Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1595208.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} + 33x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.73066\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.49000 | −0.352184 | −0.176092 | − | 0.984374i | \(-0.556346\pi\) | ||||
−0.176092 | + | 0.984374i | \(0.556346\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −188.968 | −1.45761 | −0.728807 | − | 0.684720i | \(-0.759925\pi\) | ||||
−0.728807 | + | 0.684720i | \(0.759925\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −212.860 | −0.875967 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 501.871 | 1.25058 | 0.625288 | − | 0.780394i | \(-0.284982\pi\) | ||||
0.625288 | + | 0.780394i | \(0.284982\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1061.48 | −1.74203 | −0.871013 | − | 0.491259i | \(-0.836537\pi\) | ||||
−0.871013 | + | 0.491259i | \(0.836537\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 29.5861 | 0.0248294 | 0.0124147 | − | 0.999923i | \(-0.496048\pi\) | ||||
0.0124147 | + | 0.999923i | \(0.496048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1578.33 | −1.00303 | −0.501515 | − | 0.865149i | \(-0.667224\pi\) | ||||
−0.501515 | + | 0.865149i | \(0.667224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1037.43 | 0.513347 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1295.86 | −0.510786 | −0.255393 | − | 0.966837i | \(-0.582205\pi\) | ||||
−0.255393 | + | 0.966837i | \(0.582205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2502.67 | 0.660685 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3586.63 | −0.791938 | −0.395969 | − | 0.918264i | \(-0.629591\pi\) | ||||
−0.395969 | + | 0.918264i | \(0.629591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3526.32 | 0.659048 | 0.329524 | − | 0.944147i | \(-0.393112\pi\) | ||||
0.329524 | + | 0.944147i | \(0.393112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2755.27 | −0.440432 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8413.79 | −1.01039 | −0.505193 | − | 0.863006i | \(-0.668579\pi\) | ||||
−0.505193 | + | 0.863006i | \(0.668579\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5827.54 | 0.613513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7015.12 | 0.651742 | 0.325871 | − | 0.945414i | \(-0.394343\pi\) | ||||
0.325871 | + | 0.945414i | \(0.394343\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22694.2 | 1.87173 | 0.935865 | − | 0.352358i | \(-0.114620\pi\) | ||||
0.935865 | + | 0.352358i | \(0.114620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3501.99 | −0.231244 | −0.115622 | − | 0.993293i | \(-0.536886\pi\) | ||||
−0.115622 | + | 0.993293i | \(0.536886\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18901.8 | 1.12464 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −162.428 | −0.00874449 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −27309.1 | −1.33542 | −0.667710 | − | 0.744422i | \(-0.732725\pi\) | ||||
−0.667710 | + | 0.744422i | \(0.732725\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8665.04 | 0.353251 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7925.39 | −0.296409 | −0.148204 | − | 0.988957i | \(-0.547349\pi\) | ||||
−0.148204 | + | 0.988957i | \(0.547349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7020.54 | −0.241572 | −0.120786 | − | 0.992679i | \(-0.538541\pi\) | ||||
−0.120786 | + | 0.992679i | \(0.538541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 40223.6 | 1.27682 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17631.2 | 0.479837 | 0.239919 | − | 0.970793i | \(-0.422879\pi\) | ||||
0.239919 | + | 0.970793i | \(0.422879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7114.27 | 0.179890 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13432.9 | −0.316246 | −0.158123 | − | 0.987419i | \(-0.550544\pi\) | ||||
−0.158123 | + | 0.987419i | \(0.550544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39946.8 | −0.877353 | −0.438677 | − | 0.898645i | \(-0.644553\pi\) | ||||
−0.438677 | + | 0.898645i | \(0.644553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −94837.3 | −1.82286 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 93321.2 | 1.68234 | 0.841168 | − | 0.540774i | \(-0.181869\pi\) | ||||
0.841168 | + | 0.540774i | \(0.181869\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37985.3 | 0.643284 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −58448.5 | −0.931275 | −0.465638 | − | 0.884975i | \(-0.654175\pi\) | ||||
−0.465638 | + | 0.884975i | \(0.654175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19690.6 | 0.278908 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13989.4 | −0.187208 | −0.0936038 | − | 0.995610i | \(-0.529839\pi\) | ||||
−0.0936038 | + | 0.995610i | \(0.529839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 200586. | 2.53920 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −19359.5 | −0.232106 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 110640. | 1.19394 | 0.596969 | − | 0.802264i | \(-0.296371\pi\) | ||||
0.596969 | + | 0.802264i | \(0.296371\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −106828. | −1.09546 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 198468. | 1.93592 | 0.967960 | − | 0.251103i | \(-0.0807934\pi\) | ||||
0.967960 | + | 0.251103i | \(0.0807934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 134780. | 1.25179 | 0.625897 | − | 0.779906i | \(-0.284733\pi\) | ||||
0.625897 | + | 0.779906i | \(0.284733\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 39785.5 | 0.335943 | 0.167971 | − | 0.985792i | \(-0.446278\pi\) | ||||
0.167971 | + | 0.985792i | \(0.446278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 92692.6 | 0.747272 | 0.373636 | − | 0.927575i | \(-0.378111\pi\) | ||||
0.373636 | + | 0.927575i | \(0.378111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 46191.7 | 0.355841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 66923.1 | 0.493037 | 0.246519 | − | 0.969138i | \(-0.420713\pi\) | ||||
0.246519 | + | 0.969138i | \(0.420713\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 225947. | 1.52596 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5590.81 | −0.0361916 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 90823.1 | 0.563940 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −38513.0 | −0.229533 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −58998.9 | −0.324589 | −0.162295 | − | 0.986742i | \(-0.551890\pi\) | ||||
−0.162295 | + | 0.986742i | \(0.551890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −124591. | −0.659193 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 209380. | 1.06600 | 0.533001 | − | 0.846115i | \(-0.321064\pi\) | ||||
0.533001 | + | 0.846115i | \(0.321064\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 298254. | 1.46203 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −326432. | −1.48591 | −0.742953 | − | 0.669344i | \(-0.766575\pi\) | ||||
−0.742953 | + | 0.669344i | \(0.766575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 233648. | 1.02571 | 0.512856 | − | 0.858475i | \(-0.328588\pi\) | ||||
0.512856 | + | 0.858475i | \(0.328588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19225.9 | 0.0814403 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −532727. | −2.17854 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −103771. | −0.396078 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 145336. | 0.536299 | 0.268149 | − | 0.963377i | \(-0.413588\pi\) | ||||
0.268149 | + | 0.963377i | \(0.413588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −287343. | −1.02555 | −0.512777 | − | 0.858522i | \(-0.671383\pi\) | ||||
−0.512777 | + | 0.858522i | \(0.671383\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6297.69 | −0.0217497 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 42626.2 | 0.138015 | 0.0690077 | − | 0.997616i | \(-0.478017\pi\) | ||||
0.0690077 | + | 0.997616i | \(0.478017\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 149927. | 0.470313 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 244876. | 0.744528 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −221599. | −0.653279 | −0.326639 | − | 0.945149i | \(-0.605916\pi\) | ||||
−0.326639 | + | 0.945149i | \(0.605916\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −334835. | −0.929051 | −0.464525 | − | 0.885560i | \(-0.653775\pi\) | ||||
−0.464525 | + | 0.885560i | \(0.653775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 755454. | 2.03466 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 335964. | 0.878622 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 268475. | 0.682006 | 0.341003 | − | 0.940062i | \(-0.389233\pi\) | ||||
0.341003 | + | 0.940062i | \(0.389233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 43510.4 | 0.104390 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 268052. | 0.625297 | 0.312649 | − | 0.949869i | \(-0.398784\pi\) | ||||
0.312649 | + | 0.949869i | \(0.398784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −90565.5 | −0.205479 | −0.102739 | − | 0.994708i | \(-0.532761\pi\) | ||||
−0.102739 | + | 0.994708i | \(0.532761\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 38542.8 | 0.0850776 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14848.4 | 0.0310510 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −472924. | −0.963023 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 706725. | 1.40174 | 0.700870 | − | 0.713290i | \(-0.252796\pi\) | ||||
0.700870 | + | 0.713290i | \(0.252796\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −236999. | −0.457988 | −0.228994 | − | 0.973428i | \(-0.573544\pi\) | ||||
−0.228994 | + | 0.973428i | \(0.573544\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 607901. | 1.11601 | 0.558004 | − | 0.829838i | \(-0.311567\pi\) | ||||
0.558004 | + | 0.829838i | \(0.311567\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −621060. | −1.11173 | −0.555867 | − | 0.831272i | \(-0.687613\pi\) | ||||
−0.555867 | + | 0.831272i | \(0.687613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −96795.1 | −0.168991 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 677756. | 1.15434 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 275837. | 0.447431 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −792118. | −1.25437 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.06177e6 | −1.64181 | −0.820906 | − | 0.571063i | \(-0.806531\pi\) | ||||
−0.820906 | + | 0.571063i | \(0.806531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 73746.8 | 0.111377 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −666360. | −0.960638 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 219308. | 0.308989 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31405.2 | −0.0432534 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 240721. | 0.324154 | 0.162077 | − | 0.986778i | \(-0.448181\pi\) | ||||
0.162077 | + | 0.986778i | \(0.448181\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −202494. | −0.260824 | −0.130412 | − | 0.991460i | \(-0.541630\pi\) | ||||
−0.130412 | + | 0.991460i | \(0.541630\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −284279. | −0.358225 | −0.179112 | − | 0.983829i | \(-0.557323\pi\) | ||||
−0.179112 | + | 0.983829i | \(0.557323\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 520657. | 0.641980 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −345405. | −0.416811 | −0.208406 | − | 0.978042i | \(-0.566827\pi\) | ||||
−0.208406 | + | 0.978042i | \(0.566827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −512333. | −0.592491 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.59920e6 | −1.81095 | −0.905476 | − | 0.424398i | \(-0.860486\pi\) | ||||
−0.905476 | + | 0.424398i | \(0.860486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −42246.4 | −0.0468541 | −0.0234270 | − | 0.999726i | \(-0.507458\pi\) | ||||
−0.0234270 | + | 0.999726i | \(0.507458\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −816688. | −0.887239 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.67537e6 | 1.74731 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 320882. | 0.327980 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −802841. | −0.804351 | −0.402175 | − | 0.915563i | \(-0.631746\pi\) | ||||
−0.402175 | + | 0.915563i | \(0.631746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −650354. | −0.638776 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 941153. | 0.888848 | 0.444424 | − | 0.895817i | \(-0.353408\pi\) | ||||
0.444424 | + | 0.895817i | \(0.353408\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.58993e6 | 1.47275 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 763449. | 0.693711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.53130e6 | 1.36512 | 0.682560 | − | 0.730830i | \(-0.260867\pi\) | ||||
0.682560 | + | 0.730830i | \(0.260867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 76801.7 | 0.0659315 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.25712e6 | 1.05924 | 0.529621 | − | 0.848234i | \(-0.322334\pi\) | ||||
0.529621 | + | 0.848234i | \(0.322334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −843976. | −0.698083 | −0.349041 | − | 0.937107i | \(-0.613493\pi\) | ||||
−0.349041 | + | 0.937107i | \(0.613493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.10122e6 | −0.894265 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.52070e6 | −1.19082 | −0.595408 | − | 0.803423i | \(-0.703010\pi\) | ||||
−0.595408 | + | 0.803423i | \(0.703010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −750612. | −0.577305 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.97975e6 | −1.49570 | −0.747848 | − | 0.663870i | \(-0.768913\pi\) | ||||
−0.747848 | + | 0.663870i | \(0.768913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.02901e6 | 1.50597 | 0.752986 | − | 0.658036i | \(-0.228613\pi\) | ||||
0.752986 | + | 0.658036i | \(0.228613\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.32563e6 | −0.949987 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41898e6 | −0.999384 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −607412. | −0.420485 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.23140e6 | −1.51848 | −0.759238 | − | 0.650813i | \(-0.774428\pi\) | ||||
−0.759238 | + | 0.650813i | \(0.774428\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.25602e6 | 0.826236 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.37553e6 | 0.889802 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.28847e6 | −2.72826 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.08959e6 | −0.681799 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −334318. | −0.202448 | −0.101224 | − | 0.994864i | \(-0.532276\pi\) | ||||
−0.101224 | + | 0.994864i | \(0.532276\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −739943. | −0.440861 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.39090e6 | −1.40172 | −0.700858 | − | 0.713300i | \(-0.747200\pi\) | ||||
−0.700858 | + | 0.713300i | \(0.747200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.88563e6 | 1.08791 | 0.543957 | − | 0.839113i | \(-0.316925\pi\) | ||||
0.543957 | + | 0.839113i | \(0.316925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −179636. | −0.100403 | −0.0502014 | − | 0.998739i | \(-0.515986\pi\) | ||||
−0.0502014 | + | 0.998739i | \(0.515986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.80002e6 | −0.990378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −218422. | −0.118313 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −46696.7 | −0.0249046 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −508882. | −0.263177 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 661763. | 0.337064 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −168620. | −0.0845937 | −0.0422968 | − | 0.999105i | \(-0.513468\pi\) | ||||
−0.0422968 | + | 0.999105i | \(0.513468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.79096e6 | 0.885064 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.74240e6 | −0.835744 | −0.417872 | − | 0.908506i | \(-0.637224\pi\) | ||||
−0.417872 | + | 0.908506i | \(0.637224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −367407. | −0.173640 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.76976e6 | 0.824190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −395842. | −0.181672 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.89447e6 | 1.29046 | 0.645232 | − | 0.763987i | \(-0.276761\pi\) | ||||
0.645232 | + | 0.763987i | \(0.276761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 63803.8 | 0.0280403 | 0.0140202 | − | 0.999902i | \(-0.495537\pi\) | ||||
0.0140202 | + | 0.999902i | \(0.495537\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65654e6 | −1.15093 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.79206e6 | 1.19258 | 0.596290 | − | 0.802769i | \(-0.296641\pi\) | ||||
0.596290 | + | 0.802769i | \(0.296641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30693.6 | 0.0127461 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.48391e6 | −0.607674 | −0.303837 | − | 0.952724i | \(-0.598268\pi\) | ||||
−0.303837 | + | 0.952724i | \(0.598268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15032.0 | 0.00607083 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −498619. | −0.198610 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.08188e6 | 0.419289 | 0.209644 | − | 0.977778i | \(-0.432769\pi\) | ||||
0.209644 | + | 0.977778i | \(0.432769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.49324e6 | −0.570904 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.16053e6 | 1.94652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 127750. | 0.0475434 | 0.0237717 | − | 0.999717i | \(-0.492433\pi\) | ||||
0.0237717 | + | 0.999717i | \(0.492433\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.80714e6 | 1.37958 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.61295e6 | 0.576798 | 0.288399 | − | 0.957510i | \(-0.406877\pi\) | ||||
0.288399 | + | 0.957510i | \(0.406877\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 323904. | 0.114315 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.96656e6 | −1.38171 | −0.690855 | − | 0.722993i | \(-0.742766\pi\) | ||||
−0.690855 | + | 0.722993i | \(0.742766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.83068e6 | −1.63957 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.54852e6 | −1.18898 | −0.594488 | − | 0.804104i | \(-0.702645\pi\) | ||||
−0.594488 | + | 0.804104i | \(0.702645\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38339.5 | −0.0126825 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.14950e6 | −0.375428 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 580854. | 0.184965 | 0.0924827 | − | 0.995714i | \(-0.470520\pi\) | ||||
0.0924827 | + | 0.995714i | \(0.470520\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.63741e6 | −0.514903 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.10413e6 | 0.653449 | 0.326725 | − | 0.945120i | \(-0.394055\pi\) | ||||
0.326725 | + | 0.945120i | \(0.394055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.74313e6 | −1.14808 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.22263e6 | −1.26356 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.23687e6 | 0.956790 | 0.478395 | − | 0.878145i | \(-0.341219\pi\) | ||||
0.478395 | + | 0.878145i | \(0.341219\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.79211e6 | 0.523312 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.49764e6 | 0.432049 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.28273e6 | −0.361239 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.03059e6 | 0.565049 | 0.282525 | − | 0.959260i | \(-0.408828\pi\) | ||||
0.282525 | + | 0.959260i | \(0.408828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.15883e6 | 0.593625 | 0.296813 | − | 0.954936i | \(-0.404076\pi\) | ||||
0.296813 | + | 0.954936i | \(0.404076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 745434. | 0.202562 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.32665e6 | 0.352118 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.92467e6 | 0.767245 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.49812e6 | −1.42568 | −0.712838 | − | 0.701328i | \(-0.752591\pi\) | ||||
−0.712838 | + | 0.701328i | \(0.752591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.87201e6 | −0.992470 | −0.496235 | − | 0.868188i | \(-0.665284\pi\) | ||||
−0.496235 | + | 0.868188i | \(0.665284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.04530e6 | 0.512334 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.15465e6 | −0.781250 | −0.390625 | − | 0.920550i | \(-0.627741\pi\) | ||||
−0.390625 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.02343e6 | −0.985144 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.07021e6 | −0.985389 | −0.492694 | − | 0.870202i | \(-0.663988\pi\) | ||||
−0.492694 | + | 0.870202i | \(0.663988\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −797893. | −0.188876 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 957718. | 0.224193 | 0.112096 | − | 0.993697i | \(-0.464243\pi\) | ||||
0.112096 | + | 0.993697i | \(0.464243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.52068e6 | 0.815052 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.57751e6 | 0.361183 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.38167e6 | −1.65335 | −0.826673 | − | 0.562682i | \(-0.809769\pi\) | ||||
−0.826673 | + | 0.562682i | \(0.809769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 74044.2 | 0.0164044 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.96862e6 | −0.650582 | −0.325291 | − | 0.945614i | \(-0.605462\pi\) | ||||
−0.325291 | + | 0.945614i | \(0.605462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.84593e6 | 1.48416 | 0.742079 | − | 0.670313i | \(-0.233840\pi\) | ||||
0.742079 | + | 0.670313i | \(0.233840\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.20816e6 | 0.892895 | 0.446447 | − | 0.894810i | \(-0.352689\pi\) | ||||
0.446447 | + | 0.894810i | \(0.352689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.33172e6 | −0.699417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −234018. | −0.0486068 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.13895e7 | 2.34074 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.81301e6 | 1.16978 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.73077e6 | 1.14123 | 0.570617 | − | 0.821217i | \(-0.306704\pi\) | ||||
0.570617 | + | 0.821217i | \(0.306704\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.93110e6 | 1.76012 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.34437e6 | −0.262211 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.63249e6 | 1.26723 | 0.633613 | − | 0.773650i | \(-0.281571\pi\) | ||||
0.633613 | + | 0.773650i | \(0.281571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.21658e6 | 0.230074 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.26463e6 | 0.611125 | 0.305563 | − | 0.952172i | \(-0.401156\pi\) | ||||
0.305563 | + | 0.952172i | \(0.401156\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −106114. | −0.0196633 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.53839e6 | 0.460965 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.51527e6 | 1.53090 | 0.765450 | − | 0.643495i | \(-0.222516\pi\) | ||||
0.765450 | + | 0.643495i | \(0.222516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.83824e6 | 0.327196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.24174e6 | 0.571292 | 0.285646 | − | 0.958335i | \(-0.407792\pi\) | ||||
0.285646 | + | 0.958335i | \(0.407792\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.14744e6 | −0.716573 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.04569e7 | 1.78900 | 0.894499 | − | 0.447070i | \(-0.147533\pi\) | ||||
0.894499 | + | 0.447070i | \(0.147533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.54865e6 | 1.27884 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.95004e6 | −0.662687 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.75755e6 | −0.289188 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.47393e6 | −0.240191 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −328142. | −0.0529625 | −0.0264812 | − | 0.999649i | \(-0.508430\pi\) | ||||
−0.0264812 | + | 0.999649i | \(0.508430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.42102e6 | 1.50606 | 0.753032 | − | 0.657984i | \(-0.228590\pi\) | ||||
0.753032 | + | 0.657984i | \(0.228590\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 104330. | 0.0163637 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.75709e6 | −0.739098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.68700e6 | 0.259644 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.44643e6 | −1.13535 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.47160e6 | −0.220219 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.48624e6 | 1.40644 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.08041e6 | 0.893182 | 0.446591 | − | 0.894738i | \(-0.352638\pi\) | ||||
0.446591 | + | 0.894738i | \(0.352638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 497205. | 0.0723662 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.32182e6 | 0.617587 | 0.308794 | − | 0.951129i | \(-0.400075\pi\) | ||||
0.308794 | + | 0.951129i | \(0.400075\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.49439e6 | 0.211609 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.66089e6 | 0.794338 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.76347e7 | −2.45220 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.41019e6 | −1.01203 | −0.506013 | − | 0.862526i | \(-0.668881\pi\) | ||||
−0.506013 | + | 0.862526i | \(0.668881\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.40895e7 | −3.26061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −81517.7 | −0.0109356 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.08039e7 | 1.43652 | 0.718260 | − | 0.695775i | \(-0.244939\pi\) | ||||
0.718260 | + | 0.695775i | \(0.244939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.17799e6 | −0.937660 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.77404e6 | 0.229712 | 0.114856 | − | 0.993382i | \(-0.463359\pi\) | ||||
0.114856 | + | 0.993382i | \(0.463359\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 70981.0 | 0.00911070 | 0.00455535 | − | 0.999990i | \(-0.498550\pi\) | ||||
0.00455535 | + | 0.999990i | \(0.498550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.87992e6 | −0.493669 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.04410e6 | 0.505688 | 0.252844 | − | 0.967507i | \(-0.418634\pi\) | ||||
0.252844 | + | 0.967507i | \(0.418634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.30113e6 | 0.161296 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.10449e7 | 1.35744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.37056e7 | −1.67004 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.86862e6 | −0.343620 | −0.171810 | − | 0.985130i | \(-0.554962\pi\) | ||||
−0.171810 | + | 0.985130i | \(0.554962\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.56570e6 | −0.661046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.33737e6 | −0.393040 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.23131e6 | 0.377347 | 0.188674 | − | 0.982040i | \(-0.439581\pi\) | ||||
0.188674 | + | 0.982040i | \(0.439581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.40962e6 | 0.391534 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.80078e6 | −0.432819 | −0.216409 | − | 0.976303i | \(-0.569435\pi\) | ||||
−0.216409 | + | 0.976303i | \(0.569435\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.45289e6 | 0.615801 | 0.307900 | − | 0.951419i | \(-0.400374\pi\) | ||||
0.307900 | + | 0.951419i | \(0.400374\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.75297e6 | −0.420321 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50483e7 | 1.65774 | 0.828870 | − | 0.559441i | \(-0.188984\pi\) | ||||
0.828870 | + | 0.559441i | \(0.188984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.72088e6 | −0.406539 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.71731e6 | 0.402833 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.30782e6 | 0.248056 | 0.124028 | − | 0.992279i | \(-0.460419\pi\) | ||||
0.124028 | + | 0.992279i | \(0.460419\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −381761. | −0.0403718 | −0.0201859 | − | 0.999796i | \(-0.506426\pi\) | ||||
−0.0201859 | + | 0.999796i | \(0.506426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.07208e7 | 1.12460 | 0.562302 | − | 0.826932i | \(-0.309916\pi\) | ||||
0.562302 | + | 0.826932i | \(0.309916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.24311e6 | −0.337468 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.64354e6 | 0.272876 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.34873e6 | 0.441767 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −248931. | −0.0250872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.56189e6 | 0.456112 | 0.228056 | − | 0.973648i | \(-0.426763\pi\) | ||||
0.228056 | + | 0.973648i | \(0.426763\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.82910e6 | 0.578219 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00639e7 | −1.95915 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.85933e6 | 0.277021 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.70983e6 | −0.260494 | −0.130247 | − | 0.991482i | \(-0.541577\pi\) | ||||
−0.130247 | + | 0.991482i | \(0.541577\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.10481e6 | 0.582297 | 0.291149 | − | 0.956678i | \(-0.405963\pi\) | ||||
0.291149 | + | 0.956678i | \(0.405963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.22081e7 | −1.14654 | −0.573269 | − | 0.819367i | \(-0.694325\pi\) | ||||
−0.573269 | + | 0.819367i | \(0.694325\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.97752e6 | −0.370681 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.65832e6 | 0.338321 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.26514e6 | −0.574973 | −0.287487 | − | 0.957785i | \(-0.592820\pi\) | ||||
−0.287487 | + | 0.957785i | \(0.592820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.50307e6 | 0.768532 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.85107e7 | 1.66039 | 0.830194 | − | 0.557474i | \(-0.188229\pi\) | ||||
0.830194 | + | 0.557474i | \(0.188229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.46041e6 | −0.753161 | −0.376581 | − | 0.926384i | \(-0.622900\pi\) | ||||
−0.376581 | + | 0.926384i | \(0.622900\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 172414. | 0.0152331 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.64777e6 | 0.404511 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.32156e6 | −0.114162 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.52340e6 | −0.302104 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.25182e6 | 0.617177 | 0.308588 | − | 0.951196i | \(-0.400143\pi\) | ||||
0.308588 | + | 0.951196i | \(0.400143\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.74893e6 | 0.398221 | 0.199110 | − | 0.979977i | \(-0.436195\pi\) | ||||
0.199110 | + | 0.979977i | \(0.436195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.09073e7 | −1.74030 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.11169e6 | 0.0918578 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.37712e7 | −1.12959 | −0.564793 | − | 0.825233i | \(-0.691044\pi\) | ||||
−0.564793 | + | 0.825233i | \(0.691044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.56069e6 | 0.126161 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.89882e7 | 2.32634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.64305e7 | −1.30905 | −0.654526 | − | 0.756040i | \(-0.727132\pi\) | ||||
−0.654526 | + | 0.756040i | \(0.727132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.01871e7 | 1.59676 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 207550. | 0.0161823 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.89628e6 | 0.146794 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.05170e7 | −0.808342 | −0.404171 | − | 0.914683i | \(-0.632440\pi\) | ||||
−0.404171 | + | 0.914683i | \(0.632440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.32797e7 | 1.01345 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.75041e7 | −2.82182 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.32691e6 | −0.0991349 | −0.0495674 | − | 0.998771i | \(-0.515784\pi\) | ||||
−0.0495674 | + | 0.998771i | \(0.515784\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.98643e7 | −1.47367 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.56962e6 | −0.336633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.77958e6 | 0.637787 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.65753e6 | −0.335995 | −0.167998 | − | 0.985787i | \(-0.553730\pi\) | ||||
−0.167998 | + | 0.985787i | \(0.553730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.54691e7 | −1.82463 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 231933. | 0.0165012 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.47884e6 | 0.103773 | 0.0518867 | − | 0.998653i | \(-0.483477\pi\) | ||||
0.0518867 | + | 0.998653i | \(0.483477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.74681e6 | −0.330814 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 671432. | 0.0464739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.41118e7 | 0.970115 | 0.485057 | − | 0.874482i | \(-0.338799\pi\) | ||||
0.485057 | + | 0.874482i | \(0.338799\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.84856e6 | 0.600073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.94045e6 | 0.400137 | 0.200068 | − | 0.979782i | \(-0.435884\pi\) | ||||
0.200068 | + | 0.979782i | \(0.435884\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.19780e6 | −0.615373 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.46589e7 | −0.974156 | −0.487078 | − | 0.873359i | \(-0.661937\pi\) | ||||
−0.487078 | + | 0.873359i | \(0.661937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.24413e7 | 0.815766 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.51817e6 | −0.489674 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.08263e6 | 0.393543 | 0.196771 | − | 0.980449i | \(-0.436954\pi\) | ||||
0.196771 | + | 0.980449i | \(0.436954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.40760e6 | 0.283279 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.11757e6 | 0.514856 | 0.257428 | − | 0.966297i | \(-0.417125\pi\) | ||||
0.257428 | + | 0.966297i | \(0.417125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.57044e6 | 0.224966 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.63567e7 | 1.02384 | 0.511921 | − | 0.859033i | \(-0.328934\pi\) | ||||
0.511921 | + | 0.859033i | \(0.328934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.75159e7 | −1.08923 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.41267e6 | 0.516352 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.09586e7 | −1.27805 | −0.639024 | − | 0.769187i | \(-0.720661\pi\) | ||||
−0.639024 | + | 0.769187i | \(0.720661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.16693e6 | −0.313038 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.95651e6 | −0.539126 | −0.269563 | − | 0.962983i | \(-0.586879\pi\) | ||||
−0.269563 | + | 0.962983i | \(0.586879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.72873e6 | −0.518679 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.10722e7 | −0.653717 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.74160e6 | −0.395490 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.97614e6 | −0.523221 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.42009e7 | 1.39282 | 0.696411 | − | 0.717643i | \(-0.254779\pi\) | ||||
0.696411 | + | 0.717643i | \(0.254779\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.40683e6 | −0.480773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.26463e7 | −0.718657 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.45219e6 | 0.420824 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.91659e6 | 0.552989 | 0.276494 | − | 0.961016i | \(-0.410827\pi\) | ||||
0.276494 | + | 0.961016i | \(0.410827\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −103610. | −0.00574164 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.97778e6 | 0.163988 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00481e7 | −1.09720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.90158e6 | −0.373048 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.15657e6 | −0.491883 | −0.245941 | − | 0.969285i | \(-0.579097\pi\) | ||||
−0.245941 | + | 0.969285i | \(0.579097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.49145e7 | −0.796264 | −0.398132 | − | 0.917328i | \(-0.630341\pi\) | ||||
−0.398132 | + | 0.917328i | \(0.630341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.63343e6 | 0.245853 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.58189e7 | −1.87740 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.26967e7 | −2.22426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.39549e6 | 0.486476 | 0.243238 | − | 0.969967i | \(-0.421790\pi\) | ||||
0.243238 | + | 0.969967i | \(0.421790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.59508e7 | −0.820884 | −0.410442 | − | 0.911887i | \(-0.634626\pi\) | ||||
−0.410442 | + | 0.911887i | \(0.634626\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.68518e7 | −0.856805 | −0.428403 | − | 0.903588i | \(-0.640923\pi\) | ||||
−0.428403 | + | 0.903588i | \(0.640923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.92620e6 | −0.198420 | −0.0992101 | − | 0.995067i | \(-0.531632\pi\) | ||||
−0.0992101 | + | 0.995067i | \(0.531632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.34865e6 | 0.419386 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 559229. | 0.0279240 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.82521e6 | 0.435423 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.23626e7 | 0.606322 | 0.303161 | − | 0.952939i | \(-0.401958\pi\) | ||||
0.303161 | + | 0.952939i | \(0.401958\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.64726e6 | −0.372834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.08688e7 | 0.526760 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.71626e7 | −0.822006 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.11392e7 | −0.530379 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.09031e7 | 0.516091 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.17612e6 | −0.149460 | −0.0747299 | − | 0.997204i | \(-0.523809\pi\) | ||||
−0.0747299 | + | 0.997204i | \(0.523809\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.97233e7 | 0.917334 | 0.458667 | − | 0.888608i | \(-0.348327\pi\) | ||||
0.458667 | + | 0.888608i | \(0.348327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.18456e6 | −0.193494 | −0.0967470 | − | 0.995309i | \(-0.530844\pi\) | ||||
−0.0967470 | + | 0.995309i | \(0.530844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.27771e6 | 0.334570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.89684e7 | 1.32403 | 0.662015 | − | 0.749490i | \(-0.269701\pi\) | ||||
0.662015 | + | 0.749490i | \(0.269701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.79021e6 | 0.351966 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.68352e7 | 2.10389 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.87152e7 | −0.835889 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.35508e7 | −1.04585 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.78801e7 | 1.22404 | 0.612019 | − | 0.790843i | \(-0.290358\pi\) | ||||
0.612019 | + | 0.790843i | \(0.290358\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.22504e7 | 0.534783 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.21471e7 | −1.82948 | −0.914741 | − | 0.404040i | \(-0.867606\pi\) | ||||
−0.914741 | + | 0.404040i | \(0.867606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.38615e7 | 1.89314 | 0.946568 | − | 0.322505i | \(-0.104525\pi\) | ||||
0.946568 | + | 0.322505i | \(0.104525\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.32386e7 | 0.991747 | 0.495874 | − | 0.868395i | \(-0.334848\pi\) | ||||
0.495874 | + | 0.868395i | \(0.334848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.11489e7 | 0.473126 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.90637e7 | 0.804476 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.52731e6 | 0.231945 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.55168e6 | −0.313374 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.26476e7 | −0.521925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −807970. | −0.0331576 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.35437e7 | 0.960848 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.74916e6 | 0.312778 | 0.156389 | − | 0.987696i | \(-0.450015\pi\) | ||||
0.156389 | + | 0.987696i | \(0.450015\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.22459e7 | −1.69580 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.54221e7 | −0.615668 | −0.307834 | − | 0.951440i | \(-0.599604\pi\) | ||||
−0.307834 | + | 0.951440i | \(0.599604\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.93336e7 | −1.16463 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.95661e7 | −1.55382 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.40744e7 | 0.940302 | 0.470151 | − | 0.882586i | \(-0.344199\pi\) | ||||
0.470151 | + | 0.882586i | \(0.344199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.83540e6 | 0.0712989 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.42588e7 | 0.550909 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.86893e7 | −1.09653 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.51619e7 | −0.576387 | −0.288193 | − | 0.957572i | \(-0.593055\pi\) | ||||
−0.288193 | + | 0.957572i | \(0.593055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.98333e7 | −1.12804 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.31260e7 | 0.493662 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.90390e6 | 0.182470 | 0.0912352 | − | 0.995829i | \(-0.470918\pi\) | ||||
0.0912352 | + | 0.995829i | \(0.470918\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.03521e7 | −0.383146 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.62296e7 | −0.597495 | −0.298748 | − | 0.954332i | \(-0.596569\pi\) | ||||
−0.298748 | + | 0.954332i | \(0.596569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.09062e6 | −0.332900 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.16817e7 | 1.51033 | 0.755163 | − | 0.655537i | \(-0.227558\pi\) | ||||
0.755163 | + | 0.655537i | \(0.227558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.24028e7 | 1.52837 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 986202. | 0.0353602 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.61135e7 | 0.574723 | 0.287362 | − | 0.957822i | \(-0.407222\pi\) | ||||
0.287362 | + | 0.957822i | \(0.407222\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.88212e6 | 0.348795 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.16851e7 | 2.16588 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.61942e7 | −0.565655 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.46873e6 | −0.294274 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.51707e7 | −0.521722 | −0.260861 | − | 0.965376i | \(-0.584006\pi\) | ||||
−0.260861 | + | 0.965376i | \(0.584006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 256365. | 0.00877099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.82884e7 | 0.962854 | 0.481427 | − | 0.876486i | \(-0.340119\pi\) | ||||
0.481427 | + | 0.876486i | \(0.340119\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.41519e7 | −1.49509 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.88218e7 | −0.966017 | −0.483009 | − | 0.875616i | \(-0.660456\pi\) | ||||
−0.483009 | + | 0.875616i | \(0.660456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.02086e6 | −0.234117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.97305e7 | −0.654586 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.26448e6 | −0.0747453 | −0.0373727 | − | 0.999301i | \(-0.511899\pi\) | ||||
−0.0373727 | + | 0.999301i | \(0.511899\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.63308e6 | −0.118709 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.94085e7 | −0.956053 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −995592. | −0.0322031 | −0.0161015 | − | 0.999870i | \(-0.505125\pi\) | ||||
−0.0161015 | + | 0.999870i | \(0.505125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 925721. | 0.0297925 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.57133e7 | −1.77509 | −0.887547 | − | 0.460718i | \(-0.847592\pi\) | ||||
−0.887547 | + | 0.460718i | \(0.847592\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.10569e7 | −0.667546 |
(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 | 400.6.a.ba.1.2 | 4 | ||
4.3 | odd | 2 | 200.6.a.j.1.3 | 4 | |||
5.2 | odd | 4 | 80.6.c.d.49.6 | 8 | |||
5.3 | odd | 4 | 80.6.c.d.49.3 | 8 | |||
5.4 | even | 2 | 400.6.a.z.1.3 | 4 | |||
15.2 | even | 4 | 720.6.f.n.289.7 | 8 | |||
15.8 | even | 4 | 720.6.f.n.289.8 | 8 | |||
20.3 | even | 4 | 40.6.c.a.9.6 | yes | 8 | ||
20.7 | even | 4 | 40.6.c.a.9.3 | ✓ | 8 | ||
20.19 | odd | 2 | 200.6.a.k.1.2 | 4 | |||
40.3 | even | 4 | 320.6.c.j.129.3 | 8 | |||
40.13 | odd | 4 | 320.6.c.i.129.6 | 8 | |||
40.27 | even | 4 | 320.6.c.j.129.6 | 8 | |||
40.37 | odd | 4 | 320.6.c.i.129.3 | 8 | |||
60.23 | odd | 4 | 360.6.f.b.289.8 | 8 | |||
60.47 | odd | 4 | 360.6.f.b.289.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.3 | ✓ | 8 | 20.7 | even | 4 | ||
40.6.c.a.9.6 | yes | 8 | 20.3 | even | 4 | ||
80.6.c.d.49.3 | 8 | 5.3 | odd | 4 | |||
80.6.c.d.49.6 | 8 | 5.2 | odd | 4 | |||
200.6.a.j.1.3 | 4 | 4.3 | odd | 2 | |||
200.6.a.k.1.2 | 4 | 20.19 | odd | 2 | |||
320.6.c.i.129.3 | 8 | 40.37 | odd | 4 | |||
320.6.c.i.129.6 | 8 | 40.13 | odd | 4 | |||
320.6.c.j.129.3 | 8 | 40.3 | even | 4 | |||
320.6.c.j.129.6 | 8 | 40.27 | even | 4 | |||
360.6.f.b.289.7 | 8 | 60.47 | odd | 4 | |||
360.6.f.b.289.8 | 8 | 60.23 | odd | 4 | |||
400.6.a.z.1.3 | 4 | 5.4 | even | 2 | |||
400.6.a.ba.1.2 | 4 | 1.1 | even | 1 | trivial | ||
720.6.f.n.289.7 | 8 | 15.2 | even | 4 | |||
720.6.f.n.289.8 | 8 | 15.8 | even | 4 |