Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1100,6,Mod(749,1100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1100.749");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1100.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(176.422201794\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 44) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 749.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1100.749 |
Dual form | 1100.6.b.a.749.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(551\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 7.00000i | 0.449050i | 0.974468 | + | 0.224525i | \(0.0720831\pi\) | ||||
−0.974468 | + | 0.224525i | \(0.927917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 50.0000i | 0.385678i | 0.981230 | + | 0.192839i | \(0.0617695\pi\) | ||||
−0.981230 | + | 0.192839i | \(0.938230\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 194.000 | 0.798354 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 380.000i | − 0.623627i | −0.950143 | − | 0.311814i | \(-0.899064\pi\) | ||||
0.950143 | − | 0.311814i | \(-0.100936\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1154.00i | 0.968464i | 0.874940 | + | 0.484232i | \(0.160901\pi\) | ||||
−0.874940 | + | 0.484232i | \(0.839099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1824.00 | 1.15915 | 0.579577 | − | 0.814918i | \(-0.303218\pi\) | ||||
0.579577 | + | 0.814918i | \(0.303218\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −350.000 | −0.173189 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3591.00i | 1.41545i | 0.706486 | + | 0.707727i | \(0.250279\pi\) | ||||
−0.706486 | + | 0.707727i | \(0.749721\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3059.00i | 0.807551i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8032.00 | −1.77349 | −0.886745 | − | 0.462259i | \(-0.847039\pi\) | ||||
−0.886745 | + | 0.462259i | \(0.847039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2945.00 | −0.550403 | −0.275202 | − | 0.961387i | \(-0.588745\pi\) | ||||
−0.275202 | + | 0.961387i | \(0.588745\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 847.000i | 0.135394i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6979.00i | − 0.838087i | −0.907966 | − | 0.419043i | \(-0.862366\pi\) | ||||
0.907966 | − | 0.419043i | \(-0.137634\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2660.00 | 0.280040 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −520.000 | −0.0483107 | −0.0241554 | − | 0.999708i | \(-0.507690\pi\) | ||||
−0.0241554 | + | 0.999708i | \(0.507690\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2486.00i | − 0.205036i | −0.994731 | − | 0.102518i | \(-0.967310\pi\) | ||||
0.994731 | − | 0.102518i | \(-0.0326899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6920.00i | 0.456942i | 0.973551 | + | 0.228471i | \(0.0733727\pi\) | ||||
−0.973551 | + | 0.228471i | \(0.926627\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14307.0 | 0.851252 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8078.00 | −0.434889 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 13718.0i | − 0.670812i | −0.942074 | − | 0.335406i | \(-0.891126\pi\) | ||||
0.942074 | − | 0.335406i | \(-0.108874\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12768.0i | 0.520518i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 31779.0 | 1.18853 | 0.594265 | − | 0.804269i | \(-0.297443\pi\) | ||||
0.594265 | + | 0.804269i | \(0.297443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34156.0 | 1.17528 | 0.587641 | − | 0.809121i | \(-0.300057\pi\) | ||||
0.587641 | + | 0.809121i | \(0.300057\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9700.00i | 0.307908i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 61503.0i | 1.67382i | 0.547339 | + | 0.836911i | \(0.315641\pi\) | ||||
−0.547339 | + | 0.836911i | \(0.684359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −25137.0 | −0.635610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14971.0 | −0.352456 | −0.176228 | − | 0.984349i | \(-0.556390\pi\) | ||||
−0.176228 | + | 0.984349i | \(0.556390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 36444.0i | − 0.800422i | −0.916423 | − | 0.400211i | \(-0.868937\pi\) | ||||
0.916423 | − | 0.400211i | \(-0.131063\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6050.00i | 0.116286i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 28538.0 | 0.514465 | 0.257232 | − | 0.966350i | \(-0.417189\pi\) | ||||
0.257232 | + | 0.966350i | \(0.417189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25729.0 | 0.435723 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 77482.0i | 1.23454i | 0.786751 | + | 0.617271i | \(0.211762\pi\) | ||||
−0.786751 | + | 0.617271i | \(0.788238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 56224.0i | − 0.796386i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −36271.0 | −0.485383 | −0.242691 | − | 0.970104i | \(-0.578030\pi\) | ||||
−0.242691 | + | 0.970104i | \(0.578030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19000.0 | 0.240519 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 20615.0i | − 0.247159i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 49799.0i | 0.537392i | 0.963225 | + | 0.268696i | \(0.0865927\pi\) | ||||
−0.963225 | + | 0.268696i | \(0.913407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23474.0 | 0.240713 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −153406. | −1.49637 | −0.748185 | − | 0.663490i | \(-0.769074\pi\) | ||||
−0.748185 | + | 0.663490i | \(0.769074\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 134720.i | − 1.25124i | −0.780130 | − | 0.625618i | \(-0.784847\pi\) | ||||
0.780130 | − | 0.625618i | \(-0.215153\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 169218.i | − 1.42885i | −0.699711 | − | 0.714426i | \(-0.746688\pi\) | ||||
0.699711 | − | 0.714426i | \(-0.253312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 233206. | 1.88007 | 0.940034 | − | 0.341081i | \(-0.110793\pi\) | ||||
0.940034 | + | 0.341081i | \(0.110793\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 48853.0 | 0.376343 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 94329.0i | 0.694943i | 0.937691 | + | 0.347471i | \(0.112960\pi\) | ||||
−0.937691 | + | 0.347471i | \(0.887040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 73720.0i | − 0.497875i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −57700.0 | −0.373515 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3640.00i | − 0.0216939i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 259480.i | 1.42756i | 0.700370 | + | 0.713780i | \(0.253019\pi\) | ||||
−0.700370 | + | 0.713780i | \(0.746981\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17402.0 | 0.0920714 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −85410.0 | −0.434841 | −0.217420 | − | 0.976078i | \(-0.569764\pi\) | ||||
−0.217420 | + | 0.976078i | \(0.569764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 91200.0i | 0.447060i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 427703.i | 1.94689i | 0.228926 | + | 0.973444i | \(0.426479\pi\) | ||||
−0.228926 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −309690. | −1.35953 | −0.679767 | − | 0.733428i | \(-0.737919\pi\) | ||||
−0.679767 | + | 0.733428i | \(0.737919\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −48440.0 | −0.205190 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 45980.0i | − 0.188031i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 100149.i | 0.382255i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −449846. | −1.65996 | −0.829981 | − | 0.557792i | \(-0.811649\pi\) | ||||
−0.829981 | + | 0.557792i | \(0.811649\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 405074. | 1.44575 | 0.722873 | − | 0.690981i | \(-0.242821\pi\) | ||||
0.722873 | + | 0.690981i | \(0.242821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 223876.i | 0.773177i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 339321.i | − 1.09866i | −0.835607 | − | 0.549328i | \(-0.814884\pi\) | ||||
0.835607 | − | 0.549328i | \(-0.185116\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 96026.0 | 0.301228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −179550. | −0.545910 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 271396.i | 0.800082i | 0.916497 | + | 0.400041i | \(0.131004\pi\) | ||||
−0.916497 | + | 0.400041i | \(0.868996\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 72468.0i | − 0.201074i | −0.994933 | − | 0.100537i | \(-0.967944\pi\) | ||||
0.994933 | − | 0.100537i | \(-0.0320560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 226893. | 0.611089 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 353856. | 0.925414 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 479226.i | 1.21738i | 0.793409 | + | 0.608689i | \(0.208304\pi\) | ||||
−0.793409 | + | 0.608689i | \(0.791696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 222453.i | 0.533710i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 40935.0 | 0.0954910 | 0.0477455 | − | 0.998860i | \(-0.484796\pi\) | ||||
0.0477455 | + | 0.998860i | \(0.484796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −90169.0 | −0.204579 | −0.102289 | − | 0.994755i | \(-0.532617\pi\) | ||||
−0.102289 | + | 0.994755i | \(0.532617\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 239092.i | 0.527761i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 139634.i | 0.292003i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −152950. | −0.311455 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −260375. | −0.516435 | −0.258218 | − | 0.966087i | \(-0.583135\pi\) | ||||
−0.258218 | + | 0.966087i | \(0.583135\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 524324.i | 1.01323i | 0.862173 | + | 0.506613i | \(0.169103\pi\) | ||||
−0.862173 | + | 0.506613i | \(0.830897\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 759582.i | − 1.39447i | −0.716843 | − | 0.697235i | \(-0.754413\pi\) | ||||
0.716843 | − | 0.697235i | \(-0.245587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 882736. | 1.58015 | 0.790075 | − | 0.613011i | \(-0.210042\pi\) | ||||
0.790075 | + | 0.613011i | \(0.210042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −430521. | −0.751630 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 401600.i | − 0.683996i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 696654.i | 1.13003i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 220704. | 0.349498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.15285e6 | −1.78266 | −0.891328 | − | 0.453360i | \(-0.850225\pi\) | ||||
−0.891328 | + | 0.453360i | \(0.850225\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 104797.i | − 0.158270i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 147250.i | − 0.212278i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 255108. | 0.359430 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 438520. | 0.603961 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 65893.0i | − 0.0887314i | −0.999015 | − | 0.0443657i | \(-0.985873\pi\) | ||||
0.999015 | − | 0.0443657i | \(-0.0141267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 314526.i | 0.405128i | 0.979269 | + | 0.202564i | \(0.0649274\pi\) | ||||
−0.979269 | + | 0.202564i | \(0.935073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.03846e6 | −1.30859 | −0.654293 | − | 0.756241i | \(-0.727034\pi\) | ||||
−0.654293 | + | 0.756241i | \(0.727034\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −42350.0 | −0.0522184 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 509976.i | 0.615403i | 0.951483 | + | 0.307702i | \(0.0995599\pi\) | ||||
−0.951483 | + | 0.307702i | \(0.900440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 199766.i | 0.231021i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 444494. | 0.503351 | 0.251676 | − | 0.967812i | \(-0.419018\pi\) | ||||
0.251676 | + | 0.967812i | \(0.419018\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −283464. | −0.314380 | −0.157190 | − | 0.987568i | \(-0.550244\pi\) | ||||
−0.157190 | + | 0.987568i | \(0.550244\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 923440.i | 1.00321i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 693120.i | − 0.722880i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −542374. | −0.554371 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −773807. | −0.775262 | −0.387631 | − | 0.921815i | \(-0.626706\pi\) | ||||
−0.387631 | + | 0.921815i | \(0.626706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 434511.i | 0.426775i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 387714.i | 0.366167i | 0.983097 | + | 0.183083i | \(0.0586078\pi\) | ||||
−0.983097 | + | 0.183083i | \(0.941392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 348950. | 0.323232 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.55821e6 | −1.41587 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 197602.i | − 0.176158i | −0.996113 | − | 0.0880789i | \(-0.971927\pi\) | ||||
0.996113 | − | 0.0880789i | \(-0.0280728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 253897.i | − 0.217961i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 262694. | 0.221345 | 0.110672 | − | 0.993857i | \(-0.464700\pi\) | ||||
0.110672 | + | 0.993857i | \(0.464700\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −159068. | −0.131571 | −0.0657854 | − | 0.997834i | \(-0.520955\pi\) | ||||
−0.0657854 | + | 0.997834i | \(0.520955\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 133000.i | 0.108005i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.29385e6i | − 1.01318i | −0.862188 | − | 0.506589i | \(-0.830906\pi\) | ||||
0.862188 | − | 0.506589i | \(-0.169094\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −571330. | −0.439417 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.78114e6 | −1.34565 | −0.672824 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672824 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.98279e6i | 1.47167i | 0.677161 | + | 0.735835i | \(0.263210\pi\) | ||||
−0.677161 | + | 0.735835i | \(0.736790\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 26000.0i | − 0.0186324i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 88141.0 | 0.0620774 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −348593. | −0.241316 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 578360.i | 0.393577i | 0.980446 | + | 0.196788i | \(0.0630512\pi\) | ||||
−0.980446 | + | 0.196788i | \(0.936949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 370139.i | 0.243486i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.36458e6 | 0.882716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 124300. | 0.0790779 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1.07384e6i | − 0.671945i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.07602e6i | 1.86270i | 0.364120 | + | 0.931352i | \(0.381370\pi\) | ||||
−0.364120 | + | 0.931352i | \(0.618630\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 943040. | 0.561868 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.13757e6 | −1.83947 | −0.919735 | − | 0.392540i | \(-0.871597\pi\) | ||||
−0.919735 | + | 0.392540i | \(0.871597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.61784e6i | 1.51037i | 0.655514 | + | 0.755183i | \(0.272452\pi\) | ||||
−0.655514 | + | 0.755183i | \(0.727548\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.49220e6i | 1.39294i | 0.717584 | + | 0.696472i | \(0.245248\pi\) | ||||
−0.717584 | + | 0.696472i | \(0.754752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −971872. | −0.534727 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.18453e6 | 0.641626 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.10490e6i | 1.12260i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.63244e6i | 0.844245i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −346000. | −0.176233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.70125e6 | −1.35517 | −0.677586 | − | 0.735443i | \(-0.736974\pi\) | ||||
−0.677586 | + | 0.735443i | \(0.736974\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.35393e6i | − 0.669090i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.42610e6i | 0.684031i | 0.939694 | + | 0.342016i | \(0.111110\pi\) | ||||
−0.939694 | + | 0.342016i | \(0.888890\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −660303. | −0.312064 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −356345. | −0.165953 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.55570e6i | 0.713987i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.86374e6i | − 1.27676i | −0.769721 | − | 0.638381i | \(-0.779604\pi\) | ||||
0.769721 | − | 0.638381i | \(-0.220396\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −296350. | −0.130239 | −0.0651195 | − | 0.997877i | \(-0.520743\pi\) | ||||
−0.0651195 | + | 0.997877i | \(0.520743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.16242e6 | 0.503611 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2.12114e6i | − 0.906010i | −0.891508 | − | 0.453005i | \(-0.850352\pi\) | ||||
0.891508 | − | 0.453005i | \(-0.149648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 403900.i | − 0.167727i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.47512e6 | 1.42310 | 0.711548 | − | 0.702638i | \(-0.247994\pi\) | ||||
0.711548 | + | 0.702638i | \(0.247994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 850877. | 0.343636 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 102487.i | 0.0408227i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.56190e6i | − 0.605322i | −0.953098 | − | 0.302661i | \(-0.902125\pi\) | ||||
0.953098 | − | 0.302661i | \(-0.0978750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −100880. | −0.0385691 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 685900. | 0.258718 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.93773e6i | 0.721144i | 0.932731 | + | 0.360572i | \(0.117419\pi\) | ||||
−0.932731 | + | 0.360572i | \(0.882581\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.05216e6i | 1.10600i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.07495e6 | −1.09961 | −0.549806 | − | 0.835292i | \(-0.685298\pi\) | ||||
−0.549806 | + | 0.835292i | \(0.685298\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.81636e6 | −0.641046 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.31553e6i | 1.50327i | 0.659579 | + | 0.751635i | \(0.270734\pi\) | ||||
−0.659579 | + | 0.751635i | \(0.729266\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 482284.i | − 0.163691i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.36251e6 | −0.791590 | −0.395795 | − | 0.918339i | \(-0.629531\pi\) | ||||
−0.395795 | + | 0.918339i | \(0.629531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.14401e6 | −1.37082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 597870.i | − 0.195265i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.77598e6i | − 0.565539i | −0.959188 | − | 0.282769i | \(-0.908747\pi\) | ||||
0.959188 | − | 0.282769i | \(-0.0912531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −638400. | −0.200752 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.56967e6 | 0.487468 | 0.243734 | − | 0.969842i | \(-0.421628\pi\) | ||||
0.243734 | + | 0.969842i | \(0.421628\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.11910e6i | 0.343247i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 844459.i | − 0.252693i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.29485e6 | −0.382746 | −0.191373 | − | 0.981517i | \(-0.561294\pi\) | ||||
−0.191373 | + | 0.981517i | \(0.561294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.99392e6 | −0.874250 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.58895e6i | 0.458390i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 2.16783e6i | − 0.610499i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −272916. | −0.0759441 | −0.0379720 | − | 0.999279i | \(-0.512090\pi\) | ||||
−0.0379720 | + | 0.999279i | \(0.512090\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.61801e6 | −0.719890 | −0.359945 | − | 0.932974i | \(-0.617205\pi\) | ||||
−0.359945 | + | 0.932974i | \(0.617205\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.34248e6i | 0.364802i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.70780e6i | 0.453281i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 321860. | 0.0844352 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.81037e6 | 0.728735 | 0.364368 | − | 0.931255i | \(-0.381285\pi\) | ||||
0.364368 | + | 0.931255i | \(0.381285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.98509e6i | 1.53409i | 0.641593 | + | 0.767046i | \(0.278274\pi\) | ||||
−0.641593 | + | 0.767046i | \(0.721726\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.54998e6i | 1.64073i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.50486e6 | 1.85858 | 0.929290 | − | 0.369352i | \(-0.120420\pi\) | ||||
0.929290 | + | 0.369352i | \(0.120420\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.77556e6 | 0.679601 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.56806e6i | 0.379624i | 0.981820 | + | 0.189812i | \(0.0607878\pi\) | ||||
−0.981820 | + | 0.189812i | \(0.939212\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.14892e6i | − 0.745406i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.04044e6 | 0.945831 | 0.472915 | − | 0.881108i | \(-0.343202\pi\) | ||||
0.472915 | + | 0.881108i | \(0.343202\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −62920.0 | −0.0145662 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.83552e6i | 0.649213i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 2.21132e6i | − 0.495291i | −0.968851 | − | 0.247645i | \(-0.920343\pi\) | ||||
0.968851 | − | 0.247645i | \(-0.0796568\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.53009e6 | −0.782084 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.56735e6 | −0.781795 | −0.390898 | − | 0.920434i | \(-0.627835\pi\) | ||||
−0.390898 | + | 0.920434i | \(0.627835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 747757.i | 0.162109i | 0.996710 | + | 0.0810547i | \(0.0258288\pi\) | ||||
−0.996710 | + | 0.0810547i | \(0.974171\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.44511e6i | 1.15535i | 0.816266 | + | 0.577676i | \(0.196040\pi\) | ||||
−0.816266 | + | 0.577676i | \(0.803960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.07515e6 | −0.645556 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.37525e6 | 0.493352 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 300806.i | − 0.0618207i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.66129e6i | − 0.535546i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.22046e6 | 1.23875 | 0.619375 | − | 0.785095i | \(-0.287386\pi\) | ||||
0.619375 | + | 0.785095i | \(0.287386\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.65202e6 | −0.522654 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.25685e6i | − 0.245141i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.34398e6i | 0.638913i | 0.947601 | + | 0.319457i | \(0.103500\pi\) | ||||
−0.947601 | + | 0.319457i | \(0.896500\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.89977e6 | −0.359277 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.58646e6 | 1.04576 | 0.522881 | − | 0.852406i | \(-0.324857\pi\) | ||||
0.522881 | + | 0.852406i | \(0.324857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9.26893e6i | − 1.71756i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 748550.i | − 0.135935i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.29348e6 | 1.49103 | 0.745514 | − | 0.666490i | \(-0.232204\pi\) | ||||
0.745514 | + | 0.666490i | \(0.232204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 507276. | 0.0902922 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.29951e6i | 0.933933i | 0.884275 | + | 0.466967i | \(0.154653\pi\) | ||||
−0.884275 | + | 0.466967i | \(0.845347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.58825e6i | 0.274410i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24415.0 | −0.00417698 | −0.00208849 | − | 0.999998i | \(-0.500665\pi\) | ||||
−0.00208849 | + | 0.999998i | \(0.500665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.82220e6 | 0.308705 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.57962e6i | 0.936076i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 837320.i | 0.137773i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.35458e6 | −0.546663 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.76275e6 | 0.768712 | 0.384356 | − | 0.923185i | \(-0.374424\pi\) | ||||
0.384356 | + | 0.923185i | \(0.374424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 735248.i | 0.117538i | 0.998272 | + | 0.0587692i | \(0.0187176\pi\) | ||||
−0.998272 | + | 0.0587692i | \(0.981282\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.39853e6i | − 0.533046i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.45894e6 | −1.00351 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.16513e6 | 0.948868 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 197600.i | 0.0301279i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 286545.i | 0.0428802i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.73115e6 | 0.256662 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.19649e6 | −0.469548 | −0.234774 | − | 0.972050i | \(-0.575435\pi\) | ||||
−0.234774 | + | 0.972050i | \(0.575435\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 631183.i | − 0.0918662i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 8.85902e6i | − 1.26595i | −0.774171 | − | 0.632976i | \(-0.781833\pi\) | ||||
0.774171 | − | 0.632976i | \(-0.218167\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.62626e6 | 0.938292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.46504e7 | −2.05575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.42690e6i | 0.198418i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.74512e6i | 0.238335i | 0.992874 | + | 0.119167i | \(0.0380225\pi\) | ||||
−0.992874 | + | 0.119167i | \(0.961977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −944680. | −0.127866 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −977438. | −0.131124 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.32333e7i | − 1.75953i | −0.475410 | − | 0.879764i | \(-0.657700\pi\) | ||||
0.475410 | − | 0.879764i | \(-0.342300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.28645e6i | 0.168049i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.04156e7 | −1.34867 | −0.674335 | − | 0.738426i | \(-0.735570\pi\) | ||||
−0.674335 | + | 0.738426i | \(0.735570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.48163e6 | −0.318527 | −0.159264 | − | 0.987236i | \(-0.550912\pi\) | ||||
−0.159264 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.82262e6i | − 0.231905i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.31244e7i | 1.64112i | 0.571557 | + | 0.820562i | \(0.306339\pi\) | ||||
−0.571557 | + | 0.820562i | \(0.693661\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.67027e6 | −0.454989 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.87410e6 | −0.476135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.65988e6i | − 0.202258i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.86010e6i | 0.582170i | 0.956697 | + | 0.291085i | \(0.0940163\pi\) | ||||
−0.956697 | + | 0.291085i | \(0.905984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.37168e6 | −0.638002 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.31707e6 | 0.626187 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.58559e6i | − 0.185163i | −0.995705 | − | 0.0925814i | \(-0.970488\pi\) | ||||
0.995705 | − | 0.0925814i | \(-0.0295118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.17915e6i | 0.709566i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.04294e6 | −1.02978 | −0.514888 | − | 0.857258i | \(-0.672166\pi\) | ||||
−0.514888 | + | 0.857258i | \(0.672166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 729186. | 0.0823478 | 0.0411739 | − | 0.999152i | \(-0.486890\pi\) | ||||
0.0411739 | + | 0.999152i | \(0.486890\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.19316e7i | 1.33630i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.91130e6i | 0.430873i | 0.976518 | + | 0.215437i | \(0.0691175\pi\) | ||||
−0.976518 | + | 0.215437i | \(0.930883\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.81120e6 | 0.307149 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.62960e6 | 0.284962 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.52184e6i | − 0.593516i | −0.954953 | − | 0.296758i | \(-0.904094\pi\) | ||||
0.954953 | − | 0.296758i | \(-0.0959055\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.88539e6i | 0.516638i | 0.966060 | + | 0.258319i | \(0.0831686\pi\) | ||||
−0.966060 | + | 0.258319i | \(0.916831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.11150e6 | 0.431295 | 0.215647 | − | 0.976471i | \(-0.430814\pi\) | ||||
0.215647 | + | 0.976471i | \(0.430814\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.09849e7 | −1.14305 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.81355e6i | − 0.187202i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.54493e6i | 0.156942i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.05377e6 | 0.811657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.24910e6 | 0.824771 | 0.412385 | − | 0.911009i | \(-0.364696\pi\) | ||||
0.412385 | + | 0.911009i | \(0.364696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 8.06996e6i | − 0.800502i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.43666e6i | − 0.530864i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.90437e6 | −0.281385 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.29330e6 | −0.412711 | −0.206355 | − | 0.978477i | \(-0.566160\pi\) | ||||
−0.206355 | + | 0.978477i | \(0.566160\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.63045e7i | − 1.55518i | −0.628774 | − | 0.777588i | \(-0.716443\pi\) | ||||
0.628774 | − | 0.777588i | \(-0.283557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 4.42624e6i | − 0.415695i | −0.978161 | − | 0.207847i | \(-0.933354\pi\) | ||||
0.978161 | − | 0.207847i | \(-0.0666457\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.84526e6 | 0.358355 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.03075e6 | 0.0953237 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 6.27529e6i | − 0.575905i | −0.957645 | − | 0.287952i | \(-0.907025\pi\) | ||||
0.957645 | − | 0.287952i | \(-0.0929745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 7.07014e6i | − 0.639020i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.09748e7 | 0.984422 | 0.492211 | − | 0.870476i | \(-0.336189\pi\) | ||||
0.492211 | + | 0.870476i | \(0.336189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.02025e7 | 1.79846 | 0.899229 | − | 0.437478i | \(-0.144128\pi\) | ||||
0.899229 | + | 0.437478i | \(0.144128\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.06964e6i | 0.271209i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.88429e7i | − 2.51029i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 461251. | 0.0398448 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.13288e6 | 0.354361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.14233e7i | 0.972200i | 0.873903 | + | 0.486100i | \(0.161581\pi\) | ||||
−0.873903 | + | 0.486100i | \(0.838419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.43918e6i | 0.204537i | 0.994757 | + | 0.102268i | \(0.0326101\pi\) | ||||
−0.994757 | + | 0.102268i | \(0.967390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.48995e6 | −0.207260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.20168e6 | −0.181923 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.01384e6i | 0.0831606i | 0.999135 | + | 0.0415803i | \(0.0132392\pi\) | ||||
−0.999135 | + | 0.0415803i | \(0.986761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 7.26924e6i | − 0.587621i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.21284e6 | −0.418337 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.03186e6 | −0.639913 | −0.319957 | − | 0.947432i | \(-0.603668\pi\) | ||||
−0.319957 | + | 0.947432i | \(0.603668\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.17370e6i | 0.0928376i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 600080.i | − 0.0467872i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.56983e6 | −0.276347 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −259806. | −0.0199689 | −0.00998445 | − | 0.999950i | \(-0.503178\pi\) | ||||
−0.00998445 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.27297e7i | − 0.971471i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 7.67030e6i | − 0.577117i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.92848e7 | 1.44079 | 0.720393 | − | 0.693566i | \(-0.243961\pi\) | ||||
0.720393 | + | 0.693566i | \(0.243961\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.53637e6 | 0.410725 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.05755e7i | − 0.779071i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.11146e6i | 0.226030i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −926119. | −0.0668105 | −0.0334052 | − | 0.999442i | \(-0.510635\pi\) | ||||
−0.0334052 | + | 0.999442i | \(0.510635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.73600e6 | 0.482574 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.98425e6i | − 0.141173i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.02599e7i | − 1.42168i | −0.703354 | − | 0.710840i | \(-0.748315\pi\) | ||||
0.703354 | − | 0.710840i | \(-0.251685\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −211933. | −0.0147700 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.86884e6 | 0.198570 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.10982e7i | 0.762944i | 0.924380 | + | 0.381472i | \(0.124583\pi\) | ||||
−0.924380 | + | 0.381472i | \(0.875417\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.44186e6i | 0.504676i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −624962. | −0.0420962 | −0.0210481 | − | 0.999778i | \(-0.506700\pi\) | ||||
−0.0210481 | + | 0.999778i | \(0.506700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.85184e6 | 0.324609 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46436.0i | 0.00308591i | 0.999999 | + | 0.00154295i | \(0.000491137\pi\) | ||||
−0.999999 | + | 0.00154295i | \(0.999509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.50315e7i | 0.985601i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.46090e6 | 0.551077 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.12144e6 | −0.396053 | −0.198027 | − | 0.980197i | \(-0.563453\pi\) | ||||
−0.198027 | + | 0.980197i | \(0.563453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 5.41665e6i | − 0.348131i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.26458e6i | 0.207056i | 0.994627 | + | 0.103528i | \(0.0330131\pi\) | ||||
−0.994627 | + | 0.103528i | \(0.966987\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.04158e6 | −0.191644 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.60311e7 | 1.00346 | 0.501732 | − | 0.865023i | \(-0.332696\pi\) | ||||
0.501732 | + | 0.865023i | \(0.332696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16603e7i | 0.725101i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.20760e7i | − 0.741200i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.64617e7 | −1.61362 | −0.806811 | − | 0.590810i | \(-0.798808\pi\) | ||||
−0.806811 | + | 0.590810i | \(0.798808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.71400e6 | −0.164427 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2.63836e7i | − 1.58813i | −0.607836 | − | 0.794063i | \(-0.707962\pi\) | ||||
0.607836 | − | 0.794063i | \(-0.292038\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.44265e6i | 0.145147i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −948480. | −0.0559995 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.81149e6 | −0.106269 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.45699e7i | − 1.43218i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.68115e6i | 0.326964i | 0.986546 | + | 0.163482i | \(0.0522725\pi\) | ||||
−0.986546 | + | 0.163482i | \(0.947727\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.38321e6 | 0.0791037 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.71645e6 | −0.268024 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1.29793e7i | − 0.732939i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9.99383e6i | − 0.557296i | −0.960393 | − | 0.278648i | \(-0.910114\pi\) | ||||
0.960393 | − | 0.278648i | \(-0.0898863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.98568e6 | −0.442532 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.03657e6 | −0.387507 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.40972e6i | − 0.241336i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.83886e6i | 0.0993950i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.32455e7 | −1.24873 | −0.624364 | − | 0.781134i | \(-0.714642\pi\) | ||||
−0.624364 | + | 0.781134i | \(0.714642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.27367e7 | 0.679991 | 0.339995 | − | 0.940427i | \(-0.389574\pi\) | ||||
0.339995 | + | 0.940427i | \(0.389574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.11348e6i | − 0.0590819i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 4.53446e6i | − 0.237668i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.68600e6 | 0.192020 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.85748e6 | −0.406842 | −0.203421 | − | 0.979091i | \(-0.565206\pi\) | ||||
−0.203421 | + | 0.979091i | \(0.565206\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.09499e7i | − 0.563524i | −0.959484 | − | 0.281762i | \(-0.909081\pi\) | ||||
0.959484 | − | 0.281762i | \(-0.0909188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.20638e7i | − 1.12180i | −0.827883 | − | 0.560901i | \(-0.810455\pi\) | ||||
0.827883 | − | 0.560901i | \(-0.189545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.05255e6 | −0.356418 | −0.178209 | − | 0.983993i | \(-0.557030\pi\) | ||||
−0.178209 | + | 0.983993i | \(0.557030\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.05698e6 | 0.454968 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.65103e7i | 0.824407i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 9.00876e6i | − 0.444479i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.26195e7 | 1.10937 | 0.554686 | − | 0.832060i | \(-0.312838\pi\) | ||||
0.554686 | + | 0.832060i | \(0.312838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.40019e7 | 2.14527 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.24680e7i | − 0.604264i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 732050.i | 0.0350616i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.38795e7 | −0.660853 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.50616e7 | 1.18627 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.46645e6i | 0.445466i | 0.974880 | + | 0.222733i | \(0.0714978\pi\) | ||||
−0.974880 | + | 0.222733i | \(0.928502\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 941480.i | − 0.0437884i | −0.999760 | − | 0.0218942i | \(-0.993030\pi\) | ||||
0.999760 | − | 0.0218942i | \(-0.00696970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 806423. | 0.0372889 | 0.0186445 | − | 0.999826i | \(-0.494065\pi\) | ||||
0.0186445 | + | 0.999826i | \(0.494065\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 182000. | 0.00836688 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.19485e7i | 0.546119i | 0.961997 | + | 0.273059i | \(0.0880356\pi\) | ||||
−0.961997 | + | 0.273059i | \(0.911964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 616987.i | 0.0278759i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.45310e6 | 0.155117 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.33711e7 | 1.04384 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.66101e6i | 0.429029i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 7.84853e6i | − 0.344580i | −0.985046 | − | 0.172290i | \(-0.944883\pi\) | ||||
0.985046 | − | 0.172290i | \(-0.0551165\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.04852e6 | −0.176736 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.73933e7 | −0.754991 | −0.377496 | − | 0.926011i | \(-0.623215\pi\) | ||||
−0.377496 | + | 0.926011i | \(0.623215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4.31619e7i | − 1.86294i | −0.363818 | − | 0.931470i | \(-0.618527\pi\) | ||||
0.363818 | − | 0.931470i | \(-0.381473\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.25652e6i | 0.395038i | 0.980299 | + | 0.197519i | \(0.0632884\pi\) | ||||
−0.980299 | + | 0.197519i | \(0.936712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.29740e7 | −0.550579 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.11321e6 | 0.131375 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.26221e7i | 0.529666i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.55206e6i | 0.396384i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.36542e7 | 0.976135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.58306e7 | 0.649658 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 870100.i | 0.0355099i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.47293e7i | − 1.80540i | −0.430270 | − | 0.902700i | \(-0.641582\pi\) | ||||
0.430270 | − | 0.902700i | \(-0.358418\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.97608e7 | −1.19463 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.57577e7 | 1.02828 | 0.514139 | − | 0.857707i | \(-0.328112\pi\) | ||||
0.514139 | + | 0.857707i | \(0.328112\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.37532e6i | 0.372228i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.27050e6i | − 0.167709i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.63488e7 | 1.41972 | 0.709858 | − | 0.704344i | \(-0.248759\pi\) | ||||
0.709858 | + | 0.704344i | \(0.248759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.15322e7 | −0.836447 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.68898e6i | 0.219801i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.61357e7i | − 0.998929i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.96617e6 | 0.150776 | 0.0753880 | − | 0.997154i | \(-0.475980\pi\) | ||||
0.0753880 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.60960e7 | 0.986732 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 2.19630e7i | − 0.826014i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.50528e7i | 1.30429i | 0.758094 | + | 0.652145i | \(0.226131\pi\) | ||||
−0.758094 | + | 0.652145i | \(0.773869\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.83249e7 | −0.678230 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.40738e7 | −0.518130 | −0.259065 | − | 0.965860i | \(-0.583414\pi\) | ||||
−0.259065 | + | 0.965860i | \(0.583414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.86732e6i | − 0.0683816i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.73759e7i | 1.35431i | 0.735842 | + | 0.677153i | \(0.236786\pi\) | ||||
−0.735842 | + | 0.677153i | \(0.763214\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.38487e7 | −0.499165 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.74454e7 | −0.625502 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.18424e7i | − 1.13572i | −0.823124 | − | 0.567862i | \(-0.807771\pi\) | ||||
0.823124 | − | 0.567862i | \(-0.192229\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 6.80310e6i | − 0.240119i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.13852e7 | −0.750872 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.99561e7 | −0.697056 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3.28283e7i | − 1.14073i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.16276e7i | 1.08768i | 0.839190 | + | 0.543838i | \(0.183029\pi\) | ||||
−0.839190 | + | 0.543838i | \(0.816971\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.47343e7 | −0.504103 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.73412e7 | −0.930614 | −0.465307 | − | 0.885149i | \(-0.654056\pi\) | ||||
−0.465307 | + | 0.885149i | \(0.654056\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.54845e7i | − 0.524343i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.81630e6i | 0.194944i | 0.995238 | + | 0.0974721i | \(0.0310757\pi\) | ||||
−0.995238 | + | 0.0974721i | \(0.968924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.38879e6 | −0.146348 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.52420e7 | 1.50096 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 3.81817e7i | − 1.26029i | −0.776476 | − | 0.630146i | \(-0.782995\pi\) | ||||
0.776476 | − | 0.630146i | \(-0.217005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.42200e6i | − 0.0791373i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.92723e6 | 0.290219 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.44564e6 | 0.176143 | 0.0880714 | − | 0.996114i | \(-0.471930\pi\) | ||||
0.0880714 | + | 0.996114i | \(0.471930\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1.89087e7i | − 0.608541i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.77967e6i | 0.120425i | 0.998186 | + | 0.0602125i | \(0.0191778\pi\) | ||||
−0.998186 | + | 0.0602125i | \(0.980822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.13488e7 | 0.676798 |
(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 | 1100.6.b.a.749.2 | 2 | ||
5.2 | odd | 4 | 44.6.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 1100.6.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 1100.6.b.a.749.1 | 2 | ||
15.2 | even | 4 | 396.6.a.e.1.1 | 1 | |||
20.7 | even | 4 | 176.6.a.a.1.1 | 1 | |||
40.27 | even | 4 | 704.6.a.g.1.1 | 1 | |||
40.37 | odd | 4 | 704.6.a.d.1.1 | 1 | |||
55.32 | even | 4 | 484.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
44.6.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
176.6.a.a.1.1 | 1 | 20.7 | even | 4 | |||
396.6.a.e.1.1 | 1 | 15.2 | even | 4 | |||
484.6.a.b.1.1 | 1 | 55.32 | even | 4 | |||
704.6.a.d.1.1 | 1 | 40.37 | odd | 4 | |||
704.6.a.g.1.1 | 1 | 40.27 | even | 4 | |||
1100.6.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
1100.6.b.a.749.1 | 2 | 5.4 | even | 2 | inner | ||
1100.6.b.a.749.2 | 2 | 1.1 | even | 1 | trivial |