Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(199,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.199");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.c (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: | \(72.1727189158\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.199 |
Dual form | 450.6.c.m.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 148.000i | − 1.14161i | −0.821087 | − | 0.570803i | \(-0.806632\pi\) | ||||
0.821087 | − | 0.570803i | \(-0.193368\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 384.000 | 0.956862 | 0.478431 | − | 0.878125i | \(-0.341206\pi\) | ||||
0.478431 | + | 0.878125i | \(0.341206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 334.000i | 0.548136i | 0.961710 | + | 0.274068i | \(0.0883693\pi\) | ||||
−0.961710 | + | 0.274068i | \(0.911631\pi\) | |||||||
\(14\) | −592.000 | −0.807238 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 576.000i | 0.483393i | 0.970352 | + | 0.241696i | \(0.0777038\pi\) | ||||
−0.970352 | + | 0.241696i | \(0.922296\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 664.000 | 0.421972 | 0.210986 | − | 0.977489i | \(-0.432332\pi\) | ||||
0.210986 | + | 0.977489i | \(0.432332\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 1536.00i | − 0.676604i | ||||||||
\(23\) | 3840.00i | 1.51360i | 0.653645 | + | 0.756801i | \(0.273239\pi\) | ||||
−0.653645 | + | 0.756801i | \(0.726761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1336.00 | 0.387590 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2368.00i | 0.570803i | ||||||||
\(29\) | −96.0000 | −0.0211971 | −0.0105985 | − | 0.999944i | \(-0.503374\pi\) | ||||
−0.0105985 | + | 0.999944i | \(0.503374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4564.00 | −0.852985 | −0.426493 | − | 0.904491i | \(-0.640251\pi\) | ||||
−0.426493 | + | 0.904491i | \(0.640251\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2304.00 | 0.341810 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5798.00i | 0.696264i | 0.937446 | + | 0.348132i | \(0.113184\pi\) | ||||
−0.937446 | + | 0.348132i | \(0.886816\pi\) | |||||||
\(38\) | − 2656.00i | − 0.298380i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6720.00 | −0.624323 | −0.312162 | − | 0.950029i | \(-0.601053\pi\) | ||||
−0.312162 | + | 0.950029i | \(0.601053\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14872.0i | 1.22659i | 0.789855 | + | 0.613293i | \(0.210156\pi\) | ||||
−0.789855 | + | 0.613293i | \(0.789844\pi\) | |||||||
\(44\) | −6144.00 | −0.478431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15360.0 | 1.07028 | ||||||||
\(47\) | − 19200.0i | − 1.26782i | −0.773408 | − | 0.633909i | \(-0.781450\pi\) | ||||
0.773408 | − | 0.633909i | \(-0.218550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5097.00 | −0.303266 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 5344.00i | − 0.274068i | ||||||||
\(53\) | − 7776.00i | − 0.380248i | −0.981760 | − | 0.190124i | \(-0.939111\pi\) | ||||
0.981760 | − | 0.190124i | \(-0.0608890\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9472.00 | 0.403619 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 384.000i | 0.0149886i | ||||||||
\(59\) | 13056.0 | 0.488293 | 0.244146 | − | 0.969738i | \(-0.421492\pi\) | ||||
0.244146 | + | 0.969738i | \(0.421492\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42782.0 | 1.47210 | 0.736049 | − | 0.676929i | \(-0.236689\pi\) | ||||
0.736049 | + | 0.676929i | \(0.236689\pi\) | |||||||
\(62\) | 18256.0i | 0.603151i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 36656.0i | 0.997604i | 0.866716 | + | 0.498802i | \(0.166226\pi\) | ||||
−0.866716 | + | 0.498802i | \(0.833774\pi\) | |||||||
\(68\) | − 9216.00i | − 0.241696i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 64512.0 | 1.51878 | 0.759390 | − | 0.650636i | \(-0.225498\pi\) | ||||
0.759390 | + | 0.650636i | \(0.225498\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16810.0i | 0.369199i | 0.982814 | + | 0.184600i | \(0.0590988\pi\) | ||||
−0.982814 | + | 0.184600i | \(0.940901\pi\) | |||||||
\(74\) | 23192.0 | 0.492333 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10624.0 | −0.210986 | ||||||||
\(77\) | − 56832.0i | − 1.09236i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −28076.0 | −0.506136 | −0.253068 | − | 0.967448i | \(-0.581440\pi\) | ||||
−0.253068 | + | 0.967448i | \(0.581440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26880.0i | 0.441463i | ||||||||
\(83\) | 66432.0i | 1.05848i | 0.848473 | + | 0.529239i | \(0.177523\pi\) | ||||
−0.848473 | + | 0.529239i | \(0.822477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 59488.0 | 0.867328 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 24576.0i | 0.338302i | ||||||||
\(89\) | 81792.0 | 1.09455 | 0.547275 | − | 0.836953i | \(-0.315665\pi\) | ||||
0.547275 | + | 0.836953i | \(0.315665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49432.0 | 0.625756 | ||||||||
\(92\) | − 61440.0i | − 0.756801i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −76800.0 | −0.896482 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 29938.0i | − 0.323068i | −0.986867 | − | 0.161534i | \(-0.948356\pi\) | ||||
0.986867 | − | 0.161534i | \(-0.0516441\pi\) | |||||||
\(98\) | 20388.0i | 0.214442i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 178656. | 1.74267 | 0.871333 | − | 0.490692i | \(-0.163256\pi\) | ||||
0.871333 | + | 0.490692i | \(0.163256\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 115228.i | 1.07020i | 0.844789 | + | 0.535100i | \(0.179726\pi\) | ||||
−0.844789 | + | 0.535100i | \(0.820274\pi\) | |||||||
\(104\) | −21376.0 | −0.193795 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −31104.0 | −0.268876 | ||||||||
\(107\) | − 76032.0i | − 0.642003i | −0.947079 | − | 0.321001i | \(-0.895981\pi\) | ||||
0.947079 | − | 0.321001i | \(-0.104019\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 231118. | 1.86323 | 0.931617 | − | 0.363441i | \(-0.118398\pi\) | ||||
0.931617 | + | 0.363441i | \(0.118398\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 37888.0i | − 0.285402i | ||||||||
\(113\) | − 142464.i | − 1.04956i | −0.851237 | − | 0.524782i | \(-0.824147\pi\) | ||||
0.851237 | − | 0.524782i | \(-0.175853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1536.00 | 0.0105985 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 52224.0i | − 0.345275i | ||||||||
\(119\) | 85248.0 | 0.551845 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13595.0 | −0.0844143 | ||||||||
\(122\) | − 171128.i | − 1.04093i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 73024.0 | 0.426493 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 988.000i | − 0.00543560i | −0.999996 | − | 0.00271780i | \(-0.999135\pi\) | ||||
0.999996 | − | 0.00271780i | \(-0.000865104\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 224256. | 1.14174 | 0.570868 | − | 0.821042i | \(-0.306607\pi\) | ||||
0.570868 | + | 0.821042i | \(0.306607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 98272.0i | − 0.481727i | ||||||||
\(134\) | 146624. | 0.705412 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −36864.0 | −0.170905 | ||||||||
\(137\) | − 278976.i | − 1.26989i | −0.772558 | − | 0.634944i | \(-0.781023\pi\) | ||||
0.772558 | − | 0.634944i | \(-0.218977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −177200. | −0.777905 | −0.388953 | − | 0.921258i | \(-0.627163\pi\) | ||||
−0.388953 | + | 0.921258i | \(0.627163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 258048.i | − 1.07394i | ||||||||
\(143\) | 128256.i | 0.524490i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 67240.0 | 0.261063 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 92768.0i | − 0.348132i | ||||||||
\(149\) | −236064. | −0.871092 | −0.435546 | − | 0.900166i | \(-0.643445\pi\) | ||||
−0.435546 | + | 0.900166i | \(0.643445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −482836. | −1.72329 | −0.861643 | − | 0.507515i | \(-0.830564\pi\) | ||||
−0.861643 | + | 0.507515i | \(0.830564\pi\) | |||||||
\(152\) | 42496.0i | 0.149190i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −227328. | −0.772416 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 381086.i | 1.23388i | 0.787009 | + | 0.616941i | \(0.211628\pi\) | ||||
−0.787009 | + | 0.616941i | \(0.788372\pi\) | |||||||
\(158\) | 112304.i | 0.357892i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 568320. | 1.72794 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 162920.i | − 0.480292i | −0.970737 | − | 0.240146i | \(-0.922805\pi\) | ||||
0.970737 | − | 0.240146i | \(-0.0771953\pi\) | |||||||
\(164\) | 107520. | 0.312162 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 265728. | 0.748457 | ||||||||
\(167\) | − 566016.i | − 1.57050i | −0.619180 | − | 0.785249i | \(-0.712535\pi\) | ||||
0.619180 | − | 0.785249i | \(-0.287465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 259737. | 0.699547 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 237952.i | − 0.613293i | ||||||||
\(173\) | 218208.i | 0.554313i | 0.960825 | + | 0.277157i | \(0.0893921\pi\) | ||||
−0.960825 | + | 0.277157i | \(0.910608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 98304.0 | 0.239216 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 327168.i | − 0.773964i | ||||||||
\(179\) | 412416. | 0.962062 | 0.481031 | − | 0.876704i | \(-0.340262\pi\) | ||||
0.481031 | + | 0.876704i | \(0.340262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25558.0 | −0.0579870 | −0.0289935 | − | 0.999580i | \(-0.509230\pi\) | ||||
−0.0289935 | + | 0.999580i | \(0.509230\pi\) | |||||||
\(182\) | − 197728.i | − 0.442476i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −245760. | −0.535139 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 221184.i | 0.462540i | ||||||||
\(188\) | 307200.i | 0.633909i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 400128. | 0.793625 | 0.396813 | − | 0.917900i | \(-0.370116\pi\) | ||||
0.396813 | + | 0.917900i | \(0.370116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 699650.i | − 1.35203i | −0.736886 | − | 0.676017i | \(-0.763705\pi\) | ||||
0.736886 | − | 0.676017i | \(-0.236295\pi\) | |||||||
\(194\) | −119752. | −0.228443 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 81552.0 | 0.151633 | ||||||||
\(197\) | 406368.i | 0.746026i | 0.927826 | + | 0.373013i | \(0.121675\pi\) | ||||
−0.927826 | + | 0.373013i | \(0.878325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 361996. | 0.647994 | 0.323997 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323997 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 714624.i | − 1.23225i | ||||||||
\(203\) | 14208.0i | 0.0241987i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 460912. | 0.756746 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 85504.0i | 0.137034i | ||||||||
\(209\) | 254976. | 0.403770 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 151856. | 0.234815 | 0.117407 | − | 0.993084i | \(-0.462542\pi\) | ||||
0.117407 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(212\) | 124416.i | 0.190124i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −304128. | −0.453965 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 675472.i | 0.973774i | ||||||||
\(218\) | − 924472.i | − 1.31751i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −192384. | −0.264965 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.09332e6i | 1.47227i | 0.676836 | + | 0.736134i | \(0.263351\pi\) | ||||
−0.676836 | + | 0.736134i | \(0.736649\pi\) | |||||||
\(224\) | −151552. | −0.201810 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −569856. | −0.742154 | ||||||||
\(227\) | − 566400.i | − 0.729556i | −0.931095 | − | 0.364778i | \(-0.881145\pi\) | ||||
0.931095 | − | 0.364778i | \(-0.118855\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 587206. | 0.739949 | 0.369974 | − | 0.929042i | \(-0.379366\pi\) | ||||
0.369974 | + | 0.929042i | \(0.379366\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 6144.00i | − 0.00749430i | ||||||||
\(233\) | − 579456.i | − 0.699247i | −0.936890 | − | 0.349624i | \(-0.886309\pi\) | ||||
0.936890 | − | 0.349624i | \(-0.113691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −208896. | −0.244146 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 340992.i | − 0.390213i | ||||||||
\(239\) | 584448. | 0.661837 | 0.330919 | − | 0.943659i | \(-0.392641\pi\) | ||||
0.330919 | + | 0.943659i | \(0.392641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −414130. | −0.459298 | −0.229649 | − | 0.973274i | \(-0.573758\pi\) | ||||
−0.229649 | + | 0.973274i | \(0.573758\pi\) | |||||||
\(242\) | 54380.0i | 0.0596899i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −684512. | −0.736049 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 221776.i | 0.231298i | ||||||||
\(248\) | − 292096.i | − 0.301576i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.89965e6 | −1.90322 | −0.951610 | − | 0.307309i | \(-0.900571\pi\) | ||||
−0.951610 | + | 0.307309i | \(0.900571\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.47456e6i | 1.44831i | ||||||||
\(254\) | −3952.00 | −0.00384355 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 447744.i | 0.422860i | 0.977393 | + | 0.211430i | \(0.0678121\pi\) | ||||
−0.977393 | + | 0.211430i | \(0.932188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 858104. | 0.794860 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 897024.i | − 0.807330i | ||||||||
\(263\) | 67584.0i | 0.0602496i | 0.999546 | + | 0.0301248i | \(0.00959048\pi\) | ||||
−0.999546 | + | 0.0301248i | \(0.990410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −393088. | −0.340632 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 586496.i | − 0.498802i | ||||||||
\(269\) | −564192. | −0.475386 | −0.237693 | − | 0.971340i | \(-0.576391\pi\) | ||||
−0.237693 | + | 0.971340i | \(0.576391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 720308. | 0.595792 | 0.297896 | − | 0.954598i | \(-0.403715\pi\) | ||||
0.297896 | + | 0.954598i | \(0.403715\pi\) | |||||||
\(272\) | 147456.i | 0.120848i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.11590e6 | −0.897946 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 141142.i | − 0.110524i | −0.998472 | − | 0.0552620i | \(-0.982401\pi\) | ||||
0.998472 | − | 0.0552620i | \(-0.0175994\pi\) | |||||||
\(278\) | 708800.i | 0.550062i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 584448. | 0.441550 | 0.220775 | − | 0.975325i | \(-0.429141\pi\) | ||||
0.220775 | + | 0.975325i | \(0.429141\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 177056.i | − 0.131415i | −0.997839 | − | 0.0657074i | \(-0.979070\pi\) | ||||
0.997839 | − | 0.0657074i | \(-0.0209304\pi\) | |||||||
\(284\) | −1.03219e6 | −0.759390 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 513024. | 0.370871 | ||||||||
\(287\) | 994560.i | 0.712732i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.08808e6 | 0.766331 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 268960.i | − 0.184600i | ||||||||
\(293\) | 956832.i | 0.651128i | 0.945520 | + | 0.325564i | \(0.105554\pi\) | ||||
−0.945520 | + | 0.325564i | \(0.894446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −371072. | −0.246166 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 944256.i | 0.615955i | ||||||||
\(299\) | −1.28256e6 | −0.829659 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.20106e6 | 1.40028 | ||||||||
\(302\) | 1.93134e6i | 1.21855i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 169984. | 0.105493 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.88286e6i | 1.74573i | 0.487958 | + | 0.872867i | \(0.337742\pi\) | ||||
−0.487958 | + | 0.872867i | \(0.662258\pi\) | |||||||
\(308\) | 909312.i | 0.546180i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.60045e6 | −1.52457 | −0.762285 | − | 0.647242i | \(-0.775922\pi\) | ||||
−0.762285 | + | 0.647242i | \(0.775922\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.58079e6i | 1.48899i | 0.667628 | + | 0.744495i | \(0.267310\pi\) | ||||
−0.667628 | + | 0.744495i | \(0.732690\pi\) | |||||||
\(314\) | 1.52434e6 | 0.872487 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 449216. | 0.253068 | ||||||||
\(317\) | 2.31101e6i | 1.29168i | 0.763475 | + | 0.645838i | \(0.223492\pi\) | ||||
−0.763475 | + | 0.645838i | \(0.776508\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36864.0 | −0.0202827 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 2.27328e6i | − 1.22184i | ||||||||
\(323\) | 382464.i | 0.203978i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −651680. | −0.339618 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 430080.i | − 0.220732i | ||||||||
\(329\) | −2.84160e6 | −1.44735 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −637024. | −0.319585 | −0.159792 | − | 0.987151i | \(-0.551082\pi\) | ||||
−0.159792 | + | 0.987151i | \(0.551082\pi\) | |||||||
\(332\) | − 1.06291e6i | − 0.529239i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.26406e6 | −1.11051 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.38665e6i | 1.62441i | 0.583371 | + | 0.812206i | \(0.301733\pi\) | ||||
−0.583371 | + | 0.812206i | \(0.698267\pi\) | |||||||
\(338\) | − 1.03895e6i | − 0.494655i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.75258e6 | −0.816189 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.73308e6i | − 0.795396i | ||||||||
\(344\) | −951808. | −0.433664 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 872832. | 0.391959 | ||||||||
\(347\) | 2.77824e6i | 1.23864i | 0.785138 | + | 0.619321i | \(0.212592\pi\) | ||||
−0.785138 | + | 0.619321i | \(0.787408\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.55536e6 | −0.683545 | −0.341772 | − | 0.939783i | \(-0.611027\pi\) | ||||
−0.341772 | + | 0.939783i | \(0.611027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 393216.i | − 0.169151i | ||||||||
\(353\) | − 2.11776e6i | − 0.904565i | −0.891875 | − | 0.452283i | \(-0.850610\pi\) | ||||
0.891875 | − | 0.452283i | \(-0.149390\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.30867e6 | −0.547275 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 1.64966e6i | − 0.680280i | ||||||||
\(359\) | −2.17498e6 | −0.890673 | −0.445337 | − | 0.895363i | \(-0.646916\pi\) | ||||
−0.445337 | + | 0.895363i | \(0.646916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03520e6 | −0.821939 | ||||||||
\(362\) | 102232.i | 0.0410030i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −790912. | −0.312878 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.05336e6i | 0.408235i | 0.978946 | + | 0.204117i | \(0.0654324\pi\) | ||||
−0.978946 | + | 0.204117i | \(0.934568\pi\) | |||||||
\(368\) | 983040.i | 0.378400i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.15085e6 | −0.434093 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 677098.i | 0.251988i | 0.992031 | + | 0.125994i | \(0.0402120\pi\) | ||||
−0.992031 | + | 0.125994i | \(0.959788\pi\) | |||||||
\(374\) | 884736. | 0.327065 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.22880e6 | 0.448241 | ||||||||
\(377\) | − 32064.0i | − 0.0116189i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.10748e6 | 1.82645 | 0.913227 | − | 0.407452i | \(-0.133582\pi\) | ||||
0.913227 | + | 0.407452i | \(0.133582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 1.60051e6i | − 0.561178i | ||||||||
\(383\) | − 1.63200e6i | − 0.568491i | −0.958752 | − | 0.284245i | \(-0.908257\pi\) | ||||
0.958752 | − | 0.284245i | \(-0.0917430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.79860e6 | −0.956032 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 479008.i | 0.161534i | ||||||||
\(389\) | 4.46563e6 | 1.49627 | 0.748133 | − | 0.663549i | \(-0.230950\pi\) | ||||
0.748133 | + | 0.663549i | \(0.230950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.21184e6 | −0.731664 | ||||||||
\(392\) | − 326208.i | − 0.107221i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.62547e6 | 0.527520 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 611026.i | − 0.194573i | −0.995256 | − | 0.0972867i | \(-0.968984\pi\) | ||||
0.995256 | − | 0.0972867i | \(-0.0310164\pi\) | |||||||
\(398\) | − 1.44798e6i | − 0.458201i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.09158e6 | −1.89177 | −0.945887 | − | 0.324496i | \(-0.894805\pi\) | ||||
−0.945887 | + | 0.324496i | \(0.894805\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.52438e6i | − 0.467552i | ||||||||
\(404\) | −2.85850e6 | −0.871333 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 56832.0 | 0.0171111 | ||||||||
\(407\) | 2.22643e6i | 0.666229i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.89108e6 | −0.854578 | −0.427289 | − | 0.904115i | \(-0.640531\pi\) | ||||
−0.427289 | + | 0.904115i | \(0.640531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 1.84365e6i | − 0.535100i | ||||||||
\(413\) | − 1.93229e6i | − 0.557438i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 342016. | 0.0968976 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 1.01990e6i | − 0.285508i | ||||||||
\(419\) | 2.98406e6 | 0.830373 | 0.415186 | − | 0.909736i | \(-0.363716\pi\) | ||||
0.415186 | + | 0.909736i | \(0.363716\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 822074. | 0.226051 | 0.113025 | − | 0.993592i | \(-0.463946\pi\) | ||||
0.113025 | + | 0.993592i | \(0.463946\pi\) | |||||||
\(422\) | − 607424.i | − 0.166039i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 497664. | 0.134438 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.33174e6i | − 1.68056i | ||||||||
\(428\) | 1.21651e6i | 0.321001i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.32448e6 | 1.63995 | 0.819977 | − | 0.572397i | \(-0.193986\pi\) | ||||
0.819977 | + | 0.572397i | \(0.193986\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 851902.i | 0.218358i | 0.994022 | + | 0.109179i | \(0.0348222\pi\) | ||||
−0.994022 | + | 0.109179i | \(0.965178\pi\) | |||||||
\(434\) | 2.70189e6 | 0.688562 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.69789e6 | −0.931617 | ||||||||
\(437\) | 2.54976e6i | 0.638698i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 334732. | 0.0828964 | 0.0414482 | − | 0.999141i | \(-0.486803\pi\) | ||||
0.0414482 | + | 0.999141i | \(0.486803\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 769536.i | 0.187358i | ||||||||
\(443\) | 1.76218e6i | 0.426619i | 0.976985 | + | 0.213309i | \(0.0684242\pi\) | ||||
−0.976985 | + | 0.213309i | \(0.931576\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.37330e6 | 1.04105 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 606208.i | 0.142701i | ||||||||
\(449\) | −6.51859e6 | −1.52594 | −0.762971 | − | 0.646433i | \(-0.776260\pi\) | ||||
−0.762971 | + | 0.646433i | \(0.776260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.58048e6 | −0.597392 | ||||||||
\(452\) | 2.27942e6i | 0.524782i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.26560e6 | −0.515874 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 92074.0i | − 0.0206227i | −0.999947 | − | 0.0103114i | \(-0.996718\pi\) | ||||
0.999947 | − | 0.0103114i | \(-0.00328227\pi\) | |||||||
\(458\) | − 2.34882e6i | − 0.523223i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 257568. | 0.0564468 | 0.0282234 | − | 0.999602i | \(-0.491015\pi\) | ||||
0.0282234 | + | 0.999602i | \(0.491015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3.96228e6i | − 0.858998i | −0.903067 | − | 0.429499i | \(-0.858690\pi\) | ||||
0.903067 | − | 0.429499i | \(-0.141310\pi\) | |||||||
\(464\) | −24576.0 | −0.00529927 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.31782e6 | −0.494442 | ||||||||
\(467\) | − 3.48941e6i | − 0.740388i | −0.928954 | − | 0.370194i | \(-0.879291\pi\) | ||||
0.928954 | − | 0.370194i | \(-0.120709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.42509e6 | 1.13887 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 835584.i | 0.172637i | ||||||||
\(473\) | 5.71085e6i | 1.17367i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.36397e6 | −0.275922 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 2.33779e6i | − 0.467990i | ||||||||
\(479\) | −513024. | −0.102164 | −0.0510821 | − | 0.998694i | \(-0.516267\pi\) | ||||
−0.0510821 | + | 0.998694i | \(0.516267\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.93653e6 | −0.381647 | ||||||||
\(482\) | 1.65652e6i | 0.324772i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 217520. | 0.0422071 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.14499e6i | 0.791956i | 0.918260 | + | 0.395978i | \(0.129594\pi\) | ||||
−0.918260 | + | 0.395978i | \(0.870406\pi\) | |||||||
\(488\) | 2.73805e6i | 0.520465i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.75866e6 | 0.516409 | 0.258205 | − | 0.966090i | \(-0.416869\pi\) | ||||
0.258205 | + | 0.966090i | \(0.416869\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 55296.0i | − 0.0102465i | ||||||||
\(494\) | 887104. | 0.163552 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.16838e6 | −0.213246 | ||||||||
\(497\) | − 9.54778e6i | − 1.73385i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −660896. | −0.118818 | −0.0594089 | − | 0.998234i | \(-0.518922\pi\) | ||||
−0.0594089 | + | 0.998234i | \(0.518922\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.59859e6i | 1.34578i | ||||||||
\(503\) | 944640.i | 0.166474i | 0.996530 | + | 0.0832370i | \(0.0265258\pi\) | ||||
−0.996530 | + | 0.0832370i | \(0.973474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.89824e6 | 1.02411 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15808.0i | 0.00271780i | ||||||||
\(509\) | 7.83773e6 | 1.34090 | 0.670449 | − | 0.741956i | \(-0.266102\pi\) | ||||
0.670449 | + | 0.741956i | \(0.266102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.48788e6 | 0.421480 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.79098e6 | 0.299007 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7.37280e6i | − 1.21313i | ||||||||
\(518\) | − 3.43242e6i | − 0.562051i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.29645e6 | 0.532049 | 0.266025 | − | 0.963966i | \(-0.414290\pi\) | ||||
0.266025 | + | 0.963966i | \(0.414290\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6.50238e6i | − 1.03948i | −0.854323 | − | 0.519742i | \(-0.826028\pi\) | ||||
0.854323 | − | 0.519742i | \(-0.173972\pi\) | |||||||
\(524\) | −3.58810e6 | −0.570868 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 270336. | 0.0426029 | ||||||||
\(527\) | − 2.62886e6i | − 0.412327i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.30926e6 | −1.29099 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.57235e6i | 0.240863i | ||||||||
\(533\) | − 2.24448e6i | − 0.342214i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.34598e6 | −0.352706 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.25677e6i | 0.336149i | ||||||||
\(539\) | −1.95725e6 | −0.290184 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.82714e6 | 1.44356 | 0.721778 | − | 0.692124i | \(-0.243325\pi\) | ||||
0.721778 | + | 0.692124i | \(0.243325\pi\) | |||||||
\(542\) | − 2.88123e6i | − 0.421289i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 589824. | 0.0854526 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.42580e6i | − 0.489546i | −0.969580 | − | 0.244773i | \(-0.921287\pi\) | ||||
0.969580 | − | 0.244773i | \(-0.0787135\pi\) | |||||||
\(548\) | 4.46362e6i | 0.634944i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −63744.0 | −0.00894459 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.15525e6i | 0.577809i | ||||||||
\(554\) | −564568. | −0.0781523 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.83520e6 | 0.388953 | ||||||||
\(557\) | − 6.43363e6i | − 0.878655i | −0.898327 | − | 0.439327i | \(-0.855217\pi\) | ||||
0.898327 | − | 0.439327i | \(-0.144783\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.96725e6 | −0.672336 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 2.33779e6i | − 0.312223i | ||||||||
\(563\) | − 753024.i | − 0.100124i | −0.998746 | − | 0.0500620i | \(-0.984058\pi\) | ||||
0.998746 | − | 0.0500620i | \(-0.0159419\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −708224. | −0.0929244 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.12877e6i | 0.536970i | ||||||||
\(569\) | 1.11481e7 | 1.44351 | 0.721755 | − | 0.692148i | \(-0.243336\pi\) | ||||
0.721755 | + | 0.692148i | \(0.243336\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 191024. | 0.0245187 | 0.0122594 | − | 0.999925i | \(-0.496098\pi\) | ||||
0.0122594 | + | 0.999925i | \(0.496098\pi\) | |||||||
\(572\) | − 2.05210e6i | − 0.262245i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.97824e6 | 0.503978 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.03722e7i | 1.29697i | 0.761227 | + | 0.648486i | \(0.224597\pi\) | ||||
−0.761227 | + | 0.648486i | \(0.775403\pi\) | |||||||
\(578\) | − 4.35232e6i | − 0.541878i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.83194e6 | 1.20837 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.98598e6i | − 0.363845i | ||||||||
\(584\) | −1.07584e6 | −0.130532 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.82733e6 | 0.460417 | ||||||||
\(587\) | − 2.97062e6i | − 0.355838i | −0.984045 | − | 0.177919i | \(-0.943063\pi\) | ||||
0.984045 | − | 0.177919i | \(-0.0569365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.03050e6 | −0.359936 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.48429e6i | 0.174066i | ||||||||
\(593\) | 7.55827e6i | 0.882644i | 0.897349 | + | 0.441322i | \(0.145490\pi\) | ||||
−0.897349 | + | 0.441322i | \(0.854510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.77702e6 | 0.435546 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.13024e6i | 0.586658i | ||||||||
\(599\) | −6.69158e6 | −0.762012 | −0.381006 | − | 0.924573i | \(-0.624422\pi\) | ||||
−0.381006 | + | 0.924573i | \(0.624422\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.20359e6 | −0.361785 | −0.180893 | − | 0.983503i | \(-0.557899\pi\) | ||||
−0.180893 | + | 0.983503i | \(0.557899\pi\) | |||||||
\(602\) | − 8.80422e6i | − 0.990147i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.72538e6 | 0.861643 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.35585e7i | − 1.49362i | −0.665038 | − | 0.746809i | \(-0.731585\pi\) | ||||
0.665038 | − | 0.746809i | \(-0.268415\pi\) | |||||||
\(608\) | − 679936.i | − 0.0745949i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.41280e6 | 0.694936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.07654e7i | 1.15712i | 0.815639 | + | 0.578561i | \(0.196385\pi\) | ||||
−0.815639 | + | 0.578561i | \(0.803615\pi\) | |||||||
\(614\) | 1.15315e7 | 1.23442 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.63725e6 | 0.386208 | ||||||||
\(617\) | − 9.33504e6i | − 0.987196i | −0.869690 | − | 0.493598i | \(-0.835681\pi\) | ||||
0.869690 | − | 0.493598i | \(-0.164319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.07664e6 | −0.952135 | −0.476067 | − | 0.879409i | \(-0.657938\pi\) | ||||
−0.476067 | + | 0.879409i | \(0.657938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.04018e7i | 1.07803i | ||||||||
\(623\) | − 1.21052e7i | − 1.24955i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.03232e7 | 1.05288 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 6.09738e6i | − 0.616941i | ||||||||
\(629\) | −3.33965e6 | −0.336569 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.13367e7 | −1.13348 | −0.566741 | − | 0.823896i | \(-0.691796\pi\) | ||||
−0.566741 | + | 0.823896i | \(0.691796\pi\) | |||||||
\(632\) | − 1.79686e6i | − 0.178946i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.24403e6 | 0.913352 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.70240e6i | − 0.166231i | ||||||||
\(638\) | 147456.i | 0.0143420i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.55449e7 | 1.49432 | 0.747159 | − | 0.664646i | \(-0.231418\pi\) | ||||
0.747159 | + | 0.664646i | \(0.231418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.80026e6i | 0.839399i | 0.907663 | + | 0.419699i | \(0.137864\pi\) | ||||
−0.907663 | + | 0.419699i | \(0.862136\pi\) | |||||||
\(644\) | −9.09312e6 | −0.863969 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.52986e6 | 0.144235 | ||||||||
\(647\) | 1.08449e7i | 1.01851i | 0.860615 | + | 0.509256i | \(0.170079\pi\) | ||||
−0.860615 | + | 0.509256i | \(0.829921\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.01350e6 | 0.467229 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.60672e6i | 0.240146i | ||||||||
\(653\) | 9.88771e6i | 0.907429i | 0.891147 | + | 0.453715i | \(0.149901\pi\) | ||||
−0.891147 | + | 0.453715i | \(0.850099\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.72032e6 | −0.156081 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.13664e7i | 1.02343i | ||||||||
\(659\) | 1.46150e7 | 1.31095 | 0.655476 | − | 0.755216i | \(-0.272468\pi\) | ||||
0.655476 | + | 0.755216i | \(0.272468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57792e7 | 1.40469 | 0.702347 | − | 0.711834i | \(-0.252135\pi\) | ||||
0.702347 | + | 0.711834i | \(0.252135\pi\) | |||||||
\(662\) | 2.54810e6i | 0.225980i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.25165e6 | −0.374229 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 368640.i | − 0.0320840i | ||||||||
\(668\) | 9.05626e6i | 0.785249i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.64283e7 | 1.40859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 6.64939e6i | − 0.565906i | −0.959134 | − | 0.282953i | \(-0.908686\pi\) | ||||
0.959134 | − | 0.282953i | \(-0.0913141\pi\) | |||||||
\(674\) | 1.35466e7 | 1.14863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.15579e6 | −0.349774 | ||||||||
\(677\) | 4.42550e6i | 0.371100i | 0.982635 | + | 0.185550i | \(0.0594067\pi\) | ||||
−0.982635 | + | 0.185550i | \(0.940593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.43082e6 | −0.368816 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.01030e6i | 0.577133i | ||||||||
\(683\) | 4.67827e6i | 0.383737i | 0.981421 | + | 0.191869i | \(0.0614547\pi\) | ||||
−0.981421 | + | 0.191869i | \(0.938545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.93232e6 | −0.562430 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.80723e6i | 0.306647i | ||||||||
\(689\) | 2.59718e6 | 0.208427 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.54102e6 | −0.441463 | −0.220731 | − | 0.975335i | \(-0.570844\pi\) | ||||
−0.220731 | + | 0.975335i | \(0.570844\pi\) | |||||||
\(692\) | − 3.49133e6i | − 0.277157i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.11130e7 | 0.875853 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 3.87072e6i | − 0.301793i | ||||||||
\(698\) | 6.22143e6i | 0.483339i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.53443e6 | −0.502242 | −0.251121 | − | 0.967956i | \(-0.580799\pi\) | ||||
−0.251121 | + | 0.967956i | \(0.580799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.84987e6i | 0.293804i | ||||||||
\(704\) | −1.57286e6 | −0.119608 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.47104e6 | −0.639624 | ||||||||
\(707\) | − 2.64411e7i | − 1.98944i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.86541e6 | 0.288789 | 0.144394 | − | 0.989520i | \(-0.453877\pi\) | ||||
0.144394 | + | 0.989520i | \(0.453877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.23469e6i | 0.386982i | ||||||||
\(713\) | − 1.75258e7i | − 1.29108i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.59866e6 | −0.481031 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.69990e6i | 0.629801i | ||||||||
\(719\) | −4.80614e6 | −0.346717 | −0.173358 | − | 0.984859i | \(-0.555462\pi\) | ||||
−0.173358 | + | 0.984859i | \(0.555462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.70537e7 | 1.22175 | ||||||||
\(722\) | 8.14081e6i | 0.581199i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 408928. | 0.0289935 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.90590e7i | − 1.33741i | −0.743529 | − | 0.668704i | \(-0.766850\pi\) | ||||
0.743529 | − | 0.668704i | \(-0.233150\pi\) | |||||||
\(728\) | 3.16365e6i | 0.221238i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.56627e6 | −0.592923 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5.69616e6i | − 0.391582i | −0.980646 | − | 0.195791i | \(-0.937273\pi\) | ||||
0.980646 | − | 0.195791i | \(-0.0627274\pi\) | |||||||
\(734\) | 4.21342e6 | 0.288666 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.93216e6 | 0.267570 | ||||||||
\(737\) | 1.40759e7i | 0.954570i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.84902e7 | −1.24546 | −0.622730 | − | 0.782437i | \(-0.713976\pi\) | ||||
−0.622730 | + | 0.782437i | \(0.713976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.60339e6i | 0.306950i | ||||||||
\(743\) | − 9.90336e6i | − 0.658128i | −0.944308 | − | 0.329064i | \(-0.893267\pi\) | ||||
0.944308 | − | 0.329064i | \(-0.106733\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.70839e6 | 0.178182 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 3.53894e6i | − 0.231270i | ||||||||
\(749\) | −1.12527e7 | −0.732915 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.05914e6 | −0.586121 | −0.293060 | − | 0.956094i | \(-0.594674\pi\) | ||||
−0.293060 | + | 0.956094i | \(0.594674\pi\) | |||||||
\(752\) | − 4.91520e6i | − 0.316954i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −128256. | −0.00821579 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.16677e7i | − 0.740022i | −0.929027 | − | 0.370011i | \(-0.879354\pi\) | ||||
0.929027 | − | 0.370011i | \(-0.120646\pi\) | |||||||
\(758\) | − 2.04299e7i | − 1.29150i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.27398e7 | −0.797444 | −0.398722 | − | 0.917072i | \(-0.630546\pi\) | ||||
−0.398722 | + | 0.917072i | \(0.630546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.42055e7i | − 2.12708i | ||||||||
\(764\) | −6.40205e6 | −0.396813 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.52800e6 | −0.401983 | ||||||||
\(767\) | 4.36070e6i | 0.267651i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.06783e7 | −0.651156 | −0.325578 | − | 0.945515i | \(-0.605559\pi\) | ||||
−0.325578 | + | 0.945515i | \(0.605559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.11944e7i | 0.676017i | ||||||||
\(773\) | 9.18634e6i | 0.552960i | 0.961020 | + | 0.276480i | \(0.0891679\pi\) | ||||
−0.961020 | + | 0.276480i | \(0.910832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.91603e6 | 0.114222 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 1.78625e7i | − 1.05802i | ||||||||
\(779\) | −4.46208e6 | −0.263447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.47726e7 | 1.45326 | ||||||||
\(782\) | 8.84736e6i | 0.517365i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.30483e6 | −0.0758166 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 9.28209e6i | − 0.534206i | −0.963668 | − | 0.267103i | \(-0.913934\pi\) | ||||
0.963668 | − | 0.267103i | \(-0.0860664\pi\) | |||||||
\(788\) | − 6.50189e6i | − 0.373013i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.10847e7 | −1.19819 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.42892e7i | 0.806909i | ||||||||
\(794\) | −2.44410e6 | −0.137584 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.79194e6 | −0.323997 | ||||||||
\(797\) | 21792.0i | 0.00121521i | 1.00000 | 0.000607605i | \(0.000193407\pi\) | |||||
−1.00000 | 0.000607605i | \(0.999807\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.10592e7 | 0.612854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.43663e7i | 1.33769i | ||||||||
\(803\) | 6.45504e6i | 0.353273i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.09750e6 | −0.330609 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.14340e7i | 0.616125i | ||||||||
\(809\) | −1.23085e7 | −0.661204 | −0.330602 | − | 0.943770i | \(-0.607252\pi\) | ||||
−0.330602 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.34636e7 | −1.25269 | −0.626343 | − | 0.779547i | \(-0.715449\pi\) | ||||
−0.626343 | + | 0.779547i | \(0.715449\pi\) | |||||||
\(812\) | − 227328.i | − 0.0120994i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.90573e6 | 0.471095 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.87501e6i | 0.517586i | ||||||||
\(818\) | 1.15643e7i | 0.604278i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.44206e7 | −0.746666 | −0.373333 | − | 0.927697i | \(-0.621785\pi\) | ||||
−0.373333 | + | 0.927697i | \(0.621785\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3.43419e7i | − 1.76736i | −0.468093 | − | 0.883679i | \(-0.655059\pi\) | ||||
0.468093 | − | 0.883679i | \(-0.344941\pi\) | |||||||
\(824\) | −7.37459e6 | −0.378373 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.72915e6 | −0.394168 | ||||||||
\(827\) | 2.13327e7i | 1.08463i | 0.840174 | + | 0.542316i | \(0.182453\pi\) | ||||
−0.840174 | + | 0.542316i | \(0.817547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.63751e6 | −0.133293 | −0.0666465 | − | 0.997777i | \(-0.521230\pi\) | ||||
−0.0666465 | + | 0.997777i | \(0.521230\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 1.36806e6i | − 0.0685170i | ||||||||
\(833\) | − 2.93587e6i | − 0.146597i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.07962e6 | −0.201885 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 1.19363e7i | − 0.587162i | ||||||||
\(839\) | 1.00577e7 | 0.493282 | 0.246641 | − | 0.969107i | \(-0.420673\pi\) | ||||
0.246641 | + | 0.969107i | \(0.420673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05019e7 | −0.999551 | ||||||||
\(842\) | − 3.28830e6i | − 0.159842i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.42970e6 | −0.117407 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.01206e6i | 0.0963679i | ||||||||
\(848\) | − 1.99066e6i | − 0.0950619i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.22643e7 | −1.05387 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.30748e7i | 1.08584i | 0.839785 | + | 0.542919i | \(0.182681\pi\) | ||||
−0.839785 | + | 0.542919i | \(0.817319\pi\) | |||||||
\(854\) | −2.53269e7 | −1.18833 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.86605e6 | 0.226982 | ||||||||
\(857\) | 3.51646e7i | 1.63551i | 0.575565 | + | 0.817756i | \(0.304782\pi\) | ||||
−0.575565 | + | 0.817756i | \(0.695218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.66022e7 | −0.767684 | −0.383842 | − | 0.923399i | \(-0.625399\pi\) | ||||
−0.383842 | + | 0.923399i | \(0.625399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 2.52979e7i | − 1.15962i | ||||||||
\(863\) | 2.97009e7i | 1.35751i | 0.734366 | + | 0.678754i | \(0.237480\pi\) | ||||
−0.734366 | + | 0.678754i | \(0.762520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.40761e6 | 0.154403 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 1.08076e7i | − 0.486887i | ||||||||
\(869\) | −1.07812e7 | −0.484303 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.22431e7 | −0.546822 | ||||||||
\(872\) | 1.47916e7i | 0.658753i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.01990e7 | 0.451628 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.17943e7i | − 0.517811i | −0.965903 | − | 0.258906i | \(-0.916638\pi\) | ||||
0.965903 | − | 0.258906i | \(-0.0833619\pi\) | |||||||
\(878\) | − 1.33893e6i | − 0.0586166i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.10378e7 | −0.913190 | −0.456595 | − | 0.889675i | \(-0.650931\pi\) | ||||
−0.456595 | + | 0.889675i | \(0.650931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.12192e7i | − 0.915855i | −0.888990 | − | 0.457928i | \(-0.848592\pi\) | ||||
0.888990 | − | 0.457928i | \(-0.151408\pi\) | |||||||
\(884\) | 3.07814e6 | 0.132482 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.04870e6 | 0.301665 | ||||||||
\(887\) | 2.28818e7i | 0.976520i | 0.872698 | + | 0.488260i | \(0.162368\pi\) | ||||
−0.872698 | + | 0.488260i | \(0.837632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −146224. | −0.00620532 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 1.74932e7i | − 0.736134i | ||||||||
\(893\) | − 1.27488e7i | − 0.534984i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.42483e6 | 0.100905 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.60744e7i | 1.07900i | ||||||||
\(899\) | 438144. | 0.0180808 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.47898e6 | 0.183809 | ||||||||
\(902\) | 1.03219e7i | 0.422420i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.11770e6 | 0.371077 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 9.68692e6i | − 0.390992i | −0.980705 | − | 0.195496i | \(-0.937368\pi\) | ||||
0.980705 | − | 0.195496i | \(-0.0626316\pi\) | |||||||
\(908\) | 9.06240e6i | 0.364778i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.38112e6 | 0.374506 | 0.187253 | − | 0.982312i | \(-0.440042\pi\) | ||||
0.187253 | + | 0.982312i | \(0.440042\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.55099e7i | 1.01282i | ||||||||
\(914\) | −368296. | −0.0145825 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.39530e6 | −0.369974 | ||||||||
\(917\) | − 3.31899e7i | − 1.30341i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.21870e7 | 1.64774 | 0.823872 | − | 0.566775i | \(-0.191809\pi\) | ||||
0.823872 | + | 0.566775i | \(0.191809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 1.03027e6i | − 0.0399139i | ||||||||
\(923\) | 2.15470e7i | 0.832497i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.58491e7 | −0.607403 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 98304.0i | 0.00374715i | ||||||||
\(929\) | 3.04556e7 | 1.15779 | 0.578893 | − | 0.815404i | \(-0.303485\pi\) | ||||
0.578893 | + | 0.815404i | \(0.303485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.38441e6 | −0.127970 | ||||||||
\(932\) | 9.27130e6i | 0.349624i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.39576e7 | −0.523534 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.47847e7i | 0.550128i | 0.961426 | + | 0.275064i | \(0.0886990\pi\) | ||||
−0.961426 | + | 0.275064i | \(0.911301\pi\) | |||||||
\(938\) | − 2.17004e7i | − 0.805304i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.91997e6 | −0.365205 | −0.182602 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182602 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.58048e7i | − 0.944977i | ||||||||
\(944\) | 3.34234e6 | 0.122073 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.28434e7 | 0.829913 | ||||||||
\(947\) | 2.91610e6i | 0.105664i | 0.998603 | + | 0.0528320i | \(0.0168248\pi\) | ||||
−0.998603 | + | 0.0528320i | \(0.983175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.61454e6 | −0.202371 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.45587e6i | 0.195107i | ||||||||
\(953\) | − 1.40861e7i | − 0.502410i | −0.967934 | − | 0.251205i | \(-0.919173\pi\) | ||||
0.967934 | − | 0.251205i | \(-0.0808268\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.35117e6 | −0.330919 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.05210e6i | 0.0722410i | ||||||||
\(959\) | −4.12884e7 | −1.44971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.79906e6 | −0.272417 | ||||||||
\(962\) | 7.74613e6i | 0.269865i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.62608e6 | 0.229649 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.51949e7i | 0.522553i | 0.965264 | + | 0.261276i | \(0.0841434\pi\) | ||||
−0.965264 | + | 0.261276i | \(0.915857\pi\) | |||||||
\(968\) | − 870080.i | − 0.0298449i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.61220e7 | −1.91023 | −0.955113 | − | 0.296240i | \(-0.904267\pi\) | ||||
−0.955113 | + | 0.296240i | \(0.904267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.62256e7i | 0.888062i | ||||||||
\(974\) | 1.65800e7 | 0.559997 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.09522e7 | 0.368024 | ||||||||
\(977\) | 3.45625e7i | 1.15843i | 0.815176 | + | 0.579214i | \(0.196640\pi\) | ||||
−0.815176 | + | 0.579214i | \(0.803360\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.14081e7 | 1.04733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 1.10346e7i | − 0.365156i | ||||||||
\(983\) | − 5.56385e7i | − 1.83650i | −0.395997 | − | 0.918252i | \(-0.629601\pi\) | ||||
0.395997 | − | 0.918252i | \(-0.370399\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −221184. | −0.00724538 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 3.54842e6i | − 0.115649i | ||||||||
\(989\) | −5.71085e7 | −1.85656 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.60028e7 | −1.16453 | −0.582267 | − | 0.812998i | \(-0.697834\pi\) | ||||
−0.582267 | + | 0.812998i | \(0.697834\pi\) | |||||||
\(992\) | 4.67354e6i | 0.150788i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.81911e7 | −1.22602 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.35811e7i | 0.751322i | 0.926757 | + | 0.375661i | \(0.122584\pi\) | ||||
−0.926757 | + | 0.375661i | \(0.877416\pi\) | |||||||
\(998\) | 2.64358e6i | 0.0840169i | ||||||||
\(999\) | 0 | 0 |
(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 | 450.6.c.m.199.1 | 2 | ||
3.2 | odd | 2 | 450.6.c.c.199.2 | 2 | |||
5.2 | odd | 4 | 450.6.a.v.1.1 | 1 | |||
5.3 | odd | 4 | 18.6.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 450.6.c.m.199.2 | 2 | ||
15.2 | even | 4 | 450.6.a.k.1.1 | 1 | |||
15.8 | even | 4 | 18.6.a.c.1.1 | yes | 1 | ||
15.14 | odd | 2 | 450.6.c.c.199.1 | 2 | |||
20.3 | even | 4 | 144.6.a.a.1.1 | 1 | |||
35.13 | even | 4 | 882.6.a.k.1.1 | 1 | |||
40.3 | even | 4 | 576.6.a.bi.1.1 | 1 | |||
40.13 | odd | 4 | 576.6.a.bh.1.1 | 1 | |||
45.13 | odd | 12 | 162.6.c.l.55.1 | 2 | |||
45.23 | even | 12 | 162.6.c.a.55.1 | 2 | |||
45.38 | even | 12 | 162.6.c.a.109.1 | 2 | |||
45.43 | odd | 12 | 162.6.c.l.109.1 | 2 | |||
60.23 | odd | 4 | 144.6.a.l.1.1 | 1 | |||
105.83 | odd | 4 | 882.6.a.l.1.1 | 1 | |||
120.53 | even | 4 | 576.6.a.a.1.1 | 1 | |||
120.83 | odd | 4 | 576.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.6.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
18.6.a.c.1.1 | yes | 1 | 15.8 | even | 4 | ||
144.6.a.a.1.1 | 1 | 20.3 | even | 4 | |||
144.6.a.l.1.1 | 1 | 60.23 | odd | 4 | |||
162.6.c.a.55.1 | 2 | 45.23 | even | 12 | |||
162.6.c.a.109.1 | 2 | 45.38 | even | 12 | |||
162.6.c.l.55.1 | 2 | 45.13 | odd | 12 | |||
162.6.c.l.109.1 | 2 | 45.43 | odd | 12 | |||
450.6.a.k.1.1 | 1 | 15.2 | even | 4 | |||
450.6.a.v.1.1 | 1 | 5.2 | odd | 4 | |||
450.6.c.c.199.1 | 2 | 15.14 | odd | 2 | |||
450.6.c.c.199.2 | 2 | 3.2 | odd | 2 | |||
450.6.c.m.199.1 | 2 | 1.1 | even | 1 | trivial | ||
450.6.c.m.199.2 | 2 | 5.4 | even | 2 | inner | ||
576.6.a.a.1.1 | 1 | 120.53 | even | 4 | |||
576.6.a.b.1.1 | 1 | 120.83 | odd | 4 | |||
576.6.a.bh.1.1 | 1 | 40.13 | odd | 4 | |||
576.6.a.bi.1.1 | 1 | 40.3 | even | 4 | |||
882.6.a.k.1.1 | 1 | 35.13 | even | 4 | |||
882.6.a.l.1.1 | 1 | 105.83 | odd | 4 |