Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [96,6,Mod(95,96)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(96, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("96.95");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 96 = 2^{5} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 96.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.3968467020\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 416x^{16} + 57056x^{12} + 3187216x^{8} + 63121536x^{4} + 49787136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{134}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 95.10 | ||
Root | \(1.85069 - 1.85069i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 96.95 |
Dual form | 96.6.c.a.95.9 |
$q$-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 \(\left(\mathbb{Z}/96\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −6.21400 | + | 14.2964i | −0.398629 | + | 0.917112i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 36.1786i | − | 0.647183i | −0.946197 | − | 0.323592i | \(-0.895110\pi\) | ||
0.946197 | − | 0.323592i | \(-0.104890\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 57.8847i | 0.446497i | 0.974762 | + | 0.223249i | \(0.0716662\pi\) | ||||
−0.974762 | + | 0.223249i | \(0.928334\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −165.772 | − | 177.675i | −0.682191 | − | 0.731174i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −114.418 | −0.285109 | −0.142554 | − | 0.989787i | \(-0.545532\pi\) | ||||
−0.142554 | + | 0.989787i | \(0.545532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −295.579 | −0.485082 | −0.242541 | − | 0.970141i | \(-0.577981\pi\) | ||||
−0.242541 | + | 0.970141i | \(0.577981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 517.223 | + | 224.814i | 0.593540 | + | 0.257986i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1155.61i | − | 0.969815i | −0.874566 | − | 0.484907i | \(-0.838853\pi\) | ||
0.874566 | − | 0.484907i | \(-0.161147\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1955.80i | − | 1.24291i | −0.783449 | − | 0.621456i | \(-0.786541\pi\) | ||
0.783449 | − | 0.621456i | \(-0.213459\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −827.541 | − | 359.696i | −0.409488 | − | 0.177987i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4540.43 | 1.78969 | 0.894843 | − | 0.446380i | \(-0.147287\pi\) | ||||
0.894843 | + | 0.446380i | \(0.147287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1816.11 | 0.581154 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3570.22 | − | 1265.87i | 0.942510 | − | 0.334179i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4911.55i | − | 1.08448i | −0.840222 | − | 0.542242i | \(-0.817575\pi\) | ||
0.840222 | − | 0.542242i | \(-0.182425\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1701.31i | − | 0.317965i | −0.987281 | − | 0.158982i | \(-0.949179\pi\) | ||
0.987281 | − | 0.158982i | \(-0.0508213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 710.991 | − | 1635.76i | 0.113653 | − | 0.261477i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2094.19 | 0.288965 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14990.4 | −1.80015 | −0.900076 | − | 0.435733i | \(-0.856489\pi\) | ||||
−0.900076 | + | 0.435733i | \(0.856489\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1836.73 | − | 4225.70i | 0.193367 | − | 0.444875i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 19071.6i | − | 1.77185i | −0.463824 | − | 0.885927i | \(-0.653523\pi\) | ||
0.463824 | − | 0.885927i | \(-0.346477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5939.24i | 0.489846i | 0.969543 | + | 0.244923i | \(0.0787627\pi\) | ||||
−0.969543 | + | 0.244923i | \(0.921237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6428.05 | + | 5997.42i | −0.473204 | + | 0.441502i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13287.7 | −0.877416 | −0.438708 | − | 0.898630i | \(-0.644564\pi\) | ||||
−0.438708 | + | 0.898630i | \(0.644564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13456.4 | 0.800640 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16521.0 | + | 7180.96i | 0.889429 | + | 0.386596i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13202.0i | 0.645582i | 0.946470 | + | 0.322791i | \(0.104621\pi\) | ||||
−0.946470 | + | 0.322791i | \(0.895379\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4139.47i | 0.184518i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 27960.8 | + | 12153.3i | 1.13989 | + | 0.495460i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25888.9 | −0.968242 | −0.484121 | − | 0.875001i | \(-0.660861\pi\) | ||||
−0.484121 | + | 0.875001i | \(0.660861\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5568.84 | −0.191620 | −0.0958099 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958099 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10284.7 | − | 9595.68i | 0.326467 | − | 0.304596i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10693.6i | 0.313937i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 20870.4i | − | 0.567994i | −0.958825 | − | 0.283997i | \(-0.908339\pi\) | ||
0.958825 | − | 0.283997i | \(-0.0916606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −28214.2 | + | 64911.6i | −0.713420 | + | 1.64134i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −51334.6 | −1.20855 | −0.604275 | − | 0.796776i | \(-0.706537\pi\) | ||||
−0.604275 | + | 0.796776i | \(0.706537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 73309.4 | 1.61010 | 0.805049 | − | 0.593208i | \(-0.202139\pi\) | ||||
0.805049 | + | 0.593208i | \(0.202139\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11285.3 | + | 25963.7i | −0.231665 | + | 0.532984i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6623.03i | − | 0.127300i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46469.0i | 0.837715i | 0.908052 | + | 0.418857i | \(0.137569\pi\) | ||||
−0.908052 | + | 0.418857i | \(0.862431\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4088.08 | + | 58907.3i | −0.0692320 | + | 0.997601i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −95537.3 | −1.52222 | −0.761111 | − | 0.648622i | \(-0.775346\pi\) | ||||
−0.761111 | + | 0.648622i | \(0.775346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −41808.4 | −0.627648 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 70217.3 | + | 30520.4i | 0.994595 | + | 0.432307i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 87567.6i | − | 1.17184i | −0.810369 | − | 0.585920i | \(-0.800733\pi\) | ||
0.810369 | − | 0.585920i | \(-0.199267\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 17109.5i | − | 0.216588i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24322.5 | + | 10571.9i | 0.291610 | + | 0.126750i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −70758.2 | −0.804392 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −50886.1 | −0.549124 | −0.274562 | − | 0.961569i | \(-0.588533\pi\) | ||||
−0.274562 | + | 0.961569i | \(0.588533\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18967.3 | + | 20329.2i | 0.194499 | + | 0.208464i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 69801.1i | − | 0.680862i | −0.940270 | − | 0.340431i | \(-0.889427\pi\) | ||
0.940270 | − | 0.340431i | \(-0.110573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 82496.6i | 0.766201i | 0.923707 | + | 0.383101i | \(0.125144\pi\) | ||||
−0.923707 | + | 0.383101i | \(0.874856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13013.3 | + | 29939.3i | −0.115190 | + | 0.265014i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 75209.7 | 0.635059 | 0.317530 | − | 0.948248i | \(-0.397147\pi\) | ||||
0.317530 | + | 0.948248i | \(0.397147\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 48849.4 | 0.393816 | 0.196908 | − | 0.980422i | \(-0.436910\pi\) | ||||
0.196908 | + | 0.980422i | \(0.436910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 93150.5 | − | 214308.i | 0.717592 | − | 1.65094i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 45527.2i | − | 0.335409i | −0.985837 | − | 0.167705i | \(-0.946364\pi\) | ||
0.985837 | − | 0.167705i | \(-0.0536355\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 164266.i | − | 1.15826i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 48998.8 | + | 52517.1i | 0.330918 | + | 0.354679i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 66892.1 | 0.433020 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −147960. | −0.918713 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 272655. | + | 118511.i | 1.62499 | + | 0.706312i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 178762.i | − | 1.02330i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 113221.i | − | 0.622899i | −0.950263 | − | 0.311450i | \(-0.899185\pi\) | ||
0.950263 | − | 0.311450i | \(-0.100815\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −84909.5 | − | 36906.4i | −0.449244 | − | 0.195267i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 73591.9 | 0.374672 | 0.187336 | − | 0.982296i | \(-0.440015\pi\) | ||||
0.187336 | + | 0.982296i | \(0.440015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 113211. | 0.554957 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −45797.3 | − | 129166.i | −0.216275 | − | 0.609976i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 56044.1i | − | 0.255110i | −0.991831 | − | 0.127555i | \(-0.959287\pi\) | ||
0.991831 | − | 0.127555i | \(-0.0407130\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 61631.4i | 0.270561i | 0.990807 | + | 0.135280i | \(0.0431935\pi\) | ||||
−0.990807 | + | 0.135280i | \(0.956806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 82569.8 | − | 189966.i | 0.349763 | − | 0.804689i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 33819.4 | 0.138301 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −177693. | −0.701860 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −83617.9 | + | 192377.i | −0.319158 | + | 0.734277i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 318680.i | − | 1.17595i | −0.808878 | − | 0.587976i | \(-0.799925\pi\) | ||
0.808878 | − | 0.587976i | \(-0.200075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 433550.i | 1.54738i | 0.633566 | + | 0.773689i | \(0.281591\pi\) | ||||
−0.633566 | + | 0.773689i | \(0.718409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −205323. | + | 191568.i | −0.709104 | + | 0.661598i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −61551.1 | −0.205781 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 137096. | 0.443890 | 0.221945 | − | 0.975059i | \(-0.428759\pi\) | ||||
0.221945 | + | 0.975059i | \(0.428759\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −188741. | − | 82037.5i | −0.592071 | − | 0.257347i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 262821.i | 0.799090i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 659320.i | − | 1.94369i | −0.235618 | − | 0.971846i | \(-0.575712\pi\) | ||
0.235618 | − | 0.971846i | \(-0.424288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −59179.4 | − | 25722.7i | −0.169223 | − | 0.0735540i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 163704. | 0.454222 | 0.227111 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227111 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −283926. | −0.764696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −347498. | + | 324218.i | −0.908786 | + | 0.847903i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 640742.i | 1.62768i | 0.581091 | + | 0.813838i | \(0.302626\pi\) | ||||
−0.581091 | + | 0.813838i | \(0.697374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 105125.i | 0.259484i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 160874. | − | 370118.i | 0.385969 | − | 0.887987i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −338416. | −0.789439 | −0.394719 | − | 0.918802i | \(-0.629158\pi\) | ||||
−0.394719 | + | 0.918802i | \(0.629158\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 692113. | 1.57029 | 0.785146 | − | 0.619311i | \(-0.212588\pi\) | ||||
0.785146 | + | 0.619311i | \(0.212588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 34604.8 | − | 79614.2i | 0.0763851 | − | 0.175737i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 542333.i | 1.16503i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 132222.i | 0.276503i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 73274.3 | + | 206661.i | 0.149210 | + | 0.420828i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24688.5 | −0.0489678 | −0.0244839 | − | 0.999700i | \(-0.507794\pi\) | ||||
−0.0244839 | + | 0.999700i | \(0.507794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 564427. | 1.09072 | 0.545361 | − | 0.838201i | \(-0.316392\pi\) | ||||
0.545361 | + | 0.838201i | \(0.316392\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −152880. | − | 66450.3i | −0.287915 | − | 0.125144i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 630840.i | 1.15812i | 0.815285 | + | 0.579061i | \(0.196581\pi\) | ||||
−0.815285 | + | 0.579061i | \(0.803419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 947253.i | 1.69564i | 0.530286 | + | 0.847819i | \(0.322085\pi\) | ||||
−0.530286 | + | 0.847819i | \(0.677915\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 298371. | + | 129689.i | 0.520914 | + | 0.226419i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 284304. | 0.484219 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −689985. | −1.14671 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −752677. | − | 806722.i | −1.22091 | − | 1.30857i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 223778.i | 0.354365i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 522194.i | − | 0.807469i | −0.914876 | − | 0.403734i | \(-0.867712\pi\) | ||
0.914876 | − | 0.403734i | \(-0.132288\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 318993. | − | 733898.i | 0.481762 | − | 1.10838i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 214873. | 0.317020 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 98479.8 | 0.141970 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −455545. | + | 1.04806e6i | −0.641831 | + | 1.47664i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 341574.i | 0.470439i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 335095.i | − | 0.451238i | −0.974216 | − | 0.225619i | \(-0.927560\pi\) | ||
0.974216 | − | 0.225619i | \(-0.0724404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −301060. | − | 322677.i | −0.396458 | − | 0.424925i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 542830. | 0.699196 | 0.349598 | − | 0.936900i | \(-0.386318\pi\) | ||||
0.349598 | + | 0.936900i | \(0.386318\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.13784e6 | −1.43381 | −0.716904 | − | 0.697172i | \(-0.754441\pi\) | ||||
−0.716904 | + | 0.697172i | \(0.754441\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 94685.2 | + | 41155.5i | 0.116749 | + | 0.0507456i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 36611.5i | 0.0441803i | 0.999756 | + | 0.0220901i | \(0.00703208\pi\) | ||||
−0.999756 | + | 0.0220901i | \(0.992968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 480731.i | 0.567848i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −664339. | − | 288759.i | −0.768278 | − | 0.333937i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −822358. | −0.931250 | −0.465625 | − | 0.884982i | \(-0.654170\pi\) | ||||
−0.465625 | + | 0.884982i | \(0.654170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 707488. | 0.784651 | 0.392325 | − | 0.919826i | \(-0.371671\pi\) | ||||
0.392325 | + | 0.919826i | \(0.371671\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −816757. | − | 424495.i | −0.887314 | − | 0.461166i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 486833.i | − | 0.518161i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 578093.i | 0.602914i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 593669. | − | 1.36584e6i | 0.606801 | − | 1.39605i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.89976e6 | 1.90333 | 0.951667 | − | 0.307132i | \(-0.0993692\pi\) | ||||
0.951667 | + | 0.307132i | \(0.0993692\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −519504. | −0.510256 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 259797. | − | 597708.i | 0.250198 | − | 0.575623i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.12906e6i | − | 1.06631i | −0.846017 | − | 0.533156i | \(-0.821006\pi\) | ||
0.846017 | − | 0.533156i | \(-0.178994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 867716.i | − | 0.803763i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −872661. | + | 814199.i | −0.792947 | + | 0.739825i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.90594e6 | 1.69910 | 0.849550 | − | 0.527508i | \(-0.176873\pi\) | ||||
0.849550 | + | 0.527508i | \(0.176873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 477632. | 0.417810 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.25190e6 | + | 544145.i | 1.07471 | + | 0.467129i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 220717.i | 0.185975i | 0.995667 | + | 0.0929877i | \(0.0296417\pi\) | ||||
−0.995667 | + | 0.0929877i | \(0.970358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.67935e6i | − | 1.38905i | −0.719468 | − | 0.694525i | \(-0.755614\pi\) | ||
0.719468 | − | 0.694525i | \(-0.244386\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 244604. | + | 106318.i | 0.198635 | + | 0.0863380i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −207794. | −0.165692 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 371115. | 0.290609 | 0.145304 | − | 0.989387i | \(-0.453584\pi\) | ||||
0.145304 | + | 0.989387i | \(0.453584\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −302281. | + | 282030.i | −0.232488 | + | 0.216913i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 437573.i | − | 0.330586i | −0.986244 | − | 0.165293i | \(-0.947143\pi\) | ||
0.986244 | − | 0.165293i | \(-0.0528570\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 421090.i | − | 0.312543i | −0.987714 | − | 0.156271i | \(-0.950053\pi\) | ||
0.987714 | − | 0.156271i | \(-0.0499474\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 439692. | − | 1.01159e6i | 0.320654 | − | 0.737718i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.10396e6 | 0.791128 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 84424.0 | 0.0594595 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 316207. | − | 727487.i | 0.218896 | − | 0.503608i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 913641.i | 0.621737i | 0.950453 | + | 0.310868i | \(0.100620\pi\) | ||||
−0.950453 | + | 0.310868i | \(0.899380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 936626.i | 0.626630i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −408496. | + | 144837.i | −0.268718 | + | 0.0952773i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.34205e6 | −0.868145 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −343791. | −0.218715 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 997902. | + | 433744.i | 0.624427 | + | 0.271411i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 201473.i | 0.124013i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.04561e6i | − | 0.633172i | −0.948564 | − | 0.316586i | \(-0.897463\pi\) | ||
0.948564 | − | 0.316586i | \(-0.102537\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.17940e6 | − | 512634.i | −0.702693 | − | 0.305430i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.15394e6 | −0.676522 | −0.338261 | − | 0.941052i | \(-0.609839\pi\) | ||||
−0.338261 | + | 0.941052i | \(0.609839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −423979. | −0.244615 | −0.122308 | − | 0.992492i | \(-0.539029\pi\) | ||||
−0.122308 | + | 0.992492i | \(0.539029\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −347159. | − | 372086.i | −0.197130 | − | 0.211284i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.89609e6i | − | 1.05977i | −0.848070 | − | 0.529885i | \(-0.822235\pi\) | ||
0.848070 | − | 0.529885i | \(-0.177765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 561967.i | 0.309196i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −467353. | + | 1.07523e6i | −0.253153 | + | 0.582421i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.26014e6 | −1.20539 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −536803. | −0.281907 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −303550. | + | 698369.i | −0.156986 | + | 0.361173i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 769155.i | − | 0.391764i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.53608e6i | 1.27231i | 0.771561 | + | 0.636156i | \(0.219476\pi\) | ||||
−0.771561 | + | 0.636156i | \(0.780524\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.48500e6 | + | 2.66343e6i | 1.22805 | + | 1.31623i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −755063. | −0.367596 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.10104e6 | −0.528113 | −0.264056 | − | 0.964507i | \(-0.585061\pi\) | ||||
−0.264056 | + | 0.964507i | \(0.585061\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 650874. | + | 282906.i | 0.307608 | + | 0.133704i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 194660.i | 0.0906546i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.75179e6i | 0.803981i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.34841e6 | + | 1.02075e6i | 1.06225 | + | 0.461714i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.22857e6 | −0.547742 | −0.273871 | − | 0.961766i | \(-0.588304\pi\) | ||||
−0.273871 | + | 0.961766i | \(0.588304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.38685e6 | 1.04897 | 0.524483 | − | 0.851421i | \(-0.324259\pi\) | ||||
0.524483 | + | 0.851421i | \(0.324259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.05528e6 | + | 374163.i | −0.457194 | + | 0.162104i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.30477e6i | 0.984444i | 0.870470 | + | 0.492222i | \(0.163815\pi\) | ||||
−0.870470 | + | 0.492222i | \(0.836185\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.85722e6i | 0.782153i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −415668. | + | 956314.i | −0.172614 | + | 0.397128i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.08815e6 | −1.26463 | −0.632314 | − | 0.774712i | \(-0.717895\pi\) | ||||
−0.632314 | + | 0.774712i | \(0.717895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.34906e6 | −0.544831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 919422. | − | 2.11529e6i | 0.366225 | − | 0.842563i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.65223e6i | − | 1.04203i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.24714e6i | − | 1.64601i | −0.568036 | − | 0.823004i | \(-0.692297\pi\) | ||
0.568036 | − | 0.823004i | \(-0.307703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.38856e6 | + | 3.16155e6i | −1.29553 | + | 1.20874i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −764196. | −0.288251 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.46771e6 | 1.66270 | 0.831349 | − | 0.555751i | \(-0.187569\pi\) | ||||
0.831349 | + | 0.555751i | \(0.187569\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.55565e6 | + | 1.11083e6i | 0.938478 | + | 0.407915i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.45175e6i | 0.526064i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.52600e6i | 0.903307i | 0.892193 | + | 0.451654i | \(0.149166\pi\) | ||||
−0.892193 | + | 0.451654i | \(0.850834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.61865e6 | + | 703556.i | 0.571269 | + | 0.248305i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.52845e6 | −1.22910 | −0.614551 | − | 0.788877i | \(-0.710663\pi\) | ||||
−0.614551 | + | 0.788877i | \(0.710663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −239612. | −0.0823866 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.05526e6 | − | 984561.i | 0.358163 | − | 0.334168i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.79143e6i | 0.935303i | 0.883913 | + | 0.467652i | \(0.154900\pi\) | ||||
−0.883913 | + | 0.467652i | \(0.845100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.24696e6i | − | 1.73566i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −457300. | + | 1.05210e6i | −0.149355 | + | 0.343617i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.68119e6 | 0.542155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12421e6 | −0.357989 | −0.178995 | − | 0.983850i | \(-0.557284\pi\) | ||||
−0.178995 | + | 0.983850i | \(0.557284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −703493. | + | 1.61851e6i | −0.221222 | + | 0.508958i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.16095e6i | − | 0.981651i | −0.871258 | − | 0.490825i | \(-0.836695\pi\) | ||
0.871258 | − | 0.490825i | \(-0.163305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 502871.i | 0.154239i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.13119e6 | + | 147901.i | 0.645630 | + | 0.0448058i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.71517e6 | 0.513240 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.26449e6 | −0.373772 | −0.186886 | − | 0.982382i | \(-0.559839\pi\) | ||||
−0.186886 | + | 0.982382i | \(0.559839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 801227. | + | 348258.i | 0.233965 | + | 0.101694i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.49857e6i | − | 0.432317i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.45641e6i | 0.985156i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −881105. | − | 382978.i | −0.248135 | − | 0.107853i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −984075. | −0.273838 | −0.136919 | − | 0.990582i | \(-0.543720\pi\) | ||||
−0.136919 | + | 0.990582i | \(0.543720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 994173. | 0.273374 | 0.136687 | − | 0.990614i | \(-0.456355\pi\) | ||||
0.136687 | + | 0.990614i | \(0.456355\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.20273e6 | + | 2.36090e6i | 0.598565 | + | 0.641544i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.09871e6i | − | 0.563612i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 322351.i | − | 0.0855577i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −210154. | + | 483495.i | −0.0551308 | + | 0.126838i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 243593. | 0.0631643 | 0.0315822 | − | 0.999501i | \(-0.489945\pi\) | ||||
0.0315822 | + | 0.999501i | \(0.489945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 585515. | 0.150078 | 0.0750392 | − | 0.997181i | \(-0.476092\pi\) | ||||
0.0750392 | + | 0.997181i | \(0.476092\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.10419e6 | − | 2.54037e6i | 0.279781 | − | 0.643685i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 8.88017e6i | − | 2.22442i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.89925e6i | − | 0.717999i | −0.933338 | − | 0.358999i | \(-0.883118\pi\) | ||
0.933338 | − | 0.358999i | \(-0.116882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.23069e6 | − | 2.39086e6i | −0.546189 | − | 0.585408i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.02564e6 | −0.732501 | −0.366251 | − | 0.930516i | \(-0.619359\pi\) | ||||
−0.366251 | + | 0.930516i | \(0.619359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.16808e6 | −0.758395 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.55597e6 | + | 1.98028e6i | 1.07848 | + | 0.468768i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 339862.i | − | 0.0795585i | −0.999208 | − | 0.0397793i | \(-0.987335\pi\) | ||
0.999208 | − | 0.0397793i | \(-0.0126655\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.18213e6i | 0.505172i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.19819e6 | − | 2.69408e6i | −1.41912 | − | 0.616829i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −618998. | −0.140172 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.12317e6 | −0.923508 | −0.461754 | − | 0.887008i | \(-0.652780\pi\) | ||||
−0.461754 | + | 0.887008i | \(0.652780\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.46285e6 | − | 4.12578e6i | −0.324091 | − | 0.914060i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.40750e6i | 0.308457i | 0.988035 | + | 0.154229i | \(0.0492892\pi\) | ||||
−0.988035 | + | 0.154229i | \(0.950711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 373619.i | − | 0.0809985i | −0.999180 | − | 0.0404992i | \(-0.987105\pi\) | ||
0.999180 | − | 0.0404992i | \(-0.0128948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 382478. | − | 879957.i | 0.0820304 | − | 0.188725i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.73587e6 | 1.85359 | 0.926795 | − | 0.375567i | \(-0.122552\pi\) | ||||
0.926795 | + | 0.375567i | \(0.122552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.20808e6 | 0.253608 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −851914. | + | 1.95997e6i | −0.176947 | + | 0.407097i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 679553.i | − | 0.139659i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.55194e6i | − | 0.722324i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.34568e6 | − | 2.18853e6i | 0.472033 | − | 0.440410i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.56616e6 | 1.30759 | 0.653797 | − | 0.756670i | \(-0.273175\pi\) | ||||
0.653797 | + | 0.756670i | \(0.273175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.43085e6 | 0.873221 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.75739e6 | − | 1.63317e6i | −0.732856 | − | 0.318540i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.84099e6i | 0.355383i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.03619e6i | − | 1.15329i | −0.816993 | − | 0.576647i | \(-0.804361\pi\) | ||
0.816993 | − | 0.576647i | \(-0.195639\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.42588e6 | + | 4.09702e6i | 1.78258 | + | 0.774811i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.73841e6 | −0.325424 | −0.162712 | − | 0.986674i | \(-0.552024\pi\) | ||||
−0.162712 | + | 0.986674i | \(0.552024\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.67583e6 | −1.05175 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 735482. | − | 686210.i | 0.134915 | − | 0.125876i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.97149e6i | − | 0.539614i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.57823e6i | 1.00287i | 0.865195 | + | 0.501436i | \(0.167195\pi\) | ||||
−0.865195 | + | 0.501436i | \(0.832805\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.01726e6 | + | 2.34037e6i | −0.181066 | + | 0.416573i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.61205e6 | 0.989012 | 0.494506 | − | 0.869174i | \(-0.335349\pi\) | ||||
0.494506 | + | 0.869174i | \(0.335349\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.52531e6 | −0.440642 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.76432e6 | − | 4.05911e6i | 0.304829 | − | 0.701312i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.81201e6i | 1.16542i | 0.812682 | + | 0.582708i | \(0.198007\pi\) | ||||
−0.812682 | + | 0.582708i | \(0.801993\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.24349e6i | 0.718904i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.47578e6 | − | 6.98264e6i | −0.415355 | − | 1.17146i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.98461e6 | 0.495873 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.52035e6 | 0.250159 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.16029e6 | − | 3.98157e6i | −1.49276 | − | 0.648838i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.72615e6i | 0.601404i | 0.953718 | + | 0.300702i | \(0.0972209\pi\) | ||||
−0.953718 | + | 0.300702i | \(0.902779\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.32730e6i | − | 0.212185i | −0.994356 | − | 0.106092i | \(-0.966166\pi\) | ||
0.994356 | − | 0.106092i | \(-0.0338339\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.50290e6 | − | 653246.i | −0.237976 | − | 0.103438i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.96605e6 | −0.308367 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.41791e7 | 2.20298 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.29167e6 | + | 4.59983e6i | 0.660526 | + | 0.707954i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.63717e6i | 0.859494i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.72098e6i | − | 0.411000i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.10292e6 | − | 4.83812e6i | 0.314693 | − | 0.724004i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.53964e6 | −0.228270 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.17248e6 | −1.05360 | −0.526801 | − | 0.849989i | \(-0.676609\pi\) | ||||
−0.526801 | + | 0.849989i | \(0.676609\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.30079e6 | + | 9.89470e6i | −0.625963 | + | 1.44013i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.76730e6i | − | 0.254871i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.86107e6i | 1.40914i | 0.709632 | + | 0.704572i | \(0.248861\pi\) | ||||
−0.709632 | + | 0.704572i | \(0.751139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 923160. | + | 989446.i | 0.130721 | + | 0.140107i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.60601e6 | −1.34792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.68985e6 | −0.374037 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.75339e6 | − | 3.37006e6i | −1.06846 | − | 0.464413i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.22581e6i | 1.25999i | 0.776600 | + | 0.629994i | \(0.216943\pi\) | ||||
−0.776600 | + | 0.629994i | \(0.783057\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.75551e6i | − | 0.237615i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.89029e6 | − | 821628.i | −0.253584 | − | 0.110222i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.00543e7 | −1.33685 | −0.668425 | − | 0.743780i | \(-0.733031\pi\) | ||||
−0.668425 | + | 0.743780i | \(0.733031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.64711e6 | −0.217071 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.40983e6 | − | 236637.i | −0.445426 | − | 0.0309119i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.29750e7i | 1.68007i | 0.542530 | + | 0.840036i | \(0.317466\pi\) | ||||
−0.542530 | + | 0.840036i | \(0.682534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 102836.i | − | 0.0131994i | −0.999978 | − | 0.00659972i | \(-0.997899\pi\) | ||
0.999978 | − | 0.00659972i | \(-0.00210077\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 153414. | − | 352956.i | 0.0195200 | − | 0.0449090i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.24590e6 | 1.04008 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.88650e6 | 0.861111 | 0.430556 | − | 0.902564i | \(-0.358318\pi\) | ||||
0.430556 | + | 0.902564i | \(0.358318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.50735e6 | + | 8.06925e6i | −0.434793 | + | 1.00032i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.53015e6i | − | 0.679668i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.51054e6i | − | 0.184061i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.90000e6 | − | 1.77271e6i | 0.229543 | − | 0.214165i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.07376e7 | 1.28621 | 0.643103 | − | 0.765780i | \(-0.277647\pi\) | ||||
0.643103 | + | 0.765780i | \(0.277647\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.32742e6 | −0.395202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.01873e6 | − | 3.92004e6i | −1.06213 | − | 0.461660i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.12656e7i | 1.31558i | 0.753199 | + | 0.657792i | \(0.228510\pi\) | ||||
−0.753199 | + | 0.657792i | \(0.771490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.42007e6i | − | 0.280243i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.35423e7 | − | 5.88623e6i | −1.55509 | − | 0.675930i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.18305e6 | −1.04573 | −0.522865 | − | 0.852415i | \(-0.675137\pi\) | ||||
−0.522865 | + | 0.852415i | \(0.675137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27562.1 | −0.00311261 | −0.00155631 | − | 0.999999i | \(-0.500495\pi\) | ||||
−0.00155631 | + | 0.999999i | \(0.500495\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.70816e6 | + | 3.45973e6i | −0.415303 | + | 0.387480i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.35298e6i | 0.594575i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.94174e6i | 1.09519i | 0.836743 | + | 0.547596i | \(0.184457\pi\) | ||||
−0.836743 | + | 0.547596i | \(0.815543\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.76666e6 | + | 4.06451e6i | −0.193024 | + | 0.444084i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.92756e6 | 0.425618 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.39606e7 | 1.50056 | 0.750281 | − | 0.661119i | \(-0.229918\pi\) | ||||
0.750281 | + | 0.661119i | \(0.229918\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.28757e6 | − | 9.86428e6i | 0.457113 | − | 1.05167i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.58730e7i | − | 1.67860i | −0.543671 | − | 0.839299i | \(-0.682966\pi\) | ||
0.543671 | − | 0.839299i | \(-0.317034\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.64068e6i | − | 0.801504i | −0.916187 | − | 0.400752i | \(-0.868749\pi\) | ||
0.916187 | − | 0.400752i | \(-0.131251\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.62103e7 | − | 5.74758e6i | 1.68680 | − | 0.598075i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.06882e6 | 0.523223 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −792050. | −0.0811059 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.19921e6 | − | 1.39056e6i | −0.324993 | − | 0.141260i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.73231e7i | 1.74581i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.52822e6i | 0.452746i | 0.974041 | + | 0.226373i | \(0.0726868\pi\) | ||||
−0.974041 | + | 0.226373i | \(0.927313\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.46548e6 | + | 3.24492e6i | 0.740540 | + | 0.321880i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.09618e6 | −0.403130 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.97742e6 | −0.388376 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.50986e6 | + | 9.12089e6i | 0.824461 | + | 0.883660i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.34885e6i | 0.898696i | 0.893357 | + | 0.449348i | \(0.148344\pi\) | ||||
−0.893357 | + | 0.449348i | \(0.851656\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.98305e6i | − | 0.284533i | −0.989828 | − | 0.142267i | \(-0.954561\pi\) | ||
0.989828 | − | 0.142267i | \(-0.0454390\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.33522e6 | + | 3.07191e6i | −0.126373 | + | 0.290743i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.92362e7 | 1.80659 | 0.903295 | − | 0.429020i | \(-0.141141\pi\) | ||||
0.903295 | + | 0.429020i | \(0.141141\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.96215e6 | 0.276055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −611954. | + | 1.40790e6i | −0.0565935 | + | 0.130203i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.55600e7i | − | 1.42799i | −0.700149 | − | 0.713997i | \(-0.746883\pi\) | ||
0.700149 | − | 0.713997i | \(-0.253117\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.66245e6i | − | 0.242482i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.21527e7 | − | 1.30253e7i | −1.09839 | − | 1.17726i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.76971e6 | 0.786632 | 0.393316 | − | 0.919403i | \(-0.371328\pi\) | ||||
0.393316 | + | 0.919403i | \(0.371328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.72564e6 | 0.153619 | 0.0768096 | − | 0.997046i | \(-0.475527\pi\) | ||||
0.0768096 | + | 0.997046i | \(0.475527\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.88326e6 | − | 2.12254e6i | −0.431446 | − | 0.187531i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 4.09582e6i | − | 0.359159i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.23005e7i | − | 1.94089i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.79064e6 | + | 2.08228e6i | 0.413836 | + | 0.179876i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 637173. | 0.0546325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.72691e7 | −1.46971 | −0.734855 | − | 0.678225i | \(-0.762750\pi\) | ||||
−0.734855 | + | 0.678225i | \(0.762750\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.48390e6 | − | 2.29895e6i | 0.547743 | − | 0.194209i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.63692e7i | − | 1.37264i | −0.727300 | − | 0.686320i | \(-0.759225\pi\) | ||
0.727300 | − | 0.686320i | \(-0.240775\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.94553e6i | − | 0.245182i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.37315e6 | + | 7.76049e6i | −0.278720 | + | 0.641241i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.24061e6 | −0.511889 | −0.255944 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255944 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.02760e6 | −0.165103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.07052e6 | − | 1.62669e7i | 0.571557 | − | 1.31496i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3.90224e6i | − | 0.313160i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18638e7i | 0.945211i | 0.881274 | + | 0.472605i | \(0.156686\pi\) | ||||
−0.881274 | + | 0.472605i | \(0.843314\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.17675e6 | + | 1.09791e6i | −0.0930788 | + | 0.0868431i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.22974e6 | 0.175102 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.20393e7 | −1.71837 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −523412. | − | 227504.i | −0.0405183 | − | 0.0176115i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.12864e7i | − | 0.867482i | −0.901038 | − | 0.433741i | \(-0.857193\pi\) | ||
0.901038 | − | 0.433741i | \(-0.142807\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.93182e7i | 2.23743i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.87271e6 | − | 2.98726e6i | −0.520781 | − | 0.226361i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.04042e6 | 0.304003 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.04073e7 | 0.777538 | 0.388769 | − | 0.921335i | \(-0.372900\pi\) | ||||
0.388769 | + | 0.921335i | \(0.372900\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.25641e6 | − | 7.70328e6i | 0.612515 | − | 0.571481i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.72467e6i | − | 0.569058i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.22354e6i | − | 0.0895062i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.11014e6 | − | 1.17567e7i | 0.371223 | − | 0.854061i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.42216e7 | −1.02595 | −0.512977 | − | 0.858403i | \(-0.671457\pi\) | ||||
−0.512977 | + | 0.858403i | \(0.671457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.77529e6 | −0.342107 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.39633e6 | + | 1.01145e7i | −0.312784 | + | 0.719613i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 8.91990e6i | − | 0.630253i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.21710e6i | − | 0.155578i | −0.996970 | − | 0.0777892i | \(-0.975214\pi\) | ||
0.996970 | − | 0.0777892i | \(-0.0247861\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.11441e7 | − | 9.03885e6i | 0.776649 | − | 0.629933i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.86344e6 | 0.475060 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.06428e7 | 0.731635 | 0.365818 | − | 0.930687i | \(-0.380789\pi\) | ||||
0.365818 | + | 0.930687i | \(0.380789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.95994e6 | + | 3.02518e6i | 0.475212 | + | 0.206554i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.38794e6i | 0.161940i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.00821e7i | − | 0.679111i | −0.940586 | − | 0.339555i | \(-0.889723\pi\) | ||
0.940586 | − | 0.339555i | \(-0.110277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.26463e6 | − | 3.59227e6i | −0.552940 | − | 0.240339i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.11350e7 | −1.40453 | −0.702265 | − | 0.711916i | \(-0.747828\pi\) | ||||
−0.702265 | + | 0.711916i | \(0.747828\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.15294e7 | −0.761056 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.58374e7 | + | 1.69746e7i | 1.03845 | + | 1.11301i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.35349e6i | 0.283552i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.67578e7i | − | 1.08422i | −0.840308 | − | 0.542110i | \(-0.817626\pi\) | ||
0.840308 | − | 0.542110i | \(-0.182374\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.18051e7 | + | 2.71597e7i | −0.758723 | + | 1.74557i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.56852e7 | 1.00144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.55144e6 | 0.0983998 | 0.0491999 | − | 0.998789i | \(-0.484333\pi\) | ||||
0.0491999 | + | 0.998789i | \(0.484333\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.22820e6 | − | 7.42703e6i | 0.203403 | − | 0.467962i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.06490e6i | − | 0.254441i | −0.991874 | − | 0.127221i | \(-0.959394\pi\) | ||
0.991874 | − | 0.127221i | \(-0.0406057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.82763e6i | 0.175838i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.93067e6 | + | 7.42832e6i | 0.428175 | + | 0.458920i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.65222e6 | 0.469677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.26089e7 | 1.37868 | 0.689339 | − | 0.724439i | \(-0.257901\pi\) | ||||
0.689339 | + | 0.724439i | \(0.257901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.61415e7 | + | 7.01599e6i | 0.977929 | + | 0.425063i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.50729e6i | 0.0907293i | 0.998970 | + | 0.0453647i | \(0.0144450\pi\) | ||||
−0.998970 | + | 0.0453647i | \(0.985555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.08976e6i | − | 0.184787i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.24052e7 | + | 5.39199e6i | 0.737141 | + | 0.320403i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.73003e7 | −2.20226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.87358e6 | 0.344568 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.21737e6 | − | 1.75353e7i | −0.362412 | − | 1.02214i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.95994e6i | − | 0.287278i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.44318e7i | − | 0.830585i | −0.909688 | − | 0.415293i | \(-0.863679\pi\) | ||
0.909688 | − | 0.415293i | \(-0.136321\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.18435e7 | + | 2.72480e7i | −0.677310 | + | 1.55827i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.63533e6 | 0.149759 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.64603e6 | 0.0929512 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.96801e6 | + | 6.82840e6i | −0.166551 | + | 0.383178i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.87022e7i | − | 1.04291i | −0.853278 | − | 0.521456i | \(-0.825389\pi\) | ||
0.853278 | − | 0.521456i | \(-0.174611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.53554e7i | 0.850930i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.55586e7 | + | 1.45163e7i | −0.856820 | + | 0.799418i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.38788e6 | −0.459053 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.50852e6 | 0.517158 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.15545e6 | − | 1.37154e6i | −0.170560 | − | 0.0741351i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.72136e7i | 1.46189i | 0.682435 | + | 0.730946i | \(0.260921\pi\) | ||||
−0.682435 | + | 0.730946i | \(0.739079\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.16663e7i | − | 0.622847i | −0.950271 | − | 0.311424i | \(-0.899194\pi\) | ||
0.950271 | − | 0.311424i | \(-0.100806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.40086e7 | + | 1.04355e7i | 1.27392 | + | 0.553715i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.38533e7 | −1.25792 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.16160e7 | 0.608836 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.03994e6 | + | 2.83628e6i | −0.158363 | + | 0.147754i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.60653e7i | 0.831822i | 0.909405 | + | 0.415911i | \(0.136537\pi\) | ||||
−0.909405 | + | 0.415911i | \(0.863463\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.14851e7i | 1.62034i | 0.586197 | + | 0.810169i | \(0.300625\pi\) | ||||
−0.586197 | + | 0.810169i | \(0.699375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.29124e6 | − | 2.97071e6i | 0.0660496 | − | 0.151958i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.13442e7 | 0.576779 | 0.288389 | − | 0.957513i | \(-0.406880\pi\) | ||||
0.288389 | + | 0.957513i | \(0.406880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00733e7 | −1.01446 | −0.507228 | − | 0.861812i | \(-0.669330\pi\) | ||||
−0.507228 | + | 0.861812i | \(0.669330\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.30611e6 | + | 5.30559e6i | −0.115845 | + | 0.266521i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.55503e7i | − | 0.776473i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.92259e6i | − | 0.293965i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.15363e6 | − | 6.07405e6i | −0.106257 | − | 0.299685i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.22032e7 | −0.598508 | −0.299254 | − | 0.954174i | \(-0.596738\pi\) | ||||
−0.299254 | + | 0.954174i | \(0.596738\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.61216e6 | −0.176107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.25571e6 | + | 2.71908e6i | 0.303185 | + | 0.131781i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.02721e7i | 0.494898i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.56460e6i | − | 0.410203i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.02006e6 | + | 2.61666e6i | 0.286637 | + | 0.124588i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.80629e7 | −3.22171 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −708002. | −0.0333167 | −0.0166583 | − | 0.999861i | \(-0.505303\pi\) | ||||
−0.0166583 | + | 0.999861i | \(0.505303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.17297e7 | + | 1.25720e7i | 0.548749 | + | 0.588151i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.01954e7i | − | 0.474192i | −0.971486 | − | 0.237096i | \(-0.923804\pi\) | ||
0.971486 | − | 0.237096i | \(-0.0761956\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.14505e7i | 1.45427i | 0.686496 | + | 0.727134i | \(0.259148\pi\) | ||||
−0.686496 | + | 0.727134i | \(0.740852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.85998e6 | + | 1.57826e7i | −0.315366 | + | 0.725553i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.33323e7 | 0.609364 | 0.304682 | − | 0.952454i | \(-0.401450\pi\) | ||||
0.304682 | + | 0.952454i | \(0.401450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.31812e7 | 1.05340 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −524611. | + | 1.20696e6i | −0.0237023 | + | 0.0545311i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.31687e6i | − | 0.238840i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.16885e6i | 0.275524i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.43551e6 | + | 9.04121e6i | 0.374607 | + | 0.401505i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.03476e7 | 0.456899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.28216e7 | −1.44099 | −0.720495 | − | 0.693460i | \(-0.756085\pi\) | ||||
−0.720495 | + | 0.693460i | \(0.756085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.30617e7 | − | 5.67737e6i | −0.570202 | − | 0.247842i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.61293e7i | − | 0.700125i | −0.936726 | − | 0.350062i | \(-0.886160\pi\) | ||
0.936726 | − | 0.350062i | \(-0.113840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.75882e7i | − | 0.759138i | −0.925163 | − | 0.379569i | \(-0.876072\pi\) | ||
0.925163 | − | 0.379569i | \(-0.123928\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.33904e7 | − | 5.82020e6i | −0.574690 | − | 0.249793i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.13047e7 | 0.482447 | 0.241224 | − | 0.970470i | \(-0.422451\pi\) | ||||
0.241224 | + | 0.970470i | \(0.422451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.55377e6 | 0.278123 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 467748. | − | 6.74003e6i | 0.0197387 | − | 0.284425i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.59881e7i | 1.09055i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.22434e7i | 0.510911i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.33953e6 | − | 1.91865e7i | 0.346067 | − | 0.796186i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.35606e6 | −0.344828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.52564e7 | 0.626095 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.13632e6 | − | 4.91496e6i | 0.0871860 | − | 0.200586i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.50397e7i | − | 1.01627i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.83914e6i | 0.356773i | 0.983961 | + | 0.178386i | \(0.0570877\pi\) | ||||
−0.983961 | + | 0.178386i | \(0.942912\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.24019e7 | + | 1.15711e7i | −0.497829 | + | 0.464477i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.27645e7 | −0.509575 | −0.254788 | − | 0.966997i | \(-0.582006\pi\) | ||||
−0.254788 | + | 0.966997i | \(0.582006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.09311e7 | 0.433999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.88033e6 | − | 1.25195e6i | −0.113734 | − | 0.0494351i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.25984e6i | 0.167290i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.57548e7i | 1.78710i | 0.448967 | + | 0.893548i | \(0.351792\pi\) | ||||
−0.448967 | + | 0.893548i | \(0.648208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.49484e7 | + | 6.49740e6i | 0.580690 | + | 0.252401i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.51734e7 | 0.586245 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72242e7 | −1.04617 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.46576e7 | − | 1.36757e7i | 0.560227 | − | 0.522695i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.32383e7i | 0.503259i | 0.967824 | + | 0.251630i | \(0.0809665\pi\) | ||||
−0.967824 | + | 0.251630i | \(0.919034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.63180e7i | − | 0.995126i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.17058e6 | − | 1.64971e7i | 0.269681 | − | 0.620446i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.78361e6 | 0.178948 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.71022e7 | −1.00845 | −0.504226 | − | 0.863572i | \(-0.668222\pi\) | ||||
−0.504226 | + | 0.863572i | \(0.668222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.63461e6 | − | 6.06136e6i | 0.0975107 | − | 0.224340i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.12202e7i | − | 1.14938i | −0.818373 | − | 0.574688i | \(-0.805124\pi\) | ||
0.818373 | − | 0.574688i | \(-0.194876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.65933e7i | − | 3.17106i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.47672e6 | − | 2.65097e6i | 0.272353 | − | 0.0965661i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.42016e7 | 1.23929 | 0.619643 | − | 0.784883i | \(-0.287277\pi\) | ||||
0.619643 | + | 0.784883i | \(0.287277\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.16687e7 | −0.781029 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.71072e7 | + | 1.17823e7i | 0.971928 | + | 0.422454i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.23251e7i | 1.50961i | 0.655947 | + | 0.754807i | \(0.272270\pi\) | ||||
−0.655947 | + | 0.754807i | \(0.727730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 893196.i | 0.0316912i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.03409e6 | − | 3.49207e6i | −0.283568 | − | 0.123254i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.24410e6 | 0.113906 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.57347e7 | 0.898898 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.24677e7 | − | 1.33629e7i | −0.433231 | − | 0.464339i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.04202e7i | − | 0.705897i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.63922e7i | − | 1.25153i | −0.780010 | − | 0.625767i | \(-0.784786\pi\) | ||
0.780010 | − | 0.625767i | \(-0.215214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.40445e7 | − | 3.23118e7i | 0.480505 | − | 1.10548i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.11273e7 | 1.39985 | 0.699925 | − | 0.714216i | \(-0.253217\pi\) | ||||
0.699925 | + | 0.714216i | \(0.253217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.56751e6 | −0.120805 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.33569e6 | − | 7.67433e6i | 0.112376 | − | 0.258541i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.71917e7i | − | 0.911380i | −0.890138 | − | 0.455690i | \(-0.849392\pi\) | ||
0.890138 | − | 0.455690i | \(-0.150608\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.00193e7i | 0.334102i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.09788e6 | − | 8.67934e6i | −0.268657 | − | 0.287948i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.74580e7 | 0.906326 | 0.453163 | − | 0.891428i | \(-0.350295\pi\) | ||||
0.453163 | + | 0.891428i | \(0.350295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.28229e7 | 0.749516 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.09961e7 | + | 4.77953e6i | 0.359291 | + | 0.156168i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.69667e7i | 0.876671i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.59414e7i | 1.48601i | 0.669288 | + | 0.743003i | \(0.266599\pi\) | ||||
−0.669288 | + | 0.743003i | \(0.733401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.62568e7 | − | 1.57592e7i | −1.16685 | − | 0.507180i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.42703e7 | 1.09739 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.10427e7 | 0.670445 | 0.335223 | − | 0.942139i | \(-0.391188\pi\) | ||||
0.335223 | + | 0.942139i | \(0.391188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.35191e7 | + | 1.89759e7i | −1.69666 | + | 0.601572i |
(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 | 96.6.c.a.95.10 | yes | 20 | |
3.2 | odd | 2 | inner | 96.6.c.a.95.12 | yes | 20 | |
4.3 | odd | 2 | inner | 96.6.c.a.95.11 | yes | 20 | |
8.3 | odd | 2 | 192.6.c.f.191.10 | 20 | |||
8.5 | even | 2 | 192.6.c.f.191.11 | 20 | |||
12.11 | even | 2 | inner | 96.6.c.a.95.9 | ✓ | 20 | |
24.5 | odd | 2 | 192.6.c.f.191.9 | 20 | |||
24.11 | even | 2 | 192.6.c.f.191.12 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.6.c.a.95.9 | ✓ | 20 | 12.11 | even | 2 | inner | |
96.6.c.a.95.10 | yes | 20 | 1.1 | even | 1 | trivial | |
96.6.c.a.95.11 | yes | 20 | 4.3 | odd | 2 | inner | |
96.6.c.a.95.12 | yes | 20 | 3.2 | odd | 2 | inner | |
192.6.c.f.191.9 | 20 | 24.5 | odd | 2 | |||
192.6.c.f.191.10 | 20 | 8.3 | odd | 2 | |||
192.6.c.f.191.11 | 20 | 8.5 | even | 2 | |||
192.6.c.f.191.12 | 20 | 24.11 | even | 2 |