Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(81,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.81");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.l (of order \(4\), degree \(2\), 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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 241.8 | ||
Character | \(\chi\) | \(=\) | 320.241 |
Dual form | 320.6.l.a.81.8 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −14.9697 | + | 14.9697i | −0.960307 | + | 0.960307i | −0.999242 | − | 0.0389348i | \(-0.987604\pi\) |
0.0389348 | + | 0.999242i | \(0.487604\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.6777 | + | 17.6777i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 66.6523i | 0.514127i | 0.966395 | + | 0.257063i | \(0.0827549\pi\) | ||||
−0.966395 | + | 0.257063i | \(0.917245\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 205.184i | − | 0.844379i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 34.0729 | + | 34.0729i | 0.0849040 | + | 0.0849040i | 0.748283 | − | 0.663379i | \(-0.230878\pi\) |
−0.663379 | + | 0.748283i | \(0.730878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 292.234 | − | 292.234i | 0.479593 | − | 0.479593i | −0.425409 | − | 0.905001i | \(-0.639870\pi\) |
0.905001 | + | 0.425409i | \(0.139870\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −529.259 | −0.607351 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 610.554 | 0.512391 | 0.256196 | − | 0.966625i | \(-0.417531\pi\) | ||||
0.256196 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 702.298 | − | 702.298i | 0.446311 | − | 0.446311i | −0.447815 | − | 0.894126i | \(-0.647798\pi\) |
0.894126 | + | 0.447815i | \(0.147798\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −997.765 | − | 997.765i | −0.493719 | − | 0.493719i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2859.14i | − | 1.12698i | −0.826123 | − | 0.563489i | \(-0.809459\pi\) | ||
0.826123 | − | 0.563489i | \(-0.190541\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −566.093 | − | 566.093i | −0.149444 | − | 0.149444i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4762.59 | − | 4762.59i | 1.05159 | − | 1.05159i | 0.0529987 | − | 0.998595i | \(-0.483122\pi\) |
0.998595 | − | 0.0529987i | \(-0.0168779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 775.382 | 0.144914 | 0.0724572 | − | 0.997372i | \(-0.476916\pi\) | ||||
0.0724572 | + | 0.997372i | \(0.476916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1020.12 | −0.163068 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1178.26 | + | 1178.26i | −0.162581 | + | 0.162581i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6929.77 | − | 6929.77i | −0.832174 | − | 0.832174i | 0.155640 | − | 0.987814i | \(-0.450256\pi\) |
−0.987814 | + | 0.155640i | \(0.950256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8749.32i | 0.921113i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1051.16i | − | 0.0976585i | −0.998807 | − | 0.0488292i | \(-0.984451\pi\) | ||
0.998807 | − | 0.0488292i | \(-0.0155490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5645.72 | − | 5645.72i | −0.465638 | − | 0.465638i | 0.434860 | − | 0.900498i | \(-0.356798\pi\) |
−0.900498 | + | 0.434860i | \(0.856798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3627.18 | − | 3627.18i | 0.267016 | − | 0.267016i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2247.96 | 0.148437 | 0.0742187 | − | 0.997242i | \(-0.476354\pi\) | ||||
0.0742187 | + | 0.997242i | \(0.476354\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12364.5 | 0.735674 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9139.81 | + | 9139.81i | −0.492053 | + | 0.492053i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17582.1 | + | 17582.1i | 0.859769 | + | 0.859769i | 0.991311 | − | 0.131541i | \(-0.0419926\pi\) |
−0.131541 | + | 0.991311i | \(0.541993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1204.66i | 0.0536980i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21026.4i | 0.857191i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −22506.6 | − | 22506.6i | −0.841744 | − | 0.841744i | 0.147341 | − | 0.989086i | \(-0.452928\pi\) |
−0.989086 | + | 0.147341i | \(0.952928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35680.2 | − | 35680.2i | 1.22773 | − | 1.22773i | 0.262906 | − | 0.964821i | \(-0.415319\pi\) |
0.964821 | − | 0.262906i | \(-0.0846811\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13676.0 | 0.434118 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10332.0 | 0.303321 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14570.0 | + | 14570.0i | −0.396526 | + | 0.396526i | −0.877006 | − | 0.480480i | \(-0.840462\pi\) |
0.480480 | + | 0.877006i | \(0.340462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 42800.5 | + | 42800.5i | 1.08225 | + | 1.08225i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37150.7i | 0.874624i | 0.899310 | + | 0.437312i | \(0.144070\pi\) | ||||
−0.899310 | + | 0.437312i | \(0.855930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77602.0i | 1.70438i | 0.523235 | + | 0.852188i | \(0.324725\pi\) | ||||
−0.523235 | + | 0.852188i | \(0.675275\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9356.07 | − | 9356.07i | −0.192061 | − | 0.192061i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2271.04 | + | 2271.04i | −0.0436514 | + | 0.0436514i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 103892. | 1.87290 | 0.936450 | − | 0.350800i | \(-0.114090\pi\) | ||||
0.936450 | + | 0.350800i | \(0.114090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 66808.2 | 1.13140 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 30433.5 | − | 30433.5i | 0.484905 | − | 0.484905i | −0.421789 | − | 0.906694i | \(-0.638598\pi\) |
0.906694 | + | 0.421789i | \(0.138598\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10793.2 | + | 10793.2i | 0.162032 | + | 0.162032i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 142589.i | 2.01970i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 55535.9i | 0.743188i | 0.928395 | + | 0.371594i | \(0.121189\pi\) | ||||
−0.928395 | + | 0.371594i | \(0.878811\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19478.1 | + | 19478.1i | 0.246571 | + | 0.246571i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11607.2 | + | 11607.2i | −0.139162 | + | 0.139162i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24830.0 | 0.282272 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 33028.6 | 0.356419 | 0.178209 | − | 0.983993i | \(-0.442970\pi\) | ||||
0.178209 | + | 0.983993i | \(0.442970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6991.23 | − | 6991.23i | 0.0716911 | − | 0.0716911i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −69109.8 | − | 69109.8i | −0.674119 | − | 0.674119i | 0.284544 | − | 0.958663i | \(-0.408158\pi\) |
−0.958663 | + | 0.284544i | \(0.908158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59252.8i | 0.550321i | 0.961398 | + | 0.275161i | \(0.0887310\pi\) | ||||
−0.961398 | + | 0.275161i | \(0.911269\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 35276.3i | − | 0.312256i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 132571. | + | 132571.i | 1.11941 | + | 1.11941i | 0.991828 | + | 0.127585i | \(0.0407226\pi\) |
0.127585 | + | 0.991828i | \(0.459277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −151453. | + | 151453.i | −1.22099 | + | 1.22099i | −0.253708 | + | 0.967281i | \(0.581650\pi\) |
−0.967281 | + | 0.253708i | \(0.918350\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 207473. | 1.59829 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −27934.3 | −0.205798 | −0.102899 | − | 0.994692i | \(-0.532812\pi\) | ||||
−0.102899 | + | 0.994692i | \(0.532812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 50542.9 | − | 50542.9i | 0.356382 | − | 0.356382i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −59961.8 | − | 59961.8i | −0.404958 | − | 0.404958i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 40694.8i | 0.263434i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 158729.i | − | 0.985583i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15735.6 | + | 15735.6i | 0.0937821 | + | 0.0937821i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11048.5 | + | 11048.5i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15092.5 | 0.0830333 | 0.0415166 | − | 0.999138i | \(-0.486781\pi\) | ||||
0.0415166 | + | 0.999138i | \(0.486781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 169030. | 0.894310 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 225439. | − | 225439.i | 1.14776 | − | 1.14776i | 0.160765 | − | 0.986993i | \(-0.448604\pi\) |
0.986993 | − | 0.160765i | \(-0.0513960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 46809.8 | + | 46809.8i | 0.229460 | + | 0.229460i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 20014.4i | − | 0.0945166i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 183393.i | − | 0.834798i | −0.908723 | − | 0.417399i | \(-0.862942\pi\) | ||
0.908723 | − | 0.417399i | \(-0.137058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −227165. | − | 227165.i | −0.997252 | − | 0.997252i | 0.00274377 | − | 0.999996i | \(-0.499127\pi\) |
−0.999996 | + | 0.00274377i | \(0.999127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33651.2 | + | 33651.2i | −0.142545 | + | 0.142545i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19914.6 | 0.0814386 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 168383. | 0.665086 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −185092. | + | 185092.i | −0.706473 | + | 0.706473i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 126186. | + | 126186.i | 0.465636 | + | 0.465636i | 0.900497 | − | 0.434862i | \(-0.143203\pi\) |
−0.434862 | + | 0.900497i | \(0.643203\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 406653.i | − | 1.45138i | −0.688021 | − | 0.725691i | \(-0.741520\pi\) | ||
0.688021 | − | 0.725691i | \(-0.258480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 125276.i | − | 0.432652i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13706.9 | + | 13706.9i | 0.0458259 | + | 0.0458259i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −355078. | + | 355078.i | −1.14967 | + | 1.14967i | −0.163058 | + | 0.986617i | \(0.552136\pi\) |
−0.986617 | + | 0.163058i | \(0.947864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −526399. | −1.65129 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 190568. | 0.579410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 300694. | − | 300694.i | 0.886454 | − | 0.886454i | −0.107727 | − | 0.994181i | \(-0.534357\pi\) |
0.994181 | + | 0.107727i | \(0.0343571\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18033.4 | − | 18033.4i | −0.0515665 | − | 0.0515665i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12377.8i | 0.0343441i | 0.999853 | + | 0.0171721i | \(0.00546630\pi\) | ||||
−0.999853 | + | 0.0171721i | \(0.994534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 200491.i | 0.539982i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −144100. | − | 144100.i | −0.376855 | − | 0.376855i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −207386. | + | 207386.i | −0.526823 | + | 0.526823i | −0.919624 | − | 0.392800i | \(-0.871506\pi\) |
0.392800 | + | 0.919624i | \(0.371506\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −41657.7 | −0.102825 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 673835. | 1.61667 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 66148.3 | − | 66148.3i | 0.154307 | − | 0.154307i | −0.625731 | − | 0.780039i | \(-0.715199\pi\) |
0.780039 | + | 0.625731i | \(0.215199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −100739. | − | 100739.i | −0.228560 | − | 0.228560i | 0.583531 | − | 0.812091i | \(-0.301671\pi\) |
−0.812091 | + | 0.583531i | \(0.801671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.06824e6i | 2.35799i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 245004.i | − | 0.526313i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20803.4 | + | 20803.4i | 0.0435040 | + | 0.0435040i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 37731.4 | − | 37731.4i | 0.0768331 | − | 0.0768331i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3731.48 | −0.00740113 | −0.00370056 | − | 0.999993i | \(-0.501178\pi\) | ||||
−0.00370056 | + | 0.999993i | \(0.501178\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −113488. | −0.219309 | −0.109654 | − | 0.993970i | \(-0.534974\pi\) | ||||
−0.109654 | + | 0.993970i | \(0.534974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −154668. | + | 154668.i | −0.291281 | + | 0.291281i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −299753. | − | 299753.i | −0.550298 | − | 0.550298i | 0.376228 | − | 0.926527i | \(-0.377221\pi\) |
−0.926527 | + | 0.376228i | \(0.877221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 754680.i | 1.35092i | 0.737396 | + | 0.675460i | \(0.236055\pi\) | ||||
−0.737396 | + | 0.675460i | \(0.763945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 436216.i | − | 0.761572i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 317437. | + | 317437.i | 0.540652 | + | 0.540652i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18582.1 | − | 18582.1i | 0.0308823 | − | 0.0308823i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −586650. | −0.951597 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 47858.7 | 0.0757871 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 440226. | − | 440226.i | 0.680722 | − | 0.680722i | −0.279441 | − | 0.960163i | \(-0.590149\pi\) |
0.960163 | + | 0.279441i | \(0.0901490\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −556136. | − | 556136.i | −0.839908 | − | 0.839908i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 199606.i | − | 0.294495i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 51681.0i | 0.0745043i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.16168e6 | − | 1.16168e6i | −1.63673 | − | 1.63673i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 178425. | − | 178425.i | 0.245739 | − | 0.245739i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 597053. | 0.803990 | 0.401995 | − | 0.915642i | \(-0.368317\pi\) | ||||
0.401995 | + | 0.915642i | \(0.368317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 128240. | 0.168876 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −515972. | + | 515972.i | −0.664602 | + | 0.664602i | −0.956461 | − | 0.291859i | \(-0.905726\pi\) |
0.291859 | + | 0.956461i | \(0.405726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 414064. | + | 414064.i | 0.521769 | + | 0.521769i | 0.918105 | − | 0.396336i | \(-0.129719\pi\) |
−0.396336 | + | 0.918105i | \(0.629719\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 67993.6i | − | 0.0838375i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 556837.i | − | 0.671952i | −0.941870 | − | 0.335976i | \(-0.890934\pi\) | ||
0.941870 | − | 0.335976i | \(-0.109066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39738.6 | + | 39738.6i | 0.0469400 | + | 0.0469400i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.55523e6 | + | 1.55523e6i | −1.79856 | + | 1.79856i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16833.0 | −0.0190619 | −0.00953097 | − | 0.999955i | \(-0.503034\pi\) | ||||
−0.00953097 | + | 0.999955i | \(0.503034\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 416006. | 0.461378 | 0.230689 | − | 0.973027i | \(-0.425902\pi\) | ||||
0.230689 | + | 0.973027i | \(0.425902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −862539. | + | 862539.i | −0.937050 | + | 0.937050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 218575. | + | 218575.i | 0.232641 | + | 0.232641i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 410471.i | − | 0.428095i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 911162.i | 0.931316i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.23509e6 | − | 1.23509e6i | −1.23741 | − | 1.23741i | −0.961054 | − | 0.276359i | \(-0.910872\pi\) |
−0.276359 | − | 0.961054i | \(-0.589128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 97419.3 | − | 97419.3i | 0.0956850 | − | 0.0956850i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −323141. | −0.311202 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 77341.0 | 0.0730427 | 0.0365214 | − | 0.999333i | \(-0.488372\pi\) | ||||
0.0365214 | + | 0.999333i | \(0.488372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 461885. | − | 461885.i | 0.427843 | − | 0.427843i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −977207. | − | 977207.i | −0.887943 | − | 0.887943i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.43109e6i | 1.27579i | 0.770124 | + | 0.637894i | \(0.220194\pi\) | ||||
−0.770124 | + | 0.637894i | \(0.779806\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 621622.i | 0.543766i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −831356. | − | 831356.i | −0.713689 | − | 0.713689i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.03735e6 | − | 1.03735e6i | 0.874067 | − | 0.874067i | −0.118846 | − | 0.992913i | \(-0.537919\pi\) |
0.992913 | + | 0.118846i | \(0.0379194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 654430. | 0.541302 | 0.270651 | − | 0.962677i | \(-0.412761\pi\) | ||||
0.270651 | + | 0.962677i | \(0.412761\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −583162. | −0.473568 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21295.6 | + | 21295.6i | −0.0169808 | + | 0.0169808i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.12490e6 | − | 1.12490e6i | −0.880876 | − | 0.880876i | 0.112748 | − | 0.993624i | \(-0.464035\pi\) |
−0.993624 | + | 0.112748i | \(0.964035\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 159096.i | − | 0.122363i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.15244e6i | − | 1.62617i | −0.582148 | − | 0.813083i | \(-0.697787\pi\) | ||
0.582148 | − | 0.813083i | \(-0.302213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.07730e6 | − | 1.07730e6i | −0.799597 | − | 0.799597i | 0.183435 | − | 0.983032i | \(-0.441278\pi\) |
−0.983032 | + | 0.183435i | \(0.941278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −371697. | + | 371697.i | −0.271067 | + | 0.271067i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 70062.3 | 0.0502088 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.04708e6 | −0.737455 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −494428. | + | 494428.i | −0.342271 | + | 0.342271i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 201738. | + | 201738.i | 0.137283 | + | 0.137283i | 0.772409 | − | 0.635125i | \(-0.219052\pi\) |
−0.635125 | + | 0.772409i | \(0.719052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 795729.i | − | 0.532366i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 38576.9i | − | 0.0253768i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −835538. | − | 835538.i | −0.540491 | − | 0.540491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 376300. | − | 376300.i | 0.239397 | − | 0.239397i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.06911e6 | 1.29472 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.26148e6 | 0.776483 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.33520e6 | − | 2.33520e6i | 1.41409 | − | 1.41409i | 0.697783 | − | 0.716310i | \(-0.254170\pi\) |
0.716310 | − | 0.697783i | \(-0.245830\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −886997. | − | 886997.i | −0.528477 | − | 0.528477i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.50514e6i | 0.882420i | 0.897404 | + | 0.441210i | \(0.145451\pi\) | ||||
−0.897404 | + | 0.441210i | \(0.854549\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.17646e6i | 0.678763i | 0.940649 | + | 0.339381i | \(0.110218\pi\) | ||||
−0.940649 | + | 0.339381i | \(0.889782\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 241760. | + | 241760.i | 0.137280 | + | 0.137280i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 851779. | − | 851779.i | 0.476079 | − | 0.476079i | −0.427796 | − | 0.903875i | \(-0.640710\pi\) |
0.903875 | + | 0.427796i | \(0.140710\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 324551. | 0.178569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.96911e6 | −2.14996 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 428791. | − | 428791.i | 0.228686 | − | 0.228686i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 182646. | + | 182646.i | 0.0959185 | + | 0.0959185i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.53441e6i | − | 2.34505i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 149831.i | 0.0763156i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 435282. | + | 435282.i | 0.218374 | + | 0.218374i | 0.807813 | − | 0.589439i | \(-0.200651\pi\) |
−0.589439 | + | 0.807813i | \(0.700651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.42188e6 | + | 1.42188e6i | −0.702671 | + | 0.702671i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −515126. | −0.250785 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.88013e6 | 1.38146 | 0.690728 | − | 0.723115i | \(-0.257290\pi\) | ||||
0.690728 | + | 0.723115i | \(0.257290\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 418168. | − | 418168.i | 0.197629 | − | 0.197629i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26419.5 | + | 26419.5i | 0.0123038 | + | 0.0123038i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.94435e6i | 0.892356i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.51323e6i | 0.684472i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.63293e6 | + | 2.63293e6i | 1.17386 | + | 1.17386i | 0.981282 | + | 0.192577i | \(0.0616846\pi\) |
0.192577 | + | 0.981282i | \(0.438315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.54010e6 | − | 2.54010e6i | 1.11632 | − | 1.11632i | 0.124040 | − | 0.992277i | \(-0.460415\pi\) |
0.992277 | − | 0.124040i | \(-0.0395852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −330863. | −0.143344 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.69643e6 | −0.724603 | −0.362302 | − | 0.932061i | \(-0.618009\pi\) | ||||
−0.362302 | + | 0.932061i | \(0.618009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −656738. | + | 656738.i | −0.276581 | + | 0.276581i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −609189. | − | 609189.i | −0.252977 | − | 0.252977i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.86875e6i | 1.17478i | 0.809304 | + | 0.587390i | \(0.199844\pi\) | ||||
−0.809304 | + | 0.587390i | \(0.800156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.48965e6i | 0.601613i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.37613e6 | + | 2.37613e6i | 0.946462 | + | 0.946462i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.37182e6 | + | 1.37182e6i | −0.538971 | + | 0.538971i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −231568. | −0.0897457 | −0.0448729 | − | 0.998993i | \(-0.514288\pi\) | ||||
−0.0448729 | + | 0.998993i | \(0.514288\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −215682. | −0.0824608 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.17189e6 | + | 1.17189e6i | −0.442030 | + | 0.442030i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.46826e6 | + | 1.46826e6i | 0.546427 | + | 0.546427i | 0.925405 | − | 0.378979i | \(-0.123725\pi\) |
−0.378979 | + | 0.925405i | \(0.623725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 330787.i | − | 0.121470i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.78358e6i | − | 1.00867i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −460062. | − | 460062.i | −0.164520 | − | 0.164520i | 0.620046 | − | 0.784566i | \(-0.287114\pi\) |
−0.784566 | + | 0.620046i | \(0.787114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −225930. | + | 225930.i | −0.0797375 | + | 0.0797375i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 278081. | 0.0968665 | 0.0484333 | − | 0.998826i | \(-0.484577\pi\) | ||||
0.0484333 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −80293.4 | −0.0276076 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.15841e6 | + | 1.15841e6i | −0.393175 | + | 0.393175i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.81927e6 | + | 3.81927e6i | 1.27969 | + | 1.27969i | 0.940839 | + | 0.338855i | \(0.110040\pi\) |
0.338855 | + | 0.940839i | \(0.389960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.74566e6i | − | 0.577454i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.74950e6i | 2.20440i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.83657e6 | + | 1.83657e6i | 0.592263 | + | 0.592263i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −978913. | + | 978913.i | −0.311722 | + | 0.311722i | −0.845576 | − | 0.533854i | \(-0.820743\pi\) |
0.533854 | + | 0.845576i | \(0.320743\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.40146e6 | −0.440704 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.86658e6 | −0.579677 | −0.289838 | − | 0.957076i | \(-0.593602\pi\) | ||||
−0.289838 | + | 0.957076i | \(0.593602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 226593. | − | 226593.i | 0.0694999 | − | 0.0694999i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.18101e6 | + | 1.18101e6i | 0.357781 | + | 0.357781i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 472235.i | − | 0.141310i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.49733e6i | − | 1.32937i | −0.747123 | − | 0.664686i | \(-0.768565\pi\) | ||
0.747123 | − | 0.664686i | \(-0.231435\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.74534e6 | + | 2.74534e6i | 0.801663 | + | 0.801663i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.50012e6 | − | 1.50012e6i | 0.432763 | − | 0.432763i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.07599e6 | 0.306681 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.80120e6 | 1.91534 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 289805. | − | 289805.i | 0.0806438 | − | 0.0806438i | −0.665634 | − | 0.746278i | \(-0.731839\pi\) |
0.746278 | + | 0.665634i | \(0.231839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.18738e6 | + | 3.18738e6i | 0.876452 | + | 0.876452i | 0.993166 | − | 0.116714i | \(-0.0372360\pi\) |
−0.116714 | + | 0.993166i | \(0.537236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 461245.i | − | 0.125337i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 381596.i | 0.102478i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.37816e6 | + | 2.37816e6i | 0.631207 | + | 0.631207i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −298115. | + | 298115.i | −0.0782061 | + | 0.0782061i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.40103e6 | −0.363290 | −0.181645 | − | 0.983364i | \(-0.558142\pi\) | ||||
−0.181645 | + | 0.983364i | \(0.558142\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.92875e6 | 1.26333 | 0.631666 | − | 0.775241i | \(-0.282372\pi\) | ||||
0.631666 | + | 0.775241i | \(0.282372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.52064e6 | + | 2.52064e6i | −0.638687 | + | 0.638687i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00797e6 | − | 2.00797e6i | −0.502983 | − | 0.502983i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 489017.i | 0.121105i | 0.998165 | + | 0.0605526i | \(0.0192863\pi\) | ||||
−0.998165 | + | 0.0605526i | \(0.980714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.53699e6i | − | 0.621188i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.39962e6 | + | 5.39962e6i | 1.30724 | + | 1.30724i | 0.923403 | + | 0.383833i | \(0.125396\pi\) |
0.383833 | + | 0.923403i | \(0.374604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −981746. | + | 981746.i | −0.235017 | + | 0.235017i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.77794e6 | −0.894307 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.48009e6 | −0.346475 | −0.173237 | − | 0.984880i | \(-0.555423\pi\) | ||||
−0.173237 | + | 0.984880i | \(0.555423\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35816.2 | − | 35816.2i | 0.00829159 | − | 0.00829159i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.08748e6 | + | 6.08748e6i | 1.39377 | + | 1.39377i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 688654.i | 0.155945i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5.01425e6i | − | 1.12309i | −0.827445 | − | 0.561546i | \(-0.810207\pi\) | ||
0.827445 | − | 0.561546i | \(-0.189793\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −345630. | − | 345630.i | −0.0765738 | − | 0.0765738i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.39558e6 | − | 1.39558e6i | 0.305845 | − | 0.305845i | −0.537450 | − | 0.843295i | \(-0.680612\pi\) |
0.843295 | + | 0.537450i | \(0.180612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.41497e6 | −0.957139 | −0.478570 | − | 0.878050i | \(-0.658845\pi\) | ||||
−0.478570 | + | 0.878050i | \(0.658845\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −410378. | −0.0880139 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 833822. | − | 833822.i | 0.176922 | − | 0.176922i | −0.613091 | − | 0.790013i | \(-0.710074\pi\) |
0.790013 | + | 0.613091i | \(0.210074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −971121. | − | 971121.i | −0.203864 | − | 0.203864i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.06308e7i | − | 2.20808i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 384733.i | − | 0.0790690i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 438936. | + | 438936.i | 0.0892622 | + | 0.0892622i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.60757e6 | − | 3.60757e6i | 0.725971 | − | 0.725971i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.84747e6 | 1.16447 | 0.582236 | − | 0.813020i | \(-0.302178\pi\) | ||||
0.582236 | + | 0.813020i | \(0.302178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.05023e6 | −0.798210 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.85275e6 | + | 2.85275e6i | −0.556411 | + | 0.556411i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 583868. | + | 583868.i | 0.112709 | + | 0.112709i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.71510e6i | − | 1.09195i | −0.837802 | − | 0.545974i | \(-0.816160\pi\) | ||
0.837802 | − | 0.545974i | \(-0.183840\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.00261e6i | 1.70254i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.06011e6 | − | 2.06011e6i | −0.385645 | − | 0.385645i | 0.487486 | − | 0.873131i | \(-0.337914\pi\) |
−0.873131 | + | 0.487486i | \(0.837914\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.90781e6 | − | 2.90781e6i | 0.538827 | − | 0.538827i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 247177. | 0.0453414 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.47618e6 | −0.449668 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.78177e6 | − | 4.78177e6i | 0.859680 | − | 0.859680i | −0.131620 | − | 0.991300i | \(-0.542018\pi\) |
0.991300 | + | 0.131620i | \(0.0420179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −185292. | − | 185292.i | −0.0329809 | − | 0.0329809i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.52174e6i | 0.796867i | 0.917197 | + | 0.398433i | \(0.130446\pi\) | ||||
−0.917197 | + | 0.398433i | \(0.869554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.44340e6i | − | 0.426350i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.00130e6 | − | 3.00130e6i | −0.518548 | − | 0.518548i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 296532. | − | 296532.i | 0.0507314 | − | 0.0507314i | −0.681286 | − | 0.732017i | \(-0.738579\pi\) |
0.732017 | + | 0.681286i | \(0.238579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.17235e6 | −0.876265 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −795132. | −0.133397 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.04745e6 | + | 1.04745e6i | −0.174027 | + | 0.174027i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 76594.5 | + | 76594.5i | 0.0126029 | + | 0.0126029i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.20903e6i | − | 1.01182i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 458362.i | 0.0739800i | 0.999316 | + | 0.0369900i | \(0.0117770\pi\) | ||||
−0.999316 | + | 0.0369900i | \(0.988223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.31189e6 | − | 1.31189e6i | −0.209721 | − | 0.209721i | 0.594428 | − | 0.804149i | \(-0.297379\pi\) |
−0.804149 | + | 0.594428i | \(0.797379\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 623603. | − | 623603.i | 0.0987439 | − | 0.0987439i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 473412. | 0.0742528 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.73834e6 | −0.270082 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.61800e6 | + | 4.61800e6i | −0.710751 | + | 0.710751i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −307185. | − | 307185.i | −0.0468363 | − | 0.0468363i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.68710e6i | 0.707979i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.98044e6i | 0.296364i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 421294. | + | 421294.i | 0.0624616 | + | 0.0624616i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.50591e6 | − | 7.50591e6i | 1.10258 | − | 1.10258i | 0.108481 | − | 0.994098i | \(-0.465401\pi\) |
0.994098 | − | 0.108481i | \(-0.0345988\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.01606e6 | 0.438975 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.35467e6 | −0.772221 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.64329e6 | − | 3.64329e6i | 0.520626 | − | 0.520626i | −0.397135 | − | 0.917760i | \(-0.629995\pi\) |
0.917760 | + | 0.397135i | \(0.129995\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.32100e6 | − | 7.32100e6i | −1.03667 | − | 1.03667i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.68951e6i | − | 0.938675i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.92465e6i | 0.962908i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.66764e6 | + | 3.66764e6i | 0.505422 | + | 0.505422i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.00393e6 | + | 2.00393e6i | −0.273681 | + | 0.273681i | −0.830580 | − | 0.556899i | \(-0.811991\pi\) |
0.556899 | + | 0.830580i | \(0.311991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.29974e6 | −0.446633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −622841. | −0.0835545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.20161e6 | + | 4.20161e6i | −0.558656 | + | 0.558656i | −0.928925 | − | 0.370269i | \(-0.879266\pi\) |
0.370269 | + | 0.928925i | \(0.379266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −493813. | − | 493813.i | −0.0650791 | − | 0.0650791i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.45292e6i | 0.581684i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 4.05098e6i | − | 0.524541i | −0.964994 | − | 0.262271i | \(-0.915529\pi\) | ||
0.964994 | − | 0.262271i | \(-0.0844713\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.13511e6 | − | 7.13511e6i | −0.915820 | − | 0.915820i | 0.0809020 | − | 0.996722i | \(-0.474220\pi\) |
−0.996722 | + | 0.0809020i | \(0.974220\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 55859.2 | − | 55859.2i | 0.00710735 | − | 0.00710735i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.78696e6 | 0.225396 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.29452e7 | −1.61871 | −0.809355 | − | 0.587320i | \(-0.800183\pi\) | ||||
−0.809355 | + | 0.587320i | \(0.800183\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.69888e6 | − | 1.69888e6i | 0.210604 | − | 0.210604i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.02846e6 | + | 2.02846e6i | 0.249303 | + | 0.249303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.19815e6i | 0.145996i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.11997e6i | − | 0.256118i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 243385. | + | 243385.i | 0.0291540 | + | 0.0291540i | 0.721534 | − | 0.692379i | \(-0.243438\pi\) |
−0.692379 | + | 0.721534i | \(0.743438\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 544549. | − | 544549.i | 0.0646768 | − | 0.0646768i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.97443e6 | 1.05691 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.13600e7 | −1.32661 | −0.663305 | − | 0.748349i | \(-0.730847\pi\) | ||||
−0.663305 | + | 0.748349i | \(0.730847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −719390. | + | 719390.i | −0.0833051 | + | 0.0833051i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.12973e7 | − | 1.12973e7i | −1.29730 | − | 1.29730i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.77277e6i | 0.543505i | 0.962367 | + | 0.271752i | \(0.0876032\pi\) | ||||
−0.962367 | + | 0.271752i | \(0.912397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.29410e6i | − | 0.710800i | −0.934714 | − | 0.355400i | \(-0.884345\pi\) | ||
0.934714 | − | 0.355400i | \(-0.115655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.98952e6 | + | 2.98952e6i | 0.334818 | + | 0.334818i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.80596e6 | − | 2.80596e6i | 0.311669 | − | 0.311669i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.46495e6 | 0.161380 | 0.0806901 | − | 0.996739i | \(-0.474288\pi\) | ||||
0.0806901 | + | 0.996739i | \(0.474288\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.50388e6 | −1.03838 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 656929. | − | 656929.i | 0.0711895 | − | 0.0711895i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.75338e6 | + | 6.75338e6i | 0.725888 | + | 0.725888i | 0.969798 | − | 0.243910i | \(-0.0784300\pi\) |
−0.243910 | + | 0.969798i | \(0.578430\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 556337.i | 0.0593130i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.41502e7i | 1.49641i | 0.663468 | + | 0.748205i | \(0.269084\pi\) | ||||
−0.663468 | + | 0.748205i | \(0.730916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.04550e6 | + | 5.04550e6i | 0.529271 | + | 0.529271i | 0.920355 | − | 0.391084i | \(-0.127900\pi\) |
−0.391084 | + | 0.920355i | \(0.627900\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.61854e6 | + | 1.61854e6i | −0.168420 | + | 0.168420i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.70160e6 | −0.382093 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −716431. | + | 716431.i | −0.0727789 | + | 0.0727789i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.23100e6 | − | 4.23100e6i | −0.426399 | − | 0.426399i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.77040e7i | − | 1.77010i | −0.465495 | − | 0.885051i | \(-0.654124\pi\) | ||
0.465495 | − | 0.885051i | \(-0.345876\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.31801e7i | 1.30740i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 266800. | + | 266800.i | 0.0262574 | + | 0.0262574i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.61332e6 | − | 3.61332e6i | 0.352824 | − | 0.352824i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.62274e6 | 0.738514 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.04525e7 | −1.00479 | −0.502395 | − | 0.864638i | \(-0.667548\pi\) | ||||
−0.502395 | + | 0.864638i | \(0.667548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.43319e6 | − | 5.43319e6i | 0.518236 | − | 0.518236i | −0.398801 | − | 0.917037i | \(-0.630574\pi\) |
0.917037 | + | 0.398801i | \(0.130574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.98805e6 | + | 2.98805e6i | 0.282806 | + | 0.282806i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.39010e7i | 1.30552i | 0.757563 | + | 0.652762i | \(0.226390\pi\) | ||||
−0.757563 | + | 0.652762i | \(0.773610\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.53373e6i | − | 0.142935i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −773649. | − | 773649.i | −0.0715470 | − | 0.0715470i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.15514e7 | + | 1.15514e7i | −1.06011 | + | 1.06011i | −0.0620336 | + | 0.998074i | \(0.519759\pi\) |
−0.998074 | + | 0.0620336i | \(0.980241\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.97046e6 | 0.725906 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.59227e7 | 1.43914 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.20268e7 | + | 1.20268e7i | −1.07879 | + | 1.07879i | −0.0821756 | + | 0.996618i | \(0.526187\pi\) |
−0.996618 | + | 0.0821756i | \(0.973813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.95930e6 | − | 3.95930e6i | −0.352464 | − | 0.352464i | 0.508562 | − | 0.861026i | \(-0.330177\pi\) |
−0.861026 | + | 0.508562i | \(0.830177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.34193e6i | 0.471970i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.65498e6i | 0.145123i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.36169e7 | − | 1.36169e7i | −1.18512 | − | 1.18512i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.93770e6 | + | 8.93770e6i | −0.772077 | + | 0.772077i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.43146e6 | 0.208478 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00027e7 | 0.851297 | 0.425649 | − | 0.904889i | \(-0.360046\pi\) | ||||
0.425649 | + | 0.904889i | \(0.360046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 353808. | − | 353808.i | 0.0298888 | − | 0.0298888i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −943407. | − | 943407.i | −0.0791093 | − | 0.0791093i | 0.666445 | − | 0.745554i | \(-0.267815\pi\) |
−0.745554 | + | 0.666445i | \(0.767815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.20143e6i | 0.183244i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.54479e7i | − | 1.27644i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.13632e7 | − | 1.13632e7i | −0.932069 | − | 0.932069i | 0.0657662 | − | 0.997835i | \(-0.479051\pi\) |
−0.997835 | + | 0.0657662i | \(0.979051\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.24196e6 | − | 3.24196e6i | 0.263986 | − | 0.263986i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.23968e7 | −1.00212 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.02762e7 | 0.824678 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.49054e6 | + | 2.49054e6i | −0.198426 | + | 0.198426i | −0.799325 | − | 0.600899i | \(-0.794809\pi\) |
0.600899 | + | 0.799325i | \(0.294809\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 465981. | + | 465981.i | 0.0368583 | + | 0.0368583i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.03151e6i | − | 0.630718i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 641791.i | − | 0.0500393i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.33569e6 | + | 8.33569e6i | 0.645281 | + | 0.645281i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.13666e7 | − | 1.13666e7i | 0.873643 | − | 0.873643i | −0.119224 | − | 0.992867i | \(-0.538041\pi\) |
0.992867 | + | 0.119224i | \(0.0380408\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.73352e6 | −0.742817 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.18975e6 | −0.0901536 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.60633e6 | − | 4.60633e6i | 0.346582 | − | 0.346582i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.22852e6 | − | 6.22852e6i | −0.465339 | − | 0.465339i | 0.435062 | − | 0.900401i | \(-0.356727\pi\) |
−0.900401 | + | 0.435062i | \(0.856727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.13170e7i | − | 1.58144i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.21693e6i | − | 0.163315i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 352043. | + | 352043.i | 0.0257532 | + | 0.0257532i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 251985. | − | 251985.i | 0.0183053 | − | 0.0183053i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.31572e7 | −1.67057 | −0.835283 | − | 0.549820i | \(-0.814696\pi\) | ||||
−0.835283 | + | 0.549820i | \(0.814696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.94934e6 | −0.282935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.22749e6 | + | 6.22749e6i | −0.443065 | + | 0.443065i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.97662e6 | + | 2.97662e6i | 0.210319 | + | 0.210319i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.19864e7i | 1.54283i | 0.636331 | + | 0.771416i | \(0.280451\pi\) | ||||
−0.636331 | + | 0.771416i | \(0.719549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 9.58950e6i | − | 0.668309i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.44702e6 | − | 3.44702e6i | −0.238589 | − | 0.238589i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.72418e6 | + | 7.72418e6i | −0.530998 | + | 0.530998i | −0.920869 | − | 0.389872i | \(-0.872519\pi\) |
0.389872 | + | 0.920869i | \(0.372519\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.54401e6 | −0.446813 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −992882. | −0.0673332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.11778e6 | − | 7.11778e6i | 0.479439 | − | 0.479439i | −0.425513 | − | 0.904952i | \(-0.639906\pi\) |
0.904952 | + | 0.425513i | \(0.139906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.14463e6 | + | 6.14463e6i | 0.411102 | + | 0.411102i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.83694e6i | 0.122074i | 0.998136 | + | 0.0610368i | \(0.0194407\pi\) | ||||
−0.998136 | + | 0.0610368i | \(0.980559\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.46136e6i | 0.294494i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.24448e6 | − | 6.24448e6i | −0.409444 | − | 0.409444i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.83618e6 | + | 8.83618e6i | −0.575520 | + | 0.575520i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.46486e6 | 0.159475 | 0.0797375 | − | 0.996816i | \(-0.474592\pi\) | ||||
0.0797375 | + | 0.996816i | \(0.474592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.69779e7 | 2.37659 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.18868e6 | − | 7.18868e6i | 0.458967 | − | 0.458967i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 737006. | + | 737006.i | 0.0467446 | + | 0.0467446i | 0.730093 | − | 0.683348i | \(-0.239477\pi\) |
−0.683348 | + | 0.730093i | \(0.739477\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.91668e6i | 0.183774i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.99911e7i | − | 1.87729i | −0.344887 | − | 0.938644i | \(-0.612083\pi\) | ||
0.344887 | − | 0.938644i | \(-0.387917\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00947e7 | − | 1.00947e7i | −0.627743 | − | 0.627743i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.21459e6 | − | 2.21459e6i | 0.136817 | − | 0.136817i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.31544e7 | −0.807389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.88084e7 | 1.14693 | 0.573464 | − | 0.819231i | \(-0.305599\pi\) | ||||
0.573464 | + | 0.819231i | \(0.305599\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.15777e6 | + | 1.15777e6i | −0.0701435 | + | 0.0701435i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.46987e6 | + | 4.46987e6i | 0.269058 | + | 0.269058i | 0.828721 | − | 0.559662i | \(-0.189069\pi\) |
−0.559662 | + | 0.828721i | \(0.689069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 484614.i | 0.0289829i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.38286e7i | 0.821721i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −738229. | − | 738229.i | −0.0435860 | − | 0.0435860i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.26584e6 | + | 1.26584e6i | −0.0742591 | + | 0.0742591i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.39213e6 | −0.314308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.25539e7 | −0.727118 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.97424e7 | − | 1.97424e7i | 1.13622 | − | 1.13622i | 0.147103 | − | 0.989121i | \(-0.453005\pi\) |
0.989121 | − | 0.147103i | \(-0.0469948\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.14230e7 | − | 2.14230e7i | −1.22515 | − | 1.22515i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.86188e6i | − | 0.105806i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.08539e7i | − | 1.17762i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.30550e6 | − | 9.30550e6i | −0.522182 | − | 0.522182i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.72739e7 | + | 1.72739e7i | −0.963264 | + | 0.963264i | −0.999349 | − | 0.0360843i | \(-0.988512\pi\) |
0.0360843 | + | 0.999349i | \(0.488512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.37250e6 | 0.0760580 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.13951e7 | 0.627533 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.64413e6 | + | 2.64413e6i | −0.144708 | + | 0.144708i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.36880e6 | + | 3.36880e6i | 0.183225 | + | 0.183225i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.10577e7i | 1.67875i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 164511.i | − | 0.00883740i | −0.999990 | − | 0.00441870i | \(-0.998593\pi\) | ||
0.999990 | − | 0.00441870i | \(-0.00140652\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.53151e7 | + | 1.53151e7i | 0.817650 | + | 0.817650i | 0.985767 | − | 0.168117i | \(-0.0537686\pi\) |
−0.168117 | + | 0.985767i | \(0.553769\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.79662e6 | + | 9.79662e6i | −0.519817 | + | 0.519817i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.06311e7 | 0.560643 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.92995e6 | −0.415638 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.99659e6 | − | 3.99659e6i | 0.208200 | − | 0.208200i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.42105e7 | + | 1.42105e7i | 0.735786 | + | 0.735786i | 0.971760 | − | 0.235973i | \(-0.0758277\pi\) |
−0.235973 | + | 0.971760i | \(0.575828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.30021e7i | − | 0.669136i | −0.942372 | − | 0.334568i | \(-0.891410\pi\) | ||
0.942372 | − | 0.334568i | \(-0.108590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 637577.i | − | 0.0326135i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.26007e7 | − | 2.26007e7i | −1.14910 | − | 1.14910i | −0.986729 | − | 0.162374i | \(-0.948085\pi\) |
−0.162374 | − | 0.986729i | \(-0.551915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.23018e6 | + | 4.23018e6i | −0.213783 | + | 0.213783i | −0.805872 | − | 0.592090i | \(-0.798303\pi\) |
0.592090 | + | 0.805872i | \(0.298303\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.36789e7 | 1.69182 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.54917e6 | 0.376953 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −218811. | + | 218811.i | −0.0108606 | + | 0.0108606i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −438938. | − | 438938.i | −0.0216566 | − | 0.0216566i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.41204e7i | 0.692534i | 0.938136 | + | 0.346267i | \(0.112551\pi\) | ||||
−0.938136 | + | 0.346267i | \(0.887449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2.48533e7i | − | 1.21170i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.22214e7 | + | 3.22214e7i | 1.56162 | + | 1.56162i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.54422e6 | + | 3.54422e6i | −0.170757 | + | 0.170757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.05797e7 | 0.506714 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.22538e7 | 1.53572 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.98132e7 | + | 1.98132e7i | −0.937843 | + | 0.937843i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.45744e7 | − | 1.45744e7i | −0.685830 | − | 0.685830i | 0.275477 | − | 0.961308i | \(-0.411164\pi\) |
−0.961308 | + | 0.275477i | \(0.911164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.09472e6i | − | 0.238344i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 5.14411e6i | − | 0.239253i | −0.992819 | − | 0.119627i | \(-0.961830\pi\) | ||
0.992819 | − | 0.119627i | \(-0.0381698\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.85655e7 | + | 1.85655e7i | 0.858466 | + | 0.858466i | 0.991157 | − | 0.132691i | \(-0.0423618\pi\) |
−0.132691 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.04881e6 | + | 1.04881e6i | −0.0482159 | + | 0.0482159i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.27994e7 | 1.49913 | 0.749564 | − | 0.661931i | \(-0.230263\pi\) | ||||
0.749564 | + | 0.661931i | \(0.230263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.33222e6 | −0.333192 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.56745e7 | − | 1.56745e7i | 0.708183 | − | 0.708183i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.53991e6 | + | 3.53991e6i | 0.159017 | + | 0.159017i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.51568e6i | 0.380342i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.77694e6i | − | 0.300952i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −736411. | − | 736411.i | −0.0325162 | − | 0.0325162i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.17858e7 | − | 1.17858e7i | 0.517442 | − | 0.517442i | −0.399355 | − | 0.916797i | \(-0.630766\pi\) |
0.916797 | + | 0.399355i | \(0.130766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.03991e6 | −0.263669 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.75082e6 | −0.0759981 | −0.0379991 | − | 0.999278i | \(-0.512098\pi\) | ||||
−0.0379991 | + | 0.999278i | \(0.512098\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.93751e6 | − | 3.93751e6i | 0.169950 | − | 0.169950i | −0.617008 | − | 0.786957i | \(-0.711655\pi\) |
0.786957 | + | 0.617008i | \(0.211655\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.19118e7 | + | 1.19118e7i | 0.511235 | + | 0.511235i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.95570e7i | 1.68816i | 0.536214 | + | 0.844082i | \(0.319854\pi\) | ||||
−0.536214 | + | 0.844082i | \(0.680146\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00595e6i | 0.0426896i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.27635e6 | + | 2.27635e6i | 0.0960606 | + | 0.0960606i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.57873e6 | − | 1.57873e6i | 0.0662492 | − | 0.0662492i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.33869e6 | 0.0975924 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.50155e7 | 1.03807 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.69282e6 | − | 3.69282e6i | 0.152391 | − | 0.152391i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.07348e7 | + | 1.07348e7i | 0.440538 | + | 0.440538i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.12662e7i | 0.459789i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.56165e6i | − | 0.144554i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.23900e6 | − | 2.23900e6i | −0.0903725 | − | 0.0903725i | 0.660475 | − | 0.750848i | \(-0.270355\pi\) |
−0.750848 | + | 0.660475i | \(0.770355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.41802e7 | + | 1.41802e7i | −0.569212 | + | 0.569212i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.13412e7 | −0.851968 | −0.425984 | − | 0.904731i | \(-0.640072\pi\) | ||||
−0.425984 | + | 0.904731i | \(0.640072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.07392e6 | 0.0823408 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.88840e7 | + | 1.88840e7i | −0.745662 | + | 0.745662i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.50260e7 | + | 1.50260e7i | 0.590093 | + | 0.590093i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 9.55716e6i | − | 0.373285i | −0.982428 | − | 0.186642i | \(-0.940239\pi\) | ||
0.982428 | − | 0.186642i | \(-0.0597605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.99144e7i | 2.71593i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.08567e7 | + | 1.08567e7i | 0.419464 | + | 0.419464i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.33110e6 | − | 4.33110e6i | 0.166435 | − | 0.166435i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.21577e7 | 0.464680 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.19905e7 | 1.21613 | 0.608067 | − | 0.793886i | \(-0.291945\pi\) | ||||
0.608067 | + | 0.793886i | \(0.291945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.68354e6 | − | 8.68354e6i | 0.328339 | − | 0.328339i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.25315e7 | − | 2.25315e7i | −0.847394 | − | 0.847394i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 735510.i | 0.0275144i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.44804e7i | 1.65508i | 0.561404 | + | 0.827542i | \(0.310261\pi\) | ||||
−0.561404 | + | 0.827542i | \(0.689739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.76113e7 | − | 1.76113e7i | −0.651821 | − | 0.651821i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.66460e7 | + | 2.66460e7i | −0.980974 | + | 0.980974i | −0.999822 | − | 0.0188485i | \(-0.994000\pi\) |
0.0188485 | + | 0.999822i | \(0.494000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.00542e6 | −0.110059 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.33401e6 | 0.0485935 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.00230e7 | − | 2.00230e7i | 0.725527 | − | 0.725527i | −0.244198 | − | 0.969725i | \(-0.578525\pi\) |
0.969725 | + | 0.244198i | \(0.0785248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.26779e7 | + | 2.26779e7i | 0.817407 | + | 0.817407i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.55018e7i | 0.914363i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.12385e7i | 1.11419i | 0.830449 | + | 0.557094i | \(0.188084\pi\) | ||||
−0.830449 | + | 0.557094i | \(0.811916\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −65963.9 | − | 65963.9i | −0.00234044 | − | 0.00234044i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.85843e6 | + | 4.85843e6i | −0.171481 | + | 0.171481i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.22236e7 | 0.429192 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.80279e7 | −0.979000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.72015e7 | − | 2.72015e7i | 0.945209 | − | 0.945209i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.00620e6 | − | 2.00620e6i | −0.0693515 | − | 0.0693515i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.90918e7i | − | 1.00047i | −0.865890 | − | 0.500235i | \(-0.833247\pi\) | ||
0.865890 | − | 0.500235i | \(-0.166753\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.28377e7i | 0.439217i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.56962e6 | + | 9.56962e6i | 0.325722 | + | 0.325722i | 0.850957 | − | 0.525235i | \(-0.176023\pi\) |
−0.525235 | + | 0.850957i | \(0.676023\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.51411e7 | − | 1.51411e7i | 0.512714 | − | 0.512714i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.46832e6 | −0.184223 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.40916e6 | 0.114264 | 0.0571321 | − | 0.998367i | \(-0.481804\pi\) | ||||
0.0571321 | + | 0.998367i | \(0.481804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.89227e6 | + | 1.89227e6i | −0.0630996 | + | 0.0630996i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.10757e7 | + | 3.10757e7i | 1.03098 | + | 1.03098i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.27622e6i | 0.240172i | 0.992764 | + | 0.120086i | \(0.0383170\pi\) | ||||
−0.992764 | + | 0.120086i | \(0.961683\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.05979e7i | − | 0.348039i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.24293e6 | − | 2.24293e6i | −0.0732864 | − | 0.0732864i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.61419e7 | + | 1.61419e7i | −0.524764 | + | 0.524764i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.90156e7 | 0.938529 | 0.469265 | − | 0.883058i | \(-0.344519\pi\) | ||||
0.469265 | + | 0.883058i | \(0.344519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.30321e7 | −0.419412 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.33410e7 | + | 1.33410e7i | −0.427199 | + | 0.427199i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.34377e7 | − | 3.34377e7i | −1.06537 | − | 1.06537i | −0.997709 | − | 0.0676564i | \(-0.978448\pi\) |
−0.0676564 | − | 0.997709i | \(-0.521552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.84578e6i | 0.248727i |
(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 | 320.6.l.a.241.8 | 80 | ||
4.3 | odd | 2 | 80.6.l.a.21.30 | ✓ | 80 | ||
16.3 | odd | 4 | 80.6.l.a.61.30 | yes | 80 | ||
16.13 | even | 4 | inner | 320.6.l.a.81.8 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.30 | ✓ | 80 | 4.3 | odd | 2 | ||
80.6.l.a.61.30 | yes | 80 | 16.3 | odd | 4 | ||
320.6.l.a.81.8 | 80 | 16.13 | even | 4 | inner | ||
320.6.l.a.241.8 | 80 | 1.1 | even | 1 | trivial |