Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(49,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("80.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 41x^{6} + 460x^{4} + 969x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{31}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-0.0965878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.49 |
Dual form | 80.6.c.d.49.7 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 24.1383i | − | 1.54847i | −0.632897 | − | 0.774236i | \(-0.718134\pi\) | ||
0.632897 | − | 0.774236i | \(-0.281866\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 46.7401 | − | 30.6653i | 0.836112 | − | 0.548558i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 179.876i | − | 1.38749i | −0.720223 | − | 0.693743i | \(-0.755960\pi\) | ||
0.720223 | − | 0.693743i | \(-0.244040\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −339.657 | −1.39777 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 653.681 | 1.62886 | 0.814431 | − | 0.580260i | \(-0.197049\pi\) | ||||
0.814431 | + | 0.580260i | \(0.197049\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 284.851i | 0.467477i | 0.972300 | + | 0.233738i | \(0.0750959\pi\) | ||||
−0.972300 | + | 0.233738i | \(0.924904\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −740.209 | − | 1128.23i | −0.849427 | − | 1.29470i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 383.672i | 0.321986i | 0.986956 | + | 0.160993i | \(0.0514697\pi\) | ||||
−0.986956 | + | 0.160993i | \(0.948530\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2563.29 | −1.62897 | −0.814485 | − | 0.580185i | \(-0.802980\pi\) | ||||
−0.814485 | + | 0.580185i | \(0.802980\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4341.90 | −2.14848 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 948.124i | 0.373719i | 0.982387 | + | 0.186860i | \(0.0598309\pi\) | ||||
−0.982387 | + | 0.186860i | \(0.940169\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1244.27 | − | 2866.60i | 0.398168 | − | 0.917313i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2333.13i | 0.615929i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1524.26 | 0.336561 | 0.168281 | − | 0.985739i | \(-0.446178\pi\) | ||||
0.168281 | + | 0.985739i | \(0.446178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3103.88 | −0.580098 | −0.290049 | − | 0.957012i | \(-0.593672\pi\) | ||||
−0.290049 | + | 0.957012i | \(0.593672\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 15778.7i | − | 2.52225i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5515.97 | − | 8407.43i | −0.761117 | − | 1.16009i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9991.75i | 1.19988i | 0.800046 | + | 0.599939i | \(0.204809\pi\) | ||||
−0.800046 | + | 0.599939i | \(0.795191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6875.83 | 0.723875 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15120.7 | 1.40479 | 0.702394 | − | 0.711788i | \(-0.252114\pi\) | ||||
0.702394 | + | 0.711788i | \(0.252114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1754.92i | − | 0.144739i | −0.997378 | − | 0.0723696i | \(-0.976944\pi\) | ||
0.997378 | − | 0.0723696i | \(-0.0230561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −15875.6 | + | 10415.7i | −1.16869 | + | 0.766756i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14760.7i | 0.974682i | 0.873212 | + | 0.487341i | \(0.162033\pi\) | ||||
−0.873212 | + | 0.487341i | \(0.837967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15548.5 | −0.925118 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9261.18 | 0.498587 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8704.12i | − | 0.425633i | −0.977092 | − | 0.212816i | \(-0.931736\pi\) | ||
0.977092 | − | 0.212816i | \(-0.0682636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30553.1 | − | 20045.4i | 1.36191 | − | 0.893526i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 61873.3i | 2.52241i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12632.1 | −0.472438 | −0.236219 | − | 0.971700i | \(-0.575908\pi\) | ||||
−0.236219 | + | 0.971700i | \(0.575908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43098.3 | 1.48298 | 0.741490 | − | 0.670964i | \(-0.234119\pi\) | ||||
0.741490 | + | 0.670964i | \(0.234119\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 61096.2i | 1.93938i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8735.07 | + | 13314.0i | 0.256438 | + | 0.390863i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 26125.5i | − | 0.711014i | −0.934674 | − | 0.355507i | \(-0.884308\pi\) | ||
0.934674 | − | 0.355507i | \(-0.115692\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22886.1 | 0.578694 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46285.8 | 1.08969 | 0.544844 | − | 0.838538i | \(-0.316589\pi\) | ||||
0.544844 | + | 0.838538i | \(0.316589\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 51303.2i | − | 1.12678i | −0.826192 | − | 0.563388i | \(-0.809498\pi\) | ||
0.826192 | − | 0.563388i | \(-0.190502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −69194.9 | − | 30034.6i | −1.42043 | − | 0.616551i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 117582.i | − | 2.26002i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39314.0 | 0.708729 | 0.354364 | − | 0.935107i | \(-0.384697\pi\) | ||||
0.354364 | + | 0.935107i | \(0.384697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −26218.8 | −0.444017 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 69544.8i | 1.10808i | 0.832492 | + | 0.554038i | \(0.186914\pi\) | ||||
−0.832492 | + | 0.554038i | \(0.813086\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11765.4 | + | 17932.8i | 0.176628 | + | 0.269217i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 36793.1i | − | 0.521156i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13092.2 | 0.175201 | 0.0876007 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876007 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 51238.0 | 0.648618 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 74922.5i | 0.898265i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −119808. | + | 78604.0i | −1.36200 | + | 0.893585i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 26258.1i | 0.283357i | 0.989913 | + | 0.141678i | \(0.0452499\pi\) | ||||
−0.989913 | + | 0.141678i | \(0.954750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −222027. | −2.27677 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7382.54 | 0.0720116 | 0.0360058 | − | 0.999352i | \(-0.488537\pi\) | ||||
0.0360058 | + | 0.999352i | \(0.488537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 44518.9i | − | 0.413477i | −0.978396 | − | 0.206738i | \(-0.933715\pi\) | ||
0.978396 | − | 0.206738i | \(-0.0662849\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −202941. | + | 133146.i | −1.79637 | + | 1.17857i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 194929.i | − | 1.64595i | −0.568079 | − | 0.822974i | \(-0.692313\pi\) | ||
0.568079 | − | 0.822974i | \(-0.307687\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −213783. | −1.72348 | −0.861739 | − | 0.507351i | \(-0.830625\pi\) | ||||
−0.861739 | + | 0.507351i | \(0.830625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 241184. | 1.85798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 148946.i | − | 1.09732i | −0.836046 | − | 0.548660i | \(-0.815138\pi\) | ||
0.836046 | − | 0.548660i | \(-0.184862\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 29074.5 | + | 44315.4i | 0.205007 | + | 0.312471i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 96751.8i | − | 0.653423i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 69013.4 | 0.446751 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 266248. | 1.65319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 364987.i | − | 2.17528i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −29747.8 | − | 172141.i | −0.170287 | − | 0.985395i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 116757.i | 0.642351i | 0.947020 | + | 0.321175i | \(0.104078\pi\) | ||||
−0.947020 | + | 0.321175i | \(0.895922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −42360.8 | −0.224125 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −349111. | −1.77740 | −0.888700 | − | 0.458490i | \(-0.848390\pi\) | ||||
−0.888700 | + | 0.458490i | \(0.848390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 461074.i | 2.26017i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 71546.4 | + | 109051.i | 0.337873 | + | 0.514986i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 219776.i | − | 1.00041i | −0.865907 | − | 0.500205i | \(-0.833258\pi\) | ||
0.865907 | − | 0.500205i | \(-0.166742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 126594. | 0.555744 | 0.277872 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277872 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 356299. | 1.50927 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 186202.i | 0.761455i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 71244.1 | − | 46742.0i | 0.281403 | − | 0.184624i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 375313.i | 1.43252i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 25809.9 | 0.0952403 | 0.0476202 | − | 0.998866i | \(-0.484836\pi\) | ||||
0.0476202 | + | 0.998866i | \(0.484836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 311270. | 1.11095 | 0.555475 | − | 0.831533i | \(-0.312536\pi\) | ||||
0.555475 | + | 0.831533i | \(0.312536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 130317.i | − | 0.450061i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −145076. | + | 95181.7i | −0.485027 | + | 0.318217i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 429151.i | 1.38951i | 0.719247 | + | 0.694755i | \(0.244487\pi\) | ||||
−0.719247 | + | 0.694755i | \(0.755513\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −210102. | −0.659080 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 170545. | 0.518530 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 162467.i | 0.478957i | 0.970902 | + | 0.239479i | \(0.0769765\pi\) | ||||
−0.970902 | + | 0.239479i | \(0.923023\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −483861. | − | 737500.i | −1.38360 | − | 2.10888i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 280057.i | 0.777060i | 0.921436 | + | 0.388530i | \(0.127017\pi\) | ||||
−0.921436 | + | 0.388530i | \(0.872983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 290153. | 0.781465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 870638. | 2.27692 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 742577.i | 1.88637i | 0.332271 | + | 0.943184i | \(0.392185\pi\) | ||||
−0.332271 | + | 0.943184i | \(0.607815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −515634. | − | 223815.i | −1.27276 | − | 0.552452i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 304917.i | 0.731557i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14556.0 | −0.0339554 | −0.0169777 | − | 0.999856i | \(-0.505404\pi\) | ||||
−0.0169777 | + | 0.999856i | \(0.505404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −243243. | −0.551878 | −0.275939 | − | 0.961175i | \(-0.588989\pi\) | ||||
−0.275939 | + | 0.961175i | \(0.588989\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.04032e6i | − | 2.29635i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 306400. | + | 467015.i | 0.658203 | + | 1.00323i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 250799.i | 0.524471i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 419675. | 0.854592 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −75871.1 | −0.150485 | −0.0752425 | − | 0.997165i | \(-0.523973\pi\) | ||||
−0.0752425 | + | 0.997165i | \(0.523973\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 370161.i | − | 0.715314i | −0.933853 | − | 0.357657i | \(-0.883576\pi\) | ||
0.933853 | − | 0.357657i | \(-0.116424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 321377. | − | 210850.i | 0.605241 | − | 0.397087i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 213848.i | − | 0.392590i | −0.980545 | − | 0.196295i | \(-0.937109\pi\) | ||
0.980545 | − | 0.196295i | \(-0.0628910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 466075. | 0.834302 | 0.417151 | − | 0.908837i | \(-0.363029\pi\) | ||||
0.417151 | + | 0.908837i | \(0.363029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −630626. | −1.10099 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 274178.i | − | 0.466974i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 706741. | − | 463680.i | 1.17456 | − | 0.770609i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 322037.i | − | 0.522372i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.67557e6 | −2.65337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 228211. | 0.352883 | 0.176441 | − | 0.984311i | \(-0.443541\pi\) | ||||
0.176441 | + | 0.984311i | \(0.443541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.11726e6i | − | 1.68735i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −53815.2 | − | 82025.1i | −0.0793979 | − | 0.121018i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 558315.i | 0.804878i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.23837e6 | −1.74478 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −109289. | −0.150521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 972750.i | 1.30990i | 0.755671 | + | 0.654951i | \(0.227311\pi\) | ||||
−0.755671 | + | 0.654951i | \(0.772689\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −422626. | + | 973661.i | −0.556545 | + | 1.28219i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 357063.i | − | 0.459917i | −0.973200 | − | 0.229959i | \(-0.926141\pi\) | ||
0.973200 | − | 0.229959i | \(-0.0738591\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 295196. | 0.371982 | 0.185991 | − | 0.982551i | \(-0.440451\pi\) | ||||
0.185991 | + | 0.982551i | \(0.440451\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.83822e6 | −3.49958 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 492373.i | − | 0.594162i | −0.954852 | − | 0.297081i | \(-0.903987\pi\) | ||
0.954852 | − | 0.297081i | \(-0.0960131\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 452643. | + | 689918.i | 0.534670 | + | 0.814944i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 948974.i | − | 1.09745i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −71796.0 | −0.0813028 | −0.0406514 | − | 0.999173i | \(-0.512943\pi\) | ||||
−0.0406514 | + | 0.999173i | \(0.512943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 614304. | 0.681304 | 0.340652 | − | 0.940190i | \(-0.389352\pi\) | ||||
0.340652 | + | 0.940190i | \(0.389352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.19983e6i | 1.30348i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −726736. | + | 476799.i | −0.773502 | + | 0.507481i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 730156.i | − | 0.761505i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.67869e6 | 1.71582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 244276. | 0.244735 | 0.122368 | − | 0.992485i | \(-0.460951\pi\) | ||||
0.122368 | + | 0.992485i | \(0.460951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 619771.i | 0.608737i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 432868. | − | 283997.i | 0.416875 | − | 0.273504i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 951728.i | − | 0.898835i | −0.893322 | − | 0.449418i | \(-0.851632\pi\) | ||
0.893322 | − | 0.449418i | \(-0.148368\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.79728e6 | 1.66481 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −517726. | −0.470434 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 258512.i | 0.230458i | 0.993339 | + | 0.115229i | \(0.0367602\pi\) | ||||
−0.993339 | + | 0.115229i | \(0.963240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −266915. | − | 406831.i | −0.233484 | − | 0.355877i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 316023.i | − | 0.271295i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −894716. | −0.753884 | −0.376942 | − | 0.926237i | \(-0.623024\pi\) | ||||
−0.376942 | + | 0.926237i | \(0.623024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −474149. | −0.392186 | −0.196093 | − | 0.980585i | \(-0.562825\pi\) | ||||
−0.196093 | + | 0.980585i | \(0.562825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.23680e6i | − | 1.00437i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 813358. | − | 1.87384e6i | 0.648560 | − | 1.49418i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 142752.i | − | 0.111785i | −0.998437 | − | 0.0558923i | \(-0.982200\pi\) | ||
0.998437 | − | 0.0558923i | \(-0.0178003\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.05426e6 | 0.810841 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −427838. | −0.323231 | −0.161616 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161616 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.30233e6i | 1.70884i | 0.519585 | + | 0.854419i | \(0.326087\pi\) | ||||
−0.519585 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.89737e6 | + | 2.89197e6i | 1.38369 | + | 2.10902i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.71985e6i | − | 1.94913i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27265e6 | 0.896325 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 633825. | 0.438770 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.59390e6i | 1.08465i | 0.840168 | + | 0.542326i | \(0.182456\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −590424. | + | 387367.i | −0.395011 | + | 0.259160i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.52513e6i | 1.00326i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −270074. | −0.174705 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −315668. | −0.200824 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 178202.i | − | 0.111508i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.01442e6 | − | 1.32162e6i | 1.23994 | − | 0.813501i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 322680.i | − | 0.195401i | −0.995216 | − | 0.0977005i | \(-0.968851\pi\) | ||
0.995216 | − | 0.0977005i | \(-0.0311487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.07461e6 | −0.640257 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 660204. | 0.387059 | 0.193529 | − | 0.981094i | \(-0.438006\pi\) | ||||
0.193529 | + | 0.981094i | \(0.438006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.15378e6i | 0.665677i | 0.942984 | + | 0.332838i | \(0.108006\pi\) | ||||
−0.942984 | + | 0.332838i | \(0.891994\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.87354e6 | + | 2.85564e6i | 1.06386 | + | 1.62154i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.20296e6i | 0.672364i | 0.941797 | + | 0.336182i | \(0.109136\pi\) | ||||
−0.941797 | + | 0.336182i | \(0.890864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 996381. | 0.548212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.70524e6 | −2.54870 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 983460.i | − | 0.524506i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 816556. | + | 354433.i | 0.428822 | + | 0.186134i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.16034e6i | 2.66876i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.65510e6 | 1.35236 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.82424e6 | −0.915193 | −0.457597 | − | 0.889160i | \(-0.651290\pi\) | ||||
−0.457597 | + | 0.889160i | \(0.651290\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.39377e6i | − | 1.67715i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −801149. | − | 1.22111e6i | −0.390033 | − | 0.594488i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 485867.i | − | 0.233047i | −0.993188 | − | 0.116523i | \(-0.962825\pi\) | ||
0.993188 | − | 0.116523i | \(-0.0371750\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.59530e6 | −1.69917 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.02895e6 | −0.944899 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 226383.i | − | 0.103898i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.06970e6 | − | 701809.i | 0.483853 | − | 0.317447i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.35066e6i | 1.04801i | 0.851715 | + | 0.524006i | \(0.175563\pi\) | ||||
−0.851715 | + | 0.524006i | \(0.824437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.62295e6 | 1.15273 | 0.576364 | − | 0.817193i | \(-0.304471\pi\) | ||||
0.576364 | + | 0.817193i | \(0.304471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −664597. | −0.287932 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 583638.i | 0.249291i | 0.992201 | + | 0.124646i | \(0.0397794\pi\) | ||||
−0.992201 | + | 0.124646i | \(0.960221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.16340e6 | − | 1.41937e6i | 0.911101 | − | 0.597757i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.66587e6i | − | 0.691782i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.64503e6 | 0.673654 | 0.336827 | − | 0.941567i | \(-0.390646\pi\) | ||||
0.336827 | + | 0.941567i | \(0.390646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.09433e6 | 1.65354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6.42678e6i | − | 2.55992i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.57323e6 | − | 2.39792e6i | −0.618102 | − | 0.942111i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.62251e6i | − | 1.01637i | −0.861247 | − | 0.508186i | \(-0.830316\pi\) | ||
0.861247 | − | 0.508186i | \(-0.169684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.13584e6 | −1.96357 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.56566e6 | −0.590559 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.73068e6i | − | 1.38840i | −0.719780 | − | 0.694202i | \(-0.755757\pi\) | ||
0.719780 | − | 0.694202i | \(-0.244243\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.15520e6 | + | 718062.i | −1.52586 | + | 0.263684i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 434188.i | 0.157335i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00539e6 | −1.07474 | −0.537368 | − | 0.843348i | \(-0.680582\pi\) | ||||
−0.537368 | + | 0.843348i | \(0.680582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.81831e6 | 0.994662 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 343090.i | 0.119512i | 0.998213 | + | 0.0597560i | \(0.0190323\pi\) | ||||
−0.998213 | + | 0.0597560i | \(0.980968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.60568e6 | − | 5.49578e6i | −1.23975 | − | 1.88963i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 596071.i | 0.202311i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −190583. | −0.0638572 | −0.0319286 | − | 0.999490i | \(-0.510165\pi\) | ||||
−0.0319286 | + | 0.999490i | \(0.510165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −363768. | −0.120332 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.42694e6i | 2.75225i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.83754e6 | − | 1.20558e6i | 0.592577 | − | 0.388779i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.22551e6i | 1.66400i | 0.554778 | + | 0.831999i | \(0.312803\pi\) | ||||
−0.554778 | + | 0.831999i | \(0.687197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.11295e7 | 3.49981 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.60312e6 | −0.497859 | −0.248929 | − | 0.968522i | \(-0.580079\pi\) | ||||
−0.248929 | + | 0.968522i | \(0.580079\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 884146.i | − | 0.271182i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.22547e6 | + | 804008.i | −0.371248 | + | 0.243569i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.53142e6i | 1.95444i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.58732e6 | −1.35597 | −0.677986 | − | 0.735075i | \(-0.737147\pi\) | ||||
−0.677986 | + | 0.735075i | \(0.737147\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.30501e6 | −1.54911 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.27221e6i | 0.655501i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.13261e6 | + | 3.25053e6i | 0.607844 | + | 0.926476i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.05575e6i | − | 0.860554i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.16854e6 | −1.71651 | −0.858256 | − | 0.513221i | \(-0.828452\pi\) | ||||
−0.858256 | + | 0.513221i | \(0.828452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.15589e6 | −1.69272 | −0.846361 | − | 0.532610i | \(-0.821211\pi\) | ||||
−0.846361 | + | 0.532610i | \(0.821211\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.01358e6i | − | 1.36238i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.09983e6 | + | 477393.i | 0.295362 | + | 0.128205i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.75236e6i | − | 2.05761i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.49460e6 | 1.17909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.15900e6 | −0.300532 | −0.150266 | − | 0.988646i | \(-0.548013\pi\) | ||||
−0.150266 | + | 0.988646i | \(0.548013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.73906e6i | 1.72735i | 0.504052 | + | 0.863673i | \(0.331842\pi\) | ||||
−0.504052 | + | 0.863673i | \(0.668158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.12827e6 | − | 1.71971e6i | −0.285884 | − | 0.435745i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.43031e6i | − | 0.608777i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.69068e6 | −0.913998 | −0.456999 | − | 0.889467i | \(-0.651076\pi\) | ||||
−0.456999 | + | 0.889467i | \(0.651076\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.28114e6 | 1.29310 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.55124e6i | 1.10185i | 0.834556 | + | 0.550923i | \(0.185724\pi\) | ||||
−0.834556 | + | 0.550923i | \(0.814276\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 611931. | − | 401477.i | 0.146488 | − | 0.0961082i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 623007.i | − | 0.147477i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.31419e6 | 0.775822 | 0.387911 | − | 0.921697i | \(-0.373197\pi\) | ||||
0.387911 | + | 0.921697i | \(0.373197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.88409e6 | 2.28821 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7.51352e6i | − | 1.72028i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.39487e6 | − | 1.57123e6i | 0.542317 | − | 0.355805i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.10489e6i | − | 0.919414i | −0.888071 | − | 0.459707i | \(-0.847954\pi\) | ||
0.888071 | − | 0.459707i | \(-0.152046\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −895158. | −0.198321 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.16525e6 | 1.78944 | 0.894720 | − | 0.446628i | \(-0.147375\pi\) | ||||
0.894720 | + | 0.446628i | \(0.147375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.65614e6i | 1.22622i | 0.789998 | + | 0.613109i | \(0.210081\pi\) | ||||
−0.789998 | + | 0.613109i | \(0.789919\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.29752e6 | + | 3.50188e6i | 0.492751 | + | 0.751051i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.77216e6i | 1.86129i | 0.365921 | + | 0.930646i | \(0.380754\pi\) | ||||
−0.365921 | + | 0.930646i | \(0.619246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.69936e6 | −0.986522 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.03590e7 | 2.15162 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.14716e6i | − | 0.235760i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.18943e6 | + | 7.34792e6i | −0.648603 | + | 1.49427i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.95641e6i | 0.594935i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 417978. | 0.0832367 | 0.0416184 | − | 0.999134i | \(-0.486749\pi\) | ||||
0.0416184 | + | 0.999134i | \(0.486749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.84616e6 | −0.560915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.11666e6i | − | 0.802929i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 805213. | + | 1.22731e6i | 0.155438 | + | 0.236918i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.07076e6i | − | 1.35096i | −0.737376 | − | 0.675482i | \(-0.763936\pi\) | ||
0.737376 | − | 0.675482i | \(-0.236064\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.92168e6 | 0.741652 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.00127e7 | 1.87433 | 0.937166 | − | 0.348883i | \(-0.113439\pi\) | ||||
0.937166 | + | 0.348883i | \(0.113439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 584816.i | 0.108368i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.03776e7 | + | 6.80855e6i | −1.90363 | + | 1.24894i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.32571e6i | − | 1.51193i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.74452e6 | −1.39233 | −0.696166 | − | 0.717881i | \(-0.745112\pi\) | ||||
−0.696166 | + | 0.717881i | \(0.745112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.76009e6 | 1.20326 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.20376e6i | 0.388370i | 0.980965 | + | 0.194185i | \(0.0622061\pi\) | ||||
−0.980965 | + | 0.194185i | \(0.937794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 345061. | − | 226388.i | 0.0602098 | − | 0.0395025i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.00379e6i | − | 1.21008i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.40053e6 | −0.239607 | −0.119803 | − | 0.992798i | \(-0.538226\pi\) | ||||
−0.119803 | + | 0.992798i | \(0.538226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.22823e6 | −1.56339 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.98049e6i | − | 1.00333i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.36519e6 | − | 2.08082e6i | −0.226816 | − | 0.345713i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.64881e6i | 1.58762i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.79245e7 | 2.92099 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.60571e6 | 0.259162 | 0.129581 | − | 0.991569i | \(-0.458637\pi\) | ||||
0.129581 | + | 0.991569i | \(0.458637\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.80485e6i | 0.927977i | 0.885841 | + | 0.463988i | \(0.153582\pi\) | ||||
−0.885841 | + | 0.463988i | \(0.846418\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.40252e6 | + | 1.24465e7i | −0.855456 | + | 1.97083i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.19087e6i | − | 0.186784i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.53740e6 | 0.860334 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.29057e6 | 0.660357 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.30714e6i | 0.656706i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.97755e6 | − | 9.11098e6i | −0.902898 | − | 1.37620i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 351356.i | 0.0525790i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.01637e7 | −1.50689 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.37930e6 | −1.37777 | −0.688886 | − | 0.724870i | \(-0.741900\pi\) | ||||
−0.688886 | + | 0.724870i | \(0.741900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.87146e6i | 0.854568i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.99222e6 | + | 6.55571e6i | −1.44102 | + | 0.945429i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.33685e6i | − | 0.333936i | −0.985962 | − | 0.166968i | \(-0.946602\pi\) | ||
0.985962 | − | 0.166968i | \(-0.0533976\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.46386e7 | −2.07286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.90712e6 | −0.548248 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.07166e6i | − | 0.983351i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.12730e7 | − | 7.39598e6i | 1.55348 | − | 1.01921i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.02238e6i | − | 0.959061i | −0.877525 | − | 0.479530i | \(-0.840807\pi\) | ||
0.877525 | − | 0.479530i | \(-0.159193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 499891. | 0.0676622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.05386e6 | 0.812129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.81010e6i | 0.240675i | 0.992733 | + | 0.120338i | \(0.0383977\pi\) | ||||
−0.992733 | + | 0.120338i | \(0.961602\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.56748e6 | − | 6.96175e6i | −0.601943 | − | 0.917482i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.71613e6i | 0.616068i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.62751e6 | −0.728678 | −0.364339 | − | 0.931266i | \(-0.618705\pi\) | ||||
−0.364339 | + | 0.931266i | \(0.618705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.16702e6 | 0.278145 | 0.139073 | − | 0.990282i | \(-0.455588\pi\) | ||||
0.139073 | + | 0.990282i | \(0.455588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.83140e6i | 0.233022i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.71789e6 | + | 1.17973e6i | 0.342817 | + | 0.148803i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.04992e7i | 1.31286i | 0.754387 | + | 0.656430i | \(0.227934\pi\) | ||||
−0.754387 | + | 0.656430i | \(0.772066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.93504e6 | −1.10764 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.25095e7 | 1.53744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.68972e6i | − | 0.693297i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.96693e6 | − | 4.52219e6i | −0.358441 | − | 0.546335i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.47459e7i | − | 1.76634i | −0.469050 | − | 0.883172i | \(-0.655404\pi\) | ||
0.469050 | − | 0.883172i | \(-0.344596\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.95614e6 | 0.944962 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.16192e6 | −0.607915 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.85519e6i | − | 0.566982i | −0.958975 | − | 0.283491i | \(-0.908507\pi\) | ||
0.958975 | − | 0.283491i | \(-0.0914926\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.22569e6 | − | 2.11632e6i | 0.373534 | − | 0.245069i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.12503e7i | − | 1.29189i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.48204e6 | −0.510398 | −0.255199 | − | 0.966889i | \(-0.582141\pi\) | ||||
−0.255199 | + | 0.966889i | \(0.582141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.29562e6 | 0.485110 | 0.242555 | − | 0.970138i | \(-0.422015\pi\) | ||||
0.242555 | + | 0.970138i | \(0.422015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.87372e6i | 0.993831i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.24445e7 | − | 8.16459e6i | 1.38225 | − | 0.906872i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.05706e7i | − | 1.16447i | −0.813020 | − | 0.582235i | \(-0.802178\pi\) | ||
0.813020 | − | 0.582235i | \(-0.197822\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.61820e6 | −0.723097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.20461e6 | −0.455641 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.30960e7i | − | 1.40763i | −0.710383 | − | 0.703816i | \(-0.751478\pi\) | ||
0.710383 | − | 0.703816i | \(-0.248522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.11924e7 | − | 1.70595e7i | −1.19327 | − | 1.81878i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.69519e7i | 1.79270i | 0.443351 | + | 0.896348i | \(0.353789\pi\) | ||||
−0.443351 | + | 0.896348i | \(0.646211\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.27214e7 | 1.33447 | 0.667236 | − | 0.744846i | \(-0.267477\pi\) | ||||
0.667236 | + | 0.744846i | \(0.267477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.21210e6 | −0.230184 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.35498e6i | − | 0.243090i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.66919e6 | − | 7.13368e6i | −0.682925 | − | 0.730488i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.04454e7i | 4.10866i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.83355e6 | −0.386344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.32823e6 | −0.832682 | −0.416341 | − | 0.909209i | \(-0.636688\pi\) | ||||
−0.416341 | + | 0.909209i | \(0.636688\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5.50862e6i | − | 0.546429i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.58038e6 | + | 5.45722e6i | 0.352367 | + | 0.537078i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.42900e6i | − | 0.432471i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.57213e7 | −1.52313 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.18862e6 | −0.402648 | −0.201324 | − | 0.979525i | \(-0.564524\pi\) | ||||
−0.201324 | + | 0.979525i | \(0.564524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 271198.i | 0.0258677i | 0.999916 | + | 0.0129339i | \(0.00411709\pi\) | ||||
−0.999916 | + | 0.0129339i | \(0.995883\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.97995e6 | + | 1.29901e6i | −0.187393 | + | 0.122945i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.01692e7i | 0.955052i | 0.878618 | + | 0.477526i | \(0.158466\pi\) | ||||
−0.878618 | + | 0.477526i | \(0.841534\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.25735e6 | −0.769536 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.34768e7 | 1.24633 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.95062e6i | 0.821429i | 0.911764 | + | 0.410714i | \(0.134721\pi\) | ||||
−0.911764 | + | 0.410714i | \(0.865279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.63175e7 | + | 1.07056e7i | −1.48611 | + | 0.975007i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.74255e7i | 1.57497i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.07182e7 | 0.961409 | 0.480705 | − | 0.876883i | \(-0.340381\pi\) | ||||
0.480705 | + | 0.876883i | \(0.340381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.65131e6 | 0.414068 | 0.207034 | − | 0.978334i | \(-0.433619\pi\) | ||||
0.207034 | + | 0.978334i | \(0.433619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.63806e6i | 0.233078i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.41390e7 | + | 2.15506e7i | 1.23984 | + | 1.88976i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.44519e6i | 0.125779i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.34805e7 | 2.02835 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.81725e7 | 2.41557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 9.92139e6i | − | 0.844374i | −0.906509 | − | 0.422187i | \(-0.861263\pi\) | ||
0.906509 | − | 0.422187i | \(-0.138737\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.68817e6 | + | 2.90306e6i | 0.564999 | + | 0.245243i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6.45936e6i | − | 0.541649i | −0.962629 | − | 0.270824i | \(-0.912704\pi\) | ||
0.962629 | − | 0.270824i | \(-0.0872963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.72321e6 | 0.393154 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.61888e6 | −0.712169 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.26684e7i | − | 1.03913i | −0.854432 | − | 0.519564i | \(-0.826095\pi\) | ||
0.854432 | − | 0.519564i | \(-0.173905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.73950e6 | − | 1.02723e7i | −0.548783 | − | 0.836455i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.12552e6i | − | 0.576003i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.47938e6 | 0.198973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.07160e6 | −0.324392 | −0.162196 | − | 0.986759i | \(-0.551858\pi\) | ||||
−0.162196 | + | 0.986759i | \(0.551858\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.99375e7i | 3.15898i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.91700e6 | − | 3.88204e6i | 0.464665 | − | 0.304858i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.80137e6i | 0.452323i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.18850e7 | −0.920043 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.11804e7 | −1.62795 | −0.813973 | − | 0.580903i | \(-0.802700\pi\) | ||||
−0.813973 | + | 0.580903i | \(0.802700\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.56117e7i | − | 1.95457i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.66534e7 | − | 1.09260e7i | 1.26192 | − | 0.827921i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.32794e6i | − | 0.0999150i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.87573e7 | 1.40138 | 0.700689 | − | 0.713467i | \(-0.252876\pi\) | ||||
0.700689 | + | 0.713467i | \(0.252876\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.33533e7 | −0.990637 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.94287e6i | − | 0.216794i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.70995e6 | + | 8.70310e6i | 0.417703 | + | 0.636662i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.73303e6i | 0.125895i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.82800e7 | 1.31872 | 0.659362 | − | 0.751826i | \(-0.270826\pi\) | ||||
0.659362 | + | 0.751826i | \(0.270826\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00788e6 | −0.573693 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.48282e7i | − | 1.05498i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.89660e6 | − | 4.36945e6i | 0.134008 | − | 0.308732i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.45855e6i | 0.453210i | 0.973987 | + | 0.226605i | \(0.0727626\pi\) | ||||
−0.973987 | + | 0.226605i | \(0.927237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.25906e7 | 1.57438 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 673313. | 0.0466040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.88365e6i | 0.129491i | 0.997902 | + | 0.0647454i | \(0.0206235\pi\) | ||||
−0.997902 | + | 0.0647454i | \(0.979376\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.15091e7 | + | 1.75422e7i | 0.785820 | + | 1.19775i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.70778e7i | − | 1.15814i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.24002e7 | 1.50883 | 0.754417 | − | 0.656395i | \(-0.227920\pi\) | ||||
0.754417 | + | 0.656395i | \(0.227920\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.76247e7 | −1.17917 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.22827e6i | 0.148080i | 0.997255 | + | 0.0740400i | \(0.0235893\pi\) | ||||
−0.997255 | + | 0.0740400i | \(0.976411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.20636e6 | − | 791470.i | 0.0796316 | − | 0.0522449i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 2.36214e7i | − | 1.54883i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.50630e7 | −2.28373 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.92986e7 | −1.24861 | −0.624303 | − | 0.781183i | \(-0.714617\pi\) | ||||
−0.624303 | + | 0.781183i | \(0.714617\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.89641e6i | − | 0.378966i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.45488e7 | − | 9.54520e6i | 0.928879 | − | 0.609421i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.22211e6i | 0.458062i | 0.973419 | + | 0.229031i | \(0.0735557\pi\) | ||||
−0.973419 | + | 0.229031i | \(0.926444\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.49602e7 | 0.942612 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.08001e7 | 0.676028 | 0.338014 | − | 0.941141i | \(-0.390245\pi\) | ||||
0.338014 | + | 0.941141i | \(0.390245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.84544e7i | 2.39130i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.99621e6 | − | 6.09102e6i | −0.246885 | − | 0.376302i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.59827e6i | − | 0.220854i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.50354e6 | −0.335603 | −0.167802 | − | 0.985821i | \(-0.553667\pi\) | ||||
−0.167802 | + | 0.985821i | \(0.553667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.29731e7 | −1.39182 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.91304e7i | 1.75347i | 0.480977 | + | 0.876733i | \(0.340282\pi\) | ||||
−0.480977 | + | 0.876733i | \(0.659718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.86208e6 | + | 8.89760e6i | −0.230976 | + | 0.532131i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.33832e7i | − | 2.57792i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.87586e7 | −2.28836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.02562e7 | 1.77495 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.55631e6i | 0.207298i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.31601e7 | + | 2.00586e7i | 0.762227 | + | 1.16179i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.40251e6i | 0.310927i | 0.987842 | + | 0.155464i | \(0.0496871\pi\) | ||||
−0.987842 | + | 0.155464i | \(0.950313\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.24005e6 | 0.356858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.67919e7 | −1.52251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.22766e7i | 0.693259i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.82021e6 | + | 6.44286e6i | −0.551065 | + | 0.361544i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.19820e7i | − | 1.22580i | −0.790159 | − | 0.612902i | \(-0.790002\pi\) | ||
0.790159 | − | 0.612902i | \(-0.209998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.66327e6 | −0.313834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.44686e6 | −0.244891 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 3.35360e7i | − | 1.83536i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.97128e6 | − | 5.22982e6i | 0.433549 | − | 0.284444i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.15969e7i | 1.16737i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.37377e7 | −1.81236 | −0.906178 | − | 0.422896i | \(-0.861014\pi\) | ||||
−0.906178 | + | 0.422896i | \(0.861014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.30907e6 | −0.176666 | −0.0883331 | − | 0.996091i | \(-0.528154\pi\) | ||||
−0.0883331 | + | 0.996091i | \(0.528154\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.14451e7i | 0.607289i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.98211e6 | + | 7.59373e6i | 0.262736 | + | 0.400462i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.49836e6i | 0.235776i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.74033e7 | −0.906615 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.00294e6 | 0.207263 | 0.103631 | − | 0.994616i | \(-0.466954\pi\) | ||||
0.103631 | + | 0.994616i | \(0.466954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.17703e7i | 0.605740i | 0.953032 | + | 0.302870i | \(0.0979448\pi\) | ||||
−0.953032 | + | 0.302870i | \(0.902055\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.52314e7 | − | 1.96331e7i | −2.31369 | − | 1.00428i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.12347e7i | − | 0.571214i | −0.958347 | − | 0.285607i | \(-0.907805\pi\) | ||
0.958347 | − | 0.285607i | \(-0.0921952\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.44928e7 | −1.23781 | −0.618903 | − | 0.785468i | \(-0.712423\pi\) | ||||
−0.618903 | + | 0.785468i | \(0.712423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.44578e6 | −0.173095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.96550e6i | − | 0.297875i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.58803e6 | + | 1.30899e7i | 0.426263 | + | 0.649710i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.24178e6i | − | 0.357299i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.20271e6 | −0.0589868 | −0.0294934 | − | 0.999565i | \(-0.509389\pi\) | ||||
−0.0294934 | + | 0.999565i | \(0.509389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.81878e7 | −0.886726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.03273e7i | 0.500515i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.35618e7 | − | 8.89763e6i | 0.653393 | − | 0.428679i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.78917e7i | − | 2.29378i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.55742e7 | 2.64609 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.47341e6 | −0.448418 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.92510e7i | − | 1.84705i | −0.383543 | − | 0.923523i | \(-0.625296\pi\) | ||
0.383543 | − | 0.923523i | \(-0.374704\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.06937e7 | − | 2.66984e7i | 1.90376 | − | 1.24902i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.29324e6i | − | 0.0601488i | −0.999548 | − | 0.0300744i | \(-0.990426\pi\) | ||
0.999548 | − | 0.0300744i | \(-0.00957443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.87256e7 | 1.32827 | 0.664134 | − | 0.747613i | \(-0.268800\pi\) | ||||
0.664134 | + | 0.747613i | \(0.268800\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.56525e7 | −3.01817 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.57964e6i | 0.392141i | 0.980590 | + | 0.196070i | \(0.0628181\pi\) | ||||
−0.980590 | + | 0.196070i | \(0.937182\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.27714e7 | + | 3.47081e7i | 1.03478 | + | 1.57722i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.07197e7i | − | 1.38793i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.56989e7 | 1.15442 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.44190e6 | 0.332383 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.91875e6i | − | 0.396067i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.09641e7 | + | 5.35093e6i | −1.36722 | + | 0.236270i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.79556e7i | 1.22735i | 0.789558 | + | 0.613676i | \(0.210310\pi\) | ||||
−0.789558 | + | 0.613676i | \(0.789690\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.84739e7 | 1.67955 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.36409e6 | −0.232839 | −0.116420 | − | 0.993200i | \(-0.537142\pi\) | ||||
−0.116420 | + | 0.993200i | \(0.537142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.40226e7i | − | 1.90009i | −0.312117 | − | 0.950044i | \(-0.601038\pi\) | ||
0.312117 | − | 0.950044i | \(-0.398962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.35037e6 | + | 1.42518e7i | 0.401302 | + | 0.611664i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.88424e7i | 0.804133i | 0.915610 | + | 0.402067i | \(0.131708\pi\) | ||||
−0.915610 | + | 0.402067i | \(0.868292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.10017e7 | 0.891253 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.71387e7 | −0.723243 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.78359e7i | − | 1.58773i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −680348. | + | 446364.i | −0.0283905 | + | 0.0186265i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.51913e6i | 0.270526i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.73113e6 | −0.195239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.33952e6 | 0.137048 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.61969e6i | 0.310970i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.13692e7 | + | 7.45911e6i | −0.461432 | + | 0.302737i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.40217e7i | 1.77684i | 0.459029 | + | 0.888421i | \(0.348197\pi\) | ||||
−0.459029 | + | 0.888421i | \(0.651803\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.50753e6 | −0.100655 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.02447e7 | 1.20741 | 0.603703 | − | 0.797209i | \(-0.293691\pi\) | ||||
0.603703 | + | 0.797209i | \(0.293691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.54601e7i | 1.80490i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.19017e7 | − | 4.86246e7i | −1.25968 | − | 1.92001i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.27967e7i | 2.46612i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.35173e7 | −0.918543 | −0.459272 | − | 0.888296i | \(-0.651890\pi\) | ||||
−0.459272 | + | 0.888296i | \(0.651890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.78895e6 | −0.302573 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.31846e7i | 0.509404i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.86424e7 | + | 1.24325e7i | 1.10066 | + | 0.477753i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.51211e7i | 0.577943i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.07876e7 | −1.55056 | −0.775281 | − | 0.631616i | \(-0.782392\pi\) | ||||
−0.775281 | + | 0.631616i | \(0.782392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.98551e7 | 1.50699 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.59362e7i | − | 0.599350i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.69083e6 | + | 1.17224e7i | 0.287703 | + | 0.438517i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.42613e7i | 0.530654i | 0.964159 | + | 0.265327i | \(0.0854799\pi\) | ||||
−0.964159 | + | 0.265327i | \(0.914520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.78504e7 | 1.03078 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.24934e7 | 0.828095 | 0.414048 | − | 0.910255i | \(-0.364115\pi\) | ||||
0.414048 | + | 0.910255i | \(0.364115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.43363e7i | 0.524997i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.96157e7 | − | 1.28695e7i | 0.714535 | − | 0.468794i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.45401e7i | 0.889205i | 0.895728 | + | 0.444603i | \(0.146655\pi\) | ||||
−0.895728 | + | 0.444603i | \(0.853345\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.46138e7 | 0.526742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.90375e7 | 1.04114 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.06466e7i | − | 1.44975i | −0.688882 | − | 0.724873i | \(-0.741898\pi\) | ||
0.688882 | − | 0.724873i | \(-0.258102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.54622e6 | + | 2.32661e6i | −0.125822 | + | 0.0825497i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2.40509e7i | − | 0.848891i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.95324e7 | −1.38806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.89951e7 | −0.663486 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.62089e7i | 2.30065i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.13511e7 | − | 1.73013e7i | −0.392392 | − | 0.598083i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.22263e7i | 1.45217i | 0.687606 | + | 0.726084i | \(0.258662\pi\) | ||||
−0.687606 | + | 0.726084i | \(0.741338\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.37390e7 | −0.812183 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.00999e7 | −1.36488 | −0.682442 | − | 0.730940i | \(-0.739082\pi\) | ||||
−0.682442 | + | 0.730940i | \(0.739082\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.27712e7i | − | 0.771087i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.55541e6 | − | 1.97103e7i | 0.288223 | − | 0.664019i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.75634e7i | 0.588671i | 0.955702 | + | 0.294336i | \(0.0950983\pi\) | ||||
−0.955702 | + | 0.294336i | \(0.904902\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.55813e6 | 0.285379 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.26127e7 | 2.40902 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.46862e6i | 0.114491i | 0.998360 | + | 0.0572456i | \(0.0182318\pi\) | ||||
−0.998360 | + | 0.0572456i | \(0.981768\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.55772e6 | − | 9.99527e6i | −0.215358 | − | 0.328249i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 6.40896e7i | − | 2.09409i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.66388e6 | 0.0540918 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.88098e7 | 0.608414 | 0.304207 | − | 0.952606i | \(-0.401609\pi\) | ||||
0.304207 | + | 0.952606i | \(0.401609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.40341e7i | 1.41715i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.17844e7 | − | 1.42924e7i | 0.697570 | − | 0.457663i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.29454e7i | − | 0.412455i | −0.978504 | − | 0.206227i | \(-0.933881\pi\) | ||
0.978504 | − | 0.206227i | \(-0.0661187\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.33121e7 | −0.739039 |
(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 | 80.6.c.d.49.2 | 8 | ||
3.2 | odd | 2 | 720.6.f.n.289.2 | 8 | |||
4.3 | odd | 2 | 40.6.c.a.9.7 | yes | 8 | ||
5.2 | odd | 4 | 400.6.a.ba.1.1 | 4 | |||
5.3 | odd | 4 | 400.6.a.z.1.4 | 4 | |||
5.4 | even | 2 | inner | 80.6.c.d.49.7 | 8 | ||
8.3 | odd | 2 | 320.6.c.j.129.2 | 8 | |||
8.5 | even | 2 | 320.6.c.i.129.7 | 8 | |||
12.11 | even | 2 | 360.6.f.b.289.2 | 8 | |||
15.14 | odd | 2 | 720.6.f.n.289.1 | 8 | |||
20.3 | even | 4 | 200.6.a.k.1.1 | 4 | |||
20.7 | even | 4 | 200.6.a.j.1.4 | 4 | |||
20.19 | odd | 2 | 40.6.c.a.9.2 | ✓ | 8 | ||
40.19 | odd | 2 | 320.6.c.j.129.7 | 8 | |||
40.29 | even | 2 | 320.6.c.i.129.2 | 8 | |||
60.59 | even | 2 | 360.6.f.b.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.2 | ✓ | 8 | 20.19 | odd | 2 | ||
40.6.c.a.9.7 | yes | 8 | 4.3 | odd | 2 | ||
80.6.c.d.49.2 | 8 | 1.1 | even | 1 | trivial | ||
80.6.c.d.49.7 | 8 | 5.4 | even | 2 | inner | ||
200.6.a.j.1.4 | 4 | 20.7 | even | 4 | |||
200.6.a.k.1.1 | 4 | 20.3 | even | 4 | |||
320.6.c.i.129.2 | 8 | 40.29 | even | 2 | |||
320.6.c.i.129.7 | 8 | 8.5 | even | 2 | |||
320.6.c.j.129.2 | 8 | 8.3 | odd | 2 | |||
320.6.c.j.129.7 | 8 | 40.19 | odd | 2 | |||
360.6.f.b.289.1 | 8 | 60.59 | even | 2 | |||
360.6.f.b.289.2 | 8 | 12.11 | even | 2 | |||
400.6.a.z.1.4 | 4 | 5.3 | odd | 4 | |||
400.6.a.ba.1.1 | 4 | 5.2 | odd | 4 | |||
720.6.f.n.289.1 | 8 | 15.14 | odd | 2 | |||
720.6.f.n.289.2 | 8 | 3.2 | odd | 2 |