Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.16 | ||
Root | \(4.52328i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.b.383.15 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 10.5848 | + | 11.4438i | 0.679017 | + | 0.734123i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 101.915i | − | 1.82312i | −0.411172 | − | 0.911558i | \(-0.634880\pi\) | ||
0.411172 | − | 0.911558i | \(-0.365120\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 13.9460i | − | 0.107573i | −0.998552 | − | 0.0537867i | \(-0.982871\pi\) | ||
0.998552 | − | 0.0537867i | \(-0.0171291\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.9231 | + | 242.262i | −0.0778727 | + | 0.996963i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −445.507 | −1.11013 | −0.555063 | − | 0.831808i | \(-0.687306\pi\) | ||||
−0.555063 | + | 0.831808i | \(0.687306\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −217.527 | −0.356988 | −0.178494 | − | 0.983941i | \(-0.557123\pi\) | ||||
−0.178494 | + | 0.983941i | \(0.557123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1166.30 | − | 1078.76i | 1.33839 | − | 1.23793i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1436.17i | − | 1.20527i | −0.798018 | − | 0.602634i | \(-0.794118\pi\) | ||
0.798018 | − | 0.602634i | \(-0.205882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2611.15i | 1.65939i | 0.558219 | + | 0.829694i | \(0.311485\pi\) | ||||
−0.558219 | + | 0.829694i | \(0.688515\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 159.596 | − | 147.616i | 0.0789721 | − | 0.0730442i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 696.672 | 0.274605 | 0.137303 | − | 0.990529i | \(-0.456157\pi\) | ||||
0.137303 | + | 0.990529i | \(0.456157\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7261.72 | −2.32375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2972.71 | + | 2347.75i | −0.784770 | + | 0.619787i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4602.14i | − | 1.01617i | −0.861308 | − | 0.508083i | \(-0.830354\pi\) | ||
0.861308 | − | 0.508083i | \(-0.169646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8335.61i | 1.55788i | 0.627101 | + | 0.778938i | \(0.284241\pi\) | ||||
−0.627101 | + | 0.778938i | \(0.715759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4715.61 | − | 5098.31i | −0.753794 | − | 0.814969i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1421.31 | −0.196119 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6925.77 | −0.831694 | −0.415847 | − | 0.909435i | \(-0.636515\pi\) | ||||
−0.415847 | + | 0.909435i | \(0.636515\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2302.48 | − | 2489.34i | −0.242401 | − | 0.262073i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11600.9i | 1.07778i | 0.842375 | + | 0.538891i | \(0.181157\pi\) | ||||
−0.842375 | + | 0.538891i | \(0.818843\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6050.27i | 0.499004i | 0.968374 | + | 0.249502i | \(0.0802669\pi\) | ||||
−0.968374 | + | 0.249502i | \(0.919733\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24690.2 | + | 1928.55i | 1.81758 | + | 0.141971i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13047.5 | 0.861553 | 0.430776 | − | 0.902459i | \(-0.358240\pi\) | ||||
0.430776 | + | 0.902459i | \(0.358240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16612.5 | 0.988428 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16435.3 | − | 15201.6i | 0.884815 | − | 0.818397i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37847.2i | 1.85073i | 0.379073 | + | 0.925367i | \(0.376243\pi\) | ||||
−0.379073 | + | 0.925367i | \(0.623757\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45403.9i | 2.02389i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −29881.6 | + | 27638.6i | −1.21819 | + | 1.12675i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4116.26 | −0.153947 | −0.0769737 | − | 0.997033i | \(-0.524526\pi\) | ||||
−0.0769737 | + | 0.997033i | \(0.524526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −203.748 | −0.00701083 | −0.00350541 | − | 0.999994i | \(-0.501116\pi\) | ||||
−0.00350541 | + | 0.999994i | \(0.501116\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3378.59 | + | 263.901i | 0.107247 | + | 0.00837703i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22169.3i | 0.650831i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1289.39i | 0.0350912i | 0.999846 | + | 0.0175456i | \(0.00558522\pi\) | ||||
−0.999846 | + | 0.0175456i | \(0.994415\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7374.15 | + | 7972.61i | 0.186462 | + | 0.201594i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45445.3 | −1.06990 | −0.534950 | − | 0.844884i | \(-0.679670\pi\) | ||||
−0.534950 | + | 0.844884i | \(0.679670\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 42464.1 | 0.932642 | 0.466321 | − | 0.884616i | \(-0.345579\pi\) | ||||
0.466321 | + | 0.884616i | \(0.345579\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −76864.1 | − | 83102.0i | −1.57787 | − | 1.70592i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6213.04i | 0.119420i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 28560.5i | 0.514871i | 0.966295 | + | 0.257435i | \(0.0828775\pi\) | ||||
−0.966295 | + | 0.257435i | \(0.917123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −58332.8 | − | 9168.68i | −0.987872 | − | 0.155272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7615.76 | −0.121344 | −0.0606719 | − | 0.998158i | \(-0.519324\pi\) | ||||
−0.0606719 | + | 0.998158i | \(0.519324\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −146368. | −2.19734 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 52666.2 | − | 48712.9i | 0.745991 | − | 0.689994i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15207.1i | 0.203504i | 0.994810 | + | 0.101752i | \(0.0324448\pi\) | ||||
−0.994810 | + | 0.101752i | \(0.967555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3033.63i | 0.0384024i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −95391.4 | + | 88230.9i | −1.14367 | + | 1.05782i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 266116. | 3.02526 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −87803.8 | −0.947510 | −0.473755 | − | 0.880657i | \(-0.657102\pi\) | ||||
−0.473755 | + | 0.880657i | \(0.657102\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8430.35 | − | 107929.i | 0.0864485 | − | 1.10676i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 90132.6i | − | 0.879182i | −0.898198 | − | 0.439591i | \(-0.855123\pi\) | ||
0.898198 | − | 0.439591i | \(-0.144877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 35966.5i | − | 0.334045i | −0.985953 | − | 0.167022i | \(-0.946585\pi\) | ||
0.985953 | − | 0.167022i | \(-0.0534152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15044.3 | − | 16265.3i | −0.133168 | − | 0.143975i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −162071. | −1.36850 | −0.684250 | − | 0.729247i | \(-0.739870\pi\) | ||||
−0.684250 | + | 0.729247i | \(0.739870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −209727. | −1.69079 | −0.845393 | − | 0.534145i | \(-0.820634\pi\) | ||||
−0.845393 | + | 0.534145i | \(0.820634\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −73308.0 | − | 79257.4i | −0.564734 | − | 0.610566i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 97384.1i | 0.717450i | 0.933443 | + | 0.358725i | \(0.116788\pi\) | ||||
−0.933443 | + | 0.358725i | \(0.883212\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 71001.6i | − | 0.500637i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4116.27 | − | 52698.4i | 0.0277996 | − | 0.355904i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20028.9 | −0.129655 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 37425.1 | 0.232381 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −132759. | + | 122793.i | −0.791225 | + | 0.731832i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 421595.i | 2.41335i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 136193.i | 0.749284i | 0.927169 | + | 0.374642i | \(0.122234\pi\) | ||||
−0.927169 | + | 0.374642i | \(0.877766\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −69238.4 | + | 64041.1i | −0.366330 | + | 0.338832i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −319348. | −1.62587 | −0.812936 | − | 0.582353i | \(-0.802132\pi\) | ||||
−0.812936 | + | 0.582353i | \(0.802132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 36415.1 | 0.178506 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 239271. | + | 302964.i | 1.12994 | + | 1.43073i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 340623.i | 1.55050i | 0.631652 | + | 0.775252i | \(0.282377\pi\) | ||||
−0.631652 | + | 0.775252i | \(0.717623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 434345.i | − | 1.90677i | −0.301760 | − | 0.953384i | \(-0.597574\pi\) | ||
0.301760 | − | 0.953384i | \(-0.402426\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 138105. | + | 149313.i | 0.585009 | + | 0.632485i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 96909.5 | 0.396302 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −469029. | −1.85259 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 175840. | + | 190111.i | 0.671159 | + | 0.725628i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 109904.i | − | 0.405555i | −0.979225 | − | 0.202777i | \(-0.935003\pi\) | ||
0.979225 | − | 0.202777i | \(-0.0649967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 281346.i | 1.00415i | 0.864825 | + | 0.502074i | \(0.167429\pi\) | ||||
−0.864825 | + | 0.502074i | \(0.832571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 347930. | + | 27176.7i | 1.20161 | + | 0.0938574i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 849526. | 2.84019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 486230. | 1.57432 | 0.787160 | − | 0.616749i | \(-0.211551\pi\) | ||||
0.787160 | + | 0.616749i | \(0.211551\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −433117. | + | 400606.i | −1.35867 | + | 1.25668i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9715.80i | − | 0.0295402i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 435448.i | − | 1.28371i | −0.766826 | − | 0.641855i | \(-0.778165\pi\) | ||
0.766826 | − | 0.641855i | \(-0.221835\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −519595. | + | 480593.i | −1.48578 | + | 1.37425i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 156653. | 0.434657 | 0.217328 | − | 0.976099i | \(-0.430266\pi\) | ||||
0.217328 | + | 0.976099i | \(0.430266\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −323975. | −0.872559 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −632583. | − | 49411.0i | −1.65435 | − | 0.129221i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 285352.i | − | 0.724879i | −0.932007 | − | 0.362440i | \(-0.881944\pi\) | ||
0.932007 | − | 0.362440i | \(-0.118056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 101272.i | 0.249974i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −43569.9 | − | 47105.8i | −0.104533 | − | 0.113016i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −277875. | −0.648211 | −0.324105 | − | 0.946021i | \(-0.605063\pi\) | ||||
−0.324105 | + | 0.946021i | \(0.605063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −74483.2 | −0.168990 | −0.0844951 | − | 0.996424i | \(-0.526928\pi\) | ||||
−0.0844951 | + | 0.996424i | \(0.526928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2156.64 | − | 2331.66i | −0.00476047 | − | 0.00514681i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 705842.i | 1.51627i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 639823.i | 1.33800i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 32741.7 | + | 41457.4i | 0.0666726 | + | 0.0844204i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 307683. | 0.610268 | 0.305134 | − | 0.952309i | \(-0.401299\pi\) | ||||
0.305134 | + | 0.952309i | \(0.401299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −293837. | −0.567824 | −0.283912 | − | 0.958850i | \(-0.591632\pi\) | ||||
−0.283912 | + | 0.958850i | \(0.591632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −253702. | + | 234658.i | −0.477790 | + | 0.441925i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 291128.i | − | 0.534464i | −0.963632 | − | 0.267232i | \(-0.913891\pi\) | ||
0.963632 | − | 0.267232i | \(-0.0861091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 700006.i | − | 1.25305i | −0.779400 | − | 0.626526i | \(-0.784476\pi\) | ||
0.779400 | − | 0.626526i | \(-0.215524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14755.6 | + | 13648.0i | −0.0257612 | + | 0.0238275i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −64181.5 | −0.109313 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.18231e6 | 1.96492 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13183.2 | + | 168777.i | −0.0213843 | + | 0.273771i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.16328e6i | − | 1.84213i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 933534.i | 1.44352i | 0.692142 | + | 0.721762i | \(0.256667\pi\) | ||||
−0.692142 | + | 0.721762i | \(0.743333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −481031. | − | 520069.i | −0.726480 | − | 0.785438i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 616615. | 0.909742 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 116249. | 0.167586 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 449475. | + | 485953.i | 0.633279 | + | 0.684674i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 312405.i | 0.430266i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.03626e6i | − | 1.39542i | −0.716379 | − | 0.697711i | \(-0.754202\pi\) | ||
0.716379 | − | 0.697711i | \(-0.245798\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 137414. | − | 1.75924e6i | 0.180957 | − | 2.31670i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −98404.6 | −0.126751 | −0.0633754 | − | 0.997990i | \(-0.520187\pi\) | ||||
−0.0633754 | + | 0.997990i | \(0.520187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.43694e6 | −1.81072 | −0.905360 | − | 0.424646i | \(-0.860399\pi\) | ||||
−0.905360 | + | 0.424646i | \(0.860399\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −71101.1 | + | 65763.9i | −0.0876690 | + | 0.0810882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 677501.i | 0.817561i | 0.912633 | + | 0.408780i | \(0.134046\pi\) | ||||
−0.912633 | + | 0.408780i | \(0.865954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.32974e6i | − | 1.57071i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −326842. | + | 302308.i | −0.377978 | + | 0.349606i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −510742. | −0.578371 | −0.289186 | − | 0.957273i | \(-0.593385\pi\) | ||||
−0.289186 | + | 0.957273i | \(0.593385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 385443. | 0.427481 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −512518. | − | 764601.i | −0.556792 | − | 0.830652i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.69307e6i | − | 1.80202i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 567995.i | − | 0.592382i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −80611.4 | − | 87153.5i | −0.0823945 | − | 0.0890813i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.33377e6 | 1.33628 | 0.668139 | − | 0.744037i | \(-0.267091\pi\) | ||||
0.668139 | + | 0.744037i | \(0.267091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −310372. | −0.304847 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.54928e6 | − | 1.67501e6i | −1.49203 | − | 1.61312i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 803514.i | 0.758858i | 0.925221 | + | 0.379429i | \(0.123880\pi\) | ||||
−0.925221 | + | 0.379429i | \(0.876120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 96586.9i | 0.0894682i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.11492e6 | + | 87086.6i | 1.01308 | + | 0.0791316i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −312904. | −0.278947 | −0.139474 | − | 0.990226i | \(-0.544541\pi\) | ||||
−0.139474 | + | 0.990226i | \(0.544541\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.85721e6 | 3.37410 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −174028. | + | 160965.i | −0.149397 | + | 0.138182i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.65266e6i | − | 1.39253i | −0.717786 | − | 0.696264i | \(-0.754844\pi\) | ||
0.717786 | − | 0.696264i | \(-0.245156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 969577.i | 0.801971i | 0.916084 | + | 0.400986i | \(0.131332\pi\) | ||||
−0.916084 | + | 0.400986i | \(0.868668\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −34716.4 | + | 32110.4i | −0.0281921 | + | 0.0260759i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.23515e6 | 2.57966 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 279272. | 0.218689 | 0.109345 | − | 0.994004i | \(-0.465125\pi\) | ||||
0.109345 | + | 0.994004i | \(0.465125\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.01940e6 | − | 157735.i | −1.55315 | − | 0.121316i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 388827.i | − | 0.293759i | −0.989154 | − | 0.146879i | \(-0.953077\pi\) | ||
0.989154 | − | 0.146879i | \(-0.0469230\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.06951e6i | 0.793814i | 0.917859 | + | 0.396907i | \(0.129916\pi\) | ||||
−0.917859 | + | 0.396907i | \(0.870084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.81679e6 | + | 3.04539e6i | 2.05420 | + | 2.22091i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 161786. | 0.115941 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −642728. | −0.452671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −929387. | − | 1.00481e6i | −0.643375 | − | 0.695589i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.18695e6i | − | 0.807725i | −0.914820 | − | 0.403863i | \(-0.867667\pi\) | ||
0.914820 | − | 0.403863i | \(-0.132333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 419510.i | 0.280664i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.32436e6 | − | 1.04594e6i | 0.871194 | − | 0.688041i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −151545. | −0.0980309 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 84377.2 | 0.0536796 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.03146e6 | − | 954038.i | 0.645427 | − | 0.596979i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20765.1i | 0.0127816i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 782074.i | 0.473589i | 0.971560 | + | 0.236795i | \(0.0760969\pi\) | ||||
−0.971560 | + | 0.236795i | \(0.923903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 411595. | − | 380699.i | 0.245230 | − | 0.226822i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.00278e6 | −0.587902 | −0.293951 | − | 0.955821i | \(-0.594970\pi\) | ||||
−0.293951 | + | 0.955821i | \(0.594970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.62413e6 | 0.937047 | 0.468523 | − | 0.883451i | \(-0.344786\pi\) | ||||
0.468523 | + | 0.883451i | \(0.344786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26895.6 | − | 344330.i | 0.0152723 | − | 0.195523i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.05573e6i | 1.14899i | 0.818507 | + | 0.574496i | \(0.194802\pi\) | ||||
−0.818507 | + | 0.574496i | \(0.805198\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.05028e6i | 1.12807i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.71549e6 | − | 1.85471e6i | −0.929235 | − | 1.00465i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.75006e6 | 2.00001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57962e6 | 0.829552 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.21993e6 | − | 2.40009e6i | −1.14807 | − | 1.24124i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 181960.i | − | 0.0926802i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.97905e6i | 1.49454i | 0.664521 | + | 0.747269i | \(0.268635\pi\) | ||||
−0.664521 | + | 0.747269i | \(0.731365\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 131057. | − | 1.67785e6i | 0.0647662 | − | 0.829168i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 131409. | 0.0639753 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25986.7 | 0.0124646 | 0.00623228 | − | 0.999981i | \(-0.498016\pi\) | ||||
0.00623228 | + | 0.999981i | \(0.498016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.11445e6 | + | 1.03079e6i | −0.526697 | + | 0.487161i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.71357e6i | − | 1.72944i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 466069.i | − | 0.213902i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 812531. | − | 751539.i | 0.367529 | − | 0.339941i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.98374e6 | −1.33026 | −0.665131 | − | 0.746727i | \(-0.731624\pi\) | ||||
−0.665131 | + | 0.746727i | \(0.731624\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 593510. | 0.260834 | 0.130417 | − | 0.991459i | \(-0.458368\pi\) | ||||
0.130417 | + | 0.991459i | \(0.458368\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 646643. | − | 510698.i | 0.280154 | − | 0.221257i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.49836e6i | 0.640000i | 0.947418 | + | 0.320000i | \(0.103683\pi\) | ||||
−0.947418 | + | 0.320000i | \(0.896317\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.63157e6i | 1.95055i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −212002. | − | 229207.i | −0.0880378 | − | 0.0951826i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.69341e6 | 1.92200 | 0.960998 | − | 0.276555i | \(-0.0891929\pi\) | ||||
0.960998 | + | 0.276555i | \(0.0891929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.34201e6 | −1.75357 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 396138. | + | 428287.i | 0.157790 | + | 0.170596i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.32774e6i | − | 1.70031i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.22654e6i | − | 0.862910i | −0.902135 | − | 0.431455i | \(-0.858000\pi\) | ||
0.902135 | − | 0.431455i | \(-0.142000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.81045e6 | − | 219524.i | −1.07451 | − | 0.0839298i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 527817. | 0.199090 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.53599e6 | −0.943789 | −0.471895 | − | 0.881655i | \(-0.656430\pi\) | ||||
−0.471895 | + | 0.881655i | \(0.656430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.82467e6 | + | 4.46251e6i | −1.77170 | + | 1.63871i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00109e6i | 0.362760i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.18712e6i | − | 1.13973i | −0.821740 | − | 0.569863i | \(-0.806996\pi\) | ||
0.821740 | − | 0.569863i | \(-0.193004\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.55858e6 | + | 1.44158e6i | −0.550067 | + | 0.508777i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.61862e6 | 0.912171 | 0.456086 | − | 0.889936i | \(-0.349251\pi\) | ||||
0.456086 | + | 0.889936i | \(0.349251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 633204. | 0.217717 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.46575e6 | − | 114490.i | −0.497488 | − | 0.0388588i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 226309.i | − | 0.0758276i | −0.999281 | − | 0.0379138i | \(-0.987929\pi\) | ||
0.999281 | − | 0.0379138i | \(-0.0120712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.00054e6i | − | 0.330973i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.38024e6 | − | 3.65457e6i | −1.10399 | − | 1.19359i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.91075e6 | 0.938669 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.69515e6 | 0.539800 | 0.269900 | − | 0.962888i | \(-0.413009\pi\) | ||||
0.269900 | + | 0.962888i | \(0.413009\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 385448. | + | 416729.i | 0.121209 | + | 0.131045i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.96084e6i | − | 1.23006i | −0.788504 | − | 0.615030i | \(-0.789144\pi\) | ||
0.788504 | − | 0.615030i | \(-0.210856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.81322e6i | − | 0.556144i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −934429. | + | 5.94501e6i | −0.283080 | + | 1.80100i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.08548e6 | 0.923286 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 794687. | 0.234902 | 0.117451 | − | 0.993079i | \(-0.462528\pi\) | ||||
0.117451 | + | 0.993079i | \(0.462528\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.89804e6 | + | 3.60544e6i | −1.13826 | + | 1.05282i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 57405.4i | 0.0165607i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 776162.i | 0.221224i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.97058e6 | − | 4.59746e6i | 1.39980 | − | 1.29473i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.09860e6 | 0.583976 | 0.291988 | − | 0.956422i | \(-0.405683\pi\) | ||||
0.291988 | + | 0.956422i | \(0.405683\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.09920e6 | 0.577228 | 0.288614 | − | 0.957446i | \(-0.406806\pi\) | ||||
0.288614 | + | 0.957446i | \(0.406806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −246898. | + | 3.16091e6i | −0.0670914 | + | 0.858936i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.04291e7i | 2.80074i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2841.48i | 0.000754179i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.02577e6 | + | 1.10902e6i | 0.269096 | + | 0.290934i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.13075e6 | −1.33042 | −0.665208 | − | 0.746658i | \(-0.731657\pi\) | ||||
−0.665208 | + | 0.746658i | \(0.731657\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −276424. | −0.0708527 | −0.0354264 | − | 0.999372i | \(-0.511279\pi\) | ||||
−0.0354264 | + | 0.999372i | \(0.511279\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.96458e6 | − | 5.36749e6i | −1.25794 | − | 1.36003i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.81912e6i | 0.455677i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.00849e6i | − | 0.992703i | −0.868122 | − | 0.496351i | \(-0.834673\pi\) | ||
0.868122 | − | 0.496351i | \(-0.165327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −314359. | + | 4.02458e6i | −0.0769715 | + | 0.985426i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −484754. | −0.117358 | −0.0586790 | − | 0.998277i | \(-0.518689\pi\) | ||||
−0.0586790 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.54984e6 | 0.371011 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.25773e6 | − | 1.16332e6i | 0.297727 | − | 0.275378i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.23618e6i | 1.69392i | 0.531655 | + | 0.846961i | \(0.321570\pi\) | ||||
−0.531655 | + | 0.846961i | \(0.678430\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.16827e6i | − | 1.19647i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.21967e6 | + | 2.97799e6i | −0.737168 | + | 0.681833i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 309173. | 0.0700121 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.18803e6 | −0.714055 | −0.357027 | − | 0.934094i | \(-0.616210\pi\) | ||||
−0.357027 | + | 0.934094i | \(0.616210\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.37177e6 | + | 4.26931e6i | 0.747009 | + | 0.945859i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 208368.i | 0.0456645i | 0.999739 | + | 0.0228323i | \(0.00726837\pi\) | ||||
−0.999739 | + | 0.0228323i | \(0.992732\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.76931e6i | 1.68434i | 0.539211 | + | 0.842171i | \(0.318722\pi\) | ||||
−0.539211 | + | 0.842171i | \(0.681278\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.99208e6 | + | 9.72184e6i | 1.92854 | + | 2.08505i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.32855e6 | −0.706258 | −0.353129 | − | 0.935575i | \(-0.614882\pi\) | ||||
−0.353129 | + | 0.935575i | \(0.614882\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17981.9 | 0.00377488 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.14666e6 | + | 5.56434e6i | 1.06899 | + | 1.15574i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.69544e6i | − | 0.553957i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.89615e7i | − | 3.85601i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.16894e6 | − | 716185.i | −1.84511 | − | 0.144122i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.46336e6 | 1.08798 | 0.543990 | − | 0.839092i | \(-0.316913\pi\) | ||||
0.543990 | + | 0.839092i | \(0.316913\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.50654e6 | 0.296905 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 111186. | − | 102840.i | 0.0216862 | − | 0.0200583i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.94855e6i | 1.72742i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.36280e6i | − | 1.40676i | −0.710813 | − | 0.703381i | \(-0.751673\pi\) | ||
0.710813 | − | 0.703381i | \(-0.248327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.98319e6 | − | 4.60914e6i | 0.942401 | − | 0.871660i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.98040e6 | 1.11951 | 0.559753 | − | 0.828660i | \(-0.310896\pi\) | ||||
0.559753 | + | 0.828660i | \(0.310896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.60946e6 | −1.22475 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.09997e7 | − | 859181.i | −2.01774 | − | 0.157606i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 633781.i | 0.115093i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.54433e6i | 0.277645i | 0.990317 | + | 0.138822i | \(0.0443317\pi\) | ||||
−0.990317 | + | 0.138822i | \(0.955668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.65814e6 | + | 1.79271e6i | 0.295139 | + | 0.319092i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 161847. | 0.0285222 | 0.0142611 | − | 0.999898i | \(-0.495460\pi\) | ||||
0.0142611 | + | 0.999898i | \(0.495460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.18589e6 | −1.60285 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.42922e6 | − | 3.70752e6i | −0.592482 | − | 0.640566i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.22871e6i | − | 0.552375i | −0.961104 | − | 0.276188i | \(-0.910929\pi\) | ||
0.961104 | − | 0.276188i | \(-0.0890711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 592205.i | − | 0.100327i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.13033e6 | − | 7.76218e6i | −1.02847 | − | 1.30224i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.66553e6 | −0.609003 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.81274e6 | −0.956432 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.26552e6 | − | 3.02040e6i | 0.532150 | − | 0.492205i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.06042e6i | − | 0.816755i | −0.912813 | − | 0.408378i | \(-0.866095\pi\) | ||
0.912813 | − | 0.408378i | \(-0.133905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.82857e6i | − | 0.292320i | −0.989261 | − | 0.146160i | \(-0.953309\pi\) | ||
0.989261 | − | 0.146160i | \(-0.0466914\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.15894e6 | + | 1.07195e6i | −0.183512 | + | 0.169736i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.19714e7 | 1.87766 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.95099e6 | −0.924592 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 77892.2 | − | 997213.i | 0.0119883 | − | 0.153480i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.52350e6i | − | 0.384756i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.65175e7i | 2.49494i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.94125e6 | − | 3.17995e6i | −0.440146 | − | 0.475866i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.40098e6 | −1.09728 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.75554e6 | −0.551670 | −0.275835 | − | 0.961205i | \(-0.588954\pi\) | ||||
−0.275835 | + | 0.961205i | \(0.588954\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −788391. | − | 852374.i | −0.114747 | − | 0.124060i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.13744e7i | 3.08250i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.56727e6i | 0.795562i | 0.917480 | + | 0.397781i | \(0.130220\pi\) | ||||
−0.917480 | + | 0.397781i | \(0.869780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3855.54 | − | 49360.5i | 0.000545952 | − | 0.00698954i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.20169e7 | 1.68621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 398305. | 0.0553864 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.07754e6 | + | 7.47121e6i | −1.11313 | + | 1.02958i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 356674.i | − | 0.0487117i | −0.999703 | − | 0.0243559i | \(-0.992247\pi\) | ||
0.999703 | − | 0.0243559i | \(-0.00775348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.31610e6i | − | 0.178138i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.32204e6 | + | 6.77242e6i | −0.982256 | + | 0.908524i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.13052e7 | −1.50317 | −0.751586 | − | 0.659635i | \(-0.770711\pi\) | ||||
−0.751586 | + | 0.659635i | \(0.770711\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.92493e6 | 1.30800 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −127867. | + | 813511.i | −0.0167032 | + | 0.106269i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.39855e6i | − | 0.958001i | −0.877815 | − | 0.479001i | \(-0.840999\pi\) | ||
0.877815 | − | 0.479001i | \(-0.159001\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.47941e7i | 1.89888i | 0.313953 | + | 0.949439i | \(0.398347\pi\) | ||||
−0.313953 | + | 0.949439i | \(0.601653\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.25677e6 | + | 3.52108e6i | 0.414382 | + | 0.448012i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.05904e6 | −0.638115 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 408152. | 0.0510366 | 0.0255183 | − | 0.999674i | \(-0.491876\pi\) | ||||
0.0255183 | + | 0.999674i | \(0.491876\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.11021e6 | − | 3.36263e6i | −0.385562 | − | 0.416852i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 106209.i | 0.0130534i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.68612e7i | − | 2.05455i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.37078e6 | − | 419511.i | −0.648855 | − | 0.0506819i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.26473e6 | 1.10978 | 0.554891 | − | 0.831923i | \(-0.312760\pi\) | ||||
0.554891 | + | 0.831923i | \(0.312760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.17655e7 | −2.58512 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.33163e6 | − | 3.08154e6i | 0.392363 | − | 0.362910i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.46033e6i | − | 0.637650i | −0.947814 | − | 0.318825i | \(-0.896712\pi\) | ||
0.947814 | − | 0.318825i | \(-0.103288\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.04125e6i | 0.236376i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.01076e6 | − | 7.40944e6i | 0.919894 | − | 0.850843i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.26892e7 | −1.44500 | −0.722502 | − | 0.691369i | \(-0.757008\pi\) | ||||
−0.722502 | + | 0.691369i | \(0.757008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.19942e6 | −0.474245 | −0.237122 | − | 0.971480i | \(-0.576204\pi\) | ||||
−0.237122 | + | 0.971480i | \(0.576204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −312371. | − | 24399.2i | −0.0349846 | − | 0.00273264i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3.81419e6i | − | 0.423657i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.11137e7i | 1.22430i | 0.790741 | + | 0.612150i | \(0.209695\pi\) | ||||
−0.790741 | + | 0.612150i | \(0.790305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −679350. | − | 734483.i | −0.0742250 | − | 0.0802488i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.83817e6 | −0.307564 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.84572e7 | 1.98387 | 0.991937 | − | 0.126734i | \(-0.0404495\pi\) | ||||
0.991937 | + | 0.126734i | \(0.0404495\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.25145e7 | + | 1.35301e7i | 1.33422 | + | 1.44249i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.43968e6i | − | 0.681006i | −0.940243 | − | 0.340503i | \(-0.889403\pi\) | ||
0.940243 | − | 0.340503i | \(-0.110597\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.60963e6i | − | 0.798246i | −0.916897 | − | 0.399123i | \(-0.869315\pi\) | ||
0.916897 | − | 0.399123i | \(-0.130685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.07100e6 | + | 1.63561e6i | −0.215502 | + | 0.170197i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 212079. | 0.0218916 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.02741e7 | 2.07607 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.33124e7 | − | 1.23132e7i | 1.35235 | − | 1.25084i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.94658e6i | 1.00241i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 122913.i | 0.0122892i | 0.999981 | + | 0.00614461i | \(0.00195590\pi\) | ||||
−0.999981 | + | 0.00614461i | \(0.998044\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.06832e7 | + | 9.88129e6i | −1.05972 | + | 0.980176i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.38802e7 | 1.36603 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.61366e6 | −0.352857 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 859964. | − | 1.10097e7i | 0.0833160 | − | 1.06665i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.49218e6i | 0.143441i | 0.997425 | + | 0.0717207i | \(0.0228490\pi\) | ||||
−0.997425 | + | 0.0717207i | \(0.977151\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.69300e7i | 1.61484i | 0.589980 | + | 0.807418i | \(0.299136\pi\) | ||||
−0.589980 | + | 0.807418i | \(0.700864\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.52676e6 | + | 7.05645e6i | 0.617730 | + | 0.667862i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.24710e6 | −0.211038 | −0.105519 | − | 0.994417i | \(-0.533650\pi\) | ||||
−0.105519 | + | 0.994417i | \(0.533650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.83382e6 | 0.170901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.23047e6 | + | 1.33033e6i | 0.113794 | + | 0.123029i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.12204e6i | 0.561840i | 0.959731 | + | 0.280920i | \(0.0906396\pi\) | ||||
−0.959731 | + | 0.280920i | \(0.909360\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.25465e7i | 2.96415i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −803551. | + | 1.02874e7i | −0.0726273 | + | 0.929809i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.29399e6 | 0.295467 | 0.147734 | − | 0.989027i | \(-0.452802\pi\) | ||||
0.147734 | + | 0.989027i | \(0.452802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.48328e6 | −0.310088 | −0.155044 | − | 0.987908i | \(-0.549552\pi\) | ||||
−0.155044 | + | 0.987908i | \(0.549552\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.57512e6 | + | 3.30675e6i | −0.315868 | + | 0.292158i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.71126e6i | − | 0.325437i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.20618e6i | − | 0.279045i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.18588e7 | − | 1.09686e7i | 1.02441 | − | 0.947515i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 90771.2 | 0.00778291 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.87190e6 | 0.329523 | 0.164762 | − | 0.986333i | \(-0.447315\pi\) | ||||
0.164762 | + | 0.986333i | \(0.447315\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.15870e7 | − | 1.70487e7i | 1.82361 | − | 1.44023i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 8.13996e6i | − | 0.682575i | −0.939959 | − | 0.341288i | \(-0.889137\pi\) | ||
0.939959 | − | 0.341288i | \(-0.110863\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.22451e6i | 0.101927i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.04160e6 | − | 1.12613e6i | −0.0860659 | − | 0.0930507i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.71913e7 | −1.41012 | −0.705061 | − | 0.709147i | \(-0.749080\pi\) | ||||
−0.705061 | + | 0.709147i | \(0.749080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.47147e7 | 2.82675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.52098e7 | − | 1.64442e7i | −1.22951 | − | 1.32929i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.23277e6i | − | 0.660690i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.90803e7i | 1.52016i | 0.649827 | + | 0.760082i | \(0.274841\pi\) | ||||
−0.649827 | + | 0.760082i | \(0.725159\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.50518e6 | − | 117570.i | −0.119057 | − | 0.00929956i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.42664e7 | −3.47626 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.66608e7 | 1.29902 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.75321e6 | + | 7.17122e6i | −0.600190 | + | 0.555137i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.88806e7i | − | 1.45118i | −0.688128 | − | 0.725590i | \(-0.741567\pi\) | ||
0.688128 | − | 0.725590i | \(-0.258433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.80842e7i | − | 1.38010i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.52173e7 | − | 1.40750e7i | 1.15309 | − | 1.06654i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.25699e6 | −0.0945766 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.30901e7 | −0.977975 | −0.488988 | − | 0.872291i | \(-0.662634\pi\) | ||||
−0.488988 | + | 0.872291i | \(0.662634\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.91913e6 | − | 540452.i | −0.513307 | − | 0.0400944i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.80719e6i | 0.427801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 9.87656e6i | − | 0.722505i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.40611e6 | − | 5.84485e6i | −0.392724 | − | 0.424596i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.98750e6 | 0.504080 | 0.252040 | − | 0.967717i | \(-0.418899\pi\) | ||||
0.252040 | + | 0.967717i | \(0.418899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −501589. | −0.0359344 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.07984e6 | + | 4.41095e6i | 0.290267 | + | 0.313824i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.34195e7i | 2.36132i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 481177.i | − | 0.0337652i | −0.999857 | − | 0.0168826i | \(-0.994626\pi\) | ||
0.999857 | − | 0.0168826i | \(-0.00537415\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.32506e6 | − | 1.39583e7i | 0.231729 | − | 0.972780i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.68922e6 | 0.601433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.08328e7 | −1.43215 | −0.716073 | − | 0.698025i | \(-0.754062\pi\) | ||||
−0.716073 | + | 0.698025i | \(0.754062\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.93752e7 | − | 1.79208e7i | 1.32290 | − | 1.22360i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 574433.i | − | 0.0389556i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.87155e6i | − | 0.395496i | −0.980253 | − | 0.197748i | \(-0.936637\pi\) | ||
0.980253 | − | 0.197748i | \(-0.0633627\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.50004e6 | − | 6.01212e6i | 0.434881 | − | 0.402237i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.44391e7 | 0.959550 | 0.479775 | − | 0.877392i | \(-0.340718\pi\) | ||||
0.479775 | + | 0.877392i | \(0.340718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.12009e7 | −0.739373 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 144113. | − | 1.84501e6i | 0.00944937 | − | 0.120975i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.26024e6i | 0.147214i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.23423e6i | − | 0.273952i | −0.990574 | − | 0.136976i | \(-0.956262\pi\) | ||
0.990574 | − | 0.136976i | \(-0.0437384\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.41177e7 | + | 1.52634e7i | 0.907354 | + | 0.980991i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.86734e7 | 1.83068 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.34919e7 | −0.855723 | −0.427862 | − | 0.903844i | \(-0.640733\pi\) | ||||
−0.427862 | + | 0.903844i | \(0.640733\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.28523e6 | − | 3.55185e6i | −0.206996 | − | 0.223795i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.34987e7i | − | 0.844948i | −0.906375 | − | 0.422474i | \(-0.861162\pi\) | ||
0.906375 | − | 0.422474i | \(-0.138838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.92486e6i | 0.181884i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.76972e6 | − | 3.54593e7i | 0.171113 | − | 2.19067i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 895395. | 0.0549574 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.22121e7 | 1.35449 | 0.677243 | − | 0.735760i | \(-0.263175\pi\) | ||||
0.677243 | + | 0.735760i | \(0.263175\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.19529e6 | + | 8.50505e6i | −0.557095 | + | 0.515277i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.78526e7i | − | 1.07462i | −0.843386 | − | 0.537308i | \(-0.819441\pi\) | ||
0.843386 | − | 0.537308i | \(-0.180559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.05309e7i | − | 3.62012i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.10532e6 | + | 1.02235e6i | −0.0656806 | + | 0.0607504i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.02916e7 | −1.78846 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.02462e7 | 1.18772 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.08047e7 | + | 1.36808e7i | 0.629807 | + | 0.797458i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.95543e7i | − | 2.87017i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.18718e6i | 0.240982i | 0.992714 | + | 0.120491i | \(0.0384469\pi\) | ||||
−0.992714 | + | 0.120491i | \(0.961553\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.31204e6 | − | 3.58083e6i | −0.189410 | − | 0.204782i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.35812e6 | 0.0771786 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44320.7 | 0.00250278 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.08278e7 | + | 4.41413e7i | 2.29107 | + | 2.47701i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.76856e6i | − | 0.433206i | −0.976260 | − | 0.216603i | \(-0.930502\pi\) | ||
0.976260 | − | 0.216603i | \(-0.0694978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.87384e7i | − | 1.03840i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.68411e6 | − | 287766.i | −0.202886 | − | 0.0158474i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.89180e7 | −1.03535 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −990189. | −0.0538553 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.89128e7 | − | 1.74932e7i | 1.02229 | − | 0.945550i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.07918e6i | − | 0.272849i | −0.990650 | − | 0.136424i | \(-0.956439\pi\) | ||
0.990650 | − | 0.136424i | \(-0.0435611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.12586e7i | − | 0.601080i | −0.953769 | − | 0.300540i | \(-0.902833\pi\) | ||
0.953769 | − | 0.300540i | \(-0.0971669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.10957e7 | + | 1.02628e7i | −0.588746 | + | 0.544552i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.43788e7 | −2.34035 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.57982e7 | −0.828041 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −734933. | − | 57405.5i | −0.0382858 | − | 0.00299050i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.80009e7i | − | 0.932043i | −0.884773 | − | 0.466022i | \(-0.845687\pi\) | ||
0.884773 | − | 0.466022i | \(-0.154313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.19550e6i | 0.421770i | 0.977511 | + | 0.210885i | \(0.0676346\pi\) | ||||
−0.977511 | + | 0.210885i | \(0.932365\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.42434e7 | + | 3.70225e7i | 1.75163 | + | 1.89379i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.82150e6 | −0.397673 | −0.198837 | − | 0.980033i | \(-0.563716\pi\) | ||||
−0.198837 | + | 0.980033i | \(0.563716\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.69630e6 | 0.136264 | 0.0681322 | − | 0.997676i | \(-0.478296\pi\) | ||||
0.0681322 | + | 0.997676i | \(0.478296\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.95604e6 | + | 3.19594e6i | 0.148494 | + | 0.160545i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.38584e7i | − | 1.19132i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.59653e7i | − | 0.792430i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.95699e7 | − | 2.47793e7i | −0.965551 | − | 1.22258i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.48635e7 | −0.728979 | −0.364490 | − | 0.931207i | \(-0.618757\pi\) | ||||
−0.364490 | + | 0.931207i | \(0.618757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −668562. | −0.0325951 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.44968e6 | − | 4.11567e6i | 0.215655 | − | 0.199467i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.30180e7i | 1.59078i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 521931.i | − | 0.0249980i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.22393e7 | + | 1.13206e7i | −0.582757 | + | 0.539013i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.82499e6 | −0.228388 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.77927e7 | 1.30785 | 0.653924 | − | 0.756560i | \(-0.273121\pi\) | ||||
0.653924 | + | 0.756560i | \(0.273121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.03573e6 | + | 6.44698e7i | −0.235585 | + | 3.01607i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.73505e7i | − | 0.806974i | −0.914985 | − | 0.403487i | \(-0.867798\pi\) | ||
0.914985 | − | 0.403487i | \(-0.132202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.23238e6i | 0.241945i | 0.992656 | + | 0.120972i | \(0.0386013\pi\) | ||||
−0.992656 | + | 0.120972i | \(0.961399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.71248e6 | + | 1.85145e6i | 0.0787257 | + | 0.0851148i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.61326e7 | −1.19442 | −0.597208 | − | 0.802086i | \(-0.703723\pi\) | ||||
−0.597208 | + | 0.802086i | \(0.703723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.90817e7 | −1.32154 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.80317e6 | − | 7.35528e6i | −0.307371 | − | 0.332316i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.27239e7i | − | 0.571572i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 280477.i | − | 0.0125271i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.66152e6 | − | 2.12715e7i | 0.0737851 | − | 0.944633i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.87958e6 | 0.259613 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.01424e7 | −0.445287 | −0.222644 | − | 0.974900i | \(-0.571469\pi\) | ||||
−0.222644 | + | 0.974900i | \(0.571469\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.35833e7 | − | 1.25637e7i | 0.592970 | − | 0.548459i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.18718e7i | 0.949390i | 0.880150 | + | 0.474695i | \(0.157442\pi\) | ||||
−0.880150 | + | 0.474695i | \(0.842558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.05850e7i | 0.888481i | 0.895908 | + | 0.444241i | \(0.146526\pi\) | ||||
−0.895908 | + | 0.444241i | \(0.853474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.80080e6 | + | 4.44043e6i | −0.206042 | + | 0.190576i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.39584e7 | −0.595698 | −0.297849 | − | 0.954613i | \(-0.596269\pi\) | ||||
−0.297849 | + | 0.954613i | \(0.596269\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.89935e6 | 0.0806031 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.59877e7 | + | 4.08471e6i | 1.09666 | + | 0.172372i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.40689e7i | 1.42965i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.83197e7i | 1.18176i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.60407e6 | − | 1.73425e6i | −0.0665646 | − | 0.0719667i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.83616e7 | 1.58306 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.43550e7 | 2.23063 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 893118. | + | 965599.i | 0.0364493 | + | 0.0394074i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.59097e6i | 0.308089i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.01421e7i | − | 1.21662i | −0.793699 | − | 0.608310i | \(-0.791848\pi\) | ||
0.793699 | − | 0.608310i | \(-0.208152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.18357e7 | + | 1.70558e6i | 0.876512 | + | 0.0684642i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.18404e6 | −0.246874 | −0.123437 | − | 0.992352i | \(-0.539392\pi\) | ||||
−0.123437 | + | 0.992352i | \(0.539392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.39287e6 | 0.134707 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −237632. | + | 219795.i | −0.00938323 | + | 0.00867889i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.45364e6i | 0.174901i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.31915e7i | 0.515237i | 0.966247 | + | 0.257618i | \(0.0829377\pi\) | ||||
−0.966247 | + | 0.257618i | \(0.917062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.94993e6 | + | 8.27812e6i | −0.347673 | + | 0.321575i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.88556e6 | 0.381942 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.02930e7 | 1.93265 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.71332e6 | + | 680596.i | 0.333031 | + | 0.0260130i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.61366e7i | 1.37375i | 0.726776 | + | 0.686875i | \(0.241018\pi\) | ||||
−0.726776 | + | 0.686875i | \(0.758982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.33778e7i | 1.64019i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.06143e7 | − | 1.14757e7i | −0.399195 | − | 0.431592i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.52078e7 | 2.43933 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.72568e7 | 1.75839 | 0.879195 | − | 0.476462i | \(-0.158081\pi\) | ||||
0.879195 | + | 0.476462i | \(0.158081\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.71912e7 | + | 1.85863e7i | 0.636270 | + | 0.687907i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.04002e7i | 1.11919i | 0.828768 | + | 0.559593i | \(0.189042\pi\) | ||||
−0.828768 | + | 0.559593i | \(0.810958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.08201e6i | 0.295965i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.22514e6 | − | 3.33688e6i | 0.153908 | − | 0.121552i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.23838e7 | −1.17342 | −0.586709 | − | 0.809798i | \(-0.699577\pi\) | ||||
−0.586709 | + | 0.809798i | \(0.699577\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.23707e6 | −0.332942 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.35254e7 | + | 2.17595e7i | −0.843501 | + | 0.780185i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.93465e7i | 0.690032i | 0.938597 | + | 0.345016i | \(0.112127\pi\) | ||||
−0.938597 | + | 0.345016i | \(0.887873\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3.13576e7i | − | 1.11259i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.34631e7 | + | 2.17019e7i | −0.828145 | + | 0.765981i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.75034e6 | 0.166793 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.08532e7 | −1.42698 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.06687e6 | − | 3.92636e7i | 0.106569 | − | 1.36434i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.99465e7i | 1.03521i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.67206e7i | − | 1.26282i | −0.775447 | − | 0.631412i | \(-0.782476\pi\) | ||
0.775447 | − | 0.631412i | \(-0.217524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.96937e7 | + | 4.29151e7i | 1.35804 | + | 1.46825i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.16753e7 | −1.75887 | −0.879437 | − | 0.476015i | \(-0.842081\pi\) | ||||
−0.879437 | + | 0.476015i | \(0.842081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.05738e6 | −0.205118 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.67200e7 | + | 1.80769e7i | 0.563280 | + | 0.608993i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 8.88406e6i | − | 0.297766i | −0.988855 | − | 0.148883i | \(-0.952432\pi\) | ||
0.988855 | − | 0.148883i | \(-0.0475678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.77488e6i | − | 0.225915i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.96868e6 | − | 5.08090e7i | 0.131666 | − | 1.68565i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.34925e6 | 0.209575 | 0.104787 | − | 0.994495i | \(-0.466584\pi\) | ||||
0.104787 | + | 0.994495i | \(0.466584\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.96704e7 | −0.974391 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.08232e6 | − | 1.92602e6i | 0.0680386 | − | 0.0629314i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.21506e6i | 0.137029i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.45077e7i | 1.43963i | 0.694166 | + | 0.719815i | \(0.255774\pi\) | ||||
−0.694166 | + | 0.719815i | \(0.744226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.40917e7 | + | 3.15327e7i | −1.09717 | + | 1.01482i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.13413e7 | −2.28446 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.05424e7 | −1.92895 | −0.964477 | − | 0.264166i | \(-0.914903\pi\) | ||||
−0.964477 | + | 0.264166i | \(0.914903\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.05883e7 | − | 1.62600e7i | 0.652689 | − | 0.515473i |
(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 | 384.6.c.b.383.16 | yes | 20 | |
3.2 | odd | 2 | 384.6.c.c.383.6 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.c.383.5 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.a.383.16 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.d.383.5 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.b.383.15 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.a.383.15 | ✓ | 20 | ||
24.11 | even | 2 | 384.6.c.d.383.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.15 | ✓ | 20 | 24.5 | odd | 2 | ||
384.6.c.a.383.16 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.b.383.15 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.b.383.16 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.c.c.383.5 | yes | 20 | 4.3 | odd | 2 | ||
384.6.c.c.383.6 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.d.383.5 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.d.383.6 | yes | 20 | 24.11 | even | 2 |