Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(639,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.639");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.e (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: | \(34.8774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 639.16 | ||
Character | \(\chi\) | \(=\) | 1280.639 |
Dual form | 1280.3.e.l.639.15 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 4.20423i | 1.40141i | 0.713452 | + | 0.700704i | \(0.247131\pi\) | ||||
−0.713452 | + | 0.700704i | \(0.752869\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.52118 | − | 4.76298i | −0.304237 | − | 0.952597i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.29905 | −0.471292 | −0.235646 | − | 0.971839i | \(-0.575721\pi\) | ||||
−0.235646 | + | 0.971839i | \(0.575721\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.67551 | −0.963946 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.0633 | 1.36939 | 0.684697 | − | 0.728828i | \(-0.259935\pi\) | ||||
0.684697 | + | 0.728828i | \(0.259935\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.02352 | −0.540271 | −0.270136 | − | 0.962822i | \(-0.587069\pi\) | ||||
−0.270136 | + | 0.962822i | \(0.587069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.0247 | − | 6.39540i | 1.33498 | − | 0.426360i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.9181i | 0.936359i | 0.883633 | + | 0.468180i | \(0.155090\pi\) | ||||
−0.883633 | + | 0.468180i | \(0.844910\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.8928 | −0.678569 | −0.339284 | − | 0.940684i | \(-0.610185\pi\) | ||||
−0.339284 | + | 0.940684i | \(0.610185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 13.8699i | − | 0.660473i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.49441 | −0.151931 | −0.0759655 | − | 0.997110i | \(-0.524204\pi\) | ||||
−0.0759655 | + | 0.997110i | \(0.524204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.3720 | + | 14.4907i | −0.814880 | + | 0.579629i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.36422i | 0.0505267i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.1653i | 0.453977i | 0.973897 | + | 0.226989i | \(0.0728880\pi\) | ||||
−0.973897 | + | 0.226989i | \(0.927112\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 38.2295i | − | 1.23321i | −0.787273 | − | 0.616605i | \(-0.788508\pi\) | ||
0.787273 | − | 0.616605i | \(-0.211492\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 63.3296i | 1.91908i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.01845 | + | 15.7133i | 0.143384 | + | 0.448951i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −68.5124 | −1.85169 | −0.925843 | − | 0.377908i | \(-0.876644\pi\) | ||||
−0.925843 | + | 0.377908i | \(0.876644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 29.5285i | − | 0.757140i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 57.3992 | 1.39998 | 0.699990 | − | 0.714153i | \(-0.253188\pi\) | ||||
0.699990 | + | 0.714153i | \(0.253188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 51.9027i | − | 1.20704i | −0.797348 | − | 0.603520i | \(-0.793764\pi\) | ||
0.797348 | − | 0.603520i | \(-0.206236\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.1970 | + | 41.3213i | 0.293268 | + | 0.918251i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 34.0218 | 0.723868 | 0.361934 | − | 0.932204i | \(-0.382116\pi\) | ||||
0.361934 | + | 0.932204i | \(0.382116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −38.1163 | −0.777883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −66.9233 | −1.31222 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −79.9172 | −1.50787 | −0.753936 | − | 0.656948i | \(-0.771847\pi\) | ||||
−0.753936 | + | 0.656948i | \(0.771847\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22.9141 | − | 71.7464i | −0.416620 | − | 1.30448i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 54.2042i | − | 0.950952i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −114.933 | −1.94802 | −0.974012 | − | 0.226497i | \(-0.927273\pi\) | ||||
−0.974012 | + | 0.226497i | \(0.927273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 115.485i | − | 1.89320i | −0.322404 | − | 0.946602i | \(-0.604491\pi\) | ||
0.322404 | − | 0.946602i | \(-0.395509\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 28.6209 | 0.454300 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.6841 | + | 33.4529i | 0.164370 | + | 0.514660i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 63.3874i | 0.946081i | 0.881041 | + | 0.473040i | \(0.156844\pi\) | ||||
−0.881041 | + | 0.473040i | \(0.843156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 14.6913i | − | 0.212917i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 40.1984i | − | 0.566175i | −0.959094 | − | 0.283088i | \(-0.908641\pi\) | ||
0.959094 | − | 0.283088i | \(-0.0913587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.16321i | 0.0296331i | 0.999890 | + | 0.0148165i | \(0.00471642\pi\) | ||||
−0.999890 | + | 0.0148165i | \(0.995284\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −60.9223 | − | 85.6485i | −0.812298 | − | 1.14198i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −49.6946 | −0.645385 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 78.1874i | 0.989714i | 0.868975 | + | 0.494857i | \(0.164780\pi\) | ||||
−0.868975 | + | 0.494857i | \(0.835220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −83.8151 | −1.03475 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 61.5753i | − | 0.741871i | −0.928659 | − | 0.370935i | \(-0.879037\pi\) | ||
0.928659 | − | 0.370935i | \(-0.120963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 75.8177 | − | 24.2144i | 0.891973 | − | 0.284875i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −55.3501 | −0.636208 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.04779 | 0.0679527 | 0.0339764 | − | 0.999423i | \(-0.489183\pi\) | ||||
0.0339764 | + | 0.999423i | \(0.489183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.1709 | 0.254626 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 160.725 | 1.72823 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.6123 | + | 61.4082i | 0.206445 | + | 0.646402i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 135.240i | − | 1.39422i | −0.716962 | − | 0.697112i | \(-0.754468\pi\) | ||
0.716962 | − | 0.697112i | \(-0.245532\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −130.682 | −1.32002 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 112.667i | 1.11552i | 0.830002 | + | 0.557760i | \(0.188339\pi\) | ||||
−0.830002 | + | 0.557760i | \(0.811661\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 38.6668 | 0.375406 | 0.187703 | − | 0.982226i | \(-0.439896\pi\) | ||||
0.187703 | + | 0.982226i | \(0.439896\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −66.0623 | + | 21.0987i | −0.629164 | + | 0.200940i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 198.172i | − | 1.85207i | −0.377436 | − | 0.926036i | \(-0.623194\pi\) | ||
0.377436 | − | 0.926036i | \(-0.376806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 48.3119i | 0.443229i | 0.975134 | + | 0.221614i | \(0.0711326\pi\) | ||||
−0.975134 | + | 0.221614i | \(0.928867\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 288.042i | − | 2.59497i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 75.4754i | 0.667924i | 0.942587 | + | 0.333962i | \(0.108386\pi\) | ||||
−0.942587 | + | 0.333962i | \(0.891614\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.31564 | + | 16.6438i | 0.0462230 | + | 0.144729i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 60.9327 | 0.520792 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 52.5146i | − | 0.441299i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 105.904 | 0.875239 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 241.319i | 1.96194i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 100.009 | + | 74.9884i | 0.800069 | + | 0.599908i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 69.4328 | 0.546715 | 0.273357 | − | 0.961913i | \(-0.411866\pi\) | ||||
0.273357 | + | 0.961913i | \(0.411866\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 218.211 | 1.69156 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −145.813 | −1.11308 | −0.556538 | − | 0.830822i | \(-0.687871\pi\) | ||||
−0.556538 | + | 0.830822i | \(0.687871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 42.5340 | 0.319804 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.49776 | − | 2.07523i | 0.0481316 | − | 0.0153721i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 176.955i | − | 1.29165i | −0.763487 | − | 0.645823i | \(-0.776514\pi\) | ||
0.763487 | − | 0.645823i | \(-0.223486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −56.3119 | −0.405122 | −0.202561 | − | 0.979270i | \(-0.564926\pi\) | ||||
−0.202561 | + | 0.979270i | \(0.564926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 143.035i | 1.01444i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −105.798 | −0.739844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 62.7063 | − | 20.0269i | 0.432457 | − | 0.138117i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 160.249i | − | 1.09013i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 97.1333i | − | 0.651901i | −0.945387 | − | 0.325951i | \(-0.894316\pi\) | ||
0.945387 | − | 0.325951i | \(-0.105684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 64.8671i | − | 0.429583i | −0.976660 | − | 0.214792i | \(-0.931093\pi\) | ||
0.976660 | − | 0.214792i | \(-0.0689073\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 138.098i | − | 0.902600i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −182.086 | + | 58.1541i | −1.17475 | + | 0.375188i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −235.678 | −1.50113 | −0.750566 | − | 0.660795i | \(-0.770219\pi\) | ||||
−0.750566 | + | 0.660795i | \(0.770219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 335.990i | − | 2.11314i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.5282 | 0.0716040 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 130.259i | − | 0.799135i | −0.916704 | − | 0.399568i | \(-0.869160\pi\) | ||
0.916704 | − | 0.399568i | \(-0.130840\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 301.638 | − | 96.3360i | 1.82811 | − | 0.583854i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 96.7078 | 0.579088 | 0.289544 | − | 0.957165i | \(-0.406496\pi\) | ||||
0.289544 | + | 0.957165i | \(0.406496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −119.670 | −0.708107 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 111.852 | 0.654103 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 134.520 | 0.777571 | 0.388785 | − | 0.921328i | \(-0.372895\pi\) | ||||
0.388785 | + | 0.921328i | \(0.372895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 67.2082 | − | 47.8056i | 0.384047 | − | 0.273175i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 483.206i | − | 2.72998i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.17197 | 0.0456535 | 0.0228267 | − | 0.999739i | \(-0.492733\pi\) | ||||
0.0228267 | + | 0.999739i | \(0.492733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 126.462i | 0.698682i | 0.936996 | + | 0.349341i | \(0.113595\pi\) | ||||
−0.936996 | + | 0.349341i | \(0.886405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 485.527 | 2.65315 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 104.220 | + | 326.323i | 0.563351 | + | 1.76391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 239.780i | 1.28224i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 4.50063i | − | 0.0238129i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 40.9687i | − | 0.214496i | −0.994232 | − | 0.107248i | \(-0.965796\pi\) | ||
0.994232 | − | 0.107248i | \(-0.0342039\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 152.812i | 0.791772i | 0.918300 | + | 0.395886i | \(0.129562\pi\) | ||||
−0.918300 | + | 0.395886i | \(0.870438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −140.644 | + | 44.9182i | −0.721249 | + | 0.230350i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −140.383 | −0.712605 | −0.356303 | − | 0.934371i | \(-0.615963\pi\) | ||||
−0.356303 | + | 0.934371i | \(0.615963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 108.191i | − | 0.543675i | −0.962343 | − | 0.271838i | \(-0.912369\pi\) | ||
0.962343 | − | 0.271838i | \(-0.0876313\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −266.495 | −1.32585 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 43.4331i | − | 0.213956i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −87.3147 | − | 273.391i | −0.425925 | − | 1.33362i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 30.3158 | 0.146453 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −194.209 | −0.929228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 310.419 | 1.47118 | 0.735591 | − | 0.677426i | \(-0.236904\pi\) | ||||
0.735591 | + | 0.677426i | \(0.236904\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 169.003 | 0.793443 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −247.212 | + | 78.9536i | −1.14982 | + | 0.367226i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 126.121i | 0.581203i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.09464 | −0.0415280 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 111.801i | − | 0.505888i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −339.638 | −1.52304 | −0.761520 | − | 0.648141i | \(-0.775547\pi\) | ||||
−0.761520 | + | 0.648141i | \(0.775547\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 176.738 | − | 125.715i | 0.785500 | − | 0.558731i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 143.631i | 0.632738i | 0.948636 | + | 0.316369i | \(0.102464\pi\) | ||||
−0.948636 | + | 0.316369i | \(0.897536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 153.318i | 0.669512i | 0.942305 | + | 0.334756i | \(0.108654\pi\) | ||||
−0.942305 | + | 0.334756i | \(0.891346\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 208.927i | − | 0.904448i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 40.0757i | 0.171999i | 0.996295 | + | 0.0859994i | \(0.0274083\pi\) | ||||
−0.996295 | + | 0.0859994i | \(0.972592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −51.7534 | − | 162.045i | −0.220227 | − | 0.689555i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −328.717 | −1.38699 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 246.016i | 1.02936i | 0.857383 | + | 0.514678i | \(0.172089\pi\) | ||||
−0.857383 | + | 0.514678i | \(0.827911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −235.407 | −0.976795 | −0.488397 | − | 0.872621i | \(-0.662418\pi\) | ||||
−0.488397 | + | 0.872621i | \(0.662418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 340.100i | − | 1.39959i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 57.9818 | + | 181.547i | 0.236661 | + | 0.741009i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 90.5529 | 0.366611 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 258.876 | 1.03966 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −91.4700 | −0.364422 | −0.182211 | − | 0.983259i | \(-0.558325\pi\) | ||||
−0.182211 | + | 0.983259i | \(0.558325\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −52.6375 | −0.208053 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 101.803 | + | 318.755i | 0.399226 | + | 1.25002i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 102.175i | 0.397570i | 0.980043 | + | 0.198785i | \(0.0636995\pi\) | ||||
−0.980043 | + | 0.198785i | \(0.936300\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 226.026 | 0.872686 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 114.216i | − | 0.437610i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −230.059 | −0.874748 | −0.437374 | − | 0.899280i | \(-0.644091\pi\) | ||||
−0.437374 | + | 0.899280i | \(0.644091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 121.569 | + | 380.644i | 0.458750 | + | 1.43639i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.4263i | 0.0952295i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 312.598i | − | 1.16207i | −0.813877 | − | 0.581037i | \(-0.802647\pi\) | ||
0.813877 | − | 0.581037i | \(-0.197353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 115.473i | 0.426101i | 0.977041 | + | 0.213050i | \(0.0683398\pi\) | ||||
−0.977041 | + | 0.213050i | \(0.931660\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 97.4158i | 0.356834i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −306.870 | + | 218.279i | −1.11589 | + | 0.793741i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −303.255 | −1.09478 | −0.547391 | − | 0.836877i | \(-0.684379\pi\) | ||||
−0.547391 | + | 0.836877i | \(0.684379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 331.661i | 1.18875i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −82.8094 | −0.294695 | −0.147348 | − | 0.989085i | \(-0.547074\pi\) | ||||
−0.147348 | + | 0.989085i | \(0.547074\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 336.752i | 1.18994i | 0.803749 | + | 0.594968i | \(0.202835\pi\) | ||||
−0.803749 | + | 0.594968i | \(0.797165\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −258.174 | + | 82.4546i | −0.905873 | + | 0.289314i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −189.363 | −0.659800 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.6137 | 0.123231 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 568.579 | 1.95388 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −472.607 | −1.61299 | −0.806496 | − | 0.591239i | \(-0.798639\pi\) | ||||
−0.806496 | + | 0.591239i | \(0.798639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 174.835 | + | 547.426i | 0.592660 | + | 1.85568i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.5497i | 0.0691910i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.5431 | 0.0820840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 171.230i | 0.568869i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −473.679 | −1.56330 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −550.055 | + | 175.675i | −1.80346 | + | 0.575982i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 52.5748i | − | 0.171253i | −0.996327 | − | 0.0856267i | \(-0.972711\pi\) | ||
0.996327 | − | 0.0856267i | \(-0.0272892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 162.564i | 0.526097i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 277.403i | − | 0.891971i | −0.895040 | − | 0.445985i | \(-0.852853\pi\) | ||
0.895040 | − | 0.445985i | \(-0.147147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 89.6314i | 0.286362i | 0.989696 | + | 0.143181i | \(0.0457332\pi\) | ||||
−0.989696 | + | 0.143181i | \(0.954267\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −43.5377 | − | 136.321i | −0.138215 | − | 0.432765i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −308.408 | −0.972897 | −0.486449 | − | 0.873709i | \(-0.661708\pi\) | ||||
−0.486449 | + | 0.873709i | \(0.661708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 198.314i | 0.621674i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 833.158 | 2.59551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 205.229i | − | 0.635384i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 143.083 | − | 101.776i | 0.440256 | − | 0.313157i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −203.114 | −0.621145 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −112.240 | −0.341154 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 181.666 | 0.548839 | 0.274419 | − | 0.961610i | \(-0.411514\pi\) | ||||
0.274419 | + | 0.961610i | \(0.411514\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 594.380 | 1.78493 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 301.913 | − | 96.4239i | 0.901233 | − | 0.287832i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 111.419i | 0.330621i | 0.986242 | + | 0.165310i | \(0.0528625\pi\) | ||||
−0.986242 | + | 0.165310i | \(0.947137\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −317.316 | −0.936034 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 575.864i | − | 1.68875i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 287.401 | 0.837903 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −69.9744 | + | 22.3482i | −0.202824 | + | 0.0647773i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 518.938i | − | 1.49550i | −0.663982 | − | 0.747749i | \(-0.731135\pi\) | ||
0.663982 | − | 0.747749i | \(-0.268865\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 299.596i | 0.858441i | 0.903200 | + | 0.429221i | \(0.141212\pi\) | ||||
−0.903200 | + | 0.429221i | \(0.858788\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9.58164i | − | 0.0272981i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 594.251i | 1.68343i | 0.539922 | + | 0.841715i | \(0.318454\pi\) | ||||
−0.539922 | + | 0.841715i | \(0.681546\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −191.464 | + | 61.1492i | −0.539336 | + | 0.172251i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 220.783 | 0.618440 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 229.119i | 0.638216i | 0.947718 | + | 0.319108i | \(0.103383\pi\) | ||||
−0.947718 | + | 0.319108i | \(0.896617\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −194.776 | −0.539545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 445.244i | 1.22657i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.3033 | − | 3.29064i | 0.0282283 | − | 0.00901546i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 90.0376 | 0.245334 | 0.122667 | − | 0.992448i | \(-0.460855\pi\) | ||||
0.122667 | + | 0.992448i | \(0.460855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −497.967 | −1.34950 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 263.651 | 0.710649 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −423.979 | −1.13667 | −0.568336 | − | 0.822796i | \(-0.692413\pi\) | ||||
−0.568336 | + | 0.822796i | \(0.692413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −315.268 | + | 420.459i | −0.840716 | + | 1.12122i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 92.4671i | − | 0.245271i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 410.116 | 1.08210 | 0.541051 | − | 0.840990i | \(-0.318027\pi\) | ||||
0.541051 | + | 0.840990i | \(0.318027\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 291.911i | 0.766171i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 741.842 | 1.93692 | 0.968462 | − | 0.249163i | \(-0.0801554\pi\) | ||||
0.968462 | + | 0.249163i | \(0.0801554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 75.5946 | + | 236.695i | 0.196350 | + | 0.614791i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 450.283i | 1.16352i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 179.045i | − | 0.460270i | −0.973159 | − | 0.230135i | \(-0.926083\pi\) | ||
0.973159 | − | 0.230135i | \(-0.0739168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 55.6245i | − | 0.142262i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 613.030i | − | 1.55987i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 372.405 | − | 118.937i | 0.942798 | − | 0.301107i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 81.9906 | 0.206525 | 0.103263 | − | 0.994654i | \(-0.467072\pi\) | ||||
0.103263 | + | 0.994654i | \(0.467072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 178.822i | 0.448176i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −146.981 | −0.366537 | −0.183269 | − | 0.983063i | \(-0.558668\pi\) | ||||
−0.183269 | + | 0.983063i | \(0.558668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 268.506i | 0.666268i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 127.498 | + | 399.210i | 0.314810 | + | 0.985703i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1032.02 | −2.53569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −142.051 | −0.347313 | −0.173656 | − | 0.984806i | \(-0.555558\pi\) | ||||
−0.173656 | + | 0.984806i | \(0.555558\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 743.961 | 1.81012 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 379.171 | 0.918089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −293.282 | + | 93.6673i | −0.706704 | + | 0.225704i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 236.748i | − | 0.567741i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −225.166 | −0.537389 | −0.268694 | − | 0.963225i | \(-0.586592\pi\) | ||||
−0.268694 | + | 0.963225i | \(0.586592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 360.197i | − | 0.855575i | −0.903879 | − | 0.427788i | \(-0.859293\pi\) | ||
0.903879 | − | 0.427788i | \(-0.140707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −295.157 | −0.697770 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −230.665 | − | 324.284i | −0.542741 | − | 0.763021i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 380.992i | 0.892253i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 444.797i | − | 1.03682i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 54.0689i | − | 0.125450i | −0.998031 | − | 0.0627249i | \(-0.980021\pi\) | ||
0.998031 | − | 0.0627249i | \(-0.0199791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 169.117i | − | 0.390571i | −0.980746 | − | 0.195285i | \(-0.937437\pi\) | ||
0.980746 | − | 0.195285i | \(-0.0625633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 84.1976 | + | 263.631i | 0.193558 | + | 0.606049i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45.0528 | 0.103096 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 645.558i | 1.47052i | 0.677785 | + | 0.735260i | \(0.262940\pi\) | ||||
−0.677785 | + | 0.735260i | \(0.737060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 330.678 | 0.749837 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 478.360i | − | 1.07982i | −0.841723 | − | 0.539910i | \(-0.818458\pi\) | ||
0.841723 | − | 0.539910i | \(-0.181542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.19980 | − | 28.8055i | −0.0206737 | − | 0.0647315i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 408.370 | 0.913580 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 628.735 | 1.40030 | 0.700150 | − | 0.713996i | \(-0.253116\pi\) | ||||
0.700150 | + | 0.713996i | \(0.253116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 864.623 | 1.91712 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 272.716 | 0.602022 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −35.2472 | − | 110.363i | −0.0774664 | − | 0.242555i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 121.818i | 0.266560i | 0.991078 | + | 0.133280i | \(0.0425510\pi\) | ||||
−0.991078 | + | 0.133280i | \(0.957449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.7158 | −0.0473112 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 152.537i | 0.330883i | 0.986220 | + | 0.165441i | \(0.0529049\pi\) | ||||
−0.986220 | + | 0.165441i | \(0.947095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −368.130 | −0.795097 | −0.397549 | − | 0.917581i | \(-0.630139\pi\) | ||||
−0.397549 | + | 0.917581i | \(0.630139\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −244.493 | − | 765.533i | −0.525791 | − | 1.64631i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 741.896i | 1.58864i | 0.607498 | + | 0.794321i | \(0.292173\pi\) | ||||
−0.607498 | + | 0.794321i | \(0.707827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 209.118i | − | 0.445881i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 990.842i | − | 2.10370i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 781.828i | − | 1.65291i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 262.652 | − | 186.826i | 0.552952 | − | 0.393318i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 693.323 | 1.45351 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 620.600i | 1.29562i | 0.761803 | + | 0.647808i | \(0.224314\pi\) | ||||
−0.761803 | + | 0.647808i | \(0.775686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 481.198 | 1.00041 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 48.4673i | 0.100346i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −644.145 | + | 205.724i | −1.32813 | + | 0.424174i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 525.738 | 1.07954 | 0.539772 | − | 0.841811i | \(-0.318510\pi\) | ||||
0.539772 | + | 0.841811i | \(0.318510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 547.639 | 1.11992 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 695.125 | 1.41573 | 0.707867 | − | 0.706346i | \(-0.249658\pi\) | ||||
0.707867 | + | 0.706346i | \(0.249658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −209.567 | −0.425086 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 198.791 | + | 622.437i | 0.401599 | + | 1.25745i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 132.617i | 0.266834i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 494.103 | 0.990186 | 0.495093 | − | 0.868840i | \(-0.335134\pi\) | ||||
0.495093 | + | 0.868840i | \(0.335134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 406.581i | 0.811539i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 881.187 | 1.75186 | 0.875931 | − | 0.482436i | \(-0.160248\pi\) | ||||
0.875931 | + | 0.482436i | \(0.160248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 536.633 | − | 171.388i | 1.06264 | − | 0.339382i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 503.120i | − | 0.992347i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 676.617i | 1.32931i | 0.747152 | + | 0.664653i | \(0.231421\pi\) | ||||
−0.747152 | + | 0.664653i | \(0.768579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.13654i | − | 0.0139658i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 17.5886i | − | 0.0342858i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −58.8193 | − | 184.169i | −0.114212 | − | 0.357610i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 512.482 | 0.991261 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 565.551i | 1.08969i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 139.017 | 0.266828 | 0.133414 | − | 0.991060i | \(-0.457406\pi\) | ||||
0.133414 | + | 0.991060i | \(0.457406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 506.388i | 0.968237i | 0.875002 | + | 0.484119i | \(0.160860\pi\) | ||||
−0.875002 | + | 0.484119i | \(0.839140\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 200.986 | + | 282.558i | 0.382830 | + | 0.538207i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 608.542 | 1.15473 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −516.789 | −0.976917 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 997.106 | 1.87779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −403.144 | −0.756369 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −943.888 | + | 301.455i | −1.76428 | + | 0.563468i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.3568i | 0.0639792i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −574.158 | −1.06523 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 771.126i | − | 1.42537i | −0.701484 | − | 0.712686i | \(-0.747479\pi\) | ||
0.701484 | − | 0.712686i | \(-0.252521\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −531.673 | −0.979139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 230.109 | − | 73.4913i | 0.422218 | − | 0.134846i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 551.675i | − | 1.00855i | −0.863544 | − | 0.504274i | \(-0.831760\pi\) | ||
0.863544 | − | 0.504274i | \(-0.168240\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1001.90i | 1.82495i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 169.738i | − | 0.308055i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 257.944i | − | 0.466445i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1371.94 | + | 438.164i | −2.47196 | + | 0.789484i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 971.376 | 1.74394 | 0.871972 | − | 0.489556i | \(-0.162841\pi\) | ||||
0.871972 | + | 0.489556i | \(0.162841\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 364.540i | 0.652129i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1008.09 | −1.79695 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 721.489i | 1.28151i | 0.767747 | + | 0.640754i | \(0.221378\pi\) | ||||
−0.767747 | + | 0.640754i | \(0.778622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 359.488 | − | 114.812i | 0.636262 | − | 0.203207i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 276.510 | 0.487672 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 288.369 | 0.506799 | 0.253400 | − | 0.967362i | \(-0.418451\pi\) | ||||
0.253400 | + | 0.967362i | \(0.418451\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 706.199 | 1.23678 | 0.618388 | − | 0.785873i | \(-0.287786\pi\) | ||||
0.618388 | + | 0.785873i | \(0.287786\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 172.242 | 0.300596 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 71.1882 | − | 50.6366i | 0.123806 | − | 0.0880637i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 749.954i | 1.29975i | 0.760042 | + | 0.649873i | \(0.225178\pi\) | ||||
−0.760042 | + | 0.649873i | \(0.774822\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −642.456 | −1.10960 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 203.140i | 0.349638i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1203.82 | −2.06487 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −92.6897 | − | 290.221i | −0.158444 | − | 0.496105i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 310.310i | 0.528637i | 0.964435 | + | 0.264319i | \(0.0851471\pi\) | ||||
−0.964435 | + | 0.264319i | \(0.914853\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 492.886i | 0.836818i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 590.203i | − | 0.998651i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1336i | 0.0322657i | 0.999870 | + | 0.0161329i | \(0.00513547\pi\) | ||||
−0.999870 | + | 0.0161329i | \(0.994865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −250.126 | + | 79.8843i | −0.420380 | + | 0.134259i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 454.861 | 0.761911 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 704.211i | − | 1.17564i | −0.808990 | − | 0.587822i | \(-0.799985\pi\) | ||
0.808990 | − | 0.587822i | \(-0.200015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 284.816 | 0.473903 | 0.236952 | − | 0.971521i | \(-0.423852\pi\) | ||||
0.236952 | + | 0.971521i | \(0.423852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 549.918i | − | 0.911971i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −161.099 | − | 504.419i | −0.266280 | − | 0.833750i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1114.68 | −1.83638 | −0.918191 | − | 0.396138i | \(-0.870350\pi\) | ||||
−0.918191 | + | 0.396138i | \(0.870350\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 182.602 | 0.299840 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −238.953 | −0.391085 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 81.0578 | 0.132231 | 0.0661156 | − | 0.997812i | \(-0.478939\pi\) | ||||
0.0661156 | + | 0.997812i | \(0.478939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1149.40 | − | 367.090i | 1.86894 | − | 0.596895i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 205.581i | 0.333194i | 0.986025 | + | 0.166597i | \(0.0532780\pi\) | ||||
−0.986025 | + | 0.166597i | \(0.946722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −227.970 | −0.368287 | −0.184144 | − | 0.982899i | \(-0.558951\pi\) | ||||
−0.184144 | + | 0.982899i | \(0.558951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 4.76715i | − | 0.00767658i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.9519 | −0.0320256 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 205.037 | − | 590.411i | 0.328060 | − | 0.944657i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 816.497i | − | 1.30223i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1090.59i | − | 1.73384i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 936.003i | 1.48336i | 0.670751 | + | 0.741682i | \(0.265972\pi\) | ||||
−0.670751 | + | 0.741682i | \(0.734028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1305.07i | 2.06173i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −105.620 | − | 330.707i | −0.166331 | − | 0.520799i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 267.711 | 0.420268 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 348.742i | 0.545762i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −308.970 | −0.482013 | −0.241007 | − | 0.970524i | \(-0.577478\pi\) | ||||
−0.241007 | + | 0.970524i | \(0.577478\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 556.493i | − | 0.865463i | −0.901523 | − | 0.432732i | \(-0.857550\pi\) | ||
0.901523 | − | 0.432732i | \(-0.142450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −331.939 | − | 1039.33i | −0.514633 | − | 1.61137i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 142.746 | 0.220628 | 0.110314 | − | 0.993897i | \(-0.464814\pi\) | ||||
0.110314 | + | 0.993897i | \(0.464814\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1731.28 | −2.66761 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −530.241 | −0.814502 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1034.40 | −1.58408 | −0.792040 | − | 0.610469i | \(-0.790981\pi\) | ||||
−0.792040 | + | 0.610469i | \(0.790981\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 221.808 | + | 694.504i | 0.338638 | + | 1.06031i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 18.7670i | − | 0.0285647i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −690.873 | −1.04837 | −0.524183 | − | 0.851606i | \(-0.675629\pi\) | ||||
−0.524183 | + | 0.851606i | \(0.675629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 926.204i | 1.40122i | 0.713546 | + | 0.700608i | \(0.247088\pi\) | ||||
−0.713546 | + | 0.700608i | \(0.752912\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 470.038 | 0.708956 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −64.7019 | − | 202.588i | −0.0972961 | − | 0.304644i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 46.0052i | − | 0.0689733i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1427.92i | − | 2.13440i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1739.60i | − | 2.59254i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 729.553i | − | 1.08403i | −0.840368 | − | 0.542016i | \(-0.817661\pi\) | ||
0.840368 | − | 0.542016i | \(-0.182339\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.7686 | − | 27.7919i | −0.0292868 | − | 0.0411732i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 229.836 | 0.339492 | 0.169746 | − | 0.985488i | \(-0.445705\pi\) | ||||
0.169746 | + | 0.985488i | \(0.445705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 446.162i | 0.657087i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −603.859 | −0.886724 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 76.7080i | 0.112310i | 0.998422 | + | 0.0561552i | \(0.0178842\pi\) | ||||
−0.998422 | + | 0.0561552i | \(0.982116\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −842.836 | + | 269.182i | −1.23042 | + | 0.392966i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −644.585 | −0.938260 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 561.300 | 0.814660 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1008.82 | −1.45995 | −0.729974 | − | 0.683475i | \(-0.760468\pi\) | ||||
−0.729974 | + | 0.683475i | \(0.760468\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 431.126 | 0.622116 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 85.6607 | + | 268.213i | 0.123253 | + | 0.385917i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 913.687i | 1.31088i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −168.487 | −0.241041 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 692.820i | 0.988331i | 0.869368 | + | 0.494165i | \(0.164526\pi\) | ||||
−0.869368 | + | 0.494165i | \(0.835474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 883.317 | 1.25650 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 681.275 | − | 217.583i | 0.966348 | − | 0.308628i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 371.695i | − | 0.525736i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.2200i | 0.0228773i | 0.999935 | + | 0.0114386i | \(0.00364111\pi\) | ||||
−0.999935 | + | 0.0114386i | \(0.996359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 678.316i | − | 0.954030i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 133.590i | 0.187363i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 160.938 | + | 503.912i | 0.225088 | + | 0.704773i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1034.31 | −1.44255 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1007.80i | − | 1.40168i | −0.713321 | − | 0.700838i | \(-0.752810\pi\) | ||
0.713321 | − | 0.700838i | \(-0.247190\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −127.564 | −0.176926 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 989.706i | − | 1.36889i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −190.775 | − | 268.204i | −0.263139 | − | 0.369937i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −58.2441 | −0.0801157 | −0.0400579 | − | 0.999197i | \(-0.512754\pi\) | ||||
−0.0400579 | + | 0.999197i | \(0.512754\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 675.519 | 0.926638 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 826.194 | 1.13022 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1340.52 | −1.82882 | −0.914409 | − | 0.404791i | \(-0.867344\pi\) | ||||
−0.914409 | + | 0.404791i | \(0.867344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −763.265 | + | 243.769i | −1.03846 | + | 0.331658i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 954.826i | 1.29556i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 806.666 | 1.09156 | 0.545782 | − | 0.837927i | \(-0.316233\pi\) | ||||
0.545782 | + | 0.837927i | \(0.316233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 380.705i | 0.513772i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1051.63 | −1.41538 | −0.707692 | − | 0.706521i | \(-0.750264\pi\) | ||||
−0.707692 | + | 0.706521i | \(0.750264\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −462.644 | + | 147.758i | −0.620999 | + | 0.198332i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 534.197i | 0.715123i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 653.777i | 0.872867i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 392.921i | − | 0.523196i | −0.965177 | − | 0.261598i | \(-0.915750\pi\) | ||
0.965177 | − | 0.261598i | \(-0.0842495\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 384.561i | − | 0.510705i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −308.961 | + | 98.6747i | −0.409220 | + | 0.130695i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 485.104 | 0.640825 | 0.320412 | − | 0.947278i | \(-0.396178\pi\) | ||||
0.320412 | + | 0.947278i | \(0.396178\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 221.300i | − | 0.291568i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.6127 | −0.0612519 | −0.0306260 | − | 0.999531i | \(-0.509750\pi\) | ||||
−0.0306260 | + | 0.999531i | \(0.509750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 159.383i | − | 0.208890i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −657.757 | + | 210.072i | −0.859813 | + | 0.274604i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 807.237 | 1.05246 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 859.032 | 1.11708 | 0.558538 | − | 0.829479i | \(-0.311362\pi\) | ||||
0.558538 | + | 0.829479i | \(0.311362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −429.569 | −0.557158 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1004.82 | −1.29990 | −0.649951 | − | 0.759976i | \(-0.725211\pi\) | ||||
−0.649951 | + | 0.759976i | \(0.725211\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 553.974 | + | 778.812i | 0.714805 | + | 1.00492i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 950.263i | 1.22299i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −740.036 | −0.949982 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 605.522i | − | 0.775317i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.9604 | −0.0229380 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 358.509 | + | 1122.53i | 0.456699 | + | 1.42997i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 250.881i | 0.318781i | 0.987216 | + | 0.159391i | \(0.0509529\pi\) | ||||
−0.987216 | + | 0.159391i | \(0.949047\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 967.219i | − | 1.22588i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 248.997i | − | 0.314787i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 811.115i | 1.02284i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1600.31 | + | 511.102i | −2.01297 | + | 0.642896i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 803.365 | 1.00799 | 0.503993 | − | 0.863708i | \(-0.331864\pi\) | ||||
0.503993 | + | 0.863708i | \(0.331864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 541.563i | 0.677801i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −52.4677 | −0.0655027 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.5852i | 0.0405793i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.5366 | − | 54.9088i | −0.0217845 | − | 0.0682097i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1314.23 | 1.62854 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 254.545 | 0.314642 | 0.157321 | − | 0.987548i | \(-0.449714\pi\) | ||||
0.157321 | + | 0.987548i | \(0.449714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1316.92 | 1.62382 | 0.811912 | − | 0.583779i | \(-0.198427\pi\) | ||||
0.811912 | + | 0.583779i | \(0.198427\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −485.476 | −0.597141 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −620.422 | + | 198.148i | −0.761254 | + | 0.243126i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 669.172i | 0.819060i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −201.020 | −0.245445 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 597.540i | 0.727820i | 0.931434 | + | 0.363910i | \(0.118558\pi\) | ||||
−0.931434 | + | 0.363910i | \(0.881442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1511.87 | 1.83702 | 0.918510 | − | 0.395399i | \(-0.129394\pi\) | ||||
0.918510 | + | 0.395399i | \(0.129394\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −917.693 | − | 1290.15i | −1.11236 | − | 1.56382i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 750.703i | 0.907743i | 0.891067 | + | 0.453871i | \(0.149957\pi\) | ||||
−0.891067 | + | 0.453871i | \(0.850043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 451.313i | 0.544406i | 0.962240 | + | 0.272203i | \(0.0877523\pi\) | ||||
−0.962240 | + | 0.272203i | \(0.912248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1274.95i | − | 1.53424i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 606.739i | − | 0.728379i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −147.110 | − | 460.617i | −0.176180 | − | 0.551638i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 52.1535 | 0.0623101 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1191.13i | − | 1.41970i | −0.704354 | − | 0.709849i | \(-0.748763\pi\) | ||
0.704354 | − | 0.709849i | \(-0.251237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 667.674 | 0.793905 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 348.149i | − | 0.412988i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 182.040 | + | 569.987i | 0.215432 | + | 0.674540i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −349.382 | −0.412494 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1415.78 | −1.66759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 239.411 | 0.281329 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 572.320 | 0.670949 | 0.335475 | − | 0.942049i | \(-0.391103\pi\) | ||||
0.335475 | + | 0.942049i | \(0.391103\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −170.147 | − | 532.748i | −0.199002 | − | 0.623097i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 621.587i | 0.725306i | 0.931924 | + | 0.362653i | \(0.118129\pi\) | ||||
−0.931924 | + | 0.362653i | \(0.881871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −394.083 | −0.458770 | −0.229385 | − | 0.973336i | \(-0.573671\pi\) | ||||
−0.229385 | + | 0.973336i | \(0.573671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 796.123i | − | 0.924649i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 472.620 | 0.547648 | 0.273824 | − | 0.961780i | \(-0.411711\pi\) | ||||
0.273824 | + | 0.961780i | \(0.411711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −204.629 | − | 640.715i | −0.236565 | − | 0.740711i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 149.728i | 0.172697i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1177.76i | 1.35531i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 445.203i | − | 0.511140i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1173.27i | 1.34396i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −329.933 | − | 247.390i | −0.377067 | − | 0.282732i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 407.706 | 0.464887 | 0.232443 | − | 0.972610i | \(-0.425328\pi\) | ||||
0.232443 | + | 0.972610i | \(0.425328\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1986.95i | − | 2.26046i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −843.968 | −0.957966 | −0.478983 | − | 0.877824i | \(-0.658994\pi\) | ||||
−0.478983 | + | 0.877824i | \(0.658994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 868.718i | 0.983826i | 0.870644 | + | 0.491913i | \(0.163702\pi\) | ||||
−0.870644 | + | 0.491913i | \(0.836298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2301.50 | + | 735.045i | −2.60057 | + | 0.830559i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 110.857 | 0.124979 | 0.0624896 | − | 0.998046i | \(-0.480096\pi\) | ||||
0.0624896 | + | 0.998046i | \(0.480096\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −229.062 | −0.257663 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1262.53 | −1.41699 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −438.637 | −0.491194 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.4311 | − | 38.9230i | −0.0138895 | − | 0.0434893i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 103.185i | 0.115033i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 503.305 | 0.559849 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1272.13i | − | 1.41191i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −719.888 | −0.797218 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 602.334 | − | 192.371i | 0.665562 | − | 0.212565i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 198.356i | − | 0.218694i | −0.994004 | − | 0.109347i | \(-0.965124\pi\) | ||
0.994004 | − | 0.109347i | \(-0.0348760\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 977.448i | − | 1.07530i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 964.205i | − | 1.05840i | −0.848496 | − | 0.529201i | \(-0.822492\pi\) | ||
0.848496 | − | 0.529201i | \(-0.177508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 927.529i | − | 1.01591i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −738.575 | − | 2312.56i | −0.807186 | − | 2.52738i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 481.043 | 0.524584 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1004.28i | − | 1.09279i | −0.837526 | − | 0.546397i | \(-0.815999\pi\) | ||
0.837526 | − | 0.546397i | \(-0.184001\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 221.036 | 0.239996 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 282.335i | 0.305888i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1395.73 | − | 992.795i | 1.50890 | − | 1.07329i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −335.454 | −0.361871 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.4532 | 0.0424685 | 0.0212342 | − | 0.999775i | \(-0.493240\pi\) | ||||
0.0212342 | + | 0.999775i | \(0.493240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 491.426 | 0.527847 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1166.26 | 1.25002 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1142.07 | − | 364.749i | 1.22146 | − | 0.390106i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 727.845i | − | 0.776782i | −0.921495 | − | 0.388391i | \(-0.873031\pi\) | ||
0.921495 | − | 0.388391i | \(-0.126969\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −376.831 | −0.401311 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1077.46i | − | 1.14501i | −0.819900 | − | 0.572506i | \(-0.805971\pi\) | ||
0.819900 | − | 0.572506i | \(-0.194029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −200.577 | −0.212700 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −21.4364 | + | 6.84628i | −0.0226840 | + | 0.00724474i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 153.952i | − | 0.162568i | −0.996691 | − | 0.0812840i | \(-0.974098\pi\) | ||
0.996691 | − | 0.0812840i | \(-0.0259021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 15.1934i | − | 0.0160099i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1296.62i | − | 1.36343i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1524.18i | − | 1.59935i | −0.600435 | − | 0.799673i | \(-0.705006\pi\) | ||
0.600435 | − | 0.799673i | \(-0.294994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −195.133 | + | 62.3209i | −0.204328 | + | 0.0652575i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −833.756 | −0.871219 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 583.784i | 0.608743i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −500.496 | −0.520807 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1719.24i | 1.78530i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 727.841 | − | 232.455i | 0.754239 | − | 0.240886i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −349.260 | −0.361179 | −0.180590 | − | 0.983559i | \(-0.557801\pi\) | ||||
−0.180590 | + | 0.983559i | \(0.557801\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 862.829 | 0.890433 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −745.065 | −0.767317 | −0.383659 | − | 0.923475i | \(-0.625336\pi\) | ||||
−0.383659 | + | 0.923475i | \(0.625336\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 185.776 | 0.190931 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 427.889 | + | 601.554i | 0.438861 | + | 0.616979i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1205.72i | − | 1.23410i | −0.786923 | − | 0.617051i | \(-0.788327\pi\) | ||
0.786923 | − | 0.617051i | \(-0.211673\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 91.0999 | 0.0930540 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 419.131i | − | 0.427249i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 427.425 | 0.434817 | 0.217408 | − | 0.976081i | \(-0.430240\pi\) | ||||
0.217408 | + | 0.976081i | \(0.430240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 213.549 | + | 668.643i | 0.216801 | + | 0.678825i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 471.880i | − | 0.478096i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 181.370i | 0.183387i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 924.615i | 0.933012i | 0.884518 | + | 0.466506i | \(0.154487\pi\) | ||||
−0.884518 | + | 0.466506i | \(0.845513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 763.763i | 0.769148i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −515.313 | + | 164.579i | −0.517903 | + | 0.165406i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −720.253 | −0.722420 | −0.361210 | − | 0.932484i | \(-0.617636\pi\) | ||||
−0.361210 | + | 0.932484i | \(0.617636\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 93.4661i | − | 0.0935596i |
(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 | 1280.3.e.l.639.16 | 24 | ||
4.3 | odd | 2 | 1280.3.e.k.639.9 | 24 | |||
5.4 | even | 2 | inner | 1280.3.e.l.639.9 | 24 | ||
8.3 | odd | 2 | inner | 1280.3.e.l.639.10 | 24 | ||
8.5 | even | 2 | 1280.3.e.k.639.15 | 24 | |||
16.3 | odd | 4 | 640.3.h.b.639.22 | yes | 24 | ||
16.5 | even | 4 | 640.3.h.a.639.22 | yes | 24 | ||
16.11 | odd | 4 | 640.3.h.a.639.3 | ✓ | 24 | ||
16.13 | even | 4 | 640.3.h.b.639.3 | yes | 24 | ||
20.19 | odd | 2 | 1280.3.e.k.639.16 | 24 | |||
40.19 | odd | 2 | inner | 1280.3.e.l.639.15 | 24 | ||
40.29 | even | 2 | 1280.3.e.k.639.10 | 24 | |||
80.19 | odd | 4 | 640.3.h.b.639.4 | yes | 24 | ||
80.29 | even | 4 | 640.3.h.b.639.21 | yes | 24 | ||
80.59 | odd | 4 | 640.3.h.a.639.21 | yes | 24 | ||
80.69 | even | 4 | 640.3.h.a.639.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.3.h.a.639.3 | ✓ | 24 | 16.11 | odd | 4 | ||
640.3.h.a.639.4 | yes | 24 | 80.69 | even | 4 | ||
640.3.h.a.639.21 | yes | 24 | 80.59 | odd | 4 | ||
640.3.h.a.639.22 | yes | 24 | 16.5 | even | 4 | ||
640.3.h.b.639.3 | yes | 24 | 16.13 | even | 4 | ||
640.3.h.b.639.4 | yes | 24 | 80.19 | odd | 4 | ||
640.3.h.b.639.21 | yes | 24 | 80.29 | even | 4 | ||
640.3.h.b.639.22 | yes | 24 | 16.3 | odd | 4 | ||
1280.3.e.k.639.9 | 24 | 4.3 | odd | 2 | |||
1280.3.e.k.639.10 | 24 | 40.29 | even | 2 | |||
1280.3.e.k.639.15 | 24 | 8.5 | even | 2 | |||
1280.3.e.k.639.16 | 24 | 20.19 | odd | 2 | |||
1280.3.e.l.639.9 | 24 | 5.4 | even | 2 | inner | ||
1280.3.e.l.639.10 | 24 | 8.3 | odd | 2 | inner | ||
1280.3.e.l.639.15 | 24 | 40.19 | odd | 2 | inner | ||
1280.3.e.l.639.16 | 24 | 1.1 | even | 1 | trivial |