Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,9,Mod(319,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.319");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.h (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: | \(130.361155220\) |
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: | \( x^{20} + 94 x^{18} + 5343 x^{16} + 172772 x^{14} + 36131456 x^{12} + 3044563968 x^{10} + \cdots + 11\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{140}\cdot 3^{4}\cdot 5^{12} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.2 | ||
Root | \(-3.53165 - 7.17826i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.319 |
Dual form | 320.9.h.g.319.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −134.970 | −1.66629 | −0.833145 | − | 0.553054i | \(-0.813462\pi\) | ||||
−0.833145 | + | 0.553054i | \(0.813462\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 416.235 | + | 466.234i | 0.665975 | + | 0.745974i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1863.96 | 0.776326 | 0.388163 | − | 0.921591i | \(-0.373110\pi\) | ||||
0.388163 | + | 0.921591i | \(0.373110\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11655.8 | 1.77652 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5278.32i | − | 0.360516i | −0.983619 | − | 0.180258i | \(-0.942307\pi\) | ||
0.983619 | − | 0.180258i | \(-0.0576933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 33338.9i | 1.16729i | 0.812010 | + | 0.583643i | \(0.198373\pi\) | ||||
−0.812010 | + | 0.583643i | \(0.801627\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −56179.0 | − | 62927.3i | −1.10971 | − | 1.24301i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 142617.i | 1.70756i | 0.520636 | + | 0.853779i | \(0.325695\pi\) | ||||
−0.520636 | + | 0.853779i | \(0.674305\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 70346.9i | 0.539797i | 0.962889 | + | 0.269899i | \(0.0869902\pi\) | ||||
−0.962889 | + | 0.269899i | \(0.913010\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −251578. | −1.29359 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 255957. | 0.914650 | 0.457325 | − | 0.889300i | \(-0.348808\pi\) | ||||
0.457325 | + | 0.889300i | \(0.348808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −44122.6 | + | 388125.i | −0.112954 | + | 0.993600i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −687639. | −1.29391 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −534050. | −0.755075 | −0.377537 | − | 0.925994i | \(-0.623229\pi\) | ||||
−0.377537 | + | 0.925994i | \(0.623229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.24954e6i | 1.35302i | 0.736433 | + | 0.676511i | \(0.236509\pi\) | ||||
−0.736433 | + | 0.676511i | \(0.763491\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 712412.i | 0.600725i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 775844. | + | 869041.i | 0.517014 | + | 0.579119i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 169861.i | − | 0.0906332i | −0.998973 | − | 0.0453166i | \(-0.985570\pi\) | ||
0.998973 | − | 0.0453166i | \(-0.0144297\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.49973e6i | − | 1.94504i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.36651e6 | 0.837479 | 0.418739 | − | 0.908106i | \(-0.362472\pi\) | ||||
0.418739 | + | 0.908106i | \(0.362472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.03853e6 | 1.18127 | 0.590635 | − | 0.806939i | \(-0.298877\pi\) | ||||
0.590635 | + | 0.806939i | \(0.298877\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.85153e6 | + | 5.43431e6i | 1.18312 | + | 1.32524i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.65928e6 | 0.340038 | 0.170019 | − | 0.985441i | \(-0.445617\pi\) | ||||
0.170019 | + | 0.985441i | \(0.445617\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.29046e6 | −0.397317 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.92489e7i | − | 2.84529i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 981179.i | − | 0.124350i | −0.998065 | − | 0.0621748i | \(-0.980196\pi\) | ||
0.998065 | − | 0.0621748i | \(-0.0198036\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.46093e6 | − | 2.19702e6i | 0.268936 | − | 0.240095i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 9.49469e6i | − | 0.899459i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.47526e6i | 0.616905i | 0.951240 | + | 0.308453i | \(0.0998111\pi\) | ||||
−0.951240 | + | 0.308453i | \(0.900189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41028e7 | 1.01856 | 0.509280 | − | 0.860601i | \(-0.329912\pi\) | ||||
0.509280 | + | 0.860601i | \(0.329912\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.17259e7 | 1.37916 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.55437e7 | + | 1.38768e7i | −0.870765 | + | 0.777384i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.75634e7 | 1.86409 | 0.932043 | − | 0.362347i | \(-0.118024\pi\) | ||||
0.932043 | + | 0.362347i | \(0.118024\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.45463e7 | −1.52407 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.57630e7i | − | 1.40734i | −0.710524 | − | 0.703672i | \(-0.751542\pi\) | ||
0.710524 | − | 0.703672i | \(-0.248458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.26944e6i | 0.255982i | 0.991775 | + | 0.127991i | \(0.0408529\pi\) | ||||
−0.991775 | + | 0.127991i | \(0.959147\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.95521e6 | − | 5.23851e7i | 0.188214 | − | 1.65563i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 9.83857e6i | − | 0.279878i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.72731e7i | − | 0.956945i | −0.878102 | − | 0.478473i | \(-0.841191\pi\) | ||
0.878102 | − | 0.478473i | \(-0.158809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.63368e7 | 0.379512 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.09461e7 | −0.441357 | −0.220679 | − | 0.975347i | \(-0.570827\pi\) | ||||
−0.220679 | + | 0.975347i | \(0.570827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.64928e7 | + | 5.93621e7i | −1.27379 | + | 1.13719i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.20805e7 | 1.25817 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.52812e7 | 0.402938 | 0.201469 | − | 0.979495i | \(-0.435429\pi\) | ||||
0.201469 | + | 0.979495i | \(0.435429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.21423e7i | 0.906195i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.68650e8i | − | 2.25453i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.27981e7 | + | 2.92808e7i | −0.402674 | + | 0.359492i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.35709e6i | − | 0.0153293i | −0.999971 | − | 0.00766465i | \(-0.997560\pi\) | ||
0.999971 | − | 0.00766465i | \(-0.00243976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.15229e7i | − | 0.640465i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.25091e8 | 1.20210 | 0.601052 | − | 0.799210i | \(-0.294749\pi\) | ||||
0.601052 | + | 0.799210i | \(0.294749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.55443e7 | −0.404655 | −0.202327 | − | 0.979318i | \(-0.564851\pi\) | ||||
−0.202327 | + | 0.979318i | \(0.564851\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.04715e8 | − | 1.17294e8i | −0.861496 | − | 0.964981i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.11806e7 | 0.0852959 | 0.0426480 | − | 0.999090i | \(-0.486421\pi\) | ||||
0.0426480 | + | 0.999090i | \(0.486421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.48944e7 | 0.247201 | 0.123600 | − | 0.992332i | \(-0.460556\pi\) | ||||
0.123600 | + | 0.992332i | \(0.460556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.29261e7i | 0.151021i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.55089e8i | 0.951187i | 0.879665 | + | 0.475594i | \(0.157767\pi\) | ||||
−0.879665 | + | 0.475594i | \(0.842233\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.06538e8 | + | 1.19336e8i | 0.609135 | + | 0.682305i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.88590e8i | 2.07371i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.65832e8i | 1.32562i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.86498e8 | 0.870028 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.19407e8 | −1.39548 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.99322e8 | + | 1.40980e8i | −0.816424 | + | 0.577453i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.11442e8 | −0.812786 | −0.406393 | − | 0.913698i | \(-0.633214\pi\) | ||||
−0.406393 | + | 0.913698i | \(0.633214\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.45078e8 | −1.96834 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.14013e8i | − | 0.387140i | −0.981086 | − | 0.193570i | \(-0.937993\pi\) | ||
0.981086 | − | 0.193570i | \(-0.0620067\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.31124e8i | 0.419059i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.86219e8 | − | 3.20600e8i | −0.861714 | − | 0.965226i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.96731e8i | 1.12620i | 0.826390 | + | 0.563098i | \(0.190391\pi\) | ||||
−0.826390 | + | 0.563098i | \(0.809609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.81838e8i | 0.754988i | 0.926012 | + | 0.377494i | \(0.123214\pi\) | ||||
−0.926012 | + | 0.377494i | \(0.876786\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.23952e8 | −0.566601 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.75973e8 | 0.420825 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.22290e8 | − | 2.48992e8i | −0.502861 | − | 0.563266i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.09142e8 | 0.662046 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.38854e8 | −0.890379 | −0.445190 | − | 0.895436i | \(-0.646864\pi\) | ||||
−0.445190 | + | 0.895436i | \(0.646864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.34766e8i | 1.41332i | 0.707552 | + | 0.706662i | \(0.249800\pi\) | ||||
−0.707552 | + | 0.706662i | \(0.750200\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.66231e9i | 3.03352i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.82579e8 | + | 5.20103e8i | −1.00932 | + | 0.901079i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.92920e8i | 0.646704i | 0.946279 | + | 0.323352i | \(0.104810\pi\) | ||||
−0.946279 | + | 0.323352i | \(0.895190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.32429e8i | 0.207203i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.77093e8 | 0.710067 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.78730e8 | −1.24482 | −0.622408 | − | 0.782693i | \(-0.713845\pi\) | ||||
−0.622408 | + | 0.782693i | \(0.713845\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.32150e8 | + | 2.96530e8i | −0.448125 | + | 0.400068i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.28526e8 | 0.550948 | 0.275474 | − | 0.961308i | \(-0.411165\pi\) | ||||
0.275474 | + | 0.961308i | \(0.411165\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.95749e8 | −0.362557 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.19947e8i | 0.958962i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.08766e8i | − | 0.344703i | −0.985035 | − | 0.172352i | \(-0.944863\pi\) | ||
0.985035 | − | 0.172352i | \(-0.0551366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.22427e7 | + | 7.23450e8i | −0.0876891 | + | 0.771358i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.00893e9i | − | 1.02794i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2.34312e8i | − | 0.228235i | −0.993467 | − | 0.114117i | \(-0.963596\pi\) | ||
0.993467 | − | 0.114117i | \(-0.0364040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.98225e8 | 0.184691 | 0.0923454 | − | 0.995727i | \(-0.470564\pi\) | ||||
0.0923454 | + | 0.995727i | \(0.470564\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.90345e9 | −1.69722 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.91950e7 | − | 7.07021e7i | 0.0676100 | − | 0.0603595i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.52778e8 | 0.615602 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.28173e9 | −1.00450 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.29845e9i | − | 1.72704i | −0.504317 | − | 0.863518i | \(-0.668256\pi\) | ||
0.504317 | − | 0.863518i | \(-0.331744\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.50744e8i | − | 0.469009i | −0.972115 | − | 0.234505i | \(-0.924653\pi\) | ||
0.972115 | − | 0.234505i | \(-0.0753468\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.09793e9 | − | 1.87294e9i | 1.45095 | − | 1.29535i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.18078e9i | − | 0.783981i | −0.919969 | − | 0.391990i | \(-0.871787\pi\) | ||
0.919969 | − | 0.391990i | \(-0.128213\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.61830e8i | − | 0.549553i | −0.961508 | − | 0.274776i | \(-0.911396\pi\) | ||
0.961508 | − | 0.274776i | \(-0.0886038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.06992e9 | −3.10611 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.95448e8 | −0.586185 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.85025e8 | + | 1.10335e9i | 0.557740 | + | 0.624737i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.98337e9 | 1.62490 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.71313e8 | 0.194606 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.94443e9i | − | 0.980985i | −0.871445 | − | 0.490493i | \(-0.836817\pi\) | ||
0.871445 | − | 0.490493i | \(-0.163183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.82691e9i | 2.34505i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.68097e9 | + | 1.88290e9i | 0.786697 | + | 0.881197i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.32910e9i | 1.05039i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 9.81153e8i | − | 0.426541i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.75469e9 | −1.99321 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65989e8 | 0.228870 | 0.114435 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114435 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.14283e8 | + | 4.52390e9i | −0.200665 | + | 1.76515i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.24952e9 | 0.847200 | 0.423600 | − | 0.905849i | \(-0.360766\pi\) | ||||
0.423600 | + | 0.905849i | \(0.360766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.02108e9 | 0.371295 | 0.185648 | − | 0.982616i | \(-0.440562\pi\) | ||||
0.185648 | + | 0.982616i | \(0.440562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.32791e9i | 0.466358i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.60926e9i | 0.546013i | 0.962012 | + | 0.273007i | \(0.0880181\pi\) | ||||
−0.962012 | + | 0.273007i | \(0.911982\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.90648e8 | + | 7.73610e8i | 0.226457 | + | 0.253659i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.03073e9i | 1.59455i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.14150e9i | − | 1.88227i | −0.338027 | − | 0.941136i | \(-0.609760\pi\) | ||
0.338027 | − | 0.941136i | \(-0.390240\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.57617e9 | −0.467234 | −0.233617 | − | 0.972329i | \(-0.575056\pi\) | ||||
−0.233617 | + | 0.972329i | \(0.575056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.30663e9 | 0.661536 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.53367e8 | − | 1.06789e9i | −0.264603 | − | 0.296388i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.34528e9 | −0.630098 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.82708e9 | 0.735429 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.05238e8i | − | 0.152486i | −0.997089 | − | 0.0762432i | \(-0.975707\pi\) | ||
0.997089 | − | 0.0762432i | \(-0.0242925\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.35102e9i | − | 0.329746i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.97450e9 | − | 8.01207e9i | 2.12251 | − | 1.89489i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.33383e9i | 1.68112i | 0.541720 | + | 0.840559i | \(0.317773\pi\) | ||||
−0.541720 | + | 0.840559i | \(0.682227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.16614e8i | − | 0.0703609i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.22476e9 | −1.34141 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.11216e9 | −1.69556 | −0.847780 | − | 0.530348i | \(-0.822061\pi\) | ||||
−0.847780 | + | 0.530348i | \(0.822061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.57458e8 | − | 4.08400e8i | 0.0927616 | − | 0.0828138i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.41219e9 | −0.671411 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.31912e9 | −0.251927 | −0.125964 | − | 0.992035i | \(-0.540202\pi\) | ||||
−0.125964 | + | 0.992035i | \(0.540202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.01624e9i | 0.559228i | 0.960113 | + | 0.279614i | \(0.0902064\pi\) | ||||
−0.960113 | + | 0.279614i | \(0.909794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 8.38731e9i | − | 1.50998i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.04865e9 | + | 2.32893e8i | 0.358209 | + | 0.0407217i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.19710e9i | − | 0.203334i | −0.994818 | − | 0.101667i | \(-0.967582\pi\) | ||
0.994818 | − | 0.101667i | \(-0.0324177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.45644e10i | 2.40367i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.05582e9 | 0.329732 | 0.164866 | − | 0.986316i | \(-0.447281\pi\) | ||||
0.164866 | + | 0.986316i | \(0.447281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.21382e10 | −1.89238 | −0.946189 | − | 0.323616i | \(-0.895102\pi\) | ||||
−0.946189 | + | 0.323616i | \(0.895102\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.42674e9 | − | 3.95202e9i | 0.670973 | − | 0.599017i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.41109e9 | 0.650157 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.33638e10 | −1.91575 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.83166e8i | 0.0255431i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.85830e9i | 1.20193i | 0.799275 | + | 0.600966i | \(0.205217\pi\) | ||||
−0.799275 | + | 0.600966i | \(0.794783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.48522e9 | + | 3.11146e9i | −0.460195 | + | 0.410844i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.62958e9i | 0.466477i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.53330e9i | 1.06766i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.52765e9 | 0.917051 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.68835e10 | −2.00305 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.87008e9 | + | 6.57520e9i | 0.678335 | + | 0.759818i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.27115e9 | 0.255678 | 0.127839 | − | 0.991795i | \(-0.459196\pi\) | ||||
0.127839 | + | 0.991795i | \(0.459196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.14709e9 | 0.674273 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.95031e8i | 0.106364i | 0.998585 | + | 0.0531820i | \(0.0169364\pi\) | ||||
−0.998585 | + | 0.0531820i | \(0.983064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.67741e9i | − | 1.00828i | −0.863621 | − | 0.504141i | \(-0.831809\pi\) | ||
0.863621 | − | 0.504141i | \(-0.168191\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.04306e9 | + | 1.01293e10i | 0.918488 | + | 1.02882i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.41589e9i | 0.536330i | 0.963373 | + | 0.268165i | \(0.0864173\pi\) | ||||
−0.963373 | + | 0.268165i | \(0.913583\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.81889e9i | 0.272217i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.50903e9 | −0.142128 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00327e10 | −0.921735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.29396e10 | − | 1.47100e9i | −1.15982 | − | 0.131849i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.70968e9 | −0.411908 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.09282e9 | 0.263980 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.61383e10i | 1.34445i | 0.740345 | + | 0.672227i | \(0.234662\pi\) | ||||
−0.740345 | + | 0.672227i | \(0.765338\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.97986e9i | − | 0.161012i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.56352e10 | + | 1.75133e10i | 1.24144 | + | 1.39056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.60080e10i | − | 1.24113i | −0.784154 | − | 0.620566i | \(-0.786903\pi\) | ||
0.784154 | − | 0.620566i | \(-0.213097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 2.09322e10i | − | 1.58495i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.59549e9 | 0.487786 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.50147e10 | −1.08477 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.43794e10 | − | 1.61067e10i | −1.01499 | − | 1.13692i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.34569e10 | −0.928168 | −0.464084 | − | 0.885791i | \(-0.653616\pi\) | ||||
−0.464084 | + | 0.885791i | \(0.653616\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.78901e10 | −1.20590 | −0.602951 | − | 0.797779i | \(-0.706008\pi\) | ||||
−0.602951 | + | 0.797779i | \(0.706008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.29251e10i | − | 1.51037i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.70557e10i | 1.74245i | 0.490886 | + | 0.871224i | \(0.336673\pi\) | ||||
−0.490886 | + | 0.871224i | \(0.663327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.66739e10 | − | 1.48858e10i | 1.04984 | − | 0.937257i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.58793e10i | − | 2.20887i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.50402e9i | − | 0.331361i | −0.986179 | − | 0.165681i | \(-0.947018\pi\) | ||
0.986179 | − | 0.165681i | \(-0.0529821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.20349e10 | 0.708619 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.51716e10 | −1.44972 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.38926e9 | + | 3.02579e9i | −0.190956 | + | 0.170478i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.67406e9 | 0.533267 | 0.266633 | − | 0.963798i | \(-0.414089\pi\) | ||||
0.266633 | + | 0.963798i | \(0.414089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.75835e10 | 1.48780 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.82888e9i | − | 0.0965359i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.57338e10i | − | 1.32944i | −0.747093 | − | 0.664720i | \(-0.768551\pi\) | ||
0.747093 | − | 0.664720i | \(-0.231449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.69024e10 | − | 1.90280e10i | 1.36040 | − | 0.962204i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.78046e10i | − | 0.881388i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.39099e10i | 1.64350i | 0.569849 | + | 0.821749i | \(0.307002\pi\) | ||||
−0.569849 | + | 0.821749i | \(0.692998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.85382e10 | 1.35434 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.07466e10 | −0.499433 | −0.249717 | − | 0.968319i | \(-0.580337\pi\) | ||||
−0.249717 | + | 0.968319i | \(0.580337\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.58707e9 | − | 4.09515e9i | 0.208782 | − | 0.186392i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.70722e10 | 2.09855 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.17407e10 | 1.82289 | 0.911446 | − | 0.411419i | \(-0.134967\pi\) | ||||
0.911446 | + | 0.411419i | \(0.134967\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.65038e10i | 1.56182i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.53882e10i | 0.645088i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.73780e10 | − | 1.55144e10i | 0.713856 | − | 0.637302i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.28145e10i | 0.515871i | 0.966162 | + | 0.257936i | \(0.0830422\pi\) | ||||
−0.966162 | + | 0.257936i | \(0.916958\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1.76977e10i | − | 0.698274i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.75527e10 | 1.83907 | 0.919533 | − | 0.393013i | \(-0.128567\pi\) | ||||
0.919533 | + | 0.393013i | \(0.128567\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.16584e10 | −1.57936 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.79992e9 | + | 7.61674e9i | 0.252746 | + | 0.283106i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.96581e8 | −0.0326747 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.44716e10 | 0.874518 | 0.437259 | − | 0.899336i | \(-0.355949\pi\) | ||||
0.437259 | + | 0.899336i | \(0.355949\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.35466e10i | − | 1.87657i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.39336e10i | 0.478920i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.71848e9 | − | 9.76576e9i | −0.293933 | − | 0.329241i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.80395e10i | − | 1.25803i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.99144e9i | 0.129501i | 0.997901 | + | 0.0647505i | \(0.0206252\pi\) | ||||
−0.997901 | + | 0.0647505i | \(0.979375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.14500e9 | 0.259276 | 0.129638 | − | 0.991561i | \(-0.458618\pi\) | ||||
0.129638 | + | 0.991561i | \(0.458618\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.93401e10 | 0.604085 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.53532e10 | − | 6.29263e9i | −1.69663 | − | 0.192875i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.62871e10 | 0.790734 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.37510e10 | −0.701217 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.14023e9i | 0.119982i | 0.998199 | + | 0.0599909i | \(0.0191072\pi\) | ||||
−0.998199 | + | 0.0599909i | \(0.980893\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.45166e10i | − | 0.697443i | −0.937226 | − | 0.348722i | \(-0.886616\pi\) | ||
0.937226 | − | 0.348722i | \(-0.113384\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.00024e10 | + | 3.36063e10i | 0.837913 | + | 0.938565i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.80058e10i | 0.493726i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.66902e10i | − | 1.52633i | −0.646201 | − | 0.763167i | \(-0.723643\pi\) | ||
0.646201 | − | 0.763167i | \(-0.276357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.66970e10 | −0.705843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.12919e10 | 0.552840 | 0.276420 | − | 0.961037i | \(-0.410852\pi\) | ||||
0.276420 | + | 0.961037i | \(0.410852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.05229e10 | + | 1.17870e10i | 0.268347 | + | 0.300581i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.92319e10 | 1.48363 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.16478e10 | −1.27077 | −0.635384 | − | 0.772196i | \(-0.719158\pi\) | ||||
−0.635384 | + | 0.772196i | \(0.719158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.24912e10i | − | 0.301925i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 9.91711e10i | − | 2.35501i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.89728e10 | + | 2.58658e10i | −0.675998 | + | 0.603503i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.18862e10i | 1.41883i | 0.704793 | + | 0.709413i | \(0.251040\pi\) | ||||
−0.704793 | + | 0.709413i | \(0.748960\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 9.80689e10i | − | 2.20943i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.84997e9 | −0.0409601 | −0.0204800 | − | 0.999790i | \(-0.506519\pi\) | ||||
−0.0204800 | + | 0.999790i | \(0.506519\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.89801e10 | −1.06585 | −0.532924 | − | 0.846163i | \(-0.678907\pi\) | ||||
−0.532924 | + | 0.846163i | \(0.678907\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.86304e10 | − | 7.01981e10i | 1.68182 | − | 1.50146i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.58985e9 | −0.0544511 | −0.0272255 | − | 0.999629i | \(-0.508667\pi\) | ||||
−0.0272255 | + | 0.999629i | \(0.508667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00167e10 | 1.44714 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.30322e10i | − | 1.07760i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.13166e10i | − | 0.425867i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.73034e10 | − | 3.10389e9i | −0.536342 | − | 0.0609722i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.14364e10i | − | 0.220910i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.24642e10i | 1.37652i | 0.725466 | + | 0.688258i | \(0.241624\pi\) | ||||
−0.725466 | + | 0.688258i | \(0.758376\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.66298e9 | 0.105795 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.43930e10 | −1.18318 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.32722e8 | − | 5.64869e8i | 0.0114353 | − | 0.0102089i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.78628e10 | 1.20647 | 0.603234 | − | 0.797564i | \(-0.293879\pi\) | ||||
0.603234 | + | 0.797564i | \(0.293879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.18602e11 | 2.07422 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.04720e11i | 1.80179i | 0.434032 | + | 0.900897i | \(0.357090\pi\) | ||||
−0.434032 | + | 0.900897i | \(0.642910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.61646e10i | − | 1.28933i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.86840e10 | − | 2.56079e10i | 0.477770 | − | 0.426534i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.66608e10i | − | 1.09256i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.70756e10i | 0.920552i | 0.887776 | + | 0.460276i | \(0.152250\pi\) | ||||
−0.887776 | + | 0.460276i | \(0.847750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.78379e10 | −0.918040 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.65834e10 | −0.259061 | −0.129531 | − | 0.991575i | \(-0.541347\pi\) | ||||
−0.129531 | + | 0.991575i | \(0.541347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.20673e10 | + | 5.83218e10i | 0.800571 | + | 0.896738i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.99171e10 | 0.604125 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.82746e9 | −0.0570216 | −0.0285108 | − | 0.999593i | \(-0.509076\pi\) | ||||
−0.0285108 | + | 0.999593i | \(0.509076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35499e10i | 0.198726i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.83732e10i | − | 0.698451i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.89571e10 | − | 2.12343e10i | −0.269490 | − | 0.301862i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.75818e9i | − | 0.122589i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.16740e10i | 0.574376i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.15272e10 | −0.970779 | −0.485389 | − | 0.874298i | \(-0.661322\pi\) | ||||
−0.485389 | + | 0.874298i | \(0.661322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.30293e10 | 0.307803 | 0.153902 | − | 0.988086i | \(-0.450816\pi\) | ||||
0.153902 | + | 0.988086i | \(0.450816\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.11003e10 | − | 9.76436e10i | 0.146115 | − | 1.28531i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.78206e11 | −2.31036 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.27972e10 | −0.163415 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.71300e10i | 1.09595i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.88969e10i | 0.977577i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.65374e9 | + | 5.21275e9i | 0.0568050 | + | 0.0636285i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.16250e10i | 0.380306i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.20897e10i | 0.143239i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.52906e10 | −0.645450 | −0.322725 | − | 0.946493i | \(-0.604599\pi\) | ||||
−0.322725 | + | 0.946493i | \(0.604599\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.67544e10 | −0.307748 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.45242e10 | + | 1.62689e10i | 0.164630 | + | 0.184405i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.25380e10 | −0.921945 | −0.460972 | − | 0.887415i | \(-0.652499\pi\) | ||||
−0.460972 | + | 0.887415i | \(0.652499\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.64379e11 | 1.80949 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.75688e10i | − | 0.407587i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.94755e10i | − | 0.742902i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.06889e10 | + | 9.54263e9i | −0.112658 | + | 0.100576i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 6.76291e10i | − | 0.702608i | −0.936261 | − | 0.351304i | \(-0.885738\pi\) | ||
0.936261 | − | 0.351304i | \(-0.114262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.34640e11i | 1.37888i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.01602e11 | −1.02577 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.16824e11 | −1.16278 | −0.581391 | − | 0.813624i | \(-0.697491\pi\) | ||||
−0.581391 | + | 0.813624i | \(0.697491\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.23075e10 | + | 6.45532e10i | −0.709561 | + | 0.633467i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.04510e10 | 0.294625 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.83290e9 | −0.0174860 | −0.00874298 | − | 0.999962i | \(-0.502783\pi\) | ||||
−0.00874298 | + | 0.999962i | \(0.502783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.83754e11i | − | 1.72859i | −0.502984 | − | 0.864296i | \(-0.667765\pi\) | ||
0.502984 | − | 0.864296i | \(-0.332235\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.10221e11i | 2.87774i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.12935e10 | + | 9.93432e10i | −0.103313 | + | 0.908797i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.07447e11i | 0.969374i | 0.874688 | + | 0.484687i | \(0.161066\pi\) | ||||
−0.874688 | + | 0.484687i | \(0.838934\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.78307e10i | 0.781505i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.90426e10 | −0.342637 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.17897e9 | −0.0448301 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.81174e11 | + | 1.61745e11i | −1.54693 | + | 1.38104i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.33835e10 | −0.702308 | −0.351154 | − | 0.936318i | \(-0.614211\pi\) | ||||
−0.351154 | + | 0.936318i | \(0.614211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.79015e10 | −0.730357 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.59370e11i | 1.30634i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.33128e10i | 0.673741i | 0.941551 | + | 0.336871i | \(0.109369\pi\) | ||||
−0.941551 | + | 0.336871i | \(0.890631\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.23940e11 | + | 1.10649e11i | −0.988880 | + | 0.882832i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.16321e11i | 0.915714i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.46618e10i | − | 0.579951i | −0.957034 | − | 0.289976i | \(-0.906353\pi\) | ||
0.957034 | − | 0.289976i | \(-0.0936472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.14915e11 | −0.880803 | −0.440401 | − | 0.897801i | \(-0.645164\pi\) | ||||
−0.440401 | + | 0.897801i | \(0.645164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.37831e11 | 3.31159 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.76270e10 | + | 8.69518e10i | 0.579417 | + | 0.649018i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.63432e10 | −0.267712 | −0.133856 | − | 0.991001i | \(-0.542736\pi\) | ||||
−0.133856 | + | 0.991001i | \(0.542736\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.34355e11 | 0.976754 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.53183e10i | 0.396921i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.54903e10i | 0.322164i | 0.986941 | + | 0.161082i | \(0.0514983\pi\) | ||||
−0.986941 | + | 0.161082i | \(0.948502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.32948e11 | − | 1.48918e11i | −0.929357 | − | 1.04099i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.39914e10i | − | 0.648556i | −0.945962 | − | 0.324278i | \(-0.894879\pi\) | ||
0.945962 | − | 0.324278i | \(-0.105121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.86980e10i | 0.467931i | 0.972245 | + | 0.233965i | \(0.0751702\pi\) | ||||
−0.972245 | + | 0.233965i | \(0.924830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.76006e11 | −1.18348 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.71232e10 | 0.312811 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.48694e11 | − | 3.42502e10i | −0.974483 | − | 0.224462i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.01160e10 | −0.324269 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.42251e10 | 0.154761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.95536e10i | 0.249499i | 0.992188 | + | 0.124750i | \(0.0398128\pi\) | ||||
−0.992188 | + | 0.124750i | \(0.960187\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.62439e11i | 1.63461i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.80094e10 | − | 9.85813e10i | −0.541295 | − | 0.606317i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.63612e10i | − | 0.463783i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.16845e11i | − | 2.50018i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.16726e11 | 1.87608 | 0.938040 | − | 0.346526i | \(-0.112639\pi\) | ||||
0.938040 | + | 0.346526i | \(0.112639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.41563e11 | 1.41315 | 0.706574 | − | 0.707640i | \(-0.250240\pi\) | ||||
0.706574 | + | 0.707640i | \(0.250240\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.26880e11 | − | 2.54134e11i | −1.31087 | − | 1.46833i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.42487e11 | 0.813124 | 0.406562 | − | 0.913623i | \(-0.366728\pi\) | ||||
0.406562 | + | 0.913623i | \(0.366728\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.94568e10 | 0.222404 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 3.14357e11i | − | 1.75025i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.22267e11i | 0.672447i | 0.941782 | + | 0.336224i | \(0.109150\pi\) | ||||
−0.941782 | + | 0.336224i | \(0.890850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.31566e10 | − | 4.74560e10i | 0.288796 | − | 0.257826i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.47310e10i | 0.454758i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.05381e11i | − | 0.558753i | −0.960182 | − | 0.279377i | \(-0.909872\pi\) | ||
0.960182 | − | 0.279377i | \(-0.0901278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.12360e11 | 1.11242 | 0.556209 | − | 0.831043i | \(-0.312255\pi\) | ||||
0.556209 | + | 0.831043i | \(0.312255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.41738e11 | 3.32126 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.11343e10 | + | 5.45782e10i | −0.312607 | + | 0.279083i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.36694e11 | −0.690629 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.63913e10 | −0.381364 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.44391e10i | − | 0.367207i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.80972e11i | − | 1.85709i | −0.371219 | − | 0.928545i | \(-0.621060\pi\) | ||
0.371219 | − | 0.928545i | \(-0.378940\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.03404e10 | − | 2.66890e11i | 0.146152 | − | 1.28563i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.80516e11i | − | 1.33538i | −0.744441 | − | 0.667688i | \(-0.767284\pi\) | ||
0.744441 | − | 0.667688i | \(-0.232716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.52957e9i | − | 0.0119005i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.03616e11 | −1.41168 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.79360e10 | 0.266235 | 0.133118 | − | 0.991100i | \(-0.457501\pi\) | ||||
0.133118 | + | 0.991100i | \(0.457501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.84969e11 | + | 1.65133e11i | −0.840112 | + | 0.750018i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.37815e11 | −0.618686 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.27114e10 | 0.145152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.55640e11i | 1.12129i | 0.828057 | + | 0.560644i | \(0.189446\pi\) | ||||
−0.828057 | + | 0.560644i | \(0.810554\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.14676e11i | − | 0.497210i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.31402e11 | + | 1.17311e11i | −0.563201 | + | 0.502803i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.37505e11i | 1.43004i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 2.17201e11i | − | 0.909817i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.52264e11 | −0.630556 | −0.315278 | − | 0.948999i | \(-0.602098\pi\) | ||||
−0.315278 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19492e10 | 0.0489235 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.32164e10 | − | 1.04414e11i | −0.377343 | − | 0.422670i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.33165e11 | 0.933225 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.99510e10 | −0.355976 | −0.177988 | − | 0.984033i | \(-0.556959\pi\) | ||||
−0.177988 | + | 0.984033i | \(0.556959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4.34447e11i | − | 1.70004i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.19829e11i | 1.23754i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.32461e10 | + | 8.20446e10i | 0.280259 | + | 0.313925i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.28915e11i | 3.13641i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.34871e11i | 1.25303i | 0.779409 | + | 0.626515i | \(0.215519\pi\) | ||||
−0.779409 | + | 0.626515i | \(0.784481\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.48927e10 | −0.314144 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.12735e11 | 0.778547 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.35637e10 | − | 2.07278e11i | 0.0852886 | − | 0.750243i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.68905e11 | −1.67860 | −0.839300 | − | 0.543669i | \(-0.817035\pi\) | ||||
−0.839300 | + | 0.543669i | \(0.817035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.18511e11 | −1.48182 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.75963e11i | 2.01709i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.30452e10i | 0.218392i | 0.994020 | + | 0.109196i | \(0.0348276\pi\) | ||||
−0.994020 | + | 0.109196i | \(0.965172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.28675e11 | + | 1.44132e11i | 0.440906 | + | 0.493869i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.98272e11i | − | 0.672033i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.09954e11i | − | 0.703959i | −0.936008 | − | 0.351979i | \(-0.885509\pi\) | ||
0.936008 | − | 0.351979i | \(-0.114491\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.16542e11 | 1.04993 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.18225e11 | 0.716060 | 0.358030 | − | 0.933710i | \(-0.383448\pi\) | ||||
0.358030 | + | 0.933710i | \(0.383448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.82666e11 | − | 2.04608e11i | −0.592970 | − | 0.664199i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.44143e11 | −0.784081 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.08401e10 | 0.0662175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.33771e10i | 0.167801i | 0.996474 | + | 0.0839006i | \(0.0267378\pi\) | ||||
−0.996474 | + | 0.0839006i | \(0.973262\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.16886e10i | 0.254087i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.42573e11 | + | 3.05835e11i | −1.05430 | + | 0.941238i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.91321e11i | 0.887132i | 0.896242 | + | 0.443566i | \(0.146287\pi\) | ||||
−0.896242 | + | 0.443566i | \(0.853713\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.82347e11i | 0.549453i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.92349e10 | 0.0573523 | 0.0286762 | − | 0.999589i | \(-0.490871\pi\) | ||||
0.0286762 | + | 0.999589i | \(0.490871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.50417e10 | 0.191908 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.75025e11 | + | 6.91911e11i | −2.26292 | + | 2.02025i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.49217e11 | −0.720105 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.49604e11 | 0.999703 | 0.499852 | − | 0.866111i | \(-0.333388\pi\) | ||||
0.499852 | + | 0.866111i | \(0.333388\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 9.89843e11i | − | 2.80123i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 6.52120e11i | − | 1.82646i | −0.407447 | − | 0.913229i | \(-0.633581\pi\) | ||
0.407447 | − | 0.913229i | \(-0.366419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.84979e11 | − | 5.51331e10i | −1.34436 | − | 0.152829i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.27333e10i | 0.117242i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.66477e11i | 0.452068i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.88768e11 | −0.507371 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.67233e11 | 0.977001 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.83192e11 | + | 1.63547e11i | −0.482424 | + | 0.430689i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.62094e11 | −0.943892 | −0.471946 | − | 0.881627i | \(-0.656448\pi\) | ||||
−0.471946 | + | 0.881627i | \(0.656448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.09489e12 | 2.82530 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.89079e11i | 0.738432i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.70171e11i | 1.18895i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.17430e10 | + | 5.51216e10i | −0.154568 | + | 0.137992i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.33733e11i | − | 0.331440i | −0.986173 | − | 0.165720i | \(-0.947005\pi\) | ||
0.986173 | − | 0.165720i | \(-0.0529948\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.36641e11i | 0.580634i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.94672e11 | 0.715828 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.83704e10 | 0.0922857 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.98583e11 | + | 2.22437e11i | 0.472887 | + | 0.529692i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.78041e11 | 0.419784 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.11621e11 | 0.960956 | 0.480478 | − | 0.877007i | \(-0.340463\pi\) | ||||
0.480478 | + | 0.877007i | \(0.340463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.23209e11i | 1.67178i | 0.548894 | + | 0.835892i | \(0.315049\pi\) | ||||
−0.548894 | + | 0.835892i | \(0.684951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.07100e11i | − | 0.931836i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.65758e11 | − | 4.09693e11i | −0.829016 | − | 0.928600i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.84098e11i | 0.637646i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.24316e11i | 1.60988i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.38146e11 | −1.40458 | −0.702291 | − | 0.711890i | \(-0.747840\pi\) | ||||
−0.702291 | + | 0.711890i | \(0.747840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.86794e11 | −0.625130 | −0.312565 | − | 0.949896i | \(-0.601188\pi\) | ||||
−0.312565 | + | 0.949896i | \(0.601188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.76505e11 | − | 3.14335e10i | −0.596880 | − | 0.0678541i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.21880e11 | −1.32949 | −0.664745 | − | 0.747071i | \(-0.731460\pi\) | ||||
−0.664745 | + | 0.747071i | \(0.731460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50205e11 | 1.16495 | 0.582474 | − | 0.812849i | \(-0.302085\pi\) | ||||
0.582474 | + | 0.812849i | \(0.302085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.61572e11i | 0.338814i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.26658e11i | − | 0.678442i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.78367e11 | + | 1.99793e11i | 0.366918 | + | 0.410993i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 8.59235e11i | − | 1.75069i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.29570e9i | 0.0187601i | 0.999956 | + | 0.00938003i | \(0.00298580\pi\) | ||||
−0.999956 | + | 0.00938003i | \(0.997014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.15037e11 | −0.429862 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.77474e11 | −0.549429 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.23101e11 | − | 1.37888e11i | −0.241454 | − | 0.270458i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.47625e11 | 0.675426 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.63828e12 | 3.15325 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.34771e10i | − | 0.0828977i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.76680e11i | 0.522615i | 0.965256 | + | 0.261308i | \(0.0841537\pi\) | ||||
−0.965256 | + | 0.261308i | \(0.915846\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.82287e11 | + | 3.41290e11i | −0.715361 | + | 0.638645i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 8.09328e11i | − | 1.50038i | −0.661223 | − | 0.750190i | \(-0.729962\pi\) | ||
0.661223 | − | 0.750190i | \(-0.270038\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.89123e11i | − | 0.531020i | −0.964108 | − | 0.265510i | \(-0.914460\pi\) | ||
0.964108 | − | 0.265510i | \(-0.0855403\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.95362e11 | −1.08335 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.16481e11 | 1.11142 | 0.555708 | − | 0.831378i | \(-0.312447\pi\) | ||||
0.555708 | + | 0.831378i | \(0.312447\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.43957e11 | − | 1.28519e11i | 0.257140 | − | 0.229564i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.80371e12 | 3.19220 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.96739e11 | −0.344994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.25232e12i | 2.17592i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.58180e10i | − | 0.0272329i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.71529e11 | + | 2.62780e11i | −0.633812 | + | 0.448292i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.46830e10i | 0.109343i | 0.998504 | + | 0.0546716i | \(0.0174112\pi\) | ||||
−0.998504 | + | 0.0546716i | \(0.982589\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1.19560e12i | − | 2.00277i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.16075e11 | −1.52064 | −0.760322 | − | 0.649547i | \(-0.774959\pi\) | ||||
−0.760322 | + | 0.649547i | \(0.774959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.21518e11 | −1.18687 | −0.593437 | − | 0.804881i | \(-0.702229\pi\) | ||||
−0.593437 | + | 0.804881i | \(0.702229\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.70398e11 | − | 4.19953e11i | 0.766819 | − | 0.684585i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.56512e10 | 0.0252844 | 0.0126422 | − | 0.999920i | \(-0.495976\pi\) | ||||
0.0126422 | + | 0.999920i | \(0.495976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.94119e11 | −0.630987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 8.62306e10i | − | 0.136820i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.16725e11i | 0.183551i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.09244e11 | − | 9.75287e10i | 0.170257 | − | 0.151999i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.15174e12i | − | 1.77903i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 6.67319e11i | − | 1.02163i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.39933e11 | 0.212334 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.01600e12 | −1.52807 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.25083e10 | + | 9.24194e10i | 0.122999 | + | 0.137774i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.40442e11 | −1.09411 | −0.547056 | − | 0.837096i | \(-0.684252\pi\) | ||||
−0.547056 | + | 0.837096i | \(0.684252\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.45804e12 | 2.13556 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.11646e12i | − | 1.62095i | −0.585770 | − | 0.810477i | \(-0.699208\pi\) | ||
0.585770 | − | 0.810477i | \(-0.300792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.10560e11i | 0.159116i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.92281e11 | − | 8.87452e11i | −1.13030 | − | 1.26608i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.12515e11i | − | 0.300547i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.29970e11i | 0.602804i | 0.953497 | + | 0.301402i | \(0.0974546\pi\) | ||||
−0.953497 | + | 0.301402i | \(0.902545\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.06536e11 | −0.426033 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.19230e12 | 1.64277 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.59274e10 | + | 7.49472e9i | 0.0900532 | + | 0.0102374i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.30854e11 | −0.718879 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.03621e12 | 1.39119 | 0.695594 | − | 0.718435i | \(-0.255141\pi\) | ||||
0.695594 | + | 0.718435i | \(0.255141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.61126e11i | − | 0.214471i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.34299e11i | − | 0.177233i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.13332e11 | + | 3.50970e11i | 0.409976 | + | 0.459223i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.79343e11i | 1.27051i | 0.772304 | + | 0.635253i | \(0.219104\pi\) | ||||
−0.772304 | + | 0.635253i | \(0.780896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.30616e12i | 1.68009i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.95736e11 | 0.504715 | 0.252358 | − | 0.967634i | \(-0.418794\pi\) | ||||
0.252358 | + | 0.967634i | \(0.418794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.05725e11 | 0.766000 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.33501e11 | − | 5.97586e11i | −0.668972 | − | 0.749330i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.08577e11 | 0.881022 | 0.440511 | − | 0.897747i | \(-0.354797\pi\) | ||||
0.440511 | + | 0.897747i | \(0.354797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.42355e11 | −0.298804 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 7.30979e11i | − | 0.893682i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.04943e11i | − | 0.490932i | −0.969405 | − | 0.245466i | \(-0.921059\pi\) | ||
0.969405 | − | 0.245466i | \(-0.0789411\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.07161e12 | − | 9.56694e11i | 1.28832 | − | 1.15016i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.80464e11i | − | 0.453592i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.39490e11i | 0.874295i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.08468e11 | −0.830667 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.30318e11 | 0.151530 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.03399e11 | − | 2.70862e11i | 0.349868 | − | 0.312348i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.36193e12 | 1.55758 | 0.778789 | − | 0.627286i | \(-0.215834\pi\) | ||||
0.778789 | + | 0.627286i | \(0.215834\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.35410e12 | 1.53588 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.12453e12i | − | 1.26501i | −0.774556 | − | 0.632505i | \(-0.782027\pi\) | ||
0.774556 | − | 0.632505i | \(-0.217973\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.25334e11i | 0.586117i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.74646e12 | + | 1.98540e11i | 1.93259 | + | 0.219699i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.36587e12i | − | 1.49910i | −0.661949 | − | 0.749549i | \(-0.730270\pi\) | ||
0.661949 | − | 0.749549i | \(-0.269730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.33442e11i | − | 0.145266i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.06721e11 | 0.439158 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.23632e12 | −1.32409 | −0.662046 | − | 0.749463i | \(-0.730312\pi\) | ||||
−0.662046 | + | 0.749463i | \(0.730312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.50521e11 | − | 4.91483e11i | 0.584829 | − | 0.522112i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.17437e11 | −0.439868 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.03369e12 | 1.08045 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.30551e12i | − | 1.35359i | −0.736172 | − | 0.676794i | \(-0.763369\pi\) | ||
0.736172 | − | 0.676794i | \(-0.236631\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.17818e12i | − | 2.24025i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.01814e11 | − | 3.58723e11i | 0.409952 | − | 0.365989i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.69693e12i | − | 1.71744i | −0.512441 | − | 0.858722i | \(-0.671259\pi\) | ||
0.512441 | − | 0.858722i | \(-0.328741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.16803e11i | 0.117272i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 320.9.h.g.319.2 | 20 | ||
4.3 | odd | 2 | inner | 320.9.h.g.319.20 | 20 | ||
5.4 | even | 2 | inner | 320.9.h.g.319.19 | 20 | ||
8.3 | odd | 2 | 20.9.d.c.19.7 | ✓ | 20 | ||
8.5 | even | 2 | 20.9.d.c.19.13 | yes | 20 | ||
20.19 | odd | 2 | inner | 320.9.h.g.319.1 | 20 | ||
40.3 | even | 4 | 100.9.b.g.51.4 | 20 | |||
40.13 | odd | 4 | 100.9.b.g.51.3 | 20 | |||
40.19 | odd | 2 | 20.9.d.c.19.14 | yes | 20 | ||
40.27 | even | 4 | 100.9.b.g.51.17 | 20 | |||
40.29 | even | 2 | 20.9.d.c.19.8 | yes | 20 | ||
40.37 | odd | 4 | 100.9.b.g.51.18 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.9.d.c.19.7 | ✓ | 20 | 8.3 | odd | 2 | ||
20.9.d.c.19.8 | yes | 20 | 40.29 | even | 2 | ||
20.9.d.c.19.13 | yes | 20 | 8.5 | even | 2 | ||
20.9.d.c.19.14 | yes | 20 | 40.19 | odd | 2 | ||
100.9.b.g.51.3 | 20 | 40.13 | odd | 4 | |||
100.9.b.g.51.4 | 20 | 40.3 | even | 4 | |||
100.9.b.g.51.17 | 20 | 40.27 | even | 4 | |||
100.9.b.g.51.18 | 20 | 40.37 | odd | 4 | |||
320.9.h.g.319.1 | 20 | 20.19 | odd | 2 | inner | ||
320.9.h.g.319.2 | 20 | 1.1 | even | 1 | trivial | ||
320.9.h.g.319.19 | 20 | 5.4 | even | 2 | inner | ||
320.9.h.g.319.20 | 20 | 4.3 | odd | 2 | inner |