Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,8,Mod(1,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.a (trivial) |
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: | yes |
Analytic conductor: | \(98.4012830275\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 277x^{2} + 80x + 15348 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-12.8099\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.41438 | 0.301791 | 0.150896 | − | 0.988550i | \(-0.451784\pi\) | ||||
0.150896 | + | 0.988550i | \(0.451784\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −116.342 | −0.908922 | ||||||||
\(5\) | −125.000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −834.277 | −0.576096 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −426.798 | −0.134965 | ||||||||
\(11\) | 3379.63 | 0.765588 | 0.382794 | − | 0.923834i | \(-0.374962\pi\) | ||||
0.382794 | + | 0.923834i | \(0.374962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14159.0 | −1.78743 | −0.893716 | − | 0.448633i | \(-0.851911\pi\) | ||||
−0.893716 | + | 0.448633i | \(0.851911\pi\) | |||||||
\(14\) | 1171.13 | 0.114066 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12043.2 | 0.735061 | ||||||||
\(17\) | 19538.0 | 0.964516 | 0.482258 | − | 0.876029i | \(-0.339817\pi\) | ||||
0.482258 | + | 0.876029i | \(0.339817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −38098.7 | −1.27430 | −0.637152 | − | 0.770738i | \(-0.719888\pi\) | ||||
−0.637152 | + | 0.770738i | \(0.719888\pi\) | |||||||
\(20\) | 14542.8 | 0.406482 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11539.4 | 0.231048 | ||||||||
\(23\) | −103511. | −1.77394 | −0.886969 | − | 0.461828i | \(-0.847194\pi\) | ||||
−0.886969 | + | 0.461828i | \(0.847194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | −48344.1 | −0.539432 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −39905.3 | −0.343540 | ||||||||
\(29\) | −59794.5 | −0.455269 | −0.227635 | − | 0.973747i | \(-0.573099\pi\) | ||||
−0.227635 | + | 0.973747i | \(0.573099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 68349.9 | 0.412071 | 0.206035 | − | 0.978545i | \(-0.433944\pi\) | ||||
0.206035 | + | 0.978545i | \(0.433944\pi\) | |||||||
\(32\) | 147908. | 0.797931 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 66710.3 | 0.291083 | ||||||||
\(35\) | −42875.0 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 266512. | 0.864989 | 0.432494 | − | 0.901637i | \(-0.357634\pi\) | ||||
0.432494 | + | 0.901637i | \(0.357634\pi\) | |||||||
\(38\) | −130084. | −0.384574 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 104285. | 0.257638 | ||||||||
\(41\) | −655437. | −1.48521 | −0.742604 | − | 0.669730i | \(-0.766410\pi\) | ||||
−0.742604 | + | 0.669730i | \(0.766410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −775223. | −1.48692 | −0.743459 | − | 0.668782i | \(-0.766816\pi\) | ||||
−0.743459 | + | 0.668782i | \(0.766816\pi\) | |||||||
\(44\) | −393193. | −0.695860 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −353426. | −0.535360 | ||||||||
\(47\) | 119729. | 0.168211 | 0.0841057 | − | 0.996457i | \(-0.473197\pi\) | ||||
0.0841057 | + | 0.996457i | \(0.473197\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 53349.7 | 0.0603583 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.64728e6 | 1.62464 | ||||||||
\(53\) | −224102. | −0.206767 | −0.103383 | − | 0.994642i | \(-0.532967\pi\) | ||||
−0.103383 | + | 0.994642i | \(0.532967\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −422454. | −0.342382 | ||||||||
\(56\) | −286157. | −0.217744 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −204161. | −0.137396 | ||||||||
\(59\) | 409602. | 0.259645 | 0.129823 | − | 0.991537i | \(-0.458559\pi\) | ||||
0.129823 | + | 0.991537i | \(0.458559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.42274e6 | 0.802548 | 0.401274 | − | 0.915958i | \(-0.368568\pi\) | ||||
0.401274 | + | 0.915958i | \(0.368568\pi\) | |||||||
\(62\) | 233373. | 0.124359 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.03652e6 | −0.494252 | ||||||||
\(65\) | 1.76987e6 | 0.799364 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.22037e6 | 1.71431 | 0.857153 | − | 0.515061i | \(-0.172231\pi\) | ||||
0.857153 | + | 0.515061i | \(0.172231\pi\) | |||||||
\(68\) | −2.27309e6 | −0.876670 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −146392. | −0.0510121 | ||||||||
\(71\) | −2.17619e6 | −0.721595 | −0.360798 | − | 0.932644i | \(-0.617495\pi\) | ||||
−0.360798 | + | 0.932644i | \(0.617495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.43912e6 | 1.33557 | 0.667785 | − | 0.744354i | \(-0.267242\pi\) | ||||
0.667785 | + | 0.744354i | \(0.267242\pi\) | |||||||
\(74\) | 909973. | 0.261046 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.43248e6 | 1.15824 | ||||||||
\(77\) | 1.15921e6 | 0.289365 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.63306e6 | 0.372656 | 0.186328 | − | 0.982488i | \(-0.440341\pi\) | ||||
0.186328 | + | 0.982488i | \(0.440341\pi\) | |||||||
\(80\) | −1.50540e6 | −0.328729 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.23791e6 | −0.448223 | ||||||||
\(83\) | 3.49903e6 | 0.671698 | 0.335849 | − | 0.941916i | \(-0.390977\pi\) | ||||
0.335849 | + | 0.941916i | \(0.390977\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.44225e6 | −0.431345 | ||||||||
\(86\) | −2.64691e6 | −0.448739 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.81955e6 | −0.441053 | ||||||||
\(89\) | −2.03583e6 | −0.306110 | −0.153055 | − | 0.988218i | \(-0.548911\pi\) | ||||
−0.153055 | + | 0.988218i | \(0.548911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.85652e6 | −0.675586 | ||||||||
\(92\) | 1.20427e7 | 1.61237 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 408799. | 0.0507648 | ||||||||
\(95\) | 4.76234e6 | 0.569886 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.27049e7 | 1.41342 | 0.706709 | − | 0.707505i | \(-0.250179\pi\) | ||||
0.706709 | + | 0.707505i | \(0.250179\pi\) | |||||||
\(98\) | 401698. | 0.0431131 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.81784e6 | −0.181784 | ||||||||
\(101\) | 1.86609e7 | 1.80222 | 0.901110 | − | 0.433590i | \(-0.142753\pi\) | ||||
0.901110 | + | 0.433590i | \(0.142753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.30772e6 | 0.478606 | 0.239303 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239303 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(104\) | 1.18125e7 | 1.02973 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −765171. | −0.0624005 | ||||||||
\(107\) | −1.74818e7 | −1.37957 | −0.689784 | − | 0.724015i | \(-0.742295\pi\) | ||||
−0.689784 | + | 0.724015i | \(0.742295\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 467681. | 0.0345905 | 0.0172952 | − | 0.999850i | \(-0.494494\pi\) | ||||
0.0172952 | + | 0.999850i | \(0.494494\pi\) | |||||||
\(110\) | −1.44242e6 | −0.103328 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.13083e6 | 0.277827 | ||||||||
\(113\) | 1.45523e7 | 0.948763 | 0.474382 | − | 0.880319i | \(-0.342672\pi\) | ||||
0.474382 | + | 0.880319i | \(0.342672\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.29389e7 | 0.793329 | ||||||||
\(116\) | 6.95661e6 | 0.413804 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.39854e6 | 0.0783587 | ||||||||
\(119\) | 6.70154e6 | 0.364553 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.06524e6 | −0.413874 | ||||||||
\(122\) | 4.85777e6 | 0.242202 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.95196e6 | −0.374540 | ||||||||
\(125\) | −1.95312e6 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.04101e6 | 0.0884161 | 0.0442081 | − | 0.999022i | \(-0.485924\pi\) | ||||
0.0442081 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(128\) | −2.24713e7 | −0.947093 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.04301e6 | 0.241241 | ||||||||
\(131\) | 9.14330e6 | 0.355348 | 0.177674 | − | 0.984089i | \(-0.443143\pi\) | ||||
0.177674 | + | 0.984089i | \(0.443143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.30679e7 | −0.481642 | ||||||||
\(134\) | 1.44099e7 | 0.517363 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.63001e7 | −0.555654 | ||||||||
\(137\) | −3.62725e7 | −1.20519 | −0.602596 | − | 0.798047i | \(-0.705867\pi\) | ||||
−0.602596 | + | 0.798047i | \(0.705867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.28823e7 | −0.722682 | −0.361341 | − | 0.932434i | \(-0.617681\pi\) | ||||
−0.361341 | + | 0.932434i | \(0.617681\pi\) | |||||||
\(140\) | 4.98816e6 | 0.153636 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.43036e6 | −0.217771 | ||||||||
\(143\) | −4.78521e7 | −1.36844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.47431e6 | 0.203603 | ||||||||
\(146\) | 1.51568e7 | 0.403064 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.10065e7 | −0.786207 | ||||||||
\(149\) | 7.18870e7 | 1.78032 | 0.890161 | − | 0.455646i | \(-0.150592\pi\) | ||||
0.890161 | + | 0.455646i | \(0.150592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.39974e7 | 1.51267 | 0.756333 | − | 0.654187i | \(-0.226989\pi\) | ||||
0.756333 | + | 0.654187i | \(0.226989\pi\) | |||||||
\(152\) | 3.17849e7 | 0.734122 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.95800e6 | 0.0873280 | ||||||||
\(155\) | −8.54374e6 | −0.184284 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00497e6 | 0.123840 | 0.0619202 | − | 0.998081i | \(-0.480278\pi\) | ||||
0.0619202 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(158\) | 5.57589e6 | 0.112464 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.84885e7 | −0.356846 | ||||||||
\(161\) | −3.55042e7 | −0.670486 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.83028e7 | 1.77791 | 0.888954 | − | 0.457997i | \(-0.151433\pi\) | ||||
0.888954 | + | 0.457997i | \(0.151433\pi\) | |||||||
\(164\) | 7.62549e7 | 1.34994 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.19470e7 | 0.202713 | ||||||||
\(167\) | −5.80791e7 | −0.964966 | −0.482483 | − | 0.875905i | \(-0.660265\pi\) | ||||
−0.482483 | + | 0.875905i | \(0.660265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.37728e8 | 2.19491 | ||||||||
\(170\) | −8.33878e6 | −0.130176 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.01909e7 | 1.35149 | ||||||||
\(173\) | 2.31746e7 | 0.340291 | 0.170146 | − | 0.985419i | \(-0.445576\pi\) | ||||
0.170146 | + | 0.985419i | \(0.445576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.35938e6 | 0.0755929 | ||||||||
\(176\) | 4.07017e7 | 0.562754 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.95111e6 | −0.0923814 | ||||||||
\(179\) | −3.77902e7 | −0.492486 | −0.246243 | − | 0.969208i | \(-0.579196\pi\) | ||||
−0.246243 | + | 0.969208i | \(0.579196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.09325e6 | −0.113984 | −0.0569920 | − | 0.998375i | \(-0.518151\pi\) | ||||
−0.0569920 | + | 0.998375i | \(0.518151\pi\) | |||||||
\(182\) | −1.65820e7 | −0.203886 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.63567e7 | 1.02196 | ||||||||
\(185\) | −3.33140e7 | −0.386835 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.60314e7 | 0.738422 | ||||||||
\(188\) | −1.39295e7 | −0.152891 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.62605e7 | 0.171987 | ||||||||
\(191\) | 5.34900e7 | 0.555464 | 0.277732 | − | 0.960659i | \(-0.410417\pi\) | ||||
0.277732 | + | 0.960659i | \(0.410417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.24940e7 | −0.825984 | −0.412992 | − | 0.910735i | \(-0.635516\pi\) | ||||
−0.412992 | + | 0.910735i | \(0.635516\pi\) | |||||||
\(194\) | 4.33794e7 | 0.426557 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.36875e7 | −0.129846 | ||||||||
\(197\) | −7.55328e7 | −0.703888 | −0.351944 | − | 0.936021i | \(-0.614479\pi\) | ||||
−0.351944 | + | 0.936021i | \(0.614479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.05546e6 | −0.00949412 | −0.00474706 | − | 0.999989i | \(-0.501511\pi\) | ||||
−0.00474706 | + | 0.999989i | \(0.501511\pi\) | |||||||
\(200\) | −1.30356e7 | −0.115219 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.37154e7 | 0.543895 | ||||||||
\(203\) | −2.05095e7 | −0.172076 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.19296e7 | 0.664205 | ||||||||
\(206\) | 1.81226e7 | 0.144439 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.70520e8 | −1.31387 | ||||||||
\(209\) | −1.28760e8 | −0.975593 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.14474e7 | 0.0838916 | 0.0419458 | − | 0.999120i | \(-0.486644\pi\) | ||||
0.0419458 | + | 0.999120i | \(0.486644\pi\) | |||||||
\(212\) | 2.60725e7 | 0.187935 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.96896e7 | −0.416342 | ||||||||
\(215\) | 9.69028e7 | 0.664970 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.34440e7 | 0.155748 | ||||||||
\(218\) | 1.59684e6 | 0.0104391 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.91492e7 | 0.311198 | ||||||||
\(221\) | −2.76638e8 | −1.72401 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.81598e8 | 1.70044 | 0.850222 | − | 0.526425i | \(-0.176468\pi\) | ||||
0.850222 | + | 0.526425i | \(0.176468\pi\) | |||||||
\(224\) | 5.07323e7 | 0.301590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.96872e7 | 0.286329 | ||||||||
\(227\) | 4.00301e7 | 0.227141 | 0.113571 | − | 0.993530i | \(-0.463771\pi\) | ||||
0.113571 | + | 0.993530i | \(0.463771\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.24592e8 | −0.685591 | −0.342796 | − | 0.939410i | \(-0.611374\pi\) | ||||
−0.342796 | + | 0.939410i | \(0.611374\pi\) | |||||||
\(230\) | 4.41782e7 | 0.239420 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.98852e7 | 0.262279 | ||||||||
\(233\) | 3.21485e8 | 1.66500 | 0.832500 | − | 0.554025i | \(-0.186909\pi\) | ||||
0.832500 | + | 0.554025i | \(0.186909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.49661e7 | −0.0752264 | ||||||||
\(236\) | −4.76540e7 | −0.235997 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.28816e7 | 0.110019 | ||||||||
\(239\) | 2.95076e8 | 1.39811 | 0.699054 | − | 0.715068i | \(-0.253605\pi\) | ||||
0.699054 | + | 0.715068i | \(0.253605\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00887e8 | 0.464273 | 0.232137 | − | 0.972683i | \(-0.425428\pi\) | ||||
0.232137 | + | 0.972683i | \(0.425428\pi\) | |||||||
\(242\) | −2.75378e7 | −0.124904 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.65524e8 | −0.729453 | ||||||||
\(245\) | −1.47061e7 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.39439e8 | 2.27773 | ||||||||
\(248\) | −5.70227e7 | −0.237393 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.66871e6 | −0.0269931 | ||||||||
\(251\) | 9.30364e7 | 0.371360 | 0.185680 | − | 0.982610i | \(-0.440551\pi\) | ||||
0.185680 | + | 0.982610i | \(0.440551\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.49829e8 | −1.35811 | ||||||||
\(254\) | 6.96877e6 | 0.0266832 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.59493e7 | 0.208428 | ||||||||
\(257\) | −3.64584e8 | −1.33978 | −0.669888 | − | 0.742462i | \(-0.733658\pi\) | ||||
−0.669888 | + | 0.742462i | \(0.733658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.14136e7 | 0.326935 | ||||||||
\(260\) | −2.05910e8 | −0.726559 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.12187e7 | 0.107241 | ||||||||
\(263\) | −1.11633e8 | −0.378396 | −0.189198 | − | 0.981939i | \(-0.560589\pi\) | ||||
−0.189198 | + | 0.981939i | \(0.560589\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.80128e7 | 0.0924690 | ||||||||
\(266\) | −4.46187e7 | −0.145355 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.91006e8 | −1.55817 | ||||||||
\(269\) | 1.53396e8 | 0.480487 | 0.240244 | − | 0.970713i | \(-0.422773\pi\) | ||||
0.240244 | + | 0.970713i | \(0.422773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.17128e8 | −1.27314 | −0.636571 | − | 0.771218i | \(-0.719648\pi\) | ||||
−0.636571 | + | 0.771218i | \(0.719648\pi\) | |||||||
\(272\) | 2.35301e8 | 0.708978 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.23848e8 | −0.363717 | ||||||||
\(275\) | 5.28068e7 | 0.153118 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.05683e8 | −1.14685 | −0.573426 | − | 0.819257i | \(-0.694386\pi\) | ||||
−0.573426 | + | 0.819257i | \(0.694386\pi\) | |||||||
\(278\) | −7.81288e7 | −0.218099 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.57696e7 | 0.0973781 | ||||||||
\(281\) | 1.50774e8 | 0.405371 | 0.202686 | − | 0.979244i | \(-0.435033\pi\) | ||||
0.202686 | + | 0.979244i | \(0.435033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.69597e7 | −0.0969338 | −0.0484669 | − | 0.998825i | \(-0.515434\pi\) | ||||
−0.0484669 | + | 0.998825i | \(0.515434\pi\) | |||||||
\(284\) | 2.53183e8 | 0.655874 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.63385e8 | −0.412983 | ||||||||
\(287\) | −2.24815e8 | −0.561356 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.86042e7 | −0.0697088 | ||||||||
\(290\) | 2.55202e7 | 0.0614455 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.16456e8 | −1.21393 | ||||||||
\(293\) | 6.00426e8 | 1.39451 | 0.697257 | − | 0.716822i | \(-0.254404\pi\) | ||||
0.697257 | + | 0.716822i | \(0.254404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.12003e7 | −0.116117 | ||||||||
\(296\) | −2.22345e8 | −0.498317 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.45450e8 | 0.537286 | ||||||||
\(299\) | 1.46561e9 | 3.17079 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.65901e8 | −0.562002 | ||||||||
\(302\) | 2.18511e8 | 0.456510 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.58832e8 | −0.936691 | ||||||||
\(305\) | −1.77842e8 | −0.358910 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.08890e8 | 1.79278 | 0.896390 | − | 0.443267i | \(-0.146181\pi\) | ||||
0.896390 | + | 0.443267i | \(0.146181\pi\) | |||||||
\(308\) | −1.34865e8 | −0.263010 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.91716e7 | −0.0556153 | ||||||||
\(311\) | −6.45862e8 | −1.21753 | −0.608763 | − | 0.793352i | \(-0.708334\pi\) | ||||
−0.608763 | + | 0.793352i | \(0.708334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.96603e8 | −1.65270 | −0.826352 | − | 0.563154i | \(-0.809588\pi\) | ||||
−0.826352 | + | 0.563154i | \(0.809588\pi\) | |||||||
\(314\) | 2.05033e7 | 0.0373740 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.89994e8 | −0.338715 | ||||||||
\(317\) | −8.47295e8 | −1.49392 | −0.746959 | − | 0.664870i | \(-0.768487\pi\) | ||||
−0.746959 | + | 0.664870i | \(0.768487\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.02084e8 | −0.348549 | ||||||||
\(320\) | 1.29565e8 | 0.221036 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.21225e8 | −0.202347 | ||||||||
\(323\) | −7.44374e8 | −1.22909 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.21234e8 | −0.357486 | ||||||||
\(326\) | 3.35643e8 | 0.536557 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.46816e8 | 0.855623 | ||||||||
\(329\) | 4.10669e7 | 0.0635779 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.42401e8 | 1.12523 | 0.562614 | − | 0.826720i | \(-0.309796\pi\) | ||||
0.562614 | + | 0.826720i | \(0.309796\pi\) | |||||||
\(332\) | −4.07084e8 | −0.610521 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.98304e8 | −0.291219 | ||||||||
\(335\) | −5.27546e8 | −0.766661 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.24512e8 | −1.03120 | −0.515598 | − | 0.856831i | \(-0.672430\pi\) | ||||
−0.515598 | + | 0.856831i | \(0.672430\pi\) | |||||||
\(338\) | 4.70254e8 | 0.662406 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.84137e8 | 0.392059 | ||||||||
\(341\) | 2.30998e8 | 0.315477 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 6.46750e8 | 0.856608 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.91269e7 | 0.102697 | ||||||||
\(347\) | −5.09846e8 | −0.655068 | −0.327534 | − | 0.944839i | \(-0.606218\pi\) | ||||
−0.327534 | + | 0.944839i | \(0.606218\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.76052e8 | −1.10317 | −0.551583 | − | 0.834120i | \(-0.685976\pi\) | ||||
−0.551583 | + | 0.834120i | \(0.685976\pi\) | |||||||
\(350\) | 1.82989e7 | 0.0228133 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.99874e8 | 0.610887 | ||||||||
\(353\) | −1.26670e9 | −1.53272 | −0.766358 | − | 0.642413i | \(-0.777933\pi\) | ||||
−0.766358 | + | 0.642413i | \(0.777933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.72024e8 | 0.322707 | ||||||||
\(356\) | 2.36853e8 | 0.278230 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.29030e8 | −0.148628 | ||||||||
\(359\) | −1.66558e9 | −1.89992 | −0.949961 | − | 0.312369i | \(-0.898878\pi\) | ||||
−0.949961 | + | 0.312369i | \(0.898878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.57643e8 | 0.623851 | ||||||||
\(362\) | −3.10478e7 | −0.0343994 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.65018e8 | 0.614055 | ||||||||
\(365\) | −5.54890e8 | −0.597285 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.67575e9 | 1.76961 | 0.884807 | − | 0.465957i | \(-0.154290\pi\) | ||||
0.884807 | + | 0.465957i | \(0.154290\pi\) | |||||||
\(368\) | −1.24661e9 | −1.30395 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.13747e8 | −0.116743 | ||||||||
\(371\) | −7.68672e7 | −0.0781506 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.47694e9 | 1.47360 | 0.736802 | − | 0.676109i | \(-0.236335\pi\) | ||||
0.736802 | + | 0.676109i | \(0.236335\pi\) | |||||||
\(374\) | 2.25456e8 | 0.222850 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.98868e7 | −0.0969060 | ||||||||
\(377\) | 8.46628e8 | 0.813763 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.64279e9 | −1.55005 | −0.775024 | − | 0.631932i | \(-0.782262\pi\) | ||||
−0.775024 | + | 0.631932i | \(0.782262\pi\) | |||||||
\(380\) | −5.54061e8 | −0.517982 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.82635e8 | 0.167634 | ||||||||
\(383\) | 1.89784e9 | 1.72609 | 0.863044 | − | 0.505129i | \(-0.168555\pi\) | ||||
0.863044 | + | 0.505129i | \(0.168555\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.44902e8 | −0.129408 | ||||||||
\(386\) | −2.81666e8 | −0.249275 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.47811e9 | −1.28469 | ||||||||
\(389\) | −1.05432e9 | −0.908131 | −0.454065 | − | 0.890968i | \(-0.650027\pi\) | ||||
−0.454065 | + | 0.890968i | \(0.650027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.02240e9 | −1.71099 | ||||||||
\(392\) | −9.81518e7 | −0.0822995 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.57898e8 | −0.212428 | ||||||||
\(395\) | −2.04133e8 | −0.166657 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.96848e8 | 0.238104 | 0.119052 | − | 0.992888i | \(-0.462014\pi\) | ||||
0.119052 | + | 0.992888i | \(0.462014\pi\) | |||||||
\(398\) | −3.60373e6 | −0.00286525 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.88176e8 | 0.147012 | ||||||||
\(401\) | 7.79941e8 | 0.604028 | 0.302014 | − | 0.953304i | \(-0.402341\pi\) | ||||
0.302014 | + | 0.953304i | \(0.402341\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.67763e8 | −0.736549 | ||||||||
\(404\) | −2.17105e9 | −1.63808 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.00273e7 | −0.0519310 | ||||||||
\(407\) | 9.00713e8 | 0.662225 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.75152e8 | 0.632488 | 0.316244 | − | 0.948678i | \(-0.397578\pi\) | ||||
0.316244 | + | 0.948678i | \(0.397578\pi\) | |||||||
\(410\) | 2.79739e8 | 0.200452 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.17511e8 | −0.435015 | ||||||||
\(413\) | 1.40494e8 | 0.0981367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.37378e8 | −0.300392 | ||||||||
\(416\) | −2.09422e9 | −1.42625 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.39635e8 | −0.294426 | ||||||||
\(419\) | −1.07058e9 | −0.711000 | −0.355500 | − | 0.934676i | \(-0.615689\pi\) | ||||
−0.355500 | + | 0.934676i | \(0.615689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.54184e9 | 1.66020 | 0.830100 | − | 0.557614i | \(-0.188283\pi\) | ||||
0.830100 | + | 0.557614i | \(0.188283\pi\) | |||||||
\(422\) | 3.90858e7 | 0.0253178 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.86963e8 | 0.119118 | ||||||||
\(425\) | 3.05282e8 | 0.192903 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.87999e8 | 0.303335 | ||||||||
\(428\) | 2.03387e9 | 1.25392 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.30863e8 | 0.200682 | ||||||||
\(431\) | −8.91747e8 | −0.536502 | −0.268251 | − | 0.963349i | \(-0.586446\pi\) | ||||
−0.268251 | + | 0.963349i | \(0.586446\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.03966e9 | −0.615440 | −0.307720 | − | 0.951477i | \(-0.599566\pi\) | ||||
−0.307720 | + | 0.951477i | \(0.599566\pi\) | |||||||
\(434\) | 8.00468e7 | 0.0470035 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.44109e7 | −0.0314400 | ||||||||
\(437\) | 3.94363e9 | 2.26054 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.55931e9 | −0.879641 | −0.439821 | − | 0.898086i | \(-0.644958\pi\) | ||||
−0.439821 | + | 0.898086i | \(0.644958\pi\) | |||||||
\(440\) | 3.52444e8 | 0.197245 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.44548e8 | −0.520291 | ||||||||
\(443\) | 2.79970e8 | 0.153002 | 0.0765012 | − | 0.997069i | \(-0.475625\pi\) | ||||
0.0765012 | + | 0.997069i | \(0.475625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.54479e8 | 0.136897 | ||||||||
\(446\) | 9.61482e8 | 0.513179 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.55527e8 | −0.186810 | ||||||||
\(449\) | −6.18452e8 | −0.322436 | −0.161218 | − | 0.986919i | \(-0.551542\pi\) | ||||
−0.161218 | + | 0.986919i | \(0.551542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.21514e9 | −1.13706 | ||||||||
\(452\) | −1.69305e9 | −0.862352 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.36678e8 | 0.0685494 | ||||||||
\(455\) | 6.07065e8 | 0.302131 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.07329e8 | 0.444691 | 0.222345 | − | 0.974968i | \(-0.428629\pi\) | ||||
0.222345 | + | 0.974968i | \(0.428629\pi\) | |||||||
\(458\) | −4.25404e8 | −0.206906 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.50533e9 | −0.721075 | ||||||||
\(461\) | 2.41729e9 | 1.14915 | 0.574573 | − | 0.818453i | \(-0.305168\pi\) | ||||
0.574573 | + | 0.818453i | \(0.305168\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.14336e8 | −0.147184 | −0.0735921 | − | 0.997288i | \(-0.523446\pi\) | ||||
−0.0735921 | + | 0.997288i | \(0.523446\pi\) | |||||||
\(464\) | −7.20120e8 | −0.334651 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.09767e9 | 0.502483 | ||||||||
\(467\) | −4.74332e7 | −0.0215513 | −0.0107757 | − | 0.999942i | \(-0.503430\pi\) | ||||
−0.0107757 | + | 0.999942i | \(0.503430\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.44759e9 | 0.647947 | ||||||||
\(470\) | −5.10999e7 | −0.0227027 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.41722e8 | −0.149581 | ||||||||
\(473\) | −2.61997e9 | −1.13837 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.95293e8 | −0.254861 | ||||||||
\(476\) | −7.79671e8 | −0.331350 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.00750e9 | 0.421937 | ||||||||
\(479\) | 2.08794e9 | 0.868048 | 0.434024 | − | 0.900901i | \(-0.357093\pi\) | ||||
0.434024 | + | 0.900901i | \(0.357093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.77353e9 | −1.54611 | ||||||||
\(482\) | 3.44465e8 | 0.140114 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.38326e8 | 0.376179 | ||||||||
\(485\) | −1.58811e9 | −0.632099 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.19273e9 | −0.860267 | −0.430134 | − | 0.902765i | \(-0.641534\pi\) | ||||
−0.430134 | + | 0.902765i | \(0.641534\pi\) | |||||||
\(488\) | −1.18696e9 | −0.462345 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.02123e7 | −0.0192808 | ||||||||
\(491\) | −2.19027e9 | −0.835050 | −0.417525 | − | 0.908666i | \(-0.637102\pi\) | ||||
−0.417525 | + | 0.908666i | \(0.637102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.16827e9 | −0.439115 | ||||||||
\(494\) | 1.84185e9 | 0.687400 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.23154e8 | 0.302897 | ||||||||
\(497\) | −7.46435e8 | −0.272737 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.56737e8 | 0.236614 | 0.118307 | − | 0.992977i | \(-0.462253\pi\) | ||||
0.118307 | + | 0.992977i | \(0.462253\pi\) | |||||||
\(500\) | 2.27230e8 | 0.0812964 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.17662e8 | 0.112073 | ||||||||
\(503\) | 2.58040e9 | 0.904065 | 0.452033 | − | 0.892001i | \(-0.350699\pi\) | ||||
0.452033 | + | 0.892001i | \(0.350699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.33261e9 | −0.805977 | ||||||||
\(506\) | −1.19445e9 | −0.409865 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.37455e8 | −0.0803633 | ||||||||
\(509\) | 2.07943e9 | 0.698928 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.52262e9 | 0.504798 | ||||||||
\(512\) | 3.06735e9 | 1.00999 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.24483e9 | −0.404333 | ||||||||
\(515\) | −6.63465e8 | −0.214039 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.04639e8 | 0.128781 | ||||||||
\(518\) | 3.12121e8 | 0.0986662 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.47656e9 | −0.460511 | ||||||||
\(521\) | 2.82646e9 | 0.875609 | 0.437804 | − | 0.899070i | \(-0.355756\pi\) | ||||
0.437804 | + | 0.899070i | \(0.355756\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.81610e9 | 1.47211 | 0.736055 | − | 0.676922i | \(-0.236687\pi\) | ||||
0.736055 | + | 0.676922i | \(0.236687\pi\) | |||||||
\(524\) | −1.06375e9 | −0.322983 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.81157e8 | −0.114197 | ||||||||
\(527\) | 1.33542e9 | 0.397449 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.30968e9 | 2.14686 | ||||||||
\(530\) | 9.56464e7 | 0.0279064 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.52034e9 | 0.437775 | ||||||||
\(533\) | 9.28030e9 | 2.65471 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.18523e9 | 0.616962 | ||||||||
\(536\) | −3.52096e9 | −0.987606 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.23754e8 | 0.145007 | ||||||||
\(539\) | 3.97611e8 | 0.109370 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.56108e9 | 0.423871 | 0.211936 | − | 0.977284i | \(-0.432023\pi\) | ||||
0.211936 | + | 0.977284i | \(0.432023\pi\) | |||||||
\(542\) | −1.42423e9 | −0.384223 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.88982e9 | 0.769618 | ||||||||
\(545\) | −5.84601e7 | −0.0154693 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.82511e8 | −0.0999282 | −0.0499641 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499641 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(548\) | 4.22002e9 | 1.09543 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.80303e8 | 0.0462096 | ||||||||
\(551\) | 2.27810e9 | 0.580152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.60140e8 | 0.140851 | ||||||||
\(554\) | −1.38516e9 | −0.346110 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.66217e9 | 0.656861 | ||||||||
\(557\) | 7.35207e9 | 1.80267 | 0.901335 | − | 0.433122i | \(-0.142588\pi\) | ||||
0.901335 | + | 0.433122i | \(0.142588\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.09763e10 | 2.65776 | ||||||||
\(560\) | −5.16354e8 | −0.124248 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.14798e8 | 0.122338 | ||||||||
\(563\) | −7.91584e9 | −1.86947 | −0.934733 | − | 0.355352i | \(-0.884361\pi\) | ||||
−0.934733 | + | 0.355352i | \(0.884361\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.81904e9 | −0.424300 | ||||||||
\(566\) | −1.26194e8 | −0.0292538 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.81555e9 | 0.415708 | ||||||||
\(569\) | −4.49464e9 | −1.02283 | −0.511414 | − | 0.859335i | \(-0.670878\pi\) | ||||
−0.511414 | + | 0.859335i | \(0.670878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.15052e9 | −0.483412 | −0.241706 | − | 0.970350i | \(-0.577707\pi\) | ||||
−0.241706 | + | 0.970350i | \(0.577707\pi\) | |||||||
\(572\) | 5.56721e9 | 1.24380 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.67604e8 | −0.169412 | ||||||||
\(575\) | −1.61736e9 | −0.354788 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.73438e9 | −0.375862 | −0.187931 | − | 0.982182i | \(-0.560178\pi\) | ||||
−0.187931 | + | 0.982182i | \(0.560178\pi\) | |||||||
\(578\) | −9.76656e7 | −0.0210375 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.69577e8 | −0.185059 | ||||||||
\(581\) | 1.20017e9 | 0.253878 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.57385e8 | −0.158298 | ||||||||
\(584\) | −3.70345e9 | −0.769418 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.05008e9 | 0.420852 | ||||||||
\(587\) | 2.98775e9 | 0.609692 | 0.304846 | − | 0.952402i | \(-0.401395\pi\) | ||||
0.304846 | + | 0.952402i | \(0.401395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.60405e9 | −0.525104 | ||||||||
\(590\) | −1.74817e8 | −0.0350431 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.20967e9 | 0.635819 | ||||||||
\(593\) | −5.56485e9 | −1.09588 | −0.547938 | − | 0.836519i | \(-0.684587\pi\) | ||||
−0.547938 | + | 0.836519i | \(0.684587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.37693e8 | −0.163033 | ||||||||
\(596\) | −8.36348e9 | −1.61817 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.00414e9 | 0.956919 | ||||||||
\(599\) | 5.39399e9 | 1.02545 | 0.512727 | − | 0.858552i | \(-0.328635\pi\) | ||||
0.512727 | + | 0.858552i | \(0.328635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.88616e8 | −0.110604 | −0.0553021 | − | 0.998470i | \(-0.517612\pi\) | ||||
−0.0553021 | + | 0.998470i | \(0.517612\pi\) | |||||||
\(602\) | −9.07888e8 | −0.169607 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.44558e9 | −1.37489 | ||||||||
\(605\) | 1.00815e9 | 0.185090 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.38304e9 | 0.976938 | 0.488469 | − | 0.872581i | \(-0.337556\pi\) | ||||
0.488469 | + | 0.872581i | \(0.337556\pi\) | |||||||
\(608\) | −5.63509e9 | −1.01681 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.07222e8 | −0.108316 | ||||||||
\(611\) | −1.69523e9 | −0.300667 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.87502e9 | 1.55617 | 0.778086 | − | 0.628158i | \(-0.216191\pi\) | ||||
0.778086 | + | 0.628158i | \(0.216191\pi\) | |||||||
\(614\) | 3.10330e9 | 0.541046 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.67106e8 | −0.166702 | ||||||||
\(617\) | −5.94996e6 | −0.00101980 | −0.000509901 | − | 1.00000i | \(-0.500162\pi\) | ||||
−0.000509901 | 1.00000i | \(0.500162\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.21425e9 | 1.39204 | 0.696019 | − | 0.718024i | \(-0.254953\pi\) | ||||
0.696019 | + | 0.718024i | \(0.254953\pi\) | |||||||
\(620\) | 9.93996e8 | 0.167500 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.20522e9 | −0.367439 | ||||||||
\(623\) | −6.98291e8 | −0.115699 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −3.06134e9 | −0.498772 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.98631e8 | −0.112561 | ||||||||
\(629\) | 5.20711e9 | 0.834295 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.53051e9 | 0.400964 | 0.200482 | − | 0.979697i | \(-0.435749\pi\) | ||||
0.200482 | + | 0.979697i | \(0.435749\pi\) | |||||||
\(632\) | −1.36243e9 | −0.214686 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.89299e9 | −0.450852 | ||||||||
\(635\) | −2.55126e8 | −0.0395409 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.66579e9 | −0.255347 | ||||||||
\(638\) | −6.89990e8 | −0.105189 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.80891e9 | 0.423553 | ||||||||
\(641\) | −6.96698e9 | −1.04482 | −0.522410 | − | 0.852694i | \(-0.674967\pi\) | ||||
−0.522410 | + | 0.852694i | \(0.674967\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.21823e10 | 1.80714 | 0.903572 | − | 0.428437i | \(-0.140936\pi\) | ||||
0.903572 | + | 0.428437i | \(0.140936\pi\) | |||||||
\(644\) | 4.13063e9 | 0.609419 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.54158e9 | −0.370928 | ||||||||
\(647\) | 9.95454e9 | 1.44496 | 0.722481 | − | 0.691391i | \(-0.243002\pi\) | ||||
0.722481 | + | 0.691391i | \(0.243002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.38431e9 | 0.198781 | ||||||||
\(650\) | −7.55376e8 | −0.107886 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.14367e10 | −1.61598 | ||||||||
\(653\) | −2.38576e9 | −0.335297 | −0.167649 | − | 0.985847i | \(-0.553617\pi\) | ||||
−0.167649 | + | 0.985847i | \(0.553617\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.14291e9 | −0.158916 | ||||||||
\(656\) | −7.89358e9 | −1.09172 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.40218e8 | 0.0191873 | ||||||||
\(659\) | −1.98573e8 | −0.0270284 | −0.0135142 | − | 0.999909i | \(-0.504302\pi\) | ||||
−0.0135142 | + | 0.999909i | \(0.504302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.68735e9 | 0.227247 | 0.113624 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113624 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(662\) | 2.53484e9 | 0.339584 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.91916e9 | −0.386963 | ||||||||
\(665\) | 1.63348e9 | 0.215397 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.18938e9 | 0.807620 | ||||||||
\(668\) | 6.75704e9 | 0.877079 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.80124e9 | −0.231372 | ||||||||
\(671\) | 4.80834e9 | 0.614421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.02352e9 | −0.635266 | −0.317633 | − | 0.948214i | \(-0.602888\pi\) | ||||
−0.317633 | + | 0.948214i | \(0.602888\pi\) | |||||||
\(674\) | −2.47376e9 | −0.311206 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.60235e10 | −1.99501 | ||||||||
\(677\) | 1.03907e10 | 1.28702 | 0.643510 | − | 0.765438i | \(-0.277477\pi\) | ||||
0.643510 | + | 0.765438i | \(0.277477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.35778e9 | 0.534222 | ||||||||
\(680\) | 2.03751e9 | 0.248496 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.88714e8 | 0.0952082 | ||||||||
\(683\) | −3.61608e9 | −0.434276 | −0.217138 | − | 0.976141i | \(-0.569672\pi\) | ||||
−0.217138 | + | 0.976141i | \(0.569672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.53407e9 | 0.538978 | ||||||||
\(686\) | 1.37783e8 | 0.0162952 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.33619e9 | −1.09297 | ||||||||
\(689\) | 3.17306e9 | 0.369582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.65856e10 | 1.91231 | 0.956153 | − | 0.292869i | \(-0.0946100\pi\) | ||||
0.956153 | + | 0.292869i | \(0.0946100\pi\) | |||||||
\(692\) | −2.69618e9 | −0.309298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.74081e9 | −0.197694 | ||||||||
\(695\) | 2.86028e9 | 0.323193 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.28059e10 | −1.43251 | ||||||||
\(698\) | −2.99117e9 | −0.332926 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.23520e8 | −0.0687080 | ||||||||
\(701\) | −1.42971e10 | −1.56760 | −0.783798 | − | 0.621015i | \(-0.786720\pi\) | ||||
−0.783798 | + | 0.621015i | \(0.786720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.01538e10 | −1.10226 | ||||||||
\(704\) | −3.50306e9 | −0.378394 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.32499e9 | −0.462561 | ||||||||
\(707\) | 6.40069e9 | 0.681175 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.66391e9 | 0.491460 | 0.245730 | − | 0.969338i | \(-0.420972\pi\) | ||||
0.245730 | + | 0.969338i | \(0.420972\pi\) | |||||||
\(710\) | 9.28795e8 | 0.0973903 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.69845e9 | 0.176349 | ||||||||
\(713\) | −7.07496e9 | −0.730989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.98151e9 | 0.611984 | ||||||||
\(716\) | 4.39659e9 | 0.447631 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.68694e9 | −0.573380 | ||||||||
\(719\) | −4.82173e9 | −0.483784 | −0.241892 | − | 0.970303i | \(-0.577768\pi\) | ||||
−0.241892 | + | 0.970303i | \(0.577768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.82055e9 | 0.180896 | ||||||||
\(722\) | 1.90400e9 | 0.188273 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.05793e9 | 0.103603 | ||||||||
\(725\) | −9.34289e8 | −0.0910539 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.17621e9 | 0.210054 | 0.105027 | − | 0.994469i | \(-0.466507\pi\) | ||||
0.105027 | + | 0.994469i | \(0.466507\pi\) | |||||||
\(728\) | 4.05168e9 | 0.389203 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.89461e9 | −0.180256 | ||||||||
\(731\) | −1.51463e10 | −1.43416 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.65228e9 | 0.436317 | 0.218158 | − | 0.975913i | \(-0.429995\pi\) | ||||
0.218158 | + | 0.975913i | \(0.429995\pi\) | |||||||
\(734\) | 5.72166e9 | 0.534055 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.53100e10 | −1.41548 | ||||||||
\(737\) | 1.42633e10 | 1.31245 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.05338e8 | 0.0369456 | 0.0184728 | − | 0.999829i | \(-0.494120\pi\) | ||||
0.0184728 | + | 0.999829i | \(0.494120\pi\) | |||||||
\(740\) | 3.87581e9 | 0.351603 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.62454e8 | −0.0235852 | ||||||||
\(743\) | −1.08140e10 | −0.967223 | −0.483611 | − | 0.875283i | \(-0.660675\pi\) | ||||
−0.483611 | + | 0.875283i | \(0.660675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.98588e9 | −0.796184 | ||||||||
\(746\) | 5.04282e9 | 0.444721 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.68222e9 | −0.671168 | ||||||||
\(749\) | −5.99626e9 | −0.521428 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.42070e10 | −1.22394 | −0.611972 | − | 0.790880i | \(-0.709623\pi\) | ||||
−0.611972 | + | 0.790880i | \(0.709623\pi\) | |||||||
\(752\) | 1.44192e9 | 0.123646 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.89071e9 | 0.245587 | ||||||||
\(755\) | −7.99967e9 | −0.676485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.78427e9 | 0.317064 | 0.158532 | − | 0.987354i | \(-0.449324\pi\) | ||||
0.158532 | + | 0.987354i | \(0.449324\pi\) | |||||||
\(758\) | −5.60911e9 | −0.467791 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.97311e9 | −0.328309 | ||||||||
\(761\) | −1.01511e10 | −0.834966 | −0.417483 | − | 0.908685i | \(-0.637088\pi\) | ||||
−0.417483 | + | 0.908685i | \(0.637088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.60414e8 | 0.0130740 | ||||||||
\(764\) | −6.22314e9 | −0.504874 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.47993e9 | 0.520919 | ||||||||
\(767\) | −5.79954e9 | −0.464098 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.31076e10 | −1.03939 | −0.519696 | − | 0.854351i | \(-0.673955\pi\) | ||||
−0.519696 | + | 0.854351i | \(0.673955\pi\) | |||||||
\(770\) | −4.94750e8 | −0.0390543 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.59751e9 | 0.750755 | ||||||||
\(773\) | 1.40370e10 | 1.09307 | 0.546533 | − | 0.837438i | \(-0.315947\pi\) | ||||
0.546533 | + | 0.837438i | \(0.315947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.06797e9 | 0.0824142 | ||||||||
\(776\) | −1.05994e10 | −0.814265 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.59985e9 | −0.274066 | ||||||||
\(779\) | 2.49713e10 | 1.89261 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.35474e9 | −0.552445 | ||||||||
\(782\) | −6.90524e9 | −0.516363 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.41687e9 | 0.105009 | ||||||||
\(785\) | −7.50622e8 | −0.0553831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.87288e9 | −0.283219 | −0.141610 | − | 0.989923i | \(-0.545228\pi\) | ||||
−0.141610 | + | 0.989923i | \(0.545228\pi\) | |||||||
\(788\) | 8.78764e9 | 0.639780 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.96987e8 | −0.0502956 | ||||||||
\(791\) | 4.99145e9 | 0.358599 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.01445e10 | −1.43450 | ||||||||
\(794\) | 1.01355e9 | 0.0718578 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.22794e8 | 0.00862942 | ||||||||
\(797\) | 8.56688e9 | 0.599403 | 0.299701 | − | 0.954033i | \(-0.403113\pi\) | ||||
0.299701 | + | 0.954033i | \(0.403113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.33926e9 | 0.162243 | ||||||||
\(800\) | 2.31106e9 | 0.159586 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.66302e9 | 0.182290 | ||||||||
\(803\) | 1.50026e10 | 1.02250 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.43803e9 | 0.299850 | ||||||||
\(806\) | −3.30431e9 | −0.222284 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.55684e10 | −1.03825 | ||||||||
\(809\) | 1.49503e10 | 0.992731 | 0.496365 | − | 0.868114i | \(-0.334668\pi\) | ||||
0.496365 | + | 0.868114i | \(0.334668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.61940e9 | −0.567419 | −0.283710 | − | 0.958910i | \(-0.591565\pi\) | ||||
−0.283710 | + | 0.958910i | \(0.591565\pi\) | |||||||
\(812\) | 2.38612e9 | 0.156403 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.07538e9 | 0.199854 | ||||||||
\(815\) | −1.22878e10 | −0.795104 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.95350e10 | 1.89478 | ||||||||
\(818\) | 2.98810e9 | 0.190879 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.53186e9 | −0.603711 | ||||||||
\(821\) | −2.53165e10 | −1.59663 | −0.798313 | − | 0.602243i | \(-0.794274\pi\) | ||||
−0.798313 | + | 0.602243i | \(0.794274\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.51790e9 | 0.0949171 | 0.0474586 | − | 0.998873i | \(-0.484888\pi\) | ||||
0.0474586 | + | 0.998873i | \(0.484888\pi\) | |||||||
\(824\) | −4.42811e9 | −0.275723 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.79699e8 | 0.0296168 | ||||||||
\(827\) | −1.68322e10 | −1.03484 | −0.517418 | − | 0.855733i | \(-0.673107\pi\) | ||||
−0.517418 | + | 0.855733i | \(0.673107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.54259e10 | −0.940396 | −0.470198 | − | 0.882561i | \(-0.655818\pi\) | ||||
−0.470198 | + | 0.882561i | \(0.655818\pi\) | |||||||
\(830\) | −1.49338e9 | −0.0906559 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.46761e10 | 0.883442 | ||||||||
\(833\) | 2.29863e9 | 0.137788 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.25988e9 | 0.431546 | ||||||||
\(836\) | 1.49802e10 | 0.886737 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.65536e9 | −0.214574 | ||||||||
\(839\) | 1.06044e9 | 0.0619894 | 0.0309947 | − | 0.999520i | \(-0.490132\pi\) | ||||
0.0309947 | + | 0.999520i | \(0.490132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.36745e10 | −0.792730 | ||||||||
\(842\) | 8.67880e9 | 0.501034 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.33181e9 | −0.0762509 | ||||||||
\(845\) | −1.72159e10 | −0.981595 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.76638e9 | −0.156430 | ||||||||
\(848\) | −2.69892e9 | −0.151986 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.04235e9 | 0.0582165 | ||||||||
\(851\) | −2.75869e10 | −1.53444 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.03756e10 | 1.67573 | 0.837864 | − | 0.545878i | \(-0.183804\pi\) | ||||
0.837864 | + | 0.545878i | \(0.183804\pi\) | |||||||
\(854\) | 1.66622e9 | 0.0915438 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.45847e10 | 0.794764 | ||||||||
\(857\) | 1.27509e10 | 0.692001 | 0.346001 | − | 0.938234i | \(-0.387539\pi\) | ||||
0.346001 | + | 0.938234i | \(0.387539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.08205e10 | 0.582467 | 0.291233 | − | 0.956652i | \(-0.405934\pi\) | ||||
0.291233 | + | 0.956652i | \(0.405934\pi\) | |||||||
\(860\) | −1.12739e10 | −0.604405 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.04476e9 | −0.161912 | ||||||||
\(863\) | −6.05794e9 | −0.320839 | −0.160419 | − | 0.987049i | \(-0.551285\pi\) | ||||
−0.160419 | + | 0.987049i | \(0.551285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.89682e9 | −0.152183 | ||||||||
\(866\) | −3.54981e9 | −0.185734 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.72752e9 | −0.141563 | ||||||||
\(869\) | 5.51915e9 | 0.285301 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.97560e10 | −3.06421 | ||||||||
\(872\) | −3.90175e8 | −0.0199274 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.34651e10 | 0.682211 | ||||||||
\(875\) | −6.69922e8 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.64172e9 | 0.282431 | 0.141216 | − | 0.989979i | \(-0.454899\pi\) | ||||
0.141216 | + | 0.989979i | \(0.454899\pi\) | |||||||
\(878\) | −5.32407e9 | −0.265468 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.08772e9 | −0.251671 | ||||||||
\(881\) | 1.41128e9 | 0.0695339 | 0.0347669 | − | 0.999395i | \(-0.488931\pi\) | ||||
0.0347669 | + | 0.999395i | \(0.488931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.83461e10 | 0.896773 | 0.448386 | − | 0.893840i | \(-0.351999\pi\) | ||||
0.448386 | + | 0.893840i | \(0.351999\pi\) | |||||||
\(884\) | 3.21846e10 | 1.56699 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.55923e8 | 0.0461748 | ||||||||
\(887\) | −6.77821e9 | −0.326124 | −0.163062 | − | 0.986616i | \(-0.552137\pi\) | ||||
−0.163062 | + | 0.986616i | \(0.552137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.00065e8 | 0.0334182 | ||||||||
\(890\) | 8.68889e8 | 0.0413142 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.27617e10 | −1.54557 | ||||||||
\(893\) | −4.56151e9 | −0.214353 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.72378e9 | 0.220246 | ||||||||
\(896\) | −7.70764e9 | −0.357967 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.11163e9 | −0.0973085 | ||||||||
\(899\) | −4.08695e9 | −0.187603 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.37852e9 | −0.199430 | ||||||||
\(902\) | −7.56332e9 | −0.343155 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.21407e10 | −0.546579 | ||||||||
\(905\) | 1.13666e9 | 0.0509752 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.32813e9 | −0.148107 | −0.0740535 | − | 0.997254i | \(-0.523594\pi\) | ||||
−0.0740535 | + | 0.997254i | \(0.523594\pi\) | |||||||
\(908\) | −4.65718e9 | −0.206454 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.07275e9 | 0.0911806 | ||||||||
\(911\) | −7.48533e9 | −0.328017 | −0.164009 | − | 0.986459i | \(-0.552442\pi\) | ||||
−0.164009 | + | 0.986459i | \(0.552442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.18254e10 | 0.514244 | ||||||||
\(914\) | 3.09797e9 | 0.134204 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.44953e10 | 0.623149 | ||||||||
\(917\) | 3.13615e9 | 0.134309 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.84326e10 | 1.63341 | 0.816705 | − | 0.577056i | \(-0.195799\pi\) | ||||
0.816705 | + | 0.577056i | \(0.195799\pi\) | |||||||
\(920\) | −1.07946e10 | −0.457034 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.25354e9 | 0.346802 | ||||||||
\(923\) | 3.08127e10 | 1.28980 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.16425e9 | 0.172998 | ||||||||
\(926\) | −1.07326e9 | −0.0444189 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.84406e9 | −0.363274 | ||||||||
\(929\) | −2.74203e10 | −1.12206 | −0.561032 | − | 0.827794i | \(-0.689596\pi\) | ||||
−0.561032 | + | 0.827794i | \(0.689596\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.48228e9 | −0.182043 | ||||||||
\(932\) | −3.74022e10 | −1.51336 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.61955e8 | −0.00650400 | ||||||||
\(935\) | −8.25392e9 | −0.330233 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.33959e9 | −0.0929077 | −0.0464539 | − | 0.998920i | \(-0.514792\pi\) | ||||
−0.0464539 | + | 0.998920i | \(0.514792\pi\) | |||||||
\(938\) | 4.94261e9 | 0.195545 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.74118e9 | 0.0683750 | ||||||||
\(941\) | 4.04198e10 | 1.58136 | 0.790680 | − | 0.612230i | \(-0.209727\pi\) | ||||
0.790680 | + | 0.612230i | \(0.209727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.78449e10 | 2.63467 | ||||||||
\(944\) | 4.93294e9 | 0.190855 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.94557e9 | −0.343549 | ||||||||
\(947\) | −2.68103e10 | −1.02583 | −0.512917 | − | 0.858438i | \(-0.671435\pi\) | ||||
−0.512917 | + | 0.858438i | \(0.671435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.28533e10 | −2.38724 | ||||||||
\(950\) | −2.03256e9 | −0.0769148 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.59094e9 | −0.210018 | ||||||||
\(953\) | 6.72263e9 | 0.251602 | 0.125801 | − | 0.992056i | \(-0.459850\pi\) | ||||
0.125801 | + | 0.992056i | \(0.459850\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.68625e9 | −0.248411 | ||||||||
\(956\) | −3.43297e10 | −1.27077 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.12902e9 | 0.261970 | ||||||||
\(959\) | −1.24415e10 | −0.455520 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.28409e10 | −0.830198 | ||||||||
\(962\) | −1.28843e10 | −0.466602 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.17373e10 | −0.421988 | ||||||||
\(965\) | 1.03117e10 | 0.369391 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.39023e10 | 0.850055 | 0.425027 | − | 0.905180i | \(-0.360264\pi\) | ||||
0.425027 | + | 0.905180i | \(0.360264\pi\) | |||||||
\(968\) | 6.72864e9 | 0.238431 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.42242e9 | −0.190762 | ||||||||
\(971\) | −1.65771e10 | −0.581088 | −0.290544 | − | 0.956862i | \(-0.593836\pi\) | ||||
−0.290544 | + | 0.956862i | \(0.593836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.84862e9 | −0.273148 | ||||||||
\(974\) | −7.48681e9 | −0.259621 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.71344e10 | 0.589921 | ||||||||
\(977\) | 2.03177e10 | 0.697018 | 0.348509 | − | 0.937305i | \(-0.386688\pi\) | ||||
0.348509 | + | 0.937305i | \(0.386688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.88038e9 | −0.234354 | ||||||||
\(980\) | 1.71094e9 | 0.0580689 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.47841e9 | −0.252011 | ||||||||
\(983\) | −4.78793e10 | −1.60772 | −0.803861 | − | 0.594818i | \(-0.797224\pi\) | ||||
−0.803861 | + | 0.594818i | \(0.797224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.44160e9 | 0.314788 | ||||||||
\(986\) | −3.98891e9 | −0.132521 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.27594e10 | −2.07028 | ||||||||
\(989\) | 8.02440e10 | 2.63770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.99787e10 | −0.652092 | −0.326046 | − | 0.945354i | \(-0.605716\pi\) | ||||
−0.326046 | + | 0.945354i | \(0.605716\pi\) | |||||||
\(992\) | 1.01095e10 | 0.328804 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.54861e9 | −0.0823098 | ||||||||
\(995\) | 1.31932e8 | 0.00424590 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.49634e10 | 1.43690 | 0.718450 | − | 0.695579i | \(-0.244852\pi\) | ||||
0.718450 | + | 0.695579i | \(0.244852\pi\) | |||||||
\(998\) | 2.24235e9 | 0.0714080 | ||||||||
\(999\) | 0 | 0 |
(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 | 315.8.a.g.1.3 | 4 | ||
3.2 | odd | 2 | 105.8.a.h.1.2 | ✓ | 4 | ||
15.14 | odd | 2 | 525.8.a.i.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.8.a.h.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
315.8.a.g.1.3 | 4 | 1.1 | even | 1 | trivial | ||
525.8.a.i.1.3 | 4 | 15.14 | odd | 2 |