Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,10,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.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: | \(206.014334466\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 652x + 4000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(22.2334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 210.171 | 1.49805 | 0.749027 | − | 0.662539i | \(-0.230521\pi\) | ||||
0.749027 | + | 0.662539i | \(0.230521\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9905.49 | −1.55932 | −0.779659 | − | 0.626204i | \(-0.784608\pi\) | ||||
−0.779659 | + | 0.626204i | \(0.784608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 24489.0 | 1.24417 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −36453.6 | −0.750712 | −0.375356 | − | 0.926881i | \(-0.622480\pi\) | ||||
−0.375356 | + | 0.926881i | \(0.622480\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 164867. | 1.60099 | 0.800494 | − | 0.599341i | \(-0.204571\pi\) | ||||
0.800494 | + | 0.599341i | \(0.204571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82357.1 | 0.239156 | 0.119578 | − | 0.992825i | \(-0.461846\pi\) | ||||
0.119578 | + | 0.992825i | \(0.461846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 609617. | 1.07316 | 0.536582 | − | 0.843848i | \(-0.319715\pi\) | ||||
0.536582 | + | 0.843848i | \(0.319715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08185e6 | −2.33594 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.88578e6 | −1.40513 | −0.702564 | − | 0.711620i | \(-0.747962\pi\) | ||||
−0.702564 | + | 0.711620i | \(0.747962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.01008e6 | 0.365778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 339235. | 0.0890657 | 0.0445328 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445328 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −547314. | −0.106441 | −0.0532205 | − | 0.998583i | \(-0.516949\pi\) | ||||
−0.0532205 | + | 0.998583i | \(0.516949\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.66150e6 | −1.12461 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.25687e6 | 0.461126 | 0.230563 | − | 0.973057i | \(-0.425943\pi\) | ||||
0.230563 | + | 0.973057i | \(0.425943\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.46503e7 | 2.39837 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.05812e6 | 0.113748 | 0.0568739 | − | 0.998381i | \(-0.481887\pi\) | ||||
0.0568739 | + | 0.998381i | \(0.481887\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.76158e6 | 0.301606 | 0.150803 | − | 0.988564i | \(-0.451814\pi\) | ||||
0.150803 | + | 0.988564i | \(0.451814\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.15241e7 | −0.942330 | −0.471165 | − | 0.882045i | \(-0.656166\pi\) | ||||
−0.471165 | + | 0.882045i | \(0.656166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.77651e7 | 1.43147 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.73091e7 | 0.358268 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.89593e7 | −0.852303 | −0.426151 | − | 0.904652i | \(-0.640131\pi\) | ||||
−0.426151 | + | 0.904652i | \(0.640131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.28124e8 | 1.60766 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.77960e7 | −0.943281 | −0.471640 | − | 0.881791i | \(-0.656338\pi\) | ||||
−0.471640 | + | 0.881791i | \(0.656338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.84654e7 | 0.355701 | 0.177851 | − | 0.984057i | \(-0.443086\pi\) | ||||
0.177851 | + | 0.984057i | \(0.443086\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.42575e8 | −1.94005 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.36116e8 | 0.825227 | 0.412613 | − | 0.910906i | \(-0.364616\pi\) | ||||
0.412613 | + | 0.910906i | \(0.364616\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.96337e8 | −2.10496 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.49218e8 | −1.63092 | −0.815462 | − | 0.578810i | \(-0.803517\pi\) | ||||
−0.815462 | + | 0.578810i | \(0.803517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.61345e8 | 0.664971 | 0.332486 | − | 0.943108i | \(-0.392113\pi\) | ||||
0.332486 | + | 0.943108i | \(0.392113\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.61091e8 | 1.17060 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.26975e8 | 0.366772 | 0.183386 | − | 0.983041i | \(-0.441294\pi\) | ||||
0.183386 | + | 0.983041i | \(0.441294\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.69727e8 | −0.696213 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.87494e8 | 0.664931 | 0.332466 | − | 0.943115i | \(-0.392119\pi\) | ||||
0.332466 | + | 0.943115i | \(0.392119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.12976e7 | 0.133425 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.63133e8 | −0.951385 | −0.475692 | − | 0.879612i | \(-0.657802\pi\) | ||||
−0.475692 | + | 0.879612i | \(0.657802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.63309e9 | −2.49645 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.15030e8 | −0.159454 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.71704e8 | −0.541000 | −0.270500 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270500 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.92711e8 | −0.934012 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.25673e9 | −1.20170 | −0.600851 | − | 0.799361i | \(-0.705172\pi\) | ||||
−0.600851 | + | 0.799361i | \(0.705172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.95398e9 | −1.71062 | −0.855309 | − | 0.518119i | \(-0.826633\pi\) | ||||
−0.855309 | + | 0.518119i | \(0.826633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.12306e9 | −1.56580 | −0.782899 | − | 0.622148i | \(-0.786260\pi\) | ||||
−0.782899 | + | 0.622148i | \(0.786260\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.18863e8 | −0.0806544 | −0.0403272 | − | 0.999187i | \(-0.512840\pi\) | ||||
−0.0403272 | + | 0.999187i | \(0.512840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.10484e9 | 0.690791 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.85455e9 | −1.07001 | −0.535003 | − | 0.844850i | \(-0.679689\pi\) | ||||
−0.535003 | + | 0.844850i | \(0.679689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.03742e9 | 1.99190 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.15787e8 | −0.372920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.02908e9 | −0.436432 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.32557e8 | 0.170400 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.39208e9 | 1.83924 | 0.919622 | − | 0.392805i | \(-0.128495\pi\) | ||||
0.919622 | + | 0.392805i | \(0.128495\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.42109e9 | 0.451823 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.83690e9 | −1.13831 | −0.569154 | − | 0.822231i | \(-0.692729\pi\) | ||||
−0.569154 | + | 0.822231i | \(0.692729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.03856e9 | −1.67340 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.55408e9 | −0.619430 | −0.309715 | − | 0.950829i | \(-0.600234\pi\) | ||||
−0.309715 | + | 0.950829i | \(0.600234\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.09121e9 | 0.929577 | 0.464789 | − | 0.885422i | \(-0.346130\pi\) | ||||
0.464789 | + | 0.885422i | \(0.346130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.62547e9 | −1.41166 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00999e9 | −1.20188 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.21406e10 | 2.14443 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.13643e9 | −1.01995 | −0.509974 | − | 0.860190i | \(-0.670345\pi\) | ||||
−0.509974 | + | 0.860190i | \(0.670345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.83754e9 | 0.913763 | 0.456882 | − | 0.889528i | \(-0.348966\pi\) | ||||
0.456882 | + | 0.889528i | \(0.348966\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.01684e9 | 0.297550 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.35031e9 | −0.177371 | −0.0886857 | − | 0.996060i | \(-0.528267\pi\) | ||||
−0.0886857 | + | 0.996060i | \(0.528267\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.02898e10 | −1.27680 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.86796e10 | 2.19104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.50806e9 | 0.500202 | 0.250101 | − | 0.968220i | \(-0.419536\pi\) | ||||
0.250101 | + | 0.968220i | \(0.419536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.81836e10 | −1.80908 | −0.904538 | − | 0.426393i | \(-0.859784\pi\) | ||||
−0.904538 | + | 0.426393i | \(0.859784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.65766e10 | 1.56316 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.49289e10 | 1.33520 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.77143e9 | 0.829375 | 0.414687 | − | 0.909964i | \(-0.363891\pi\) | ||||
0.414687 | + | 0.909964i | \(0.363891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.84522e10 | −1.41309 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.65866e9 | −0.484784 | −0.242392 | − | 0.970178i | \(-0.577932\pi\) | ||||
−0.242392 | + | 0.970178i | \(0.577932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.32873e9 | −0.507546 | −0.253773 | − | 0.967264i | \(-0.581672\pi\) | ||||
−0.253773 | + | 0.967264i | \(0.581672\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.08432e9 | 0.532860 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00221e9 | −0.179537 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00053e10 | −0.570364 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.06956e9 | −0.438732 | −0.219366 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219366 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.12603e9 | 0.162176 | 0.0810878 | − | 0.996707i | \(-0.474161\pi\) | ||||
0.0810878 | + | 0.996707i | \(0.474161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.40133e10 | −1.13594 | −0.567968 | − | 0.823051i | \(-0.692270\pi\) | ||||
−0.567968 | + | 0.823051i | \(0.692270\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.73605e9 | −0.440093 | −0.220046 | − | 0.975489i | \(-0.570621\pi\) | ||||
−0.220046 | + | 0.975489i | \(0.570621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.86077e10 | 1.23623 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.36029e9 | −0.138882 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.61808e10 | −1.74822 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.22227e10 | −0.805637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.39305e10 | 0.831151 | 0.415576 | − | 0.909559i | \(-0.363580\pi\) | ||||
0.415576 | + | 0.909559i | \(0.363580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.33956e10 | −2.44321 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.42141e9 | 0.165975 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.39101e10 | 0.996163 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.35779e10 | 0.382885 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.02289e10 | −0.547773 | −0.273886 | − | 0.961762i | \(-0.588309\pi\) | ||||
−0.273886 | + | 0.961762i | \(0.588309\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.42152e10 | −1.10524 | −0.552618 | − | 0.833434i | \(-0.686371\pi\) | ||||
−0.552618 | + | 0.833434i | \(0.686371\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.89483e10 | −1.17619 | −0.588096 | − | 0.808791i | \(-0.700122\pi\) | ||||
−0.588096 | + | 0.808791i | \(0.700122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.58909e10 | 1.75362 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.68132e10 | 1.48512 | 0.742559 | − | 0.669781i | \(-0.233612\pi\) | ||||
0.742559 | + | 0.669781i | \(0.233612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.66865e10 | 0.549444 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.21153e10 | 0.438431 | 0.219216 | − | 0.975676i | \(-0.429650\pi\) | ||||
0.219216 | + | 0.975676i | \(0.429650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.97637e10 | 1.90500 | 0.952502 | − | 0.304532i | \(-0.0985002\pi\) | ||||
0.952502 | + | 0.304532i | \(0.0985002\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.65703e10 | −1.40874 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00506e11 | 1.71812 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.04229e10 | 0.996104 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.97276e10 | 0.790799 | 0.395399 | − | 0.918509i | \(-0.370606\pi\) | ||||
0.395399 | + | 0.918509i | \(0.370606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.87435e10 | 1.05485 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.81308e10 | 0.831204 | 0.415602 | − | 0.909547i | \(-0.363571\pi\) | ||||
0.415602 | + | 0.909547i | \(0.363571\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.20718e10 | −0.719041 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.30753e9 | 0.110813 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.23476e10 | 0.416909 | 0.208454 | − | 0.978032i | \(-0.433157\pi\) | ||||
0.208454 | + | 0.978032i | \(0.433157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.18354e11 | −1.42523 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.24220e9 | 0.0726863 | 0.0363431 | − | 0.999339i | \(-0.488429\pi\) | ||||
0.0363431 | + | 0.999339i | \(0.488429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.05816e10 | −0.907557 | −0.453779 | − | 0.891114i | \(-0.649924\pi\) | ||||
−0.453779 | + | 0.891114i | \(0.649924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.43228e11 | −3.73982 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.07976e10 | −0.722536 | −0.361268 | − | 0.932462i | \(-0.617656\pi\) | ||||
−0.361268 | + | 0.932462i | \(0.617656\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.34031e10 | −0.132430 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.15619e10 | 0.780385 | 0.390193 | − | 0.920733i | \(-0.372408\pi\) | ||||
0.390193 | + | 0.920733i | \(0.372408\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.89301e11 | −1.75434 | −0.877168 | − | 0.480184i | \(-0.840570\pi\) | ||||
−0.877168 | + | 0.480184i | \(0.840570\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.03867e10 | −0.177369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.11805e11 | −0.942805 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.91387e10 | −0.810447 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.39489e10 | −0.427640 | −0.213820 | − | 0.976873i | \(-0.568591\pi\) | ||||
−0.213820 | + | 0.976873i | \(0.568591\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.68209e10 | −0.274594 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.10903e11 | −2.24959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.69768e10 | −0.470300 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.64129e11 | −1.80022 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.30037e11 | 0.835496 | 0.417748 | − | 0.908563i | \(-0.362819\pi\) | ||||
0.417748 | + | 0.908563i | \(0.362819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.10671e11 | −2.56260 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.09580e9 | −0.0127036 | −0.00635182 | − | 0.999980i | \(-0.502022\pi\) | ||||
−0.00635182 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.43788e11 | −1.43570 | −0.717848 | − | 0.696200i | \(-0.754873\pi\) | ||||
−0.717848 | + | 0.696200i | \(0.754873\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.46483e11 | −1.92715 | −0.963573 | − | 0.267445i | \(-0.913821\pi\) | ||||
−0.963573 | + | 0.267445i | \(0.913821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.23664e10 | −0.0668626 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.46207e11 | −2.34565 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.02063e10 | 0.256653 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.49816e10 | −0.120825 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.12262e11 | 1.46939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.43303e11 | 0.656189 | 0.328094 | − | 0.944645i | \(-0.393594\pi\) | ||||
0.328094 | + | 0.944645i | \(0.393594\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.28735e11 | 0.573718 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.34820e11 | 1.41409 | 0.707044 | − | 0.707170i | \(-0.250028\pi\) | ||||
0.707044 | + | 0.707170i | \(0.250028\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.89773e11 | −1.60293 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.99515e10 | 0.0799064 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.72469e11 | −0.672804 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.22101e10 | 0.341425 | 0.170713 | − | 0.985321i | \(-0.445393\pi\) | ||||
0.170713 | + | 0.985321i | \(0.445393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.71738e11 | −1.70211 | −0.851053 | − | 0.525080i | \(-0.824035\pi\) | ||||
−0.851053 | + | 0.525080i | \(0.824035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.66528e11 | 0.585606 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.01029e11 | −1.37464 | −0.687322 | − | 0.726353i | \(-0.741214\pi\) | ||||
−0.687322 | + | 0.726353i | \(0.741214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.71455e11 | −0.558654 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.36110e10 | 0.0750220 | 0.0375110 | − | 0.999296i | \(-0.488057\pi\) | ||||
0.0375110 | + | 0.999296i | \(0.488057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.89457e10 | 0.151681 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.16284e11 | −0.653799 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.23035e11 | −0.354022 | −0.177011 | − | 0.984209i | \(-0.556643\pi\) | ||||
−0.177011 | + | 0.984209i | \(0.556643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.04012e10 | 0.141521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.84966e11 | 1.32901 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.39248e11 | −0.639968 | −0.319984 | − | 0.947423i | \(-0.603678\pi\) | ||||
−0.319984 | + | 0.947423i | \(0.603678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.59287e10 | 0.142593 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.90629e11 | 1.47041 | 0.735205 | − | 0.677845i | \(-0.237086\pi\) | ||||
0.735205 | + | 0.677845i | \(0.237086\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.13326e12 | 2.75529 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.30525e10 | 0.125983 | 0.0629914 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629914 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.65584e11 | 0.375249 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.10395e11 | 0.687293 | 0.343646 | − | 0.939099i | \(-0.388338\pi\) | ||||
0.343646 | + | 0.939099i | \(0.388338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.55307e11 | −0.336045 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.06407e11 | −1.70525 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.09351e11 | −0.422979 | −0.211489 | − | 0.977380i | \(-0.567831\pi\) | ||||
−0.211489 | + | 0.977380i | \(0.567831\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.26913e12 | −2.50685 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.43868e11 | 0.857244 | 0.428622 | − | 0.903484i | \(-0.358999\pi\) | ||||
0.428622 | + | 0.903484i | \(0.358999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.02338e10 | −0.170411 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.91632e11 | −0.346172 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.56031e11 | 0.805823 | 0.402912 | − | 0.915239i | \(-0.367998\pi\) | ||||
0.402912 | + | 0.915239i | \(0.367998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.36794e11 | −0.927940 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.69663e11 | 1.47087 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.59856e11 | 1.39256 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.12392e12 | 1.78144 | 0.890720 | − | 0.454552i | \(-0.150201\pi\) | ||||
0.890720 | + | 0.454552i | \(0.150201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02822e12 | −1.59521 | −0.797605 | − | 0.603180i | \(-0.793900\pi\) | ||||
−0.797605 | + | 0.603180i | \(0.793900\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.71994e11 | −1.17242 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.81018e11 | −0.554652 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.26313e12 | −1.80048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.37714e12 | 1.92234 | 0.961171 | − | 0.275953i | \(-0.0889934\pi\) | ||||
0.961171 | + | 0.275953i | \(0.0889934\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.94790e11 | 0.266299 | 0.133150 | − | 0.991096i | \(-0.457491\pi\) | ||||
0.133150 | + | 0.991096i | \(0.457491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.14961e12 | −1.50793 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.32533e11 | 0.684315 | 0.342157 | − | 0.939643i | \(-0.388842\pi\) | ||||
0.342157 | + | 0.939643i | \(0.388842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.41461e12 | 1.78099 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.26633e11 | −0.896393 | −0.448196 | − | 0.893935i | \(-0.647933\pi\) | ||||
−0.448196 | + | 0.893935i | \(0.647933\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.28970e12 | −1.52794 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.34830e11 | 1.08549 | 0.542743 | − | 0.839899i | \(-0.317386\pi\) | ||||
0.542743 | + | 0.839899i | \(0.317386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.50258e10 | −0.0853918 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.22688e12 | 1.36887 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.09190e12 | −1.17101 | −0.585503 | − | 0.810670i | \(-0.699103\pi\) | ||||
−0.585503 | + | 0.810670i | \(0.699103\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.31870e10 | 0.0874779 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.93683e11 | 1.02469 | 0.512347 | − | 0.858779i | \(-0.328776\pi\) | ||||
0.512347 | + | 0.858779i | \(0.328776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.95734e11 | 0.703605 | 0.351802 | − | 0.936074i | \(-0.385569\pi\) | ||||
0.351802 | + | 0.936074i | \(0.385569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.87957e12 | −1.82866 | −0.914328 | − | 0.404975i | \(-0.867280\pi\) | ||||
−0.914328 | + | 0.404975i | \(0.867280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.34830e12 | −1.28679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.83795e11 | −0.265712 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.46484e11 | −0.226419 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.19896e12 | −1.06041 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.29011e11 | 0.198768 | 0.0993838 | − | 0.995049i | \(-0.468313\pi\) | ||||
0.0993838 | + | 0.995049i | \(0.468313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.66683e11 | 0.738256 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.92591e12 | 3.28230 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.81410e11 | 0.387824 | 0.193912 | − | 0.981019i | \(-0.437882\pi\) | ||||
0.193912 | + | 0.981019i | \(0.437882\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.47465e11 | 0.749330 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.70320e12 | 1.32251 | 0.661257 | − | 0.750160i | \(-0.270023\pi\) | ||||
0.661257 | + | 0.750160i | \(0.270023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.79384e10 | 0.0213006 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.45917e12 | 2.54313 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.06075e12 | −1.48789 | −0.743947 | − | 0.668238i | \(-0.767049\pi\) | ||||
−0.743947 | + | 0.668238i | \(0.767049\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.82168e12 | −2.71010 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.97493e11 | 0.416176 | 0.208088 | − | 0.978110i | \(-0.433276\pi\) | ||||
0.208088 | + | 0.978110i | \(0.433276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.48392e12 | 2.34170 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.46938e11 | −0.559270 | −0.279635 | − | 0.960106i | \(-0.590213\pi\) | ||||
−0.279635 | + | 0.960106i | \(0.590213\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.59820e12 | −1.03690 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.15760e11 | 0.392540 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.14917e12 | 0.707418 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.05367e12 | 1.24245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.31013e11 | 0.434666 | 0.217333 | − | 0.976098i | \(-0.430264\pi\) | ||||
0.217333 | + | 0.976098i | \(0.430264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.04453e12 | −0.610467 | −0.305233 | − | 0.952278i | \(-0.598734\pi\) | ||||
−0.305233 | + | 0.952278i | \(0.598734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.50751e10 | −0.0254559 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.75502e12 | 0.974386 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.15003e12 | −1.17360 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.39315e11 | 0.182109 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.39946e12 | −0.726233 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.10575e12 | −1.07462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88034e12 | −0.943733 | −0.471866 | − | 0.881670i | \(-0.656420\pi\) | ||||
−0.471866 | + | 0.881670i | \(0.656420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.54029e12 | −0.760331 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.08624e12 | 0.518780 | 0.259390 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259390 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.41977e11 | 0.442553 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.06804e11 | 0.0955821 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.25775e12 | −0.571914 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.11965e12 | 0.933072 | 0.466536 | − | 0.884502i | \(-0.345502\pi\) | ||||
0.466536 | + | 0.884502i | \(0.345502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.11476e12 | 0.482868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.30978e11 | −0.268956 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.04489e12 | −1.27727 | −0.638636 | − | 0.769509i | \(-0.720501\pi\) | ||||
−0.638636 | + | 0.769509i | \(0.720501\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.67178e12 | 1.08562 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.25275e12 | 1.30090 | 0.650452 | − | 0.759548i | \(-0.274580\pi\) | ||||
0.650452 | + | 0.759548i | \(0.274580\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.35916e12 | 0.535066 | 0.267533 | − | 0.963549i | \(-0.413792\pi\) | ||||
0.267533 | + | 0.963549i | \(0.413792\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.69599e12 | −0.657245 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.35782e12 | −0.885564 | −0.442782 | − | 0.896629i | \(-0.646008\pi\) | ||||
−0.442782 | + | 0.896629i | \(0.646008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.57002e11 | 0.242948 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.84777e12 | −1.03684 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.78474e12 | 0.639834 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.37065e12 | 0.824130 | 0.412065 | − | 0.911154i | \(-0.364808\pi\) | ||||
0.412065 | + | 0.911154i | \(0.364808\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.33652e11 | −0.114229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.04690e12 | −1.70169 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.56707e12 | 1.51667 | 0.758336 | − | 0.651864i | \(-0.226013\pi\) | ||||
0.758336 | + | 0.651864i | \(0.226013\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.04624e12 | −0.659283 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.30493e12 | 1.68368 | 0.841839 | − | 0.539729i | \(-0.181473\pi\) | ||||
0.841839 | + | 0.539729i | \(0.181473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.71307e12 | −0.848255 | −0.424128 | − | 0.905602i | \(-0.639419\pi\) | ||||
−0.424128 | + | 0.905602i | \(0.639419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.33335e12 | 1.02672 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00734e12 | 1.19814 | 0.599069 | − | 0.800698i | \(-0.295538\pi\) | ||||
0.599069 | + | 0.800698i | \(0.295538\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.06237e11 | −0.208052 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.19728e12 | −1.50866 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.24954e12 | −0.643459 | −0.321730 | − | 0.946832i | \(-0.604264\pi\) | ||||
−0.321730 | + | 0.946832i | \(0.604264\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.19664e12 | 0.332414 | 0.166207 | − | 0.986091i | \(-0.446848\pi\) | ||||
0.166207 | + | 0.986091i | \(0.446848\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.36723e12 | 1.19563 | 0.597817 | − | 0.801633i | \(-0.296035\pi\) | ||||
0.597817 | + | 0.801633i | \(0.296035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.90478e12 | −0.513965 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.57811e12 | 1.48351 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.67058e12 | −1.20689 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.32940e11 | 0.110281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.78790e12 | −0.700077 | −0.350039 | − | 0.936735i | \(-0.613832\pi\) | ||||
−0.350039 | + | 0.936735i | \(0.613832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.02950e12 | 1.24511 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.52355e12 | 2.29177 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.55199e12 | −2.02915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.28295e12 | −0.534115 | −0.267058 | − | 0.963681i | \(-0.586051\pi\) | ||||
−0.267058 | + | 0.963681i | \(0.586051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.29995e12 | 0.530603 | 0.265301 | − | 0.964166i | \(-0.414529\pi\) | ||||
0.265301 | + | 0.964166i | \(0.414529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.85647e12 | −0.416503 | −0.208251 | − | 0.978075i | \(-0.566777\pi\) | ||||
−0.208251 | + | 0.978075i | \(0.566777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.20048e12 | 0.708132 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.13942e12 | 0.248640 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.75397e12 | 1.66884 | 0.834420 | − | 0.551129i | \(-0.185803\pi\) | ||||
0.834420 | + | 0.551129i | \(0.185803\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.95117e12 | 0.827336 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.42166e12 | −1.53291 | −0.766455 | − | 0.642298i | \(-0.777981\pi\) | ||||
−0.766455 | + | 0.642298i | \(0.777981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.79783e12 | 1.18130 | 0.590648 | − | 0.806929i | \(-0.298872\pi\) | ||||
0.590648 | + | 0.806929i | \(0.298872\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.85369e12 | 0.573583 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.39724e11 | −0.125149 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.25153e12 | −0.820593 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.40220e12 | −0.267029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.32456e12 | −1.18840 | −0.594200 | − | 0.804318i | \(-0.702531\pi\) | ||||
−0.594200 | + | 0.804318i | \(0.702531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.95066e12 | −0.905762 | −0.452881 | − | 0.891571i | \(-0.649604\pi\) | ||||
−0.452881 | + | 0.891571i | \(0.649604\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.67246e12 | 0.843591 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.29277e12 | −1.65571 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.32611e12 | −1.28819 | −0.644095 | − | 0.764945i | \(-0.722766\pi\) | ||||
−0.644095 | + | 0.764945i | \(0.722766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.02875e13 | −1.76200 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.07176e12 | −1.36453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.66806e12 | 0.945765 | 0.472882 | − | 0.881126i | \(-0.343214\pi\) | ||||
0.472882 | + | 0.881126i | \(0.343214\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.84274e12 | 1.45642 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.69501e11 | 0.0272034 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.40422e13 | 2.22479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.20985e12 | −0.658470 | −0.329235 | − | 0.944248i | \(-0.606791\pi\) | ||||
−0.329235 | + | 0.944248i | \(0.606791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.20468e12 | 0.494863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.24486e13 | 1.87384 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.19654e13 | 1.77835 | 0.889176 | − | 0.457566i | \(-0.151279\pi\) | ||||
0.889176 | + | 0.457566i | \(0.151279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.10949e12 | 0.456326 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.03211e12 | 0.149563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.64799e12 | 0.656794 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.07118e11 | 0.0568120 | 0.0284060 | − | 0.999596i | \(-0.490957\pi\) | ||||
0.0284060 | + | 0.999596i | \(0.490957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.93551e13 | 2.66740 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.09675e13 | 2.85380 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.44424e12 | −0.855592 | −0.427796 | − | 0.903875i | \(-0.640710\pi\) | ||||
−0.427796 | + | 0.903875i | \(0.640710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.07838e13 | −1.41416 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.56864e11 | 0.0721308 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.46122e12 | 0.698749 | 0.349375 | − | 0.936983i | \(-0.386394\pi\) | ||||
0.349375 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.96192e12 | −0.619507 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.88201e12 | 0.232125 | 0.116062 | − | 0.993242i | \(-0.462973\pi\) | ||||
0.116062 | + | 0.993242i | \(0.462973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.11234e13 | 2.57384 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.36704e13 | −1.64563 | −0.822813 | − | 0.568312i | \(-0.807597\pi\) | ||||
−0.822813 | + | 0.568312i | \(0.807597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.04042e12 | 0.827287 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.10300e13 | 2.44158 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.52585e12 | −0.978043 | −0.489021 | − | 0.872272i | \(-0.662646\pi\) | ||||
−0.489021 | + | 0.872272i | \(0.662646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.04513e13 | 1.18466 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.50792e12 | −0.830975 | −0.415487 | − | 0.909599i | \(-0.636389\pi\) | ||||
−0.415487 | + | 0.909599i | \(0.636389\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.44479e13 | 1.58022 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.61560e13 | −1.74624 | −0.873118 | − | 0.487509i | \(-0.837906\pi\) | ||||
−0.873118 | + | 0.487509i | \(0.837906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.17740e12 | 0.125766 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.44747e13 | −1.51018 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.11830e12 | 0.115317 | 0.0576583 | − | 0.998336i | \(-0.481637\pi\) | ||||
0.0576583 | + | 0.998336i | \(0.481637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.22174e13 | 1.24519 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.73165e13 | −1.74442 | −0.872212 | − | 0.489129i | \(-0.837315\pi\) | ||||
−0.872212 | + | 0.489129i | \(0.837315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.09440e13 | −1.07716 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.25466e12 | 0.122070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.27302e13 | 1.22435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.42654e11 | 0.0325783 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.88515e11 | 0.0361012 | 0.0180506 | − | 0.999837i | \(-0.494254\pi\) | ||||
0.0180506 | + | 0.999837i | \(0.494254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.79853e12 | 0.624552 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.83702e13 | 1.66848 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.34166e12 | 0.569474 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.08432e12 | −0.0951910 | −0.0475955 | − | 0.998867i | \(-0.515156\pi\) | ||||
−0.0475955 | + | 0.998867i | \(0.515156\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.59624e12 | −0.225363 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.37906e13 | −1.18368 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.88161e12 | −0.499202 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.31193e12 | 0.108888 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.06803e12 | 0.333900 | 0.166950 | − | 0.985965i | \(-0.446608\pi\) | ||||
0.166950 | + | 0.985965i | \(0.446608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.87468e12 | −0.395688 | −0.197844 | − | 0.980234i | \(-0.563394\pi\) | ||||
−0.197844 | + | 0.980234i | \(0.563394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.69359e13 | −1.35957 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.12198e12 | 0.323673 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.99926e13 | −3.10600 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.03829e12 | −0.0797582 | −0.0398791 | − | 0.999205i | \(-0.512697\pi\) | ||||
−0.0398791 | + | 0.999205i | \(0.512697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.10923e13 | −0.842794 | −0.421397 | − | 0.906876i | \(-0.638460\pi\) | ||||
−0.421397 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.45526e13 | 1.08184 | 0.540922 | − | 0.841073i | \(-0.318075\pi\) | ||||
0.540922 | + | 0.841073i | \(0.318075\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.37985e13 | 1.01470 | 0.507348 | − | 0.861741i | \(-0.330626\pi\) | ||||
0.507348 | + | 0.861741i | \(0.330626\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.48796e13 | −1.08240 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.75736e12 | 0.342345 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.52829e11 | −0.0389337 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.20234e11 | −0.0641165 | −0.0320582 | − | 0.999486i | \(-0.510206\pi\) | ||||
−0.0320582 | + | 0.999486i | \(0.510206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.43921e13 | −0.992067 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.71420e13 | 1.16906 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.01936e13 | 0.680536 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.97855e13 | −2.62809 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.91330e12 | −0.647941 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.46964e12 | −0.483091 | −0.241545 | − | 0.970390i | \(-0.577654\pi\) | ||||
−0.241545 | + | 0.970390i | \(0.577654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.05568e13 | 1.30179 | 0.650897 | − | 0.759166i | \(-0.274393\pi\) | ||||
0.650897 | + | 0.759166i | \(0.274393\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.05923e12 | 0.0663775 | 0.0331888 | − | 0.999449i | \(-0.489434\pi\) | ||||
0.0331888 | + | 0.999449i | \(0.489434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.28469e12 | −0.265709 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.53023e13 | −0.939092 | −0.469546 | − | 0.882908i | \(-0.655582\pi\) | ||||
−0.469546 | + | 0.882908i | \(0.655582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.34982e13 | −1.41237 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.62869e12 | −0.275340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.24410e13 | 1.32118 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.15516e13 | −0.673095 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.74558e11 | −0.00996416 | −0.00498208 | − | 0.999988i | \(-0.501586\pi\) | ||||
−0.00498208 | + | 0.999988i | \(0.501586\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.13385e13 | −0.640629 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.59039e12 | 0.480420 | 0.240210 | − | 0.970721i | \(-0.422784\pi\) | ||||
0.240210 | + | 0.970721i | \(0.422784\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.70227e13 | 0.942336 | 0.471168 | − | 0.882043i | \(-0.343833\pi\) | ||||
0.471168 | + | 0.882043i | \(0.343833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.01246e13 | 1.09162 | 0.545810 | − | 0.837909i | \(-0.316222\pi\) | ||||
0.545810 | + | 0.837909i | \(0.316222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.34112e13 | −2.86797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.83253e12 | 0.522655 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.92177e13 | −1.01127 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.53428e13 | −3.37002 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.85668e11 | −0.00948023 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.03214e12 | −0.203833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.40766e13 | −0.704535 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.10130e13 | 1.03099 | 0.515495 | − | 0.856893i | \(-0.327608\pi\) | ||||
0.515495 | + | 0.856893i | \(0.327608\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.07761e13 | −1.49512 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.95345e12 | −0.0939656 | −0.0469828 | − | 0.998896i | \(-0.514961\pi\) | ||||
−0.0469828 | + | 0.998896i | \(0.514961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.04802e13 | −0.499172 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.80064e13 | 1.77499 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.47656e12 | 0.114533 | 0.0572663 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572663 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.73301e13 | 1.25162 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.75744e13 | −2.61109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.78510e13 | −2.12830 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.40844e13 | 1.94184 | 0.970922 | − | 0.239395i | \(-0.0769490\pi\) | ||||
0.970922 | + | 0.239395i | \(0.0769490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.52146e13 | 1.53621 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.40477e11 | −0.0190308 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.92250e12 | 0.208621 | 0.104310 | − | 0.994545i | \(-0.466736\pi\) | ||||
0.104310 | + | 0.994545i | \(0.466736\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.12372e13 | −2.15075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.54680e13 | −0.643103 | −0.321552 | − | 0.946892i | \(-0.604204\pi\) | ||||
−0.321552 | + | 0.946892i | \(0.604204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.88116e12 | −0.159830 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.49107e12 | −0.221862 | −0.110931 | − | 0.993828i | \(-0.535383\pi\) | ||||
−0.110931 | + | 0.993828i | \(0.535383\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.66004e13 | 1.06461 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.28207e13 | −2.88697 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.76932e13 | −0.694845 | −0.347422 | − | 0.937709i | \(-0.612943\pi\) | ||||
−0.347422 | + | 0.937709i | \(0.612943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.59905e12 | −0.100164 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.52994e13 | 0.965888 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.61401e13 | −0.988670 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.19916e13 | −1.94812 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.89231e13 | −1.06372 | −0.531858 | − | 0.846834i | \(-0.678506\pi\) | ||||
−0.531858 | + | 0.846834i | \(0.678506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.05519e13 | 0.384481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.69482e13 | −0.972843 | −0.486422 | − | 0.873724i | \(-0.661698\pi\) | ||||
−0.486422 | + | 0.873724i | \(0.661698\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.05255e13 | −1.44951 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.90598e13 | 1.37153 | 0.685764 | − | 0.727824i | \(-0.259468\pi\) | ||||
0.685764 | + | 0.727824i | \(0.259468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.05282e13 | 0.714216 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.91084e12 | −0.100348 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.03830e12 | −0.308742 | −0.154371 | − | 0.988013i | \(-0.549335\pi\) | ||||
−0.154371 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.56285e13 | 2.20123 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.27509e13 | −0.423795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.89096e13 | −1.61088 | −0.805439 | − | 0.592678i | \(-0.798071\pi\) | ||||
−0.805439 | + | 0.592678i | \(0.798071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.01181e13 | 0.983007 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.01445e13 | 1.28676 | 0.643380 | − | 0.765547i | \(-0.277532\pi\) | ||||
0.643380 | + | 0.765547i | \(0.277532\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.30984e12 | 0.168670 |
(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 | 400.10.a.u.1.3 | 3 | ||
4.3 | odd | 2 | 25.10.a.d.1.2 | yes | 3 | ||
5.2 | odd | 4 | 400.10.c.q.49.2 | 6 | |||
5.3 | odd | 4 | 400.10.c.q.49.5 | 6 | |||
5.4 | even | 2 | 400.10.a.y.1.1 | 3 | |||
12.11 | even | 2 | 225.10.a.m.1.2 | 3 | |||
20.3 | even | 4 | 25.10.b.c.24.2 | 6 | |||
20.7 | even | 4 | 25.10.b.c.24.5 | 6 | |||
20.19 | odd | 2 | 25.10.a.c.1.2 | ✓ | 3 | ||
60.23 | odd | 4 | 225.10.b.m.199.5 | 6 | |||
60.47 | odd | 4 | 225.10.b.m.199.2 | 6 | |||
60.59 | even | 2 | 225.10.a.p.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.2 | ✓ | 3 | 20.19 | odd | 2 | ||
25.10.a.d.1.2 | yes | 3 | 4.3 | odd | 2 | ||
25.10.b.c.24.2 | 6 | 20.3 | even | 4 | |||
25.10.b.c.24.5 | 6 | 20.7 | even | 4 | |||
225.10.a.m.1.2 | 3 | 12.11 | even | 2 | |||
225.10.a.p.1.2 | 3 | 60.59 | even | 2 | |||
225.10.b.m.199.2 | 6 | 60.47 | odd | 4 | |||
225.10.b.m.199.5 | 6 | 60.23 | odd | 4 | |||
400.10.a.u.1.3 | 3 | 1.1 | even | 1 | trivial | ||
400.10.a.y.1.1 | 3 | 5.4 | even | 2 | |||
400.10.c.q.49.2 | 6 | 5.2 | odd | 4 | |||
400.10.c.q.49.5 | 6 | 5.3 | odd | 4 |