Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,10,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(12.8758959041\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(22.2334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −21.4187 | −0.946580 | −0.473290 | − | 0.880907i | \(-0.656934\pi\) | ||||
−0.473290 | + | 0.880907i | \(0.656934\pi\) | |||||||
\(3\) | 210.171 | 1.49805 | 0.749027 | − | 0.662539i | \(-0.230521\pi\) | ||||
0.749027 | + | 0.662539i | \(0.230521\pi\) | |||||||
\(4\) | −53.2406 | −0.103986 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4501.59 | −1.41803 | ||||||||
\(7\) | −9905.49 | −1.55932 | −0.779659 | − | 0.626204i | \(-0.784608\pi\) | ||||
−0.779659 | + | 0.626204i | \(0.784608\pi\) | |||||||
\(8\) | 12106.7 | 1.04501 | ||||||||
\(9\) | 24489.0 | 1.24417 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36453.6 | 0.750712 | 0.375356 | − | 0.926881i | \(-0.377520\pi\) | ||||
0.375356 | + | 0.926881i | \(0.377520\pi\) | |||||||
\(12\) | −11189.6 | −0.155776 | ||||||||
\(13\) | −164867. | −1.60099 | −0.800494 | − | 0.599341i | \(-0.795429\pi\) | ||||
−0.800494 | + | 0.599341i | \(0.795429\pi\) | |||||||
\(14\) | 212162. | 1.47602 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −232050. | −0.885201 | ||||||||
\(17\) | −82357.1 | −0.239156 | −0.119578 | − | 0.992825i | \(-0.538154\pi\) | ||||
−0.119578 | + | 0.992825i | \(0.538154\pi\) | |||||||
\(18\) | −524521. | −1.17771 | ||||||||
\(19\) | −609617. | −1.07316 | −0.536582 | − | 0.843848i | \(-0.680285\pi\) | ||||
−0.536582 | + | 0.843848i | \(0.680285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08185e6 | −2.33594 | ||||||||
\(22\) | −780787. | −0.710609 | ||||||||
\(23\) | −1.88578e6 | −1.40513 | −0.702564 | − | 0.711620i | \(-0.747962\pi\) | ||||
−0.702564 | + | 0.711620i | \(0.747962\pi\) | |||||||
\(24\) | 2.54448e6 | 1.56548 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.53123e6 | 1.51546 | ||||||||
\(27\) | 1.01008e6 | 0.365778 | ||||||||
\(28\) | 527374. | 0.162147 | ||||||||
\(29\) | 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 | \(-0.483051\pi\) | ||||
0.0532205 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(32\) | −1.22842e6 | −0.207097 | ||||||||
\(33\) | 7.66150e6 | 1.12461 | ||||||||
\(34\) | 1.76398e6 | 0.226380 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.30381e6 | −0.129376 | ||||||||
\(37\) | −5.25687e6 | −0.461126 | −0.230563 | − | 0.973057i | \(-0.574057\pi\) | ||||
−0.230563 | + | 0.973057i | \(0.574057\pi\) | |||||||
\(38\) | 1.30572e7 | 1.01584 | ||||||||
\(39\) | −3.46503e7 | −2.39837 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.05812e6 | 0.113748 | 0.0568739 | − | 0.998381i | \(-0.481887\pi\) | ||||
0.0568739 | + | 0.998381i | \(0.481887\pi\) | |||||||
\(42\) | 4.45904e7 | 2.21116 | ||||||||
\(43\) | 6.76158e6 | 0.301606 | 0.150803 | − | 0.988564i | \(-0.451814\pi\) | ||||
0.150803 | + | 0.988564i | \(0.451814\pi\) | |||||||
\(44\) | −1.94081e6 | −0.0780632 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.03909e7 | 1.33007 | ||||||||
\(47\) | −3.15241e7 | −0.942330 | −0.471165 | − | 0.882045i | \(-0.656166\pi\) | ||||
−0.471165 | + | 0.882045i | \(0.656166\pi\) | |||||||
\(48\) | −4.87703e7 | −1.32608 | ||||||||
\(49\) | 5.77651e7 | 1.43147 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.73091e7 | −0.358268 | ||||||||
\(52\) | 8.77761e6 | 0.166480 | ||||||||
\(53\) | 4.89593e7 | 0.852303 | 0.426151 | − | 0.904652i | \(-0.359869\pi\) | ||||
0.426151 | + | 0.904652i | \(0.359869\pi\) | |||||||
\(54\) | −2.16345e7 | −0.346238 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.19923e8 | −1.62950 | ||||||||
\(57\) | −1.28124e8 | −1.60766 | ||||||||
\(58\) | −7.26597e6 | −0.0843078 | ||||||||
\(59\) | 8.77960e7 | 0.943281 | 0.471640 | − | 0.881791i | \(-0.343662\pi\) | ||||
0.471640 | + | 0.881791i | \(0.343662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.84654e7 | 0.355701 | 0.177851 | − | 0.984057i | \(-0.443086\pi\) | ||||
0.177851 | + | 0.984057i | \(0.443086\pi\) | |||||||
\(62\) | −1.17227e7 | −0.100755 | ||||||||
\(63\) | −2.42575e8 | −1.94005 | ||||||||
\(64\) | 1.45121e8 | 1.08124 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.64099e8 | −1.06453 | ||||||||
\(67\) | 1.36116e8 | 0.825227 | 0.412613 | − | 0.910906i | \(-0.364616\pi\) | ||||
0.412613 | + | 0.910906i | \(0.364616\pi\) | |||||||
\(68\) | 4.38474e6 | 0.0248687 | ||||||||
\(69\) | −3.96337e8 | −2.10496 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.49218e8 | 1.63092 | 0.815462 | − | 0.578810i | \(-0.196483\pi\) | ||||
0.815462 | + | 0.578810i | \(0.196483\pi\) | |||||||
\(72\) | 2.96481e8 | 1.30017 | ||||||||
\(73\) | −1.61345e8 | −0.664971 | −0.332486 | − | 0.943108i | \(-0.607887\pi\) | ||||
−0.332486 | + | 0.943108i | \(0.607887\pi\) | |||||||
\(74\) | 1.12595e8 | 0.436492 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.24564e7 | 0.111594 | ||||||||
\(77\) | −3.61091e8 | −1.17060 | ||||||||
\(78\) | 7.42163e8 | 2.27025 | ||||||||
\(79\) | −1.26975e8 | −0.366772 | −0.183386 | − | 0.983041i | \(-0.558706\pi\) | ||||
−0.183386 | + | 0.983041i | \(0.558706\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.69727e8 | −0.696213 | ||||||||
\(82\) | −4.40822e7 | −0.107671 | ||||||||
\(83\) | 2.87494e8 | 0.664931 | 0.332466 | − | 0.943115i | \(-0.392119\pi\) | ||||
0.332466 | + | 0.943115i | \(0.392119\pi\) | |||||||
\(84\) | 1.10839e8 | 0.242904 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.44824e8 | −0.285494 | ||||||||
\(87\) | 7.12976e7 | 0.133425 | ||||||||
\(88\) | 4.41333e8 | 0.784502 | ||||||||
\(89\) | −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 | ||||||||
\(92\) | 1.00400e8 | 0.146113 | ||||||||
\(93\) | 1.15030e8 | 0.159454 | ||||||||
\(94\) | 6.75205e8 | 0.891991 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.58179e8 | −0.310242 | ||||||||
\(97\) | 4.71704e8 | 0.541000 | 0.270500 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270500 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(98\) | −1.23725e9 | −1.35500 | ||||||||
\(99\) | 8.92711e8 | 0.934012 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.25673e9 | −1.20170 | −0.600851 | − | 0.799361i | \(-0.705172\pi\) | ||||
−0.600851 | + | 0.799361i | \(0.705172\pi\) | |||||||
\(102\) | 3.70738e8 | 0.339130 | ||||||||
\(103\) | −1.95398e9 | −1.71062 | −0.855309 | − | 0.518119i | \(-0.826633\pi\) | ||||
−0.855309 | + | 0.518119i | \(0.826633\pi\) | |||||||
\(104\) | −1.99599e9 | −1.67305 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.04864e9 | −0.806773 | ||||||||
\(107\) | −2.12306e9 | −1.56580 | −0.782899 | − | 0.622148i | \(-0.786260\pi\) | ||||
−0.782899 | + | 0.622148i | \(0.786260\pi\) | |||||||
\(108\) | −5.37771e7 | −0.0380356 | ||||||||
\(109\) | −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 | ||||||||
\(112\) | 2.29857e9 | 1.38031 | ||||||||
\(113\) | 1.85455e9 | 1.07001 | 0.535003 | − | 0.844850i | \(-0.320311\pi\) | ||||
0.535003 | + | 0.844850i | \(0.320311\pi\) | |||||||
\(114\) | 2.74425e9 | 1.52178 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.80611e7 | −0.00926154 | ||||||||
\(117\) | −4.03742e9 | −1.99190 | ||||||||
\(118\) | −1.88047e9 | −0.892891 | ||||||||
\(119\) | 8.15787e8 | 0.372920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.02908e9 | −0.436432 | ||||||||
\(122\) | −8.23877e8 | −0.336700 | ||||||||
\(123\) | 4.32557e8 | 0.170400 | ||||||||
\(124\) | −2.91393e7 | −0.0110683 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.19564e9 | 1.83642 | ||||||||
\(127\) | 5.39208e9 | 1.83924 | 0.919622 | − | 0.392805i | \(-0.128495\pi\) | ||||
0.919622 | + | 0.392805i | \(0.128495\pi\) | |||||||
\(128\) | −2.47934e9 | −0.816379 | ||||||||
\(129\) | 1.42109e9 | 0.451823 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.83690e9 | 1.13831 | 0.569154 | − | 0.822231i | \(-0.307271\pi\) | ||||
0.569154 | + | 0.822231i | \(0.307271\pi\) | |||||||
\(132\) | −4.07903e8 | −0.116943 | ||||||||
\(133\) | 6.03856e9 | 1.67340 | ||||||||
\(134\) | −2.91543e9 | −0.781143 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.97072e8 | −0.249920 | ||||||||
\(137\) | 2.55408e9 | 0.619430 | 0.309715 | − | 0.950829i | \(-0.399766\pi\) | ||||
0.309715 | + | 0.950829i | \(0.399766\pi\) | |||||||
\(138\) | 8.48901e9 | 1.99251 | ||||||||
\(139\) | −4.09121e9 | −0.929577 | −0.464789 | − | 0.885422i | \(-0.653870\pi\) | ||||
−0.464789 | + | 0.885422i | \(0.653870\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.62547e9 | −1.41166 | ||||||||
\(142\) | −7.47978e9 | −1.54380 | ||||||||
\(143\) | −6.00999e9 | −1.20188 | ||||||||
\(144\) | −5.68267e9 | −1.10134 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.45580e9 | 0.629449 | ||||||||
\(147\) | 1.21406e10 | 2.14443 | ||||||||
\(148\) | 2.79879e8 | 0.0479504 | ||||||||
\(149\) | −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 | \(-0.651034\pi\) | ||||
−0.456882 | + | 0.889528i | \(0.651034\pi\) | |||||||
\(152\) | −7.38046e9 | −1.12147 | ||||||||
\(153\) | −2.01684e9 | −0.297550 | ||||||||
\(154\) | 7.73408e9 | 1.10807 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.84480e9 | 0.249396 | ||||||||
\(157\) | 1.35031e9 | 0.177371 | 0.0886857 | − | 0.996060i | \(-0.471733\pi\) | ||||
0.0886857 | + | 0.996060i | \(0.471733\pi\) | |||||||
\(158\) | 2.71963e9 | 0.347179 | ||||||||
\(159\) | 1.02898e10 | 1.27680 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.86796e10 | 2.19104 | ||||||||
\(162\) | 5.77720e9 | 0.659022 | ||||||||
\(163\) | 4.50806e9 | 0.500202 | 0.250101 | − | 0.968220i | \(-0.419536\pi\) | ||||
0.250101 | + | 0.968220i | \(0.419536\pi\) | |||||||
\(164\) | −1.09575e8 | −0.0118281 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.15773e9 | −0.629411 | ||||||||
\(167\) | −1.81836e10 | −1.80908 | −0.904538 | − | 0.426393i | \(-0.859784\pi\) | ||||
−0.904538 | + | 0.426393i | \(0.859784\pi\) | |||||||
\(168\) | −2.52043e10 | −2.44109 | ||||||||
\(169\) | 1.65766e10 | 1.56316 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.49289e10 | −1.33520 | ||||||||
\(172\) | −3.59991e8 | −0.0313627 | ||||||||
\(173\) | −9.77143e9 | −0.829375 | −0.414687 | − | 0.909964i | \(-0.636109\pi\) | ||||
−0.414687 | + | 0.909964i | \(0.636109\pi\) | |||||||
\(174\) | −1.52710e9 | −0.126298 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.45906e9 | −0.664531 | ||||||||
\(177\) | 1.84522e10 | 1.41309 | ||||||||
\(178\) | 1.20616e10 | 0.900562 | ||||||||
\(179\) | 6.65866e9 | 0.484784 | 0.242392 | − | 0.970178i | \(-0.422068\pi\) | ||||
0.242392 | + | 0.970178i | \(0.422068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.32873e9 | −0.507546 | −0.253773 | − | 0.967264i | \(-0.581672\pi\) | ||||
−0.253773 | + | 0.967264i | \(0.581672\pi\) | |||||||
\(182\) | −3.49785e10 | −2.36309 | ||||||||
\(183\) | 8.08432e9 | 0.532860 | ||||||||
\(184\) | −2.28306e10 | −1.46837 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.46378e9 | −0.150936 | ||||||||
\(187\) | −3.00221e9 | −0.179537 | ||||||||
\(188\) | 1.67836e9 | 0.0979887 | ||||||||
\(189\) | −1.00053e10 | −0.570364 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.06956e9 | 0.438732 | 0.219366 | − | 0.975643i | \(-0.429601\pi\) | ||||
0.219366 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(192\) | 3.05003e10 | 1.61975 | ||||||||
\(193\) | −3.12603e9 | −0.162176 | −0.0810878 | − | 0.996707i | \(-0.525839\pi\) | ||||
−0.0810878 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(194\) | −1.01033e10 | −0.512100 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.07545e9 | −0.148853 | ||||||||
\(197\) | 2.40133e10 | 1.13594 | 0.567968 | − | 0.823051i | \(-0.307730\pi\) | ||||
0.567968 | + | 0.823051i | \(0.307730\pi\) | |||||||
\(198\) | −1.91207e10 | −0.884117 | ||||||||
\(199\) | 9.73605e9 | 0.440093 | 0.220046 | − | 0.975489i | \(-0.429379\pi\) | ||||
0.220046 | + | 0.975489i | \(0.429379\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.86077e10 | 1.23623 | ||||||||
\(202\) | 2.69175e10 | 1.13751 | ||||||||
\(203\) | −3.36029e9 | −0.138882 | ||||||||
\(204\) | 9.21546e8 | 0.0372547 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.18517e10 | 1.61924 | ||||||||
\(207\) | −4.61808e10 | −1.74822 | ||||||||
\(208\) | 3.82574e10 | 1.41720 | ||||||||
\(209\) | −2.22227e10 | −0.805637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.39305e10 | −0.831151 | −0.415576 | − | 0.909559i | \(-0.636420\pi\) | ||||
−0.415576 | + | 0.909559i | \(0.636420\pi\) | |||||||
\(212\) | −2.60662e9 | −0.0886272 | ||||||||
\(213\) | 7.33956e10 | 2.44321 | ||||||||
\(214\) | 4.54732e10 | 1.48215 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.22287e10 | 0.382242 | ||||||||
\(217\) | −5.42141e9 | −0.165975 | ||||||||
\(218\) | 2.54589e9 | 0.0763459 | ||||||||
\(219\) | −3.39101e10 | −0.996163 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.35779e10 | 0.382885 | ||||||||
\(222\) | 2.36643e10 | 0.653890 | ||||||||
\(223\) | −2.02289e10 | −0.547773 | −0.273886 | − | 0.961762i | \(-0.588309\pi\) | ||||
−0.273886 | + | 0.961762i | \(0.588309\pi\) | |||||||
\(224\) | 1.21681e10 | 0.322930 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.97220e10 | −1.01285 | ||||||||
\(227\) | −4.42152e10 | −1.10524 | −0.552618 | − | 0.833434i | \(-0.686371\pi\) | ||||
−0.552618 | + | 0.833434i | \(0.686371\pi\) | |||||||
\(228\) | 6.82140e9 | 0.167173 | ||||||||
\(229\) | −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 | ||||||||
\(232\) | 4.10702e9 | 0.0930746 | ||||||||
\(233\) | −6.68132e10 | −1.48512 | −0.742559 | − | 0.669781i | \(-0.766388\pi\) | ||||
−0.742559 | + | 0.669781i | \(0.766388\pi\) | |||||||
\(234\) | 8.64761e10 | 1.88549 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.67431e9 | −0.0980876 | ||||||||
\(237\) | −2.66865e10 | −0.549444 | ||||||||
\(238\) | −1.74731e10 | −0.352999 | ||||||||
\(239\) | −2.21153e10 | −0.438431 | −0.219216 | − | 0.975676i | \(-0.570350\pi\) | ||||
−0.219216 | + | 0.975676i | \(0.570350\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.97637e10 | 1.90500 | 0.952502 | − | 0.304532i | \(-0.0985002\pi\) | ||||
0.952502 | + | 0.304532i | \(0.0985002\pi\) | |||||||
\(242\) | 2.20416e10 | 0.413118 | ||||||||
\(243\) | −7.65703e10 | −1.40874 | ||||||||
\(244\) | −2.04792e9 | −0.0369878 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.26480e9 | −0.161298 | ||||||||
\(247\) | 1.00506e11 | 1.71812 | ||||||||
\(248\) | 6.62616e9 | 0.111232 | ||||||||
\(249\) | 6.04229e10 | 0.996104 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.97276e10 | −0.790799 | −0.395399 | − | 0.918509i | \(-0.629394\pi\) | ||||
−0.395399 | + | 0.918509i | \(0.629394\pi\) | |||||||
\(252\) | 1.29149e10 | 0.201738 | ||||||||
\(253\) | −6.87435e10 | −1.05485 | ||||||||
\(254\) | −1.15491e11 | −1.74099 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.11977e10 | −0.308467 | ||||||||
\(257\) | −5.81308e10 | −0.831204 | −0.415602 | − | 0.909547i | \(-0.636429\pi\) | ||||
−0.415602 | + | 0.909547i | \(0.636429\pi\) | |||||||
\(258\) | −3.04379e10 | −0.427686 | ||||||||
\(259\) | 5.20718e10 | 0.719041 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.30753e9 | 0.110813 | ||||||||
\(262\) | −8.21814e10 | −1.07750 | ||||||||
\(263\) | 3.23476e10 | 0.416909 | 0.208454 | − | 0.978032i | \(-0.433157\pi\) | ||||
0.208454 | + | 0.978032i | \(0.433157\pi\) | |||||||
\(264\) | 9.27555e10 | 1.17523 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.29338e11 | −1.58401 | ||||||||
\(267\) | −1.18354e11 | −1.42523 | ||||||||
\(268\) | −7.24691e9 | −0.0858116 | ||||||||
\(269\) | 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 | \(-0.350076\pi\) | ||||
0.453779 | + | 0.891114i | \(0.350076\pi\) | |||||||
\(272\) | 1.91110e10 | 0.211701 | ||||||||
\(273\) | 3.43228e11 | 3.73982 | ||||||||
\(274\) | −5.47050e10 | −0.586340 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.11012e10 | 0.218885 | ||||||||
\(277\) | 7.07976e10 | 0.722536 | 0.361268 | − | 0.932462i | \(-0.382344\pi\) | ||||
0.361268 | + | 0.932462i | \(0.382344\pi\) | |||||||
\(278\) | 8.76284e10 | 0.879920 | ||||||||
\(279\) | 1.34031e10 | 0.132430 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.15619e10 | 0.780385 | 0.390193 | − | 0.920733i | \(-0.372408\pi\) | ||||
0.390193 | + | 0.920733i | \(0.372408\pi\) | |||||||
\(282\) | 1.41909e11 | 1.33625 | ||||||||
\(283\) | −1.89301e11 | −1.75434 | −0.877168 | − | 0.480184i | \(-0.840570\pi\) | ||||
−0.877168 | + | 0.480184i | \(0.840570\pi\) | |||||||
\(284\) | −1.85926e10 | −0.169593 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.28726e11 | 1.13768 | ||||||||
\(287\) | −2.03867e10 | −0.177369 | ||||||||
\(288\) | −3.00828e10 | −0.257663 | ||||||||
\(289\) | −1.11805e11 | −0.942805 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.91387e10 | 0.810447 | ||||||||
\(292\) | 8.59011e9 | 0.0691474 | ||||||||
\(293\) | 5.39489e10 | 0.427640 | 0.213820 | − | 0.976873i | \(-0.431409\pi\) | ||||
0.213820 | + | 0.976873i | \(0.431409\pi\) | |||||||
\(294\) | −2.60035e11 | −2.02987 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.36433e10 | −0.481881 | ||||||||
\(297\) | 3.68209e10 | 0.274594 | ||||||||
\(298\) | 1.31434e11 | 0.965462 | ||||||||
\(299\) | 3.10903e11 | 2.24959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.69768e10 | −0.470300 | ||||||||
\(302\) | 1.25032e11 | 0.864950 | ||||||||
\(303\) | −2.64129e11 | −1.80022 | ||||||||
\(304\) | 1.41462e11 | 0.949966 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.31980e10 | 0.281655 | ||||||||
\(307\) | 1.30037e11 | 0.835496 | 0.417748 | − | 0.908563i | \(-0.362819\pi\) | ||||
0.417748 | + | 0.908563i | \(0.362819\pi\) | |||||||
\(308\) | 1.92247e10 | 0.121725 | ||||||||
\(309\) | −4.10671e11 | −2.56260 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.09580e9 | 0.0127036 | 0.00635182 | − | 0.999980i | \(-0.497978\pi\) | ||||
0.00635182 | + | 0.999980i | \(0.497978\pi\) | |||||||
\(312\) | −4.19500e11 | −2.50632 | ||||||||
\(313\) | 2.43788e11 | 1.43570 | 0.717848 | − | 0.696200i | \(-0.245127\pi\) | ||||
0.717848 | + | 0.696200i | \(0.245127\pi\) | |||||||
\(314\) | −2.89217e10 | −0.167896 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.76022e9 | 0.0381390 | ||||||||
\(317\) | 3.46483e11 | 1.92715 | 0.963573 | − | 0.267445i | \(-0.0861794\pi\) | ||||
0.963573 | + | 0.267445i | \(0.0861794\pi\) | |||||||
\(318\) | −2.20395e11 | −1.20859 | ||||||||
\(319\) | 1.23664e10 | 0.0668626 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.46207e11 | −2.34565 | ||||||||
\(322\) | −4.00092e11 | −2.07400 | ||||||||
\(323\) | 5.02063e10 | 0.256653 | ||||||||
\(324\) | 1.43604e10 | 0.0723961 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.65566e10 | −0.473481 | ||||||||
\(327\) | −2.49816e10 | −0.120825 | ||||||||
\(328\) | 2.49170e10 | 0.118868 | ||||||||
\(329\) | 3.12262e11 | 1.46939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.43303e11 | −0.656189 | −0.328094 | − | 0.944645i | \(-0.606406\pi\) | ||||
−0.328094 | + | 0.944645i | \(0.606406\pi\) | |||||||
\(332\) | −1.53063e10 | −0.0691433 | ||||||||
\(333\) | −1.28735e11 | −0.573718 | ||||||||
\(334\) | 3.89470e11 | 1.71244 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.83094e11 | 2.06778 | ||||||||
\(337\) | −3.34820e11 | −1.41409 | −0.707044 | − | 0.707170i | \(-0.749972\pi\) | ||||
−0.707044 | + | 0.707170i | \(0.749972\pi\) | |||||||
\(338\) | −3.55048e11 | −1.47966 | ||||||||
\(339\) | 3.89773e11 | 1.60293 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.99515e10 | 0.0799064 | ||||||||
\(342\) | 3.19757e11 | 1.26387 | ||||||||
\(343\) | −1.72469e11 | −0.672804 | ||||||||
\(344\) | 8.18604e10 | 0.315182 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.09291e11 | 0.785070 | ||||||||
\(347\) | 9.22101e10 | 0.341425 | 0.170713 | − | 0.985321i | \(-0.445393\pi\) | ||||
0.170713 | + | 0.985321i | \(0.445393\pi\) | |||||||
\(348\) | −3.79592e9 | −0.0138743 | ||||||||
\(349\) | −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 | ||||||||
\(352\) | −4.47805e10 | −0.155470 | ||||||||
\(353\) | 4.01029e11 | 1.37464 | 0.687322 | − | 0.726353i | \(-0.258786\pi\) | ||||
0.687322 | + | 0.726353i | \(0.258786\pi\) | |||||||
\(354\) | −3.95222e11 | −1.33760 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.99816e10 | 0.0989303 | ||||||||
\(357\) | 1.71455e11 | 0.558654 | ||||||||
\(358\) | −1.42620e11 | −0.458887 | ||||||||
\(359\) | −2.36110e10 | −0.0750220 | −0.0375110 | − | 0.999296i | \(-0.511943\pi\) | ||||
−0.0375110 | + | 0.999296i | \(0.511943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.89457e10 | 0.151681 | ||||||||
\(362\) | 1.56972e11 | 0.480433 | ||||||||
\(363\) | −2.16284e11 | −0.653799 | ||||||||
\(364\) | −8.69465e10 | −0.259595 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.73155e11 | −0.504395 | ||||||||
\(367\) | −1.23035e11 | −0.354022 | −0.177011 | − | 0.984209i | \(-0.556643\pi\) | ||||
−0.177011 | + | 0.984209i | \(0.556643\pi\) | |||||||
\(368\) | 4.37596e11 | 1.24382 | ||||||||
\(369\) | 5.04012e10 | 0.141521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.84966e11 | −1.32901 | ||||||||
\(372\) | −6.12424e9 | −0.0165809 | ||||||||
\(373\) | 2.39248e11 | 0.639968 | 0.319984 | − | 0.947423i | \(-0.396322\pi\) | ||||
0.319984 | + | 0.947423i | \(0.396322\pi\) | |||||||
\(374\) | 6.43034e10 | 0.169946 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.81653e11 | −0.984745 | ||||||||
\(377\) | −5.59287e10 | −0.142593 | ||||||||
\(378\) | 2.14300e11 | 0.539896 | ||||||||
\(379\) | −5.90629e11 | −1.47041 | −0.735205 | − | 0.677845i | \(-0.762914\pi\) | ||||
−0.735205 | + | 0.677845i | \(0.762914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.13326e12 | 2.75529 | ||||||||
\(382\) | −1.72839e11 | −0.415295 | ||||||||
\(383\) | 5.30525e10 | 0.125983 | 0.0629914 | − | 0.998014i | \(-0.479936\pi\) | ||||
0.0629914 | + | 0.998014i | \(0.479936\pi\) | |||||||
\(384\) | −5.21087e11 | −1.22298 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.69554e10 | 0.153512 | ||||||||
\(387\) | 1.65584e11 | 0.375249 | ||||||||
\(388\) | −2.51138e10 | −0.0562562 | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 6.99345e11 | 1.49591 | ||||||||
\(393\) | 8.06407e11 | 1.70525 | ||||||||
\(394\) | −5.14333e11 | −1.07525 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.75285e10 | −0.0971238 | ||||||||
\(397\) | 2.09351e11 | 0.422979 | 0.211489 | − | 0.977380i | \(-0.432169\pi\) | ||||
0.211489 | + | 0.977380i | \(0.432169\pi\) | |||||||
\(398\) | −2.08533e11 | −0.416583 | ||||||||
\(399\) | 1.26913e12 | 2.50685 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.43868e11 | 0.857244 | 0.428622 | − | 0.903484i | \(-0.358999\pi\) | ||||
0.428622 | + | 0.903484i | \(0.358999\pi\) | |||||||
\(402\) | −6.12739e11 | −1.17020 | ||||||||
\(403\) | −9.02338e10 | −0.170411 | ||||||||
\(404\) | 6.69092e10 | 0.124960 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.19730e10 | 0.131463 | ||||||||
\(407\) | −1.91632e11 | −0.346172 | ||||||||
\(408\) | −2.09556e11 | −0.374394 | ||||||||
\(409\) | 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 | ||||||||
\(412\) | 1.04031e11 | 0.177880 | ||||||||
\(413\) | −8.69663e11 | −1.47087 | ||||||||
\(414\) | 9.89132e11 | 1.65483 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.02526e11 | 0.331559 | ||||||||
\(417\) | −8.59856e11 | −1.39256 | ||||||||
\(418\) | 4.75982e11 | 0.762600 | ||||||||
\(419\) | −1.12392e12 | −1.78144 | −0.890720 | − | 0.454552i | \(-0.849799\pi\) | ||||
−0.890720 | + | 0.454552i | \(0.849799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02822e12 | −1.59521 | −0.797605 | − | 0.603180i | \(-0.793900\pi\) | ||||
−0.797605 | + | 0.603180i | \(0.793900\pi\) | |||||||
\(422\) | 5.12559e11 | 0.786751 | ||||||||
\(423\) | −7.71994e11 | −1.17242 | ||||||||
\(424\) | 5.92736e11 | 0.890666 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.57204e12 | −2.31270 | ||||||||
\(427\) | −3.81018e11 | −0.554652 | ||||||||
\(428\) | 1.13033e11 | 0.162820 | ||||||||
\(429\) | −1.26313e12 | −1.80048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.37714e12 | −1.92234 | −0.961171 | − | 0.275953i | \(-0.911007\pi\) | ||||
−0.961171 | + | 0.275953i | \(0.911007\pi\) | |||||||
\(432\) | −2.34389e11 | −0.323787 | ||||||||
\(433\) | −1.94790e11 | −0.266299 | −0.133150 | − | 0.991096i | \(-0.542509\pi\) | ||||
−0.133150 | + | 0.991096i | \(0.542509\pi\) | |||||||
\(434\) | 1.16119e11 | 0.157109 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.32835e9 | 0.00838689 | ||||||||
\(437\) | 1.14961e12 | 1.50793 | ||||||||
\(438\) | 7.26309e11 | 0.942948 | ||||||||
\(439\) | −5.32533e11 | −0.684315 | −0.342157 | − | 0.939643i | \(-0.611158\pi\) | ||||
−0.342157 | + | 0.939643i | \(0.611158\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.41461e12 | 1.78099 | ||||||||
\(442\) | −2.90821e11 | −0.362432 | ||||||||
\(443\) | −7.26633e11 | −0.896393 | −0.448196 | − | 0.893935i | \(-0.647933\pi\) | ||||
−0.448196 | + | 0.893935i | \(0.647933\pi\) | |||||||
\(444\) | 5.88225e10 | 0.0718323 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.33276e11 | 0.518511 | ||||||||
\(447\) | −1.28970e12 | −1.52794 | ||||||||
\(448\) | −1.43749e12 | −1.68599 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | −9.87374e10 | −0.111265 | ||||||||
\(453\) | −1.22688e12 | −1.36887 | ||||||||
\(454\) | 9.47031e11 | 1.04620 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.55116e12 | −1.68002 | ||||||||
\(457\) | 1.09190e12 | 1.17101 | 0.585503 | − | 0.810670i | \(-0.300897\pi\) | ||||
0.585503 | + | 0.810670i | \(0.300897\pi\) | |||||||
\(458\) | 1.04841e12 | 1.11336 | ||||||||
\(459\) | −8.31870e10 | −0.0874779 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.93683e11 | 1.02469 | 0.512347 | − | 0.858779i | \(-0.328776\pi\) | ||||
0.512347 | + | 0.858779i | \(0.328776\pi\) | |||||||
\(462\) | 1.62548e12 | 1.65994 | ||||||||
\(463\) | 6.95734e11 | 0.703605 | 0.351802 | − | 0.936074i | \(-0.385569\pi\) | ||||
0.351802 | + | 0.936074i | \(0.385569\pi\) | |||||||
\(464\) | −7.87197e10 | −0.0788411 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.43105e12 | 1.40578 | ||||||||
\(467\) | −1.87957e12 | −1.82866 | −0.914328 | − | 0.404975i | \(-0.867280\pi\) | ||||
−0.914328 | + | 0.404975i | \(0.867280\pi\) | |||||||
\(468\) | 2.14955e11 | 0.207129 | ||||||||
\(469\) | −1.34830e12 | −1.28679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.83795e11 | 0.265712 | ||||||||
\(472\) | 1.06292e12 | 0.985739 | ||||||||
\(473\) | 2.46484e11 | 0.226419 | ||||||||
\(474\) | 5.71589e11 | 0.520093 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.34330e10 | −0.0387783 | ||||||||
\(477\) | 1.19896e12 | 1.06041 | ||||||||
\(478\) | 4.73679e11 | 0.415010 | ||||||||
\(479\) | −2.29011e11 | −0.198768 | −0.0993838 | − | 0.995049i | \(-0.531687\pi\) | ||||
−0.0993838 | + | 0.995049i | \(0.531687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.66683e11 | 0.738256 | ||||||||
\(482\) | −2.13681e12 | −1.80324 | ||||||||
\(483\) | 3.92591e12 | 3.28230 | ||||||||
\(484\) | 5.47890e10 | 0.0453826 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.64003e12 | 1.33349 | ||||||||
\(487\) | 4.81410e11 | 0.387824 | 0.193912 | − | 0.981019i | \(-0.437882\pi\) | ||||
0.193912 | + | 0.981019i | \(0.437882\pi\) | |||||||
\(488\) | 4.65689e11 | 0.371712 | ||||||||
\(489\) | 9.47465e11 | 0.749330 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.70320e12 | −1.32251 | −0.661257 | − | 0.750160i | \(-0.729977\pi\) | ||||
−0.661257 | + | 0.750160i | \(0.729977\pi\) | |||||||
\(492\) | −2.30296e10 | −0.0177192 | ||||||||
\(493\) | −2.79384e10 | −0.0213006 | ||||||||
\(494\) | −2.15270e12 | −1.62634 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.27004e11 | −0.0942217 | ||||||||
\(497\) | −3.45917e12 | −2.54313 | ||||||||
\(498\) | −1.29418e12 | −0.942892 | ||||||||
\(499\) | 2.06075e12 | 1.48789 | 0.743947 | − | 0.668238i | \(-0.232951\pi\) | ||||
0.743947 | + | 0.668238i | \(0.232951\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.82168e12 | −2.71010 | ||||||||
\(502\) | 1.06510e12 | 0.748555 | ||||||||
\(503\) | 5.97493e11 | 0.416176 | 0.208088 | − | 0.978110i | \(-0.433276\pi\) | ||||
0.208088 | + | 0.978110i | \(0.433276\pi\) | |||||||
\(504\) | −2.93679e12 | −2.02738 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.47239e12 | 0.998497 | ||||||||
\(507\) | 3.48392e12 | 2.34170 | ||||||||
\(508\) | −2.87077e11 | −0.191255 | ||||||||
\(509\) | −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 | ||||||||
\(512\) | 1.72345e12 | 1.10837 | ||||||||
\(513\) | −6.15760e11 | −0.392540 | ||||||||
\(514\) | 1.24508e12 | 0.786801 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.56597e10 | −0.0469830 | ||||||||
\(517\) | −1.14917e12 | −0.707418 | ||||||||
\(518\) | −1.11531e12 | −0.680630 | ||||||||
\(519\) | −2.05367e12 | −1.24245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.31013e11 | 0.434666 | 0.217333 | − | 0.976098i | \(-0.430264\pi\) | ||||
0.217333 | + | 0.976098i | \(0.430264\pi\) | |||||||
\(522\) | −1.77936e11 | −0.104893 | ||||||||
\(523\) | −1.04453e12 | −0.610467 | −0.305233 | − | 0.952278i | \(-0.598734\pi\) | ||||
−0.305233 | + | 0.952278i | \(0.598734\pi\) | |||||||
\(524\) | −2.04279e11 | −0.118368 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.92842e11 | −0.394638 | ||||||||
\(527\) | −4.50751e10 | −0.0254559 | ||||||||
\(528\) | −1.77785e12 | −0.995504 | ||||||||
\(529\) | 1.75502e12 | 0.974386 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.15003e12 | 1.17360 | ||||||||
\(532\) | −3.21496e11 | −0.174010 | ||||||||
\(533\) | −3.39315e11 | −0.182109 | ||||||||
\(534\) | 2.53500e12 | 1.34909 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.64792e12 | 0.862371 | ||||||||
\(537\) | 1.39946e12 | 0.726233 | ||||||||
\(538\) | −1.33700e11 | −0.0688034 | ||||||||
\(539\) | 2.10575e12 | 1.07462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88034e12 | −0.943733 | −0.471866 | − | 0.881670i | \(-0.656420\pi\) | ||||
−0.471866 | + | 0.881670i | \(0.656420\pi\) | |||||||
\(542\) | −1.72595e12 | −0.859076 | ||||||||
\(543\) | −1.54029e12 | −0.760331 | ||||||||
\(544\) | 1.01169e11 | 0.0495284 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.35148e12 | −3.54004 | ||||||||
\(547\) | 1.08624e12 | 0.518780 | 0.259390 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259390 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(548\) | −1.35981e11 | −0.0644117 | ||||||||
\(549\) | 9.41977e11 | 0.442553 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.06804e11 | −0.0955821 | ||||||||
\(552\) | −4.79834e12 | −2.19971 | ||||||||
\(553\) | 1.25775e12 | 0.571914 | ||||||||
\(554\) | −1.51639e12 | −0.683938 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.17819e11 | 0.0966626 | ||||||||
\(557\) | −2.11965e12 | −0.933072 | −0.466536 | − | 0.884502i | \(-0.654498\pi\) | ||||
−0.466536 | + | 0.884502i | \(0.654498\pi\) | |||||||
\(558\) | −2.87078e11 | −0.125356 | ||||||||
\(559\) | −1.11476e12 | −0.482868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.30978e11 | −0.268956 | ||||||||
\(562\) | −1.74695e12 | −0.738697 | ||||||||
\(563\) | −3.04489e12 | −1.27727 | −0.638636 | − | 0.769509i | \(-0.720501\pi\) | ||||
−0.638636 | + | 0.769509i | \(0.720501\pi\) | |||||||
\(564\) | 3.52744e11 | 0.146792 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.05456e12 | 1.66062 | ||||||||
\(567\) | 2.67178e12 | 1.08562 | ||||||||
\(568\) | 4.22788e12 | 1.70433 | ||||||||
\(569\) | 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 | \(-0.586208\pi\) | ||||
−0.267533 | + | 0.963549i | \(0.586208\pi\) | |||||||
\(572\) | 3.19975e11 | 0.124978 | ||||||||
\(573\) | 1.69599e12 | 0.657245 | ||||||||
\(574\) | 4.36655e11 | 0.167894 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.55386e12 | 1.34524 | ||||||||
\(577\) | 2.35782e12 | 0.885564 | 0.442782 | − | 0.896629i | \(-0.353992\pi\) | ||||
0.442782 | + | 0.896629i | \(0.353992\pi\) | |||||||
\(578\) | 2.39472e12 | 0.892440 | ||||||||
\(579\) | −6.57002e11 | −0.242948 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.84777e12 | −1.03684 | ||||||||
\(582\) | −2.12342e12 | −0.767154 | ||||||||
\(583\) | 1.78474e12 | 0.639834 | ||||||||
\(584\) | −1.95336e12 | −0.694902 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.15551e12 | −0.404796 | ||||||||
\(587\) | 2.37065e12 | 0.824130 | 0.412065 | − | 0.911154i | \(-0.364808\pi\) | ||||
0.412065 | + | 0.911154i | \(0.364808\pi\) | |||||||
\(588\) | −6.46371e11 | −0.222989 | ||||||||
\(589\) | −3.33652e11 | −0.114229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.04690e12 | 1.70169 | ||||||||
\(592\) | 1.21986e12 | 0.408189 | ||||||||
\(593\) | −4.56707e12 | −1.51667 | −0.758336 | − | 0.651864i | \(-0.773987\pi\) | ||||
−0.758336 | + | 0.651864i | \(0.773987\pi\) | |||||||
\(594\) | −7.88655e11 | −0.259925 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.26707e11 | 0.106060 | ||||||||
\(597\) | 2.04624e12 | 0.659283 | ||||||||
\(598\) | −6.65912e12 | −2.12942 | ||||||||
\(599\) | −5.30493e12 | −1.68368 | −0.841839 | − | 0.539729i | \(-0.818527\pi\) | ||||
−0.841839 | + | 0.539729i | \(0.818527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.71307e12 | −0.848255 | −0.424128 | − | 0.905602i | \(-0.639419\pi\) | ||||
−0.424128 | + | 0.905602i | \(0.639419\pi\) | |||||||
\(602\) | 1.43455e12 | 0.445177 | ||||||||
\(603\) | 3.33335e12 | 1.02672 | ||||||||
\(604\) | 3.10794e11 | 0.0950182 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.65730e12 | 1.70405 | ||||||||
\(607\) | 4.00734e12 | 1.19814 | 0.599069 | − | 0.800698i | \(-0.295538\pi\) | ||||
0.599069 | + | 0.800698i | \(0.295538\pi\) | |||||||
\(608\) | 7.48868e11 | 0.222249 | ||||||||
\(609\) | −7.06237e11 | −0.208052 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.19728e12 | 1.50866 | ||||||||
\(612\) | 1.07378e11 | 0.0309409 | ||||||||
\(613\) | 2.24954e12 | 0.643459 | 0.321730 | − | 0.946832i | \(-0.395736\pi\) | ||||
0.321730 | + | 0.946832i | \(0.395736\pi\) | |||||||
\(614\) | −2.78522e12 | −0.790864 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.37162e12 | −1.22329 | ||||||||
\(617\) | −1.19664e12 | −0.332414 | −0.166207 | − | 0.986091i | \(-0.553152\pi\) | ||||
−0.166207 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(618\) | 8.79602e12 | 2.42571 | ||||||||
\(619\) | −4.36723e12 | −1.19563 | −0.597817 | − | 0.801633i | \(-0.703965\pi\) | ||||
−0.597817 | + | 0.801633i | \(0.703965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.90478e12 | −0.513965 | ||||||||
\(622\) | −4.48893e10 | −0.0120250 | ||||||||
\(623\) | 5.57811e12 | 1.48351 | ||||||||
\(624\) | 8.04060e12 | 2.12304 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.22161e12 | −1.35900 | ||||||||
\(627\) | −4.67058e12 | −1.20689 | ||||||||
\(628\) | −7.18911e10 | −0.0184441 | ||||||||
\(629\) | 4.32940e11 | 0.110281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.78790e12 | 0.700077 | 0.350039 | − | 0.936735i | \(-0.386168\pi\) | ||||
0.350039 | + | 0.936735i | \(0.386168\pi\) | |||||||
\(632\) | −1.53725e12 | −0.383281 | ||||||||
\(633\) | −5.02950e12 | −1.24511 | ||||||||
\(634\) | −7.42120e12 | −1.82420 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.47837e11 | −0.132768 | ||||||||
\(637\) | −9.52355e12 | −2.29177 | ||||||||
\(638\) | −2.64871e11 | −0.0632909 | ||||||||
\(639\) | 8.55199e12 | 2.02915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.28295e12 | −0.534115 | −0.267058 | − | 0.963681i | \(-0.586051\pi\) | ||||
−0.267058 | + | 0.963681i | \(0.586051\pi\) | |||||||
\(642\) | 9.55716e12 | 2.22035 | ||||||||
\(643\) | 2.29995e12 | 0.530603 | 0.265301 | − | 0.964166i | \(-0.414529\pi\) | ||||
0.265301 | + | 0.964166i | \(0.414529\pi\) | |||||||
\(644\) | −9.94512e11 | −0.227837 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.07535e12 | −0.242943 | ||||||||
\(647\) | −1.85647e12 | −0.416503 | −0.208251 | − | 0.978075i | \(-0.566777\pi\) | ||||
−0.208251 | + | 0.978075i | \(0.566777\pi\) | |||||||
\(648\) | −3.26551e12 | −0.727550 | ||||||||
\(649\) | 3.20048e12 | 0.708132 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.13942e12 | −0.248640 | ||||||||
\(652\) | −2.40012e11 | −0.0520138 | ||||||||
\(653\) | −7.75397e12 | −1.66884 | −0.834420 | − | 0.551129i | \(-0.814197\pi\) | ||||
−0.834420 | + | 0.551129i | \(0.814197\pi\) | |||||||
\(654\) | 5.35073e11 | 0.114370 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.77587e11 | −0.100690 | ||||||||
\(657\) | −3.95117e12 | −0.827336 | ||||||||
\(658\) | −6.68824e12 | −1.39090 | ||||||||
\(659\) | 7.42166e12 | 1.53291 | 0.766455 | − | 0.642298i | \(-0.222019\pi\) | ||||
0.766455 | + | 0.642298i | \(0.222019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.79783e12 | 1.18130 | 0.590648 | − | 0.806929i | \(-0.298872\pi\) | ||||
0.590648 | + | 0.806929i | \(0.298872\pi\) | |||||||
\(662\) | 3.06936e12 | 0.621135 | ||||||||
\(663\) | 2.85369e12 | 0.573583 | ||||||||
\(664\) | 3.48060e12 | 0.694861 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.75734e12 | 0.543070 | ||||||||
\(667\) | −6.39724e11 | −0.125149 | ||||||||
\(668\) | 9.68108e11 | 0.188118 | ||||||||
\(669\) | −4.25153e12 | −0.820593 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.40220e12 | 0.267029 | ||||||||
\(672\) | 2.55739e12 | 0.483766 | ||||||||
\(673\) | 6.32456e12 | 1.18840 | 0.594200 | − | 0.804318i | \(-0.297469\pi\) | ||||
0.594200 | + | 0.804318i | \(0.297469\pi\) | |||||||
\(674\) | 7.17139e12 | 1.33855 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.82546e11 | −0.162546 | ||||||||
\(677\) | 4.95066e12 | 0.905762 | 0.452881 | − | 0.891571i | \(-0.350396\pi\) | ||||
0.452881 | + | 0.891571i | \(0.350396\pi\) | |||||||
\(678\) | −8.34843e12 | −1.51730 | ||||||||
\(679\) | −4.67246e12 | −0.843591 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.29277e12 | −1.65571 | ||||||||
\(682\) | −4.27336e11 | −0.0756379 | ||||||||
\(683\) | −7.32611e12 | −1.28819 | −0.644095 | − | 0.764945i | \(-0.722766\pi\) | ||||
−0.644095 | + | 0.764945i | \(0.722766\pi\) | |||||||
\(684\) | 7.94824e11 | 0.138841 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.69406e12 | 0.636863 | ||||||||
\(687\) | −1.02875e13 | −1.76200 | ||||||||
\(688\) | −1.56903e12 | −0.266982 | ||||||||
\(689\) | −8.07176e12 | −1.36453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.66806e12 | −0.945765 | −0.472882 | − | 0.881126i | \(-0.656786\pi\) | ||||
−0.472882 | + | 0.881126i | \(0.656786\pi\) | |||||||
\(692\) | 5.20237e11 | 0.0862430 | ||||||||
\(693\) | −8.84274e12 | −1.45642 | ||||||||
\(694\) | −1.97502e12 | −0.323187 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.63178e11 | 0.139431 | ||||||||
\(697\) | −1.69501e11 | −0.0272034 | ||||||||
\(698\) | 1.01040e13 | 1.61118 | ||||||||
\(699\) | −1.40422e13 | −2.22479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.20985e12 | −0.658470 | −0.329235 | − | 0.944248i | \(-0.606791\pi\) | ||||
−0.329235 | + | 0.944248i | \(0.606791\pi\) | |||||||
\(702\) | 3.56681e12 | 0.554323 | ||||||||
\(703\) | 3.20468e12 | 0.494863 | ||||||||
\(704\) | 5.29018e12 | 0.811696 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.58952e12 | −1.30121 | ||||||||
\(707\) | 1.24486e13 | 1.87384 | ||||||||
\(708\) | −9.82407e11 | −0.146941 | ||||||||
\(709\) | 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 | ||||||||
\(712\) | −6.81769e12 | −0.994208 | ||||||||
\(713\) | −1.03211e12 | −0.149563 | ||||||||
\(714\) | −3.67234e12 | −0.528811 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.54511e11 | −0.0504105 | ||||||||
\(717\) | −4.64799e12 | −0.656794 | ||||||||
\(718\) | 5.05715e11 | 0.0710143 | ||||||||
\(719\) | −4.07118e11 | −0.0568120 | −0.0284060 | − | 0.999596i | \(-0.509043\pi\) | ||||
−0.0284060 | + | 0.999596i | \(0.509043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.93551e13 | 2.66740 | ||||||||
\(722\) | −1.04835e12 | −0.143579 | ||||||||
\(723\) | 2.09675e13 | 2.85380 | ||||||||
\(724\) | 3.90186e11 | 0.0527774 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.63251e12 | 0.618873 | ||||||||
\(727\) | −6.44424e12 | −0.855592 | −0.427796 | − | 0.903875i | \(-0.640710\pi\) | ||||
−0.427796 | + | 0.903875i | \(0.640710\pi\) | |||||||
\(728\) | 1.97713e13 | 2.60882 | ||||||||
\(729\) | −1.07838e13 | −1.41416 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.56864e11 | −0.0721308 | ||||||||
\(732\) | −4.30414e11 | −0.0554098 | ||||||||
\(733\) | −5.46122e12 | −0.698749 | −0.349375 | − | 0.936983i | \(-0.613606\pi\) | ||||
−0.349375 | + | 0.936983i | \(0.613606\pi\) | |||||||
\(734\) | 2.63524e12 | 0.335110 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.31654e12 | 0.290998 | ||||||||
\(737\) | 4.96192e12 | 0.619507 | ||||||||
\(738\) | −1.07953e12 | −0.133961 | ||||||||
\(739\) | −1.88201e12 | −0.232125 | −0.116062 | − | 0.993242i | \(-0.537027\pi\) | ||||
−0.116062 | + | 0.993242i | \(0.537027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.11234e13 | 2.57384 | ||||||||
\(742\) | 1.03873e13 | 1.25802 | ||||||||
\(743\) | −1.36704e13 | −1.64563 | −0.822813 | − | 0.568312i | \(-0.807597\pi\) | ||||
−0.822813 | + | 0.568312i | \(0.807597\pi\) | |||||||
\(744\) | 1.39263e12 | 0.166632 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.12437e12 | −0.605781 | ||||||||
\(747\) | 7.04042e12 | 0.827287 | ||||||||
\(748\) | 1.59840e11 | 0.0186693 | ||||||||
\(749\) | 2.10300e13 | 2.44158 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.52585e12 | 0.978043 | 0.489021 | − | 0.872272i | \(-0.337354\pi\) | ||||
0.489021 | + | 0.872272i | \(0.337354\pi\) | |||||||
\(752\) | 7.31518e12 | 0.834152 | ||||||||
\(753\) | −1.04513e13 | −1.18466 | ||||||||
\(754\) | 1.19792e12 | 0.134976 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.32688e11 | 0.0593096 | ||||||||
\(757\) | 7.50792e12 | 0.830975 | 0.415487 | − | 0.909599i | \(-0.363611\pi\) | ||||
0.415487 | + | 0.909599i | \(0.363611\pi\) | |||||||
\(758\) | 1.26505e13 | 1.39186 | ||||||||
\(759\) | −1.44479e13 | −1.58022 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.61560e13 | −1.74624 | −0.873118 | − | 0.487509i | \(-0.837906\pi\) | ||||
−0.873118 | + | 0.487509i | \(0.837906\pi\) | |||||||
\(762\) | −2.42729e13 | −2.60810 | ||||||||
\(763\) | 1.17740e12 | 0.125766 | ||||||||
\(764\) | −4.29628e11 | −0.0456218 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.13631e12 | −0.119253 | ||||||||
\(767\) | −1.44747e13 | −1.51018 | ||||||||
\(768\) | −4.45514e12 | −0.462100 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 1.66432e11 | 0.0168639 | ||||||||
\(773\) | 1.73165e13 | 1.74442 | 0.872212 | − | 0.489129i | \(-0.162685\pi\) | ||||
0.872212 | + | 0.489129i | \(0.162685\pi\) | |||||||
\(774\) | −3.54659e12 | −0.355203 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.71078e12 | 0.565351 | ||||||||
\(777\) | 1.09440e13 | 1.07716 | ||||||||
\(778\) | −6.64825e12 | −0.650578 | ||||||||
\(779\) | −1.25466e12 | −0.122070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.27302e13 | 1.22435 | ||||||||
\(782\) | −3.32648e12 | −0.318093 | ||||||||
\(783\) | 3.42654e11 | 0.0325783 | ||||||||
\(784\) | −1.34044e13 | −1.26714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.72722e13 | −1.61416 | ||||||||
\(787\) | 3.88515e11 | 0.0361012 | 0.0180506 | − | 0.999837i | \(-0.494254\pi\) | ||||
0.0180506 | + | 0.999837i | \(0.494254\pi\) | |||||||
\(788\) | −1.27848e12 | −0.118121 | ||||||||
\(789\) | 6.79853e12 | 0.624552 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.83702e13 | −1.66848 | ||||||||
\(792\) | 1.08078e13 | 0.976053 | ||||||||
\(793\) | −6.34166e12 | −0.569474 | ||||||||
\(794\) | −4.48403e12 | −0.400383 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.18353e11 | −0.0457633 | ||||||||
\(797\) | 1.08432e12 | 0.0951910 | 0.0475955 | − | 0.998867i | \(-0.484844\pi\) | ||||
0.0475955 | + | 0.998867i | \(0.484844\pi\) | |||||||
\(798\) | −2.71831e13 | −2.37294 | ||||||||
\(799\) | 2.59624e12 | 0.225363 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.37906e13 | −1.18368 | ||||||||
\(802\) | −9.50706e12 | −0.811450 | ||||||||
\(803\) | −5.88161e12 | −0.499202 | ||||||||
\(804\) | −1.52309e12 | −0.128551 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.93269e12 | 0.161307 | ||||||||
\(807\) | 1.31193e12 | 0.108888 | ||||||||
\(808\) | −1.52149e13 | −1.25579 | ||||||||
\(809\) | 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 | \(-0.436606\pi\) | ||||
0.197844 | + | 0.980234i | \(0.436606\pi\) | |||||||
\(812\) | 1.78904e11 | 0.0144417 | ||||||||
\(813\) | 1.69359e13 | 1.35957 | ||||||||
\(814\) | 4.10449e12 | 0.327680 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.01658e12 | 0.317140 | ||||||||
\(817\) | −4.12198e12 | −0.323673 | ||||||||
\(818\) | −9.76758e12 | −0.762777 | ||||||||
\(819\) | 3.99926e13 | 3.10600 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.03829e12 | −0.0797582 | −0.0398791 | − | 0.999205i | \(-0.512697\pi\) | ||||
−0.0398791 | + | 0.999205i | \(0.512697\pi\) | |||||||
\(822\) | −1.14974e13 | −0.878370 | ||||||||
\(823\) | −1.10923e13 | −0.842794 | −0.421397 | − | 0.906876i | \(-0.638460\pi\) | ||||
−0.421397 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(824\) | −2.36563e13 | −1.78761 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.86270e13 | 1.39230 | ||||||||
\(827\) | 1.45526e13 | 1.08184 | 0.540922 | − | 0.841073i | \(-0.318075\pi\) | ||||
0.540922 | + | 0.841073i | \(0.318075\pi\) | |||||||
\(828\) | 2.45870e12 | 0.181789 | ||||||||
\(829\) | 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 | ||||||||
\(832\) | −2.39256e13 | −1.73104 | ||||||||
\(833\) | −4.75736e12 | −0.342345 | ||||||||
\(834\) | 1.84170e13 | 1.31817 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.18315e12 | 0.0837746 | ||||||||
\(837\) | 5.52829e11 | 0.0389337 | ||||||||
\(838\) | 2.40728e13 | 1.68628 | ||||||||
\(839\) | 9.20234e11 | 0.0641165 | 0.0320582 | − | 0.999486i | \(-0.489794\pi\) | ||||
0.0320582 | + | 0.999486i | \(0.489794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.43921e13 | −0.992067 | ||||||||
\(842\) | 2.20232e13 | 1.50999 | ||||||||
\(843\) | 1.71420e13 | 1.16906 | ||||||||
\(844\) | 1.27407e12 | 0.0864277 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.65351e13 | 1.10979 | ||||||||
\(847\) | 1.01936e13 | 0.680536 | ||||||||
\(848\) | −1.13610e13 | −0.754460 | ||||||||
\(849\) | −3.97855e13 | −2.62809 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.91330e12 | 0.647941 | ||||||||
\(852\) | −3.90762e12 | −0.254059 | ||||||||
\(853\) | 7.46964e12 | 0.483091 | 0.241545 | − | 0.970390i | \(-0.422346\pi\) | ||||
0.241545 | + | 0.970390i | \(0.422346\pi\) | |||||||
\(854\) | 8.16090e12 | 0.525022 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.57033e13 | −1.63628 | ||||||||
\(857\) | −2.05568e13 | −1.30179 | −0.650897 | − | 0.759166i | \(-0.725607\pi\) | ||||
−0.650897 | + | 0.759166i | \(0.725607\pi\) | |||||||
\(858\) | 2.70545e13 | 1.70430 | ||||||||
\(859\) | −1.05923e12 | −0.0663775 | −0.0331888 | − | 0.999449i | \(-0.510566\pi\) | ||||
−0.0331888 | + | 0.999449i | \(0.510566\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.28469e12 | −0.265709 | ||||||||
\(862\) | 2.94965e13 | 1.81965 | ||||||||
\(863\) | −1.53023e13 | −0.939092 | −0.469546 | − | 0.882908i | \(-0.655582\pi\) | ||||
−0.469546 | + | 0.882908i | \(0.655582\pi\) | |||||||
\(864\) | −1.24080e12 | −0.0757514 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.17213e12 | 0.252074 | ||||||||
\(867\) | −2.34982e13 | −1.41237 | ||||||||
\(868\) | 2.88639e11 | 0.0172590 | ||||||||
\(869\) | −4.62869e12 | −0.275340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.24410e13 | −1.32118 | ||||||||
\(872\) | −1.43904e12 | −0.0842847 | ||||||||
\(873\) | 1.15516e13 | 0.673095 | ||||||||
\(874\) | −2.46230e13 | −1.42738 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.80539e12 | 0.103587 | ||||||||
\(877\) | 1.74558e11 | 0.00996416 | 0.00498208 | − | 0.999988i | \(-0.498414\pi\) | ||||
0.00498208 | + | 0.999988i | \(0.498414\pi\) | |||||||
\(878\) | 1.14061e13 | 0.647759 | ||||||||
\(879\) | 1.13385e13 | 0.640629 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.59039e12 | 0.480420 | 0.240210 | − | 0.970721i | \(-0.422784\pi\) | ||||
0.240210 | + | 0.970721i | \(0.422784\pi\) | |||||||
\(882\) | −3.02990e13 | −1.68585 | ||||||||
\(883\) | 1.70227e13 | 0.942336 | 0.471168 | − | 0.882043i | \(-0.343833\pi\) | ||||
0.471168 | + | 0.882043i | \(0.343833\pi\) | |||||||
\(884\) | −7.22898e11 | −0.0398145 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.55635e13 | 0.848508 | ||||||||
\(887\) | 2.01246e13 | 1.09162 | 0.545810 | − | 0.837909i | \(-0.316222\pi\) | ||||
0.545810 | + | 0.837909i | \(0.316222\pi\) | |||||||
\(888\) | −1.33760e13 | −0.721885 | ||||||||
\(889\) | −5.34112e13 | −2.86797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.83253e12 | −0.522655 | ||||||||
\(892\) | 1.07700e12 | 0.0569604 | ||||||||
\(893\) | 1.92177e13 | 1.01127 | ||||||||
\(894\) | 2.76237e13 | 1.44632 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.45591e13 | 1.27299 | ||||||||
\(897\) | 6.53428e13 | 3.37002 | ||||||||
\(898\) | −2.00228e13 | −1.02750 | ||||||||
\(899\) | 1.85668e11 | 0.00948023 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.03214e12 | −0.203833 | ||||||||
\(902\) | −1.60695e12 | −0.0808302 | ||||||||
\(903\) | −1.40766e13 | −0.704535 | ||||||||
\(904\) | 2.24525e13 | 1.11817 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.62782e13 | 1.29574 | ||||||||
\(907\) | 2.10130e13 | 1.03099 | 0.515495 | − | 0.856893i | \(-0.327608\pi\) | ||||
0.515495 | + | 0.856893i | \(0.327608\pi\) | |||||||
\(908\) | 2.35404e12 | 0.114929 | ||||||||
\(909\) | −3.07761e13 | −1.49512 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.95345e12 | 0.0939656 | 0.0469828 | − | 0.998896i | \(-0.485039\pi\) | ||||
0.0469828 | + | 0.998896i | \(0.485039\pi\) | |||||||
\(912\) | 2.97312e13 | 1.42310 | ||||||||
\(913\) | 1.04802e13 | 0.499172 | ||||||||
\(914\) | −2.33870e13 | −1.10845 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.60604e12 | 0.122307 | ||||||||
\(917\) | −3.80064e13 | −1.77499 | ||||||||
\(918\) | 1.78175e12 | 0.0828048 | ||||||||
\(919\) | −2.47656e12 | −0.114533 | −0.0572663 | − | 0.998359i | \(-0.518238\pi\) | ||||
−0.0572663 | + | 0.998359i | \(0.518238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.73301e13 | 1.25162 | ||||||||
\(922\) | −2.12834e13 | −0.969954 | ||||||||
\(923\) | −5.75744e13 | −2.61109 | ||||||||
\(924\) | 4.04048e12 | 0.182351 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.49017e13 | −0.666018 | ||||||||
\(927\) | −4.78510e13 | −2.12830 | ||||||||
\(928\) | −4.16725e11 | −0.0184452 | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 3.55718e12 | 0.154431 | ||||||||
\(933\) | 4.40477e11 | 0.0190308 | ||||||||
\(934\) | 4.02578e13 | 1.73097 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.88798e13 | −2.08156 | ||||||||
\(937\) | −4.92250e12 | −0.208621 | −0.104310 | − | 0.994545i | \(-0.533264\pi\) | ||||
−0.104310 | + | 0.994545i | \(0.533264\pi\) | |||||||
\(938\) | 2.88787e13 | 1.21805 | ||||||||
\(939\) | 5.12372e13 | 2.15075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.54680e13 | −0.643103 | −0.321552 | − | 0.946892i | \(-0.604204\pi\) | ||||
−0.321552 | + | 0.946892i | \(0.604204\pi\) | |||||||
\(942\) | −6.07852e12 | −0.251518 | ||||||||
\(943\) | −3.88116e12 | −0.159830 | ||||||||
\(944\) | −2.03731e13 | −0.834993 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.27936e12 | −0.214324 | ||||||||
\(947\) | −5.49107e12 | −0.221862 | −0.110931 | − | 0.993828i | \(-0.535383\pi\) | ||||
−0.110931 | + | 0.993828i | \(0.535383\pi\) | |||||||
\(948\) | 1.42080e12 | 0.0571343 | ||||||||
\(949\) | 2.66004e13 | 1.06461 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.28207e13 | 2.88697 | ||||||||
\(952\) | 9.87649e12 | 0.389705 | ||||||||
\(953\) | 1.76932e13 | 0.694845 | 0.347422 | − | 0.937709i | \(-0.387057\pi\) | ||||
0.347422 | + | 0.937709i | \(0.387057\pi\) | |||||||
\(954\) | −2.56802e13 | −1.00376 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.17743e12 | 0.0455905 | ||||||||
\(957\) | 2.59905e12 | 0.100164 | ||||||||
\(958\) | 4.90510e12 | 0.188150 | ||||||||
\(959\) | −2.52994e13 | −0.965888 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.61401e13 | −0.988670 | ||||||||
\(962\) | −1.85632e13 | −0.698819 | ||||||||
\(963\) | −5.19916e13 | −1.94812 | ||||||||
\(964\) | −5.31148e12 | −0.198093 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.40878e13 | −3.10696 | ||||||||
\(967\) | −2.89231e13 | −1.06372 | −0.531858 | − | 0.846834i | \(-0.678506\pi\) | ||||
−0.531858 | + | 0.846834i | \(0.678506\pi\) | |||||||
\(968\) | −1.24588e13 | −0.456076 | ||||||||
\(969\) | 1.05519e13 | 0.384481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.69482e13 | 0.972843 | 0.486422 | − | 0.873724i | \(-0.338302\pi\) | ||||
0.486422 | + | 0.873724i | \(0.338302\pi\) | |||||||
\(972\) | 4.07665e12 | 0.146489 | ||||||||
\(973\) | 4.05255e13 | 1.44951 | ||||||||
\(974\) | −1.03112e13 | −0.367107 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.92590e12 | −0.314867 | ||||||||
\(977\) | −3.90598e13 | −1.37153 | −0.685764 | − | 0.727824i | \(-0.740532\pi\) | ||||
−0.685764 | + | 0.727824i | \(0.740532\pi\) | |||||||
\(978\) | −2.02934e13 | −0.709301 | ||||||||
\(979\) | −2.05282e13 | −0.714216 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.91084e12 | −0.100348 | ||||||||
\(982\) | 3.64804e13 | 1.25187 | ||||||||
\(983\) | −9.03830e12 | −0.308742 | −0.154371 | − | 0.988013i | \(-0.549335\pi\) | ||||
−0.154371 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(984\) | 5.23684e12 | 0.178070 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.98404e11 | 0.0201627 | ||||||||
\(987\) | 6.56285e13 | 2.20123 | ||||||||
\(988\) | −5.35098e12 | −0.178660 | ||||||||
\(989\) | −1.27509e13 | −0.423795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.89096e13 | 1.61088 | 0.805439 | − | 0.592678i | \(-0.201929\pi\) | ||||
0.805439 | + | 0.592678i | \(0.201929\pi\) | |||||||
\(992\) | −6.72333e11 | −0.0220436 | ||||||||
\(993\) | −3.01181e13 | −0.983007 | ||||||||
\(994\) | 7.40909e13 | 2.40728 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.21695e12 | −0.103580 | ||||||||
\(997\) | −4.01445e13 | −1.28676 | −0.643380 | − | 0.765547i | \(-0.722468\pi\) | ||||
−0.643380 | + | 0.765547i | \(0.722468\pi\) | |||||||
\(998\) | −4.41384e13 | −1.40841 | ||||||||
\(999\) | −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 | 25.10.a.c.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 225.10.a.p.1.2 | 3 | |||
4.3 | odd | 2 | 400.10.a.y.1.1 | 3 | |||
5.2 | odd | 4 | 25.10.b.c.24.2 | 6 | |||
5.3 | odd | 4 | 25.10.b.c.24.5 | 6 | |||
5.4 | even | 2 | 25.10.a.d.1.2 | yes | 3 | ||
15.2 | even | 4 | 225.10.b.m.199.5 | 6 | |||
15.8 | even | 4 | 225.10.b.m.199.2 | 6 | |||
15.14 | odd | 2 | 225.10.a.m.1.2 | 3 | |||
20.3 | even | 4 | 400.10.c.q.49.2 | 6 | |||
20.7 | even | 4 | 400.10.c.q.49.5 | 6 | |||
20.19 | odd | 2 | 400.10.a.u.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.10.a.c.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
25.10.a.d.1.2 | yes | 3 | 5.4 | even | 2 | ||
25.10.b.c.24.2 | 6 | 5.2 | odd | 4 | |||
25.10.b.c.24.5 | 6 | 5.3 | odd | 4 | |||
225.10.a.m.1.2 | 3 | 15.14 | odd | 2 | |||
225.10.a.p.1.2 | 3 | 3.2 | odd | 2 | |||
225.10.b.m.199.2 | 6 | 15.8 | even | 4 | |||
225.10.b.m.199.5 | 6 | 15.2 | even | 4 | |||
400.10.a.u.1.3 | 3 | 20.19 | odd | 2 | |||
400.10.a.y.1.1 | 3 | 4.3 | odd | 2 | |||
400.10.c.q.49.2 | 6 | 20.3 | even | 4 | |||
400.10.c.q.49.5 | 6 | 20.7 | even | 4 |