Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,10,Mod(1,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("15.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(7.72553754246\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 60 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-7.26209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 38.7863 | 1.71413 | 0.857063 | − | 0.515211i | \(-0.172286\pi\) | ||||
0.857063 | + | 0.515211i | \(0.172286\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 992.374 | 1.93823 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | −3141.69 | −0.989652 | ||||||||
\(7\) | 12272.1 | 1.93187 | 0.965936 | − | 0.258780i | \(-0.0833204\pi\) | ||||
0.965936 | + | 0.258780i | \(0.0833204\pi\) | |||||||
\(8\) | 18631.9 | 1.60825 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 24241.4 | 0.766581 | ||||||||
\(11\) | −65897.9 | −1.35708 | −0.678538 | − | 0.734565i | \(-0.737386\pi\) | ||||
−0.678538 | + | 0.734565i | \(0.737386\pi\) | |||||||
\(12\) | −80382.3 | −1.11904 | ||||||||
\(13\) | −112300. | −1.09052 | −0.545260 | − | 0.838267i | \(-0.683569\pi\) | ||||
−0.545260 | + | 0.838267i | \(0.683569\pi\) | |||||||
\(14\) | 475990. | 3.31147 | ||||||||
\(15\) | −50625.0 | −0.258199 | ||||||||
\(16\) | 214567. | 0.818508 | ||||||||
\(17\) | 96634.7 | 0.280616 | 0.140308 | − | 0.990108i | \(-0.455191\pi\) | ||||
0.140308 | + | 0.990108i | \(0.455191\pi\) | |||||||
\(18\) | 254477. | 0.571376 | ||||||||
\(19\) | −181332. | −0.319214 | −0.159607 | − | 0.987181i | \(-0.551023\pi\) | ||||
−0.159607 | + | 0.987181i | \(0.551023\pi\) | |||||||
\(20\) | 620234. | 0.866803 | ||||||||
\(21\) | −994042. | −1.11537 | ||||||||
\(22\) | −2.55593e6 | −2.32620 | ||||||||
\(23\) | 244145. | 0.181916 | 0.0909582 | − | 0.995855i | \(-0.471007\pi\) | ||||
0.0909582 | + | 0.995855i | \(0.471007\pi\) | |||||||
\(24\) | −1.50919e6 | −0.928521 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | −4.35569e6 | −1.86929 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 1.21785e7 | 3.74442 | ||||||||
\(29\) | −5.26461e6 | −1.38221 | −0.691107 | − | 0.722752i | \(-0.742877\pi\) | ||||
−0.691107 | + | 0.722752i | \(0.742877\pi\) | |||||||
\(30\) | −1.96355e6 | −0.442586 | ||||||||
\(31\) | 1.83457e6 | 0.356784 | 0.178392 | − | 0.983959i | \(-0.442910\pi\) | ||||
0.178392 | + | 0.983959i | \(0.442910\pi\) | |||||||
\(32\) | −1.21730e6 | −0.205221 | ||||||||
\(33\) | 5.33773e6 | 0.783508 | ||||||||
\(34\) | 3.74810e6 | 0.481012 | ||||||||
\(35\) | 7.67008e6 | 0.863960 | ||||||||
\(36\) | 6.51097e6 | 0.646077 | ||||||||
\(37\) | 6.36194e6 | 0.558061 | 0.279030 | − | 0.960282i | \(-0.409987\pi\) | ||||
0.279030 | + | 0.960282i | \(0.409987\pi\) | |||||||
\(38\) | −7.03318e6 | −0.547174 | ||||||||
\(39\) | 9.09628e6 | 0.629612 | ||||||||
\(40\) | 1.16449e7 | 0.719230 | ||||||||
\(41\) | 1.57111e6 | 0.0868319 | 0.0434159 | − | 0.999057i | \(-0.486176\pi\) | ||||
0.0434159 | + | 0.999057i | \(0.486176\pi\) | |||||||
\(42\) | −3.85552e7 | −1.91188 | ||||||||
\(43\) | −1.99504e7 | −0.889903 | −0.444952 | − | 0.895555i | \(-0.646779\pi\) | ||||
−0.444952 | + | 0.895555i | \(0.646779\pi\) | |||||||
\(44\) | −6.53953e7 | −2.63033 | ||||||||
\(45\) | 4.10062e6 | 0.149071 | ||||||||
\(46\) | 9.46946e6 | 0.311828 | ||||||||
\(47\) | 3.00961e7 | 0.899643 | 0.449821 | − | 0.893119i | \(-0.351488\pi\) | ||||
0.449821 | + | 0.893119i | \(0.351488\pi\) | |||||||
\(48\) | −1.73799e7 | −0.472566 | ||||||||
\(49\) | 1.10251e8 | 2.73213 | ||||||||
\(50\) | 1.51509e7 | 0.342825 | ||||||||
\(51\) | −7.82741e6 | −0.162014 | ||||||||
\(52\) | −1.11443e8 | −2.11368 | ||||||||
\(53\) | −2.57306e6 | −0.0447929 | −0.0223964 | − | 0.999749i | \(-0.507130\pi\) | ||||
−0.0223964 | + | 0.999749i | \(0.507130\pi\) | |||||||
\(54\) | −2.06126e7 | −0.329884 | ||||||||
\(55\) | −4.11862e7 | −0.606903 | ||||||||
\(56\) | 2.28653e8 | 3.10693 | ||||||||
\(57\) | 1.46879e7 | 0.184299 | ||||||||
\(58\) | −2.04195e8 | −2.36929 | ||||||||
\(59\) | −1.19004e8 | −1.27858 | −0.639290 | − | 0.768965i | \(-0.720772\pi\) | ||||
−0.639290 | + | 0.768965i | \(0.720772\pi\) | |||||||
\(60\) | −5.02389e7 | −0.500449 | ||||||||
\(61\) | 1.92875e8 | 1.78358 | 0.891790 | − | 0.452449i | \(-0.149450\pi\) | ||||
0.891790 | + | 0.452449i | \(0.149450\pi\) | |||||||
\(62\) | 7.11559e7 | 0.611573 | ||||||||
\(63\) | 8.05174e7 | 0.643958 | ||||||||
\(64\) | −1.57073e8 | −1.17028 | ||||||||
\(65\) | −7.01874e7 | −0.487696 | ||||||||
\(66\) | 2.07030e8 | 1.34303 | ||||||||
\(67\) | −1.20193e8 | −0.728691 | −0.364345 | − | 0.931264i | \(-0.618707\pi\) | ||||
−0.364345 | + | 0.931264i | \(0.618707\pi\) | |||||||
\(68\) | 9.58978e7 | 0.543899 | ||||||||
\(69\) | −1.97757e7 | −0.105030 | ||||||||
\(70\) | 2.97494e8 | 1.48094 | ||||||||
\(71\) | −699549. | −0.00326705 | −0.00163352 | − | 0.999999i | \(-0.500520\pi\) | ||||
−0.00163352 | + | 0.999999i | \(0.500520\pi\) | |||||||
\(72\) | 1.22244e8 | 0.536082 | ||||||||
\(73\) | −8.91287e7 | −0.367337 | −0.183669 | − | 0.982988i | \(-0.558797\pi\) | ||||
−0.183669 | + | 0.982988i | \(0.558797\pi\) | |||||||
\(74\) | 2.46756e8 | 0.956587 | ||||||||
\(75\) | −3.16406e7 | −0.115470 | ||||||||
\(76\) | −1.79949e8 | −0.618711 | ||||||||
\(77\) | −8.08707e8 | −2.62170 | ||||||||
\(78\) | 3.52811e8 | 1.07924 | ||||||||
\(79\) | 4.31205e8 | 1.24555 | 0.622776 | − | 0.782400i | \(-0.286005\pi\) | ||||
0.622776 | + | 0.782400i | \(0.286005\pi\) | |||||||
\(80\) | 1.34104e8 | 0.366048 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 6.09375e7 | 0.148841 | ||||||||
\(83\) | −1.69761e7 | −0.0392633 | −0.0196316 | − | 0.999807i | \(-0.506249\pi\) | ||||
−0.0196316 | + | 0.999807i | \(0.506249\pi\) | |||||||
\(84\) | −9.86461e8 | −2.16184 | ||||||||
\(85\) | 6.03967e7 | 0.125495 | ||||||||
\(86\) | −7.73800e8 | −1.52541 | ||||||||
\(87\) | 4.26433e8 | 0.798022 | ||||||||
\(88\) | −1.22780e9 | −2.18251 | ||||||||
\(89\) | −3.09863e6 | −0.00523498 | −0.00261749 | − | 0.999997i | \(-0.500833\pi\) | ||||
−0.00261749 | + | 0.999997i | \(0.500833\pi\) | |||||||
\(90\) | 1.59048e8 | 0.255527 | ||||||||
\(91\) | −1.37816e9 | −2.10675 | ||||||||
\(92\) | 2.42283e8 | 0.352596 | ||||||||
\(93\) | −1.48600e8 | −0.205989 | ||||||||
\(94\) | 1.16732e9 | 1.54210 | ||||||||
\(95\) | −1.13332e8 | −0.142757 | ||||||||
\(96\) | 9.86009e7 | 0.118484 | ||||||||
\(97\) | 5.72609e8 | 0.656727 | 0.328364 | − | 0.944551i | \(-0.393503\pi\) | ||||
0.328364 | + | 0.944551i | \(0.393503\pi\) | |||||||
\(98\) | 4.27624e9 | 4.68322 | ||||||||
\(99\) | −4.32356e8 | −0.452359 | ||||||||
\(100\) | 3.87646e8 | 0.387646 | ||||||||
\(101\) | 1.78445e9 | 1.70631 | 0.853156 | − | 0.521655i | \(-0.174685\pi\) | ||||
0.853156 | + | 0.521655i | \(0.174685\pi\) | |||||||
\(102\) | −3.03596e8 | −0.277712 | ||||||||
\(103\) | 1.16632e9 | 1.02106 | 0.510528 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510528 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(104\) | −2.09236e9 | −1.75383 | ||||||||
\(105\) | −6.21276e8 | −0.498807 | ||||||||
\(106\) | −9.97995e7 | −0.0767807 | ||||||||
\(107\) | −1.72229e9 | −1.27022 | −0.635109 | − | 0.772422i | \(-0.719045\pi\) | ||||
−0.635109 | + | 0.772422i | \(0.719045\pi\) | |||||||
\(108\) | −5.27388e8 | −0.373013 | ||||||||
\(109\) | 2.08468e9 | 1.41456 | 0.707279 | − | 0.706934i | \(-0.249922\pi\) | ||||
0.707279 | + | 0.706934i | \(0.249922\pi\) | |||||||
\(110\) | −1.59746e9 | −1.04031 | ||||||||
\(111\) | −5.15317e8 | −0.322197 | ||||||||
\(112\) | 2.63319e9 | 1.58125 | ||||||||
\(113\) | −1.81995e9 | −1.05004 | −0.525020 | − | 0.851090i | \(-0.675942\pi\) | ||||
−0.525020 | + | 0.851090i | \(0.675942\pi\) | |||||||
\(114\) | 5.69688e8 | 0.315911 | ||||||||
\(115\) | 1.52590e8 | 0.0813555 | ||||||||
\(116\) | −5.22446e9 | −2.67905 | ||||||||
\(117\) | −7.36799e8 | −0.363507 | ||||||||
\(118\) | −4.61573e9 | −2.19165 | ||||||||
\(119\) | 1.18591e9 | 0.542115 | ||||||||
\(120\) | −9.43241e8 | −0.415247 | ||||||||
\(121\) | 1.98458e9 | 0.841656 | ||||||||
\(122\) | 7.48092e9 | 3.05728 | ||||||||
\(123\) | −1.27260e8 | −0.0501324 | ||||||||
\(124\) | 1.82058e9 | 0.691530 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | 3.12297e9 | 1.10382 | ||||||||
\(127\) | −3.74913e9 | −1.27883 | −0.639417 | − | 0.768860i | \(-0.720824\pi\) | ||||
−0.639417 | + | 0.768860i | \(0.720824\pi\) | |||||||
\(128\) | −5.46900e9 | −1.80079 | ||||||||
\(129\) | 1.61598e9 | 0.513786 | ||||||||
\(130\) | −2.72231e9 | −0.835972 | ||||||||
\(131\) | −1.96598e9 | −0.583256 | −0.291628 | − | 0.956532i | \(-0.594197\pi\) | ||||
−0.291628 | + | 0.956532i | \(0.594197\pi\) | |||||||
\(132\) | 5.29702e9 | 1.51862 | ||||||||
\(133\) | −2.22532e9 | −0.616682 | ||||||||
\(134\) | −4.66184e9 | −1.24907 | ||||||||
\(135\) | −3.32151e8 | −0.0860663 | ||||||||
\(136\) | 1.80049e9 | 0.451300 | ||||||||
\(137\) | −3.63223e8 | −0.0880909 | −0.0440455 | − | 0.999030i | \(-0.514025\pi\) | ||||
−0.0440455 | + | 0.999030i | \(0.514025\pi\) | |||||||
\(138\) | −7.67026e8 | −0.180034 | ||||||||
\(139\) | 4.55580e9 | 1.03514 | 0.517569 | − | 0.855642i | \(-0.326837\pi\) | ||||
0.517569 | + | 0.855642i | \(0.326837\pi\) | |||||||
\(140\) | 7.61159e9 | 1.67455 | ||||||||
\(141\) | −2.43779e9 | −0.519409 | ||||||||
\(142\) | −2.71329e7 | −0.00560014 | ||||||||
\(143\) | 7.40032e9 | 1.47992 | ||||||||
\(144\) | 1.40777e9 | 0.272836 | ||||||||
\(145\) | −3.29038e9 | −0.618145 | ||||||||
\(146\) | −3.45697e9 | −0.629662 | ||||||||
\(147\) | −8.93036e9 | −1.57740 | ||||||||
\(148\) | 6.31342e9 | 1.08165 | ||||||||
\(149\) | 8.79830e9 | 1.46238 | 0.731191 | − | 0.682173i | \(-0.238965\pi\) | ||||
0.731191 | + | 0.682173i | \(0.238965\pi\) | |||||||
\(150\) | −1.22722e9 | −0.197930 | ||||||||
\(151\) | −2.70702e8 | −0.0423736 | −0.0211868 | − | 0.999776i | \(-0.506744\pi\) | ||||
−0.0211868 | + | 0.999776i | \(0.506744\pi\) | |||||||
\(152\) | −3.37856e9 | −0.513376 | ||||||||
\(153\) | 6.34020e8 | 0.0935388 | ||||||||
\(154\) | −3.13667e10 | −4.49392 | ||||||||
\(155\) | 1.14660e9 | 0.159559 | ||||||||
\(156\) | 9.02692e9 | 1.22033 | ||||||||
\(157\) | 9.73240e9 | 1.27841 | 0.639207 | − | 0.769035i | \(-0.279263\pi\) | ||||
0.639207 | + | 0.769035i | \(0.279263\pi\) | |||||||
\(158\) | 1.67248e10 | 2.13504 | ||||||||
\(159\) | 2.08418e8 | 0.0258612 | ||||||||
\(160\) | −7.60810e8 | −0.0917775 | ||||||||
\(161\) | 2.99617e9 | 0.351439 | ||||||||
\(162\) | 1.66962e9 | 0.190459 | ||||||||
\(163\) | 7.76823e9 | 0.861941 | 0.430971 | − | 0.902366i | \(-0.358171\pi\) | ||||
0.430971 | + | 0.902366i | \(0.358171\pi\) | |||||||
\(164\) | 1.55913e9 | 0.168300 | ||||||||
\(165\) | 3.33608e9 | 0.350396 | ||||||||
\(166\) | −6.58440e8 | −0.0673023 | ||||||||
\(167\) | −8.41748e9 | −0.837448 | −0.418724 | − | 0.908114i | \(-0.637522\pi\) | ||||
−0.418724 | + | 0.908114i | \(0.637522\pi\) | |||||||
\(168\) | −1.85209e10 | −1.79379 | ||||||||
\(169\) | 2.00674e9 | 0.189235 | ||||||||
\(170\) | 2.34256e9 | 0.215115 | ||||||||
\(171\) | −1.18972e9 | −0.106405 | ||||||||
\(172\) | −1.97982e10 | −1.72484 | ||||||||
\(173\) | 3.59838e8 | 0.0305422 | 0.0152711 | − | 0.999883i | \(-0.495139\pi\) | ||||
0.0152711 | + | 0.999883i | \(0.495139\pi\) | |||||||
\(174\) | 1.65398e10 | 1.36791 | ||||||||
\(175\) | 4.79380e9 | 0.386375 | ||||||||
\(176\) | −1.41395e10 | −1.11078 | ||||||||
\(177\) | 9.63934e9 | 0.738189 | ||||||||
\(178\) | −1.20184e8 | −0.00897342 | ||||||||
\(179\) | −8.65338e9 | −0.630009 | −0.315005 | − | 0.949090i | \(-0.602006\pi\) | ||||
−0.315005 | + | 0.949090i | \(0.602006\pi\) | |||||||
\(180\) | 4.06935e9 | 0.288934 | ||||||||
\(181\) | 6.09713e9 | 0.422252 | 0.211126 | − | 0.977459i | \(-0.432287\pi\) | ||||
0.211126 | + | 0.977459i | \(0.432287\pi\) | |||||||
\(182\) | −5.34535e10 | −3.61123 | ||||||||
\(183\) | −1.56229e10 | −1.02975 | ||||||||
\(184\) | 4.54888e9 | 0.292566 | ||||||||
\(185\) | 3.97621e9 | 0.249572 | ||||||||
\(186\) | −5.76363e9 | −0.353092 | ||||||||
\(187\) | −6.36802e9 | −0.380818 | ||||||||
\(188\) | 2.98666e10 | 1.74371 | ||||||||
\(189\) | −6.52191e9 | −0.371789 | ||||||||
\(190\) | −4.39574e9 | −0.244704 | ||||||||
\(191\) | −2.96238e10 | −1.61061 | −0.805306 | − | 0.592859i | \(-0.797999\pi\) | ||||
−0.805306 | + | 0.592859i | \(0.797999\pi\) | |||||||
\(192\) | 1.27229e10 | 0.675662 | ||||||||
\(193\) | −4.63438e8 | −0.0240427 | −0.0120214 | − | 0.999928i | \(-0.503827\pi\) | ||||
−0.0120214 | + | 0.999928i | \(0.503827\pi\) | |||||||
\(194\) | 2.22094e10 | 1.12571 | ||||||||
\(195\) | 5.68518e9 | 0.281571 | ||||||||
\(196\) | 1.09411e11 | 5.29550 | ||||||||
\(197\) | 1.23414e10 | 0.583803 | 0.291902 | − | 0.956448i | \(-0.405712\pi\) | ||||
0.291902 | + | 0.956448i | \(0.405712\pi\) | |||||||
\(198\) | −1.67695e10 | −0.775400 | ||||||||
\(199\) | −1.00354e10 | −0.453624 | −0.226812 | − | 0.973939i | \(-0.572830\pi\) | ||||
−0.226812 | + | 0.973939i | \(0.572830\pi\) | |||||||
\(200\) | 7.27809e9 | 0.321649 | ||||||||
\(201\) | 9.73565e9 | 0.420710 | ||||||||
\(202\) | 6.92122e10 | 2.92484 | ||||||||
\(203\) | −6.46080e10 | −2.67026 | ||||||||
\(204\) | −7.76772e9 | −0.314020 | ||||||||
\(205\) | 9.81943e8 | 0.0388324 | ||||||||
\(206\) | 4.52371e10 | 1.75022 | ||||||||
\(207\) | 1.60183e9 | 0.0606388 | ||||||||
\(208\) | −2.40958e10 | −0.892599 | ||||||||
\(209\) | 1.19494e10 | 0.433198 | ||||||||
\(210\) | −2.40970e10 | −0.855019 | ||||||||
\(211\) | −3.56268e10 | −1.23739 | −0.618693 | − | 0.785633i | \(-0.712338\pi\) | ||||
−0.618693 | + | 0.785633i | \(0.712338\pi\) | |||||||
\(212\) | −2.55344e9 | −0.0868189 | ||||||||
\(213\) | 5.66635e7 | 0.00188623 | ||||||||
\(214\) | −6.68011e10 | −2.17732 | ||||||||
\(215\) | −1.24690e10 | −0.397977 | ||||||||
\(216\) | −9.90176e9 | −0.309507 | ||||||||
\(217\) | 2.25140e10 | 0.689262 | ||||||||
\(218\) | 8.08571e10 | 2.42473 | ||||||||
\(219\) | 7.21943e9 | 0.212082 | ||||||||
\(220\) | −4.08721e10 | −1.17632 | ||||||||
\(221\) | −1.08521e10 | −0.306018 | ||||||||
\(222\) | −1.99872e10 | −0.552286 | ||||||||
\(223\) | −3.41646e10 | −0.925133 | −0.462566 | − | 0.886585i | \(-0.653071\pi\) | ||||
−0.462566 | + | 0.886585i | \(0.653071\pi\) | |||||||
\(224\) | −1.49388e10 | −0.396460 | ||||||||
\(225\) | 2.56289e9 | 0.0666667 | ||||||||
\(226\) | −7.05889e10 | −1.79990 | ||||||||
\(227\) | 3.64936e10 | 0.912221 | 0.456110 | − | 0.889923i | \(-0.349242\pi\) | ||||
0.456110 | + | 0.889923i | \(0.349242\pi\) | |||||||
\(228\) | 1.45759e10 | 0.357213 | ||||||||
\(229\) | 3.87446e10 | 0.931005 | 0.465502 | − | 0.885047i | \(-0.345874\pi\) | ||||
0.465502 | + | 0.885047i | \(0.345874\pi\) | |||||||
\(230\) | 5.91841e9 | 0.139454 | ||||||||
\(231\) | 6.55052e10 | 1.51364 | ||||||||
\(232\) | −9.80898e10 | −2.22294 | ||||||||
\(233\) | −2.68717e10 | −0.597302 | −0.298651 | − | 0.954362i | \(-0.596537\pi\) | ||||
−0.298651 | + | 0.954362i | \(0.596537\pi\) | |||||||
\(234\) | −2.85777e10 | −0.623097 | ||||||||
\(235\) | 1.88101e10 | 0.402332 | ||||||||
\(236\) | −1.18097e11 | −2.47818 | ||||||||
\(237\) | −3.49276e10 | −0.719120 | ||||||||
\(238\) | 4.59971e10 | 0.929254 | ||||||||
\(239\) | 1.34711e10 | 0.267063 | 0.133531 | − | 0.991045i | \(-0.457368\pi\) | ||||
0.133531 | + | 0.991045i | \(0.457368\pi\) | |||||||
\(240\) | −1.08624e10 | −0.211338 | ||||||||
\(241\) | −1.85860e10 | −0.354902 | −0.177451 | − | 0.984130i | \(-0.556785\pi\) | ||||
−0.177451 | + | 0.984130i | \(0.556785\pi\) | |||||||
\(242\) | 7.69745e10 | 1.44271 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 1.91405e11 | 3.45699 | ||||||||
\(245\) | 6.89071e10 | 1.22185 | ||||||||
\(246\) | −4.93593e9 | −0.0859333 | ||||||||
\(247\) | 2.03635e10 | 0.348110 | ||||||||
\(248\) | 3.41815e10 | 0.573797 | ||||||||
\(249\) | 1.37506e9 | 0.0226687 | ||||||||
\(250\) | 9.46930e9 | 0.153316 | ||||||||
\(251\) | 4.30327e10 | 0.684332 | 0.342166 | − | 0.939640i | \(-0.388839\pi\) | ||||
0.342166 | + | 0.939640i | \(0.388839\pi\) | |||||||
\(252\) | 7.99034e10 | 1.24814 | ||||||||
\(253\) | −1.60886e10 | −0.246875 | ||||||||
\(254\) | −1.45415e11 | −2.19208 | ||||||||
\(255\) | −4.89213e9 | −0.0724548 | ||||||||
\(256\) | −1.31701e11 | −1.91650 | ||||||||
\(257\) | −6.26858e8 | −0.00896335 | −0.00448168 | − | 0.999990i | \(-0.501427\pi\) | ||||
−0.00448168 | + | 0.999990i | \(0.501427\pi\) | |||||||
\(258\) | 6.26778e10 | 0.880694 | ||||||||
\(259\) | 7.80745e10 | 1.07810 | ||||||||
\(260\) | −6.96521e10 | −0.945267 | ||||||||
\(261\) | −3.45411e10 | −0.460738 | ||||||||
\(262\) | −7.62532e10 | −0.999774 | ||||||||
\(263\) | 6.21446e10 | 0.800944 | 0.400472 | − | 0.916309i | \(-0.368846\pi\) | ||||
0.400472 | + | 0.916309i | \(0.368846\pi\) | |||||||
\(264\) | 9.94521e10 | 1.26007 | ||||||||
\(265\) | −1.60816e9 | −0.0200320 | ||||||||
\(266\) | −8.63120e10 | −1.05707 | ||||||||
\(267\) | 2.50989e8 | 0.00302242 | ||||||||
\(268\) | −1.19277e11 | −1.41237 | ||||||||
\(269\) | −5.44876e10 | −0.634472 | −0.317236 | − | 0.948347i | \(-0.602755\pi\) | ||||
−0.317236 | + | 0.948347i | \(0.602755\pi\) | |||||||
\(270\) | −1.28829e10 | −0.147529 | ||||||||
\(271\) | −9.74930e10 | −1.09802 | −0.549012 | − | 0.835815i | \(-0.684996\pi\) | ||||
−0.549012 | + | 0.835815i | \(0.684996\pi\) | |||||||
\(272\) | 2.07346e10 | 0.229687 | ||||||||
\(273\) | 1.11631e11 | 1.21633 | ||||||||
\(274\) | −1.40881e10 | −0.150999 | ||||||||
\(275\) | −2.57414e10 | −0.271415 | ||||||||
\(276\) | −1.96249e10 | −0.203571 | ||||||||
\(277\) | 1.43195e11 | 1.46140 | 0.730702 | − | 0.682697i | \(-0.239193\pi\) | ||||
0.730702 | + | 0.682697i | \(0.239193\pi\) | |||||||
\(278\) | 1.76702e11 | 1.77436 | ||||||||
\(279\) | 1.20366e10 | 0.118928 | ||||||||
\(280\) | 1.42908e11 | 1.38946 | ||||||||
\(281\) | 6.51280e10 | 0.623146 | 0.311573 | − | 0.950222i | \(-0.399144\pi\) | ||||
0.311573 | + | 0.950222i | \(0.399144\pi\) | |||||||
\(282\) | −9.45526e10 | −0.890333 | ||||||||
\(283\) | −1.65431e11 | −1.53312 | −0.766561 | − | 0.642171i | \(-0.778034\pi\) | ||||
−0.766561 | + | 0.642171i | \(0.778034\pi\) | |||||||
\(284\) | −6.94214e8 | −0.00633229 | ||||||||
\(285\) | 9.17992e9 | 0.0824208 | ||||||||
\(286\) | 2.87031e11 | 2.53677 | ||||||||
\(287\) | 1.92808e10 | 0.167748 | ||||||||
\(288\) | −7.98667e9 | −0.0684069 | ||||||||
\(289\) | −1.09250e11 | −0.921254 | ||||||||
\(290\) | −1.27622e11 | −1.05958 | ||||||||
\(291\) | −4.63813e10 | −0.379162 | ||||||||
\(292\) | −8.84490e10 | −0.711984 | ||||||||
\(293\) | 5.64261e10 | 0.447277 | 0.223638 | − | 0.974672i | \(-0.428207\pi\) | ||||
0.223638 | + | 0.974672i | \(0.428207\pi\) | |||||||
\(294\) | −3.46375e11 | −2.70386 | ||||||||
\(295\) | −7.43776e10 | −0.571799 | ||||||||
\(296\) | 1.18535e11 | 0.897499 | ||||||||
\(297\) | 3.50208e10 | 0.261169 | ||||||||
\(298\) | 3.41253e11 | 2.50671 | ||||||||
\(299\) | −2.74174e10 | −0.198384 | ||||||||
\(300\) | −3.13993e10 | −0.223808 | ||||||||
\(301\) | −2.44833e11 | −1.71918 | ||||||||
\(302\) | −1.04995e10 | −0.0726338 | ||||||||
\(303\) | −1.44541e11 | −0.985140 | ||||||||
\(304\) | −3.89078e10 | −0.261279 | ||||||||
\(305\) | 1.20547e11 | 0.797641 | ||||||||
\(306\) | 2.45913e10 | 0.160337 | ||||||||
\(307\) | 1.79360e10 | 0.115240 | 0.0576200 | − | 0.998339i | \(-0.481649\pi\) | ||||
0.0576200 | + | 0.998339i | \(0.481649\pi\) | |||||||
\(308\) | −8.02540e11 | −5.08146 | ||||||||
\(309\) | −9.44717e10 | −0.589507 | ||||||||
\(310\) | 4.44725e10 | 0.273504 | ||||||||
\(311\) | 3.19953e11 | 1.93938 | 0.969692 | − | 0.244330i | \(-0.0785680\pi\) | ||||
0.969692 | + | 0.244330i | \(0.0785680\pi\) | |||||||
\(312\) | 1.69481e11 | 1.01257 | ||||||||
\(313\) | −3.16987e11 | −1.86677 | −0.933387 | − | 0.358872i | \(-0.883162\pi\) | ||||
−0.933387 | + | 0.358872i | \(0.883162\pi\) | |||||||
\(314\) | 3.77483e11 | 2.19136 | ||||||||
\(315\) | 5.03234e10 | 0.287987 | ||||||||
\(316\) | 4.27917e11 | 2.41417 | ||||||||
\(317\) | −3.08157e11 | −1.71398 | −0.856990 | − | 0.515334i | \(-0.827668\pi\) | ||||
−0.856990 | + | 0.515334i | \(0.827668\pi\) | |||||||
\(318\) | 8.08376e9 | 0.0443293 | ||||||||
\(319\) | 3.46927e11 | 1.87577 | ||||||||
\(320\) | −9.81703e10 | −0.523366 | ||||||||
\(321\) | 1.39505e11 | 0.733361 | ||||||||
\(322\) | 1.16210e11 | 0.602412 | ||||||||
\(323\) | −1.75229e10 | −0.0895768 | ||||||||
\(324\) | 4.27185e10 | 0.215359 | ||||||||
\(325\) | −4.38671e10 | −0.218104 | ||||||||
\(326\) | 3.01301e11 | 1.47748 | ||||||||
\(327\) | −1.68859e11 | −0.816696 | ||||||||
\(328\) | 2.92728e10 | 0.139647 | ||||||||
\(329\) | 3.69343e11 | 1.73800 | ||||||||
\(330\) | 1.29394e11 | 0.600623 | ||||||||
\(331\) | −1.79184e11 | −0.820490 | −0.410245 | − | 0.911975i | \(-0.634557\pi\) | ||||
−0.410245 | + | 0.911975i | \(0.634557\pi\) | |||||||
\(332\) | −1.68466e10 | −0.0761013 | ||||||||
\(333\) | 4.17407e10 | 0.186020 | ||||||||
\(334\) | −3.26482e11 | −1.43549 | ||||||||
\(335\) | −7.51207e10 | −0.325880 | ||||||||
\(336\) | −2.13288e11 | −0.912937 | ||||||||
\(337\) | −9.73351e10 | −0.411088 | −0.205544 | − | 0.978648i | \(-0.565896\pi\) | ||||
−0.205544 | + | 0.978648i | \(0.565896\pi\) | |||||||
\(338\) | 7.78340e10 | 0.324373 | ||||||||
\(339\) | 1.47416e11 | 0.606241 | ||||||||
\(340\) | 5.99361e10 | 0.243239 | ||||||||
\(341\) | −1.20894e11 | −0.484183 | ||||||||
\(342\) | −4.61447e10 | −0.182391 | ||||||||
\(343\) | 8.57794e11 | 3.34626 | ||||||||
\(344\) | −3.71713e11 | −1.43118 | ||||||||
\(345\) | −1.23598e10 | −0.0469706 | ||||||||
\(346\) | 1.39568e10 | 0.0523531 | ||||||||
\(347\) | −3.47750e11 | −1.28761 | −0.643806 | − | 0.765189i | \(-0.722646\pi\) | ||||
−0.643806 | + | 0.765189i | \(0.722646\pi\) | |||||||
\(348\) | 4.23182e11 | 1.54675 | ||||||||
\(349\) | −1.10131e11 | −0.397372 | −0.198686 | − | 0.980063i | \(-0.563667\pi\) | ||||
−0.198686 | + | 0.980063i | \(0.563667\pi\) | |||||||
\(350\) | 1.85934e11 | 0.662295 | ||||||||
\(351\) | 5.96807e10 | 0.209871 | ||||||||
\(352\) | 8.02172e10 | 0.278500 | ||||||||
\(353\) | −3.40052e11 | −1.16563 | −0.582814 | − | 0.812606i | \(-0.698048\pi\) | ||||
−0.582814 | + | 0.812606i | \(0.698048\pi\) | |||||||
\(354\) | 3.73874e11 | 1.26535 | ||||||||
\(355\) | −4.37218e8 | −0.00146107 | ||||||||
\(356\) | −3.07500e9 | −0.0101466 | ||||||||
\(357\) | −9.60589e10 | −0.312990 | ||||||||
\(358\) | −3.35632e11 | −1.07992 | ||||||||
\(359\) | −2.75063e11 | −0.873993 | −0.436996 | − | 0.899463i | \(-0.643958\pi\) | ||||
−0.436996 | + | 0.899463i | \(0.643958\pi\) | |||||||
\(360\) | 7.64025e10 | 0.239743 | ||||||||
\(361\) | −2.89807e11 | −0.898102 | ||||||||
\(362\) | 2.36485e11 | 0.723793 | ||||||||
\(363\) | −1.60751e11 | −0.485930 | ||||||||
\(364\) | −1.36765e12 | −4.08336 | ||||||||
\(365\) | −5.57054e10 | −0.164278 | ||||||||
\(366\) | −6.05954e11 | −1.76512 | ||||||||
\(367\) | −2.12218e11 | −0.610639 | −0.305320 | − | 0.952250i | \(-0.598763\pi\) | ||||
−0.305320 | + | 0.952250i | \(0.598763\pi\) | |||||||
\(368\) | 5.23854e10 | 0.148900 | ||||||||
\(369\) | 1.03081e10 | 0.0289440 | ||||||||
\(370\) | 1.54222e11 | 0.427799 | ||||||||
\(371\) | −3.15769e10 | −0.0865341 | ||||||||
\(372\) | −1.47467e11 | −0.399255 | ||||||||
\(373\) | 6.08324e11 | 1.62721 | 0.813607 | − | 0.581415i | \(-0.197501\pi\) | ||||
0.813607 | + | 0.581415i | \(0.197501\pi\) | |||||||
\(374\) | −2.46992e11 | −0.652770 | ||||||||
\(375\) | −1.97754e10 | −0.0516398 | ||||||||
\(376\) | 5.60748e11 | 1.44685 | ||||||||
\(377\) | 5.91215e11 | 1.50733 | ||||||||
\(378\) | −2.52960e11 | −0.637294 | ||||||||
\(379\) | 4.64136e11 | 1.15550 | 0.577749 | − | 0.816214i | \(-0.303931\pi\) | ||||
0.577749 | + | 0.816214i | \(0.303931\pi\) | |||||||
\(380\) | −1.12468e11 | −0.276696 | ||||||||
\(381\) | 3.03680e11 | 0.738335 | ||||||||
\(382\) | −1.14900e12 | −2.76079 | ||||||||
\(383\) | 5.22749e11 | 1.24136 | 0.620681 | − | 0.784063i | \(-0.286856\pi\) | ||||
0.620681 | + | 0.784063i | \(0.286856\pi\) | |||||||
\(384\) | 4.42989e11 | 1.03969 | ||||||||
\(385\) | −5.05442e11 | −1.17246 | ||||||||
\(386\) | −1.79750e10 | −0.0412123 | ||||||||
\(387\) | −1.30894e11 | −0.296634 | ||||||||
\(388\) | 5.68242e11 | 1.27289 | ||||||||
\(389\) | −1.18899e11 | −0.263271 | −0.131636 | − | 0.991298i | \(-0.542023\pi\) | ||||
−0.131636 | + | 0.991298i | \(0.542023\pi\) | |||||||
\(390\) | 2.20507e11 | 0.482649 | ||||||||
\(391\) | 2.35928e10 | 0.0510487 | ||||||||
\(392\) | 2.05419e12 | 4.39394 | ||||||||
\(393\) | 1.59245e11 | 0.336743 | ||||||||
\(394\) | 4.78677e11 | 1.00071 | ||||||||
\(395\) | 2.69503e11 | 0.557028 | ||||||||
\(396\) | −4.29059e11 | −0.876776 | ||||||||
\(397\) | −2.76954e11 | −0.559564 | −0.279782 | − | 0.960064i | \(-0.590262\pi\) | ||||
−0.279782 | + | 0.960064i | \(0.590262\pi\) | |||||||
\(398\) | −3.89236e11 | −0.777569 | ||||||||
\(399\) | 1.80251e11 | 0.356041 | ||||||||
\(400\) | 8.38152e10 | 0.163702 | ||||||||
\(401\) | −1.53482e11 | −0.296421 | −0.148210 | − | 0.988956i | \(-0.547351\pi\) | ||||
−0.148210 | + | 0.988956i | \(0.547351\pi\) | |||||||
\(402\) | 3.77609e11 | 0.721150 | ||||||||
\(403\) | −2.06021e11 | −0.389080 | ||||||||
\(404\) | 1.77084e12 | 3.30723 | ||||||||
\(405\) | 2.69042e10 | 0.0496904 | ||||||||
\(406\) | −2.50590e12 | −4.57717 | ||||||||
\(407\) | −4.19238e11 | −0.757331 | ||||||||
\(408\) | −1.45840e11 | −0.260558 | ||||||||
\(409\) | −1.52364e11 | −0.269232 | −0.134616 | − | 0.990898i | \(-0.542980\pi\) | ||||
−0.134616 | + | 0.990898i | \(0.542980\pi\) | |||||||
\(410\) | 3.80859e10 | 0.0665636 | ||||||||
\(411\) | 2.94211e10 | 0.0508593 | ||||||||
\(412\) | 1.15742e12 | 1.97904 | ||||||||
\(413\) | −1.46043e12 | −2.47006 | ||||||||
\(414\) | 6.21291e10 | 0.103943 | ||||||||
\(415\) | −1.06101e10 | −0.0175591 | ||||||||
\(416\) | 1.36702e11 | 0.223797 | ||||||||
\(417\) | −3.69020e11 | −0.597637 | ||||||||
\(418\) | 4.63472e11 | 0.742557 | ||||||||
\(419\) | −9.09824e11 | −1.44210 | −0.721049 | − | 0.692885i | \(-0.756340\pi\) | ||||
−0.721049 | + | 0.692885i | \(0.756340\pi\) | |||||||
\(420\) | −6.16538e11 | −0.966804 | ||||||||
\(421\) | 9.88529e11 | 1.53363 | 0.766814 | − | 0.641869i | \(-0.221841\pi\) | ||||
0.766814 | + | 0.641869i | \(0.221841\pi\) | |||||||
\(422\) | −1.38183e12 | −2.12104 | ||||||||
\(423\) | 1.97461e11 | 0.299881 | ||||||||
\(424\) | −4.79411e10 | −0.0720380 | ||||||||
\(425\) | 3.77479e10 | 0.0561233 | ||||||||
\(426\) | 2.19776e9 | 0.00323324 | ||||||||
\(427\) | 2.36699e12 | 3.44565 | ||||||||
\(428\) | −1.70915e12 | −2.46198 | ||||||||
\(429\) | −5.99426e11 | −0.854432 | ||||||||
\(430\) | −4.83625e11 | −0.682183 | ||||||||
\(431\) | 2.03278e11 | 0.283755 | 0.141878 | − | 0.989884i | \(-0.454686\pi\) | ||||
0.141878 | + | 0.989884i | \(0.454686\pi\) | |||||||
\(432\) | −1.14030e11 | −0.157522 | ||||||||
\(433\) | −2.10847e11 | −0.288251 | −0.144126 | − | 0.989559i | \(-0.546037\pi\) | ||||
−0.144126 | + | 0.989559i | \(0.546037\pi\) | |||||||
\(434\) | 8.73234e11 | 1.18148 | ||||||||
\(435\) | 2.66521e11 | 0.356886 | ||||||||
\(436\) | 2.06879e12 | 2.74174 | ||||||||
\(437\) | −4.42712e10 | −0.0580704 | ||||||||
\(438\) | 2.80015e11 | 0.363536 | ||||||||
\(439\) | 2.11413e11 | 0.271670 | 0.135835 | − | 0.990732i | \(-0.456628\pi\) | ||||
0.135835 | + | 0.990732i | \(0.456628\pi\) | |||||||
\(440\) | −7.67377e11 | −0.976050 | ||||||||
\(441\) | 7.23359e11 | 0.910711 | ||||||||
\(442\) | −4.20911e11 | −0.524553 | ||||||||
\(443\) | 1.45517e12 | 1.79514 | 0.897569 | − | 0.440874i | \(-0.145331\pi\) | ||||
0.897569 | + | 0.440874i | \(0.145331\pi\) | |||||||
\(444\) | −5.11387e11 | −0.624491 | ||||||||
\(445\) | −1.93665e9 | −0.00234115 | ||||||||
\(446\) | −1.32512e12 | −1.58579 | ||||||||
\(447\) | −7.12663e11 | −0.844306 | ||||||||
\(448\) | −1.92761e12 | −2.26084 | ||||||||
\(449\) | −2.19470e11 | −0.254840 | −0.127420 | − | 0.991849i | \(-0.540670\pi\) | ||||
−0.127420 | + | 0.991849i | \(0.540670\pi\) | |||||||
\(450\) | 9.94049e10 | 0.114275 | ||||||||
\(451\) | −1.03533e11 | −0.117837 | ||||||||
\(452\) | −1.80607e12 | −2.03522 | ||||||||
\(453\) | 2.19269e10 | 0.0244644 | ||||||||
\(454\) | 1.41545e12 | 1.56366 | ||||||||
\(455\) | −8.61348e11 | −0.942166 | ||||||||
\(456\) | 2.73663e11 | 0.296397 | ||||||||
\(457\) | 7.40816e11 | 0.794488 | 0.397244 | − | 0.917713i | \(-0.369967\pi\) | ||||
0.397244 | + | 0.917713i | \(0.369967\pi\) | |||||||
\(458\) | 1.50276e12 | 1.59586 | ||||||||
\(459\) | −5.13556e10 | −0.0540046 | ||||||||
\(460\) | 1.51427e11 | 0.157686 | ||||||||
\(461\) | 2.80170e11 | 0.288913 | 0.144457 | − | 0.989511i | \(-0.453857\pi\) | ||||
0.144457 | + | 0.989511i | \(0.453857\pi\) | |||||||
\(462\) | 2.54070e12 | 2.59457 | ||||||||
\(463\) | −5.07092e10 | −0.0512828 | −0.0256414 | − | 0.999671i | \(-0.508163\pi\) | ||||
−0.0256414 | + | 0.999671i | \(0.508163\pi\) | |||||||
\(464\) | −1.12961e12 | −1.13135 | ||||||||
\(465\) | −9.28749e10 | −0.0921213 | ||||||||
\(466\) | −1.04225e12 | −1.02385 | ||||||||
\(467\) | 1.77228e12 | 1.72427 | 0.862135 | − | 0.506678i | \(-0.169127\pi\) | ||||
0.862135 | + | 0.506678i | \(0.169127\pi\) | |||||||
\(468\) | −7.31180e11 | −0.704560 | ||||||||
\(469\) | −1.47503e12 | −1.40774 | ||||||||
\(470\) | 7.29572e11 | 0.689649 | ||||||||
\(471\) | −7.88324e11 | −0.738092 | ||||||||
\(472\) | −2.21728e12 | −2.05627 | ||||||||
\(473\) | 1.31469e12 | 1.20767 | ||||||||
\(474\) | −1.35471e12 | −1.23266 | ||||||||
\(475\) | −7.08327e10 | −0.0638429 | ||||||||
\(476\) | 1.17687e12 | 1.05074 | ||||||||
\(477\) | −1.68819e10 | −0.0149310 | ||||||||
\(478\) | 5.22495e11 | 0.457779 | ||||||||
\(479\) | −7.79555e11 | −0.676608 | −0.338304 | − | 0.941037i | \(-0.609853\pi\) | ||||
−0.338304 | + | 0.941037i | \(0.609853\pi\) | |||||||
\(480\) | 6.16256e10 | 0.0529877 | ||||||||
\(481\) | −7.14444e11 | −0.608577 | ||||||||
\(482\) | −7.20880e11 | −0.608347 | ||||||||
\(483\) | −2.42690e11 | −0.202904 | ||||||||
\(484\) | 1.96945e12 | 1.63132 | ||||||||
\(485\) | 3.57880e11 | 0.293697 | ||||||||
\(486\) | −1.35239e11 | −0.109961 | ||||||||
\(487\) | −1.33958e12 | −1.07916 | −0.539582 | − | 0.841933i | \(-0.681418\pi\) | ||||
−0.539582 | + | 0.841933i | \(0.681418\pi\) | |||||||
\(488\) | 3.59364e12 | 2.86844 | ||||||||
\(489\) | −6.29226e11 | −0.497642 | ||||||||
\(490\) | 2.67265e12 | 2.09440 | ||||||||
\(491\) | −9.76349e11 | −0.758121 | −0.379061 | − | 0.925372i | \(-0.623753\pi\) | ||||
−0.379061 | + | 0.925372i | \(0.623753\pi\) | |||||||
\(492\) | −1.26289e11 | −0.0971682 | ||||||||
\(493\) | −5.08744e11 | −0.387872 | ||||||||
\(494\) | 7.89825e11 | 0.596705 | ||||||||
\(495\) | −2.70222e11 | −0.202301 | ||||||||
\(496\) | 3.93637e11 | 0.292031 | ||||||||
\(497\) | −8.58495e9 | −0.00631152 | ||||||||
\(498\) | 5.33336e10 | 0.0388570 | ||||||||
\(499\) | 1.32057e12 | 0.953472 | 0.476736 | − | 0.879046i | \(-0.341820\pi\) | ||||
0.476736 | + | 0.879046i | \(0.341820\pi\) | |||||||
\(500\) | 2.42279e11 | 0.173361 | ||||||||
\(501\) | 6.81815e11 | 0.483501 | ||||||||
\(502\) | 1.66908e12 | 1.17303 | ||||||||
\(503\) | −1.16421e12 | −0.810917 | −0.405459 | − | 0.914113i | \(-0.632888\pi\) | ||||
−0.405459 | + | 0.914113i | \(0.632888\pi\) | |||||||
\(504\) | 1.50019e12 | 1.03564 | ||||||||
\(505\) | 1.11528e12 | 0.763086 | ||||||||
\(506\) | −6.24017e11 | −0.423174 | ||||||||
\(507\) | −1.62546e11 | −0.109255 | ||||||||
\(508\) | −3.72054e12 | −2.47868 | ||||||||
\(509\) | 8.32285e11 | 0.549594 | 0.274797 | − | 0.961502i | \(-0.411389\pi\) | ||||
0.274797 | + | 0.961502i | \(0.411389\pi\) | |||||||
\(510\) | −1.89747e11 | −0.124197 | ||||||||
\(511\) | −1.09380e12 | −0.709649 | ||||||||
\(512\) | −2.30806e12 | −1.48434 | ||||||||
\(513\) | 9.63671e10 | 0.0614329 | ||||||||
\(514\) | −2.43135e10 | −0.0153643 | ||||||||
\(515\) | 7.28949e11 | 0.456630 | ||||||||
\(516\) | 1.60366e12 | 0.995835 | ||||||||
\(517\) | −1.98327e12 | −1.22088 | ||||||||
\(518\) | 3.02822e12 | 1.84800 | ||||||||
\(519\) | −2.91469e10 | −0.0176335 | ||||||||
\(520\) | −1.30773e12 | −0.784335 | ||||||||
\(521\) | 2.43459e12 | 1.44763 | 0.723813 | − | 0.689997i | \(-0.242388\pi\) | ||||
0.723813 | + | 0.689997i | \(0.242388\pi\) | |||||||
\(522\) | −1.33972e12 | −0.789763 | ||||||||
\(523\) | −1.07631e12 | −0.629043 | −0.314522 | − | 0.949250i | \(-0.601844\pi\) | ||||
−0.314522 | + | 0.949250i | \(0.601844\pi\) | |||||||
\(524\) | −1.95099e12 | −1.13048 | ||||||||
\(525\) | −3.88298e11 | −0.223073 | ||||||||
\(526\) | 2.41036e12 | 1.37292 | ||||||||
\(527\) | 1.77283e11 | 0.100119 | ||||||||
\(528\) | 1.14530e12 | 0.641308 | ||||||||
\(529\) | −1.74155e12 | −0.966906 | ||||||||
\(530\) | −6.23747e10 | −0.0343374 | ||||||||
\(531\) | −7.80787e11 | −0.426194 | ||||||||
\(532\) | −2.20835e12 | −1.19527 | ||||||||
\(533\) | −1.76435e11 | −0.0946919 | ||||||||
\(534\) | 9.73494e9 | 0.00518081 | ||||||||
\(535\) | −1.07643e12 | −0.568059 | ||||||||
\(536\) | −2.23943e12 | −1.17191 | ||||||||
\(537\) | 7.00923e11 | 0.363736 | ||||||||
\(538\) | −2.11337e12 | −1.08757 | ||||||||
\(539\) | −7.26533e12 | −3.70771 | ||||||||
\(540\) | −3.29618e11 | −0.166816 | ||||||||
\(541\) | −3.12532e12 | −1.56858 | −0.784291 | − | 0.620393i | \(-0.786973\pi\) | ||||
−0.784291 | + | 0.620393i | \(0.786973\pi\) | |||||||
\(542\) | −3.78139e12 | −1.88215 | ||||||||
\(543\) | −4.93867e11 | −0.243787 | ||||||||
\(544\) | −1.17633e11 | −0.0575883 | ||||||||
\(545\) | 1.30293e12 | 0.632610 | ||||||||
\(546\) | 4.32974e12 | 2.08495 | ||||||||
\(547\) | 1.59061e12 | 0.759663 | 0.379832 | − | 0.925056i | \(-0.375982\pi\) | ||||
0.379832 | + | 0.925056i | \(0.375982\pi\) | |||||||
\(548\) | −3.60453e11 | −0.170741 | ||||||||
\(549\) | 1.26546e12 | 0.594527 | ||||||||
\(550\) | −9.98411e11 | −0.465240 | ||||||||
\(551\) | 9.54641e11 | 0.441223 | ||||||||
\(552\) | −3.68460e11 | −0.168913 | ||||||||
\(553\) | 5.29180e12 | 2.40625 | ||||||||
\(554\) | 5.55402e12 | 2.50503 | ||||||||
\(555\) | −3.22073e11 | −0.144091 | ||||||||
\(556\) | 4.52106e12 | 2.00633 | ||||||||
\(557\) | 3.76617e12 | 1.65787 | 0.828937 | − | 0.559343i | \(-0.188946\pi\) | ||||
0.828937 | + | 0.559343i | \(0.188946\pi\) | |||||||
\(558\) | 4.66854e11 | 0.203858 | ||||||||
\(559\) | 2.24042e12 | 0.970458 | ||||||||
\(560\) | 1.64574e12 | 0.707158 | ||||||||
\(561\) | 5.15810e11 | 0.219865 | ||||||||
\(562\) | 2.52607e12 | 1.06815 | ||||||||
\(563\) | −2.32486e12 | −0.975234 | −0.487617 | − | 0.873058i | \(-0.662134\pi\) | ||||
−0.487617 | + | 0.873058i | \(0.662134\pi\) | |||||||
\(564\) | −2.41919e12 | −1.00673 | ||||||||
\(565\) | −1.13747e12 | −0.469592 | ||||||||
\(566\) | −6.41643e12 | −2.62797 | ||||||||
\(567\) | 5.28275e11 | 0.214653 | ||||||||
\(568\) | −1.30339e10 | −0.00525422 | ||||||||
\(569\) | 3.30244e11 | 0.132078 | 0.0660388 | − | 0.997817i | \(-0.478964\pi\) | ||||
0.0660388 | + | 0.997817i | \(0.478964\pi\) | |||||||
\(570\) | 3.56055e11 | 0.141280 | ||||||||
\(571\) | 3.83190e12 | 1.50852 | 0.754261 | − | 0.656575i | \(-0.227995\pi\) | ||||
0.754261 | + | 0.656575i | \(0.227995\pi\) | |||||||
\(572\) | 7.34388e12 | 2.86843 | ||||||||
\(573\) | 2.39953e12 | 0.929887 | ||||||||
\(574\) | 7.47832e11 | 0.287542 | ||||||||
\(575\) | 9.53690e10 | 0.0363833 | ||||||||
\(576\) | −1.03055e12 | −0.390094 | ||||||||
\(577\) | −1.66616e12 | −0.625786 | −0.312893 | − | 0.949788i | \(-0.601298\pi\) | ||||
−0.312893 | + | 0.949788i | \(0.601298\pi\) | |||||||
\(578\) | −4.23738e12 | −1.57915 | ||||||||
\(579\) | 3.75384e10 | 0.0138811 | ||||||||
\(580\) | −3.26529e12 | −1.19811 | ||||||||
\(581\) | −2.08333e11 | −0.0758517 | ||||||||
\(582\) | −1.79896e12 | −0.649931 | ||||||||
\(583\) | 1.69559e11 | 0.0607874 | ||||||||
\(584\) | −1.66064e12 | −0.590769 | ||||||||
\(585\) | −4.60499e11 | −0.162565 | ||||||||
\(586\) | 2.18856e12 | 0.766689 | ||||||||
\(587\) | 2.00482e12 | 0.696953 | 0.348476 | − | 0.937318i | \(-0.386699\pi\) | ||||
0.348476 | + | 0.937318i | \(0.386699\pi\) | |||||||
\(588\) | −8.86226e12 | −3.05736 | ||||||||
\(589\) | −3.32665e11 | −0.113891 | ||||||||
\(590\) | −2.88483e12 | −0.980136 | ||||||||
\(591\) | −9.99654e11 | −0.337059 | ||||||||
\(592\) | 1.36506e12 | 0.456777 | ||||||||
\(593\) | 1.46848e12 | 0.487666 | 0.243833 | − | 0.969817i | \(-0.421595\pi\) | ||||
0.243833 | + | 0.969817i | \(0.421595\pi\) | |||||||
\(594\) | 1.35833e12 | 0.447678 | ||||||||
\(595\) | 7.41195e11 | 0.242441 | ||||||||
\(596\) | 8.73121e12 | 2.83443 | ||||||||
\(597\) | 8.12868e11 | 0.261900 | ||||||||
\(598\) | −1.06342e12 | −0.340055 | ||||||||
\(599\) | 5.67302e12 | 1.80050 | 0.900251 | − | 0.435370i | \(-0.143383\pi\) | ||||
0.900251 | + | 0.435370i | \(0.143383\pi\) | |||||||
\(600\) | −5.89525e11 | −0.185704 | ||||||||
\(601\) | 2.23747e12 | 0.699555 | 0.349778 | − | 0.936833i | \(-0.386257\pi\) | ||||
0.349778 | + | 0.936833i | \(0.386257\pi\) | |||||||
\(602\) | −9.49617e12 | −2.94689 | ||||||||
\(603\) | −7.88587e11 | −0.242897 | ||||||||
\(604\) | −2.68638e11 | −0.0821299 | ||||||||
\(605\) | 1.24036e12 | 0.376400 | ||||||||
\(606\) | −5.60619e12 | −1.68865 | ||||||||
\(607\) | 7.87986e11 | 0.235597 | 0.117798 | − | 0.993038i | \(-0.462416\pi\) | ||||
0.117798 | + | 0.993038i | \(0.462416\pi\) | |||||||
\(608\) | 2.20734e11 | 0.0655094 | ||||||||
\(609\) | 5.23324e12 | 1.54168 | ||||||||
\(610\) | 4.67557e12 | 1.36726 | ||||||||
\(611\) | −3.37979e12 | −0.981079 | ||||||||
\(612\) | 6.29185e11 | 0.181300 | ||||||||
\(613\) | −4.35930e12 | −1.24694 | −0.623468 | − | 0.781848i | \(-0.714277\pi\) | ||||
−0.623468 | + | 0.781848i | \(0.714277\pi\) | |||||||
\(614\) | 6.95671e11 | 0.197536 | ||||||||
\(615\) | −7.95374e10 | −0.0224199 | ||||||||
\(616\) | −1.50678e13 | −4.21634 | ||||||||
\(617\) | −2.04791e12 | −0.568889 | −0.284444 | − | 0.958693i | \(-0.591809\pi\) | ||||
−0.284444 | + | 0.958693i | \(0.591809\pi\) | |||||||
\(618\) | −3.66421e12 | −1.01049 | ||||||||
\(619\) | −6.31079e12 | −1.72773 | −0.863865 | − | 0.503723i | \(-0.831963\pi\) | ||||
−0.863865 | + | 0.503723i | \(0.831963\pi\) | |||||||
\(620\) | 1.13786e12 | 0.309262 | ||||||||
\(621\) | −1.29748e11 | −0.0350098 | ||||||||
\(622\) | 1.24098e13 | 3.32435 | ||||||||
\(623\) | −3.80268e10 | −0.0101133 | ||||||||
\(624\) | 1.95176e12 | 0.515342 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | −1.22947e13 | −3.19989 | ||||||||
\(627\) | −9.67899e11 | −0.250107 | ||||||||
\(628\) | 9.65818e12 | 2.47786 | ||||||||
\(629\) | 6.14784e11 | 0.156601 | ||||||||
\(630\) | 1.95186e12 | 0.493646 | ||||||||
\(631\) | 4.94106e12 | 1.24076 | 0.620380 | − | 0.784301i | \(-0.286978\pi\) | ||||
0.620380 | + | 0.784301i | \(0.286978\pi\) | |||||||
\(632\) | 8.03418e12 | 2.00316 | ||||||||
\(633\) | 2.88577e12 | 0.714405 | ||||||||
\(634\) | −1.19523e13 | −2.93798 | ||||||||
\(635\) | −2.34321e12 | −0.571912 | ||||||||
\(636\) | 2.06829e11 | 0.0501249 | ||||||||
\(637\) | −1.23812e13 | −2.97945 | ||||||||
\(638\) | 1.34560e13 | 3.21531 | ||||||||
\(639\) | −4.58974e9 | −0.00108902 | ||||||||
\(640\) | −3.41813e12 | −0.805338 | ||||||||
\(641\) | −6.55819e11 | −0.153434 | −0.0767172 | − | 0.997053i | \(-0.524444\pi\) | ||||
−0.0767172 | + | 0.997053i | \(0.524444\pi\) | |||||||
\(642\) | 5.41089e12 | 1.25707 | ||||||||
\(643\) | 5.76324e11 | 0.132959 | 0.0664794 | − | 0.997788i | \(-0.478823\pi\) | ||||
0.0664794 | + | 0.997788i | \(0.478823\pi\) | |||||||
\(644\) | 2.97332e12 | 0.681171 | ||||||||
\(645\) | 1.00999e12 | 0.229772 | ||||||||
\(646\) | −6.79649e11 | −0.153546 | ||||||||
\(647\) | −3.52372e12 | −0.790556 | −0.395278 | − | 0.918562i | \(-0.629352\pi\) | ||||
−0.395278 | + | 0.918562i | \(0.629352\pi\) | |||||||
\(648\) | 8.02043e11 | 0.178694 | ||||||||
\(649\) | 7.84212e12 | 1.73513 | ||||||||
\(650\) | −1.70144e12 | −0.373858 | ||||||||
\(651\) | −1.82364e12 | −0.397945 | ||||||||
\(652\) | 7.70899e12 | 1.67064 | ||||||||
\(653\) | −4.37841e11 | −0.0942338 | −0.0471169 | − | 0.998889i | \(-0.515003\pi\) | ||||
−0.0471169 | + | 0.998889i | \(0.515003\pi\) | |||||||
\(654\) | −6.54942e12 | −1.39992 | ||||||||
\(655\) | −1.22874e12 | −0.260840 | ||||||||
\(656\) | 3.37108e11 | 0.0710725 | ||||||||
\(657\) | −5.84774e11 | −0.122446 | ||||||||
\(658\) | 1.43254e13 | 2.97914 | ||||||||
\(659\) | 1.98477e12 | 0.409945 | 0.204972 | − | 0.978768i | \(-0.434290\pi\) | ||||
0.204972 | + | 0.978768i | \(0.434290\pi\) | |||||||
\(660\) | 3.31064e12 | 0.679148 | ||||||||
\(661\) | 2.80945e12 | 0.572420 | 0.286210 | − | 0.958167i | \(-0.407604\pi\) | ||||
0.286210 | + | 0.958167i | \(0.407604\pi\) | |||||||
\(662\) | −6.94988e12 | −1.40642 | ||||||||
\(663\) | 8.79016e11 | 0.176679 | ||||||||
\(664\) | −3.16297e11 | −0.0631450 | ||||||||
\(665\) | −1.39083e12 | −0.275788 | ||||||||
\(666\) | 1.61896e12 | 0.318862 | ||||||||
\(667\) | −1.28533e12 | −0.251447 | ||||||||
\(668\) | −8.35328e12 | −1.62317 | ||||||||
\(669\) | 2.76733e12 | 0.534126 | ||||||||
\(670\) | −2.91365e12 | −0.558600 | ||||||||
\(671\) | −1.27101e13 | −2.42045 | ||||||||
\(672\) | 1.21004e12 | 0.228896 | ||||||||
\(673\) | −2.08224e12 | −0.391258 | −0.195629 | − | 0.980678i | \(-0.562675\pi\) | ||||
−0.195629 | + | 0.980678i | \(0.562675\pi\) | |||||||
\(674\) | −3.77526e12 | −0.704657 | ||||||||
\(675\) | −2.07594e11 | −0.0384900 | ||||||||
\(676\) | 1.99144e12 | 0.366781 | ||||||||
\(677\) | −6.44805e12 | −1.17972 | −0.589861 | − | 0.807505i | \(-0.700817\pi\) | ||||
−0.589861 | + | 0.807505i | \(0.700817\pi\) | |||||||
\(678\) | 5.71770e12 | 1.03917 | ||||||||
\(679\) | 7.02712e12 | 1.26871 | ||||||||
\(680\) | 1.12531e12 | 0.201828 | ||||||||
\(681\) | −2.95598e12 | −0.526671 | ||||||||
\(682\) | −4.68902e12 | −0.829952 | ||||||||
\(683\) | −4.02024e12 | −0.706902 | −0.353451 | − | 0.935453i | \(-0.614992\pi\) | ||||
−0.353451 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(684\) | −1.18064e12 | −0.206237 | ||||||||
\(685\) | −2.27015e11 | −0.0393955 | ||||||||
\(686\) | 3.32706e13 | 5.73591 | ||||||||
\(687\) | −3.13832e12 | −0.537516 | ||||||||
\(688\) | −4.28069e12 | −0.728392 | ||||||||
\(689\) | 2.88954e11 | 0.0488476 | ||||||||
\(690\) | −4.79391e11 | −0.0805136 | ||||||||
\(691\) | −8.43146e12 | −1.40686 | −0.703431 | − | 0.710763i | \(-0.748350\pi\) | ||||
−0.703431 | + | 0.710763i | \(0.748350\pi\) | |||||||
\(692\) | 3.57094e11 | 0.0591978 | ||||||||
\(693\) | −5.30592e12 | −0.873900 | ||||||||
\(694\) | −1.34879e13 | −2.20713 | ||||||||
\(695\) | 2.84737e12 | 0.462927 | ||||||||
\(696\) | 7.94527e12 | 1.28342 | ||||||||
\(697\) | 1.51824e11 | 0.0243664 | ||||||||
\(698\) | −4.27159e12 | −0.681145 | ||||||||
\(699\) | 2.17661e12 | 0.344853 | ||||||||
\(700\) | 4.75724e12 | 0.748883 | ||||||||
\(701\) | 6.55956e12 | 1.02599 | 0.512995 | − | 0.858391i | \(-0.328536\pi\) | ||||
0.512995 | + | 0.858391i | \(0.328536\pi\) | |||||||
\(702\) | 2.31479e12 | 0.359745 | ||||||||
\(703\) | −1.15362e12 | −0.178141 | ||||||||
\(704\) | 1.03507e13 | 1.58816 | ||||||||
\(705\) | −1.52362e12 | −0.232287 | ||||||||
\(706\) | −1.31894e13 | −1.99803 | ||||||||
\(707\) | 2.18990e13 | 3.29638 | ||||||||
\(708\) | 9.56583e12 | 1.43078 | ||||||||
\(709\) | −5.30959e12 | −0.789138 | −0.394569 | − | 0.918866i | \(-0.629106\pi\) | ||||
−0.394569 | + | 0.918866i | \(0.629106\pi\) | |||||||
\(710\) | −1.69581e10 | −0.00250446 | ||||||||
\(711\) | 2.82914e12 | 0.415184 | ||||||||
\(712\) | −5.77335e10 | −0.00841914 | ||||||||
\(713\) | 4.47899e11 | 0.0649049 | ||||||||
\(714\) | −3.72577e12 | −0.536505 | ||||||||
\(715\) | 4.62520e12 | 0.661840 | ||||||||
\(716\) | −8.58739e12 | −1.22110 | ||||||||
\(717\) | −1.09116e12 | −0.154189 | ||||||||
\(718\) | −1.06687e13 | −1.49813 | ||||||||
\(719\) | 1.02053e13 | 1.42411 | 0.712056 | − | 0.702123i | \(-0.247764\pi\) | ||||
0.712056 | + | 0.702123i | \(0.247764\pi\) | |||||||
\(720\) | 8.79858e11 | 0.122016 | ||||||||
\(721\) | 1.43132e13 | 1.97255 | ||||||||
\(722\) | −1.12405e13 | −1.53946 | ||||||||
\(723\) | 1.50546e12 | 0.204903 | ||||||||
\(724\) | 6.05063e12 | 0.818422 | ||||||||
\(725\) | −2.05649e12 | −0.276443 | ||||||||
\(726\) | −6.23493e12 | −0.832946 | ||||||||
\(727\) | −7.45813e12 | −0.990206 | −0.495103 | − | 0.868834i | \(-0.664870\pi\) | ||||
−0.495103 | + | 0.868834i | \(0.664870\pi\) | |||||||
\(728\) | −2.56777e13 | −3.38817 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −2.16061e12 | −0.281594 | ||||||||
\(731\) | −1.92790e12 | −0.249721 | ||||||||
\(732\) | −1.55038e13 | −1.99589 | ||||||||
\(733\) | −1.06610e13 | −1.36405 | −0.682024 | − | 0.731329i | \(-0.738900\pi\) | ||||
−0.682024 | + | 0.731329i | \(0.738900\pi\) | |||||||
\(734\) | −8.23114e12 | −1.04671 | ||||||||
\(735\) | −5.58148e12 | −0.705433 | ||||||||
\(736\) | −2.97196e11 | −0.0373330 | ||||||||
\(737\) | 7.92047e12 | 0.988889 | ||||||||
\(738\) | 3.99811e11 | 0.0496136 | ||||||||
\(739\) | 2.33179e12 | 0.287601 | 0.143800 | − | 0.989607i | \(-0.454068\pi\) | ||||
0.143800 | + | 0.989607i | \(0.454068\pi\) | |||||||
\(740\) | 3.94589e12 | 0.483729 | ||||||||
\(741\) | −1.64944e12 | −0.200981 | ||||||||
\(742\) | −1.22475e12 | −0.148330 | ||||||||
\(743\) | −7.80869e12 | −0.940001 | −0.470001 | − | 0.882666i | \(-0.655746\pi\) | ||||
−0.470001 | + | 0.882666i | \(0.655746\pi\) | |||||||
\(744\) | −2.76870e12 | −0.331282 | ||||||||
\(745\) | 5.49894e12 | 0.653997 | ||||||||
\(746\) | 2.35946e13 | 2.78925 | ||||||||
\(747\) | −1.11380e11 | −0.0130878 | ||||||||
\(748\) | −6.31946e12 | −0.738113 | ||||||||
\(749\) | −2.11361e13 | −2.45390 | ||||||||
\(750\) | −7.67013e11 | −0.0885171 | ||||||||
\(751\) | 4.20664e12 | 0.482565 | 0.241283 | − | 0.970455i | \(-0.422432\pi\) | ||||
0.241283 | + | 0.970455i | \(0.422432\pi\) | |||||||
\(752\) | 6.45763e12 | 0.736364 | ||||||||
\(753\) | −3.48565e12 | −0.395099 | ||||||||
\(754\) | 2.29310e13 | 2.58376 | ||||||||
\(755\) | −1.69189e11 | −0.0189501 | ||||||||
\(756\) | −6.47217e12 | −0.720613 | ||||||||
\(757\) | −1.54834e13 | −1.71370 | −0.856848 | − | 0.515570i | \(-0.827580\pi\) | ||||
−0.856848 | + | 0.515570i | \(0.827580\pi\) | |||||||
\(758\) | 1.80021e13 | 1.98067 | ||||||||
\(759\) | 1.30318e12 | 0.142533 | ||||||||
\(760\) | −2.11160e12 | −0.229589 | ||||||||
\(761\) | 9.77615e12 | 1.05666 | 0.528332 | − | 0.849038i | \(-0.322818\pi\) | ||||
0.528332 | + | 0.849038i | \(0.322818\pi\) | |||||||
\(762\) | 1.17786e13 | 1.26560 | ||||||||
\(763\) | 2.55835e13 | 2.73275 | ||||||||
\(764\) | −2.93979e13 | −3.12174 | ||||||||
\(765\) | 3.96263e11 | 0.0418318 | ||||||||
\(766\) | 2.02755e13 | 2.12785 | ||||||||
\(767\) | 1.33641e13 | 1.39432 | ||||||||
\(768\) | 1.06678e13 | 1.10649 | ||||||||
\(769\) | 3.35411e12 | 0.345867 | 0.172933 | − | 0.984934i | \(-0.444675\pi\) | ||||
0.172933 | + | 0.984934i | \(0.444675\pi\) | |||||||
\(770\) | −1.96042e13 | −2.00974 | ||||||||
\(771\) | 5.07755e10 | 0.00517499 | ||||||||
\(772\) | −4.59904e11 | −0.0466003 | ||||||||
\(773\) | −6.04474e12 | −0.608933 | −0.304467 | − | 0.952523i | \(-0.598478\pi\) | ||||
−0.304467 | + | 0.952523i | \(0.598478\pi\) | |||||||
\(774\) | −5.07690e12 | −0.508469 | ||||||||
\(775\) | 7.16627e11 | 0.0713568 | ||||||||
\(776\) | 1.06688e13 | 1.05618 | ||||||||
\(777\) | −6.32403e12 | −0.622443 | ||||||||
\(778\) | −4.61163e12 | −0.451280 | ||||||||
\(779\) | −2.84892e11 | −0.0277180 | ||||||||
\(780\) | 5.64182e12 | 0.545750 | ||||||||
\(781\) | 4.60988e10 | 0.00443364 | ||||||||
\(782\) | 9.15078e11 | 0.0875040 | ||||||||
\(783\) | 2.79783e12 | 0.266007 | ||||||||
\(784\) | 2.36563e13 | 2.23627 | ||||||||
\(785\) | 6.08275e12 | 0.571724 | ||||||||
\(786\) | 6.17651e12 | 0.577220 | ||||||||
\(787\) | 4.16503e12 | 0.387019 | 0.193509 | − | 0.981098i | \(-0.438013\pi\) | ||||
0.193509 | + | 0.981098i | \(0.438013\pi\) | |||||||
\(788\) | 1.22473e13 | 1.13155 | ||||||||
\(789\) | −5.03371e12 | −0.462425 | ||||||||
\(790\) | 1.04530e13 | 0.954817 | ||||||||
\(791\) | −2.23346e13 | −2.02854 | ||||||||
\(792\) | −8.05562e12 | −0.727504 | ||||||||
\(793\) | −2.16599e13 | −1.94503 | ||||||||
\(794\) | −1.07420e13 | −0.959164 | ||||||||
\(795\) | 1.30261e11 | 0.0115655 | ||||||||
\(796\) | −9.95887e12 | −0.879228 | ||||||||
\(797\) | 2.14334e13 | 1.88160 | 0.940802 | − | 0.338957i | \(-0.110074\pi\) | ||||
0.940802 | + | 0.338957i | \(0.110074\pi\) | |||||||
\(798\) | 6.99128e12 | 0.610300 | ||||||||
\(799\) | 2.90833e12 | 0.252454 | ||||||||
\(800\) | −4.75506e11 | −0.0410441 | ||||||||
\(801\) | −2.03301e10 | −0.00174499 | ||||||||
\(802\) | −5.95301e12 | −0.508103 | ||||||||
\(803\) | 5.87339e12 | 0.498504 | ||||||||
\(804\) | 9.66140e12 | 0.815432 | ||||||||
\(805\) | 1.87261e12 | 0.157168 | ||||||||
\(806\) | −7.99080e12 | −0.666933 | ||||||||
\(807\) | 4.41350e12 | 0.366313 | ||||||||
\(808\) | 3.32478e13 | 2.74417 | ||||||||
\(809\) | −1.82139e11 | −0.0149498 | −0.00747490 | − | 0.999972i | \(-0.502379\pi\) | ||||
−0.00747490 | + | 0.999972i | \(0.502379\pi\) | |||||||
\(810\) | 1.04351e12 | 0.0851756 | ||||||||
\(811\) | −1.32191e13 | −1.07302 | −0.536511 | − | 0.843894i | \(-0.680258\pi\) | ||||
−0.536511 | + | 0.843894i | \(0.680258\pi\) | |||||||
\(812\) | −6.41153e13 | −5.17558 | ||||||||
\(813\) | 7.89693e12 | 0.633944 | ||||||||
\(814\) | −1.62607e13 | −1.29816 | ||||||||
\(815\) | 4.85514e12 | 0.385472 | ||||||||
\(816\) | −1.67950e12 | −0.132610 | ||||||||
\(817\) | 3.61763e12 | 0.284070 | ||||||||
\(818\) | −5.90963e12 | −0.461498 | ||||||||
\(819\) | −9.04209e12 | −0.702249 | ||||||||
\(820\) | 9.74455e11 | 0.0752661 | ||||||||
\(821\) | −1.15652e13 | −0.888398 | −0.444199 | − | 0.895928i | \(-0.646512\pi\) | ||||
−0.444199 | + | 0.895928i | \(0.646512\pi\) | |||||||
\(822\) | 1.14113e12 | 0.0871793 | ||||||||
\(823\) | 9.35914e12 | 0.711110 | 0.355555 | − | 0.934655i | \(-0.384292\pi\) | ||||
0.355555 | + | 0.934655i | \(0.384292\pi\) | |||||||
\(824\) | 2.17307e13 | 1.64211 | ||||||||
\(825\) | 2.08505e12 | 0.156702 | ||||||||
\(826\) | −5.66448e13 | −4.23399 | ||||||||
\(827\) | −2.25652e13 | −1.67751 | −0.838753 | − | 0.544512i | \(-0.816715\pi\) | ||||
−0.838753 | + | 0.544512i | \(0.816715\pi\) | |||||||
\(828\) | 1.58962e12 | 0.117532 | ||||||||
\(829\) | 1.22484e13 | 0.900705 | 0.450353 | − | 0.892851i | \(-0.351298\pi\) | ||||
0.450353 | + | 0.892851i | \(0.351298\pi\) | |||||||
\(830\) | −4.11525e11 | −0.0300985 | ||||||||
\(831\) | −1.15988e13 | −0.843742 | ||||||||
\(832\) | 1.76392e13 | 1.27622 | ||||||||
\(833\) | 1.06541e13 | 0.766681 | ||||||||
\(834\) | −1.43129e13 | −1.02442 | ||||||||
\(835\) | −5.26092e12 | −0.374518 | ||||||||
\(836\) | 1.18582e13 | 0.839638 | ||||||||
\(837\) | −9.74963e11 | −0.0686631 | ||||||||
\(838\) | −3.52887e13 | −2.47194 | ||||||||
\(839\) | 4.67277e12 | 0.325571 | 0.162786 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162786 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(840\) | −1.15756e13 | −0.802205 | ||||||||
\(841\) | 1.32090e13 | 0.910516 | ||||||||
\(842\) | 3.83414e13 | 2.62883 | ||||||||
\(843\) | −5.27537e12 | −0.359773 | ||||||||
\(844\) | −3.53551e13 | −2.39834 | ||||||||
\(845\) | 1.25421e12 | 0.0846285 | ||||||||
\(846\) | 7.65876e12 | 0.514034 | ||||||||
\(847\) | 2.43550e13 | 1.62597 | ||||||||
\(848\) | −5.52094e11 | −0.0366633 | ||||||||
\(849\) | 1.33999e13 | 0.885149 | ||||||||
\(850\) | 1.46410e12 | 0.0962024 | ||||||||
\(851\) | 1.55323e12 | 0.101520 | ||||||||
\(852\) | 5.62314e10 | 0.00365595 | ||||||||
\(853\) | 4.04678e12 | 0.261721 | 0.130861 | − | 0.991401i | \(-0.458226\pi\) | ||||
0.130861 | + | 0.991401i | \(0.458226\pi\) | |||||||
\(854\) | 9.18067e13 | 5.90628 | ||||||||
\(855\) | −7.43573e11 | −0.0475857 | ||||||||
\(856\) | −3.20895e13 | −2.04282 | ||||||||
\(857\) | −2.35372e13 | −1.49053 | −0.745267 | − | 0.666766i | \(-0.767678\pi\) | ||||
−0.745267 | + | 0.666766i | \(0.767678\pi\) | |||||||
\(858\) | −2.32495e13 | −1.46460 | ||||||||
\(859\) | 2.19727e13 | 1.37694 | 0.688470 | − | 0.725265i | \(-0.258283\pi\) | ||||
0.688470 | + | 0.725265i | \(0.258283\pi\) | |||||||
\(860\) | −1.23739e13 | −0.771371 | ||||||||
\(861\) | −1.56175e12 | −0.0968494 | ||||||||
\(862\) | 7.88441e12 | 0.486392 | ||||||||
\(863\) | −2.06939e13 | −1.26997 | −0.634984 | − | 0.772525i | \(-0.718993\pi\) | ||||
−0.634984 | + | 0.772525i | \(0.718993\pi\) | |||||||
\(864\) | 6.46921e11 | 0.0394947 | ||||||||
\(865\) | 2.24899e11 | 0.0136589 | ||||||||
\(866\) | −8.17796e12 | −0.494099 | ||||||||
\(867\) | 8.84922e12 | 0.531887 | ||||||||
\(868\) | 2.23423e13 | 1.33595 | ||||||||
\(869\) | −2.84155e13 | −1.69031 | ||||||||
\(870\) | 1.03374e13 | 0.611748 | ||||||||
\(871\) | 1.34977e13 | 0.794652 | ||||||||
\(872\) | 3.88416e13 | 2.27496 | ||||||||
\(873\) | 3.75689e12 | 0.218909 | ||||||||
\(874\) | −1.71711e12 | −0.0995400 | ||||||||
\(875\) | 2.99612e12 | 0.172792 | ||||||||
\(876\) | 7.16437e12 | 0.411064 | ||||||||
\(877\) | −8.18344e12 | −0.467130 | −0.233565 | − | 0.972341i | \(-0.575039\pi\) | ||||
−0.233565 | + | 0.972341i | \(0.575039\pi\) | |||||||
\(878\) | 8.19991e12 | 0.465676 | ||||||||
\(879\) | −4.57052e12 | −0.258235 | ||||||||
\(880\) | −8.83719e12 | −0.496755 | ||||||||
\(881\) | 2.43747e13 | 1.36316 | 0.681581 | − | 0.731743i | \(-0.261293\pi\) | ||||
0.681581 | + | 0.731743i | \(0.261293\pi\) | |||||||
\(882\) | 2.80564e13 | 1.56107 | ||||||||
\(883\) | −1.17064e13 | −0.648039 | −0.324019 | − | 0.946050i | \(-0.605034\pi\) | ||||
−0.324019 | + | 0.946050i | \(0.605034\pi\) | |||||||
\(884\) | −1.07693e13 | −0.593133 | ||||||||
\(885\) | 6.02459e12 | 0.330128 | ||||||||
\(886\) | 5.64407e13 | 3.07709 | ||||||||
\(887\) | 2.83247e13 | 1.53642 | 0.768210 | − | 0.640198i | \(-0.221148\pi\) | ||||
0.768210 | + | 0.640198i | \(0.221148\pi\) | |||||||
\(888\) | −9.60134e12 | −0.518171 | ||||||||
\(889\) | −4.60098e13 | −2.47055 | ||||||||
\(890\) | −7.51153e10 | −0.00401304 | ||||||||
\(891\) | −2.83669e12 | −0.150786 | ||||||||
\(892\) | −3.39040e13 | −1.79312 | ||||||||
\(893\) | −5.45738e12 | −0.287179 | ||||||||
\(894\) | −2.76415e13 | −1.44725 | ||||||||
\(895\) | −5.40836e12 | −0.281749 | ||||||||
\(896\) | −6.71163e13 | −3.47890 | ||||||||
\(897\) | 2.22081e12 | 0.114537 | ||||||||
\(898\) | −8.51244e12 | −0.436828 | ||||||||
\(899\) | −9.65827e12 | −0.493152 | ||||||||
\(900\) | 2.54335e12 | 0.129215 | ||||||||
\(901\) | −2.48647e11 | −0.0125696 | ||||||||
\(902\) | −4.01565e12 | −0.201988 | ||||||||
\(903\) | 1.98315e13 | 0.992569 | ||||||||
\(904\) | −3.39091e13 | −1.68872 | ||||||||
\(905\) | 3.81070e12 | 0.188837 | ||||||||
\(906\) | 8.50462e11 | 0.0419351 | ||||||||
\(907\) | 5.36313e12 | 0.263139 | 0.131570 | − | 0.991307i | \(-0.457998\pi\) | ||||
0.131570 | + | 0.991307i | \(0.457998\pi\) | |||||||
\(908\) | 3.62153e13 | 1.76809 | ||||||||
\(909\) | 1.17078e13 | 0.568771 | ||||||||
\(910\) | −3.34085e13 | −1.61499 | ||||||||
\(911\) | 3.43721e13 | 1.65338 | 0.826691 | − | 0.562656i | \(-0.190220\pi\) | ||||
0.826691 | + | 0.562656i | \(0.190220\pi\) | |||||||
\(912\) | 3.15153e12 | 0.150850 | ||||||||
\(913\) | 1.11869e12 | 0.0532833 | ||||||||
\(914\) | 2.87335e13 | 1.36185 | ||||||||
\(915\) | −9.76432e12 | −0.460519 | ||||||||
\(916\) | 3.84492e13 | 1.80450 | ||||||||
\(917\) | −2.41268e13 | −1.12678 | ||||||||
\(918\) | −1.99189e12 | −0.0925708 | ||||||||
\(919\) | −2.98037e13 | −1.37832 | −0.689160 | − | 0.724609i | \(-0.742020\pi\) | ||||
−0.689160 | + | 0.724609i | \(0.742020\pi\) | |||||||
\(920\) | 2.84305e12 | 0.130840 | ||||||||
\(921\) | −1.45282e12 | −0.0665339 | ||||||||
\(922\) | 1.08668e13 | 0.495234 | ||||||||
\(923\) | 7.85592e10 | 0.00356278 | ||||||||
\(924\) | 6.50057e13 | 2.93378 | ||||||||
\(925\) | 2.48513e12 | 0.111612 | ||||||||
\(926\) | −1.96682e12 | −0.0879053 | ||||||||
\(927\) | 7.65221e12 | 0.340352 | ||||||||
\(928\) | 6.40859e12 | 0.283659 | ||||||||
\(929\) | −2.03150e13 | −0.894843 | −0.447421 | − | 0.894323i | \(-0.647658\pi\) | ||||
−0.447421 | + | 0.894323i | \(0.647658\pi\) | |||||||
\(930\) | −3.60227e12 | −0.157908 | ||||||||
\(931\) | −1.99921e13 | −0.872136 | ||||||||
\(932\) | −2.66668e13 | −1.15771 | ||||||||
\(933\) | −2.59162e13 | −1.11970 | ||||||||
\(934\) | 6.87399e13 | 2.95562 | ||||||||
\(935\) | −3.98001e12 | −0.170307 | ||||||||
\(936\) | −1.37280e13 | −0.584609 | ||||||||
\(937\) | 2.73553e13 | 1.15935 | 0.579674 | − | 0.814848i | \(-0.303180\pi\) | ||||
0.579674 | + | 0.814848i | \(0.303180\pi\) | |||||||
\(938\) | −5.72107e13 | −2.41304 | ||||||||
\(939\) | 2.56759e13 | 1.07778 | ||||||||
\(940\) | 1.86666e13 | 0.779813 | ||||||||
\(941\) | −4.24123e13 | −1.76335 | −0.881675 | − | 0.471857i | \(-0.843584\pi\) | ||||
−0.881675 | + | 0.471857i | \(0.843584\pi\) | |||||||
\(942\) | −3.05761e13 | −1.26518 | ||||||||
\(943\) | 3.83578e11 | 0.0157961 | ||||||||
\(944\) | −2.55344e13 | −1.04653 | ||||||||
\(945\) | −4.07619e12 | −0.166269 | ||||||||
\(946\) | 5.09918e13 | 2.07009 | ||||||||
\(947\) | 9.23741e12 | 0.373229 | 0.186614 | − | 0.982433i | \(-0.440248\pi\) | ||||
0.186614 | + | 0.982433i | \(0.440248\pi\) | |||||||
\(948\) | −3.46613e13 | −1.39382 | ||||||||
\(949\) | 1.00091e13 | 0.400589 | ||||||||
\(950\) | −2.74734e12 | −0.109435 | ||||||||
\(951\) | 2.49607e13 | 0.989566 | ||||||||
\(952\) | 2.20958e13 | 0.871855 | ||||||||
\(953\) | 1.11343e13 | 0.437265 | 0.218633 | − | 0.975807i | \(-0.429840\pi\) | ||||
0.218633 | + | 0.975807i | \(0.429840\pi\) | |||||||
\(954\) | −6.54784e11 | −0.0255936 | ||||||||
\(955\) | −1.85149e13 | −0.720288 | ||||||||
\(956\) | 1.33684e13 | 0.517629 | ||||||||
\(957\) | −2.81011e13 | −1.08298 | ||||||||
\(958\) | −3.02360e13 | −1.15979 | ||||||||
\(959\) | −4.45752e12 | −0.170180 | ||||||||
\(960\) | 7.95180e12 | 0.302165 | ||||||||
\(961\) | −2.30740e13 | −0.872705 | ||||||||
\(962\) | −2.77106e13 | −1.04318 | ||||||||
\(963\) | −1.12999e13 | −0.423406 | ||||||||
\(964\) | −1.84442e13 | −0.687882 | ||||||||
\(965\) | −2.89649e11 | −0.0107522 | ||||||||
\(966\) | −9.41304e12 | −0.347803 | ||||||||
\(967\) | −5.48630e12 | −0.201772 | −0.100886 | − | 0.994898i | \(-0.532168\pi\) | ||||
−0.100886 | + | 0.994898i | \(0.532168\pi\) | |||||||
\(968\) | 3.69766e13 | 1.35359 | ||||||||
\(969\) | 1.41936e12 | 0.0517172 | ||||||||
\(970\) | 1.38808e13 | 0.503435 | ||||||||
\(971\) | −2.07887e13 | −0.750484 | −0.375242 | − | 0.926927i | \(-0.622440\pi\) | ||||
−0.375242 | + | 0.926927i | \(0.622440\pi\) | |||||||
\(972\) | −3.46019e12 | −0.124338 | ||||||||
\(973\) | 5.59093e13 | 1.99975 | ||||||||
\(974\) | −5.19572e13 | −1.84982 | ||||||||
\(975\) | 3.55324e12 | 0.125922 | ||||||||
\(976\) | 4.13847e13 | 1.45987 | ||||||||
\(977\) | 2.25372e13 | 0.791362 | 0.395681 | − | 0.918388i | \(-0.370509\pi\) | ||||
0.395681 | + | 0.918388i | \(0.370509\pi\) | |||||||
\(978\) | −2.44053e13 | −0.853022 | ||||||||
\(979\) | 2.04193e11 | 0.00710427 | ||||||||
\(980\) | 6.83816e13 | 2.36822 | ||||||||
\(981\) | 1.36776e13 | 0.471519 | ||||||||
\(982\) | −3.78689e13 | −1.29952 | ||||||||
\(983\) | −2.20727e13 | −0.753989 | −0.376994 | − | 0.926216i | \(-0.623042\pi\) | ||||
−0.376994 | + | 0.926216i | \(0.623042\pi\) | |||||||
\(984\) | −2.37110e12 | −0.0806253 | ||||||||
\(985\) | 7.71338e12 | 0.261085 | ||||||||
\(986\) | −1.97323e13 | −0.664861 | ||||||||
\(987\) | −2.99168e13 | −1.00343 | ||||||||
\(988\) | 2.02082e13 | 0.674717 | ||||||||
\(989\) | −4.87077e12 | −0.161888 | ||||||||
\(990\) | −1.04809e13 | −0.346770 | ||||||||
\(991\) | −5.27788e13 | −1.73831 | −0.869157 | − | 0.494536i | \(-0.835338\pi\) | ||||
−0.869157 | + | 0.494536i | \(0.835338\pi\) | |||||||
\(992\) | −2.23321e12 | −0.0732195 | ||||||||
\(993\) | 1.45139e13 | 0.473710 | ||||||||
\(994\) | −3.32978e11 | −0.0108188 | ||||||||
\(995\) | −6.27213e12 | −0.202867 | ||||||||
\(996\) | 1.36458e12 | 0.0439371 | ||||||||
\(997\) | −4.19157e13 | −1.34353 | −0.671767 | − | 0.740763i | \(-0.734464\pi\) | ||||
−0.671767 | + | 0.740763i | \(0.734464\pi\) | |||||||
\(998\) | 5.12199e13 | 1.63437 | ||||||||
\(999\) | −3.38099e12 | −0.107399 |
(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 | 15.10.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 45.10.a.d.1.1 | 2 | |||
4.3 | odd | 2 | 240.10.a.r.1.1 | 2 | |||
5.2 | odd | 4 | 75.10.b.f.49.4 | 4 | |||
5.3 | odd | 4 | 75.10.b.f.49.1 | 4 | |||
5.4 | even | 2 | 75.10.a.f.1.1 | 2 | |||
15.2 | even | 4 | 225.10.b.i.199.1 | 4 | |||
15.8 | even | 4 | 225.10.b.i.199.4 | 4 | |||
15.14 | odd | 2 | 225.10.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
45.10.a.d.1.1 | 2 | 3.2 | odd | 2 | |||
75.10.a.f.1.1 | 2 | 5.4 | even | 2 | |||
75.10.b.f.49.1 | 4 | 5.3 | odd | 4 | |||
75.10.b.f.49.4 | 4 | 5.2 | odd | 4 | |||
225.10.a.k.1.2 | 2 | 15.14 | odd | 2 | |||
225.10.b.i.199.1 | 4 | 15.2 | even | 4 | |||
225.10.b.i.199.4 | 4 | 15.8 | even | 4 | |||
240.10.a.r.1.1 | 2 | 4.3 | odd | 2 |