Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0816 | 0.710714 | 0.355357 | − | 0.934731i | \(-0.384359\pi\) | ||||
0.355357 | + | 0.934731i | \(0.384359\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −253.381 | −0.494885 | ||||||||
\(5\) | 2048.36 | 1.46569 | 0.732843 | − | 0.680398i | \(-0.238193\pi\) | ||||
0.732843 | + | 0.680398i | \(0.238193\pi\) | |||||||
\(6\) | −1302.61 | −0.410331 | ||||||||
\(7\) | −8880.78 | −1.39801 | −0.699004 | − | 0.715118i | \(-0.746373\pi\) | ||||
−0.699004 | + | 0.715118i | \(0.746373\pi\) | |||||||
\(8\) | −12308.6 | −1.06244 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 32940.9 | 1.04168 | ||||||||
\(11\) | 70959.2 | 1.46131 | 0.730654 | − | 0.682748i | \(-0.239215\pi\) | ||||
0.730654 | + | 0.682748i | \(0.239215\pi\) | |||||||
\(12\) | 20523.9 | 0.285722 | ||||||||
\(13\) | −57764.1 | −0.560936 | −0.280468 | − | 0.959863i | \(-0.590490\pi\) | ||||
−0.280468 | + | 0.959863i | \(0.590490\pi\) | |||||||
\(14\) | −142817. | −0.993584 | ||||||||
\(15\) | −165917. | −0.846214 | ||||||||
\(16\) | −68210.6 | −0.260203 | ||||||||
\(17\) | 574690. | 1.66884 | 0.834418 | − | 0.551132i | \(-0.185804\pi\) | ||||
0.834418 | + | 0.551132i | \(0.185804\pi\) | |||||||
\(18\) | 105512. | 0.236905 | ||||||||
\(19\) | −675543. | −1.18922 | −0.594610 | − | 0.804015i | \(-0.702693\pi\) | ||||
−0.594610 | + | 0.804015i | \(0.702693\pi\) | |||||||
\(20\) | −519016. | −0.725347 | ||||||||
\(21\) | 719343. | 0.807141 | ||||||||
\(22\) | 1.14114e6 | 1.03857 | ||||||||
\(23\) | 325234. | 0.242337 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(24\) | 996995. | 0.613398 | ||||||||
\(25\) | 2.24265e6 | 1.14823 | ||||||||
\(26\) | −928941. | −0.398665 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 2.25022e6 | 0.691854 | ||||||||
\(29\) | −2.59800e6 | −0.682101 | −0.341050 | − | 0.940045i | \(-0.610783\pi\) | ||||
−0.341050 | + | 0.940045i | \(0.610783\pi\) | |||||||
\(30\) | −2.66822e6 | −0.601416 | ||||||||
\(31\) | 3.69152e6 | 0.717922 | 0.358961 | − | 0.933352i | \(-0.383131\pi\) | ||||
0.358961 | + | 0.933352i | \(0.383131\pi\) | |||||||
\(32\) | 5.20505e6 | 0.877506 | ||||||||
\(33\) | −5.74770e6 | −0.843687 | ||||||||
\(34\) | 9.24195e6 | 1.18607 | ||||||||
\(35\) | −1.81910e7 | −2.04904 | ||||||||
\(36\) | −1.66244e6 | −0.164962 | ||||||||
\(37\) | −1.59909e7 | −1.40271 | −0.701353 | − | 0.712814i | \(-0.747420\pi\) | ||||
−0.701353 | + | 0.712814i | \(0.747420\pi\) | |||||||
\(38\) | −1.08638e7 | −0.845195 | ||||||||
\(39\) | 4.67889e6 | 0.323856 | ||||||||
\(40\) | −2.52124e7 | −1.55720 | ||||||||
\(41\) | 2.01221e7 | 1.11210 | 0.556052 | − | 0.831147i | \(-0.312316\pi\) | ||||
0.556052 | + | 0.831147i | \(0.312316\pi\) | |||||||
\(42\) | 1.15682e7 | 0.573646 | ||||||||
\(43\) | −2.99619e7 | −1.33647 | −0.668237 | − | 0.743948i | \(-0.732951\pi\) | ||||
−0.668237 | + | 0.743948i | \(0.732951\pi\) | |||||||
\(44\) | −1.79797e7 | −0.723180 | ||||||||
\(45\) | 1.34393e7 | 0.488562 | ||||||||
\(46\) | 5.23028e6 | 0.172232 | ||||||||
\(47\) | 1.30817e7 | 0.391041 | 0.195521 | − | 0.980700i | \(-0.437360\pi\) | ||||
0.195521 | + | 0.980700i | \(0.437360\pi\) | |||||||
\(48\) | 5.52506e6 | 0.150228 | ||||||||
\(49\) | 3.85146e7 | 0.954428 | ||||||||
\(50\) | 3.60654e7 | 0.816067 | ||||||||
\(51\) | −4.65499e7 | −0.963503 | ||||||||
\(52\) | 1.46364e7 | 0.277599 | ||||||||
\(53\) | −4.33294e7 | −0.754295 | −0.377148 | − | 0.926153i | \(-0.623095\pi\) | ||||
−0.377148 | + | 0.926153i | \(0.623095\pi\) | |||||||
\(54\) | −8.54643e6 | −0.136777 | ||||||||
\(55\) | 1.45350e8 | 2.14182 | ||||||||
\(56\) | 1.09310e8 | 1.48529 | ||||||||
\(57\) | 5.47190e7 | 0.686596 | ||||||||
\(58\) | −4.17801e7 | −0.484779 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | 4.20403e7 | 0.418779 | ||||||||
\(61\) | 1.48079e8 | 1.36934 | 0.684668 | − | 0.728855i | \(-0.259947\pi\) | ||||
0.684668 | + | 0.728855i | \(0.259947\pi\) | |||||||
\(62\) | 5.93656e7 | 0.510238 | ||||||||
\(63\) | −5.82668e7 | −0.466003 | ||||||||
\(64\) | 1.18630e8 | 0.883859 | ||||||||
\(65\) | −1.18322e8 | −0.822156 | ||||||||
\(66\) | −9.24323e7 | −0.599620 | ||||||||
\(67\) | 2.62228e7 | 0.158980 | 0.0794899 | − | 0.996836i | \(-0.474671\pi\) | ||||
0.0794899 | + | 0.996836i | \(0.474671\pi\) | |||||||
\(68\) | −1.45616e8 | −0.825883 | ||||||||
\(69\) | −2.63439e7 | −0.139913 | ||||||||
\(70\) | −2.92541e8 | −1.45628 | ||||||||
\(71\) | −3.59885e8 | −1.68074 | −0.840372 | − | 0.542010i | \(-0.817663\pi\) | ||||
−0.840372 | + | 0.542010i | \(0.817663\pi\) | |||||||
\(72\) | −8.07566e7 | −0.354145 | ||||||||
\(73\) | −3.34147e8 | −1.37716 | −0.688580 | − | 0.725160i | \(-0.741766\pi\) | ||||
−0.688580 | + | 0.725160i | \(0.741766\pi\) | |||||||
\(74\) | −2.57160e8 | −0.996922 | ||||||||
\(75\) | −1.81654e8 | −0.662934 | ||||||||
\(76\) | 1.71170e8 | 0.588527 | ||||||||
\(77\) | −6.30173e8 | −2.04292 | ||||||||
\(78\) | 7.52442e7 | 0.230169 | ||||||||
\(79\) | −6.43140e8 | −1.85773 | −0.928867 | − | 0.370413i | \(-0.879216\pi\) | ||||
−0.928867 | + | 0.370413i | \(0.879216\pi\) | |||||||
\(80\) | −1.39720e8 | −0.381376 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 3.23596e8 | 0.790388 | ||||||||
\(83\) | −3.84290e8 | −0.888808 | −0.444404 | − | 0.895826i | \(-0.646585\pi\) | ||||
−0.444404 | + | 0.895826i | \(0.646585\pi\) | |||||||
\(84\) | −1.82268e8 | −0.399442 | ||||||||
\(85\) | 1.17717e9 | 2.44599 | ||||||||
\(86\) | −4.81835e8 | −0.949852 | ||||||||
\(87\) | 2.10438e8 | 0.393811 | ||||||||
\(88\) | −8.73407e8 | −1.55255 | ||||||||
\(89\) | 3.95175e8 | 0.667628 | 0.333814 | − | 0.942639i | \(-0.391664\pi\) | ||||
0.333814 | + | 0.942639i | \(0.391664\pi\) | |||||||
\(90\) | 2.16125e8 | 0.347228 | ||||||||
\(91\) | 5.12990e8 | 0.784193 | ||||||||
\(92\) | −8.24081e7 | −0.119929 | ||||||||
\(93\) | −2.99013e8 | −0.414493 | ||||||||
\(94\) | 2.10374e8 | 0.277918 | ||||||||
\(95\) | −1.38375e9 | −1.74302 | ||||||||
\(96\) | −4.21609e8 | −0.506628 | ||||||||
\(97\) | −3.41540e8 | −0.391714 | −0.195857 | − | 0.980632i | \(-0.562749\pi\) | ||||
−0.195857 | + | 0.980632i | \(0.562749\pi\) | |||||||
\(98\) | 6.19377e8 | 0.678325 | ||||||||
\(99\) | 4.65564e8 | 0.487103 | ||||||||
\(100\) | −5.68245e8 | −0.568245 | ||||||||
\(101\) | −1.26167e9 | −1.20643 | −0.603213 | − | 0.797580i | \(-0.706113\pi\) | ||||
−0.603213 | + | 0.797580i | \(0.706113\pi\) | |||||||
\(102\) | −7.48598e8 | −0.684775 | ||||||||
\(103\) | −3.05119e8 | −0.267117 | −0.133559 | − | 0.991041i | \(-0.542640\pi\) | ||||
−0.133559 | + | 0.991041i | \(0.542640\pi\) | |||||||
\(104\) | 7.10994e8 | 0.595958 | ||||||||
\(105\) | 1.47347e9 | 1.18301 | ||||||||
\(106\) | −6.96807e8 | −0.536088 | ||||||||
\(107\) | −1.23762e9 | −0.912769 | −0.456385 | − | 0.889783i | \(-0.650856\pi\) | ||||
−0.456385 | + | 0.889783i | \(0.650856\pi\) | |||||||
\(108\) | 1.34657e8 | 0.0952407 | ||||||||
\(109\) | −9.06241e8 | −0.614928 | −0.307464 | − | 0.951560i | \(-0.599480\pi\) | ||||
−0.307464 | + | 0.951560i | \(0.599480\pi\) | |||||||
\(110\) | 2.33746e9 | 1.52222 | ||||||||
\(111\) | 1.29527e9 | 0.809852 | ||||||||
\(112\) | 6.05764e8 | 0.363766 | ||||||||
\(113\) | −1.77528e9 | −1.02427 | −0.512135 | − | 0.858905i | \(-0.671145\pi\) | ||||
−0.512135 | + | 0.858905i | \(0.671145\pi\) | |||||||
\(114\) | 8.79970e8 | 0.487973 | ||||||||
\(115\) | 6.66195e8 | 0.355190 | ||||||||
\(116\) | 6.58285e8 | 0.337562 | ||||||||
\(117\) | −3.78990e8 | −0.186979 | ||||||||
\(118\) | −1.94867e8 | −0.0925271 | ||||||||
\(119\) | −5.10370e9 | −2.33305 | ||||||||
\(120\) | 2.04220e9 | 0.899048 | ||||||||
\(121\) | 2.67727e9 | 1.13542 | ||||||||
\(122\) | 2.38136e9 | 0.973207 | ||||||||
\(123\) | −1.62989e9 | −0.642074 | ||||||||
\(124\) | −9.35362e8 | −0.355289 | ||||||||
\(125\) | 5.93043e8 | 0.217266 | ||||||||
\(126\) | −9.37024e8 | −0.331195 | ||||||||
\(127\) | 4.23992e9 | 1.44624 | 0.723120 | − | 0.690722i | \(-0.242707\pi\) | ||||
0.723120 | + | 0.690722i | \(0.242707\pi\) | |||||||
\(128\) | −7.57231e8 | −0.249335 | ||||||||
\(129\) | 2.42691e9 | 0.771614 | ||||||||
\(130\) | −1.90280e9 | −0.584318 | ||||||||
\(131\) | −1.60747e9 | −0.476895 | −0.238447 | − | 0.971155i | \(-0.576638\pi\) | ||||
−0.238447 | + | 0.971155i | \(0.576638\pi\) | |||||||
\(132\) | 1.45636e9 | 0.417528 | ||||||||
\(133\) | 5.99935e9 | 1.66254 | ||||||||
\(134\) | 4.21705e8 | 0.112989 | ||||||||
\(135\) | −1.08858e9 | −0.282071 | ||||||||
\(136\) | −7.07362e9 | −1.77303 | ||||||||
\(137\) | −6.17427e9 | −1.49742 | −0.748709 | − | 0.662899i | \(-0.769326\pi\) | ||||
−0.748709 | + | 0.662899i | \(0.769326\pi\) | |||||||
\(138\) | −4.23653e8 | −0.0994384 | ||||||||
\(139\) | −6.22009e9 | −1.41329 | −0.706643 | − | 0.707571i | \(-0.749791\pi\) | ||||
−0.706643 | + | 0.707571i | \(0.749791\pi\) | |||||||
\(140\) | 4.60926e9 | 1.01404 | ||||||||
\(141\) | −1.05961e9 | −0.225768 | ||||||||
\(142\) | −5.78754e9 | −1.19453 | ||||||||
\(143\) | −4.09890e9 | −0.819700 | ||||||||
\(144\) | −4.47530e8 | −0.0867343 | ||||||||
\(145\) | −5.32164e9 | −0.999746 | ||||||||
\(146\) | −5.37363e9 | −0.978768 | ||||||||
\(147\) | −3.11968e9 | −0.551039 | ||||||||
\(148\) | 4.05181e9 | 0.694178 | ||||||||
\(149\) | 1.18843e10 | 1.97531 | 0.987657 | − | 0.156630i | \(-0.0500630\pi\) | ||||
0.987657 | + | 0.156630i | \(0.0500630\pi\) | |||||||
\(150\) | −2.92130e9 | −0.471156 | ||||||||
\(151\) | −7.78951e9 | −1.21931 | −0.609654 | − | 0.792667i | \(-0.708692\pi\) | ||||
−0.609654 | + | 0.792667i | \(0.708692\pi\) | |||||||
\(152\) | 8.31497e9 | 1.26347 | ||||||||
\(153\) | 3.77054e9 | 0.556279 | ||||||||
\(154\) | −1.01342e10 | −1.45193 | ||||||||
\(155\) | 7.56155e9 | 1.05225 | ||||||||
\(156\) | −1.18554e9 | −0.160272 | ||||||||
\(157\) | 9.52831e9 | 1.25161 | 0.625803 | − | 0.779981i | \(-0.284771\pi\) | ||||
0.625803 | + | 0.779981i | \(0.284771\pi\) | |||||||
\(158\) | −1.03427e10 | −1.32032 | ||||||||
\(159\) | 3.50968e9 | 0.435492 | ||||||||
\(160\) | 1.06618e10 | 1.28615 | ||||||||
\(161\) | −2.88833e9 | −0.338789 | ||||||||
\(162\) | 6.92261e8 | 0.0789682 | ||||||||
\(163\) | −6.42572e9 | −0.712981 | −0.356490 | − | 0.934299i | \(-0.616027\pi\) | ||||
−0.356490 | + | 0.934299i | \(0.616027\pi\) | |||||||
\(164\) | −5.09856e9 | −0.550364 | ||||||||
\(165\) | −1.17733e10 | −1.23658 | ||||||||
\(166\) | −6.18001e9 | −0.631688 | ||||||||
\(167\) | 1.74275e9 | 0.173385 | 0.0866925 | − | 0.996235i | \(-0.472370\pi\) | ||||
0.0866925 | + | 0.996235i | \(0.472370\pi\) | |||||||
\(168\) | −8.85409e9 | −0.857535 | ||||||||
\(169\) | −7.26781e9 | −0.685351 | ||||||||
\(170\) | 1.89308e10 | 1.73840 | ||||||||
\(171\) | −4.43224e9 | −0.396406 | ||||||||
\(172\) | 7.59178e9 | 0.661402 | ||||||||
\(173\) | −1.30581e9 | −0.110834 | −0.0554168 | − | 0.998463i | \(-0.517649\pi\) | ||||
−0.0554168 | + | 0.998463i | \(0.517649\pi\) | |||||||
\(174\) | 3.38419e9 | 0.279887 | ||||||||
\(175\) | −1.99164e10 | −1.60524 | ||||||||
\(176\) | −4.84017e9 | −0.380237 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | 6.35506e9 | 0.474493 | ||||||||
\(179\) | −9.50453e9 | −0.691978 | −0.345989 | − | 0.938239i | \(-0.612456\pi\) | ||||
−0.345989 | + | 0.938239i | \(0.612456\pi\) | |||||||
\(180\) | −3.40526e9 | −0.241782 | ||||||||
\(181\) | 6.40309e9 | 0.443441 | 0.221721 | − | 0.975110i | \(-0.428833\pi\) | ||||
0.221721 | + | 0.975110i | \(0.428833\pi\) | |||||||
\(182\) | 8.24972e9 | 0.557337 | ||||||||
\(183\) | −1.19944e10 | −0.790587 | ||||||||
\(184\) | −4.00316e9 | −0.257468 | ||||||||
\(185\) | −3.27552e10 | −2.05593 | ||||||||
\(186\) | −4.80862e9 | −0.294586 | ||||||||
\(187\) | 4.07796e10 | 2.43868 | ||||||||
\(188\) | −3.31465e9 | −0.193521 | ||||||||
\(189\) | 4.71961e9 | 0.269047 | ||||||||
\(190\) | −2.22530e10 | −1.23879 | ||||||||
\(191\) | 2.35967e10 | 1.28293 | 0.641463 | − | 0.767154i | \(-0.278328\pi\) | ||||
0.641463 | + | 0.767154i | \(0.278328\pi\) | |||||||
\(192\) | −9.60899e9 | −0.510296 | ||||||||
\(193\) | −1.82705e9 | −0.0947857 | −0.0473928 | − | 0.998876i | \(-0.515091\pi\) | ||||
−0.0473928 | + | 0.998876i | \(0.515091\pi\) | |||||||
\(194\) | −5.49253e9 | −0.278397 | ||||||||
\(195\) | 9.58405e9 | 0.474672 | ||||||||
\(196\) | −9.75888e9 | −0.472332 | ||||||||
\(197\) | 1.08956e10 | 0.515409 | 0.257705 | − | 0.966224i | \(-0.417034\pi\) | ||||
0.257705 | + | 0.966224i | \(0.417034\pi\) | |||||||
\(198\) | 7.48702e9 | 0.346191 | ||||||||
\(199\) | 3.90626e10 | 1.76572 | 0.882862 | − | 0.469633i | \(-0.155614\pi\) | ||||
0.882862 | + | 0.469633i | \(0.155614\pi\) | |||||||
\(200\) | −2.76038e10 | −1.21993 | ||||||||
\(201\) | −2.12405e9 | −0.0917871 | ||||||||
\(202\) | −2.02898e10 | −0.857424 | ||||||||
\(203\) | 2.30723e10 | 0.953583 | ||||||||
\(204\) | 1.17949e10 | 0.476824 | ||||||||
\(205\) | 4.12172e10 | 1.63000 | ||||||||
\(206\) | −4.90681e9 | −0.189844 | ||||||||
\(207\) | 2.13386e9 | 0.0807791 | ||||||||
\(208\) | 3.94013e9 | 0.145957 | ||||||||
\(209\) | −4.79360e10 | −1.73782 | ||||||||
\(210\) | 2.36958e10 | 0.840785 | ||||||||
\(211\) | −1.23713e10 | −0.429678 | −0.214839 | − | 0.976649i | \(-0.568923\pi\) | ||||
−0.214839 | + | 0.976649i | \(0.568923\pi\) | |||||||
\(212\) | 1.09789e10 | 0.373290 | ||||||||
\(213\) | 2.91507e10 | 0.970378 | ||||||||
\(214\) | −1.99030e10 | −0.648718 | ||||||||
\(215\) | −6.13726e10 | −1.95885 | ||||||||
\(216\) | 6.54128e9 | 0.204466 | ||||||||
\(217\) | −3.27836e10 | −1.00366 | ||||||||
\(218\) | −1.45738e10 | −0.437038 | ||||||||
\(219\) | 2.70659e10 | 0.795104 | ||||||||
\(220\) | −3.68290e10 | −1.05995 | ||||||||
\(221\) | −3.31965e10 | −0.936110 | ||||||||
\(222\) | 2.08300e10 | 0.575573 | ||||||||
\(223\) | 8.76793e9 | 0.237424 | 0.118712 | − | 0.992929i | \(-0.462123\pi\) | ||||
0.118712 | + | 0.992929i | \(0.462123\pi\) | |||||||
\(224\) | −4.62249e10 | −1.22676 | ||||||||
\(225\) | 1.47140e10 | 0.382745 | ||||||||
\(226\) | −2.85494e10 | −0.727963 | ||||||||
\(227\) | 1.40496e10 | 0.351195 | 0.175597 | − | 0.984462i | \(-0.443814\pi\) | ||||
0.175597 | + | 0.984462i | \(0.443814\pi\) | |||||||
\(228\) | −1.38648e10 | −0.339786 | ||||||||
\(229\) | 5.68805e10 | 1.36680 | 0.683398 | − | 0.730046i | \(-0.260501\pi\) | ||||
0.683398 | + | 0.730046i | \(0.260501\pi\) | |||||||
\(230\) | 1.07135e10 | 0.252439 | ||||||||
\(231\) | 5.10440e10 | 1.17948 | ||||||||
\(232\) | 3.19777e10 | 0.724689 | ||||||||
\(233\) | −7.66188e10 | −1.70307 | −0.851537 | − | 0.524294i | \(-0.824329\pi\) | ||||
−0.851537 | + | 0.524294i | \(0.824329\pi\) | |||||||
\(234\) | −6.09478e9 | −0.132888 | ||||||||
\(235\) | 2.67959e10 | 0.573143 | ||||||||
\(236\) | 3.07031e9 | 0.0644286 | ||||||||
\(237\) | 5.20943e10 | 1.07256 | ||||||||
\(238\) | −8.20757e10 | −1.65813 | ||||||||
\(239\) | −2.35739e9 | −0.0467348 | −0.0233674 | − | 0.999727i | \(-0.507439\pi\) | ||||
−0.0233674 | + | 0.999727i | \(0.507439\pi\) | |||||||
\(240\) | 1.13173e10 | 0.220187 | ||||||||
\(241\) | −6.47507e10 | −1.23642 | −0.618212 | − | 0.786011i | \(-0.712143\pi\) | ||||
−0.618212 | + | 0.786011i | \(0.712143\pi\) | |||||||
\(242\) | 4.30548e10 | 0.806960 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −3.75205e10 | −0.677665 | ||||||||
\(245\) | 7.88917e10 | 1.39889 | ||||||||
\(246\) | −2.62113e10 | −0.456331 | ||||||||
\(247\) | 3.90222e10 | 0.667075 | ||||||||
\(248\) | −4.54373e10 | −0.762747 | ||||||||
\(249\) | 3.11275e10 | 0.513154 | ||||||||
\(250\) | 9.53710e9 | 0.154414 | ||||||||
\(251\) | 7.83882e10 | 1.24658 | 0.623288 | − | 0.781992i | \(-0.285796\pi\) | ||||
0.623288 | + | 0.781992i | \(0.285796\pi\) | |||||||
\(252\) | 1.47637e10 | 0.230618 | ||||||||
\(253\) | 2.30783e10 | 0.354129 | ||||||||
\(254\) | 6.81848e10 | 1.02786 | ||||||||
\(255\) | −9.53509e10 | −1.41219 | ||||||||
\(256\) | −7.29158e10 | −1.06107 | ||||||||
\(257\) | 1.12417e11 | 1.60743 | 0.803716 | − | 0.595013i | \(-0.202853\pi\) | ||||
0.803716 | + | 0.595013i | \(0.202853\pi\) | |||||||
\(258\) | 3.90287e10 | 0.548397 | ||||||||
\(259\) | 1.42012e11 | 1.96099 | ||||||||
\(260\) | 2.99805e10 | 0.406873 | ||||||||
\(261\) | −1.70455e10 | −0.227367 | ||||||||
\(262\) | −2.58508e10 | −0.338936 | ||||||||
\(263\) | −3.79023e10 | −0.488501 | −0.244250 | − | 0.969712i | \(-0.578542\pi\) | ||||
−0.244250 | + | 0.969712i | \(0.578542\pi\) | |||||||
\(264\) | 7.07460e10 | 0.896363 | ||||||||
\(265\) | −8.87541e10 | −1.10556 | ||||||||
\(266\) | 9.64793e10 | 1.18159 | ||||||||
\(267\) | −3.20092e10 | −0.385455 | ||||||||
\(268\) | −6.64436e9 | −0.0786768 | ||||||||
\(269\) | −4.07264e10 | −0.474232 | −0.237116 | − | 0.971481i | \(-0.576202\pi\) | ||||
−0.237116 | + | 0.971481i | \(0.576202\pi\) | |||||||
\(270\) | −1.75062e10 | −0.200472 | ||||||||
\(271\) | −9.29803e10 | −1.04720 | −0.523599 | − | 0.851965i | \(-0.675411\pi\) | ||||
−0.523599 | + | 0.851965i | \(0.675411\pi\) | |||||||
\(272\) | −3.92000e10 | −0.434236 | ||||||||
\(273\) | −4.15522e10 | −0.452754 | ||||||||
\(274\) | −9.92923e10 | −1.06424 | ||||||||
\(275\) | 1.59136e11 | 1.67793 | ||||||||
\(276\) | 6.67506e9 | 0.0692411 | ||||||||
\(277\) | 6.68436e10 | 0.682183 | 0.341091 | − | 0.940030i | \(-0.389203\pi\) | ||||
0.341091 | + | 0.940030i | \(0.389203\pi\) | |||||||
\(278\) | −1.00029e11 | −1.00444 | ||||||||
\(279\) | 2.42201e10 | 0.239307 | ||||||||
\(280\) | 2.23905e11 | 2.17698 | ||||||||
\(281\) | 1.78845e11 | 1.71119 | 0.855595 | − | 0.517647i | \(-0.173192\pi\) | ||||
0.855595 | + | 0.517647i | \(0.173192\pi\) | |||||||
\(282\) | −1.70403e10 | −0.160456 | ||||||||
\(283\) | 8.69585e10 | 0.805885 | 0.402943 | − | 0.915225i | \(-0.367987\pi\) | ||||
0.402943 | + | 0.915225i | \(0.367987\pi\) | |||||||
\(284\) | 9.11882e10 | 0.831776 | ||||||||
\(285\) | 1.12084e11 | 1.00633 | ||||||||
\(286\) | −6.59169e10 | −0.582572 | ||||||||
\(287\) | −1.78700e11 | −1.55473 | ||||||||
\(288\) | 3.41504e10 | 0.292502 | ||||||||
\(289\) | 2.11681e11 | 1.78501 | ||||||||
\(290\) | −8.55806e10 | −0.710533 | ||||||||
\(291\) | 2.76648e10 | 0.226156 | ||||||||
\(292\) | 8.46666e10 | 0.681537 | ||||||||
\(293\) | −1.40207e11 | −1.11139 | −0.555693 | − | 0.831387i | \(-0.687547\pi\) | ||||
−0.555693 | + | 0.831387i | \(0.687547\pi\) | |||||||
\(294\) | −5.01696e10 | −0.391631 | ||||||||
\(295\) | −2.48207e10 | −0.190816 | ||||||||
\(296\) | 1.96826e11 | 1.49028 | ||||||||
\(297\) | −3.77106e10 | −0.281229 | ||||||||
\(298\) | 1.91119e11 | 1.40388 | ||||||||
\(299\) | −1.87868e10 | −0.135936 | ||||||||
\(300\) | 4.60278e10 | 0.328076 | ||||||||
\(301\) | 2.66085e11 | 1.86840 | ||||||||
\(302\) | −1.25268e11 | −0.866580 | ||||||||
\(303\) | 1.02196e11 | 0.696531 | ||||||||
\(304\) | 4.60792e10 | 0.309438 | ||||||||
\(305\) | 3.03319e11 | 2.00702 | ||||||||
\(306\) | 6.06365e10 | 0.395355 | ||||||||
\(307\) | −1.99661e11 | −1.28283 | −0.641417 | − | 0.767192i | \(-0.721653\pi\) | ||||
−0.641417 | + | 0.767192i | \(0.721653\pi\) | |||||||
\(308\) | 1.59674e11 | 1.01101 | ||||||||
\(309\) | 2.47147e10 | 0.154220 | ||||||||
\(310\) | 1.21602e11 | 0.747848 | ||||||||
\(311\) | −1.99334e11 | −1.20826 | −0.604130 | − | 0.796886i | \(-0.706479\pi\) | ||||
−0.604130 | + | 0.796886i | \(0.706479\pi\) | |||||||
\(312\) | −5.75905e10 | −0.344077 | ||||||||
\(313\) | −1.31175e11 | −0.772508 | −0.386254 | − | 0.922393i | \(-0.626231\pi\) | ||||
−0.386254 | + | 0.922393i | \(0.626231\pi\) | |||||||
\(314\) | 1.53231e11 | 0.889534 | ||||||||
\(315\) | −1.19351e11 | −0.683014 | ||||||||
\(316\) | 1.62960e11 | 0.919366 | ||||||||
\(317\) | 8.58630e10 | 0.477573 | 0.238786 | − | 0.971072i | \(-0.423250\pi\) | ||||
0.238786 | + | 0.971072i | \(0.423250\pi\) | |||||||
\(318\) | 5.64414e10 | 0.309511 | ||||||||
\(319\) | −1.84352e11 | −0.996760 | ||||||||
\(320\) | 2.42996e11 | 1.29546 | ||||||||
\(321\) | 1.00247e11 | 0.526987 | ||||||||
\(322\) | −4.64490e10 | −0.240782 | ||||||||
\(323\) | −3.88228e11 | −1.98461 | ||||||||
\(324\) | −1.09072e10 | −0.0549873 | ||||||||
\(325\) | −1.29544e11 | −0.644086 | ||||||||
\(326\) | −1.03336e11 | −0.506725 | ||||||||
\(327\) | 7.34055e10 | 0.355029 | ||||||||
\(328\) | −2.47674e11 | −1.18154 | ||||||||
\(329\) | −1.16175e11 | −0.546679 | ||||||||
\(330\) | −1.89335e11 | −0.878855 | ||||||||
\(331\) | −8.30618e10 | −0.380343 | −0.190171 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190171 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(332\) | 9.73720e10 | 0.439858 | ||||||||
\(333\) | −1.04917e11 | −0.467568 | ||||||||
\(334\) | 2.80263e10 | 0.123227 | ||||||||
\(335\) | 5.37136e10 | 0.233015 | ||||||||
\(336\) | −4.90668e10 | −0.210020 | ||||||||
\(337\) | −1.49661e11 | −0.632083 | −0.316042 | − | 0.948745i | \(-0.602354\pi\) | ||||
−0.316042 | + | 0.948745i | \(0.602354\pi\) | |||||||
\(338\) | −1.16878e11 | −0.487089 | ||||||||
\(339\) | 1.43798e11 | 0.591362 | ||||||||
\(340\) | −2.98273e11 | −1.21048 | ||||||||
\(341\) | 2.61947e11 | 1.04911 | ||||||||
\(342\) | −7.12776e10 | −0.281732 | ||||||||
\(343\) | 1.63318e10 | 0.0637104 | ||||||||
\(344\) | 3.68788e11 | 1.41992 | ||||||||
\(345\) | −5.39618e10 | −0.205069 | ||||||||
\(346\) | −2.09995e10 | −0.0787710 | ||||||||
\(347\) | −2.38151e11 | −0.881801 | −0.440900 | − | 0.897556i | \(-0.645341\pi\) | ||||
−0.440900 | + | 0.897556i | \(0.645341\pi\) | |||||||
\(348\) | −5.33211e10 | −0.194891 | ||||||||
\(349\) | 2.91117e11 | 1.05040 | 0.525199 | − | 0.850980i | \(-0.323991\pi\) | ||||
0.525199 | + | 0.850980i | \(0.323991\pi\) | |||||||
\(350\) | −3.20289e11 | −1.14087 | ||||||||
\(351\) | 3.06982e10 | 0.107952 | ||||||||
\(352\) | 3.69347e11 | 1.28231 | ||||||||
\(353\) | 4.63430e11 | 1.58854 | 0.794270 | − | 0.607565i | \(-0.207854\pi\) | ||||
0.794270 | + | 0.607565i | \(0.207854\pi\) | |||||||
\(354\) | 1.57842e10 | 0.0534205 | ||||||||
\(355\) | −7.37174e11 | −2.46344 | ||||||||
\(356\) | −1.00130e11 | −0.330399 | ||||||||
\(357\) | 4.13399e11 | 1.34699 | ||||||||
\(358\) | −1.52848e11 | −0.491798 | ||||||||
\(359\) | −3.43784e11 | −1.09235 | −0.546173 | − | 0.837672i | \(-0.683916\pi\) | ||||
−0.546173 | + | 0.837672i | \(0.683916\pi\) | |||||||
\(360\) | −1.65418e11 | −0.519066 | ||||||||
\(361\) | 1.33671e11 | 0.414242 | ||||||||
\(362\) | 1.02972e11 | 0.315160 | ||||||||
\(363\) | −2.16859e11 | −0.655536 | ||||||||
\(364\) | −1.29982e11 | −0.388086 | ||||||||
\(365\) | −6.84453e11 | −2.01849 | ||||||||
\(366\) | −1.92890e11 | −0.561881 | ||||||||
\(367\) | −5.88441e11 | −1.69319 | −0.846595 | − | 0.532237i | \(-0.821352\pi\) | ||||
−0.846595 | + | 0.532237i | \(0.821352\pi\) | |||||||
\(368\) | −2.21844e10 | −0.0630568 | ||||||||
\(369\) | 1.32021e11 | 0.370701 | ||||||||
\(370\) | −5.26757e11 | −1.46118 | ||||||||
\(371\) | 3.84799e11 | 1.05451 | ||||||||
\(372\) | 7.57643e10 | 0.205126 | ||||||||
\(373\) | −4.80252e11 | −1.28463 | −0.642317 | − | 0.766439i | \(-0.722027\pi\) | ||||
−0.642317 | + | 0.766439i | \(0.722027\pi\) | |||||||
\(374\) | 6.55802e11 | 1.73321 | ||||||||
\(375\) | −4.80365e10 | −0.125438 | ||||||||
\(376\) | −1.61017e11 | −0.415456 | ||||||||
\(377\) | 1.50071e11 | 0.382615 | ||||||||
\(378\) | 7.58990e10 | 0.191215 | ||||||||
\(379\) | 7.91147e10 | 0.196961 | 0.0984806 | − | 0.995139i | \(-0.468602\pi\) | ||||
0.0984806 | + | 0.995139i | \(0.468602\pi\) | |||||||
\(380\) | 3.50618e11 | 0.862596 | ||||||||
\(381\) | −3.43433e11 | −0.834988 | ||||||||
\(382\) | 3.79474e11 | 0.911793 | ||||||||
\(383\) | 5.13977e11 | 1.22053 | 0.610266 | − | 0.792197i | \(-0.291063\pi\) | ||||
0.610266 | + | 0.792197i | \(0.291063\pi\) | |||||||
\(384\) | 6.13357e10 | 0.143954 | ||||||||
\(385\) | −1.29082e12 | −2.99428 | ||||||||
\(386\) | −2.93819e10 | −0.0673655 | ||||||||
\(387\) | −1.96580e11 | −0.445492 | ||||||||
\(388\) | 8.65400e10 | 0.193854 | ||||||||
\(389\) | 5.24137e11 | 1.16057 | 0.580286 | − | 0.814413i | \(-0.302941\pi\) | ||||
0.580286 | + | 0.814413i | \(0.302941\pi\) | |||||||
\(390\) | 1.54127e11 | 0.337356 | ||||||||
\(391\) | 1.86909e11 | 0.404421 | ||||||||
\(392\) | −4.74060e11 | −1.01402 | ||||||||
\(393\) | 1.30205e11 | 0.275335 | ||||||||
\(394\) | 1.75219e11 | 0.366309 | ||||||||
\(395\) | −1.31738e12 | −2.72286 | ||||||||
\(396\) | −1.17965e11 | −0.241060 | ||||||||
\(397\) | 1.37630e11 | 0.278071 | 0.139036 | − | 0.990287i | \(-0.455600\pi\) | ||||
0.139036 | + | 0.990287i | \(0.455600\pi\) | |||||||
\(398\) | 6.28191e11 | 1.25492 | ||||||||
\(399\) | −4.85947e11 | −0.959867 | ||||||||
\(400\) | −1.52972e11 | −0.298774 | ||||||||
\(401\) | 9.21929e11 | 1.78052 | 0.890261 | − | 0.455450i | \(-0.150522\pi\) | ||||
0.890261 | + | 0.455450i | \(0.150522\pi\) | |||||||
\(402\) | −3.41581e10 | −0.0652344 | ||||||||
\(403\) | −2.13237e11 | −0.402708 | ||||||||
\(404\) | 3.19685e11 | 0.597043 | ||||||||
\(405\) | 8.81751e10 | 0.162854 | ||||||||
\(406\) | 3.71040e11 | 0.677725 | ||||||||
\(407\) | −1.13471e12 | −2.04978 | ||||||||
\(408\) | 5.72963e11 | 1.02366 | ||||||||
\(409\) | −2.01994e11 | −0.356931 | −0.178466 | − | 0.983946i | \(-0.557113\pi\) | ||||
−0.178466 | + | 0.983946i | \(0.557113\pi\) | |||||||
\(410\) | 6.62840e11 | 1.15846 | ||||||||
\(411\) | 5.00116e11 | 0.864535 | ||||||||
\(412\) | 7.73115e10 | 0.132192 | ||||||||
\(413\) | 1.07612e11 | 0.182005 | ||||||||
\(414\) | 3.43159e10 | 0.0574108 | ||||||||
\(415\) | −7.87164e11 | −1.30271 | ||||||||
\(416\) | −3.00665e11 | −0.492225 | ||||||||
\(417\) | 5.03827e11 | 0.815961 | ||||||||
\(418\) | −7.70889e11 | −1.23509 | ||||||||
\(419\) | 5.01944e11 | 0.795596 | 0.397798 | − | 0.917473i | \(-0.369775\pi\) | ||||
0.397798 | + | 0.917473i | \(0.369775\pi\) | |||||||
\(420\) | −3.73350e11 | −0.585457 | ||||||||
\(421\) | −7.66121e11 | −1.18858 | −0.594289 | − | 0.804251i | \(-0.702567\pi\) | ||||
−0.594289 | + | 0.804251i | \(0.702567\pi\) | |||||||
\(422\) | −1.98950e11 | −0.305379 | ||||||||
\(423\) | 8.58287e10 | 0.130347 | ||||||||
\(424\) | 5.33323e11 | 0.801390 | ||||||||
\(425\) | 1.28883e12 | 1.91622 | ||||||||
\(426\) | 4.68791e11 | 0.689661 | ||||||||
\(427\) | −1.31506e12 | −1.91434 | ||||||||
\(428\) | 3.13590e11 | 0.451716 | ||||||||
\(429\) | 3.32011e11 | 0.473254 | ||||||||
\(430\) | −9.86972e11 | −1.39218 | ||||||||
\(431\) | −2.97428e11 | −0.415177 | −0.207589 | − | 0.978216i | \(-0.566562\pi\) | ||||
−0.207589 | + | 0.978216i | \(0.566562\pi\) | |||||||
\(432\) | 3.62499e10 | 0.0500761 | ||||||||
\(433\) | 1.09804e12 | 1.50114 | 0.750569 | − | 0.660792i | \(-0.229779\pi\) | ||||
0.750569 | + | 0.660792i | \(0.229779\pi\) | |||||||
\(434\) | −5.27213e11 | −0.713316 | ||||||||
\(435\) | 4.31053e11 | 0.577203 | ||||||||
\(436\) | 2.29625e11 | 0.304319 | ||||||||
\(437\) | −2.19709e11 | −0.288192 | ||||||||
\(438\) | 4.35264e11 | 0.565092 | ||||||||
\(439\) | −8.54029e11 | −1.09744 | −0.548722 | − | 0.836005i | \(-0.684886\pi\) | ||||
−0.548722 | + | 0.836005i | \(0.684886\pi\) | |||||||
\(440\) | −1.78905e12 | −2.27555 | ||||||||
\(441\) | 2.52694e11 | 0.318143 | ||||||||
\(442\) | −5.33853e11 | −0.665307 | ||||||||
\(443\) | −3.63618e11 | −0.448568 | −0.224284 | − | 0.974524i | \(-0.572004\pi\) | ||||
−0.224284 | + | 0.974524i | \(0.572004\pi\) | |||||||
\(444\) | −3.28196e11 | −0.400784 | ||||||||
\(445\) | 8.09460e11 | 0.978533 | ||||||||
\(446\) | 1.41003e11 | 0.168741 | ||||||||
\(447\) | −9.62630e11 | −1.14045 | ||||||||
\(448\) | −1.05352e12 | −1.23564 | ||||||||
\(449\) | −2.76604e11 | −0.321181 | −0.160590 | − | 0.987021i | \(-0.551340\pi\) | ||||
−0.160590 | + | 0.987021i | \(0.551340\pi\) | |||||||
\(450\) | 2.36625e11 | 0.272022 | ||||||||
\(451\) | 1.42785e12 | 1.62513 | ||||||||
\(452\) | 4.49823e11 | 0.506896 | ||||||||
\(453\) | 6.30950e11 | 0.703968 | ||||||||
\(454\) | 2.25941e11 | 0.249599 | ||||||||
\(455\) | 1.05079e12 | 1.14938 | ||||||||
\(456\) | −6.73513e11 | −0.729464 | ||||||||
\(457\) | −2.71605e11 | −0.291283 | −0.145642 | − | 0.989337i | \(-0.546525\pi\) | ||||
−0.145642 | + | 0.989337i | \(0.546525\pi\) | |||||||
\(458\) | 9.14731e11 | 0.971402 | ||||||||
\(459\) | −3.05414e11 | −0.321168 | ||||||||
\(460\) | −1.68801e11 | −0.175778 | ||||||||
\(461\) | 5.93856e11 | 0.612388 | 0.306194 | − | 0.951969i | \(-0.400944\pi\) | ||||
0.306194 | + | 0.951969i | \(0.400944\pi\) | |||||||
\(462\) | 8.20871e11 | 0.838274 | ||||||||
\(463\) | −1.90507e11 | −0.192662 | −0.0963310 | − | 0.995349i | \(-0.530711\pi\) | ||||
−0.0963310 | + | 0.995349i | \(0.530711\pi\) | |||||||
\(464\) | 1.77211e11 | 0.177485 | ||||||||
\(465\) | −6.12486e11 | −0.607516 | ||||||||
\(466\) | −1.23215e12 | −1.21040 | ||||||||
\(467\) | −6.17353e11 | −0.600631 | −0.300315 | − | 0.953840i | \(-0.597092\pi\) | ||||
−0.300315 | + | 0.953840i | \(0.597092\pi\) | |||||||
\(468\) | 9.60291e10 | 0.0925330 | ||||||||
\(469\) | −2.32879e11 | −0.222255 | ||||||||
\(470\) | 4.30922e11 | 0.407341 | ||||||||
\(471\) | −7.71793e11 | −0.722615 | ||||||||
\(472\) | 1.49147e11 | 0.138317 | ||||||||
\(473\) | −2.12607e12 | −1.95300 | ||||||||
\(474\) | 8.37762e11 | 0.762286 | ||||||||
\(475\) | −1.51500e12 | −1.36550 | ||||||||
\(476\) | 1.29318e12 | 1.15459 | ||||||||
\(477\) | −2.84284e11 | −0.251432 | ||||||||
\(478\) | −3.79107e10 | −0.0332151 | ||||||||
\(479\) | −2.05297e11 | −0.178186 | −0.0890928 | − | 0.996023i | \(-0.528397\pi\) | ||||
−0.0890928 | + | 0.996023i | \(0.528397\pi\) | |||||||
\(480\) | −8.63607e11 | −0.742558 | ||||||||
\(481\) | 9.23703e11 | 0.786828 | ||||||||
\(482\) | −1.04130e12 | −0.878745 | ||||||||
\(483\) | 2.33954e11 | 0.195600 | ||||||||
\(484\) | −6.78369e11 | −0.561904 | ||||||||
\(485\) | −6.99597e11 | −0.574130 | ||||||||
\(486\) | −5.60732e10 | −0.0455923 | ||||||||
\(487\) | −1.89086e12 | −1.52328 | −0.761640 | − | 0.648001i | \(-0.775605\pi\) | ||||
−0.761640 | + | 0.648001i | \(0.775605\pi\) | |||||||
\(488\) | −1.82265e12 | −1.45483 | ||||||||
\(489\) | 5.20484e11 | 0.411640 | ||||||||
\(490\) | 1.26871e12 | 0.994212 | ||||||||
\(491\) | 1.01893e12 | 0.791187 | 0.395594 | − | 0.918426i | \(-0.370539\pi\) | ||||
0.395594 | + | 0.918426i | \(0.370539\pi\) | |||||||
\(492\) | 4.12983e11 | 0.317753 | ||||||||
\(493\) | −1.49305e12 | −1.13831 | ||||||||
\(494\) | 6.27540e11 | 0.474100 | ||||||||
\(495\) | 9.53641e11 | 0.713940 | ||||||||
\(496\) | −2.51801e11 | −0.186805 | ||||||||
\(497\) | 3.19606e12 | 2.34969 | ||||||||
\(498\) | 5.00581e11 | 0.364705 | ||||||||
\(499\) | 1.51606e12 | 1.09462 | 0.547311 | − | 0.836929i | \(-0.315651\pi\) | ||||
0.547311 | + | 0.836929i | \(0.315651\pi\) | |||||||
\(500\) | −1.50266e11 | −0.107522 | ||||||||
\(501\) | −1.41163e11 | −0.100104 | ||||||||
\(502\) | 1.26061e12 | 0.885959 | ||||||||
\(503\) | −2.25319e12 | −1.56943 | −0.784713 | − | 0.619859i | \(-0.787190\pi\) | ||||
−0.784713 | + | 0.619859i | \(0.787190\pi\) | |||||||
\(504\) | 7.17181e11 | 0.495098 | ||||||||
\(505\) | −2.58436e12 | −1.76824 | ||||||||
\(506\) | 3.71137e11 | 0.251685 | ||||||||
\(507\) | 5.88692e11 | 0.395688 | ||||||||
\(508\) | −1.07432e12 | −0.715724 | ||||||||
\(509\) | −1.89541e11 | −0.125162 | −0.0625812 | − | 0.998040i | \(-0.519933\pi\) | ||||
−0.0625812 | + | 0.998040i | \(0.519933\pi\) | |||||||
\(510\) | −1.53340e12 | −1.00367 | ||||||||
\(511\) | 2.96748e12 | 1.92528 | ||||||||
\(512\) | −7.84903e11 | −0.504779 | ||||||||
\(513\) | 3.59011e11 | 0.228865 | ||||||||
\(514\) | 1.80785e12 | 1.14242 | ||||||||
\(515\) | −6.24993e11 | −0.391510 | ||||||||
\(516\) | −6.14934e11 | −0.381861 | ||||||||
\(517\) | 9.28264e11 | 0.571431 | ||||||||
\(518\) | 2.28378e12 | 1.39371 | ||||||||
\(519\) | 1.05770e11 | 0.0639898 | ||||||||
\(520\) | 1.45637e12 | 0.873488 | ||||||||
\(521\) | 2.48369e11 | 0.147682 | 0.0738411 | − | 0.997270i | \(-0.476474\pi\) | ||||
0.0738411 | + | 0.997270i | \(0.476474\pi\) | |||||||
\(522\) | −2.74119e11 | −0.161593 | ||||||||
\(523\) | −2.94791e11 | −0.172289 | −0.0861443 | − | 0.996283i | \(-0.527455\pi\) | ||||
−0.0861443 | + | 0.996283i | \(0.527455\pi\) | |||||||
\(524\) | 4.07303e11 | 0.236008 | ||||||||
\(525\) | 1.61323e12 | 0.926787 | ||||||||
\(526\) | −6.09531e11 | −0.347184 | ||||||||
\(527\) | 2.12148e12 | 1.19809 | ||||||||
\(528\) | 3.92054e11 | 0.219530 | ||||||||
\(529\) | −1.69538e12 | −0.941273 | ||||||||
\(530\) | −1.42731e12 | −0.785737 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −1.52012e12 | −0.822766 | ||||||||
\(533\) | −1.16233e12 | −0.623819 | ||||||||
\(534\) | −5.14760e11 | −0.273948 | ||||||||
\(535\) | −2.53509e12 | −1.33783 | ||||||||
\(536\) | −3.22765e11 | −0.168906 | ||||||||
\(537\) | 7.69867e11 | 0.399513 | ||||||||
\(538\) | −6.54947e11 | −0.337044 | ||||||||
\(539\) | 2.73297e12 | 1.39471 | ||||||||
\(540\) | 2.75826e11 | 0.139593 | ||||||||
\(541\) | 2.55667e11 | 0.128318 | 0.0641590 | − | 0.997940i | \(-0.479564\pi\) | ||||
0.0641590 | + | 0.997940i | \(0.479564\pi\) | |||||||
\(542\) | −1.49527e12 | −0.744259 | ||||||||
\(543\) | −5.18650e11 | −0.256021 | ||||||||
\(544\) | 2.99129e12 | 1.46441 | ||||||||
\(545\) | −1.85631e12 | −0.901292 | ||||||||
\(546\) | −6.68227e11 | −0.321779 | ||||||||
\(547\) | −2.11030e12 | −1.00786 | −0.503932 | − | 0.863743i | \(-0.668114\pi\) | ||||
−0.503932 | + | 0.863743i | \(0.668114\pi\) | |||||||
\(548\) | 1.56445e12 | 0.741051 | ||||||||
\(549\) | 9.71548e11 | 0.456445 | ||||||||
\(550\) | 2.55917e12 | 1.19253 | ||||||||
\(551\) | 1.75506e12 | 0.811167 | ||||||||
\(552\) | 3.24256e11 | 0.148649 | ||||||||
\(553\) | 5.71158e12 | 2.59713 | ||||||||
\(554\) | 1.07495e12 | 0.484837 | ||||||||
\(555\) | 2.65317e12 | 1.18699 | ||||||||
\(556\) | 1.57605e12 | 0.699414 | ||||||||
\(557\) | −4.44566e12 | −1.95699 | −0.978493 | − | 0.206279i | \(-0.933865\pi\) | ||||
−0.978493 | + | 0.206279i | \(0.933865\pi\) | |||||||
\(558\) | 3.89498e11 | 0.170079 | ||||||||
\(559\) | 1.73072e12 | 0.749677 | ||||||||
\(560\) | 1.24082e12 | 0.533167 | ||||||||
\(561\) | −3.30315e12 | −1.40798 | ||||||||
\(562\) | 2.87612e12 | 1.21617 | ||||||||
\(563\) | 4.54146e12 | 1.90506 | 0.952528 | − | 0.304452i | \(-0.0984732\pi\) | ||||
0.952528 | + | 0.304452i | \(0.0984732\pi\) | |||||||
\(564\) | 2.68486e11 | 0.111729 | ||||||||
\(565\) | −3.63641e12 | −1.50126 | ||||||||
\(566\) | 1.39843e12 | 0.572754 | ||||||||
\(567\) | −3.82288e11 | −0.155334 | ||||||||
\(568\) | 4.42967e12 | 1.78568 | ||||||||
\(569\) | −3.69150e12 | −1.47638 | −0.738190 | − | 0.674593i | \(-0.764319\pi\) | ||||
−0.738190 | + | 0.674593i | \(0.764319\pi\) | |||||||
\(570\) | 1.80249e12 | 0.715216 | ||||||||
\(571\) | 2.45410e10 | 0.00966117 | 0.00483058 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483058 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(572\) | 1.03858e12 | 0.405658 | ||||||||
\(573\) | −1.91133e12 | −0.740697 | ||||||||
\(574\) | −2.87378e12 | −1.10497 | ||||||||
\(575\) | 7.29384e11 | 0.278260 | ||||||||
\(576\) | 7.78328e11 | 0.294620 | ||||||||
\(577\) | 2.34560e12 | 0.880974 | 0.440487 | − | 0.897759i | \(-0.354806\pi\) | ||||
0.440487 | + | 0.897759i | \(0.354806\pi\) | |||||||
\(578\) | 3.40418e12 | 1.26864 | ||||||||
\(579\) | 1.47991e11 | 0.0547245 | ||||||||
\(580\) | 1.34840e12 | 0.494760 | ||||||||
\(581\) | 3.41280e12 | 1.24256 | ||||||||
\(582\) | 4.44895e11 | 0.160733 | ||||||||
\(583\) | −3.07462e12 | −1.10226 | ||||||||
\(584\) | 4.11287e12 | 1.46315 | ||||||||
\(585\) | −7.76308e11 | −0.274052 | ||||||||
\(586\) | −2.25475e12 | −0.789878 | ||||||||
\(587\) | −2.42490e12 | −0.842990 | −0.421495 | − | 0.906831i | \(-0.638495\pi\) | ||||
−0.421495 | + | 0.906831i | \(0.638495\pi\) | |||||||
\(588\) | 7.90469e11 | 0.272701 | ||||||||
\(589\) | −2.49378e12 | −0.853767 | ||||||||
\(590\) | −3.99157e11 | −0.135616 | ||||||||
\(591\) | −8.82542e11 | −0.297572 | ||||||||
\(592\) | 1.09075e12 | 0.364988 | ||||||||
\(593\) | 2.29186e12 | 0.761101 | 0.380551 | − | 0.924760i | \(-0.375734\pi\) | ||||
0.380551 | + | 0.924760i | \(0.375734\pi\) | |||||||
\(594\) | −6.06448e11 | −0.199873 | ||||||||
\(595\) | −1.04542e13 | −3.41951 | ||||||||
\(596\) | −3.01127e12 | −0.977555 | ||||||||
\(597\) | −3.16407e12 | −1.01944 | ||||||||
\(598\) | −3.02123e11 | −0.0966113 | ||||||||
\(599\) | −5.21413e12 | −1.65486 | −0.827430 | − | 0.561569i | \(-0.810198\pi\) | ||||
−0.827430 | + | 0.561569i | \(0.810198\pi\) | |||||||
\(600\) | 2.23591e12 | 0.704325 | ||||||||
\(601\) | 1.28472e12 | 0.401674 | 0.200837 | − | 0.979625i | \(-0.435634\pi\) | ||||
0.200837 | + | 0.979625i | \(0.435634\pi\) | |||||||
\(602\) | 4.27907e12 | 1.32790 | ||||||||
\(603\) | 1.72048e11 | 0.0529933 | ||||||||
\(604\) | 1.97372e12 | 0.603418 | ||||||||
\(605\) | 5.48400e12 | 1.66417 | ||||||||
\(606\) | 1.64347e12 | 0.495034 | ||||||||
\(607\) | 1.50667e12 | 0.450474 | 0.225237 | − | 0.974304i | \(-0.427684\pi\) | ||||
0.225237 | + | 0.974304i | \(0.427684\pi\) | |||||||
\(608\) | −3.51624e12 | −1.04355 | ||||||||
\(609\) | −1.86886e12 | −0.550551 | ||||||||
\(610\) | 4.87787e12 | 1.42642 | ||||||||
\(611\) | −7.55650e11 | −0.219349 | ||||||||
\(612\) | −9.55385e11 | −0.275294 | ||||||||
\(613\) | 7.34445e11 | 0.210081 | 0.105041 | − | 0.994468i | \(-0.466503\pi\) | ||||
0.105041 | + | 0.994468i | \(0.466503\pi\) | |||||||
\(614\) | −3.21087e12 | −0.911728 | ||||||||
\(615\) | −3.33859e12 | −0.941078 | ||||||||
\(616\) | 7.75653e12 | 2.17047 | ||||||||
\(617\) | 6.90093e11 | 0.191701 | 0.0958505 | − | 0.995396i | \(-0.469443\pi\) | ||||
0.0958505 | + | 0.995396i | \(0.469443\pi\) | |||||||
\(618\) | 3.97452e11 | 0.109606 | ||||||||
\(619\) | −2.37314e12 | −0.649704 | −0.324852 | − | 0.945765i | \(-0.605314\pi\) | ||||
−0.324852 | + | 0.945765i | \(0.605314\pi\) | |||||||
\(620\) | −1.91596e12 | −0.520742 | ||||||||
\(621\) | −1.72842e11 | −0.0466378 | ||||||||
\(622\) | −3.20562e12 | −0.858727 | ||||||||
\(623\) | −3.50946e12 | −0.933349 | ||||||||
\(624\) | −3.19150e11 | −0.0842684 | ||||||||
\(625\) | −3.16540e12 | −0.829792 | ||||||||
\(626\) | −2.10951e12 | −0.549032 | ||||||||
\(627\) | 3.88282e12 | 1.00333 | ||||||||
\(628\) | −2.41430e12 | −0.619401 | ||||||||
\(629\) | −9.18984e12 | −2.34089 | ||||||||
\(630\) | −1.91936e12 | −0.485427 | ||||||||
\(631\) | 3.82877e12 | 0.961450 | 0.480725 | − | 0.876871i | \(-0.340374\pi\) | ||||
0.480725 | + | 0.876871i | \(0.340374\pi\) | |||||||
\(632\) | 7.91614e12 | 1.97372 | ||||||||
\(633\) | 1.00207e12 | 0.248075 | ||||||||
\(634\) | 1.38082e12 | 0.339418 | ||||||||
\(635\) | 8.68487e12 | 2.11973 | ||||||||
\(636\) | −8.89288e11 | −0.215519 | ||||||||
\(637\) | −2.22476e12 | −0.535373 | ||||||||
\(638\) | −2.96468e12 | −0.708411 | ||||||||
\(639\) | −2.36121e12 | −0.560248 | ||||||||
\(640\) | −1.55108e12 | −0.365447 | ||||||||
\(641\) | −8.41400e12 | −1.96853 | −0.984263 | − | 0.176708i | \(-0.943455\pi\) | ||||
−0.984263 | + | 0.176708i | \(0.943455\pi\) | |||||||
\(642\) | 1.61214e12 | 0.374537 | ||||||||
\(643\) | 6.56454e12 | 1.51445 | 0.757225 | − | 0.653155i | \(-0.226555\pi\) | ||||
0.757225 | + | 0.653155i | \(0.226555\pi\) | |||||||
\(644\) | 7.31848e11 | 0.167662 | ||||||||
\(645\) | 4.97118e12 | 1.13094 | ||||||||
\(646\) | −6.24334e12 | −1.41049 | ||||||||
\(647\) | −1.08070e12 | −0.242458 | −0.121229 | − | 0.992625i | \(-0.538684\pi\) | ||||
−0.121229 | + | 0.992625i | \(0.538684\pi\) | |||||||
\(648\) | −5.29844e11 | −0.118048 | ||||||||
\(649\) | −8.59839e11 | −0.190246 | ||||||||
\(650\) | −2.08329e12 | −0.457761 | ||||||||
\(651\) | 2.65547e12 | 0.579464 | ||||||||
\(652\) | 1.62816e12 | 0.352844 | ||||||||
\(653\) | 4.48631e12 | 0.965562 | 0.482781 | − | 0.875741i | \(-0.339627\pi\) | ||||
0.482781 | + | 0.875741i | \(0.339627\pi\) | |||||||
\(654\) | 1.18048e12 | 0.252324 | ||||||||
\(655\) | −3.29268e12 | −0.698978 | ||||||||
\(656\) | −1.37254e12 | −0.289373 | ||||||||
\(657\) | −2.19234e12 | −0.459054 | ||||||||
\(658\) | −1.86829e12 | −0.388532 | ||||||||
\(659\) | −2.37848e12 | −0.491264 | −0.245632 | − | 0.969363i | \(-0.578995\pi\) | ||||
−0.245632 | + | 0.969363i | \(0.578995\pi\) | |||||||
\(660\) | 2.98315e12 | 0.611965 | ||||||||
\(661\) | −7.15743e12 | −1.45831 | −0.729157 | − | 0.684347i | \(-0.760087\pi\) | ||||
−0.729157 | + | 0.684347i | \(0.760087\pi\) | |||||||
\(662\) | −1.33577e12 | −0.270315 | ||||||||
\(663\) | 2.68892e12 | 0.540463 | ||||||||
\(664\) | 4.73007e12 | 0.944302 | ||||||||
\(665\) | 1.22888e13 | 2.43676 | ||||||||
\(666\) | −1.68723e12 | −0.332307 | ||||||||
\(667\) | −8.44958e11 | −0.165298 | ||||||||
\(668\) | −4.41581e11 | −0.0858057 | ||||||||
\(669\) | −7.10202e11 | −0.137077 | ||||||||
\(670\) | 8.63803e11 | 0.165607 | ||||||||
\(671\) | 1.05076e13 | 2.00102 | ||||||||
\(672\) | 3.74422e12 | 0.708271 | ||||||||
\(673\) | 3.34043e12 | 0.627675 | 0.313838 | − | 0.949477i | \(-0.398385\pi\) | ||||
0.313838 | + | 0.949477i | \(0.398385\pi\) | |||||||
\(674\) | −2.40679e12 | −0.449231 | ||||||||
\(675\) | −1.19183e12 | −0.220978 | ||||||||
\(676\) | 1.84153e12 | 0.339170 | ||||||||
\(677\) | 1.16108e10 | 0.00212429 | 0.00106214 | − | 0.999999i | \(-0.499662\pi\) | ||||
0.00106214 | + | 0.999999i | \(0.499662\pi\) | |||||||
\(678\) | 2.31250e12 | 0.420290 | ||||||||
\(679\) | 3.03315e12 | 0.547620 | ||||||||
\(680\) | −1.44893e13 | −2.59871 | ||||||||
\(681\) | −1.13802e12 | −0.202763 | ||||||||
\(682\) | 4.21254e12 | 0.745614 | ||||||||
\(683\) | −2.75359e12 | −0.484179 | −0.242090 | − | 0.970254i | \(-0.577833\pi\) | ||||
−0.242090 | + | 0.970254i | \(0.577833\pi\) | |||||||
\(684\) | 1.12305e12 | 0.196176 | ||||||||
\(685\) | −1.26471e13 | −2.19474 | ||||||||
\(686\) | 2.62642e11 | 0.0452799 | ||||||||
\(687\) | −4.60732e12 | −0.789120 | ||||||||
\(688\) | 2.04372e12 | 0.347755 | ||||||||
\(689\) | 2.50288e12 | 0.423111 | ||||||||
\(690\) | −8.67793e11 | −0.145746 | ||||||||
\(691\) | 3.09917e12 | 0.517124 | 0.258562 | − | 0.965995i | \(-0.416751\pi\) | ||||
0.258562 | + | 0.965995i | \(0.416751\pi\) | |||||||
\(692\) | 3.30867e11 | 0.0548499 | ||||||||
\(693\) | −4.13457e12 | −0.680974 | ||||||||
\(694\) | −3.82986e12 | −0.626708 | ||||||||
\(695\) | −1.27410e13 | −2.07143 | ||||||||
\(696\) | −2.59019e12 | −0.418399 | ||||||||
\(697\) | 1.15640e13 | 1.85592 | ||||||||
\(698\) | 4.68164e12 | 0.746532 | ||||||||
\(699\) | 6.20612e12 | 0.983270 | ||||||||
\(700\) | 5.04645e12 | 0.794411 | ||||||||
\(701\) | 2.89435e12 | 0.452710 | 0.226355 | − | 0.974045i | \(-0.427319\pi\) | ||||
0.226355 | + | 0.974045i | \(0.427319\pi\) | |||||||
\(702\) | 4.93677e11 | 0.0767231 | ||||||||
\(703\) | 1.08026e13 | 1.66812 | ||||||||
\(704\) | 8.41786e12 | 1.29159 | ||||||||
\(705\) | −2.17047e12 | −0.330904 | ||||||||
\(706\) | 7.45271e12 | 1.12900 | ||||||||
\(707\) | 1.12046e13 | 1.68659 | ||||||||
\(708\) | −2.48695e11 | −0.0371979 | ||||||||
\(709\) | −3.07176e12 | −0.456540 | −0.228270 | − | 0.973598i | \(-0.573307\pi\) | ||||
−0.228270 | + | 0.973598i | \(0.573307\pi\) | |||||||
\(710\) | −1.18550e13 | −1.75080 | ||||||||
\(711\) | −4.21964e12 | −0.619245 | ||||||||
\(712\) | −4.86404e12 | −0.709312 | ||||||||
\(713\) | 1.20061e12 | 0.173979 | ||||||||
\(714\) | 6.64813e12 | 0.957322 | ||||||||
\(715\) | −8.39601e12 | −1.20142 | ||||||||
\(716\) | 2.40827e12 | 0.342450 | ||||||||
\(717\) | 1.90949e11 | 0.0269824 | ||||||||
\(718\) | −5.52860e12 | −0.776346 | ||||||||
\(719\) | −7.37377e12 | −1.02899 | −0.514493 | − | 0.857495i | \(-0.672020\pi\) | ||||
−0.514493 | + | 0.857495i | \(0.672020\pi\) | |||||||
\(720\) | −9.16702e11 | −0.127125 | ||||||||
\(721\) | 2.70970e12 | 0.373432 | ||||||||
\(722\) | 2.14964e12 | 0.294408 | ||||||||
\(723\) | 5.24481e12 | 0.713850 | ||||||||
\(724\) | −1.62242e12 | −0.219453 | ||||||||
\(725\) | −5.82640e12 | −0.783212 | ||||||||
\(726\) | −3.48744e12 | −0.465899 | ||||||||
\(727\) | 1.76907e11 | 0.0234877 | 0.0117438 | − | 0.999931i | \(-0.496262\pi\) | ||||
0.0117438 | + | 0.999931i | \(0.496262\pi\) | |||||||
\(728\) | −6.31418e12 | −0.833155 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −1.10071e13 | −1.43457 | ||||||||
\(731\) | −1.72188e13 | −2.23036 | ||||||||
\(732\) | 3.03916e12 | 0.391250 | ||||||||
\(733\) | 7.53574e12 | 0.964180 | 0.482090 | − | 0.876122i | \(-0.339878\pi\) | ||||
0.482090 | + | 0.876122i | \(0.339878\pi\) | |||||||
\(734\) | −9.46309e12 | −1.20337 | ||||||||
\(735\) | −6.39023e12 | −0.807650 | ||||||||
\(736\) | 1.69286e12 | 0.212652 | ||||||||
\(737\) | 1.86075e12 | 0.232319 | ||||||||
\(738\) | 2.12311e12 | 0.263463 | ||||||||
\(739\) | 9.74013e12 | 1.20134 | 0.600669 | − | 0.799498i | \(-0.294901\pi\) | ||||
0.600669 | + | 0.799498i | \(0.294901\pi\) | |||||||
\(740\) | 8.29955e12 | 1.01745 | ||||||||
\(741\) | −3.16079e12 | −0.385136 | ||||||||
\(742\) | 6.18819e12 | 0.749456 | ||||||||
\(743\) | −6.04164e12 | −0.727286 | −0.363643 | − | 0.931538i | \(-0.618467\pi\) | ||||
−0.363643 | + | 0.931538i | \(0.618467\pi\) | |||||||
\(744\) | 3.68042e12 | 0.440372 | ||||||||
\(745\) | 2.43434e13 | 2.89519 | ||||||||
\(746\) | −7.72323e12 | −0.913007 | ||||||||
\(747\) | −2.52133e12 | −0.296269 | ||||||||
\(748\) | −1.03328e13 | −1.20687 | ||||||||
\(749\) | 1.09910e13 | 1.27606 | ||||||||
\(750\) | −7.72505e11 | −0.0891508 | ||||||||
\(751\) | −1.86477e12 | −0.213917 | −0.106958 | − | 0.994264i | \(-0.534111\pi\) | ||||
−0.106958 | + | 0.994264i | \(0.534111\pi\) | |||||||
\(752\) | −8.92308e11 | −0.101750 | ||||||||
\(753\) | −6.34944e12 | −0.719711 | ||||||||
\(754\) | 2.41339e12 | 0.271930 | ||||||||
\(755\) | −1.59557e13 | −1.78712 | ||||||||
\(756\) | −1.19586e12 | −0.133147 | ||||||||
\(757\) | −1.42975e13 | −1.58244 | −0.791222 | − | 0.611528i | \(-0.790555\pi\) | ||||
−0.791222 | + | 0.611528i | \(0.790555\pi\) | |||||||
\(758\) | 1.27229e12 | 0.139983 | ||||||||
\(759\) | −1.86934e12 | −0.204457 | ||||||||
\(760\) | 1.70320e13 | 1.85185 | ||||||||
\(761\) | 7.40971e11 | 0.0800885 | 0.0400442 | − | 0.999198i | \(-0.487250\pi\) | ||||
0.0400442 | + | 0.999198i | \(0.487250\pi\) | |||||||
\(762\) | −5.52297e12 | −0.593437 | ||||||||
\(763\) | 8.04813e12 | 0.859675 | ||||||||
\(764\) | −5.97897e12 | −0.634901 | ||||||||
\(765\) | 7.72342e12 | 0.815330 | ||||||||
\(766\) | 8.26559e12 | 0.867449 | ||||||||
\(767\) | 6.99949e11 | 0.0730276 | ||||||||
\(768\) | 5.90618e12 | 0.612606 | ||||||||
\(769\) | −2.78398e12 | −0.287076 | −0.143538 | − | 0.989645i | \(-0.545848\pi\) | ||||
−0.143538 | + | 0.989645i | \(0.545848\pi\) | |||||||
\(770\) | −2.07585e13 | −2.12808 | ||||||||
\(771\) | −9.10577e12 | −0.928051 | ||||||||
\(772\) | 4.62941e11 | 0.0469080 | ||||||||
\(773\) | 7.72432e11 | 0.0778131 | 0.0389065 | − | 0.999243i | \(-0.487613\pi\) | ||||
0.0389065 | + | 0.999243i | \(0.487613\pi\) | |||||||
\(774\) | −3.16132e12 | −0.316617 | ||||||||
\(775\) | 8.27877e12 | 0.824343 | ||||||||
\(776\) | 4.20388e12 | 0.416171 | ||||||||
\(777\) | −1.15030e13 | −1.13218 | ||||||||
\(778\) | 8.42898e12 | 0.824835 | ||||||||
\(779\) | −1.35933e13 | −1.32254 | ||||||||
\(780\) | −2.42842e12 | −0.234908 | ||||||||
\(781\) | −2.55372e13 | −2.45608 | ||||||||
\(782\) | 3.00579e12 | 0.287428 | ||||||||
\(783\) | 1.38069e12 | 0.131270 | ||||||||
\(784\) | −2.62711e12 | −0.248345 | ||||||||
\(785\) | 1.95174e13 | 1.83446 | ||||||||
\(786\) | 2.09391e12 | 0.195685 | ||||||||
\(787\) | −1.05342e12 | −0.0978851 | −0.0489425 | − | 0.998802i | \(-0.515585\pi\) | ||||
−0.0489425 | + | 0.998802i | \(0.515585\pi\) | |||||||
\(788\) | −2.76074e12 | −0.255068 | ||||||||
\(789\) | 3.07009e12 | 0.282036 | ||||||||
\(790\) | −2.11856e13 | −1.93517 | ||||||||
\(791\) | 1.57659e13 | 1.43194 | ||||||||
\(792\) | −5.73042e12 | −0.517516 | ||||||||
\(793\) | −8.55367e12 | −0.768110 | ||||||||
\(794\) | 2.21331e12 | 0.197629 | ||||||||
\(795\) | 7.18908e12 | 0.638295 | ||||||||
\(796\) | −9.89774e12 | −0.873831 | ||||||||
\(797\) | −5.36649e12 | −0.471116 | −0.235558 | − | 0.971860i | \(-0.575692\pi\) | ||||
−0.235558 | + | 0.971860i | \(0.575692\pi\) | |||||||
\(798\) | −7.81482e12 | −0.682191 | ||||||||
\(799\) | 7.51790e12 | 0.652583 | ||||||||
\(800\) | 1.16731e13 | 1.00758 | ||||||||
\(801\) | 2.59274e12 | 0.222543 | ||||||||
\(802\) | 1.48261e13 | 1.26544 | ||||||||
\(803\) | −2.37108e13 | −2.01246 | ||||||||
\(804\) | 5.38193e11 | 0.0454241 | ||||||||
\(805\) | −5.91633e12 | −0.496559 | ||||||||
\(806\) | −3.42920e12 | −0.286210 | ||||||||
\(807\) | 3.29884e12 | 0.273798 | ||||||||
\(808\) | 1.55294e13 | 1.28175 | ||||||||
\(809\) | 6.93954e12 | 0.569590 | 0.284795 | − | 0.958589i | \(-0.408075\pi\) | ||||
0.284795 | + | 0.958589i | \(0.408075\pi\) | |||||||
\(810\) | 1.41800e12 | 0.115743 | ||||||||
\(811\) | −1.68670e12 | −0.136913 | −0.0684565 | − | 0.997654i | \(-0.521807\pi\) | ||||
−0.0684565 | + | 0.997654i | \(0.521807\pi\) | |||||||
\(812\) | −5.84609e12 | −0.471914 | ||||||||
\(813\) | 7.53141e12 | 0.604601 | ||||||||
\(814\) | −1.82479e13 | −1.45681 | ||||||||
\(815\) | −1.31622e13 | −1.04501 | ||||||||
\(816\) | 3.17520e12 | 0.250706 | ||||||||
\(817\) | 2.02405e13 | 1.58936 | ||||||||
\(818\) | −3.24840e12 | −0.253676 | ||||||||
\(819\) | 3.36573e12 | 0.261398 | ||||||||
\(820\) | −1.04437e13 | −0.806661 | ||||||||
\(821\) | 2.02395e13 | 1.55473 | 0.777365 | − | 0.629050i | \(-0.216556\pi\) | ||||
0.777365 | + | 0.629050i | \(0.216556\pi\) | |||||||
\(822\) | 8.04268e12 | 0.614437 | ||||||||
\(823\) | 8.31956e11 | 0.0632123 | 0.0316061 | − | 0.999500i | \(-0.489938\pi\) | ||||
0.0316061 | + | 0.999500i | \(0.489938\pi\) | |||||||
\(824\) | 3.75558e12 | 0.283795 | ||||||||
\(825\) | −1.28901e13 | −0.968751 | ||||||||
\(826\) | 1.73057e12 | 0.129354 | ||||||||
\(827\) | 1.16197e13 | 0.863813 | 0.431906 | − | 0.901918i | \(-0.357841\pi\) | ||||
0.431906 | + | 0.901918i | \(0.357841\pi\) | |||||||
\(828\) | −5.40680e11 | −0.0399764 | ||||||||
\(829\) | 2.32301e13 | 1.70827 | 0.854135 | − | 0.520051i | \(-0.174087\pi\) | ||||
0.854135 | + | 0.520051i | \(0.174087\pi\) | |||||||
\(830\) | −1.26589e13 | −0.925857 | ||||||||
\(831\) | −5.41433e12 | −0.393858 | ||||||||
\(832\) | −6.85253e12 | −0.495788 | ||||||||
\(833\) | 2.21340e13 | 1.59278 | ||||||||
\(834\) | 8.10236e12 | 0.579915 | ||||||||
\(835\) | 3.56978e12 | 0.254128 | ||||||||
\(836\) | 1.21461e13 | 0.860020 | ||||||||
\(837\) | −1.96182e12 | −0.138164 | ||||||||
\(838\) | 8.07208e12 | 0.565441 | ||||||||
\(839\) | 1.50688e13 | 1.04990 | 0.524952 | − | 0.851132i | \(-0.324083\pi\) | ||||
0.524952 | + | 0.851132i | \(0.324083\pi\) | |||||||
\(840\) | −1.81363e13 | −1.25688 | ||||||||
\(841\) | −7.75753e12 | −0.534738 | ||||||||
\(842\) | −1.23205e13 | −0.844739 | ||||||||
\(843\) | −1.44864e13 | −0.987955 | ||||||||
\(844\) | 3.13465e12 | 0.212642 | ||||||||
\(845\) | −1.48871e13 | −1.00451 | ||||||||
\(846\) | 1.38027e12 | 0.0926395 | ||||||||
\(847\) | −2.37762e13 | −1.58733 | ||||||||
\(848\) | 2.95553e12 | 0.196270 | ||||||||
\(849\) | −7.04364e12 | −0.465278 | ||||||||
\(850\) | 2.07264e13 | 1.36188 | ||||||||
\(851\) | −5.20079e12 | −0.339928 | ||||||||
\(852\) | −7.38625e12 | −0.480226 | ||||||||
\(853\) | −2.01905e13 | −1.30580 | −0.652900 | − | 0.757444i | \(-0.726448\pi\) | ||||
−0.652900 | + | 0.757444i | \(0.726448\pi\) | |||||||
\(854\) | −2.11483e13 | −1.36055 | ||||||||
\(855\) | −9.07881e12 | −0.581007 | ||||||||
\(856\) | 1.52334e13 | 0.969759 | ||||||||
\(857\) | −5.74789e11 | −0.0363994 | −0.0181997 | − | 0.999834i | \(-0.505793\pi\) | ||||
−0.0181997 | + | 0.999834i | \(0.505793\pi\) | |||||||
\(858\) | 5.33927e12 | 0.336348 | ||||||||
\(859\) | 1.93738e13 | 1.21407 | 0.607037 | − | 0.794674i | \(-0.292358\pi\) | ||||
0.607037 | + | 0.794674i | \(0.292358\pi\) | |||||||
\(860\) | 1.55507e13 | 0.969407 | ||||||||
\(861\) | 1.44747e13 | 0.897624 | ||||||||
\(862\) | −4.78312e12 | −0.295072 | ||||||||
\(863\) | −4.19691e12 | −0.257562 | −0.128781 | − | 0.991673i | \(-0.541106\pi\) | ||||
−0.128781 | + | 0.991673i | \(0.541106\pi\) | |||||||
\(864\) | −2.76618e12 | −0.168876 | ||||||||
\(865\) | −2.67476e12 | −0.162447 | ||||||||
\(866\) | 1.76582e13 | 1.06688 | ||||||||
\(867\) | −1.71462e13 | −1.03058 | ||||||||
\(868\) | 8.30674e12 | 0.496697 | ||||||||
\(869\) | −4.56367e13 | −2.71472 | ||||||||
\(870\) | 6.93203e12 | 0.410227 | ||||||||
\(871\) | −1.51474e12 | −0.0891775 | ||||||||
\(872\) | 1.11545e13 | 0.653322 | ||||||||
\(873\) | −2.24085e12 | −0.130571 | ||||||||
\(874\) | −3.53328e12 | −0.204822 | ||||||||
\(875\) | −5.26668e12 | −0.303739 | ||||||||
\(876\) | −6.85800e12 | −0.393485 | ||||||||
\(877\) | 1.32466e13 | 0.756148 | 0.378074 | − | 0.925775i | \(-0.376586\pi\) | ||||
0.378074 | + | 0.925775i | \(0.376586\pi\) | |||||||
\(878\) | −1.37342e13 | −0.779969 | ||||||||
\(879\) | 1.13568e13 | 0.641659 | ||||||||
\(880\) | −9.91441e12 | −0.557308 | ||||||||
\(881\) | 2.43165e13 | 1.35991 | 0.679955 | − | 0.733254i | \(-0.261999\pi\) | ||||
0.679955 | + | 0.733254i | \(0.261999\pi\) | |||||||
\(882\) | 4.06373e12 | 0.226108 | ||||||||
\(883\) | 1.97916e13 | 1.09562 | 0.547809 | − | 0.836604i | \(-0.315462\pi\) | ||||
0.547809 | + | 0.836604i | \(0.315462\pi\) | |||||||
\(884\) | 8.41137e12 | 0.463267 | ||||||||
\(885\) | 2.01048e12 | 0.110168 | ||||||||
\(886\) | −5.84757e12 | −0.318804 | ||||||||
\(887\) | −5.09160e12 | −0.276184 | −0.138092 | − | 0.990419i | \(-0.544097\pi\) | ||||
−0.138092 | + | 0.990419i | \(0.544097\pi\) | |||||||
\(888\) | −1.59429e13 | −0.860416 | ||||||||
\(889\) | −3.76538e13 | −2.02186 | ||||||||
\(890\) | 1.30174e13 | 0.695457 | ||||||||
\(891\) | 3.05456e12 | 0.162368 | ||||||||
\(892\) | −2.22163e12 | −0.117498 | ||||||||
\(893\) | −8.83722e12 | −0.465033 | ||||||||
\(894\) | −1.54807e13 | −0.810533 | ||||||||
\(895\) | −1.94687e13 | −1.01422 | ||||||||
\(896\) | 6.72480e12 | 0.348573 | ||||||||
\(897\) | 1.52173e12 | 0.0784824 | ||||||||
\(898\) | −4.44823e12 | −0.228268 | ||||||||
\(899\) | −9.59058e12 | −0.489695 | ||||||||
\(900\) | −3.72825e12 | −0.189415 | ||||||||
\(901\) | −2.49010e13 | −1.25879 | ||||||||
\(902\) | 2.29621e13 | 1.15500 | ||||||||
\(903\) | −2.15529e13 | −1.07872 | ||||||||
\(904\) | 2.18512e13 | 1.08822 | ||||||||
\(905\) | 1.31158e13 | 0.649945 | ||||||||
\(906\) | 1.01467e13 | 0.500320 | ||||||||
\(907\) | 3.51115e12 | 0.172273 | 0.0861364 | − | 0.996283i | \(-0.472548\pi\) | ||||
0.0861364 | + | 0.996283i | \(0.472548\pi\) | |||||||
\(908\) | −3.55991e12 | −0.173801 | ||||||||
\(909\) | −8.27784e12 | −0.402142 | ||||||||
\(910\) | 1.68984e13 | 0.816881 | ||||||||
\(911\) | −5.93968e12 | −0.285713 | −0.142857 | − | 0.989743i | \(-0.545629\pi\) | ||||
−0.142857 | + | 0.989743i | \(0.545629\pi\) | |||||||
\(912\) | −3.73242e12 | −0.178654 | ||||||||
\(913\) | −2.72689e13 | −1.29882 | ||||||||
\(914\) | −4.36786e12 | −0.207019 | ||||||||
\(915\) | −2.45689e13 | −1.15875 | ||||||||
\(916\) | −1.44125e13 | −0.676408 | ||||||||
\(917\) | 1.42756e13 | 0.666703 | ||||||||
\(918\) | −4.91155e12 | −0.228258 | ||||||||
\(919\) | −1.16149e12 | −0.0537151 | −0.0268576 | − | 0.999639i | \(-0.508550\pi\) | ||||
−0.0268576 | + | 0.999639i | \(0.508550\pi\) | |||||||
\(920\) | −8.19991e12 | −0.377367 | ||||||||
\(921\) | 1.61725e13 | 0.740645 | ||||||||
\(922\) | 9.55016e12 | 0.435233 | ||||||||
\(923\) | 2.07885e13 | 0.942789 | ||||||||
\(924\) | −1.29336e13 | −0.583708 | ||||||||
\(925\) | −3.58620e13 | −1.61064 | ||||||||
\(926\) | −3.06366e12 | −0.136928 | ||||||||
\(927\) | −2.00189e12 | −0.0890391 | ||||||||
\(928\) | −1.35227e13 | −0.598548 | ||||||||
\(929\) | −7.37213e12 | −0.324730 | −0.162365 | − | 0.986731i | \(-0.551912\pi\) | ||||
−0.162365 | + | 0.986731i | \(0.551912\pi\) | |||||||
\(930\) | −9.84977e12 | −0.431770 | ||||||||
\(931\) | −2.60183e13 | −1.13502 | ||||||||
\(932\) | 1.94138e13 | 0.842827 | ||||||||
\(933\) | 1.61461e13 | 0.697589 | ||||||||
\(934\) | −9.92804e12 | −0.426877 | ||||||||
\(935\) | 8.35312e13 | 3.57435 | ||||||||
\(936\) | 4.66483e12 | 0.198653 | ||||||||
\(937\) | 3.78723e13 | 1.60507 | 0.802534 | − | 0.596606i | \(-0.203485\pi\) | ||||
0.802534 | + | 0.596606i | \(0.203485\pi\) | |||||||
\(938\) | −3.74507e12 | −0.157960 | ||||||||
\(939\) | 1.06252e13 | 0.446008 | ||||||||
\(940\) | −6.78958e12 | −0.283640 | ||||||||
\(941\) | −6.80763e12 | −0.283037 | −0.141518 | − | 0.989936i | \(-0.545198\pi\) | ||||
−0.141518 | + | 0.989936i | \(0.545198\pi\) | |||||||
\(942\) | −1.24117e13 | −0.513573 | ||||||||
\(943\) | 6.54437e12 | 0.269504 | ||||||||
\(944\) | 8.26533e11 | 0.0338755 | ||||||||
\(945\) | 9.66745e12 | 0.394338 | ||||||||
\(946\) | −3.41907e13 | −1.38803 | ||||||||
\(947\) | −3.21838e12 | −0.130036 | −0.0650179 | − | 0.997884i | \(-0.520710\pi\) | ||||
−0.0650179 | + | 0.997884i | \(0.520710\pi\) | |||||||
\(948\) | −1.31997e13 | −0.530796 | ||||||||
\(949\) | 1.93017e13 | 0.772499 | ||||||||
\(950\) | −2.43637e13 | −0.970482 | ||||||||
\(951\) | −6.95491e12 | −0.275727 | ||||||||
\(952\) | 6.28192e13 | 2.47871 | ||||||||
\(953\) | 2.57077e13 | 1.00959 | 0.504796 | − | 0.863239i | \(-0.331568\pi\) | ||||
0.504796 | + | 0.863239i | \(0.331568\pi\) | |||||||
\(954\) | −4.57175e12 | −0.178696 | ||||||||
\(955\) | 4.83345e13 | 1.88037 | ||||||||
\(956\) | 5.97319e11 | 0.0231284 | ||||||||
\(957\) | 1.49325e13 | 0.575480 | ||||||||
\(958\) | −3.30151e12 | −0.126639 | ||||||||
\(959\) | 5.48323e13 | 2.09340 | ||||||||
\(960\) | −1.96827e13 | −0.747934 | ||||||||
\(961\) | −1.28123e13 | −0.484588 | ||||||||
\(962\) | 1.48546e13 | 0.559209 | ||||||||
\(963\) | −8.12004e12 | −0.304256 | ||||||||
\(964\) | 1.64066e13 | 0.611889 | ||||||||
\(965\) | −3.74245e12 | −0.138926 | ||||||||
\(966\) | 3.76237e12 | 0.139016 | ||||||||
\(967\) | 8.66214e12 | 0.318571 | 0.159285 | − | 0.987233i | \(-0.449081\pi\) | ||||
0.159285 | + | 0.987233i | \(0.449081\pi\) | |||||||
\(968\) | −3.29533e13 | −1.20631 | ||||||||
\(969\) | 3.14465e13 | 1.14582 | ||||||||
\(970\) | −1.12507e13 | −0.408042 | ||||||||
\(971\) | −2.16854e12 | −0.0782852 | −0.0391426 | − | 0.999234i | \(-0.512463\pi\) | ||||
−0.0391426 | + | 0.999234i | \(0.512463\pi\) | |||||||
\(972\) | 8.83486e11 | 0.0317469 | ||||||||
\(973\) | 5.52392e13 | 1.97579 | ||||||||
\(974\) | −3.04081e13 | −1.08262 | ||||||||
\(975\) | 1.04931e13 | 0.371863 | ||||||||
\(976\) | −1.01006e13 | −0.356305 | ||||||||
\(977\) | −4.24310e13 | −1.48990 | −0.744951 | − | 0.667120i | \(-0.767527\pi\) | ||||
−0.744951 | + | 0.667120i | \(0.767527\pi\) | |||||||
\(978\) | 8.37022e12 | 0.292558 | ||||||||
\(979\) | 2.80413e13 | 0.975610 | ||||||||
\(980\) | −1.99897e13 | −0.692291 | ||||||||
\(981\) | −5.94585e12 | −0.204976 | ||||||||
\(982\) | 1.63861e13 | 0.562308 | ||||||||
\(983\) | −5.52491e13 | −1.88727 | −0.943635 | − | 0.330987i | \(-0.892618\pi\) | ||||
−0.943635 | + | 0.330987i | \(0.892618\pi\) | |||||||
\(984\) | 2.00616e13 | 0.682162 | ||||||||
\(985\) | 2.23180e13 | 0.755428 | ||||||||
\(986\) | −2.40106e13 | −0.809016 | ||||||||
\(987\) | 9.41020e12 | 0.315625 | ||||||||
\(988\) | −9.88749e12 | −0.330126 | ||||||||
\(989\) | −9.74460e12 | −0.323878 | ||||||||
\(990\) | 1.53361e13 | 0.507407 | ||||||||
\(991\) | 2.15925e13 | 0.711167 | 0.355584 | − | 0.934644i | \(-0.384282\pi\) | ||||
0.355584 | + | 0.934644i | \(0.384282\pi\) | |||||||
\(992\) | 1.92145e13 | 0.629981 | ||||||||
\(993\) | 6.72801e12 | 0.219591 | ||||||||
\(994\) | 5.13978e13 | 1.66996 | ||||||||
\(995\) | 8.00143e13 | 2.58800 | ||||||||
\(996\) | −7.88713e12 | −0.253952 | ||||||||
\(997\) | 3.54323e12 | 0.113572 | 0.0567860 | − | 0.998386i | \(-0.481915\pi\) | ||||
0.0567860 | + | 0.998386i | \(0.481915\pi\) | |||||||
\(998\) | 2.43807e13 | 0.777964 | ||||||||
\(999\) | 8.49825e12 | 0.269951 |
(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 | 177.10.a.b.1.15 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.15 | ✓ | 21 | 1.1 | even | 1 | trivial |