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: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.3468 | −0.722431 | −0.361216 | − | 0.932482i | \(-0.617638\pi\) | ||||
−0.361216 | + | 0.932482i | \(0.617638\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | −244.784 | −0.478093 | ||||||||
\(5\) | −1401.93 | −1.00314 | −0.501569 | − | 0.865118i | \(-0.667244\pi\) | ||||
−0.501569 | + | 0.865118i | \(0.667244\pi\) | |||||||
\(6\) | −1324.09 | −0.417096 | ||||||||
\(7\) | 3361.75 | 0.529205 | 0.264602 | − | 0.964358i | \(-0.414759\pi\) | ||||
0.264602 | + | 0.964358i | \(0.414759\pi\) | |||||||
\(8\) | 12371.0 | 1.06782 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 22917.0 | 0.724698 | ||||||||
\(11\) | 31144.9 | 0.641387 | 0.320693 | − | 0.947183i | \(-0.396084\pi\) | ||||
0.320693 | + | 0.947183i | \(0.396084\pi\) | |||||||
\(12\) | −19827.5 | −0.276027 | ||||||||
\(13\) | 181333. | 1.76089 | 0.880445 | − | 0.474148i | \(-0.157244\pi\) | ||||
0.880445 | + | 0.474148i | \(0.157244\pi\) | |||||||
\(14\) | −54953.6 | −0.382314 | ||||||||
\(15\) | −113556. | −0.579162 | ||||||||
\(16\) | −76895.6 | −0.293334 | ||||||||
\(17\) | 560395. | 1.62733 | 0.813663 | − | 0.581337i | \(-0.197470\pi\) | ||||
0.813663 | + | 0.581337i | \(0.197470\pi\) | |||||||
\(18\) | −107251. | −0.240810 | ||||||||
\(19\) | −392444. | −0.690854 | −0.345427 | − | 0.938446i | \(-0.612266\pi\) | ||||
−0.345427 | + | 0.938446i | \(0.612266\pi\) | |||||||
\(20\) | 343169. | 0.479593 | ||||||||
\(21\) | 272301. | 0.305536 | ||||||||
\(22\) | −509118. | −0.463358 | ||||||||
\(23\) | −2.10816e6 | −1.57082 | −0.785412 | − | 0.618974i | \(-0.787549\pi\) | ||||
−0.785412 | + | 0.618974i | \(0.787549\pi\) | |||||||
\(24\) | 1.00205e6 | 0.616507 | ||||||||
\(25\) | 12274.7 | 0.00628466 | ||||||||
\(26\) | −2.96421e6 | −1.27212 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −822901. | −0.253009 | ||||||||
\(29\) | −1.57396e6 | −0.413239 | −0.206620 | − | 0.978421i | \(-0.566246\pi\) | ||||
−0.206620 | + | 0.978421i | \(0.566246\pi\) | |||||||
\(30\) | 1.85627e6 | 0.418404 | ||||||||
\(31\) | −2.88698e6 | −0.561457 | −0.280729 | − | 0.959787i | \(-0.590576\pi\) | ||||
−0.280729 | + | 0.959787i | \(0.590576\pi\) | |||||||
\(32\) | −5.07694e6 | −0.855907 | ||||||||
\(33\) | 2.52274e6 | 0.370305 | ||||||||
\(34\) | −9.16064e6 | −1.17563 | ||||||||
\(35\) | −4.71292e6 | −0.530865 | ||||||||
\(36\) | −1.60603e6 | −0.159364 | ||||||||
\(37\) | −2.17752e6 | −0.191009 | −0.0955046 | − | 0.995429i | \(-0.530446\pi\) | ||||
−0.0955046 | + | 0.995429i | \(0.530446\pi\) | |||||||
\(38\) | 6.41518e6 | 0.499094 | ||||||||
\(39\) | 1.46880e7 | 1.01665 | ||||||||
\(40\) | −1.73432e7 | −1.07117 | ||||||||
\(41\) | 1.94028e7 | 1.07235 | 0.536177 | − | 0.844106i | \(-0.319868\pi\) | ||||
0.536177 | + | 0.844106i | \(0.319868\pi\) | |||||||
\(42\) | −4.45124e6 | −0.220729 | ||||||||
\(43\) | 1.36630e7 | 0.609452 | 0.304726 | − | 0.952440i | \(-0.401435\pi\) | ||||
0.304726 | + | 0.952440i | \(0.401435\pi\) | |||||||
\(44\) | −7.62377e6 | −0.306643 | ||||||||
\(45\) | −9.19804e6 | −0.334379 | ||||||||
\(46\) | 3.44615e7 | 1.13481 | ||||||||
\(47\) | 1.56640e7 | 0.468234 | 0.234117 | − | 0.972208i | \(-0.424780\pi\) | ||||
0.234117 | + | 0.972208i | \(0.424780\pi\) | |||||||
\(48\) | −6.22855e6 | −0.169356 | ||||||||
\(49\) | −2.90523e7 | −0.719942 | ||||||||
\(50\) | −200652. | −0.00454023 | ||||||||
\(51\) | 4.53920e7 | 0.939537 | ||||||||
\(52\) | −4.43874e7 | −0.841870 | ||||||||
\(53\) | 7.05119e7 | 1.22750 | 0.613749 | − | 0.789501i | \(-0.289661\pi\) | ||||
0.613749 | + | 0.789501i | \(0.289661\pi\) | |||||||
\(54\) | −8.68733e6 | −0.139032 | ||||||||
\(55\) | −4.36629e7 | −0.643399 | ||||||||
\(56\) | 4.15880e7 | 0.565096 | ||||||||
\(57\) | −3.17879e7 | −0.398865 | ||||||||
\(58\) | 2.57291e7 | 0.298537 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | 2.77967e7 | 0.276893 | ||||||||
\(61\) | 1.38031e8 | 1.27641 | 0.638207 | − | 0.769865i | \(-0.279676\pi\) | ||||
0.638207 | + | 0.769865i | \(0.279676\pi\) | |||||||
\(62\) | 4.71928e7 | 0.405614 | ||||||||
\(63\) | 2.20564e7 | 0.176402 | ||||||||
\(64\) | 1.22362e8 | 0.911668 | ||||||||
\(65\) | −2.54216e8 | −1.76641 | ||||||||
\(66\) | −4.12386e7 | −0.267520 | ||||||||
\(67\) | 2.09373e8 | 1.26936 | 0.634678 | − | 0.772777i | \(-0.281133\pi\) | ||||
0.634678 | + | 0.772777i | \(0.281133\pi\) | |||||||
\(68\) | −1.37176e8 | −0.778013 | ||||||||
\(69\) | −1.70761e8 | −0.906915 | ||||||||
\(70\) | 7.70410e7 | 0.383513 | ||||||||
\(71\) | −1.48646e8 | −0.694210 | −0.347105 | − | 0.937826i | \(-0.612835\pi\) | ||||
−0.347105 | + | 0.937826i | \(0.612835\pi\) | |||||||
\(72\) | 8.11658e7 | 0.355940 | ||||||||
\(73\) | −2.48240e8 | −1.02310 | −0.511552 | − | 0.859252i | \(-0.670929\pi\) | ||||
−0.511552 | + | 0.859252i | \(0.670929\pi\) | |||||||
\(74\) | 3.55954e7 | 0.137991 | ||||||||
\(75\) | 994253. | 0.00362845 | ||||||||
\(76\) | 9.60639e7 | 0.330293 | ||||||||
\(77\) | 1.04701e8 | 0.339425 | ||||||||
\(78\) | −2.40101e8 | −0.734460 | ||||||||
\(79\) | −5.22199e8 | −1.50839 | −0.754196 | − | 0.656650i | \(-0.771973\pi\) | ||||
−0.754196 | + | 0.656650i | \(0.771973\pi\) | |||||||
\(80\) | 1.07802e8 | 0.294254 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −3.17173e8 | −0.774702 | ||||||||
\(83\) | 6.25714e8 | 1.44719 | 0.723593 | − | 0.690226i | \(-0.242489\pi\) | ||||
0.723593 | + | 0.690226i | \(0.242489\pi\) | |||||||
\(84\) | −6.66549e7 | −0.146075 | ||||||||
\(85\) | −7.85633e8 | −1.63243 | ||||||||
\(86\) | −2.23346e8 | −0.440287 | ||||||||
\(87\) | −1.27490e8 | −0.238584 | ||||||||
\(88\) | 3.85292e8 | 0.684886 | ||||||||
\(89\) | −6.80185e8 | −1.14914 | −0.574569 | − | 0.818456i | \(-0.694830\pi\) | ||||
−0.574569 | + | 0.818456i | \(0.694830\pi\) | |||||||
\(90\) | 1.50358e8 | 0.241566 | ||||||||
\(91\) | 6.09596e8 | 0.931871 | ||||||||
\(92\) | 5.16042e8 | 0.751000 | ||||||||
\(93\) | −2.33846e8 | −0.324157 | ||||||||
\(94\) | −2.56056e8 | −0.338267 | ||||||||
\(95\) | 5.50178e8 | 0.693021 | ||||||||
\(96\) | −4.11232e8 | −0.494158 | ||||||||
\(97\) | 9.35972e7 | 0.107347 | 0.0536735 | − | 0.998559i | \(-0.482907\pi\) | ||||
0.0536735 | + | 0.998559i | \(0.482907\pi\) | |||||||
\(98\) | 4.74910e8 | 0.520109 | ||||||||
\(99\) | 2.04342e8 | 0.213796 | ||||||||
\(100\) | −3.00465e6 | −0.00300465 | ||||||||
\(101\) | 1.18057e9 | 1.12888 | 0.564438 | − | 0.825475i | \(-0.309093\pi\) | ||||
0.564438 | + | 0.825475i | \(0.309093\pi\) | |||||||
\(102\) | −7.42012e8 | −0.678751 | ||||||||
\(103\) | −1.32026e8 | −0.115582 | −0.0577912 | − | 0.998329i | \(-0.518406\pi\) | ||||
−0.0577912 | + | 0.998329i | \(0.518406\pi\) | |||||||
\(104\) | 2.24327e9 | 1.88031 | ||||||||
\(105\) | −3.81747e8 | −0.306495 | ||||||||
\(106\) | −1.15264e9 | −0.886783 | ||||||||
\(107\) | 1.39713e9 | 1.03041 | 0.515205 | − | 0.857067i | \(-0.327716\pi\) | ||||
0.515205 | + | 0.857067i | \(0.327716\pi\) | |||||||
\(108\) | −1.30088e8 | −0.0920091 | ||||||||
\(109\) | 9.61582e8 | 0.652480 | 0.326240 | − | 0.945287i | \(-0.394218\pi\) | ||||
0.326240 | + | 0.945287i | \(0.394218\pi\) | |||||||
\(110\) | 7.13747e8 | 0.464812 | ||||||||
\(111\) | −1.76379e8 | −0.110279 | ||||||||
\(112\) | −2.58504e8 | −0.155233 | ||||||||
\(113\) | −3.28060e9 | −1.89278 | −0.946391 | − | 0.323024i | \(-0.895301\pi\) | ||||
−0.946391 | + | 0.323024i | \(0.895301\pi\) | |||||||
\(114\) | 5.19630e8 | 0.288152 | ||||||||
\(115\) | 2.95548e9 | 1.57575 | ||||||||
\(116\) | 3.85279e8 | 0.197567 | ||||||||
\(117\) | 1.18973e9 | 0.586963 | ||||||||
\(118\) | 1.98079e8 | 0.0940525 | ||||||||
\(119\) | 1.88391e9 | 0.861188 | ||||||||
\(120\) | −1.40480e9 | −0.618441 | ||||||||
\(121\) | −1.38794e9 | −0.588623 | ||||||||
\(122\) | −2.25636e9 | −0.922122 | ||||||||
\(123\) | 1.57163e9 | 0.619124 | ||||||||
\(124\) | 7.06686e8 | 0.268429 | ||||||||
\(125\) | 2.72093e9 | 0.996833 | ||||||||
\(126\) | −3.60551e8 | −0.127438 | ||||||||
\(127\) | 5.47584e9 | 1.86781 | 0.933907 | − | 0.357516i | \(-0.116376\pi\) | ||||
0.933907 | + | 0.357516i | \(0.116376\pi\) | |||||||
\(128\) | 5.99170e8 | 0.197290 | ||||||||
\(129\) | 1.10671e9 | 0.351867 | ||||||||
\(130\) | 4.15561e9 | 1.27611 | ||||||||
\(131\) | 3.05429e9 | 0.906128 | 0.453064 | − | 0.891478i | \(-0.350331\pi\) | ||||
0.453064 | + | 0.891478i | \(0.350331\pi\) | |||||||
\(132\) | −6.17525e8 | −0.177040 | ||||||||
\(133\) | −1.31930e9 | −0.365603 | ||||||||
\(134\) | −3.42256e9 | −0.917023 | ||||||||
\(135\) | −7.45042e8 | −0.193054 | ||||||||
\(136\) | 6.93263e9 | 1.73769 | ||||||||
\(137\) | −6.36427e9 | −1.54350 | −0.771748 | − | 0.635928i | \(-0.780618\pi\) | ||||
−0.771748 | + | 0.635928i | \(0.780618\pi\) | |||||||
\(138\) | 2.79138e9 | 0.655184 | ||||||||
\(139\) | 2.77153e9 | 0.629728 | 0.314864 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(140\) | 1.15365e9 | 0.253803 | ||||||||
\(141\) | 1.26879e9 | 0.270335 | ||||||||
\(142\) | 2.42988e9 | 0.501519 | ||||||||
\(143\) | 5.64761e9 | 1.12941 | ||||||||
\(144\) | −5.04512e8 | −0.0977779 | ||||||||
\(145\) | 2.20657e9 | 0.414536 | ||||||||
\(146\) | 4.05792e9 | 0.739122 | ||||||||
\(147\) | −2.35323e9 | −0.415659 | ||||||||
\(148\) | 5.33021e8 | 0.0913202 | ||||||||
\(149\) | 1.14918e10 | 1.91008 | 0.955040 | − | 0.296478i | \(-0.0958123\pi\) | ||||
0.955040 | + | 0.296478i | \(0.0958123\pi\) | |||||||
\(150\) | −1.62528e7 | −0.00262130 | ||||||||
\(151\) | −4.20609e9 | −0.658388 | −0.329194 | − | 0.944262i | \(-0.606777\pi\) | ||||
−0.329194 | + | 0.944262i | \(0.606777\pi\) | |||||||
\(152\) | −4.85490e9 | −0.737708 | ||||||||
\(153\) | 3.67675e9 | 0.542442 | ||||||||
\(154\) | −1.71153e9 | −0.245211 | ||||||||
\(155\) | 4.04734e9 | 0.563219 | ||||||||
\(156\) | −3.59538e9 | −0.486054 | ||||||||
\(157\) | −4.77264e9 | −0.626917 | −0.313459 | − | 0.949602i | \(-0.601488\pi\) | ||||
−0.313459 | + | 0.949602i | \(0.601488\pi\) | |||||||
\(158\) | 8.53626e9 | 1.08971 | ||||||||
\(159\) | 5.71146e9 | 0.708697 | ||||||||
\(160\) | 7.11749e9 | 0.858593 | ||||||||
\(161\) | −7.08708e9 | −0.831287 | ||||||||
\(162\) | −7.03674e8 | −0.0802701 | ||||||||
\(163\) | −8.24908e9 | −0.915295 | −0.457648 | − | 0.889134i | \(-0.651308\pi\) | ||||
−0.457648 | + | 0.889134i | \(0.651308\pi\) | |||||||
\(164\) | −4.74950e9 | −0.512685 | ||||||||
\(165\) | −3.53669e9 | −0.371467 | ||||||||
\(166\) | −1.02284e10 | −1.04549 | ||||||||
\(167\) | 4.76936e9 | 0.474499 | 0.237250 | − | 0.971449i | \(-0.423754\pi\) | ||||
0.237250 | + | 0.971449i | \(0.423754\pi\) | |||||||
\(168\) | 3.36863e9 | 0.326258 | ||||||||
\(169\) | 2.22772e10 | 2.10073 | ||||||||
\(170\) | 1.28426e10 | 1.17932 | ||||||||
\(171\) | −2.57482e9 | −0.230285 | ||||||||
\(172\) | −3.34449e9 | −0.291375 | ||||||||
\(173\) | −7.56434e9 | −0.642042 | −0.321021 | − | 0.947072i | \(-0.604026\pi\) | ||||
−0.321021 | + | 0.947072i | \(0.604026\pi\) | |||||||
\(174\) | 2.08405e9 | 0.172360 | ||||||||
\(175\) | 4.12645e7 | 0.00332587 | ||||||||
\(176\) | −2.39491e9 | −0.188140 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | 1.11188e10 | 0.830173 | ||||||||
\(179\) | 2.65450e10 | 1.93261 | 0.966303 | − | 0.257407i | \(-0.0828682\pi\) | ||||
0.966303 | + | 0.257407i | \(0.0828682\pi\) | |||||||
\(180\) | 2.25153e9 | 0.159864 | ||||||||
\(181\) | −5.67564e9 | −0.393062 | −0.196531 | − | 0.980498i | \(-0.562968\pi\) | ||||
−0.196531 | + | 0.980498i | \(0.562968\pi\) | |||||||
\(182\) | −9.96492e9 | −0.673213 | ||||||||
\(183\) | 1.11805e10 | 0.736938 | ||||||||
\(184\) | −2.60799e10 | −1.67736 | ||||||||
\(185\) | 3.05272e9 | 0.191608 | ||||||||
\(186\) | 3.82262e9 | 0.234181 | ||||||||
\(187\) | 1.74535e10 | 1.04375 | ||||||||
\(188\) | −3.83430e9 | −0.223859 | ||||||||
\(189\) | 1.78657e9 | 0.101845 | ||||||||
\(190\) | −8.99362e9 | −0.500660 | ||||||||
\(191\) | −1.78592e9 | −0.0970985 | −0.0485493 | − | 0.998821i | \(-0.515460\pi\) | ||||
−0.0485493 | + | 0.998821i | \(0.515460\pi\) | |||||||
\(192\) | 9.91132e9 | 0.526352 | ||||||||
\(193\) | −9.29193e9 | −0.482056 | −0.241028 | − | 0.970518i | \(-0.577485\pi\) | ||||
−0.241028 | + | 0.970518i | \(0.577485\pi\) | |||||||
\(194\) | −1.53001e9 | −0.0775509 | ||||||||
\(195\) | −2.05915e10 | −1.01984 | ||||||||
\(196\) | 7.11152e9 | 0.344200 | ||||||||
\(197\) | 2.37061e9 | 0.112141 | 0.0560703 | − | 0.998427i | \(-0.482143\pi\) | ||||
0.0560703 | + | 0.998427i | \(0.482143\pi\) | |||||||
\(198\) | −3.34032e9 | −0.154453 | ||||||||
\(199\) | −2.86581e10 | −1.29541 | −0.647706 | − | 0.761890i | \(-0.724271\pi\) | ||||
−0.647706 | + | 0.761890i | \(0.724271\pi\) | |||||||
\(200\) | 1.51850e8 | 0.00671089 | ||||||||
\(201\) | 1.69592e10 | 0.732863 | ||||||||
\(202\) | −1.92985e10 | −0.815535 | ||||||||
\(203\) | −5.29124e9 | −0.218688 | ||||||||
\(204\) | −1.11112e10 | −0.449186 | ||||||||
\(205\) | −2.72014e10 | −1.07572 | ||||||||
\(206\) | 2.15820e9 | 0.0835004 | ||||||||
\(207\) | −1.38316e10 | −0.523608 | ||||||||
\(208\) | −1.39437e10 | −0.516528 | ||||||||
\(209\) | −1.22226e10 | −0.443105 | ||||||||
\(210\) | 6.24032e9 | 0.221422 | ||||||||
\(211\) | −7.11025e9 | −0.246953 | −0.123476 | − | 0.992348i | \(-0.539404\pi\) | ||||
−0.123476 | + | 0.992348i | \(0.539404\pi\) | |||||||
\(212\) | −1.72602e10 | −0.586859 | ||||||||
\(213\) | −1.20403e10 | −0.400802 | ||||||||
\(214\) | −2.28385e10 | −0.744400 | ||||||||
\(215\) | −1.91546e10 | −0.611364 | ||||||||
\(216\) | 6.57443e9 | 0.205502 | ||||||||
\(217\) | −9.70530e9 | −0.297126 | ||||||||
\(218\) | −1.57187e10 | −0.471372 | ||||||||
\(219\) | −2.01075e10 | −0.590689 | ||||||||
\(220\) | 1.06880e10 | 0.307605 | ||||||||
\(221\) | 1.01618e11 | 2.86554 | ||||||||
\(222\) | 2.88322e9 | 0.0796691 | ||||||||
\(223\) | 1.40377e10 | 0.380124 | 0.190062 | − | 0.981772i | \(-0.439131\pi\) | ||||
0.190062 | + | 0.981772i | \(0.439131\pi\) | |||||||
\(224\) | −1.70674e10 | −0.452950 | ||||||||
\(225\) | 8.05345e7 | 0.00209489 | ||||||||
\(226\) | 5.36272e10 | 1.36740 | ||||||||
\(227\) | 6.18630e10 | 1.54637 | 0.773187 | − | 0.634178i | \(-0.218661\pi\) | ||||
0.773187 | + | 0.634178i | \(0.218661\pi\) | |||||||
\(228\) | 7.78117e9 | 0.190695 | ||||||||
\(229\) | −1.23510e9 | −0.0296786 | −0.0148393 | − | 0.999890i | \(-0.504724\pi\) | ||||
−0.0148393 | + | 0.999890i | \(0.504724\pi\) | |||||||
\(230\) | −4.83125e10 | −1.13837 | ||||||||
\(231\) | 8.48080e9 | 0.195967 | ||||||||
\(232\) | −1.94713e10 | −0.441266 | ||||||||
\(233\) | 1.31833e10 | 0.293036 | 0.146518 | − | 0.989208i | \(-0.453193\pi\) | ||||
0.146518 | + | 0.989208i | \(0.453193\pi\) | |||||||
\(234\) | −1.94482e10 | −0.424041 | ||||||||
\(235\) | −2.19598e10 | −0.469703 | ||||||||
\(236\) | 2.96613e9 | 0.0622424 | ||||||||
\(237\) | −4.22981e10 | −0.870870 | ||||||||
\(238\) | −3.07957e10 | −0.622149 | ||||||||
\(239\) | 7.31541e10 | 1.45027 | 0.725133 | − | 0.688608i | \(-0.241778\pi\) | ||||
0.725133 | + | 0.688608i | \(0.241778\pi\) | |||||||
\(240\) | 8.73197e9 | 0.169888 | ||||||||
\(241\) | 6.96186e10 | 1.32938 | 0.664689 | − | 0.747120i | \(-0.268564\pi\) | ||||
0.664689 | + | 0.747120i | \(0.268564\pi\) | |||||||
\(242\) | 2.26883e10 | 0.425240 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | −3.37877e10 | −0.610245 | ||||||||
\(245\) | 4.07292e10 | 0.722201 | ||||||||
\(246\) | −2.56910e10 | −0.447274 | ||||||||
\(247\) | −7.11631e10 | −1.21652 | ||||||||
\(248\) | −3.57147e10 | −0.599535 | ||||||||
\(249\) | 5.06829e10 | 0.835534 | ||||||||
\(250\) | −4.44784e10 | −0.720143 | ||||||||
\(251\) | −5.79655e10 | −0.921802 | −0.460901 | − | 0.887452i | \(-0.652474\pi\) | ||||
−0.460901 | + | 0.887452i | \(0.652474\pi\) | |||||||
\(252\) | −5.39905e9 | −0.0843364 | ||||||||
\(253\) | −6.56583e10 | −1.00751 | ||||||||
\(254\) | −8.95121e10 | −1.34937 | ||||||||
\(255\) | −6.36363e10 | −0.942484 | ||||||||
\(256\) | −7.24438e10 | −1.05420 | ||||||||
\(257\) | 1.10867e10 | 0.158527 | 0.0792633 | − | 0.996854i | \(-0.474743\pi\) | ||||
0.0792633 | + | 0.996854i | \(0.474743\pi\) | |||||||
\(258\) | −1.80910e10 | −0.254200 | ||||||||
\(259\) | −7.32026e9 | −0.101083 | ||||||||
\(260\) | 6.22279e10 | 0.844511 | ||||||||
\(261\) | −1.03267e10 | −0.137746 | ||||||||
\(262\) | −4.99277e10 | −0.654615 | ||||||||
\(263\) | 1.03693e11 | 1.33644 | 0.668222 | − | 0.743962i | \(-0.267056\pi\) | ||||
0.668222 | + | 0.743962i | \(0.267056\pi\) | |||||||
\(264\) | 3.12087e10 | 0.395419 | ||||||||
\(265\) | −9.88525e10 | −1.23135 | ||||||||
\(266\) | 2.15662e10 | 0.264123 | ||||||||
\(267\) | −5.50950e10 | −0.663455 | ||||||||
\(268\) | −5.12510e10 | −0.606871 | ||||||||
\(269\) | 4.72847e10 | 0.550599 | 0.275299 | − | 0.961359i | \(-0.411223\pi\) | ||||
0.275299 | + | 0.961359i | \(0.411223\pi\) | |||||||
\(270\) | 1.21790e10 | 0.139468 | ||||||||
\(271\) | 1.34795e10 | 0.151814 | 0.0759070 | − | 0.997115i | \(-0.475815\pi\) | ||||
0.0759070 | + | 0.997115i | \(0.475815\pi\) | |||||||
\(272\) | −4.30920e10 | −0.477349 | ||||||||
\(273\) | 4.93773e10 | 0.538016 | ||||||||
\(274\) | 1.04035e11 | 1.11507 | ||||||||
\(275\) | 3.82295e8 | 0.00403090 | ||||||||
\(276\) | 4.17994e10 | 0.433590 | ||||||||
\(277\) | 1.74328e11 | 1.77913 | 0.889564 | − | 0.456810i | \(-0.151008\pi\) | ||||
0.889564 | + | 0.456810i | \(0.151008\pi\) | |||||||
\(278\) | −4.53055e10 | −0.454935 | ||||||||
\(279\) | −1.89415e10 | −0.187152 | ||||||||
\(280\) | −5.83033e10 | −0.566869 | ||||||||
\(281\) | 1.10032e11 | 1.05278 | 0.526392 | − | 0.850242i | \(-0.323545\pi\) | ||||
0.526392 | + | 0.850242i | \(0.323545\pi\) | |||||||
\(282\) | −2.07405e10 | −0.195298 | ||||||||
\(283\) | −8.34242e10 | −0.773131 | −0.386566 | − | 0.922262i | \(-0.626339\pi\) | ||||
−0.386566 | + | 0.922262i | \(0.626339\pi\) | |||||||
\(284\) | 3.63862e10 | 0.331897 | ||||||||
\(285\) | 4.45644e10 | 0.400116 | ||||||||
\(286\) | −9.23200e10 | −0.815922 | ||||||||
\(287\) | 6.52274e10 | 0.567495 | ||||||||
\(288\) | −3.33098e10 | −0.285302 | ||||||||
\(289\) | 1.95455e11 | 1.64819 | ||||||||
\(290\) | −3.60703e10 | −0.299474 | ||||||||
\(291\) | 7.58137e9 | 0.0619769 | ||||||||
\(292\) | 6.07652e10 | 0.489139 | ||||||||
\(293\) | 8.47020e10 | 0.671412 | 0.335706 | − | 0.941967i | \(-0.391025\pi\) | ||||
0.335706 | + | 0.941967i | \(0.391025\pi\) | |||||||
\(294\) | 3.84677e10 | 0.300285 | ||||||||
\(295\) | 1.69877e10 | 0.130597 | ||||||||
\(296\) | −2.69380e10 | −0.203963 | ||||||||
\(297\) | 1.65517e10 | 0.123435 | ||||||||
\(298\) | −1.87854e11 | −1.37990 | ||||||||
\(299\) | −3.82279e11 | −2.76605 | ||||||||
\(300\) | −2.43377e8 | −0.00173474 | ||||||||
\(301\) | 4.59317e10 | 0.322525 | ||||||||
\(302\) | 6.87558e10 | 0.475640 | ||||||||
\(303\) | 9.56263e10 | 0.651757 | ||||||||
\(304\) | 3.01772e10 | 0.202651 | ||||||||
\(305\) | −1.93509e11 | −1.28042 | ||||||||
\(306\) | −6.01030e10 | −0.391877 | ||||||||
\(307\) | −2.10679e11 | −1.35363 | −0.676814 | − | 0.736154i | \(-0.736640\pi\) | ||||
−0.676814 | + | 0.736154i | \(0.736640\pi\) | |||||||
\(308\) | −2.56292e10 | −0.162277 | ||||||||
\(309\) | −1.06941e10 | −0.0667316 | ||||||||
\(310\) | −6.61608e10 | −0.406887 | ||||||||
\(311\) | 2.21798e11 | 1.34442 | 0.672211 | − | 0.740359i | \(-0.265345\pi\) | ||||
0.672211 | + | 0.740359i | \(0.265345\pi\) | |||||||
\(312\) | 1.81704e11 | 1.08560 | ||||||||
\(313\) | −2.84657e11 | −1.67638 | −0.838189 | − | 0.545380i | \(-0.816385\pi\) | ||||
−0.838189 | + | 0.545380i | \(0.816385\pi\) | |||||||
\(314\) | 7.80172e10 | 0.452905 | ||||||||
\(315\) | −3.09215e10 | −0.176955 | ||||||||
\(316\) | 1.27826e11 | 0.721152 | ||||||||
\(317\) | 3.66864e9 | 0.0204051 | 0.0102026 | − | 0.999948i | \(-0.496752\pi\) | ||||
0.0102026 | + | 0.999948i | \(0.496752\pi\) | |||||||
\(318\) | −9.33639e10 | −0.511985 | ||||||||
\(319\) | −4.90207e10 | −0.265046 | ||||||||
\(320\) | −1.71543e11 | −0.914528 | ||||||||
\(321\) | 1.13168e11 | 0.594907 | ||||||||
\(322\) | 1.15851e11 | 0.600548 | ||||||||
\(323\) | −2.19924e11 | −1.12424 | ||||||||
\(324\) | −1.05371e10 | −0.0531215 | ||||||||
\(325\) | 2.22582e9 | 0.0110666 | ||||||||
\(326\) | 1.34846e11 | 0.661238 | ||||||||
\(327\) | 7.78881e10 | 0.376709 | ||||||||
\(328\) | 2.40032e11 | 1.14508 | ||||||||
\(329\) | 5.26584e10 | 0.247791 | ||||||||
\(330\) | 5.78135e10 | 0.268359 | ||||||||
\(331\) | 1.19871e11 | 0.548895 | 0.274447 | − | 0.961602i | \(-0.411505\pi\) | ||||
0.274447 | + | 0.961602i | \(0.411505\pi\) | |||||||
\(332\) | −1.53165e11 | −0.691890 | ||||||||
\(333\) | −1.42867e10 | −0.0636697 | ||||||||
\(334\) | −7.79635e10 | −0.342793 | ||||||||
\(335\) | −2.93525e11 | −1.27334 | ||||||||
\(336\) | −2.09388e10 | −0.0896241 | ||||||||
\(337\) | −2.27970e11 | −0.962816 | −0.481408 | − | 0.876497i | \(-0.659874\pi\) | ||||
−0.481408 | + | 0.876497i | \(0.659874\pi\) | |||||||
\(338\) | −3.64161e11 | −1.51764 | ||||||||
\(339\) | −2.65729e11 | −1.09280 | ||||||||
\(340\) | 1.92310e11 | 0.780454 | ||||||||
\(341\) | −8.99148e10 | −0.360111 | ||||||||
\(342\) | 4.20900e10 | 0.166365 | ||||||||
\(343\) | −2.33325e11 | −0.910201 | ||||||||
\(344\) | 1.69025e11 | 0.650785 | ||||||||
\(345\) | 2.39394e11 | 0.909761 | ||||||||
\(346\) | 1.23652e11 | 0.463831 | ||||||||
\(347\) | 2.82682e11 | 1.04668 | 0.523341 | − | 0.852123i | \(-0.324685\pi\) | ||||
0.523341 | + | 0.852123i | \(0.324685\pi\) | |||||||
\(348\) | 3.12076e10 | 0.114065 | ||||||||
\(349\) | −2.13705e11 | −0.771082 | −0.385541 | − | 0.922691i | \(-0.625985\pi\) | ||||
−0.385541 | + | 0.922691i | \(0.625985\pi\) | |||||||
\(350\) | −6.74540e8 | −0.00240271 | ||||||||
\(351\) | 9.63679e10 | 0.338884 | ||||||||
\(352\) | −1.58121e11 | −0.548968 | ||||||||
\(353\) | −1.01077e11 | −0.346472 | −0.173236 | − | 0.984880i | \(-0.555422\pi\) | ||||
−0.173236 | + | 0.984880i | \(0.555422\pi\) | |||||||
\(354\) | 1.60444e10 | 0.0543012 | ||||||||
\(355\) | 2.08391e11 | 0.696388 | ||||||||
\(356\) | 1.66498e11 | 0.549395 | ||||||||
\(357\) | 1.52596e11 | 0.497207 | ||||||||
\(358\) | −4.33924e11 | −1.39617 | ||||||||
\(359\) | 6.52223e10 | 0.207239 | 0.103619 | − | 0.994617i | \(-0.466958\pi\) | ||||
0.103619 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(360\) | −1.13789e11 | −0.357057 | ||||||||
\(361\) | −1.68676e11 | −0.522721 | ||||||||
\(362\) | 9.27782e10 | 0.283960 | ||||||||
\(363\) | −1.12423e11 | −0.339842 | ||||||||
\(364\) | −1.49219e11 | −0.445521 | ||||||||
\(365\) | 3.48015e11 | 1.02631 | ||||||||
\(366\) | −1.82765e11 | −0.532387 | ||||||||
\(367\) | 5.97288e11 | 1.71865 | 0.859323 | − | 0.511434i | \(-0.170885\pi\) | ||||
0.859323 | + | 0.511434i | \(0.170885\pi\) | |||||||
\(368\) | 1.62108e11 | 0.460775 | ||||||||
\(369\) | 1.27302e11 | 0.357451 | ||||||||
\(370\) | −4.99021e10 | −0.138424 | ||||||||
\(371\) | 2.37043e11 | 0.649598 | ||||||||
\(372\) | 5.72416e10 | 0.154977 | ||||||||
\(373\) | −5.35635e11 | −1.43278 | −0.716389 | − | 0.697701i | \(-0.754206\pi\) | ||||
−0.716389 | + | 0.697701i | \(0.754206\pi\) | |||||||
\(374\) | −2.85307e11 | −0.754034 | ||||||||
\(375\) | 2.20395e11 | 0.575522 | ||||||||
\(376\) | 1.93779e11 | 0.499990 | ||||||||
\(377\) | −2.85411e11 | −0.727669 | ||||||||
\(378\) | −2.92046e10 | −0.0735763 | ||||||||
\(379\) | 3.00653e11 | 0.748496 | 0.374248 | − | 0.927329i | \(-0.377901\pi\) | ||||
0.374248 | + | 0.927329i | \(0.377901\pi\) | |||||||
\(380\) | −1.34675e11 | −0.331329 | ||||||||
\(381\) | 4.43543e11 | 1.07838 | ||||||||
\(382\) | 2.91940e10 | 0.0701470 | ||||||||
\(383\) | 1.30463e11 | 0.309809 | 0.154905 | − | 0.987929i | \(-0.450493\pi\) | ||||
0.154905 | + | 0.987929i | \(0.450493\pi\) | |||||||
\(384\) | 4.85328e10 | 0.113906 | ||||||||
\(385\) | −1.46784e11 | −0.340490 | ||||||||
\(386\) | 1.51893e11 | 0.348253 | ||||||||
\(387\) | 8.96432e10 | 0.203151 | ||||||||
\(388\) | −2.29111e10 | −0.0513219 | ||||||||
\(389\) | 7.22330e11 | 1.59942 | 0.799710 | − | 0.600386i | \(-0.204986\pi\) | ||||
0.799710 | + | 0.600386i | \(0.204986\pi\) | |||||||
\(390\) | 3.36604e11 | 0.736764 | ||||||||
\(391\) | −1.18140e12 | −2.55624 | ||||||||
\(392\) | −3.59404e11 | −0.768769 | ||||||||
\(393\) | 2.47397e11 | 0.523153 | ||||||||
\(394\) | −3.87518e10 | −0.0810139 | ||||||||
\(395\) | 7.32085e11 | 1.51312 | ||||||||
\(396\) | −5.00195e10 | −0.102214 | ||||||||
\(397\) | 6.36817e11 | 1.28664 | 0.643321 | − | 0.765597i | \(-0.277556\pi\) | ||||
0.643321 | + | 0.765597i | \(0.277556\pi\) | |||||||
\(398\) | 4.68466e11 | 0.935846 | ||||||||
\(399\) | −1.06863e11 | −0.211081 | ||||||||
\(400\) | −9.43873e8 | −0.00184350 | ||||||||
\(401\) | 3.75683e11 | 0.725557 | 0.362778 | − | 0.931875i | \(-0.381828\pi\) | ||||
0.362778 | + | 0.931875i | \(0.381828\pi\) | |||||||
\(402\) | −2.77228e11 | −0.529443 | ||||||||
\(403\) | −5.23506e11 | −0.988664 | ||||||||
\(404\) | −2.88985e11 | −0.539708 | ||||||||
\(405\) | −6.03484e10 | −0.111460 | ||||||||
\(406\) | 8.64946e10 | 0.157987 | ||||||||
\(407\) | −6.78186e10 | −0.122511 | ||||||||
\(408\) | 5.61543e11 | 1.00326 | ||||||||
\(409\) | −4.30578e11 | −0.760847 | −0.380424 | − | 0.924812i | \(-0.624222\pi\) | ||||
−0.380424 | + | 0.924812i | \(0.624222\pi\) | |||||||
\(410\) | 4.44654e11 | 0.777132 | ||||||||
\(411\) | −5.15506e11 | −0.891138 | ||||||||
\(412\) | 3.23178e10 | 0.0552592 | ||||||||
\(413\) | −4.07355e10 | −0.0688966 | ||||||||
\(414\) | 2.26102e11 | 0.378271 | ||||||||
\(415\) | −8.77206e11 | −1.45173 | ||||||||
\(416\) | −9.20617e11 | −1.50716 | ||||||||
\(417\) | 2.24494e11 | 0.363574 | ||||||||
\(418\) | 1.99800e11 | 0.320113 | ||||||||
\(419\) | −4.21627e11 | −0.668291 | −0.334146 | − | 0.942521i | \(-0.608448\pi\) | ||||
−0.334146 | + | 0.942521i | \(0.608448\pi\) | |||||||
\(420\) | 9.34454e10 | 0.146533 | ||||||||
\(421\) | 5.44686e11 | 0.845039 | 0.422519 | − | 0.906354i | \(-0.361146\pi\) | ||||
0.422519 | + | 0.906354i | \(0.361146\pi\) | |||||||
\(422\) | 1.16230e11 | 0.178406 | ||||||||
\(423\) | 1.02772e11 | 0.156078 | ||||||||
\(424\) | 8.72300e11 | 1.31075 | ||||||||
\(425\) | 6.87870e9 | 0.0102272 | ||||||||
\(426\) | 1.96820e11 | 0.289552 | ||||||||
\(427\) | 4.64024e11 | 0.675485 | ||||||||
\(428\) | −3.41995e11 | −0.492632 | ||||||||
\(429\) | 4.57456e11 | 0.652066 | ||||||||
\(430\) | 3.13115e11 | 0.441668 | ||||||||
\(431\) | 1.30392e11 | 0.182013 | 0.0910067 | − | 0.995850i | \(-0.470992\pi\) | ||||
0.0910067 | + | 0.995850i | \(0.470992\pi\) | |||||||
\(432\) | −4.08655e10 | −0.0564521 | ||||||||
\(433\) | 1.21450e12 | 1.66035 | 0.830177 | − | 0.557501i | \(-0.188240\pi\) | ||||
0.830177 | + | 0.557501i | \(0.188240\pi\) | |||||||
\(434\) | 1.58650e11 | 0.214653 | ||||||||
\(435\) | 1.78732e11 | 0.239332 | ||||||||
\(436\) | −2.35380e11 | −0.311946 | ||||||||
\(437\) | 8.27333e11 | 1.08521 | ||||||||
\(438\) | 3.28692e11 | 0.426732 | ||||||||
\(439\) | −2.42493e11 | −0.311608 | −0.155804 | − | 0.987788i | \(-0.549797\pi\) | ||||
−0.155804 | + | 0.987788i | \(0.549797\pi\) | |||||||
\(440\) | −5.40152e11 | −0.687035 | ||||||||
\(441\) | −1.90612e11 | −0.239981 | ||||||||
\(442\) | −1.66113e12 | −2.07016 | ||||||||
\(443\) | 7.51319e11 | 0.926846 | 0.463423 | − | 0.886137i | \(-0.346621\pi\) | ||||
0.463423 | + | 0.886137i | \(0.346621\pi\) | |||||||
\(444\) | 4.31747e10 | 0.0527237 | ||||||||
\(445\) | 9.53570e11 | 1.15274 | ||||||||
\(446\) | −2.29471e11 | −0.274613 | ||||||||
\(447\) | 9.30839e11 | 1.10278 | ||||||||
\(448\) | 4.11350e11 | 0.482459 | ||||||||
\(449\) | 4.50564e11 | 0.523176 | 0.261588 | − | 0.965180i | \(-0.415754\pi\) | ||||
0.261588 | + | 0.965180i | \(0.415754\pi\) | |||||||
\(450\) | −1.31648e9 | −0.00151341 | ||||||||
\(451\) | 6.04300e11 | 0.687794 | ||||||||
\(452\) | 8.03038e11 | 0.904926 | ||||||||
\(453\) | −3.40693e11 | −0.380120 | ||||||||
\(454\) | −1.01126e12 | −1.11715 | ||||||||
\(455\) | −8.54609e11 | −0.934795 | ||||||||
\(456\) | −3.93247e11 | −0.425916 | ||||||||
\(457\) | −8.20512e11 | −0.879958 | −0.439979 | − | 0.898008i | \(-0.645014\pi\) | ||||
−0.439979 | + | 0.898008i | \(0.645014\pi\) | |||||||
\(458\) | 2.01899e10 | 0.0214407 | ||||||||
\(459\) | 2.97817e11 | 0.313179 | ||||||||
\(460\) | −7.23454e11 | −0.753356 | ||||||||
\(461\) | −3.57199e11 | −0.368346 | −0.184173 | − | 0.982894i | \(-0.558961\pi\) | ||||
−0.184173 | + | 0.982894i | \(0.558961\pi\) | |||||||
\(462\) | −1.38634e11 | −0.141573 | ||||||||
\(463\) | 8.01850e11 | 0.810922 | 0.405461 | − | 0.914112i | \(-0.367111\pi\) | ||||
0.405461 | + | 0.914112i | \(0.367111\pi\) | |||||||
\(464\) | 1.21030e11 | 0.121217 | ||||||||
\(465\) | 3.27834e11 | 0.325174 | ||||||||
\(466\) | −2.15504e11 | −0.211699 | ||||||||
\(467\) | −9.38973e10 | −0.0913540 | −0.0456770 | − | 0.998956i | \(-0.514544\pi\) | ||||
−0.0456770 | + | 0.998956i | \(0.514544\pi\) | |||||||
\(468\) | −2.91226e11 | −0.280623 | ||||||||
\(469\) | 7.03858e11 | 0.671749 | ||||||||
\(470\) | 3.58972e11 | 0.339328 | ||||||||
\(471\) | −3.86584e11 | −0.361951 | ||||||||
\(472\) | −1.49903e11 | −0.139018 | ||||||||
\(473\) | 4.25534e11 | 0.390894 | ||||||||
\(474\) | 6.91437e11 | 0.629144 | ||||||||
\(475\) | −4.81714e9 | −0.00434178 | ||||||||
\(476\) | −4.61150e11 | −0.411728 | ||||||||
\(477\) | 4.62629e11 | 0.409166 | ||||||||
\(478\) | −1.19583e12 | −1.04772 | ||||||||
\(479\) | 1.82709e11 | 0.158580 | 0.0792902 | − | 0.996852i | \(-0.474735\pi\) | ||||
0.0792902 | + | 0.996852i | \(0.474735\pi\) | |||||||
\(480\) | 5.76517e11 | 0.495709 | ||||||||
\(481\) | −3.94856e11 | −0.336346 | ||||||||
\(482\) | −1.13804e12 | −0.960384 | ||||||||
\(483\) | −5.74054e11 | −0.479944 | ||||||||
\(484\) | 3.39746e11 | 0.281417 | ||||||||
\(485\) | −1.31216e11 | −0.107684 | ||||||||
\(486\) | −5.69976e10 | −0.0463440 | ||||||||
\(487\) | 7.57497e10 | 0.0610240 | 0.0305120 | − | 0.999534i | \(-0.490286\pi\) | ||||
0.0305120 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(488\) | 1.70757e12 | 1.36298 | ||||||||
\(489\) | −6.68175e11 | −0.528446 | ||||||||
\(490\) | −6.65790e11 | −0.521741 | ||||||||
\(491\) | 2.98778e11 | 0.231997 | 0.115998 | − | 0.993249i | \(-0.462993\pi\) | ||||
0.115998 | + | 0.993249i | \(0.462993\pi\) | |||||||
\(492\) | −3.84710e11 | −0.295999 | ||||||||
\(493\) | −8.82038e11 | −0.672475 | ||||||||
\(494\) | 1.16329e12 | 0.878851 | ||||||||
\(495\) | −2.86472e11 | −0.214466 | ||||||||
\(496\) | 2.21996e11 | 0.164694 | ||||||||
\(497\) | −4.99710e11 | −0.367379 | ||||||||
\(498\) | −8.28500e11 | −0.603616 | ||||||||
\(499\) | 1.82082e12 | 1.31466 | 0.657331 | − | 0.753602i | \(-0.271685\pi\) | ||||
0.657331 | + | 0.753602i | \(0.271685\pi\) | |||||||
\(500\) | −6.66040e11 | −0.476579 | ||||||||
\(501\) | 3.86318e11 | 0.273952 | ||||||||
\(502\) | 9.47547e11 | 0.665938 | ||||||||
\(503\) | 1.20304e12 | 0.837964 | 0.418982 | − | 0.907994i | \(-0.362387\pi\) | ||||
0.418982 | + | 0.907994i | \(0.362387\pi\) | |||||||
\(504\) | 2.72859e11 | 0.188365 | ||||||||
\(505\) | −1.65508e12 | −1.13242 | ||||||||
\(506\) | 1.07330e12 | 0.727853 | ||||||||
\(507\) | 1.80446e12 | 1.21286 | ||||||||
\(508\) | −1.34040e12 | −0.892989 | ||||||||
\(509\) | −2.85545e12 | −1.88558 | −0.942788 | − | 0.333391i | \(-0.891807\pi\) | ||||
−0.942788 | + | 0.333391i | \(0.891807\pi\) | |||||||
\(510\) | 1.04025e12 | 0.680880 | ||||||||
\(511\) | −8.34521e11 | −0.541431 | ||||||||
\(512\) | 8.77446e11 | 0.564294 | ||||||||
\(513\) | −2.08561e11 | −0.132955 | ||||||||
\(514\) | −1.81231e11 | −0.114525 | ||||||||
\(515\) | 1.85091e11 | 0.115945 | ||||||||
\(516\) | −2.70904e11 | −0.168225 | ||||||||
\(517\) | 4.87854e11 | 0.300319 | ||||||||
\(518\) | 1.19662e11 | 0.0730254 | ||||||||
\(519\) | −6.12712e11 | −0.370683 | ||||||||
\(520\) | −3.14489e12 | −1.88621 | ||||||||
\(521\) | 2.69409e12 | 1.60193 | 0.800963 | − | 0.598713i | \(-0.204321\pi\) | ||||
0.800963 | + | 0.598713i | \(0.204321\pi\) | |||||||
\(522\) | 1.68808e11 | 0.0995123 | ||||||||
\(523\) | 7.79450e11 | 0.455544 | 0.227772 | − | 0.973714i | \(-0.426856\pi\) | ||||
0.227772 | + | 0.973714i | \(0.426856\pi\) | |||||||
\(524\) | −7.47640e11 | −0.433214 | ||||||||
\(525\) | 3.34242e9 | 0.00192019 | ||||||||
\(526\) | −1.69505e12 | −0.965488 | ||||||||
\(527\) | −1.61785e12 | −0.913673 | ||||||||
\(528\) | −1.93988e11 | −0.108623 | ||||||||
\(529\) | 2.64317e12 | 1.46749 | ||||||||
\(530\) | 1.61592e12 | 0.889565 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | 3.22942e11 | 0.174792 | ||||||||
\(533\) | 3.51838e12 | 1.88830 | ||||||||
\(534\) | 9.00624e11 | 0.479301 | ||||||||
\(535\) | −1.95868e12 | −1.03364 | ||||||||
\(536\) | 2.59014e12 | 1.35544 | ||||||||
\(537\) | 2.15014e12 | 1.11579 | ||||||||
\(538\) | −7.72951e11 | −0.397770 | ||||||||
\(539\) | −9.04831e11 | −0.461762 | ||||||||
\(540\) | 1.82374e11 | 0.0922978 | ||||||||
\(541\) | −1.13636e12 | −0.570335 | −0.285167 | − | 0.958478i | \(-0.592049\pi\) | ||||
−0.285167 | + | 0.958478i | \(0.592049\pi\) | |||||||
\(542\) | −2.20346e11 | −0.109675 | ||||||||
\(543\) | −4.59727e11 | −0.226934 | ||||||||
\(544\) | −2.84509e12 | −1.39284 | ||||||||
\(545\) | −1.34807e12 | −0.654527 | ||||||||
\(546\) | −8.07158e11 | −0.388680 | ||||||||
\(547\) | 1.13181e12 | 0.540542 | 0.270271 | − | 0.962784i | \(-0.412887\pi\) | ||||
0.270271 | + | 0.962784i | \(0.412887\pi\) | |||||||
\(548\) | 1.55787e12 | 0.737935 | ||||||||
\(549\) | 9.05620e11 | 0.425472 | ||||||||
\(550\) | −6.24928e9 | −0.00291205 | ||||||||
\(551\) | 6.17689e11 | 0.285488 | ||||||||
\(552\) | −2.11247e12 | −0.968423 | ||||||||
\(553\) | −1.75550e12 | −0.798248 | ||||||||
\(554\) | −2.84969e12 | −1.28530 | ||||||||
\(555\) | 2.47270e11 | 0.110625 | ||||||||
\(556\) | −6.78426e11 | −0.301069 | ||||||||
\(557\) | 2.12002e11 | 0.0933238 | 0.0466619 | − | 0.998911i | \(-0.485142\pi\) | ||||
0.0466619 | + | 0.998911i | \(0.485142\pi\) | |||||||
\(558\) | 3.09632e11 | 0.135205 | ||||||||
\(559\) | 2.47756e12 | 1.07318 | ||||||||
\(560\) | 3.62403e11 | 0.155721 | ||||||||
\(561\) | 1.41373e12 | 0.602606 | ||||||||
\(562\) | −1.79866e12 | −0.760563 | ||||||||
\(563\) | −3.99743e12 | −1.67684 | −0.838422 | − | 0.545022i | \(-0.816521\pi\) | ||||
−0.838422 | + | 0.545022i | \(0.816521\pi\) | |||||||
\(564\) | −3.10578e11 | −0.129245 | ||||||||
\(565\) | 4.59916e12 | 1.89872 | ||||||||
\(566\) | 1.36372e12 | 0.558534 | ||||||||
\(567\) | 1.44712e11 | 0.0588005 | ||||||||
\(568\) | −1.83889e12 | −0.741292 | ||||||||
\(569\) | 2.47154e12 | 0.988469 | 0.494235 | − | 0.869329i | \(-0.335448\pi\) | ||||
0.494235 | + | 0.869329i | \(0.335448\pi\) | |||||||
\(570\) | −7.28483e11 | −0.289056 | ||||||||
\(571\) | −3.38809e12 | −1.33381 | −0.666903 | − | 0.745145i | \(-0.732380\pi\) | ||||
−0.666903 | + | 0.745145i | \(0.732380\pi\) | |||||||
\(572\) | −1.38244e12 | −0.539964 | ||||||||
\(573\) | −1.44660e11 | −0.0560599 | ||||||||
\(574\) | −1.06626e12 | −0.409976 | ||||||||
\(575\) | −2.58770e10 | −0.00987209 | ||||||||
\(576\) | 8.02817e11 | 0.303889 | ||||||||
\(577\) | −2.44916e12 | −0.919869 | −0.459934 | − | 0.887953i | \(-0.652127\pi\) | ||||
−0.459934 | + | 0.887953i | \(0.652127\pi\) | |||||||
\(578\) | −3.19506e12 | −1.19070 | ||||||||
\(579\) | −7.52646e11 | −0.278315 | ||||||||
\(580\) | −5.40133e11 | −0.198187 | ||||||||
\(581\) | 2.10349e12 | 0.765858 | ||||||||
\(582\) | −1.23931e11 | −0.0447740 | ||||||||
\(583\) | 2.19609e12 | 0.787301 | ||||||||
\(584\) | −3.07097e12 | −1.09249 | ||||||||
\(585\) | −1.66791e12 | −0.588805 | ||||||||
\(586\) | −1.38460e12 | −0.485049 | ||||||||
\(587\) | −4.46433e12 | −1.55197 | −0.775987 | − | 0.630749i | \(-0.782748\pi\) | ||||
−0.775987 | + | 0.630749i | \(0.782748\pi\) | |||||||
\(588\) | 5.76034e11 | 0.198724 | ||||||||
\(589\) | 1.13298e12 | 0.387885 | ||||||||
\(590\) | −2.77693e11 | −0.0943476 | ||||||||
\(591\) | 1.92020e11 | 0.0647444 | ||||||||
\(592\) | 1.67442e11 | 0.0560294 | ||||||||
\(593\) | −3.99401e12 | −1.32637 | −0.663183 | − | 0.748457i | \(-0.730795\pi\) | ||||
−0.663183 | + | 0.748457i | \(0.730795\pi\) | |||||||
\(594\) | −2.70566e11 | −0.0891733 | ||||||||
\(595\) | −2.64110e12 | −0.863890 | ||||||||
\(596\) | −2.81302e12 | −0.913196 | ||||||||
\(597\) | −2.32130e12 | −0.747906 | ||||||||
\(598\) | 6.24901e12 | 1.99828 | ||||||||
\(599\) | 9.60826e11 | 0.304947 | 0.152473 | − | 0.988308i | \(-0.451276\pi\) | ||||
0.152473 | + | 0.988308i | \(0.451276\pi\) | |||||||
\(600\) | 1.22999e10 | 0.00387453 | ||||||||
\(601\) | 8.37458e11 | 0.261835 | 0.130918 | − | 0.991393i | \(-0.458208\pi\) | ||||
0.130918 | + | 0.991393i | \(0.458208\pi\) | |||||||
\(602\) | −7.50833e11 | −0.233002 | ||||||||
\(603\) | 1.37369e12 | 0.423119 | ||||||||
\(604\) | 1.02958e12 | 0.314771 | ||||||||
\(605\) | 1.94579e12 | 0.590470 | ||||||||
\(606\) | −1.56318e12 | −0.470850 | ||||||||
\(607\) | 2.20940e11 | 0.0660578 | 0.0330289 | − | 0.999454i | \(-0.489485\pi\) | ||||
0.0330289 | + | 0.999454i | \(0.489485\pi\) | |||||||
\(608\) | 1.99241e12 | 0.591307 | ||||||||
\(609\) | −4.28590e11 | −0.126260 | ||||||||
\(610\) | 3.16325e12 | 0.925015 | ||||||||
\(611\) | 2.84041e12 | 0.824508 | ||||||||
\(612\) | −9.00010e11 | −0.259338 | ||||||||
\(613\) | −5.34560e12 | −1.52906 | −0.764530 | − | 0.644588i | \(-0.777029\pi\) | ||||
−0.764530 | + | 0.644588i | \(0.777029\pi\) | |||||||
\(614\) | 3.44392e12 | 0.977903 | ||||||||
\(615\) | −2.20331e12 | −0.621066 | ||||||||
\(616\) | 1.29525e12 | 0.362445 | ||||||||
\(617\) | 1.02111e12 | 0.283656 | 0.141828 | − | 0.989891i | \(-0.454702\pi\) | ||||
0.141828 | + | 0.989891i | \(0.454702\pi\) | |||||||
\(618\) | 1.74814e11 | 0.0482090 | ||||||||
\(619\) | 6.46932e12 | 1.77113 | 0.885566 | − | 0.464514i | \(-0.153771\pi\) | ||||
0.885566 | + | 0.464514i | \(0.153771\pi\) | |||||||
\(620\) | −9.90723e11 | −0.269271 | ||||||||
\(621\) | −1.12036e12 | −0.302305 | ||||||||
\(622\) | −3.62568e12 | −0.971253 | ||||||||
\(623\) | −2.28661e12 | −0.608129 | ||||||||
\(624\) | −1.12944e12 | −0.298218 | ||||||||
\(625\) | −3.83852e12 | −1.00625 | ||||||||
\(626\) | 4.65321e12 | 1.21107 | ||||||||
\(627\) | −9.90033e11 | −0.255827 | ||||||||
\(628\) | 1.16826e12 | 0.299725 | ||||||||
\(629\) | −1.22027e12 | −0.310834 | ||||||||
\(630\) | 5.05466e11 | 0.127838 | ||||||||
\(631\) | 2.92249e12 | 0.733873 | 0.366936 | − | 0.930246i | \(-0.380407\pi\) | ||||
0.366936 | + | 0.930246i | \(0.380407\pi\) | |||||||
\(632\) | −6.46010e12 | −1.61069 | ||||||||
\(633\) | −5.75931e11 | −0.142578 | ||||||||
\(634\) | −5.99704e10 | −0.0147413 | ||||||||
\(635\) | −7.67672e12 | −1.87367 | ||||||||
\(636\) | −1.39807e12 | −0.338823 | ||||||||
\(637\) | −5.26814e12 | −1.26774 | ||||||||
\(638\) | 8.01330e11 | 0.191478 | ||||||||
\(639\) | −9.75267e11 | −0.231403 | ||||||||
\(640\) | −8.39993e11 | −0.197909 | ||||||||
\(641\) | 9.07867e11 | 0.212403 | 0.106202 | − | 0.994345i | \(-0.466131\pi\) | ||||
0.106202 | + | 0.994345i | \(0.466131\pi\) | |||||||
\(642\) | −1.84992e12 | −0.429780 | ||||||||
\(643\) | −7.71700e12 | −1.78033 | −0.890163 | − | 0.455643i | \(-0.849409\pi\) | ||||
−0.890163 | + | 0.455643i | \(0.849409\pi\) | |||||||
\(644\) | 1.73480e12 | 0.397433 | ||||||||
\(645\) | −1.55152e12 | −0.352971 | ||||||||
\(646\) | 3.59504e12 | 0.812189 | ||||||||
\(647\) | −6.56641e12 | −1.47319 | −0.736595 | − | 0.676334i | \(-0.763568\pi\) | ||||
−0.736595 | + | 0.676334i | \(0.763568\pi\) | |||||||
\(648\) | 5.32529e11 | 0.118647 | ||||||||
\(649\) | −3.77394e11 | −0.0835015 | ||||||||
\(650\) | −3.63848e10 | −0.00799485 | ||||||||
\(651\) | −7.86129e11 | −0.171546 | ||||||||
\(652\) | 2.01924e12 | 0.437597 | ||||||||
\(653\) | −6.60194e12 | −1.42090 | −0.710448 | − | 0.703750i | \(-0.751508\pi\) | ||||
−0.710448 | + | 0.703750i | \(0.751508\pi\) | |||||||
\(654\) | −1.27322e12 | −0.272146 | ||||||||
\(655\) | −4.28189e12 | −0.908971 | ||||||||
\(656\) | −1.49199e12 | −0.314557 | ||||||||
\(657\) | −1.62871e12 | −0.341034 | ||||||||
\(658\) | −8.60794e11 | −0.179012 | ||||||||
\(659\) | −3.09082e12 | −0.638394 | −0.319197 | − | 0.947688i | \(-0.603413\pi\) | ||||
−0.319197 | + | 0.947688i | \(0.603413\pi\) | |||||||
\(660\) | 8.65725e11 | 0.177596 | ||||||||
\(661\) | −4.17896e12 | −0.851456 | −0.425728 | − | 0.904851i | \(-0.639982\pi\) | ||||
−0.425728 | + | 0.904851i | \(0.639982\pi\) | |||||||
\(662\) | −1.95951e12 | −0.396539 | ||||||||
\(663\) | 8.23108e12 | 1.65442 | ||||||||
\(664\) | 7.74068e12 | 1.54534 | ||||||||
\(665\) | 1.84956e12 | 0.366750 | ||||||||
\(666\) | 2.33541e11 | 0.0459970 | ||||||||
\(667\) | 3.31814e12 | 0.649126 | ||||||||
\(668\) | −1.16746e12 | −0.226855 | ||||||||
\(669\) | 1.13706e12 | 0.219465 | ||||||||
\(670\) | 4.79819e12 | 0.919900 | ||||||||
\(671\) | 4.29896e12 | 0.818676 | ||||||||
\(672\) | −1.38246e12 | −0.261511 | ||||||||
\(673\) | −4.82850e12 | −0.907287 | −0.453644 | − | 0.891183i | \(-0.649876\pi\) | ||||
−0.453644 | + | 0.891183i | \(0.649876\pi\) | |||||||
\(674\) | 3.72657e12 | 0.695568 | ||||||||
\(675\) | 6.52329e9 | 0.00120948 | ||||||||
\(676\) | −5.45311e12 | −1.00435 | ||||||||
\(677\) | 8.64207e12 | 1.58114 | 0.790568 | − | 0.612375i | \(-0.209786\pi\) | ||||
0.790568 | + | 0.612375i | \(0.209786\pi\) | |||||||
\(678\) | 4.34380e12 | 0.789471 | ||||||||
\(679\) | 3.14650e11 | 0.0568086 | ||||||||
\(680\) | −9.71904e12 | −1.74314 | ||||||||
\(681\) | 5.01090e12 | 0.892799 | ||||||||
\(682\) | 1.46982e12 | 0.260156 | ||||||||
\(683\) | 2.80206e12 | 0.492703 | 0.246351 | − | 0.969181i | \(-0.420768\pi\) | ||||
0.246351 | + | 0.969181i | \(0.420768\pi\) | |||||||
\(684\) | 6.30275e11 | 0.110098 | ||||||||
\(685\) | 8.92224e12 | 1.54834 | ||||||||
\(686\) | 3.81410e12 | 0.657558 | ||||||||
\(687\) | −1.00043e11 | −0.0171349 | ||||||||
\(688\) | −1.05063e12 | −0.178773 | ||||||||
\(689\) | 1.27862e13 | 2.16149 | ||||||||
\(690\) | −3.91331e12 | −0.657239 | ||||||||
\(691\) | 5.96570e12 | 0.995429 | 0.497714 | − | 0.867341i | \(-0.334173\pi\) | ||||
0.497714 | + | 0.867341i | \(0.334173\pi\) | |||||||
\(692\) | 1.85163e12 | 0.306956 | ||||||||
\(693\) | 6.86945e11 | 0.113142 | ||||||||
\(694\) | −4.62093e12 | −0.756156 | ||||||||
\(695\) | −3.88548e12 | −0.631704 | ||||||||
\(696\) | −1.57718e12 | −0.254765 | ||||||||
\(697\) | 1.08733e13 | 1.74507 | ||||||||
\(698\) | 3.49338e12 | 0.557053 | ||||||||
\(699\) | 1.06785e12 | 0.169185 | ||||||||
\(700\) | −1.01009e10 | −0.00159008 | ||||||||
\(701\) | 6.02618e12 | 0.942565 | 0.471283 | − | 0.881982i | \(-0.343791\pi\) | ||||
0.471283 | + | 0.881982i | \(0.343791\pi\) | |||||||
\(702\) | −1.57530e12 | −0.244820 | ||||||||
\(703\) | 8.54554e11 | 0.131959 | ||||||||
\(704\) | 3.81095e12 | 0.584732 | ||||||||
\(705\) | −1.77874e12 | −0.271183 | ||||||||
\(706\) | 1.65229e12 | 0.250302 | ||||||||
\(707\) | 3.96878e12 | 0.597406 | ||||||||
\(708\) | 2.40257e11 | 0.0359357 | ||||||||
\(709\) | 9.37965e12 | 1.39405 | 0.697025 | − | 0.717047i | \(-0.254507\pi\) | ||||
0.697025 | + | 0.717047i | \(0.254507\pi\) | |||||||
\(710\) | −3.40652e12 | −0.503093 | ||||||||
\(711\) | −3.42615e12 | −0.502797 | ||||||||
\(712\) | −8.41454e12 | −1.22707 | ||||||||
\(713\) | 6.08621e12 | 0.881950 | ||||||||
\(714\) | −2.49446e12 | −0.359198 | ||||||||
\(715\) | −7.91753e12 | −1.13296 | ||||||||
\(716\) | −6.49777e12 | −0.923966 | ||||||||
\(717\) | 5.92548e12 | 0.837312 | ||||||||
\(718\) | −1.06617e12 | −0.149716 | ||||||||
\(719\) | 2.94327e12 | 0.410724 | 0.205362 | − | 0.978686i | \(-0.434163\pi\) | ||||
0.205362 | + | 0.978686i | \(0.434163\pi\) | |||||||
\(720\) | 7.07289e11 | 0.0980846 | ||||||||
\(721\) | −4.43838e11 | −0.0611668 | ||||||||
\(722\) | 2.75730e12 | 0.377630 | ||||||||
\(723\) | 5.63911e12 | 0.767517 | ||||||||
\(724\) | 1.38930e12 | 0.187920 | ||||||||
\(725\) | −1.93199e10 | −0.00259707 | ||||||||
\(726\) | 1.83776e12 | 0.245512 | ||||||||
\(727\) | 4.80339e12 | 0.637739 | 0.318870 | − | 0.947799i | \(-0.396697\pi\) | ||||
0.318870 | + | 0.947799i | \(0.396697\pi\) | |||||||
\(728\) | 7.54129e12 | 0.995071 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −5.68891e12 | −0.741441 | ||||||||
\(731\) | 7.65670e12 | 0.991776 | ||||||||
\(732\) | −2.73680e12 | −0.352325 | ||||||||
\(733\) | −3.39490e12 | −0.434370 | −0.217185 | − | 0.976130i | \(-0.569687\pi\) | ||||
−0.217185 | + | 0.976130i | \(0.569687\pi\) | |||||||
\(734\) | −9.76371e12 | −1.24160 | ||||||||
\(735\) | 3.29906e12 | 0.416963 | ||||||||
\(736\) | 1.07030e13 | 1.34448 | ||||||||
\(737\) | 6.52090e12 | 0.814148 | ||||||||
\(738\) | −2.08098e12 | −0.258234 | ||||||||
\(739\) | 2.13168e12 | 0.262919 | 0.131460 | − | 0.991322i | \(-0.458034\pi\) | ||||
0.131460 | + | 0.991322i | \(0.458034\pi\) | |||||||
\(740\) | −7.47257e11 | −0.0916067 | ||||||||
\(741\) | −5.76421e12 | −0.702357 | ||||||||
\(742\) | −3.87488e12 | −0.469290 | ||||||||
\(743\) | 2.82447e12 | 0.340006 | 0.170003 | − | 0.985444i | \(-0.445622\pi\) | ||||
0.170003 | + | 0.985444i | \(0.445622\pi\) | |||||||
\(744\) | −2.89289e12 | −0.346142 | ||||||||
\(745\) | −1.61107e13 | −1.91607 | ||||||||
\(746\) | 8.75588e12 | 1.03508 | ||||||||
\(747\) | 4.10531e12 | 0.482396 | ||||||||
\(748\) | −4.27232e12 | −0.499007 | ||||||||
\(749\) | 4.69680e12 | 0.545298 | ||||||||
\(750\) | −3.60275e12 | −0.415775 | ||||||||
\(751\) | −2.42385e12 | −0.278052 | −0.139026 | − | 0.990289i | \(-0.544397\pi\) | ||||
−0.139026 | + | 0.990289i | \(0.544397\pi\) | |||||||
\(752\) | −1.20449e12 | −0.137349 | ||||||||
\(753\) | −4.69520e12 | −0.532203 | ||||||||
\(754\) | 4.66554e12 | 0.525691 | ||||||||
\(755\) | 5.89663e12 | 0.660454 | ||||||||
\(756\) | −4.37323e11 | −0.0486916 | ||||||||
\(757\) | 3.90640e12 | 0.432359 | 0.216180 | − | 0.976354i | \(-0.430640\pi\) | ||||
0.216180 | + | 0.976354i | \(0.430640\pi\) | |||||||
\(758\) | −4.91470e12 | −0.540737 | ||||||||
\(759\) | −5.31832e12 | −0.581684 | ||||||||
\(760\) | 6.80622e12 | 0.740023 | ||||||||
\(761\) | 6.76565e12 | 0.731272 | 0.365636 | − | 0.930758i | \(-0.380852\pi\) | ||||
0.365636 | + | 0.930758i | \(0.380852\pi\) | |||||||
\(762\) | −7.25048e12 | −0.779057 | ||||||||
\(763\) | 3.23259e12 | 0.345295 | ||||||||
\(764\) | 4.37165e11 | 0.0464222 | ||||||||
\(765\) | −5.15454e12 | −0.544144 | ||||||||
\(766\) | −2.13265e12 | −0.223816 | ||||||||
\(767\) | −2.19728e12 | −0.229248 | ||||||||
\(768\) | −5.86795e12 | −0.608640 | ||||||||
\(769\) | 1.08276e13 | 1.11651 | 0.558255 | − | 0.829669i | \(-0.311471\pi\) | ||||
0.558255 | + | 0.829669i | \(0.311471\pi\) | |||||||
\(770\) | 2.39943e12 | 0.245980 | ||||||||
\(771\) | 8.98021e11 | 0.0915254 | ||||||||
\(772\) | 2.27451e12 | 0.230468 | ||||||||
\(773\) | −1.93513e13 | −1.94941 | −0.974704 | − | 0.223500i | \(-0.928252\pi\) | ||||
−0.974704 | + | 0.223500i | \(0.928252\pi\) | |||||||
\(774\) | −1.46537e12 | −0.146762 | ||||||||
\(775\) | −3.54369e10 | −0.00352857 | ||||||||
\(776\) | 1.15789e12 | 0.114627 | ||||||||
\(777\) | −5.92941e11 | −0.0583602 | ||||||||
\(778\) | −1.18078e13 | −1.15547 | ||||||||
\(779\) | −7.61453e12 | −0.740840 | ||||||||
\(780\) | 5.04046e12 | 0.487579 | ||||||||
\(781\) | −4.62957e12 | −0.445257 | ||||||||
\(782\) | 1.93121e13 | 1.84671 | ||||||||
\(783\) | −8.36465e11 | −0.0795280 | ||||||||
\(784\) | 2.23399e12 | 0.211183 | ||||||||
\(785\) | 6.69090e12 | 0.628884 | ||||||||
\(786\) | −4.04414e12 | −0.377942 | ||||||||
\(787\) | 1.80989e13 | 1.68177 | 0.840885 | − | 0.541214i | \(-0.182035\pi\) | ||||
0.840885 | + | 0.541214i | \(0.182035\pi\) | |||||||
\(788\) | −5.80288e11 | −0.0536137 | ||||||||
\(789\) | 8.39917e12 | 0.771596 | ||||||||
\(790\) | −1.19672e13 | −1.09313 | ||||||||
\(791\) | −1.10285e13 | −1.00167 | ||||||||
\(792\) | 2.52790e12 | 0.228295 | ||||||||
\(793\) | 2.50296e13 | 2.24763 | ||||||||
\(794\) | −1.04099e13 | −0.929510 | ||||||||
\(795\) | −8.00706e12 | −0.710920 | ||||||||
\(796\) | 7.01503e12 | 0.619328 | ||||||||
\(797\) | 5.88413e12 | 0.516559 | 0.258279 | − | 0.966070i | \(-0.416844\pi\) | ||||
0.258279 | + | 0.966070i | \(0.416844\pi\) | |||||||
\(798\) | 1.74686e12 | 0.152492 | ||||||||
\(799\) | 8.77804e12 | 0.761969 | ||||||||
\(800\) | −6.23180e10 | −0.00537909 | ||||||||
\(801\) | −4.46270e12 | −0.383046 | ||||||||
\(802\) | −6.14119e12 | −0.524165 | ||||||||
\(803\) | −7.73142e12 | −0.656205 | ||||||||
\(804\) | −4.15133e12 | −0.350377 | ||||||||
\(805\) | 9.93557e12 | 0.833895 | ||||||||
\(806\) | 8.55762e12 | 0.714242 | ||||||||
\(807\) | 3.83006e12 | 0.317888 | ||||||||
\(808\) | 1.46048e13 | 1.20544 | ||||||||
\(809\) | −8.22827e12 | −0.675368 | −0.337684 | − | 0.941260i | \(-0.609643\pi\) | ||||
−0.337684 | + | 0.941260i | \(0.609643\pi\) | |||||||
\(810\) | 9.86500e11 | 0.0805220 | ||||||||
\(811\) | 1.36302e13 | 1.10639 | 0.553196 | − | 0.833051i | \(-0.313408\pi\) | ||||
0.553196 | + | 0.833051i | \(0.313408\pi\) | |||||||
\(812\) | 1.29521e12 | 0.104553 | ||||||||
\(813\) | 1.09184e12 | 0.0876498 | ||||||||
\(814\) | 1.10861e12 | 0.0885056 | ||||||||
\(815\) | 1.15646e13 | 0.918167 | ||||||||
\(816\) | −3.49045e12 | −0.275598 | ||||||||
\(817\) | −5.36197e12 | −0.421042 | ||||||||
\(818\) | 7.03856e12 | 0.549660 | ||||||||
\(819\) | 3.99956e12 | 0.310624 | ||||||||
\(820\) | 6.65845e12 | 0.514294 | ||||||||
\(821\) | −2.06555e13 | −1.58668 | −0.793342 | − | 0.608776i | \(-0.791661\pi\) | ||||
−0.793342 | + | 0.608776i | \(0.791661\pi\) | |||||||
\(822\) | 8.42684e12 | 0.643786 | ||||||||
\(823\) | 2.84174e12 | 0.215916 | 0.107958 | − | 0.994155i | \(-0.465569\pi\) | ||||
0.107958 | + | 0.994155i | \(0.465569\pi\) | |||||||
\(824\) | −1.63329e12 | −0.123421 | ||||||||
\(825\) | 3.09659e10 | 0.00232724 | ||||||||
\(826\) | 6.65893e11 | 0.0497730 | ||||||||
\(827\) | −4.68952e12 | −0.348621 | −0.174311 | − | 0.984691i | \(-0.555770\pi\) | ||||
−0.174311 | + | 0.984691i | \(0.555770\pi\) | |||||||
\(828\) | 3.38575e12 | 0.250333 | ||||||||
\(829\) | 2.39047e13 | 1.75788 | 0.878939 | − | 0.476935i | \(-0.158252\pi\) | ||||
0.878939 | + | 0.476935i | \(0.158252\pi\) | |||||||
\(830\) | 1.43395e13 | 1.04877 | ||||||||
\(831\) | 1.41205e13 | 1.02718 | ||||||||
\(832\) | 2.21883e13 | 1.60535 | ||||||||
\(833\) | −1.62808e13 | −1.17158 | ||||||||
\(834\) | −3.66975e12 | −0.262657 | ||||||||
\(835\) | −6.68629e12 | −0.475988 | ||||||||
\(836\) | 2.99190e12 | 0.211845 | ||||||||
\(837\) | −1.53426e12 | −0.108052 | ||||||||
\(838\) | 6.89224e12 | 0.482794 | ||||||||
\(839\) | −2.47263e13 | −1.72278 | −0.861392 | − | 0.507940i | \(-0.830407\pi\) | ||||
−0.861392 | + | 0.507940i | \(0.830407\pi\) | |||||||
\(840\) | −4.72257e12 | −0.327282 | ||||||||
\(841\) | −1.20298e13 | −0.829233 | ||||||||
\(842\) | −8.90384e12 | −0.610482 | ||||||||
\(843\) | 8.91256e12 | 0.607825 | ||||||||
\(844\) | 1.74047e12 | 0.118066 | ||||||||
\(845\) | −3.12311e13 | −2.10733 | ||||||||
\(846\) | −1.67998e12 | −0.112756 | ||||||||
\(847\) | −4.66591e12 | −0.311502 | ||||||||
\(848\) | −5.42206e12 | −0.360067 | ||||||||
\(849\) | −6.75736e12 | −0.446368 | ||||||||
\(850\) | −1.12444e11 | −0.00738844 | ||||||||
\(851\) | 4.59055e12 | 0.300042 | ||||||||
\(852\) | 2.94728e12 | 0.191621 | ||||||||
\(853\) | −1.17423e13 | −0.759420 | −0.379710 | − | 0.925106i | \(-0.623976\pi\) | ||||
−0.379710 | + | 0.925106i | \(0.623976\pi\) | |||||||
\(854\) | −7.58529e12 | −0.487991 | ||||||||
\(855\) | 3.60972e12 | 0.231007 | ||||||||
\(856\) | 1.72838e13 | 1.10029 | ||||||||
\(857\) | 2.65634e11 | 0.0168217 | 0.00841084 | − | 0.999965i | \(-0.497323\pi\) | ||||
0.00841084 | + | 0.999965i | \(0.497323\pi\) | |||||||
\(858\) | −7.47792e12 | −0.471073 | ||||||||
\(859\) | 4.27853e12 | 0.268117 | 0.134059 | − | 0.990973i | \(-0.457199\pi\) | ||||
0.134059 | + | 0.990973i | \(0.457199\pi\) | |||||||
\(860\) | 4.68873e12 | 0.292289 | ||||||||
\(861\) | 5.28342e12 | 0.327643 | ||||||||
\(862\) | −2.13149e12 | −0.131492 | ||||||||
\(863\) | 1.26461e13 | 0.776081 | 0.388041 | − | 0.921642i | \(-0.373152\pi\) | ||||
0.388041 | + | 0.921642i | \(0.373152\pi\) | |||||||
\(864\) | −2.69809e12 | −0.164719 | ||||||||
\(865\) | 1.06047e13 | 0.644057 | ||||||||
\(866\) | −1.98531e13 | −1.19949 | ||||||||
\(867\) | 1.58319e13 | 0.951582 | ||||||||
\(868\) | 2.37570e12 | 0.142054 | ||||||||
\(869\) | −1.62638e13 | −0.967463 | ||||||||
\(870\) | −2.92169e12 | −0.172901 | ||||||||
\(871\) | 3.79662e13 | 2.23520 | ||||||||
\(872\) | 1.18957e13 | 0.696731 | ||||||||
\(873\) | 6.14091e11 | 0.0357824 | ||||||||
\(874\) | −1.35242e13 | −0.783989 | ||||||||
\(875\) | 9.14708e12 | 0.527529 | ||||||||
\(876\) | 4.92198e12 | 0.282404 | ||||||||
\(877\) | −1.31246e13 | −0.749185 | −0.374593 | − | 0.927189i | \(-0.622217\pi\) | ||||
−0.374593 | + | 0.927189i | \(0.622217\pi\) | |||||||
\(878\) | 3.96397e12 | 0.225115 | ||||||||
\(879\) | 6.86086e12 | 0.387640 | ||||||||
\(880\) | 3.35749e12 | 0.188731 | ||||||||
\(881\) | −9.07975e12 | −0.507788 | −0.253894 | − | 0.967232i | \(-0.581711\pi\) | ||||
−0.253894 | + | 0.967232i | \(0.581711\pi\) | |||||||
\(882\) | 3.11589e12 | 0.173370 | ||||||||
\(883\) | −1.54949e12 | −0.0857757 | −0.0428879 | − | 0.999080i | \(-0.513656\pi\) | ||||
−0.0428879 | + | 0.999080i | \(0.513656\pi\) | |||||||
\(884\) | −2.48745e13 | −1.37000 | ||||||||
\(885\) | 1.37600e12 | 0.0754004 | ||||||||
\(886\) | −1.22816e13 | −0.669582 | ||||||||
\(887\) | −5.54485e12 | −0.300769 | −0.150385 | − | 0.988628i | \(-0.548051\pi\) | ||||
−0.150385 | + | 0.988628i | \(0.548051\pi\) | |||||||
\(888\) | −2.18198e12 | −0.117758 | ||||||||
\(889\) | 1.84084e13 | 0.988456 | ||||||||
\(890\) | −1.55878e13 | −0.832778 | ||||||||
\(891\) | 1.34069e12 | 0.0712652 | ||||||||
\(892\) | −3.43621e12 | −0.181735 | ||||||||
\(893\) | −6.14725e12 | −0.323481 | ||||||||
\(894\) | −1.52162e13 | −0.796686 | ||||||||
\(895\) | −3.72141e13 | −1.93867 | ||||||||
\(896\) | 2.01426e12 | 0.104407 | ||||||||
\(897\) | −3.09646e13 | −1.59698 | ||||||||
\(898\) | −7.36525e12 | −0.377958 | ||||||||
\(899\) | 4.54398e12 | 0.232016 | ||||||||
\(900\) | −1.97135e10 | −0.00100155 | ||||||||
\(901\) | 3.95145e13 | 1.99754 | ||||||||
\(902\) | −9.87834e12 | −0.496883 | ||||||||
\(903\) | 3.72046e12 | 0.186210 | ||||||||
\(904\) | −4.05842e13 | −2.02115 | ||||||||
\(905\) | 7.95683e12 | 0.394295 | ||||||||
\(906\) | 5.56922e12 | 0.274611 | ||||||||
\(907\) | −8.14492e12 | −0.399627 | −0.199813 | − | 0.979834i | \(-0.564034\pi\) | ||||
−0.199813 | + | 0.979834i | \(0.564034\pi\) | |||||||
\(908\) | −1.51431e13 | −0.739311 | ||||||||
\(909\) | 7.74573e12 | 0.376292 | ||||||||
\(910\) | 1.39701e13 | 0.675325 | ||||||||
\(911\) | −1.57553e13 | −0.757867 | −0.378934 | − | 0.925424i | \(-0.623709\pi\) | ||||
−0.378934 | + | 0.925424i | \(0.623709\pi\) | |||||||
\(912\) | 2.44435e12 | 0.117000 | ||||||||
\(913\) | 1.94878e13 | 0.928207 | ||||||||
\(914\) | 1.34127e13 | 0.635709 | ||||||||
\(915\) | −1.56742e13 | −0.739250 | ||||||||
\(916\) | 3.02333e11 | 0.0141891 | ||||||||
\(917\) | 1.02677e13 | 0.479527 | ||||||||
\(918\) | −4.86834e12 | −0.226250 | ||||||||
\(919\) | 1.43731e12 | 0.0664708 | 0.0332354 | − | 0.999448i | \(-0.489419\pi\) | ||||
0.0332354 | + | 0.999448i | \(0.489419\pi\) | |||||||
\(920\) | 3.65621e13 | 1.68262 | ||||||||
\(921\) | −1.70650e13 | −0.781518 | ||||||||
\(922\) | 5.83904e12 | 0.266104 | ||||||||
\(923\) | −2.69545e13 | −1.22243 | ||||||||
\(924\) | −2.07596e12 | −0.0936905 | ||||||||
\(925\) | −2.67284e10 | −0.00120043 | ||||||||
\(926\) | −1.31076e13 | −0.585835 | ||||||||
\(927\) | −8.66223e11 | −0.0385275 | ||||||||
\(928\) | 7.99087e12 | 0.353695 | ||||||||
\(929\) | −2.20360e13 | −0.970651 | −0.485325 | − | 0.874334i | \(-0.661299\pi\) | ||||
−0.485325 | + | 0.874334i | \(0.661299\pi\) | |||||||
\(930\) | −5.35903e12 | −0.234916 | ||||||||
\(931\) | 1.14014e13 | 0.497375 | ||||||||
\(932\) | −3.22705e12 | −0.140099 | ||||||||
\(933\) | 1.79656e13 | 0.776203 | ||||||||
\(934\) | 1.53492e12 | 0.0659969 | ||||||||
\(935\) | −2.44685e13 | −1.04702 | ||||||||
\(936\) | 1.47181e13 | 0.626772 | ||||||||
\(937\) | −9.91396e12 | −0.420164 | −0.210082 | − | 0.977684i | \(-0.567373\pi\) | ||||
−0.210082 | + | 0.977684i | \(0.567373\pi\) | |||||||
\(938\) | −1.15058e13 | −0.485293 | ||||||||
\(939\) | −2.30572e13 | −0.967857 | ||||||||
\(940\) | 5.37540e12 | 0.224562 | ||||||||
\(941\) | 1.18619e11 | 0.00493175 | 0.00246587 | − | 0.999997i | \(-0.499215\pi\) | ||||
0.00246587 | + | 0.999997i | \(0.499215\pi\) | |||||||
\(942\) | 6.31939e12 | 0.261485 | ||||||||
\(943\) | −4.09042e13 | −1.68448 | ||||||||
\(944\) | 9.31772e11 | 0.0381888 | ||||||||
\(945\) | −2.50464e12 | −0.102165 | ||||||||
\(946\) | −6.95610e12 | −0.282394 | ||||||||
\(947\) | 3.13848e13 | 1.26807 | 0.634037 | − | 0.773302i | \(-0.281397\pi\) | ||||
0.634037 | + | 0.773302i | \(0.281397\pi\) | |||||||
\(948\) | 1.03539e13 | 0.416357 | ||||||||
\(949\) | −4.50142e13 | −1.80157 | ||||||||
\(950\) | 7.87446e10 | 0.00313664 | ||||||||
\(951\) | 2.97160e11 | 0.0117809 | ||||||||
\(952\) | 2.33057e13 | 0.919594 | ||||||||
\(953\) | −3.04762e13 | −1.19686 | −0.598430 | − | 0.801175i | \(-0.704209\pi\) | ||||
−0.598430 | + | 0.801175i | \(0.704209\pi\) | |||||||
\(954\) | −7.56247e12 | −0.295594 | ||||||||
\(955\) | 2.50373e12 | 0.0974032 | ||||||||
\(956\) | −1.79069e13 | −0.693363 | ||||||||
\(957\) | −3.97068e12 | −0.153025 | ||||||||
\(958\) | −2.98669e12 | −0.114563 | ||||||||
\(959\) | −2.13950e13 | −0.816826 | ||||||||
\(960\) | −1.38949e13 | −0.528003 | ||||||||
\(961\) | −1.81050e13 | −0.684766 | ||||||||
\(962\) | 6.45462e12 | 0.242987 | ||||||||
\(963\) | 9.16657e12 | 0.343470 | ||||||||
\(964\) | −1.70415e13 | −0.635567 | ||||||||
\(965\) | 1.30266e13 | 0.483569 | ||||||||
\(966\) | 9.38391e12 | 0.346726 | ||||||||
\(967\) | 1.60103e13 | 0.588815 | 0.294408 | − | 0.955680i | \(-0.404878\pi\) | ||||
0.294408 | + | 0.955680i | \(0.404878\pi\) | |||||||
\(968\) | −1.71702e13 | −0.628544 | ||||||||
\(969\) | −1.78138e13 | −0.649083 | ||||||||
\(970\) | 2.14496e12 | 0.0777942 | ||||||||
\(971\) | −1.63968e13 | −0.591932 | −0.295966 | − | 0.955198i | \(-0.595642\pi\) | ||||
−0.295966 | + | 0.955198i | \(0.595642\pi\) | |||||||
\(972\) | −8.53508e11 | −0.0306697 | ||||||||
\(973\) | 9.31718e12 | 0.333255 | ||||||||
\(974\) | −1.23826e12 | −0.0440856 | ||||||||
\(975\) | 1.80291e11 | 0.00638930 | ||||||||
\(976\) | −1.06140e13 | −0.374415 | ||||||||
\(977\) | −1.57320e13 | −0.552407 | −0.276204 | − | 0.961099i | \(-0.589076\pi\) | ||||
−0.276204 | + | 0.961099i | \(0.589076\pi\) | |||||||
\(978\) | 1.09225e13 | 0.381766 | ||||||||
\(979\) | −2.11843e13 | −0.737042 | ||||||||
\(980\) | −9.96984e12 | −0.345280 | ||||||||
\(981\) | 6.30894e12 | 0.217493 | ||||||||
\(982\) | −4.88405e12 | −0.167602 | ||||||||
\(983\) | 1.51445e13 | 0.517326 | 0.258663 | − | 0.965968i | \(-0.416718\pi\) | ||||
0.258663 | + | 0.965968i | \(0.416718\pi\) | |||||||
\(984\) | 1.94426e13 | 0.661113 | ||||||||
\(985\) | −3.32343e12 | −0.112492 | ||||||||
\(986\) | 1.44185e13 | 0.485817 | ||||||||
\(987\) | 4.26533e12 | 0.143062 | ||||||||
\(988\) | 1.74196e13 | 0.581609 | ||||||||
\(989\) | −2.88038e13 | −0.957341 | ||||||||
\(990\) | 4.68289e12 | 0.154937 | ||||||||
\(991\) | 3.91091e13 | 1.28809 | 0.644046 | − | 0.764987i | \(-0.277255\pi\) | ||||
0.644046 | + | 0.764987i | \(0.277255\pi\) | |||||||
\(992\) | 1.46570e13 | 0.480555 | ||||||||
\(993\) | 9.70957e12 | 0.316905 | ||||||||
\(994\) | 8.16864e12 | 0.265406 | ||||||||
\(995\) | 4.01765e13 | 1.29948 | ||||||||
\(996\) | −1.24063e13 | −0.399463 | ||||||||
\(997\) | 3.21837e12 | 0.103159 | 0.0515796 | − | 0.998669i | \(-0.483574\pi\) | ||||
0.0515796 | + | 0.998669i | \(0.483574\pi\) | |||||||
\(998\) | −2.97645e13 | −0.949753 | ||||||||
\(999\) | −1.15722e12 | −0.0367597 |
(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.d.1.7 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.d.1.7 | ✓ | 22 | 1.1 | even | 1 | trivial |