Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
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, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.18 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.83 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 46.3046i | − | 1.44702i | −0.690315 | − | 0.723509i | \(-0.742528\pi\) | ||
0.690315 | − | 0.723509i | \(-0.257472\pi\) | |||||||
\(3\) | 140.296 | 0.577350 | ||||||||
\(4\) | −1120.11 | −1.09386 | ||||||||
\(5\) | 3858.39 | 1.23469 | 0.617343 | − | 0.786694i | \(-0.288209\pi\) | ||||
0.617343 | + | 0.786694i | \(0.288209\pi\) | |||||||
\(6\) | − | 6496.35i | − | 0.835436i | ||||||
\(7\) | 22459.5 | 1.33632 | 0.668158 | − | 0.744020i | \(-0.267083\pi\) | ||||
0.668158 | + | 0.744020i | \(0.267083\pi\) | |||||||
\(8\) | 4450.45i | 0.135817i | ||||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | − | 178661.i | − | 1.78661i | ||||||
\(11\) | − | 173626.i | − | 1.07808i | −0.842280 | − | 0.539041i | \(-0.818787\pi\) | ||
0.842280 | − | 0.539041i | \(-0.181213\pi\) | |||||||
\(12\) | −157147. | −0.631540 | ||||||||
\(13\) | − | 674974.i | − | 1.81790i | −0.416904 | − | 0.908950i | \(-0.636885\pi\) | ||
0.416904 | − | 0.908950i | \(-0.363115\pi\) | |||||||
\(14\) | − | 1.03998e6i | − | 1.93367i | ||||||
\(15\) | 541318. | 0.712846 | ||||||||
\(16\) | −940919. | −0.897330 | ||||||||
\(17\) | 2.43219e6 | 1.71298 | 0.856490 | − | 0.516164i | \(-0.172640\pi\) | ||||
0.856490 | + | 0.516164i | \(0.172640\pi\) | |||||||
\(18\) | − | 911413.i | − | 0.482339i | ||||||
\(19\) | 1.33829e6 | 0.540483 | 0.270242 | − | 0.962793i | \(-0.412896\pi\) | ||||
0.270242 | + | 0.962793i | \(0.412896\pi\) | |||||||
\(20\) | −4.32184e6 | −1.35057 | ||||||||
\(21\) | 3.15097e6 | 0.771522 | ||||||||
\(22\) | −8.03968e6 | −1.56000 | ||||||||
\(23\) | − | 562371.i | − | 0.0873742i | −0.999045 | − | 0.0436871i | \(-0.986090\pi\) | ||
0.999045 | − | 0.0436871i | \(-0.0139105\pi\) | |||||||
\(24\) | 624381.i | 0.0784140i | ||||||||
\(25\) | 5.12158e6 | 0.524450 | ||||||||
\(26\) | −3.12544e7 | −2.63053 | ||||||||
\(27\) | 2.76145e6 | 0.192450 | ||||||||
\(28\) | −2.51571e7 | −1.46174 | ||||||||
\(29\) | 7.41792e6 | 0.361653 | 0.180827 | − | 0.983515i | \(-0.442123\pi\) | ||||
0.180827 | + | 0.983515i | \(0.442123\pi\) | |||||||
\(30\) | − | 2.50655e7i | − | 1.03150i | ||||||
\(31\) | 3.31206e7i | 1.15688i | 0.815724 | + | 0.578442i | \(0.196339\pi\) | ||||
−0.815724 | + | 0.578442i | \(0.803661\pi\) | |||||||
\(32\) | 4.81261e7i | 1.43427i | ||||||||
\(33\) | − | 2.43591e7i | − | 0.622431i | ||||||
\(34\) | − | 1.12621e8i | − | 2.47871i | ||||||
\(35\) | 8.66574e7 | 1.64993 | ||||||||
\(36\) | −2.20472e7 | −0.364620 | ||||||||
\(37\) | 7.74043e7i | 1.11624i | 0.829761 | + | 0.558119i | \(0.188477\pi\) | ||||
−0.829761 | + | 0.558119i | \(0.811523\pi\) | |||||||
\(38\) | − | 6.19690e7i | − | 0.782089i | ||||||
\(39\) | − | 9.46962e7i | − | 1.04957i | ||||||
\(40\) | 1.71716e7i | 0.167691i | ||||||||
\(41\) | 1.51747e8 | 1.30979 | 0.654894 | − | 0.755720i | \(-0.272713\pi\) | ||||
0.654894 | + | 0.755720i | \(0.272713\pi\) | |||||||
\(42\) | − | 1.45905e8i | − | 1.11641i | ||||||
\(43\) | 1.64287e8i | 1.11754i | 0.829324 | + | 0.558768i | \(0.188726\pi\) | ||||
−0.829324 | + | 0.558768i | \(0.811274\pi\) | |||||||
\(44\) | 1.94481e8i | 1.17927i | ||||||||
\(45\) | 7.59448e7 | 0.411562 | ||||||||
\(46\) | −2.60403e7 | −0.126432 | ||||||||
\(47\) | − | 2.27468e8i | − | 0.991817i | −0.868375 | − | 0.495909i | \(-0.834835\pi\) | ||
0.868375 | − | 0.495909i | \(-0.165165\pi\) | |||||||
\(48\) | −1.32007e8 | −0.518074 | ||||||||
\(49\) | 2.21952e8 | 0.785740 | ||||||||
\(50\) | − | 2.37152e8i | − | 0.758888i | ||||||
\(51\) | 3.41226e8 | 0.988989 | ||||||||
\(52\) | 7.56047e8i | 1.98853i | ||||||||
\(53\) | −6.16906e8 | −1.47516 | −0.737581 | − | 0.675258i | \(-0.764032\pi\) | ||||
−0.737581 | + | 0.675258i | \(0.764032\pi\) | |||||||
\(54\) | − | 1.27868e8i | − | 0.278479i | ||||||
\(55\) | − | 6.69918e8i | − | 1.33109i | ||||||
\(56\) | 9.99547e7i | 0.181494i | ||||||||
\(57\) | 1.87757e8 | 0.312048 | ||||||||
\(58\) | − | 3.43484e8i | − | 0.523318i | ||||||
\(59\) | −6.62524e8 | + | 2.68661e8i | −0.926705 | + | 0.375790i | ||||
\(60\) | −6.06337e8 | −0.779754 | ||||||||
\(61\) | 5.94808e8i | 0.704251i | 0.935953 | + | 0.352126i | \(0.114541\pi\) | ||||
−0.935953 | + | 0.352126i | \(0.885459\pi\) | |||||||
\(62\) | 1.53363e9 | 1.67403 | ||||||||
\(63\) | 4.42069e8 | 0.445439 | ||||||||
\(64\) | 1.26496e9 | 1.17808 | ||||||||
\(65\) | − | 2.60431e9i | − | 2.24454i | ||||||
\(66\) | −1.12794e9 | −0.900668 | ||||||||
\(67\) | 1.29950e9i | 0.962500i | 0.876583 | + | 0.481250i | \(0.159817\pi\) | ||||
−0.876583 | + | 0.481250i | \(0.840183\pi\) | |||||||
\(68\) | −2.72432e9 | −1.87376 | ||||||||
\(69\) | − | 7.88984e7i | − | 0.0504455i | ||||||
\(70\) | − | 4.01263e9i | − | 2.38748i | ||||||
\(71\) | 2.19554e9 | 1.21688 | 0.608442 | − | 0.793599i | \(-0.291795\pi\) | ||||
0.608442 | + | 0.793599i | \(0.291795\pi\) | |||||||
\(72\) | 8.75982e7i | 0.0452723i | ||||||||
\(73\) | 1.44021e8i | 0.0694723i | 0.999397 | + | 0.0347361i | \(0.0110591\pi\) | ||||
−0.999397 | + | 0.0347361i | \(0.988941\pi\) | |||||||
\(74\) | 3.58417e9 | 1.61521 | ||||||||
\(75\) | 7.18538e8 | 0.302791 | ||||||||
\(76\) | −1.49904e9 | −0.591213 | ||||||||
\(77\) | − | 3.89955e9i | − | 1.44066i | ||||||
\(78\) | −4.38487e9 | −1.51874 | ||||||||
\(79\) | −5.52548e9 | −1.79570 | −0.897851 | − | 0.440298i | \(-0.854873\pi\) | ||||
−0.897851 | + | 0.440298i | \(0.854873\pi\) | |||||||
\(80\) | −3.63044e9 | −1.10792 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | − | 7.02659e9i | − | 1.89529i | ||||||
\(83\) | − | 2.03540e9i | − | 0.516726i | −0.966048 | − | 0.258363i | \(-0.916817\pi\) | ||
0.966048 | − | 0.258363i | \(-0.0831831\pi\) | |||||||
\(84\) | −3.52945e9 | −0.843937 | ||||||||
\(85\) | 9.38433e9 | 2.11499 | ||||||||
\(86\) | 7.60724e9 | 1.61709 | ||||||||
\(87\) | 1.04071e9 | 0.208801 | ||||||||
\(88\) | 7.72714e8 | 0.146422 | ||||||||
\(89\) | 2.60902e8i | 0.0467227i | 0.999727 | + | 0.0233614i | \(0.00743683\pi\) | ||||
−0.999727 | + | 0.0233614i | \(0.992563\pi\) | |||||||
\(90\) | − | 3.51659e9i | − | 0.595537i | ||||||
\(91\) | − | 1.51595e10i | − | 2.42929i | ||||||
\(92\) | 6.29918e8i | 0.0955752i | ||||||||
\(93\) | 4.64669e9i | 0.667927i | ||||||||
\(94\) | −1.05328e10 | −1.43518 | ||||||||
\(95\) | 5.16365e9 | 0.667327 | ||||||||
\(96\) | 6.75191e9i | 0.828076i | ||||||||
\(97\) | − | 9.73345e9i | − | 1.13347i | −0.823902 | − | 0.566733i | \(-0.808207\pi\) | ||
0.823902 | − | 0.566733i | \(-0.191793\pi\) | |||||||
\(98\) | − | 1.02774e10i | − | 1.13698i | ||||||
\(99\) | − | 3.41748e9i | − | 0.359360i | ||||||
\(100\) | −5.73674e9 | −0.573674 | ||||||||
\(101\) | 2.01714e10i | 1.91924i | 0.281293 | + | 0.959622i | \(0.409237\pi\) | ||||
−0.281293 | + | 0.959622i | \(0.590763\pi\) | |||||||
\(102\) | − | 1.58003e10i | − | 1.43108i | ||||||
\(103\) | − | 8.11267e9i | − | 0.699806i | −0.936786 | − | 0.349903i | \(-0.886215\pi\) | ||
0.936786 | − | 0.349903i | \(-0.113785\pi\) | |||||||
\(104\) | 3.00394e9 | 0.246902 | ||||||||
\(105\) | 1.21577e10 | 0.952588 | ||||||||
\(106\) | 2.85656e10i | 2.13459i | ||||||||
\(107\) | 7.83502e9 | 0.558626 | 0.279313 | − | 0.960200i | \(-0.409893\pi\) | ||||
0.279313 | + | 0.960200i | \(0.409893\pi\) | |||||||
\(108\) | −3.09313e9 | −0.210513 | ||||||||
\(109\) | − | 1.58300e10i | − | 1.02884i | −0.857537 | − | 0.514422i | \(-0.828007\pi\) | ||
0.857537 | − | 0.514422i | \(-0.171993\pi\) | |||||||
\(110\) | −3.10203e10 | −1.92611 | ||||||||
\(111\) | 1.08595e10i | 0.644460i | ||||||||
\(112\) | −2.11325e10 | −1.19912 | ||||||||
\(113\) | 3.34226e10i | 1.81405i | 0.421082 | + | 0.907023i | \(0.361651\pi\) | ||||
−0.421082 | + | 0.907023i | \(0.638349\pi\) | |||||||
\(114\) | − | 8.69400e9i | − | 0.451539i | ||||||
\(115\) | − | 2.16985e9i | − | 0.107880i | ||||||
\(116\) | −8.30891e9 | −0.395598 | ||||||||
\(117\) | − | 1.32855e10i | − | 0.605967i | ||||||
\(118\) | 1.24402e10 | + | 3.06779e10i | 0.543774 | + | 1.34096i | ||||
\(119\) | 5.46256e10 | 2.28908 | ||||||||
\(120\) | 2.40911e9i | 0.0968166i | ||||||||
\(121\) | −4.20859e9 | −0.162259 | ||||||||
\(122\) | 2.75423e10 | 1.01906 | ||||||||
\(123\) | 2.12895e10 | 0.756207 | ||||||||
\(124\) | − | 3.70988e10i | − | 1.26547i | ||||||
\(125\) | −1.79186e10 | −0.587155 | ||||||||
\(126\) | − | 2.04698e10i | − | 0.644557i | ||||||
\(127\) | −1.60679e10 | −0.486341 | −0.243171 | − | 0.969984i | \(-0.578188\pi\) | ||||
−0.243171 | + | 0.969984i | \(0.578188\pi\) | |||||||
\(128\) | − | 9.29216e9i | − | 0.270437i | ||||||
\(129\) | 2.30488e10i | 0.645209i | ||||||||
\(130\) | −1.20592e11 | −3.24788 | ||||||||
\(131\) | − | 3.56195e10i | − | 0.923276i | −0.887068 | − | 0.461638i | \(-0.847262\pi\) | ||
0.887068 | − | 0.461638i | \(-0.152738\pi\) | |||||||
\(132\) | 2.72849e10i | 0.680852i | ||||||||
\(133\) | 3.00573e10 | 0.722256 | ||||||||
\(134\) | 6.01726e10 | 1.39275 | ||||||||
\(135\) | 1.06548e10 | 0.237615 | ||||||||
\(136\) | 1.08243e10i | 0.232652i | ||||||||
\(137\) | 4.47286e10 | 0.926793 | 0.463396 | − | 0.886151i | \(-0.346631\pi\) | ||||
0.463396 | + | 0.886151i | \(0.346631\pi\) | |||||||
\(138\) | −3.65336e9 | −0.0729956 | ||||||||
\(139\) | −3.73592e10 | −0.719986 | −0.359993 | − | 0.932955i | \(-0.617221\pi\) | ||||
−0.359993 | + | 0.932955i | \(0.617221\pi\) | |||||||
\(140\) | −9.70661e10 | −1.80479 | ||||||||
\(141\) | − | 3.19129e10i | − | 0.572626i | ||||||
\(142\) | − | 1.01663e11i | − | 1.76085i | ||||||
\(143\) | −1.17193e11 | −1.95984 | ||||||||
\(144\) | −1.85201e10 | −0.299110 | ||||||||
\(145\) | 2.86213e10 | 0.446528 | ||||||||
\(146\) | 6.66883e9 | 0.100528 | ||||||||
\(147\) | 3.11390e10 | 0.453647 | ||||||||
\(148\) | − | 8.67015e10i | − | 1.22101i | ||||||
\(149\) | 5.72721e10i | 0.779852i | 0.920846 | + | 0.389926i | \(0.127499\pi\) | ||||
−0.920846 | + | 0.389926i | \(0.872501\pi\) | |||||||
\(150\) | − | 3.32716e10i | − | 0.438144i | ||||||
\(151\) | 8.23203e10i | 1.04863i | 0.851525 | + | 0.524315i | \(0.175678\pi\) | ||||
−0.851525 | + | 0.524315i | \(0.824322\pi\) | |||||||
\(152\) | 5.95599e9i | 0.0734068i | ||||||||
\(153\) | 4.78727e10 | 0.570993 | ||||||||
\(154\) | −1.80567e11 | −2.08466 | ||||||||
\(155\) | 1.27792e11i | 1.42839i | ||||||||
\(156\) | 1.06070e11i | 1.14808i | ||||||||
\(157\) | 6.15806e10i | 0.645573i | 0.946472 | + | 0.322787i | \(0.104620\pi\) | ||||
−0.946472 | + | 0.322787i | \(0.895380\pi\) | |||||||
\(158\) | 2.55855e11i | 2.59841i | ||||||||
\(159\) | −8.65496e10 | −0.851686 | ||||||||
\(160\) | 1.85689e11i | 1.77087i | ||||||||
\(161\) | − | 1.26305e10i | − | 0.116760i | ||||||
\(162\) | − | 1.79393e10i | − | 0.160780i | ||||||
\(163\) | −1.86475e11 | −1.62063 | −0.810314 | − | 0.585996i | \(-0.800703\pi\) | ||||
−0.810314 | + | 0.585996i | \(0.800703\pi\) | |||||||
\(164\) | −1.69974e11 | −1.43273 | ||||||||
\(165\) | − | 9.39869e10i | − | 0.768506i | ||||||
\(166\) | −9.42485e10 | −0.747712 | ||||||||
\(167\) | −1.33552e11 | −1.02818 | −0.514090 | − | 0.857736i | \(-0.671870\pi\) | ||||
−0.514090 | + | 0.857736i | \(0.671870\pi\) | |||||||
\(168\) | 1.40233e10i | 0.104786i | ||||||||
\(169\) | −3.17731e11 | −2.30476 | ||||||||
\(170\) | − | 4.34537e11i | − | 3.06043i | ||||||
\(171\) | 2.63416e10 | 0.180161 | ||||||||
\(172\) | − | 1.84020e11i | − | 1.22243i | ||||||
\(173\) | − | 7.52751e10i | − | 0.485759i | −0.970056 | − | 0.242879i | \(-0.921908\pi\) | ||
0.970056 | − | 0.242879i | \(-0.0780919\pi\) | |||||||
\(174\) | − | 4.81894e10i | − | 0.302138i | ||||||
\(175\) | 1.15028e11 | 0.700830 | ||||||||
\(176\) | 1.63368e11i | 0.967395i | ||||||||
\(177\) | −9.29495e10 | + | 3.76921e10i | −0.535033 | + | 0.216962i | ||||
\(178\) | 1.20810e10 | 0.0676086 | ||||||||
\(179\) | − | 1.98766e11i | − | 1.08162i | −0.841143 | − | 0.540812i | \(-0.818117\pi\) | ||
0.841143 | − | 0.540812i | \(-0.181883\pi\) | |||||||
\(180\) | −8.50667e10 | −0.450191 | ||||||||
\(181\) | 1.84058e11 | 0.947460 | 0.473730 | − | 0.880670i | \(-0.342907\pi\) | ||||
0.473730 | + | 0.880670i | \(0.342907\pi\) | |||||||
\(182\) | −7.01956e11 | −3.51522 | ||||||||
\(183\) | 8.34493e10i | 0.406600i | ||||||||
\(184\) | 2.50280e9 | 0.0118669 | ||||||||
\(185\) | 2.98656e11i | 1.37820i | ||||||||
\(186\) | 2.15163e11 | 0.966502 | ||||||||
\(187\) | − | 4.22291e11i | − | 1.84673i | ||||||
\(188\) | 2.54790e11i | 1.08491i | ||||||||
\(189\) | 6.20206e10 | 0.257174 | ||||||||
\(190\) | − | 2.39101e11i | − | 0.965634i | ||||||
\(191\) | 1.52877e11i | 0.601418i | 0.953716 | + | 0.300709i | \(0.0972233\pi\) | ||||
−0.953716 | + | 0.300709i | \(0.902777\pi\) | |||||||
\(192\) | 1.77469e11 | 0.680167 | ||||||||
\(193\) | −1.45253e11 | −0.542423 | −0.271212 | − | 0.962520i | \(-0.587424\pi\) | ||||
−0.271212 | + | 0.962520i | \(0.587424\pi\) | |||||||
\(194\) | −4.50703e11 | −1.64014 | ||||||||
\(195\) | − | 3.65375e11i | − | 1.29588i | ||||||
\(196\) | −2.48611e11 | −0.859489 | ||||||||
\(197\) | −3.18108e11 | −1.07212 | −0.536061 | − | 0.844180i | \(-0.680088\pi\) | ||||
−0.536061 | + | 0.844180i | \(0.680088\pi\) | |||||||
\(198\) | −1.58245e11 | −0.520001 | ||||||||
\(199\) | 4.37270e11 | 1.40115 | 0.700574 | − | 0.713580i | \(-0.252927\pi\) | ||||
0.700574 | + | 0.713580i | \(0.252927\pi\) | |||||||
\(200\) | 2.27933e10i | 0.0712292i | ||||||||
\(201\) | 1.82314e11i | 0.555700i | ||||||||
\(202\) | 9.34030e11 | 2.77718 | ||||||||
\(203\) | 1.66602e11 | 0.483283 | ||||||||
\(204\) | −3.82212e11 | −1.08182 | ||||||||
\(205\) | 5.85500e11 | 1.61718 | ||||||||
\(206\) | −3.75654e11 | −1.01263 | ||||||||
\(207\) | − | 1.10691e10i | − | 0.0291247i | ||||||
\(208\) | 6.35096e11i | 1.63126i | ||||||||
\(209\) | − | 2.32362e11i | − | 0.582685i | ||||||
\(210\) | − | 5.62957e11i | − | 1.37841i | ||||||
\(211\) | 1.61677e11i | 0.386577i | 0.981142 | + | 0.193289i | \(0.0619153\pi\) | ||||
−0.981142 | + | 0.193289i | \(0.938085\pi\) | |||||||
\(212\) | 6.91005e11 | 1.61362 | ||||||||
\(213\) | 3.08025e11 | 0.702568 | ||||||||
\(214\) | − | 3.62797e11i | − | 0.808342i | ||||||
\(215\) | 6.33885e11i | 1.37981i | ||||||||
\(216\) | 1.22897e10i | 0.0261380i | ||||||||
\(217\) | 7.43871e11i | 1.54596i | ||||||||
\(218\) | −7.33003e11 | −1.48876 | ||||||||
\(219\) | 2.02056e10i | 0.0401098i | ||||||||
\(220\) | 7.50383e11i | 1.45603i | ||||||||
\(221\) | − | 1.64166e12i | − | 3.11403i | ||||||
\(222\) | 5.02845e11 | 0.932545 | ||||||||
\(223\) | 7.52806e11 | 1.36508 | 0.682541 | − | 0.730847i | \(-0.260875\pi\) | ||||
0.682541 | + | 0.730847i | \(0.260875\pi\) | |||||||
\(224\) | 1.08089e12i | 1.91664i | ||||||||
\(225\) | 1.00808e11 | 0.174817 | ||||||||
\(226\) | 1.54762e12 | 2.62496 | ||||||||
\(227\) | − | 1.24261e11i | − | 0.206160i | −0.994673 | − | 0.103080i | \(-0.967130\pi\) | ||
0.994673 | − | 0.103080i | \(-0.0328698\pi\) | |||||||
\(228\) | −2.10309e11 | −0.341337 | ||||||||
\(229\) | − | 8.21422e11i | − | 1.30433i | −0.758075 | − | 0.652167i | \(-0.773860\pi\) | ||
0.758075 | − | 0.652167i | \(-0.226140\pi\) | |||||||
\(230\) | −1.00474e11 | −0.156104 | ||||||||
\(231\) | − | 5.47091e11i | − | 0.831764i | ||||||
\(232\) | 3.30131e10i | 0.0491186i | ||||||||
\(233\) | 3.61168e11i | 0.525932i | 0.964805 | + | 0.262966i | \(0.0847007\pi\) | ||||
−0.964805 | + | 0.262966i | \(0.915299\pi\) | |||||||
\(234\) | −6.15180e11 | −0.876845 | ||||||||
\(235\) | − | 8.77662e11i | − | 1.22458i | ||||||
\(236\) | 7.42101e11 | − | 3.00931e11i | 1.01369 | − | 0.411061i | ||||
\(237\) | −7.75203e11 | −1.03675 | ||||||||
\(238\) | − | 2.52941e12i | − | 3.31234i | ||||||
\(239\) | 1.31812e12 | 1.69031 | 0.845156 | − | 0.534520i | \(-0.179507\pi\) | ||||
0.845156 | + | 0.534520i | \(0.179507\pi\) | |||||||
\(240\) | −5.09336e11 | −0.639659 | ||||||||
\(241\) | −9.65434e11 | −1.18751 | −0.593755 | − | 0.804646i | \(-0.702355\pi\) | ||||
−0.593755 | + | 0.804646i | \(0.702355\pi\) | |||||||
\(242\) | 1.94877e11i | 0.234792i | ||||||||
\(243\) | 5.43536e10 | 0.0641500 | ||||||||
\(244\) | − | 6.66252e11i | − | 0.770352i | ||||||
\(245\) | 8.56378e11 | 0.970142 | ||||||||
\(246\) | − | 9.85803e11i | − | 1.09424i | ||||||
\(247\) | − | 9.03311e11i | − | 0.982545i | ||||||
\(248\) | −1.47402e11 | −0.157124 | ||||||||
\(249\) | − | 2.85559e11i | − | 0.298332i | ||||||
\(250\) | 8.29711e11i | 0.849624i | ||||||||
\(251\) | −1.73925e12 | −1.74580 | −0.872898 | − | 0.487902i | \(-0.837762\pi\) | ||||
−0.872898 | + | 0.487902i | \(0.837762\pi\) | |||||||
\(252\) | −4.95168e11 | −0.487247 | ||||||||
\(253\) | −9.76422e10 | −0.0941965 | ||||||||
\(254\) | 7.44018e11i | 0.703745i | ||||||||
\(255\) | 1.31659e12 | 1.22109 | ||||||||
\(256\) | 8.65047e11 | 0.786756 | ||||||||
\(257\) | 2.30940e11 | 0.205984 | 0.102992 | − | 0.994682i | \(-0.467158\pi\) | ||||
0.102992 | + | 0.994682i | \(0.467158\pi\) | |||||||
\(258\) | 1.06727e12 | 0.933629 | ||||||||
\(259\) | 1.73846e12i | 1.49165i | ||||||||
\(260\) | 2.91713e12i | 2.45521i | ||||||||
\(261\) | 1.46007e11 | 0.120551 | ||||||||
\(262\) | −1.64935e12 | −1.33600 | ||||||||
\(263\) | −1.00273e12 | −0.796906 | −0.398453 | − | 0.917189i | \(-0.630453\pi\) | ||||
−0.398453 | + | 0.917189i | \(0.630453\pi\) | |||||||
\(264\) | 1.08409e11 | 0.0845366 | ||||||||
\(265\) | −2.38027e12 | −1.82136 | ||||||||
\(266\) | − | 1.39179e12i | − | 1.04512i | ||||||
\(267\) | 3.66036e10i | 0.0269754i | ||||||||
\(268\) | − | 1.45558e12i | − | 1.05284i | ||||||
\(269\) | 1.38574e12i | 0.983827i | 0.870644 | + | 0.491914i | \(0.163702\pi\) | ||||
−0.870644 | + | 0.491914i | \(0.836298\pi\) | |||||||
\(270\) | − | 4.93364e11i | − | 0.343834i | ||||||
\(271\) | −3.34414e11 | −0.228791 | −0.114395 | − | 0.993435i | \(-0.536493\pi\) | ||||
−0.114395 | + | 0.993435i | \(0.536493\pi\) | |||||||
\(272\) | −2.28849e12 | −1.53711 | ||||||||
\(273\) | − | 2.12683e12i | − | 1.40255i | ||||||
\(274\) | − | 2.07114e12i | − | 1.34109i | ||||||
\(275\) | − | 8.89240e11i | − | 0.565399i | ||||||
\(276\) | 8.83751e10i | 0.0551804i | ||||||||
\(277\) | 6.23330e11 | 0.382225 | 0.191113 | − | 0.981568i | \(-0.438790\pi\) | ||||
0.191113 | + | 0.981568i | \(0.438790\pi\) | |||||||
\(278\) | 1.72990e12i | 1.04183i | ||||||||
\(279\) | 6.51913e11i | 0.385628i | ||||||||
\(280\) | 3.85665e11i | 0.224088i | ||||||||
\(281\) | −1.04987e12 | −0.599247 | −0.299623 | − | 0.954058i | \(-0.596861\pi\) | ||||
−0.299623 | + | 0.954058i | \(0.596861\pi\) | |||||||
\(282\) | −1.47771e12 | −0.828600 | ||||||||
\(283\) | − | 1.82074e12i | − | 1.00304i | −0.865147 | − | 0.501518i | \(-0.832775\pi\) | ||
0.865147 | − | 0.501518i | \(-0.167225\pi\) | |||||||
\(284\) | −2.45925e12 | −1.33110 | ||||||||
\(285\) | 7.24440e11 | 0.385282 | ||||||||
\(286\) | 5.42657e12i | 2.83593i | ||||||||
\(287\) | 3.40816e12 | 1.75029 | ||||||||
\(288\) | 9.47266e11i | 0.478090i | ||||||||
\(289\) | 3.89954e12 | 1.93430 | ||||||||
\(290\) | − | 1.32529e12i | − | 0.646134i | ||||||
\(291\) | − | 1.36557e12i | − | 0.654407i | ||||||
\(292\) | − | 1.61320e11i | − | 0.0759929i | ||||||
\(293\) | −1.89086e12 | −0.875631 | −0.437816 | − | 0.899065i | \(-0.644248\pi\) | ||||
−0.437816 | + | 0.899065i | \(0.644248\pi\) | |||||||
\(294\) | − | 1.44188e12i | − | 0.656435i | ||||||
\(295\) | −2.55628e12 | + | 1.03660e12i | −1.14419 | + | 0.463982i | ||||
\(296\) | −3.44484e11 | −0.151604 | ||||||||
\(297\) | − | 4.79459e11i | − | 0.207477i | ||||||
\(298\) | 2.65196e12 | 1.12846 | ||||||||
\(299\) | −3.79585e11 | −0.158838 | ||||||||
\(300\) | −8.04843e11 | −0.331211 | ||||||||
\(301\) | 3.68980e12i | 1.49338i | ||||||||
\(302\) | 3.81180e12 | 1.51739 | ||||||||
\(303\) | 2.82998e12i | 1.10808i | ||||||||
\(304\) | −1.25922e12 | −0.484992 | ||||||||
\(305\) | 2.29500e12i | 0.869529i | ||||||||
\(306\) | − | 2.21673e12i | − | 0.826237i | ||||||
\(307\) | 3.11488e12 | 1.14222 | 0.571109 | − | 0.820874i | \(-0.306513\pi\) | ||||
0.571109 | + | 0.820874i | \(0.306513\pi\) | |||||||
\(308\) | 4.36793e12i | 1.57588i | ||||||||
\(309\) | − | 1.13818e12i | − | 0.404033i | ||||||
\(310\) | 5.91737e12 | 2.06690 | ||||||||
\(311\) | −6.95987e11 | −0.239221 | −0.119610 | − | 0.992821i | \(-0.538165\pi\) | ||||
−0.119610 | + | 0.992821i | \(0.538165\pi\) | |||||||
\(312\) | 4.21441e11 | 0.142549 | ||||||||
\(313\) | − | 2.00121e12i | − | 0.666149i | −0.942900 | − | 0.333075i | \(-0.891914\pi\) | ||
0.942900 | − | 0.333075i | \(-0.108086\pi\) | |||||||
\(314\) | 2.85146e12 | 0.934156 | ||||||||
\(315\) | 1.70568e12 | 0.549977 | ||||||||
\(316\) | 6.18916e12 | 1.96425 | ||||||||
\(317\) | 4.25638e12 | 1.32967 | 0.664835 | − | 0.746990i | \(-0.268502\pi\) | ||||
0.664835 | + | 0.746990i | \(0.268502\pi\) | |||||||
\(318\) | 4.00764e12i | 1.23240i | ||||||||
\(319\) | − | 1.28794e12i | − | 0.389891i | ||||||
\(320\) | 4.88070e12 | 1.45456 | ||||||||
\(321\) | 1.09922e12 | 0.322523 | ||||||||
\(322\) | −5.84852e11 | −0.168953 | ||||||||
\(323\) | 3.25497e12 | 0.925837 | ||||||||
\(324\) | −4.33955e11 | −0.121540 | ||||||||
\(325\) | − | 3.45693e12i | − | 0.953397i | ||||||
\(326\) | 8.63465e12i | 2.34508i | ||||||||
\(327\) | − | 2.22089e12i | − | 0.594003i | ||||||
\(328\) | 6.75343e11i | 0.177892i | ||||||||
\(329\) | − | 5.10881e12i | − | 1.32538i | ||||||
\(330\) | −4.35202e12 | −1.11204 | ||||||||
\(331\) | −1.32140e12 | −0.332578 | −0.166289 | − | 0.986077i | \(-0.553179\pi\) | ||||
−0.166289 | + | 0.986077i | \(0.553179\pi\) | |||||||
\(332\) | 2.27988e12i | 0.565226i | ||||||||
\(333\) | 1.52355e12i | 0.372079i | ||||||||
\(334\) | 6.18409e12i | 1.48780i | ||||||||
\(335\) | 5.01397e12i | 1.18839i | ||||||||
\(336\) | −2.96481e12 | −0.692310 | ||||||||
\(337\) | − | 2.23788e12i | − | 0.514858i | −0.966297 | − | 0.257429i | \(-0.917125\pi\) | ||
0.966297 | − | 0.257429i | \(-0.0828754\pi\) | |||||||
\(338\) | 1.47124e13i | 3.33503i | ||||||||
\(339\) | 4.68906e12i | 1.04734i | ||||||||
\(340\) | −1.05115e13 | −2.31351 | ||||||||
\(341\) | 5.75060e12 | 1.24721 | ||||||||
\(342\) | − | 1.21973e12i | − | 0.260696i | ||||||
\(343\) | −1.35932e12 | −0.286320 | ||||||||
\(344\) | −7.31152e11 | −0.151780 | ||||||||
\(345\) | − | 3.04421e11i | − | 0.0622844i | ||||||
\(346\) | −3.48558e12 | −0.702902 | ||||||||
\(347\) | − | 3.33102e12i | − | 0.662110i | −0.943611 | − | 0.331055i | \(-0.892595\pi\) | ||
0.943611 | − | 0.331055i | \(-0.107405\pi\) | |||||||
\(348\) | −1.16571e12 | −0.228399 | ||||||||
\(349\) | − | 5.35080e11i | − | 0.103346i | −0.998664 | − | 0.0516728i | \(-0.983545\pi\) | ||
0.998664 | − | 0.0516728i | \(-0.0164553\pi\) | |||||||
\(350\) | − | 5.32632e12i | − | 1.01411i | ||||||
\(351\) | − | 1.86391e12i | − | 0.349855i | ||||||
\(352\) | 8.35595e12 | 1.54626 | ||||||||
\(353\) | − | 1.27435e12i | − | 0.232496i | −0.993220 | − | 0.116248i | \(-0.962913\pi\) | ||
0.993220 | − | 0.116248i | \(-0.0370868\pi\) | |||||||
\(354\) | 1.74532e12 | + | 4.30399e12i | 0.313948 | + | 0.774203i | ||||
\(355\) | 8.47124e12 | 1.50247 | ||||||||
\(356\) | − | 2.92240e11i | − | 0.0511081i | ||||||
\(357\) | 7.66376e12 | 1.32160 | ||||||||
\(358\) | −9.20376e12 | −1.56513 | ||||||||
\(359\) | −7.50199e12 | −1.25807 | −0.629034 | − | 0.777378i | \(-0.716549\pi\) | ||||
−0.629034 | + | 0.777378i | \(0.716549\pi\) | |||||||
\(360\) | 3.37988e11i | 0.0558971i | ||||||||
\(361\) | −4.34004e12 | −0.707878 | ||||||||
\(362\) | − | 8.52270e12i | − | 1.37099i | ||||||
\(363\) | −5.90449e11 | −0.0936805 | ||||||||
\(364\) | 1.69804e13i | 2.65730i | ||||||||
\(365\) | 5.55690e11i | 0.0857764i | ||||||||
\(366\) | 3.86408e12 | 0.588357 | ||||||||
\(367\) | − | 2.92715e12i | − | 0.439657i | −0.975539 | − | 0.219829i | \(-0.929450\pi\) | ||
0.975539 | − | 0.219829i | \(-0.0705498\pi\) | |||||||
\(368\) | 5.29145e11i | 0.0784036i | ||||||||
\(369\) | 2.98684e12 | 0.436596 | ||||||||
\(370\) | 1.38291e13 | 1.99428 | ||||||||
\(371\) | −1.38554e13 | −1.97128 | ||||||||
\(372\) | − | 5.20482e12i | − | 0.730619i | ||||||
\(373\) | 8.19998e12 | 1.13571 | 0.567856 | − | 0.823128i | \(-0.307773\pi\) | ||||
0.567856 | + | 0.823128i | \(0.307773\pi\) | |||||||
\(374\) | −1.95540e13 | −2.67225 | ||||||||
\(375\) | −2.51390e12 | −0.338994 | ||||||||
\(376\) | 1.01234e12 | 0.134706 | ||||||||
\(377\) | − | 5.00690e12i | − | 0.657449i | ||||||
\(378\) | − | 2.87184e12i | − | 0.372135i | ||||||
\(379\) | 7.57176e12 | 0.968279 | 0.484140 | − | 0.874991i | \(-0.339133\pi\) | ||||
0.484140 | + | 0.874991i | \(0.339133\pi\) | |||||||
\(380\) | −5.78387e12 | −0.729963 | ||||||||
\(381\) | −2.25427e12 | −0.280789 | ||||||||
\(382\) | 7.07892e12 | 0.870262 | ||||||||
\(383\) | 6.28768e12 | 0.762951 | 0.381475 | − | 0.924379i | \(-0.375416\pi\) | ||||
0.381475 | + | 0.924379i | \(0.375416\pi\) | |||||||
\(384\) | − | 1.30365e12i | − | 0.156137i | ||||||
\(385\) | − | 1.50460e13i | − | 1.77876i | ||||||
\(386\) | 6.72588e12i | 0.784896i | ||||||||
\(387\) | 3.23366e12i | 0.372512i | ||||||||
\(388\) | 1.09026e13i | 1.23985i | ||||||||
\(389\) | −8.97532e12 | −1.00763 | −0.503816 | − | 0.863811i | \(-0.668071\pi\) | ||||
−0.503816 | + | 0.863811i | \(0.668071\pi\) | |||||||
\(390\) | −1.69185e13 | −1.87517 | ||||||||
\(391\) | − | 1.36779e12i | − | 0.149670i | ||||||
\(392\) | 9.87786e11i | 0.106717i | ||||||||
\(393\) | − | 4.99728e12i | − | 0.533054i | ||||||
\(394\) | 1.47299e13i | 1.55138i | ||||||||
\(395\) | −2.13195e13 | −2.21713 | ||||||||
\(396\) | 3.82796e12i | 0.393090i | ||||||||
\(397\) | − | 3.49967e12i | − | 0.354874i | −0.984132 | − | 0.177437i | \(-0.943219\pi\) | ||
0.984132 | − | 0.177437i | \(-0.0567806\pi\) | |||||||
\(398\) | − | 2.02476e13i | − | 2.02749i | ||||||
\(399\) | 4.21692e12 | 0.416995 | ||||||||
\(400\) | −4.81899e12 | −0.470605 | ||||||||
\(401\) | − | 5.14383e11i | − | 0.0496095i | −0.999692 | − | 0.0248047i | \(-0.992104\pi\) | ||
0.999692 | − | 0.0248047i | \(-0.00789641\pi\) | |||||||
\(402\) | 8.44198e12 | 0.804107 | ||||||||
\(403\) | 2.23555e13 | 2.10310 | ||||||||
\(404\) | − | 2.25943e13i | − | 2.09938i | ||||||
\(405\) | 1.49482e12 | 0.137187 | ||||||||
\(406\) | − | 7.71445e12i | − | 0.699319i | ||||||
\(407\) | 1.34394e13 | 1.20339 | ||||||||
\(408\) | 1.51861e12i | 0.134322i | ||||||||
\(409\) | − | 1.55003e13i | − | 1.35433i | −0.735832 | − | 0.677164i | \(-0.763209\pi\) | ||
0.735832 | − | 0.677164i | \(-0.236791\pi\) | |||||||
\(410\) | − | 2.71113e13i | − | 2.34009i | ||||||
\(411\) | 6.27525e12 | 0.535084 | ||||||||
\(412\) | 9.08711e12i | 0.765490i | ||||||||
\(413\) | −1.48799e13 | + | 6.03399e12i | −1.23837 | + | 0.502174i | ||||
\(414\) | −5.12552e11 | −0.0421440 | ||||||||
\(415\) | − | 7.85339e12i | − | 0.637994i | ||||||
\(416\) | 3.24839e13 | 2.60736 | ||||||||
\(417\) | −5.24135e12 | −0.415684 | ||||||||
\(418\) | −1.07594e13 | −0.843156 | ||||||||
\(419\) | 9.66126e12i | 0.748107i | 0.927407 | + | 0.374054i | \(0.122032\pi\) | ||||
−0.927407 | + | 0.374054i | \(0.877968\pi\) | |||||||
\(420\) | −1.36180e13 | −1.04200 | ||||||||
\(421\) | 1.11554e13i | 0.843479i | 0.906717 | + | 0.421740i | \(0.138580\pi\) | ||||
−0.906717 | + | 0.421740i | \(0.861420\pi\) | |||||||
\(422\) | 7.48638e12 | 0.559384 | ||||||||
\(423\) | − | 4.47726e12i | − | 0.330606i | ||||||
\(424\) | − | 2.74551e12i | − | 0.200352i | ||||||
\(425\) | 1.24566e13 | 0.898372 | ||||||||
\(426\) | − | 1.42630e13i | − | 1.01663i | ||||||
\(427\) | 1.33591e13i | 0.941102i | ||||||||
\(428\) | −8.77611e12 | −0.611059 | ||||||||
\(429\) | −1.64417e13 | −1.13152 | ||||||||
\(430\) | 2.93517e13 | 1.99660 | ||||||||
\(431\) | 1.68009e13i | 1.12966i | 0.825208 | + | 0.564828i | \(0.191058\pi\) | ||||
−0.825208 | + | 0.564828i | \(0.808942\pi\) | |||||||
\(432\) | −2.59830e12 | −0.172691 | ||||||||
\(433\) | −2.13329e13 | −1.40156 | −0.700779 | − | 0.713378i | \(-0.747164\pi\) | ||||
−0.700779 | + | 0.713378i | \(0.747164\pi\) | |||||||
\(434\) | 3.44446e13 | 2.23703 | ||||||||
\(435\) | 4.01545e12 | 0.257803 | ||||||||
\(436\) | 1.77314e13i | 1.12541i | ||||||||
\(437\) | − | 7.52615e11i | − | 0.0472243i | ||||||
\(438\) | 9.35611e11 | 0.0580396 | ||||||||
\(439\) | −3.77036e12 | −0.231239 | −0.115619 | − | 0.993294i | \(-0.536885\pi\) | ||||
−0.115619 | + | 0.993294i | \(0.536885\pi\) | |||||||
\(440\) | 2.98144e12 | 0.180785 | ||||||||
\(441\) | 4.36868e12 | 0.261913 | ||||||||
\(442\) | −7.60164e13 | −4.50605 | ||||||||
\(443\) | − | 2.05445e13i | − | 1.20414i | −0.798443 | − | 0.602070i | \(-0.794343\pi\) | ||
0.798443 | − | 0.602070i | \(-0.205657\pi\) | |||||||
\(444\) | − | 1.21639e13i | − | 0.704949i | ||||||
\(445\) | 1.00666e12i | 0.0576879i | ||||||||
\(446\) | − | 3.48584e13i | − | 1.97530i | ||||||
\(447\) | 8.03506e12i | 0.450247i | ||||||||
\(448\) | 2.84103e13 | 1.57429 | ||||||||
\(449\) | 6.79517e12 | 0.372365 | 0.186182 | − | 0.982515i | \(-0.440388\pi\) | ||||
0.186182 | + | 0.982515i | \(0.440388\pi\) | |||||||
\(450\) | − | 4.66787e12i | − | 0.252963i | ||||||
\(451\) | − | 2.63473e13i | − | 1.41206i | ||||||
\(452\) | − | 3.74371e13i | − | 1.98431i | ||||||
\(453\) | 1.15492e13i | 0.605426i | ||||||||
\(454\) | −5.75384e12 | −0.298318 | ||||||||
\(455\) | − | 5.84915e13i | − | 2.99941i | ||||||
\(456\) | 8.35603e11i | 0.0423814i | ||||||||
\(457\) | 2.65198e13i | 1.33042i | 0.746657 | + | 0.665209i | \(0.231658\pi\) | ||||
−0.746657 | + | 0.665209i | \(0.768342\pi\) | |||||||
\(458\) | −3.80356e13 | −1.88739 | ||||||||
\(459\) | 6.71636e12 | 0.329663 | ||||||||
\(460\) | 2.43047e12i | 0.118005i | ||||||||
\(461\) | 2.21723e13 | 1.06490 | 0.532448 | − | 0.846463i | \(-0.321272\pi\) | ||||
0.532448 | + | 0.846463i | \(0.321272\pi\) | |||||||
\(462\) | −2.53328e13 | −1.20358 | ||||||||
\(463\) | − | 7.92214e11i | − | 0.0372338i | −0.999827 | − | 0.0186169i | \(-0.994074\pi\) | ||
0.999827 | − | 0.0186169i | \(-0.00592629\pi\) | |||||||
\(464\) | −6.97966e12 | −0.324522 | ||||||||
\(465\) | 1.79288e13i | 0.824680i | ||||||||
\(466\) | 1.67237e13 | 0.761032 | ||||||||
\(467\) | 3.39537e13i | 1.52863i | 0.644842 | + | 0.764316i | \(0.276923\pi\) | ||||
−0.644842 | + | 0.764316i | \(0.723077\pi\) | |||||||
\(468\) | 1.48813e13i | 0.662843i | ||||||||
\(469\) | 2.91860e13i | 1.28620i | ||||||||
\(470\) | −4.06398e13 | −1.77199 | ||||||||
\(471\) | 8.63951e12i | 0.372722i | ||||||||
\(472\) | −1.19566e12 | − | 2.94853e12i | −0.0510386 | − | 0.125862i | ||||
\(473\) | 2.85245e13 | 1.20479 | ||||||||
\(474\) | 3.58954e13i | 1.50019i | ||||||||
\(475\) | 6.85416e12 | 0.283456 | ||||||||
\(476\) | −6.11868e13 | −2.50393 | ||||||||
\(477\) | −1.21426e13 | −0.491721 | ||||||||
\(478\) | − | 6.10352e13i | − | 2.44591i | ||||||
\(479\) | −4.75640e13 | −1.88626 | −0.943128 | − | 0.332430i | \(-0.892131\pi\) | ||||
−0.943128 | + | 0.332430i | \(0.892131\pi\) | |||||||
\(480\) | 2.60515e13i | 1.02241i | ||||||||
\(481\) | 5.22459e13 | 2.02921 | ||||||||
\(482\) | 4.47040e13i | 1.71835i | ||||||||
\(483\) | − | 1.77202e12i | − | 0.0674112i | ||||||
\(484\) | 4.71410e12 | 0.177489 | ||||||||
\(485\) | − | 3.75555e13i | − | 1.39947i | ||||||
\(486\) | − | 2.51682e12i | − | 0.0928262i | ||||||
\(487\) | 3.51604e13 | 1.28354 | 0.641769 | − | 0.766898i | \(-0.278201\pi\) | ||||
0.641769 | + | 0.766898i | \(0.278201\pi\) | |||||||
\(488\) | −2.64716e12 | −0.0956493 | ||||||||
\(489\) | −2.61618e13 | −0.935670 | ||||||||
\(490\) | − | 3.96542e13i | − | 1.40381i | ||||||
\(491\) | −1.27897e13 | −0.448182 | −0.224091 | − | 0.974568i | \(-0.571941\pi\) | ||||
−0.224091 | + | 0.974568i | \(0.571941\pi\) | |||||||
\(492\) | −2.38467e13 | −0.827185 | ||||||||
\(493\) | 1.80418e13 | 0.619504 | ||||||||
\(494\) | −4.18274e13 | −1.42176 | ||||||||
\(495\) | − | 1.31860e13i | − | 0.443697i | ||||||
\(496\) | − | 3.11638e13i | − | 1.03811i | ||||||
\(497\) | 4.93106e13 | 1.62614 | ||||||||
\(498\) | −1.32227e13 | −0.431692 | ||||||||
\(499\) | −1.52080e13 | −0.491553 | −0.245776 | − | 0.969327i | \(-0.579043\pi\) | ||||
−0.245776 | + | 0.969327i | \(0.579043\pi\) | |||||||
\(500\) | 2.00708e13 | 0.642266 | ||||||||
\(501\) | −1.87369e13 | −0.593621 | ||||||||
\(502\) | 8.05353e13i | 2.52620i | ||||||||
\(503\) | − | 2.33946e13i | − | 0.726568i | −0.931678 | − | 0.363284i | \(-0.881656\pi\) | ||
0.931678 | − | 0.363284i | \(-0.118344\pi\) | |||||||
\(504\) | 1.96741e12i | 0.0604981i | ||||||||
\(505\) | 7.78294e13i | 2.36966i | ||||||||
\(506\) | 4.52128e12i | 0.136304i | ||||||||
\(507\) | −4.45764e13 | −1.33066 | ||||||||
\(508\) | 1.79979e13 | 0.531989 | ||||||||
\(509\) | 5.67471e13i | 1.66094i | 0.557060 | + | 0.830472i | \(0.311929\pi\) | ||||
−0.557060 | + | 0.830472i | \(0.688071\pi\) | |||||||
\(510\) | − | 6.09639e13i | − | 1.76694i | ||||||
\(511\) | 3.23463e12i | 0.0928369i | ||||||||
\(512\) | − | 4.95708e13i | − | 1.40889i | ||||||
\(513\) | 3.69562e12 | 0.104016 | ||||||||
\(514\) | − | 1.06936e13i | − | 0.298063i | ||||||
\(515\) | − | 3.13019e13i | − | 0.864041i | ||||||
\(516\) | − | 2.58173e13i | − | 0.705769i | ||||||
\(517\) | −3.94944e13 | −1.06926 | ||||||||
\(518\) | 8.04986e13 | 2.15844 | ||||||||
\(519\) | − | 1.05608e13i | − | 0.280453i | ||||||
\(520\) | 1.15904e13 | 0.304846 | ||||||||
\(521\) | −4.25643e13 | −1.10881 | −0.554405 | − | 0.832247i | \(-0.687054\pi\) | ||||
−0.554405 | + | 0.832247i | \(0.687054\pi\) | |||||||
\(522\) | − | 6.76079e12i | − | 0.174439i | ||||||
\(523\) | −3.59058e13 | −0.917606 | −0.458803 | − | 0.888538i | \(-0.651722\pi\) | ||||
−0.458803 | + | 0.888538i | \(0.651722\pi\) | |||||||
\(524\) | 3.98979e13i | 1.00993i | ||||||||
\(525\) | 1.61380e13 | 0.404625 | ||||||||
\(526\) | 4.64312e13i | 1.15314i | ||||||||
\(527\) | 8.05555e13i | 1.98172i | ||||||||
\(528\) | 2.29199e13i | 0.558526i | ||||||||
\(529\) | 4.11103e13 | 0.992366 | ||||||||
\(530\) | 1.10217e14i | 2.63554i | ||||||||
\(531\) | −1.30405e13 | + | 5.28806e12i | −0.308902 | + | 0.125263i | ||||
\(532\) | −3.36675e13 | −0.790047 | ||||||||
\(533\) | − | 1.02425e14i | − | 2.38107i | ||||||
\(534\) | 1.69491e12 | 0.0390338 | ||||||||
\(535\) | 3.02306e13 | 0.689728 | ||||||||
\(536\) | −5.78334e12 | −0.130724 | ||||||||
\(537\) | − | 2.78861e13i | − | 0.624476i | ||||||
\(538\) | 6.41659e13 | 1.42362 | ||||||||
\(539\) | − | 3.85366e13i | − | 0.847091i | ||||||
\(540\) | −1.19345e13 | −0.259918 | ||||||||
\(541\) | − | 6.83733e13i | − | 1.47537i | −0.675147 | − | 0.737683i | \(-0.735920\pi\) | ||
0.675147 | − | 0.737683i | \(-0.264080\pi\) | |||||||
\(542\) | 1.54849e13i | 0.331064i | ||||||||
\(543\) | 2.58226e13 | 0.547016 | ||||||||
\(544\) | 1.17052e14i | 2.45688i | ||||||||
\(545\) | − | 6.10785e13i | − | 1.27030i | ||||||
\(546\) | −9.84817e13 | −2.02952 | ||||||||
\(547\) | −1.27448e13 | −0.260253 | −0.130127 | − | 0.991497i | \(-0.541538\pi\) | ||||
−0.130127 | + | 0.991497i | \(0.541538\pi\) | |||||||
\(548\) | −5.01011e13 | −1.01378 | ||||||||
\(549\) | 1.17076e13i | 0.234750i | ||||||||
\(550\) | −4.11759e13 | −0.818143 | ||||||||
\(551\) | 9.92733e12 | 0.195468 | ||||||||
\(552\) | 3.51133e11 | 0.00685136 | ||||||||
\(553\) | −1.24099e14 | −2.39963 | ||||||||
\(554\) | − | 2.88630e13i | − | 0.553087i | ||||||
\(555\) | 4.19003e13i | 0.795706i | ||||||||
\(556\) | 4.18465e13 | 0.787563 | ||||||||
\(557\) | −3.48486e13 | −0.649993 | −0.324997 | − | 0.945715i | \(-0.605363\pi\) | ||||
−0.324997 | + | 0.945715i | \(0.605363\pi\) | |||||||
\(558\) | 3.01865e13 | 0.558010 | ||||||||
\(559\) | 1.10890e14 | 2.03157 | ||||||||
\(560\) | −8.15376e13 | −1.48053 | ||||||||
\(561\) | − | 5.92458e13i | − | 1.06621i | ||||||
\(562\) | 4.86140e13i | 0.867121i | ||||||||
\(563\) | 1.65945e12i | 0.0293374i | 0.999892 | + | 0.0146687i | \(0.00466935\pi\) | ||||
−0.999892 | + | 0.0146687i | \(0.995331\pi\) | |||||||
\(564\) | 3.57461e13i | 0.626372i | ||||||||
\(565\) | 1.28958e14i | 2.23978i | ||||||||
\(566\) | −8.43088e13 | −1.45141 | ||||||||
\(567\) | 8.70125e12 | 0.148480 | ||||||||
\(568\) | 9.77112e12i | 0.165273i | ||||||||
\(569\) | 9.52495e13i | 1.59699i | 0.602003 | + | 0.798493i | \(0.294369\pi\) | ||||
−0.602003 | + | 0.798493i | \(0.705631\pi\) | |||||||
\(570\) | − | 3.35449e13i | − | 0.557509i | ||||||
\(571\) | 3.48630e12i | 0.0574360i | 0.999588 | + | 0.0287180i | \(0.00914248\pi\) | ||||
−0.999588 | + | 0.0287180i | \(0.990858\pi\) | |||||||
\(572\) | 1.31269e14 | 2.14380 | ||||||||
\(573\) | 2.14481e13i | 0.347229i | ||||||||
\(574\) | − | 1.57813e14i | − | 2.53270i | ||||||
\(575\) | − | 2.88022e12i | − | 0.0458234i | ||||||
\(576\) | 2.48982e13 | 0.392694 | ||||||||
\(577\) | 5.15438e13 | 0.805930 | 0.402965 | − | 0.915215i | \(-0.367980\pi\) | ||||
0.402965 | + | 0.915215i | \(0.367980\pi\) | |||||||
\(578\) | − | 1.80566e14i | − | 2.79897i | ||||||
\(579\) | −2.03784e13 | −0.313168 | ||||||||
\(580\) | −3.20590e13 | −0.488439 | ||||||||
\(581\) | − | 4.57141e13i | − | 0.690509i | ||||||
\(582\) | −6.32319e13 | −0.946938 | ||||||||
\(583\) | 1.07111e14i | 1.59035i | ||||||||
\(584\) | −6.40958e11 | −0.00943551 | ||||||||
\(585\) | − | 5.12607e13i | − | 0.748179i | ||||||
\(586\) | 8.75555e13i | 1.26705i | ||||||||
\(587\) | 4.23890e13i | 0.608223i | 0.952636 | + | 0.304112i | \(0.0983596\pi\) | ||||
−0.952636 | + | 0.304112i | \(0.901640\pi\) | |||||||
\(588\) | −3.48792e13 | −0.496226 | ||||||||
\(589\) | 4.43250e13i | 0.625276i | ||||||||
\(590\) | 4.79994e13 | + | 1.18367e14i | 0.671391 | + | 1.65566i | ||||
\(591\) | −4.46294e13 | −0.618989 | ||||||||
\(592\) | − | 7.28312e13i | − | 1.00163i | ||||||
\(593\) | 4.77928e13 | 0.651762 | 0.325881 | − | 0.945411i | \(-0.394339\pi\) | ||||
0.325881 | + | 0.945411i | \(0.394339\pi\) | |||||||
\(594\) | −2.22012e13 | −0.300223 | ||||||||
\(595\) | 2.10767e14 | 2.82630 | ||||||||
\(596\) | − | 6.41512e13i | − | 0.853048i | ||||||
\(597\) | 6.13473e13 | 0.808953 | ||||||||
\(598\) | 1.75765e13i | 0.229841i | ||||||||
\(599\) | −4.04491e13 | −0.524536 | −0.262268 | − | 0.964995i | \(-0.584470\pi\) | ||||
−0.262268 | + | 0.964995i | \(0.584470\pi\) | |||||||
\(600\) | 3.19782e12i | 0.0411242i | ||||||||
\(601\) | 1.44431e14i | 1.84199i | 0.389572 | + | 0.920996i | \(0.372623\pi\) | ||||
−0.389572 | + | 0.920996i | \(0.627377\pi\) | |||||||
\(602\) | 1.70855e14 | 2.16095 | ||||||||
\(603\) | 2.55780e13i | 0.320833i | ||||||||
\(604\) | − | 9.22080e13i | − | 1.14705i | ||||||
\(605\) | −1.62384e13 | −0.200339 | ||||||||
\(606\) | 1.31041e14 | 1.60341 | ||||||||
\(607\) | −6.25111e13 | −0.758601 | −0.379301 | − | 0.925274i | \(-0.623835\pi\) | ||||
−0.379301 | + | 0.925274i | \(0.623835\pi\) | |||||||
\(608\) | 6.44067e13i | 0.775199i | ||||||||
\(609\) | 2.33737e13 | 0.279023 | ||||||||
\(610\) | 1.06269e14 | 1.25822 | ||||||||
\(611\) | −1.53535e14 | −1.80302 | ||||||||
\(612\) | −5.36228e13 | −0.624587 | ||||||||
\(613\) | 9.96934e13i | 1.15177i | 0.817532 | + | 0.575883i | \(0.195342\pi\) | ||||
−0.817532 | + | 0.575883i | \(0.804658\pi\) | |||||||
\(614\) | − | 1.44233e14i | − | 1.65281i | ||||||
\(615\) | 8.21434e13 | 0.933678 | ||||||||
\(616\) | 1.73547e13 | 0.195666 | ||||||||
\(617\) | 1.57532e14 | 1.76174 | 0.880870 | − | 0.473358i | \(-0.156958\pi\) | ||||
0.880870 | + | 0.473358i | \(0.156958\pi\) | |||||||
\(618\) | −5.27028e13 | −0.584643 | ||||||||
\(619\) | 9.05151e12 | 0.0996019 | 0.0498009 | − | 0.998759i | \(-0.484141\pi\) | ||||
0.0498009 | + | 0.998759i | \(0.484141\pi\) | |||||||
\(620\) | − | 1.43142e14i | − | 1.56246i | ||||||
\(621\) | − | 1.55296e12i | − | 0.0168152i | ||||||
\(622\) | 3.22274e13i | 0.346157i | ||||||||
\(623\) | 5.85973e12i | 0.0624363i | ||||||||
\(624\) | 8.91015e13i | 0.941807i | ||||||||
\(625\) | −1.19152e14 | −1.24940 | ||||||||
\(626\) | −9.26653e13 | −0.963930 | ||||||||
\(627\) | − | 3.25995e13i | − | 0.336413i | ||||||
\(628\) | − | 6.89772e13i | − | 0.706167i | ||||||
\(629\) | 1.88262e14i | 1.91209i | ||||||||
\(630\) | − | 7.89807e13i | − | 0.795826i | ||||||
\(631\) | 1.60900e14 | 1.60845 | 0.804227 | − | 0.594322i | \(-0.202580\pi\) | ||||
0.804227 | + | 0.594322i | \(0.202580\pi\) | |||||||
\(632\) | − | 2.45909e13i | − | 0.243887i | ||||||
\(633\) | 2.26827e13i | 0.223190i | ||||||||
\(634\) | − | 1.97090e14i | − | 1.92406i | ||||||
\(635\) | −6.19964e13 | −0.600479 | ||||||||
\(636\) | 9.69453e13 | 0.931625 | ||||||||
\(637\) | − | 1.49812e14i | − | 1.42840i | ||||||
\(638\) | −5.96377e13 | −0.564180 | ||||||||
\(639\) | 4.32147e13 | 0.405628 | ||||||||
\(640\) | − | 3.58528e13i | − | 0.333905i | ||||||
\(641\) | −6.48002e13 | −0.598806 | −0.299403 | − | 0.954127i | \(-0.596787\pi\) | ||||
−0.299403 | + | 0.954127i | \(0.596787\pi\) | |||||||
\(642\) | − | 5.08991e13i | − | 0.466697i | ||||||
\(643\) | −7.74552e13 | −0.704686 | −0.352343 | − | 0.935871i | \(-0.614615\pi\) | ||||
−0.352343 | + | 0.935871i | \(0.614615\pi\) | |||||||
\(644\) | 1.41476e13i | 0.127719i | ||||||||
\(645\) | 8.89315e13i | 0.796631i | ||||||||
\(646\) | − | 1.50720e14i | − | 1.33970i | ||||||
\(647\) | 1.06247e14 | 0.937119 | 0.468559 | − | 0.883432i | \(-0.344773\pi\) | ||||
0.468559 | + | 0.883432i | \(0.344773\pi\) | |||||||
\(648\) | 1.72420e12i | 0.0150908i | ||||||||
\(649\) | 4.66466e13 | + | 1.15031e14i | 0.405132 | + | 0.999063i | ||||
\(650\) | −1.60072e14 | −1.37958 | ||||||||
\(651\) | 1.04362e14i | 0.892561i | ||||||||
\(652\) | 2.08873e14 | 1.77274 | ||||||||
\(653\) | 1.19468e14 | 1.00620 | 0.503100 | − | 0.864228i | \(-0.332193\pi\) | ||||
0.503100 | + | 0.864228i | \(0.332193\pi\) | |||||||
\(654\) | −1.02837e14 | −0.859533 | ||||||||
\(655\) | − | 1.37434e14i | − | 1.13996i | ||||||
\(656\) | −1.42782e14 | −1.17531 | ||||||||
\(657\) | 2.83477e12i | 0.0231574i | ||||||||
\(658\) | −2.36561e14 | −1.91785 | ||||||||
\(659\) | 2.02038e14i | 1.62557i | 0.582566 | + | 0.812784i | \(0.302049\pi\) | ||||
−0.582566 | + | 0.812784i | \(0.697951\pi\) | |||||||
\(660\) | 1.05276e14i | 0.840638i | ||||||||
\(661\) | −6.65042e13 | −0.527038 | −0.263519 | − | 0.964654i | \(-0.584883\pi\) | ||||
−0.263519 | + | 0.964654i | \(0.584883\pi\) | |||||||
\(662\) | 6.11868e13i | 0.481247i | ||||||||
\(663\) | − | 2.30319e14i | − | 1.79788i | ||||||
\(664\) | 9.05847e12 | 0.0701802 | ||||||||
\(665\) | 1.15973e14 | 0.891760 | ||||||||
\(666\) | 7.05473e13 | 0.538405 | ||||||||
\(667\) | − | 4.17162e12i | − | 0.0315992i | ||||||
\(668\) | 1.49594e14 | 1.12469 | ||||||||
\(669\) | 1.05616e14 | 0.788131 | ||||||||
\(670\) | 2.32170e14 | 1.71962 | ||||||||
\(671\) | 1.03274e14 | 0.759240 | ||||||||
\(672\) | 1.51644e14i | 1.10657i | ||||||||
\(673\) | − | 1.75283e14i | − | 1.26959i | −0.772679 | − | 0.634796i | \(-0.781084\pi\) | ||
0.772679 | − | 0.634796i | \(-0.218916\pi\) | |||||||
\(674\) | −1.03624e14 | −0.745009 | ||||||||
\(675\) | 1.41430e13 | 0.100930 | ||||||||
\(676\) | 3.55895e14 | 2.52109 | ||||||||
\(677\) | −1.00815e13 | −0.0708898 | −0.0354449 | − | 0.999372i | \(-0.511285\pi\) | ||||
−0.0354449 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(678\) | 2.17125e14 | 1.51552 | ||||||||
\(679\) | − | 2.18608e14i | − | 1.51467i | ||||||
\(680\) | 4.17645e13i | 0.287252i | ||||||||
\(681\) | − | 1.74333e13i | − | 0.119027i | ||||||
\(682\) | − | 2.66279e14i | − | 1.80474i | ||||||
\(683\) | − | 1.10610e14i | − | 0.744204i | −0.928192 | − | 0.372102i | \(-0.878637\pi\) | ||
0.928192 | − | 0.372102i | \(-0.121363\pi\) | |||||||
\(684\) | −2.95055e13 | −0.197071 | ||||||||
\(685\) | 1.72581e14 | 1.14430 | ||||||||
\(686\) | 6.29427e13i | 0.414310i | ||||||||
\(687\) | − | 1.15242e14i | − | 0.753058i | ||||||
\(688\) | − | 1.54581e14i | − | 1.00280i | ||||||
\(689\) | 4.16396e14i | 2.68170i | ||||||||
\(690\) | −1.40961e13 | −0.0901266 | ||||||||
\(691\) | 1.58453e13i | 0.100580i | 0.998735 | + | 0.0502898i | \(0.0160145\pi\) | ||||
−0.998735 | + | 0.0502898i | \(0.983985\pi\) | |||||||
\(692\) | 8.43166e13i | 0.531352i | ||||||||
\(693\) | − | 7.67548e13i | − | 0.480219i | ||||||
\(694\) | −1.54241e14 | −0.958084 | ||||||||
\(695\) | −1.44147e14 | −0.888956 | ||||||||
\(696\) | 4.63161e12i | 0.0283586i | ||||||||
\(697\) | 3.69077e14 | 2.24364 | ||||||||
\(698\) | −2.47766e13 | −0.149543 | ||||||||
\(699\) | 5.06704e13i | 0.303647i | ||||||||
\(700\) | −1.28844e14 | −0.766610 | ||||||||
\(701\) | 4.46930e13i | 0.264028i | 0.991248 | + | 0.132014i | \(0.0421443\pi\) | ||||
−0.991248 | + | 0.132014i | \(0.957856\pi\) | |||||||
\(702\) | −8.63073e13 | −0.506247 | ||||||||
\(703\) | 1.03589e14i | 0.603308i | ||||||||
\(704\) | − | 2.19630e14i | − | 1.27007i | ||||||
\(705\) | − | 1.23133e14i | − | 0.707013i | ||||||
\(706\) | −5.90083e13 | −0.336426 | ||||||||
\(707\) | 4.53040e14i | 2.56472i | ||||||||
\(708\) | 1.04114e14 | − | 4.22194e13i | 0.585252 | − | 0.237326i | ||||
\(709\) | −2.60393e14 | −1.45344 | −0.726720 | − | 0.686933i | \(-0.758956\pi\) | ||||
−0.726720 | + | 0.686933i | \(0.758956\pi\) | |||||||
\(710\) | − | 3.92257e14i | − | 2.17410i | ||||||
\(711\) | −1.08758e14 | −0.598568 | ||||||||
\(712\) | −1.16113e12 | −0.00634574 | ||||||||
\(713\) | 1.86260e13 | 0.101082 | ||||||||
\(714\) | − | 3.54867e14i | − | 1.91238i | ||||||
\(715\) | −4.52177e14 | −2.41979 | ||||||||
\(716\) | 2.22640e14i | 1.18315i | ||||||||
\(717\) | 1.84928e14 | 0.975902 | ||||||||
\(718\) | 3.47376e14i | 1.82045i | ||||||||
\(719\) | − | 2.80920e14i | − | 1.46197i | −0.682393 | − | 0.730985i | \(-0.739061\pi\) | ||
0.682393 | − | 0.730985i | \(-0.260939\pi\) | |||||||
\(720\) | −7.14579e13 | −0.369307 | ||||||||
\(721\) | − | 1.82206e14i | − | 0.935162i | ||||||
\(722\) | 2.00964e14i | 1.02431i | ||||||||
\(723\) | −1.35447e14 | −0.685609 | ||||||||
\(724\) | −2.06165e14 | −1.03639 | ||||||||
\(725\) | 3.79915e13 | 0.189669 | ||||||||
\(726\) | 2.73405e13i | 0.135557i | ||||||||
\(727\) | 2.03091e14 | 1.00004 | 0.500022 | − | 0.866013i | \(-0.333325\pi\) | ||||
0.500022 | + | 0.866013i | \(0.333325\pi\) | |||||||
\(728\) | 6.74668e13 | 0.329939 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | 2.57310e13 | 0.124120 | ||||||||
\(731\) | 3.99577e14i | 1.91432i | ||||||||
\(732\) | − | 9.34726e13i | − | 0.444763i | ||||||
\(733\) | −4.22591e13 | −0.199710 | −0.0998551 | − | 0.995002i | \(-0.531838\pi\) | ||||
−0.0998551 | + | 0.995002i | \(0.531838\pi\) | |||||||
\(734\) | −1.35540e14 | −0.636192 | ||||||||
\(735\) | 1.20147e14 | 0.560112 | ||||||||
\(736\) | 2.70647e13 | 0.125318 | ||||||||
\(737\) | 2.25626e14 | 1.03765 | ||||||||
\(738\) | − | 1.38304e14i | − | 0.631763i | ||||||
\(739\) | 7.28618e13i | 0.330581i | 0.986245 | + | 0.165290i | \(0.0528561\pi\) | ||||
−0.986245 | + | 0.165290i | \(0.947144\pi\) | |||||||
\(740\) | − | 3.34529e14i | − | 1.50756i | ||||||
\(741\) | − | 1.26731e14i | − | 0.567273i | ||||||
\(742\) | 6.41568e14i | 2.85248i | ||||||||
\(743\) | 1.84631e14 | 0.815381 | 0.407690 | − | 0.913120i | \(-0.366334\pi\) | ||||
0.407690 | + | 0.913120i | \(0.366334\pi\) | |||||||
\(744\) | −2.06799e13 | −0.0907158 | ||||||||
\(745\) | 2.20978e14i | 0.962872i | ||||||||
\(746\) | − | 3.79696e14i | − | 1.64340i | ||||||
\(747\) | − | 4.00629e13i | − | 0.172242i | ||||||
\(748\) | 4.73013e14i | 2.02007i | ||||||||
\(749\) | 1.75970e14 | 0.746501 | ||||||||
\(750\) | 1.16405e14i | 0.490531i | ||||||||
\(751\) | 7.80965e13i | 0.326913i | 0.986551 | + | 0.163456i | \(0.0522643\pi\) | ||||
−0.986551 | + | 0.163456i | \(0.947736\pi\) | |||||||
\(752\) | 2.14029e14i | 0.889988i | ||||||||
\(753\) | −2.44010e14 | −1.00794 | ||||||||
\(754\) | −2.31842e14 | −0.951341 | ||||||||
\(755\) | 3.17624e14i | 1.29473i | ||||||||
\(756\) | −6.94701e13 | −0.281312 | ||||||||
\(757\) | 3.97360e14 | 1.59847 | 0.799236 | − | 0.601017i | \(-0.205238\pi\) | ||||
0.799236 | + | 0.601017i | \(0.205238\pi\) | |||||||
\(758\) | − | 3.50607e14i | − | 1.40112i | ||||||
\(759\) | −1.36988e13 | −0.0543844 | ||||||||
\(760\) | 2.29806e13i | 0.0906344i | ||||||||
\(761\) | −1.06320e14 | −0.416575 | −0.208287 | − | 0.978068i | \(-0.566789\pi\) | ||||
−0.208287 | + | 0.978068i | \(0.566789\pi\) | |||||||
\(762\) | 1.04383e14i | 0.406307i | ||||||||
\(763\) | − | 3.55534e14i | − | 1.37486i | ||||||
\(764\) | − | 1.71240e14i | − | 0.657867i | ||||||
\(765\) | 1.84712e14 | 0.704997 | ||||||||
\(766\) | − | 2.91148e14i | − | 1.10400i | ||||||
\(767\) | 1.81339e14 | + | 4.47186e14i | 0.683148 | + | 1.68466i | ||||
\(768\) | 1.21363e14 | 0.454234 | ||||||||
\(769\) | − | 2.09290e13i | − | 0.0778246i | −0.999243 | − | 0.0389123i | \(-0.987611\pi\) | ||
0.999243 | − | 0.0389123i | \(-0.0123893\pi\) | |||||||
\(770\) | −6.96698e14 | −2.57390 | ||||||||
\(771\) | 3.24000e13 | 0.118925 | ||||||||
\(772\) | 1.62700e14 | 0.593335 | ||||||||
\(773\) | 1.46588e14i | 0.531132i | 0.964093 | + | 0.265566i | \(0.0855588\pi\) | ||||
−0.964093 | + | 0.265566i | \(0.914441\pi\) | |||||||
\(774\) | 1.49733e14 | 0.539031 | ||||||||
\(775\) | 1.69630e14i | 0.606727i | ||||||||
\(776\) | 4.33182e13 | 0.153944 | ||||||||
\(777\) | 2.43899e14i | 0.861202i | ||||||||
\(778\) | 4.15598e14i | 1.45806i | ||||||||
\(779\) | 2.03082e14 | 0.707919 | ||||||||
\(780\) | 4.09261e14i | 1.41752i | ||||||||
\(781\) | − | 3.81202e14i | − | 1.31190i | ||||||
\(782\) | −6.33349e13 | −0.216576 | ||||||||
\(783\) | 2.04842e13 | 0.0696002 | ||||||||
\(784\) | −2.08839e14 | −0.705068 | ||||||||
\(785\) | 2.37602e14i | 0.797080i | ||||||||
\(786\) | −2.31397e14 | −0.771338 | ||||||||
\(787\) | 1.49665e14 | 0.495732 | 0.247866 | − | 0.968794i | \(-0.420271\pi\) | ||||
0.247866 | + | 0.968794i | \(0.420271\pi\) | |||||||
\(788\) | 3.56317e14 | 1.17275 | ||||||||
\(789\) | −1.40680e14 | −0.460094 | ||||||||
\(790\) | 9.87189e14i | 3.20823i | ||||||||
\(791\) | 7.50654e14i | 2.42414i | ||||||||
\(792\) | 1.52093e13 | 0.0488072 | ||||||||
\(793\) | 4.01480e14 | 1.28026 | ||||||||
\(794\) | −1.62051e14 | −0.513509 | ||||||||
\(795\) | −3.33942e14 | −1.05156 | ||||||||
\(796\) | −4.89791e14 | −1.53266 | ||||||||
\(797\) | − | 3.79427e13i | − | 0.117988i | −0.998258 | − | 0.0589938i | \(-0.981211\pi\) | ||
0.998258 | − | 0.0589938i | \(-0.0187892\pi\) | |||||||
\(798\) | − | 1.95263e14i | − | 0.603399i | ||||||
\(799\) | − | 5.53245e14i | − | 1.69896i | ||||||
\(800\) | 2.46482e14i | 0.752202i | ||||||||
\(801\) | 5.13534e12i | 0.0155742i | ||||||||
\(802\) | −2.38183e13 | −0.0717858 | ||||||||
\(803\) | 2.50058e13 | 0.0748968 | ||||||||
\(804\) | − | 2.04212e14i | − | 0.607858i | ||||||
\(805\) | − | 4.87336e13i | − | 0.144161i | ||||||
\(806\) | − | 1.03516e15i | − | 3.04322i | ||||||
\(807\) | 1.94413e14i | 0.568013i | ||||||||
\(808\) | −8.97720e13 | −0.260666 | ||||||||
\(809\) | − | 2.30150e14i | − | 0.664154i | −0.943252 | − | 0.332077i | \(-0.892251\pi\) | ||
0.943252 | − | 0.332077i | \(-0.107749\pi\) | |||||||
\(810\) | − | 6.92170e13i | − | 0.198512i | ||||||
\(811\) | − | 2.99669e14i | − | 0.854156i | −0.904215 | − | 0.427078i | \(-0.859543\pi\) | ||
0.904215 | − | 0.427078i | \(-0.140457\pi\) | |||||||
\(812\) | −1.86614e14 | −0.528644 | ||||||||
\(813\) | −4.69170e13 | −0.132092 | ||||||||
\(814\) | − | 6.22306e14i | − | 1.74133i | ||||||
\(815\) | −7.19495e14 | −2.00097 | ||||||||
\(816\) | −3.21066e14 | −0.887450 | ||||||||
\(817\) | 2.19864e14i | 0.604009i | ||||||||
\(818\) | −7.17735e14 | −1.95974 | ||||||||
\(819\) | − | 2.98385e14i | − | 0.809763i | ||||||
\(820\) | −6.55826e14 | −1.76897 | ||||||||
\(821\) | − | 4.71250e14i | − | 1.26338i | −0.775219 | − | 0.631692i | \(-0.782361\pi\) | ||
0.775219 | − | 0.631692i | \(-0.217639\pi\) | |||||||
\(822\) | − | 2.90573e14i | − | 0.774276i | ||||||
\(823\) | 2.72158e13i | 0.0720811i | 0.999350 | + | 0.0360406i | \(0.0114745\pi\) | ||||
−0.999350 | + | 0.0360406i | \(0.988525\pi\) | |||||||
\(824\) | 3.61050e13 | 0.0950455 | ||||||||
\(825\) | − | 1.24757e14i | − | 0.326433i | ||||||
\(826\) | 2.79401e14 | + | 6.89008e14i | 0.726654 | + | 1.79194i | ||||
\(827\) | −7.11843e13 | −0.184016 | −0.0920082 | − | 0.995758i | \(-0.529329\pi\) | ||||
−0.0920082 | + | 0.995758i | \(0.529329\pi\) | |||||||
\(828\) | 1.23987e13i | 0.0318584i | ||||||||
\(829\) | −3.08006e14 | −0.786659 | −0.393330 | − | 0.919398i | \(-0.628677\pi\) | ||||
−0.393330 | + | 0.919398i | \(0.628677\pi\) | |||||||
\(830\) | −3.63648e14 | −0.923189 | ||||||||
\(831\) | 8.74508e13 | 0.220678 | ||||||||
\(832\) | − | 8.53813e14i | − | 2.14164i | ||||||
\(833\) | 5.39829e14 | 1.34596 | ||||||||
\(834\) | 2.42699e14i | 0.601502i | ||||||||
\(835\) | −5.15298e14 | −1.26948 | ||||||||
\(836\) | 2.60272e14i | 0.637376i | ||||||||
\(837\) | 9.14608e13i | 0.222642i | ||||||||
\(838\) | 4.47361e14 | 1.08252 | ||||||||
\(839\) | 6.69515e14i | 1.61046i | 0.592961 | + | 0.805231i | \(0.297959\pi\) | ||||
−0.592961 | + | 0.805231i | \(0.702041\pi\) | |||||||
\(840\) | 5.41072e13i | 0.129378i | ||||||||
\(841\) | −3.65682e14 | −0.869207 | ||||||||
\(842\) | 5.16545e14 | 1.22053 | ||||||||
\(843\) | −1.47293e14 | −0.345975 | ||||||||
\(844\) | − | 1.81096e14i | − | 0.422861i | ||||||
\(845\) | −1.22593e15 | −2.84566 | ||||||||
\(846\) | −2.07318e14 | −0.478392 | ||||||||
\(847\) | −9.45227e13 | −0.216830 | ||||||||
\(848\) | 5.80459e14 | 1.32371 | ||||||||
\(849\) | − | 2.55443e14i | − | 0.579104i | ||||||
\(850\) | − | 5.76799e14i | − | 1.29996i | ||||||
\(851\) | 4.35299e13 | 0.0975304 | ||||||||
\(852\) | −3.45023e14 | −0.768511 | ||||||||
\(853\) | −1.00160e14 | −0.221794 | −0.110897 | − | 0.993832i | \(-0.535372\pi\) | ||||
−0.110897 | + | 0.993832i | \(0.535372\pi\) | |||||||
\(854\) | 6.18586e14 | 1.36179 | ||||||||
\(855\) | 1.01636e14 | 0.222442 | ||||||||
\(856\) | 3.48694e13i | 0.0758709i | ||||||||
\(857\) | − | 6.30075e14i | − | 1.36298i | −0.731829 | − | 0.681488i | \(-0.761333\pi\) | ||
0.731829 | − | 0.681488i | \(-0.238667\pi\) | |||||||
\(858\) | 7.61327e14i | 1.63732i | ||||||||
\(859\) | − | 4.84948e14i | − | 1.03688i | −0.855113 | − | 0.518441i | \(-0.826512\pi\) | ||
0.855113 | − | 0.518441i | \(-0.173488\pi\) | |||||||
\(860\) | − | 7.10022e14i | − | 1.50931i | ||||||
\(861\) | 4.78151e14 | 1.01053 | ||||||||
\(862\) | 7.77959e14 | 1.63463 | ||||||||
\(863\) | 4.17348e14i | 0.871855i | 0.899982 | + | 0.435927i | \(0.143580\pi\) | ||||
−0.899982 | + | 0.435927i | \(0.856420\pi\) | |||||||
\(864\) | 1.32898e14i | 0.276025i | ||||||||
\(865\) | − | 2.90441e14i | − | 0.599760i | ||||||
\(866\) | 9.87812e14i | 2.02808i | ||||||||
\(867\) | 5.47090e14 | 1.11677 | ||||||||
\(868\) | − | 8.33219e14i | − | 1.69107i | ||||||
\(869\) | 9.59367e14i | 1.93591i | ||||||||
\(870\) | − | 1.85934e14i | − | 0.373046i | ||||||
\(871\) | 8.77126e14 | 1.74973 | ||||||||
\(872\) | 7.04508e13 | 0.139734 | ||||||||
\(873\) | − | 1.91584e14i | − | 0.377822i | ||||||
\(874\) | −3.48495e13 | −0.0683344 | ||||||||
\(875\) | −4.02441e14 | −0.784625 | ||||||||
\(876\) | − | 2.26325e13i | − | 0.0438745i | ||||||
\(877\) | 2.00146e14 | 0.385788 | 0.192894 | − | 0.981220i | \(-0.438213\pi\) | ||||
0.192894 | + | 0.981220i | \(0.438213\pi\) | |||||||
\(878\) | 1.74585e14i | 0.334606i | ||||||||
\(879\) | −2.65280e14 | −0.505546 | ||||||||
\(880\) | 6.30338e14i | 1.19443i | ||||||||
\(881\) | − | 1.00087e15i | − | 1.88581i | −0.333057 | − | 0.942907i | \(-0.608080\pi\) | ||
0.333057 | − | 0.942907i | \(-0.391920\pi\) | |||||||
\(882\) | − | 2.02290e14i | − | 0.378993i | ||||||
\(883\) | −4.29843e13 | −0.0800767 | −0.0400383 | − | 0.999198i | \(-0.512748\pi\) | ||||
−0.0400383 | + | 0.999198i | \(0.512748\pi\) | |||||||
\(884\) | 1.83885e15i | 3.40631i | ||||||||
\(885\) | −3.58636e14 | + | 1.45431e14i | −0.660598 | + | 0.267880i | ||||
\(886\) | −9.51304e14 | −1.74241 | ||||||||
\(887\) | − | 9.55737e14i | − | 1.74068i | −0.492447 | − | 0.870342i | \(-0.663898\pi\) | ||
0.492447 | − | 0.870342i | \(-0.336102\pi\) | |||||||
\(888\) | −4.83298e13 | −0.0875286 | ||||||||
\(889\) | −3.60877e14 | −0.649906 | ||||||||
\(890\) | 4.66132e13 | 0.0834754 | ||||||||
\(891\) | − | 6.72663e13i | − | 0.119787i | ||||||
\(892\) | −8.43228e14 | −1.49321 | ||||||||
\(893\) | − | 3.04419e14i | − | 0.536061i | ||||||
\(894\) | 3.72060e14 | 0.651516 | ||||||||
\(895\) | − | 7.66917e14i | − | 1.33547i | ||||||
\(896\) | − | 2.08697e14i | − | 0.361390i | ||||||
\(897\) | −5.32544e13 | −0.0917050 | ||||||||
\(898\) | − | 3.14648e14i | − | 0.538819i | ||||||
\(899\) | 2.45686e14i | 0.418390i | ||||||||
\(900\) | −1.12916e14 | −0.191225 | ||||||||
\(901\) | −1.50043e15 | −2.52692 | ||||||||
\(902\) | −1.22000e15 | −2.04327 | ||||||||
\(903\) | 5.17665e14i | 0.862203i | ||||||||
\(904\) | −1.48746e14 | −0.246378 | ||||||||
\(905\) | 7.10166e14 | 1.16982 | ||||||||
\(906\) | 5.34781e14 | 0.876063 | ||||||||
\(907\) | 8.58784e14 | 1.39910 | 0.699548 | − | 0.714586i | \(-0.253385\pi\) | ||||
0.699548 | + | 0.714586i | \(0.253385\pi\) | |||||||
\(908\) | 1.39186e14i | 0.225510i | ||||||||
\(909\) | 3.97035e14i | 0.639748i | ||||||||
\(910\) | −2.70842e15 | −4.34020 | ||||||||
\(911\) | −4.42625e14 | −0.705415 | −0.352707 | − | 0.935734i | \(-0.614739\pi\) | ||||
−0.352707 | + | 0.935734i | \(0.614739\pi\) | |||||||
\(912\) | −1.76664e14 | −0.280010 | ||||||||
\(913\) | −3.53399e14 | −0.557073 | ||||||||
\(914\) | 1.22799e15 | 1.92514 | ||||||||
\(915\) | 3.21980e14i | 0.502023i | ||||||||
\(916\) | 9.20085e14i | 1.42676i | ||||||||
\(917\) | − | 7.99995e14i | − | 1.23379i | ||||||
\(918\) | − | 3.10998e14i | − | 0.477028i | ||||||
\(919\) | 7.03055e14i | 1.07254i | 0.844048 | + | 0.536268i | \(0.180166\pi\) | ||||
−0.844048 | + | 0.536268i | \(0.819834\pi\) | |||||||
\(920\) | 9.65680e12 | 0.0146519 | ||||||||
\(921\) | 4.37005e14 | 0.659460 | ||||||||
\(922\) | − | 1.02668e15i | − | 1.54092i | ||||||
\(923\) | − | 1.48193e15i | − | 2.21217i | ||||||
\(924\) | 6.12804e14i | 0.909833i | ||||||||
\(925\) | 3.96432e14i | 0.585410i | ||||||||
\(926\) | −3.66831e13 | −0.0538780 | ||||||||
\(927\) | − | 1.59682e14i | − | 0.233269i | ||||||
\(928\) | 3.56996e14i | 0.518708i | ||||||||
\(929\) | − | 3.10138e14i | − | 0.448204i | −0.974566 | − | 0.224102i | \(-0.928055\pi\) | ||
0.974566 | − | 0.224102i | \(-0.0719449\pi\) | |||||||
\(930\) | 8.30184e14 | 1.19333 | ||||||||
\(931\) | 2.97036e14 | 0.424679 | ||||||||
\(932\) | − | 4.04548e14i | − | 0.575296i | ||||||
\(933\) | −9.76442e13 | −0.138114 | ||||||||
\(934\) | 1.57221e15 | 2.21196 | ||||||||
\(935\) | − | 1.62936e15i | − | 2.28013i | ||||||
\(936\) | 5.91265e13 | 0.0823006 | ||||||||
\(937\) | − | 3.54299e14i | − | 0.490538i | −0.969455 | − | 0.245269i | \(-0.921124\pi\) | ||
0.969455 | − | 0.245269i | \(-0.0788763\pi\) | |||||||
\(938\) | 1.35144e15 | 1.86116 | ||||||||
\(939\) | − | 2.80762e14i | − | 0.384601i | ||||||
\(940\) | 9.83081e14i | 1.33952i | ||||||||
\(941\) | 4.65865e14i | 0.631411i | 0.948857 | + | 0.315705i | \(0.102241\pi\) | ||||
−0.948857 | + | 0.315705i | \(0.897759\pi\) | |||||||
\(942\) | 4.00049e14 | 0.539335 | ||||||||
\(943\) | − | 8.53381e13i | − | 0.114442i | ||||||
\(944\) | 6.23381e14 | − | 2.52788e14i | 0.831561 | − | 0.337208i | ||||
\(945\) | 2.39300e14 | 0.317529 | ||||||||
\(946\) | − | 1.32082e15i | − | 1.74336i | ||||||
\(947\) | 8.40312e14 | 1.10329 | 0.551646 | − | 0.834078i | \(-0.314000\pi\) | ||||
0.551646 | + | 0.834078i | \(0.314000\pi\) | |||||||
\(948\) | 8.68315e14 | 1.13406 | ||||||||
\(949\) | 9.72104e13 | 0.126294 | ||||||||
\(950\) | − | 3.17379e14i | − | 0.410166i | ||||||
\(951\) | 5.97154e14 | 0.767686 | ||||||||
\(952\) | 2.43108e14i | 0.310896i | ||||||||
\(953\) | 1.13658e15 | 1.44589 | 0.722947 | − | 0.690903i | \(-0.242787\pi\) | ||||
0.722947 | + | 0.690903i | \(0.242787\pi\) | |||||||
\(954\) | 5.62256e14i | 0.711529i | ||||||||
\(955\) | 5.89861e14i | 0.742562i | ||||||||
\(956\) | −1.47645e15 | −1.84896 | ||||||||
\(957\) | − | 1.80694e14i | − | 0.225104i | ||||||
\(958\) | 2.20243e15i | 2.72945i | ||||||||
\(959\) | 1.00458e15 | 1.23849 | ||||||||
\(960\) | 6.84744e14 | 0.839792 | ||||||||
\(961\) | −2.77345e14 | −0.338379 | ||||||||
\(962\) | − | 2.41922e15i | − | 2.93630i | ||||||
\(963\) | 1.54217e14 | 0.186209 | ||||||||
\(964\) | 1.08139e15 | 1.29897 | ||||||||
\(965\) | −5.60443e14 | −0.669723 | ||||||||
\(966\) | −8.20524e13 | −0.0975451 | ||||||||
\(967\) | − | 8.59747e14i | − | 1.01681i | −0.861119 | − | 0.508403i | \(-0.830236\pi\) | ||
0.861119 | − | 0.508403i | \(-0.169764\pi\) | |||||||
\(968\) | − | 1.87301e13i | − | 0.0220376i | ||||||
\(969\) | 4.56660e14 | 0.534532 | ||||||||
\(970\) | −1.73899e15 | −2.02506 | ||||||||
\(971\) | 1.16181e15 | 1.34598 | 0.672989 | − | 0.739652i | \(-0.265010\pi\) | ||||
0.672989 | + | 0.739652i | \(0.265010\pi\) | |||||||
\(972\) | −6.08821e13 | −0.0701711 | ||||||||
\(973\) | −8.39068e14 | −0.962128 | ||||||||
\(974\) | − | 1.62809e15i | − | 1.85730i | ||||||
\(975\) | − | 4.84994e14i | − | 0.550444i | ||||||
\(976\) | − | 5.59666e14i | − | 0.631946i | ||||||
\(977\) | 4.63358e14i | 0.520528i | 0.965537 | + | 0.260264i | \(0.0838096\pi\) | ||||
−0.965537 | + | 0.260264i | \(0.916190\pi\) | |||||||
\(978\) | 1.21141e15i | 1.35393i | ||||||||
\(979\) | 4.52995e13 | 0.0503709 | ||||||||
\(980\) | −9.59240e14 | −1.06120 | ||||||||
\(981\) | − | 3.11583e14i | − | 0.342948i | ||||||
\(982\) | 5.92223e14i | 0.648527i | ||||||||
\(983\) | − | 7.27851e14i | − | 0.793003i | −0.918034 | − | 0.396502i | \(-0.870224\pi\) | ||
0.918034 | − | 0.396502i | \(-0.129776\pi\) | |||||||
\(984\) | 9.47480e13i | 0.102706i | ||||||||
\(985\) | −1.22739e15 | −1.32373 | ||||||||
\(986\) | − | 8.35416e14i | − | 0.896434i | ||||||
\(987\) | − | 7.16747e14i | − | 0.765209i | ||||||
\(988\) | 1.01181e15i | 1.07477i | ||||||||
\(989\) | 9.23903e13 | 0.0976438 | ||||||||
\(990\) | −6.10572e14 | −0.642038 | ||||||||
\(991\) | − | 1.04062e15i | − | 1.08874i | −0.838844 | − | 0.544371i | \(-0.816768\pi\) | ||
0.838844 | − | 0.544371i | \(-0.183232\pi\) | |||||||
\(992\) | −1.59397e15 | −1.65928 | ||||||||
\(993\) | −1.85387e14 | −0.192014 | ||||||||
\(994\) | − | 2.28330e15i | − | 2.35305i | ||||||
\(995\) | 1.68716e15 | 1.72998 | ||||||||
\(996\) | 3.19859e14i | 0.326333i | ||||||||
\(997\) | −1.48321e15 | −1.50566 | −0.752828 | − | 0.658217i | \(-0.771311\pi\) | ||||
−0.752828 | + | 0.658217i | \(0.771311\pi\) | |||||||
\(998\) | 7.04201e14i | 0.711286i | ||||||||
\(999\) | 2.13748e14i | 0.214820i |
(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 | 177.11.c.a.58.18 | ✓ | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.83 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.18 | ✓ | 100 | 1.1 | even | 1 | trivial | |
177.11.c.a.58.83 | yes | 100 | 59.58 | odd | 2 | inner |