Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (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: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.22 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.13 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.4666i | 0.670832i | 0.942070 | + | 0.335416i | \(0.108877\pi\) | ||||
−0.942070 | + | 0.335416i | \(0.891123\pi\) | |||||||
\(3\) | − | 198.865i | − | 0.818374i | −0.912451 | − | 0.409187i | \(-0.865812\pi\) | ||
0.912451 | − | 0.409187i | \(-0.134188\pi\) | |||||||
\(4\) | 563.184 | 0.549985 | ||||||||
\(5\) | − | 4591.08i | − | 1.46914i | −0.678531 | − | 0.734572i | \(-0.737383\pi\) | ||
0.678531 | − | 0.734572i | \(-0.262617\pi\) | |||||||
\(6\) | 4268.96 | 0.548991 | ||||||||
\(7\) | 9954.72i | 0.592296i | 0.955142 | + | 0.296148i | \(0.0957022\pi\) | ||||
−0.955142 | + | 0.296148i | \(0.904298\pi\) | |||||||
\(8\) | 34071.5i | 1.03978i | ||||||||
\(9\) | 19501.8 | 0.330264 | ||||||||
\(10\) | 98554.8 | 0.985548 | ||||||||
\(11\) | 281457. | 1.74763 | 0.873813 | − | 0.486262i | \(-0.161640\pi\) | ||||
0.873813 | + | 0.486262i | \(0.161640\pi\) | |||||||
\(12\) | − | 111998.i | − | 0.450093i | ||||||
\(13\) | −387846. | −1.04458 | −0.522291 | − | 0.852768i | \(-0.674922\pi\) | ||||
−0.522291 | + | 0.852768i | \(0.674922\pi\) | |||||||
\(14\) | −213694. | −0.397331 | ||||||||
\(15\) | −913004. | −1.20231 | ||||||||
\(16\) | −154698. | −0.147532 | ||||||||
\(17\) | 790905. | 0.557032 | 0.278516 | − | 0.960432i | \(-0.410158\pi\) | ||||
0.278516 | + | 0.960432i | \(0.410158\pi\) | |||||||
\(18\) | 418637.i | 0.221552i | ||||||||
\(19\) | − | 2.97737e6i | − | 1.20244i | −0.799082 | − | 0.601222i | \(-0.794681\pi\) | ||
0.799082 | − | 0.601222i | \(-0.205319\pi\) | |||||||
\(20\) | − | 2.58562e6i | − | 0.808007i | ||||||
\(21\) | 1.97965e6 | 0.484720 | ||||||||
\(22\) | 6.04193e6i | 1.17236i | ||||||||
\(23\) | −3.73725e6 | −0.580648 | −0.290324 | − | 0.956928i | \(-0.593763\pi\) | ||||
−0.290324 | + | 0.956928i | \(0.593763\pi\) | |||||||
\(24\) | 6.77562e6 | 0.850928 | ||||||||
\(25\) | −1.13123e7 | −1.15838 | ||||||||
\(26\) | − | 8.32573e6i | − | 0.700738i | ||||||
\(27\) | − | 1.56210e7i | − | 1.08865i | ||||||
\(28\) | 5.60635e6i | 0.325754i | ||||||||
\(29\) | − | 2.26181e7i | − | 1.10272i | −0.834266 | − | 0.551362i | \(-0.814108\pi\) | ||
0.834266 | − | 0.551362i | \(-0.185892\pi\) | |||||||
\(30\) | − | 1.95991e7i | − | 0.806547i | ||||||
\(31\) | 2.79032e7 | 0.974644 | 0.487322 | − | 0.873222i | \(-0.337974\pi\) | ||||
0.487322 | + | 0.873222i | \(0.337974\pi\) | |||||||
\(32\) | 3.15683e7i | 0.940810i | ||||||||
\(33\) | − | 5.59719e7i | − | 1.43021i | ||||||
\(34\) | 1.69781e7i | 0.373674i | ||||||||
\(35\) | 4.57029e7 | 0.870169 | ||||||||
\(36\) | 1.09831e7 | 0.181640 | ||||||||
\(37\) | − | 7.96095e6i | − | 0.114804i | −0.998351 | − | 0.0574019i | \(-0.981718\pi\) | ||
0.998351 | − | 0.0574019i | \(-0.0182816\pi\) | |||||||
\(38\) | 6.39141e7 | 0.806638 | ||||||||
\(39\) | 7.71289e7i | 0.854858i | ||||||||
\(40\) | 1.56425e8 | 1.52759 | ||||||||
\(41\) | 5.43511e7 | 0.469126 | 0.234563 | − | 0.972101i | \(-0.424634\pi\) | ||||
0.234563 | + | 0.972101i | \(0.424634\pi\) | |||||||
\(42\) | 4.24963e7i | 0.325166i | ||||||||
\(43\) | −9.52801e7 | − | 1.11952e8i | −0.648126 | − | 0.761533i | ||||
\(44\) | 1.58512e8 | 0.961168 | ||||||||
\(45\) | − | 8.95340e7i | − | 0.485205i | ||||||
\(46\) | − | 8.02262e7i | − | 0.389517i | ||||||
\(47\) | −6.95452e7 | −0.303234 | −0.151617 | − | 0.988439i | \(-0.548448\pi\) | ||||
−0.151617 | + | 0.988439i | \(0.548448\pi\) | |||||||
\(48\) | 3.07641e7i | 0.120736i | ||||||||
\(49\) | 1.83379e8 | 0.649185 | ||||||||
\(50\) | − | 2.42838e8i | − | 0.777081i | ||||||
\(51\) | − | 1.57283e8i | − | 0.455860i | ||||||
\(52\) | −2.18429e8 | −0.574504 | ||||||||
\(53\) | −3.43114e8 | −0.820463 | −0.410232 | − | 0.911981i | \(-0.634552\pi\) | ||||
−0.410232 | + | 0.911981i | \(0.634552\pi\) | |||||||
\(54\) | 3.35330e8 | 0.730303 | ||||||||
\(55\) | − | 1.29219e9i | − | 2.56751i | ||||||
\(56\) | −3.39172e8 | −0.615857 | ||||||||
\(57\) | −5.92095e8 | −0.984049 | ||||||||
\(58\) | 4.85535e8 | 0.739743 | ||||||||
\(59\) | 4.88010e8 | 0.682604 | 0.341302 | − | 0.939954i | \(-0.389132\pi\) | ||||
0.341302 | + | 0.939954i | \(0.389132\pi\) | |||||||
\(60\) | −5.14189e8 | −0.661252 | ||||||||
\(61\) | 8.46701e8i | 1.00249i | 0.865305 | + | 0.501246i | \(0.167125\pi\) | ||||
−0.865305 | + | 0.501246i | \(0.832875\pi\) | |||||||
\(62\) | 5.98988e8i | 0.653822i | ||||||||
\(63\) | 1.94135e8i | 0.195614i | ||||||||
\(64\) | −8.36077e8 | −0.778657 | ||||||||
\(65\) | 1.78063e9i | 1.53464i | ||||||||
\(66\) | 1.20153e9 | 0.959431 | ||||||||
\(67\) | −8.00338e8 | −0.592788 | −0.296394 | − | 0.955066i | \(-0.595784\pi\) | ||||
−0.296394 | + | 0.955066i | \(0.595784\pi\) | |||||||
\(68\) | 4.45425e8 | 0.306359 | ||||||||
\(69\) | 7.43208e8i | 0.475188i | ||||||||
\(70\) | 9.81086e8i | 0.583737i | ||||||||
\(71\) | − | 1.08276e9i | − | 0.600125i | −0.953920 | − | 0.300063i | \(-0.902992\pi\) | ||
0.953920 | − | 0.300063i | \(-0.0970076\pi\) | |||||||
\(72\) | 6.64454e8i | 0.343402i | ||||||||
\(73\) | − | 1.82954e9i | − | 0.882525i | −0.897378 | − | 0.441263i | \(-0.854531\pi\) | ||
0.897378 | − | 0.441263i | \(-0.145469\pi\) | |||||||
\(74\) | 1.70895e8 | 0.0770140 | ||||||||
\(75\) | 2.24963e9i | 0.947992i | ||||||||
\(76\) | − | 1.67681e9i | − | 0.661326i | ||||||
\(77\) | 2.80183e9i | 1.03511i | ||||||||
\(78\) | −1.65570e9 | −0.573466 | ||||||||
\(79\) | −4.40059e9 | −1.43013 | −0.715065 | − | 0.699058i | \(-0.753603\pi\) | ||||
−0.715065 | + | 0.699058i | \(0.753603\pi\) | |||||||
\(80\) | 7.10232e8i | 0.216746i | ||||||||
\(81\) | −1.95491e9 | −0.560662 | ||||||||
\(82\) | 1.16673e9i | 0.314704i | ||||||||
\(83\) | 4.62097e9 | 1.17312 | 0.586561 | − | 0.809905i | \(-0.300482\pi\) | ||||
0.586561 | + | 0.809905i | \(0.300482\pi\) | |||||||
\(84\) | 1.11491e9 | 0.266589 | ||||||||
\(85\) | − | 3.63111e9i | − | 0.818360i | ||||||
\(86\) | 2.40322e9 | − | 2.04534e9i | 0.510860 | − | 0.434784i | ||||
\(87\) | −4.49795e9 | −0.902441 | ||||||||
\(88\) | 9.58965e9i | 1.81714i | ||||||||
\(89\) | 7.45253e9i | 1.33461i | 0.744786 | + | 0.667304i | \(0.232552\pi\) | ||||
−0.744786 | + | 0.667304i | \(0.767448\pi\) | |||||||
\(90\) | 1.92199e9 | 0.325491 | ||||||||
\(91\) | − | 3.86090e9i | − | 0.618702i | ||||||
\(92\) | −2.10476e9 | −0.319348 | ||||||||
\(93\) | − | 5.54897e9i | − | 0.797623i | ||||||
\(94\) | − | 1.49290e9i | − | 0.203419i | ||||||
\(95\) | −1.36693e10 | −1.76656 | ||||||||
\(96\) | 6.27783e9 | 0.769934 | ||||||||
\(97\) | 1.42418e9 | 0.165846 | 0.0829232 | − | 0.996556i | \(-0.473574\pi\) | ||||
0.0829232 | + | 0.996556i | \(0.473574\pi\) | |||||||
\(98\) | 3.93652e9i | 0.435494i | ||||||||
\(99\) | 5.48890e9 | 0.577178 | ||||||||
\(100\) | −6.37094e9 | −0.637094 | ||||||||
\(101\) | 6.64206e9 | 0.631969 | 0.315985 | − | 0.948764i | \(-0.397665\pi\) | ||||
0.315985 | + | 0.948764i | \(0.397665\pi\) | |||||||
\(102\) | 3.37634e9 | 0.305805 | ||||||||
\(103\) | 4.24087e8 | 0.0365822 | 0.0182911 | − | 0.999833i | \(-0.494177\pi\) | ||||
0.0182911 | + | 0.999833i | \(0.494177\pi\) | |||||||
\(104\) | − | 1.32145e10i | − | 1.08613i | ||||||
\(105\) | − | 9.08870e9i | − | 0.712123i | ||||||
\(106\) | − | 7.36550e9i | − | 0.550393i | ||||||
\(107\) | −2.47617e10 | −1.76547 | −0.882736 | − | 0.469868i | \(-0.844301\pi\) | ||||
−0.882736 | + | 0.469868i | \(0.844301\pi\) | |||||||
\(108\) | − | 8.79750e9i | − | 0.598743i | ||||||
\(109\) | 1.78573e10 | 1.16060 | 0.580300 | − | 0.814403i | \(-0.302935\pi\) | ||||
0.580300 | + | 0.814403i | \(0.302935\pi\) | |||||||
\(110\) | 2.77389e10 | 1.72237 | ||||||||
\(111\) | −1.58315e9 | −0.0939524 | ||||||||
\(112\) | − | 1.53998e9i | − | 0.0873827i | ||||||
\(113\) | 7.64076e9i | 0.414710i | 0.978266 | + | 0.207355i | \(0.0664855\pi\) | ||||
−0.978266 | + | 0.207355i | \(0.933515\pi\) | |||||||
\(114\) | − | 1.27103e10i | − | 0.660131i | ||||||
\(115\) | 1.71580e10i | 0.853056i | ||||||||
\(116\) | − | 1.27382e10i | − | 0.606482i | ||||||
\(117\) | −7.56367e9 | −0.344988 | ||||||||
\(118\) | 1.04759e10i | 0.457913i | ||||||||
\(119\) | 7.87324e9i | 0.329928i | ||||||||
\(120\) | − | 3.11074e10i | − | 1.25014i | ||||||
\(121\) | 5.32806e10 | 2.05420 | ||||||||
\(122\) | −1.81758e10 | −0.672503 | ||||||||
\(123\) | − | 1.08085e10i | − | 0.383920i | ||||||
\(124\) | 1.57147e10 | 0.536039 | ||||||||
\(125\) | 7.10112e9i | 0.232689i | ||||||||
\(126\) | −4.16741e9 | −0.131224 | ||||||||
\(127\) | 4.24675e10 | 1.28540 | 0.642700 | − | 0.766118i | \(-0.277814\pi\) | ||||
0.642700 | + | 0.766118i | \(0.277814\pi\) | |||||||
\(128\) | 1.43782e10i | 0.418462i | ||||||||
\(129\) | −2.22633e10 | + | 1.89479e10i | −0.623219 | + | 0.530410i | ||||
\(130\) | −3.82241e10 | −1.02949 | ||||||||
\(131\) | − | 1.39356e10i | − | 0.361217i | −0.983555 | − | 0.180609i | \(-0.942193\pi\) | ||
0.983555 | − | 0.180609i | \(-0.0578067\pi\) | |||||||
\(132\) | − | 3.15225e10i | − | 0.786595i | ||||||
\(133\) | 2.96389e10 | 0.712203 | ||||||||
\(134\) | − | 1.71806e10i | − | 0.397661i | ||||||
\(135\) | −7.17171e10 | −1.59939 | ||||||||
\(136\) | 2.69473e10i | 0.579190i | ||||||||
\(137\) | 1.51743e10i | 0.314417i | 0.987565 | + | 0.157208i | \(0.0502494\pi\) | ||||
−0.987565 | + | 0.157208i | \(0.949751\pi\) | |||||||
\(138\) | −1.59542e10 | −0.318771 | ||||||||
\(139\) | 9.42053e10 | 1.81552 | 0.907760 | − | 0.419490i | \(-0.137791\pi\) | ||||
0.907760 | + | 0.419490i | \(0.137791\pi\) | |||||||
\(140\) | 2.57392e10 | 0.478580 | ||||||||
\(141\) | 1.38301e10i | 0.248159i | ||||||||
\(142\) | 2.32433e10 | 0.402583 | ||||||||
\(143\) | −1.09162e11 | −1.82554 | ||||||||
\(144\) | −3.01689e9 | −0.0487245 | ||||||||
\(145\) | −1.03842e11 | −1.62006 | ||||||||
\(146\) | 3.92740e10 | 0.592026 | ||||||||
\(147\) | − | 3.64676e10i | − | 0.531276i | ||||||
\(148\) | − | 4.48348e9i | − | 0.0631403i | ||||||
\(149\) | 8.46017e10i | 1.15199i | 0.817454 | + | 0.575994i | \(0.195385\pi\) | ||||
−0.817454 | + | 0.575994i | \(0.804615\pi\) | |||||||
\(150\) | −4.82919e10 | −0.635943 | ||||||||
\(151\) | 9.79693e10i | 1.24797i | 0.781435 | + | 0.623986i | \(0.214488\pi\) | ||||
−0.781435 | + | 0.623986i | \(0.785512\pi\) | |||||||
\(152\) | 1.01443e11 | 1.25028 | ||||||||
\(153\) | 1.54240e10 | 0.183967 | ||||||||
\(154\) | −6.01457e10 | −0.694386 | ||||||||
\(155\) | − | 1.28106e11i | − | 1.43189i | ||||||
\(156\) | 4.34378e10i | 0.470159i | ||||||||
\(157\) | 1.82495e11i | 1.91317i | 0.291455 | + | 0.956584i | \(0.405861\pi\) | ||||
−0.291455 | + | 0.956584i | \(0.594139\pi\) | |||||||
\(158\) | − | 9.44658e10i | − | 0.959377i | ||||||
\(159\) | 6.82333e10i | 0.671446i | ||||||||
\(160\) | 1.44933e11 | 1.38219 | ||||||||
\(161\) | − | 3.72033e10i | − | 0.343916i | ||||||
\(162\) | − | 4.19652e10i | − | 0.376110i | ||||||
\(163\) | 3.99764e10i | 0.347429i | 0.984796 | + | 0.173714i | \(0.0555770\pi\) | ||||
−0.984796 | + | 0.173714i | \(0.944423\pi\) | |||||||
\(164\) | 3.06097e10 | 0.258012 | ||||||||
\(165\) | −2.56971e11 | −2.10119 | ||||||||
\(166\) | 9.91967e10i | 0.786967i | ||||||||
\(167\) | −1.57900e11 | −1.21563 | −0.607813 | − | 0.794080i | \(-0.707953\pi\) | ||||
−0.607813 | + | 0.794080i | \(0.707953\pi\) | |||||||
\(168\) | 6.74494e10i | 0.504002i | ||||||||
\(169\) | 1.25658e10 | 0.0911497 | ||||||||
\(170\) | 7.79475e10 | 0.548982 | ||||||||
\(171\) | − | 5.80640e10i | − | 0.397124i | ||||||
\(172\) | −5.36602e10 | − | 6.30495e10i | −0.356460 | − | 0.418831i | ||||
\(173\) | −1.39091e11 | −0.897569 | −0.448784 | − | 0.893640i | \(-0.648143\pi\) | ||||
−0.448784 | + | 0.893640i | \(0.648143\pi\) | |||||||
\(174\) | − | 9.65559e10i | − | 0.605386i | ||||||
\(175\) | − | 1.12611e11i | − | 0.686107i | ||||||
\(176\) | −4.35410e10 | −0.257831 | ||||||||
\(177\) | − | 9.70481e10i | − | 0.558626i | ||||||
\(178\) | −1.59981e11 | −0.895297 | ||||||||
\(179\) | 3.01180e11i | 1.63893i | 0.573130 | + | 0.819465i | \(0.305729\pi\) | ||||
−0.573130 | + | 0.819465i | \(0.694271\pi\) | |||||||
\(180\) | − | 5.04242e10i | − | 0.266856i | ||||||
\(181\) | −3.06485e11 | −1.57767 | −0.788836 | − | 0.614603i | \(-0.789316\pi\) | ||||
−0.788836 | + | 0.614603i | \(0.789316\pi\) | |||||||
\(182\) | 8.28804e10 | 0.415045 | ||||||||
\(183\) | 1.68379e11 | 0.820413 | ||||||||
\(184\) | − | 1.27334e11i | − | 0.603746i | ||||||
\(185\) | −3.65493e10 | −0.168663 | ||||||||
\(186\) | 1.19118e11 | 0.535071 | ||||||||
\(187\) | 2.22606e11 | 0.973483 | ||||||||
\(188\) | −3.91668e10 | −0.166774 | ||||||||
\(189\) | 1.55503e11 | 0.644805 | ||||||||
\(190\) | − | 2.93434e11i | − | 1.18507i | ||||||
\(191\) | 3.13253e11i | 1.23234i | 0.787615 | + | 0.616168i | \(0.211316\pi\) | ||||
−0.787615 | + | 0.616168i | \(0.788684\pi\) | |||||||
\(192\) | 1.66266e11i | 0.637233i | ||||||||
\(193\) | 3.96142e11 | 1.47933 | 0.739664 | − | 0.672976i | \(-0.234984\pi\) | ||||
0.739664 | + | 0.672976i | \(0.234984\pi\) | |||||||
\(194\) | 3.05723e10i | 0.111255i | ||||||||
\(195\) | 3.54105e11 | 1.25591 | ||||||||
\(196\) | 1.03276e11 | 0.357042 | ||||||||
\(197\) | 2.34601e11 | 0.790677 | 0.395339 | − | 0.918535i | \(-0.370627\pi\) | ||||
0.395339 | + | 0.918535i | \(0.370627\pi\) | |||||||
\(198\) | 1.17828e11i | 0.387189i | ||||||||
\(199\) | 1.92218e11i | 0.615925i | 0.951399 | + | 0.307962i | \(0.0996471\pi\) | ||||
−0.951399 | + | 0.307962i | \(0.900353\pi\) | |||||||
\(200\) | − | 3.85428e11i | − | 1.20446i | ||||||
\(201\) | 1.59159e11i | 0.485122i | ||||||||
\(202\) | 1.42583e11i | 0.423945i | ||||||||
\(203\) | 2.25157e11 | 0.653140 | ||||||||
\(204\) | − | 8.85795e10i | − | 0.250716i | ||||||
\(205\) | − | 2.49530e11i | − | 0.689213i | ||||||
\(206\) | 9.10372e9i | 0.0245405i | ||||||||
\(207\) | −7.28830e10 | −0.191767 | ||||||||
\(208\) | 5.99991e10 | 0.154109 | ||||||||
\(209\) | − | 8.38002e11i | − | 2.10142i | ||||||
\(210\) | 1.95104e11 | 0.477715 | ||||||||
\(211\) | − | 2.97067e11i | − | 0.710301i | −0.934809 | − | 0.355150i | \(-0.884430\pi\) | ||
0.934809 | − | 0.355150i | \(-0.115570\pi\) | |||||||
\(212\) | −1.93236e11 | −0.451242 | ||||||||
\(213\) | −2.15324e11 | −0.491127 | ||||||||
\(214\) | − | 5.31549e11i | − | 1.18434i | ||||||
\(215\) | −5.13979e11 | + | 4.37438e11i | −1.11880 | + | 0.952191i | ||||
\(216\) | 5.32230e11 | 1.13196 | ||||||||
\(217\) | 2.77769e11i | 0.577278i | ||||||||
\(218\) | 3.83335e11i | 0.778568i | ||||||||
\(219\) | −3.63831e11 | −0.722236 | ||||||||
\(220\) | − | 7.27741e11i | − | 1.41209i | ||||||
\(221\) | −3.06749e11 | −0.581865 | ||||||||
\(222\) | − | 3.39849e10i | − | 0.0630263i | ||||||
\(223\) | 5.72221e11i | 1.03762i | 0.854889 | + | 0.518811i | \(0.173625\pi\) | ||||
−0.854889 | + | 0.518811i | \(0.826375\pi\) | |||||||
\(224\) | −3.14254e11 | −0.557238 | ||||||||
\(225\) | −2.20611e11 | −0.382573 | ||||||||
\(226\) | −1.64021e11 | −0.278200 | ||||||||
\(227\) | − | 2.30229e11i | − | 0.381972i | −0.981593 | − | 0.190986i | \(-0.938831\pi\) | ||
0.981593 | − | 0.190986i | \(-0.0611685\pi\) | |||||||
\(228\) | −3.33458e11 | −0.541212 | ||||||||
\(229\) | 1.23658e11 | 0.196357 | 0.0981785 | − | 0.995169i | \(-0.468698\pi\) | ||||
0.0981785 | + | 0.995169i | \(0.468698\pi\) | |||||||
\(230\) | −3.68324e11 | −0.572257 | ||||||||
\(231\) | 5.57185e11 | 0.847109 | ||||||||
\(232\) | 7.70634e11 | 1.14659 | ||||||||
\(233\) | − | 1.29810e12i | − | 1.89029i | −0.326654 | − | 0.945144i | \(-0.605921\pi\) | ||
0.326654 | − | 0.945144i | \(-0.394079\pi\) | |||||||
\(234\) | − | 1.62366e11i | − | 0.231429i | ||||||
\(235\) | 3.19287e11i | 0.445495i | ||||||||
\(236\) | 2.74840e11 | 0.375422 | ||||||||
\(237\) | 8.75123e11i | 1.17038i | ||||||||
\(238\) | −1.69012e11 | −0.221326 | ||||||||
\(239\) | −3.98118e11 | −0.510531 | −0.255266 | − | 0.966871i | \(-0.582163\pi\) | ||||
−0.255266 | + | 0.966871i | \(0.582163\pi\) | |||||||
\(240\) | 1.41240e11 | 0.177379 | ||||||||
\(241\) | − | 8.56905e11i | − | 1.05402i | −0.849860 | − | 0.527008i | \(-0.823314\pi\) | ||
0.849860 | − | 0.527008i | \(-0.176686\pi\) | |||||||
\(242\) | 1.14375e12i | 1.37802i | ||||||||
\(243\) | − | 5.33641e11i | − | 0.629822i | ||||||
\(244\) | 4.76849e11i | 0.551355i | ||||||||
\(245\) | − | 8.41905e11i | − | 0.953746i | ||||||
\(246\) | 2.32023e11 | 0.257546 | ||||||||
\(247\) | 1.15476e12i | 1.25605i | ||||||||
\(248\) | 9.50704e11i | 1.01341i | ||||||||
\(249\) | − | 9.18949e11i | − | 0.960052i | ||||||
\(250\) | −1.52437e11 | −0.156095 | ||||||||
\(251\) | 6.33616e11 | 0.636000 | 0.318000 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.318000 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(252\) | 1.09334e11i | 0.107585i | ||||||||
\(253\) | −1.05188e12 | −1.01476 | ||||||||
\(254\) | 9.11634e11i | 0.862287i | ||||||||
\(255\) | −7.22099e11 | −0.669724 | ||||||||
\(256\) | −1.16479e12 | −1.05937 | ||||||||
\(257\) | 1.61085e12i | 1.43678i | 0.695641 | + | 0.718390i | \(0.255121\pi\) | ||||
−0.695641 | + | 0.718390i | \(0.744879\pi\) | |||||||
\(258\) | −4.06746e11 | − | 4.77917e11i | −0.355816 | − | 0.418075i | ||||
\(259\) | 7.92490e10 | 0.0679978 | ||||||||
\(260\) | 1.00282e12i | 0.844029i | ||||||||
\(261\) | − | 4.41094e11i | − | 0.364190i | ||||||
\(262\) | 2.99150e11 | 0.242316 | ||||||||
\(263\) | 7.22918e10i | 0.0574527i | 0.999587 | + | 0.0287263i | \(0.00914513\pi\) | ||||
−0.999587 | + | 0.0287263i | \(0.990855\pi\) | |||||||
\(264\) | 1.90705e12 | 1.48710 | ||||||||
\(265\) | 1.57526e12i | 1.20538i | ||||||||
\(266\) | 6.36247e11i | 0.477769i | ||||||||
\(267\) | 1.48205e12 | 1.09221 | ||||||||
\(268\) | −4.50738e11 | −0.326024 | ||||||||
\(269\) | −1.04098e12 | −0.739063 | −0.369531 | − | 0.929218i | \(-0.620482\pi\) | ||||
−0.369531 | + | 0.929218i | \(0.620482\pi\) | |||||||
\(270\) | − | 1.53952e12i | − | 1.07292i | ||||||
\(271\) | 2.43860e12 | 1.66838 | 0.834190 | − | 0.551477i | \(-0.185936\pi\) | ||||
0.834190 | + | 0.551477i | \(0.185936\pi\) | |||||||
\(272\) | −1.22352e11 | −0.0821800 | ||||||||
\(273\) | −7.67797e11 | −0.506329 | ||||||||
\(274\) | −3.25741e11 | −0.210921 | ||||||||
\(275\) | −3.18394e12 | −2.02442 | ||||||||
\(276\) | 4.18563e11i | 0.261346i | ||||||||
\(277\) | − | 1.02076e12i | − | 0.625931i | −0.949764 | − | 0.312966i | \(-0.898678\pi\) | ||
0.949764 | − | 0.312966i | \(-0.101322\pi\) | |||||||
\(278\) | 2.02227e12i | 1.21791i | ||||||||
\(279\) | 5.44162e11 | 0.321890 | ||||||||
\(280\) | 1.55717e12i | 0.904783i | ||||||||
\(281\) | −3.03748e12 | −1.73373 | −0.866867 | − | 0.498539i | \(-0.833870\pi\) | ||||
−0.866867 | + | 0.498539i | \(0.833870\pi\) | |||||||
\(282\) | −2.96886e11 | −0.166473 | ||||||||
\(283\) | 2.97432e12 | 1.63853 | 0.819267 | − | 0.573413i | \(-0.194381\pi\) | ||||
0.819267 | + | 0.573413i | \(0.194381\pi\) | |||||||
\(284\) | − | 6.09795e11i | − | 0.330060i | ||||||
\(285\) | 2.71835e12i | 1.44571i | ||||||||
\(286\) | − | 2.34334e12i | − | 1.22463i | ||||||
\(287\) | 5.41050e11i | 0.277861i | ||||||||
\(288\) | 6.15638e11i | 0.310716i | ||||||||
\(289\) | −1.39046e12 | −0.689716 | ||||||||
\(290\) | − | 2.22913e12i | − | 1.08679i | ||||||
\(291\) | − | 2.83219e11i | − | 0.135724i | ||||||
\(292\) | − | 1.03037e12i | − | 0.485375i | ||||||
\(293\) | 1.21603e12 | 0.563128 | 0.281564 | − | 0.959542i | \(-0.409147\pi\) | ||||
0.281564 | + | 0.959542i | \(0.409147\pi\) | |||||||
\(294\) | 7.82836e11 | 0.356397 | ||||||||
\(295\) | − | 2.24049e12i | − | 1.00284i | ||||||
\(296\) | 2.71241e11 | 0.119371 | ||||||||
\(297\) | − | 4.39663e12i | − | 1.90256i | ||||||
\(298\) | −1.81611e12 | −0.772790 | ||||||||
\(299\) | 1.44948e12 | 0.606534 | ||||||||
\(300\) | 1.26696e12i | 0.521381i | ||||||||
\(301\) | 1.11445e12 | − | 9.48487e11i | 0.451053 | − | 0.383883i | ||||
\(302\) | −2.10307e12 | −0.837180 | ||||||||
\(303\) | − | 1.32087e12i | − | 0.517187i | ||||||
\(304\) | 4.60595e11i | 0.177399i | ||||||||
\(305\) | 3.88727e12 | 1.47280 | ||||||||
\(306\) | 3.31102e11i | 0.123411i | ||||||||
\(307\) | 1.99500e12 | 0.731561 | 0.365781 | − | 0.930701i | \(-0.380802\pi\) | ||||
0.365781 | + | 0.930701i | \(0.380802\pi\) | |||||||
\(308\) | 1.57794e12i | 0.569296i | ||||||||
\(309\) | − | 8.43361e10i | − | 0.0299379i | ||||||
\(310\) | 2.75000e12 | 0.960559 | ||||||||
\(311\) | −4.26280e12 | −1.46519 | −0.732593 | − | 0.680667i | \(-0.761690\pi\) | ||||
−0.732593 | + | 0.680667i | \(0.761690\pi\) | |||||||
\(312\) | −2.62790e12 | −0.888863 | ||||||||
\(313\) | − | 3.58899e12i | − | 1.19468i | −0.801989 | − | 0.597339i | \(-0.796225\pi\) | ||
0.801989 | − | 0.597339i | \(-0.203775\pi\) | |||||||
\(314\) | −3.91756e12 | −1.28341 | ||||||||
\(315\) | 8.91287e11 | 0.287385 | ||||||||
\(316\) | −2.47834e12 | −0.786550 | ||||||||
\(317\) | 5.45005e12 | 1.70257 | 0.851283 | − | 0.524706i | \(-0.175825\pi\) | ||||
0.851283 | + | 0.524706i | \(0.175825\pi\) | |||||||
\(318\) | −1.46474e12 | −0.450427 | ||||||||
\(319\) | − | 6.36603e12i | − | 1.92715i | ||||||
\(320\) | 3.83849e12i | 1.14396i | ||||||||
\(321\) | 4.92423e12i | 1.44482i | ||||||||
\(322\) | 7.98629e11 | 0.230710 | ||||||||
\(323\) | − | 2.35482e12i | − | 0.669799i | ||||||
\(324\) | −1.10097e12 | −0.308355 | ||||||||
\(325\) | 4.38744e12 | 1.21003 | ||||||||
\(326\) | −8.58158e11 | −0.233066 | ||||||||
\(327\) | − | 3.55119e12i | − | 0.949805i | ||||||
\(328\) | 1.85182e12i | 0.487787i | ||||||||
\(329\) | − | 6.92304e11i | − | 0.179604i | ||||||
\(330\) | − | 5.51630e12i | − | 1.40954i | ||||||
\(331\) | 5.62247e12i | 1.41510i | 0.706663 | + | 0.707550i | \(0.250200\pi\) | ||||
−0.706663 | + | 0.707550i | \(0.749800\pi\) | |||||||
\(332\) | 2.60246e12 | 0.645199 | ||||||||
\(333\) | − | 1.55252e11i | − | 0.0379155i | ||||||
\(334\) | − | 3.38958e12i | − | 0.815481i | ||||||
\(335\) | 3.67441e12i | 0.870891i | ||||||||
\(336\) | −3.06248e11 | −0.0715117 | ||||||||
\(337\) | 2.77529e12 | 0.638496 | 0.319248 | − | 0.947671i | \(-0.396570\pi\) | ||||
0.319248 | + | 0.947671i | \(0.396570\pi\) | |||||||
\(338\) | 2.69744e11i | 0.0611461i | ||||||||
\(339\) | 1.51948e12 | 0.339388 | ||||||||
\(340\) | − | 2.04498e12i | − | 0.450085i | ||||||
\(341\) | 7.85355e12 | 1.70331 | ||||||||
\(342\) | 1.24644e12 | 0.266403 | ||||||||
\(343\) | 4.63745e12i | 0.976806i | ||||||||
\(344\) | 3.81436e12 | − | 3.24633e12i | 0.791826 | − | 0.673908i | ||||
\(345\) | 3.41213e12 | 0.698119 | ||||||||
\(346\) | − | 2.98581e12i | − | 0.602118i | ||||||
\(347\) | 6.90565e12i | 1.37264i | 0.727299 | + | 0.686321i | \(0.240775\pi\) | ||||
−0.727299 | + | 0.686321i | \(0.759225\pi\) | |||||||
\(348\) | −2.53318e12 | −0.496329 | ||||||||
\(349\) | − | 1.08800e12i | − | 0.210137i | −0.994465 | − | 0.105069i | \(-0.966494\pi\) | ||
0.994465 | − | 0.105069i | \(-0.0335063\pi\) | |||||||
\(350\) | 2.41738e12 | 0.460262 | ||||||||
\(351\) | 6.05853e12i | 1.13719i | ||||||||
\(352\) | 8.88513e12i | 1.64418i | ||||||||
\(353\) | −7.47744e12 | −1.36420 | −0.682102 | − | 0.731257i | \(-0.738934\pi\) | ||||
−0.682102 | + | 0.731257i | \(0.738934\pi\) | |||||||
\(354\) | 2.08329e12 | 0.374744 | ||||||||
\(355\) | −4.97105e12 | −0.881670 | ||||||||
\(356\) | 4.19715e12i | 0.734014i | ||||||||
\(357\) | 1.56571e12 | 0.270004 | ||||||||
\(358\) | −6.46531e12 | −1.09945 | ||||||||
\(359\) | −7.05719e12 | −1.18348 | −0.591738 | − | 0.806130i | \(-0.701558\pi\) | ||||
−0.591738 | + | 0.806130i | \(0.701558\pi\) | |||||||
\(360\) | 3.05056e12 | 0.504506 | ||||||||
\(361\) | −2.73367e12 | −0.445872 | ||||||||
\(362\) | − | 6.57920e12i | − | 1.05835i | ||||||
\(363\) | − | 1.05956e13i | − | 1.68110i | ||||||
\(364\) | − | 2.17440e12i | − | 0.340276i | ||||||
\(365\) | −8.39955e12 | −1.29656 | ||||||||
\(366\) | 3.61453e12i | 0.550359i | ||||||||
\(367\) | −2.86369e11 | −0.0430127 | −0.0215063 | − | 0.999769i | \(-0.506846\pi\) | ||||
−0.0215063 | + | 0.999769i | \(0.506846\pi\) | |||||||
\(368\) | 5.78147e11 | 0.0856642 | ||||||||
\(369\) | 1.05994e12 | 0.154935 | ||||||||
\(370\) | − | 7.84590e11i | − | 0.113145i | ||||||
\(371\) | − | 3.41560e12i | − | 0.485957i | ||||||
\(372\) | − | 3.12509e12i | − | 0.438681i | ||||||
\(373\) | − | 9.31022e12i | − | 1.28948i | −0.764400 | − | 0.644742i | \(-0.776965\pi\) | ||
0.764400 | − | 0.644742i | \(-0.223035\pi\) | |||||||
\(374\) | 4.77859e12i | 0.653043i | ||||||||
\(375\) | 1.41216e12 | 0.190427 | ||||||||
\(376\) | − | 2.36951e12i | − | 0.315296i | ||||||
\(377\) | 8.77235e12i | 1.15189i | ||||||||
\(378\) | 3.33812e12i | 0.432556i | ||||||||
\(379\) | −9.20492e12 | −1.17713 | −0.588564 | − | 0.808450i | \(-0.700307\pi\) | ||||
−0.588564 | + | 0.808450i | \(0.700307\pi\) | |||||||
\(380\) | −7.69836e12 | −0.971583 | ||||||||
\(381\) | − | 8.44530e12i | − | 1.05194i | ||||||
\(382\) | −6.72449e12 | −0.826690 | ||||||||
\(383\) | − | 5.91711e12i | − | 0.717985i | −0.933340 | − | 0.358993i | \(-0.883120\pi\) | ||
0.933340 | − | 0.358993i | \(-0.116880\pi\) | |||||||
\(384\) | 2.85933e12 | 0.342458 | ||||||||
\(385\) | 1.28634e13 | 1.52073 | ||||||||
\(386\) | 8.50383e12i | 0.992380i | ||||||||
\(387\) | −1.85813e12 | − | 2.18326e12i | −0.214053 | − | 0.251507i | ||||
\(388\) | 8.02076e11 | 0.0912130 | ||||||||
\(389\) | 1.45448e13i | 1.63290i | 0.577417 | + | 0.816449i | \(0.304061\pi\) | ||||
−0.577417 | + | 0.816449i | \(0.695939\pi\) | |||||||
\(390\) | 7.60143e12i | 0.842504i | ||||||||
\(391\) | −2.95581e12 | −0.323440 | ||||||||
\(392\) | 6.24798e12i | 0.675009i | ||||||||
\(393\) | −2.77130e12 | −0.295611 | ||||||||
\(394\) | 5.03610e12i | 0.530411i | ||||||||
\(395\) | 2.02035e13i | 2.10107i | ||||||||
\(396\) | 3.09127e12 | 0.317439 | ||||||||
\(397\) | 1.45663e12 | 0.147705 | 0.0738526 | − | 0.997269i | \(-0.476471\pi\) | ||||
0.0738526 | + | 0.997269i | \(0.476471\pi\) | |||||||
\(398\) | −4.12626e12 | −0.413182 | ||||||||
\(399\) | − | 5.89414e12i | − | 0.582849i | ||||||
\(400\) | 1.75000e12 | 0.170899 | ||||||||
\(401\) | 8.65402e11 | 0.0834634 | 0.0417317 | − | 0.999129i | \(-0.486713\pi\) | ||||
0.0417317 | + | 0.999129i | \(0.486713\pi\) | |||||||
\(402\) | −3.41661e12 | −0.325436 | ||||||||
\(403\) | −1.08221e13 | −1.01809 | ||||||||
\(404\) | 3.74071e12 | 0.347574 | ||||||||
\(405\) | 8.97512e12i | 0.823693i | ||||||||
\(406\) | 4.83337e12i | 0.438147i | ||||||||
\(407\) | − | 2.24066e12i | − | 0.200634i | ||||||
\(408\) | 5.35887e12 | 0.473994 | ||||||||
\(409\) | 2.00482e12i | 0.175170i | 0.996157 | + | 0.0875849i | \(0.0279149\pi\) | ||||
−0.996157 | + | 0.0875849i | \(0.972085\pi\) | |||||||
\(410\) | 5.35657e12 | 0.462346 | ||||||||
\(411\) | 3.01763e12 | 0.257311 | ||||||||
\(412\) | 2.38839e11 | 0.0201196 | ||||||||
\(413\) | 4.85801e12i | 0.404304i | ||||||||
\(414\) | − | 1.56455e12i | − | 0.128644i | ||||||
\(415\) | − | 2.12152e13i | − | 1.72348i | ||||||
\(416\) | − | 1.22436e13i | − | 0.982752i | ||||||
\(417\) | − | 1.87341e13i | − | 1.48577i | ||||||
\(418\) | 1.79891e13 | 1.40970 | ||||||||
\(419\) | 1.47181e12i | 0.113968i | 0.998375 | + | 0.0569839i | \(0.0181484\pi\) | ||||
−0.998375 | + | 0.0569839i | \(0.981852\pi\) | |||||||
\(420\) | − | 5.11861e12i | − | 0.391657i | ||||||
\(421\) | − | 2.78330e12i | − | 0.210450i | −0.994448 | − | 0.105225i | \(-0.966444\pi\) | ||
0.994448 | − | 0.105225i | \(-0.0335563\pi\) | |||||||
\(422\) | 6.37703e12 | 0.476492 | ||||||||
\(423\) | −1.35625e12 | −0.100147 | ||||||||
\(424\) | − | 1.16904e13i | − | 0.853100i | ||||||
\(425\) | −8.94699e12 | −0.645257 | ||||||||
\(426\) | − | 4.62227e12i | − | 0.329463i | ||||||
\(427\) | −8.42867e12 | −0.593772 | ||||||||
\(428\) | −1.39454e13 | −0.970983 | ||||||||
\(429\) | 2.17085e13i | 1.49397i | ||||||||
\(430\) | −9.39031e12 | − | 1.10334e13i | −0.638760 | − | 0.750527i | ||||
\(431\) | −1.09047e13 | −0.733210 | −0.366605 | − | 0.930377i | \(-0.619480\pi\) | ||||
−0.366605 | + | 0.930377i | \(0.619480\pi\) | |||||||
\(432\) | 2.41654e12i | 0.160611i | ||||||||
\(433\) | − | 7.48067e12i | − | 0.491474i | −0.969336 | − | 0.245737i | \(-0.920970\pi\) | ||
0.969336 | − | 0.245737i | \(-0.0790300\pi\) | |||||||
\(434\) | −5.96276e12 | −0.387256 | ||||||||
\(435\) | 2.06504e13i | 1.32582i | ||||||||
\(436\) | 1.00569e13 | 0.638313 | ||||||||
\(437\) | 1.11272e13i | 0.698197i | ||||||||
\(438\) | − | 7.81022e12i | − | 0.484499i | ||||||
\(439\) | −1.29772e13 | −0.795902 | −0.397951 | − | 0.917407i | \(-0.630279\pi\) | ||||
−0.397951 | + | 0.917407i | \(0.630279\pi\) | |||||||
\(440\) | 4.40268e13 | 2.66965 | ||||||||
\(441\) | 3.57621e12 | 0.214402 | ||||||||
\(442\) | − | 6.58487e12i | − | 0.390333i | ||||||
\(443\) | −7.54555e12 | −0.442254 | −0.221127 | − | 0.975245i | \(-0.570974\pi\) | ||||
−0.221127 | + | 0.975245i | \(0.570974\pi\) | |||||||
\(444\) | −8.91607e11 | −0.0516724 | ||||||||
\(445\) | 3.42151e13 | 1.96073 | ||||||||
\(446\) | −1.22836e13 | −0.696070 | ||||||||
\(447\) | 1.68243e13 | 0.942757 | ||||||||
\(448\) | − | 8.32291e12i | − | 0.461196i | ||||||
\(449\) | − | 2.77542e13i | − | 1.52089i | −0.649405 | − | 0.760443i | \(-0.724982\pi\) | ||
0.649405 | − | 0.760443i | \(-0.275018\pi\) | |||||||
\(450\) | − | 4.73576e12i | − | 0.256642i | ||||||
\(451\) | 1.52975e13 | 0.819856 | ||||||||
\(452\) | 4.30316e12i | 0.228084i | ||||||||
\(453\) | 1.94826e13 | 1.02131 | ||||||||
\(454\) | 4.94225e12 | 0.256239 | ||||||||
\(455\) | −1.77257e13 | −0.908962 | ||||||||
\(456\) | − | 2.01735e13i | − | 1.02319i | ||||||
\(457\) | 2.13666e13i | 1.07190i | 0.844249 | + | 0.535951i | \(0.180047\pi\) | ||||
−0.844249 | + | 0.535951i | \(0.819953\pi\) | |||||||
\(458\) | 2.65453e12i | 0.131723i | ||||||||
\(459\) | − | 1.23547e13i | − | 0.606414i | ||||||
\(460\) | 9.66312e12i | 0.469168i | ||||||||
\(461\) | 1.20763e13 | 0.580004 | 0.290002 | − | 0.957026i | \(-0.406344\pi\) | ||||
0.290002 | + | 0.957026i | \(0.406344\pi\) | |||||||
\(462\) | 1.19609e13i | 0.568268i | ||||||||
\(463\) | − | 1.51558e13i | − | 0.712320i | −0.934425 | − | 0.356160i | \(-0.884086\pi\) | ||
0.934425 | − | 0.356160i | \(-0.115914\pi\) | |||||||
\(464\) | 3.49899e12i | 0.162687i | ||||||||
\(465\) | −2.54757e13 | −1.17182 | ||||||||
\(466\) | 2.78658e13 | 1.26807 | ||||||||
\(467\) | 3.12334e13i | 1.40616i | 0.711111 | + | 0.703080i | \(0.248192\pi\) | ||||
−0.711111 | + | 0.703080i | \(0.751808\pi\) | |||||||
\(468\) | −4.25974e12 | −0.189738 | ||||||||
\(469\) | − | 7.96715e12i | − | 0.351106i | ||||||
\(470\) | −6.85402e12 | −0.298852 | ||||||||
\(471\) | 3.62919e13 | 1.56569 | ||||||||
\(472\) | 1.66272e13i | 0.709757i | ||||||||
\(473\) | −2.68172e13 | − | 3.15096e13i | −1.13268 | − | 1.33087i | ||||
\(474\) | −1.87859e13 | −0.785129 | ||||||||
\(475\) | 3.36811e13i | 1.39289i | ||||||||
\(476\) | 4.43409e12i | 0.181455i | ||||||||
\(477\) | −6.69132e12 | −0.270969 | ||||||||
\(478\) | − | 8.54625e12i | − | 0.342481i | ||||||
\(479\) | −4.43874e13 | −1.76028 | −0.880141 | − | 0.474713i | \(-0.842552\pi\) | ||||
−0.880141 | + | 0.474713i | \(0.842552\pi\) | |||||||
\(480\) | − | 2.88220e13i | − | 1.13114i | ||||||
\(481\) | 3.08762e12i | 0.119922i | ||||||||
\(482\) | 1.83948e13 | 0.707067 | ||||||||
\(483\) | −7.39843e12 | −0.281452 | ||||||||
\(484\) | 3.00068e13 | 1.12978 | ||||||||
\(485\) | − | 6.53852e12i | − | 0.243652i | ||||||
\(486\) | 1.14555e13 | 0.422505 | ||||||||
\(487\) | −1.37180e13 | −0.500779 | −0.250389 | − | 0.968145i | \(-0.580559\pi\) | ||||
−0.250389 | + | 0.968145i | \(0.580559\pi\) | |||||||
\(488\) | −2.88483e13 | −1.04237 | ||||||||
\(489\) | 7.94991e12 | 0.284327 | ||||||||
\(490\) | 1.80729e13 | 0.639803 | ||||||||
\(491\) | − | 4.55887e13i | − | 1.59753i | −0.601641 | − | 0.798766i | \(-0.705486\pi\) | ||
0.601641 | − | 0.798766i | \(-0.294514\pi\) | |||||||
\(492\) | − | 6.08719e12i | − | 0.211150i | ||||||
\(493\) | − | 1.78888e13i | − | 0.614252i | ||||||
\(494\) | −2.47888e13 | −0.842599 | ||||||||
\(495\) | − | 2.52000e13i | − | 0.847957i | ||||||
\(496\) | −4.31659e12 | −0.143791 | ||||||||
\(497\) | 1.07786e13 | 0.355452 | ||||||||
\(498\) | 1.97267e13 | 0.644034 | ||||||||
\(499\) | 5.81864e13i | 1.88070i | 0.340214 | + | 0.940348i | \(0.389501\pi\) | ||||
−0.340214 | + | 0.940348i | \(0.610499\pi\) | |||||||
\(500\) | 3.99924e12i | 0.127976i | ||||||||
\(501\) | 3.14008e13i | 0.994837i | ||||||||
\(502\) | 1.36016e13i | 0.426649i | ||||||||
\(503\) | 2.77763e13i | 0.862650i | 0.902197 | + | 0.431325i | \(0.141954\pi\) | ||||
−0.902197 | + | 0.431325i | \(0.858046\pi\) | |||||||
\(504\) | −6.61445e12 | −0.203395 | ||||||||
\(505\) | − | 3.04942e13i | − | 0.928454i | ||||||
\(506\) | − | 2.25802e13i | − | 0.680731i | ||||||
\(507\) | − | 2.49889e12i | − | 0.0745946i | ||||||
\(508\) | 2.39171e13 | 0.706951 | ||||||||
\(509\) | 1.00508e13 | 0.294180 | 0.147090 | − | 0.989123i | \(-0.453009\pi\) | ||||
0.147090 | + | 0.989123i | \(0.453009\pi\) | |||||||
\(510\) | − | 1.55010e13i | − | 0.449272i | ||||||
\(511\) | 1.82125e13 | 0.522717 | ||||||||
\(512\) | − | 1.02809e13i | − | 0.292200i | ||||||
\(513\) | −4.65095e13 | −1.30905 | ||||||||
\(514\) | −3.45796e13 | −0.963838 | ||||||||
\(515\) | − | 1.94702e12i | − | 0.0537445i | ||||||
\(516\) | −1.25383e13 | + | 1.06711e13i | −0.342761 | + | 0.291717i | ||||
\(517\) | −1.95740e13 | −0.529940 | ||||||||
\(518\) | 1.70121e12i | 0.0456151i | ||||||||
\(519\) | 2.76603e13i | 0.734547i | ||||||||
\(520\) | −6.06686e13 | −1.59569 | ||||||||
\(521\) | 5.84779e13i | 1.52336i | 0.647953 | + | 0.761681i | \(0.275625\pi\) | ||||
−0.647953 | + | 0.761681i | \(0.724375\pi\) | |||||||
\(522\) | 9.46879e12 | 0.244310 | ||||||||
\(523\) | 9.90764e12i | 0.253199i | 0.991954 | + | 0.126599i | \(0.0404063\pi\) | ||||
−0.991954 | + | 0.126599i | \(0.959594\pi\) | |||||||
\(524\) | − | 7.84830e12i | − | 0.198664i | ||||||
\(525\) | −2.23944e13 | −0.561492 | ||||||||
\(526\) | −1.55186e12 | −0.0385411 | ||||||||
\(527\) | 2.20688e13 | 0.542907 | ||||||||
\(528\) | 8.65877e12i | 0.211002i | ||||||||
\(529\) | −2.74595e13 | −0.662847 | ||||||||
\(530\) | −3.38155e13 | −0.808606 | ||||||||
\(531\) | 9.51706e12 | 0.225440 | ||||||||
\(532\) | 1.66922e13 | 0.391701 | ||||||||
\(533\) | −2.10798e13 | −0.490040 | ||||||||
\(534\) | 3.18145e13i | 0.732688i | ||||||||
\(535\) | 1.13683e14i | 2.59373i | ||||||||
\(536\) | − | 2.72687e13i | − | 0.616369i | ||||||
\(537\) | 5.98940e13 | 1.34126 | ||||||||
\(538\) | − | 2.23463e13i | − | 0.495787i | ||||||
\(539\) | 5.16132e13 | 1.13453 | ||||||||
\(540\) | −4.03900e13 | −0.879639 | ||||||||
\(541\) | 7.39783e13 | 1.59631 | 0.798157 | − | 0.602450i | \(-0.205809\pi\) | ||||
0.798157 | + | 0.602450i | \(0.205809\pi\) | |||||||
\(542\) | 5.23486e13i | 1.11920i | ||||||||
\(543\) | 6.09492e13i | 1.29113i | ||||||||
\(544\) | 2.49676e13i | 0.524061i | ||||||||
\(545\) | − | 8.19841e13i | − | 1.70509i | ||||||
\(546\) | − | 1.64820e13i | − | 0.339662i | ||||||
\(547\) | −9.16879e13 | −1.87230 | −0.936150 | − | 0.351601i | \(-0.885637\pi\) | ||||
−0.936150 | + | 0.351601i | \(0.885637\pi\) | |||||||
\(548\) | 8.54593e12i | 0.172924i | ||||||||
\(549\) | 1.65122e13i | 0.331087i | ||||||||
\(550\) | − | 6.83484e13i | − | 1.35805i | ||||||
\(551\) | −6.73426e13 | −1.32596 | ||||||||
\(552\) | −2.53222e13 | −0.494090 | ||||||||
\(553\) | − | 4.38067e13i | − | 0.847061i | ||||||
\(554\) | 2.19124e13 | 0.419894 | ||||||||
\(555\) | 7.26837e12i | 0.138030i | ||||||||
\(556\) | 5.30549e13 | 0.998509 | ||||||||
\(557\) | 3.64850e13 | 0.680515 | 0.340258 | − | 0.940332i | \(-0.389486\pi\) | ||||
0.340258 | + | 0.940332i | \(0.389486\pi\) | |||||||
\(558\) | 1.16813e13i | 0.215934i | ||||||||
\(559\) | 3.69540e13 | + | 4.34200e13i | 0.677021 | + | 0.795483i | ||||
\(560\) | −7.07017e12 | −0.128378 | ||||||||
\(561\) | − | 4.42685e13i | − | 0.796673i | ||||||
\(562\) | − | 6.52045e13i | − | 1.16304i | ||||||
\(563\) | 6.24849e13 | 1.10467 | 0.552336 | − | 0.833622i | \(-0.313737\pi\) | ||||
0.552336 | + | 0.833622i | \(0.313737\pi\) | |||||||
\(564\) | 7.78890e12i | 0.136484i | ||||||||
\(565\) | 3.50793e13 | 0.609268 | ||||||||
\(566\) | 6.38485e13i | 1.09918i | ||||||||
\(567\) | − | 1.94606e13i | − | 0.332078i | ||||||
\(568\) | 3.68913e13 | 0.623997 | ||||||||
\(569\) | −3.57357e13 | −0.599158 | −0.299579 | − | 0.954072i | \(-0.596846\pi\) | ||||
−0.299579 | + | 0.954072i | \(0.596846\pi\) | |||||||
\(570\) | −5.83538e13 | −0.969828 | ||||||||
\(571\) | 2.48707e13i | 0.409740i | 0.978789 | + | 0.204870i | \(0.0656771\pi\) | ||||
−0.978789 | + | 0.204870i | \(0.934323\pi\) | |||||||
\(572\) | −6.14782e13 | −1.00402 | ||||||||
\(573\) | 6.22951e13 | 1.00851 | ||||||||
\(574\) | −1.16145e13 | −0.186398 | ||||||||
\(575\) | 4.22771e13 | 0.672614 | ||||||||
\(576\) | −1.63050e13 | −0.257162 | ||||||||
\(577\) | − | 1.12449e13i | − | 0.175824i | −0.996128 | − | 0.0879120i | \(-0.971981\pi\) | ||
0.996128 | − | 0.0879120i | \(-0.0280194\pi\) | |||||||
\(578\) | − | 2.98485e13i | − | 0.462683i | ||||||
\(579\) | − | 7.87788e13i | − | 1.21064i | ||||||
\(580\) | −5.84820e13 | −0.891009 | ||||||||
\(581\) | 4.60005e13i | 0.694836i | ||||||||
\(582\) | 6.07976e12 | 0.0910483 | ||||||||
\(583\) | −9.65718e13 | −1.43386 | ||||||||
\(584\) | 6.23351e13 | 0.917631 | ||||||||
\(585\) | 3.47254e13i | 0.506836i | ||||||||
\(586\) | 2.61041e13i | 0.377764i | ||||||||
\(587\) | 8.96698e13i | 1.28664i | 0.765599 | + | 0.643318i | \(0.222443\pi\) | ||||
−0.765599 | + | 0.643318i | \(0.777557\pi\) | |||||||
\(588\) | − | 2.05380e13i | − | 0.292194i | ||||||
\(589\) | − | 8.30782e13i | − | 1.17195i | ||||||
\(590\) | 4.80958e13 | 0.672740 | ||||||||
\(591\) | − | 4.66540e13i | − | 0.647070i | ||||||
\(592\) | 1.23155e12i | 0.0169372i | ||||||||
\(593\) | − | 3.41621e13i | − | 0.465877i | −0.972491 | − | 0.232939i | \(-0.925166\pi\) | ||
0.972491 | − | 0.232939i | \(-0.0748341\pi\) | |||||||
\(594\) | 9.43809e13 | 1.27630 | ||||||||
\(595\) | 3.61467e13 | 0.484711 | ||||||||
\(596\) | 4.76464e13i | 0.633576i | ||||||||
\(597\) | 3.82253e13 | 0.504057 | ||||||||
\(598\) | 3.11154e13i | 0.406883i | ||||||||
\(599\) | 3.96588e13 | 0.514288 | 0.257144 | − | 0.966373i | \(-0.417219\pi\) | ||||
0.257144 | + | 0.966373i | \(0.417219\pi\) | |||||||
\(600\) | −7.66482e13 | −0.985702 | ||||||||
\(601\) | − | 1.06834e14i | − | 1.36250i | −0.732052 | − | 0.681249i | \(-0.761437\pi\) | ||
0.732052 | − | 0.681249i | \(-0.238563\pi\) | |||||||
\(602\) | 2.03608e13 | + | 2.39234e13i | 0.257521 | + | 0.302581i | ||||
\(603\) | −1.56080e13 | −0.195777 | ||||||||
\(604\) | 5.51748e13i | 0.686366i | ||||||||
\(605\) | − | 2.44615e14i | − | 3.01791i | ||||||
\(606\) | 2.83547e13 | 0.346946 | ||||||||
\(607\) | − | 9.01507e13i | − | 1.09402i | −0.837126 | − | 0.547011i | \(-0.815766\pi\) | ||
0.837126 | − | 0.547011i | \(-0.184234\pi\) | |||||||
\(608\) | 9.39907e13 | 1.13127 | ||||||||
\(609\) | − | 4.47759e13i | − | 0.534512i | ||||||
\(610\) | 8.34465e13i | 0.988004i | ||||||||
\(611\) | 2.69728e13 | 0.316753 | ||||||||
\(612\) | 8.68658e12 | 0.101179 | ||||||||
\(613\) | −8.92183e13 | −1.03075 | −0.515373 | − | 0.856966i | \(-0.672346\pi\) | ||||
−0.515373 | + | 0.856966i | \(0.672346\pi\) | |||||||
\(614\) | 4.28259e13i | 0.490755i | ||||||||
\(615\) | −4.96228e13 | −0.564034 | ||||||||
\(616\) | −9.54624e13 | −1.07629 | ||||||||
\(617\) | 9.22488e13 | 1.03166 | 0.515828 | − | 0.856692i | \(-0.327484\pi\) | ||||
0.515828 | + | 0.856692i | \(0.327484\pi\) | |||||||
\(618\) | 1.81041e12 | 0.0200833 | ||||||||
\(619\) | −3.98980e13 | −0.439034 | −0.219517 | − | 0.975609i | \(-0.570448\pi\) | ||||
−0.219517 | + | 0.975609i | \(0.570448\pi\) | |||||||
\(620\) | − | 7.21472e13i | − | 0.787519i | ||||||
\(621\) | 5.83796e13i | 0.632125i | ||||||||
\(622\) | − | 9.15079e13i | − | 0.982894i | ||||||
\(623\) | −7.41879e13 | −0.790483 | ||||||||
\(624\) | − | 1.19317e13i | − | 0.126119i | ||||||
\(625\) | −7.78704e13 | −0.816530 | ||||||||
\(626\) | 7.70436e13 | 0.801428 | ||||||||
\(627\) | −1.66649e14 | −1.71975 | ||||||||
\(628\) | 1.02778e14i | 1.05221i | ||||||||
\(629\) | − | 6.29635e12i | − | 0.0639493i | ||||||
\(630\) | 1.91329e13i | 0.192787i | ||||||||
\(631\) | − | 1.53005e12i | − | 0.0152954i | −0.999971 | − | 0.00764769i | \(-0.997566\pi\) | ||
0.999971 | − | 0.00764769i | \(-0.00243436\pi\) | |||||||
\(632\) | − | 1.49935e14i | − | 1.48702i | ||||||
\(633\) | −5.90762e13 | −0.581292 | ||||||||
\(634\) | 1.16994e14i | 1.14214i | ||||||||
\(635\) | − | 1.94972e14i | − | 1.88844i | ||||||
\(636\) | 3.84279e13i | 0.369285i | ||||||||
\(637\) | −7.11226e13 | −0.678126 | ||||||||
\(638\) | 1.36657e14 | 1.29279 | ||||||||
\(639\) | − | 2.11158e13i | − | 0.198200i | ||||||
\(640\) | 6.60116e13 | 0.614781 | ||||||||
\(641\) | − | 2.31328e13i | − | 0.213766i | −0.994272 | − | 0.106883i | \(-0.965913\pi\) | ||
0.994272 | − | 0.106883i | \(-0.0340870\pi\) | |||||||
\(642\) | −1.05706e14 | −0.969229 | ||||||||
\(643\) | 1.53455e14 | 1.39613 | 0.698063 | − | 0.716036i | \(-0.254045\pi\) | ||||
0.698063 | + | 0.716036i | \(0.254045\pi\) | |||||||
\(644\) | − | 2.09523e13i | − | 0.189149i | ||||||
\(645\) | 8.69910e13 | + | 1.02212e14i | 0.779249 | + | 0.915598i | ||||
\(646\) | 5.05500e13 | 0.449323 | ||||||||
\(647\) | 1.02218e14i | 0.901587i | 0.892628 | + | 0.450793i | \(0.148859\pi\) | ||||
−0.892628 | + | 0.450793i | \(0.851141\pi\) | |||||||
\(648\) | − | 6.66066e13i | − | 0.582964i | ||||||
\(649\) | 1.37354e14 | 1.19294 | ||||||||
\(650\) | 9.41836e13i | 0.811724i | ||||||||
\(651\) | 5.52385e13 | 0.472429 | ||||||||
\(652\) | 2.25141e13i | 0.191081i | ||||||||
\(653\) | − | 4.90839e13i | − | 0.413403i | −0.978404 | − | 0.206701i | \(-0.933727\pi\) | ||
0.978404 | − | 0.206701i | \(-0.0662729\pi\) | |||||||
\(654\) | 7.62319e13 | 0.637160 | ||||||||
\(655\) | −6.39793e13 | −0.530680 | ||||||||
\(656\) | −8.40804e12 | −0.0692110 | ||||||||
\(657\) | − | 3.56792e13i | − | 0.291466i | ||||||
\(658\) | 1.48614e13 | 0.120484 | ||||||||
\(659\) | 1.76149e14 | 1.41727 | 0.708635 | − | 0.705575i | \(-0.249311\pi\) | ||||
0.708635 | + | 0.705575i | \(0.249311\pi\) | |||||||
\(660\) | −1.44722e14 | −1.15562 | ||||||||
\(661\) | 9.18643e13 | 0.728014 | 0.364007 | − | 0.931396i | \(-0.381408\pi\) | ||||
0.364007 | + | 0.931396i | \(0.381408\pi\) | |||||||
\(662\) | −1.20695e14 | −0.949295 | ||||||||
\(663\) | 6.10016e13i | 0.476183i | ||||||||
\(664\) | 1.57443e14i | 1.21979i | ||||||||
\(665\) | − | 1.36074e14i | − | 1.04633i | ||||||
\(666\) | 3.33274e12 | 0.0254350 | ||||||||
\(667\) | 8.45297e13i | 0.640295i | ||||||||
\(668\) | −8.89269e13 | −0.668576 | ||||||||
\(669\) | 1.13795e14 | 0.849163 | ||||||||
\(670\) | −7.88772e13 | −0.584222 | ||||||||
\(671\) | 2.38310e14i | 1.75198i | ||||||||
\(672\) | 6.24941e13i | 0.456029i | ||||||||
\(673\) | 1.28168e14i | 0.928336i | 0.885747 | + | 0.464168i | \(0.153647\pi\) | ||||
−0.885747 | + | 0.464168i | \(0.846353\pi\) | |||||||
\(674\) | 5.95760e13i | 0.428324i | ||||||||
\(675\) | 1.76710e14i | 1.26108i | ||||||||
\(676\) | 7.07684e12 | 0.0501310 | ||||||||
\(677\) | − | 2.96060e13i | − | 0.208179i | −0.994568 | − | 0.104089i | \(-0.966807\pi\) | ||
0.994568 | − | 0.104089i | \(-0.0331928\pi\) | |||||||
\(678\) | 3.26181e13i | 0.227672i | ||||||||
\(679\) | 1.41773e13i | 0.0982303i | ||||||||
\(680\) | 1.23717e14 | 0.850913 | ||||||||
\(681\) | −4.57846e13 | −0.312596 | ||||||||
\(682\) | 1.68589e14i | 1.14264i | ||||||||
\(683\) | −1.89445e14 | −1.27462 | −0.637309 | − | 0.770608i | \(-0.719953\pi\) | ||||
−0.637309 | + | 0.770608i | \(0.719953\pi\) | |||||||
\(684\) | − | 3.27007e13i | − | 0.218412i | ||||||
\(685\) | 6.96663e13 | 0.461924 | ||||||||
\(686\) | −9.95503e13 | −0.655273 | ||||||||
\(687\) | − | 2.45913e13i | − | 0.160694i | ||||||
\(688\) | 1.47397e13 | + | 1.73188e13i | 0.0956194 | + | 0.112350i | ||||
\(689\) | 1.33075e14 | 0.857040 | ||||||||
\(690\) | 7.32468e13i | 0.468320i | ||||||||
\(691\) | − | 1.36965e14i | − | 0.869399i | −0.900575 | − | 0.434700i | \(-0.856855\pi\) | ||
0.900575 | − | 0.434700i | \(-0.143145\pi\) | |||||||
\(692\) | −7.83337e13 | −0.493649 | ||||||||
\(693\) | 5.46405e13i | 0.341860i | ||||||||
\(694\) | −1.48241e14 | −0.920812 | ||||||||
\(695\) | − | 4.32503e14i | − | 2.66726i | ||||||
\(696\) | − | 1.53252e14i | − | 0.938339i | ||||||
\(697\) | 4.29866e13 | 0.261318 | ||||||||
\(698\) | 2.33558e13 | 0.140967 | ||||||||
\(699\) | −2.58146e14 | −1.54696 | ||||||||
\(700\) | − | 6.34209e13i | − | 0.377348i | ||||||
\(701\) | 5.00960e13 | 0.295946 | 0.147973 | − | 0.988991i | \(-0.452725\pi\) | ||||
0.147973 | + | 0.988991i | \(0.452725\pi\) | |||||||
\(702\) | −1.30056e14 | −0.762861 | ||||||||
\(703\) | −2.37027e13 | −0.138045 | ||||||||
\(704\) | −2.35320e14 | −1.36080 | ||||||||
\(705\) | 6.34950e13 | 0.364581 | ||||||||
\(706\) | − | 1.60515e14i | − | 0.915151i | ||||||
\(707\) | 6.61199e13i | 0.374313i | ||||||||
\(708\) | − | 5.46560e13i | − | 0.307236i | ||||||
\(709\) | 5.61827e13 | 0.313596 | 0.156798 | − | 0.987631i | \(-0.449883\pi\) | ||||
0.156798 | + | 0.987631i | \(0.449883\pi\) | |||||||
\(710\) | − | 1.06712e14i | − | 0.591452i | ||||||
\(711\) | −8.58193e13 | −0.472321 | ||||||||
\(712\) | −2.53919e14 | −1.38770 | ||||||||
\(713\) | −1.04281e14 | −0.565925 | ||||||||
\(714\) | 3.36105e13i | 0.181127i | ||||||||
\(715\) | 5.01170e14i | 2.68198i | ||||||||
\(716\) | 1.69620e14i | 0.901386i | ||||||||
\(717\) | 7.91717e13i | 0.417806i | ||||||||
\(718\) | − | 1.51494e14i | − | 0.793914i | ||||||
\(719\) | 1.13106e14 | 0.588628 | 0.294314 | − | 0.955709i | \(-0.404909\pi\) | ||||
0.294314 | + | 0.955709i | \(0.404909\pi\) | |||||||
\(720\) | 1.38508e13i | 0.0715833i | ||||||||
\(721\) | 4.22167e12i | 0.0216675i | ||||||||
\(722\) | − | 5.86827e13i | − | 0.299105i | ||||||
\(723\) | −1.70408e14 | −0.862579 | ||||||||
\(724\) | −1.72608e14 | −0.867696 | ||||||||
\(725\) | 2.55864e14i | 1.27738i | ||||||||
\(726\) | 2.27452e14 | 1.12774 | ||||||||
\(727\) | − | 1.64326e14i | − | 0.809161i | −0.914502 | − | 0.404581i | \(-0.867418\pi\) | ||
0.914502 | − | 0.404581i | \(-0.132582\pi\) | |||||||
\(728\) | 1.31546e14 | 0.643313 | ||||||||
\(729\) | −2.21558e14 | −1.07609 | ||||||||
\(730\) | − | 1.80310e14i | − | 0.869772i | ||||||
\(731\) | −7.53575e13 | − | 8.85432e13i | −0.361027 | − | 0.424198i | ||||
\(732\) | 9.48284e13 | 0.451215 | ||||||||
\(733\) | − | 7.12596e13i | − | 0.336762i | −0.985722 | − | 0.168381i | \(-0.946146\pi\) | ||
0.985722 | − | 0.168381i | \(-0.0538539\pi\) | |||||||
\(734\) | − | 6.14738e12i | − | 0.0288543i | ||||||
\(735\) | −1.67425e14 | −0.780521 | ||||||||
\(736\) | − | 1.17979e14i | − | 0.546280i | ||||||
\(737\) | −2.25261e14 | −1.03597 | ||||||||
\(738\) | 2.27534e13i | 0.103936i | ||||||||
\(739\) | 1.25433e14i | 0.569100i | 0.958661 | + | 0.284550i | \(0.0918442\pi\) | ||||
−0.958661 | + | 0.284550i | \(0.908156\pi\) | |||||||
\(740\) | −2.05840e13 | −0.0927622 | ||||||||
\(741\) | 2.29641e14 | 1.02792 | ||||||||
\(742\) | 7.33215e13 | 0.325996 | ||||||||
\(743\) | 2.75150e14i | 1.21514i | 0.794267 | + | 0.607569i | \(0.207855\pi\) | ||||
−0.794267 | + | 0.607569i | \(0.792145\pi\) | |||||||
\(744\) | 1.89062e14 | 0.829352 | ||||||||
\(745\) | 3.88413e14 | 1.69244 | ||||||||
\(746\) | 1.99859e14 | 0.865026 | ||||||||
\(747\) | 9.01171e13 | 0.387440 | ||||||||
\(748\) | 1.25368e14 | 0.535401 | ||||||||
\(749\) | − | 2.46496e14i | − | 1.04568i | ||||||
\(750\) | 3.03144e13i | 0.127744i | ||||||||
\(751\) | − | 1.89466e14i | − | 0.793106i | −0.918012 | − | 0.396553i | \(-0.870206\pi\) | ||
0.918012 | − | 0.396553i | \(-0.129794\pi\) | |||||||
\(752\) | 1.07585e13 | 0.0447367 | ||||||||
\(753\) | − | 1.26004e14i | − | 0.520486i | ||||||
\(754\) | −1.88313e14 | −0.772721 | ||||||||
\(755\) | 4.49784e14 | 1.83345 | ||||||||
\(756\) | 8.75767e13 | 0.354633 | ||||||||
\(757\) | 2.42227e14i | 0.974415i | 0.873286 | + | 0.487207i | \(0.161984\pi\) | ||||
−0.873286 | + | 0.487207i | \(0.838016\pi\) | |||||||
\(758\) | − | 1.97598e14i | − | 0.789655i | ||||||
\(759\) | 2.09181e14i | 0.830450i | ||||||||
\(760\) | − | 4.65734e14i | − | 1.83684i | ||||||
\(761\) | − | 3.33654e14i | − | 1.30729i | −0.756800 | − | 0.653646i | \(-0.773238\pi\) | ||
0.756800 | − | 0.653646i | \(-0.226762\pi\) | |||||||
\(762\) | 1.81292e14 | 0.705674 | ||||||||
\(763\) | 1.77764e14i | 0.687419i | ||||||||
\(764\) | 1.76419e14i | 0.677766i | ||||||||
\(765\) | − | 7.08129e13i | − | 0.270275i | ||||||
\(766\) | 1.27020e14 | 0.481647 | ||||||||
\(767\) | −1.89273e14 | −0.713035 | ||||||||
\(768\) | 2.31637e14i | 0.866965i | ||||||||
\(769\) | −3.02892e14 | −1.12631 | −0.563153 | − | 0.826353i | \(-0.690412\pi\) | ||||
−0.563153 | + | 0.826353i | \(0.690412\pi\) | |||||||
\(770\) | 2.76134e14i | 1.02015i | ||||||||
\(771\) | 3.20342e14 | 1.17582 | ||||||||
\(772\) | 2.23101e14 | 0.813608 | ||||||||
\(773\) | 3.06858e14i | 1.11183i | 0.831238 | + | 0.555917i | \(0.187633\pi\) | ||||
−0.831238 | + | 0.555917i | \(0.812367\pi\) | |||||||
\(774\) | 4.68671e13 | − | 3.98877e13i | 0.168719 | − | 0.143593i | ||||
\(775\) | −3.15651e14 | −1.12901 | ||||||||
\(776\) | 4.85239e13i | 0.172444i | ||||||||
\(777\) | − | 1.57599e13i | − | 0.0556477i | ||||||
\(778\) | −3.12227e14 | −1.09540 | ||||||||
\(779\) | − | 1.61823e14i | − | 0.564097i | ||||||
\(780\) | 1.99426e14 | 0.690731 | ||||||||
\(781\) | − | 3.04751e14i | − | 1.04879i | ||||||
\(782\) | − | 6.34513e13i | − | 0.216973i | ||||||
\(783\) | −3.53318e14 | −1.20048 | ||||||||
\(784\) | −2.83684e13 | −0.0957756 | ||||||||
\(785\) | 8.37849e14 | 2.81072 | ||||||||
\(786\) | − | 5.94903e13i | − | 0.198305i | ||||||
\(787\) | −1.41766e14 | −0.469568 | −0.234784 | − | 0.972048i | \(-0.575438\pi\) | ||||
−0.234784 | + | 0.972048i | \(0.575438\pi\) | |||||||
\(788\) | 1.32124e14 | 0.434860 | ||||||||
\(789\) | 1.43763e13 | 0.0470178 | ||||||||
\(790\) | −4.33700e14 | −1.40946 | ||||||||
\(791\) | −7.60616e13 | −0.245631 | ||||||||
\(792\) | 1.87015e14i | 0.600137i | ||||||||
\(793\) | − | 3.28389e14i | − | 1.04718i | ||||||
\(794\) | 3.12688e13i | 0.0990853i | ||||||||
\(795\) | 3.13264e14 | 0.986450 | ||||||||
\(796\) | 1.08254e14i | 0.338749i | ||||||||
\(797\) | 1.45208e14 | 0.451541 | 0.225771 | − | 0.974180i | \(-0.427510\pi\) | ||||
0.225771 | + | 0.974180i | \(0.427510\pi\) | |||||||
\(798\) | 1.26527e14 | 0.390993 | ||||||||
\(799\) | −5.50037e13 | −0.168911 | ||||||||
\(800\) | − | 3.57112e14i | − | 1.08982i | ||||||
\(801\) | 1.45337e14i | 0.440773i | ||||||||
\(802\) | 1.85773e13i | 0.0559899i | ||||||||
\(803\) | − | 5.14936e14i | − | 1.54232i | ||||||
\(804\) | 8.96360e13i | 0.266810i | ||||||||
\(805\) | −1.70803e14 | −0.505262 | ||||||||
\(806\) | − | 2.32315e14i | − | 0.682970i | ||||||
\(807\) | 2.07015e14i | 0.604830i | ||||||||
\(808\) | 2.26305e14i | 0.657109i | ||||||||
\(809\) | 2.60445e14 | 0.751578 | 0.375789 | − | 0.926705i | \(-0.377372\pi\) | ||||
0.375789 | + | 0.926705i | \(0.377372\pi\) | |||||||
\(810\) | −1.92666e14 | −0.552559 | ||||||||
\(811\) | − | 8.94059e13i | − | 0.254837i | −0.991849 | − | 0.127418i | \(-0.959331\pi\) | ||
0.991849 | − | 0.127418i | \(-0.0406691\pi\) | |||||||
\(812\) | 1.26805e14 | 0.359217 | ||||||||
\(813\) | − | 4.84953e14i | − | 1.36536i | ||||||
\(814\) | 4.80995e13 | 0.134592 | ||||||||
\(815\) | 1.83535e14 | 0.510423 | ||||||||
\(816\) | 2.43315e13i | 0.0672540i | ||||||||
\(817\) | −3.33322e14 | + | 2.83684e14i | −0.915701 | + | 0.779336i | ||||
\(818\) | −4.30368e13 | −0.117510 | ||||||||
\(819\) | − | 7.52943e13i | − | 0.204335i | ||||||
\(820\) | − | 1.40531e14i | − | 0.379057i | ||||||
\(821\) | −2.08933e14 | −0.560133 | −0.280066 | − | 0.959981i | \(-0.590357\pi\) | ||||
−0.280066 | + | 0.959981i | \(0.590357\pi\) | |||||||
\(822\) | 6.47784e13i | 0.172612i | ||||||||
\(823\) | −1.38434e14 | −0.366643 | −0.183321 | − | 0.983053i | \(-0.558685\pi\) | ||||
−0.183321 | + | 0.983053i | \(0.558685\pi\) | |||||||
\(824\) | 1.44493e13i | 0.0380374i | ||||||||
\(825\) | 6.33174e14i | 1.65673i | ||||||||
\(826\) | −1.04285e14 | −0.271220 | ||||||||
\(827\) | −5.75359e14 | −1.48734 | −0.743672 | − | 0.668545i | \(-0.766918\pi\) | ||||
−0.743672 | + | 0.668545i | \(0.766918\pi\) | |||||||
\(828\) | −4.10466e13 | −0.105469 | ||||||||
\(829\) | − | 4.82281e14i | − | 1.23176i | −0.787838 | − | 0.615882i | \(-0.788800\pi\) | ||
0.787838 | − | 0.615882i | \(-0.211200\pi\) | |||||||
\(830\) | 4.55419e14 | 1.15617 | ||||||||
\(831\) | −2.02994e14 | −0.512246 | ||||||||
\(832\) | 3.24269e14 | 0.813371 | ||||||||
\(833\) | 1.45035e14 | 0.361617 | ||||||||
\(834\) | 4.02158e14 | 0.996705 | ||||||||
\(835\) | 7.24931e14i | 1.78593i | ||||||||
\(836\) | − | 4.71949e14i | − | 1.15575i | ||||||
\(837\) | − | 4.35876e14i | − | 1.06105i | ||||||
\(838\) | −3.15948e13 | −0.0764532 | ||||||||
\(839\) | 3.87972e14i | 0.933235i | 0.884459 | + | 0.466617i | \(0.154527\pi\) | ||||
−0.884459 | + | 0.466617i | \(0.845473\pi\) | |||||||
\(840\) | 3.09665e14 | 0.740451 | ||||||||
\(841\) | −9.08732e13 | −0.216001 | ||||||||
\(842\) | 5.97480e13 | 0.141177 | ||||||||
\(843\) | 6.04049e14i | 1.41884i | ||||||||
\(844\) | − | 1.67304e14i | − | 0.390655i | ||||||
\(845\) | − | 5.76904e13i | − | 0.133912i | ||||||
\(846\) | − | 2.91142e13i | − | 0.0671820i | ||||||
\(847\) | 5.30393e14i | 1.21669i | ||||||||
\(848\) | 5.30792e13 | 0.121045 | ||||||||
\(849\) | − | 5.91487e14i | − | 1.34093i | ||||||
\(850\) | − | 1.92062e14i | − | 0.432859i | ||||||
\(851\) | 2.97521e13i | 0.0666606i | ||||||||
\(852\) | −1.21267e14 | −0.270112 | ||||||||
\(853\) | 1.80811e14 | 0.400388 | 0.200194 | − | 0.979756i | \(-0.435843\pi\) | ||||
0.200194 | + | 0.979756i | \(0.435843\pi\) | |||||||
\(854\) | − | 1.80935e14i | − | 0.398321i | ||||||
\(855\) | −2.66576e14 | −0.583432 | ||||||||
\(856\) | − | 8.43667e14i | − | 1.83570i | ||||||
\(857\) | −5.32140e14 | −1.15112 | −0.575562 | − | 0.817758i | \(-0.695217\pi\) | ||||
−0.575562 | + | 0.817758i | \(0.695217\pi\) | |||||||
\(858\) | −4.66007e14 | −1.00220 | ||||||||
\(859\) | 3.55149e14i | 0.759355i | 0.925119 | + | 0.379678i | \(0.123965\pi\) | ||||
−0.925119 | + | 0.379678i | \(0.876035\pi\) | |||||||
\(860\) | −2.89465e14 | + | 2.46358e14i | −0.615324 | + | 0.523691i | ||||
\(861\) | 1.07596e14 | 0.227395 | ||||||||
\(862\) | − | 2.34087e14i | − | 0.491860i | ||||||
\(863\) | − | 6.43274e13i | − | 0.134382i | −0.997740 | − | 0.0671911i | \(-0.978596\pi\) | ||
0.997740 | − | 0.0671911i | \(-0.0214037\pi\) | |||||||
\(864\) | 4.93129e14 | 1.02422 | ||||||||
\(865\) | 6.38576e14i | 1.31866i | ||||||||
\(866\) | 1.60585e14 | 0.329697 | ||||||||
\(867\) | 2.76514e14i | 0.564445i | ||||||||
\(868\) | 1.56435e14i | 0.317494i | ||||||||
\(869\) | −1.23858e15 | −2.49933 | ||||||||
\(870\) | −4.43295e14 | −0.889399 | ||||||||
\(871\) | 3.10408e14 | 0.619215 | ||||||||
\(872\) | 6.08424e14i | 1.20677i | ||||||||
\(873\) | 2.77740e13 | 0.0547731 | ||||||||
\(874\) | −2.38863e14 | −0.468373 | ||||||||
\(875\) | −7.06897e13 | −0.137821 | ||||||||
\(876\) | −2.04904e14 | −0.397219 | ||||||||
\(877\) | −1.44366e14 | −0.278271 | −0.139136 | − | 0.990273i | \(-0.544432\pi\) | ||||
−0.139136 | + | 0.990273i | \(0.544432\pi\) | |||||||
\(878\) | − | 2.78577e14i | − | 0.533916i | ||||||
\(879\) | − | 2.41826e14i | − | 0.460849i | ||||||
\(880\) | 1.99900e14i | 0.378790i | ||||||||
\(881\) | 1.81950e14 | 0.342825 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(882\) | 7.67691e13i | 0.143828i | ||||||||
\(883\) | −8.24418e13 | −0.153583 | −0.0767917 | − | 0.997047i | \(-0.524468\pi\) | ||||
−0.0767917 | + | 0.997047i | \(0.524468\pi\) | |||||||
\(884\) | −1.72756e14 | −0.320017 | ||||||||
\(885\) | −4.45555e14 | −0.820701 | ||||||||
\(886\) | − | 1.61977e14i | − | 0.296678i | ||||||
\(887\) | − | 5.40678e13i | − | 0.0984738i | −0.998787 | − | 0.0492369i | \(-0.984321\pi\) | ||
0.998787 | − | 0.0492369i | \(-0.0156789\pi\) | |||||||
\(888\) | − | 5.39404e13i | − | 0.0976897i | ||||||
\(889\) | 4.22753e14i | 0.761338i | ||||||||
\(890\) | 7.34483e14i | 1.31532i | ||||||||
\(891\) | −5.50222e14 | −0.979827 | ||||||||
\(892\) | 3.22266e14i | 0.570676i | ||||||||
\(893\) | 2.07062e14i | 0.364622i | ||||||||
\(894\) | 3.61161e14i | 0.632431i | ||||||||
\(895\) | 1.38274e15 | 2.40782 | ||||||||
\(896\) | −1.43131e14 | −0.247853 | ||||||||
\(897\) | − | 2.88250e14i | − | 0.496372i | ||||||
\(898\) | 5.95788e14 | 1.02026 | ||||||||
\(899\) | − | 6.31119e14i | − | 1.07476i | ||||||
\(900\) | −1.24244e14 | −0.210409 | ||||||||
\(901\) | −2.71371e14 | −0.457024 | ||||||||
\(902\) | 3.28385e14i | 0.549985i | ||||||||
\(903\) | −1.88621e14 | − | 2.21625e14i | −0.314160 | − | 0.369130i | ||||
\(904\) | −2.60332e14 | −0.431206 | ||||||||
\(905\) | 1.40710e15i | 2.31783i | ||||||||
\(906\) | 4.18227e14i | 0.685126i | ||||||||
\(907\) | 4.99564e14 | 0.813869 | 0.406934 | − | 0.913457i | \(-0.366598\pi\) | ||||
0.406934 | + | 0.913457i | \(0.366598\pi\) | |||||||
\(908\) | − | 1.29662e14i | − | 0.210079i | ||||||
\(909\) | 1.29532e14 | 0.208717 | ||||||||
\(910\) | − | 3.80510e14i | − | 0.609760i | ||||||
\(911\) | 4.54424e14i | 0.724218i | 0.932136 | + | 0.362109i | \(0.117943\pi\) | ||||
−0.932136 | + | 0.362109i | \(0.882057\pi\) | |||||||
\(912\) | 9.15961e13 | 0.145179 | ||||||||
\(913\) | 1.30060e15 | 2.05018 | ||||||||
\(914\) | −4.58669e14 | −0.719066 | ||||||||
\(915\) | − | 7.73041e14i | − | 1.20530i | ||||||
\(916\) | 6.96425e13 | 0.107993 | ||||||||
\(917\) | 1.38725e14 | 0.213948 | ||||||||
\(918\) | 2.65214e14 | 0.406802 | ||||||||
\(919\) | −2.26663e14 | −0.345783 | −0.172892 | − | 0.984941i | \(-0.555311\pi\) | ||||
−0.172892 | + | 0.984941i | \(0.555311\pi\) | |||||||
\(920\) | −5.84599e14 | −0.886990 | ||||||||
\(921\) | − | 3.96735e14i | − | 0.598691i | ||||||
\(922\) | 2.59238e14i | 0.389085i | ||||||||
\(923\) | 4.19945e14i | 0.626879i | ||||||||
\(924\) | 3.13798e14 | 0.465897 | ||||||||
\(925\) | 9.00570e13i | 0.132987i | ||||||||
\(926\) | 3.25345e14 | 0.477847 | ||||||||
\(927\) | 8.27045e12 | 0.0120818 | ||||||||
\(928\) | 7.14017e14 | 1.03745 | ||||||||
\(929\) | − | 3.65769e14i | − | 0.528601i | −0.964440 | − | 0.264301i | \(-0.914859\pi\) | ||
0.964440 | − | 0.264301i | \(-0.0851411\pi\) | |||||||
\(930\) | − | 5.46878e14i | − | 0.786096i | ||||||
\(931\) | − | 5.45986e14i | − | 0.780609i | ||||||
\(932\) | − | 7.31069e14i | − | 1.03963i | ||||||
\(933\) | 8.47721e14i | 1.19907i | ||||||||
\(934\) | −6.70475e14 | −0.943296 | ||||||||
\(935\) | − | 1.02200e15i | − | 1.43019i | ||||||
\(936\) | − | 2.57705e14i | − | 0.358711i | ||||||
\(937\) | 8.60901e14i | 1.19194i | 0.803006 | + | 0.595971i | \(0.203233\pi\) | ||||
−0.803006 | + | 0.595971i | \(0.796767\pi\) | |||||||
\(938\) | 1.71028e14 | 0.235533 | ||||||||
\(939\) | −7.13725e14 | −0.977694 | ||||||||
\(940\) | 1.79818e14i | 0.245015i | ||||||||
\(941\) | 8.07504e14 | 1.09445 | 0.547226 | − | 0.836985i | \(-0.315684\pi\) | ||||
0.547226 | + | 0.836985i | \(0.315684\pi\) | |||||||
\(942\) | 7.79064e14i | 1.05031i | ||||||||
\(943\) | −2.03124e14 | −0.272397 | ||||||||
\(944\) | −7.54945e13 | −0.100706 | ||||||||
\(945\) | − | 7.13924e14i | − | 0.947312i | ||||||
\(946\) | 6.76404e14 | − | 5.75675e14i | 0.892793 | − | 0.759839i | ||||
\(947\) | −7.85028e14 | −1.03071 | −0.515354 | − | 0.856978i | \(-0.672339\pi\) | ||||
−0.515354 | + | 0.856978i | \(0.672339\pi\) | |||||||
\(948\) | 4.92856e14i | 0.643692i | ||||||||
\(949\) | 7.09578e14i | 0.921869i | ||||||||
\(950\) | −7.23018e14 | −0.934397 | ||||||||
\(951\) | − | 1.08382e15i | − | 1.39334i | ||||||
\(952\) | −2.68253e14 | −0.343052 | ||||||||
\(953\) | − | 6.08840e13i | − | 0.0774530i | −0.999250 | − | 0.0387265i | \(-0.987670\pi\) | ||
0.999250 | − | 0.0387265i | \(-0.0123301\pi\) | |||||||
\(954\) | − | 1.43640e14i | − | 0.181775i | ||||||
\(955\) | 1.43817e15 | 1.81048 | ||||||||
\(956\) | −2.24214e14 | −0.280784 | ||||||||
\(957\) | −1.26598e15 | −1.57713 | ||||||||
\(958\) | − | 9.52847e14i | − | 1.18085i | ||||||
\(959\) | −1.51056e14 | −0.186228 | ||||||||
\(960\) | 7.63341e14 | 0.936187 | ||||||||
\(961\) | −4.10385e13 | −0.0500697 | ||||||||
\(962\) | −6.62807e13 | −0.0804474 | ||||||||
\(963\) | −4.82896e14 | −0.583072 | ||||||||
\(964\) | − | 4.82595e14i | − | 0.579693i | ||||||
\(965\) | − | 1.81872e15i | − | 2.17335i | ||||||
\(966\) | − | 1.58819e14i | − | 0.188807i | ||||||
\(967\) | −5.32825e14 | −0.630162 | −0.315081 | − | 0.949065i | \(-0.602032\pi\) | ||||
−0.315081 | + | 0.949065i | \(0.602032\pi\) | |||||||
\(968\) | 1.81535e15i | 2.13591i | ||||||||
\(969\) | −4.68291e14 | −0.548146 | ||||||||
\(970\) | 1.40360e14 | 0.163450 | ||||||||
\(971\) | 4.42449e14 | 0.512587 | 0.256293 | − | 0.966599i | \(-0.417499\pi\) | ||||
0.256293 | + | 0.966599i | \(0.417499\pi\) | |||||||
\(972\) | − | 3.00539e14i | − | 0.346393i | ||||||
\(973\) | 9.37787e14i | 1.07533i | ||||||||
\(974\) | − | 2.94479e14i | − | 0.335938i | ||||||
\(975\) | − | 8.72509e14i | − | 0.990254i | ||||||
\(976\) | − | 1.30983e14i | − | 0.147900i | ||||||
\(977\) | 6.32036e14 | 0.710017 | 0.355008 | − | 0.934863i | \(-0.384478\pi\) | ||||
0.355008 | + | 0.934863i | \(0.384478\pi\) | |||||||
\(978\) | 1.70658e14i | 0.190735i | ||||||||
\(979\) | 2.09757e15i | 2.33239i | ||||||||
\(980\) | − | 4.74148e14i | − | 0.524546i | ||||||
\(981\) | 3.48248e14 | 0.383305 | ||||||||
\(982\) | 9.78635e14 | 1.07168 | ||||||||
\(983\) | − | 1.01322e15i | − | 1.10392i | −0.833871 | − | 0.551959i | \(-0.813880\pi\) | ||
0.833871 | − | 0.551959i | \(-0.186120\pi\) | |||||||
\(984\) | 3.68263e14 | 0.399192 | ||||||||
\(985\) | − | 1.07707e15i | − | 1.16162i | ||||||
\(986\) | 3.84012e14 | 0.412060 | ||||||||
\(987\) | −1.37675e14 | −0.146984 | ||||||||
\(988\) | 6.50343e14i | 0.690809i | ||||||||
\(989\) | 3.56086e14 | + | 4.18392e14i | 0.376334 | + | 0.442183i | ||||
\(990\) | 5.40958e14 | 0.568837 | ||||||||
\(991\) | − | 5.40127e14i | − | 0.565103i | −0.959252 | − | 0.282552i | \(-0.908819\pi\) | ||
0.959252 | − | 0.282552i | \(-0.0911809\pi\) | |||||||
\(992\) | 8.80858e14i | 0.916954i | ||||||||
\(993\) | 1.11811e15 | 1.15808 | ||||||||
\(994\) | 2.31380e14i | 0.238448i | ||||||||
\(995\) | 8.82485e14 | 0.904882 | ||||||||
\(996\) | − | 5.17538e14i | − | 0.528014i | ||||||
\(997\) | − | 7.73067e14i | − | 0.784768i | −0.919801 | − | 0.392384i | \(-0.871650\pi\) | ||
0.919801 | − | 0.392384i | \(-0.128350\pi\) | |||||||
\(998\) | −1.24906e15 | −1.26163 | ||||||||
\(999\) | −1.24358e14 | −0.124982 |
(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 | 43.11.b.b.42.22 | yes | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.13 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.13 | ✓ | 34 | 43.42 | odd | 2 | inner | |
43.11.b.b.42.22 | yes | 34 | 1.1 | even | 1 | trivial |