Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,15,Mod(22,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.22");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(28.5956626749\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.12 | ||
Character | \(\chi\) | \(=\) | 23.22 |
Dual form | 23.15.b.b.22.11 |
$q$-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 \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −54.1371 | −0.422946 | −0.211473 | − | 0.977384i | \(-0.567826\pi\) | ||||
−0.211473 | + | 0.977384i | \(0.567826\pi\) | |||||||
\(3\) | −3497.25 | −1.59911 | −0.799555 | − | 0.600593i | \(-0.794931\pi\) | ||||
−0.799555 | + | 0.600593i | \(0.794931\pi\) | |||||||
\(4\) | −13453.2 | −0.821117 | ||||||||
\(5\) | − | 104018.i | − | 1.33143i | −0.746206 | − | 0.665716i | \(-0.768126\pi\) | ||
0.746206 | − | 0.665716i | \(-0.231874\pi\) | |||||||
\(6\) | 189331. | 0.676337 | ||||||||
\(7\) | − | 363656.i | − | 0.441575i | −0.975322 | − | 0.220787i | \(-0.929137\pi\) | ||
0.975322 | − | 0.220787i | \(-0.0708627\pi\) | |||||||
\(8\) | 1.61530e6 | 0.770234 | ||||||||
\(9\) | 7.44782e6 | 1.55715 | ||||||||
\(10\) | 5.63123e6i | 0.563123i | ||||||||
\(11\) | 1.70377e7i | 0.874302i | 0.899388 | + | 0.437151i | \(0.144012\pi\) | ||||
−0.899388 | + | 0.437151i | \(0.855988\pi\) | |||||||
\(12\) | 4.70492e7 | 1.31306 | ||||||||
\(13\) | 4.63838e7 | 0.739202 | 0.369601 | − | 0.929191i | \(-0.379494\pi\) | ||||
0.369601 | + | 0.929191i | \(0.379494\pi\) | |||||||
\(14\) | 1.96873e7i | 0.186762i | ||||||||
\(15\) | 3.63778e8i | 2.12911i | ||||||||
\(16\) | 1.32969e8 | 0.495350 | ||||||||
\(17\) | − | 7.43123e8i | − | 1.81100i | −0.424347 | − | 0.905500i | \(-0.639496\pi\) | ||
0.424347 | − | 0.905500i | \(-0.360504\pi\) | |||||||
\(18\) | −4.03203e8 | −0.658591 | ||||||||
\(19\) | − | 1.19078e9i | − | 1.33216i | −0.745880 | − | 0.666080i | \(-0.767971\pi\) | ||
0.745880 | − | 0.666080i | \(-0.232029\pi\) | |||||||
\(20\) | 1.39937e9i | 1.09326i | ||||||||
\(21\) | 1.27180e9i | 0.706127i | ||||||||
\(22\) | − | 9.22370e8i | − | 0.369782i | ||||||
\(23\) | 3.02387e9 | − | 1.56494e9i | 0.888114 | − | 0.459624i | ||||
\(24\) | −5.64910e9 | −1.23169 | ||||||||
\(25\) | −4.71624e9 | −0.772709 | ||||||||
\(26\) | −2.51108e9 | −0.312642 | ||||||||
\(27\) | −9.31965e9 | −0.890950 | ||||||||
\(28\) | 4.89233e9i | 0.362585i | ||||||||
\(29\) | 1.91522e10 | 1.11028 | 0.555139 | − | 0.831758i | \(-0.312665\pi\) | ||||
0.555139 | + | 0.831758i | \(0.312665\pi\) | |||||||
\(30\) | − | 1.96939e10i | − | 0.900496i | ||||||
\(31\) | 1.15243e10 | 0.418873 | 0.209436 | − | 0.977822i | \(-0.432837\pi\) | ||||
0.209436 | + | 0.977822i | \(0.432837\pi\) | |||||||
\(32\) | −3.36636e10 | −0.979740 | ||||||||
\(33\) | − | 5.95851e10i | − | 1.39811i | ||||||
\(34\) | 4.02305e10i | 0.765955i | ||||||||
\(35\) | −3.78268e10 | −0.587927 | ||||||||
\(36\) | −1.00197e11 | −1.27860 | ||||||||
\(37\) | − | 4.82300e10i | − | 0.508049i | −0.967198 | − | 0.254024i | \(-0.918246\pi\) | ||
0.967198 | − | 0.254024i | \(-0.0817543\pi\) | |||||||
\(38\) | 6.44654e10i | 0.563432i | ||||||||
\(39\) | −1.62216e11 | −1.18207 | ||||||||
\(40\) | − | 1.68020e11i | − | 1.02551i | ||||||
\(41\) | −2.83740e11 | −1.45691 | −0.728456 | − | 0.685093i | \(-0.759762\pi\) | ||||
−0.728456 | + | 0.685093i | \(0.759762\pi\) | |||||||
\(42\) | − | 6.88514e10i | − | 0.298653i | ||||||
\(43\) | 2.89161e11i | 1.06380i | 0.846807 | + | 0.531900i | \(0.178522\pi\) | ||||
−0.846807 | + | 0.531900i | \(0.821478\pi\) | |||||||
\(44\) | − | 2.29211e11i | − | 0.717904i | ||||||
\(45\) | − | 7.74707e11i | − | 2.07324i | ||||||
\(46\) | −1.63704e11 | + | 8.47212e10i | −0.375624 | + | 0.194396i | ||||
\(47\) | 1.70535e11 | 0.336612 | 0.168306 | − | 0.985735i | \(-0.446170\pi\) | ||||
0.168306 | + | 0.985735i | \(0.446170\pi\) | |||||||
\(48\) | −4.65028e11 | −0.792119 | ||||||||
\(49\) | 5.45977e11 | 0.805012 | ||||||||
\(50\) | 2.55324e11 | 0.326814 | ||||||||
\(51\) | 2.59889e12i | 2.89599i | ||||||||
\(52\) | −6.24010e11 | −0.606971 | ||||||||
\(53\) | − | 2.00801e12i | − | 1.70937i | −0.519151 | − | 0.854683i | \(-0.673752\pi\) | ||
0.519151 | − | 0.854683i | \(-0.326248\pi\) | |||||||
\(54\) | 5.04538e11 | 0.376823 | ||||||||
\(55\) | 1.77223e12 | 1.16407 | ||||||||
\(56\) | − | 5.87412e11i | − | 0.340116i | ||||||
\(57\) | 4.16446e12i | 2.13027i | ||||||||
\(58\) | −1.03684e12 | −0.469587 | ||||||||
\(59\) | 1.84293e12 | 0.740532 | 0.370266 | − | 0.928926i | \(-0.379267\pi\) | ||||
0.370266 | + | 0.928926i | \(0.379267\pi\) | |||||||
\(60\) | − | 4.89397e12i | − | 1.74824i | ||||||
\(61\) | 2.15010e12i | 0.684149i | 0.939673 | + | 0.342075i | \(0.111130\pi\) | ||||
−0.939673 | + | 0.342075i | \(0.888870\pi\) | |||||||
\(62\) | −6.23891e11 | −0.177161 | ||||||||
\(63\) | − | 2.70844e12i | − | 0.687600i | ||||||
\(64\) | −3.56122e11 | −0.0809728 | ||||||||
\(65\) | − | 4.82476e12i | − | 0.984197i | ||||||
\(66\) | 3.22576e12i | 0.591323i | ||||||||
\(67\) | − | 3.48837e12i | − | 0.575571i | −0.957695 | − | 0.287786i | \(-0.907081\pi\) | ||
0.957695 | − | 0.287786i | \(-0.0929191\pi\) | |||||||
\(68\) | 9.99737e12i | 1.48704i | ||||||||
\(69\) | −1.05752e13 | + | 5.47299e12i | −1.42019 | + | 0.734989i | ||||
\(70\) | 2.04783e12 | 0.248661 | ||||||||
\(71\) | 5.84451e12 | 0.642599 | 0.321299 | − | 0.946978i | \(-0.395880\pi\) | ||||
0.321299 | + | 0.946978i | \(0.395880\pi\) | |||||||
\(72\) | 1.20304e13 | 1.19937 | ||||||||
\(73\) | 1.12981e13 | 1.02270 | 0.511348 | − | 0.859374i | \(-0.329146\pi\) | ||||
0.511348 | + | 0.859374i | \(0.329146\pi\) | |||||||
\(74\) | 2.61103e12i | 0.214877i | ||||||||
\(75\) | 1.64939e13 | 1.23565 | ||||||||
\(76\) | 1.60198e13i | 1.09386i | ||||||||
\(77\) | 6.19585e12 | 0.386070 | ||||||||
\(78\) | 8.78190e12 | 0.499950 | ||||||||
\(79\) | 1.67367e13i | 0.871528i | 0.900061 | + | 0.435764i | \(0.143522\pi\) | ||||
−0.900061 | + | 0.435764i | \(0.856478\pi\) | |||||||
\(80\) | − | 1.38312e13i | − | 0.659524i | ||||||
\(81\) | −3.02950e12 | −0.132427 | ||||||||
\(82\) | 1.53608e13 | 0.616195 | ||||||||
\(83\) | − | 2.84328e13i | − | 1.04779i | −0.851784 | − | 0.523894i | \(-0.824479\pi\) | ||
0.851784 | − | 0.523894i | \(-0.175521\pi\) | |||||||
\(84\) | − | 1.71097e13i | − | 0.579813i | ||||||
\(85\) | −7.72982e13 | −2.41122 | ||||||||
\(86\) | − | 1.56543e13i | − | 0.449930i | ||||||
\(87\) | −6.69800e13 | −1.77546 | ||||||||
\(88\) | 2.75209e13i | 0.673417i | ||||||||
\(89\) | − | 7.66878e13i | − | 1.73379i | −0.498492 | − | 0.866894i | \(-0.666113\pi\) | ||
0.498492 | − | 0.866894i | \(-0.333887\pi\) | |||||||
\(90\) | 4.19404e13i | 0.876869i | ||||||||
\(91\) | − | 1.68678e13i | − | 0.326413i | ||||||
\(92\) | −4.06807e13 | + | 2.10534e13i | −0.729245 | + | 0.377405i | ||||
\(93\) | −4.03034e13 | −0.669824 | ||||||||
\(94\) | −9.23228e12 | −0.142369 | ||||||||
\(95\) | −1.23863e14 | −1.77368 | ||||||||
\(96\) | 1.17730e14 | 1.56671 | ||||||||
\(97\) | − | 1.08940e14i | − | 1.34829i | −0.738597 | − | 0.674147i | \(-0.764511\pi\) | ||
0.738597 | − | 0.674147i | \(-0.235489\pi\) | |||||||
\(98\) | −2.95576e13 | −0.340476 | ||||||||
\(99\) | 1.26893e14i | 1.36142i | ||||||||
\(100\) | 6.34485e13 | 0.634485 | ||||||||
\(101\) | −1.92236e13 | −0.179302 | −0.0896509 | − | 0.995973i | \(-0.528575\pi\) | ||||
−0.0896509 | + | 0.995973i | \(0.528575\pi\) | |||||||
\(102\) | − | 1.40696e14i | − | 1.22485i | ||||||
\(103\) | − | 4.69048e13i | − | 0.381379i | −0.981650 | − | 0.190689i | \(-0.938928\pi\) | ||
0.981650 | − | 0.190689i | \(-0.0610723\pi\) | |||||||
\(104\) | 7.49237e13 | 0.569358 | ||||||||
\(105\) | 1.32290e14 | 0.940160 | ||||||||
\(106\) | 1.08708e14i | 0.722969i | ||||||||
\(107\) | 8.43182e13i | 0.525091i | 0.964920 | + | 0.262546i | \(0.0845620\pi\) | ||||
−0.964920 | + | 0.262546i | \(0.915438\pi\) | |||||||
\(108\) | 1.25379e14 | 0.731574 | ||||||||
\(109\) | 3.64514e13i | 0.199402i | 0.995017 | + | 0.0997008i | \(0.0317885\pi\) | ||||
−0.995017 | + | 0.0997008i | \(0.968211\pi\) | |||||||
\(110\) | −9.59431e13 | −0.492340 | ||||||||
\(111\) | 1.68673e14i | 0.812426i | ||||||||
\(112\) | − | 4.83551e13i | − | 0.218734i | ||||||
\(113\) | 2.47998e14i | 1.05414i | 0.849821 | + | 0.527072i | \(0.176710\pi\) | ||||
−0.849821 | + | 0.527072i | \(0.823290\pi\) | |||||||
\(114\) | − | 2.25452e14i | − | 0.900990i | ||||||
\(115\) | −1.62782e14 | − | 3.14537e14i | −0.611958 | − | 1.18246i | ||||
\(116\) | −2.57657e14 | −0.911668 | ||||||||
\(117\) | 3.45458e14 | 1.15105 | ||||||||
\(118\) | −9.97706e13 | −0.313205 | ||||||||
\(119\) | −2.70241e14 | −0.799692 | ||||||||
\(120\) | 5.87609e14i | 1.63991i | ||||||||
\(121\) | 8.94675e13 | 0.235596 | ||||||||
\(122\) | − | 1.16400e14i | − | 0.289358i | ||||||
\(123\) | 9.92310e14 | 2.32976 | ||||||||
\(124\) | −1.55038e14 | −0.343944 | ||||||||
\(125\) | − | 1.44301e14i | − | 0.302622i | ||||||
\(126\) | 1.46627e14i | 0.290817i | ||||||||
\(127\) | 3.36880e14 | 0.632192 | 0.316096 | − | 0.948727i | \(-0.397628\pi\) | ||||
0.316096 | + | 0.948727i | \(0.397628\pi\) | |||||||
\(128\) | 5.70824e14 | 1.01399 | ||||||||
\(129\) | − | 1.01127e15i | − | 1.70113i | ||||||
\(130\) | 2.61198e14i | 0.416262i | ||||||||
\(131\) | 6.45474e13 | 0.0974944 | 0.0487472 | − | 0.998811i | \(-0.484477\pi\) | ||||
0.0487472 | + | 0.998811i | \(0.484477\pi\) | |||||||
\(132\) | 8.01609e14i | 1.14801i | ||||||||
\(133\) | −4.33035e14 | −0.588249 | ||||||||
\(134\) | 1.88850e14i | 0.243435i | ||||||||
\(135\) | 9.69412e14i | 1.18624i | ||||||||
\(136\) | − | 1.20036e15i | − | 1.39489i | ||||||
\(137\) | 1.27294e15i | 1.40528i | 0.711544 | + | 0.702641i | \(0.247996\pi\) | ||||
−0.711544 | + | 0.702641i | \(0.752004\pi\) | |||||||
\(138\) | 5.72513e14 | − | 2.96292e14i | 0.600664 | − | 0.310861i | ||||
\(139\) | −4.66027e14 | −0.464845 | −0.232422 | − | 0.972615i | \(-0.574665\pi\) | ||||
−0.232422 | + | 0.972615i | \(0.574665\pi\) | |||||||
\(140\) | 5.08891e14 | 0.482757 | ||||||||
\(141\) | −5.96405e14 | −0.538279 | ||||||||
\(142\) | −3.16405e14 | −0.271784 | ||||||||
\(143\) | 7.90273e14i | 0.646286i | ||||||||
\(144\) | 9.90332e14 | 0.771335 | ||||||||
\(145\) | − | 1.99217e15i | − | 1.47826i | ||||||
\(146\) | −6.11647e14 | −0.432545 | ||||||||
\(147\) | −1.90942e15 | −1.28730 | ||||||||
\(148\) | 6.48847e14i | 0.417167i | ||||||||
\(149\) | − | 3.72395e14i | − | 0.228402i | −0.993458 | − | 0.114201i | \(-0.963569\pi\) | ||
0.993458 | − | 0.114201i | \(-0.0364308\pi\) | |||||||
\(150\) | −8.92931e14 | −0.522612 | ||||||||
\(151\) | −3.57307e15 | −1.99619 | −0.998097 | − | 0.0616603i | \(-0.980360\pi\) | ||||
−0.998097 | + | 0.0616603i | \(0.980360\pi\) | |||||||
\(152\) | − | 1.92347e15i | − | 1.02608i | ||||||
\(153\) | − | 5.53464e15i | − | 2.82000i | ||||||
\(154\) | −3.35425e14 | −0.163287 | ||||||||
\(155\) | − | 1.19873e15i | − | 0.557700i | ||||||
\(156\) | 2.18232e15 | 0.970614 | ||||||||
\(157\) | 9.97719e14i | 0.424337i | 0.977233 | + | 0.212168i | \(0.0680525\pi\) | ||||
−0.977233 | + | 0.212168i | \(0.931947\pi\) | |||||||
\(158\) | − | 9.06078e14i | − | 0.368609i | ||||||
\(159\) | 7.02252e15i | 2.73346i | ||||||||
\(160\) | 3.50162e15i | 1.30446i | ||||||||
\(161\) | −5.69099e14 | − | 1.09965e15i | −0.202958 | − | 0.392169i | ||||
\(162\) | 1.64008e14 | 0.0560094 | ||||||||
\(163\) | −6.93882e14 | −0.226972 | −0.113486 | − | 0.993540i | \(-0.536202\pi\) | ||||
−0.113486 | + | 0.993540i | \(0.536202\pi\) | |||||||
\(164\) | 3.81720e15 | 1.19629 | ||||||||
\(165\) | −6.19792e15 | −1.86148 | ||||||||
\(166\) | 1.53927e15i | 0.443157i | ||||||||
\(167\) | 5.06681e15 | 1.39868 | 0.699341 | − | 0.714788i | \(-0.253477\pi\) | ||||
0.699341 | + | 0.714788i | \(0.253477\pi\) | |||||||
\(168\) | 2.05433e15i | 0.543883i | ||||||||
\(169\) | −1.78592e15 | −0.453580 | ||||||||
\(170\) | 4.18470e15 | 1.01982 | ||||||||
\(171\) | − | 8.86872e15i | − | 2.07438i | ||||||
\(172\) | − | 3.89013e15i | − | 0.873504i | ||||||
\(173\) | −5.99671e15 | −1.29297 | −0.646487 | − | 0.762925i | \(-0.723763\pi\) | ||||
−0.646487 | + | 0.762925i | \(0.723763\pi\) | |||||||
\(174\) | 3.62610e15 | 0.750922 | ||||||||
\(175\) | 1.71509e15i | 0.341209i | ||||||||
\(176\) | 2.26549e15i | 0.433085i | ||||||||
\(177\) | −6.44518e15 | −1.18419 | ||||||||
\(178\) | 4.15165e15i | 0.733299i | ||||||||
\(179\) | 6.80266e15 | 1.15533 | 0.577667 | − | 0.816273i | \(-0.303963\pi\) | ||||
0.577667 | + | 0.816273i | \(0.303963\pi\) | |||||||
\(180\) | 1.04223e16i | 1.70237i | ||||||||
\(181\) | − | 7.23728e15i | − | 1.13717i | −0.822625 | − | 0.568585i | \(-0.807491\pi\) | ||
0.822625 | − | 0.568585i | \(-0.192509\pi\) | |||||||
\(182\) | 9.13171e14i | 0.138055i | ||||||||
\(183\) | − | 7.51946e15i | − | 1.09403i | ||||||
\(184\) | 4.88445e15 | − | 2.52784e15i | 0.684055 | − | 0.354018i | ||||
\(185\) | −5.01679e15 | −0.676432 | ||||||||
\(186\) | 2.18191e15 | 0.283299 | ||||||||
\(187\) | 1.26611e16 | 1.58336 | ||||||||
\(188\) | −2.29424e15 | −0.276398 | ||||||||
\(189\) | 3.38914e15i | 0.393421i | ||||||||
\(190\) | 6.70556e15 | 0.750171 | ||||||||
\(191\) | 5.10982e15i | 0.551026i | 0.961297 | + | 0.275513i | \(0.0888477\pi\) | ||||
−0.961297 | + | 0.275513i | \(0.911152\pi\) | |||||||
\(192\) | 1.24545e15 | 0.129484 | ||||||||
\(193\) | −1.05662e16 | −1.05930 | −0.529649 | − | 0.848217i | \(-0.677676\pi\) | ||||
−0.529649 | + | 0.848217i | \(0.677676\pi\) | |||||||
\(194\) | 5.89769e15i | 0.570256i | ||||||||
\(195\) | 1.68734e16i | 1.57384i | ||||||||
\(196\) | −7.34513e15 | −0.661009 | ||||||||
\(197\) | 9.62662e15 | 0.836007 | 0.418004 | − | 0.908445i | \(-0.362730\pi\) | ||||
0.418004 | + | 0.908445i | \(0.362730\pi\) | |||||||
\(198\) | − | 6.86964e15i | − | 0.575808i | ||||||
\(199\) | − | 8.89744e15i | − | 0.719936i | −0.932965 | − | 0.359968i | \(-0.882788\pi\) | ||
0.932965 | − | 0.359968i | \(-0.117212\pi\) | |||||||
\(200\) | −7.61814e15 | −0.595167 | ||||||||
\(201\) | 1.21997e16i | 0.920402i | ||||||||
\(202\) | 1.04071e15 | 0.0758350 | ||||||||
\(203\) | − | 6.96480e15i | − | 0.490271i | ||||||
\(204\) | − | 3.49633e16i | − | 2.37794i | ||||||
\(205\) | 2.95141e16i | 1.93978i | ||||||||
\(206\) | 2.53929e15i | 0.161303i | ||||||||
\(207\) | 2.25212e16 | − | 1.16554e16i | 1.38293 | − | 0.715705i | ||||
\(208\) | 6.16763e15 | 0.366164 | ||||||||
\(209\) | 2.02881e16 | 1.16471 | ||||||||
\(210\) | −7.16179e15 | −0.397637 | ||||||||
\(211\) | 1.84823e16 | 0.992610 | 0.496305 | − | 0.868148i | \(-0.334690\pi\) | ||||
0.496305 | + | 0.868148i | \(0.334690\pi\) | |||||||
\(212\) | 2.70141e16i | 1.40359i | ||||||||
\(213\) | −2.04397e16 | −1.02759 | ||||||||
\(214\) | − | 4.56474e15i | − | 0.222085i | ||||||
\(215\) | 3.00779e16 | 1.41638 | ||||||||
\(216\) | −1.50540e16 | −0.686239 | ||||||||
\(217\) | − | 4.19088e15i | − | 0.184964i | ||||||
\(218\) | − | 1.97337e15i | − | 0.0843360i | ||||||
\(219\) | −3.95124e16 | −1.63540 | ||||||||
\(220\) | −2.38421e16 | −0.955840 | ||||||||
\(221\) | − | 3.44689e16i | − | 1.33869i | ||||||
\(222\) | − | 9.13144e15i | − | 0.343612i | ||||||
\(223\) | −3.22061e16 | −1.17437 | −0.587185 | − | 0.809453i | \(-0.699764\pi\) | ||||
−0.587185 | + | 0.809453i | \(0.699764\pi\) | |||||||
\(224\) | 1.22420e16i | 0.432629i | ||||||||
\(225\) | −3.51257e16 | −1.20323 | ||||||||
\(226\) | − | 1.34259e16i | − | 0.445846i | ||||||
\(227\) | 4.70834e16i | 1.51596i | 0.652280 | + | 0.757978i | \(0.273813\pi\) | ||||
−0.652280 | + | 0.757978i | \(0.726187\pi\) | |||||||
\(228\) | − | 5.60253e16i | − | 1.74920i | ||||||
\(229\) | 2.22913e15i | 0.0674975i | 0.999430 | + | 0.0337488i | \(0.0107446\pi\) | ||||
−0.999430 | + | 0.0337488i | \(0.989255\pi\) | |||||||
\(230\) | 8.81254e15 | + | 1.70281e16i | 0.258825 | + | 0.500118i | ||||
\(231\) | −2.16685e16 | −0.617368 | ||||||||
\(232\) | 3.09364e16 | 0.855174 | ||||||||
\(233\) | −4.84546e16 | −1.29970 | −0.649850 | − | 0.760062i | \(-0.725169\pi\) | ||||
−0.649850 | + | 0.760062i | \(0.725169\pi\) | |||||||
\(234\) | −1.87021e16 | −0.486832 | ||||||||
\(235\) | − | 1.77388e16i | − | 0.448176i | ||||||
\(236\) | −2.47932e16 | −0.608063 | ||||||||
\(237\) | − | 5.85326e16i | − | 1.39367i | ||||||
\(238\) | 1.46301e16 | 0.338226 | ||||||||
\(239\) | −2.85573e15 | −0.0641108 | −0.0320554 | − | 0.999486i | \(-0.510205\pi\) | ||||
−0.0320554 | + | 0.999486i | \(0.510205\pi\) | |||||||
\(240\) | 4.83713e16i | 1.05465i | ||||||||
\(241\) | − | 1.91486e15i | − | 0.0405526i | −0.999794 | − | 0.0202763i | \(-0.993545\pi\) | ||
0.999794 | − | 0.0202763i | \(-0.00645459\pi\) | |||||||
\(242\) | −4.84351e15 | −0.0996443 | ||||||||
\(243\) | 5.51705e16 | 1.10271 | ||||||||
\(244\) | − | 2.89257e16i | − | 0.561766i | ||||||
\(245\) | − | 5.67915e16i | − | 1.07182i | ||||||
\(246\) | −5.37207e16 | −0.985363 | ||||||||
\(247\) | − | 5.52330e16i | − | 0.984736i | ||||||
\(248\) | 1.86152e16 | 0.322630 | ||||||||
\(249\) | 9.94367e16i | 1.67553i | ||||||||
\(250\) | 7.81205e15i | 0.127993i | ||||||||
\(251\) | 4.33087e16i | 0.690015i | 0.938600 | + | 0.345008i | \(0.112124\pi\) | ||||
−0.938600 | + | 0.345008i | \(0.887876\pi\) | |||||||
\(252\) | 3.64372e16i | 0.564600i | ||||||||
\(253\) | 2.66629e16 | + | 5.15197e16i | 0.401850 | + | 0.776480i | ||||
\(254\) | −1.82377e16 | −0.267383 | ||||||||
\(255\) | 2.70332e17 | 3.85581 | ||||||||
\(256\) | −2.50680e16 | −0.347889 | ||||||||
\(257\) | 1.08722e17 | 1.46820 | 0.734101 | − | 0.679041i | \(-0.237604\pi\) | ||||
0.734101 | + | 0.679041i | \(0.237604\pi\) | |||||||
\(258\) | 5.47471e16i | 0.719488i | ||||||||
\(259\) | −1.75391e16 | −0.224342 | ||||||||
\(260\) | 6.49083e16i | 0.808141i | ||||||||
\(261\) | 1.42642e17 | 1.72887 | ||||||||
\(262\) | −3.49441e15 | −0.0412349 | ||||||||
\(263\) | − | 6.64568e16i | − | 0.763570i | −0.924251 | − | 0.381785i | \(-0.875309\pi\) | ||
0.924251 | − | 0.381785i | \(-0.124691\pi\) | |||||||
\(264\) | − | 9.62476e16i | − | 1.07687i | ||||||
\(265\) | −2.08869e17 | −2.27590 | ||||||||
\(266\) | 2.34432e16 | 0.248797 | ||||||||
\(267\) | 2.68197e17i | 2.77252i | ||||||||
\(268\) | 4.69297e16i | 0.472611i | ||||||||
\(269\) | −9.83762e16 | −0.965215 | −0.482607 | − | 0.875837i | \(-0.660310\pi\) | ||||
−0.482607 | + | 0.875837i | \(0.660310\pi\) | |||||||
\(270\) | − | 5.24811e16i | − | 0.501714i | ||||||
\(271\) | −6.73653e16 | −0.627554 | −0.313777 | − | 0.949497i | \(-0.601594\pi\) | ||||
−0.313777 | + | 0.949497i | \(0.601594\pi\) | |||||||
\(272\) | − | 9.88126e16i | − | 0.897078i | ||||||
\(273\) | 5.89908e16i | 0.521971i | ||||||||
\(274\) | − | 6.89132e16i | − | 0.594358i | ||||||
\(275\) | − | 8.03538e16i | − | 0.675581i | ||||||
\(276\) | 1.42271e17 | − | 7.36291e16i | 1.16614 | − | 0.603512i | ||||
\(277\) | −8.87282e16 | −0.709093 | −0.354547 | − | 0.935038i | \(-0.615365\pi\) | ||||
−0.354547 | + | 0.935038i | \(0.615365\pi\) | |||||||
\(278\) | 2.52293e16 | 0.196604 | ||||||||
\(279\) | 8.58308e16 | 0.652249 | ||||||||
\(280\) | −6.11015e16 | −0.452841 | ||||||||
\(281\) | − | 2.50651e17i | − | 1.81187i | −0.423422 | − | 0.905933i | \(-0.639171\pi\) | ||
0.423422 | − | 0.905933i | \(-0.360829\pi\) | |||||||
\(282\) | 3.22876e16 | 0.227663 | ||||||||
\(283\) | − | 2.29216e16i | − | 0.157667i | −0.996888 | − | 0.0788334i | \(-0.974880\pi\) | ||
0.996888 | − | 0.0788334i | \(-0.0251195\pi\) | |||||||
\(284\) | −7.86273e16 | −0.527649 | ||||||||
\(285\) | 4.33179e17 | 2.83631 | ||||||||
\(286\) | − | 4.27830e16i | − | 0.273344i | ||||||
\(287\) | 1.03184e17i | 0.643336i | ||||||||
\(288\) | −2.50720e17 | −1.52561 | ||||||||
\(289\) | −3.83854e17 | −2.27972 | ||||||||
\(290\) | 1.07850e17i | 0.625223i | ||||||||
\(291\) | 3.80990e17i | 2.15607i | ||||||||
\(292\) | −1.51996e17 | −0.839752 | ||||||||
\(293\) | 2.28366e17i | 1.23185i | 0.787805 | + | 0.615924i | \(0.211217\pi\) | ||||
−0.787805 | + | 0.615924i | \(0.788783\pi\) | |||||||
\(294\) | 1.03370e17 | 0.544459 | ||||||||
\(295\) | − | 1.91698e17i | − | 0.985967i | ||||||
\(296\) | − | 7.79058e16i | − | 0.391316i | ||||||
\(297\) | − | 1.58785e17i | − | 0.778959i | ||||||
\(298\) | 2.01604e16i | 0.0966017i | ||||||||
\(299\) | 1.40259e17 | − | 7.25879e16i | 0.656496 | − | 0.339755i | ||||
\(300\) | −2.21895e17 | −1.01461 | ||||||||
\(301\) | 1.05155e17 | 0.469748 | ||||||||
\(302\) | 1.93435e17 | 0.844282 | ||||||||
\(303\) | 6.72298e16 | 0.286723 | ||||||||
\(304\) | − | 1.58337e17i | − | 0.659885i | ||||||
\(305\) | 2.23650e17 | 0.910898 | ||||||||
\(306\) | 2.99629e17i | 1.19271i | ||||||||
\(307\) | 1.77181e17 | 0.689362 | 0.344681 | − | 0.938720i | \(-0.387987\pi\) | ||||
0.344681 | + | 0.938720i | \(0.387987\pi\) | |||||||
\(308\) | −8.33539e16 | −0.317008 | ||||||||
\(309\) | 1.64038e17i | 0.609867i | ||||||||
\(310\) | 6.48960e16i | 0.235877i | ||||||||
\(311\) | −3.98607e17 | −1.41652 | −0.708259 | − | 0.705952i | \(-0.750519\pi\) | ||||
−0.708259 | + | 0.705952i | \(0.750519\pi\) | |||||||
\(312\) | −2.62027e17 | −0.910467 | ||||||||
\(313\) | − | 4.75005e17i | − | 1.61394i | −0.590591 | − | 0.806971i | \(-0.701105\pi\) | ||
0.590591 | − | 0.806971i | \(-0.298895\pi\) | |||||||
\(314\) | − | 5.40136e16i | − | 0.179471i | ||||||
\(315\) | −2.81727e17 | −0.915492 | ||||||||
\(316\) | − | 2.25162e17i | − | 0.715626i | ||||||
\(317\) | 5.59180e17 | 1.73835 | 0.869174 | − | 0.494507i | \(-0.164651\pi\) | ||||
0.869174 | + | 0.494507i | \(0.164651\pi\) | |||||||
\(318\) | − | 3.80179e17i | − | 1.15611i | ||||||
\(319\) | 3.26308e17i | 0.970719i | ||||||||
\(320\) | 3.70432e16i | 0.107810i | ||||||||
\(321\) | − | 2.94882e17i | − | 0.839679i | ||||||
\(322\) | 3.08094e16 | + | 5.95318e16i | 0.0858404 | + | 0.165866i | ||||
\(323\) | −8.84897e17 | −2.41254 | ||||||||
\(324\) | 4.07564e16 | 0.108738 | ||||||||
\(325\) | −2.18757e17 | −0.571188 | ||||||||
\(326\) | 3.75648e16 | 0.0959969 | ||||||||
\(327\) | − | 1.27480e17i | − | 0.318865i | ||||||
\(328\) | −4.58324e17 | −1.12216 | ||||||||
\(329\) | − | 6.20162e16i | − | 0.148639i | ||||||
\(330\) | 3.35537e17 | 0.787306 | ||||||||
\(331\) | −3.39881e17 | −0.780784 | −0.390392 | − | 0.920649i | \(-0.627661\pi\) | ||||
−0.390392 | + | 0.920649i | \(0.627661\pi\) | |||||||
\(332\) | 3.82512e17i | 0.860356i | ||||||||
\(333\) | − | 3.59208e17i | − | 0.791109i | ||||||
\(334\) | −2.74302e17 | −0.591567 | ||||||||
\(335\) | −3.62854e17 | −0.766334 | ||||||||
\(336\) | 1.69110e17i | 0.349780i | ||||||||
\(337\) | 7.58375e17i | 1.53630i | 0.640273 | + | 0.768148i | \(0.278821\pi\) | ||||
−0.640273 | + | 0.768148i | \(0.721179\pi\) | |||||||
\(338\) | 9.66842e16 | 0.191840 | ||||||||
\(339\) | − | 8.67313e17i | − | 1.68569i | ||||||
\(340\) | 1.03991e18 | 1.97989 | ||||||||
\(341\) | 1.96347e17i | 0.366221i | ||||||||
\(342\) | 4.80126e17i | 0.877350i | ||||||||
\(343\) | − | 4.45188e17i | − | 0.797048i | ||||||
\(344\) | 4.67081e17i | 0.819375i | ||||||||
\(345\) | 5.69290e17 | + | 1.10002e18i | 0.978588 | + | 1.89089i | ||||
\(346\) | 3.24644e17 | 0.546858 | ||||||||
\(347\) | 1.07300e18 | 1.77131 | 0.885655 | − | 0.464343i | \(-0.153710\pi\) | ||||
0.885655 | + | 0.464343i | \(0.153710\pi\) | |||||||
\(348\) | 9.01093e17 | 1.45786 | ||||||||
\(349\) | −1.14112e17 | −0.180947 | −0.0904737 | − | 0.995899i | \(-0.528838\pi\) | ||||
−0.0904737 | + | 0.995899i | \(0.528838\pi\) | |||||||
\(350\) | − | 9.28499e16i | − | 0.144313i | ||||||
\(351\) | −4.32281e17 | −0.658592 | ||||||||
\(352\) | − | 5.73550e17i | − | 0.856589i | ||||||
\(353\) | 5.45475e17 | 0.798642 | 0.399321 | − | 0.916811i | \(-0.369246\pi\) | ||||
0.399321 | + | 0.916811i | \(0.369246\pi\) | |||||||
\(354\) | 3.48923e17 | 0.500849 | ||||||||
\(355\) | − | 6.07935e17i | − | 0.855576i | ||||||
\(356\) | 1.03169e18i | 1.42364i | ||||||||
\(357\) | 9.45102e17 | 1.27880 | ||||||||
\(358\) | −3.68276e17 | −0.488644 | ||||||||
\(359\) | 4.94984e17i | 0.644066i | 0.946728 | + | 0.322033i | \(0.104366\pi\) | ||||
−0.946728 | + | 0.322033i | \(0.895634\pi\) | |||||||
\(360\) | − | 1.25138e18i | − | 1.59688i | ||||||
\(361\) | −6.18952e17 | −0.774652 | ||||||||
\(362\) | 3.91805e17i | 0.480961i | ||||||||
\(363\) | −3.12890e17 | −0.376744 | ||||||||
\(364\) | 2.26925e17i | 0.268023i | ||||||||
\(365\) | − | 1.17521e18i | − | 1.36165i | ||||||
\(366\) | 4.07082e17i | 0.462715i | ||||||||
\(367\) | 2.94484e17i | 0.328397i | 0.986427 | + | 0.164198i | \(0.0525037\pi\) | ||||
−0.986427 | + | 0.164198i | \(0.947496\pi\) | |||||||
\(368\) | 4.02083e17 | − | 2.08089e17i | 0.439927 | − | 0.227675i | ||||
\(369\) | −2.11324e18 | −2.26863 | ||||||||
\(370\) | 2.71594e17 | 0.286094 | ||||||||
\(371\) | −7.30225e17 | −0.754813 | ||||||||
\(372\) | 5.42208e17 | 0.550004 | ||||||||
\(373\) | 1.93366e18i | 1.92495i | 0.271379 | + | 0.962473i | \(0.412520\pi\) | ||||
−0.271379 | + | 0.962473i | \(0.587480\pi\) | |||||||
\(374\) | −6.85434e17 | −0.669676 | ||||||||
\(375\) | 5.04658e17i | 0.483926i | ||||||||
\(376\) | 2.75465e17 | 0.259270 | ||||||||
\(377\) | 8.88351e17 | 0.820720 | ||||||||
\(378\) | − | 1.83478e17i | − | 0.166396i | ||||||
\(379\) | − | 1.54669e18i | − | 1.37698i | −0.725244 | − | 0.688492i | \(-0.758273\pi\) | ||
0.725244 | − | 0.688492i | \(-0.241727\pi\) | |||||||
\(380\) | 1.66635e18 | 1.45640 | ||||||||
\(381\) | −1.17816e18 | −1.01095 | ||||||||
\(382\) | − | 2.76631e17i | − | 0.233054i | ||||||
\(383\) | − | 4.10276e17i | − | 0.339379i | −0.985498 | − | 0.169690i | \(-0.945724\pi\) | ||
0.985498 | − | 0.169690i | \(-0.0542765\pi\) | |||||||
\(384\) | −1.99632e18 | −1.62148 | ||||||||
\(385\) | − | 6.44481e17i | − | 0.514026i | ||||||
\(386\) | 5.72023e17 | 0.448025 | ||||||||
\(387\) | 2.15362e18i | 1.65650i | ||||||||
\(388\) | 1.46559e18i | 1.10711i | ||||||||
\(389\) | − | 7.29254e17i | − | 0.541043i | −0.962714 | − | 0.270522i | \(-0.912804\pi\) | ||
0.962714 | − | 0.270522i | \(-0.0871961\pi\) | |||||||
\(390\) | − | 9.13476e17i | − | 0.665649i | ||||||
\(391\) | −1.16294e18 | − | 2.24711e18i | −0.832379 | − | 1.60837i | ||||
\(392\) | 8.81916e17 | 0.620047 | ||||||||
\(393\) | −2.25739e17 | −0.155904 | ||||||||
\(394\) | −5.21157e17 | −0.353586 | ||||||||
\(395\) | 1.74092e18 | 1.16038 | ||||||||
\(396\) | − | 1.70712e18i | − | 1.11789i | ||||||
\(397\) | −6.73100e17 | −0.433058 | −0.216529 | − | 0.976276i | \(-0.569474\pi\) | ||||
−0.216529 | + | 0.976276i | \(0.569474\pi\) | |||||||
\(398\) | 4.81681e17i | 0.304494i | ||||||||
\(399\) | 1.51443e18 | 0.940675 | ||||||||
\(400\) | −6.27116e17 | −0.382761 | ||||||||
\(401\) | 1.76399e18i | 1.05800i | 0.848622 | + | 0.529000i | \(0.177433\pi\) | ||||
−0.848622 | + | 0.529000i | \(0.822567\pi\) | |||||||
\(402\) | − | 6.60457e17i | − | 0.389280i | ||||||
\(403\) | 5.34541e17 | 0.309632 | ||||||||
\(404\) | 2.58618e17 | 0.147228 | ||||||||
\(405\) | 3.15123e17i | 0.176317i | ||||||||
\(406\) | 3.77054e17i | 0.207358i | ||||||||
\(407\) | 8.21727e17 | 0.444188 | ||||||||
\(408\) | 4.19798e18i | 2.23059i | ||||||||
\(409\) | −3.07282e18 | −1.60500 | −0.802499 | − | 0.596654i | \(-0.796496\pi\) | ||||
−0.802499 | + | 0.596654i | \(0.796496\pi\) | |||||||
\(410\) | − | 1.59780e18i | − | 0.820421i | ||||||
\(411\) | − | 4.45179e18i | − | 2.24720i | ||||||
\(412\) | 6.31018e17i | 0.313157i | ||||||||
\(413\) | − | 6.70191e17i | − | 0.327000i | ||||||
\(414\) | −1.21923e18 | + | 6.30988e17i | −0.584904 | + | 0.302704i | ||||
\(415\) | −2.95753e18 | −1.39506 | ||||||||
\(416\) | −1.56145e18 | −0.724226 | ||||||||
\(417\) | 1.62982e18 | 0.743338 | ||||||||
\(418\) | −1.09834e18 | −0.492610 | ||||||||
\(419\) | 2.33105e17i | 0.102814i | 0.998678 | + | 0.0514071i | \(0.0163706\pi\) | ||||
−0.998678 | + | 0.0514071i | \(0.983629\pi\) | |||||||
\(420\) | −1.77972e18 | −0.771981 | ||||||||
\(421\) | − | 1.17297e18i | − | 0.500394i | −0.968195 | − | 0.250197i | \(-0.919505\pi\) | ||
0.968195 | − | 0.250197i | \(-0.0804954\pi\) | |||||||
\(422\) | −1.00058e18 | −0.419820 | ||||||||
\(423\) | 1.27012e18 | 0.524156 | ||||||||
\(424\) | − | 3.24353e18i | − | 1.31661i | ||||||
\(425\) | 3.50475e18i | 1.39938i | ||||||||
\(426\) | 1.10655e18 | 0.434613 | ||||||||
\(427\) | 7.81898e17 | 0.302103 | ||||||||
\(428\) | − | 1.13435e18i | − | 0.431161i | ||||||
\(429\) | − | 2.76378e18i | − | 1.03348i | ||||||
\(430\) | −1.62833e18 | −0.599051 | ||||||||
\(431\) | 3.91693e18i | 1.41777i | 0.705325 | + | 0.708884i | \(0.250801\pi\) | ||||
−0.705325 | + | 0.708884i | \(0.749199\pi\) | |||||||
\(432\) | −1.23923e18 | −0.441332 | ||||||||
\(433\) | − | 2.71222e18i | − | 0.950408i | −0.879876 | − | 0.475204i | \(-0.842374\pi\) | ||
0.879876 | − | 0.475204i | \(-0.157626\pi\) | |||||||
\(434\) | 2.26882e17i | 0.0782297i | ||||||||
\(435\) | 6.96713e18i | 2.36390i | ||||||||
\(436\) | − | 4.90387e17i | − | 0.163732i | ||||||
\(437\) | −1.86350e18 | − | 3.60077e18i | −0.612293 | − | 1.18311i | ||||
\(438\) | 2.13909e18 | 0.691686 | ||||||||
\(439\) | 1.52974e18 | 0.486818 | 0.243409 | − | 0.969924i | \(-0.421734\pi\) | ||||
0.243409 | + | 0.969924i | \(0.421734\pi\) | |||||||
\(440\) | 2.86267e18 | 0.896608 | ||||||||
\(441\) | 4.06634e18 | 1.25353 | ||||||||
\(442\) | 1.86605e18i | 0.566195i | ||||||||
\(443\) | 4.44473e18 | 1.32745 | 0.663727 | − | 0.747975i | \(-0.268974\pi\) | ||||
0.663727 | + | 0.747975i | \(0.268974\pi\) | |||||||
\(444\) | − | 2.26918e18i | − | 0.667096i | ||||||
\(445\) | −7.97692e18 | −2.30842 | ||||||||
\(446\) | 1.74355e18 | 0.496695 | ||||||||
\(447\) | 1.30236e18i | 0.365240i | ||||||||
\(448\) | 1.29506e17i | 0.0357556i | ||||||||
\(449\) | −2.67135e18 | −0.726118 | −0.363059 | − | 0.931766i | \(-0.618268\pi\) | ||||
−0.363059 | + | 0.931766i | \(0.618268\pi\) | |||||||
\(450\) | 1.90160e18 | 0.508900 | ||||||||
\(451\) | − | 4.83427e18i | − | 1.27378i | ||||||
\(452\) | − | 3.33637e18i | − | 0.865575i | ||||||
\(453\) | 1.24959e19 | 3.19213 | ||||||||
\(454\) | − | 2.54896e18i | − | 0.641168i | ||||||
\(455\) | −1.75455e18 | −0.434597 | ||||||||
\(456\) | 6.72685e18i | 1.64081i | ||||||||
\(457\) | 6.73286e18i | 1.61728i | 0.588302 | + | 0.808641i | \(0.299797\pi\) | ||||
−0.588302 | + | 0.808641i | \(0.700203\pi\) | |||||||
\(458\) | − | 1.20679e17i | − | 0.0285478i | ||||||
\(459\) | 6.92564e18i | 1.61351i | ||||||||
\(460\) | 2.18993e18 | + | 4.23153e18i | 0.502489 | + | 0.970940i | ||||
\(461\) | 1.59506e18 | 0.360471 | 0.180235 | − | 0.983624i | \(-0.442314\pi\) | ||||
0.180235 | + | 0.983624i | \(0.442314\pi\) | |||||||
\(462\) | 1.17307e18 | 0.261113 | ||||||||
\(463\) | 2.18155e18 | 0.478298 | 0.239149 | − | 0.970983i | \(-0.423132\pi\) | ||||
0.239149 | + | 0.970983i | \(0.423132\pi\) | |||||||
\(464\) | 2.54665e18 | 0.549976 | ||||||||
\(465\) | 4.19228e18i | 0.891825i | ||||||||
\(466\) | 2.62319e18 | 0.549703 | ||||||||
\(467\) | − | 1.58011e18i | − | 0.326189i | −0.986610 | − | 0.163095i | \(-0.947852\pi\) | ||
0.986610 | − | 0.163095i | \(-0.0521476\pi\) | |||||||
\(468\) | −4.64751e18 | −0.945147 | ||||||||
\(469\) | −1.26857e18 | −0.254158 | ||||||||
\(470\) | 9.60324e17i | 0.189554i | ||||||||
\(471\) | − | 3.48928e18i | − | 0.678561i | ||||||
\(472\) | 2.97687e18 | 0.570382 | ||||||||
\(473\) | −4.92663e18 | −0.930083 | ||||||||
\(474\) | 3.16878e18i | 0.589446i | ||||||||
\(475\) | 5.61601e18i | 1.02937i | ||||||||
\(476\) | 3.63560e18 | 0.656640 | ||||||||
\(477\) | − | 1.49553e19i | − | 2.66174i | ||||||
\(478\) | 1.54601e17 | 0.0271154 | ||||||||
\(479\) | 1.91799e18i | 0.331511i | 0.986167 | + | 0.165755i | \(0.0530062\pi\) | ||||
−0.986167 | + | 0.165755i | \(0.946994\pi\) | |||||||
\(480\) | − | 1.22461e19i | − | 2.08597i | ||||||
\(481\) | − | 2.23709e18i | − | 0.375551i | ||||||
\(482\) | 1.03665e17i | 0.0171515i | ||||||||
\(483\) | 1.99029e18 | + | 3.84575e18i | 0.324553 | + | 0.627121i | ||||
\(484\) | −1.20362e18 | −0.193452 | ||||||||
\(485\) | −1.13317e19 | −1.79516 | ||||||||
\(486\) | −2.98677e18 | −0.466389 | ||||||||
\(487\) | −5.60381e18 | −0.862543 | −0.431271 | − | 0.902222i | \(-0.641935\pi\) | ||||
−0.431271 | + | 0.902222i | \(0.641935\pi\) | |||||||
\(488\) | 3.47306e18i | 0.526955i | ||||||||
\(489\) | 2.42668e18 | 0.362953 | ||||||||
\(490\) | 3.07453e18i | 0.453321i | ||||||||
\(491\) | −7.91090e18 | −1.14989 | −0.574944 | − | 0.818193i | \(-0.694976\pi\) | ||||
−0.574944 | + | 0.818193i | \(0.694976\pi\) | |||||||
\(492\) | −1.33497e19 | −1.91301 | ||||||||
\(493\) | − | 1.42324e19i | − | 2.01071i | ||||||
\(494\) | 2.99015e18i | 0.416490i | ||||||||
\(495\) | 1.31992e19 | 1.81264 | ||||||||
\(496\) | 1.53238e18 | 0.207489 | ||||||||
\(497\) | − | 2.12539e18i | − | 0.283755i | ||||||
\(498\) | − | 5.38321e18i | − | 0.708657i | ||||||
\(499\) | 1.50726e19 | 1.95652 | 0.978261 | − | 0.207376i | \(-0.0664923\pi\) | ||||
0.978261 | + | 0.207376i | \(0.0664923\pi\) | |||||||
\(500\) | 1.94131e18i | 0.248488i | ||||||||
\(501\) | −1.77199e19 | −2.23665 | ||||||||
\(502\) | − | 2.34460e18i | − | 0.291839i | ||||||
\(503\) | 5.74019e18i | 0.704613i | 0.935885 | + | 0.352306i | \(0.114602\pi\) | ||||
−0.935885 | + | 0.352306i | \(0.885398\pi\) | |||||||
\(504\) | − | 4.37494e18i | − | 0.529613i | ||||||
\(505\) | 1.99960e18i | 0.238728i | ||||||||
\(506\) | −1.44345e18 | − | 2.78913e18i | −0.169961 | − | 0.328409i | ||||
\(507\) | 6.24580e18 | 0.725325 | ||||||||
\(508\) | −4.53211e18 | −0.519104 | ||||||||
\(509\) | 5.37325e18 | 0.607033 | 0.303516 | − | 0.952826i | \(-0.401839\pi\) | ||||
0.303516 | + | 0.952826i | \(0.401839\pi\) | |||||||
\(510\) | −1.46350e19 | −1.63080 | ||||||||
\(511\) | − | 4.10863e18i | − | 0.451597i | ||||||
\(512\) | −7.99527e18 | −0.866849 | ||||||||
\(513\) | 1.10977e19i | 1.18689i | ||||||||
\(514\) | −5.88589e18 | −0.620970 | ||||||||
\(515\) | −4.87894e18 | −0.507780 | ||||||||
\(516\) | 1.36048e19i | 1.39683i | ||||||||
\(517\) | 2.90553e18i | 0.294300i | ||||||||
\(518\) | 9.49517e17 | 0.0948843 | ||||||||
\(519\) | 2.09720e19 | 2.06761 | ||||||||
\(520\) | − | 7.79342e18i | − | 0.758062i | ||||||
\(521\) | 2.80563e18i | 0.269257i | 0.990896 | + | 0.134628i | \(0.0429841\pi\) | ||||
−0.990896 | + | 0.134628i | \(0.957016\pi\) | |||||||
\(522\) | −7.72221e18 | −0.731220 | ||||||||
\(523\) | 1.31581e19i | 1.22936i | 0.788775 | + | 0.614682i | \(0.210716\pi\) | ||||
−0.788775 | + | 0.614682i | \(0.789284\pi\) | |||||||
\(524\) | −8.68368e17 | −0.0800543 | ||||||||
\(525\) | − | 5.99811e18i | − | 0.545631i | ||||||
\(526\) | 3.59777e18i | 0.322949i | ||||||||
\(527\) | − | 8.56396e18i | − | 0.758579i | ||||||
\(528\) | − | 7.92299e18i | − | 0.692551i | ||||||
\(529\) | 6.69477e18 | − | 9.46435e18i | 0.577492 | − | 0.816397i | ||||
\(530\) | 1.13076e19 | 0.962584 | ||||||||
\(531\) | 1.37258e19 | 1.15312 | ||||||||
\(532\) | 5.82569e18 | 0.483021 | ||||||||
\(533\) | −1.31609e19 | −1.07695 | ||||||||
\(534\) | − | 1.45194e19i | − | 1.17263i | ||||||
\(535\) | 8.77061e18 | 0.699123 | ||||||||
\(536\) | − | 5.63476e18i | − | 0.443324i | ||||||
\(537\) | −2.37906e19 | −1.84751 | ||||||||
\(538\) | 5.32580e18 | 0.408234 | ||||||||
\(539\) | 9.30219e18i | 0.703823i | ||||||||
\(540\) | − | 1.30417e19i | − | 0.974040i | ||||||
\(541\) | 7.93256e18 | 0.584834 | 0.292417 | − | 0.956291i | \(-0.405541\pi\) | ||||
0.292417 | + | 0.956291i | \(0.405541\pi\) | |||||||
\(542\) | 3.64696e18 | 0.265421 | ||||||||
\(543\) | 2.53106e19i | 1.81846i | ||||||||
\(544\) | 2.50162e19i | 1.77431i | ||||||||
\(545\) | 3.79160e18 | 0.265489 | ||||||||
\(546\) | − | 3.19359e18i | − | 0.220765i | ||||||
\(547\) | −3.44897e18 | −0.235385 | −0.117692 | − | 0.993050i | \(-0.537550\pi\) | ||||
−0.117692 | + | 0.993050i | \(0.537550\pi\) | |||||||
\(548\) | − | 1.71251e19i | − | 1.15390i | ||||||
\(549\) | 1.60136e19i | 1.06533i | ||||||||
\(550\) | 4.35012e18i | 0.285734i | ||||||||
\(551\) | − | 2.28060e19i | − | 1.47907i | ||||||
\(552\) | −1.70822e19 | + | 8.84050e18i | −1.09388 | + | 0.566114i | ||||
\(553\) | 6.08641e18 | 0.384845 | ||||||||
\(554\) | 4.80348e18 | 0.299908 | ||||||||
\(555\) | 1.75450e19 | 1.08169 | ||||||||
\(556\) | 6.26955e18 | 0.381692 | ||||||||
\(557\) | − | 2.53328e19i | − | 1.52299i | −0.648173 | − | 0.761493i | \(-0.724466\pi\) | ||
0.648173 | − | 0.761493i | \(-0.275534\pi\) | |||||||
\(558\) | −4.64663e18 | −0.275866 | ||||||||
\(559\) | 1.34124e19i | 0.786364i | ||||||||
\(560\) | −5.02981e18 | −0.291229 | ||||||||
\(561\) | −4.42790e19 | −2.53197 | ||||||||
\(562\) | 1.35695e19i | 0.766321i | ||||||||
\(563\) | − | 3.60984e17i | − | 0.0201340i | −0.999949 | − | 0.0100670i | \(-0.996796\pi\) | ||
0.999949 | − | 0.0100670i | \(-0.00320448\pi\) | |||||||
\(564\) | 8.02355e18 | 0.441990 | ||||||||
\(565\) | 2.57963e19 | 1.40352 | ||||||||
\(566\) | 1.24091e18i | 0.0666845i | ||||||||
\(567\) | 1.10170e18i | 0.0584764i | ||||||||
\(568\) | 9.44062e18 | 0.494951 | ||||||||
\(569\) | 2.25204e19i | 1.16625i | 0.812383 | + | 0.583124i | \(0.198170\pi\) | ||||
−0.812383 | + | 0.583124i | \(0.801830\pi\) | |||||||
\(570\) | −2.34511e19 | −1.19961 | ||||||||
\(571\) | 1.93126e19i | 0.975862i | 0.872882 | + | 0.487931i | \(0.162248\pi\) | ||||
−0.872882 | + | 0.487931i | \(0.837752\pi\) | |||||||
\(572\) | − | 1.06317e19i | − | 0.530676i | ||||||
\(573\) | − | 1.78703e19i | − | 0.881151i | ||||||
\(574\) | − | 5.58606e18i | − | 0.272096i | ||||||
\(575\) | −1.42613e19 | + | 7.38063e18i | −0.686254 | + | 0.355156i | ||||
\(576\) | −2.65233e18 | −0.126087 | ||||||||
\(577\) | −1.40650e19 | −0.660553 | −0.330277 | − | 0.943884i | \(-0.607142\pi\) | ||||
−0.330277 | + | 0.943884i | \(0.607142\pi\) | |||||||
\(578\) | 2.07807e19 | 0.964197 | ||||||||
\(579\) | 3.69527e19 | 1.69393 | ||||||||
\(580\) | 2.68010e19i | 1.21382i | ||||||||
\(581\) | −1.03398e19 | −0.462677 | ||||||||
\(582\) | − | 2.06257e19i | − | 0.911901i | ||||||
\(583\) | 3.42118e19 | 1.49450 | ||||||||
\(584\) | 1.82498e19 | 0.787714 | ||||||||
\(585\) | − | 3.59339e19i | − | 1.53255i | ||||||
\(586\) | − | 1.23630e19i | − | 0.521005i | ||||||
\(587\) | 2.38786e19 | 0.994358 | 0.497179 | − | 0.867648i | \(-0.334369\pi\) | ||||
0.497179 | + | 0.867648i | \(0.334369\pi\) | |||||||
\(588\) | 2.56878e19 | 1.05703 | ||||||||
\(589\) | − | 1.37229e19i | − | 0.558006i | ||||||
\(590\) | 1.03779e19i | 0.417011i | ||||||||
\(591\) | −3.36667e19 | −1.33687 | ||||||||
\(592\) | − | 6.41312e18i | − | 0.251662i | ||||||
\(593\) | 3.48176e18 | 0.135025 | 0.0675127 | − | 0.997718i | \(-0.478494\pi\) | ||||
0.0675127 | + | 0.997718i | \(0.478494\pi\) | |||||||
\(594\) | 8.59616e18i | 0.329457i | ||||||||
\(595\) | 2.81100e19i | 1.06473i | ||||||||
\(596\) | 5.00990e18i | 0.187545i | ||||||||
\(597\) | 3.11166e19i | 1.15126i | ||||||||
\(598\) | −7.59320e18 | + | 3.92969e18i | −0.277662 | + | 0.143698i | ||||
\(599\) | −4.69083e19 | −1.69536 | −0.847679 | − | 0.530509i | \(-0.822001\pi\) | ||||
−0.847679 | + | 0.530509i | \(0.822001\pi\) | |||||||
\(600\) | 2.66426e19 | 0.951737 | ||||||||
\(601\) | 4.46391e18 | 0.157614 | 0.0788068 | − | 0.996890i | \(-0.474889\pi\) | ||||
0.0788068 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(602\) | −5.69278e18 | −0.198678 | ||||||||
\(603\) | − | 2.59808e19i | − | 0.896253i | ||||||
\(604\) | 4.80691e19 | 1.63911 | ||||||||
\(605\) | − | 9.30623e18i | − | 0.313680i | ||||||
\(606\) | −3.63962e18 | −0.121268 | ||||||||
\(607\) | −1.82390e19 | −0.600732 | −0.300366 | − | 0.953824i | \(-0.597109\pi\) | ||||
−0.300366 | + | 0.953824i | \(0.597109\pi\) | |||||||
\(608\) | 4.00860e19i | 1.30517i | ||||||||
\(609\) | 2.43577e19i | 0.783997i | ||||||||
\(610\) | −1.21077e19 | −0.385260 | ||||||||
\(611\) | 7.91008e18 | 0.248824 | ||||||||
\(612\) | 7.44585e19i | 2.31555i | ||||||||
\(613\) | 2.82394e18i | 0.0868226i | 0.999057 | + | 0.0434113i | \(0.0138226\pi\) | ||||
−0.999057 | + | 0.0434113i | \(0.986177\pi\) | |||||||
\(614\) | −9.59203e18 | −0.291563 | ||||||||
\(615\) | − | 1.03218e20i | − | 3.10192i | ||||||
\(616\) | 1.00081e19 | 0.297364 | ||||||||
\(617\) | − | 4.24441e19i | − | 1.24687i | −0.781875 | − | 0.623435i | \(-0.785736\pi\) | ||
0.781875 | − | 0.623435i | \(-0.214264\pi\) | |||||||
\(618\) | − | 8.88053e18i | − | 0.257941i | ||||||
\(619\) | − | 3.21398e19i | − | 0.923013i | −0.887137 | − | 0.461507i | \(-0.847309\pi\) | ||
0.887137 | − | 0.461507i | \(-0.152691\pi\) | |||||||
\(620\) | 1.61268e19i | 0.457937i | ||||||||
\(621\) | −2.81814e19 | + | 1.45847e19i | −0.791264 | + | 0.409502i | ||||
\(622\) | 2.15794e19 | 0.599111 | ||||||||
\(623\) | −2.78880e19 | −0.765598 | ||||||||
\(624\) | −2.15698e19 | −0.585536 | ||||||||
\(625\) | −4.37956e19 | −1.17563 | ||||||||
\(626\) | 2.57154e19i | 0.682610i | ||||||||
\(627\) | −7.09528e19 | −1.86250 | ||||||||
\(628\) | − | 1.34225e19i | − | 0.348430i | ||||||
\(629\) | −3.58408e19 | −0.920076 | ||||||||
\(630\) | 1.52519e19 | 0.387204 | ||||||||
\(631\) | − | 2.19634e19i | − | 0.551434i | −0.961239 | − | 0.275717i | \(-0.911085\pi\) | ||
0.961239 | − | 0.275717i | \(-0.0889152\pi\) | |||||||
\(632\) | 2.70348e19i | 0.671280i | ||||||||
\(633\) | −6.46373e19 | −1.58729 | ||||||||
\(634\) | −3.02723e19 | −0.735227 | ||||||||
\(635\) | − | 3.50416e19i | − | 0.841721i | ||||||
\(636\) | − | 9.44753e19i | − | 2.24449i | ||||||
\(637\) | 2.53245e19 | 0.595066 | ||||||||
\(638\) | − | 1.76654e19i | − | 0.410561i | ||||||
\(639\) | 4.35289e19 | 1.00062 | ||||||||
\(640\) | − | 5.93760e19i | − | 1.35005i | ||||||
\(641\) | − | 1.83694e19i | − | 0.413132i | −0.978433 | − | 0.206566i | \(-0.933771\pi\) | ||
0.978433 | − | 0.206566i | \(-0.0662288\pi\) | |||||||
\(642\) | 1.59640e19i | 0.355139i | ||||||||
\(643\) | 1.12644e19i | 0.247873i | 0.992290 | + | 0.123937i | \(0.0395519\pi\) | ||||
−0.992290 | + | 0.123937i | \(0.960448\pi\) | |||||||
\(644\) | 7.65620e18 | + | 1.47938e19i | 0.166653 | + | 0.322016i | ||||
\(645\) | −1.05190e20 | −2.26494 | ||||||||
\(646\) | 4.79057e19 | 1.02037 | ||||||||
\(647\) | −5.58592e18 | −0.117697 | −0.0588484 | − | 0.998267i | \(-0.518743\pi\) | ||||
−0.0588484 | + | 0.998267i | \(0.518743\pi\) | |||||||
\(648\) | −4.89355e18 | −0.102000 | ||||||||
\(649\) | 3.13992e19i | 0.647448i | ||||||||
\(650\) | 1.18429e19 | 0.241582 | ||||||||
\(651\) | 1.46566e19i | 0.295777i | ||||||||
\(652\) | 9.33492e18 | 0.186371 | ||||||||
\(653\) | 6.34906e19 | 1.25406 | 0.627028 | − | 0.778996i | \(-0.284271\pi\) | ||||
0.627028 | + | 0.778996i | \(0.284271\pi\) | |||||||
\(654\) | 6.90138e18i | 0.134863i | ||||||||
\(655\) | − | 6.71410e18i | − | 0.129807i | ||||||
\(656\) | −3.77287e19 | −0.721681 | ||||||||
\(657\) | 8.41463e19 | 1.59249 | ||||||||
\(658\) | 3.35737e18i | 0.0628664i | ||||||||
\(659\) | 4.28614e19i | 0.794087i | 0.917800 | + | 0.397044i | \(0.129964\pi\) | ||||
−0.917800 | + | 0.397044i | \(0.870036\pi\) | |||||||
\(660\) | 8.33818e19 | 1.52849 | ||||||||
\(661\) | 1.01826e20i | 1.84692i | 0.383700 | + | 0.923458i | \(0.374650\pi\) | ||||
−0.383700 | + | 0.923458i | \(0.625350\pi\) | |||||||
\(662\) | 1.84002e19 | 0.330229 | ||||||||
\(663\) | 1.20546e20i | 2.14072i | ||||||||
\(664\) | − | 4.59274e19i | − | 0.807041i | ||||||
\(665\) | 4.50434e19i | 0.783213i | ||||||||
\(666\) | 1.94465e19i | 0.334596i | ||||||||
\(667\) | 5.79137e19 | − | 2.99720e19i | 0.986053 | − | 0.510310i | ||||
\(668\) | −6.81647e19 | −1.14848 | ||||||||
\(669\) | 1.12633e20 | 1.87795 | ||||||||
\(670\) | 1.96438e19 | 0.324118 | ||||||||
\(671\) | −3.66328e19 | −0.598153 | ||||||||
\(672\) | − | 4.28133e19i | − | 0.691821i | ||||||
\(673\) | −9.87680e19 | −1.57947 | −0.789734 | − | 0.613449i | \(-0.789781\pi\) | ||||
−0.789734 | + | 0.613449i | \(0.789781\pi\) | |||||||
\(674\) | − | 4.10562e19i | − | 0.649770i | ||||||
\(675\) | 4.39537e19 | 0.688445 | ||||||||
\(676\) | 2.40262e19 | 0.372442 | ||||||||
\(677\) | − | 8.03279e18i | − | 0.123238i | −0.998100 | − | 0.0616192i | \(-0.980374\pi\) | ||
0.998100 | − | 0.0616192i | \(-0.0196264\pi\) | |||||||
\(678\) | 4.69538e19i | 0.712956i | ||||||||
\(679\) | −3.96166e19 | −0.595373 | ||||||||
\(680\) | −1.24860e20 | −1.85720 | ||||||||
\(681\) | − | 1.64663e20i | − | 2.42418i | ||||||
\(682\) | − | 1.06297e19i | − | 0.154892i | ||||||
\(683\) | 5.80621e19 | 0.837428 | 0.418714 | − | 0.908118i | \(-0.362481\pi\) | ||||
0.418714 | + | 0.908118i | \(0.362481\pi\) | |||||||
\(684\) | 1.19312e20i | 1.70331i | ||||||||
\(685\) | 1.32409e20 | 1.87104 | ||||||||
\(686\) | 2.41012e19i | 0.337108i | ||||||||
\(687\) | − | 7.79585e18i | − | 0.107936i | ||||||
\(688\) | 3.84495e19i | 0.526953i | ||||||||
\(689\) | − | 9.31392e19i | − | 1.26357i | ||||||
\(690\) | −3.08197e19 | − | 5.95517e19i | −0.413890 | − | 0.799743i | ||||
\(691\) | −2.22123e19 | −0.295289 | −0.147644 | − | 0.989040i | \(-0.547169\pi\) | ||||
−0.147644 | + | 0.989040i | \(0.547169\pi\) | |||||||
\(692\) | 8.06748e19 | 1.06168 | ||||||||
\(693\) | 4.61456e19 | 0.601170 | ||||||||
\(694\) | −5.80893e19 | −0.749168 | ||||||||
\(695\) | 4.84753e19i | 0.618909i | ||||||||
\(696\) | −1.08193e20 | −1.36752 | ||||||||
\(697\) | 2.10854e20i | 2.63847i | ||||||||
\(698\) | 6.17768e18 | 0.0765310 | ||||||||
\(699\) | 1.69458e20 | 2.07837 | ||||||||
\(700\) | − | 2.30734e19i | − | 0.280173i | ||||||
\(701\) | − | 1.23169e20i | − | 1.48073i | −0.672206 | − | 0.740364i | \(-0.734653\pi\) | ||
0.672206 | − | 0.740364i | \(-0.265347\pi\) | |||||||
\(702\) | 2.34024e19 | 0.278549 | ||||||||
\(703\) | −5.74314e19 | −0.676802 | ||||||||
\(704\) | − | 6.06750e18i | − | 0.0707947i | ||||||
\(705\) | 6.20369e19i | 0.716682i | ||||||||
\(706\) | −2.95304e19 | −0.337782 | ||||||||
\(707\) | 6.99077e18i | 0.0791752i | ||||||||
\(708\) | 8.67081e19 | 0.972360 | ||||||||
\(709\) | − | 1.16029e20i | − | 1.28837i | −0.764868 | − | 0.644187i | \(-0.777196\pi\) | ||
0.764868 | − | 0.644187i | \(-0.222804\pi\) | |||||||
\(710\) | 3.29118e19i | 0.361862i | ||||||||
\(711\) | 1.24652e20i | 1.35710i | ||||||||
\(712\) | − | 1.23874e20i | − | 1.33542i | ||||||
\(713\) | 3.48480e19 | − | 1.80348e19i | 0.372007 | − | 0.192524i | ||||
\(714\) | −5.11650e19 | −0.540861 | ||||||||
\(715\) | 8.22026e19 | 0.860485 | ||||||||
\(716\) | −9.15174e19 | −0.948664 | ||||||||
\(717\) | 9.98720e18 | 0.102520 | ||||||||
\(718\) | − | 2.67970e19i | − | 0.272405i | ||||||
\(719\) | −1.06708e20 | −1.07422 | −0.537110 | − | 0.843513i | \(-0.680484\pi\) | ||||
−0.537110 | + | 0.843513i | \(0.680484\pi\) | |||||||
\(720\) | − | 1.03012e20i | − | 1.02698i | ||||||
\(721\) | −1.70572e19 | −0.168407 | ||||||||
\(722\) | 3.35083e19 | 0.327636 | ||||||||
\(723\) | 6.69676e18i | 0.0648481i | ||||||||
\(724\) | 9.73644e19i | 0.933749i | ||||||||
\(725\) | −9.03263e19 | −0.857922 | ||||||||
\(726\) | 1.69390e19 | 0.159342 | ||||||||
\(727\) | 1.19170e20i | 1.11027i | 0.831761 | + | 0.555133i | \(0.187333\pi\) | ||||
−0.831761 | + | 0.555133i | \(0.812667\pi\) | |||||||
\(728\) | − | 2.72464e19i | − | 0.251414i | ||||||
\(729\) | −1.78455e20 | −1.63094 | ||||||||
\(730\) | 6.36223e19i | 0.575903i | ||||||||
\(731\) | 2.14882e20 | 1.92654 | ||||||||
\(732\) | 1.01161e20i | 0.898326i | ||||||||
\(733\) | − | 1.34342e20i | − | 1.18163i | −0.806805 | − | 0.590817i | \(-0.798805\pi\) | ||
0.806805 | − | 0.590817i | \(-0.201195\pi\) | |||||||
\(734\) | − | 1.59425e19i | − | 0.138894i | ||||||
\(735\) | 1.98614e20i | 1.71395i | ||||||||
\(736\) | −1.01794e20 | + | 5.26815e19i | −0.870120 | + | 0.450312i | ||||
\(737\) | 5.94337e19 | 0.503223 | ||||||||
\(738\) | 1.14405e20 | 0.959509 | ||||||||
\(739\) | 1.35112e20 | 1.12249 | 0.561246 | − | 0.827649i | \(-0.310322\pi\) | ||||
0.561246 | + | 0.827649i | \(0.310322\pi\) | |||||||
\(740\) | 6.74918e19 | 0.555430 | ||||||||
\(741\) | 1.93164e20i | 1.57470i | ||||||||
\(742\) | 3.95322e19 | 0.319245 | ||||||||
\(743\) | − | 2.12605e20i | − | 1.70079i | −0.526142 | − | 0.850397i | \(-0.676362\pi\) | ||
0.526142 | − | 0.850397i | \(-0.323638\pi\) | |||||||
\(744\) | −6.51019e19 | −0.515921 | ||||||||
\(745\) | −3.87358e19 | −0.304102 | ||||||||
\(746\) | − | 1.04683e20i | − | 0.814147i | ||||||
\(747\) | − | 2.11762e20i | − | 1.63157i | ||||||
\(748\) | −1.70332e20 | −1.30012 | ||||||||
\(749\) | 3.06628e19 | 0.231867 | ||||||||
\(750\) | − | 2.73207e19i | − | 0.204674i | ||||||
\(751\) | − | 1.82216e20i | − | 1.35240i | −0.736717 | − | 0.676201i | \(-0.763625\pi\) | ||
0.736717 | − | 0.676201i | \(-0.236375\pi\) | |||||||
\(752\) | 2.26760e19 | 0.166741 | ||||||||
\(753\) | − | 1.51461e20i | − | 1.10341i | ||||||
\(754\) | −4.80927e19 | −0.347120 | ||||||||
\(755\) | 3.71664e20i | 2.65780i | ||||||||
\(756\) | − | 4.55948e19i | − | 0.323045i | ||||||
\(757\) | − | 9.81424e19i | − | 0.688946i | −0.938796 | − | 0.344473i | \(-0.888058\pi\) | ||
0.938796 | − | 0.344473i | \(-0.111942\pi\) | |||||||
\(758\) | 8.37333e19i | 0.582390i | ||||||||
\(759\) | −9.32470e19 | − | 1.80178e20i | −0.642603 | − | 1.24168i | ||||
\(760\) | −2.00075e20 | −1.36615 | ||||||||
\(761\) | −1.75838e19 | −0.118965 | −0.0594827 | − | 0.998229i | \(-0.518945\pi\) | ||||
−0.0594827 | + | 0.998229i | \(0.518945\pi\) | |||||||
\(762\) | 6.37819e19 | 0.427575 | ||||||||
\(763\) | 1.32558e19 | 0.0880507 | ||||||||
\(764\) | − | 6.87433e19i | − | 0.452457i | ||||||
\(765\) | −5.75703e20 | −3.75464 | ||||||||
\(766\) | 2.22112e19i | 0.143539i | ||||||||
\(767\) | 8.54819e19 | 0.547403 | ||||||||
\(768\) | 8.76692e19 | 0.556312 | ||||||||
\(769\) | − | 7.00513e19i | − | 0.440486i | −0.975445 | − | 0.220243i | \(-0.929315\pi\) | ||
0.975445 | − | 0.220243i | \(-0.0706850\pi\) | |||||||
\(770\) | 3.48903e19i | 0.217405i | ||||||||
\(771\) | −3.80228e20 | −2.34782 | ||||||||
\(772\) | 1.42149e20 | 0.869807 | ||||||||
\(773\) | − | 1.64802e20i | − | 0.999325i | −0.866220 | − | 0.499662i | \(-0.833457\pi\) | ||
0.866220 | − | 0.499662i | \(-0.166543\pi\) | |||||||
\(774\) | − | 1.16590e20i | − | 0.700610i | ||||||
\(775\) | −5.43514e19 | −0.323667 | ||||||||
\(776\) | − | 1.75970e20i | − | 1.03850i | ||||||
\(777\) | 6.13388e19 | 0.358747 | ||||||||
\(778\) | 3.94797e19i | 0.228832i | ||||||||
\(779\) | 3.37872e20i | 1.94084i | ||||||||
\(780\) | − | 2.27001e20i | − | 1.29231i | ||||||
\(781\) | 9.95769e19i | 0.561825i | ||||||||
\(782\) | 6.29583e19 | + | 1.21652e20i | 0.352051 | + | 0.680255i | ||||
\(783\) | −1.78491e20 | −0.989202 | ||||||||
\(784\) | 7.25983e19 | 0.398762 | ||||||||
\(785\) | 1.03781e20 | 0.564975 | ||||||||
\(786\) | 1.22208e19 | 0.0659391 | ||||||||
\(787\) | 7.47706e19i | 0.399860i | 0.979810 | + | 0.199930i | \(0.0640714\pi\) | ||||
−0.979810 | + | 0.199930i | \(0.935929\pi\) | |||||||
\(788\) | −1.29509e20 | −0.686460 | ||||||||
\(789\) | 2.32416e20i | 1.22103i | ||||||||
\(790\) | −9.42485e19 | −0.490778 | ||||||||
\(791\) | 9.01861e19 | 0.465483 | ||||||||
\(792\) | 2.04971e20i | 1.04861i | ||||||||
\(793\) | 9.97301e19i | 0.505724i | ||||||||
\(794\) | 3.64397e19 | 0.183160 | ||||||||
\(795\) | 7.30469e20 | 3.63942 | ||||||||
\(796\) | 1.19699e20i | 0.591151i | ||||||||
\(797\) | 2.69481e20i | 1.31923i | 0.751605 | + | 0.659614i | \(0.229280\pi\) | ||||
−0.751605 | + | 0.659614i | \(0.770720\pi\) | |||||||
\(798\) | −8.19869e19 | −0.397854 | ||||||||
\(799\) | − | 1.26729e20i | − | 0.609604i | ||||||
\(800\) | 1.58766e20 | 0.757054 | ||||||||
\(801\) | − | 5.71157e20i | − | 2.69978i | ||||||
\(802\) | − | 9.54973e19i | − | 0.447477i | ||||||
\(803\) | 1.92494e20i | 0.894144i | ||||||||
\(804\) | − | 1.64125e20i | − | 0.755758i | ||||||
\(805\) | −1.14383e20 | + | 5.91966e19i | −0.522146 | + | 0.270225i | ||||
\(806\) | −2.89385e19 | −0.130957 | ||||||||
\(807\) | 3.44046e20 | 1.54348 | ||||||||
\(808\) | −3.10518e19 | −0.138104 | ||||||||
\(809\) | 6.11606e19 | 0.269670 | 0.134835 | − | 0.990868i | \(-0.456950\pi\) | ||||
0.134835 | + | 0.990868i | \(0.456950\pi\) | |||||||
\(810\) | − | 1.70598e19i | − | 0.0745727i | ||||||
\(811\) | −3.22032e17 | −0.00139557 | −0.000697786 | − | 1.00000i | \(-0.500222\pi\) | ||||
−0.000697786 | 1.00000i | \(0.500222\pi\) | ||||||||
\(812\) | 9.36987e19i | 0.402570i | ||||||||
\(813\) | 2.35593e20 | 1.00353 | ||||||||
\(814\) | −4.44859e19 | −0.187867 | ||||||||
\(815\) | 7.21763e19i | 0.302198i | ||||||||
\(816\) | 3.45573e20i | 1.43453i | ||||||||
\(817\) | 3.44327e20 | 1.41715 | ||||||||
\(818\) | 1.66354e20 | 0.678827 | ||||||||
\(819\) | − | 1.25628e20i | − | 0.508275i | ||||||
\(820\) | − | 3.97058e20i | − | 1.59278i | ||||||
\(821\) | 1.31502e20 | 0.523033 | 0.261517 | − | 0.965199i | \(-0.415777\pi\) | ||||
0.261517 | + | 0.965199i | \(0.415777\pi\) | |||||||
\(822\) | 2.41007e20i | 0.950444i | ||||||||
\(823\) | 7.77131e19 | 0.303875 | 0.151938 | − | 0.988390i | \(-0.451449\pi\) | ||||
0.151938 | + | 0.988390i | \(0.451449\pi\) | |||||||
\(824\) | − | 7.57652e19i | − | 0.293751i | ||||||
\(825\) | 2.81018e20i | 1.08033i | ||||||||
\(826\) | 3.62822e19i | 0.138303i | ||||||||
\(827\) | 2.75747e20i | 1.04225i | 0.853481 | + | 0.521125i | \(0.174487\pi\) | ||||
−0.853481 | + | 0.521125i | \(0.825513\pi\) | |||||||
\(828\) | −3.02982e20 | + | 1.56802e20i | −1.13555 | + | 0.587677i | ||||
\(829\) | −4.59792e20 | −1.70876 | −0.854378 | − | 0.519652i | \(-0.826062\pi\) | ||||
−0.854378 | + | 0.519652i | \(0.826062\pi\) | |||||||
\(830\) | 1.60112e20 | 0.590033 | ||||||||
\(831\) | 3.10305e20 | 1.13392 | ||||||||
\(832\) | −1.65183e19 | −0.0598553 | ||||||||
\(833\) | − | 4.05728e20i | − | 1.45788i | ||||||
\(834\) | −8.82334e19 | −0.314392 | ||||||||
\(835\) | − | 5.27040e20i | − | 1.86225i | ||||||
\(836\) | −2.72940e20 | −0.956364 | ||||||||
\(837\) | −1.07402e20 | −0.373195 | ||||||||
\(838\) | − | 1.26196e19i | − | 0.0434848i | ||||||
\(839\) | − | 2.54217e20i | − | 0.868702i | −0.900744 | − | 0.434351i | \(-0.856978\pi\) | ||
0.900744 | − | 0.434351i | \(-0.143022\pi\) | |||||||
\(840\) | 2.13688e20 | 0.724143 | ||||||||
\(841\) | 6.92470e19 | 0.232718 | ||||||||
\(842\) | 6.35011e19i | 0.211640i | ||||||||
\(843\) | 8.76592e20i | 2.89737i | ||||||||
\(844\) | −2.48646e20 | −0.815049 | ||||||||
\(845\) | 1.85768e20i | 0.603911i | ||||||||
\(846\) | −6.87603e19 | −0.221690 | ||||||||
\(847\) | − | 3.25354e19i | − | 0.104033i | ||||||
\(848\) | − | 2.67004e20i | − | 0.846734i | ||||||
\(849\) | 8.01627e19i | 0.252127i | ||||||||
\(850\) | − | 1.89737e20i | − | 0.591860i | ||||||
\(851\) | −7.54770e19 | − | 1.45841e20i | −0.233511 | − | 0.451205i | ||||
\(852\) | 2.74980e20 | 0.843768 | ||||||||
\(853\) | −1.16392e20 | −0.354224 | −0.177112 | − | 0.984191i | \(-0.556676\pi\) | ||||
−0.177112 | + | 0.984191i | \(0.556676\pi\) | |||||||
\(854\) | −4.23297e19 | −0.127773 | ||||||||
\(855\) | −9.22507e20 | −2.76189 | ||||||||
\(856\) | 1.36199e20i | 0.404443i | ||||||||
\(857\) | 1.42230e20 | 0.418914 | 0.209457 | − | 0.977818i | \(-0.432830\pi\) | ||||
0.209457 | + | 0.977818i | \(0.432830\pi\) | |||||||
\(858\) | 1.49623e20i | 0.437107i | ||||||||
\(859\) | −2.67639e20 | −0.775527 | −0.387764 | − | 0.921759i | \(-0.626752\pi\) | ||||
−0.387764 | + | 0.921759i | \(0.626752\pi\) | |||||||
\(860\) | −4.04644e20 | −1.16301 | ||||||||
\(861\) | − | 3.60859e20i | − | 1.02876i | ||||||
\(862\) | − | 2.12051e20i | − | 0.599639i | ||||||
\(863\) | −3.07709e20 | −0.863106 | −0.431553 | − | 0.902087i | \(-0.642034\pi\) | ||||
−0.431553 | + | 0.902087i | \(0.642034\pi\) | |||||||
\(864\) | 3.13733e20 | 0.872899 | ||||||||
\(865\) | 6.23766e20i | 1.72151i | ||||||||
\(866\) | 1.46832e20i | 0.401971i | ||||||||
\(867\) | 1.34244e21 | 3.64552 | ||||||||
\(868\) | 5.63806e19i | 0.151877i | ||||||||
\(869\) | −2.85155e20 | −0.761978 | ||||||||
\(870\) | − | 3.77180e20i | − | 0.999801i | ||||||
\(871\) | − | 1.61804e20i | − | 0.425464i | ||||||
\(872\) | 5.88798e19i | 0.153586i | ||||||||
\(873\) | − | 8.11364e20i | − | 2.09950i | ||||||
\(874\) | 1.00884e20 | + | 1.94935e20i | 0.258967 | + | 0.500391i | ||||
\(875\) | −5.24760e19 | −0.133630 | ||||||||
\(876\) | 5.31567e20 | 1.34286 | ||||||||
\(877\) | −1.79409e19 | −0.0449622 | −0.0224811 | − | 0.999747i | \(-0.507157\pi\) | ||||
−0.0224811 | + | 0.999747i | \(0.507157\pi\) | |||||||
\(878\) | −8.28158e19 | −0.205898 | ||||||||
\(879\) | − | 7.98652e20i | − | 1.96986i | ||||||
\(880\) | 2.35652e20 | 0.576623 | ||||||||
\(881\) | 4.03729e20i | 0.980073i | 0.871702 | + | 0.490037i | \(0.163017\pi\) | ||||
−0.871702 | + | 0.490037i | \(0.836983\pi\) | |||||||
\(882\) | −2.20140e20 | −0.530174 | ||||||||
\(883\) | −3.53907e19 | −0.0845598 | −0.0422799 | − | 0.999106i | \(-0.513462\pi\) | ||||
−0.0422799 | + | 0.999106i | \(0.513462\pi\) | |||||||
\(884\) | 4.63716e20i | 1.09922i | ||||||||
\(885\) | 6.70415e20i | 1.57667i | ||||||||
\(886\) | −2.40625e20 | −0.561441 | ||||||||
\(887\) | 3.83746e20 | 0.888339 | 0.444169 | − | 0.895943i | \(-0.353499\pi\) | ||||
0.444169 | + | 0.895943i | \(0.353499\pi\) | |||||||
\(888\) | 2.72456e20i | 0.625758i | ||||||||
\(889\) | − | 1.22508e20i | − | 0.279160i | ||||||
\(890\) | 4.31847e20 | 0.976337 | ||||||||
\(891\) | − | 5.16157e19i | − | 0.115781i | ||||||
\(892\) | 4.33275e20 | 0.964294 | ||||||||
\(893\) | − | 2.03070e20i | − | 0.448421i | ||||||
\(894\) | − | 7.05060e19i | − | 0.154477i | ||||||
\(895\) | − | 7.07600e20i | − | 1.53825i | ||||||
\(896\) | − | 2.07584e20i | − | 0.447751i | ||||||
\(897\) | −4.90521e20 | + | 2.53858e20i | −1.04981 | + | 0.543306i | ||||
\(898\) | 1.44619e20 | 0.307108 | ||||||||
\(899\) | 2.20715e20 | 0.465065 | ||||||||
\(900\) | 4.72553e20 | 0.987990 | ||||||||
\(901\) | −1.49220e21 | −3.09566 | ||||||||
\(902\) | 2.61713e20i | 0.538740i | ||||||||
\(903\) | −3.67754e20 | −0.751178 | ||||||||
\(904\) | 4.00591e20i | 0.811937i | ||||||||
\(905\) | −7.52808e20 | −1.51406 | ||||||||
\(906\) | −6.76493e20 | −1.35010 | ||||||||
\(907\) | 4.78981e20i | 0.948565i | 0.880373 | + | 0.474283i | \(0.157293\pi\) | ||||
−0.880373 | + | 0.474283i | \(0.842707\pi\) | |||||||
\(908\) | − | 6.33421e20i | − | 1.24478i | ||||||
\(909\) | −1.43174e20 | −0.279200 | ||||||||
\(910\) | 9.49863e19 | 0.183811 | ||||||||
\(911\) | 7.46334e19i | 0.143319i | 0.997429 | + | 0.0716596i | \(0.0228295\pi\) | ||||
−0.997429 | + | 0.0716596i | \(0.977170\pi\) | |||||||
\(912\) | 5.53746e20i | 1.05523i | ||||||||
\(913\) | 4.84429e20 | 0.916083 | ||||||||
\(914\) | − | 3.64497e20i | − | 0.684023i | ||||||
\(915\) | −7.82160e20 | −1.45663 | ||||||||
\(916\) | − | 2.99889e19i | − | 0.0554233i | ||||||
\(917\) | − | 2.34731e19i | − | 0.0430511i | ||||||
\(918\) | − | 3.74934e20i | − | 0.682427i | ||||||
\(919\) | 4.69237e20i | 0.847585i | 0.905759 | + | 0.423793i | \(0.139301\pi\) | ||||
−0.905759 | + | 0.423793i | \(0.860699\pi\) | |||||||
\(920\) | −2.62941e20 | − | 5.08071e20i | −0.471350 | − | 0.910772i | ||||
\(921\) | −6.19645e20 | −1.10237 | ||||||||
\(922\) | −8.63518e19 | −0.152460 | ||||||||
\(923\) | 2.71091e20 | 0.475010 | ||||||||
\(924\) | 2.91510e20 | 0.506932 | ||||||||
\(925\) | 2.27464e20i | 0.392574i | ||||||||
\(926\) | −1.18103e20 | −0.202294 | ||||||||
\(927\) | − | 3.49338e20i | − | 0.593865i | ||||||
\(928\) | −6.44731e20 | −1.08778 | ||||||||
\(929\) | 4.93994e20 | 0.827202 | 0.413601 | − | 0.910458i | \(-0.364271\pi\) | ||||
0.413601 | + | 0.910458i | \(0.364271\pi\) | |||||||
\(930\) | − | 2.26958e20i | − | 0.377193i | ||||||
\(931\) | − | 6.50139e20i | − | 1.07240i | ||||||
\(932\) | 6.51868e20 | 1.06721 | ||||||||
\(933\) | 1.39403e21 | 2.26517 | ||||||||
\(934\) | 8.55426e19i | 0.137960i | ||||||||
\(935\) | − | 1.31698e21i | − | 2.10814i | ||||||
\(936\) | 5.58018e20 | 0.886578 | ||||||||
\(937\) | − | 9.88783e20i | − | 1.55928i | −0.626229 | − | 0.779639i | \(-0.715402\pi\) | ||
0.626229 | − | 0.779639i | \(-0.284598\pi\) | |||||||
\(938\) | 6.86765e19 | 0.107495 | ||||||||
\(939\) | 1.66121e21i | 2.58087i | ||||||||
\(940\) | 2.38643e20i | 0.368004i | ||||||||
\(941\) | 3.99115e18i | 0.00610901i | 0.999995 | + | 0.00305450i | \(0.000972280\pi\) | ||||
−0.999995 | + | 0.00305450i | \(0.999028\pi\) | |||||||
\(942\) | 1.88899e20i | 0.286995i | ||||||||
\(943\) | −8.57993e20 | + | 4.44035e20i | −1.29390 | + | 0.669631i | ||||
\(944\) | 2.45053e20 | 0.366822 | ||||||||
\(945\) | 3.52532e20 | 0.523813 | ||||||||
\(946\) | 2.66713e20 | 0.393375 | ||||||||
\(947\) | −7.76261e20 | −1.13647 | −0.568235 | − | 0.822866i | \(-0.692374\pi\) | ||||
−0.568235 | + | 0.822866i | \(0.692374\pi\) | |||||||
\(948\) | 7.87450e20i | 1.14436i | ||||||||
\(949\) | 5.24050e20 | 0.755978 | ||||||||
\(950\) | − | 3.04034e20i | − | 0.435369i | ||||||
\(951\) | −1.95559e21 | −2.77981 | ||||||||
\(952\) | −4.36520e20 | −0.615950 | ||||||||
\(953\) | − | 4.14059e20i | − | 0.579979i | −0.957030 | − | 0.289989i | \(-0.906348\pi\) | ||
0.957030 | − | 0.289989i | \(-0.0936518\pi\) | |||||||
\(954\) | 8.09636e20i | 1.12577i | ||||||||
\(955\) | 5.31513e20 | 0.733653 | ||||||||
\(956\) | 3.84186e19 | 0.0526425 | ||||||||
\(957\) | − | 1.14118e21i | − | 1.55229i | ||||||
\(958\) | − | 1.03834e20i | − | 0.140211i | ||||||
\(959\) | 4.62912e20 | 0.620537 | ||||||||
\(960\) | − | 1.29549e20i | − | 0.172400i | ||||||
\(961\) | −6.24135e20 | −0.824546 | ||||||||
\(962\) | 1.21110e20i | 0.158838i | ||||||||
\(963\) | 6.27986e20i | 0.817648i | ||||||||
\(964\) | 2.57610e19i | 0.0332984i | ||||||||
\(965\) | 1.09908e21i | 1.41038i | ||||||||
\(966\) | −1.07748e20 | − | 2.08198e20i | −0.137268 | − | 0.265238i | ||||
\(967\) | −2.33192e20 | −0.294936 | −0.147468 | − | 0.989067i | \(-0.547112\pi\) | ||||
−0.147468 | + | 0.989067i | \(0.547112\pi\) | |||||||
\(968\) | 1.44517e20 | 0.181464 | ||||||||
\(969\) | 3.09471e21 | 3.85792 | ||||||||
\(970\) | 6.13466e20 | 0.759256 | ||||||||
\(971\) | − | 9.46454e20i | − | 1.16296i | −0.813560 | − | 0.581480i | \(-0.802474\pi\) | ||
0.813560 | − | 0.581480i | \(-0.197526\pi\) | |||||||
\(972\) | −7.42219e20 | −0.905458 | ||||||||
\(973\) | 1.69474e20i | 0.205264i | ||||||||
\(974\) | 3.03374e20 | 0.364809 | ||||||||
\(975\) | 7.65050e20 | 0.913393 | ||||||||
\(976\) | 2.85898e20i | 0.338893i | ||||||||
\(977\) | 4.23888e20i | 0.498872i | 0.968391 | + | 0.249436i | \(0.0802452\pi\) | ||||
−0.968391 | + | 0.249436i | \(0.919755\pi\) | |||||||
\(978\) | −1.31373e20 | −0.153510 | ||||||||
\(979\) | 1.30658e21 | 1.51586 | ||||||||
\(980\) | 7.64026e20i | 0.880087i | ||||||||
\(981\) | 2.71483e20i | 0.310499i | ||||||||
\(982\) | 4.28273e20 | 0.486340 | ||||||||
\(983\) | 1.64800e21i | 1.85816i | 0.369879 | + | 0.929080i | \(0.379399\pi\) | ||||
−0.369879 | + | 0.929080i | \(0.620601\pi\) | |||||||
\(984\) | 1.60288e21 | 1.79446 | ||||||||
\(985\) | − | 1.00134e21i | − | 1.11309i | ||||||
\(986\) | 7.70501e20i | 0.850423i | ||||||||
\(987\) | 2.16886e20i | 0.237691i | ||||||||
\(988\) | 7.43059e20i | 0.808583i | ||||||||
\(989\) | 4.52519e20 | + | 8.74385e20i | 0.488948 | + | 0.944776i | ||||
\(990\) | −7.14567e20 | −0.766649 | ||||||||
\(991\) | −1.64342e21 | −1.75078 | −0.875392 | − | 0.483414i | \(-0.839397\pi\) | ||||
−0.875392 | + | 0.483414i | \(0.839397\pi\) | |||||||
\(992\) | −3.87949e20 | −0.410386 | ||||||||
\(993\) | 1.18865e21 | 1.24856 | ||||||||
\(994\) | 1.15062e20i | 0.120013i | ||||||||
\(995\) | −9.25495e20 | −0.958545 | ||||||||
\(996\) | − | 1.33774e21i | − | 1.37580i | ||||||
\(997\) | 8.30679e20 | 0.848335 | 0.424167 | − | 0.905584i | \(-0.360567\pi\) | ||||
0.424167 | + | 0.905584i | \(0.360567\pi\) | |||||||
\(998\) | −8.15987e20 | −0.827503 | ||||||||
\(999\) | 4.49487e20i | 0.452646i |
(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 | 23.15.b.b.22.12 | yes | 24 | |
23.22 | odd | 2 | inner | 23.15.b.b.22.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.15.b.b.22.11 | ✓ | 24 | 23.22 | odd | 2 | inner | |
23.15.b.b.22.12 | yes | 24 | 1.1 | even | 1 | trivial |