Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,39,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(36.5853876134\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.7 | ||
Root | \(0.500000 - 5.46285e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.8 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −173179. | − | 494861.i | −0.330313 | − | 0.943872i | ||||
\(3\) | 8.74057e8i | 0.752031i | 0.926613 | + | 0.376015i | \(0.122706\pi\) | ||||
−0.926613 | + | 0.376015i | \(0.877294\pi\) | |||||||
\(4\) | −2.14896e11 | + | 1.71399e11i | −0.781787 | + | 0.623546i | ||||
\(5\) | 2.48589e13 | 1.30332 | 0.651661 | − | 0.758510i | \(-0.274072\pi\) | ||||
0.651661 | + | 0.758510i | \(0.274072\pi\) | |||||||
\(6\) | 4.32536e14 | − | 1.51368e14i | 0.709821 | − | 0.248405i | ||||
\(7\) | 8.29070e15i | 0.727324i | 0.931531 | + | 0.363662i | \(0.118474\pi\) | ||||
−0.931531 | + | 0.363662i | \(0.881526\pi\) | |||||||
\(8\) | 1.22034e17 | + | 7.66608e16i | 0.846781 | + | 0.531941i | ||||
\(9\) | 5.86877e17 | 0.434449 | ||||||||
\(10\) | −4.30504e18 | − | 1.23017e19i | −0.430504 | − | 1.23017i | ||||
\(11\) | − | 3.43238e19i | − | 0.561222i | −0.959822 | − | 0.280611i | \(-0.909463\pi\) | ||
0.959822 | − | 0.280611i | \(-0.0905370\pi\) | |||||||
\(12\) | −1.49812e20 | − | 1.87831e20i | −0.468926 | − | 0.587928i | ||||
\(13\) | 9.38699e20 | 0.642100 | 0.321050 | − | 0.947062i | \(-0.395964\pi\) | ||||
0.321050 | + | 0.947062i | \(0.395964\pi\) | |||||||
\(14\) | 4.10274e21 | − | 1.43577e21i | 0.686501 | − | 0.240245i | ||||
\(15\) | 2.17281e22i | 0.980139i | ||||||||
\(16\) | 1.68027e22 | − | 7.36659e22i | 0.222382 | − | 0.974960i | ||||
\(17\) | −2.90046e23 | −1.21321 | −0.606607 | − | 0.795002i | \(-0.707470\pi\) | ||||
−0.606607 | + | 0.795002i | \(0.707470\pi\) | |||||||
\(18\) | −1.01635e23 | − | 2.90422e23i | −0.143504 | − | 0.410064i | ||||
\(19\) | 3.13139e24i | 1.58278i | 0.611315 | + | 0.791388i | \(0.290641\pi\) | ||||
−0.611315 | + | 0.791388i | \(0.709359\pi\) | |||||||
\(20\) | −5.34208e24 | + | 4.26079e24i | −1.01892 | + | 0.812681i | ||||
\(21\) | −7.24654e24 | −0.546971 | ||||||||
\(22\) | −1.69855e25 | + | 5.94416e24i | −0.529721 | + | 0.185379i | ||||
\(23\) | − | 4.99393e25i | − | 0.669289i | −0.942345 | − | 0.334644i | \(-0.891384\pi\) | ||
0.942345 | − | 0.334644i | \(-0.108616\pi\) | |||||||
\(24\) | −6.70059e25 | + | 1.06665e26i | −0.400036 | + | 0.636806i | ||||
\(25\) | 2.54167e26 | 0.698649 | ||||||||
\(26\) | −1.62563e26 | − | 4.64525e26i | −0.212094 | − | 0.606060i | ||||
\(27\) | 1.69368e27i | 1.07875i | ||||||||
\(28\) | −1.42102e27 | − | 1.78164e27i | −0.453520 | − | 0.568613i | ||||
\(29\) | 8.62415e27 | 1.41304 | 0.706520 | − | 0.707693i | \(-0.250264\pi\) | ||||
0.706520 | + | 0.707693i | \(0.250264\pi\) | |||||||
\(30\) | 1.07524e28 | − | 3.76285e27i | 0.925125 | − | 0.323752i | ||||
\(31\) | − | 1.05953e28i | − | 0.488925i | −0.969659 | − | 0.244462i | \(-0.921389\pi\) | ||
0.969659 | − | 0.244462i | \(-0.0786115\pi\) | |||||||
\(32\) | −3.93642e28 | + | 4.44240e27i | −0.993692 | + | 0.112142i | ||||
\(33\) | 3.00009e28 | 0.422056 | ||||||||
\(34\) | 5.02299e28 | + | 1.43532e29i | 0.400740 | + | 1.14512i | ||||
\(35\) | 2.06098e29i | 0.947938i | ||||||||
\(36\) | −1.26117e29 | + | 1.00590e29i | −0.339647 | + | 0.270899i | ||||
\(37\) | −4.26856e29 | −0.683045 | −0.341522 | − | 0.939874i | \(-0.610943\pi\) | ||||
−0.341522 | + | 0.939874i | \(0.610943\pi\) | |||||||
\(38\) | 1.54960e30 | − | 5.42292e29i | 1.49394 | − | 0.522811i | ||||
\(39\) | 8.20476e29i | 0.482879i | ||||||||
\(40\) | 3.03363e30 | + | 1.90570e30i | 1.10363 | + | 0.693291i | ||||
\(41\) | 8.28192e30 | 1.88468 | 0.942340 | − | 0.334656i | \(-0.108620\pi\) | ||||
0.942340 | + | 0.334656i | \(0.108620\pi\) | |||||||
\(42\) | 1.25495e30 | + | 3.58603e30i | 0.180671 | + | 0.516270i | ||||
\(43\) | 3.48399e29i | 0.0320757i | 0.999871 | + | 0.0160378i | \(0.00510522\pi\) | ||||
−0.999871 | + | 0.0160378i | \(0.994895\pi\) | |||||||
\(44\) | 5.88306e30 | + | 7.37605e30i | 0.349947 | + | 0.438756i | ||||
\(45\) | 1.45891e31 | 0.566228 | ||||||||
\(46\) | −2.47130e31 | + | 8.64844e30i | −0.631723 | + | 0.221075i | ||||
\(47\) | 1.09265e32i | 1.85618i | 0.372356 | + | 0.928090i | \(0.378550\pi\) | ||||
−0.372356 | + | 0.928090i | \(0.621450\pi\) | |||||||
\(48\) | 6.43881e31 | + | 1.46865e31i | 0.733200 | + | 0.167238i | ||||
\(49\) | 6.11992e31 | 0.470999 | ||||||||
\(50\) | −4.40164e31 | − | 1.25777e32i | −0.230773 | − | 0.659435i | ||||
\(51\) | − | 2.53517e32i | − | 0.912375i | ||||||
\(52\) | −2.01723e32 | + | 1.60892e32i | −0.501986 | + | 0.400379i | ||||
\(53\) | −3.01382e32 | −0.522247 | −0.261123 | − | 0.965305i | \(-0.584093\pi\) | ||||
−0.261123 | + | 0.965305i | \(0.584093\pi\) | |||||||
\(54\) | 8.38138e32 | − | 2.93311e32i | 1.01820 | − | 0.356325i | ||||
\(55\) | − | 8.53252e32i | − | 0.731453i | ||||||
\(56\) | −6.35572e32 | + | 1.01175e33i | −0.386894 | + | 0.615885i | ||||
\(57\) | −2.73702e33 | −1.19030 | ||||||||
\(58\) | −1.49352e33 | − | 4.26775e33i | −0.466745 | − | 1.33373i | ||||
\(59\) | 1.34443e33i | 0.303634i | 0.988409 | + | 0.151817i | \(0.0485125\pi\) | ||||
−0.988409 | + | 0.151817i | \(0.951487\pi\) | |||||||
\(60\) | −3.72417e33 | − | 4.66928e33i | −0.611161 | − | 0.766260i | ||||
\(61\) | −2.87786e33 | −0.344987 | −0.172494 | − | 0.985011i | \(-0.555182\pi\) | ||||
−0.172494 | + | 0.985011i | \(0.555182\pi\) | |||||||
\(62\) | −5.24321e33 | + | 1.83489e33i | −0.461482 | + | 0.161498i | ||||
\(63\) | 4.86562e33i | 0.315986i | ||||||||
\(64\) | 9.01542e33 | + | 1.87105e34i | 0.434077 | + | 0.900876i | ||||
\(65\) | 2.33350e34 | 0.836864 | ||||||||
\(66\) | −5.19553e33 | − | 1.48463e34i | −0.139411 | − | 0.398367i | ||||
\(67\) | 9.77943e33i | 0.197193i | 0.995127 | + | 0.0985966i | \(0.0314354\pi\) | ||||
−0.995127 | + | 0.0985966i | \(0.968565\pi\) | |||||||
\(68\) | 6.23298e34 | − | 4.97136e34i | 0.948475 | − | 0.756495i | ||||
\(69\) | 4.36498e34 | 0.503326 | ||||||||
\(70\) | 1.01990e35 | − | 3.56918e34i | 0.894732 | − | 0.313116i | ||||
\(71\) | 2.88061e35i | 1.93008i | 0.262097 | + | 0.965042i | \(0.415586\pi\) | ||||
−0.262097 | + | 0.965042i | \(0.584414\pi\) | |||||||
\(72\) | 7.16189e34 | + | 4.49905e34i | 0.367884 | + | 0.231102i | ||||
\(73\) | −3.46504e35 | −1.36954 | −0.684768 | − | 0.728761i | \(-0.740096\pi\) | ||||
−0.684768 | + | 0.728761i | \(0.740096\pi\) | |||||||
\(74\) | 7.39226e34 | + | 2.11234e35i | 0.225618 | + | 0.644706i | ||||
\(75\) | 2.22156e35i | 0.525406i | ||||||||
\(76\) | −5.36717e35 | − | 6.72924e35i | −0.986933 | − | 1.23739i | ||||
\(77\) | 2.84568e35 | 0.408190 | ||||||||
\(78\) | 4.06021e35 | − | 1.42089e35i | 0.455776 | − | 0.159501i | ||||
\(79\) | 4.41569e35i | 0.389121i | 0.980891 | + | 0.194560i | \(0.0623280\pi\) | ||||
−0.980891 | + | 0.194560i | \(0.937672\pi\) | |||||||
\(80\) | 4.17696e35 | − | 1.83125e36i | 0.289835 | − | 1.27069i | ||||
\(81\) | −6.87593e35 | −0.376804 | ||||||||
\(82\) | −1.43425e36 | − | 4.09840e36i | −0.622534 | − | 1.77890i | ||||
\(83\) | 3.81913e36i | 1.31668i | 0.752721 | + | 0.658340i | \(0.228741\pi\) | ||||
−0.752721 | + | 0.658340i | \(0.771259\pi\) | |||||||
\(84\) | 1.55725e36 | − | 1.24205e36i | 0.427614 | − | 0.341061i | ||||
\(85\) | −7.21023e36 | −1.58121 | ||||||||
\(86\) | 1.72409e35 | − | 6.03354e34i | 0.0302753 | − | 0.0105950i | ||||
\(87\) | 7.53800e36i | 1.06265i | ||||||||
\(88\) | 2.63129e36 | − | 4.18867e36i | 0.298537 | − | 0.475232i | ||||
\(89\) | −3.10884e36 | −0.284569 | −0.142285 | − | 0.989826i | \(-0.545445\pi\) | ||||
−0.142285 | + | 0.989826i | \(0.545445\pi\) | |||||||
\(90\) | −2.52653e36 | − | 7.21957e36i | −0.187032 | − | 0.534446i | ||||
\(91\) | 7.78247e36i | 0.467015i | ||||||||
\(92\) | 8.55954e36 | + | 1.07318e37i | 0.417332 | + | 0.523241i | ||||
\(93\) | 9.26091e36 | 0.367687 | ||||||||
\(94\) | 5.40707e37 | − | 1.89223e37i | 1.75200 | − | 0.613120i | ||||
\(95\) | 7.78430e37i | 2.06287i | ||||||||
\(96\) | −3.88291e36 | − | 3.44065e37i | −0.0843342 | − | 0.747287i | ||||
\(97\) | 4.23861e37 | 0.756067 | 0.378034 | − | 0.925792i | \(-0.376600\pi\) | ||||
0.378034 | + | 0.925792i | \(0.376600\pi\) | |||||||
\(98\) | −1.05984e37 | − | 3.02851e37i | −0.155577 | − | 0.444563i | ||||
\(99\) | − | 2.01438e37i | − | 0.243822i | ||||||
\(100\) | −5.46195e37 | + | 4.35640e37i | −0.546195 | + | 0.435640i | ||||
\(101\) | −1.82770e37 | −0.151286 | −0.0756431 | − | 0.997135i | \(-0.524101\pi\) | ||||
−0.0756431 | + | 0.997135i | \(0.524101\pi\) | |||||||
\(102\) | −1.25455e38 | + | 4.39038e37i | −0.861165 | + | 0.301369i | ||||
\(103\) | − | 7.94465e37i | − | 0.453072i | −0.974003 | − | 0.226536i | \(-0.927260\pi\) | ||
0.974003 | − | 0.226536i | \(-0.0727402\pi\) | |||||||
\(104\) | 1.14553e38 | + | 7.19615e37i | 0.543718 | + | 0.341560i | ||||
\(105\) | −1.80141e38 | −0.712879 | ||||||||
\(106\) | 5.21930e37 | + | 1.49142e38i | 0.172505 | + | 0.492934i | ||||
\(107\) | − | 4.96685e38i | − | 1.37338i | −0.726952 | − | 0.686688i | \(-0.759064\pi\) | ||
0.726952 | − | 0.686688i | \(-0.240936\pi\) | |||||||
\(108\) | −2.90296e38 | − | 3.63966e38i | −0.672650 | − | 0.843353i | ||||
\(109\) | −4.87318e38 | −0.947783 | −0.473892 | − | 0.880583i | \(-0.657151\pi\) | ||||
−0.473892 | + | 0.880583i | \(0.657151\pi\) | |||||||
\(110\) | −4.22241e38 | + | 1.47765e38i | −0.690397 | + | 0.241608i | ||||
\(111\) | − | 3.73097e38i | − | 0.513671i | ||||||
\(112\) | 6.10741e38 | + | 1.39306e38i | 0.709112 | + | 0.161744i | ||||
\(113\) | 1.83355e39 | 1.79805 | 0.899027 | − | 0.437893i | \(-0.144275\pi\) | ||||
0.899027 | + | 0.437893i | \(0.144275\pi\) | |||||||
\(114\) | 4.73994e38 | + | 1.35444e39i | 0.393170 | + | 1.12349i | ||||
\(115\) | − | 1.24144e39i | − | 0.872299i | ||||||
\(116\) | −1.85329e39 | + | 1.47817e39i | −1.10470 | + | 0.881095i | ||||
\(117\) | 5.50901e38 | 0.278960 | ||||||||
\(118\) | 6.65307e38 | − | 2.32828e38i | 0.286592 | − | 0.100294i | ||||
\(119\) | − | 2.40468e39i | − | 0.882401i | ||||||
\(120\) | −1.66569e39 | + | 2.65157e39i | −0.521376 | + | 0.829963i | ||||
\(121\) | 2.56231e39 | 0.685030 | ||||||||
\(122\) | 4.98385e38 | + | 1.42414e39i | 0.113954 | + | 0.325624i | ||||
\(123\) | 7.23887e39i | 1.41734i | ||||||||
\(124\) | 1.81603e39 | + | 2.27689e39i | 0.304867 | + | 0.382235i | ||||
\(125\) | −2.72530e39 | −0.392757 | ||||||||
\(126\) | 2.40780e39 | − | 8.42623e38i | 0.298250 | − | 0.104374i | ||||
\(127\) | − | 5.95566e39i | − | 0.634833i | −0.948286 | − | 0.317416i | \(-0.897185\pi\) | ||
0.948286 | − | 0.317416i | \(-0.102815\pi\) | |||||||
\(128\) | 7.69779e39 | − | 7.70164e39i | 0.706930 | − | 0.707283i | ||||
\(129\) | −3.04520e38 | −0.0241219 | ||||||||
\(130\) | −4.04114e39 | − | 1.15476e40i | −0.276427 | − | 0.789892i | ||||
\(131\) | − | 1.99604e40i | − | 1.18036i | −0.807271 | − | 0.590181i | \(-0.799056\pi\) | ||
0.807271 | − | 0.590181i | \(-0.200944\pi\) | |||||||
\(132\) | −6.44708e39 | + | 5.14213e39i | −0.329958 | + | 0.263171i | ||||
\(133\) | −2.59614e40 | −1.15119 | ||||||||
\(134\) | 4.83945e39 | − | 1.69359e39i | 0.186125 | − | 0.0651355i | ||||
\(135\) | 4.21031e40i | 1.40596i | ||||||||
\(136\) | −3.53955e40 | − | 2.22352e40i | −1.02733 | − | 0.645359i | ||||
\(137\) | 1.58039e40 | 0.399093 | 0.199546 | − | 0.979888i | \(-0.436053\pi\) | ||||
0.199546 | + | 0.979888i | \(0.436053\pi\) | |||||||
\(138\) | −7.55922e39 | − | 2.16005e40i | −0.166255 | − | 0.475075i | ||||
\(139\) | 1.01319e41i | 1.94272i | 0.237608 | + | 0.971361i | \(0.423637\pi\) | ||||
−0.237608 | + | 0.971361i | \(0.576363\pi\) | |||||||
\(140\) | −3.53249e40 | − | 4.42895e40i | −0.591083 | − | 0.741086i | ||||
\(141\) | −9.55034e40 | −1.39590 | ||||||||
\(142\) | 1.42550e41 | − | 4.98861e40i | 1.82175 | − | 0.637531i | ||||
\(143\) | − | 3.22197e40i | − | 0.360361i | ||||||
\(144\) | 9.86110e39 | − | 4.32328e40i | 0.0966136 | − | 0.423571i | ||||
\(145\) | 2.14387e41 | 1.84165 | ||||||||
\(146\) | 6.00072e40 | + | 1.71471e41i | 0.452375 | + | 1.29267i | ||||
\(147\) | 5.34916e40i | 0.354206i | ||||||||
\(148\) | 9.17297e40 | − | 7.31627e40i | 0.533995 | − | 0.425910i | ||||
\(149\) | −6.34117e40 | −0.324811 | −0.162405 | − | 0.986724i | \(-0.551925\pi\) | ||||
−0.162405 | + | 0.986724i | \(0.551925\pi\) | |||||||
\(150\) | 1.09936e41 | − | 3.84728e40i | 0.495916 | − | 0.173548i | ||||
\(151\) | 1.44167e41i | 0.573195i | 0.958051 | + | 0.286598i | \(0.0925243\pi\) | ||||
−0.958051 | + | 0.286598i | \(0.907476\pi\) | |||||||
\(152\) | −2.40055e41 | + | 3.82137e41i | −0.841944 | + | 1.34026i | ||||
\(153\) | −1.70221e41 | −0.527080 | ||||||||
\(154\) | −4.92812e40 | − | 1.40822e41i | −0.134830 | − | 0.385279i | ||||
\(155\) | − | 2.63388e41i | − | 0.637227i | ||||||
\(156\) | −1.40629e41 | − | 1.76317e41i | −0.301097 | − | 0.377509i | ||||
\(157\) | −3.82249e40 | −0.0724859 | −0.0362429 | − | 0.999343i | \(-0.511539\pi\) | ||||
−0.0362429 | + | 0.999343i | \(0.511539\pi\) | |||||||
\(158\) | 2.18515e41 | − | 7.64706e40i | 0.367280 | − | 0.128532i | ||||
\(159\) | − | 2.63425e41i | − | 0.392746i | ||||||
\(160\) | −9.78551e41 | + | 1.10433e41i | −1.29510 | + | 0.146157i | ||||
\(161\) | 4.14031e41 | 0.486790 | ||||||||
\(162\) | 1.19077e41 | + | 3.40262e41i | 0.124463 | + | 0.355655i | ||||
\(163\) | − | 1.81527e42i | − | 1.68801i | −0.536333 | − | 0.844006i | \(-0.680191\pi\) | ||
0.536333 | − | 0.844006i | \(-0.319809\pi\) | |||||||
\(164\) | −1.77975e42 | + | 1.41951e42i | −1.47342 | + | 1.17518i | ||||
\(165\) | 7.45791e41 | 0.550075 | ||||||||
\(166\) | 1.88993e42 | − | 6.61393e41i | 1.24278 | − | 0.434916i | ||||
\(167\) | − | 1.97076e42i | − | 1.15617i | −0.815978 | − | 0.578083i | \(-0.803801\pi\) | ||
0.815978 | − | 0.578083i | \(-0.196199\pi\) | |||||||
\(168\) | −8.84324e41 | − | 5.55526e41i | −0.463164 | − | 0.290956i | ||||
\(169\) | −1.25605e42 | −0.587707 | ||||||||
\(170\) | 1.24866e42 | + | 3.56806e42i | 0.522294 | + | 1.49246i | ||||
\(171\) | 1.83774e42i | 0.687636i | ||||||||
\(172\) | −5.97152e40 | − | 7.48695e40i | −0.0200007 | − | 0.0250764i | ||||
\(173\) | 6.85037e41 | 0.205513 | 0.102756 | − | 0.994707i | \(-0.467234\pi\) | ||||
0.102756 | + | 0.994707i | \(0.467234\pi\) | |||||||
\(174\) | 3.73026e42 | − | 1.30542e42i | 1.00300 | − | 0.351007i | ||||
\(175\) | 2.10722e42i | 0.508145i | ||||||||
\(176\) | −2.52849e42 | − | 5.76732e41i | −0.547168 | − | 0.124805i | ||||
\(177\) | −1.17511e42 | −0.228342 | ||||||||
\(178\) | 5.38386e41 | + | 1.53844e42i | 0.0939969 | + | 0.268597i | ||||
\(179\) | 4.61389e42i | 0.724202i | 0.932139 | + | 0.362101i | \(0.117940\pi\) | ||||
−0.932139 | + | 0.362101i | \(0.882060\pi\) | |||||||
\(180\) | −3.13514e42 | + | 2.50056e42i | −0.442669 | + | 0.353069i | ||||
\(181\) | 1.22705e43 | 1.55945 | 0.779723 | − | 0.626124i | \(-0.215360\pi\) | ||||
0.779723 | + | 0.626124i | \(0.215360\pi\) | |||||||
\(182\) | 3.85124e42 | − | 1.34776e42i | 0.440802 | − | 0.154261i | ||||
\(183\) | − | 2.51541e42i | − | 0.259441i | ||||||
\(184\) | 3.82839e42 | − | 6.09429e42i | 0.356022 | − | 0.566741i | ||||
\(185\) | −1.06112e43 | −0.890227 | ||||||||
\(186\) | −1.60380e42 | − | 4.58286e42i | −0.121452 | − | 0.347049i | ||||
\(187\) | 9.95549e42i | 0.680882i | ||||||||
\(188\) | −1.87278e43 | − | 2.34805e43i | −1.15741 | − | 1.45114i | ||||
\(189\) | −1.40418e43 | −0.784602 | ||||||||
\(190\) | 3.85214e43 | − | 1.34808e43i | 1.94708 | − | 0.681391i | ||||
\(191\) | 1.43427e43i | 0.656142i | 0.944653 | + | 0.328071i | \(0.106399\pi\) | ||||
−0.944653 | + | 0.328071i | \(0.893601\pi\) | |||||||
\(192\) | −1.63540e43 | + | 7.87999e42i | −0.677487 | + | 0.326439i | ||||
\(193\) | −1.36311e43 | −0.511614 | −0.255807 | − | 0.966728i | \(-0.582341\pi\) | ||||
−0.255807 | + | 0.966728i | \(0.582341\pi\) | |||||||
\(194\) | −7.34038e42 | − | 2.09752e43i | −0.249739 | − | 0.713630i | ||||
\(195\) | 2.03961e43i | 0.629347i | ||||||||
\(196\) | −1.31515e43 | + | 1.04895e43i | −0.368221 | + | 0.293689i | ||||
\(197\) | −3.49713e43 | −0.888901 | −0.444450 | − | 0.895804i | \(-0.646601\pi\) | ||||
−0.444450 | + | 0.895804i | \(0.646601\pi\) | |||||||
\(198\) | −9.96839e42 | + | 3.48849e42i | −0.230137 | + | 0.0805376i | ||||
\(199\) | − | 6.86906e43i | − | 1.44108i | −0.693412 | − | 0.720541i | \(-0.743893\pi\) | ||
0.693412 | − | 0.720541i | \(-0.256107\pi\) | |||||||
\(200\) | 3.10170e43 | + | 1.94847e43i | 0.591603 | + | 0.371640i | ||||
\(201\) | −8.54777e42 | −0.148295 | ||||||||
\(202\) | 3.16520e42 | + | 9.04458e42i | 0.0499718 | + | 0.142795i | ||||
\(203\) | 7.15002e43i | 1.02774i | ||||||||
\(204\) | 4.34525e43 | + | 5.44797e43i | 0.568908 | + | 0.713283i | ||||
\(205\) | 2.05879e44 | 2.45635 | ||||||||
\(206\) | −3.93149e43 | + | 1.37585e43i | −0.427642 | + | 0.149656i | ||||
\(207\) | − | 2.93082e43i | − | 0.290772i | ||||||
\(208\) | 1.57727e43 | − | 6.91501e43i | 0.142791 | − | 0.626022i | ||||
\(209\) | 1.07481e44 | 0.888288 | ||||||||
\(210\) | 3.11966e43 | + | 8.91446e43i | 0.235473 | + | 0.672866i | ||||
\(211\) | − | 1.16874e44i | − | 0.806032i | −0.915193 | − | 0.403016i | \(-0.867962\pi\) | ||
0.915193 | − | 0.403016i | \(-0.132038\pi\) | |||||||
\(212\) | 6.47657e43 | − | 5.16565e43i | 0.408286 | − | 0.325645i | ||||
\(213\) | −2.51782e44 | −1.45148 | ||||||||
\(214\) | −2.45790e44 | + | 8.60155e43i | −1.29629 | + | 0.453644i | ||||
\(215\) | 8.66081e42i | 0.0418050i | ||||||||
\(216\) | −1.29839e44 | + | 2.06687e44i | −0.573832 | + | 0.913466i | ||||
\(217\) | 8.78426e43 | 0.355607 | ||||||||
\(218\) | 8.43933e43 | + | 2.41154e44i | 0.313065 | + | 0.894586i | ||||
\(219\) | − | 3.02864e44i | − | 1.02993i | ||||||
\(220\) | 1.46246e44 | + | 1.83360e44i | 0.456094 | + | 0.571840i | ||||
\(221\) | −2.72266e44 | −0.779005 | ||||||||
\(222\) | −1.84631e44 | + | 6.46125e43i | −0.484839 | + | 0.169672i | ||||
\(223\) | − | 5.64827e44i | − | 1.36183i | −0.732362 | − | 0.680915i | \(-0.761582\pi\) | ||
0.732362 | − | 0.680915i | \(-0.238418\pi\) | |||||||
\(224\) | −3.68306e43 | − | 3.26357e44i | −0.0815635 | − | 0.722737i | ||||
\(225\) | 1.49165e44 | 0.303528 | ||||||||
\(226\) | −3.17533e44 | − | 9.07352e44i | −0.593920 | − | 1.69713i | ||||
\(227\) | 3.96498e44i | 0.681946i | 0.940073 | + | 0.340973i | \(0.110756\pi\) | ||||
−0.940073 | + | 0.340973i | \(0.889244\pi\) | |||||||
\(228\) | 5.88174e44 | − | 4.69121e44i | 0.930558 | − | 0.742204i | ||||
\(229\) | −1.89874e44 | −0.276435 | −0.138217 | − | 0.990402i | \(-0.544137\pi\) | ||||
−0.138217 | + | 0.990402i | \(0.544137\pi\) | |||||||
\(230\) | −6.14338e44 | + | 2.14991e44i | −0.823338 | + | 0.288131i | ||||
\(231\) | 2.48729e44i | 0.306972i | ||||||||
\(232\) | 1.05244e45 | + | 6.61134e44i | 1.19654 | + | 0.751654i | ||||
\(233\) | 6.08866e44 | 0.637910 | 0.318955 | − | 0.947770i | \(-0.396668\pi\) | ||||
0.318955 | + | 0.947770i | \(0.396668\pi\) | |||||||
\(234\) | −9.54045e43 | − | 2.72619e44i | −0.0921441 | − | 0.263302i | ||||
\(235\) | 2.71620e45i | 2.41920i | ||||||||
\(236\) | −2.30434e44 | − | 2.88913e44i | −0.189330 | − | 0.237377i | ||||
\(237\) | −3.85957e44 | −0.292631 | ||||||||
\(238\) | −1.18998e45 | + | 4.16441e44i | −0.832873 | + | 0.291468i | ||||
\(239\) | − | 1.41312e45i | − | 0.913308i | −0.889644 | − | 0.456654i | \(-0.849048\pi\) | ||
0.889644 | − | 0.456654i | \(-0.150952\pi\) | |||||||
\(240\) | 1.60062e45 | + | 3.65090e44i | 0.955596 | + | 0.217965i | ||||
\(241\) | −4.00978e44 | −0.221206 | −0.110603 | − | 0.993865i | \(-0.535278\pi\) | ||||
−0.110603 | + | 0.993865i | \(0.535278\pi\) | |||||||
\(242\) | −4.43738e44 | − | 1.26799e45i | −0.226274 | − | 0.646581i | ||||
\(243\) | 1.68692e45i | 0.795382i | ||||||||
\(244\) | 6.18441e44 | − | 4.93262e44i | 0.269706 | − | 0.215115i | ||||
\(245\) | 1.52134e45 | 0.613864 | ||||||||
\(246\) | 3.58223e45 | − | 1.25362e45i | 1.33779 | − | 0.468165i | ||||
\(247\) | 2.93944e45i | 1.01630i | ||||||||
\(248\) | 8.12246e44 | − | 1.29299e45i | 0.260079 | − | 0.414012i | ||||
\(249\) | −3.33813e45 | −0.990184 | ||||||||
\(250\) | 4.71965e44 | + | 1.34864e45i | 0.129733 | + | 0.370712i | ||||
\(251\) | − | 1.16135e45i | − | 0.295911i | −0.988994 | − | 0.147956i | \(-0.952731\pi\) | ||
0.988994 | − | 0.147956i | \(-0.0472693\pi\) | |||||||
\(252\) | −8.33961e44 | − | 1.04560e45i | −0.197031 | − | 0.247033i | ||||
\(253\) | −1.71411e45 | −0.375619 | ||||||||
\(254\) | −2.94722e45 | + | 1.03140e45i | −0.599201 | + | 0.209693i | ||||
\(255\) | − | 6.30215e45i | − | 1.18912i | ||||||
\(256\) | −5.14433e45 | − | 2.47557e45i | −0.901093 | − | 0.433626i | ||||
\(257\) | 2.46040e45 | 0.400199 | 0.200099 | − | 0.979776i | \(-0.435873\pi\) | ||||
0.200099 | + | 0.979776i | \(0.435873\pi\) | |||||||
\(258\) | 5.27365e43 | + | 1.50695e44i | 0.00796778 | + | 0.0227680i | ||||
\(259\) | − | 3.53894e45i | − | 0.496795i | ||||||
\(260\) | −5.01460e45 | + | 3.99960e45i | −0.654249 | + | 0.521823i | ||||
\(261\) | 5.06131e45 | 0.613894 | ||||||||
\(262\) | −9.87762e45 | + | 3.45673e45i | −1.11411 | + | 0.389888i | ||||
\(263\) | − | 6.11021e45i | − | 0.641057i | −0.947239 | − | 0.320529i | \(-0.896139\pi\) | ||
0.947239 | − | 0.320529i | \(-0.103861\pi\) | |||||||
\(264\) | 3.66114e45 | + | 2.29990e45i | 0.357389 | + | 0.224509i | ||||
\(265\) | −7.49202e45 | −0.680656 | ||||||||
\(266\) | 4.49597e45 | + | 1.28473e46i | 0.380253 | + | 1.08658i | ||||
\(267\) | − | 2.71730e45i | − | 0.214005i | ||||||
\(268\) | −1.67618e45 | − | 2.10156e45i | −0.122959 | − | 0.154163i | ||||
\(269\) | 1.24324e46 | 0.849694 | 0.424847 | − | 0.905265i | \(-0.360328\pi\) | ||||
0.424847 | + | 0.905265i | \(0.360328\pi\) | |||||||
\(270\) | 2.08352e46 | − | 7.29138e45i | 1.32705 | − | 0.464406i | ||||
\(271\) | 5.17900e45i | 0.307489i | 0.988111 | + | 0.153745i | \(0.0491333\pi\) | ||||
−0.988111 | + | 0.153745i | \(0.950867\pi\) | |||||||
\(272\) | −4.87356e45 | + | 2.13665e46i | −0.269797 | + | 1.18284i | ||||
\(273\) | −6.80232e45 | −0.351210 | ||||||||
\(274\) | −2.73691e45 | − | 7.82073e45i | −0.131825 | − | 0.376692i | ||||
\(275\) | − | 8.72398e45i | − | 0.392097i | ||||||
\(276\) | −9.38016e45 | + | 7.48152e45i | −0.393494 | + | 0.313847i | ||||
\(277\) | 3.30132e46 | 1.29292 | 0.646461 | − | 0.762947i | \(-0.276248\pi\) | ||||
0.646461 | + | 0.762947i | \(0.276248\pi\) | |||||||
\(278\) | 5.01389e46 | − | 1.75464e46i | 1.83368 | − | 0.641706i | ||||
\(279\) | − | 6.21815e45i | − | 0.212413i | ||||||
\(280\) | −1.57996e46 | + | 2.51509e46i | −0.504248 | + | 0.802696i | ||||
\(281\) | 5.17847e45 | 0.154448 | 0.0772238 | − | 0.997014i | \(-0.475394\pi\) | ||||
0.0772238 | + | 0.997014i | \(0.475394\pi\) | |||||||
\(282\) | 1.65392e46 | + | 4.72609e46i | 0.461085 | + | 1.31755i | ||||
\(283\) | − | 8.63166e45i | − | 0.224984i | −0.993653 | − | 0.112492i | \(-0.964117\pi\) | ||
0.993653 | − | 0.112492i | \(-0.0358833\pi\) | |||||||
\(284\) | −4.93734e46 | − | 6.19032e46i | −1.20349 | − | 1.50891i | ||||
\(285\) | −6.80392e46 | −1.55134 | ||||||||
\(286\) | −1.59443e46 | + | 5.57978e45i | −0.340134 | + | 0.119032i | ||||
\(287\) | 6.86629e46i | 1.37077i | ||||||||
\(288\) | −2.31019e46 | + | 2.60714e45i | −0.431709 | + | 0.0487200i | ||||
\(289\) | 2.69712e46 | 0.471890 | ||||||||
\(290\) | −3.71273e46 | − | 1.06092e47i | −0.608319 | − | 1.73828i | ||||
\(291\) | 3.70478e46i | 0.568586i | ||||||||
\(292\) | 7.44622e46 | − | 5.93903e46i | 1.07069 | − | 0.853968i | ||||
\(293\) | −9.90073e46 | −1.33408 | −0.667041 | − | 0.745021i | \(-0.732439\pi\) | ||||
−0.667041 | + | 0.745021i | \(0.732439\pi\) | |||||||
\(294\) | 2.64709e46 | − | 9.26361e45i | 0.334325 | − | 0.116999i | ||||
\(295\) | 3.34211e46i | 0.395733i | ||||||||
\(296\) | −5.20910e46 | − | 3.27232e46i | −0.578389 | − | 0.363340i | ||||
\(297\) | 5.81337e46 | 0.605418 | ||||||||
\(298\) | 1.09816e46 | + | 3.13799e46i | 0.107289 | + | 0.306580i | ||||
\(299\) | − | 4.68780e46i | − | 0.429750i | ||||||
\(300\) | −3.80774e46 | − | 4.77405e46i | −0.327615 | − | 0.410755i | ||||
\(301\) | −2.88847e45 | −0.0233294 | ||||||||
\(302\) | 7.13423e46 | − | 2.49666e46i | 0.541023 | − | 0.189334i | ||||
\(303\) | − | 1.59752e46i | − | 0.113772i | ||||||
\(304\) | 2.30677e47 | + | 5.26158e46i | 1.54314 | + | 0.351980i | ||||
\(305\) | −7.15404e46 | −0.449629 | ||||||||
\(306\) | 2.94788e46 | + | 8.42358e46i | 0.174101 | + | 0.497496i | ||||
\(307\) | − | 1.39496e46i | − | 0.0774344i | −0.999250 | − | 0.0387172i | \(-0.987673\pi\) | ||
0.999250 | − | 0.0387172i | \(-0.0123272\pi\) | |||||||
\(308\) | −6.11526e46 | + | 4.87747e46i | −0.319118 | + | 0.254525i | ||||
\(309\) | 6.94408e46 | 0.340724 | ||||||||
\(310\) | −1.30340e47 | + | 4.56133e46i | −0.601460 | + | 0.210484i | ||||
\(311\) | 2.37380e47i | 1.03038i | 0.857077 | + | 0.515189i | \(0.172278\pi\) | ||||
−0.857077 | + | 0.515189i | \(0.827722\pi\) | |||||||
\(312\) | −6.28984e46 | + | 1.00126e47i | −0.256863 | + | 0.408893i | ||||
\(313\) | 1.06109e47 | 0.407764 | 0.203882 | − | 0.978995i | \(-0.434644\pi\) | ||||
0.203882 | + | 0.978995i | \(0.434644\pi\) | |||||||
\(314\) | 6.61976e45 | + | 1.89160e46i | 0.0239430 | + | 0.0684174i | ||||
\(315\) | 1.20954e47i | 0.411831i | ||||||||
\(316\) | −7.56845e46 | − | 9.48915e46i | −0.242634 | − | 0.304209i | ||||
\(317\) | 4.62385e46 | 0.139598 | 0.0697988 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0697988 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(318\) | −1.30359e47 | + | 4.56196e46i | −0.370701 | + | 0.129729i | ||||
\(319\) | − | 2.96014e47i | − | 0.793028i | ||||||
\(320\) | 2.24113e47 | + | 4.65121e47i | 0.565742 | + | 1.17413i | ||||
\(321\) | 4.34131e47 | 1.03282 | ||||||||
\(322\) | −7.17016e46 | − | 2.04888e47i | −0.160793 | − | 0.459467i | ||||
\(323\) | − | 9.08249e47i | − | 1.92025i | ||||||
\(324\) | 1.47761e47 | − | 1.17853e47i | 0.294581 | − | 0.234955i | ||||
\(325\) | 2.38586e47 | 0.448603 | ||||||||
\(326\) | −8.98303e47 | + | 3.14366e47i | −1.59327 | + | 0.557572i | ||||
\(327\) | − | 4.25944e47i | − | 0.712762i | ||||||
\(328\) | 1.01068e48 | + | 6.34899e47i | 1.59591 | + | 1.00254i | ||||
\(329\) | −9.05879e47 | −1.35004 | ||||||||
\(330\) | −1.29155e47 | − | 3.69062e47i | −0.181697 | − | 0.519200i | ||||
\(331\) | − | 4.13158e47i | − | 0.548763i | −0.961621 | − | 0.274381i | \(-0.911527\pi\) | ||
0.961621 | − | 0.274381i | \(-0.0884730\pi\) | |||||||
\(332\) | −6.54594e47 | − | 8.20715e47i | −0.821010 | − | 1.02936i | ||||
\(333\) | −2.50512e47 | −0.296748 | ||||||||
\(334\) | −9.75251e47 | + | 3.41294e47i | −1.09127 | + | 0.381897i | ||||
\(335\) | 2.43106e47i | 0.257006i | ||||||||
\(336\) | −1.21761e47 | + | 5.33822e47i | −0.121636 | + | 0.533274i | ||||
\(337\) | −5.69409e47 | −0.537596 | −0.268798 | − | 0.963197i | \(-0.586626\pi\) | ||||
−0.268798 | + | 0.963197i | \(0.586626\pi\) | |||||||
\(338\) | 2.17522e47 | + | 6.21572e47i | 0.194127 | + | 0.554720i | ||||
\(339\) | 1.60263e48i | 1.35219i | ||||||||
\(340\) | 1.54945e48 | − | 1.23583e48i | 1.23617 | − | 0.985957i | ||||
\(341\) | −3.63672e47 | −0.274395 | ||||||||
\(342\) | 9.09426e47 | − | 3.18258e47i | 0.649040 | − | 0.227135i | ||||
\(343\) | 1.58463e48i | 1.06989i | ||||||||
\(344\) | −2.67085e46 | + | 4.25165e46i | −0.0170624 | + | 0.0271611i | ||||
\(345\) | 1.08509e48 | 0.655996 | ||||||||
\(346\) | −1.18634e47 | − | 3.38998e47i | −0.0678834 | − | 0.193977i | ||||
\(347\) | − | 2.72748e48i | − | 1.47741i | −0.674029 | − | 0.738705i | \(-0.735438\pi\) | ||
0.674029 | − | 0.738705i | \(-0.264562\pi\) | |||||||
\(348\) | −1.29200e48 | − | 1.61988e48i | −0.662610 | − | 0.830766i | ||||
\(349\) | 2.78256e48 | 1.35133 | 0.675665 | − | 0.737209i | \(-0.263857\pi\) | ||||
0.675665 | + | 0.737209i | \(0.263857\pi\) | |||||||
\(350\) | 1.04278e48 | − | 3.64927e47i | 0.479623 | − | 0.167847i | ||||
\(351\) | 1.58986e48i | 0.692666i | ||||||||
\(352\) | 1.52480e47 | + | 1.35113e48i | 0.0629365 | + | 0.557682i | ||||
\(353\) | −8.40990e47 | −0.328906 | −0.164453 | − | 0.986385i | \(-0.552586\pi\) | ||||
−0.164453 | + | 0.986385i | \(0.552586\pi\) | |||||||
\(354\) | 2.03505e47 | + | 5.81516e47i | 0.0754244 | + | 0.215526i | ||||
\(355\) | 7.16088e48i | 2.51552i | ||||||||
\(356\) | 6.68077e47 | − | 5.32852e47i | 0.222473 | − | 0.177442i | ||||
\(357\) | 2.10183e48 | 0.663593 | ||||||||
\(358\) | 2.28323e48 | − | 7.99029e47i | 0.683554 | − | 0.239213i | ||||
\(359\) | − | 1.99311e48i | − | 0.565896i | −0.959135 | − | 0.282948i | \(-0.908688\pi\) | ||
0.959135 | − | 0.282948i | \(-0.0913124\pi\) | |||||||
\(360\) | 1.78037e48 | + | 1.11841e48i | 0.479471 | + | 0.301200i | ||||
\(361\) | −5.89148e48 | −1.50518 | ||||||||
\(362\) | −2.12500e48 | − | 6.07220e48i | −0.515105 | − | 1.47192i | ||||
\(363\) | 2.23960e48i | 0.515164i | ||||||||
\(364\) | −1.33391e48 | − | 1.67242e48i | −0.291205 | − | 0.365106i | ||||
\(365\) | −8.61370e48 | −1.78495 | ||||||||
\(366\) | −1.24478e48 | + | 4.35617e47i | −0.244879 | + | 0.0856967i | ||||
\(367\) | − | 8.38448e48i | − | 1.56610i | −0.621956 | − | 0.783052i | \(-0.713662\pi\) | ||
0.621956 | − | 0.783052i | \(-0.286338\pi\) | |||||||
\(368\) | −3.67882e48 | − | 8.39114e47i | −0.652529 | − | 0.148838i | ||||
\(369\) | 4.86047e48 | 0.818798 | ||||||||
\(370\) | 1.83763e48 | + | 5.25106e48i | 0.294053 | + | 0.840260i | ||||
\(371\) | − | 2.49867e48i | − | 0.379843i | ||||||
\(372\) | −1.99013e48 | + | 1.58731e48i | −0.287453 | + | 0.229269i | ||||
\(373\) | 3.37603e47 | 0.0463382 | 0.0231691 | − | 0.999732i | \(-0.492624\pi\) | ||||
0.0231691 | + | 0.999732i | \(0.492624\pi\) | |||||||
\(374\) | 4.92658e48 | − | 1.72408e48i | 0.642665 | − | 0.224904i | ||||
\(375\) | − | 2.38207e48i | − | 0.295366i | ||||||
\(376\) | −8.37631e48 | + | 1.33340e49i | −0.987379 | + | 1.57178i | ||||
\(377\) | 8.09548e48 | 0.907313 | ||||||||
\(378\) | 2.43175e48 | + | 6.94874e48i | 0.259164 | + | 0.740563i | ||||
\(379\) | − | 4.59288e48i | − | 0.465522i | −0.972534 | − | 0.232761i | \(-0.925224\pi\) | ||
0.972534 | − | 0.232761i | \(-0.0747760\pi\) | |||||||
\(380\) | −1.33422e49 | − | 1.67281e49i | −1.28629 | − | 1.61272i | ||||
\(381\) | 5.20559e48 | 0.477414 | ||||||||
\(382\) | 7.09765e48 | − | 2.48386e48i | 0.619314 | − | 0.216732i | ||||
\(383\) | − | 8.86033e48i | − | 0.735653i | −0.929894 | − | 0.367826i | \(-0.880102\pi\) | ||
0.929894 | − | 0.367826i | \(-0.119898\pi\) | |||||||
\(384\) | 6.73167e48 | + | 6.72830e48i | 0.531899 | + | 0.531633i | ||||
\(385\) | 7.07405e48 | 0.532003 | ||||||||
\(386\) | 2.36062e48 | + | 6.74550e48i | 0.168993 | + | 0.482898i | ||||
\(387\) | 2.04467e47i | 0.0139353i | ||||||||
\(388\) | −9.10860e48 | + | 7.26493e48i | −0.591083 | + | 0.471442i | ||||
\(389\) | −9.88367e48 | −0.610768 | −0.305384 | − | 0.952229i | \(-0.598785\pi\) | ||||
−0.305384 | + | 0.952229i | \(0.598785\pi\) | |||||||
\(390\) | 1.00932e49 | − | 3.53218e48i | 0.594023 | − | 0.207881i | ||||
\(391\) | 1.44847e49i | 0.811991i | ||||||||
\(392\) | 7.46838e48 | + | 4.69158e48i | 0.398833 | + | 0.250544i | ||||
\(393\) | 1.74465e49 | 0.887668 | ||||||||
\(394\) | 6.05629e48 | + | 1.73059e49i | 0.293615 | + | 0.839008i | ||||
\(395\) | 1.09769e49i | 0.507150i | ||||||||
\(396\) | 3.45263e48 | + | 4.32883e48i | 0.152034 | + | 0.190617i | ||||
\(397\) | 4.11516e48 | 0.172730 | 0.0863649 | − | 0.996264i | \(-0.472475\pi\) | ||||
0.0863649 | + | 0.996264i | \(0.472475\pi\) | |||||||
\(398\) | −3.39923e49 | + | 1.18958e49i | −1.36020 | + | 0.476008i | ||||
\(399\) | − | 2.26918e49i | − | 0.865731i | ||||||
\(400\) | 4.27069e48 | − | 1.87234e49i | 0.155367 | − | 0.681155i | ||||
\(401\) | −4.33161e49 | −1.50282 | −0.751409 | − | 0.659837i | \(-0.770625\pi\) | ||||
−0.751409 | + | 0.659837i | \(0.770625\pi\) | |||||||
\(402\) | 1.48029e48 | + | 4.22995e48i | 0.0489839 | + | 0.139972i | ||||
\(403\) | − | 9.94582e48i | − | 0.313939i | ||||||
\(404\) | 3.92766e48 | − | 3.13266e48i | 0.118274 | − | 0.0943339i | ||||
\(405\) | −1.70928e49 | −0.491098 | ||||||||
\(406\) | 3.53826e49 | − | 1.23823e49i | 0.970053 | − | 0.339475i | ||||
\(407\) | 1.46513e49i | 0.383339i | ||||||||
\(408\) | 1.94348e49 | − | 3.09377e49i | 0.485330 | − | 0.772582i | ||||
\(409\) | 4.65038e49 | 1.10852 | 0.554262 | − | 0.832342i | \(-0.313000\pi\) | ||||
0.554262 | + | 0.832342i | \(0.313000\pi\) | |||||||
\(410\) | −3.56540e49 | − | 1.01882e50i | −0.811363 | − | 2.31848i | ||||
\(411\) | 1.38135e49i | 0.300130i | ||||||||
\(412\) | 1.36170e49 | + | 1.70727e49i | 0.282511 | + | 0.354206i | ||||
\(413\) | −1.11463e49 | −0.220841 | ||||||||
\(414\) | −1.45035e49 | + | 5.07557e48i | −0.274451 | + | 0.0960457i | ||||
\(415\) | 9.49393e49i | 1.71606i | ||||||||
\(416\) | −3.69512e49 | + | 4.17008e48i | −0.638050 | + | 0.0720063i | ||||
\(417\) | −8.85588e49 | −1.46099 | ||||||||
\(418\) | −1.86135e49 | − | 5.31883e49i | −0.293413 | − | 0.838429i | ||||
\(419\) | − | 3.58312e49i | − | 0.539752i | −0.962895 | − | 0.269876i | \(-0.913017\pi\) | ||
0.962895 | − | 0.269876i | \(-0.0869827\pi\) | |||||||
\(420\) | 3.87116e49 | − | 3.08760e49i | 0.557319 | − | 0.444513i | ||||
\(421\) | 7.60449e49 | 1.04643 | 0.523215 | − | 0.852201i | \(-0.324732\pi\) | ||||
0.523215 | + | 0.852201i | \(0.324732\pi\) | |||||||
\(422\) | −5.78365e49 | + | 2.02402e49i | −0.760791 | + | 0.266243i | ||||
\(423\) | 6.41248e49i | 0.806416i | ||||||||
\(424\) | −3.67788e49 | − | 2.31042e49i | −0.442229 | − | 0.277805i | ||||
\(425\) | −7.37202e49 | −0.847612 | ||||||||
\(426\) | 4.36033e49 | + | 1.24597e50i | 0.479443 | + | 1.37001i | ||||
\(427\) | − | 2.38595e49i | − | 0.250918i | ||||||
\(428\) | 8.51314e49 | + | 1.06736e50i | 0.856363 | + | 1.07369i | ||||
\(429\) | 2.81619e49 | 0.271002 | ||||||||
\(430\) | 4.28590e48 | − | 1.49987e48i | 0.0394585 | − | 0.0138087i | ||||
\(431\) | − | 1.44601e50i | − | 1.27381i | −0.770944 | − | 0.636903i | \(-0.780215\pi\) | ||
0.770944 | − | 0.636903i | \(-0.219785\pi\) | |||||||
\(432\) | 1.24767e50 | + | 2.84584e49i | 1.05174 | + | 0.239894i | ||||
\(433\) | 4.40370e49 | 0.355261 | 0.177631 | − | 0.984097i | \(-0.443157\pi\) | ||||
0.177631 | + | 0.984097i | \(0.443157\pi\) | |||||||
\(434\) | −1.52125e49 | − | 4.34698e49i | −0.117462 | − | 0.335647i | ||||
\(435\) | 1.87386e50i | 1.38497i | ||||||||
\(436\) | 1.04723e50 | − | 8.35258e49i | 0.740965 | − | 0.590986i | ||||
\(437\) | 1.56380e50 | 1.05933 | ||||||||
\(438\) | −1.49875e50 | + | 5.24496e49i | −0.972125 | + | 0.340200i | ||||
\(439\) | − | 6.15859e49i | − | 0.382521i | −0.981539 | − | 0.191261i | \(-0.938742\pi\) | ||
0.981539 | − | 0.191261i | \(-0.0612576\pi\) | |||||||
\(440\) | 6.54110e49 | − | 1.04126e50i | 0.389090 | − | 0.619380i | ||||
\(441\) | 3.59164e49 | 0.204625 | ||||||||
\(442\) | 4.71508e49 | + | 1.34734e50i | 0.257315 | + | 0.735281i | ||||
\(443\) | − | 2.28103e50i | − | 1.19250i | −0.802797 | − | 0.596252i | \(-0.796656\pi\) | ||
0.802797 | − | 0.596252i | \(-0.203344\pi\) | |||||||
\(444\) | 6.39484e49 | + | 8.01770e49i | 0.320297 | + | 0.401581i | ||||
\(445\) | −7.72823e49 | −0.370886 | ||||||||
\(446\) | −2.79511e50 | + | 9.78162e49i | −1.28539 | + | 0.449830i | ||||
\(447\) | − | 5.54254e49i | − | 0.244268i | ||||||
\(448\) | −1.55123e50 | + | 7.47441e49i | −0.655229 | + | 0.315715i | ||||
\(449\) | 2.44924e49 | 0.0991632 | 0.0495816 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495816 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(450\) | −2.58322e49 | − | 7.38157e49i | −0.100259 | − | 0.286491i | ||||
\(451\) | − | 2.84267e50i | − | 1.05772i | ||||||
\(452\) | −3.94023e50 | + | 3.14269e50i | −1.40569 | + | 1.12117i | ||||
\(453\) | −1.26010e50 | −0.431061 | ||||||||
\(454\) | 1.96211e50 | − | 6.86651e49i | 0.643669 | − | 0.225255i | ||||
\(455\) | 1.93464e50i | 0.608671i | ||||||||
\(456\) | −3.34009e50 | − | 2.09822e50i | −1.00792 | − | 0.633168i | ||||
\(457\) | −1.46647e49 | −0.0424489 | −0.0212244 | − | 0.999775i | \(-0.506756\pi\) | ||||
−0.0212244 | + | 0.999775i | \(0.506756\pi\) | |||||||
\(458\) | 3.28823e49 | + | 9.39614e49i | 0.0913099 | + | 0.260919i | ||||
\(459\) | − | 4.91247e50i | − | 1.30876i | ||||||
\(460\) | 2.12781e50 | + | 2.66780e50i | 0.543918 | + | 0.681952i | ||||
\(461\) | −1.75960e50 | −0.431614 | −0.215807 | − | 0.976436i | \(-0.569238\pi\) | ||||
−0.215807 | + | 0.976436i | \(0.569238\pi\) | |||||||
\(462\) | 1.23086e50 | − | 4.30746e49i | 0.289742 | − | 0.101397i | ||||
\(463\) | 1.98320e50i | 0.448051i | 0.974583 | + | 0.224026i | \(0.0719200\pi\) | ||||
−0.974583 | + | 0.224026i | \(0.928080\pi\) | |||||||
\(464\) | 1.44909e50 | − | 6.35305e50i | 0.314234 | − | 1.37766i | ||||
\(465\) | 2.30216e50 | 0.479214 | ||||||||
\(466\) | −1.05443e50 | − | 3.01304e50i | −0.210710 | − | 0.602105i | ||||
\(467\) | 4.93368e50i | 0.946564i | 0.880911 | + | 0.473282i | \(0.156931\pi\) | ||||
−0.880911 | + | 0.473282i | \(0.843069\pi\) | |||||||
\(468\) | −1.18386e50 | + | 9.44238e49i | −0.218087 | + | 0.173944i | ||||
\(469\) | −8.10782e49 | −0.143423 | ||||||||
\(470\) | 1.34414e51 | − | 4.70388e50i | 2.28341 | − | 0.799093i | ||||
\(471\) | − | 3.34108e49i | − | 0.0545116i | ||||||
\(472\) | −1.03065e50 | + | 1.64067e50i | −0.161516 | + | 0.257112i | ||||
\(473\) | 1.19584e49 | 0.0180016 | ||||||||
\(474\) | 6.68396e49 | + | 1.90995e50i | 0.0966597 | + | 0.276206i | ||||
\(475\) | 7.95897e50i | 1.10580i | ||||||||
\(476\) | 4.12160e50 | + | 5.16757e50i | 0.550217 | + | 0.689849i | ||||
\(477\) | −1.76874e50 | −0.226890 | ||||||||
\(478\) | −6.99295e50 | + | 2.44722e50i | −0.862046 | + | 0.301677i | ||||
\(479\) | 7.53198e50i | 0.892349i | 0.894946 | + | 0.446174i | \(0.147214\pi\) | ||||
−0.894946 | + | 0.446174i | \(0.852786\pi\) | |||||||
\(480\) | −9.65248e49 | − | 8.55309e50i | −0.109915 | − | 0.973956i | ||||
\(481\) | −4.00690e50 | −0.438583 | ||||||||
\(482\) | 6.94410e49 | + | 1.98428e50i | 0.0730672 | + | 0.208790i | ||||
\(483\) | 3.61887e50i | 0.366081i | ||||||||
\(484\) | −5.50630e50 | + | 4.39177e50i | −0.535548 | + | 0.427148i | ||||
\(485\) | 1.05367e51 | 0.985399 | ||||||||
\(486\) | 8.34791e50 | − | 2.92139e50i | 0.750738 | − | 0.262725i | ||||
\(487\) | − | 5.87321e50i | − | 0.507955i | −0.967210 | − | 0.253978i | \(-0.918261\pi\) | ||
0.967210 | − | 0.253978i | \(-0.0817390\pi\) | |||||||
\(488\) | −3.51197e50 | − | 2.20619e50i | −0.292129 | − | 0.183513i | ||||
\(489\) | 1.58664e51 | 1.26944 | ||||||||
\(490\) | −2.63465e50 | − | 7.52853e50i | −0.202767 | − | 0.579408i | ||||
\(491\) | 1.41059e51i | 1.04437i | 0.852833 | + | 0.522184i | \(0.174883\pi\) | ||||
−0.852833 | + | 0.522184i | \(0.825117\pi\) | |||||||
\(492\) | −1.24073e51 | − | 1.55560e51i | −0.883775 | − | 1.10806i | ||||
\(493\) | −2.50140e51 | −1.71432 | ||||||||
\(494\) | 1.45461e51 | − | 5.09049e50i | 0.959257 | − | 0.335697i | ||||
\(495\) | − | 5.00754e50i | − | 0.317779i | ||||||
\(496\) | −7.80514e50 | − | 1.78030e50i | −0.476682 | − | 0.108728i | ||||
\(497\) | −2.38823e51 | −1.40380 | ||||||||
\(498\) | 5.78095e50 | + | 1.65191e51i | 0.327070 | + | 0.934607i | ||||
\(499\) | − | 1.49434e51i | − | 0.813840i | −0.913464 | − | 0.406920i | \(-0.866603\pi\) | ||
0.913464 | − | 0.406920i | \(-0.133397\pi\) | |||||||
\(500\) | 5.85656e50 | − | 4.67114e50i | 0.307052 | − | 0.244902i | ||||
\(501\) | 1.72255e51 | 0.869473 | ||||||||
\(502\) | −5.74705e50 | + | 2.01121e50i | −0.279302 | + | 0.0977433i | ||||
\(503\) | − | 1.77067e51i | − | 0.828603i | −0.910140 | − | 0.414302i | \(-0.864026\pi\) | ||
0.910140 | − | 0.414302i | \(-0.135974\pi\) | |||||||
\(504\) | −3.73002e50 | + | 5.93771e50i | −0.168086 | + | 0.267571i | ||||
\(505\) | −4.54347e50 | −0.197175 | ||||||||
\(506\) | 2.96847e50 | + | 8.48244e50i | 0.124072 | + | 0.354536i | ||||
\(507\) | − | 1.09786e51i | − | 0.441974i | ||||||
\(508\) | 1.02079e51 | + | 1.27985e51i | 0.395847 | + | 0.496304i | ||||
\(509\) | 3.68200e51 | 1.37545 | 0.687727 | − | 0.725970i | \(-0.258609\pi\) | ||||
0.687727 | + | 0.725970i | \(0.258609\pi\) | |||||||
\(510\) | −3.11869e51 | + | 1.09140e51i | −1.12238 | + | 0.392781i | ||||
\(511\) | − | 2.87276e51i | − | 0.996097i | ||||||
\(512\) | −3.34171e50 | + | 2.97444e51i | −0.111645 | + | 0.993748i | ||||
\(513\) | −5.30359e51 | −1.70742 | ||||||||
\(514\) | −4.26089e50 | − | 1.21755e51i | −0.132191 | − | 0.377736i | ||||
\(515\) | − | 1.97495e51i | − | 0.590499i | ||||||
\(516\) | 6.54402e49 | − | 5.21945e49i | 0.0188582 | − | 0.0150411i | ||||
\(517\) | 3.75038e51 | 1.04173 | ||||||||
\(518\) | −1.75128e51 | + | 6.12870e50i | −0.468911 | + | 0.164098i | ||||
\(519\) | 5.98762e50i | 0.154552i | ||||||||
\(520\) | 2.84767e51 | + | 1.78888e51i | 0.708640 | + | 0.445162i | ||||
\(521\) | 3.66204e51 | 0.878630 | 0.439315 | − | 0.898333i | \(-0.355221\pi\) | ||||
0.439315 | + | 0.898333i | \(0.355221\pi\) | |||||||
\(522\) | −8.76513e50 | − | 2.50464e51i | −0.202777 | − | 0.579437i | ||||
\(523\) | 6.86846e51i | 1.53224i | 0.642696 | + | 0.766121i | \(0.277816\pi\) | ||||
−0.642696 | + | 0.766121i | \(0.722184\pi\) | |||||||
\(524\) | 3.42119e51 | + | 4.28941e51i | 0.736009 | + | 0.922791i | ||||
\(525\) | −1.84183e51 | −0.382141 | ||||||||
\(526\) | −3.02370e51 | + | 1.05816e51i | −0.605076 | + | 0.211749i | ||||
\(527\) | 3.07313e51i | 0.593171i | ||||||||
\(528\) | 5.04096e50 | − | 2.21005e51i | 0.0938575 | − | 0.411488i | ||||
\(529\) | 3.07354e51 | 0.552053 | ||||||||
\(530\) | 1.29746e51 | + | 3.70751e51i | 0.224829 | + | 0.642451i | ||||
\(531\) | 7.89016e50i | 0.131914i | ||||||||
\(532\) | 5.57901e51 | − | 4.44976e51i | 0.899986 | − | 0.717820i | ||||
\(533\) | 7.77423e51 | 1.21015 | ||||||||
\(534\) | −1.34468e51 | + | 4.70579e50i | −0.201993 | + | 0.0706886i | ||||
\(535\) | − | 1.23471e52i | − | 1.78995i | ||||||
\(536\) | −7.49699e50 | + | 1.19342e51i | −0.104895 | + | 0.166980i | ||||
\(537\) | −4.03280e51 | −0.544623 | ||||||||
\(538\) | −2.15303e51 | − | 6.15232e51i | −0.280665 | − | 0.802002i | ||||
\(539\) | − | 2.10059e51i | − | 0.264335i | ||||||
\(540\) | −7.21643e51 | − | 9.04779e51i | −0.876680 | − | 1.09916i | ||||
\(541\) | −1.11502e52 | −1.30778 | −0.653889 | − | 0.756591i | \(-0.726864\pi\) | ||||
−0.653889 | + | 0.756591i | \(0.726864\pi\) | |||||||
\(542\) | 2.56288e51 | − | 8.96895e50i | 0.290230 | − | 0.101568i | ||||
\(543\) | 1.07251e52i | 1.17275i | ||||||||
\(544\) | 1.14174e52 | − | 1.28850e51i | 1.20556 | − | 0.136052i | ||||
\(545\) | −1.21142e52 | −1.23527 | ||||||||
\(546\) | 1.17802e51 | + | 3.36620e51i | 0.116009 | + | 0.331497i | ||||
\(547\) | − | 6.56803e50i | − | 0.0624706i | −0.999512 | − | 0.0312353i | \(-0.990056\pi\) | ||
0.999512 | − | 0.0312353i | \(-0.00994412\pi\) | |||||||
\(548\) | −3.39620e51 | + | 2.70877e51i | −0.312005 | + | 0.248853i | ||||
\(549\) | −1.68895e51 | −0.149879 | ||||||||
\(550\) | −4.31715e51 | + | 1.51081e51i | −0.370089 | + | 0.129515i | ||||
\(551\) | 2.70056e52i | 2.23652i | ||||||||
\(552\) | 5.32676e51 | + | 3.34623e51i | 0.426207 | + | 0.267740i | ||||
\(553\) | −3.66092e51 | −0.283017 | ||||||||
\(554\) | −5.71720e51 | − | 1.63370e52i | −0.427069 | − | 1.22035i | ||||
\(555\) | − | 9.27478e51i | − | 0.669479i | ||||||
\(556\) | −1.73660e52 | − | 2.17731e52i | −1.21138 | − | 1.51880i | ||||
\(557\) | −4.22504e51 | −0.284828 | −0.142414 | − | 0.989807i | \(-0.545486\pi\) | ||||
−0.142414 | + | 0.989807i | \(0.545486\pi\) | |||||||
\(558\) | −3.07712e51 | + | 1.07685e51i | −0.200491 | + | 0.0701628i | ||||
\(559\) | 3.27042e50i | 0.0205958i | ||||||||
\(560\) | 1.51824e52 | + | 3.46299e51i | 0.924202 | + | 0.210804i | ||||
\(561\) | −8.70166e51 | −0.512045 | ||||||||
\(562\) | −8.96802e50 | − | 2.56262e51i | −0.0510160 | − | 0.145779i | ||||
\(563\) | 9.30319e50i | 0.0511650i | 0.999673 | + | 0.0255825i | \(0.00814404\pi\) | ||||
−0.999673 | + | 0.0255825i | \(0.991856\pi\) | |||||||
\(564\) | 2.05233e52 | − | 1.63692e52i | 1.09130 | − | 0.870410i | ||||
\(565\) | 4.55801e52 | 2.34344 | ||||||||
\(566\) | −4.27147e51 | + | 1.49482e51i | −0.212356 | + | 0.0743152i | ||||
\(567\) | − | 5.70062e51i | − | 0.274059i | ||||||
\(568\) | −2.20830e52 | + | 3.51533e52i | −1.02669 | + | 1.63436i | ||||
\(569\) | 3.90477e52 | 1.75575 | 0.877875 | − | 0.478891i | \(-0.158961\pi\) | ||||
0.877875 | + | 0.478891i | \(0.158961\pi\) | |||||||
\(570\) | 1.17830e52 | + | 3.36699e52i | 0.512427 | + | 1.46427i | ||||
\(571\) | − | 2.40636e51i | − | 0.101222i | −0.998718 | − | 0.0506109i | \(-0.983883\pi\) | ||
0.998718 | − | 0.0506109i | \(-0.0161168\pi\) | |||||||
\(572\) | 5.52243e51 | + | 6.92389e51i | 0.224701 | + | 0.281725i | ||||
\(573\) | −1.25364e52 | −0.493439 | ||||||||
\(574\) | 3.39785e52 | − | 1.18910e52i | 1.29383 | − | 0.452784i | ||||
\(575\) | − | 1.26929e52i | − | 0.467598i | ||||||
\(576\) | 5.29094e51 | + | 1.09807e52i | 0.188584 | + | 0.391385i | ||||
\(577\) | −3.01356e52 | −1.03930 | −0.519649 | − | 0.854380i | \(-0.673937\pi\) | ||||
−0.519649 | + | 0.854380i | \(0.673937\pi\) | |||||||
\(578\) | −4.67084e51 | − | 1.33470e52i | −0.155871 | − | 0.445404i | ||||
\(579\) | − | 1.19144e52i | − | 0.384749i | ||||||
\(580\) | −4.60709e52 | + | 3.67457e52i | −1.43977 | + | 1.14835i | ||||
\(581\) | −3.16632e52 | −0.957654 | ||||||||
\(582\) | 1.83335e52 | − | 6.41591e51i | 0.536672 | − | 0.187811i | ||||
\(583\) | 1.03446e52i | 0.293096i | ||||||||
\(584\) | −4.22852e52 | − | 2.65633e52i | −1.15970 | − | 0.728513i | ||||
\(585\) | 1.36948e52 | 0.363575 | ||||||||
\(586\) | 1.71460e52 | + | 4.89948e52i | 0.440664 | + | 1.25920i | ||||
\(587\) | 1.52217e51i | 0.0378739i | 0.999821 | + | 0.0189369i | \(0.00602817\pi\) | ||||
−0.999821 | + | 0.0189369i | \(0.993972\pi\) | |||||||
\(588\) | −9.16839e51 | − | 1.14951e52i | −0.220864 | − | 0.276914i | ||||
\(589\) | 3.31781e52 | 0.773858 | ||||||||
\(590\) | 1.65388e52 | − | 5.78784e51i | 0.373522 | − | 0.130716i | ||||
\(591\) | − | 3.05669e52i | − | 0.668481i | ||||||
\(592\) | −7.17234e51 | + | 3.14448e52i | −0.151897 | + | 0.665941i | ||||
\(593\) | −5.13722e52 | −1.05363 | −0.526816 | − | 0.849979i | \(-0.676614\pi\) | ||||
−0.526816 | + | 0.849979i | \(0.676614\pi\) | |||||||
\(594\) | −1.00675e52 | − | 2.87681e52i | −0.199977 | − | 0.571437i | ||||
\(595\) | − | 5.97778e52i | − | 1.15005i | ||||||
\(596\) | 1.36269e52 | − | 1.08687e52i | 0.253933 | − | 0.202534i | ||||
\(597\) | 6.00395e52 | 1.08374 | ||||||||
\(598\) | −2.31981e52 | + | 8.11828e51i | −0.405629 | + | 0.141952i | ||||
\(599\) | − | 5.89348e52i | − | 0.998302i | −0.866515 | − | 0.499151i | \(-0.833645\pi\) | ||
0.866515 | − | 0.499151i | \(-0.166355\pi\) | |||||||
\(600\) | −1.70307e52 | + | 2.71106e52i | −0.279485 | + | 0.444904i | ||||
\(601\) | −4.61306e52 | −0.733456 | −0.366728 | − | 0.930328i | \(-0.619522\pi\) | ||||
−0.366728 | + | 0.930328i | \(0.619522\pi\) | |||||||
\(602\) | 5.00222e50 | + | 1.42939e51i | 0.00770601 | + | 0.0220200i | ||||
\(603\) | 5.73932e51i | 0.0856705i | ||||||||
\(604\) | −2.47100e52 | − | 3.09808e52i | −0.357413 | − | 0.448117i | ||||
\(605\) | 6.36962e52 | 0.892815 | ||||||||
\(606\) | −7.90547e51 | + | 2.76656e51i | −0.107386 | + | 0.0375803i | ||||
\(607\) | 2.29323e52i | 0.301899i | 0.988541 | + | 0.150950i | \(0.0482332\pi\) | ||||
−0.988541 | + | 0.150950i | \(0.951767\pi\) | |||||||
\(608\) | −1.39109e52 | − | 1.23265e53i | −0.177495 | − | 1.57279i | ||||
\(609\) | −6.24952e52 | −0.772891 | ||||||||
\(610\) | 1.23893e52 | + | 3.54025e52i | 0.148518 | + | 0.424392i | ||||
\(611\) | 1.02567e53i | 1.19185i | ||||||||
\(612\) | 3.65799e52 | − | 2.91758e52i | 0.412065 | − | 0.328659i | ||||
\(613\) | 9.31597e52 | 1.01737 | 0.508685 | − | 0.860953i | \(-0.330132\pi\) | ||||
0.508685 | + | 0.860953i | \(0.330132\pi\) | |||||||
\(614\) | −6.90313e51 | + | 2.41579e51i | −0.0730882 | + | 0.0255776i | ||||
\(615\) | 1.79950e53i | 1.84725i | ||||||||
\(616\) | 3.47270e52 | + | 2.18152e52i | 0.345648 | + | 0.217133i | ||||
\(617\) | −1.79910e53 | −1.73635 | −0.868175 | − | 0.496258i | \(-0.834707\pi\) | ||||
−0.868175 | + | 0.496258i | \(0.834707\pi\) | |||||||
\(618\) | −1.20257e52 | − | 3.43635e52i | −0.112546 | − | 0.321600i | ||||
\(619\) | 5.33732e52i | 0.484397i | 0.970227 | + | 0.242198i | \(0.0778685\pi\) | ||||
−0.970227 | + | 0.242198i | \(0.922132\pi\) | |||||||
\(620\) | 4.51444e52 | + | 5.66010e52i | 0.397340 | + | 0.498175i | ||||
\(621\) | 8.45814e52 | 0.721995 | ||||||||
\(622\) | 1.17470e53 | − | 4.11092e52i | 0.972544 | − | 0.340347i | ||||
\(623\) | − | 2.57744e52i | − | 0.206974i | ||||||
\(624\) | 6.04411e52 | + | 1.37862e52i | 0.470788 | + | 0.107384i | ||||
\(625\) | −1.60213e53 | −1.21054 | ||||||||
\(626\) | −1.83758e52 | − | 5.25091e52i | −0.134690 | − | 0.384877i | ||||
\(627\) | 9.39448e52i | 0.668020i | ||||||||
\(628\) | 8.21439e51 | − | 6.55171e51i | 0.0566685 | − | 0.0451983i | ||||
\(629\) | 1.23808e53 | 0.828680 | ||||||||
\(630\) | 5.98553e52 | − | 2.09467e52i | 0.388716 | − | 0.136033i | ||||
\(631\) | − | 8.87768e52i | − | 0.559425i | −0.960084 | − | 0.279712i | \(-0.909761\pi\) | ||
0.960084 | − | 0.279712i | \(-0.0902391\pi\) | |||||||
\(632\) | −3.38511e52 | + | 5.38865e52i | −0.206989 | + | 0.329500i | ||||
\(633\) | 1.02155e53 | 0.606161 | ||||||||
\(634\) | −8.00754e51 | − | 2.28816e52i | −0.0461108 | − | 0.131762i | ||||
\(635\) | − | 1.48051e53i | − | 0.827392i | ||||||
\(636\) | 4.51507e52 | + | 5.66089e52i | 0.244895 | + | 0.307043i | ||||
\(637\) | 5.74476e52 | 0.302429 | ||||||||
\(638\) | −1.46485e53 | + | 5.12633e52i | −0.748517 | + | 0.261947i | ||||
\(639\) | 1.69056e53i | 0.838523i | ||||||||
\(640\) | 1.91359e53 | − | 1.91454e53i | 0.921358 | − | 0.921818i | ||||
\(641\) | −1.08361e53 | −0.506487 | −0.253244 | − | 0.967403i | \(-0.581497\pi\) | ||||
−0.253244 | + | 0.967403i | \(0.581497\pi\) | |||||||
\(642\) | −7.51824e52 | − | 2.14834e53i | −0.341154 | − | 0.974851i | ||||
\(643\) | 4.88969e52i | 0.215413i | 0.994183 | + | 0.107707i | \(0.0343507\pi\) | ||||
−0.994183 | + | 0.107707i | \(0.965649\pi\) | |||||||
\(644\) | −8.89737e52 | + | 7.09645e52i | −0.380566 | + | 0.303536i | ||||
\(645\) | −7.57004e51 | −0.0314386 | ||||||||
\(646\) | −4.49456e53 | + | 1.57290e53i | −1.81247 | + | 0.634282i | ||||
\(647\) | − | 2.37610e53i | − | 0.930430i | −0.885198 | − | 0.465215i | \(-0.845977\pi\) | ||
0.885198 | − | 0.465215i | \(-0.154023\pi\) | |||||||
\(648\) | −8.39097e52 | − | 5.27114e52i | −0.319071 | − | 0.200438i | ||||
\(649\) | 4.61461e52 | 0.170406 | ||||||||
\(650\) | −4.13182e52 | − | 1.18067e53i | −0.148179 | − | 0.423423i | ||||
\(651\) | 7.67794e52i | 0.267427i | ||||||||
\(652\) | 3.11135e53 | + | 3.90093e53i | 1.05255 | + | 1.31967i | ||||
\(653\) | −2.60826e53 | −0.857039 | −0.428519 | − | 0.903533i | \(-0.640965\pi\) | ||||
−0.428519 | + | 0.903533i | \(0.640965\pi\) | |||||||
\(654\) | −2.10783e53 | + | 7.37645e52i | −0.672756 | + | 0.235435i | ||||
\(655\) | − | 4.96194e53i | − | 1.53839i | ||||||
\(656\) | 1.39159e53 | − | 6.10095e53i | 0.419118 | − | 1.83749i | ||||
\(657\) | −2.03355e53 | −0.594994 | ||||||||
\(658\) | 1.56879e53 | + | 4.48284e53i | 0.445937 | + | 1.27427i | ||||
\(659\) | 4.78396e51i | 0.0132119i | 0.999978 | + | 0.00660593i | \(0.00210275\pi\) | ||||
−0.999978 | + | 0.00660593i | \(0.997897\pi\) | |||||||
\(660\) | −1.60267e53 | + | 1.27828e53i | −0.430042 | + | 0.342997i | ||||
\(661\) | 6.97248e53 | 1.81786 | 0.908928 | − | 0.416953i | \(-0.136902\pi\) | ||||
0.908928 | + | 0.416953i | \(0.136902\pi\) | |||||||
\(662\) | −2.04456e53 | + | 7.15503e52i | −0.517961 | + | 0.181263i | ||||
\(663\) | − | 2.37976e53i | − | 0.585836i | ||||||
\(664\) | −2.92777e53 | + | 4.66063e53i | −0.700397 | + | 1.11494i | ||||
\(665\) | −6.45373e53 | −1.50037 | ||||||||
\(666\) | 4.33834e52 | + | 1.23969e53i | 0.0980198 | + | 0.280092i | ||||
\(667\) | − | 4.30684e53i | − | 0.945731i | ||||||
\(668\) | 3.37786e53 | + | 4.23508e53i | 0.720923 | + | 0.903876i | ||||
\(669\) | 4.93691e53 | 1.02414 | ||||||||
\(670\) | 1.20303e53 | − | 4.21008e52i | 0.242581 | − | 0.0848925i | ||||
\(671\) | 9.87791e52i | 0.193614i | ||||||||
\(672\) | 2.85254e53 | − | 3.21920e52i | 0.543520 | − | 0.0613383i | ||||
\(673\) | 6.26013e53 | 1.15957 | 0.579785 | − | 0.814770i | \(-0.303137\pi\) | ||||
0.579785 | + | 0.814770i | \(0.303137\pi\) | |||||||
\(674\) | 9.86097e52 | + | 2.81778e53i | 0.177575 | + | 0.507422i | ||||
\(675\) | 4.30479e53i | 0.753668i | ||||||||
\(676\) | 2.69921e53 | − | 2.15286e53i | 0.459462 | − | 0.366462i | ||||
\(677\) | −3.55253e52 | −0.0587968 | −0.0293984 | − | 0.999568i | \(-0.509359\pi\) | ||||
−0.0293984 | + | 0.999568i | \(0.509359\pi\) | |||||||
\(678\) | 7.93077e53 | − | 2.77542e53i | 1.27630 | − | 0.446646i | ||||
\(679\) | 3.51410e53i | 0.549906i | ||||||||
\(680\) | −8.79893e53 | − | 5.52742e53i | −1.33894 | − | 0.841111i | ||||
\(681\) | −3.46562e53 | −0.512844 | ||||||||
\(682\) | 6.29803e52 | + | 1.79967e53i | 0.0906362 | + | 0.258994i | ||||
\(683\) | 8.24124e53i | 1.15345i | 0.816938 | + | 0.576726i | \(0.195670\pi\) | ||||
−0.816938 | + | 0.576726i | \(0.804330\pi\) | |||||||
\(684\) | −3.14987e53 | − | 3.94923e53i | −0.428772 | − | 0.537585i | ||||
\(685\) | 3.92868e53 | 0.520146 | ||||||||
\(686\) | 7.84173e53 | − | 2.74425e53i | 1.00984 | − | 0.353400i | ||||
\(687\) | − | 1.65961e53i | − | 0.207887i | ||||||
\(688\) | 2.56651e52 | + | 5.85404e51i | 0.0312725 | + | 0.00713305i | ||||
\(689\) | −2.82907e53 | −0.335335 | ||||||||
\(690\) | −1.87914e53 | − | 5.36966e53i | −0.216684 | − | 0.619176i | ||||
\(691\) | − | 1.44384e54i | − | 1.61970i | −0.586635 | − | 0.809852i | \(-0.699548\pi\) | ||
0.586635 | − | 0.809852i | \(-0.300452\pi\) | |||||||
\(692\) | −1.47212e53 | + | 1.17415e53i | −0.160667 | + | 0.128146i | ||||
\(693\) | 1.67006e53 | 0.177338 | ||||||||
\(694\) | −1.34972e54 | + | 4.72342e53i | −1.39449 | + | 0.488007i | ||||
\(695\) | 2.51869e54i | 2.53199i | ||||||||
\(696\) | −5.77869e53 | + | 9.19892e53i | −0.565267 | + | 0.899832i | ||||
\(697\) | −2.40214e54 | −2.28652 | ||||||||
\(698\) | −4.81881e53 | − | 1.37698e54i | −0.446361 | − | 1.27548i | ||||
\(699\) | 5.32184e53i | 0.479728i | ||||||||
\(700\) | −3.61176e53 | − | 4.52834e53i | −0.316851 | − | 0.397261i | ||||
\(701\) | 2.24485e54 | 1.91666 | 0.958332 | − | 0.285657i | \(-0.0922119\pi\) | ||||
0.958332 | + | 0.285657i | \(0.0922119\pi\) | |||||||
\(702\) | 7.86759e53 | − | 2.75330e53i | 0.653788 | − | 0.228796i | ||||
\(703\) | − | 1.33666e54i | − | 1.08111i | ||||||
\(704\) | 6.42214e53 | − | 3.09444e53i | 0.505591 | − | 0.243613i | ||||
\(705\) | −2.37411e54 | −1.81931 | ||||||||
\(706\) | 1.45642e53 | + | 4.16173e53i | 0.108642 | + | 0.310445i | ||||
\(707\) | − | 1.51529e53i | − | 0.110034i | ||||||
\(708\) | 2.52527e53 | − | 2.01413e53i | 0.178515 | − | 0.142382i | ||||
\(709\) | −2.25437e53 | −0.155148 | −0.0775740 | − | 0.996987i | \(-0.524717\pi\) | ||||
−0.0775740 | + | 0.996987i | \(0.524717\pi\) | |||||||
\(710\) | 3.54364e54 | − | 1.24011e54i | 2.37433 | − | 0.830909i | ||||
\(711\) | 2.59147e53i | 0.169053i | ||||||||
\(712\) | −3.79384e53 | − | 2.38326e53i | −0.240968 | − | 0.151374i | ||||
\(713\) | −5.29123e53 | −0.327232 | ||||||||
\(714\) | −3.63993e53 | − | 1.04011e54i | −0.219193 | − | 0.626346i | ||||
\(715\) | − | 8.00947e53i | − | 0.469666i | ||||||
\(716\) | −7.90816e53 | − | 9.91507e53i | −0.451573 | − | 0.566172i | ||||
\(717\) | 1.23514e54 | 0.686836 | ||||||||
\(718\) | −9.86311e53 | + | 3.45165e53i | −0.534133 | + | 0.186923i | ||||
\(719\) | 1.91687e54i | 1.01098i | 0.862832 | + | 0.505492i | \(0.168689\pi\) | ||||
−0.862832 | + | 0.505492i | \(0.831311\pi\) | |||||||
\(720\) | 2.45136e53 | − | 1.07472e54i | 0.125919 | − | 0.552049i | ||||
\(721\) | 6.58667e53 | 0.329531 | ||||||||
\(722\) | 1.02028e54 | + | 2.91546e54i | 0.497179 | + | 1.42069i | ||||
\(723\) | − | 3.50478e53i | − | 0.166354i | ||||||
\(724\) | −2.63689e54 | + | 2.10316e54i | −1.21916 | + | 0.972386i | ||||
\(725\) | 2.19198e54 | 0.987219 | ||||||||
\(726\) | 1.10829e54 | − | 3.87853e53i | 0.486249 | − | 0.170165i | ||||
\(727\) | − | 5.13707e53i | − | 0.219564i | −0.993956 | − | 0.109782i | \(-0.964985\pi\) | ||
0.993956 | − | 0.109782i | \(-0.0350153\pi\) | |||||||
\(728\) | −5.96611e53 | + | 9.49726e53i | −0.248425 | + | 0.395460i | ||||
\(729\) | −2.40330e54 | −0.974956 | ||||||||
\(730\) | 1.49171e54 | + | 4.26258e54i | 0.589591 | + | 1.68476i | ||||
\(731\) | − | 1.01052e53i | − | 0.0389147i | ||||||
\(732\) | 4.31139e53 | + | 5.40552e53i | 0.161773 | + | 0.202828i | ||||
\(733\) | 5.27598e54 | 1.92898 | 0.964489 | − | 0.264121i | \(-0.0850820\pi\) | ||||
0.964489 | + | 0.264121i | \(0.0850820\pi\) | |||||||
\(734\) | −4.14915e54 | + | 1.45202e54i | −1.47820 | + | 0.517304i | ||||
\(735\) | 1.32974e54i | 0.461645i | ||||||||
\(736\) | 2.21850e53 | + | 1.96582e54i | 0.0750553 | + | 0.665067i | ||||
\(737\) | 3.35667e53 | 0.110669 | ||||||||
\(738\) | −8.41731e53 | − | 2.40525e54i | −0.270460 | − | 0.772840i | ||||
\(739\) | − | 4.03673e54i | − | 1.26411i | −0.774923 | − | 0.632056i | \(-0.782211\pi\) | ||
0.774923 | − | 0.632056i | \(-0.217789\pi\) | |||||||
\(740\) | 2.28030e54 | − | 1.81875e54i | 0.695968 | − | 0.555097i | ||||
\(741\) | −2.56923e54 | −0.764289 | ||||||||
\(742\) | −1.23649e54 | + | 4.32716e53i | −0.358523 | + | 0.125467i | ||||
\(743\) | − | 5.79693e54i | − | 1.63837i | −0.573533 | − | 0.819183i | \(-0.694428\pi\) | ||
0.573533 | − | 0.819183i | \(-0.305572\pi\) | |||||||
\(744\) | 1.13015e54 | + | 7.09949e53i | 0.311350 | + | 0.195588i | ||||
\(745\) | −1.57635e54 | −0.423333 | ||||||||
\(746\) | −5.84658e52 | − | 1.67066e53i | −0.0153061 | − | 0.0437373i | ||||
\(747\) | 2.24136e54i | 0.572031i | ||||||||
\(748\) | −1.70636e54 | − | 2.13939e54i | −0.424561 | − | 0.532305i | ||||
\(749\) | 4.11787e54 | 0.998890 | ||||||||
\(750\) | −1.17879e54 | + | 4.12524e53i | −0.278787 | + | 0.0975630i | ||||
\(751\) | − | 1.76746e54i | − | 0.407559i | −0.979017 | − | 0.203779i | \(-0.934677\pi\) | ||
0.979017 | − | 0.203779i | \(-0.0653226\pi\) | |||||||
\(752\) | 8.04907e54 | + | 1.83594e54i | 1.80970 | + | 0.412780i | ||||
\(753\) | 1.01508e54 | 0.222535 | ||||||||
\(754\) | −1.40197e54 | − | 4.00614e54i | −0.299697 | − | 0.856387i | ||||
\(755\) | 3.58382e54i | 0.747058i | ||||||||
\(756\) | 3.01753e54 | − | 2.40675e54i | 0.613391 | − | 0.489235i | ||||
\(757\) | −4.76640e54 | −0.944863 | −0.472431 | − | 0.881367i | \(-0.656624\pi\) | ||||
−0.472431 | + | 0.881367i | \(0.656624\pi\) | |||||||
\(758\) | −2.27283e54 | + | 7.95390e53i | −0.439393 | + | 0.153768i | ||||
\(759\) | − | 1.49823e54i | − | 0.282477i | ||||||
\(760\) | −5.96751e54 | + | 9.49950e54i | −1.09732 | + | 1.74680i | ||||
\(761\) | −5.99263e54 | −1.07475 | −0.537377 | − | 0.843342i | \(-0.680585\pi\) | ||||
−0.537377 | + | 0.843342i | \(0.680585\pi\) | |||||||
\(762\) | −9.01498e53 | − | 2.57604e54i | −0.157696 | − | 0.450617i | ||||
\(763\) | − | 4.04021e54i | − | 0.689346i | ||||||
\(764\) | −2.45833e54 | − | 3.08219e54i | −0.409134 | − | 0.512963i | ||||
\(765\) | −4.23152e54 | −0.686956 | ||||||||
\(766\) | −4.38463e54 | + | 1.53442e54i | −0.694362 | + | 0.242996i | ||||
\(767\) | 1.26202e54i | 0.194964i | ||||||||
\(768\) | 2.16379e54 | − | 4.49644e54i | 0.326100 | − | 0.677650i | ||||
\(769\) | 9.26319e53 | 0.136195 | 0.0680974 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680974 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(770\) | −1.22508e54 | − | 3.50067e54i | −0.175728 | − | 0.502143i | ||||
\(771\) | 2.15053e54i | 0.300962i | ||||||||
\(772\) | 2.92927e54 | − | 2.33636e54i | 0.399973 | − | 0.319015i | ||||
\(773\) | 2.05382e54 | 0.273623 | 0.136811 | − | 0.990597i | \(-0.456315\pi\) | ||||
0.136811 | + | 0.990597i | \(0.456315\pi\) | |||||||
\(774\) | 1.01183e53 | − | 3.54094e52i | 0.0131531 | − | 0.00460300i | ||||
\(775\) | − | 2.69298e54i | − | 0.341587i | ||||||
\(776\) | 5.17254e54 | + | 3.24935e54i | 0.640223 | + | 0.402183i | ||||
\(777\) | 3.09323e54 | 0.373605 | ||||||||
\(778\) | 1.71164e54 | + | 4.89104e54i | 0.201744 | + | 0.576486i | ||||
\(779\) | 2.59340e55i | 2.98303i | ||||||||
\(780\) | −3.49588e54 | − | 4.38305e54i | −0.392427 | − | 0.492016i | ||||
\(781\) | 9.88735e54 | 1.08320 | ||||||||
\(782\) | 7.16791e54 | − | 2.50845e54i | 0.766415 | − | 0.268211i | ||||
\(783\) | 1.46066e55i | 1.52432i | ||||||||
\(784\) | 1.02831e54 | − | 4.50829e54i | 0.104742 | − | 0.459205i | ||||
\(785\) | −9.50230e53 | −0.0944725 | ||||||||
\(786\) | −3.02137e54 | − | 8.63360e54i | −0.293208 | − | 0.837845i | ||||
\(787\) | − | 1.53224e55i | − | 1.45147i | −0.687975 | − | 0.725734i | \(-0.741500\pi\) | ||
0.687975 | − | 0.725734i | \(-0.258500\pi\) | |||||||
\(788\) | 7.51519e54 | − | 5.99404e54i | 0.694931 | − | 0.554270i | ||||
\(789\) | 5.34067e54 | 0.482095 | ||||||||
\(790\) | 5.43205e54 | − | 1.90097e54i | 0.478684 | − | 0.167518i | ||||
\(791\) | 1.52014e55i | 1.30777i | ||||||||
\(792\) | 1.54424e54 | − | 2.45823e54i | 0.129699 | − | 0.206464i | ||||
\(793\) | −2.70145e54 | −0.221516 | ||||||||
\(794\) | −7.12659e53 | − | 2.03643e54i | −0.0570548 | − | 0.163035i | ||||
\(795\) | − | 6.54845e54i | − | 0.511874i | ||||||
\(796\) | 1.17735e55 | + | 1.47613e55i | 0.898581 | + | 1.12662i | ||||
\(797\) | −1.54598e55 | −1.15211 | −0.576057 | − | 0.817409i | \(-0.695409\pi\) | ||||
−0.576057 | + | 0.817409i | \(0.695409\pi\) | |||||||
\(798\) | −1.12293e55 | + | 3.92974e54i | −0.817139 | + | 0.285962i | ||||
\(799\) | − | 3.16918e55i | − | 2.25194i | ||||||
\(800\) | −1.00051e55 | + | 1.12911e54i | −0.694242 | + | 0.0783478i | ||||
\(801\) | −1.82450e54 | −0.123631 | ||||||||
\(802\) | 7.50144e54 | + | 2.14354e55i | 0.496400 | + | 1.41847i | ||||
\(803\) | 1.18933e55i | 0.768613i | ||||||||
\(804\) | 1.83688e54 | − | 1.46508e54i | 0.115935 | − | 0.0924690i | ||||
\(805\) | 1.02924e55 | 0.634444 | ||||||||
\(806\) | −4.92180e54 | + | 1.72241e54i | −0.296318 | + | 0.103698i | ||||
\(807\) | 1.08666e55i | 0.638996i | ||||||||
\(808\) | −2.23042e54 | − | 1.40113e54i | −0.128106 | − | 0.0804754i | ||||
\(809\) | −1.04749e55 | −0.587664 | −0.293832 | − | 0.955857i | \(-0.594931\pi\) | ||||
−0.293832 | + | 0.955857i | \(0.594931\pi\) | |||||||
\(810\) | 2.96011e54 | + | 8.45855e54i | 0.162216 | + | 0.463533i | ||||
\(811\) | − | 5.70326e54i | − | 0.305300i | −0.988280 | − | 0.152650i | \(-0.951219\pi\) | ||
0.988280 | − | 0.152650i | \(-0.0487808\pi\) | |||||||
\(812\) | −1.22551e55 | − | 1.53651e55i | −0.640842 | − | 0.803472i | ||||
\(813\) | −4.52674e54 | −0.231241 | ||||||||
\(814\) | 7.25037e54 | − | 2.53730e54i | 0.361823 | − | 0.126622i | ||||
\(815\) | − | 4.51255e55i | − | 2.20002i | ||||||
\(816\) | −1.86755e55 | − | 4.25976e54i | −0.889529 | − | 0.202896i | ||||
\(817\) | −1.09097e54 | −0.0507686 | ||||||||
\(818\) | −8.05348e54 | − | 2.30129e55i | −0.366160 | − | 1.04631i | ||||
\(819\) | 4.56735e54i | 0.202894i | ||||||||
\(820\) | −4.42427e55 | + | 3.52875e55i | −1.92034 | + | 1.53164i | ||||
\(821\) | −2.76428e54 | −0.117236 | −0.0586182 | − | 0.998280i | \(-0.518669\pi\) | ||||
−0.0586182 | + | 0.998280i | \(0.518669\pi\) | |||||||
\(822\) | 6.83576e54 | − | 2.39221e54i | 0.283284 | − | 0.0991368i | ||||
\(823\) | 2.17970e54i | 0.0882675i | 0.999026 | + | 0.0441337i | \(0.0140528\pi\) | ||||
−0.999026 | + | 0.0441337i | \(0.985947\pi\) | |||||||
\(824\) | 6.09044e54 | − | 9.69518e54i | 0.241008 | − | 0.383653i | ||||
\(825\) | 7.62525e54 | 0.294869 | ||||||||
\(826\) | 1.93030e54 | + | 5.51586e54i | 0.0729465 | + | 0.208445i | ||||
\(827\) | − | 1.73081e55i | − | 0.639213i | −0.947550 | − | 0.319607i | \(-0.896449\pi\) | ||
0.947550 | − | 0.319607i | \(-0.103551\pi\) | |||||||
\(828\) | 5.02339e54 | + | 6.29821e54i | 0.181310 | + | 0.227322i | ||||
\(829\) | 4.08994e55 | 1.44272 | 0.721358 | − | 0.692562i | \(-0.243518\pi\) | ||||
0.721358 | + | 0.692562i | \(0.243518\pi\) | |||||||
\(830\) | 4.69817e55 | − | 1.64415e55i | 1.61974 | − | 0.566836i | ||||
\(831\) | 2.88554e55i | 0.972318i | ||||||||
\(832\) | 8.46277e54 | + | 1.75635e55i | 0.278721 | + | 0.578453i | ||||
\(833\) | −1.77506e55 | −0.571423 | ||||||||
\(834\) | 1.53365e55 | + | 4.38242e55i | 0.482583 | + | 1.37898i | ||||
\(835\) | − | 4.89909e55i | − | 1.50686i | ||||||
\(836\) | −2.30973e55 | + | 1.84222e55i | −0.694452 | + | 0.553888i | ||||
\(837\) | 1.79451e55 | 0.527428 | ||||||||
\(838\) | −1.77314e55 | + | 6.20520e54i | −0.509457 | + | 0.178287i | ||||
\(839\) | 8.42036e54i | 0.236512i | 0.992983 | + | 0.118256i | \(0.0377304\pi\) | ||||
−0.992983 | + | 0.118256i | \(0.962270\pi\) | |||||||
\(840\) | −2.19833e55 | − | 1.38098e55i | −0.603652 | − | 0.379210i | ||||
\(841\) | 3.71262e55 | 0.996681 | ||||||||
\(842\) | −1.31694e55 | − | 3.76316e55i | −0.345649 | − | 0.987696i | ||||
\(843\) | 4.52627e54i | 0.116149i | ||||||||
\(844\) | 2.00321e55 | + | 2.51158e55i | 0.502598 | + | 0.630146i | ||||
\(845\) | −3.12241e55 | −0.765972 | ||||||||
\(846\) | 3.17328e55 | − | 1.11051e55i | 0.761153 | − | 0.266370i | ||||
\(847\) | 2.12433e55i | 0.498239i | ||||||||
\(848\) | −5.06402e54 | + | 2.22016e55i | −0.116138 | + | 0.509169i | ||||
\(849\) | 7.54456e54 | 0.169195 | ||||||||
\(850\) | 1.27668e55 | + | 3.64812e55i | 0.279977 | + | 0.800036i | ||||
\(851\) | 2.13169e55i | 0.457154i | ||||||||
\(852\) | 5.41069e55 | − | 4.31551e55i | 1.13475 | − | 0.905065i | ||||
\(853\) | −7.89307e55 | −1.61888 | −0.809440 | − | 0.587203i | \(-0.800229\pi\) | ||||
−0.809440 | + | 0.587203i | \(0.800229\pi\) | |||||||
\(854\) | −1.18071e55 | + | 4.13196e54i | −0.236834 | + | 0.0828813i | ||||
\(855\) | 4.56842e55i | 0.896211i | ||||||||
\(856\) | 3.80763e55 | − | 6.06125e55i | 0.730556 | − | 1.16295i | ||||
\(857\) | 2.89450e55 | 0.543173 | 0.271587 | − | 0.962414i | \(-0.412452\pi\) | ||||
0.271587 | + | 0.962414i | \(0.412452\pi\) | |||||||
\(858\) | −4.87705e54 | − | 1.39362e55i | −0.0895155 | − | 0.255791i | ||||
\(859\) | 7.81007e55i | 1.40212i | 0.713102 | + | 0.701060i | \(0.247289\pi\) | ||||
−0.713102 | + | 0.701060i | \(0.752711\pi\) | |||||||
\(860\) | −1.48445e54 | − | 1.86117e54i | −0.0260673 | − | 0.0326826i | ||||
\(861\) | −6.00152e55 | −1.03086 | ||||||||
\(862\) | −7.15573e55 | + | 2.50419e55i | −1.20231 | + | 0.420754i | ||||
\(863\) | − | 3.27212e55i | − | 0.537804i | −0.963168 | − | 0.268902i | \(-0.913339\pi\) | ||
0.963168 | − | 0.268902i | \(-0.0866608\pi\) | |||||||
\(864\) | −7.52402e54 | − | 6.66705e55i | −0.120973 | − | 1.07195i | ||||
\(865\) | 1.70293e55 | 0.267849 | ||||||||
\(866\) | −7.62629e54 | − | 2.17922e55i | −0.117347 | − | 0.335321i | ||||
\(867\) | 2.35743e55i | 0.354876i | ||||||||
\(868\) | −1.88770e55 | + | 1.50561e55i | −0.278009 | + | 0.221737i | ||||
\(869\) | 1.51563e55 | 0.218383 | ||||||||
\(870\) | 9.27301e55 | − | 3.24514e55i | 1.30724 | − | 0.457475i | ||||
\(871\) | 9.17994e54i | 0.126618i | ||||||||
\(872\) | −5.94694e55 | − | 3.73582e55i | −0.802565 | − | 0.504165i | ||||
\(873\) | 2.48754e55 | 0.328473 | ||||||||
\(874\) | −2.70817e55 | − | 7.73861e55i | −0.349911 | − | 0.999875i | ||||
\(875\) | − | 2.25946e55i | − | 0.285662i | ||||||
\(876\) | 5.19105e55 | + | 6.50842e55i | 0.642210 | + | 0.805188i | ||||
\(877\) | −3.40864e55 | −0.412657 | −0.206328 | − | 0.978483i | \(-0.566152\pi\) | ||||
−0.206328 | + | 0.978483i | \(0.566152\pi\) | |||||||
\(878\) | −3.04764e55 | + | 1.06654e55i | −0.361051 | + | 0.126352i | ||||
\(879\) | − | 8.65380e55i | − | 1.00327i | ||||||
\(880\) | −6.28556e55 | − | 1.43369e55i | −0.713137 | − | 0.162662i | ||||
\(881\) | 7.74971e55 | 0.860485 | 0.430243 | − | 0.902713i | \(-0.358428\pi\) | ||||
0.430243 | + | 0.902713i | \(0.358428\pi\) | |||||||
\(882\) | −6.21996e54 | − | 1.77736e55i | −0.0675903 | − | 0.193140i | ||||
\(883\) | − | 1.28708e56i | − | 1.36884i | −0.729088 | − | 0.684420i | \(-0.760055\pi\) | ||
0.729088 | − | 0.684420i | \(-0.239945\pi\) | |||||||
\(884\) | 5.85089e55 | − | 4.66661e55i | 0.609016 | − | 0.485745i | ||||
\(885\) | −2.92120e55 | −0.297604 | ||||||||
\(886\) | −1.12879e56 | + | 3.95026e55i | −1.12557 | + | 0.393899i | ||||
\(887\) | 1.67612e56i | 1.63590i | 0.575287 | + | 0.817952i | \(0.304890\pi\) | ||||
−0.575287 | + | 0.817952i | \(0.695110\pi\) | |||||||
\(888\) | 2.86019e55 | − | 4.55305e55i | 0.273243 | − | 0.434967i | ||||
\(889\) | 4.93766e55 | 0.461729 | ||||||||
\(890\) | 1.33837e55 | + | 3.82440e55i | 0.122508 | + | 0.350068i | ||||
\(891\) | 2.36008e55i | 0.211471i | ||||||||
\(892\) | 9.68108e55 | + | 1.21379e56i | 0.849164 | + | 1.06466i | ||||
\(893\) | −3.42150e56 | −2.93791 | ||||||||
\(894\) | −2.74279e55 | + | 9.59852e54i | −0.230557 | + | 0.0806847i | ||||
\(895\) | 1.14696e56i | 0.943869i | ||||||||
\(896\) | 6.38519e55 | + | 6.38200e55i | 0.514425 | + | 0.514167i | ||||
\(897\) | 4.09740e55 | 0.323186 | ||||||||
\(898\) | −4.24156e54 | − | 1.21203e55i | −0.0327549 | − | 0.0935973i | ||||
\(899\) | − | 9.13757e55i | − | 0.690870i | ||||||
\(900\) | −3.20549e55 | + | 2.55667e55i | −0.237294 | + | 0.189263i | ||||
\(901\) | 8.74147e55 | 0.633597 | ||||||||
\(902\) | −1.40673e56 | + | 4.92291e55i | −0.998355 | + | 0.349380i | ||||
\(903\) | − | 2.52469e54i | − | 0.0175445i | ||||||
\(904\) | 2.23756e56 | + | 1.40562e56i | 1.52256 | + | 0.956459i | ||||
\(905\) | 3.05032e56 | 2.03246 | ||||||||
\(906\) | 2.18222e55 | + | 6.23572e55i | 0.142385 | + | 0.406866i | ||||
\(907\) | − | 8.02498e55i | − | 0.512750i | −0.966577 | − | 0.256375i | \(-0.917472\pi\) | ||
0.966577 | − | 0.256375i | \(-0.0825281\pi\) | |||||||
\(908\) | −6.79593e55 | − | 8.52058e55i | −0.425224 | − | 0.533136i | ||||
\(909\) | −1.07264e55 | −0.0657262 | ||||||||
\(910\) | 9.57375e55 | − | 3.35038e55i | 0.574508 | − | 0.201052i | ||||
\(911\) | − | 2.48458e56i | − | 1.46017i | −0.683357 | − | 0.730084i | \(-0.739481\pi\) | ||
0.683357 | − | 0.730084i | \(-0.260519\pi\) | |||||||
\(912\) | −4.59892e55 | + | 2.01625e56i | −0.264700 | + | 1.16049i | ||||
\(913\) | 1.31087e56 | 0.738949 | ||||||||
\(914\) | 2.53962e54 | + | 7.25700e54i | 0.0140214 | + | 0.0400663i | ||||
\(915\) | − | 6.25304e55i | − | 0.338135i | ||||||
\(916\) | 4.08032e55 | − | 3.25443e55i | 0.216113 | − | 0.172370i | ||||
\(917\) | 1.65486e56 | 0.858506 | ||||||||
\(918\) | −2.43099e56 | + | 8.50736e55i | −1.23530 | + | 0.432299i | ||||
\(919\) | − | 2.64953e56i | − | 1.31879i | −0.751799 | − | 0.659393i | \(-0.770814\pi\) | ||
0.751799 | − | 0.659393i | \(-0.229186\pi\) | |||||||
\(920\) | 9.51695e55 | − | 1.51497e56i | 0.464012 | − | 0.738646i | ||||
\(921\) | 1.21928e55 | 0.0582331 | ||||||||
\(922\) | 3.04725e55 | + | 8.70756e55i | 0.142568 | + | 0.407389i | ||||
\(923\) | 2.70403e56i | 1.23931i | ||||||||
\(924\) | −4.26318e55 | − | 5.34508e55i | −0.191411 | − | 0.239986i | ||||
\(925\) | −1.08493e56 | −0.477209 | ||||||||
\(926\) | 9.81408e55 | − | 3.43449e55i | 0.422903 | − | 0.147997i | ||||
\(927\) | − | 4.66253e55i | − | 0.196837i | ||||||
\(928\) | −3.39483e56 | + | 3.83119e55i | −1.40413 | + | 0.158461i | ||||
\(929\) | −3.18645e56 | −1.29125 | −0.645623 | − | 0.763657i | \(-0.723402\pi\) | ||||
−0.645623 | + | 0.763657i | \(0.723402\pi\) | |||||||
\(930\) | −3.98686e55 | − | 1.13925e56i | −0.158291 | − | 0.452317i | ||||
\(931\) | 1.91639e56i | 0.745486i | ||||||||
\(932\) | −1.30843e56 | + | 1.04359e56i | −0.498710 | + | 0.397766i | ||||
\(933\) | −2.07483e56 | −0.774876 | ||||||||
\(934\) | 2.44148e56 | − | 8.54409e55i | 0.893435 | − | 0.312662i | ||||
\(935\) | 2.47483e56i | 0.887409i | ||||||||
\(936\) | 6.72286e55 | + | 4.22325e55i | 0.236218 | + | 0.148390i | ||||
\(937\) | 4.73831e55 | 0.163144 | 0.0815721 | − | 0.996667i | \(-0.474006\pi\) | ||||
0.0815721 | + | 0.996667i | \(0.474006\pi\) | |||||||
\(938\) | 1.40410e55 | + | 4.01224e55i | 0.0473746 | + | 0.135373i | ||||
\(939\) | 9.27451e55i | 0.306651i | ||||||||
\(940\) | −4.65553e56 | − | 5.83700e56i | −1.50848 | − | 1.89130i | ||||
\(941\) | 7.71396e55 | 0.244948 | 0.122474 | − | 0.992472i | \(-0.460917\pi\) | ||||
0.122474 | + | 0.992472i | \(0.460917\pi\) | |||||||
\(942\) | −1.65337e55 | + | 5.78604e54i | −0.0514520 | + | 0.0180059i | ||||
\(943\) | − | 4.13593e56i | − | 1.26140i | ||||||
\(944\) | 9.90388e55 | + | 2.25901e55i | 0.296031 | + | 0.0675227i | ||||
\(945\) | −3.49064e56 | −1.02259 | ||||||||
\(946\) | −2.07094e54 | − | 5.91773e54i | −0.00594615 | − | 0.0169912i | ||||
\(947\) | 6.04705e55i | 0.170174i | 0.996374 | + | 0.0850872i | \(0.0271169\pi\) | ||||
−0.996374 | + | 0.0850872i | \(0.972883\pi\) | |||||||
\(948\) | 8.29405e55 | − | 6.61526e55i | 0.228775 | − | 0.182469i | ||||
\(949\) | −3.25263e56 | −0.879379 | ||||||||
\(950\) | 3.93858e56 | − | 1.37833e56i | 1.04374 | − | 0.365261i | ||||
\(951\) | 4.04151e55i | 0.104982i | ||||||||
\(952\) | 1.84345e56 | − | 2.93453e56i | 0.469385 | − | 0.747200i | ||||
\(953\) | 2.68288e56 | 0.669633 | 0.334817 | − | 0.942283i | \(-0.391326\pi\) | ||||
0.334817 | + | 0.942283i | \(0.391326\pi\) | |||||||
\(954\) | 3.06309e55 | + | 8.75280e55i | 0.0749446 | + | 0.214155i | ||||
\(955\) | 3.56544e56i | 0.855164i | ||||||||
\(956\) | 2.42206e56 | + | 3.03673e56i | 0.569489 | + | 0.714013i | ||||
\(957\) | 2.58733e56 | 0.596382 | ||||||||
\(958\) | 3.72728e56 | − | 1.30438e56i | 0.842263 | − | 0.294754i | ||||
\(959\) | 1.31025e56i | 0.290270i | ||||||||
\(960\) | −4.06543e56 | + | 1.95888e56i | −0.882983 | + | 0.425455i | ||||
\(961\) | 3.57357e56 | 0.760953 | ||||||||
\(962\) | 6.93911e55 | + | 1.98286e56i | 0.144870 | + | 0.413966i | ||||
\(963\) | − | 2.91493e56i | − | 0.596663i | ||||||
\(964\) | 8.61686e55 | − | 6.87272e55i | 0.172936 | − | 0.137932i | ||||
\(965\) | −3.38854e56 | −0.666798 | ||||||||
\(966\) | 1.79084e56 | − | 6.26712e55i | 0.345534 | − | 0.120921i | ||||
\(967\) | 8.89441e56i | 1.68273i | 0.540469 | + | 0.841364i | \(0.318247\pi\) | ||||
−0.540469 | + | 0.841364i | \(0.681753\pi\) | |||||||
\(968\) | 3.12689e56 | + | 1.96429e56i | 0.580071 | + | 0.364396i | ||||
\(969\) | 7.93861e56 | 1.44408 | ||||||||
\(970\) | −1.82474e56 | − | 5.21420e56i | −0.325490 | − | 0.930090i | ||||
\(971\) | 5.57103e56i | 0.974473i | 0.873270 | + | 0.487236i | \(0.161995\pi\) | ||||
−0.873270 | + | 0.487236i | \(0.838005\pi\) | |||||||
\(972\) | −2.89137e56 | − | 3.62513e56i | −0.495957 | − | 0.621819i | ||||
\(973\) | −8.40007e56 | −1.41299 | ||||||||
\(974\) | −2.90642e56 | + | 1.01712e56i | −0.479444 | + | 0.167784i | ||||
\(975\) | 2.08538e56i | 0.337363i | ||||||||
\(976\) | −4.83558e55 | + | 2.12000e56i | −0.0767188 | + | 0.336349i | ||||
\(977\) | 1.05425e57 | 1.64039 | 0.820193 | − | 0.572087i | \(-0.193866\pi\) | ||||
0.820193 | + | 0.572087i | \(0.193866\pi\) | |||||||
\(978\) | −2.74774e56 | − | 7.85168e56i | −0.419311 | − | 1.19819i | ||||
\(979\) | 1.06707e56i | 0.159706i | ||||||||
\(980\) | −3.26931e56 | + | 2.60757e56i | −0.479911 | + | 0.382772i | ||||
\(981\) | −2.85996e56 | −0.411764 | ||||||||
\(982\) | 6.98047e56 | − | 2.44285e56i | 0.985749 | − | 0.344968i | ||||
\(983\) | − | 1.19742e57i | − | 1.65855i | −0.558838 | − | 0.829277i | \(-0.688753\pi\) | ||
0.558838 | − | 0.829277i | \(-0.311247\pi\) | |||||||
\(984\) | −5.54938e56 | + | 8.83388e56i | −0.753941 | + | 1.20018i | ||||
\(985\) | −8.69348e56 | −1.15852 | ||||||||
\(986\) | 4.33190e56 | + | 1.23785e57i | 0.566262 | + | 1.61810i | ||||
\(987\) | − | 7.91790e56i | − | 1.01528i | ||||||
\(988\) | −5.03816e56 | − | 6.31673e56i | −0.633710 | − | 0.794530i | ||||
\(989\) | 1.73988e55 | 0.0214679 | ||||||||
\(990\) | −2.47803e56 | + | 8.67200e55i | −0.299943 | + | 0.104967i | ||||
\(991\) | 6.67252e56i | 0.792302i | 0.918185 | + | 0.396151i | \(0.129654\pi\) | ||||
−0.918185 | + | 0.396151i | \(0.870346\pi\) | |||||||
\(992\) | 4.70686e55 | + | 4.17077e56i | 0.0548289 | + | 0.485841i | ||||
\(993\) | 3.61124e56 | 0.412686 | ||||||||
\(994\) | 4.13591e56 | + | 1.18184e57i | 0.463692 | + | 1.32500i | ||||
\(995\) | − | 1.70757e57i | − | 1.87820i | ||||||
\(996\) | 7.17351e56 | − | 5.72152e56i | 0.774113 | − | 0.617425i | ||||
\(997\) | 5.88054e55 | 0.0622600 | 0.0311300 | − | 0.999515i | \(-0.490089\pi\) | ||||
0.0311300 | + | 0.999515i | \(0.490089\pi\) | |||||||
\(998\) | −7.39489e56 | + | 2.58788e56i | −0.768160 | + | 0.268822i | ||||
\(999\) | − | 7.22960e56i | − | 0.736835i |
(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 | 4.39.b.a.3.7 | ✓ | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.8 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.7 | ✓ | 18 | 1.1 | even | 1 | trivial | |
4.39.b.a.3.8 | yes | 18 | 4.3 | odd | 2 | inner |