Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,16,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(11.4154804080\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 6354 x^{12} + 136110 x^{11} + 41390651 x^{10} - 1368564777 x^{9} + \cdots + 24\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.13 | ||
Root | \(-93.3164 + 5.91227i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.16.b.a.5.14 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 180.633 | − | 11.8245i | 0.997864 | − | 0.0653220i | ||||
\(3\) | − | 1858.96i | − | 0.490750i | −0.969428 | − | 0.245375i | \(-0.921089\pi\) | ||
0.969428 | − | 0.245375i | \(-0.0789111\pi\) | |||||||
\(4\) | 32488.4 | − | 4271.80i | 0.991466 | − | 0.130365i | ||||
\(5\) | 290191.i | 1.66115i | 0.556907 | + | 0.830575i | \(0.311988\pi\) | ||||
−0.556907 | + | 0.830575i | \(0.688012\pi\) | |||||||
\(6\) | −21981.3 | − | 335789.i | −0.0320568 | − | 0.489702i | ||||
\(7\) | 1.26027e6 | 0.578402 | 0.289201 | − | 0.957268i | \(-0.406610\pi\) | ||||
0.289201 | + | 0.957268i | \(0.406610\pi\) | |||||||
\(8\) | 5.81795e6 | − | 1.15579e6i | 0.980833 | − | 0.194851i | ||||
\(9\) | 1.08932e7 | 0.759164 | ||||||||
\(10\) | 3.43137e6 | + | 5.24180e7i | 0.108510 | + | 1.65760i | ||||
\(11\) | − | 9.81513e7i | − | 1.51863i | −0.650725 | − | 0.759314i | \(-0.725535\pi\) | ||
0.650725 | − | 0.759314i | \(-0.274465\pi\) | |||||||
\(12\) | −7.94110e6 | − | 6.03946e7i | −0.0639766 | − | 0.486562i | ||||
\(13\) | 3.04482e8i | 1.34582i | 0.739726 | + | 0.672908i | \(0.234955\pi\) | ||||
−0.739726 | + | 0.672908i | \(0.765045\pi\) | |||||||
\(14\) | 2.27647e8 | − | 1.49022e7i | 0.577166 | − | 0.0377824i | ||||
\(15\) | 5.39453e8 | 0.815210 | ||||||||
\(16\) | 1.03725e9 | − | 2.77567e8i | 0.966010 | − | 0.258505i | ||||
\(17\) | 6.26054e8 | 0.370037 | 0.185018 | − | 0.982735i | \(-0.440766\pi\) | ||||
0.185018 | + | 0.982735i | \(0.440766\pi\) | |||||||
\(18\) | 1.96766e9 | − | 1.28807e8i | 0.757543 | − | 0.0495901i | ||||
\(19\) | 5.70219e8i | 0.146349i | 0.997319 | + | 0.0731745i | \(0.0233130\pi\) | ||||
−0.997319 | + | 0.0731745i | \(0.976687\pi\) | |||||||
\(20\) | 1.23964e9 | + | 9.42783e9i | 0.216556 | + | 1.64697i | ||||
\(21\) | − | 2.34280e9i | − | 0.283851i | ||||||
\(22\) | −1.16059e9 | − | 1.77293e10i | −0.0991997 | − | 1.51538i | ||||
\(23\) | −2.03517e10 | −1.24636 | −0.623178 | − | 0.782080i | \(-0.714159\pi\) | ||||
−0.623178 | + | 0.782080i | \(0.714159\pi\) | |||||||
\(24\) | −2.14856e9 | − | 1.08153e10i | −0.0956232 | − | 0.481344i | ||||
\(25\) | −5.36932e10 | −1.75942 | ||||||||
\(26\) | 3.60035e9 | + | 5.49993e10i | 0.0879114 | + | 1.34294i | ||||
\(27\) | − | 4.69240e10i | − | 0.863310i | ||||||
\(28\) | 4.09442e10 | − | 5.38364e9i | 0.573466 | − | 0.0754033i | ||||
\(29\) | 3.55070e10i | 0.382234i | 0.981567 | + | 0.191117i | \(0.0612110\pi\) | ||||
−0.981567 | + | 0.191117i | \(0.938789\pi\) | |||||||
\(30\) | 9.74429e10 | − | 6.37879e9i | 0.813469 | − | 0.0532511i | ||||
\(31\) | −1.37553e11 | −0.897958 | −0.448979 | − | 0.893542i | \(-0.648212\pi\) | ||||
−0.448979 | + | 0.893542i | \(0.648212\pi\) | |||||||
\(32\) | 1.84078e11 | − | 6.24027e10i | 0.947061 | − | 0.321054i | ||||
\(33\) | −1.82459e11 | −0.745267 | ||||||||
\(34\) | 1.13086e11 | − | 7.40280e9i | 0.369247 | − | 0.0241715i | ||||
\(35\) | 3.65720e11i | 0.960812i | ||||||||
\(36\) | 3.53901e11 | − | 4.65334e10i | 0.752685 | − | 0.0989684i | ||||
\(37\) | − | 6.95044e11i | − | 1.20365i | −0.798629 | − | 0.601824i | \(-0.794441\pi\) | ||
0.798629 | − | 0.601824i | \(-0.205559\pi\) | |||||||
\(38\) | 6.74257e9 | + | 1.03000e11i | 0.00955980 | + | 0.146036i | ||||
\(39\) | 5.66019e11 | 0.660460 | ||||||||
\(40\) | 3.35399e11 | + | 1.68832e12i | 0.323677 | + | 1.62931i | ||||
\(41\) | −6.94552e11 | −0.556962 | −0.278481 | − | 0.960442i | \(-0.589831\pi\) | ||||
−0.278481 | + | 0.960442i | \(0.589831\pi\) | |||||||
\(42\) | −2.77025e10 | − | 4.23186e11i | −0.0185417 | − | 0.283245i | ||||
\(43\) | − | 1.01781e12i | − | 0.571025i | −0.958375 | − | 0.285513i | \(-0.907836\pi\) | ||
0.958375 | − | 0.285513i | \(-0.0921639\pi\) | |||||||
\(44\) | −4.19283e11 | − | 3.18878e12i | −0.197976 | − | 1.50567i | ||||
\(45\) | 3.16110e12i | 1.26108i | ||||||||
\(46\) | −3.67619e12 | + | 2.40650e11i | −1.24370 | + | 0.0814145i | ||||
\(47\) | 2.94174e12 | 0.846974 | 0.423487 | − | 0.905902i | \(-0.360806\pi\) | ||||
0.423487 | + | 0.905902i | \(0.360806\pi\) | |||||||
\(48\) | −5.15987e11 | − | 1.92820e12i | −0.126861 | − | 0.474070i | ||||
\(49\) | −3.15927e12 | −0.665451 | ||||||||
\(50\) | −9.69874e12 | + | 6.34897e11i | −1.75566 | + | 0.114929i | ||||
\(51\) | − | 1.16381e12i | − | 0.181596i | ||||||
\(52\) | 1.30068e12 | + | 9.89211e12i | 0.175447 | + | 1.33433i | ||||
\(53\) | − | 5.17445e12i | − | 0.605056i | −0.953141 | − | 0.302528i | \(-0.902169\pi\) | ||
0.953141 | − | 0.302528i | \(-0.0978305\pi\) | |||||||
\(54\) | −5.54855e11 | − | 8.47601e12i | −0.0563931 | − | 0.861467i | ||||
\(55\) | 2.84826e13 | 2.52267 | ||||||||
\(56\) | 7.33221e12 | − | 1.45661e12i | 0.567316 | − | 0.112702i | ||||
\(57\) | 1.06001e12 | 0.0718208 | ||||||||
\(58\) | 4.19854e11 | + | 6.41373e12i | 0.0249683 | + | 0.381417i | ||||
\(59\) | 2.55439e13i | 1.33628i | 0.744035 | + | 0.668140i | \(0.232909\pi\) | ||||
−0.744035 | + | 0.668140i | \(0.767091\pi\) | |||||||
\(60\) | 1.75259e13 | − | 2.30443e12i | 0.808253 | − | 0.106275i | ||||
\(61\) | − | 8.74172e12i | − | 0.356142i | −0.984018 | − | 0.178071i | \(-0.943014\pi\) | ||
0.984018 | − | 0.178071i | \(-0.0569856\pi\) | |||||||
\(62\) | −2.48465e13 | + | 1.62650e12i | −0.896040 | + | 0.0586564i | ||||
\(63\) | 1.37284e13 | 0.439102 | ||||||||
\(64\) | 3.25127e13 | − | 1.34486e13i | 0.924066 | − | 0.382233i | ||||
\(65\) | −8.83578e13 | −2.23560 | ||||||||
\(66\) | −3.29581e13 | + | 2.15750e12i | −0.743675 | + | 0.0486823i | ||||
\(67\) | − | 6.72032e13i | − | 1.35466i | −0.735681 | − | 0.677328i | \(-0.763138\pi\) | ||
0.735681 | − | 0.677328i | \(-0.236862\pi\) | |||||||
\(68\) | 2.03395e13 | − | 2.67438e12i | 0.366879 | − | 0.0482398i | ||||
\(69\) | 3.78330e13i | 0.611650i | ||||||||
\(70\) | 4.32447e12 | + | 6.60610e13i | 0.0627621 | + | 0.958760i | ||||
\(71\) | −2.21325e13 | −0.288797 | −0.144399 | − | 0.989520i | \(-0.546125\pi\) | ||||
−0.144399 | + | 0.989520i | \(0.546125\pi\) | |||||||
\(72\) | 6.33759e13 | − | 1.25902e13i | 0.744613 | − | 0.147924i | ||||
\(73\) | −1.27473e14 | −1.35050 | −0.675252 | − | 0.737587i | \(-0.735965\pi\) | ||||
−0.675252 | + | 0.737587i | \(0.735965\pi\) | |||||||
\(74\) | −8.21858e12 | − | 1.25548e14i | −0.0786247 | − | 1.20108i | ||||
\(75\) | 9.98134e13i | 0.863435i | ||||||||
\(76\) | 2.43586e12 | + | 1.85255e13i | 0.0190788 | + | 0.145100i | ||||
\(77\) | − | 1.23698e14i | − | 0.878377i | ||||||
\(78\) | 1.02242e14 | − | 6.69292e12i | 0.659049 | − | 0.0431425i | ||||
\(79\) | 7.24152e13 | 0.424255 | 0.212127 | − | 0.977242i | \(-0.431961\pi\) | ||||
0.212127 | + | 0.977242i | \(0.431961\pi\) | |||||||
\(80\) | 8.05475e13 | + | 3.00999e14i | 0.429415 | + | 1.60469i | ||||
\(81\) | 6.90753e13 | 0.335494 | ||||||||
\(82\) | −1.25459e14 | + | 8.21276e12i | −0.555773 | + | 0.0363819i | ||||
\(83\) | − | 1.55075e14i | − | 0.627274i | −0.949543 | − | 0.313637i | \(-0.898453\pi\) | ||
0.949543 | − | 0.313637i | \(-0.101547\pi\) | |||||||
\(84\) | −1.00080e13 | − | 7.61137e13i | −0.0370042 | − | 0.281429i | ||||
\(85\) | 1.81675e14i | 0.614686i | ||||||||
\(86\) | −1.20352e13 | − | 1.83851e14i | −0.0373005 | − | 0.569806i | ||||
\(87\) | 6.60061e13 | 0.187581 | ||||||||
\(88\) | −1.13442e14 | − | 5.71040e14i | −0.295906 | − | 1.48952i | ||||
\(89\) | 6.61821e14 | 1.58604 | 0.793022 | − | 0.609192i | \(-0.208506\pi\) | ||||
0.793022 | + | 0.609192i | \(0.208506\pi\) | |||||||
\(90\) | 3.73786e13 | + | 5.70998e14i | 0.0823766 | + | 1.25839i | ||||
\(91\) | 3.83730e14i | 0.778423i | ||||||||
\(92\) | −6.61194e14 | + | 8.69385e13i | −1.23572 | + | 0.162481i | ||||
\(93\) | 2.55705e14i | 0.440673i | ||||||||
\(94\) | 5.31374e14 | − | 3.47847e13i | 0.845165 | − | 0.0553260i | ||||
\(95\) | −1.65472e14 | −0.243107 | ||||||||
\(96\) | −1.16004e14 | − | 3.42194e14i | −0.157558 | − | 0.464770i | ||||
\(97\) | 4.81808e14 | 0.605460 | 0.302730 | − | 0.953076i | \(-0.402102\pi\) | ||||
0.302730 | + | 0.953076i | \(0.402102\pi\) | |||||||
\(98\) | −5.70668e14 | + | 3.73569e13i | −0.664030 | + | 0.0434686i | ||||
\(99\) | − | 1.06918e15i | − | 1.15289i | ||||||
\(100\) | −1.74440e15 | + | 2.29366e14i | −1.74440 | + | 0.229366i | ||||
\(101\) | − | 1.19918e15i | − | 1.11294i | −0.830867 | − | 0.556471i | \(-0.812155\pi\) | ||
0.830867 | − | 0.556471i | \(-0.187845\pi\) | |||||||
\(102\) | −1.37615e13 | − | 2.10222e14i | −0.0118622 | − | 0.181208i | ||||
\(103\) | −1.94385e15 | −1.55734 | −0.778670 | − | 0.627434i | \(-0.784105\pi\) | ||||
−0.778670 | + | 0.627434i | \(0.784105\pi\) | |||||||
\(104\) | 3.51916e14 | + | 1.77146e15i | 0.262234 | + | 1.32002i | ||||
\(105\) | 6.79859e14 | 0.471519 | ||||||||
\(106\) | −6.11855e13 | − | 9.34676e14i | −0.0395234 | − | 0.603764i | ||||
\(107\) | 3.00752e15i | 1.81063i | 0.424739 | + | 0.905316i | \(0.360366\pi\) | ||||
−0.424739 | + | 0.905316i | \(0.639634\pi\) | |||||||
\(108\) | −2.00450e14 | − | 1.52448e15i | −0.112545 | − | 0.855943i | ||||
\(109\) | 1.05051e15i | 0.550427i | 0.961383 | + | 0.275214i | \(0.0887486\pi\) | ||||
−0.961383 | + | 0.275214i | \(0.911251\pi\) | |||||||
\(110\) | 5.14489e15 | − | 3.36794e14i | 2.51728 | − | 0.164786i | ||||
\(111\) | −1.29206e15 | −0.590691 | ||||||||
\(112\) | 1.30721e15 | − | 3.49811e14i | 0.558742 | − | 0.149520i | ||||
\(113\) | 1.90217e15 | 0.760607 | 0.380303 | − | 0.924862i | \(-0.375820\pi\) | ||||
0.380303 | + | 0.924862i | \(0.375820\pi\) | |||||||
\(114\) | 1.91473e14 | − | 1.25342e13i | 0.0716674 | − | 0.00469148i | ||||
\(115\) | − | 5.90588e15i | − | 2.07039i | ||||||
\(116\) | 1.51679e14 | + | 1.15356e15i | 0.0498299 | + | 0.378972i | ||||
\(117\) | 3.31677e15i | 1.02170i | ||||||||
\(118\) | 3.02045e14 | + | 4.61407e15i | 0.0872885 | + | 1.33343i | ||||
\(119\) | 7.89000e14 | 0.214030 | ||||||||
\(120\) | 3.13851e15 | − | 6.23493e14i | 0.799584 | − | 0.158844i | ||||
\(121\) | −5.45644e15 | −1.30623 | ||||||||
\(122\) | −1.03367e14 | − | 1.57904e15i | −0.0232639 | − | 0.355381i | ||||
\(123\) | 1.29114e15i | 0.273329i | ||||||||
\(124\) | −4.46886e15 | + | 5.87597e14i | −0.890295 | + | 0.117062i | ||||
\(125\) | − | 6.72534e15i | − | 1.26151i | ||||||
\(126\) | 2.47980e15 | − | 1.62332e14i | 0.438164 | − | 0.0286830i | ||||
\(127\) | −4.55964e15 | −0.759281 | −0.379640 | − | 0.925134i | \(-0.623952\pi\) | ||||
−0.379640 | + | 0.925134i | \(0.623952\pi\) | |||||||
\(128\) | 5.71383e15 | − | 2.81371e15i | 0.897124 | − | 0.441778i | ||||
\(129\) | −1.89208e15 | −0.280231 | ||||||||
\(130\) | −1.59603e16 | + | 1.04479e15i | −2.23083 | + | 0.146034i | ||||
\(131\) | 1.02016e16i | 1.34627i | 0.739519 | + | 0.673136i | \(0.235053\pi\) | ||||
−0.739519 | + | 0.673136i | \(0.764947\pi\) | |||||||
\(132\) | −5.92781e15 | + | 7.79430e14i | −0.738907 | + | 0.0971567i | ||||
\(133\) | 7.18632e14i | 0.0846485i | ||||||||
\(134\) | −7.94647e14 | − | 1.21391e16i | −0.0884888 | − | 1.35176i | ||||
\(135\) | 1.36169e16 | 1.43409 | ||||||||
\(136\) | 3.64235e15 | − | 7.23585e14i | 0.362944 | − | 0.0721021i | ||||
\(137\) | 1.00633e15 | 0.0949148 | 0.0474574 | − | 0.998873i | \(-0.484888\pi\) | ||||
0.0474574 | + | 0.998873i | \(0.484888\pi\) | |||||||
\(138\) | 4.47358e14 | + | 6.83389e15i | 0.0399542 | + | 0.610344i | ||||
\(139\) | − | 7.02401e15i | − | 0.594257i | −0.954837 | − | 0.297129i | \(-0.903971\pi\) | ||
0.954837 | − | 0.297129i | \(-0.0960290\pi\) | |||||||
\(140\) | 1.56228e15 | + | 1.18816e16i | 0.125256 | + | 0.952612i | ||||
\(141\) | − | 5.46857e15i | − | 0.415653i | ||||||
\(142\) | −3.99786e15 | + | 2.61707e14i | −0.288181 | + | 0.0188648i | ||||
\(143\) | 2.98853e16 | 2.04379 | ||||||||
\(144\) | 1.12989e16 | − | 3.02359e15i | 0.733360 | − | 0.196248i | ||||
\(145\) | −1.03038e16 | −0.634948 | ||||||||
\(146\) | −2.30258e16 | + | 1.50731e15i | −1.34762 | + | 0.0882177i | ||||
\(147\) | 5.87296e15i | 0.326570i | ||||||||
\(148\) | −2.96909e15 | − | 2.25808e16i | −0.156913 | − | 1.19338i | ||||
\(149\) | 2.85325e16i | 1.43365i | 0.697255 | + | 0.716824i | \(0.254405\pi\) | ||||
−0.697255 | + | 0.716824i | \(0.745595\pi\) | |||||||
\(150\) | 1.18025e15 | + | 1.80296e16i | 0.0564013 | + | 0.861591i | ||||
\(151\) | 2.85155e15 | 0.129644 | 0.0648222 | − | 0.997897i | \(-0.479352\pi\) | ||||
0.0648222 | + | 0.997897i | \(0.479352\pi\) | |||||||
\(152\) | 6.59051e14 | + | 3.31750e15i | 0.0285162 | + | 0.143544i | ||||
\(153\) | 6.81972e15 | 0.280919 | ||||||||
\(154\) | −1.46267e15 | − | 2.23438e16i | −0.0573773 | − | 0.876501i | ||||
\(155\) | − | 3.99165e16i | − | 1.49164i | ||||||
\(156\) | 1.83890e16 | − | 2.41792e15i | 0.654824 | − | 0.0861008i | ||||
\(157\) | − | 9.50020e15i | − | 0.322467i | −0.986916 | − | 0.161233i | \(-0.948453\pi\) | ||
0.986916 | − | 0.161233i | \(-0.0515472\pi\) | |||||||
\(158\) | 1.30806e16 | − | 8.56277e14i | 0.423349 | − | 0.0277132i | ||||
\(159\) | −9.61910e15 | −0.296931 | ||||||||
\(160\) | 1.81087e16 | + | 5.34178e16i | 0.533319 | + | 1.57321i | ||||
\(161\) | −2.56487e16 | −0.720895 | ||||||||
\(162\) | 1.24773e16 | − | 8.16784e14i | 0.334778 | − | 0.0219151i | ||||
\(163\) | 6.08927e16i | 1.56012i | 0.625705 | + | 0.780060i | \(0.284812\pi\) | ||||
−0.625705 | + | 0.780060i | \(0.715188\pi\) | |||||||
\(164\) | −2.25649e16 | + | 2.96699e15i | −0.552209 | + | 0.0726084i | ||||
\(165\) | − | 5.29481e16i | − | 1.23800i | ||||||
\(166\) | −1.83370e15 | − | 2.80117e16i | −0.0409748 | − | 0.625934i | ||||
\(167\) | −5.75741e16 | −1.22985 | −0.614927 | − | 0.788584i | \(-0.710814\pi\) | ||||
−0.614927 | + | 0.788584i | \(0.710814\pi\) | |||||||
\(168\) | −2.70778e15 | − | 1.36303e16i | −0.0553086 | − | 0.278410i | ||||
\(169\) | −4.15231e16 | −0.811222 | ||||||||
\(170\) | 2.14823e15 | + | 3.28165e16i | 0.0401525 | + | 0.613374i | ||||
\(171\) | 6.21149e15i | 0.111103i | ||||||||
\(172\) | −4.34790e15 | − | 3.30671e16i | −0.0744417 | − | 0.566152i | ||||
\(173\) | 2.16370e16i | 0.354692i | 0.984149 | + | 0.177346i | \(0.0567512\pi\) | ||||
−0.984149 | + | 0.177346i | \(0.943249\pi\) | |||||||
\(174\) | 1.19229e16 | − | 7.80492e14i | 0.187181 | − | 0.0122532i | ||||
\(175\) | −6.76681e16 | −1.01765 | ||||||||
\(176\) | −2.72436e16 | − | 1.01807e17i | −0.392572 | − | 1.46701i | ||||
\(177\) | 4.74851e16 | 0.655780 | ||||||||
\(178\) | 1.19547e17 | − | 7.82573e15i | 1.58266 | − | 0.103604i | ||||
\(179\) | − | 6.49679e16i | − | 0.824710i | −0.911023 | − | 0.412355i | \(-0.864706\pi\) | ||
0.911023 | − | 0.412355i | \(-0.135294\pi\) | |||||||
\(180\) | 1.35036e16 | + | 1.02699e17i | 0.164401 | + | 1.25032i | ||||
\(181\) | 6.33200e16i | 0.739523i | 0.929127 | + | 0.369761i | \(0.120561\pi\) | ||||
−0.929127 | + | 0.369761i | \(0.879439\pi\) | |||||||
\(182\) | 4.53743e15 | + | 6.93142e16i | 0.0508481 | + | 0.776760i | ||||
\(183\) | −1.62505e16 | −0.174777 | ||||||||
\(184\) | −1.18405e17 | + | 2.35222e16i | −1.22247 | + | 0.242854i | ||||
\(185\) | 2.01695e17 | 1.99944 | ||||||||
\(186\) | 3.02359e15 | + | 4.61887e16i | 0.0287857 | + | 0.439732i | ||||
\(187\) | − | 6.14481e16i | − | 0.561948i | ||||||
\(188\) | 9.55723e16 | − | 1.25665e16i | 0.839746 | − | 0.110416i | ||||
\(189\) | − | 5.91371e16i | − | 0.499340i | ||||||
\(190\) | −2.98897e16 | + | 1.95663e15i | −0.242588 | + | 0.0158803i | ||||
\(191\) | 7.61809e16 | 0.594423 | 0.297212 | − | 0.954812i | \(-0.403943\pi\) | ||||
0.297212 | + | 0.954812i | \(0.403943\pi\) | |||||||
\(192\) | −2.50004e16 | − | 6.04398e16i | −0.187581 | − | 0.453486i | ||||
\(193\) | 1.31762e17 | 0.950849 | 0.475425 | − | 0.879756i | \(-0.342294\pi\) | ||||
0.475425 | + | 0.879756i | \(0.342294\pi\) | |||||||
\(194\) | 8.70302e16 | − | 5.69715e15i | 0.604167 | − | 0.0395499i | ||||
\(195\) | 1.64254e17i | 1.09712i | ||||||||
\(196\) | −1.02640e17 | + | 1.34958e16i | −0.659772 | + | 0.0867515i | ||||
\(197\) | 1.38251e17i | 0.855406i | 0.903919 | + | 0.427703i | \(0.140677\pi\) | ||||
−0.903919 | + | 0.427703i | \(0.859323\pi\) | |||||||
\(198\) | −1.26426e16 | − | 1.93129e17i | −0.0753089 | − | 1.15042i | ||||
\(199\) | −1.07768e16 | −0.0618150 | −0.0309075 | − | 0.999522i | \(-0.509840\pi\) | ||||
−0.0309075 | + | 0.999522i | \(0.509840\pi\) | |||||||
\(200\) | −3.12384e17 | + | 6.20578e16i | −1.72569 | + | 0.342824i | ||||
\(201\) | −1.24928e17 | −0.664798 | ||||||||
\(202\) | −1.41797e16 | − | 2.16611e17i | −0.0726996 | − | 1.11057i | ||||
\(203\) | 4.47486e16i | 0.221085i | ||||||||
\(204\) | −4.97156e15 | − | 3.78103e16i | −0.0236737 | − | 0.180046i | ||||
\(205\) | − | 2.01553e17i | − | 0.925198i | ||||||
\(206\) | −3.51123e17 | + | 2.29851e16i | −1.55401 | + | 0.101728i | ||||
\(207\) | −2.21695e17 | −0.946189 | ||||||||
\(208\) | 8.45142e16 | + | 3.15822e17i | 0.347900 | + | 1.30007i | ||||
\(209\) | 5.59677e16 | 0.222249 | ||||||||
\(210\) | 1.22805e17 | − | 8.03902e15i | 0.470512 | − | 0.0308005i | ||||
\(211\) | − | 3.20233e17i | − | 1.18399i | −0.805942 | − | 0.591995i | \(-0.798340\pi\) | ||
0.805942 | − | 0.591995i | \(-0.201660\pi\) | |||||||
\(212\) | −2.21042e16 | − | 1.68109e17i | −0.0788781 | − | 0.599892i | ||||
\(213\) | 4.11435e16i | 0.141727i | ||||||||
\(214\) | 3.55625e16 | + | 5.43256e17i | 0.118274 | + | 1.80676i | ||||
\(215\) | 2.95361e17 | 0.948558 | ||||||||
\(216\) | −5.42341e16 | − | 2.73002e17i | −0.168217 | − | 0.846763i | ||||
\(217\) | −1.73354e17 | −0.519381 | ||||||||
\(218\) | 1.24218e16 | + | 1.89756e17i | 0.0359550 | + | 0.549252i | ||||
\(219\) | 2.36967e17i | 0.662761i | ||||||||
\(220\) | 9.25354e17 | − | 1.21672e17i | 2.50114 | − | 0.328867i | ||||
\(221\) | 1.90622e17i | 0.498002i | ||||||||
\(222\) | −2.33388e17 | + | 1.52780e16i | −0.589429 | + | 0.0385851i | ||||
\(223\) | 2.84887e17 | 0.695642 | 0.347821 | − | 0.937561i | \(-0.386922\pi\) | ||||
0.347821 | + | 0.937561i | \(0.386922\pi\) | |||||||
\(224\) | 2.31989e17 | − | 7.86445e16i | 0.547782 | − | 0.185698i | ||||
\(225\) | −5.84889e17 | −1.33569 | ||||||||
\(226\) | 3.43593e17 | − | 2.24922e16i | 0.758982 | − | 0.0496843i | ||||
\(227\) | − | 2.22335e17i | − | 0.475132i | −0.971371 | − | 0.237566i | \(-0.923650\pi\) | ||
0.971371 | − | 0.237566i | \(-0.0763496\pi\) | |||||||
\(228\) | 3.44381e16 | − | 4.52816e15i | 0.0712079 | − | 0.00936291i | ||||
\(229\) | − | 1.88161e17i | − | 0.376499i | −0.982121 | − | 0.188250i | \(-0.939719\pi\) | ||
0.982121 | − | 0.188250i | \(-0.0602814\pi\) | |||||||
\(230\) | −6.98344e16 | − | 1.06680e18i | −0.135242 | − | 2.06596i | ||||
\(231\) | −2.29949e17 | −0.431064 | ||||||||
\(232\) | 4.10385e16 | + | 2.06578e17i | 0.0744787 | + | 0.374908i | ||||
\(233\) | −4.12831e17 | −0.725442 | −0.362721 | − | 0.931898i | \(-0.618152\pi\) | ||||
−0.362721 | + | 0.931898i | \(0.618152\pi\) | |||||||
\(234\) | 3.92193e16 | + | 5.99117e17i | 0.0667392 | + | 1.01951i | ||||
\(235\) | 8.53666e17i | 1.40695i | ||||||||
\(236\) | 1.09118e17 | + | 8.29880e17i | 0.174204 | + | 1.32488i | ||||
\(237\) | − | 1.34617e17i | − | 0.208203i | ||||||
\(238\) | 1.42519e17 | − | 9.32956e15i | 0.213573 | − | 0.0139809i | ||||
\(239\) | 6.47168e17 | 0.939795 | 0.469897 | − | 0.882721i | \(-0.344291\pi\) | ||||
0.469897 | + | 0.882721i | \(0.344291\pi\) | |||||||
\(240\) | 5.59545e17 | − | 1.49735e17i | 0.787501 | − | 0.210736i | ||||
\(241\) | −2.19632e17 | −0.299618 | −0.149809 | − | 0.988715i | \(-0.547866\pi\) | ||||
−0.149809 | + | 0.988715i | \(0.547866\pi\) | |||||||
\(242\) | −9.85611e17 | + | 6.45199e16i | −1.30344 | + | 0.0853254i | ||||
\(243\) | − | 8.01717e17i | − | 1.02795i | ||||||
\(244\) | −3.73429e16 | − | 2.84004e17i | −0.0464284 | − | 0.353103i | ||||
\(245\) | − | 9.16792e17i | − | 1.10541i | ||||||
\(246\) | 1.52672e16 | + | 2.33223e17i | 0.0178544 | + | 0.272746i | ||||
\(247\) | −1.73621e17 | −0.196959 | ||||||||
\(248\) | −8.00274e17 | + | 1.58981e17i | −0.880747 | + | 0.174968i | ||||
\(249\) | −2.88279e17 | −0.307835 | ||||||||
\(250\) | −7.95241e16 | − | 1.21482e18i | −0.0824040 | − | 1.25881i | ||||
\(251\) | 2.91655e17i | 0.293303i | 0.989188 | + | 0.146652i | \(0.0468497\pi\) | ||||
−0.989188 | + | 0.146652i | \(0.953150\pi\) | |||||||
\(252\) | 4.46013e17 | − | 5.86449e16i | 0.435355 | − | 0.0572435i | ||||
\(253\) | 1.99755e18i | 1.89275i | ||||||||
\(254\) | −8.23620e17 | + | 5.39156e16i | −0.757659 | + | 0.0495977i | ||||
\(255\) | 3.37727e17 | 0.301658 | ||||||||
\(256\) | 9.98834e17 | − | 5.75811e17i | 0.866351 | − | 0.499436i | ||||
\(257\) | 8.57227e17 | 0.722101 | 0.361050 | − | 0.932546i | \(-0.382418\pi\) | ||||
0.361050 | + | 0.932546i | \(0.382418\pi\) | |||||||
\(258\) | −3.41771e17 | + | 2.23729e16i | −0.279632 | + | 0.0183052i | ||||
\(259\) | − | 8.75946e17i | − | 0.696192i | ||||||
\(260\) | −2.87060e18 | + | 3.77447e17i | −2.21652 | + | 0.291444i | ||||
\(261\) | 3.86784e17i | 0.290178i | ||||||||
\(262\) | 1.20629e17 | + | 1.84274e18i | 0.0879411 | + | 1.34340i | ||||
\(263\) | 3.80213e17 | 0.269376 | 0.134688 | − | 0.990888i | \(-0.456997\pi\) | ||||
0.134688 | + | 0.990888i | \(0.456997\pi\) | |||||||
\(264\) | −1.06154e18 | + | 2.10884e17i | −0.730982 | + | 0.145216i | ||||
\(265\) | 1.50158e18 | 1.00509 | ||||||||
\(266\) | 8.49749e15 | + | 1.29808e17i | 0.00552941 | + | 0.0844677i | ||||
\(267\) | − | 1.23030e18i | − | 0.778352i | ||||||
\(268\) | −2.87078e17 | − | 2.18332e18i | −0.176600 | − | 1.34310i | ||||
\(269\) | − | 1.59898e18i | − | 0.956536i | −0.878214 | − | 0.478268i | \(-0.841265\pi\) | ||
0.878214 | − | 0.478268i | \(-0.158735\pi\) | |||||||
\(270\) | 2.45966e18 | − | 1.61014e17i | 1.43102 | − | 0.0936774i | ||||
\(271\) | −4.79907e17 | −0.271574 | −0.135787 | − | 0.990738i | \(-0.543356\pi\) | ||||
−0.135787 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(272\) | 6.49372e17 | − | 1.73772e17i | 0.357459 | − | 0.0956563i | ||||
\(273\) | 7.13339e17 | 0.382011 | ||||||||
\(274\) | 1.81775e17 | − | 1.18993e16i | 0.0947121 | − | 0.00620002i | ||||
\(275\) | 5.27006e18i | 2.67190i | ||||||||
\(276\) | 1.61615e17 | + | 1.22913e18i | 0.0797377 | + | 0.606430i | ||||
\(277\) | − | 6.67858e17i | − | 0.320690i | −0.987061 | − | 0.160345i | \(-0.948739\pi\) | ||
0.987061 | − | 0.160345i | \(-0.0512607\pi\) | |||||||
\(278\) | −8.30557e16 | − | 1.26877e18i | −0.0388180 | − | 0.592988i | ||||
\(279\) | −1.49838e18 | −0.681698 | ||||||||
\(280\) | 4.22694e17 | + | 2.12774e18i | 0.187215 | + | 0.942396i | ||||
\(281\) | 4.04339e18 | 1.74361 | 0.871803 | − | 0.489857i | \(-0.162951\pi\) | ||||
0.871803 | + | 0.489857i | \(0.162951\pi\) | |||||||
\(282\) | −6.46634e16 | − | 9.87803e17i | −0.0271513 | − | 0.414765i | ||||
\(283\) | − | 1.73833e18i | − | 0.710777i | −0.934719 | − | 0.355388i | \(-0.884349\pi\) | ||
0.934719 | − | 0.355388i | \(-0.115651\pi\) | |||||||
\(284\) | −7.19049e17 | + | 9.45457e16i | −0.286333 | + | 0.0376491i | ||||
\(285\) | 3.07606e17i | 0.119305i | ||||||||
\(286\) | 5.39826e18 | − | 3.53380e17i | 2.03943 | − | 0.133505i | ||||
\(287\) | −8.75326e17 | −0.322148 | ||||||||
\(288\) | 2.00520e18 | − | 6.79764e17i | 0.718975 | − | 0.243733i | ||||
\(289\) | −2.47048e18 | −0.863073 | ||||||||
\(290\) | −1.86121e18 | + | 1.21838e17i | −0.633591 | + | 0.0414760i | ||||
\(291\) | − | 8.95661e17i | − | 0.297130i | ||||||
\(292\) | −4.14138e18 | + | 5.44538e17i | −1.33898 | + | 0.176058i | ||||
\(293\) | 8.46641e17i | 0.266804i | 0.991062 | + | 0.133402i | \(0.0425901\pi\) | ||||
−0.991062 | + | 0.133402i | \(0.957410\pi\) | |||||||
\(294\) | 6.94450e16 | + | 1.06085e18i | 0.0213322 | + | 0.325873i | ||||
\(295\) | −7.41261e18 | −2.21976 | ||||||||
\(296\) | −8.03323e17 | − | 4.04373e18i | −0.234532 | − | 1.18058i | ||||
\(297\) | −4.60566e18 | −1.31105 | ||||||||
\(298\) | 3.37383e17 | + | 5.15390e18i | 0.0936487 | + | 1.43059i | ||||
\(299\) | − | 6.19673e18i | − | 1.67737i | ||||||
\(300\) | 4.26383e17 | + | 3.24277e18i | 0.112562 | + | 0.856066i | ||||
\(301\) | − | 1.28273e18i | − | 0.330282i | ||||||
\(302\) | 5.15083e17 | − | 3.37183e16i | 0.129368 | − | 0.00846863i | ||||
\(303\) | −2.22922e18 | −0.546177 | ||||||||
\(304\) | 1.58274e17 | + | 5.91457e17i | 0.0378319 | + | 0.141374i | ||||
\(305\) | 2.53677e18 | 0.591605 | ||||||||
\(306\) | 1.23186e18 | − | 8.06400e16i | 0.280319 | − | 0.0183502i | ||||
\(307\) | 2.23744e18i | 0.496836i | 0.968653 | + | 0.248418i | \(0.0799106\pi\) | ||||
−0.968653 | + | 0.248418i | \(0.920089\pi\) | |||||||
\(308\) | −5.28411e17 | − | 4.01873e18i | −0.114510 | − | 0.870881i | ||||
\(309\) | 3.61354e18i | 0.764265i | ||||||||
\(310\) | −4.71994e17 | − | 7.21023e18i | −0.0974371 | − | 1.48846i | ||||
\(311\) | 8.89953e18 | 1.79335 | 0.896673 | − | 0.442694i | \(-0.145977\pi\) | ||||
0.896673 | + | 0.442694i | \(0.145977\pi\) | |||||||
\(312\) | 3.29307e18 | − | 6.54197e17i | 0.647801 | − | 0.128691i | ||||
\(313\) | −4.42301e18 | −0.849445 | −0.424722 | − | 0.905324i | \(-0.639628\pi\) | ||||
−0.424722 | + | 0.905324i | \(0.639628\pi\) | |||||||
\(314\) | −1.12335e17 | − | 1.71605e18i | −0.0210642 | − | 0.321778i | ||||
\(315\) | 3.98385e18i | 0.729414i | ||||||||
\(316\) | 2.35265e18 | − | 3.09343e17i | 0.420634 | − | 0.0553080i | ||||
\(317\) | 7.11739e18i | 1.24273i | 0.783522 | + | 0.621364i | \(0.213421\pi\) | ||||
−0.783522 | + | 0.621364i | \(0.786579\pi\) | |||||||
\(318\) | −1.73752e18 | + | 1.13741e17i | −0.296297 | + | 0.0193961i | ||||
\(319\) | 3.48506e18 | 0.580471 | ||||||||
\(320\) | 3.90266e18 | + | 9.43488e18i | 0.634945 | + | 1.53501i | ||||
\(321\) | 5.59086e18 | 0.888568 | ||||||||
\(322\) | −4.63300e18 | + | 3.03285e17i | −0.719355 | + | 0.0470903i | ||||
\(323\) | 3.56988e17i | 0.0541545i | ||||||||
\(324\) | 2.24414e18 | − | 2.95076e17i | 0.332631 | − | 0.0437367i | ||||
\(325\) | − | 1.63486e19i | − | 2.36785i | ||||||
\(326\) | 7.20028e17 | + | 1.09992e19i | 0.101910 | + | 1.55679i | ||||
\(327\) | 1.95285e18 | 0.270122 | ||||||||
\(328\) | −4.04087e18 | + | 8.02754e17i | −0.546287 | + | 0.108525i | ||||
\(329\) | 3.70740e18 | 0.489891 | ||||||||
\(330\) | −6.26086e17 | − | 9.56415e18i | −0.0808686 | − | 1.23536i | ||||
\(331\) | 6.49509e18i | 0.820116i | 0.912060 | + | 0.410058i | \(0.134491\pi\) | ||||
−0.912060 | + | 0.410058i | \(0.865509\pi\) | |||||||
\(332\) | −6.62451e17 | − | 5.03814e18i | −0.0817745 | − | 0.621921i | ||||
\(333\) | − | 7.57124e18i | − | 0.913766i | ||||||
\(334\) | −1.03998e19 | + | 6.80787e17i | −1.22723 | + | 0.0803364i | ||||
\(335\) | 1.95018e19 | 2.25029 | ||||||||
\(336\) | −6.50285e17 | − | 2.43006e18i | −0.0733768 | − | 0.274203i | ||||
\(337\) | −8.36981e18 | −0.923616 | −0.461808 | − | 0.886980i | \(-0.652799\pi\) | ||||
−0.461808 | + | 0.886980i | \(0.652799\pi\) | |||||||
\(338\) | −7.50044e18 | + | 4.90992e17i | −0.809490 | + | 0.0529906i | ||||
\(339\) | − | 3.53605e18i | − | 0.373268i | ||||||
\(340\) | 7.76080e17 | + | 5.90233e18i | 0.0801336 | + | 0.609441i | ||||
\(341\) | 1.35010e19i | 1.36366i | ||||||||
\(342\) | 7.34480e16 | + | 1.12200e18i | 0.00725746 | + | 0.110866i | ||||
\(343\) | −9.96478e18 | −0.963300 | ||||||||
\(344\) | −1.17638e18 | − | 5.92159e18i | −0.111265 | − | 0.560080i | ||||
\(345\) | −1.09788e19 | −1.01604 | ||||||||
\(346\) | 2.55848e17 | + | 3.90835e18i | 0.0231692 | + | 0.353935i | ||||
\(347\) | − | 5.36645e18i | − | 0.475572i | −0.971318 | − | 0.237786i | \(-0.923578\pi\) | ||
0.971318 | − | 0.237786i | \(-0.0764216\pi\) | |||||||
\(348\) | 2.14443e18 | − | 2.81965e17i | 0.185981 | − | 0.0244540i | ||||
\(349\) | 1.57562e19i | 1.33740i | 0.743534 | + | 0.668699i | \(0.233148\pi\) | ||||
−0.743534 | + | 0.668699i | \(0.766852\pi\) | |||||||
\(350\) | −1.22231e19 | + | 8.00144e17i | −1.01548 | + | 0.0664749i | ||||
\(351\) | 1.42875e19 | 1.16186 | ||||||||
\(352\) | −6.12491e18 | − | 1.80675e19i | −0.487562 | − | 1.43823i | ||||
\(353\) | −9.01560e18 | −0.702561 | −0.351281 | − | 0.936270i | \(-0.614254\pi\) | ||||
−0.351281 | + | 0.936270i | \(0.614254\pi\) | |||||||
\(354\) | 8.57737e18 | − | 5.61490e17i | 0.654379 | − | 0.0428368i | ||||
\(355\) | − | 6.42266e18i | − | 0.479736i | ||||||
\(356\) | 2.15015e19 | − | 2.82717e18i | 1.57251 | − | 0.206765i | ||||
\(357\) | − | 1.46672e18i | − | 0.105035i | ||||||
\(358\) | −7.68216e17 | − | 1.17353e19i | −0.0538717 | − | 0.822949i | ||||
\(359\) | −1.68743e19 | −1.15882 | −0.579412 | − | 0.815035i | \(-0.696718\pi\) | ||||
−0.579412 | + | 0.815035i | \(0.696718\pi\) | |||||||
\(360\) | 3.65356e18 | + | 1.83911e19i | 0.245724 | + | 1.23691i | ||||
\(361\) | 1.48560e19 | 0.978582 | ||||||||
\(362\) | 7.48730e17 | + | 1.14377e19i | 0.0483071 | + | 0.737943i | ||||
\(363\) | 1.01433e19i | 0.641032i | ||||||||
\(364\) | 1.63922e18 | + | 1.24668e19i | 0.101479 | + | 0.771780i | ||||
\(365\) | − | 3.69914e19i | − | 2.24339i | ||||||
\(366\) | −2.93537e18 | + | 1.92155e17i | −0.174403 | + | 0.0114168i | ||||
\(367\) | −1.10764e19 | −0.644768 | −0.322384 | − | 0.946609i | \(-0.604484\pi\) | ||||
−0.322384 | + | 0.946609i | \(0.604484\pi\) | |||||||
\(368\) | −2.11097e19 | + | 5.64898e18i | −1.20399 | + | 0.322189i | ||||
\(369\) | −7.56588e18 | −0.422826 | ||||||||
\(370\) | 3.64328e19 | − | 2.38496e18i | 1.99517 | − | 0.130607i | ||||
\(371\) | − | 6.52123e18i | − | 0.349965i | ||||||
\(372\) | 1.09232e18 | + | 8.30743e18i | 0.0574483 | + | 0.436913i | ||||
\(373\) | 2.00597e19i | 1.03397i | 0.855995 | + | 0.516984i | \(0.172945\pi\) | ||||
−0.855995 | + | 0.516984i | \(0.827055\pi\) | |||||||
\(374\) | −7.26595e17 | − | 1.10995e19i | −0.0367076 | − | 0.560748i | ||||
\(375\) | −1.25021e19 | −0.619084 | ||||||||
\(376\) | 1.71149e19 | − | 3.40002e18i | 0.830740 | − | 0.165034i | ||||
\(377\) | −1.08112e19 | −0.514417 | ||||||||
\(378\) | −6.99269e17 | − | 1.06821e19i | −0.0326179 | − | 0.498274i | ||||
\(379\) | 1.03163e19i | 0.471770i | 0.971781 | + | 0.235885i | \(0.0757988\pi\) | ||||
−0.971781 | + | 0.235885i | \(0.924201\pi\) | |||||||
\(380\) | −5.37592e18 | + | 7.06864e17i | −0.241033 | + | 0.0316927i | ||||
\(381\) | 8.47618e18i | 0.372617i | ||||||||
\(382\) | 1.37608e19 | − | 9.00804e17i | 0.593154 | − | 0.0388289i | ||||
\(383\) | 1.58453e18 | 0.0669744 | 0.0334872 | − | 0.999439i | \(-0.489339\pi\) | ||||
0.0334872 | + | 0.999439i | \(0.489339\pi\) | |||||||
\(384\) | −5.23057e18 | − | 1.06218e19i | −0.216803 | − | 0.440264i | ||||
\(385\) | 3.58959e19 | 1.45911 | ||||||||
\(386\) | 2.38006e19 | − | 1.55803e18i | 0.948818 | − | 0.0621113i | ||||
\(387\) | − | 1.10872e19i | − | 0.433502i | ||||||
\(388\) | 1.56531e19 | − | 2.05818e18i | 0.600293 | − | 0.0789308i | ||||
\(389\) | 1.37817e18i | 0.0518420i | 0.999664 | + | 0.0259210i | \(0.00825183\pi\) | ||||
−0.999664 | + | 0.0259210i | \(0.991748\pi\) | |||||||
\(390\) | 1.94222e18 | + | 2.96696e19i | 0.0716662 | + | 1.09478i | ||||
\(391\) | −1.27413e19 | −0.461198 | ||||||||
\(392\) | −1.83805e19 | + | 3.65144e18i | −0.652697 | + | 0.129664i | ||||
\(393\) | 1.89643e19 | 0.660683 | ||||||||
\(394\) | 1.63476e18 | + | 2.49727e19i | 0.0558768 | + | 0.853579i | ||||
\(395\) | 2.10142e19i | 0.704751i | ||||||||
\(396\) | −4.56732e18 | − | 3.47359e19i | −0.150296 | − | 1.14305i | ||||
\(397\) | − | 2.02566e19i | − | 0.654092i | −0.945008 | − | 0.327046i | \(-0.893947\pi\) | ||
0.945008 | − | 0.327046i | \(-0.106053\pi\) | |||||||
\(398\) | −1.94665e18 | + | 1.27431e17i | −0.0616830 | + | 0.00403788i | ||||
\(399\) | 1.33591e18 | 0.0415413 | ||||||||
\(400\) | −5.56930e19 | + | 1.49035e19i | −1.69961 | + | 0.454818i | ||||
\(401\) | −9.25607e17 | −0.0277232 | −0.0138616 | − | 0.999904i | \(-0.504412\pi\) | ||||
−0.0138616 | + | 0.999904i | \(0.504412\pi\) | |||||||
\(402\) | −2.25661e19 | + | 1.47722e18i | −0.663378 | + | 0.0434259i | ||||
\(403\) | − | 4.18822e19i | − | 1.20849i | ||||||
\(404\) | −5.12264e18 | − | 3.89593e19i | −0.145089 | − | 1.10345i | ||||
\(405\) | 2.00450e19i | 0.557306i | ||||||||
\(406\) | 5.29131e17 | + | 8.08305e18i | 0.0144417 | + | 0.220613i | ||||
\(407\) | −6.82195e19 | −1.82789 | ||||||||
\(408\) | −1.34512e18 | − | 6.77098e18i | −0.0353841 | − | 0.178115i | ||||
\(409\) | 4.94945e19 | 1.27830 | 0.639148 | − | 0.769083i | \(-0.279287\pi\) | ||||
0.639148 | + | 0.769083i | \(0.279287\pi\) | |||||||
\(410\) | −2.38327e18 | − | 3.64070e19i | −0.0604357 | − | 0.923222i | ||||
\(411\) | − | 1.87072e18i | − | 0.0465795i | ||||||
\(412\) | −6.31525e19 | + | 8.30373e18i | −1.54405 | + | 0.203022i | ||||
\(413\) | 3.21923e19i | 0.772907i | ||||||||
\(414\) | −4.00454e19 | + | 2.62144e18i | −0.944169 | + | 0.0618070i | ||||
\(415\) | 4.50015e19 | 1.04200 | ||||||||
\(416\) | 1.90005e19 | + | 5.60485e19i | 0.432080 | + | 1.27457i | ||||
\(417\) | −1.30574e19 | −0.291632 | ||||||||
\(418\) | 1.01096e19 | − | 6.61793e17i | 0.221775 | − | 0.0145178i | ||||
\(419\) | 6.22046e19i | 1.34035i | 0.742205 | + | 0.670173i | \(0.233780\pi\) | ||||
−0.742205 | + | 0.670173i | \(0.766220\pi\) | |||||||
\(420\) | 2.20875e19 | − | 2.90422e18i | 0.467495 | − | 0.0614695i | ||||
\(421\) | − | 3.79369e19i | − | 0.788762i | −0.918947 | − | 0.394381i | \(-0.870959\pi\) | ||
0.918947 | − | 0.394381i | \(-0.129041\pi\) | |||||||
\(422\) | −3.78661e18 | − | 5.78446e19i | −0.0773406 | − | 1.18146i | ||||
\(423\) | 3.20449e19 | 0.642992 | ||||||||
\(424\) | −5.98056e18 | − | 3.01047e19i | −0.117896 | − | 0.593459i | ||||
\(425\) | −3.36148e19 | −0.651049 | ||||||||
\(426\) | 4.86503e17 | + | 7.43186e18i | 0.00925792 | + | 0.141425i | ||||
\(427\) | − | 1.10170e19i | − | 0.205993i | ||||||
\(428\) | 1.28475e19 | + | 9.77094e19i | 0.236043 | + | 1.79518i | ||||
\(429\) | − | 5.55555e19i | − | 1.00299i | ||||||
\(430\) | 5.33518e19 | − | 3.49250e18i | 0.946532 | − | 0.0619617i | ||||
\(431\) | 9.10237e19 | 1.58699 | 0.793497 | − | 0.608574i | \(-0.208258\pi\) | ||||
0.793497 | + | 0.608574i | \(0.208258\pi\) | |||||||
\(432\) | −1.30246e19 | − | 4.86717e19i | −0.223170 | − | 0.833966i | ||||
\(433\) | 7.12134e19 | 1.19923 | 0.599615 | − | 0.800288i | \(-0.295320\pi\) | ||||
0.599615 | + | 0.800288i | \(0.295320\pi\) | |||||||
\(434\) | −3.13134e19 | + | 2.04983e18i | −0.518271 | + | 0.0339270i | ||||
\(435\) | 1.91544e19i | 0.311601i | ||||||||
\(436\) | 4.48755e18 | + | 3.41292e19i | 0.0717564 | + | 0.545730i | ||||
\(437\) | − | 1.16049e19i | − | 0.182403i | ||||||
\(438\) | 2.80202e18 | + | 4.28040e19i | 0.0432928 | + | 0.661345i | ||||
\(439\) | −5.81164e19 | −0.882704 | −0.441352 | − | 0.897334i | \(-0.645501\pi\) | ||||
−0.441352 | + | 0.897334i | \(0.645501\pi\) | |||||||
\(440\) | 1.65710e20 | − | 3.29198e19i | 2.47431 | − | 0.491544i | ||||
\(441\) | −3.44145e19 | −0.505187 | ||||||||
\(442\) | 2.25402e18 | + | 3.44326e19i | 0.0325305 | + | 0.496938i | ||||
\(443\) | − | 1.24589e20i | − | 1.76788i | −0.467605 | − | 0.883938i | \(-0.654883\pi\) | ||
0.467605 | − | 0.883938i | \(-0.345117\pi\) | |||||||
\(444\) | −4.19769e19 | + | 5.51942e18i | −0.585650 | + | 0.0770054i | ||||
\(445\) | 1.92054e20i | 2.63466i | ||||||||
\(446\) | 5.14599e19 | − | 3.36866e18i | 0.694156 | − | 0.0454407i | ||||
\(447\) | 5.30407e19 | 0.703563 | ||||||||
\(448\) | 4.09749e19 | − | 1.69489e19i | 0.534482 | − | 0.221084i | ||||
\(449\) | −1.49517e20 | −1.91797 | −0.958985 | − | 0.283456i | \(-0.908519\pi\) | ||||
−0.958985 | + | 0.283456i | \(0.908519\pi\) | |||||||
\(450\) | −1.05650e20 | + | 6.91604e18i | −1.33283 | + | 0.0872497i | ||||
\(451\) | 6.81712e19i | 0.845818i | ||||||||
\(452\) | 6.17983e19 | − | 8.12567e18i | 0.754116 | − | 0.0991564i | ||||
\(453\) | − | 5.30092e18i | − | 0.0636230i | ||||||
\(454\) | −2.62901e18 | − | 4.01610e19i | −0.0310366 | − | 0.474117i | ||||
\(455\) | −1.11355e20 | −1.29308 | ||||||||
\(456\) | 6.16711e18 | − | 1.22515e18i | 0.0704442 | − | 0.0139944i | ||||
\(457\) | −9.69974e19 | −1.08990 | −0.544952 | − | 0.838467i | \(-0.683452\pi\) | ||||
−0.544952 | + | 0.838467i | \(0.683452\pi\) | |||||||
\(458\) | −2.22492e18 | − | 3.39881e19i | −0.0245937 | − | 0.375695i | ||||
\(459\) | − | 2.93770e19i | − | 0.319457i | ||||||
\(460\) | −2.52287e19 | − | 1.91872e20i | −0.269906 | − | 2.05272i | ||||
\(461\) | − | 1.55135e20i | − | 1.63288i | −0.577431 | − | 0.816439i | \(-0.695945\pi\) | ||
0.577431 | − | 0.816439i | \(-0.304055\pi\) | |||||||
\(462\) | −4.15363e19 | + | 2.71904e18i | −0.430143 | + | 0.0281579i | ||||
\(463\) | 8.54675e19 | 0.870850 | 0.435425 | − | 0.900225i | \(-0.356598\pi\) | ||||
0.435425 | + | 0.900225i | \(0.356598\pi\) | |||||||
\(464\) | 9.85559e18 | + | 3.68295e19i | 0.0988093 | + | 0.369242i | ||||
\(465\) | −7.42032e19 | −0.732024 | ||||||||
\(466\) | −7.45707e19 | + | 4.88153e18i | −0.723892 | + | 0.0473873i | ||||
\(467\) | 8.76389e19i | 0.837183i | 0.908175 | + | 0.418591i | \(0.137476\pi\) | ||||
−0.908175 | + | 0.418591i | \(0.862524\pi\) | |||||||
\(468\) | 1.41686e19 | + | 1.07756e20i | 0.133193 | + | 1.01298i | ||||
\(469\) | − | 8.46944e19i | − | 0.783535i | ||||||
\(470\) | 1.00942e19 | + | 1.54200e20i | 0.0919048 | + | 1.40395i | ||||
\(471\) | −1.76605e19 | −0.158251 | ||||||||
\(472\) | 2.95233e19 | + | 1.48613e20i | 0.260376 | + | 1.31067i | ||||
\(473\) | −9.98999e19 | −0.867174 | ||||||||
\(474\) | −1.59178e18 | − | 2.43162e19i | −0.0136002 | − | 0.207759i | ||||
\(475\) | − | 3.06168e19i | − | 0.257489i | ||||||
\(476\) | 2.56333e19 | − | 3.37045e18i | 0.212203 | − | 0.0279020i | ||||
\(477\) | − | 5.63662e19i | − | 0.459337i | ||||||
\(478\) | 1.16900e20 | − | 7.65247e18i | 0.937788 | − | 0.0613892i | ||||
\(479\) | 1.65573e20 | 1.30759 | 0.653797 | − | 0.756670i | \(-0.273175\pi\) | ||||
0.653797 | + | 0.756670i | \(0.273175\pi\) | |||||||
\(480\) | 9.93016e19 | − | 3.36633e19i | 0.772053 | − | 0.261727i | ||||
\(481\) | 2.11628e20 | 1.61989 | ||||||||
\(482\) | −3.96727e19 | + | 2.59705e18i | −0.298978 | + | 0.0195716i | ||||
\(483\) | 4.76800e19i | 0.353780i | ||||||||
\(484\) | −1.77271e20 | + | 2.33088e19i | −1.29508 | + | 0.170286i | ||||
\(485\) | 1.39816e20i | 1.00576i | ||||||||
\(486\) | −9.47993e18 | − | 1.44816e20i | −0.0671480 | − | 1.02576i | ||||
\(487\) | −2.31728e20 | −1.61626 | −0.808131 | − | 0.589003i | \(-0.799521\pi\) | ||||
−0.808131 | + | 0.589003i | \(0.799521\pi\) | |||||||
\(488\) | −1.01036e19 | − | 5.08589e19i | −0.0693946 | − | 0.349316i | ||||
\(489\) | 1.13197e20 | 0.765629 | ||||||||
\(490\) | −1.08406e19 | − | 1.65603e20i | −0.0722078 | − | 1.10305i | ||||
\(491\) | 4.55837e19i | 0.299019i | 0.988760 | + | 0.149509i | \(0.0477694\pi\) | ||||
−0.988760 | + | 0.149509i | \(0.952231\pi\) | |||||||
\(492\) | 5.51551e18 | + | 4.19472e19i | 0.0356326 | + | 0.270997i | ||||
\(493\) | 2.22293e19i | 0.141441i | ||||||||
\(494\) | −3.13617e19 | + | 2.05299e18i | −0.196538 | + | 0.0128657i | ||||
\(495\) | 3.10266e20 | 1.91512 | ||||||||
\(496\) | −1.42676e20 | + | 3.81801e19i | −0.867437 | + | 0.232127i | ||||
\(497\) | −2.78930e19 | −0.167041 | ||||||||
\(498\) | −5.20726e19 | + | 3.40877e18i | −0.307177 | + | 0.0201084i | ||||
\(499\) | − | 8.94164e19i | − | 0.519593i | −0.965663 | − | 0.259796i | \(-0.916345\pi\) | ||
0.965663 | − | 0.259796i | \(-0.0836554\pi\) | |||||||
\(500\) | −2.87293e19 | − | 2.18495e20i | −0.164456 | − | 1.25074i | ||||
\(501\) | 1.07028e20i | 0.603551i | ||||||||
\(502\) | 3.44869e18 | + | 5.26825e19i | 0.0191592 | + | 0.292677i | ||||
\(503\) | −7.58265e19 | −0.415012 | −0.207506 | − | 0.978234i | \(-0.566535\pi\) | ||||
−0.207506 | + | 0.978234i | \(0.566535\pi\) | |||||||
\(504\) | 7.98710e19 | − | 1.58671e19i | 0.430686 | − | 0.0855595i | ||||
\(505\) | 3.47990e20 | 1.84876 | ||||||||
\(506\) | 2.36201e19 | + | 3.60823e20i | 0.123638 | + | 1.88871i | ||||
\(507\) | 7.71898e19i | 0.398108i | ||||||||
\(508\) | −1.48135e20 | + | 1.94779e19i | −0.752801 | + | 0.0989836i | ||||
\(509\) | 2.19542e20i | 1.09934i | 0.835381 | + | 0.549672i | \(0.185247\pi\) | ||||
−0.835381 | + | 0.549672i | \(0.814753\pi\) | |||||||
\(510\) | 6.10045e19 | − | 3.99347e18i | 0.301013 | − | 0.0197049i | ||||
\(511\) | −1.60651e20 | −0.781134 | ||||||||
\(512\) | 1.73613e20 | − | 1.15821e20i | 0.831876 | − | 0.554962i | ||||
\(513\) | 2.67570e19 | 0.126345 | ||||||||
\(514\) | 1.54843e20 | − | 1.01363e19i | 0.720558 | − | 0.0471690i | ||||
\(515\) | − | 5.64087e20i | − | 2.58697i | ||||||
\(516\) | −6.14705e19 | + | 8.08257e18i | −0.277839 | + | 0.0365323i | ||||
\(517\) | − | 2.88736e20i | − | 1.28624i | ||||||
\(518\) | −1.03577e19 | − | 1.58225e20i | −0.0454767 | − | 0.694705i | ||||
\(519\) | 4.02223e19 | 0.174065 | ||||||||
\(520\) | −5.14061e20 | + | 1.02123e20i | −2.19275 | + | 0.435609i | ||||
\(521\) | −2.44441e19 | −0.102776 | −0.0513879 | − | 0.998679i | \(-0.516364\pi\) | ||||
−0.0513879 | + | 0.998679i | \(0.516364\pi\) | |||||||
\(522\) | 4.57354e18 | + | 6.98659e19i | 0.0189550 | + | 0.289558i | ||||
\(523\) | 2.97518e20i | 1.21549i | 0.794133 | + | 0.607744i | \(0.207925\pi\) | ||||
−0.794133 | + | 0.607744i | \(0.792075\pi\) | |||||||
\(524\) | 4.35791e19 | + | 3.31433e20i | 0.175507 | + | 1.33478i | ||||
\(525\) | 1.25792e20i | 0.499412i | ||||||||
\(526\) | 6.86788e19 | − | 4.49584e18i | 0.268800 | − | 0.0175962i | ||||
\(527\) | −8.61154e19 | −0.332278 | ||||||||
\(528\) | −1.89255e20 | + | 5.06448e19i | −0.719935 | + | 0.192655i | ||||
\(529\) | 1.47557e20 | 0.553406 | ||||||||
\(530\) | 2.71234e20 | − | 1.77555e19i | 1.00294 | − | 0.0656543i | ||||
\(531\) | 2.78254e20i | 1.01446i | ||||||||
\(532\) | 3.06985e18 | + | 2.33472e19i | 0.0110352 | + | 0.0839261i | ||||
\(533\) | − | 2.11478e20i | − | 0.749569i | ||||||
\(534\) | −1.45477e19 | − | 2.22232e20i | −0.0508435 | − | 0.776690i | ||||
\(535\) | −8.72755e20 | −3.00773 | ||||||||
\(536\) | −7.76725e19 | − | 3.90985e20i | −0.263956 | − | 1.32869i | ||||
\(537\) | −1.20773e20 | −0.404727 | ||||||||
\(538\) | −1.89072e19 | − | 2.88828e20i | −0.0624828 | − | 0.954493i | ||||
\(539\) | 3.10087e20i | 1.01057i | ||||||||
\(540\) | 4.42391e20 | − | 5.81687e19i | 1.42185 | − | 0.186955i | ||||
\(541\) | − | 2.64565e20i | − | 0.838596i | −0.907849 | − | 0.419298i | \(-0.862276\pi\) | ||
0.907849 | − | 0.419298i | \(-0.137724\pi\) | |||||||
\(542\) | −8.66870e19 | + | 5.67469e18i | −0.270994 | + | 0.0177397i | ||||
\(543\) | 1.17709e20 | 0.362921 | ||||||||
\(544\) | 1.15243e20 | − | 3.90675e19i | 0.350447 | − | 0.118802i | ||||
\(545\) | −3.04847e20 | −0.914342 | ||||||||
\(546\) | 1.28852e20 | − | 8.43491e18i | 0.381195 | − | 0.0249537i | ||||
\(547\) | − | 2.07387e20i | − | 0.605169i | −0.953123 | − | 0.302584i | \(-0.902151\pi\) | ||
0.953123 | − | 0.302584i | \(-0.0978494\pi\) | |||||||
\(548\) | 3.26939e19 | − | 4.29882e18i | 0.0941048 | − | 0.0123736i | ||||
\(549\) | − | 9.52251e19i | − | 0.270370i | ||||||
\(550\) | 6.23160e19 | + | 9.51944e20i | 0.174534 | + | 2.66619i | ||||
\(551\) | −2.02468e19 | −0.0559395 | ||||||||
\(552\) | 4.37269e19 | + | 2.20111e20i | 0.119181 | + | 0.599927i | ||||
\(553\) | 9.12630e19 | 0.245390 | ||||||||
\(554\) | −7.89711e18 | − | 1.20637e20i | −0.0209481 | − | 0.320005i | ||||
\(555\) | − | 3.74944e20i | − | 0.981225i | ||||||
\(556\) | −3.00052e19 | − | 2.28199e20i | −0.0774703 | − | 0.589186i | ||||
\(557\) | 3.53993e20i | 0.901738i | 0.892590 | + | 0.450869i | \(0.148886\pi\) | ||||
−0.892590 | + | 0.450869i | \(0.851114\pi\) | |||||||
\(558\) | −2.70657e20 | + | 1.77177e19i | −0.680242 | + | 0.0445298i | ||||
\(559\) | 3.09906e20 | 0.768495 | ||||||||
\(560\) | 1.01512e20 | + | 3.79341e20i | 0.248374 | + | 0.928154i | ||||
\(561\) | −1.14229e20 | −0.275776 | ||||||||
\(562\) | 7.30368e20 | − | 4.78112e19i | 1.73988 | − | 0.113896i | ||||
\(563\) | 1.16560e20i | 0.273992i | 0.990572 | + | 0.136996i | \(0.0437447\pi\) | ||||
−0.990572 | + | 0.136996i | \(0.956255\pi\) | |||||||
\(564\) | −2.33606e19 | − | 1.77665e20i | −0.0541866 | − | 0.412106i | ||||
\(565\) | 5.51991e20i | 1.26348i | ||||||||
\(566\) | −2.05549e19 | − | 3.13999e20i | −0.0464294 | − | 0.709259i | ||||
\(567\) | 8.70538e19 | 0.194050 | ||||||||
\(568\) | −1.28766e20 | + | 2.55805e19i | −0.283262 | + | 0.0562725i | ||||
\(569\) | 1.44331e20 | 0.313341 | 0.156670 | − | 0.987651i | \(-0.449924\pi\) | ||||
0.156670 | + | 0.987651i | \(0.449924\pi\) | |||||||
\(570\) | 3.63730e18 | + | 5.55638e19i | 0.00779324 | + | 0.119050i | ||||
\(571\) | − | 2.46922e20i | − | 0.522142i | −0.965320 | − | 0.261071i | \(-0.915924\pi\) | ||
0.965320 | − | 0.261071i | \(-0.0840756\pi\) | |||||||
\(572\) | 9.70924e20 | − | 1.27664e20i | 2.02635 | − | 0.266439i | ||||
\(573\) | − | 1.41617e20i | − | 0.291714i | ||||||
\(574\) | −1.58112e20 | + | 1.03503e19i | −0.321460 | + | 0.0210433i | ||||
\(575\) | 1.09275e21 | 2.19286 | ||||||||
\(576\) | 3.54166e20 | − | 1.46498e20i | 0.701518 | − | 0.290177i | ||||
\(577\) | 1.52447e20 | 0.298059 | 0.149029 | − | 0.988833i | \(-0.452385\pi\) | ||||
0.149029 | + | 0.988833i | \(0.452385\pi\) | |||||||
\(578\) | −4.46249e20 | + | 2.92123e19i | −0.861229 | + | 0.0563776i | ||||
\(579\) | − | 2.44941e20i | − | 0.466630i | ||||||
\(580\) | −3.34754e20 | + | 4.40158e19i | −0.629529 | + | 0.0827749i | ||||
\(581\) | − | 1.95437e20i | − | 0.362816i | ||||||
\(582\) | −1.05908e19 | − | 1.61786e20i | −0.0194091 | − | 0.296495i | ||||
\(583\) | −5.07880e20 | −0.918854 | ||||||||
\(584\) | −7.41630e20 | + | 1.47331e20i | −1.32462 | + | 0.263147i | ||||
\(585\) | −9.62497e20 | −1.69719 | ||||||||
\(586\) | 1.00111e19 | + | 1.52931e20i | 0.0174281 | + | 0.266234i | ||||
\(587\) | 7.28116e20i | 1.25145i | 0.780042 | + | 0.625727i | \(0.215198\pi\) | ||||
−0.780042 | + | 0.625727i | \(0.784802\pi\) | |||||||
\(588\) | 2.50881e19 | + | 1.90803e20i | 0.0425733 | + | 0.323784i | ||||
\(589\) | − | 7.84351e19i | − | 0.131415i | ||||||
\(590\) | −1.33896e21 | + | 8.76507e19i | −2.21502 | + | 0.144999i | ||||
\(591\) | 2.57004e20 | 0.419791 | ||||||||
\(592\) | −1.92922e20 | − | 7.20931e20i | −0.311149 | − | 1.16274i | ||||
\(593\) | 6.32845e19 | 0.100783 | 0.0503915 | − | 0.998730i | \(-0.483953\pi\) | ||||
0.0503915 | + | 0.998730i | \(0.483953\pi\) | |||||||
\(594\) | −8.31932e20 | + | 5.44598e19i | −1.30825 | + | 0.0856402i | ||||
\(595\) | 2.28960e20i | 0.355536i | ||||||||
\(596\) | 1.21885e20 | + | 9.26973e20i | 0.186897 | + | 1.42141i | ||||
\(597\) | 2.00337e19i | 0.0303357i | ||||||||
\(598\) | −7.32734e19 | − | 1.11933e21i | −0.109569 | − | 1.67379i | ||||
\(599\) | 7.33623e20 | 1.08336 | 0.541679 | − | 0.840586i | \(-0.317789\pi\) | ||||
0.541679 | + | 0.840586i | \(0.317789\pi\) | |||||||
\(600\) | 1.15363e20 | + | 5.80709e20i | 0.168241 | + | 0.846885i | ||||
\(601\) | −1.96003e20 | −0.282295 | −0.141148 | − | 0.989989i | \(-0.545079\pi\) | ||||
−0.141148 | + | 0.989989i | \(0.545079\pi\) | |||||||
\(602\) | −1.51676e19 | − | 2.31702e20i | −0.0215747 | − | 0.329577i | ||||
\(603\) | − | 7.32056e20i | − | 1.02841i | ||||||
\(604\) | 9.26422e19 | − | 1.21812e19i | 0.128538 | − | 0.0169011i | ||||
\(605\) | − | 1.58341e21i | − | 2.16984i | ||||||
\(606\) | −4.02670e20 | + | 2.63595e19i | −0.545011 | + | 0.0356774i | ||||
\(607\) | 2.86277e20 | 0.382711 | 0.191356 | − | 0.981521i | \(-0.438712\pi\) | ||||
0.191356 | + | 0.981521i | \(0.438712\pi\) | |||||||
\(608\) | 3.55832e19 | + | 1.04965e20i | 0.0469860 | + | 0.138601i | ||||
\(609\) | 8.31858e19 | 0.108497 | ||||||||
\(610\) | 4.58223e20 | − | 2.99961e19i | 0.590341 | − | 0.0386448i | ||||
\(611\) | 8.95705e20i | 1.13987i | ||||||||
\(612\) | 2.21561e20 | − | 2.91325e19i | 0.278521 | − | 0.0366219i | ||||
\(613\) | 1.49673e21i | 1.85862i | 0.369303 | + | 0.929309i | \(0.379596\pi\) | ||||
−0.369303 | + | 0.929309i | \(0.620404\pi\) | |||||||
\(614\) | 2.64567e19 | + | 4.04154e20i | 0.0324543 | + | 0.495775i | ||||
\(615\) | −3.74678e20 | −0.454041 | ||||||||
\(616\) | −1.42968e20 | − | 7.19666e20i | −0.171153 | − | 0.861541i | ||||
\(617\) | 2.70955e20 | 0.320448 | 0.160224 | − | 0.987081i | \(-0.448778\pi\) | ||||
0.160224 | + | 0.987081i | \(0.448778\pi\) | |||||||
\(618\) | 4.27284e19 | + | 6.52723e20i | 0.0499233 | + | 0.762633i | ||||
\(619\) | 9.61598e19i | 0.110998i | 0.998459 | + | 0.0554988i | \(0.0176749\pi\) | ||||
−0.998459 | + | 0.0554988i | \(0.982325\pi\) | |||||||
\(620\) | −1.70515e20 | − | 1.29682e21i | −0.194458 | − | 1.47891i | ||||
\(621\) | 9.54985e20i | 1.07599i | ||||||||
\(622\) | 1.60755e21 | − | 1.05233e20i | 1.78952 | − | 0.117145i | ||||
\(623\) | 8.34076e20 | 0.917371 | ||||||||
\(624\) | 5.87101e20 | − | 1.57108e20i | 0.638011 | − | 0.170732i | ||||
\(625\) | 3.13047e20 | 0.336132 | ||||||||
\(626\) | −7.98940e20 | + | 5.23000e19i | −0.847630 | + | 0.0554874i | ||||
\(627\) | − | 1.04042e20i | − | 0.109069i | ||||||
\(628\) | −4.05829e19 | − | 3.08646e20i | −0.0420384 | − | 0.319715i | ||||
\(629\) | − | 4.35135e20i | − | 0.445394i | ||||||
\(630\) | 4.71072e19 | + | 7.19614e20i | 0.0476468 | + | 0.727856i | ||||
\(631\) | −6.38381e20 | −0.638057 | −0.319029 | − | 0.947745i | \(-0.603357\pi\) | ||||
−0.319029 | + | 0.947745i | \(0.603357\pi\) | |||||||
\(632\) | 4.21308e20 | − | 8.36966e19i | 0.416123 | − | 0.0826665i | ||||
\(633\) | −5.95301e20 | −0.581044 | ||||||||
\(634\) | 8.41598e19 | + | 1.28563e21i | 0.0811775 | + | 1.24007i | ||||
\(635\) | − | 1.32317e21i | − | 1.26128i | ||||||
\(636\) | −3.12509e20 | + | 4.10909e19i | −0.294397 | + | 0.0387094i | ||||
\(637\) | − | 9.61940e20i | − | 0.895575i | ||||||
\(638\) | 6.29516e20 | − | 4.12092e19i | 0.579231 | − | 0.0379175i | ||||
\(639\) | −2.41093e20 | −0.219245 | ||||||||
\(640\) | 8.16512e20 | + | 1.65810e21i | 0.733859 | + | 1.49026i | ||||
\(641\) | −7.24707e20 | −0.643765 | −0.321882 | − | 0.946780i | \(-0.604316\pi\) | ||||
−0.321882 | + | 0.946780i | \(0.604316\pi\) | |||||||
\(642\) | 1.00989e21 | − | 6.61093e19i | 0.886670 | − | 0.0580430i | ||||
\(643\) | − | 2.26091e19i | − | 0.0196201i | −0.999952 | − | 0.00981006i | \(-0.996877\pi\) | ||
0.999952 | − | 0.00981006i | \(-0.00312269\pi\) | |||||||
\(644\) | −8.33286e20 | + | 1.09566e20i | −0.714743 | + | 0.0939794i | ||||
\(645\) | − | 5.49063e20i | − | 0.465505i | ||||||
\(646\) | 4.22122e18 | + | 6.44837e19i | 0.00353748 | + | 0.0540388i | ||||
\(647\) | −1.14582e21 | −0.949148 | −0.474574 | − | 0.880215i | \(-0.657398\pi\) | ||||
−0.474574 | + | 0.880215i | \(0.657398\pi\) | |||||||
\(648\) | 4.01876e20 | − | 7.98363e19i | 0.329064 | − | 0.0653714i | ||||
\(649\) | 2.50717e21 | 2.02931 | ||||||||
\(650\) | −1.93314e20 | − | 2.95309e21i | −0.154673 | − | 2.36280i | ||||
\(651\) | 3.22258e20i | 0.254886i | ||||||||
\(652\) | 2.60121e20 | + | 1.97830e21i | 0.203385 | + | 1.54681i | ||||
\(653\) | 1.94286e21i | 1.50173i | 0.660454 | + | 0.750866i | \(0.270364\pi\) | ||||
−0.660454 | + | 0.750866i | \(0.729636\pi\) | |||||||
\(654\) | 3.52748e20 | − | 2.30915e19i | 0.269545 | − | 0.0176449i | ||||
\(655\) | −2.96041e21 | −2.23636 | ||||||||
\(656\) | −7.20421e20 | + | 1.92785e20i | −0.538031 | + | 0.143977i | ||||
\(657\) | −1.38858e21 | −1.02525 | ||||||||
\(658\) | 6.69677e20 | − | 4.38383e19i | 0.488845 | − | 0.0320007i | ||||
\(659\) | 8.62593e20i | 0.622537i | 0.950322 | + | 0.311269i | \(0.100754\pi\) | ||||
−0.950322 | + | 0.311269i | \(0.899246\pi\) | |||||||
\(660\) | −2.26183e20 | − | 1.72020e21i | −0.161392 | − | 1.22743i | ||||
\(661\) | − | 1.45427e21i | − | 1.02597i | −0.858398 | − | 0.512984i | \(-0.828540\pi\) | ||
0.858398 | − | 0.512984i | \(-0.171460\pi\) | |||||||
\(662\) | 7.68014e19 | + | 1.17323e21i | 0.0535716 | + | 0.818364i | ||||
\(663\) | 3.54359e20 | 0.244395 | ||||||||
\(664\) | −1.79234e20 | − | 9.02221e20i | −0.122225 | − | 0.615251i | ||||
\(665\) | −2.08540e20 | −0.140614 | ||||||||
\(666\) | −8.95264e19 | − | 1.36761e21i | −0.0596890 | − | 0.911815i | ||||
\(667\) | − | 7.22629e20i | − | 0.476400i | ||||||
\(668\) | −1.87049e21 | + | 2.45945e20i | −1.21936 | + | 0.160330i | ||||
\(669\) | − | 5.29593e20i | − | 0.341387i | ||||||
\(670\) | 3.52265e21 | − | 2.30599e20i | 2.24548 | − | 0.146993i | ||||
\(671\) | −8.58011e20 | −0.540847 | ||||||||
\(672\) | −1.46197e20 | − | 4.31258e20i | −0.0911316 | − | 0.268824i | ||||
\(673\) | 2.10999e21 | 1.30067 | 0.650336 | − | 0.759647i | \(-0.274628\pi\) | ||||
0.650336 | + | 0.759647i | \(0.274628\pi\) | |||||||
\(674\) | −1.51186e21 | + | 9.89692e19i | −0.921643 | + | 0.0603324i | ||||
\(675\) | 2.51950e21i | 1.51892i | ||||||||
\(676\) | −1.34902e21 | + | 1.77378e20i | −0.804299 | + | 0.105755i | ||||
\(677\) | 1.82037e21i | 1.07336i | 0.843786 | + | 0.536680i | \(0.180322\pi\) | ||||
−0.843786 | + | 0.536680i | \(0.819678\pi\) | |||||||
\(678\) | −4.18122e19 | − | 6.38727e20i | −0.0243826 | − | 0.372471i | ||||
\(679\) | 6.07209e20 | 0.350199 | ||||||||
\(680\) | 2.09978e20 | + | 1.05698e21i | 0.119772 | + | 0.602905i | ||||
\(681\) | −4.13312e20 | −0.233171 | ||||||||
\(682\) | 1.59643e20 | + | 2.43872e21i | 0.0890772 | + | 1.36075i | ||||
\(683\) | − | 1.88174e21i | − | 1.03850i | −0.854624 | − | 0.519248i | \(-0.826212\pi\) | ||
0.854624 | − | 0.519248i | \(-0.173788\pi\) | |||||||
\(684\) | 2.65342e19 | + | 2.01801e20i | 0.0144839 | + | 0.110155i | ||||
\(685\) | 2.92026e20i | 0.157668i | ||||||||
\(686\) | −1.79996e21 | + | 1.17829e20i | −0.961243 | + | 0.0629247i | ||||
\(687\) | −3.49784e20 | −0.184767 | ||||||||
\(688\) | −2.82512e20 | − | 1.05572e21i | −0.147613 | − | 0.551616i | ||||
\(689\) | 1.57553e21 | 0.814294 | ||||||||
\(690\) | −1.98313e21 | + | 1.29819e20i | −1.01387 | + | 0.0663699i | ||||
\(691\) | − | 3.50914e21i | − | 1.77466i | −0.461135 | − | 0.887330i | \(-0.652558\pi\) | ||
0.461135 | − | 0.887330i | \(-0.347442\pi\) | |||||||
\(692\) | 9.24290e19 | + | 7.02951e20i | 0.0462394 | + | 0.351665i | ||||
\(693\) | − | 1.34746e21i | − | 0.666832i | ||||||
\(694\) | −6.34558e19 | − | 9.69356e20i | −0.0310653 | − | 0.474556i | ||||
\(695\) | 2.03830e21 | 0.987150 | ||||||||
\(696\) | 3.84020e20 | − | 7.62890e19i | 0.183986 | − | 0.0365504i | ||||
\(697\) | −4.34827e20 | −0.206097 | ||||||||
\(698\) | 1.86310e20 | + | 2.84608e21i | 0.0873614 | + | 1.33454i | ||||
\(699\) | 7.67436e20i | 0.356011i | ||||||||
\(700\) | −2.19843e21 | + | 2.89064e20i | −1.00897 | + | 0.132666i | ||||
\(701\) | 4.75438e20i | 0.215878i | 0.994158 | + | 0.107939i | \(0.0344251\pi\) | ||||
−0.994158 | + | 0.107939i | \(0.965575\pi\) | |||||||
\(702\) | 2.58079e21 | − | 1.68943e20i | 1.15938 | − | 0.0758948i | ||||
\(703\) | 3.96327e20 | 0.176153 | ||||||||
\(704\) | −1.32000e21 | − | 3.19116e21i | −0.580469 | − | 1.40331i | ||||
\(705\) | 1.58693e21 | 0.690461 | ||||||||
\(706\) | −1.62851e21 | + | 1.06605e20i | −0.701061 | + | 0.0458927i | ||||
\(707\) | − | 1.51129e21i | − | 0.643728i | ||||||
\(708\) | 1.54271e21 | − | 2.02847e20i | 0.650184 | − | 0.0854907i | ||||
\(709\) | 2.02240e21i | 0.843373i | 0.906742 | + | 0.421687i | \(0.138562\pi\) | ||||
−0.906742 | + | 0.421687i | \(0.861438\pi\) | |||||||
\(710\) | −7.59449e19 | − | 1.16014e21i | −0.0313373 | − | 0.478711i | ||||
\(711\) | 7.88832e20 | 0.322079 | ||||||||
\(712\) | 3.85044e21 | − | 7.64924e20i | 1.55564 | − | 0.309042i | ||||
\(713\) | 2.79943e21 | 1.11918 | ||||||||
\(714\) | −1.73433e19 | − | 2.64937e20i | −0.00686111 | − | 0.104811i | ||||
\(715\) | 8.67243e21i | 3.39505i | ||||||||
\(716\) | −2.77530e20 | − | 2.11070e21i | −0.107513 | − | 0.817672i | ||||
\(717\) | − | 1.20306e21i | − | 0.461205i | ||||||
\(718\) | −3.04805e21 | + | 1.99531e20i | −1.15635 | + | 0.0756967i | ||||
\(719\) | 4.23037e21 | 1.58822 | 0.794112 | − | 0.607772i | \(-0.207936\pi\) | ||||
0.794112 | + | 0.607772i | \(0.207936\pi\) | |||||||
\(720\) | 8.77418e20 | + | 3.27884e21i | 0.325997 | + | 1.21822i | ||||
\(721\) | −2.44978e21 | −0.900768 | ||||||||
\(722\) | 2.68348e21 | − | 1.75665e20i | 0.976492 | − | 0.0639229i | ||||
\(723\) | 4.08287e20i | 0.147037i | ||||||||
\(724\) | 2.70490e20 | + | 2.05716e21i | 0.0964078 | + | 0.733212i | ||||
\(725\) | − | 1.90648e21i | − | 0.672509i | ||||||
\(726\) | 1.19940e20 | + | 1.83221e21i | 0.0418735 | + | 0.639663i | ||||
\(727\) | −7.62091e20 | −0.263329 | −0.131664 | − | 0.991294i | \(-0.542032\pi\) | ||||
−0.131664 | + | 0.991294i | \(0.542032\pi\) | |||||||
\(728\) | 4.43510e20 | + | 2.23252e21i | 0.151676 | + | 0.763503i | ||||
\(729\) | −4.99204e20 | −0.168975 | ||||||||
\(730\) | −4.37407e20 | − | 6.68187e21i | −0.146543 | − | 2.23860i | ||||
\(731\) | − | 6.37207e20i | − | 0.211300i | ||||||
\(732\) | −5.27952e20 | + | 6.94189e19i | −0.173285 | + | 0.0227848i | ||||
\(733\) | − | 2.81226e21i | − | 0.913641i | −0.889559 | − | 0.456821i | \(-0.848988\pi\) | ||
0.889559 | − | 0.456821i | \(-0.151012\pi\) | |||||||
\(734\) | −2.00076e21 | + | 1.30974e20i | −0.643391 | + | 0.0421175i | ||||
\(735\) | −1.70428e21 | −0.542482 | ||||||||
\(736\) | −3.74631e21 | + | 1.27000e21i | −1.18038 | + | 0.400148i | ||||
\(737\) | −6.59608e21 | −2.05722 | ||||||||
\(738\) | −1.36664e21 | + | 8.94630e19i | −0.421923 | + | 0.0276198i | ||||
\(739\) | − | 5.97793e21i | − | 1.82691i | −0.406939 | − | 0.913455i | \(-0.633404\pi\) | ||
0.406939 | − | 0.913455i | \(-0.366596\pi\) | |||||||
\(740\) | 6.55276e21 | − | 8.61602e20i | 1.98238 | − | 0.260657i | ||||
\(741\) | 3.22755e20i | 0.0966576i | ||||||||
\(742\) | −7.71105e19 | − | 1.17795e21i | −0.0228604 | − | 0.349218i | ||||
\(743\) | 2.28812e21 | 0.671527 | 0.335764 | − | 0.941946i | \(-0.391006\pi\) | ||||
0.335764 | + | 0.941946i | \(0.391006\pi\) | |||||||
\(744\) | 2.95540e20 | + | 1.48768e21i | 0.0858656 | + | 0.432227i | ||||
\(745\) | −8.27986e21 | −2.38150 | ||||||||
\(746\) | 2.37196e20 | + | 3.62343e21i | 0.0675409 | + | 1.03176i | ||||
\(747\) | − | 1.68926e21i | − | 0.476204i | ||||||
\(748\) | −2.62494e20 | − | 1.99635e21i | −0.0732583 | − | 0.557152i | ||||
\(749\) | 3.79030e21i | 1.04727i | ||||||||
\(750\) | −2.25830e21 | + | 1.47832e20i | −0.617762 | + | 0.0404398i | ||||
\(751\) | −3.94337e21 | −1.06799 | −0.533996 | − | 0.845487i | \(-0.679310\pi\) | ||||
−0.533996 | + | 0.845487i | \(0.679310\pi\) | |||||||
\(752\) | 3.05130e21 | − | 8.16531e20i | 0.818185 | − | 0.218947i | ||||
\(753\) | 5.42176e20 | 0.143939 | ||||||||
\(754\) | −1.95286e21 | + | 1.27838e20i | −0.513318 | + | 0.0336027i | ||||
\(755\) | 8.27493e20i | 0.215359i | ||||||||
\(756\) | −2.52622e20 | − | 1.92127e21i | −0.0650965 | − | 0.495079i | ||||
\(757\) | 1.52988e21i | 0.390336i | 0.980770 | + | 0.195168i | \(0.0625253\pi\) | ||||
−0.980770 | + | 0.195168i | \(0.937475\pi\) | |||||||
\(758\) | 1.21986e20 | + | 1.86346e21i | 0.0308169 | + | 0.470762i | ||||
\(759\) | 3.71336e21 | 0.928868 | ||||||||
\(760\) | −9.62709e20 | + | 1.91251e20i | −0.238448 | + | 0.0473697i | ||||
\(761\) | 1.44614e21 | 0.354671 | 0.177336 | − | 0.984150i | \(-0.443252\pi\) | ||||
0.177336 | + | 0.984150i | \(0.443252\pi\) | |||||||
\(762\) | 1.00227e20 | + | 1.53108e21i | 0.0243401 | + | 0.371822i | ||||
\(763\) | 1.32393e21i | 0.318368i | ||||||||
\(764\) | 2.47499e21 | − | 3.25430e20i | 0.589351 | − | 0.0774920i | ||||
\(765\) | 1.97902e21i | 0.466648i | ||||||||
\(766\) | 2.86218e20 | − | 1.87363e19i | 0.0668314 | − | 0.00437490i | ||||
\(767\) | −7.77765e21 | −1.79839 | ||||||||
\(768\) | −1.07041e21 | − | 1.85679e21i | −0.245099 | − | 0.425162i | ||||
\(769\) | 1.78954e21 | 0.405782 | 0.202891 | − | 0.979201i | \(-0.434966\pi\) | ||||
0.202891 | + | 0.979201i | \(0.434966\pi\) | |||||||
\(770\) | 6.48398e21 | − | 4.24453e20i | 1.45600 | − | 0.0953123i | ||||
\(771\) | − | 1.59355e21i | − | 0.354371i | ||||||
\(772\) | 4.28074e21 | − | 5.62862e20i | 0.942735 | − | 0.123957i | ||||
\(773\) | − | 4.44104e21i | − | 0.968586i | −0.874906 | − | 0.484293i | \(-0.839077\pi\) | ||
0.874906 | − | 0.484293i | \(-0.160923\pi\) | |||||||
\(774\) | −1.31101e20 | − | 2.00272e21i | −0.0283172 | − | 0.432576i | ||||
\(775\) | 7.38563e21 | 1.57988 | ||||||||
\(776\) | 2.80313e21 | − | 5.56867e20i | 0.593855 | − | 0.117975i | ||||
\(777\) | −1.62835e21 | −0.341657 | ||||||||
\(778\) | 1.62963e19 | + | 2.48943e20i | 0.00338642 | + | 0.0517313i | ||||
\(779\) | − | 3.96047e20i | − | 0.0815108i | ||||||
\(780\) | 7.01658e20 | + | 5.33633e21i | 0.143026 | + | 1.08776i | ||||
\(781\) | 2.17234e21i | 0.438576i | ||||||||
\(782\) | −2.30149e21 | + | 1.50660e20i | −0.460213 | + | 0.0301264i | ||||
\(783\) | 1.66613e21 | 0.329986 | ||||||||
\(784\) | −3.27694e21 | + | 8.76911e20i | −0.642833 | + | 0.172022i | ||||
\(785\) | 2.75687e21 | 0.535666 | ||||||||
\(786\) | 3.42558e21 | − | 2.24245e20i | 0.659272 | − | 0.0431571i | ||||
\(787\) | 3.43008e21i | 0.653874i | 0.945046 | + | 0.326937i | \(0.106017\pi\) | ||||
−0.945046 | + | 0.326937i | \(0.893983\pi\) | |||||||
\(788\) | 5.90582e20 | + | 4.49156e21i | 0.111515 | + | 0.848106i | ||||
\(789\) | − | 7.06800e20i | − | 0.132196i | ||||||
\(790\) | 2.48484e20 | + | 3.79586e21i | 0.0460357 | + | 0.703245i | ||||
\(791\) | 2.39725e21 | 0.439936 | ||||||||
\(792\) | −1.23574e21 | − | 6.22043e21i | −0.224641 | − | 1.13079i | ||||
\(793\) | 2.66169e21 | 0.479302 | ||||||||
\(794\) | −2.39526e20 | − | 3.65901e21i | −0.0427266 | − | 0.652695i | ||||
\(795\) | − | 2.79138e21i | − | 0.493247i | ||||||
\(796\) | −3.50122e20 | + | 4.60365e19i | −0.0612875 | + | 0.00805851i | ||||
\(797\) | − | 1.81349e21i | − | 0.314469i | −0.987561 | − | 0.157234i | \(-0.949742\pi\) | ||
0.987561 | − | 0.157234i | \(-0.0502578\pi\) | |||||||
\(798\) | 2.41309e20 | − | 1.57965e19i | 0.0414525 | − | 0.00271356i | ||||
\(799\) | 1.84169e21 | 0.313412 | ||||||||
\(800\) | −9.88375e21 | + | 3.35060e21i | −1.66628 | + | 0.564869i | ||||
\(801\) | 7.20933e21 | 1.20407 | ||||||||
\(802\) | −1.67195e20 | + | 1.09449e19i | −0.0276640 | + | 0.00181094i | ||||
\(803\) | 1.25116e22i | 2.05091i | ||||||||
\(804\) | −4.05871e21 | + | 5.33667e20i | −0.659124 | + | 0.0866663i | ||||
\(805\) | − | 7.44303e21i | − | 1.19751i | ||||||
\(806\) | −4.95238e20 | − | 7.56530e21i | −0.0789408 | − | 1.20591i | ||||
\(807\) | −2.97244e21 | −0.469420 | ||||||||
\(808\) | −1.38599e21 | − | 6.97675e21i | −0.216858 | − | 1.09161i | ||||
\(809\) | 1.55831e21 | 0.241568 | 0.120784 | − | 0.992679i | \(-0.461459\pi\) | ||||
0.120784 | + | 0.992679i | \(0.461459\pi\) | |||||||
\(810\) | 2.37023e20 | + | 3.62079e21i | 0.0364043 | + | 0.556116i | ||||
\(811\) | − | 2.19869e21i | − | 0.334586i | −0.985907 | − | 0.167293i | \(-0.946497\pi\) | ||
0.985907 | − | 0.167293i | \(-0.0535027\pi\) | |||||||
\(812\) | 1.91157e20 | + | 1.45381e21i | 0.0288217 | + | 0.219198i | ||||
\(813\) | 8.92129e20i | 0.133275i | ||||||||
\(814\) | −1.23227e22 | + | 8.06665e20i | −1.82399 | + | 0.119402i | ||||
\(815\) | −1.76705e22 | −2.59159 | ||||||||
\(816\) | −3.23036e20 | − | 1.20716e21i | −0.0469434 | − | 0.175423i | ||||
\(817\) | 5.80377e20 | 0.0835689 | ||||||||
\(818\) | 8.94032e21 | − | 5.85249e20i | 1.27557 | − | 0.0835009i | ||||
\(819\) | 4.18004e21i | 0.590951i | ||||||||
\(820\) | −8.60992e20 | − | 6.54811e21i | −0.120613 | − | 0.917302i | ||||
\(821\) | 4.69997e21i | 0.652411i | 0.945299 | + | 0.326205i | \(0.105770\pi\) | ||||
−0.945299 | + | 0.326205i | \(0.894230\pi\) | |||||||
\(822\) | −2.21204e19 | − | 3.37913e20i | −0.00304266 | − | 0.0464800i | ||||
\(823\) | 5.67810e21 | 0.773934 | 0.386967 | − | 0.922094i | \(-0.373523\pi\) | ||||
0.386967 | + | 0.922094i | \(0.373523\pi\) | |||||||
\(824\) | −1.13092e22 | + | 2.24667e21i | −1.52749 | + | 0.303449i | ||||
\(825\) | 9.79682e21 | 1.31124 | ||||||||
\(826\) | 3.80660e20 | + | 5.81499e21i | 0.0504878 | + | 0.771256i | ||||
\(827\) | − | 1.14459e22i | − | 1.50438i | −0.658946 | − | 0.752190i | \(-0.728997\pi\) | ||
0.658946 | − | 0.752190i | \(-0.271003\pi\) | |||||||
\(828\) | −7.20250e21 | + | 9.47036e20i | −0.938115 | + | 0.123350i | ||||
\(829\) | 8.78189e21i | 1.13352i | 0.823883 | + | 0.566760i | \(0.191803\pi\) | ||||
−0.823883 | + | 0.566760i | \(0.808197\pi\) | |||||||
\(830\) | 8.12874e21 | − | 5.32122e20i | 1.03977 | − | 0.0680652i | ||||
\(831\) | −1.24152e21 | −0.157379 | ||||||||
\(832\) | 4.09485e21 | + | 9.89951e21i | 0.514415 | + | 1.24362i | ||||
\(833\) | −1.97787e21 | −0.246242 | ||||||||
\(834\) | −2.35859e21 | + | 1.54397e20i | −0.291009 | + | 0.0190500i | ||||
\(835\) | − | 1.67075e22i | − | 2.04297i | ||||||
\(836\) | 1.81830e21 | − | 2.39083e20i | 0.220353 | − | 0.0289735i | ||||
\(837\) | 6.45452e21i | 0.775217i | ||||||||
\(838\) | 7.35541e20 | + | 1.12362e22i | 0.0875541 | + | 1.33748i | ||||
\(839\) | 4.73338e21 | 0.558414 | 0.279207 | − | 0.960231i | \(-0.409928\pi\) | ||||
0.279207 | + | 0.960231i | \(0.409928\pi\) | |||||||
\(840\) | 3.95538e21 | − | 7.85772e20i | 0.462481 | − | 0.0918759i | ||||
\(841\) | 7.36844e21 | 0.853897 | ||||||||
\(842\) | −4.48586e20 | − | 6.85264e21i | −0.0515235 | − | 0.787078i | ||||
\(843\) | − | 7.51650e21i | − | 0.855675i | ||||||
\(844\) | −1.36797e21 | − | 1.04039e22i | −0.154351 | − | 1.17389i | ||||
\(845\) | − | 1.20496e22i | − | 1.34756i | ||||||
\(846\) | 5.78835e21 | − | 3.78916e20i | 0.641619 | − | 0.0420015i | ||||
\(847\) | −6.87661e21 | −0.755525 | ||||||||
\(848\) | −1.43626e21 | − | 5.36718e21i | −0.156410 | − | 0.584490i | ||||
\(849\) | −3.23148e21 | −0.348814 | ||||||||
\(850\) | −6.07194e21 | + | 3.97480e20i | −0.649659 | + | 0.0425278i | ||||
\(851\) | 1.41453e22i | 1.50018i | ||||||||
\(852\) | 1.75757e20 | + | 1.33668e21i | 0.0184763 | + | 0.140518i | ||||
\(853\) | 6.81363e21i | 0.710004i | 0.934865 | + | 0.355002i | \(0.115520\pi\) | ||||
−0.934865 | + | 0.355002i | \(0.884480\pi\) | |||||||
\(854\) | −1.30270e20 | − | 1.99002e21i | −0.0134559 | − | 0.205553i | ||||
\(855\) | −1.80252e21 | −0.184558 | ||||||||
\(856\) | 3.47605e21 | + | 1.74976e22i | 0.352803 | + | 1.77593i | ||||
\(857\) | −1.20231e22 | −1.20965 | −0.604825 | − | 0.796359i | \(-0.706757\pi\) | ||||
−0.604825 | + | 0.796359i | \(0.706757\pi\) | |||||||
\(858\) | −6.56919e20 | − | 1.00351e22i | −0.0655174 | − | 1.00085i | ||||
\(859\) | 1.96935e22i | 1.94704i | 0.228606 | + | 0.973519i | \(0.426583\pi\) | ||||
−0.228606 | + | 0.973519i | \(0.573417\pi\) | |||||||
\(860\) | 9.59578e21 | − | 1.26172e21i | 0.940463 | − | 0.123659i | ||||
\(861\) | 1.62720e21i | 0.158094i | ||||||||
\(862\) | 1.64419e22 | − | 1.07631e21i | 1.58360 | − | 0.103666i | ||||
\(863\) | −1.75887e22 | −1.67939 | −0.839695 | − | 0.543058i | \(-0.817266\pi\) | ||||
−0.839695 | + | 0.543058i | \(0.817266\pi\) | |||||||
\(864\) | −2.92819e21 | − | 8.63770e21i | −0.277170 | − | 0.817607i | ||||
\(865\) | −6.27886e21 | −0.589197 | ||||||||
\(866\) | 1.28635e22 | − | 8.42066e20i | 1.19667 | − | 0.0783361i | ||||
\(867\) | 4.59252e21i | 0.423553i | ||||||||
\(868\) | −5.63199e21 | + | 7.40533e20i | −0.514948 | + | 0.0677090i | ||||
\(869\) | − | 7.10765e21i | − | 0.644285i | ||||||
\(870\) | 2.26492e20 | + | 3.45991e21i | 0.0203544 | + | 0.310935i | ||||
\(871\) | 2.04621e22 | 1.82312 | ||||||||
\(872\) | 1.21416e21 | + | 6.11179e21i | 0.107251 | + | 0.539877i | ||||
\(873\) | 5.24841e21 | 0.459644 | ||||||||
\(874\) | −1.37223e20 | − | 2.09623e21i | −0.0119149 | − | 0.182013i | ||||
\(875\) | − | 8.47577e21i | − | 0.729657i | ||||||
\(876\) | 1.01227e21 | + | 7.69867e21i | 0.0864008 | + | 0.657105i | ||||
\(877\) | − | 1.93194e22i | − | 1.63492i | −0.575983 | − | 0.817462i | \(-0.695380\pi\) | ||
0.575983 | − | 0.817462i | \(-0.304620\pi\) | |||||||
\(878\) | −1.04977e22 | + | 6.87200e20i | −0.880819 | + | 0.0576600i | ||||
\(879\) | 1.57387e21 | 0.130934 | ||||||||
\(880\) | 2.95435e22 | − | 7.90585e21i | 2.43692 | − | 0.652121i | ||||
\(881\) | 4.62940e21 | 0.378621 | 0.189311 | − | 0.981917i | \(-0.439375\pi\) | ||||
0.189311 | + | 0.981917i | \(0.439375\pi\) | |||||||
\(882\) | −6.21638e21 | + | 4.06936e20i | −0.504108 | + | 0.0329998i | ||||
\(883\) | − | 5.41532e21i | − | 0.435431i | −0.976012 | − | 0.217715i | \(-0.930140\pi\) | ||
0.976012 | − | 0.217715i | \(-0.0698604\pi\) | |||||||
\(884\) | 8.14298e20 | + | 6.19299e21i | 0.0649220 | + | 0.493752i | ||||
\(885\) | 1.37798e22i | 1.08935i | ||||||||
\(886\) | −1.47321e21 | − | 2.25048e22i | −0.115481 | − | 1.76410i | ||||
\(887\) | −1.26185e22 | −0.980797 | −0.490399 | − | 0.871498i | \(-0.663149\pi\) | ||||
−0.490399 | + | 0.871498i | \(0.663149\pi\) | |||||||
\(888\) | −7.51714e21 | + | 1.49334e21i | −0.579369 | + | 0.115097i | ||||
\(889\) | −5.74639e21 | −0.439169 | ||||||||
\(890\) | 2.27095e21 | + | 3.46913e22i | 0.172101 | + | 2.62903i | ||||
\(891\) | − | 6.77983e21i | − | 0.509491i | ||||||
\(892\) | 9.25550e21 | − | 1.21698e21i | 0.689706 | − | 0.0906873i | ||||
\(893\) | 1.67743e21i | 0.123954i | ||||||||
\(894\) | 9.58089e21 | − | 6.27182e20i | 0.702060 | − | 0.0459581i | ||||
\(895\) | 1.88531e22 | 1.36997 | ||||||||
\(896\) | 7.20099e21 | − | 3.54604e21i | 0.518898 | − | 0.255525i | ||||
\(897\) | −1.15195e22 | −0.823169 | ||||||||
\(898\) | −2.70076e22 | + | 1.76797e21i | −1.91387 | + | 0.125286i | ||||
\(899\) | − | 4.88408e21i | − | 0.343230i | ||||||
\(900\) | −1.90021e22 | + | 2.49853e21i | −1.32429 | + | 0.174127i | ||||
\(901\) | − | 3.23949e21i | − | 0.223893i | ||||||
\(902\) | 8.06093e20 | + | 1.23140e22i | 0.0552505 | + | 0.844012i | ||||
\(903\) | −2.38454e21 | −0.162086 | ||||||||
\(904\) | 1.10667e22 | − | 2.19850e21i | 0.746028 | − | 0.148205i | ||||
\(905\) | −1.83749e22 | −1.22846 | ||||||||
\(906\) | −6.26809e19 | − | 9.57519e20i | −0.00415598 | − | 0.0634871i | ||||
\(907\) | 1.94803e22i | 1.28098i | 0.767967 | + | 0.640489i | \(0.221268\pi\) | ||||
−0.767967 | + | 0.640489i | \(0.778732\pi\) | |||||||
\(908\) | −9.49771e20 | − | 7.22330e21i | −0.0619405 | − | 0.471077i | ||||
\(909\) | − | 1.30628e22i | − | 0.844906i | ||||||
\(910\) | −2.01144e22 | + | 1.31672e21i | −1.29031 | + | 0.0844663i | ||||
\(911\) | 1.13836e22 | 0.724254 | 0.362127 | − | 0.932129i | \(-0.382051\pi\) | ||||
0.362127 | + | 0.932129i | \(0.382051\pi\) | |||||||
\(912\) | 1.09949e21 | − | 2.94225e20i | 0.0693796 | − | 0.0185660i | ||||
\(913\) | −1.52209e22 | −0.952595 | ||||||||
\(914\) | −1.75209e22 | + | 1.14695e21i | −1.08758 | + | 0.0711947i | ||||
\(915\) | − | 4.71575e21i | − | 0.290330i | ||||||
\(916\) | −8.03787e20 | − | 6.11305e21i | −0.0490823 | − | 0.373286i | ||||
\(917\) | 1.28568e22i | 0.778686i | ||||||||
\(918\) | −3.47369e20 | − | 5.30644e21i | −0.0208675 | − | 0.318774i | ||||
\(919\) | 2.62399e22 | 1.56349 | 0.781746 | − | 0.623597i | \(-0.214329\pi\) | ||||
0.781746 | + | 0.623597i | \(0.214329\pi\) | |||||||
\(920\) | −6.82594e21 | − | 3.43601e22i | −0.403417 | − | 2.03070i | ||||
\(921\) | 4.15930e21 | 0.243822 | ||||||||
\(922\) | −1.83440e21 | − | 2.80225e22i | −0.106663 | − | 1.62939i | ||||
\(923\) | − | 6.73894e21i | − | 0.388668i | ||||||
\(924\) | −7.47066e21 | + | 9.82295e20i | −0.427385 | + | 0.0561956i | ||||
\(925\) | 3.73191e22i | 2.11772i | ||||||||
\(926\) | 1.54382e22 | − | 1.01061e21i | 0.868990 | − | 0.0568856i | ||||
\(927\) | −2.11747e22 | −1.18228 | ||||||||
\(928\) | 2.21573e21 | + | 6.53607e21i | 0.122718 | + | 0.361999i | ||||
\(929\) | 2.40119e22 | 1.31920 | 0.659598 | − | 0.751618i | \(-0.270726\pi\) | ||||
0.659598 | + | 0.751618i | \(0.270726\pi\) | |||||||
\(930\) | −1.34035e22 | + | 8.77419e20i | −0.730461 | + | 0.0478173i | ||||
\(931\) | − | 1.80148e21i | − | 0.0973881i | ||||||
\(932\) | −1.34122e22 | + | 1.76353e21i | −0.719251 | + | 0.0945722i | ||||
\(933\) | − | 1.65439e22i | − | 0.880085i | ||||||
\(934\) | 1.03629e21 | + | 1.58305e22i | 0.0546864 | + | 0.835395i | ||||
\(935\) | 1.78317e22 | 0.933479 | ||||||||
\(936\) | 3.83348e21 | + | 1.92968e22i | 0.199078 | + | 1.00211i | ||||
\(937\) | −1.34584e22 | −0.693341 | −0.346671 | − | 0.937987i | \(-0.612688\pi\) | ||||
−0.346671 | + | 0.937987i | \(0.612688\pi\) | |||||||
\(938\) | −1.00147e21 | − | 1.52986e22i | −0.0511821 | − | 0.781862i | ||||
\(939\) | 8.22219e21i | 0.416865i | ||||||||
\(940\) | 3.64669e21 | + | 2.77342e22i | 0.183417 | + | 1.39494i | ||||
\(941\) | − | 1.34511e21i | − | 0.0671172i | −0.999437 | − | 0.0335586i | \(-0.989316\pi\) | ||
0.999437 | − | 0.0335586i | \(-0.0106840\pi\) | |||||||
\(942\) | −3.19006e21 | + | 2.08827e20i | −0.157913 | + | 0.0103373i | ||||
\(943\) | 1.41353e22 | 0.694174 | ||||||||
\(944\) | 7.09016e21 | + | 2.64953e22i | 0.345435 | + | 1.29086i | ||||
\(945\) | 1.71611e22 | 0.829479 | ||||||||
\(946\) | −1.80452e22 | + | 1.18127e21i | −0.865322 | + | 0.0566456i | ||||
\(947\) | − | 2.00072e22i | − | 0.951835i | −0.879490 | − | 0.475917i | \(-0.842116\pi\) | ||
0.879490 | − | 0.475917i | \(-0.157884\pi\) | |||||||
\(948\) | −5.75057e20 | − | 4.37349e21i | −0.0271424 | − | 0.206426i | ||||
\(949\) | − | 3.88131e22i | − | 1.81753i | ||||||
\(950\) | −3.62030e20 | − | 5.53040e21i | −0.0168197 | − | 0.256939i | ||||
\(951\) | 1.32309e22 | 0.609869 | ||||||||
\(952\) | 4.59036e21 | − | 9.11915e20i | 0.209928 | − | 0.0417040i | ||||
\(953\) | 2.84287e22 | 1.28991 | 0.644956 | − | 0.764220i | \(-0.276876\pi\) | ||||
0.644956 | + | 0.764220i | \(0.276876\pi\) | |||||||
\(954\) | −6.66505e20 | − | 1.01816e22i | −0.0300048 | − | 0.458356i | ||||
\(955\) | 2.21070e22i | 0.987426i | ||||||||
\(956\) | 2.10254e22 | − | 2.76457e21i | 0.931775 | − | 0.122516i | ||||
\(957\) | − | 6.47859e21i | − | 0.284866i | ||||||
\(958\) | 2.99079e22 | − | 1.95782e21i | 1.30480 | − | 0.0854147i | ||||
\(959\) | 1.26825e21 | 0.0548989 | ||||||||
\(960\) | 1.75391e22 | − | 7.25490e21i | 0.753308 | − | 0.311600i | ||||
\(961\) | −4.54454e21 | −0.193671 | ||||||||
\(962\) | 3.82270e22 | − | 2.50241e21i | 1.61643 | − | 0.105814i | ||||
\(963\) | 3.27614e22i | 1.37457i | ||||||||
\(964\) | −7.13548e21 | + | 9.38223e20i | −0.297061 | + | 0.0390596i | ||||
\(965\) | 3.82362e22i | 1.57950i | ||||||||
\(966\) | 5.63794e20 | + | 8.61257e21i | 0.0231096 | + | 0.353024i | ||||
\(967\) | −1.28151e22 | −0.521222 | −0.260611 | − | 0.965444i | \(-0.583924\pi\) | ||||
−0.260611 | + | 0.965444i | \(0.583924\pi\) | |||||||
\(968\) | −3.17453e22 | + | 6.30648e21i | −1.28119 | + | 0.254520i | ||||
\(969\) | 6.63626e20 | 0.0265763 | ||||||||
\(970\) | 1.65326e21 | + | 2.52554e22i | 0.0656982 | + | 1.00361i | ||||
\(971\) | 9.93289e20i | 0.0391680i | 0.999808 | + | 0.0195840i | \(0.00623418\pi\) | ||||
−0.999808 | + | 0.0195840i | \(0.993766\pi\) | |||||||
\(972\) | −3.42477e21 | − | 2.60465e22i | −0.134009 | − | 1.01918i | ||||
\(973\) | − | 8.85218e21i | − | 0.343719i | ||||||
\(974\) | −4.18577e22 | + | 2.74008e21i | −1.61281 | + | 0.105577i | ||||
\(975\) | −3.03913e22 | −1.16202 | ||||||||
\(976\) | −2.42642e21 | − | 9.06731e21i | −0.0920644 | − | 0.344037i | ||||
\(977\) | −5.30610e21 | −0.199787 | −0.0998933 | − | 0.994998i | \(-0.531850\pi\) | ||||
−0.0998933 | + | 0.994998i | \(0.531850\pi\) | |||||||
\(978\) | 2.04471e22 | − | 1.33850e21i | 0.763994 | − | 0.0500124i | ||||
\(979\) | − | 6.49586e22i | − | 2.40861i | ||||||
\(980\) | −3.91635e21 | − | 2.97851e22i | −0.144107 | − | 1.09598i | ||||
\(981\) | 1.14433e22i | 0.417865i | ||||||||
\(982\) | 5.39007e20 | + | 8.23391e21i | 0.0195325 | + | 0.298380i | ||||
\(983\) | −3.43620e22 | −1.23574 | −0.617870 | − | 0.786281i | \(-0.712004\pi\) | ||||
−0.617870 | + | 0.786281i | \(0.712004\pi\) | |||||||
\(984\) | 1.49229e21 | + | 7.51181e21i | 0.0532585 | + | 0.268091i | ||||
\(985\) | −4.01193e22 | −1.42096 | ||||||||
\(986\) | 2.62851e20 | + | 4.01534e21i | 0.00923918 | + | 0.141139i | ||||
\(987\) | − | 6.89190e21i | − | 0.240414i | ||||||
\(988\) | −5.64066e21 | + | 7.41674e20i | −0.195278 | + | 0.0256765i | ||||
\(989\) | 2.07143e22i | 0.711701i | ||||||||
\(990\) | 5.60442e22 | − | 3.66876e21i | 1.91103 | − | 0.125099i | ||||
\(991\) | −3.47863e22 | −1.17722 | −0.588608 | − | 0.808418i | \(-0.700324\pi\) | ||||
−0.588608 | + | 0.808418i | \(0.700324\pi\) | |||||||
\(992\) | −2.53205e22 | + | 8.58366e21i | −0.850421 | + | 0.288293i | ||||
\(993\) | 1.20741e22 | 0.402472 | ||||||||
\(994\) | −5.03840e21 | + | 3.29822e20i | −0.166684 | + | 0.0109114i | ||||
\(995\) | − | 3.12734e21i | − | 0.102684i | ||||||
\(996\) | −9.36571e21 | + | 1.23147e21i | −0.305208 | + | 0.0401309i | ||||
\(997\) | − | 5.81285e21i | − | 0.188008i | −0.995572 | − | 0.0940038i | \(-0.970033\pi\) | ||
0.995572 | − | 0.0940038i | \(-0.0299666\pi\) | |||||||
\(998\) | −1.05731e21 | − | 1.61515e22i | −0.0339408 | − | 0.518483i | ||||
\(999\) | −3.26143e22 | −1.03912 |
(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 | 8.16.b.a.5.13 | ✓ | 14 | |
3.2 | odd | 2 | 72.16.d.b.37.2 | 14 | |||
4.3 | odd | 2 | 32.16.b.a.17.9 | 14 | |||
8.3 | odd | 2 | 32.16.b.a.17.6 | 14 | |||
8.5 | even | 2 | inner | 8.16.b.a.5.14 | yes | 14 | |
24.5 | odd | 2 | 72.16.d.b.37.1 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.16.b.a.5.13 | ✓ | 14 | 1.1 | even | 1 | trivial | |
8.16.b.a.5.14 | yes | 14 | 8.5 | even | 2 | inner | |
32.16.b.a.17.6 | 14 | 8.3 | odd | 2 | |||
32.16.b.a.17.9 | 14 | 4.3 | odd | 2 | |||
72.16.d.b.37.1 | 14 | 24.5 | odd | 2 | |||
72.16.d.b.37.2 | 14 | 3.2 | odd | 2 |