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 | 3.4 | ||
Root | \(0.500000 + 4.81893e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −453236. | + | 263543.i | −0.864479 | + | 0.502669i | ||||
\(3\) | − | 7.71029e8i | − | 0.663386i | −0.943387 | − | 0.331693i | \(-0.892380\pi\) | ||
0.943387 | − | 0.331693i | \(-0.107620\pi\) | |||||||
\(4\) | 1.35968e11 | − | 2.38895e11i | 0.494648 | − | 0.869093i | ||||
\(5\) | −2.10588e13 | −1.10409 | −0.552045 | − | 0.833814i | \(-0.686152\pi\) | ||||
−0.552045 | + | 0.833814i | \(0.686152\pi\) | |||||||
\(6\) | 2.03199e14 | + | 3.49458e14i | 0.333464 | + | 0.573484i | ||||
\(7\) | − | 5.85221e15i | − | 0.513402i | −0.966491 | − | 0.256701i | \(-0.917364\pi\) | ||
0.966491 | − | 0.256701i | \(-0.0826355\pi\) | |||||||
\(8\) | 1.33358e15 | + | 1.44109e17i | 0.00925358 | + | 0.999957i | ||||
\(9\) | 7.56367e17 | 0.559918 | ||||||||
\(10\) | 9.54463e18 | − | 5.54992e18i | 0.954463 | − | 0.554992i | ||||
\(11\) | − | 6.60292e19i | − | 1.07963i | −0.841783 | − | 0.539815i | \(-0.818494\pi\) | ||
0.841783 | − | 0.539815i | \(-0.181506\pi\) | |||||||
\(12\) | −1.84195e20 | − | 1.04835e20i | −0.576545 | − | 0.328143i | ||||
\(13\) | 1.72571e21 | 1.18044 | 0.590221 | − | 0.807242i | \(-0.299041\pi\) | ||||
0.590221 | + | 0.807242i | \(0.299041\pi\) | |||||||
\(14\) | 1.54231e21 | + | 2.65243e21i | 0.258071 | + | 0.443825i | ||||
\(15\) | 1.62370e22i | 0.732438i | ||||||||
\(16\) | −3.85834e22 | − | 6.49639e22i | −0.510647 | − | 0.859791i | ||||
\(17\) | 2.34447e23 | 0.980654 | 0.490327 | − | 0.871539i | \(-0.336877\pi\) | ||||
0.490327 | + | 0.871539i | \(0.336877\pi\) | |||||||
\(18\) | −3.42813e23 | + | 1.99335e23i | −0.484038 | + | 0.281454i | ||||
\(19\) | 2.63164e24i | 1.33018i | 0.746765 | + | 0.665088i | \(0.231606\pi\) | ||||
−0.746765 | + | 0.665088i | \(0.768394\pi\) | |||||||
\(20\) | −2.86332e24 | + | 5.03084e24i | −0.546136 | + | 0.959557i | ||||
\(21\) | −4.51222e24 | −0.340584 | ||||||||
\(22\) | 1.74016e25 | + | 2.99268e25i | 0.542697 | + | 0.933318i | ||||
\(23\) | 9.74799e23i | 0.0130643i | 0.999979 | + | 0.00653215i | \(0.00207926\pi\) | ||||
−0.999979 | + | 0.00653215i | \(0.997921\pi\) | |||||||
\(24\) | 1.11112e26 | − | 1.02823e24i | 0.663358 | − | 0.00613870i | ||||
\(25\) | 7.96770e25 | 0.219015 | ||||||||
\(26\) | −7.82155e26 | + | 4.54800e26i | −1.02047 | + | 0.593372i | ||||
\(27\) | − | 1.62473e27i | − | 1.03483i | ||||||
\(28\) | −1.39806e27 | − | 7.95713e26i | −0.446194 | − | 0.253953i | ||||
\(29\) | 4.55931e27 | 0.747029 | 0.373515 | − | 0.927624i | \(-0.378153\pi\) | ||||
0.373515 | + | 0.927624i | \(0.378153\pi\) | |||||||
\(30\) | −4.27914e27 | − | 7.35918e27i | −0.368174 | − | 0.633178i | ||||
\(31\) | − | 2.63620e28i | − | 1.21648i | −0.793753 | − | 0.608241i | \(-0.791876\pi\) | ||
0.793753 | − | 0.608241i | \(-0.208124\pi\) | |||||||
\(32\) | 3.46082e28 | + | 1.92756e28i | 0.873634 | + | 0.486584i | ||||
\(33\) | −5.09104e28 | −0.716213 | ||||||||
\(34\) | −1.06260e29 | + | 6.17870e28i | −0.847755 | + | 0.492944i | ||||
\(35\) | 1.23241e29i | 0.566842i | ||||||||
\(36\) | 1.02841e29 | − | 1.80692e29i | 0.276962 | − | 0.486621i | ||||
\(37\) | −1.68618e29 | −0.269818 | −0.134909 | − | 0.990858i | \(-0.543074\pi\) | ||||
−0.134909 | + | 0.990858i | \(0.543074\pi\) | |||||||
\(38\) | −6.93552e29 | − | 1.19276e30i | −0.668638 | − | 1.14991i | ||||
\(39\) | − | 1.33057e30i | − | 0.783090i | ||||||
\(40\) | −2.80837e28 | − | 3.03477e30i | −0.0102168 | − | 1.10404i | ||||
\(41\) | −3.77960e30 | −0.860107 | −0.430053 | − | 0.902804i | \(-0.641505\pi\) | ||||
−0.430053 | + | 0.902804i | \(0.641505\pi\) | |||||||
\(42\) | 2.04510e30 | − | 1.18917e30i | 0.294428 | − | 0.171201i | ||||
\(43\) | − | 2.13020e31i | − | 1.96119i | −0.196051 | − | 0.980594i | \(-0.562812\pi\) | ||
0.196051 | − | 0.980594i | \(-0.437188\pi\) | |||||||
\(44\) | −1.57740e31 | − | 8.97785e30i | −0.938300 | − | 0.534037i | ||||
\(45\) | −1.59282e31 | −0.618200 | ||||||||
\(46\) | −2.56902e29 | − | 4.41814e29i | −0.00656702 | − | 0.0112938i | ||||
\(47\) | 1.21346e31i | 0.206141i | 0.994674 | + | 0.103071i | \(0.0328668\pi\) | ||||
−0.994674 | + | 0.103071i | \(0.967133\pi\) | |||||||
\(48\) | −5.00890e31 | + | 2.97489e31i | −0.570373 | + | 0.338756i | ||||
\(49\) | 9.56864e31 | 0.736419 | ||||||||
\(50\) | −3.61125e31 | + | 2.09983e31i | −0.189333 | + | 0.110092i | ||||
\(51\) | − | 1.80766e32i | − | 0.650553i | ||||||
\(52\) | 2.34641e32 | − | 4.12263e32i | 0.583903 | − | 1.02591i | ||||
\(53\) | −5.52099e32 | −0.956700 | −0.478350 | − | 0.878169i | \(-0.658765\pi\) | ||||
−0.478350 | + | 0.878169i | \(0.658765\pi\) | |||||||
\(54\) | 4.28186e32 | + | 7.36384e32i | 0.520176 | + | 0.894588i | ||||
\(55\) | 1.39050e33i | 1.19201i | ||||||||
\(56\) | 8.43357e32 | − | 7.80440e30i | 0.513380 | − | 0.00475080i | ||||
\(57\) | 2.02907e33 | 0.882420 | ||||||||
\(58\) | −2.06645e33 | + | 1.20158e33i | −0.645791 | + | 0.375508i | ||||
\(59\) | 3.38179e33i | 0.763763i | 0.924211 | + | 0.381881i | \(0.124724\pi\) | ||||
−0.924211 | + | 0.381881i | \(0.875276\pi\) | |||||||
\(60\) | 3.87892e33 | + | 2.20770e33i | 0.636557 | + | 0.362299i | ||||
\(61\) | 2.82365e33 | 0.338488 | 0.169244 | − | 0.985574i | \(-0.445867\pi\) | ||||
0.169244 | + | 0.985574i | \(0.445867\pi\) | |||||||
\(62\) | 6.94752e33 | + | 1.19482e34i | 0.611487 | + | 1.05162i | ||||
\(63\) | − | 4.42642e33i | − | 0.287463i | ||||||
\(64\) | −2.07656e34 | + | 3.84362e32i | −0.999829 | + | 0.0185064i | ||||
\(65\) | −3.63415e34 | −1.30331 | ||||||||
\(66\) | 2.30744e34 | − | 1.34171e34i | 0.619151 | − | 0.360018i | ||||
\(67\) | − | 9.12806e34i | − | 1.84059i | −0.391224 | − | 0.920296i | \(-0.627948\pi\) | ||
0.391224 | − | 0.920296i | \(-0.372052\pi\) | |||||||
\(68\) | 3.18773e34 | − | 5.60082e34i | 0.485078 | − | 0.852280i | ||||
\(69\) | 7.51598e32 | 0.00866668 | ||||||||
\(70\) | −3.24793e34 | − | 5.58572e34i | −0.284934 | − | 0.490023i | ||||
\(71\) | 3.38934e34i | 0.227095i | 0.993533 | + | 0.113547i | \(0.0362213\pi\) | ||||
−0.993533 | + | 0.113547i | \(0.963779\pi\) | |||||||
\(72\) | 1.00868e33 | + | 1.08999e35i | 0.00518125 | + | 0.559894i | ||||
\(73\) | −4.50107e35 | −1.77902 | −0.889511 | − | 0.456914i | \(-0.848955\pi\) | ||||
−0.889511 | + | 0.456914i | \(0.848955\pi\) | |||||||
\(74\) | 7.64238e34 | − | 4.44382e34i | 0.233252 | − | 0.135629i | ||||
\(75\) | − | 6.14333e34i | − | 0.145291i | ||||||
\(76\) | 6.28686e35 | + | 3.57819e35i | 1.15605 | + | 0.657968i | ||||
\(77\) | −3.86417e35 | −0.554285 | ||||||||
\(78\) | 3.50664e35 | + | 6.03064e35i | 0.393635 | + | 0.676964i | ||||
\(79\) | − | 1.73909e36i | − | 1.53252i | −0.642531 | − | 0.766260i | \(-0.722115\pi\) | ||
0.642531 | − | 0.766260i | \(-0.277885\pi\) | |||||||
\(80\) | 8.12522e35 | + | 1.36807e36i | 0.563800 | + | 0.949286i | ||||
\(81\) | −2.30971e35 | −0.126573 | ||||||||
\(82\) | 1.71305e36 | − | 9.96088e35i | 0.743544 | − | 0.432349i | ||||
\(83\) | 2.19300e36i | 0.756059i | 0.925794 | + | 0.378029i | \(0.123398\pi\) | ||||
−0.925794 | + | 0.378029i | \(0.876602\pi\) | |||||||
\(84\) | −6.13517e35 | + | 1.07795e36i | −0.168469 | + | 0.295999i | ||||
\(85\) | −4.93719e36 | −1.08273 | ||||||||
\(86\) | 5.61399e36 | + | 9.65482e36i | 0.985828 | + | 1.69541i | ||||
\(87\) | − | 3.51536e36i | − | 0.495569i | ||||||
\(88\) | 9.51541e36 | − | 8.80554e34i | 1.07958 | − | 0.00999045i | ||||
\(89\) | −1.76726e37 | −1.61767 | −0.808836 | − | 0.588035i | \(-0.799902\pi\) | ||||
−0.808836 | + | 0.588035i | \(0.799902\pi\) | |||||||
\(90\) | 7.21924e36 | − | 4.19777e36i | 0.534421 | − | 0.310750i | ||||
\(91\) | − | 1.00992e37i | − | 0.606041i | ||||||
\(92\) | 2.32874e35 | + | 1.32541e35i | 0.0113541 | + | 0.00646223i | ||||
\(93\) | −2.03258e37 | −0.806997 | ||||||||
\(94\) | −3.19799e36 | − | 5.49983e36i | −0.103621 | − | 0.178205i | ||||
\(95\) | − | 5.54194e37i | − | 1.46863i | ||||||
\(96\) | 1.48620e37 | − | 2.66839e37i | 0.322794 | − | 0.579557i | ||||
\(97\) | −1.37640e37 | −0.245517 | −0.122758 | − | 0.992437i | \(-0.539174\pi\) | ||||
−0.122758 | + | 0.992437i | \(0.539174\pi\) | |||||||
\(98\) | −4.33685e37 | + | 2.52175e37i | −0.636618 | + | 0.370175i | ||||
\(99\) | − | 4.99423e37i | − | 0.604505i | ||||||
\(100\) | 1.08335e37 | − | 1.90344e37i | 0.108335 | − | 0.190344i | ||||
\(101\) | 2.42651e36 | 0.0200852 | 0.0100426 | − | 0.999950i | \(-0.496803\pi\) | ||||
0.0100426 | + | 0.999950i | \(0.496803\pi\) | |||||||
\(102\) | 4.76396e37 | + | 8.19295e37i | 0.327013 | + | 0.562389i | ||||
\(103\) | 2.01919e38i | 1.15151i | 0.817621 | + | 0.575757i | \(0.195293\pi\) | ||||
−0.817621 | + | 0.575757i | \(0.804707\pi\) | |||||||
\(104\) | 2.30138e36 | + | 2.48691e38i | 0.0109233 | + | 1.18039i | ||||
\(105\) | 9.50222e37 | 0.376035 | ||||||||
\(106\) | 2.50231e38 | − | 1.45502e38i | 0.827047 | − | 0.480903i | ||||
\(107\) | 4.85956e38i | 1.34371i | 0.740683 | + | 0.671855i | \(0.234502\pi\) | ||||
−0.740683 | + | 0.671855i | \(0.765498\pi\) | |||||||
\(108\) | −3.88138e38 | − | 2.20910e38i | −0.899363 | − | 0.511876i | ||||
\(109\) | 7.12284e38 | 1.38532 | 0.692660 | − | 0.721265i | \(-0.256439\pi\) | ||||
0.692660 | + | 0.721265i | \(0.256439\pi\) | |||||||
\(110\) | −3.66457e38 | − | 6.30224e38i | −0.599186 | − | 1.03047i | ||||
\(111\) | 1.30009e38i | 0.178994i | ||||||||
\(112\) | −3.80183e38 | + | 2.25798e38i | −0.441418 | + | 0.262167i | ||||
\(113\) | 5.09915e38 | 0.500043 | 0.250021 | − | 0.968240i | \(-0.419562\pi\) | ||||
0.250021 | + | 0.968240i | \(0.419562\pi\) | |||||||
\(114\) | −9.19649e38 | + | 5.34749e38i | −0.762834 | + | 0.443565i | ||||
\(115\) | − | 2.05281e37i | − | 0.0144242i | ||||||
\(116\) | 6.19920e38 | − | 1.08920e39i | 0.369516 | − | 0.649238i | ||||
\(117\) | 1.30527e39 | 0.660951 | ||||||||
\(118\) | −8.91248e38 | − | 1.53275e39i | −0.383920 | − | 0.660257i | ||||
\(119\) | − | 1.37204e39i | − | 0.503470i | ||||||
\(120\) | −2.33989e39 | + | 2.16533e37i | −0.732407 | + | 0.00677768i | ||||
\(121\) | −6.19427e38 | −0.165603 | ||||||||
\(122\) | −1.27978e39 | + | 7.44154e38i | −0.292616 | + | 0.170148i | ||||
\(123\) | 2.91418e39i | 0.570583i | ||||||||
\(124\) | −6.29773e39 | − | 3.58438e39i | −1.05724 | − | 0.601730i | ||||
\(125\) | 5.98326e39 | 0.862278 | ||||||||
\(126\) | 1.16655e39 | + | 2.00621e39i | 0.144499 | + | 0.248506i | ||||
\(127\) | 2.60707e39i | 0.277896i | 0.990300 | + | 0.138948i | \(0.0443721\pi\) | ||||
−0.990300 | + | 0.138948i | \(0.955628\pi\) | |||||||
\(128\) | 9.31043e39 | − | 5.64685e39i | 0.855028 | − | 0.518581i | ||||
\(129\) | −1.64244e40 | −1.30103 | ||||||||
\(130\) | 1.64713e40 | − | 9.57756e39i | 1.12669 | − | 0.655136i | ||||
\(131\) | − | 1.54564e40i | − | 0.914018i | −0.889462 | − | 0.457009i | \(-0.848921\pi\) | ||
0.889462 | − | 0.457009i | \(-0.151079\pi\) | |||||||
\(132\) | −6.92218e39 | + | 1.21622e40i | −0.354273 | + | 0.622456i | ||||
\(133\) | 1.54009e40 | 0.682914 | ||||||||
\(134\) | 2.40564e40 | + | 4.13717e40i | 0.925208 | + | 1.59115i | ||||
\(135\) | 3.42148e40i | 1.14254i | ||||||||
\(136\) | 3.12655e38 | + | 3.37860e40i | 0.00907456 | + | 0.980612i | ||||
\(137\) | −5.33423e40 | −1.34704 | −0.673521 | − | 0.739168i | \(-0.735219\pi\) | ||||
−0.673521 | + | 0.739168i | \(0.735219\pi\) | |||||||
\(138\) | −3.40651e38 | + | 1.98079e38i | −0.00749217 | + | 0.00435647i | ||||
\(139\) | − | 2.93279e40i | − | 0.562342i | −0.959658 | − | 0.281171i | \(-0.909277\pi\) | ||
0.959658 | − | 0.281171i | \(-0.0907228\pi\) | |||||||
\(140\) | 2.94416e40 | + | 1.67568e40i | 0.492639 | + | 0.280387i | ||||
\(141\) | 9.35611e39 | 0.136751 | ||||||||
\(142\) | −8.93238e39 | − | 1.53617e40i | −0.114153 | − | 0.196318i | ||||
\(143\) | − | 1.13948e41i | − | 1.27444i | ||||||
\(144\) | −2.91832e40 | − | 4.91366e40i | −0.285921 | − | 0.481412i | ||||
\(145\) | −9.60139e40 | −0.824787 | ||||||||
\(146\) | 2.04005e41 | − | 1.18623e41i | 1.53793 | − | 0.894259i | ||||
\(147\) | − | 7.37769e40i | − | 0.488530i | ||||||
\(148\) | −2.29266e40 | + | 4.02820e40i | −0.133465 | + | 0.234497i | ||||
\(149\) | −2.76794e41 | −1.41781 | −0.708904 | − | 0.705305i | \(-0.750810\pi\) | ||||
−0.708904 | + | 0.705305i | \(0.750810\pi\) | |||||||
\(150\) | 1.61903e40 | + | 2.78438e40i | 0.0730334 | + | 0.125601i | ||||
\(151\) | − | 7.95011e40i | − | 0.316090i | −0.987432 | − | 0.158045i | \(-0.949481\pi\) | ||
0.987432 | − | 0.158045i | \(-0.0505192\pi\) | |||||||
\(152\) | −3.79244e41 | + | 3.50951e39i | −1.33012 | + | 0.0123089i | ||||
\(153\) | 1.77328e41 | 0.549086 | ||||||||
\(154\) | 1.75138e41 | − | 1.01838e41i | 0.479167 | − | 0.278622i | ||||
\(155\) | 5.55152e41i | 1.34310i | ||||||||
\(156\) | −3.17867e41 | − | 1.80915e41i | −0.680578 | − | 0.387354i | ||||
\(157\) | 1.04378e42 | 1.97932 | 0.989658 | − | 0.143448i | \(-0.0458189\pi\) | ||||
0.989658 | + | 0.143448i | \(0.0458189\pi\) | |||||||
\(158\) | 4.58324e41 | + | 7.88216e41i | 0.770350 | + | 1.32483i | ||||
\(159\) | 4.25684e41i | 0.634662i | ||||||||
\(160\) | −7.28808e41 | − | 4.05922e41i | −0.964570 | − | 0.537233i | ||||
\(161\) | 5.70473e39 | 0.00670724 | ||||||||
\(162\) | 1.04684e41 | − | 6.08707e40i | 0.109420 | − | 0.0636243i | ||||
\(163\) | − | 3.11913e41i | − | 0.290047i | −0.989428 | − | 0.145024i | \(-0.953674\pi\) | ||
0.989428 | − | 0.145024i | \(-0.0463259\pi\) | |||||||
\(164\) | −5.13903e41 | + | 9.02925e41i | −0.425450 | + | 0.747513i | ||||
\(165\) | 1.07211e42 | 0.790763 | ||||||||
\(166\) | −5.77951e41 | − | 9.93948e41i | −0.380047 | − | 0.653597i | ||||
\(167\) | 7.61829e41i | 0.446935i | 0.974711 | + | 0.223468i | \(0.0717377\pi\) | ||||
−0.974711 | + | 0.223468i | \(0.928262\pi\) | |||||||
\(168\) | −6.01742e39 | − | 6.50252e41i | −0.00315162 | − | 0.340569i | ||||
\(169\) | 8.40873e41 | 0.393444 | ||||||||
\(170\) | 2.23771e42 | − | 1.30116e42i | 0.935998 | − | 0.544255i | ||||
\(171\) | 1.99049e42i | 0.744790i | ||||||||
\(172\) | −5.08892e42 | − | 2.89638e42i | −1.70446 | − | 0.970097i | ||||
\(173\) | −1.46553e42 | −0.439661 | −0.219830 | − | 0.975538i | \(-0.570550\pi\) | ||||
−0.219830 | + | 0.975538i | \(0.570550\pi\) | |||||||
\(174\) | 9.26450e41 | + | 1.59329e42i | 0.249107 | + | 0.428409i | ||||
\(175\) | − | 4.66287e41i | − | 0.112442i | ||||||
\(176\) | −4.28952e42 | + | 2.54763e42i | −0.928256 | + | 0.551310i | ||||
\(177\) | 2.60746e42 | 0.506670 | ||||||||
\(178\) | 8.00986e42 | − | 4.65750e42i | 1.39844 | − | 0.813153i | ||||
\(179\) | − | 8.38708e42i | − | 1.31645i | −0.752823 | − | 0.658223i | \(-0.771308\pi\) | ||
0.752823 | − | 0.658223i | \(-0.228692\pi\) | |||||||
\(180\) | −2.16572e42 | + | 3.80516e42i | −0.305791 | + | 0.537274i | ||||
\(181\) | −1.42214e43 | −1.80738 | −0.903692 | − | 0.428183i | \(-0.859154\pi\) | ||||
−0.903692 | + | 0.428183i | \(0.859154\pi\) | |||||||
\(182\) | 2.66159e42 | + | 4.57734e42i | 0.304638 | + | 0.523910i | ||||
\(183\) | − | 2.17711e42i | − | 0.224549i | ||||||
\(184\) | −1.40477e41 | + | 1.29997e39i | −0.0130637 | + | 0.000120892i | ||||
\(185\) | 3.55090e42 | 0.297904 | ||||||||
\(186\) | 9.21239e42 | − | 5.35673e42i | 0.697632 | − | 0.405653i | ||||
\(187\) | − | 1.54804e43i | − | 1.05874i | ||||||
\(188\) | 2.89889e42 | + | 1.64991e42i | 0.179156 | + | 0.101967i | ||||
\(189\) | −9.50824e42 | −0.531283 | ||||||||
\(190\) | 1.46054e43 | + | 2.51181e43i | 0.738236 | + | 1.26960i | ||||
\(191\) | 3.06221e43i | 1.40088i | 0.713710 | + | 0.700441i | \(0.247013\pi\) | ||||
−0.713710 | + | 0.700441i | \(0.752987\pi\) | |||||||
\(192\) | 2.96354e41 | + | 1.60109e43i | 0.0122769 | + | 0.663273i | ||||
\(193\) | 6.68211e42 | 0.250798 | 0.125399 | − | 0.992106i | \(-0.459979\pi\) | ||||
0.125399 | + | 0.992106i | \(0.459979\pi\) | |||||||
\(194\) | 6.23833e42 | − | 3.62741e42i | 0.212244 | − | 0.123414i | ||||
\(195\) | 2.80203e43i | 0.864601i | ||||||||
\(196\) | 1.30103e43 | − | 2.28590e43i | 0.364268 | − | 0.640017i | ||||
\(197\) | −1.41772e43 | −0.360357 | −0.180179 | − | 0.983634i | \(-0.557668\pi\) | ||||
−0.180179 | + | 0.983634i | \(0.557668\pi\) | |||||||
\(198\) | 1.31620e43 | + | 2.26357e43i | 0.303866 | + | 0.522582i | ||||
\(199\) | − | 4.86430e43i | − | 1.02050i | −0.860027 | − | 0.510249i | \(-0.829553\pi\) | ||
0.860027 | − | 0.510249i | \(-0.170447\pi\) | |||||||
\(200\) | 1.06256e41 | + | 1.14822e43i | 0.00202667 | + | 0.219005i | ||||
\(201\) | −7.03800e43 | −1.22102 | ||||||||
\(202\) | −1.09978e42 | + | 6.39490e41i | −0.0173632 | + | 0.0100962i | ||||
\(203\) | − | 2.66821e43i | − | 0.383526i | ||||||
\(204\) | −4.31839e43 | − | 2.45783e43i | −0.565391 | − | 0.321795i | ||||
\(205\) | 7.95940e43 | 0.949635 | ||||||||
\(206\) | −5.32143e43 | − | 9.15168e43i | −0.578830 | − | 0.995460i | ||||
\(207\) | 7.37306e41i | 0.00731495i | ||||||||
\(208\) | −6.65838e43 | − | 1.12109e44i | −0.602789 | − | 1.01493i | ||||
\(209\) | 1.73766e44 | 1.43610 | ||||||||
\(210\) | −4.30675e43 | + | 2.50425e43i | −0.325075 | + | 0.189021i | ||||
\(211\) | − | 1.85839e44i | − | 1.28166i | −0.767685 | − | 0.640828i | \(-0.778591\pi\) | ||
0.767685 | − | 0.640828i | \(-0.221409\pi\) | |||||||
\(212\) | −7.50677e43 | + | 1.31894e44i | −0.473229 | + | 0.831461i | ||||
\(213\) | 2.61328e43 | 0.150651 | ||||||||
\(214\) | −1.28070e44 | − | 2.20253e44i | −0.675441 | − | 1.16161i | ||||
\(215\) | 4.48595e44i | 2.16533i | ||||||||
\(216\) | 2.34138e44 | − | 2.16670e42i | 1.03478 | − | 0.00957587i | ||||
\(217\) | −1.54276e44 | −0.624544 | ||||||||
\(218\) | −3.22833e44 | + | 1.87718e44i | −1.19758 | + | 0.696357i | ||||
\(219\) | 3.47045e44i | 1.18018i | ||||||||
\(220\) | 3.32183e44 | + | 1.89063e44i | 1.03597 | + | 0.589625i | ||||
\(221\) | 4.04589e44 | 1.15761 | ||||||||
\(222\) | −3.42631e43 | − | 5.89249e43i | −0.0899747 | − | 0.154736i | ||||
\(223\) | − | 4.08148e43i | − | 0.0984068i | −0.998789 | − | 0.0492034i | \(-0.984332\pi\) | ||
0.998789 | − | 0.0492034i | \(-0.0156682\pi\) | |||||||
\(224\) | 1.12805e44 | − | 2.02535e44i | 0.249813 | − | 0.448525i | ||||
\(225\) | 6.02650e43 | 0.122630 | ||||||||
\(226\) | −2.31112e44 | + | 1.34385e44i | −0.432276 | + | 0.251356i | ||||
\(227\) | − | 5.84772e44i | − | 1.00576i | −0.864355 | − | 0.502881i | \(-0.832273\pi\) | ||
0.864355 | − | 0.502881i | \(-0.167727\pi\) | |||||||
\(228\) | 2.75889e44 | − | 4.84735e44i | 0.436487 | − | 0.766906i | ||||
\(229\) | 3.69037e44 | 0.537273 | 0.268637 | − | 0.963242i | \(-0.413427\pi\) | ||||
0.268637 | + | 0.963242i | \(0.413427\pi\) | |||||||
\(230\) | 5.41006e42 | + | 9.30409e42i | 0.00725058 | + | 0.0124694i | ||||
\(231\) | 2.97939e44i | 0.367705i | ||||||||
\(232\) | 6.08022e42 | + | 6.57038e44i | 0.00691269 | + | 0.746997i | ||||
\(233\) | −1.17874e45 | −1.23497 | −0.617483 | − | 0.786585i | \(-0.711847\pi\) | ||||
−0.617483 | + | 0.786585i | \(0.711847\pi\) | |||||||
\(234\) | −5.91596e44 | + | 3.43996e44i | −0.571379 | + | 0.332240i | ||||
\(235\) | − | 2.55540e44i | − | 0.227599i | ||||||
\(236\) | 8.07891e44 | + | 4.59815e44i | 0.663781 | + | 0.377794i | ||||
\(237\) | −1.34088e45 | −1.01665 | ||||||||
\(238\) | 3.61591e44 | + | 6.21856e44i | 0.253079 | + | 0.435239i | ||||
\(239\) | − | 2.12120e45i | − | 1.37095i | −0.728096 | − | 0.685476i | \(-0.759594\pi\) | ||
0.728096 | − | 0.685476i | \(-0.240406\pi\) | |||||||
\(240\) | 1.05482e45 | − | 6.26477e44i | 0.629744 | − | 0.374017i | ||||
\(241\) | −7.92479e44 | −0.437184 | −0.218592 | − | 0.975816i | \(-0.570146\pi\) | ||||
−0.218592 | + | 0.975816i | \(0.570146\pi\) | |||||||
\(242\) | 2.80747e44 | − | 1.63246e44i | 0.143160 | − | 0.0832435i | ||||
\(243\) | − | 2.01668e45i | − | 0.950862i | ||||||
\(244\) | 3.83925e44 | − | 6.74555e44i | 0.167433 | − | 0.294178i | ||||
\(245\) | −2.01504e45 | −0.813072 | ||||||||
\(246\) | −7.68012e44 | − | 1.32081e45i | −0.286814 | − | 0.493257i | ||||
\(247\) | 4.54146e45i | 1.57020i | ||||||||
\(248\) | 3.79900e45 | − | 3.51558e43i | 1.21643 | − | 0.0112568i | ||||
\(249\) | 1.69087e45 | 0.501559 | ||||||||
\(250\) | −2.71183e45 | + | 1.57685e45i | −0.745421 | + | 0.433440i | ||||
\(251\) | − | 3.02682e45i | − | 0.771232i | −0.922659 | − | 0.385616i | \(-0.873989\pi\) | ||
0.922659 | − | 0.385616i | \(-0.126011\pi\) | |||||||
\(252\) | −1.05745e45 | − | 6.01850e44i | −0.249832 | − | 0.142193i | ||||
\(253\) | 6.43653e43 | 0.0141046 | ||||||||
\(254\) | −6.87077e44 | − | 1.18162e45i | −0.139690 | − | 0.240236i | ||||
\(255\) | 3.80671e45i | 0.718269i | ||||||||
\(256\) | −2.73163e45 | + | 5.01306e45i | −0.478479 | + | 0.878099i | ||||
\(257\) | 4.45369e45 | 0.724420 | 0.362210 | − | 0.932096i | \(-0.382022\pi\) | ||||
0.362210 | + | 0.932096i | \(0.382022\pi\) | |||||||
\(258\) | 7.44414e45 | − | 4.32855e45i | 1.12471 | − | 0.653985i | ||||
\(259\) | 9.86790e44i | 0.138525i | ||||||||
\(260\) | −4.94127e45 | + | 8.68179e45i | −0.644682 | + | 1.13270i | ||||
\(261\) | 3.44851e45 | 0.418275 | ||||||||
\(262\) | 4.07344e45 | + | 7.00541e45i | 0.459448 | + | 0.790149i | ||||
\(263\) | 3.76990e45i | 0.395522i | 0.980250 | + | 0.197761i | \(0.0633669\pi\) | ||||
−0.980250 | + | 0.197761i | \(0.936633\pi\) | |||||||
\(264\) | −6.78932e43 | − | 7.33665e45i | −0.00662753 | − | 0.716182i | ||||
\(265\) | 1.16266e46 | 1.05628 | ||||||||
\(266\) | −6.98026e45 | + | 4.05882e45i | −0.590365 | + | 0.343280i | ||||
\(267\) | 1.36261e46i | 1.07314i | ||||||||
\(268\) | −2.18064e46 | − | 1.24112e46i | −1.59965 | − | 0.910445i | ||||
\(269\) | 1.92563e45 | 0.131607 | 0.0658034 | − | 0.997833i | \(-0.479039\pi\) | ||||
0.0658034 | + | 0.997833i | \(0.479039\pi\) | |||||||
\(270\) | −9.01709e45 | − | 1.55074e46i | −0.574321 | − | 0.987705i | ||||
\(271\) | − | 1.36328e46i | − | 0.809413i | −0.914447 | − | 0.404706i | \(-0.867374\pi\) | ||
0.914447 | − | 0.404706i | \(-0.132626\pi\) | |||||||
\(272\) | −9.04577e45 | − | 1.52306e46i | −0.500768 | − | 0.843157i | ||||
\(273\) | −7.78680e45 | −0.402040 | ||||||||
\(274\) | 2.41767e46 | − | 1.40580e46i | 1.16449 | − | 0.677116i | ||||
\(275\) | − | 5.26101e45i | − | 0.236455i | ||||||
\(276\) | 1.02193e44 | − | 1.79553e44i | 0.00428696 | − | 0.00753216i | ||||
\(277\) | 2.26152e44 | 0.00885697 | 0.00442849 | − | 0.999990i | \(-0.498590\pi\) | ||||
0.00442849 | + | 0.999990i | \(0.498590\pi\) | |||||||
\(278\) | 7.72918e45 | + | 1.32925e46i | 0.282672 | + | 0.486133i | ||||
\(279\) | − | 1.99393e46i | − | 0.681130i | ||||||
\(280\) | −1.77601e46 | + | 1.64352e44i | −0.566818 | + | 0.00524532i | ||||
\(281\) | 3.24869e45 | 0.0968920 | 0.0484460 | − | 0.998826i | \(-0.484573\pi\) | ||||
0.0484460 | + | 0.998826i | \(0.484573\pi\) | |||||||
\(282\) | −4.24052e45 | + | 2.46574e45i | −0.118219 | + | 0.0687407i | ||||
\(283\) | 1.26031e46i | 0.328500i | 0.986419 | + | 0.164250i | \(0.0525203\pi\) | ||||
−0.986419 | + | 0.164250i | \(0.947480\pi\) | |||||||
\(284\) | 8.09695e45 | + | 4.60841e45i | 0.197366 | + | 0.112332i | ||||
\(285\) | −4.27299e46 | −0.974271 | ||||||||
\(286\) | 3.00301e46 | + | 5.16451e46i | 0.640622 | + | 1.10173i | ||||
\(287\) | 2.21190e46i | 0.441580i | ||||||||
\(288\) | 2.61765e46 | + | 1.45794e46i | 0.489163 | + | 0.272448i | ||||
\(289\) | −2.19006e45 | −0.0383175 | ||||||||
\(290\) | 4.35169e46 | − | 2.53038e46i | 0.713011 | − | 0.414595i | ||||
\(291\) | 1.06124e46i | 0.162873i | ||||||||
\(292\) | −6.12000e46 | + | 1.07528e47i | −0.879990 | + | 1.54614i | ||||
\(293\) | 7.59287e46 | 1.02311 | 0.511554 | − | 0.859251i | \(-0.329070\pi\) | ||||
0.511554 | + | 0.859251i | \(0.329070\pi\) | |||||||
\(294\) | 1.94434e46 | + | 3.34384e46i | 0.245569 | + | 0.422324i | ||||
\(295\) | − | 7.12166e46i | − | 0.843263i | ||||||
\(296\) | −2.24866e44 | − | 2.42994e46i | −0.00249679 | − | 0.269807i | ||||
\(297\) | −1.07279e47 | −1.11723 | ||||||||
\(298\) | 1.25453e47 | − | 7.29472e46i | 1.22567 | − | 0.712688i | ||||
\(299\) | 1.68222e45i | 0.0154217i | ||||||||
\(300\) | −1.46761e46 | − | 8.35294e45i | −0.126272 | − | 0.0718680i | ||||
\(301\) | −1.24664e47 | −1.00688 | ||||||||
\(302\) | 2.09520e46 | + | 3.60328e46i | 0.158889 | + | 0.273254i | ||||
\(303\) | − | 1.87091e45i | − | 0.0133242i | ||||||
\(304\) | 1.70962e47 | − | 1.01538e47i | 1.14367 | − | 0.679250i | ||||
\(305\) | −5.94628e46 | −0.373722 | ||||||||
\(306\) | −8.03715e46 | + | 4.67337e46i | −0.474674 | + | 0.276009i | ||||
\(307\) | − | 1.02618e47i | − | 0.569630i | −0.958582 | − | 0.284815i | \(-0.908068\pi\) | ||
0.958582 | − | 0.284815i | \(-0.0919322\pi\) | |||||||
\(308\) | −5.25403e46 | + | 9.23130e46i | −0.274176 | + | 0.481725i | ||||
\(309\) | 1.55685e47 | 0.763899 | ||||||||
\(310\) | −1.46307e47 | − | 2.51615e47i | −0.675137 | − | 1.16109i | ||||
\(311\) | 9.56462e46i | 0.415165i | 0.978218 | + | 0.207582i | \(0.0665595\pi\) | ||||
−0.978218 | + | 0.207582i | \(0.933441\pi\) | |||||||
\(312\) | 1.91748e47 | − | 1.77443e45i | 0.783056 | − | 0.00724638i | ||||
\(313\) | −1.07456e47 | −0.412941 | −0.206471 | − | 0.978453i | \(-0.566198\pi\) | ||||
−0.206471 | + | 0.978453i | \(0.566198\pi\) | |||||||
\(314\) | −4.73078e47 | + | 2.75081e47i | −1.71108 | + | 0.994941i | ||||
\(315\) | 9.32153e46i | 0.317385i | ||||||||
\(316\) | −4.15458e47 | − | 2.36460e47i | −1.33190 | − | 0.758058i | ||||
\(317\) | 3.42063e47 | 1.03271 | 0.516357 | − | 0.856373i | \(-0.327288\pi\) | ||||
0.516357 | + | 0.856373i | \(0.327288\pi\) | |||||||
\(318\) | −1.12186e47 | − | 1.92935e47i | −0.319025 | − | 0.548652i | ||||
\(319\) | − | 3.01048e47i | − | 0.806516i | ||||||
\(320\) | 4.37300e47 | − | 8.09422e45i | 1.10390 | − | 0.0204327i | ||||
\(321\) | 3.74686e47 | 0.891399 | ||||||||
\(322\) | −2.58559e45 | + | 1.50344e45i | −0.00579827 | + | 0.00337152i | ||||
\(323\) | 6.16982e47i | 1.30444i | ||||||||
\(324\) | −3.14045e46 | + | 5.51776e46i | −0.0626091 | + | 0.110004i | ||||
\(325\) | 1.37500e47 | 0.258534 | ||||||||
\(326\) | 8.22026e46 | + | 1.41370e47i | 0.145798 | + | 0.250740i | ||||
\(327\) | − | 5.49191e47i | − | 0.919002i | ||||||
\(328\) | −5.04040e45 | − | 5.44674e47i | −0.00795906 | − | 0.860070i | ||||
\(329\) | 7.10142e46 | 0.105833 | ||||||||
\(330\) | −4.85921e47 | + | 2.82549e47i | −0.683598 | + | 0.397492i | ||||
\(331\) | 6.65915e47i | 0.884477i | 0.896897 | + | 0.442239i | \(0.145816\pi\) | ||||
−0.896897 | + | 0.442239i | \(0.854184\pi\) | |||||||
\(332\) | 5.23897e47 | + | 2.98178e47i | 0.657086 | + | 0.373983i | ||||
\(333\) | −1.27537e47 | −0.151076 | ||||||||
\(334\) | −2.00775e47 | − | 3.45288e47i | −0.224661 | − | 0.386366i | ||||
\(335\) | 1.92226e48i | 2.03218i | ||||||||
\(336\) | 1.74097e47 | + | 2.93132e47i | 0.173918 | + | 0.292831i | ||||
\(337\) | 1.21390e48 | 1.14608 | 0.573041 | − | 0.819527i | \(-0.305763\pi\) | ||||
0.573041 | + | 0.819527i | \(0.305763\pi\) | |||||||
\(338\) | −3.81114e47 | + | 2.21607e47i | −0.340124 | + | 0.197772i | ||||
\(339\) | − | 3.93159e47i | − | 0.331722i | ||||||
\(340\) | −6.71299e47 | + | 1.17947e48i | −0.535570 | + | 0.940994i | ||||
\(341\) | −1.74066e48 | −1.31335 | ||||||||
\(342\) | −5.24580e47 | − | 9.02161e47i | −0.374383 | − | 0.643855i | ||||
\(343\) | − | 1.32038e48i | − | 0.891481i | ||||||
\(344\) | 3.06981e48 | − | 2.84079e46i | 1.96110 | − | 0.0181480i | ||||
\(345\) | −1.58278e46 | −0.00956880 | ||||||||
\(346\) | 6.64230e47 | − | 3.86230e47i | 0.380078 | − | 0.221004i | ||||
\(347\) | − | 3.05531e48i | − | 1.65499i | −0.561475 | − | 0.827494i | \(-0.689766\pi\) | ||
0.561475 | − | 0.827494i | \(-0.310234\pi\) | |||||||
\(348\) | −8.39801e47 | − | 4.77976e47i | −0.430696 | − | 0.245132i | ||||
\(349\) | −2.47433e48 | −1.20164 | −0.600819 | − | 0.799385i | \(-0.705159\pi\) | ||||
−0.600819 | + | 0.799385i | \(0.705159\pi\) | |||||||
\(350\) | 1.22887e47 | + | 2.11338e47i | 0.0565213 | + | 0.0972041i | ||||
\(351\) | − | 2.80381e48i | − | 1.22156i | ||||||
\(352\) | 1.27275e48 | − | 2.28515e48i | 0.525332 | − | 0.943202i | ||||
\(353\) | −1.23870e48 | −0.484446 | −0.242223 | − | 0.970221i | \(-0.577877\pi\) | ||||
−0.242223 | + | 0.970221i | \(0.577877\pi\) | |||||||
\(354\) | −1.18179e48 | + | 6.87178e47i | −0.438005 | + | 0.254687i | ||||
\(355\) | − | 7.13756e47i | − | 0.250733i | ||||||
\(356\) | −2.40290e48 | + | 4.22189e48i | −0.800178 | + | 1.40591i | ||||
\(357\) | −1.05788e48 | −0.333995 | ||||||||
\(358\) | 2.21036e48 | + | 3.80132e48i | 0.661736 | + | 1.13804i | ||||
\(359\) | 3.55217e48i | 1.00855i | 0.863542 | + | 0.504276i | \(0.168241\pi\) | ||||
−0.863542 | + | 0.504276i | \(0.831759\pi\) | |||||||
\(360\) | −2.12416e46 | − | 2.29540e48i | −0.00572056 | − | 0.618174i | ||||
\(361\) | −3.01141e48 | −0.769366 | ||||||||
\(362\) | 6.44567e48 | − | 3.74796e48i | 1.56245 | − | 0.908516i | ||||
\(363\) | 4.77596e47i | 0.109859i | ||||||||
\(364\) | −2.41265e48 | − | 1.37317e48i | −0.526707 | − | 0.299777i | ||||
\(365\) | 9.47873e48 | 1.96420 | ||||||||
\(366\) | 5.73764e47 | + | 9.86746e47i | 0.112874 | + | 0.194118i | ||||
\(367\) | 6.71115e48i | 1.25355i | 0.779200 | + | 0.626775i | \(0.215625\pi\) | ||||
−0.779200 | + | 0.626775i | \(0.784375\pi\) | |||||||
\(368\) | 6.33268e46 | − | 3.76111e46i | 0.0112326 | − | 0.00667125i | ||||
\(369\) | −2.85876e48 | −0.481589 | ||||||||
\(370\) | −1.60940e48 | + | 9.35817e47i | −0.257532 | + | 0.149747i | ||||
\(371\) | 3.23100e48i | 0.491171i | ||||||||
\(372\) | −2.76366e48 | + | 4.85573e48i | −0.399180 | + | 0.701356i | ||||
\(373\) | −9.25968e47 | −0.127095 | −0.0635475 | − | 0.997979i | \(-0.520241\pi\) | ||||
−0.0635475 | + | 0.997979i | \(0.520241\pi\) | |||||||
\(374\) | 4.07975e48 | + | 7.01627e48i | 0.532198 | + | 0.915262i | ||||
\(375\) | − | 4.61326e48i | − | 0.572024i | ||||||
\(376\) | −1.74870e48 | + | 1.61824e46i | −0.206133 | + | 0.00190755i | ||||
\(377\) | 7.86807e48 | 0.881825 | ||||||||
\(378\) | 4.30948e48 | − | 2.50583e48i | 0.459283 | − | 0.267059i | ||||
\(379\) | − | 4.71994e48i | − | 0.478401i | −0.970970 | − | 0.239200i | \(-0.923115\pi\) | ||
0.970970 | − | 0.239200i | \(-0.0768853\pi\) | |||||||
\(380\) | −1.32394e49 | − | 7.53525e48i | −1.27638 | − | 0.726456i | ||||
\(381\) | 2.01013e48 | 0.184353 | ||||||||
\(382\) | −8.07026e48 | − | 1.38791e49i | −0.704180 | − | 1.21103i | ||||
\(383\) | 1.08626e49i | 0.901899i | 0.892549 | + | 0.450950i | \(0.148915\pi\) | ||||
−0.892549 | + | 0.450950i | \(0.851085\pi\) | |||||||
\(384\) | −4.35388e48 | − | 7.17861e48i | −0.344020 | − | 0.567214i | ||||
\(385\) | 8.13750e48 | 0.611980 | ||||||||
\(386\) | −3.02857e48 | + | 1.76102e48i | −0.216810 | + | 0.126068i | ||||
\(387\) | − | 1.61121e49i | − | 1.09810i | ||||||
\(388\) | −1.87146e48 | + | 3.28814e48i | −0.121444 | + | 0.213377i | ||||
\(389\) | 1.64050e49 | 1.01376 | 0.506879 | − | 0.862017i | \(-0.330799\pi\) | ||||
0.506879 | + | 0.862017i | \(0.330799\pi\) | |||||||
\(390\) | −7.38457e48 | − | 1.26998e49i | −0.434608 | − | 0.747430i | ||||
\(391\) | 2.28539e47i | 0.0128116i | ||||||||
\(392\) | 1.27606e47 | + | 1.37893e49i | 0.00681451 | + | 0.736387i | ||||
\(393\) | −1.19174e49 | −0.606347 | ||||||||
\(394\) | 6.42563e48 | − | 3.73631e48i | 0.311521 | − | 0.181140i | ||||
\(395\) | 3.66231e49i | 1.69204i | ||||||||
\(396\) | −1.19310e49 | − | 6.79055e48i | −0.525372 | − | 0.299017i | ||||
\(397\) | −2.06187e49 | −0.865450 | −0.432725 | − | 0.901526i | \(-0.642448\pi\) | ||||
−0.432725 | + | 0.901526i | \(0.642448\pi\) | |||||||
\(398\) | 1.28195e49 | + | 2.20468e49i | 0.512972 | + | 0.882199i | ||||
\(399\) | − | 1.18746e49i | − | 0.453036i | ||||||
\(400\) | −3.07421e48 | − | 5.17613e48i | −0.111839 | − | 0.188307i | ||||
\(401\) | −2.28768e49 | −0.793694 | −0.396847 | − | 0.917885i | \(-0.629896\pi\) | ||||
−0.396847 | + | 0.917885i | \(0.629896\pi\) | |||||||
\(402\) | 3.18987e49 | − | 1.85482e49i | 1.05555 | − | 0.613770i | ||||
\(403\) | − | 4.54932e49i | − | 1.43599i | ||||||
\(404\) | 3.29927e47 | − | 5.79679e47i | 0.00993508 | − | 0.0174559i | ||||
\(405\) | 4.86397e48 | 0.139748 | ||||||||
\(406\) | 7.03188e48 | + | 1.20933e49i | 0.192787 | + | 0.331550i | ||||
\(407\) | 1.11337e49i | 0.291304i | ||||||||
\(408\) | 2.60500e49 | − | 2.41066e47i | 0.650525 | − | 0.00601994i | ||||
\(409\) | 1.28628e49 | 0.306614 | 0.153307 | − | 0.988179i | \(-0.451008\pi\) | ||||
0.153307 | + | 0.988179i | \(0.451008\pi\) | |||||||
\(410\) | −3.60748e49 | + | 2.09765e49i | −0.820940 | + | 0.477352i | ||||
\(411\) | 4.11285e49i | 0.893610i | ||||||||
\(412\) | 4.82373e49 | + | 2.74544e49i | 1.00077 | + | 0.569594i | ||||
\(413\) | 1.97910e49 | 0.392117 | ||||||||
\(414\) | −1.94312e47 | − | 3.34174e47i | −0.00367700 | − | 0.00632362i | ||||
\(415\) | − | 4.61821e49i | − | 0.834757i | ||||||
\(416\) | 5.97238e49 | + | 3.32641e49i | 1.03127 | + | 0.574385i | ||||
\(417\) | −2.26127e49 | −0.373050 | ||||||||
\(418\) | −7.87568e49 | + | 4.57947e49i | −1.24148 | + | 0.721882i | ||||
\(419\) | − | 9.99261e48i | − | 0.150526i | −0.997164 | − | 0.0752632i | \(-0.976020\pi\) | ||
0.997164 | − | 0.0752632i | \(-0.0239797\pi\) | |||||||
\(420\) | 1.29200e49 | − | 2.27003e49i | 0.186005 | − | 0.326810i | ||||
\(421\) | −9.06625e49 | −1.24758 | −0.623789 | − | 0.781593i | \(-0.714408\pi\) | ||||
−0.623789 | + | 0.781593i | \(0.714408\pi\) | |||||||
\(422\) | 4.89767e49 | + | 8.42291e49i | 0.644248 | + | 1.10796i | ||||
\(423\) | 9.17819e48i | 0.115422i | ||||||||
\(424\) | −7.36269e47 | − | 7.95625e49i | −0.00885290 | − | 0.956659i | ||||
\(425\) | 1.86801e49 | 0.214777 | ||||||||
\(426\) | −1.18443e49 | + | 6.88712e48i | −0.130235 | + | 0.0757278i | ||||
\(427\) | − | 1.65246e49i | − | 0.173781i | ||||||
\(428\) | 1.16092e50 | + | 6.60744e49i | 1.16781 | + | 0.664663i | ||||
\(429\) | −8.78568e49 | −0.845448 | ||||||||
\(430\) | −1.18224e50 | − | 2.03319e50i | −1.08844 | − | 1.87188i | ||||
\(431\) | − | 3.03034e49i | − | 0.266946i | −0.991052 | − | 0.133473i | \(-0.957387\pi\) | ||
0.991052 | − | 0.133473i | \(-0.0426130\pi\) | |||||||
\(432\) | −1.05549e50 | + | 6.26874e49i | −0.889736 | + | 0.528432i | ||||
\(433\) | 8.65125e49 | 0.697925 | 0.348963 | − | 0.937137i | \(-0.386534\pi\) | ||||
0.348963 | + | 0.937137i | \(0.386534\pi\) | |||||||
\(434\) | 6.99234e49 | − | 4.06584e49i | 0.539905 | − | 0.313939i | ||||
\(435\) | 7.40295e49i | 0.547153i | ||||||||
\(436\) | 9.68477e49 | − | 1.70161e50i | 0.685245 | − | 1.20397i | ||||
\(437\) | −2.56533e48 | −0.0173778 | ||||||||
\(438\) | −9.14615e49 | − | 1.57293e50i | −0.593239 | − | 1.02024i | ||||
\(439\) | − | 1.84517e50i | − | 1.14607i | −0.819531 | − | 0.573034i | \(-0.805766\pi\) | ||
0.819531 | − | 0.573034i | \(-0.194234\pi\) | |||||||
\(440\) | −2.00384e50 | + | 1.85434e48i | −1.19196 | + | 0.0110304i | ||||
\(441\) | 7.23740e49 | 0.412334 | ||||||||
\(442\) | −1.83374e50 | + | 1.06627e50i | −1.00073 | + | 0.581892i | ||||
\(443\) | 6.98396e49i | 0.365116i | 0.983195 | + | 0.182558i | \(0.0584377\pi\) | ||||
−0.983195 | + | 0.182558i | \(0.941562\pi\) | |||||||
\(444\) | 3.10585e49 | + | 1.76771e49i | 0.155562 | + | 0.0885390i | ||||
\(445\) | 3.72165e50 | 1.78605 | ||||||||
\(446\) | 1.07565e49 | + | 1.84987e49i | 0.0494660 | + | 0.0850706i | ||||
\(447\) | 2.13416e50i | 0.940555i | ||||||||
\(448\) | 2.24937e48 | + | 1.21525e50i | 0.00950120 | + | 0.513314i | ||||
\(449\) | 3.84894e49 | 0.155833 | 0.0779167 | − | 0.996960i | \(-0.475173\pi\) | ||||
0.0779167 | + | 0.996960i | \(0.475173\pi\) | |||||||
\(450\) | −2.73143e49 | + | 1.58824e49i | −0.106011 | + | 0.0616424i | ||||
\(451\) | 2.49564e50i | 0.928598i | ||||||||
\(452\) | 6.93320e49 | − | 1.21816e50i | 0.247345 | − | 0.434584i | ||||
\(453\) | −6.12977e49 | −0.209690 | ||||||||
\(454\) | 1.54113e50 | + | 2.65040e50i | 0.505566 | + | 0.869461i | ||||
\(455\) | 2.12678e50i | 0.669124i | ||||||||
\(456\) | 2.70593e48 | + | 2.92408e50i | 0.00816555 | + | 0.882382i | ||||
\(457\) | −2.70676e50 | −0.783505 | −0.391753 | − | 0.920071i | \(-0.628131\pi\) | ||||
−0.391753 | + | 0.920071i | \(0.628131\pi\) | |||||||
\(458\) | −1.67261e50 | + | 9.72571e49i | −0.464462 | + | 0.270071i | ||||
\(459\) | − | 3.80913e50i | − | 1.01481i | ||||||
\(460\) | −4.90406e48 | − | 2.79117e48i | −0.0125360 | − | 0.00713488i | ||||
\(461\) | 4.88810e50 | 1.19901 | 0.599505 | − | 0.800371i | \(-0.295364\pi\) | ||||
0.599505 | + | 0.800371i | \(0.295364\pi\) | |||||||
\(462\) | −7.85198e49 | − | 1.35037e50i | −0.184834 | − | 0.317873i | ||||
\(463\) | 2.76683e50i | 0.625092i | 0.949903 | + | 0.312546i | \(0.101182\pi\) | ||||
−0.949903 | + | 0.312546i | \(0.898818\pi\) | |||||||
\(464\) | −1.75914e50 | − | 2.96191e50i | −0.381468 | − | 0.642289i | ||||
\(465\) | 4.28038e50 | 0.890998 | ||||||||
\(466\) | 5.34246e50 | − | 3.10648e50i | 1.06760 | − | 0.620779i | ||||
\(467\) | 1.19702e49i | 0.0229658i | 0.999934 | + | 0.0114829i | \(0.00365520\pi\) | ||||
−0.999934 | + | 0.0114829i | \(0.996345\pi\) | |||||||
\(468\) | 1.77475e50 | − | 3.11822e50i | 0.326938 | − | 0.574429i | ||||
\(469\) | −5.34194e50 | −0.944963 | ||||||||
\(470\) | 6.73459e49 | + | 1.15820e50i | 0.114407 | + | 0.196754i | ||||
\(471\) | − | 8.04783e50i | − | 1.31305i | ||||||
\(472\) | −4.87347e50 | + | 4.50989e48i | −0.763730 | + | 0.00706754i | ||||
\(473\) | −1.40655e51 | −2.11736 | ||||||||
\(474\) | 6.07737e50 | − | 3.53381e50i | 0.878875 | − | 0.511040i | ||||
\(475\) | 2.09682e50i | 0.291328i | ||||||||
\(476\) | −3.27772e50 | − | 1.86553e50i | −0.437562 | − | 0.249040i | ||||
\(477\) | −4.17589e50 | −0.535674 | ||||||||
\(478\) | 5.59029e50 | + | 9.61405e50i | 0.689135 | + | 1.18516i | ||||
\(479\) | − | 1.20440e51i | − | 1.42690i | −0.700704 | − | 0.713452i | \(-0.747131\pi\) | ||
0.700704 | − | 0.713452i | \(-0.252869\pi\) | |||||||
\(480\) | −3.12977e50 | + | 5.61932e50i | −0.356393 | + | 0.639883i | ||||
\(481\) | −2.90987e50 | −0.318505 | ||||||||
\(482\) | 3.59180e50 | − | 2.08853e50i | 0.377936 | − | 0.219759i | ||||
\(483\) | − | 4.39851e48i | − | 0.00444949i | ||||||
\(484\) | −8.42221e49 | + | 1.47978e50i | −0.0819152 | + | 0.143924i | ||||
\(485\) | 2.89854e50 | 0.271073 | ||||||||
\(486\) | 5.31482e50 | + | 9.14031e50i | 0.477969 | + | 0.822000i | ||||
\(487\) | 4.39009e50i | 0.379685i | 0.981815 | + | 0.189842i | \(0.0607977\pi\) | ||||
−0.981815 | + | 0.189842i | \(0.939202\pi\) | |||||||
\(488\) | 3.76557e48 | + | 4.06913e50i | 0.00313223 | + | 0.338474i | ||||
\(489\) | −2.40494e50 | −0.192414 | ||||||||
\(490\) | 9.13291e50 | − | 5.31052e50i | 0.702884 | − | 0.408706i | ||||
\(491\) | − | 1.00454e51i | − | 0.743738i | −0.928285 | − | 0.371869i | \(-0.878717\pi\) | ||
0.928285 | − | 0.371869i | \(-0.121283\pi\) | |||||||
\(492\) | 6.96181e50 | + | 3.96234e50i | 0.495890 | + | 0.282238i | ||||
\(493\) | 1.06892e51 | 0.732577 | ||||||||
\(494\) | −1.19687e51 | − | 2.05835e51i | −0.789288 | − | 1.35740i | ||||
\(495\) | 1.05173e51i | 0.667428i | ||||||||
\(496\) | −1.71258e51 | + | 1.01713e51i | −1.04592 | + | 0.621193i | ||||
\(497\) | 1.98352e50 | 0.116591 | ||||||||
\(498\) | −7.66362e50 | + | 4.45617e50i | −0.433587 | + | 0.252118i | ||||
\(499\) | 4.17141e50i | 0.227181i | 0.993528 | + | 0.113591i | \(0.0362352\pi\) | ||||
−0.993528 | + | 0.113591i | \(0.963765\pi\) | |||||||
\(500\) | 8.13530e50 | − | 1.42937e51i | 0.426524 | − | 0.749400i | ||||
\(501\) | 5.87392e50 | 0.296491 | ||||||||
\(502\) | 7.97697e50 | + | 1.37186e51i | 0.387675 | + | 0.666714i | ||||
\(503\) | 3.05468e51i | 1.42947i | 0.699397 | + | 0.714733i | \(0.253452\pi\) | ||||
−0.699397 | + | 0.714733i | \(0.746548\pi\) | |||||||
\(504\) | 6.37887e50 | − | 5.90299e48i | 0.287451 | − | 0.00266006i | ||||
\(505\) | −5.10994e49 | −0.0221758 | ||||||||
\(506\) | −2.91727e49 | + | 1.69630e49i | −0.0121932 | + | 0.00708996i | ||||
\(507\) | − | 6.48337e50i | − | 0.261006i | ||||||
\(508\) | 6.22816e50 | + | 3.54478e50i | 0.241518 | + | 0.137461i | ||||
\(509\) | −8.74606e48 | −0.00326719 | −0.00163360 | − | 0.999999i | \(-0.500520\pi\) | ||||
−0.00163360 | + | 0.999999i | \(0.500520\pi\) | |||||||
\(510\) | −1.00323e51 | − | 1.72534e51i | −0.361051 | − | 0.620928i | ||||
\(511\) | 2.63412e51i | 0.913353i | ||||||||
\(512\) | −8.30827e49 | − | 2.99200e51i | −0.0277576 | − | 0.999615i | ||||
\(513\) | 4.27570e51 | 1.37650 | ||||||||
\(514\) | −2.01857e51 | + | 1.17374e51i | −0.626246 | + | 0.364144i | ||||
\(515\) | − | 4.25217e51i | − | 1.27138i | ||||||
\(516\) | −2.23319e51 | + | 3.92371e51i | −0.643549 | + | 1.13071i | ||||
\(517\) | 8.01237e50 | 0.222557 | ||||||||
\(518\) | −2.60062e50 | − | 4.47249e50i | −0.0696324 | − | 0.119752i | ||||
\(519\) | 1.12996e51i | 0.291665i | ||||||||
\(520\) | −4.84644e49 | − | 5.23714e51i | −0.0120603 | − | 1.30326i | ||||
\(521\) | −1.90170e51 | −0.456275 | −0.228137 | − | 0.973629i | \(-0.573264\pi\) | ||||
−0.228137 | + | 0.973629i | \(0.573264\pi\) | |||||||
\(522\) | −1.56299e51 | + | 9.08833e50i | −0.361590 | + | 0.210254i | ||||
\(523\) | 3.74720e51i | 0.835939i | 0.908461 | + | 0.417970i | \(0.137258\pi\) | ||||
−0.908461 | + | 0.417970i | \(0.862742\pi\) | |||||||
\(524\) | −3.69246e51 | − | 2.10158e51i | −0.794367 | − | 0.452117i | ||||
\(525\) | −3.59521e50 | −0.0745928 | ||||||||
\(526\) | −9.93531e50 | − | 1.70865e51i | −0.198816 | − | 0.341920i | ||||
\(527\) | − | 6.18049e51i | − | 1.19295i | ||||||
\(528\) | 1.96430e51 | + | 3.30734e51i | 0.365732 | + | 0.615793i | ||||
\(529\) | 5.56652e51 | 0.999829 | ||||||||
\(530\) | −5.26958e51 | + | 3.06411e51i | −0.913134 | + | 0.530960i | ||||
\(531\) | 2.55787e51i | 0.427645i | ||||||||
\(532\) | 2.09403e51 | − | 3.67920e51i | 0.337802 | − | 0.593517i | ||||
\(533\) | −6.52250e51 | −1.01531 | ||||||||
\(534\) | −3.59106e51 | − | 6.17583e51i | −0.539435 | − | 0.927708i | ||||
\(535\) | − | 1.02337e52i | − | 1.48358i | ||||||
\(536\) | 1.31544e52 | − | 1.21730e50i | 1.84051 | − | 0.0170321i | ||||
\(537\) | −6.46667e51 | −0.873312 | ||||||||
\(538\) | −8.72763e50 | + | 5.07486e50i | −0.113771 | + | 0.0661547i | ||||
\(539\) | − | 6.31810e51i | − | 0.795060i | ||||||
\(540\) | 8.17374e51 | + | 4.65212e51i | 0.992978 | + | 0.565157i | ||||
\(541\) | 7.19752e51 | 0.844179 | 0.422090 | − | 0.906554i | \(-0.361297\pi\) | ||||
0.422090 | + | 0.906554i | \(0.361297\pi\) | |||||||
\(542\) | 3.59285e51 | + | 6.17890e51i | 0.406867 | + | 0.699720i | ||||
\(543\) | 1.09651e52i | 1.19899i | ||||||||
\(544\) | 8.11380e51 | + | 4.51911e51i | 0.856732 | + | 0.477171i | ||||
\(545\) | −1.49999e52 | −1.52952 | ||||||||
\(546\) | 3.52926e51 | − | 2.05216e51i | 0.347555 | − | 0.202093i | ||||
\(547\) | 1.48668e52i | 1.41403i | 0.707200 | + | 0.707013i | \(0.249958\pi\) | ||||
−0.707200 | + | 0.707013i | \(0.750042\pi\) | |||||||
\(548\) | −7.25284e51 | + | 1.27432e52i | −0.666312 | + | 1.17071i | ||||
\(549\) | 2.13571e51 | 0.189526 | ||||||||
\(550\) | 1.38650e51 | + | 2.38448e51i | 0.118859 | + | 0.204410i | ||||
\(551\) | 1.19985e52i | 0.993680i | ||||||||
\(552\) | 1.00232e48 | + | 1.08312e50i | 8.01978e−5 | + | 0.00866631i | ||||
\(553\) | −1.01775e52 | −0.786799 | ||||||||
\(554\) | −1.02500e50 | + | 5.96009e49i | −0.00765667 | + | 0.00445212i | ||||
\(555\) | − | 2.73785e51i | − | 0.197625i | ||||||
\(556\) | −7.00629e51 | − | 3.98766e51i | −0.488728 | − | 0.278161i | ||||
\(557\) | 2.50750e52 | 1.69041 | 0.845205 | − | 0.534443i | \(-0.179479\pi\) | ||||
0.845205 | + | 0.534443i | \(0.179479\pi\) | |||||||
\(558\) | 5.25487e51 | + | 9.03721e51i | 0.342383 | + | 0.588823i | ||||
\(559\) | − | 3.67611e52i | − | 2.31507i | ||||||
\(560\) | 8.00621e51 | − | 4.75505e51i | 0.487365 | − | 0.289456i | ||||
\(561\) | −1.19358e52 | −0.702357 | ||||||||
\(562\) | −1.47242e51 | + | 8.56170e50i | −0.0837611 | + | 0.0487046i | ||||
\(563\) | − | 1.49382e52i | − | 0.821561i | −0.911734 | − | 0.410780i | \(-0.865256\pi\) | ||
0.911734 | − | 0.410780i | \(-0.134744\pi\) | |||||||
\(564\) | 1.27213e51 | − | 2.23512e51i | 0.0676438 | − | 0.118850i | ||||
\(565\) | −1.07382e52 | −0.552092 | ||||||||
\(566\) | −3.32146e51 | − | 5.71218e51i | −0.165127 | − | 0.283981i | ||||
\(567\) | 1.35169e51i | 0.0649828i | ||||||||
\(568\) | −4.88435e51 | + | 4.51996e49i | −0.227085 | + | 0.00210144i | ||||
\(569\) | −1.47975e52 | −0.665358 | −0.332679 | − | 0.943040i | \(-0.607953\pi\) | ||||
−0.332679 | + | 0.943040i | \(0.607953\pi\) | |||||||
\(570\) | 1.93667e52 | − | 1.12612e52i | 0.842237 | − | 0.489736i | ||||
\(571\) | 9.93138e51i | 0.417757i | 0.977942 | + | 0.208878i | \(0.0669813\pi\) | ||||
−0.977942 | + | 0.208878i | \(0.933019\pi\) | |||||||
\(572\) | −2.72214e52 | − | 1.54932e52i | −1.10761 | − | 0.630400i | ||||
\(573\) | 2.36105e52 | 0.929326 | ||||||||
\(574\) | −5.82932e51 | − | 1.00251e52i | −0.221969 | − | 0.381737i | ||||
\(575\) | 7.76691e49i | 0.00286127i | ||||||||
\(576\) | −1.57064e52 | + | 2.90719e50i | −0.559822 | + | 0.0103621i | ||||
\(577\) | 1.11265e52 | 0.383724 | 0.191862 | − | 0.981422i | \(-0.438547\pi\) | ||||
0.191862 | + | 0.981422i | \(0.438547\pi\) | |||||||
\(578\) | 9.92614e50 | − | 5.77176e50i | 0.0331247 | − | 0.0192610i | ||||
\(579\) | − | 5.15209e51i | − | 0.166376i | ||||||
\(580\) | −1.30548e52 | + | 2.29372e52i | −0.407979 | + | 0.716817i | ||||
\(581\) | 1.28339e52 | 0.388162 | ||||||||
\(582\) | −2.79683e51 | − | 4.80993e51i | −0.0818710 | − | 0.140800i | ||||
\(583\) | 3.64547e52i | 1.03288i | ||||||||
\(584\) | −6.00254e50 | − | 6.48645e52i | −0.0164623 | − | 1.77895i | ||||
\(585\) | −2.74875e52 | −0.729750 | ||||||||
\(586\) | −3.44136e52 | + | 2.00105e52i | −0.884455 | + | 0.514284i | ||||
\(587\) | 5.20780e52i | 1.29578i | 0.761735 | + | 0.647889i | \(0.224348\pi\) | ||||
−0.761735 | + | 0.647889i | \(0.775652\pi\) | |||||||
\(588\) | −1.76249e52 | − | 1.00313e52i | −0.424578 | − | 0.241650i | ||||
\(589\) | 6.93753e52 | 1.61813 | ||||||||
\(590\) | 1.87687e52 | + | 3.22779e52i | 0.423882 | + | 0.728983i | ||||
\(591\) | 1.09311e52i | 0.239056i | ||||||||
\(592\) | 6.50586e51 | + | 1.09541e52i | 0.137782 | + | 0.231987i | ||||
\(593\) | 6.27741e52 | 1.28748 | 0.643741 | − | 0.765243i | \(-0.277381\pi\) | ||||
0.643741 | + | 0.765243i | \(0.277381\pi\) | |||||||
\(594\) | 4.86229e52 | − | 2.82728e52i | 0.965825 | − | 0.561598i | ||||
\(595\) | 2.88935e52i | 0.555876i | ||||||||
\(596\) | −3.76351e52 | + | 6.61246e52i | −0.701316 | + | 1.23221i | ||||
\(597\) | −3.75051e52 | −0.676984 | ||||||||
\(598\) | −4.43339e50 | − | 7.62444e50i | −0.00775199 | − | 0.0133317i | ||||
\(599\) | − | 6.62193e52i | − | 1.12170i | −0.827919 | − | 0.560848i | \(-0.810475\pi\) | ||
0.827919 | − | 0.560848i | \(-0.189525\pi\) | |||||||
\(600\) | 8.85309e51 | − | 8.19262e49i | 0.145285 | − | 0.00134446i | ||||
\(601\) | −3.86015e52 | −0.613747 | −0.306873 | − | 0.951750i | \(-0.599283\pi\) | ||||
−0.306873 | + | 0.951750i | \(0.599283\pi\) | |||||||
\(602\) | 5.65021e52 | − | 3.28543e52i | 0.870424 | − | 0.506126i | ||||
\(603\) | − | 6.90416e52i | − | 1.03058i | ||||||
\(604\) | −1.89924e52 | − | 1.08096e52i | −0.274712 | − | 0.156353i | ||||
\(605\) | 1.30444e52 | 0.182841 | ||||||||
\(606\) | 4.93065e50 | + | 8.47962e50i | 0.00669767 | + | 0.0115185i | ||||
\(607\) | 4.71183e52i | 0.620303i | 0.950687 | + | 0.310152i | \(0.100380\pi\) | ||||
−0.950687 | + | 0.310152i | \(0.899620\pi\) | |||||||
\(608\) | −5.07265e52 | + | 9.10765e52i | −0.647243 | + | 1.16209i | ||||
\(609\) | −2.05726e52 | −0.254426 | ||||||||
\(610\) | 2.69507e52 | − | 1.56710e52i | 0.323075 | − | 0.187858i | ||||
\(611\) | 2.09408e52i | 0.243338i | ||||||||
\(612\) | 2.41109e52 | − | 4.23627e52i | 0.271604 | − | 0.477207i | ||||
\(613\) | 3.99927e52 | 0.436749 | 0.218374 | − | 0.975865i | \(-0.429925\pi\) | ||||
0.218374 | + | 0.975865i | \(0.429925\pi\) | |||||||
\(614\) | 2.70442e52 | + | 4.65100e52i | 0.286335 | + | 0.492433i | ||||
\(615\) | − | 6.13692e52i | − | 0.629975i | ||||||
\(616\) | −5.15319e50 | − | 5.56862e52i | −0.00512912 | − | 0.554261i | ||||
\(617\) | −1.53502e53 | −1.48148 | −0.740740 | − | 0.671792i | \(-0.765525\pi\) | ||||
−0.740740 | + | 0.671792i | \(0.765525\pi\) | |||||||
\(618\) | −7.05621e52 | + | 4.10298e52i | −0.660375 | + | 0.383988i | ||||
\(619\) | − | 3.66312e52i | − | 0.332452i | −0.986088 | − | 0.166226i | \(-0.946842\pi\) | ||
0.986088 | − | 0.166226i | \(-0.0531581\pi\) | |||||||
\(620\) | 1.32623e53 | + | 7.54828e52i | 1.16728 | + | 0.664364i | ||||
\(621\) | 1.58378e51 | 0.0135193 | ||||||||
\(622\) | −2.52069e52 | − | 4.33503e52i | −0.208690 | − | 0.358901i | ||||
\(623\) | 1.03424e53i | 0.830516i | ||||||||
\(624\) | −8.64393e52 | + | 5.13380e52i | −0.673293 | + | 0.399882i | ||||
\(625\) | −1.54987e53 | −1.17105 | ||||||||
\(626\) | 4.87029e52 | − | 2.83193e52i | 0.356979 | − | 0.207573i | ||||
\(627\) | − | 1.33978e53i | − | 0.952688i | ||||||
\(628\) | 1.41920e53 | − | 2.49353e53i | 0.979064 | − | 1.72021i | ||||
\(629\) | −3.95321e52 | −0.264599 | ||||||||
\(630\) | −2.45663e52 | − | 4.22485e52i | −0.159540 | − | 0.274373i | ||||
\(631\) | − | 1.54525e53i | − | 0.973733i | −0.873476 | − | 0.486867i | \(-0.838140\pi\) | ||
0.873476 | − | 0.486867i | \(-0.161860\pi\) | |||||||
\(632\) | 2.50618e53 | − | 2.31921e51i | 1.53245 | − | 0.0141813i | ||||
\(633\) | −1.43288e53 | −0.850233 | ||||||||
\(634\) | −1.55035e53 | + | 9.01484e52i | −0.892759 | + | 0.519113i | ||||
\(635\) | − | 5.49020e52i | − | 0.306823i | ||||||
\(636\) | 1.01694e53 | + | 5.78793e52i | 0.551580 | + | 0.313934i | ||||
\(637\) | 1.65127e53 | 0.869300 | ||||||||
\(638\) | 7.93392e52 | + | 1.36446e53i | 0.405410 | + | 0.697216i | ||||
\(639\) | 2.56359e52i | 0.127154i | ||||||||
\(640\) | −1.96067e53 | + | 1.18916e53i | −0.944028 | + | 0.572560i | ||||
\(641\) | −5.03488e52 | −0.235335 | −0.117667 | − | 0.993053i | \(-0.537542\pi\) | ||||
−0.117667 | + | 0.993053i | \(0.537542\pi\) | |||||||
\(642\) | −1.69821e53 | + | 9.87460e52i | −0.770595 | + | 0.448078i | ||||
\(643\) | 3.21557e52i | 0.141661i | 0.997488 | + | 0.0708304i | \(0.0225649\pi\) | ||||
−0.997488 | + | 0.0708304i | \(0.977435\pi\) | |||||||
\(644\) | 7.75660e50 | − | 1.36283e51i | 0.00331772 | − | 0.00582922i | ||||
\(645\) | 3.45879e53 | 1.43645 | ||||||||
\(646\) | −1.62602e53 | − | 2.79639e53i | −0.655702 | − | 1.12766i | ||||
\(647\) | 3.24139e53i | 1.26926i | 0.772817 | + | 0.634629i | \(0.218847\pi\) | ||||
−0.772817 | + | 0.634629i | \(0.781153\pi\) | |||||||
\(648\) | −3.08018e50 | − | 3.32849e52i | −0.00117125 | − | 0.126568i | ||||
\(649\) | 2.23297e53 | 0.824582 | ||||||||
\(650\) | −6.23198e52 | + | 3.62371e52i | −0.223497 | + | 0.129957i | ||||
\(651\) | 1.18951e53i | 0.414314i | ||||||||
\(652\) | −7.45143e52 | − | 4.24101e52i | −0.252078 | − | 0.143471i | ||||
\(653\) | 2.13563e53 | 0.701740 | 0.350870 | − | 0.936424i | \(-0.385886\pi\) | ||||
0.350870 | + | 0.936424i | \(0.385886\pi\) | |||||||
\(654\) | 1.44736e53 | + | 2.48913e53i | 0.461954 | + | 0.794458i | ||||
\(655\) | 3.25495e53i | 1.00916i | ||||||||
\(656\) | 1.45830e53 | + | 2.45538e53i | 0.439211 | + | 0.739511i | ||||
\(657\) | −3.40446e53 | −0.996107 | ||||||||
\(658\) | −3.21862e52 | + | 1.87153e52i | −0.0914908 | + | 0.0531992i | ||||
\(659\) | 1.46403e53i | 0.404320i | 0.979352 | + | 0.202160i | \(0.0647962\pi\) | ||||
−0.979352 | + | 0.202160i | \(0.935204\pi\) | |||||||
\(660\) | 1.45773e53 | − | 2.56122e53i | 0.391149 | − | 0.687247i | ||||
\(661\) | 6.49219e53 | 1.69264 | 0.846318 | − | 0.532677i | \(-0.178814\pi\) | ||||
0.846318 | + | 0.532677i | \(0.178814\pi\) | |||||||
\(662\) | −1.75497e53 | − | 3.01816e53i | −0.444599 | − | 0.764612i | ||||
\(663\) | − | 3.11950e53i | − | 0.767940i | ||||||
\(664\) | −3.16032e53 | + | 2.92455e51i | −0.756026 | + | 0.00699625i | ||||
\(665\) | −3.24326e53 | −0.753999 | ||||||||
\(666\) | 5.78044e52 | − | 3.36116e52i | 0.130602 | − | 0.0759414i | ||||
\(667\) | 4.44442e51i | 0.00975942i | ||||||||
\(668\) | 1.81997e53 | + | 1.03584e53i | 0.388429 | + | 0.221076i | ||||
\(669\) | −3.14694e52 | −0.0652817 | ||||||||
\(670\) | −5.06600e53 | − | 8.71239e53i | −1.02151 | − | 1.75678i | ||||
\(671\) | − | 1.86443e53i | − | 0.365443i | ||||||
\(672\) | −1.56160e53 | − | 8.69758e52i | −0.297545 | − | 0.165723i | ||||
\(673\) | −7.05868e53 | −1.30749 | −0.653743 | − | 0.756716i | \(-0.726802\pi\) | ||||
−0.653743 | + | 0.756716i | \(0.726802\pi\) | |||||||
\(674\) | −5.50185e53 | + | 3.19916e53i | −0.990764 | + | 0.576100i | ||||
\(675\) | − | 1.29453e53i | − | 0.226643i | ||||||
\(676\) | 1.14332e53 | − | 2.00880e53i | 0.194616 | − | 0.341940i | ||||
\(677\) | 7.23413e53 | 1.19730 | 0.598648 | − | 0.801012i | \(-0.295705\pi\) | ||||
0.598648 | + | 0.801012i | \(0.295705\pi\) | |||||||
\(678\) | 1.03614e53 | + | 1.78194e53i | 0.166746 | + | 0.286766i | ||||
\(679\) | 8.05498e52i | 0.126049i | ||||||||
\(680\) | −6.58414e51 | − | 7.11494e53i | −0.0100191 | − | 1.08268i | ||||
\(681\) | −4.50876e53 | −0.667210 | ||||||||
\(682\) | 7.88930e53 | − | 4.58739e53i | 1.13536 | − | 0.660181i | ||||
\(683\) | − | 5.58560e53i | − | 0.781765i | −0.920440 | − | 0.390883i | \(-0.872170\pi\) | ||
0.920440 | − | 0.390883i | \(-0.127830\pi\) | |||||||
\(684\) | 4.75517e53 | + | 2.70642e53i | 0.647292 | + | 0.368409i | ||||
\(685\) | 1.12333e54 | 1.48726 | ||||||||
\(686\) | 3.47978e53 | + | 5.98445e53i | 0.448120 | + | 0.770666i | ||||
\(687\) | − | 2.84538e53i | − | 0.356420i | ||||||
\(688\) | −1.38386e54 | + | 8.21902e53i | −1.68621 | + | 1.00147i | ||||
\(689\) | −9.52765e53 | −1.12933 | ||||||||
\(690\) | 7.17372e51 | − | 4.17131e51i | 0.00827203 | − | 0.00480994i | ||||
\(691\) | − | 2.35453e53i | − | 0.264132i | −0.991241 | − | 0.132066i | \(-0.957839\pi\) | ||
0.991241 | − | 0.132066i | \(-0.0421612\pi\) | |||||||
\(692\) | −1.99264e53 | + | 3.50106e53i | −0.217477 | + | 0.382106i | ||||
\(693\) | −2.92273e53 | −0.310354 | ||||||||
\(694\) | 8.05205e53 | + | 1.38477e54i | 0.831911 | + | 1.43070i | ||||
\(695\) | 6.17613e53i | 0.620876i | ||||||||
\(696\) | 5.06595e53 | − | 4.68802e51i | 0.495548 | − | 0.00458579i | ||||
\(697\) | −8.86117e53 | −0.843467 | ||||||||
\(698\) | 1.12145e54 | − | 6.52092e53i | 1.03879 | − | 0.604027i | ||||
\(699\) | 9.08840e53i | 0.819259i | ||||||||
\(700\) | −1.11393e53 | − | 6.34000e52i | −0.0977230 | − | 0.0556194i | ||||
\(701\) | −1.17774e54 | −1.00556 | −0.502779 | − | 0.864415i | \(-0.667689\pi\) | ||||
−0.502779 | + | 0.864415i | \(0.667689\pi\) | |||||||
\(702\) | 7.38925e53 | + | 1.27079e54i | 0.614038 | + | 1.05601i | ||||
\(703\) | − | 4.43743e53i | − | 0.358906i | ||||||
\(704\) | 2.53791e52 | + | 1.37114e54i | 0.0199800 | + | 1.07945i | ||||
\(705\) | −1.97029e53 | −0.150986 | ||||||||
\(706\) | 5.61422e53 | − | 3.26450e53i | 0.418793 | − | 0.243516i | ||||
\(707\) | − | 1.42004e52i | − | 0.0103118i | ||||||
\(708\) | 3.54530e53 | − | 6.22907e53i | 0.250623 | − | 0.440343i | ||||
\(709\) | 2.04205e54 | 1.40536 | 0.702679 | − | 0.711507i | \(-0.251987\pi\) | ||||
0.702679 | + | 0.711507i | \(0.251987\pi\) | |||||||
\(710\) | 1.88106e53 | + | 3.23500e53i | 0.126036 | + | 0.216753i | ||||
\(711\) | − | 1.31539e54i | − | 0.858086i | ||||||
\(712\) | −2.35678e52 | − | 2.54678e54i | −0.0149693 | − | 1.61760i | ||||
\(713\) | 2.56976e52 | 0.0158925 | ||||||||
\(714\) | 4.79469e53 | − | 2.78797e53i | 0.288732 | − | 0.167889i | ||||
\(715\) | 2.39960e54i | 1.40710i | ||||||||
\(716\) | −2.00363e54 | − | 1.14037e54i | −1.14411 | − | 0.651177i | ||||
\(717\) | −1.63551e54 | −0.909470 | ||||||||
\(718\) | −9.36149e53 | − | 1.60997e54i | −0.506968 | − | 0.871873i | ||||
\(719\) | − | 2.98403e54i | − | 1.57382i | −0.617069 | − | 0.786909i | \(-0.711680\pi\) | ||
0.617069 | − | 0.786909i | \(-0.288320\pi\) | |||||||
\(720\) | 6.14564e53 | + | 1.03476e54i | 0.315682 | + | 0.531523i | ||||
\(721\) | 1.18167e54 | 0.591190 | ||||||||
\(722\) | 1.36488e54 | − | 7.93637e53i | 0.665101 | − | 0.386736i | ||||
\(723\) | 6.11024e53i | 0.290022i | ||||||||
\(724\) | −1.93366e54 | + | 3.39742e54i | −0.894019 | + | 1.57079i | ||||
\(725\) | 3.63273e53 | 0.163610 | ||||||||
\(726\) | −1.25867e53 | − | 2.16464e53i | −0.0552226 | − | 0.0949706i | ||||
\(727\) | 3.16380e54i | 1.35224i | 0.736789 | + | 0.676122i | \(0.236341\pi\) | ||||
−0.736789 | + | 0.676122i | \(0.763659\pi\) | |||||||
\(728\) | 1.45539e54 | − | 1.34682e52i | 0.606015 | − | 0.00560805i | ||||
\(729\) | −1.86692e54 | −0.757362 | ||||||||
\(730\) | −4.29610e54 | + | 2.49806e54i | −1.69801 | + | 0.987343i | ||||
\(731\) | − | 4.99419e54i | − | 1.92325i | ||||||
\(732\) | −5.20101e53 | − | 2.96017e53i | −0.195154 | − | 0.111073i | ||||
\(733\) | 5.32886e54 | 1.94831 | 0.974156 | − | 0.225874i | \(-0.0725239\pi\) | ||||
0.974156 | + | 0.225874i | \(0.0725239\pi\) | |||||||
\(734\) | −1.76868e54 | − | 3.04173e54i | −0.630121 | − | 1.08367i | ||||
\(735\) | 1.55366e54i | 0.539381i | ||||||||
\(736\) | −1.87898e52 | + | 3.37360e52i | −0.00635689 | + | 0.0114134i | ||||
\(737\) | −6.02719e54 | −1.98716 | ||||||||
\(738\) | 1.29569e54 | − | 7.53407e53i | 0.416324 | − | 0.242080i | ||||
\(739\) | 3.62860e54i | 1.13630i | 0.822924 | + | 0.568152i | \(0.192341\pi\) | ||||
−0.822924 | + | 0.568152i | \(0.807659\pi\) | |||||||
\(740\) | 4.82808e53 | − | 8.48292e53i | 0.147357 | − | 0.258906i | ||||
\(741\) | 3.50160e54 | 1.04165 | ||||||||
\(742\) | −8.51509e53 | − | 1.46441e54i | −0.246897 | − | 0.424607i | ||||
\(743\) | − | 5.37861e54i | − | 1.52014i | −0.649844 | − | 0.760068i | \(-0.725166\pi\) | ||
0.649844 | − | 0.760068i | \(-0.274834\pi\) | |||||||
\(744\) | −2.71061e52 | − | 2.92913e54i | −0.00746761 | − | 0.806963i | ||||
\(745\) | 5.82896e54 | 1.56539 | ||||||||
\(746\) | 4.19682e53 | − | 2.44033e53i | 0.109871 | − | 0.0638867i | ||||
\(747\) | 1.65871e54i | 0.423331i | ||||||||
\(748\) | −3.69818e54 | − | 2.10483e54i | −0.920148 | − | 0.523706i | ||||
\(749\) | 2.84392e54 | 0.689863 | ||||||||
\(750\) | 1.21579e54 | + | 2.09090e54i | 0.287539 | + | 0.494502i | ||||
\(751\) | 7.31050e54i | 1.68573i | 0.538124 | + | 0.842866i | \(0.319133\pi\) | ||||
−0.538124 | + | 0.842866i | \(0.680867\pi\) | |||||||
\(752\) | 7.88310e53 | − | 4.68193e53i | 0.177239 | − | 0.105266i | ||||
\(753\) | −2.33376e54 | −0.511625 | ||||||||
\(754\) | −3.56609e54 | + | 2.07358e54i | −0.762319 | + | 0.443266i | ||||
\(755\) | 1.67420e54i | 0.348992i | ||||||||
\(756\) | −1.29281e54 | + | 2.27147e54i | −0.262798 | + | 0.461735i | ||||
\(757\) | 3.78254e54 | 0.749828 | 0.374914 | − | 0.927060i | \(-0.377672\pi\) | ||||
0.374914 | + | 0.927060i | \(0.377672\pi\) | |||||||
\(758\) | 1.24391e54 | + | 2.13925e54i | 0.240477 | + | 0.413567i | ||||
\(759\) | − | 4.96275e52i | − | 0.00935682i | ||||||
\(760\) | 7.98643e54 | − | 7.39063e52i | 1.46857 | − | 0.0135901i | ||||
\(761\) | −8.00697e54 | −1.43602 | −0.718009 | − | 0.696034i | \(-0.754946\pi\) | ||||
−0.718009 | + | 0.696034i | \(0.754946\pi\) | |||||||
\(762\) | −9.11063e53 | + | 5.29756e53i | −0.159369 | + | 0.0926684i | ||||
\(763\) | − | 4.16844e54i | − | 0.711225i | ||||||
\(764\) | 7.31546e54 | + | 4.16362e54i | 1.21750 | + | 0.692943i | ||||
\(765\) | −3.73433e54 | −0.606241 | ||||||||
\(766\) | −2.86277e54 | − | 4.92333e54i | −0.453357 | − | 0.779673i | ||||
\(767\) | 5.83600e54i | 0.901578i | ||||||||
\(768\) | 3.86521e54 | + | 2.10617e54i | 0.582519 | + | 0.317417i | ||||
\(769\) | −1.97586e54 | −0.290506 | −0.145253 | − | 0.989395i | \(-0.546400\pi\) | ||||
−0.145253 | + | 0.989395i | \(0.546400\pi\) | |||||||
\(770\) | −3.68821e54 | + | 2.14458e54i | −0.529044 | + | 0.307623i | ||||
\(771\) | − | 3.43392e54i | − | 0.480571i | ||||||
\(772\) | 9.08551e53 | − | 1.59632e54i | 0.124057 | − | 0.217967i | ||||
\(773\) | 1.38648e54 | 0.184716 | 0.0923580 | − | 0.995726i | \(-0.470560\pi\) | ||||
0.0923580 | + | 0.995726i | \(0.470560\pi\) | |||||||
\(774\) | 4.24624e54 | + | 7.30258e54i | 0.551983 | + | 0.949289i | ||||
\(775\) | − | 2.10044e54i | − | 0.266427i | ||||||
\(776\) | −1.83554e52 | − | 1.98351e54i | −0.00227191 | − | 0.245506i | ||||
\(777\) | 7.60843e53 | 0.0918958 | ||||||||
\(778\) | −7.43534e54 | + | 4.32343e54i | −0.876372 | + | 0.509584i | ||||
\(779\) | − | 9.94656e54i | − | 1.14409i | ||||||
\(780\) | 6.69391e54 | + | 3.80986e54i | 0.751419 | + | 0.427673i | ||||
\(781\) | 2.23796e54 | 0.245178 | ||||||||
\(782\) | −6.02300e52 | − | 1.03582e53i | −0.00643998 | − | 0.0110753i | ||||
\(783\) | − | 7.40763e54i | − | 0.773047i | ||||||
\(784\) | −3.69191e54 | − | 6.21616e54i | −0.376050 | − | 0.633166i | ||||
\(785\) | −2.19808e55 | −2.18534 | ||||||||
\(786\) | 5.40137e54 | − | 3.14074e54i | 0.524174 | − | 0.304792i | ||||
\(787\) | − | 3.64802e54i | − | 0.345571i | −0.984959 | − | 0.172786i | \(-0.944723\pi\) | ||
0.984959 | − | 0.172786i | \(-0.0552768\pi\) | |||||||
\(788\) | −1.92765e54 | + | 3.38686e54i | −0.178250 | + | 0.313184i | ||||
\(789\) | 2.90670e54 | 0.262384 | ||||||||
\(790\) | −9.65178e54 | − | 1.65989e55i | −0.850536 | − | 1.46273i | ||||
\(791\) | − | 2.98413e54i | − | 0.256723i | ||||||
\(792\) | 7.19714e54 | − | 6.66021e52i | 0.604479 | − | 0.00559384i | ||||
\(793\) | 4.87281e54 | 0.399566 | ||||||||
\(794\) | 9.34515e54 | − | 5.43393e54i | 0.748164 | − | 0.435035i | ||||
\(795\) | − | 8.96442e54i | − | 0.700724i | ||||||
\(796\) | −1.16206e55 | − | 6.61388e54i | −0.886908 | − | 0.504787i | ||||
\(797\) | −1.78465e54 | −0.132998 | −0.0664988 | − | 0.997787i | \(-0.521183\pi\) | ||||
−0.0664988 | + | 0.997787i | \(0.521183\pi\) | |||||||
\(798\) | 3.12946e54 | + | 5.38198e54i | 0.227727 | + | 0.391640i | ||||
\(799\) | 2.84492e54i | 0.202154i | ||||||||
\(800\) | 2.75748e54 | + | 1.53582e54i | 0.191338 | + | 0.106569i | ||||
\(801\) | −1.33670e55 | −0.905764 | ||||||||
\(802\) | 1.03686e55 | − | 6.02904e54i | 0.686131 | − | 0.398965i | ||||
\(803\) | 2.97202e55i | 1.92069i | ||||||||
\(804\) | −9.56941e54 | + | 1.68134e55i | −0.603977 | + | 1.06118i | ||||
\(805\) | −1.20135e53 | −0.00740540 | ||||||||
\(806\) | 1.19894e55 | + | 2.06191e55i | 0.721826 | + | 1.24138i | ||||
\(807\) | − | 1.48471e54i | − | 0.0873062i | ||||||
\(808\) | 3.23594e51 | + | 3.49681e53i | 0.000185860 | + | 0.0200843i | ||||
\(809\) | 2.37044e55 | 1.32986 | 0.664932 | − | 0.746904i | \(-0.268461\pi\) | ||||
0.664932 | + | 0.746904i | \(0.268461\pi\) | |||||||
\(810\) | −2.20453e54 | + | 1.28187e54i | −0.120809 | + | 0.0702470i | ||||
\(811\) | 1.98008e55i | 1.05995i | 0.848012 | + | 0.529977i | \(0.177799\pi\) | ||||
−0.848012 | + | 0.529977i | \(0.822201\pi\) | |||||||
\(812\) | −6.37421e54 | − | 3.62790e54i | −0.333320 | − | 0.189710i | ||||
\(813\) | −1.05113e55 | −0.536954 | ||||||||
\(814\) | −2.93422e54 | − | 5.04621e54i | −0.146430 | − | 0.251826i | ||||
\(815\) | 6.56853e54i | 0.320238i | ||||||||
\(816\) | −1.17432e55 | + | 6.97455e54i | −0.559339 | + | 0.332203i | ||||
\(817\) | 5.60592e55 | 2.60872 | ||||||||
\(818\) | −5.82987e54 | + | 3.38989e54i | −0.265061 | + | 0.154125i | ||||
\(819\) | − | 7.63873e54i | − | 0.339334i | ||||||
\(820\) | 1.08222e55 | − | 1.90146e55i | 0.469735 | − | 0.825322i | ||||
\(821\) | 1.25594e55 | 0.532658 | 0.266329 | − | 0.963882i | \(-0.414189\pi\) | ||||
0.266329 | + | 0.963882i | \(0.414189\pi\) | |||||||
\(822\) | −1.08391e55 | − | 1.86409e55i | −0.449190 | − | 0.772507i | ||||
\(823\) | 2.31895e55i | 0.939064i | 0.882916 | + | 0.469532i | \(0.155577\pi\) | ||||
−0.882916 | + | 0.469532i | \(0.844423\pi\) | |||||||
\(824\) | −2.90983e55 | + | 2.69275e53i | −1.15146 | + | 0.0106556i | ||||
\(825\) | −4.05639e54 | −0.156861 | ||||||||
\(826\) | −8.96998e54 | + | 5.21578e54i | −0.338977 | + | 0.197105i | ||||
\(827\) | − | 2.00297e55i | − | 0.739724i | −0.929087 | − | 0.369862i | \(-0.879405\pi\) | ||
0.929087 | − | 0.369862i | \(-0.120595\pi\) | |||||||
\(828\) | 1.76138e53 | + | 1.00250e53i | 0.00635737 | + | 0.00361832i | ||||
\(829\) | −3.56852e54 | −0.125879 | −0.0629394 | − | 0.998017i | \(-0.520047\pi\) | ||||
−0.0629394 | + | 0.998017i | \(0.520047\pi\) | |||||||
\(830\) | 1.21710e55 | + | 2.09314e55i | 0.419606 | + | 0.721630i | ||||
\(831\) | − | 1.74370e53i | − | 0.00587559i | ||||||
\(832\) | −3.58355e55 | + | 6.63299e53i | −1.18024 | + | 0.0218457i | ||||
\(833\) | 2.24334e55 | 0.722172 | ||||||||
\(834\) | 1.02489e55 | − | 5.95942e54i | 0.322494 | − | 0.187521i | ||||
\(835\) | − | 1.60432e55i | − | 0.493457i | ||||||
\(836\) | 2.36265e55 | − | 4.15116e55i | 0.710363 | − | 1.24810i | ||||
\(837\) | −4.28310e55 | −1.25885 | ||||||||
\(838\) | 2.63349e54 | + | 4.52901e54i | 0.0756649 | + | 0.130127i | ||||
\(839\) | − | 1.33460e55i | − | 0.374865i | −0.982278 | − | 0.187432i | \(-0.939983\pi\) | ||
0.982278 | − | 0.187432i | \(-0.0600165\pi\) | |||||||
\(840\) | 1.26720e53 | + | 1.36936e55i | 0.00347967 | + | 0.376019i | ||||
\(841\) | −1.64624e55 | −0.441947 | ||||||||
\(842\) | 4.10915e55 | − | 2.38935e55i | 1.07851 | − | 0.627119i | ||||
\(843\) | − | 2.50483e54i | − | 0.0642769i | ||||||
\(844\) | −4.43960e55 | − | 2.52682e55i | −1.11388 | − | 0.633968i | ||||
\(845\) | −1.77078e55 | −0.434398 | ||||||||
\(846\) | −2.41885e54 | − | 4.15989e54i | −0.0580193 | − | 0.0997803i | ||||
\(847\) | 3.62502e54i | 0.0850209i | ||||||||
\(848\) | 2.13019e55 | + | 3.58665e55i | 0.488536 | + | 0.822561i | ||||
\(849\) | 9.71735e54 | 0.217922 | ||||||||
\(850\) | −8.46648e54 | + | 4.92301e54i | −0.185671 | + | 0.107962i | ||||
\(851\) | − | 1.64369e53i | − | 0.00352499i | ||||||
\(852\) | 3.55322e54 | − | 6.24298e54i | 0.0745194 | − | 0.130930i | ||||
\(853\) | 2.02762e55 | 0.415867 | 0.207933 | − | 0.978143i | \(-0.433326\pi\) | ||||
0.207933 | + | 0.978143i | \(0.433326\pi\) | |||||||
\(854\) | 4.35495e54 | + | 7.48954e54i | 0.0873541 | + | 0.150230i | ||||
\(855\) | − | 4.19174e55i | − | 0.822315i | ||||||
\(856\) | −7.00307e55 | + | 6.48062e53i | −1.34365 | + | 0.0124341i | ||||
\(857\) | −8.02526e55 | −1.50600 | −0.752998 | − | 0.658023i | \(-0.771393\pi\) | ||||
−0.752998 | + | 0.658023i | \(0.771393\pi\) | |||||||
\(858\) | 3.98199e55 | − | 2.31541e55i | 0.730872 | − | 0.424980i | ||||
\(859\) | 4.83819e55i | 0.868586i | 0.900772 | + | 0.434293i | \(0.143002\pi\) | ||||
−0.900772 | + | 0.434293i | \(0.856998\pi\) | |||||||
\(860\) | 1.07167e56 | + | 6.09944e55i | 1.88187 | + | 1.07107i | ||||
\(861\) | 1.70544e55 | 0.292938 | ||||||||
\(862\) | 7.98627e54 | + | 1.37346e55i | 0.134186 | + | 0.230769i | ||||
\(863\) | 5.23121e55i | 0.859799i | 0.902877 | + | 0.429900i | \(0.141451\pi\) | ||||
−0.902877 | + | 0.429900i | \(0.858549\pi\) | |||||||
\(864\) | 3.13176e55 | − | 5.62288e55i | 0.503532 | − | 0.904061i | ||||
\(865\) | 3.08623e55 | 0.485425 | ||||||||
\(866\) | −3.92106e55 | + | 2.27998e55i | −0.603342 | + | 0.350825i | ||||
\(867\) | 1.68860e54i | 0.0254193i | ||||||||
\(868\) | −2.09765e55 | + | 3.68557e55i | −0.308929 | + | 0.542787i | ||||
\(869\) | −1.14831e56 | −1.65456 | ||||||||
\(870\) | −1.95100e55 | − | 3.35528e55i | −0.275037 | − | 0.473002i | ||||
\(871\) | − | 1.57524e56i | − | 2.17271i | ||||||
\(872\) | 9.49889e53 | + | 1.02647e56i | 0.0128192 | + | 1.38526i | ||||
\(873\) | −1.04106e55 | −0.137469 | ||||||||
\(874\) | 1.16270e54 | − | 6.76074e53i | 0.0150228 | − | 0.00873529i | ||||
\(875\) | − | 3.50153e55i | − | 0.442695i | ||||||
\(876\) | 8.29072e55 | + | 4.71870e55i | 1.02569 | + | 0.583773i | ||||
\(877\) | 4.25545e55 | 0.515173 | 0.257586 | − | 0.966255i | \(-0.417073\pi\) | ||||
0.257586 | + | 0.966255i | \(0.417073\pi\) | |||||||
\(878\) | 4.86282e55 | + | 8.36298e55i | 0.576093 | + | 0.990752i | ||||
\(879\) | − | 5.85432e55i | − | 0.678716i | ||||||
\(880\) | 9.03323e55 | − | 5.36502e55i | 1.02488 | − | 0.608696i | ||||
\(881\) | 1.17792e56 | 1.30789 | 0.653947 | − | 0.756541i | \(-0.273112\pi\) | ||||
0.653947 | + | 0.756541i | \(0.273112\pi\) | |||||||
\(882\) | −3.28025e55 | + | 1.90737e55i | −0.356454 | + | 0.207268i | ||||
\(883\) | 1.62280e56i | 1.72589i | 0.505301 | + | 0.862943i | \(0.331382\pi\) | ||||
−0.505301 | + | 0.862943i | \(0.668618\pi\) | |||||||
\(884\) | 5.50110e55 | − | 9.66541e55i | 0.572607 | − | 1.00607i | ||||
\(885\) | −5.49100e55 | −0.559409 | ||||||||
\(886\) | −1.84058e55 | − | 3.16538e55i | −0.183532 | − | 0.315635i | ||||
\(887\) | 4.37192e55i | 0.426701i | 0.976976 | + | 0.213351i | \(0.0684376\pi\) | ||||
−0.976976 | + | 0.213351i | \(0.931562\pi\) | |||||||
\(888\) | −1.87355e55 | + | 1.73378e53i | −0.178986 | + | 0.00165633i | ||||
\(889\) | 1.52572e55 | 0.142672 | ||||||||
\(890\) | −1.68678e56 | + | 9.80815e55i | −1.54401 | + | 0.897794i | ||||
\(891\) | 1.52508e55i | 0.136652i | ||||||||
\(892\) | −9.75043e54 | − | 5.54949e54i | −0.0855247 | − | 0.0486767i | ||||
\(893\) | −3.19339e55 | −0.274204 | ||||||||
\(894\) | −5.62444e55 | − | 9.67279e55i | −0.472788 | − | 0.813090i | ||||
\(895\) | 1.76622e56i | 1.45347i | ||||||||
\(896\) | −3.30466e55 | − | 5.44867e55i | −0.266241 | − | 0.438973i | ||||
\(897\) | 1.29704e54 | 0.0102305 | ||||||||
\(898\) | −1.74448e55 | + | 1.01436e55i | −0.134715 | + | 0.0783326i | ||||
\(899\) | − | 1.20192e56i | − | 0.908747i | ||||||
\(900\) | 8.19410e54 | − | 1.43970e55i | 0.0606588 | − | 0.106577i | ||||
\(901\) | −1.29438e56 | −0.938192 | ||||||||
\(902\) | −6.57709e55 | − | 1.13111e56i | −0.466777 | − | 0.802753i | ||||
\(903\) | 9.61193e55i | 0.667949i | ||||||||
\(904\) | 6.80013e53 | + | 7.34833e55i | 0.00462718 | + | 0.500021i | ||||
\(905\) | 2.99487e56 | 1.99551 | ||||||||
\(906\) | 2.77823e55 | − | 1.61546e55i | 0.181273 | − | 0.105405i | ||||
\(907\) | − | 2.07283e56i | − | 1.32442i | −0.749319 | − | 0.662210i | \(-0.769619\pi\) | ||
0.749319 | − | 0.662210i | \(-0.230381\pi\) | |||||||
\(908\) | −1.39699e56 | − | 7.95102e55i | −0.874102 | − | 0.497499i | ||||
\(909\) | 1.83533e54 | 0.0112461 | ||||||||
\(910\) | −5.60499e55 | − | 9.63935e55i | −0.336348 | − | 0.578444i | ||||
\(911\) | − | 2.22241e55i | − | 0.130609i | −0.997865 | − | 0.0653046i | \(-0.979198\pi\) | ||
0.997865 | − | 0.0653046i | \(-0.0208019\pi\) | |||||||
\(912\) | −7.82885e55 | − | 1.31817e56i | −0.450605 | − | 0.758697i | ||||
\(913\) | 1.44802e56 | 0.816265 | ||||||||
\(914\) | 1.22680e56 | − | 7.13348e55i | 0.677324 | − | 0.393844i | ||||
\(915\) | 4.58475e55i | 0.247922i | ||||||||
\(916\) | 5.01771e55 | − | 8.81609e55i | 0.265761 | − | 0.466941i | ||||
\(917\) | −9.04544e55 | −0.469258 | ||||||||
\(918\) | 1.00387e56 | + | 1.72643e56i | 0.510113 | + | 0.877281i | ||||
\(919\) | − | 2.55150e56i | − | 1.26999i | −0.772516 | − | 0.634996i | \(-0.781002\pi\) | ||
0.772516 | − | 0.634996i | \(-0.218998\pi\) | |||||||
\(920\) | 2.95829e54 | − | 2.73760e52i | 0.0144236 | − | 0.000133475i | ||||
\(921\) | −7.91211e55 | −0.377885 | ||||||||
\(922\) | −2.21546e56 | + | 1.28823e56i | −1.03652 | + | 0.602705i | ||||
\(923\) | 5.84903e55i | 0.268072i | ||||||||
\(924\) | 7.11760e55 | + | 4.05101e55i | 0.319570 | + | 0.181884i | ||||
\(925\) | −1.34350e55 | −0.0590942 | ||||||||
\(926\) | −7.29180e55 | − | 1.25403e56i | −0.314214 | − | 0.540379i | ||||
\(927\) | 1.52725e56i | 0.644754i | ||||||||
\(928\) | 1.57790e56 | + | 8.78835e55i | 0.652630 | + | 0.363493i | ||||
\(929\) | 1.87803e56 | 0.761035 | 0.380517 | − | 0.924774i | \(-0.375746\pi\) | ||||
0.380517 | + | 0.924774i | \(0.375746\pi\) | |||||||
\(930\) | −1.94002e56 | + | 1.12807e56i | −0.770249 | + | 0.447877i | ||||
\(931\) | 2.51813e56i | 0.979566i | ||||||||
\(932\) | −1.60270e56 | + | 2.81594e56i | −0.610873 | + | 1.07330i | ||||
\(933\) | 7.37459e55 | 0.275415 | ||||||||
\(934\) | −3.15467e54 | − | 5.42533e54i | −0.0115442 | − | 0.0198534i | ||||
\(935\) | 3.25999e56i | 1.16895i | ||||||||
\(936\) | 1.74069e54 | + | 1.88101e56i | 0.00611617 | + | 0.660923i | ||||
\(937\) | 2.48823e56 | 0.856719 | 0.428359 | − | 0.903608i | \(-0.359092\pi\) | ||||
0.428359 | + | 0.903608i | \(0.359092\pi\) | |||||||
\(938\) | 2.42116e56 | − | 1.40783e56i | 0.816901 | − | 0.475004i | ||||
\(939\) | 8.28517e55i | 0.273940i | ||||||||
\(940\) | −6.10472e55 | − | 3.47452e55i | −0.197805 | − | 0.112581i | ||||
\(941\) | −3.78718e56 | −1.20258 | −0.601289 | − | 0.799032i | \(-0.705346\pi\) | ||||
−0.601289 | + | 0.799032i | \(0.705346\pi\) | |||||||
\(942\) | 2.12095e56 | + | 3.64757e56i | 0.660030 | + | 1.13511i | ||||
\(943\) | − | 3.68435e54i | − | 0.0112367i | ||||||
\(944\) | 2.19694e56 | − | 1.30481e56i | 0.656676 | − | 0.390013i | ||||
\(945\) | 2.00233e56 | 0.586584 | ||||||||
\(946\) | 6.37500e56 | − | 3.70688e56i | 1.83041 | − | 1.06433i | ||||
\(947\) | − | 3.77159e56i | − | 1.06139i | −0.847563 | − | 0.530695i | \(-0.821931\pi\) | ||
0.847563 | − | 0.530695i | \(-0.178069\pi\) | |||||||
\(948\) | −1.82317e56 | + | 3.20330e56i | −0.502885 | + | 0.883567i | ||||
\(949\) | −7.76755e56 | −2.10003 | ||||||||
\(950\) | −5.52602e55 | − | 9.50352e55i | −0.146441 | − | 0.251847i | ||||
\(951\) | − | 2.63740e56i | − | 0.685088i | ||||||
\(952\) | 1.97723e56 | − | 1.82972e54i | 0.503448 | − | 0.00465890i | ||||
\(953\) | −1.20914e56 | −0.301794 | −0.150897 | − | 0.988549i | \(-0.548216\pi\) | ||||
−0.150897 | + | 0.988549i | \(0.548216\pi\) | |||||||
\(954\) | 1.89267e56 | − | 1.10053e56i | 0.463079 | − | 0.269267i | ||||
\(955\) | − | 6.44867e56i | − | 1.54670i | ||||||
\(956\) | −5.06744e56 | − | 2.88415e56i | −1.19148 | − | 0.678138i | ||||
\(957\) | −2.32117e56 | −0.535032 | ||||||||
\(958\) | 3.17411e56 | + | 5.45876e56i | 0.717260 | + | 1.23353i | ||||
\(959\) | 3.12171e56i | 0.691574i | ||||||||
\(960\) | −6.24088e54 | − | 3.37171e56i | −0.0135548 | − | 0.732313i | ||||
\(961\) | −2.25335e56 | −0.479827 | ||||||||
\(962\) | 1.31886e56 | − | 7.66875e55i | 0.275341 | − | 0.160103i | ||||
\(963\) | 3.67561e56i | 0.752368i | ||||||||
\(964\) | −1.07752e56 | + | 1.89319e56i | −0.216252 | + | 0.379953i | ||||
\(965\) | −1.40717e56 | −0.276904 | ||||||||
\(966\) | 1.15920e54 | + | 1.99356e54i | 0.00223662 | + | 0.00384649i | ||||
\(967\) | − | 4.33299e56i | − | 0.819756i | −0.912140 | − | 0.409878i | \(-0.865571\pi\) | ||
0.912140 | − | 0.409878i | \(-0.134429\pi\) | |||||||
\(968\) | −8.26056e53 | − | 8.92650e55i | −0.00153242 | − | 0.165596i | ||||
\(969\) | 4.75711e56 | 0.865349 | ||||||||
\(970\) | −1.31372e56 | + | 7.63890e55i | −0.234337 | + | 0.136260i | ||||
\(971\) | − | 1.05882e57i | − | 1.85206i | −0.377450 | − | 0.926030i | \(-0.623199\pi\) | ||
0.377450 | − | 0.926030i | \(-0.376801\pi\) | |||||||
\(972\) | −4.81774e56 | − | 2.74203e56i | −0.826388 | − | 0.470342i | ||||
\(973\) | −1.71633e56 | −0.288707 | ||||||||
\(974\) | −1.15698e56 | − | 1.98975e56i | −0.190856 | − | 0.328230i | ||||
\(975\) | − | 1.06016e56i | − | 0.171508i | ||||||
\(976\) | −1.08946e56 | − | 1.83435e56i | −0.172848 | − | 0.291029i | ||||
\(977\) | −4.13148e55 | −0.0642849 | −0.0321424 | − | 0.999483i | \(-0.510233\pi\) | ||||
−0.0321424 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(978\) | 1.09000e56 | − | 6.33805e55i | 0.166337 | − | 0.0967203i | ||||
\(979\) | 1.16691e57i | 1.74649i | ||||||||
\(980\) | −2.73981e56 | + | 4.81383e56i | −0.402184 | + | 0.706636i | ||||
\(981\) | 5.38748e56 | 0.775666 | ||||||||
\(982\) | 2.64741e56 | + | 4.55295e56i | 0.373854 | + | 0.642946i | ||||
\(983\) | − | 6.30241e55i | − | 0.0872950i | −0.999047 | − | 0.0436475i | \(-0.986102\pi\) | ||
0.999047 | − | 0.0436475i | \(-0.0138979\pi\) | |||||||
\(984\) | −4.19959e56 | + | 3.88629e54i | −0.570559 | + | 0.00527994i | ||||
\(985\) | 2.98556e56 | 0.397867 | ||||||||
\(986\) | −4.84473e56 | + | 2.81707e56i | −0.633298 | + | 0.368244i | ||||
\(987\) | − | 5.47539e55i | − | 0.0702085i | ||||||
\(988\) | 1.08493e57 | + | 6.17493e56i | 1.36465 | + | 0.776694i | ||||
\(989\) | 2.07651e55 | 0.0256216 | ||||||||
\(990\) | −2.77176e56 | − | 4.76681e56i | −0.335495 | − | 0.576978i | ||||
\(991\) | 7.77140e56i | 0.922783i | 0.887197 | + | 0.461392i | \(0.152650\pi\) | ||||
−0.887197 | + | 0.461392i | \(0.847350\pi\) | |||||||
\(992\) | 5.08143e56 | − | 9.12340e56i | 0.591921 | − | 1.06276i | ||||
\(993\) | 5.13439e56 | 0.586750 | ||||||||
\(994\) | −8.99001e55 | + | 5.22742e55i | −0.100790 | + | 0.0586066i | ||||
\(995\) | 1.02437e57i | 1.12672i | ||||||||
\(996\) | 2.29904e56 | − | 4.03939e56i | 0.248095 | − | 0.435902i | ||||
\(997\) | 5.00009e55 | 0.0529383 | 0.0264692 | − | 0.999650i | \(-0.491574\pi\) | ||||
0.0264692 | + | 0.999650i | \(0.491574\pi\) | |||||||
\(998\) | −1.09935e56 | − | 1.89063e56i | −0.114197 | − | 0.196393i | ||||
\(999\) | 2.73958e56i | 0.279216i |
(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.3.4 | yes | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.3 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.3 | ✓ | 18 | 4.3 | odd | 2 | inner | |
4.39.b.a.3.4 | yes | 18 | 1.1 | even | 1 | trivial |