Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,43,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 43, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 43);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 43 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(33.5183121516\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 33864221333 x^{10} + \cdots + 25\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(-104257. i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.43.b.b.2.12 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.75326e6i | − | 1.78969i | −0.446374 | − | 0.894847i | \(-0.647285\pi\) | ||
0.446374 | − | 0.894847i | \(-0.352715\pi\) | |||||||
\(3\) | 1.02269e10 | − | 2.19746e9i | 0.977685 | − | 0.210075i | ||||
\(4\) | −9.68891e12 | −2.20300 | ||||||||
\(5\) | 5.14242e14i | 1.07844i | 0.842164 | + | 0.539222i | \(0.181282\pi\) | ||||
−0.842164 | + | 0.539222i | \(0.818718\pi\) | |||||||
\(6\) | −8.24764e15 | − | 3.83843e16i | −0.375970 | − | 1.74976i | ||||
\(7\) | 7.24611e17 | 1.29732 | 0.648659 | − | 0.761079i | \(-0.275330\pi\) | ||||
0.648659 | + | 0.761079i | \(0.275330\pi\) | |||||||
\(8\) | 1.98580e19i | 2.15301i | ||||||||
\(9\) | 9.97613e19 | − | 4.49466e19i | 0.911737 | − | 0.410775i | ||||
\(10\) | 1.93008e21 | 1.93008 | ||||||||
\(11\) | − | 5.80883e21i | − | 0.784950i | −0.919763 | − | 0.392475i | \(-0.871619\pi\) | ||
0.919763 | − | 0.392475i | \(-0.128381\pi\) | |||||||
\(12\) | −9.90878e22 | + | 2.12910e22i | −2.15384 | + | 0.462796i | ||||
\(13\) | −2.70188e23 | −1.09359 | −0.546797 | − | 0.837265i | \(-0.684153\pi\) | ||||
−0.546797 | + | 0.837265i | \(0.684153\pi\) | |||||||
\(14\) | − | 2.71965e24i | − | 2.32180i | ||||||
\(15\) | 1.13003e24 | + | 5.25912e24i | 0.226554 | + | 1.05438i | ||||
\(16\) | 3.19198e25 | 1.65022 | ||||||||
\(17\) | − | 9.64744e25i | − | 1.39632i | −0.715942 | − | 0.698160i | \(-0.754003\pi\) | ||
0.715942 | − | 0.698160i | \(-0.245997\pi\) | |||||||
\(18\) | −1.68696e26 | − | 3.74430e26i | −0.735161 | − | 1.63173i | ||||
\(19\) | 4.61773e26 | 0.646551 | 0.323275 | − | 0.946305i | \(-0.395216\pi\) | ||||
0.323275 | + | 0.946305i | \(0.395216\pi\) | |||||||
\(20\) | − | 4.98245e27i | − | 2.37582i | ||||||
\(21\) | 7.41055e27 | − | 1.59230e27i | 1.26837 | − | 0.272534i | ||||
\(22\) | −2.18020e28 | −1.40482 | ||||||||
\(23\) | − | 3.87491e28i | − | 0.981695i | −0.871245 | − | 0.490848i | \(-0.836687\pi\) | ||
0.871245 | − | 0.490848i | \(-0.163313\pi\) | |||||||
\(24\) | 4.36371e28 | + | 2.03086e29i | 0.452293 | + | 2.10496i | ||||
\(25\) | −3.70714e28 | −0.163042 | ||||||||
\(26\) | 1.01409e30i | 1.95720i | ||||||||
\(27\) | 9.21484e29 | − | 6.78887e29i | 0.805098 | − | 0.593142i | ||||
\(28\) | −7.02069e30 | −2.85799 | ||||||||
\(29\) | − | 4.99222e30i | − | 0.972604i | −0.873791 | − | 0.486302i | \(-0.838346\pi\) | ||
0.873791 | − | 0.486302i | \(-0.161654\pi\) | |||||||
\(30\) | 1.97388e31 | − | 4.24128e30i | 1.88702 | − | 0.405463i | ||||
\(31\) | −6.62101e30 | −0.317928 | −0.158964 | − | 0.987284i | \(-0.550815\pi\) | ||||
−0.158964 | + | 0.987284i | \(0.550815\pi\) | |||||||
\(32\) | − | 3.24671e31i | − | 0.800377i | ||||||
\(33\) | −1.27647e31 | − | 5.94065e31i | −0.164899 | − | 0.767435i | ||||
\(34\) | −3.62093e32 | −2.49898 | ||||||||
\(35\) | 3.72626e32i | 1.39908i | ||||||||
\(36\) | −9.66578e32 | + | 4.35483e32i | −2.00856 | + | 0.904938i | ||||
\(37\) | 1.25696e33 | 1.46922 | 0.734609 | − | 0.678491i | \(-0.237366\pi\) | ||||
0.734609 | + | 0.678491i | \(0.237366\pi\) | |||||||
\(38\) | − | 1.73315e33i | − | 1.15713i | ||||||
\(39\) | −2.76320e33 | + | 5.93727e32i | −1.06919 | + | 0.229737i | ||||
\(40\) | −1.02118e34 | −2.32190 | ||||||||
\(41\) | − | 6.68342e33i | − | 0.904769i | −0.891823 | − | 0.452385i | \(-0.850573\pi\) | ||
0.891823 | − | 0.452385i | \(-0.149427\pi\) | |||||||
\(42\) | −5.97633e33 | − | 2.78137e34i | −0.487753 | − | 2.26999i | ||||
\(43\) | 1.15443e34 | 0.574820 | 0.287410 | − | 0.957808i | \(-0.407206\pi\) | ||||
0.287410 | + | 0.957808i | \(0.407206\pi\) | |||||||
\(44\) | 5.62812e34i | 1.72925i | ||||||||
\(45\) | 2.31134e34 | + | 5.13015e34i | 0.442998 | + | 0.983257i | ||||
\(46\) | −1.45435e35 | −1.75693 | ||||||||
\(47\) | 6.11246e34i | 0.470069i | 0.971987 | + | 0.235034i | \(0.0755203\pi\) | ||||
−0.971987 | + | 0.235034i | \(0.924480\pi\) | |||||||
\(48\) | 3.26442e35 | − | 7.01426e34i | 1.61339 | − | 0.346670i | ||||
\(49\) | 2.13088e35 | 0.683033 | ||||||||
\(50\) | 1.39139e35i | 0.291795i | ||||||||
\(51\) | −2.11999e35 | − | 9.86637e35i | −0.293332 | − | 1.36516i | ||||
\(52\) | 2.61783e36 | 2.40919 | ||||||||
\(53\) | 1.29204e36i | 0.797043i | 0.917159 | + | 0.398522i | \(0.130477\pi\) | ||||
−0.917159 | + | 0.398522i | \(0.869523\pi\) | |||||||
\(54\) | −2.54804e36 | − | 3.45857e36i | −1.06154 | − | 1.44088i | ||||
\(55\) | 2.98715e36 | 0.846525 | ||||||||
\(56\) | 1.43893e37i | 2.79313i | ||||||||
\(57\) | 4.72252e36 | − | 1.01473e36i | 0.632123 | − | 0.135824i | ||||
\(58\) | −1.87371e37 | −1.74066 | ||||||||
\(59\) | 6.95742e36i | 0.451394i | 0.974198 | + | 0.225697i | \(0.0724660\pi\) | ||||
−0.974198 | + | 0.225697i | \(0.927534\pi\) | |||||||
\(60\) | −1.09487e37 | − | 5.09551e37i | −0.499100 | − | 2.32280i | ||||
\(61\) | −4.26930e37 | −1.37540 | −0.687701 | − | 0.725994i | \(-0.741380\pi\) | ||||
−0.687701 | + | 0.725994i | \(0.741380\pi\) | |||||||
\(62\) | 2.48504e37i | 0.568994i | ||||||||
\(63\) | 7.22882e37 | − | 3.25688e37i | 1.18281 | − | 0.532905i | ||||
\(64\) | 1.85273e37 | 0.217788 | ||||||||
\(65\) | − | 1.38942e38i | − | 1.17938i | ||||||
\(66\) | −2.22968e38 | + | 4.79091e37i | −1.37347 | + | 0.295118i | ||||
\(67\) | −1.36227e38 | −0.611917 | −0.305959 | − | 0.952045i | \(-0.598977\pi\) | ||||
−0.305959 | + | 0.952045i | \(0.598977\pi\) | |||||||
\(68\) | 9.34731e38i | 3.07609i | ||||||||
\(69\) | −8.51495e37 | − | 3.96284e38i | −0.206230 | − | 0.959789i | ||||
\(70\) | 1.39856e39 | 2.50393 | ||||||||
\(71\) | − | 7.56050e38i | − | 1.00491i | −0.864605 | − | 0.502453i | \(-0.832431\pi\) | ||
0.864605 | − | 0.502453i | \(-0.167569\pi\) | |||||||
\(72\) | 8.92547e38 | + | 1.98106e39i | 0.884400 | + | 1.96297i | ||||
\(73\) | 7.90940e38 | 0.586629 | 0.293314 | − | 0.956016i | \(-0.405242\pi\) | ||||
0.293314 | + | 0.956016i | \(0.405242\pi\) | |||||||
\(74\) | − | 4.71771e39i | − | 2.62945i | ||||||
\(75\) | −3.79127e38 | + | 8.14630e37i | −0.159404 | + | 0.0342510i | ||||
\(76\) | −4.47407e39 | −1.42435 | ||||||||
\(77\) | − | 4.20914e39i | − | 1.01833i | ||||||
\(78\) | 2.22841e39 | + | 1.03710e40i | 0.411158 | + | 1.91352i | ||||
\(79\) | −1.56636e38 | −0.0221168 | −0.0110584 | − | 0.999939i | \(-0.503520\pi\) | ||||
−0.0110584 | + | 0.999939i | \(0.503520\pi\) | |||||||
\(80\) | 1.64145e40i | 1.77967i | ||||||||
\(81\) | 7.93213e39 | − | 8.96786e39i | 0.662528 | − | 0.749037i | ||||
\(82\) | −2.50846e40 | −1.61926 | ||||||||
\(83\) | − | 2.41146e40i | − | 1.20681i | −0.797433 | − | 0.603407i | \(-0.793809\pi\) | ||
0.797433 | − | 0.603407i | \(-0.206191\pi\) | |||||||
\(84\) | −7.18002e40 | + | 1.54277e40i | −2.79422 | + | 0.600393i | ||||
\(85\) | 4.96112e40 | 1.50585 | ||||||||
\(86\) | − | 4.33289e40i | − | 1.02875i | ||||||
\(87\) | −1.09702e40 | − | 5.10551e40i | −0.204320 | − | 0.950901i | ||||
\(88\) | 1.15352e41 | 1.69000 | ||||||||
\(89\) | 1.04630e41i | 1.20912i | 0.796561 | + | 0.604558i | \(0.206650\pi\) | ||||
−0.796561 | + | 0.604558i | \(0.793350\pi\) | |||||||
\(90\) | 1.92548e41 | − | 8.67506e40i | 1.75973 | − | 0.792830i | ||||
\(91\) | −1.95781e41 | −1.41874 | ||||||||
\(92\) | 3.75436e41i | 2.16268i | ||||||||
\(93\) | −6.77126e40 | + | 1.45494e40i | −0.310834 | + | 0.0667888i | ||||
\(94\) | 2.29417e41 | 0.841279 | ||||||||
\(95\) | 2.37463e41i | 0.697269i | ||||||||
\(96\) | −7.13453e40 | − | 3.32039e41i | −0.168139 | − | 0.782517i | ||||
\(97\) | 3.83536e41 | 0.727109 | 0.363554 | − | 0.931573i | \(-0.381563\pi\) | ||||
0.363554 | + | 0.931573i | \(0.381563\pi\) | |||||||
\(98\) | − | 7.99776e41i | − | 1.22242i | ||||||
\(99\) | −2.61087e41 | − | 5.79497e41i | −0.322438 | − | 0.715668i | ||||
\(100\) | 3.59181e41 | 0.359181 | ||||||||
\(101\) | 6.85959e41i | 0.556608i | 0.960493 | + | 0.278304i | \(0.0897723\pi\) | ||||
−0.960493 | + | 0.278304i | \(0.910228\pi\) | |||||||
\(102\) | −3.70310e42 | + | 7.95686e41i | −2.44322 | + | 0.524974i | ||||
\(103\) | −5.84455e41 | −0.314174 | −0.157087 | − | 0.987585i | \(-0.550210\pi\) | ||||
−0.157087 | + | 0.987585i | \(0.550210\pi\) | |||||||
\(104\) | − | 5.36539e42i | − | 2.35451i | ||||||
\(105\) | 8.18830e41 | + | 3.81082e42i | 0.293913 | + | 1.36786i | ||||
\(106\) | 4.84935e42 | 1.42646 | ||||||||
\(107\) | 6.02787e42i | 1.45581i | 0.685678 | + | 0.727905i | \(0.259506\pi\) | ||||
−0.685678 | + | 0.727905i | \(0.740494\pi\) | |||||||
\(108\) | −8.92817e42 | + | 6.57767e42i | −1.77363 | + | 1.30669i | ||||
\(109\) | −6.41559e42 | −1.05022 | −0.525110 | − | 0.851034i | \(-0.675976\pi\) | ||||
−0.525110 | + | 0.851034i | \(0.675976\pi\) | |||||||
\(110\) | − | 1.12115e43i | − | 1.51502i | ||||||
\(111\) | 1.28549e43 | − | 2.76212e42i | 1.43643 | − | 0.308646i | ||||
\(112\) | 2.31295e43 | 2.14086 | ||||||||
\(113\) | − | 9.33215e42i | − | 0.716695i | −0.933588 | − | 0.358347i | \(-0.883340\pi\) | ||
0.933588 | − | 0.358347i | \(-0.116660\pi\) | |||||||
\(114\) | −3.80853e42 | − | 1.77248e43i | −0.243084 | − | 1.13131i | ||||
\(115\) | 1.99264e43 | 1.05870 | ||||||||
\(116\) | 4.83692e43i | 2.14265i | ||||||||
\(117\) | −2.69543e43 | + | 1.21440e43i | −0.997069 | + | 0.449220i | ||||
\(118\) | 2.61130e43 | 0.807857 | ||||||||
\(119\) | − | 6.99065e43i | − | 1.81147i | ||||||
\(120\) | −1.04435e44 | + | 2.24400e43i | −2.27008 | + | 0.487773i | ||||
\(121\) | 2.10212e43 | 0.383853 | ||||||||
\(122\) | 1.60238e44i | 2.46155i | ||||||||
\(123\) | −1.46866e43 | − | 6.83509e43i | −0.190070 | − | 0.884580i | ||||
\(124\) | 6.41504e43 | 0.700396 | ||||||||
\(125\) | 9.78615e43i | 0.902613i | ||||||||
\(126\) | −1.22239e44 | − | 2.71316e44i | −0.953737 | − | 2.11687i | ||||
\(127\) | 1.66541e43 | 0.110064 | 0.0550318 | − | 0.998485i | \(-0.482474\pi\) | ||||
0.0550318 | + | 0.998485i | \(0.482474\pi\) | |||||||
\(128\) | − | 2.12330e44i | − | 1.19015i | ||||||
\(129\) | 1.18063e44 | − | 2.53682e43i | 0.561993 | − | 0.120755i | ||||
\(130\) | −5.21486e44 | −2.11073 | ||||||||
\(131\) | − | 3.25643e44i | − | 1.12213i | −0.827770 | − | 0.561067i | \(-0.810391\pi\) | ||
0.827770 | − | 0.561067i | \(-0.189609\pi\) | |||||||
\(132\) | 1.23676e44 | + | 5.75584e44i | 0.363272 | + | 1.69066i | ||||
\(133\) | 3.34606e44 | 0.838782 | ||||||||
\(134\) | 5.11296e44i | 1.09514i | ||||||||
\(135\) | 3.49112e44 | + | 4.73866e44i | 0.639670 | + | 0.868253i | ||||
\(136\) | 1.91579e45 | 3.00628 | ||||||||
\(137\) | 4.99119e44i | 0.671541i | 0.941944 | + | 0.335770i | \(0.108997\pi\) | ||||
−0.941944 | + | 0.335770i | \(0.891003\pi\) | |||||||
\(138\) | −1.48736e45 | + | 3.19588e44i | −1.71773 | + | 0.369088i | ||||
\(139\) | −2.62476e44 | −0.260483 | −0.130241 | − | 0.991482i | \(-0.541575\pi\) | ||||
−0.130241 | + | 0.991482i | \(0.541575\pi\) | |||||||
\(140\) | − | 3.61034e45i | − | 3.08219i | ||||||
\(141\) | 1.34319e44 | + | 6.25118e44i | 0.0987497 | + | 0.459579i | ||||
\(142\) | −2.83765e45 | −1.79847 | ||||||||
\(143\) | 1.56948e45i | 0.858416i | ||||||||
\(144\) | 3.18437e45 | − | 1.43469e45i | 1.50456 | − | 0.677867i | ||||
\(145\) | 2.56721e45 | 1.04890 | ||||||||
\(146\) | − | 2.96860e45i | − | 1.04989i | ||||||
\(147\) | 2.17924e45 | − | 4.68253e44i | 0.667792 | − | 0.143488i | ||||
\(148\) | −1.21786e46 | −3.23669 | ||||||||
\(149\) | 7.13567e45i | 1.64635i | 0.567785 | + | 0.823177i | \(0.307801\pi\) | ||||
−0.567785 | + | 0.823177i | \(0.692199\pi\) | |||||||
\(150\) | 3.05752e44 | + | 1.42296e45i | 0.0612988 | + | 0.285284i | ||||
\(151\) | −7.92644e43 | −0.0138217 | −0.00691086 | − | 0.999976i | \(-0.502200\pi\) | ||||
−0.00691086 | + | 0.999976i | \(0.502200\pi\) | |||||||
\(152\) | 9.16987e45i | 1.39203i | ||||||||
\(153\) | −4.33619e45 | − | 9.62441e45i | −0.573573 | − | 1.27308i | ||||
\(154\) | −1.57980e46 | −1.82250 | ||||||||
\(155\) | − | 3.40480e45i | − | 0.342868i | ||||||
\(156\) | 2.67723e46 | − | 5.75257e45i | 2.35543 | − | 0.506111i | ||||
\(157\) | 2.05387e46 | 1.58009 | 0.790044 | − | 0.613051i | \(-0.210058\pi\) | ||||
0.790044 | + | 0.613051i | \(0.210058\pi\) | |||||||
\(158\) | 5.87895e44i | 0.0395823i | ||||||||
\(159\) | 2.83920e45 | + | 1.32136e46i | 0.167439 | + | 0.779257i | ||||
\(160\) | 1.66960e46 | 0.863162 | ||||||||
\(161\) | − | 2.80780e46i | − | 1.27357i | ||||||
\(162\) | −3.36587e46 | − | 2.97713e46i | −1.34055 | − | 1.18572i | ||||
\(163\) | 2.41150e46 | 0.844011 | 0.422006 | − | 0.906593i | \(-0.361326\pi\) | ||||
0.422006 | + | 0.906593i | \(0.361326\pi\) | |||||||
\(164\) | 6.47551e46i | 1.99321i | ||||||||
\(165\) | 3.05493e46 | − | 6.56413e45i | 0.827635 | − | 0.177834i | ||||
\(166\) | −9.05084e46 | −2.15983 | ||||||||
\(167\) | 1.27577e46i | 0.268366i | 0.990957 | + | 0.134183i | \(0.0428409\pi\) | ||||
−0.990957 | + | 0.134183i | \(0.957159\pi\) | |||||||
\(168\) | 3.16199e46 | + | 1.47159e47i | 0.586768 | + | 2.73080i | ||||
\(169\) | 1.19607e46 | 0.195946 | ||||||||
\(170\) | − | 1.86204e47i | − | 2.69501i | ||||||
\(171\) | 4.60670e46 | − | 2.07551e46i | 0.589484 | − | 0.265587i | ||||
\(172\) | −1.11852e47 | −1.26633 | ||||||||
\(173\) | 8.07502e44i | 0.00809423i | 0.999992 | + | 0.00404711i | \(0.00128824\pi\) | ||||
−0.999992 | + | 0.00404711i | \(0.998712\pi\) | |||||||
\(174\) | −1.91623e47 | + | 4.11740e46i | −1.70182 | + | 0.365670i | ||||
\(175\) | −2.68624e46 | −0.211517 | ||||||||
\(176\) | − | 1.85417e47i | − | 1.29534i | ||||||
\(177\) | 1.52887e46 | + | 7.11531e46i | 0.0948267 | + | 0.441322i | ||||
\(178\) | 3.92705e47 | 2.16395 | ||||||||
\(179\) | − | 6.10839e45i | − | 0.0299236i | −0.999888 | − | 0.0149618i | \(-0.995237\pi\) | ||
0.999888 | − | 0.0149618i | \(-0.00476266\pi\) | |||||||
\(180\) | −2.23944e47 | − | 4.97055e47i | −0.975925 | − | 2.16612i | ||||
\(181\) | 1.05779e47 | 0.410346 | 0.205173 | − | 0.978726i | \(-0.434224\pi\) | ||||
0.205173 | + | 0.978726i | \(0.434224\pi\) | |||||||
\(182\) | 7.34818e47i | 2.53911i | ||||||||
\(183\) | −4.36618e47 | + | 9.38161e46i | −1.34471 | + | 0.288938i | ||||
\(184\) | 7.69478e47 | 2.11360 | ||||||||
\(185\) | 6.46383e47i | 1.58447i | ||||||||
\(186\) | 5.46077e46 | + | 2.54143e47i | 0.119531 | + | 0.556297i | ||||
\(187\) | −5.60403e47 | −1.09604 | ||||||||
\(188\) | − | 5.92231e47i | − | 1.03556i | ||||||
\(189\) | 6.67718e47 | − | 4.91929e47i | 1.04447 | − | 0.769493i | ||||
\(190\) | 8.91260e47 | 1.24790 | ||||||||
\(191\) | 6.70025e46i | 0.0840215i | 0.999117 | + | 0.0420107i | \(0.0133764\pi\) | ||||
−0.999117 | + | 0.0420107i | \(0.986624\pi\) | |||||||
\(192\) | 1.89478e47 | − | 4.07130e46i | 0.212928 | − | 0.0457517i | ||||
\(193\) | −2.34629e47 | −0.236416 | −0.118208 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118208 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(194\) | − | 1.43951e48i | − | 1.30130i | ||||||
\(195\) | −3.05320e47 | − | 1.42095e48i | −0.247758 | − | 1.15306i | ||||
\(196\) | −2.06459e48 | −1.50472 | ||||||||
\(197\) | 2.09534e48i | 1.37235i | 0.727439 | + | 0.686173i | \(0.240711\pi\) | ||||
−0.727439 | + | 0.686173i | \(0.759289\pi\) | |||||||
\(198\) | −2.17500e48 | + | 9.79927e47i | −1.28083 | + | 0.577065i | ||||
\(199\) | −6.04782e47 | −0.320394 | −0.160197 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160197 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(200\) | − | 7.36163e47i | − | 0.351030i | ||||||
\(201\) | −1.39319e48 | + | 2.99354e47i | −0.598263 | + | 0.128549i | ||||
\(202\) | 2.57458e48 | 0.996158 | ||||||||
\(203\) | − | 3.61742e48i | − | 1.26178i | ||||||
\(204\) | 2.05403e48 | + | 9.55944e48i | 0.646211 | + | 3.00745i | ||||
\(205\) | 3.43690e48 | 0.975743 | ||||||||
\(206\) | 2.19361e48i | 0.562274i | ||||||||
\(207\) | −1.74164e48 | − | 3.86566e48i | −0.403256 | − | 0.895048i | ||||
\(208\) | −8.62436e48 | −1.80467 | ||||||||
\(209\) | − | 2.68236e48i | − | 0.507510i | ||||||
\(210\) | 1.43030e49 | − | 3.07328e48i | 2.44806 | − | 0.526014i | ||||
\(211\) | −1.12281e49 | −1.73930 | −0.869652 | − | 0.493665i | \(-0.835657\pi\) | ||||
−0.869652 | + | 0.493665i | \(0.835657\pi\) | |||||||
\(212\) | − | 1.25184e49i | − | 1.75589i | ||||||
\(213\) | −1.66139e48 | − | 7.73208e48i | −0.211106 | − | 0.982482i | ||||
\(214\) | 2.26242e49 | 2.60545 | ||||||||
\(215\) | 5.93659e48i | 0.619911i | ||||||||
\(216\) | 1.34813e49 | + | 1.82988e49i | 1.27704 | + | 1.73338i | ||||
\(217\) | −4.79766e48 | −0.412454 | ||||||||
\(218\) | 2.40794e49i | 1.87957i | ||||||||
\(219\) | 8.08889e48 | − | 1.73806e48i | 0.573538 | − | 0.123236i | ||||
\(220\) | −2.89422e49 | −1.86490 | ||||||||
\(221\) | 2.60662e49i | 1.52701i | ||||||||
\(222\) | −1.03670e49 | − | 4.82477e49i | −0.552382 | − | 2.57077i | ||||
\(223\) | −1.04880e49 | −0.508500 | −0.254250 | − | 0.967139i | \(-0.581829\pi\) | ||||
−0.254250 | + | 0.967139i | \(0.581829\pi\) | |||||||
\(224\) | − | 2.35261e49i | − | 1.03834i | ||||||
\(225\) | −3.69829e48 | + | 1.66623e48i | −0.148651 | + | 0.0669735i | ||||
\(226\) | −3.50260e49 | −1.28266 | ||||||||
\(227\) | 4.72205e49i | 1.57611i | 0.615602 | + | 0.788057i | \(0.288913\pi\) | ||||
−0.615602 | + | 0.788057i | \(0.711087\pi\) | |||||||
\(228\) | −4.57560e49 | + | 9.83159e48i | −1.39257 | + | 0.299221i | ||||
\(229\) | 5.59139e49 | 1.55230 | 0.776148 | − | 0.630550i | \(-0.217171\pi\) | ||||
0.776148 | + | 0.630550i | \(0.217171\pi\) | |||||||
\(230\) | − | 7.47890e49i | − | 1.89475i | ||||||
\(231\) | −9.24943e48 | − | 4.30466e49i | −0.213926 | − | 0.995606i | ||||
\(232\) | 9.91354e49 | 2.09402 | ||||||||
\(233\) | − | 3.55371e49i | − | 0.685817i | −0.939369 | − | 0.342908i | \(-0.888588\pi\) | ||
0.939369 | − | 0.342908i | \(-0.111412\pi\) | |||||||
\(234\) | 4.55797e49 | + | 1.01167e50i | 0.803967 | + | 1.78445i | ||||
\(235\) | −3.14329e49 | −0.506943 | ||||||||
\(236\) | − | 6.74098e49i | − | 0.994423i | ||||||
\(237\) | −1.60190e48 | + | 3.44201e47i | −0.0216233 | + | 0.00464619i | ||||
\(238\) | −2.62377e50 | −3.24198 | ||||||||
\(239\) | 1.54845e50i | 1.75203i | 0.482283 | + | 0.876015i | \(0.339808\pi\) | ||||
−0.482283 | + | 0.876015i | \(0.660192\pi\) | |||||||
\(240\) | 3.60703e49 | + | 1.67870e50i | 0.373864 | + | 1.73995i | ||||
\(241\) | 1.92291e50 | 1.82642 | 0.913210 | − | 0.407488i | \(-0.133595\pi\) | ||||
0.913210 | + | 0.407488i | \(0.133595\pi\) | |||||||
\(242\) | − | 7.88980e49i | − | 0.686979i | ||||||
\(243\) | 6.14149e49 | − | 1.09144e50i | 0.490390 | − | 0.871503i | ||||
\(244\) | 4.13648e50 | 3.03001 | ||||||||
\(245\) | 1.09579e50i | 0.736613i | ||||||||
\(246\) | −2.56539e50 | + | 5.51224e49i | −1.58313 | + | 0.340166i | ||||
\(247\) | −1.24765e50 | −0.707063 | ||||||||
\(248\) | − | 1.31480e50i | − | 0.684501i | ||||||
\(249\) | −5.29909e49 | − | 2.46619e50i | −0.253522 | − | 1.17988i | ||||
\(250\) | 3.67299e50 | 1.61540 | ||||||||
\(251\) | − | 4.15830e50i | − | 1.68177i | −0.541212 | − | 0.840886i | \(-0.682034\pi\) | ||
0.541212 | − | 0.840886i | \(-0.317966\pi\) | |||||||
\(252\) | −7.00394e50 | + | 3.15556e50i | −2.60574 | + | 1.17399i | ||||
\(253\) | −2.25087e50 | −0.770582 | ||||||||
\(254\) | − | 6.25073e49i | − | 0.196980i | ||||||
\(255\) | 5.07371e50 | − | 1.09019e50i | 1.47225 | − | 0.316342i | ||||
\(256\) | −7.15445e50 | −1.91222 | ||||||||
\(257\) | 5.11943e50i | 1.26074i | 0.776294 | + | 0.630371i | \(0.217097\pi\) | ||||
−0.776294 | + | 0.630371i | \(0.782903\pi\) | |||||||
\(258\) | −9.52136e49 | − | 4.43122e50i | −0.216115 | − | 1.00579i | ||||
\(259\) | 9.10810e50 | 1.90604 | ||||||||
\(260\) | 1.34620e51i | 2.59817i | ||||||||
\(261\) | −2.24383e50 | − | 4.98031e50i | −0.399521 | − | 0.886759i | ||||
\(262\) | −1.22222e51 | −2.00828 | ||||||||
\(263\) | 5.17583e50i | 0.785071i | 0.919737 | + | 0.392536i | \(0.128402\pi\) | ||||
−0.919737 | + | 0.392536i | \(0.871598\pi\) | |||||||
\(264\) | 1.17969e51 | − | 2.53480e50i | 1.65229 | − | 0.355027i | ||||
\(265\) | −6.64420e50 | −0.859566 | ||||||||
\(266\) | − | 1.25586e51i | − | 1.50116i | ||||||
\(267\) | 2.29921e50 | + | 1.07005e51i | 0.254005 | + | 1.18213i | ||||
\(268\) | 1.31989e51 | 1.34806 | ||||||||
\(269\) | 4.39733e50i | 0.415328i | 0.978200 | + | 0.207664i | \(0.0665861\pi\) | ||||
−0.978200 | + | 0.207664i | \(0.933414\pi\) | |||||||
\(270\) | 1.77854e51 | − | 1.31031e51i | 1.55391 | − | 1.14481i | ||||
\(271\) | −4.50806e50 | −0.364447 | −0.182224 | − | 0.983257i | \(-0.558330\pi\) | ||||
−0.182224 | + | 0.983257i | \(0.558330\pi\) | |||||||
\(272\) | − | 3.07945e51i | − | 2.30423i | ||||||
\(273\) | −2.00224e51 | + | 4.30222e50i | −1.38708 | + | 0.298042i | ||||
\(274\) | 1.87332e51 | 1.20185 | ||||||||
\(275\) | 2.15342e50i | 0.127980i | ||||||||
\(276\) | 8.25006e50 | + | 3.83956e51i | 0.454325 | + | 2.11442i | ||||
\(277\) | 1.80963e51 | 0.923667 | 0.461834 | − | 0.886967i | \(-0.347192\pi\) | ||||
0.461834 | + | 0.886967i | \(0.347192\pi\) | |||||||
\(278\) | 9.85140e50i | 0.466184i | ||||||||
\(279\) | −6.60521e50 | + | 2.97592e50i | −0.289867 | + | 0.130597i | ||||
\(280\) | −7.39959e51 | −3.01224 | ||||||||
\(281\) | − | 2.73994e51i | − | 1.03492i | −0.855706 | − | 0.517462i | \(-0.826877\pi\) | ||
0.855706 | − | 0.517462i | \(-0.173123\pi\) | |||||||
\(282\) | 2.34623e51 | − | 5.04134e50i | 0.822506 | − | 0.176732i | ||||
\(283\) | −3.95811e51 | −1.28817 | −0.644084 | − | 0.764955i | \(-0.722761\pi\) | ||||
−0.644084 | + | 0.764955i | \(0.722761\pi\) | |||||||
\(284\) | 7.32530e51i | 2.21381i | ||||||||
\(285\) | 5.21815e50 | + | 2.42852e51i | 0.146479 | + | 0.681709i | ||||
\(286\) | 5.89065e51 | 1.53630 | ||||||||
\(287\) | − | 4.84288e51i | − | 1.17377i | ||||||
\(288\) | −1.45929e51 | − | 3.23897e51i | −0.328775 | − | 0.729733i | ||||
\(289\) | −4.53361e51 | −0.949707 | ||||||||
\(290\) | − | 9.63541e51i | − | 1.87721i | ||||||
\(291\) | 3.92239e51 | − | 8.42804e50i | 0.710883 | − | 0.152747i | ||||
\(292\) | −7.66334e51 | −1.29234 | ||||||||
\(293\) | − | 2.96723e51i | − | 0.465726i | −0.972510 | − | 0.232863i | \(-0.925191\pi\) | ||
0.972510 | − | 0.232863i | \(-0.0748094\pi\) | |||||||
\(294\) | −1.75747e51 | − | 8.17925e51i | −0.256800 | − | 1.19514i | ||||
\(295\) | −3.57780e51 | −0.486804 | ||||||||
\(296\) | 2.49607e52i | 3.16323i | ||||||||
\(297\) | −3.94354e51 | − | 5.35274e51i | −0.465587 | − | 0.631962i | ||||
\(298\) | 2.67820e52 | 2.94647 | ||||||||
\(299\) | 1.04695e52i | 1.07358i | ||||||||
\(300\) | 3.67333e51 | − | 7.89287e50i | 0.351166 | − | 0.0754551i | ||||
\(301\) | 8.36516e51 | 0.745724 | ||||||||
\(302\) | 2.97500e50i | 0.0247367i | ||||||||
\(303\) | 1.50737e51 | + | 7.01526e51i | 0.116930 | + | 0.544188i | ||||
\(304\) | 1.47397e52 | 1.06695 | ||||||||
\(305\) | − | 2.19545e52i | − | 1.48329i | ||||||
\(306\) | −3.61229e52 | + | 1.62748e52i | −2.27842 | + | 1.02652i | ||||
\(307\) | 8.53677e51 | 0.502791 | 0.251395 | − | 0.967884i | \(-0.419111\pi\) | ||||
0.251395 | + | 0.967884i | \(0.419111\pi\) | |||||||
\(308\) | 4.07820e52i | 2.24338i | ||||||||
\(309\) | −5.97719e51 | + | 1.28432e51i | −0.307163 | + | 0.0660000i | ||||
\(310\) | −1.27791e52 | −0.613628 | ||||||||
\(311\) | − | 3.00572e52i | − | 1.34890i | −0.738320 | − | 0.674450i | \(-0.764381\pi\) | ||
0.738320 | − | 0.674450i | \(-0.235619\pi\) | |||||||
\(312\) | −1.17902e52 | − | 5.48714e52i | −0.494624 | − | 2.30197i | ||||
\(313\) | 5.27239e51 | 0.206812 | 0.103406 | − | 0.994639i | \(-0.467026\pi\) | ||||
0.103406 | + | 0.994639i | \(0.467026\pi\) | |||||||
\(314\) | − | 7.70872e52i | − | 2.82787i | ||||||
\(315\) | 1.67482e52 | + | 3.71736e52i | 0.574709 | + | 1.27560i | ||||
\(316\) | 1.51763e51 | 0.0487233 | ||||||||
\(317\) | 5.15943e52i | 1.55009i | 0.631906 | + | 0.775045i | \(0.282273\pi\) | ||||
−0.631906 | + | 0.775045i | \(0.717727\pi\) | |||||||
\(318\) | 4.95940e52 | − | 1.06563e52i | 1.39463 | − | 0.299664i | ||||
\(319\) | −2.89990e52 | −0.763446 | ||||||||
\(320\) | 9.52753e51i | 0.234872i | ||||||||
\(321\) | 1.32460e52 | + | 6.16467e52i | 0.305830 | + | 1.42332i | ||||
\(322\) | −1.05384e53 | −2.27930 | ||||||||
\(323\) | − | 4.45492e52i | − | 0.902791i | ||||||
\(324\) | −7.68537e52 | + | 8.68887e52i | −1.45955 | + | 1.65013i | ||||
\(325\) | 1.00163e52 | 0.178301 | ||||||||
\(326\) | − | 9.05100e52i | − | 1.51052i | ||||||
\(327\) | −6.56118e52 | + | 1.40980e52i | −1.02678 | + | 0.220625i | ||||
\(328\) | 1.32719e53 | 1.94797 | ||||||||
\(329\) | 4.42916e52i | 0.609828i | ||||||||
\(330\) | −2.46369e52 | − | 1.14660e53i | −0.318268 | − | 1.48121i | ||||
\(331\) | 7.26343e52 | 0.880550 | 0.440275 | − | 0.897863i | \(-0.354881\pi\) | ||||
0.440275 | + | 0.897863i | \(0.354881\pi\) | |||||||
\(332\) | 2.33644e53i | 2.65861i | ||||||||
\(333\) | 1.25396e53 | − | 5.64961e52i | 1.33954 | − | 0.603517i | ||||
\(334\) | 4.78830e52 | 0.480292 | ||||||||
\(335\) | − | 7.00537e52i | − | 0.659919i | ||||||
\(336\) | 2.36544e53 | − | 5.08261e52i | 2.09308 | − | 0.449741i | ||||
\(337\) | 9.67459e52 | 0.804275 | 0.402137 | − | 0.915579i | \(-0.368267\pi\) | ||||
0.402137 | + | 0.915579i | \(0.368267\pi\) | |||||||
\(338\) | − | 4.48917e52i | − | 0.350683i | ||||||
\(339\) | −2.05070e52 | − | 9.54392e52i | −0.150560 | − | 0.700702i | ||||
\(340\) | −4.80678e53 | −3.31740 | ||||||||
\(341\) | 3.84603e52i | 0.249558i | ||||||||
\(342\) | −7.78992e52 | − | 1.72902e53i | −0.475319 | − | 1.05500i | ||||
\(343\) | −7.16533e52 | −0.411206 | ||||||||
\(344\) | 2.29247e53i | 1.23759i | ||||||||
\(345\) | 2.03786e53 | − | 4.37875e52i | 1.03508 | − | 0.222407i | ||||
\(346\) | 3.03076e51 | 0.0144862 | ||||||||
\(347\) | − | 5.77439e52i | − | 0.259769i | −0.991529 | − | 0.129884i | \(-0.958539\pi\) | ||
0.991529 | − | 0.129884i | \(-0.0414606\pi\) | |||||||
\(348\) | 1.06289e53 | + | 4.94668e53i | 0.450117 | + | 2.09484i | ||||
\(349\) | −2.86857e53 | −1.14375 | −0.571875 | − | 0.820341i | \(-0.693784\pi\) | ||||
−0.571875 | + | 0.820341i | \(0.693784\pi\) | |||||||
\(350\) | 1.00821e53i | 0.378551i | ||||||||
\(351\) | −2.48974e53 | + | 1.83427e53i | −0.880450 | + | 0.648656i | ||||
\(352\) | −1.88596e53 | −0.628256 | ||||||||
\(353\) | 7.09859e52i | 0.222794i | 0.993776 | + | 0.111397i | \(0.0355325\pi\) | ||||
−0.993776 | + | 0.111397i | \(0.964467\pi\) | |||||||
\(354\) | 2.67056e53 | − | 5.73823e52i | 0.789830 | − | 0.169711i | ||||
\(355\) | 3.88793e53 | 1.08373 | ||||||||
\(356\) | − | 1.01375e54i | − | 2.66368i | ||||||
\(357\) | −1.53617e53 | − | 7.14929e53i | −0.380545 | − | 1.77105i | ||||
\(358\) | −2.29264e52 | −0.0535540 | ||||||||
\(359\) | 1.69674e53i | 0.373793i | 0.982380 | + | 0.186896i | \(0.0598429\pi\) | ||||
−0.982380 | + | 0.186896i | \(0.940157\pi\) | |||||||
\(360\) | −1.01874e54 | + | 4.58985e53i | −2.11696 | + | 0.953776i | ||||
\(361\) | −2.96861e53 | −0.581972 | ||||||||
\(362\) | − | 3.97017e53i | − | 0.734393i | ||||||
\(363\) | 2.14982e53 | − | 4.61932e52i | 0.375287 | − | 0.0806379i | ||||
\(364\) | 1.89691e54 | 3.12548 | ||||||||
\(365\) | 4.06735e53i | 0.632646i | ||||||||
\(366\) | 3.52116e53 | + | 1.63874e54i | 0.517110 | + | 2.40662i | ||||
\(367\) | −7.62830e53 | −1.05789 | −0.528945 | − | 0.848656i | \(-0.677412\pi\) | ||||
−0.528945 | + | 0.848656i | \(0.677412\pi\) | |||||||
\(368\) | − | 1.23686e54i | − | 1.62001i | ||||||
\(369\) | −3.00397e53 | − | 6.66747e53i | −0.371656 | − | 0.824912i | ||||
\(370\) | 2.42604e54 | 2.83571 | ||||||||
\(371\) | 9.36225e53i | 1.03402i | ||||||||
\(372\) | 6.56061e53 | − | 1.40968e53i | 0.684767 | − | 0.147136i | ||||
\(373\) | −1.96577e54 | −1.93931 | −0.969656 | − | 0.244473i | \(-0.921385\pi\) | ||||
−0.969656 | + | 0.244473i | \(0.921385\pi\) | |||||||
\(374\) | 2.10334e54i | 1.96158i | ||||||||
\(375\) | 2.15047e53 | + | 1.00082e54i | 0.189616 | + | 0.882471i | ||||
\(376\) | −1.21381e54 | −1.01206 | ||||||||
\(377\) | 1.34884e54i | 1.06363i | ||||||||
\(378\) | −1.84634e54 | − | 2.50612e54i | −1.37716 | − | 1.86928i | ||||
\(379\) | 1.43891e54 | 1.01534 | 0.507670 | − | 0.861552i | \(-0.330507\pi\) | ||||
0.507670 | + | 0.861552i | \(0.330507\pi\) | |||||||
\(380\) | − | 2.30076e54i | − | 1.53608i | ||||||
\(381\) | 1.70321e53 | − | 3.65968e52i | 0.107608 | − | 0.0231216i | ||||
\(382\) | 2.51478e53 | 0.150373 | ||||||||
\(383\) | − | 1.88455e54i | − | 1.06668i | −0.845901 | − | 0.533340i | \(-0.820937\pi\) | ||
0.845901 | − | 0.533340i | \(-0.179063\pi\) | |||||||
\(384\) | −4.66586e53 | − | 2.17148e54i | −0.250021 | − | 1.16359i | ||||
\(385\) | 2.16452e54 | 1.09821 | ||||||||
\(386\) | 8.80623e53i | 0.423113i | ||||||||
\(387\) | 1.15168e54 | − | 5.18878e53i | 0.524084 | − | 0.236121i | ||||
\(388\) | −3.71604e54 | −1.60182 | ||||||||
\(389\) | 7.46859e53i | 0.304998i | 0.988304 | + | 0.152499i | \(0.0487321\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(390\) | −5.33320e54 | + | 1.14594e54i | −2.06363 | + | 0.443411i | ||||
\(391\) | −3.73829e54 | −1.37076 | ||||||||
\(392\) | 4.23150e54i | 1.47057i | ||||||||
\(393\) | −7.15588e53 | − | 3.33033e54i | −0.235733 | − | 1.09709i | ||||
\(394\) | 7.86435e54 | 2.45608 | ||||||||
\(395\) | − | 8.05487e52i | − | 0.0238517i | ||||||
\(396\) | 2.52965e54 | + | 5.61469e54i | 0.710331 | + | 1.57662i | ||||
\(397\) | −3.44358e53 | −0.0917084 | −0.0458542 | − | 0.998948i | \(-0.514601\pi\) | ||||
−0.0458542 | + | 0.998948i | \(0.514601\pi\) | |||||||
\(398\) | 2.26991e54i | 0.573407i | ||||||||
\(399\) | 3.42199e54 | − | 7.35283e53i | 0.820064 | − | 0.176207i | ||||
\(400\) | −1.18331e54 | −0.269054 | ||||||||
\(401\) | − | 3.13021e54i | − | 0.675370i | −0.941259 | − | 0.337685i | \(-0.890356\pi\) | ||
0.941259 | − | 0.337685i | \(-0.109644\pi\) | |||||||
\(402\) | 1.12355e54 | + | 5.22899e54i | 0.230063 | + | 1.07071i | ||||
\(403\) | 1.78892e54 | 0.347684 | ||||||||
\(404\) | − | 6.64620e54i | − | 1.22621i | ||||||
\(405\) | 4.61165e54 | + | 4.07904e54i | 0.807794 | + | 0.714500i | ||||
\(406\) | −1.35771e55 | −2.25819 | ||||||||
\(407\) | − | 7.30148e54i | − | 1.15326i | ||||||
\(408\) | 1.95926e55 | − | 4.20986e54i | 2.93920 | − | 0.631545i | ||||
\(409\) | −7.57120e54 | −1.07889 | −0.539443 | − | 0.842022i | \(-0.681365\pi\) | ||||
−0.539443 | + | 0.842022i | \(0.681365\pi\) | |||||||
\(410\) | − | 1.28996e55i | − | 1.74628i | ||||||
\(411\) | 1.09679e54 | + | 5.10446e54i | 0.141074 | + | 0.656555i | ||||
\(412\) | 5.66273e54 | 0.692125 | ||||||||
\(413\) | 5.04143e54i | 0.585602i | ||||||||
\(414\) | −1.45088e55 | + | 6.53682e54i | −1.60186 | + | 0.721704i | ||||
\(415\) | 1.24008e55 | 1.30148 | ||||||||
\(416\) | 8.77224e54i | 0.875287i | ||||||||
\(417\) | −2.68432e54 | + | 5.76781e53i | −0.254670 | + | 0.0547209i | ||||
\(418\) | −1.00676e55 | −0.908288 | ||||||||
\(419\) | 5.92571e54i | 0.508447i | 0.967146 | + | 0.254223i | \(0.0818199\pi\) | ||||
−0.967146 | + | 0.254223i | \(0.918180\pi\) | |||||||
\(420\) | −7.93357e54 | − | 3.69227e55i | −0.647491 | − | 3.01341i | ||||
\(421\) | 1.70784e55 | 1.32594 | 0.662968 | − | 0.748648i | \(-0.269297\pi\) | ||||
0.662968 | + | 0.748648i | \(0.269297\pi\) | |||||||
\(422\) | 4.21421e55i | 3.11282i | ||||||||
\(423\) | 2.74734e54 | + | 6.09788e54i | 0.193092 | + | 0.428579i | ||||
\(424\) | −2.56572e55 | −1.71604 | ||||||||
\(425\) | 3.57644e54i | 0.227658i | ||||||||
\(426\) | −2.90205e55 | + | 6.23563e54i | −1.75834 | + | 0.377814i | ||||
\(427\) | −3.09358e55 | −1.78433 | ||||||||
\(428\) | − | 5.84035e55i | − | 3.20715i | ||||||
\(429\) | 3.44886e54 | + | 1.60509e55i | 0.180332 | + | 0.839261i | ||||
\(430\) | 2.22816e55 | 1.10945 | ||||||||
\(431\) | 6.55253e54i | 0.310732i | 0.987857 | + | 0.155366i | \(0.0496557\pi\) | ||||
−0.987857 | + | 0.155366i | \(0.950344\pi\) | |||||||
\(432\) | 2.94136e55 | − | 2.16700e55i | 1.32859 | − | 0.978812i | ||||
\(433\) | 4.18498e54 | 0.180073 | 0.0900364 | − | 0.995938i | \(-0.471302\pi\) | ||||
0.0900364 | + | 0.995938i | \(0.471302\pi\) | |||||||
\(434\) | 1.80069e55i | 0.738166i | ||||||||
\(435\) | 2.62547e55 | − | 5.64135e54i | 1.02549 | − | 0.220348i | ||||
\(436\) | 6.21601e55 | 2.31364 | ||||||||
\(437\) | − | 1.78933e55i | − | 0.634716i | ||||||
\(438\) | −6.52338e54 | − | 3.03597e55i | −0.220555 | − | 1.02646i | ||||
\(439\) | −4.80865e55 | −1.54977 | −0.774887 | − | 0.632100i | \(-0.782193\pi\) | ||||
−0.774887 | + | 0.632100i | \(0.782193\pi\) | |||||||
\(440\) | 5.93186e55i | 1.82257i | ||||||||
\(441\) | 2.12580e55 | − | 9.57758e54i | 0.622747 | − | 0.280573i | ||||
\(442\) | 9.78333e55 | 2.73287 | ||||||||
\(443\) | − | 2.85134e55i | − | 0.759574i | −0.925074 | − | 0.379787i | \(-0.875997\pi\) | ||
0.925074 | − | 0.379787i | \(-0.124003\pi\) | |||||||
\(444\) | −1.24550e56 | + | 2.67620e55i | −3.16446 | + | 0.679948i | ||||
\(445\) | −5.38054e55 | −1.30396 | ||||||||
\(446\) | 3.93642e55i | 0.910059i | ||||||||
\(447\) | 1.56804e55 | + | 7.29761e55i | 0.345858 | + | 1.60962i | ||||
\(448\) | 1.34251e55 | 0.282540 | ||||||||
\(449\) | − | 8.34240e55i | − | 1.67540i | −0.546133 | − | 0.837698i | \(-0.683901\pi\) | ||
0.546133 | − | 0.837698i | \(-0.316099\pi\) | |||||||
\(450\) | 6.25380e54 | + | 1.38807e55i | 0.119862 | + | 0.266040i | ||||
\(451\) | −3.88229e55 | −0.710199 | ||||||||
\(452\) | 9.04183e55i | 1.57888i | ||||||||
\(453\) | −8.10632e53 | + | 1.74180e53i | −0.0135133 | + | 0.00290360i | ||||
\(454\) | 1.77231e56 | 2.82076 | ||||||||
\(455\) | − | 1.00679e56i | − | 1.53003i | ||||||
\(456\) | 2.01504e55 | + | 9.37796e55i | 0.292430 | + | 1.36096i | ||||
\(457\) | 2.64725e55 | 0.366906 | 0.183453 | − | 0.983028i | \(-0.441273\pi\) | ||||
0.183453 | + | 0.983028i | \(0.441273\pi\) | |||||||
\(458\) | − | 2.09859e56i | − | 2.77814i | ||||||
\(459\) | −6.54952e55 | − | 8.88996e55i | −0.828215 | − | 1.12417i | ||||
\(460\) | −1.93065e56 | −2.33233 | ||||||||
\(461\) | 1.49317e56i | 1.72342i | 0.507405 | + | 0.861708i | \(0.330605\pi\) | ||||
−0.507405 | + | 0.861708i | \(0.669395\pi\) | |||||||
\(462\) | −1.61565e56 | + | 3.47155e55i | −1.78183 | + | 0.382862i | ||||
\(463\) | 4.17276e55 | 0.439767 | 0.219883 | − | 0.975526i | \(-0.429432\pi\) | ||||
0.219883 | + | 0.975526i | \(0.429432\pi\) | |||||||
\(464\) | − | 1.59351e56i | − | 1.60501i | ||||||
\(465\) | −7.48192e54 | − | 3.48207e55i | −0.0720280 | − | 0.335217i | ||||
\(466\) | −1.33380e56 | −1.22740 | ||||||||
\(467\) | 1.06470e56i | 0.936644i | 0.883558 | + | 0.468322i | \(0.155141\pi\) | ||||
−0.883558 | + | 0.468322i | \(0.844859\pi\) | |||||||
\(468\) | 2.61158e56 | − | 1.17662e56i | 2.19655 | − | 0.989634i | ||||
\(469\) | −9.87117e55 | −0.793851 | ||||||||
\(470\) | 1.17976e56i | 0.907272i | ||||||||
\(471\) | 2.10048e56 | − | 4.51331e55i | 1.54483 | − | 0.331937i | ||||
\(472\) | −1.38160e56 | −0.971854 | ||||||||
\(473\) | − | 6.70591e55i | − | 0.451205i | ||||||
\(474\) | 1.29187e54 | + | 6.01236e54i | 0.00831525 | + | 0.0386990i | ||||
\(475\) | −1.71186e55 | −0.105415 | ||||||||
\(476\) | 6.77317e56i | 3.99067i | ||||||||
\(477\) | 5.80726e55 | + | 1.28895e56i | 0.327405 | + | 0.726694i | ||||
\(478\) | 5.81174e56 | 3.13560 | ||||||||
\(479\) | 2.60939e56i | 1.34739i | 0.739010 | + | 0.673694i | \(0.235293\pi\) | ||||
−0.739010 | + | 0.673694i | \(0.764707\pi\) | |||||||
\(480\) | 1.70749e56 | − | 3.66887e55i | 0.843901 | − | 0.181329i | ||||
\(481\) | −3.39616e56 | −1.60673 | ||||||||
\(482\) | − | 7.21718e56i | − | 3.26873i | ||||||
\(483\) | −6.17003e55 | − | 2.87152e56i | −0.267546 | − | 1.24515i | ||||
\(484\) | −2.03672e56 | −0.845628 | ||||||||
\(485\) | 1.97230e56i | 0.784146i | ||||||||
\(486\) | −4.09646e56 | − | 2.30506e56i | −1.55972 | − | 0.877648i | ||||
\(487\) | 2.29921e56 | 0.838438 | 0.419219 | − | 0.907885i | \(-0.362304\pi\) | ||||
0.419219 | + | 0.907885i | \(0.362304\pi\) | |||||||
\(488\) | − | 8.47795e56i | − | 2.96125i | ||||||
\(489\) | 2.46623e56 | − | 5.29918e55i | 0.825178 | − | 0.177306i | ||||
\(490\) | 4.11278e56 | 1.31831 | ||||||||
\(491\) | 5.52415e56i | 1.69650i | 0.529595 | + | 0.848251i | \(0.322344\pi\) | ||||
−0.529595 | + | 0.848251i | \(0.677656\pi\) | |||||||
\(492\) | 1.42297e56 | + | 6.62246e56i | 0.418724 | + | 1.94873i | ||||
\(493\) | −4.81622e56 | −1.35807 | ||||||||
\(494\) | 4.68277e56i | 1.26543i | ||||||||
\(495\) | 2.98002e56 | − | 1.34262e56i | 0.771808 | − | 0.347731i | ||||
\(496\) | −2.11342e56 | −0.524650 | ||||||||
\(497\) | − | 5.47843e56i | − | 1.30368i | ||||||
\(498\) | −9.25623e56 | + | 1.98889e56i | −2.11163 | + | 0.453726i | ||||
\(499\) | 6.53739e56 | 1.42986 | 0.714929 | − | 0.699198i | \(-0.246459\pi\) | ||||
0.714929 | + | 0.699198i | \(0.246459\pi\) | |||||||
\(500\) | − | 9.48171e56i | − | 1.98846i | ||||||
\(501\) | 2.80346e55 | + | 1.30472e56i | 0.0563770 | + | 0.262377i | ||||
\(502\) | −1.56072e57 | −3.00986 | ||||||||
\(503\) | 1.45999e56i | 0.270036i | 0.990843 | + | 0.135018i | \(0.0431092\pi\) | ||||
−0.990843 | + | 0.135018i | \(0.956891\pi\) | |||||||
\(504\) | 6.46750e56 | + | 1.43550e57i | 1.14735 | + | 2.54660i | ||||
\(505\) | −3.52749e56 | −0.600271 | ||||||||
\(506\) | 8.44809e56i | 1.37911i | ||||||||
\(507\) | 1.22321e56 | − | 2.62832e55i | 0.191573 | − | 0.0411634i | ||||
\(508\) | −1.61360e56 | −0.242470 | ||||||||
\(509\) | − | 8.80675e56i | − | 1.26982i | −0.772586 | − | 0.634910i | \(-0.781037\pi\) | ||
0.772586 | − | 0.634910i | \(-0.218963\pi\) | |||||||
\(510\) | −4.09175e56 | − | 1.90429e57i | −0.566155 | − | 2.63488i | ||||
\(511\) | 5.73124e56 | 0.761044 | ||||||||
\(512\) | 1.75141e57i | 2.23213i | ||||||||
\(513\) | 4.25516e56 | − | 3.13491e56i | 0.520537 | − | 0.383496i | ||||
\(514\) | 1.92145e57 | 2.25634 | ||||||||
\(515\) | − | 3.00552e56i | − | 0.338819i | ||||||
\(516\) | −1.14390e57 | + | 2.45790e56i | −1.23807 | + | 0.266024i | ||||
\(517\) | 3.55063e56 | 0.368981 | ||||||||
\(518\) | − | 3.41850e57i | − | 3.41123i | ||||||
\(519\) | 1.77445e54 | + | 8.25827e54i | 0.00170040 | + | 0.00791361i | ||||
\(520\) | 2.75911e57 | 2.53921 | ||||||||
\(521\) | 3.72877e56i | 0.329590i | 0.986328 | + | 0.164795i | \(0.0526962\pi\) | ||||
−0.986328 | + | 0.164795i | \(0.947304\pi\) | |||||||
\(522\) | −1.86924e57 | + | 8.42168e56i | −1.58703 | + | 0.715020i | ||||
\(523\) | −7.07575e56 | −0.577081 | −0.288540 | − | 0.957468i | \(-0.593170\pi\) | ||||
−0.288540 | + | 0.957468i | \(0.593170\pi\) | |||||||
\(524\) | 3.15513e57i | 2.47206i | ||||||||
\(525\) | −2.74720e56 | + | 5.90290e55i | −0.206797 | + | 0.0444345i | ||||
\(526\) | 1.94262e57 | 1.40504 | ||||||||
\(527\) | 6.38758e56i | 0.443929i | ||||||||
\(528\) | −4.07446e56 | − | 1.89625e57i | −0.272118 | − | 1.26643i | ||||
\(529\) | 5.65154e55 | 0.0362742 | ||||||||
\(530\) | 2.49374e57i | 1.53836i | ||||||||
\(531\) | 3.12712e56 | + | 6.94082e56i | 0.185421 | + | 0.411553i | ||||
\(532\) | −3.24196e57 | −1.84784 | ||||||||
\(533\) | 1.80578e57i | 0.989450i | ||||||||
\(534\) | 4.01617e57 | − | 8.62953e56i | 2.11566 | − | 0.454591i | ||||
\(535\) | −3.09979e57 | −1.57001 | ||||||||
\(536\) | − | 2.70519e57i | − | 1.31746i | ||||||
\(537\) | −1.34229e55 | − | 6.24701e55i | −0.00628619 | − | 0.0292558i | ||||
\(538\) | 1.65043e57 | 0.743310 | ||||||||
\(539\) | − | 1.23779e57i | − | 0.536147i | ||||||
\(540\) | −3.38252e57 | − | 4.59124e57i | −1.40919 | − | 1.91276i | ||||
\(541\) | −4.09025e57 | −1.63911 | −0.819554 | − | 0.573002i | \(-0.805779\pi\) | ||||
−0.819554 | + | 0.573002i | \(0.805779\pi\) | |||||||
\(542\) | 1.69199e57i | 0.652249i | ||||||||
\(543\) | 1.08180e57 | − | 2.32445e56i | 0.401189 | − | 0.0862034i | ||||
\(544\) | −3.13225e57 | −1.11758 | ||||||||
\(545\) | − | 3.29917e57i | − | 1.13260i | ||||||
\(546\) | 1.61473e57 | + | 7.51494e57i | 0.533403 | + | 2.48245i | ||||
\(547\) | 4.71343e57 | 1.49832 | 0.749158 | − | 0.662392i | \(-0.230459\pi\) | ||||
0.749158 | + | 0.662392i | \(0.230459\pi\) | |||||||
\(548\) | − | 4.83592e57i | − | 1.47941i | ||||||
\(549\) | −4.25911e57 | + | 1.91890e57i | −1.25400 | + | 0.564980i | ||||
\(550\) | 8.08233e56 | 0.229045 | ||||||||
\(551\) | − | 2.30527e57i | − | 0.628838i | ||||||
\(552\) | 7.86940e57 | − | 1.69090e57i | 2.06643 | − | 0.444014i | ||||
\(553\) | −1.13500e56 | −0.0286925 | ||||||||
\(554\) | − | 6.79202e57i | − | 1.65308i | ||||||
\(555\) | 1.42040e57 | + | 6.61052e57i | 0.332858 | + | 1.54911i | ||||
\(556\) | 2.54311e57 | 0.573844 | ||||||||
\(557\) | 5.99960e57i | 1.30366i | 0.758366 | + | 0.651829i | \(0.225998\pi\) | ||||
−0.758366 | + | 0.651829i | \(0.774002\pi\) | |||||||
\(558\) | 1.11694e57 | + | 2.47911e57i | 0.233728 | + | 0.518772i | ||||
\(559\) | −3.11914e57 | −0.628619 | ||||||||
\(560\) | 1.18942e58i | 2.30879i | ||||||||
\(561\) | −5.73121e57 | + | 1.23146e57i | −1.07158 | + | 0.230251i | ||||
\(562\) | −1.02837e58 | −1.85220 | ||||||||
\(563\) | − | 6.67422e57i | − | 1.15804i | −0.815313 | − | 0.579021i | \(-0.803435\pi\) | ||
0.815313 | − | 0.579021i | \(-0.196565\pi\) | |||||||
\(564\) | −1.30140e57 | − | 6.05671e57i | −0.217546 | − | 1.01245i | ||||
\(565\) | 4.79898e57 | 0.772915 | ||||||||
\(566\) | 1.48558e58i | 2.30543i | ||||||||
\(567\) | 5.74771e57 | − | 6.49821e57i | 0.859510 | − | 0.971739i | ||||
\(568\) | 1.50136e58 | 2.16357 | ||||||||
\(569\) | − | 6.97280e57i | − | 0.968389i | −0.874961 | − | 0.484194i | \(-0.839113\pi\) | ||
0.874961 | − | 0.484194i | \(-0.160887\pi\) | |||||||
\(570\) | 9.11486e57 | − | 1.95851e57i | 1.22005 | − | 0.262152i | ||||
\(571\) | 8.05857e57 | 1.03968 | 0.519840 | − | 0.854263i | \(-0.325991\pi\) | ||||
0.519840 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(572\) | − | 1.52065e58i | − | 1.89109i | ||||||
\(573\) | 1.47235e56 | + | 6.85230e56i | 0.0176508 | + | 0.0821466i | ||||
\(574\) | −1.81766e58 | −2.10069 | ||||||||
\(575\) | 1.43648e57i | 0.160057i | ||||||||
\(576\) | 1.84831e57 | − | 8.32739e56i | 0.198565 | − | 0.0894616i | ||||
\(577\) | −2.72612e57 | −0.282392 | −0.141196 | − | 0.989982i | \(-0.545095\pi\) | ||||
−0.141196 | + | 0.989982i | \(0.545095\pi\) | |||||||
\(578\) | 1.70158e58i | 1.69968i | ||||||||
\(579\) | −2.39953e57 | + | 5.15587e56i | −0.231141 | + | 0.0496652i | ||||
\(580\) | −2.48735e58 | −2.31073 | ||||||||
\(581\) | − | 1.74737e58i | − | 1.56562i | ||||||
\(582\) | −3.16326e57 | − | 1.47218e58i | −0.273371 | − | 1.27226i | ||||
\(583\) | 7.50522e57 | 0.625639 | ||||||||
\(584\) | 1.57065e58i | 1.26301i | ||||||||
\(585\) | −6.24497e57 | − | 1.38611e58i | −0.484459 | − | 1.07528i | ||||
\(586\) | −1.11368e58 | −0.833507 | ||||||||
\(587\) | 1.30204e58i | 0.940206i | 0.882611 | + | 0.470103i | \(0.155783\pi\) | ||||
−0.882611 | + | 0.470103i | \(0.844217\pi\) | |||||||
\(588\) | −2.11145e58 | + | 4.53686e57i | −1.47115 | + | 0.316105i | ||||
\(589\) | −3.05740e57 | −0.205557 | ||||||||
\(590\) | 1.34284e58i | 0.871229i | ||||||||
\(591\) | 4.60442e57 | + | 2.14289e58i | 0.288296 | + | 1.34172i | ||||
\(592\) | 4.01220e58 | 2.42453 | ||||||||
\(593\) | 2.47365e58i | 1.44275i | 0.692547 | + | 0.721373i | \(0.256489\pi\) | ||||
−0.692547 | + | 0.721373i | \(0.743511\pi\) | |||||||
\(594\) | −2.00902e58 | + | 1.48011e58i | −1.13102 | + | 0.833258i | ||||
\(595\) | 3.59489e58 | 1.95357 | ||||||||
\(596\) | − | 6.91369e58i | − | 3.62692i | ||||||
\(597\) | −6.18507e57 | + | 1.32899e57i | −0.313245 | + | 0.0673068i | ||||
\(598\) | 3.92949e58 | 1.92137 | ||||||||
\(599\) | 1.19346e58i | 0.563434i | 0.959498 | + | 0.281717i | \(0.0909039\pi\) | ||||
−0.959498 | + | 0.281717i | \(0.909096\pi\) | |||||||
\(600\) | −1.61769e57 | − | 7.52869e57i | −0.0737426 | − | 0.343197i | ||||
\(601\) | −2.72028e58 | −1.19743 | −0.598715 | − | 0.800962i | \(-0.704322\pi\) | ||||
−0.598715 | + | 0.800962i | \(0.704322\pi\) | |||||||
\(602\) | − | 3.13966e58i | − | 1.33462i | ||||||
\(603\) | −1.35902e58 | + | 6.12294e57i | −0.557908 | + | 0.251360i | ||||
\(604\) | 7.67985e56 | 0.0304493 | ||||||||
\(605\) | 1.08100e58i | 0.413964i | ||||||||
\(606\) | 2.63301e58 | − | 5.65754e57i | 0.973929 | − | 0.209268i | ||||
\(607\) | 3.19838e58 | 1.14279 | 0.571396 | − | 0.820675i | \(-0.306402\pi\) | ||||
0.571396 | + | 0.820675i | \(0.306402\pi\) | |||||||
\(608\) | − | 1.49924e58i | − | 0.517484i | ||||||
\(609\) | −7.94914e57 | − | 3.69951e58i | −0.265068 | − | 1.23362i | ||||
\(610\) | −8.24010e58 | −2.65464 | ||||||||
\(611\) | − | 1.65151e58i | − | 0.514064i | ||||||
\(612\) | 4.20130e58 | + | 9.32500e58i | 1.26358 | + | 2.80459i | ||||
\(613\) | −3.27172e58 | −0.950836 | −0.475418 | − | 0.879760i | \(-0.657703\pi\) | ||||
−0.475418 | + | 0.879760i | \(0.657703\pi\) | |||||||
\(614\) | − | 3.20407e58i | − | 0.899842i | ||||||
\(615\) | 3.51489e58 | − | 7.55245e57i | 0.953970 | − | 0.204979i | ||||
\(616\) | 8.35851e58 | 2.19247 | ||||||||
\(617\) | 5.56508e58i | 1.41086i | 0.708781 | + | 0.705429i | \(0.249246\pi\) | ||||
−0.708781 | + | 0.705429i | \(0.750754\pi\) | |||||||
\(618\) | 4.82038e57 | + | 2.24339e58i | 0.118120 | + | 0.549727i | ||||
\(619\) | 8.02722e58 | 1.90135 | 0.950674 | − | 0.310193i | \(-0.100394\pi\) | ||||
0.950674 | + | 0.310193i | \(0.100394\pi\) | |||||||
\(620\) | 3.29888e58i | 0.755338i | ||||||||
\(621\) | −2.63062e58 | − | 3.57067e58i | −0.582284 | − | 0.790361i | ||||
\(622\) | −1.12812e59 | −2.41412 | ||||||||
\(623\) | 7.58164e58i | 1.56861i | ||||||||
\(624\) | −8.82007e58 | + | 1.89517e58i | −1.76440 | + | 0.379115i | ||||
\(625\) | −5.87536e58 | −1.13646 | ||||||||
\(626\) | − | 1.97886e58i | − | 0.370131i | ||||||
\(627\) | −5.89438e57 | − | 2.74323e58i | −0.106615 | − | 0.496185i | ||||
\(628\) | −1.98998e59 | −3.48094 | ||||||||
\(629\) | − | 1.21265e59i | − | 2.05150i | ||||||
\(630\) | 1.39522e59 | − | 6.28605e58i | 2.28293 | − | 1.02855i | ||||
\(631\) | 8.71597e58 | 1.37943 | 0.689714 | − | 0.724082i | \(-0.257736\pi\) | ||||
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(632\) | − | 3.11047e57i | − | 0.0476176i | ||||||
\(633\) | −1.14829e59 | + | 2.46734e58i | −1.70049 | + | 0.365385i | ||||
\(634\) | 1.93647e59 | 2.77419 | ||||||||
\(635\) | 8.56426e57i | 0.118697i | ||||||||
\(636\) | −2.75087e58 | − | 1.28025e59i | −0.368868 | − | 1.71671i | ||||
\(637\) | −5.75739e58 | −0.746961 | ||||||||
\(638\) | 1.08841e59i | 1.36633i | ||||||||
\(639\) | −3.39819e58 | − | 7.54246e58i | −0.412790 | − | 0.916210i | ||||
\(640\) | 1.09189e59 | 1.28351 | ||||||||
\(641\) | 7.65162e57i | 0.0870432i | 0.999052 | + | 0.0435216i | \(0.0138577\pi\) | ||||
−0.999052 | + | 0.0435216i | \(0.986142\pi\) | |||||||
\(642\) | 2.31376e59 | − | 4.97157e58i | 2.54731 | − | 0.547341i | ||||
\(643\) | −1.02721e59 | −1.09453 | −0.547265 | − | 0.836959i | \(-0.684331\pi\) | ||||
−0.547265 | + | 0.836959i | \(0.684331\pi\) | |||||||
\(644\) | 2.72045e59i | 2.80568i | ||||||||
\(645\) | 1.30454e58 | + | 6.07131e58i | 0.130228 | + | 0.606078i | ||||
\(646\) | −1.67205e59 | −1.61572 | ||||||||
\(647\) | − | 1.70616e59i | − | 1.59599i | −0.602666 | − | 0.797994i | \(-0.705895\pi\) | ||
0.602666 | − | 0.797994i | \(-0.294105\pi\) | |||||||
\(648\) | 1.78083e59 | + | 1.57516e59i | 1.61268 | + | 1.42643i | ||||
\(649\) | 4.04145e58 | 0.354322 | ||||||||
\(650\) | − | 3.75936e58i | − | 0.319105i | ||||||
\(651\) | −4.90654e58 | + | 1.05427e58i | −0.403250 | + | 0.0866463i | ||||
\(652\) | −2.33648e59 | −1.85936 | ||||||||
\(653\) | 2.62640e58i | 0.202388i | 0.994867 | + | 0.101194i | \(0.0322663\pi\) | ||||
−0.994867 | + | 0.101194i | \(0.967734\pi\) | |||||||
\(654\) | 5.29135e58 | + | 2.46258e59i | 0.394851 | + | 1.83763i | ||||
\(655\) | 1.67460e59 | 1.21016 | ||||||||
\(656\) | − | 2.13334e59i | − | 1.49307i | ||||||
\(657\) | 7.89052e58 | − | 3.55500e58i | 0.534851 | − | 0.240972i | ||||
\(658\) | 1.66238e59 | 1.09141 | ||||||||
\(659\) | − | 3.75568e58i | − | 0.238833i | −0.992844 | − | 0.119417i | \(-0.961898\pi\) | ||
0.992844 | − | 0.119417i | \(-0.0381024\pi\) | |||||||
\(660\) | −2.95990e59 | + | 6.35993e58i | −1.82328 | + | 0.391769i | ||||
\(661\) | −9.80098e58 | −0.584843 | −0.292421 | − | 0.956290i | \(-0.594461\pi\) | ||||
−0.292421 | + | 0.956290i | \(0.594461\pi\) | |||||||
\(662\) | − | 2.72615e59i | − | 1.57591i | ||||||
\(663\) | 5.72795e58 | + | 2.66578e59i | 0.320786 | + | 1.49293i | ||||
\(664\) | 4.78867e59 | 2.59828 | ||||||||
\(665\) | 1.72068e59i | 0.904579i | ||||||||
\(666\) | −2.12045e59 | − | 4.70645e59i | −1.08011 | − | 2.39737i | ||||
\(667\) | −1.93444e59 | −0.954801 | ||||||||
\(668\) | − | 1.23608e59i | − | 0.591210i | ||||||
\(669\) | −1.07260e59 | + | 2.30470e58i | −0.497153 | + | 0.106823i | ||||
\(670\) | −2.62930e59 | −1.18105 | ||||||||
\(671\) | 2.47996e59i | 1.07962i | ||||||||
\(672\) | −5.16976e58 | − | 2.40600e59i | −0.218130 | − | 1.01517i | ||||
\(673\) | 1.25195e59 | 0.512003 | 0.256001 | − | 0.966676i | \(-0.417595\pi\) | ||||
0.256001 | + | 0.966676i | \(0.417595\pi\) | |||||||
\(674\) | − | 3.63112e59i | − | 1.43941i | ||||||
\(675\) | −3.41607e58 | + | 2.51673e58i | −0.131265 | + | 0.0967069i | ||||
\(676\) | −1.15886e59 | −0.431669 | ||||||||
\(677\) | − | 4.16483e59i | − | 1.50395i | −0.659189 | − | 0.751977i | \(-0.729100\pi\) | ||
0.659189 | − | 0.751977i | \(-0.270900\pi\) | |||||||
\(678\) | −3.58208e59 | + | 7.69681e58i | −1.25404 | + | 0.269456i | ||||
\(679\) | 2.77914e59 | 0.943291 | ||||||||
\(680\) | 9.85178e59i | 3.24211i | ||||||||
\(681\) | 1.03765e59 | + | 4.82921e59i | 0.331103 | + | 1.54094i | ||||
\(682\) | 1.44352e59 | 0.446632 | ||||||||
\(683\) | 2.02654e59i | 0.608025i | 0.952668 | + | 0.304012i | \(0.0983264\pi\) | ||||
−0.952668 | + | 0.304012i | \(0.901674\pi\) | |||||||
\(684\) | −4.46339e59 | + | 2.01094e59i | −1.29863 | + | 0.585088i | ||||
\(685\) | −2.56668e59 | −0.724219 | ||||||||
\(686\) | 2.68934e59i | 0.735933i | ||||||||
\(687\) | 5.71828e59 | − | 1.22869e59i | 1.51766 | − | 0.326099i | ||||
\(688\) | 3.68494e59 | 0.948577 | ||||||||
\(689\) | − | 3.49093e59i | − | 0.871641i | ||||||
\(690\) | −1.64346e59 | − | 7.64862e59i | −0.398041 | − | 1.85247i | ||||
\(691\) | 4.07236e59 | 0.956768 | 0.478384 | − | 0.878151i | \(-0.341223\pi\) | ||||
0.478384 | + | 0.878151i | \(0.341223\pi\) | |||||||
\(692\) | − | 7.82381e57i | − | 0.0178316i | ||||||
\(693\) | −1.89187e59 | − | 4.19910e59i | −0.418304 | − | 0.928449i | ||||
\(694\) | −2.16728e59 | −0.464906 | ||||||||
\(695\) | − | 1.34976e59i | − | 0.280916i | ||||||
\(696\) | 1.01385e60 | − | 2.17846e59i | 2.04729 | − | 0.439902i | ||||
\(697\) | −6.44779e59 | −1.26335 | ||||||||
\(698\) | 1.07665e60i | 2.04696i | ||||||||
\(699\) | −7.80914e58 | − | 3.63436e59i | −0.144073 | − | 0.670513i | ||||
\(700\) | 2.60267e59 | 0.465973 | ||||||||
\(701\) | − | 6.37311e59i | − | 1.10732i | −0.832743 | − | 0.553660i | \(-0.813231\pi\) | ||
0.832743 | − | 0.553660i | \(-0.186769\pi\) | |||||||
\(702\) | 6.88450e59 | + | 9.34464e59i | 1.16089 | + | 1.57574i | ||||
\(703\) | 5.80431e59 | 0.949924 | ||||||||
\(704\) | − | 1.07622e59i | − | 0.170952i | ||||||
\(705\) | −3.21462e59 | + | 6.90725e58i | −0.495631 | + | 0.106496i | ||||
\(706\) | 2.66429e59 | 0.398733 | ||||||||
\(707\) | 4.97054e59i | 0.722098i | ||||||||
\(708\) | −1.48130e59 | − | 6.89396e59i | −0.208903 | − | 0.972232i | ||||
\(709\) | 9.41879e59 | 1.28951 | 0.644754 | − | 0.764390i | \(-0.276960\pi\) | ||||
0.644754 | + | 0.764390i | \(0.276960\pi\) | |||||||
\(710\) | − | 1.45924e60i | − | 1.93955i | ||||||
\(711\) | −1.56262e58 | + | 7.04024e57i | −0.0201647 | + | 0.00908502i | ||||
\(712\) | −2.07775e60 | −2.60323 | ||||||||
\(713\) | 2.56558e59i | 0.312108i | ||||||||
\(714\) | −2.68331e60 | + | 5.76563e59i | −3.16963 | + | 0.681058i | ||||
\(715\) | −8.07091e59 | −0.925754 | ||||||||
\(716\) | 5.91836e58i | 0.0659217i | ||||||||
\(717\) | 3.40266e59 | + | 1.58359e60i | 0.368058 | + | 1.71293i | ||||
\(718\) | 6.36829e59 | 0.668975 | ||||||||
\(719\) | − | 3.75591e59i | − | 0.383185i | −0.981475 | − | 0.191592i | \(-0.938635\pi\) | ||
0.981475 | − | 0.191592i | \(-0.0613652\pi\) | |||||||
\(720\) | 7.37776e59 | + | 1.63754e60i | 0.731042 | + | 1.62259i | ||||
\(721\) | −4.23503e59 | −0.407583 | ||||||||
\(722\) | 1.11420e60i | 1.04155i | ||||||||
\(723\) | 1.96655e60 | − | 4.22552e59i | 1.78566 | − | 0.383686i | ||||
\(724\) | −1.02488e60 | −0.903993 | ||||||||
\(725\) | 1.85069e59i | 0.158575i | ||||||||
\(726\) | −1.73375e59 | − | 8.06884e59i | −0.144317 | − | 0.671649i | ||||
\(727\) | −2.28875e60 | −1.85087 | −0.925435 | − | 0.378905i | \(-0.876301\pi\) | ||||
−0.925435 | + | 0.378905i | \(0.876301\pi\) | |||||||
\(728\) | − | 3.88782e60i | − | 3.05455i | ||||||
\(729\) | 3.88246e59 | − | 1.25117e60i | 0.296366 | − | 0.955074i | ||||
\(730\) | 1.52658e60 | 1.13224 | ||||||||
\(731\) | − | 1.11373e60i | − | 0.802632i | ||||||
\(732\) | 4.23035e60 | − | 9.08975e59i | 2.96240 | − | 0.636531i | ||||
\(733\) | −4.64225e58 | −0.0315897 | −0.0157948 | − | 0.999875i | \(-0.505028\pi\) | ||||
−0.0157948 | + | 0.999875i | \(0.505028\pi\) | |||||||
\(734\) | 2.86310e60i | 1.89330i | ||||||||
\(735\) | 2.40795e59 | + | 1.12066e60i | 0.154744 | + | 0.720176i | ||||
\(736\) | −1.25807e60 | −0.785726 | ||||||||
\(737\) | 7.91320e59i | 0.480325i | ||||||||
\(738\) | −2.50247e60 | + | 1.12747e60i | −1.47634 | + | 0.665151i | ||||
\(739\) | −7.61542e59 | −0.436677 | −0.218339 | − | 0.975873i | \(-0.570064\pi\) | ||||
−0.218339 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(740\) | − | 6.26275e60i | − | 3.49059i | ||||||
\(741\) | −1.27597e60 | + | 2.74167e59i | −0.691285 | + | 0.148536i | ||||
\(742\) | 3.51389e60 | 1.85058 | ||||||||
\(743\) | 3.20623e60i | 1.64146i | 0.571319 | + | 0.820728i | \(0.306432\pi\) | ||||
−0.571319 | + | 0.820728i | \(0.693568\pi\) | |||||||
\(744\) | −2.88922e59 | − | 1.34464e60i | −0.143797 | − | 0.669226i | ||||
\(745\) | −3.66946e60 | −1.77550 | ||||||||
\(746\) | 7.37805e60i | 3.47077i | ||||||||
\(747\) | −1.08387e60 | − | 2.40571e60i | −0.495729 | − | 1.10030i | ||||
\(748\) | 5.42970e60 | 2.41458 | ||||||||
\(749\) | 4.36787e60i | 1.88865i | ||||||||
\(750\) | 3.75635e60 | − | 8.07126e59i | 1.57935 | − | 0.339355i | ||||
\(751\) | 3.65531e60 | 1.49447 | 0.747233 | − | 0.664563i | \(-0.231382\pi\) | ||||
0.747233 | + | 0.664563i | \(0.231382\pi\) | |||||||
\(752\) | 1.95109e60i | 0.775715i | ||||||||
\(753\) | −9.13769e59 | − | 4.25266e60i | −0.353299 | − | 1.64424i | ||||
\(754\) | 5.06254e60 | 1.90358 | ||||||||
\(755\) | − | 4.07611e58i | − | 0.0149060i | ||||||
\(756\) | −6.46946e60 | + | 4.76626e60i | −2.30097 | + | 1.69520i | ||||
\(757\) | −4.13891e59 | −0.143177 | −0.0715884 | − | 0.997434i | \(-0.522807\pi\) | ||||
−0.0715884 | + | 0.997434i | \(0.522807\pi\) | |||||||
\(758\) | − | 5.40061e60i | − | 1.81715i | ||||||
\(759\) | −2.30195e60 | + | 4.94619e59i | −0.753387 | + | 0.161880i | ||||
\(760\) | −4.71553e60 | −1.50122 | ||||||||
\(761\) | − | 3.07895e60i | − | 0.953508i | −0.879037 | − | 0.476754i | \(-0.841813\pi\) | ||
0.879037 | − | 0.476754i | \(-0.158187\pi\) | |||||||
\(762\) | −1.37357e59 | − | 6.39258e59i | −0.0413806 | − | 0.192585i | ||||
\(763\) | −4.64881e60 | −1.36247 | ||||||||
\(764\) | − | 6.49181e59i | − | 0.185100i | ||||||
\(765\) | 4.94928e60 | − | 2.22985e60i | 1.37294 | − | 0.618566i | ||||
\(766\) | −7.07322e60 | −1.90903 | ||||||||
\(767\) | − | 1.87981e60i | − | 0.493642i | ||||||
\(768\) | −7.31681e60 | + | 1.57216e60i | −1.86955 | + | 0.401709i | ||||
\(769\) | 6.16064e60 | 1.53170 | 0.765848 | − | 0.643021i | \(-0.222319\pi\) | ||||
0.765848 | + | 0.643021i | \(0.222319\pi\) | |||||||
\(770\) | − | 8.12400e60i | − | 1.96546i | ||||||
\(771\) | 1.12497e60 | + | 5.23561e60i | 0.264850 | + | 1.23261i | ||||
\(772\) | 2.27330e60 | 0.520826 | ||||||||
\(773\) | − | 3.23420e60i | − | 0.721104i | −0.932739 | − | 0.360552i | \(-0.882588\pi\) | ||
0.932739 | − | 0.360552i | \(-0.117412\pi\) | |||||||
\(774\) | −1.94749e60 | − | 4.32255e60i | −0.422585 | − | 0.937950i | ||||
\(775\) | 2.45450e59 | 0.0518356 | ||||||||
\(776\) | 7.61624e60i | 1.56547i | ||||||||
\(777\) | 9.31479e60 | − | 2.00147e60i | 1.86351 | − | 0.400412i | ||||
\(778\) | 2.80316e60 | 0.545853 | ||||||||
\(779\) | − | 3.08622e60i | − | 0.584979i | ||||||
\(780\) | 2.95821e60 | + | 1.37675e61i | 0.545812 | + | 2.54020i | ||||
\(781\) | −4.39177e60 | −0.788801 | ||||||||
\(782\) | 1.40308e61i | 2.45324i | ||||||||
\(783\) | −3.38915e60 | − | 4.60025e60i | −0.576892 | − | 0.783042i | ||||
\(784\) | 6.80174e60 | 1.12715 | ||||||||
\(785\) | 1.05619e61i | 1.70404i | ||||||||
\(786\) | −1.24996e61 | + | 2.68579e60i | −1.96346 | + | 0.421889i | ||||
\(787\) | −6.93462e60 | −1.06060 | −0.530302 | − | 0.847809i | \(-0.677922\pi\) | ||||
−0.530302 | + | 0.847809i | \(0.677922\pi\) | |||||||
\(788\) | − | 2.03015e61i | − | 3.02328i | ||||||
\(789\) | 1.13737e60 | + | 5.29328e60i | 0.164924 | + | 0.767553i | ||||
\(790\) | −3.02320e59 | −0.0426873 | ||||||||
\(791\) | − | 6.76218e60i | − | 0.929781i | ||||||
\(792\) | 1.15076e61 | − | 5.18465e60i | 1.54084 | − | 0.694210i | ||||
\(793\) | 1.15351e61 | 1.50413 | ||||||||
\(794\) | 1.29246e60i | 0.164130i | ||||||||
\(795\) | −6.79498e60 | + | 1.46004e60i | −0.840385 | + | 0.180574i | ||||
\(796\) | 5.85968e60 | 0.705829 | ||||||||
\(797\) | 3.79547e60i | 0.445288i | 0.974900 | + | 0.222644i | \(0.0714688\pi\) | ||||
−0.974900 | + | 0.222644i | \(0.928531\pi\) | |||||||
\(798\) | −2.75971e60 | − | 1.28436e61i | −0.315357 | − | 1.46766i | ||||
\(799\) | 5.89696e60 | 0.656366 | ||||||||
\(800\) | 1.20360e60i | 0.130495i | ||||||||
\(801\) | 4.70277e60 | + | 1.04381e61i | 0.496674 | + | 1.10239i | ||||
\(802\) | −1.17485e61 | −1.20870 | ||||||||
\(803\) | − | 4.59443e60i | − | 0.460475i | ||||||
\(804\) | 1.34984e61 | − | 2.90041e60i | 1.31797 | − | 0.283193i | ||||
\(805\) | 1.44389e61 | 1.37348 | ||||||||
\(806\) | − | 6.71427e60i | − | 0.622248i | ||||||
\(807\) | 9.66296e59 | + | 4.49712e60i | 0.0872501 | + | 0.406060i | ||||
\(808\) | −1.36218e61 | −1.19838 | ||||||||
\(809\) | − | 1.00290e61i | − | 0.859683i | −0.902904 | − | 0.429842i | \(-0.858569\pi\) | ||
0.902904 | − | 0.429842i | \(-0.141431\pi\) | |||||||
\(810\) | 1.53097e61 | − | 1.73087e61i | 1.27874 | − | 1.44570i | ||||
\(811\) | −2.23570e61 | −1.81960 | −0.909800 | − | 0.415047i | \(-0.863765\pi\) | ||||
−0.909800 | + | 0.415047i | \(0.863765\pi\) | |||||||
\(812\) | 3.50489e61i | 2.77970i | ||||||||
\(813\) | −4.61037e60 | + | 9.90629e59i | −0.356315 | + | 0.0765613i | ||||
\(814\) | −2.74044e61 | −2.06399 | ||||||||
\(815\) | 1.24010e61i | 0.910219i | ||||||||
\(816\) | −6.76696e60 | − | 3.14933e61i | −0.484061 | − | 2.25281i | ||||
\(817\) | 5.33086e60 | 0.371650 | ||||||||
\(818\) | 2.84167e61i | 1.93087i | ||||||||
\(819\) | −1.95314e61 | + | 8.79970e60i | −1.29352 | + | 0.582782i | ||||
\(820\) | −3.32998e61 | −2.14956 | ||||||||
\(821\) | 1.21036e61i | 0.761566i | 0.924664 | + | 0.380783i | \(0.124345\pi\) | ||||
−0.924664 | + | 0.380783i | \(0.875655\pi\) | |||||||
\(822\) | 1.91584e61 | − | 4.11655e60i | 1.17503 | − | 0.252479i | ||||
\(823\) | 4.76830e60 | 0.285080 | 0.142540 | − | 0.989789i | \(-0.454473\pi\) | ||||
0.142540 | + | 0.989789i | \(0.454473\pi\) | |||||||
\(824\) | − | 1.16061e61i | − | 0.676417i | ||||||
\(825\) | 4.73204e59 | + | 2.20228e60i | 0.0268854 | + | 0.125124i | ||||
\(826\) | 1.89218e61 | 1.04805 | ||||||||
\(827\) | − | 2.41842e61i | − | 1.30592i | −0.757394 | − | 0.652958i | \(-0.773528\pi\) | ||
0.757394 | − | 0.652958i | \(-0.226472\pi\) | |||||||
\(828\) | 1.68746e61 | + | 3.74540e61i | 0.888373 | + | 1.97179i | ||||
\(829\) | 1.24242e61 | 0.637710 | 0.318855 | − | 0.947803i | \(-0.396702\pi\) | ||||
0.318855 | + | 0.947803i | \(0.396702\pi\) | |||||||
\(830\) | − | 4.65432e61i | − | 2.32925i | ||||||
\(831\) | 1.85070e61 | − | 3.97660e60i | 0.903056 | − | 0.194039i | ||||
\(832\) | −5.00586e60 | −0.238171 | ||||||||
\(833\) | − | 2.05576e61i | − | 0.953733i | ||||||
\(834\) | 2.16481e60 | + | 1.00750e61i | 0.0979337 | + | 0.455781i | ||||
\(835\) | −6.56056e60 | −0.289417 | ||||||||
\(836\) | 2.59891e61i | 1.11805i | ||||||||
\(837\) | −6.10116e60 | + | 4.49492e60i | −0.255963 | + | 0.188576i | ||||
\(838\) | 2.22407e61 | 0.909964 | ||||||||
\(839\) | 8.63752e60i | 0.344658i | 0.985039 | + | 0.172329i | \(0.0551291\pi\) | ||||
−0.985039 | + | 0.172329i | \(0.944871\pi\) | |||||||
\(840\) | −7.56751e61 | + | 1.62603e61i | −2.94502 | + | 0.632796i | ||||
\(841\) | 1.42378e60 | 0.0540415 | ||||||||
\(842\) | − | 6.40995e61i | − | 2.37302i | ||||||
\(843\) | −6.02091e60 | − | 2.80212e61i | −0.217412 | − | 1.01183i | ||||
\(844\) | 1.08788e62 | 3.83169 | ||||||||
\(845\) | 6.15070e60i | 0.211317i | ||||||||
\(846\) | 2.28869e61 | − | 1.03115e61i | 0.767025 | − | 0.345576i | ||||
\(847\) | 1.52322e61 | 0.497979 | ||||||||
\(848\) | 4.12416e61i | 1.31529i | ||||||||
\(849\) | −4.04793e61 | + | 8.69778e60i | −1.25942 | + | 0.270612i | ||||
\(850\) | 1.34233e61 | 0.407439 | ||||||||
\(851\) | − | 4.87061e61i | − | 1.44232i | ||||||
\(852\) | 1.60971e61 | + | 7.49154e61i | 0.465066 | + | 2.16441i | ||||
\(853\) | 1.30531e61 | 0.367946 | 0.183973 | − | 0.982931i | \(-0.441104\pi\) | ||||
0.183973 | + | 0.982931i | \(0.441104\pi\) | |||||||
\(854\) | 1.16110e62i | 3.19341i | ||||||||
\(855\) | 1.06731e61 | + | 2.36896e61i | 0.286420 | + | 0.635726i | ||||
\(856\) | −1.19701e62 | −3.13437 | ||||||||
\(857\) | − | 2.13574e61i | − | 0.545695i | −0.962057 | − | 0.272848i | \(-0.912034\pi\) | ||
0.962057 | − | 0.272848i | \(-0.0879655\pi\) | |||||||
\(858\) | 6.02433e61 | − | 1.29445e61i | 1.50202 | − | 0.322739i | ||||
\(859\) | −7.92701e61 | −1.92865 | −0.964324 | − | 0.264724i | \(-0.914719\pi\) | ||||
−0.964324 | + | 0.264724i | \(0.914719\pi\) | |||||||
\(860\) | − | 5.75191e61i | − | 1.36567i | ||||||
\(861\) | −1.06420e61 | − | 4.95279e61i | −0.246581 | − | 1.14758i | ||||
\(862\) | 2.45933e61 | 0.556115 | ||||||||
\(863\) | 6.53731e61i | 1.44269i | 0.692577 | + | 0.721344i | \(0.256475\pi\) | ||||
−0.692577 | + | 0.721344i | \(0.743525\pi\) | |||||||
\(864\) | −2.20415e61 | − | 2.99180e61i | −0.474737 | − | 0.644382i | ||||
\(865\) | −4.15252e59 | −0.00872917 | ||||||||
\(866\) | − | 1.57073e61i | − | 0.322275i | ||||||
\(867\) | −4.63650e61 | + | 9.96243e60i | −0.928515 | + | 0.199510i | ||||
\(868\) | 4.64841e61 | 0.908636 | ||||||||
\(869\) | 9.09871e59i | 0.0173606i | ||||||||
\(870\) | −2.11734e61 | − | 9.85407e61i | −0.394355 | − | 1.83532i | ||||
\(871\) | 3.68069e61 | 0.669189 | ||||||||
\(872\) | − | 1.27401e62i | − | 2.26113i | ||||||
\(873\) | 3.82620e61 | − | 1.72386e61i | 0.662932 | − | 0.298678i | ||||
\(874\) | −6.71580e61 | −1.13595 | ||||||||
\(875\) | 7.09115e61i | 1.17098i | ||||||||
\(876\) | −7.83725e61 | + | 1.68399e61i | −1.26351 | + | 0.271489i | ||||
\(877\) | 5.89907e61 | 0.928522 | 0.464261 | − | 0.885698i | \(-0.346320\pi\) | ||||
0.464261 | + | 0.885698i | \(0.346320\pi\) | |||||||
\(878\) | 1.80481e62i | 2.77362i | ||||||||
\(879\) | −6.52036e60 | − | 3.03456e61i | −0.0978375 | − | 0.455334i | ||||
\(880\) | 9.53492e61 | 1.39695 | ||||||||
\(881\) | 3.46249e61i | 0.495330i | 0.968846 | + | 0.247665i | \(0.0796633\pi\) | ||||
−0.968846 | + | 0.247665i | \(0.920337\pi\) | |||||||
\(882\) | −3.59472e61 | − | 7.97867e61i | −0.502139 | − | 1.11453i | ||||
\(883\) | 2.64433e59 | 0.00360696 | 0.00180348 | − | 0.999998i | \(-0.499426\pi\) | ||||
0.00180348 | + | 0.999998i | \(0.499426\pi\) | |||||||
\(884\) | − | 2.52553e62i | − | 3.36400i | ||||||
\(885\) | −3.65899e61 | + | 7.86207e60i | −0.475941 | + | 0.102265i | ||||
\(886\) | −1.07018e62 | −1.35941 | ||||||||
\(887\) | 3.59415e61i | 0.445862i | 0.974834 | + | 0.222931i | \(0.0715625\pi\) | ||||
−0.974834 | + | 0.222931i | \(0.928437\pi\) | |||||||
\(888\) | 5.48502e61 | + | 2.55272e62i | 0.664517 | + | 3.09265i | ||||
\(889\) | 1.20678e61 | 0.142787 | ||||||||
\(890\) | 2.01945e62i | 2.33369i | ||||||||
\(891\) | −5.20927e61 | − | 4.60764e61i | −0.587957 | − | 0.520052i | ||||
\(892\) | 1.01617e62 | 1.12023 | ||||||||
\(893\) | 2.82257e61i | 0.303923i | ||||||||
\(894\) | 2.73898e62 | − | 5.88524e61i | 2.88072 | − | 0.618980i | ||||
\(895\) | 3.14119e60 | 0.0322709 | ||||||||
\(896\) | − | 1.53857e62i | − | 1.54400i | ||||||
\(897\) | 2.30064e61 | + | 1.07071e62i | 0.225531 | + | 1.04962i | ||||
\(898\) | −3.13112e62 | −2.99845 | ||||||||
\(899\) | 3.30536e61i | 0.309218i | ||||||||
\(900\) | 3.58324e61 | − | 1.61440e61i | 0.327479 | − | 0.147543i | ||||
\(901\) | 1.24649e62 | 1.11293 | ||||||||
\(902\) | 1.45712e62i | 1.27104i | ||||||||
\(903\) | 8.55500e61 | − | 1.83821e61i | 0.729083 | − | 0.156658i | ||||
\(904\) | 1.85317e62 | 1.54305 | ||||||||
\(905\) | 5.43961e61i | 0.442535i | ||||||||
\(906\) | 6.53744e59 | + | 3.04251e60i | 0.00519656 | + | 0.0241847i | ||||
\(907\) | 1.24353e62 | 0.965834 | 0.482917 | − | 0.875666i | \(-0.339577\pi\) | ||||
0.482917 | + | 0.875666i | \(0.339577\pi\) | |||||||
\(908\) | − | 4.57515e62i | − | 3.47218i | ||||||
\(909\) | 3.08315e61 | + | 6.84322e61i | 0.228641 | + | 0.507480i | ||||
\(910\) | −3.77875e62 | −2.73828 | ||||||||
\(911\) | − | 1.51904e62i | − | 1.07568i | −0.843047 | − | 0.537840i | \(-0.819241\pi\) | ||
0.843047 | − | 0.537840i | \(-0.180759\pi\) | |||||||
\(912\) | 1.50742e62 | − | 3.23899e61i | 1.04314 | − | 0.224139i | ||||
\(913\) | −1.40078e62 | −0.947289 | ||||||||
\(914\) | − | 9.93581e61i | − | 0.656649i | ||||||
\(915\) | −4.82442e61 | − | 2.24527e62i | −0.311603 | − | 1.45019i | ||||
\(916\) | −5.41745e62 | −3.41971 | ||||||||
\(917\) | − | 2.35965e62i | − | 1.45576i | ||||||
\(918\) | −3.33663e62 | + | 2.45820e62i | −2.01193 | + | 1.48225i | ||||
\(919\) | 8.87370e61 | 0.522972 | 0.261486 | − | 0.965207i | \(-0.415787\pi\) | ||||
0.261486 | + | 0.965207i | \(0.415787\pi\) | |||||||
\(920\) | 3.95698e62i | 2.27939i | ||||||||
\(921\) | 8.73049e61 | − | 1.87592e61i | 0.491571 | − | 0.105624i | ||||
\(922\) | 5.60426e62 | 3.08439 | ||||||||
\(923\) | 2.04276e62i | 1.09896i | ||||||||
\(924\) | 8.96168e61 | + | 4.17075e62i | 0.471279 | + | 2.19332i | ||||
\(925\) | −4.65974e61 | −0.239544 | ||||||||
\(926\) | − | 1.56614e62i | − | 0.787047i | ||||||
\(927\) | −5.83060e61 | + | 2.62693e61i | −0.286444 | + | 0.129055i | ||||
\(928\) | −1.62083e62 | −0.778450 | ||||||||
\(929\) | 1.48660e62i | 0.698012i | 0.937120 | + | 0.349006i | \(0.113481\pi\) | ||||
−0.937120 | + | 0.349006i | \(0.886519\pi\) | |||||||
\(930\) | −1.30691e62 | + | 2.80816e61i | −0.599935 | + | 0.128908i | ||||
\(931\) | 9.83983e61 | 0.441616 | ||||||||
\(932\) | 3.44316e62i | 1.51086i | ||||||||
\(933\) | −6.60494e61 | − | 3.07393e62i | −0.283370 | − | 1.31880i | ||||
\(934\) | 3.99611e62 | 1.67631 | ||||||||
\(935\) | − | 2.88183e62i | − | 1.18202i | ||||||
\(936\) | −2.41156e62 | − | 5.35258e62i | −0.967174 | − | 2.14670i | ||||
\(937\) | −1.79061e62 | −0.702214 | −0.351107 | − | 0.936335i | \(-0.614195\pi\) | ||||
−0.351107 | + | 0.936335i | \(0.614195\pi\) | |||||||
\(938\) | 3.70491e62i | 1.42075i | ||||||||
\(939\) | 5.39204e61 | − | 1.15859e61i | 0.202197 | − | 0.0434461i | ||||
\(940\) | 3.04550e62 | 1.11680 | ||||||||
\(941\) | 1.27200e62i | 0.456148i | 0.973644 | + | 0.228074i | \(0.0732429\pi\) | ||||
−0.973644 | + | 0.228074i | \(0.926757\pi\) | |||||||
\(942\) | −1.69396e62 | − | 7.88366e62i | −0.594065 | − | 2.76477i | ||||
\(943\) | −2.58976e62 | −0.888208 | ||||||||
\(944\) | 2.22080e62i | 0.744898i | ||||||||
\(945\) | 2.52971e62 | + | 3.43369e62i | 0.829855 | + | 1.12640i | ||||
\(946\) | −2.51690e62 | −0.807519 | ||||||||
\(947\) | − | 9.15420e61i | − | 0.287257i | −0.989632 | − | 0.143628i | \(-0.954123\pi\) | ||
0.989632 | − | 0.143628i | \(-0.0458770\pi\) | |||||||
\(948\) | 1.55207e61 | − | 3.33493e60i | 0.0476361 | − | 0.0102356i | ||||
\(949\) | −2.13702e62 | −0.641533 | ||||||||
\(950\) | 6.42504e61i | 0.188660i | ||||||||
\(951\) | 1.13376e62 | + | 5.27651e62i | 0.325635 | + | 1.51550i | ||||
\(952\) | 1.38820e63 | 3.90010 | ||||||||
\(953\) | − | 1.84564e62i | − | 0.507220i | −0.967307 | − | 0.253610i | \(-0.918382\pi\) | ||
0.967307 | − | 0.253610i | \(-0.0816180\pi\) | |||||||
\(954\) | 4.83778e62 | − | 2.17962e62i | 1.30056 | − | 0.585955i | ||||
\(955\) | −3.44555e61 | −0.0906125 | ||||||||
\(956\) | − | 1.50028e63i | − | 3.85973i | ||||||
\(957\) | −2.96571e62 | + | 6.37241e61i | −0.746410 | + | 0.160381i | ||||
\(958\) | 9.79370e62 | 2.41141 | ||||||||
\(959\) | 3.61668e62i | 0.871202i | ||||||||
\(960\) | 2.09364e61 | + | 9.74374e61i | 0.0493407 | + | 0.229631i | ||||
\(961\) | −3.89864e62 | −0.898922 | ||||||||
\(962\) | 1.27467e63i | 2.87555i | ||||||||
\(963\) | 2.70932e62 | + | 6.01349e62i | 0.598010 | + | 1.32732i | ||||
\(964\) | −1.86309e63 | −4.02361 | ||||||||
\(965\) | − | 1.20656e62i | − | 0.254962i | ||||||
\(966\) | −1.07776e63 | + | 2.31577e62i | −2.22844 | + | 0.478825i | ||||
\(967\) | 1.81165e62 | 0.366538 | 0.183269 | − | 0.983063i | \(-0.441332\pi\) | ||||
0.183269 | + | 0.983063i | \(0.441332\pi\) | |||||||
\(968\) | 4.17438e62i | 0.826437i | ||||||||
\(969\) | −9.78952e61 | − | 4.55602e62i | −0.189654 | − | 0.882646i | ||||
\(970\) | 7.40256e62 | 1.40338 | ||||||||
\(971\) | − | 3.31204e62i | − | 0.614457i | −0.951636 | − | 0.307228i | \(-0.900598\pi\) | ||
0.951636 | − | 0.307228i | \(-0.0994016\pi\) | |||||||
\(972\) | −5.95043e62 | + | 1.05749e63i | −1.08033 | + | 1.91992i | ||||
\(973\) | −1.90193e62 | −0.337929 | ||||||||
\(974\) | − | 8.62955e62i | − | 1.50055i | ||||||
\(975\) | 1.02436e62 | − | 2.20103e61i | 0.174323 | − | 0.0374567i | ||||
\(976\) | −1.36275e63 | −2.26971 | ||||||||
\(977\) | − | 5.30049e62i | − | 0.864033i | −0.901866 | − | 0.432016i | \(-0.857802\pi\) | ||
0.901866 | − | 0.432016i | \(-0.142198\pi\) | |||||||
\(978\) | −1.98892e62 | − | 9.25640e62i | −0.317323 | − | 1.47681i | ||||
\(979\) | 6.07780e62 | 0.949095 | ||||||||
\(980\) | − | 1.06170e63i | − | 1.62276i | ||||||
\(981\) | −6.40028e62 | + | 2.88359e62i | −0.957524 | + | 0.431404i | ||||
\(982\) | 2.07336e63 | 3.03622 | ||||||||
\(983\) | − | 1.81769e62i | − | 0.260552i | −0.991478 | − | 0.130276i | \(-0.958414\pi\) | ||
0.991478 | − | 0.130276i | \(-0.0415864\pi\) | |||||||
\(984\) | 1.35731e63 | − | 2.91645e62i | 1.90450 | − | 0.409221i | ||||
\(985\) | −1.07751e63 | −1.48000 | ||||||||
\(986\) | 1.80765e63i | 2.43052i | ||||||||
\(987\) | 9.73291e61 | + | 4.52967e62i | 0.128110 | + | 0.596220i | ||||
\(988\) | 1.20884e63 | 1.55766 | ||||||||
\(989\) | − | 4.47333e62i | − | 0.564298i | ||||||
\(990\) | −5.03920e62 | − | 1.11848e63i | −0.622332 | − | 1.38130i | ||||
\(991\) | −3.13176e62 | −0.378653 | −0.189326 | − | 0.981914i | \(-0.560630\pi\) | ||||
−0.189326 | + | 0.981914i | \(0.560630\pi\) | |||||||
\(992\) | 2.14965e62i | 0.254462i | ||||||||
\(993\) | 7.42826e62 | − | 1.59611e62i | 0.860901 | − | 0.184982i | ||||
\(994\) | −2.05620e63 | −2.33319 | ||||||||
\(995\) | − | 3.11005e62i | − | 0.345527i | ||||||
\(996\) | 5.13424e62 | + | 2.38946e63i | 0.558509 | + | 2.59929i | ||||
\(997\) | −3.77697e62 | −0.402295 | −0.201148 | − | 0.979561i | \(-0.564467\pi\) | ||||
−0.201148 | + | 0.979561i | \(0.564467\pi\) | |||||||
\(998\) | − | 2.45365e63i | − | 2.55901i | ||||||
\(999\) | 1.15827e63 | − | 8.53335e62i | 1.18286 | − | 0.871454i |
(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 | 3.43.b.b.2.1 | ✓ | 12 | |
3.2 | odd | 2 | inner | 3.43.b.b.2.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.43.b.b.2.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
3.43.b.b.2.12 | yes | 12 | 3.2 | odd | 2 | inner |