Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,33,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, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
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: | \(25.9466620569\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 72511313626452 x^{12} + \cdots + 62\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{182}\cdot 3^{20}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(-2.77300e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.33.b.b.3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −61401.1 | + | 22910.1i | −0.936907 | + | 0.349580i | ||||
\(3\) | − | 4.43679e7i | − | 1.03069i | −0.856982 | − | 0.515346i | \(-0.827663\pi\) | ||
0.856982 | − | 0.515346i | \(-0.172337\pi\) | |||||||
\(4\) | 3.24522e9 | − | 2.81341e9i | 0.755588 | − | 0.655048i | ||||
\(5\) | 1.39224e11 | 0.912416 | 0.456208 | − | 0.889873i | \(-0.349207\pi\) | ||||
0.456208 | + | 0.889873i | \(0.349207\pi\) | |||||||
\(6\) | 1.01647e12 | + | 2.72424e12i | 0.360310 | + | 0.965663i | ||||
\(7\) | 2.23454e13i | 0.672388i | 0.941793 | + | 0.336194i | \(0.109140\pi\) | ||||
−0.941793 | + | 0.336194i | \(0.890860\pi\) | |||||||
\(8\) | −1.34805e14 | + | 2.47095e14i | −0.478923 | + | 0.877857i | ||||
\(9\) | −1.15494e14 | −0.0623277 | ||||||||
\(10\) | −8.54848e15 | + | 3.18962e15i | −0.854848 | + | 0.318962i | ||||
\(11\) | 1.78893e16i | 0.389323i | 0.980870 | + | 0.194661i | \(0.0623608\pi\) | ||||
−0.980870 | + | 0.194661i | \(0.937639\pi\) | |||||||
\(12\) | −1.24825e17 | − | 1.43984e17i | −0.675153 | − | 0.778779i | ||||
\(13\) | 2.16497e17 | 0.325355 | 0.162677 | − | 0.986679i | \(-0.447987\pi\) | ||||
0.162677 | + | 0.986679i | \(0.447987\pi\) | |||||||
\(14\) | −5.11935e17 | − | 1.37203e18i | −0.235053 | − | 0.629965i | ||||
\(15\) | − | 6.17706e18i | − | 0.940420i | ||||||
\(16\) | 2.61621e18 | − | 1.82603e19i | 0.141825 | − | 0.989892i | ||||
\(17\) | −6.14938e19 | −1.26371 | −0.631857 | − | 0.775085i | \(-0.717707\pi\) | ||||
−0.631857 | + | 0.775085i | \(0.717707\pi\) | |||||||
\(18\) | 7.09149e18 | − | 2.64599e18i | 0.0583952 | − | 0.0217885i | ||||
\(19\) | 4.44940e20i | 1.54257i | 0.636492 | + | 0.771283i | \(0.280385\pi\) | ||||
−0.636492 | + | 0.771283i | \(0.719615\pi\) | |||||||
\(20\) | 4.51812e20 | − | 3.91693e20i | 0.689410 | − | 0.597676i | ||||
\(21\) | 9.91420e20 | 0.693025 | ||||||||
\(22\) | −4.09845e20 | − | 1.09842e21i | −0.136100 | − | 0.364759i | ||||
\(23\) | 8.74399e21i | 1.42582i | 0.701256 | + | 0.712909i | \(0.252623\pi\) | ||||
−0.701256 | + | 0.712909i | \(0.747377\pi\) | |||||||
\(24\) | 1.09631e22 | + | 5.98102e21i | 0.904801 | + | 0.493623i | ||||
\(25\) | −3.89986e21 | −0.167498 | ||||||||
\(26\) | −1.32931e22 | + | 4.95995e21i | −0.304827 | + | 0.113738i | ||||
\(27\) | − | 7.70904e22i | − | 0.966452i | ||||||
\(28\) | 6.28668e22 | + | 7.25159e22i | 0.440446 | + | 0.508048i | ||||
\(29\) | 4.53622e23 | 1.81270 | 0.906351 | − | 0.422526i | \(-0.138856\pi\) | ||||
0.906351 | + | 0.422526i | \(0.138856\pi\) | |||||||
\(30\) | 1.41517e23 | + | 3.79279e23i | 0.328752 | + | 0.881086i | ||||
\(31\) | 1.07502e24i | 1.47785i | 0.673789 | + | 0.738924i | \(0.264666\pi\) | ||||
−0.673789 | + | 0.738924i | \(0.735334\pi\) | |||||||
\(32\) | 2.57706e23 | + | 1.18114e24i | 0.213169 | + | 0.977015i | ||||
\(33\) | 7.93711e23 | 0.401272 | ||||||||
\(34\) | 3.77579e24 | − | 1.40883e24i | 1.18398 | − | 0.441769i | ||||
\(35\) | 3.11101e24i | 0.613497i | ||||||||
\(36\) | −3.74805e23 | + | 3.24933e23i | −0.0470940 | + | 0.0408276i | ||||
\(37\) | −9.58490e23 | −0.0776891 | −0.0388445 | − | 0.999245i | \(-0.512368\pi\) | ||||
−0.0388445 | + | 0.999245i | \(0.512368\pi\) | |||||||
\(38\) | −1.01936e25 | − | 2.73198e25i | −0.539251 | − | 1.44524i | ||||
\(39\) | − | 9.60551e24i | − | 0.335341i | ||||||
\(40\) | −1.87680e25 | + | 3.44014e25i | −0.436977 | + | 0.800970i | ||||
\(41\) | −1.42325e25 | −0.223223 | −0.111612 | − | 0.993752i | \(-0.535601\pi\) | ||||
−0.111612 | + | 0.993752i | \(0.535601\pi\) | |||||||
\(42\) | −6.08743e25 | + | 2.27135e25i | −0.649300 | + | 0.242268i | ||||
\(43\) | − | 1.36563e26i | − | 0.999625i | −0.866134 | − | 0.499813i | \(-0.833402\pi\) | ||
0.866134 | − | 0.499813i | \(-0.166598\pi\) | |||||||
\(44\) | 5.03298e25 | + | 5.80547e25i | 0.255025 | + | 0.294168i | ||||
\(45\) | −1.60796e25 | −0.0568688 | ||||||||
\(46\) | −2.00325e26 | − | 5.36891e26i | −0.498438 | − | 1.33586i | ||||
\(47\) | 1.63099e26i | 0.287663i | 0.989602 | + | 0.143832i | \(0.0459424\pi\) | ||||
−0.989602 | + | 0.143832i | \(0.954058\pi\) | |||||||
\(48\) | −8.10171e26 | − | 1.16076e26i | −1.02027 | − | 0.146178i | ||||
\(49\) | 6.05110e26 | 0.547895 | ||||||||
\(50\) | 2.39456e26 | − | 8.93461e25i | 0.156930 | − | 0.0585539i | ||||
\(51\) | 2.72836e27i | 1.30250i | ||||||||
\(52\) | 7.02580e26 | − | 6.09093e26i | 0.245834 | − | 0.213123i | ||||
\(53\) | 6.59943e27 | 1.70252 | 0.851261 | − | 0.524743i | \(-0.175838\pi\) | ||||
0.851261 | + | 0.524743i | \(0.175838\pi\) | |||||||
\(54\) | 1.76615e27 | + | 4.73344e27i | 0.337852 | + | 0.905475i | ||||
\(55\) | 2.49061e27i | 0.355224i | ||||||||
\(56\) | −5.52143e27 | − | 3.01227e27i | −0.590260 | − | 0.322022i | ||||
\(57\) | 1.97411e28 | 1.58991 | ||||||||
\(58\) | −2.78529e28 | + | 1.03925e28i | −1.69833 | + | 0.633684i | ||||
\(59\) | − | 2.05929e26i | − | 0.00955181i | −0.999989 | − | 0.00477590i | \(-0.998480\pi\) | ||
0.999989 | − | 0.00477590i | \(-0.00152022\pi\) | |||||||
\(60\) | −1.73786e28 | − | 2.00460e28i | −0.616020 | − | 0.710570i | ||||
\(61\) | 1.66456e28 | 0.452919 | 0.226460 | − | 0.974021i | \(-0.427285\pi\) | ||||
0.226460 | + | 0.974021i | \(0.427285\pi\) | |||||||
\(62\) | −2.46288e28 | − | 6.60074e28i | −0.516626 | − | 1.38460i | ||||
\(63\) | − | 2.58077e27i | − | 0.0419084i | ||||||
\(64\) | −4.28834e28 | − | 6.66192e28i | −0.541265 | − | 0.840852i | ||||
\(65\) | 3.01414e28 | 0.296859 | ||||||||
\(66\) | −4.87347e28 | + | 1.81840e28i | −0.375955 | + | 0.140277i | ||||
\(67\) | 2.31454e29i | 1.40368i | 0.712336 | + | 0.701839i | \(0.247637\pi\) | ||||
−0.712336 | + | 0.701839i | \(0.752363\pi\) | |||||||
\(68\) | −1.99561e29 | + | 1.73007e29i | −0.954847 | + | 0.827793i | ||||
\(69\) | 3.87953e29 | 1.46958 | ||||||||
\(70\) | −7.12735e28 | − | 1.91019e29i | −0.214466 | − | 0.574789i | ||||
\(71\) | − | 3.68248e29i | − | 0.883095i | −0.897238 | − | 0.441547i | \(-0.854430\pi\) | ||
0.897238 | − | 0.441547i | \(-0.145570\pi\) | |||||||
\(72\) | 1.55692e28 | − | 2.85381e28i | 0.0298502 | − | 0.0547148i | ||||
\(73\) | 2.79454e29 | 0.429679 | 0.214840 | − | 0.976649i | \(-0.431077\pi\) | ||||
0.214840 | + | 0.976649i | \(0.431077\pi\) | |||||||
\(74\) | 5.88523e28 | − | 2.19591e28i | 0.0727874 | − | 0.0271585i | ||||
\(75\) | 1.73029e29i | 0.172639i | ||||||||
\(76\) | 1.25180e30 | + | 1.44393e30i | 1.01045 | + | 1.16554i | ||||
\(77\) | −3.99743e29 | −0.261776 | ||||||||
\(78\) | 2.20063e29 | + | 5.89789e29i | 0.117229 | + | 0.314183i | ||||
\(79\) | 2.19129e30i | 0.952063i | 0.879428 | + | 0.476032i | \(0.157925\pi\) | ||||
−0.879428 | + | 0.476032i | \(0.842075\pi\) | |||||||
\(80\) | 3.64239e29 | − | 2.54226e30i | 0.129404 | − | 0.903193i | ||||
\(81\) | −3.63436e30 | −1.05844 | ||||||||
\(82\) | 8.73891e29 | − | 3.26068e29i | 0.209139 | − | 0.0780344i | ||||
\(83\) | − | 3.91771e30i | − | 0.772294i | −0.922437 | − | 0.386147i | \(-0.873806\pi\) | ||
0.922437 | − | 0.386147i | \(-0.126194\pi\) | |||||||
\(84\) | 3.21738e30 | − | 2.78927e30i | 0.523641 | − | 0.453965i | ||||
\(85\) | −8.56139e30 | −1.15303 | ||||||||
\(86\) | 3.12866e30 | + | 8.38511e30i | 0.349449 | + | 0.936555i | ||||
\(87\) | − | 2.01263e31i | − | 1.86834i | ||||||
\(88\) | −4.42035e30 | − | 2.41156e30i | −0.341770 | − | 0.186456i | ||||
\(89\) | −2.76276e31 | −1.78280 | −0.891400 | − | 0.453217i | \(-0.850276\pi\) | ||||
−0.891400 | + | 0.453217i | \(0.850276\pi\) | |||||||
\(90\) | 9.87302e29 | − | 3.68384e29i | 0.0532807 | − | 0.0198802i | ||||
\(91\) | 4.83771e30i | 0.218765i | ||||||||
\(92\) | 2.46004e31 | + | 2.83762e31i | 0.933979 | + | 1.07733i | ||||
\(93\) | 4.76964e31 | 1.52321 | ||||||||
\(94\) | −3.73660e30 | − | 1.00144e31i | −0.100561 | − | 0.269514i | ||||
\(95\) | 6.19462e31i | 1.40746i | ||||||||
\(96\) | 5.24047e31 | − | 1.14339e31i | 1.00700 | − | 0.219712i | ||||
\(97\) | 2.89803e30 | 0.0471798 | 0.0235899 | − | 0.999722i | \(-0.492490\pi\) | ||||
0.0235899 | + | 0.999722i | \(0.492490\pi\) | |||||||
\(98\) | −3.71544e31 | + | 1.38631e31i | −0.513326 | + | 0.191533i | ||||
\(99\) | − | 2.06611e30i | − | 0.0242656i | ||||||
\(100\) | −1.26559e31 | + | 1.09719e31i | −0.126559 | + | 0.109719i | ||||
\(101\) | 2.75294e31 | 0.234777 | 0.117388 | − | 0.993086i | \(-0.462548\pi\) | ||||
0.117388 | + | 0.993086i | \(0.462548\pi\) | |||||||
\(102\) | −6.25068e31 | − | 1.67524e32i | −0.455328 | − | 1.22032i | ||||
\(103\) | 6.01350e30i | 0.0374742i | 0.999824 | + | 0.0187371i | \(0.00596455\pi\) | ||||
−0.999824 | + | 0.0187371i | \(0.994035\pi\) | |||||||
\(104\) | −2.91848e31 | + | 5.34952e31i | −0.155820 | + | 0.285615i | ||||
\(105\) | 1.38029e32 | 0.632327 | ||||||||
\(106\) | −4.05212e32 | + | 1.51194e32i | −1.59510 | + | 0.595168i | ||||
\(107\) | − | 1.74148e32i | − | 0.589900i | −0.955513 | − | 0.294950i | \(-0.904697\pi\) | ||
0.955513 | − | 0.294950i | \(-0.0953030\pi\) | |||||||
\(108\) | −2.16887e32 | − | 2.50176e32i | −0.633072 | − | 0.730239i | ||||
\(109\) | 5.59935e32 | 1.41031 | 0.705153 | − | 0.709055i | \(-0.250878\pi\) | ||||
0.705153 | + | 0.709055i | \(0.250878\pi\) | |||||||
\(110\) | −5.70601e31 | − | 1.52926e32i | −0.124179 | − | 0.332812i | ||||
\(111\) | 4.25262e31i | 0.0800736i | ||||||||
\(112\) | 4.08034e32 | + | 5.84604e31i | 0.665591 | + | 0.0953616i | ||||
\(113\) | −7.28604e32 | −1.03095 | −0.515474 | − | 0.856905i | \(-0.672384\pi\) | ||||
−0.515474 | + | 0.856905i | \(0.672384\pi\) | |||||||
\(114\) | −1.21212e33 | + | 4.52270e32i | −1.48960 | + | 0.555802i | ||||
\(115\) | 1.21737e33i | 1.30094i | ||||||||
\(116\) | 1.47211e33 | − | 1.27622e33i | 1.36966 | − | 1.18741i | ||||
\(117\) | −2.50042e31 | −0.0202786 | ||||||||
\(118\) | 4.71785e30 | + | 1.26443e31i | 0.00333912 | + | 0.00894915i | ||||
\(119\) | − | 1.37411e33i | − | 0.849706i | ||||||
\(120\) | 1.52632e33 | + | 8.32699e32i | 0.825554 | + | 0.450389i | ||||
\(121\) | 1.79135e33 | 0.848428 | ||||||||
\(122\) | −1.02206e33 | + | 3.81351e32i | −0.424343 | + | 0.158332i | ||||
\(123\) | 6.31466e32i | 0.230075i | ||||||||
\(124\) | 3.02447e33 | + | 3.48868e33i | 0.968060 | + | 1.11664i | ||||
\(125\) | −3.78450e33 | −1.06524 | ||||||||
\(126\) | 5.91257e31 | + | 1.58462e32i | 0.0146503 | + | 0.0392642i | ||||
\(127\) | − | 1.27122e33i | − | 0.277563i | −0.990323 | − | 0.138781i | \(-0.955681\pi\) | ||
0.990323 | − | 0.138781i | \(-0.0443185\pi\) | |||||||
\(128\) | 4.15934e33 | + | 3.10803e33i | 0.801060 | + | 0.598585i | ||||
\(129\) | −6.05901e33 | −1.03031 | ||||||||
\(130\) | −1.85072e33 | + | 6.90543e32i | −0.278129 | + | 0.103776i | ||||
\(131\) | − | 5.79109e33i | − | 0.769874i | −0.922943 | − | 0.384937i | \(-0.874223\pi\) | ||
0.922943 | − | 0.384937i | \(-0.125777\pi\) | |||||||
\(132\) | 2.57577e33 | − | 2.23303e33i | 0.303196 | − | 0.262852i | ||||
\(133\) | −9.94237e33 | −1.03720 | ||||||||
\(134\) | −5.30262e33 | − | 1.42115e34i | −0.490697 | − | 1.31511i | ||||
\(135\) | − | 1.07328e34i | − | 0.881806i | ||||||
\(136\) | 8.28967e33 | − | 1.51948e34i | 0.605222 | − | 1.10936i | ||||
\(137\) | 5.24158e33 | 0.340356 | 0.170178 | − | 0.985413i | \(-0.445566\pi\) | ||||
0.170178 | + | 0.985413i | \(0.445566\pi\) | |||||||
\(138\) | −2.38207e34 | + | 8.88803e33i | −1.37686 | + | 0.513736i | ||||
\(139\) | 3.31449e34i | 1.70679i | 0.521267 | + | 0.853394i | \(0.325460\pi\) | ||||
−0.521267 | + | 0.853394i | \(0.674540\pi\) | |||||||
\(140\) | 8.75254e33 | + | 1.00959e34i | 0.401870 | + | 0.463551i | ||||
\(141\) | 7.23635e33 | 0.296492 | ||||||||
\(142\) | 8.43660e33 | + | 2.26109e34i | 0.308712 | + | 0.827377i | ||||
\(143\) | 3.87297e33i | 0.126668i | ||||||||
\(144\) | −3.02158e32 | + | 2.10896e33i | −0.00883964 | + | 0.0616977i | ||||
\(145\) | 6.31549e34 | 1.65394 | ||||||||
\(146\) | −1.71588e34 | + | 6.40231e33i | −0.402569 | + | 0.150207i | ||||
\(147\) | − | 2.68475e34i | − | 0.564711i | ||||||
\(148\) | −3.11051e33 | + | 2.69662e33i | −0.0587009 | + | 0.0508900i | ||||
\(149\) | 5.60725e34 | 0.950100 | 0.475050 | − | 0.879959i | \(-0.342430\pi\) | ||||
0.475050 | + | 0.879959i | \(0.342430\pi\) | |||||||
\(150\) | −3.96410e33 | − | 1.06242e34i | −0.0603511 | − | 0.161746i | ||||
\(151\) | 2.77124e34i | 0.379353i | 0.981847 | + | 0.189676i | \(0.0607439\pi\) | ||||
−0.981847 | + | 0.189676i | \(0.939256\pi\) | |||||||
\(152\) | −1.09942e35 | − | 5.99801e34i | −1.35415 | − | 0.738771i | ||||
\(153\) | 7.10220e33 | 0.0787644 | ||||||||
\(154\) | 2.45447e34 | − | 9.15815e33i | 0.245260 | − | 0.0915117i | ||||
\(155\) | 1.49668e35i | 1.34841i | ||||||||
\(156\) | −2.70242e34 | − | 3.11720e34i | −0.219664 | − | 0.253380i | ||||
\(157\) | −8.55727e34 | −0.627973 | −0.313986 | − | 0.949428i | \(-0.601665\pi\) | ||||
−0.313986 | + | 0.949428i | \(0.601665\pi\) | |||||||
\(158\) | −5.02025e34 | − | 1.34547e35i | −0.332822 | − | 0.891994i | ||||
\(159\) | − | 2.92803e35i | − | 1.75478i | ||||||
\(160\) | 3.58787e34 | + | 1.64442e35i | 0.194499 | + | 0.891444i | ||||
\(161\) | −1.95388e35 | −0.958703 | ||||||||
\(162\) | 2.23154e35 | − | 8.32634e34i | 0.991662 | − | 0.370011i | ||||
\(163\) | 1.94005e35i | 0.781287i | 0.920542 | + | 0.390644i | \(0.127748\pi\) | ||||
−0.920542 | + | 0.390644i | \(0.872252\pi\) | |||||||
\(164\) | −4.61876e34 | + | 4.00418e34i | −0.168665 | + | 0.146222i | ||||
\(165\) | 1.10503e35 | 0.366127 | ||||||||
\(166\) | 8.97550e34 | + | 2.40552e35i | 0.269979 | + | 0.723567i | ||||
\(167\) | − | 3.97663e35i | − | 1.08655i | −0.839553 | − | 0.543277i | \(-0.817183\pi\) | ||
0.839553 | − | 0.543277i | \(-0.182817\pi\) | |||||||
\(168\) | −1.33648e35 | + | 2.44975e35i | −0.331906 | + | 0.608377i | ||||
\(169\) | −3.95908e35 | −0.894144 | ||||||||
\(170\) | 5.25679e35 | − | 1.96142e35i | 1.08028 | − | 0.403077i | ||||
\(171\) | − | 5.13881e34i | − | 0.0961446i | ||||||
\(172\) | −3.84207e35 | − | 4.43177e35i | −0.654802 | − | 0.755304i | ||||
\(173\) | −1.09919e35 | −0.170740 | −0.0853698 | − | 0.996349i | \(-0.527207\pi\) | ||||
−0.0853698 | + | 0.996349i | \(0.527207\pi\) | |||||||
\(174\) | 4.61095e35 | + | 1.23578e36i | 0.653134 | + | 1.75046i | ||||
\(175\) | − | 8.71440e34i | − | 0.112623i | ||||||
\(176\) | 3.26663e35 | + | 4.68022e34i | 0.385388 | + | 0.0552158i | ||||
\(177\) | −9.13665e33 | −0.00984498 | ||||||||
\(178\) | 1.69636e36 | − | 6.32950e35i | 1.67032 | − | 0.623231i | ||||
\(179\) | 1.77396e36i | 1.59696i | 0.602021 | + | 0.798480i | \(0.294362\pi\) | ||||
−0.602021 | + | 0.798480i | \(0.705638\pi\) | |||||||
\(180\) | −5.21817e34 | + | 4.52383e34i | −0.0429693 | + | 0.0372517i | ||||
\(181\) | 7.69778e34 | 0.0580107 | 0.0290054 | − | 0.999579i | \(-0.490766\pi\) | ||||
0.0290054 | + | 0.999579i | \(0.490766\pi\) | |||||||
\(182\) | −1.10832e35 | − | 2.97041e35i | −0.0764758 | − | 0.204962i | ||||
\(183\) | − | 7.38529e35i | − | 0.466821i | ||||||
\(184\) | −2.16059e36 | − | 1.17873e36i | −1.25166 | − | 0.682858i | ||||
\(185\) | −1.33444e35 | −0.0708847 | ||||||||
\(186\) | −2.92861e36 | + | 1.09273e36i | −1.42710 | + | 0.532483i | ||||
\(187\) | − | 1.10008e36i | − | 0.491993i | ||||||
\(188\) | 4.58863e35 | + | 5.29291e35i | 0.188433 | + | 0.217355i | ||||
\(189\) | 1.72262e36 | 0.649831 | ||||||||
\(190\) | −1.41919e36 | − | 3.80356e36i | −0.492021 | − | 1.31866i | ||||
\(191\) | − | 1.79749e36i | − | 0.572971i | −0.958085 | − | 0.286486i | \(-0.907513\pi\) | ||
0.958085 | − | 0.286486i | \(-0.0924871\pi\) | |||||||
\(192\) | −2.95576e36 | + | 1.90265e36i | −0.866660 | + | 0.557878i | ||||
\(193\) | 2.10472e36 | 0.567908 | 0.283954 | − | 0.958838i | \(-0.408354\pi\) | ||||
0.283954 | + | 0.958838i | \(0.408354\pi\) | |||||||
\(194\) | −1.77942e35 | + | 6.63942e34i | −0.0442030 | + | 0.0164931i | ||||
\(195\) | − | 1.33731e36i | − | 0.305970i | ||||||
\(196\) | 1.96372e36 | − | 1.70242e36i | 0.413982 | − | 0.358897i | ||||
\(197\) | −1.10393e36 | −0.214528 | −0.107264 | − | 0.994231i | \(-0.534209\pi\) | ||||
−0.107264 | + | 0.994231i | \(0.534209\pi\) | |||||||
\(198\) | 4.73348e34 | + | 1.26862e35i | 0.00848277 | + | 0.0227346i | ||||
\(199\) | 8.49051e36i | 1.40373i | 0.712309 | + | 0.701866i | \(0.247650\pi\) | ||||
−0.712309 | + | 0.701866i | \(0.752350\pi\) | |||||||
\(200\) | 5.25721e35 | − | 9.63635e35i | 0.0802186 | − | 0.147039i | ||||
\(201\) | 1.02691e37 | 1.44676 | ||||||||
\(202\) | −1.69034e36 | + | 6.30701e35i | −0.219964 | + | 0.0820732i | ||||
\(203\) | 1.01364e37i | 1.21884i | ||||||||
\(204\) | 7.67598e36 | + | 8.85412e36i | 0.853200 | + | 0.984154i | ||||
\(205\) | −1.98150e36 | −0.203672 | ||||||||
\(206\) | −1.37770e35 | − | 3.69236e35i | −0.0131002 | − | 0.0351098i | ||||
\(207\) | − | 1.00988e36i | − | 0.0888680i | ||||||
\(208\) | 5.66401e35 | − | 3.95329e36i | 0.0461436 | − | 0.322066i | ||||
\(209\) | −7.95966e36 | −0.600557 | ||||||||
\(210\) | −8.47514e36 | + | 3.16226e36i | −0.592431 | + | 0.221049i | ||||
\(211\) | − | 2.37381e37i | − | 1.53790i | −0.639312 | − | 0.768948i | \(-0.720781\pi\) | ||
0.639312 | − | 0.768948i | \(-0.279219\pi\) | |||||||
\(212\) | 2.14166e37 | − | 1.85669e37i | 1.28640 | − | 1.11523i | ||||
\(213\) | −1.63384e37 | −0.910200 | ||||||||
\(214\) | 3.98975e36 | + | 1.06929e37i | 0.206217 | + | 0.552681i | ||||
\(215\) | − | 1.90128e37i | − | 0.912074i | ||||||
\(216\) | 1.90486e37 | + | 1.03922e37i | 0.848406 | + | 0.462857i | ||||
\(217\) | −2.40218e37 | −0.993687 | ||||||||
\(218\) | −3.43806e37 | + | 1.28282e37i | −1.32133 | + | 0.493015i | ||||
\(219\) | − | 1.23988e37i | − | 0.442867i | ||||||
\(220\) | 7.00710e36 | + | 8.08259e36i | 0.232689 | + | 0.268403i | ||||
\(221\) | −1.33132e37 | −0.411156 | ||||||||
\(222\) | −9.74279e35 | − | 2.61116e36i | −0.0279921 | − | 0.0750214i | ||||
\(223\) | 5.19320e37i | 1.38854i | 0.719716 | + | 0.694268i | \(0.244272\pi\) | ||||
−0.719716 | + | 0.694268i | \(0.755728\pi\) | |||||||
\(224\) | −2.63930e37 | + | 5.75855e36i | −0.656933 | + | 0.143333i | ||||
\(225\) | 4.50412e35 | 0.0104397 | ||||||||
\(226\) | 4.47371e37 | − | 1.66924e37i | 0.965902 | − | 0.360399i | ||||
\(227\) | − | 2.16268e37i | − | 0.435090i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) | ||
0.976050 | − | 0.217545i | \(-0.0698049\pi\) | |||||||
\(228\) | 6.40642e37 | − | 5.55397e37i | 1.20132 | − | 1.04147i | ||||
\(229\) | 3.92200e37 | 0.685709 | 0.342854 | − | 0.939389i | \(-0.388606\pi\) | ||||
0.342854 | + | 0.939389i | \(0.388606\pi\) | |||||||
\(230\) | −2.78900e37 | − | 7.47478e37i | −0.454782 | − | 1.21886i | ||||
\(231\) | 1.77358e37i | 0.269811i | ||||||||
\(232\) | −6.11505e37 | + | 1.12088e38i | −0.868145 | + | 1.59129i | ||||
\(233\) | −1.54117e37 | −0.204247 | −0.102124 | − | 0.994772i | \(-0.532564\pi\) | ||||
−0.102124 | + | 0.994772i | \(0.532564\pi\) | |||||||
\(234\) | 1.53528e36 | − | 5.72847e35i | 0.0189992 | − | 0.00708900i | ||||
\(235\) | 2.27072e37i | 0.262468i | ||||||||
\(236\) | −5.79363e35 | − | 6.68286e35i | −0.00625689 | − | 0.00721723i | ||||
\(237\) | 9.72229e37 | 0.981285 | ||||||||
\(238\) | 3.14809e37 | + | 8.43716e37i | 0.297040 | + | 0.796095i | ||||
\(239\) | 2.42617e37i | 0.214070i | 0.994255 | + | 0.107035i | \(0.0341357\pi\) | ||||
−0.994255 | + | 0.107035i | \(0.965864\pi\) | |||||||
\(240\) | −1.12795e38 | − | 1.61605e37i | −0.930914 | − | 0.133375i | ||||
\(241\) | 1.91142e38 | 1.47599 | 0.737996 | − | 0.674805i | \(-0.235772\pi\) | ||||
0.737996 | + | 0.674805i | \(0.235772\pi\) | |||||||
\(242\) | −1.09991e38 | + | 4.10400e37i | −0.794897 | + | 0.296593i | ||||
\(243\) | 1.83989e37i | 0.124477i | ||||||||
\(244\) | 5.40185e37 | − | 4.68307e37i | 0.342220 | − | 0.296684i | ||||
\(245\) | 8.42456e37 | 0.499908 | ||||||||
\(246\) | −1.44669e37 | − | 3.87727e37i | −0.0804295 | − | 0.215558i | ||||
\(247\) | 9.63280e37i | 0.501882i | ||||||||
\(248\) | −2.65632e38 | − | 1.44918e38i | −1.29734 | − | 0.707776i | ||||
\(249\) | −1.73821e38 | −0.795998 | ||||||||
\(250\) | 2.32373e38 | − | 8.67033e37i | 0.998033 | − | 0.372388i | ||||
\(251\) | − | 4.00964e38i | − | 1.61557i | −0.589477 | − | 0.807785i | \(-0.700666\pi\) | ||
0.589477 | − | 0.807785i | \(-0.299334\pi\) | |||||||
\(252\) | −7.26076e36 | − | 8.37518e36i | −0.0274520 | − | 0.0316654i | ||||
\(253\) | −1.56424e38 | −0.555104 | ||||||||
\(254\) | 2.91238e37 | + | 7.80543e37i | 0.0970304 | + | 0.260050i | ||||
\(255\) | 3.79851e38i | 1.18842i | ||||||||
\(256\) | −3.26593e38 | − | 9.55456e37i | −0.959771 | − | 0.280783i | ||||
\(257\) | −5.30332e38 | −1.46426 | −0.732129 | − | 0.681166i | \(-0.761473\pi\) | ||||
−0.732129 | + | 0.681166i | \(0.761473\pi\) | |||||||
\(258\) | 3.72030e38 | − | 1.38812e38i | 0.965301 | − | 0.360175i | ||||
\(259\) | − | 2.14179e37i | − | 0.0522372i | ||||||
\(260\) | 9.78157e37 | − | 8.48001e37i | 0.224303 | − | 0.194457i | ||||
\(261\) | −5.23909e37 | −0.112982 | ||||||||
\(262\) | 1.32674e38 | + | 3.55579e38i | 0.269133 | + | 0.721300i | ||||
\(263\) | − | 9.05669e38i | − | 1.72853i | −0.503034 | − | 0.864267i | \(-0.667783\pi\) | ||
0.503034 | − | 0.864267i | \(-0.332217\pi\) | |||||||
\(264\) | −1.06996e38 | + | 1.96122e38i | −0.192179 | + | 0.352260i | ||||
\(265\) | 9.18797e38 | 1.55341 | ||||||||
\(266\) | 6.10473e38 | − | 2.27781e38i | 0.971762 | − | 0.362586i | ||||
\(267\) | 1.22578e39i | 1.83752i | ||||||||
\(268\) | 6.51174e38 | + | 7.51119e38i | 0.919475 | + | 1.06060i | ||||
\(269\) | −7.91984e38 | −1.05361 | −0.526805 | − | 0.849986i | \(-0.676610\pi\) | ||||
−0.526805 | + | 0.849986i | \(0.676610\pi\) | |||||||
\(270\) | 2.45889e38 | + | 6.59006e38i | 0.308262 | + | 0.826170i | ||||
\(271\) | − | 7.17026e38i | − | 0.847278i | −0.905831 | − | 0.423639i | \(-0.860752\pi\) | ||
0.905831 | − | 0.423639i | \(-0.139248\pi\) | |||||||
\(272\) | −1.60881e38 | + | 1.12289e39i | −0.179227 | + | 1.25094i | ||||
\(273\) | 2.14639e38 | 0.225479 | ||||||||
\(274\) | −3.21839e38 | + | 1.20085e38i | −0.318881 | + | 0.118982i | ||||
\(275\) | − | 6.97657e37i | − | 0.0652107i | ||||||
\(276\) | 1.25899e39 | − | 1.09147e39i | 1.11040 | − | 0.962645i | ||||
\(277\) | −1.07006e39 | −0.890698 | −0.445349 | − | 0.895357i | \(-0.646920\pi\) | ||||
−0.445349 | + | 0.895357i | \(0.646920\pi\) | |||||||
\(278\) | −7.59352e38 | − | 2.03513e39i | −0.596659 | − | 1.59910i | ||||
\(279\) | − | 1.24159e38i | − | 0.0921108i | ||||||
\(280\) | −7.68714e38 | − | 4.19379e38i | −0.538563 | − | 0.293818i | ||||
\(281\) | −9.83963e38 | −0.651145 | −0.325573 | − | 0.945517i | \(-0.605557\pi\) | ||||
−0.325573 | + | 0.945517i | \(0.605557\pi\) | |||||||
\(282\) | −4.44320e38 | + | 1.65785e38i | −0.277786 | + | 0.103648i | ||||
\(283\) | 8.98302e38i | 0.530688i | 0.964154 | + | 0.265344i | \(0.0854855\pi\) | ||||
−0.964154 | + | 0.265344i | \(0.914514\pi\) | |||||||
\(284\) | −1.03603e39 | − | 1.19505e39i | −0.578469 | − | 0.667256i | ||||
\(285\) | 2.74842e39 | 1.45066 | ||||||||
\(286\) | −8.87300e37 | − | 2.37805e38i | −0.0442807 | − | 0.118676i | ||||
\(287\) | − | 3.18031e38i | − | 0.150093i | ||||||
\(288\) | −2.97636e37 | − | 1.36415e38i | −0.0132864 | − | 0.0608951i | ||||
\(289\) | 1.41358e39 | 0.596973 | ||||||||
\(290\) | −3.87778e39 | + | 1.44688e39i | −1.54958 | + | 0.578184i | ||||
\(291\) | − | 1.28580e38i | − | 0.0486278i | ||||||
\(292\) | 9.06890e38 | − | 7.86218e38i | 0.324660 | − | 0.281460i | ||||
\(293\) | −3.27044e38 | −0.110847 | −0.0554235 | − | 0.998463i | \(-0.517651\pi\) | ||||
−0.0554235 | + | 0.998463i | \(0.517651\pi\) | |||||||
\(294\) | 6.15078e38 | + | 1.64847e39i | 0.197412 | + | 0.529081i | ||||
\(295\) | − | 2.86702e37i | − | 0.00871522i | ||||||
\(296\) | 1.29209e38 | − | 2.36838e38i | 0.0372071 | − | 0.0681999i | ||||
\(297\) | 1.37909e39 | 0.376262 | ||||||||
\(298\) | −3.44291e39 | + | 1.28462e39i | −0.890155 | + | 0.332136i | ||||
\(299\) | 1.89304e39i | 0.463897i | ||||||||
\(300\) | 4.86801e38 | + | 5.61517e38i | 0.113087 | + | 0.130444i | ||||
\(301\) | 3.05155e39 | 0.672136 | ||||||||
\(302\) | −6.34894e38 | − | 1.70157e39i | −0.132614 | − | 0.355418i | ||||
\(303\) | − | 1.22142e39i | − | 0.241983i | ||||||
\(304\) | 8.12473e39 | + | 1.16406e39i | 1.52697 | + | 0.218775i | ||||
\(305\) | 2.31745e39 | 0.413251 | ||||||||
\(306\) | −4.36083e38 | + | 1.62712e38i | −0.0737949 | + | 0.0275345i | ||||
\(307\) | 1.67228e39i | 0.268592i | 0.990941 | + | 0.134296i | \(0.0428774\pi\) | ||||
−0.990941 | + | 0.134296i | \(0.957123\pi\) | |||||||
\(308\) | −1.29726e39 | + | 1.12464e39i | −0.197795 | + | 0.171476i | ||||
\(309\) | 2.66807e38 | 0.0386244 | ||||||||
\(310\) | −3.42891e39 | − | 9.18979e39i | −0.471378 | − | 1.26334i | ||||
\(311\) | 1.74120e39i | 0.227344i | 0.993518 | + | 0.113672i | \(0.0362613\pi\) | ||||
−0.993518 | + | 0.113672i | \(0.963739\pi\) | |||||||
\(312\) | 2.37347e39 | + | 1.29487e39i | 0.294381 | + | 0.160603i | ||||
\(313\) | −1.14924e40 | −1.35426 | −0.677128 | − | 0.735866i | \(-0.736776\pi\) | ||||
−0.677128 | + | 0.735866i | \(0.736776\pi\) | |||||||
\(314\) | 5.25426e39 | − | 1.96048e39i | 0.588352 | − | 0.219527i | ||||
\(315\) | − | 3.59304e38i | − | 0.0382379i | ||||||
\(316\) | 6.16498e39 | + | 7.11122e39i | 0.623647 | + | 0.719367i | ||||
\(317\) | −1.00613e40 | −0.967623 | −0.483811 | − | 0.875172i | \(-0.660748\pi\) | ||||
−0.483811 | + | 0.875172i | \(0.660748\pi\) | |||||||
\(318\) | 6.70815e39 | + | 1.79784e40i | 0.613435 | + | 1.64406i | ||||
\(319\) | 8.11498e39i | 0.705726i | ||||||||
\(320\) | −5.97038e39 | − | 9.27496e39i | −0.493858 | − | 0.767207i | ||||
\(321\) | −7.72659e39 | −0.608006 | ||||||||
\(322\) | 1.19970e40 | − | 4.47636e39i | 0.898215 | − | 0.335143i | ||||
\(323\) | − | 2.73611e40i | − | 1.94936i | ||||||
\(324\) | −1.17943e40 | + | 1.02249e40i | −0.799746 | + | 0.693331i | ||||
\(325\) | −8.44307e38 | −0.0544962 | ||||||||
\(326\) | −4.44467e39 | − | 1.19121e40i | −0.273122 | − | 0.731993i | ||||
\(327\) | − | 2.48432e40i | − | 1.45359i | ||||||
\(328\) | 1.91861e39 | − | 3.51677e39i | 0.106907 | − | 0.195958i | ||||
\(329\) | −3.64451e39 | −0.193421 | ||||||||
\(330\) | −6.78502e39 | + | 2.53164e39i | −0.343027 | + | 0.127991i | ||||
\(331\) | 4.73509e39i | 0.228076i | 0.993476 | + | 0.114038i | \(0.0363786\pi\) | ||||
−0.993476 | + | 0.114038i | \(0.963621\pi\) | |||||||
\(332\) | −1.10221e40 | − | 1.27138e40i | −0.505889 | − | 0.583536i | ||||
\(333\) | 1.10700e38 | 0.00484218 | ||||||||
\(334\) | 9.11049e39 | + | 2.44169e40i | 0.379838 | + | 1.01800i | ||||
\(335\) | 3.22238e40i | 1.28074i | ||||||||
\(336\) | 2.59377e39 | − | 1.81036e40i | 0.0982885 | − | 0.686020i | ||||
\(337\) | 3.62976e40 | 1.31159 | 0.655797 | − | 0.754937i | \(-0.272333\pi\) | ||||
0.655797 | + | 0.754937i | \(0.272333\pi\) | |||||||
\(338\) | 2.43092e40 | − | 9.07029e39i | 0.837729 | − | 0.312575i | ||||
\(339\) | 3.23267e40i | 1.06259i | ||||||||
\(340\) | −2.77836e40 | + | 2.40867e40i | −0.871217 | + | 0.755291i | ||||
\(341\) | −1.92313e40 | −0.575360 | ||||||||
\(342\) | 1.17731e39 | + | 3.15529e39i | 0.0336102 | + | 0.0900785i | ||||
\(343\) | 3.82003e40i | 1.04079i | ||||||||
\(344\) | 3.37439e40 | + | 1.84093e40i | 0.877528 | + | 0.478744i | ||||
\(345\) | 5.40122e40 | 1.34087 | ||||||||
\(346\) | 6.74913e39 | − | 2.51825e39i | 0.159967 | − | 0.0596871i | ||||
\(347\) | − | 2.25109e40i | − | 0.509473i | −0.967011 | − | 0.254736i | \(-0.918011\pi\) | ||
0.967011 | − | 0.254736i | \(-0.0819887\pi\) | |||||||
\(348\) | −5.66235e40 | − | 6.53143e40i | −1.22385 | − | 1.41169i | ||||
\(349\) | 3.78768e40 | 0.781928 | 0.390964 | − | 0.920406i | \(-0.372142\pi\) | ||||
0.390964 | + | 0.920406i | \(0.372142\pi\) | |||||||
\(350\) | 1.99648e39 | + | 5.35074e39i | 0.0393709 | + | 0.105518i | ||||
\(351\) | − | 1.66898e40i | − | 0.314440i | ||||||
\(352\) | −2.11297e40 | + | 4.61017e39i | −0.380374 | + | 0.0829917i | ||||
\(353\) | 4.87419e40 | 0.838508 | 0.419254 | − | 0.907869i | \(-0.362292\pi\) | ||||
0.419254 | + | 0.907869i | \(0.362292\pi\) | |||||||
\(354\) | 5.61001e38 | − | 2.09321e38i | 0.00922383 | − | 0.00344161i | ||||
\(355\) | − | 5.12689e40i | − | 0.805750i | ||||||
\(356\) | −8.96577e40 | + | 7.77276e40i | −1.34706 | + | 1.16782i | ||||
\(357\) | −6.09662e40 | −0.875786 | ||||||||
\(358\) | −4.06414e40 | − | 1.08923e41i | −0.558265 | − | 1.49620i | ||||
\(359\) | 5.11945e40i | 0.672531i | 0.941767 | + | 0.336265i | \(0.109164\pi\) | ||||
−0.941767 | + | 0.336265i | \(0.890836\pi\) | |||||||
\(360\) | 2.16760e39 | − | 3.97317e39i | 0.0272358 | − | 0.0499226i | ||||
\(361\) | −1.14773e41 | −1.37951 | ||||||||
\(362\) | −4.72652e39 | + | 1.76357e39i | −0.0543506 | + | 0.0202794i | ||||
\(363\) | − | 7.94786e40i | − | 0.874468i | ||||||
\(364\) | 1.36104e40 | + | 1.56994e40i | 0.143301 | + | 0.165296i | ||||
\(365\) | 3.89066e40 | 0.392046 | ||||||||
\(366\) | 1.69198e40 | + | 4.53465e40i | 0.163191 | + | 0.437367i | ||||
\(367\) | − | 1.13981e41i | − | 1.05239i | −0.850364 | − | 0.526196i | \(-0.823618\pi\) | ||
0.850364 | − | 0.526196i | \(-0.176382\pi\) | |||||||
\(368\) | 1.59668e41 | + | 2.28761e40i | 1.41141 | + | 0.202217i | ||||
\(369\) | 1.64377e39 | 0.0139130 | ||||||||
\(370\) | 8.19363e39 | − | 3.05722e39i | 0.0664124 | − | 0.0247799i | ||||
\(371\) | 1.47467e41i | 1.14476i | ||||||||
\(372\) | 1.54786e41 | − | 1.34190e41i | 1.15092 | − | 0.997773i | ||||
\(373\) | −1.95796e41 | −1.39464 | −0.697319 | − | 0.716761i | \(-0.745624\pi\) | ||||
−0.697319 | + | 0.716761i | \(0.745624\pi\) | |||||||
\(374\) | 2.52029e40 | + | 6.75462e40i | 0.171991 | + | 0.460951i | ||||
\(375\) | 1.67911e41i | 1.09794i | ||||||||
\(376\) | −4.03008e40 | − | 2.19865e40i | −0.252527 | − | 0.137769i | ||||
\(377\) | 9.82077e40 | 0.589772 | ||||||||
\(378\) | −1.05771e41 | + | 3.94653e40i | −0.608831 | + | 0.227168i | ||||
\(379\) | 1.25171e40i | 0.0690679i | 0.999404 | + | 0.0345339i | \(0.0109947\pi\) | ||||
−0.999404 | + | 0.0345339i | \(0.989005\pi\) | |||||||
\(380\) | 1.74280e41 | + | 2.01029e41i | 0.921955 | + | 1.06346i | ||||
\(381\) | −5.64014e40 | −0.286082 | ||||||||
\(382\) | 4.11807e40 | + | 1.10368e41i | 0.200299 | + | 0.536821i | ||||
\(383\) | − | 2.07290e41i | − | 0.966938i | −0.875362 | − | 0.483469i | \(-0.839377\pi\) | ||
0.875362 | − | 0.483469i | \(-0.160623\pi\) | |||||||
\(384\) | 1.37897e41 | − | 1.84541e41i | 0.616957 | − | 0.825646i | ||||
\(385\) | −5.56537e40 | −0.238848 | ||||||||
\(386\) | −1.29232e41 | + | 4.82194e40i | −0.532077 | + | 0.198529i | ||||
\(387\) | 1.57722e40i | 0.0623043i | ||||||||
\(388\) | 9.40477e39 | − | 8.15335e39i | 0.0356484 | − | 0.0309050i | ||||
\(389\) | 2.02435e41 | 0.736361 | 0.368181 | − | 0.929754i | \(-0.379981\pi\) | ||||
0.368181 | + | 0.929754i | \(0.379981\pi\) | |||||||
\(390\) | 3.06380e40 | + | 8.21125e40i | 0.106961 | + | 0.286666i | ||||
\(391\) | − | 5.37701e41i | − | 1.80183i | ||||||
\(392\) | −8.15718e40 | + | 1.49519e41i | −0.262400 | + | 0.480973i | ||||
\(393\) | −2.56939e41 | −0.793503 | ||||||||
\(394\) | 6.77827e40 | − | 2.52912e40i | 0.200992 | − | 0.0749946i | ||||
\(395\) | 3.05079e41i | 0.868677i | ||||||||
\(396\) | −5.81282e39 | − | 6.70500e39i | −0.0158951 | − | 0.0183348i | ||||
\(397\) | 1.88519e40 | 0.0495115 | 0.0247558 | − | 0.999694i | \(-0.492119\pi\) | ||||
0.0247558 | + | 0.999694i | \(0.492119\pi\) | |||||||
\(398\) | −1.94518e41 | − | 5.21327e41i | −0.490717 | − | 1.31517i | ||||
\(399\) | 4.41123e41i | 1.06904i | ||||||||
\(400\) | −1.02029e40 | + | 7.12125e40i | −0.0237554 | + | 0.165805i | ||||
\(401\) | 7.93687e41 | 1.77558 | 0.887788 | − | 0.460252i | \(-0.152241\pi\) | ||||
0.887788 | + | 0.460252i | \(0.152241\pi\) | |||||||
\(402\) | −6.30535e41 | + | 2.35266e41i | −1.35548 | + | 0.505758i | ||||
\(403\) | 2.32738e41i | 0.480825i | ||||||||
\(404\) | 8.93391e40 | − | 7.74515e40i | 0.177394 | − | 0.153790i | ||||
\(405\) | −5.05988e41 | −0.965740 | ||||||||
\(406\) | −2.32225e41 | − | 6.22385e41i | −0.426082 | − | 1.14194i | ||||
\(407\) | − | 1.71467e40i | − | 0.0302461i | ||||||
\(408\) | −6.74162e41 | − | 3.67796e41i | −1.14341 | − | 0.623798i | ||||
\(409\) | 1.31441e41 | 0.214367 | 0.107183 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107183 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(410\) | 1.21666e41 | − | 4.53963e40i | 0.190822 | − | 0.0711998i | ||||
\(411\) | − | 2.32558e41i | − | 0.350802i | ||||||
\(412\) | 1.69184e40 | + | 1.95152e40i | 0.0245474 | + | 0.0283150i | ||||
\(413\) | 4.60157e39 | 0.00642252 | ||||||||
\(414\) | 2.31365e40 | + | 6.20079e40i | 0.0310665 | + | 0.0832610i | ||||
\(415\) | − | 5.45437e41i | − | 0.704653i | ||||||
\(416\) | 5.57925e40 | + | 2.55713e41i | 0.0693557 | + | 0.317877i | ||||
\(417\) | 1.47057e42 | 1.75917 | ||||||||
\(418\) | 4.88732e41 | − | 1.82356e41i | 0.562665 | − | 0.209943i | ||||
\(419\) | 7.01171e41i | 0.776961i | 0.921457 | + | 0.388481i | \(0.127000\pi\) | ||||
−0.921457 | + | 0.388481i | \(0.873000\pi\) | |||||||
\(420\) | 4.47935e41 | − | 3.88332e41i | 0.477779 | − | 0.414204i | ||||
\(421\) | −8.56023e41 | −0.878966 | −0.439483 | − | 0.898251i | \(-0.644838\pi\) | ||||
−0.439483 | + | 0.898251i | \(0.644838\pi\) | |||||||
\(422\) | 5.43842e41 | + | 1.45755e42i | 0.537618 | + | 1.44086i | ||||
\(423\) | − | 1.88370e40i | − | 0.0179294i | ||||||
\(424\) | −8.89636e41 | + | 1.63068e42i | −0.815378 | + | 1.49457i | ||||
\(425\) | 2.39817e41 | 0.211669 | ||||||||
\(426\) | 1.00320e42 | − | 3.74315e41i | 0.852772 | − | 0.318188i | ||||
\(427\) | 3.71952e41i | 0.304537i | ||||||||
\(428\) | −4.89950e41 | − | 5.65150e41i | −0.386413 | − | 0.445721i | ||||
\(429\) | 1.71836e41 | 0.130556 | ||||||||
\(430\) | 4.35584e41 | + | 1.16740e42i | 0.318843 | + | 0.854528i | ||||
\(431\) | 5.29035e41i | 0.373120i | 0.982444 | + | 0.186560i | \(0.0597338\pi\) | ||||
−0.982444 | + | 0.186560i | \(0.940266\pi\) | |||||||
\(432\) | −1.40769e42 | − | 2.01685e41i | −0.956683 | − | 0.137067i | ||||
\(433\) | 2.07497e41 | 0.135896 | 0.0679478 | − | 0.997689i | \(-0.478355\pi\) | ||||
0.0679478 | + | 0.997689i | \(0.478355\pi\) | |||||||
\(434\) | 1.47496e42 | − | 5.50341e41i | 0.930991 | − | 0.347373i | ||||
\(435\) | − | 2.80205e42i | − | 1.70470i | ||||||
\(436\) | 1.81711e42 | − | 1.57533e42i | 1.06561 | − | 0.923818i | ||||
\(437\) | −3.89055e42 | −2.19942 | ||||||||
\(438\) | 2.84057e41 | + | 7.61299e41i | 0.154818 | + | 0.414925i | ||||
\(439\) | 2.85946e42i | 1.50263i | 0.659944 | + | 0.751315i | \(0.270580\pi\) | ||||
−0.659944 | + | 0.751315i | \(0.729420\pi\) | |||||||
\(440\) | −6.15416e41 | − | 3.35747e41i | −0.311836 | − | 0.170125i | ||||
\(441\) | −6.98868e40 | −0.0341490 | ||||||||
\(442\) | 8.17446e41 | − | 3.05007e41i | 0.385214 | − | 0.143732i | ||||
\(443\) | − | 2.21579e42i | − | 1.00709i | −0.863969 | − | 0.503545i | \(-0.832029\pi\) | ||
0.863969 | − | 0.503545i | \(-0.167971\pi\) | |||||||
\(444\) | 1.19644e41 | + | 1.38007e41i | 0.0524520 | + | 0.0605026i | ||||
\(445\) | −3.84641e42 | −1.62665 | ||||||||
\(446\) | −1.18977e42 | − | 3.18868e42i | −0.485405 | − | 1.30093i | ||||
\(447\) | − | 2.48782e42i | − | 0.979261i | ||||||
\(448\) | 1.48863e42 | − | 9.58248e41i | 0.565379 | − | 0.363940i | ||||
\(449\) | 8.69610e40 | 0.0318701 | 0.0159350 | − | 0.999873i | \(-0.494928\pi\) | ||||
0.0159350 | + | 0.999873i | \(0.494928\pi\) | |||||||
\(450\) | −2.76558e40 | + | 1.03190e40i | −0.00978107 | + | 0.00364953i | ||||
\(451\) | − | 2.54609e41i | − | 0.0869059i | ||||||
\(452\) | −2.36448e42 | + | 2.04986e42i | −0.778971 | + | 0.675320i | ||||
\(453\) | 1.22954e42 | 0.390996 | ||||||||
\(454\) | 4.95473e41 | + | 1.32791e42i | 0.152099 | + | 0.407639i | ||||
\(455\) | 6.73523e41i | 0.199604i | ||||||||
\(456\) | −2.66120e42 | + | 4.87792e42i | −0.761446 | + | 1.39572i | ||||
\(457\) | 4.54305e42 | 1.25513 | 0.627565 | − | 0.778564i | \(-0.284052\pi\) | ||||
0.627565 | + | 0.778564i | \(0.284052\pi\) | |||||||
\(458\) | −2.40815e42 | + | 8.98533e41i | −0.642445 | + | 0.239710i | ||||
\(459\) | 4.74059e42i | 1.22132i | ||||||||
\(460\) | 3.42496e42 | + | 3.95064e42i | 0.852177 | + | 0.982973i | ||||
\(461\) | 4.18043e42 | 1.00463 | 0.502315 | − | 0.864684i | \(-0.332482\pi\) | ||||
0.502315 | + | 0.864684i | \(0.332482\pi\) | |||||||
\(462\) | −4.06328e41 | − | 1.08900e42i | −0.0943204 | − | 0.252787i | ||||
\(463\) | 1.57491e42i | 0.353150i | 0.984287 | + | 0.176575i | \(0.0565018\pi\) | ||||
−0.984287 | + | 0.176575i | \(0.943498\pi\) | |||||||
\(464\) | 1.18677e42 | − | 8.28327e42i | 0.257087 | − | 1.79438i | ||||
\(465\) | 6.64047e42 | 1.38980 | ||||||||
\(466\) | 9.46297e41 | − | 3.53084e41i | 0.191361 | − | 0.0714008i | ||||
\(467\) | − | 3.22443e42i | − | 0.630061i | −0.949082 | − | 0.315031i | \(-0.897985\pi\) | ||
0.949082 | − | 0.315031i | \(-0.102015\pi\) | |||||||
\(468\) | −8.11441e40 | + | 7.03469e40i | −0.0153223 | + | 0.0132835i | ||||
\(469\) | −5.17193e42 | −0.943815 | ||||||||
\(470\) | −5.20223e41 | − | 1.39425e42i | −0.0917537 | − | 0.245908i | ||||
\(471\) | 3.79668e42i | 0.647247i | ||||||||
\(472\) | 5.08840e40 | + | 2.77603e40i | 0.00838512 | + | 0.00457458i | ||||
\(473\) | 2.44301e42 | 0.389177 | ||||||||
\(474\) | −5.96959e42 | + | 2.22738e42i | −0.919372 | + | 0.343038i | ||||
\(475\) | − | 1.73520e42i | − | 0.258376i | ||||||
\(476\) | −3.86592e42 | − | 4.45928e42i | −0.556598 | − | 0.642027i | ||||
\(477\) | −7.62198e41 | −0.106114 | ||||||||
\(478\) | −5.55838e41 | − | 1.48970e42i | −0.0748346 | − | 0.200563i | ||||
\(479\) | 6.21903e42i | 0.809756i | 0.914371 | + | 0.404878i | \(0.132686\pi\) | ||||
−0.914371 | + | 0.404878i | \(0.867314\pi\) | |||||||
\(480\) | 7.29597e42 | − | 1.59187e42i | 0.918805 | − | 0.200469i | ||||
\(481\) | −2.07510e41 | −0.0252765 | ||||||||
\(482\) | −1.17363e43 | + | 4.37908e42i | −1.38287 | + | 0.515977i | ||||
\(483\) | 8.66897e42i | 0.988128i | ||||||||
\(484\) | 5.81334e42 | − | 5.03980e42i | 0.641061 | − | 0.555761i | ||||
\(485\) | 4.03475e41 | 0.0430475 | ||||||||
\(486\) | −4.21519e41 | − | 1.12971e42i | −0.0435148 | − | 0.116624i | ||||
\(487\) | − | 1.91998e43i | − | 1.91793i | −0.283517 | − | 0.958967i | \(-0.591501\pi\) | ||
0.283517 | − | 0.958967i | \(-0.408499\pi\) | |||||||
\(488\) | −2.24390e42 | + | 4.11303e42i | −0.216914 | + | 0.397598i | ||||
\(489\) | 8.60760e42 | 0.805267 | ||||||||
\(490\) | −5.17277e42 | + | 1.93007e42i | −0.468367 | + | 0.174758i | ||||
\(491\) | − | 4.78448e42i | − | 0.419306i | −0.977776 | − | 0.209653i | \(-0.932767\pi\) | ||
0.977776 | − | 0.209653i | \(-0.0672334\pi\) | |||||||
\(492\) | 1.77657e42 | + | 2.04925e42i | 0.150710 | + | 0.173841i | ||||
\(493\) | −2.78950e43 | −2.29074 | ||||||||
\(494\) | −2.20688e42 | − | 5.91465e42i | −0.175448 | − | 0.470216i | ||||
\(495\) | − | 2.87652e41i | − | 0.0221403i | ||||||
\(496\) | 1.96302e43 | + | 2.81248e42i | 1.46291 | + | 0.209596i | ||||
\(497\) | 8.22867e42 | 0.593782 | ||||||||
\(498\) | 1.06728e43 | − | 3.98225e42i | 0.745776 | − | 0.278265i | ||||
\(499\) | − | 1.53323e43i | − | 1.03752i | −0.854919 | − | 0.518762i | \(-0.826393\pi\) | ||
0.854919 | − | 0.518762i | \(-0.173607\pi\) | |||||||
\(500\) | −1.22816e43 | + | 1.06474e43i | −0.804885 | + | 0.697785i | ||||
\(501\) | −1.76435e43 | −1.11990 | ||||||||
\(502\) | 9.18612e42 | + | 2.46196e43i | 0.564771 | + | 1.51364i | ||||
\(503\) | 2.93216e42i | 0.174623i | 0.996181 | + | 0.0873113i | \(0.0278275\pi\) | ||||
−0.996181 | + | 0.0873113i | \(0.972173\pi\) | |||||||
\(504\) | 6.37695e41 | + | 3.47901e41i | 0.0367895 | + | 0.0200709i | ||||
\(505\) | 3.83274e42 | 0.214214 | ||||||||
\(506\) | 9.60459e42 | − | 3.58368e42i | 0.520080 | − | 0.194053i | ||||
\(507\) | 1.75656e43i | 0.921588i | ||||||||
\(508\) | −3.57646e42 | − | 4.12539e42i | −0.181817 | − | 0.209723i | ||||
\(509\) | −2.81958e43 | −1.38899 | −0.694496 | − | 0.719497i | \(-0.744373\pi\) | ||||
−0.694496 | + | 0.719497i | \(0.744373\pi\) | |||||||
\(510\) | −8.70242e42 | − | 2.33233e43i | −0.415449 | − | 1.11344i | ||||
\(511\) | 6.24451e42i | 0.288911i | ||||||||
\(512\) | 2.22421e43 | − | 1.61567e42i | 0.997372 | − | 0.0724492i | ||||
\(513\) | 3.43006e43 | 1.49082 | ||||||||
\(514\) | 3.25630e43 | − | 1.21499e43i | 1.37187 | − | 0.511876i | ||||
\(515\) | 8.37221e41i | 0.0341920i | ||||||||
\(516\) | −1.96628e43 | + | 1.70465e43i | −0.778487 | + | 0.674900i | ||||
\(517\) | −2.91772e42 | −0.111994 | ||||||||
\(518\) | 4.90685e41 | + | 1.31508e42i | 0.0182611 | + | 0.0489414i | ||||
\(519\) | 4.87687e42i | 0.175980i | ||||||||
\(520\) | −4.06321e42 | + | 7.44779e42i | −0.142173 | + | 0.260600i | ||||
\(521\) | 3.53836e43 | 1.20060 | 0.600300 | − | 0.799775i | \(-0.295048\pi\) | ||||
0.600300 | + | 0.799775i | \(0.295048\pi\) | |||||||
\(522\) | 3.21686e42 | − | 1.20028e42i | 0.105853 | − | 0.0394961i | ||||
\(523\) | 4.38521e43i | 1.39947i | 0.714402 | + | 0.699735i | \(0.246699\pi\) | ||||
−0.714402 | + | 0.699735i | \(0.753301\pi\) | |||||||
\(524\) | −1.62927e43 | − | 1.87934e43i | −0.504304 | − | 0.581707i | ||||
\(525\) | −3.86640e42 | −0.116080 | ||||||||
\(526\) | 2.07490e43 | + | 5.56091e43i | 0.604261 | + | 1.61947i | ||||
\(527\) | − | 6.61071e43i | − | 1.86758i | ||||||
\(528\) | 2.07652e42 | − | 1.44934e43i | 0.0569105 | − | 0.397216i | ||||
\(529\) | −3.88484e43 | −1.03296 | ||||||||
\(530\) | −5.64151e43 | + | 2.10497e43i | −1.45540 | + | 0.543040i | ||||
\(531\) | 2.37837e40i | 0.000595342i | ||||||||
\(532\) | −3.22652e43 | + | 2.79720e43i | −0.783698 | + | 0.679417i | ||||
\(533\) | −3.08129e42 | −0.0726268 | ||||||||
\(534\) | −2.80827e43 | − | 7.52642e43i | −0.642360 | − | 1.72158i | ||||
\(535\) | − | 2.42455e43i | − | 0.538234i | ||||||
\(536\) | −5.71910e43 | − | 3.12011e43i | −1.23223 | − | 0.672254i | ||||
\(537\) | 7.87067e43 | 1.64598 | ||||||||
\(538\) | 4.86287e43 | − | 1.81444e43i | 0.987135 | − | 0.368321i | ||||
\(539\) | 1.08250e43i | 0.213308i | ||||||||
\(540\) | −3.01958e43 | − | 3.48304e43i | −0.577625 | − | 0.666282i | ||||
\(541\) | −3.92683e43 | −0.729266 | −0.364633 | − | 0.931151i | \(-0.618805\pi\) | ||||
−0.364633 | + | 0.931151i | \(0.618805\pi\) | |||||||
\(542\) | 1.64271e43 | + | 4.40262e43i | 0.296192 | + | 0.793821i | ||||
\(543\) | − | 3.41535e42i | − | 0.0597912i | ||||||
\(544\) | −1.58473e43 | − | 7.26328e43i | −0.269385 | − | 1.23467i | ||||
\(545\) | 7.79561e43 | 1.28679 | ||||||||
\(546\) | −1.31791e43 | + | 4.91740e42i | −0.211253 | + | 0.0788230i | ||||
\(547\) | − | 4.32555e43i | − | 0.673356i | −0.941620 | − | 0.336678i | \(-0.890697\pi\) | ||
0.941620 | − | 0.336678i | \(-0.109303\pi\) | |||||||
\(548\) | 1.70101e43 | − | 1.47467e43i | 0.257168 | − | 0.222949i | ||||
\(549\) | −1.92247e42 | −0.0282294 | ||||||||
\(550\) | 1.59834e42 | + | 4.28369e42i | 0.0227964 | + | 0.0610963i | ||||
\(551\) | 2.01835e44i | 2.79621i | ||||||||
\(552\) | −5.22980e43 | + | 9.58611e43i | −0.703817 | + | 1.29008i | ||||
\(553\) | −4.89652e43 | −0.640156 | ||||||||
\(554\) | 6.57026e43 | − | 2.45151e43i | 0.834500 | − | 0.311370i | ||||
\(555\) | 5.92065e42i | 0.0730604i | ||||||||
\(556\) | 9.32500e43 | + | 1.07563e44i | 1.11803 | + | 1.28963i | ||||
\(557\) | 4.56437e43 | 0.531738 | 0.265869 | − | 0.964009i | \(-0.414341\pi\) | ||||
0.265869 | + | 0.964009i | \(0.414341\pi\) | |||||||
\(558\) | 2.84449e42 | + | 7.62349e42i | 0.0322001 | + | 0.0862992i | ||||
\(559\) | − | 2.95654e43i | − | 0.325233i | ||||||
\(560\) | 5.68079e43 | + | 8.13907e42i | 0.607296 | + | 0.0870094i | ||||
\(561\) | −4.88083e43 | −0.507093 | ||||||||
\(562\) | 6.04164e43 | − | 2.25427e43i | 0.610062 | − | 0.227627i | ||||
\(563\) | 1.65440e42i | 0.0162370i | 0.999967 | + | 0.00811850i | \(0.00258423\pi\) | ||||
−0.999967 | + | 0.00811850i | \(0.997416\pi\) | |||||||
\(564\) | 2.34836e43 | − | 2.03588e43i | 0.224026 | − | 0.194217i | ||||
\(565\) | −1.01439e44 | −0.940653 | ||||||||
\(566\) | −2.05802e43 | − | 5.51567e43i | −0.185518 | − | 0.497205i | ||||
\(567\) | − | 8.12113e43i | − | 0.711684i | ||||||
\(568\) | 9.09922e43 | + | 4.96417e43i | 0.775231 | + | 0.422935i | ||||
\(569\) | 1.25234e44 | 1.03735 | 0.518676 | − | 0.854971i | \(-0.326425\pi\) | ||||
0.518676 | + | 0.854971i | \(0.326425\pi\) | |||||||
\(570\) | −1.68756e44 | + | 6.29666e43i | −1.35913 | + | 0.507122i | ||||
\(571\) | − | 1.77620e44i | − | 1.39096i | −0.718546 | − | 0.695479i | \(-0.755192\pi\) | ||
0.718546 | − | 0.695479i | \(-0.244808\pi\) | |||||||
\(572\) | 1.08962e43 | + | 1.25687e43i | 0.0829737 | + | 0.0957089i | ||||
\(573\) | −7.97510e43 | −0.590557 | ||||||||
\(574\) | 7.28612e42 | + | 1.95275e43i | 0.0524694 | + | 0.140623i | ||||
\(575\) | − | 3.41003e43i | − | 0.238821i | ||||||
\(576\) | 4.95280e42 | + | 7.69415e42i | 0.0337358 | + | 0.0524084i | ||||
\(577\) | −2.47656e44 | −1.64072 | −0.820361 | − | 0.571845i | \(-0.806228\pi\) | ||||
−0.820361 | + | 0.571845i | \(0.806228\pi\) | |||||||
\(578\) | −8.67954e43 | + | 3.23852e43i | −0.559308 | + | 0.208690i | ||||
\(579\) | − | 9.33822e43i | − | 0.585339i | ||||||
\(580\) | 2.04952e44 | − | 1.77681e44i | 1.24969 | − | 1.08341i | ||||
\(581\) | 8.75429e43 | 0.519281 | ||||||||
\(582\) | 2.94577e42 | + | 7.89494e42i | 0.0169993 | + | 0.0455597i | ||||
\(583\) | 1.18059e44i | 0.662831i | ||||||||
\(584\) | −3.76718e43 | + | 6.90515e43i | −0.205783 | + | 0.377197i | ||||
\(585\) | −3.48117e42 | −0.0185025 | ||||||||
\(586\) | 2.00808e43 | − | 7.49260e42i | 0.103853 | − | 0.0387499i | ||||
\(587\) | 1.66894e44i | 0.839909i | 0.907545 | + | 0.419954i | \(0.137954\pi\) | ||||
−0.907545 | + | 0.419954i | \(0.862046\pi\) | |||||||
\(588\) | −7.55329e43 | − | 8.71261e43i | −0.369913 | − | 0.426689i | ||||
\(589\) | −4.78320e44 | −2.27968 | ||||||||
\(590\) | 6.56836e41 | + | 1.76038e42i | 0.00304667 | + | 0.00816535i | ||||
\(591\) | 4.89793e43i | 0.221112i | ||||||||
\(592\) | −2.50761e42 | + | 1.75023e43i | −0.0110183 | + | 0.0769038i | ||||
\(593\) | 2.26180e44 | 0.967338 | 0.483669 | − | 0.875251i | \(-0.339304\pi\) | ||||
0.483669 | + | 0.875251i | \(0.339304\pi\) | |||||||
\(594\) | −8.46778e43 | + | 3.15951e43i | −0.352522 | + | 0.131534i | ||||
\(595\) | − | 1.91308e44i | − | 0.775285i | ||||||
\(596\) | 1.81968e44 | − | 1.57755e44i | 0.717884 | − | 0.622361i | ||||
\(597\) | 3.76706e44 | 1.44682 | ||||||||
\(598\) | −4.33698e43 | − | 1.16235e44i | −0.162169 | − | 0.434628i | ||||
\(599\) | 3.91427e44i | 1.42502i | 0.701661 | + | 0.712510i | \(0.252442\pi\) | ||||
−0.701661 | + | 0.712510i | \(0.747558\pi\) | |||||||
\(600\) | −4.27545e43 | − | 2.33251e43i | −0.151552 | − | 0.0826807i | ||||
\(601\) | 2.39574e44 | 0.826891 | 0.413446 | − | 0.910529i | \(-0.364325\pi\) | ||||
0.413446 | + | 0.910529i | \(0.364325\pi\) | |||||||
\(602\) | −1.87369e44 | + | 6.99113e43i | −0.629728 | + | 0.234965i | ||||
\(603\) | − | 2.67316e43i | − | 0.0874879i | ||||||
\(604\) | 7.79663e43 | + | 8.99330e43i | 0.248494 | + | 0.286634i | ||||
\(605\) | 2.49398e44 | 0.774119 | ||||||||
\(606\) | 2.79829e43 | + | 7.49967e43i | 0.0845923 | + | 0.226715i | ||||
\(607\) | − | 3.33012e44i | − | 0.980486i | −0.871586 | − | 0.490243i | \(-0.836908\pi\) | ||
0.871586 | − | 0.490243i | \(-0.163092\pi\) | |||||||
\(608\) | −5.25536e44 | + | 1.14664e44i | −1.50711 | + | 0.328828i | ||||
\(609\) | 4.49730e44 | 1.25625 | ||||||||
\(610\) | −1.42294e44 | + | 5.30930e43i | −0.387177 | + | 0.144464i | ||||
\(611\) | 3.53103e43i | 0.0935927i | ||||||||
\(612\) | 2.30482e43 | − | 1.99814e43i | 0.0595134 | − | 0.0515944i | ||||
\(613\) | −2.76813e44 | −0.696337 | −0.348169 | − | 0.937432i | \(-0.613196\pi\) | ||||
−0.348169 | + | 0.937432i | \(0.613196\pi\) | |||||||
\(614\) | −3.83120e43 | − | 1.02680e44i | −0.0938945 | − | 0.251646i | ||||
\(615\) | 8.79150e43i | 0.209924i | ||||||||
\(616\) | 5.38874e43 | − | 9.87745e43i | 0.125371 | − | 0.229802i | ||||
\(617\) | −2.34450e44 | −0.531481 | −0.265741 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265741 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(618\) | −1.63822e43 | + | 6.11256e42i | −0.0361874 | + | 0.0135023i | ||||
\(619\) | 7.46890e44i | 1.60771i | 0.594828 | + | 0.803853i | \(0.297220\pi\) | ||||
−0.594828 | + | 0.803853i | \(0.702780\pi\) | |||||||
\(620\) | 4.21078e44 | + | 4.85707e44i | 0.883273 | + | 1.01884i | ||||
\(621\) | 6.74078e44 | 1.37799 | ||||||||
\(622\) | −3.98911e43 | − | 1.06912e44i | −0.0794749 | − | 0.213000i | ||||
\(623\) | − | 6.17350e44i | − | 1.19873i | ||||||
\(624\) | −1.75399e44 | − | 2.51301e43i | −0.331951 | − | 0.0475598i | ||||
\(625\) | −4.36091e44 | −0.804447 | ||||||||
\(626\) | 7.05645e44 | − | 2.63291e44i | 1.26881 | − | 0.473421i | ||||
\(627\) | 3.53154e44i | 0.618989i | ||||||||
\(628\) | −2.77702e44 | + | 2.40751e44i | −0.474488 | + | 0.411352i | ||||
\(629\) | 5.89412e43 | 0.0981768 | ||||||||
\(630\) | 8.23169e42 | + | 2.20617e43i | 0.0133672 | + | 0.0358253i | ||||
\(631\) | − | 3.23311e44i | − | 0.511859i | −0.966695 | − | 0.255930i | \(-0.917619\pi\) | ||
0.966695 | − | 0.255930i | \(-0.0823815\pi\) | |||||||
\(632\) | −5.41455e44 | − | 2.95396e44i | −0.835775 | − | 0.455965i | ||||
\(633\) | −1.05321e45 | −1.58510 | ||||||||
\(634\) | 6.17775e44 | − | 2.30505e44i | 0.906572 | − | 0.338262i | ||||
\(635\) | − | 1.76984e44i | − | 0.253253i | ||||||
\(636\) | −8.23775e44 | − | 9.50212e44i | −1.14946 | − | 1.32589i | ||||
\(637\) | 1.31004e44 | 0.178260 | ||||||||
\(638\) | −1.85915e44 | − | 4.98269e44i | −0.246708 | − | 0.661200i | ||||
\(639\) | 4.25307e43i | 0.0550413i | ||||||||
\(640\) | 5.79078e44 | + | 4.32711e44i | 0.730899 | + | 0.546158i | ||||
\(641\) | −8.79742e44 | −1.08300 | −0.541498 | − | 0.840702i | \(-0.682143\pi\) | ||||
−0.541498 | + | 0.840702i | \(0.682143\pi\) | |||||||
\(642\) | 4.74421e44 | − | 1.77017e44i | 0.569644 | − | 0.212547i | ||||
\(643\) | − | 1.22266e45i | − | 1.43196i | −0.698123 | − | 0.715978i | \(-0.745981\pi\) | ||
0.698123 | − | 0.715978i | \(-0.254019\pi\) | |||||||
\(644\) | −6.34078e44 | + | 5.49706e44i | −0.724384 | + | 0.627996i | ||||
\(645\) | −8.43557e44 | −0.940068 | ||||||||
\(646\) | 6.26844e44 | + | 1.68000e45i | 0.681458 | + | 1.82637i | ||||
\(647\) | 1.76718e44i | 0.187419i | 0.995600 | + | 0.0937094i | \(0.0298724\pi\) | ||||
−0.995600 | + | 0.0937094i | \(0.970128\pi\) | |||||||
\(648\) | 4.89929e44 | − | 8.98031e44i | 0.506913 | − | 0.929161i | ||||
\(649\) | 3.68392e42 | 0.00371874 | ||||||||
\(650\) | 5.18414e43 | − | 1.93431e43i | 0.0510579 | − | 0.0190508i | ||||
\(651\) | 1.06580e45i | 1.02419i | ||||||||
\(652\) | 5.45815e44 | + | 6.29589e44i | 0.511780 | + | 0.590331i | ||||
\(653\) | 6.63007e44 | 0.606606 | 0.303303 | − | 0.952894i | \(-0.401910\pi\) | ||||
0.303303 | + | 0.952894i | \(0.401910\pi\) | |||||||
\(654\) | 5.69159e44 | + | 1.52540e45i | 0.508147 | + | 1.36188i | ||||
\(655\) | − | 8.06256e44i | − | 0.702445i | ||||||
\(656\) | −3.72352e43 | + | 2.59889e44i | −0.0316587 | + | 0.220967i | ||||
\(657\) | −3.22754e43 | −0.0267809 | ||||||||
\(658\) | 2.23777e44 | − | 8.34959e43i | 0.181218 | − | 0.0676162i | ||||
\(659\) | − | 1.59975e45i | − | 1.26440i | −0.774804 | − | 0.632202i | \(-0.782151\pi\) | ||
0.774804 | − | 0.632202i | \(-0.217849\pi\) | |||||||
\(660\) | 3.58608e44 | − | 3.10891e44i | 0.276641 | − | 0.239831i | ||||
\(661\) | 2.05812e45 | 1.54970 | 0.774850 | − | 0.632145i | \(-0.217825\pi\) | ||||
0.774850 | + | 0.632145i | \(0.217825\pi\) | |||||||
\(662\) | −1.08481e44 | − | 2.90740e44i | −0.0797309 | − | 0.213686i | ||||
\(663\) | 5.90680e44i | 0.423775i | ||||||||
\(664\) | 9.68045e44 | + | 5.28127e44i | 0.677964 | + | 0.369870i | ||||
\(665\) | −1.38421e45 | −0.946360 | ||||||||
\(666\) | −6.79712e42 | + | 2.53615e42i | −0.00453667 | + | 0.00169273i | ||||
\(667\) | 3.96647e45i | 2.58458i | ||||||||
\(668\) | −1.11879e45 | − | 1.29050e45i | −0.711745 | − | 0.820987i | ||||
\(669\) | 2.30412e45 | 1.43115 | ||||||||
\(670\) | −7.38250e44 | − | 1.97858e45i | −0.447720 | − | 1.19993i | ||||
\(671\) | 2.97777e44i | 0.176332i | ||||||||
\(672\) | 2.55495e44 | + | 1.17101e45i | 0.147732 | + | 0.677096i | ||||
\(673\) | −1.30868e45 | −0.738911 | −0.369455 | − | 0.929249i | \(-0.620456\pi\) | ||||
−0.369455 | + | 0.929249i | \(0.620456\pi\) | |||||||
\(674\) | −2.22871e45 | + | 8.31581e44i | −1.22884 | + | 0.458507i | ||||
\(675\) | 3.00642e44i | 0.161879i | ||||||||
\(676\) | −1.28481e45 | + | 1.11385e45i | −0.675604 | + | 0.585707i | ||||
\(677\) | 4.37637e44 | 0.224748 | 0.112374 | − | 0.993666i | \(-0.464155\pi\) | ||||
0.112374 | + | 0.993666i | \(0.464155\pi\) | |||||||
\(678\) | −7.40607e44 | − | 1.98489e45i | −0.371460 | − | 0.995548i | ||||
\(679\) | 6.47578e43i | 0.0317231i | ||||||||
\(680\) | 1.15412e45 | − | 2.11547e45i | 0.552214 | − | 1.01220i | ||||
\(681\) | −9.59539e44 | −0.448445 | ||||||||
\(682\) | 1.18083e45 | − | 4.40592e44i | 0.539058 | − | 0.201134i | ||||
\(683\) | − | 4.04925e45i | − | 1.80569i | −0.429963 | − | 0.902846i | \(-0.641474\pi\) | ||
0.429963 | − | 0.902846i | \(-0.358526\pi\) | |||||||
\(684\) | −1.44576e44 | − | 1.66766e44i | −0.0629793 | − | 0.0726457i | ||||
\(685\) | 7.29751e44 | 0.310546 | ||||||||
\(686\) | −8.75173e44 | − | 2.34554e45i | −0.363838 | − | 0.975119i | ||||
\(687\) | − | 1.74011e45i | − | 0.706755i | ||||||
\(688\) | −2.49368e45 | − | 3.57278e44i | −0.989521 | − | 0.141772i | ||||
\(689\) | 1.42875e45 | 0.553924 | ||||||||
\(690\) | −3.31641e45 | + | 1.23742e45i | −1.25627 | + | 0.468741i | ||||
\(691\) | − | 7.76543e44i | − | 0.287420i | −0.989620 | − | 0.143710i | \(-0.954097\pi\) | ||
0.989620 | − | 0.143710i | \(-0.0459032\pi\) | |||||||
\(692\) | −3.56711e44 | + | 3.09246e44i | −0.129009 | + | 0.111843i | ||||
\(693\) | 4.61682e43 | 0.0163159 | ||||||||
\(694\) | 5.15726e44 | + | 1.38219e45i | 0.178102 | + | 0.477328i | ||||
\(695\) | 4.61455e45i | 1.55730i | ||||||||
\(696\) | 4.97310e45 | + | 2.71312e45i | 1.64013 | + | 0.894791i | ||||
\(697\) | 8.75211e44 | 0.282090 | ||||||||
\(698\) | −2.32568e45 | + | 8.67761e44i | −0.732594 | + | 0.273346i | ||||
\(699\) | 6.83786e44i | 0.210516i | ||||||||
\(700\) | −2.45172e44 | − | 2.82802e44i | −0.0737737 | − | 0.0850969i | ||||
\(701\) | 1.30382e45 | 0.383467 | 0.191734 | − | 0.981447i | \(-0.438589\pi\) | ||||
0.191734 | + | 0.981447i | \(0.438589\pi\) | |||||||
\(702\) | 3.82365e44 | + | 1.02477e45i | 0.109922 | + | 0.294601i | ||||
\(703\) | − | 4.26471e44i | − | 0.119841i | ||||||
\(704\) | 1.19177e45 | − | 7.67154e44i | 0.327363 | − | 0.210727i | ||||
\(705\) | 1.00747e45 | 0.270524 | ||||||||
\(706\) | −2.99281e45 | + | 1.11668e45i | −0.785603 | + | 0.293126i | ||||
\(707\) | 6.15156e44i | 0.157861i | ||||||||
\(708\) | −2.96505e43 | + | 2.57051e43i | −0.00743874 | + | 0.00644893i | ||||
\(709\) | 6.95799e44 | 0.170665 | 0.0853324 | − | 0.996353i | \(-0.472805\pi\) | ||||
0.0853324 | + | 0.996353i | \(0.472805\pi\) | |||||||
\(710\) | 1.17457e45 | + | 3.14796e45i | 0.281674 | + | 0.754912i | ||||
\(711\) | − | 2.53081e44i | − | 0.0593399i | ||||||
\(712\) | 3.72433e45 | − | 6.82663e45i | 0.853825 | − | 1.56504i | ||||
\(713\) | −9.39997e45 | −2.10714 | ||||||||
\(714\) | 3.74339e45 | − | 1.39674e45i | 0.820529 | − | 0.306157i | ||||
\(715\) | 5.39209e44i | 0.115574i | ||||||||
\(716\) | 4.99086e45 | + | 5.75688e45i | 1.04609 | + | 1.20664i | ||||
\(717\) | 1.07644e45 | 0.220640 | ||||||||
\(718\) | −1.17287e45 | − | 3.14340e45i | −0.235103 | − | 0.630099i | ||||
\(719\) | − | 8.60509e44i | − | 0.168692i | −0.996437 | − | 0.0843458i | \(-0.973120\pi\) | ||
0.996437 | − | 0.0843458i | \(-0.0268800\pi\) | |||||||
\(720\) | −4.20675e43 | + | 2.93617e44i | −0.00806542 | + | 0.0562939i | ||||
\(721\) | −1.34374e44 | −0.0251972 | ||||||||
\(722\) | 7.04721e45 | − | 2.62946e45i | 1.29247 | − | 0.482250i | ||||
\(723\) | − | 8.48059e45i | − | 1.52129i | ||||||
\(724\) | 2.49810e44 | − | 2.16570e44i | 0.0438322 | − | 0.0379998i | ||||
\(725\) | −1.76906e45 | −0.303623 | ||||||||
\(726\) | 1.82086e45 | + | 4.88007e45i | 0.305697 | + | 0.819295i | ||||
\(727\) | 7.29693e45i | 1.19837i | 0.800612 | + | 0.599183i | \(0.204508\pi\) | ||||
−0.800612 | + | 0.599183i | \(0.795492\pi\) | |||||||
\(728\) | −1.19537e45 | − | 6.52147e44i | −0.192044 | − | 0.104772i | ||||
\(729\) | −5.91822e45 | −0.930145 | ||||||||
\(730\) | −2.38891e45 | + | 8.91352e44i | −0.367310 | + | 0.137051i | ||||
\(731\) | 8.39777e45i | 1.26324i | ||||||||
\(732\) | −2.07778e45 | − | 2.39669e45i | −0.305790 | − | 0.352724i | ||||
\(733\) | 1.38096e45 | 0.198846 | 0.0994228 | − | 0.995045i | \(-0.468300\pi\) | ||||
0.0994228 | + | 0.995045i | \(0.468300\pi\) | |||||||
\(734\) | 2.61132e45 | + | 6.99859e45i | 0.367895 | + | 0.985992i | ||||
\(735\) | − | 3.73780e45i | − | 0.515251i | ||||||
\(736\) | −1.03279e46 | + | 2.25338e45i | −1.39305 | + | 0.303941i | ||||
\(737\) | −4.14054e45 | −0.546484 | ||||||||
\(738\) | −1.00930e44 | + | 3.76590e43i | −0.0130352 | + | 0.00486370i | ||||
\(739\) | − | 1.34106e46i | − | 1.69487i | −0.530897 | − | 0.847437i | \(-0.678145\pi\) | ||
0.530897 | − | 0.847437i | \(-0.321855\pi\) | |||||||
\(740\) | −4.33057e44 | + | 3.75433e44i | −0.0535596 | + | 0.0464329i | ||||
\(741\) | 4.27388e45 | 0.517286 | ||||||||
\(742\) | −3.37848e45 | − | 9.05464e45i | −0.400184 | − | 1.07253i | ||||
\(743\) | − | 6.23466e45i | − | 0.722756i | −0.932419 | − | 0.361378i | \(-0.882306\pi\) | ||
0.932419 | − | 0.361378i | \(-0.117694\pi\) | |||||||
\(744\) | −6.42972e45 | + | 1.17855e46i | −0.729499 | + | 1.33716i | ||||
\(745\) | 7.80661e45 | 0.866886 | ||||||||
\(746\) | 1.20221e46 | − | 4.48569e45i | 1.30665 | − | 0.487538i | ||||
\(747\) | 4.52474e44i | 0.0481353i | ||||||||
\(748\) | −3.09498e45 | − | 3.57001e45i | −0.322279 | − | 0.371744i | ||||
\(749\) | 3.89141e45 | 0.396642 | ||||||||
\(750\) | −3.84685e45 | − | 1.03099e46i | −0.383817 | − | 1.02867i | ||||
\(751\) | 3.87283e45i | 0.378259i | 0.981952 | + | 0.189130i | \(0.0605666\pi\) | ||||
−0.981952 | + | 0.189130i | \(0.939433\pi\) | |||||||
\(752\) | 2.97823e45 | + | 4.26701e44i | 0.284755 | + | 0.0407979i | ||||
\(753\) | −1.77900e46 | −1.66516 | ||||||||
\(754\) | −6.03006e45 | + | 2.24995e45i | −0.552561 | + | 0.206172i | ||||
\(755\) | 3.85822e45i | 0.346127i | ||||||||
\(756\) | 5.59028e45 | − | 4.84643e45i | 0.491004 | − | 0.425670i | ||||
\(757\) | 8.44667e45 | 0.726359 | 0.363180 | − | 0.931719i | \(-0.381691\pi\) | ||||
0.363180 | + | 0.931719i | \(0.381691\pi\) | |||||||
\(758\) | −2.86767e44 | − | 7.68563e44i | −0.0241447 | − | 0.0647101i | ||||
\(759\) | 6.94020e45i | 0.572141i | ||||||||
\(760\) | −1.53066e46 | − | 8.35065e45i | −1.23555 | − | 0.674066i | ||||
\(761\) | 1.41451e46 | 1.11802 | 0.559012 | − | 0.829160i | \(-0.311181\pi\) | ||||
0.559012 | + | 0.829160i | \(0.311181\pi\) | |||||||
\(762\) | 3.46311e45 | − | 1.29216e45i | 0.268032 | − | 0.100009i | ||||
\(763\) | 1.25120e46i | 0.948273i | ||||||||
\(764\) | −5.05708e45 | − | 5.83326e45i | −0.375323 | − | 0.432930i | ||||
\(765\) | 9.88793e44 | 0.0718658 | ||||||||
\(766\) | 4.74904e45 | + | 1.27278e46i | 0.338022 | + | 0.905930i | ||||
\(767\) | − | 4.45830e43i | − | 0.00310773i | ||||||
\(768\) | −4.23916e45 | + | 1.44903e46i | −0.289401 | + | 0.989229i | ||||
\(769\) | 1.81104e46 | 1.21089 | 0.605447 | − | 0.795885i | \(-0.292994\pi\) | ||||
0.605447 | + | 0.795885i | \(0.292994\pi\) | |||||||
\(770\) | 3.41720e45 | − | 1.27503e45i | 0.223779 | − | 0.0834967i | ||||
\(771\) | 2.35297e46i | 1.50920i | ||||||||
\(772\) | 6.83030e45 | − | 5.92144e45i | 0.429104 | − | 0.372007i | ||||
\(773\) | 1.38738e46 | 0.853738 | 0.426869 | − | 0.904313i | \(-0.359616\pi\) | ||||
0.426869 | + | 0.904313i | \(0.359616\pi\) | |||||||
\(774\) | −3.61343e44 | − | 9.68433e44i | −0.0217803 | − | 0.0583733i | ||||
\(775\) | − | 4.19243e45i | − | 0.247536i | ||||||
\(776\) | −3.90669e44 | + | 7.16089e44i | −0.0225955 | + | 0.0414171i | ||||
\(777\) | −9.50266e44 | −0.0538405 | ||||||||
\(778\) | −1.24297e46 | + | 4.63779e45i | −0.689902 | + | 0.257417i | ||||
\(779\) | − | 6.33261e45i | − | 0.344337i | ||||||
\(780\) | −3.76241e45 | − | 4.33988e45i | −0.200425 | − | 0.231187i | ||||
\(781\) | 6.58770e45 | 0.343809 | ||||||||
\(782\) | 1.23188e46 | + | 3.30155e46i | 0.629883 | + | 1.68814i | ||||
\(783\) | − | 3.49699e46i | − | 1.75189i | ||||||
\(784\) | 1.58310e45 | − | 1.10495e46i | 0.0777053 | − | 0.542356i | ||||
\(785\) | −1.19137e46 | −0.572972 | ||||||||
\(786\) | 1.57763e46 | − | 5.88649e45i | 0.743439 | − | 0.277393i | ||||
\(787\) | 2.35867e46i | 1.08911i | 0.838726 | + | 0.544554i | \(0.183301\pi\) | ||||
−0.838726 | + | 0.544554i | \(0.816699\pi\) | |||||||
\(788\) | −3.58251e45 | + | 3.10581e45i | −0.162094 | + | 0.140526i | ||||
\(789\) | −4.01827e46 | −1.78159 | ||||||||
\(790\) | −6.98938e45 | − | 1.87322e46i | −0.303672 | − | 0.813869i | ||||
\(791\) | − | 1.62810e46i | − | 0.693197i | ||||||
\(792\) | 5.10526e44 | + | 2.78522e44i | 0.0213017 | + | 0.0116214i | ||||
\(793\) | 3.60371e45 | 0.147360 | ||||||||
\(794\) | −1.15753e45 | + | 4.31898e44i | −0.0463877 | + | 0.0173082i | ||||
\(795\) | − | 4.07651e46i | − | 1.60109i | ||||||
\(796\) | 2.38873e46 | + | 2.75536e46i | 0.919512 | + | 1.06064i | ||||
\(797\) | −4.29181e46 | −1.61923 | −0.809613 | − | 0.586964i | \(-0.800323\pi\) | ||||
−0.809613 | + | 0.586964i | \(0.800323\pi\) | |||||||
\(798\) | −1.01062e46 | − | 2.70854e46i | −0.373714 | − | 1.00159i | ||||
\(799\) | − | 1.00296e46i | − | 0.363524i | ||||||
\(800\) | −1.00502e45 | − | 4.60628e45i | −0.0357054 | − | 0.163648i | ||||
\(801\) | 3.19083e45 | 0.111118 | ||||||||
\(802\) | −4.87333e46 | + | 1.81834e46i | −1.66355 | + | 0.620706i | ||||
\(803\) | 4.99923e45i | 0.167284i | ||||||||
\(804\) | 3.33256e46 | − | 2.88912e46i | 1.09315 | − | 0.947697i | ||||
\(805\) | −2.72026e46 | −0.874736 | ||||||||
\(806\) | −5.33205e45 | − | 1.42904e46i | −0.168087 | − | 0.450488i | ||||
\(807\) | 3.51387e46i | 1.08595i | ||||||||
\(808\) | −3.71110e45 | + | 6.80237e45i | −0.112440 | + | 0.206100i | ||||
\(809\) | 1.17845e46 | 0.350054 | 0.175027 | − | 0.984564i | \(-0.443999\pi\) | ||||
0.175027 | + | 0.984564i | \(0.443999\pi\) | |||||||
\(810\) | 3.10682e46 | − | 1.15922e46i | 0.904808 | − | 0.337603i | ||||
\(811\) | 1.09029e46i | 0.311321i | 0.987811 | + | 0.155660i | \(0.0497505\pi\) | ||||
−0.987811 | + | 0.155660i | \(0.950249\pi\) | |||||||
\(812\) | 2.85178e46 | + | 3.28948e46i | 0.798397 | + | 0.920939i | ||||
\(813\) | −3.18130e46 | −0.873284 | ||||||||
\(814\) | 3.92832e44 | + | 1.05283e45i | 0.0105734 | + | 0.0283378i | ||||
\(815\) | 2.70100e46i | 0.712859i | ||||||||
\(816\) | 4.98205e46 | + | 7.13796e45i | 1.28933 | + | 0.184728i | ||||
\(817\) | 6.07623e46 | 1.54199 | ||||||||
\(818\) | −8.07062e45 | + | 3.01132e45i | −0.200842 | + | 0.0749384i | ||||
\(819\) | − | 5.58728e44i | − | 0.0136351i | ||||||
\(820\) | −6.43041e45 | + | 5.57476e45i | −0.153892 | + | 0.133415i | ||||
\(821\) | 2.63391e46 | 0.618173 | 0.309087 | − | 0.951034i | \(-0.399977\pi\) | ||||
0.309087 | + | 0.951034i | \(0.399977\pi\) | |||||||
\(822\) | 5.32792e45 | + | 1.42793e46i | 0.122633 | + | 0.328669i | ||||
\(823\) | − | 1.90934e46i | − | 0.431007i | −0.976503 | − | 0.215504i | \(-0.930861\pi\) | ||
0.976503 | − | 0.215504i | \(-0.0691393\pi\) | |||||||
\(824\) | −1.48590e45 | − | 8.10650e44i | −0.0328969 | − | 0.0179473i | ||||
\(825\) | −3.09536e45 | −0.0672122 | ||||||||
\(826\) | −2.82542e44 | + | 1.05422e44i | −0.00601730 | + | 0.00224518i | ||||
\(827\) | − | 2.78507e46i | − | 0.581766i | −0.956759 | − | 0.290883i | \(-0.906051\pi\) | ||
0.956759 | − | 0.290883i | \(-0.0939490\pi\) | |||||||
\(828\) | −2.84121e45 | − | 3.27729e45i | −0.0582127 | − | 0.0671475i | ||||
\(829\) | −1.97696e46 | −0.397306 | −0.198653 | − | 0.980070i | \(-0.563657\pi\) | ||||
−0.198653 | + | 0.980070i | \(0.563657\pi\) | |||||||
\(830\) | 1.24960e46 | + | 3.34905e46i | 0.246333 | + | 0.660194i | ||||
\(831\) | 4.74762e46i | 0.918036i | ||||||||
\(832\) | −9.28411e45 | − | 1.44228e46i | −0.176103 | − | 0.273575i | ||||
\(833\) | −3.72105e46 | −0.692382 | ||||||||
\(834\) | −9.02946e46 | + | 3.36909e46i | −1.64818 | + | 0.614972i | ||||
\(835\) | − | 5.53640e46i | − | 0.991389i | ||||||
\(836\) | −2.58309e46 | + | 2.23938e46i | −0.453773 | + | 0.393393i | ||||
\(837\) | 8.28738e46 | 1.42827 | ||||||||
\(838\) | −1.60639e46 | − | 4.30527e46i | −0.271610 | − | 0.727940i | ||||
\(839\) | − | 7.36571e45i | − | 0.122187i | −0.998132 | − | 0.0610933i | \(-0.980541\pi\) | ||
0.998132 | − | 0.0610933i | \(-0.0194587\pi\) | |||||||
\(840\) | −1.86070e46 | + | 3.41063e46i | −0.302836 | + | 0.555093i | ||||
\(841\) | 1.43150e47 | 2.28589 | ||||||||
\(842\) | 5.25608e46 | − | 1.96116e46i | 0.823509 | − | 0.307269i | ||||
\(843\) | 4.36564e46i | 0.671131i | ||||||||
\(844\) | −6.67850e46 | − | 7.70355e46i | −1.00739 | − | 1.16201i | ||||
\(845\) | −5.51198e46 | −0.815831 | ||||||||
\(846\) | 4.31557e44 | + | 1.15661e45i | 0.00626776 | + | 0.0167982i | ||||
\(847\) | 4.00285e46i | 0.570472i | ||||||||
\(848\) | 1.72655e46 | − | 1.20507e47i | 0.241461 | − | 1.68531i | ||||
\(849\) | 3.98558e46 | 0.546976 | ||||||||
\(850\) | −1.47251e46 | + | 5.49423e45i | −0.198314 | + | 0.0739953i | ||||
\(851\) | − | 8.38102e45i | − | 0.110771i | ||||||
\(852\) | −5.30219e46 | + | 4.59667e46i | −0.687735 | + | 0.596224i | ||||
\(853\) | −8.98888e46 | −1.14425 | −0.572125 | − | 0.820166i | \(-0.693881\pi\) | ||||
−0.572125 | + | 0.820166i | \(0.693881\pi\) | |||||||
\(854\) | −8.52144e45 | − | 2.28383e46i | −0.106460 | − | 0.285323i | ||||
\(855\) | − | 7.15444e45i | − | 0.0877238i | ||||||
\(856\) | 4.30311e46 | + | 2.34760e46i | 0.517848 | + | 0.282517i | ||||
\(857\) | −8.55308e45 | −0.101025 | −0.0505126 | − | 0.998723i | \(-0.516085\pi\) | ||||
−0.0505126 | + | 0.998723i | \(0.516085\pi\) | |||||||
\(858\) | −1.05509e46 | + | 3.93677e45i | −0.122319 | + | 0.0456398i | ||||
\(859\) | 4.31181e46i | 0.490647i | 0.969441 | + | 0.245323i | \(0.0788942\pi\) | ||||
−0.969441 | + | 0.245323i | \(0.921106\pi\) | |||||||
\(860\) | −5.34907e46 | − | 6.17007e46i | −0.597452 | − | 0.689151i | ||||
\(861\) | −1.41104e46 | −0.154699 | ||||||||
\(862\) | −1.21202e46 | − | 3.24833e46i | −0.130435 | − | 0.349578i | ||||
\(863\) | − | 2.29879e45i | − | 0.0242843i | −0.999926 | − | 0.0121422i | \(-0.996135\pi\) | ||
0.999926 | − | 0.0121422i | \(-0.00386507\pi\) | |||||||
\(864\) | 9.10545e46 | − | 1.98667e46i | 0.944238 | − | 0.206018i | ||||
\(865\) | −1.53033e46 | −0.155785 | ||||||||
\(866\) | −1.27405e46 | + | 4.75377e45i | −0.127322 | + | 0.0475064i | ||||
\(867\) | − | 6.27176e46i | − | 0.615296i | ||||||
\(868\) | −7.79561e46 | + | 6.75831e46i | −0.750817 | + | 0.650912i | ||||
\(869\) | −3.92005e46 | −0.370660 | ||||||||
\(870\) | 6.41953e46 | + | 1.72049e47i | 0.595930 | + | 1.59715i | ||||
\(871\) | 5.01089e46i | 0.456693i | ||||||||
\(872\) | −7.54820e46 | + | 1.38357e47i | −0.675429 | + | 1.23805i | ||||
\(873\) | −3.34707e44 | −0.00294061 | ||||||||
\(874\) | 2.38884e47 | − | 8.91328e46i | 2.06065 | − | 0.768873i | ||||
\(875\) | − | 8.45663e46i | − | 0.716257i | ||||||
\(876\) | −3.48829e46 | − | 4.02369e46i | −0.290099 | − | 0.334625i | ||||
\(877\) | 1.35870e46 | 0.110951 | 0.0554753 | − | 0.998460i | \(-0.482333\pi\) | ||||
0.0554753 | + | 0.998460i | \(0.482333\pi\) | |||||||
\(878\) | −6.55105e46 | − | 1.75574e47i | −0.525289 | − | 1.40782i | ||||
\(879\) | 1.45103e46i | 0.114249i | ||||||||
\(880\) | 4.54792e46 | + | 6.51597e45i | 0.351634 | + | 0.0503798i | ||||
\(881\) | −1.55064e45 | −0.0117733 | −0.00588663 | − | 0.999983i | \(-0.501874\pi\) | ||||
−0.00588663 | + | 0.999983i | \(0.501874\pi\) | |||||||
\(882\) | 4.29113e45 | − | 1.60111e45i | 0.0319944 | − | 0.0119378i | ||||
\(883\) | − | 1.25584e46i | − | 0.0919523i | −0.998943 | − | 0.0459761i | \(-0.985360\pi\) | ||
0.998943 | − | 0.0459761i | \(-0.0146398\pi\) | |||||||
\(884\) | −4.32043e46 | + | 3.74555e46i | −0.310664 | + | 0.269327i | ||||
\(885\) | −1.27204e45 | −0.00898271 | ||||||||
\(886\) | 5.07639e46 | + | 1.36052e47i | 0.352059 | + | 0.943550i | ||||
\(887\) | − | 2.45267e47i | − | 1.67056i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) | ||
0.549825 | − | 0.835280i | \(-0.314694\pi\) | |||||||
\(888\) | −1.05080e46 | − | 5.73275e45i | −0.0702931 | − | 0.0383491i | ||||
\(889\) | 2.84059e46 | 0.186630 | ||||||||
\(890\) | 2.36174e47 | − | 8.81215e46i | 1.52402 | − | 0.568646i | ||||
\(891\) | − | 6.50161e46i | − | 0.412076i | ||||||
\(892\) | 1.46106e47 | + | 1.68531e47i | 0.909558 | + | 1.04916i | ||||
\(893\) | −7.25691e46 | −0.443740 | ||||||||
\(894\) | 5.69961e46 | + | 1.52755e47i | 0.342330 | + | 0.917476i | ||||
\(895\) | 2.46976e47i | 1.45709i | ||||||||
\(896\) | −6.94502e46 | + | 9.29422e46i | −0.402481 | + | 0.538623i | ||||
\(897\) | 8.39905e46 | 0.478135 | ||||||||
\(898\) | −5.33950e45 | + | 1.99228e45i | −0.0298593 | + | 0.0111411i | ||||
\(899\) | 4.87653e47i | 2.67890i | ||||||||
\(900\) | 1.46169e45 | − | 1.26719e45i | 0.00788814 | − | 0.00683853i | ||||
\(901\) | −4.05824e47 | −2.15150 | ||||||||
\(902\) | 5.83311e45 | + | 1.56333e46i | 0.0303806 | + | 0.0814227i | ||||
\(903\) | − | 1.35391e47i | − | 0.692766i | ||||||
\(904\) | 9.82195e46 | − | 1.80034e47i | 0.493745 | − | 0.905025i | ||||
\(905\) | 1.07171e46 | 0.0529299 | ||||||||
\(906\) | −7.54953e46 | + | 2.81689e46i | −0.366327 | + | 0.136684i | ||||
\(907\) | − | 2.67546e47i | − | 1.27550i | −0.770242 | − | 0.637752i | \(-0.779864\pi\) | ||
0.770242 | − | 0.637752i | \(-0.220136\pi\) | |||||||
\(908\) | −6.08451e46 | − | 7.01840e46i | −0.285005 | − | 0.328749i | ||||
\(909\) | −3.17949e45 | −0.0146331 | ||||||||
\(910\) | −1.54305e46 | − | 4.13551e46i | −0.0697777 | − | 0.187011i | ||||
\(911\) | 6.22236e46i | 0.276478i | 0.990399 | + | 0.138239i | \(0.0441443\pi\) | ||||
−0.990399 | + | 0.138239i | \(0.955856\pi\) | |||||||
\(912\) | 5.16469e46 | − | 3.60478e47i | 0.225490 | − | 1.57384i | ||||
\(913\) | 7.00850e46 | 0.300672 | ||||||||
\(914\) | −2.78949e47 | + | 1.04082e47i | −1.17594 | + | 0.438768i | ||||
\(915\) | − | 1.02821e47i | − | 0.425934i | ||||||
\(916\) | 1.27278e47 | − | 1.10342e47i | 0.518113 | − | 0.449172i | ||||
\(917\) | 1.29404e47 | 0.517654 | ||||||||
\(918\) | −1.08607e47 | − | 2.91077e47i | −0.426949 | − | 1.14426i | ||||
\(919\) | − | 2.14141e47i | − | 0.827278i | −0.910441 | − | 0.413639i | \(-0.864258\pi\) | ||
0.910441 | − | 0.413639i | \(-0.135742\pi\) | |||||||
\(920\) | −3.00806e47 | − | 1.64107e47i | −1.14204 | − | 0.623050i | ||||
\(921\) | 7.41954e46 | 0.276836 | ||||||||
\(922\) | −2.56683e47 | + | 9.57740e46i | −0.941245 | + | 0.351199i | ||||
\(923\) | − | 7.97245e46i | − | 0.287319i | ||||||
\(924\) | 4.98980e46 | + | 5.75566e46i | 0.176739 | + | 0.203866i | ||||
\(925\) | 3.73798e45 | 0.0130127 | ||||||||
\(926\) | −3.60812e46 | − | 9.67010e46i | −0.123454 | − | 0.330868i | ||||
\(927\) | − | 6.94526e44i | − | 0.00233568i | ||||||
\(928\) | 1.16901e47 | + | 5.35791e47i | 0.386413 | + | 1.77104i | ||||
\(929\) | 3.58125e47 | 1.16354 | 0.581772 | − | 0.813352i | \(-0.302360\pi\) | ||||
0.581772 | + | 0.813352i | \(0.302360\pi\) | |||||||
\(930\) | −4.07732e47 | + | 1.52134e47i | −1.30211 | + | 0.485845i | ||||
\(931\) | 2.69238e47i | 0.845164i | ||||||||
\(932\) | −5.00145e46 | + | 4.33595e46i | −0.154327 | + | 0.133792i | ||||
\(933\) | 7.72537e46 | 0.234322 | ||||||||
\(934\) | 7.38719e46 | + | 1.97983e47i | 0.220257 | + | 0.590308i | ||||
\(935\) | − | 1.53157e47i | − | 0.448902i | ||||||
\(936\) | 3.37068e45 | − | 6.17839e45i | 0.00971191 | − | 0.0178017i | ||||
\(937\) | −1.81846e47 | −0.515074 | −0.257537 | − | 0.966268i | \(-0.582911\pi\) | ||||
−0.257537 | + | 0.966268i | \(0.582911\pi\) | |||||||
\(938\) | 3.17562e47 | − | 1.18489e47i | 0.884267 | − | 0.329939i | ||||
\(939\) | 5.09893e47i | 1.39582i | ||||||||
\(940\) | 6.38845e46 | + | 7.36898e46i | 0.171929 | + | 0.198318i | ||||
\(941\) | 3.72510e47 | 0.985607 | 0.492803 | − | 0.870141i | \(-0.335972\pi\) | ||||
0.492803 | + | 0.870141i | \(0.335972\pi\) | |||||||
\(942\) | −8.69823e46 | − | 2.33121e47i | −0.226265 | − | 0.606410i | ||||
\(943\) | − | 1.24449e47i | − | 0.318276i | ||||||
\(944\) | −3.76032e45 | − | 5.38755e44i | −0.00945526 | − | 0.00135469i | ||||
\(945\) | 2.39829e47 | 0.592916 | ||||||||
\(946\) | −1.50004e47 | + | 5.59696e46i | −0.364622 | + | 0.136048i | ||||
\(947\) | 2.05570e47i | 0.491316i | 0.969357 | + | 0.245658i | \(0.0790040\pi\) | ||||
−0.969357 | + | 0.245658i | \(0.920996\pi\) | |||||||
\(948\) | 3.15510e47 | − | 2.73528e47i | 0.741447 | − | 0.642788i | ||||
\(949\) | 6.05008e46 | 0.139798 | ||||||||
\(950\) | 3.97537e46 | + | 1.06543e47i | 0.0903232 | + | 0.242075i | ||||
\(951\) | 4.46399e47i | 0.997322i | ||||||||
\(952\) | 3.39534e47 | + | 1.85236e47i | 0.745920 | + | 0.406944i | ||||
\(953\) | −9.72774e46 | −0.210148 | −0.105074 | − | 0.994464i | \(-0.533508\pi\) | ||||
−0.105074 | + | 0.994464i | \(0.533508\pi\) | |||||||
\(954\) | 4.67998e46 | − | 1.74620e46i | 0.0994191 | − | 0.0370954i | ||||
\(955\) | − | 2.50253e47i | − | 0.522788i | ||||||
\(956\) | 6.82582e46 | + | 7.87348e46i | 0.140226 | + | 0.161749i | ||||
\(957\) | 3.60045e47 | 0.727387 | ||||||||
\(958\) | −1.42478e47 | − | 3.81855e47i | −0.283075 | − | 0.758666i | ||||
\(959\) | 1.17125e47i | 0.228851i | ||||||||
\(960\) | −4.11511e47 | + | 2.64894e47i | −0.790754 | + | 0.509016i | ||||
\(961\) | −6.26524e47 | −1.18403 | ||||||||
\(962\) | 1.27413e46 | − | 4.75407e45i | 0.0236817 | − | 0.00883617i | ||||
\(963\) | 2.01131e46i | 0.0367671i | ||||||||
\(964\) | 6.20299e47 | − | 5.37761e47i | 1.11524 | − | 0.966845i | ||||
\(965\) | 2.93027e47 | 0.518168 | ||||||||
\(966\) | −1.98607e47 | − | 5.32284e47i | −0.345430 | − | 0.925784i | ||||
\(967\) | − | 4.63298e47i | − | 0.792568i | −0.918128 | − | 0.396284i | \(-0.870300\pi\) | ||
0.918128 | − | 0.396284i | \(-0.129700\pi\) | |||||||
\(968\) | −2.41483e47 | + | 4.42633e47i | −0.406332 | + | 0.744798i | ||||
\(969\) | −1.21395e48 | −2.00919 | ||||||||
\(970\) | −2.47738e46 | + | 9.24364e45i | −0.0403315 | + | 0.0150486i | ||||
\(971\) | − | 8.04985e47i | − | 1.28908i | −0.764570 | − | 0.644540i | \(-0.777049\pi\) | ||
0.764570 | − | 0.644540i | \(-0.222951\pi\) | |||||||
\(972\) | 5.17635e46 | + | 5.97084e46i | 0.0815386 | + | 0.0940536i | ||||
\(973\) | −7.40636e47 | −1.14762 | ||||||||
\(974\) | 4.39869e47 | + | 1.17889e48i | 0.670472 | + | 1.79693i | ||||
\(975\) | 3.74602e46i | 0.0561689i | ||||||||
\(976\) | 4.35483e46 | − | 3.03952e47i | 0.0642354 | − | 0.448341i | ||||
\(977\) | −4.45450e47 | −0.646377 | −0.323189 | − | 0.946335i | \(-0.604755\pi\) | ||||
−0.323189 | + | 0.946335i | \(0.604755\pi\) | |||||||
\(978\) | −5.28516e47 | + | 1.97201e47i | −0.754460 | + | 0.281505i | ||||
\(979\) | − | 4.94237e47i | − | 0.694085i | ||||||
\(980\) | 2.73396e47 | − | 2.37017e47i | 0.377724 | − | 0.327463i | ||||
\(981\) | −6.46694e46 | −0.0879012 | ||||||||
\(982\) | 1.09613e47 | + | 2.93773e47i | 0.146581 | + | 0.392851i | ||||
\(983\) | 1.72322e47i | 0.226718i | 0.993554 | + | 0.113359i | \(0.0361610\pi\) | ||||
−0.993554 | + | 0.113359i | \(0.963839\pi\) | |||||||
\(984\) | −1.56032e47 | − | 8.51248e46i | −0.201972 | − | 0.110188i | ||||
\(985\) | −1.53694e47 | −0.195738 | ||||||||
\(986\) | 1.71278e48 | − | 6.39076e47i | 2.14621 | − | 0.800796i | ||||
\(987\) | 1.61699e47i | 0.199358i | ||||||||
\(988\) | 2.71010e47 | + | 3.12606e47i | 0.328756 | + | 0.379216i | ||||
\(989\) | 1.19410e48 | 1.42528 | ||||||||
\(990\) | 6.59012e45 | + | 1.76621e46i | 0.00773981 | + | 0.0207434i | ||||
\(991\) | − | 1.30834e48i | − | 1.51197i | −0.654591 | − | 0.755983i | \(-0.727159\pi\) | ||
0.654591 | − | 0.755983i | \(-0.272841\pi\) | |||||||
\(992\) | −1.26975e48 | + | 2.77039e47i | −1.44388 | + | 0.315032i | ||||
\(993\) | 2.10086e47 | 0.235077 | ||||||||
\(994\) | −5.05249e47 | + | 1.88519e47i | −0.556318 | + | 0.207574i | ||||
\(995\) | 1.18208e48i | 1.28079i | ||||||||
\(996\) | −5.64087e47 | + | 4.89029e47i | −0.601446 | + | 0.521417i | ||||
\(997\) | −8.48188e47 | −0.889958 | −0.444979 | − | 0.895541i | \(-0.646789\pi\) | ||||
−0.444979 | + | 0.895541i | \(0.646789\pi\) | |||||||
\(998\) | 3.51264e47 | + | 9.41419e47i | 0.362698 | + | 0.972063i | ||||
\(999\) | 7.38904e46i | 0.0750828i |
(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 | 4.33.b.b.3.2 | yes | 14 | |
3.2 | odd | 2 | 36.33.d.b.19.13 | 14 | |||
4.3 | odd | 2 | inner | 4.33.b.b.3.1 | ✓ | 14 | |
12.11 | even | 2 | 36.33.d.b.19.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.33.b.b.3.1 | ✓ | 14 | 4.3 | odd | 2 | inner | |
4.33.b.b.3.2 | yes | 14 | 1.1 | even | 1 | trivial | |
36.33.d.b.19.13 | 14 | 3.2 | odd | 2 | |||
36.33.d.b.19.14 | 14 | 12.11 | even | 2 |