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 | 3.4 | ||
Root | \(2.55660e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.33.b.b.3.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −56022.2 | + | 34007.1i | −0.854830 | + | 0.518908i | ||||
\(3\) | 4.09055e7i | 0.950259i | 0.879916 | + | 0.475130i | \(0.157599\pi\) | ||||
−0.879916 | + | 0.475130i | \(0.842401\pi\) | |||||||
\(4\) | 1.98200e9 | − | 3.81031e9i | 0.461470 | − | 0.887156i | ||||
\(5\) | −2.17196e11 | −1.42342 | −0.711709 | − | 0.702475i | \(-0.752078\pi\) | ||||
−0.711709 | + | 0.702475i | \(0.752078\pi\) | |||||||
\(6\) | −1.39108e12 | − | 2.29162e12i | −0.493097 | − | 0.812310i | ||||
\(7\) | 2.81808e12i | 0.0847977i | 0.999101 | + | 0.0423988i | \(0.0135000\pi\) | ||||
−0.999101 | + | 0.0423988i | \(0.986500\pi\) | |||||||
\(8\) | 1.85418e13 | + | 2.80864e14i | 0.0658738 | + | 0.997828i | ||||
\(9\) | 1.79757e14 | 0.0970076 | ||||||||
\(10\) | 1.21678e16 | − | 7.38622e15i | 1.21678 | − | 0.738622i | ||||
\(11\) | − | 6.95526e16i | − | 1.51367i | −0.653607 | − | 0.756834i | \(-0.726745\pi\) | ||
0.653607 | − | 0.756834i | \(-0.273255\pi\) | |||||||
\(12\) | 1.55863e17 | + | 8.10747e16i | 0.843028 | + | 0.438516i | ||||
\(13\) | −7.08184e17 | −1.06427 | −0.532136 | − | 0.846659i | \(-0.678610\pi\) | ||||
−0.532136 | + | 0.846659i | \(0.678610\pi\) | |||||||
\(14\) | −9.58347e16 | − | 1.57875e17i | −0.0440022 | − | 0.0724876i | ||||
\(15\) | − | 8.88453e18i | − | 1.35262i | ||||||
\(16\) | −1.05901e19 | − | 1.51040e19i | −0.574091 | − | 0.818791i | ||||
\(17\) | 6.55998e19 | 1.34809 | 0.674046 | − | 0.738689i | \(-0.264555\pi\) | ||||
0.674046 | + | 0.738689i | \(0.264555\pi\) | |||||||
\(18\) | −1.00704e19 | + | 6.11302e18i | −0.0829251 | + | 0.0503380i | ||||
\(19\) | − | 1.83995e20i | − | 0.637894i | −0.947773 | − | 0.318947i | \(-0.896671\pi\) | ||
0.947773 | − | 0.318947i | \(-0.103329\pi\) | |||||||
\(20\) | −4.30482e20 | + | 8.27584e20i | −0.656864 | + | 1.26279i | ||||
\(21\) | −1.15275e20 | −0.0805798 | ||||||||
\(22\) | 2.36528e21 | + | 3.89649e21i | 0.785454 | + | 1.29393i | ||||
\(23\) | 7.92873e20i | 0.129288i | 0.997908 | + | 0.0646440i | \(0.0205912\pi\) | ||||
−0.997908 | + | 0.0646440i | \(0.979409\pi\) | |||||||
\(24\) | −1.14889e22 | + | 7.58463e20i | −0.948195 | + | 0.0625972i | ||||
\(25\) | 2.38911e22 | 1.02612 | ||||||||
\(26\) | 3.96740e22 | − | 2.40833e22i | 0.909771 | − | 0.552259i | ||||
\(27\) | 8.31519e22i | 1.04244i | ||||||||
\(28\) | 1.07377e22 | + | 5.58542e21i | 0.0752288 | + | 0.0391316i | ||||
\(29\) | −1.45523e23 | −0.581519 | −0.290760 | − | 0.956796i | \(-0.593908\pi\) | ||||
−0.290760 | + | 0.956796i | \(0.593908\pi\) | |||||||
\(30\) | 3.02137e23 | + | 4.97731e23i | 0.701882 | + | 1.15626i | ||||
\(31\) | 1.34887e24i | 1.85431i | 0.374673 | + | 0.927157i | \(0.377755\pi\) | ||||
−0.374673 | + | 0.927157i | \(0.622245\pi\) | |||||||
\(32\) | 1.10693e24 | + | 4.86021e23i | 0.915628 | + | 0.402027i | ||||
\(33\) | 2.84509e24 | 1.43838 | ||||||||
\(34\) | −3.67504e24 | + | 2.23086e24i | −1.15239 | + | 0.699535i | ||||
\(35\) | − | 6.12075e23i | − | 0.120702i | ||||||
\(36\) | 3.56278e23 | − | 6.84930e23i | 0.0447661 | − | 0.0860609i | ||||
\(37\) | −2.62567e24 | −0.212820 | −0.106410 | − | 0.994322i | \(-0.533936\pi\) | ||||
−0.106410 | + | 0.994322i | \(0.533936\pi\) | |||||||
\(38\) | 6.25715e24 | + | 1.03078e25i | 0.331008 | + | 0.545291i | ||||
\(39\) | − | 2.89686e25i | − | 1.01133i | ||||||
\(40\) | −4.02721e24 | − | 6.10025e25i | −0.0937659 | − | 1.42033i | ||||
\(41\) | −1.80745e25 | −0.283481 | −0.141740 | − | 0.989904i | \(-0.545270\pi\) | ||||
−0.141740 | + | 0.989904i | \(0.545270\pi\) | |||||||
\(42\) | 6.45795e24 | − | 3.92017e24i | 0.0688820 | − | 0.0418135i | ||||
\(43\) | 1.56149e26i | 1.14300i | 0.820603 | + | 0.571498i | \(0.193638\pi\) | ||||
−0.820603 | + | 0.571498i | \(0.806362\pi\) | |||||||
\(44\) | −2.65017e26 | − | 1.37853e26i | −1.34286 | − | 0.698512i | ||||
\(45\) | −3.90426e25 | −0.138082 | ||||||||
\(46\) | −2.69633e25 | − | 4.44185e25i | −0.0670885 | − | 0.110519i | ||||
\(47\) | − | 8.64218e26i | − | 1.52425i | −0.647427 | − | 0.762127i | \(-0.724155\pi\) | ||
0.647427 | − | 0.762127i | \(-0.275845\pi\) | |||||||
\(48\) | 6.17839e26 | − | 4.33194e26i | 0.778064 | − | 0.545536i | ||||
\(49\) | 1.09649e27 | 0.992809 | ||||||||
\(50\) | −1.33843e27 | + | 8.12470e26i | −0.877156 | + | 0.532460i | ||||
\(51\) | 2.68339e27i | 1.28104i | ||||||||
\(52\) | −1.40362e27 | + | 2.69840e27i | −0.491129 | + | 0.944175i | ||||
\(53\) | 5.50243e27 | 1.41952 | 0.709759 | − | 0.704444i | \(-0.248804\pi\) | ||||
0.709759 | + | 0.704444i | \(0.248804\pi\) | |||||||
\(54\) | −2.82776e27 | − | 4.65835e27i | −0.540931 | − | 0.891111i | ||||
\(55\) | 1.51066e28i | 2.15458i | ||||||||
\(56\) | −7.91495e26 | + | 5.22522e25i | −0.0846135 | + | 0.00558594i | ||||
\(57\) | 7.52642e27 | 0.606165 | ||||||||
\(58\) | 8.15252e27 | − | 4.94882e27i | 0.497100 | − | 0.301755i | ||||
\(59\) | − | 9.48554e27i | − | 0.439977i | −0.975502 | − | 0.219988i | \(-0.929398\pi\) | ||
0.975502 | − | 0.219988i | \(-0.0706020\pi\) | |||||||
\(60\) | −3.38528e28 | − | 1.76091e28i | −1.19998 | − | 0.624191i | ||||
\(61\) | 3.04221e28 | 0.827774 | 0.413887 | − | 0.910328i | \(-0.364171\pi\) | ||||
0.413887 | + | 0.910328i | \(0.364171\pi\) | |||||||
\(62\) | −4.58712e28 | − | 7.55666e28i | −0.962218 | − | 1.58512i | ||||
\(63\) | 5.06569e26i | 0.00822602i | ||||||||
\(64\) | −7.85406e28 | + | 1.04154e28i | −0.991321 | + | 0.131461i | ||||
\(65\) | 1.53815e29 | 1.51490 | ||||||||
\(66\) | −1.59388e29 | + | 9.67532e28i | −1.22957 | + | 0.746384i | ||||
\(67\) | 7.40203e28i | 0.448905i | 0.974485 | + | 0.224452i | \(0.0720593\pi\) | ||||
−0.974485 | + | 0.224452i | \(0.927941\pi\) | |||||||
\(68\) | 1.30019e29 | − | 2.49955e29i | 0.622103 | − | 1.19597i | ||||
\(69\) | −3.24329e28 | −0.122857 | ||||||||
\(70\) | 2.08149e28 | + | 3.42898e28i | 0.0626334 | + | 0.103180i | ||||
\(71\) | 2.60149e29i | 0.623863i | 0.950105 | + | 0.311932i | \(0.100976\pi\) | ||||
−0.950105 | + | 0.311932i | \(0.899024\pi\) | |||||||
\(72\) | 3.33302e27 | + | 5.04872e28i | 0.00639026 | + | 0.0967969i | ||||
\(73\) | 3.70906e29 | 0.570293 | 0.285147 | − | 0.958484i | \(-0.407958\pi\) | ||||
0.285147 | + | 0.958484i | \(0.407958\pi\) | |||||||
\(74\) | 1.47095e29 | − | 8.92914e28i | 0.181925 | − | 0.110434i | ||||
\(75\) | 9.77280e29i | 0.975077i | ||||||||
\(76\) | −7.01078e29 | − | 3.64678e29i | −0.565912 | − | 0.294369i | ||||
\(77\) | 1.96004e29 | 0.128355 | ||||||||
\(78\) | 9.85140e29 | + | 1.62289e30i | 0.524789 | + | 0.864519i | ||||
\(79\) | − | 2.10671e30i | − | 0.915317i | −0.889128 | − | 0.457659i | \(-0.848688\pi\) | ||
0.889128 | − | 0.457659i | \(-0.151312\pi\) | |||||||
\(80\) | 2.30013e30 | + | 3.28054e30i | 0.817172 | + | 1.16548i | ||||
\(81\) | −3.06828e30 | −0.893582 | ||||||||
\(82\) | 1.01257e30 | − | 6.14660e29i | 0.242328 | − | 0.147100i | ||||
\(83\) | − | 6.24724e30i | − | 1.23151i | −0.787937 | − | 0.615756i | \(-0.788851\pi\) | ||
0.787937 | − | 0.615756i | \(-0.211149\pi\) | |||||||
\(84\) | −2.28475e29 | + | 4.39233e29i | −0.0371851 | + | 0.0714868i | ||||
\(85\) | −1.42480e31 | −1.91890 | ||||||||
\(86\) | −5.31019e30 | − | 8.74783e30i | −0.593110 | − | 0.977068i | ||||
\(87\) | − | 5.95270e30i | − | 0.552594i | ||||||
\(88\) | 1.95348e31 | − | 1.28963e30i | 1.51038 | − | 0.0997110i | ||||
\(89\) | 1.03445e31 | 0.667526 | 0.333763 | − | 0.942657i | \(-0.391682\pi\) | ||||
0.333763 | + | 0.942657i | \(0.391682\pi\) | |||||||
\(90\) | 2.18725e30 | − | 1.32773e30i | 0.118037 | − | 0.0716520i | ||||
\(91\) | − | 1.99572e30i | − | 0.0902477i | ||||||
\(92\) | 3.02109e30 | + | 1.57147e30i | 0.114699 | + | 0.0596625i | ||||
\(93\) | −5.51763e31 | −1.76208 | ||||||||
\(94\) | 2.93896e31 | + | 4.84153e31i | 0.790947 | + | 1.30298i | ||||
\(95\) | 3.99630e31i | 0.907990i | ||||||||
\(96\) | −1.98809e31 | + | 4.52794e31i | −0.382030 | + | 0.870084i | ||||
\(97\) | 1.05656e32 | 1.72007 | 0.860036 | − | 0.510233i | \(-0.170441\pi\) | ||||
0.860036 | + | 0.510233i | \(0.170441\pi\) | |||||||
\(98\) | −6.14275e31 | + | 3.72883e31i | −0.848684 | + | 0.515176i | ||||
\(99\) | − | 1.25026e31i | − | 0.146837i | ||||||
\(100\) | 4.73522e31 | − | 9.10326e31i | 0.473522 | − | 0.910326i | ||||
\(101\) | 9.75597e31 | 0.832010 | 0.416005 | − | 0.909362i | \(-0.363430\pi\) | ||||
0.416005 | + | 0.909362i | \(0.363430\pi\) | |||||||
\(102\) | −9.12545e31 | − | 1.50329e32i | −0.664740 | − | 1.09507i | ||||
\(103\) | 1.75898e31i | 0.109614i | 0.998497 | + | 0.0548068i | \(0.0174543\pi\) | ||||
−0.998497 | + | 0.0548068i | \(0.982546\pi\) | |||||||
\(104\) | −1.31310e31 | − | 1.98903e32i | −0.0701076 | − | 1.06196i | ||||
\(105\) | 2.50373e31 | 0.114699 | ||||||||
\(106\) | −3.08258e32 | + | 1.87122e32i | −1.21345 | + | 0.736599i | ||||
\(107\) | 2.30757e32i | 0.781653i | 0.920464 | + | 0.390827i | \(0.127811\pi\) | ||||
−0.920464 | + | 0.390827i | \(0.872189\pi\) | |||||||
\(108\) | 3.16834e32 | + | 1.64807e32i | 0.924808 | + | 0.481055i | ||||
\(109\) | −3.17192e32 | −0.798910 | −0.399455 | − | 0.916753i | \(-0.630801\pi\) | ||||
−0.399455 | + | 0.916753i | \(0.630801\pi\) | |||||||
\(110\) | −5.13731e32 | − | 8.46302e32i | −1.11803 | − | 1.84180i | ||||
\(111\) | − | 1.07404e32i | − | 0.202234i | ||||||
\(112\) | 4.25643e31 | − | 2.98438e31i | 0.0694316 | − | 0.0486816i | ||||
\(113\) | 1.38155e33 | 1.95485 | 0.977424 | − | 0.211288i | \(-0.0677658\pi\) | ||||
0.977424 | + | 0.211288i | \(0.0677658\pi\) | |||||||
\(114\) | −4.21646e32 | + | 2.55952e32i | −0.518168 | + | 0.314544i | ||||
\(115\) | − | 1.72209e32i | − | 0.184031i | ||||||
\(116\) | −2.88426e32 | + | 5.54488e32i | −0.268353 | + | 0.515898i | ||||
\(117\) | −1.27301e32 | −0.103242 | ||||||||
\(118\) | 3.22576e32 | + | 5.31400e32i | 0.228307 | + | 0.376105i | ||||
\(119\) | 1.84865e32i | 0.114315i | ||||||||
\(120\) | 2.49534e33 | − | 1.64735e32i | 1.34968 | − | 0.0891019i | ||||
\(121\) | −2.72619e33 | −1.29119 | ||||||||
\(122\) | −1.70431e33 | + | 1.03457e33i | −0.707606 | + | 0.429538i | ||||
\(123\) | − | 7.39345e32i | − | 0.269380i | ||||||
\(124\) | 5.13961e33 | + | 2.67346e33i | 1.64507 | + | 0.855710i | ||||
\(125\) | −1.32074e32 | −0.0371755 | ||||||||
\(126\) | −1.72270e31 | − | 2.83791e31i | −0.00426855 | − | 0.00703185i | ||||
\(127\) | 5.38941e33i | 1.17674i | 0.808590 | + | 0.588372i | \(0.200231\pi\) | ||||
−0.808590 | + | 0.588372i | \(0.799769\pi\) | |||||||
\(128\) | 4.04581e33 | − | 3.25444e33i | 0.779195 | − | 0.626781i | ||||
\(129\) | −6.38737e33 | −1.08614 | ||||||||
\(130\) | −8.61704e33 | + | 5.23080e33i | −1.29498 | + | 0.786094i | ||||
\(131\) | − | 1.38685e34i | − | 1.84370i | −0.387550 | − | 0.921849i | \(-0.626679\pi\) | ||
0.387550 | − | 0.921849i | \(-0.373321\pi\) | |||||||
\(132\) | 5.63895e33 | − | 1.08407e34i | 0.663767 | − | 1.27606i | ||||
\(133\) | 5.18512e32 | 0.0540919 | ||||||||
\(134\) | −2.51722e33 | − | 4.14678e33i | −0.232940 | − | 0.383737i | ||||
\(135\) | − | 1.80603e34i | − | 1.48383i | ||||||
\(136\) | 1.21634e33 | + | 1.84246e34i | 0.0888039 | + | 1.34516i | ||||
\(137\) | −1.41446e34 | −0.918461 | −0.459231 | − | 0.888317i | \(-0.651875\pi\) | ||||
−0.459231 | + | 0.888317i | \(0.651875\pi\) | |||||||
\(138\) | 1.81696e33 | − | 1.10295e33i | 0.105022 | − | 0.0637515i | ||||
\(139\) | 1.36246e34i | 0.701596i | 0.936451 | + | 0.350798i | \(0.114090\pi\) | ||||
−0.936451 | + | 0.350798i | \(0.885910\pi\) | |||||||
\(140\) | −2.33219e33 | − | 1.21313e33i | −0.107082 | − | 0.0557005i | ||||
\(141\) | 3.53513e34 | 1.44844 | ||||||||
\(142\) | −8.84694e33 | − | 1.45741e34i | −0.323727 | − | 0.533297i | ||||
\(143\) | 4.92560e34i | 1.61095i | ||||||||
\(144\) | −1.90365e33 | − | 2.71506e33i | −0.0556913 | − | 0.0794290i | ||||
\(145\) | 3.16071e34 | 0.827745 | ||||||||
\(146\) | −2.07790e34 | + | 1.26134e34i | −0.487504 | + | 0.295929i | ||||
\(147\) | 4.48524e34i | 0.943426i | ||||||||
\(148\) | −5.20406e33 | + | 1.00046e34i | −0.0982098 | + | 0.188804i | ||||
\(149\) | 1.20034e34 | 0.203388 | 0.101694 | − | 0.994816i | \(-0.467574\pi\) | ||||
0.101694 | + | 0.994816i | \(0.467574\pi\) | |||||||
\(150\) | −3.32345e34 | − | 5.47494e34i | −0.505975 | − | 0.833525i | ||||
\(151\) | 4.78649e34i | 0.655219i | 0.944813 | + | 0.327609i | \(0.106243\pi\) | ||||
−0.944813 | + | 0.327609i | \(0.893757\pi\) | |||||||
\(152\) | 5.16775e34 | − | 3.41160e33i | 0.636509 | − | 0.0420205i | ||||
\(153\) | 1.17920e34 | 0.130775 | ||||||||
\(154\) | −1.09806e34 | + | 6.66555e33i | −0.109722 | + | 0.0666046i | ||||
\(155\) | − | 2.92970e35i | − | 2.63946i | ||||||
\(156\) | −1.10379e35 | − | 5.74158e34i | −0.897211 | − | 0.466700i | ||||
\(157\) | 7.13932e34 | 0.523917 | 0.261959 | − | 0.965079i | \(-0.415632\pi\) | ||||
0.261959 | + | 0.965079i | \(0.415632\pi\) | |||||||
\(158\) | 7.16432e34 | + | 1.18023e35i | 0.474965 | + | 0.782441i | ||||
\(159\) | 2.25080e35i | 1.34891i | ||||||||
\(160\) | −2.40420e35 | − | 1.05562e35i | −1.30332 | − | 0.572252i | ||||
\(161\) | −2.23438e33 | −0.0109633 | ||||||||
\(162\) | 1.71892e35 | − | 1.04343e35i | 0.763861 | − | 0.463686i | ||||
\(163\) | − | 9.56621e34i | − | 0.385246i | −0.981273 | − | 0.192623i | \(-0.938301\pi\) | ||
0.981273 | − | 0.192623i | \(-0.0616995\pi\) | |||||||
\(164\) | −3.58235e34 | + | 6.88692e34i | −0.130818 | + | 0.251492i | ||||
\(165\) | −6.17942e35 | −2.04741 | ||||||||
\(166\) | 2.12451e35 | + | 3.49984e35i | 0.639041 | + | 1.05273i | ||||
\(167\) | − | 1.85412e35i | − | 0.506609i | −0.967387 | − | 0.253305i | \(-0.918482\pi\) | ||
0.967387 | − | 0.253305i | \(-0.0815175\pi\) | |||||||
\(168\) | −2.13741e33 | − | 3.23765e34i | −0.00530809 | − | 0.0804047i | ||||
\(169\) | 5.87451e34 | 0.132674 | ||||||||
\(170\) | 7.98205e35 | − | 4.84534e35i | 1.64033 | − | 0.995731i | ||||
\(171\) | − | 3.30744e34i | − | 0.0618806i | ||||||
\(172\) | 5.94977e35 | + | 3.09488e35i | 1.01402 | + | 0.527458i | ||||
\(173\) | −2.05267e35 | −0.318846 | −0.159423 | − | 0.987210i | \(-0.550963\pi\) | ||||
−0.159423 | + | 0.987210i | \(0.550963\pi\) | |||||||
\(174\) | 2.02434e35 | + | 3.33483e35i | 0.286745 | + | 0.472374i | ||||
\(175\) | 6.73271e34i | 0.0870123i | ||||||||
\(176\) | −1.05052e36 | + | 7.36570e35i | −1.23938 | + | 0.868984i | ||||
\(177\) | 3.88011e35 | 0.418092 | ||||||||
\(178\) | −5.79519e35 | + | 3.51786e35i | −0.570621 | + | 0.346384i | ||||
\(179\) | 1.25998e35i | 0.113426i | 0.998391 | + | 0.0567132i | \(0.0180621\pi\) | ||||
−0.998391 | + | 0.0567132i | \(0.981938\pi\) | |||||||
\(180\) | −7.73823e34 | + | 1.48764e35i | −0.0637208 | + | 0.122501i | ||||
\(181\) | −1.20858e35 | −0.0910789 | −0.0455394 | − | 0.998963i | \(-0.514501\pi\) | ||||
−0.0455394 | + | 0.998963i | \(0.514501\pi\) | |||||||
\(182\) | 6.78686e34 | + | 1.11804e35i | 0.0468302 | + | 0.0771465i | ||||
\(183\) | 1.24443e36i | 0.786600i | ||||||||
\(184\) | −2.22689e35 | + | 1.47013e34i | −0.129007 | + | 0.00851669i | ||||
\(185\) | 5.70285e35 | 0.302931 | ||||||||
\(186\) | 3.09109e36 | − | 1.87639e36i | 1.50628 | − | 0.914356i | ||||
\(187\) | − | 4.56263e36i | − | 2.04056i | ||||||
\(188\) | −3.29293e36 | − | 1.71288e36i | −1.35225 | − | 0.703397i | ||||
\(189\) | −2.34328e35 | −0.0883966 | ||||||||
\(190\) | −1.35903e36 | − | 2.23882e36i | −0.471163 | − | 0.776177i | ||||
\(191\) | 2.97958e36i | 0.949776i | 0.880046 | + | 0.474888i | \(0.157511\pi\) | ||||
−0.880046 | + | 0.474888i | \(0.842489\pi\) | |||||||
\(192\) | −4.26049e35 | − | 3.21274e36i | −0.124922 | − | 0.942012i | ||||
\(193\) | −1.00262e35 | −0.0270532 | −0.0135266 | − | 0.999909i | \(-0.504306\pi\) | ||||
−0.0135266 | + | 0.999909i | \(0.504306\pi\) | |||||||
\(194\) | −5.91908e36 | + | 3.59306e36i | −1.47037 | + | 0.892559i | ||||
\(195\) | 6.29188e36i | 1.43955i | ||||||||
\(196\) | 2.17323e36 | − | 4.17795e36i | 0.458151 | − | 0.880777i | ||||
\(197\) | 9.62694e36 | 1.87081 | 0.935403 | − | 0.353585i | \(-0.115037\pi\) | ||||
0.935403 | + | 0.353585i | \(0.115037\pi\) | |||||||
\(198\) | 4.25177e35 | + | 7.00421e35i | 0.0761950 | + | 0.125521i | ||||
\(199\) | − | 1.60787e36i | − | 0.265828i | −0.991128 | − | 0.132914i | \(-0.957567\pi\) | ||
0.991128 | − | 0.132914i | \(-0.0424335\pi\) | |||||||
\(200\) | 4.42985e35 | + | 6.71015e36i | 0.0675942 | + | 1.02389i | ||||
\(201\) | −3.02784e36 | −0.426576 | ||||||||
\(202\) | −5.46551e36 | + | 3.31773e36i | −0.711228 | + | 0.431736i | ||||
\(203\) | − | 4.10095e35i | − | 0.0493115i | ||||||
\(204\) | 1.02245e37 | + | 5.31848e36i | 1.13648 | + | 0.591159i | ||||
\(205\) | 3.92570e36 | 0.403511 | ||||||||
\(206\) | −5.98178e35 | − | 9.85417e35i | −0.0568794 | − | 0.0937011i | ||||
\(207\) | 1.42525e35i | 0.0125419i | ||||||||
\(208\) | 7.49975e36 | + | 1.06964e37i | 0.610989 | + | 0.871416i | ||||
\(209\) | −1.27973e37 | −0.965560 | ||||||||
\(210\) | −1.40264e36 | + | 8.51446e35i | −0.0980479 | + | 0.0595180i | ||||
\(211\) | 3.10011e36i | 0.200843i | 0.994945 | + | 0.100422i | \(0.0320192\pi\) | ||||
−0.994945 | + | 0.100422i | \(0.967981\pi\) | |||||||
\(212\) | 1.09058e37 | − | 2.09660e37i | 0.655065 | − | 1.25933i | ||||
\(213\) | −1.06416e37 | −0.592832 | ||||||||
\(214\) | −7.84738e36 | − | 1.29275e37i | −0.405606 | − | 0.668181i | ||||
\(215\) | − | 3.39151e37i | − | 1.62696i | ||||||
\(216\) | −2.33543e37 | + | 1.54179e36i | −1.04018 | + | 0.0686696i | ||||
\(217\) | −3.80122e36 | −0.157242 | ||||||||
\(218\) | 1.77698e37 | − | 1.07868e37i | 0.682933 | − | 0.414561i | ||||
\(219\) | 1.51721e37i | 0.541926i | ||||||||
\(220\) | 5.75606e37 | + | 2.99412e37i | 1.91145 | + | 0.994274i | ||||
\(221\) | −4.64567e37 | −1.43474 | ||||||||
\(222\) | 3.65251e36 | + | 6.01702e36i | 0.104941 | + | 0.172876i | ||||
\(223\) | − | 1.15242e37i | − | 0.308129i | −0.988061 | − | 0.154065i | \(-0.950764\pi\) | ||
0.988061 | − | 0.154065i | \(-0.0492364\pi\) | |||||||
\(224\) | −1.36964e36 | + | 3.11940e36i | −0.0340910 | + | 0.0776431i | ||||
\(225\) | 4.29460e36 | 0.0995412 | ||||||||
\(226\) | −7.73977e37 | + | 4.69827e37i | −1.67106 | + | 1.01439i | ||||
\(227\) | − | 4.61854e37i | − | 0.929160i | −0.885531 | − | 0.464580i | \(-0.846205\pi\) | ||
0.885531 | − | 0.464580i | \(-0.153795\pi\) | |||||||
\(228\) | 1.49173e37 | − | 2.86780e37i | 0.279727 | − | 0.537763i | ||||
\(229\) | 3.72281e37 | 0.650883 | 0.325441 | − | 0.945562i | \(-0.394487\pi\) | ||||
0.325441 | + | 0.945562i | \(0.394487\pi\) | |||||||
\(230\) | 5.85634e36 | + | 9.64752e36i | 0.0954950 | + | 0.157315i | ||||
\(231\) | 8.01767e36i | 0.121971i | ||||||||
\(232\) | −2.69826e36 | − | 4.08722e37i | −0.0383069 | − | 0.580256i | ||||
\(233\) | 7.06883e37 | 0.936813 | 0.468407 | − | 0.883513i | \(-0.344828\pi\) | ||||
0.468407 | + | 0.883513i | \(0.344828\pi\) | |||||||
\(234\) | 7.13168e36 | − | 4.32915e36i | 0.0882548 | − | 0.0535733i | ||||
\(235\) | 1.87705e38i | 2.16965i | ||||||||
\(236\) | −3.61428e37 | − | 1.88003e37i | −0.390328 | − | 0.203036i | ||||
\(237\) | 8.61762e37 | 0.869789 | ||||||||
\(238\) | −6.28673e36 | − | 1.03565e37i | −0.0593190 | − | 0.0977200i | ||||
\(239\) | − | 1.27048e37i | − | 0.112099i | −0.998428 | − | 0.0560493i | \(-0.982150\pi\) | ||
0.998428 | − | 0.0560493i | \(-0.0178504\pi\) | |||||||
\(240\) | −1.34192e38 | + | 9.40882e37i | −1.10751 | + | 0.776525i | ||||
\(241\) | 4.54592e37 | 0.351034 | 0.175517 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175517 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(242\) | 1.52727e38 | − | 9.27098e37i | 1.10375 | − | 0.670008i | ||||
\(243\) | 2.85725e37i | 0.193307i | ||||||||
\(244\) | 6.02965e37 | − | 1.15917e38i | 0.381993 | − | 0.734365i | ||||
\(245\) | −2.38153e38 | −1.41318 | ||||||||
\(246\) | 2.51430e37 | + | 4.14197e37i | 0.139783 | + | 0.230274i | ||||
\(247\) | 1.30302e38i | 0.678892i | ||||||||
\(248\) | −3.78849e38 | + | 2.50105e37i | −1.85029 | + | 0.122151i | ||||
\(249\) | 2.55547e38 | 1.17026 | ||||||||
\(250\) | 7.39907e36 | − | 4.49146e36i | 0.0317787 | − | 0.0192907i | ||||
\(251\) | − | 1.86541e38i | − | 0.751612i | −0.926698 | − | 0.375806i | \(-0.877366\pi\) | ||
0.926698 | − | 0.375806i | \(-0.122634\pi\) | |||||||
\(252\) | 1.93018e36 | + | 1.00402e36i | 0.00729777 | + | 0.00379606i | ||||
\(253\) | 5.51464e37 | 0.195699 | ||||||||
\(254\) | −1.83279e38 | − | 3.01927e38i | −0.610622 | − | 1.00592i | ||||
\(255\) | − | 5.82823e38i | − | 1.82345i | ||||||
\(256\) | −1.15981e38 | + | 3.19907e38i | −0.340838 | + | 0.940122i | ||||
\(257\) | −1.69751e38 | −0.468687 | −0.234344 | − | 0.972154i | \(-0.575294\pi\) | ||||
−0.234344 | + | 0.972154i | \(0.575294\pi\) | |||||||
\(258\) | 3.57834e38 | − | 2.17216e38i | 0.928468 | − | 0.563608i | ||||
\(259\) | − | 7.39932e36i | − | 0.0180466i | ||||||
\(260\) | 3.04861e38 | − | 5.86082e38i | 0.699082 | − | 1.34395i | ||||
\(261\) | −2.61588e37 | −0.0564118 | ||||||||
\(262\) | 4.71629e38 | + | 7.76945e38i | 0.956709 | + | 1.57605i | ||||
\(263\) | 2.65236e38i | 0.506221i | 0.967437 | + | 0.253110i | \(0.0814536\pi\) | ||||
−0.967437 | + | 0.253110i | \(0.918546\pi\) | |||||||
\(264\) | 5.27531e37 | + | 7.99081e38i | 0.0947513 | + | 1.43525i | ||||
\(265\) | −1.19511e39 | −2.02057 | ||||||||
\(266\) | −2.90482e37 | + | 1.76331e37i | −0.0462394 | + | 0.0280687i | ||||
\(267\) | 4.23146e38i | 0.634322i | ||||||||
\(268\) | 2.82040e38 | + | 1.46708e38i | 0.398249 | + | 0.207156i | ||||
\(269\) | 1.81625e38 | 0.241624 | 0.120812 | − | 0.992675i | \(-0.461450\pi\) | ||||
0.120812 | + | 0.992675i | \(0.461450\pi\) | |||||||
\(270\) | 6.14178e38 | + | 1.01178e39i | 0.769970 | + | 1.26842i | ||||
\(271\) | 1.02031e39i | 1.20566i | 0.797870 | + | 0.602829i | \(0.205960\pi\) | ||||
−0.797870 | + | 0.602829i | \(0.794040\pi\) | |||||||
\(272\) | −6.94709e38 | − | 9.90821e38i | −0.773928 | − | 1.10381i | ||||
\(273\) | 8.16358e37 | 0.0857587 | ||||||||
\(274\) | 7.92410e38 | − | 4.81017e38i | 0.785129 | − | 0.476597i | ||||
\(275\) | − | 1.66169e39i | − | 1.55320i | ||||||
\(276\) | −6.42819e37 | + | 1.23579e38i | −0.0566948 | + | 0.108993i | ||||
\(277\) | 1.47642e39 | 1.22895 | 0.614475 | − | 0.788937i | \(-0.289368\pi\) | ||||
0.614475 | + | 0.788937i | \(0.289368\pi\) | |||||||
\(278\) | −4.63334e38 | − | 7.63280e38i | −0.364064 | − | 0.599745i | ||||
\(279\) | 2.42469e38i | 0.179883i | ||||||||
\(280\) | 1.71910e38 | − | 1.13490e37i | 0.120440 | − | 0.00795113i | ||||
\(281\) | −5.86616e38 | −0.388197 | −0.194099 | − | 0.980982i | \(-0.562178\pi\) | ||||
−0.194099 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(282\) | −1.98046e39 | + | 1.20220e39i | −1.23817 | + | 0.751605i | ||||
\(283\) | − | 2.31347e39i | − | 1.36673i | −0.730078 | − | 0.683363i | \(-0.760516\pi\) | ||
0.730078 | − | 0.683363i | \(-0.239484\pi\) | |||||||
\(284\) | 9.91249e38 | + | 5.15615e38i | 0.553464 | + | 0.287894i | ||||
\(285\) | −1.63471e39 | −0.862825 | ||||||||
\(286\) | −1.67506e39 | − | 2.75943e39i | −0.835936 | − | 1.37709i | ||||
\(287\) | − | 5.09352e37i | − | 0.0240385i | ||||||
\(288\) | 1.98978e38 | + | 8.73657e37i | 0.0888229 | + | 0.0389997i | ||||
\(289\) | 1.93542e39 | 0.817351 | ||||||||
\(290\) | −1.77070e39 | + | 1.07487e39i | −0.707581 | + | 0.429523i | ||||
\(291\) | 4.32192e39i | 1.63451i | ||||||||
\(292\) | 7.35135e38 | − | 1.41327e39i | 0.263173 | − | 0.505939i | ||||
\(293\) | 9.55731e38 | 0.323932 | 0.161966 | − | 0.986796i | \(-0.448217\pi\) | ||||
0.161966 | + | 0.986796i | \(0.448217\pi\) | |||||||
\(294\) | −1.52530e39 | − | 2.51273e39i | −0.489551 | − | 0.806469i | ||||
\(295\) | 2.06022e39i | 0.626271i | ||||||||
\(296\) | −4.86846e37 | − | 7.37454e38i | −0.0140192 | − | 0.212357i | ||||
\(297\) | 5.78343e39 | 1.57791 | ||||||||
\(298\) | −6.72457e38 | + | 4.08202e38i | −0.173862 | + | 0.105539i | ||||
\(299\) | − | 5.61500e38i | − | 0.137598i | ||||||
\(300\) | 3.72374e39 | + | 1.93697e39i | 0.865045 | + | 0.449969i | ||||
\(301\) | −4.40041e38 | −0.0969235 | ||||||||
\(302\) | −1.62775e39 | − | 2.68150e39i | −0.339998 | − | 0.560101i | ||||
\(303\) | 3.99073e39i | 0.790625i | ||||||||
\(304\) | −2.77907e39 | + | 1.94853e39i | −0.522302 | + | 0.366210i | ||||
\(305\) | −6.60756e39 | −1.17827 | ||||||||
\(306\) | −6.60615e38 | + | 4.01013e38i | −0.111791 | + | 0.0678603i | ||||
\(307\) | − | 1.81430e39i | − | 0.291404i | −0.989329 | − | 0.145702i | \(-0.953456\pi\) | ||
0.989329 | − | 0.145702i | \(-0.0465440\pi\) | |||||||
\(308\) | 3.88480e38 | − | 7.46837e38i | 0.0592322 | − | 0.113871i | ||||
\(309\) | −7.19519e38 | −0.104161 | ||||||||
\(310\) | 9.96306e39 | + | 1.64128e40i | 1.36964 | + | 2.25629i | ||||
\(311\) | − | 1.20307e40i | − | 1.57082i | −0.618976 | − | 0.785410i | \(-0.712452\pi\) | ||
0.618976 | − | 0.785410i | \(-0.287548\pi\) | |||||||
\(312\) | 8.13624e39 | − | 5.37131e38i | 1.00914 | − | 0.0666204i | ||||
\(313\) | 9.36962e39 | 1.10411 | 0.552055 | − | 0.833808i | \(-0.313844\pi\) | ||||
0.552055 | + | 0.833808i | \(0.313844\pi\) | |||||||
\(314\) | −3.99960e39 | + | 2.42788e39i | −0.447860 | + | 0.271865i | ||||
\(315\) | − | 1.10025e38i | − | 0.0117091i | ||||||
\(316\) | −8.02722e39 | − | 4.17550e39i | −0.812029 | − | 0.422391i | ||||
\(317\) | −1.26999e40 | −1.22138 | −0.610692 | − | 0.791868i | \(-0.709109\pi\) | ||||
−0.610692 | + | 0.791868i | \(0.709109\pi\) | |||||||
\(318\) | −7.65433e39 | − | 1.26095e40i | −0.699960 | − | 1.15309i | ||||
\(319\) | 1.01215e40i | 0.880227i | ||||||||
\(320\) | 1.70587e40 | − | 2.26220e39i | 1.41106 | − | 0.187124i | ||||
\(321\) | −9.43923e39 | −0.742773 | ||||||||
\(322\) | 1.25175e38 | − | 7.59847e37i | 0.00937178 | − | 0.00568895i | ||||
\(323\) | − | 1.20700e40i | − | 0.859940i | ||||||
\(324\) | −6.08132e39 | + | 1.16911e40i | −0.412361 | + | 0.792747i | ||||
\(325\) | −1.69193e40 | −1.09207 | ||||||||
\(326\) | 3.25320e39 | + | 5.35920e39i | 0.199907 | + | 0.329320i | ||||
\(327\) | − | 1.29749e40i | − | 0.759172i | ||||||
\(328\) | −3.35133e38 | − | 5.07646e39i | −0.0186739 | − | 0.282865i | ||||
\(329\) | 2.43543e39 | 0.129253 | ||||||||
\(330\) | 3.46185e40 | − | 2.10144e40i | 1.75019 | − | 1.06242i | ||||
\(331\) | 1.76393e39i | 0.0849637i | 0.999097 | + | 0.0424818i | \(0.0135265\pi\) | ||||
−0.999097 | + | 0.0424818i | \(0.986474\pi\) | |||||||
\(332\) | −2.38039e40 | − | 1.23820e40i | −1.09254 | − | 0.568305i | ||||
\(333\) | −4.71982e38 | −0.0206451 | ||||||||
\(334\) | 6.30531e39 | + | 1.03872e40i | 0.262883 | + | 0.433065i | ||||
\(335\) | − | 1.60769e40i | − | 0.638979i | ||||||
\(336\) | 1.22077e39 | + | 1.74112e39i | 0.0462602 | + | 0.0659780i | ||||
\(337\) | 8.12789e38 | 0.0293697 | 0.0146848 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146848 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(338\) | −3.29103e39 | + | 1.99775e39i | −0.113413 | + | 0.0688453i | ||||
\(339\) | 5.65132e40i | 1.85761i | ||||||||
\(340\) | −2.82395e40 | + | 5.42893e40i | −0.885513 | + | 1.70236i | ||||
\(341\) | 9.38175e40 | 2.80681 | ||||||||
\(342\) | 1.12477e39 | + | 1.85290e39i | 0.0321103 | + | 0.0528974i | ||||
\(343\) | 6.20234e39i | 0.168986i | ||||||||
\(344\) | −4.38567e40 | + | 2.89529e39i | −1.14051 | + | 0.0752935i | ||||
\(345\) | 7.04430e39 | 0.174877 | ||||||||
\(346\) | 1.14995e40 | − | 6.98054e39i | 0.272559 | − | 0.165452i | ||||
\(347\) | 7.06291e40i | 1.59850i | 0.601000 | + | 0.799249i | \(0.294769\pi\) | ||||
−0.601000 | + | 0.799249i | \(0.705231\pi\) | |||||||
\(348\) | −2.26816e40 | − | 1.17982e40i | −0.490237 | − | 0.255005i | ||||
\(349\) | −1.82205e40 | −0.376143 | −0.188071 | − | 0.982155i | \(-0.560224\pi\) | ||||
−0.188071 | + | 0.982155i | \(0.560224\pi\) | |||||||
\(350\) | −2.28960e39 | − | 3.77181e39i | −0.0451514 | − | 0.0743808i | ||||
\(351\) | − | 5.88868e40i | − | 1.10944i | ||||||
\(352\) | 3.38040e40 | − | 7.69896e40i | 0.608535 | − | 1.38596i | ||||
\(353\) | −2.49744e40 | −0.429636 | −0.214818 | − | 0.976654i | \(-0.568916\pi\) | ||||
−0.214818 | + | 0.976654i | \(0.568916\pi\) | |||||||
\(354\) | −2.17372e40 | + | 1.31951e40i | −0.357398 | + | 0.216951i | ||||
\(355\) | − | 5.65035e40i | − | 0.888018i | ||||||
\(356\) | 2.05027e40 | − | 3.94156e40i | 0.308043 | − | 0.592199i | ||||
\(357\) | −7.56200e39 | −0.108629 | ||||||||
\(358\) | −4.28482e39 | − | 7.05866e39i | −0.0588578 | − | 0.0969603i | ||||
\(359\) | 8.95589e40i | 1.17651i | 0.808674 | + | 0.588257i | \(0.200186\pi\) | ||||
−0.808674 | + | 0.588257i | \(0.799814\pi\) | |||||||
\(360\) | −7.23920e38 | − | 1.09656e40i | −0.00909601 | − | 0.137782i | ||||
\(361\) | 4.93443e40 | 0.593091 | ||||||||
\(362\) | 6.77072e39 | − | 4.11003e39i | 0.0778570 | − | 0.0472615i | ||||
\(363\) | − | 1.11516e41i | − | 1.22696i | ||||||
\(364\) | −7.60429e39 | − | 3.95550e39i | −0.0800638 | − | 0.0416466i | ||||
\(365\) | −8.05594e40 | −0.811765 | ||||||||
\(366\) | −4.23196e40 | − | 6.97158e40i | −0.408173 | − | 0.672409i | ||||
\(367\) | − | 1.14387e40i | − | 0.105614i | −0.998605 | − | 0.0528069i | \(-0.983183\pi\) | ||
0.998605 | − | 0.0528069i | \(-0.0168168\pi\) | |||||||
\(368\) | 1.19756e40 | − | 8.39662e39i | 0.105860 | − | 0.0742232i | ||||
\(369\) | −3.24901e39 | −0.0274998 | ||||||||
\(370\) | −3.19486e40 | + | 1.93937e40i | −0.258955 | + | 0.157193i | ||||
\(371\) | 1.55063e40i | 0.120372i | ||||||||
\(372\) | −1.09359e41 | + | 2.10239e41i | −0.813146 | + | 1.56324i | ||||
\(373\) | −1.08315e41 | −0.771519 | −0.385760 | − | 0.922599i | \(-0.626061\pi\) | ||||
−0.385760 | + | 0.922599i | \(0.626061\pi\) | |||||||
\(374\) | 1.55162e41 | + | 2.55609e41i | 1.05886 | + | 1.74433i | ||||
\(375\) | − | 5.40255e39i | − | 0.0353264i | ||||||
\(376\) | 2.42727e41 | − | 1.60242e40i | 1.52094 | − | 0.100408i | ||||
\(377\) | 1.03057e41 | 0.618894 | ||||||||
\(378\) | 1.31276e40 | − | 7.96883e39i | 0.0755641 | − | 0.0458697i | ||||
\(379\) | − | 9.31410e40i | − | 0.513941i | −0.966419 | − | 0.256971i | \(-0.917276\pi\) | ||
0.966419 | − | 0.256971i | \(-0.0827244\pi\) | |||||||
\(380\) | 1.52271e41 | + | 7.92066e40i | 0.805528 | + | 0.419010i | ||||
\(381\) | −2.20457e41 | −1.11821 | ||||||||
\(382\) | −1.01327e41 | − | 1.66923e41i | −0.492846 | − | 0.811897i | ||||
\(383\) | 7.96910e39i | 0.0371731i | 0.999827 | + | 0.0185866i | \(0.00591663\pi\) | ||||
−0.999827 | + | 0.0185866i | \(0.994083\pi\) | |||||||
\(384\) | 1.33124e41 | + | 1.65496e41i | 0.595605 | + | 0.740437i | ||||
\(385\) | −4.25714e40 | −0.182703 | ||||||||
\(386\) | 5.61688e39 | − | 3.40962e39i | 0.0231259 | − | 0.0140381i | ||||
\(387\) | 2.80690e40i | 0.110879i | ||||||||
\(388\) | 2.09410e41 | − | 4.02582e41i | 0.793761 | − | 1.52597i | ||||
\(389\) | 9.70371e39 | 0.0352975 | 0.0176488 | − | 0.999844i | \(-0.494382\pi\) | ||||
0.0176488 | + | 0.999844i | \(0.494382\pi\) | |||||||
\(390\) | −2.13969e41 | − | 3.52485e41i | −0.746993 | − | 1.23057i | ||||
\(391\) | 5.20123e40i | 0.174292i | ||||||||
\(392\) | 2.03308e40 | + | 3.07963e41i | 0.0654001 | + | 0.990653i | ||||
\(393\) | 5.67300e41 | 1.75199 | ||||||||
\(394\) | −5.39322e41 | + | 3.27385e41i | −1.59922 | + | 0.970775i | ||||
\(395\) | 4.57570e41i | 1.30288i | ||||||||
\(396\) | −4.76386e40 | − | 2.47801e40i | −0.130268 | − | 0.0677610i | ||||
\(397\) | −5.94309e41 | −1.56086 | −0.780430 | − | 0.625243i | \(-0.785000\pi\) | ||||
−0.780430 | + | 0.625243i | \(0.785000\pi\) | |||||||
\(398\) | 5.46790e40 | + | 9.00762e40i | 0.137940 | + | 0.227238i | ||||
\(399\) | 2.12100e40i | 0.0514014i | ||||||||
\(400\) | −2.53010e41 | − | 3.60853e41i | −0.589085 | − | 0.840176i | ||||
\(401\) | −8.19907e40 | −0.183423 | −0.0917117 | − | 0.995786i | \(-0.529234\pi\) | ||||
−0.0917117 | + | 0.995786i | \(0.529234\pi\) | |||||||
\(402\) | 1.69626e41 | − | 1.02968e41i | 0.364650 | − | 0.221353i | ||||
\(403\) | − | 9.55248e41i | − | 1.97349i | ||||||
\(404\) | 1.93363e41 | − | 3.71732e41i | 0.383947 | − | 0.738123i | ||||
\(405\) | 6.66418e41 | 1.27194 | ||||||||
\(406\) | 1.39462e40 | + | 2.29744e40i | 0.0255881 | + | 0.0421529i | ||||
\(407\) | 1.82622e41i | 0.322138i | ||||||||
\(408\) | −7.53667e41 | + | 4.97550e40i | −1.27825 | + | 0.0843867i | ||||
\(409\) | 7.15084e41 | 1.16623 | 0.583115 | − | 0.812390i | \(-0.301834\pi\) | ||||
0.583115 | + | 0.812390i | \(0.301834\pi\) | |||||||
\(410\) | −2.19926e41 | + | 1.33502e41i | −0.344934 | + | 0.209385i | ||||
\(411\) | − | 5.78592e41i | − | 0.872776i | ||||||
\(412\) | 6.70224e40 | + | 3.48629e40i | 0.0972444 | + | 0.0505834i | ||||
\(413\) | 2.67310e40 | 0.0373090 | ||||||||
\(414\) | −4.84685e39 | − | 7.98453e39i | −0.00650810 | − | 0.0107212i | ||||
\(415\) | 1.35688e42i | 1.75296i | ||||||||
\(416\) | −7.83907e41 | − | 3.44192e41i | −0.974476 | − | 0.427866i | ||||
\(417\) | −5.57322e41 | −0.666698 | ||||||||
\(418\) | 7.16935e41 | − | 4.35201e41i | 0.825390 | − | 0.501036i | ||||
\(419\) | 1.14174e42i | 1.26515i | 0.774498 | + | 0.632576i | \(0.218003\pi\) | ||||
−0.774498 | + | 0.632576i | \(0.781997\pi\) | |||||||
\(420\) | 4.96238e40 | − | 9.53997e40i | 0.0529299 | − | 0.101756i | ||||
\(421\) | 2.75721e39 | 0.00283110 | 0.00141555 | − | 0.999999i | \(-0.499549\pi\) | ||||
0.00141555 | + | 0.999999i | \(0.499549\pi\) | |||||||
\(422\) | −1.05426e41 | − | 1.73675e41i | −0.104219 | − | 0.171687i | ||||
\(423\) | − | 1.55349e41i | − | 0.147864i | ||||||
\(424\) | 1.02025e41 | + | 1.54543e42i | 0.0935090 | + | 1.41644i | ||||
\(425\) | 1.56725e42 | 1.38330 | ||||||||
\(426\) | 5.96163e41 | − | 3.61889e41i | 0.506770 | − | 0.307625i | ||||
\(427\) | 8.57317e40i | 0.0701933i | ||||||||
\(428\) | 8.79254e41 | + | 4.57359e41i | 0.693448 | + | 0.360709i | ||||
\(429\) | −2.01484e42 | −1.53082 | ||||||||
\(430\) | 1.15335e42 | + | 1.89999e42i | 0.844243 | + | 1.39078i | ||||
\(431\) | − | 1.37954e42i | − | 0.972967i | −0.873690 | − | 0.486484i | \(-0.838279\pi\) | ||
0.873690 | − | 0.486484i | \(-0.161721\pi\) | |||||||
\(432\) | 1.25593e42 | − | 8.80588e41i | 0.853542 | − | 0.598457i | ||||
\(433\) | −1.83219e42 | −1.19995 | −0.599976 | − | 0.800018i | \(-0.704823\pi\) | ||||
−0.599976 | + | 0.800018i | \(0.704823\pi\) | |||||||
\(434\) | 2.12953e41 | − | 1.29269e41i | 0.134415 | − | 0.0815938i | ||||
\(435\) | 1.29290e42i | 0.786572i | ||||||||
\(436\) | −6.28673e41 | + | 1.20860e42i | −0.368673 | + | 0.708758i | ||||
\(437\) | 1.45885e41 | 0.0824721 | ||||||||
\(438\) | −5.15960e41 | − | 8.49974e41i | −0.281210 | − | 0.463255i | ||||
\(439\) | − | 3.54955e42i | − | 1.86527i | −0.360827 | − | 0.932633i | \(-0.617506\pi\) | ||
0.360827 | − | 0.932633i | \(-0.382494\pi\) | |||||||
\(440\) | −4.24288e42 | + | 2.80103e41i | −2.14990 | + | 0.141930i | ||||
\(441\) | 1.97101e41 | 0.0963101 | ||||||||
\(442\) | 2.60260e42 | − | 1.57986e42i | 1.22646 | − | 0.744495i | ||||
\(443\) | − | 3.06452e42i | − | 1.39285i | −0.717631 | − | 0.696423i | \(-0.754774\pi\) | ||
0.717631 | − | 0.696423i | \(-0.245226\pi\) | |||||||
\(444\) | −4.09243e41 | − | 2.12875e41i | −0.179413 | − | 0.0933248i | ||||
\(445\) | −2.24678e42 | −0.950168 | ||||||||
\(446\) | 3.91905e41 | + | 6.45610e41i | 0.159890 | + | 0.263398i | ||||
\(447\) | 4.91006e41i | 0.193271i | ||||||||
\(448\) | −2.93515e40 | − | 2.21333e41i | −0.0111476 | − | 0.0840617i | ||||
\(449\) | 2.68427e42 | 0.983749 | 0.491875 | − | 0.870666i | \(-0.336312\pi\) | ||||
0.491875 | + | 0.870666i | \(0.336312\pi\) | |||||||
\(450\) | −2.40593e41 | + | 1.46047e41i | −0.0850908 | + | 0.0516527i | ||||
\(451\) | 1.25713e42i | 0.429095i | ||||||||
\(452\) | 2.73824e42 | − | 5.26415e42i | 0.902103 | − | 1.73425i | ||||
\(453\) | −1.95794e42 | −0.622628 | ||||||||
\(454\) | 1.57063e42 | + | 2.58740e42i | 0.482148 | + | 0.794274i | ||||
\(455\) | 4.33462e41i | 0.128460i | ||||||||
\(456\) | 1.39553e41 | + | 2.11390e42i | 0.0399304 | + | 0.604848i | ||||
\(457\) | 1.28397e42 | 0.354729 | 0.177365 | − | 0.984145i | \(-0.443243\pi\) | ||||
0.177365 | + | 0.984145i | \(0.443243\pi\) | |||||||
\(458\) | −2.08560e42 | + | 1.26602e42i | −0.556394 | + | 0.337748i | ||||
\(459\) | 5.45474e42i | 1.40531i | ||||||||
\(460\) | −6.56169e41 | − | 3.41318e41i | −0.163264 | − | 0.0849246i | ||||
\(461\) | −5.93149e42 | −1.42544 | −0.712721 | − | 0.701448i | \(-0.752537\pi\) | ||||
−0.712721 | + | 0.701448i | \(0.752537\pi\) | |||||||
\(462\) | −2.72658e41 | − | 4.49167e41i | −0.0632917 | − | 0.104264i | ||||
\(463\) | 2.14282e42i | 0.480495i | 0.970712 | + | 0.240248i | \(0.0772286\pi\) | ||||
−0.970712 | + | 0.240248i | \(0.922771\pi\) | |||||||
\(464\) | 1.54111e42 | + | 2.19799e42i | 0.333845 | + | 0.476143i | ||||
\(465\) | 1.19841e43 | 2.50817 | ||||||||
\(466\) | −3.96011e42 | + | 2.40391e42i | −0.800816 | + | 0.486120i | ||||
\(467\) | 2.77518e42i | 0.542278i | 0.962540 | + | 0.271139i | \(0.0874003\pi\) | ||||
−0.962540 | + | 0.271139i | \(0.912600\pi\) | |||||||
\(468\) | −2.52310e41 | + | 4.85056e41i | −0.0476433 | + | 0.0915922i | ||||
\(469\) | −2.08595e41 | −0.0380661 | ||||||||
\(470\) | −6.38330e42 | − | 1.05156e43i | −1.12585 | − | 1.85468i | ||||
\(471\) | 2.92038e42i | 0.497857i | ||||||||
\(472\) | 2.66414e42 | − | 1.75879e41i | 0.439021 | − | 0.0289829i | ||||
\(473\) | 1.08606e43 | 1.73012 | ||||||||
\(474\) | −4.82778e42 | + | 2.93061e42i | −0.743522 | + | 0.451340i | ||||
\(475\) | − | 4.39585e42i | − | 0.654554i | ||||||
\(476\) | 7.04392e41 | + | 3.66402e41i | 0.101415 | + | 0.0527529i | ||||
\(477\) | 9.89102e41 | 0.137704 | ||||||||
\(478\) | 4.32052e41 | + | 7.11748e41i | 0.0581688 | + | 0.0958252i | ||||
\(479\) | − | 9.77483e42i | − | 1.27274i | −0.771383 | − | 0.636372i | \(-0.780434\pi\) | ||
0.771383 | − | 0.636372i | \(-0.219566\pi\) | |||||||
\(480\) | 4.31807e42 | − | 9.83452e42i | 0.543788 | − | 1.23849i | ||||
\(481\) | 1.85945e42 | 0.226498 | ||||||||
\(482\) | −2.54672e42 | + | 1.54594e42i | −0.300074 | + | 0.182154i | ||||
\(483\) | − | 9.13984e40i | − | 0.0104180i | ||||||
\(484\) | −5.40330e42 | + | 1.03876e43i | −0.595845 | + | 1.14549i | ||||
\(485\) | −2.29481e43 | −2.44838 | ||||||||
\(486\) | −9.71669e41 | − | 1.60069e42i | −0.100309 | − | 0.165245i | ||||
\(487\) | 4.78815e42i | 0.478304i | 0.970982 | + | 0.239152i | \(0.0768695\pi\) | ||||
−0.970982 | + | 0.239152i | \(0.923131\pi\) | |||||||
\(488\) | 5.64081e41 | + | 8.54446e42i | 0.0545286 | + | 0.825976i | ||||
\(489\) | 3.91311e42 | 0.366084 | ||||||||
\(490\) | 1.33418e43 | − | 8.09889e42i | 1.20803 | − | 0.733311i | ||||
\(491\) | 4.17934e42i | 0.366272i | 0.983088 | + | 0.183136i | \(0.0586248\pi\) | ||||
−0.983088 | + | 0.183136i | \(0.941375\pi\) | |||||||
\(492\) | −2.81713e42 | − | 1.46538e42i | −0.238982 | − | 0.124311i | ||||
\(493\) | −9.54628e42 | −0.783941 | ||||||||
\(494\) | −4.43121e42 | − | 7.29982e42i | −0.352283 | − | 0.580338i | ||||
\(495\) | 2.71551e42i | 0.209011i | ||||||||
\(496\) | 2.03734e43 | − | 1.42847e43i | 1.51830 | − | 1.06455i | ||||
\(497\) | −7.33121e41 | −0.0529021 | ||||||||
\(498\) | −1.43163e43 | + | 8.69041e42i | −1.00037 | + | 0.607254i | ||||
\(499\) | − | 2.18612e43i | − | 1.47933i | −0.672975 | − | 0.739665i | \(-0.734984\pi\) | ||
0.672975 | − | 0.739665i | \(-0.265016\pi\) | |||||||
\(500\) | −2.61770e41 | + | 5.03242e41i | −0.0171554 | + | 0.0329805i | ||||
\(501\) | 7.58436e42 | 0.481410 | ||||||||
\(502\) | 6.34371e42 | + | 1.04504e43i | 0.390017 | + | 0.642501i | ||||
\(503\) | 8.88151e41i | 0.0528931i | 0.999650 | + | 0.0264466i | \(0.00841918\pi\) | ||||
−0.999650 | + | 0.0264466i | \(0.991581\pi\) | |||||||
\(504\) | −1.42277e41 | + | 9.39271e39i | −0.00820816 | + | 0.000541879i | ||||
\(505\) | −2.11896e43 | −1.18430 | ||||||||
\(506\) | −3.08942e42 | + | 1.87537e42i | −0.167289 | + | 0.101550i | ||||
\(507\) | 2.40300e42i | 0.126074i | ||||||||
\(508\) | 2.05353e43 | + | 1.06818e43i | 1.04396 | + | 0.543032i | ||||
\(509\) | 1.41679e43 | 0.697946 | 0.348973 | − | 0.937133i | \(-0.386530\pi\) | ||||
0.348973 | + | 0.937133i | \(0.386530\pi\) | |||||||
\(510\) | 1.98201e43 | + | 3.26510e43i | 0.946202 | + | 1.55874i | ||||
\(511\) | 1.04524e42i | 0.0483595i | ||||||||
\(512\) | −4.38160e42 | − | 2.18661e43i | −0.196478 | − | 0.980508i | ||||
\(513\) | 1.52995e43 | 0.664967 | ||||||||
\(514\) | 9.50984e42 | − | 5.77276e42i | 0.400648 | − | 0.243205i | ||||
\(515\) | − | 3.82043e42i | − | 0.156026i | ||||||
\(516\) | −1.26598e43 | + | 2.43379e43i | −0.501222 | + | 0.963578i | ||||
\(517\) | −6.01086e43 | −2.30721 | ||||||||
\(518\) | 2.51630e41 | + | 4.14526e41i | 0.00936453 | + | 0.0154268i | ||||
\(519\) | − | 8.39655e42i | − | 0.302987i | ||||||
\(520\) | 2.85201e42 | + | 4.32010e43i | 0.0997923 | + | 1.51161i | ||||
\(521\) | 4.87247e43 | 1.65328 | 0.826639 | − | 0.562733i | \(-0.190250\pi\) | ||||
0.826639 | + | 0.562733i | \(0.190250\pi\) | |||||||
\(522\) | 1.46547e42 | − | 8.89586e41i | 0.0482225 | − | 0.0292725i | ||||
\(523\) | − | 1.24274e42i | − | 0.0396601i | −0.999803 | − | 0.0198300i | \(-0.993687\pi\) | ||
0.999803 | − | 0.0198300i | \(-0.00631251\pi\) | |||||||
\(524\) | −5.28433e43 | − | 2.74874e43i | −1.63565 | − | 0.850810i | ||||
\(525\) | −2.75405e42 | −0.0826843 | ||||||||
\(526\) | −9.01990e42 | − | 1.48591e43i | −0.262682 | − | 0.432733i | ||||
\(527\) | 8.84856e43i | 2.49979i | ||||||||
\(528\) | −3.01298e43 | − | 4.29723e43i | −0.825760 | − | 1.17773i | ||||
\(529\) | 3.69803e43 | 0.983285 | ||||||||
\(530\) | 6.69525e43 | − | 4.06422e43i | 1.72724 | − | 1.04849i | ||||
\(531\) | − | 1.70509e42i | − | 0.0426811i | ||||||
\(532\) | 1.02769e42 | − | 1.97569e42i | 0.0249618 | − | 0.0479880i | ||||
\(533\) | 1.28000e43 | 0.301700 | ||||||||
\(534\) | −1.43900e43 | − | 2.37055e43i | −0.329155 | − | 0.542238i | ||||
\(535\) | − | 5.01195e43i | − | 1.11262i | ||||||
\(536\) | −2.07896e43 | + | 1.37247e42i | −0.447930 | + | 0.0295710i | ||||
\(537\) | −5.15400e42 | −0.107784 | ||||||||
\(538\) | −1.01750e43 | + | 6.17656e42i | −0.206548 | + | 0.125381i | ||||
\(539\) | − | 7.62635e43i | − | 1.50278i | ||||||
\(540\) | −6.88152e43 | − | 3.57954e43i | −1.31639 | − | 0.684742i | ||||
\(541\) | −5.93941e43 | −1.10303 | −0.551515 | − | 0.834165i | \(-0.685950\pi\) | ||||
−0.551515 | + | 0.834165i | \(0.685950\pi\) | |||||||
\(542\) | −3.46979e43 | − | 5.71601e43i | −0.625625 | − | 1.03063i | ||||
\(543\) | − | 4.94376e42i | − | 0.0865485i | ||||||
\(544\) | 7.26141e43 | + | 3.18828e43i | 1.23435 | + | 0.541969i | ||||
\(545\) | 6.88929e43 | 1.13718 | ||||||||
\(546\) | −4.57341e42 | + | 2.77620e42i | −0.0733092 | + | 0.0445009i | ||||
\(547\) | 1.03500e44i | 1.61118i | 0.592476 | + | 0.805588i | \(0.298150\pi\) | ||||
−0.592476 | + | 0.805588i | \(0.701850\pi\) | |||||||
\(548\) | −2.80345e43 | + | 5.38952e43i | −0.423842 | + | 0.814819i | ||||
\(549\) | 5.46859e42 | 0.0803004 | ||||||||
\(550\) | 5.65094e43 | + | 9.30916e43i | 0.805967 | + | 1.32772i | ||||
\(551\) | 2.67755e43i | 0.370948i | ||||||||
\(552\) | −6.01365e41 | − | 9.10922e42i | −0.00809306 | − | 0.122590i | ||||
\(553\) | 5.93687e42 | 0.0776168 | ||||||||
\(554\) | −8.27123e43 | + | 5.02089e43i | −1.05054 | + | 0.637711i | ||||
\(555\) | 2.33278e43i | 0.287863i | ||||||||
\(556\) | 5.19139e43 | + | 2.70039e43i | 0.622425 | + | 0.323765i | ||||
\(557\) | 3.46931e43 | 0.404166 | 0.202083 | − | 0.979368i | \(-0.435229\pi\) | ||||
0.202083 | + | 0.979368i | \(0.435229\pi\) | |||||||
\(558\) | −8.24568e42 | − | 1.35836e43i | −0.0933425 | − | 0.153769i | ||||
\(559\) | − | 1.10582e44i | − | 1.21646i | ||||||
\(560\) | −9.24481e42 | + | 6.48195e42i | −0.0988301 | + | 0.0692943i | ||||
\(561\) | 1.86637e44 | 1.93906 | ||||||||
\(562\) | 3.28635e43 | − | 1.99491e43i | 0.331843 | − | 0.201439i | ||||
\(563\) | 1.44724e44i | 1.42038i | 0.704008 | + | 0.710192i | \(0.251392\pi\) | ||||
−0.704008 | + | 0.710192i | \(0.748608\pi\) | |||||||
\(564\) | 7.00662e43 | − | 1.34699e44i | 0.668410 | − | 1.28499i | ||||
\(565\) | −3.00068e44 | −2.78256 | ||||||||
\(566\) | 7.86746e43 | + | 1.29606e44i | 0.709205 | + | 1.16832i | ||||
\(567\) | − | 8.64664e42i | − | 0.0757737i | ||||||
\(568\) | −7.30665e43 | + | 4.82364e42i | −0.622508 | + | 0.0410962i | ||||
\(569\) | −8.69359e43 | −0.720117 | −0.360059 | − | 0.932930i | \(-0.617243\pi\) | ||||
−0.360059 | + | 0.932930i | \(0.617243\pi\) | |||||||
\(570\) | 9.15800e43 | − | 5.55918e43i | 0.737569 | − | 0.447727i | ||||
\(571\) | − | 1.65234e44i | − | 1.29396i | −0.762506 | − | 0.646981i | \(-0.776031\pi\) | ||
0.762506 | − | 0.646981i | \(-0.223969\pi\) | |||||||
\(572\) | 1.87681e44 | + | 9.76253e43i | 1.42917 | + | 0.743406i | ||||
\(573\) | −1.21881e44 | −0.902533 | ||||||||
\(574\) | 1.73216e42 | + | 2.85350e42i | 0.0124738 | + | 0.0205488i | ||||
\(575\) | 1.89426e43i | 0.132665i | ||||||||
\(576\) | −1.41182e43 | + | 1.87225e42i | −0.0961657 | + | 0.0127528i | ||||
\(577\) | −8.34544e43 | −0.552887 | −0.276443 | − | 0.961030i | \(-0.589156\pi\) | ||||
−0.276443 | + | 0.961030i | \(0.589156\pi\) | |||||||
\(578\) | −1.08426e44 | + | 6.58180e43i | −0.698697 | + | 0.424130i | ||||
\(579\) | − | 4.10126e42i | − | 0.0257075i | ||||||
\(580\) | 6.26451e43 | − | 1.20433e44i | 0.381979 | − | 0.734339i | ||||
\(581\) | 1.76052e43 | 0.104429 | ||||||||
\(582\) | −1.46976e44 | − | 2.42123e44i | −0.848162 | − | 1.39723i | ||||
\(583\) | − | 3.82709e44i | − | 2.14868i | ||||||
\(584\) | 6.87727e42 | + | 1.04174e44i | 0.0375674 | + | 0.569054i | ||||
\(585\) | 2.76493e43 | 0.146957 | ||||||||
\(586\) | −5.35421e43 | + | 3.25017e43i | −0.276907 | + | 0.168091i | ||||
\(587\) | 6.43456e42i | 0.0323824i | 0.999869 | + | 0.0161912i | \(0.00515405\pi\) | ||||
−0.999869 | + | 0.0161912i | \(0.994846\pi\) | |||||||
\(588\) | 1.70901e44 | + | 8.88972e43i | 0.836966 | + | 0.435363i | ||||
\(589\) | 2.48186e44 | 1.18286 | ||||||||
\(590\) | −7.00623e43 | − | 1.15418e44i | −0.324977 | − | 0.535355i | ||||
\(591\) | 3.93795e44i | 1.77775i | ||||||||
\(592\) | 2.78061e43 | + | 3.96581e43i | 0.122178 | + | 0.174255i | ||||
\(593\) | 6.27744e43 | 0.268477 | 0.134239 | − | 0.990949i | \(-0.457141\pi\) | ||||
0.134239 | + | 0.990949i | \(0.457141\pi\) | |||||||
\(594\) | −3.24000e44 | + | 1.96678e44i | −1.34885 | + | 0.818789i | ||||
\(595\) | − | 4.01520e43i | − | 0.162718i | ||||||
\(596\) | 2.37907e43 | − | 4.57367e43i | 0.0938572 | − | 0.180437i | ||||
\(597\) | 6.57707e43 | 0.252606 | ||||||||
\(598\) | 1.90950e43 | + | 3.14564e43i | 0.0714004 | + | 0.117623i | ||||
\(599\) | 5.41478e43i | 0.197129i | 0.995131 | + | 0.0985647i | \(0.0314251\pi\) | ||||
−0.995131 | + | 0.0985647i | \(0.968575\pi\) | |||||||
\(600\) | −2.74482e44 | + | 1.81206e43i | −0.972959 | + | 0.0642320i | ||||
\(601\) | −4.48094e44 | −1.54660 | −0.773299 | − | 0.634042i | \(-0.781395\pi\) | ||||
−0.773299 | + | 0.634042i | \(0.781395\pi\) | |||||||
\(602\) | 2.46520e43 | − | 1.49645e43i | 0.0828531 | − | 0.0502943i | ||||
\(603\) | 1.33057e43i | 0.0435472i | ||||||||
\(604\) | 1.82380e44 | + | 9.48682e43i | 0.581281 | + | 0.302364i | ||||
\(605\) | 5.92118e44 | 1.83790 | ||||||||
\(606\) | −1.35713e44 | − | 2.23570e44i | −0.410262 | − | 0.675850i | ||||
\(607\) | − | 1.09513e44i | − | 0.322440i | −0.986919 | − | 0.161220i | \(-0.948457\pi\) | ||
0.986919 | − | 0.161220i | \(-0.0515428\pi\) | |||||||
\(608\) | 8.94255e43 | − | 2.03669e44i | 0.256451 | − | 0.584074i | ||||
\(609\) | 1.67752e43 | 0.0468587 | ||||||||
\(610\) | 3.70170e44 | − | 2.24704e44i | 1.00722 | − | 0.611412i | ||||
\(611\) | 6.12025e44i | 1.62222i | ||||||||
\(612\) | 2.33718e43 | − | 4.49312e43i | 0.0603488 | − | 0.116018i | ||||
\(613\) | 1.27103e44 | 0.319734 | 0.159867 | − | 0.987139i | \(-0.448894\pi\) | ||||
0.159867 | + | 0.987139i | \(0.448894\pi\) | |||||||
\(614\) | 6.16991e43 | + | 1.01641e44i | 0.151212 | + | 0.249101i | ||||
\(615\) | 1.60583e44i | 0.383440i | ||||||||
\(616\) | 3.63428e42 | + | 5.50505e43i | 0.00845526 | + | 0.128077i | ||||
\(617\) | 6.26067e44 | 1.41925 | 0.709624 | − | 0.704581i | \(-0.248865\pi\) | ||||
0.709624 | + | 0.704581i | \(0.248865\pi\) | |||||||
\(618\) | 4.03090e43 | − | 2.44688e43i | 0.0890403 | − | 0.0540501i | ||||
\(619\) | 2.94769e44i | 0.634500i | 0.948342 | + | 0.317250i | \(0.102759\pi\) | ||||
−0.948342 | + | 0.317250i | \(0.897241\pi\) | |||||||
\(620\) | −1.11630e45 | − | 5.80665e44i | −2.34161 | − | 1.21803i | ||||
\(621\) | −6.59289e43 | −0.134775 | ||||||||
\(622\) | 4.09131e44 | + | 6.73989e44i | 0.815111 | + | 1.34278i | ||||
\(623\) | 2.91515e43i | 0.0566046i | ||||||||
\(624\) | −4.37543e44 | + | 3.06781e44i | −0.828071 | + | 0.580598i | ||||
\(625\) | −5.27573e44 | −0.973201 | ||||||||
\(626\) | −5.24906e44 | + | 3.18634e44i | −0.943827 | + | 0.572931i | ||||
\(627\) | − | 5.23482e44i | − | 0.917532i | ||||||
\(628\) | 1.41501e44 | − | 2.72030e44i | 0.241772 | − | 0.464796i | ||||
\(629\) | −1.72243e44 | −0.286900 | ||||||||
\(630\) | 3.74163e42 | + | 6.16383e42i | 0.00607592 | + | 0.0100093i | ||||
\(631\) | − | 3.61763e44i | − | 0.572736i | −0.958120 | − | 0.286368i | \(-0.907552\pi\) | ||
0.958120 | − | 0.286368i | \(-0.0924479\pi\) | |||||||
\(632\) | 5.91699e44 | − | 3.90623e43i | 0.913329 | − | 0.0602954i | ||||
\(633\) | −1.26812e44 | −0.190853 | ||||||||
\(634\) | 7.11476e44 | − | 4.31887e44i | 1.04408 | − | 0.633786i | ||||
\(635\) | − | 1.17056e45i | − | 1.67500i | ||||||
\(636\) | 8.57624e44 | + | 4.46108e44i | 1.19669 | + | 0.622481i | ||||
\(637\) | −7.76514e44 | −1.05662 | ||||||||
\(638\) | −3.44204e44 | − | 5.67029e44i | −0.456756 | − | 0.752444i | ||||
\(639\) | 4.67637e43i | 0.0605195i | ||||||||
\(640\) | −8.78735e44 | + | 7.06851e44i | −1.10912 | + | 0.892172i | ||||
\(641\) | −7.60593e44 | −0.936319 | −0.468159 | − | 0.883644i | \(-0.655083\pi\) | ||||
−0.468159 | + | 0.883644i | \(0.655083\pi\) | |||||||
\(642\) | 5.28806e44 | − | 3.21001e44i | 0.634945 | − | 0.385431i | ||||
\(643\) | − | 1.05982e45i | − | 1.24124i | −0.784112 | − | 0.620619i | \(-0.786881\pi\) | ||
0.784112 | − | 0.620619i | \(-0.213119\pi\) | |||||||
\(644\) | −4.42853e42 | + | 8.51366e42i | −0.00505924 | + | 0.00972618i | ||||
\(645\) | 1.38731e45 | 1.54603 | ||||||||
\(646\) | 4.10467e44 | + | 6.76189e44i | 0.446229 | + | 0.735103i | ||||
\(647\) | 4.77969e44i | 0.506911i | 0.967347 | + | 0.253455i | \(0.0815671\pi\) | ||||
−0.967347 | + | 0.253455i | \(0.918433\pi\) | |||||||
\(648\) | −5.68914e43 | − | 8.61768e44i | −0.0588636 | − | 0.891641i | ||||
\(649\) | −6.59744e44 | −0.665979 | ||||||||
\(650\) | 9.47857e44 | − | 5.75378e44i | 0.933532 | − | 0.566682i | ||||
\(651\) | − | 1.55491e44i | − | 0.149420i | ||||||
\(652\) | −3.64502e44 | − | 1.89602e44i | −0.341774 | − | 0.177779i | ||||
\(653\) | −1.50534e45 | −1.37729 | −0.688643 | − | 0.725101i | \(-0.741793\pi\) | ||||
−0.688643 | + | 0.725101i | \(0.741793\pi\) | |||||||
\(654\) | 4.41239e44 | + | 7.26882e44i | 0.393940 | + | 0.648963i | ||||
\(655\) | 3.01219e45i | 2.62435i | ||||||||
\(656\) | 1.91411e44 | + | 2.72997e44i | 0.162744 | + | 0.232111i | ||||
\(657\) | 6.66730e43 | 0.0553228 | ||||||||
\(658\) | −1.36438e44 | + | 8.28220e43i | −0.110490 | + | 0.0670705i | ||||
\(659\) | 1.35593e45i | 1.07169i | 0.844315 | + | 0.535847i | \(0.180008\pi\) | ||||
−0.844315 | + | 0.535847i | \(0.819992\pi\) | |||||||
\(660\) | −1.22476e45 | + | 2.35455e45i | −0.944818 | + | 1.81637i | ||||
\(661\) | 1.79337e45 | 1.35035 | 0.675176 | − | 0.737657i | \(-0.264068\pi\) | ||||
0.675176 | + | 0.737657i | \(0.264068\pi\) | |||||||
\(662\) | −5.99862e43 | − | 9.88191e43i | −0.0440883 | − | 0.0726295i | ||||
\(663\) | − | 1.90034e45i | − | 1.36337i | ||||||
\(664\) | 1.75462e45 | − | 1.15835e44i | 1.22884 | − | 0.0811243i | ||||
\(665\) | −1.12619e44 | −0.0769954 | ||||||||
\(666\) | 2.64415e43 | − | 1.60508e43i | 0.0176481 | − | 0.0107129i | ||||
\(667\) | − | 1.15381e44i | − | 0.0751835i | ||||||
\(668\) | −7.06475e44 | − | 3.67485e44i | −0.449441 | − | 0.233785i | ||||
\(669\) | 4.71403e44 | 0.292802 | ||||||||
\(670\) | 5.46731e44 | + | 9.00665e44i | 0.331571 | + | 0.546218i | ||||
\(671\) | − | 2.11594e45i | − | 1.25297i | ||||||
\(672\) | −1.27601e44 | − | 5.60260e43i | −0.0737811 | − | 0.0323952i | ||||
\(673\) | −1.07392e45 | −0.606361 | −0.303181 | − | 0.952933i | \(-0.598049\pi\) | ||||
−0.303181 | + | 0.952933i | \(0.598049\pi\) | |||||||
\(674\) | −4.55342e43 | + | 2.76406e43i | −0.0251061 | + | 0.0152401i | ||||
\(675\) | 1.98659e45i | 1.06967i | ||||||||
\(676\) | 1.16433e44 | − | 2.23837e44i | 0.0612248 | − | 0.117702i | ||||
\(677\) | 1.73726e45 | 0.892165 | 0.446083 | − | 0.894992i | \(-0.352819\pi\) | ||||
0.446083 | + | 0.894992i | \(0.352819\pi\) | |||||||
\(678\) | −1.92185e45 | − | 3.16599e45i | −0.963929 | − | 1.58794i | ||||
\(679\) | 2.97747e44i | 0.145858i | ||||||||
\(680\) | −2.64184e44 | − | 4.00175e45i | −0.126405 | − | 1.91473i | ||||
\(681\) | 1.88924e45 | 0.882943 | ||||||||
\(682\) | −5.25586e45 | + | 3.19046e45i | −2.39935 | + | 1.45648i | ||||
\(683\) | − | 3.65073e45i | − | 1.62798i | −0.580882 | − | 0.813988i | \(-0.697292\pi\) | ||
0.580882 | − | 0.813988i | \(-0.302708\pi\) | |||||||
\(684\) | −1.26024e44 | − | 6.55534e43i | −0.0548978 | − | 0.0285560i | ||||
\(685\) | 3.07215e45 | 1.30735 | ||||||||
\(686\) | −2.10924e44 | − | 3.47469e44i | −0.0876879 | − | 0.144454i | ||||
\(687\) | 1.52283e45i | 0.618507i | ||||||||
\(688\) | 2.35849e45 | − | 1.65364e45i | 0.935876 | − | 0.656185i | ||||
\(689\) | −3.89674e45 | −1.51075 | ||||||||
\(690\) | −3.94637e44 | + | 2.39557e44i | −0.149490 | + | 0.0907450i | ||||
\(691\) | 4.60791e45i | 1.70551i | 0.522309 | + | 0.852756i | \(0.325071\pi\) | ||||
−0.522309 | + | 0.852756i | \(0.674929\pi\) | |||||||
\(692\) | −4.06838e44 | + | 7.82130e44i | −0.147138 | + | 0.282866i | ||||
\(693\) | 3.52332e43 | 0.0124515 | ||||||||
\(694\) | −2.40189e45 | − | 3.95680e45i | −0.829473 | − | 1.36644i | ||||
\(695\) | − | 2.95921e45i | − | 0.998664i | ||||||
\(696\) | 1.67190e45 | − | 1.10374e44i | 0.551394 | − | 0.0364014i | ||||
\(697\) | −1.18568e45 | −0.382158 | ||||||||
\(698\) | 1.02075e45 | − | 6.19626e44i | 0.321538 | − | 0.195183i | ||||
\(699\) | 2.89154e45i | 0.890215i | ||||||||
\(700\) | 2.56537e44 | + | 1.33442e44i | 0.0771935 | + | 0.0401536i | ||||
\(701\) | 2.86431e45 | 0.842425 | 0.421212 | − | 0.906962i | \(-0.361605\pi\) | ||||
0.421212 | + | 0.906962i | \(0.361605\pi\) | |||||||
\(702\) | 2.00257e45 | + | 3.29897e45i | 0.575697 | + | 0.948383i | ||||
\(703\) | 4.83110e44i | 0.135756i | ||||||||
\(704\) | 7.24421e44 | + | 5.46270e45i | 0.198989 | + | 1.50053i | ||||
\(705\) | −7.67817e45 | −2.06173 | ||||||||
\(706\) | 1.39912e45 | − | 8.49309e44i | 0.367265 | − | 0.222941i | ||||
\(707\) | 2.74931e44i | 0.0705525i | ||||||||
\(708\) | 7.69037e44 | − | 1.47844e45i | 0.192937 | − | 0.370913i | ||||
\(709\) | 6.73611e45 | 1.65223 | 0.826113 | − | 0.563504i | \(-0.190547\pi\) | ||||
0.826113 | + | 0.563504i | \(0.190547\pi\) | |||||||
\(710\) | 1.92152e45 | + | 3.16545e45i | 0.460799 | + | 0.759104i | ||||
\(711\) | − | 3.78696e44i | − | 0.0887928i | ||||||
\(712\) | 1.91805e44 | + | 2.90538e45i | 0.0439724 | + | 0.666076i | ||||
\(713\) | −1.06948e45 | −0.239741 | ||||||||
\(714\) | 4.23640e44 | − | 2.57162e44i | 0.0928593 | − | 0.0563684i | ||||
\(715\) | − | 1.06982e46i | − | 2.29306i | ||||||
\(716\) | 4.80090e44 | + | 2.49727e44i | 0.100627 | + | 0.0523428i | ||||
\(717\) | 5.19695e44 | 0.106523 | ||||||||
\(718\) | −3.04564e45 | − | 5.01728e45i | −0.610502 | − | 1.00572i | ||||
\(719\) | 6.36501e45i | 1.24778i | 0.781514 | + | 0.623888i | \(0.214448\pi\) | ||||
−0.781514 | + | 0.623888i | \(0.785552\pi\) | |||||||
\(720\) | 4.13465e44 | + | 5.89700e44i | 0.0792719 | + | 0.113061i | ||||
\(721\) | −4.95693e43 | −0.00929498 | ||||||||
\(722\) | −2.76437e45 | + | 1.67806e45i | −0.506992 | + | 0.307760i | ||||
\(723\) | 1.85953e45i | 0.333573i | ||||||||
\(724\) | −2.39540e44 | + | 4.60505e44i | −0.0420301 | + | 0.0808012i | ||||
\(725\) | −3.47672e45 | −0.596707 | ||||||||
\(726\) | 3.79235e45 | + | 6.24738e45i | 0.636681 | + | 1.04885i | ||||
\(727\) | − | 8.93864e45i | − | 1.46798i | −0.679159 | − | 0.733991i | \(-0.737655\pi\) | ||
0.679159 | − | 0.733991i | \(-0.262345\pi\) | |||||||
\(728\) | 5.60524e44 | − | 3.70042e43i | 0.0900517 | − | 0.00594496i | ||||
\(729\) | −6.85435e45 | −1.07727 | ||||||||
\(730\) | 4.51311e45 | − | 2.73959e45i | 0.693921 | − | 0.421231i | ||||
\(731\) | 1.02434e46i | 1.54086i | ||||||||
\(732\) | 4.74167e45 | + | 2.46646e45i | 0.697837 | + | 0.362992i | ||||
\(733\) | −3.50667e45 | −0.504930 | −0.252465 | − | 0.967606i | \(-0.581241\pi\) | ||||
−0.252465 | + | 0.967606i | \(0.581241\pi\) | |||||||
\(734\) | 3.88998e44 | + | 6.40822e44i | 0.0548038 | + | 0.0902818i | ||||
\(735\) | − | 9.74176e45i | − | 1.34289i | ||||||
\(736\) | −3.85353e44 | + | 8.77652e44i | −0.0519773 | + | 0.118380i | ||||
\(737\) | 5.14831e45 | 0.679492 | ||||||||
\(738\) | 1.82017e44 | − | 1.10490e44i | 0.0235077 | − | 0.0142699i | ||||
\(739\) | 3.33091e45i | 0.420971i | 0.977597 | + | 0.210486i | \(0.0675045\pi\) | ||||
−0.977597 | + | 0.210486i | \(0.932496\pi\) | |||||||
\(740\) | 1.13030e45 | − | 2.17296e45i | 0.139794 | − | 0.268747i | ||||
\(741\) | −5.33009e45 | −0.645124 | ||||||||
\(742\) | −5.27324e44 | − | 8.68695e44i | −0.0624619 | − | 0.102898i | ||||
\(743\) | − | 5.60428e45i | − | 0.649679i | −0.945769 | − | 0.324840i | \(-0.894690\pi\) | ||
0.945769 | − | 0.324840i | \(-0.105310\pi\) | |||||||
\(744\) | −1.02307e45 | − | 1.54970e46i | −0.116075 | − | 1.75825i | ||||
\(745\) | −2.60710e45 | −0.289505 | ||||||||
\(746\) | 6.06803e45 | − | 3.68348e45i | 0.659518 | − | 0.400347i | ||||
\(747\) | − | 1.12299e45i | − | 0.119466i | ||||||
\(748\) | −1.73850e46 | − | 9.04313e45i | −1.81030 | − | 0.941658i | ||||
\(749\) | −6.50290e44 | −0.0662824 | ||||||||
\(750\) | 1.83725e44 | + | 3.02663e44i | 0.0183311 | + | 0.0301980i | ||||
\(751\) | 1.89091e46i | 1.84685i | 0.383775 | + | 0.923427i | \(0.374624\pi\) | ||||
−0.383775 | + | 0.923427i | \(0.625376\pi\) | |||||||
\(752\) | −1.30532e46 | + | 9.15217e45i | −1.24805 | + | 0.875061i | ||||
\(753\) | 7.63054e45 | 0.714226 | ||||||||
\(754\) | −5.77348e45 | + | 3.50468e45i | −0.529050 | + | 0.321149i | ||||
\(755\) | − | 1.03961e46i | − | 0.932650i | ||||||
\(756\) | −4.64438e44 | + | 8.92862e44i | −0.0407924 | + | 0.0784216i | ||||
\(757\) | 2.00538e46 | 1.72450 | 0.862250 | − | 0.506483i | \(-0.169055\pi\) | ||||
0.862250 | + | 0.506483i | \(0.169055\pi\) | |||||||
\(758\) | 3.16746e45 | + | 5.21796e45i | 0.266688 | + | 0.439333i | ||||
\(759\) | 2.25579e45i | 0.185965i | ||||||||
\(760\) | −1.12242e46 | + | 7.40987e44i | −0.906017 | + | 0.0598127i | ||||
\(761\) | 1.36781e46 | 1.08112 | 0.540558 | − | 0.841307i | \(-0.318213\pi\) | ||||
0.540558 | + | 0.841307i | \(0.318213\pi\) | |||||||
\(762\) | 1.23505e46 | − | 7.49711e45i | 0.955881 | − | 0.580249i | ||||
\(763\) | − | 8.93871e44i | − | 0.0677457i | ||||||
\(764\) | 1.13531e46 | + | 5.90552e45i | 0.842600 | + | 0.438293i | ||||
\(765\) | −2.56118e45 | −0.186148 | ||||||||
\(766\) | −2.71006e44 | − | 4.46446e44i | −0.0192894 | − | 0.0317767i | ||||
\(767\) | 6.71750e45i | 0.468255i | ||||||||
\(768\) | −1.30860e46 | − | 4.74427e45i | −0.893360 | − | 0.323884i | ||||
\(769\) | 1.11734e46 | 0.747071 | 0.373536 | − | 0.927616i | \(-0.378145\pi\) | ||||
0.373536 | + | 0.927616i | \(0.378145\pi\) | |||||||
\(770\) | 2.38494e45 | − | 1.44773e45i | 0.156180 | − | 0.0948062i | ||||
\(771\) | − | 6.94377e45i | − | 0.445374i | ||||||
\(772\) | −1.98719e44 | + | 3.82028e44i | −0.0124842 | + | 0.0240004i | ||||
\(773\) | −2.18678e46 | −1.34565 | −0.672827 | − | 0.739800i | \(-0.734920\pi\) | ||||
−0.672827 | + | 0.739800i | \(0.734920\pi\) | |||||||
\(774\) | −9.54545e44 | − | 1.57248e45i | −0.0575362 | − | 0.0947831i | ||||
\(775\) | 3.22261e46i | 1.90274i | ||||||||
\(776\) | 1.95906e45 | + | 2.96749e46i | 0.113308 | + | 1.71634i | ||||
\(777\) | 3.02673e44 | 0.0171490 | ||||||||
\(778\) | −5.43623e44 | + | 3.29996e44i | −0.0301734 | + | 0.0183162i | ||||
\(779\) | 3.32561e45i | 0.180831i | ||||||||
\(780\) | 2.39740e46 | + | 1.24705e46i | 1.27711 | + | 0.664309i | ||||
\(781\) | 1.80941e46 | 0.944321 | ||||||||
\(782\) | −1.76879e45 | − | 2.91384e45i | −0.0904415 | − | 0.148990i | ||||
\(783\) | − | 1.21005e46i | − | 0.606200i | ||||||
\(784\) | −1.16119e46 | − | 1.65614e46i | −0.569963 | − | 0.812904i | ||||
\(785\) | −1.55063e46 | −0.745753 | ||||||||
\(786\) | −3.17813e46 | + | 1.92922e46i | −1.49765 | + | 0.909121i | ||||
\(787\) | 1.68275e46i | 0.777007i | 0.921447 | + | 0.388503i | \(0.127008\pi\) | ||||
−0.921447 | + | 0.388503i | \(0.872992\pi\) | |||||||
\(788\) | 1.90806e46 | − | 3.66816e46i | 0.863320 | − | 1.65970i | ||||
\(789\) | −1.08496e46 | −0.481041 | ||||||||
\(790\) | −1.55606e46 | − | 2.56341e46i | −0.676074 | − | 1.11374i | ||||
\(791\) | 3.89332e45i | 0.165767i | ||||||||
\(792\) | 3.51152e45 | − | 2.31821e44i | 0.146518 | − | 0.00967273i | ||||
\(793\) | −2.15444e46 | −0.880976 | ||||||||
\(794\) | 3.32945e46 | − | 2.02107e46i | 1.33427 | − | 0.809942i | ||||
\(795\) | − | 4.88865e46i | − | 1.92006i | ||||||
\(796\) | −6.12647e45 | − | 3.18679e45i | −0.235831 | − | 0.122672i | ||||
\(797\) | −3.48117e45 | −0.131339 | −0.0656693 | − | 0.997841i | \(-0.520918\pi\) | ||||
−0.0656693 | + | 0.997841i | \(0.520918\pi\) | |||||||
\(798\) | −7.21292e44 | − | 1.18823e45i | −0.0266726 | − | 0.0439394i | ||||
\(799\) | − | 5.66925e46i | − | 2.05483i | ||||||
\(800\) | 2.64457e46 | + | 1.16116e46i | 0.939541 | + | 0.412527i | ||||
\(801\) | 1.85949e45 | 0.0647551 | ||||||||
\(802\) | 4.59330e45 | − | 2.78827e45i | 0.156796 | − | 0.0951798i | ||||
\(803\) | − | 2.57975e46i | − | 0.863234i | ||||||
\(804\) | −6.00117e45 | + | 1.15370e46i | −0.196852 | + | 0.378439i | ||||
\(805\) | 4.85298e44 | 0.0156054 | ||||||||
\(806\) | 3.24853e46 | + | 5.35151e46i | 1.02406 | + | 1.68700i | ||||
\(807\) | 7.42948e45i | 0.229605i | ||||||||
\(808\) | 1.80893e45 | + | 2.74010e46i | 0.0548076 | + | 0.830203i | ||||
\(809\) | −2.87821e46 | −0.854961 | −0.427481 | − | 0.904025i | \(-0.640599\pi\) | ||||
−0.427481 | + | 0.904025i | \(0.640599\pi\) | |||||||
\(810\) | −3.73342e46 | + | 2.26630e46i | −1.08729 | + | 0.660019i | ||||
\(811\) | 4.47972e46i | 1.27914i | 0.768733 | + | 0.639569i | \(0.220887\pi\) | ||||
−0.768733 | + | 0.639569i | \(0.779113\pi\) | |||||||
\(812\) | −1.56259e45 | − | 8.12807e44i | −0.0437470 | − | 0.0227558i | ||||
\(813\) | −4.17364e46 | −1.14569 | ||||||||
\(814\) | −6.21045e45 | − | 1.02309e46i | −0.167160 | − | 0.275374i | ||||
\(815\) | 2.07775e46i | 0.548366i | ||||||||
\(816\) | 4.05301e46 | − | 2.84175e46i | 1.04890 | − | 0.735432i | ||||
\(817\) | 2.87307e46 | 0.729111 | ||||||||
\(818\) | −4.00606e46 | + | 2.43180e46i | −0.996929 | + | 0.605166i | ||||
\(819\) | − | 3.58744e44i | − | 0.00875472i | ||||||
\(820\) | 7.78073e45 | − | 1.49581e46i | 0.186208 | − | 0.357977i | ||||
\(821\) | −2.72426e46 | −0.639378 | −0.319689 | − | 0.947523i | \(-0.603578\pi\) | ||||
−0.319689 | + | 0.947523i | \(0.603578\pi\) | |||||||
\(822\) | 1.96762e46 | + | 3.24140e46i | 0.452890 | + | 0.746076i | ||||
\(823\) | − | 1.08853e46i | − | 0.245721i | −0.992424 | − | 0.122861i | \(-0.960793\pi\) | ||
0.992424 | − | 0.122861i | \(-0.0392068\pi\) | |||||||
\(824\) | −4.94033e45 | + | 3.26146e44i | −0.109376 | + | 0.00722066i | ||||
\(825\) | 6.79724e46 | 1.47594 | ||||||||
\(826\) | −1.49753e45 | + | 9.09043e44i | −0.0318929 | + | 0.0193599i | ||||
\(827\) | 3.00168e46i | 0.627013i | 0.949586 | + | 0.313507i | \(0.101504\pi\) | ||||
−0.949586 | + | 0.313507i | \(0.898496\pi\) | |||||||
\(828\) | 5.43062e44 | + | 2.82483e44i | 0.0111266 | + | 0.00578772i | ||||
\(829\) | 7.52687e46 | 1.51266 | 0.756331 | − | 0.654189i | \(-0.226990\pi\) | ||||
0.756331 | + | 0.654189i | \(0.226990\pi\) | |||||||
\(830\) | −4.61435e46 | − | 7.60152e46i | −0.909622 | − | 1.49848i | ||||
\(831\) | 6.03938e46i | 1.16782i | ||||||||
\(832\) | 5.56212e46 | − | 7.37605e45i | 1.05503 | − | 0.139911i | ||||
\(833\) | 7.19292e46 | 1.33840 | ||||||||
\(834\) | 3.12224e46 | − | 1.89529e46i | 0.569914 | − | 0.345955i | ||||
\(835\) | 4.02707e46i | 0.721117i | ||||||||
\(836\) | −2.53643e46 | + | 4.87618e46i | −0.445576 | + | 0.856602i | ||||
\(837\) | −1.12161e47 | −1.93301 | ||||||||
\(838\) | −3.88273e46 | − | 6.39628e46i | −0.656497 | − | 1.08149i | ||||
\(839\) | − | 5.53407e46i | − | 0.918023i | −0.888430 | − | 0.459011i | \(-0.848204\pi\) | ||
0.888430 | − | 0.459011i | \(-0.151796\pi\) | |||||||
\(840\) | 4.64237e44 | + | 7.03206e45i | 0.00755563 | + | 0.114450i | ||||
\(841\) | −4.14463e46 | −0.661835 | ||||||||
\(842\) | −1.54465e44 | + | 9.37647e43i | −0.00242011 | + | 0.00146908i | ||||
\(843\) | − | 2.39958e46i | − | 0.368888i | ||||||
\(844\) | 1.18124e46 | + | 6.14440e45i | 0.178179 | + | 0.0926831i | ||||
\(845\) | −1.27592e46 | −0.188850 | ||||||||
\(846\) | 5.28298e45 | + | 8.70300e45i | 0.0767279 | + | 0.126399i | ||||
\(847\) | − | 7.68260e45i | − | 0.109490i | ||||||
\(848\) | −5.82714e46 | − | 8.31089e46i | −0.814933 | − | 1.16229i | ||||
\(849\) | 9.46339e46 | 1.29874 | ||||||||
\(850\) | −8.78009e46 | + | 5.32978e46i | −1.18249 | + | 0.717805i | ||||
\(851\) | − | 2.08182e45i | − | 0.0275150i | ||||||
\(852\) | −2.10915e46 | + | 4.05476e46i | −0.273574 | + | 0.525934i | ||||
\(853\) | −5.02319e45 | −0.0639433 | −0.0319717 | − | 0.999489i | \(-0.510179\pi\) | ||||
−0.0319717 | + | 0.999489i | \(0.510179\pi\) | |||||||
\(854\) | −2.91549e45 | − | 4.80288e45i | −0.0364238 | − | 0.0600034i | ||||
\(855\) | 7.18364e45i | 0.0880819i | ||||||||
\(856\) | −6.48112e46 | + | 4.27865e45i | −0.779955 | + | 0.0514904i | ||||
\(857\) | 9.46054e46 | 1.11744 | 0.558718 | − | 0.829357i | \(-0.311293\pi\) | ||||
0.558718 | + | 0.829357i | \(0.311293\pi\) | |||||||
\(858\) | 1.12876e47 | − | 6.85191e46i | 1.30859 | − | 0.794356i | ||||
\(859\) | 1.91602e46i | 0.218026i | 0.994040 | + | 0.109013i | \(0.0347691\pi\) | ||||
−0.994040 | + | 0.109013i | \(0.965231\pi\) | |||||||
\(860\) | −1.29227e47 | − | 6.72196e46i | −1.44337 | − | 0.750793i | ||||
\(861\) | 2.08353e45 | 0.0228428 | ||||||||
\(862\) | 4.69142e46 | + | 7.72848e46i | 0.504880 | + | 0.831722i | ||||
\(863\) | − | 9.20747e46i | − | 0.972675i | −0.873771 | − | 0.486338i | \(-0.838333\pi\) | ||
0.873771 | − | 0.486338i | \(-0.161667\pi\) | |||||||
\(864\) | −4.04135e46 | + | 9.20430e46i | −0.419090 | + | 0.954488i | ||||
\(865\) | 4.45832e46 | 0.453851 | ||||||||
\(866\) | 1.02643e47 | − | 6.23075e46i | 1.02575 | − | 0.622664i | ||||
\(867\) | 7.91692e46i | 0.776696i | ||||||||
\(868\) | −7.53401e45 | + | 1.44838e46i | −0.0725622 | + | 0.139498i | ||||
\(869\) | −1.46527e47 | −1.38549 | ||||||||
\(870\) | −4.39680e46 | − | 7.24313e46i | −0.408158 | − | 0.672385i | ||||
\(871\) | − | 5.24200e46i | − | 0.477756i | ||||||
\(872\) | −5.88131e45 | − | 8.90876e46i | −0.0526272 | − | 0.797175i | ||||
\(873\) | 1.89924e46 | 0.166860 | ||||||||
\(874\) | −8.17278e45 | + | 4.96112e45i | −0.0704996 | + | 0.0427954i | ||||
\(875\) | − | 3.72194e44i | − | 0.00315240i | ||||||
\(876\) | 5.78104e46 | + | 3.00711e46i | 0.480773 | + | 0.250082i | ||||
\(877\) | −1.63787e47 | −1.33748 | −0.668739 | − | 0.743497i | \(-0.733166\pi\) | ||||
−0.668739 | + | 0.743497i | \(0.733166\pi\) | |||||||
\(878\) | 1.20710e47 | + | 1.98853e47i | 0.967901 | + | 1.59449i | ||||
\(879\) | 3.90947e46i | 0.307819i | ||||||||
\(880\) | 2.28170e47 | − | 1.59980e47i | 1.76415 | − | 1.23693i | ||||
\(881\) | 3.60559e46 | 0.273755 | 0.136877 | − | 0.990588i | \(-0.456293\pi\) | ||||
0.136877 | + | 0.990588i | \(0.456293\pi\) | |||||||
\(882\) | −1.10420e46 | + | 6.70285e45i | −0.0823288 | + | 0.0499760i | ||||
\(883\) | − | 1.54388e47i | − | 1.13042i | −0.824945 | − | 0.565212i | \(-0.808794\pi\) | ||
0.824945 | − | 0.565212i | \(-0.191206\pi\) | |||||||
\(884\) | −9.20770e46 | + | 1.77014e47i | −0.662087 | + | 1.27283i | ||||
\(885\) | −8.42745e46 | −0.595119 | ||||||||
\(886\) | 1.04216e47 | + | 1.71681e47i | 0.722759 | + | 1.19065i | ||||
\(887\) | 1.06318e47i | 0.724150i | 0.932149 | + | 0.362075i | \(0.117932\pi\) | ||||
−0.932149 | + | 0.362075i | \(0.882068\pi\) | |||||||
\(888\) | 3.01659e46 | − | 1.99147e45i | 0.201795 | − | 0.0133219i | ||||
\(889\) | −1.51878e46 | −0.0997852 | ||||||||
\(890\) | 1.25869e47 | − | 7.64065e46i | 0.812232 | − | 0.493049i | ||||
\(891\) | 2.13407e47i | 1.35259i | ||||||||
\(892\) | −4.39107e46 | − | 2.28409e46i | −0.273358 | − | 0.142192i | ||||
\(893\) | −1.59012e47 | −0.972313 | ||||||||
\(894\) | −1.66977e46 | − | 2.75072e46i | −0.100290 | − | 0.165214i | ||||
\(895\) | − | 2.73662e46i | − | 0.161453i | ||||||
\(896\) | 9.17124e45 | + | 1.14014e46i | 0.0531496 | + | 0.0660739i | ||||
\(897\) | 2.29685e46 | 0.130753 | ||||||||
\(898\) | −1.50378e47 | + | 9.12843e46i | −0.840939 | + | 0.510475i | ||||
\(899\) | − | 1.96292e47i | − | 1.07832i | ||||||
\(900\) | 8.51189e45 | − | 1.63638e46i | 0.0459352 | − | 0.0883086i | ||||
\(901\) | 3.60958e47 | 1.91364 | ||||||||
\(902\) | −4.27512e46 | − | 7.04269e46i | −0.222661 | − | 0.366804i | ||||
\(903\) | − | 1.80001e46i | − | 0.0921024i | ||||||
\(904\) | 2.56165e46 | + | 3.88028e47i | 0.128773 | + | 1.95060i | ||||
\(905\) | 2.62499e46 | 0.129643 | ||||||||
\(906\) | 1.09688e47 | − | 6.65840e46i | 0.532241 | − | 0.323086i | ||||
\(907\) | 1.29696e47i | 0.618314i | 0.951011 | + | 0.309157i | \(0.100047\pi\) | ||||
−0.951011 | + | 0.309157i | \(0.899953\pi\) | |||||||
\(908\) | −1.75980e47 | − | 9.15393e46i | −0.824310 | − | 0.428779i | ||||
\(909\) | 1.75371e46 | 0.0807113 | ||||||||
\(910\) | −1.47408e46 | − | 2.42835e46i | −0.0666590 | − | 0.109812i | ||||
\(911\) | − | 3.45293e47i | − | 1.53424i | −0.641503 | − | 0.767120i | \(-0.721689\pi\) | ||
0.641503 | − | 0.767120i | \(-0.278311\pi\) | |||||||
\(912\) | −7.97057e46 | − | 1.13679e47i | −0.347994 | − | 0.496322i | ||||
\(913\) | −4.34512e47 | −1.86410 | ||||||||
\(914\) | −7.19310e46 | + | 4.36643e46i | −0.303233 | + | 0.184072i | ||||
\(915\) | − | 2.70286e47i | − | 1.11966i | ||||||
\(916\) | 7.37859e46 | − | 1.41850e47i | 0.300363 | − | 0.577434i | ||||
\(917\) | 3.90826e46 | 0.156341 | ||||||||
\(918\) | −1.85500e47 | − | 3.05586e47i | −0.729224 | − | 1.20130i | ||||
\(919\) | 4.17823e47i | 1.61415i | 0.590447 | + | 0.807076i | \(0.298951\pi\) | ||||
−0.590447 | + | 0.807076i | \(0.701049\pi\) | |||||||
\(920\) | 4.83673e46 | − | 3.19307e45i | 0.183631 | − | 0.0121228i | ||||
\(921\) | 7.42149e46 | 0.276909 | ||||||||
\(922\) | 3.32295e47 | − | 2.01713e47i | 1.21851 | − | 0.739672i | ||||
\(923\) | − | 1.84234e47i | − | 0.663960i | ||||||
\(924\) | 3.05498e46 | + | 1.58910e46i | 0.108207 | + | 0.0562859i | ||||
\(925\) | −6.27302e46 | −0.218378 | ||||||||
\(926\) | −7.28710e46 | − | 1.20045e47i | −0.249333 | − | 0.410742i | ||||
\(927\) | 3.16189e45i | 0.0106334i | ||||||||
\(928\) | −1.61083e47 | − | 7.07273e46i | −0.532455 | − | 0.233786i | ||||
\(929\) | 1.68290e47 | 0.546772 | 0.273386 | − | 0.961904i | \(-0.411856\pi\) | ||||
0.273386 | + | 0.961904i | \(0.411856\pi\) | |||||||
\(930\) | −6.71374e47 | + | 4.07544e47i | −2.14406 | + | 1.30151i | ||||
\(931\) | − | 2.01748e47i | − | 0.633307i | ||||||
\(932\) | 1.40104e47 | − | 2.69344e47i | 0.432311 | − | 0.831099i | ||||
\(933\) | 4.92124e47 | 1.49269 | ||||||||
\(934\) | −9.43761e46 | − | 1.55472e47i | −0.281392 | − | 0.463555i | ||||
\(935\) | 9.90987e47i | 2.90457i | ||||||||
\(936\) | −2.36039e45 | − | 3.57542e46i | −0.00680097 | − | 0.103018i | ||||
\(937\) | 9.90873e46 | 0.280663 | 0.140331 | − | 0.990105i | \(-0.455183\pi\) | ||||
0.140331 | + | 0.990105i | \(0.455183\pi\) | |||||||
\(938\) | 1.16859e46 | − | 7.09371e45i | 0.0325400 | − | 0.0197528i | ||||
\(939\) | 3.83269e47i | 1.04919i | ||||||||
\(940\) | 7.15213e47 | + | 3.72031e47i | 1.92482 | + | 1.00123i | ||||
\(941\) | 1.96858e47 | 0.520858 | 0.260429 | − | 0.965493i | \(-0.416136\pi\) | ||||
0.260429 | + | 0.965493i | \(0.416136\pi\) | |||||||
\(942\) | −9.93137e46 | − | 1.63606e47i | −0.258342 | − | 0.425583i | ||||
\(943\) | − | 1.43307e46i | − | 0.0366507i | ||||||
\(944\) | −1.43270e47 | + | 1.00453e47i | −0.360249 | + | 0.252587i | ||||
\(945\) | 5.08952e46 | 0.125825 | ||||||||
\(946\) | −6.08434e47 | + | 3.69338e47i | −1.47896 | + | 0.897771i | ||||
\(947\) | 3.79998e47i | 0.908200i | 0.890951 | + | 0.454100i | \(0.150039\pi\) | ||||
−0.890951 | + | 0.454100i | \(0.849961\pi\) | |||||||
\(948\) | 1.70801e47 | − | 3.28358e47i | 0.401381 | − | 0.771638i | ||||
\(949\) | −2.62670e47 | −0.606947 | ||||||||
\(950\) | 1.49490e47 | + | 2.46265e47i | 0.339653 | + | 0.559533i | ||||
\(951\) | − | 5.19497e47i | − | 1.16063i | ||||||
\(952\) | −5.19219e46 | + | 3.42773e45i | −0.114067 | + | 0.00753036i | ||||
\(953\) | 7.54445e47 | 1.62982 | 0.814912 | − | 0.579584i | \(-0.196785\pi\) | ||||
0.814912 | + | 0.579584i | \(0.196785\pi\) | |||||||
\(954\) | −5.54116e46 | + | 3.36365e46i | −0.117714 | + | 0.0714557i | ||||
\(955\) | − | 6.47154e47i | − | 1.35193i | ||||||
\(956\) | −4.84090e46 | − | 2.51808e46i | −0.0994489 | − | 0.0517301i | ||||
\(957\) | −4.14026e47 | −0.836443 | ||||||||
\(958\) | 3.32414e47 | + | 5.47607e47i | 0.660436 | + | 1.08798i | ||||
\(959\) | − | 3.98605e46i | − | 0.0778834i | ||||||
\(960\) | 9.25363e46 | + | 6.97796e47i | 0.177817 | + | 1.34088i | ||||
\(961\) | −1.29031e48 | −2.43848 | ||||||||
\(962\) | −1.04171e47 | + | 6.32347e46i | −0.193617 | + | 0.117531i | ||||
\(963\) | 4.14802e46i | 0.0758263i | ||||||||
\(964\) | 9.00999e46 | − | 1.73213e47i | 0.161991 | − | 0.311422i | ||||
\(965\) | 2.17765e46 | 0.0385080 | ||||||||
\(966\) | 3.10820e45 | + | 5.12033e45i | 0.00540598 | + | 0.00890562i | ||||
\(967\) | − | 8.33368e47i | − | 1.42565i | −0.701342 | − | 0.712825i | \(-0.747415\pi\) | ||
0.701342 | − | 0.712825i | \(-0.252585\pi\) | |||||||
\(968\) | −5.05485e46 | − | 7.65687e47i | −0.0850555 | − | 1.28838i | ||||
\(969\) | 4.93731e47 | 0.817166 | ||||||||
\(970\) | 1.28560e48 | − | 7.80399e47i | 2.09295 | − | 1.27048i | ||||
\(971\) | 8.37495e47i | 1.34114i | 0.741846 | + | 0.670571i | \(0.233951\pi\) | ||||
−0.741846 | + | 0.670571i | \(0.766049\pi\) | |||||||
\(972\) | 1.08870e47 | + | 5.66306e46i | 0.171494 | + | 0.0892054i | ||||
\(973\) | −3.83952e46 | −0.0594937 | ||||||||
\(974\) | −1.62831e47 | − | 2.68243e47i | −0.248196 | − | 0.408869i | ||||
\(975\) | − | 6.92094e47i | − | 1.03775i | ||||||
\(976\) | −3.22174e47 | − | 4.59496e47i | −0.475218 | − | 0.677774i | ||||
\(977\) | −7.41388e45 | −0.0107580 | −0.00537901 | − | 0.999986i | \(-0.501712\pi\) | ||||
−0.00537901 | + | 0.999986i | \(0.501712\pi\) | |||||||
\(978\) | −2.19221e47 | + | 1.33074e47i | −0.312940 | + | 0.189964i | ||||
\(979\) | − | 7.19485e47i | − | 1.01041i | ||||||
\(980\) | −4.72018e47 | + | 9.07435e47i | −0.652141 | + | 1.25371i | ||||
\(981\) | −5.70175e46 | −0.0775004 | ||||||||
\(982\) | −1.42127e47 | − | 2.34136e47i | −0.190061 | − | 0.313100i | ||||
\(983\) | 5.93909e47i | 0.781382i | 0.920522 | + | 0.390691i | \(0.127764\pi\) | ||||
−0.920522 | + | 0.390691i | \(0.872236\pi\) | |||||||
\(984\) | 2.07655e47 | − | 1.37088e46i | 0.268795 | − | 0.0177451i | ||||
\(985\) | −2.09093e48 | −2.66294 | ||||||||
\(986\) | 5.34803e47 | − | 3.24642e47i | 0.670137 | − | 0.406793i | ||||
\(987\) | 9.96226e46i | 0.122824i | ||||||||
\(988\) | 4.96492e47 | + | 2.58259e47i | 0.602284 | + | 0.313288i | ||||
\(989\) | −1.23807e47 | −0.147776 | ||||||||
\(990\) | −9.23468e46 | − | 1.52129e47i | −0.108457 | − | 0.178669i | ||||
\(991\) | 5.19983e47i | 0.600911i | 0.953796 | + | 0.300456i | \(0.0971388\pi\) | ||||
−0.953796 | + | 0.300456i | \(0.902861\pi\) | |||||||
\(992\) | −6.55579e47 | + | 1.49310e48i | −0.745484 | + | 1.69786i | ||||
\(993\) | −7.21545e46 | −0.0807375 | ||||||||
\(994\) | 4.10710e46 | − | 2.49313e46i | 0.0452224 | − | 0.0274513i | ||||
\(995\) | 3.49223e47i | 0.378385i | ||||||||
\(996\) | 5.06493e47 | − | 9.73711e47i | 0.540037 | − | 1.03820i | ||||
\(997\) | 1.07840e48 | 1.13150 | 0.565752 | − | 0.824575i | \(-0.308586\pi\) | ||||
0.565752 | + | 0.824575i | \(0.308586\pi\) | |||||||
\(998\) | 7.43436e47 | + | 1.22471e48i | 0.767636 | + | 1.26458i | ||||
\(999\) | − | 2.18329e47i | − | 0.221852i |
(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.3.4 | yes | 14 | |
3.2 | odd | 2 | 36.33.d.b.19.11 | 14 | |||
4.3 | odd | 2 | inner | 4.33.b.b.3.3 | ✓ | 14 | |
12.11 | even | 2 | 36.33.d.b.19.12 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.33.b.b.3.3 | ✓ | 14 | 4.3 | odd | 2 | inner | |
4.33.b.b.3.4 | yes | 14 | 1.1 | even | 1 | trivial | |
36.33.d.b.19.11 | 14 | 3.2 | odd | 2 | |||
36.33.d.b.19.12 | 14 | 12.11 | even | 2 |