LMFDB - Embedded newform 81.9.f.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(8,81)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not 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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-28.3033 - 4.99063i) q^{2} +(535.607 + 194.945i) q^{4} +(-187.097 - 222.974i) q^{5} +(1603.17 - 583.507i) q^{7} +(-7814.83 - 4511.89i) q^{8} +(4182.68 + 7244.61i) q^{10} +(-14031.5 + 16722.1i) q^{11} +(-920.446 - 5220.11i) q^{13} +(-48287.1 + 8514.32i) q^{14} +(86890.4 + 72909.7i) q^{16} +(62632.7 - 36161.0i) q^{17} +(-90477.4 + 156711. i) q^{19} +(-56742.9 - 155900. i) q^{20} +(480590. - 403263. i) q^{22} +(177170. - 486771. i) q^{23} +(53119.4 - 301255. i) q^{25} +152340. i q^{26} +972423. q^{28} +(774286. + 136527. i) q^{29} +(139553. + 50793.3i) q^{31} +(-610520. - 727589. i) q^{32} +(-1.95318e6 + 710898. i) q^{34} +(-430056. - 248293. i) q^{35} +(740801. + 1.28311e6i) q^{37} +(3.34289e6 - 3.98391e6i) q^{38} +(456098. + 2.58666e6i) q^{40} +(-2.88334e6 + 508410. i) q^{41} +(-4.56281e6 - 3.82865e6i) q^{43} +(-1.07752e7 + 6.22109e6i) q^{44} +(-7.44379e6 + 1.28930e7i) q^{46} +(-115922. - 318492. i) q^{47} +(-2.18641e6 + 1.83462e6i) q^{49} +(-3.00690e6 + 8.26140e6i) q^{50} +(524637. - 2.97536e6i) q^{52} +7.93536e6i q^{53} +6.35383e6 q^{55} +(-1.51612e7 - 2.67334e6i) q^{56} +(-2.12334e7 - 7.72834e6i) q^{58} +(-3.57747e6 - 4.26346e6i) q^{59} +(1.32571e7 - 4.82519e6i) q^{61} +(-3.69632e6 - 2.13407e6i) q^{62} +(-870121. - 1.50709e6i) q^{64} +(-991734. + 1.18190e6i) q^{65} +(-422568. - 2.39650e6i) q^{67} +(4.05959e7 - 7.15815e6i) q^{68} +(1.09328e7 + 9.17375e6i) q^{70} +(-6.54312e6 + 3.77767e6i) q^{71} +(-1.24346e7 + 2.15374e7i) q^{73} +(-1.45636e7 - 4.00131e7i) q^{74} +(-7.90104e7 + 6.62976e7i) q^{76} +(-1.27374e7 + 3.49958e7i) q^{77} +(2.88661e6 - 1.63708e7i) q^{79} -3.30155e7i q^{80} +8.41451e7 q^{82} +(-8.88369e7 - 1.56643e7i) q^{83} +(-1.97813e7 - 7.19982e6i) q^{85} +(1.10035e8 + 1.31135e8i) q^{86} +(1.85102e8 - 6.73715e7i) q^{88} +(-8.49243e7 - 4.90311e7i) q^{89} +(-4.52160e6 - 7.83165e6i) q^{91} +(1.89787e8 - 2.26180e8i) q^{92} +(1.69149e6 + 9.59289e6i) q^{94} +(5.18706e7 - 9.14618e6i) q^{95} +(-2.32866e7 - 1.95398e7i) q^{97} +(7.10385e7 - 4.10141e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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 $

$2$	−28.3033	−	4.99063i	−1.76895	−	0.311914i	−0.808116	−	0.589024i	$-0.799512\pi$
$2$	−28.3033	−	4.99063i	−1.76895	−	0.311914i	−0.960838	+	0.277110i	$0.910624\pi$
$3$		0			0
$3$		0			0
$4$	535.607	+	194.945i	2.09222	+	0.761504i
$5$	−187.097	−	222.974i	−0.299355	−	0.356758i	0.595309	−	0.803497i	$-0.297030\pi$
$5$	−187.097	−	222.974i	−0.299355	−	0.356758i	−0.894664	+	0.446739i	$0.852585\pi$
$6$		0			0
$7$	1603.17	−	583.507i	0.667710	−	0.243027i	0.0141487	−	0.999900i	$-0.495496\pi$
$7$	1603.17	−	583.507i	0.667710	−	0.243027i	0.653562	+	0.756873i	$0.273274\pi$
$8$	−7814.83	−	4511.89i	−1.90792	−	1.10154i
$9$		0			0
$10$	4182.68	+	7244.61i	0.418268	+	0.724461i
$11$	−14031.5	+	16722.1i	−0.958369	+	1.14214i	0.0314069	+	0.999507i	$0.490001\pi$
$11$	−14031.5	+	16722.1i	−0.958369	+	1.14214i	−0.989776	+	0.142633i	$0.954443\pi$
$12$		0			0
$13$	−920.446	−	5220.11i	−0.0322274	−	0.182770i	0.964445	−	0.264284i	$-0.0851357\pi$
$13$	−920.446	−	5220.11i	−0.0322274	−	0.182770i	−0.996672	+	0.0815137i	$0.974025\pi$
$14$	−48287.1	+	8514.32i	−1.25695	+	0.221635i
$15$		0			0
$16$	86890.4	+	72909.7i	1.32584	+	1.11251i
$17$	62632.7	−	36161.0i	0.749903	−	0.432957i	−0.0757556	−	0.997126i	$-0.524137\pi$
$17$	62632.7	−	36161.0i	0.749903	−	0.432957i	0.825659	+	0.564170i	$0.190804\pi$
$18$		0			0
$19$	−90477.4	+	156711.i	−0.694266	+	1.20250i	0.276162	+	0.961111i	$0.410937\pi$
$19$	−90477.4	+	156711.i	−0.694266	+	1.20250i	−0.970428	+	0.241392i	$0.922396\pi$
$20$	−56742.9	−	155900.i	−0.354643	−	0.974374i
$21$		0			0
$22$	480590.	−	403263.i	2.05156	−	1.72146i
$23$	177170.	−	486771.i	0.633110	−	1.73946i	−0.0392472	−	0.999230i	$-0.512496\pi$
$23$	177170.	−	486771.i	0.633110	−	1.73946i	0.672357	−	0.740227i	$-0.265282\pi$
$24$		0			0
$25$	53119.4	−	301255.i	0.135986	−	0.771213i
$26$			152340.i			0.333365i
$27$		0			0
$28$	972423.			1.58206
$29$	774286.	+	136527.i	1.09474	+	0.193031i	0.691723	−	0.722163i	$-0.256852\pi$
$29$	774286.	+	136527.i	1.09474	+	0.193031i	0.403013	+	0.915194i	$0.367963\pi$
$30$		0			0
$31$	139553.	+	50793.3i	0.151110	+	0.0549996i	0.416468	−	0.909150i	$-0.363268\pi$
$31$	139553.	+	50793.3i	0.151110	+	0.0549996i	−0.265358	+	0.964150i	$0.585490\pi$
$32$	−610520.	−	727589.i	−0.582237	−	0.693883i
$33$		0			0
$34$	−1.95318e6	+	710898.i	−1.46159	+	0.531975i
$35$	−430056.	−	248293.i	−0.286584	−	0.165460i
$36$		0			0
$37$	740801.	+	1.28311e6i	0.395271	+	0.684629i	0.993136	−	0.116968i	$-0.0373174\pi$
$37$	740801.	+	1.28311e6i	0.395271	+	0.684629i	−0.597865	+	0.801597i	$0.703984\pi$
$38$	3.34289e6	−	3.98391e6i	1.60320	−	1.91062i
$39$		0			0
$40$	456098.	+	2.58666e6i	0.178163	+	1.01041i
$41$	−2.88334e6	+	508410.i	−1.02038	+	0.179920i	−0.658717	−	0.752391i	$-0.728900\pi$
$41$	−2.88334e6	+	508410.i	−1.02038	+	0.179920i	−0.361659	+	0.932311i	$0.617789\pi$
$42$		0			0
$43$	−4.56281e6	−	3.82865e6i	−1.33462	−	1.11988i	−0.982973	−	0.183751i	$-0.941176\pi$
$43$	−4.56281e6	−	3.82865e6i	−1.33462	−	1.11988i	−0.351651	−	0.936131i	$-0.614379\pi$
$44$	−1.07752e7	+	6.22109e6i	−2.87486	+	1.65980i
$45$		0			0
$46$	−7.44379e6	+	1.28930e7i	−1.66250	+	2.87954i
$47$	−115922.	−	318492.i	−0.0237560	−	0.0652691i	0.927248	−	0.374448i	$-0.122168\pi$
$47$	−115922.	−	318492.i	−0.0237560	−	0.0652691i	−0.951004	+	0.309179i	$0.899946\pi$
$48$		0			0
$49$	−2.18641e6	+	1.83462e6i	−0.379269	+	0.318245i
$50$	−3.00690e6	+	8.26140e6i	−0.481105	+	1.32182i
$51$		0			0
$52$	524637.	−	2.97536e6i	0.0717539	−	0.406936i
$53$			7.93536e6i			1.00569i	0.864377	+	0.502844i	$0.167713\pi$
$53$			7.93536e6i			1.00569i	−0.864377	+	0.502844i	$0.832287\pi$
$54$		0			0
$55$	6.35383e6			0.694360
$56$	−1.51612e7	−	2.67334e6i	−1.54164	−	0.271832i
$57$		0			0
$58$	−2.12334e7	−	7.72834e6i	−1.87633	−	0.682927i
$59$	−3.57747e6	−	4.26346e6i	−0.295235	−	0.351847i	0.597953	−	0.801531i	$-0.295981\pi$
$59$	−3.57747e6	−	4.26346e6i	−0.295235	−	0.351847i	−0.893188	+	0.449684i	$0.851537\pi$
$60$		0			0
$61$	1.32571e7	−	4.82519e6i	0.957479	−	0.348494i	0.184434	−	0.982845i	$-0.440955\pi$
$61$	1.32571e7	−	4.82519e6i	0.957479	−	0.348494i	0.773045	+	0.634351i	$0.218733\pi$
$62$	−3.69632e6	−	2.13407e6i	−0.250152	−	0.144425i
$63$		0			0
$64$	−870121.	−	1.50709e6i	−0.0518633	−	0.0898298i
$65$	−991734.	+	1.18190e6i	−0.0555574	+	0.0662107i
$66$		0			0
$67$	−422568.	−	2.39650e6i	−0.0209700	−	0.118927i	0.972526	−	0.232795i	$-0.0747870\pi$
$67$	−422568.	−	2.39650e6i	−0.0209700	−	0.118927i	−0.993496	+	0.113868i	$0.963676\pi$
$68$	4.05959e7	−	7.15815e6i	1.89866	−	0.334785i
$69$		0			0
$70$	1.09328e7	+	9.17375e6i	0.455345	+	0.382080i
$71$	−6.54312e6	+	3.77767e6i	−0.257485	+	0.148659i	−0.623187	−	0.782073i	$-0.714162\pi$
$71$	−6.54312e6	+	3.77767e6i	−0.257485	+	0.148659i	0.365702	+	0.930732i	$0.380829\pi$
$72$		0			0
$73$	−1.24346e7	+	2.15374e7i	−0.437866	+	0.758406i	−0.997525	−	0.0703173i	$-0.977599\pi$
$73$	−1.24346e7	+	2.15374e7i	−0.437866	+	0.758406i	0.559659	+	0.828723i	$0.310932\pi$
$74$	−1.45636e7	−	4.00131e7i	−0.485670	−	1.33437i
$75$		0			0
$76$	−7.90104e7	+	6.62976e7i	−2.36826	+	1.98721i
$77$	−1.27374e7	+	3.49958e7i	−0.362342	+	0.995528i
$78$		0			0
$79$	2.88661e6	−	1.63708e7i	0.0741106	−	0.420302i	−0.925069	−	0.379799i	$-0.875993\pi$
$79$	2.88661e6	−	1.63708e7i	0.0741106	−	0.420302i	0.999179	−	0.0405026i	$-0.0128959\pi$
$80$		−	3.30155e7i		−	0.806041i
$81$		0			0
$82$	8.41451e7			1.86112
$83$	−8.88369e7	−	1.56643e7i	−1.87189	−	0.330065i	−0.881929	−	0.471382i	$-0.843755\pi$
$83$	−8.88369e7	−	1.56643e7i	−1.87189	−	0.330065i	−0.989964	+	0.141317i	$0.954866\pi$
$84$		0			0
$85$	−1.97813e7	−	7.19982e6i	−0.378948	−	0.137926i
$86$	1.10035e8	+	1.31135e8i	2.01158	+	2.39731i
$87$		0			0
$88$	1.85102e8	−	6.73715e7i	3.08660	−	1.12343i
$89$	−8.49243e7	−	4.90311e7i	−1.35354	−	0.781468i	−0.364799	−	0.931086i	$-0.618862\pi$
$89$	−8.49243e7	−	4.90311e7i	−1.35354	−	0.781468i	−0.988744	+	0.149618i	$0.952196\pi$
$90$		0			0
$91$	−4.52160e6	−	7.83165e6i	−0.0659367	−	0.114206i
$92$	1.89787e8	−	2.26180e8i	2.64921	−	3.15720i
$93$		0			0
$94$	1.69149e6	+	9.59289e6i	0.0216649	+	0.122868i
$95$	5.18706e7	−	9.14618e6i	0.636835	−	0.112291i
$96$		0			0
$97$	−2.32866e7	−	1.95398e7i	−0.263038	−	0.220715i	0.501724	−	0.865028i	$-0.332699\pi$
$97$	−2.32866e7	−	1.95398e7i	−0.263038	−	0.220715i	−0.764762	+	0.644312i	$0.777144\pi$
$98$	7.10385e7	−	4.10141e7i	0.770175	−	0.444661i
$99$		0			0
$100$	8.71793e7	−	1.50999e8i	0.871793	−	1.50999i
$101$	4.34937e7	+	1.19498e8i	0.417966	+	1.14835i	0.952854	+	0.303430i	$0.0981317\pi$
$101$	4.34937e7	+	1.19498e8i	0.417966	+	1.14835i	−0.534888	+	0.844923i	$0.679646\pi$
$102$		0			0
$103$	−5.56755e7	+	4.67173e7i	−0.494670	+	0.415077i	−0.855696	−	0.517478i	$-0.826871\pi$
$103$	−5.56755e7	+	4.67173e7i	−0.494670	+	0.415077i	0.361026	+	0.932556i	$0.382426\pi$
$104$	−1.63594e7	+	4.49472e7i	−0.139841	+	0.384210i
$105$		0			0
$106$	3.96024e7	−	2.24597e8i	0.313688	−	1.77901i
$107$			1.92468e8i			1.46833i	0.678971	+	0.734165i	$0.262426\pi$
$107$			1.92468e8i			1.46833i	−0.678971	+	0.734165i	$0.737574\pi$
$108$		0			0
$109$	−2.41150e8			−1.70837			−0.854183	−	0.519972i	$-0.825942\pi$
$109$	−2.41150e8			−1.70837			−0.854183	+	0.519972i	$0.825942\pi$
$110$	−1.79834e8	−	3.17096e7i	−1.22829	−	0.216581i
$111$		0			0
$112$	1.81844e8	+	6.61857e7i	1.15565	+	0.420622i
$113$	−6.85578e7	−	8.17040e7i	−0.420478	−	0.501106i	0.513672	−	0.857987i	$-0.328285\pi$
$113$	−6.85578e7	−	8.17040e7i	−0.420478	−	0.501106i	−0.934150	+	0.356880i	$0.883840\pi$
$114$		0			0
$115$	−1.41685e8	+	5.15692e7i	−0.810090	+	0.294848i
$116$	3.88097e8	+	2.24068e8i	2.14343	+	1.23751i
$117$		0			0
$118$	7.99766e7	+	1.38524e8i	0.412511	+	0.714489i
$119$	7.93108e7	−	9.45189e7i	0.395498	−	0.471336i
$120$		0			0
$121$	−4.55220e7	−	2.58168e8i	−0.212364	−	1.20437i
$122$	−3.99300e8	+	7.04074e7i	−1.80244	+	0.317818i
$123$		0			0
$124$	6.48439e7	+	5.44105e7i	0.274272	+	0.230142i
$125$	−1.75577e8	+	1.01370e8i	−0.719165	+	0.415210i
$126$		0			0
$127$	−6.82968e7	+	1.18293e8i	−0.262534	+	0.454722i	−0.966915	−	0.255100i	$-0.917891\pi$
$127$	−6.82968e7	+	1.18293e8i	−0.262534	+	0.454722i	0.704381	+	0.709822i	$0.251225\pi$
$128$	1.00268e8	+	2.75483e8i	0.373526	+	1.02626i
$129$		0			0
$130$	3.39677e7	−	2.85023e7i	0.118930	−	0.0997945i
$131$	−1.23713e7	+	3.39898e7i	−0.0420078	+	0.115415i	−0.958923	−	0.283667i	$-0.908449\pi$
$131$	−1.23713e7	+	3.39898e7i	−0.0420078	+	0.115415i	0.916915	+	0.399082i	$0.130671\pi$
$132$		0			0
$133$	−5.36086e7	+	3.04030e8i	−0.171328	+	0.971649i
$134$			6.99378e7i			0.216917i
$135$		0			0
$136$	−6.52618e8			−1.90767
$137$	−1.65916e8	−	2.92554e7i	−0.470983	−	0.0830470i	−0.0668810	−	0.997761i	$-0.521305\pi$
$137$	−1.65916e8	−	2.92554e7i	−0.470983	−	0.0830470i	−0.404102	+	0.914714i	$0.632416\pi$
$138$		0			0
$139$	−4.57066e7	−	1.66359e7i	−0.122439	−	0.0445642i	0.280074	−	0.959978i	$-0.409641\pi$
$139$	−4.57066e7	−	1.66359e7i	−0.122439	−	0.0445642i	−0.402513	+	0.915414i	$0.631863\pi$
$140$	−1.81937e8	−	2.16825e8i	−0.473598	−	0.564412i
$141$		0			0
$142$	2.04044e8	−	7.42661e7i	0.501847	−	0.182657i
$143$	1.00206e8	+	5.78541e7i	0.239635	+	0.138353i
$144$		0			0
$145$	−1.14425e8	−	1.98189e8i	−0.258849	−	0.448340i
$146$	4.59425e8	−	5.47522e8i	1.01112	−	1.20501i
$147$		0			0
$148$	1.46643e8	+	8.31656e8i	0.305644	+	1.73339i
$149$	−8.99841e7	+	1.58666e7i	−0.182566	+	0.0321914i	−0.264184	−	0.964472i	$-0.585103\pi$
$149$	−8.99841e7	+	1.58666e7i	−0.182566	+	0.0321914i	0.0816174	+	0.996664i	$0.473991\pi$
$150$		0			0
$151$	−2.11839e8	−	1.77754e8i	−0.407472	−	0.341910i	0.415901	−	0.909410i	$-0.363466\pi$
$151$	−2.11839e8	−	1.77754e8i	−0.407472	−	0.341910i	−0.823373	+	0.567500i	$0.807911\pi$
$152$	1.41413e9	−	8.16448e8i	2.64920	−	1.52952i
$153$		0			0
$154$	5.35162e8	−	9.26928e8i	0.951487	−	1.64802i
$155$	−1.47845e7	−	4.06200e7i	−0.0256141	−	0.0703741i
$156$		0			0
$157$	−2.13728e8	+	1.79339e8i	−0.351774	+	0.295173i	−0.801502	−	0.597992i	$-0.795965\pi$
$157$	−2.13728e8	+	1.79339e8i	−0.351774	+	0.295173i	0.449728	+	0.893166i	$0.351521\pi$
$158$	−1.63401e8	+	4.48941e8i	−0.262196	+	0.720379i
$159$		0			0
$160$	−4.80067e7	+	2.72260e8i	−0.0732525	+	0.415435i
$161$		−	8.83758e8i		−	1.31532i
$162$		0			0
$163$	5.57443e8			0.789677			0.394839	−	0.918750i	$-0.370800\pi$
$163$	5.57443e8			0.789677			0.394839	+	0.918750i	$0.370800\pi$
$164$	−1.64345e9	−	2.89784e8i	−2.27185	−	0.400589i
$165$		0			0
$166$	2.43620e9	+	8.86704e8i	3.20834	+	1.16774i
$167$	−1.63677e8	−	1.95063e8i	−0.210437	−	0.250789i	0.650493	−	0.759512i	$-0.274562\pi$
$167$	−1.63677e8	−	1.95063e8i	−0.210437	−	0.250789i	−0.860930	+	0.508723i	$0.830118\pi$
$168$		0			0
$169$	7.40134e8	−	2.69387e8i	0.907326	−	0.330240i
$170$	5.23945e8	+	3.02500e8i	0.627321	+	0.362184i
$171$		0			0
$172$	−1.69750e9	−	2.94015e9i	−1.93952	−	3.35936i
$173$	−6.78132e8	+	8.08167e8i	−0.757060	+	0.902229i	−0.997658	−	0.0683961i	$-0.978212\pi$
$173$	−6.78132e8	+	8.08167e8i	−0.757060	+	0.902229i	0.240599	+	0.970625i	$0.422656\pi$
$174$		0			0
$175$	−9.06249e7	−	5.13960e8i	−0.0966263	−	0.547995i
$176$	−2.43840e9	+	4.29956e8i	−2.54129	+	0.448098i
$177$		0			0
$178$	2.15894e9	+	1.81157e9i	2.15060	+	1.80457i
$179$	1.33649e8	−	7.71622e7i	0.130183	−	0.0751609i	−0.433494	−	0.901156i	$-0.642720\pi$
$179$	1.33649e8	−	7.71622e7i	0.130183	−	0.0751609i	0.563677	+	0.825995i	$0.309386\pi$
$180$		0			0
$181$	−9.02439e8	+	1.56307e9i	−0.840821	+	1.45634i	0.0483806	+	0.998829i	$0.484594\pi$
$181$	−9.02439e8	+	1.56307e9i	−0.840821	+	1.45634i	−0.889202	+	0.457516i	$0.848739\pi$
$182$	8.88913e7	+	2.44227e8i	0.0810166	+	0.222591i
$183$		0			0
$184$	−3.58081e9	+	3.00466e9i	−3.12399	+	2.62134i
$185$	1.47497e8	−	4.05244e8i	0.125920	−	0.345963i
$186$		0			0
$187$	−2.74143e8	+	1.55474e9i	−0.224187	+	1.27143i
$188$		−	1.93185e8i		−	0.154647i
$189$		0			0
$190$	−1.51375e9			−1.16156
$191$	−5.78554e8	−	1.02015e8i	−0.434721	−	0.0766530i	−0.0479945	−	0.998848i	$-0.515283\pi$
$191$	−5.78554e8	−	1.02015e8i	−0.434721	−	0.0766530i	−0.386726	+	0.922195i	$0.626394\pi$
$192$		0			0
$193$	1.70927e8	+	6.22125e7i	0.123192	+	0.0448382i	0.402881	−	0.915253i	$-0.368009\pi$
$193$	1.70927e8	+	6.22125e7i	0.123192	+	0.0448382i	−0.279689	+	0.960091i	$0.590231\pi$
$194$	5.61570e8	+	6.69253e8i	0.396458	+	0.472480i
$195$		0			0
$196$	−1.52871e9	+	5.56404e8i	−1.03586	+	0.377021i
$197$	5.83796e8	+	3.37055e8i	0.387611	+	0.223787i	0.681125	−	0.732168i	$-0.261491\pi$
$197$	5.83796e8	+	3.37055e8i	0.387611	+	0.223787i	−0.293513	+	0.955955i	$0.594825\pi$
$198$		0			0
$199$	−5.70801e8	−	9.88657e8i	−0.363976	−	0.630425i	0.624635	−	0.780917i	$-0.285248\pi$
$199$	−5.70801e8	−	9.88657e8i	−0.363976	−	0.630425i	−0.988611	+	0.150492i	$0.951914\pi$
$200$	−1.77435e9	+	2.11459e9i	−1.10897	+	1.32162i
$201$		0			0
$202$	−6.34644e8	−	3.59925e9i	−0.381175	−	2.16175i
$203$	1.32098e9	−	2.32924e8i	0.777878	−	0.137161i
$204$		0			0
$205$	6.52826e8	+	5.47786e8i	0.369643	+	0.310167i
$206$	1.80895e9	−	1.04440e9i	1.00452	−	0.579958i
$207$		0			0
$208$	3.00619e8	−	5.20687e8i	0.160606	−	0.278178i
$209$	−1.35101e9	−	3.71186e9i	−0.708064	−	1.94539i
$210$		0			0
$211$	−5.29066e8	+	4.43939e8i	−0.266919	+	0.223972i	−0.766417	−	0.642343i	$-0.777962\pi$
$211$	−5.29066e8	+	4.43939e8i	−0.266919	+	0.223972i	0.499498	+	0.866315i	$0.333518\pi$
$212$	−1.54696e9	+	4.25023e9i	−0.765835	+	2.10411i
$213$		0			0
$214$	9.60537e8	−	5.44748e9i	0.457993	−	2.59741i
$215$			1.73372e9i			0.811380i
$216$		0			0
$217$	2.53366e8			0.114264
$218$	6.82533e9	+	1.20349e9i	3.02202	+	0.532864i
$219$		0			0
$220$	3.40316e9	+	1.23865e9i	1.45275	+	0.528758i
$221$	−2.46414e8	−	2.93665e8i	−0.103299	−	0.123107i
$222$		0			0
$223$	3.54611e8	−	1.29068e8i	0.143395	−	0.0521914i	−0.269326	−	0.963049i	$-0.586801\pi$
$223$	3.54611e8	−	1.29068e8i	0.143395	−	0.0521914i	0.412720	+	0.910858i	$0.364579\pi$
$224$	−1.40332e9	−	8.10209e8i	−0.557398	−	0.321814i
$225$		0			0
$226$	1.53266e9	+	2.65464e9i	0.587504	+	1.01759i
$227$	1.51069e9	−	1.80037e9i	0.568947	−	0.678044i	−0.402468	−	0.915434i	$-0.631847\pi$
$227$	1.51069e9	−	1.80037e9i	0.568947	−	0.678044i	0.971414	+	0.237390i	$0.0762919\pi$
$228$		0			0
$229$	−1.50142e8	−	8.51496e8i	−0.0545958	−	0.309628i	0.945265	−	0.326303i	$-0.105803\pi$
$229$	−1.50142e8	−	8.51496e8i	−0.0545958	−	0.309628i	−0.999861	+	0.0166750i	$0.994692\pi$
$230$	4.26752e9	−	7.52478e8i	1.52498	−	0.268895i
$231$		0			0
$232$	−5.43491e9	−	4.56043e9i	−1.87603	−	1.57418i
$233$	−2.47836e9	+	1.43088e9i	−0.840892	+	0.485489i	−0.857567	−	0.514372i	$-0.828025\pi$
$233$	−2.47836e9	+	1.43088e9i	−0.840892	+	0.485489i	0.0166752	+	0.999861i	$0.494692\pi$
$234$		0			0
$235$	−4.93268e7	+	8.54365e7i	−0.0161738	+	0.0280138i
$236$	−1.08498e9	−	2.98095e9i	−0.349762	−	0.960962i
$237$		0			0
$238$	−2.71646e9	+	2.27938e9i	−0.846635	+	0.710411i
$239$	5.27337e8	−	1.44885e9i	0.161620	−	0.444049i	−0.832277	−	0.554361i	$-0.812963\pi$
$239$	5.27337e8	−	1.44885e9i	0.161620	−	0.444049i	0.993897	+	0.110312i	$0.0351850\pi$
$240$		0			0
$241$	1.16177e8	−	6.58874e8i	0.0344392	−	0.195314i	−0.962734	−	0.270449i	$-0.912828\pi$
$241$	1.16177e8	−	6.58874e8i	0.0344392	−	0.195314i	0.997173	+	0.0751351i	$0.0239388\pi$
$242$			7.53419e9i			2.19672i
$243$		0			0
$244$	8.04124e9			2.26863
$245$	8.18142e8	+	1.44261e8i	0.227073	+	0.0400390i
$246$		0			0
$247$	9.01330e8	+	3.28057e8i	0.242156	+	0.0881378i
$248$	−8.61411e8	−	1.02659e9i	−0.227721	−	0.271388i
$249$		0			0
$250$	5.47531e9	−	1.99285e9i	1.40168	−	0.510170i
$251$	−4.85125e9	−	2.80087e9i	−1.22225	−	0.705664i	−0.256850	−	0.966451i	$-0.582685\pi$
$251$	−4.85125e9	−	2.80087e9i	−1.22225	−	0.705664i	−0.965396	+	0.260787i	$0.916018\pi$
$252$		0			0
$253$	5.65386e9	+	9.79277e9i	1.37995	+	2.39014i
$254$	2.52338e9	−	3.00725e9i	0.606245	−	0.722494i
$255$		0			0
$256$	−1.38571e9	−	7.85874e9i	−0.322635	−	1.82976i
$257$	1.85295e9	−	3.26725e8i	0.424748	−	0.0748945i	0.0428117	−	0.999083i	$-0.486368\pi$
$257$	1.85295e9	−	3.26725e8i	0.424748	−	0.0748945i	0.381936	+	0.924189i	$0.375257\pi$
$258$		0			0
$259$	1.93633e9	+	1.62478e9i	0.430310	+	0.361073i
$260$	−7.61586e8	+	4.39702e8i	−0.166658	+	0.0962199i
$261$		0			0
$262$	5.19779e8	−	9.00283e8i	0.110310	−	0.191062i
$263$	−2.38076e9	−	6.54109e9i	−0.497615	−	1.36719i	−0.893573	−	0.448917i	$-0.851810\pi$
$263$	−2.38076e9	−	6.54109e9i	−0.497615	−	1.36719i	0.395959	−	0.918268i	$-0.370412\pi$
$264$		0			0
$265$	1.76938e9	−	1.48468e9i	0.358787	−	0.301058i
$266$	3.03460e9	−	8.33749e9i	0.606143	−	1.66536i
$267$		0			0
$268$	2.40856e8	−	1.36596e9i	0.0466894	−	0.264789i
$269$			2.31396e8i			0.0441923i	0.999756	+	0.0220962i	$0.00703400\pi$
$269$			2.31396e8i			0.0441923i	−0.999756	+	0.0220962i	$0.992966\pi$
$270$		0			0
$271$	−9.67160e9			−1.79317			−0.896584	−	0.442873i	$-0.853959\pi$
$271$	−9.67160e9			−1.79317			−0.896584	+	0.442873i	$0.853959\pi$
$272$	8.07866e9	+	1.42449e9i	1.47592	+	0.260245i
$273$		0			0
$274$	4.54995e9	+	1.65605e9i	0.807244	+	0.293813i
$275$	4.29226e9	+	5.11532e9i	0.750508	+	0.894421i
$276$		0			0
$277$	5.32215e9	−	1.93710e9i	0.903999	−	0.329029i	0.152145	−	0.988358i	$-0.451382\pi$
$277$	5.32215e9	−	1.93710e9i	0.903999	−	0.329029i	0.751854	+	0.659329i	$0.229160\pi$
$278$	1.21062e9	+	6.98954e8i	0.202689	+	0.117022i
$279$		0			0
$280$	2.24054e9	+	3.88073e9i	0.364519	+	0.631366i
$281$	−4.17573e9	+	4.97645e9i	−0.669742	+	0.798168i	−0.988749	−	0.149585i	$-0.952206\pi$
$281$	−4.17573e9	+	4.97645e9i	−0.669742	+	0.798168i	0.319007	+	0.947752i	$0.396651\pi$
$282$		0			0
$283$	−1.66850e9	−	9.46252e9i	−0.260124	−	1.47524i	−0.782570	−	0.622563i	$-0.786092\pi$
$283$	−1.66850e9	−	9.46252e9i	−0.260124	−	1.47524i	0.522446	−	0.852672i	$-0.325020\pi$
$284$	−4.24098e9	+	7.47799e8i	−0.651917	+	0.114951i
$285$		0			0
$286$	−2.54743e9	−	2.13755e9i	−0.380749	−	0.319486i
$287$	−4.32583e9	+	2.49752e9i	−0.637590	+	0.368113i
$288$		0			0
$289$	−8.72644e8	+	1.51146e9i	−0.125097	+	0.216674i
$290$	2.24950e9	+	6.18045e9i	0.318049	+	0.873832i
$291$		0			0
$292$	−1.08587e10	+	9.11151e9i	−1.49364	+	1.25331i
$293$	−6.63524e8	+	1.82302e9i	−0.0900298	+	0.247355i	−0.976533	−	0.215367i	$-0.930905\pi$
$293$	−6.63524e8	+	1.82302e9i	−0.0900298	+	0.247355i	0.886503	+	0.462722i	$0.153127\pi$
$294$		0			0
$295$	−2.81305e8	+	1.59536e9i	−0.0371441	+	0.210655i
$296$		−	1.33697e10i		−	1.74162i
$297$		0			0
$298$	2.62603e9			0.332993
$299$	−2.70407e9	−	4.76801e8i	−0.338325	−	0.0596558i
$300$		0			0
$301$	−9.54902e9	−	3.47556e9i	−1.16330	−	0.423408i
$302$	5.10863e9	+	6.08822e9i	0.614153	+	0.731919i
$303$		0			0
$304$	−1.92874e10	+	7.02004e9i	−2.25829	+	0.821949i
$305$	−3.55626e9	−	2.05321e9i	−0.410954	−	0.237265i
$306$		0			0
$307$	−5.77919e9	−	1.00098e10i	−0.650599	−	1.12687i	−0.982978	−	0.183724i	$-0.941185\pi$
$307$	−5.77919e9	−	1.00098e10i	−0.650599	−	1.12687i	0.332379	−	0.943146i	$-0.392149\pi$
$308$	−1.36445e10	+	1.62609e10i	−1.51620	+	1.80693i
$309$		0			0
$310$	2.15729e8	+	1.22346e9i	0.0233594	+	0.132478i
$311$	1.21888e10	−	2.14922e9i	1.30293	−	0.229742i	0.521240	−	0.853410i	$-0.325470\pi$
$311$	1.21888e10	−	2.14922e9i	1.30293	−	0.229742i	0.781689	+	0.623669i	$0.214359\pi$
$312$		0			0
$313$	3.57248e9	+	2.99766e9i	0.372213	+	0.312324i	0.809636	−	0.586932i	$-0.199664\pi$
$313$	3.57248e9	+	2.99766e9i	0.372213	+	0.312324i	−0.437423	+	0.899256i	$0.644109\pi$
$314$	6.94423e9	−	4.00925e9i	0.714341	−	0.412425i
$315$		0			0
$316$	4.73750e9	−	8.20558e9i	0.475117	−	0.822927i
$317$	−1.06178e9	−	2.91722e9i	−0.105147	−	0.288889i	0.875951	−	0.482400i	$-0.160235\pi$
$317$	−1.06178e9	−	2.91722e9i	−0.105147	−	0.288889i	−0.981098	+	0.193511i	$0.938013\pi$
$318$		0			0
$319$	−1.31474e10	+	1.10320e10i	−1.26963	+	1.06535i
$320$	−1.73245e8	+	4.75987e8i	−0.0165219	+	0.0453937i
$321$		0			0
$322$	−4.41051e9	+	2.50132e10i	−0.410266	+	2.32673i
$323$			1.30870e10i			1.20235i
$324$		0			0
$325$	−1.62148e9			−0.145337
$326$	−1.57774e10	−	2.78199e9i	−1.39690	−	0.246312i
$327$		0			0
$328$	2.48267e10	+	9.03617e9i	2.14498	+	0.780708i
$329$	−3.71685e8	−	4.42957e8i	−0.0317243	−	0.0378075i
$330$		0			0
$331$	−1.13426e10	+	4.12838e9i	−0.944935	+	0.343928i	−0.768113	−	0.640315i	$-0.778804\pi$
$331$	−1.13426e10	+	4.12838e9i	−0.944935	+	0.343928i	−0.176822	+	0.984243i	$0.556582\pi$
$332$	−4.45280e10	−	2.57083e10i	−3.66506	−	2.11602i
$333$		0			0
$334$	3.65911e9	+	6.33776e9i	0.294028	+	0.509272i
$335$	−4.55296e8	+	5.42601e8i	−0.0361505	+	0.0430825i
$336$		0			0
$337$	−1.30056e9	−	7.37582e9i	−0.100835	−	0.571861i	−0.992803	−	0.119763i	$-0.961787\pi$
$337$	−1.30056e9	−	7.37582e9i	−0.100835	−	0.571861i	0.891968	−	0.452099i	$-0.149324\pi$
$338$	−2.22926e10	+	3.93079e9i	−1.70802	+	0.301171i
$339$		0			0
$340$	−9.19146e9	−	7.71255e9i	−0.687810	−	0.577141i
$341$	−2.80751e9	+	1.62092e9i	−0.207636	+	0.119879i
$342$		0			0
$343$	−7.35223e9	+	1.27344e10i	−0.531181	+	0.920033i
$344$	1.83831e10	+	5.05072e10i	1.31276	+	3.60678i
$345$		0			0
$346$	2.32266e10	−	1.94895e10i	1.62062	−	1.35986i
$347$	−2.04973e8	+	5.63159e8i	−0.0141377	+	0.0388430i	−0.946561	−	0.322526i	$-0.895468\pi$
$347$	−2.04973e8	+	5.63159e8i	−0.0141377	+	0.0388430i	0.932423	+	0.361369i	$0.117690\pi$
$348$		0			0
$349$	8.38797e7	−	4.75705e8i	0.00565399	−	0.0320654i	−0.981850	−	0.189658i	$-0.939262\pi$
$349$	8.38797e7	−	4.75705e8i	0.00565399	−	0.0320654i	0.987504	+	0.157592i	$0.0503732\pi$
$350$			1.49990e10i			0.999517i
$351$		0			0
$352$	2.07333e10			1.35051
$353$	−1.31078e10	−	2.31126e9i	−0.844172	−	0.148850i	−0.265196	−	0.964195i	$-0.585437\pi$
$353$	−1.31078e10	−	2.31126e9i	−0.844172	−	0.148850i	−0.578977	+	0.815344i	$0.696548\pi$
$354$		0			0
$355$	2.06652e9	+	7.52151e8i	0.130115	+	0.0473578i
$356$	−3.59277e10	−	4.28170e10i	−2.23681	−	2.66573i
$357$		0			0
$358$	−4.16778e9	+	1.51695e9i	−0.253731	+	0.0923504i
$359$	2.82913e10	+	1.63340e10i	1.70324	+	0.983365i	0.942440	+	0.334375i	$0.108525\pi$
$359$	2.82913e10	+	1.63340e10i	1.70324	+	0.983365i	0.760798	+	0.648989i	$0.224808\pi$
$360$		0			0
$361$	−7.88054e9	−	1.36495e10i	−0.464010	−	0.803688i
$362$	3.33427e10	−	3.97362e10i	1.94163	−	2.31394i
$363$		0			0
$364$	−8.95062e8	−	5.07615e9i	−0.0509856	−	0.289154i
$365$	7.12875e9	−	1.25699e9i	0.401645	−	0.0708208i
$366$		0			0
$367$	7.91011e9	+	6.63737e9i	0.436032	+	0.365874i	0.834222	−	0.551429i	$-0.185917\pi$
$367$	7.91011e9	+	6.63737e9i	0.436032	+	0.365874i	−0.398190	+	0.917303i	$0.630362\pi$
$368$	5.08847e10	−	2.93783e10i	2.77457	−	1.60190i
$369$		0			0
$370$	−6.19707e9	+	1.07336e10i	−0.330658	+	0.572717i
$371$	4.63034e9	+	1.27217e10i	0.244409	+	0.671508i
$372$		0			0
$373$	2.89391e10	−	2.42828e10i	1.49503	−	1.25448i	0.606997	−	0.794704i	$-0.292374\pi$
$373$	2.89391e10	−	2.42828e10i	1.49503	−	1.25448i	0.888035	−	0.459776i	$-0.152070\pi$
$374$	1.55183e10	−	4.26361e10i	0.793152	−	2.17917i
$375$		0			0
$376$	−5.31095e8	+	3.01199e9i	−0.0265718	+	0.150696i
$377$		−	4.16752e9i		−	0.206306i
$378$		0			0
$379$	1.35560e10			0.657013			0.328507	−	0.944502i	$-0.393455\pi$
$379$	1.35560e10			0.657013			0.328507	+	0.944502i	$0.393455\pi$
$380$	2.95653e10	+	5.21315e9i	1.41791	+	0.250015i
$381$		0			0
$382$	1.58658e10	+	5.77469e9i	0.745092	+	0.271191i
$383$	2.92494e9	+	3.48581e9i	0.135932	+	0.161998i	0.829716	−	0.558185i	$-0.188502\pi$
$383$	2.92494e9	+	3.48581e9i	0.135932	+	0.161998i	−0.693784	+	0.720183i	$0.744058\pi$
$384$		0			0
$385$	1.01863e10	−	3.70750e9i	0.463631	−	0.168748i
$386$	−4.52732e9	−	2.61385e9i	−0.203935	−	0.117742i
$387$		0			0
$388$	−8.66328e9	−	1.50052e10i	−0.382257	−	0.662088i
$389$	−3.84156e9	+	4.57819e9i	−0.167768	+	0.199938i	−0.843377	−	0.537322i	$-0.819436\pi$
$389$	−3.84156e9	+	4.57819e9i	−0.167768	+	0.199938i	0.675610	+	0.737260i	$0.263881\pi$
$390$		0			0
$391$	−6.50548e9	−	3.68944e10i	−0.278338	−	1.57853i
$392$	2.53640e10	−	4.47236e9i	1.07417	−	0.189405i
$393$		0			0
$394$	−1.48412e10	−	1.24533e10i	−0.615864	−	0.516771i
$395$	−4.19033e9	+	2.41929e9i	−0.172131	+	0.0993801i
$396$		0			0
$397$	−1.70315e10	+	2.94993e10i	−0.685630	+	1.18755i	0.287609	+	0.957748i	$0.407140\pi$
$397$	−1.70315e10	+	2.94993e10i	−0.685630	+	1.18755i	−0.973238	+	0.229797i	$0.926194\pi$
$398$	1.12215e10	+	3.08309e10i	0.447218	+	1.22872i
$399$		0			0
$400$	2.65800e10	−	2.23032e10i	1.03828	−	0.871221i
$401$	6.92397e9	−	1.90234e10i	0.267780	−	0.735719i	−0.730808	−	0.682583i	$-0.760856\pi$
$401$	6.92397e9	−	1.90234e10i	0.267780	−	0.735719i	0.998587	−	0.0531351i	$-0.0169214\pi$
$402$		0			0
$403$	1.36695e8	−	7.75236e8i	0.00518242	−	0.0293910i
$404$			7.24829e10i			2.72088i
$405$		0			0
$406$	−3.85504e10			−1.41881
$407$	−3.18507e10	−	5.61614e9i	−1.16076	−	0.204673i
$408$		0			0
$409$	−2.51758e9	−	9.16325e8i	−0.0899685	−	0.0327458i	0.296644	−	0.954988i	$-0.404133\pi$
$409$	−2.51758e9	−	9.16325e8i	−0.0899685	−	0.0327458i	−0.386612	+	0.922242i	$0.626355\pi$
$410$	−1.57433e10	−	1.87621e10i	−0.557135	−	0.663968i
$411$		0			0
$412$	−3.89275e10	+	1.41685e10i	−1.35104	+	0.491738i
$413$	−8.22306e9	−	4.74758e9i	−0.282640	−	0.163182i
$414$		0			0
$415$	1.31284e10	+	2.27390e10i	0.442608	+	0.766620i
$416$	−3.23614e9	+	3.85669e9i	−0.108057	+	0.128778i
$417$		0			0
$418$	1.97134e10	+	1.11800e11i	0.645738	+	3.66216i
$419$	−3.23402e10	+	5.70245e9i	−1.04927	+	0.185014i	−0.671590	−	0.740923i	$-0.734388\pi$
$419$	−3.23402e10	+	5.70245e9i	−1.04927	+	0.185014i	−0.377678	+	0.925937i	$0.623277\pi$
$420$		0			0
$421$	4.17265e9	+	3.50127e9i	0.132826	+	0.111454i	0.706780	−	0.707433i	$-0.250147\pi$
$421$	4.17265e9	+	3.50127e9i	0.132826	+	0.111454i	−0.573954	+	0.818887i	$0.694591\pi$
$422$	1.71898e10	−	9.92456e9i	0.542028	−	0.312940i
$423$		0			0
$424$	3.58035e10	−	6.20134e10i	1.10780	−	1.91877i
$425$	−7.56667e9	−	2.07893e10i	−0.231926	−	0.637211i
$426$		0			0
$427$	1.84379e10	−	1.54712e10i	0.554625	−	0.465386i
$428$	−3.75207e10	+	1.03087e11i	−1.11814	+	3.07206i
$429$		0			0
$430$	8.65234e9	−	4.90698e10i	0.253081	−	1.43529i
$431$		−	2.94401e10i		−	0.853160i	−0.904450	−	0.426580i	$-0.859718\pi$
$431$		−	2.94401e10i		−	0.853160i	0.904450	−	0.426580i	$-0.140282\pi$
$432$		0			0
$433$	4.76142e10			1.35452			0.677259	−	0.735745i	$-0.263168\pi$
$433$	4.76142e10			1.35452			0.677259	+	0.735745i	$0.263168\pi$
$434$	−7.17109e9	−	1.26446e9i	−0.202128	−	0.0356406i
$435$		0			0
$436$	−1.29162e11	−	4.70110e10i	−3.57427	−	1.30093i
$437$	6.02527e10	+	7.18064e10i	1.65216	+	1.96896i
$438$		0			0
$439$	3.09810e10	−	1.12761e10i	0.834136	−	0.303601i	0.110581	−	0.993867i	$-0.464729\pi$
$439$	3.09810e10	−	1.12761e10i	0.834136	−	0.303601i	0.723555	+	0.690266i	$0.242507\pi$
$440$	−4.96541e10	−	2.86678e10i	−1.32478	−	0.764863i
$441$		0			0
$442$	5.50875e9	+	9.54144e9i	0.144333	+	0.249991i
$443$	2.33646e10	−	2.78448e10i	0.606657	−	0.722986i	−0.372058	−	0.928210i	$-0.621348\pi$
$443$	2.33646e10	−	2.78448e10i	0.606657	−	0.722986i	0.978715	+	0.205224i	$0.0657922\pi$
$444$		0			0
$445$	4.95646e9	+	2.81095e10i	0.126395	+	0.716824i
$446$	−1.06808e10	+	1.88331e9i	−0.269938	+	0.0475973i
$447$		0			0
$448$	−2.27435e9	−	1.90841e9i	−0.0564607	−	0.0473761i
$449$	−1.86178e10	+	1.07490e10i	−0.458082	+	0.264474i	−0.711237	−	0.702952i	$-0.751865\pi$
$449$	−1.86178e10	+	1.07490e10i	−0.458082	+	0.264474i	0.253156	+	0.967426i	$0.418532\pi$
$450$		0			0
$451$	3.19558e10	−	5.53491e10i	0.772403	−	1.33784i
$452$	−2.07923e10	−	5.71263e10i	−0.498136	−	1.36862i
$453$		0			0
$454$	−5.17424e10	+	4.34170e10i	−1.21793	+	1.02197i
$455$	−9.00272e8	+	2.47348e9i	−0.0210053	+	0.0577115i
$456$		0			0
$457$	−8.26923e9	+	4.68971e10i	−0.189583	+	1.07518i	0.730340	+	0.683083i	$0.239361\pi$
$457$	−8.26923e9	+	4.68971e10i	−0.189583	+	1.07518i	−0.919924	+	0.392097i	$0.871750\pi$
$458$			2.48494e10i			0.564747i
$459$		0			0
$460$	−8.59407e10			−1.91941
$461$	2.28332e10	+	4.02612e9i	0.505550	+	0.0891420i	0.420605	−	0.907244i	$-0.361818\pi$
$461$	2.28332e10	+	4.02612e9i	0.505550	+	0.0891420i	0.0849442	+	0.996386i	$0.472929\pi$
$462$		0			0
$463$	−5.45630e10	−	1.98593e10i	−1.18734	−	0.432155i	−0.328549	−	0.944487i	$-0.606560\pi$
$463$	−5.45630e10	−	1.98593e10i	−1.18734	−	0.432155i	−0.858788	+	0.512332i	$0.828782\pi$
$464$	5.73238e10	+	6.83158e10i	1.23670	+	1.47384i
$465$		0			0
$466$	7.72866e10	−	2.81300e10i	1.63893	−	0.596522i
$467$	−2.44829e10	−	1.41352e10i	−0.514748	−	0.297190i	0.220035	−	0.975492i	$-0.429383\pi$
$467$	−2.44829e10	−	1.41352e10i	−0.514748	−	0.297190i	−0.734783	+	0.678302i	$0.762716\pi$
$468$		0			0
$469$	−2.07583e9	−	3.59544e9i	−0.0429042	−	0.0743123i
$470$	1.82249e9	−	2.17196e9i	0.0373486	−	0.0445103i
$471$		0			0
$472$	8.72101e9	+	4.94593e10i	0.175711	+	0.996506i
$473$	1.28046e11	−	2.25780e10i	2.55812	−	0.451066i
$474$		0			0
$475$	4.24040e10	+	3.55812e10i	0.832976	+	0.698950i
$476$	6.09054e10	−	3.51638e10i	1.18639	−	0.684964i
$477$		0			0
$478$	−2.21560e10	+	3.83753e10i	−0.424404	+	0.735090i
$479$	1.20930e10	+	3.32253e10i	0.229717	+	0.631143i	0.999978	−	0.00658596i	$-0.00209639\pi$
$479$	1.20930e10	+	3.32253e10i	0.229717	+	0.631143i	−0.770261	+	0.637729i	$0.779874\pi$
$480$		0			0
$481$	6.01608e9	−	5.04809e9i	0.112391	−	0.0943077i
$482$	−6.57639e9	+	1.80685e10i	−0.121843	+	0.334760i
$483$		0			0
$484$	2.59467e10	−	1.47151e11i	0.472825	−	2.68152i
$485$			8.84812e9i			0.159913i
$486$		0			0
$487$	−2.17167e10			−0.386081			−0.193041	−	0.981191i	$-0.561835\pi$
$487$	−2.17167e10			−0.386081			−0.193041	+	0.981191i	$0.561835\pi$
$488$	−1.25373e11	−	2.21066e10i	−2.21067	−	0.389800i
$489$		0			0
$490$	−2.24361e10	−	8.16609e9i	−0.389192	−	0.141654i
$491$	−4.06287e10	−	4.84194e10i	−0.699048	−	0.833094i	0.293370	−	0.955999i	$-0.405223\pi$
$491$	−4.06287e10	−	4.84194e10i	−0.699048	−	0.833094i	−0.992418	+	0.122905i	$0.960779\pi$
$492$		0			0
$493$	5.34325e10	−	1.94479e10i	0.904520	−	0.329218i
$494$	−2.38734e10	−	1.37833e10i	−0.400872	−	0.231444i
$495$		0			0
$496$	8.42252e9	+	1.45882e10i	0.139160	+	0.241033i
$497$	−8.28545e9	+	9.87421e9i	−0.135797	+	0.161837i
$498$		0			0
$499$	1.24947e9	+	7.08608e9i	0.0201522	+	0.114289i	0.993225	−	0.116211i	$-0.0370749\pi$
$499$	1.24947e9	+	7.08608e9i	0.0201522	+	0.114289i	−0.973072	+	0.230500i	$0.925964\pi$
$500$	−1.13802e11	+	2.00664e10i	−1.82083	+	0.321062i
$501$		0			0
$502$	1.23328e11	+	1.03485e11i	1.94199	+	1.62952i
$503$	9.78717e10	−	5.65063e10i	1.52892	−	0.882723i	0.529514	−	0.848301i	$-0.322374\pi$
$503$	9.78717e10	−	5.65063e10i	1.52892	−	0.882723i	0.999407	−	0.0344225i	$-0.0109592\pi$
$504$		0			0
$505$	1.85074e10	−	3.20557e10i	0.284563	−	0.492878i
$506$	−1.11151e11	−	3.05384e11i	−1.69555	−	4.65847i
$507$		0			0
$508$	−5.96410e10	+	5.00447e10i	−0.895550	+	0.751456i
$509$	−3.43800e8	+	9.44583e8i	−0.00512195	+	0.0140724i	−0.942227	−	0.334974i	$-0.891272\pi$
$509$	−3.43800e8	+	9.44583e8i	−0.00512195	+	0.0140724i	0.937105	+	0.349047i	$0.113495\pi$
$510$		0			0
$511$	−7.36762e9	+	4.17838e10i	−0.108055	+	0.612809i
$512$			1.54294e11i			2.24527i
$513$		0			0
$514$	−5.40751e10			−0.774721
$515$	2.08335e10	+	3.67350e9i	0.296164	+	0.0522217i
$516$		0			0
$517$	6.95240e9	+	2.53047e9i	0.0973134	+	0.0354192i
$518$	−4.66959e10	−	5.56500e10i	−0.648574	−	0.772941i
$519$		0			0
$520$	1.30828e10	−	4.76176e9i	0.178932	−	0.0651260i
$521$	2.65062e10	+	1.53034e10i	0.359746	+	0.207700i	0.668970	−	0.743290i	$-0.266736\pi$
$521$	2.65062e10	+	1.53034e10i	0.359746	+	0.207700i	−0.309223	+	0.950990i	$0.600069\pi$
$522$		0			0
$523$	4.85845e10	+	8.41508e10i	0.649368	+	1.12474i	0.983274	+	0.182132i	$0.0582998\pi$
$523$	4.85845e10	+	8.41508e10i	0.649368	+	1.12474i	−0.333906	+	0.942606i	$0.608367\pi$
$524$	−1.32523e10	+	1.57935e10i	−0.175779	+	0.209485i
$525$		0			0
$526$	3.47392e10	+	1.97016e11i	0.453813	+	2.57370i
$527$	1.05773e10	−	1.86507e9i	0.137130	−	0.0241798i
$528$		0			0
$529$	−1.45567e11	−	1.22145e11i	−1.85883	−	1.55975i
$530$	−5.74886e10	+	3.31911e10i	−0.728582	+	0.420647i
$531$		0			0
$532$	−8.79823e10	+	1.52390e11i	−1.09837	+	1.90243i
$533$	5.30791e9	+	1.45834e10i	0.0657680	+	0.180696i
$534$		0			0
$535$	4.29153e10	−	3.60102e10i	0.523838	−	0.439553i
$536$	−7.51047e9	+	2.06348e10i	−0.0909930	+	0.250001i
$537$		0			0
$538$	1.15481e9	−	6.54927e9i	0.0137842	−	0.0781742i
$539$		−	6.23037e10i		−	0.738174i
$540$		0			0
$541$	1.49873e11			1.74958			0.874790	−	0.484501i	$-0.160999\pi$
$541$	1.49873e11			1.74958			0.874790	+	0.484501i	$0.160999\pi$
$542$	2.73738e11	+	4.82674e10i	3.17203	+	0.559315i
$543$		0			0
$544$	−6.45488e10	−	2.34939e10i	−0.737043	−	0.268262i
$545$	4.51184e10	+	5.37701e10i	0.511409	+	0.609473i
$546$		0			0
$547$	−1.05734e11	+	3.84841e10i	−1.18104	+	0.429865i	−0.856570	−	0.516030i	$-0.827409\pi$
$547$	−1.05734e11	+	3.84841e10i	−1.18104	+	0.429865i	−0.324473	+	0.945895i	$0.605187\pi$
$548$	−8.31624e10	−	4.80138e10i	−0.922157	−	0.532408i
$549$		0			0
$550$	−9.59564e10	−	1.66201e11i	−1.04863	−	1.81628i
$551$	−9.14507e10	+	1.08987e11i	−0.992158	+	1.18241i
$552$		0			0
$553$	−4.92474e9	−	2.79296e10i	−0.0526602	−	0.298651i
$554$	−1.60302e11	+	2.82655e10i	−1.70176	+	0.300066i
$555$		0			0
$556$	−2.12377e10	−	1.78206e10i	−0.222233	−	0.186476i
$557$	4.90294e9	−	2.83072e9i	0.0509373	−	0.0294087i	−0.474315	−	0.880355i	$-0.657304\pi$
$557$	4.90294e9	−	2.83072e9i	0.0509373	−	0.0294087i	0.525252	+	0.850946i	$0.323971\pi$
$558$		0			0
$559$	−1.57862e10	+	2.73424e10i	−0.161670	+	0.280021i
$560$	−1.92648e10	−	5.29295e10i	−0.195890	−	0.538202i
$561$		0			0
$562$	1.43023e11	−	1.20010e11i	1.43370	−	1.20302i
$563$	1.81468e10	−	4.98578e10i	0.180620	−	0.496249i	−0.816032	−	0.578006i	$-0.803831\pi$
$563$	1.81468e10	−	4.98578e10i	0.180620	−	0.496249i	0.996652	+	0.0817570i	$0.0260531\pi$
$564$		0			0
$565$	−5.39088e9	+	3.05732e10i	−0.0529012	+	0.300018i
$566$			2.76147e11i			2.69076i
$567$		0			0
$568$	6.81777e10			0.655012
$569$	8.35693e10	+	1.47355e10i	0.797256	+	0.140578i	0.557414	−	0.830234i	$-0.311793\pi$
$569$	8.35693e10	+	1.47355e10i	0.797256	+	0.140578i	0.239841	+	0.970812i	$0.422905\pi$
$570$		0			0
$571$	1.52155e10	+	5.53797e9i	0.143133	+	0.0520963i	0.412593	−	0.910915i	$-0.364623\pi$
$571$	1.52155e10	+	5.53797e9i	0.143133	+	0.0520963i	−0.269460	+	0.963012i	$0.586845\pi$
$572$	4.23928e10	+	5.05218e10i	0.396012	+	0.471948i
$573$		0			0
$574$	1.34899e11	−	4.90993e10i	1.24269	−	0.452301i
$575$	−1.37231e11	−	7.92304e10i	−1.25540	−	0.724804i
$576$		0			0
$577$	−3.80191e10	−	6.58511e10i	−0.343004	−	0.594100i	0.641985	−	0.766717i	$-0.278111\pi$
$577$	−3.80191e10	−	6.58511e10i	−0.343004	−	0.594100i	−0.984989	+	0.172617i	$0.944778\pi$
$578$	3.22418e10	−	3.84243e10i	0.288874	−	0.344266i
$579$		0			0
$580$	−2.26506e10	−	1.28458e11i	−0.200156	−	1.13514i
$581$	−1.51561e11	+	2.67243e10i	−1.33010	+	0.234532i
$582$		0			0
$583$	−1.32696e11	−	1.11345e11i	−1.14864	−	0.963819i
$584$	1.94349e11	−	1.12207e11i	1.67082	−	0.964650i
$585$		0			0
$586$	2.78779e10	−	4.82860e10i	0.236412	−	0.409478i
$587$	−1.47692e9	−	4.05781e9i	−0.0124396	−	0.0341774i	0.933317	−	0.359052i	$-0.116900\pi$
$587$	−1.47692e9	−	4.05781e9i	−0.0124396	−	0.0341774i	−0.945757	+	0.324875i	$0.894678\pi$
$588$		0			0
$589$	−2.05863e10	+	1.72740e10i	−0.171048	+	0.143526i
$590$	1.59237e10	−	4.37500e10i	0.131412	−	0.361053i
$591$		0			0
$592$	−2.91823e10	+	1.65501e11i	−0.237593	+	1.34745i
$593$		−	5.01514e10i		−	0.405568i	−0.979223	−	0.202784i	$-0.935001\pi$
$593$		−	5.01514e10i		−	0.405568i	0.979223	−	0.202784i	$-0.0649990\pi$
$594$		0			0
$595$	−3.59141e10			−0.286547
$596$	−5.12893e10	−	9.04368e9i	−0.406482	−	0.0716738i
$597$		0			0
$598$	7.41546e10	+	2.69901e10i	0.579873	+	0.211057i
$599$	−8.26157e10	−	9.84575e10i	−0.641734	−	0.764789i	0.342909	−	0.939369i	$-0.388588\pi$
$599$	−8.26157e10	−	9.84575e10i	−0.641734	−	0.764789i	−0.984643	+	0.174580i	$0.944143\pi$
$600$		0			0
$601$	−7.25846e10	+	2.64186e10i	−0.556348	+	0.202494i	−0.604865	−	0.796328i	$-0.706773\pi$
$601$	−7.25846e10	+	2.64186e10i	−0.556348	+	0.202494i	0.0485165	+	0.998822i	$0.484551\pi$
$602$	2.52923e11	+	1.46025e11i	1.92576	+	1.11184i
$603$		0			0
$604$	−7.88101e10	−	1.36503e11i	−0.592154	−	1.02564i
$605$	−4.90477e10	+	5.84527e10i	−0.366098	+	0.436298i
$606$		0			0
$607$	3.40959e10	+	1.93367e11i	0.251158	+	1.42439i	0.805745	+	0.592262i	$0.201765\pi$
$607$	3.40959e10	+	1.93367e11i	0.251158	+	1.42439i	−0.554587	+	0.832125i	$0.687124\pi$
$608$	1.69260e11	−	2.98451e10i	1.23862	−	0.218403i
$609$		0			0
$610$	9.04069e10	+	7.58604e10i	0.652953	+	0.547893i
$611$	−1.55586e9	+	8.98279e8i	−0.0111637	+	0.00644535i
$612$		0			0
$613$	1.29617e10	−	2.24503e10i	0.0917951	−	0.158994i	−0.816471	−	0.577386i	$-0.804073\pi$
$613$	1.29617e10	−	2.24503e10i	0.0917951	−	0.158994i	0.908267	+	0.418392i	$0.137406\pi$
$614$	1.13614e11	+	3.12153e11i	0.799393	+	2.19631i
$615$		0			0
$616$	2.57438e11	−	2.16016e11i	1.78793	−	1.50025i
$617$	−9.09516e10	+	2.49887e11i	−0.627581	+	1.72426i	0.0600420	+	0.998196i	$0.480877\pi$
$617$	−9.09516e10	+	2.49887e11i	−0.627581	+	1.72426i	−0.687623	+	0.726068i	$0.741346\pi$
$618$		0			0
$619$	−3.76883e10	+	2.13741e11i	−0.256711	+	1.45588i	0.534931	+	0.844896i	$0.320337\pi$
$619$	−3.76883e10	+	2.13741e11i	−0.256711	+	1.45588i	−0.791642	+	0.610985i	$0.790774\pi$
$620$		−	2.46385e10i		−	0.166743i
$621$		0			0
$622$	−3.55710e11			−2.37648
$623$	−1.64758e11	−	2.90513e10i	−1.09369	−	0.192848i
$624$		0			0
$625$	−5.68341e10	−	2.06859e10i	−0.372468	−	0.135567i
$626$	−8.61525e10	−	1.02673e11i	−0.561010	−	0.668586i
$627$		0			0
$628$	−1.49436e11	+	5.43902e10i	−0.960762	+	0.349689i
$629$	9.27967e10	+	5.35762e10i	0.592830	+	0.342271i
$630$		0			0
$631$	−3.48237e10	−	6.03164e10i	−0.219663	−	0.380468i	0.735042	−	0.678022i	$-0.237163\pi$
$631$	−3.48237e10	−	6.03164e10i	−0.219663	−	0.380468i	−0.954705	+	0.297554i	$0.903829\pi$
$632$	−9.64216e10	+	1.14911e11i	−0.604375	+	0.720266i
$633$		0			0
$634$	1.54931e10	+	8.78657e10i	0.0958917	+	0.543829i
$635$	3.91545e10	−	6.90399e9i	0.240817	−	0.0424624i
$636$		0			0
$637$	1.15894e10	+	9.72464e9i	0.0703886	+	0.0590630i
$638$	4.27171e11	−	2.46627e11i	2.57821	−	1.48853i
$639$		0			0
$640$	4.26657e10	−	7.38992e10i	0.254308	−	0.440474i
$641$	8.61283e10	+	2.36636e11i	0.510169	+	1.40168i	0.881062	+	0.473001i	$0.156829\pi$
$641$	8.61283e10	+	2.36636e11i	0.510169	+	1.40168i	−0.370893	+	0.928676i	$0.620948\pi$
$642$		0			0
$643$	−1.59790e11	+	1.34080e11i	−0.934773	+	0.784368i	−0.976668	−	0.214754i	$-0.931105\pi$
$643$	−1.59790e11	+	1.34080e11i	−0.934773	+	0.784368i	0.0418951	+	0.999122i	$0.486660\pi$
$644$	1.72284e11	−	4.73347e11i	1.00162	−	2.75192i
$645$		0			0
$646$	6.53124e10	−	3.70405e11i	0.375030	−	2.12690i
$647$		−	3.24590e11i		−	1.85233i	−0.377119	−	0.926165i	$-0.623085\pi$
$647$		−	3.24590e11i		−	1.85233i	0.377119	−	0.926165i	$-0.376915\pi$
$648$		0			0
$649$	1.21491e11			0.684802
$650$	4.58931e10	+	8.09219e9i	0.257095	+	0.0453328i
$651$		0			0
$652$	2.98570e11	+	1.08671e11i	1.65218	+	0.601343i
$653$	−1.13196e11	−	1.34902e11i	−0.622555	−	0.741933i	0.358952	−	0.933356i	$-0.383134\pi$
$653$	−1.13196e11	−	1.34902e11i	−0.622555	−	0.741933i	−0.981508	+	0.191423i	$0.938690\pi$
$654$		0			0
$655$	9.89347e9	−	3.60093e9i	0.0537506	−	0.0195636i
$656$	−2.87602e11	−	1.66047e11i	−1.55302	−	0.896636i
$657$		0			0
$658$	8.30927e9	+	1.43921e10i	0.0443261	+	0.0767750i
$659$	−4.46693e10	+	5.32348e10i	−0.236847	+	0.282263i	−0.871355	−	0.490653i	$-0.836758\pi$
$659$	−4.46693e10	+	5.32348e10i	−0.236847	+	0.282263i	0.634508	+	0.772916i	$0.281203\pi$
$660$		0			0
$661$	−4.78874e10	−	2.71583e11i	−0.250851	−	1.42264i	−0.806503	−	0.591230i	$-0.798642\pi$
$661$	−4.78874e10	−	2.71583e11i	−0.250851	−	1.42264i	0.555652	−	0.831415i	$-0.312469\pi$
$662$	3.41637e11	−	6.02398e10i	1.77882	−	0.313654i
$663$		0			0
$664$	6.23569e11	+	5.23237e11i	3.20784	+	2.69169i
$665$	7.78206e10	−	4.49298e10i	0.397931	−	0.229746i
$666$		0			0
$667$	2.03638e11	−	3.52711e11i	1.02886	−	1.78203i
$668$	−4.96400e10	−	1.36385e11i	−0.249302	−	0.684952i
$669$		0			0
$670$	1.55943e10	−	1.30852e10i	0.0773867	−	0.0649351i
$671$	−1.05330e11	+	2.89391e11i	−0.519589	+	1.42756i
$672$		0			0
$673$	−3.73237e10	+	2.11673e11i	−0.181939	+	1.03183i	0.747887	+	0.663826i	$0.231068\pi$
$673$	−3.73237e10	+	2.11673e11i	−0.181939	+	1.03183i	−0.929826	+	0.367999i	$0.880043\pi$
$674$			2.15250e11i			1.04305i
$675$		0			0
$676$	4.48937e11			2.14980
$677$	−9.14852e10	−	1.61313e10i	−0.435508	−	0.0767918i	−0.0484040	−	0.998828i	$-0.515413\pi$
$677$	−9.14852e10	−	1.61313e10i	−0.435508	−	0.0767918i	−0.387104	+	0.922036i	$0.626525\pi$
$678$		0			0
$679$	−4.87340e10	−	1.77377e10i	−0.229273	−	0.0834485i
$680$	1.22103e11	+	1.45517e11i	0.571071	+	0.680576i
$681$		0			0
$682$	8.75510e10	−	3.18660e10i	0.404691	−	0.147296i
$683$	−1.32662e11	−	7.65922e10i	−0.609624	−	0.351967i	0.163194	−	0.986594i	$-0.447820\pi$
$683$	−1.32662e11	−	7.65922e10i	−0.609624	−	0.351967i	−0.772818	+	0.634627i	$0.781154\pi$
$684$		0			0
$685$	2.45192e10	+	4.24684e10i	0.111364	+	0.192887i
$686$	2.71645e11	−	3.23734e11i	1.22661	−	1.46181i
$687$		0			0
$688$	−1.17319e11	−	6.65346e11i	−0.523616	−	2.96957i
$689$	4.14234e10	−	7.30407e9i	0.183810	−	0.0324107i
$690$		0			0
$691$	−3.13641e11	−	2.63176e11i	−1.37569	−	1.15434i	−0.970776	−	0.239987i	$-0.922857\pi$
$691$	−3.13641e11	−	2.63176e11i	−1.37569	−	1.15434i	−0.404914	−	0.914355i	$-0.632699\pi$
$692$	−5.20761e11	+	3.00661e11i	−2.27098	+	1.31115i
$693$		0			0
$694$	8.61192e9	−	1.49163e10i	0.0371246	−	0.0643017i
$695$	4.84222e9	+	1.33039e10i	0.0207542	+	0.0570216i
$696$		0			0
$697$	−1.62206e11	+	1.36107e11i	−0.687285	+	0.576701i
$698$	−4.74814e9	+	1.30454e10i	−0.0200033	+	0.0549586i
$699$		0			0
$700$	5.16545e10	−	2.92947e11i	0.215137	−	1.22011i
$701$		−	2.56831e11i		−	1.06359i	−0.846872	−	0.531797i	$-0.821517\pi$
$701$		−	2.56831e11i		−	1.06359i	0.846872	−	0.531797i	$-0.178483\pi$
$702$		0			0
$703$	−2.68103e11			−1.09769
$704$	3.74108e10	+	6.59653e9i	0.152302	+	0.0268550i
$705$		0			0
$706$	3.59459e11	+	1.30832e11i	1.44687	+	0.526619i
$707$	1.39456e11	+	1.66197e11i	0.558161	+	0.665190i
$708$		0			0
$709$	−9.95062e9	+	3.62173e9i	−0.0393790	+	0.0143328i	−0.361635	−	0.932320i	$-0.617781\pi$
$709$	−9.95062e9	+	3.62173e9i	−0.0393790	+	0.0143328i	0.322256	+	0.946653i	$0.395559\pi$
$710$	−5.47355e10	−	3.16016e10i	−0.215395	−	0.124358i
$711$		0			0
$712$	4.42446e11	+	7.66339e11i	1.72163	+	2.98195i
$713$	4.94494e10	−	5.89315e10i	0.191339	−	0.228029i
$714$		0			0
$715$	−5.84836e9	−	3.31677e10i	−0.0223774	−	0.126909i
$716$	8.66256e10	−	1.52744e10i	0.329605	−	0.0581183i
$717$		0			0
$718$	−7.19219e11	−	6.03497e11i	−2.70622	−	2.27079i
$719$	−2.39785e11	+	1.38440e11i	−0.897235	+	0.518019i	−0.876302	−	0.481762i	$-0.839997\pi$
$719$	−2.39785e11	+	1.38440e11i	−0.897235	+	0.518019i	−0.0209326	+	0.999781i	$0.506664\pi$
$720$		0			0
$721$	−6.19976e10	+	1.07383e11i	−0.229421	+	0.397369i
$722$	1.54925e11	+	4.25654e11i	0.570130	+	1.56642i
$723$		0			0
$724$	−7.88065e11	+	6.61265e11i	−2.86819	+	2.40670i
$725$	8.22592e10	−	2.26005e11i	0.297737	−	0.818025i
$726$		0			0
$727$	−6.32423e10	+	3.58665e11i	−0.226397	+	1.28396i	0.633601	+	0.773660i	$0.281576\pi$
$727$	−6.32423e10	+	3.58665e11i	−0.226397	+	1.28396i	−0.859997	+	0.510298i	$0.829535\pi$
$728$			8.16040e10i			0.290526i
$729$		0			0
$730$	−2.08040e11			−0.732581
$731$	−4.24229e11	−	7.48030e10i	−1.48570	−	0.261969i
$732$		0			0
$733$	2.28719e11	+	8.32470e10i	0.792295	+	0.288372i	0.706290	−	0.707923i	$-0.250368\pi$
$733$	2.28719e11	+	8.32470e10i	0.792295	+	0.288372i	0.0860054	+	0.996295i	$0.472590\pi$
$734$	−1.90757e11	−	2.27336e11i	−0.657199	−	0.783219i
$735$		0			0
$736$	−4.62335e11	+	1.68276e11i	−1.57560	+	0.573471i
$737$	4.60038e10	+	2.65603e10i	0.155928	+	0.0900249i
$738$		0			0
$739$	2.35023e11	+	4.07071e11i	0.788010	+	1.36487i	0.927184	+	0.374606i	$0.122222\pi$
$739$	2.35023e11	+	4.07071e11i	0.788010	+	1.36487i	−0.139174	+	0.990268i	$0.544445\pi$
$740$	1.58001e11	−	1.88298e11i	0.526905	−	0.627941i
$741$		0			0
$742$	−6.75641e10	−	3.83175e11i	−0.222895	−	1.26410i
$743$	−2.71960e11	+	4.79538e10i	−0.892379	+	0.157351i	−0.600992	−	0.799255i	$-0.705228\pi$
$743$	−2.71960e11	+	4.79538e10i	−0.892379	+	0.157351i	−0.291387	+	0.956605i	$0.594117\pi$
$744$		0			0
$745$	2.03736e10	+	1.70955e10i	0.0661368	+	0.0554953i
$746$	−9.40259e11	+	5.42859e11i	−3.03593	+	1.75280i
$747$		0			0
$748$	−4.49921e11	+	7.79287e11i	−1.43724	+	2.48938i
$749$	1.12307e11	+	3.08560e11i	0.356844	+	0.980420i
$750$		0			0
$751$	2.16654e11	−	1.81794e11i	0.681093	−	0.571505i	−0.235232	−	0.971939i	$-0.575585\pi$
$751$	2.16654e11	−	1.81794e11i	0.681093	−	0.571505i	0.916326	+	0.400434i	$0.131141\pi$
$752$	1.31487e10	−	3.61257e10i	0.0411160	−	0.112965i
$753$		0			0
$754$	−2.07985e10	+	1.17954e11i	−0.0643499	+	0.364946i
$755$			8.04917e10i			0.247721i
$756$		0			0
$757$	4.15637e11			1.26570			0.632849	−	0.774275i	$-0.281885\pi$
$757$	4.15637e11			1.26570			0.632849	+	0.774275i	$0.281885\pi$
$758$	−3.83678e11	−	6.76529e10i	−1.16223	−	0.204932i
$759$		0			0
$760$	−4.46626e11	−	1.62559e11i	−1.33872	−	0.487254i
$761$	1.10440e11	+	1.31617e11i	0.329296	+	0.392440i	0.905136	−	0.425123i	$-0.139769\pi$
$761$	1.10440e11	+	1.31617e11i	0.329296	+	0.392440i	−0.575840	+	0.817563i	$0.695325\pi$
$762$		0			0
$763$	−3.86605e11	+	1.40713e11i	−1.14069	+	0.415179i
$764$	−2.89990e11	−	1.67426e11i	−0.851158	−	0.491416i
$765$		0			0
$766$	−6.53891e10	−	1.13257e11i	−0.189929	−	0.328966i
$767$	−1.89628e10	+	2.25990e10i	−0.0547926	+	0.0652993i
$768$		0			0
$769$	7.94270e9	+	4.50453e10i	0.0227124	+	0.128808i	0.994056	−	0.108872i	$-0.0347240\pi$
$769$	7.94270e9	+	4.50453e10i	0.0227124	+	0.128808i	−0.971343	+	0.237681i	$0.923613\pi$
$770$	−3.06808e11	+	5.40985e10i	−0.872778	+	0.153894i
$771$		0			0
$772$	7.94219e10	+	6.66429e10i	0.223600	+	0.187622i
$773$	3.95630e11	−	2.28417e11i	1.10808	−	0.639751i	0.169749	−	0.985487i	$-0.445704\pi$
$773$	3.95630e11	−	2.28417e11i	1.10808	−	0.639751i	0.938332	+	0.345736i	$0.112371\pi$
$774$		0			0
$775$	2.27147e10	−	3.93430e10i	0.0629652	−	0.109059i
$776$	9.38192e10	+	2.57766e11i	0.258729	+	0.710852i
$777$		0			0
$778$	1.31577e11	−	1.10406e11i	0.359137	−	0.301352i
$779$	1.81203e11	−	4.97852e11i	0.492058	−	1.35192i
$780$		0			0
$781$	2.86391e10	−	1.62421e11i	0.0769761	−	0.436553i
$782$			1.07670e12i			2.87917i
$783$		0			0
$784$	−3.23739e11			−0.856902
$785$	7.99759e10	+	1.41019e10i	0.210611	+	0.0371364i
$786$		0			0
$787$	−1.72921e11	−	6.29382e10i	−0.450765	−	0.164065i	0.106654	−	0.994296i	$-0.465986\pi$
$787$	−1.72921e11	−	6.29382e10i	−0.450765	−	0.164065i	−0.557419	+	0.830231i	$0.688208\pi$
$788$	2.46978e11	+	2.94337e11i	0.640551	+	0.763379i
$789$		0			0
$790$	1.30674e11	−	4.75614e10i	0.335491	−	0.122109i
$791$	−1.57585e11	−	9.09817e10i	−0.402540	−	0.232406i
$792$		0			0
$793$	−3.73905e10	−	6.47622e10i	−0.0945514	−	0.163768i
$794$	6.29266e11	−	7.49930e11i	1.58326	−	1.88686i
$795$		0			0
$796$	−1.12991e11	−	6.40807e11i	−0.281445	−	1.59615i
$797$	7.64594e10	−	1.34819e10i	0.189495	−	0.0334131i	−0.0780951	−	0.996946i	$-0.524884\pi$
$797$	7.64594e10	−	1.34819e10i	0.189495	−	0.0334131i	0.267590	+	0.963533i	$0.413773\pi$
$798$		0			0
$799$	−1.87775e10	−	1.57562e10i	−0.0460734	−	0.0386602i
$800$	−2.51620e11	+	1.45273e11i	−0.614308	+	0.354671i
$801$		0			0
$802$	−2.90910e11	+	5.03871e11i	−0.703171	+	1.21793i
$803$	−1.85674e11	−	5.10134e11i	−0.446568	−	1.22694i
$804$		0			0
$805$	−1.97055e11	+	1.65349e11i	−0.469249	+	0.393747i
$806$	−7.73783e9	+	2.12595e10i	−0.0183349	+	0.0503748i
$807$		0			0
$808$	1.99266e11	−	1.13010e12i	0.467507	−	2.65137i
$809$			2.24143e11i			0.523276i	0.965166	+	0.261638i	$0.0842627\pi$
$809$			2.24143e11i			0.523276i	−0.965166	+	0.261638i	$0.915737\pi$
$810$		0			0
$811$	3.41908e11			0.790362			0.395181	−	0.918603i	$-0.370682\pi$
$811$	3.41908e11			0.790362			0.395181	+	0.918603i	$0.370682\pi$
$812$	7.52933e11	+	1.32762e11i	1.73194	+	0.305387i
$813$		0			0
$814$	8.73451e11	+	3.17910e11i	1.98949	+	0.724114i
$815$	−1.04296e11	−	1.24295e11i	−0.236394	−	0.281724i
$816$		0			0
$817$	1.01283e12	−	3.68638e11i	2.27325	−	0.827394i
$818$	6.66827e10	+	3.84993e10i	0.148936	+	0.0859883i
$819$		0			0
$820$	2.42870e11	+	4.20663e11i	0.537178	+	0.930420i
$821$	−5.42482e10	+	6.46505e10i	−0.119402	+	0.142298i	−0.822434	−	0.568860i	$-0.807385\pi$
$821$	−5.42482e10	+	6.46505e10i	−0.119402	+	0.142298i	0.703032	+	0.711158i	$0.251829\pi$
$822$		0			0
$823$	−7.46715e10	−	4.23483e11i	−0.162763	−	0.923075i	−0.951341	−	0.308140i	$-0.900293\pi$
$823$	−7.46715e10	−	4.23483e11i	−0.162763	−	0.923075i	0.788578	−	0.614935i	$-0.210818\pi$
$824$	6.45878e11	−	1.13886e11i	1.40101	−	0.247036i
$825$		0			0
$826$	2.09046e11	+	1.75410e11i	0.449078	+	0.376821i
$827$	4.79698e11	−	2.76954e11i	1.02552	−	0.592086i	0.109824	−	0.993951i	$-0.464971\pi$
$827$	4.79698e11	−	2.76954e11i	1.02552	−	0.592086i	0.915699	+	0.401865i	$0.131638\pi$
$828$		0			0
$829$	1.30117e11	−	2.25369e11i	0.275496	−	0.477172i	−0.694764	−	0.719237i	$-0.744491\pi$
$829$	1.30117e11	−	2.25369e11i	0.275496	−	0.477172i	0.970260	+	0.242065i	$0.0778247\pi$
$830$	−2.58094e11	−	7.09108e11i	−0.543834	−	1.49417i
$831$		0			0
$832$	−7.06629e9	+	5.92932e9i	−0.0147468	+	0.0123741i
$833$	−7.05992e10	+	1.93970e11i	−0.146629	+	0.402860i
$834$		0			0
$835$	−1.28703e10	+	7.29913e10i	−0.0264755	+	0.150150i
$836$		−	2.25147e12i		−	4.60937i
$837$		0			0
$838$	9.43792e11			1.91382
$839$	9.55859e11	+	1.68544e11i	1.92906	+	0.340146i	0.999587	−	0.0287397i	$-0.00914940\pi$
$839$	9.55859e11	+	1.68544e11i	1.92906	+	0.340146i	0.929475	+	0.368885i	$0.120261\pi$
$840$		0			0
$841$	1.10800e11	+	4.03281e10i	0.221492	+	0.0806164i
$842$	−1.00626e11	−	1.19922e11i	−0.200199	−	0.238588i
$843$		0			0
$844$	−3.69915e11	+	1.34638e11i	−0.729008	+	0.265337i
$845$	−1.98543e11	−	1.14629e11i	−0.389429	−	0.224837i
$846$		0			0
$847$	−2.23623e11	−	3.87326e11i	−0.434492	−	0.752563i
$848$	−5.78564e11	+	6.89506e11i	−1.11884	+	1.33338i
$849$		0			0
$850$	1.10410e11	+	6.26166e11i	0.211511	+	1.19954i
$851$	7.55827e11	−	1.33273e11i	1.44113	−	0.254111i
$852$		0			0
$853$	2.70884e11	+	2.27299e11i	0.511667	+	0.429340i	0.861715	−	0.507392i	$-0.169390\pi$
$853$	2.70884e11	+	2.27299e11i	0.511667	+	0.429340i	−0.350048	+	0.936732i	$0.613835\pi$
$854$	−5.99064e11	+	3.45870e11i	−1.12627	+	0.650251i
$855$		0			0
$856$	8.68395e11	−	1.50410e12i	1.61742	−	2.80145i
$857$	−3.75060e10	−	1.03047e11i	−0.0695308	−	0.191034i	0.900060	−	0.435766i	$-0.143522\pi$
$857$	−3.75060e10	−	1.03047e11i	−0.0695308	−	0.191034i	−0.969591	+	0.244732i	$0.921300\pi$
$858$		0			0
$859$	−4.13197e11	+	3.46713e11i	−0.758900	+	0.636792i	−0.937840	−	0.347068i	$-0.887177\pi$
$859$	−4.13197e11	+	3.46713e11i	−0.758900	+	0.636792i	0.178941	+	0.983860i	$0.442733\pi$
$860$	−3.37980e11	+	9.28591e11i	−0.617869	+	1.69758i
$861$		0			0
$862$	−1.46925e11	+	8.33252e11i	−0.266113	+	1.50920i
$863$		−	1.87437e11i		−	0.337919i	−0.985623	−	0.168960i	$-0.945959\pi$
$863$		−	1.87437e11i		−	0.337919i	0.985623	−	0.168960i	$-0.0540407\pi$
$864$		0			0
$865$	3.07077e11			0.548507
$866$	−1.34764e12	−	2.37625e11i	−2.39608	−	0.422494i
$867$		0			0
$868$	1.35705e11	+	4.93925e10i	0.239065	+	0.0870126i
$869$	2.33250e11	+	2.77977e11i	0.409018	+	0.487449i
$870$		0			0
$871$	−1.21211e10	+	4.41171e9i	−0.0210605	+	0.00766538i
$872$	1.88454e12	+	1.08804e12i	3.25942	+	1.88183i
$873$		0			0
$874$	−1.34699e12	−	2.33305e12i	−2.30844	−	3.99833i
$875$	−2.22331e11	+	2.64964e11i	−0.379287	+	0.452016i
$876$		0			0
$877$	5.14818e10	+	2.91968e11i	0.0870273	+	0.493557i	0.996901	+	0.0786704i	$0.0250675\pi$
$877$	5.14818e10	+	2.91968e11i	0.0870273	+	0.493557i	−0.909873	+	0.414886i	$0.863821\pi$
$878$	−9.33137e11	+	1.64537e11i	−1.57025	+	0.276877i
$879$		0			0
$880$	5.52087e11	+	4.63256e11i	0.920612	+	0.772485i
$881$	−1.28985e11	+	7.44694e10i	−0.214109	+	0.123616i	−0.603220	−	0.797575i	$-0.706116\pi$
$881$	−1.28985e11	+	7.44694e10i	−0.214109	+	0.123616i	0.389111	+	0.921191i	$0.372782\pi$
$882$		0			0
$883$	−5.34296e11	+	9.25428e11i	−0.878900	+	1.52230i	−0.0263503	+	0.999653i	$0.508389\pi$
$883$	−5.34296e11	+	9.25428e11i	−0.878900	+	1.52230i	−0.852550	+	0.522646i	$0.824945\pi$
$884$	−7.47327e10	−	2.05326e11i	−0.122377	−	0.336229i
$885$		0			0
$886$	−8.00258e11	+	6.71496e11i	−1.29866	+	1.08970i
$887$	−9.73447e10	+	2.67452e11i	−0.157260	+	0.432068i	−0.993153	−	0.116825i	$-0.962728\pi$
$887$	−9.73447e10	+	2.67452e11i	−0.157260	+	0.432068i	0.835893	+	0.548893i	$0.184951\pi$
$888$		0			0
$889$	−4.04664e10	+	2.29497e11i	−0.0647870	+	0.367425i
$890$		−	8.20325e11i		−	1.30745i
$891$		0			0
$892$	2.15093e11			0.339756
$893$	6.03997e10	+	1.06501e10i	0.0949793	+	0.0167474i
$894$		0			0
$895$	−4.22104e10	−	1.53633e10i	−0.0657851	−	0.0239438i
$896$	3.21493e11	+	3.83140e11i	0.498815	+	0.594465i
$897$		0			0
$898$	5.80588e11	−	2.11317e11i	0.892818	−	0.324959i
$899$	1.01119e11	+	5.83813e10i	0.154809	+	0.0893790i
$900$		0			0
$901$	2.86950e11	+	4.97013e11i	0.435419	+	0.754168i
$902$	−1.18068e12	+	1.40708e12i	−1.78364	+	2.12565i
$903$		0			0
$904$	1.67128e11	+	9.47828e11i	0.250250	+	1.41924i
$905$	5.17367e11	−	9.12258e10i	0.771267	−	0.135995i
$906$		0			0
$907$	−7.35713e11	−	6.17337e11i	−1.08713	−	0.912206i	−0.0906324	−	0.995884i	$-0.528889\pi$
$907$	−7.35713e11	−	6.17337e11i	−1.08713	−	0.912206i	−0.996493	+	0.0836780i	$0.973333\pi$
$908$	1.16011e12	−	6.69789e11i	1.70669	−	0.985359i
$909$		0			0
$910$	3.78249e10	−	6.55146e10i	0.0551584	−	0.0955372i
$911$	−5.94476e10	−	1.63331e11i	−0.0863099	−	0.237134i	0.889027	−	0.457854i	$-0.151382\pi$
$911$	−5.94476e10	−	1.63331e11i	−0.0863099	−	0.237134i	−0.975337	+	0.220719i	$0.929159\pi$
$912$		0			0
$913$	1.50845e12	−	1.26574e12i	2.17094	−	1.82164i
$914$	4.68092e11	−	1.28607e12i	0.670729	−	1.84281i
$915$		0			0
$916$	8.55779e10	−	4.85336e11i	0.121557	−	0.689384i
$917$			6.17103e10i			0.0872731i
$918$		0			0
$919$	−1.17205e12			−1.64318			−0.821591	−	0.570078i	$-0.806913\pi$
$919$	−1.17205e12			−1.64318			−0.821591	+	0.570078i	$0.806913\pi$
$920$	1.33992e12	+	2.36264e11i	1.87037	+	0.329797i
$921$		0			0
$922$	−6.26162e11	−	2.27904e11i	−0.866489	−	0.315376i
$923$	2.57424e10	+	3.06786e10i	0.0354685	+	0.0422697i
$924$		0			0
$925$	4.25893e11	−	1.55012e11i	0.581746	−	0.211738i
$926$	1.44520e12	+	8.34386e11i	1.96555	+	1.13481i
$927$		0			0
$928$	−3.73381e11	−	6.46715e11i	−0.503454	−	0.872008i
$929$	−1.89184e11	+	2.25461e11i	−0.253993	+	0.302697i	−0.877941	−	0.478769i	$-0.841083\pi$
$929$	−1.89184e11	+	2.25461e11i	−0.253993	+	0.302697i	0.623948	+	0.781466i	$0.285528\pi$
$930$		0			0
$931$	−8.96847e10	−	5.08627e11i	−0.119377	−	0.677019i
$932$	−1.60637e12	+	2.83246e11i	−2.12903	+	0.375405i
$933$		0			0
$934$	6.22401e11	+	5.22257e11i	0.817868	+	0.686272i
$935$	3.97957e11	−	2.29761e11i	0.520703	−	0.300628i
$936$		0			0
$937$	2.74794e11	−	4.75958e11i	0.356492	−	0.617462i	−0.630880	−	0.775880i	$-0.717306\pi$
$937$	2.74794e11	−	4.75958e11i	0.356492	−	0.617462i	0.987372	+	0.158418i	$0.0506394\pi$
$938$	4.08092e10	+	1.12122e11i	0.0527165	+	0.144837i
$939$		0			0
$940$	−4.30752e10	+	3.61444e10i	−0.0551716	+	0.0462945i
$941$	9.58200e10	−	2.63263e11i	0.122208	−	0.335762i	−0.863471	−	0.504399i	$-0.831714\pi$
$941$	9.58200e10	−	2.63263e11i	0.122208	−	0.335762i	0.985678	+	0.168636i	$0.0539364\pi$
$942$		0			0
$943$	−2.63362e11	+	1.49360e12i	−0.333048	+	1.88881i
$944$		−	6.31285e11i		−	0.794946i
$945$		0			0
$946$	−3.73680e12			−4.66590
$947$	−6.37988e11	−	1.12494e11i	−0.793254	−	0.139872i	−0.237685	−	0.971342i	$-0.576389\pi$
$947$	−6.37988e11	−	1.12494e11i	−0.793254	−	0.139872i	−0.555569	+	0.831470i	$0.687500\pi$
$948$		0			0
$949$	1.23873e11	+	4.50860e10i	0.152725	+	0.0555875i
$950$	−1.02260e12	−	1.21869e12i	−1.25548	−	1.49623i
$951$		0			0
$952$	−1.04626e12	+	3.80807e11i	−1.27377	+	0.463615i
$953$	8.40866e11	+	4.85474e11i	1.01942	+	0.588565i	0.913937	−	0.405855i	$-0.133026\pi$
$953$	8.40866e11	+	4.85474e11i	1.01942	+	0.588565i	0.105488	+	0.994421i	$0.466360\pi$
$954$		0			0
$955$	8.54992e10	+	1.48089e11i	0.102789	+	0.178036i
$956$	5.64890e11	−	6.73210e11i	0.676290	−	0.805971i
$957$		0			0
$958$	−1.76457e11	−	1.00074e12i	−0.209497	−	1.18811i
$959$	−2.83062e11	+	4.99115e10i	−0.334663	+	0.0590101i
$960$		0			0
$961$	−6.36457e11	−	5.34051e11i	−0.746235	−	0.626166i
$962$	−1.95468e11	+	1.12853e11i	−0.228231	+	0.131769i
$963$		0			0
$964$	1.90670e11	−	3.30249e11i	0.220787	−	0.382414i
$965$	−1.81083e10	−	4.97521e10i	−0.0208818	−	0.0573723i
$966$		0			0
$967$	−4.10530e11	+	3.44475e11i	−0.469504	+	0.393960i	−0.846613	−	0.532208i	$-0.821362\pi$
$967$	−4.10530e11	+	3.44475e11i	−0.469504	+	0.393960i	0.377110	+	0.926169i	$0.376918\pi$
$968$	−8.09080e11	+	2.22293e12i	−0.921489	+	2.53177i
$969$		0			0
$970$	4.41577e10	−	2.50431e11i	0.0498792	−	0.282879i
$971$			1.01673e12i			1.14374i	0.820344	+	0.571870i	$0.193782\pi$
$971$			1.01673e12i			1.14374i	−0.820344	+	0.571870i	$0.806218\pi$
$972$		0			0
$973$	−8.29828e10			−0.0925841
$974$	6.14654e11	+	1.08380e11i	0.682960	+	0.120424i
$975$		0			0
$976$	1.50372e12	+	5.47308e11i	1.65717	+	0.603161i
$977$	9.56365e10	+	1.13975e11i	0.104965	+	0.125093i	0.815969	−	0.578095i	$-0.196204\pi$
$977$	9.56365e10	+	1.13975e11i	0.104965	+	0.125093i	−0.711004	+	0.703188i	$0.751759\pi$
$978$		0			0
$979$	2.01151e12	−	7.32131e11i	2.18974	−	0.797000i
$980$	4.10080e11	+	2.36760e11i	0.444595	+	0.256687i
$981$		0			0
$982$	9.08282e11	+	1.57319e12i	0.976731	+	1.69175i
$983$	−9.20447e10	+	1.09695e11i	−0.0985791	+	0.117482i	−0.813079	−	0.582154i	$-0.802210\pi$
$983$	−9.20447e10	+	1.09695e11i	−0.0985791	+	0.117482i	0.714499	+	0.699636i	$0.246654\pi$
$984$		0			0
$985$	−3.40722e10	−	1.93233e11i	−0.0361956	−	0.205275i
$986$	−1.60937e12	+	2.83776e11i	−1.70274	+	0.300239i
$987$		0			0
$988$	4.18806e11	+	3.51420e11i	0.439526	+	0.368806i
$989$	−2.67207e12	+	1.54272e12i	−2.79295	+	1.61251i
$990$		0			0
$991$	3.15899e11	−	5.47153e11i	0.327532	−	0.567302i	−0.654490	−	0.756071i	$-0.727117\pi$
$991$	3.15899e11	−	5.47153e11i	0.327532	−	0.567302i	0.982021	+	0.188769i	$0.0604498\pi$
$992$	−4.82434e10	−	1.32548e11i	−0.0498186	−	0.136876i
$993$		0			0
$994$	2.83784e11	−	2.38123e11i	0.290698	−	0.243925i
$995$	−1.13649e11	+	3.12249e11i	−0.115951	+	0.318572i
$996$		0			0
$997$	−2.46421e11	+	1.39752e12i	−0.249400	+	1.41442i	0.560647	+	0.828055i	$0.310553\pi$
$997$	−2.46421e11	+	1.39752e12i	−0.249400	+	1.41442i	−0.810047	+	0.586365i	$0.800558\pi$
$998$		−	2.06795e11i		−	0.208457i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.1		138
3.2	odd	2		27.9.f.a.2.23	✓	138
27.13	even	9		27.9.f.a.14.23	yes	138
27.14	odd	18	inner	81.9.f.a.71.1		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.23	✓	138	3.2	odd	2
27.9.f.a.14.23	yes	138	27.13	even	9
81.9.f.a.8.1		138	1.1	even	1	trivial
81.9.f.a.71.1		138	27.14	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-28.3033 - 4.99063i) q^{2} +(535.607 + 194.945i) q^{4} +(-187.097 - 222.974i) q^{5} +(1603.17 - 583.507i) q^{7} +(-7814.83 - 4511.89i) q^{8} +(4182.68 + 7244.61i) q^{10} +(-14031.5 + 16722.1i) q^{11} +(-920.446 - 5220.11i) q^{13} +(-48287.1 + 8514.32i) q^{14} +(86890.4 + 72909.7i) q^{16} +(62632.7 - 36161.0i) q^{17} +(-90477.4 + 156711. i) q^{19} +(-56742.9 - 155900. i) q^{20} +(480590. - 403263. i) q^{22} +(177170. - 486771. i) q^{23} +(53119.4 - 301255. i) q^{25} +152340. i q^{26} +972423. q^{28} +(774286. + 136527. i) q^{29} +(139553. + 50793.3i) q^{31} +(-610520. - 727589. i) q^{32} +(-1.95318e6 + 710898. i) q^{34} +(-430056. - 248293. i) q^{35} +(740801. + 1.28311e6i) q^{37} +(3.34289e6 - 3.98391e6i) q^{38} +(456098. + 2.58666e6i) q^{40} +(-2.88334e6 + 508410. i) q^{41} +(-4.56281e6 - 3.82865e6i) q^{43} +(-1.07752e7 + 6.22109e6i) q^{44} +(-7.44379e6 + 1.28930e7i) q^{46} +(-115922. - 318492. i) q^{47} +(-2.18641e6 + 1.83462e6i) q^{49} +(-3.00690e6 + 8.26140e6i) q^{50} +(524637. - 2.97536e6i) q^{52} +7.93536e6i q^{53} +6.35383e6 q^{55} +(-1.51612e7 - 2.67334e6i) q^{56} +(-2.12334e7 - 7.72834e6i) q^{58} +(-3.57747e6 - 4.26346e6i) q^{59} +(1.32571e7 - 4.82519e6i) q^{61} +(-3.69632e6 - 2.13407e6i) q^{62} +(-870121. - 1.50709e6i) q^{64} +(-991734. + 1.18190e6i) q^{65} +(-422568. - 2.39650e6i) q^{67} +(4.05959e7 - 7.15815e6i) q^{68} +(1.09328e7 + 9.17375e6i) q^{70} +(-6.54312e6 + 3.77767e6i) q^{71} +(-1.24346e7 + 2.15374e7i) q^{73} +(-1.45636e7 - 4.00131e7i) q^{74} +(-7.90104e7 + 6.62976e7i) q^{76} +(-1.27374e7 + 3.49958e7i) q^{77} +(2.88661e6 - 1.63708e7i) q^{79} -3.30155e7i q^{80} +8.41451e7 q^{82} +(-8.88369e7 - 1.56643e7i) q^{83} +(-1.97813e7 - 7.19982e6i) q^{85} +(1.10035e8 + 1.31135e8i) q^{86} +(1.85102e8 - 6.73715e7i) q^{88} +(-8.49243e7 - 4.90311e7i) q^{89} +(-4.52160e6 - 7.83165e6i) q^{91} +(1.89787e8 - 2.26180e8i) q^{92} +(1.69149e6 + 9.59289e6i) q^{94} +(5.18706e7 - 9.14618e6i) q^{95} +(-2.32866e7 - 1.95398e7i) q^{97} +(7.10385e7 - 4.10141e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

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