LMFDB - Embedded newform 81.9.f.a.8.4

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			8.4
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-25.1387 - 4.43262i) q^{2} +(371.742 + 135.303i) q^{4} +(546.503 + 651.297i) q^{5} +(-3663.86 + 1333.53i) q^{7} +(-3086.08 - 1781.75i) q^{8} +(-10851.4 - 18795.2i) q^{10} +(7165.64 - 8539.67i) q^{11} +(-6824.34 - 38702.7i) q^{13} +(98015.5 - 17282.8i) q^{14} +(-7898.09 - 6627.28i) q^{16} +(-109614. + 63285.8i) q^{17} +(-62328.9 + 107957. i) q^{19} +(115036. + 316059. i) q^{20} +(-217988. + 182913. i) q^{22} +(84577.6 - 232375. i) q^{23} +(-57691.0 + 327182. i) q^{25} +1.00318e6i q^{26} -1.54244e6 q^{28} +(177273. + 31258.0i) q^{29} +(557486. + 202908. i) q^{31} +(755557. + 900438. i) q^{32} +(3.03608e6 - 1.10504e6i) q^{34} +(-2.87084e6 - 1.65748e6i) q^{35} +(-229672. - 397803. i) q^{37} +(2.04540e6 - 2.43761e6i) q^{38} +(-526104. - 2.98368e6i) q^{40} +(981871. - 173130. i) q^{41} +(-2.11904e6 - 1.77809e6i) q^{43} +(3.81922e6 - 2.20503e6i) q^{44} +(-3.15620e6 + 5.46670e6i) q^{46} +(1.21462e6 + 3.33714e6i) q^{47} +(7.22944e6 - 6.06622e6i) q^{49} +(2.90055e6 - 7.96919e6i) q^{50} +(2.69971e6 - 1.53108e7i) q^{52} -6.97006e6i q^{53} +9.47791e6 q^{55} +(1.36830e7 + 2.41268e6i) q^{56} +(-4.31784e6 - 1.57157e6i) q^{58} +(7.66416e6 + 9.13379e6i) q^{59} +(-4.95543e6 + 1.80363e6i) q^{61} +(-1.31150e7 - 7.57197e6i) q^{62} +(-1.36827e7 - 2.36991e7i) q^{64} +(2.14775e7 - 2.55958e7i) q^{65} +(-5.51669e6 - 3.12867e7i) q^{67} +(-4.93110e7 + 8.69486e6i) q^{68} +(6.48220e7 + 5.43921e7i) q^{70} +(2.14530e7 - 1.23859e7i) q^{71} +(2.29304e6 - 3.97166e6i) q^{73} +(4.01033e6 + 1.10183e7i) q^{74} +(-3.77772e7 + 3.16988e7i) q^{76} +(-1.48659e7 + 4.08438e7i) q^{77} +(1.68902e6 - 9.57891e6i) q^{79} -8.76584e6i q^{80} -2.54503e7 q^{82} +(2.39486e7 + 4.22279e6i) q^{83} +(-1.01122e8 - 3.68056e7i) q^{85} +(4.53882e7 + 5.40916e7i) q^{86} +(-3.73292e7 + 1.35867e7i) q^{88} +(2.53853e7 + 1.46562e7i) q^{89} +(7.66148e7 + 1.32701e8i) q^{91} +(6.28822e7 - 7.49401e7i) q^{92} +(-1.57416e7 - 8.92752e7i) q^{94} +(-1.04375e8 + 1.84041e7i) q^{95} +(8.60715e7 + 7.22226e7i) q^{97} +(-2.08628e8 + 1.20451e8i) 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 $

$2$	−25.1387	−	4.43262i	−1.57117	−	0.277039i	−0.680864	−	0.732410i	$-0.738396\pi$
$2$	−25.1387	−	4.43262i	−1.57117	−	0.277039i	−0.890302	+	0.455371i	$0.849507\pi$
$3$		0			0
$3$		0			0
$4$	371.742	+	135.303i	1.45212	+	0.528528i
$5$	546.503	+	651.297i	0.874405	+	1.04208i	0.998757	+	0.0498377i	$0.0158704\pi$
$5$	546.503	+	651.297i	0.874405	+	1.04208i	−0.124352	+	0.992238i	$0.539685\pi$
$6$		0			0
$7$	−3663.86	+	1333.53i	−1.52597	+	0.555408i	−0.962631	−	0.270817i	$-0.912706\pi$
$7$	−3663.86	+	1333.53i	−1.52597	+	0.555408i	−0.563340	+	0.826225i	$0.690484\pi$
$8$	−3086.08	−	1781.75i	−0.753437	−	0.434997i
$9$		0			0
$10$	−10851.4	−	18795.2i	−1.08514	−	1.87952i
$11$	7165.64	−	8539.67i	0.489423	−	0.583271i	−0.463648	−	0.886020i	$-0.653460\pi$
$11$	7165.64	−	8539.67i	0.489423	−	0.583271i	0.953071	+	0.302748i	$0.0979042\pi$
$12$		0			0
$13$	−6824.34	−	38702.7i	−0.238939	−	1.35509i	−0.834158	−	0.551526i	$-0.814046\pi$
$13$	−6824.34	−	38702.7i	−0.238939	−	1.35509i	0.595219	−	0.803564i	$-0.297065\pi$
$14$	98015.5	−	17282.8i	2.55142	−	0.449885i
$15$		0			0
$16$	−7898.09	−	6627.28i	−0.120515	−	0.101124i
$17$	−109614.	+	63285.8i	−1.31242	+	0.757723i	−0.982496	−	0.186286i	$-0.940355\pi$
$17$	−109614.	+	63285.8i	−1.31242	+	0.757723i	−0.329920	+	0.944009i	$0.607022\pi$
$18$		0			0
$19$	−62328.9	+	107957.i	−0.478272	+	0.828391i	−0.999690	−	0.0249102i	$-0.992070\pi$
$19$	−62328.9	+	107957.i	−0.478272	+	0.828391i	0.521418	+	0.853302i	$0.325403\pi$
$20$	115036.	+	316059.i	0.718974	+	1.97537i
$21$		0			0
$22$	−217988.	+	182913.i	−0.930553	+	0.780827i
$23$	84577.6	−	232375.i	0.302235	−	0.830383i	−0.691876	−	0.722016i	$-0.743216\pi$
$23$	84577.6	−	232375.i	0.302235	−	0.830383i	0.994111	−	0.108367i	$-0.0345621\pi$
$24$		0			0
$25$	−57691.0	+	327182.i	−0.147689	+	0.837586i
$26$			1.00318e6i			2.19527i
$27$		0			0
$28$	−1.54244e6			−2.50944
$29$	177273.	+	31258.0i	0.250640	+	0.0441946i	0.297556	−	0.954704i	$-0.403828\pi$
$29$	177273.	+	31258.0i	0.250640	+	0.0441946i	−0.0469165	+	0.998899i	$0.514939\pi$
$30$		0			0
$31$	557486.	+	202908.i	0.603653	+	0.219712i	0.625724	−	0.780045i	$-0.284804\pi$
$31$	557486.	+	202908.i	0.603653	+	0.219712i	−0.0220706	+	0.999756i	$0.507026\pi$
$32$	755557.	+	900438.i	0.720555	+	0.858724i
$33$		0			0
$34$	3.03608e6	−	1.10504e6i	2.27194	−	0.826919i
$35$	−2.87084e6	−	1.65748e6i	−1.91310	−	1.10453i
$36$		0			0
$37$	−229672.	−	397803.i	−0.122546	−	0.212257i	0.798225	−	0.602360i	$-0.205773\pi$
$37$	−229672.	−	397803.i	−0.122546	−	0.212257i	−0.920771	+	0.390103i	$0.872439\pi$
$38$	2.04540e6	−	2.43761e6i	0.980941	−	1.16904i
$39$		0			0
$40$	−526104.	−	2.98368e6i	−0.205509	−	1.16550i
$41$	981871.	−	173130.i	0.347471	−	0.0612686i	0.00281108	−	0.999996i	$-0.499105\pi$
$41$	981871.	−	173130.i	0.347471	−	0.0612686i	0.344660	+	0.938727i	$0.387994\pi$
$42$		0			0
$43$	−2.11904e6	−	1.77809e6i	−0.619820	−	0.520091i	0.277927	−	0.960602i	$-0.410353\pi$
$43$	−2.11904e6	−	1.77809e6i	−0.619820	−	0.520091i	−0.897747	+	0.440512i	$0.854797\pi$
$44$	3.81922e6	−	2.20503e6i	1.01898	−	0.588306i
$45$		0			0
$46$	−3.15620e6	+	5.46670e6i	−0.704909	+	1.22094i
$47$	1.21462e6	+	3.33714e6i	0.248914	+	0.683885i	0.999727	+	0.0233703i	$0.00743968\pi$
$47$	1.21462e6	+	3.33714e6i	0.248914	+	0.683885i	−0.750813	+	0.660515i	$0.770338\pi$
$48$		0			0
$49$	7.22944e6	−	6.06622e6i	1.25407	−	1.05229i
$50$	2.90055e6	−	7.96919e6i	0.464088	−	1.27507i
$51$		0			0
$52$	2.69971e6	−	1.53108e7i	0.369235	−	2.09404i
$53$		−	6.97006e6i		−	0.883350i	−0.897175	−	0.441675i	$-0.854384\pi$
$53$		−	6.97006e6i		−	0.883350i	0.897175	−	0.441675i	$-0.145616\pi$
$54$		0			0
$55$	9.47791e6			1.03577
$56$	1.36830e7	+	2.41268e6i	1.39132	+	0.245328i
$57$		0			0
$58$	−4.31784e6	−	1.57157e6i	−0.381553	−	0.138874i
$59$	7.66416e6	+	9.13379e6i	0.632494	+	0.753777i	0.983165	−	0.182722i	$-0.0584908\pi$
$59$	7.66416e6	+	9.13379e6i	0.632494	+	0.753777i	−0.350671	+	0.936499i	$0.614046\pi$
$60$		0			0
$61$	−4.95543e6	+	1.80363e6i	−0.357900	+	0.130265i	−0.514711	−	0.857364i	$-0.672101\pi$
$61$	−4.95543e6	+	1.80363e6i	−0.357900	+	0.130265i	0.156811	+	0.987629i	$0.449879\pi$
$62$	−1.31150e7	−	7.57197e6i	−0.887571	−	0.512439i
$63$		0			0
$64$	−1.36827e7	−	2.36991e7i	−0.815551	−	1.41258i
$65$	2.14775e7	−	2.55958e7i	1.20318	−	1.43389i
$66$		0			0
$67$	−5.51669e6	−	3.12867e7i	−0.273766	−	1.55260i	−0.742854	−	0.669453i	$-0.766528\pi$
$67$	−5.51669e6	−	3.12867e7i	−0.273766	−	1.55260i	0.469088	−	0.883151i	$-0.344583\pi$
$68$	−4.93110e7	+	8.69486e6i	−2.30626	+	0.406656i
$69$		0			0
$70$	6.48220e7	+	5.43921e7i	2.69979	+	2.26540i
$71$	2.14530e7	−	1.23859e7i	0.844217	−	0.487409i	−0.0144782	−	0.999895i	$-0.504609\pi$
$71$	2.14530e7	−	1.23859e7i	0.844217	−	0.487409i	0.858696	+	0.512486i	$0.171275\pi$
$72$		0			0
$73$	2.29304e6	−	3.97166e6i	0.0807459	−	0.139856i	−0.822825	−	0.568295i	$-0.807603\pi$
$73$	2.29304e6	−	3.97166e6i	0.0807459	−	0.139856i	0.903571	+	0.428439i	$0.140936\pi$
$74$	4.01033e6	+	1.10183e7i	0.133737	+	0.367441i
$75$		0			0
$76$	−3.77772e7	+	3.16988e7i	−1.13234	+	0.950143i
$77$	−1.48659e7	+	4.08438e7i	−0.422891	+	1.16188i
$78$		0			0
$79$	1.68902e6	−	9.57891e6i	0.0433637	−	0.245928i	−0.955419	−	0.295253i	$-0.904596\pi$
$79$	1.68902e6	−	9.57891e6i	0.0433637	−	0.245928i	0.998783	+	0.0493253i	$0.0157071\pi$
$80$		−	8.76584e6i		−	0.214010i
$81$		0			0
$82$	−2.54503e7			−0.562909
$83$	2.39486e7	+	4.22279e6i	0.504625	+	0.0889789i	0.420165	−	0.907448i	$-0.361972\pi$
$83$	2.39486e7	+	4.22279e6i	0.504625	+	0.0889789i	0.0844600	+	0.996427i	$0.473083\pi$
$84$		0			0
$85$	−1.01122e8	−	3.68056e7i	−1.93719	−	0.705079i
$86$	4.53882e7	+	5.40916e7i	0.829754	+	0.988863i
$87$		0			0
$88$	−3.73292e7	+	1.35867e7i	−0.622470	+	0.226561i
$89$	2.53853e7	+	1.46562e7i	0.404597	+	0.233594i	0.688466	−	0.725269i	$-0.258285\pi$
$89$	2.53853e7	+	1.46562e7i	0.404597	+	0.233594i	−0.283869	+	0.958863i	$0.591618\pi$
$90$		0			0
$91$	7.66148e7	+	1.32701e8i	1.11724	+	1.93512i
$92$	6.28822e7	−	7.49401e7i	0.877761	−	1.04608i
$93$		0			0
$94$	−1.57416e7	−	8.92752e7i	−0.201622	−	1.14346i
$95$	−1.04375e8	+	1.84041e7i	−1.28145	+	0.225954i
$96$		0			0
$97$	8.60715e7	+	7.22226e7i	0.972238	+	0.815805i	0.982900	−	0.184139i	$-0.0589495\pi$
$97$	8.60715e7	+	7.22226e7i	0.972238	+	0.815805i	−0.0106623	+	0.999943i	$0.503394\pi$
$98$	−2.08628e8	+	1.20451e8i	−2.26187	+	1.30589i
$99$		0			0
$100$	−6.57150e7	+	1.13822e8i	−0.657150	+	1.13822i
$101$	1.90295e7	+	5.22830e7i	0.182869	+	0.502430i	0.996925	−	0.0783568i	$-0.0249673\pi$
$101$	1.90295e7	+	5.22830e7i	0.182869	+	0.502430i	−0.814056	+	0.580787i	$0.802745\pi$
$102$		0			0
$103$	1.00395e8	−	8.42412e7i	0.891995	−	0.748473i	−0.0766144	−	0.997061i	$-0.524411\pi$
$103$	1.00395e8	−	8.42412e7i	0.891995	−	0.748473i	0.968609	+	0.248588i	$0.0799666\pi$
$104$	−4.78981e7	+	1.31599e8i	−0.409435	+	1.12491i
$105$		0			0
$106$	−3.08956e7	+	1.75218e8i	−0.244722	+	1.38789i
$107$		−	1.08497e8i		−	0.827717i	−0.910341	−	0.413858i	$-0.864181\pi$
$107$		−	1.08497e8i		−	0.827717i	0.910341	−	0.413858i	$-0.135819\pi$
$108$		0			0
$109$	−1.06383e8			−0.753642			−0.376821	−	0.926286i	$-0.622983\pi$
$109$	−1.06383e8			−0.753642			−0.376821	+	0.926286i	$0.622983\pi$
$110$	−2.38262e8	−	4.20120e7i	−1.62736	−	0.286948i
$111$		0			0
$112$	3.77752e7	+	1.37490e7i	0.240068	+	0.0873776i
$113$	−1.07489e8	−	1.28100e8i	−0.659248	−	0.785661i	0.328030	−	0.944667i	$-0.393615\pi$
$113$	−1.07489e8	−	1.28100e8i	−0.659248	−	0.785661i	−0.987278	+	0.159007i	$0.949171\pi$
$114$		0			0
$115$	1.97567e8	−	7.19086e7i	1.12960	−	0.411140i
$116$	6.16705e7	+	3.56055e7i	0.340601	+	0.196646i
$117$		0			0
$118$	−1.52180e8	−	2.63583e8i	−0.784927	−	1.35953i
$119$	3.17217e8	−	3.78045e8i	1.58186	−	1.88519i
$120$		0			0
$121$	1.56434e7	+	8.87179e7i	0.0729774	+	0.413875i
$122$	1.32568e8	−	2.33753e7i	0.598409	−	0.105516i
$123$		0			0
$124$	1.79787e8	+	1.50859e8i	0.760452	+	0.638095i
$125$	4.29968e7	−	2.48242e7i	0.176115	−	0.101680i
$126$		0			0
$127$	2.29807e8	−	3.98037e8i	0.883381	−	1.53006i	0.0358234	−	0.999358i	$-0.488595\pi$
$127$	2.29807e8	−	3.98037e8i	0.883381	−	1.53006i	0.847558	−	0.530703i	$-0.178072\pi$
$128$	1.35997e8	+	3.73648e8i	0.506628	+	1.39195i
$129$		0			0
$130$	−6.53371e8	+	5.48244e8i	−2.28763	+	1.91955i
$131$	1.27572e8	−	3.50502e8i	0.433183	−	1.19016i	−0.510664	−	0.859780i	$-0.670601\pi$
$131$	1.27572e8	−	3.50502e8i	0.433183	−	1.19016i	0.943848	−	0.330381i	$-0.107177\pi$
$132$		0			0
$133$	8.44000e7	−	4.78656e8i	0.269734	−	1.52974i
$134$			8.10959e8i			2.51524i
$135$		0			0
$136$	4.51037e8			1.31843
$137$	−7.16013e7	−	1.26252e7i	−0.203254	−	0.0358391i	0.0710942	−	0.997470i	$-0.477351\pi$
$137$	−7.16013e7	−	1.26252e7i	−0.203254	−	0.0358391i	−0.274348	+	0.961630i	$0.588462\pi$
$138$		0			0
$139$	6.06880e8	+	2.20886e8i	1.62571	+	0.591711i	0.984458	−	0.175617i	$-0.0561922\pi$
$139$	6.06880e8	+	2.20886e8i	1.62571	+	0.591711i	0.641254	+	0.767329i	$0.278414\pi$
$140$	−8.42950e8	−	1.00459e9i	−2.19427	−	2.61503i
$141$		0			0
$142$	−5.94201e8	+	2.16271e8i	−1.46144	+	0.531919i
$143$	−3.79409e8	−	2.19052e8i	−0.907327	−	0.523846i
$144$		0			0
$145$	7.65220e7	+	1.32540e8i	0.173107	+	0.299830i
$146$	−7.52489e7	+	8.96781e7i	−0.165611	+	0.197367i
$147$		0			0
$148$	−3.15547e7	−	1.78956e8i	−0.0657684	−	0.372991i
$149$	−8.44613e6	+	1.48928e6i	−0.0171361	+	0.00302156i	−0.182210	−	0.983260i	$-0.558325\pi$
$149$	−8.44613e6	+	1.48928e6i	−0.0171361	+	0.00302156i	0.165074	+	0.986281i	$0.447214\pi$
$150$		0			0
$151$	−1.49154e8	−	1.25155e8i	−0.286898	−	0.240736i	0.487968	−	0.872862i	$-0.337738\pi$
$151$	−1.49154e8	−	1.25155e8i	−0.286898	−	0.240736i	−0.774866	+	0.632125i	$0.782183\pi$
$152$	3.84703e8	−	2.22109e8i	0.720695	−	0.416094i
$153$		0			0
$154$	5.54754e8	−	9.60862e8i	0.986320	−	1.70836i
$155$	1.72515e8	+	4.73980e8i	0.298881	+	0.821170i
$156$		0			0
$157$	−6.99474e8	+	5.86928e8i	−1.15126	+	0.966020i	−0.999748	−	0.0224353i	$-0.992858\pi$
$157$	−6.99474e8	+	5.86928e8i	−1.15126	+	0.966020i	−0.151510	+	0.988456i	$0.548414\pi$
$158$	−8.49194e7	+	2.33314e8i	−0.136263	+	0.374380i
$159$		0			0
$160$	−1.73538e8	+	9.84185e8i	−0.264798	+	1.50175i
$161$			9.64177e8i			1.43500i
$162$		0			0
$163$	1.26949e8			0.179837			0.0899183	−	0.995949i	$-0.471339\pi$
$163$	1.26949e8			0.179837			0.0899183	+	0.995949i	$0.471339\pi$
$164$	3.88428e8	+	6.84904e7i	0.536952	+	0.0946791i
$165$		0			0
$166$	−5.83318e8	−	2.12311e8i	−0.768198	−	0.279601i
$167$	8.12252e8	+	9.68005e8i	1.04430	+	1.24455i	0.968915	+	0.247393i	$0.0795739\pi$
$167$	8.12252e8	+	9.68005e8i	1.04430	+	1.24455i	0.0753843	+	0.997155i	$0.475982\pi$
$168$		0			0
$169$	−6.84794e8	+	2.49244e8i	−0.839485	+	0.305547i
$170$	2.37894e9	+	1.37348e9i	2.84831	+	1.64447i
$171$		0			0
$172$	−5.47157e8	−	9.47703e8i	−0.625170	−	1.08283i
$173$	2.95566e8	−	3.52242e8i	0.329966	−	0.393239i	−0.575398	−	0.817873i	$-0.695153\pi$
$173$	2.95566e8	−	3.52242e8i	0.329966	−	0.393239i	0.905365	+	0.424635i	$0.139597\pi$
$174$		0			0
$175$	−2.24937e8	−	1.27568e9i	−0.239833	−	1.36016i
$176$	−1.13190e8	+	1.99584e7i	−0.117966	+	0.0208006i
$177$		0			0
$178$	−5.73187e8	−	4.80961e8i	−0.570974	−	0.479104i
$179$	1.30805e9	−	7.55204e8i	1.27413	−	0.735618i	0.298365	−	0.954452i	$-0.403559\pi$
$179$	1.30805e9	−	7.55204e8i	1.27413	−	0.735618i	0.975762	+	0.218834i	$0.0702254\pi$
$180$		0			0
$181$	5.45421e8	−	9.44697e8i	0.508180	−	0.880193i	−0.491775	−	0.870722i	$-0.663652\pi$
$181$	5.45421e8	−	9.44697e8i	0.508180	−	0.880193i	0.999955	−	0.00947115i	$-0.00301481\pi$
$182$	−1.33778e9	−	3.67552e9i	−1.21927	−	3.34991i
$183$		0			0
$184$	−6.75047e8	+	5.66432e8i	−0.588929	+	0.494170i
$185$	1.33572e8	−	3.66986e8i	0.114032	−	0.313301i
$186$		0			0
$187$	−2.45016e8	+	1.38955e9i	−0.200368	+	1.13634i
$188$			1.40490e9i			1.12464i
$189$		0			0
$190$	2.70542e9			2.07597
$191$	−1.12748e9	−	1.98806e8i	−0.847182	−	0.149381i	−0.266827	−	0.963745i	$-0.585975\pi$
$191$	−1.12748e9	−	1.98806e8i	−0.847182	−	0.149381i	−0.580355	+	0.814364i	$0.697086\pi$
$192$		0			0
$193$	2.83300e8	+	1.03113e8i	0.204182	+	0.0743163i	0.442087	−	0.896972i	$-0.354238\pi$
$193$	2.83300e8	+	1.03113e8i	0.204182	+	0.0743163i	−0.237905	+	0.971289i	$0.576461\pi$
$194$	−1.84359e9	−	2.19710e9i	−1.30154	−	1.55111i
$195$		0			0
$196$	3.50827e9	−	1.27691e9i	2.37722	−	0.865236i
$197$	−3.88205e6	−	2.24130e6i	−0.00257749	−	0.00148811i	0.498711	−	0.866769i	$-0.333807\pi$
$197$	−3.88205e6	−	2.24130e6i	−0.00257749	−	0.00148811i	−0.501288	+	0.865280i	$0.667140\pi$
$198$		0			0
$199$	−8.90147e8	−	1.54178e9i	−0.567609	−	0.983128i	−0.996802	−	0.0799151i	$-0.974535\pi$
$199$	−8.90147e8	−	1.54178e9i	−0.567609	−	0.983128i	0.429192	−	0.903213i	$-0.358798\pi$
$200$	7.60995e8	−	9.06918e8i	0.475622	−	0.566824i
$201$		0			0
$202$	−2.46624e8	−	1.39868e9i	−0.148126	−	0.840062i
$203$	−6.91186e8	+	1.21875e8i	−0.407015	+	0.0717678i
$204$		0			0
$205$	6.49355e8	+	5.44874e8i	0.367677	+	0.308518i
$206$	−2.89720e9	+	1.67270e9i	−1.60883	+	0.928857i
$207$		0			0
$208$	−2.02595e8	+	3.50904e8i	−0.108237	+	0.187472i
$209$	4.75290e8	+	1.30585e9i	0.249100	+	0.684396i
$210$		0			0
$211$	−8.22862e6	+	6.90463e6i	−0.00415142	+	0.00348346i	−0.644861	−	0.764300i	$-0.723085\pi$
$211$	−8.22862e6	+	6.90463e6i	−0.00415142	+	0.00348346i	0.640710	+	0.767783i	$0.278640\pi$
$212$	9.43071e8	−	2.59107e9i	0.466875	−	1.28273i
$213$		0			0
$214$	−4.80925e8	+	2.72746e9i	−0.229310	+	1.30048i
$215$		−	2.35186e9i		−	1.10067i
$216$		0			0
$217$	−2.31314e9			−1.04319
$218$	2.67432e9	+	4.71555e8i	1.18410	+	0.208788i
$219$		0			0
$220$	3.52334e9	+	1.28239e9i	1.50406	+	0.547432i
$221$	3.19738e9	+	3.81049e9i	1.34037	+	1.59739i
$222$		0			0
$223$	1.40723e9	−	5.12190e8i	0.569044	−	0.207115i	−0.0414439	−	0.999141i	$-0.513196\pi$
$223$	1.40723e9	−	5.12190e8i	0.569044	−	0.207115i	0.610488	+	0.792026i	$0.290974\pi$
$224$	−3.96902e9	−	2.29151e9i	−1.57649	−	0.910186i
$225$		0			0
$226$	2.13430e9	+	3.69672e9i	0.818129	+	1.41704i
$227$	−3.27780e8	+	3.90632e8i	−0.123446	+	0.147118i	−0.824228	−	0.566258i	$-0.808390\pi$
$227$	−3.27780e8	+	3.90632e8i	−0.123446	+	0.147118i	0.700781	+	0.713376i	$0.252835\pi$
$228$		0			0
$229$	−6.73079e8	−	3.81722e9i	−0.244751	−	1.38805i	−0.821070	−	0.570827i	$-0.806623\pi$
$229$	−6.73079e8	−	3.81722e9i	−0.244751	−	1.38805i	0.576319	−	0.817225i	$-0.304488\pi$
$230$	−5.28532e9	+	9.31945e8i	−1.88869	+	0.333026i
$231$		0			0
$232$	−4.91384e8	−	4.12320e8i	−0.169617	−	0.142325i
$233$	−3.57343e9	+	2.06312e9i	−1.21244	+	0.700004i	−0.963291	−	0.268460i	$-0.913485\pi$
$233$	−3.57343e9	+	2.06312e9i	−1.21244	+	0.700004i	−0.249152	+	0.968464i	$0.580152\pi$
$234$		0			0
$235$	−1.50968e9	+	2.61484e9i	−0.495009	+	0.857380i
$236$	1.61326e9	+	4.43240e9i	0.520064	+	1.42886i
$237$		0			0
$238$	−9.65014e9	+	8.09743e9i	−3.00764	+	2.52371i
$239$	−3.57255e8	+	9.81550e8i	−0.109493	+	0.300830i	−0.982323	−	0.187195i	$-0.940060\pi$
$239$	−3.57255e8	+	9.81550e8i	−0.109493	+	0.300830i	0.872830	+	0.488025i	$0.162283\pi$
$240$		0			0
$241$	2.50680e8	−	1.42168e9i	0.0743109	−	0.421438i	−0.924844	−	0.380345i	$-0.875805\pi$
$241$	2.50680e8	−	1.42168e9i	0.0743109	−	0.421438i	0.999155	−	0.0410924i	$-0.0130838\pi$
$242$		−	2.29959e9i		−	0.670485i
$243$		0			0
$244$	−2.08618e9			−0.588562
$245$	7.90183e9	+	1.39331e9i	2.19312	+	0.386707i
$246$		0			0
$247$	4.60358e9	+	1.67556e9i	1.23682	+	0.450167i
$248$	−1.35891e9	−	1.61949e9i	−0.359241	−	0.428126i
$249$		0			0
$250$	−1.19092e9	+	4.33459e8i	−0.304875	+	0.110966i
$251$	5.61404e8	+	3.24127e8i	0.141443	+	0.0816619i	0.569051	−	0.822302i	$-0.307311\pi$
$251$	5.61404e8	+	3.24127e8i	0.141443	+	0.0816619i	−0.427609	+	0.903964i	$0.640644\pi$
$252$		0			0
$253$	−1.37836e9	−	2.38738e9i	−0.336418	−	0.582693i
$254$	−7.54138e9	+	8.98747e9i	−1.81182	+	2.15925i
$255$		0			0
$256$	−5.46039e8	−	3.09674e9i	−0.127135	−	0.721016i
$257$	−1.80140e8	+	3.17636e7i	−0.0412932	+	0.00728110i	−0.194257	−	0.980951i	$-0.562229\pi$
$257$	−1.80140e8	+	3.17636e7i	−0.0412932	+	0.00728110i	0.152963	+	0.988232i	$0.451118\pi$
$258$		0			0
$259$	1.37197e9	+	1.15122e9i	0.304892	+	0.255834i
$260$	1.14473e10	−	6.60909e9i	2.50501	−	1.44627i
$261$		0			0
$262$	−4.76064e9	+	8.24568e9i	−1.01032	+	1.74993i
$263$	−3.06731e9	−	8.42736e9i	−0.641112	−	1.76144i	−0.648203	−	0.761467i	$-0.724479\pi$
$263$	−3.06731e9	−	8.42736e9i	−0.641112	−	1.76144i	0.00709088	−	0.999975i	$-0.497743\pi$
$264$		0			0
$265$	4.53958e9	−	3.80916e9i	0.920518	−	0.772406i
$266$	−4.24340e9	+	1.16587e10i	−0.847594	+	2.32874i
$267$		0			0
$268$	2.18240e9	−	1.23770e10i	0.423054	−	2.39926i
$269$			6.71344e9i			1.28214i	0.767482	+	0.641071i	$0.221510\pi$
$269$			6.71344e9i			1.28214i	−0.767482	+	0.641071i	$0.778490\pi$
$270$		0			0
$271$	−8.11138e9			−1.50390			−0.751948	−	0.659223i	$-0.770885\pi$
$271$	−8.11138e9			−1.50390			−0.751948	+	0.659223i	$0.770885\pi$
$272$	1.28516e9	+	2.26608e8i	0.234790	+	0.0413999i
$273$		0			0
$274$	1.74400e9	+	6.34763e8i	0.309417	+	0.112618i
$275$	2.38063e9	+	2.83713e9i	0.416257	+	0.496076i
$276$		0			0
$277$	−8.39877e9	+	3.05690e9i	−1.42658	+	0.519234i	−0.935950	−	0.352133i	$-0.885456\pi$
$277$	−8.39877e9	+	3.05690e9i	−1.42658	+	0.519234i	−0.490632	+	0.871367i	$0.663234\pi$
$278$	−1.42770e10	−	8.24286e9i	−2.39034	−	1.38006i
$279$		0			0
$280$	5.90642e9	+	1.02302e10i	0.960931	+	1.66438i
$281$	6.85448e9	−	8.16885e9i	1.09938	−	1.31019i	0.152612	−	0.988286i	$-0.451231\pi$
$281$	6.85448e9	−	8.16885e9i	1.09938	−	1.31019i	0.946771	−	0.321908i	$-0.104324\pi$
$282$		0			0
$283$	−1.27797e9	−	7.24775e9i	−0.199240	−	1.12995i	−0.906250	−	0.422742i	$-0.861068\pi$
$283$	−1.27797e9	−	7.24775e9i	−0.199240	−	1.12995i	0.707010	−	0.707203i	$-0.250043\pi$
$284$	9.65083e9	−	1.70170e9i	1.48351	−	0.261583i
$285$		0			0
$286$	8.56687e9	+	7.18845e9i	1.28044	+	1.07441i
$287$	−3.36656e9	+	1.94368e9i	−0.496202	+	0.286483i
$288$		0			0
$289$	4.52231e9	−	7.83286e9i	0.648289	−	1.12287i
$290$	−1.33616e9	−	3.67107e9i	−0.188915	−	0.519040i
$291$		0			0
$292$	1.38980e9	−	1.16618e9i	0.191170	−	0.160411i
$293$	−4.58166e8	+	1.25880e9i	−0.0621659	+	0.170799i	−0.966887	−	0.255205i	$-0.917857\pi$
$293$	−4.58166e8	+	1.25880e9i	−0.0621659	+	0.170799i	0.904721	+	0.426005i	$0.140079\pi$
$294$		0			0
$295$	−1.76032e9	+	9.98329e9i	−0.232437	+	1.31821i
$296$			1.63687e9i			0.213229i
$297$		0			0
$298$	2.18926e8			0.0277608
$299$	−9.57074e9	−	1.68758e9i	−1.19746	−	0.211144i
$300$		0			0
$301$	1.01350e10	+	3.68884e9i	1.23469	+	0.449390i
$302$	3.19477e9	+	3.80738e9i	0.384072	+	0.457719i
$303$		0			0
$304$	1.20774e9	−	4.39581e8i	0.141410	−	0.0514689i
$305$	−3.88286e9	−	2.24177e9i	−0.448696	−	0.259055i
$306$		0			0
$307$	1.71939e9	+	2.97808e9i	0.193563	+	0.335261i	0.946428	−	0.322914i	$-0.104662\pi$
$307$	1.71939e9	+	2.97808e9i	0.193563	+	0.335261i	−0.752866	+	0.658174i	$0.771329\pi$
$308$	−1.10526e10	+	1.31720e10i	−1.22818	+	1.46368i
$309$		0			0
$310$	−2.23581e9	−	1.26799e10i	−0.242096	−	1.37300i
$311$	8.85574e9	−	1.56151e9i	0.946637	−	0.166918i	0.321041	−	0.947065i	$-0.395967\pi$
$311$	8.85574e9	−	1.56151e9i	0.946637	−	0.166918i	0.625596	+	0.780148i	$0.284856\pi$
$312$		0			0
$313$	−1.97299e9	−	1.65553e9i	−0.205564	−	0.172489i	0.534194	−	0.845362i	$-0.320615\pi$
$313$	−1.97299e9	−	1.65553e9i	−0.205564	−	0.172489i	−0.739757	+	0.672874i	$0.765060\pi$
$314$	2.01855e10	−	1.16541e10i	2.07644	−	1.19883i
$315$		0			0
$316$	1.92394e9	−	3.33236e9i	0.192949	−	0.334198i
$317$	1.17183e9	+	3.21958e9i	0.116045	+	0.318832i	0.984094	−	0.177646i	$-0.0568483\pi$
$317$	1.17183e9	+	3.21958e9i	0.116045	+	0.318832i	−0.868049	+	0.496479i	$0.834626\pi$
$318$		0			0
$319$	1.53721e9	−	1.28987e9i	0.148446	−	0.124561i
$320$	7.95753e9	−	2.18631e10i	0.758889	−	2.08503i
$321$		0			0
$322$	4.27383e9	−	2.42381e10i	0.397552	−	2.25463i
$323$		−	1.57781e10i		−	1.44959i
$324$		0			0
$325$	1.30565e10			1.17029
$326$	−3.19132e9	−	5.62716e8i	−0.282553	−	0.0498217i
$327$		0			0
$328$	−3.33860e9	−	1.21515e9i	−0.288449	−	0.104987i
$329$	−8.90039e9	−	1.06071e10i	−0.759671	−	0.905340i
$330$		0			0
$331$	1.73076e10	−	6.29946e9i	1.44187	−	0.524797i	0.501560	−	0.865123i	$-0.332760\pi$
$331$	1.73076e10	−	6.29946e9i	1.44187	−	0.524797i	0.940307	+	0.340326i	$0.110538\pi$
$332$	8.33137e9	+	4.81012e9i	0.685747	+	0.395916i
$333$		0			0
$334$	−1.61281e10	−	2.79347e10i	−1.29598	−	2.24470i
$335$	1.73621e10	−	2.06913e10i	1.37855	−	1.64289i
$336$		0			0
$337$	−8.07216e8	−	4.57795e9i	−0.0625850	−	0.354937i	−0.999978	−	0.00666321i	$-0.997879\pi$
$337$	−8.07216e8	−	4.57795e9i	−0.0625850	−	0.354937i	0.937393	−	0.348274i	$-0.113232\pi$
$338$	1.83196e10	−	3.23024e9i	1.40362	−	0.247496i
$339$		0			0
$340$	−3.26116e10	−	2.73644e10i	−2.44037	−	2.04772i
$341$	5.72752e9	−	3.30678e9i	0.423593	−	0.244562i
$342$		0			0
$343$	−7.15965e9	+	1.24009e10i	−0.517268	+	0.895934i
$344$	3.37142e9	+	9.26290e9i	0.240757	+	0.661475i
$345$		0			0
$346$	−8.99148e9	+	7.54475e9i	−0.627374	+	0.526430i
$347$	−9.72752e9	+	2.67261e10i	−0.670941	+	1.84339i	−0.152450	+	0.988311i	$0.548716\pi$
$347$	−9.72752e9	+	2.67261e10i	−0.670941	+	1.84339i	−0.518490	+	0.855083i	$0.673506\pi$
$348$		0			0
$349$	−2.37527e9	+	1.34708e10i	−0.160107	+	0.908013i	0.793860	+	0.608101i	$0.208068\pi$
$349$	−2.37527e9	+	1.34708e10i	−0.160107	+	0.908013i	−0.953967	+	0.299912i	$0.903043\pi$
$350$			3.30660e10i			2.20348i
$351$		0			0
$352$	1.31035e10			0.853525
$353$	−2.21431e10	−	3.90442e9i	−1.42606	−	0.251453i	−0.593255	−	0.805015i	$-0.702157\pi$
$353$	−2.21431e10	−	3.90442e9i	−1.42606	−	0.251453i	−0.832808	+	0.553562i	$0.813268\pi$
$354$		0			0
$355$	1.97910e10	+	7.20334e9i	1.24611	+	0.453545i
$356$	7.45377e9	+	8.88306e9i	0.464062	+	0.553048i
$357$		0			0
$358$	−3.62302e10	+	1.31867e10i	−2.20566	+	0.802794i
$359$	−5.81312e8	−	3.35621e8i	−0.0349970	−	0.0202056i	0.482399	−	0.875951i	$-0.339765\pi$
$359$	−5.81312e8	−	3.35621e8i	−0.0349970	−	0.0202056i	−0.517396	+	0.855746i	$0.673099\pi$
$360$		0			0
$361$	7.22003e8	+	1.25055e9i	0.0425118	+	0.0736327i
$362$	−1.78986e10	+	2.13308e10i	−1.04228	+	1.24214i
$363$		0			0
$364$	1.05261e10	+	5.96967e10i	0.599603	+	3.40052i
$365$	3.83989e9	−	6.77076e8i	0.216345	−	0.0381475i
$366$		0			0
$367$	−1.44482e8	−	1.21235e8i	−0.00796436	−	0.00668289i	0.638797	−	0.769376i	$-0.279432\pi$
$367$	−1.44482e8	−	1.21235e8i	−0.00796436	−	0.00668289i	−0.646761	+	0.762693i	$0.723877\pi$
$368$	−2.20802e9	+	1.27480e9i	−0.120396	+	0.0695105i
$369$		0			0
$370$	−4.98452e9	+	8.63345e9i	−0.265960	+	0.460657i
$371$	9.29482e9	+	2.55373e10i	0.490620	+	1.34797i
$372$		0			0
$373$	1.47010e10	−	1.23356e10i	0.759470	−	0.637271i	−0.178519	−	0.983937i	$-0.557130\pi$
$373$	1.47010e10	−	1.23356e10i	0.759470	−	0.637271i	0.937989	+	0.346665i	$0.112686\pi$
$374$	1.23187e10	−	3.38454e10i	0.629621	−	1.72987i
$375$		0			0
$376$	2.19753e9	−	1.24628e10i	0.109947	−	0.623541i
$377$		−	7.07426e9i		−	0.350199i
$378$		0			0
$379$	−3.09946e10			−1.50221			−0.751103	−	0.660185i	$-0.770478\pi$
$379$	−3.09946e10			−1.50221			−0.751103	+	0.660185i	$0.770478\pi$
$380$	−4.12907e10	−	7.28067e9i	−1.98024	−	0.349170i
$381$		0			0
$382$	2.74622e10	+	9.99542e9i	1.28968	+	0.469405i
$383$	8.91482e9	+	1.06243e10i	0.414302	+	0.493746i	0.932325	−	0.361620i	$-0.117776\pi$
$383$	8.91482e9	+	1.06243e10i	0.414302	+	0.493746i	−0.518023	+	0.855367i	$0.673332\pi$
$384$		0			0
$385$	−3.47257e10	+	1.26391e10i	−1.58055	+	0.575273i
$386$	−6.66473e9	−	3.84788e9i	−0.300216	−	0.173330i
$387$		0			0
$388$	2.22245e10	+	3.84940e10i	0.980630	+	1.69850i
$389$	−1.64333e10	+	1.95845e10i	−0.717673	+	0.855290i	−0.994402	−	0.105658i	$-0.966305\pi$
$389$	−1.64333e10	+	1.95845e10i	−0.717673	+	0.855290i	0.276729	+	0.960948i	$0.410749\pi$
$390$		0			0
$391$	5.43514e9	+	3.08242e10i	0.232543	+	1.31882i
$392$	−3.31191e10	+	5.83979e9i	−1.40260	+	0.247316i
$393$		0			0
$394$	8.76547e7	+	7.35510e7i	0.00363739	+	0.00305213i
$395$	7.16177e9	−	4.13485e9i	0.294193	−	0.169852i
$396$		0			0
$397$	1.40601e10	−	2.43528e10i	0.566012	−	0.980362i	−0.430943	−	0.902379i	$-0.641819\pi$
$397$	1.40601e10	−	2.43528e10i	0.566012	−	0.980362i	0.996955	−	0.0779823i	$-0.0248478\pi$
$398$	1.55430e10	+	4.27040e10i	0.619444	+	1.70191i
$399$		0			0
$400$	2.62398e9	−	2.20178e9i	0.102499	−	0.0860069i
$401$	6.59080e9	−	1.81081e10i	0.254894	−	0.700317i	−0.744568	−	0.667546i	$-0.767345\pi$
$401$	6.59080e9	−	1.81081e10i	0.254894	−	0.700317i	0.999463	−	0.0327706i	$-0.0104331\pi$
$402$		0			0
$403$	4.04864e9	−	2.29610e10i	0.153493	−	0.870502i
$404$			2.20106e10i			0.826239i
$405$		0			0
$406$	1.79157e10			0.659371
$407$	−5.04286e9	−	8.89192e8i	−0.183780	−	0.0324054i
$408$		0			0
$409$	−4.65542e10	−	1.69444e10i	−1.66367	−	0.605525i	−0.672733	−	0.739885i	$-0.734880\pi$
$409$	−4.65542e10	−	1.69444e10i	−1.66367	−	0.605525i	−0.990933	+	0.134360i	$0.957102\pi$
$410$	−1.39087e10	−	1.65757e10i	−0.492211	−	0.586594i
$411$		0			0
$412$	4.87191e10	−	1.77323e10i	1.69087	−	0.615427i
$413$	−4.02606e10	−	2.32445e10i	−1.38382	−	0.798950i
$414$		0			0
$415$	1.03377e10	+	1.79055e10i	0.348524	+	0.603661i
$416$	2.96932e10	−	3.53870e10i	0.991480	−	1.18160i
$417$		0			0
$418$	−6.15981e9	−	3.49340e10i	−0.201773	−	1.14431i
$419$	−1.30485e8	+	2.30080e7i	−0.00423354	+	0.000746487i	−0.175765	−	0.984432i	$-0.556240\pi$
$419$	−1.30485e8	+	2.30080e7i	−0.00423354	+	0.000746487i	0.171531	+	0.985179i	$0.445129\pi$
$420$		0			0
$421$	−1.35983e10	−	1.14103e10i	−0.432868	−	0.363220i	0.400164	−	0.916443i	$-0.368953\pi$
$421$	−1.35983e10	−	1.14103e10i	−0.432868	−	0.363220i	−0.833033	+	0.553224i	$0.813397\pi$
$422$	2.37462e8	−	1.37099e8i	0.00748763	−	0.00432298i
$423$		0			0
$424$	−1.24189e10	+	2.15101e10i	−0.384255	+	0.665549i
$425$	−1.43822e10	−	3.95148e10i	−0.440829	−	1.21117i
$426$		0			0
$427$	1.57508e10	−	1.32165e10i	0.473795	−	0.397561i
$428$	1.46800e10	−	4.03329e10i	0.437472	−	1.20194i
$429$		0			0
$430$	−1.04249e10	+	5.91225e10i	−0.304928	+	1.72933i
$431$			8.67445e9i			0.251381i	0.992069	+	0.125691i	$0.0401147\pi$
$431$			8.67445e9i			0.251381i	−0.992069	+	0.125691i	$0.959885\pi$
$432$		0			0
$433$	−4.02004e10			−1.14361			−0.571807	−	0.820388i	$-0.693757\pi$
$433$	−4.02004e10			−1.14361			−0.571807	+	0.820388i	$0.693757\pi$
$434$	5.81491e10	+	1.02533e10i	1.63902	+	0.289004i
$435$		0			0
$436$	−3.95470e10	−	1.43939e10i	−1.09438	−	0.398321i
$437$	1.98148e10	+	2.36144e10i	0.543332	+	0.647517i
$438$		0			0
$439$	3.68034e10	−	1.33954e10i	0.990901	−	0.360659i	0.204832	−	0.978797i	$-0.434335\pi$
$439$	3.68034e10	−	1.33954e10i	0.990901	−	0.360659i	0.786069	+	0.618138i	$0.212113\pi$
$440$	−2.92496e10	−	1.68872e10i	−0.780385	−	0.450555i
$441$		0			0
$442$	−6.34873e10	−	1.09963e11i	−1.66340	−	2.88110i
$443$	1.64364e10	−	1.95882e10i	0.426768	−	0.508603i	−0.509219	−	0.860637i	$-0.670066\pi$
$443$	1.64364e10	−	1.95882e10i	0.426768	−	0.508603i	0.935987	+	0.352034i	$0.114510\pi$
$444$		0			0
$445$	4.32761e9	+	2.45431e10i	0.110359	+	0.625877i
$446$	−3.76462e10	+	6.63804e9i	−0.951441	+	0.167765i
$447$		0			0
$448$	8.17349e10	+	6.85838e10i	2.02906	+	1.70259i
$449$	2.68255e8	−	1.54877e8i	0.00660028	−	0.00381067i	−0.496696	−	0.867924i	$-0.665454\pi$
$449$	2.68255e8	−	1.54877e8i	0.00660028	−	0.00381067i	0.503297	+	0.864114i	$0.332120\pi$
$450$		0			0
$451$	5.55726e9	−	9.62545e9i	0.134324	−	0.232656i
$452$	−2.26257e10	−	6.21637e10i	−0.542062	−	1.48930i
$453$		0			0
$454$	9.97146e9	−	8.36705e9i	0.234712	−	0.196947i
$455$	−4.45574e10	+	1.22420e11i	−1.03962	+	2.85633i
$456$		0			0
$457$	−1.30511e10	+	7.40165e10i	−0.299214	+	1.69693i	0.350347	+	0.936620i	$0.386064\pi$
$457$	−1.30511e10	+	7.40165e10i	−0.299214	+	1.69693i	−0.649562	+	0.760309i	$0.725048\pi$
$458$			9.89434e10i			2.24866i
$459$		0			0
$460$	8.31736e10			1.85761
$461$	1.17413e10	+	2.07030e9i	0.259962	+	0.0458384i	0.302110	−	0.953273i	$-0.402309\pi$
$461$	1.17413e10	+	2.07030e9i	0.259962	+	0.0458384i	−0.0421478	+	0.999111i	$0.513420\pi$
$462$		0			0
$463$	−4.36052e10	−	1.58710e10i	−0.948886	−	0.345366i	−0.179217	−	0.983810i	$-0.557356\pi$
$463$	−4.36052e10	−	1.58710e10i	−0.948886	−	0.345366i	−0.769669	+	0.638443i	$0.779579\pi$
$464$	−1.19296e9	−	1.42172e9i	−0.0257368	−	0.0306719i
$465$		0			0
$466$	9.89762e10	−	3.60244e10i	2.09888	−	0.763929i
$467$	−3.51264e10	−	2.02802e10i	−0.738526	−	0.426388i	0.0830074	−	0.996549i	$-0.473547\pi$
$467$	−3.51264e10	−	2.02802e10i	−0.738526	−	0.426388i	−0.821533	+	0.570161i	$0.806881\pi$
$468$		0			0
$469$	6.19343e10	+	1.07273e11i	1.28009	+	2.21718i
$470$	4.95418e10	−	5.90417e10i	1.01527	−	1.20995i
$471$		0			0
$472$	−7.37808e9	−	4.18432e10i	−0.148654	−	0.843056i
$473$	−3.03685e10	+	5.35479e9i	−0.606708	+	0.106979i
$474$		0			0
$475$	−3.17257e10	−	2.66210e10i	−0.623213	−	0.522938i
$476$	1.69074e11	−	9.76147e10i	3.29343	−	1.90146i
$477$		0			0
$478$	1.33318e10	−	2.30913e10i	0.255373	−	0.442320i
$479$	−1.09639e10	−	3.01231e10i	−0.208269	−	0.572214i	0.790944	−	0.611889i	$-0.209590\pi$
$479$	−1.09639e10	−	3.01231e10i	−0.208269	−	0.572214i	−0.999213	+	0.0396750i	$0.987368\pi$
$480$		0			0
$481$	−1.38287e10	+	1.16037e10i	−0.258346	+	0.216778i
$482$	−1.26035e10	+	3.46279e10i	−0.233509	+	0.641562i
$483$		0			0
$484$	−6.18851e9	+	3.50968e10i	−0.112773	+	0.639567i
$485$			9.55281e10i			1.72649i
$486$		0			0
$487$	−6.91591e10			−1.22951			−0.614757	−	0.788716i	$-0.710746\pi$
$487$	−6.91591e10			−1.22951			−0.614757	+	0.788716i	$0.710746\pi$
$488$	1.85064e10	+	3.26319e9i	0.326320	+	0.0575390i
$489$		0			0
$490$	−1.92465e11	−	7.00516e10i	−3.33863	−	1.21516i
$491$	−9.90310e9	−	1.18021e10i	−0.170391	−	0.203064i	0.674091	−	0.738648i	$-0.264536\pi$
$491$	−9.90310e9	−	1.18021e10i	−0.170391	−	0.203064i	−0.844481	+	0.535585i	$0.820091\pi$
$492$		0			0
$493$	−2.14098e10	+	7.79253e9i	−0.362431	+	0.131914i
$494$	−1.08301e11	−	6.25273e10i	−1.81854	−	1.04993i
$495$		0			0
$496$	−3.05835e9	−	5.29721e9i	−0.0505312	−	0.0875226i
$497$	−6.20837e10	+	7.39884e10i	−1.01754	+	1.21266i
$498$		0			0
$499$	−8.68063e9	−	4.92303e10i	−0.140007	−	0.794018i	−0.971241	−	0.238097i	$-0.923477\pi$
$499$	−8.68063e9	−	4.92303e10i	−0.140007	−	0.794018i	0.831235	−	0.555922i	$-0.187635\pi$
$500$	1.93426e10	−	3.41061e9i	0.309481	−	0.0545698i
$501$		0			0
$502$	−1.26762e10	−	1.06366e10i	−0.199606	−	0.167490i
$503$	3.52695e10	−	2.03628e10i	0.550969	−	0.318102i	−0.198544	−	0.980092i	$-0.563621\pi$
$503$	3.52695e10	−	2.03628e10i	0.550969	−	0.318102i	0.749513	+	0.661990i	$0.230288\pi$
$504$		0			0
$505$	−2.36521e10	+	4.09667e10i	−0.363668	+	0.629891i
$506$	2.40676e10	+	6.61253e10i	0.367140	+	1.00871i
$507$		0			0
$508$	1.39285e11	−	1.16874e11i	2.09145	−	1.75494i
$509$	1.69845e10	−	4.66645e10i	0.253035	−	0.695209i	−0.746519	−	0.665364i	$-0.768276\pi$
$509$	1.69845e10	−	4.66645e10i	0.253035	−	0.695209i	0.999555	−	0.0298452i	$-0.00950142\pi$
$510$		0			0
$511$	−3.10502e9	+	1.76095e10i	−0.0455388	+	0.258263i
$512$		−	2.15246e10i		−	0.313224i
$513$		0			0
$514$	4.66928e9			0.0668955
$515$	1.09732e11	+	1.93487e10i	1.55993	+	0.275058i
$516$		0			0
$517$	3.72016e10	+	1.35403e10i	0.520715	+	0.189525i
$518$	−2.93865e10	−	3.50215e10i	−0.408159	−	0.486425i
$519$		0			0
$520$	−1.11886e11	+	4.07233e10i	−1.53026	+	0.556968i
$521$	1.21235e11	+	6.99950e10i	1.64542	+	0.949984i	0.978860	+	0.204532i	$0.0655674\pi$
$521$	1.21235e11	+	6.99950e10i	1.64542	+	0.949984i	0.666560	+	0.745451i	$0.267766\pi$
$522$		0			0
$523$	−1.76459e10	−	3.05635e10i	−0.235850	−	0.408504i	0.723669	−	0.690147i	$-0.242454\pi$
$523$	−1.76459e10	−	3.05635e10i	−0.235850	−	0.408504i	−0.959519	+	0.281642i	$0.909121\pi$
$524$	9.48482e10	−	1.13036e11i	1.25807	−	1.49931i
$525$		0			0
$526$	3.97527e10	+	2.25449e11i	0.519306	+	2.94513i
$527$	−7.39497e10	+	1.30393e10i	−0.958724	+	0.169049i
$528$		0			0
$529$	1.31449e10	+	1.10298e10i	0.167855	+	0.140847i
$530$	−1.31004e11	+	7.56349e10i	−1.66027	+	0.958559i
$531$		0			0
$532$	9.61387e10	−	1.66517e11i	1.20020	−	2.07880i
$533$	−1.34012e10	−	3.68196e10i	−0.166049	−	0.456216i
$534$		0			0
$535$	7.06637e10	−	5.92939e10i	0.862544	−	0.723760i
$536$	−3.87201e10	+	1.06383e11i	−0.469113	+	1.28888i
$537$		0			0
$538$	2.97581e10	−	1.68767e11i	0.355203	−	2.01446i
$539$		−	1.05205e11i		−	1.24647i
$540$		0			0
$541$	1.20221e10			0.140343			0.0701714	−	0.997535i	$-0.477645\pi$
$541$	1.20221e10			0.140343			0.0701714	+	0.997535i	$0.477645\pi$
$542$	2.03909e11	+	3.59547e10i	2.36287	+	0.416638i
$543$		0			0
$544$	−1.39805e11	−	5.08848e10i	−1.59634	−	0.581021i
$545$	−5.81385e10	−	6.92868e10i	−0.658989	−	0.785352i
$546$		0			0
$547$	−1.41913e10	+	5.16522e9i	−0.158516	+	0.0576951i	−0.420059	−	0.907497i	$-0.637991\pi$
$547$	−1.41913e10	+	5.16522e9i	−0.158516	+	0.0576951i	0.261543	+	0.965192i	$0.415769\pi$
$548$	−2.49090e10	−	1.43812e10i	−0.276207	−	0.159468i
$549$		0			0
$550$	−4.72700e10	−	8.18741e10i	−0.516577	−	0.894738i
$551$	−1.44237e10	+	1.71895e10i	−0.156484	+	0.186491i
$552$		0			0
$553$	6.58548e9	+	3.73481e10i	0.0704185	+	0.399363i
$554$	2.24684e11	−	3.96178e10i	2.38525	−	0.420583i
$555$		0			0
$556$	1.95717e11	+	1.64226e11i	2.04799	+	1.71847i
$557$	1.29584e10	−	7.48156e9i	0.134627	−	0.0777269i	−0.431174	−	0.902269i	$-0.641900\pi$
$557$	1.29584e10	−	7.48156e9i	0.134627	−	0.0777269i	0.565801	+	0.824542i	$0.308567\pi$
$558$		0			0
$559$	−5.43557e10	+	9.41469e10i	−0.556670	+	0.964181i
$560$	1.16895e10	+	3.21168e10i	0.118863	+	0.326573i
$561$		0			0
$562$	−2.08522e11	+	1.74971e11i	−2.09029	+	1.75396i
$563$	1.44475e10	−	3.96943e10i	0.143800	−	0.395089i	−0.846794	−	0.531921i	$-0.821470\pi$
$563$	1.44475e10	−	3.96943e10i	0.143800	−	0.395089i	0.990594	+	0.136833i	$0.0436924\pi$
$564$		0			0
$565$	2.46883e10	−	1.40014e11i	0.242268	−	1.37397i
$566$			1.87863e11i			1.83053i
$567$		0			0
$568$	−8.82741e10			−0.848086
$569$	−1.41148e11	−	2.48882e10i	−1.34656	−	0.237435i	−0.546553	−	0.837425i	$-0.684060\pi$
$569$	−1.41148e11	−	2.48882e10i	−1.34656	−	0.237435i	−0.800008	+	0.599990i	$0.795171\pi$
$570$		0			0
$571$	2.84027e10	+	1.03377e10i	0.267187	+	0.0972482i	0.472140	−	0.881524i	$-0.343482\pi$
$571$	2.84027e10	+	1.03377e10i	0.267187	+	0.0972482i	−0.204953	+	0.978772i	$0.565704\pi$
$572$	−1.11404e11	−	1.32766e11i	−1.04068	−	1.24023i
$573$		0			0
$574$	9.32464e10	−	3.39389e10i	0.858983	−	0.312644i
$575$	7.11496e10	+	4.10782e10i	0.650880	+	0.375786i
$576$		0			0
$577$	−1.41011e10	−	2.44238e10i	−0.127218	−	0.220349i	0.795380	−	0.606112i	$-0.207272\pi$
$577$	−1.41011e10	−	2.44238e10i	−0.127218	−	0.220349i	−0.922598	+	0.385763i	$0.873938\pi$
$578$	−1.48405e11	+	1.76862e11i	−1.32965	+	1.58461i
$579$		0			0
$580$	1.05134e10	+	5.96244e10i	0.0929032	+	0.526880i
$581$	−9.33756e10	+	1.64646e10i	−0.819462	+	0.144493i
$582$		0			0
$583$	−5.95220e10	−	4.99449e10i	−0.515233	−	0.432332i
$584$	−1.41530e10	+	8.17124e9i	−0.121674	+	0.0702484i
$585$		0			0
$586$	1.70975e10	−	2.96137e10i	0.144991	−	0.251132i
$587$	−5.88935e10	−	1.61809e11i	−0.496038	−	1.36285i	−0.895074	−	0.445918i	$-0.852877\pi$
$587$	−5.88935e10	−	1.61809e11i	−0.496038	−	1.36285i	0.399036	−	0.916935i	$-0.369345\pi$
$588$		0			0
$589$	−5.66529e10	+	4.75374e10i	−0.470718	+	0.394979i
$590$	8.85043e10	−	2.43164e11i	0.730393	−	2.00674i
$591$		0			0
$592$	−8.22387e8	+	4.66399e9i	−0.00669559	+	0.0379726i
$593$			5.60671e10i			0.453408i	0.973964	+	0.226704i	$0.0727950\pi$
$593$			5.60671e10i			0.453408i	−0.973964	+	0.226704i	$0.927205\pi$
$594$		0			0
$595$	4.19580e11			3.34770
$596$	−3.34129e9	−	5.89160e8i	−0.0264807	−	0.00466926i
$597$		0			0
$598$	2.33115e11	+	8.48470e10i	1.82291	+	0.663486i
$599$	8.07351e10	+	9.62163e10i	0.627126	+	0.747380i	0.982278	−	0.187429i	$-0.0600153\pi$
$599$	8.07351e10	+	9.62163e10i	0.627126	+	0.747380i	−0.355152	+	0.934809i	$0.615571\pi$
$600$		0			0
$601$	−1.60390e11	+	5.83772e10i	−1.22936	+	0.447451i	−0.873379	−	0.487042i	$-0.838076\pi$
$601$	−1.60390e11	+	5.83772e10i	−1.22936	+	0.447451i	−0.355983	+	0.934493i	$0.615854\pi$
$602$	−2.38429e11	−	1.37657e11i	−1.81540	−	1.04812i
$603$		0			0
$604$	−3.85131e10	−	6.67066e10i	−0.289375	−	0.501212i
$605$	−4.92326e10	+	5.86731e10i	−0.367478	+	0.437943i
$606$		0			0
$607$	−2.34693e10	−	1.33101e11i	−0.172880	−	0.980452i	−0.940562	−	0.339621i	$-0.889701\pi$
$607$	−2.34693e10	−	1.33101e11i	−0.172880	−	0.980452i	0.767682	−	0.640831i	$-0.221410\pi$
$608$	−1.44301e11	+	2.54442e10i	−1.05598	+	0.186198i
$609$		0			0
$610$	8.76729e10	+	7.35663e10i	0.633208	+	0.531324i
$611$	1.20867e11	−	6.97829e10i	0.867251	−	0.500707i
$612$		0			0
$613$	4.51983e10	−	7.82858e10i	0.320096	−	0.554423i	−0.660411	−	0.750904i	$-0.729618\pi$
$613$	4.51983e10	−	7.82858e10i	0.320096	−	0.554423i	0.980508	+	0.196481i	$0.0629514\pi$
$614$	−3.00226e10	−	8.24863e10i	−0.211239	−	0.580375i
$615$		0			0
$616$	1.18651e11	−	9.95597e10i	0.824038	−	0.691450i
$617$	6.73455e10	−	1.85030e11i	0.464695	−	1.27674i	−0.457223	−	0.889352i	$-0.651156\pi$
$617$	6.73455e10	−	1.85030e11i	0.464695	−	1.27674i	0.921918	−	0.387386i	$-0.126622\pi$
$618$		0			0
$619$	−1.36246e10	+	7.72687e10i	−0.0928025	+	0.526309i	0.902596	+	0.430488i	$0.141659\pi$
$619$	−1.36246e10	+	7.72687e10i	−0.0928025	+	0.526309i	−0.995399	+	0.0958207i	$0.969452\pi$
$620$			1.99540e11i			1.35040i
$621$		0			0
$622$	−2.29543e11			−1.53357
$623$	−1.12553e11	−	1.98461e10i	−0.747144	−	0.131742i
$624$		0			0
$625$	1.61616e11	+	5.88236e10i	1.05917	+	0.385506i
$626$	4.22599e10	+	5.03634e10i	0.275189	+	0.327957i
$627$		0			0
$628$	−3.39437e11	+	1.23545e11i	−2.18233	+	0.794304i
$629$	5.03506e10	+	2.90699e10i	0.321664	+	0.185713i
$630$		0			0
$631$	3.10276e10	+	5.37415e10i	0.195718	+	0.338994i	0.947136	−	0.320833i	$-0.103963\pi$
$631$	3.10276e10	+	5.37415e10i	0.195718	+	0.338994i	−0.751417	+	0.659827i	$0.770630\pi$
$632$	−2.22796e10	+	2.65518e10i	−0.139650	+	0.166428i
$633$		0			0
$634$	−1.51871e10	−	8.61302e10i	−0.0939977	−	0.533088i
$635$	3.84831e11	−	6.78561e10i	2.36687	−	0.417344i
$636$		0			0
$637$	−2.84115e11	−	2.38401e11i	−1.72559	−	1.44794i
$638$	−4.43608e10	+	2.56117e10i	−0.267742	+	0.154581i
$639$		0			0
$640$	−1.69033e11	+	2.92775e11i	−1.00752	+	1.74507i
$641$	−9.42691e10	−	2.59002e11i	−0.558390	−	1.53416i	−0.821973	−	0.569526i	$-0.807127\pi$
$641$	−9.42691e10	−	2.59002e11i	−0.558390	−	1.53416i	0.263584	−	0.964637i	$-0.415096\pi$
$642$		0			0
$643$	2.14606e11	−	1.80076e11i	1.25545	−	1.05345i	0.259297	−	0.965798i	$-0.416509\pi$
$643$	2.14606e11	−	1.80076e11i	1.25545	−	1.05345i	0.996151	−	0.0876483i	$-0.0279352\pi$
$644$	−1.30456e11	+	3.58425e11i	−0.758440	+	2.08380i
$645$		0			0
$646$	−6.99385e10	+	3.96641e11i	−0.401593	+	2.27755i
$647$			1.18701e11i			0.677390i	0.940896	+	0.338695i	$0.109985\pi$
$647$			1.18701e11i			0.677390i	−0.940896	+	0.338695i	$0.890015\pi$
$648$		0			0
$649$	1.32918e11			0.749213
$650$	−3.28224e11	−	5.78747e10i	−1.83872	−	0.324217i
$651$		0			0
$652$	4.71922e10	+	1.71766e10i	0.261144	+	0.0950486i
$653$	1.10090e11	+	1.31200e11i	0.605473	+	0.721574i	0.978500	−	0.206246i	$-0.0661247\pi$
$653$	1.10090e11	+	1.31200e11i	0.605473	+	0.721574i	−0.373027	+	0.927820i	$0.621680\pi$
$654$		0			0
$655$	2.98000e11	−	1.08463e11i	1.61902	−	0.589274i
$656$	−8.90229e9	−	5.13974e9i	−0.0480713	−	0.0277540i
$657$		0			0
$658$	1.76727e11	+	3.06100e11i	0.942754	+	1.63290i
$659$	−1.32926e11	+	1.58415e11i	−0.704805	+	0.839954i	−0.993061	−	0.117600i	$-0.962480\pi$
$659$	−1.32926e11	+	1.58415e11i	−0.704805	+	0.839954i	0.288256	+	0.957553i	$0.406924\pi$
$660$		0			0
$661$	4.95574e10	+	2.81054e11i	0.259599	+	1.47226i	0.783986	+	0.620779i	$0.213184\pi$
$661$	4.95574e10	+	2.81054e11i	0.259599	+	1.47226i	−0.524387	+	0.851480i	$0.675705\pi$
$662$	−4.63013e11	+	8.16417e10i	−2.41080	+	0.425089i
$663$		0			0
$664$	−6.63834e10	−	5.57023e10i	−0.341497	−	0.286550i
$665$	3.57872e11	−	2.06618e11i	1.82996	−	1.05653i
$666$		0			0
$667$	2.22569e10	−	3.85501e10i	0.112450	−	0.194770i
$668$	1.70975e11	+	4.69749e11i	0.858669	+	2.35917i
$669$		0			0
$670$	−5.28176e11	+	4.43192e11i	−2.62107	+	2.19934i
$671$	−2.01064e10	+	5.52419e10i	−0.0991847	+	0.272508i
$672$		0			0
$673$	−1.42595e10	+	8.08695e10i	−0.0695093	+	0.394207i	0.930127	+	0.367238i	$0.119697\pi$
$673$	−1.42595e10	+	8.08695e10i	−0.0695093	+	0.394207i	−0.999636	+	0.0269688i	$0.991415\pi$
$674$			1.18662e11i			0.575004i
$675$		0			0
$676$	−2.88290e11			−1.38052
$677$	−1.47869e11	−	2.60732e10i	−0.703916	−	0.124119i	−0.189778	−	0.981827i	$-0.560777\pi$
$677$	−1.47869e11	−	2.60732e10i	−0.703916	−	0.124119i	−0.514138	+	0.857708i	$0.671888\pi$
$678$		0			0
$679$	−4.11665e11	−	1.49834e11i	−1.93671	−	0.704905i
$680$	2.46493e11	+	2.93759e11i	1.15284	+	1.37390i
$681$		0			0
$682$	−1.58640e11	+	5.77402e10i	−0.733288	+	0.266895i
$683$	2.82988e11	+	1.63383e11i	1.30043	+	0.750801i	0.980477	−	0.196634i	$-0.0630010\pi$
$683$	2.82988e11	+	1.63383e11i	1.30043	+	0.750801i	0.319949	+	0.947435i	$0.396334\pi$
$684$		0			0
$685$	−3.09076e10	−	5.35335e10i	−0.140379	−	0.243144i
$686$	2.34952e11	−	2.80005e11i	1.06092	−	1.26436i
$687$		0			0
$688$	4.95249e9	+	2.80870e10i	0.0221039	+	0.125358i
$689$	−2.69760e11	+	4.75660e10i	−1.19702	+	0.211067i
$690$		0			0
$691$	−1.88959e11	−	1.58555e11i	−0.828810	−	0.695454i	0.126207	−	0.992004i	$-0.459720\pi$
$691$	−1.88959e11	−	1.58555e11i	−0.828810	−	0.695454i	−0.955017	+	0.296550i	$0.904164\pi$
$692$	1.57534e11	−	9.09522e10i	0.686988	−	0.396633i
$693$		0			0
$694$	3.63004e11	−	6.28741e11i	1.56485	−	2.71040i
$695$	1.87799e11	+	5.15975e11i	0.804924	+	2.21151i
$696$		0			0
$697$	−9.66704e10	+	8.11161e10i	−0.409602	+	0.343697i
$698$	1.19422e11	−	3.28109e11i	0.503110	−	1.38228i
$699$		0			0
$700$	8.89851e10	−	5.04660e11i	0.370617	−	2.10187i
$701$		−	3.69835e11i		−	1.53157i	−0.643098	−	0.765784i	$-0.722351\pi$
$701$		−	3.69835e11i		−	1.53157i	0.643098	−	0.765784i	$-0.277649\pi$
$702$		0			0
$703$	5.72608e10			0.234442
$704$	−3.00428e11	−	5.29735e10i	−1.22306	−	0.215659i
$705$		0			0
$706$	5.39340e11	+	1.96304e11i	2.17092	+	0.790150i
$707$	−1.39443e11	−	1.66181e11i	−0.558107	−	0.665126i
$708$		0			0
$709$	2.54355e11	−	9.25776e10i	1.00660	−	0.366371i	0.214471	−	0.976730i	$-0.431197\pi$
$709$	2.54355e11	−	9.25776e10i	1.00660	−	0.366371i	0.792125	+	0.610359i	$0.208975\pi$
$710$	−4.65590e11	−	2.68808e11i	−1.83219	−	1.05781i
$711$		0			0
$712$	−5.22274e10	−	9.04605e10i	−0.203226	−	0.351997i
$713$	9.43018e10	−	1.12384e11i	0.364890	−	0.434859i
$714$		0			0
$715$	−6.46805e10	−	3.66821e11i	−0.247485	−	1.40356i
$716$	5.88440e11	−	1.03758e11i	2.23898	−	0.394792i
$717$		0			0
$718$	1.31257e10	+	1.10138e10i	0.0493884	+	0.0414418i
$719$	−4.07092e9	+	2.35035e9i	−0.0152327	+	0.00879462i	−0.507597	−	0.861595i	$-0.669466\pi$
$719$	−4.07092e9	+	2.35035e9i	−0.0152327	+	0.00879462i	0.492364	+	0.870389i	$0.336133\pi$
$720$		0			0
$721$	−2.55494e11	+	4.42528e11i	−0.945451	+	1.63757i
$722$	−1.26070e10	−	3.46374e10i	−0.0463940	−	0.127467i
$723$		0			0
$724$	3.30577e11	−	2.77387e11i	1.20314	−	1.00956i
$725$	−2.04541e10	+	5.61972e10i	−0.0740335	+	0.203405i
$726$		0			0
$727$	5.52832e10	−	3.13527e11i	0.197905	−	1.12237i	−0.710317	−	0.703882i	$-0.751448\pi$
$727$	5.52832e10	−	3.13527e11i	0.197905	−	1.12237i	0.908221	−	0.418490i	$-0.137441\pi$
$728$		−	5.46033e11i		−	1.94399i
$729$		0			0
$730$	−9.95309e10			−0.350483
$731$	3.44805e11	+	6.07983e10i	1.20755	+	0.212923i
$732$		0			0
$733$	3.96308e11	+	1.44244e11i	1.37283	+	0.499669i	0.919997	−	0.391926i	$-0.128191\pi$
$733$	3.96308e11	+	1.44244e11i	1.37283	+	0.499669i	0.452833	+	0.891595i	$0.350413\pi$
$734$	3.09470e9	+	3.68812e9i	0.0106619	+	0.0127064i
$735$		0			0
$736$	2.73143e11	−	9.94158e10i	0.930847	−	0.338800i
$737$	−3.06709e11	−	1.77079e11i	−1.03958	−	0.600200i
$738$		0			0
$739$	1.39500e11	+	2.41621e11i	0.467731	+	0.810134i	0.999320	−	0.0368686i	$-0.0117383\pi$
$739$	1.39500e11	+	2.41621e11i	0.467731	+	0.810134i	−0.531589	+	0.847002i	$0.678405\pi$
$740$	9.93086e10	−	1.18351e11i	0.331177	−	0.394681i
$741$		0			0
$742$	−1.20462e11	−	6.83174e11i	−0.397406	−	2.25380i
$743$	−7.10841e9	+	1.25340e9i	−0.0233248	+	0.00411279i	−0.185298	−	0.982682i	$-0.559325\pi$
$743$	−7.10841e9	+	1.25340e9i	−0.0233248	+	0.00411279i	0.161974	+	0.986795i	$0.448214\pi$
$744$		0			0
$745$	−5.58580e9	−	4.68705e9i	−0.0181326	−	0.0152151i
$746$	−4.24242e11	+	2.44936e11i	−1.36980	+	0.790856i
$747$		0			0
$748$	−2.79094e11	+	4.83404e11i	−0.891546	+	1.54420i
$749$	1.44684e11	+	3.97517e11i	0.459721	+	1.26307i
$750$		0			0
$751$	−6.48985e10	+	5.44563e10i	−0.204021	+	0.171194i	−0.739073	−	0.673625i	$-0.764736\pi$
$751$	−6.48985e10	+	5.44563e10i	−0.204021	+	0.171194i	0.535052	+	0.844819i	$0.320292\pi$
$752$	1.25230e10	−	3.44067e10i	0.0391595	−	0.107590i
$753$		0			0
$754$	−3.13575e10	+	1.77837e11i	−0.0970189	+	0.550221i
$755$		−	1.65542e11i		−	0.509471i
$756$		0			0
$757$	−4.60417e11			−1.40206			−0.701032	−	0.713130i	$-0.747277\pi$
$757$	−4.60417e11			−1.40206			−0.701032	+	0.713130i	$0.747277\pi$
$758$	7.79163e11	+	1.37388e11i	2.36022	+	0.416170i
$759$		0			0
$760$	3.54901e11	+	1.29173e11i	1.06378	+	0.387185i
$761$	−7.37481e9	−	8.78895e9i	−0.0219893	−	0.0262059i	0.754938	−	0.655797i	$-0.227667\pi$
$761$	−7.37481e9	−	8.78895e9i	−0.0219893	−	0.0262059i	−0.776927	+	0.629591i	$0.783223\pi$
$762$		0			0
$763$	3.89771e11	−	1.41865e11i	1.15004	−	0.418579i
$764$	−3.92234e11	−	2.26457e11i	−1.15126	−	0.664678i
$765$		0			0
$766$	−1.77013e11	−	3.06596e11i	−0.514151	−	0.890535i
$767$	3.01200e11	−	3.58956e11i	0.870308	−	1.03719i
$768$		0			0
$769$	−4.42064e10	−	2.50707e11i	−0.126410	−	0.716904i	−0.980461	−	0.196715i	$-0.936973\pi$
$769$	−4.42064e10	−	2.50707e11i	−0.126410	−	0.716904i	0.854051	−	0.520189i	$-0.174139\pi$
$770$	9.28982e11	−	1.63805e11i	2.64268	−	0.465976i
$771$		0			0
$772$	9.13633e10	+	7.66629e10i	0.257219	+	0.215832i
$773$	−1.20697e11	+	6.96843e10i	−0.338047	+	0.195172i	−0.659408	−	0.751785i	$-0.729193\pi$
$773$	−1.20697e11	+	6.96843e10i	−0.338047	+	0.195172i	0.321361	+	0.946957i	$0.395860\pi$
$774$		0			0
$775$	−9.85500e10	+	1.70694e11i	−0.273181	+	0.473163i
$776$	−1.36941e11	−	3.76242e11i	−0.377647	−	1.03758i
$777$		0			0
$778$	4.99922e11	−	4.19484e11i	1.36453	−	1.14498i
$779$	−4.25083e10	+	1.16791e11i	−0.115431	+	0.317145i
$780$		0			0
$781$	4.79529e10	−	2.71954e11i	0.128887	−	0.730957i
$782$		−	7.98970e11i		−	2.13650i
$783$		0			0
$784$	−9.73013e10			−0.257546
$785$	−7.64530e11	−	1.34807e11i	−2.01333	−	0.355005i
$786$		0			0
$787$	2.58977e11	+	9.42598e10i	0.675090	+	0.245713i	0.656738	−	0.754119i	$-0.271936\pi$
$787$	2.58977e11	+	9.42598e10i	0.675090	+	0.245713i	0.0183521	+	0.999832i	$0.494158\pi$
$788$	−1.13987e9	−	1.35844e9i	−0.00295631	−	0.00352319i
$789$		0			0
$790$	−1.98366e11	+	7.21992e10i	−0.509282	+	0.185363i
$791$	5.64649e11	+	3.26000e11i	1.44236	+	0.832744i
$792$		0			0
$793$	1.03623e11	+	1.79480e11i	0.262037	+	0.453862i
$794$	−4.61398e11	+	5.49873e11i	−1.16090	+	1.38350i
$795$		0			0
$796$	−1.22298e11	−	6.93585e11i	−0.304625	−	1.72762i
$797$	−1.29154e11	+	2.27733e10i	−0.320091	+	0.0564407i	−0.331385	−	0.943496i	$-0.607516\pi$
$797$	−1.29154e11	+	2.27733e10i	−0.320091	+	0.0564407i	0.0112943	+	0.999936i	$0.496405\pi$
$798$		0			0
$799$	−3.44333e11	−	2.88930e11i	−0.844874	−	0.708933i
$800$	−3.38196e11	+	1.95257e11i	−0.825674	+	0.476703i
$801$		0			0
$802$	−2.45950e11	+	4.25998e11i	−0.594496	+	1.02970i
$803$	−1.74856e10	−	4.80413e10i	−0.0420551	−	0.115545i
$804$		0			0
$805$	−6.27966e11	+	5.26926e11i	−1.49538	+	1.25478i
$806$	−2.03555e11	+	5.59262e11i	−0.482326	+	1.32518i
$807$		0			0
$808$	3.44288e10	−	1.95255e11i	0.0807748	−	0.458097i
$809$		−	1.21681e11i		−	0.284072i	−0.989862	−	0.142036i	$-0.954635\pi$
$809$		−	1.21681e11i		−	0.284072i	0.989862	−	0.142036i	$-0.0453648\pi$
$810$		0			0
$811$	9.29506e10			0.214867			0.107433	−	0.994212i	$-0.465737\pi$
$811$	9.29506e10			0.214867			0.107433	+	0.994212i	$0.465737\pi$
$812$	−2.73433e11	−	4.82136e10i	−0.628966	−	0.110904i
$813$		0			0
$814$	1.22829e11	+	4.47062e10i	0.279772	+	0.101829i
$815$	6.93779e10	+	8.26814e10i	0.157250	+	0.187403i
$816$		0			0
$817$	3.24034e11	−	1.17939e11i	0.727281	−	0.264709i
$818$	1.09520e12	+	6.32316e11i	2.44614	+	1.41228i
$819$		0			0
$820$	1.67670e11	+	2.90413e11i	0.370851	+	0.642333i
$821$	6.00692e10	−	7.15877e10i	0.132215	−	0.157567i	−0.695875	−	0.718163i	$-0.744983\pi$
$821$	6.00692e10	−	7.15877e10i	0.132215	−	0.157567i	0.828090	+	0.560596i	$0.189428\pi$
$822$		0			0
$823$	−7.89598e9	−	4.47804e10i	−0.0172110	−	0.0976086i	0.974992	−	0.222239i	$-0.0713366\pi$
$823$	−7.89598e9	−	4.47804e10i	−0.0172110	−	0.0976086i	−0.992203	+	0.124631i	$0.960225\pi$
$824$	−4.59923e11	+	8.10968e10i	−0.997645	+	0.175912i
$825$		0			0
$826$	9.09063e11	+	7.62795e11i	1.95287	+	1.63865i
$827$	−2.41268e11	+	1.39296e11i	−0.515795	+	0.297794i	−0.735212	−	0.677837i	$-0.762918\pi$
$827$	−2.41268e11	+	1.39296e11i	−0.515795	+	0.297794i	0.219418	+	0.975631i	$0.429584\pi$
$828$		0			0
$829$	8.05320e10	−	1.39486e11i	0.170510	−	0.295332i	−0.768088	−	0.640344i	$-0.778792\pi$
$829$	8.05320e10	−	1.39486e11i	0.170510	−	0.295332i	0.938598	+	0.345012i	$0.112125\pi$
$830$	−1.80508e11	−	4.95942e11i	−0.380351	−	1.04501i
$831$		0			0
$832$	−8.23844e11	+	6.91287e11i	−1.71930	+	1.44266i
$833$	−4.08544e11	+	1.12247e12i	−0.848513	+	2.33127i
$834$		0			0
$835$	−1.86560e11	+	1.05804e12i	−0.383772	+	2.17648i
$836$			5.49747e11i			1.12548i
$837$		0			0
$838$	3.38220e9			0.00685840
$839$	3.62946e11	+	6.39972e10i	0.732478	+	0.129156i	0.527433	−	0.849597i	$-0.323155\pi$
$839$	3.62946e11	+	6.39972e10i	0.732478	+	0.129156i	0.205045	+	0.978753i	$0.434266\pi$
$840$		0			0
$841$	−4.39629e11	−	1.60012e11i	−0.878825	−	0.319866i
$842$	2.91265e11	+	3.47116e11i	0.579482	+	0.690600i
$843$		0			0
$844$	−3.99314e9	+	1.45339e9i	−0.00786947	+	0.00286425i
$845$	−5.36574e11	−	3.09791e11i	−1.05245	−	0.607634i
$846$		0			0
$847$	−1.75623e11	−	3.04189e11i	−0.341231	−	0.591030i
$848$	−4.61925e10	+	5.50501e10i	−0.0893282	+	0.106457i
$849$		0			0
$850$	1.86395e11	+	1.05710e12i	0.357075	+	2.02507i
$851$	−1.11865e11	+	1.97248e10i	−0.213292	+	0.0376092i
$852$		0			0
$853$	−7.35866e11	−	6.17465e11i	−1.38996	−	1.16632i	−0.965356	−	0.260936i	$-0.915969\pi$
$853$	−7.35866e11	−	6.17465e11i	−1.38996	−	1.16632i	−0.424604	−	0.905379i	$-0.639587\pi$
$854$	−4.54537e11	+	2.62427e11i	−0.854551	+	0.493375i
$855$		0			0
$856$	−1.93314e11	+	3.34829e11i	−0.360054	+	0.623632i
$857$	−1.83325e11	−	5.03683e11i	−0.339860	−	0.933756i	−0.985434	−	0.170059i	$-0.945604\pi$
$857$	−1.83325e11	−	5.03683e11i	−0.339860	−	0.933756i	0.645574	−	0.763697i	$-0.276618\pi$
$858$		0			0
$859$	3.19597e11	−	2.68174e11i	0.586990	−	0.492543i	−0.300244	−	0.953862i	$-0.597068\pi$
$859$	3.19597e11	−	2.68174e11i	0.586990	−	0.492543i	0.887234	+	0.461319i	$0.152624\pi$
$860$	3.18214e11	−	8.74285e11i	0.581735	−	1.59830i
$861$		0			0
$862$	3.84506e10	−	2.18064e11i	0.0696424	−	0.394962i
$863$			1.90539e11i			0.343512i	0.985140	+	0.171756i	$0.0549441\pi$
$863$			1.90539e11i			0.343512i	−0.985140	+	0.171756i	$0.945056\pi$
$864$		0			0
$865$	3.90942e11			0.698309
$866$	1.01058e12	+	1.78193e11i	1.79681	+	0.316825i
$867$		0			0
$868$	−8.59891e11	−	3.12975e11i	−1.51483	−	0.551354i
$869$	−6.96979e10	−	8.30627e10i	−0.122219	−	0.145655i
$870$		0			0
$871$	−1.17323e12	+	4.27022e11i	−2.03851	+	0.741955i
$872$	3.28305e11	+	1.89547e11i	0.567822	+	0.327832i
$873$		0			0
$874$	−3.93445e11	−	6.81466e11i	−0.674277	−	1.16788i
$875$	−1.24430e11	+	1.48290e11i	−0.212273	+	0.252977i
$876$		0			0
$877$	−1.69490e11	−	9.61225e11i	−0.286514	−	1.62490i	−0.699828	−	0.714312i	$-0.746740\pi$
$877$	−1.69490e11	−	9.61225e11i	−0.286514	−	1.62490i	0.413314	−	0.910589i	$-0.364371\pi$
$878$	−9.84566e11	+	1.73606e11i	−1.65679	+	0.292136i
$879$		0			0
$880$	−7.48574e10	−	6.28128e10i	−0.124826	−	0.104741i
$881$	8.30379e11	−	4.79419e11i	1.37839	−	0.795815i	0.386426	−	0.922320i	$-0.373710\pi$
$881$	8.30379e11	−	4.79419e11i	1.37839	−	0.795815i	0.991966	+	0.126506i	$0.0403762\pi$
$882$		0			0
$883$	6.56496e10	−	1.13709e11i	0.107991	−	0.187047i	−0.806965	−	0.590599i	$-0.798891\pi$
$883$	6.56496e10	−	1.13709e11i	0.107991	−	0.187047i	0.914956	+	0.403553i	$0.132225\pi$
$884$	6.73030e11	+	1.84913e12i	1.10211	+	3.02803i
$885$		0			0
$886$	−5.00016e11	+	4.19564e11i	−0.811427	+	0.680868i
$887$	−8.69002e10	+	2.38756e11i	−0.140387	+	0.385710i	−0.989883	−	0.141885i	$-0.954684\pi$
$887$	−8.69002e10	+	2.38756e11i	−0.140387	+	0.385710i	0.849496	+	0.527595i	$0.176906\pi$
$888$		0			0
$889$	−3.11183e11	+	1.76481e12i	−0.498206	+	2.82547i
$890$		−	6.36163e11i		−	1.01393i
$891$		0			0
$892$	5.92428e11			0.935785
$893$	−4.35973e11	−	7.68738e10i	−0.685573	−	0.120885i
$894$		0			0
$895$	1.20672e12	+	4.39209e11i	1.88067	+	0.684509i
$896$	−9.96546e11	−	1.18764e12i	−1.54620	−	1.84269i
$897$		0			0
$898$	−7.43008e9	+	2.70433e9i	−0.0114258	+	0.00415866i
$899$	9.24847e10	+	5.33961e10i	0.141589	+	0.0817467i
$900$		0			0
$901$	4.41106e11	+	7.64018e11i	0.669335	+	1.15932i
$902$	−1.82368e11	+	2.17338e11i	−0.275500	+	0.328329i
$903$		0			0
$904$	1.03476e11	+	5.86844e11i	0.154941	+	0.878716i
$905$	9.13353e11	−	1.61049e11i	1.36158	−	0.240084i
$906$		0			0
$907$	5.49245e11	+	4.60871e11i	0.811591	+	0.681005i	0.950987	−	0.309231i	$-0.100072\pi$
$907$	5.49245e11	+	4.60871e11i	0.811591	+	0.681005i	−0.139396	+	0.990237i	$0.544516\pi$
$908$	−1.74703e11	+	1.00865e11i	−0.257015	+	0.148388i
$909$		0			0
$910$	1.66276e12	−	2.87998e12i	2.42473	−	4.19975i
$911$	−2.82777e11	−	7.76924e11i	−0.410555	−	1.12799i	−0.956897	−	0.290428i	$-0.906202\pi$
$911$	−2.82777e11	−	7.76924e11i	−0.410555	−	1.12799i	0.546342	−	0.837562i	$-0.316020\pi$
$912$		0			0
$913$	2.07668e11	−	1.74255e11i	0.298874	−	0.250785i
$914$	6.56174e11	−	1.80282e12i	0.940231	−	2.58326i
$915$		0			0
$916$	2.66270e11	−	1.51009e12i	0.378217	−	2.14497i
$917$			1.45431e12i			2.05675i
$918$		0			0
$919$	1.09601e12			1.53658			0.768288	−	0.640104i	$-0.221109\pi$
$919$	1.09601e12			1.53658			0.768288	+	0.640104i	$0.221109\pi$
$920$	−7.37831e11	−	1.30099e11i	−1.02992	−	0.181604i
$921$		0			0
$922$	−2.85982e11	−	1.04089e11i	−0.395745	−	0.144039i
$923$	−6.25770e11	−	7.45764e11i	−0.862200	−	1.02753i
$924$		0			0
$925$	1.43404e11	−	5.21948e10i	0.195882	−	0.0712952i
$926$	1.02583e12	+	5.92260e11i	1.39518	+	0.805506i
$927$		0			0
$928$	1.05794e11	+	1.83240e11i	0.142649	+	0.247075i
$929$	−4.47446e11	+	5.33245e11i	−0.600727	+	0.715919i	−0.977630	−	0.210334i	$-0.932545\pi$
$929$	−4.47446e11	+	5.33245e11i	−0.600727	+	0.715919i	0.376902	+	0.926253i	$0.376989\pi$
$930$		0			0
$931$	2.04287e11	+	1.15857e12i	0.271920	+	1.54214i
$932$	−1.60754e12	+	2.83453e11i	−2.13058	+	0.375679i
$933$		0			0
$934$	7.93135e11	+	6.65519e11i	1.04222	+	0.874527i
$935$	−1.03891e12	+	5.99817e11i	−1.35936	+	0.784825i
$936$		0			0
$937$	−1.55285e11	+	2.68961e11i	−0.201452	+	0.348925i	−0.948996	−	0.315287i	$-0.897899\pi$
$937$	−1.55285e11	+	2.68961e11i	−0.201452	+	0.348925i	0.747545	+	0.664212i	$0.231233\pi$
$938$	−1.08144e12	−	2.97124e12i	−1.39699	−	3.83819i
$939$		0			0
$940$	−9.15007e11	+	7.67782e11i	−1.17196	+	0.983392i
$941$	−6.34290e10	+	1.74270e11i	−0.0808964	+	0.222261i	−0.973546	−	0.228489i	$-0.926621\pi$
$941$	−6.34290e10	+	1.74270e11i	−0.0808964	+	0.222261i	0.892650	+	0.450750i	$0.148844\pi$
$942$		0			0
$943$	4.28131e10	−	2.42805e11i	0.0541415	−	0.307052i
$944$		−	1.22932e11i		−	0.154802i
$945$		0			0
$946$	7.87160e11			0.982876
$947$	−6.64181e11	−	1.17113e11i	−0.825822	−	0.145615i	−0.255263	−	0.966872i	$-0.582162\pi$
$947$	−6.64181e11	−	1.17113e11i	−0.825822	−	0.145615i	−0.570559	+	0.821257i	$0.693273\pi$
$948$		0			0
$949$	−1.69363e11	−	6.16430e10i	−0.208811	−	0.0760009i
$950$	6.79541e11	+	8.09845e11i	0.834297	+	0.994277i
$951$		0			0
$952$	−1.65254e12	+	6.01474e11i	−2.01188	+	0.732266i
$953$	−5.06794e11	−	2.92598e11i	−0.614412	−	0.354731i	0.160278	−	0.987072i	$-0.448761\pi$
$953$	−5.06794e11	−	2.92598e11i	−0.614412	−	0.354731i	−0.774690	+	0.632341i	$0.782094\pi$
$954$		0			0
$955$	−4.86692e11	−	8.42975e11i	−0.585114	−	1.01345i
$956$	−2.65614e11	+	3.16546e11i	−0.317994	+	0.378971i
$957$		0			0
$958$	1.42094e11	+	8.05854e11i	0.168699	+	0.956741i
$959$	2.79173e11	−	4.92258e10i	0.330065	−	0.0581994i
$960$		0			0
$961$	−3.83733e11	−	3.21990e11i	−0.449920	−	0.377528i
$962$	3.99070e11	−	2.30403e11i	0.465960	−	0.269022i
$963$		0			0
$964$	2.85546e11	−	4.94581e11i	0.330650	−	0.572702i
$965$	8.76675e10	+	2.40864e11i	0.101095	+	0.277756i
$966$		0			0
$967$	4.53600e11	−	3.80616e11i	0.518761	−	0.435292i	−0.345438	−	0.938441i	$-0.612270\pi$
$967$	4.53600e11	−	3.80616e11i	0.518761	−	0.435292i	0.864200	+	0.503149i	$0.167825\pi$
$968$	1.09796e11	−	3.01663e11i	0.125051	−	0.343574i
$969$		0			0
$970$	4.23440e11	−	2.40145e12i	0.478305	−	2.71260i
$971$		−	1.22816e12i		−	1.38158i	−0.723053	−	0.690792i	$-0.757262\pi$
$971$		−	1.22816e12i		−	1.38158i	0.723053	−	0.690792i	$-0.242738\pi$
$972$		0			0
$973$	−2.51808e12			−2.80943
$974$	1.73857e12	+	3.06556e11i	1.93177	+	0.340623i
$975$		0			0
$976$	5.10916e10	+	1.85958e10i	0.0563054	+	0.0204935i
$977$	3.07346e11	+	3.66281e11i	0.337326	+	0.402009i	0.907866	−	0.419261i	$-0.137711\pi$
$977$	3.07346e11	+	3.66281e11i	0.337326	+	0.402009i	−0.570540	+	0.821270i	$0.693266\pi$
$978$		0			0
$979$	3.07061e11	−	1.11761e11i	0.334268	−	0.121664i
$980$	2.74893e12	+	1.58709e12i	2.98029	+	1.72067i
$981$		0			0
$982$	1.96637e11	+	3.40585e11i	0.211455	+	0.366251i
$983$	6.20840e11	−	7.39888e11i	0.664914	−	0.792414i	−0.323168	−	0.946342i	$-0.604748\pi$
$983$	6.20840e11	−	7.39888e11i	0.664914	−	0.792414i	0.988082	+	0.153928i	$0.0491923\pi$
$984$		0			0
$985$	−6.61799e8	−	3.75325e9i	−0.000703042	−	0.00398715i
$986$	5.72755e11	−	1.00992e11i	0.605984	−	0.106851i
$987$		0			0
$988$	1.48464e12	+	1.24576e12i	1.55809	+	1.30739i
$989$	−5.92406e11	+	3.42026e11i	−0.619205	+	0.357498i
$990$		0			0
$991$	4.11018e10	−	7.11905e10i	0.0426154	−	0.0738120i	−0.843931	−	0.536452i	$-0.819764\pi$
$991$	4.11018e10	−	7.11905e10i	0.0426154	−	0.0738120i	0.886546	+	0.462640i	$0.153098\pi$
$992$	2.38506e11	+	6.55291e11i	0.246294	+	0.676686i
$993$		0			0
$994$	1.88866e12	−	1.58478e12i	1.93468	−	1.62339i
$995$	5.17689e11	−	1.42234e12i	0.528173	−	1.45114i
$996$		0			0
$997$	−1.37239e11	+	7.78323e11i	−0.138899	+	0.787734i	0.833166	+	0.553022i	$0.186526\pi$
$997$	−1.37239e11	+	7.78323e11i	−0.138899	+	0.787734i	−0.972065	+	0.234711i	$0.924586\pi$
$998$			1.27606e12i			1.28632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.4		138
3.2	odd	2		27.9.f.a.2.20	✓	138
27.13	even	9		27.9.f.a.14.20	yes	138
27.14	odd	18	inner	81.9.f.a.71.4		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.20	✓	138	3.2	odd	2
27.9.f.a.14.20	yes	138	27.13	even	9
81.9.f.a.8.4		138	1.1	even	1	trivial
81.9.f.a.71.4		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+(-25.1387 - 4.43262i) q^{2} +(371.742 + 135.303i) q^{4} +(546.503 + 651.297i) q^{5} +(-3663.86 + 1333.53i) q^{7} +(-3086.08 - 1781.75i) q^{8} +(-10851.4 - 18795.2i) q^{10} +(7165.64 - 8539.67i) q^{11} +(-6824.34 - 38702.7i) q^{13} +(98015.5 - 17282.8i) q^{14} +(-7898.09 - 6627.28i) q^{16} +(-109614. + 63285.8i) q^{17} +(-62328.9 + 107957. i) q^{19} +(115036. + 316059. i) q^{20} +(-217988. + 182913. i) q^{22} +(84577.6 - 232375. i) q^{23} +(-57691.0 + 327182. i) q^{25} +1.00318e6i q^{26} -1.54244e6 q^{28} +(177273. + 31258.0i) q^{29} +(557486. + 202908. i) q^{31} +(755557. + 900438. i) q^{32} +(3.03608e6 - 1.10504e6i) q^{34} +(-2.87084e6 - 1.65748e6i) q^{35} +(-229672. - 397803. i) q^{37} +(2.04540e6 - 2.43761e6i) q^{38} +(-526104. - 2.98368e6i) q^{40} +(981871. - 173130. i) q^{41} +(-2.11904e6 - 1.77809e6i) q^{43} +(3.81922e6 - 2.20503e6i) q^{44} +(-3.15620e6 + 5.46670e6i) q^{46} +(1.21462e6 + 3.33714e6i) q^{47} +(7.22944e6 - 6.06622e6i) q^{49} +(2.90055e6 - 7.96919e6i) q^{50} +(2.69971e6 - 1.53108e7i) q^{52} -6.97006e6i q^{53} +9.47791e6 q^{55} +(1.36830e7 + 2.41268e6i) q^{56} +(-4.31784e6 - 1.57157e6i) q^{58} +(7.66416e6 + 9.13379e6i) q^{59} +(-4.95543e6 + 1.80363e6i) q^{61} +(-1.31150e7 - 7.57197e6i) q^{62} +(-1.36827e7 - 2.36991e7i) q^{64} +(2.14775e7 - 2.55958e7i) q^{65} +(-5.51669e6 - 3.12867e7i) q^{67} +(-4.93110e7 + 8.69486e6i) q^{68} +(6.48220e7 + 5.43921e7i) q^{70} +(2.14530e7 - 1.23859e7i) q^{71} +(2.29304e6 - 3.97166e6i) q^{73} +(4.01033e6 + 1.10183e7i) q^{74} +(-3.77772e7 + 3.16988e7i) q^{76} +(-1.48659e7 + 4.08438e7i) q^{77} +(1.68902e6 - 9.57891e6i) q^{79} -8.76584e6i q^{80} -2.54503e7 q^{82} +(2.39486e7 + 4.22279e6i) q^{83} +(-1.01122e8 - 3.68056e7i) q^{85} +(4.53882e7 + 5.40916e7i) q^{86} +(-3.73292e7 + 1.35867e7i) q^{88} +(2.53853e7 + 1.46562e7i) q^{89} +(7.66148e7 + 1.32701e8i) q^{91} +(6.28822e7 - 7.49401e7i) q^{92} +(-1.57416e7 - 8.92752e7i) q^{94} +(-1.04375e8 + 1.84041e7i) q^{95} +(8.60715e7 + 7.22226e7i) q^{97} +(-2.08628e8 + 1.20451e8i) 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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