LMFDB - Embedded newform 81.9.f.a.8.2

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			8.2
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-26.8116 - 4.72761i) q^{2} +(455.951 + 165.953i) q^{4} +(-232.968 - 277.641i) q^{5} +(45.0827 - 16.4088i) q^{7} +(-5404.32 - 3120.19i) q^{8} +(4933.68 + 8545.38i) q^{10} +(735.313 - 876.312i) q^{11} +(6621.57 + 37552.8i) q^{13} +(-1286.31 + 226.812i) q^{14} +(34993.7 + 29363.2i) q^{16} +(-67597.9 + 39027.7i) q^{17} +(113236. - 196131. i) q^{19} +(-60146.9 - 165252. i) q^{20} +(-23857.8 + 20019.1i) q^{22} +(82558.0 - 226826. i) q^{23} +(45021.1 - 255328. i) q^{25} -1.03816e6i q^{26} +23278.6 q^{28} +(-572834. - 101006. i) q^{29} +(-24300.0 - 8844.49i) q^{31} +(227456. + 271071. i) q^{32} +(1.99692e6 - 726818. i) q^{34} +(-15058.6 - 8694.08i) q^{35} +(-1.45625e6 - 2.52229e6i) q^{37} +(-3.96328e6 + 4.72325e6i) q^{38} +(392744. + 2.22736e6i) q^{40} +(-535074. + 94347.9i) q^{41} +(4.54620e6 + 3.81472e6i) q^{43} +(480693. - 277528. i) q^{44} +(-3.28586e6 + 5.69128e6i) q^{46} +(3.01327e6 + 8.27890e6i) q^{47} +(-4.41433e6 + 3.70406e6i) q^{49} +(-2.41418e6 + 6.63290e6i) q^{50} +(-3.21287e6 + 1.82211e7i) q^{52} -3.89255e6i q^{53} -414605. q^{55} +(-294840. - 51988.2i) q^{56} +(1.48811e7 + 5.41627e6i) q^{58} +(-2.64580e6 - 3.15314e6i) q^{59} +(-1.75097e7 + 6.37302e6i) q^{61} +(609710. + 352016. i) q^{62} +(-1.06641e7 - 1.84708e7i) q^{64} +(8.88358e6 - 1.05870e7i) q^{65} +(-493265. - 2.79744e6i) q^{67} +(-3.72981e7 + 6.57666e6i) q^{68} +(362643. + 304293. i) q^{70} +(-893484. + 515853. i) q^{71} +(-1.26668e7 + 2.19395e7i) q^{73} +(2.71199e7 + 7.45114e7i) q^{74} +(8.41786e7 - 7.06343e7i) q^{76} +(18770.7 - 51572.1i) q^{77} +(-1.00312e7 + 5.68895e7i) q^{79} -1.65564e7i q^{80} +1.47922e7 q^{82} +(-1.09503e7 - 1.93083e6i) q^{83} +(2.65838e7 + 9.67572e6i) q^{85} +(-1.03856e8 - 1.23771e8i) q^{86} +(-6.70813e6 + 2.44156e6i) q^{88} +(2.45007e7 + 1.41455e7i) q^{89} +(914714. + 1.58433e6i) q^{91} +(7.52848e7 - 8.97209e7i) q^{92} +(-4.16513e7 - 2.36216e8i) q^{94} +(-8.08344e7 + 1.42533e7i) q^{95} +(-4.04609e7 - 3.39507e7i) q^{97} +(1.35867e8 - 7.84427e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−26.8116	−	4.72761i	−1.67573	−	0.295476i	−0.746609	−	0.665263i	$-0.768320\pi$
$2$	−26.8116	−	4.72761i	−1.67573	−	0.295476i	−0.929117	+	0.369787i	$0.879431\pi$
$3$		0			0
$3$		0			0
$4$	455.951	+	165.953i	1.78106	+	0.648252i
$5$	−232.968	−	277.641i	−0.372749	−	0.444225i	0.546763	−	0.837288i	$-0.315860\pi$
$5$	−232.968	−	277.641i	−0.372749	−	0.444225i	−0.919512	+	0.393063i	$0.871416\pi$
$6$		0			0
$7$	45.0827	−	16.4088i	0.0187766	−	0.00683414i	−0.332615	−	0.943063i	$-0.607931\pi$
$7$	45.0827	−	16.4088i	0.0187766	−	0.00683414i	0.351391	+	0.936229i	$0.385709\pi$
$8$	−5404.32	−	3120.19i	−1.31941	−	0.761764i
$9$		0			0
$10$	4933.68	+	8545.38i	0.493368	+	0.854538i
$11$	735.313	−	876.312i	0.0502229	−	0.0598533i	−0.740348	−	0.672224i	$-0.765339\pi$
$11$	735.313	−	876.312i	0.0502229	−	0.0598533i	0.790571	+	0.612370i	$0.209784\pi$
$12$		0			0
$13$	6621.57	+	37552.8i	0.231840	+	1.31483i	0.849168	+	0.528123i	$0.177104\pi$
$13$	6621.57	+	37552.8i	0.231840	+	1.31483i	−0.617328	+	0.786706i	$0.711785\pi$
$14$	−1286.31	+	226.812i	−0.0334838	+	0.00590410i
$15$		0			0
$16$	34993.7	+	29363.2i	0.533962	+	0.448047i
$17$	−67597.9	+	39027.7i	−0.809352	+	0.467280i	−0.846731	−	0.532022i	$-0.821433\pi$
$17$	−67597.9	+	39027.7i	−0.809352	+	0.467280i	0.0373788	+	0.999301i	$0.488099\pi$
$18$		0			0
$19$	113236.	−	196131.i	0.868903	−	1.50498i	0.00578360	−	0.999983i	$-0.498159\pi$
$19$	113236.	−	196131.i	0.868903	−	1.50498i	0.863119	−	0.505000i	$-0.168508\pi$
$20$	−60146.9	−	165252.i	−0.375918	−	1.03283i
$21$		0			0
$22$	−23857.8	+	20019.1i	−0.101845	+	0.0854581i
$23$	82558.0	−	226826.i	0.295018	−	0.810554i	−0.700296	−	0.713853i	$-0.746949\pi$
$23$	82558.0	−	226826.i	0.295018	−	0.810554i	0.995313	−	0.0967014i	$-0.0308292\pi$
$24$		0			0
$25$	45021.1	−	255328.i	0.115254	−	0.653639i
$26$		−	1.03816e6i		−	2.27179i
$27$		0			0
$28$	23278.6			0.0378725
$29$	−572834.	−	101006.i	−0.809910	−	0.142809i	−0.246667	−	0.969100i	$-0.579335\pi$
$29$	−572834.	−	101006.i	−0.809910	−	0.142809i	−0.563243	+	0.826291i	$0.690447\pi$
$30$		0			0
$31$	−24300.0	−	8844.49i	−0.0263124	−	0.00957693i	0.328830	−	0.944389i	$-0.393346\pi$
$31$	−24300.0	−	8844.49i	−0.0263124	−	0.00957693i	−0.355143	+	0.934812i	$0.615568\pi$
$32$	227456.	+	271071.i	0.216919	+	0.258514i
$33$		0			0
$34$	1.99692e6	−	726818.i	1.49432	−	0.543889i
$35$	−15058.6	−	8694.08i	−0.0100349	−	0.00579364i
$36$		0			0
$37$	−1.45625e6	−	2.52229e6i	−0.777013	−	1.34583i	−0.933656	−	0.358171i	$-0.883401\pi$
$37$	−1.45625e6	−	2.52229e6i	−0.777013	−	1.34583i	0.156643	−	0.987655i	$-0.449933\pi$
$38$	−3.96328e6	+	4.72325e6i	−1.90073	+	2.26520i
$39$		0			0
$40$	392744.	+	2.22736e6i	0.153416	+	0.870064i
$41$	−535074.	+	94347.9i	−0.189356	+	0.0333885i	−0.267522	−	0.963552i	$-0.586205\pi$
$41$	−535074.	+	94347.9i	−0.189356	+	0.0333885i	0.0781660	+	0.996940i	$0.475094\pi$
$42$		0			0
$43$	4.54620e6	+	3.81472e6i	1.32976	+	1.11581i	0.984133	+	0.177435i	$0.0567799\pi$
$43$	4.54620e6	+	3.81472e6i	1.32976	+	1.11581i	0.345632	+	0.938370i	$0.387665\pi$
$44$	480693.	−	277528.i	0.128250	−	0.0740451i
$45$		0			0
$46$	−3.28586e6	+	5.69128e6i	−0.733868	+	1.27110i
$47$	3.01327e6	+	8.27890e6i	0.617515	+	1.69661i	0.712989	+	0.701175i	$0.247341\pi$
$47$	3.01327e6	+	8.27890e6i	0.617515	+	1.69661i	−0.0954743	+	0.995432i	$0.530437\pi$
$48$		0			0
$49$	−4.41433e6	+	3.70406e6i	−0.765739	+	0.642531i
$50$	−2.41418e6	+	6.63290e6i	−0.386269	+	1.06126i
$51$		0			0
$52$	−3.21287e6	+	1.82211e7i	−0.439420	+	2.49208i
$53$		−	3.89255e6i		−	0.493322i	−0.969102	−	0.246661i	$-0.920667\pi$
$53$		−	3.89255e6i		−	0.493322i	0.969102	−	0.246661i	$-0.0793335\pi$
$54$		0			0
$55$	−414605.			−0.0453089
$56$	−294840.	−	51988.2i	−0.0299802	−	0.00528631i
$57$		0			0
$58$	1.48811e7	+	5.41627e6i	1.31499	+	0.478618i
$59$	−2.64580e6	−	3.15314e6i	−0.218348	−	0.260217i	0.645741	−	0.763557i	$-0.276549\pi$
$59$	−2.64580e6	−	3.15314e6i	−0.218348	−	0.260217i	−0.864088	+	0.503340i	$0.832104\pi$
$60$		0			0
$61$	−1.75097e7	+	6.37302e6i	−1.26462	+	0.460284i	−0.885317	−	0.464989i	$-0.846058\pi$
$61$	−1.75097e7	+	6.37302e6i	−1.26462	+	0.460284i	−0.379303	+	0.925273i	$0.623836\pi$
$62$	609710.	+	352016.i	0.0412626	+	0.0238230i
$63$		0			0
$64$	−1.06641e7	−	1.84708e7i	−0.635631	−	1.10094i
$65$	8.88358e6	−	1.05870e7i	0.497662	−	0.593090i
$66$		0			0
$67$	−493265.	−	2.79744e6i	−0.0244783	−	0.138823i	0.970119	−	0.242628i	$-0.0780094\pi$
$67$	−493265.	−	2.79744e6i	−0.0244783	−	0.138823i	−0.994598	+	0.103805i	$0.966898\pi$
$68$	−3.72981e7	+	6.57666e6i	−1.74442	+	0.307588i
$69$		0			0
$70$	362643.	+	304293.i	0.0151038	+	0.0126736i
$71$	−893484.	+	515853.i	−0.0351603	+	0.0202998i	−0.517477	−	0.855697i	$-0.673129\pi$
$71$	−893484.	+	515853.i	−0.0351603	+	0.0202998i	0.482317	+	0.875997i	$0.339795\pi$
$72$		0			0
$73$	−1.26668e7	+	2.19395e7i	−0.446042	+	0.772567i	−0.998124	−	0.0612227i	$-0.980500\pi$
$73$	−1.26668e7	+	2.19395e7i	−0.446042	+	0.772567i	0.552082	+	0.833790i	$0.313833\pi$
$74$	2.71199e7	+	7.45114e7i	0.904402	+	2.48482i
$75$		0			0
$76$	8.41786e7	−	7.06343e7i	2.52318	−	2.11720i
$77$	18770.7	−	51572.1i	0.000533971	−	0.00146707i
$78$		0			0
$79$	−1.00312e7	+	5.68895e7i	−0.257539	+	1.46057i	0.531932	+	0.846787i	$0.321466\pi$
$79$	−1.00312e7	+	5.68895e7i	−0.257539	+	1.46057i	−0.789471	+	0.613788i	$0.789645\pi$
$80$		−	1.65564e7i		−	0.404209i
$81$		0			0
$82$	1.47922e7			0.327174
$83$	−1.09503e7	−	1.93083e6i	−0.230735	−	0.0406848i	0.0570850	−	0.998369i	$-0.481819\pi$
$83$	−1.09503e7	−	1.93083e6i	−0.230735	−	0.0406848i	−0.287820	+	0.957684i	$0.592931\pi$
$84$		0			0
$85$	2.65838e7	+	9.67572e6i	0.509263	+	0.185356i
$86$	−1.03856e8	−	1.23771e8i	−1.89863	−	2.26270i
$87$		0			0
$88$	−6.70813e6	+	2.44156e6i	−0.111859	+	0.0407133i
$89$	2.45007e7	+	1.41455e7i	0.390497	+	0.225454i	0.682376	−	0.731002i	$-0.260947\pi$
$89$	2.45007e7	+	1.41455e7i	0.390497	+	0.225454i	−0.291878	+	0.956455i	$0.594280\pi$
$90$		0			0
$91$	914714.	+	1.58433e6i	0.0133389	+	0.0231036i
$92$	7.52848e7	−	8.97209e7i	1.05089	−	1.25240i
$93$		0			0
$94$	−4.16513e7	−	2.36216e8i	−0.533479	−	3.02551i
$95$	−8.08344e7	+	1.42533e7i	−0.992434	+	0.174993i
$96$		0			0
$97$	−4.04609e7	−	3.39507e7i	−0.457034	−	0.383497i	0.385005	−	0.922915i	$-0.374200\pi$
$97$	−4.04609e7	−	3.39507e7i	−0.457034	−	0.383497i	−0.842038	+	0.539418i	$0.818644\pi$
$98$	1.35867e8	−	7.84427e7i	1.47302	−	0.850449i
$99$		0			0
$100$	6.28997e7	−	1.08945e8i	0.628997	−	1.08945i
$101$	5.95975e7	+	1.63743e8i	0.572721	+	1.57354i	0.800187	+	0.599751i	$0.204734\pi$
$101$	5.95975e7	+	1.63743e8i	0.572721	+	1.57354i	−0.227466	+	0.973786i	$0.573044\pi$
$102$		0			0
$103$	−3.63871e7	+	3.05324e7i	−0.323294	+	0.271276i	−0.789961	−	0.613157i	$-0.789899\pi$
$103$	−3.63871e7	+	3.05324e7i	−0.323294	+	0.271276i	0.466667	+	0.884433i	$0.345455\pi$
$104$	8.13867e7	−	2.23608e8i	0.695697	−	1.91141i
$105$		0			0
$106$	−1.84025e7	+	1.04366e8i	−0.145765	+	0.826673i
$107$			4.68870e6i			0.0357698i	0.999840	+	0.0178849i	$0.00569325\pi$
$107$			4.68870e6i			0.0357698i	−0.999840	+	0.0178849i	$0.994307\pi$
$108$		0			0
$109$	−1.85151e8			−1.31166			−0.655829	−	0.754910i	$-0.727681\pi$
$109$	−1.85151e8			−1.31166			−0.655829	+	0.754910i	$0.727681\pi$
$110$	1.11162e7	+	1.96009e6i	0.0759253	+	0.0133877i
$111$		0			0
$112$	2.05943e6	+	749570.i	0.0130880	+	0.00476365i
$113$	1.32652e8	+	1.58089e8i	0.813582	+	0.969590i	0.999917	−	0.0128966i	$-0.00410522\pi$
$113$	1.32652e8	+	1.58089e8i	0.813582	+	0.969590i	−0.186334	+	0.982486i	$0.559661\pi$
$114$		0			0
$115$	−8.22096e7	+	2.99219e7i	−0.470036	+	0.171079i
$116$	−2.44422e8	−	1.41117e8i	−1.34992	−	0.779378i
$117$		0			0
$118$	5.60313e7	+	9.70491e7i	0.289003	+	0.500569i
$119$	−2.40710e6	+	2.86867e6i	−0.0120035	+	0.0143052i
$120$		0			0
$121$	3.69958e7	+	2.09814e8i	0.172588	+	0.978796i
$122$	4.99593e8	−	8.80917e7i	2.25516	−	0.397645i
$123$		0			0
$124$	−9.61186e6	−	8.06531e6i	−0.0406556	−	0.0341141i
$125$	−2.03986e8	+	1.17771e8i	−0.835527	+	0.482392i
$126$		0			0
$127$	7.48482e7	−	1.29641e8i	0.287718	−	0.498342i	−0.685547	−	0.728028i	$-0.740437\pi$
$127$	7.48482e7	−	1.29641e8i	0.287718	−	0.498342i	0.973265	+	0.229687i	$0.0737702\pi$
$128$	1.67617e8	+	4.60523e8i	0.624420	+	1.71558i
$129$		0			0
$130$	−2.88234e8	+	2.41857e8i	−1.00919	+	0.846810i
$131$	−1.04070e8	+	2.85930e8i	−0.353379	+	0.970900i	0.627898	+	0.778296i	$0.283915\pi$
$131$	−1.04070e8	+	2.85930e8i	−0.353379	+	0.970900i	−0.981277	+	0.192604i	$0.938307\pi$
$132$		0			0
$133$	1.88673e6	−	1.07002e7i	0.00602981	−	0.0341967i
$134$			7.73359e7i			0.239862i
$135$		0			0
$136$	4.87094e8			1.42383
$137$	−3.96451e8	−	6.99051e7i	−1.12540	−	0.198439i	−0.420191	−	0.907436i	$-0.638037\pi$
$137$	−3.96451e8	−	6.99051e7i	−1.12540	−	0.198439i	−0.705211	+	0.708997i	$0.749148\pi$
$138$		0			0
$139$	−1.03082e8	−	3.75187e7i	−0.276136	−	0.100505i	0.200240	−	0.979747i	$-0.435828\pi$
$139$	−1.03082e8	−	3.75187e7i	−0.276136	−	0.100505i	−0.476376	+	0.879242i	$0.658050\pi$
$140$	−5.42317e6	−	6.46308e6i	−0.0141170	−	0.0168239i
$141$		0			0
$142$	2.63945e7	−	9.60681e6i	0.0649172	−	0.0236279i
$143$	3.77769e7	+	2.18105e7i	0.0903405	+	0.0521581i
$144$		0			0
$145$	1.05409e8	+	1.82573e8i	0.238454	+	0.413015i
$146$	4.43339e8	−	5.28351e8i	0.975718	−	1.16282i
$147$		0			0
$148$	−2.45396e8	−	1.39171e9i	−0.511471	−	2.90070i
$149$	7.89944e7	−	1.39288e7i	0.160270	−	0.0282599i	−0.0929375	−	0.995672i	$-0.529626\pi$
$149$	7.89944e7	−	1.39288e7i	0.160270	−	0.0282599i	0.253207	+	0.967412i	$0.418515\pi$
$150$		0			0
$151$	−9.13846e7	−	7.66808e7i	−0.175778	−	0.147496i	0.550654	−	0.834734i	$-0.314378\pi$
$151$	−9.13846e7	−	7.66808e7i	−0.175778	−	0.147496i	−0.726432	+	0.687238i	$0.758823\pi$
$152$	−1.22393e9	+	7.06637e8i	−2.29289	+	1.32380i
$153$		0			0
$154$	−747086.	+	1.29399e6i	−0.00132827	+	0.00230064i
$155$	3.20555e6	+	8.80717e6i	0.00555361	+	0.0152584i
$156$		0			0
$157$	−2.39241e8	+	2.00747e8i	−0.393765	+	0.330408i	−0.818078	−	0.575108i	$-0.804960\pi$
$157$	−2.39241e8	+	2.00747e8i	−0.393765	+	0.330408i	0.424313	+	0.905516i	$0.360516\pi$
$158$	5.37903e8	−	1.47788e9i	0.863129	−	2.37143i
$159$		0			0
$160$	2.22704e7	−	1.26302e8i	0.0339820	−	0.192721i
$161$		−	1.15806e7i		−	0.0172357i
$162$		0			0
$163$	1.16396e9			1.64887			0.824436	−	0.565956i	$-0.191493\pi$
$163$	1.16396e9			1.64887			0.824436	+	0.565956i	$0.191493\pi$
$164$	−2.59625e8	−	4.57788e7i	−0.358898	−	0.0632833i
$165$		0			0
$166$	2.84467e8	+	1.03538e8i	0.374627	+	0.136353i
$167$	−5.15616e8	−	6.14487e8i	−0.662919	−	0.790036i	0.324882	−	0.945754i	$-0.394675\pi$
$167$	−5.15616e8	−	6.14487e8i	−0.662919	−	0.790036i	−0.987802	+	0.155718i	$0.950231\pi$
$168$		0			0
$169$	−5.99833e8	+	2.18321e8i	−0.735332	+	0.267639i
$170$	−6.67012e8	−	3.85100e8i	−0.798616	−	0.461081i
$171$		0			0
$172$	1.43978e9	+	2.49378e9i	1.64507	+	2.84934i
$173$	5.52802e8	−	6.58804e8i	0.617142	−	0.735482i	−0.363434	−	0.931620i	$-0.618396\pi$
$173$	5.52802e8	−	6.58804e8i	0.617142	−	0.735482i	0.980576	+	0.196138i	$0.0628402\pi$
$174$		0			0
$175$	−2.15993e6	−	1.22496e7i	−0.00230297	−	0.0130608i
$176$	5.14627e7	−	9.07426e6i	0.0536342	−	0.00945716i
$177$		0			0
$178$	−5.90029e8	−	4.95093e8i	−0.587751	−	0.493181i
$179$	−1.09637e9	+	6.32988e8i	−1.06793	+	0.616571i	−0.927616	−	0.373535i	$-0.878145\pi$
$179$	−1.09637e9	+	6.32988e8i	−1.06793	+	0.616571i	−0.140317	+	0.990107i	$0.544812\pi$
$180$		0			0
$181$	−4.48587e8	+	7.76975e8i	−0.417957	+	0.723924i	−0.995734	−	0.0922715i	$-0.970587\pi$
$181$	−4.48587e8	+	7.76975e8i	−0.417957	+	0.723924i	0.577776	+	0.816195i	$0.303921\pi$
$182$	−1.70349e7	−	4.68029e7i	−0.0155258	−	0.0426567i
$183$		0			0
$184$	−1.15391e9	+	9.68246e8i	−1.00670	+	0.844723i
$185$	−3.61032e8	+	9.91928e8i	−0.308219	+	0.846824i
$186$		0			0
$187$	−1.55052e7	+	8.79344e7i	−0.0126798	+	0.0719105i
$188$			4.27483e9i			3.42206i
$189$		0			0
$190$	2.23468e9			1.71475
$191$	1.06750e9	+	1.88229e8i	0.802112	+	0.141434i	0.559652	−	0.828727i	$-0.310935\pi$
$191$	1.06750e9	+	1.88229e8i	0.802112	+	0.141434i	0.242460	+	0.970161i	$0.422046\pi$
$192$		0			0
$193$	1.93844e9	+	7.05533e8i	1.39708	+	0.508497i	0.927311	−	0.374291i	$-0.122114\pi$
$193$	1.93844e9	+	7.05533e8i	1.39708	+	0.508497i	0.469772	+	0.882788i	$0.344336\pi$
$194$	9.24315e8	+	1.10156e9i	0.652549	+	0.777678i
$195$		0			0
$196$	−2.62742e9	+	9.56302e8i	−1.78035	+	0.647993i
$197$	−6.54025e8	−	3.77601e8i	−0.434240	−	0.250708i	0.266912	−	0.963721i	$-0.413997\pi$
$197$	−6.54025e8	−	3.77601e8i	−0.434240	−	0.250708i	−0.701151	+	0.713013i	$0.747330\pi$
$198$		0			0
$199$	−5.49207e8	−	9.51255e8i	−0.350206	−	0.606575i	0.636079	−	0.771624i	$-0.280555\pi$
$199$	−5.49207e8	−	9.51255e8i	−0.350206	−	0.606575i	−0.986285	+	0.165049i	$0.947222\pi$
$200$	−1.03998e9	+	1.23940e9i	−0.649986	+	0.774624i
$201$		0			0
$202$	−8.23793e8	−	4.67197e9i	−0.494781	−	2.80604i
$203$	−2.74823e7	+	4.84587e6i	−0.0161834	+	0.00285356i
$204$		0			0
$205$	1.50850e8	+	1.26578e8i	0.0854142	+	0.0716710i
$206$	1.11994e9	−	6.46598e8i	0.621908	−	0.359059i
$207$		0			0
$208$	−8.70958e8	+	1.50854e9i	−0.465312	+	0.805943i
$209$	−8.86078e7	−	2.43448e8i	−0.0464394	−	0.127591i
$210$		0			0
$211$	−1.86890e9	+	1.56819e9i	−0.942878	+	0.791169i	−0.978084	−	0.208212i	$-0.933236\pi$
$211$	−1.86890e9	+	1.56819e9i	−0.942878	+	0.791169i	0.0352059	+	0.999380i	$0.488791\pi$
$212$	6.45979e8	−	1.77481e9i	0.319797	−	0.878636i
$213$		0			0
$214$	2.21663e7	−	1.25712e8i	0.0105691	−	0.0599405i
$215$		−	2.15092e9i		−	1.00663i
$216$		0			0
$217$	−1.24064e6			−0.000559508
$218$	4.96420e9	+	8.75323e8i	2.19798	+	0.387563i
$219$		0			0
$220$	−1.89039e8	−	6.88047e7i	−0.0806978	−	0.0293716i
$221$	−1.91320e9	−	2.28007e9i	−0.802032	−	0.955825i
$222$		0			0
$223$	9.26509e8	−	3.37222e8i	0.374654	−	0.136363i	−0.147828	−	0.989013i	$-0.547228\pi$
$223$	9.26509e8	−	3.37222e8i	0.374654	−	0.136363i	0.522482	+	0.852650i	$0.325006\pi$
$224$	1.47023e7	+	8.48836e6i	0.00583972	+	0.00337156i
$225$		0			0
$226$	−2.80924e9	−	4.86575e9i	−1.07685	−	1.86516i
$227$	−3.27828e9	+	3.90690e9i	−1.23465	+	1.47139i	−0.403845	+	0.914828i	$0.632326\pi$
$227$	−3.27828e9	+	3.90690e9i	−1.23465	+	1.47139i	−0.830802	+	0.556567i	$0.812118\pi$
$228$		0			0
$229$	−1.05431e8	−	5.97931e8i	−0.0383378	−	0.217425i	0.959620	−	0.281299i	$-0.0907654\pi$
$229$	−1.05431e8	−	5.97931e8i	−0.0383378	−	0.217425i	−0.997958	+	0.0638746i	$0.979654\pi$
$230$	2.34563e9	−	4.13598e8i	0.838201	−	0.147798i
$231$		0			0
$232$	2.78062e9	+	2.33322e9i	0.959821	+	0.805385i
$233$	4.38788e9	−	2.53335e9i	1.48878	−	0.859549i	0.488865	−	0.872359i	$-0.337411\pi$
$233$	4.38788e9	−	2.53335e9i	1.48878	−	0.859549i	0.999918	+	0.0128098i	$0.00407761\pi$
$234$		0			0
$235$	1.59656e9	−	2.76533e9i	0.523498	−	0.906725i
$236$	−6.83083e8	−	1.87676e9i	−0.220204	−	0.605006i
$237$		0			0
$238$	7.81002e7	−	6.55338e7i	0.0243413	−	0.0204248i
$239$	−2.49741e8	+	6.86157e8i	−0.0765416	+	0.210296i	−0.972062	−	0.234724i	$-0.924581\pi$
$239$	−2.49741e8	+	6.86157e8i	−0.0765416	+	0.210296i	0.895520	+	0.445020i	$0.146804\pi$
$240$		0			0
$241$	−5.18746e8	+	2.94195e9i	−0.153775	+	0.872103i	0.806122	+	0.591750i	$0.201563\pi$
$241$	−5.18746e8	+	2.94195e9i	−0.153775	+	0.872103i	−0.959897	+	0.280353i	$0.909548\pi$
$242$		−	5.80034e9i		−	1.69119i
$243$		0			0
$244$	−9.04119e9			−2.55074
$245$	2.05680e9	+	3.62669e8i	0.570857	+	0.100657i
$246$		0			0
$247$	8.11507e9	+	2.95364e9i	2.18024	+	0.793543i
$248$	1.03729e8	+	1.23619e8i	0.0274216	+	0.0326798i
$249$		0			0
$250$	6.02598e9	−	2.19328e9i	1.54265	−	0.561479i
$251$	−3.51134e9	−	2.02727e9i	−0.884663	−	0.510760i	−0.0124699	−	0.999922i	$-0.503969\pi$
$251$	−3.51134e9	−	2.02727e9i	−0.884663	−	0.510760i	−0.872193	+	0.489162i	$0.837303\pi$
$252$		0			0
$253$	−1.38065e8	−	2.39135e8i	−0.0336977	−	0.0583661i
$254$	−2.61969e9	+	3.12203e9i	−0.629384	+	0.750070i
$255$		0			0
$256$	−1.36877e9	−	7.76271e9i	−0.318693	−	1.80740i
$257$	−5.64026e9	+	9.94531e8i	−1.29291	+	0.227974i	−0.777452	−	0.628943i	$-0.783488\pi$
$257$	−5.64026e9	+	9.94531e8i	−1.29291	+	0.227974i	−0.515454	+	0.856917i	$0.672377\pi$
$258$		0			0
$259$	−1.07039e8	−	8.98166e7i	−0.0237873	−	0.0199599i
$260$	5.80742e9	−	3.35292e9i	1.27084	−	0.733718i
$261$		0			0
$262$	4.14205e9	−	7.17424e9i	0.879043	−	1.52255i
$263$	−4.21791e8	−	1.15886e9i	−0.0881606	−	0.242219i	0.887775	−	0.460277i	$-0.152250\pi$
$263$	−4.21791e8	−	1.15886e9i	−0.0881606	−	0.242219i	−0.975936	+	0.218058i	$0.930028\pi$
$264$		0			0
$265$	−1.08073e9	+	9.06841e8i	−0.219146	+	0.183885i
$266$	−1.01173e8	+	2.77969e8i	−0.0202086	+	0.0555227i
$267$		0			0
$268$	2.39338e8	−	1.35736e9i	0.0463952	−	0.263120i
$269$		−	4.85339e9i		−	0.926907i	−0.886121	−	0.463453i	$-0.846610\pi$
$269$		−	4.85339e9i		−	0.926907i	0.886121	−	0.463453i	$-0.153390\pi$
$270$		0			0
$271$	−4.20942e9			−0.780450			−0.390225	−	0.920719i	$-0.627603\pi$
$271$	−4.20942e9			−0.780450			−0.390225	+	0.920719i	$0.627603\pi$
$272$	−3.51148e9	−	6.19169e8i	−0.641526	−	0.113118i
$273$		0			0
$274$	1.02990e10	+	3.74854e9i	1.82723	+	0.665058i
$275$	−1.90642e8	−	2.27198e8i	−0.0333340	−	0.0397260i
$276$		0			0
$277$	−7.60895e9	+	2.76943e9i	−1.29243	+	0.470405i	−0.894523	−	0.447023i	$-0.852484\pi$
$277$	−7.60895e9	+	2.76943e9i	−1.29243	+	0.470405i	−0.397903	+	0.917427i	$0.630262\pi$
$278$	2.58642e9	+	1.49327e9i	0.433031	+	0.250011i
$279$		0			0
$280$	5.42543e7	+	9.39712e7i	0.00882677	+	0.0152884i
$281$	2.83468e9	−	3.37824e9i	0.454652	−	0.541833i	−0.489213	−	0.872164i	$-0.662716\pi$
$281$	2.83468e9	−	3.37824e9i	0.454652	−	0.541833i	0.943865	+	0.330331i	$0.107160\pi$
$282$		0			0
$283$	−2.00162e8	−	1.13517e9i	−0.0312058	−	0.176977i	0.965221	−	0.261434i	$-0.0841955\pi$
$283$	−2.00162e8	−	1.13517e9i	−0.0312058	−	0.176977i	−0.996427	+	0.0844573i	$0.973084\pi$
$284$	−4.92992e8	+	8.69278e7i	−0.0757821	+	0.0133624i
$285$		0			0
$286$	−9.09749e8	−	7.63370e8i	−0.135974	−	0.114096i
$287$	−2.25744e7	+	1.30334e7i	−0.00332728	+	0.00192101i
$288$		0			0
$289$	−4.41562e8	+	7.64808e8i	−0.0632995	+	0.109638i
$290$	−1.96304e9	−	5.39342e9i	−0.277548	−	0.762557i
$291$		0			0
$292$	−9.41636e9	+	7.90127e9i	−1.29524	+	1.08684i
$293$	−2.31044e9	+	6.34787e9i	−0.313490	+	0.861306i	0.678456	+	0.734641i	$0.262649\pi$
$293$	−2.31044e9	+	6.34787e9i	−0.313490	+	0.861306i	−0.991946	+	0.126665i	$0.959573\pi$
$294$		0			0
$295$	−2.59053e8	+	1.46916e9i	−0.0342059	+	0.193991i
$296$			1.81751e10i			2.36760i
$297$		0			0
$298$	−2.18382e9			−0.276918
$299$	9.06463e9	+	1.59834e9i	1.13414	+	0.199979i
$300$		0			0
$301$	2.67550e8	+	9.73802e7i	0.0325941	+	0.0118633i
$302$	2.08765e9	+	2.48797e9i	0.250975	+	0.299100i
$303$		0			0
$304$	9.72160e9	−	3.53837e9i	1.13826	−	0.414294i
$305$	5.84862e9	+	3.37670e9i	0.675856	+	0.390205i
$306$		0			0
$307$	5.52672e7	+	9.57256e7i	0.00622177	+	0.0107764i	0.869120	−	0.494602i	$-0.164686\pi$
$307$	5.52672e7	+	9.57256e7i	0.00622177	+	0.0107764i	−0.862898	+	0.505379i	$0.831353\pi$
$308$	1.71170e7	−	2.03993e7i	0.00190207	−	0.00226680i
$309$		0			0
$310$	−4.43090e7	−	2.51289e8i	−0.00479784	−	0.0272099i
$311$	−1.59059e10	+	2.80464e9i	−1.70026	+	0.299803i	−0.937787	−	0.347212i	$-0.887128\pi$
$311$	−1.59059e10	+	2.80464e9i	−1.70026	+	0.299803i	−0.762478	+	0.647014i	$0.776017\pi$
$312$		0			0
$313$	−5.82416e9	−	4.88705e9i	−0.606814	−	0.509178i	0.286814	−	0.957986i	$-0.407404\pi$
$313$	−5.82416e9	−	4.88705e9i	−0.606814	−	0.509178i	−0.893628	+	0.448809i	$0.851848\pi$
$314$	7.36349e9	−	4.25131e9i	0.757470	−	0.437325i
$315$		0			0
$316$	−1.40147e10	+	2.42741e10i	−1.40551	+	2.43442i
$317$	5.26808e9	+	1.44739e10i	0.521693	+	1.43334i	0.868635	+	0.495453i	$0.164998\pi$
$317$	5.26808e9	+	1.44739e10i	0.521693	+	1.43334i	−0.346942	+	0.937887i	$0.612780\pi$
$318$		0			0
$319$	−5.09725e8	+	4.27710e8i	−0.0492236	+	0.0413035i
$320$	−2.64384e9	+	7.26390e9i	−0.252136	+	0.692739i
$321$		0			0
$322$	−5.47486e7	+	3.10495e8i	−0.00509272	+	0.0288823i
$323$			1.76774e10i			1.62408i
$324$		0			0
$325$	9.88638e9			0.886143
$326$	−3.12076e10	−	5.50274e9i	−2.76306	−	0.487201i
$327$		0			0
$328$	3.18609e9	+	1.15964e9i	0.275273	+	0.100191i
$329$	2.71693e8	+	3.23791e8i	0.0231897	+	0.0276364i
$330$		0			0
$331$	−1.41892e9	+	5.16445e8i	−0.118208	+	0.0430241i	−0.400447	−	0.916320i	$-0.631145\pi$
$331$	−1.41892e9	+	5.16445e8i	−0.118208	+	0.0430241i	0.282239	+	0.959344i	$0.408923\pi$
$332$	−4.67237e9	−	2.69760e9i	−0.384579	−	0.222037i
$333$		0			0
$334$	1.09194e10	+	1.89130e10i	0.877434	+	1.51976i
$335$	−6.61769e8	+	7.88666e8i	−0.0525445	+	0.0626201i
$336$		0			0
$337$	3.82656e9	+	2.17015e10i	0.296680	+	1.68256i	0.660293	+	0.751008i	$0.270432\pi$
$337$	3.82656e9	+	2.17015e10i	0.296680	+	1.68256i	−0.363613	+	0.931550i	$0.618457\pi$
$338$	1.71146e10	−	3.01777e9i	1.31129	−	0.231217i
$339$		0			0
$340$	1.05152e10	+	8.82331e9i	0.786869	+	0.660261i
$341$	−2.56187e7	+	1.47909e7i	−0.00189469	+	0.00109390i
$342$		0			0
$343$	−2.76517e8	+	4.78941e8i	−0.0199777	+	0.0346024i
$344$	−1.26665e10	−	3.48009e10i	−0.904530	−	2.48518i
$345$		0			0
$346$	−1.79361e10	+	1.50502e10i	−1.25148	+	1.05012i
$347$	−3.05748e9	+	8.40036e9i	−0.210885	+	0.579402i	−0.999364	−	0.0356598i	$-0.988647\pi$
$347$	−3.05748e9	+	8.40036e9i	−0.210885	+	0.579402i	0.788479	+	0.615062i	$0.210869\pi$
$348$		0			0
$349$	9.86509e8	−	5.59477e9i	0.0664966	−	0.377121i	−0.933339	−	0.358996i	$-0.883119\pi$
$349$	9.86509e8	−	5.59477e9i	0.0664966	−	0.377121i	0.999836	−	0.0181249i	$-0.00576965\pi$
$350$			3.38643e8i			0.0225668i
$351$		0			0
$352$	4.04794e8			0.0263672
$353$	−2.49535e9	−	4.39998e8i	−0.160706	−	0.0283368i	0.0927161	−	0.995693i	$-0.470445\pi$
$353$	−2.49535e9	−	4.39998e8i	−0.160706	−	0.0283368i	−0.253422	+	0.967356i	$0.581556\pi$
$354$		0			0
$355$	3.51375e8	+	1.27890e8i	0.0221237	+	0.00805236i
$356$	8.82363e9	+	1.05156e10i	0.549348	+	0.654687i
$357$		0			0
$358$	3.23879e10	−	1.17882e10i	1.97174	−	0.717656i
$359$	−1.19526e10	−	6.90083e9i	−0.719589	−	0.415455i	0.0950126	−	0.995476i	$-0.469711\pi$
$359$	−1.19526e10	−	6.90083e9i	−0.719589	−	0.415455i	−0.814601	+	0.580021i	$0.803044\pi$
$360$		0			0
$361$	−1.71531e10	−	2.97101e10i	−1.00998	−	1.74934i
$362$	1.57006e10	−	1.87112e10i	0.914284	−	1.08960i
$363$		0			0
$364$	1.54141e8	+	8.74176e8i	0.00878036	+	0.0497959i
$365$	9.04227e9	−	1.59440e9i	0.509455	−	0.0898307i
$366$		0			0
$367$	−2.16338e10	−	1.81529e10i	−1.19253	−	1.00065i	−0.999812	−	0.0193960i	$-0.993826\pi$
$367$	−2.16338e10	−	1.81529e10i	−1.19253	−	1.00065i	−0.192717	−	0.981254i	$-0.561730\pi$
$368$	9.54936e9	−	5.51333e9i	0.520695	−	0.300623i
$369$		0			0
$370$	1.43693e10	−	2.48884e10i	0.766706	−	1.32797i
$371$	−6.38719e7	−	1.75487e8i	−0.00337143	−	0.00926293i
$372$		0			0
$373$	−1.20599e8	+	1.01195e8i	−0.00623030	+	0.00522784i	−0.645897	−	0.763424i	$-0.723517\pi$
$373$	−1.20599e8	+	1.01195e8i	−0.00623030	+	0.00522784i	0.639667	+	0.768652i	$0.279072\pi$
$374$	8.31439e8	−	2.28436e9i	0.0424956	−	0.116756i
$375$		0			0
$376$	9.54702e9	−	5.41438e10i	0.477657	−	2.70893i
$377$		−	2.21804e10i		−	1.09800i
$378$		0			0
$379$	1.13180e10			0.548547			0.274273	−	0.961652i	$-0.411563\pi$
$379$	1.13180e10			0.548547			0.274273	+	0.961652i	$0.411563\pi$
$380$	−3.92219e10	−	6.91588e9i	−1.88102	−	0.331675i
$381$		0			0
$382$	−2.77316e10	−	1.00935e10i	−1.30233	−	0.474009i
$383$	2.31264e10	+	2.75610e10i	1.07476	+	1.28085i	0.957712	+	0.287729i	$0.0929003\pi$
$383$	2.31264e10	+	2.75610e10i	1.07476	+	1.28085i	0.117053	+	0.993126i	$0.462655\pi$
$384$		0			0
$385$	−1.86915e7	+	6.80315e6i	−0.000850748	+	0.000309647i
$386$	−4.86371e10	−	2.80806e10i	−2.19088	−	1.26490i
$387$		0			0
$388$	−1.28140e10	−	2.21944e10i	−0.565401	−	0.979303i
$389$	1.87472e10	−	2.23420e10i	0.818724	−	0.975717i	−0.181247	−	0.983438i	$-0.558013\pi$
$389$	1.87472e10	−	2.23420e10i	0.818724	−	0.975717i	0.999970	+	0.00772084i	$0.00245765\pi$
$390$		0			0
$391$	3.27175e9	+	1.85550e10i	0.139982	+	0.793879i
$392$	3.54138e10	−	6.24441e9i	1.49978	−	0.264452i
$393$		0			0
$394$	1.57503e10	+	1.32161e10i	0.653588	+	0.548426i
$395$	1.81318e10	−	1.04684e10i	0.744822	−	0.430023i
$396$		0			0
$397$	3.13372e9	−	5.42776e9i	0.126153	−	0.218504i	−0.796030	−	0.605257i	$-0.793070\pi$
$397$	3.13372e9	−	5.42776e9i	0.126153	−	0.218504i	0.922183	+	0.386754i	$0.126404\pi$
$398$	1.02280e10	+	2.81011e10i	0.407621	+	1.11993i
$399$		0			0
$400$	9.07270e9	−	7.61290e9i	0.354402	−	0.297379i
$401$	6.92919e9	−	1.90378e10i	0.267982	−	0.736274i	−0.730589	−	0.682818i	$-0.760754\pi$
$401$	6.92919e9	−	1.90378e10i	0.267982	−	0.736274i	0.998570	−	0.0534557i	$-0.0170236\pi$
$402$		0			0
$403$	1.71231e8	−	9.71099e8i	0.00649176	−	0.0368166i
$404$			8.45491e10i			3.17383i
$405$		0			0
$406$	7.59754e8			0.0279621
$407$	−3.28112e9	−	5.78549e8i	−0.119576	−	0.0210845i
$408$		0			0
$409$	1.05073e10	+	3.82434e9i	0.375489	+	0.136667i	0.522869	−	0.852413i	$-0.324862\pi$
$409$	1.05073e10	+	3.82434e9i	0.375489	+	0.136667i	−0.147380	+	0.989080i	$0.547084\pi$
$410$	−3.44612e9	−	4.10693e9i	−0.121954	−	0.145339i
$411$		0			0
$412$	−2.16576e10	+	7.88274e9i	−0.751661	+	0.273582i
$413$	−1.71019e8	−	9.87378e7i	−0.00587820	−	0.00339378i
$414$		0			0
$415$	2.01499e9	+	3.49007e9i	0.0679331	+	0.117664i
$416$	−8.67337e9	+	1.03365e10i	−0.289611	+	0.345145i
$417$		0			0
$418$	1.22479e9	+	6.94614e9i	0.0401196	+	0.227530i
$419$	−2.72177e10	+	4.79921e9i	−0.883070	+	0.155709i	−0.596752	−	0.802425i	$-0.703543\pi$
$419$	−2.72177e10	+	4.79921e9i	−0.883070	+	0.155709i	−0.286318	+	0.958135i	$0.592431\pi$
$420$		0			0
$421$	1.08291e10	+	9.08671e9i	0.344719	+	0.289253i	0.798665	−	0.601776i	$-0.205540\pi$
$421$	1.08291e10	+	9.08671e9i	0.344719	+	0.289253i	−0.453947	+	0.891029i	$0.649984\pi$
$422$	5.75219e10	−	3.32103e10i	1.81378	−	1.04718i
$423$		0			0
$424$	−1.21455e10	+	2.10366e10i	−0.375795	+	0.650897i
$425$	6.92150e9	+	1.90167e10i	0.212151	+	0.582880i
$426$		0			0
$427$	−6.84812e8	+	5.74626e8i	−0.0205997	+	0.0172852i
$428$	−7.78101e8	+	2.13782e9i	−0.0231879	+	0.0637082i
$429$		0			0
$430$	−1.01687e10	+	5.76696e10i	−0.297435	+	1.68684i
$431$		−	1.89465e10i		−	0.549059i	−0.961579	−	0.274529i	$-0.911478\pi$
$431$		−	1.89465e10i		−	0.549059i	0.961579	−	0.274529i	$-0.0885220\pi$
$432$		0			0
$433$	−2.31085e10			−0.657385			−0.328692	−	0.944437i	$-0.606608\pi$
$433$	−2.31085e10			−0.657385			−0.328692	+	0.944437i	$0.606608\pi$
$434$	3.32635e7	+	5.86526e6i	0.000937582	+	0.000165321i
$435$		0			0
$436$	−8.44199e10	−	3.07263e10i	−2.33614	−	0.850285i
$437$	−3.51391e10	−	4.18771e10i	−0.963529	−	1.14829i
$438$		0			0
$439$	5.42623e9	−	1.97498e9i	0.146097	−	0.0531748i	−0.267937	−	0.963436i	$-0.586342\pi$
$439$	5.42623e9	−	1.97498e9i	0.146097	−	0.0531748i	0.414033	+	0.910262i	$0.364120\pi$
$440$	2.24066e9	+	1.29364e9i	0.0597812	+	0.0345147i
$441$		0			0
$442$	4.05168e10	+	7.01771e10i	1.06156	+	1.83868i
$443$	3.44173e10	−	4.10170e10i	0.893639	−	1.06500i	−0.103879	−	0.994590i	$-0.533126\pi$
$443$	3.44173e10	−	4.10170e10i	0.893639	−	1.06500i	0.997518	−	0.0704077i	$-0.0224300\pi$
$444$		0			0
$445$	−1.78052e9	−	1.00978e10i	−0.0454053	−	0.257507i
$446$	−2.64355e10	+	4.66128e9i	−0.668109	+	0.117806i
$447$		0			0
$448$	−7.83850e8	−	6.57728e8i	−0.0194590	−	0.0163280i
$449$	−7.73947e9	+	4.46839e9i	−0.190426	+	0.109942i	−0.592182	−	0.805804i	$-0.701733\pi$
$449$	−7.73947e9	+	4.46839e9i	−0.190426	+	0.109942i	0.401756	+	0.915747i	$0.368400\pi$
$450$		0			0
$451$	−3.10769e8	+	5.38267e8i	−0.00751157	+	0.0130104i
$452$	3.42477e10	+	9.40949e10i	0.820499	+	2.25430i
$453$		0			0
$454$	1.06366e11	−	8.92520e10i	2.50369	−	2.10085i
$455$	2.26775e8	−	6.23061e8i	0.00529116	−	0.0145373i
$456$		0			0
$457$	3.14572e9	−	1.78403e10i	0.0721200	−	0.409013i	−0.927280	−	0.374369i	$-0.877859\pi$
$457$	3.14572e9	−	1.78403e10i	0.0721200	−	0.409013i	0.999400	−	0.0346436i	$-0.0110296\pi$
$458$			1.65299e10i			0.375672i
$459$		0			0
$460$	−4.24492e10			−0.948064
$461$	5.93869e10	+	1.04715e10i	1.31488	+	0.231849i	0.786728	−	0.617299i	$-0.211773\pi$
$461$	5.93869e10	+	1.04715e10i	1.31488	+	0.231849i	0.528154	+	0.849149i	$0.322884\pi$
$462$		0			0
$463$	2.44870e10	+	8.91255e9i	0.532859	+	0.193945i	0.594414	−	0.804159i	$-0.297384\pi$
$463$	2.44870e10	+	8.91255e9i	0.532859	+	0.193945i	−0.0615554	+	0.998104i	$0.519606\pi$
$464$	−1.70797e10	−	2.03548e10i	−0.368476	−	0.439133i
$465$		0			0
$466$	−1.29623e11	+	4.71789e10i	−2.74877	+	1.00047i
$467$	6.40285e10	+	3.69669e10i	1.34619	+	0.777222i	0.987707	−	0.156315i	$-0.0499615\pi$
$467$	6.40285e10	+	3.69669e10i	1.34619	+	0.777222i	0.358481	+	0.933537i	$0.383295\pi$
$468$		0			0
$469$	−6.81403e7	−	1.18022e8i	−0.00140836	−	0.00243934i
$470$	−5.58798e10	+	6.65950e10i	−1.14515	+	1.36474i
$471$		0			0
$472$	4.46036e9	+	2.52960e10i	0.0898674	+	0.509664i
$473$	6.68576e9	−	1.17888e9i	0.133569	−	0.0235519i
$474$		0			0
$475$	−4.49796e10	−	3.77424e10i	−0.883571	−	0.741404i
$476$	−1.57358e9	+	9.08509e8i	−0.0306522	+	0.0176971i
$477$		0			0
$478$	9.93983e9	−	1.72163e10i	0.190400	−	0.329783i
$479$	−2.67599e10	−	7.35221e10i	−0.508326	−	1.39661i	−0.882963	−	0.469442i	$-0.844455\pi$
$479$	−2.67599e10	−	7.35221e10i	−0.508326	−	1.39661i	0.374638	−	0.927171i	$-0.377767\pi$
$480$		0			0
$481$	8.50766e10	−	7.13878e10i	1.58939	−	1.33365i
$482$	2.78168e10	−	7.64261e10i	0.515371	−	1.41597i
$483$		0			0
$484$	−1.79508e10	+	1.01804e11i	−0.327117	+	1.85517i
$485$			1.91430e10i			0.345974i
$486$		0			0
$487$	7.64909e9			0.135986			0.0679930	−	0.997686i	$-0.478340\pi$
$487$	7.64909e9			0.135986			0.0679930	+	0.997686i	$0.478340\pi$
$488$	1.14513e11	+	2.01918e10i	2.01919	+	0.356037i
$489$		0			0
$490$	−5.34315e10	−	1.94475e10i	−0.926858	−	0.337349i
$491$	−6.03897e10	−	7.19697e10i	−1.03905	−	1.23829i	−0.970615	−	0.240638i	$-0.922643\pi$
$491$	−6.03897e10	−	7.19697e10i	−1.03905	−	1.23829i	−0.0684368	−	0.997655i	$-0.521801\pi$
$492$		0			0
$493$	4.26644e10	−	1.55286e10i	0.722234	−	0.262872i
$494$	−2.03615e11	−	1.17557e11i	−3.41901	−	1.97397i
$495$		0			0
$496$	−5.90646e8	−	1.02303e9i	−0.00975890	−	0.0169029i
$497$	−3.18161e7	+	3.79170e7i	−0.000521461	+	0.000621453i
$498$		0			0
$499$	1.38187e9	+	7.83698e9i	0.0222877	+	0.126400i	0.993922	−	0.110090i	$-0.0351140\pi$
$499$	1.38187e9	+	7.83698e9i	0.0222877	+	0.126400i	−0.971634	+	0.236490i	$0.924003\pi$
$500$	−1.12552e11	+	1.98460e10i	−1.80083	+	0.317536i
$501$		0			0
$502$	8.45605e10	+	7.09547e10i	1.33154	+	1.11729i
$503$	−1.30492e10	+	7.53394e9i	−0.203850	+	0.117693i	−0.598450	−	0.801160i	$-0.704217\pi$
$503$	−1.30492e10	+	7.53394e9i	−0.203850	+	0.117693i	0.394600	+	0.918853i	$0.370883\pi$
$504$		0			0
$505$	3.15774e10	−	5.46936e10i	0.485524	−	0.840952i
$506$	2.57120e9	+	7.06431e9i	0.0392223	+	0.107762i
$507$		0			0
$508$	5.56414e10	−	4.66886e10i	0.835493	−	0.701062i
$509$	−2.81492e10	+	7.73393e10i	−0.419368	+	1.15220i	0.532697	+	0.846306i	$0.321179\pi$
$509$	−2.81492e10	+	7.73393e10i	−0.419368	+	1.15220i	−0.952065	+	0.305897i	$0.901044\pi$
$510$		0			0
$511$	−2.11053e8	+	1.19694e9i	−0.00309534	+	0.0175545i
$512$			8.91417e10i			1.29718i
$513$		0			0
$514$	1.55926e11			2.23392
$515$	1.69541e10	+	2.98946e9i	0.241015	+	0.0424975i
$516$		0			0
$517$	9.47060e9	+	3.44702e9i	0.132561	+	0.0482482i
$518$	2.44528e9	+	2.91417e9i	0.0339633	+	0.0404758i
$519$		0			0
$520$	−8.10432e10	+	2.94973e10i	−1.10842	+	0.403431i
$521$	1.88229e10	+	1.08674e10i	0.255468	+	0.147494i	0.622265	−	0.782806i	$-0.286213\pi$
$521$	1.88229e10	+	1.08674e10i	0.255468	+	0.147494i	−0.366798	+	0.930301i	$0.619546\pi$
$522$		0			0
$523$	−1.73044e10	−	2.99720e10i	−0.231286	−	0.400599i	0.726901	−	0.686742i	$-0.240960\pi$
$523$	−1.73044e10	−	2.99720e10i	−0.231286	−	0.400599i	−0.958187	+	0.286144i	$0.907627\pi$
$524$	−9.49016e10	+	1.13099e11i	−1.25878	+	1.50015i
$525$		0			0
$526$	5.83026e9	+	3.30650e10i	0.0761631	+	0.431943i
$527$	1.98781e9	−	3.50505e8i	0.0257711	−	0.00454414i
$528$		0			0
$529$	1.53554e10	+	1.28847e10i	0.196082	+	0.164532i
$530$	3.32633e10	−	1.92046e10i	0.421563	−	0.243389i
$531$		0			0
$532$	2.63598e9	−	4.56565e9i	0.0329075	−	0.0569975i
$533$	−7.08606e9	−	1.94688e10i	−0.0878003	−	0.241229i
$534$		0			0
$535$	1.30177e9	−	1.09232e9i	0.0158899	−	0.0133332i
$536$	−6.06278e9	+	1.66574e10i	−0.0734535	+	0.201812i
$537$		0			0
$538$	−2.29449e10	+	1.30127e11i	−0.273878	+	1.55324i
$539$			6.59198e9i			0.0781017i
$540$		0			0
$541$	−9.13064e10			−1.06589			−0.532944	−	0.846150i	$-0.678915\pi$
$541$	−9.13064e10			−1.06589			−0.532944	+	0.846150i	$0.678915\pi$
$542$	1.12861e11	+	1.99005e10i	1.30782	+	0.230604i
$543$		0			0
$544$	−2.59548e10	−	9.44678e9i	−0.296362	−	0.107867i
$545$	4.31344e10	+	5.14055e10i	0.488919	+	0.582671i
$546$		0			0
$547$	1.12692e11	−	4.10164e10i	1.25876	−	0.458150i	0.375406	−	0.926861i	$-0.377503\pi$
$547$	1.12692e11	−	4.10164e10i	1.25876	−	0.458150i	0.883352	+	0.468710i	$0.155281\pi$
$548$	−1.69161e11	−	9.76654e10i	−1.87577	−	1.08298i
$549$		0			0
$550$	4.03731e9	+	6.99283e9i	0.0441206	+	0.0764192i
$551$	−8.46760e10	+	1.00913e11i	−0.918659	+	1.09481i
$552$		0			0
$553$	4.81255e8	+	2.72933e9i	0.00514606	+	0.0291847i
$554$	2.17101e11	−	3.82808e10i	2.30474	−	0.406389i
$555$		0			0
$556$	−4.07740e10	−	3.42134e10i	−0.426662	−	0.358012i
$557$	1.09462e11	−	6.31979e10i	1.13721	−	0.656571i	0.191475	−	0.981498i	$-0.438673\pi$
$557$	1.09462e11	−	6.31979e10i	1.13721	−	0.656571i	0.945739	+	0.324927i	$0.105340\pi$
$558$		0			0
$559$	−1.13150e11	+	1.95982e11i	−1.15880	+	2.00710i
$560$	−2.71670e8	−	7.46406e8i	−0.00276242	−	0.00758968i
$561$		0			0
$562$	−9.19734e10	+	7.71748e10i	−0.921970	+	0.773625i
$563$	5.52101e10	−	1.51689e11i	0.549522	−	1.50980i	−0.284836	−	0.958576i	$-0.591939\pi$
$563$	5.52101e10	−	1.51689e11i	0.549522	−	1.50980i	0.834358	−	0.551223i	$-0.185839\pi$
$564$		0			0
$565$	1.29882e10	−	7.36595e10i	0.127454	−	0.722828i
$566$			3.13821e10i			0.305785i
$567$		0			0
$568$	6.43823e9			0.0618548
$569$	−9.00791e10	−	1.58834e10i	−0.859360	−	0.151528i	−0.273432	−	0.961891i	$-0.588159\pi$
$569$	−9.00791e10	−	1.58834e10i	−0.859360	−	0.151528i	−0.585928	+	0.810363i	$0.699270\pi$
$570$		0			0
$571$	−1.11458e11	−	4.05674e10i	−1.04850	−	0.381622i	−0.240402	−	0.970673i	$-0.577279\pi$
$571$	−1.11458e11	−	4.05674e10i	−1.04850	−	0.381622i	−0.808095	+	0.589052i	$0.799501\pi$
$572$	1.36049e10	+	1.62137e10i	0.127090	+	0.151460i
$573$		0			0
$574$	6.66874e8	−	2.42722e8i	0.00614322	−	0.00223595i
$575$	−5.41981e10	−	3.12913e10i	−0.495807	−	0.286255i
$576$		0			0
$577$	1.67766e10	+	2.90579e10i	0.151356	+	0.262157i	0.931726	−	0.363161i	$-0.118303\pi$
$577$	1.67766e10	+	2.90579e10i	0.151356	+	0.262157i	−0.780370	+	0.625318i	$0.784969\pi$
$578$	1.54547e10	−	1.84182e10i	0.138468	−	0.165020i
$579$		0			0
$580$	1.77627e10	+	1.00737e11i	0.156963	+	0.890182i
$581$	−5.25352e8	+	9.26337e7i	−0.00461048	+	0.000812951i
$582$		0			0
$583$	−3.41109e9	−	2.86224e9i	−0.0295270	−	0.0247761i
$584$	1.36911e11	−	7.90456e10i	1.17703	−	0.679557i
$585$		0			0
$586$	9.19568e10	−	1.59274e11i	0.779818	−	1.35068i
$587$	−3.65161e10	−	1.00327e11i	−0.307562	−	0.845019i	−0.993131	−	0.117011i	$-0.962669\pi$
$587$	−3.65161e10	−	1.00327e11i	−0.307562	−	0.845019i	0.685569	−	0.728008i	$-0.259553\pi$
$588$		0			0
$589$	−4.48632e9	+	3.76447e9i	−0.0372760	+	0.0312783i
$590$	1.38913e10	−	3.81659e10i	0.114639	−	0.314969i
$591$		0			0
$592$	2.31032e10	−	1.31025e11i	0.188098	−	1.06676i
$593$			2.28708e11i			1.84953i	0.380534	+	0.924767i	$0.375740\pi$
$593$			2.28708e11i			1.84953i	−0.380534	+	0.924767i	$0.624260\pi$
$594$		0			0
$595$	1.35724e9			0.0108290
$596$	3.83291e10	+	6.75845e9i	0.303769	+	0.0535627i
$597$		0			0
$598$	−2.35481e11	−	8.57081e10i	−1.84141	−	0.670219i
$599$	7.32940e10	+	8.73484e10i	0.569326	+	0.678496i	0.971493	−	0.237070i	$-0.0761871\pi$
$599$	7.32940e10	+	8.73484e10i	0.569326	+	0.678496i	−0.402166	+	0.915567i	$0.631743\pi$
$600$		0			0
$601$	1.29784e11	−	4.72377e10i	0.994775	−	0.362069i	0.207208	−	0.978297i	$-0.433562\pi$
$601$	1.29784e11	−	4.72377e10i	0.994775	−	0.362069i	0.787567	+	0.616228i	$0.211340\pi$
$602$	−6.71307e9	−	3.87579e9i	−0.0511134	−	0.0295103i
$603$		0			0
$604$	−2.89415e10	−	5.01282e10i	−0.217457	−	0.376647i
$605$	4.96339e10	−	5.91514e10i	0.370474	−	0.441513i
$606$		0			0
$607$	3.56398e10	+	2.02123e11i	0.262531	+	1.48889i	0.775975	+	0.630763i	$0.217258\pi$
$607$	3.56398e10	+	2.02123e11i	0.262531	+	1.48889i	−0.513445	+	0.858123i	$0.671631\pi$
$608$	7.89217e10	−	1.39160e10i	0.577540	−	0.101836i
$609$		0			0
$610$	−1.40847e11	−	1.18185e11i	−1.01725	−	0.853576i
$611$	−2.90943e11	+	1.67976e11i	−2.08758	+	1.20527i
$612$		0			0
$613$	−7.92167e10	+	1.37207e11i	−0.561016	+	0.971707i	0.436393	+	0.899756i	$0.356256\pi$
$613$	−7.92167e10	+	1.37207e11i	−0.561016	+	0.971707i	−0.997408	+	0.0719511i	$0.977077\pi$
$614$	−1.02925e9	−	2.82784e9i	−0.00724181	−	0.0198967i
$615$		0			0
$616$	−2.62358e8	+	2.20144e8i	−0.00182209	+	0.00152892i
$617$	−3.39972e10	+	9.34066e10i	−0.234586	+	0.644521i	0.765413	+	0.643539i	$0.222535\pi$
$617$	−3.39972e10	+	9.34066e10i	−0.234586	+	0.644521i	−1.00000		0.000981684i	$0.999688\pi$
$618$		0			0
$619$	−1.69349e10	+	9.60425e10i	−0.115351	+	0.654185i	0.871226	+	0.490883i	$0.163326\pi$
$619$	−1.69349e10	+	9.60425e10i	−0.115351	+	0.654185i	−0.986576	+	0.163302i	$0.947785\pi$
$620$			4.54761e9i			0.0307763i
$621$		0			0
$622$	4.39722e11			2.93776
$623$	1.33667e9	+	2.35690e8i	0.00887301	+	0.00156455i
$624$		0			0
$625$	−1.49478e10	−	5.44056e9i	−0.0979619	−	0.0356552i
$626$	1.33051e11	+	1.58564e11i	0.866405	+	1.03254i
$627$		0			0
$628$	−1.42397e11	+	5.18282e10i	−0.915506	+	0.333217i
$629$	1.96879e11	+	1.13668e11i	1.25775	+	0.726165i
$630$		0			0
$631$	4.93554e10	+	8.54861e10i	0.311327	+	0.539235i	0.978650	−	0.205534i	$-0.0658931\pi$
$631$	4.93554e10	+	8.54861e10i	0.311327	+	0.539235i	−0.667323	+	0.744769i	$0.732560\pi$
$632$	2.31717e11	−	2.76150e11i	1.45241	−	1.73092i
$633$		0			0
$634$	−7.28186e10	−	4.12975e11i	−0.450697	−	2.55603i
$635$	−5.34309e10	+	9.42130e9i	−0.328622	+	0.0579450i
$636$		0			0
$637$	−1.68328e11	−	1.41244e11i	−1.02235	−	0.857851i
$638$	1.56886e10	−	9.05782e9i	0.0946895	−	0.0546690i
$639$		0			0
$640$	8.88105e10	−	1.53824e11i	0.529352	−	0.916865i
$641$	−2.47911e10	−	6.81129e10i	−0.146846	−	0.403457i	0.844361	−	0.535775i	$-0.179980\pi$
$641$	−2.47911e10	−	6.81129e10i	−0.146846	−	0.403457i	−0.991207	+	0.132318i	$0.957758\pi$
$642$		0			0
$643$	−1.83351e11	+	1.53850e11i	−1.07261	+	0.900023i	−0.995286	−	0.0969835i	$-0.969081\pi$
$643$	−1.83351e11	+	1.53850e11i	−1.07261	+	0.900023i	−0.0773195	+	0.997006i	$0.524636\pi$
$644$	1.92183e9	−	5.28019e9i	0.0111731	−	0.0306977i
$645$		0			0
$646$	8.35718e10	−	4.73959e11i	0.479877	−	2.72152i
$647$			2.53520e11i			1.44676i	0.690452	+	0.723378i	$0.257411\pi$
$647$			2.53520e11i			1.44676i	−0.690452	+	0.723378i	$0.742589\pi$
$648$		0			0
$649$	−4.70863e9			−0.0265409
$650$	−2.65070e11	−	4.67390e10i	−1.48493	−	0.261834i
$651$		0			0
$652$	5.30708e11	+	1.93162e11i	2.93674	+	1.06888i
$653$	−2.00231e11	−	2.38626e11i	−1.10123	−	1.31239i	−0.945873	−	0.324537i	$-0.894792\pi$
$653$	−2.00231e11	−	2.38626e11i	−1.10123	−	1.31239i	−0.155357	−	0.987858i	$-0.549653\pi$
$654$		0			0
$655$	1.03631e11	−	3.77185e10i	0.563020	−	0.204922i
$656$	−2.14946e10	−	1.24099e10i	−0.116068	−	0.0670121i
$657$		0			0
$658$	−5.75377e9	−	9.96582e9i	−0.0306937	−	0.0531630i
$659$	1.13446e11	−	1.35200e11i	0.601518	−	0.716861i	−0.376258	−	0.926515i	$-0.622789\pi$
$659$	1.13446e11	−	1.35200e11i	0.601518	−	0.716861i	0.977776	+	0.209654i	$0.0672338\pi$
$660$		0			0
$661$	−4.61200e10	−	2.61560e11i	−0.241593	−	1.37014i	−0.828275	−	0.560322i	$-0.810677\pi$
$661$	−4.61200e10	−	2.61560e11i	−0.241593	−	1.37014i	0.586682	−	0.809817i	$-0.300434\pi$
$662$	4.04851e10	−	7.13862e9i	0.210797	−	0.0371691i
$663$		0			0
$664$	5.31544e10	+	4.46018e10i	0.273443	+	0.229446i
$665$	−3.41035e9	+	1.96897e9i	−0.0174387	+	0.0100682i
$666$		0			0
$667$	−7.02029e10	+	1.21595e11i	−0.354692	+	0.614345i
$668$	−1.33120e11	−	3.65744e11i	−0.668555	−	1.83684i
$669$		0			0
$670$	2.14716e10	−	1.80168e10i	0.106553	−	0.0894085i
$671$	−7.29038e9	+	2.00301e10i	−0.0359633	+	0.0988084i
$672$		0			0
$673$	−6.55793e9	+	3.71918e10i	−0.0319673	+	0.181296i	−0.996611	−	0.0822631i	$-0.973785\pi$
$673$	−6.55793e9	+	3.71918e10i	−0.0319673	+	0.181296i	0.964643	+	0.263559i	$0.0848963\pi$
$674$		−	5.99942e11i		−	2.90717i
$675$		0			0
$676$	−3.09725e11			−1.48317
$677$	−3.97150e10	−	7.00282e9i	−0.189060	−	0.0333364i	0.0783163	−	0.996929i	$-0.475046\pi$
$677$	−3.97150e10	−	7.00282e9i	−0.189060	−	0.0333364i	−0.267376	+	0.963592i	$0.586157\pi$
$678$		0			0
$679$	−2.38117e9	−	8.66676e8i	−0.0112024	−	0.00407735i
$680$	−1.13478e11	−	1.35237e11i	−0.530731	−	0.632500i
$681$		0			0
$682$	7.56804e8	−	2.75454e8i	0.00349821	−	0.00127324i
$683$	−1.59856e10	−	9.22927e9i	−0.0734590	−	0.0424116i	0.462821	−	0.886452i	$-0.346837\pi$
$683$	−1.59856e10	−	9.22927e9i	−0.0734590	−	0.0424116i	−0.536280	+	0.844040i	$0.680171\pi$
$684$		0			0
$685$	7.29521e10	+	1.26357e11i	0.331341	+	0.573900i
$686$	9.67811e9	−	1.15339e10i	0.0437013	−	0.0520812i
$687$		0			0
$688$	4.70762e10	+	2.66982e11i	0.210110	+	1.19159i
$689$	1.46176e11	−	2.57748e10i	0.648634	−	0.114372i
$690$		0			0
$691$	1.16645e11	+	9.78767e10i	0.511627	+	0.429306i	0.861701	−	0.507416i	$-0.169399\pi$
$691$	1.16645e11	+	9.78767e10i	0.511627	+	0.429306i	−0.350074	+	0.936722i	$0.613844\pi$
$692$	3.61381e11	−	2.08643e11i	1.57594	−	0.909872i
$693$		0			0
$694$	1.21690e11	−	2.10773e11i	0.524585	−	0.908607i
$695$	1.35981e10	+	3.73604e10i	0.0582825	+	0.160130i
$696$		0			0
$697$	3.24877e10	−	2.72604e10i	0.137654	−	0.115505i
$698$	−5.28998e10	+	1.45341e11i	−0.222860	+	0.612303i
$699$		0			0
$700$	1.04803e9	−	5.94366e9i	0.00436497	−	0.0247549i
$701$			2.37952e11i			0.985409i	0.870197	+	0.492705i	$0.163992\pi$
$701$			2.37952e11i			0.985409i	−0.870197	+	0.492705i	$0.836008\pi$
$702$		0			0
$703$	−6.59600e11			−2.70059
$704$	−2.40276e10	−	4.23672e9i	−0.0978184	−	0.0172480i
$705$		0			0
$706$	6.48242e10	+	2.35941e10i	0.260927	+	0.0949696i
$707$	5.37364e9	+	6.40405e9i	0.0215075	+	0.0256317i
$708$		0			0
$709$	1.08444e11	−	3.94705e10i	0.429162	−	0.156202i	−0.118402	−	0.992966i	$-0.537777\pi$
$709$	1.08444e11	−	3.94705e10i	0.429162	−	0.156202i	0.547564	+	0.836763i	$0.315555\pi$
$710$	−8.81632e9	−	5.09010e9i	−0.0346940	−	0.0200306i
$711$		0			0
$712$	−8.82731e10	−	1.52893e11i	−0.343485	−	0.594934i
$713$	−4.01233e9	+	4.78170e9i	−0.0155252	+	0.0185023i
$714$		0			0
$715$	−2.74534e9	−	1.55696e10i	−0.0105044	−	0.0595734i
$716$	−6.04936e11	+	1.06666e11i	−2.30174	+	0.405860i
$717$		0			0
$718$	2.87844e11	+	2.41530e11i	1.08308	+	0.908809i
$719$	1.29764e11	−	7.49192e10i	0.485555	−	0.280335i	−0.237174	−	0.971467i	$-0.576221\pi$
$719$	1.29764e11	−	7.49192e10i	0.485555	−	0.280335i	0.722728	+	0.691132i	$0.242888\pi$
$720$		0			0
$721$	−1.13943e9	+	1.97355e9i	−0.00421644	+	0.00730309i
$722$	3.19445e11	+	8.77669e11i	1.17557	+	3.22985i
$723$		0			0
$724$	−3.33475e11	+	2.79818e11i	−1.21369	+	1.01841i
$725$	−5.15793e10	+	1.41713e11i	−0.186691	+	0.512929i
$726$		0			0
$727$	−2.75911e10	+	1.56477e11i	−0.0987715	+	0.560161i	0.894755	+	0.446558i	$0.147350\pi$
$727$	−2.75911e10	+	1.56477e11i	−0.0987715	+	0.560161i	−0.993526	+	0.113603i	$0.963761\pi$
$728$		−	1.14163e10i		−	0.0406444i
$729$		0			0
$730$	−2.49976e11			−0.880250
$731$	−4.56193e11	−	8.04391e10i	−1.59764	−	0.281707i
$732$		0			0
$733$	4.15930e11	+	1.51386e11i	1.44080	+	0.524409i	0.940007	−	0.341156i	$-0.110818\pi$
$733$	4.15930e11	+	1.51386e11i	1.44080	+	0.524409i	0.500796	+	0.865565i	$0.333041\pi$
$734$	4.94218e11	+	5.88985e11i	1.70268	+	2.02918i
$735$		0			0
$736$	8.02644e10	−	2.92138e10i	0.273534	−	0.0995583i
$737$	−2.81414e9	−	1.62474e9i	−0.00953839	−	0.00550699i
$738$		0			0
$739$	1.80473e11	+	3.12589e11i	0.605111	+	1.04808i	0.992034	+	0.125971i	$0.0402045\pi$
$739$	1.80473e11	+	3.12589e11i	0.605111	+	1.04808i	−0.386923	+	0.922112i	$0.626462\pi$
$740$	−3.29226e11	+	3.92356e11i	−1.09791	+	1.30844i
$741$		0			0
$742$	8.82877e8	+	5.00704e9i	0.00291262	+	0.0165183i
$743$	−2.53589e11	+	4.47146e10i	−0.832100	+	0.146722i	−0.573441	−	0.819247i	$-0.694392\pi$
$743$	−2.53589e11	+	4.47146e10i	−0.832100	+	0.146722i	−0.258659	+	0.965969i	$0.583281\pi$
$744$		0			0
$745$	−2.22704e10	−	1.86871e10i	−0.0722941	−	0.0606620i
$746$	3.71186e9	−	2.14305e9i	0.0119850	−	0.00691952i
$747$		0			0
$748$	−2.16626e10	+	3.75206e10i	−0.0691996	+	0.119857i
$749$	7.69357e7	+	2.11379e8i	0.000244456	+	0.000671637i
$750$		0			0
$751$	−1.36650e11	+	1.14663e11i	−0.429587	+	0.360466i	−0.831796	−	0.555082i	$-0.812687\pi$
$751$	−1.36650e11	+	1.14663e11i	−0.429587	+	0.360466i	0.402209	+	0.915548i	$0.368243\pi$
$752$	−1.37650e11	+	3.78189e11i	−0.430431	+	1.18260i
$753$		0			0
$754$	−1.04860e11	+	5.94691e11i	−0.324433	+	1.83995i
$755$			4.32363e10i			0.133064i
$756$		0			0
$757$	1.50495e11			0.458289			0.229144	−	0.973392i	$-0.426407\pi$
$757$	1.50495e11			0.458289			0.229144	+	0.973392i	$0.426407\pi$
$758$	−3.03455e11	−	5.35072e10i	−0.919214	−	0.162082i
$759$		0			0
$760$	4.81328e11	+	1.75189e11i	1.44274	+	0.525113i
$761$	2.79893e10	+	3.33563e10i	0.0834551	+	0.0994579i	0.806156	−	0.591703i	$-0.201544\pi$
$761$	2.79893e10	+	3.33563e10i	0.0834551	+	0.0994579i	−0.722701	+	0.691161i	$0.757100\pi$
$762$		0			0
$763$	−8.34712e9	+	3.03810e9i	−0.0246285	+	0.00896405i
$764$	4.55491e11	+	2.62978e11i	1.33692	+	0.771873i
$765$		0			0
$766$	−4.89759e11	−	8.48288e11i	−1.42255	−	2.46393i
$767$	1.00890e11	−	1.20236e11i	0.291519	−	0.347419i
$768$		0			0
$769$	4.72911e10	+	2.68201e11i	0.135230	+	0.766929i	0.974699	+	0.223521i	$0.0717552\pi$
$769$	4.72911e10	+	2.68201e11i	0.135230	+	0.766929i	−0.839469	+	0.543408i	$0.817134\pi$
$770$	5.33312e8	−	9.40373e7i	0.00151711	−	0.000267508i
$771$		0			0
$772$	7.66747e11	+	6.43377e11i	2.15865	+	1.81132i
$773$	9.19339e10	−	5.30781e10i	0.257489	−	0.148661i	−0.365700	−	0.930733i	$-0.619170\pi$
$773$	9.19339e10	−	5.30781e10i	0.257489	−	0.148661i	0.623188	+	0.782072i	$0.285837\pi$
$774$		0			0
$775$	−3.35226e9	+	5.80628e9i	−0.00929246	+	0.0160950i
$776$	1.12731e11	+	3.09726e11i	0.310883	+	0.854143i
$777$		0			0
$778$	−6.08266e11	+	5.10396e11i	−1.66026	+	1.39312i
$779$	−4.20852e10	+	1.15628e11i	−0.114282	+	0.313988i
$780$		0			0
$781$	−2.04942e8	+	1.16228e9i	−0.000550842	+	0.00312398i
$782$		−	5.12958e11i		−	1.37169i
$783$		0			0
$784$	−2.63237e11			−0.696759
$785$	1.11471e11	+	1.96554e10i	0.293551	+	0.0517610i
$786$		0			0
$787$	3.73249e11	+	1.35851e11i	0.972970	+	0.354132i	0.779103	−	0.626896i	$-0.215675\pi$
$787$	3.73249e11	+	1.35851e11i	0.972970	+	0.354132i	0.193867	+	0.981028i	$0.437897\pi$
$788$	−2.35539e11	−	2.80705e11i	−0.610884	−	0.728023i
$789$		0			0
$790$	−5.35633e11	+	1.94954e11i	−1.37518	+	0.500524i
$791$	8.57438e9	+	4.95042e9i	0.0219027	+	0.0126455i
$792$		0			0
$793$	−3.55267e11	−	6.15340e11i	−0.898383	−	1.55605i
$794$	−1.09680e11	+	1.30712e11i	−0.275961	+	0.328877i
$795$		0			0
$796$	−9.25484e10	−	5.24868e11i	−0.230524	−	1.30737i
$797$	3.00279e11	−	5.29473e10i	0.744204	−	0.131223i	0.211326	−	0.977416i	$-0.432222\pi$
$797$	3.00279e11	−	5.29473e10i	0.744204	−	0.131223i	0.532878	+	0.846192i	$0.321111\pi$
$798$		0			0
$799$	−5.26797e11	−	4.42035e11i	−1.29258	−	1.08460i
$800$	7.94523e10	−	4.58718e10i	0.193975	−	0.111992i
$801$		0			0
$802$	−2.75786e11	+	4.77676e11i	−0.666615	+	1.15461i
$803$	9.91182e9	+	2.72325e10i	0.0238392	+	0.0654976i
$804$		0			0
$805$	−3.21525e9	+	2.69792e9i	−0.00765652	+	0.00642458i
$806$	−9.18196e9	+	2.52272e10i	−0.0217568	+	0.0597763i
$807$		0			0
$808$	1.88824e11	−	1.07087e12i	0.443008	−	2.51243i
$809$		−	8.23751e11i		−	1.92310i	−0.274630	−	0.961550i	$-0.588555\pi$
$809$		−	8.23751e11i		−	1.92310i	0.274630	−	0.961550i	$-0.411445\pi$
$810$		0			0
$811$	1.98978e11			0.459962			0.229981	−	0.973195i	$-0.426134\pi$
$811$	1.98978e11			0.459962			0.229981	+	0.973195i	$0.426134\pi$
$812$	−1.33348e10	−	2.35128e9i	−0.0306734	−	0.00540854i
$813$		0			0
$814$	8.52368e10	+	3.10237e10i	0.194147	+	0.0706636i
$815$	−2.71165e11	−	3.23162e11i	−0.614615	−	0.732470i
$816$		0			0
$817$	1.26298e12	−	4.59687e11i	2.83470	−	1.03175i
$818$	−2.63637e11	−	1.52211e11i	−0.588834	−	0.339964i
$819$		0			0
$820$	4.77742e10	+	8.27474e10i	0.105667	+	0.183020i
$821$	2.60503e11	−	3.10456e11i	0.573378	−	0.683325i	−0.398943	−	0.916976i	$-0.630623\pi$
$821$	2.60503e11	−	3.10456e11i	0.573378	−	0.683325i	0.972321	+	0.233651i	$0.0750672\pi$
$822$		0			0
$823$	−7.72259e10	−	4.37970e11i	−0.168331	−	0.954651i	−0.945563	−	0.325438i	$-0.894488\pi$
$823$	−7.72259e10	−	4.37970e11i	−0.168331	−	0.954651i	0.777233	−	0.629213i	$-0.216623\pi$
$824$	2.91914e11	−	5.14723e10i	0.633208	−	0.111652i
$825$		0			0
$826$	4.11850e9	+	3.45583e9i	0.00884747	+	0.00742391i
$827$	−1.18380e11	+	6.83468e10i	−0.253079	+	0.146115i	−0.621173	−	0.783673i	$-0.713344\pi$
$827$	−1.18380e11	+	6.83468e10i	−0.253079	+	0.146115i	0.368094	+	0.929789i	$0.380010\pi$
$828$		0			0
$829$	7.12170e10	−	1.23352e11i	0.150788	−	0.261172i	−0.780730	−	0.624869i	$-0.785152\pi$
$829$	7.12170e10	−	1.23352e11i	0.150788	−	0.261172i	0.931517	+	0.363697i	$0.118486\pi$
$830$	−3.75256e10	−	1.03101e11i	−0.0790705	−	0.217245i
$831$		0			0
$832$	6.23017e11	−	5.22773e11i	1.30019	−	1.09099i
$833$	1.53839e11	−	4.22668e11i	0.319510	−	0.877848i
$834$		0			0
$835$	−5.04845e10	+	2.86312e11i	−0.103851	+	0.588971i
$836$		−	1.25705e11i		−	0.257352i
$837$		0			0
$838$	7.52439e11			1.52579
$839$	−2.90620e11	−	5.12441e10i	−0.586512	−	0.103418i	−0.127486	−	0.991840i	$-0.540691\pi$
$839$	−2.90620e11	−	5.12441e10i	−0.586512	−	0.103418i	−0.459027	+	0.888422i	$0.651802\pi$
$840$		0			0
$841$	−1.52141e11	−	5.53748e10i	−0.304132	−	0.110695i
$842$	−2.47388e11	−	2.94825e11i	−0.492187	−	0.586565i
$843$		0			0
$844$	−1.11237e12	+	4.04870e11i	−2.19220	+	0.797895i
$845$	2.00357e11	+	1.15676e11i	0.392986	+	0.226891i
$846$		0			0
$847$	5.11065e9	+	8.85191e9i	0.00992985	+	0.0171990i
$848$	1.14298e11	−	1.36215e11i	0.221032	−	0.263415i
$849$		0			0
$850$	−9.56732e10	−	5.42590e11i	−0.183280	−	1.03943i
$851$	−6.92348e11	+	1.22080e11i	−1.32010	+	0.232769i
$852$		0			0
$853$	−3.69467e11	−	3.10020e11i	−0.697878	−	0.585589i	0.223291	−	0.974752i	$-0.428320\pi$
$853$	−3.69467e11	−	3.10020e11i	−0.697878	−	0.585589i	−0.921169	+	0.389162i	$0.872764\pi$
$854$	2.10775e10	−	1.21691e10i	0.0396267	−	0.0228785i
$855$		0			0
$856$	1.46296e10	−	2.53392e10i	0.0272482	−	0.0471953i
$857$	−1.34367e11	−	3.69170e11i	−0.249097	−	0.684389i	−0.999720	−	0.0236580i	$-0.992469\pi$
$857$	−1.34367e11	−	3.69170e11i	−0.249097	−	0.684389i	0.750623	−	0.660731i	$-0.229754\pi$
$858$		0			0
$859$	5.22766e11	−	4.38652e11i	0.960140	−	0.805653i	−0.0208363	−	0.999783i	$-0.506633\pi$
$859$	5.22766e11	−	4.38652e11i	0.960140	−	0.805653i	0.980976	+	0.194130i	$0.0621884\pi$
$860$	3.56950e11	−	9.80713e11i	0.652550	−	1.79287i
$861$		0			0
$862$	−8.95714e10	+	5.07985e11i	−0.162233	+	0.920072i
$863$			5.66894e11i			1.02202i	0.859575	+	0.511009i	$0.170728\pi$
$863$			5.66894e11i			1.02202i	−0.859575	+	0.511009i	$0.829272\pi$
$864$		0			0
$865$	−3.11696e11			−0.556759
$866$	6.19575e11	+	1.09248e11i	1.10160	+	0.194241i
$867$		0			0
$868$	−5.65670e8	−	2.05887e8i	−0.000996517	−	0.000362702i
$869$	4.24769e10	+	5.06220e10i	0.0744859	+	0.0887688i
$870$		0			0
$871$	1.01786e11	−	3.70469e10i	0.176854	−	0.0643694i
$872$	1.00062e12	+	5.77706e11i	1.73062	+	0.999174i
$873$		0			0
$874$	7.44157e11	+	1.28892e12i	1.27532	+	2.20892i
$875$	−7.26376e9	+	8.65662e9i	−0.0123917	+	0.0147678i
$876$		0			0
$877$	−7.39775e10	−	4.19547e11i	−0.125055	−	0.709222i	−0.981275	−	0.192611i	$-0.938304\pi$
$877$	−7.39775e10	−	4.19547e11i	−0.125055	−	0.709222i	0.856220	−	0.516611i	$-0.172807\pi$
$878$	−1.54823e11	+	2.72994e10i	−0.260530	+	0.0459384i
$879$		0			0
$880$	−1.45086e10	−	1.21741e10i	−0.0241932	−	0.0203005i
$881$	−3.90690e11	+	2.25565e11i	−0.648528	+	0.374428i	−0.787892	−	0.615813i	$-0.788828\pi$
$881$	−3.90690e11	+	2.25565e11i	−0.648528	+	0.374428i	0.139364	+	0.990241i	$0.455494\pi$
$882$		0			0
$883$	4.88112e10	−	8.45435e10i	0.0802929	−	0.139071i	−0.823083	−	0.567921i	$-0.807748\pi$
$883$	4.88112e10	−	8.45435e10i	0.0802929	−	0.139071i	0.903376	+	0.428850i	$0.141081\pi$
$884$	−4.93944e11	−	1.35710e12i	−0.808851	−	2.22230i
$885$		0			0
$886$	−1.11670e12	+	9.37019e11i	−1.81217	+	1.52060i
$887$	−1.65794e11	+	4.55516e11i	−0.267840	+	0.735884i	0.730742	+	0.682653i	$0.239174\pi$
$887$	−1.65794e11	+	4.55516e11i	−0.267840	+	0.735884i	−0.998582	+	0.0532308i	$0.983048\pi$
$888$		0			0
$889$	1.24711e9	−	7.07273e9i	0.00199664	−	0.0113235i
$890$			2.79157e11i			0.444927i
$891$		0			0
$892$	4.78406e11			0.755678
$893$	1.96496e12	+	3.46476e11i	3.08993	+	0.544837i
$894$		0			0
$895$	4.31162e11	+	1.56930e11i	0.671968	+	0.244576i
$896$	1.51132e10	+	1.80112e10i	0.0234490	+	0.0279455i
$897$		0			0
$898$	2.28633e11	−	8.32155e10i	0.351587	−	0.127967i
$899$	1.30265e10	+	7.52088e9i	0.0199430	+	0.0115141i
$900$		0			0
$901$	1.51917e11	+	2.63128e11i	0.230519	+	0.399271i
$902$	1.08769e10	−	1.29626e10i	0.0164316	−	0.0195824i
$903$		0			0
$904$	−2.23629e11	−	1.26826e12i	−0.334854	−	1.89905i
$905$	3.20226e11	−	5.64645e10i	0.477378	−	0.0841747i
$906$		0			0
$907$	−2.27187e11	−	1.90633e11i	−0.335703	−	0.281688i	0.459316	−	0.888273i	$-0.348095\pi$
$907$	−2.27187e11	−	1.90633e11i	−0.335703	−	0.281688i	−0.795019	+	0.606585i	$0.792539\pi$
$908$	−2.14310e12	+	1.23732e12i	−3.15281	+	1.82028i
$909$		0			0
$910$	−9.02580e9	+	1.56332e10i	−0.0131620	+	0.0227972i
$911$	−1.30456e10	−	3.58424e10i	−0.0189404	−	0.0520383i	0.929862	−	0.367908i	$-0.119926\pi$
$911$	−1.30456e10	−	3.58424e10i	−0.0189404	−	0.0520383i	−0.948803	+	0.315870i	$0.897704\pi$
$912$		0			0
$913$	−9.74392e9	+	8.17612e9i	−0.0140233	+	0.0117670i
$914$	−1.68684e11	+	4.63455e11i	−0.241707	+	0.664084i
$915$		0			0
$916$	5.11566e10	−	2.90124e11i	0.0726641	−	0.412099i
$917$			1.45981e10i			0.0206453i
$918$		0			0
$919$	9.13877e11			1.28123			0.640613	−	0.767864i	$-0.278680\pi$
$919$	9.13877e11			1.28123			0.640613	+	0.767864i	$0.278680\pi$
$920$	5.37649e11	+	9.48020e10i	0.750494	+	0.132332i
$921$		0			0
$922$	−1.54275e12	−	5.61516e11i	−2.13488	−	0.777032i
$923$	−2.52880e10	−	3.01371e10i	−0.0348424	−	0.0415235i
$924$		0			0
$925$	−7.09573e11	+	2.58264e11i	−0.969238	+	0.352774i
$926$	−6.14402e11	−	3.54725e11i	−0.835620	−	0.482445i
$927$		0			0
$928$	−1.02915e11	−	1.78253e11i	−0.138767	−	0.240351i
$929$	−5.41065e11	+	6.44816e11i	−0.726418	+	0.865711i	−0.995238	−	0.0974796i	$-0.968922\pi$
$929$	−5.41065e11	+	6.44816e11i	−0.726418	+	0.865711i	0.268820	+	0.963190i	$0.413366\pi$
$930$		0			0
$931$	2.26619e11	+	1.28522e12i	0.301646	+	1.71072i
$932$	2.42108e12	−	4.26901e11i	3.20882	−	0.565801i
$933$		0			0
$934$	−1.54194e12	−	1.29384e12i	−2.02619	−	1.70018i
$935$	2.80264e10	−	1.61810e10i	0.0366708	−	0.0211719i
$936$		0			0
$937$	6.18994e11	−	1.07213e12i	0.803023	−	1.39088i	−0.114595	−	0.993412i	$-0.536557\pi$
$937$	6.18994e11	−	1.07213e12i	0.803023	−	1.39088i	0.917618	−	0.397464i	$-0.130110\pi$
$938$	1.26899e9	+	3.48651e9i	0.00163925	+	0.00450381i
$939$		0			0
$940$	1.18687e12	−	9.95901e11i	1.52017	−	1.27557i
$941$	2.09574e11	−	5.75800e11i	0.267288	−	0.734367i	−0.731341	−	0.682012i	$-0.761105\pi$
$941$	2.09574e11	−	5.75800e11i	0.267288	−	0.734367i	0.998629	−	0.0523549i	$-0.0166727\pi$
$942$		0			0
$943$	−2.27740e10	+	1.29158e11i	−0.0288000	+	0.163333i
$944$		−	1.88029e11i		−	0.236776i
$945$		0			0
$946$	−1.84829e11			−0.230784
$947$	−2.33000e9	−	4.10843e8i	−0.00289706	−	0.000510829i	0.172199	−	0.985062i	$-0.444913\pi$
$947$	−2.33000e9	−	4.10843e8i	−0.00289706	−	0.000510829i	−0.175097	+	0.984551i	$0.556024\pi$
$948$		0			0
$949$	−9.07766e11	−	3.30400e11i	−1.11920	−	0.407357i
$950$	1.02754e12	+	1.22458e12i	1.26156	+	1.50346i
$951$		0			0
$952$	2.19595e10	−	7.99262e9i	0.0267347	−	0.00973063i
$953$	5.08444e11	+	2.93550e11i	0.616413	+	0.355886i	0.775471	−	0.631383i	$-0.217512\pi$
$953$	5.08444e11	+	2.93550e11i	0.616413	+	0.355886i	−0.159058	+	0.987269i	$0.550846\pi$
$954$		0			0
$955$	−1.96434e11	−	3.40233e11i	−0.236158	−	0.409038i
$956$	−2.27739e11	+	2.71409e11i	−0.272650	+	0.324932i
$957$		0			0
$958$	3.69891e11	+	2.09776e12i	0.439149	+	2.49054i
$959$	−1.90202e10	+	3.35377e9i	−0.0224874	+	0.00396514i
$960$		0			0
$961$	−6.52840e11	−	5.47798e11i	−0.765444	−	0.642284i
$962$	−2.61853e12	+	1.51181e12i	−3.05744	+	1.76521i
$963$		0			0
$964$	−7.24748e11	+	1.25530e12i	−0.839226	+	1.45358i
$965$	−2.55709e11	−	7.02555e11i	−0.294875	−	0.810161i
$966$		0			0
$967$	−1.15318e12	+	9.67637e11i	−1.31884	+	1.10664i	−0.332293	+	0.943176i	$0.607822\pi$
$967$	−1.15318e12	+	9.67637e11i	−1.31884	+	1.10664i	−0.986549	+	0.163464i	$0.947733\pi$
$968$	4.54720e11	−	1.24933e12i	0.517896	−	1.42291i
$969$		0			0
$970$	9.05007e10	−	5.13255e11i	0.102227	−	0.579758i
$971$		−	1.51594e12i		−	1.70532i	−0.522468	−	0.852659i	$-0.674989\pi$
$971$		−	1.51594e12i		−	1.70532i	0.522468	−	0.852659i	$-0.325011\pi$
$972$		0			0
$973$	−5.26285e9			−0.00587177
$974$	−2.05084e11	−	3.61619e10i	−0.227875	−	0.0401805i
$975$		0			0
$976$	−7.99863e11	−	2.91126e11i	−0.881488	−	0.320835i
$977$	8.51500e11	+	1.01478e12i	0.934559	+	1.11376i	0.993309	+	0.115491i	$0.0368442\pi$
$977$	8.51500e11	+	1.01478e12i	0.934559	+	1.11376i	−0.0587497	+	0.998273i	$0.518711\pi$
$978$		0			0
$979$	3.04115e10	−	1.10689e10i	0.0331061	−	0.0120496i
$980$	8.77613e11	+	5.06690e11i	0.951478	+	0.549336i
$981$		0			0
$982$	1.27890e12	+	2.21512e12i	1.37528	+	2.38206i
$983$	−2.92069e11	+	3.48074e11i	−0.312803	+	0.372784i	−0.899424	−	0.437078i	$-0.856014\pi$
$983$	−2.92069e11	+	3.48074e11i	−0.312803	+	0.372784i	0.586621	+	0.809862i	$0.300458\pi$
$984$		0			0
$985$	4.75295e10	+	2.69553e11i	0.0504915	+	0.286351i
$986$	−1.21732e12	+	2.14645e11i	−1.28794	+	0.227098i
$987$		0			0
$988$	3.20991e12	+	2.69343e12i	3.36872	+	2.82669i
$989$	1.24060e12	−	7.16262e11i	1.29672	−	0.748664i
$990$		0			0
$991$	−1.84309e11	+	3.19233e11i	−0.191097	+	0.330989i	−0.945614	−	0.325291i	$-0.894538\pi$
$991$	−1.84309e11	+	3.19233e11i	−0.191097	+	0.330989i	0.754517	+	0.656280i	$0.227871\pi$
$992$	−3.12970e9	−	8.59877e9i	−0.00323188	−	0.00887952i
$993$		0			0
$994$	1.03230e9	−	8.66202e8i	0.00105745	−	0.000887306i
$995$	−1.36159e11	+	3.74094e11i	−0.138917	+	0.381671i
$996$		0			0
$997$	−2.63940e11	+	1.49688e12i	−0.267131	+	1.51498i	0.495766	+	0.868456i	$0.334887\pi$
$997$	−2.63940e11	+	1.49688e12i	−0.267131	+	1.51498i	−0.762897	+	0.646520i	$0.776224\pi$
$998$		−	2.16655e11i		−	0.218397i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.2		138
3.2	odd	2		27.9.f.a.2.22	✓	138
27.13	even	9		27.9.f.a.14.22	yes	138
27.14	odd	18	inner	81.9.f.a.71.2		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.22	✓	138	3.2	odd	2
27.9.f.a.14.22	yes	138	27.13	even	9
81.9.f.a.8.2		138	1.1	even	1	trivial
81.9.f.a.71.2		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)

\(f(q)\)	\(=\)	\(q+(-26.8116 - 4.72761i) q^{2} +(455.951 + 165.953i) q^{4} +(-232.968 - 277.641i) q^{5} +(45.0827 - 16.4088i) q^{7} +(-5404.32 - 3120.19i) q^{8} +(4933.68 + 8545.38i) q^{10} +(735.313 - 876.312i) q^{11} +(6621.57 + 37552.8i) q^{13} +(-1286.31 + 226.812i) q^{14} +(34993.7 + 29363.2i) q^{16} +(-67597.9 + 39027.7i) q^{17} +(113236. - 196131. i) q^{19} +(-60146.9 - 165252. i) q^{20} +(-23857.8 + 20019.1i) q^{22} +(82558.0 - 226826. i) q^{23} +(45021.1 - 255328. i) q^{25} -1.03816e6i q^{26} +23278.6 q^{28} +(-572834. - 101006. i) q^{29} +(-24300.0 - 8844.49i) q^{31} +(227456. + 271071. i) q^{32} +(1.99692e6 - 726818. i) q^{34} +(-15058.6 - 8694.08i) q^{35} +(-1.45625e6 - 2.52229e6i) q^{37} +(-3.96328e6 + 4.72325e6i) q^{38} +(392744. + 2.22736e6i) q^{40} +(-535074. + 94347.9i) q^{41} +(4.54620e6 + 3.81472e6i) q^{43} +(480693. - 277528. i) q^{44} +(-3.28586e6 + 5.69128e6i) q^{46} +(3.01327e6 + 8.27890e6i) q^{47} +(-4.41433e6 + 3.70406e6i) q^{49} +(-2.41418e6 + 6.63290e6i) q^{50} +(-3.21287e6 + 1.82211e7i) q^{52} -3.89255e6i q^{53} -414605. q^{55} +(-294840. - 51988.2i) q^{56} +(1.48811e7 + 5.41627e6i) q^{58} +(-2.64580e6 - 3.15314e6i) q^{59} +(-1.75097e7 + 6.37302e6i) q^{61} +(609710. + 352016. i) q^{62} +(-1.06641e7 - 1.84708e7i) q^{64} +(8.88358e6 - 1.05870e7i) q^{65} +(-493265. - 2.79744e6i) q^{67} +(-3.72981e7 + 6.57666e6i) q^{68} +(362643. + 304293. i) q^{70} +(-893484. + 515853. i) q^{71} +(-1.26668e7 + 2.19395e7i) q^{73} +(2.71199e7 + 7.45114e7i) q^{74} +(8.41786e7 - 7.06343e7i) q^{76} +(18770.7 - 51572.1i) q^{77} +(-1.00312e7 + 5.68895e7i) q^{79} -1.65564e7i q^{80} +1.47922e7 q^{82} +(-1.09503e7 - 1.93083e6i) q^{83} +(2.65838e7 + 9.67572e6i) q^{85} +(-1.03856e8 - 1.23771e8i) q^{86} +(-6.70813e6 + 2.44156e6i) q^{88} +(2.45007e7 + 1.41455e7i) q^{89} +(914714. + 1.58433e6i) q^{91} +(7.52848e7 - 8.97209e7i) q^{92} +(-4.16513e7 - 2.36216e8i) q^{94} +(-8.08344e7 + 1.42533e7i) q^{95} +(-4.04609e7 - 3.39507e7i) q^{97} +(1.35867e8 - 7.84427e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 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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