LMFDB - Embedded newform 1053.2.e.j.352.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1053,2,Mod(352,1053)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1053, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1053.352"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1053 = 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1053.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,0,-3,5,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.40824733284$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 351)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$-0.651388 - 1.12824i$ of defining polynomial
Character	$\chi$	$=$	1053.352
Dual form			1053.2.e.j.703.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.651388 - 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(2.15139 - 3.72631i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} -5.60555 q^{10} +(-0.651388 - 1.12824i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(0.651388 - 1.12824i) q^{14} +(1.65139 + 2.86029i) q^{16} -4.30278 q^{17} -5.30278 q^{19} +(-0.651388 - 1.12824i) q^{20} +(-0.848612 + 1.46984i) q^{22} +(1.95416 - 3.38471i) q^{23} +(-6.75694 - 11.7034i) q^{25} +1.30278 q^{26} +0.302776 q^{28} +(0.197224 + 0.341603i) q^{29} +(-3.60555 + 6.24500i) q^{31} +(-0.848612 + 1.46984i) q^{32} +(2.80278 + 4.85455i) q^{34} +4.30278 q^{35} +4.21110 q^{37} +(3.45416 + 5.98279i) q^{38} +(-6.45416 + 11.1789i) q^{40} +(4.50000 - 7.79423i) q^{41} +(-0.348612 - 0.603814i) q^{43} -0.394449 q^{44} -5.09167 q^{46} +(-0.454163 - 0.786634i) q^{47} +(3.00000 - 5.19615i) q^{49} +(-8.80278 + 15.2469i) q^{50} +(0.151388 + 0.262211i) q^{52} +12.9083 q^{53} -5.60555 q^{55} +(-1.50000 - 2.59808i) q^{56} +(0.256939 - 0.445032i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-1.19722 - 2.07365i) q^{61} +9.39445 q^{62} +8.81665 q^{64} +(2.15139 + 3.72631i) q^{65} +(6.75694 - 11.7034i) q^{67} +(-0.651388 + 1.12824i) q^{68} +(-2.80278 - 4.85455i) q^{70} -13.8167 q^{71} -10.9083 q^{73} +(-2.74306 - 4.75112i) q^{74} +(-0.802776 + 1.39045i) q^{76} +(0.651388 - 1.12824i) q^{77} +(6.95416 + 12.0450i) q^{79} +14.2111 q^{80} -11.7250 q^{82} +(-0.197224 - 0.341603i) q^{83} +(-9.25694 + 16.0335i) q^{85} +(-0.454163 + 0.786634i) q^{86} +(1.95416 + 3.38471i) q^{88} -8.60555 q^{89} -1.00000 q^{91} +(-0.591673 - 1.02481i) q^{92} +(-0.591673 + 1.02481i) q^{94} +(-11.4083 + 19.7598i) q^{95} +(7.21110 + 12.4900i) q^{97} -7.81665 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} - 8 q^{10} + q^{11} - 2 q^{13} - q^{14} + 3 q^{16} - 10 q^{17} - 14 q^{19} + q^{20} - 7 q^{22} - 3 q^{23} - 9 q^{25} - 2 q^{26} - 6 q^{28} + 8 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 - 8 * q^10 + q^11 - 2 * q^13 - q^14 + 3 * q^16 - 10 * q^17 - 14 * q^19 + q^20 - 7 * q^22 - 3 * q^23 - 9 * q^25 - 2 * q^26 - 6 * q^28 + 8 * q^29 - 7 * q^32 + 4 * q^34 + 10 * q^35 - 12 * q^37 + 3 * q^38 - 15 * q^40 + 18 * q^41 - 5 * q^43 - 16 * q^44 - 42 * q^46 + 9 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^52 + 30 * q^53 - 8 * q^55 - 6 * q^56 - 17 * q^58 + 6 * q^59 - 12 * q^61 + 52 * q^62 - 8 * q^64 + 5 * q^65 + 9 * q^67 + q^68 - 4 * q^70 - 12 * q^71 - 22 * q^73 - 29 * q^74 + 4 * q^76 - q^77 + 17 * q^79 + 28 * q^80 + 18 * q^82 - 8 * q^83 - 19 * q^85 + 9 * q^86 - 3 * q^88 - 20 * q^89 - 4 * q^91 - 24 * q^92 - 24 * q^94 - 24 * q^95 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times$.

$n$	$326$	$730$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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 $

$2$	−0.651388	−	1.12824i	−0.460601	−	0.797784i	0.538390	−	0.842696i	$-0.319033\pi$
$2$	−0.651388	−	1.12824i	−0.460601	−	0.797784i	−0.998991	+	0.0449118i	$0.985699\pi$
$3$		0			0
$3$		0			0
$4$	0.151388	−	0.262211i	0.0756939	−	0.131106i
$5$	2.15139	−	3.72631i	0.962130	−	1.66646i	0.244994	−	0.969525i	$-0.421214\pi$
$5$	2.15139	−	3.72631i	0.962130	−	1.66646i	0.717136	−	0.696933i	$-0.245453\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$	−5.60555			−1.77263
$11$	−0.651388	−	1.12824i	−0.196401	−	0.340176i	0.750958	−	0.660350i	$-0.229592\pi$
$11$	−0.651388	−	1.12824i	−0.196401	−	0.340176i	−0.947359	+	0.320174i	$0.896259\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	0.651388	−	1.12824i	0.174091	−	0.301534i
$15$		0			0
$16$	1.65139	+	2.86029i	0.412847	+	0.715072i
$17$	−4.30278			−1.04358			−0.521788	−	0.853075i	$-0.674735\pi$
$17$	−4.30278			−1.04358			−0.521788	+	0.853075i	$0.674735\pi$
$18$		0			0
$19$	−5.30278			−1.21654			−0.608270	−	0.793730i	$-0.708136\pi$
$19$	−5.30278			−1.21654			−0.608270	+	0.793730i	$0.708136\pi$
$20$	−0.651388	−	1.12824i	−0.145655	−	0.252281i
$21$		0			0
$22$	−0.848612	+	1.46984i	−0.180925	+	0.313371i
$23$	1.95416	−	3.38471i	0.407471	−	0.705761i	−0.587134	−	0.809489i	$-0.699744\pi$
$23$	1.95416	−	3.38471i	0.407471	−	0.705761i	0.994606	+	0.103729i	$0.0330773\pi$
$24$		0			0
$25$	−6.75694	−	11.7034i	−1.35139	−	2.34067i
$26$	1.30278			0.255495
$27$		0			0
$28$	0.302776			0.0572192
$29$	0.197224	+	0.341603i	0.0366236	+	0.0634340i	0.883756	−	0.467948i	$-0.155006\pi$
$29$	0.197224	+	0.341603i	0.0366236	+	0.0634340i	−0.847133	+	0.531382i	$0.821673\pi$
$30$		0			0
$31$	−3.60555	+	6.24500i	−0.647576	+	1.12163i	0.336124	+	0.941818i	$0.390884\pi$
$31$	−3.60555	+	6.24500i	−0.647576	+	1.12163i	−0.983700	+	0.179817i	$0.942449\pi$
$32$	−0.848612	+	1.46984i	−0.150015	+	0.259833i
$33$		0			0
$34$	2.80278	+	4.85455i	0.480672	+	0.832548i
$35$	4.30278			0.727302
$36$		0			0
$37$	4.21110			0.692301			0.346150	−	0.938179i	$-0.387489\pi$
$37$	4.21110			0.692301			0.346150	+	0.938179i	$0.387489\pi$
$38$	3.45416	+	5.98279i	0.560339	+	0.970536i
$39$		0			0
$40$	−6.45416	+	11.1789i	−1.02049	+	1.76755i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−0.348612	−	0.603814i	−0.0531629	−	0.0920808i	0.838219	−	0.545333i	$-0.183597\pi$
$43$	−0.348612	−	0.603814i	−0.0531629	−	0.0920808i	−0.891382	+	0.453253i	$0.850264\pi$
$44$	−0.394449			−0.0594654
$45$		0			0
$46$	−5.09167			−0.750726
$47$	−0.454163	−	0.786634i	−0.0662465	−	0.114742i	0.831000	−	0.556273i	$-0.187769\pi$
$47$	−0.454163	−	0.786634i	−0.0662465	−	0.114742i	−0.897246	+	0.441530i	$0.854436\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−8.80278	+	15.2469i	−1.24490	+	2.15623i
$51$		0			0
$52$	0.151388	+	0.262211i	0.0209937	+	0.0363622i
$53$	12.9083			1.77310			0.886548	−	0.462638i	$-0.153097\pi$
$53$	12.9083			1.77310			0.886548	+	0.462638i	$0.153097\pi$
$54$		0			0
$55$	−5.60555			−0.755852
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$		0			0
$58$	0.256939	−	0.445032i	0.0337378	−	0.0584355i
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	−1.19722	−	2.07365i	−0.153289	−	0.265504i	0.779146	−	0.626843i	$-0.215653\pi$
$61$	−1.19722	−	2.07365i	−0.153289	−	0.265504i	−0.932435	+	0.361339i	$0.882320\pi$
$62$	9.39445			1.19310
$63$		0			0
$64$	8.81665			1.10208
$65$	2.15139	+	3.72631i	0.266847	+	0.462192i
$66$		0			0
$67$	6.75694	−	11.7034i	0.825491	−	1.42979i	−0.0760516	−	0.997104i	$-0.524231\pi$
$67$	6.75694	−	11.7034i	0.825491	−	1.42979i	0.901543	−	0.432689i	$-0.142435\pi$
$68$	−0.651388	+	1.12824i	−0.0789924	+	0.136819i
$69$		0			0
$70$	−2.80278	−	4.85455i	−0.334996	−	0.580230i
$71$	−13.8167			−1.63974			−0.819868	−	0.572553i	$-0.805953\pi$
$71$	−13.8167			−1.63974			−0.819868	+	0.572553i	$0.805953\pi$
$72$		0			0
$73$	−10.9083			−1.27672			−0.638362	−	0.769737i	$-0.720388\pi$
$73$	−10.9083			−1.27672			−0.638362	+	0.769737i	$0.720388\pi$
$74$	−2.74306	−	4.75112i	−0.318874	−	0.552307i
$75$		0			0
$76$	−0.802776	+	1.39045i	−0.0920847	+	0.159495i
$77$	0.651388	−	1.12824i	0.0742325	−	0.128575i
$78$		0			0
$79$	6.95416	+	12.0450i	0.782405	+	1.35516i	0.930537	+	0.366197i	$0.119340\pi$
$79$	6.95416	+	12.0450i	0.782405	+	1.35516i	−0.148133	+	0.988967i	$0.547326\pi$
$80$	14.2111			1.58885
$81$		0			0
$82$	−11.7250			−1.29481
$83$	−0.197224	−	0.341603i	−0.0216482	−	0.0374958i	0.854998	−	0.518631i	$-0.173558\pi$
$83$	−0.197224	−	0.341603i	−0.0216482	−	0.0374958i	−0.876647	+	0.481135i	$0.840225\pi$
$84$		0			0
$85$	−9.25694	+	16.0335i	−1.00406	+	1.73908i
$86$	−0.454163	+	0.786634i	−0.0489737	+	0.0848249i
$87$		0			0
$88$	1.95416	+	3.38471i	0.208315	+	0.360811i
$89$	−8.60555			−0.912187			−0.456093	−	0.889932i	$-0.650752\pi$
$89$	−8.60555			−0.912187			−0.456093	+	0.889932i	$0.650752\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$	−0.591673	−	1.02481i	−0.0616862	−	0.106844i
$93$		0			0
$94$	−0.591673	+	1.02481i	−0.0610264	+	0.105701i
$95$	−11.4083	+	19.7598i	−1.17047	+	2.02731i
$96$		0			0
$97$	7.21110	+	12.4900i	0.732177	+	1.26817i	0.955951	+	0.293526i	$0.0948287\pi$
$97$	7.21110	+	12.4900i	0.732177	+	1.26817i	−0.223775	+	0.974641i	$0.571838\pi$
$98$	−7.81665			−0.789601
$99$		0			0
$100$	−4.09167			−0.409167
$101$	−5.40833	−	9.36750i	−0.538149	−	0.932101i	−0.999004	−	0.0446254i	$-0.985791\pi$
$101$	−5.40833	−	9.36750i	−0.538149	−	0.932101i	0.460855	−	0.887475i	$-0.347543\pi$
$102$		0			0
$103$	−2.75694	+	4.77516i	−0.271649	+	0.470510i	−0.969284	−	0.245943i	$-0.920902\pi$
$103$	−2.75694	+	4.77516i	−0.271649	+	0.470510i	0.697635	+	0.716453i	$0.254236\pi$
$104$	1.50000	−	2.59808i	0.147087	−	0.254762i
$105$		0			0
$106$	−8.40833	−	14.5636i	−0.816689	−	1.41455i
$107$	9.90833			0.957874			0.478937	−	0.877849i	$-0.341022\pi$
$107$	9.90833			0.957874			0.478937	+	0.877849i	$0.341022\pi$
$108$		0			0
$109$	1.48612			0.142345			0.0711723	−	0.997464i	$-0.477326\pi$
$109$	1.48612			0.142345			0.0711723	+	0.997464i	$0.477326\pi$
$110$	3.65139	+	6.32439i	0.348146	+	0.603007i
$111$		0			0
$112$	−1.65139	+	2.86029i	−0.156041	+	0.270272i
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$		0			0
$115$	−8.40833	−	14.5636i	−0.784081	−	1.35807i
$116$	0.119429			0.0110887
$117$		0			0
$118$	−3.90833			−0.359791
$119$	−2.15139	−	3.72631i	−0.197217	−	0.341591i
$120$		0			0
$121$	4.65139	−	8.05644i	0.422853	−	0.732404i
$122$	−1.55971	+	2.70151i	−0.141210	+	0.244583i
$123$		0			0
$124$	1.09167	+	1.89083i	0.0980351	+	0.169802i
$125$	−36.6333			−3.27658
$126$		0			0
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	−4.04584	−	7.00759i	−0.357605	−	0.619390i
$129$		0			0
$130$	2.80278	−	4.85455i	0.245820	−	0.425772i
$131$	−7.10555	+	12.3072i	−0.620815	+	1.07528i	0.368519	+	0.929620i	$0.379865\pi$
$131$	−7.10555	+	12.3072i	−0.620815	+	1.07528i	−0.989334	+	0.145663i	$0.953469\pi$
$132$		0			0
$133$	−2.65139	−	4.59234i	−0.229904	−	0.398206i
$134$	−17.6056			−1.52089
$135$		0			0
$136$	12.9083			1.10688
$137$	−3.90833	−	6.76942i	−0.333911	−	0.578351i	0.649364	−	0.760478i	$-0.275035\pi$
$137$	−3.90833	−	6.76942i	−0.333911	−	0.578351i	−0.983275	+	0.182127i	$0.941702\pi$
$138$		0			0
$139$	7.01388	−	12.1484i	0.594909	−	1.03041i	−0.398650	−	0.917103i	$-0.630521\pi$
$139$	7.01388	−	12.1484i	0.594909	−	1.03041i	0.993560	−	0.113310i	$-0.0361454\pi$
$140$	0.651388	−	1.12824i	0.0550523	−	0.0953534i
$141$		0			0
$142$	9.00000	+	15.5885i	0.755263	+	1.30815i
$143$	1.30278			0.108944
$144$		0			0
$145$	1.69722			0.140947
$146$	7.10555	+	12.3072i	0.588060	+	1.01855i
$147$		0			0
$148$	0.637510	−	1.10420i	0.0524030	−	0.0907646i
$149$	4.04584	−	7.00759i	0.331448	−	0.574085i	−0.651348	−	0.758779i	$-0.725796\pi$
$149$	4.04584	−	7.00759i	0.331448	−	0.574085i	0.982796	+	0.184695i	$0.0591296\pi$
$150$		0			0
$151$	−5.10555	−	8.84307i	−0.415484	−	0.719639i	0.579995	−	0.814620i	$-0.303054\pi$
$151$	−5.10555	−	8.84307i	−0.415484	−	0.719639i	−0.995479	+	0.0949807i	$0.969721\pi$
$152$	15.9083			1.29034
$153$		0			0
$154$	−1.69722			−0.136766
$155$	15.5139	+	26.8708i	1.24610	+	2.15832i
$156$		0			0
$157$	5.65139	−	9.78849i	0.451030	−	0.781207i	−0.547420	−	0.836858i	$-0.684390\pi$
$157$	5.65139	−	9.78849i	0.451030	−	0.781207i	0.998450	+	0.0556511i	$0.0177235\pi$
$158$	9.05971	−	15.6919i	0.720752	−	1.24838i
$159$		0			0
$160$	3.65139	+	6.32439i	0.288668	+	0.499987i
$161$	3.90833			0.308019
$162$		0			0
$163$	22.7250			1.77996			0.889979	−	0.456002i	$-0.150719\pi$
$163$	22.7250			1.77996			0.889979	+	0.456002i	$0.150719\pi$
$164$	−1.36249	−	2.35990i	−0.106393	−	0.184277i
$165$		0			0
$166$	−0.256939	+	0.445032i	−0.0199423	+	0.0345411i
$167$	−10.1056	+	17.5033i	−0.781991	+	1.35445i	0.148789	+	0.988869i	$0.452462\pi$
$167$	−10.1056	+	17.5033i	−0.781991	+	1.35445i	−0.930780	+	0.365579i	$0.880871\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	24.1194			1.84988
$171$		0			0
$172$	−0.211103			−0.0160964
$173$	1.95416	+	3.38471i	0.148572	+	0.257335i	0.930700	−	0.365783i	$-0.119199\pi$
$173$	1.95416	+	3.38471i	0.148572	+	0.257335i	−0.782128	+	0.623118i	$0.785866\pi$
$174$		0			0
$175$	6.75694	−	11.7034i	0.510777	−	0.884691i
$176$	2.15139	−	3.72631i	0.162167	−	0.280881i
$177$		0			0
$178$	5.60555	+	9.70910i	0.420154	+	0.727728i
$179$	−3.51388			−0.262640			−0.131320	−	0.991340i	$-0.541921\pi$
$179$	−3.51388			−0.262640			−0.131320	+	0.991340i	$0.541921\pi$
$180$		0			0
$181$	−3.09167			−0.229802			−0.114901	−	0.993377i	$-0.536655\pi$
$181$	−3.09167			−0.229802			−0.114901	+	0.993377i	$0.536655\pi$
$182$	0.651388	+	1.12824i	0.0482841	+	0.0836305i
$183$		0			0
$184$	−5.86249	+	10.1541i	−0.432189	+	0.748572i
$185$	9.05971	−	15.6919i	0.666083	−	1.15369i
$186$		0			0
$187$	2.80278	+	4.85455i	0.204959	+	0.355000i
$188$	−0.275019			−0.0200578
$189$		0			0
$190$	29.7250			2.15648
$191$	−0.848612	−	1.46984i	−0.0614034	−	0.106354i	0.833690	−	0.552233i	$-0.186224\pi$
$191$	−0.848612	−	1.46984i	−0.0614034	−	0.106354i	−0.895093	+	0.445880i	$0.852891\pi$
$192$		0			0
$193$	5.65139	−	9.78849i	0.406796	−	0.704591i	−0.587733	−	0.809055i	$-0.699979\pi$
$193$	5.65139	−	9.78849i	0.406796	−	0.704591i	0.994529	+	0.104464i	$0.0333127\pi$
$194$	9.39445	−	16.2717i	0.674482	−	1.16824i
$195$		0			0
$196$	−0.908327	−	1.57327i	−0.0648805	−	0.112376i
$197$	−1.81665			−0.129431			−0.0647156	−	0.997904i	$-0.520614\pi$
$197$	−1.81665			−0.129431			−0.0647156	+	0.997904i	$0.520614\pi$
$198$		0			0
$199$	7.09167			0.502715			0.251358	−	0.967894i	$-0.419123\pi$
$199$	7.09167			0.502715			0.251358	+	0.967894i	$0.419123\pi$
$200$	20.2708	+	35.1101i	1.43336	+	2.48266i
$201$		0			0
$202$	−7.04584	+	12.2037i	−0.495743	+	0.858653i
$203$	−0.197224	+	0.341603i	−0.0138424	+	0.0239758i
$204$		0			0
$205$	−19.3625	−	33.5368i	−1.35233	−	2.34231i
$206$	7.18335			0.500487
$207$		0			0
$208$	−3.30278			−0.229006
$209$	3.45416	+	5.98279i	0.238929	+	0.413838i
$210$		0			0
$211$	−5.55971	+	9.62971i	−0.382747	+	0.662936i	−0.991454	−	0.130458i	$-0.958355\pi$
$211$	−5.55971	+	9.62971i	−0.382747	+	0.662936i	0.608707	+	0.793395i	$0.291688\pi$
$212$	1.95416	−	3.38471i	0.134212	−	0.232463i
$213$		0			0
$214$	−6.45416	−	11.1789i	−0.441198	−	0.764177i
$215$	−3.00000			−0.204598
$216$		0			0
$217$	−7.21110			−0.489522
$218$	−0.968042	−	1.67670i	−0.0655641	−	0.113560i
$219$		0			0
$220$	−0.848612	+	1.46984i	−0.0572134	+	0.0990966i
$221$	2.15139	−	3.72631i	0.144718	−	0.250659i
$222$		0			0
$223$	9.16527	+	15.8747i	0.613752	+	1.06305i	0.990602	+	0.136775i	$0.0436737\pi$
$223$	9.16527	+	15.8747i	0.613752	+	1.06305i	−0.376851	+	0.926274i	$0.622993\pi$
$224$	−1.69722			−0.113401
$225$		0			0
$226$	−3.90833			−0.259978
$227$	−3.05971	−	5.29958i	−0.203080	−	0.351746i	0.746439	−	0.665454i	$-0.231762\pi$
$227$	−3.05971	−	5.29958i	−0.203080	−	0.351746i	−0.949519	+	0.313708i	$0.898429\pi$
$228$		0			0
$229$	3.95416	−	6.84881i	0.261298	−	0.452582i	−0.705289	−	0.708920i	$-0.749183\pi$
$229$	3.95416	−	6.84881i	0.261298	−	0.452582i	0.966587	+	0.256338i	$0.0825160\pi$
$230$	−10.9542	+	18.9732i	−0.722296	+	1.25105i
$231$		0			0
$232$	−0.591673	−	1.02481i	−0.0388452	−	0.0672819i
$233$	10.0278			0.656940			0.328470	−	0.944514i	$-0.393467\pi$
$233$	10.0278			0.656940			0.328470	+	0.944514i	$0.393467\pi$
$234$		0			0
$235$	−3.90833			−0.254951
$236$	−0.454163	−	0.786634i	−0.0295635	−	0.0512055i
$237$		0			0
$238$	−2.80278	+	4.85455i	−0.181677	+	0.314674i
$239$	2.40833	−	4.17134i	0.155782	−	0.269822i	−0.777562	−	0.628807i	$-0.783544\pi$
$239$	2.40833	−	4.17134i	0.155782	−	0.269822i	0.933343	+	0.358985i	$0.116877\pi$
$240$		0			0
$241$	5.25694	+	9.10529i	0.338629	+	0.586523i	0.984175	−	0.177198i	$-0.0567034\pi$
$241$	5.25694	+	9.10529i	0.338629	+	0.586523i	−0.645546	+	0.763721i	$0.723370\pi$
$242$	−12.1194			−0.779066
$243$		0			0
$244$	−0.724981			−0.0464121
$245$	−12.9083	−	22.3579i	−0.824683	−	1.42839i
$246$		0			0
$247$	2.65139	−	4.59234i	0.168704	−	0.292203i
$248$	10.8167	−	18.7350i	0.686858	−	1.18967i
$249$		0			0
$250$	23.8625	+	41.3310i	1.50920	+	2.61400i
$251$	−0.908327			−0.0573331			−0.0286665	−	0.999589i	$-0.509126\pi$
$251$	−0.908327			−0.0573331			−0.0286665	+	0.999589i	$0.509126\pi$
$252$		0			0
$253$	−5.09167			−0.320111
$254$	−7.16527	−	12.4106i	−0.449589	−	0.778711i
$255$		0			0
$256$	3.54584	−	6.14157i	0.221615	−	0.383848i
$257$	3.65139	−	6.32439i	0.227767	−	0.394505i	−0.729379	−	0.684110i	$-0.760191\pi$
$257$	3.65139	−	6.32439i	0.227767	−	0.394505i	0.957146	+	0.289606i	$0.0935241\pi$
$258$		0			0
$259$	2.10555	+	3.64692i	0.130833	+	0.226609i
$260$	1.30278			0.0807947
$261$		0			0
$262$	18.5139			1.14379
$263$	−8.54584	−	14.8018i	−0.526959	−	0.912720i	−0.999506	−	0.0314144i	$-0.989999\pi$
$263$	−8.54584	−	14.8018i	−0.526959	−	0.912720i	0.472548	−	0.881305i	$-0.343334\pi$
$264$		0			0
$265$	27.7708	−	48.1005i	1.70595	−	2.95479i
$266$	−3.45416	+	5.98279i	−0.211788	+	0.366828i
$267$		0			0
$268$	−2.04584	−	3.54349i	−0.124969	−	0.216453i
$269$	16.9361			1.03261			0.516306	−	0.856404i	$-0.327307\pi$
$269$	16.9361			1.03261			0.516306	+	0.856404i	$0.327307\pi$
$270$		0			0
$271$	15.4222			0.936832			0.468416	−	0.883508i	$-0.344825\pi$
$271$	15.4222			0.936832			0.468416	+	0.883508i	$0.344825\pi$
$272$	−7.10555	−	12.3072i	−0.430837	−	0.746232i
$273$		0			0
$274$	−5.09167	+	8.81904i	−0.307599	+	0.532777i
$275$	−8.80278	+	15.2469i	−0.530827	+	0.919420i
$276$		0			0
$277$	8.90833	+	15.4297i	0.535249	+	0.927079i	0.999151	+	0.0411926i	$0.0131157\pi$
$277$	8.90833	+	15.4297i	0.535249	+	0.927079i	−0.463902	+	0.885887i	$0.653551\pi$
$278$	−18.2750			−1.09606
$279$		0			0
$280$	−12.9083			−0.771420
$281$	−5.21110	−	9.02589i	−0.310868	−	0.538440i	0.667682	−	0.744446i	$-0.267286\pi$
$281$	−5.21110	−	9.02589i	−0.310868	−	0.538440i	−0.978551	+	0.206007i	$0.933953\pi$
$282$		0			0
$283$	6.24306	−	10.8133i	0.371111	−	0.642784i	−0.618625	−	0.785686i	$-0.712310\pi$
$283$	6.24306	−	10.8133i	0.371111	−	0.642784i	0.989737	+	0.142902i	$0.0456434\pi$
$284$	−2.09167	+	3.62288i	−0.124118	+	0.214979i
$285$		0			0
$286$	−0.848612	−	1.46984i	−0.0501795	−	0.0869134i
$287$	9.00000			0.531253
$288$		0			0
$289$	1.51388			0.0890517
$290$	−1.10555	−	1.91487i	−0.0649202	−	0.112445i
$291$		0			0
$292$	−1.65139	+	2.86029i	−0.0966402	+	0.167386i
$293$	9.31665	−	16.1369i	0.544285	−	0.942729i	−0.454367	−	0.890815i	$-0.650134\pi$
$293$	9.31665	−	16.1369i	0.544285	−	0.942729i	0.998652	−	0.0519141i	$-0.0165322\pi$
$294$		0			0
$295$	−6.45416	−	11.1789i	−0.375776	−	0.650863i
$296$	−12.6333			−0.734296
$297$		0			0
$298$	−10.5416			−0.610660
$299$	1.95416	+	3.38471i	0.113012	+	0.195743i
$300$		0			0
$301$	0.348612	−	0.603814i	0.0200937	−	0.0348033i
$302$	−6.65139	+	11.5205i	−0.382744	+	0.662933i
$303$		0			0
$304$	−8.75694	−	15.1675i	−0.502245	−	0.869914i
$305$	−10.3028			−0.589935
$306$		0			0
$307$	7.09167			0.404743			0.202372	−	0.979309i	$-0.435135\pi$
$307$	7.09167			0.404743			0.202372	+	0.979309i	$0.435135\pi$
$308$	−0.197224	−	0.341603i	−0.0112379	−	0.0194646i
$309$		0			0
$310$	20.2111	−	35.0067i	1.14791	−	1.98824i
$311$	−3.45416	+	5.98279i	−0.195868	+	0.339253i	−0.947185	−	0.320689i	$-0.896086\pi$
$311$	−3.45416	+	5.98279i	−0.195868	+	0.339253i	0.751317	+	0.659942i	$0.229419\pi$
$312$		0			0
$313$	−2.30278	−	3.98852i	−0.130161	−	0.225445i	0.793578	−	0.608469i	$-0.208216\pi$
$313$	−2.30278	−	3.98852i	−0.130161	−	0.225445i	−0.923738	+	0.383024i	$0.874883\pi$
$314$	−14.7250			−0.830979
$315$		0			0
$316$	4.21110			0.236893
$317$	0.0597147	+	0.103429i	0.00335391	+	0.00580915i	0.867697	−	0.497093i	$-0.165599\pi$
$317$	0.0597147	+	0.103429i	0.00335391	+	0.00580915i	−0.864344	+	0.502902i	$0.832266\pi$
$318$		0			0
$319$	0.256939	−	0.445032i	0.0143858	−	0.0249170i
$320$	18.9680	−	32.8536i	1.06035	−	1.83657i
$321$		0			0
$322$	−2.54584	−	4.40952i	−0.141874	−	0.245733i
$323$	22.8167			1.26955
$324$		0			0
$325$	13.5139			0.749615
$326$	−14.8028	−	25.6392i	−0.819850	−	1.42002i
$327$		0			0
$328$	−13.5000	+	23.3827i	−0.745413	+	1.29109i
$329$	0.454163	−	0.786634i	0.0250388	−	0.0433685i
$330$		0			0
$331$	−7.31665	−	12.6728i	−0.402160	−	0.696561i	0.591827	−	0.806065i	$-0.298407\pi$
$331$	−7.31665	−	12.6728i	−0.402160	−	0.696561i	−0.993986	+	0.109504i	$0.965074\pi$
$332$	−0.119429			−0.00655454
$333$		0			0
$334$	26.3305			1.44074
$335$	−29.0736	−	50.3569i	−1.58846	−	2.75129i
$336$		0			0
$337$	−0.802776	+	1.39045i	−0.0437300	+	0.0757425i	−0.887062	−	0.461650i	$-0.847257\pi$
$337$	−0.802776	+	1.39045i	−0.0437300	+	0.0757425i	0.843332	+	0.537393i	$0.180591\pi$
$338$	−0.651388	+	1.12824i	−0.0354308	+	0.0613680i
$339$		0			0
$340$	2.80278	+	4.85455i	0.152002	+	0.263275i
$341$	9.39445			0.508738
$342$		0			0
$343$	13.0000			0.701934
$344$	1.04584	+	1.81144i	0.0563877	+	0.0976664i
$345$		0			0
$346$	2.54584	−	4.40952i	0.136865	−	0.237057i
$347$	−7.50000	+	12.9904i	−0.402621	+	0.697360i	−0.994041	−	0.109003i	$-0.965234\pi$
$347$	−7.50000	+	12.9904i	−0.402621	+	0.697360i	0.591420	+	0.806363i	$0.298567\pi$
$348$		0			0
$349$	−3.15139	−	5.45836i	−0.168690	−	0.292180i	0.769270	−	0.638924i	$-0.220620\pi$
$349$	−3.15139	−	5.45836i	−0.168690	−	0.292180i	−0.937960	+	0.346745i	$0.887287\pi$
$350$	−17.6056			−0.941056
$351$		0			0
$352$	2.21110			0.117852
$353$	1.89445	+	3.28128i	0.100831	+	0.174645i	0.912027	−	0.410129i	$-0.134516\pi$
$353$	1.89445	+	3.28128i	0.100831	+	0.174645i	−0.811196	+	0.584774i	$0.801183\pi$
$354$		0			0
$355$	−29.7250	+	51.4852i	−1.57764	+	2.73255i
$356$	−1.30278	+	2.25647i	−0.0690470	+	0.119593i
$357$		0			0
$358$	2.28890	+	3.96449i	0.120972	+	0.209530i
$359$	1.18335			0.0624546			0.0312273	−	0.999512i	$-0.490058\pi$
$359$	1.18335			0.0624546			0.0312273	+	0.999512i	$0.490058\pi$
$360$		0			0
$361$	9.11943			0.479970
$362$	2.01388	+	3.48814i	0.105847	+	0.183333i
$363$		0			0
$364$	−0.151388	+	0.262211i	−0.00793488	+	0.0137436i
$365$	−23.4680	+	40.6478i	−1.22837	+	2.12761i
$366$		0			0
$367$	−0.0138782	−	0.0240377i	−0.000724436	−	0.00125476i	0.865663	−	0.500627i	$-0.166897\pi$
$367$	−0.0138782	−	0.0240377i	−0.000724436	−	0.00125476i	−0.866387	+	0.499372i	$0.833564\pi$
$368$	12.9083			0.672893
$369$		0			0
$370$	−23.6056			−1.22719
$371$	6.45416	+	11.1789i	0.335083	+	0.580382i
$372$		0			0
$373$	−10.0597	+	17.4239i	−0.520872	+	0.902177i	0.478833	+	0.877906i	$0.341060\pi$
$373$	−10.0597	+	17.4239i	−0.520872	+	0.902177i	−0.999705	+	0.0242713i	$0.992273\pi$
$374$	3.65139	−	6.32439i	0.188809	−	0.327026i
$375$		0			0
$376$	1.36249	+	2.35990i	0.0702651	+	0.121703i
$377$	−0.394449			−0.0203151
$378$		0			0
$379$	−18.2111			−0.935442			−0.467721	−	0.883876i	$-0.654925\pi$
$379$	−18.2111			−0.935442			−0.467721	+	0.883876i	$0.654925\pi$
$380$	3.45416	+	5.98279i	0.177195	+	0.306910i
$381$		0			0
$382$	−1.10555	+	1.91487i	−0.0565649	+	0.0979733i
$383$	11.6056	−	20.1014i	0.593016	−	1.02713i	−0.400808	−	0.916162i	$-0.631270\pi$
$383$	11.6056	−	20.1014i	0.593016	−	1.02713i	0.993824	−	0.110972i	$-0.0353962\pi$
$384$		0			0
$385$	−2.80278	−	4.85455i	−0.142843	−	0.247411i
$386$	−14.7250			−0.749482
$387$		0			0
$388$	4.36669			0.221685
$389$	12.1194	+	20.9915i	0.614479	+	1.06431i	0.990476	+	0.137688i	$0.0439673\pi$
$389$	12.1194	+	20.9915i	0.614479	+	1.06431i	−0.375996	+	0.926621i	$0.622699\pi$
$390$		0			0
$391$	−8.40833	+	14.5636i	−0.425227	+	0.736515i
$392$	−9.00000	+	15.5885i	−0.454569	+	0.787336i
$393$		0			0
$394$	1.18335	+	2.04962i	0.0596161	+	0.103258i
$395$	59.8444			3.01110
$396$		0			0
$397$	−22.6333			−1.13593			−0.567967	−	0.823052i	$-0.692270\pi$
$397$	−22.6333			−1.13593			−0.567967	+	0.823052i	$0.692270\pi$
$398$	−4.61943	−	8.00109i	−0.231551	−	0.401058i
$399$		0			0
$400$	22.3167	−	38.6536i	1.11583	−	1.93268i
$401$	16.3028	−	28.2372i	0.814122	−	1.41010i	−0.0958350	−	0.995397i	$-0.530552\pi$
$401$	16.3028	−	28.2372i	0.814122	−	1.41010i	0.909957	−	0.414703i	$-0.136115\pi$
$402$		0			0
$403$	−3.60555	−	6.24500i	−0.179605	−	0.311086i
$404$	−3.27502			−0.162938
$405$		0			0
$406$	0.513878			0.0255033
$407$	−2.74306	−	4.75112i	−0.135968	−	0.235504i
$408$		0			0
$409$	−3.60555	+	6.24500i	−0.178283	+	0.308795i	−0.941293	−	0.337592i	$-0.890388\pi$
$409$	−3.60555	+	6.24500i	−0.178283	+	0.308795i	0.763010	+	0.646387i	$0.223721\pi$
$410$	−25.2250	+	43.6909i	−1.24577	+	2.15774i
$411$		0			0
$412$	0.834734	+	1.44580i	0.0411244	+	0.0712295i
$413$	3.00000			0.147620
$414$		0			0
$415$	−1.69722			−0.0833135
$416$	−0.848612	−	1.46984i	−0.0416066	−	0.0720648i
$417$		0			0
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	12.3944	−	21.4678i	0.605508	−	1.04877i	−0.386462	−	0.922305i	$-0.626303\pi$
$419$	12.3944	−	21.4678i	0.605508	−	1.04877i	0.991971	−	0.126466i	$-0.0403635\pi$
$420$		0			0
$421$	−16.9083	−	29.2861i	−0.824061	−	1.42732i	−0.902634	−	0.430408i	$-0.858370\pi$
$421$	−16.9083	−	29.2861i	−0.824061	−	1.42732i	0.0785731	−	0.996908i	$-0.474964\pi$
$422$	14.4861			0.705173
$423$		0			0
$424$	−38.7250			−1.88065
$425$	29.0736	+	50.3569i	1.41028	+	2.44267i
$426$		0			0
$427$	1.19722	−	2.07365i	0.0579377	−	0.100351i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$		0			0
$430$	1.95416	+	3.38471i	0.0942381	+	0.163225i
$431$	−28.8167			−1.38805			−0.694025	−	0.719951i	$-0.744164\pi$
$431$	−28.8167			−1.38805			−0.694025	+	0.719951i	$0.744164\pi$
$432$		0			0
$433$	−9.88057			−0.474830			−0.237415	−	0.971408i	$-0.576300\pi$
$433$	−9.88057			−0.474830			−0.237415	+	0.971408i	$0.576300\pi$
$434$	4.69722	+	8.13583i	0.225474	+	0.390532i
$435$		0			0
$436$	0.224981	−	0.389678i	0.0107746	−	0.0186622i
$437$	−10.3625	+	17.9484i	−0.495705	+	0.858586i
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$	16.8167			0.801703
$441$		0			0
$442$	−5.60555			−0.266629
$443$	11.0139	+	19.0766i	0.523285	+	0.906356i	0.999633	+	0.0270994i	$0.00862706\pi$
$443$	11.0139	+	19.0766i	0.523285	+	0.906356i	−0.476348	+	0.879257i	$0.658040\pi$
$444$		0			0
$445$	−18.5139	+	32.0670i	−0.877642	+	1.52012i
$446$	11.9403	−	20.6812i	0.565389	−	0.979282i
$447$		0			0
$448$	4.40833	+	7.63545i	0.208274	+	0.360741i
$449$	−29.6056			−1.39717			−0.698586	−	0.715526i	$-0.746187\pi$
$449$	−29.6056			−1.39717			−0.698586	+	0.715526i	$0.746187\pi$
$450$		0			0
$451$	−11.7250			−0.552108
$452$	−0.454163	−	0.786634i	−0.0213621	−	0.0370002i
$453$		0			0
$454$	−3.98612	+	6.90417i	−0.187078	+	0.324029i
$455$	−2.15139	+	3.72631i	−0.100859	+	0.174692i
$456$		0			0
$457$	−17.5000	−	30.3109i	−0.818615	−	1.41788i	−0.906702	−	0.421771i	$-0.861409\pi$
$457$	−17.5000	−	30.3109i	−0.818615	−	1.41788i	0.0880870	−	0.996113i	$-0.471925\pi$
$458$	−10.3028			−0.481417
$459$		0			0
$460$	−5.09167			−0.237400
$461$	13.1653	+	22.8029i	0.613168	+	1.06204i	0.990703	+	0.136042i	$0.0434383\pi$
$461$	13.1653	+	22.8029i	0.613168	+	1.06204i	−0.377535	+	0.925995i	$0.623228\pi$
$462$		0			0
$463$	11.2569	−	19.4976i	0.523154	−	0.906130i	−0.476483	−	0.879184i	$-0.658088\pi$
$463$	11.2569	−	19.4976i	0.523154	−	0.906130i	0.999637	−	0.0269460i	$-0.00857820\pi$
$464$	−0.651388	+	1.12824i	−0.0302399	+	0.0523771i
$465$		0			0
$466$	−6.53196	−	11.3137i	−0.302587	−	0.524096i
$467$	16.8167			0.778182			0.389091	−	0.921199i	$-0.372789\pi$
$467$	16.8167			0.778182			0.389091	+	0.921199i	$0.372789\pi$
$468$		0			0
$469$	13.5139			0.624013
$470$	2.54584	+	4.40952i	0.117431	+	0.203396i
$471$		0			0
$472$	−4.50000	+	7.79423i	−0.207129	+	0.358758i
$473$	−0.454163	+	0.786634i	−0.0208825	+	0.0361695i
$474$		0			0
$475$	35.8305	+	62.0603i	1.64402	+	2.84752i
$476$	−1.30278			−0.0597126
$477$		0			0
$478$	−6.27502			−0.287013
$479$	8.86249	+	15.3503i	0.404938	+	0.701372i	0.994314	−	0.106486i	$-0.0339599\pi$
$479$	8.86249	+	15.3503i	0.404938	+	0.701372i	−0.589377	+	0.807858i	$0.700627\pi$
$480$		0			0
$481$	−2.10555	+	3.64692i	−0.0960049	+	0.166285i
$482$	6.84861	−	11.8621i	0.311946	−	0.540306i
$483$		0			0
$484$	−1.40833	−	2.43929i	−0.0640149	−	0.110877i
$485$	62.0555			2.81780
$486$		0			0
$487$	42.4222			1.92233			0.961167	−	0.275968i	$-0.0889984\pi$
$487$	42.4222			1.92233			0.961167	+	0.275968i	$0.0889984\pi$
$488$	3.59167	+	6.22096i	0.162587	+	0.281610i
$489$		0			0
$490$	−16.8167	+	29.1273i	−0.759699	+	1.31584i
$491$	−19.9542	+	34.5616i	−0.900519	+	1.55974i	−0.0736967	+	0.997281i	$0.523480\pi$
$491$	−19.9542	+	34.5616i	−0.900519	+	1.55974i	−0.826822	+	0.562464i	$0.809854\pi$
$492$		0			0
$493$	−0.848612	−	1.46984i	−0.0382196	−	0.0661982i
$494$	−6.90833			−0.310820
$495$		0			0
$496$	−23.8167			−1.06940
$497$	−6.90833	−	11.9656i	−0.309881	−	0.536729i
$498$		0			0
$499$	−8.44029	+	14.6190i	−0.377839	+	0.654436i	−0.990748	−	0.135717i	$-0.956666\pi$
$499$	−8.44029	+	14.6190i	−0.377839	+	0.654436i	0.612909	+	0.790154i	$0.289999\pi$
$500$	−5.54584	+	9.60567i	−0.248017	+	0.429579i
$501$		0			0
$502$	0.591673	+	1.02481i	0.0264077	+	0.0457394i
$503$	4.02776			0.179589			0.0897944	−	0.995960i	$-0.471379\pi$
$503$	4.02776			0.179589			0.0897944	+	0.995960i	$0.471379\pi$
$504$		0			0
$505$	−46.5416			−2.07108
$506$	3.31665	+	5.74461i	0.147443	+	0.255379i
$507$		0			0
$508$	1.66527	−	2.88433i	0.0738842	−	0.127971i
$509$	−9.51388	+	16.4785i	−0.421695	+	0.730398i	−0.996105	−	0.0881700i	$-0.971898\pi$
$509$	−9.51388	+	16.4785i	−0.421695	+	0.730398i	0.574410	+	0.818568i	$0.305231\pi$
$510$		0			0
$511$	−5.45416	−	9.44689i	−0.241278	−	0.417906i
$512$	−25.4222			−1.12351
$513$		0			0
$514$	−9.51388			−0.419639
$515$	11.8625	+	20.5464i	0.522724	+	0.905384i
$516$		0			0
$517$	−0.591673	+	1.02481i	−0.0260218	+	0.0450710i
$518$	2.74306	−	4.75112i	0.120523	−	0.208752i
$519$		0			0
$520$	−6.45416	−	11.1789i	−0.283034	−	0.490229i
$521$	−32.4500			−1.42166			−0.710829	−	0.703365i	$-0.751680\pi$
$521$	−32.4500			−1.42166			−0.710829	+	0.703365i	$0.751680\pi$
$522$		0			0
$523$	5.90833			0.258353			0.129177	−	0.991622i	$-0.458767\pi$
$523$	5.90833			0.258353			0.129177	+	0.991622i	$0.458767\pi$
$524$	2.15139	+	3.72631i	0.0939838	+	0.162785i
$525$		0			0
$526$	−11.1333	+	19.2835i	−0.485435	+	0.840799i
$527$	15.5139	−	26.8708i	0.675795	−	1.17051i
$528$		0			0
$529$	3.86249	+	6.69003i	0.167934	+	0.290871i
$530$	−72.3583			−3.14304
$531$		0			0
$532$	−1.60555			−0.0696095
$533$	4.50000	+	7.79423i	0.194917	+	0.337606i
$534$		0			0
$535$	21.3167	−	36.9215i	0.921599	−	1.59626i
$536$	−20.2708	+	35.1101i	−0.875566	+	1.51652i
$537$		0			0
$538$	−11.0320	−	19.1079i	−0.475621	−	0.823801i
$539$	−7.81665			−0.336687
$540$		0			0
$541$	−32.3028			−1.38880			−0.694402	−	0.719587i	$-0.744331\pi$
$541$	−32.3028			−1.38880			−0.694402	+	0.719587i	$0.744331\pi$
$542$	−10.0458	−	17.3999i	−0.431506	−	0.747390i
$543$		0			0
$544$	3.65139	−	6.32439i	0.156552	−	0.271156i
$545$	3.19722	−	5.53776i	0.136954	−	0.237211i
$546$		0			0
$547$	18.7569	+	32.4880i	0.801989	+	1.38909i	0.918305	+	0.395873i	$0.129558\pi$
$547$	18.7569	+	32.4880i	0.801989	+	1.38909i	−0.116316	+	0.993212i	$0.537109\pi$
$548$	−2.36669			−0.101100
$549$		0			0
$550$	22.9361			0.977998
$551$	−1.04584	−	1.81144i	−0.0445541	−	0.0771700i
$552$		0			0
$553$	−6.95416	+	12.0450i	−0.295721	+	0.512204i
$554$	11.6056	−	20.1014i	0.493073	−	0.854027i
$555$		0			0
$556$	−2.12363	−	3.67824i	−0.0900620	−	0.155992i
$557$	12.6333			0.535290			0.267645	−	0.963518i	$-0.413754\pi$
$557$	12.6333			0.535290			0.267645	+	0.963518i	$0.413754\pi$
$558$		0			0
$559$	0.697224			0.0294894
$560$	7.10555	+	12.3072i	0.300264	+	0.520073i
$561$		0			0
$562$	−6.78890	+	11.7587i	−0.286372	+	0.496011i
$563$	9.31665	−	16.1369i	0.392650	−	0.680090i	−0.600148	−	0.799889i	$-0.704892\pi$
$563$	9.31665	−	16.1369i	0.392650	−	0.680090i	0.992798	+	0.119799i	$0.0382250\pi$
$564$		0			0
$565$	−6.45416	−	11.1789i	−0.271529	−	0.470301i
$566$	−16.2666			−0.683737
$567$		0			0
$568$	41.4500			1.73920
$569$	13.6194	+	23.5895i	0.570956	+	0.988925i	0.996468	+	0.0839723i	$0.0267607\pi$
$569$	13.6194	+	23.5895i	0.570956	+	0.988925i	−0.425512	+	0.904953i	$0.639906\pi$
$570$		0			0
$571$	9.81665	−	17.0029i	0.410814	−	0.711551i	−0.584165	−	0.811635i	$-0.698578\pi$
$571$	9.81665	−	17.0029i	0.410814	−	0.711551i	0.994979	+	0.100084i	$0.0319112\pi$
$572$	0.197224	−	0.341603i	0.00824636	−	0.0142831i
$573$		0			0
$574$	−5.86249	−	10.1541i	−0.244696	−	0.423825i
$575$	−52.8167			−2.20261
$576$		0			0
$577$	−3.09167			−0.128708			−0.0643540	−	0.997927i	$-0.520499\pi$
$577$	−3.09167			−0.128708			−0.0643540	+	0.997927i	$0.520499\pi$
$578$	−0.986122	−	1.70801i	−0.0410173	−	0.0710440i
$579$		0			0
$580$	0.256939	−	0.445032i	0.0106688	−	0.0184789i
$581$	0.197224	−	0.341603i	0.00818225	−	0.0141721i
$582$		0			0
$583$	−8.40833	−	14.5636i	−0.348237	−	0.603165i
$584$	32.7250			1.35417
$585$		0			0
$586$	−24.2750			−1.00279
$587$	−9.05971	−	15.6919i	−0.373934	−	0.647673i	0.616232	−	0.787564i	$-0.288658\pi$
$587$	−9.05971	−	15.6919i	−0.373934	−	0.647673i	−0.990167	+	0.139891i	$0.955325\pi$
$588$		0			0
$589$	19.1194	−	33.1158i	0.787802	−	1.36451i
$590$	−8.40833	+	14.5636i	−0.346165	+	0.599576i
$591$		0			0
$592$	6.95416	+	12.0450i	0.285814	+	0.495045i
$593$	24.1194			0.990466			0.495233	−	0.868760i	$-0.335083\pi$
$593$	24.1194			0.990466			0.495233	+	0.868760i	$0.335083\pi$
$594$		0			0
$595$	−18.5139			−0.758995
$596$	−1.22498	−	2.12173i	−0.0501772	−	0.0869094i
$597$		0			0
$598$	2.54584	−	4.40952i	0.104107	−	0.180319i
$599$	−3.11943	+	5.40301i	−0.127456	+	0.220761i	−0.922690	−	0.385542i	$-0.874015\pi$
$599$	−3.11943	+	5.40301i	−0.127456	+	0.220761i	0.795234	+	0.606303i	$0.207348\pi$
$600$		0			0
$601$	−7.65139	−	13.2526i	−0.312107	−	0.540585i	0.666712	−	0.745316i	$-0.267701\pi$
$601$	−7.65139	−	13.2526i	−0.312107	−	0.540585i	−0.978818	+	0.204731i	$0.934368\pi$
$602$	−0.908327			−0.0370206
$603$		0			0
$604$	−3.09167			−0.125798
$605$	−20.0139	−	34.6651i	−0.813680	−	1.40933i
$606$		0			0
$607$	12.9542	−	22.4373i	0.525793	−	0.910701i	−0.473755	−	0.880657i	$-0.657102\pi$
$607$	12.9542	−	22.4373i	0.525793	−	0.910701i	0.999549	−	0.0300441i	$-0.00956479\pi$
$608$	4.50000	−	7.79423i	0.182499	−	0.316098i
$609$		0			0
$610$	6.71110	+	11.6240i	0.271725	+	0.470641i
$611$	0.908327			0.0367470
$612$		0			0
$613$	−11.4222			−0.461339			−0.230669	−	0.973032i	$-0.574092\pi$
$613$	−11.4222			−0.461339			−0.230669	+	0.973032i	$0.574092\pi$
$614$	−4.61943	−	8.00109i	−0.186425	−	0.322898i
$615$		0			0
$616$	−1.95416	+	3.38471i	−0.0787355	+	0.136374i
$617$	2.34861	−	4.06792i	0.0945516	−	0.163768i	−0.814870	−	0.579644i	$-0.803192\pi$
$617$	2.34861	−	4.06792i	0.0945516	−	0.163768i	0.909421	+	0.415876i	$0.136525\pi$
$618$		0			0
$619$	1.60555	+	2.78090i	0.0645326	+	0.111774i	0.896487	−	0.443071i	$-0.146111\pi$
$619$	1.60555	+	2.78090i	0.0645326	+	0.111774i	−0.831954	+	0.554845i	$0.812778\pi$
$620$	9.39445			0.377290
$621$		0			0
$622$	9.00000			0.360867
$623$	−4.30278	−	7.45263i	−0.172387	−	0.298583i
$624$		0			0
$625$	−45.0278	+	77.9904i	−1.80111	+	3.11961i
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	−1.71110	−	2.96372i	−0.0682804	−	0.118265i
$629$	−18.1194			−0.722469
$630$		0			0
$631$	−30.4500			−1.21219			−0.606097	−	0.795391i	$-0.707266\pi$
$631$	−30.4500			−1.21219			−0.606097	+	0.795391i	$0.707266\pi$
$632$	−20.8625	−	36.1349i	−0.829865	−	1.43737i
$633$		0			0
$634$	0.0777949	−	0.134745i	0.00308963	−	0.00535140i
$635$	23.6653	−	40.9894i	0.939127	−	1.62662i
$636$		0			0
$637$	3.00000	+	5.19615i	0.118864	+	0.205879i
$638$	−0.669468			−0.0265045
$639$		0			0
$640$	−34.8167			−1.37625
$641$	14.6056	+	25.2976i	0.576885	+	0.999193i	0.995834	+	0.0911839i	$0.0290651\pi$
$641$	14.6056	+	25.2976i	0.576885	+	0.999193i	−0.418949	+	0.908010i	$0.637602\pi$
$642$		0			0
$643$	−15.4083	+	26.6880i	−0.607645	+	1.05247i	0.383982	+	0.923340i	$0.374552\pi$
$643$	−15.4083	+	26.6880i	−0.607645	+	1.05247i	−0.991627	+	0.129132i	$0.958781\pi$
$644$	0.591673	−	1.02481i	0.0233152	−	0.0403831i
$645$		0			0
$646$	−14.8625	−	25.7426i	−0.584757	−	1.01283i
$647$	−3.51388			−0.138145			−0.0690724	−	0.997612i	$-0.522004\pi$
$647$	−3.51388			−0.138145			−0.0690724	+	0.997612i	$0.522004\pi$
$648$		0			0
$649$	−3.90833			−0.153415
$650$	−8.80278	−	15.2469i	−0.345273	−	0.598031i
$651$		0			0
$652$	3.44029	−	5.95875i	0.134732	−	0.233363i
$653$	−5.09167	+	8.81904i	−0.199253	+	0.345116i	−0.948286	−	0.317416i	$-0.897185\pi$
$653$	−5.09167	+	8.81904i	−0.199253	+	0.345116i	0.749034	+	0.662532i	$0.230518\pi$
$654$		0			0
$655$	30.5736	+	52.9550i	1.19461	+	2.06912i
$656$	29.7250			1.16057
$657$		0			0
$658$	−1.18335			−0.0461316
$659$	−1.10555	−	1.91487i	−0.0430662	−	0.0745928i	0.843689	−	0.536833i	$-0.180379\pi$
$659$	−1.10555	−	1.91487i	−0.0430662	−	0.0745928i	−0.886755	+	0.462240i	$0.847046\pi$
$660$		0			0
$661$	12.1056	−	20.9674i	0.470851	−	0.815539i	−0.528593	−	0.848876i	$-0.677280\pi$
$661$	12.1056	−	20.9674i	0.470851	−	0.815539i	0.999444	+	0.0333370i	$0.0106135\pi$
$662$	−9.53196	+	16.5098i	−0.370470	+	0.641673i
$663$		0			0
$664$	0.591673	+	1.02481i	0.0229614	+	0.0397703i
$665$	−22.8167			−0.884792
$666$		0			0
$667$	1.54163			0.0596923
$668$	3.05971	+	5.29958i	0.118384	+	0.205047i
$669$		0			0
$670$	−37.8764	+	65.6038i	−1.46329	+	2.53450i
$671$	−1.55971	+	2.70151i	−0.0602121	+	0.104290i
$672$		0			0
$673$	−13.5139	−	23.4067i	−0.520922	−	0.902263i	−0.999704	−	0.0243292i	$-0.992255\pi$
$673$	−13.5139	−	23.4067i	−0.520922	−	0.902263i	0.478782	−	0.877934i	$-0.341078\pi$
$674$	2.09167			0.0805682
$675$		0			0
$676$	−0.302776			−0.0116452
$677$	−0.197224	−	0.341603i	−0.00757995	−	0.0131289i	0.862211	−	0.506550i	$-0.169079\pi$
$677$	−0.197224	−	0.341603i	−0.00757995	−	0.0131289i	−0.869790	+	0.493421i	$0.835746\pi$
$678$		0			0
$679$	−7.21110	+	12.4900i	−0.276737	+	0.479322i
$680$	27.7708	−	48.1005i	1.06496	−	1.84457i
$681$		0			0
$682$	−6.11943	−	10.5992i	−0.234325	−	0.405863i
$683$	35.4500			1.35646			0.678228	−	0.734852i	$-0.262748\pi$
$683$	35.4500			1.35646			0.678228	+	0.734852i	$0.262748\pi$
$684$		0			0
$685$	−33.6333			−1.28506
$686$	−8.46804	−	14.6671i	−0.323311	−	0.559992i
$687$		0			0
$688$	1.15139	−	1.99426i	0.0438962	−	0.0760305i
$689$	−6.45416	+	11.1789i	−0.245884	+	0.425884i
$690$		0			0
$691$	−19.1194	−	33.1158i	−0.727337	−	1.25979i	−0.958005	−	0.286753i	$-0.907424\pi$
$691$	−19.1194	−	33.1158i	−0.727337	−	1.25979i	0.230667	−	0.973033i	$-0.425909\pi$
$692$	1.18335			0.0449841
$693$		0			0
$694$	19.5416			0.741790
$695$	−30.1791	−	52.2718i	−1.14476	−	1.98278i
$696$		0			0
$697$	−19.3625	+	33.5368i	−0.733407	+	1.27030i
$698$	−4.10555	+	7.11102i	−0.155397	+	0.269156i
$699$		0			0
$700$	−2.04584	−	3.54349i	−0.0773254	−	0.133931i
$701$	−35.8444			−1.35382			−0.676912	−	0.736064i	$-0.736682\pi$
$701$	−35.8444			−1.35382			−0.676912	+	0.736064i	$0.736682\pi$
$702$		0			0
$703$	−22.3305			−0.842212
$704$	−5.74306	−	9.94727i	−0.216450	−	0.374902i
$705$		0			0
$706$	2.46804	−	4.27477i	0.0928860	−	0.160883i
$707$	5.40833	−	9.36750i	0.203401	−	0.352301i
$708$		0			0
$709$	18.7569	+	32.4880i	0.704432	+	1.22011i	0.966896	+	0.255170i	$0.0821314\pi$
$709$	18.7569	+	32.4880i	0.704432	+	1.22011i	−0.262465	+	0.964942i	$0.584535\pi$
$710$	77.4500			2.90665
$711$		0			0
$712$	25.8167			0.967520
$713$	14.0917	+	24.4075i	0.527737	+	0.914068i
$714$		0			0
$715$	2.80278	−	4.85455i	0.104818	−	0.181550i
$716$	−0.531958	+	0.921379i	−0.0198802	+	0.0344335i
$717$		0			0
$718$	−0.770817	−	1.33509i	−0.0287666	−	0.0498253i
$719$	1.81665			0.0677498			0.0338749	−	0.999426i	$-0.489215\pi$
$719$	1.81665			0.0677498			0.0338749	+	0.999426i	$0.489215\pi$
$720$		0			0
$721$	−5.51388			−0.205348
$722$	−5.94029	−	10.2889i	−0.221075	−	0.382912i
$723$		0			0
$724$	−0.468042	+	0.810672i	−0.0173946	+	0.0301284i
$725$	2.66527	−	4.61638i	0.0989855	−	0.171448i
$726$		0			0
$727$	−3.40833	−	5.90340i	−0.126408	−	0.218945i	0.795875	−	0.605462i	$-0.207011\pi$
$727$	−3.40833	−	5.90340i	−0.126408	−	0.218945i	−0.922282	+	0.386517i	$0.873678\pi$
$728$	3.00000			0.111187
$729$		0			0
$730$	61.1472			2.26316
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	−1.39445	+	2.41526i	−0.0515051	+	0.0892095i	−0.890629	−	0.454732i	$-0.849735\pi$
$733$	−1.39445	+	2.41526i	−0.0515051	+	0.0892095i	0.839123	+	0.543941i	$0.183069\pi$
$734$	−0.0180802	+	0.0313158i	−0.000667351	+	0.00115589i
$735$		0			0
$736$	3.31665	+	5.74461i	0.122253	+	0.211749i
$737$	−17.6056			−0.648509
$738$		0			0
$739$	41.9083			1.54162			0.770811	−	0.637063i	$-0.219851\pi$
$739$	41.9083			1.54162			0.770811	+	0.637063i	$0.219851\pi$
$740$	−2.74306	−	4.75112i	−0.100837	−	0.174655i
$741$		0			0
$742$	8.40833	−	14.5636i	0.308679	−	0.534648i
$743$	2.54584	−	4.40952i	0.0933977	−	0.161770i	−0.815541	−	0.578699i	$-0.803561\pi$
$743$	2.54584	−	4.40952i	0.0933977	−	0.161770i	0.908939	+	0.416930i	$0.136894\pi$
$744$		0			0
$745$	−17.4083	−	30.1521i	−0.637792	−	1.10469i
$746$	26.2111			0.959657
$747$		0			0
$748$	1.69722			0.0620567
$749$	4.95416	+	8.58086i	0.181021	+	0.313538i
$750$		0			0
$751$	16.2708	−	28.1819i	0.593731	−	1.02837i	−0.399994	−	0.916518i	$-0.630988\pi$
$751$	16.2708	−	28.1819i	0.593731	−	1.02837i	0.993725	−	0.111854i	$-0.0356788\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$		0			0
$754$	0.256939	+	0.445032i	0.00935717	+	0.0162071i
$755$	−43.9361			−1.59900
$756$		0			0
$757$	15.9361			0.579207			0.289603	−	0.957147i	$-0.406477\pi$
$757$	15.9361			0.579207			0.289603	+	0.957147i	$0.406477\pi$
$758$	11.8625	+	20.5464i	0.430865	+	0.746280i
$759$		0			0
$760$	34.2250	−	59.2794i	1.24147	−	2.15029i
$761$	−14.2111	+	24.6144i	−0.515152	+	0.892270i	0.484693	+	0.874684i	$0.338931\pi$
$761$	−14.2111	+	24.6144i	−0.515152	+	0.892270i	−0.999845	+	0.0175854i	$0.994402\pi$
$762$		0			0
$763$	0.743061	+	1.28702i	0.0269006	+	0.0465932i
$764$	−0.513878			−0.0185915
$765$		0			0
$766$	−30.2389			−1.09257
$767$	1.50000	+	2.59808i	0.0541619	+	0.0938111i
$768$		0			0
$769$	7.01388	−	12.1484i	0.252927	−	0.438082i	−0.711403	−	0.702784i	$-0.751940\pi$
$769$	7.01388	−	12.1484i	0.252927	−	0.438082i	0.964330	+	0.264702i	$0.0852734\pi$
$770$	−3.65139	+	6.32439i	−0.131587	+	0.227915i
$771$		0			0
$772$	−1.71110	−	2.96372i	−0.0615839	−	0.106666i
$773$	11.4861			0.413127			0.206564	−	0.978433i	$-0.433772\pi$
$773$	11.4861			0.413127			0.206564	+	0.978433i	$0.433772\pi$
$774$		0			0
$775$	97.4500			3.50051
$776$	−21.6333	−	37.4700i	−0.776590	−	1.34509i
$777$		0			0
$778$	15.7889	−	27.3472i	0.566059	−	0.980444i
$779$	−23.8625	+	41.3310i	−0.854962	+	1.48084i
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	21.9083			0.783440
$783$		0			0
$784$	19.8167			0.707738
$785$	−24.3167	−	42.1177i	−0.867899	−	1.50324i
$786$		0			0
$787$	−21.0139	+	36.3971i	−0.749064	+	1.29742i	0.199208	+	0.979957i	$0.436163\pi$
$787$	−21.0139	+	36.3971i	−0.749064	+	1.29742i	−0.948272	+	0.317459i	$0.897170\pi$
$788$	−0.275019	+	0.476347i	−0.00979716	+	0.0169692i
$789$		0			0
$790$	−38.9819	−	67.5187i	−1.38691	−	2.40221i
$791$	3.00000			0.106668
$792$		0			0
$793$	2.39445			0.0850294
$794$	14.7431	+	25.5357i	0.523212	+	0.906229i
$795$		0			0
$796$	1.07359	−	1.85952i	0.0380525	−	0.0659088i
$797$	−18.1972	+	31.5185i	−0.644579	+	1.11644i	0.339820	+	0.940491i	$0.389634\pi$
$797$	−18.1972	+	31.5185i	−0.644579	+	1.11644i	−0.984399	+	0.175953i	$0.943699\pi$
$798$		0			0
$799$	1.95416	+	3.38471i	0.0691333	+	0.119742i
$800$	22.9361			0.810913
$801$		0			0
$802$	−42.4777			−1.49994
$803$	7.10555	+	12.3072i	0.250749	+	0.434311i
$804$		0			0
$805$	8.40833	−	14.5636i	0.296355	−	0.513301i
$806$	−4.69722	+	8.13583i	−0.165453	+	0.286572i
$807$		0			0
$808$	16.2250	+	28.1025i	0.570793	+	0.988642i
$809$	43.5416			1.53084			0.765421	−	0.643530i	$-0.222531\pi$
$809$	43.5416			1.53084			0.765421	+	0.643530i	$0.222531\pi$
$810$		0			0
$811$	−32.8167			−1.15235			−0.576174	−	0.817327i	$-0.695455\pi$
$811$	−32.8167			−1.15235			−0.576174	+	0.817327i	$0.695455\pi$
$812$	0.0597147	+	0.103429i	0.00209558	+	0.00362964i
$813$		0			0
$814$	−3.57359	+	6.18964i	−0.125254	+	0.216947i
$815$	48.8902	−	84.6804i	1.71255	−	2.96622i
$816$		0			0
$817$	1.84861	+	3.20189i	0.0646748	+	0.112020i
$818$	9.39445			0.328469
$819$		0			0
$820$	−11.7250			−0.409454
$821$	−4.30278	−	7.45263i	−0.150168	−	0.260098i	0.781121	−	0.624379i	$-0.214648\pi$
$821$	−4.30278	−	7.45263i	−0.150168	−	0.260098i	−0.931289	+	0.364281i	$0.881315\pi$
$822$		0			0
$823$	−5.89445	+	10.2095i	−0.205468	+	0.355880i	−0.950282	−	0.311392i	$-0.899205\pi$
$823$	−5.89445	+	10.2095i	−0.205468	+	0.355880i	0.744814	+	0.667272i	$0.232538\pi$
$824$	8.27082	−	14.3255i	0.288128	−	0.499052i
$825$		0			0
$826$	−1.95416	−	3.38471i	−0.0679940	−	0.117769i
$827$	−23.6056			−0.820845			−0.410423	−	0.911895i	$-0.634619\pi$
$827$	−23.6056			−0.820845			−0.410423	+	0.911895i	$0.634619\pi$
$828$		0			0
$829$	17.6333			0.612430			0.306215	−	0.951962i	$-0.400937\pi$
$829$	17.6333			0.612430			0.306215	+	0.951962i	$0.400937\pi$
$830$	1.10555	+	1.91487i	0.0383742	+	0.0664661i
$831$		0			0
$832$	−4.40833	+	7.63545i	−0.152831	+	0.264711i
$833$	−12.9083	+	22.3579i	−0.447247	+	0.774655i
$834$		0			0
$835$	43.4819	+	75.3129i	1.50475	+	2.60631i
$836$	2.09167			0.0723420
$837$		0			0
$838$	−32.2944			−1.11559
$839$	16.0458	+	27.7922i	0.553964	+	0.959493i	0.997983	+	0.0634763i	$0.0202187\pi$
$839$	16.0458	+	27.7922i	0.553964	+	0.959493i	−0.444020	+	0.896017i	$0.646448\pi$
$840$		0			0
$841$	14.4222	−	24.9800i	0.497317	−	0.861379i
$842$	−22.0278	+	38.1532i	−0.759127	+	1.31485i
$843$		0			0
$844$	1.68335	+	2.91564i	0.0579432	+	0.100361i
$845$	−4.30278			−0.148020
$846$		0			0
$847$	9.30278			0.319647
$848$	21.3167	+	36.9215i	0.732017	+	1.26789i
$849$		0			0
$850$	37.8764	−	65.6038i	1.29915	−	2.25019i
$851$	8.22918	−	14.2534i	0.282093	−	0.488599i
$852$		0			0
$853$	17.0597	+	29.5483i	0.584114	+	1.01171i	0.994985	+	0.100021i	$0.0318910\pi$
$853$	17.0597	+	29.5483i	0.584114	+	1.01171i	−0.410872	+	0.911693i	$0.634776\pi$
$854$	−3.11943			−0.106745
$855$		0			0
$856$	−29.7250			−1.01598
$857$	−15.5736	−	26.9743i	−0.531984	−	0.921423i	−0.999303	−	0.0373342i	$-0.988113\pi$
$857$	−15.5736	−	26.9743i	−0.531984	−	0.921423i	0.467319	−	0.884089i	$-0.345220\pi$
$858$		0			0
$859$	−4.19722	+	7.26981i	−0.143207	+	0.248043i	−0.928703	−	0.370825i	$-0.879075\pi$
$859$	−4.19722	+	7.26981i	−0.143207	+	0.248043i	0.785495	+	0.618868i	$0.212408\pi$
$860$	−0.454163	+	0.786634i	−0.0154868	+	0.0268240i
$861$		0			0
$862$	18.7708	+	32.5120i	0.639337	+	1.10736i
$863$	21.3944			0.728276			0.364138	−	0.931345i	$-0.381364\pi$
$863$	21.3944			0.728276			0.364138	+	0.931345i	$0.381364\pi$
$864$		0			0
$865$	16.8167			0.571783
$866$	6.43608	+	11.1476i	0.218707	+	0.378812i
$867$		0			0
$868$	−1.09167	+	1.89083i	−0.0370538	+	0.0641791i
$869$	9.05971	−	15.6919i	0.307330	−	0.532311i
$870$		0			0
$871$	6.75694	+	11.7034i	0.228950	+	0.396553i
$872$	−4.45837			−0.150979
$873$		0			0
$874$	27.0000			0.913289
$875$	−18.3167	−	31.7254i	−0.619216	−	1.07251i
$876$		0			0
$877$	−1.31665	+	2.28051i	−0.0444602	+	0.0770074i	−0.887399	−	0.461002i	$-0.847490\pi$
$877$	−1.31665	+	2.28051i	−0.0444602	+	0.0770074i	0.842939	+	0.538009i	$0.180823\pi$
$878$	18.2389	−	31.5906i	0.615532	−	1.06613i
$879$		0			0
$880$	−9.25694	−	16.0335i	−0.312051	−	0.540489i
$881$	−19.9722			−0.672882			−0.336441	−	0.941705i	$-0.609223\pi$
$881$	−19.9722			−0.672882			−0.336441	+	0.941705i	$0.609223\pi$
$882$		0			0
$883$	−17.6972			−0.595559			−0.297780	−	0.954635i	$-0.596246\pi$
$883$	−17.6972			−0.595559			−0.297780	+	0.954635i	$0.596246\pi$
$884$	−0.651388	−	1.12824i	−0.0219085	−	0.0379467i
$885$		0			0
$886$	14.3486	−	24.8525i	0.482051	−	0.834937i
$887$	−0.591673	+	1.02481i	−0.0198664	+	0.0344097i	−0.875788	−	0.482696i	$-0.839657\pi$
$887$	−0.591673	+	1.02481i	−0.0198664	+	0.0344097i	0.855921	+	0.517106i	$0.172991\pi$
$888$		0			0
$889$	5.50000	+	9.52628i	0.184464	+	0.319501i
$890$	48.2389			1.61697
$891$		0			0
$892$	5.55004			0.185829
$893$	2.40833	+	4.17134i	0.0805916	+	0.139589i
$894$		0			0
$895$	−7.55971	+	13.0938i	−0.252693	+	0.437678i
$896$	4.04584	−	7.00759i	0.135162	−	0.234107i
$897$		0			0
$898$	19.2847	+	33.4021i	0.643539	+	1.11464i
$899$	−2.84441			−0.0948664
$900$		0			0
$901$	−55.5416			−1.85036
$902$	7.63751	+	13.2286i	0.254301	+	0.440463i
$903$		0			0
$904$	−4.50000	+	7.79423i	−0.149668	+	0.259232i
$905$	−6.65139	+	11.5205i	−0.221100	+	0.382956i
$906$		0			0
$907$	−7.39445	−	12.8076i	−0.245529	−	0.425268i	0.716751	−	0.697329i	$-0.245628\pi$
$907$	−7.39445	−	12.8076i	−0.245529	−	0.425268i	−0.962280	+	0.272061i	$0.912295\pi$
$908$	−1.85281			−0.0614878
$909$		0			0
$910$	5.60555			0.185822
$911$	1.83473	+	3.17785i	0.0607874	+	0.105287i	0.894818	−	0.446432i	$-0.147305\pi$
$911$	1.83473	+	3.17785i	0.0607874	+	0.105287i	−0.834030	+	0.551719i	$0.813972\pi$
$912$		0			0
$913$	−0.256939	+	0.445032i	−0.00850344	+	0.0147284i
$914$	−22.7986	+	39.4883i	−0.754110	+	1.30616i
$915$		0			0
$916$	−1.19722	−	2.07365i	−0.0395574	−	0.0685154i
$917$	−14.2111			−0.469292
$918$		0			0
$919$	8.78890			0.289919			0.144959	−	0.989438i	$-0.453695\pi$
$919$	8.78890			0.289919			0.144959	+	0.989438i	$0.453695\pi$
$920$	25.2250	+	43.6909i	0.831643	+	1.44045i
$921$		0			0
$922$	17.1514	−	29.7071i	0.564851	−	0.978350i
$923$	6.90833	−	11.9656i	0.227390	−	0.393852i
$924$		0			0
$925$	−28.4542	−	49.2841i	−0.935567	−	1.62045i
$926$	−29.3305			−0.963861
$927$		0			0
$928$	−0.669468			−0.0219764
$929$	9.59167	+	16.6133i	0.314693	+	0.545064i	0.979372	−	0.202065i	$-0.0647652\pi$
$929$	9.59167	+	16.6133i	0.314693	+	0.545064i	−0.664680	+	0.747129i	$0.731432\pi$
$930$		0			0
$931$	−15.9083	+	27.5540i	−0.521374	+	0.903047i
$932$	1.51808	−	2.62939i	0.0497264	−	0.0861286i
$933$		0			0
$934$	−10.9542	−	18.9732i	−0.358431	−	0.620821i
$935$	24.1194			0.788790
$936$		0			0
$937$	57.5416			1.87980			0.939902	−	0.341445i	$-0.110916\pi$
$937$	57.5416			1.87980			0.939902	+	0.341445i	$0.110916\pi$
$938$	−8.80278	−	15.2469i	−0.287421	−	0.497827i
$939$		0			0
$940$	−0.591673	+	1.02481i	−0.0192982	+	0.0334255i
$941$	−15.5139	+	26.8708i	−0.505738	+	0.875964i	0.494240	+	0.869326i	$0.335446\pi$
$941$	−15.5139	+	26.8708i	−0.505738	+	0.875964i	−0.999978	+	0.00663836i	$0.997887\pi$
$942$		0			0
$943$	−17.5875	−	30.4624i	−0.572727	−	0.991992i
$944$	9.90833			0.322489
$945$		0			0
$946$	1.18335			0.0384739
$947$	24.3167	+	42.1177i	0.790185	+	1.36864i	0.925852	+	0.377886i	$0.123349\pi$
$947$	24.3167	+	42.1177i	0.790185	+	1.36864i	−0.135667	+	0.990754i	$0.543318\pi$
$948$		0			0
$949$	5.45416	−	9.44689i	0.177050	−	0.306659i
$950$	46.6791	−	80.8506i	1.51447	−	2.62314i
$951$		0			0
$952$	6.45416	+	11.1789i	0.209181	+	0.362311i
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$		0			0
$955$	−7.30278			−0.236312
$956$	−0.729183	−	1.26298i	−0.0235835	−	0.0408477i
$957$		0			0
$958$	11.5458	−	19.9980i	0.373029	−	0.646105i
$959$	3.90833	−	6.76942i	0.126206	−	0.218596i
$960$		0			0
$961$	−10.5000	−	18.1865i	−0.338710	−	0.586662i
$962$	5.48612			0.176880
$963$		0			0
$964$	3.18335			0.102529
$965$	−24.3167	−	42.1177i	−0.782781	−	1.35582i
$966$		0			0
$967$	−1.90833	+	3.30532i	−0.0613677	+	0.106292i	−0.895077	−	0.445912i	$-0.852880\pi$
$967$	−1.90833	+	3.30532i	−0.0613677	+	0.106292i	0.833709	+	0.552204i	$0.186213\pi$
$968$	−13.9542	+	24.1693i	−0.448504	+	0.776831i
$969$		0			0
$970$	−40.4222	−	70.0133i	−1.29788	−	2.24799i
$971$	−42.0000			−1.34784			−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000			−1.34784			−0.673922	+	0.738802i	$0.735392\pi$
$972$		0			0
$973$	14.0278			0.449709
$974$	−27.6333	−	47.8623i	−0.885428	−	1.53361i
$975$		0			0
$976$	3.95416	−	6.84881i	0.126570	−	0.219225i
$977$	5.09167	−	8.81904i	0.162897	−	0.282146i	−0.773009	−	0.634395i	$-0.781249\pi$
$977$	5.09167	−	8.81904i	0.162897	−	0.282146i	0.935906	+	0.352249i	$0.114583\pi$
$978$		0			0
$979$	5.60555	+	9.70910i	0.179154	+	0.310304i
$980$	−7.81665			−0.249694
$981$		0			0
$982$	51.9916			1.65912
$983$	−21.5139	−	37.2631i	−0.686186	−	1.18851i	−0.973062	−	0.230542i	$-0.925950\pi$
$983$	−21.5139	−	37.2631i	−0.686186	−	1.18851i	0.286876	−	0.957968i	$-0.407383\pi$
$984$		0			0
$985$	−3.90833	+	6.76942i	−0.124530	+	0.215692i
$986$	−1.10555	+	1.91487i	−0.0352079	+	0.0609819i
$987$		0			0
$988$	−0.802776	−	1.39045i	−0.0255397	−	0.0442360i
$989$	−2.72498			−0.0866493
$990$		0			0
$991$	−11.4222			−0.362838			−0.181419	−	0.983406i	$-0.558069\pi$
$991$	−11.4222			−0.362838			−0.181419	+	0.983406i	$0.558069\pi$
$992$	−6.11943	−	10.5992i	−0.194292	−	0.336524i
$993$		0			0
$994$	−9.00000	+	15.5885i	−0.285463	+	0.494436i
$995$	15.2569	−	26.4258i	0.483677	−	0.837754i
$996$		0			0
$997$	22.6653	+	39.2574i	0.717816	+	1.24329i	0.961863	+	0.273531i	$0.0881915\pi$
$997$	22.6653	+	39.2574i	0.717816	+	1.24329i	−0.244047	+	0.969763i	$0.578475\pi$
$998$	21.9916			0.696132
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1053.2.e.j.352.1		4
3.2	odd	2		1053.2.e.f.352.2		4
9.2	odd	6		1053.2.e.f.703.2		4
9.4	even	3		351.2.a.b.1.2	✓	2
9.5	odd	6		351.2.a.d.1.1	yes	2
9.7	even	3	inner	1053.2.e.j.703.1		4
36.23	even	6		5616.2.a.bz.1.2		2
36.31	odd	6		5616.2.a.bi.1.1		2
45.4	even	6		8775.2.a.bd.1.1		2
45.14	odd	6		8775.2.a.w.1.2		2
117.77	odd	6		4563.2.a.i.1.2		2
117.103	even	6		4563.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.a.b.1.2	✓	2	9.4	even	3
351.2.a.d.1.1	yes	2	9.5	odd	6
1053.2.e.f.352.2		4	3.2	odd	2
1053.2.e.f.703.2		4	9.2	odd	6
1053.2.e.j.352.1		4	1.1	even	1	trivial
1053.2.e.j.703.1		4	9.7	even	3	inner
4563.2.a.i.1.2		2	117.77	odd	6
4563.2.a.q.1.1		2	117.103	even	6
5616.2.a.bi.1.1		2	36.31	odd	6
5616.2.a.bz.1.2		2	36.23	even	6
8775.2.a.w.1.2		2	45.14	odd	6
8775.2.a.bd.1.1		2	45.4	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1053.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.651388 - 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(2.15139 - 3.72631i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} -5.60555 q^{10} +(-0.651388 - 1.12824i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(0.651388 - 1.12824i) q^{14} +(1.65139 + 2.86029i) q^{16} -4.30278 q^{17} -5.30278 q^{19} +(-0.651388 - 1.12824i) q^{20} +(-0.848612 + 1.46984i) q^{22} +(1.95416 - 3.38471i) q^{23} +(-6.75694 - 11.7034i) q^{25} +1.30278 q^{26} +0.302776 q^{28} +(0.197224 + 0.341603i) q^{29} +(-3.60555 + 6.24500i) q^{31} +(-0.848612 + 1.46984i) q^{32} +(2.80278 + 4.85455i) q^{34} +4.30278 q^{35} +4.21110 q^{37} +(3.45416 + 5.98279i) q^{38} +(-6.45416 + 11.1789i) q^{40} +(4.50000 - 7.79423i) q^{41} +(-0.348612 - 0.603814i) q^{43} -0.394449 q^{44} -5.09167 q^{46} +(-0.454163 - 0.786634i) q^{47} +(3.00000 - 5.19615i) q^{49} +(-8.80278 + 15.2469i) q^{50} +(0.151388 + 0.262211i) q^{52} +12.9083 q^{53} -5.60555 q^{55} +(-1.50000 - 2.59808i) q^{56} +(0.256939 - 0.445032i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-1.19722 - 2.07365i) q^{61} +9.39445 q^{62} +8.81665 q^{64} +(2.15139 + 3.72631i) q^{65} +(6.75694 - 11.7034i) q^{67} +(-0.651388 + 1.12824i) q^{68} +(-2.80278 - 4.85455i) q^{70} -13.8167 q^{71} -10.9083 q^{73} +(-2.74306 - 4.75112i) q^{74} +(-0.802776 + 1.39045i) q^{76} +(0.651388 - 1.12824i) q^{77} +(6.95416 + 12.0450i) q^{79} +14.2111 q^{80} -11.7250 q^{82} +(-0.197224 - 0.341603i) q^{83} +(-9.25694 + 16.0335i) q^{85} +(-0.454163 + 0.786634i) q^{86} +(1.95416 + 3.38471i) q^{88} -8.60555 q^{89} -1.00000 q^{91} +(-0.591673 - 1.02481i) q^{92} +(-0.591673 + 1.02481i) q^{94} +(-11.4083 + 19.7598i) q^{95} +(7.21110 + 12.4900i) q^{97} -7.81665 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 3 q^{4} + 5 q^{5} + 2 q^{7} - 12 q^{8} - 8 q^{10} + q^{11} - 2 q^{13} - q^{14} + 3 q^{16} - 10 q^{17} - 14 q^{19} + q^{20} - 7 q^{22} - 3 q^{23} - 9 q^{25} - 2 q^{26} - 6 q^{28} + 8 q^{29}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q + q^2 - 3 * q^4 + 5 * q^5 + 2 * q^7 - 12 * q^8 - 8 * q^10 + q^11 - 2 * q^13 - q^14 + 3 * q^16 - 10 * q^17 - 14 * q^19 + q^20 - 7 * q^22 - 3 * q^23 - 9 * q^25 - 2 * q^26 - 6 * q^28 + 8 * q^29 - 7 * q^32 + 4 * q^34 + 10 * q^35 - 12 * q^37 + 3 * q^38 - 15 * q^40 + 18 * q^41 - 5 * q^43 - 16 * q^44 - 42 * q^46 + 9 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^52 + 30 * q^53 - 8 * q^55 - 6 * q^56 - 17 * q^58 + 6 * q^59 - 12 * q^61 + 52 * q^62 - 8 * q^64 + 5 * q^65 + 9 * q^67 + q^68 - 4 * q^70 - 12 * q^71 - 22 * q^73 - 29 * q^74 + 4 * q^76 - q^77 + 17 * q^79 + 28 * q^80 + 18 * q^82 - 8 * q^83 - 19 * q^85 + 9 * q^86 - 3 * q^88 - 20 * q^89 - 4 * q^91 - 24 * q^92 - 24 * q^94 - 24 * q^95 + 12 * q^98

Introduction

L-functions

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Database

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