LMFDB - Embedded newform 728.2.c.a.365.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 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("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.17
Character	$\chi$	$=$	728.365
Dual form			728.2.c.a.365.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.182514 - 1.40239i) q^{2} -0.275879i q^{3} +(-1.93338 - 0.511911i) q^{4} -3.61620i q^{5} +(-0.386890 - 0.0503520i) q^{6} -1.00000 q^{7} +(-1.07077 + 2.61791i) q^{8} +2.92389 q^{9} +(-5.07131 - 0.660008i) q^{10} -5.52552i q^{11} +(-0.141226 + 0.533379i) q^{12} -1.00000i q^{13} +(-0.182514 + 1.40239i) q^{14} -0.997636 q^{15} +(3.47589 + 1.97944i) q^{16} +3.52124 q^{17} +(0.533652 - 4.10043i) q^{18} +1.10679i q^{19} +(-1.85117 + 6.99148i) q^{20} +0.275879i q^{21} +(-7.74891 - 1.00849i) q^{22} -7.91353 q^{23} +(0.722228 + 0.295403i) q^{24} -8.07691 q^{25} +(-1.40239 - 0.182514i) q^{26} -1.63428i q^{27} +(1.93338 + 0.511911i) q^{28} +10.0364i q^{29} +(-0.182083 + 1.39907i) q^{30} -5.12736 q^{31} +(3.41033 - 4.51327i) q^{32} -1.52438 q^{33} +(0.642678 - 4.93815i) q^{34} +3.61620i q^{35} +(-5.65298 - 1.49677i) q^{36} +3.62244i q^{37} +(1.55215 + 0.202005i) q^{38} -0.275879 q^{39} +(9.46689 + 3.87211i) q^{40} +1.03995 q^{41} +(0.386890 + 0.0503520i) q^{42} -8.73661i q^{43} +(-2.82857 + 10.6829i) q^{44} -10.5734i q^{45} +(-1.44433 + 11.0978i) q^{46} +13.4664 q^{47} +(0.546086 - 0.958928i) q^{48} +1.00000 q^{49} +(-1.47415 + 11.3269i) q^{50} -0.971439i q^{51} +(-0.511911 + 1.93338i) q^{52} -2.23708i q^{53} +(-2.29189 - 0.298279i) q^{54} -19.9814 q^{55} +(1.07077 - 2.61791i) q^{56} +0.305341 q^{57} +(14.0749 + 1.83178i) q^{58} +4.78728i q^{59} +(1.92881 + 0.510701i) q^{60} +0.861749i q^{61} +(-0.935817 + 7.19054i) q^{62} -2.92389 q^{63} +(-5.70692 - 5.60634i) q^{64} -3.61620 q^{65} +(-0.278221 + 2.13777i) q^{66} -4.23522i q^{67} +(-6.80789 - 1.80257i) q^{68} +2.18318i q^{69} +(5.07131 + 0.660008i) q^{70} +0.866345 q^{71} +(-3.13080 + 7.65449i) q^{72} -5.70186 q^{73} +(5.08007 + 0.661148i) q^{74} +2.22825i q^{75} +(0.566578 - 2.13984i) q^{76} +5.52552i q^{77} +(-0.0503520 + 0.386890i) q^{78} -7.29555 q^{79} +(7.15804 - 12.5695i) q^{80} +8.32081 q^{81} +(0.189806 - 1.45841i) q^{82} -7.27650i q^{83} +(0.141226 - 0.533379i) q^{84} -12.7335i q^{85} +(-12.2521 - 1.59456i) q^{86} +2.76883 q^{87} +(14.4653 + 5.91654i) q^{88} +7.66208 q^{89} +(-14.8280 - 1.92979i) q^{90} +1.00000i q^{91} +(15.2998 + 4.05103i) q^{92} +1.41453i q^{93} +(2.45781 - 18.8851i) q^{94} +4.00238 q^{95} +(-1.24512 - 0.940841i) q^{96} +12.7857 q^{97} +(0.182514 - 1.40239i) q^{98} -16.1560i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) $ 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	0.182514	−	1.40239i	0.129057	−	0.991637i
$2$	0.182514	−	1.40239i	0.129057	−	0.991637i
$3$		−	0.275879i		−	0.159279i	−0.996824	−	0.0796395i	$-0.974623\pi$
$3$		−	0.275879i		−	0.159279i	0.996824	−	0.0796395i	$-0.0253769\pi$
$4$	−1.93338	−	0.511911i	−0.966689	−	0.255956i
$5$		−	3.61620i		−	1.61721i	−0.588349	−	0.808607i	$-0.700222\pi$
$5$		−	3.61620i		−	1.61721i	0.588349	−	0.808607i	$-0.299778\pi$
$6$	−0.386890	−	0.0503520i	−0.157947	−	0.0205561i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−1.07077	+	2.61791i	−0.378573	+	0.925571i
$9$	2.92389			0.974630
$10$	−5.07131	−	0.660008i	−1.60369	−	0.208713i
$11$		−	5.52552i		−	1.66601i	−0.553269	−	0.833003i	$-0.686620\pi$
$11$		−	5.52552i		−	1.66601i	0.553269	−	0.833003i	$-0.313380\pi$
$12$	−0.141226	+	0.533379i	−0.0407684	+	0.153973i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−0.182514	+	1.40239i	−0.0487790	+	0.374804i
$15$	−0.997636			−0.257588
$16$	3.47589	+	1.97944i	0.868973	+	0.494859i
$17$	3.52124			0.854027			0.427014	−	0.904245i	$-0.359566\pi$
$17$	3.52124			0.854027			0.427014	+	0.904245i	$0.359566\pi$
$18$	0.533652	−	4.10043i	0.125783	−	0.966479i
$19$			1.10679i			0.253915i	0.991908	+	0.126958i	$0.0405212\pi$
$19$			1.10679i			0.253915i	−0.991908	+	0.126958i	$0.959479\pi$
$20$	−1.85117	+	6.99148i	−0.413935	+	1.56334i
$21$			0.275879i			0.0602018i
$22$	−7.74891	−	1.00849i	−1.65207	−	0.215010i
$23$	−7.91353			−1.65009			−0.825043	−	0.565070i	$-0.808849\pi$
$23$	−7.91353			−1.65009			−0.825043	+	0.565070i	$0.808849\pi$
$24$	0.722228	+	0.295403i	0.147424	+	0.0602988i
$25$	−8.07691			−1.61538
$26$	−1.40239	−	0.182514i	−0.275031	−	0.0357940i
$27$		−	1.63428i		−	0.314517i
$28$	1.93338	+	0.511911i	0.365374	+	0.0967421i
$29$			10.0364i			1.86371i	0.362833	+	0.931854i	$0.381809\pi$
$29$			10.0364i			1.86371i	−0.362833	+	0.931854i	$0.618191\pi$
$30$	−0.182083	+	1.39907i	−0.0332436	+	0.255434i
$31$	−5.12736			−0.920901			−0.460450	−	0.887685i	$-0.652312\pi$
$31$	−5.12736			−0.920901			−0.460450	+	0.887685i	$0.652312\pi$
$32$	3.41033	−	4.51327i	0.602868	−	0.797841i
$33$	−1.52438			−0.265360
$34$	0.642678	−	4.93815i	0.110218	−	0.846885i
$35$			3.61620i			0.611249i
$36$	−5.65298	−	1.49677i	−0.942164	−	0.249462i
$37$			3.62244i			0.595526i	0.954640	+	0.297763i	$0.0962405\pi$
$37$			3.62244i			0.595526i	−0.954640	+	0.297763i	$0.903760\pi$
$38$	1.55215	+	0.202005i	0.251792	+	0.0327695i
$39$	−0.275879			−0.0441761
$40$	9.46689	+	3.87211i	1.49685	+	0.612234i
$41$	1.03995			0.162413			0.0812064	−	0.996697i	$-0.474123\pi$
$41$	1.03995			0.162413			0.0812064	+	0.996697i	$0.474123\pi$
$42$	0.386890	+	0.0503520i	0.0596984	+	0.00776948i
$43$		−	8.73661i		−	1.33232i	−0.745809	−	0.666160i	$-0.767937\pi$
$43$		−	8.73661i		−	1.33232i	0.745809	−	0.666160i	$-0.232063\pi$
$44$	−2.82857	+	10.6829i	−0.426424	+	1.61051i
$45$		−	10.5734i		−	1.57619i
$46$	−1.44433	+	11.0978i	−0.212955	+	1.63629i
$47$	13.4664			1.96427			0.982136	−	0.188171i	$-0.0602559\pi$
$47$	13.4664			1.96427			0.982136	+	0.188171i	$0.0602559\pi$
$48$	0.546086	−	0.958928i	0.0788207	−	0.138409i
$49$	1.00000			0.142857
$50$	−1.47415	+	11.3269i	−0.208476	+	1.60187i
$51$		−	0.971439i		−	0.136029i
$52$	−0.511911	+	1.93338i	−0.0709893	+	0.268111i
$53$		−	2.23708i		−	0.307286i	−0.988126	−	0.153643i	$-0.950899\pi$
$53$		−	2.23708i		−	0.307286i	0.988126	−	0.153643i	$-0.0491006\pi$
$54$	−2.29189	−	0.298279i	−0.311887	−	0.0405907i
$55$	−19.9814			−2.69429
$56$	1.07077	−	2.61791i	0.143087	−	0.349833i
$57$	0.305341			0.0404434
$58$	14.0749	+	1.83178i	1.84812	+	0.240525i
$59$			4.78728i			0.623251i	0.950205	+	0.311626i	$0.100873\pi$
$59$			4.78728i			0.623251i	−0.950205	+	0.311626i	$0.899127\pi$
$60$	1.92881	+	0.510701i	0.249008	+	0.0659312i
$61$			0.861749i			0.110336i	0.998477	+	0.0551678i	$0.0175694\pi$
$61$			0.861749i			0.110336i	−0.998477	+	0.0551678i	$0.982431\pi$
$62$	−0.935817	+	7.19054i	−0.118849	+	0.913200i
$63$	−2.92389			−0.368376
$64$	−5.70692	−	5.60634i	−0.713365	−	0.700793i
$65$	−3.61620			−0.448534
$66$	−0.278221	+	2.13777i	−0.0342466	+	0.263141i
$67$		−	4.23522i		−	0.517414i	−0.965956	−	0.258707i	$-0.916704\pi$
$67$		−	4.23522i		−	0.517414i	0.965956	−	0.258707i	$-0.0832965\pi$
$68$	−6.80789	−	1.80257i	−0.825578	−	0.218593i
$69$			2.18318i			0.262824i
$70$	5.07131	+	0.660008i	0.606138	+	0.0788861i
$71$	0.866345			0.102816			0.0514081	−	0.998678i	$-0.483629\pi$
$71$	0.866345			0.102816			0.0514081	+	0.998678i	$0.483629\pi$
$72$	−3.13080	+	7.65449i	−0.368969	+	0.902090i
$73$	−5.70186			−0.667352			−0.333676	−	0.942688i	$-0.608289\pi$
$73$	−5.70186			−0.667352			−0.333676	+	0.942688i	$0.608289\pi$
$74$	5.08007	+	0.661148i	0.590546	+	0.0768569i
$75$			2.22825i			0.257297i
$76$	0.566578	−	2.13984i	0.0649910	−	0.245457i
$77$			5.52552i			0.629691i
$78$	−0.0503520	+	0.386890i	−0.00570124	+	0.0438066i
$79$	−7.29555			−0.820814			−0.410407	−	0.911902i	$-0.634613\pi$
$79$	−7.29555			−0.820814			−0.410407	+	0.911902i	$0.634613\pi$
$80$	7.15804	−	12.5695i	0.800293	−	1.40532i
$81$	8.32081			0.924534
$82$	0.189806	−	1.45841i	0.0209605	−	0.161054i
$83$		−	7.27650i		−	0.798700i	−0.916799	−	0.399350i	$-0.869236\pi$
$83$		−	7.27650i		−	0.798700i	0.916799	−	0.399350i	$-0.130764\pi$
$84$	0.141226	−	0.533379i	0.0154090	−	0.0581964i
$85$		−	12.7335i		−	1.38115i
$86$	−12.2521	−	1.59456i	−1.32118	−	0.171945i
$87$	2.76883			0.296850
$88$	14.4653	+	5.91654i	1.54201	+	0.630705i
$89$	7.66208			0.812178			0.406089	−	0.913833i	$-0.366892\pi$
$89$	7.66208			0.812178			0.406089	+	0.913833i	$0.366892\pi$
$90$	−14.8280	−	1.92979i	−1.56300	−	0.203418i
$91$			1.00000i			0.104828i
$92$	15.2998	+	4.05103i	1.59512	+	0.422349i
$93$			1.41453i			0.146680i
$94$	2.45781	−	18.8851i	0.253503	−	1.94785i
$95$	4.00238			0.410635
$96$	−1.24512	−	0.940841i	−0.127079	−	0.0960242i
$97$	12.7857			1.29819			0.649097	−	0.760706i	$-0.275147\pi$
$97$	12.7857			1.29819			0.649097	+	0.760706i	$0.275147\pi$
$98$	0.182514	−	1.40239i	0.0184367	−	0.141662i
$99$		−	16.1560i		−	1.62374i
$100$	15.6157	+	4.13466i	1.56157	+	0.413466i
$101$		−	9.46158i		−	0.941462i	−0.882277	−	0.470731i	$-0.843990\pi$
$101$		−	9.46158i		−	0.941462i	0.882277	−	0.470731i	$-0.156010\pi$
$102$	−1.36233	−	0.177302i	−0.134891	−	0.0175555i
$103$	0.503322			0.0495938			0.0247969	−	0.999693i	$-0.492106\pi$
$103$	0.503322			0.0495938			0.0247969	+	0.999693i	$0.492106\pi$
$104$	2.61791	+	1.07077i	0.256707	+	0.104997i
$105$	0.997636			0.0973593
$106$	−3.13725	−	0.408299i	−0.304716	−	0.0396575i
$107$			3.29814i			0.318843i	0.987211	+	0.159422i	$0.0509629\pi$
$107$			3.29814i			0.318843i	−0.987211	+	0.159422i	$0.949037\pi$
$108$	−0.836606	+	3.15968i	−0.0805025	+	0.304040i
$109$		−	17.1603i		−	1.64366i	−0.569735	−	0.821829i	$-0.692954\pi$
$109$		−	17.1603i		−	1.64366i	0.569735	−	0.821829i	$-0.307046\pi$
$110$	−3.64689	+	28.0216i	−0.347717	+	2.67176i
$111$	0.999358			0.0948548
$112$	−3.47589	−	1.97944i	−0.328441	−	0.187039i
$113$	4.38117			0.412146			0.206073	−	0.978537i	$-0.433932\pi$
$113$	4.38117			0.412146			0.206073	+	0.978537i	$0.433932\pi$
$114$	0.0557290	−	0.428206i	0.00521950	−	0.0401051i
$115$			28.6169i			2.66854i
$116$	5.13773	−	19.4041i	0.477027	−	1.80163i
$117$		−	2.92389i		−	0.270314i
$118$	6.71362	+	0.873748i	0.618039	+	0.0804350i
$119$	−3.52124			−0.322792
$120$	1.06823	−	2.61172i	0.0975161	−	0.238416i
$121$	−19.5313			−1.77558
$122$	1.20851	+	0.157282i	0.109413	+	0.0142396i
$123$		−	0.286901i		−	0.0258689i
$124$	9.91312	+	2.62475i	0.890224	+	0.235710i
$125$			11.1267i			0.995204i
$126$	−0.533652	+	4.10043i	−0.0475415	+	0.365295i
$127$	−0.951245			−0.0844094			−0.0422047	−	0.999109i	$-0.513438\pi$
$127$	−0.951245			−0.0844094			−0.0422047	+	0.999109i	$0.513438\pi$
$128$	−8.90386	+	6.98007i	−0.786997	+	0.616957i
$129$	−2.41025			−0.212211
$130$	−0.660008	+	5.07131i	−0.0578866	+	0.444783i
$131$			6.18131i			0.540063i	0.962851	+	0.270032i	$0.0870342\pi$
$131$			6.18131i			0.540063i	−0.962851	+	0.270032i	$0.912966\pi$
$132$	2.94719	+	0.780346i	0.256520	+	0.0679204i
$133$		−	1.10679i		−	0.0959709i
$134$	−5.93942	−	0.772988i	−0.513087	−	0.0667760i
$135$	−5.90988			−0.508642
$136$	−3.77043	+	9.21831i	−0.323312	+	0.790463i
$137$	2.69492			0.230242			0.115121	−	0.993351i	$-0.463274\pi$
$137$	2.69492			0.230242			0.115121	+	0.993351i	$0.463274\pi$
$138$	3.06166	+	0.398462i	0.260626	+	0.0339193i
$139$			10.0486i			0.852314i	0.904649	+	0.426157i	$0.140133\pi$
$139$			10.0486i			0.852314i	−0.904649	+	0.426157i	$0.859867\pi$
$140$	1.85117	−	6.99148i	0.156453	−	0.590888i
$141$		−	3.71510i		−	0.312868i
$142$	0.158120	−	1.21495i	0.0132692	−	0.101956i
$143$	−5.52552			−0.462067
$144$	10.1631	+	5.78765i	0.846928	+	0.482304i
$145$	36.2936			3.01402
$146$	−1.04067	+	7.99621i	−0.0861266	+	0.661771i
$147$		−	0.275879i		−	0.0227542i
$148$	1.85437	−	7.00355i	0.152428	−	0.575688i
$149$		−	11.6165i		−	0.951664i	−0.879536	−	0.475832i	$-0.842147\pi$
$149$		−	11.6165i		−	0.951664i	0.879536	−	0.475832i	$-0.157853\pi$
$150$	3.12487	+	0.406688i	0.255145	+	0.0332059i
$151$	4.16990			0.339342			0.169671	−	0.985501i	$-0.445730\pi$
$151$	4.16990			0.339342			0.169671	+	0.985501i	$0.445730\pi$
$152$	−2.89748	−	1.18511i	−0.235017	−	0.0961254i
$153$	10.2957			0.832361
$154$	7.74891	+	1.00849i	0.624425	+	0.0812661i
$155$			18.5416i			1.48929i
$156$	0.533379	+	0.141226i	0.0427045	+	0.0113071i
$157$		−	19.3608i		−	1.54516i	−0.634918	−	0.772580i	$-0.718966\pi$
$157$		−	19.3608i		−	1.54516i	0.634918	−	0.772580i	$-0.281034\pi$
$158$	−1.33154	+	10.2312i	−0.105932	+	0.813950i
$159$	−0.617164			−0.0489443
$160$	−16.3209	−	12.3325i	−1.29028	−	0.974966i
$161$	7.91353			0.623674
$162$	1.51867	−	11.6690i	0.119318	−	0.916802i
$163$		−	10.0263i		−	0.785320i	−0.919684	−	0.392660i	$-0.871555\pi$
$163$		−	10.0263i		−	0.785320i	0.919684	−	0.392660i	$-0.128445\pi$
$164$	−2.01061	−	0.532362i	−0.157003	−	0.0415705i
$165$			5.51245i			0.429144i
$166$	−10.2045	−	1.32807i	−0.792020	−	0.103078i
$167$	15.3016			1.18407			0.592037	−	0.805911i	$-0.298324\pi$
$167$	15.3016			1.18407			0.592037	+	0.805911i	$0.298324\pi$
$168$	−0.722228	−	0.295403i	−0.0557211	−	0.0227908i
$169$	−1.00000			−0.0769231
$170$	−17.8573	−	2.32405i	−1.36959	−	0.178247i
$171$			3.23613i			0.247473i
$172$	−4.47237	+	16.8912i	−0.341015	+	1.28794i
$173$		−	12.8175i		−	0.974498i	−0.873263	−	0.487249i	$-0.838000\pi$
$173$		−	12.8175i		−	0.974498i	0.873263	−	0.487249i	$-0.162000\pi$
$174$	0.505351	−	3.88297i	0.0383106	−	0.294367i
$175$	8.07691			0.610557
$176$	10.9374	−	19.2061i	0.824438	−	1.44771i
$177$	1.32071			0.0992709
$178$	1.39844	−	10.7452i	0.104817	−	0.805386i
$179$			7.47709i			0.558864i	0.960165	+	0.279432i	$0.0901462\pi$
$179$			7.47709i			0.558864i	−0.960165	+	0.279432i	$0.909854\pi$
$180$	−5.41263	+	20.4423i	−0.403434	+	1.52368i
$181$			22.4833i			1.67117i	0.549360	+	0.835585i	$0.314871\pi$
$181$			22.4833i			1.67117i	−0.549360	+	0.835585i	$0.685129\pi$
$182$	1.40239	+	0.182514i	0.103952	+	0.0135289i
$183$	0.237739			0.0175742
$184$	8.47355	−	20.7169i	0.624678	−	1.52727i
$185$	13.0995			0.963093
$186$	1.98372	+	0.258173i	0.145454	+	0.0189301i
$187$		−	19.4567i		−	1.42281i
$188$	−26.0356	−	6.89359i	−1.89884	−	0.502767i
$189$			1.63428i			0.118876i
$190$	0.730491	−	5.61288i	0.0529954	−	0.407201i
$191$	−11.6789			−0.845057			−0.422528	−	0.906350i	$-0.638857\pi$
$191$	−11.6789			−0.845057			−0.422528	+	0.906350i	$0.638857\pi$
$192$	−1.54668	+	1.57442i	−0.111622	+	0.113624i
$193$	−11.6391			−0.837800			−0.418900	−	0.908032i	$-0.637584\pi$
$193$	−11.6391			−0.837800			−0.418900	+	0.908032i	$0.637584\pi$
$194$	2.33358	−	17.9305i	0.167541	−	1.28734i
$195$			0.997636i			0.0714422i
$196$	−1.93338	−	0.511911i	−0.138098	−	0.0365651i
$197$			5.59686i			0.398760i	0.979922	+	0.199380i	$0.0638927\pi$
$197$			5.59686i			0.398760i	−0.979922	+	0.199380i	$0.936107\pi$
$198$	−22.6570	−	2.94870i	−1.61016	−	0.209555i
$199$	20.2542			1.43578			0.717890	−	0.696156i	$-0.245108\pi$
$199$	20.2542			1.43578			0.717890	+	0.696156i	$0.245108\pi$
$200$	8.64848	−	21.1446i	0.611540	−	1.49515i
$201$	−1.16841			−0.0824133
$202$	−13.2688	−	1.72687i	−0.933589	−	0.121502i
$203$		−	10.0364i		−	0.704415i
$204$	−0.497291	+	1.87816i	−0.0348173	+	0.131497i
$205$		−	3.76066i		−	0.262656i
$206$	0.0918635	−	0.705852i	0.00640043	−	0.0491790i
$207$	−23.1383			−1.60822
$208$	1.97944	−	3.47589i	0.137249	−	0.241010i
$209$	6.11559			0.423024
$210$	0.182083	−	1.39907i	0.0125649	−	0.0965451i
$211$		−	12.3571i		−	0.850695i	−0.905030	−	0.425347i	$-0.860152\pi$
$211$		−	12.3571i		−	0.850695i	0.905030	−	0.425347i	$-0.139848\pi$
$212$	−1.14519	+	4.32511i	−0.0786516	+	0.297050i
$213$		−	0.239007i		−	0.0163765i
$214$	4.62527	+	0.601958i	0.316177	+	0.0411490i
$215$	−31.5933			−2.15465
$216$	4.27840	+	1.74993i	0.291108	+	0.119068i
$217$	5.12736			0.348068
$218$	−24.0654	−	3.13200i	−1.62991	−	0.212126i
$219$			1.57303i			0.106295i
$220$	38.6315	+	10.2287i	2.60454	+	0.689618i
$221$		−	3.52124i		−	0.236865i
$222$	0.182397	−	1.40149i	0.0122417	−	0.0940616i
$223$	14.7408			0.987120			0.493560	−	0.869712i	$-0.335695\pi$
$223$	14.7408			0.987120			0.493560	+	0.869712i	$0.335695\pi$
$224$	−3.41033	+	4.51327i	−0.227863	+	0.301556i
$225$	−23.6160			−1.57440
$226$	0.799627	−	6.14410i	0.0531904	−	0.408700i
$227$		−	0.323771i		−	0.0214894i	−0.999942	−	0.0107447i	$-0.996580\pi$
$227$		−	0.323771i		−	0.0214894i	0.999942	−	0.0107447i	$-0.00342021\pi$
$228$	−0.590339	−	0.156307i	−0.0390961	−	0.0103517i
$229$		−	22.2035i		−	1.46725i	−0.679556	−	0.733624i	$-0.737827\pi$
$229$		−	22.2035i		−	1.46725i	0.679556	−	0.733624i	$-0.262173\pi$
$230$	40.1320	+	5.22300i	2.64622	+	0.344394i
$231$	1.52438			0.100297
$232$	−26.2743	−	10.7466i	−1.72499	−	0.705550i
$233$	17.2053			1.12716			0.563579	−	0.826062i	$-0.309424\pi$
$233$	17.2053			1.12716			0.563579	+	0.826062i	$0.309424\pi$
$234$	−4.10043	−	0.533652i	−0.268053	−	0.0348859i
$235$		−	48.6971i		−	3.17665i
$236$	2.45066	−	9.25562i	0.159525	−	0.602490i
$237$			2.01269i			0.130738i
$238$	−0.642678	+	4.93815i	−0.0416586	+	0.320093i
$239$	−14.0545			−0.909112			−0.454556	−	0.890718i	$-0.650202\pi$
$239$	−14.0545			−0.909112			−0.454556	+	0.890718i	$0.650202\pi$
$240$	−3.46768	−	1.97476i	−0.223837	−	0.127470i
$241$	14.8607			0.957262			0.478631	−	0.878016i	$-0.341133\pi$
$241$	14.8607			0.957262			0.478631	+	0.878016i	$0.341133\pi$
$242$	−3.56475	+	27.3905i	−0.229151	+	1.76073i
$243$		−	7.19838i		−	0.461776i
$244$	0.441139	−	1.66609i	0.0282410	−	0.106660i
$245$		−	3.61620i		−	0.231031i
$246$	−0.402345	−	0.0523635i	−0.0256526	−	0.00333857i
$247$	1.10679			0.0704234
$248$	5.49021	−	13.4230i	0.348628	−	0.852360i
$249$	−2.00744			−0.127216
$250$	15.6040	+	2.03079i	0.986881	+	0.128438i
$251$			25.9434i			1.63753i	0.574128	+	0.818766i	$0.305341\pi$
$251$			25.9434i			1.63753i	−0.574128	+	0.818766i	$0.694659\pi$
$252$	5.65298	+	1.49677i	0.356104	+	0.0942878i
$253$			43.7263i			2.74905i
$254$	−0.173616	+	1.33401i	−0.0108936	+	0.0837035i
$255$	−3.51292			−0.219988
$256$	8.16367	+	13.7606i	0.510230	+	0.860038i
$257$	18.1892			1.13461			0.567306	−	0.823507i	$-0.307985\pi$
$257$	18.1892			1.13461			0.567306	+	0.823507i	$0.307985\pi$
$258$	−0.439905	+	3.38010i	−0.0273873	+	0.210436i
$259$		−	3.62244i		−	0.225088i
$260$	6.99148	+	1.85117i	0.433593	+	0.114805i
$261$			29.3453i			1.81643i
$262$	8.66858	+	1.12818i	0.535547	+	0.0696990i
$263$	−26.5683			−1.63827			−0.819135	−	0.573601i	$-0.805546\pi$
$263$	−26.5683			−1.63827			−0.819135	+	0.573601i	$0.805546\pi$
$264$	1.63225	−	3.99068i	0.100458	−	0.245610i
$265$	−8.08972			−0.496948
$266$	−1.55215	−	0.202005i	−0.0951683	−	0.0123857i
$267$		−	2.11381i		−	0.129363i
$268$	−2.16806	+	8.18828i	−0.132435	+	0.500179i
$269$			25.0750i			1.52885i	0.644713	+	0.764425i	$0.276977\pi$
$269$			25.0750i			1.52885i	−0.644713	+	0.764425i	$0.723023\pi$
$270$	−1.07864	+	8.28794i	−0.0656438	+	0.504388i
$271$	2.65065			0.161016			0.0805079	−	0.996754i	$-0.474346\pi$
$271$	2.65065			0.161016			0.0805079	+	0.996754i	$0.474346\pi$
$272$	12.2395	+	6.97008i	0.742127	+	0.422623i
$273$	0.275879			0.0166970
$274$	0.491861	−	3.77931i	0.0297144	−	0.228317i
$275$			44.6291i			2.69123i
$276$	1.11760	−	4.22091i	0.0672713	−	0.254069i
$277$			18.7189i			1.12471i	0.826895	+	0.562356i	$0.190105\pi$
$277$			18.7189i			1.12471i	−0.826895	+	0.562356i	$0.809895\pi$
$278$	14.0921	+	1.83402i	0.845186	+	0.109997i
$279$	−14.9918			−0.897538
$280$	−9.46689	−	3.87211i	−0.565755	−	0.231403i
$281$	−14.3291			−0.854803			−0.427402	−	0.904062i	$-0.640571\pi$
$281$	−14.3291			−0.854803			−0.427402	+	0.904062i	$0.640571\pi$
$282$	−5.21000	−	0.678058i	−0.310251	−	0.0403778i
$283$		−	14.4237i		−	0.857400i	−0.903447	−	0.428700i	$-0.858972\pi$
$283$		−	14.4237i		−	0.857400i	0.903447	−	0.428700i	$-0.141028\pi$
$284$	−1.67497	−	0.443492i	−0.0993912	−	0.0263164i
$285$		−	1.10417i		−	0.0654056i
$286$	−1.00849	+	7.74891i	−0.0596330	+	0.458203i
$287$	−1.03995			−0.0613862
$288$	9.97144	−	13.1963i	0.587573	−	0.777600i
$289$	−4.60084			−0.270637
$290$	6.62409	−	50.8976i	0.388980	−	2.98881i
$291$		−	3.52732i		−	0.206775i
$292$	11.0238	+	2.91885i	0.645122	+	0.170813i
$293$			4.97250i			0.290497i	0.989395	+	0.145248i	$0.0463981\pi$
$293$			4.97250i			0.290497i	−0.989395	+	0.145248i	$0.953602\pi$
$294$	−0.386890	−	0.0503520i	−0.0225639	−	0.00293659i
$295$	17.3118			1.00793
$296$	−9.48323	−	3.87879i	−0.551202	−	0.225450i
$297$	−9.03024			−0.523988
$298$	−16.2909	−	2.12019i	−0.943706	−	0.122819i
$299$			7.91353i			0.457651i
$300$	1.14067	−	4.30805i	0.0658565	−	0.248726i
$301$			8.73661i			0.503570i
$302$	0.761066	−	5.84781i	0.0437944	−	0.336504i
$303$	−2.61026			−0.149955
$304$	−2.19082	+	3.84708i	−0.125652	+	0.220645i
$305$	3.11626			0.178436
$306$	1.87912	−	14.4386i	0.107422	−	0.825400i
$307$			2.53252i			0.144539i	0.997385	+	0.0722693i	$0.0230241\pi$
$307$			2.53252i			0.144539i	−0.997385	+	0.0722693i	$0.976976\pi$
$308$	2.82857	−	10.6829i	0.161173	−	0.608715i
$309$		−	0.138856i		−	0.00789925i
$310$	26.0024	+	3.38410i	1.47684	+	0.192204i
$311$	21.4305			1.21521			0.607607	−	0.794238i	$-0.292129\pi$
$311$	21.4305			1.21521			0.607607	+	0.794238i	$0.292129\pi$
$312$	0.295403	−	0.722228i	0.0167239	−	0.0408881i
$313$	−31.4457			−1.77742			−0.888708	−	0.458473i	$-0.848397\pi$
$313$	−31.4457			−1.77742			−0.888708	+	0.458473i	$0.848397\pi$
$314$	−27.1513	−	3.53362i	−1.53224	−	0.199414i
$315$			10.5734i			0.595742i
$316$	14.1051	+	3.73468i	0.793471	+	0.210092i
$317$		−	20.0491i		−	1.12607i	−0.826433	−	0.563036i	$-0.809633\pi$
$317$		−	20.0491i		−	1.12607i	0.826433	−	0.563036i	$-0.190367\pi$
$318$	−0.112641	+	0.865502i	−0.00631661	+	0.0485349i
$319$	55.4562			3.10495
$320$	−20.2737	+	20.6374i	−1.13333	+	1.15366i
$321$	0.909889			0.0507851
$322$	1.44433	−	11.0978i	0.0804895	−	0.618458i
$323$			3.89728i			0.216850i
$324$	−16.0873	−	4.25952i	−0.893737	−	0.236640i
$325$			8.07691i			0.448026i
$326$	−14.0607	−	1.82994i	−0.778752	−	0.101351i
$327$	−4.73417			−0.261800
$328$	−1.11354	+	2.72249i	−0.0614851	+	0.150325i
$329$	−13.4664			−0.742425
$330$	7.73059	+	1.00610i	0.425555	+	0.0553841i
$331$			25.2112i			1.38573i	0.721065	+	0.692867i	$0.243653\pi$
$331$			25.2112i			1.38573i	−0.721065	+	0.692867i	$0.756347\pi$
$332$	−3.72492	+	14.0682i	−0.204432	+	0.772094i
$333$			10.5916i			0.580417i
$334$	2.79276	−	21.4588i	0.152813	−	1.17417i
$335$	−15.3154			−0.836770
$336$	−0.546086	+	0.958928i	−0.0297914	+	0.0523138i
$337$	−16.0856			−0.876236			−0.438118	−	0.898918i	$-0.644355\pi$
$337$	−16.0856			−0.876236			−0.438118	+	0.898918i	$0.644355\pi$
$338$	−0.182514	+	1.40239i	−0.00992747	+	0.0762798i
$339$		−	1.20868i		−	0.0656463i
$340$	−6.51844	+	24.6187i	−0.353512	+	1.33514i
$341$			28.3313i			1.53423i
$342$	4.53831	+	0.590641i	0.245404	+	0.0319382i
$343$	−1.00000			−0.0539949
$344$	22.8717	+	9.35487i	1.23316	+	0.504381i
$345$	7.89482			0.425043
$346$	−17.9751	−	2.33938i	−0.966348	−	0.125766i
$347$		−	5.29694i		−	0.284355i	−0.989841	−	0.142177i	$-0.954590\pi$
$347$		−	5.29694i		−	0.284355i	0.989841	−	0.142177i	$-0.0454104\pi$
$348$	−5.35319	−	1.41740i	−0.286961	−	0.0759804i
$349$			19.0084i			1.01749i	0.860916	+	0.508747i	$0.169891\pi$
$349$			19.0084i			1.01749i	−0.860916	+	0.508747i	$0.830109\pi$
$350$	1.47415	−	11.3269i	0.0787967	−	0.605451i
$351$	−1.63428			−0.0872314
$352$	−24.9382	−	18.8439i	−1.32921	−	1.00438i
$353$	2.67801			0.142536			0.0712680	−	0.997457i	$-0.477295\pi$
$353$	2.67801			0.142536			0.0712680	+	0.997457i	$0.477295\pi$
$354$	0.241049	−	1.85215i	0.0128116	−	0.0984407i
$355$		−	3.13288i		−	0.166276i
$356$	−14.8137	−	3.92230i	−0.785123	−	0.207882i
$357$			0.971439i			0.0514140i
$358$	10.4858	+	1.36468i	0.554190	+	0.0721254i
$359$	22.7147			1.19884			0.599418	−	0.800436i	$-0.295399\pi$
$359$	22.7147			1.19884			0.599418	+	0.800436i	$0.295399\pi$
$360$	27.6802	+	11.3216i	1.45887	+	0.596702i
$361$	17.7750			0.935527
$362$	31.5303	+	4.10353i	1.65720	+	0.215677i
$363$			5.38829i			0.282812i
$364$	0.511911	−	1.93338i	0.0268314	−	0.101336i
$365$			20.6191i			1.07925i
$366$	0.0433907	−	0.333402i	0.00226807	−	0.0174272i
$367$	−3.18895			−0.166462			−0.0832310	−	0.996530i	$-0.526524\pi$
$367$	−3.18895			−0.166462			−0.0832310	+	0.996530i	$0.526524\pi$
$368$	−27.5066	−	15.6643i	−1.43388	−	0.816559i
$369$	3.04070			0.158292
$370$	2.39084	−	18.3705i	0.124294	−	0.955039i
$371$			2.23708i			0.116143i
$372$	0.724116	−	2.73483i	0.0375436	−	0.141794i
$373$		−	22.8764i		−	1.18450i	−0.805756	−	0.592248i	$-0.798240\pi$
$373$		−	22.8764i		−	1.18450i	0.805756	−	0.592248i	$-0.201760\pi$
$374$	−27.2858	−	3.55113i	−1.41092	−	0.183624i
$375$	3.06963			0.158515
$376$	−14.4193	+	35.2538i	−0.743621	+	1.81807i
$377$	10.0364			0.516900
$378$	2.29189	+	0.298279i	0.117882	+	0.0153418i
$379$			14.0537i			0.721891i	0.932587	+	0.360946i	$0.117546\pi$
$379$			14.0537i			0.721891i	−0.932587	+	0.360946i	$0.882454\pi$
$380$	−7.73810	−	2.04886i	−0.396956	−	0.105104i
$381$			0.262429i			0.0134446i
$382$	−2.13157	+	16.3784i	−0.109061	+	0.837990i
$383$	−5.29338			−0.270479			−0.135239	−	0.990813i	$-0.543180\pi$
$383$	−5.29338			−0.270479			−0.135239	+	0.990813i	$0.543180\pi$
$384$	1.92566	+	2.45639i	0.0982683	+	0.125352i
$385$	19.9814			1.01835
$386$	−2.12430	+	16.3225i	−0.108124	+	0.830794i
$387$		−	25.5449i		−	1.29852i
$388$	−24.7196	−	6.54516i	−1.25495	−	0.332280i
$389$		−	21.1015i		−	1.06989i	−0.844887	−	0.534945i	$-0.820332\pi$
$389$		−	21.1015i		−	1.06989i	0.844887	−	0.534945i	$-0.179668\pi$
$390$	1.39907	+	0.182083i	0.0708447	+	0.00922012i
$391$	−27.8655			−1.40922
$392$	−1.07077	+	2.61791i	−0.0540819	+	0.132224i
$393$	1.70530			0.0860208
$394$	7.84896	+	1.02151i	0.395425	+	0.0514628i
$395$			26.3822i			1.32743i
$396$	−8.27044	+	31.2356i	−0.415605	+	1.56965i
$397$			28.3687i			1.42378i	0.702289	+	0.711892i	$0.252162\pi$
$397$			28.3687i			1.42378i	−0.702289	+	0.711892i	$0.747838\pi$
$398$	3.69668	−	28.4042i	0.185298	−	1.42377i
$399$	−0.305341			−0.0152862
$400$	−28.0745	−	15.9877i	−1.40372	−	0.799386i
$401$	−29.0290			−1.44964			−0.724819	−	0.688940i	$-0.758077\pi$
$401$	−29.0290			−1.44964			−0.724819	+	0.688940i	$0.758077\pi$
$402$	−0.213252	+	1.63856i	−0.0106360	+	0.0817241i
$403$			5.12736i			0.255412i
$404$	−4.84349	+	18.2928i	−0.240973	+	0.910101i
$405$		−	30.0897i		−	1.49517i
$406$	−14.0749	−	1.83178i	−0.698525	−	0.0909098i
$407$	20.0159			0.992150
$408$	2.54314	+	1.04018i	0.125904	+	0.0514968i
$409$	−34.4641			−1.70414			−0.852069	−	0.523429i	$-0.824652\pi$
$409$	−34.4641			−1.70414			−0.852069	+	0.523429i	$0.824652\pi$
$410$	−5.27390	−	0.686375i	−0.260460	−	0.0338976i
$411$		−	0.743472i		−	0.0366728i
$412$	−0.973111	−	0.257656i	−0.0479417	−	0.0126938i
$413$		−	4.78728i		−	0.235567i
$414$	−4.22307	+	32.4488i	−0.207553	+	1.59477i
$415$	−26.3133			−1.29167
$416$	−4.51327	−	3.41033i	−0.221281	−	0.167205i
$417$	2.77221			0.135756
$418$	1.11618	−	8.57642i	0.0545943	−	0.419486i
$419$		−	4.27902i		−	0.209044i	−0.994523	−	0.104522i	$-0.966669\pi$
$419$		−	4.27902i		−	0.209044i	0.994523	−	0.104522i	$-0.0333312\pi$
$420$	−1.92881	−	0.510701i	−0.0941161	−	0.0249197i
$421$		−	7.01406i		−	0.341844i	−0.985285	−	0.170922i	$-0.945325\pi$
$421$		−	7.01406i		−	0.341844i	0.985285	−	0.170922i	$-0.0546747\pi$
$422$	−17.3294	−	2.25534i	−0.843581	−	0.109788i
$423$	39.3742			1.91444
$424$	5.85647	+	2.39539i	0.284415	+	0.116330i
$425$	−28.4408			−1.37958
$426$	−0.335180	−	0.0436222i	−0.0162395	−	0.00211350i
$427$		−	0.861749i		−	0.0417029i
$428$	1.68836	−	6.37655i	0.0816097	−	0.308222i
$429$			1.52438i			0.0735976i
$430$	−5.76623	+	44.3061i	−0.278073	+	2.13663i
$431$	−29.6150			−1.42651			−0.713253	−	0.700906i	$-0.752779\pi$
$431$	−29.6150			−1.42651			−0.713253	+	0.700906i	$0.752779\pi$
$432$	3.23495	−	5.68058i	0.155642	−	0.273307i
$433$	11.8181			0.567939			0.283970	−	0.958833i	$-0.408348\pi$
$433$	11.8181			0.567939			0.283970	+	0.958833i	$0.408348\pi$
$434$	0.935817	−	7.19054i	0.0449206	−	0.345157i
$435$		−	10.0126i		−	0.480070i
$436$	−8.78455	+	33.1773i	−0.420703	+	1.58890i
$437$		−	8.75862i		−	0.418982i
$438$	2.20599	+	0.287100i	0.105406	+	0.0137182i
$439$	15.2077			0.725822			0.362911	−	0.931824i	$-0.381783\pi$
$439$	15.2077			0.725822			0.362911	+	0.931824i	$0.381783\pi$
$440$	21.3954	−	52.3095i	1.01999	−	2.49376i
$441$	2.92389			0.139233
$442$	−4.93815	−	0.642678i	−0.234884	−	0.0305691i
$443$			14.9404i			0.709842i	0.934896	+	0.354921i	$0.115492\pi$
$443$			14.9404i			0.709842i	−0.934896	+	0.354921i	$0.884508\pi$
$444$	−1.93214	−	0.511582i	−0.0916951	−	0.0242786i
$445$		−	27.7076i		−	1.31347i
$446$	2.69041	−	20.6724i	0.127395	−	0.978865i
$447$	−3.20477			−0.151580
$448$	5.70692	+	5.60634i	0.269627	+	0.264875i
$449$	29.9678			1.41427			0.707133	−	0.707081i	$-0.249988\pi$
$449$	29.9678			1.41427			0.707133	+	0.707081i	$0.249988\pi$
$450$	−4.31026	+	33.1188i	−0.203187	+	1.56123i
$451$		−	5.74625i		−	0.270581i
$452$	−8.47046	−	2.24277i	−0.398417	−	0.105491i
$453$		−	1.15039i		−	0.0540500i
$454$	−0.454052	−	0.0590928i	−0.0213097	−	0.00277336i
$455$	3.61620			0.169530
$456$	−0.326949	+	0.799355i	−0.0153108	+	0.0374332i
$457$	11.0522			0.517001			0.258501	−	0.966011i	$-0.416772\pi$
$457$	11.0522			0.517001			0.258501	+	0.966011i	$0.416772\pi$
$458$	−31.1379	−	4.05245i	−1.45498	−	0.189359i
$459$		−	5.75470i		−	0.268606i
$460$	14.6493	−	55.3273i	0.683028	−	2.57965i
$461$			41.6333i			1.93906i	0.244977	+	0.969529i	$0.421220\pi$
$461$			41.6333i			1.93906i	−0.244977	+	0.969529i	$0.578780\pi$
$462$	0.278221	−	2.13777i	0.0129440	−	0.0994578i
$463$	36.3379			1.68877			0.844384	−	0.535739i	$-0.179967\pi$
$463$	36.3379			1.68877			0.844384	+	0.535739i	$0.179967\pi$
$464$	−19.8664	+	34.8854i	−0.922272	+	1.61951i
$465$	5.11524			0.237213
$466$	3.14022	−	24.1285i	0.145468	−	1.11773i
$467$			8.62570i			0.399150i	0.979883	+	0.199575i	$0.0639561\pi$
$467$			8.62570i			0.399150i	−0.979883	+	0.199575i	$0.936044\pi$
$468$	−1.49677	+	5.65298i	−0.0691883	+	0.261309i
$469$			4.23522i			0.195564i
$470$	−68.2922	−	8.88792i	−3.15008	−	0.409969i
$471$	−5.34124			−0.246112
$472$	−12.5327	−	5.12606i	−0.576863	−	0.235946i
$473$	−48.2743			−2.21965
$474$	2.82257	+	0.367345i	0.129645	+	0.0168727i
$475$		−	8.93944i		−	0.410170i
$476$	6.80789	+	1.80257i	0.312039	+	0.0826204i
$477$		−	6.54097i		−	0.299490i
$478$	−2.56515	+	19.7099i	−0.117327	+	0.901509i
$479$	14.0769			0.643191			0.321595	−	0.946877i	$-0.395781\pi$
$479$	14.0769			0.643191			0.321595	+	0.946877i	$0.395781\pi$
$480$	−3.40227	+	4.50260i	−0.155292	+	0.205515i
$481$	3.62244			0.165169
$482$	2.71229	−	20.8404i	0.123541	−	0.949256i
$483$		−	2.18318i		−	0.0993382i
$484$	37.7614	+	9.99831i	1.71643	+	0.454469i
$485$		−	46.2358i		−	2.09946i
$486$	−10.0949	−	1.31381i	−0.457915	−	0.0595955i
$487$	30.9096			1.40065			0.700324	−	0.713826i	$-0.253039\pi$
$487$	30.9096			1.40065			0.700324	+	0.713826i	$0.253039\pi$
$488$	−2.25598	−	0.922732i	−0.102124	−	0.0417701i
$489$	−2.76605			−0.125085
$490$	−5.07131	−	0.660008i	−0.229099	−	0.0298161i
$491$			30.4626i			1.37476i	0.726300	+	0.687378i	$0.241238\pi$
$491$			30.4626i			1.37476i	−0.726300	+	0.687378i	$0.758762\pi$
$492$	−0.146868	+	0.554687i	−0.00662130	+	0.0250072i
$493$			35.3405i			1.59166i
$494$	0.202005	−	1.55215i	0.00908864	−	0.0698344i
$495$	−58.4234			−2.62593
$496$	−17.8222	−	10.1493i	−0.800238	−	0.455716i
$497$	−0.866345			−0.0388609
$498$	−0.366386	+	2.81520i	−0.0164182	+	0.126152i
$499$			9.18401i			0.411133i	0.978643	+	0.205566i	$0.0659036\pi$
$499$			9.18401i			0.411133i	−0.978643	+	0.205566i	$0.934096\pi$
$500$	5.69589	−	21.5121i	0.254728	−	0.962052i
$501$		−	4.22140i		−	0.188598i
$502$	36.3826	+	4.73504i	1.62384	+	0.211335i
$503$	3.80294			0.169565			0.0847824	−	0.996399i	$-0.472980\pi$
$503$	3.80294			0.169565			0.0847824	+	0.996399i	$0.472980\pi$
$504$	3.13080	−	7.65449i	0.139457	−	0.340958i
$505$	−34.2150			−1.52255
$506$	61.3212	+	7.98068i	2.72606	+	0.354785i
$507$			0.275879i			0.0122522i
$508$	1.83912	+	0.486953i	0.0815976	+	0.0216051i
$509$		−	28.6024i		−	1.26778i	−0.773423	−	0.633890i	$-0.781457\pi$
$509$		−	28.6024i		−	1.26778i	0.773423	−	0.633890i	$-0.218543\pi$
$510$	−0.641158	+	4.92647i	−0.0283910	+	0.218148i
$511$	5.70186			0.252235
$512$	20.7877	−	8.93712i	0.918695	−	0.394969i
$513$	1.80880			0.0798607
$514$	3.31979	−	25.5083i	0.146430	−	1.12512i
$515$		−	1.82011i		−	0.0802038i
$516$	4.65992	+	1.23383i	0.205142	+	0.0543165i
$517$		−	74.4087i		−	3.27249i
$518$	−5.08007	−	0.661148i	−0.223205	−	0.0290492i
$519$	−3.53609			−0.155217
$520$	3.87211	−	9.46689i	0.169803	−	0.415151i
$521$	20.2308			0.886327			0.443164	−	0.896441i	$-0.353856\pi$
$521$	20.2308			0.886327			0.443164	+	0.896441i	$0.353856\pi$
$522$	41.1534	+	5.35593i	1.80124	+	0.234423i
$523$		−	25.8242i		−	1.12921i	−0.825360	−	0.564607i	$-0.809028\pi$
$523$		−	25.8242i		−	1.12921i	0.825360	−	0.564607i	$-0.190972\pi$
$524$	3.16428	−	11.9508i	0.138232	−	0.522073i
$525$		−	2.22825i		−	0.0972489i
$526$	−4.84909	+	37.2590i	−0.211430	+	1.62457i
$527$	−18.0547			−0.786475
$528$	−5.29857	−	3.01740i	−0.230591	−	0.131316i
$529$	39.6240			1.72278
$530$	−1.47649	+	11.3449i	−0.0641346	+	0.492792i
$531$			13.9975i			0.607439i
$532$	−0.566578	+	2.13984i	−0.0245643	+	0.0927739i
$533$		−	1.03995i		−	0.0450452i
$534$	−2.96438	−	0.385800i	−0.128281	−	0.0166952i
$535$	11.9267			0.515638
$536$	11.0874	+	4.53493i	0.478904	+	0.195879i
$537$	2.06278			0.0890154
$538$	35.1648	+	4.57655i	1.51606	+	0.197309i
$539$		−	5.52552i		−	0.238001i
$540$	11.4260	+	3.02534i	0.491698	+	0.130190i
$541$			7.96843i			0.342589i	0.985220	+	0.171295i	$0.0547950\pi$
$541$			7.96843i			0.342589i	−0.985220	+	0.171295i	$0.945205\pi$
$542$	0.483782	−	3.71724i	0.0207802	−	0.159669i
$543$	6.20268			0.266183
$544$	12.0086	−	15.8923i	0.514865	−	0.681378i
$545$	−62.0550			−2.65815
$546$	0.0503520	−	0.386890i	0.00215486	−	0.0165574i
$547$			14.9906i			0.640953i	0.947256	+	0.320477i	$0.103843\pi$
$547$			14.9906i			0.640953i	−0.947256	+	0.320477i	$0.896157\pi$
$548$	−5.21029	−	1.37956i	−0.222572	−	0.0589318i
$549$			2.51966i			0.107536i
$550$	62.5872	+	8.14545i	2.66873	+	0.347323i
$551$	−11.1082			−0.473224
$552$	−5.71537	−	2.33768i	−0.243262	−	0.0994982i
$553$	7.29555			0.310238
$554$	26.2512	+	3.41647i	1.11531	+	0.145152i
$555$		−	3.61388i		−	0.153401i
$556$	5.14401	−	19.4278i	0.218155	−	0.823922i
$557$		−	4.35114i		−	0.184364i	−0.995742	−	0.0921819i	$-0.970616\pi$
$557$		−	4.35114i		−	0.184364i	0.995742	−	0.0921819i	$-0.0293841\pi$
$558$	−2.73623	+	21.0244i	−0.115834	+	0.890032i
$559$	−8.73661			−0.369519
$560$	−7.15804	+	12.5695i	−0.302482	+	0.531160i
$561$	−5.36770			−0.226625
$562$	−2.61527	+	20.0950i	−0.110318	+	0.847654i
$563$		−	19.3697i		−	0.816334i	−0.912907	−	0.408167i	$-0.866168\pi$
$563$		−	19.3697i		−	0.816334i	0.912907	−	0.408167i	$-0.133832\pi$
$564$	−1.90180	+	7.18268i	−0.0800802	+	0.302445i
$565$		−	15.8432i		−	0.666529i
$566$	−20.2276	−	2.63253i	−0.850230	−	0.110654i
$567$	−8.32081			−0.349441
$568$	−0.927653	+	2.26801i	−0.0389235	+	0.0951637i
$569$	37.1682			1.55817			0.779087	−	0.626916i	$-0.215683\pi$
$569$	37.1682			1.55817			0.779087	+	0.626916i	$0.215683\pi$
$570$	−1.54848	−	0.201527i	−0.0648586	−	0.00844106i
$571$		−	21.5095i		−	0.900143i	−0.892992	−	0.450072i	$-0.851398\pi$
$571$		−	21.5095i		−	0.900143i	0.892992	−	0.450072i	$-0.148602\pi$
$572$	10.6829	+	2.82857i	0.446675	+	0.118269i
$573$			3.22197i			0.134600i
$574$	−0.189806	+	1.45841i	−0.00792233	+	0.0608729i
$575$	63.9169			2.66552
$576$	−16.6864	−	16.3923i	−0.695267	−	0.683014i
$577$	−15.0168			−0.625159			−0.312579	−	0.949892i	$-0.601193\pi$
$577$	−15.0168			−0.625159			−0.312579	+	0.949892i	$0.601193\pi$
$578$	−0.839718	+	6.45215i	−0.0349277	+	0.268374i
$579$			3.21099i			0.133444i
$580$	−70.1691	−	18.5791i	−2.91361	−	0.771454i
$581$			7.27650i			0.301880i
$582$	−4.94667	−	0.643786i	−0.205046	−	0.0266858i
$583$	−12.3610			−0.511941
$584$	6.10536	−	14.9270i	0.252642	−	0.617682i
$585$	−10.5734			−0.437155
$586$	6.97337	+	0.907552i	0.288067	+	0.0374906i
$587$		−	16.8666i		−	0.696161i	−0.937465	−	0.348080i	$-0.886834\pi$
$587$		−	16.8666i		−	0.696161i	0.937465	−	0.348080i	$-0.113166\pi$
$588$	−0.141226	+	0.533379i	−0.00582406	+	0.0219962i
$589$		−	5.67491i		−	0.233831i
$590$	3.15965	−	24.2778i	0.130081	−	0.999502i
$591$	1.54406			0.0635141
$592$	−7.17039	+	12.5912i	−0.294701	+	0.517496i
$593$	−24.9466			−1.02443			−0.512217	−	0.858856i	$-0.671176\pi$
$593$	−24.9466			−1.02443			−0.512217	+	0.858856i	$0.671176\pi$
$594$	−1.64815	+	12.6639i	−0.0676243	+	0.519606i
$595$			12.7335i			0.522024i
$596$	−5.94664	+	22.4592i	−0.243584	+	0.919963i
$597$		−	5.58771i		−	0.228690i
$598$	11.0978	+	1.44433i	0.453824	+	0.0590632i
$599$	18.5685			0.758687			0.379343	−	0.925256i	$-0.376150\pi$
$599$	18.5685			0.758687			0.379343	+	0.925256i	$0.376150\pi$
$600$	−5.83337	−	2.38594i	−0.238146	−	0.0974056i
$601$	−1.28859			−0.0525625			−0.0262813	−	0.999655i	$-0.508367\pi$
$601$	−1.28859			−0.0525625			−0.0262813	+	0.999655i	$0.508367\pi$
$602$	12.2521	+	1.59456i	0.499358	+	0.0649893i
$603$		−	12.3833i		−	0.504288i
$604$	−8.06199	−	2.13462i	−0.328038	−	0.0868564i
$605$			70.6292i			2.87149i
$606$	−0.476409	+	3.66059i	−0.0193528	+	0.148701i
$607$	4.75102			0.192838			0.0964190	−	0.995341i	$-0.469261\pi$
$607$	4.75102			0.192838			0.0964190	+	0.995341i	$0.469261\pi$
$608$	4.99524	+	3.77452i	0.202584	+	0.153077i
$609$	−2.76883			−0.112199
$610$	0.568762	−	4.37020i	0.0230285	−	0.176944i
$611$		−	13.4664i		−	0.544791i
$612$	−19.9055	−	5.27050i	−0.804634	−	0.213047i
$613$		−	10.0018i		−	0.403967i	−0.979389	−	0.201984i	$-0.935261\pi$
$613$		−	10.0018i		−	0.403967i	0.979389	−	0.201984i	$-0.0647388\pi$
$614$	3.55158	+	0.462222i	0.143330	+	0.0186537i
$615$	−1.03749			−0.0418356
$616$	−14.4653	−	5.91654i	−0.582824	−	0.238384i
$617$	−13.2245			−0.532396			−0.266198	−	0.963918i	$-0.585768\pi$
$617$	−13.2245			−0.532396			−0.266198	+	0.963918i	$0.585768\pi$
$618$	−0.194730	−	0.0253432i	−0.00783319	−	0.00101945i
$619$			23.6609i			0.951011i	0.879713	+	0.475506i	$0.157735\pi$
$619$			23.6609i			0.951011i	−0.879713	+	0.475506i	$0.842265\pi$
$620$	9.49164	−	35.8478i	0.381193	−	1.43968i
$621$			12.9329i			0.518980i
$622$	3.91138	−	30.0539i	0.156832	−	1.20505i
$623$	−7.66208			−0.306975
$624$	−0.958928	−	0.546086i	−0.0383878	−	0.0218609i
$625$	−0.148100			−0.00592399
$626$	−5.73929	+	44.0990i	−0.229388	+	1.76255i
$627$		−	1.68716i		−	0.0673789i
$628$	−9.91101	+	37.4317i	−0.395492	+	1.49369i
$629$			12.7555i			0.508595i
$630$	14.8280	+	1.92979i	0.590760	+	0.0768848i
$631$	14.7571			0.587469			0.293735	−	0.955887i	$-0.405102\pi$
$631$	14.7571			0.587469			0.293735	+	0.955887i	$0.405102\pi$
$632$	7.81184	−	19.0991i	0.310738	−	0.759722i
$633$	−3.40906			−0.135498
$634$	−28.1166	−	3.65925i	−1.11665	−	0.145328i
$635$			3.43989i			0.136508i
$636$	1.19321	+	0.315933i	0.0473139	+	0.0125276i
$637$		−	1.00000i		−	0.0396214i
$638$	10.1215	−	77.7710i	0.400716	−	3.07898i
$639$	2.53310			0.100208
$640$	25.2413	+	32.1981i	0.997751	+	1.27274i
$641$	−13.7361			−0.542542			−0.271271	−	0.962503i	$-0.587444\pi$
$641$	−13.7361			−0.542542			−0.271271	+	0.962503i	$0.587444\pi$
$642$	0.166068	−	1.27602i	0.00655417	−	0.0503604i
$643$			25.9351i			1.02278i	0.859349	+	0.511390i	$0.170869\pi$
$643$			25.9351i			1.02278i	−0.859349	+	0.511390i	$0.829131\pi$
$644$	−15.2998	−	4.05103i	−0.602898	−	0.159633i
$645$			8.71595i			0.343190i
$646$	5.46549	+	0.711309i	0.215037	+	0.0279861i
$647$	12.2027			0.479737			0.239868	−	0.970805i	$-0.422896\pi$
$647$	12.2027			0.479737			0.239868	+	0.970805i	$0.422896\pi$
$648$	−8.90964	+	21.7831i	−0.350004	+	0.855722i
$649$	26.4522			1.03834
$650$	11.3269	+	1.47415i	0.444279	+	0.0578210i
$651$		−	1.41453i		−	0.0554399i
$652$	−5.13257	+	19.3846i	−0.201007	+	0.759160i
$653$			11.5584i			0.452316i	0.974091	+	0.226158i	$0.0726166\pi$
$653$			11.5584i			0.452316i	−0.974091	+	0.226158i	$0.927383\pi$
$654$	−0.864054	+	6.63914i	−0.0337872	+	0.259611i
$655$	22.3528			0.873398
$656$	3.61475	+	2.05851i	0.141132	+	0.0803714i
$657$	−16.6716			−0.650422
$658$	−2.45781	+	18.8851i	−0.0958153	+	0.736216i
$659$			30.8839i			1.20307i	0.798848	+	0.601533i	$0.205443\pi$
$659$			30.8839i			1.20307i	−0.798848	+	0.601533i	$0.794557\pi$
$660$	2.82189	−	10.6576i	0.109842	−	0.414848i
$661$		−	29.5707i		−	1.15017i	−0.818094	−	0.575084i	$-0.804969\pi$
$661$		−	29.5707i		−	1.15017i	0.818094	−	0.575084i	$-0.195031\pi$
$662$	35.3559	+	4.60141i	1.37415	+	0.178839i
$663$	−0.971439			−0.0377276
$664$	19.0492	+	7.79143i	0.739254	+	0.302366i
$665$	−4.00238			−0.155205
$666$	14.8536	+	1.93312i	0.575564	+	0.0749070i
$667$		−	79.4232i		−	3.07528i
$668$	−29.5838	−	7.83307i	−1.14463	−	0.303070i
$669$		−	4.06670i		−	0.157228i
$670$	−2.79528	+	21.4781i	−0.107991	+	0.829772i
$671$	4.76161			0.183820
$672$	1.24512	+	0.940841i	0.0480315	+	0.0362937i
$673$	−40.3299			−1.55460			−0.777301	−	0.629128i	$-0.783412\pi$
$673$	−40.3299			−1.55460			−0.777301	+	0.629128i	$0.783412\pi$
$674$	−2.93584	+	22.5582i	−0.113084	+	0.868908i
$675$			13.1999i			0.508065i
$676$	1.93338	+	0.511911i	0.0743607	+	0.0196889i
$677$		−	29.4826i		−	1.13311i	−0.824025	−	0.566553i	$-0.808277\pi$
$677$		−	29.4826i		−	1.13311i	0.824025	−	0.566553i	$-0.191723\pi$
$678$	−1.69503	−	0.220601i	−0.0650973	−	0.00847212i
$679$	−12.7857			−0.490671
$680$	33.3352	+	13.6346i	1.27835	+	0.522864i
$681$	−0.0893217			−0.00342282
$682$	39.7314	+	5.17087i	1.52140	+	0.198003i
$683$		−	6.90366i		−	0.264161i	−0.991239	−	0.132081i	$-0.957834\pi$
$683$		−	6.90366i		−	0.264161i	0.991239	−	0.132081i	$-0.0421658\pi$
$684$	1.65661	−	6.25667i	0.0633422	−	0.239230i
$685$		−	9.74535i		−	0.372351i
$686$	−0.182514	+	1.40239i	−0.00696843	+	0.0535434i
$687$	−6.12549			−0.233702
$688$	17.2935	−	30.3675i	0.659310	−	1.15775i
$689$	−2.23708			−0.0852258
$690$	1.44092	−	11.0716i	0.0548548	−	0.421488i
$691$		−	48.0500i		−	1.82791i	−0.405816	−	0.913955i	$-0.633012\pi$
$691$		−	48.0500i		−	1.82791i	0.405816	−	0.913955i	$-0.366988\pi$
$692$	−6.56143	+	24.7811i	−0.249428	+	0.942036i
$693$			16.1560i			0.613716i
$694$	−7.42836	−	0.966768i	−0.281977	−	0.0366980i
$695$	36.3379			1.37837
$696$	−2.96477	+	7.24855i	−0.112379	+	0.274756i
$697$	3.66191			0.138705
$698$	26.6571	+	3.46930i	1.00898	+	0.131315i
$699$		−	4.74659i		−	0.179533i
$700$	−15.6157	−	4.13466i	−0.590218	−	0.156275i
$701$		−	1.98674i		−	0.0750381i	−0.999296	−	0.0375190i	$-0.988055\pi$
$701$		−	1.98674i		−	0.0750381i	0.999296	−	0.0375190i	$-0.0119455\pi$
$702$	−0.298279	+	2.29189i	−0.0112578	+	0.0865019i
$703$	−4.00928			−0.151213
$704$	−30.9779	+	31.5337i	−1.16753	+	1.18847i
$705$	−13.4345			−0.505974
$706$	0.488775	−	3.75560i	0.0183953	−	0.141344i
$707$			9.46158i			0.355839i
$708$	−2.55344	−	0.676088i	−0.0959640	−	0.0254089i
$709$			16.3537i			0.614175i	0.951681	+	0.307087i	$0.0993544\pi$
$709$			16.3537i			0.614175i	−0.951681	+	0.307087i	$0.900646\pi$
$710$	−4.39350	−	0.571795i	−0.164885	−	0.0214591i
$711$	−21.3314			−0.799990
$712$	−8.20429	+	20.0586i	−0.307469	+	0.751729i
$713$	40.5755			1.51957
$714$	1.36233	+	0.177302i	0.0509840	+	0.00663534i
$715$			19.9814i			0.747261i
$716$	3.82761	−	14.4560i	0.143044	−	0.540248i
$717$			3.87736i			0.144803i
$718$	4.14576	−	31.8548i	0.154718	−	1.18881i
$719$	−42.8271			−1.59718			−0.798590	−	0.601875i	$-0.794421\pi$
$719$	−42.8271			−1.59718			−0.798590	+	0.601875i	$0.794421\pi$
$720$	20.9293	−	36.7519i	0.779989	−	1.36966i
$721$	−0.503322			−0.0187447
$722$	3.24419	−	24.9274i	0.120736	−	0.927703i
$723$		−	4.09976i		−	0.152472i
$724$	11.5095	−	43.4687i	0.427746	−	1.61550i
$725$		−	81.0629i		−	3.01060i
$726$	7.55647	+	0.983441i	0.280447	+	0.0364989i
$727$	13.1739			0.488594			0.244297	−	0.969700i	$-0.421443\pi$
$727$	13.1739			0.488594			0.244297	+	0.969700i	$0.421443\pi$
$728$	−2.61791	−	1.07077i	−0.0970262	−	0.0396853i
$729$	22.9765			0.850983
$730$	28.9159	+	3.76328i	1.07023	+	0.139285i
$731$		−	30.7637i		−	1.13784i
$732$	−0.459639	−	0.121701i	−0.0169887	−	0.00449821i
$733$		−	6.15717i		−	0.227420i	−0.993514	−	0.113710i	$-0.963726\pi$
$733$		−	6.15717i		−	0.227420i	0.993514	−	0.113710i	$-0.0362735\pi$
$734$	−0.582030	+	4.47215i	−0.0214831	+	0.165070i
$735$	−0.997636			−0.0367983
$736$	−26.9878	+	35.7159i	−0.994783	+	1.31651i
$737$	−23.4018			−0.862015
$738$	0.554971	−	4.26423i	0.0204288	−	0.156969i
$739$			10.2396i			0.376669i	0.982105	+	0.188334i	$0.0603088\pi$
$739$			10.2396i			0.376669i	−0.982105	+	0.188334i	$0.939691\pi$
$740$	−25.3262	−	6.70577i	−0.931011	−	0.246509i
$741$		−	0.305341i		−	0.0112170i
$742$	3.13725	+	0.408299i	0.115172	+	0.0149891i
$743$	19.4710			0.714321			0.357161	−	0.934043i	$-0.383745\pi$
$743$	19.4710			0.714321			0.357161	+	0.934043i	$0.383745\pi$
$744$	−3.70312	−	1.51464i	−0.135763	−	0.0555292i
$745$	−42.0077			−1.53904
$746$	−32.0816	−	4.17528i	−1.17459	−	0.152868i
$747$		−	21.2757i		−	0.778437i
$748$	−9.96010	+	37.6171i	−0.364177	+	1.37542i
$749$		−	3.29814i		−	0.120511i
$750$	0.560252	−	4.30481i	0.0204575	−	0.157190i
$751$	22.0975			0.806350			0.403175	−	0.915123i	$-0.367907\pi$
$751$	22.0975			0.806350			0.403175	+	0.915123i	$0.367907\pi$
$752$	46.8077	+	26.6558i	1.70690	+	0.972038i
$753$	7.15725			0.260825
$754$	1.83178	−	14.0749i	0.0667096	−	0.512577i
$755$		−	15.0792i		−	0.548788i
$756$	0.836606	−	3.15968i	0.0304271	−	0.114916i
$757$		−	1.15259i		−	0.0418916i	−0.999781	−	0.0209458i	$-0.993332\pi$
$757$		−	1.15259i		−	0.0418916i	0.999781	−	0.0209458i	$-0.00666775\pi$
$758$	19.7088	+	2.56501i	0.715854	+	0.0931652i
$759$	12.0632			0.437866
$760$	−4.28561	+	10.4779i	−0.155455	+	0.380072i
$761$	52.0968			1.88851			0.944253	−	0.329220i	$-0.106786\pi$
$761$	52.0968			1.88851			0.944253	+	0.329220i	$0.106786\pi$
$762$	0.368027	+	0.0478971i	0.0133322	+	0.00173513i
$763$			17.1603i			0.621244i
$764$	22.5798	+	5.97857i	0.816907	+	0.216297i
$765$		−	37.2314i		−	1.34611i
$766$	−0.966117	+	7.42336i	−0.0349072	+	0.268217i
$767$	4.78728			0.172859
$768$	3.79627	−	2.25219i	0.136986	−	0.0812689i
$769$	−3.53413			−0.127444			−0.0637220	−	0.997968i	$-0.520297\pi$
$769$	−3.53413			−0.127444			−0.0637220	+	0.997968i	$0.520297\pi$
$770$	3.64689	−	28.0216i	0.131425	−	1.00983i
$771$		−	5.01804i		−	0.180720i
$772$	22.5028	+	5.95819i	0.809892	+	0.214440i
$773$		−	32.9280i		−	1.18434i	−0.805814	−	0.592168i	$-0.798272\pi$
$773$		−	32.9280i		−	1.18434i	0.805814	−	0.592168i	$-0.201728\pi$
$774$	−35.8238	−	4.66231i	−1.28766	−	0.167583i
$775$	41.4132			1.48761
$776$	−13.6905	+	33.4719i	−0.491461	+	1.20157i
$777$	−0.999358			−0.0358518
$778$	−29.5925	−	3.85133i	−1.06094	−	0.138077i
$779$			1.15101i			0.0412390i
$780$	0.510701	−	1.92881i	0.0182860	−	0.0690623i
$781$		−	4.78700i		−	0.171292i
$782$	−5.08585	+	39.0782i	−0.181870	+	1.39743i
$783$	16.4022			0.586168
$784$	3.47589	+	1.97944i	0.124139	+	0.0706941i
$785$	−70.0125			−2.49885
$786$	0.311241	−	2.39148i	0.0111016	−	0.0853014i
$787$		−	17.5105i		−	0.624182i	−0.950052	−	0.312091i	$-0.898971\pi$
$787$		−	17.5105i		−	0.624182i	0.950052	−	0.312091i	$-0.101029\pi$
$788$	2.86509	−	10.8208i	0.102065	−	0.385476i
$789$			7.32964i			0.260942i
$790$	36.9980	+	4.81513i	1.31633	+	0.171315i
$791$	−4.38117			−0.155777
$792$	42.2950	+	17.2993i	1.50289	+	0.614704i
$793$	0.861749			0.0306016
$794$	39.7839	+	5.17769i	1.41188	+	0.183749i
$795$			2.23179i			0.0791534i
$796$	−39.1590	−	10.3683i	−1.38795	−	0.367496i
$797$			33.4031i			1.18320i	0.806232	+	0.591600i	$0.201503\pi$
$797$			33.4031i			1.18320i	−0.806232	+	0.591600i	$0.798497\pi$
$798$	−0.0557290	+	0.428206i	−0.00197279	+	0.0151583i
$799$	47.4184			1.67754
$800$	−27.5450	+	36.4533i	−0.973861	+	1.28882i
$801$	22.4031			0.791574
$802$	−5.29820	+	40.7098i	−0.187086	+	1.43751i
$803$			31.5057i			1.11181i
$804$	2.25898	+	0.598122i	0.0796680	+	0.0210942i
$805$		−	28.6169i		−	1.00861i
$806$	7.19054	+	0.935817i	0.253276	+	0.0329627i
$807$	6.91768			0.243514
$808$	24.7696	+	10.1311i	0.871390	+	0.356412i
$809$	11.3668			0.399636			0.199818	−	0.979833i	$-0.435965\pi$
$809$	11.3668			0.399636			0.199818	+	0.979833i	$0.435965\pi$
$810$	−42.1974	−	5.49180i	−1.48267	−	0.192962i
$811$			32.5379i			1.14256i	0.820756	+	0.571279i	$0.193553\pi$
$811$			32.5379i			1.14256i	−0.820756	+	0.571279i	$0.806447\pi$
$812$	−5.13773	+	19.4041i	−0.180299	+	0.680950i
$813$		−	0.731261i		−	0.0256465i
$814$	3.65318	−	28.0700i	0.128044	−	0.983852i
$815$	−36.2571			−1.27003
$816$	1.92290	−	3.37662i	0.0673150	−	0.118205i
$817$	9.66959			0.338296
$818$	−6.29018	+	48.3319i	−0.219931	+	1.68989i
$819$			2.92389i			0.102169i
$820$	−1.92513	+	7.27078i	−0.0672283	+	0.253907i
$821$			34.1067i			1.19033i	0.803603	+	0.595166i	$0.202914\pi$
$821$			34.1067i			1.19033i	−0.803603	+	0.595166i	$0.797086\pi$
$822$	−1.04264	−	0.135694i	−0.0363661	−	0.00473288i
$823$	−35.0649			−1.22229			−0.611143	−	0.791520i	$-0.709290\pi$
$823$	−35.0649			−1.22229			−0.611143	+	0.791520i	$0.709290\pi$
$824$	−0.538940	+	1.31765i	−0.0187749	+	0.0459026i
$825$	12.3122			0.428657
$826$	−6.71362	−	0.873748i	−0.233597	−	0.0304016i
$827$			22.8625i			0.795006i	0.917601	+	0.397503i	$0.130123\pi$
$827$			22.8625i			0.795006i	−0.917601	+	0.397503i	$0.869877\pi$
$828$	44.7351	+	11.8448i	1.55465	+	0.411634i
$829$			45.9793i			1.59693i	0.602042	+	0.798464i	$0.294354\pi$
$829$			45.9793i			1.59693i	−0.602042	+	0.798464i	$0.705646\pi$
$830$	−4.80255	+	36.9014i	−0.166699	+	1.28087i
$831$	5.16417			0.179143
$832$	−5.60634	+	5.70692i	−0.194365	+	0.197852i
$833$	3.52124			0.122004
$834$	0.505969	−	3.88771i	0.0175203	−	0.134621i
$835$		−	55.3337i		−	1.91490i
$836$	−11.8237	−	3.13064i	−0.408932	−	0.108275i
$837$			8.37954i			0.289639i
$838$	−6.00084	−	0.780983i	−0.207296	−	0.0269786i
$839$	−23.4652			−0.810108			−0.405054	−	0.914293i	$-0.632747\pi$
$839$	−23.4652			−0.810108			−0.405054	+	0.914293i	$0.632747\pi$
$840$	−1.06823	+	2.61172i	−0.0368576	+	0.0901129i
$841$	−71.7288			−2.47341
$842$	−9.83643	−	1.28017i	−0.338986	−	0.0441175i
$843$			3.95311i			0.136152i
$844$	−6.32572	+	23.8908i	−0.217740	+	0.822357i
$845$			3.61620i			0.124401i
$846$	7.18636	−	55.2179i	0.247072	−	1.89843i
$847$	19.5313			0.671104
$848$	4.42815	−	7.77584i	0.152063	−	0.267024i
$849$	−3.97920			−0.136566
$850$	−5.19085	+	39.8850i	−0.178045	+	1.36804i
$851$		−	28.6663i		−	0.982669i
$852$	−0.122350	+	0.462090i	−0.00419165	+	0.0158309i
$853$		−	1.79276i		−	0.0613831i	−0.999529	−	0.0306915i	$-0.990229\pi$
$853$		−	1.79276i		−	0.0613831i	0.999529	−	0.0306915i	$-0.00977095\pi$
$854$	−1.20851	−	0.157282i	−0.0413542	−	0.00538206i
$855$	11.7025			0.400217
$856$	−8.63424	−	3.53154i	−0.295112	−	0.120705i
$857$	−22.0714			−0.753943			−0.376972	−	0.926225i	$-0.623035\pi$
$857$	−22.0714			−0.753943			−0.376972	+	0.926225i	$0.623035\pi$
$858$	2.13777	+	0.278221i	0.0729821	+	0.00949829i
$859$		−	4.52672i		−	0.154450i	−0.997014	−	0.0772248i	$-0.975394\pi$
$859$		−	4.52672i		−	0.154450i	0.997014	−	0.0772248i	$-0.0246059\pi$
$860$	61.0818	+	16.1730i	2.08287	+	0.551494i
$861$			0.286901i			0.00977754i
$862$	−5.40517	+	41.5317i	−0.184101	+	1.41458i
$863$	51.4286			1.75065			0.875325	−	0.483534i	$-0.160647\pi$
$863$	51.4286			1.75065			0.875325	+	0.483534i	$0.160647\pi$
$864$	−7.37595	−	5.57344i	−0.250935	−	0.189612i
$865$	−46.3507			−1.57597
$866$	2.15696	−	16.5735i	0.0732966	−	0.563190i
$867$			1.26928i			0.0431069i
$868$	−9.91312	−	2.62475i	−0.336473	−	0.0890899i
$869$			40.3117i			1.36748i
$870$	−14.0416	−	1.82745i	−0.476055	−	0.0619564i
$871$	−4.23522			−0.143505
$872$	44.9241	+	18.3747i	1.52132	+	0.622245i
$873$	37.3841			1.26526
$874$	−12.2830	−	1.59857i	−0.415478	−	0.0540726i
$875$		−	11.1267i		−	0.376152i
$876$	0.805250	−	3.04125i	0.0272069	−	0.102754i
$877$			38.9877i			1.31652i	0.752791	+	0.658260i	$0.228707\pi$
$877$			38.9877i			1.31652i	−0.752791	+	0.658260i	$0.771293\pi$
$878$	2.77562	−	21.3270i	0.0936725	−	0.719752i
$879$	1.37181			0.0462700
$880$	−69.4531	−	39.5518i	−2.34126	−	1.33329i
$881$	36.2082			1.21989			0.609943	−	0.792445i	$-0.291192\pi$
$881$	36.2082			1.21989			0.609943	+	0.792445i	$0.291192\pi$
$882$	0.533652	−	4.10043i	0.0179690	−	0.138068i
$883$		−	49.4027i		−	1.66253i	−0.555875	−	0.831266i	$-0.687617\pi$
$883$		−	49.4027i		−	1.66253i	0.555875	−	0.831266i	$-0.312383\pi$
$884$	−1.80257	+	6.80789i	−0.0606268	+	0.228974i
$885$		−	4.77596i		−	0.160542i
$886$	20.9523	+	2.72685i	0.703906	+	0.0916102i
$887$	27.1660			0.912146			0.456073	−	0.889942i	$-0.349256\pi$
$887$	27.1660			0.912146			0.456073	+	0.889942i	$0.349256\pi$
$888$	−1.07008	+	2.61623i	−0.0359095	+	0.0877949i
$889$	0.951245			0.0319037
$890$	−38.8568	−	5.05703i	−1.30248	−	0.169512i
$891$		−	45.9768i		−	1.54028i
$892$	−28.4996	−	7.54600i	−0.954237	−	0.252659i
$893$			14.9044i			0.498758i
$894$	−0.584916	+	4.49432i	−0.0195625	+	0.150313i
$895$	27.0387			0.903803
$896$	8.90386	−	6.98007i	0.297457	−	0.233188i
$897$	2.18318			0.0728943
$898$	5.46954	−	42.0264i	0.182521	−	1.40244i
$899$		−	51.4601i		−	1.71629i
$900$	45.6586	+	12.0893i	1.52195	+	0.402976i
$901$		−	7.87730i		−	0.262431i
$902$	−8.05847	−	1.04877i	−0.268318	−	0.0349203i
$903$	2.41025			0.0802081
$904$	−4.69122	+	11.4695i	−0.156028	+	0.381471i
$905$	81.3041			2.70264
$906$	−1.61329	−	0.209963i	−0.0535980	−	0.00697554i
$907$			22.3716i			0.742838i	0.928465	+	0.371419i	$0.121129\pi$
$907$			22.3716i			0.742838i	−0.928465	+	0.371419i	$0.878871\pi$
$908$	−0.165742	+	0.625971i	−0.00550034	+	0.0207736i
$909$		−	27.6646i		−	0.917577i
$910$	0.660008	−	5.07131i	0.0218791	−	0.168112i
$911$	9.55929			0.316713			0.158357	−	0.987382i	$-0.449380\pi$
$911$	9.55929			0.316713			0.158357	+	0.987382i	$0.449380\pi$
$912$	1.06133	+	0.604402i	0.0351442	+	0.0200138i
$913$	−40.2064			−1.33064
$914$	2.01719	−	15.4995i	0.0667227	−	0.512677i
$915$		−	0.859711i		−	0.0284212i
$916$	−11.3662	+	42.9277i	−0.375550	+	1.41837i
$917$		−	6.18131i		−	0.204125i
$918$	−8.07031	−	1.05032i	−0.266360	−	0.0346656i
$919$	−60.0820			−1.98192			−0.990961	−	0.134148i	$-0.957170\pi$
$919$	−60.0820			−1.98192			−0.990961	+	0.134148i	$0.957170\pi$
$920$	−74.9166	−	30.6420i	−2.46993	−	1.01024i
$921$	0.698671			0.0230220
$922$	58.3860	+	7.59868i	1.92284	+	0.250249i
$923$		−	0.866345i		−	0.0285161i
$924$	−2.94719	−	0.780346i	−0.0969556	−	0.0256715i
$925$		−	29.2581i		−	0.962002i
$926$	6.63219	−	50.9598i	0.217947	−	1.67464i
$927$	1.47166			0.0483356
$928$	45.2969	+	34.2274i	1.48694	+	1.12357i
$929$	10.2401			0.335966			0.167983	−	0.985790i	$-0.446275\pi$
$929$	10.2401			0.335966			0.167983	+	0.985790i	$0.446275\pi$
$930$	0.933604	−	7.17354i	0.0306141	−	0.235230i
$931$			1.10679i			0.0362736i
$932$	−33.2644	−	8.80760i	−1.08961	−	0.288502i
$933$		−	5.91225i		−	0.193558i
$934$	12.0966	+	1.57431i	0.395812	+	0.0515131i
$935$	−70.3593			−2.30100
$936$	7.65449	+	3.13080i	0.250195	+	0.102334i
$937$	34.9995			1.14338			0.571692	−	0.820469i	$-0.306287\pi$
$937$	34.9995			1.14338			0.571692	+	0.820469i	$0.306287\pi$
$938$	5.93942	+	0.772988i	0.193929	+	0.0252390i
$939$			8.67523i			0.283105i
$940$	−24.9286	+	94.1499i	−0.813081	+	3.07083i
$941$			20.3362i			0.662941i	0.943466	+	0.331471i	$0.107545\pi$
$941$			20.3362i			0.662941i	−0.943466	+	0.331471i	$0.892455\pi$
$942$	−0.974854	+	7.49049i	−0.0317625	+	0.244053i
$943$	−8.22967			−0.267995
$944$	−9.47612	+	16.6401i	−0.308421	+	0.541589i
$945$	5.90988			0.192249
$946$	−8.81075	+	67.6992i	−0.286462	+	2.20109i
$947$			19.1433i			0.622073i	0.950398	+	0.311036i	$0.100676\pi$
$947$			19.1433i			0.622073i	−0.950398	+	0.311036i	$0.899324\pi$
$948$	1.03032	−	3.89130i	0.0334633	−	0.126383i
$949$			5.70186i			0.185090i
$950$	−12.5366	−	1.63158i	−0.406740	−	0.0529353i
$951$	−5.53114			−0.179360
$952$	3.77043	−	9.21831i	0.122200	−	0.298767i
$953$	41.8842			1.35676			0.678382	−	0.734710i	$-0.262682\pi$
$953$	41.8842			1.35676			0.678382	+	0.734710i	$0.262682\pi$
$954$	−9.17297	−	1.19382i	−0.296986	−	0.0386514i
$955$			42.2333i			1.36664i
$956$	27.1727	+	7.19467i	0.878828	+	0.232692i
$957$		−	15.2992i		−	0.494553i
$958$	2.56924	−	19.7413i	0.0830083	−	0.637812i
$959$	−2.69492			−0.0870234
$960$	5.69342	+	5.59309i	0.183754	+	0.180516i
$961$	−4.71019			−0.151941
$962$	0.661148	−	5.08007i	0.0213163	−	0.163788i
$963$			9.64340i			0.310754i
$964$	−28.7313	−	7.60736i	−0.925374	−	0.245017i
$965$			42.0893i			1.35490i
$966$	−3.06166	−	0.398462i	−0.0985074	−	0.0128203i
$967$	−48.0006			−1.54360			−0.771798	−	0.635868i	$-0.780642\pi$
$967$	−48.0006			−1.54360			−0.771798	+	0.635868i	$0.780642\pi$
$968$	20.9135	−	51.1313i	0.672185	−	1.64342i
$969$	1.07518			0.0345397
$970$	−64.8404	−	8.43869i	−2.08190	−	0.270950i
$971$		−	2.14847i		−	0.0689477i	−0.999406	−	0.0344739i	$-0.989024\pi$
$971$		−	2.14847i		−	0.0689477i	0.999406	−	0.0344739i	$-0.0109755\pi$
$972$	−3.68493	+	13.9172i	−0.118194	+	0.446394i
$973$		−	10.0486i		−	0.322145i
$974$	5.64144	−	43.3472i	0.180763	−	1.38893i
$975$	2.22825			0.0713612
$976$	−1.70578	+	2.99535i	−0.0546006	+	0.0958787i
$977$	8.19821			0.262284			0.131142	−	0.991364i	$-0.458136\pi$
$977$	8.19821			0.262284			0.131142	+	0.991364i	$0.458136\pi$
$978$	−0.504843	+	3.87907i	−0.0161431	+	0.124039i
$979$		−	42.3369i		−	1.35309i
$980$	−1.85117	+	6.99148i	−0.0591336	+	0.223335i
$981$		−	50.1748i		−	1.60196i
$982$	42.7203	+	5.55985i	1.36326	+	0.177422i
$983$	7.16077			0.228393			0.114196	−	0.993458i	$-0.463571\pi$
$983$	7.16077			0.228393			0.114196	+	0.993458i	$0.463571\pi$
$984$	0.751080	+	0.307204i	0.0239436	+	0.00979329i
$985$	20.2394			0.644880
$986$	49.5611	+	6.45015i	1.57835	+	0.205415i
$987$			3.71510i			0.118253i
$988$	−2.13984	−	0.566578i	−0.0680775	−	0.0180253i
$989$			69.1374i			2.19844i
$990$	−10.6631	+	81.9321i	−0.338896	+	2.60397i
$991$	22.3913			0.711284			0.355642	−	0.934622i	$-0.384262\pi$
$991$	22.3913			0.711284			0.355642	+	0.934622i	$0.384262\pi$
$992$	−17.4860	+	23.1412i	−0.555181	+	0.734733i
$993$	6.95526			0.220719
$994$	−0.158120	+	1.21495i	−0.00501527	+	0.0385359i
$995$		−	73.2432i		−	2.32196i
$996$	3.88113	+	1.02763i	0.122978	+	0.0325617i
$997$			57.3479i			1.81623i	0.418725	+	0.908113i	$0.362477\pi$
$997$			57.3479i			1.81623i	−0.418725	+	0.908113i	$0.637523\pi$
$998$	12.8795	+	1.67621i	0.407694	+	0.0530596i
$999$	5.92008			0.187303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.a.365.17	✓	34
4.3	odd	2		2912.2.c.a.1457.19		34
8.3	odd	2		2912.2.c.a.1457.16		34
8.5	even	2	inner	728.2.c.a.365.18	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.a.365.17	✓	34	1.1	even	1	trivial
728.2.c.a.365.18	yes	34	8.5	even	2	inner
2912.2.c.a.1457.16		34	8.3	odd	2
2912.2.c.a.1457.19		34	4.3	odd	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.182514 - 1.40239i) q^{2} -0.275879i q^{3} +(-1.93338 - 0.511911i) q^{4} -3.61620i q^{5} +(-0.386890 - 0.0503520i) q^{6} -1.00000 q^{7} +(-1.07077 + 2.61791i) q^{8} +2.92389 q^{9} +(-5.07131 - 0.660008i) q^{10} -5.52552i q^{11} +(-0.141226 + 0.533379i) q^{12} -1.00000i q^{13} +(-0.182514 + 1.40239i) q^{14} -0.997636 q^{15} +(3.47589 + 1.97944i) q^{16} +3.52124 q^{17} +(0.533652 - 4.10043i) q^{18} +1.10679i q^{19} +(-1.85117 + 6.99148i) q^{20} +0.275879i q^{21} +(-7.74891 - 1.00849i) q^{22} -7.91353 q^{23} +(0.722228 + 0.295403i) q^{24} -8.07691 q^{25} +(-1.40239 - 0.182514i) q^{26} -1.63428i q^{27} +(1.93338 + 0.511911i) q^{28} +10.0364i q^{29} +(-0.182083 + 1.39907i) q^{30} -5.12736 q^{31} +(3.41033 - 4.51327i) q^{32} -1.52438 q^{33} +(0.642678 - 4.93815i) q^{34} +3.61620i q^{35} +(-5.65298 - 1.49677i) q^{36} +3.62244i q^{37} +(1.55215 + 0.202005i) q^{38} -0.275879 q^{39} +(9.46689 + 3.87211i) q^{40} +1.03995 q^{41} +(0.386890 + 0.0503520i) q^{42} -8.73661i q^{43} +(-2.82857 + 10.6829i) q^{44} -10.5734i q^{45} +(-1.44433 + 11.0978i) q^{46} +13.4664 q^{47} +(0.546086 - 0.958928i) q^{48} +1.00000 q^{49} +(-1.47415 + 11.3269i) q^{50} -0.971439i q^{51} +(-0.511911 + 1.93338i) q^{52} -2.23708i q^{53} +(-2.29189 - 0.298279i) q^{54} -19.9814 q^{55} +(1.07077 - 2.61791i) q^{56} +0.305341 q^{57} +(14.0749 + 1.83178i) q^{58} +4.78728i q^{59} +(1.92881 + 0.510701i) q^{60} +0.861749i q^{61} +(-0.935817 + 7.19054i) q^{62} -2.92389 q^{63} +(-5.70692 - 5.60634i) q^{64} -3.61620 q^{65} +(-0.278221 + 2.13777i) q^{66} -4.23522i q^{67} +(-6.80789 - 1.80257i) q^{68} +2.18318i q^{69} +(5.07131 + 0.660008i) q^{70} +0.866345 q^{71} +(-3.13080 + 7.65449i) q^{72} -5.70186 q^{73} +(5.08007 + 0.661148i) q^{74} +2.22825i q^{75} +(0.566578 - 2.13984i) q^{76} +5.52552i q^{77} +(-0.0503520 + 0.386890i) q^{78} -7.29555 q^{79} +(7.15804 - 12.5695i) q^{80} +8.32081 q^{81} +(0.189806 - 1.45841i) q^{82} -7.27650i q^{83} +(0.141226 - 0.533379i) q^{84} -12.7335i q^{85} +(-12.2521 - 1.59456i) q^{86} +2.76883 q^{87} +(14.4653 + 5.91654i) q^{88} +7.66208 q^{89} +(-14.8280 - 1.92979i) q^{90} +1.00000i q^{91} +(15.2998 + 4.05103i) q^{92} +1.41453i q^{93} +(2.45781 - 18.8851i) q^{94} +4.00238 q^{95} +(-1.24512 - 0.940841i) q^{96} +12.7857 q^{97} +(0.182514 - 1.40239i) q^{98} -16.1560i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) \) 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

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