LMFDB - Embedded newform 465.2.e.a.371.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(371,465)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("465.371"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.21
Character	$\chi$	$=$	465.371
Dual form			465.2.e.a.371.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.201763i q^{2} +(-0.798995 - 1.53675i) q^{3} +1.95929 q^{4} -1.00000i q^{5} +(-0.310060 + 0.161208i) q^{6} -3.41472 q^{7} -0.798839i q^{8} +(-1.72321 + 2.45571i) q^{9} -0.201763 q^{10} -5.52310 q^{11} +(-1.56546 - 3.01095i) q^{12} -5.36545i q^{13} +0.688964i q^{14} +(-1.53675 + 0.798995i) q^{15} +3.75741 q^{16} -3.84562 q^{17} +(0.495472 + 0.347681i) q^{18} +3.81652 q^{19} -1.95929i q^{20} +(2.72834 + 5.24758i) q^{21} +1.11436i q^{22} +0.602484 q^{23} +(-1.22762 + 0.638268i) q^{24} -1.00000 q^{25} -1.08255 q^{26} +(5.15066 + 0.686052i) q^{27} -6.69043 q^{28} +3.16401 q^{29} +(0.161208 + 0.310060i) q^{30} +(-5.42120 - 1.26910i) q^{31} -2.35578i q^{32} +(4.41293 + 8.48763i) q^{33} +0.775903i q^{34} +3.41472i q^{35} +(-3.37628 + 4.81146i) q^{36} +0.170000i q^{37} -0.770033i q^{38} +(-8.24536 + 4.28696i) q^{39} -0.798839 q^{40} -8.16253i q^{41} +(1.05877 - 0.550479i) q^{42} +2.74434i q^{43} -10.8214 q^{44} +(2.45571 + 1.72321i) q^{45} -0.121559i q^{46} -12.0573i q^{47} +(-3.00215 - 5.77420i) q^{48} +4.66030 q^{49} +0.201763i q^{50} +(3.07263 + 5.90976i) q^{51} -10.5125i q^{52} +9.95009 q^{53} +(0.138420 - 1.03921i) q^{54} +5.52310i q^{55} +2.72781i q^{56} +(-3.04938 - 5.86505i) q^{57} -0.638381i q^{58} -3.14445i q^{59} +(-3.01095 + 1.56546i) q^{60} +8.27031i q^{61} +(-0.256058 + 1.09380i) q^{62} +(5.88429 - 8.38557i) q^{63} +7.03950 q^{64} -5.36545 q^{65} +(1.71249 - 0.890365i) q^{66} -9.06536 q^{67} -7.53468 q^{68} +(-0.481382 - 0.925869i) q^{69} +0.688964 q^{70} +13.1481i q^{71} +(1.96172 + 1.37657i) q^{72} +5.65479i q^{73} +0.0342997 q^{74} +(0.798995 + 1.53675i) q^{75} +7.47768 q^{76} +18.8598 q^{77} +(0.864951 + 1.66361i) q^{78} -16.0055i q^{79} -3.75741i q^{80} +(-3.06106 - 8.46345i) q^{81} -1.64690 q^{82} -4.72868 q^{83} +(5.34562 + 10.2815i) q^{84} +3.84562i q^{85} +0.553706 q^{86} +(-2.52803 - 4.86230i) q^{87} +4.41206i q^{88} +14.4724 q^{89} +(0.347681 - 0.495472i) q^{90} +18.3215i q^{91} +1.18044 q^{92} +(2.38121 + 9.34504i) q^{93} -2.43271 q^{94} -3.81652i q^{95} +(-3.62026 + 1.88226i) q^{96} +11.8891 q^{97} -0.940276i q^{98} +(9.51748 - 13.5631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 52 q^{4} + 16 q^{7} + 4 q^{10} + 68 q^{16} - 28 q^{18} - 8 q^{19} - 44 q^{25} - 56 q^{28} - 16 q^{31} + 4 q^{33} + 12 q^{36} - 20 q^{39} - 36 q^{40} - 4 q^{45} + 92 q^{49} + 8 q^{51} - 12 q^{63}+ \cdots + 16 q^{97}+O(q^{100}) $ 44 * q - 52 * q^4 + 16 * q^7 + 4 * q^10 + 68 * q^16 - 28 * q^18 - 8 * q^19 - 44 * q^25 - 56 * q^28 - 16 * q^31 + 4 * q^33 + 12 * q^36 - 20 * q^39 - 36 * q^40 - 4 * q^45 + 92 * q^49 + 8 * q^51 - 12 * q^63 - 52 * q^64 + 40 * q^66 - 32 * q^67 + 12 * q^69 - 24 * q^72 + 48 * q^76 - 88 * q^78 - 4 * q^81 + 36 * q^87 + 16 * q^90 - 20 * q^93 + 32 * q^94 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	0.201763i		−	0.142668i	−0.997452	−	0.0713340i	$-0.977274\pi$
$2$		−	0.201763i		−	0.142668i	0.997452	−	0.0713340i	$-0.0227256\pi$
$3$	−0.798995	−	1.53675i	−0.461300	−	0.887244i
$3$	−0.798995	−	1.53675i	−0.461300	−	0.887244i
$4$	1.95929			0.979646
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.310060	+	0.161208i	−0.126581	+	0.0658127i
$7$	−3.41472			−1.29064			−0.645321	−	0.763911i	$-0.723276\pi$
$7$	−3.41472			−1.29064			−0.645321	+	0.763911i	$0.723276\pi$
$8$		−	0.798839i		−	0.282432i
$9$	−1.72321	+	2.45571i	−0.574405	+	0.818571i
$10$	−0.201763			−0.0638031
$11$	−5.52310			−1.66528			−0.832638	−	0.553817i	$-0.813171\pi$
$11$	−5.52310			−1.66528			−0.832638	+	0.553817i	$0.813171\pi$
$12$	−1.56546	−	3.01095i	−0.451910	−	0.869185i
$13$		−	5.36545i		−	1.48811i	−0.668120	−	0.744054i	$-0.732901\pi$
$13$		−	5.36545i		−	1.48811i	0.668120	−	0.744054i	$-0.267099\pi$
$14$			0.688964i			0.184133i
$15$	−1.53675	+	0.798995i	−0.396788	+	0.206300i
$16$	3.75741			0.939352
$17$	−3.84562			−0.932699			−0.466349	−	0.884601i	$-0.654431\pi$
$17$	−3.84562			−0.932699			−0.466349	+	0.884601i	$0.654431\pi$
$18$	0.495472	+	0.347681i	0.116784	+	0.0819492i
$19$	3.81652			0.875570			0.437785	−	0.899080i	$-0.355763\pi$
$19$	3.81652			0.875570			0.437785	+	0.899080i	$0.355763\pi$
$20$		−	1.95929i		−	0.438111i
$21$	2.72834	+	5.24758i	0.595373	+	1.14511i
$22$			1.11436i			0.237582i
$23$	0.602484			0.125627			0.0628133	−	0.998025i	$-0.479993\pi$
$23$	0.602484			0.125627			0.0628133	+	0.998025i	$0.479993\pi$
$24$	−1.22762	+	0.638268i	−0.250586	+	0.130286i
$25$	−1.00000			−0.200000
$26$	−1.08255			−0.212305
$27$	5.15066	+	0.686052i	0.991246	+	0.132031i
$28$	−6.69043			−1.26437
$29$	3.16401			0.587542			0.293771	−	0.955876i	$-0.405090\pi$
$29$	3.16401			0.587542			0.293771	+	0.955876i	$0.405090\pi$
$30$	0.161208	+	0.310060i	0.0294324	+	0.0566089i
$31$	−5.42120	−	1.26910i	−0.973676	−	0.227938i
$31$	−5.42120	−	1.26910i	−0.973676	−	0.227938i
$32$		−	2.35578i		−	0.416448i
$33$	4.41293	+	8.48763i	0.768192	+	1.47751i
$34$			0.775903i			0.133066i
$35$			3.41472i			0.577193i
$36$	−3.37628	+	4.81146i	−0.562713	+	0.801910i
$37$			0.170000i			0.0279478i	0.999902	+	0.0139739i	$0.00444818\pi$
$37$			0.170000i			0.0279478i	−0.999902	+	0.0139739i	$0.995552\pi$
$38$		−	0.770033i		−	0.124916i
$39$	−8.24536	+	4.28696i	−1.32031	+	0.686464i
$40$	−0.798839			−0.126308
$41$		−	8.16253i		−	1.27477i	−0.770544	−	0.637386i	$-0.780016\pi$
$41$		−	8.16253i		−	1.27477i	0.770544	−	0.637386i	$-0.219984\pi$
$42$	1.05877	−	0.550479i	0.163371	−	0.0849407i
$43$			2.74434i			0.418507i	0.977861	+	0.209254i	$0.0671035\pi$
$43$			2.74434i			0.418507i	−0.977861	+	0.209254i	$0.932897\pi$
$44$	−10.8214			−1.63138
$45$	2.45571	+	1.72321i	0.366076	+	0.256882i
$46$		−	0.121559i		−	0.0179229i
$47$		−	12.0573i		−	1.75874i	−0.476143	−	0.879368i	$-0.657966\pi$
$47$		−	12.0573i		−	1.75874i	0.476143	−	0.879368i	$-0.342034\pi$
$48$	−3.00215	−	5.77420i	−0.433323	−	0.833435i
$49$	4.66030			0.665757
$50$			0.201763i			0.0285336i
$51$	3.07263	+	5.90976i	0.430254	+	0.827532i
$52$		−	10.5125i		−	1.45782i
$53$	9.95009			1.36675			0.683375	−	0.730068i	$-0.260511\pi$
$53$	9.95009			1.36675			0.683375	+	0.730068i	$0.260511\pi$
$54$	0.138420	−	1.03921i	0.0188366	−	0.141419i
$55$			5.52310i			0.744734i
$56$			2.72781i			0.364519i
$57$	−3.04938	−	5.86505i	−0.403900	−	0.776845i
$58$		−	0.638381i		−	0.0838235i
$59$		−	3.14445i		−	0.409372i	−0.978828	−	0.204686i	$-0.934383\pi$
$59$		−	3.14445i		−	0.409372i	0.978828	−	0.204686i	$-0.0656174\pi$
$60$	−3.01095	+	1.56546i	−0.388711	+	0.202100i
$61$			8.27031i			1.05891i	0.848339	+	0.529453i	$0.177603\pi$
$61$			8.27031i			1.05891i	−0.848339	+	0.529453i	$0.822397\pi$
$62$	−0.256058	+	1.09380i	−0.0325194	+	0.138912i
$63$	5.88429	−	8.38557i	0.741351	−	1.05648i
$64$	7.03950			0.879938
$65$	−5.36545			−0.665502
$66$	1.71249	−	0.890365i	0.210793	−	0.109596i
$67$	−9.06536			−1.10751			−0.553755	−	0.832680i	$-0.686806\pi$
$67$	−9.06536			−1.10751			−0.553755	+	0.832680i	$0.686806\pi$
$68$	−7.53468			−0.913715
$69$	−0.481382	−	0.925869i	−0.0579516	−	0.111462i
$70$	0.688964			0.0823469
$71$			13.1481i			1.56039i	0.625534	+	0.780197i	$0.284881\pi$
$71$			13.1481i			1.56039i	−0.625534	+	0.780197i	$0.715119\pi$
$72$	1.96172	+	1.37657i	0.231191	+	0.162230i
$73$			5.65479i			0.661843i	0.943658	+	0.330921i	$0.107359\pi$
$73$			5.65479i			0.661843i	−0.943658	+	0.330921i	$0.892641\pi$
$74$	0.0342997			0.00398726
$75$	0.798995	+	1.53675i	0.0922600	+	0.177449i
$76$	7.47768			0.857749
$77$	18.8598			2.14928
$78$	0.864951	+	1.66361i	0.0979364	+	0.188367i
$79$		−	16.0055i		−	1.80076i	−0.435102	−	0.900381i	$-0.643288\pi$
$79$		−	16.0055i		−	1.80076i	0.435102	−	0.900381i	$-0.356712\pi$
$80$		−	3.75741i		−	0.420091i
$81$	−3.06106	−	8.46345i	−0.340118	−	0.940383i
$82$	−1.64690			−0.181869
$83$	−4.72868			−0.519040			−0.259520	−	0.965738i	$-0.583564\pi$
$83$	−4.72868			−0.519040			−0.259520	+	0.965738i	$0.583564\pi$
$84$	5.34562	+	10.2815i	0.583255	+	1.12181i
$85$			3.84562i			0.417116i
$86$	0.553706			0.0597076
$87$	−2.52803	−	4.86230i	−0.271033	−	0.521294i
$88$			4.41206i			0.470328i
$89$	14.4724			1.53407			0.767036	−	0.641604i	$-0.221731\pi$
$89$	14.4724			1.53407			0.767036	+	0.641604i	$0.221731\pi$
$90$	0.347681	−	0.495472i	0.0366488	−	0.0522274i
$91$			18.3215i			1.92061i
$92$	1.18044			0.123070
$93$	2.38121	+	9.34504i	0.246920	+	0.969036i
$94$	−2.43271			−0.250915
$95$		−	3.81652i		−	0.391567i
$96$	−3.62026	+	1.88226i	−0.369491	+	0.192107i
$97$	11.8891			1.20715			0.603576	−	0.797305i	$-0.293742\pi$
$97$	11.8891			1.20715			0.603576	+	0.797305i	$0.293742\pi$
$98$		−	0.940276i		−	0.0949823i
$99$	9.51748	−	13.5631i	0.956543	−	1.36315i
$100$	−1.95929			−0.195929
$101$		−	16.0808i		−	1.60010i	−0.599932	−	0.800051i	$-0.704806\pi$
$101$		−	16.0808i		−	1.60010i	0.599932	−	0.800051i	$-0.295194\pi$
$102$	1.19237	−	0.619943i	0.118062	−	0.0613835i
$103$	5.67209			0.558888			0.279444	−	0.960162i	$-0.409850\pi$
$103$	5.67209			0.558888			0.279444	+	0.960162i	$0.409850\pi$
$104$	−4.28613			−0.420289
$105$	5.24758	−	2.72834i	0.512111	−	0.266259i
$106$		−	2.00756i		−	0.194992i
$107$			12.5868i			1.21681i	0.793625	+	0.608407i	$0.208191\pi$
$107$			12.5868i			1.21681i	−0.793625	+	0.608407i	$0.791809\pi$
$108$	10.0917	+	1.34418i	0.971070	+	0.129343i
$109$	1.32741			0.127143			0.0635713	−	0.997977i	$-0.479751\pi$
$109$	1.32741			0.127143			0.0635713	+	0.997977i	$0.479751\pi$
$110$	1.11436			0.106250
$111$	0.261248	−	0.135829i	0.0247965	−	0.0128923i
$112$	−12.8305			−1.21237
$113$		−	8.59400i		−	0.808455i	−0.914658	−	0.404228i	$-0.867540\pi$
$113$		−	8.59400i		−	0.808455i	0.914658	−	0.404228i	$-0.132460\pi$
$114$	−1.18335	+	0.615252i	−0.110831	+	0.0576237i
$115$		−	0.602484i		−	0.0561820i
$116$	6.19922			0.575583
$117$	13.1760	+	9.24582i	1.21812	+	0.854776i
$118$	−0.634434			−0.0584044
$119$	13.1317			1.20378
$120$	0.638268	+	1.22762i	0.0582656	+	0.112066i
$121$	19.5046			1.77315
$122$	1.66864			0.151072
$123$	−12.5438	+	6.52182i	−1.13103	+	0.588052i
$124$	−10.6217	−	2.48654i	−0.953857	−	0.223298i
$125$			1.00000i			0.0894427i
$126$	−1.69190	−	1.18723i	−0.150726	−	0.105767i
$127$		−	19.2401i		−	1.70728i	−0.520861	−	0.853642i	$-0.674389\pi$
$127$		−	19.2401i		−	1.70728i	0.520861	−	0.853642i	$-0.325611\pi$
$128$		−	6.13188i		−	0.541987i
$129$	4.21737	−	2.19271i	0.371318	−	0.193057i
$130$			1.08255i			0.0949458i
$131$		−	1.59424i		−	0.139289i	−0.997572	−	0.0696445i	$-0.977814\pi$
$131$		−	1.59424i		−	0.139289i	0.997572	−	0.0696445i	$-0.0221865\pi$
$132$	8.64621	+	16.6297i	0.752556	+	1.44743i
$133$	−13.0323			−1.13005
$134$			1.82905i			0.158006i
$135$	0.686052	−	5.15066i	0.0590459	−	0.443299i
$136$			3.07203i			0.263424i
$137$	−2.52659			−0.215861			−0.107931	−	0.994158i	$-0.534422\pi$
$137$	−2.52659			−0.215861			−0.107931	+	0.994158i	$0.534422\pi$
$138$	−0.186806	+	0.0971251i	−0.0159020	+	0.00826784i
$139$			2.96805i			0.251747i	0.992046	+	0.125873i	$0.0401733\pi$
$139$			2.96805i			0.251747i	−0.992046	+	0.125873i	$0.959827\pi$
$140$			6.69043i			0.565444i
$141$	−18.5291	+	9.63371i	−1.56043	+	0.811304i
$142$	2.65280			0.222618
$143$			29.6339i			2.47811i
$144$	−6.47482	+	9.22712i	−0.539568	+	0.768926i
$145$		−	3.16401i		−	0.262757i
$146$	1.14093			0.0944238
$147$	−3.72356	−	7.16173i	−0.307114	−	0.590689i
$148$			0.333079i			0.0273790i
$149$		−	12.1619i		−	0.996345i	−0.867078	−	0.498173i	$-0.834005\pi$
$149$		−	12.1619i		−	0.996345i	0.867078	−	0.498173i	$-0.165995\pi$
$150$	0.310060	−	0.161208i	0.0253163	−	0.0131625i
$151$			17.3762i			1.41405i	0.707186	+	0.707027i	$0.249964\pi$
$151$			17.3762i			1.41405i	−0.707186	+	0.707027i	$0.750036\pi$
$152$		−	3.04879i		−	0.247289i
$153$	6.62682	−	9.44373i	0.535747	−	0.763480i
$154$		−	3.80522i		−	0.306633i
$155$	−1.26910	+	5.42120i	−0.101937	+	0.435441i
$156$	−16.1551	+	8.39941i	−1.29344	+	0.672491i
$157$	−2.45570			−0.195986			−0.0979931	−	0.995187i	$-0.531242\pi$
$157$	−2.45570			−0.195986			−0.0979931	+	0.995187i	$0.531242\pi$
$158$	−3.22932			−0.256911
$159$	−7.95007	−	15.2908i	−0.630482	−	1.21264i
$160$	−2.35578			−0.186241
$161$	−2.05731			−0.162139
$162$	−1.70761	+	0.617609i	−0.134163	+	0.0485239i
$163$	−14.5145			−1.13686			−0.568431	−	0.822731i	$-0.692449\pi$
$163$	−14.5145			−1.13686			−0.568431	+	0.822731i	$0.692449\pi$
$164$		−	15.9928i		−	1.24883i
$165$	8.48763	−	4.41293i	0.660761	−	0.343546i
$166$			0.954073i			0.0740505i
$167$	−4.86683			−0.376606			−0.188303	−	0.982111i	$-0.560299\pi$
$167$	−4.86683			−0.376606			−0.188303	+	0.982111i	$0.560299\pi$
$168$	4.19197	−	2.17951i	0.323417	−	0.168152i
$169$	−15.7880			−1.21446
$170$	0.775903			0.0595091
$171$	−6.57669	+	9.37229i	−0.502932	+	0.716717i
$172$			5.37696i			0.409989i
$173$		−	5.02438i		−	0.381996i	−0.981590	−	0.190998i	$-0.938828\pi$
$173$		−	5.02438i		−	0.381996i	0.981590	−	0.190998i	$-0.0611725\pi$
$174$	−0.981033	+	0.510063i	−0.0743719	+	0.0386678i
$175$	3.41472			0.258128
$176$	−20.7525			−1.56428
$177$	−4.83224	+	2.51240i	−0.363213	+	0.188843i
$178$		−	2.92000i		−	0.218863i
$179$	10.7634			0.804498			0.402249	−	0.915530i	$-0.368229\pi$
$179$	10.7634			0.804498			0.402249	+	0.915530i	$0.368229\pi$
$180$	4.81146	+	3.37628i	0.358625	+	0.251653i
$181$		−	5.42864i		−	0.403508i	−0.979436	−	0.201754i	$-0.935336\pi$
$181$		−	5.42864i		−	0.403508i	0.979436	−	0.201754i	$-0.0646641\pi$
$182$	3.69660			0.274010
$183$	12.7094	−	6.60794i	0.939508	−	0.488473i
$184$		−	0.481288i		−	0.0354810i
$185$	0.170000			0.0124986
$186$	1.88548	−	0.480440i	0.138250	−	0.0352276i
$187$	21.2397			1.55320
$188$		−	23.6237i		−	1.72294i
$189$	−17.5881	−	2.34267i	−1.27934	−	0.170404i
$190$	−0.770033			−0.0558641
$191$			11.4538i			0.828769i	0.910102	+	0.414384i	$0.136003\pi$
$191$			11.4538i			0.828769i	−0.910102	+	0.414384i	$0.863997\pi$
$192$	−5.62453	−	10.8180i	−0.405915	−	0.780720i
$193$	7.30048			0.525500			0.262750	−	0.964864i	$-0.415371\pi$
$193$	7.30048			0.525500			0.262750	+	0.964864i	$0.415371\pi$
$194$		−	2.39878i		−	0.172222i
$195$	4.28696	+	8.24536i	0.306996	+	0.590463i
$196$	9.13089			0.652206
$197$	−13.8583			−0.987360			−0.493680	−	0.869644i	$-0.664349\pi$
$197$	−13.8583			−0.987360			−0.493680	+	0.869644i	$0.664349\pi$
$198$	−2.73654	−	1.92028i	−0.194478	−	0.136468i
$199$		−	8.09096i		−	0.573553i	−0.957998	−	0.286776i	$-0.907416\pi$
$199$		−	8.09096i		−	0.573553i	0.957998	−	0.286776i	$-0.0925837\pi$
$200$			0.798839i			0.0564864i
$201$	7.24318	+	13.9312i	0.510894	+	0.982632i
$202$	−3.24452			−0.228283
$203$	−10.8042			−0.758307
$204$	6.02017	+	11.5789i	0.421496	+	0.810688i
$205$	−8.16253			−0.570096
$206$		−	1.14442i		−	0.0797355i
$207$	−1.03821	+	1.47953i	−0.0721606	+	0.102834i
$208$		−	20.1602i		−	1.39786i
$209$	−21.0790			−1.45807
$210$	−0.550479	−	1.05877i	−0.0379866	−	0.0730619i
$211$	3.67305			0.252863			0.126432	−	0.991975i	$-0.459648\pi$
$211$	3.67305			0.252863			0.126432	+	0.991975i	$0.459648\pi$
$212$	19.4951			1.33893
$213$	20.2054	−	10.5053i	1.38445	−	0.719809i
$214$	2.53955			0.173600
$215$	2.74434			0.187162
$216$	0.548045	−	4.11455i	0.0372897	−	0.279960i
$217$	18.5119	+	4.33363i	1.25667	+	0.294186i
$218$		−	0.267822i		−	0.0181392i
$219$	8.69001	−	4.51814i	0.587216	−	0.305308i
$220$			10.8214i			0.729576i
$221$			20.6335i			1.38796i
$222$	−0.0274053	−	0.0527101i	−0.00183932	−	0.00353767i
$223$			19.5370i			1.30829i	0.756368	+	0.654146i	$0.226972\pi$
$223$			19.5370i			1.30829i	−0.756368	+	0.654146i	$0.773028\pi$
$224$			8.04434i			0.537485i
$225$	1.72321	−	2.45571i	0.114881	−	0.163714i
$226$	−1.73395			−0.115341
$227$			8.83421i			0.586347i	0.956059	+	0.293174i	$0.0947114\pi$
$227$			8.83421i			0.586347i	−0.956059	+	0.293174i	$0.905289\pi$
$228$	−5.97463	−	11.4913i	−0.395679	−	0.761033i
$229$			8.35398i			0.552047i	0.961151	+	0.276023i	$0.0890167\pi$
$229$			8.35398i			0.552047i	−0.961151	+	0.276023i	$0.910983\pi$
$230$	−0.121559			−0.00801537
$231$	−15.0689	−	28.9829i	−0.991461	−	1.90693i
$232$		−	2.52754i		−	0.165941i
$233$			10.8745i			0.712415i	0.934407	+	0.356207i	$0.115930\pi$
$233$			10.8745i			0.712415i	−0.934407	+	0.356207i	$0.884070\pi$
$234$	1.86546	−	2.65843i	0.121949	−	0.173787i
$235$	−12.0573			−0.786530
$236$		−	6.16089i		−	0.401040i
$237$	−24.5965	+	12.7883i	−1.59772	+	0.830691i
$238$		−	2.64949i		−	0.171741i
$239$	−27.7384			−1.79425			−0.897125	−	0.441778i	$-0.854348\pi$
$239$	−27.7384			−1.79425			−0.897125	+	0.441778i	$0.854348\pi$
$240$	−5.77420	+	3.00215i	−0.372723	+	0.193788i
$241$		−	9.09295i		−	0.585728i	−0.956154	−	0.292864i	$-0.905392\pi$
$241$		−	9.09295i		−	0.585728i	0.956154	−	0.292864i	$-0.0946084\pi$
$242$		−	3.93531i		−	0.252971i
$243$	−10.5604	+	11.4663i	−0.677453	+	0.735566i
$244$			16.2040i			1.03735i
$245$		−	4.66030i		−	0.297736i
$246$	1.31586	+	2.53087i	0.0838963	+	0.161362i
$247$		−	20.4773i		−	1.30294i
$248$	−1.01381	+	4.33066i	−0.0643769	+	0.274997i
$249$	3.77819	+	7.26681i	0.239433	+	0.460516i
$250$	0.201763			0.0127606
$251$	−1.41006			−0.0890021			−0.0445011	−	0.999009i	$-0.514170\pi$
$251$	−1.41006			−0.0890021			−0.0445011	+	0.999009i	$0.514170\pi$
$252$	11.5290	−	16.4298i	0.726262	−	1.03498i
$253$	−3.32758			−0.209203
$254$	−3.88194			−0.243575
$255$	5.90976	−	3.07263i	0.370083	−	0.192415i
$256$	12.8418			0.802614
$257$		−	4.38857i		−	0.273752i	−0.990588	−	0.136876i	$-0.956294\pi$
$257$		−	4.38857i		−	0.273752i	0.990588	−	0.136876i	$-0.0437061\pi$
$258$	−0.442408	−	0.850909i	−0.0275431	−	0.0529753i
$259$		−	0.580502i		−	0.0360706i
$260$	−10.5125			−0.651956
$261$	−5.45227	+	7.76991i	−0.337487	+	0.480945i
$262$	−0.321658			−0.0198721
$263$	11.4053			0.703281			0.351640	−	0.936135i	$-0.385624\pi$
$263$	11.4053			0.703281			0.351640	+	0.936135i	$0.385624\pi$
$264$	6.78025	−	3.52522i	0.417296	−	0.216962i
$265$		−	9.95009i		−	0.611229i
$266$			2.62945i			0.161222i
$267$	−11.5634	−	22.2405i	−0.707667	−	1.36110i
$268$	−17.7617			−1.08497
$269$	13.8325			0.843385			0.421693	−	0.906739i	$-0.361436\pi$
$269$	13.8325			0.843385			0.421693	+	0.906739i	$0.361436\pi$
$270$	−1.03921	−	0.138420i	−0.0632445	−	0.00842397i
$271$		−	28.8651i		−	1.75343i	−0.481009	−	0.876716i	$-0.659730\pi$
$271$		−	28.8651i		−	1.75343i	0.481009	−	0.876716i	$-0.340270\pi$
$272$	−14.4495			−0.876132
$273$	28.1556	−	14.6388i	1.70405	−	0.885979i
$274$			0.509773i			0.0307965i
$275$	5.52310			0.333055
$276$	−0.943167	−	1.81405i	−0.0567720	−	0.109193i
$277$			1.53175i			0.0920340i	0.998941	+	0.0460170i	$0.0146528\pi$
$277$			1.53175i			0.0920340i	−0.998941	+	0.0460170i	$0.985347\pi$
$278$	0.598842			0.0359162
$279$	12.4584	−	11.1260i	0.745867	−	0.666094i
$280$	2.72781			0.163018
$281$		−	15.0431i		−	0.897397i	−0.893683	−	0.448699i	$-0.851888\pi$
$281$		−	15.0431i		−	0.897397i	0.893683	−	0.448699i	$-0.148112\pi$
$282$	1.94373	+	3.73848i	0.115747	+	0.222623i
$283$	−15.7091			−0.933812			−0.466906	−	0.884307i	$-0.654631\pi$
$283$	−15.7091			−0.933812			−0.466906	+	0.884307i	$0.654631\pi$
$284$			25.7610i			1.52863i
$285$	−5.86505	+	3.04938i	−0.347415	+	0.180630i
$286$	5.97902			0.353547
$287$			27.8727i			1.64528i
$288$	5.78513	+	4.05952i	0.340892	+	0.239210i
$289$	−2.21124			−0.130073
$290$	−0.638381			−0.0374870
$291$	−9.49931	−	18.2706i	−0.556859	−	1.07104i
$292$			11.0794i			0.648371i
$293$			18.6303i			1.08840i	0.838957	+	0.544198i	$0.183166\pi$
$293$			18.6303i			1.08840i	−0.838957	+	0.544198i	$0.816834\pi$
$294$	−1.44497	+	0.751276i	−0.0842725	+	0.0438153i
$295$	−3.14445			−0.183077
$296$	0.135803			0.00789336
$297$	−28.4476	−	3.78913i	−1.65070	−	0.219868i
$298$	−2.45383			−0.142147
$299$		−	3.23260i		−	0.186946i
$300$	1.56546	+	3.01095i	0.0903821	+	0.173837i
$301$		−	9.37114i		−	0.540143i
$302$	3.50587			0.201740
$303$	−24.7122	+	12.8485i	−1.41968	+	0.738127i
$304$	14.3402			0.822468
$305$	8.27031			0.473557
$306$	−1.90540	−	1.33705i	−0.108924	−	0.0764339i
$307$	1.28244			0.0731927			0.0365963	−	0.999330i	$-0.488348\pi$
$307$	1.28244			0.0731927			0.0365963	+	0.999330i	$0.488348\pi$
$308$	36.9519			2.10553
$309$	−4.53197	−	8.71660i	−0.257815	−	0.495870i
$310$	1.09380	+	0.256058i	0.0621235	+	0.0145431i
$311$			16.6104i			0.941892i	0.882162	+	0.470946i	$0.156087\pi$
$311$			16.6104i			0.941892i	−0.882162	+	0.470946i	$0.843913\pi$
$312$	3.42459	+	6.58672i	0.193879	+	0.372899i
$313$			5.80608i			0.328179i	0.986445	+	0.164090i	$0.0524686\pi$
$313$			5.80608i			0.328179i	−0.986445	+	0.164090i	$0.947531\pi$
$314$			0.495470i			0.0279610i
$315$	−8.38557	−	5.88429i	−0.472473	−	0.331542i
$316$		−	31.3595i		−	1.76411i
$317$			10.9825i			0.616841i	0.951250	+	0.308421i	$0.0998004\pi$
$317$			10.9825i			0.616841i	−0.951250	+	0.308421i	$0.900200\pi$
$318$	−3.08512	+	1.60403i	−0.173005	+	0.0899496i
$319$	−17.4751			−0.978420
$320$		−	7.03950i		−	0.393520i
$321$	19.3428	−	10.0568i	1.07961	−	0.561316i
$322$			0.415090i			0.0231321i
$323$	−14.6769			−0.816643
$324$	−5.99751	−	16.5824i	−0.333195	−	0.921242i
$325$			5.36545i			0.297621i
$326$			2.92849i			0.162194i
$327$	−1.06059	−	2.03990i	−0.0586509	−	0.112807i
$328$	−6.52054			−0.360037
$329$			41.1722i			2.26990i
$330$	−0.890365	−	1.71249i	−0.0490130	−	0.0942695i
$331$		−	10.7832i		−	0.592700i	−0.955079	−	0.296350i	$-0.904231\pi$
$331$		−	10.7832i		−	0.592700i	0.955079	−	0.296350i	$-0.0957695\pi$
$332$	−9.26487			−0.508476
$333$	−0.417471	−	0.292946i	−0.0228773	−	0.0160534i
$334$			0.981946i			0.0537297i
$335$			9.06536i			0.495294i
$336$	10.2515	+	19.7173i	0.559265	+	1.07567i
$337$			12.1769i			0.663317i	0.943400	+	0.331658i	$0.107608\pi$
$337$			12.1769i			0.663317i	−0.943400	+	0.331658i	$0.892392\pi$
$338$			3.18544i			0.173265i
$339$	−13.2068	+	6.86656i	−0.717297	+	0.372940i
$340$			7.53468i			0.408626i
$341$	29.9418	+	7.00938i	1.62144	+	0.379579i
$342$	1.89098	+	1.32693i	0.102253	+	0.0717523i
$343$	7.98942			0.431388
$344$	2.19228			0.118200
$345$	−0.925869	+	0.481382i	−0.0498471	+	0.0259167i
$346$	−1.01373			−0.0544987
$347$	−7.87830			−0.422930			−0.211465	−	0.977386i	$-0.567823\pi$
$347$	−7.87830			−0.422930			−0.211465	+	0.977386i	$0.567823\pi$
$348$	−4.95315	−	9.52667i	−0.265517	−	0.510683i
$349$	−9.28266			−0.496889			−0.248445	−	0.968646i	$-0.579919\pi$
$349$	−9.28266			−0.496889			−0.248445	+	0.968646i	$0.579919\pi$
$350$		−	0.688964i		−	0.0368267i
$351$	3.68098	−	27.6356i	0.196476	−	1.47508i
$352$			13.0112i			0.693500i
$353$	−17.1351			−0.912008			−0.456004	−	0.889978i	$-0.650720\pi$
$353$	−17.1351			−0.912008			−0.456004	+	0.889978i	$0.650720\pi$
$354$	0.506909	+	0.974967i	0.0269419	+	0.0518189i
$355$	13.1481			0.697829
$356$	28.3557			1.50285
$357$	−10.4922	−	20.1802i	−0.555304	−	1.06805i
$358$		−	2.17167i		−	0.114776i
$359$			3.89759i			0.205707i	0.994697	+	0.102854i	$0.0327973\pi$
$359$			3.89759i			0.205707i	−0.994697	+	0.102854i	$0.967203\pi$
$360$	1.37657	−	1.96172i	0.0725517	−	0.103392i
$361$	−4.43416			−0.233377
$362$	−1.09530			−0.0575676
$363$	−15.5841	−	29.9737i	−0.817952	−	1.57321i
$364$			35.8971i			1.88152i
$365$	5.65479			0.295985
$366$	−1.33324	−	2.56429i	−0.0696895	−	0.134038i
$367$			19.2092i			1.00271i	0.865241	+	0.501356i	$0.167165\pi$
$367$			19.2092i			1.00271i	−0.865241	+	0.501356i	$0.832835\pi$
$368$	2.26378			0.118008
$369$	20.0448	+	14.0658i	1.04349	+	0.732236i
$370$		−	0.0342997i		−	0.00178316i
$371$	−33.9768			−1.76399
$372$	4.66549	+	18.3097i	0.241894	+	0.949312i
$373$	−13.1666			−0.681743			−0.340871	−	0.940110i	$-0.610722\pi$
$373$	−13.1666			−0.681743			−0.340871	+	0.940110i	$0.610722\pi$
$374$		−	4.28539i		−	0.221592i
$375$	1.53675	−	0.798995i	0.0793575	−	0.0412599i
$376$	−9.63183			−0.496723
$377$		−	16.9763i		−	0.874326i
$378$	−0.472665	+	3.54862i	−0.0243113	+	0.182521i
$379$	−1.75444			−0.0901197			−0.0450598	−	0.998984i	$-0.514348\pi$
$379$	−1.75444			−0.0901197			−0.0450598	+	0.998984i	$0.514348\pi$
$380$		−	7.47768i		−	0.383597i
$381$	−29.5673	+	15.3727i	−1.51478	+	0.787570i
$382$	2.31096			0.118239
$383$	37.2282			1.90227			0.951137	−	0.308769i	$-0.0999170\pi$
$383$	37.2282			1.90227			0.951137	+	0.308769i	$0.0999170\pi$
$384$	−9.42318	+	4.89934i	−0.480875	+	0.250018i
$385$		−	18.8598i		−	0.961185i
$386$		−	1.47297i		−	0.0749720i
$387$	−6.73931	−	4.72908i	−0.342578	−	0.240393i
$388$	23.2942			1.18258
$389$	18.6634			0.946273			0.473137	−	0.880989i	$-0.343122\pi$
$389$	18.6634			0.946273			0.473137	+	0.880989i	$0.343122\pi$
$390$	1.66361	−	0.864951i	0.0842402	−	0.0437985i
$391$	−2.31692			−0.117172
$392$		−	3.72283i		−	0.188031i
$393$	−2.44994	+	1.27379i	−0.123583	+	0.0642540i
$394$			2.79608i			0.140865i
$395$	−16.0055			−0.805325
$396$	18.6475	−	26.5742i	0.937073	−	1.33540i
$397$	22.9613			1.15239			0.576197	−	0.817311i	$-0.304536\pi$
$397$	22.9613			1.15239			0.576197	+	0.817311i	$0.304536\pi$
$398$	−1.63246			−0.0818276
$399$	10.4128	+	20.0275i	0.521291	+	1.00263i
$400$	−3.75741			−0.187870
$401$	−16.5051			−0.824228			−0.412114	−	0.911132i	$-0.635209\pi$
$401$	−16.5051			−0.824228			−0.412114	+	0.911132i	$0.635209\pi$
$402$	2.81080	−	1.46141i	0.140190	−	0.0728883i
$403$	−6.80931	+	29.0871i	−0.339196	+	1.44893i
$404$		−	31.5070i		−	1.56753i
$405$	−8.46345	+	3.06106i	−0.420552	+	0.152105i
$406$			2.17989i			0.108186i
$407$		−	0.938926i		−	0.0465408i
$408$	4.72094	−	2.45453i	0.233722	−	0.121518i
$409$		−	4.07927i		−	0.201707i	−0.994901	−	0.100854i	$-0.967843\pi$
$409$		−	4.07927i		−	0.201707i	0.994901	−	0.100854i	$-0.0321573\pi$
$410$			1.64690i			0.0813344i
$411$	2.01873	+	3.88275i	0.0995768	+	0.191522i
$412$	11.1133			0.547512
$413$			10.7374i			0.528353i
$414$	0.298514	+	0.209472i	0.0146712	+	0.0102950i
$415$			4.72868i			0.232122i
$416$	−12.6398			−0.619719
$417$	4.56115	−	2.37145i	0.223361	−	0.116131i
$418$			4.25297i			0.208019i
$419$			10.1501i			0.495865i	0.968777	+	0.247932i	$0.0797511\pi$
$419$			10.1501i			0.495865i	−0.968777	+	0.247932i	$0.920249\pi$
$420$	10.2815	−	5.34562i	0.501687	−	0.260839i
$421$	18.7017			0.911465			0.455732	−	0.890117i	$-0.349377\pi$
$421$	18.7017			0.911465			0.455732	+	0.890117i	$0.349377\pi$
$422$		−	0.741086i		−	0.0360755i
$423$	29.6092	+	20.7773i	1.43965	+	1.01023i
$424$		−	7.94852i		−	0.386014i
$425$	3.84562			0.186540
$426$	−2.11958	−	4.07670i	−0.102694	−	0.197517i
$427$		−	28.2408i		−	1.36667i
$428$			24.6612i			1.19205i
$429$	45.5399	−	23.6773i	2.19869	−	1.14315i
$430$		−	0.553706i		−	0.0267021i
$431$		−	19.9381i		−	0.960383i	−0.877164	−	0.480191i	$-0.840567\pi$
$431$		−	19.9381i		−	0.960383i	0.877164	−	0.480191i	$-0.159433\pi$
$432$	19.3531	+	2.57778i	0.931128	+	0.124023i
$433$			6.72332i			0.323102i	0.986864	+	0.161551i	$0.0516497\pi$
$433$			6.72332i			0.323102i	−0.986864	+	0.161551i	$0.948350\pi$
$434$	0.874366	−	3.73501i	0.0419709	−	0.179286i
$435$	−4.86230	+	2.52803i	−0.233130	+	0.121210i
$436$	2.60078			0.124555
$437$	2.29939			0.109995
$438$	−0.911595	−	1.75332i	−0.0435577	−	0.0837770i
$439$	7.90203			0.377144			0.188572	−	0.982059i	$-0.439614\pi$
$439$	7.90203			0.377144			0.188572	+	0.982059i	$0.439614\pi$
$440$	4.41206			0.210337
$441$	−8.03070	+	11.4444i	−0.382414	+	0.544970i
$442$	4.16307			0.198017
$443$		−	30.0456i		−	1.42751i	−0.700395	−	0.713756i	$-0.746993\pi$
$443$		−	30.0456i		−	1.42751i	0.700395	−	0.713756i	$-0.253007\pi$
$444$	0.511860	−	0.266129i	0.0242918	−	0.0126299i
$445$		−	14.4724i		−	0.686058i
$446$	3.94184			0.186652
$447$	−18.6899	+	9.71733i	−0.884002	+	0.459614i
$448$	−24.0379			−1.13569
$449$	−6.94742			−0.327869			−0.163934	−	0.986471i	$-0.552419\pi$
$449$	−6.94742			−0.327869			−0.163934	+	0.986471i	$0.552419\pi$
$450$	−0.495472	−	0.347681i	−0.0233568	−	0.0163898i
$451$			45.0824i			2.12285i
$452$		−	16.8382i		−	0.792000i
$453$	26.7029	−	13.8835i	1.25461	−	0.652303i
$454$	1.78242			0.0836530
$455$	18.3215			0.858925
$456$	−4.68523	+	2.43596i	−0.219406	+	0.114074i
$457$			2.23418i			0.104511i	0.998634	+	0.0522553i	$0.0166409\pi$
$457$			2.23418i			0.104511i	−0.998634	+	0.0522553i	$0.983359\pi$
$458$	1.68552			0.0787594
$459$	−19.8075	−	2.63829i	−0.924534	−	0.123145i
$460$		−	1.18044i		−	0.0550384i
$461$	31.3859			1.46179			0.730893	−	0.682492i	$-0.239104\pi$
$461$	31.3859			1.46179			0.730893	+	0.682492i	$0.239104\pi$
$462$	−5.84767	+	3.04035i	−0.272058	+	0.141450i
$463$		−	21.3200i		−	0.990826i	−0.868658	−	0.495413i	$-0.835017\pi$
$463$		−	21.3200i		−	0.990826i	0.868658	−	0.495413i	$-0.164983\pi$
$464$	11.8885			0.551909
$465$	9.34504	−	2.38121i	0.433366	−	0.110426i
$466$	2.19408			0.101639
$467$			4.55754i			0.210898i	0.994425	+	0.105449i	$0.0336280\pi$
$467$			4.55754i			0.210898i	−0.994425	+	0.105449i	$0.966372\pi$
$468$	25.8156	+	18.1153i	1.19333	+	0.837378i
$469$	30.9557			1.42940
$470$			2.43271i			0.112213i
$471$	1.96209	+	3.77380i	0.0904084	+	0.173888i
$472$	−2.51191			−0.115620
$473$		−	15.1572i		−	0.696931i
$474$	2.58021	+	4.96267i	0.118513	+	0.227943i
$475$	−3.81652			−0.175114
$476$	25.7288			1.17928
$477$	−17.1461	+	24.4346i	−0.785068	+	1.11878i
$478$			5.59659i			0.255982i
$479$			3.24882i			0.148443i	0.997242	+	0.0742213i	$0.0236471\pi$
$479$			3.24882i			0.148443i	−0.997242	+	0.0742213i	$0.976353\pi$
$480$	1.88226	+	3.62026i	0.0859130	+	0.165241i
$481$	0.912125			0.0415893
$482$	−1.83462			−0.0835647
$483$	1.64378	+	3.16158i	0.0747947	+	0.143857i
$484$	38.2152			1.73705
$485$		−	11.8891i		−	0.539855i
$486$	2.31348	+	2.13071i	0.104942	+	0.0966509i
$487$		−	1.18688i		−	0.0537825i	−0.999638	−	0.0268913i	$-0.991439\pi$
$487$		−	1.18688i		−	0.0537825i	0.999638	−	0.0268913i	$-0.00856079\pi$
$488$	6.60665			0.299069
$489$	11.5970	+	22.3052i	0.524434	+	1.00867i
$490$	−0.940276			−0.0424774
$491$	11.3973			0.514352			0.257176	−	0.966365i	$-0.417208\pi$
$491$	11.3973			0.514352			0.257176	+	0.966365i	$0.417208\pi$
$492$	−24.5769	+	12.7781i	−1.10801	+	0.576083i
$493$	−12.1676			−0.548000
$494$	−4.13157			−0.185888
$495$	−13.5631	−	9.51748i	−0.609618	−	0.427779i
$496$	−20.3696	−	4.76854i	−0.914624	−	0.214114i
$497$		−	44.8971i		−	2.01391i
$498$	1.46617	−	0.762300i	0.0657008	−	0.0341595i
$499$		−	33.2882i		−	1.49018i	−0.666962	−	0.745092i	$-0.732406\pi$
$499$		−	33.2882i		−	1.49018i	0.666962	−	0.745092i	$-0.267594\pi$
$500$			1.95929i			0.0876222i
$501$	3.88857	+	7.47911i	0.173728	+	0.334142i
$502$			0.284498i			0.0126978i
$503$		−	3.39826i		−	0.151521i	−0.997126	−	0.0757605i	$-0.975862\pi$
$503$		−	3.39826i		−	0.151521i	0.997126	−	0.0757605i	$-0.0241384\pi$
$504$	−6.69872	−	4.70060i	−0.298385	−	0.209381i
$505$	−16.0808			−0.715587
$506$			0.671383i			0.0298466i
$507$	12.6146	+	24.2623i	0.560232	+	1.07753i
$508$		−	37.6970i		−	1.67253i
$509$	5.33341			0.236399			0.118200	−	0.992990i	$-0.462288\pi$
$509$	5.33341			0.236399			0.118200	+	0.992990i	$0.462288\pi$
$510$	−0.619943	−	1.19237i	−0.0274515	−	0.0527991i
$511$		−	19.3095i		−	0.854202i
$512$		−	14.8548i		−	0.656494i
$513$	19.6576	+	2.61833i	0.867905	+	0.115602i
$514$	−0.885452			−0.0390556
$515$		−	5.67209i		−	0.249942i
$516$	8.26305	−	4.29616i	0.363761	−	0.189128i
$517$			66.5935i			2.92878i
$518$	−0.117124			−0.00514612
$519$	−7.72123	+	4.01445i	−0.338924	+	0.176215i
$520$			4.28613i			0.187959i
$521$		−	4.82120i		−	0.211221i	−0.994408	−	0.105610i	$-0.966320\pi$
$521$		−	4.82120i		−	0.211221i	0.994408	−	0.105610i	$-0.0336796\pi$
$522$	1.56768	+	1.10007i	0.0686155	+	0.0481486i
$523$		−	4.88434i		−	0.213577i	−0.994282	−	0.106789i	$-0.965943\pi$
$523$		−	4.88434i		−	0.213577i	0.994282	−	0.106789i	$-0.0340568\pi$
$524$		−	3.12357i		−	0.136454i
$525$	−2.72834	−	5.24758i	−0.119075	−	0.229023i
$526$		−	2.30117i		−	0.100336i
$527$	20.8478	+	4.88048i	0.908146	+	0.212597i
$528$	16.5812	+	31.8915i	0.721602	+	1.38790i
$529$	−22.6370			−0.984218
$530$	−2.00756			−0.0872029
$531$	7.72187	+	5.41856i	0.335100	+	0.235146i
$532$	−25.5342			−1.10705
$533$	−43.7956			−1.89700
$534$	−4.48731	+	2.33306i	−0.194185	+	0.100962i
$535$	12.5868			0.544176
$536$			7.24176i			0.312796i
$537$	−8.59994	−	16.5408i	−0.371115	−	0.713786i
$538$		−	2.79090i		−	0.120324i
$539$	−25.7393			−1.10867
$540$	1.34418	−	10.0917i	0.0578441	−	0.434276i
$541$	17.1172			0.735926			0.367963	−	0.929840i	$-0.380055\pi$
$541$	17.1172			0.735926			0.367963	+	0.929840i	$0.380055\pi$
$542$	−5.82392			−0.250159
$543$	−8.34247	+	4.33745i	−0.358010	+	0.186138i
$544$			9.05944i			0.388420i
$545$		−	1.32741i		−	0.0568599i
$546$	−2.95356	−	5.68076i	−0.126401	−	0.243114i
$547$	30.1072			1.28729			0.643646	−	0.765323i	$-0.277421\pi$
$547$	30.1072			1.28729			0.643646	+	0.765323i	$0.277421\pi$
$548$	−4.95033			−0.211468
$549$	−20.3095	−	14.2515i	−0.866789	−	0.608240i
$550$		−	1.11436i		−	0.0475163i
$551$	12.0755			0.514435
$552$	−0.739620	+	0.384546i	−0.0314803	+	0.0163674i
$553$			54.6544i			2.32414i
$554$	0.309051			0.0131303
$555$	−0.135829	−	0.261248i	−0.00576562	−	0.0110893i
$556$			5.81527i			0.246622i
$557$	−33.9958			−1.44045			−0.720224	−	0.693742i	$-0.755961\pi$
$557$	−33.9958			−1.44045			−0.720224	+	0.693742i	$0.755961\pi$
$558$	−2.24481	−	2.51365i	−0.0950304	−	0.106411i
$559$	14.7246			0.622784
$560$			12.8305i			0.542187i
$561$	−16.9704	−	32.6402i	−0.716492	−	1.37807i
$562$	−3.03515			−0.128030
$563$			3.73852i			0.157560i	0.996892	+	0.0787799i	$0.0251024\pi$
$563$			3.73852i			0.157560i	−0.996892	+	0.0787799i	$0.974898\pi$
$564$	−36.3038	+	18.8752i	−1.52867	+	0.794791i
$565$	−8.59400			−0.361552
$566$			3.16953i			0.133225i
$567$	10.4527	+	28.9003i	0.438970	+	1.21370i
$568$	10.5032			0.440705
$569$	10.3915			0.435633			0.217816	−	0.975990i	$-0.430107\pi$
$569$	10.3915			0.435633			0.217816	+	0.975990i	$0.430107\pi$
$570$	0.615252	+	1.18335i	0.0257701	+	0.0495651i
$571$		−	22.0116i		−	0.921158i	−0.887619	−	0.460579i	$-0.847642\pi$
$571$		−	22.0116i		−	0.921158i	0.887619	−	0.460579i	$-0.152358\pi$
$572$			58.0614i			2.42767i
$573$	17.6017	−	9.15153i	0.735320	−	0.382311i
$574$	5.62369			0.234728
$575$	−0.602484			−0.0251253
$576$	−12.1306	+	17.2870i	−0.505441	+	0.720292i
$577$	−29.5326			−1.22946			−0.614730	−	0.788738i	$-0.710735\pi$
$577$	−29.5326			−1.22946			−0.614730	+	0.788738i	$0.710735\pi$
$578$			0.446146i			0.0185572i
$579$	−5.83304	−	11.2190i	−0.242413	−	0.466247i
$580$		−	6.19922i		−	0.257409i
$581$	16.1471			0.669895
$582$	−3.68632	+	1.91661i	−0.152803	+	0.0794460i
$583$	−54.9553			−2.27602
$584$	4.51726			0.186926
$585$	9.24582	−	13.1760i	0.382268	−	0.544761i
$586$	3.75892			0.155279
$587$	−2.05907			−0.0849868			−0.0424934	−	0.999097i	$-0.513530\pi$
$587$	−2.05907			−0.0849868			−0.0424934	+	0.999097i	$0.513530\pi$
$588$	−7.29553	−	14.0319i	−0.300863	−	0.578666i
$589$	−20.6901	−	4.84356i	−0.852521	−	0.199575i
$590$			0.634434i			0.0261192i
$591$	11.0727	+	21.2967i	0.455469	+	0.876030i
$592$			0.638759i			0.0262528i
$593$		−	14.6809i		−	0.602872i	−0.953486	−	0.301436i	$-0.902534\pi$
$593$		−	14.6809i		−	0.602872i	0.953486	−	0.301436i	$-0.0974660\pi$
$594$	−0.764507	+	5.73968i	−0.0313681	+	0.235502i
$595$		−	13.1317i		−	0.538347i
$596$		−	23.8288i		−	0.976066i
$597$	−12.4338	+	6.46463i	−0.508881	+	0.264580i
$598$	−0.652219			−0.0266712
$599$			28.2690i			1.15504i	0.816377	+	0.577520i	$0.195979\pi$
$599$			28.2690i			1.15504i	−0.816377	+	0.577520i	$0.804021\pi$
$600$	1.22762	−	0.638268i	0.0501173	−	0.0260572i
$601$		−	20.6504i		−	0.842347i	−0.906980	−	0.421174i	$-0.861618\pi$
$601$		−	20.6504i		−	0.842347i	0.906980	−	0.421174i	$-0.138382\pi$
$602$	−1.89075			−0.0770612
$603$	15.6216	−	22.2619i	0.636159	−	0.906576i
$604$			34.0450i			1.38527i
$605$		−	19.5046i		−	0.792975i
$606$	2.59235	+	4.98602i	0.105307	+	0.202543i
$607$	28.9558			1.17528			0.587640	−	0.809123i	$-0.300057\pi$
$607$	28.9558			1.17528			0.587640	+	0.809123i	$0.300057\pi$
$608$		−	8.99090i		−	0.364629i
$609$	8.63251	+	16.6034i	0.349807	+	0.672803i
$610$		−	1.66864i		−	0.0675614i
$611$	−64.6927			−2.61719
$612$	12.9839	−	18.5030i	0.524842	−	0.747940i
$613$			16.7793i			0.677711i	0.940838	+	0.338855i	$0.110040\pi$
$613$			16.7793i			0.677711i	−0.940838	+	0.338855i	$0.889960\pi$
$614$		−	0.258749i		−	0.0104423i
$615$	6.52182	+	12.5438i	0.262985	+	0.505814i
$616$		−	15.0660i		−	0.607025i
$617$			13.3708i			0.538288i	0.963100	+	0.269144i	$0.0867408\pi$
$617$			13.3708i			0.538288i	−0.963100	+	0.269144i	$0.913259\pi$
$618$	−1.75869	+	0.914385i	−0.0707448	+	0.0367819i
$619$		−	37.4460i		−	1.50508i	−0.658546	−	0.752540i	$-0.728828\pi$
$619$		−	37.4460i		−	1.50508i	0.658546	−	0.752540i	$-0.271172\pi$
$620$	−2.48654	+	10.6217i	−0.0998620	+	0.426578i
$621$	3.10319	+	0.413336i	0.124527	+	0.0165866i
$622$	3.35137			0.134378
$623$	−49.4192			−1.97994
$624$	−30.9812	+	16.1079i	−1.24024	+	0.644831i
$625$	1.00000			0.0400000
$626$	1.17145			0.0468207
$627$	16.8420	+	32.3932i	0.672606	+	1.29366i
$628$	−4.81143			−0.191997
$629$		−	0.653754i		−	0.0260669i
$630$	−1.18723	+	1.69190i	−0.0473005	+	0.0674068i
$631$			7.75486i			0.308716i	0.988015	+	0.154358i	$0.0493309\pi$
$631$			7.75486i			0.308716i	−0.988015	+	0.154358i	$0.950669\pi$
$632$	−12.7858			−0.508593
$633$	−2.93475	−	5.64457i	−0.116646	−	0.224352i
$634$	2.21587			0.0880035
$635$	−19.2401			−0.763520
$636$	−15.5765	−	29.9592i	−0.617649	−	1.18796i
$637$		−	25.0046i		−	0.990718i
$638$			3.52584i			0.139589i
$639$	−32.2880	−	22.6570i	−1.27729	−	0.896298i
$640$	−6.13188			−0.242384
$641$	35.0575			1.38469			0.692345	−	0.721567i	$-0.256578\pi$
$641$	35.0575			1.38469			0.692345	+	0.721567i	$0.256578\pi$
$642$	−2.02909	−	3.90267i	−0.0800818	−	0.154026i
$643$			19.2597i			0.759527i	0.925084	+	0.379764i	$0.123995\pi$
$643$			19.2597i			0.759527i	−0.925084	+	0.379764i	$0.876005\pi$
$644$	−4.03088			−0.158839
$645$	−2.19271	−	4.21737i	−0.0863379	−	0.166059i
$646$			2.96125i			0.116509i
$647$	17.8111			0.700226			0.350113	−	0.936707i	$-0.386143\pi$
$647$	17.8111			0.700226			0.350113	+	0.936707i	$0.386143\pi$
$648$	−6.76093	+	2.44529i	−0.265594	+	0.0960602i
$649$			17.3671i			0.681718i
$650$	1.08255			0.0424611
$651$	−8.13116	−	31.9107i	−0.318685	−	1.25068i
$652$	−28.4381			−1.11372
$653$			28.7340i			1.12445i	0.826985	+	0.562224i	$0.190054\pi$
$653$			28.7340i			1.12445i	−0.826985	+	0.562224i	$0.809946\pi$
$654$	−0.411576	+	0.213988i	−0.0160939	+	0.00836761i
$655$	−1.59424			−0.0622919
$656$		−	30.6699i		−	1.19746i
$657$	−13.8865	−	9.74441i	−0.541765	−	0.380166i
$658$	8.30703			0.323842
$659$		−	10.6520i		−	0.414943i	−0.978241	−	0.207472i	$-0.933477\pi$
$659$		−	10.6520i		−	0.414943i	0.978241	−	0.207472i	$-0.0665234\pi$
$660$	16.6297	−	8.64621i	0.647312	−	0.336553i
$661$	−4.73139			−0.184030			−0.0920149	−	0.995758i	$-0.529331\pi$
$661$	−4.73139			−0.184030			−0.0920149	+	0.995758i	$0.529331\pi$
$662$	−2.17566			−0.0845593
$663$	31.7085	−	16.4860i	1.23146	−	0.640264i
$664$			3.77745i			0.146594i
$665$			13.0323i			0.505373i
$666$	−0.0591057	+	0.0842302i	−0.00229030	+	0.00326386i
$667$	1.90627			0.0738110
$668$	−9.53553			−0.368941
$669$	30.0235	−	15.6099i	1.16078	−	0.603515i
$670$	1.82905			0.0706626
$671$		−	45.6778i		−	1.76337i
$672$	12.3622	−	6.42738i	0.476880	−	0.247942i
$673$		−	33.3886i		−	1.28704i	−0.765431	−	0.643519i	$-0.777474\pi$
$673$		−	33.3886i		−	1.28704i	0.765431	−	0.643519i	$-0.222526\pi$
$674$	2.45684			0.0946341
$675$	−5.15066	−	0.686052i	−0.198249	−	0.0264062i
$676$	−30.9334			−1.18974
$677$	−3.88792			−0.149425			−0.0747124	−	0.997205i	$-0.523804\pi$
$677$	−3.88792			−0.149425			−0.0747124	+	0.997205i	$0.523804\pi$
$678$	1.38542	+	2.66465i	0.0532067	+	0.102335i
$679$	−40.5978			−1.55800
$680$	3.07203			0.117807
$681$	13.5760	−	7.05849i	0.520233	−	0.270482i
$682$	1.41423	−	6.04115i	0.0541538	−	0.231328i
$683$		−	20.8458i		−	0.797642i	−0.917029	−	0.398821i	$-0.869420\pi$
$683$		−	20.8458i		−	0.797642i	0.917029	−	0.398821i	$-0.130580\pi$
$684$	−12.8856	+	18.3630i	−0.492695	+	0.702128i
$685$			2.52659i			0.0965362i
$686$		−	1.61197i		−	0.0615453i
$687$	12.8380	−	6.67479i	0.489800	−	0.254659i
$688$			10.3116i			0.393126i
$689$		−	53.3867i		−	2.03387i
$690$	0.0971251	+	0.186806i	0.00369749	+	0.00711159i
$691$	36.7507			1.39806			0.699031	−	0.715092i	$-0.253615\pi$
$691$	36.7507			1.39806			0.699031	+	0.715092i	$0.253615\pi$
$692$		−	9.84422i		−	0.374221i
$693$	−32.4995	+	46.3143i	−1.23455	+	1.75934i
$694$			1.58955i			0.0603385i
$695$	2.96805			0.112584
$696$	−3.88420	+	2.01949i	−0.147230	+	0.0765485i
$697$			31.3899i			1.18898i
$698$			1.87290i			0.0708902i
$699$	16.7115	−	8.68870i	0.632086	−	0.328637i
$700$	6.69043			0.252874
$701$			49.1806i			1.85753i	0.370675	+	0.928763i	$0.379126\pi$
$701$			49.1806i			1.85753i	−0.370675	+	0.928763i	$0.620874\pi$
$702$	−5.57585	−	0.742685i	−0.210447	−	0.0280308i
$703$			0.648808i			0.0244703i
$704$	−38.8799			−1.46534
$705$	9.63371	+	18.5291i	0.362826	+	0.697845i
$706$			3.45722i			0.130114i
$707$			54.9115i			2.06516i
$708$	−9.46777	+	4.92252i	−0.355820	+	0.185000i
$709$			1.66844i			0.0626598i	0.999509	+	0.0313299i	$0.00997424\pi$
$709$			1.66844i			0.0626598i	−0.999509	+	0.0313299i	$0.990026\pi$
$710$		−	2.65280i		−	0.0995579i
$711$	39.3050	+	27.5810i	1.47405	+	1.03437i
$712$		−	11.5611i		−	0.433271i
$713$	−3.26619	−	0.764615i	−0.122320	−	0.0286350i
$714$	−4.07161	+	2.11693i	−0.152376	+	0.0792241i
$715$	29.6339			1.10824
$716$	21.0887			0.788123
$717$	22.1628	+	42.6271i	0.827687	+	1.59194i
$718$	0.786390			0.0293478
$719$	7.94686			0.296368			0.148184	−	0.988960i	$-0.452657\pi$
$719$	7.94686			0.296368			0.148184	+	0.988960i	$0.452657\pi$
$720$	9.22712	+	6.47482i	0.343874	+	0.241302i
$721$	−19.3686			−0.721324
$722$			0.894650i			0.0332954i
$723$	−13.9736	+	7.26522i	−0.519684	+	0.270196i
$724$		−	10.6363i		−	0.395294i
$725$	−3.16401			−0.117508
$726$	−6.04759	+	3.14429i	−0.224447	+	0.116696i
$727$	38.1861			1.41624			0.708121	−	0.706091i	$-0.249543\pi$
$727$	38.1861			1.41624			0.708121	+	0.706091i	$0.249543\pi$
$728$	14.6359			0.542443
$729$	26.0587	+	7.06724i	0.965136	+	0.261750i
$730$		−	1.14093i		−	0.0422276i
$731$		−	10.5537i		−	0.390341i
$732$	24.9015	−	12.9469i	0.920385	−	0.478530i
$733$	−17.0233			−0.628771			−0.314385	−	0.949295i	$-0.601798\pi$
$733$	−17.0233			−0.628771			−0.314385	+	0.949295i	$0.601798\pi$
$734$	3.87571			0.143055
$735$	−7.16173	+	3.72356i	−0.264164	+	0.137345i
$736$		−	1.41932i		−	0.0523169i
$737$	50.0689			1.84431
$738$	2.83796	−	4.04431i	0.104467	−	0.148873i
$739$		−	40.6135i		−	1.49399i	−0.664829	−	0.746995i	$-0.731496\pi$
$739$		−	40.6135i		−	1.49399i	0.664829	−	0.746995i	$-0.268504\pi$
$740$	0.333079			0.0122442
$741$	−31.4686	+	16.3613i	−1.15603	+	0.601047i
$742$			6.85525i			0.251664i
$743$	−39.0607			−1.43300			−0.716499	−	0.697589i	$-0.754256\pi$
$743$	−39.0607			−1.43300			−0.716499	+	0.697589i	$0.754256\pi$
$744$	7.46518	−	1.90220i	0.273687	−	0.0697382i
$745$	−12.1619			−0.445579
$746$			2.65654i			0.0972629i
$747$	8.14854	−	11.6123i	0.298139	−	0.424871i
$748$	41.6148			1.52159
$749$		−	42.9804i		−	1.57047i
$750$	−0.161208	−	0.310060i	−0.00588647	−	0.0113218i
$751$	−8.65187			−0.315711			−0.157856	−	0.987462i	$-0.550458\pi$
$751$	−8.65187			−0.315711			−0.157856	+	0.987462i	$0.550458\pi$
$752$		−	45.3041i		−	1.65207i
$753$	1.12663	+	2.16691i	0.0410567	+	0.0789666i
$754$	−3.42520			−0.124738
$755$	17.3762			0.632384
$756$	−34.4601	−	4.58998i	−1.25330	−	0.166936i
$757$			29.5370i			1.07354i	0.843728	+	0.536771i	$0.180356\pi$
$757$			29.5370i			1.07354i	−0.843728	+	0.536771i	$0.819644\pi$
$758$			0.353982i			0.0128572i
$759$	2.65872	+	5.11367i	0.0965054	+	0.185614i
$760$	−3.04879			−0.110591
$761$	−34.4500			−1.24881			−0.624406	−	0.781100i	$-0.714659\pi$
$761$	−34.4500			−1.24881			−0.624406	+	0.781100i	$0.714659\pi$
$762$	3.10165	+	5.96558i	0.112361	+	0.216110i
$763$	−4.53273			−0.164096
$764$			22.4414i			0.811900i
$765$	−9.44373	−	6.62682i	−0.341439	−	0.239593i
$766$		−	7.51128i		−	0.271394i
$767$	−16.8714			−0.609190
$768$	−10.2605	−	19.7347i	−0.370246	−	0.712115i
$769$	−6.16604			−0.222353			−0.111176	−	0.993801i	$-0.535462\pi$
$769$	−6.16604			−0.222353			−0.111176	+	0.993801i	$0.535462\pi$
$770$	−3.80522			−0.137130
$771$	−6.74415	+	3.50645i	−0.242885	+	0.126282i
$772$	14.3038			0.514804
$773$	23.7137			0.852924			0.426462	−	0.904505i	$-0.359760\pi$
$773$	23.7137			0.852924			0.426462	+	0.904505i	$0.359760\pi$
$774$	−0.954154	+	1.35974i	−0.0342964	+	0.0488750i
$775$	5.42120	+	1.26910i	0.194735	+	0.0455875i
$776$		−	9.49745i		−	0.340939i
$777$	−0.892087	+	0.463818i	−0.0320035	+	0.0166394i
$778$		−	3.76559i		−	0.135003i
$779$		−	31.1525i		−	1.11615i
$780$	8.39941	+	16.1551i	0.300747	+	0.578444i
$781$		−	72.6183i		−	2.59849i
$782$			0.467470i			0.0167167i
$783$	16.2968	+	2.17068i	0.582399	+	0.0775737i
$784$	17.5106			0.625380
$785$			2.45570i			0.0876477i
$786$	0.257003	+	0.494308i	0.00916699	+	0.0176314i
$787$		−	54.1761i		−	1.93117i	−0.260088	−	0.965585i	$-0.583752\pi$
$787$		−	54.1761i		−	1.93117i	0.260088	−	0.965585i	$-0.416248\pi$
$788$	−27.1524			−0.967263
$789$	−9.11277	−	17.5271i	−0.324423	−	0.623982i
$790$			3.22932i			0.114894i
$791$			29.3461i			1.04343i
$792$	−10.8348	−	7.60294i	−0.384997	−	0.270159i
$793$	44.3739			1.57576
$794$		−	4.63274i		−	0.164410i
$795$	−15.2908	+	7.95007i	−0.542310	+	0.281960i
$796$		−	15.8525i		−	0.561878i
$797$	−28.4993			−1.00950			−0.504748	−	0.863267i	$-0.668414\pi$
$797$	−28.4993			−1.00950			−0.504748	+	0.863267i	$0.668414\pi$
$798$	4.04081	−	2.10091i	0.143043	−	0.0743715i
$799$			46.3677i			1.64037i
$800$			2.35578i			0.0832895i
$801$	−24.9391	+	35.5401i	−0.881179	+	1.25575i
$802$			3.33013i			0.117591i
$803$		−	31.2319i		−	1.10215i
$804$	14.1915	+	27.2953i	0.500495	+	0.962631i
$805$			2.05731i			0.0725108i
$806$	5.86871	+	1.37387i	0.206717	+	0.0483924i
$807$	−11.0521	−	21.2572i	−0.389053	−	0.748289i
$808$	−12.8460			−0.451920
$809$	12.8525			0.451870			0.225935	−	0.974142i	$-0.427456\pi$
$809$	12.8525			0.451870			0.225935	+	0.974142i	$0.427456\pi$
$810$	0.617609	+	1.70761i	0.0217006	+	0.0599993i
$811$	21.3271			0.748897			0.374448	−	0.927248i	$-0.377832\pi$
$811$	21.3271			0.748897			0.374448	+	0.927248i	$0.377832\pi$
$812$	−21.1686			−0.742872
$813$	−44.3585	+	23.0631i	−1.55572	+	0.808857i
$814$	−0.189441			−0.00663989
$815$			14.5145i			0.508420i
$816$	11.5451	+	22.2054i	0.404160	+	0.777343i
$817$			10.4738i			0.366433i
$818$	−0.823047			−0.0287771
$819$	−44.9923	−	31.5719i	−1.57216	−	1.10321i
$820$	−15.9928			−0.558492
$821$	3.12888			0.109198			0.0545992	−	0.998508i	$-0.482612\pi$
$821$	3.12888			0.109198			0.0545992	+	0.998508i	$0.482612\pi$
$822$	0.783395	−	0.407306i	0.0273240	−	0.0142064i
$823$		−	19.0857i		−	0.665285i	−0.943053	−	0.332643i	$-0.892060\pi$
$823$		−	19.0857i		−	0.665285i	0.943053	−	0.332643i	$-0.107940\pi$
$824$		−	4.53109i		−	0.157848i
$825$	−4.41293	−	8.48763i	−0.153638	−	0.295501i
$826$	2.16641			0.0753791
$827$	−19.3892			−0.674229			−0.337114	−	0.941464i	$-0.609451\pi$
$827$	−19.3892			−0.674229			−0.337114	+	0.941464i	$0.609451\pi$
$828$	−2.03416	+	2.89883i	−0.0706918	+	0.100741i
$829$		−	21.4665i		−	0.745564i	−0.927919	−	0.372782i	$-0.878404\pi$
$829$		−	21.4665i		−	0.745564i	0.927919	−	0.372782i	$-0.121596\pi$
$830$	0.954073			0.0331164
$831$	2.35392	−	1.22386i	0.0816567	−	0.0424553i
$832$		−	37.7701i		−	1.30944i
$833$	−17.9217			−0.620951
$834$	−0.478472	−	0.920272i	−0.0165681	−	0.0318664i
$835$			4.86683i			0.168423i
$836$	−41.3000			−1.42839
$837$	−27.0521	−	10.2559i	−0.935057	−	0.354497i
$838$	2.04792			0.0707441
$839$		−	42.0203i		−	1.45070i	−0.688378	−	0.725352i	$-0.741677\pi$
$839$		−	42.0203i		−	1.45070i	0.688378	−	0.725352i	$-0.258323\pi$
$840$	−2.17951	−	4.19197i	−0.0752001	−	0.144637i
$841$	−18.9890			−0.654794
$842$		−	3.77331i		−	0.130037i
$843$	−23.1175	+	12.0194i	−0.796211	+	0.413969i
$844$	7.19658			0.247717
$845$			15.7880i			0.543125i
$846$	4.19209	−	5.97405i	0.144127	−	0.205392i
$847$	−66.6027			−2.28850
$848$	37.3865			1.28386
$849$	12.5515	+	24.1411i	0.430767	+	0.828519i
$850$		−	0.775903i		−	0.0266133i
$851$			0.102422i			0.00351099i
$852$	39.5882	−	20.5829i	1.35627	−	0.705158i
$853$	−19.0375			−0.651832			−0.325916	−	0.945399i	$-0.605673\pi$
$853$	−19.0375			−0.651832			−0.325916	+	0.945399i	$0.605673\pi$
$854$	−5.69795			−0.194980
$855$	9.37229	+	6.57669i	0.320525	+	0.224918i
$856$	10.0548			0.343667
$857$		−	50.8253i		−	1.73616i	−0.496425	−	0.868080i	$-0.665354\pi$
$857$		−	50.8253i		−	1.73616i	0.496425	−	0.868080i	$-0.334646\pi$
$858$	−4.77721	−	9.18828i	−0.163091	−	0.313683i
$859$			47.9644i			1.63652i	0.574846	+	0.818262i	$0.305062\pi$
$859$			47.9644i			1.63652i	−0.574846	+	0.818262i	$0.694938\pi$
$860$	5.37696			0.183353
$861$	42.8335	−	22.2702i	1.45976	−	0.758965i
$862$	−4.02276			−0.137016
$863$	27.7409			0.944312			0.472156	−	0.881515i	$-0.343476\pi$
$863$	27.7409			0.944312			0.472156	+	0.881515i	$0.343476\pi$
$864$	1.61619	−	12.1338i	0.0549839	−	0.412802i
$865$	−5.02438			−0.170834
$866$	1.35652			0.0460964
$867$	1.76677	+	3.39813i	0.0600026	+	0.115406i
$868$	36.2701	+	8.49084i	1.23109	+	0.288198i
$869$			88.4001i			2.99877i
$870$	0.510063	+	0.981033i	0.0172928	+	0.0332601i
$871$			48.6397i			1.64809i
$872$		−	1.06039i		−	0.0359092i
$873$	−20.4874	+	29.1962i	−0.693395	+	0.988141i
$874$		−	0.463933i		−	0.0156928i
$875$		−	3.41472i		−	0.115439i
$876$	17.0263	−	8.85236i	0.575264	−	0.299094i
$877$	19.4005			0.655107			0.327553	−	0.944833i	$-0.393776\pi$
$877$	19.4005			0.655107			0.327553	+	0.944833i	$0.393776\pi$
$878$		−	1.59434i		−	0.0538063i
$879$	28.6302	−	14.8855i	0.965673	−	0.502077i
$880$			20.7525i			0.699567i
$881$	34.8845			1.17529			0.587644	−	0.809119i	$-0.300056\pi$
$881$	34.8845			1.17529			0.587644	+	0.809119i	$0.300056\pi$
$882$	2.30905	+	1.62030i	0.0777497	+	0.0545583i
$883$		−	34.1812i		−	1.15029i	−0.818052	−	0.575145i	$-0.804946\pi$
$883$		−	34.1812i		−	1.15029i	0.818052	−	0.575145i	$-0.195054\pi$
$884$			40.4269i			1.35971i
$885$	2.51240	+	4.83224i	0.0844533	+	0.162434i
$886$	−6.06210			−0.203660
$887$		−	16.4346i		−	0.551818i	−0.961184	−	0.275909i	$-0.911021\pi$
$887$		−	16.4346i		−	0.551818i	0.961184	−	0.275909i	$-0.0889789\pi$
$888$	−0.108505	−	0.208695i	−0.00364121	−	0.00700334i
$889$			65.6995i			2.20349i
$890$	−2.92000			−0.0978786
$891$	16.9065	+	46.7444i	0.566390	+	1.56600i
$892$			38.2786i			1.28166i
$893$		−	46.0169i		−	1.53990i
$894$	1.96060	+	3.77093i	0.0655722	+	0.126119i
$895$		−	10.7634i		−	0.359782i
$896$			20.9386i			0.699511i
$897$	−4.96770	+	2.58283i	−0.165867	+	0.0862382i
$898$			1.40173i			0.0467764i
$899$	−17.1527	−	4.01546i	−0.572076	−	0.133923i
$900$	3.37628	−	4.81146i	0.112543	−	0.160382i
$901$	−38.2642			−1.27477
$902$	9.09597			0.302863
$903$	−14.4011	+	7.48749i	−0.479239	+	0.249168i
$904$	−6.86522			−0.228334
$905$	−5.42864			−0.180454
$906$	−2.80117	−	5.38766i	−0.0930628	−	0.178993i
$907$	−9.91018			−0.329062			−0.164531	−	0.986372i	$-0.552611\pi$
$907$	−9.91018			−0.329062			−0.164531	+	0.986372i	$0.552611\pi$
$908$			17.3088i			0.574413i
$909$	39.4899	+	27.7107i	1.30980	+	0.919106i
$910$		−	3.69660i		−	0.122541i
$911$	36.7115			1.21631			0.608153	−	0.793820i	$-0.291911\pi$
$911$	36.7115			1.21631			0.608153	+	0.793820i	$0.291911\pi$
$912$	−11.4578	−	22.0374i	−0.379405	−	0.729730i
$913$	26.1170			0.864346
$914$	0.450775			0.0149103
$915$	−6.60794	−	12.7094i	−0.218452	−	0.420161i
$916$			16.3679i			0.540810i
$917$			5.44386i			0.179772i
$918$	−0.532310	+	3.99642i	−0.0175688	+	0.131901i
$919$	43.3049			1.42850			0.714249	−	0.699891i	$-0.246768\pi$
$919$	43.3049			1.42850			0.714249	+	0.699891i	$0.246768\pi$
$920$	−0.481288			−0.0158676
$921$	−1.02466	−	1.97079i	−0.0337638	−	0.0649398i
$922$		−	6.33251i		−	0.208550i
$923$	70.5455			2.32203
$924$	−29.5244	−	56.7859i	−0.971280	−	1.86812i
$925$		−	0.170000i		−	0.00558956i
$926$	−4.30159			−0.141359
$927$	−9.77424	+	13.9290i	−0.321028	+	0.457490i
$928$		−	7.45373i		−	0.244681i
$929$	−54.5896			−1.79103			−0.895513	−	0.445036i	$-0.853191\pi$
$929$	−54.5896			−1.79103			−0.895513	+	0.445036i	$0.853191\pi$
$930$	−0.480440	−	1.88548i	−0.0157543	−	0.0618275i
$931$	17.7861			0.582917
$932$			21.3064i			0.697914i
$933$	25.5261	−	13.2717i	0.835688	−	0.434495i
$934$	0.919544			0.0300884
$935$		−	21.2397i		−	0.694613i
$936$	7.38592	−	10.5255i	0.241416	−	0.344037i
$937$	6.22153			0.203248			0.101624	−	0.994823i	$-0.467596\pi$
$937$	6.22153			0.203248			0.101624	+	0.994823i	$0.467596\pi$
$938$		−	6.24571i		−	0.203930i
$939$	8.92251	−	4.63903i	0.291175	−	0.151389i
$940$	−23.6237			−0.770521
$941$	−31.6467			−1.03165			−0.515826	−	0.856693i	$-0.672515\pi$
$941$	−31.6467			−1.03165			−0.515826	+	0.856693i	$0.672515\pi$
$942$	0.761414	−	0.395878i	0.0248082	−	0.0128984i
$943$		−	4.91779i		−	0.160145i
$944$		−	11.8150i		−	0.384545i
$945$	−2.34267	+	17.5881i	−0.0762072	+	0.572140i
$946$	−3.05817			−0.0994297
$947$	55.3508			1.79866			0.899330	−	0.437270i	$-0.144055\pi$
$947$	55.3508			1.79866			0.899330	+	0.437270i	$0.144055\pi$
$948$	−48.1918	+	25.0561i	−1.56520	+	0.813783i
$949$	30.3405			0.984893
$950$			0.770033i			0.0249832i
$951$	16.8775	−	8.77500i	0.547289	−	0.284549i
$952$		−	10.4901i		−	0.339986i
$953$	6.97490			0.225939			0.112970	−	0.993598i	$-0.463964\pi$
$953$	6.97490			0.225939			0.112970	+	0.993598i	$0.463964\pi$
$954$	4.92999	+	3.45946i	0.159614	+	0.112004i
$955$	11.4538			0.370637
$956$	−54.3476			−1.75773
$957$	13.9626	+	26.8550i	0.451345	+	0.868098i
$958$	0.655493			0.0211780
$959$	8.62760			0.278600
$960$	−10.8180	+	5.62453i	−0.349149	+	0.181531i
$961$	27.7788	+	13.7601i	0.896089	+	0.443875i
$962$		−	0.184033i		−	0.00593347i
$963$	−30.9096	−	21.6898i	−0.996049	−	0.698944i
$964$		−	17.8157i		−	0.573806i
$965$		−	7.30048i		−	0.235011i
$966$	0.637891	−	0.331655i	0.0205238	−	0.0106708i
$967$			48.1269i			1.54766i	0.633394	+	0.773829i	$0.281661\pi$
$967$			48.1269i			1.54766i	−0.633394	+	0.773829i	$0.718339\pi$
$968$		−	15.5810i		−	0.500793i
$969$	11.7267	+	22.5547i	0.376717	+	0.724562i
$970$	−2.39878			−0.0770201
$971$			40.9765i			1.31500i	0.753455	+	0.657500i	$0.228386\pi$
$971$			40.9765i			1.31500i	−0.753455	+	0.657500i	$0.771614\pi$
$972$	−20.6910	+	22.4659i	−0.663664	+	0.720594i
$973$		−	10.1350i		−	0.324915i
$974$	−0.239468			−0.00767305
$975$	8.24536	−	4.28696i	0.264063	−	0.137293i
$976$			31.0749i			0.994685i
$977$			45.4140i			1.45292i	0.687208	+	0.726461i	$0.258836\pi$
$977$			45.4140i			1.45292i	−0.687208	+	0.726461i	$0.741164\pi$
$978$	4.50036	−	2.33985i	0.143906	−	0.0748200i
$979$	−79.9325			−2.55466
$980$		−	9.13089i		−	0.291675i
$981$	−2.28741	+	3.25974i	−0.0730314	+	0.104075i
$982$		−	2.29955i		−	0.0733816i
$983$	49.8783			1.59087			0.795436	−	0.606038i	$-0.207242\pi$
$983$	49.8783			1.59087			0.795436	+	0.606038i	$0.207242\pi$
$984$	5.20988	+	10.0205i	0.166085	+	0.319441i
$985$			13.8583i			0.441561i
$986$			2.45497i			0.0781821i
$987$	63.2715	−	32.8964i	2.01395	−	1.04710i
$988$		−	40.1211i		−	1.27642i
$989$			1.65342i			0.0525757i
$990$	−1.92028	+	2.73654i	−0.0610304	+	0.0869730i
$991$			40.6979i			1.29281i	0.762994	+	0.646406i	$0.223729\pi$
$991$			40.6979i			1.29281i	−0.762994	+	0.646406i	$0.776271\pi$
$992$	−2.98973	+	12.7712i	−0.0949241	+	0.405485i
$993$	−16.5712	+	8.61574i	−0.525870	+	0.273412i
$994$	−9.05857			−0.287321
$995$	−8.09096			−0.256501
$996$	7.40258	+	14.2378i	0.234560	+	0.451142i
$997$	21.6870			0.686835			0.343418	−	0.939183i	$-0.388415\pi$
$997$	21.6870			0.686835			0.343418	+	0.939183i	$0.388415\pi$
$998$	−6.71632			−0.212601
$999$	−0.116629	+	0.875612i	−0.00368997	+	0.0277031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.e.a.371.21	✓	44
3.2	odd	2	inner	465.2.e.a.371.24	yes	44
31.30	odd	2	inner	465.2.e.a.371.22	yes	44
93.92	even	2	inner	465.2.e.a.371.23	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.e.a.371.21	✓	44	1.1	even	1	trivial
465.2.e.a.371.22	yes	44	31.30	odd	2	inner
465.2.e.a.371.23	yes	44	93.92	even	2	inner
465.2.e.a.371.24	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.201763i q^{2} +(-0.798995 - 1.53675i) q^{3} +1.95929 q^{4} -1.00000i q^{5} +(-0.310060 + 0.161208i) q^{6} -3.41472 q^{7} -0.798839i q^{8} +(-1.72321 + 2.45571i) q^{9} -0.201763 q^{10} -5.52310 q^{11} +(-1.56546 - 3.01095i) q^{12} -5.36545i q^{13} +0.688964i q^{14} +(-1.53675 + 0.798995i) q^{15} +3.75741 q^{16} -3.84562 q^{17} +(0.495472 + 0.347681i) q^{18} +3.81652 q^{19} -1.95929i q^{20} +(2.72834 + 5.24758i) q^{21} +1.11436i q^{22} +0.602484 q^{23} +(-1.22762 + 0.638268i) q^{24} -1.00000 q^{25} -1.08255 q^{26} +(5.15066 + 0.686052i) q^{27} -6.69043 q^{28} +3.16401 q^{29} +(0.161208 + 0.310060i) q^{30} +(-5.42120 - 1.26910i) q^{31} -2.35578i q^{32} +(4.41293 + 8.48763i) q^{33} +0.775903i q^{34} +3.41472i q^{35} +(-3.37628 + 4.81146i) q^{36} +0.170000i q^{37} -0.770033i q^{38} +(-8.24536 + 4.28696i) q^{39} -0.798839 q^{40} -8.16253i q^{41} +(1.05877 - 0.550479i) q^{42} +2.74434i q^{43} -10.8214 q^{44} +(2.45571 + 1.72321i) q^{45} -0.121559i q^{46} -12.0573i q^{47} +(-3.00215 - 5.77420i) q^{48} +4.66030 q^{49} +0.201763i q^{50} +(3.07263 + 5.90976i) q^{51} -10.5125i q^{52} +9.95009 q^{53} +(0.138420 - 1.03921i) q^{54} +5.52310i q^{55} +2.72781i q^{56} +(-3.04938 - 5.86505i) q^{57} -0.638381i q^{58} -3.14445i q^{59} +(-3.01095 + 1.56546i) q^{60} +8.27031i q^{61} +(-0.256058 + 1.09380i) q^{62} +(5.88429 - 8.38557i) q^{63} +7.03950 q^{64} -5.36545 q^{65} +(1.71249 - 0.890365i) q^{66} -9.06536 q^{67} -7.53468 q^{68} +(-0.481382 - 0.925869i) q^{69} +0.688964 q^{70} +13.1481i q^{71} +(1.96172 + 1.37657i) q^{72} +5.65479i q^{73} +0.0342997 q^{74} +(0.798995 + 1.53675i) q^{75} +7.47768 q^{76} +18.8598 q^{77} +(0.864951 + 1.66361i) q^{78} -16.0055i q^{79} -3.75741i q^{80} +(-3.06106 - 8.46345i) q^{81} -1.64690 q^{82} -4.72868 q^{83} +(5.34562 + 10.2815i) q^{84} +3.84562i q^{85} +0.553706 q^{86} +(-2.52803 - 4.86230i) q^{87} +4.41206i q^{88} +14.4724 q^{89} +(0.347681 - 0.495472i) q^{90} +18.3215i q^{91} +1.18044 q^{92} +(2.38121 + 9.34504i) q^{93} -2.43271 q^{94} -3.81652i q^{95} +(-3.62026 + 1.88226i) q^{96} +11.8891 q^{97} -0.940276i q^{98} +(9.51748 - 13.5631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 52 q^{4} + 16 q^{7} + 4 q^{10} + 68 q^{16} - 28 q^{18} - 8 q^{19} - 44 q^{25} - 56 q^{28} - 16 q^{31} + 4 q^{33} + 12 q^{36} - 20 q^{39} - 36 q^{40} - 4 q^{45} + 92 q^{49} + 8 q^{51} - 12 q^{63}+ \cdots + 16 q^{97}+O(q^{100}) \) 44 * q - 52 * q^4 + 16 * q^7 + 4 * q^10 + 68 * q^16 - 28 * q^18 - 8 * q^19 - 44 * q^25 - 56 * q^28 - 16 * q^31 + 4 * q^33 + 12 * q^36 - 20 * q^39 - 36 * q^40 - 4 * q^45 + 92 * q^49 + 8 * q^51 - 12 * q^63 - 52 * q^64 + 40 * q^66 - 32 * q^67 + 12 * q^69 - 24 * q^72 + 48 * q^76 - 88 * q^78 - 4 * q^81 + 36 * q^87 + 16 * q^90 - 20 * q^93 + 32 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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