LMFDB - Embedded newform 153.2.f.b.64.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,2,Mod(55,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.55"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.3
Root			$0.222191i$ of defining polynomial
Character	$\chi$	$=$	153.64
Dual form			153.2.f.b.55.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.222191i q^{2} +1.95063 q^{4} +(0.450006 + 0.450006i) q^{5} +(-1.22219 + 1.22219i) q^{7} +0.877796i q^{8} +(-0.0999875 + 0.0999875i) q^{10} +(3.50062 - 3.50062i) q^{11} -2.50625 q^{13} +(-0.271560 - 0.271560i) q^{14} +3.70622 q^{16} +(-2.17845 + 3.50062i) q^{17} +0.950631i q^{19} +(0.877796 + 0.877796i) q^{20} +(0.777809 + 0.777809i) q^{22} +(-1.50062 + 1.50062i) q^{23} -4.59499i q^{25} -0.556867i q^{26} +(-2.38404 + 2.38404i) q^{28} +(-6.77906 - 6.77906i) q^{29} +(-3.72844 - 3.72844i) q^{31} +2.57908i q^{32} +(-0.777809 - 0.484032i) q^{34} -1.09999 q^{35} +(-6.00125 - 6.00125i) q^{37} -0.211222 q^{38} +(-0.395014 + 0.395014i) q^{40} +(-4.89439 + 4.89439i) q^{41} +7.15061i q^{43} +(6.82843 - 6.82843i) q^{44} +(-0.333426 - 0.333426i) q^{46} +8.10124 q^{47} +4.01250i q^{49} +1.02097 q^{50} -4.88877 q^{52} -6.44438i q^{53} +3.15061 q^{55} +(-1.07283 - 1.07283i) q^{56} +(1.50625 - 1.50625i) q^{58} +10.1125i q^{59} +(2.09999 - 2.09999i) q^{61} +(0.828427 - 0.828427i) q^{62} +6.83940 q^{64} +(-1.12783 - 1.12783i) q^{65} +7.70129 q^{67} +(-4.24934 + 6.82843i) q^{68} -0.244408i q^{70} +(-0.271560 - 0.271560i) q^{71} +(4.60624 + 4.60624i) q^{73} +(1.33343 - 1.33343i) q^{74} +1.85433i q^{76} +8.55687i q^{77} +(1.67782 - 1.67782i) q^{79} +(1.66782 + 1.66782i) q^{80} +(-1.08749 - 1.08749i) q^{82} -13.3581i q^{83} +(-2.55562 + 0.594989i) q^{85} -1.58880 q^{86} +(3.07283 + 3.07283i) q^{88} -1.98875 q^{89} +(3.06311 - 3.06311i) q^{91} +(-2.92717 + 2.92717i) q^{92} +1.80002i q^{94} +(-0.427790 + 0.427790i) q^{95} +(2.15061 + 2.15061i) q^{97} -0.891542 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{13} - 24 q^{14} + 12 q^{16} + 4 q^{17} + 12 q^{20} + 12 q^{22} + 16 q^{23} - 8 q^{28} - 4 q^{29} - 8 q^{31} - 12 q^{34} - 8 q^{35} + 8 q^{37} - 24 q^{38} + 36 q^{40}+ \cdots + 76 q^{98}+O(q^{100}) $ 8 * q - 12 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^13 - 24 * q^14 + 12 * q^16 + 4 * q^17 + 12 * q^20 + 12 * q^22 + 16 * q^23 - 8 * q^28 - 4 * q^29 - 8 * q^31 - 12 * q^34 - 8 * q^35 + 8 * q^37 - 24 * q^38 + 36 * q^40 - 28 * q^41 + 32 * q^44 - 20 * q^46 + 8 * q^47 + 60 * q^50 - 16 * q^52 - 4 * q^55 + 24 * q^56 - 4 * q^58 + 16 * q^61 - 16 * q^62 + 4 * q^64 - 16 * q^65 + 8 * q^67 - 60 * q^68 - 24 * q^71 + 20 * q^73 + 28 * q^74 + 20 * q^79 - 60 * q^80 - 40 * q^82 - 32 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 36 * q^91 - 56 * q^92 - 8 * q^95 - 12 * q^97 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			0.222191i			0.157113i	0.996910	+	0.0785565i	$0.0250311\pi$
$2$			0.222191i			0.157113i	−0.996910	+	0.0785565i	$0.974969\pi$
$3$		0			0
$3$		0			0
$4$	1.95063			0.975315
$5$	0.450006	+	0.450006i	0.201249	+	0.201249i	0.800535	−	0.599286i	$-0.204549\pi$
$5$	0.450006	+	0.450006i	0.201249	+	0.201249i	−0.599286	+	0.800535i	$0.704549\pi$
$6$		0			0
$7$	−1.22219	+	1.22219i	−0.461945	+	0.461945i	−0.899293	−	0.437348i	$-0.855918\pi$
$7$	−1.22219	+	1.22219i	−0.461945	+	0.461945i	0.437348	+	0.899293i	$0.355918\pi$
$8$			0.877796i			0.310348i
$9$		0			0
$10$	−0.0999875	+	0.0999875i	−0.0316188	+	0.0316188i
$11$	3.50062	−	3.50062i	1.05548	−	1.05548i	0.0571102	−	0.998368i	$-0.481811\pi$
$11$	3.50062	−	3.50062i	1.05548	−	1.05548i	0.998368	−	0.0571102i	$-0.0181886\pi$
$12$		0			0
$13$	−2.50625			−0.695108			−0.347554	−	0.937660i	$-0.612988\pi$
$13$	−2.50625			−0.695108			−0.347554	+	0.937660i	$0.612988\pi$
$14$	−0.271560	−	0.271560i	−0.0725776	−	0.0725776i
$15$		0			0
$16$	3.70622			0.926556
$17$	−2.17845	+	3.50062i	−0.528351	+	0.849026i
$17$	−2.17845	+	3.50062i	−0.528351	+	0.849026i
$18$		0			0
$19$			0.950631i			0.218090i	0.994037	+	0.109045i	$0.0347792\pi$
$19$			0.950631i			0.218090i	−0.994037	+	0.109045i	$0.965221\pi$
$20$	0.877796	+	0.877796i	0.196281	+	0.196281i
$21$		0			0
$22$	0.777809	+	0.777809i	0.165829	+	0.165829i
$23$	−1.50062	+	1.50062i	−0.312902	+	0.312902i	−0.846033	−	0.533131i	$-0.821015\pi$
$23$	−1.50062	+	1.50062i	−0.312902	+	0.312902i	0.533131	+	0.846033i	$0.321015\pi$
$24$		0			0
$25$		−	4.59499i		−	0.918998i
$26$		−	0.556867i		−	0.109211i
$27$		0			0
$28$	−2.38404	+	2.38404i	−0.450542	+	0.450542i
$29$	−6.77906	−	6.77906i	−1.25884	−	1.25884i	−0.951648	−	0.307192i	$-0.900611\pi$
$29$	−6.77906	−	6.77906i	−1.25884	−	1.25884i	−0.307192	−	0.951648i	$-0.599389\pi$
$30$		0			0
$31$	−3.72844	−	3.72844i	−0.669648	−	0.669648i	0.287987	−	0.957634i	$-0.407014\pi$
$31$	−3.72844	−	3.72844i	−0.669648	−	0.669648i	−0.957634	+	0.287987i	$0.907014\pi$
$32$			2.57908i			0.455922i
$33$		0			0
$34$	−0.777809	−	0.484032i	−0.133393	−	0.0830108i
$35$	−1.09999			−0.185932
$36$		0			0
$37$	−6.00125	−	6.00125i	−0.986599	−	0.986599i	0.0133121	−	0.999911i	$-0.495763\pi$
$37$	−6.00125	−	6.00125i	−0.986599	−	0.986599i	−0.999911	+	0.0133121i	$0.995763\pi$
$38$	−0.211222			−0.0342647
$39$		0			0
$40$	−0.395014	+	0.395014i	−0.0624572	+	0.0624572i
$41$	−4.89439	+	4.89439i	−0.764375	+	0.764375i	−0.977110	−	0.212735i	$-0.931763\pi$
$41$	−4.89439	+	4.89439i	−0.764375	+	0.764375i	0.212735	+	0.977110i	$0.431763\pi$
$42$		0			0
$43$			7.15061i			1.09046i	0.838287	+	0.545229i	$0.183557\pi$
$43$			7.15061i			1.09046i	−0.838287	+	0.545229i	$0.816443\pi$
$44$	6.82843	−	6.82843i	1.02942	−	1.02942i
$45$		0			0
$46$	−0.333426	−	0.333426i	−0.0491610	−	0.0491610i
$47$	8.10124			1.18169			0.590843	−	0.806786i	$-0.298795\pi$
$47$	8.10124			1.18169			0.590843	+	0.806786i	$0.298795\pi$
$48$		0			0
$49$			4.01250i			0.573214i
$50$	1.02097			0.144387
$51$		0			0
$52$	−4.88877			−0.677950
$53$		−	6.44438i		−	0.885204i	−0.896718	−	0.442602i	$-0.854055\pi$
$53$		−	6.44438i		−	0.885204i	0.896718	−	0.442602i	$-0.145945\pi$
$54$		0			0
$55$	3.15061			0.424828
$56$	−1.07283	−	1.07283i	−0.143364	−	0.143364i
$57$		0			0
$58$	1.50625	−	1.50625i	0.197780	−	0.197780i
$59$			10.1125i			1.31653i	0.752785	+	0.658267i	$0.228710\pi$
$59$			10.1125i			1.31653i	−0.752785	+	0.658267i	$0.771290\pi$
$60$		0			0
$61$	2.09999	−	2.09999i	0.268876	−	0.268876i	−0.559771	−	0.828647i	$-0.689111\pi$
$61$	2.09999	−	2.09999i	0.268876	−	0.268876i	0.828647	+	0.559771i	$0.189111\pi$
$62$	0.828427	−	0.828427i	0.105210	−	0.105210i
$63$		0			0
$64$	6.83940			0.854925
$65$	−1.12783	−	1.12783i	−0.139890	−	0.139890i
$66$		0			0
$67$	7.70129			0.940862			0.470431	−	0.882437i	$-0.344098\pi$
$67$	7.70129			0.940862			0.470431	+	0.882437i	$0.344098\pi$
$68$	−4.24934	+	6.82843i	−0.515309	+	0.828068i
$69$		0			0
$70$		−	0.244408i		−	0.0292123i
$71$	−0.271560	−	0.271560i	−0.0322283	−	0.0322283i	0.690809	−	0.723037i	$-0.257255\pi$
$71$	−0.271560	−	0.271560i	−0.0322283	−	0.0322283i	−0.723037	+	0.690809i	$0.757255\pi$
$72$		0			0
$73$	4.60624	+	4.60624i	0.539119	+	0.539119i	0.923270	−	0.384151i	$-0.125506\pi$
$73$	4.60624	+	4.60624i	0.539119	+	0.539119i	−0.384151	+	0.923270i	$0.625506\pi$
$74$	1.33343	−	1.33343i	0.155008	−	0.155008i
$75$		0			0
$76$			1.85433i			0.212706i
$77$			8.55687i			0.975145i
$78$		0			0
$79$	1.67782	−	1.67782i	0.188770	−	0.188770i	−0.606394	−	0.795164i	$-0.707385\pi$
$79$	1.67782	−	1.67782i	0.188770	−	0.188770i	0.795164	+	0.606394i	$0.207385\pi$
$80$	1.66782	+	1.66782i	0.186468	+	0.186468i
$81$		0			0
$82$	−1.08749	−	1.08749i	−0.120093	−	0.120093i
$83$		−	13.3581i		−	1.46625i	−0.680096	−	0.733123i	$-0.738062\pi$
$83$		−	13.3581i		−	1.46625i	0.680096	−	0.733123i	$-0.261938\pi$
$84$		0			0
$85$	−2.55562	+	0.594989i	−0.277196	+	0.0645356i
$86$	−1.58880			−0.171325
$87$		0			0
$88$	3.07283	+	3.07283i	0.327565	+	0.327565i
$89$	−1.98875			−0.210807			−0.105404	−	0.994430i	$-0.533613\pi$
$89$	−1.98875			−0.210807			−0.105404	+	0.994430i	$0.533613\pi$
$90$		0			0
$91$	3.06311	−	3.06311i	0.321102	−	0.321102i
$92$	−2.92717	+	2.92717i	−0.305178	+	0.305178i
$93$		0			0
$94$			1.80002i			0.185658i
$95$	−0.427790	+	0.427790i	−0.0438903	+	0.0438903i
$96$		0			0
$97$	2.15061	+	2.15061i	0.218361	+	0.218361i	0.807807	−	0.589446i	$-0.200654\pi$
$97$	2.15061	+	2.15061i	0.218361	+	0.218361i	−0.589446	+	0.807807i	$0.700654\pi$
$98$	−0.891542			−0.0900594
$99$		0			0
$100$		−	8.96313i		−	0.896313i
$101$	18.5456			1.84536			0.922679	−	0.385569i	$-0.125995\pi$
$101$	18.5456			1.84536			0.922679	+	0.385569i	$0.125995\pi$
$102$		0			0
$103$	3.39501			0.334521			0.167260	−	0.985913i	$-0.446508\pi$
$103$	3.39501			0.334521			0.167260	+	0.985913i	$0.446508\pi$
$104$		−	2.19998i		−	0.215725i
$105$		0			0
$106$	1.43189			0.139077
$107$	9.30065	+	9.30065i	0.899128	+	0.899128i	0.995359	−	0.0962313i	$-0.0306788\pi$
$107$	9.30065	+	9.30065i	0.899128	+	0.899128i	−0.0962313	+	0.995359i	$0.530679\pi$
$108$		0			0
$109$	−12.2963	+	12.2963i	−1.17777	+	1.17777i	−0.197458	+	0.980311i	$0.563269\pi$
$109$	−12.2963	+	12.2963i	−1.17777	+	1.17777i	−0.980311	+	0.197458i	$0.936731\pi$
$110$			0.700037i			0.0667460i
$111$		0			0
$112$	−4.52971	+	4.52971i	−0.428018	+	0.428018i
$113$	0.548744	−	0.548744i	0.0516215	−	0.0516215i	−0.680825	−	0.732446i	$-0.738378\pi$
$113$	0.548744	−	0.548744i	0.0516215	−	0.0516215i	0.732446	+	0.680825i	$0.238378\pi$
$114$		0			0
$115$	−1.35058			−0.125942
$116$	−13.2234	−	13.2234i	−1.22777	−	1.22777i
$117$		0			0
$118$	−2.24691			−0.206845
$119$	−1.61596	−	6.94091i	−0.148134	−	0.636272i
$120$		0			0
$121$		−	13.5087i		−	1.22807i
$122$	0.466599	+	0.466599i	0.0422439	+	0.0422439i
$123$		0			0
$124$	−7.27281	−	7.27281i	−0.653118	−	0.653118i
$125$	4.31780	−	4.31780i	0.386196	−	0.386196i
$126$		0			0
$127$			10.8519i			0.962950i	0.876460	+	0.481475i	$0.159899\pi$
$127$			10.8519i			0.962950i	−0.876460	+	0.481475i	$0.840101\pi$
$128$			6.67782i			0.590242i
$129$		0			0
$130$	0.250594	−	0.250594i	0.0219785	−	0.0219785i
$131$	−0.499375	−	0.499375i	−0.0436306	−	0.0436306i	0.684955	−	0.728585i	$-0.259822\pi$
$131$	−0.499375	−	0.499375i	−0.0436306	−	0.0436306i	−0.728585	+	0.684955i	$0.759822\pi$
$132$		0			0
$133$	−1.16185	−	1.16185i	−0.100745	−	0.100745i
$134$			1.71116i			0.147822i
$135$		0			0
$136$	−3.07283	−	1.91223i	−0.263493	−	0.163972i
$137$	−12.3125			−1.05192			−0.525962	−	0.850508i	$-0.676295\pi$
$137$	−12.3125			−1.05192			−0.525962	+	0.850508i	$0.676295\pi$
$138$		0			0
$139$	9.43591	+	9.43591i	0.800344	+	0.800344i	0.983149	−	0.182805i	$-0.0585178\pi$
$139$	9.43591	+	9.43591i	0.800344	+	0.800344i	−0.182805	+	0.983149i	$0.558518\pi$
$140$	−2.14567			−0.181342
$141$		0			0
$142$	0.0603384	−	0.0603384i	0.00506348	−	0.00506348i
$143$	−8.77343	+	8.77343i	−0.733671	+	0.733671i
$144$		0			0
$145$		−	6.10124i		−	0.506680i
$146$	−1.02347	+	1.02347i	−0.0847026	+	0.0847026i
$147$		0			0
$148$	−11.7062	−	11.7062i	−0.962246	−	0.962246i
$149$	0.356892			0.0292377			0.0146189	−	0.999893i	$-0.495347\pi$
$149$	0.356892			0.0292377			0.0146189	+	0.999893i	$0.495347\pi$
$150$		0			0
$151$		−	9.13317i		−	0.743247i	−0.928384	−	0.371624i	$-0.878801\pi$
$151$		−	9.13317i		−	0.743247i	0.928384	−	0.371624i	$-0.121199\pi$
$152$	−0.834460			−0.0676837
$153$		0			0
$154$	−1.90126			−0.153208
$155$		−	3.35564i		−	0.269532i
$156$		0			0
$157$	−17.5975			−1.40443			−0.702216	−	0.711964i	$-0.747806\pi$
$157$	−17.5975			−1.40443			−0.702216	+	0.711964i	$0.747806\pi$
$158$	0.372797	+	0.372797i	0.0296582	+	0.0296582i
$159$		0			0
$160$	−1.16060	+	1.16060i	−0.0917538	+	0.0917538i
$161$		−	3.66810i		−	0.289087i
$162$		0			0
$163$	11.7309	−	11.7309i	0.918838	−	0.918838i	−0.0781070	−	0.996945i	$-0.524888\pi$
$163$	11.7309	−	11.7309i	0.918838	−	0.918838i	0.996945	+	0.0781070i	$0.0248876\pi$
$164$	−9.54715	+	9.54715i	−0.745507	+	0.745507i
$165$		0			0
$166$	2.96806			0.230366
$167$	−10.0575	−	10.0575i	−0.778272	−	0.778272i	0.201265	−	0.979537i	$-0.435495\pi$
$167$	−10.0575	−	10.0575i	−0.778272	−	0.778272i	−0.979537	+	0.201265i	$0.935495\pi$
$168$		0			0
$169$	−6.71872			−0.516825
$170$	−0.132201	−	0.567836i	−0.0101394	−	0.0435510i
$171$		0			0
$172$			13.9482i			1.06354i
$173$	−1.33877	−	1.33877i	−0.101785	−	0.101785i	0.654381	−	0.756165i	$-0.272929\pi$
$173$	−1.33877	−	1.33877i	−0.101785	−	0.101785i	−0.756165	+	0.654381i	$0.772929\pi$
$174$		0			0
$175$	5.61596	+	5.61596i	0.424526	+	0.424526i
$176$	12.9741	−	12.9741i	0.977959	−	0.977959i
$177$		0			0
$178$		−	0.441884i		−	0.0331206i
$179$			22.2469i			1.66281i	0.555666	+	0.831406i	$0.312464\pi$
$179$			22.2469i			1.66281i	−0.555666	+	0.831406i	$0.687536\pi$
$180$		0			0
$181$	8.21247	−	8.21247i	0.610428	−	0.610428i	−0.332629	−	0.943058i	$-0.607936\pi$
$181$	8.21247	−	8.21247i	0.610428	−	0.610428i	0.943058	+	0.332629i	$0.107936\pi$
$182$	0.680598	+	0.680598i	0.0504493	+	0.0504493i
$183$		0			0
$184$	−1.31724	−	1.31724i	−0.0971084	−	0.0971084i
$185$		−	5.40120i		−	0.397104i
$186$		0			0
$187$	4.62845	+	19.8803i	0.338466	+	1.45379i
$188$	15.8025			1.15252
$189$		0			0
$190$	−0.0950512	−	0.0950512i	−0.00689574	−	0.00689574i
$191$	6.63311			0.479955			0.239978	−	0.970778i	$-0.422860\pi$
$191$	6.63311			0.479955			0.239978	+	0.970778i	$0.422860\pi$
$192$		0			0
$193$	−2.06311	+	2.06311i	−0.148506	+	0.148506i	−0.777450	−	0.628944i	$-0.783487\pi$
$193$	−2.06311	+	2.06311i	−0.148506	+	0.148506i	0.628944	+	0.777450i	$0.283487\pi$
$194$	−0.477846	+	0.477846i	−0.0343074	+	0.0343074i
$195$		0			0
$196$			7.82690i			0.559064i
$197$	−3.20685	+	3.20685i	−0.228478	+	0.228478i	−0.812057	−	0.583578i	$-0.801652\pi$
$197$	−3.20685	+	3.20685i	−0.228478	+	0.228478i	0.583578	+	0.812057i	$0.301652\pi$
$198$		0			0
$199$	1.73969	+	1.73969i	0.123323	+	0.123323i	0.766075	−	0.642752i	$-0.222207\pi$
$199$	1.73969	+	1.73969i	0.123323	+	0.123323i	−0.642752	+	0.766075i	$0.722207\pi$
$200$	4.03346			0.285209
$201$		0			0
$202$			4.12068i			0.289930i
$203$	16.5706			1.16303
$204$		0			0
$205$	−4.40501			−0.307659
$206$			0.754343i			0.0525576i
$207$		0			0
$208$	−9.28872			−0.644057
$209$	3.32780	+	3.32780i	0.230189	+	0.230189i
$210$		0			0
$211$	14.0741	−	14.0741i	0.968900	−	0.968900i	−0.0306308	−	0.999531i	$-0.509752\pi$
$211$	14.0741	−	14.0741i	0.968900	−	0.968900i	0.999531	+	0.0306308i	$0.00975162\pi$
$212$		−	12.5706i		−	0.863353i
$213$		0			0
$214$	−2.06652	+	2.06652i	−0.141265	+	0.141265i
$215$	−3.21782	+	3.21782i	−0.219453	+	0.219453i
$216$		0			0
$217$	9.11373			0.618681
$218$	−2.73213	−	2.73213i	−0.185043	−	0.185043i
$219$		0			0
$220$	6.14567			0.414341
$221$	5.45973	−	8.77343i	0.367261	−	0.590165i
$222$		0			0
$223$		−	14.3631i		−	0.961823i	−0.876769	−	0.480911i	$-0.840306\pi$
$223$		−	14.3631i		−	0.961823i	0.876769	−	0.480911i	$-0.159694\pi$
$224$	−3.15213	−	3.15213i	−0.210611	−	0.210611i
$225$		0			0
$226$	0.121926	+	0.121926i	0.00811041	+	0.00811041i
$227$	−7.68935	+	7.68935i	−0.510360	+	0.510360i	−0.914637	−	0.404277i	$-0.867523\pi$
$227$	−7.68935	+	7.68935i	−0.510360	+	0.510360i	0.404277	+	0.914637i	$0.367523\pi$
$228$		0			0
$229$			18.9900i			1.25489i	0.778659	+	0.627447i	$0.215900\pi$
$229$			18.9900i			1.25489i	−0.778659	+	0.627447i	$0.784100\pi$
$230$		−	0.300087i		−	0.0197872i
$231$		0			0
$232$	5.95063	−	5.95063i	0.390678	−	0.390678i
$233$	−5.00687	−	5.00687i	−0.328011	−	0.328011i	0.523819	−	0.851830i	$-0.324507\pi$
$233$	−5.00687	−	5.00687i	−0.328011	−	0.328011i	−0.851830	+	0.523819i	$0.824507\pi$
$234$		0			0
$235$	3.64561	+	3.64561i	0.237813	+	0.237813i
$236$			19.7257i			1.28404i
$237$		0			0
$238$	1.54221	−	0.359051i	0.0999667	−	0.0232738i
$239$	5.28872			0.342099			0.171049	−	0.985262i	$-0.445284\pi$
$239$	5.28872			0.342099			0.171049	+	0.985262i	$0.445284\pi$
$240$		0			0
$241$	−4.09999	−	4.09999i	−0.264103	−	0.264103i	0.562615	−	0.826719i	$-0.309795\pi$
$241$	−4.09999	−	4.09999i	−0.264103	−	0.264103i	−0.826719	+	0.562615i	$0.809795\pi$
$242$	3.00153			0.192945
$243$		0			0
$244$	4.09630	−	4.09630i	0.262239	−	0.262239i
$245$	−1.80565	+	1.80565i	−0.115359	+	0.115359i
$246$		0			0
$247$		−	2.38252i		−	0.151596i
$248$	3.27281	−	3.27281i	0.207824	−	0.207824i
$249$		0			0
$250$	0.959379	+	0.959379i	0.0606765	+	0.0606765i
$251$	−8.33190			−0.525905			−0.262952	−	0.964809i	$-0.584696\pi$
$251$	−8.33190			−0.525905			−0.262952	+	0.964809i	$0.584696\pi$
$252$		0			0
$253$			10.5062i			0.660522i
$254$	−2.41120			−0.151292
$255$		0			0
$256$	12.1950			0.762190
$257$		−	4.25565i		−	0.265460i	−0.991152	−	0.132730i	$-0.957626\pi$
$257$		−	4.25565i		−	0.265460i	0.991152	−	0.132730i	$-0.0423744\pi$
$258$		0			0
$259$	14.6694			0.911509
$260$	−2.19998	−	2.19998i	−0.136437	−	0.136437i
$261$		0			0
$262$	0.110957	−	0.110957i	0.00685494	−	0.00685494i
$263$			9.09999i			0.561129i	0.959835	+	0.280565i	$0.0905217\pi$
$263$			9.09999i			0.561129i	−0.959835	+	0.280565i	$0.909478\pi$
$264$		0			0
$265$	2.90001	−	2.90001i	0.178146	−	0.178146i
$266$	0.258154	−	0.258154i	0.0158284	−	0.0158284i
$267$		0			0
$268$	15.0224			0.917637
$269$	15.1194	+	15.1194i	0.921843	+	0.921843i	0.997160	−	0.0753162i	$-0.0239966\pi$
$269$	15.1194	+	15.1194i	0.921843	+	0.921843i	−0.0753162	+	0.997160i	$0.523997\pi$
$270$		0			0
$271$	−19.3213			−1.17368			−0.586842	−	0.809702i	$-0.699629\pi$
$271$	−19.3213			−1.17368			−0.586842	+	0.809702i	$0.699629\pi$
$272$	−8.07381	+	12.9741i	−0.489546	+	0.786670i
$273$		0			0
$274$		−	2.73572i		−	0.165271i
$275$	−16.0853	−	16.0853i	−0.969982	−	0.969982i
$276$		0			0
$277$	2.36183	+	2.36183i	0.141908	+	0.141908i	0.774492	−	0.632584i	$-0.218006\pi$
$277$	2.36183	+	2.36183i	0.141908	+	0.141908i	−0.632584	+	0.774492i	$0.718006\pi$
$278$	−2.09658	+	2.09658i	−0.125744	+	0.125744i
$279$		0			0
$280$		−	0.965565i		−	0.0577035i
$281$		−	4.67754i		−	0.279039i	−0.990219	−	0.139519i	$-0.955444\pi$
$281$		−	4.67754i		−	0.279039i	0.990219	−	0.139519i	$-0.0445558\pi$
$282$		0			0
$283$	−7.11221	+	7.11221i	−0.422777	+	0.422777i	−0.886159	−	0.463382i	$-0.846636\pi$
$283$	−7.11221	+	7.11221i	−0.422777	+	0.422777i	0.463382	+	0.886159i	$0.346636\pi$
$284$	−0.529714	−	0.529714i	−0.0314327	−	0.0314327i
$285$		0			0
$286$	−1.94938	−	1.94938i	−0.115269	−	0.115269i
$287$		−	11.9638i		−	0.706198i
$288$		0			0
$289$	−7.50875	−	15.2518i	−0.441691	−	0.897167i
$290$	1.35564			0.0796061
$291$		0			0
$292$	8.98507	+	8.98507i	0.525811	+	0.525811i
$293$	5.76934			0.337048			0.168524	−	0.985698i	$-0.446100\pi$
$293$	5.76934			0.337048			0.168524	+	0.985698i	$0.446100\pi$
$294$		0			0
$295$	−4.55068	+	4.55068i	−0.264951	+	0.264951i
$296$	5.26787	−	5.26787i	0.306189	−	0.306189i
$297$		0			0
$298$			0.0792983i			0.00459363i
$299$	3.76094	−	3.76094i	0.217501	−	0.217501i
$300$		0			0
$301$	−8.73941	−	8.73941i	−0.503731	−	0.503731i
$302$	2.02931			0.116774
$303$		0			0
$304$			3.52325i			0.202072i
$305$	1.89001			0.108222
$306$		0			0
$307$	−13.2375			−0.755502			−0.377751	−	0.925907i	$-0.623302\pi$
$307$	−13.2375			−0.755502			−0.377751	+	0.925907i	$0.623302\pi$
$308$			16.6913i			0.951074i
$309$		0			0
$310$	0.745595			0.0423469
$311$	0.915918	+	0.915918i	0.0519370	+	0.0519370i	0.732598	−	0.680661i	$-0.238307\pi$
$311$	0.915918	+	0.915918i	0.0519370	+	0.0519370i	−0.680661	+	0.732598i	$0.738307\pi$
$312$		0			0
$313$	−13.5062	+	13.5062i	−0.763418	+	0.763418i	−0.976939	−	0.213520i	$-0.931507\pi$
$313$	−13.5062	+	13.5062i	−0.763418	+	0.763418i	0.213520	+	0.976939i	$0.431507\pi$
$314$		−	3.91001i		−	0.220655i
$315$		0			0
$316$	3.27281	−	3.27281i	0.184110	−	0.184110i
$317$	10.6803	−	10.6803i	0.599867	−	0.599867i	−0.340410	−	0.940277i	$-0.610566\pi$
$317$	10.6803	−	10.6803i	0.599867	−	0.599867i	0.940277	+	0.340410i	$0.110566\pi$
$318$		0			0
$319$	−47.4619			−2.65735
$320$	3.07777	+	3.07777i	0.172053	+	0.172053i
$321$		0			0
$322$	0.815020			0.0454193
$323$	−3.32780	−	2.07090i	−0.185164	−	0.115228i
$324$		0			0
$325$			11.5162i			0.638803i
$326$	2.60651	+	2.60651i	0.144361	+	0.144361i
$327$		0			0
$328$	−4.29628	−	4.29628i	−0.237222	−	0.237222i
$329$	−9.90126	+	9.90126i	−0.545874	+	0.545874i
$330$		0			0
$331$		−	22.6769i		−	1.24644i	−0.782048	−	0.623218i	$-0.785825\pi$
$331$		−	22.6769i		−	1.24644i	0.782048	−	0.623218i	$-0.214175\pi$
$332$		−	26.0568i		−	1.43005i
$333$		0			0
$334$	2.23469	−	2.23469i	0.122277	−	0.122277i
$335$	3.46563	+	3.46563i	0.189347	+	0.189347i
$336$		0			0
$337$	1.14317	+	1.14317i	0.0622725	+	0.0622725i	0.737557	−	0.675285i	$-0.235979\pi$
$337$	1.14317	+	1.14317i	0.0622725	+	0.0622725i	−0.675285	+	0.737557i	$0.735979\pi$
$338$		−	1.49284i		−	0.0811999i
$339$		0			0
$340$	−4.98507	+	1.16060i	−0.270353	+	0.0629426i
$341$	−26.1037			−1.41360
$342$		0			0
$343$	−13.4594	−	13.4594i	−0.726738	−	0.726738i
$344$	−6.27677			−0.338421
$345$		0			0
$346$	0.297464	−	0.297464i	0.0159917	−	0.0159917i
$347$	10.8616	−	10.8616i	0.583082	−	0.583082i	−0.352667	−	0.935749i	$-0.614725\pi$
$347$	10.8616	−	10.8616i	0.583082	−	0.583082i	0.935749	+	0.352667i	$0.114725\pi$
$348$		0			0
$349$		−	15.1087i		−	0.808749i	−0.914594	−	0.404374i	$-0.867489\pi$
$349$		−	15.1087i		−	0.808749i	0.914594	−	0.404374i	$-0.132511\pi$
$350$	−1.24782	+	1.24782i	−0.0666986	+	0.0666986i
$351$		0			0
$352$	9.02840	+	9.02840i	0.481215	+	0.481215i
$353$	−31.2482			−1.66317			−0.831586	−	0.555396i	$-0.812567\pi$
$353$	−31.2482			−1.66317			−0.831586	+	0.555396i	$0.812567\pi$
$354$		0			0
$355$		−	0.244408i		−	0.0129718i
$356$	−3.87932			−0.205604
$357$		0			0
$358$	−4.94307			−0.261249
$359$			2.72503i			0.143822i	0.997411	+	0.0719108i	$0.0229097\pi$
$359$			2.72503i			0.143822i	−0.997411	+	0.0719108i	$0.977090\pi$
$360$		0			0
$361$	18.0963			0.952437
$362$	1.82474	+	1.82474i	0.0959062	+	0.0959062i
$363$		0			0
$364$	5.97501	−	5.97501i	0.313175	−	0.313175i
$365$			4.14567i			0.216994i
$366$		0			0
$367$	−13.0472	+	13.0472i	−0.681059	+	0.681059i	−0.960239	−	0.279180i	$-0.909937\pi$
$367$	−13.0472	+	13.0472i	−0.681059	+	0.681059i	0.279180	+	0.960239i	$0.409937\pi$
$368$	−5.56165	+	5.56165i	−0.289921	+	0.289921i
$369$		0			0
$370$	1.20010			0.0623902
$371$	7.87627	+	7.87627i	0.408916	+	0.408916i
$372$		0			0
$373$	24.4049			1.26364			0.631820	−	0.775115i	$-0.282308\pi$
$373$	24.4049			1.26364			0.631820	+	0.775115i	$0.282308\pi$
$374$	−4.41723	+	1.02840i	−0.228410	+	0.0531774i
$375$		0			0
$376$			7.11123i			0.366734i
$377$	16.9900	+	16.9900i	0.875030	+	0.875030i
$378$		0			0
$379$	−4.16526	−	4.16526i	−0.213955	−	0.213955i	0.591990	−	0.805945i	$-0.298342\pi$
$379$	−4.16526	−	4.16526i	−0.213955	−	0.213955i	−0.805945	+	0.591990i	$0.798342\pi$
$380$	−0.834460	+	0.834460i	−0.0428069	+	0.0428069i
$381$		0			0
$382$			1.47382i			0.0754072i
$383$		−	30.7756i		−	1.57256i	−0.617871	−	0.786279i	$-0.712005\pi$
$383$		−	30.7756i		−	1.57256i	0.617871	−	0.786279i	$-0.287995\pi$
$384$		0			0
$385$	−3.85064	+	3.85064i	−0.196247	+	0.196247i
$386$	−0.458406	−	0.458406i	−0.0233323	−	0.0233323i
$387$		0			0
$388$	4.19504	+	4.19504i	0.212971	+	0.212971i
$389$			19.5244i			0.989925i	0.868914	+	0.494963i	$0.164818\pi$
$389$			19.5244i			0.989925i	−0.868914	+	0.494963i	$0.835182\pi$
$390$		0			0
$391$	−1.98409	−	8.52215i	−0.100340	−	0.430984i
$392$	−3.52215			−0.177896
$393$		0			0
$394$	−0.712534	−	0.712534i	−0.0358969	−	0.0358969i
$395$	1.51006			0.0759794
$396$		0			0
$397$	0.639421	−	0.639421i	0.0320916	−	0.0320916i	−0.690879	−	0.722971i	$-0.742776\pi$
$397$	0.639421	−	0.639421i	0.0320916	−	0.0320916i	0.722971	+	0.690879i	$0.242776\pi$
$398$	−0.386543	+	0.386543i	−0.0193757	+	0.0193757i
$399$		0			0
$400$		−	17.0301i		−	0.851503i
$401$	−0.894389	+	0.894389i	−0.0446637	+	0.0446637i	−0.729086	−	0.684422i	$-0.760055\pi$
$401$	−0.894389	+	0.894389i	−0.0446637	+	0.0446637i	0.684422	+	0.729086i	$0.260055\pi$
$402$		0			0
$403$	9.34440	+	9.34440i	0.465477	+	0.465477i
$404$	36.1757			1.79981
$405$		0			0
$406$			3.68185i			0.182727i
$407$	−42.0162			−2.08267
$408$		0			0
$409$	28.6350			1.41591			0.707954	−	0.706258i	$-0.249618\pi$
$409$	28.6350			1.41591			0.707954	+	0.706258i	$0.249618\pi$
$410$		−	0.978756i		−	0.0483373i
$411$		0			0
$412$	6.62242			0.326263
$413$	−12.3594	−	12.3594i	−0.608166	−	0.608166i
$414$		0			0
$415$	6.01125	−	6.01125i	0.295081	−	0.295081i
$416$		−	6.46382i		−	0.316915i
$417$		0			0
$418$	−0.739409	+	0.739409i	−0.0361657	+	0.0361657i
$419$	16.9409	−	16.9409i	0.827618	−	0.827618i	−0.159569	−	0.987187i	$-0.551010\pi$
$419$	16.9409	−	16.9409i	0.827618	−	0.827618i	0.987187	+	0.159569i	$0.0510105\pi$
$420$		0			0
$421$	12.5312			0.610735			0.305368	−	0.952235i	$-0.401221\pi$
$421$	12.5312			0.610735			0.305368	+	0.952235i	$0.401221\pi$
$422$	3.12714	+	3.12714i	0.152227	+	0.152227i
$423$		0			0
$424$	5.65685			0.274721
$425$	16.0853	+	10.0099i	0.780253	+	0.485553i
$426$		0			0
$427$			5.13317i			0.248412i
$428$	18.1421	+	18.1421i	0.876933	+	0.876933i
$429$		0			0
$430$	−0.714971	−	0.714971i	−0.0344790	−	0.0344790i
$431$	−12.4965	+	12.4965i	−0.601937	+	0.601937i	−0.940826	−	0.338890i	$-0.889949\pi$
$431$	−12.4965	+	12.4965i	−0.601937	+	0.601937i	0.338890	+	0.940826i	$0.389949\pi$
$432$		0			0
$433$		−	14.0076i		−	0.673160i	−0.941655	−	0.336580i	$-0.890730\pi$
$433$		−	14.0076i		−	0.673160i	0.941655	−	0.336580i	$-0.109270\pi$
$434$			2.02499i			0.0972028i
$435$		0			0
$436$	−23.9855	+	23.9855i	−1.14870	+	1.14870i
$437$	−1.42654	−	1.42654i	−0.0682407	−	0.0682407i
$438$		0			0
$439$	8.18407	+	8.18407i	0.390604	+	0.390604i	0.874903	−	0.484299i	$-0.160925\pi$
$439$	8.18407	+	8.18407i	0.390604	+	0.390604i	−0.484299	+	0.874903i	$0.660925\pi$
$440$			2.76559i			0.131844i
$441$		0			0
$442$	1.94938	+	1.21310i	0.0927226	+	0.0577015i
$443$	35.6174			1.69223			0.846117	−	0.532997i	$-0.178934\pi$
$443$	35.6174			1.69223			0.846117	+	0.532997i	$0.178934\pi$
$444$		0			0
$445$	−0.894951	−	0.894951i	−0.0424248	−	0.0424248i
$446$	3.19135			0.151115
$447$		0			0
$448$	−8.35905	+	8.35905i	−0.394928	+	0.394928i
$449$	15.6596	−	15.6596i	0.739024	−	0.739024i	−0.233365	−	0.972389i	$-0.574974\pi$
$449$	15.6596	−	15.6596i	0.739024	−	0.739024i	0.972389	+	0.233365i	$0.0749738\pi$
$450$		0			0
$451$			34.2668i			1.61356i
$452$	1.07040	−	1.07040i	0.0503473	−	0.0503473i
$453$		0			0
$454$	−1.70851	−	1.70851i	−0.0801842	−	0.0801842i
$455$	2.75684			0.129243
$456$		0			0
$457$		−	9.90632i		−	0.463398i	−0.972787	−	0.231699i	$-0.925572\pi$
$457$		−	9.90632i		−	0.463398i	0.972787	−	0.231699i	$-0.0744285\pi$
$458$	−4.21941			−0.197160
$459$		0			0
$460$	−2.63449			−0.122834
$461$		−	9.62367i		−	0.448219i	−0.974564	−	0.224109i	$-0.928053\pi$
$461$		−	9.62367i		−	0.448219i	0.974564	−	0.224109i	$-0.0719473\pi$
$462$		0			0
$463$	−15.3013			−0.711113			−0.355557	−	0.934655i	$-0.615709\pi$
$463$	−15.3013			−0.711113			−0.355557	+	0.934655i	$0.615709\pi$
$464$	−25.1247	−	25.1247i	−1.16639	−	1.16639i
$465$		0			0
$466$	1.11248	−	1.11248i	0.0515348	−	0.0515348i
$467$			22.3150i			1.03261i	0.856404	+	0.516307i	$0.172693\pi$
$467$			22.3150i			1.03261i	−0.856404	+	0.516307i	$0.827307\pi$
$468$		0			0
$469$	−9.41245	+	9.41245i	−0.434626	+	0.434626i
$470$	−0.810022	+	0.810022i	−0.0373636	+	0.0373636i
$471$		0			0
$472$	−8.87670			−0.408583
$473$	25.0316	+	25.0316i	1.15095	+	1.15095i
$474$		0			0
$475$	4.36814			0.200424
$476$	−3.15213	−	13.5392i	−0.144478	−	0.620566i
$477$		0			0
$478$			1.17511i			0.0537481i
$479$	−11.0006	−	11.0006i	−0.502629	−	0.502629i	0.409625	−	0.912254i	$-0.365659\pi$
$479$	−11.0006	−	11.0006i	−0.502629	−	0.502629i	−0.912254	+	0.409625i	$0.865659\pi$
$480$		0			0
$481$	15.0406	+	15.0406i	0.685793	+	0.685793i
$482$	0.910982	−	0.910982i	0.0414941	−	0.0414941i
$483$		0			0
$484$		−	26.3506i		−	1.19775i
$485$			1.93557i			0.0878898i
$486$		0			0
$487$	0.0209669	−	0.0209669i	0.000950100	−	0.000950100i	−0.706632	−	0.707582i	$-0.749786\pi$
$487$	0.0209669	−	0.0209669i	0.000950100	−	0.000950100i	0.707582	+	0.706632i	$0.249786\pi$
$488$	1.84336	+	1.84336i	0.0834450	+	0.0834450i
$489$		0			0
$490$	−0.401200	−	0.401200i	−0.0181243	−	0.0181243i
$491$			6.66935i			0.300984i	0.988611	+	0.150492i	$0.0480857\pi$
$491$			6.66935i			0.300984i	−0.988611	+	0.150492i	$0.951914\pi$
$492$		0			0
$493$	38.4987	−	8.96313i	1.73390	−	0.403679i
$494$	0.529375			0.0238177
$495$		0			0
$496$	−13.8184	−	13.8184i	−0.620466	−	0.620466i
$497$	0.663798			0.0297754
$498$		0			0
$499$	13.1853	−	13.1853i	0.590256	−	0.590256i	−0.347445	−	0.937701i	$-0.612951\pi$
$499$	13.1853	−	13.1853i	0.590256	−	0.590256i	0.937701	+	0.347445i	$0.112951\pi$
$500$	8.42244	−	8.42244i	0.376663	−	0.376663i
$501$		0			0
$502$		−	1.85128i		−	0.0826265i
$503$	−18.2007	+	18.2007i	−0.811527	+	0.811527i	−0.984863	−	0.173335i	$-0.944546\pi$
$503$	−18.2007	+	18.2007i	−0.811527	+	0.811527i	0.173335	+	0.984863i	$0.444546\pi$
$504$		0			0
$505$	8.34564	+	8.34564i	0.371376	+	0.371376i
$506$	−2.33440			−0.103777
$507$		0			0
$508$			21.1680i			0.939180i
$509$	−41.1950			−1.82594			−0.912968	−	0.408032i	$-0.866215\pi$
$509$	−41.1950			−1.82594			−0.912968	+	0.408032i	$0.866215\pi$
$510$		0			0
$511$	−11.2594			−0.498087
$512$			16.0653i			0.709992i
$513$		0			0
$514$	0.945570			0.0417073
$515$	1.52778	+	1.52778i	0.0673219	+	0.0673219i
$516$		0			0
$517$	28.3594	−	28.3594i	1.24724	−	1.24724i
$518$			3.25940i			0.143210i
$519$		0			0
$520$	0.990002	−	0.990002i	0.0434145	−	0.0434145i
$521$	6.35127	−	6.35127i	0.278254	−	0.278254i	−0.554158	−	0.832412i	$-0.686960\pi$
$521$	6.35127	−	6.35127i	0.278254	−	0.278254i	0.832412	+	0.554158i	$0.186960\pi$
$522$		0			0
$523$	5.38995			0.235686			0.117843	−	0.993032i	$-0.462402\pi$
$523$	5.38995			0.235686			0.117843	+	0.993032i	$0.462402\pi$
$524$	−0.974097	−	0.974097i	−0.0425536	−	0.0425536i
$525$		0			0
$526$	−2.02194			−0.0881607
$527$	21.1741	−	4.92966i	0.922357	−	0.214740i
$528$		0			0
$529$			18.4963i			0.804185i
$530$	0.644358	+	0.644358i	0.0279891	+	0.0279891i
$531$		0			0
$532$	−2.26635	−	2.26635i	−0.0982586	−	0.0982586i
$533$	12.2666	−	12.2666i	0.531323	−	0.531323i
$534$		0			0
$535$			8.37070i			0.361897i
$536$			6.76016i			0.291994i
$537$		0			0
$538$	−3.35939	+	3.35939i	−0.144834	+	0.144834i
$539$	14.0462	+	14.0462i	0.605015	+	0.605015i
$540$		0			0
$541$	−0.868076	−	0.868076i	−0.0373215	−	0.0373215i	0.688200	−	0.725521i	$-0.258401\pi$
$541$	−0.868076	−	0.868076i	−0.0373215	−	0.0373215i	−0.725521	+	0.688200i	$0.758401\pi$
$542$		−	4.29302i		−	0.184401i
$543$		0			0
$544$	−9.02840	−	5.61839i	−0.387090	−	0.240887i
$545$	−11.0668			−0.474050
$546$		0			0
$547$	−9.56534	−	9.56534i	−0.408984	−	0.408984i	0.472400	−	0.881384i	$-0.343388\pi$
$547$	−9.56534	−	9.56534i	−0.408984	−	0.408984i	−0.881384	+	0.472400i	$0.843388\pi$
$548$	−24.0171			−1.02596
$549$		0			0
$550$	3.57402	−	3.57402i	0.152397	−	0.152397i
$551$	6.44438	−	6.44438i	0.274540	−	0.274540i
$552$		0			0
$553$			4.10124i			0.174402i
$554$	−0.524778	+	0.524778i	−0.0222957	+	0.0222957i
$555$		0			0
$556$	18.4060	+	18.4060i	0.780588	+	0.780588i
$557$	−18.3599			−0.777936			−0.388968	−	0.921251i	$-0.627168\pi$
$557$	−18.3599			−0.777936			−0.388968	+	0.921251i	$0.627168\pi$
$558$		0			0
$559$		−	17.9212i		−	0.757986i
$560$	−4.07680			−0.172276
$561$		0			0
$562$	1.03931			0.0438406
$563$			3.33315i			0.140475i	0.997530	+	0.0702377i	$0.0223758\pi$
$563$			3.33315i			0.140475i	−0.997530	+	0.0702377i	$0.977624\pi$
$564$		0			0
$565$	0.493877			0.0207775
$566$	−1.58027	−	1.58027i	−0.0664237	−	0.0664237i
$567$		0			0
$568$	0.238375	−	0.238375i	0.0100020	−	0.0100020i
$569$		−	29.4369i		−	1.23406i	−0.786940	−	0.617029i	$-0.788336\pi$
$569$		−	29.4369i		−	1.23406i	0.786940	−	0.617029i	$-0.211664\pi$
$570$		0			0
$571$	−18.2628	+	18.2628i	−0.764275	+	0.764275i	−0.977092	−	0.212817i	$-0.931736\pi$
$571$	−18.2628	+	18.2628i	−0.764275	+	0.764275i	0.212817	+	0.977092i	$0.431736\pi$
$572$	−17.1137	+	17.1137i	−0.715561	+	0.715561i
$573$		0			0
$574$	2.65824			0.110953
$575$	6.89535	+	6.89535i	0.287556	+	0.287556i
$576$		0			0
$577$	−22.1850			−0.923575			−0.461788	−	0.886990i	$-0.652792\pi$
$577$	−22.1850			−0.923575			−0.461788	+	0.886990i	$0.652792\pi$
$578$	3.38883	−	1.66838i	0.140957	−	0.0693954i
$579$		0			0
$580$		−	11.9013i		−	0.494173i
$581$	16.3262	+	16.3262i	0.677325	+	0.677325i
$582$		0			0
$583$	−22.5594	−	22.5594i	−0.934313	−	0.934313i
$584$	−4.04334	+	4.04334i	−0.167314	+	0.167314i
$585$		0			0
$586$			1.28190i			0.0529547i
$587$		−	32.1482i		−	1.32690i	−0.748222	−	0.663448i	$-0.769092\pi$
$587$		−	32.1482i		−	1.32690i	0.748222	−	0.663448i	$-0.230908\pi$
$588$		0			0
$589$	3.54437	−	3.54437i	0.146043	−	0.146043i
$590$	−1.01112	−	1.01112i	−0.0416272	−	0.0416272i
$591$		0			0
$592$	−22.2420	−	22.2420i	−0.914139	−	0.914139i
$593$		−	29.3406i		−	1.20488i	−0.798166	−	0.602438i	$-0.794196\pi$
$593$		−	29.3406i		−	1.20488i	0.798166	−	0.602438i	$-0.205804\pi$
$594$		0			0
$595$	2.39626	−	3.85064i	0.0982372	−	0.157861i
$596$	0.696164			0.0285160
$597$		0			0
$598$	0.835648	+	0.835648i	0.0341722	+	0.0341722i
$599$	−36.2632			−1.48167			−0.740836	−	0.671686i	$-0.765570\pi$
$599$	−36.2632			−1.48167			−0.740836	+	0.671686i	$0.765570\pi$
$600$		0			0
$601$	−32.3418	+	32.3418i	−1.31925	+	1.31925i	−0.404882	+	0.914369i	$0.632687\pi$
$601$	−32.3418	+	32.3418i	−1.31925	+	1.31925i	−0.914369	+	0.404882i	$0.867313\pi$
$602$	1.94182	−	1.94182i	0.0791427	−	0.0791427i
$603$		0			0
$604$		−	17.8155i		−	0.724900i
$605$	6.07902	−	6.07902i	0.247147	−	0.247147i
$606$		0			0
$607$	−23.8041	−	23.8041i	−0.966177	−	0.966177i	0.0332698	−	0.999446i	$-0.489408\pi$
$607$	−23.8041	−	23.8041i	−0.966177	−	0.966177i	−0.999446	+	0.0332698i	$0.989408\pi$
$608$	−2.45176			−0.0994318
$609$		0			0
$610$			0.419945i			0.0170031i
$611$	−20.3037			−0.821400
$612$		0			0
$613$	−5.89120			−0.237943			−0.118972	−	0.992898i	$-0.537960\pi$
$613$	−5.89120			−0.237943			−0.118972	+	0.992898i	$0.537960\pi$
$614$		−	2.94125i		−	0.118699i
$615$		0			0
$616$	−7.51118			−0.302634
$617$	24.9028	+	24.9028i	1.00255	+	1.00255i	0.999997	+	0.00255180i	$0.000812263\pi$
$617$	24.9028	+	24.9028i	1.00255	+	1.00255i	0.00255180	+	0.999997i	$0.499188\pi$
$618$		0			0
$619$	−23.2134	+	23.2134i	−0.933027	+	0.933027i	−0.997894	−	0.0648669i	$-0.979338\pi$
$619$	−23.2134	+	23.2134i	−0.933027	+	0.933027i	0.0648669	+	0.997894i	$0.479338\pi$
$620$		−	6.54562i		−	0.262878i
$621$		0			0
$622$	−0.203509	+	0.203509i	−0.00815997	+	0.00815997i
$623$	2.43064	−	2.43064i	0.0973814	−	0.0973814i
$624$		0			0
$625$	−19.0889			−0.763555
$626$	−3.00097	−	3.00097i	−0.119943	−	0.119943i
$627$		0			0
$628$	−34.3262			−1.36976
$629$	34.0815	−	7.93473i	1.35892	−	0.316378i
$630$		0			0
$631$		−	10.7057i		−	0.426186i	−0.977032	−	0.213093i	$-0.931646\pi$
$631$		−	10.7057i		−	0.426186i	0.977032	−	0.213093i	$-0.0683537\pi$
$632$	1.47278	+	1.47278i	0.0585842	+	0.0585842i
$633$		0			0
$634$	2.37308	+	2.37308i	0.0942468	+	0.0942468i
$635$	−4.88342	+	4.88342i	−0.193793	+	0.193793i
$636$		0			0
$637$		−	10.0563i		−	0.398446i
$638$		−	10.5456i		−	0.417505i
$639$		0			0
$640$	−3.00506	+	3.00506i	−0.118785	+	0.118785i
$641$	26.1231	+	26.1231i	1.03180	+	1.03180i	0.999477	+	0.0323232i	$0.0102906\pi$
$641$	26.1231	+	26.1231i	1.03180	+	1.03180i	0.0323232	+	0.999477i	$0.489709\pi$
$642$		0			0
$643$	27.7990	+	27.7990i	1.09629	+	1.09629i	0.994841	+	0.101444i	$0.0323462\pi$
$643$	27.7990	+	27.7990i	1.09629	+	1.09629i	0.101444	+	0.994841i	$0.467654\pi$
$644$		−	7.15511i		−	0.281951i
$645$		0			0
$646$	0.460136	−	0.739409i	0.0181038	−	0.0290917i
$647$	14.8806			0.585016			0.292508	−	0.956263i	$-0.405510\pi$
$647$	14.8806			0.585016			0.292508	+	0.956263i	$0.405510\pi$
$648$		0			0
$649$	35.4000	+	35.4000i	1.38957	+	1.38957i
$650$	−2.55880			−0.100364
$651$		0			0
$652$	22.8827	−	22.8827i	0.896157	−	0.896157i
$653$	−17.1762	+	17.1762i	−0.672155	+	0.672155i	−0.958212	−	0.286057i	$-0.907655\pi$
$653$	−17.1762	+	17.1762i	−0.672155	+	0.672155i	0.286057	+	0.958212i	$0.407655\pi$
$654$		0			0
$655$		−	0.449444i		−	0.0175612i
$656$	−18.1397	+	18.1397i	−0.708236	+	0.708236i
$657$		0			0
$658$	−2.19998	−	2.19998i	−0.0857640	−	0.0857640i
$659$	−9.14192			−0.356119			−0.178059	−	0.984020i	$-0.556982\pi$
$659$	−9.14192			−0.356119			−0.178059	+	0.984020i	$0.556982\pi$
$660$		0			0
$661$			16.7951i			0.653253i	0.945153	+	0.326627i	$0.105912\pi$
$661$			16.7951i			0.653253i	−0.945153	+	0.326627i	$0.894088\pi$
$662$	5.03861			0.195831
$663$		0			0
$664$	11.7257			0.455046
$665$		−	1.04568i		−	0.0405498i
$666$		0			0
$667$	20.3456			0.787787
$668$	−19.6185	−	19.6185i	−0.759061	−	0.759061i
$669$		0			0
$670$	−0.770032	+	0.770032i	−0.0297490	+	0.0297490i
$671$		−	14.7025i		−	0.567585i
$672$		0			0
$673$	13.1743	−	13.1743i	0.507834	−	0.507834i	−0.406027	−	0.913861i	$-0.633086\pi$
$673$	13.1743	−	13.1743i	0.507834	−	0.507834i	0.913861	+	0.406027i	$0.133086\pi$
$674$	−0.254003	+	0.254003i	−0.00978382	+	0.00978382i
$675$		0			0
$676$	−13.1057			−0.504067
$677$	7.63748	+	7.63748i	0.293532	+	0.293532i	0.838474	−	0.544942i	$-0.183448\pi$
$677$	7.63748	+	7.63748i	0.293532	+	0.293532i	−0.544942	+	0.838474i	$0.683448\pi$
$678$		0			0
$679$	−5.25690			−0.201741
$680$	−0.522279	−	2.24331i	−0.0200285	−	0.0860270i
$681$		0			0
$682$		−	5.80002i		−	0.222094i
$683$	−15.7118	−	15.7118i	−0.601197	−	0.601197i	0.339433	−	0.940630i	$-0.389765\pi$
$683$	−15.7118	−	15.7118i	−0.601197	−	0.601197i	−0.940630	+	0.339433i	$0.889765\pi$
$684$		0			0
$685$	−5.54068	−	5.54068i	−0.211699	−	0.211699i
$686$	2.99056	−	2.99056i	0.114180	−	0.114180i
$687$		0			0
$688$			26.5017i			1.01037i
$689$			16.1512i			0.615313i
$690$		0			0
$691$	27.2528	−	27.2528i	1.03675	−	1.03675i	0.0374473	−	0.999299i	$-0.488077\pi$
$691$	27.2528	−	27.2528i	1.03675	−	1.03675i	0.999299	−	0.0374473i	$-0.0119226\pi$
$692$	−2.61145	−	2.61145i	−0.0992724	−	0.0992724i
$693$		0			0
$694$	2.41336	+	2.41336i	0.0916098	+	0.0916098i
$695$			8.49244i			0.322137i
$696$		0			0
$697$	−6.47126	−	27.7956i	−0.245116	−	1.05283i
$698$	3.35702			0.127065
$699$		0			0
$700$	10.9547	+	10.9547i	0.414047	+	0.414047i
$701$	18.0843			0.683034			0.341517	−	0.939876i	$-0.389059\pi$
$701$	18.0843			0.683034			0.341517	+	0.939876i	$0.389059\pi$
$702$		0			0
$703$	5.70497	−	5.70497i	0.215167	−	0.215167i
$704$	23.9422	−	23.9422i	0.902354	−	0.902354i
$705$		0			0
$706$		−	6.94307i		−	0.261306i
$707$	−22.6663	+	22.6663i	−0.852454	+	0.852454i
$708$		0			0
$709$	36.9544	+	36.9544i	1.38785	+	1.38785i	0.829821	+	0.558030i	$0.188443\pi$
$709$	36.9544	+	36.9544i	1.38785	+	1.38785i	0.558030	+	0.829821i	$0.311557\pi$
$710$	0.0543053			0.00203804
$711$		0			0
$712$		−	1.74572i		−	0.0654236i
$713$	11.1900			0.419068
$714$		0			0
$715$	−7.89620			−0.295301
$716$			43.3955i			1.62177i
$717$		0			0
$718$	−0.605478			−0.0225962
$719$	−1.59686	−	1.59686i	−0.0595530	−	0.0595530i	0.676703	−	0.736256i	$-0.263408\pi$
$719$	−1.59686	−	1.59686i	−0.0595530	−	0.0595530i	−0.736256	+	0.676703i	$0.763408\pi$
$720$		0			0
$721$	−4.14936	+	4.14936i	−0.154530	+	0.154530i
$722$			4.02084i			0.149640i
$723$		0			0
$724$	16.0195	−	16.0195i	0.595360	−	0.595360i
$725$	−31.1497	+	31.1497i	−1.15687	+	1.15687i
$726$		0			0
$727$	39.5601			1.46720			0.733601	−	0.679581i	$-0.237838\pi$
$727$	39.5601			1.46720			0.733601	+	0.679581i	$0.237838\pi$
$728$	2.68879	+	2.68879i	0.0996532	+	0.0996532i
$729$		0			0
$730$	−0.921132			−0.0340926
$731$	−25.0316	−	15.5772i	−0.925827	−	0.576144i
$732$		0			0
$733$			13.5137i			0.499139i	0.968357	+	0.249570i	$0.0802892\pi$
$733$			13.5137i			0.499139i	−0.968357	+	0.249570i	$0.919711\pi$
$734$	−2.89898	−	2.89898i	−0.107003	−	0.107003i
$735$		0			0
$736$	−3.87024	−	3.87024i	−0.142659	−	0.142659i
$737$	26.9593	−	26.9593i	0.993059	−	0.993059i
$738$		0			0
$739$		−	10.7282i		−	0.394642i	−0.980339	−	0.197321i	$-0.936776\pi$
$739$		−	10.7282i		−	0.394642i	0.980339	−	0.197321i	$-0.0632241\pi$
$740$		−	10.5357i		−	0.387302i
$741$		0			0
$742$	−1.75004	+	1.75004i	−0.0642460	+	0.0642460i
$743$	31.1071	+	31.1071i	1.14121	+	1.14121i	0.988229	+	0.152981i	$0.0488875\pi$
$743$	31.1071	+	31.1071i	1.14121	+	1.14121i	0.152981	+	0.988229i	$0.451113\pi$
$744$		0			0
$745$	0.160604	+	0.160604i	0.00588406	+	0.00588406i
$746$			5.42257i			0.198534i
$747$		0			0
$748$	9.02840	+	38.7791i	0.330111	+	1.41791i
$749$	−22.7343			−0.830695
$750$		0			0
$751$	8.84217	+	8.84217i	0.322655	+	0.322655i	0.849785	−	0.527129i	$-0.176732\pi$
$751$	8.84217	+	8.84217i	0.322655	+	0.322655i	−0.527129	+	0.849785i	$0.676732\pi$
$752$	30.0250			1.09490
$753$		0			0
$754$	−3.77503	+	3.77503i	−0.137479	+	0.137479i
$755$	4.10999	−	4.10999i	0.149578	−	0.149578i
$756$		0			0
$757$		−	35.8474i		−	1.30290i	−0.758693	−	0.651449i	$-0.774162\pi$
$757$		−	35.8474i		−	1.30290i	0.758693	−	0.651449i	$-0.225838\pi$
$758$	0.925485	−	0.925485i	0.0336151	−	0.0336151i
$759$		0			0
$760$	−0.375512	−	0.375512i	−0.0136213	−	0.0136213i
$761$	−23.4468			−0.849944			−0.424972	−	0.905206i	$-0.639716\pi$
$761$	−23.4468			−0.849944			−0.424972	+	0.905206i	$0.639716\pi$
$762$		0			0
$763$		−	30.0568i		−	1.08813i
$764$	12.9388			0.468108
$765$		0			0
$766$	6.83807			0.247070
$767$		−	25.3444i		−	0.915133i
$768$		0			0
$769$	−22.8938			−0.825573			−0.412786	−	0.910828i	$-0.635444\pi$
$769$	−22.8938			−0.825573			−0.412786	+	0.910828i	$0.635444\pi$
$770$	−0.855580	−	0.855580i	−0.0308330	−	0.0308330i
$771$		0			0
$772$	−4.02438	+	4.02438i	−0.144840	+	0.144840i
$773$		−	34.1287i		−	1.22753i	−0.789491	−	0.613763i	$-0.789655\pi$
$773$		−	34.1287i		−	1.22753i	0.789491	−	0.613763i	$-0.210345\pi$
$774$		0			0
$775$	−17.1321	+	17.1321i	−0.615405	+	0.615405i
$776$	−1.88779	+	1.88779i	−0.0677678	+	0.0677678i
$777$		0			0
$778$	−4.33815			−0.155530
$779$	−4.65276	−	4.65276i	−0.166702	−	0.166702i
$780$		0			0
$781$	−1.90126			−0.0680325
$782$	1.89355	−	0.440849i	0.0677132	−	0.0157647i
$783$		0			0
$784$			14.8712i			0.531115i
$785$	−7.91898	−	7.91898i	−0.282640	−	0.282640i
$786$		0			0
$787$	9.31474	+	9.31474i	0.332035	+	0.332035i	0.853359	−	0.521324i	$-0.174562\pi$
$787$	9.31474	+	9.31474i	0.332035	+	0.332035i	−0.521324	+	0.853359i	$0.674562\pi$
$788$	−6.25538	+	6.25538i	−0.222839	+	0.222839i
$789$		0			0
$790$			0.335522i			0.0119373i
$791$			1.34134i			0.0476926i
$792$		0			0
$793$	−5.26309	+	5.26309i	−0.186898	+	0.186898i
$794$	0.142074	+	0.142074i	0.00504202	+	0.00504202i
$795$		0			0
$796$	3.39349	+	3.39349i	0.120279	+	0.120279i
$797$			36.3506i			1.28761i	0.765191	+	0.643803i	$0.222644\pi$
$797$			36.3506i			1.28761i	−0.765191	+	0.643803i	$0.777356\pi$
$798$		0			0
$799$	−17.6481	+	28.3594i	−0.624345	+	1.00328i
$800$	11.8509			0.418991
$801$		0			0
$802$	−0.198726	−	0.198726i	−0.00701724	−	0.00701724i
$803$	32.2494			1.13806
$804$		0			0
$805$	1.65067	−	1.65067i	0.0581784	−	0.0581784i
$806$	−2.07624	+	2.07624i	−0.0731326	+	0.0731326i
$807$		0			0
$808$			16.2793i			0.572703i
$809$	31.9094	−	31.9094i	1.12187	−	1.12187i	0.130415	−	0.991460i	$-0.458369\pi$
$809$	31.9094	−	31.9094i	1.12187	−	1.12187i	0.991460	−	0.130415i	$-0.0416309\pi$
$810$		0			0
$811$	−2.35336	−	2.35336i	−0.0826376	−	0.0826376i	0.664580	−	0.747217i	$-0.268611\pi$
$811$	−2.35336	−	2.35336i	−0.0826376	−	0.0826376i	−0.747217	+	0.664580i	$0.768611\pi$
$812$	32.3232			1.13432
$813$		0			0
$814$		−	9.33565i		−	0.327214i
$815$	10.5580			0.369830
$816$		0			0
$817$	−6.79759			−0.237817
$818$			6.36244i			0.222458i
$819$		0			0
$820$	−8.59255			−0.300065
$821$	5.28197	+	5.28197i	0.184342	+	0.184342i	0.793245	−	0.608903i	$-0.208390\pi$
$821$	5.28197	+	5.28197i	0.184342	+	0.184342i	−0.608903	+	0.793245i	$0.708390\pi$
$822$		0			0
$823$	38.3134	−	38.3134i	1.33552	−	1.33552i	0.435178	−	0.900345i	$-0.356686\pi$
$823$	38.3134	−	38.3134i	1.33552	−	1.33552i	0.900345	−	0.435178i	$-0.143314\pi$
$824$			2.98013i			0.103818i
$825$		0			0
$826$	2.74615	−	2.74615i	0.0955508	−	0.0955508i
$827$	−3.50062	+	3.50062i	−0.121729	+	0.121729i	−0.765347	−	0.643618i	$-0.777433\pi$
$827$	−3.50062	+	3.50062i	−0.121729	+	0.121729i	0.643618	+	0.765347i	$0.277433\pi$
$828$		0			0
$829$	0.0762440			0.00264806			0.00132403	−	0.999999i	$-0.499579\pi$
$829$	0.0762440			0.00264806			0.00132403	+	0.999999i	$0.499579\pi$
$830$	1.33565	+	1.33565i	0.0463610	+	0.0463610i
$831$		0			0
$832$	−17.1412			−0.594265
$833$	−14.0462	−	8.74101i	−0.486674	−	0.302858i
$834$		0			0
$835$		−	9.05187i		−	0.313253i
$836$	6.49131	+	6.49131i	0.224507	+	0.224507i
$837$		0			0
$838$	3.76412	+	3.76412i	0.130030	+	0.130030i
$839$	−25.7725	+	25.7725i	−0.889766	+	0.889766i	−0.994500	−	0.104734i	$-0.966601\pi$
$839$	−25.7725	+	25.7725i	−0.889766	+	0.889766i	0.104734	+	0.994500i	$0.466601\pi$
$840$		0			0
$841$			62.9113i			2.16935i
$842$			2.78433i			0.0959545i
$843$		0			0
$844$	27.4533	−	27.4533i	0.944983	−	0.944983i
$845$	−3.02347	−	3.02347i	−0.104010	−	0.104010i
$846$		0			0
$847$	16.5103	+	16.5103i	0.567300	+	0.567300i
$848$		−	23.8843i		−	0.820191i
$849$		0			0
$850$	−2.22412	+	3.57402i	−0.0762867	+	0.122588i
$851$	18.0112			0.617418
$852$		0			0
$853$	−28.2619	−	28.2619i	−0.967669	−	0.967669i	0.0318244	−	0.999493i	$-0.489868\pi$
$853$	−28.2619	−	28.2619i	−0.967669	−	0.967669i	−0.999493	+	0.0318244i	$0.989868\pi$
$854$	−1.14055			−0.0390287
$855$		0			0
$856$	−8.16407	+	8.16407i	−0.279042	+	0.279042i
$857$	2.09277	−	2.09277i	0.0714875	−	0.0714875i	−0.670459	−	0.741947i	$-0.733903\pi$
$857$	2.09277	−	2.09277i	0.0714875	−	0.0714875i	0.741947	+	0.670459i	$0.233903\pi$
$858$		0			0
$859$		−	22.4494i		−	0.765963i	−0.923756	−	0.382981i	$-0.874897\pi$
$859$		−	22.4494i		−	0.765963i	0.923756	−	0.382981i	$-0.125103\pi$
$860$	−6.27677	+	6.27677i	−0.214036	+	0.214036i
$861$		0			0
$862$	−2.77662	−	2.77662i	−0.0945721	−	0.0945721i
$863$	−27.8981			−0.949661			−0.474831	−	0.880077i	$-0.657491\pi$
$863$	−27.8981			−0.949661			−0.474831	+	0.880077i	$0.657491\pi$
$864$		0			0
$865$		−	1.20491i		−	0.0409682i
$866$	3.11236			0.105762
$867$		0			0
$868$	17.7775			0.603409
$869$		−	11.7468i		−	0.398484i
$870$		0			0
$871$	−19.3013			−0.654001
$872$	−10.7936	−	10.7936i	−0.365518	−	0.365518i
$873$		0			0
$874$	0.316965	−	0.316965i	0.0107215	−	0.0107215i
$875$			10.5544i			0.356803i
$876$		0			0
$877$	14.6344	−	14.6344i	0.494167	−	0.494167i	−0.415449	−	0.909616i	$-0.636376\pi$
$877$	14.6344	−	14.6344i	0.494167	−	0.494167i	0.909616	+	0.415449i	$0.136376\pi$
$878$	−1.81843	+	1.81843i	−0.0613690	+	0.0613690i
$879$		0			0
$880$	11.6768			0.393627
$881$	−15.7260	−	15.7260i	−0.529822	−	0.529822i	0.390697	−	0.920519i	$-0.372234\pi$
$881$	−15.7260	−	15.7260i	−0.529822	−	0.529822i	−0.920519	+	0.390697i	$0.872234\pi$
$882$		0			0
$883$	4.23253			0.142436			0.0712180	−	0.997461i	$-0.477311\pi$
$883$	4.23253			0.142436			0.0712180	+	0.997461i	$0.477311\pi$
$884$	10.6499	−	17.1137i	0.358195	−	0.575597i
$885$		0			0
$886$			7.91388i			0.265872i
$887$	−25.6713	−	25.6713i	−0.861957	−	0.861957i	0.129608	−	0.991565i	$-0.458628\pi$
$887$	−25.6713	−	25.6713i	−0.861957	−	0.861957i	−0.991565	+	0.129608i	$0.958628\pi$
$888$		0			0
$889$	−13.2631	−	13.2631i	−0.444830	−	0.444830i
$890$	0.198850	−	0.198850i	0.00666548	−	0.00666548i
$891$		0			0
$892$		−	28.0171i		−	0.938081i
$893$			7.70129i			0.257714i
$894$		0			0
$895$	−10.0112	+	10.0112i	−0.334639	+	0.334639i
$896$	−8.16158	−	8.16158i	−0.272659	−	0.272659i
$897$		0			0
$898$	3.47943	+	3.47943i	0.116110	+	0.116110i
$899$			50.5506i			1.68596i
$900$		0			0
$901$	22.5594	+	14.0387i	0.751561	+	0.467698i
$902$	−7.61380			−0.253512
$903$		0			0
$904$	0.481686	+	0.481686i	0.0160206	+	0.0160206i
$905$	7.39133			0.245696
$906$		0			0
$907$	−17.2334	+	17.2334i	−0.572227	+	0.572227i	−0.932750	−	0.360523i	$-0.882598\pi$
$907$	−17.2334	+	17.2334i	−0.572227	+	0.572227i	0.360523	+	0.932750i	$0.382598\pi$
$908$	−14.9991	+	14.9991i	−0.497762	+	0.497762i
$909$		0			0
$910$			0.612546i			0.0203057i
$911$	−19.0337	+	19.0337i	−0.630616	+	0.630616i	−0.948223	−	0.317606i	$-0.897121\pi$
$911$	−19.0337	+	19.0337i	−0.630616	+	0.630616i	0.317606	+	0.948223i	$0.397121\pi$
$912$		0			0
$913$	−46.7618	−	46.7618i	−1.54759	−	1.54759i
$914$	2.20110			0.0728059
$915$		0			0
$916$			37.0425i			1.22392i
$917$	1.22066			0.0403099
$918$		0			0
$919$	−23.8000			−0.785088			−0.392544	−	0.919733i	$-0.628405\pi$
$919$	−23.8000			−0.785088			−0.392544	+	0.919733i	$0.628405\pi$
$920$		−	1.18553i		−	0.0390859i
$921$		0			0
$922$	2.13830			0.0704210
$923$	0.680598	+	0.680598i	0.0224021	+	0.0224021i
$924$		0			0
$925$	−27.5757	+	27.5757i	−0.906683	+	0.906683i
$926$		−	3.39983i		−	0.111725i
$927$		0			0
$928$	17.4838	−	17.4838i	0.573932	−	0.573932i
$929$	−4.12061	+	4.12061i	−0.135193	+	0.135193i	−0.771465	−	0.636272i	$-0.780476\pi$
$929$	−4.12061	+	4.12061i	−0.135193	+	0.135193i	0.636272	+	0.771465i	$0.280476\pi$
$930$		0			0
$931$	−3.81440			−0.125012
$932$	−9.76656	−	9.76656i	−0.319914	−	0.319914i
$933$		0			0
$934$	−4.95819			−0.162237
$935$	−6.86342	+	11.0291i	−0.224458	+	0.360690i
$936$		0			0
$937$		−	55.4424i		−	1.81123i	−0.424106	−	0.905613i	$-0.639411\pi$
$937$		−	55.4424i		−	1.81123i	0.424106	−	0.905613i	$-0.360589\pi$
$938$	−2.09136	−	2.09136i	−0.0682855	−	0.0682855i
$939$		0			0
$940$	7.11123	+	7.11123i	0.231943	+	0.231943i
$941$	−14.9692	+	14.9692i	−0.487981	+	0.487981i	−0.907669	−	0.419688i	$-0.862140\pi$
$941$	−14.9692	+	14.9692i	−0.487981	+	0.487981i	0.419688	+	0.907669i	$0.362140\pi$
$942$		0			0
$943$		−	14.6893i		−	0.478349i
$944$			37.4791i			1.21984i
$945$		0			0
$946$	−5.56180	+	5.56180i	−0.180830	+	0.180830i
$947$	−26.5753	−	26.5753i	−0.863580	−	0.863580i	0.128172	−	0.991752i	$-0.459089\pi$
$947$	−26.5753	−	26.5753i	−0.863580	−	0.863580i	−0.991752	+	0.128172i	$0.959089\pi$
$948$		0			0
$949$	−11.5444	−	11.5444i	−0.374746	−	0.374746i
$950$			0.970563i			0.0314892i
$951$		0			0
$952$	6.09270	−	1.41848i	0.197466	−	0.0459732i
$953$	−21.2794			−0.689307			−0.344654	−	0.938730i	$-0.612004\pi$
$953$	−21.2794			−0.689307			−0.344654	+	0.938730i	$0.612004\pi$
$954$		0			0
$955$	2.98494	+	2.98494i	0.0965904	+	0.0965904i
$956$	10.3163			0.333654
$957$		0			0
$958$	2.44423	−	2.44423i	0.0789695	−	0.0789695i
$959$	15.0482	−	15.0482i	0.485931	−	0.485931i
$960$		0			0
$961$		−	3.19748i		−	0.103144i
$962$	−3.34190	+	3.34190i	−0.107747	+	0.107747i
$963$		0			0
$964$	−7.99756	−	7.99756i	−0.257584	−	0.257584i
$965$	−1.85683			−0.0597734
$966$		0			0
$967$			26.2320i			0.843563i	0.906697	+	0.421782i	$0.138595\pi$
$967$			26.2320i			0.843563i	−0.906697	+	0.421782i	$0.861405\pi$
$968$	11.8579			0.381128
$969$		0			0
$970$	−0.430067			−0.0138086
$971$		−	20.8243i		−	0.668285i	−0.942523	−	0.334142i	$-0.891553\pi$
$971$		−	20.8243i		−	0.668285i	0.942523	−	0.334142i	$-0.108447\pi$
$972$		0			0
$973$	−23.0650			−0.739429
$974$	0.00465866	+	0.00465866i	0.000149273	+	0.000149273i
$975$		0			0
$976$	7.78302	−	7.78302i	0.249128	−	0.249128i
$977$		−	16.2900i		−	0.521162i	−0.965452	−	0.260581i	$-0.916086\pi$
$977$		−	16.2900i		−	0.521162i	0.965452	−	0.260581i	$-0.0839141\pi$
$978$		0			0
$979$	−6.96188	+	6.96188i	−0.222503	+	0.222503i
$980$	−3.52215	+	3.52215i	−0.112511	+	0.112511i
$981$		0			0
$982$	−1.48187			−0.0472884
$983$	0.658791	+	0.658791i	0.0210122	+	0.0210122i	0.717535	−	0.696523i	$-0.245270\pi$
$983$	0.658791	+	0.658791i	0.0210122	+	0.0210122i	−0.696523	+	0.717535i	$0.745270\pi$
$984$		0			0
$985$	−2.88620			−0.0919621
$986$	1.99153	+	8.55409i	0.0634232	+	0.272418i
$987$		0			0
$988$		−	4.64741i		−	0.147854i
$989$	−10.7304	−	10.7304i	−0.341206	−	0.341206i
$990$		0			0
$991$	−15.3422	−	15.3422i	−0.487362	−	0.487362i	0.420111	−	0.907473i	$-0.361991\pi$
$991$	−15.3422	−	15.3422i	−0.487362	−	0.487362i	−0.907473	+	0.420111i	$0.861991\pi$
$992$	9.61596	−	9.61596i	0.305307	−	0.305307i
$993$		0			0
$994$			0.147490i			0.00467810i
$995$			1.56574i			0.0496373i
$996$		0			0
$997$	2.28190	−	2.28190i	0.0722684	−	0.0722684i	−0.670049	−	0.742317i	$-0.733727\pi$
$997$	2.28190	−	2.28190i	0.0722684	−	0.0722684i	0.742317	+	0.670049i	$0.233727\pi$
$998$	2.92966	+	2.92966i	0.0927369	+	0.0927369i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.f.b.64.3		8
3.2	odd	2		51.2.e.a.13.2	yes	8
4.3	odd	2		2448.2.be.x.1441.3		8
12.11	even	2		816.2.bd.e.625.3		8
17.2	even	8		2601.2.a.bf.1.2		4
17.4	even	4	inner	153.2.f.b.55.2		8
17.15	even	8		2601.2.a.be.1.2		4
51.2	odd	8		867.2.a.k.1.3		4
51.5	even	16		867.2.h.i.733.4		16
51.8	odd	8		867.2.d.f.577.4		8
51.11	even	16		867.2.h.i.757.4		16
51.14	even	16		867.2.h.k.712.2		16
51.20	even	16		867.2.h.k.712.1		16
51.23	even	16		867.2.h.i.757.3		16
51.26	odd	8		867.2.d.f.577.3		8
51.29	even	16		867.2.h.i.733.3		16
51.32	odd	8		867.2.a.l.1.3		4
51.38	odd	4		51.2.e.a.4.3	✓	8
51.41	even	16		867.2.h.k.688.1		16
51.44	even	16		867.2.h.k.688.2		16
51.47	odd	4		867.2.e.g.616.3		8
51.50	odd	2		867.2.e.g.829.2		8
68.55	odd	4		2448.2.be.x.1585.3		8
204.191	even	4		816.2.bd.e.769.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.3	✓	8	51.38	odd	4
51.2.e.a.13.2	yes	8	3.2	odd	2
153.2.f.b.55.2		8	17.4	even	4	inner
153.2.f.b.64.3		8	1.1	even	1	trivial
816.2.bd.e.625.3		8	12.11	even	2
816.2.bd.e.769.3		8	204.191	even	4
867.2.a.k.1.3		4	51.2	odd	8
867.2.a.l.1.3		4	51.32	odd	8
867.2.d.f.577.3		8	51.26	odd	8
867.2.d.f.577.4		8	51.8	odd	8
867.2.e.g.616.3		8	51.47	odd	4
867.2.e.g.829.2		8	51.50	odd	2
867.2.h.i.733.3		16	51.29	even	16
867.2.h.i.733.4		16	51.5	even	16
867.2.h.i.757.3		16	51.23	even	16
867.2.h.i.757.4		16	51.11	even	16
867.2.h.k.688.1		16	51.41	even	16
867.2.h.k.688.2		16	51.44	even	16
867.2.h.k.712.1		16	51.20	even	16
867.2.h.k.712.2		16	51.14	even	16
2448.2.be.x.1441.3		8	4.3	odd	2
2448.2.be.x.1585.3		8	68.55	odd	4
2601.2.a.be.1.2		4	17.15	even	8
2601.2.a.bf.1.2		4	17.2	even	8

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.222191i q^{2} +1.95063 q^{4} +(0.450006 + 0.450006i) q^{5} +(-1.22219 + 1.22219i) q^{7} +0.877796i q^{8} +(-0.0999875 + 0.0999875i) q^{10} +(3.50062 - 3.50062i) q^{11} -2.50625 q^{13} +(-0.271560 - 0.271560i) q^{14} +3.70622 q^{16} +(-2.17845 + 3.50062i) q^{17} +0.950631i q^{19} +(0.877796 + 0.877796i) q^{20} +(0.777809 + 0.777809i) q^{22} +(-1.50062 + 1.50062i) q^{23} -4.59499i q^{25} -0.556867i q^{26} +(-2.38404 + 2.38404i) q^{28} +(-6.77906 - 6.77906i) q^{29} +(-3.72844 - 3.72844i) q^{31} +2.57908i q^{32} +(-0.777809 - 0.484032i) q^{34} -1.09999 q^{35} +(-6.00125 - 6.00125i) q^{37} -0.211222 q^{38} +(-0.395014 + 0.395014i) q^{40} +(-4.89439 + 4.89439i) q^{41} +7.15061i q^{43} +(6.82843 - 6.82843i) q^{44} +(-0.333426 - 0.333426i) q^{46} +8.10124 q^{47} +4.01250i q^{49} +1.02097 q^{50} -4.88877 q^{52} -6.44438i q^{53} +3.15061 q^{55} +(-1.07283 - 1.07283i) q^{56} +(1.50625 - 1.50625i) q^{58} +10.1125i q^{59} +(2.09999 - 2.09999i) q^{61} +(0.828427 - 0.828427i) q^{62} +6.83940 q^{64} +(-1.12783 - 1.12783i) q^{65} +7.70129 q^{67} +(-4.24934 + 6.82843i) q^{68} -0.244408i q^{70} +(-0.271560 - 0.271560i) q^{71} +(4.60624 + 4.60624i) q^{73} +(1.33343 - 1.33343i) q^{74} +1.85433i q^{76} +8.55687i q^{77} +(1.67782 - 1.67782i) q^{79} +(1.66782 + 1.66782i) q^{80} +(-1.08749 - 1.08749i) q^{82} -13.3581i q^{83} +(-2.55562 + 0.594989i) q^{85} -1.58880 q^{86} +(3.07283 + 3.07283i) q^{88} -1.98875 q^{89} +(3.06311 - 3.06311i) q^{91} +(-2.92717 + 2.92717i) q^{92} +1.80002i q^{94} +(-0.427790 + 0.427790i) q^{95} +(2.15061 + 2.15061i) q^{97} -0.891542 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{13} - 24 q^{14} + 12 q^{16} + 4 q^{17} + 12 q^{20} + 12 q^{22} + 16 q^{23} - 8 q^{28} - 4 q^{29} - 8 q^{31} - 12 q^{34} - 8 q^{35} + 8 q^{37} - 24 q^{38} + 36 q^{40}+ \cdots + 76 q^{98}+O(q^{100}) \) 8 * q - 12 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^13 - 24 * q^14 + 12 * q^16 + 4 * q^17 + 12 * q^20 + 12 * q^22 + 16 * q^23 - 8 * q^28 - 4 * q^29 - 8 * q^31 - 12 * q^34 - 8 * q^35 + 8 * q^37 - 24 * q^38 + 36 * q^40 - 28 * q^41 + 32 * q^44 - 20 * q^46 + 8 * q^47 + 60 * q^50 - 16 * q^52 - 4 * q^55 + 24 * q^56 - 4 * q^58 + 16 * q^61 - 16 * q^62 + 4 * q^64 - 16 * q^65 + 8 * q^67 - 60 * q^68 - 24 * q^71 + 20 * q^73 + 28 * q^74 + 20 * q^79 - 60 * q^80 - 40 * q^82 - 32 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 36 * q^91 - 56 * q^92 - 8 * q^95 - 12 * q^97 + 76 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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