LMFDB - Embedded newform 855.2.da.b.244.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(199,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.199"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.da (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			244.6
Character	$\chi$	$=$	855.244
Dual form			855.2.da.b.424.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04072 - 1.24028i) q^{2} +(-0.107903 - 0.611947i) q^{4} +(-2.23519 - 0.0626993i) q^{5} +(-1.93288 + 1.11595i) q^{7} +(1.93303 + 1.11604i) q^{8} +(-2.40397 + 2.70701i) q^{10} +(2.82239 - 4.88852i) q^{11} +(1.60766 - 4.41702i) q^{13} +(-0.627496 + 3.55871i) q^{14} +(4.56376 - 1.66107i) q^{16} +(0.505129 - 0.601990i) q^{17} +(2.63014 - 3.47597i) q^{19} +(0.202814 + 1.37458i) q^{20} +(-3.12582 - 8.58813i) q^{22} +(-5.05247 + 0.890886i) q^{23} +(4.99214 + 0.280289i) q^{25} +(-3.80521 - 6.59082i) q^{26} +(0.891466 + 1.06241i) q^{28} +(2.32611 - 1.95184i) q^{29} +(-4.05208 - 7.01841i) q^{31} +(1.16257 - 3.19413i) q^{32} +(-0.220938 - 1.25300i) q^{34} +(4.39033 - 2.37317i) q^{35} +0.985141i q^{37} +(-1.57393 - 6.87961i) q^{38} +(-4.25071 - 2.61575i) q^{40} +(1.33247 - 0.484978i) q^{41} +(-1.49862 - 0.264247i) q^{43} +(-3.29606 - 1.19967i) q^{44} +(-4.15324 + 7.19363i) q^{46} +(0.617523 + 0.735935i) q^{47} +(-1.00930 + 1.74817i) q^{49} +(5.54304 - 5.89994i) q^{50} +(-2.87645 - 0.507196i) q^{52} +(4.34421 - 0.766002i) q^{53} +(-6.61508 + 10.7498i) q^{55} -4.98176 q^{56} -4.91635i q^{58} +(7.56739 + 6.34980i) q^{59} +(0.363973 + 2.06420i) q^{61} +(-12.9219 - 2.27847i) q^{62} +(2.10495 + 3.64588i) q^{64} +(-3.87038 + 9.77207i) q^{65} +(2.08785 + 2.48820i) q^{67} +(-0.422891 - 0.244156i) q^{68} +(1.62570 - 7.91504i) q^{70} +(-1.24628 + 7.06798i) q^{71} +(-5.18587 - 14.2481i) q^{73} +(1.22185 + 1.02525i) q^{74} +(-2.41091 - 1.23444i) q^{76} +12.5986i q^{77} +(1.25893 - 0.458214i) q^{79} +(-10.3050 + 3.42667i) q^{80} +(0.785214 - 2.15736i) q^{82} +(6.51723 - 3.76273i) q^{83} +(-1.16680 + 1.31389i) q^{85} +(-1.88738 + 1.58370i) q^{86} +(10.9115 - 6.29977i) q^{88} +(-3.19776 - 1.16389i) q^{89} +(1.82175 + 10.3317i) q^{91} +(1.09035 + 2.99571i) q^{92} +1.55543 q^{94} +(-6.09681 + 7.60453i) q^{95} +(-8.20200 + 9.77477i) q^{97} +(1.11781 + 3.07117i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49}+ \cdots + 63 q^{95}+O(q^{100}) $ 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	1.04072	−	1.24028i	0.735899	−	0.877010i	−0.260173	−	0.965562i	$-0.583780\pi$
$2$	1.04072	−	1.24028i	0.735899	−	0.877010i	0.996072	+	0.0885521i	$0.0282240\pi$
$3$		0			0
$3$		0			0
$4$	−0.107903	−	0.611947i	−0.0539514	−	0.305973i
$5$	−2.23519	−	0.0626993i	−0.999607	−	0.0280400i
$5$	−2.23519	−	0.0626993i	−0.999607	−	0.0280400i
$6$		0			0
$7$	−1.93288	+	1.11595i	−0.730562	+	0.421790i	−0.818628	−	0.574325i	$-0.805265\pi$
$7$	−1.93288	+	1.11595i	−0.730562	+	0.421790i	0.0880659	+	0.996115i	$0.471931\pi$
$8$	1.93303	+	1.11604i	0.683429	+	0.394578i
$9$		0			0
$10$	−2.40397	+	2.70701i	−0.760201	+	0.856031i
$11$	2.82239	−	4.88852i	0.850983	−	1.47395i	−0.0293397	−	0.999569i	$-0.509340\pi$
$11$	2.82239	−	4.88852i	0.850983	−	1.47395i	0.880322	−	0.474376i	$-0.157326\pi$
$12$		0			0
$13$	1.60766	−	4.41702i	0.445886	−	1.22506i	−0.489678	−	0.871903i	$-0.662886\pi$
$13$	1.60766	−	4.41702i	0.445886	−	1.22506i	0.935564	−	0.353158i	$-0.114892\pi$
$14$	−0.627496	+	3.55871i	−0.167705	+	0.951105i
$15$		0			0
$16$	4.56376	−	1.66107i	1.14094	−	0.415268i
$17$	0.505129	−	0.601990i	0.122512	−	0.146004i	−0.701302	−	0.712864i	$-0.747398\pi$
$17$	0.505129	−	0.601990i	0.122512	−	0.146004i	0.823814	+	0.566860i	$0.191842\pi$
$18$		0			0
$19$	2.63014	−	3.47597i	0.603396	−	0.797442i
$19$	2.63014	−	3.47597i	0.603396	−	0.797442i
$20$	0.202814	+	1.37458i	0.0453507	+	0.307366i
$21$		0			0
$22$	−3.12582	−	8.58813i	−0.666428	−	1.83099i
$23$	−5.05247	+	0.890886i	−1.05351	+	0.185763i	−0.673476	−	0.739209i	$-0.735200\pi$
$23$	−5.05247	+	0.890886i	−1.05351	+	0.185763i	−0.380036	+	0.924972i	$0.624088\pi$
$24$		0			0
$25$	4.99214	+	0.280289i	0.998428	+	0.0560579i
$26$	−3.80521	−	6.59082i	−0.746264	−	1.29257i
$27$		0			0
$28$	0.891466	+	1.06241i	0.168471	+	0.200776i
$29$	2.32611	−	1.95184i	0.431949	−	0.362448i	−0.400738	−	0.916193i	$-0.631246\pi$
$29$	2.32611	−	1.95184i	0.431949	−	0.362448i	0.832686	+	0.553745i	$0.186802\pi$
$30$		0			0
$31$	−4.05208	−	7.01841i	−0.727775	−	1.26054i	−0.957822	−	0.287364i	$-0.907221\pi$
$31$	−4.05208	−	7.01841i	−0.727775	−	1.26054i	0.230047	−	0.973180i	$-0.426112\pi$
$32$	1.16257	−	3.19413i	0.205515	−	0.564647i
$33$		0			0
$34$	−0.220938	−	1.25300i	−0.0378906	−	0.214888i
$35$	4.39033	−	2.37317i	0.742101	−	0.401139i
$36$		0			0
$37$			0.985141i			0.161956i	0.996716	+	0.0809781i	$0.0258044\pi$
$37$			0.985141i			0.161956i	−0.996716	+	0.0809781i	$0.974196\pi$
$38$	−1.57393	−	6.87961i	−0.255326	−	1.11602i
$39$		0			0
$40$	−4.25071	−	2.61575i	−0.672097	−	0.413586i
$41$	1.33247	−	0.484978i	0.208096	−	0.0757409i	−0.235869	−	0.971785i	$-0.575794\pi$
$41$	1.33247	−	0.484978i	0.208096	−	0.0757409i	0.443965	+	0.896044i	$0.353571\pi$
$42$		0			0
$43$	−1.49862	−	0.264247i	−0.228537	−	0.0402973i	0.0582066	−	0.998305i	$-0.481462\pi$
$43$	−1.49862	−	0.264247i	−0.228537	−	0.0402973i	−0.286744	+	0.958007i	$0.592573\pi$
$44$	−3.29606	−	1.19967i	−0.496900	−	0.180857i
$45$		0			0
$46$	−4.15324	+	7.19363i	−0.612363	+	1.06064i
$47$	0.617523	+	0.735935i	0.0900749	+	0.107347i	0.809199	−	0.587534i	$-0.199901\pi$
$47$	0.617523	+	0.735935i	0.0900749	+	0.107347i	−0.719124	+	0.694881i	$0.755457\pi$
$48$		0			0
$49$	−1.00930	+	1.74817i	−0.144186	+	0.249738i
$50$	5.54304	−	5.89994i	0.783905	−	0.834378i
$51$		0			0
$52$	−2.87645	−	0.507196i	−0.398892	−	0.0703355i
$53$	4.34421	−	0.766002i	0.596723	−	0.105218i	0.132875	−	0.991133i	$-0.457579\pi$
$53$	4.34421	−	0.766002i	0.596723	−	0.105218i	0.463849	+	0.885914i	$0.346468\pi$
$54$		0			0
$55$	−6.61508	+	10.7498i	−0.891977	+	1.44950i
$56$	−4.98176			−0.665716
$57$		0			0
$58$		−	4.91635i		−	0.645548i
$59$	7.56739	+	6.34980i	0.985191	+	0.826673i	0.984864	−	0.173327i	$-0.0554516\pi$
$59$	7.56739	+	6.34980i	0.985191	+	0.826673i	0.000326502		1.00000i	$0.499896\pi$
$60$		0			0
$61$	0.363973	+	2.06420i	0.0466020	+	0.264293i	0.999202	−	0.0399312i	$-0.0127139\pi$
$61$	0.363973	+	2.06420i	0.0466020	+	0.264293i	−0.952600	+	0.304224i	$0.901603\pi$
$62$	−12.9219	−	2.27847i	−1.64108	−	0.289366i
$63$		0			0
$64$	2.10495	+	3.64588i	0.263118	+	0.455735i
$65$	−3.87038	+	9.77207i	−0.480061	+	1.21208i
$66$		0			0
$67$	2.08785	+	2.48820i	0.255071	+	0.303982i	0.878350	−	0.478017i	$-0.158644\pi$
$67$	2.08785	+	2.48820i	0.255071	+	0.303982i	−0.623279	+	0.781999i	$0.714200\pi$
$68$	−0.422891	−	0.244156i	−0.0512830	−	0.0296083i
$69$		0			0
$70$	1.62570	−	7.91504i	0.194308	−	0.946028i
$71$	−1.24628	+	7.06798i	−0.147906	+	0.838815i	0.817082	+	0.576521i	$0.195590\pi$
$71$	−1.24628	+	7.06798i	−0.147906	+	0.838815i	−0.964988	+	0.262294i	$0.915521\pi$
$72$		0			0
$73$	−5.18587	−	14.2481i	−0.606960	−	1.66761i	−0.736829	−	0.676079i	$-0.763678\pi$
$73$	−5.18587	−	14.2481i	−0.606960	−	1.66761i	0.129869	−	0.991531i	$-0.458544\pi$
$74$	1.22185	+	1.02525i	0.142037	+	0.119183i
$75$		0			0
$76$	−2.41091	−	1.23444i	−0.276550	−	0.141600i
$77$			12.5986i			1.43574i
$78$		0			0
$79$	1.25893	−	0.458214i	0.141641	−	0.0515531i	−0.270227	−	0.962797i	$-0.587099\pi$
$79$	1.25893	−	0.458214i	0.141641	−	0.0515531i	0.411868	+	0.911244i	$0.364877\pi$
$80$	−10.3050	+	3.42667i	−1.15214	+	0.383113i
$81$		0			0
$82$	0.785214	−	2.15736i	0.0867123	−	0.238240i
$83$	6.51723	−	3.76273i	0.715359	−	0.413013i	−0.0976829	−	0.995218i	$-0.531143\pi$
$83$	6.51723	−	3.76273i	0.715359	−	0.413013i	0.813042	+	0.582205i	$0.197810\pi$
$84$		0			0
$85$	−1.16680	+	1.31389i	−0.126558	+	0.142511i
$86$	−1.88738	+	1.58370i	−0.203522	+	0.170775i
$87$		0			0
$88$	10.9115	−	6.29977i	1.16317	−	0.671558i
$89$	−3.19776	−	1.16389i	−0.338962	−	0.123372i	0.166930	−	0.985969i	$-0.446614\pi$
$89$	−3.19776	−	1.16389i	−0.338962	−	0.123372i	−0.505892	+	0.862597i	$0.668837\pi$
$90$		0			0
$91$	1.82175	+	10.3317i	0.190971	+	1.08305i
$92$	1.09035	+	2.99571i	0.113677	+	0.312324i
$93$		0			0
$94$	1.55543			0.160431
$95$	−6.09681	+	7.60453i	−0.625519	+	0.780209i
$96$		0			0
$97$	−8.20200	+	9.77477i	−0.832787	+	0.992477i	0.167191	+	0.985924i	$0.446530\pi$
$97$	−8.20200	+	9.77477i	−0.832787	+	0.992477i	−0.999979	+	0.00655264i	$0.997914\pi$
$98$	1.11781	+	3.07117i	0.112916	+	0.310235i
$99$		0			0
$100$	−0.367143	−	3.08517i	−0.0367143	−	0.308517i
$101$	5.23691	+	1.90608i	0.521092	+	0.189662i	0.589156	−	0.808019i	$-0.299460\pi$
$101$	5.23691	+	1.90608i	0.521092	+	0.189662i	−0.0680647	+	0.997681i	$0.521682\pi$
$102$		0			0
$103$	2.86453	+	1.65384i	0.282251	+	0.162958i	0.634442	−	0.772971i	$-0.281230\pi$
$103$	2.86453	+	1.65384i	0.282251	+	0.162958i	−0.352191	+	0.935928i	$0.614563\pi$
$104$	8.03721	−	6.74402i	0.788114	−	0.661306i
$105$		0			0
$106$	3.57104	−	6.18523i	0.346850	−	0.600763i
$107$	5.77870	−	3.33633i	0.558648	−	0.322536i	−0.193955	−	0.981010i	$-0.562131\pi$
$107$	5.77870	−	3.33633i	0.558648	−	0.322536i	0.752603	+	0.658475i	$0.228798\pi$
$108$		0			0
$109$	−2.72302	+	15.4430i	−0.260818	+	1.47917i	0.519866	+	0.854248i	$0.325982\pi$
$109$	−2.72302	+	15.4430i	−0.260818	+	1.47917i	−0.780684	+	0.624925i	$0.785129\pi$
$110$	6.44833	+	19.3921i	0.614825	+	1.84896i
$111$		0			0
$112$	−6.96755	+	8.30360i	−0.658371	+	0.784616i
$113$		−	6.58139i		−	0.619125i	−0.950879	−	0.309562i	$-0.899817\pi$
$113$		−	6.58139i		−	0.619125i	0.950879	−	0.309562i	$-0.100183\pi$
$114$		0			0
$115$	11.3491	−	1.67451i	1.05831	−	0.156149i
$116$	−1.44542	−	1.21285i	−0.134204	−	0.112610i
$117$		0			0
$118$	15.7510	−	2.77733i	1.45000	−	0.255674i
$119$	−0.304565	+	1.72728i	−0.0279195	+	0.158339i
$120$		0			0
$121$	−10.4318	−	18.0684i	−0.948343	−	1.64258i
$122$	2.93897	+	1.69682i	0.266082	+	0.153623i
$123$		0			0
$124$	−3.85766	+	3.23696i	−0.346428	+	0.290688i
$125$	−11.1408	−	0.939503i	−0.996463	−	0.0840317i
$126$		0			0
$127$	−0.456461	+	1.25412i	−0.0405044	+	0.111285i	−0.958296	−	0.285778i	$-0.907748\pi$
$127$	−0.456461	+	1.25412i	−0.0405044	+	0.111285i	0.917792	+	0.397062i	$0.129970\pi$
$128$	13.4075	+	2.36411i	1.18507	+	0.208960i
$129$		0			0
$130$	8.09213	+	14.9703i	0.709727	+	1.31298i
$131$	−10.5552	−	8.85684i	−0.922210	−	0.773826i	0.0521924	−	0.998637i	$-0.483379\pi$
$131$	−10.5552	−	8.85684i	−0.922210	−	0.773826i	−0.974402	+	0.224811i	$0.927824\pi$
$132$		0			0
$133$	−1.20475	+	9.65376i	−0.104465	+	0.837087i
$134$	5.25892			0.454302
$135$		0			0
$136$	1.64827	−	0.599922i	0.141338	−	0.0514429i
$137$	11.5639	−	2.03902i	0.987969	−	0.174206i	0.343762	−	0.939057i	$-0.388299\pi$
$137$	11.5639	−	2.03902i	0.987969	−	0.174206i	0.644207	+	0.764851i	$0.277187\pi$
$138$		0			0
$139$	−8.77809	−	3.19496i	−0.744548	−	0.270993i	−0.0582382	−	0.998303i	$-0.518548\pi$
$139$	−8.77809	−	3.19496i	−0.744548	−	0.270993i	−0.686310	+	0.727309i	$0.740771\pi$
$140$	−1.92598	−	2.43058i	−0.162775	−	0.205421i
$141$		0			0
$142$	7.46925	+	8.90151i	0.626806	+	0.746998i
$143$	−17.0553	−	20.3257i	−1.42623	−	1.69972i
$144$		0			0
$145$	−5.32168	+	4.21689i	−0.441942	+	0.350194i
$146$	−23.0686	−	8.39629i	−1.90917	−	0.694882i
$147$		0			0
$148$	0.602854	−	0.106299i	0.0495543	−	0.00873776i
$149$	−16.9364	+	6.16435i	−1.38748	+	0.505003i	−0.924439	−	0.381331i	$-0.875466\pi$
$149$	−16.9364	+	6.16435i	−1.38748	+	0.505003i	−0.463046	+	0.886334i	$0.653244\pi$
$150$		0			0
$151$	−13.0159			−1.05922			−0.529611	−	0.848241i	$-0.677662\pi$
$151$	−13.0159			−1.05922			−0.529611	+	0.848241i	$0.677662\pi$
$152$	8.96345	−	3.78382i	0.727032	−	0.306908i
$153$		0			0
$154$	15.6258	+	13.1116i	1.25916	+	1.05656i
$155$	8.61711	+	15.9415i	0.692143	+	1.28045i
$156$		0			0
$157$	10.3475	+	1.82454i	0.825821	+	0.145614i	0.570558	−	0.821257i	$-0.306727\pi$
$157$	10.3475	+	1.82454i	0.825821	+	0.145614i	0.255263	+	0.966872i	$0.417838\pi$
$158$	0.741880	−	2.03830i	0.0590208	−	0.162158i
$159$		0			0
$160$	−2.79883	+	7.06658i	−0.221267	+	0.558662i
$161$	8.77165	−	7.36029i	0.691303	−	0.580072i
$162$		0			0
$163$	−3.13838	−	1.81195i	−0.245817	−	0.141923i	0.372030	−	0.928221i	$-0.378662\pi$
$163$	−3.13838	−	1.81195i	−0.245817	−	0.141923i	−0.617847	+	0.786298i	$0.711995\pi$
$164$	−0.440558	−	0.763068i	−0.0344018	−	0.0595856i
$165$		0			0
$166$	2.11577	−	11.9991i	0.164216	−	0.931313i
$167$	−10.4783	+	1.84761i	−0.810835	+	0.142972i	−0.563669	−	0.826001i	$-0.690611\pi$
$167$	−10.4783	+	1.84761i	−0.810835	+	0.142972i	−0.247166	+	0.968973i	$0.579499\pi$
$168$		0			0
$169$	−6.96691	−	5.84593i	−0.535916	−	0.449687i
$170$	0.415276	+	2.81455i	0.0318502	+	0.215866i
$171$		0			0
$172$			0.945588i			0.0721004i
$173$	−12.4770	+	14.8695i	−0.948611	+	1.13051i	0.0427156	+	0.999087i	$0.486399\pi$
$173$	−12.4770	+	14.8695i	−0.948611	+	1.13051i	−0.991326	+	0.131423i	$0.958045\pi$
$174$		0			0
$175$	−9.96202	+	5.02922i	−0.753058	+	0.380173i
$176$	4.76052	−	26.9982i	0.358838	−	2.03507i
$177$		0			0
$178$	−4.77152	+	2.75484i	−0.357640	+	0.206484i
$179$	−1.03526	+	1.79312i	−0.0773789	+	0.134024i	−0.902118	−	0.431489i	$-0.857988\pi$
$179$	−1.03526	+	1.79312i	−0.0773789	+	0.134024i	0.824739	+	0.565513i	$0.191322\pi$
$180$		0			0
$181$	16.5714	−	13.9051i	1.23174	−	1.03356i	0.233619	−	0.972328i	$-0.424943\pi$
$181$	16.5714	−	13.9051i	1.23174	−	1.03356i	0.998124	−	0.0612273i	$-0.0195014\pi$
$182$	14.7101	+	8.49287i	1.09038	+	0.629533i
$183$		0			0
$184$	−10.7608	−	3.91662i	−0.793299	−	0.288737i
$185$	0.0617676	−	2.20198i	0.00454125	−	0.161892i
$186$		0			0
$187$	−1.51717	−	4.16839i	−0.110946	−	0.304823i
$188$	0.383721	−	0.457300i	0.0279857	−	0.0333521i
$189$		0			0
$190$	3.08669	+	15.4759i	0.223932	+	1.12274i
$191$	22.4061			1.62125			0.810626	−	0.585565i	$-0.199127\pi$
$191$	22.4061			1.62125			0.810626	+	0.585565i	$0.199127\pi$
$192$		0			0
$193$	6.70316	+	18.4168i	0.482504	+	1.32567i	0.907339	+	0.420399i	$0.138110\pi$
$193$	6.70316	+	18.4168i	0.482504	+	1.32567i	−0.424835	+	0.905271i	$0.639668\pi$
$194$	3.58747	+	20.3455i	0.257565	+	1.46073i
$195$		0			0
$196$	1.17869	+	0.429009i	0.0841923	+	0.0306435i
$197$	−13.3885	+	7.72984i	−0.953890	+	0.550729i	−0.894287	−	0.447494i	$-0.852317\pi$
$197$	−13.3885	+	7.72984i	−0.953890	+	0.550729i	−0.0596028	+	0.998222i	$0.518983\pi$
$198$		0			0
$199$	1.05175	−	0.882524i	0.0745566	−	0.0625604i	−0.604748	−	0.796417i	$-0.706726\pi$
$199$	1.05175	−	0.882524i	0.0745566	−	0.0625604i	0.679304	+	0.733857i	$0.262282\pi$
$200$	9.33714	+	6.11321i	0.660235	+	0.432269i
$201$		0			0
$202$	7.81421	−	4.51154i	0.549806	−	0.317431i
$203$	−2.31795	+	6.36852i	−0.162688	+	0.446982i
$204$		0			0
$205$	−3.00872	+	1.00047i	−0.210138	+	0.0698761i
$206$	5.03239	−	1.83164i	0.350623	−	0.127617i
$207$		0			0
$208$		−	22.8287i		−	1.58288i
$209$	−9.56906	−	22.6681i	−0.661905	−	1.56798i
$210$		0			0
$211$	7.33250	+	6.15270i	0.504790	+	0.423569i	0.859291	−	0.511486i	$-0.170905\pi$
$211$	7.33250	+	6.15270i	0.504790	+	0.423569i	−0.354501	+	0.935056i	$0.615349\pi$
$212$	−0.937505	−	2.57577i	−0.0643881	−	0.176905i
$213$		0			0
$214$	1.87601	−	10.6394i	0.128241	−	0.727293i
$215$	3.33313	+	0.684604i	0.227318	+	0.0466896i
$216$		0			0
$217$	15.6644	+	9.04385i	1.06337	+	0.613936i
$218$	16.3198	+	19.4491i	1.10531	+	1.31726i
$219$		0			0
$220$	7.29210	+	2.88814i	0.491633	+	0.194719i
$221$	−1.84692	−	3.19896i	−0.124237	−	0.215186i
$222$		0			0
$223$	−6.43818	−	1.13522i	−0.431132	−	0.0760203i	−0.0461291	−	0.998935i	$-0.514689\pi$
$223$	−6.43818	−	1.13522i	−0.431132	−	0.0760203i	−0.385003	+	0.922915i	$0.625800\pi$
$224$	1.31738	+	7.47124i	0.0880213	+	0.499194i
$225$		0			0
$226$	−8.16276	−	6.84937i	−0.542979	−	0.455613i
$227$		−	8.88867i		−	0.589962i	−0.955503	−	0.294981i	$-0.904687\pi$
$227$		−	8.88867i		−	0.589962i	0.955503	−	0.294981i	$-0.0953133\pi$
$228$		0			0
$229$	7.22494			0.477438			0.238719	−	0.971089i	$-0.423273\pi$
$229$	7.22494			0.477438			0.238719	+	0.971089i	$0.423273\pi$
$230$	9.73432	−	15.8187i	0.641862	−	1.04306i
$231$		0			0
$232$	6.67477	−	1.17694i	0.438220	−	0.0772701i
$233$	24.5985	+	4.33738i	1.61150	+	0.284151i	0.905592	−	0.424151i	$-0.139427\pi$
$233$	24.5985	+	4.33738i	1.61150	+	0.284151i	0.705910	+	0.708302i	$0.250538\pi$
$234$		0			0
$235$	−1.33414	−	1.68367i	−0.0870295	−	0.109831i
$236$	3.06920	−	5.31600i	0.199788	−	0.346042i
$237$		0			0
$238$	1.82534	+	2.17535i	0.118319	+	0.141007i
$239$	−8.40936	+	14.5654i	−0.543956	+	0.942160i	0.454715	+	0.890637i	$0.349741\pi$
$239$	−8.40936	+	14.5654i	−0.543956	+	0.942160i	−0.998672	+	0.0515232i	$0.983592\pi$
$240$		0			0
$241$	10.1922	+	3.70965i	0.656536	+	0.238959i	0.648740	−	0.761010i	$-0.275296\pi$
$241$	10.1922	+	3.70965i	0.656536	+	0.238959i	0.00779570	+	0.999970i	$0.497519\pi$
$242$	−33.2664	−	5.86576i	−2.13844	−	0.377065i
$243$		0			0
$244$	1.22390	−	0.445465i	0.0783524	−	0.0285179i
$245$	2.36560	−	3.84420i	0.151132	−	0.245597i
$246$		0			0
$247$	−11.1250	−	17.2056i	−0.707869	−	1.09476i
$248$		−	18.0891i		−	1.14866i
$249$		0			0
$250$	−12.7597	+	12.8399i	−0.806993	+	0.812069i
$251$	−1.10625	−	6.27388i	−0.0698262	−	0.396004i	−0.999611	−	0.0278997i	$-0.991118\pi$
$251$	−1.10625	−	6.27388i	−0.0698262	−	0.396004i	0.929785	−	0.368104i	$-0.119993\pi$
$252$		0			0
$253$	−9.90491	+	27.2135i	−0.622717	+	1.71090i
$254$	1.08041	+	1.87132i	0.0677909	+	0.117417i
$255$		0			0
$256$	10.4357	−	8.75656i	0.652229	−	0.547285i
$257$	8.77180	+	10.4538i	0.547170	+	0.652092i	0.966779	−	0.255613i	$-0.0822774\pi$
$257$	8.77180	+	10.4538i	0.547170	+	0.652092i	−0.419609	+	0.907705i	$0.637833\pi$
$258$		0			0
$259$	−1.09937	−	1.90416i	−0.0683115	−	0.118319i
$260$	6.39761	+	1.31403i	0.396763	+	0.0814927i
$261$		0			0
$262$	−21.9699	+	3.87389i	−1.35731	+	0.239330i
$263$	3.49596	+	9.60508i	0.215570	+	0.592274i	0.999595	−	0.0284550i	$-0.00905874\pi$
$263$	3.49596	+	9.60508i	0.215570	+	0.592274i	−0.784025	+	0.620730i	$0.786837\pi$
$264$		0			0
$265$	−9.75816	+	1.43978i	−0.599439	+	0.0884450i
$266$	10.7195	+	11.5411i	0.657258	+	0.707628i
$267$		0			0
$268$	1.29736	−	1.54613i	0.0792490	−	0.0944452i
$269$	13.5785	−	4.94217i	0.827895	−	0.301329i	0.106900	−	0.994270i	$-0.465907\pi$
$269$	13.5785	−	4.94217i	0.827895	−	0.301329i	0.720995	+	0.692941i	$0.243685\pi$
$270$		0			0
$271$	−2.81404	+	15.9592i	−0.170941	+	0.969453i	0.771785	+	0.635884i	$0.219364\pi$
$271$	−2.81404	+	15.9592i	−0.170941	+	0.969453i	−0.942725	+	0.333570i	$0.891747\pi$
$272$	1.30534	−	3.58639i	0.0791479	−	0.217457i
$273$		0			0
$274$	9.50578	−	16.4645i	0.574265	−	0.994657i
$275$	15.4600	−	23.6131i	0.932271	−	1.42392i
$276$		0			0
$277$	24.7634	+	14.2971i	1.48789	+	0.859032i	0.999904	−	0.0138211i	$-0.00439952\pi$
$277$	24.7634	+	14.2971i	1.48789	+	0.859032i	0.487983	+	0.872853i	$0.337733\pi$
$278$	−13.0982	+	7.56223i	−0.785576	+	0.453552i
$279$		0			0
$280$	11.1352	+	0.312353i	0.665455	+	0.0186667i
$281$	−1.24639	−	7.06866i	−0.0743537	−	0.421681i	−0.999150	−	0.0412185i	$-0.986876\pi$
$281$	−1.24639	−	7.06866i	−0.0743537	−	0.421681i	0.924796	−	0.380462i	$-0.124235\pi$
$282$		0			0
$283$	6.66290	−	7.94053i	0.396068	−	0.472016i	−0.530749	−	0.847529i	$-0.678089\pi$
$283$	6.66290	−	7.94053i	0.396068	−	0.472016i	0.926817	+	0.375514i	$0.122534\pi$
$284$	4.45970			0.264635
$285$		0			0
$286$	−42.9592			−2.54023
$287$	−2.03429	+	2.42438i	−0.120080	+	0.143106i
$288$		0			0
$289$	2.84478	+	16.1336i	0.167340	+	0.949033i
$290$	−0.308251	+	10.9890i	−0.0181012	+	0.645294i
$291$		0			0
$292$	−8.15949	+	4.71088i	−0.477498	+	0.275684i
$293$	−7.87266	−	4.54528i	−0.459926	−	0.265538i	0.252087	−	0.967704i	$-0.418883\pi$
$293$	−7.87266	−	4.54528i	−0.459926	−	0.265538i	−0.712013	+	0.702166i	$0.752216\pi$
$294$		0			0
$295$	−16.5164	−	14.6675i	−0.961624	−	0.853973i
$296$	−1.09945	+	1.90431i	−0.0639044	+	0.110686i
$297$		0			0
$298$	−9.98051	+	27.4212i	−0.578156	+	1.58847i
$299$	−4.18761	+	23.7491i	−0.242175	+	1.37345i
$300$		0			0
$301$	3.19155	−	1.16163i	0.183958	−	0.0669551i
$302$	−13.5459	+	16.1434i	−0.779480	+	0.928948i
$303$		0			0
$304$	6.22951	−	20.2323i	0.357287	−	1.16040i
$305$	−0.684125	−	4.63669i	−0.0391729	−	0.265496i
$306$		0			0
$307$	5.01541	+	13.7797i	0.286245	+	0.786450i	0.996584	+	0.0825907i	$0.0263194\pi$
$307$	5.01541	+	13.7797i	0.286245	+	0.786450i	−0.710339	+	0.703860i	$0.751458\pi$
$308$	7.70967	−	1.35942i	0.439299	−	0.0774603i
$309$		0			0
$310$	28.7399	+	5.90301i	1.63232	+	0.335268i
$311$	−15.7905	−	27.3500i	−0.895400	−	1.55088i	−0.833309	−	0.552807i	$-0.813557\pi$
$311$	−15.7905	−	27.3500i	−0.895400	−	1.55088i	−0.0620906	−	0.998071i	$-0.519777\pi$
$312$		0			0
$313$	5.77911	+	6.88727i	0.326654	+	0.389292i	0.904230	−	0.427046i	$-0.140446\pi$
$313$	5.77911	+	6.88727i	0.326654	+	0.389292i	−0.577576	+	0.816337i	$0.696001\pi$
$314$	13.0318	−	10.9350i	0.735426	−	0.617095i
$315$		0			0
$316$	−0.416244	−	0.720957i	−0.0234156	−	0.0405570i
$317$	3.56399	−	9.79199i	0.200174	−	0.549973i	−0.798470	−	0.602035i	$-0.794357\pi$
$317$	3.56399	−	9.79199i	0.200174	−	0.549973i	0.998644	+	0.0520614i	$0.0165791\pi$
$318$		0			0
$319$	−2.97642	−	16.8801i	−0.166648	−	0.945106i
$320$	−4.47636	−	8.28120i	−0.250236	−	0.462933i
$321$		0			0
$322$		−	18.5393i		−	1.03315i
$323$	−0.763934	−	3.33913i	−0.0425064	−	0.185794i
$324$		0			0
$325$	9.26372	−	21.5998i	0.513859	−	1.19814i
$326$	−5.51349	+	2.00675i	−0.305364	+	0.111143i
$327$		0			0
$328$	3.11695	+	0.549603i	0.172105	+	0.0303467i
$329$	−2.01487	−	0.733352i	−0.111083	−	0.0404310i
$330$		0			0
$331$	2.01528	−	3.49056i	0.110770	−	0.191859i	−0.805311	−	0.592852i	$-0.798002\pi$
$331$	2.01528	−	3.49056i	0.110770	−	0.191859i	0.916081	+	0.400994i	$0.131335\pi$
$332$	−3.00582	−	3.58219i	−0.164966	−	0.196598i
$333$		0			0
$334$	−8.61341	+	14.9189i	−0.471305	+	0.816324i
$335$	−4.51072	−	5.69250i	−0.246447	−	0.311015i
$336$		0			0
$337$	−24.4051	−	4.30328i	−1.32943	−	0.234414i	−0.536590	−	0.843843i	$-0.680288\pi$
$337$	−24.4051	−	4.30328i	−1.32943	−	0.234414i	−0.792841	+	0.609429i	$0.791399\pi$
$338$	−14.5012	+	2.55695i	−0.788760	+	0.139080i
$339$		0			0
$340$	0.929932	+	0.572250i	0.0504326	+	0.0310346i
$341$	−45.7462			−2.47730
$342$		0			0
$343$		−	20.1287i		−	1.08685i
$344$	−2.60197	−	2.18331i	−0.140289	−	0.117716i
$345$		0			0
$346$	5.45732	+	30.9500i	0.293387	+	1.66388i
$347$	28.1891	+	4.97049i	1.51327	+	0.266830i	0.867783	−	0.496943i	$-0.165544\pi$
$347$	28.1891	+	4.97049i	1.51327	+	0.266830i	0.645485	+	0.763773i	$0.276655\pi$
$348$		0			0
$349$	5.11084	+	8.85223i	0.273577	+	0.473849i	0.969775	−	0.244001i	$-0.0784599\pi$
$349$	5.11084	+	8.85223i	0.273577	+	0.473849i	−0.696198	+	0.717850i	$0.745127\pi$
$350$	−4.13002	+	17.5897i	−0.220759	+	0.940208i
$351$		0			0
$352$	−12.3333	−	14.6983i	−0.657369	−	0.783422i
$353$	15.4082	+	8.89593i	0.820096	+	0.473483i	0.850450	−	0.526057i	$-0.176330\pi$
$353$	15.4082	+	8.89593i	0.820096	+	0.473483i	−0.0303537	+	0.999539i	$0.509663\pi$
$354$		0			0
$355$	3.22882	−	15.7201i	0.171368	−	0.834338i
$356$	−0.367192	+	2.08245i	−0.0194611	+	0.110369i
$357$		0			0
$358$	1.14656	+	3.15014i	0.0605975	+	0.166490i
$359$	−0.659251	−	0.553177i	−0.0347939	−	0.0291956i	0.625225	−	0.780445i	$-0.285007\pi$
$359$	−0.659251	−	0.553177i	−0.0347939	−	0.0291956i	−0.660019	+	0.751249i	$0.729452\pi$
$360$		0			0
$361$	−5.16469	−	18.2846i	−0.271826	−	0.962346i
$362$		−	35.0244i		−	1.84084i
$363$		0			0
$364$	6.12586	−	2.22963i	0.321082	−	0.116864i
$365$	10.6981	+	32.1723i	0.559962	+	1.68397i
$366$		0			0
$367$	7.28874	−	20.0256i	0.380469	−	1.04533i	−0.590690	−	0.806899i	$-0.701144\pi$
$367$	7.28874	−	20.0256i	0.380469	−	1.04533i	0.971159	−	0.238432i	$-0.0766334\pi$
$368$	−21.5784	+	12.4583i	−1.12485	+	0.649434i
$369$		0			0
$370$	−2.66678	−	2.36825i	−0.138639	−	0.123119i
$371$	−7.54204	+	6.32852i	−0.391563	+	0.328561i
$372$		0			0
$373$	12.2737	−	7.08623i	0.635509	−	0.366911i	−0.147374	−	0.989081i	$-0.547082\pi$
$373$	12.2737	−	7.08623i	0.635509	−	0.366911i	0.782882	+	0.622170i	$0.213749\pi$
$374$	−6.74891	−	2.45640i	−0.348978	−	0.127018i
$375$		0			0
$376$	0.372360	+	2.11176i	0.0192030	+	0.108906i
$377$	−4.88171	−	13.4124i	−0.251421	−	0.690774i
$378$		0			0
$379$	3.54496			0.182092			0.0910462	−	0.995847i	$-0.470979\pi$
$379$	3.54496			0.182092			0.0910462	+	0.995847i	$0.470979\pi$
$380$	5.31143	+	2.91037i	0.272471	+	0.149299i
$381$		0			0
$382$	23.3185	−	27.7899i	1.19308	−	1.42185i
$383$	−2.63645	−	7.24358i	−0.134716	−	0.370130i	0.853931	−	0.520387i	$-0.174212\pi$
$383$	−2.63645	−	7.24358i	−0.134716	−	0.370130i	−0.988647	+	0.150257i	$0.951990\pi$
$384$		0			0
$385$	0.789923	−	28.1603i	0.0402582	−	1.43518i
$386$	29.8181	+	10.8529i	1.51770	+	0.552398i
$387$		0			0
$388$	6.86665	+	3.96447i	0.348602	+	0.201265i
$389$	1.37878	−	1.15693i	0.0699070	−	0.0586589i	−0.607165	−	0.794576i	$-0.707693\pi$
$389$	1.37878	−	1.15693i	0.0699070	−	0.0586589i	0.677072	+	0.735917i	$0.263249\pi$
$390$		0			0
$391$	−2.01584	+	3.49155i	−0.101946	+	0.176575i
$392$	−3.90203	+	2.25284i	−0.197082	+	0.113786i
$393$		0			0
$394$	−4.34647	+	24.6500i	−0.218972	+	1.24185i
$395$	−2.84268	+	0.945260i	−0.143031	+	0.0475612i
$396$		0			0
$397$	−11.3616	+	13.5403i	−0.570224	+	0.679567i	−0.971677	−	0.236313i	$-0.924061\pi$
$397$	−11.3616	+	13.5403i	−0.570224	+	0.679567i	0.401453	+	0.915880i	$0.368505\pi$
$398$		−	2.22292i		−	0.111425i
$399$		0			0
$400$	23.2485	−	7.01313i	1.16243	−	0.350657i
$401$	20.7714	+	17.4293i	1.03727	+	0.870375i	0.991698	−	0.128586i	$-0.0410437\pi$
$401$	20.7714	+	17.4293i	1.03727	+	0.870375i	0.0455746	+	0.998961i	$0.485488\pi$
$402$		0			0
$403$	−37.5148	+	6.61488i	−1.86875	+	0.329510i
$404$	0.601342	−	3.41038i	0.0299179	−	0.169673i
$405$		0			0
$406$	5.48641	+	9.50273i	0.272286	+	0.471613i
$407$	4.81588	+	2.78045i	0.238715	+	0.137822i
$408$		0			0
$409$	−25.9468	+	21.7720i	−1.28299	+	1.07655i	−0.290162	+	0.956977i	$0.593709\pi$
$409$	−25.9468	+	21.7720i	−1.28299	+	1.07655i	−0.992825	+	0.119577i	$0.961846\pi$
$410$	−1.89037	+	4.77287i	−0.0933585	+	0.235715i
$411$		0			0
$412$	0.702970	−	1.93140i	0.0346329	−	0.0951530i
$413$	−21.7130	−	3.82858i	−1.06843	−	0.188392i
$414$		0			0
$415$	−14.8032	+	8.00178i	−0.726659	+	0.392792i
$416$	−12.2395	−	10.2702i	−0.600091	−	0.503536i
$417$		0			0
$418$	−38.0734	−	11.7227i	−1.86223	−	0.573378i
$419$	−23.2338			−1.13505			−0.567524	−	0.823357i	$-0.692099\pi$
$419$	−23.2338			−1.13505			−0.567524	+	0.823357i	$0.692099\pi$
$420$		0			0
$421$	−18.1808	+	6.61727i	−0.886077	+	0.322506i	−0.744660	−	0.667444i	$-0.767388\pi$
$421$	−18.1808	+	6.61727i	−0.886077	+	0.322506i	−0.141418	+	0.989950i	$0.545166\pi$
$422$	15.2621	−	2.69113i	0.742949	−	0.131002i
$423$		0			0
$424$	9.25238	+	3.36759i	0.449335	+	0.163545i
$425$	2.69041	−	2.86363i	0.130504	−	0.138907i
$426$		0			0
$427$	−3.00706	−	3.58367i	−0.145522	−	0.173426i
$428$	−2.66520	−	3.17626i	−0.128827	−	0.153530i
$429$		0			0
$430$	4.31795	−	3.42153i	0.208230	−	0.165001i
$431$	−12.2685	−	4.46538i	−0.590955	−	0.215090i	0.0291947	−	0.999574i	$-0.490706\pi$
$431$	−12.2685	−	4.46538i	−0.590955	−	0.215090i	−0.620149	+	0.784484i	$0.712928\pi$
$432$		0			0
$433$	5.74031	−	1.01217i	0.275862	−	0.0486418i	−0.0340058	−	0.999422i	$-0.510826\pi$
$433$	5.74031	−	1.01217i	0.275862	−	0.0486418i	0.309867	+	0.950780i	$0.399715\pi$
$434$	27.5191	−	10.0161i	1.32096	−	0.480790i
$435$		0			0
$436$	9.74413			0.466659
$437$	−10.1920	+	19.9054i	−0.487550	+	0.952203i
$438$		0			0
$439$	4.97166	+	4.17172i	0.237284	+	0.199105i	0.753674	−	0.657249i	$-0.228280\pi$
$439$	4.97166	+	4.17172i	0.237284	+	0.199105i	−0.516390	+	0.856354i	$0.672724\pi$
$440$	−24.7843	+	13.3970i	−1.18155	+	0.638679i
$441$		0			0
$442$	−5.88973	−	1.03852i	−0.280146	−	0.0493973i
$443$	−3.14771	+	8.64826i	−0.149552	+	0.410891i	−0.991735	−	0.128300i	$-0.959048\pi$
$443$	−3.14771	+	8.64826i	−0.149552	+	0.410891i	0.842183	+	0.539191i	$0.181270\pi$
$444$		0			0
$445$	7.07463	+	2.80201i	0.335369	+	0.132828i
$446$	−8.10832	+	6.80369i	−0.383940	+	0.322164i
$447$		0			0
$448$	−8.13724	−	4.69804i	−0.384449	−	0.221961i
$449$	8.73231	+	15.1248i	0.412103	+	0.713783i	0.995120	−	0.0986770i	$-0.0314611\pi$
$449$	8.73231	+	15.1248i	0.412103	+	0.713783i	−0.583017	+	0.812460i	$0.698128\pi$
$450$		0			0
$451$	1.38991	−	7.88259i	0.0654485	−	0.371177i
$452$	−4.02746	+	0.710150i	−0.189436	+	0.0334026i
$453$		0			0
$454$	−11.0244	−	9.25060i	−0.517402	−	0.434152i
$455$	−3.42417	−	23.2074i	−0.160528	−	1.08798i
$456$		0			0
$457$		−	0.381827i		−	0.0178611i	−0.999960	−	0.00893055i	$-0.997157\pi$
$457$		−	0.381827i		−	0.0178611i	0.999960	−	0.00893055i	$-0.00284272\pi$
$458$	7.51913	−	8.96095i	0.351346	−	0.418718i
$459$		0			0
$460$	−2.24931	−	6.76434i	−0.104875	−	0.315389i
$461$	−1.47897	+	8.38766i	−0.0688826	+	0.390652i	0.930802	+	0.365525i	$0.119110\pi$
$461$	−1.47897	+	8.38766i	−0.0688826	+	0.390652i	−0.999684	+	0.0251278i	$0.992001\pi$
$462$		0			0
$463$	−32.0583	+	18.5089i	−1.48988	+	0.860181i	−0.999933	−	0.0115723i	$-0.996316\pi$
$463$	−32.0583	+	18.5089i	−1.48988	+	0.860181i	−0.489945	+	0.871754i	$0.662983\pi$
$464$	7.37368	−	12.7716i	0.342314	−	0.592906i
$465$		0			0
$466$	30.9797	−	25.9950i	1.43511	−	1.20420i
$467$	−22.4636	−	12.9694i	−1.03949	−	0.600151i	−0.119803	−	0.992798i	$-0.538226\pi$
$467$	−22.4636	−	12.9694i	−1.03949	−	0.600151i	−0.919689	+	0.392647i	$0.871560\pi$
$468$		0			0
$469$	−6.81228	−	2.47947i	−0.314562	−	0.114491i
$470$	−3.47668	−	0.0975244i	−0.160367	−	0.00449847i
$471$		0			0
$472$	7.54140	+	20.7198i	0.347121	+	0.953707i
$473$	−5.52147	+	6.58023i	−0.253877	+	0.302559i
$474$		0			0
$475$	14.1043	−	16.6153i	0.647150	−	0.762362i
$476$	1.08986			0.0499539
$477$		0			0
$478$	9.31344	+	25.5885i	0.425987	+	1.17039i
$479$	2.05579	+	11.6589i	0.0939313	+	0.532711i	0.995070	+	0.0991792i	$0.0316217\pi$
$479$	2.05579	+	11.6589i	0.0939313	+	0.532711i	−0.901138	+	0.433532i	$0.857267\pi$
$480$		0			0
$481$	4.35139	+	1.58378i	0.198406	+	0.0722139i
$482$	15.2082	−	8.78045i	0.692714	−	0.399938i
$483$		0			0
$484$	−9.93126	+	8.33332i	−0.451421	+	0.378787i
$485$	18.9459	−	21.3342i	0.860289	−	0.968736i
$486$		0			0
$487$	25.4449	−	14.6906i	1.15302	−	0.665696i	0.203398	−	0.979096i	$-0.434801\pi$
$487$	25.4449	−	14.6906i	1.15302	−	0.665696i	0.949621	+	0.313400i	$0.101468\pi$
$488$	−1.60014	+	4.39636i	−0.0724351	+	0.199014i
$489$		0			0
$490$	−2.30597	−	6.93473i	−0.104173	−	0.313279i
$491$	−4.52780	+	1.64798i	−0.204337	+	0.0743725i	−0.442161	−	0.896936i	$-0.645788\pi$
$491$	−4.52780	+	1.64798i	−0.204337	+	0.0743725i	0.237824	+	0.971308i	$0.423566\pi$
$492$		0			0
$493$		−	2.38623i		−	0.107470i
$494$	−32.9177	−	4.10801i	−1.48104	−	0.184828i
$495$		0			0
$496$	−30.1508	−	25.2995i	−1.35381	−	1.13598i
$497$	−5.47862	−	15.0524i	−0.245750	−	0.675191i
$498$		0			0
$499$	−0.0326851	+	0.185366i	−0.00146318	+	0.00829813i	−0.985531	−	0.169498i	$-0.945786\pi$
$499$	−0.0326851	+	0.185366i	−0.00146318	+	0.00829813i	0.984067	+	0.177796i	$0.0568966\pi$
$500$	0.627196	+	6.91895i	0.0280491	+	0.309425i
$501$		0			0
$502$	−8.93266	−	5.15728i	−0.398684	−	0.230181i
$503$	1.46289	+	1.74340i	0.0652269	+	0.0777343i	0.797671	−	0.603093i	$-0.206065\pi$
$503$	1.46289	+	1.74340i	0.0652269	+	0.0777343i	−0.732444	+	0.680827i	$0.761621\pi$
$504$		0			0
$505$	−11.5860	−	4.58879i	−0.515569	−	0.204199i
$506$	23.4442	+	40.6065i	1.04222	+	1.80518i
$507$		0			0
$508$	0.816707	+	0.144007i	0.0362355	+	0.00638930i
$509$	−0.742270	−	4.20962i	−0.0329006	−	0.186588i	0.963928	−	0.266161i	$-0.0857554\pi$
$509$	−0.742270	−	4.20962i	−0.0329006	−	0.186588i	−0.996829	+	0.0795731i	$0.974644\pi$
$510$		0			0
$511$	25.9238	+	21.7527i	1.14680	+	0.962282i
$512$			5.17245i			0.228592i
$513$		0			0
$514$	22.0946			0.974552
$515$	−6.29908	−	3.87625i	−0.277571	−	0.170808i
$516$		0			0
$517$	5.34052	−	0.941679i	0.234876	−	0.0414150i
$518$	−3.50583	−	0.618172i	−0.154037	−	0.0271609i
$519$		0			0
$520$	−18.3875	+	14.5702i	−0.806347	+	0.638947i
$521$	16.1637	−	27.9963i	0.708143	−	1.22654i	−0.257402	−	0.966304i	$-0.582866\pi$
$521$	16.1637	−	27.9963i	0.708143	−	1.22654i	0.965545	−	0.260236i	$-0.0838002\pi$
$522$		0			0
$523$	−18.9726	−	22.6107i	−0.829613	−	0.988695i	−0.999995	−	0.00331656i	$-0.998944\pi$
$523$	−18.9726	−	22.6107i	−0.829613	−	0.988695i	0.170381	−	0.985378i	$-0.445500\pi$
$524$	−4.28099	+	7.41488i	−0.187016	+	0.323921i
$525$		0			0
$526$	15.5513	+	5.66021i	0.678069	+	0.246797i
$527$	−6.27183	−	1.10589i	−0.273205	−	0.0481735i
$528$		0			0
$529$	3.12081	−	1.13588i	0.135687	−	0.0493861i
$530$	−8.36977	+	13.6013i	−0.363559	+	0.590801i
$531$		0			0
$532$	6.03758	−	0.304422i	0.261762	−	0.0131984i
$533$		−	6.66521i		−	0.288702i
$534$		0			0
$535$	−13.1257	+	7.09502i	−0.567472	+	0.306744i
$536$	1.25895	+	7.13988i	0.0543785	+	0.308396i
$537$		0			0
$538$	8.00171	−	21.9845i	0.344978	−	0.947820i
$539$	5.69730	+	9.86802i	0.245400	+	0.425046i
$540$		0			0
$541$	14.4594	−	12.1328i	0.621656	−	0.521632i	−0.276667	−	0.960966i	$-0.589230\pi$
$541$	14.4594	−	12.1328i	0.621656	−	0.521632i	0.898324	+	0.439334i	$0.144786\pi$
$542$	16.8653	+	20.0992i	0.724425	+	0.863336i
$543$		0			0
$544$	−1.33558	−	2.31330i	−0.0572627	−	0.0991819i
$545$	7.05473	−	34.3473i	0.302192	−	1.47128i
$546$		0			0
$547$	24.7374	−	4.36188i	1.05770	−	0.186500i	0.382362	−	0.924012i	$-0.375111\pi$
$547$	24.7374	−	4.36188i	1.05770	−	0.186500i	0.675334	+	0.737512i	$0.264000\pi$
$548$	−2.49555	−	6.85647i	−0.106605	−	0.292894i
$549$		0			0
$550$	−13.1974	−	43.7492i	−0.562738	−	1.86547i
$551$	−0.666523	−	13.2191i	−0.0283949	−	0.563153i
$552$		0			0
$553$	−1.92203	+	2.29058i	−0.0817328	+	0.0974054i
$554$	43.5042	−	15.8342i	1.84831	−	0.672731i
$555$		0			0
$556$	−1.00797	+	5.71647i	−0.0427473	+	0.242432i
$557$	9.63578	−	26.4741i	0.408281	−	1.12174i	−0.549812	−	0.835288i	$-0.685301\pi$
$557$	9.63578	−	26.4741i	0.408281	−	1.12174i	0.958094	−	0.286455i	$-0.0924770\pi$
$558$		0			0
$559$	−3.57646	+	6.19461i	−0.151268	+	0.262004i
$560$	16.0944	−	18.1232i	0.680113	−	0.765847i
$561$		0			0
$562$	−10.0643	−	5.81060i	−0.424535	−	0.245105i
$563$	17.6927	−	10.2149i	0.745656	−	0.430505i	−0.0784660	−	0.996917i	$-0.525002\pi$
$563$	17.6927	−	10.2149i	0.745656	−	0.430505i	0.824122	+	0.566412i	$0.191669\pi$
$564$		0			0
$565$	−0.412648	+	14.7106i	−0.0173602	+	0.618881i
$566$	−2.91428	−	16.5277i	−0.122496	−	0.694711i
$567$		0			0
$568$	−10.2972	+	12.2717i	−0.432061	+	0.514910i
$569$	−35.8386			−1.50243			−0.751217	−	0.660056i	$-0.770533\pi$
$569$	−35.8386			−1.50243			−0.751217	+	0.660056i	$0.770533\pi$
$570$		0			0
$571$	−2.82827			−0.118359			−0.0591797	−	0.998247i	$-0.518848\pi$
$571$	−2.82827			−0.118359			−0.0591797	+	0.998247i	$0.518848\pi$
$572$	−10.5979	+	12.6301i	−0.443121	+	0.528091i
$573$		0			0
$574$	0.889778	+	5.04618i	0.0371386	+	0.210624i
$575$	−25.4723	+	3.03127i	−1.06227	+	0.126413i
$576$		0			0
$577$	37.5103	−	21.6566i	1.56157	−	0.901575i	0.564476	−	0.825449i	$-0.309078\pi$
$577$	37.5103	−	21.6566i	1.56157	−	0.901575i	0.997098	−	0.0761261i	$-0.0242552\pi$
$578$	22.9707	+	13.2622i	0.955457	+	0.551633i
$579$		0			0
$580$	3.15474	+	2.80157i	0.130993	+	0.116329i
$581$	−8.39804	+	14.5458i	−0.348409	+	0.603463i
$582$		0			0
$583$	8.51645	−	23.3987i	0.352715	−	0.969077i
$584$	5.87690	−	33.3296i	0.243188	−	1.37919i
$585$		0			0
$586$	−13.8306	+	5.03394i	−0.571338	+	0.207950i
$587$	−15.7959	+	18.8249i	−0.651968	+	0.776985i	−0.986209	−	0.165502i	$-0.947075\pi$
$587$	−15.7959	+	18.8249i	−0.651968	+	0.776985i	0.334242	+	0.942487i	$0.391520\pi$
$588$		0			0
$589$	−35.0533	−	4.37452i	−1.44435	−	0.180249i
$590$	−35.3807	+	5.22029i	−1.45660	+	0.214916i
$591$		0			0
$592$	1.63639	+	4.49595i	0.0672553	+	0.184782i
$593$	0.308954	−	0.0544770i	0.0126872	−	0.00223710i	−0.167301	−	0.985906i	$-0.553505\pi$
$593$	0.308954	−	0.0544770i	0.0126872	−	0.00223710i	0.179988	+	0.983669i	$0.442394\pi$
$594$		0			0
$595$	0.789060	−	3.84169i	0.0323483	−	0.157494i
$596$	5.59974	+	9.69903i	0.229374	+	0.397288i
$597$		0			0
$598$	25.0974	+	29.9099i	1.02631	+	1.22311i
$599$	18.7653	−	15.7460i	0.766731	−	0.643364i	−0.173139	−	0.984897i	$-0.555391\pi$
$599$	18.7653	−	15.7460i	0.766731	−	0.643364i	0.939869	+	0.341534i	$0.110946\pi$
$600$		0			0
$601$	3.91522	+	6.78137i	0.159705	+	0.276618i	0.934762	−	0.355273i	$-0.115612\pi$
$601$	3.91522	+	6.78137i	0.159705	+	0.276618i	−0.775057	+	0.631891i	$0.782279\pi$
$602$	1.88076	−	5.16734i	0.0766539	−	0.210605i
$603$		0			0
$604$	1.40445	+	7.96506i	0.0571464	+	0.324094i
$605$	22.1841	+	41.0403i	0.901912	+	1.66852i
$606$		0			0
$607$			12.4142i			0.503876i	0.967743	+	0.251938i	$0.0810680\pi$
$607$			12.4142i			0.503876i	−0.967743	+	0.251938i	$0.918932\pi$
$608$	−8.04496	−	12.4421i	−0.326266	−	0.504592i
$609$		0			0
$610$	−6.46277	−	3.97698i	−0.261670	−	0.161023i
$611$	4.24341	−	1.54447i	0.171670	−	0.0624827i
$612$		0			0
$613$	1.04244	+	0.183811i	0.0421039	+	0.00742405i	0.194660	−	0.980871i	$-0.437640\pi$
$613$	1.04244	+	0.183811i	0.0421039	+	0.00742405i	−0.152557	+	0.988295i	$0.548751\pi$
$614$	22.3103	+	8.12030i	0.900372	+	0.327709i
$615$		0			0
$616$	−14.0605	+	24.3535i	−0.566513	+	0.981229i
$617$	18.3761	+	21.8998i	0.739794	+	0.881652i	0.996392	−	0.0848661i	$-0.0270462\pi$
$617$	18.3761	+	21.8998i	0.739794	+	0.881652i	−0.256598	+	0.966518i	$0.582602\pi$
$618$		0			0
$619$	4.70978	−	8.15758i	0.189302	−	0.327881i	−0.755716	−	0.654900i	$-0.772711\pi$
$619$	4.70978	−	8.15758i	0.189302	−	0.327881i	0.945018	+	0.327019i	$0.106044\pi$
$620$	8.82556	−	6.99335i	0.354443	−	0.280860i
$621$		0			0
$622$	−50.3552	−	8.87898i	−2.01906	−	0.356015i
$623$	7.47975	−	1.31888i	0.299670	−	0.0528399i
$624$		0			0
$625$	24.8429	+	2.79849i	0.993715	+	0.111939i
$626$	14.5566			0.581797
$627$		0			0
$628$		−	6.52899i		−	0.260535i
$629$	0.593045	+	0.497624i	0.0236462	+	0.0198416i
$630$		0			0
$631$	−6.88134	−	39.0260i	−0.273942	−	1.55360i	−0.742304	−	0.670064i	$-0.766267\pi$
$631$	−6.88134	−	39.0260i	−0.273942	−	1.55360i	0.468362	−	0.883537i	$-0.344844\pi$
$632$	2.94493	+	0.519271i	0.117143	+	0.0206555i
$633$		0			0
$634$	−8.43570	−	14.6111i	−0.335024	−	0.580279i
$635$	1.09891	−	2.77457i	0.0436089	−	0.110105i
$636$		0			0
$637$	6.09907	+	7.26858i	0.241654	+	0.287992i
$638$	−24.0337	−	13.8759i	−0.951503	−	0.549350i
$639$		0			0
$640$	−29.8201	−	6.12487i	−1.17874	−	0.242107i
$641$	−3.41320	+	19.3572i	−0.134813	+	0.764565i	0.840176	+	0.542314i	$0.182452\pi$
$641$	−3.41320	+	19.3572i	−0.134813	+	0.764565i	−0.974989	+	0.222251i	$0.928660\pi$
$642$		0			0
$643$	9.81994	+	26.9801i	0.387261	+	1.06399i	0.968229	+	0.250064i	$0.0804516\pi$
$643$	9.81994	+	26.9801i	0.387261	+	1.06399i	−0.580969	+	0.813926i	$0.697326\pi$
$644$	−5.45059	−	4.57359i	−0.214783	−	0.180225i
$645$		0			0
$646$	−4.93650	−	2.52760i	−0.194224	−	0.0994472i
$647$			17.4412i			0.685686i	0.939393	+	0.342843i	$0.111390\pi$
$647$			17.4412i			0.685686i	−0.939393	+	0.342843i	$0.888610\pi$
$648$		0			0
$649$	52.3993	−	19.0718i	2.05685	−	0.748633i
$650$	−17.1488	−	33.9689i	−0.672632	−	1.33237i
$651$		0			0
$652$	−0.770175	+	2.11604i	−0.0301624	+	0.0828704i
$653$	−26.2837	+	15.1749i	−1.02856	+	0.593839i	−0.916572	−	0.399871i	$-0.869055\pi$
$653$	−26.2837	+	15.1749i	−1.02856	+	0.593839i	−0.111988	+	0.993710i	$0.535722\pi$
$654$		0			0
$655$	23.0375	+	20.4585i	0.900149	+	0.799381i
$656$	5.27547	−	4.42665i	0.205973	−	0.172832i
$657$		0			0
$658$	−3.00647	+	1.73579i	−0.117204	+	0.0676680i
$659$	−6.14432	−	2.23635i	−0.239349	−	0.0871158i	0.219561	−	0.975599i	$-0.429538\pi$
$659$	−6.14432	−	2.23635i	−0.239349	−	0.0871158i	−0.458909	+	0.888483i	$0.651760\pi$
$660$		0			0
$661$	4.13276	+	23.4381i	0.160746	+	0.911635i	0.953343	+	0.301889i	$0.0976174\pi$
$661$	4.13276	+	23.4381i	0.160746	+	0.911635i	−0.792597	+	0.609746i	$0.791272\pi$
$662$	−2.23194	−	6.13220i	−0.0867467	−	0.238335i
$663$		0			0
$664$	16.7973			0.651863
$665$	3.29813	−	21.5024i	0.127896	−	0.833828i
$666$		0			0
$667$	−10.0137	+	11.9339i	−0.387734	+	0.462083i
$668$	2.26127	+	6.21280i	0.0874913	+	0.240380i
$669$		0			0
$670$	−11.7547	−	0.329731i	−0.454123	−	0.0127386i
$671$	11.1181	+	4.04667i	0.429211	+	0.156220i
$672$		0			0
$673$	43.2343	+	24.9614i	1.66656	+	0.962189i	0.969471	+	0.245206i	$0.0788555\pi$
$673$	43.2343	+	24.9614i	1.66656	+	0.962189i	0.697090	+	0.716984i	$0.254478\pi$
$674$	−30.7361	+	25.7906i	−1.18391	+	0.993418i
$675$		0			0
$676$	−2.82565	+	4.89417i	−0.108679	+	0.188237i
$677$	29.9494	−	17.2913i	1.15105	−	0.664558i	0.201906	−	0.979405i	$-0.435286\pi$
$677$	29.9494	−	17.2913i	1.15105	−	0.664558i	0.949143	+	0.314847i	$0.101953\pi$
$678$		0			0
$679$	4.94536	−	28.0465i	0.189786	−	1.07633i
$680$	−3.72181	+	1.23759i	−0.142725	+	0.0474595i
$681$		0			0
$682$	−47.6089	+	56.7381i	−1.82304	+	2.17261i
$683$		−	21.1277i		−	0.808429i	−0.914664	−	0.404214i	$-0.867545\pi$
$683$		−	21.1277i		−	0.808429i	0.914664	−	0.404214i	$-0.132455\pi$
$684$		0			0
$685$	−25.9753	+	3.83256i	−0.992466	+	0.146435i
$686$	−24.9652	−	20.9483i	−0.953174	−	0.799808i
$687$		0			0
$688$	−7.27827	+	1.28336i	−0.277482	+	0.0489275i
$689$	3.60059	−	20.4199i	0.137171	−	0.777938i
$690$		0			0
$691$	−13.9430	−	24.1500i	−0.530418	−	0.918711i	−0.999370	−	0.0354873i	$-0.988702\pi$
$691$	−13.9430	−	24.1500i	−0.530418	−	0.918711i	0.468952	−	0.883224i	$-0.344632\pi$
$692$	10.4457	+	6.03081i	0.397085	+	0.229257i
$693$		0			0
$694$	35.5017	−	29.7894i	1.34762	−	1.13079i
$695$	19.4204	+	7.69173i	0.736656	+	0.291764i
$696$		0			0
$697$	0.381116	−	1.04711i	0.0144358	−	0.0396620i
$698$	16.2982	+	2.87381i	0.616895	+	0.108775i
$699$		0			0
$700$	4.15254	+	5.55356i	0.156951	+	0.209905i
$701$	30.1319	+	25.2837i	1.13807	+	0.954952i	0.999374	−	0.0353834i	$-0.0112652\pi$
$701$	30.1319	+	25.2837i	1.13807	+	0.954952i	0.138694	+	0.990335i	$0.455710\pi$
$702$		0			0
$703$	3.42432	+	2.59106i	0.129151	+	0.0977237i
$704$	23.7639			0.895637
$705$		0			0
$706$	27.0690	−	9.85232i	1.01876	−	0.370797i
$707$	−12.2494	+	2.15990i	−0.460687	+	0.0812316i
$708$		0			0
$709$	4.02970	+	1.46669i	0.151339	+	0.0550828i	0.416579	−	0.909100i	$-0.363229\pi$
$709$	4.02970	+	1.46669i	0.151339	+	0.0550828i	−0.265240	+	0.964182i	$0.585451\pi$
$710$	−16.1371	−	20.3649i	−0.605613	−	0.764280i
$711$		0			0
$712$	−4.88243	−	5.81865i	−0.182977	−	0.218063i
$713$	26.7256	+	31.8503i	1.00088	+	1.19280i
$714$		0			0
$715$	36.8473	+	46.5010i	1.37801	+	1.73904i
$716$	1.20900	+	0.440041i	0.0451825	+	0.0164451i
$717$		0			0
$718$	−1.37219	+	0.241954i	−0.0512096	+	0.00902964i
$719$	3.69536	−	1.34500i	0.137814	−	0.0501600i	−0.272193	−	0.962243i	$-0.587749\pi$
$719$	3.69536	−	1.34500i	0.137814	−	0.0501600i	0.410006	+	0.912083i	$0.365527\pi$
$720$		0			0
$721$	−7.38242			−0.274936
$722$	−28.0530	−	12.6234i	−1.04402	−	0.469795i
$723$		0			0
$724$	−10.2973	−	8.64043i	−0.382695	−	0.321119i
$725$	12.1594	−	9.09188i	0.451587	−	0.337664i
$726$		0			0
$727$	−19.7527	−	3.48294i	−0.732587	−	0.129175i	−0.205104	−	0.978740i	$-0.565753\pi$
$727$	−19.7527	−	3.48294i	−0.732587	−	0.129175i	−0.527483	+	0.849565i	$0.676864\pi$
$728$	−8.00900	+	22.0046i	−0.296833	+	0.815543i
$729$		0			0
$730$	51.0363	+	20.2137i	1.88894	+	0.748142i
$731$	−0.916071	+	0.768675i	−0.0338821	+	0.0284305i
$732$		0			0
$733$	−0.178212	−	0.102891i	−0.00658241	−	0.00380036i	0.496705	−	0.867919i	$-0.334543\pi$
$733$	−0.178212	−	0.102891i	−0.00658241	−	0.00380036i	−0.503288	+	0.864119i	$0.667876\pi$
$734$	−17.2519	−	29.8811i	−0.636778	−	1.10293i
$735$		0			0
$736$	−3.02823	+	17.1739i	−0.111622	+	0.633039i
$737$	18.0563	−	3.18382i	0.665114	−	0.117278i
$738$		0			0
$739$	−24.9819	−	20.9623i	−0.918976	−	0.771112i	0.0548297	−	0.998496i	$-0.482538\pi$
$739$	−24.9819	−	20.9623i	−0.918976	−	0.771112i	−0.973805	+	0.227384i	$0.926983\pi$
$740$	−1.35416	+	0.199801i	−0.0497798	+	0.00734482i
$741$		0			0
$742$			15.9404i			0.585192i
$743$	19.0010	−	22.6445i	0.697078	−	0.830745i	−0.295114	−	0.955462i	$-0.595358\pi$
$743$	19.0010	−	22.6445i	0.697078	−	0.830745i	0.992192	+	0.124717i	$0.0398021\pi$
$744$		0			0
$745$	38.2426	−	12.7166i	1.40110	−	0.465900i
$746$	3.98457	−	22.5976i	0.145885	−	0.827357i
$747$		0			0
$748$	−2.38712	+	1.37821i	−0.0872819	+	0.0503922i
$749$	−7.44637	+	12.8975i	−0.272085	+	0.471264i
$750$		0			0
$751$	−28.3787	+	23.8126i	−1.03555	+	0.868932i	−0.991501	−	0.130097i	$-0.958471\pi$
$751$	−28.3787	+	23.8126i	−1.03555	+	0.868932i	−0.0440520	+	0.999029i	$0.514027\pi$
$752$	4.04067	+	2.33288i	0.147348	+	0.0850714i
$753$		0			0
$754$	−21.7156	−	7.90384i	−0.790836	−	0.287841i
$755$	29.0931	+	0.816089i	1.05880	+	0.0297005i
$756$		0			0
$757$	−10.4480	−	28.7057i	−0.379740	−	1.04333i	−0.971464	−	0.237187i	$-0.923775\pi$
$757$	−10.4480	−	28.7057i	−0.379740	−	1.04333i	0.591724	−	0.806141i	$-0.298447\pi$
$758$	3.68931	−	4.39674i	0.134002	−	0.159697i
$759$		0			0
$760$	−20.2722	+	7.89554i	−0.735351	+	0.286401i
$761$	46.0692			1.67001			0.835004	−	0.550244i	$-0.185465\pi$
$761$	46.0692			1.67001			0.835004	+	0.550244i	$0.185465\pi$
$762$		0			0
$763$	−11.9704	−	32.8883i	−0.433357	−	1.19064i
$764$	−2.41768	−	13.7114i	−0.0874687	−	0.496060i
$765$		0			0
$766$	−11.7279	−	4.26859i	−0.423745	−	0.154231i
$767$	40.2130	−	23.2170i	1.45201	−	0.838317i
$768$		0			0
$769$	−11.2761	+	9.46178i	−0.406627	+	0.341200i	−0.823048	−	0.567971i	$-0.807728\pi$
$769$	−11.2761	+	9.46178i	−0.406627	+	0.341200i	0.416422	+	0.909172i	$0.363284\pi$
$770$	−34.1045	−	30.2866i	−1.22904	−	1.09145i
$771$		0			0
$772$	10.5468	−	6.08920i	0.379588	−	0.219155i
$773$	3.03195	−	8.33022i	0.109052	−	0.299617i	−0.873148	−	0.487454i	$-0.837926\pi$
$773$	3.03195	−	8.33022i	0.109052	−	0.299617i	0.982200	+	0.187837i	$0.0601478\pi$
$774$		0			0
$775$	−18.2614	−	36.1726i	−0.655967	−	1.29936i
$776$	−26.7637	+	9.74119i	−0.960761	+	0.349688i
$777$		0			0
$778$		−	2.91412i		−	0.104476i
$779$	1.81881	−	5.90717i	0.0651656	−	0.211646i
$780$		0			0
$781$	31.0345	+	26.0410i	1.11050	+	0.931822i
$782$	2.23257	+	6.13393i	0.0798364	+	0.219349i
$783$		0			0
$784$	−1.70239	+	9.65474i	−0.0607997	+	0.344812i
$785$	−23.0142	−	4.72698i	−0.821413	−	0.168713i
$786$		0			0
$787$	−11.4182	−	6.59229i	−0.407014	−	0.234990i	0.282492	−	0.959270i	$-0.408839\pi$
$787$	−11.4182	−	6.59229i	−0.407014	−	0.234990i	−0.689506	+	0.724280i	$0.742172\pi$
$788$	6.17491	+	7.35897i	0.219972	+	0.262152i
$789$		0			0
$790$	−1.78604	+	4.50947i	−0.0635445	+	0.160440i
$791$	7.34451	+	12.7211i	0.261141	+	0.452309i
$792$		0			0
$793$	9.70274	+	1.71085i	0.344554	+	0.0607542i
$794$	4.96946	+	28.1832i	0.176360	+	1.00018i
$795$		0			0
$796$	−0.653544	−	0.548389i	−0.0231643	−	0.0194371i
$797$			38.1858i			1.35261i	0.736621	+	0.676306i	$0.236420\pi$
$797$			38.1858i			1.35261i	−0.736621	+	0.676306i	$0.763580\pi$
$798$		0			0
$799$	0.754954			0.0267084
$800$	6.69897	−	15.6197i	0.236844	−	0.552238i
$801$		0			0
$802$	43.2343	−	7.62337i	1.52666	−	0.269191i
$803$	−84.2886	−	14.8623i	−2.97448	−	0.524481i
$804$		0			0
$805$	−20.0678	+	15.9017i	−0.707296	+	0.560460i
$806$	−30.8381	+	53.4131i	−1.08622	+	1.88140i
$807$		0			0
$808$	7.99585	+	9.52908i	0.281293	+	0.335232i
$809$	−21.8833	+	37.9031i	−0.769377	+	1.33260i	0.168524	+	0.985698i	$0.446100\pi$
$809$	−21.8833	+	37.9031i	−0.769377	+	1.33260i	−0.937901	+	0.346903i	$0.887233\pi$
$810$		0			0
$811$	5.59328	+	2.03579i	0.196407	+	0.0714862i	0.438351	−	0.898804i	$-0.355563\pi$
$811$	5.59328	+	2.03579i	0.196407	+	0.0714862i	−0.241944	+	0.970290i	$0.577785\pi$
$812$	4.14731	+	0.731282i	0.145542	+	0.0256630i
$813$		0			0
$814$	8.46052	−	3.07938i	0.296541	−	0.107932i
$815$	6.90127	+	4.24682i	0.241741	+	0.148759i
$816$		0			0
$817$	−4.86010	+	4.51415i	−0.170033	+	0.157930i
$818$			54.8398i			1.91743i
$819$		0			0
$820$	0.936886	+	1.73322i	0.0327175	+	0.0605268i
$821$	1.38401	+	7.84911i	0.0483023	+	0.273936i	0.999388	−	0.0349926i	$-0.0111408\pi$
$821$	1.38401	+	7.84911i	0.0483023	+	0.273936i	−0.951085	+	0.308928i	$0.900030\pi$
$822$		0			0
$823$	9.64179	−	26.4906i	0.336092	−	0.923404i	−0.650400	−	0.759592i	$-0.725399\pi$
$823$	9.64179	−	26.4906i	0.336092	−	0.923404i	0.986492	−	0.163812i	$-0.0523791\pi$
$824$	3.69149	+	6.39384i	0.128599	+	0.222740i
$825$		0			0
$826$	−27.3456	+	22.9457i	−0.951475	+	0.798382i
$827$	−35.0380	−	41.7566i	−1.21839	−	1.45202i	−0.853600	−	0.520929i	$-0.825585\pi$
$827$	−35.0380	−	41.7566i	−1.21839	−	1.45202i	−0.364789	−	0.931090i	$-0.618859\pi$
$828$		0			0
$829$	4.20261	+	7.27913i	0.145963	+	0.252815i	0.929732	−	0.368238i	$-0.120039\pi$
$829$	4.20261	+	7.27913i	0.145963	+	0.252815i	−0.783769	+	0.621052i	$0.786705\pi$
$830$	−5.48148	+	26.6877i	−0.190265	+	0.926342i
$831$		0			0
$832$	19.4880	−	3.43625i	0.675623	−	0.119131i
$833$	0.542549	+	1.49064i	0.0187982	+	0.0516477i
$834$		0			0
$835$	23.5368	−	3.47277i	0.814525	−	0.120180i
$836$	−12.8391	+	8.30170i	−0.444050	+	0.287120i
$837$		0			0
$838$	−24.1799	+	28.8165i	−0.835280	+	0.995448i
$839$	−35.4409	+	12.8994i	−1.22356	+	0.445338i	−0.871386	−	0.490597i	$-0.836779\pi$
$839$	−35.4409	+	12.8994i	−1.22356	+	0.445338i	−0.352171	+	0.935936i	$0.614556\pi$
$840$		0			0
$841$	−3.43468	+	19.4790i	−0.118437	+	0.671690i
$842$	−10.7138	+	29.4360i	−0.369222	+	1.01443i
$843$		0			0
$844$	2.97393	−	5.15099i	0.102367	−	0.177304i
$845$	15.2058	+	13.5036i	0.523096	+	0.464537i
$846$		0			0
$847$	40.3268	+	23.2827i	1.38565	+	0.800003i
$848$	18.5536	−	10.7119i	0.637132	−	0.367848i
$849$		0			0
$850$	−0.751751	−	6.31709i	−0.0257848	−	0.216674i
$851$	−0.877648	−	4.97739i	−0.0300854	−	0.170623i
$852$		0			0
$853$	−26.5455	+	31.6357i	−0.908902	+	1.08319i	0.0873063	+	0.996182i	$0.472174\pi$
$853$	−26.5455	+	31.6357i	−0.908902	+	1.08319i	−0.996208	+	0.0870051i	$0.972270\pi$
$854$	−7.57426			−0.259186
$855$		0			0
$856$	14.8939			0.509062
$857$	2.20780	−	2.63115i	0.0754170	−	0.0898785i	−0.727017	−	0.686620i	$-0.759094\pi$
$857$	2.20780	−	2.63115i	0.0754170	−	0.0898785i	0.802434	+	0.596741i	$0.203538\pi$
$858$		0			0
$859$	5.26017	+	29.8319i	0.179475	+	1.01785i	0.932851	+	0.360262i	$0.117313\pi$
$859$	5.26017	+	29.8319i	0.179475	+	1.01785i	−0.753377	+	0.657589i	$0.771576\pi$
$860$	0.0592877	−	2.11357i	0.00202169	−	0.0720721i
$861$		0			0
$862$	−18.3064	+	10.5692i	−0.623519	+	0.359989i
$863$	20.6624	+	11.9295i	0.703358	+	0.406084i	0.808597	−	0.588363i	$-0.200227\pi$
$863$	20.6624	+	11.9295i	0.703358	+	0.406084i	−0.105239	+	0.994447i	$0.533561\pi$
$864$		0			0
$865$	28.8208	−	32.4539i	0.979937	−	1.10347i
$866$	4.71867	−	8.17297i	0.160347	−	0.277729i
$867$		0			0
$868$	3.84412	−	10.5616i	0.130478	−	0.358485i
$869$	1.31321	−	7.44757i	0.0445475	−	0.252642i
$870$		0			0
$871$	14.3470	−	5.22188i	0.486129	−	0.176936i
$872$	−22.4986	+	26.8128i	−0.761900	+	0.907997i
$873$		0			0
$874$	14.0812	+	33.3568i	0.476304	+	1.12831i
$875$	22.5823	−	10.6166i	0.763422	−	0.358908i
$876$		0			0
$877$	4.54055	+	12.4751i	0.153324	+	0.421253i	0.992445	−	0.122691i	$-0.0391525\pi$
$877$	4.54055	+	12.4751i	0.153324	+	0.421253i	−0.839121	+	0.543944i	$0.816930\pi$
$878$	10.3482	−	1.82466i	0.349234	−	0.0615794i
$879$		0			0
$880$	−12.3334	+	60.0477i	−0.415760	+	2.02421i
$881$	10.0999	+	17.4935i	0.340274	+	0.589371i	0.984483	−	0.175478i	$-0.0561470\pi$
$881$	10.0999	+	17.4935i	0.340274	+	0.589371i	−0.644210	+	0.764849i	$0.722814\pi$
$882$		0			0
$883$	37.4427	+	44.6225i	1.26005	+	1.50167i	0.781922	+	0.623376i	$0.214239\pi$
$883$	37.4427	+	44.6225i	1.26005	+	1.50167i	0.478126	+	0.878291i	$0.341316\pi$
$884$	−1.75831	+	1.47540i	−0.0591383	+	0.0496229i
$885$		0			0
$886$	7.45038	+	12.9044i	0.250300	+	0.433533i
$887$	−15.7612	+	43.3035i	−0.529208	+	1.45399i	0.330797	+	0.943702i	$0.392683\pi$
$887$	−15.7612	+	43.3035i	−0.529208	+	1.45399i	−0.860005	+	0.510286i	$0.829540\pi$
$888$		0			0
$889$	−0.517247	−	2.93345i	−0.0173479	−	0.0983849i
$890$	10.8380	−	5.85841i	0.363289	−	0.196374i
$891$		0			0
$892$			4.06232i			0.136016i
$893$	4.18226	−	0.210874i	0.139954	−	0.00705664i
$894$		0			0
$895$	2.42643	−	3.94305i	0.0811065	−	0.131802i
$896$	−28.5534	+	10.3926i	−0.953903	+	0.347192i
$897$		0			0
$898$	27.8468	+	4.91015i	0.929261	+	0.163854i
$899$	−23.1244	−	8.41660i	−0.771243	−	0.280709i
$900$		0			0
$901$	1.73326	−	3.00210i	0.0577434	−	0.100015i
$902$	−8.33011	−	9.92744i	−0.277362	−	0.330548i
$903$		0			0
$904$	7.34506	−	12.7220i	0.244293	−	0.423128i
$905$	−37.9121	+	30.0414i	−1.26024	+	0.998611i
$906$		0			0
$907$	−43.0236	−	7.58622i	−1.42857	−	0.251896i	−0.594743	−	0.803916i	$-0.702746\pi$
$907$	−43.0236	−	7.58622i	−1.42857	−	0.251896i	−0.833831	+	0.552020i	$0.813857\pi$
$908$	−5.43939	+	0.959112i	−0.180513	+	0.0318292i
$909$		0			0
$910$	−32.3473	−	19.9055i	−1.07230	−	0.659860i
$911$	30.7689			1.01942			0.509709	−	0.860347i	$-0.329753\pi$
$911$	30.7689			1.01942			0.509709	+	0.860347i	$0.329753\pi$
$912$		0			0
$913$		−	42.4795i		−	1.40587i
$914$	−0.473572	−	0.397374i	−0.0156644	−	0.0131440i
$915$		0			0
$916$	−0.779591	−	4.42128i	−0.0257584	−	0.146083i
$917$	30.2857	+	5.34019i	1.00012	+	0.176349i
$918$		0			0
$919$	6.04713	+	10.4739i	0.199476	+	0.345503i	0.948359	−	0.317200i	$-0.102743\pi$
$919$	6.04713	+	10.4739i	0.199476	+	0.345503i	−0.748882	+	0.662703i	$0.769409\pi$
$920$	23.8069	+	9.42908i	0.784891	+	0.310868i
$921$		0			0
$922$	8.86385	+	10.5635i	0.291915	+	0.347891i
$923$	29.2158	+	16.8678i	0.961650	+	0.555209i
$924$		0			0
$925$	−0.276125	+	4.91796i	−0.00907892	+	0.161702i
$926$	−10.4075	+	59.0238i	−0.342012	+	1.93964i
$927$		0			0
$928$	−3.53016	−	9.69905i	−0.115883	−	0.318387i
$929$	12.2297	+	10.2619i	0.401242	+	0.336682i	0.820974	−	0.570966i	$-0.193431\pi$
$929$	12.2297	+	10.2619i	0.401242	+	0.336682i	−0.419731	+	0.907648i	$0.637876\pi$
$930$		0			0
$931$	3.42195	+	8.10624i	0.112150	+	0.265671i
$932$		−	15.5210i		−	0.508407i
$933$		0			0
$934$	−39.4639	+	14.3637i	−1.29130	+	0.469995i
$935$	3.12980	+	9.41226i	0.102356	+	0.307814i
$936$		0			0
$937$	1.22430	−	3.36373i	0.0399961	−	0.109888i	−0.918087	−	0.396379i	$-0.870267\pi$
$937$	1.22430	−	3.36373i	0.0399961	−	0.109888i	0.958083	+	0.286491i	$0.0924888\pi$
$938$	−10.1649	+	5.86870i	−0.331895	+	0.191620i
$939$		0			0
$940$	−0.886360	+	0.998094i	−0.0289099	+	0.0325542i
$941$	−26.5863	+	22.3086i	−0.866689	+	0.727238i	−0.963398	−	0.268074i	$-0.913613\pi$
$941$	−26.5863	+	22.3086i	−0.866689	+	0.727238i	0.0967092	+	0.995313i	$0.469168\pi$
$942$		0			0
$943$	−6.30018	+	3.63741i	−0.205162	+	0.118450i
$944$	45.0833	+	16.4090i	1.46733	+	0.534066i
$945$		0			0
$946$	2.41503	+	13.6963i	0.0785195	+	0.445306i
$947$	−15.3805	−	42.2576i	−0.499800	−	1.37319i	−0.891469	−	0.453082i	$-0.850324\pi$
$947$	−15.3805	−	42.2576i	−0.499800	−	1.37319i	0.391669	−	0.920106i	$-0.371898\pi$
$948$		0			0
$949$	−71.2711			−2.31356
$950$	−5.92901	−	34.7851i	−0.192362	−	1.12858i
$951$		0			0
$952$	−2.51644	+	2.99897i	−0.0815582	+	0.0971972i
$953$	0.572365	+	1.57256i	0.0185407	+	0.0509402i	0.948618	−	0.316424i	$-0.102482\pi$
$953$	0.572365	+	1.57256i	0.0185407	+	0.0509402i	−0.930077	+	0.367365i	$0.880260\pi$
$954$		0			0
$955$	−50.0820	−	1.40485i	−1.62061	−	0.0454598i
$956$	9.82067	+	3.57443i	0.317623	+	0.115605i
$957$		0			0
$958$	16.5998	+	9.58393i	0.536317	+	0.309643i
$959$	−20.0762	+	16.8459i	−0.648294	+	0.543984i
$960$		0			0
$961$	−17.3387	+	30.0315i	−0.559313	+	0.968758i
$962$	6.49289	−	3.74867i	0.209339	−	0.120862i
$963$		0			0
$964$	1.17034	−	6.63735i	0.0376942	−	0.213775i
$965$	−13.8281	−	41.5853i	−0.445143	−	1.33868i
$966$		0			0
$967$	−11.6789	+	13.9183i	−0.375568	+	0.447584i	−0.920410	−	0.390954i	$-0.872145\pi$
$967$	−11.6789	+	13.9183i	−0.375568	+	0.447584i	0.544842	+	0.838538i	$0.316589\pi$
$968$		−	46.5689i		−	1.49678i
$969$		0			0
$970$	−6.74302	−	45.7011i	−0.216505	−	1.46737i
$971$	−3.56175	−	2.98867i	−0.114302	−	0.0959108i	0.583845	−	0.811865i	$-0.301547\pi$
$971$	−3.56175	−	2.98867i	−0.114302	−	0.0959108i	−0.698147	+	0.715954i	$0.745992\pi$
$972$		0			0
$973$	20.5325	−	3.62043i	0.658240	−	0.116066i
$974$	8.26050	−	46.8476i	0.264683	−	1.50109i
$975$		0			0
$976$	5.08987	+	8.81591i	0.162923	+	0.282190i
$977$	−11.8979	−	6.86928i	−0.380649	−	0.219768i	0.297452	−	0.954737i	$-0.403863\pi$
$977$	−11.8979	−	6.86928i	−0.380649	−	0.219768i	−0.678100	+	0.734969i	$0.737197\pi$
$978$		0			0
$979$	−14.7150	+	12.3474i	−0.470295	+	0.394624i
$980$	−2.60770	−	1.03282i	−0.0832999	−	0.0329922i
$981$		0			0
$982$	−2.66820	+	7.33082i	−0.0851457	+	0.233936i
$983$	−8.28423	−	1.46073i	−0.264226	−	0.0465901i	0.0399657	−	0.999201i	$-0.487275\pi$
$983$	−8.28423	−	1.46073i	−0.264226	−	0.0465901i	−0.304191	+	0.952611i	$0.598386\pi$
$984$		0			0
$985$	30.4104	−	16.4382i	0.968957	−	0.523765i
$986$	−2.95959	−	2.48339i	−0.0942526	−	0.0790873i
$987$		0			0
$988$	−9.32848	+	8.66446i	−0.296778	+	0.275653i
$989$	7.80714			0.248253
$990$		0			0
$991$	−17.4575	+	6.35400i	−0.554555	+	0.201841i	−0.604069	−	0.796932i	$-0.706455\pi$
$991$	−17.4575	+	6.35400i	−0.554555	+	0.201841i	0.0495142	+	0.998773i	$0.484233\pi$
$992$	−27.1285	+	4.78348i	−0.861330	+	0.151876i
$993$		0			0
$994$	−24.3708	−	8.87026i	−0.772996	−	0.281348i
$995$	−2.40619	+	1.90666i	−0.0762815	+	0.0604453i
$996$		0			0
$997$	24.7222	+	29.4628i	0.782960	+	0.933096i	0.999063	−	0.0432750i	$-0.0137792\pi$
$997$	24.7222	+	29.4628i	0.782960	+	0.933096i	−0.216103	+	0.976371i	$0.569335\pi$
$998$	0.195890	+	0.233452i	0.00620079	+	0.00738981i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.244.6		48
3.2	odd	2		95.2.p.a.54.3	yes	48
5.4	even	2	inner	855.2.da.b.244.3		48
15.2	even	4		475.2.l.f.301.3		48
15.8	even	4		475.2.l.f.301.6		48
15.14	odd	2		95.2.p.a.54.6	yes	48
19.6	even	9	inner	855.2.da.b.424.3		48
57.5	odd	18		1805.2.b.k.1084.19		24
57.14	even	18		1805.2.b.l.1084.6		24
57.44	odd	18		95.2.p.a.44.6	yes	48
95.44	even	18	inner	855.2.da.b.424.6		48
285.14	even	18		1805.2.b.l.1084.19		24
285.44	odd	18		95.2.p.a.44.3	✓	48
285.62	even	36		9025.2.a.cu.1.6		24
285.119	odd	18		1805.2.b.k.1084.6		24
285.128	odd	36		9025.2.a.ct.1.6		24
285.158	even	36		475.2.l.f.101.6		48
285.233	even	36		9025.2.a.cu.1.19		24
285.242	odd	36		9025.2.a.ct.1.19		24
285.272	even	36		475.2.l.f.101.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.3	✓	48	285.44	odd	18
95.2.p.a.44.6	yes	48	57.44	odd	18
95.2.p.a.54.3	yes	48	3.2	odd	2
95.2.p.a.54.6	yes	48	15.14	odd	2
475.2.l.f.101.3		48	285.272	even	36
475.2.l.f.101.6		48	285.158	even	36
475.2.l.f.301.3		48	15.2	even	4
475.2.l.f.301.6		48	15.8	even	4
855.2.da.b.244.3		48	5.4	even	2	inner
855.2.da.b.244.6		48	1.1	even	1	trivial
855.2.da.b.424.3		48	19.6	even	9	inner
855.2.da.b.424.6		48	95.44	even	18	inner
1805.2.b.k.1084.6		24	285.119	odd	18
1805.2.b.k.1084.19		24	57.5	odd	18
1805.2.b.l.1084.6		24	57.14	even	18
1805.2.b.l.1084.19		24	285.14	even	18
9025.2.a.ct.1.6		24	285.128	odd	36
9025.2.a.ct.1.19		24	285.242	odd	36
9025.2.a.cu.1.6		24	285.62	even	36
9025.2.a.cu.1.19		24	285.233	even	36

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04072 - 1.24028i) q^{2} +(-0.107903 - 0.611947i) q^{4} +(-2.23519 - 0.0626993i) q^{5} +(-1.93288 + 1.11595i) q^{7} +(1.93303 + 1.11604i) q^{8} +(-2.40397 + 2.70701i) q^{10} +(2.82239 - 4.88852i) q^{11} +(1.60766 - 4.41702i) q^{13} +(-0.627496 + 3.55871i) q^{14} +(4.56376 - 1.66107i) q^{16} +(0.505129 - 0.601990i) q^{17} +(2.63014 - 3.47597i) q^{19} +(0.202814 + 1.37458i) q^{20} +(-3.12582 - 8.58813i) q^{22} +(-5.05247 + 0.890886i) q^{23} +(4.99214 + 0.280289i) q^{25} +(-3.80521 - 6.59082i) q^{26} +(0.891466 + 1.06241i) q^{28} +(2.32611 - 1.95184i) q^{29} +(-4.05208 - 7.01841i) q^{31} +(1.16257 - 3.19413i) q^{32} +(-0.220938 - 1.25300i) q^{34} +(4.39033 - 2.37317i) q^{35} +0.985141i q^{37} +(-1.57393 - 6.87961i) q^{38} +(-4.25071 - 2.61575i) q^{40} +(1.33247 - 0.484978i) q^{41} +(-1.49862 - 0.264247i) q^{43} +(-3.29606 - 1.19967i) q^{44} +(-4.15324 + 7.19363i) q^{46} +(0.617523 + 0.735935i) q^{47} +(-1.00930 + 1.74817i) q^{49} +(5.54304 - 5.89994i) q^{50} +(-2.87645 - 0.507196i) q^{52} +(4.34421 - 0.766002i) q^{53} +(-6.61508 + 10.7498i) q^{55} -4.98176 q^{56} -4.91635i q^{58} +(7.56739 + 6.34980i) q^{59} +(0.363973 + 2.06420i) q^{61} +(-12.9219 - 2.27847i) q^{62} +(2.10495 + 3.64588i) q^{64} +(-3.87038 + 9.77207i) q^{65} +(2.08785 + 2.48820i) q^{67} +(-0.422891 - 0.244156i) q^{68} +(1.62570 - 7.91504i) q^{70} +(-1.24628 + 7.06798i) q^{71} +(-5.18587 - 14.2481i) q^{73} +(1.22185 + 1.02525i) q^{74} +(-2.41091 - 1.23444i) q^{76} +12.5986i q^{77} +(1.25893 - 0.458214i) q^{79} +(-10.3050 + 3.42667i) q^{80} +(0.785214 - 2.15736i) q^{82} +(6.51723 - 3.76273i) q^{83} +(-1.16680 + 1.31389i) q^{85} +(-1.88738 + 1.58370i) q^{86} +(10.9115 - 6.29977i) q^{88} +(-3.19776 - 1.16389i) q^{89} +(1.82175 + 10.3317i) q^{91} +(1.09035 + 2.99571i) q^{92} +1.55543 q^{94} +(-6.09681 + 7.60453i) q^{95} +(-8.20200 + 9.77477i) q^{97} +(1.11781 + 3.07117i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49}+ \cdots + 63 q^{95}+O(q^{100}) \) 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Introduction

L-functions

Modular forms

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Database

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