LMFDB - Embedded newform 855.2.da.b.244.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(199,855)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			244.3
Character	$\chi$	$=$	855.244
Dual form			855.2.da.b.424.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04072 + 1.24028i) q^{2} +(-0.107903 - 0.611947i) q^{4} +(2.12183 + 0.705562i) q^{5} +(1.93288 - 1.11595i) q^{7} +(-1.93303 - 1.11604i) q^{8} +O(q^{10})$	\(q+(-1.04072 + 1.24028i) q^{2} +(-0.107903 - 0.611947i) q^{4} +(2.12183 + 0.705562i) q^{5} +(1.93288 - 1.11595i) q^{7} +(-1.93303 - 1.11604i) q^{8} +(-3.08333 + 1.89738i) q^{10} +(2.82239 - 4.88852i) q^{11} +(-1.60766 + 4.41702i) q^{13} +(-0.627496 + 3.55871i) q^{14} +(4.56376 - 1.66107i) q^{16} +(-0.505129 + 0.601990i) q^{17} +(2.63014 - 3.47597i) q^{19} +(0.202814 - 1.37458i) q^{20} +(3.12582 + 8.58813i) q^{22} +(5.05247 - 0.890886i) q^{23} +(4.00437 + 2.99417i) q^{25} +(-3.80521 - 6.59082i) q^{26} +(-0.891466 - 1.06241i) q^{28} +(2.32611 - 1.95184i) q^{29} +(-4.05208 - 7.01841i) q^{31} +(-1.16257 + 3.19413i) q^{32} +(-0.220938 - 1.25300i) q^{34} +(4.88863 - 1.00410i) q^{35} -0.985141i q^{37} +(1.57393 + 6.87961i) q^{38} +(-3.31414 - 3.73191i) q^{40} +(1.33247 - 0.484978i) q^{41} +(1.49862 + 0.264247i) q^{43} +(-3.29606 - 1.19967i) q^{44} +(-4.15324 + 7.19363i) q^{46} +(-0.617523 - 0.735935i) q^{47} +(-1.00930 + 1.74817i) q^{49} +(-7.88102 + 1.85045i) q^{50} +(2.87645 + 0.507196i) q^{52} +(-4.34421 + 0.766002i) q^{53} +(9.43780 - 8.38127i) q^{55} -4.98176 q^{56} +4.91635i q^{58} +(7.56739 + 6.34980i) q^{59} +(0.363973 + 2.06420i) q^{61} +(12.9219 + 2.27847i) q^{62} +(2.10495 + 3.64588i) q^{64} +(-6.52768 + 8.23788i) q^{65} +(-2.08785 - 2.48820i) q^{67} +(0.422891 + 0.244156i) q^{68} +(-3.84233 + 7.10825i) q^{70} +(-1.24628 + 7.06798i) q^{71} +(5.18587 + 14.2481i) q^{73} +(1.22185 + 1.02525i) q^{74} +(-2.41091 - 1.23444i) q^{76} -12.5986i q^{77} +(1.25893 - 0.458214i) q^{79} +(10.8555 - 0.304509i) q^{80} +(-0.785214 + 2.15736i) q^{82} +(-6.51723 + 3.76273i) q^{83} +(-1.49654 + 0.920923i) q^{85} +(-1.88738 + 1.58370i) q^{86} +(-10.9115 + 6.29977i) q^{88} +(-3.19776 - 1.16389i) q^{89} +(1.82175 + 10.3317i) q^{91} +(-1.09035 - 2.99571i) q^{92} +1.55543 q^{94} +(8.03324 - 5.51970i) q^{95} +(8.20200 - 9.77477i) q^{97} +(-1.11781 - 3.07117i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) $ 48 * q - 18 * q^4 + 6 * q^5	$ 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}+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

Display 100 coefficients 10 coefficients

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	−0.996072	−	0.0885521i	$-0.971776\pi$
$2$	−1.04072	+	1.24028i	−0.735899	+	0.877010i	0.260173	+	0.965562i	$0.416220\pi$
$3$		0			0
$3$		0			0
$4$	−0.107903	−	0.611947i	−0.0539514	−	0.305973i
$5$	2.12183	+	0.705562i	0.948913	+	0.315537i
$5$	2.12183	+	0.705562i	0.948913	+	0.315537i
$6$		0			0
$7$	1.93288	−	1.11595i	0.730562	−	0.421790i	−0.0880659	−	0.996115i	$-0.528069\pi$
$7$	1.93288	−	1.11595i	0.730562	−	0.421790i	0.818628	+	0.574325i	$0.194735\pi$
$8$	−1.93303	−	1.11604i	−0.683429	−	0.394578i
$9$		0			0
$10$	−3.08333	+	1.89738i	−0.975033	+	0.600003i
$11$	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	$0.337114\pi$
$13$	−1.60766	+	4.41702i	−0.445886	+	1.22506i	−0.935564	+	0.353158i	$0.885108\pi$
$14$	−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	−0.823814	−	0.566860i	$-0.808158\pi$
$17$	−0.505129	+	0.601990i	−0.122512	+	0.146004i	0.701302	+	0.712864i	$0.252602\pi$
$18$		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	0.380036	−	0.924972i	$-0.375912\pi$
$23$	5.05247	−	0.890886i	1.05351	−	0.185763i	0.673476	+	0.739209i	$0.264800\pi$
$24$		0			0
$25$	4.00437	+	2.99417i	0.800873	+	0.598834i
$26$	−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
$35$	4.88863	−	1.00410i	0.826330	−	0.169723i
$36$		0			0
$37$		−	0.985141i		−	0.161956i	−0.996716	−	0.0809781i	$-0.974196\pi$
$37$		−	0.985141i		−	0.161956i	0.996716	−	0.0809781i	$-0.0258044\pi$
$38$	1.57393	+	6.87961i	0.255326	+	1.11602i
$39$		0			0
$40$	−3.31414	−	3.73191i	−0.524011	−	0.590067i
$41$	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	0.286744	−	0.958007i	$-0.407427\pi$
$43$	1.49862	+	0.264247i	0.228537	+	0.0402973i	−0.0582066	+	0.998305i	$0.518538\pi$
$44$	−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	0.719124	−	0.694881i	$-0.244543\pi$
$47$	−0.617523	−	0.735935i	−0.0900749	−	0.107347i	−0.809199	+	0.587534i	$0.800099\pi$
$48$		0			0
$49$	−1.00930	+	1.74817i	−0.144186	+	0.249738i
$50$	−7.88102	+	1.85045i	−1.11454	+	0.261693i
$51$		0			0
$52$	2.87645	+	0.507196i	0.398892	+	0.0703355i
$53$	−4.34421	+	0.766002i	−0.596723	+	0.105218i	−0.463849	−	0.885914i	$-0.653532\pi$
$53$	−4.34421	+	0.766002i	−0.596723	+	0.105218i	−0.132875	+	0.991133i	$0.542421\pi$
$54$		0			0
$55$	9.43780	−	8.38127i	1.27259	−	1.13013i
$56$	−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
$65$	−6.52768	+	8.23788i	−0.809659	+	1.02178i
$66$		0			0
$67$	−2.08785	−	2.48820i	−0.255071	−	0.303982i	0.623279	−	0.781999i	$-0.285800\pi$
$67$	−2.08785	−	2.48820i	−0.255071	−	0.303982i	−0.878350	+	0.478017i	$0.841356\pi$
$68$	0.422891	+	0.244156i	0.0512830	+	0.0296083i
$69$		0			0
$70$	−3.84233	+	7.10825i	−0.459246	+	0.849599i
$71$	−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	$0.236322\pi$
$73$	5.18587	+	14.2481i	0.606960	+	1.66761i	−0.129869	+	0.991531i	$0.541456\pi$
$74$	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	$0.364877\pi$
$80$	10.8555	−	0.304509i	1.21369	−	0.0340451i
$81$		0			0
$82$	−0.785214	+	2.15736i	−0.0867123	+	0.238240i
$83$	−6.51723	+	3.76273i	−0.715359	+	0.413013i	−0.813042	−	0.582205i	$-0.802190\pi$
$83$	−6.51723	+	3.76273i	−0.715359	+	0.413013i	0.0976829	+	0.995218i	$0.468857\pi$
$84$		0			0
$85$	−1.49654	+	0.920923i	−0.162323	+	0.0998881i
$86$	−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
$95$	8.03324	−	5.51970i	0.824193	−	0.566309i
$96$		0			0
$97$	8.20200	−	9.77477i	0.832787	−	0.992477i	−0.167191	−	0.985924i	$-0.553470\pi$
$97$	8.20200	−	9.77477i	0.832787	−	0.992477i	0.999979	−	0.00655264i	$-0.00208579\pi$
$98$	−1.11781	−	3.07117i	−0.112916	−	0.310235i
$99$		0			0
$100$	1.40019	−	2.77354i	0.140019	−	0.277354i
$101$	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	0.352191	−	0.935928i	$-0.385437\pi$
$103$	−2.86453	−	1.65384i	−0.282251	−	0.162958i	−0.634442	+	0.772971i	$0.718770\pi$
$104$	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	−0.752603	−	0.658475i	$-0.771202\pi$
$107$	−5.77870	+	3.33633i	−0.558648	+	0.322536i	0.193955	+	0.981010i	$0.437869\pi$
$108$		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	$0.785129\pi$
$110$	0.573027	+	20.4280i	0.0546360	+	1.94774i
$111$		0			0
$112$	6.96755	−	8.30360i	0.658371	−	0.784616i
$113$			6.58139i			0.619125i	0.950879	+	0.309562i	$0.100183\pi$
$113$			6.58139i			0.619125i	−0.950879	+	0.309562i	$0.899817\pi$
$114$		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
$125$	6.38403	+	9.17846i	0.571005	+	0.820946i
$126$		0			0
$127$	0.456461	−	1.25412i	0.0405044	−	0.111285i	−0.917792	−	0.397062i	$-0.870030\pi$
$127$	0.456461	−	1.25412i	0.0405044	−	0.111285i	0.958296	+	0.285778i	$0.0922518\pi$
$128$	−13.4075	−	2.36411i	−1.18507	−	0.208960i
$129$		0			0
$130$	−3.42380	−	16.6695i	−0.300287	−	1.46201i
$131$	−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	−0.644207	−	0.764851i	$-0.722813\pi$
$137$	−11.5639	+	2.03902i	−0.987969	+	0.174206i	−0.343762	+	0.939057i	$0.611701\pi$
$138$		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	$0.740771\pi$
$140$	−1.14195	−	2.88324i	−0.0965124	−	0.243678i
$141$		0			0
$142$	−7.46925	−	8.90151i	−0.626806	−	0.746998i
$143$	17.0553	+	20.3257i	1.42623	+	1.69972i
$144$		0			0
$145$	6.31277	−	2.50027i	0.524247	−	0.207636i
$146$	−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
$155$	−3.64592	−	17.7509i	−0.292848	−	1.42579i
$156$		0			0
$157$	−10.3475	−	1.82454i	−0.825821	−	0.145614i	−0.255263	−	0.966872i	$-0.582162\pi$
$157$	−10.3475	−	1.82454i	−0.825821	−	0.145614i	−0.570558	+	0.821257i	$0.693273\pi$
$158$	−0.741880	+	2.03830i	−0.0590208	+	0.162158i
$159$		0			0
$160$	−4.72043	+	5.95714i	−0.373183	+	0.470954i
$161$	8.77165	−	7.36029i	0.691303	−	0.580072i
$162$		0			0
$163$	3.13838	+	1.81195i	0.245817	+	0.141923i	0.617847	−	0.786298i	$-0.288005\pi$
$163$	3.13838	+	1.81195i	0.245817	+	0.141923i	−0.372030	+	0.928221i	$0.621338\pi$
$164$	−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	0.247166	−	0.968973i	$-0.420501\pi$
$167$	10.4783	−	1.84761i	0.810835	−	0.142972i	0.563669	+	0.826001i	$0.309389\pi$
$168$		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	$-0.513601\pi$
$173$	12.4770	−	14.8695i	0.948611	−	1.13051i	0.991326	−	0.131423i	$-0.0419546\pi$
$174$		0			0
$175$	11.0813	+	1.31871i	0.837669	+	0.0996849i
$176$	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
$185$	0.695078	−	2.09031i	0.0511031	−	0.153682i
$186$		0			0
$187$	1.51717	+	4.16839i	0.110946	+	0.304823i
$188$	−0.383721	+	0.457300i	−0.0279857	+	0.0333521i
$189$		0			0
$190$	−1.51437	+	15.7079i	−0.109864	+	1.13957i
$191$	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	$-0.861890\pi$
$193$	−6.70316	−	18.4168i	−0.482504	−	1.32567i	0.424835	−	0.905271i	$-0.360332\pi$
$194$	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	0.0596028	−	0.998222i	$-0.481017\pi$
$197$	13.3885	−	7.72984i	0.953890	−	0.550729i	0.894287	+	0.447494i	$0.147683\pi$
$198$		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	$0.262282\pi$
$200$	−4.39896	−	10.2568i	−0.311053	−	0.725268i
$201$		0			0
$202$	−7.81421	+	4.51154i	−0.549806	+	0.317431i
$203$	2.31795	−	6.36852i	0.162688	−	0.446982i
$204$		0			0
$205$	3.16946	−	0.0889064i	0.221364	−	0.00620949i
$206$	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
$215$	2.99338	+	1.61806i	0.204147	+	0.110351i
$216$		0			0
$217$	−15.6644	−	9.04385i	−1.06337	−	0.613936i
$218$	−16.3198	−	19.4491i	−1.10531	−	1.31726i
$219$		0			0
$220$	−6.14726	−	4.87107i	−0.414448	−	0.328407i
$221$	−1.84692	−	3.19896i	−0.124237	−	0.215186i
$222$		0			0
$223$	6.43818	+	1.13522i	0.431132	+	0.0760203i	0.385003	−	0.922915i	$-0.374200\pi$
$223$	6.43818	+	1.13522i	0.431132	+	0.0760203i	0.0461291	+	0.998935i	$0.485311\pi$
$224$	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	$0.0953133\pi$
$227$			8.88867i			0.589962i	−0.955503	+	0.294981i	$0.904687\pi$
$228$		0			0
$229$	7.22494			0.477438			0.238719	−	0.971089i	$-0.423273\pi$
$229$	7.22494			0.477438			0.238719	+	0.971089i	$0.423273\pi$
$230$	−13.8880	+	12.3333i	−0.915751	+	0.813235i
$231$		0			0
$232$	−6.67477	+	1.17694i	−0.438220	+	0.0772701i
$233$	−24.5985	−	4.33738i	−1.61150	−	0.284151i	−0.705910	−	0.708302i	$-0.749462\pi$
$233$	−24.5985	−	4.33738i	−1.61150	−	0.284151i	−0.905592	+	0.424151i	$0.860573\pi$
$234$		0			0
$235$	−0.791034	−	1.99723i	−0.0516013	−	0.130285i
$236$	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
$245$	−3.37502	+	2.99719i	−0.215622	+	0.191484i
$246$		0			0
$247$	11.1250	+	17.2056i	0.707869	+	1.09476i
$248$			18.0891i			1.14866i
$249$		0			0
$250$	−18.0278	−	1.63421i	−1.14018	−	0.103356i
$251$	−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	0.419609	−	0.907705i	$-0.362167\pi$
$257$	−8.77180	−	10.4538i	−0.547170	−	0.652092i	−0.966779	+	0.255613i	$0.917723\pi$
$258$		0			0
$259$	−1.09937	−	1.90416i	−0.0683115	−	0.118319i
$260$	5.74550	+	3.10570i	0.356321	+	0.192607i
$261$		0			0
$262$	21.9699	−	3.87389i	1.35731	−	0.239330i
$263$	−3.49596	−	9.60508i	−0.215570	−	0.592274i	0.784025	−	0.620730i	$-0.213163\pi$
$263$	−3.49596	−	9.60508i	−0.215570	−	0.592274i	−0.999595	+	0.0284550i	$0.990941\pi$
$264$		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
$275$	25.9390	−	11.1247i	1.56418	−	0.670846i
$276$		0			0
$277$	−24.7634	−	14.2971i	−1.48789	−	0.859032i	−0.487983	−	0.872853i	$-0.662267\pi$
$277$	−24.7634	−	14.2971i	−1.48789	−	0.859032i	−0.999904	+	0.0138211i	$0.995600\pi$
$278$	13.0982	−	7.56223i	0.785576	−	0.453552i
$279$		0			0
$280$	−10.5705	−	3.51494i	−0.631707	−	0.210058i
$281$	−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	−0.926817	−	0.375514i	$-0.877466\pi$
$283$	−6.66290	+	7.94053i	−0.396068	+	0.472016i	0.530749	+	0.847529i	$0.321911\pi$
$284$	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
$290$	−3.46879	+	10.4317i	−0.203694	+	0.612569i
$291$		0			0
$292$	8.15949	−	4.71088i	0.477498	−	0.275684i
$293$	7.87266	+	4.54528i	0.459926	+	0.265538i	0.712013	−	0.702166i	$-0.247784\pi$
$293$	7.87266	+	4.54528i	0.459926	+	0.265538i	−0.252087	+	0.967704i	$0.581117\pi$
$294$		0			0
$295$	11.5766	+	18.8125i	0.674015	+	1.09531i
$296$	−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	$-0.973681\pi$
$307$	−5.01541	−	13.7797i	−0.286245	−	0.786450i	0.710339	−	0.703860i	$-0.248542\pi$
$308$	−7.70967	+	1.35942i	−0.439299	+	0.0774603i
$309$		0			0
$310$	25.8104	+	13.9517i	1.46593	+	0.792404i
$311$	−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	0.577576	−	0.816337i	$-0.303999\pi$
$313$	−5.77911	−	6.88727i	−0.326654	−	0.389292i	−0.904230	+	0.427046i	$0.859554\pi$
$314$	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	−0.998644	−	0.0520614i	$-0.983421\pi$
$317$	−3.56399	+	9.79199i	−0.200174	+	0.549973i	0.798470	+	0.602035i	$0.205643\pi$
$318$		0			0
$319$	−2.97642	−	16.8801i	−0.166648	−	0.945106i
$320$	1.89396	+	9.22112i	0.105876	+	0.515476i
$321$		0			0
$322$			18.5393i			1.03315i
$323$	0.763934	+	3.33913i	0.0425064	+	0.185794i
$324$		0			0
$325$	−19.6630	+	12.8737i	−1.09071	+	0.714107i
$326$	−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
$335$	−2.67449	−	6.75265i	−0.146123	−	0.368937i
$336$		0			0
$337$	24.4051	+	4.30328i	1.32943	+	0.234414i	0.792841	−	0.609429i	$-0.208601\pi$
$337$	24.4051	+	4.30328i	1.32943	+	0.234414i	0.536590	+	0.843843i	$0.319712\pi$
$338$	14.5012	−	2.55695i	0.788760	−	0.139080i
$339$		0			0
$340$	0.725037	+	0.816434i	0.0393206	+	0.0442773i
$341$	−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	−0.645485	−	0.763773i	$-0.723345\pi$
$347$	−28.1891	−	4.97049i	−1.51327	−	0.266830i	−0.867783	+	0.496943i	$0.834456\pi$
$348$		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	$0.745127\pi$
$350$	−13.1681	+	12.3715i	−0.703865	+	0.661287i
$351$		0			0
$352$	12.3333	+	14.6983i	0.657369	+	0.783422i
$353$	−15.4082	−	8.89593i	−0.820096	−	0.473483i	0.0303537	−	0.999539i	$-0.490337\pi$
$353$	−15.4082	−	8.89593i	−0.820096	−	0.473483i	−0.850450	+	0.526057i	$0.823670\pi$
$354$		0			0
$355$	−7.63129	+	14.1178i	−0.405027	+	0.749293i
$356$	−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
$365$	0.950676	+	33.8910i	0.0497607	+	1.77394i
$366$		0			0
$367$	−7.28874	+	20.0256i	−0.380469	+	1.04533i	0.590690	+	0.806899i	$0.298856\pi$
$367$	−7.28874	+	20.0256i	−0.380469	+	1.04533i	−0.971159	+	0.238432i	$0.923367\pi$
$368$	21.5784	−	12.4583i	1.12485	−	0.649434i
$369$		0			0
$370$	1.86918	+	3.03751i	0.0971743	+	0.157913i
$371$	−7.54204	+	6.32852i	−0.391563	+	0.328561i
$372$		0			0
$373$	−12.2737	+	7.08623i	−0.635509	+	0.366911i	−0.782882	−	0.622170i	$-0.786251\pi$
$373$	−12.2737	+	7.08623i	−0.635509	+	0.366911i	0.147374	+	0.989081i	$0.452918\pi$
$374$	−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	$0.470979\pi$
$380$	−4.24457	−	4.32032i	−0.217742	−	0.221628i
$381$		0			0
$382$	−23.3185	+	27.7899i	−1.19308	+	1.42185i
$383$	2.63645	+	7.24358i	0.134716	+	0.370130i	0.988647	−	0.150257i	$-0.0480101\pi$
$383$	2.63645	+	7.24358i	0.134716	+	0.370130i	−0.853931	+	0.520387i	$0.825788\pi$
$384$		0			0
$385$	8.88909	−	26.7322i	0.453030	−	1.36240i
$386$	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
$395$	2.99454	−	0.0839999i	0.150672	−	0.00422649i
$396$		0			0
$397$	11.3616	−	13.5403i	0.570224	−	0.679567i	−0.401453	−	0.915880i	$-0.631495\pi$
$397$	11.3616	−	13.5403i	0.570224	−	0.679567i	0.971677	+	0.236313i	$0.0759390\pi$
$398$			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	$0.961846\pi$
$410$	−3.18824	+	4.02354i	−0.157456	+	0.198708i
$411$		0			0
$412$	−0.702970	+	1.93140i	−0.0346329	+	0.0951530i
$413$	21.7130	+	3.82858i	1.06843	+	0.188392i
$414$		0			0
$415$	−16.4833	+	3.38558i	−0.809135	+	0.166191i
$416$	−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
$425$	−3.82518	+	0.898144i	−0.185549	+	0.0435664i
$426$		0			0
$427$	3.00706	+	3.58367i	0.145522	+	0.173426i
$428$	2.66520	+	3.17626i	0.128827	+	0.153530i
$429$		0			0
$430$	−5.12211	+	2.02869i	−0.247010	+	0.0978320i
$431$	−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	−0.309867	−	0.950780i	$-0.600285\pi$
$433$	−5.74031	+	1.01217i	−0.275862	+	0.0486418i	0.0340058	+	0.999422i	$0.489174\pi$
$434$	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	$0.672724\pi$
$440$	−27.5973	+	5.66833i	−1.31565	+	0.270227i
$441$		0			0
$442$	5.88973	+	1.03852i	0.280146	+	0.0493973i
$443$	3.14771	−	8.64826i	0.149552	−	0.410891i	−0.842183	−	0.539191i	$-0.818730\pi$
$443$	3.14771	−	8.64826i	0.149552	−	0.410891i	0.991735	+	0.128300i	$0.0409522\pi$
$444$		0			0
$445$	−5.96393	−	4.72580i	−0.282717	−	0.224024i
$446$	−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	$0.00284272\pi$
$457$			0.381827i			0.0178611i	−0.999960	+	0.00893055i	$0.997157\pi$
$458$	−7.51913	+	8.96095i	−0.351346	+	0.418718i
$459$		0			0
$460$	−0.199883	−	7.12571i	−0.00931961	−	0.332238i
$461$	−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	0.489945	−	0.871754i	$-0.337017\pi$
$463$	32.0583	−	18.5089i	1.48988	−	0.860181i	0.999933	+	0.0115723i	$0.00368365\pi$
$464$	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	0.919689	−	0.392647i	$-0.128440\pi$
$467$	22.4636	+	12.9694i	1.03949	+	0.600151i	0.119803	+	0.992798i	$0.461774\pi$
$468$		0			0
$469$	−6.81228	−	2.47947i	−0.314562	−	0.114491i
$470$	3.30037	+	1.09745i	0.152235	+	0.0506217i
$471$		0			0
$472$	−7.54140	−	20.7198i	−0.347121	−	0.953707i
$473$	5.52147	−	6.58023i	0.253877	−	0.302559i
$474$		0			0
$475$	20.9397	−	6.04395i	0.960779	−	0.277315i
$476$	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
$485$	24.3000	−	14.9534i	1.10341	−	0.679000i
$486$		0			0
$487$	−25.4449	+	14.6906i	−1.15302	+	0.665696i	−0.949621	−	0.313400i	$-0.898532\pi$
$487$	−25.4449	+	14.6906i	−1.15302	+	0.665696i	−0.203398	+	0.979096i	$0.565199\pi$
$488$	1.60014	−	4.39636i	0.0724351	−	0.199014i
$489$		0			0
$490$	−0.204918	−	7.30520i	−0.00925726	−	0.330015i
$491$	−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	$0.0568966\pi$
$500$	4.92787	−	4.89707i	0.220381	−	0.219004i
$501$		0			0
$502$	8.93266	+	5.15728i	0.398684	+	0.230181i
$503$	−1.46289	−	1.74340i	−0.0652269	−	0.0777343i	0.732444	−	0.680827i	$-0.238379\pi$
$503$	−1.46289	−	1.74340i	−0.0652269	−	0.0777343i	−0.797671	+	0.603093i	$0.793935\pi$
$504$		0			0
$505$	9.76699	+	7.73934i	0.434626	+	0.344396i
$506$	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
$515$	−4.91118	−	5.53028i	−0.216412	−	0.243693i
$516$		0			0
$517$	−5.34052	+	0.941679i	−0.234876	+	0.0414150i
$518$	3.50583	+	0.618172i	0.154037	+	0.0271609i
$519$		0			0
$520$	21.8120	−	8.63895i	0.956518	−	0.378843i
$521$	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	$0.00105569\pi$
$523$	18.9726	+	22.6107i	0.829613	+	0.988695i	−0.170381	+	0.985378i	$0.554500\pi$
$524$	−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
$530$	11.9412	−	10.6044i	0.518694	−	0.460628i
$531$		0			0
$532$	−6.03758	+	0.304422i	−0.261762	+	0.0131984i
$533$			6.66521i			0.288702i
$534$		0			0
$535$	−14.6154	+	3.00192i	−0.631880	+	0.129784i
$536$	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
$545$	−16.6738	+	30.8463i	−0.714227	+	1.32131i
$546$		0			0
$547$	−24.7374	+	4.36188i	−1.05770	+	0.186500i	−0.675334	−	0.737512i	$-0.736000\pi$
$547$	−24.7374	+	4.36188i	−1.05770	+	0.186500i	−0.382362	+	0.924012i	$0.624889\pi$
$548$	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	$0.314699\pi$
$557$	−9.63578	+	26.4741i	−0.408281	+	1.12174i	−0.958094	+	0.286455i	$0.907523\pi$
$558$		0			0
$559$	−3.57646	+	6.19461i	−0.151268	+	0.262004i
$560$	20.6427	−	12.7028i	0.872312	−	0.536793i
$561$		0			0
$562$	10.0643	+	5.81060i	0.424535	+	0.245105i
$563$	−17.6927	+	10.2149i	−0.745656	+	0.430505i	−0.824122	−	0.566412i	$-0.808331\pi$
$563$	−17.6927	+	10.2149i	−0.745656	+	0.430505i	0.0784660	+	0.996917i	$0.474998\pi$
$564$		0			0
$565$	−4.64357	+	13.9646i	−0.195357	+	0.587496i
$566$	−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
$575$	22.8994	+	11.5605i	0.954970	+	0.482107i
$576$		0			0
$577$	−37.5103	+	21.6566i	−1.56157	+	0.901575i	−0.564476	+	0.825449i	$0.690922\pi$
$577$	−37.5103	+	21.6566i	−1.56157	+	0.901575i	−0.997098	+	0.0761261i	$0.975745\pi$
$578$	−22.9707	−	13.2622i	−0.955457	−	0.551633i
$579$		0			0
$580$	−2.21120	−	3.59330i	−0.0918150	−	0.149204i
$581$	−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	−0.334242	−	0.942487i	$-0.608480\pi$
$587$	15.7959	−	18.8249i	0.651968	−	0.776985i	0.986209	+	0.165502i	$0.0529246\pi$
$588$		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	−0.179988	−	0.983669i	$-0.557606\pi$
$593$	−0.308954	+	0.0544770i	−0.0126872	+	0.00223710i	0.167301	+	0.985906i	$0.446495\pi$
$594$		0			0
$595$	−1.86494	+	3.45011i	−0.0764550	+	0.141441i
$596$	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
$605$	−9.38616	−	45.6983i	−0.381602	−	1.85790i
$606$		0			0
$607$		−	12.4142i		−	0.503876i	−0.967743	−	0.251938i	$-0.918932\pi$
$607$		−	12.4142i		−	0.503876i	0.967743	−	0.251938i	$-0.0810680\pi$
$608$	8.04496	+	12.4421i	0.326266	+	0.504592i
$609$		0			0
$610$	−5.03881	−	5.67399i	−0.204015	−	0.229733i
$611$	4.24341	−	1.54447i	0.171670	−	0.0624827i
$612$		0			0
$613$	−1.04244	−	0.183811i	−0.0421039	−	0.00742405i	0.152557	−	0.988295i	$-0.451249\pi$
$613$	−1.04244	−	0.183811i	−0.0421039	−	0.00742405i	−0.194660	+	0.980871i	$0.562360\pi$
$614$	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	0.256598	−	0.966518i	$-0.417398\pi$
$617$	−18.3761	−	21.8998i	−0.739794	−	0.881652i	−0.996392	+	0.0848661i	$0.972954\pi$
$618$		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	$0.106044\pi$
$620$	−10.4692	+	4.14648i	−0.420453	+	0.166527i
$621$		0			0
$622$	50.3552	+	8.87898i	2.01906	+	0.356015i
$623$	−7.47975	+	1.31888i	−0.299670	+	0.0528399i
$624$		0			0
$625$	7.06989	+	23.9795i	0.282796	+	0.959180i
$626$	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
$635$	1.85339	−	2.33897i	0.0735497	−	0.0928191i
$636$		0			0
$637$	−6.09907	−	7.26858i	−0.241654	−	0.287992i
$638$	24.0337	+	13.8759i	0.951503	+	0.549350i
$639$		0			0
$640$	−26.7805	−	14.4761i	−1.05859	−	0.572217i
$641$	−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	$-0.919548\pi$
$643$	−9.81994	−	26.9801i	−0.387261	−	1.06399i	0.580969	−	0.813926i	$-0.302674\pi$
$644$	−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	$-0.888610\pi$
$647$		−	17.4412i		−	0.685686i	0.939393	−	0.342843i	$-0.111390\pi$
$648$		0			0
$649$	52.3993	−	19.0718i	2.05685	−	0.748633i
$650$	4.49658	−	37.7855i	0.176370	−	1.48207i
$651$		0			0
$652$	0.770175	−	2.11604i	0.0301624	−	0.0828704i
$653$	26.2837	−	15.1749i	1.02856	−	0.593839i	0.111988	−	0.993710i	$-0.464278\pi$
$653$	26.2837	−	15.1749i	1.02856	−	0.593839i	0.916572	+	0.399871i	$0.130945\pi$
$654$		0			0
$655$	−16.1473	−	26.2401i	−0.630927	−	1.02529i
$656$	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
$665$	9.36761	−	19.6336i	0.363260	−	0.761360i
$666$		0			0
$667$	10.0137	−	11.9339i	0.387734	−	0.462083i
$668$	−2.26127	−	6.21280i	−0.0874913	−	0.240380i
$669$		0			0
$670$	11.1586	+	3.71049i	0.431093	+	0.143349i
$671$	11.1181	+	4.04667i	0.429211	+	0.156220i
$672$		0			0
$673$	−43.2343	−	24.9614i	−1.66656	−	0.962189i	−0.969471	−	0.245206i	$-0.921144\pi$
$673$	−43.2343	−	24.9614i	−1.66656	−	0.962189i	−0.697090	−	0.716984i	$-0.745522\pi$
$674$	−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	−0.949143	−	0.314847i	$-0.898047\pi$
$677$	−29.9494	+	17.2913i	−1.15105	+	0.664558i	−0.201906	+	0.979405i	$0.564714\pi$
$678$		0			0
$679$	4.94536	−	28.0465i	0.189786	−	1.07633i
$680$	3.92064	−	0.109978i	0.150350	−	0.00421746i
$681$		0			0
$682$	47.6089	−	56.7381i	1.82304	−	2.17261i
$683$			21.1277i			0.808429i	0.914664	+	0.404214i	$0.132455\pi$
$683$			21.1277i			0.808429i	−0.914664	+	0.404214i	$0.867545\pi$
$684$		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
$695$	−16.3714	−	12.9727i	−0.621003	−	0.492081i
$696$		0			0
$697$	−0.381116	+	1.04711i	−0.0144358	+	0.0396620i
$698$	−16.2982	−	2.87381i	−0.616895	−	0.108775i
$699$		0			0
$700$	−0.388727	−	6.92347i	−0.0146925	−	0.261683i
$701$	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	$0.585451\pi$
$710$	−9.56795	−	24.1575i	−0.359079	−	0.906616i
$711$		0			0
$712$	4.88243	+	5.81865i	0.182977	+	0.218063i
$713$	−26.7256	−	31.8503i	−1.00088	−	1.19280i
$714$		0			0
$715$	21.8474	+	55.1612i	0.817047	+	2.06291i
$716$	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
$725$	15.1588	−	0.851106i	0.562982	−	0.0316093i
$726$		0			0
$727$	19.7527	+	3.48294i	0.732587	+	0.129175i	0.527483	−	0.849565i	$-0.323136\pi$
$727$	19.7527	+	3.48294i	0.732587	+	0.129175i	0.205104	+	0.978740i	$0.434247\pi$
$728$	8.00900	−	22.0046i	0.296833	−	0.815543i
$729$		0			0
$730$	−43.0237	−	34.0919i	−1.59238	−	1.26180i
$731$	−0.916071	+	0.768675i	−0.0338821	+	0.0284305i
$732$		0			0
$733$	0.178212	+	0.102891i	0.00658241	+	0.00380036i	0.503288	−	0.864119i	$-0.332124\pi$
$733$	0.178212	+	0.102891i	0.00658241	+	0.00380036i	−0.496705	+	0.867919i	$0.665457\pi$
$734$	−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	−0.992192	−	0.124717i	$-0.960198\pi$
$743$	−19.0010	+	22.6445i	−0.697078	+	0.830745i	0.295114	+	0.955462i	$0.404642\pi$
$744$		0			0
$745$	−40.2856	+	1.13005i	−1.47595	+	0.0414019i
$746$	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
$755$	−27.6177	−	9.18354i	−1.00511	−	0.334223i
$756$		0			0
$757$	10.4480	+	28.7057i	0.379740	+	1.04333i	0.971464	+	0.237187i	$0.0762252\pi$
$757$	10.4480	+	28.7057i	0.379740	+	1.04333i	−0.591724	+	0.806141i	$0.701553\pi$
$758$	−3.68931	+	4.39674i	−0.134002	+	0.159697i
$759$		0			0
$760$	−21.6887	+	1.70437i	−0.786731	+	0.0618239i
$761$	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	$0.363284\pi$
$770$	23.9043	+	38.8456i	0.861451	+	1.39990i
$771$		0			0
$772$	−10.5468	+	6.08920i	−0.379588	+	0.219155i
$773$	−3.03195	+	8.33022i	−0.109052	+	0.299617i	−0.982200	−	0.187837i	$-0.939852\pi$
$773$	−3.03195	+	8.33022i	−0.109052	+	0.299617i	0.873148	+	0.487454i	$0.162074\pi$
$774$		0			0
$775$	4.78830	−	40.2369i	0.172001	−	1.44535i
$776$	−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
$785$	−20.6684	−	11.1722i	−0.737685	−	0.398752i
$786$		0			0
$787$	11.4182	+	6.59229i	0.407014	+	0.234990i	0.689506	−	0.724280i	$-0.257828\pi$
$787$	11.4182	+	6.59229i	0.407014	+	0.234990i	−0.282492	+	0.959270i	$0.591161\pi$
$788$	−6.17491	−	7.35897i	−0.219972	−	0.262152i
$789$		0			0
$790$	−3.01229	+	3.80149i	−0.107173	+	0.135251i
$791$	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	$-0.763580\pi$
$797$		−	38.1858i		−	1.35261i	0.736621	−	0.676306i	$-0.236420\pi$
$798$		0			0
$799$	0.754954			0.0267084
$800$	−14.2191	+	9.30953i	−0.502721	+	0.329141i
$801$		0			0
$802$	−43.2343	+	7.62337i	−1.52666	+	0.269191i
$803$	84.2886	+	14.8623i	2.97448	+	0.524481i
$804$		0			0
$805$	23.8051	−	9.42838i	0.839020	−	0.332307i
$806$	−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
$815$	5.38069	+	6.05897i	0.188477	+	0.212237i
$816$		0			0
$817$	4.86010	−	4.51415i	0.170033	−	0.157930i
$818$		−	54.8398i		−	1.91743i
$819$		0			0
$820$	−0.396399	−	1.92995i	−0.0138429	−	0.0673966i
$821$	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	$0.274601\pi$
$823$	−9.64179	+	26.4906i	−0.336092	+	0.923404i	−0.986492	+	0.163812i	$0.947621\pi$
$824$	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	$0.174415\pi$
$827$	35.0380	+	41.7566i	1.21839	+	1.45202i	0.364789	+	0.931090i	$0.381141\pi$
$828$		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	$0.786705\pi$
$830$	12.9554	−	23.9674i	0.449690	−	0.831919i
$831$		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
$845$	−10.6580	−	17.3197i	−0.366645	−	0.595815i
$846$		0			0
$847$	−40.3268	−	23.2827i	−1.38565	−	0.800003i
$848$	−18.5536	+	10.7119i	−0.637132	+	0.367848i
$849$		0			0
$850$	2.86699	−	5.67901i	0.0983368	−	0.194788i
$851$	−0.877648	−	4.97739i	−0.0300854	−	0.170623i
$852$		0			0
$853$	26.5455	−	31.6357i	0.908902	−	1.08319i	−0.0873063	−	0.996182i	$-0.527826\pi$
$853$	26.5455	−	31.6357i	0.908902	−	1.08319i	0.996208	−	0.0870051i	$-0.0277297\pi$
$854$	−7.57426			−0.259186
$855$		0			0
$856$	14.8939			0.509062
$857$	−2.20780	+	2.63115i	−0.0754170	+	0.0898785i	−0.802434	−	0.596741i	$-0.796462\pi$
$857$	−2.20780	+	2.63115i	−0.0754170	+	0.0898785i	0.727017	+	0.686620i	$0.240906\pi$
$858$		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	$0.771576\pi$
$860$	0.667171	−	2.00638i	0.0227503	−	0.0684171i
$861$		0			0
$862$	18.3064	−	10.5692i	0.623519	−	0.359989i
$863$	−20.6624	−	11.9295i	−0.703358	−	0.406084i	0.105239	−	0.994447i	$-0.466439\pi$
$863$	−20.6624	−	11.9295i	−0.703358	−	0.406084i	−0.808597	+	0.588363i	$0.799773\pi$
$864$		0			0
$865$	36.9656	−	22.7474i	1.25687	−	0.773435i
$866$	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	0.839121	−	0.543944i	$-0.183070\pi$
$877$	−4.54055	−	12.4751i	−0.153324	−	0.421253i	−0.992445	+	0.122691i	$0.960848\pi$
$878$	−10.3482	+	1.82466i	−0.349234	+	0.0615794i
$879$		0			0
$880$	29.1500	−	53.9270i	0.982645	−	1.81788i
$881$	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	$-0.785761\pi$
$883$	−37.4427	−	44.6225i	−1.26005	−	1.50167i	−0.478126	−	0.878291i	$-0.658684\pi$
$884$	−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	$-0.607317\pi$
$887$	15.7612	−	43.3035i	0.529208	−	1.45399i	0.860005	−	0.510286i	$-0.170460\pi$
$888$		0			0
$889$	−0.517247	−	2.93345i	−0.0173479	−	0.0983849i
$890$	12.0681	−	2.47871i	0.404523	−	0.0830865i
$891$		0			0
$892$		−	4.06232i		−	0.136016i
$893$	−4.18226	+	0.210874i	−0.139954	+	0.00705664i
$894$		0			0
$895$	−3.46181	+	3.07427i	−0.115715	+	0.102761i
$896$	−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
$905$	44.9727	−	17.8121i	1.49494	−	0.592094i
$906$		0			0
$907$	43.0236	+	7.58622i	1.42857	+	0.251896i	0.833831	−	0.552020i	$-0.186143\pi$
$907$	43.0236	+	7.58622i	1.42857	+	0.251896i	0.594743	+	0.803916i	$0.297254\pi$
$908$	5.43939	−	0.959112i	0.180513	−	0.0318292i
$909$		0			0
$910$	−25.2201	−	28.3993i	−0.836039	−	0.941429i
$911$	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	$0.769409\pi$
$920$	−20.0693	−	15.9028i	−0.661665	−	0.524301i
$921$		0			0
$922$	−8.86385	−	10.5635i	−0.291915	−	0.347891i
$923$	−29.2158	−	16.8678i	−0.961650	−	0.555209i
$924$		0			0
$925$	2.94968	−	3.94486i	0.0969849	−	0.129706i
$926$	−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
$935$	0.278128	+	9.91508i	0.00909576	+	0.324258i
$936$		0			0
$937$	−1.22430	+	3.36373i	−0.0399961	+	0.109888i	−0.958083	−	0.286491i	$-0.907511\pi$
$937$	−1.22430	+	3.36373i	−0.0399961	+	0.109888i	0.918087	+	0.396379i	$0.129733\pi$
$938$	10.1649	−	5.86870i	0.331895	−	0.191620i
$939$		0			0
$940$	−1.13685	+	0.699577i	−0.0370798	+	0.0228177i
$941$	−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	$0.149676\pi$
$947$	15.3805	+	42.2576i	0.499800	+	1.37319i	−0.391669	+	0.920106i	$0.628102\pi$
$948$		0			0
$949$	−71.2711			−2.31356
$950$	−14.2961	+	32.2611i	−0.463828	+	1.04669i
$951$		0			0
$952$	2.51644	−	2.99897i	0.0815582	−	0.0971972i
$953$	−0.572365	−	1.57256i	−0.0185407	−	0.0509402i	0.930077	−	0.367365i	$-0.119740\pi$
$953$	−0.572365	−	1.57256i	−0.0185407	−	0.0509402i	−0.948618	+	0.316424i	$0.897518\pi$
$954$		0			0
$955$	47.5421	+	15.8089i	1.53843	+	0.511564i
$956$	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
$965$	−1.22883	−	43.8069i	−0.0395573	−	1.41019i
$966$		0			0
$967$	11.6789	−	13.9183i	0.375568	−	0.447584i	−0.544842	−	0.838538i	$-0.683411\pi$
$967$	11.6789	−	13.9183i	0.375568	−	0.447584i	0.920410	+	0.390954i	$0.127855\pi$
$968$			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	0.678100	−	0.734969i	$-0.262803\pi$
$977$	11.8979	+	6.86928i	0.380649	+	0.219768i	−0.297452	+	0.954737i	$0.596137\pi$
$978$		0			0
$979$	−14.7150	+	12.3474i	−0.470295	+	0.394624i
$980$	2.19830	+	1.74193i	0.0702220	+	0.0556438i
$981$		0			0
$982$	2.66820	−	7.33082i	0.0851457	−	0.233936i
$983$	8.28423	+	1.46073i	0.264226	+	0.0465901i	0.304191	−	0.952611i	$-0.401614\pi$
$983$	8.28423	+	1.46073i	0.264226	+	0.0465901i	−0.0399657	+	0.999201i	$0.512725\pi$
$984$		0			0
$985$	33.8620	−	6.95505i	1.07893	−	0.221606i
$986$	−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
$995$	2.85432	−	1.13049i	0.0904879	−	0.0358391i
$996$		0			0
$997$	−24.7222	−	29.4628i	−0.782960	−	0.933096i	0.216103	−	0.976371i	$-0.430665\pi$
$997$	−24.7222	−	29.4628i	−0.782960	−	0.933096i	−0.999063	+	0.0432750i	$0.986221\pi$
$998$	−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.244.3		48
3.2	odd	2		95.2.p.a.54.6	yes	48
5.4	even	2	inner	855.2.da.b.244.6		48
15.2	even	4		475.2.l.f.301.6		48
15.8	even	4		475.2.l.f.301.3		48
15.14	odd	2		95.2.p.a.54.3	yes	48
19.6	even	9	inner	855.2.da.b.424.6		48
57.5	odd	18		1805.2.b.k.1084.6		24
57.14	even	18		1805.2.b.l.1084.19		24
57.44	odd	18		95.2.p.a.44.3	✓	48
95.44	even	18	inner	855.2.da.b.424.3		48
285.14	even	18		1805.2.b.l.1084.6		24
285.44	odd	18		95.2.p.a.44.6	yes	48
285.62	even	36		9025.2.a.cu.1.19		24
285.119	odd	18		1805.2.b.k.1084.19		24
285.128	odd	36		9025.2.a.ct.1.19		24
285.158	even	36		475.2.l.f.101.3		48
285.233	even	36		9025.2.a.cu.1.6		24
285.242	odd	36		9025.2.a.ct.1.6		24
285.272	even	36		475.2.l.f.101.6		48

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

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

\(f(q)\)	\(=\)	\(q+(-1.04072 + 1.24028i) q^{2} +(-0.107903 - 0.611947i) q^{4} +(2.12183 + 0.705562i) q^{5} +(1.93288 - 1.11595i) q^{7} +(-1.93303 - 1.11604i) q^{8} +O(q^{10})\)	\(q+(-1.04072 + 1.24028i) q^{2} +(-0.107903 - 0.611947i) q^{4} +(2.12183 + 0.705562i) q^{5} +(1.93288 - 1.11595i) q^{7} +(-1.93303 - 1.11604i) q^{8} +(-3.08333 + 1.89738i) q^{10} +(2.82239 - 4.88852i) q^{11} +(-1.60766 + 4.41702i) q^{13} +(-0.627496 + 3.55871i) q^{14} +(4.56376 - 1.66107i) q^{16} +(-0.505129 + 0.601990i) q^{17} +(2.63014 - 3.47597i) q^{19} +(0.202814 - 1.37458i) q^{20} +(3.12582 + 8.58813i) q^{22} +(5.05247 - 0.890886i) q^{23} +(4.00437 + 2.99417i) q^{25} +(-3.80521 - 6.59082i) q^{26} +(-0.891466 - 1.06241i) q^{28} +(2.32611 - 1.95184i) q^{29} +(-4.05208 - 7.01841i) q^{31} +(-1.16257 + 3.19413i) q^{32} +(-0.220938 - 1.25300i) q^{34} +(4.88863 - 1.00410i) q^{35} -0.985141i q^{37} +(1.57393 + 6.87961i) q^{38} +(-3.31414 - 3.73191i) q^{40} +(1.33247 - 0.484978i) q^{41} +(1.49862 + 0.264247i) q^{43} +(-3.29606 - 1.19967i) q^{44} +(-4.15324 + 7.19363i) q^{46} +(-0.617523 - 0.735935i) q^{47} +(-1.00930 + 1.74817i) q^{49} +(-7.88102 + 1.85045i) q^{50} +(2.87645 + 0.507196i) q^{52} +(-4.34421 + 0.766002i) q^{53} +(9.43780 - 8.38127i) q^{55} -4.98176 q^{56} +4.91635i q^{58} +(7.56739 + 6.34980i) q^{59} +(0.363973 + 2.06420i) q^{61} +(12.9219 + 2.27847i) q^{62} +(2.10495 + 3.64588i) q^{64} +(-6.52768 + 8.23788i) q^{65} +(-2.08785 - 2.48820i) q^{67} +(0.422891 + 0.244156i) q^{68} +(-3.84233 + 7.10825i) q^{70} +(-1.24628 + 7.06798i) q^{71} +(5.18587 + 14.2481i) q^{73} +(1.22185 + 1.02525i) q^{74} +(-2.41091 - 1.23444i) q^{76} -12.5986i q^{77} +(1.25893 - 0.458214i) q^{79} +(10.8555 - 0.304509i) q^{80} +(-0.785214 + 2.15736i) q^{82} +(-6.51723 + 3.76273i) q^{83} +(-1.49654 + 0.920923i) q^{85} +(-1.88738 + 1.58370i) q^{86} +(-10.9115 + 6.29977i) q^{88} +(-3.19776 - 1.16389i) q^{89} +(1.82175 + 10.3317i) q^{91} +(-1.09035 - 2.99571i) q^{92} +1.55543 q^{94} +(8.03324 - 5.51970i) q^{95} +(8.20200 - 9.77477i) q^{97} +(-1.11781 - 3.07117i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 48 * q - 18 * q^4 + 6 * q^5	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) 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

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