LMFDB - Embedded newform 441.2.bb.f.46.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(37,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 32])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			46.1
Character	$\chi$	$=$	441.46
Dual form			441.2.bb.f.163.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00262 + 2.55465i) q^{2} +(-4.05486 - 3.76236i) q^{4} +(1.62281 + 1.10641i) q^{5} +(1.40782 - 2.24010i) q^{7} +(8.73185 - 4.20504i) q^{8} +(-4.45356 + 3.03638i) q^{10} +(-2.60758 + 0.393029i) q^{11} +(1.31197 + 1.64516i) q^{13} +(4.31114 + 5.84246i) q^{14} +(1.16088 + 15.4908i) q^{16} +(7.39542 + 2.28118i) q^{17} +(2.72747 + 4.72412i) q^{19} +(-2.41754 - 10.5919i) q^{20} +(1.61037 - 7.05551i) q^{22} +(-2.66318 + 0.821483i) q^{23} +(-0.417347 - 1.06338i) q^{25} +(-5.51821 + 1.70214i) q^{26} +(-14.1366 + 3.78655i) q^{28} +(1.03128 + 4.51833i) q^{29} +(-0.390994 + 0.677221i) q^{31} +(-22.2155 - 6.85257i) q^{32} +(-13.2424 + 16.6055i) q^{34} +(4.76309 - 2.07762i) q^{35} +(6.16124 - 5.71680i) q^{37} +(-14.8031 + 2.23121i) q^{38} +(18.8226 + 2.83705i) q^{40} +(1.43808 - 0.692542i) q^{41} +(-4.24459 - 2.04409i) q^{43} +(12.0521 + 8.21698i) q^{44} +(0.571574 - 7.62713i) q^{46} +(-2.00825 + 5.11693i) q^{47} +(-3.03608 - 6.30731i) q^{49} +3.13501 q^{50} +(0.869824 - 11.6070i) q^{52} +(2.53557 + 2.35267i) q^{53} +(-4.66645 - 2.24725i) q^{55} +(2.87318 - 25.4801i) q^{56} +(-12.5767 - 1.89563i) q^{58} +(-1.82008 + 1.24091i) q^{59} +(7.21614 - 6.69560i) q^{61} +(-1.33804 - 1.67785i) q^{62} +(20.4087 - 25.5917i) q^{64} +(0.308853 + 4.12135i) q^{65} +(1.83620 - 3.18040i) q^{67} +(-21.4047 - 37.0741i) q^{68} +(0.531987 + 14.2511i) q^{70} +(-1.29074 + 5.65511i) q^{71} +(5.44147 + 13.8646i) q^{73} +(8.42698 + 21.4716i) q^{74} +(6.71433 - 29.4174i) q^{76} +(-2.79058 + 6.39455i) q^{77} +(5.58327 + 9.67050i) q^{79} +(-15.2554 + 26.4231i) q^{80} +(0.327347 + 4.36814i) q^{82} +(2.89258 - 3.62718i) q^{83} +(9.47741 + 11.8843i) q^{85} +(9.47766 - 8.79398i) q^{86} +(-21.1163 + 14.3968i) q^{88} +(-13.0708 - 1.97011i) q^{89} +(5.53234 - 0.622853i) q^{91} +(13.8895 + 6.68885i) q^{92} +(-11.0584 - 10.2607i) q^{94} +(-0.800659 + 10.6840i) q^{95} +0.286958 q^{97} +(19.1570 - 1.43224i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55}+ \cdots + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00262	+	2.55465i	−0.708963	+	1.80641i	−0.129207	+	0.991618i	$0.541243\pi$
$2$	−1.00262	+	2.55465i	−0.708963	+	1.80641i	−0.579755	+	0.814791i	$0.696852\pi$
$3$		0			0
$3$		0			0
$4$	−4.05486	−	3.76236i	−2.02743	−	1.88118i
$5$	1.62281	+	1.10641i	0.725742	+	0.494802i	0.868956	−	0.494889i	$-0.164791\pi$
$5$	1.62281	+	1.10641i	0.725742	+	0.494802i	−0.143214	+	0.989692i	$0.545744\pi$
$6$		0			0
$7$	1.40782	−	2.24010i	0.532106	−	0.846678i
$7$	1.40782	−	2.24010i	0.532106	−	0.846678i
$8$	8.73185	−	4.20504i	3.08718	−	1.48671i
$9$		0			0
$10$	−4.45356	+	3.03638i	−1.40834	+	0.960189i
$11$	−2.60758	+	0.393029i	−0.786215	+	0.118503i	−0.529866	−	0.848081i	$-0.677758\pi$
$11$	−2.60758	+	0.393029i	−0.786215	+	0.118503i	−0.256349	+	0.966584i	$0.582520\pi$
$12$		0			0
$13$	1.31197	+	1.64516i	0.363875	+	0.456285i	0.929742	−	0.368212i	$-0.120030\pi$
$13$	1.31197	+	1.64516i	0.363875	+	0.456285i	−0.565867	+	0.824497i	$0.691458\pi$
$14$	4.31114	+	5.84246i	1.15220	+	1.56146i
$15$		0			0
$16$	1.16088	+	15.4908i	0.290220	+	3.87271i
$17$	7.39542	+	2.28118i	1.79365	+	0.553268i	0.998581	−	0.0532489i	$-0.0169577\pi$
$17$	7.39542	+	2.28118i	1.79365	+	0.553268i	0.795070	+	0.606517i	$0.207434\pi$
$18$		0			0
$19$	2.72747	+	4.72412i	0.625725	+	1.08379i	0.988400	+	0.151872i	$0.0485302\pi$
$19$	2.72747	+	4.72412i	0.625725	+	1.08379i	−0.362675	+	0.931916i	$0.618136\pi$
$20$	−2.41754	−	10.5919i	−0.540578	−	2.36843i
$21$		0			0
$22$	1.61037	−	7.05551i	0.343333	−	1.50424i
$23$	−2.66318	+	0.821483i	−0.555312	+	0.171291i	−0.559694	−	0.828699i	$-0.689081\pi$
$23$	−2.66318	+	0.821483i	−0.555312	+	0.171291i	0.00438222	+	0.999990i	$0.498605\pi$
$24$		0			0
$25$	−0.417347	−	1.06338i	−0.0834693	−	0.212676i
$26$	−5.51821	+	1.70214i	−1.08221	+	0.333818i
$27$		0			0
$28$	−14.1366	+	3.78655i	−2.67156	+	0.715592i
$29$	1.03128	+	4.51833i	0.191504	+	0.839032i	0.975803	+	0.218650i	$0.0701653\pi$
$29$	1.03128	+	4.51833i	0.191504	+	0.839032i	−0.784300	+	0.620382i	$0.786978\pi$
$30$		0			0
$31$	−0.390994	+	0.677221i	−0.0702245	+	0.121632i	−0.899000	−	0.437949i	$-0.855705\pi$
$31$	−0.390994	+	0.677221i	−0.0702245	+	0.121632i	0.828775	+	0.559582i	$0.189038\pi$
$32$	−22.2155	−	6.85257i	−3.92718	−	1.21137i
$33$		0			0
$34$	−13.2424	+	16.6055i	−2.27106	+	2.84782i
$35$	4.76309	−	2.07762i	0.805110	−	0.351182i
$36$		0			0
$37$	6.16124	−	5.71680i	1.01290	−	0.939835i	0.0147067	−	0.999892i	$-0.495319\pi$
$37$	6.16124	−	5.71680i	1.01290	−	0.939835i	0.998195	+	0.0600565i	$0.0191281\pi$
$38$	−14.8031	+	2.23121i	−2.40138	+	0.361950i
$39$		0			0
$40$	18.8226	+	2.83705i	2.97612	+	0.448577i
$41$	1.43808	−	0.692542i	0.224590	−	0.108157i	−0.318205	−	0.948022i	$-0.603080\pi$
$41$	1.43808	−	0.692542i	0.224590	−	0.108157i	0.542795	+	0.839865i	$0.317366\pi$
$42$		0			0
$43$	−4.24459	−	2.04409i	−0.647294	−	0.311720i	0.0812760	−	0.996692i	$-0.474100\pi$
$43$	−4.24459	−	2.04409i	−0.647294	−	0.311720i	−0.728570	+	0.684971i	$0.759815\pi$
$44$	12.0521	+	8.21698i	1.81692	+	1.23876i
$45$		0			0
$46$	0.571574	−	7.62713i	0.0842740	−	1.12456i
$47$	−2.00825	+	5.11693i	−0.292933	+	0.746382i	0.706326	+	0.707887i	$0.250351\pi$
$47$	−2.00825	+	5.11693i	−0.292933	+	0.746382i	−0.999259	+	0.0384945i	$0.987744\pi$
$48$		0			0
$49$	−3.03608	−	6.30731i	−0.433726	−	0.901045i
$50$	3.13501			0.443357
$51$		0			0
$52$	0.869824	−	11.6070i	0.120623	−	1.60960i
$53$	2.53557	+	2.35267i	0.348288	+	0.323164i	0.834845	−	0.550485i	$-0.185557\pi$
$53$	2.53557	+	2.35267i	0.348288	+	0.323164i	−0.486557	+	0.873649i	$0.661748\pi$
$54$		0			0
$55$	−4.66645	−	2.24725i	−0.629225	−	0.303019i
$56$	2.87318	−	25.4801i	0.383945	−	3.40493i
$57$		0			0
$58$	−12.5767	−	1.89563i	−1.65140	−	0.248909i
$59$	−1.82008	+	1.24091i	−0.236954	+	0.161553i	−0.675976	−	0.736924i	$-0.736278\pi$
$59$	−1.82008	+	1.24091i	−0.236954	+	0.161553i	0.439022	+	0.898477i	$0.355325\pi$
$60$		0			0
$61$	7.21614	−	6.69560i	0.923932	−	0.857284i	−0.0661449	−	0.997810i	$-0.521070\pi$
$61$	7.21614	−	6.69560i	0.923932	−	0.857284i	0.990077	+	0.140526i	$0.0448795\pi$
$62$	−1.33804	−	1.67785i	−0.169931	−	0.213087i
$63$		0			0
$64$	20.4087	−	25.5917i	2.55109	−	3.19897i
$65$	0.308853	+	4.12135i	0.0383085	+	0.511191i
$66$		0			0
$67$	1.83620	−	3.18040i	0.224328	−	0.388547i	−0.731790	−	0.681531i	$-0.761315\pi$
$67$	1.83620	−	3.18040i	0.224328	−	0.388547i	0.956118	+	0.292983i	$0.0946480\pi$
$68$	−21.4047	−	37.0741i	−2.59571	−	4.49589i
$69$		0			0
$70$	0.531987	+	14.2511i	0.0635846	+	1.70333i
$71$	−1.29074	+	5.65511i	−0.153183	+	0.671139i	0.838765	+	0.544493i	$0.183278\pi$
$71$	−1.29074	+	5.65511i	−0.153183	+	0.671139i	−0.991948	+	0.126645i	$0.959579\pi$
$72$		0			0
$73$	5.44147	+	13.8646i	0.636876	+	1.62273i	0.774738	+	0.632282i	$0.217882\pi$
$73$	5.44147	+	13.8646i	0.636876	+	1.62273i	−0.137862	+	0.990451i	$0.544023\pi$
$74$	8.42698	+	21.4716i	0.979617	+	2.49602i
$75$		0			0
$76$	6.71433	−	29.4174i	0.770186	−	3.37441i
$77$	−2.79058	+	6.39455i	−0.318016	+	0.728727i
$78$		0			0
$79$	5.58327	+	9.67050i	0.628167	+	1.08802i	0.987919	+	0.154969i	$0.0495277\pi$
$79$	5.58327	+	9.67050i	0.628167	+	1.08802i	−0.359753	+	0.933048i	$0.617139\pi$
$80$	−15.2554	+	26.4231i	−1.70560	+	2.95419i
$81$		0			0
$82$	0.327347	+	4.36814i	0.0361494	+	0.482380i
$83$	2.89258	−	3.62718i	0.317502	−	0.398135i	−0.597313	−	0.802008i	$-0.703765\pi$
$83$	2.89258	−	3.62718i	0.317502	−	0.398135i	0.914815	+	0.403874i	$0.132336\pi$
$84$		0			0
$85$	9.47741	+	11.8843i	1.02797	+	1.28903i
$86$	9.47766	−	8.79398i	1.02200	−	0.948279i
$87$		0			0
$88$	−21.1163	+	14.3968i	−2.25100	+	1.53471i
$89$	−13.0708	−	1.97011i	−1.38550	−	0.208831i	−0.586399	−	0.810023i	$-0.699455\pi$
$89$	−13.0708	−	1.97011i	−1.38550	−	0.208831i	−0.799105	+	0.601192i	$0.794693\pi$
$90$		0			0
$91$	5.53234	−	0.622853i	0.579946	−	0.0652928i
$92$	13.8895	+	6.68885i	1.44808	+	0.697361i
$93$		0			0
$94$	−11.0584	−	10.2607i	−1.14059	−	1.05831i
$95$	−0.800659	+	10.6840i	−0.0821459	+	1.09616i
$96$		0			0
$97$	0.286958			0.0291361			0.0145681	−	0.999894i	$-0.495363\pi$
$97$	0.286958			0.0291361			0.0145681	+	0.999894i	$0.495363\pi$
$98$	19.1570	−	1.43224i	1.93515	−	0.144678i
$99$		0			0
$100$	−2.30854	+	5.88207i	−0.230854	+	0.588207i
$101$	1.28197	−	17.1066i	0.127560	−	1.70217i	−0.455899	−	0.890032i	$-0.650682\pi$
$101$	1.28197	−	17.1066i	0.127560	−	1.70217i	0.583459	−	0.812142i	$-0.301699\pi$
$102$		0			0
$103$	−12.4145	−	8.46406i	−1.22324	−	0.833989i	−0.232877	−	0.972506i	$-0.574814\pi$
$103$	−12.4145	−	8.46406i	−1.22324	−	0.833989i	−0.990360	+	0.138517i	$0.955766\pi$
$104$	18.3739	+	8.84839i	1.80171	+	0.867656i
$105$		0			0
$106$	−8.55247	+	4.11865i	−0.830689	+	0.400039i
$107$	−4.87053	−	0.734115i	−0.470852	−	0.0709695i	−0.0906696	−	0.995881i	$-0.528901\pi$
$107$	−4.87053	−	0.734115i	−0.470852	−	0.0709695i	−0.380182	+	0.924911i	$0.624139\pi$
$108$		0			0
$109$	1.35946	−	0.204905i	0.130212	−	0.0196263i	−0.0836128	−	0.996498i	$-0.526646\pi$
$109$	1.35946	−	0.204905i	0.130212	−	0.0196263i	0.213825	+	0.976872i	$0.431408\pi$
$110$	10.4196	−	9.66800i	0.993472	−	0.921807i
$111$		0			0
$112$	36.3353	+	19.2079i	3.43337	+	1.81497i
$113$	−5.43368	+	6.81362i	−0.511158	+	0.640972i	−0.968705	−	0.248214i	$-0.920157\pi$
$113$	−5.43368	+	6.81362i	−0.511158	+	0.640972i	0.457548	+	0.889185i	$0.348728\pi$
$114$		0			0
$115$	−5.23073	−	1.61347i	−0.487768	−	0.150457i
$116$	12.8179	−	22.2012i	1.19011	−	2.06133i
$117$		0			0
$118$	−1.34523	−	5.89382i	−0.123838	−	0.542571i
$119$	15.5215	−	13.3550i	1.42285	−	1.22425i
$120$		0			0
$121$	−3.86630	+	1.19260i	−0.351482	+	0.108418i
$122$	9.86981	+	25.1479i	0.893571	+	2.27678i
$123$		0			0
$124$	4.13337	−	1.27498i	0.371188	−	0.114496i
$125$	2.68452	−	11.7617i	0.240111	−	1.05199i
$126$		0			0
$127$	1.42041	+	6.22321i	0.126041	+	0.552220i	0.998032	+	0.0626998i	$0.0199711\pi$
$127$	1.42041	+	6.22321i	0.126041	+	0.552220i	−0.871992	+	0.489521i	$0.837172\pi$
$128$	21.6672	+	37.5287i	1.91513	+	3.31710i
$129$		0			0
$130$	−10.8383	−	3.34316i	−0.950579	−	0.293215i
$131$	0.565680	+	7.54847i	0.0494237	+	0.659513i	0.965815	+	0.259231i	$0.0834689\pi$
$131$	0.565680	+	7.54847i	0.0494237	+	0.659513i	−0.916392	+	0.400282i	$0.868912\pi$
$132$		0			0
$133$	14.4223	+	0.540910i	1.25057	+	0.0469029i
$134$	6.28377	+	7.87960i	0.542835	+	0.680693i
$135$		0			0
$136$	74.1681	−	11.1790i	6.35986	−	0.958595i
$137$	10.5639	−	7.20233i	0.902534	−	0.615337i	−0.0206120	−	0.999788i	$-0.506561\pi$
$137$	10.5639	−	7.20233i	0.902534	−	0.615337i	0.923146	+	0.384451i	$0.125609\pi$
$138$		0			0
$139$	10.5063	−	5.05956i	0.891132	−	0.429147i	0.0684541	−	0.997654i	$-0.478193\pi$
$139$	10.5063	−	5.05956i	0.891132	−	0.429147i	0.822678	+	0.568508i	$0.192479\pi$
$140$	−27.1304	−	9.49602i	−2.29294	−	0.802560i
$141$		0			0
$142$	−13.1527	−	8.96735i	−1.10375	−	0.752523i
$143$	−4.06766	−	3.77424i	−0.340155	−	0.315618i
$144$		0			0
$145$	−3.32556	+	8.47339i	−0.276173	+	0.703677i
$146$	−40.8750			−3.38284
$147$		0			0
$148$	−46.4916			−3.82159
$149$	4.81589	−	12.2707i	0.394533	−	1.00525i	−0.586246	−	0.810133i	$-0.699395\pi$
$149$	4.81589	−	12.2707i	0.394533	−	1.00525i	0.980779	−	0.195121i	$-0.0625101\pi$
$150$		0			0
$151$	2.99764	+	2.78140i	0.243945	+	0.226347i	0.792663	−	0.609659i	$-0.208694\pi$
$151$	2.99764	+	2.78140i	0.243945	+	0.226347i	−0.548719	+	0.836007i	$0.684884\pi$
$152$	43.6810	+	29.7812i	3.54300	+	2.41557i
$153$		0			0
$154$	−13.5379	−	13.5403i	−1.09092	−	1.09111i
$155$	−1.38379	+	0.666399i	−0.111149	+	0.0535265i
$156$		0			0
$157$	−5.33071	+	3.63441i	−0.425437	+	0.290058i	−0.757049	−	0.653358i	$-0.773360\pi$
$157$	−5.33071	+	3.63441i	−0.425437	+	0.290058i	0.331613	+	0.943416i	$0.392407\pi$
$158$	−30.3026	+	4.56739i	−2.41075	+	0.363362i
$159$		0			0
$160$	−28.4697	−	35.6999i	−2.25073	−	2.82232i
$161$	−1.90908	+	7.12229i	−0.150457	+	0.561315i
$162$		0			0
$163$	−1.59257	−	21.2513i	−0.124740	−	1.66453i	−0.611685	−	0.791101i	$-0.709508\pi$
$163$	−1.59257	−	21.2513i	−0.124740	−	1.66453i	0.486946	−	0.873432i	$-0.338111\pi$
$164$	−8.43680	−	2.60241i	−0.658803	−	0.203214i
$165$		0			0
$166$	6.36599	+	11.0262i	0.494097	+	0.855801i
$167$	−2.68891	−	11.7809i	−0.208074	−	0.911631i	−0.965847	−	0.259113i	$-0.916570\pi$
$167$	−2.68891	−	11.7809i	−0.208074	−	0.911631i	0.757773	−	0.652518i	$-0.226287\pi$
$168$		0			0
$169$	1.90749	−	8.35727i	0.146730	−	0.642867i
$170$	−39.8625	+	12.2959i	−3.05731	+	0.943056i
$171$		0			0
$172$	9.52063	+	24.2582i	0.725941	+	1.84967i
$173$	−14.4541	+	4.45849i	−1.09892	+	0.338973i	−0.790615	−	0.612314i	$-0.790239\pi$
$173$	−14.4541	+	4.45849i	−1.09892	+	0.338973i	−0.308308	+	0.951287i	$0.599763\pi$
$174$		0			0
$175$	−2.96963	−	0.562154i	−0.224483	−	0.0424948i
$176$	−9.11544	−	39.9374i	−0.687102	−	3.01039i
$177$		0			0
$178$	18.1381	−	31.4160i	1.35950	−	2.35473i
$179$	−9.56093	−	2.94916i	−0.714618	−	0.220430i	−0.0839351	−	0.996471i	$-0.526749\pi$
$179$	−9.56093	−	2.94916i	−0.714618	−	0.220430i	−0.630683	+	0.776041i	$0.717225\pi$
$180$		0			0
$181$	−0.755969	+	0.947955i	−0.0561907	+	0.0704609i	−0.809133	−	0.587626i	$-0.800063\pi$
$181$	−0.755969	+	0.947955i	−0.0561907	+	0.0704609i	0.752942	+	0.658087i	$0.228634\pi$
$182$	−3.95569	+	14.7577i	−0.293215	+	1.09391i
$183$		0			0
$184$	−19.8001	+	18.3718i	−1.45969	+	1.35439i
$185$	16.3236	−	2.46039i	1.20014	−	0.180892i
$186$		0			0
$187$	−20.1807	−	3.04175i	−1.47576	−	0.222435i
$188$	27.3949	−	13.1927i	1.99798	−	0.962176i
$189$		0			0
$190$	−26.4912	−	12.7575i	−1.92187	−	0.925526i
$191$	−15.9211	−	10.8548i	−1.15201	−	0.785429i	−0.172144	−	0.985072i	$-0.555069\pi$
$191$	−15.9211	−	10.8548i	−1.15201	−	0.785429i	−0.979869	+	0.199643i	$0.936022\pi$
$192$		0			0
$193$	−1.43572	+	19.1584i	−0.103346	+	1.37905i	0.668722	+	0.743513i	$0.266842\pi$
$193$	−1.43572	+	19.1584i	−0.103346	+	1.37905i	−0.772068	+	0.635540i	$0.780777\pi$
$194$	−0.287711	+	0.733075i	−0.0206564	+	0.0526318i
$195$		0			0
$196$	−11.4195	+	36.9981i	−0.815679	+	2.64272i
$197$	−6.02438			−0.429219			−0.214610	−	0.976700i	$-0.568848\pi$
$197$	−6.02438			−0.429219			−0.214610	+	0.976700i	$0.568848\pi$
$198$		0			0
$199$	0.922189	−	12.3058i	0.0653722	−	0.872332i	−0.864072	−	0.503369i	$-0.832094\pi$
$199$	0.922189	−	12.3058i	0.0653722	−	0.872332i	0.929444	−	0.368963i	$-0.120287\pi$
$200$	−8.11577	−	7.53033i	−0.573871	−	0.532475i
$201$		0			0
$202$	42.4161	+	20.4265i	2.98439	+	1.43720i
$203$	11.5734	+	4.05083i	0.812290	+	0.284313i
$204$		0			0
$205$	3.09996	+	0.467244i	0.216511	+	0.0326337i
$206$	34.0698	−	23.2284i	2.37375	−	1.61840i
$207$		0			0
$208$	−23.9619	+	22.2334i	−1.66146	+	1.54161i
$209$	−8.96882	−	11.2465i	−0.620386	−	0.777940i
$210$		0			0
$211$	8.73027	−	10.9474i	0.601017	−	0.753651i	−0.384519	−	0.923117i	$-0.625633\pi$
$211$	8.73027	−	10.9474i	0.601017	−	0.753651i	0.985536	+	0.169466i	$0.0542042\pi$
$212$	−1.42981	−	19.0795i	−0.0981997	−	1.31038i
$213$		0			0
$214$	6.75872	−	11.7064i	0.462017	−	0.800236i
$215$	−4.62655	−	8.01343i	−0.315528	−	0.546511i
$216$		0			0
$217$	0.966592	+	1.82927i	0.0656165	+	0.124179i
$218$	−0.839564	+	3.67837i	−0.0568625	+	0.249131i
$219$		0			0
$220$	10.4669	+	26.6691i	0.705676	+	1.79803i
$221$	5.94965	+	15.1595i	0.400217	+	1.01974i
$222$		0			0
$223$	1.29428	−	5.67062i	0.0866715	−	0.379733i	−0.912925	−	0.408127i	$-0.866182\pi$
$223$	1.29428	−	5.67062i	0.0866715	−	0.379733i	0.999597	+	0.0283940i	$0.00903930\pi$
$224$	−46.6258	+	40.1177i	−3.11532	+	2.68047i
$225$		0			0
$226$	−11.9585	−	20.7126i	−0.795464	−	1.37778i
$227$	8.53849	−	14.7891i	0.566720	−	0.981587i	−0.430168	−	0.902749i	$-0.641546\pi$
$227$	8.53849	−	14.7891i	0.566720	−	0.981587i	0.996887	−	0.0788382i	$-0.0251211\pi$
$228$		0			0
$229$	−0.0321065	−	0.428431i	−0.00212166	−	0.0283115i	0.996042	−	0.0888783i	$-0.0283282\pi$
$229$	−0.0321065	−	0.428431i	−0.00212166	−	0.0283115i	−0.998164	+	0.0605668i	$0.980709\pi$
$230$	9.36630	−	11.7450i	0.617595	−	0.774440i
$231$		0			0
$232$	28.0047	+	35.1168i	1.83860	+	2.30553i
$233$	−10.9126	+	10.1254i	−0.714907	+	0.663337i	−0.951281	−	0.308326i	$-0.900231\pi$
$233$	−10.9126	+	10.1254i	−0.714907	+	0.663337i	0.236374	+	0.971662i	$0.424041\pi$
$234$		0			0
$235$	−8.92044	+	6.08185i	−0.581905	+	0.396736i
$236$	12.0489	+	1.81608i	0.784317	+	0.118217i
$237$		0			0
$238$	18.5550	+	53.0420i	1.20274	+	3.43820i
$239$	−8.15721	−	3.92830i	−0.527646	−	0.254101i	0.151042	−	0.988527i	$-0.451737\pi$
$239$	−8.15721	−	3.92830i	−0.527646	−	0.254101i	−0.678688	+	0.734426i	$0.737451\pi$
$240$		0			0
$241$	5.69089	+	5.28037i	0.366582	+	0.340139i	0.841859	−	0.539698i	$-0.181461\pi$
$241$	5.69089	+	5.28037i	0.366582	+	0.340139i	−0.475277	+	0.879836i	$0.657652\pi$
$242$	0.829788	−	11.0728i	0.0533408	−	0.711784i
$243$		0			0
$244$	−54.4517			−3.48591
$245$	2.05151	−	13.5947i	0.131066	−	0.868534i
$246$		0			0
$247$	−4.19357	+	10.6850i	−0.266830	+	0.679872i
$248$	−0.566359	+	7.55753i	−0.0359638	+	0.479904i
$249$		0			0
$250$	27.3553	+	18.6505i	1.73010	+	1.17956i
$251$	2.25422	+	1.08557i	0.142285	+	0.0685208i	0.503671	−	0.863895i	$-0.331982\pi$
$251$	2.25422	+	1.08557i	0.142285	+	0.0685208i	−0.361387	+	0.932416i	$0.617697\pi$
$252$		0			0
$253$	6.62159	−	3.18879i	0.416296	−	0.200478i
$254$	−17.3222	−	2.61091i	−1.08689	−	0.163823i
$255$		0			0
$256$	−52.8619	+	7.96764i	−3.30387	+	0.497978i
$257$	−8.81597	+	8.18003i	−0.549925	+	0.510256i	−0.905474	−	0.424402i	$-0.860484\pi$
$257$	−8.81597	+	8.18003i	−0.549925	+	0.510256i	0.355549	+	0.934658i	$0.384294\pi$
$258$		0			0
$259$	−4.13226	−	21.8500i	−0.256766	−	1.35769i
$260$	14.2537	−	17.8735i	0.883975	−	1.10847i
$261$		0			0
$262$	−19.8508	−	6.12317i	−1.22639	−	0.378291i
$263$	−1.29549	+	2.24386i	−0.0798836	+	0.138362i	−0.903200	−	0.429221i	$-0.858788\pi$
$263$	−1.29549	+	2.24386i	−0.0798836	+	0.138362i	0.823316	+	0.567583i	$0.192122\pi$
$264$		0			0
$265$	1.51173	+	6.62332i	0.0928648	+	0.406867i
$266$	−15.8420	+	36.3015i	−0.971334	+	2.22579i
$267$		0			0
$268$	−19.4113	+	5.98761i	−1.18574	+	0.365751i
$269$	−5.53096	−	14.0927i	−0.337229	−	0.859245i	−0.994417	−	0.105518i	$-0.966350\pi$
$269$	−5.53096	−	14.0927i	−0.337229	−	0.859245i	0.657189	−	0.753726i	$-0.271745\pi$
$270$		0			0
$271$	−7.53727	+	2.32494i	−0.457856	+	0.141230i	−0.515100	−	0.857130i	$-0.672245\pi$
$271$	−7.53727	+	2.32494i	−0.457856	+	0.141230i	0.0572433	+	0.998360i	$0.481769\pi$
$272$	−26.7523	+	117.209i	−1.62210	+	7.10687i
$273$		0			0
$274$	7.80781	+	34.2082i	0.471687	+	2.06660i
$275$	1.50620	+	2.60882i	0.0908276	+	0.157318i
$276$		0			0
$277$	1.15421	+	0.356026i	0.0693496	+	0.0213915i	0.329236	−	0.944248i	$-0.393209\pi$
$277$	1.15421	+	0.356026i	0.0693496	+	0.0213915i	−0.259886	+	0.965639i	$0.583685\pi$
$278$	2.39153	+	31.9127i	0.143434	+	1.91400i
$279$		0			0
$280$	32.8542	−	38.1704i	1.96341	−	2.28112i
$281$	−11.3165	−	14.1904i	−0.675085	−	0.846530i	0.319806	−	0.947483i	$-0.396382\pi$
$281$	−11.3165	−	14.1904i	−0.675085	−	0.846530i	−0.994891	+	0.100953i	$0.967811\pi$
$282$		0			0
$283$	−10.2154	+	1.53973i	−0.607245	+	0.0915274i	−0.445465	−	0.895299i	$-0.646962\pi$
$283$	−10.2154	+	1.53973i	−0.607245	+	0.0915274i	−0.161780	+	0.986827i	$0.551723\pi$
$284$	26.5104	−	18.0745i	1.57310	−	1.07252i
$285$		0			0
$286$	13.7202	−	6.60729i	0.811292	−	0.390698i
$287$	0.473195	−	4.19641i	0.0279318	−	0.247706i
$288$		0			0
$289$	35.4423	+	24.1642i	2.08484	+	1.42142i
$290$	−18.3122	−	16.9913i	−1.07533	−	0.997762i
$291$		0			0
$292$	30.0994	−	76.6919i	1.76143	−	4.48806i
$293$	−0.832475			−0.0486337			−0.0243169	−	0.999704i	$-0.507741\pi$
$293$	−0.832475			−0.0486337			−0.0243169	+	0.999704i	$0.507741\pi$
$294$		0			0
$295$	−4.32659			−0.251904
$296$	29.7597	−	75.8264i	1.72975	−	4.40732i
$297$		0			0
$298$	26.5188	+	24.6058i	1.53619	+	1.42538i
$299$	−4.84548	−	3.30359i	−0.280222	−	0.191052i
$300$		0			0
$301$	−10.5546	+	6.63059i	−0.608356	+	0.382181i
$302$	−10.1110	+	4.86921i	−0.581824	+	0.280191i
$303$		0			0
$304$	−70.0144	+	47.7350i	−4.01560	+	2.73779i
$305$	19.1185	−	2.88165i	1.09472	−	0.165003i
$306$		0			0
$307$	−15.6748	−	19.6556i	−0.894610	−	1.12181i	−0.991960	−	0.126556i	$-0.959608\pi$
$307$	−15.6748	−	19.6556i	−0.894610	−	1.12181i	0.0973492	−	0.995250i	$-0.468964\pi$
$308$	35.3740	−	15.4298i	2.01562	−	0.879196i
$309$		0			0
$310$	−0.314990	−	4.20325i	−0.0178902	−	0.238728i
$311$	14.4006	+	4.44200i	0.816583	+	0.251882i	0.674786	−	0.738013i	$-0.264236\pi$
$311$	14.4006	+	4.44200i	0.816583	+	0.251882i	0.141797	+	0.989896i	$0.454712\pi$
$312$		0			0
$313$	−11.5723	−	20.0439i	−0.654107	−	1.13295i	−0.982117	−	0.188272i	$-0.939711\pi$
$313$	−11.5723	−	20.0439i	−0.654107	−	1.13295i	0.328010	−	0.944674i	$-0.393622\pi$
$314$	−3.93994	−	17.2620i	−0.222344	−	0.974152i
$315$		0			0
$316$	13.7445	−	60.2188i	0.773191	−	3.38757i
$317$	3.05986	−	0.943843i	0.171859	−	0.0530115i	−0.207631	−	0.978207i	$-0.566575\pi$
$317$	3.05986	−	0.943843i	0.171859	−	0.0530115i	0.379491	+	0.925196i	$0.376099\pi$
$318$		0			0
$319$	−4.46498	−	11.3766i	−0.249991	−	0.636966i
$320$	61.4345	−	18.9500i	3.43429	−	1.05934i
$321$		0			0
$322$	−16.2808	−	12.0180i	−0.907296	−	0.669738i
$323$	9.39421	+	41.1587i	0.522708	+	2.29013i
$324$		0			0
$325$	1.20189	−	2.08173i	0.0666686	−	0.115473i
$326$	55.8864	+	17.2387i	3.09526	+	0.954762i
$327$		0			0
$328$	9.64492	−	12.0943i	0.532551	−	0.667798i
$329$	8.63518	+	11.7024i	0.476073	+	0.645174i
$330$		0			0
$331$	−14.9403	+	13.8626i	−0.821194	+	0.761957i	−0.974060	−	0.226290i	$-0.927340\pi$
$331$	−14.9403	+	13.8626i	−0.821194	+	0.761957i	0.152866	+	0.988247i	$0.451150\pi$
$332$	−25.3758	+	3.82478i	−1.39268	+	0.209912i
$333$		0			0
$334$	32.7919	+	4.94259i	1.79429	+	0.270446i
$335$	6.49863	−	3.12958i	0.355058	−	0.170987i
$336$		0			0
$337$	7.04355	+	3.39199i	0.383686	+	0.184774i	0.615777	−	0.787921i	$-0.288842\pi$
$337$	7.04355	+	3.39199i	0.383686	+	0.184774i	−0.232090	+	0.972694i	$0.574557\pi$
$338$	19.4374	+	13.2522i	1.05725	+	0.720823i
$339$		0			0
$340$	6.28343	−	83.8466i	0.340767	−	4.54722i
$341$	0.753379	−	1.91958i	0.0407978	−	0.103951i
$342$		0			0
$343$	−18.4033	−	2.07845i	−0.993683	−	0.112226i
$344$	−45.6586			−2.46175
$345$		0			0
$346$	3.10215	−	41.3953i	0.166772	−	2.22542i
$347$	20.4713	+	18.9946i	1.09896	+	1.01968i	0.999697	+	0.0246206i	$0.00783777\pi$
$347$	20.4713	+	18.9946i	1.09896	+	1.01968i	0.0992592	+	0.995062i	$0.468353\pi$
$348$		0			0
$349$	7.45595	+	3.59059i	0.399108	+	0.192200i	0.622661	−	0.782492i	$-0.286051\pi$
$349$	7.45595	+	3.59059i	0.399108	+	0.192200i	−0.223554	+	0.974692i	$0.571766\pi$
$350$	4.41353	−	7.02272i	0.235913	−	0.375380i
$351$		0			0
$352$	60.6219	+	9.13728i	3.23116	+	0.487019i
$353$	−8.31737	+	5.67069i	−0.442689	+	0.301820i	−0.764074	−	0.645128i	$-0.776804\pi$
$353$	−8.31737	+	5.67069i	−0.442689	+	0.301820i	0.321385	+	0.946948i	$0.395852\pi$
$354$		0			0
$355$	−8.35151	+	7.74907i	−0.443252	+	0.411278i
$356$	45.5881	+	57.1656i	2.41616	+	3.02977i
$357$		0			0
$358$	17.1201	−	21.4679i	0.904825	−	1.13461i
$359$	−2.31317	−	30.8671i	−0.122084	−	1.62910i	−0.636301	−	0.771441i	$-0.719536\pi$
$359$	−2.31317	−	30.8671i	−0.122084	−	1.62910i	0.514216	−	0.857661i	$-0.328083\pi$
$360$		0			0
$361$	−5.37822	+	9.31534i	−0.283064	+	0.490281i
$362$	−1.66374	−	2.88168i	−0.0874441	−	0.151458i
$363$		0			0
$364$	−24.7762	−	18.2891i	−1.29863	−	0.958607i
$365$	−6.50954	+	28.5202i	−0.340725	+	1.49281i
$366$		0			0
$367$	7.60620	+	19.3803i	0.397041	+	1.01164i	0.979974	+	0.199123i	$0.0638094\pi$
$367$	7.60620	+	19.3803i	0.397041	+	1.01164i	−0.582934	+	0.812520i	$0.698095\pi$
$368$	−15.8171	−	40.3013i	−0.824523	−	2.10085i
$369$		0			0
$370$	−10.0811	+	44.1680i	−0.524089	+	2.29618i
$371$	8.83984	−	2.36780i	0.458942	−	0.122930i
$372$		0			0
$373$	1.11045	+	1.92335i	0.0574968	+	0.0995874i	0.893341	−	0.449379i	$-0.148355\pi$
$373$	1.11045	+	1.92335i	0.0574968	+	0.0995874i	−0.835844	+	0.548967i	$0.815021\pi$
$374$	28.0043	−	48.5049i	1.44807	−	2.50813i
$375$		0			0
$376$	3.98117	+	53.1251i	0.205313	+	2.73972i
$377$	−6.08036	+	7.62453i	−0.313154	+	0.392683i
$378$		0			0
$379$	−1.83216	−	2.29746i	−0.0941118	−	0.118012i	0.732546	−	0.680718i	$-0.238332\pi$
$379$	−1.83216	−	2.29746i	−0.0941118	−	0.118012i	−0.826658	+	0.562705i	$0.809761\pi$
$380$	43.4438	−	40.3100i	2.22862	−	2.06786i
$381$		0			0
$382$	43.6932	−	29.7895i	2.23554	−	1.52416i
$383$	−7.88201	−	1.18802i	−0.402752	−	0.0607051i	−0.0554570	−	0.998461i	$-0.517662\pi$
$383$	−7.88201	−	1.18802i	−0.402752	−	0.0607051i	−0.347295	+	0.937756i	$0.612900\pi$
$384$		0			0
$385$	−11.6036	+	7.28960i	−0.591373	+	0.371512i
$386$	−47.5035	−	22.8765i	−2.41786	−	1.16438i
$387$		0			0
$388$	−1.16357	−	1.07964i	−0.0590715	−	0.0548103i
$389$	−1.58516	+	21.1524i	−0.0803706	+	1.07247i	0.800569	+	0.599241i	$0.204531\pi$
$389$	−1.58516	+	21.1524i	−0.0803706	+	1.07247i	−0.880939	+	0.473229i	$0.843088\pi$
$390$		0			0
$391$	−21.5693			−1.09081
$392$	−53.0331	−	42.3077i	−2.67858	−	2.13686i
$393$		0			0
$394$	6.04019	−	15.3902i	0.304301	−	0.775345i
$395$	−1.63899	+	21.8708i	−0.0824664	+	1.10044i
$396$		0			0
$397$	6.55751	+	4.47083i	0.329112	+	0.224385i	0.716591	−	0.697494i	$-0.245702\pi$
$397$	6.55751	+	4.47083i	0.329112	+	0.224385i	−0.387479	+	0.921879i	$0.626654\pi$
$398$	30.5122	+	14.6939i	1.52944	+	0.736540i
$399$		0			0
$400$	15.9882	−	7.69951i	0.799410	−	0.384975i
$401$	−27.8295	−	4.19462i	−1.38974	−	0.209469i	−0.588830	−	0.808257i	$-0.700411\pi$
$401$	−27.8295	−	4.19462i	−1.38974	−	0.209469i	−0.800908	+	0.598787i	$0.795649\pi$
$402$		0			0
$403$	−1.62711	+	0.245247i	−0.0810520	+	0.0122166i
$404$	−69.5595	+	64.5418i	−3.46072	+	3.21107i
$405$		0			0
$406$	−21.9522	+	25.5044i	−1.08947	+	1.26576i
$407$	−13.8191	+	17.3286i	−0.684985	+	0.858944i
$408$		0			0
$409$	−11.8769	−	3.66353i	−0.587273	−	0.181150i	−0.0131426	−	0.999914i	$-0.504184\pi$
$409$	−11.8769	−	3.66353i	−0.587273	−	0.181150i	−0.574130	+	0.818764i	$0.694660\pi$
$410$	−4.30174	+	7.45083i	−0.212448	+	0.367970i
$411$		0			0
$412$	18.4942	+	81.0284i	0.911144	+	3.99198i
$413$	0.217412	+	5.82413i	0.0106982	+	0.286587i
$414$		0			0
$415$	8.70725	−	2.68583i	0.427422	−	0.131842i
$416$	−17.8725	−	45.5383i	−0.876270	−	2.23270i
$417$		0			0
$418$	37.7233	−	11.6361i	1.84511	−	0.569140i
$419$	−1.96081	+	8.59089i	−0.0957920	+	0.419692i	−0.999972	−	0.00745902i	$-0.997626\pi$
$419$	−1.96081	+	8.59089i	−0.0957920	+	0.419692i	0.904180	+	0.427151i	$0.140483\pi$
$420$		0			0
$421$	−1.65715	−	7.26046i	−0.0807647	−	0.353853i	0.918357	−	0.395753i	$-0.129516\pi$
$421$	−1.65715	−	7.26046i	−0.0807647	−	0.353853i	−0.999122	+	0.0418994i	$0.986659\pi$
$422$	19.2136	+	33.2789i	0.935303	+	1.61999i
$423$		0			0
$424$	32.0333	+	9.88097i	1.55568	+	0.479862i
$425$	−0.660682	−	8.81619i	−0.0320478	−	0.427648i
$426$		0			0
$427$	−4.83977	−	25.5911i	−0.234213	−	1.23844i
$428$	16.9873	+	21.3014i	0.821113	+	1.02964i
$429$		0			0
$430$	25.1102	−	3.78475i	1.21092	−	0.182517i
$431$	−13.4148	+	9.14605i	−0.646168	+	0.440550i	−0.841551	−	0.540177i	$-0.818357\pi$
$431$	−13.4148	+	9.14605i	−0.646168	+	0.440550i	0.195384	+	0.980727i	$0.437405\pi$
$432$		0			0
$433$	−2.29606	+	1.10572i	−0.110342	+	0.0531377i	−0.488240	−	0.872709i	$-0.662361\pi$
$433$	−2.29606	+	1.10572i	−0.110342	+	0.0531377i	0.377899	+	0.925847i	$0.376647\pi$
$434$	−5.64227	+	0.635230i	−0.270837	+	0.0304920i
$435$		0			0
$436$	−6.28333	−	4.28390i	−0.300917	−	0.205162i
$437$	−11.1445	−	10.3406i	−0.533116	−	0.494659i
$438$		0			0
$439$	−6.74813	+	17.1940i	−0.322071	+	0.820623i	0.674530	+	0.738247i	$0.264346\pi$
$439$	−6.74813	+	17.1940i	−0.322071	+	0.820623i	−0.996601	+	0.0823761i	$0.973749\pi$
$440$	−50.1965			−2.39303
$441$		0			0
$442$	−44.6924			−2.12580
$443$	−0.0408306	+	0.104035i	−0.00193992	+	0.00494284i	−0.931840	−	0.362868i	$-0.881797\pi$
$443$	−0.0408306	+	0.104035i	−0.00193992	+	0.00494284i	0.929901	+	0.367811i	$0.119893\pi$
$444$		0			0
$445$	−19.0317	−	17.6588i	−0.902188	−	0.837108i
$446$	13.1887	+	8.99194i	0.624505	+	0.425781i
$447$		0			0
$448$	−28.5962	−	81.7462i	−1.35104	−	3.86214i
$449$	31.2561	−	15.0522i	1.47507	−	0.710355i	0.488327	−	0.872660i	$-0.337607\pi$
$449$	31.2561	−	15.0522i	1.47507	−	0.710355i	0.986741	+	0.162305i	$0.0518929\pi$
$450$		0			0
$451$	−3.47771	+	2.37107i	−0.163759	+	0.111649i
$452$	47.6681	−	7.18481i	2.24212	−	0.337945i
$453$		0			0
$454$	29.2200	+	36.6408i	1.37136	+	1.71964i
$455$	9.66705	+	5.11027i	0.453198	+	0.239573i
$456$		0			0
$457$	0.481692	+	6.42773i	0.0225326	+	0.300676i	0.997072	+	0.0764622i	$0.0243625\pi$
$457$	0.481692	+	6.42773i	0.0225326	+	0.300676i	−0.974540	+	0.224214i	$0.928018\pi$
$458$	1.12668	+	0.347535i	0.0526464	+	0.0162393i
$459$		0			0
$460$	15.1394	+	26.2223i	0.705880	+	1.22262i
$461$	0.797540	+	3.49425i	0.0371451	+	0.162743i	0.990099	−	0.140373i	$-0.0448301\pi$
$461$	0.797540	+	3.49425i	0.0371451	+	0.162743i	−0.952954	+	0.303116i	$0.901973\pi$
$462$		0			0
$463$	−4.15107	+	18.1870i	−0.192917	+	0.845224i	0.782111	+	0.623139i	$0.214143\pi$
$463$	−4.15107	+	18.1870i	−0.192917	+	0.845224i	−0.975028	+	0.222084i	$0.928714\pi$
$464$	−68.7955	+	21.2206i	−3.19375	+	0.985142i
$465$		0			0
$466$	−14.9256	−	38.0298i	−0.691414	−	1.76169i
$467$	29.4973	−	9.09871i	1.36497	−	0.421038i	0.476180	−	0.879348i	$-0.342021\pi$
$467$	29.4973	−	9.09871i	1.36497	−	0.421038i	0.888792	+	0.458310i	$0.151545\pi$
$468$		0			0
$469$	−4.53936	−	8.59070i	−0.209608	−	0.396682i
$470$	−6.59313	−	28.8864i	−0.304118	−	1.33243i
$471$		0			0
$472$	−10.6746	+	18.4889i	−0.491338	+	0.851022i
$473$	11.8715	+	3.66187i	0.545852	+	0.168373i
$474$		0			0
$475$	3.88524	−	4.87194i	0.178267	−	0.223540i
$476$	−113.184	−	4.24497i	−5.18776	−	0.194568i
$477$		0			0
$478$	18.2140	−	16.9002i	0.833091	−	0.772996i
$479$	37.2936	−	5.62111i	1.70399	−	0.256835i	0.776347	−	0.630306i	$-0.217071\pi$
$479$	37.2936	−	5.62111i	1.70399	−	0.256835i	0.927642	+	0.373471i	$0.121833\pi$
$480$		0			0
$481$	17.4884	+	2.63595i	0.797402	+	0.120189i
$482$	−19.1953	+	9.24398i	−0.874323	+	0.421052i
$483$		0			0
$484$	20.1643	+	9.71060i	0.916558	+	0.441391i
$485$	0.465677	+	0.317493i	0.0211453	+	0.0144166i
$486$		0			0
$487$	−2.12852	+	28.4031i	−0.0964525	+	1.28707i	0.713534	+	0.700621i	$0.247093\pi$
$487$	−2.12852	+	28.4031i	−0.0964525	+	1.28707i	−0.809987	+	0.586449i	$0.800526\pi$
$488$	34.8550	−	88.8091i	1.57781	−	4.02020i
$489$		0			0
$490$	32.6728	+	18.8713i	1.47601	+	0.852518i
$491$	17.3428			0.782671			0.391336	−	0.920248i	$-0.372013\pi$
$491$	17.3428			0.782671			0.391336	+	0.920248i	$0.372013\pi$
$492$		0			0
$493$	−2.68040	+	35.7674i	−0.120719	+	1.61088i
$494$	−23.0919	−	21.4262i	−1.03895	−	0.964008i
$495$		0			0
$496$	−10.9446	−	5.27065i	−0.491428	−	0.236659i
$497$	10.8509	+	10.8528i	0.486728	+	0.486814i
$498$		0			0
$499$	−16.6572	−	2.51067i	−0.745678	−	0.112393i	−0.234797	−	0.972044i	$-0.575443\pi$
$499$	−16.6572	−	2.51067i	−0.745678	−	0.112393i	−0.510881	+	0.859651i	$0.670681\pi$
$500$	−55.1369	+	37.5917i	−2.46580	+	1.68115i
$501$		0			0
$502$	−5.03339	+	4.67031i	−0.224651	+	0.208446i
$503$	−25.7194	−	32.2511i	−1.14677	−	1.43800i	−0.880462	−	0.474117i	$-0.842767\pi$
$503$	−25.7194	−	32.2511i	−1.14677	−	1.43800i	−0.266309	−	0.963888i	$-0.585804\pi$
$504$		0			0
$505$	21.0074	−	26.3424i	0.934815	−	1.17222i
$506$	1.50726	+	20.1130i	0.0670059	+	0.894131i
$507$		0			0
$508$	17.6544	−	30.5783i	0.783287	−	1.35669i
$509$	21.6358	+	37.4742i	0.958988	+	1.66102i	0.724965	+	0.688785i	$0.241856\pi$
$509$	21.6358	+	37.4742i	0.958988	+	1.66102i	0.234023	+	0.972231i	$0.424811\pi$
$510$		0			0
$511$	38.7188	+	7.32950i	1.71282	+	0.324238i
$512$	13.3605	−	58.5360i	0.590454	−	2.58695i
$513$		0			0
$514$	−12.0580	−	30.7232i	−0.531854	−	1.35514i
$515$	−10.7816	−	27.4711i	−0.475094	−	1.21052i
$516$		0			0
$517$	3.22556	−	14.1321i	0.141860	−	0.621530i
$518$	59.9622	+	11.3509i	2.63459	+	0.498730i
$519$		0			0
$520$	20.0273	+	34.6883i	0.878256	+	1.52118i
$521$	6.87049	−	11.9000i	0.301002	−	0.521350i	−0.675361	−	0.737487i	$-0.736012\pi$
$521$	6.87049	−	11.9000i	0.301002	−	0.521350i	0.976363	+	0.216137i	$0.0693457\pi$
$522$		0			0
$523$	−1.99863	−	26.6698i	−0.0873938	−	1.16619i	−0.852657	−	0.522472i	$-0.825010\pi$
$523$	−1.99863	−	26.6698i	−0.0873938	−	1.16619i	0.765263	−	0.643718i	$-0.222609\pi$
$524$	26.1063	−	32.7363i	1.14046	−	1.43009i
$525$		0			0
$526$	−4.43338	−	5.55928i	−0.193305	−	0.242396i
$527$	−4.43642	+	4.11640i	−0.193254	+	0.179313i
$528$		0			0
$529$	−12.5858	+	8.58085i	−0.547208	+	0.373080i
$530$	−18.4359	−	2.77877i	−0.800806	−	0.120702i
$531$		0			0
$532$	−56.4453	−	56.4552i	−2.44721	−	2.44764i
$533$	3.02606	+	1.45727i	0.131073	+	0.0631214i
$534$		0			0
$535$	−7.09170	−	6.58014i	−0.306601	−	0.284484i
$536$	2.65976	−	35.4921i	0.114884	−	1.53302i
$537$		0			0
$538$	41.5472			1.79123
$539$	10.3958	+	15.2536i	0.447778	+	0.657017i
$540$		0			0
$541$	−7.34435	+	18.7131i	−0.315758	+	0.804538i	0.681588	+	0.731736i	$0.261290\pi$
$541$	−7.34435	+	18.7131i	−0.315758	+	0.804538i	−0.997346	+	0.0728026i	$0.976806\pi$
$542$	1.61765	−	21.5861i	0.0694842	−	0.927203i
$543$		0			0
$544$	−148.661	−	101.355i	−6.37377	−	4.34557i
$545$	2.43284	+	1.17160i	0.104212	+	0.0501856i
$546$		0			0
$547$	0.751658	−	0.361980i	0.0321386	−	0.0154771i	−0.417745	−	0.908564i	$-0.637180\pi$
$547$	0.751658	−	0.361980i	0.0321386	−	0.0154771i	0.449884	+	0.893087i	$0.351465\pi$
$548$	−69.9328	−	10.5407i	−2.98738	−	0.450276i
$549$		0			0
$550$	−8.17478	+	1.23215i	−0.348574	+	0.0525391i
$551$	−18.5323	+	17.1955i	−0.789504	+	0.732553i
$552$		0			0
$553$	29.5231	+	1.10727i	1.25545	+	0.0470859i
$554$	−2.06676	+	2.59163i	−0.0878082	+	0.110108i
$555$		0			0
$556$	−61.6374	−	19.0126i	−2.61401	−	0.806315i
$557$	−14.1490	+	24.5068i	−0.599513	+	1.03839i	0.393380	+	0.919376i	$0.371306\pi$
$557$	−14.1490	+	24.5068i	−0.599513	+	1.03839i	−0.992893	+	0.119011i	$0.962028\pi$
$558$		0			0
$559$	−2.20593	−	9.66481i	−0.0933009	−	0.408778i
$560$	37.7135	+	71.3725i	1.59368	+	3.01604i
$561$		0			0
$562$	47.5977	−	14.6820i	2.00779	−	0.619321i
$563$	8.05541	+	20.5249i	0.339495	+	0.865020i	0.994042	+	0.108998i	$0.0347642\pi$
$563$	8.05541	+	20.5249i	0.339495	+	0.865020i	−0.654547	+	0.756021i	$0.727141\pi$
$564$		0			0
$565$	−16.3565	+	5.04531i	−0.688123	+	0.212258i
$566$	6.30879	−	27.6406i	0.265178	−	1.16182i
$567$		0			0
$568$	12.5094	+	54.8072i	0.524882	+	2.29966i
$569$	−2.01868	−	3.49646i	−0.0846275	−	0.146579i	0.820605	−	0.571496i	$-0.193637\pi$
$569$	−2.01868	−	3.49646i	−0.0846275	−	0.146579i	−0.905232	+	0.424917i	$0.860303\pi$
$570$		0			0
$571$	−33.6551	−	10.3812i	−1.40842	−	0.434441i	−0.504973	−	0.863135i	$-0.668497\pi$
$571$	−33.6551	−	10.3812i	−1.40842	−	0.434441i	−0.903449	+	0.428695i	$0.858974\pi$
$572$	2.29375	+	30.6080i	0.0959067	+	1.27979i
$573$		0			0
$574$	10.2459	+	5.41627i	0.427656	+	0.226071i
$575$	1.98502	+	2.48914i	0.0827810	+	0.103804i
$576$		0			0
$577$	−19.0426	+	2.87021i	−0.792753	+	0.119488i	−0.532921	−	0.846165i	$-0.678906\pi$
$577$	−19.0426	+	2.87021i	−0.792753	+	0.119488i	−0.259833	+	0.965654i	$0.583667\pi$
$578$	−97.2662	+	66.3150i	−4.04574	+	2.75834i
$579$		0			0
$580$	45.3647	−	21.8465i	1.88366	−	0.907125i
$581$	−4.05300	−	11.5861i	−0.168147	−	0.480672i
$582$		0			0
$583$	−7.53638	−	5.13822i	−0.312125	−	0.212803i
$584$	105.815	+	98.1824i	4.37867	+	4.06282i
$585$		0			0
$586$	0.834660	−	2.12668i	0.0344795	−	0.0878523i
$587$	−26.6941			−1.10178			−0.550892	−	0.834577i	$-0.685712\pi$
$587$	−26.6941			−1.10178			−0.550892	+	0.834577i	$0.685712\pi$
$588$		0			0
$589$	−4.26570			−0.175765
$590$	4.33795	−	11.0529i	0.178591	−	0.455041i
$591$		0			0
$592$	95.7105	+	88.8063i	3.93368	+	3.64992i
$593$	−22.3898	−	15.2651i	−0.919441	−	0.626864i	0.00835012	−	0.999965i	$-0.497342\pi$
$593$	−22.3898	−	15.2651i	−0.919441	−	0.626864i	−0.927791	+	0.373101i	$0.878294\pi$
$594$		0			0
$595$	39.9645	−	4.49937i	1.63838	−	0.184456i
$596$	−65.6946	+	31.6368i	−2.69095	+	1.29590i
$597$		0			0
$598$	13.2977	−	9.06623i	0.543784	−	0.370746i
$599$	29.6592	−	4.47040i	1.21184	−	0.182656i	0.488138	−	0.872767i	$-0.337676\pi$
$599$	29.6592	−	4.47040i	1.21184	−	0.182656i	0.723703	+	0.690111i	$0.242438\pi$
$600$		0			0
$601$	−10.3796	−	13.0156i	−0.423391	−	0.530916i	0.523691	−	0.851909i	$-0.324555\pi$
$601$	−10.3796	−	13.0156i	−0.423391	−	0.530916i	−0.947082	+	0.320993i	$0.895983\pi$
$602$	−6.35654	−	33.6112i	−0.259073	−	1.36989i
$603$		0			0
$604$	−1.69037	−	22.5564i	−0.0687802	−	0.917807i
$605$	−7.59376	−	2.34236i	−0.308730	−	0.0952307i
$606$		0			0
$607$	−1.85040	−	3.20499i	−0.0751056	−	0.130087i	0.826027	−	0.563631i	$-0.190596\pi$
$607$	−1.85040	−	3.20499i	−0.0751056	−	0.130087i	−0.901132	+	0.433544i	$0.857263\pi$
$608$	−28.2197	−	123.639i	−1.14446	−	5.01421i
$609$		0			0
$610$	−11.8071	+	51.7302i	−0.478055	+	2.09450i
$611$	−11.0529	+	3.40938i	−0.447154	+	0.137929i
$612$		0			0
$613$	−4.06433	−	10.3557i	−0.164157	−	0.418264i	0.824999	−	0.565134i	$-0.191175\pi$
$613$	−4.06433	−	10.3557i	−0.164157	−	0.418264i	−0.989156	+	0.146870i	$0.953080\pi$
$614$	65.9292	−	20.3365i	2.66068	−	0.820713i
$615$		0			0
$616$	2.52239	+	67.5708i	0.101630	+	2.72250i
$617$	−6.26447	−	27.4464i	−0.252198	−	1.10495i	−0.929377	−	0.369133i	$-0.879655\pi$
$617$	−6.26447	−	27.4464i	−0.252198	−	1.10495i	0.677179	−	0.735819i	$-0.263202\pi$
$618$		0			0
$619$	5.62821	−	9.74834i	0.226217	−	0.391819i	−0.730467	−	0.682948i	$-0.760698\pi$
$619$	5.62821	−	9.74834i	0.226217	−	0.391819i	0.956684	+	0.291129i	$0.0940309\pi$
$620$	8.11832	+	2.50417i	0.326039	+	0.100570i
$621$		0			0
$622$	−25.7861	+	32.3348i	−1.03393	+	1.29651i
$623$	−22.8146	+	26.5063i	−0.914048	+	1.06195i
$624$		0			0
$625$	13.1827	−	12.2318i	0.527308	−	0.489270i
$626$	62.8077	−	9.46673i	2.51030	−	0.378367i
$627$		0			0
$628$	35.2892	+	5.31900i	1.40819	+	0.212251i
$629$	58.6060	−	28.2232i	2.33677	−	1.12533i
$630$		0			0
$631$	41.7178	+	20.0903i	1.66076	+	0.799780i	0.998734	+	0.0502999i	$0.0160177\pi$
$631$	41.7178	+	20.0903i	1.66076	+	0.799780i	0.662027	+	0.749480i	$0.269697\pi$
$632$	89.4171	+	60.9635i	3.55682	+	2.42500i
$633$		0			0
$634$	−0.656711	+	8.76319i	−0.0260813	+	0.348031i
$635$	−4.58038	+	11.6706i	−0.181767	+	0.463135i
$636$		0			0
$637$	6.39329	−	13.2698i	0.253311	−	0.525770i
$638$	33.5398			1.32785
$639$		0			0
$640$	−6.36049	+	84.8748i	−0.251420	+	3.35497i
$641$	3.49450	+	3.24242i	0.138024	+	0.128068i	0.746164	−	0.665762i	$-0.231893\pi$
$641$	3.49450	+	3.24242i	0.138024	+	0.128068i	−0.608140	+	0.793830i	$0.708084\pi$
$642$		0			0
$643$	−40.8484	−	19.6716i	−1.61090	−	0.775770i	−0.611029	−	0.791608i	$-0.709244\pi$
$643$	−40.8484	−	19.6716i	−1.61090	−	0.775770i	−0.999875	+	0.0158379i	$0.994958\pi$
$644$	34.5377	−	21.6972i	1.36097	−	0.854991i
$645$		0			0
$646$	−114.565	−	17.2679i	−4.50749	−	0.679395i
$647$	−17.4007	+	11.8636i	−0.684092	+	0.466406i	−0.854828	−	0.518911i	$-0.826338\pi$
$647$	−17.4007	+	11.8636i	−0.684092	+	0.466406i	0.170737	+	0.985317i	$0.445385\pi$
$648$		0			0
$649$	4.25829	−	3.95111i	0.167152	−	0.155095i
$650$	4.11303	+	5.15758i	0.161326	+	0.202297i
$651$		0			0
$652$	−73.4975	+	92.1630i	−2.87839	+	3.60938i
$653$	0.841479	+	11.2288i	0.0329296	+	0.439415i	0.989164	+	0.146814i	$0.0469018\pi$
$653$	0.841479	+	11.2288i	0.0329296	+	0.439415i	−0.956235	+	0.292601i	$0.905479\pi$
$654$		0			0
$655$	−7.43373	+	12.8756i	−0.290460	+	0.503091i
$656$	12.3975	+	21.4731i	0.484041	+	0.838383i
$657$		0			0
$658$	−38.5534	+	10.3267i	−1.50297	+	0.402577i
$659$	2.22799	−	9.76147i	0.0867902	−	0.380253i	−0.912814	−	0.408375i	$-0.866096\pi$
$659$	2.22799	−	9.76147i	0.0867902	−	0.380253i	0.999604	+	0.0281221i	$0.00895274\pi$
$660$		0			0
$661$	15.0468	+	38.3386i	0.585253	+	1.49120i	0.849947	+	0.526868i	$0.176634\pi$
$661$	15.0468	+	38.3386i	0.585253	+	1.49120i	−0.264694	+	0.964332i	$0.585271\pi$
$662$	−20.4345	−	52.0662i	−0.794209	−	2.02361i
$663$		0			0
$664$	10.0051	−	43.8354i	0.388275	−	1.70114i
$665$	22.8061	+	16.8348i	0.884384	+	0.652825i
$666$		0			0
$667$	−6.45821	−	11.1859i	−0.250063	−	0.433122i
$668$	−33.4207	+	57.8864i	−1.29309	+	2.23969i
$669$		0			0
$670$	1.47927	+	19.7395i	0.0571492	+	0.762604i
$671$	−16.1851	+	20.2955i	−0.624819	+	0.783498i
$672$		0			0
$673$	−16.8858	−	21.1741i	−0.650901	−	0.816203i	0.341418	−	0.939912i	$-0.389093\pi$
$673$	−16.8858	−	21.1741i	−0.650901	−	0.816203i	−0.992319	+	0.123708i	$0.960521\pi$
$674$	−15.7274	+	14.5929i	−0.605796	+	0.562097i
$675$		0			0
$676$	−39.1777	+	26.7109i	−1.50683	+	1.02734i
$677$	−5.63331	−	0.849085i	−0.216506	−	0.0326330i	0.0398935	−	0.999204i	$-0.487298\pi$
$677$	−5.63331	−	0.849085i	−0.216506	−	0.0326330i	−0.256399	+	0.966571i	$0.582536\pi$
$678$		0			0
$679$	0.403985	−	0.642813i	0.0155035	−	0.0246689i
$680$	132.729	+	63.9190i	5.08993	+	2.45118i
$681$		0			0
$682$	4.14849	+	3.84924i	0.158854	+	0.147395i
$683$	2.41079	−	32.1698i	0.0922465	−	1.23094i	−0.738485	−	0.674270i	$-0.764458\pi$
$683$	2.41079	−	32.1698i	0.0922465	−	1.23094i	0.830731	−	0.556674i	$-0.187923\pi$
$684$		0			0
$685$	25.1119			0.959476
$686$	23.7613	−	44.9299i	0.907210	−	1.71543i
$687$		0			0
$688$	26.7372	−	68.1253i	1.01935	−	2.59725i
$689$	−0.543916	+	7.25805i	−0.0207215	+	0.276510i
$690$		0			0
$691$	13.0523	+	8.89894i	0.496535	+	0.338532i	0.785556	−	0.618791i	$-0.212377\pi$
$691$	13.0523	+	8.89894i	0.496535	+	0.338532i	−0.289021	+	0.957323i	$0.593330\pi$
$692$	75.3837	+	36.3029i	2.86566	+	1.38003i
$693$		0			0
$694$	−69.0495	+	33.2525i	−2.62108	+	1.26225i
$695$	22.6477	+	3.41358i	0.859074	+	0.129485i
$696$		0			0
$697$	12.2150	−	1.84111i	0.462676	−	0.0697372i
$698$	−16.6482	+	15.4473i	−0.630144	+	0.584689i
$699$		0			0
$700$	9.92640	+	13.4523i	0.375183	+	0.508448i
$701$	21.2222	−	26.6118i	0.801552	−	1.00511i	−0.198137	−	0.980174i	$-0.563489\pi$
$701$	21.2222	−	26.6118i	0.801552	−	1.00511i	0.999689	−	0.0249398i	$-0.00793941\pi$
$702$		0			0
$703$	43.8115	+	13.5140i	1.65238	+	0.509692i
$704$	−43.1591	+	74.7538i	−1.62662	+	2.81739i
$705$		0			0
$706$	−6.14740	−	26.9335i	−0.231360	−	1.01366i
$707$	−36.5158	−	26.9548i	−1.37332	−	1.01374i
$708$		0			0
$709$	26.9344	−	8.30816i	1.01154	−	0.312020i	0.255688	−	0.966759i	$-0.417698\pi$
$709$	26.9344	−	8.30816i	1.01154	−	0.312020i	0.755854	+	0.654740i	$0.227222\pi$
$710$	−11.4227	−	29.1046i	−0.428686	−	1.09228i
$711$		0			0
$712$	−122.417	+	37.7606i	−4.58776	+	1.41514i
$713$	0.484962	−	2.12476i	0.0181620	−	0.0795727i
$714$		0			0
$715$	−2.42517	−	10.6254i	−0.0906963	−	0.397366i
$716$	27.6725	+	47.9301i	1.03417	+	1.79123i
$717$		0			0
$718$	81.1737	+	25.0388i	3.02938	+	0.934439i
$719$	−1.78788	−	23.8576i	−0.0666766	−	0.889737i	−0.925811	−	0.377987i	$-0.876616\pi$
$719$	−1.78788	−	23.8576i	−0.0666766	−	0.889737i	0.859134	−	0.511750i	$-0.171003\pi$
$720$		0			0
$721$	−36.4377	+	15.8938i	−1.35701	+	0.591917i
$722$	−18.4051	−	23.0792i	−0.684966	−	0.858920i
$723$		0			0
$724$	6.63190	−	0.999598i	0.246472	−	0.0371497i
$725$	4.37431	−	2.98235i	0.162458	−	0.110762i
$726$		0			0
$727$	−36.7941	+	17.7191i	−1.36462	+	0.657165i	−0.965661	−	0.259806i	$-0.916341\pi$
$727$	−36.7941	+	17.7191i	−1.36462	+	0.657165i	−0.398955	+	0.916970i	$0.630627\pi$
$728$	45.6884	−	28.7023i	1.69332	−	1.06378i
$729$		0			0
$730$	−66.3323	−	45.2246i	−2.45507	−	1.67384i
$731$	−26.7276	−	24.7996i	−0.988555	−	0.917245i
$732$		0			0
$733$	−1.79465	+	4.57270i	−0.0662870	+	0.168896i	−0.960179	−	0.279386i	$-0.909869\pi$
$733$	−1.79465	+	4.57270i	−0.0662870	+	0.168896i	0.893892	+	0.448283i	$0.147964\pi$
$734$	−57.1360			−2.10893
$735$		0			0
$736$	64.7931			2.38831
$737$	−3.53806	+	9.01482i	−0.130326	+	0.332065i
$738$		0			0
$739$	22.3263	+	20.7158i	0.821286	+	0.762042i	0.974077	−	0.226217i	$-0.0726357\pi$
$739$	22.3263	+	20.7158i	0.821286	+	0.762042i	−0.152791	+	0.988259i	$0.548826\pi$
$740$	−75.4469	−	51.4389i	−2.77348	−	1.89093i
$741$		0			0
$742$	−2.81416	+	24.9567i	−0.103311	+	0.916189i
$743$	6.71032	−	3.23152i	0.246178	−	0.118553i	−0.306727	−	0.951798i	$-0.599234\pi$
$743$	6.71032	−	3.23152i	0.246178	−	0.118553i	0.552904	+	0.833245i	$0.313519\pi$
$744$		0			0
$745$	21.3917	−	14.5846i	0.783732	−	0.534339i
$746$	−6.02685	+	0.908401i	−0.220659	+	0.0332589i
$747$		0			0
$748$	70.3858	+	88.2610i	2.57356	+	3.22714i
$749$	−8.50133	+	9.87697i	−0.310632	+	0.360897i
$750$		0			0
$751$	1.17990	+	15.7446i	0.0430551	+	0.574530i	0.976459	+	0.215703i	$0.0692043\pi$
$751$	1.17990	+	15.7446i	0.0430551	+	0.574530i	−0.933404	+	0.358827i	$0.883177\pi$
$752$	−81.5970	−	25.1693i	−2.97554	−	0.917831i
$753$		0			0
$754$	−13.3817	−	23.1777i	−0.487331	−	0.844082i
$755$	1.78722	+	7.83031i	0.0650435	+	0.284974i
$756$		0			0
$757$	0.368738	−	1.61555i	0.0134020	−	0.0587181i	−0.967785	−	0.251779i	$-0.918984\pi$
$757$	0.368738	−	1.61555i	0.0134020	−	0.0587181i	0.981187	+	0.193061i	$0.0618415\pi$
$758$	7.70616	−	2.37704i	0.279900	−	0.0863379i
$759$		0			0
$760$	37.9356	+	96.6583i	1.37607	+	3.50617i
$761$	−11.3387	+	3.49753i	−0.411028	+	0.126785i	−0.493372	−	0.869819i	$-0.664236\pi$
$761$	−11.3387	+	3.49753i	−0.411028	+	0.126785i	0.0823435	+	0.996604i	$0.473760\pi$
$762$		0			0
$763$	1.45486	−	3.33378i	0.0526696	−	0.120691i
$764$	23.7181	+	103.916i	0.858091	+	3.75954i
$765$		0			0
$766$	10.9377	−	18.9446i	0.395194	−	0.684496i
$767$	−4.42938	−	1.36628i	−0.159936	−	0.0493336i
$768$		0			0
$769$	7.06702	−	8.86177i	0.254843	−	0.319564i	−0.637908	−	0.770112i	$-0.720200\pi$
$769$	7.06702	−	8.86177i	0.254843	−	0.319564i	0.892752	+	0.450549i	$0.148772\pi$
$770$	−6.98830	−	36.9518i	−0.251841	−	1.33165i
$771$		0			0
$772$	77.9025	−	72.2830i	2.80377	−	2.60152i
$773$	−41.1071	+	6.19590i	−1.47852	+	0.222851i	−0.838245	−	0.545294i	$-0.816418\pi$
$773$	−41.1071	+	6.19590i	−1.47852	+	0.222851i	−0.640276	+	0.768145i	$0.721180\pi$
$774$		0			0
$775$	0.883324	+	0.133140i	0.0317299	+	0.00478252i
$776$	2.50567	−	1.20667i	0.0899484	−	0.0433168i
$777$		0			0
$778$	−52.4477	−	25.2575i	−1.88034	−	0.905524i
$779$	7.19397	+	4.90477i	0.257751	+	0.175731i
$780$		0			0
$781$	1.14309	−	15.2535i	0.0409029	−	0.545812i
$782$	21.6259	−	55.1019i	0.773341	−	1.97044i
$783$		0			0
$784$	94.1811	−	54.3535i	3.36361	−	1.94120i
$785$	−12.6719			−0.452278
$786$		0			0
$787$	1.54702	−	20.6435i	0.0551452	−	0.735862i	−0.899273	−	0.437388i	$-0.855903\pi$
$787$	1.54702	−	20.6435i	0.0551452	−	0.735862i	0.954418	−	0.298474i	$-0.0964775\pi$
$788$	24.4280	+	22.6659i	0.870212	+	0.807439i
$789$		0			0
$790$	−54.2288	−	26.1152i	−1.92937	−	0.929137i
$791$	7.61353	+	21.7643i	0.270706	+	0.773851i
$792$		0			0
$793$	20.4827	+	3.08727i	0.727361	+	0.109632i
$794$	−17.9961	+	12.2695i	−0.638658	+	0.435430i
$795$		0			0
$796$	−50.0380	+	46.4285i	−1.77355	+	1.64561i
$797$	−9.56712	−	11.9968i	−0.338885	−	0.424948i	0.582964	−	0.812498i	$-0.301893\pi$
$797$	−9.56712	−	11.9968i	−0.338885	−	0.424948i	−0.921849	+	0.387550i	$0.873321\pi$
$798$		0			0
$799$	−26.5245	+	33.2607i	−0.938369	+	1.17668i
$800$	1.98466	+	26.4834i	0.0701683	+	0.936330i
$801$		0			0
$802$	38.6183	−	66.8889i	1.36366	−	2.36193i
$803$	−19.6383	−	34.0145i	−0.693020	−	1.20035i
$804$		0			0
$805$	−10.9783	+	9.44588i	−0.386933	+	0.332923i
$806$	1.00486	−	4.40257i	0.0353946	−	0.155074i
$807$		0			0
$808$	−60.7401	−	154.763i	−2.13683	−	5.44455i
$809$	−2.30023	−	5.86088i	−0.0808716	−	0.206058i	0.884719	−	0.466125i	$-0.154350\pi$
$809$	−2.30023	−	5.86088i	−0.0808716	−	0.206058i	−0.965590	+	0.260068i	$0.916255\pi$
$810$		0			0
$811$	7.37127	−	32.2957i	0.258840	−	1.13405i	−0.663653	−	0.748041i	$-0.730995\pi$
$811$	7.37127	−	32.2957i	0.258840	−	1.13405i	0.922493	−	0.386013i	$-0.126148\pi$
$812$	−31.6876	−	59.9687i	−1.11202	−	2.10449i
$813$		0			0
$814$	−30.4130	−	52.6769i	−1.06597	−	1.84632i
$815$	20.9283	−	36.2489i	0.733086	−	1.26974i
$816$		0			0
$817$	−1.92049	−	25.6272i	−0.0671894	−	0.896581i
$818$	21.2671	−	26.6680i	0.743585	−	0.932426i
$819$		0			0
$820$	−10.8120	−	13.5578i	−0.377570	−	0.473458i
$821$	22.5244	−	20.8996i	0.786106	−	0.729400i	−0.181080	−	0.983468i	$-0.557959\pi$
$821$	22.5244	−	20.8996i	0.786106	−	0.729400i	0.967186	+	0.254069i	$0.0817689\pi$
$822$		0			0
$823$	8.83916	−	6.02644i	0.308114	−	0.210068i	−0.399384	−	0.916784i	$-0.630776\pi$
$823$	8.83916	−	6.02644i	0.308114	−	0.210068i	0.707498	+	0.706715i	$0.249824\pi$
$824$	−143.993	−	21.7035i	−5.01624	−	0.756077i
$825$		0			0
$826$	−15.0966	−	5.28401i	−0.525277	−	0.183854i
$827$	−43.1858	−	20.7972i	−1.50172	−	0.723190i	−0.511059	−	0.859546i	$-0.670747\pi$
$827$	−43.1858	−	20.7972i	−1.50172	−	0.723190i	−0.990660	+	0.136356i	$0.956461\pi$
$828$		0			0
$829$	28.2917	+	26.2509i	0.982611	+	0.911730i	0.996105	−	0.0881788i	$-0.0281047\pi$
$829$	28.2917	+	26.2509i	0.982611	+	0.911730i	−0.0134932	+	0.999909i	$0.504295\pi$
$830$	−1.86876	+	24.9368i	−0.0648655	+	0.865570i
$831$		0			0
$832$	68.8781			2.38792
$833$	−8.06493	−	53.5711i	−0.279433	−	1.85613i
$834$		0			0
$835$	8.67091	−	22.0931i	0.300069	−	0.764564i
$836$	−5.94624	+	79.3471i	−0.205655	+	2.74428i
$837$		0			0
$838$	−19.9807	−	13.6226i	−0.690223	−	0.470586i
$839$	14.8545	+	7.15355i	0.512834	+	0.246968i	0.672358	−	0.740226i	$-0.265282\pi$
$839$	14.8545	+	7.15355i	0.512834	+	0.246968i	−0.159524	+	0.987194i	$0.550996\pi$
$840$		0			0
$841$	6.77636	−	3.26332i	0.233667	−	0.112528i
$842$	20.2094	+	3.04608i	0.696463	+	0.104975i
$843$		0			0
$844$	−76.5881	+	11.5438i	−2.63627	+	0.397354i
$845$	12.3421	−	11.4518i	0.424580	−	0.393953i
$846$		0			0
$847$	−2.77153	+	10.3398i	−0.0952308	+	0.355281i
$848$	−33.5013	+	42.0094i	−1.15044	+	1.44261i
$849$		0			0
$850$	23.1847	+	7.15153i	0.795228	+	0.245295i
$851$	−11.7123	+	20.2862i	−0.401491	+	0.695402i
$852$		0			0
$853$	1.76191	+	7.71945i	0.0603268	+	0.264309i	0.996093	−	0.0883127i	$-0.0281475\pi$
$853$	1.76191	+	7.71945i	0.0603268	+	0.264309i	−0.935766	+	0.352621i	$0.885290\pi$
$854$	70.2286	+	13.2943i	2.40317	+	0.454923i
$855$		0			0
$856$	−45.6157	+	14.0706i	−1.55911	+	0.480923i
$857$	14.3869	+	36.6571i	0.491446	+	1.25218i	0.934588	+	0.355732i	$0.115768\pi$
$857$	14.3869	+	36.6571i	0.491446	+	1.25218i	−0.443142	+	0.896451i	$0.646136\pi$
$858$		0			0
$859$	−6.72958	+	2.07580i	−0.229610	+	0.0708254i	−0.407425	−	0.913239i	$-0.633573\pi$
$859$	−6.72958	+	2.07580i	−0.229610	+	0.0708254i	0.177815	+	0.984064i	$0.443097\pi$
$860$	−11.3894	+	49.9001i	−0.388374	+	1.70158i
$861$		0			0
$862$	−9.91492	−	43.4401i	−0.337704	−	1.47958i
$863$	4.17379	+	7.22921i	0.142077	+	0.246085i	0.928279	−	0.371885i	$-0.121289\pi$
$863$	4.17379	+	7.22921i	0.142077	+	0.246085i	−0.786201	+	0.617970i	$0.787955\pi$
$864$		0			0
$865$	−28.3891	−	8.75688i	−0.965259	−	0.297743i
$866$	−0.522648	−	6.97425i	−0.0177603	−	0.236995i
$867$		0			0
$868$	2.96298	−	11.0541i	0.100570	−	0.375201i
$869$	−18.3596	−	23.0222i	−0.622807	−	0.780975i
$870$		0			0
$871$	7.64130	−	1.15174i	0.258916	−	0.0390252i
$872$	11.0089	−	7.50576i	0.372809	−	0.254177i
$873$		0			0
$874$	37.5904	−	18.1026i	1.27152	−	0.612329i
$875$	−22.5679	−	22.5719i	−0.762936	−	0.763069i
$876$		0			0
$877$	18.4287	+	12.5645i	0.622295	+	0.424273i	0.832997	−	0.553277i	$-0.186623\pi$
$877$	18.4287	+	12.5645i	0.622295	+	0.424273i	−0.210703	+	0.977550i	$0.567575\pi$
$878$	−37.1587	−	34.4782i	−1.25404	−	1.16358i
$879$		0			0
$880$	29.3946	−	74.8961i	0.990890	−	2.52475i
$881$	10.3865			0.349931			0.174966	−	0.984575i	$-0.444019\pi$
$881$	10.3865			0.349931			0.174966	+	0.984575i	$0.444019\pi$
$882$		0			0
$883$	44.8617			1.50972			0.754859	−	0.655887i	$-0.227705\pi$
$883$	44.8617			1.50972			0.754859	+	0.655887i	$0.227705\pi$
$884$	32.9104	−	83.8543i	1.10690	−	2.82032i
$885$		0			0
$886$	−0.224834	−	0.208615i	−0.00755345	−	0.00700857i
$887$	22.1968	+	15.1336i	0.745297	+	0.508135i	0.875420	−	0.483363i	$-0.160585\pi$
$887$	22.1968	+	15.1336i	0.745297	+	0.508135i	−0.130123	+	0.991498i	$0.541537\pi$
$888$		0			0
$889$	15.9403	+	5.57931i	0.534620	+	0.187124i
$890$	64.1936	−	30.9140i	2.15178	−	1.03624i
$891$		0			0
$892$	−26.5830	+	18.1240i	−0.890066	+	0.606837i
$893$	−29.6505	+	4.46909i	−0.992215	+	0.149552i
$894$		0			0
$895$	−12.2526	−	15.3642i	−0.409558	−	0.513570i
$896$	114.572	+	4.29703i	3.82757	+	0.143554i
$897$		0			0
$898$	7.11477	+	94.9400i	0.237423	+	3.16819i
$899$	−3.46313	−	1.06823i	−0.115502	−	0.0356276i
$900$		0			0
$901$	13.3848	+	23.1831i	0.445911	+	0.772340i
$902$	−2.57039	−	11.2616i	−0.0855847	−	0.374971i
$903$		0			0
$904$	−18.7946	+	82.3444i	−0.625098	+	2.73873i
$905$	−2.27562	+	0.701936i	−0.0756442	+	0.0233331i
$906$		0			0
$907$	10.5948	+	26.9951i	0.351795	+	0.896359i	0.991778	+	0.127970i	$0.0408461\pi$
$907$	10.5948	+	26.9951i	0.351795	+	0.896359i	−0.639983	+	0.768389i	$0.721059\pi$
$908$	−90.2643	+	27.8429i	−2.99553	+	0.923998i
$909$		0			0
$910$	−22.7474	+	19.5722i	−0.754068	+	0.648813i
$911$	7.34460	+	32.1788i	0.243338	+	1.06613i	0.937956	+	0.346753i	$0.112716\pi$
$911$	7.34460	+	32.1788i	0.243338	+	1.06613i	−0.694619	+	0.719378i	$0.744427\pi$
$912$		0			0
$913$	−6.11704	+	10.5950i	−0.202445	+	0.350644i
$914$	−16.9035	−	5.21405i	−0.559119	−	0.172465i
$915$		0			0
$916$	−1.48173	+	1.85803i	−0.0489576	+	0.0613909i
$917$	17.7057	+	9.35972i	0.584694	+	0.309085i
$918$		0			0
$919$	−22.9729	+	21.3157i	−0.757806	+	0.703141i	−0.961168	−	0.275962i	$-0.911003\pi$
$919$	−22.9729	+	21.3157i	−0.757806	+	0.703141i	0.203363	+	0.979103i	$0.434813\pi$
$920$	−52.4586	+	7.90687i	−1.72951	+	0.260682i
$921$		0			0
$922$	−9.72621	−	1.46599i	−0.320316	−	0.0482798i
$923$	−10.9970	+	5.29586i	−0.361970	+	0.174315i
$924$		0			0
$925$	−8.65051	−	4.16587i	−0.284427	−	0.136973i
$926$	−42.2995	−	28.8393i	−1.39005	−	0.947719i
$927$		0			0
$928$	8.05179	−	107.444i	0.264313	−	3.52701i
$929$	15.8622	−	40.4162i	0.520421	−	1.32601i	−0.393203	−	0.919452i	$-0.628633\pi$
$929$	15.8622	−	40.4162i	0.520421	−	1.32601i	0.913624	−	0.406559i	$-0.133272\pi$
$930$		0			0
$931$	21.5157	−	31.5458i	0.705148	−	1.03387i
$932$	82.3444			2.69728
$933$		0			0
$934$	−6.33073	+	84.4778i	−0.207148	+	2.76420i
$935$	−29.3840	−	27.2644i	−0.960959	−	0.891640i
$936$		0			0
$937$	33.5480	+	16.1559i	1.09597	+	0.527789i	0.892388	−	0.451270i	$-0.149029\pi$
$937$	33.5480	+	16.1559i	1.09597	+	0.527789i	0.203578	+	0.979059i	$0.434743\pi$
$938$	26.4975	−	2.98320i	0.865174	−	0.0974048i
$939$		0			0
$940$	59.0532	+	8.90084i	1.92610	+	0.290314i
$941$	−41.1832	+	28.0782i	−1.34253	+	0.915323i	−0.999710	−	0.0240766i	$-0.992335\pi$
$941$	−41.1832	+	28.0782i	−1.34253	+	0.915323i	−0.342823	+	0.939400i	$0.611383\pi$
$942$		0			0
$943$	−3.26095	+	3.02572i	−0.106191	+	0.0985310i
$944$	−21.3356	−	26.7540i	−0.694415	−	0.870769i
$945$		0			0
$946$	−21.2575	+	26.6560i	−0.691139	+	0.866661i
$947$	−0.876939	−	11.7019i	−0.0284967	−	0.380262i	−0.993159	−	0.116772i	$-0.962745\pi$
$947$	−0.876939	−	11.7019i	−0.0284967	−	0.380262i	0.964662	−	0.263490i	$-0.0848736\pi$
$948$		0			0
$949$	−15.6705	+	27.1421i	−0.508685	+	0.881069i
$950$	8.55065	+	14.8102i	0.277420	+	0.480505i
$951$		0			0
$952$	79.3733	−	181.882i	2.57250	−	5.89483i
$953$	−12.5074	+	54.7984i	−0.405154	+	1.77509i	0.200840	+	0.979624i	$0.435633\pi$
$953$	−12.5074	+	54.7984i	−0.405154	+	1.77509i	−0.605994	+	0.795469i	$0.707224\pi$
$954$		0			0
$955$	−13.8270	−	35.2306i	−0.447431	−	1.14004i
$956$	18.2966	+	46.6191i	0.591755	+	1.50777i
$957$		0			0
$958$	−23.0316	+	100.908i	−0.744116	+	3.26018i
$959$	−1.26188	−	33.8037i	−0.0407482	−	1.09158i
$960$		0			0
$961$	15.1942	+	26.3172i	0.490137	+	0.848942i
$962$	−24.2682	+	42.0338i	−0.782439	+	1.35522i
$963$		0			0
$964$	−3.20909	−	42.8223i	−0.103358	−	1.37921i
$965$	−23.5270	+	29.5019i	−0.757361	+	0.949700i
$966$		0			0
$967$	6.80866	+	8.53779i	0.218952	+	0.274557i	0.879161	−	0.476525i	$-0.158104\pi$
$967$	6.80866	+	8.53779i	0.218952	+	0.274557i	−0.660209	+	0.751082i	$0.729532\pi$
$968$	−28.7450	+	26.6715i	−0.923900	+	0.857254i
$969$		0			0
$970$	−1.27798	+	0.871314i	−0.0410336	+	0.0279762i
$971$	40.1308	+	6.04875i	1.28786	+	0.194114i	0.757039	−	0.653370i	$-0.226645\pi$
$971$	40.1308	+	6.04875i	1.28786	+	0.194114i	0.530821	+	0.847484i	$0.321884\pi$
$972$		0			0
$973$	3.45706	−	30.6581i	0.110828	−	0.982853i
$974$	−70.4259	−	33.9153i	−2.25659	−	1.08672i
$975$		0			0
$976$	112.098	+	104.011i	3.58816	+	3.32932i
$977$	3.44403	−	45.9574i	0.110184	−	1.47031i	−0.618676	−	0.785646i	$-0.712331\pi$
$977$	3.44403	−	45.9574i	0.110184	−	1.47031i	0.728861	−	0.684662i	$-0.240050\pi$
$978$		0			0
$979$	34.8575			1.11405
$980$	−59.4668	+	47.4061i	−1.89960	+	1.51433i
$981$		0			0
$982$	−17.3884	+	44.3048i	−0.554885	+	1.41382i
$983$	−1.97153	+	26.3082i	−0.0628819	+	0.839101i	0.873210	+	0.487345i	$0.162035\pi$
$983$	−1.97153	+	26.3082i	−0.0628819	+	0.839101i	−0.936092	+	0.351756i	$0.885585\pi$
$984$		0			0
$985$	−9.77641	−	6.66544i	−0.311502	−	0.212379i
$986$	−88.6857	−	42.7088i	−2.82433	−	1.36013i
$987$		0			0
$988$	57.2053	−	27.5486i	1.81994	−	0.876438i
$989$	12.9833	+	1.95692i	0.412845	+	0.0622264i
$990$		0			0
$991$	16.1905	−	2.44033i	0.514310	−	0.0775197i	0.113241	−	0.993568i	$-0.463877\pi$
$991$	16.1905	−	2.44033i	0.514310	−	0.0775197i	0.401069	+	0.916048i	$0.368639\pi$
$992$	13.3268	−	12.3655i	0.423126	−	0.392604i
$993$		0			0
$994$	−38.6044	+	16.8389i	−1.22446	+	0.534097i
$995$	15.1118	−	18.9496i	0.479075	−	0.600741i
$996$		0			0
$997$	−29.1045	−	8.97755i	−0.921749	−	0.284322i	−0.202668	−	0.979248i	$-0.564961\pi$
$997$	−29.1045	−	8.97755i	−0.921749	−	0.284322i	−0.719082	+	0.694926i	$0.755437\pi$
$998$	23.1148	−	40.0360i	0.731686	−	1.26732i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.46.1	✓	72
3.2	odd	2	inner	441.2.bb.f.46.6	yes	72
49.16	even	21	inner	441.2.bb.f.163.1	yes	72
147.65	odd	42	inner	441.2.bb.f.163.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.46.1	✓	72	1.1	even	1	trivial
441.2.bb.f.46.6	yes	72	3.2	odd	2	inner
441.2.bb.f.163.1	yes	72	49.16	even	21	inner
441.2.bb.f.163.6	yes	72	147.65	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00262 + 2.55465i) q^{2} +(-4.05486 - 3.76236i) q^{4} +(1.62281 + 1.10641i) q^{5} +(1.40782 - 2.24010i) q^{7} +(8.73185 - 4.20504i) q^{8} +(-4.45356 + 3.03638i) q^{10} +(-2.60758 + 0.393029i) q^{11} +(1.31197 + 1.64516i) q^{13} +(4.31114 + 5.84246i) q^{14} +(1.16088 + 15.4908i) q^{16} +(7.39542 + 2.28118i) q^{17} +(2.72747 + 4.72412i) q^{19} +(-2.41754 - 10.5919i) q^{20} +(1.61037 - 7.05551i) q^{22} +(-2.66318 + 0.821483i) q^{23} +(-0.417347 - 1.06338i) q^{25} +(-5.51821 + 1.70214i) q^{26} +(-14.1366 + 3.78655i) q^{28} +(1.03128 + 4.51833i) q^{29} +(-0.390994 + 0.677221i) q^{31} +(-22.2155 - 6.85257i) q^{32} +(-13.2424 + 16.6055i) q^{34} +(4.76309 - 2.07762i) q^{35} +(6.16124 - 5.71680i) q^{37} +(-14.8031 + 2.23121i) q^{38} +(18.8226 + 2.83705i) q^{40} +(1.43808 - 0.692542i) q^{41} +(-4.24459 - 2.04409i) q^{43} +(12.0521 + 8.21698i) q^{44} +(0.571574 - 7.62713i) q^{46} +(-2.00825 + 5.11693i) q^{47} +(-3.03608 - 6.30731i) q^{49} +3.13501 q^{50} +(0.869824 - 11.6070i) q^{52} +(2.53557 + 2.35267i) q^{53} +(-4.66645 - 2.24725i) q^{55} +(2.87318 - 25.4801i) q^{56} +(-12.5767 - 1.89563i) q^{58} +(-1.82008 + 1.24091i) q^{59} +(7.21614 - 6.69560i) q^{61} +(-1.33804 - 1.67785i) q^{62} +(20.4087 - 25.5917i) q^{64} +(0.308853 + 4.12135i) q^{65} +(1.83620 - 3.18040i) q^{67} +(-21.4047 - 37.0741i) q^{68} +(0.531987 + 14.2511i) q^{70} +(-1.29074 + 5.65511i) q^{71} +(5.44147 + 13.8646i) q^{73} +(8.42698 + 21.4716i) q^{74} +(6.71433 - 29.4174i) q^{76} +(-2.79058 + 6.39455i) q^{77} +(5.58327 + 9.67050i) q^{79} +(-15.2554 + 26.4231i) q^{80} +(0.327347 + 4.36814i) q^{82} +(2.89258 - 3.62718i) q^{83} +(9.47741 + 11.8843i) q^{85} +(9.47766 - 8.79398i) q^{86} +(-21.1163 + 14.3968i) q^{88} +(-13.0708 - 1.97011i) q^{89} +(5.53234 - 0.622853i) q^{91} +(13.8895 + 6.68885i) q^{92} +(-11.0584 - 10.2607i) q^{94} +(-0.800659 + 10.6840i) q^{95} +0.286958 q^{97} +(19.1570 - 1.43224i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55}+ \cdots + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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