LMFDB - Embedded newform 738.2.ba.a.233.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,-4,0,4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$3$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			233.1
Character	$\chi$	$=$	738.233
Dual form			738.2.ba.a.719.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.587785 - 0.809017i) q^{4} +(-0.524441 + 3.31119i) q^{5} +(2.69206 - 3.15200i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.71220 - 1.97053i) q^{10} +(-2.99794 - 4.89220i) q^{11} +(0.336584 - 4.27671i) q^{13} +(1.58628 + 3.82962i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(1.09484 - 4.56035i) q^{17} +(-0.0711129 - 0.903575i) q^{19} +(2.98707 - 1.52199i) q^{20} +(5.72002 - 0.450175i) q^{22} +(2.00966 + 6.18509i) q^{23} +(-5.93364 - 1.92796i) q^{25} +(3.65777 + 2.24148i) q^{26} +(-4.13237 - 0.325225i) q^{28} +(-2.14178 - 8.92115i) q^{29} +(-2.40301 + 3.30746i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.56625 + 3.04587i) q^{34} +(9.02502 + 10.5669i) q^{35} +(0.547981 - 0.398132i) q^{37} +(0.837376 + 0.346852i) q^{38} +3.35246i q^{40} +(6.00083 - 2.23385i) q^{41} +(5.17218 + 2.63536i) q^{43} +(-2.19572 + 5.30095i) q^{44} +(-6.42332 - 1.01735i) q^{46} +(-6.05205 + 5.16894i) q^{47} +(-1.59286 - 10.0569i) q^{49} +(4.41164 - 4.41164i) q^{50} +(-3.65777 + 2.24148i) q^{52} +(6.95935 - 1.67079i) q^{53} +(17.7712 - 7.36108i) q^{55} +(2.16583 - 3.53432i) q^{56} +(8.92115 + 2.14178i) q^{58} +(4.86267 - 1.57998i) q^{59} +(-3.21439 - 6.30859i) q^{61} +(-1.85603 - 3.64265i) q^{62} +(0.951057 - 0.309017i) q^{64} +(13.9845 + 3.35737i) q^{65} +(1.56772 - 2.55829i) q^{67} +(-4.33293 + 1.79476i) q^{68} +(-13.5125 + 3.24406i) q^{70} +(-0.0803081 + 0.0492129i) q^{71} +(4.33705 - 4.33705i) q^{73} +(0.105960 + 0.669003i) q^{74} +(-0.689209 + 0.588640i) q^{76} +(-23.4908 - 3.72058i) q^{77} +(-3.21784 + 7.76856i) q^{79} +(-2.98707 - 1.52199i) q^{80} +(-0.733948 + 6.36092i) q^{82} +8.41626i q^{83} +(14.5260 + 6.01687i) q^{85} +(-4.69624 + 3.41202i) q^{86} +(-3.72634 - 4.36298i) q^{88} +(-7.81737 - 6.67667i) q^{89} +(-12.5741 - 12.5741i) q^{91} +(3.82259 - 5.26135i) q^{92} +(-1.85799 - 7.73907i) q^{94} +(3.02920 + 0.238403i) q^{95} +(11.0760 + 6.78737i) q^{97} +(9.68390 + 3.14649i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{11}{40}\right)$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$		0			0
$3$		0			0
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−0.524441	+	3.31119i	−0.234537	+	1.48081i	0.536436	+	0.843941i	$0.319770\pi$
$5$	−0.524441	+	3.31119i	−0.234537	+	1.48081i	−0.770973	+	0.636867i	$0.780230\pi$
$6$		0			0
$7$	2.69206	−	3.15200i	1.01750	−	1.19134i	0.0361064	−	0.999348i	$-0.488504\pi$
$7$	2.69206	−	3.15200i	1.01750	−	1.19134i	0.981396	−	0.191994i	$-0.0614955\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$		0			0
$10$	−2.71220	−	1.97053i	−0.857672	−	0.623136i
$11$	−2.99794	−	4.89220i	−0.903913	−	1.47505i	−0.879800	−	0.475343i	$-0.842324\pi$
$11$	−2.99794	−	4.89220i	−0.903913	−	1.47505i	−0.0241131	−	0.999709i	$-0.507676\pi$
$12$		0			0
$13$	0.336584	−	4.27671i	0.0933517	−	1.18615i	−0.754641	−	0.656138i	$-0.772189\pi$
$13$	0.336584	−	4.27671i	0.0933517	−	1.18615i	0.847993	−	0.530008i	$-0.177811\pi$
$14$	1.58628	+	3.82962i	0.423951	+	1.02351i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	1.09484	−	4.56035i	0.265539	−	1.10605i	−0.667023	−	0.745037i	$-0.732432\pi$
$17$	1.09484	−	4.56035i	0.265539	−	1.10605i	0.932562	−	0.361011i	$-0.117568\pi$
$18$		0			0
$19$	−0.0711129	−	0.903575i	−0.0163144	−	0.207294i	−0.999672	−	0.0256133i	$-0.991846\pi$
$19$	−0.0711129	−	0.903575i	−0.0163144	−	0.207294i	0.983358	−	0.181681i	$-0.0581539\pi$
$20$	2.98707	−	1.52199i	0.667928	−	0.340326i
$21$		0			0
$22$	5.72002	−	0.450175i	1.21951	−	0.0959776i
$23$	2.00966	+	6.18509i	0.419042	+	1.28968i	0.908585	+	0.417700i	$0.137164\pi$
$23$	2.00966	+	6.18509i	0.419042	+	1.28968i	−0.489543	+	0.871979i	$0.662836\pi$
$24$		0			0
$25$	−5.93364	−	1.92796i	−1.18673	−	0.385591i
$26$	3.65777	+	2.24148i	0.717348	+	0.439591i
$27$		0			0
$28$	−4.13237	−	0.325225i	−0.780945	−	0.0614617i
$29$	−2.14178	−	8.92115i	−0.397719	−	1.65662i	−0.708181	−	0.706031i	$-0.750484\pi$
$29$	−2.14178	−	8.92115i	−0.397719	−	1.65662i	0.310462	−	0.950586i	$-0.399516\pi$
$30$		0			0
$31$	−2.40301	+	3.30746i	−0.431594	+	0.594038i	−0.968318	−	0.249720i	$-0.919661\pi$
$31$	−2.40301	+	3.30746i	−0.431594	+	0.594038i	0.536725	+	0.843758i	$0.319661\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	3.56625	+	3.04587i	0.611608	+	0.522362i
$35$	9.02502	+	10.5669i	1.52551	+	1.78614i
$36$		0			0
$37$	0.547981	−	0.398132i	0.0900875	−	0.0654524i	−0.541830	−	0.840488i	$-0.682268\pi$
$37$	0.547981	−	0.398132i	0.0900875	−	0.0654524i	0.631917	+	0.775036i	$0.282268\pi$
$38$	0.837376	+	0.346852i	0.135840	+	0.0562669i
$39$		0			0
$40$			3.35246i			0.530071i
$41$	6.00083	−	2.23385i	0.937172	−	0.348868i
$41$	6.00083	−	2.23385i	0.937172	−	0.348868i
$42$		0			0
$43$	5.17218	+	2.63536i	0.788749	+	0.401888i	0.801473	−	0.598031i	$-0.204050\pi$
$43$	5.17218	+	2.63536i	0.788749	+	0.401888i	−0.0127235	+	0.999919i	$0.504050\pi$
$44$	−2.19572	+	5.30095i	−0.331018	+	0.799148i
$45$		0			0
$46$	−6.42332	−	1.01735i	−0.947066	−	0.150001i
$47$	−6.05205	+	5.16894i	−0.882783	+	0.753968i	−0.970226	−	0.242202i	$-0.922130\pi$
$47$	−6.05205	+	5.16894i	−0.882783	+	0.753968i	0.0874430	+	0.996170i	$0.472130\pi$
$48$		0			0
$49$	−1.59286	−	10.0569i	−0.227551	−	1.43670i
$50$	4.41164	−	4.41164i	0.623900	−	0.623900i
$51$		0			0
$52$	−3.65777	+	2.24148i	−0.507241	+	0.310838i
$53$	6.95935	−	1.67079i	0.955940	−	0.229501i	0.274675	−	0.961537i	$-0.411430\pi$
$53$	6.95935	−	1.67079i	0.955940	−	0.229501i	0.681266	+	0.732036i	$0.261430\pi$
$54$		0			0
$55$	17.7712	−	7.36108i	2.39627	−	0.992568i
$56$	2.16583	−	3.53432i	0.289422	−	0.472293i
$57$		0			0
$58$	8.92115	+	2.14178i	1.17141	+	0.281229i
$59$	4.86267	−	1.57998i	0.633066	−	0.205696i	0.0251330	−	0.999684i	$-0.491999\pi$
$59$	4.86267	−	1.57998i	0.633066	−	0.205696i	0.607933	+	0.793989i	$0.291999\pi$
$60$		0			0
$61$	−3.21439	−	6.30859i	−0.411560	−	0.807733i	0.588439	−	0.808541i	$-0.299743\pi$
$61$	−3.21439	−	6.30859i	−0.411560	−	0.807733i	−1.00000		0.000808802i	$0.999743\pi$
$62$	−1.85603	−	3.64265i	−0.235715	−	0.462618i
$63$		0			0
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	13.9845	+	3.35737i	1.73456	+	0.416431i
$66$		0			0
$67$	1.56772	−	2.55829i	0.191528	−	0.312545i	−0.742433	−	0.669920i	$-0.766328\pi$
$67$	1.56772	−	2.55829i	0.191528	−	0.312545i	0.933961	+	0.357375i	$0.116328\pi$
$68$	−4.33293	+	1.79476i	−0.525445	+	0.217647i
$69$		0			0
$70$	−13.5125	+	3.24406i	−1.61505	+	0.387740i
$71$	−0.0803081	+	0.0492129i	−0.00953082	+	0.00584049i	−0.527256	−	0.849707i	$-0.676779\pi$
$71$	−0.0803081	+	0.0492129i	−0.00953082	+	0.00584049i	0.517725	+	0.855547i	$0.326779\pi$
$72$		0			0
$73$	4.33705	−	4.33705i	0.507613	−	0.507613i	−0.406180	−	0.913793i	$-0.633139\pi$
$73$	4.33705	−	4.33705i	0.507613	−	0.507613i	0.913793	+	0.406180i	$0.133139\pi$
$74$	0.105960	+	0.669003i	0.0123176	+	0.0777700i
$75$		0			0
$76$	−0.689209	+	0.588640i	−0.0790576	+	0.0675216i
$77$	−23.4908	−	3.72058i	−2.67703	−	0.423999i
$78$		0			0
$79$	−3.21784	+	7.76856i	−0.362035	+	0.874031i	0.632967	+	0.774179i	$0.281837\pi$
$79$	−3.21784	+	7.76856i	−0.362035	+	0.874031i	−0.995002	+	0.0998520i	$0.968163\pi$
$80$	−2.98707	−	1.52199i	−0.333964	−	0.170163i
$81$		0			0
$82$	−0.733948	+	6.36092i	−0.0810510	+	0.702446i
$83$			8.41626i			0.923804i	0.886931	+	0.461902i	$0.152833\pi$
$83$			8.41626i			0.923804i	−0.886931	+	0.461902i	$0.847167\pi$
$84$		0			0
$85$	14.5260	+	6.01687i	1.57557	+	0.652621i
$86$	−4.69624	+	3.41202i	−0.506408	+	0.367927i
$87$		0			0
$88$	−3.72634	−	4.36298i	−0.397229	−	0.465096i
$89$	−7.81737	−	6.67667i	−0.828640	−	0.707725i	0.130257	−	0.991480i	$-0.458420\pi$
$89$	−7.81737	−	6.67667i	−0.828640	−	0.707725i	−0.958897	+	0.283755i	$0.908420\pi$
$90$		0			0
$91$	−12.5741	−	12.5741i	−1.31812	−	1.31812i
$92$	3.82259	−	5.26135i	0.398533	−	0.548534i
$93$		0			0
$94$	−1.85799	−	7.73907i	−0.191637	−	0.798224i
$95$	3.02920	+	0.238403i	0.310789	+	0.0244597i
$96$		0			0
$97$	11.0760	+	6.78737i	1.12460	+	0.689153i	0.955072	−	0.296373i	$-0.0957772\pi$
$97$	11.0760	+	6.78737i	1.12460	+	0.689153i	0.169523	+	0.985526i	$0.445777\pi$
$98$	9.68390	+	3.14649i	0.978221	+	0.317843i
$99$		0			0
$100$	1.92796	+	5.93364i	0.192796	+	0.593364i
$101$	−12.0827	+	0.950930i	−1.20227	+	0.0946210i	−0.663727	−	0.747975i	$-0.731026\pi$
$101$	−12.0827	+	0.950930i	−1.20227	+	0.0946210i	−0.538547	+	0.842596i	$0.681026\pi$
$102$		0			0
$103$	−6.06981	+	3.09272i	−0.598076	+	0.304735i	−0.726696	−	0.686959i	$-0.758945\pi$
$103$	−6.06981	+	3.09272i	−0.598076	+	0.304735i	0.128620	+	0.991694i	$0.458945\pi$
$104$	−0.336584	−	4.27671i	−0.0330048	−	0.419366i
$105$		0			0
$106$	−1.67079	+	6.95935i	−0.162282	+	0.675952i
$107$	4.00645	−	12.3306i	0.387318	−	1.19204i	−0.547466	−	0.836828i	$-0.684408\pi$
$107$	4.00645	−	12.3306i	0.387318	−	1.19204i	0.934785	−	0.355215i	$-0.115592\pi$
$108$		0			0
$109$	5.08994	+	12.2882i	0.487528	+	1.17700i	0.955960	+	0.293497i	$0.0948192\pi$
$109$	5.08994	+	12.2882i	0.487528	+	1.17700i	−0.468432	+	0.883500i	$0.655181\pi$
$110$	−1.50919	+	19.1761i	−0.143896	+	1.82837i
$111$		0			0
$112$	2.16583	+	3.53432i	0.204652	+	0.333962i
$113$	−2.76727	−	2.01054i	−0.260323	−	0.189136i	0.449966	−	0.893045i	$-0.351436\pi$
$113$	−2.76727	−	2.01054i	−0.260323	−	0.189136i	−0.710289	+	0.703910i	$0.751436\pi$
$114$		0			0
$115$	−21.5339	+	3.41064i	−2.00805	+	0.318044i
$116$	−5.95846	+	6.97646i	−0.553229	+	0.647748i
$117$		0			0
$118$	−0.799836	+	5.04997i	−0.0736309	+	0.464887i
$119$	−11.4268	−	15.7277i	−1.04750	−	1.44175i
$120$		0			0
$121$	−9.95203	+	19.5320i	−0.904730	+	1.77563i
$122$	7.08030			0.641020
$123$		0			0
$124$	4.08825			0.367135
$125$	1.88574	−	3.70097i	0.168666	−	0.331025i
$126$		0			0
$127$	3.94529	+	5.43022i	0.350088	+	0.481854i	0.947354	−	0.320189i	$-0.103746\pi$
$127$	3.94529	+	5.43022i	0.350088	+	0.481854i	−0.597266	+	0.802043i	$0.703746\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$		0			0
$130$	−9.34026	+	10.9360i	−0.819195	+	0.959154i
$131$	16.5821	−	2.62635i	1.44879	−	0.229466i	0.618055	−	0.786135i	$-0.287921\pi$
$131$	16.5821	−	2.62635i	1.44879	−	0.229466i	0.830734	+	0.556670i	$0.187921\pi$
$132$		0			0
$133$	−3.03950	−	2.20833i	−0.263558	−	0.191486i
$134$	1.56772	+	2.55829i	0.135431	+	0.221003i
$135$		0			0
$136$	0.367968	−	4.67548i	0.0315530	−	0.400919i
$137$	1.00674	+	2.43049i	0.0860118	+	0.207651i	0.961033	−	0.276434i	$-0.0891527\pi$
$137$	1.00674	+	2.43049i	0.0860118	+	0.207651i	−0.875021	+	0.484085i	$0.839153\pi$
$138$		0			0
$139$	−1.48170	+	4.56021i	−0.125676	+	0.386792i	−0.994024	−	0.109164i	$-0.965183\pi$
$139$	−1.48170	+	4.56021i	−0.125676	+	0.386792i	0.868347	+	0.495957i	$0.165183\pi$
$140$	3.24406	−	13.5125i	0.274173	−	1.14201i
$141$		0			0
$142$	−0.00738987	−	0.0938972i	−0.000620144	−	0.00787968i
$143$	−21.9316	+	11.1747i	−1.83401	+	0.934475i
$144$		0			0
$145$	30.6629	−	2.41322i	2.54641	−	0.200407i
$146$	1.89536	+	5.83332i	0.156861	+	0.482769i
$147$		0			0
$148$	−0.644190	−	0.209310i	−0.0529521	−	0.0172052i
$149$	−17.0518	−	10.4493i	−1.39694	−	0.856044i	−0.398799	−	0.917038i	$-0.630573\pi$
$149$	−17.0518	−	10.4493i	−1.39694	−	0.856044i	−0.998138	+	0.0609945i	$0.980573\pi$
$150$		0			0
$151$	17.4501	+	1.37335i	1.42007	+	0.111762i	0.765109	−	0.643901i	$-0.222685\pi$
$151$	17.4501	+	1.37335i	1.42007	+	0.111762i	0.654961	+	0.755663i	$0.272685\pi$
$152$	−0.211588	−	0.881326i	−0.0171620	−	0.0714850i
$153$		0			0
$154$	13.9797	−	19.2414i	1.12651	−	1.55051i
$155$	−9.69139	−	9.69139i	−0.778431	−	0.778431i
$156$		0			0
$157$	−11.6067	−	9.91302i	−0.926312	−	0.791145i	0.0519215	−	0.998651i	$-0.483465\pi$
$157$	−11.6067	−	9.91302i	−0.926312	−	0.791145i	−0.978234	+	0.207506i	$0.933465\pi$
$158$	−5.46097	−	6.39397i	−0.434451	−	0.508677i
$159$		0			0
$160$	2.71220	−	1.97053i	0.214418	−	0.155784i
$161$	24.9055	+	10.3162i	1.96283	+	0.813029i
$162$		0			0
$163$		−	23.0982i		−	1.80919i	−0.426275	−	0.904594i	$-0.640174\pi$
$163$		−	23.0982i		−	1.80919i	0.426275	−	0.904594i	$-0.359826\pi$
$164$	−5.33442	−	3.54175i	−0.416548	−	0.276564i
$165$		0			0
$166$	−7.49894	−	3.82090i	−0.582031	−	0.296559i
$167$	−4.25881	+	10.2817i	−0.329557	+	0.795621i	0.669068	+	0.743201i	$0.266693\pi$
$167$	−4.25881	+	10.2817i	−0.329557	+	0.795621i	−0.998625	+	0.0524198i	$0.983307\pi$
$168$		0			0
$169$	−5.33701	−	0.845299i	−0.410539	−	0.0650230i
$170$	−11.9557	+	10.2112i	−0.916963	+	0.783160i
$171$		0			0
$172$	−0.908081	−	5.73340i	−0.0692406	−	0.437168i
$173$	−0.621089	+	0.621089i	−0.0472205	+	0.0472205i	−0.730323	−	0.683102i	$-0.760630\pi$
$173$	−0.621089	+	0.621089i	−0.0472205	+	0.0472205i	0.683102	+	0.730323i	$0.260630\pi$
$174$		0			0
$175$	−22.0506	+	13.5126i	−1.66687	+	1.02146i
$176$	5.57917	−	1.33944i	0.420546	−	0.100964i
$177$		0			0
$178$	9.49797	−	3.93419i	0.711903	−	0.294880i
$179$	−8.60405	+	14.0405i	−0.643097	+	1.04944i	0.350511	+	0.936558i	$0.386008\pi$
$179$	−8.60405	+	14.0405i	−0.643097	+	1.04944i	−0.993609	+	0.112881i	$0.963992\pi$
$180$		0			0
$181$	18.4127	+	4.42049i	1.36860	+	0.328572i	0.850153	−	0.526536i	$-0.176509\pi$
$181$	18.4127	+	4.42049i	1.36860	+	0.328572i	0.518450	+	0.855108i	$0.326509\pi$
$182$	16.9121	−	5.49507i	1.25361	−	0.407322i
$183$		0			0
$184$	2.95247	+	5.79456i	0.217659	+	0.427180i
$185$	1.03090	+	2.02326i	0.0757936	+	0.148753i
$186$		0			0
$187$	−25.5924	+	8.31548i	−1.87150	+	0.608088i
$188$	7.73907	+	1.85799i	0.564430	+	0.135508i
$189$		0			0
$190$	−1.58765	+	2.59081i	−0.115180	+	0.187957i
$191$	12.8401	−	5.31856i	0.929079	−	0.384837i	0.133750	−	0.991015i	$-0.457298\pi$
$191$	12.8401	−	5.31856i	0.929079	−	0.384837i	0.795329	+	0.606178i	$0.207298\pi$
$192$		0			0
$193$	−9.33692	+	2.24160i	−0.672086	+	0.161354i	−0.555105	−	0.831780i	$-0.687322\pi$
$193$	−9.33692	+	2.24160i	−0.672086	+	0.161354i	−0.116981	+	0.993134i	$0.537322\pi$
$194$	−11.0760	+	6.78737i	−0.795209	+	0.487305i
$195$		0			0
$196$	−7.19994	+	7.19994i	−0.514281	+	0.514281i
$197$	−0.269225	−	1.69982i	−0.0191815	−	0.121107i	0.976240	−	0.216694i	$-0.0695273\pi$
$197$	−0.269225	−	1.69982i	−0.0191815	−	0.121107i	−0.995421	+	0.0955867i	$0.969527\pi$
$198$		0			0
$199$	−13.3316	+	11.3862i	−0.945049	+	0.807148i	−0.981357	−	0.192193i	$-0.938440\pi$
$199$	−13.3316	+	11.3862i	−0.945049	+	0.807148i	0.0363086	+	0.999341i	$0.488440\pi$
$200$	−6.16219	−	0.975995i	−0.435732	−	0.0690132i
$201$		0			0
$202$	4.63815	−	11.1975i	0.326339	−	0.787852i
$203$	−33.8852	−	17.2654i	−2.37828	−	1.21179i
$204$		0			0
$205$	4.24960	+	21.0414i	0.296805	+	1.46959i
$206$		−	6.81231i		−	0.474636i
$207$		0			0
$208$	3.96338	+	1.64169i	0.274811	+	0.113830i
$209$	−4.20727	+	3.05676i	−0.291023	+	0.211441i
$210$		0			0
$211$	−15.2678	−	17.8763i	−1.05108	−	1.23065i	−0.972294	−	0.233762i	$-0.924896\pi$
$211$	−15.2678	−	17.8763i	−1.05108	−	1.23065i	−0.0787839	−	0.996892i	$-0.525104\pi$
$212$	−5.44230	−	4.64817i	−0.373779	−	0.319237i
$213$		0			0
$214$	9.16774	+	9.16774i	0.626694	+	0.626694i
$215$	−11.4387	+	15.7440i	−0.780110	+	1.07373i
$216$		0			0
$217$	3.95606	+	16.4782i	0.268555	+	1.11861i
$218$	−13.2597	−	1.04356i	−0.898058	−	0.0706787i
$219$		0			0
$220$	−16.4009	−	10.0505i	−1.10575	−	0.677604i
$221$	−19.1348	−	6.21727i	−1.28715	−	0.418219i
$222$		0			0
$223$	−4.27822	−	13.1670i	−0.286491	−	0.881727i	−0.985948	−	0.167053i	$-0.946575\pi$
$223$	−4.27822	−	13.1670i	−0.286491	−	0.881727i	0.699457	−	0.714674i	$-0.253425\pi$
$224$	−4.13237	+	0.325225i	−0.276106	+	0.0217300i
$225$		0			0
$226$	3.04772	−	1.55289i	0.202731	−	0.103297i
$227$	0.921030	+	11.7028i	0.0611309	+	0.776742i	0.948722	+	0.316110i	$0.102377\pi$
$227$	0.921030	+	11.7028i	0.0611309	+	0.776742i	−0.887591	+	0.460632i	$0.847623\pi$
$228$		0			0
$229$	5.50621	−	22.9350i	0.363860	−	1.51559i	−0.427374	−	0.904075i	$-0.640561\pi$
$229$	5.50621	−	22.9350i	0.363860	−	1.51559i	0.791235	−	0.611513i	$-0.209439\pi$
$230$	6.73730	−	20.7353i	0.444244	−	1.36724i
$231$		0			0
$232$	−3.51099	−	8.47627i	−0.230508	−	0.556495i
$233$	1.24845	−	15.8631i	0.0817890	−	1.03923i	−0.809897	−	0.586572i	$-0.800477\pi$
$233$	1.24845	−	15.8631i	0.0817890	−	1.03923i	0.891686	−	0.452655i	$-0.149523\pi$
$234$		0			0
$235$	−13.9414	−	22.7503i	−0.909436	−	1.48407i
$236$	−4.13643	−	3.00530i	−0.269259	−	0.195628i
$237$		0			0
$238$	19.2011	−	3.04116i	1.24462	−	0.197129i
$239$	−0.784194	+	0.918173i	−0.0507253	+	0.0593917i	−0.785189	−	0.619257i	$-0.787434\pi$
$239$	−0.784194	+	0.918173i	−0.0507253	+	0.0593917i	0.734463	+	0.678648i	$0.237434\pi$
$240$		0			0
$241$	−1.09112	+	6.88906i	−0.0702852	+	0.443764i	0.927300	+	0.374318i	$0.122123\pi$
$241$	−1.09112	+	6.88906i	−0.0702852	+	0.443764i	−0.997586	+	0.0694457i	$0.977877\pi$
$242$	−12.8850	−	17.7347i	−0.828278	−	1.14003i
$243$		0			0
$244$	−3.21439	+	6.30859i	−0.205780	+	0.403866i
$245$	34.1356			2.18084
$246$		0			0
$247$	−3.88826			−0.247404
$248$	−1.85603	+	3.64265i	−0.117858	+	0.231309i
$249$		0			0
$250$	2.44148	+	3.36041i	0.154413	+	0.212531i
$251$	−0.571112	+	3.60586i	−0.0360483	+	0.227600i	−0.999135	−	0.0415927i	$-0.986757\pi$
$251$	−0.571112	+	3.60586i	−0.0360483	+	0.227600i	0.963086	+	0.269193i	$0.0867568\pi$
$252$		0			0
$253$	24.2338	−	28.3742i	1.52357	−	1.78387i
$254$	−6.62949	+	1.05001i	−0.415971	+	0.0658833i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−2.87261	−	4.68767i	−0.179188	−	0.292409i	0.750417	−	0.660964i	$-0.229853\pi$
$257$	−2.87261	−	4.68767i	−0.179188	−	0.292409i	−0.929606	+	0.368555i	$0.879853\pi$
$258$		0			0
$259$	0.220288	−	2.79903i	0.0136880	−	0.173923i
$260$	−5.50369	−	13.2871i	−0.341325	−	0.824030i
$261$		0			0
$262$	−5.18804	+	15.9671i	−0.320518	+	0.986453i
$263$	−1.84495	+	7.68477i	−0.113765	+	0.473863i	0.886180	+	0.463341i	$0.153349\pi$
$263$	−1.84495	+	7.68477i	−0.113765	+	0.473863i	−0.999945	+	0.0105224i	$0.996651\pi$
$264$		0			0
$265$	1.88254	+	23.9199i	0.115644	+	1.46939i
$266$	3.34754	−	1.70566i	0.205251	−	0.104581i
$267$		0			0
$268$	−2.99118	+	0.235411i	−0.182716	+	0.0143800i
$269$	8.14938	+	25.0812i	0.496876	+	1.52923i	0.814012	+	0.580848i	$0.197279\pi$
$269$	8.14938	+	25.0812i	0.496876	+	1.52923i	−0.317136	+	0.948380i	$0.602721\pi$
$270$		0			0
$271$	23.2537	+	7.55557i	1.41256	+	0.458968i	0.913230	−	0.407444i	$-0.133580\pi$
$271$	23.2537	+	7.55557i	1.41256	+	0.458968i	0.499329	+	0.866412i	$0.333580\pi$
$272$	3.99883	+	2.45048i	0.242464	+	0.148582i
$273$		0			0
$274$	−2.62263	−	0.206406i	−0.158439	−	0.0124694i
$275$	8.35677	+	34.8084i	0.503932	+	2.09903i
$276$		0			0
$277$	2.63074	−	3.62090i	0.158066	−	0.217559i	−0.722637	−	0.691227i	$-0.757070\pi$
$277$	2.63074	−	3.62090i	0.158066	−	0.217559i	0.880703	+	0.473668i	$0.157070\pi$
$278$	−3.39050	−	3.39050i	−0.203349	−	0.203349i
$279$		0			0
$280$	10.5669	+	9.02502i	0.631496	+	0.539348i
$281$	−4.58824	−	5.37213i	−0.273711	−	0.320475i	0.606476	−	0.795102i	$-0.292583\pi$
$281$	−4.58824	−	5.37213i	−0.273711	−	0.320475i	−0.880187	+	0.474627i	$0.842583\pi$
$282$		0			0
$283$	6.26927	−	4.55489i	0.372669	−	0.270760i	−0.385648	−	0.922646i	$-0.626022\pi$
$283$	6.26927	−	4.55489i	0.372669	−	0.270760i	0.758317	+	0.651886i	$0.226022\pi$
$284$	0.0870179	+	0.0360440i	0.00516357	+	0.00213882i
$285$		0			0
$286$		−	24.6144i		−	1.45548i
$287$	9.11351	−	24.9282i	0.537953	−	1.47147i
$288$		0			0
$289$	−4.45101	−	2.26790i	−0.261824	−	0.133406i
$290$	−11.7704	+	28.4164i	−0.691185	+	1.66867i
$291$		0			0
$292$	−6.05800	−	0.959493i	−0.354518	−	0.0561501i
$293$	15.2807	−	13.0509i	0.892706	−	0.762443i	−0.0794346	−	0.996840i	$-0.525311\pi$
$293$	15.2807	−	13.0509i	0.892706	−	0.762443i	0.972141	+	0.234397i	$0.0753115\pi$
$294$		0			0
$295$	2.68142	+	16.9298i	0.156118	+	0.985692i
$296$	0.478953	−	0.478953i	0.0278386	−	0.0278386i
$297$		0			0
$298$	17.0518	−	10.4493i	0.987784	−	0.605315i
$299$	27.1282	−	6.51291i	1.56887	−	0.376652i
$300$		0			0
$301$	22.2304	−	9.20814i	1.28134	−	0.530749i
$302$	−9.14585	+	14.9247i	−0.526284	+	0.858818i
$303$		0			0
$304$	0.881326	+	0.211588i	0.0505475	+	0.0121354i
$305$	22.5747	−	7.33496i	1.29262	−	0.419999i
$306$		0			0
$307$	1.38311	+	2.71451i	0.0789384	+	0.154925i	0.927102	−	0.374809i	$-0.122292\pi$
$307$	1.38311	+	2.71451i	0.0789384	+	0.154925i	−0.848164	+	0.529734i	$0.822292\pi$
$308$	10.7975	+	21.1914i	0.615247	+	1.20749i
$309$		0			0
$310$	13.0349	−	4.23529i	0.740332	−	0.240548i
$311$	15.7832	+	3.78920i	0.894981	+	0.214866i	0.654746	−	0.755849i	$-0.272776\pi$
$311$	15.7832	+	3.78920i	0.894981	+	0.214866i	0.240235	+	0.970715i	$0.422776\pi$
$312$		0			0
$313$	−15.2839	+	24.9410i	−0.863896	+	1.40975i	0.0477884	+	0.998857i	$0.484783\pi$
$313$	−15.2839	+	24.9410i	−0.863896	+	1.40975i	−0.911684	+	0.410892i	$0.865217\pi$
$314$	14.1019	−	5.84119i	0.795815	−	0.329637i
$315$		0			0
$316$	8.17629	−	1.96295i	0.459952	−	0.110425i
$317$	4.58710	−	2.81098i	0.257637	−	0.157880i	−0.387682	−	0.921793i	$-0.626724\pi$
$317$	4.58710	−	2.81098i	0.257637	−	0.157880i	0.645320	+	0.763913i	$0.276724\pi$
$318$		0			0
$319$	−37.2231	+	37.2231i	−2.08409	+	2.08409i
$320$	0.524441	+	3.31119i	0.0293171	+	0.185101i
$321$		0			0
$322$	−20.4986	+	17.5075i	−1.14234	+	0.975654i
$323$	−4.19848	−	0.664974i	−0.233610	−	0.0370001i
$324$		0			0
$325$	−10.2425	+	24.7275i	−0.568151	+	1.37164i
$326$	20.5806	+	10.4863i	1.13985	+	0.580785i
$327$		0			0
$328$	5.57750	−	3.14508i	0.307966	−	0.173658i
$329$			32.9911i			1.81886i
$330$		0			0
$331$	14.9483	+	6.19178i	0.821631	+	0.340331i	0.753584	−	0.657351i	$-0.228323\pi$
$331$	14.9483	+	6.19178i	0.821631	+	0.340331i	0.0680470	+	0.997682i	$0.478323\pi$
$332$	6.80890	−	4.94695i	0.373687	−	0.271499i
$333$		0			0
$334$	−7.22759	−	8.46242i	−0.395476	−	0.463043i
$335$	7.64880	+	6.53269i	0.417899	+	0.356919i
$336$		0			0
$337$	0.0679988	+	0.0679988i	0.00370413	+	0.00370413i	0.708956	−	0.705252i	$-0.249166\pi$
$337$	0.0679988	+	0.0679988i	0.00370413	+	0.00370413i	−0.705252	+	0.708956i	$0.749166\pi$
$338$	3.17612	−	4.37155i	0.172758	−	0.237781i
$339$		0			0
$340$	−3.67042	−	15.2884i	−0.199057	−	0.829130i
$341$	23.3848	+	1.84043i	1.26636	+	0.0996647i
$342$		0			0
$343$	−11.2471	−	6.89223i	−0.607286	−	0.372146i
$344$	5.52076	+	1.79380i	0.297659	+	0.0967154i
$345$		0			0
$346$	−0.271426	−	0.835362i	−0.0145919	−	0.0449094i
$347$	12.2404	−	0.963338i	0.657098	−	0.0517147i	0.254473	−	0.967080i	$-0.418098\pi$
$347$	12.2404	−	0.963338i	0.657098	−	0.0517147i	0.402625	+	0.915365i	$0.368098\pi$
$348$		0			0
$349$	−8.48565	+	4.32366i	−0.454227	+	0.231440i	−0.666108	−	0.745855i	$-0.732041\pi$
$349$	−8.48565	+	4.32366i	−0.454227	+	0.231440i	0.211881	+	0.977295i	$0.432041\pi$
$350$	−2.02908	−	25.7819i	−0.108459	−	1.37810i
$351$		0			0
$352$	−1.33944	+	5.57917i	−0.0713924	+	0.297371i
$353$	1.94763	−	5.99420i	0.103662	−	0.319039i	−0.885752	−	0.464159i	$-0.846357\pi$
$353$	1.94763	−	5.99420i	0.103662	−	0.319039i	0.989414	+	0.145120i	$0.0463567\pi$
$354$		0			0
$355$	−0.120836	−	0.291724i	−0.00641332	−	0.0154831i
$356$	−0.806601	+	10.2488i	−0.0427498	+	0.543187i
$357$		0			0
$358$	−8.60405	−	14.0405i	−0.454738	−	0.742066i
$359$	15.7536	+	11.4456i	0.831441	+	0.604077i	0.919967	−	0.391997i	$-0.128216\pi$
$359$	15.7536	+	11.4456i	0.831441	+	0.604077i	−0.0885260	+	0.996074i	$0.528216\pi$
$360$		0			0
$361$	17.9547	−	2.84374i	0.944984	−	0.149671i
$362$	−12.2979	+	14.3989i	−0.646361	+	0.756792i
$363$		0			0
$364$	−2.78178	+	17.5635i	−0.145805	+	0.920577i
$365$	12.0863	+	16.6353i	0.632624	+	0.870732i
$366$		0			0
$367$	4.69761	−	9.21958i	0.245213	−	0.481258i	−0.735292	−	0.677750i	$-0.762955\pi$
$367$	4.69761	−	9.21958i	0.245213	−	0.481258i	0.980505	+	0.196492i	$0.0629550\pi$
$368$	−6.50338			−0.339012
$369$		0			0
$370$	−2.27076			−0.118051
$371$	13.4686	−	26.4337i	0.699257	−	1.37237i
$372$		0			0
$373$	−7.24526	−	9.97224i	−0.375145	−	0.516343i	0.579145	−	0.815225i	$-0.303387\pi$
$373$	−7.24526	−	9.97224i	−0.375145	−	0.516343i	−0.954290	+	0.298881i	$0.903387\pi$
$374$	4.20957	−	26.5782i	0.217671	−	1.37432i
$375$		0			0
$376$	−5.16894	+	6.05205i	−0.266568	+	0.312111i
$377$	−38.8741	+	6.15705i	−2.00212	+	0.317104i
$378$		0			0
$379$	12.4910	+	9.07524i	0.641619	+	0.466164i	0.860406	−	0.509609i	$-0.170210\pi$
$379$	12.4910	+	9.07524i	0.641619	+	0.466164i	−0.218787	+	0.975773i	$0.570210\pi$
$380$	−1.58765	−	2.59081i	−0.0814446	−	0.132905i
$381$		0			0
$382$	−1.09043	+	13.8552i	−0.0557912	+	0.708895i
$383$	6.60571	+	15.9476i	0.337536	+	0.814884i	0.997951	+	0.0639831i	$0.0203804\pi$
$383$	6.60571	+	15.9476i	0.337536	+	0.814884i	−0.660415	+	0.750901i	$0.729620\pi$
$384$		0			0
$385$	24.6391	−	75.8313i	1.25572	−	3.86472i
$386$	2.24160	−	9.33692i	0.114094	−	0.475237i
$387$		0			0
$388$	−1.01920	−	12.9502i	−0.0517421	−	0.657445i
$389$	25.4872	−	12.9864i	1.29225	−	0.658435i	0.333519	−	0.942744i	$-0.391764\pi$
$389$	25.4872	−	12.9864i	1.29225	−	0.658435i	0.958733	+	0.284309i	$0.0917640\pi$
$390$		0			0
$391$	30.4064	−	2.39304i	1.53772	−	0.121021i
$392$	−3.14649	−	9.68390i	−0.158922	−	0.489111i
$393$		0			0
$394$	1.63677	+	0.531820i	0.0824595	+	0.0267927i
$395$	−24.0356	−	14.7290i	−1.20936	−	0.741098i
$396$		0			0
$397$	−22.0600	−	1.73616i	−1.10716	−	0.0871352i	−0.488328	−	0.872660i	$-0.662393\pi$
$397$	−22.0600	−	1.73616i	−1.10716	−	0.0871352i	−0.618830	+	0.785525i	$0.712393\pi$
$398$	−4.09280	−	17.0477i	−0.205153	−	0.854526i
$399$		0			0
$400$	3.66719	−	5.04746i	0.183360	−	0.252373i
$401$	−11.1658	−	11.1658i	−0.557592	−	0.557592i	0.371029	−	0.928621i	$-0.379005\pi$
$401$	−11.1658	−	11.1658i	−0.557592	−	0.557592i	−0.928621	+	0.371029i	$0.879005\pi$
$402$		0			0
$403$	13.3362	+	11.3902i	0.664325	+	0.567387i
$404$	7.87135	+	9.21617i	0.391614	+	0.458522i
$405$		0			0
$406$	30.7671	−	22.3536i	1.52695	−	1.10939i
$407$	−3.59055	−	1.48726i	−0.177977	−	0.0737205i
$408$		0			0
$409$			25.9397i			1.28263i	0.767276	+	0.641317i	$0.221612\pi$
$409$			25.9397i			1.28263i	−0.767276	+	0.641317i	$0.778388\pi$
$410$	−20.6773	−	5.76616i	−1.02118	−	0.284771i
$411$		0			0
$412$	6.06981	+	3.09272i	0.299038	+	0.152367i
$413$	8.11051	−	19.5805i	0.399092	−	0.963494i
$414$		0			0
$415$	−27.8678	−	4.41383i	−1.36798	−	0.216666i
$416$	−3.26209	+	2.78609i	−0.159937	+	0.136599i
$417$		0			0
$418$	−0.813534	−	5.13645i	−0.0397912	−	0.251232i
$419$	−13.9094	+	13.9094i	−0.679519	+	0.679519i	−0.959891	−	0.280372i	$-0.909542\pi$
$419$	−13.9094	+	13.9094i	−0.679519	+	0.679519i	0.280372	+	0.959891i	$0.409542\pi$
$420$		0			0
$421$	−18.8840	+	11.5721i	−0.920350	+	0.563991i	−0.900042	−	0.435803i	$-0.856465\pi$
$421$	−18.8840	+	11.5721i	−0.920350	+	0.563991i	−0.0203078	+	0.999794i	$0.506465\pi$
$422$	22.8593	−	5.48804i	1.11277	−	0.267153i
$423$		0			0
$424$	6.61230	−	2.73890i	0.321122	−	0.133013i
$425$	−15.2886	+	24.9487i	−0.741605	+	1.21019i
$426$		0			0
$427$	−28.5380	−	6.85136i	−1.38105	−	0.331561i
$428$	−12.3306	+	4.00645i	−0.596021	+	0.193659i
$429$		0			0
$430$	−8.83493	−	17.3395i	−0.426058	−	0.836186i
$431$	10.0457	+	19.7158i	0.483884	+	0.949676i	0.995879	+	0.0906880i	$0.0289066\pi$
$431$	10.0457	+	19.7158i	0.483884	+	0.949676i	−0.511995	+	0.858988i	$0.671093\pi$
$432$		0			0
$433$	2.18970	−	0.711476i	0.105230	−	0.0341914i	−0.255929	−	0.966696i	$-0.582381\pi$
$433$	2.18970	−	0.711476i	0.105230	−	0.0341914i	0.361159	+	0.932504i	$0.382381\pi$
$434$	−16.4782	−	3.95606i	−0.790977	−	0.189897i
$435$		0			0
$436$	6.94958	−	11.3407i	0.332824	−	0.543120i
$437$	5.44578	−	2.25571i	0.260507	−	0.107905i
$438$		0			0
$439$	−0.503069	+	0.120776i	−0.0240102	+	0.00576433i	−0.245433	−	0.969414i	$-0.578930\pi$
$439$	−0.503069	+	0.120776i	−0.0240102	+	0.00576433i	0.221422	+	0.975178i	$0.428930\pi$
$440$	16.4009	−	10.0505i	0.781882	−	0.479138i
$441$		0			0
$442$	14.2266	−	14.2266i	0.676692	−	0.676692i
$443$	2.63663	+	16.6470i	0.125270	+	0.790924i	0.967697	+	0.252114i	$0.0811259\pi$
$443$	2.63663	+	16.6470i	0.125270	+	0.790924i	−0.842427	+	0.538810i	$0.818874\pi$
$444$		0			0
$445$	26.2074	−	22.3833i	1.24235	−	1.06107i
$446$	13.6741	+	2.16577i	0.647490	+	0.102552i
$447$		0			0
$448$	1.58628	−	3.82962i	0.0749447	−	0.180932i
$449$	−15.7089	−	8.00407i	−0.741348	−	0.377735i	0.0421656	−	0.999111i	$-0.486574\pi$
$449$	−15.7089	−	8.00407i	−0.741348	−	0.377735i	−0.783513	+	0.621375i	$0.786574\pi$
$450$		0			0
$451$	−28.9185	−	22.6603i	−1.36172	−	1.06703i
$452$			3.42054i			0.160888i
$453$		0			0
$454$	−10.8454	−	4.49232i	−0.509000	−	0.210835i
$455$	48.2294	−	35.0407i	2.26103	−	1.64274i
$456$		0			0
$457$	−14.6151	−	17.1121i	−0.683666	−	0.800470i	0.304719	−	0.952442i	$-0.401438\pi$
$457$	−14.6151	−	17.1121i	−0.683666	−	0.800470i	−0.988385	+	0.151972i	$0.951438\pi$
$458$	17.9355	+	15.3183i	0.838069	+	0.715779i
$459$		0			0
$460$	15.4166	+	15.4166i	0.718802	+	0.718802i
$461$	−8.06635	+	11.1024i	−0.375687	+	0.517089i	−0.954436	−	0.298417i	$-0.903541\pi$
$461$	−8.06635	+	11.1024i	−0.375687	+	0.517089i	0.578748	+	0.815506i	$0.303541\pi$
$462$		0			0
$463$	3.01437	+	12.5558i	0.140090	+	0.583516i	0.997612	+	0.0690689i	$0.0220028\pi$
$463$	3.01437	+	12.5558i	0.140090	+	0.583516i	−0.857522	+	0.514447i	$0.827997\pi$
$464$	9.14637	+	0.719835i	0.424610	+	0.0334175i
$465$		0			0
$466$	13.5674	+	8.31409i	0.628496	+	0.385143i
$467$	−9.85235	−	3.20122i	−0.455912	−	0.148135i	0.0720531	−	0.997401i	$-0.477045\pi$
$467$	−9.85235	−	3.20122i	−0.455912	−	0.148135i	−0.527965	+	0.849266i	$0.677045\pi$
$468$		0			0
$469$	−3.84332	−	11.8285i	−0.177468	−	0.546190i
$470$	26.5999	−	2.09346i	1.22696	−	0.0965641i
$471$		0			0
$472$	4.55564	−	2.32121i	0.209690	−	0.106843i
$473$	−2.61321	−	33.2039i	−0.120155	−	1.52672i
$474$		0			0
$475$	−1.32010	+	5.49859i	−0.0605701	+	0.252293i
$476$	−6.00744	+	18.4890i	−0.275350	+	0.847441i
$477$		0			0
$478$	−0.462081	−	1.11556i	−0.0211351	−	0.0510247i
$479$	0.588599	−	7.47886i	0.0268938	−	0.341718i	−0.968720	−	0.248157i	$-0.920175\pi$
$479$	0.588599	−	7.47886i	0.0268938	−	0.341718i	0.995614	−	0.0935608i	$-0.0298249\pi$
$480$		0			0
$481$	−1.51825	−	2.47756i	−0.0692263	−	0.112967i
$482$	−5.64284	−	4.09976i	−0.257024	−	0.186739i
$483$		0			0
$484$	21.6514	−	3.42924i	0.984152	−	0.155874i
$485$	−28.2829	+	33.1151i	−1.28426	+	1.50368i
$486$		0			0
$487$	−5.14611	+	32.4912i	−0.233192	+	1.47232i	0.541885	+	0.840453i	$0.317711\pi$
$487$	−5.14611	+	32.4912i	−0.233192	+	1.47232i	−0.775078	+	0.631866i	$0.782289\pi$
$488$	−4.16170	−	5.72808i	−0.188391	−	0.259298i
$489$		0			0
$490$	−15.4972	+	30.4151i	−0.700094	+	1.37401i
$491$	17.3214			0.781706			0.390853	−	0.920453i	$-0.372180\pi$
$491$	17.3214			0.781706			0.390853	+	0.920453i	$0.372180\pi$
$492$		0			0
$493$	−43.0285			−1.93791
$494$	1.76524	−	3.46447i	0.0794217	−	0.155874i
$495$		0			0
$496$	−2.40301	−	3.30746i	−0.107898	−	0.148509i
$497$	−0.0610754	+	0.385615i	−0.00273960	+	0.0172972i
$498$		0			0
$499$	0.967637	−	1.13296i	0.0433174	−	0.0507181i	−0.738324	−	0.674446i	$-0.764383\pi$
$499$	0.967637	−	1.13296i	0.0433174	−	0.0507181i	0.781642	+	0.623728i	$0.214383\pi$
$500$	−4.10256	+	0.649782i	−0.183472	+	0.0290591i
$501$		0			0
$502$	−2.95357	−	2.14589i	−0.131824	−	0.0957758i
$503$	12.6648	+	20.6671i	0.564697	+	0.921502i	0.999777	+	0.0211104i	$0.00672014\pi$
$503$	12.6648	+	20.6671i	0.564697	+	0.921502i	−0.435080	+	0.900392i	$0.643280\pi$
$504$		0			0
$505$	3.18795	−	40.5068i	0.141862	−	1.80253i
$506$	14.2796	+	34.4741i	0.634807	+	1.53256i
$507$		0			0
$508$	2.07416	−	6.38361i	0.0920260	−	0.283227i
$509$	−3.27680	+	13.6489i	−0.145242	+	0.604975i	0.851503	+	0.524350i	$0.175692\pi$
$509$	−3.27680	+	13.6489i	−0.145242	+	0.604975i	−0.996745	+	0.0806249i	$0.974308\pi$
$510$		0			0
$511$	−1.99477	−	25.3460i	−0.0882434	−	1.12124i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$		0			0
$514$	5.48089	−	0.431355i	0.241751	−	0.0190263i
$515$	−7.05733	−	21.7202i	−0.310983	−	0.957107i
$516$		0			0
$517$	43.4312	+	14.1116i	1.91010	+	0.620630i
$518$	2.39394	+	1.46701i	0.105184	+	0.0644567i
$519$		0			0
$520$	14.3375	+	1.12839i	0.628741	+	0.0494830i
$521$	0.907412	+	3.77964i	0.0397544	+	0.165589i	0.988716	−	0.149803i	$-0.0478640\pi$
$521$	0.907412	+	3.77964i	0.0397544	+	0.165589i	−0.948961	+	0.315392i	$0.897864\pi$
$522$		0			0
$523$	−9.08962	+	12.5108i	−0.397461	+	0.547059i	−0.960105	−	0.279641i	$-0.909784\pi$
$523$	−9.08962	+	12.5108i	−0.397461	+	0.547059i	0.562643	+	0.826700i	$0.309784\pi$
$524$	−11.8715	−	11.8715i	−0.518609	−	0.518609i
$525$		0			0
$526$	−6.00959	−	5.13268i	−0.262031	−	0.223795i
$527$	12.4523	+	14.5797i	0.542429	+	0.635103i
$528$		0			0
$529$	−15.6092	+	11.3407i	−0.678660	+	0.493075i
$530$	−22.1675	−	9.18207i	−0.962894	−	0.398844i
$531$		0			0
$532$			3.75703i			0.162888i
$533$	−7.53372	−	26.4157i	−0.326322	−	1.14419i
$534$		0			0
$535$	38.7277	+	19.7328i	1.67435	+	0.853122i
$536$	1.14822	−	2.77204i	0.0495954	−	0.119734i
$537$		0			0
$538$	−26.0473	−	4.12548i	−1.12298	−	0.177862i
$539$	−44.4250	+	37.9425i	−1.91352	+	1.63430i
$540$		0			0
$541$	4.80054	+	30.3094i	0.206392	+	1.30310i	0.845495	+	0.533984i	$0.179306\pi$
$541$	4.80054	+	30.3094i	0.206392	+	1.30310i	−0.639103	+	0.769121i	$0.720694\pi$
$542$	−17.2890	+	17.2890i	−0.742626	+	0.742626i
$543$		0			0
$544$	−3.99883	+	2.45048i	−0.171448	+	0.105064i
$545$	−43.3579	+	10.4093i	−1.85725	+	0.445886i
$546$		0			0
$547$	−19.6988	+	8.15951i	−0.842260	+	0.348875i	−0.761744	−	0.647878i	$-0.775657\pi$
$547$	−19.6988	+	8.15951i	−0.842260	+	0.348875i	−0.0805155	+	0.996753i	$0.525657\pi$
$548$	1.37456	−	2.24308i	0.0587183	−	0.0958195i
$549$		0			0
$550$	−34.8084	−	8.35677i	−1.48424	−	0.356334i
$551$	−7.90863	+	2.56967i	−0.336919	+	0.109472i
$552$		0			0
$553$	15.8238	+	31.0560i	0.672898	+	1.32064i
$554$	2.03192	+	3.98786i	0.0863279	+	0.169428i
$555$		0			0
$556$	4.56021	−	1.48170i	0.193396	−	0.0628382i
$557$	−2.50107	−	0.600453i	−0.105974	−	0.0254420i	0.180112	−	0.983646i	$-0.442354\pi$
$557$	−2.50107	−	0.600453i	−0.105974	−	0.0254420i	−0.286085	+	0.958204i	$0.592354\pi$
$558$		0			0
$559$	13.0115	−	21.2329i	0.550329	−	0.898055i
$560$	−12.8386	+	5.31794i	−0.542532	+	0.224724i
$561$		0			0
$562$	6.86962	−	1.64925i	0.289778	−	0.0695694i
$563$	8.63660	−	5.29251i	0.363989	−	0.223053i	−0.328463	−	0.944517i	$-0.606531\pi$
$563$	8.63660	−	5.29251i	0.363989	−	0.223053i	0.692452	+	0.721464i	$0.256531\pi$
$564$		0			0
$565$	8.10855	−	8.10855i	0.341129	−	0.341129i
$566$	1.21225	+	7.65384i	0.0509546	+	0.321715i
$567$		0			0
$568$	−0.0716208	+	0.0611699i	−0.00300514	+	0.00256663i
$569$	−14.4664	−	2.29125i	−0.606462	−	0.0960541i	−0.154351	−	0.988016i	$-0.549329\pi$
$569$	−14.4664	−	2.29125i	−0.606462	−	0.0960541i	−0.452111	+	0.891962i	$0.649329\pi$
$570$		0			0
$571$	9.76049	−	23.5639i	0.408464	−	0.986119i	−0.577078	−	0.816689i	$-0.695807\pi$
$571$	9.76049	−	23.5639i	0.408464	−	0.986119i	0.985542	−	0.169430i	$-0.0541927\pi$
$572$	21.9316	+	11.1747i	0.917005	+	0.467237i
$573$		0			0
$574$	18.0738	+	19.4374i	0.754384	+	0.811300i
$575$		−	40.5746i		−	1.69208i
$576$		0			0
$577$	29.8021	+	12.3444i	1.24068	+	0.513906i	0.903926	−	0.427688i	$-0.140672\pi$
$577$	29.8021	+	12.3444i	1.24068	+	0.513906i	0.336751	+	0.941594i	$0.390672\pi$
$578$	4.04143	−	2.93627i	0.168101	−	0.122133i
$579$		0			0
$580$	−19.9755	−	23.3883i	−0.829438	−	0.971147i
$581$	26.5280	+	22.6571i	1.10057	+	0.939973i
$582$		0			0
$583$	−29.0376	−	29.0376i	−1.20261	−	1.20261i
$584$	3.60519	−	4.96212i	0.149184	−	0.205334i
$585$		0			0
$586$	4.69118	+	19.5402i	0.193791	+	0.807197i
$587$	−3.97684	−	0.312984i	−0.164142	−	0.0129182i	−0.00387806	−	0.999992i	$-0.501234\pi$
$587$	−3.97684	−	0.312984i	−0.164142	−	0.0129182i	−0.160264	+	0.987074i	$0.551234\pi$
$588$		0			0
$589$	3.15942	+	1.93610i	0.130182	+	0.0797755i
$590$	−16.3019	−	5.29681i	−0.671139	−	0.218066i
$591$		0			0
$592$	0.209310	+	0.644190i	0.00860259	+	0.0264761i
$593$	41.0938	−	3.23415i	1.68752	−	0.132811i	0.801973	−	0.597361i	$-0.203784\pi$
$593$	41.0938	−	3.23415i	1.68752	−	0.132811i	0.885547	+	0.464550i	$0.153784\pi$
$594$		0			0
$595$	58.0700	−	29.5881i	2.38064	−	1.21299i
$596$	1.56909	+	19.9372i	0.0642724	+	0.816658i
$597$		0			0
$598$	−6.51291	+	27.1282i	−0.266333	+	1.10936i
$599$	2.52358	−	7.76677i	0.103111	−	0.317342i	−0.886172	−	0.463357i	$-0.846645\pi$
$599$	2.52358	−	7.76677i	0.103111	−	0.317342i	0.989282	+	0.146015i	$0.0466448\pi$
$600$		0			0
$601$	9.21654	+	22.2507i	0.375951	+	0.907625i	0.992716	+	0.120478i	$0.0384428\pi$
$601$	9.21654	+	22.2507i	0.375951	+	0.907625i	−0.616765	+	0.787147i	$0.711557\pi$
$602$	−1.88789	+	23.9879i	−0.0769445	+	0.977672i
$603$		0			0
$604$	−9.14585	−	14.9247i	−0.372139	−	0.607276i
$605$	−59.4547	−	43.1964i	−2.41718	−	1.75618i
$606$		0			0
$607$	−8.36936	+	1.32558i	−0.339702	+	0.0538035i	−0.323955	−	0.946073i	$-0.605013\pi$
$607$	−8.36936	+	1.32558i	−0.339702	+	0.0538035i	−0.0157469	+	0.999876i	$0.505013\pi$
$608$	−0.588640	+	0.689209i	−0.0238725	+	0.0279511i
$609$		0			0
$610$	−3.71320	+	23.4442i	−0.150343	+	0.949228i
$611$	20.0690	+	27.6227i	0.811907	+	1.11749i
$612$		0			0
$613$	−2.45977	+	4.82758i	−0.0993493	+	0.194984i	−0.935331	−	0.353773i	$-0.884899\pi$
$613$	−2.45977	+	4.82758i	−0.0993493	+	0.194984i	0.835982	+	0.548757i	$0.184899\pi$
$614$	−3.04657			−0.122949
$615$		0			0
$616$	−23.7836			−0.958270
$617$	20.2744	−	39.7908i	0.816219	−	1.60192i	0.0177807	−	0.999842i	$-0.494340\pi$
$617$	20.2744	−	39.7908i	0.816219	−	1.60192i	0.798438	−	0.602077i	$-0.205660\pi$
$618$		0			0
$619$	7.53064	+	10.3650i	0.302682	+	0.416606i	0.933082	−	0.359665i	$-0.117109\pi$
$619$	7.53064	+	10.3650i	0.302682	+	0.416606i	−0.630399	+	0.776271i	$0.717109\pi$
$620$	−2.14404	+	13.5370i	−0.0861068	+	0.543657i
$621$		0			0
$622$	−10.5416	+	12.3426i	−0.422680	+	0.494895i
$623$	−42.0897	+	6.66635i	−1.68629	+	0.267082i
$624$		0			0
$625$	−13.9716	−	10.1510i	−0.558865	−	0.406039i
$626$	−15.2839	−	24.9410i	−0.610866	−	0.996843i
$627$		0			0
$628$	−1.19758	+	15.2167i	−0.0477887	+	0.607213i
$629$	−1.21567	−	2.93488i	−0.0484718	−	0.117021i
$630$		0			0
$631$	−6.81991	+	20.9895i	−0.271496	+	0.835580i	0.718629	+	0.695394i	$0.244770\pi$
$631$	−6.81991	+	20.9895i	−0.271496	+	0.835580i	−0.990125	+	0.140186i	$0.955230\pi$
$632$	−1.96295	+	8.17629i	−0.0780821	+	0.325236i
$633$		0			0
$634$	0.422100	+	5.36329i	0.0167637	+	0.213004i
$635$	−20.0496	+	10.2158i	−0.795642	+	0.405400i
$636$		0			0
$637$	−43.5465	+	3.42719i	−1.72538	+	0.135790i
$638$	−16.2671	−	50.0650i	−0.644020	−	1.98209i
$639$		0			0
$640$	−3.18838	−	1.03597i	−0.126032	−	0.0409502i
$641$	36.2211	+	22.1963i	1.43065	+	0.876701i	0.999671	−	0.0256625i	$-0.00816953\pi$
$641$	36.2211	+	22.1963i	1.43065	+	0.876701i	0.430976	+	0.902364i	$0.358170\pi$
$642$		0			0
$643$	−23.6112	−	1.85824i	−0.931136	−	0.0732820i	−0.396190	−	0.918168i	$-0.629668\pi$
$643$	−23.6112	−	1.85824i	−0.931136	−	0.0732820i	−0.534946	+	0.844886i	$0.679668\pi$
$644$	−6.29310	−	26.2127i	−0.247983	−	1.03292i
$645$		0			0
$646$	2.49856	−	3.43898i	0.0983047	−	0.135305i
$647$	−18.9808	−	18.9808i	−0.746213	−	0.746213i	0.227553	−	0.973766i	$-0.426927\pi$
$647$	−18.9808	−	18.9808i	−0.746213	−	0.746213i	−0.973766	+	0.227553i	$0.926927\pi$
$648$		0			0
$649$	−22.3076	−	19.0525i	−0.875648	−	0.747874i
$650$	−17.3824	−	20.3522i	−0.681794	−	0.798279i
$651$		0			0
$652$	−18.6868	+	13.5768i	−0.731832	+	0.531707i
$653$	32.6642	+	13.5300i	1.27825	+	0.529469i	0.915463	−	0.402403i	$-0.131825\pi$
$653$	32.6642	+	13.5300i	1.27825	+	0.529469i	0.362788	+	0.931872i	$0.381825\pi$
$654$		0			0
$655$			56.2840i			2.19920i
$656$	0.270156	+	6.39742i	0.0105478	+	0.249777i
$657$		0			0
$658$	−29.3953	−	14.9777i	−1.14595	−	0.583890i
$659$	16.4756	−	39.7755i	0.641797	−	1.54943i	−0.182457	−	0.983214i	$-0.558405\pi$
$659$	16.4756	−	39.7755i	0.641797	−	1.54943i	0.824254	−	0.566221i	$-0.191595\pi$
$660$		0			0
$661$	17.2819	+	2.73718i	0.672187	+	0.106464i	0.483192	−	0.875514i	$-0.339477\pi$
$661$	17.2819	+	2.73718i	0.672187	+	0.106464i	0.188994	+	0.981978i	$0.439477\pi$
$662$	−12.3033	+	10.5080i	−0.478181	+	0.408405i
$663$		0			0
$664$	1.31659	+	8.31264i	0.0510937	+	0.322593i
$665$	8.90623	−	8.90623i	0.345369	−	0.345369i
$666$		0			0
$667$	50.8739	−	31.1755i	1.96984	−	1.20712i
$668$	10.8213	−	2.59797i	0.418690	−	0.100519i
$669$		0			0
$670$	−9.29316	+	3.84935i	−0.359026	+	0.148713i
$671$	−21.2263	+	34.6382i	−0.819433	+	1.33719i
$672$		0			0
$673$	−8.54684	−	2.05191i	−0.329456	−	0.0790955i	0.0653429	−	0.997863i	$-0.479186\pi$
$673$	−8.54684	−	2.05191i	−0.329456	−	0.0790955i	−0.394799	+	0.918767i	$0.629186\pi$
$674$	−0.0914582	+	0.0297166i	−0.00352284	+	0.00114464i
$675$		0			0
$676$	2.45315	+	4.81459i	0.0943521	+	0.185176i
$677$	−16.3913	−	32.1697i	−0.629969	−	1.23638i	−0.956648	−	0.291248i	$-0.905930\pi$
$677$	−16.3913	−	32.1697i	−0.629969	−	1.23638i	0.326679	−	0.945135i	$-0.394070\pi$
$678$		0			0
$679$	51.2110	−	16.6394i	1.96530	−	0.638563i
$680$	15.2884	+	3.67042i	0.586284	+	0.140754i
$681$		0			0
$682$	−12.2563	+	20.0005i	−0.469319	+	0.765859i
$683$	−30.8564	+	12.7811i	−1.18069	+	0.489056i	−0.884711	−	0.466139i	$-0.845645\pi$
$683$	−30.8564	+	12.7811i	−1.18069	+	0.489056i	−0.295975	+	0.955196i	$0.595645\pi$
$684$		0			0
$685$	−8.57579	+	2.05886i	−0.327664	+	0.0786651i
$686$	11.2471	−	6.89223i	0.429416	−	0.263147i
$687$		0			0
$688$	−4.10466	+	4.10466i	−0.156489	+	0.156489i
$689$	−4.80309	−	30.3255i	−0.182983	−	1.15531i
$690$		0			0
$691$	−18.9440	+	16.1797i	−0.720665	+	0.615506i	−0.932234	−	0.361857i	$-0.882143\pi$
$691$	−18.9440	+	16.1797i	−0.720665	+	0.615506i	0.211568	+	0.977363i	$0.432143\pi$
$692$	0.867538	+	0.137405i	0.0329788	+	0.00522334i
$693$		0			0
$694$	−4.69867	+	11.3436i	−0.178359	+	0.430597i
$695$	−14.3227	−	7.29776i	−0.543289	−	0.276820i
$696$		0			0
$697$	−3.61715	−	29.8116i	−0.137009	−	1.12919i
$698$		−	9.52367i		−	0.360476i
$699$		0			0
$700$	23.8930	+	9.89680i	0.903070	+	0.374064i
$701$	19.9347	−	14.4834i	0.752923	−	0.547031i	−0.143808	−	0.989606i	$-0.545935\pi$
$701$	19.9347	−	14.4834i	0.752923	−	0.547031i	0.896732	+	0.442575i	$0.145935\pi$
$702$		0			0
$703$	−0.398710	−	0.466830i	−0.0150376	−	0.0176068i
$704$	−4.36298	−	3.72634i	−0.164436	−	0.140442i
$705$		0			0
$706$	4.45667	+	4.45667i	0.167729	+	0.167729i
$707$	−29.5300	+	40.6446i	−1.11059	+	1.52860i
$708$		0			0
$709$	−2.20827	−	9.19810i	−0.0829333	−	0.345442i	0.915440	−	0.402454i	$-0.131843\pi$
$709$	−2.20827	−	9.19810i	−0.0829333	−	0.345442i	−0.998373	+	0.0570120i	$0.981843\pi$
$710$	0.314787	+	0.0247743i	0.0118137	+	0.000929761i
$711$		0			0
$712$	−8.76559	−	5.37156i	−0.328504	−	0.201308i
$713$	−25.2862	−	8.21597i	−0.946974	−	0.307691i
$714$		0			0
$715$	−25.4997	−	78.4800i	−0.953634	−	2.93498i
$716$	16.4164	−	1.29200i	0.613509	−	0.0482842i
$717$		0			0
$718$	−17.3501	+	8.84031i	−0.647500	+	0.329917i
$719$	−1.60607	−	20.4071i	−0.0598963	−	0.761055i	−0.951383	−	0.308009i	$-0.900337\pi$
$719$	−1.60607	−	20.4071i	−0.0598963	−	0.761055i	0.891487	−	0.453046i	$-0.149663\pi$
$720$		0			0
$721$	−6.59203	+	27.4578i	−0.245500	+	1.02258i
$722$	−5.61746	+	17.2888i	−0.209060	+	0.643422i
$723$		0			0
$724$	−7.24644	−	17.4945i	−0.269312	−	0.650176i
$725$	−4.49105	+	57.0642i	−0.166793	+	2.11931i
$726$		0			0
$727$	18.6558	+	30.4436i	0.691907	+	1.12909i	0.984925	+	0.172982i	$0.0553404\pi$
$727$	18.6558	+	30.4436i	0.691907	+	1.12909i	−0.293018	+	0.956107i	$0.594660\pi$
$728$	−14.3863	−	10.4522i	−0.533191	−	0.387386i
$729$		0			0
$730$	−20.3092	+	3.21667i	−0.751678	+	0.119054i
$731$	17.6809	−	20.7016i	0.653951	−	0.765678i
$732$		0			0
$733$	−4.62459	+	29.1985i	−0.170813	+	1.07847i	0.742092	+	0.670298i	$0.233834\pi$
$733$	−4.62459	+	29.1985i	−0.170813	+	1.07847i	−0.912905	+	0.408173i	$0.866166\pi$
$734$	6.08204	+	8.37121i	0.224492	+	0.308987i
$735$		0			0
$736$	2.95247	−	5.79456i	0.108830	−	0.213590i
$737$	−17.2156			−0.634145
$738$		0			0
$739$	−36.7156			−1.35061			−0.675303	−	0.737541i	$-0.735987\pi$
$739$	−36.7156			−1.35061			−0.675303	+	0.737541i	$0.735987\pi$
$740$	1.03090	−	2.02326i	0.0378968	−	0.0743767i
$741$		0			0
$742$	17.4380	+	24.0013i	0.640168	+	0.881116i
$743$	−0.825200	+	5.21011i	−0.0302736	+	0.191140i	−0.998191	−	0.0601303i	$-0.980848\pi$
$743$	−0.825200	+	5.21011i	−0.0302736	+	0.191140i	0.967917	+	0.251271i	$0.0808484\pi$
$744$		0			0
$745$	43.5424	−	50.9816i	1.59527	−	1.86782i
$746$	12.1746	−	1.92827i	0.445744	−	0.0705990i
$747$		0			0
$748$	21.7702	+	15.8170i	0.795998	+	0.578326i
$749$	−28.0804	−	45.8230i	−1.02603	−	1.67434i
$750$		0			0
$751$	3.04607	−	38.7039i	0.111153	−	1.41233i	−0.648112	−	0.761545i	$-0.724441\pi$
$751$	3.04607	−	38.7039i	0.111153	−	1.41233i	0.759265	−	0.650782i	$-0.225559\pi$
$752$	−3.04577	−	7.35314i	−0.111068	−	0.268141i
$753$		0			0
$754$	12.1625	−	37.4323i	0.442932	−	1.36320i
$755$	−13.6990	+	57.0603i	−0.498557	+	2.07664i
$756$		0			0
$757$	0.943382	+	11.9868i	0.0342878	+	0.435668i	0.989971	+	0.141271i	$0.0451188\pi$
$757$	0.943382	+	11.9868i	0.0342878	+	0.435668i	−0.955683	+	0.294397i	$0.904881\pi$
$758$	−13.7569	+	7.00949i	−0.499673	+	0.254596i
$759$		0			0
$760$	3.02920	−	0.238403i	0.109881	−	0.00864780i
$761$	1.63942	+	5.04561i	0.0594289	+	0.182903i	0.976364	−	0.216133i	$-0.0693446\pi$
$761$	1.63942	+	5.04561i	0.0594289	+	0.182903i	−0.916935	+	0.399037i	$0.869345\pi$
$762$		0			0
$763$	52.4348	+	17.0371i	1.89827	+	0.616785i
$764$	−11.8500	−	7.26172i	−0.428720	−	0.262720i
$765$		0			0
$766$	−17.2083	−	1.35433i	−0.621762	−	0.0489338i
$767$	−5.12041	−	21.3280i	−0.184887	−	0.770110i
$768$		0			0
$769$	−5.13211	+	7.06375i	−0.185069	+	0.254725i	−0.891463	−	0.453093i	$-0.850321\pi$
$769$	−5.13211	+	7.06375i	−0.185069	+	0.254725i	0.706394	+	0.707818i	$0.250321\pi$
$770$	56.3802	+	56.3802i	2.03180	+	2.03180i
$771$		0			0
$772$	7.30159	+	6.23615i	0.262790	+	0.224444i
$773$	−2.91939	−	3.41816i	−0.105003	−	0.122943i	0.705416	−	0.708794i	$-0.250760\pi$
$773$	−2.91939	−	3.41816i	−0.105003	−	0.122943i	−0.810419	+	0.585851i	$0.800760\pi$
$774$		0			0
$775$	20.6352	−	14.9924i	0.741240	−	0.538542i
$776$	12.0014	+	4.97114i	0.430825	+	0.178454i
$777$		0			0
$778$			28.6049i			1.02554i
$779$	−2.44518	−	5.26334i	−0.0876078	−	0.188579i
$780$		0			0
$781$	0.481518	+	0.245346i	0.0172301	+	0.00877916i
$782$	−11.6720	+	28.1787i	−0.417390	+	1.00767i
$783$		0			0
$784$	10.0569	+	1.59286i	0.359175	+	0.0568877i
$785$	38.9109	−	33.2330i	1.38879	−	1.18614i
$786$		0			0
$787$	2.03917	+	12.8748i	0.0726886	+	0.458938i	0.997007	+	0.0773150i	$0.0246347\pi$
$787$	2.03917	+	12.8748i	0.0726886	+	0.458938i	−0.924318	+	0.381623i	$0.875365\pi$
$788$	−1.21694	+	1.21694i	−0.0433515	+	0.0433515i
$789$		0			0
$790$	24.0356	−	14.7290i	0.855148	−	0.524035i
$791$	−13.7869	+	3.30994i	−0.490205	+	0.117688i
$792$		0			0
$793$	−28.0619	+	11.6236i	−0.996508	+	0.412767i
$794$	11.5619	−	18.8674i	0.410318	−	0.669578i
$795$		0			0
$796$	17.0477	+	4.09280i	0.604241	+	0.145065i
$797$	−10.2746	+	3.33841i	−0.363944	+	0.118253i	−0.485280	−	0.874359i	$-0.661282\pi$
$797$	−10.2746	+	3.33841i	−0.363944	+	0.118253i	0.121336	+	0.992612i	$0.461282\pi$
$798$		0			0
$799$	16.9461	+	33.2587i	0.599511	+	1.17661i
$800$	2.83245	+	5.55899i	0.100142	+	0.196540i
$801$		0			0
$802$	15.0179	−	4.87962i	0.530301	−	0.172305i
$803$	−34.2199	−	8.21548i	−1.20760	−	0.289918i
$804$		0			0
$805$	−47.2203	+	77.0565i	−1.66430	+	2.71588i
$806$	−16.2033	+	6.71162i	−0.570736	+	0.236407i
$807$		0			0
$808$	−11.7852	+	2.82937i	−0.414601	+	0.0995370i
$809$	−23.1693	+	14.1981i	−0.814588	+	0.499180i	−0.866325	−	0.499481i	$-0.833524\pi$
$809$	−23.1693	+	14.1981i	−0.814588	+	0.499180i	0.0517374	+	0.998661i	$0.483524\pi$
$810$		0			0
$811$	24.5700	−	24.5700i	0.862769	−	0.862769i	−0.128890	−	0.991659i	$-0.541141\pi$
$811$	24.5700	−	24.5700i	0.862769	−	0.862769i	0.991659	+	0.128890i	$0.0411414\pi$
$812$	5.94925	+	37.5621i	0.208778	+	1.31817i
$813$		0			0
$814$	2.95523	−	2.52401i	0.103581	−	0.0884664i
$815$	76.4823	+	12.1136i	2.67906	+	0.424321i
$816$		0			0
$817$	2.01343	−	4.86086i	0.0704411	−	0.170060i
$818$	−23.1124	−	11.7764i	−0.808106	−	0.411751i
$819$		0			0
$820$	14.5250	−	15.8058i	0.507234	−	0.551963i
$821$			37.0336i			1.29248i	0.763134	+	0.646240i	$0.223659\pi$
$821$			37.0336i			1.29248i	−0.763134	+	0.646240i	$0.776341\pi$
$822$		0			0
$823$	3.38901	+	1.40377i	0.118133	+	0.0489324i	0.440967	−	0.897523i	$-0.354636\pi$
$823$	3.38901	+	1.40377i	0.118133	+	0.0489324i	−0.322834	+	0.946456i	$0.604636\pi$
$824$	−5.51127	+	4.00417i	−0.191994	+	0.139492i
$825$		0			0
$826$	13.7643	+	16.1159i	0.478920	+	0.560743i
$827$	−27.8306	−	23.7696i	−0.967766	−	0.826550i	0.0171025	−	0.999854i	$-0.494556\pi$
$827$	−27.8306	−	23.7696i	−0.967766	−	0.826550i	−0.984868	+	0.173303i	$0.944556\pi$
$828$		0			0
$829$	−0.877505	−	0.877505i	−0.0304770	−	0.0304770i	0.691704	−	0.722181i	$-0.256860\pi$
$829$	−0.877505	−	0.877505i	−0.0304770	−	0.0304770i	−0.722181	+	0.691704i	$0.756860\pi$
$830$	16.5845	−	22.8266i	0.575655	−	0.792322i
$831$		0			0
$832$	−1.00147	−	4.17140i	−0.0347196	−	0.144617i
$833$	−47.6069	−	3.74674i	−1.64948	−	0.129817i
$834$		0			0
$835$	−31.8111	−	19.4939i	−1.10087	−	0.674613i
$836$	4.94595	+	1.60704i	0.171059	+	0.0555805i
$837$		0			0
$838$	−6.07863	−	18.7081i	−0.209983	−	0.646261i
$839$	23.9120	−	1.88192i	0.825535	−	0.0649710i	0.341350	−	0.939936i	$-0.389116\pi$
$839$	23.9120	−	1.88192i	0.825535	−	0.0649710i	0.484185	+	0.874965i	$0.339116\pi$
$840$		0			0
$841$	−49.1606	+	25.0486i	−1.69519	+	0.863744i
$842$	−1.73769	−	22.0794i	−0.0598847	−	0.760907i
$843$		0			0
$844$	−5.48804	+	22.8593i	−0.188906	+	0.786850i
$845$	5.59789	−	17.2285i	0.192573	−	0.592680i
$846$		0			0
$847$	34.7732	+	83.9500i	1.19482	+	2.88455i
$848$	−0.561540	+	7.13504i	−0.0192834	+	0.245018i
$849$		0			0
$850$	−15.2886	−	24.9487i	−0.524394	−	0.855733i
$851$	3.56373	+	2.58920i	0.122163	+	0.0887567i
$852$		0			0
$853$	44.8319	−	7.10067i	1.53501	−	0.243122i	0.669046	−	0.743221i	$-0.266703\pi$
$853$	44.8319	−	7.10067i	1.53501	−	0.243122i	0.865968	+	0.500099i	$0.166703\pi$
$854$	19.0606	−	22.3171i	0.652240	−	0.763674i
$855$		0			0
$856$	2.02820	−	12.8055i	0.0693223	−	0.437684i
$857$	−14.1039	−	19.4124i	−0.481780	−	0.663114i	0.497066	−	0.867713i	$-0.334411\pi$
$857$	−14.1039	−	19.4124i	−0.481780	−	0.663114i	−0.978846	+	0.204599i	$0.934411\pi$
$858$		0			0
$859$	−3.83546	+	7.52751i	−0.130864	+	0.256835i	−0.947136	−	0.320833i	$-0.896037\pi$
$859$	−3.83546	+	7.52751i	−0.130864	+	0.256835i	0.816272	+	0.577668i	$0.196037\pi$
$860$	19.4606			0.663601
$861$		0			0
$862$	−22.1276			−0.753667
$863$	0.0611847	−	0.120082i	0.00208275	−	0.00408763i	−0.889963	−	0.456033i	$-0.849270\pi$
$863$	0.0611847	−	0.120082i	0.00208275	−	0.00408763i	0.892046	+	0.451945i	$0.149270\pi$
$864$		0			0
$865$	−1.73082	−	2.38226i	−0.0588495	−	0.0809994i
$866$	−0.360172	+	2.27404i	−0.0122392	+	0.0772750i
$867$		0			0
$868$	11.0058	−	12.8861i	0.373561	−	0.437384i
$869$	47.6522	−	7.54737i	1.61649	−	0.256027i
$870$		0			0
$871$	−10.4134	−	7.56577i	−0.352844	−	0.256356i
$872$	6.94958	+	11.3407i	0.235342	+	0.384044i
$873$		0			0
$874$	−0.462475	+	5.87630i	−0.0156434	+	0.198769i
$875$	−6.58893	−	15.9071i	−0.222746	−	0.537757i
$876$		0			0
$877$	−1.28573	+	3.95708i	−0.0434161	+	0.133621i	−0.970415	−	0.241443i	$-0.922379\pi$
$877$	−1.28573	+	3.95708i	−0.0434161	+	0.133621i	0.926999	+	0.375064i	$0.122379\pi$
$878$	0.120776	−	0.503069i	0.00407600	−	0.0169778i
$879$		0			0
$880$	1.50919	+	19.1761i	0.0508749	+	0.646427i
$881$	21.7708	−	11.0928i	0.733475	−	0.373724i	−0.0470133	−	0.998894i	$-0.514970\pi$
$881$	21.7708	−	11.0928i	0.733475	−	0.373724i	0.780489	+	0.625170i	$0.214970\pi$
$882$		0			0
$883$	−42.9638	+	3.38133i	−1.44585	+	0.113791i	−0.776949	−	0.629563i	$-0.783234\pi$
$883$	−42.9638	+	3.38133i	−1.44585	+	0.113791i	−0.668898	+	0.743354i	$0.733234\pi$
$884$	6.21727	+	19.1348i	0.209109	+	0.643573i
$885$		0			0
$886$	−16.0296	−	5.20834i	−0.538526	−	0.174978i
$887$	−27.6449	−	16.9408i	−0.928225	−	0.568817i	−0.0258012	−	0.999667i	$-0.508214\pi$
$887$	−27.6449	−	16.9408i	−0.928225	−	0.568817i	−0.902423	+	0.430850i	$0.858214\pi$
$888$		0			0
$889$	27.7370	+	2.18295i	0.930268	+	0.0732137i
$890$	8.04571	+	33.5128i	0.269693	+	1.12335i
$891$		0			0
$892$	−8.13765	+	11.2005i	−0.272469	+	0.375021i
$893$	5.10091	+	5.10091i	0.170695	+	0.170695i
$894$		0			0
$895$	−41.9785	−	35.8531i	−1.40319	−	1.19844i
$896$	2.69206	+	3.15200i	0.0899354	+	0.105301i
$897$		0			0
$898$	14.2634	−	10.3629i	0.475974	−	0.345816i
$899$	34.6531	+	14.3538i	1.15575	+	0.478725i
$900$		0			0
$901$		−	33.5663i		−	1.11826i
$902$	33.3192	−	15.4791i	1.10941	−	0.515396i
$903$		0			0
$904$	−3.04772	−	1.55289i	−0.101366	−	0.0516484i
$905$	−24.2934	+	58.6495i	−0.807541	+	1.94958i
$906$		0			0
$907$	−24.1273	−	3.82138i	−0.801132	−	0.126887i	−0.257574	−	0.966258i	$-0.582923\pi$
$907$	−24.1273	−	3.82138i	−0.801132	−	0.126887i	−0.543558	+	0.839372i	$0.682923\pi$
$908$	8.92639	−	7.62386i	0.296233	−	0.253007i
$909$		0			0
$910$	9.32582	+	58.8809i	0.309148	+	1.95188i
$911$	−26.7892	+	26.7892i	−0.887567	+	0.887567i	−0.994289	−	0.106722i	$-0.965965\pi$
$911$	−26.7892	+	26.7892i	−0.887567	+	0.887567i	0.106722	+	0.994289i	$0.465965\pi$
$912$		0			0
$913$	41.1740	−	25.2315i	1.36266	−	0.835039i
$914$	21.8821	−	5.25343i	0.723796	−	0.173768i
$915$		0			0
$916$	−21.7913	+	9.02624i	−0.720004	+	0.298235i
$917$	36.3618	−	59.3371i	1.20077	−	1.95949i
$918$		0			0
$919$	−18.4365	−	4.42622i	−0.608165	−	0.146008i	−0.0823458	−	0.996604i	$-0.526241\pi$
$919$	−18.4365	−	4.42622i	−0.608165	−	0.146008i	−0.525819	+	0.850596i	$0.676241\pi$
$920$	−20.7353	+	6.73730i	−0.683621	+	0.222122i
$921$		0			0
$922$	−6.23024	−	12.2275i	−0.205182	−	0.402693i
$923$	0.183439	+	0.360019i	0.00603796	+	0.0118502i
$924$		0			0
$925$	−4.01910	+	1.30589i	−0.132147	+	0.0429373i
$926$	−12.5558	−	3.01437i	−0.412608	−	0.0990585i
$927$		0			0
$928$	−4.79374	+	7.82268i	−0.157362	+	0.256792i
$929$	−11.4718	+	4.75177i	−0.376377	+	0.155900i	−0.562849	−	0.826560i	$-0.690295\pi$
$929$	−11.4718	+	4.75177i	−0.376377	+	0.155900i	0.186472	+	0.982460i	$0.440295\pi$
$930$		0			0
$931$	−8.97389	+	2.15444i	−0.294107	+	0.0706089i
$932$	−13.5674	+	8.31409i	−0.444413	+	0.272337i
$933$		0			0
$934$	7.32518	−	7.32518i	0.239687	−	0.239687i
$935$	−14.1124	−	89.1022i	−0.461525	−	2.91395i
$936$		0			0
$937$	17.4091	−	14.8688i	0.568730	−	0.485741i	−0.317961	−	0.948104i	$-0.602998\pi$
$937$	17.4091	−	14.8688i	0.568730	−	0.485741i	0.886691	+	0.462363i	$0.152998\pi$
$938$	12.2841	+	1.94561i	0.401091	+	0.0635265i
$939$		0			0
$940$	−10.2108	+	24.6511i	−0.333040	+	0.804031i
$941$	51.9730	+	26.4816i	1.69427	+	0.863274i	0.987836	+	0.155497i	$0.0496978\pi$
$941$	51.9730	+	26.4816i	1.69427	+	0.863274i	0.706435	+	0.707778i	$0.250302\pi$
$942$		0			0
$943$	25.8761	+	32.6264i	0.842643	+	1.06246i
$944$			5.11291i			0.166411i
$945$		0			0
$946$	30.7713	+	12.7459i	1.00046	+	0.414405i
$947$	−17.7558	+	12.9003i	−0.576986	+	0.419205i	−0.837636	−	0.546229i	$-0.816063\pi$
$947$	−17.7558	+	12.9003i	−0.576986	+	0.419205i	0.260651	+	0.965433i	$0.416063\pi$
$948$		0			0
$949$	−17.0885	−	20.0081i	−0.554717	−	0.649490i
$950$	−4.29997	−	3.67252i	−0.139510	−	0.119152i
$951$		0			0
$952$	−13.7465	−	13.7465i	−0.445526	−	0.445526i
$953$	34.1697	−	47.0306i	1.10687	−	1.52347i	0.280913	−	0.959733i	$-0.409363\pi$
$953$	34.1697	−	47.0306i	1.10687	−	1.52347i	0.825954	−	0.563738i	$-0.190637\pi$
$954$		0			0
$955$	10.8769	+	45.3054i	0.351967	+	1.46605i
$956$	1.20375	+	0.0947375i	0.0389322	+	0.00306403i
$957$		0			0
$958$	6.39650	+	3.91978i	0.206661	+	0.126642i
$959$	10.3711	+	3.36978i	0.334900	+	0.108816i
$960$		0			0
$961$	4.41469	+	13.5870i	0.142409	+	0.438291i
$962$	2.89679	−	0.227983i	0.0933964	−	0.00735046i
$963$		0			0
$964$	6.21471	−	3.16655i	0.200162	−	0.101988i
$965$	−2.52569	−	32.0919i	−0.0813047	−	1.03307i
$966$		0			0
$967$	4.56648	−	19.0208i	0.146848	−	0.611667i	−0.849598	−	0.527431i	$-0.823155\pi$
$967$	4.56648	−	19.0208i	0.146848	−	0.611667i	0.996446	−	0.0842355i	$-0.0268448\pi$
$968$	−6.77404	+	20.8483i	−0.217726	+	0.670091i
$969$		0			0
$970$	−16.6656	−	40.2342i	−0.535099	−	1.29184i
$971$	−2.22399	+	28.2585i	−0.0713712	+	0.906857i	0.852147	+	0.523303i	$0.175300\pi$
$971$	−2.22399	+	28.2585i	−0.0713712	+	0.906857i	−0.923518	+	0.383555i	$0.874700\pi$
$972$		0			0
$973$	10.3849	+	16.9467i	0.332926	+	0.543286i
$974$	−26.6136	−	19.3359i	−0.852756	−	0.619563i
$975$		0			0
$976$	6.99313	−	1.10760i	0.223845	−	0.0354535i
$977$	−19.6889	+	23.0527i	−0.629902	+	0.737521i	−0.979957	−	0.199208i	$-0.936163\pi$
$977$	−19.6889	+	23.0527i	−0.629902	+	0.737521i	0.350055	+	0.936729i	$0.386163\pi$
$978$		0			0
$979$	−9.22754	+	58.2604i	−0.294913	+	1.86201i
$980$	−20.0644	−	27.6163i	−0.640934	−	0.882170i
$981$		0			0
$982$	−7.86377	+	15.4335i	−0.250943	+	0.492503i
$983$	51.5993			1.64576			0.822880	−	0.568215i	$-0.192366\pi$
$983$	51.5993			1.64576			0.822880	+	0.568215i	$0.192366\pi$
$984$		0			0
$985$	5.76961			0.183835
$986$	19.5345	−	38.3387i	0.622106	−	1.22095i
$987$		0			0
$988$	2.28546	+	3.14567i	0.0727103	+	0.100077i
$989$	−5.90560	+	37.2865i	−0.187787	+	1.18564i
$990$		0			0
$991$	−15.0516	+	17.6232i	−0.478131	+	0.559819i	−0.946079	−	0.323937i	$-0.894993\pi$
$991$	−15.0516	+	17.6232i	−0.478131	+	0.559819i	0.467948	+	0.883756i	$0.344993\pi$
$992$	4.03791	−	0.639543i	0.128204	−	0.0203055i
$993$		0			0
$994$	−0.315857	−	0.229484i	−0.0100184	−	0.00727879i
$995$	−30.7103	−	50.1147i	−0.973582	−	1.58874i
$996$		0			0
$997$	−2.67156	+	33.9454i	−0.0846093	+	1.07506i	0.797281	+	0.603608i	$0.206271\pi$
$997$	−2.67156	+	33.9454i	−0.0846093	+	1.07506i	−0.881890	+	0.471455i	$0.843729\pi$
$998$	0.570174	+	1.37652i	0.0180486	+	0.0435731i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.a.233.1	✓	48
3.2	odd	2		738.2.ba.b.233.3	yes	48
41.22	odd	40		738.2.ba.b.719.3	yes	48
123.104	even	40	inner	738.2.ba.a.719.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.a.233.1	✓	48	1.1	even	1	trivial
738.2.ba.a.719.1	yes	48	123.104	even	40	inner
738.2.ba.b.233.3	yes	48	3.2	odd	2
738.2.ba.b.719.3	yes	48	41.22	odd	40

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.587785 - 0.809017i) q^{4} +(-0.524441 + 3.31119i) q^{5} +(2.69206 - 3.15200i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.71220 - 1.97053i) q^{10} +(-2.99794 - 4.89220i) q^{11} +(0.336584 - 4.27671i) q^{13} +(1.58628 + 3.82962i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(1.09484 - 4.56035i) q^{17} +(-0.0711129 - 0.903575i) q^{19} +(2.98707 - 1.52199i) q^{20} +(5.72002 - 0.450175i) q^{22} +(2.00966 + 6.18509i) q^{23} +(-5.93364 - 1.92796i) q^{25} +(3.65777 + 2.24148i) q^{26} +(-4.13237 - 0.325225i) q^{28} +(-2.14178 - 8.92115i) q^{29} +(-2.40301 + 3.30746i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.56625 + 3.04587i) q^{34} +(9.02502 + 10.5669i) q^{35} +(0.547981 - 0.398132i) q^{37} +(0.837376 + 0.346852i) q^{38} +3.35246i q^{40} +(6.00083 - 2.23385i) q^{41} +(5.17218 + 2.63536i) q^{43} +(-2.19572 + 5.30095i) q^{44} +(-6.42332 - 1.01735i) q^{46} +(-6.05205 + 5.16894i) q^{47} +(-1.59286 - 10.0569i) q^{49} +(4.41164 - 4.41164i) q^{50} +(-3.65777 + 2.24148i) q^{52} +(6.95935 - 1.67079i) q^{53} +(17.7712 - 7.36108i) q^{55} +(2.16583 - 3.53432i) q^{56} +(8.92115 + 2.14178i) q^{58} +(4.86267 - 1.57998i) q^{59} +(-3.21439 - 6.30859i) q^{61} +(-1.85603 - 3.64265i) q^{62} +(0.951057 - 0.309017i) q^{64} +(13.9845 + 3.35737i) q^{65} +(1.56772 - 2.55829i) q^{67} +(-4.33293 + 1.79476i) q^{68} +(-13.5125 + 3.24406i) q^{70} +(-0.0803081 + 0.0492129i) q^{71} +(4.33705 - 4.33705i) q^{73} +(0.105960 + 0.669003i) q^{74} +(-0.689209 + 0.588640i) q^{76} +(-23.4908 - 3.72058i) q^{77} +(-3.21784 + 7.76856i) q^{79} +(-2.98707 - 1.52199i) q^{80} +(-0.733948 + 6.36092i) q^{82} +8.41626i q^{83} +(14.5260 + 6.01687i) q^{85} +(-4.69624 + 3.41202i) q^{86} +(-3.72634 - 4.36298i) q^{88} +(-7.81737 - 6.67667i) q^{89} +(-12.5741 - 12.5741i) q^{91} +(3.82259 - 5.26135i) q^{92} +(-1.85799 - 7.73907i) q^{94} +(3.02920 + 0.238403i) q^{95} +(11.0760 + 6.78737i) q^{97} +(9.68390 + 3.14649i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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