LMFDB - Embedded newform 168.2.p.a.139.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(139,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.139"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.20457921756784916168704.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 - 4x^12 - 4x^10 + 16x^8 - 16x^6 - 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.6
Root			$-1.40199 - 0.185533i$ of defining polynomial
Character	$\chi$	$=$	168.139
Dual form			168.2.p.a.139.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.185533 - 1.40199i) q^{2} +1.00000i q^{3} +(-1.93115 + 0.520231i) q^{4} -3.84444 q^{5} +(1.40199 - 0.185533i) q^{6} +(-1.62140 - 2.09071i) q^{7} +(1.08765 + 2.61094i) q^{8} -1.00000 q^{9} +(0.713272 + 5.38987i) q^{10} -4.54637 q^{11} +(-0.520231 - 1.93115i) q^{12} +1.81625 q^{13} +(-2.63033 + 2.66108i) q^{14} -3.84444i q^{15} +(3.45872 - 2.00929i) q^{16} -3.49124i q^{17} +(0.185533 + 1.40199i) q^{18} +1.68700i q^{19} +(7.42422 - 2.00000i) q^{20} +(2.09071 - 1.62140i) q^{21} +(0.843502 + 6.37397i) q^{22} +5.00632i q^{23} +(-2.61094 + 1.08765i) q^{24} +9.77975 q^{25} +(-0.336975 - 2.54637i) q^{26} -1.00000i q^{27} +(4.21882 + 3.19398i) q^{28} -1.81625i q^{29} +(-5.38987 + 0.713272i) q^{30} -5.34329 q^{31} +(-3.45872 - 4.47630i) q^{32} -4.54637i q^{33} +(-4.89469 + 0.647741i) q^{34} +(6.23338 + 8.03761i) q^{35} +(1.93115 - 0.520231i) q^{36} -1.42654i q^{37} +(2.36516 - 0.312995i) q^{38} +1.81625i q^{39} +(-4.18142 - 10.0376i) q^{40} -8.97551i q^{41} +(-2.66108 - 2.63033i) q^{42} -8.03761 q^{43} +(8.77975 - 2.36516i) q^{44} +3.84444 q^{45} +(7.01881 - 0.928837i) q^{46} -4.83580 q^{47} +(2.00929 + 3.45872i) q^{48} +(-1.74213 + 6.77975i) q^{49} +(-1.81447 - 13.7111i) q^{50} +3.49124 q^{51} +(-3.50747 + 0.944872i) q^{52} +5.87263i q^{53} +(-1.40199 + 0.185533i) q^{54} +17.4783 q^{55} +(3.69520 - 6.50734i) q^{56} -1.68700 q^{57} +(-2.54637 + 0.336975i) q^{58} -8.46675i q^{59} +(2.00000 + 7.42422i) q^{60} -3.01955 q^{61} +(0.991357 + 7.49124i) q^{62} +(1.62140 + 2.09071i) q^{63} +(-5.63402 + 5.67959i) q^{64} -6.98249 q^{65} +(-6.37397 + 0.843502i) q^{66} -4.42914 q^{67} +(1.81625 + 6.74213i) q^{68} -5.00632 q^{69} +(10.1122 - 10.2304i) q^{70} +1.47928i q^{71} +(-1.08765 - 2.61094i) q^{72} -6.98249i q^{73} +(-2.00000 + 0.264671i) q^{74} +9.77975i q^{75} +(-0.877633 - 3.25787i) q^{76} +(7.37148 + 9.50514i) q^{77} +(2.54637 - 0.336975i) q^{78} -2.97813i q^{79} +(-13.2968 + 7.72462i) q^{80} +1.00000 q^{81} +(-12.5836 + 1.66525i) q^{82} +10.5770i q^{83} +(-3.19398 + 4.21882i) q^{84} +13.4219i q^{85} +(1.49124 + 11.2687i) q^{86} +1.81625 q^{87} +(-4.94487 - 11.8703i) q^{88} +15.9580i q^{89} +(-0.713272 - 5.38987i) q^{90} +(-2.94487 - 3.79726i) q^{91} +(-2.60444 - 9.66797i) q^{92} -5.34329i q^{93} +(0.897201 + 6.77975i) q^{94} -6.48559i q^{95} +(4.47630 - 3.45872i) q^{96} +11.6085i q^{97} +(9.82836 + 1.18459i) q^{98} +4.54637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 2 q^{4} - 10 q^{8} - 16 q^{9} - 8 q^{11} - 14 q^{14} + 18 q^{16} - 2 q^{18} + 8 q^{22} + 16 q^{25} - 10 q^{28} - 16 q^{30} - 18 q^{32} + 24 q^{35} - 2 q^{36} - 4 q^{42} - 8 q^{43} + 52 q^{46}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 + 2 * q^4 - 10 * q^8 - 16 * q^9 - 8 * q^11 - 14 * q^14 + 18 * q^16 - 2 * q^18 + 8 * q^22 + 16 * q^25 - 10 * q^28 - 16 * q^30 - 18 * q^32 + 24 * q^35 - 2 * q^36 - 4 * q^42 - 8 * q^43 + 52 * q^46 - 8 * q^49 - 34 * q^50 + 50 * q^56 - 16 * q^57 + 24 * q^58 + 32 * q^60 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 10 * q^72 - 32 * q^74 - 24 * q^78 + 16 * q^81 + 8 * q^84 - 32 * q^86 - 88 * q^88 - 56 * q^91 + 44 * q^92 + 66 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.185533	−	1.40199i	−0.131192	−	0.991357i
$2$	−0.185533	−	1.40199i	−0.131192	−	0.991357i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.93115	+	0.520231i	−0.965577	+	0.260116i
$5$	−3.84444			−1.71929			−0.859644	−	0.510894i	$-0.829314\pi$
$5$	−3.84444			−1.71929			−0.859644	+	0.510894i	$0.829314\pi$
$6$	1.40199	−	0.185533i	0.572360	−	0.0757436i
$7$	−1.62140	−	2.09071i	−0.612831	−	0.790214i
$7$	−1.62140	−	2.09071i	−0.612831	−	0.790214i
$8$	1.08765	+	2.61094i	0.384543	+	0.923107i
$9$	−1.00000			−0.333333
$10$	0.713272	+	5.38987i	0.225556	+	1.70443i
$11$	−4.54637			−1.37078			−0.685391	−	0.728175i	$-0.740369\pi$
$11$	−4.54637			−1.37078			−0.685391	+	0.728175i	$0.740369\pi$
$12$	−0.520231	−	1.93115i	−0.150178	−	0.557476i
$13$	1.81625			0.503738			0.251869	−	0.967761i	$-0.418955\pi$
$13$	1.81625			0.503738			0.251869	+	0.967761i	$0.418955\pi$
$14$	−2.63033	+	2.66108i	−0.702986	+	0.711204i
$15$		−	3.84444i		−	0.992631i
$16$	3.45872	−	2.00929i	0.864680	−	0.502324i
$17$		−	3.49124i		−	0.846751i	−0.905954	−	0.423375i	$-0.860845\pi$
$17$		−	3.49124i		−	0.846751i	0.905954	−	0.423375i	$-0.139155\pi$
$18$	0.185533	+	1.40199i	0.0437306	+	0.330452i
$19$			1.68700i			0.387025i	0.981098	+	0.193513i	$0.0619881\pi$
$19$			1.68700i			0.387025i	−0.981098	+	0.193513i	$0.938012\pi$
$20$	7.42422	−	2.00000i	1.66011	−	0.447214i
$21$	2.09071	−	1.62140i	0.456230	−	0.353818i
$22$	0.843502	+	6.37397i	0.179835	+	1.35893i
$23$			5.00632i			1.04389i	0.852979	+	0.521945i	$0.174793\pi$
$23$			5.00632i			1.04389i	−0.852979	+	0.521945i	$0.825207\pi$
$24$	−2.61094	+	1.08765i	−0.532956	+	0.222016i
$25$	9.77975			1.95595
$26$	−0.336975	−	2.54637i	−0.0660863	−	0.499384i
$27$		−	1.00000i		−	0.192450i
$28$	4.21882	+	3.19398i	0.797283	+	0.603606i
$29$		−	1.81625i		−	0.337270i	−0.985679	−	0.168635i	$-0.946064\pi$
$29$		−	1.81625i		−	0.337270i	0.985679	−	0.168635i	$-0.0539359\pi$
$30$	−5.38987	+	0.713272i	−0.984052	+	0.130225i
$31$	−5.34329			−0.959683			−0.479842	−	0.877355i	$-0.659306\pi$
$31$	−5.34329			−0.959683			−0.479842	+	0.877355i	$0.659306\pi$
$32$	−3.45872	−	4.47630i	−0.611421	−	0.791306i
$33$		−	4.54637i		−	0.791422i
$34$	−4.89469	+	0.647741i	−0.839433	+	0.111087i
$35$	6.23338	+	8.03761i	1.05363	+	1.35860i
$36$	1.93115	−	0.520231i	0.321859	−	0.0867052i
$37$		−	1.42654i		−	0.234522i	−0.993101	−	0.117261i	$-0.962589\pi$
$37$		−	1.42654i		−	0.234522i	0.993101	−	0.117261i	$-0.0374114\pi$
$38$	2.36516	−	0.312995i	0.383680	−	0.0507745i
$39$			1.81625i			0.290833i
$40$	−4.18142	−	10.0376i	−0.661140	−	1.58709i
$41$		−	8.97551i		−	1.40174i	−0.713290	−	0.700869i	$-0.752796\pi$
$41$		−	8.97551i		−	1.40174i	0.713290	−	0.700869i	$-0.247204\pi$
$42$	−2.66108	−	2.63033i	−0.410614	−	0.405869i
$43$	−8.03761			−1.22572			−0.612862	−	0.790190i	$-0.709982\pi$
$43$	−8.03761			−1.22572			−0.612862	+	0.790190i	$0.709982\pi$
$44$	8.77975	−	2.36516i	1.32360	−	0.356562i
$45$	3.84444			0.573096
$46$	7.01881	−	0.928837i	1.03487	−	0.136950i
$47$	−4.83580			−0.705374			−0.352687	−	0.935741i	$-0.614732\pi$
$47$	−4.83580			−0.705374			−0.352687	+	0.935741i	$0.614732\pi$
$48$	2.00929	+	3.45872i	0.290017	+	0.499223i
$49$	−1.74213	+	6.77975i	−0.248876	+	0.968535i
$50$	−1.81447	−	13.7111i	−0.256604	−	1.93904i
$51$	3.49124			0.488872
$52$	−3.50747	+	0.944872i	−0.486398	+	0.131030i
$53$			5.87263i			0.806668i	0.915053	+	0.403334i	$0.132149\pi$
$53$			5.87263i			0.806668i	−0.915053	+	0.403334i	$0.867851\pi$
$54$	−1.40199	+	0.185533i	−0.190787	+	0.0252479i
$55$	17.4783			2.35677
$56$	3.69520	−	6.50734i	0.493792	−	0.869580i
$57$	−1.68700			−0.223449
$58$	−2.54637	+	0.336975i	−0.334355	+	0.0442470i
$59$		−	8.46675i		−	1.10228i	−0.834414	−	0.551139i	$-0.814194\pi$
$59$		−	8.46675i		−	1.10228i	0.834414	−	0.551139i	$-0.185806\pi$
$60$	2.00000	+	7.42422i	0.258199	+	0.958462i
$61$	−3.01955			−0.386613			−0.193307	−	0.981138i	$-0.561921\pi$
$61$	−3.01955			−0.386613			−0.193307	+	0.981138i	$0.561921\pi$
$62$	0.991357	+	7.49124i	0.125903	+	0.951389i
$63$	1.62140	+	2.09071i	0.204277	+	0.263405i
$64$	−5.63402	+	5.67959i	−0.704253	+	0.709949i
$65$	−6.98249			−0.866071
$66$	−6.37397	+	0.843502i	−0.784581	+	0.103828i
$67$	−4.42914			−0.541105			−0.270553	−	0.962705i	$-0.587206\pi$
$67$	−4.42914			−0.541105			−0.270553	+	0.962705i	$0.587206\pi$
$68$	1.81625	+	6.74213i	0.220253	+	0.817604i
$69$	−5.00632			−0.602690
$70$	10.1122	−	10.2304i	1.20863	−	1.22276i
$71$			1.47928i			0.175558i	0.996140	+	0.0877791i	$0.0279769\pi$
$71$			1.47928i			0.175558i	−0.996140	+	0.0877791i	$0.972023\pi$
$72$	−1.08765	−	2.61094i	−0.128181	−	0.307702i
$73$		−	6.98249i		−	0.817238i	−0.912705	−	0.408619i	$-0.866010\pi$
$73$		−	6.98249i		−	0.817238i	0.912705	−	0.408619i	$-0.133990\pi$
$74$	−2.00000	+	0.264671i	−0.232495	+	0.0307674i
$75$			9.77975i			1.12927i
$76$	−0.877633	−	3.25787i	−0.100671	−	0.373703i
$77$	7.37148	+	9.50514i	0.840058	+	1.08321i
$78$	2.54637	−	0.336975i	0.288320	−	0.0381549i
$79$		−	2.97813i		−	0.335065i	−0.985867	−	0.167533i	$-0.946420\pi$
$79$		−	2.97813i		−	0.335065i	0.985867	−	0.167533i	$-0.0535800\pi$
$80$	−13.2968	+	7.72462i	−1.48663	+	0.863639i
$81$	1.00000			0.111111
$82$	−12.5836	+	1.66525i	−1.38962	+	0.183897i
$83$			10.5770i			1.16098i	0.814268	+	0.580489i	$0.197138\pi$
$83$			10.5770i			1.16098i	−0.814268	+	0.580489i	$0.802862\pi$
$84$	−3.19398	+	4.21882i	−0.348492	+	0.460312i
$85$			13.4219i			1.45581i
$86$	1.49124	+	11.2687i	0.160805	+	1.21513i
$87$	1.81625			0.194723
$88$	−4.94487	−	11.8703i	−0.527125	−	1.26538i
$89$			15.9580i			1.69154i	0.533544	+	0.845772i	$0.320860\pi$
$89$			15.9580i			1.69154i	−0.533544	+	0.845772i	$0.679140\pi$
$90$	−0.713272	−	5.38987i	−0.0751854	−	0.568143i
$91$	−2.94487	−	3.79726i	−0.308707	−	0.398061i
$92$	−2.60444	−	9.66797i	−0.271532	−	1.00796i
$93$		−	5.34329i		−	0.554073i
$94$	0.897201	+	6.77975i	0.0925392	+	0.699278i
$95$		−	6.48559i		−	0.665408i
$96$	4.47630	−	3.45872i	0.456860	−	0.353004i
$97$			11.6085i			1.17866i	0.807892	+	0.589331i	$0.200609\pi$
$97$			11.6085i			1.17866i	−0.807892	+	0.589331i	$0.799391\pi$
$98$	9.82836	+	1.18459i	0.992815	+	0.119661i
$99$	4.54637			0.456928
$100$	−18.8862	+	5.08773i	−1.88862	+	0.508773i
$101$	11.5333			1.14761			0.573805	−	0.818992i	$-0.305467\pi$
$101$	11.5333			1.14761			0.573805	+	0.818992i	$0.305467\pi$
$102$	−0.647741	−	4.89469i	−0.0641359	−	0.484647i
$103$	−1.14230			−0.112555			−0.0562773	−	0.998415i	$-0.517923\pi$
$103$	−1.14230			−0.112555			−0.0562773	+	0.998415i	$0.517923\pi$
$104$	1.97545	+	4.74213i	0.193709	+	0.465004i
$105$	−8.03761	+	6.23338i	−0.784391	+	0.608315i
$106$	8.23338	−	1.08957i	0.799696	−	0.105828i
$107$	0.0796192			0.00769707			0.00384854	−	0.999993i	$-0.498775\pi$
$107$	0.0796192			0.00769707			0.00384854	+	0.999993i	$0.498775\pi$
$108$	0.520231	+	1.93115i	0.0500593	+	0.185825i
$109$		−	20.1081i		−	1.92601i	−0.269489	−	0.963004i	$-0.586855\pi$
$109$		−	20.1081i		−	1.92601i	0.269489	−	0.963004i	$-0.413145\pi$
$110$	−3.24280	−	24.5044i	−0.309189	−	2.33640i
$111$	1.42654			0.135401
$112$	−9.80881	−	3.97331i	−0.926846	−	0.375442i
$113$	4.98249			0.468713			0.234356	−	0.972151i	$-0.424702\pi$
$113$	4.98249			0.468713			0.234356	+	0.972151i	$0.424702\pi$
$114$	0.312995	+	2.36516i	0.0293147	+	0.221518i
$115$		−	19.2465i		−	1.79475i
$116$	0.944872	+	3.50747i	0.0877292	+	0.325660i
$117$	−1.81625			−0.167913
$118$	−11.8703	+	1.57086i	−1.09275	+	0.144610i
$119$	−7.29918	+	5.66070i	−0.669114	+	0.518915i
$120$	10.0376	−	4.18142i	0.916305	−	0.381710i
$121$	9.66949			0.879045
$122$	0.560226	+	4.23338i	0.0507205	+	0.383272i
$123$	8.97551			0.809294
$124$	10.3187	−	2.77975i	0.926649	−	0.249629i
$125$	−18.3755			−1.64355
$126$	2.63033	−	2.66108i	0.234329	−	0.237068i
$127$			5.38471i			0.477816i	0.971042	+	0.238908i	$0.0767894\pi$
$127$			5.38471i			0.477816i	−0.971042	+	0.238908i	$0.923211\pi$
$128$	9.00803	+	6.84510i	0.796205	+	0.605027i
$129$		−	8.03761i		−	0.707673i
$130$	1.29548	+	9.78938i	0.113621	+	0.858586i
$131$		−	13.0927i		−	1.14392i	−0.820282	−	0.571959i	$-0.806184\pi$
$131$		−	13.0927i		−	1.14392i	0.820282	−	0.571959i	$-0.193816\pi$
$132$	2.36516	+	8.77975i	0.205861	+	0.764179i
$133$	3.52704	−	2.73531i	0.305833	−	0.237181i
$134$	0.821752	+	6.20961i	0.0709885	+	0.536428i
$135$			3.84444i			0.330877i
$136$	9.11543	−	3.79726i	0.781642	−	0.325612i
$137$	−19.5595			−1.67108			−0.835540	−	0.549429i	$-0.814845\pi$
$137$	−19.5595			−1.67108			−0.835540	+	0.549429i	$0.814845\pi$
$138$	0.928837	+	7.01881i	0.0790679	+	0.597481i
$139$		−	14.5910i		−	1.23759i	−0.785553	−	0.618795i	$-0.787621\pi$
$139$		−	14.5910i		−	1.23759i	0.785553	−	0.618795i	$-0.212379\pi$
$140$	−16.2190	−	12.2791i	−1.37076	−	1.03777i
$141$		−	4.83580i		−	0.407248i
$142$	2.07394	−	0.274455i	0.174041	−	0.0230318i
$143$	−8.25737			−0.690516
$144$	−3.45872	+	2.00929i	−0.288227	+	0.167441i
$145$			6.98249i			0.579864i
$146$	−9.78938	+	1.29548i	−0.810175	+	0.107215i
$147$	−6.77975	−	1.74213i	−0.559184	−	0.143689i
$148$	0.742132	+	2.75488i	0.0610029	+	0.226449i
$149$		−	18.3973i		−	1.50717i	−0.657352	−	0.753584i	$-0.728324\pi$
$149$		−	18.3973i		−	1.50717i	0.657352	−	0.753584i	$-0.271676\pi$
$150$	13.7111	−	1.81447i	1.11951	−	0.148151i
$151$			9.88759i			0.804641i	0.915499	+	0.402320i	$0.131796\pi$
$151$			9.88759i			0.804641i	−0.915499	+	0.402320i	$0.868204\pi$
$152$	−4.40467	+	1.83488i	−0.357266	+	0.148828i
$153$			3.49124i			0.282250i
$154$	11.9585	−	12.0983i	0.963641	−	0.974906i
$155$	20.5420			1.64997
$156$	−0.944872	−	3.50747i	−0.0756503	−	0.280822i
$157$	12.3582			0.986294			0.493147	−	0.869946i	$-0.335846\pi$
$157$	12.3582			0.986294			0.493147	+	0.869946i	$0.335846\pi$
$158$	−4.17531	+	0.552541i	−0.332169	+	0.0439578i
$159$	−5.87263			−0.465730
$160$	13.2968	+	17.2089i	1.05121	+	1.36048i
$161$	10.4668	−	8.11723i	0.824896	−	0.639728i
$162$	−0.185533	−	1.40199i	−0.0145769	−	0.110151i
$163$	−3.57086			−0.279692			−0.139846	−	0.990173i	$-0.544661\pi$
$163$	−3.57086			−0.279692			−0.139846	+	0.990173i	$0.544661\pi$
$164$	4.66934	+	17.3331i	0.364614	+	1.35349i
$165$			17.4783i			1.36068i
$166$	14.8289	−	1.96239i	1.15094	−	0.152311i
$167$	19.5788			1.51505			0.757525	−	0.652806i	$-0.226408\pi$
$167$	19.5788			1.51505			0.757525	+	0.652806i	$0.226408\pi$
$168$	6.50734	+	3.69520i	0.502052	+	0.285091i
$169$	−9.70122			−0.746248
$170$	18.8174	−	2.49020i	1.44323	−	0.190990i
$171$		−	1.68700i		−	0.129008i
$172$	15.5219	−	4.18142i	1.18353	−	0.318830i
$173$	−5.49424			−0.417719			−0.208860	−	0.977946i	$-0.566975\pi$
$173$	−5.49424			−0.417719			−0.208860	+	0.977946i	$0.566975\pi$
$174$	−0.336975	−	2.54637i	−0.0255460	−	0.193040i
$175$	−15.8569	−	20.4466i	−1.19867	−	1.54562i
$176$	−15.7246	+	9.13500i	−1.18529	+	0.688576i
$177$	8.46675			0.636400
$178$	22.3730	−	2.96074i	1.67692	−	0.221917i
$179$	10.0306			0.749725			0.374862	−	0.927080i	$-0.377690\pi$
$179$	10.0306			0.749725			0.374862	+	0.927080i	$0.377690\pi$
$180$	−7.42422	+	2.00000i	−0.553368	+	0.149071i
$181$	−24.2481			−1.80235			−0.901174	−	0.433458i	$-0.857293\pi$
$181$	−24.2481			−1.80235			−0.901174	+	0.433458i	$0.857293\pi$
$182$	−4.77735	+	4.83320i	−0.354121	+	0.358261i
$183$		−	3.01955i		−	0.223211i
$184$	−13.0712	+	5.44513i	−0.963621	+	0.401420i
$185$			5.48426i			0.403211i
$186$	−7.49124	+	0.991357i	−0.549285	+	0.0726899i
$187$			15.8725i			1.16071i
$188$	9.33868	−	2.51574i	0.681093	−	0.183479i
$189$	−2.09071	+	1.62140i	−0.152077	+	0.117939i
$190$	−9.09274	+	1.20329i	−0.659657	+	0.0872960i
$191$		−	8.49422i		−	0.614620i	−0.951609	−	0.307310i	$-0.900571\pi$
$191$		−	8.49422i		−	0.614620i	0.951609	−	0.307310i	$-0.0994288\pi$
$192$	−5.67959	−	5.63402i	−0.409889	−	0.406601i
$193$	−11.2955			−0.813067			−0.406533	−	0.913636i	$-0.633262\pi$
$193$	−11.2955			−0.813067			−0.406533	+	0.913636i	$0.633262\pi$
$194$	16.2750	−	2.15376i	1.16848	−	0.154631i
$195$		−	6.98249i		−	0.500026i
$196$	−0.162709	−	13.9991i	−0.0116221	−	0.999932i
$197$		−	2.38473i		−	0.169905i	−0.996385	−	0.0849526i	$-0.972926\pi$
$197$		−	2.38473i		−	0.169905i	0.996385	−	0.0849526i	$-0.0270739\pi$
$198$	−0.843502	−	6.37397i	−0.0599451	−	0.452978i
$199$	−2.46338			−0.174624			−0.0873120	−	0.996181i	$-0.527828\pi$
$199$	−2.46338			−0.174624			−0.0873120	+	0.996181i	$0.527828\pi$
$200$	10.6370	+	25.5343i	0.752147	+	1.80555i
$201$		−	4.42914i		−	0.312407i
$202$	−2.13981	−	16.1696i	−0.150557	−	1.13769i
$203$	−3.79726	+	2.94487i	−0.266515	+	0.206690i
$204$	−6.74213	+	1.81625i	−0.472044	+	0.127163i
$205$			34.5058i			2.40999i
$206$	0.211935	+	1.60150i	0.0147662	+	0.111582i
$207$		−	5.00632i		−	0.347963i
$208$	6.28191	−	3.64939i	0.435572	−	0.253040i
$209$		−	7.66975i		−	0.530528i
$210$	10.2304	+	10.1122i	0.705963	+	0.697806i
$211$	−0.0376150			−0.00258952			−0.00129476	−	0.999999i	$-0.500412\pi$
$211$	−0.0376150			−0.00258952			−0.00129476	+	0.999999i	$0.500412\pi$
$212$	−3.05513	−	11.3410i	−0.209827	−	0.778901i
$213$	−1.47928			−0.101359
$214$	−0.0147720	−	0.111625i	−0.00100979	−	0.00763055i
$215$	30.9002			2.10737
$216$	2.61094	−	1.08765i	0.177652	−	0.0740054i
$217$	8.66361	+	11.1713i	0.588124	+	0.758355i
$218$	−28.1914	+	3.73072i	−1.90936	+	0.252676i
$219$	6.98249			0.471833
$220$	−33.7532	+	9.09274i	−2.27564	+	0.613033i
$221$		−	6.34099i		−	0.426541i
$222$	−0.264671	−	2.00000i	−0.0177636	−	0.134231i
$223$	−12.9144			−0.864812			−0.432406	−	0.901679i	$-0.642335\pi$
$223$	−12.9144			−0.864812			−0.432406	+	0.901679i	$0.642335\pi$
$224$	−3.75068	+	14.4890i	−0.250603	+	0.968090i
$225$	−9.77975			−0.651983
$226$	−0.924416	−	6.98540i	−0.0614913	−	0.464662i
$227$		−	1.48426i		−	0.0985141i	−0.998786	−	0.0492571i	$-0.984315\pi$
$227$		−	1.48426i		−	0.0985141i	0.998786	−	0.0492571i	$-0.0156854\pi$
$228$	3.25787	−	0.877633i	0.215758	−	0.0581226i
$229$	−4.66934			−0.308559			−0.154279	−	0.988027i	$-0.549306\pi$
$229$	−4.66934			−0.308559			−0.154279	+	0.988027i	$0.549306\pi$
$230$	−26.9834	+	3.57086i	−1.77923	+	0.235456i
$231$	−9.50514	+	7.37148i	−0.625392	+	0.485008i
$232$	4.74213	−	1.97545i	0.311336	−	0.129695i
$233$	−8.35650			−0.547452			−0.273726	−	0.961808i	$-0.588256\pi$
$233$	−8.35650			−0.547452			−0.273726	+	0.961808i	$0.588256\pi$
$234$	0.336975	+	2.54637i	0.0220288	+	0.166461i
$235$	18.5910			1.21274
$236$	4.40467	+	16.3506i	0.286720	+	1.06433i
$237$	2.97813			0.193450
$238$	9.29048	+	9.18313i	0.602213	+	0.595254i
$239$		−	19.8547i		−	1.28430i	−0.766580	−	0.642148i	$-0.778043\pi$
$239$		−	19.8547i		−	1.28430i	0.766580	−	0.642148i	$-0.221957\pi$
$240$	−7.72462	−	13.2968i	−0.498622	−	0.858308i
$241$			6.57701i			0.423662i	0.977306	+	0.211831i	$0.0679427\pi$
$241$			6.57701i			0.423662i	−0.977306	+	0.211831i	$0.932057\pi$
$242$	−1.79401	−	13.5565i	−0.115323	−	0.871447i
$243$			1.00000i			0.0641500i
$244$	5.83121	−	1.57086i	0.373305	−	0.100564i
$245$	6.69753	−	26.0644i	0.427889	−	1.66519i
$246$	−1.66525	−	12.5836i	−0.106173	−	0.802300i
$247$			3.06403i			0.194960i
$248$	−5.81164	−	13.9510i	−0.369040	−	0.885890i
$249$	−10.5770			−0.670291
$250$	3.40926	+	25.7622i	0.215620	+	1.62935i
$251$			4.85827i			0.306652i	0.988176	+	0.153326i	$0.0489984\pi$
$251$			4.85827i			0.306652i	−0.988176	+	0.153326i	$0.951002\pi$
$252$	−4.21882	−	3.19398i	−0.265761	−	0.201202i
$253$		−	22.7606i		−	1.43094i
$254$	7.54931	−	0.999042i	0.473686	−	0.0626855i
$255$	−13.4219			−0.840511
$256$	7.92547	−	13.8992i	0.495342	−	0.868698i
$257$			9.20998i			0.574503i	0.957855	+	0.287251i	$0.0927415\pi$
$257$			9.20998i			0.574503i	−0.957855	+	0.287251i	$0.907259\pi$
$258$	−11.2687	+	1.49124i	−0.701556	+	0.0928408i
$259$	−2.98249	+	2.31300i	−0.185323	+	0.143723i
$260$	13.4843	−	3.63251i	0.836259	−	0.225279i
$261$			1.81625i			0.112423i
$262$	−18.3559	+	2.42914i	−1.13403	+	0.150073i
$263$			3.90849i			0.241008i	0.992713	+	0.120504i	$0.0384511\pi$
$263$			3.90849i			0.241008i	−0.992713	+	0.120504i	$0.961549\pi$
$264$	11.8703	−	4.94487i	0.730567	−	0.304336i
$265$		−	22.5770i		−	1.38689i
$266$	−4.48926	−	4.43738i	−0.275254	−	0.272073i
$267$	−15.9580			−0.976613
$268$	8.55335	−	2.30418i	0.522479	−	0.140750i
$269$	9.24872			0.563905			0.281952	−	0.959428i	$-0.409018\pi$
$269$	9.24872			0.563905			0.281952	+	0.959428i	$0.409018\pi$
$270$	5.38987	−	0.713272i	0.328017	−	0.0434083i
$271$	16.5201			1.00352			0.501762	−	0.865006i	$-0.332685\pi$
$271$	16.5201			1.00352			0.501762	+	0.865006i	$0.332685\pi$
$272$	−7.01494	−	12.0752i	−0.425343	−	0.732168i
$273$	3.79726	−	2.94487i	0.229821	−	0.178232i
$274$	3.62893	+	27.4222i	0.219232	+	1.65664i
$275$	−44.4624			−2.68118
$276$	9.66797	−	2.60444i	0.581944	−	0.156769i
$277$			3.26465i			0.196154i	0.995179	+	0.0980769i	$0.0312691\pi$
$277$			3.26465i			0.196154i	−0.995179	+	0.0980769i	$0.968731\pi$
$278$	−20.4564	+	2.70711i	−1.22689	+	0.162361i
$279$	5.34329			0.319894
$280$	−14.2060	+	25.0171i	−0.848970	+	1.49506i
$281$	19.1680			1.14347			0.571733	−	0.820440i	$-0.306271\pi$
$281$	19.1680			1.14347			0.571733	+	0.820440i	$0.306271\pi$
$282$	−6.77975	+	0.897201i	−0.403728	+	0.0534276i
$283$			20.2780i			1.20540i	0.797968	+	0.602700i	$0.205908\pi$
$283$			20.2780i			1.20540i	−0.797968	+	0.602700i	$0.794092\pi$
$284$	−0.769567	−	2.85672i	−0.0456654	−	0.169515i
$285$	6.48559			0.384173
$286$	1.53201	+	11.5767i	0.0905899	+	0.684548i
$287$	−18.7652	+	14.5529i	−1.10767	+	0.859029i
$288$	3.45872	+	4.47630i	0.203807	+	0.263769i
$289$	4.81122			0.283013
$290$	9.78938	−	1.29548i	0.574852	−	0.0760734i
$291$	−11.6085			−0.680501
$292$	3.63251	+	13.4843i	0.212576	+	0.789107i
$293$	5.07037			0.296214			0.148107	−	0.988971i	$-0.452682\pi$
$293$	5.07037			0.296214			0.148107	+	0.988971i	$0.452682\pi$
$294$	−1.18459	+	9.82836i	−0.0690864	+	0.573202i
$295$			32.5500i			1.89513i
$296$	3.72462	−	1.55158i	0.216489	−	0.0901839i
$297$			4.54637i			0.263807i
$298$	−25.7929	+	3.41331i	−1.49414	+	0.197728i
$299$			9.09274i			0.525847i
$300$	−5.08773	−	18.8862i	−0.293740	−	1.09040i
$301$	13.0322	+	16.8043i	0.751162	+	0.968585i
$302$	13.8623	−	1.83448i	0.797686	−	0.105562i
$303$			11.5333i			0.662573i
$304$	3.38969	+	5.83488i	0.194412	+	0.334653i
$305$	11.6085			0.664700
$306$	4.89469	−	0.647741i	0.279811	−	0.0370289i
$307$			15.2465i			0.870164i	0.900391	+	0.435082i	$0.143281\pi$
$307$			15.2465i			0.870164i	−0.900391	+	0.435082i	$0.856719\pi$
$308$	−19.1803	−	14.5210i	−1.09290	−	0.827412i
$309$		−	1.14230i		−	0.0649834i
$310$	−3.81122	−	28.7997i	−0.216463	−	1.63571i
$311$	−8.91481			−0.505513			−0.252756	−	0.967530i	$-0.581337\pi$
$311$	−8.91481			−0.505513			−0.252756	+	0.967530i	$0.581337\pi$
$312$	−4.74213	+	1.97545i	−0.268470	+	0.111838i
$313$		−	24.9335i		−	1.40932i	−0.709543	−	0.704662i	$-0.751098\pi$
$313$		−	24.9335i		−	1.40932i	0.709543	−	0.704662i	$-0.248902\pi$
$314$	−2.29286	−	17.3261i	−0.129394	−	0.977769i
$315$	−6.23338	−	8.03761i	−0.351211	−	0.452868i
$316$	1.54931	+	5.75122i	0.0871558	+	0.323532i
$317$			16.1127i			0.904980i	0.891769	+	0.452490i	$0.149464\pi$
$317$			16.1127i			0.904980i	−0.891769	+	0.452490i	$0.850536\pi$
$318$	1.08957	+	8.23338i	0.0610999	+	0.461705i
$319$			8.25737i			0.462324i
$320$	21.6597	−	21.8349i	1.21081	−	1.22061i
$321$			0.0796192i			0.00444391i
$322$	−13.3222	−	13.1683i	−0.742418	−	0.733839i
$323$	5.88974			0.327714
$324$	−1.93115	+	0.520231i	−0.107286	+	0.0289017i
$325$	17.7625			0.985287
$326$	0.662513	+	5.00632i	0.0366932	+	0.277274i
$327$	20.1081			1.11198
$328$	23.4345	−	9.76223i	1.29395	−	0.539029i
$329$	7.84076	+	10.1103i	0.432275	+	0.557396i
$330$	24.5044	−	3.24280i	1.34892	−	0.178510i
$331$	22.3802			1.23012			0.615062	−	0.788479i	$-0.289131\pi$
$331$	22.3802			1.23012			0.615062	+	0.788479i	$0.289131\pi$
$332$	−5.50249	−	20.4258i	−0.301988	−	1.12101i
$333$			1.42654i			0.0781741i
$334$	−3.63251	−	27.4492i	−0.198762	−	1.50196i
$335$	17.0276			0.930315
$336$	3.97331	−	9.80881i	0.216762	−	0.535115i
$337$	2.22051			0.120959			0.0604795	−	0.998169i	$-0.480737\pi$
$337$	2.22051			0.120959			0.0604795	+	0.998169i	$0.480737\pi$
$338$	1.79990	+	13.6010i	0.0979015	+	0.739798i
$339$			4.98249i			0.270612i
$340$	−6.98249	−	25.9197i	−0.378679	−	1.40570i
$341$	24.2926			1.31552
$342$	−2.36516	+	0.312995i	−0.127893	+	0.0169248i
$343$	16.9992	−	7.35038i	0.917869	−	0.396883i
$344$	−8.74213	−	20.9857i	−0.471344	−	1.13148i
$345$	19.2465			1.03620
$346$	1.01936	+	7.70287i	0.0548013	+	0.414109i
$347$	−17.4186			−0.935080			−0.467540	−	0.883972i	$-0.654860\pi$
$347$	−17.4186			−0.935080			−0.467540	+	0.883972i	$0.654860\pi$
$348$	−3.50747	+	0.944872i	−0.188020	+	0.0506505i
$349$	−29.0839			−1.55683			−0.778413	−	0.627753i	$-0.783975\pi$
$349$	−29.0839			−1.55683			−0.778413	+	0.627753i	$0.783975\pi$
$350$	−25.7240	+	26.0247i	−1.37500	+	1.39108i
$351$		−	1.81625i		−	0.0969445i
$352$	15.7246	+	20.3509i	0.838125	+	1.08471i
$353$		−	7.02449i		−	0.373876i	−0.982372	−	0.186938i	$-0.940144\pi$
$353$		−	7.02449i		−	0.373876i	0.982372	−	0.186938i	$-0.0598563\pi$
$354$	−1.57086	−	11.8703i	−0.0834904	−	0.630900i
$355$		−	5.68700i		−	0.301835i
$356$	−8.30185	−	30.8174i	−0.439997	−	1.63332i
$357$	−5.66070	−	7.29918i	−0.299596	−	0.386313i
$358$	−1.86102	−	14.0629i	−0.0983577	−	0.743245i
$359$		−	11.1509i		−	0.588521i	−0.955725	−	0.294260i	$-0.904927\pi$
$359$		−	11.1509i		−	0.588521i	0.955725	−	0.294260i	$-0.0950733\pi$
$360$	4.18142	+	10.0376i	0.220380	+	0.529029i
$361$	16.1540			0.850211
$362$	4.49883	+	33.9956i	0.236453	+	1.78677i
$363$			9.66949i			0.507517i
$364$	7.66246	+	5.80108i	0.401622	+	0.304059i
$365$			26.8438i			1.40507i
$366$	−4.23338	+	0.560226i	−0.221282	+	0.0292835i
$367$	−6.42880			−0.335581			−0.167790	−	0.985823i	$-0.553663\pi$
$367$	−6.42880			−0.335581			−0.167790	+	0.985823i	$0.553663\pi$
$368$	10.0592	+	17.3154i	0.524370	+	0.902630i
$369$			8.97551i			0.467246i
$370$	7.68889	−	1.01751i	0.399726	−	0.0528980i
$371$	12.2780	−	9.52188i	0.637440	−	0.494351i
$372$	2.77975	+	10.3187i	0.144123	+	0.535001i
$373$		−	1.75527i		−	0.0908842i	−0.998967	−	0.0454421i	$-0.985530\pi$
$373$		−	1.75527i		−	0.0908842i	0.998967	−	0.0454421i	$-0.0144697\pi$
$374$	22.2531	−	2.94487i	1.15068	−	0.152276i
$375$		−	18.3755i		−	0.948905i
$376$	−5.25967	−	12.6260i	−0.271247	−	0.651136i
$377$		−	3.29878i		−	0.169896i
$378$	2.66108	+	2.63033i	0.136871	+	0.135290i
$379$	−19.0061			−0.976280			−0.488140	−	0.872765i	$-0.662324\pi$
$379$	−19.0061			−0.976280			−0.488140	+	0.872765i	$0.662324\pi$
$380$	3.37401	+	12.5247i	0.173083	+	0.642503i
$381$	−5.38471			−0.275867
$382$	−11.9088	+	1.57596i	−0.609308	+	0.0806330i
$383$	−28.4936			−1.45595			−0.727977	−	0.685602i	$-0.759539\pi$
$383$	−28.4936			−1.45595			−0.727977	+	0.685602i	$0.759539\pi$
$384$	−6.84510	+	9.00803i	−0.349312	+	0.459689i
$385$	−28.3392	−	36.5420i	−1.44430	−	1.86235i
$386$	2.09569	+	15.8362i	0.106668	+	0.806039i
$387$	8.03761			0.408575
$388$	−6.03909	−	22.4178i	−0.306589	−	1.13809i
$389$			29.3858i			1.48992i	0.667110	+	0.744960i	$0.267531\pi$
$389$			29.3858i			1.48992i	−0.667110	+	0.744960i	$0.732469\pi$
$390$	−9.78938	+	1.29548i	−0.495705	+	0.0655993i
$391$	17.4783			0.883914
$392$	−19.5964	+	2.82540i	−0.989765	+	0.142704i
$393$	13.0927			0.660442
$394$	−3.34337	+	0.442447i	−0.168437	+	0.0222902i
$395$			11.4492i			0.576074i
$396$	−8.77975	+	2.36516i	−0.441199	+	0.118854i
$397$	15.5442			0.780143			0.390071	−	0.920785i	$-0.372450\pi$
$397$	15.5442			0.780143			0.390071	+	0.920785i	$0.372450\pi$
$398$	0.457038	+	3.45363i	0.0229092	+	0.173115i
$399$	2.73531	+	3.52704i	0.136937	+	0.176573i
$400$	33.8254	−	19.6504i	1.69127	−	0.982520i
$401$	−15.5595			−0.777004			−0.388502	−	0.921448i	$-0.627007\pi$
$401$	−15.5595			−0.777004			−0.388502	+	0.921448i	$0.627007\pi$
$402$	−6.20961	+	0.821752i	−0.309707	+	0.0409852i
$403$	−9.70478			−0.483429
$404$	−22.2726	+	6.00000i	−1.10811	+	0.298511i
$405$	−3.84444			−0.191032
$406$	4.83320	+	4.77735i	0.239868	+	0.237096i
$407$			6.48559i			0.321479i
$408$	3.79726	+	9.11543i	0.187992	+	0.451281i
$409$			18.3565i			0.907670i	0.891086	+	0.453835i	$0.149945\pi$
$409$			18.3565i			0.907670i	−0.891086	+	0.453835i	$0.850055\pi$
$410$	48.3769	−	6.40198i	2.38916	−	0.316171i
$411$		−	19.5595i		−	0.964799i
$412$	2.20597	−	0.594262i	0.108680	−	0.0292772i
$413$	−17.7015	+	13.7280i	−0.871035	+	0.675510i
$414$	−7.01881	+	0.928837i	−0.344956	+	0.0456499i
$415$		−	40.6627i		−	1.99605i
$416$	−6.28191	−	8.13010i	−0.307996	−	0.398611i
$417$	14.5910			0.714523
$418$	−10.7529	+	1.42299i	−0.525942	+	0.0696008i
$419$		−	21.1680i		−	1.03412i	−0.855948	−	0.517062i	$-0.827026\pi$
$419$		−	21.1680i		−	1.03412i	0.855948	−	0.517062i	$-0.172974\pi$
$420$	12.2791	−	16.2190i	0.599158	−	0.791408i
$421$		−	2.20597i		−	0.107512i	−0.998554	−	0.0537561i	$-0.982881\pi$
$421$		−	2.20597i		−	0.107512i	0.998554	−	0.0537561i	$-0.0171193\pi$
$422$	0.00697882	+	0.0527358i	0.000339724	+	0.00256714i
$423$	4.83580			0.235125
$424$	−15.3331	+	6.38738i	−0.744641	+	0.310199i
$425$		−	34.1435i		−	1.65620i
$426$	0.274455	+	2.07394i	0.0132974	+	0.100482i
$427$	4.89589	+	6.31300i	0.236929	+	0.305507i
$428$	−0.153757	+	0.0414204i	−0.00743212	+	0.00200213i
$429$		−	8.25737i		−	0.398669i
$430$	−5.73300	−	43.3217i	−0.276470	−	2.08916i
$431$		−	17.4255i		−	0.839358i	−0.907673	−	0.419679i	$-0.862143\pi$
$431$		−	17.4255i		−	0.839358i	0.907673	−	0.419679i	$-0.137857\pi$
$432$	−2.00929	−	3.45872i	−0.0966722	−	0.166408i
$433$		−	2.18549i		−	0.105028i	−0.998620	−	0.0525139i	$-0.983277\pi$
$433$		−	2.18549i		−	0.105028i	0.998620	−	0.0525139i	$-0.0167234\pi$
$434$	14.0546	−	14.2189i	0.674644	−	0.682531i
$435$	−6.98249			−0.334785
$436$	10.4609	+	38.8319i	0.500985	+	1.85971i
$437$	−8.44568			−0.404012
$438$	−1.29548	−	9.78938i	−0.0619006	−	0.467755i
$439$	−27.5128			−1.31311			−0.656556	−	0.754277i	$-0.727987\pi$
$439$	−27.5128			−1.31311			−0.656556	+	0.754277i	$0.727987\pi$
$440$	19.0103	+	45.6347i	0.906280	+	2.17555i
$441$	1.74213	−	6.77975i	0.0829587	−	0.322845i
$442$	−8.89000	+	1.17646i	−0.422854	+	0.0559586i
$443$	3.37840			0.160513			0.0802563	−	0.996774i	$-0.474426\pi$
$443$	3.37840			0.160513			0.0802563	+	0.996774i	$0.474426\pi$
$444$	−2.75488	+	0.742132i	−0.130741	+	0.0352200i
$445$		−	61.3496i		−	2.90825i
$446$	2.39605	+	18.1059i	0.113456	+	0.857338i
$447$	18.3973			0.870163
$448$	21.0094	+	2.57022i	0.992600	+	0.121432i
$449$	1.76553			0.0833206			0.0416603	−	0.999132i	$-0.486735\pi$
$449$	1.76553			0.0833206			0.0416603	+	0.999132i	$0.486735\pi$
$450$	1.81447	+	13.7111i	0.0855348	+	0.646348i
$451$			40.8060i			1.92148i
$452$	−9.62195	+	2.59205i	−0.452579	+	0.121920i
$453$	−9.88759			−0.464560
$454$	−2.08093	+	0.275380i	−0.0976627	+	0.0129242i
$455$	11.3214	+	14.5984i	0.530755	+	0.684381i
$456$	−1.83488	−	4.40467i	−0.0859259	−	0.206268i
$457$	−24.4178			−1.14222			−0.571108	−	0.820875i	$-0.693486\pi$
$457$	−24.4178			−1.14222			−0.571108	+	0.820875i	$0.693486\pi$
$458$	0.866317	+	6.54637i	0.0404803	+	0.305892i
$459$	−3.49124			−0.162957
$460$	10.0126	+	37.1680i	0.466841	+	1.73297i
$461$	−7.77884			−0.362297			−0.181148	−	0.983456i	$-0.557981\pi$
$461$	−7.77884			−0.362297			−0.181148	+	0.983456i	$0.557981\pi$
$462$	12.0983	+	11.9585i	0.562862	+	0.556358i
$463$		−	16.5615i		−	0.769678i	−0.922984	−	0.384839i	$-0.874257\pi$
$463$		−	16.5615i		−	0.769678i	0.922984	−	0.384839i	$-0.125743\pi$
$464$	−3.64939	−	6.28191i	−0.169419	−	0.291630i
$465$			20.5420i			0.952612i
$466$	1.55041	+	11.7157i	0.0718212	+	0.542721i
$467$			14.1103i			0.652945i	0.945207	+	0.326472i	$0.105860\pi$
$467$			14.1103i			0.652945i	−0.945207	+	0.326472i	$0.894140\pi$
$468$	3.50747	−	0.944872i	0.162133	−	0.0436767i
$469$	7.18140	+	9.26004i	0.331606	+	0.427589i
$470$	−3.44924	−	26.0644i	−0.159102	−	1.20226i
$471$			12.3582i			0.569437i
$472$	22.1062	−	9.20888i	1.01752	−	0.423873i
$473$	36.5420			1.68020
$474$	−0.552541	−	4.17531i	−0.0253791	−	0.191778i
$475$			16.4985i			0.757002i
$476$	11.1510	−	14.7289i	0.511104	−	0.675100i
$477$		−	5.87263i		−	0.268889i
$478$	−27.8362	+	3.68371i	−1.27320	+	0.168489i
$479$	−8.74757			−0.399687			−0.199843	−	0.979828i	$-0.564043\pi$
$479$	−8.74757			−0.399687			−0.199843	+	0.979828i	$0.564043\pi$
$480$	−17.2089	+	13.2968i	−0.785475	+	0.606915i
$481$		−	2.59097i		−	0.118138i
$482$	9.22090	−	1.22025i	0.420001	−	0.0555810i
$483$	8.11723	+	10.4668i	0.369347	+	0.476254i
$484$	−18.6733	+	5.03037i	−0.848786	+	0.228653i
$485$		−	44.6281i		−	2.02646i
$486$	1.40199	−	0.185533i	0.0635956	−	0.00841595i
$487$			31.0252i			1.40589i	0.711246	+	0.702943i	$0.248131\pi$
$487$			31.0252i			1.40589i	−0.711246	+	0.702943i	$0.751869\pi$
$488$	−3.28422	−	7.88386i	−0.148670	−	0.356885i
$489$		−	3.57086i		−	0.161480i
$490$	−37.7846	−	4.55407i	−1.70693	−	0.205732i
$491$	−22.0446			−0.994859			−0.497429	−	0.867505i	$-0.665723\pi$
$491$	−22.0446			−0.994859			−0.497429	+	0.867505i	$0.665723\pi$
$492$	−17.3331	+	4.66934i	−0.781436	+	0.210510i
$493$	−6.34099			−0.285584
$494$	4.29574	−	0.568479i	0.193275	−	0.0255771i
$495$	−17.4783			−0.785590
$496$	−18.4809	+	10.7362i	−0.829819	+	0.482072i
$497$	3.09274	−	2.39850i	0.138728	−	0.107587i
$498$	1.96239	+	14.8289i	0.0879366	+	0.664497i
$499$	40.6409			1.81934			0.909668	−	0.415337i	$-0.136336\pi$
$499$	40.6409			1.81934			0.909668	+	0.415337i	$0.136336\pi$
$500$	35.4859	−	9.55949i	1.58698	−	0.427514i
$501$			19.5788i			0.874715i
$502$	6.81125	−	0.901371i	0.304001	−	0.0402301i
$503$	−33.1848			−1.47964			−0.739818	−	0.672807i	$-0.765088\pi$
$503$	−33.1848			−1.47964			−0.739818	+	0.672807i	$0.765088\pi$
$504$	−3.69520	+	6.50734i	−0.164597	+	0.289860i
$505$	−44.3392			−1.97307
$506$	−31.9101	+	4.22284i	−1.41858	+	0.187728i
$507$		−	9.70122i		−	0.430846i
$508$	−2.80130	−	10.3987i	−0.124287	−	0.461368i
$509$	−35.5240			−1.57457			−0.787287	−	0.616586i	$-0.788515\pi$
$509$	−35.5240			−1.57457			−0.787287	+	0.616586i	$0.788515\pi$
$510$	2.49020	+	18.8174i	0.110268	+	0.833247i
$511$	−14.5984	+	11.3214i	−0.645793	+	0.500829i
$512$	−20.9569	−	8.53268i	−0.926175	−	0.377095i
$513$	1.68700			0.0744831
$514$	12.9123	−	1.70876i	0.569537	−	0.0753700i
$515$	4.39152			0.193514
$516$	4.18142	+	15.5219i	0.184077	+	0.683313i
$517$	21.9853			0.966914
$518$	3.79615	+	3.75228i	0.166793	+	0.164866i
$519$		−	5.49424i		−	0.241170i
$520$	−7.59452	−	18.2309i	−0.333042	−	0.799476i
$521$			26.4737i			1.15984i	0.814675	+	0.579918i	$0.196915\pi$
$521$			26.4737i			1.15984i	−0.814675	+	0.579918i	$0.803085\pi$
$522$	2.54637	−	0.336975i	0.111452	−	0.0147490i
$523$		−	41.7100i		−	1.82385i	−0.410358	−	0.911924i	$-0.634596\pi$
$523$		−	41.7100i		−	1.82385i	0.410358	−	0.911924i	$-0.365404\pi$
$524$	6.81125	+	25.2841i	0.297551	+	1.10454i
$525$	20.4466	−	15.8569i	0.892363	−	0.692051i
$526$	5.47967	−	0.725155i	0.238925	−	0.0316183i
$527$			18.6547i			0.812613i
$528$	−9.13500	−	15.7246i	−0.397550	−	0.684326i
$529$	−2.06320			−0.0897043
$530$	−31.6528	+	4.18878i	−1.37491	+	0.181949i
$531$			8.46675i			0.367426i
$532$	−5.38826	+	7.11718i	−0.233611	+	0.308569i
$533$		−	16.3018i		−	0.706110i
$534$	2.96074	+	22.3730i	0.128124	+	0.968173i
$535$	−0.306091			−0.0132335
$536$	−4.81736	−	11.5642i	−0.208078	−	0.499498i
$537$			10.0306i			0.432854i
$538$	−1.71594	−	12.9666i	−0.0739796	−	0.559031i
$539$	7.92038	−	30.8232i	0.341155	−	1.32765i
$540$	−2.00000	−	7.42422i	−0.0860663	−	0.319487i
$541$			10.3187i			0.443637i	0.975088	+	0.221818i	$0.0711992\pi$
$541$			10.3187i			0.443637i	−0.975088	+	0.221818i	$0.928801\pi$
$542$	−3.06502	−	23.1610i	−0.131654	−	0.994850i
$543$		−	24.2481i		−	1.04059i
$544$	−15.6279	+	12.0752i	−0.670039	+	0.517721i
$545$			77.3045i			3.31136i
$546$	−4.83320	−	4.77735i	−0.206842	−	0.204452i
$547$	19.6461			0.840006			0.420003	−	0.907523i	$-0.362029\pi$
$547$	19.6461			0.840006			0.420003	+	0.907523i	$0.362029\pi$
$548$	37.7724	−	10.1755i	1.61356	−	0.434674i
$549$	3.01955			0.128871
$550$	8.24924	+	62.3358i	0.351749	+	2.65801i
$551$	3.06403			0.130532
$552$	−5.44513	−	13.0712i	−0.231760	−	0.556347i
$553$	−6.22640	+	4.82873i	−0.264773	+	0.205339i
$554$	4.57701	−	0.605701i	0.194458	−	0.0257337i
$555$	−5.48426			−0.232794
$556$	7.59068	+	28.1774i	0.321916	+	1.19499i
$557$			30.0989i			1.27533i	0.770314	+	0.637665i	$0.220100\pi$
$557$			30.0989i			1.27533i	−0.770314	+	0.637665i	$0.779900\pi$
$558$	−0.991357	−	7.49124i	−0.0419675	−	0.317130i
$559$	−14.5984			−0.617445
$560$	37.7094	+	15.2752i	1.59351	+	0.645493i
$561$	−15.8725			−0.670137
$562$	−3.55629	−	26.8733i	−0.150013	−	1.13358i
$563$			6.35650i			0.267894i	0.990988	+	0.133947i	$0.0427653\pi$
$563$			6.35650i			0.267894i	−0.990988	+	0.133947i	$0.957235\pi$
$564$	2.51574	+	9.33868i	0.105932	+	0.393229i
$565$	−19.1549			−0.805852
$566$	28.4295	−	3.76223i	1.19498	−	0.158139i
$567$	−1.62140	−	2.09071i	−0.0680923	−	0.0878015i
$568$	−3.86231	+	1.60894i	−0.162059	+	0.0675097i
$569$	−37.7589			−1.58294			−0.791469	−	0.611210i	$-0.790683\pi$
$569$	−37.7589			−1.58294			−0.791469	+	0.611210i	$0.790683\pi$
$570$	−1.20329	−	9.09274i	−0.0504004	−	0.380853i
$571$	−29.0324			−1.21497			−0.607484	−	0.794332i	$-0.707821\pi$
$571$	−29.0324			−1.21497			−0.607484	+	0.794332i	$0.707821\pi$
$572$	15.9463	−	4.29574i	0.666746	−	0.179614i
$573$	8.49422			0.354851
$574$	23.8846	+	23.6086i	0.996922	+	0.985402i
$575$			48.9605i			2.04179i
$576$	5.63402	−	5.67959i	0.234751	−	0.236650i
$577$		−	38.4060i		−	1.59886i	−0.600758	−	0.799431i	$-0.705134\pi$
$577$		−	38.4060i		−	1.59886i	0.600758	−	0.799431i	$-0.294866\pi$
$578$	−0.892640	−	6.74528i	−0.0371289	−	0.280567i
$579$		−	11.2955i		−	0.469424i
$580$	−3.63251	−	13.4843i	−0.150832	−	0.559904i
$581$	22.1134	−	17.1495i	0.917420	−	0.711483i
$582$	2.15376	+	16.2750i	0.0892761	+	0.674619i
$583$		−	26.6992i		−	1.10577i
$584$	18.2309	−	7.59452i	0.754398	−	0.314263i
$585$	6.98249			0.288690
$586$	−0.940721	−	7.10861i	−0.0388608	−	0.293654i
$587$		−	0.157054i		−	0.00648231i	−0.999995	−	0.00324116i	$-0.998968\pi$
$587$		−	0.157054i		−	0.00648231i	0.999995	−	0.00324116i	$-0.00103169\pi$
$588$	13.9991	−	0.162709i	0.577311	−	0.00671002i
$589$		−	9.01416i		−	0.371422i
$590$	45.6347	−	6.03909i	1.87875	−	0.248626i
$591$	2.38473			0.0980948
$592$	−2.86635	−	4.93401i	−0.117806	−	0.202787i
$593$		−	37.5927i		−	1.54375i	−0.635776	−	0.771874i	$-0.719320\pi$
$593$		−	37.5927i		−	1.54375i	0.635776	−	0.771874i	$-0.280680\pi$
$594$	6.37397	−	0.843502i	0.261527	−	0.0346093i
$595$	28.0613	−	21.7622i	1.15040	−	0.892165i
$596$	9.57086	+	35.5281i	0.392038	+	1.45529i
$597$		−	2.46338i		−	0.100819i
$598$	12.7479	−	1.68700i	0.521302	−	0.0689868i
$599$		−	18.7569i		−	0.766387i	−0.923668	−	0.383194i	$-0.874824\pi$
$599$		−	18.7569i		−	0.766387i	0.923668	−	0.383194i	$-0.125176\pi$
$600$	−25.5343	+	10.6370i	−1.04244	+	0.434252i
$601$		−	2.44051i		−	0.0995503i	−0.998760	−	0.0497751i	$-0.984150\pi$
$601$		−	2.44051i		−	0.0995503i	0.998760	−	0.0497751i	$-0.0158505\pi$
$602$	21.1416	−	21.3887i	0.861667	−	0.871740i
$603$	4.42914			0.180368
$604$	−5.14383	−	19.0945i	−0.209300	−	0.776943i
$605$	−37.1738			−1.51133
$606$	16.1696	−	2.13981i	0.656846	−	0.0869240i
$607$	40.4839			1.64319			0.821596	−	0.570070i	$-0.193084\pi$
$607$	40.4839			1.64319			0.821596	+	0.570070i	$0.193084\pi$
$608$	7.55154	−	5.83488i	0.306255	−	0.236635i
$609$	−2.94487	−	3.79726i	−0.119332	−	0.153873i
$610$	−2.15376	−	16.2750i	−0.0872031	−	0.658955i
$611$	−8.78304			−0.355324
$612$	−1.81625	−	6.74213i	−0.0734177	−	0.272535i
$613$			8.57378i			0.346292i	0.984896	+	0.173146i	$0.0553932\pi$
$613$			8.57378i			0.346292i	−0.984896	+	0.173146i	$0.944607\pi$
$614$	21.3754	−	2.82873i	0.862643	−	0.114158i
$615$	−34.5058			−1.39141
$616$	−16.7998	+	29.5848i	−0.676881	+	1.19201i
$617$	31.3390			1.26166			0.630830	−	0.775921i	$-0.282715\pi$
$617$	31.3390			1.26166			0.630830	+	0.775921i	$0.282715\pi$
$618$	−1.60150	+	0.211935i	−0.0644217	+	0.00852528i
$619$		−	41.5595i		−	1.67042i	−0.549933	−	0.835209i	$-0.685347\pi$
$619$		−	41.5595i		−	1.67042i	0.549933	−	0.835209i	$-0.314653\pi$
$620$	−39.6698	+	10.6866i	−1.59318	+	0.429183i
$621$	5.00632			0.200897
$622$	1.65399	+	12.4985i	0.0663191	+	0.501143i
$623$	33.3635	−	25.8743i	1.33668	−	1.03663i
$624$	3.64939	+	6.28191i	0.146093	+	0.251478i
$625$	21.7447			0.869789
$626$	−34.9565	+	4.62599i	−1.39714	+	0.184892i
$627$	7.66975			0.306300
$628$	−23.8657	+	6.42914i	−0.952343	+	0.256551i
$629$	−4.98041			−0.198582
$630$	−10.1122	+	10.2304i	−0.402878	+	0.407588i
$631$		−	48.0528i		−	1.91295i	−0.291814	−	0.956475i	$-0.594259\pi$
$631$		−	48.0528i		−	1.91295i	0.291814	−	0.956475i	$-0.405741\pi$
$632$	7.77571	−	3.23917i	0.309301	−	0.128847i
$633$		−	0.0376150i		−	0.00149506i
$634$	22.5899	−	2.98944i	0.897158	−	0.118726i
$635$		−	20.7012i		−	0.821503i
$636$	11.3410	−	3.05513i	0.449698	−	0.121144i
$637$	−3.16416	+	12.3137i	−0.125368	+	0.487888i
$638$	11.5767	−	1.53201i	0.458328	−	0.0606530i
$639$		−	1.47928i		−	0.0585194i
$640$	−34.6309	−	26.3156i	−1.36891	−	1.04021i
$641$	−26.9335			−1.06381			−0.531905	−	0.846804i	$-0.678524\pi$
$641$	−26.9335			−1.06381			−0.531905	+	0.846804i	$0.678524\pi$
$642$	0.111625	−	0.0147720i	0.00440550	−	0.000583004i
$643$			20.2780i			0.799685i	0.916584	+	0.399843i	$0.130935\pi$
$643$			20.2780i			0.799685i	−0.916584	+	0.399843i	$0.869065\pi$
$644$	−15.9901	+	21.1208i	−0.630097	+	0.832275i
$645$			30.9002i			1.21669i
$646$	−1.09274	−	8.25737i	−0.0429934	−	0.324882i
$647$	16.3928			0.644466			0.322233	−	0.946660i	$-0.395567\pi$
$647$	16.3928			0.644466			0.322233	+	0.946660i	$0.395567\pi$
$648$	1.08765	+	2.61094i	0.0427270	+	0.102567i
$649$			38.4930i			1.51098i
$650$	−3.29553	−	24.9029i	−0.129261	−	0.976771i
$651$	−11.1713	+	8.66361i	−0.437837	+	0.339553i
$652$	6.89589	−	1.85767i	0.270064	−	0.0727522i
$653$			27.4567i			1.07447i	0.843434	+	0.537233i	$0.180530\pi$
$653$			27.4567i			1.07447i	−0.843434	+	0.537233i	$0.819470\pi$
$654$	−3.73072	−	28.1914i	−0.145883	−	1.10237i
$655$			50.3343i			1.96672i
$656$	−18.0344	−	31.0438i	−0.704127	−	1.21206i
$657$			6.98249i			0.272413i
$658$	12.7198	−	12.8685i	0.495868	−	0.501665i
$659$	34.1059			1.32858			0.664288	−	0.747477i	$-0.268735\pi$
$659$	34.1059			1.32858			0.664288	+	0.747477i	$0.268735\pi$
$660$	−9.09274	−	33.7532i	−0.353935	−	1.31384i
$661$	−42.0551			−1.63575			−0.817877	−	0.575393i	$-0.804849\pi$
$661$	−42.0551			−1.63575			−0.817877	+	0.575393i	$0.804849\pi$
$662$	−4.15226	−	31.3768i	−0.161382	−	1.21949i
$663$	6.34099			0.246263
$664$	−27.6159	+	11.5041i	−1.07171	+	0.446446i
$665$	−13.5595	+	10.5157i	−0.525815	+	0.407783i
$666$	2.00000	−	0.264671i	0.0774984	−	0.0102558i
$667$	9.09274			0.352072
$668$	−37.8096	+	10.1855i	−1.46290	+	0.394088i
$669$		−	12.9144i		−	0.499300i
$670$	−3.15918	−	23.8725i	−0.122050	−	0.922275i
$671$	13.7280			0.529963
$672$	−14.4890	−	3.75068i	−0.558927	−	0.144686i
$673$	43.0405			1.65909			0.829544	−	0.558441i	$-0.188600\pi$
$673$	43.0405			1.65909			0.829544	+	0.558441i	$0.188600\pi$
$674$	−0.411978	−	3.11313i	−0.0158688	−	0.119913i
$675$		−	9.77975i		−	0.376423i
$676$	18.7346	−	5.04688i	0.720560	−	0.194111i
$677$	5.91811			0.227451			0.113726	−	0.993512i	$-0.463722\pi$
$677$	5.91811			0.227451			0.113726	+	0.993512i	$0.463722\pi$
$678$	6.98540	−	0.924416i	0.268273	−	0.0355020i
$679$	24.2700	−	18.8220i	0.931395	−	0.722321i
$680$	−35.0438	+	14.5984i	−1.34387	+	0.559821i
$681$	1.48426			0.0568772
$682$	−4.50708	−	34.0580i	−0.172585	−	1.30415i
$683$	−1.50261			−0.0574958			−0.0287479	−	0.999587i	$-0.509152\pi$
$683$	−1.50261			−0.0574958			−0.0287479	+	0.999587i	$0.509152\pi$
$684$	0.877633	+	3.25787i	0.0335571	+	0.124568i
$685$	75.1954			2.87307
$686$	−13.4591	−	22.4689i	−0.513870	−	0.857868i
$687$		−	4.66934i		−	0.178146i
$688$	−27.7998	+	16.1499i	−1.05986	+	0.615711i
$689$			10.6662i			0.406350i
$690$	−3.57086	−	26.9834i	−0.135940	−	1.02724i
$691$			8.62599i			0.328148i	0.986448	+	0.164074i	$0.0524636\pi$
$691$			8.62599i			0.328148i	−0.986448	+	0.164074i	$0.947536\pi$
$692$	10.6102	−	2.85827i	0.403340	−	0.108655i
$693$	−7.37148	−	9.50514i	−0.280019	−	0.361070i
$694$	3.23173	+	24.4207i	0.122675	+	0.926998i
$695$			56.0941i			2.12777i
$696$	1.97545	+	4.74213i	0.0748794	+	0.179750i
$697$	−31.3357			−1.18692
$698$	5.39603	+	40.7754i	0.204243	+	1.54337i
$699$		−	8.35650i		−	0.316072i
$700$	41.2590	+	31.2363i	1.55945	+	1.18062i
$701$			10.4065i			0.393050i	0.980499	+	0.196525i	$0.0629656\pi$
$701$			10.4065i			0.393050i	−0.980499	+	0.196525i	$0.937034\pi$
$702$	−2.54637	+	0.336975i	−0.0961066	+	0.0127183i
$703$	2.40659			0.0907661
$704$	25.6144	−	25.8215i	0.965378	−	0.973186i
$705$			18.5910i			0.700176i
$706$	−9.84827	+	1.30328i	−0.370645	+	0.0490494i
$707$	−18.7001	−	24.1128i	−0.703291	−	0.906857i
$708$	−16.3506	+	4.40467i	−0.614494	+	0.165538i
$709$			34.8737i			1.30971i	0.755755	+	0.654855i	$0.227270\pi$
$709$			34.8737i			1.30971i	−0.755755	+	0.654855i	$0.772730\pi$
$710$	−7.97313	+	1.05513i	−0.299226	+	0.0395982i
$711$			2.97813i			0.111688i
$712$	−41.6654	+	17.3568i	−1.56148	+	0.650472i
$713$		−	26.7502i		−	1.00180i
$714$	−9.18313	+	9.29048i	−0.343670	+	0.347688i
$715$	31.7450			1.18719
$716$	−19.3707	+	5.21825i	−0.723918	+	0.195015i
$717$	19.8547			0.741489
$718$	−15.6334	+	2.06886i	−0.583434	+	0.0772091i
$719$	−8.74757			−0.326229			−0.163115	−	0.986607i	$-0.552154\pi$
$719$	−8.74757			−0.326229			−0.163115	+	0.986607i	$0.552154\pi$
$720$	13.2968	−	7.72462i	0.495544	−	0.287880i
$721$	1.85213	+	2.38823i	0.0689769	+	0.0889422i
$722$	−2.99710	−	22.6478i	−0.111541	−	0.842863i
$723$	−6.57701			−0.244602
$724$	46.8268	−	12.6146i	1.74031	−	0.468819i
$725$		−	17.7625i		−	0.659683i
$726$	13.5565	−	1.79401i	0.503130	−	0.0665820i
$727$	23.7851			0.882140			0.441070	−	0.897473i	$-0.354599\pi$
$727$	23.7851			0.882140			0.441070	+	0.897473i	$0.354599\pi$
$728$	6.71142	−	11.8190i	0.248742	−	0.438041i
$729$	−1.00000			−0.0370370
$730$	37.6347	−	4.98041i	1.39292	−	0.184333i
$731$			28.0613i			1.03788i
$732$	1.57086	+	5.83121i	0.0580608	+	0.215528i
$733$	−4.79132			−0.176971			−0.0884857	−	0.996077i	$-0.528203\pi$
$733$	−4.79132			−0.176971			−0.0884857	+	0.996077i	$0.528203\pi$
$734$	1.19276	+	9.01312i	0.0440254	+	0.332680i
$735$	26.0644	+	6.69753i	0.961398	+	0.247042i
$736$	22.4098	−	17.3154i	0.826035	−	0.638256i
$737$	20.1365			0.741738
$738$	12.5836	−	1.66525i	0.463208	−	0.0612988i
$739$	13.7563			0.506035			0.253018	−	0.967462i	$-0.418577\pi$
$739$	13.7563			0.506035			0.253018	+	0.967462i	$0.418577\pi$
$740$	−2.85309	−	10.5910i	−0.104882	−	0.389332i
$741$	−3.06403			−0.112560
$742$	−15.6276	−	15.4470i	−0.573706	−	0.567076i
$743$		−	11.5310i		−	0.423033i	−0.977374	−	0.211517i	$-0.932160\pi$
$743$		−	11.5310i		−	0.423033i	0.977374	−	0.211517i	$-0.0678402\pi$
$744$	13.9510	−	5.81164i	0.511469	−	0.213065i
$745$			70.7275i			2.59125i
$746$	−2.46087	+	0.325660i	−0.0900987	+	0.0119233i
$747$		−	10.5770i		−	0.386992i
$748$	−8.25737	−	30.6522i	−0.301919	−	1.12076i
$749$	−0.129094	−	0.166461i	−0.00471701	−	0.00608234i
$750$	−25.7622	+	3.40926i	−0.940704	+	0.124488i
$751$			40.8541i			1.49079i	0.666625	+	0.745393i	$0.267738\pi$
$751$			40.8541i			1.49079i	−0.666625	+	0.745393i	$0.732262\pi$
$752$	−16.7257	+	9.71655i	−0.609923	+	0.354326i
$753$	−4.85827			−0.177045
$754$	−4.62486	+	0.612033i	−0.168427	+	0.0222889i
$755$		−	38.0123i		−	1.38341i
$756$	3.19398	−	4.21882i	0.116164	−	0.153437i
$757$		−	27.8196i		−	1.01112i	−0.862791	−	0.505561i	$-0.831286\pi$
$757$		−	27.8196i		−	1.01112i	0.862791	−	0.505561i	$-0.168714\pi$
$758$	3.52627	+	26.6464i	0.128080	+	0.967842i
$759$	22.7606			0.826156
$760$	16.9335	−	7.05407i	0.614243	−	0.255878i
$761$		−	26.4737i		−	0.959672i	−0.877358	−	0.479836i	$-0.840696\pi$
$761$		−	26.4737i		−	0.959672i	0.877358	−	0.479836i	$-0.159304\pi$
$762$	0.999042	+	7.54931i	0.0361915	+	0.273483i
$763$	−42.0402	+	32.6033i	−1.52196	+	1.18032i
$764$	4.41896	+	16.4036i	0.159872	+	0.593463i
$765$		−	13.4219i		−	0.485269i
$766$	5.28650	+	39.9477i	0.191009	+	1.44337i
$767$		−	15.3778i		−	0.555259i
$768$	13.8992	+	7.92547i	0.501543	+	0.285986i
$769$			31.5945i			1.13933i	0.821878	+	0.569664i	$0.192927\pi$
$769$			31.5945i			1.13933i	−0.821878	+	0.569664i	$0.807073\pi$
$770$	−45.9736	+	46.5111i	−1.65678	+	1.67614i
$771$	−9.20998			−0.331689
$772$	21.8133	−	5.87626i	0.785079	−	0.211491i
$773$	33.5413			1.20640			0.603199	−	0.797591i	$-0.293893\pi$
$773$	33.5413			1.20640			0.603199	+	0.797591i	$0.293893\pi$
$774$	−1.49124	−	11.2687i	−0.0536016	−	0.405044i
$775$	−52.2560			−1.87709
$776$	−30.3090	+	12.6260i	−1.08803	+	0.453247i
$777$	−2.31300	−	2.98249i	−0.0829782	−	0.106996i
$778$	41.1986	−	5.45204i	1.47704	−	0.195465i
$779$	15.1417			0.542509
$780$	3.63251	+	13.4843i	0.130065	+	0.482814i
$781$		−	6.72535i		−	0.240652i
$782$	−3.24280	−	24.5044i	−0.115962	−	0.876274i
$783$	−1.81625			−0.0649076
$784$	7.59696	+	26.9497i	0.271320	+	0.962489i
$785$	−47.5105			−1.69572
$786$	−2.42914	−	18.3559i	−0.0866445	−	0.654733i
$787$		−	1.03147i		−	0.0367679i	−0.999831	−	0.0183840i	$-0.994148\pi$
$787$		−	1.03147i		−	0.0367679i	0.999831	−	0.0183840i	$-0.00585213\pi$
$788$	1.24061	+	4.60529i	0.0441950	+	0.164057i
$789$	−3.90849			−0.139146
$790$	16.0517	−	2.12421i	0.571095	−	0.0755761i
$791$	−8.07860	−	10.4169i	−0.287242	−	0.370384i
$792$	4.94487	+	11.8703i	0.175708	+	0.421793i
$793$	−5.48426			−0.194752
$794$	−2.88397	−	21.7929i	−0.102348	−	0.773400i
$795$	22.5770			0.800724
$796$	4.75716	−	1.28152i	0.168613	−	0.0454224i
$797$	22.2199			0.787070			0.393535	−	0.919310i	$-0.371252\pi$
$797$	22.2199			0.787070			0.393535	+	0.919310i	$0.371252\pi$
$798$	4.43738	−	4.48926i	0.157082	−	0.158918i
$799$			16.8830i			0.597276i
$800$	−33.8254	−	43.7771i	−1.19591	−	1.54775i
$801$		−	15.9580i		−	0.563848i
$802$	2.88680	+	21.8143i	0.101937	+	0.770288i
$803$			31.7450i			1.12026i
$804$	2.30418	+	8.55335i	0.0812620	+	0.301653i
$805$	−40.2388	+	31.2062i	−1.41823	+	1.09988i
$806$	1.80056	+	13.6060i	0.0634219	+	0.479251i
$807$			9.24872i			0.325570i
$808$	12.5443	+	30.1128i	0.441305	+	1.05937i
$809$	−52.4790			−1.84506			−0.922532	−	0.385920i	$-0.873884\pi$
$809$	−52.4790			−1.84506			−0.922532	+	0.385920i	$0.873884\pi$
$810$	0.713272	+	5.38987i	0.0250618	+	0.189381i
$811$			4.40548i			0.154697i	0.997004	+	0.0773487i	$0.0246455\pi$
$811$			4.40548i			0.154697i	−0.997004	+	0.0773487i	$0.975355\pi$
$812$	5.80108	−	7.66246i	0.203578	−	0.268900i
$813$			16.5201i			0.579384i
$814$	9.09274	−	1.20329i	0.318700	−	0.0421754i
$815$	13.7280			0.480870
$816$	12.0752	−	7.01494i	0.422718	−	0.245572i
$817$		−	13.5595i		−	0.474387i
$818$	25.7356	−	3.40574i	0.899825	−	0.119079i
$819$	2.94487	+	3.79726i	0.102902	+	0.132687i
$820$	−17.9510	−	66.6361i	−0.626877	−	2.32703i
$821$		−	21.2067i		−	0.740119i	−0.929008	−	0.370060i	$-0.879337\pi$
$821$		−	21.2067i		−	0.740119i	0.929008	−	0.370060i	$-0.120663\pi$
$822$	−27.4222	+	3.62893i	−0.956460	+	0.126574i
$823$			29.3609i			1.02346i	0.859148	+	0.511728i	$0.170994\pi$
$823$			29.3609i			1.02346i	−0.859148	+	0.511728i	$0.829006\pi$
$824$	−1.24243	−	2.98249i	−0.0432821	−	0.103900i
$825$		−	44.4624i		−	1.54798i
$826$	22.5307	+	22.2704i	0.783944	+	0.774885i
$827$	−28.2161			−0.981171			−0.490585	−	0.871393i	$-0.663217\pi$
$827$	−28.2161			−0.981171			−0.490585	+	0.871393i	$0.663217\pi$
$828$	2.60444	+	9.66797i	0.0905106	+	0.335985i
$829$	−9.77173			−0.339386			−0.169693	−	0.985497i	$-0.554278\pi$
$829$	−9.77173			−0.339386			−0.169693	+	0.985497i	$0.554278\pi$
$830$	−57.0087	+	7.54428i	−1.97880	+	0.261866i
$831$	−3.26465			−0.113249
$832$	−10.2328	+	10.3156i	−0.354759	+	0.357629i
$833$	23.6698	+	6.08221i	0.820108	+	0.210736i
$834$	−2.70711	−	20.4564i	−0.0937395	−	0.708347i
$835$	−75.2694			−2.60481
$836$	3.99004	+	14.8115i	0.137999	+	0.512266i
$837$			5.34329i			0.184691i
$838$	−29.6773	+	3.92736i	−1.02519	+	0.135668i
$839$	−35.0785			−1.21104			−0.605522	−	0.795828i	$-0.707036\pi$
$839$	−35.0785			−1.21104			−0.605522	+	0.795828i	$0.707036\pi$
$840$	−25.0171	−	14.2060i	−0.863172	−	0.490153i
$841$	25.7012			0.886249
$842$	−3.09274	+	0.409280i	−0.106583	+	0.0141047i
$843$			19.1680i			0.660180i
$844$	0.0726403	−	0.0195685i	0.00250038	−	0.000673575i
$845$	37.2958			1.28301
$846$	−0.897201	−	6.77975i	−0.0308464	−	0.233093i
$847$	−15.6781	−	20.2161i	−0.538706	−	0.694633i
$848$	11.7998	+	20.3118i	0.405209	+	0.697510i
$849$	−20.2780			−0.695938
$850$	−47.8688	+	6.33475i	−1.64189	+	0.217280i
$851$	7.14173			0.244815
$852$	2.85672	−	0.769567i	0.0978695	−	0.0263649i
$853$	18.3536			0.628416			0.314208	−	0.949354i	$-0.398261\pi$
$853$	18.3536			0.628416			0.314208	+	0.949354i	$0.398261\pi$
$854$	7.94241	−	8.03526i	0.271784	−	0.274961i
$855$			6.48559i			0.221803i
$856$	0.0865980	+	0.207881i	0.00295986	+	0.00710522i
$857$		−	7.62775i		−	0.260559i	−0.991477	−	0.130279i	$-0.958413\pi$
$857$		−	7.62775i		−	0.260559i	0.991477	−	0.130279i	$-0.0415874\pi$
$858$	−11.5767	+	1.53201i	−0.395224	+	0.0523021i
$859$		−	13.9075i		−	0.474518i	−0.971446	−	0.237259i	$-0.923751\pi$
$859$		−	13.9075i		−	0.474518i	0.971446	−	0.237259i	$-0.0762491\pi$
$860$	−59.6730	+	16.0752i	−2.03483	+	0.548161i
$861$	−14.5529	−	18.7652i	−0.495961	−	0.639516i
$862$	−24.4304	+	3.23301i	−0.832104	+	0.110117i
$863$		−	13.3074i		−	0.452989i	−0.974012	−	0.226494i	$-0.927274\pi$
$863$		−	13.3074i		−	0.452989i	0.974012	−	0.226494i	$-0.0727265\pi$
$864$	−4.47630	+	3.45872i	−0.152287	+	0.117668i
$865$	21.1223			0.718179
$866$	−3.06403	+	0.405480i	−0.104120	+	0.0137788i
$867$			4.81122i			0.163398i
$868$	−22.5424	−	17.0664i	−0.765139	−	0.579270i
$869$			13.5397i			0.459302i
$870$	1.29548	+	9.78938i	0.0439210	+	0.331891i
$871$	−8.04444			−0.272575
$872$	52.5011	−	21.8706i	1.77791	−	0.740633i
$873$		−	11.6085i		−	0.392887i
$874$	1.56695	+	11.8408i	0.0530030	+	0.400520i
$875$	29.7940	+	38.4178i	1.00722	+	1.29876i
$876$	−13.4843	+	3.63251i	−0.455591	+	0.122731i
$877$		−	25.0885i		−	0.847179i	−0.905854	−	0.423589i	$-0.860770\pi$
$877$		−	25.0885i		−	0.847179i	0.905854	−	0.423589i	$-0.139230\pi$
$878$	5.10453	+	38.5726i	0.172269	+	1.30176i
$879$			5.07037i			0.171019i
$880$	60.4524	−	35.1190i	2.03785	−	1.18386i
$881$			5.29180i			0.178285i	0.996019	+	0.0891426i	$0.0284127\pi$
$881$			5.29180i			0.178285i	−0.996019	+	0.0891426i	$0.971587\pi$
$882$	−9.82836	−	1.18459i	−0.330938	−	0.0398871i
$883$	−21.5219			−0.724269			−0.362134	−	0.932126i	$-0.617952\pi$
$883$	−21.5219			−0.724269			−0.362134	+	0.932126i	$0.617952\pi$
$884$	3.29878	+	12.2454i	0.110950	+	0.411858i
$885$	−32.5500			−1.09415
$886$	−0.626805	−	4.73648i	−0.0210579	−	0.159125i
$887$	−14.7656			−0.495780			−0.247890	−	0.968788i	$-0.579737\pi$
$887$	−14.7656			−0.495780			−0.247890	+	0.968788i	$0.579737\pi$
$888$	1.55158	+	3.72462i	0.0520677	+	0.124990i
$889$	11.2579	−	8.73076i	0.377577	−	0.292820i
$890$	−86.0116	+	11.3824i	−2.88311	+	0.381538i
$891$	−4.54637			−0.152309
$892$	24.9397	−	6.71848i	0.835043	−	0.224951i
$893$		−	8.15802i		−	0.272998i
$894$	−3.41331	−	25.7929i	−0.114158	−	0.862643i
$895$	−38.5622			−1.28899
$896$	−0.294507	−	29.9318i	−0.00983880	−	0.999952i
$897$	−9.09274			−0.303598
$898$	−0.327565	−	2.47526i	−0.0109310	−	0.0826005i
$899$			9.70478i			0.323672i
$900$	18.8862	−	5.08773i	0.629540	−	0.169591i
$901$	20.5028			0.683047
$902$	57.2096	−	7.57086i	1.90487	−	0.252082i
$903$	−16.8043	+	13.0322i	−0.559213	+	0.433684i
$904$	5.41922	+	13.0090i	0.180240	+	0.432672i
$905$	93.2205			3.09875
$906$	1.83448	+	13.8623i	0.0609464	+	0.460544i
$907$	46.8609			1.55599			0.777995	−	0.628271i	$-0.216237\pi$
$907$	46.8609			1.55599			0.777995	+	0.628271i	$0.216237\pi$
$908$	0.772161	+	2.86635i	0.0256251	+	0.0951230i
$909$	−11.5333			−0.382536
$910$	18.3663	−	18.5810i	0.608836	−	0.615953i
$911$		−	54.6440i		−	1.81044i	−0.424945	−	0.905219i	$-0.639707\pi$
$911$		−	54.6440i		−	1.81044i	0.424945	−	0.905219i	$-0.360293\pi$
$912$	−5.83488	+	3.38969i	−0.193212	+	0.112244i
$913$		−	48.0870i		−	1.59145i
$914$	4.53030	+	34.2335i	0.149849	+	1.13234i
$915$			11.6085i			0.383764i
$916$	9.01722	−	2.42914i	0.297937	−	0.0802610i
$917$	−27.3731	+	21.2286i	−0.903940	+	0.701029i
$918$	0.647741	+	4.89469i	0.0213786	+	0.161549i
$919$		−	28.6186i		−	0.944041i	−0.881588	−	0.472020i	$-0.843525\pi$
$919$		−	28.6186i		−	0.944041i	0.881588	−	0.472020i	$-0.156475\pi$
$920$	50.2515	−	20.9335i	1.65674	−	0.690157i
$921$	−15.2465			−0.502389
$922$	1.44323	+	10.9059i	0.0475304	+	0.359166i
$923$			2.68675i			0.0884353i
$924$	14.5210	−	19.1803i	0.477707	−	0.630987i
$925$		−	13.9512i		−	0.458714i
$926$	−23.2191	+	3.07271i	−0.763026	+	0.100975i
$927$	1.14230			0.0375182
$928$	−8.13010	+	6.28191i	−0.266884	+	0.206214i
$929$			29.6885i			0.974048i	0.873389	+	0.487024i	$0.161918\pi$
$929$			29.6885i			0.974048i	−0.873389	+	0.487024i	$0.838082\pi$
$930$	28.7997	−	3.81122i	0.944378	−	0.124975i
$931$	−11.4375	−	2.93899i	−0.374848	−	0.0963214i
$932$	16.1377	−	4.34731i	0.528608	−	0.142401i
$933$		−	8.91481i		−	0.291858i
$934$	19.7824	−	2.61792i	0.647301	−	0.0856609i
$935$		−	61.0209i		−	1.99560i
$936$	−1.97545	−	4.74213i	−0.0645697	−	0.155001i
$937$		−	32.4055i		−	1.05864i	−0.848422	−	0.529320i	$-0.822447\pi$
$937$		−	32.4055i		−	1.05864i	0.848422	−	0.529320i	$-0.177553\pi$
$938$	11.6501	−	11.7863i	0.380389	−	0.384836i
$939$	24.9335			0.813674
$940$	−35.9020	+	9.67160i	−1.17100	+	0.315453i
$941$	−10.5656			−0.344429			−0.172214	−	0.985060i	$-0.555092\pi$
$941$	−10.5656			−0.344429			−0.172214	+	0.985060i	$0.555092\pi$
$942$	17.3261	−	2.29286i	0.564515	−	0.0747054i
$943$	44.9342			1.46326
$944$	−17.0122	−	29.2841i	−0.553700	−	0.953117i
$945$	8.03761	−	6.23338i	0.261464	−	0.202772i
$946$	−6.77975	−	51.2315i	−0.220429	−	1.66568i
$947$	−3.44186			−0.111845			−0.0559226	−	0.998435i	$-0.517810\pi$
$947$	−3.44186			−0.111845			−0.0559226	+	0.998435i	$0.517810\pi$
$948$	−5.75122	+	1.54931i	−0.186791	+	0.0503194i
$949$		−	12.6820i		−	0.411674i
$950$	23.1307	−	3.06101i	0.750459	−	0.0993124i
$951$	−16.1127			−0.522491
$952$	−22.7187	−	12.9008i	−0.736318	−	0.418119i
$953$	−38.5559			−1.24895			−0.624475	−	0.781045i	$-0.714687\pi$
$953$	−38.5559			−1.24895			−0.624475	+	0.781045i	$0.714687\pi$
$954$	−8.23338	+	1.08957i	−0.266565	+	0.0352761i
$955$			32.6555i			1.05671i
$956$	10.3291	+	38.3426i	0.334066	+	1.24009i
$957$	−8.25737			−0.266923
$958$	1.62296	+	12.2640i	0.0524356	+	0.396232i
$959$	31.7137	+	40.8932i	1.02409	+	1.32051i
$960$	21.8349	+	21.6597i	0.704718	+	0.699063i
$961$	−2.44924			−0.0790077
$962$	−3.63251	+	0.480710i	−0.117117	+	0.0154987i
$963$	−0.0796192			−0.00256569
$964$	−3.42157	−	12.7012i	−0.110201	−	0.409079i
$965$	43.4248			1.39790
$966$	13.1683	−	13.3222i	0.423682	−	0.428635i
$967$			10.0322i			0.322614i	0.986904	+	0.161307i	$0.0515709\pi$
$967$			10.0322i			0.322614i	−0.986904	+	0.161307i	$0.948429\pi$
$968$	10.5170	+	25.2465i	0.338031	+	0.811452i
$969$			5.88974i			0.189206i
$970$	−62.5682	+	8.28000i	−2.00894	+	0.265855i
$971$			28.4807i			0.913989i	0.889469	+	0.456995i	$0.151074\pi$
$971$			28.4807i			0.913989i	−0.889469	+	0.456995i	$0.848926\pi$
$972$	−0.520231	−	1.93115i	−0.0166864	−	0.0619418i
$973$	−30.5055	+	23.6578i	−0.977960	+	0.758433i
$974$	43.4970	−	5.75620i	1.39373	−	0.184441i
$975$			17.7625i			0.568856i
$976$	−10.4438	+	6.06716i	−0.334297	+	0.194205i
$977$	8.98249			0.287375			0.143688	−	0.989623i	$-0.454104\pi$
$977$	8.98249			0.287375			0.143688	+	0.989623i	$0.454104\pi$
$978$	−5.00632	+	0.662513i	−0.160084	+	0.0211848i
$979$		−	72.5510i		−	2.31874i
$980$	0.625527	+	53.8186i	0.0199817	+	1.71917i
$981$			20.1081i			0.642002i
$982$	4.09000	+	30.9063i	0.130517	+	0.986260i
$983$	11.1768			0.356484			0.178242	−	0.983987i	$-0.442959\pi$
$983$	11.1768			0.356484			0.178242	+	0.983987i	$0.442959\pi$
$984$	9.76223	+	23.4345i	0.311209	+	0.747065i
$985$			9.16797i			0.292116i
$986$	1.17646	+	8.89000i	0.0374662	+	0.283115i
$987$	−10.1103	+	7.84076i	−0.321813	+	0.249574i
$988$	−1.59400	−	5.91712i	−0.0507120	−	0.188249i
$989$		−	40.2388i		−	1.27952i
$990$	3.24280	+	24.5044i	0.103063	+	0.778800i
$991$			21.5500i			0.684559i	0.939598	+	0.342279i	$0.111199\pi$
$991$			21.5500i			0.684559i	−0.939598	+	0.342279i	$0.888801\pi$
$992$	18.4809	+	23.9182i	0.586770	+	0.759403i
$993$			22.3802i			0.710213i
$994$	−3.93648	−	3.89099i	−0.124858	−	0.123415i
$995$	9.47031			0.300229
$996$	20.4258	−	5.50249i	0.647218	−	0.174353i
$997$	−38.2116			−1.21017			−0.605087	−	0.796159i	$-0.706862\pi$
$997$	−38.2116			−1.21017			−0.605087	+	0.796159i	$0.706862\pi$
$998$	−7.54023	−	56.9781i	−0.238682	−	1.80361i
$999$	−1.42654			−0.0451338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.p.a.139.6	yes	16
3.2	odd	2		504.2.p.g.307.12		16
4.3	odd	2		672.2.p.a.559.1		16
7.6	odd	2	inner	168.2.p.a.139.5	✓	16
8.3	odd	2	inner	168.2.p.a.139.8	yes	16
8.5	even	2		672.2.p.a.559.8		16
12.11	even	2		2016.2.p.g.559.16		16
21.20	even	2		504.2.p.g.307.11		16
24.5	odd	2		2016.2.p.g.559.1		16
24.11	even	2		504.2.p.g.307.9		16
28.27	even	2		672.2.p.a.559.16		16
56.13	odd	2		672.2.p.a.559.9		16
56.27	even	2	inner	168.2.p.a.139.7	yes	16
84.83	odd	2		2016.2.p.g.559.2		16
168.83	odd	2		504.2.p.g.307.10		16
168.125	even	2		2016.2.p.g.559.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.p.a.139.5	✓	16	7.6	odd	2	inner
168.2.p.a.139.6	yes	16	1.1	even	1	trivial
168.2.p.a.139.7	yes	16	56.27	even	2	inner
168.2.p.a.139.8	yes	16	8.3	odd	2	inner
504.2.p.g.307.9		16	24.11	even	2
504.2.p.g.307.10		16	168.83	odd	2
504.2.p.g.307.11		16	21.20	even	2
504.2.p.g.307.12		16	3.2	odd	2
672.2.p.a.559.1		16	4.3	odd	2
672.2.p.a.559.8		16	8.5	even	2
672.2.p.a.559.9		16	56.13	odd	2
672.2.p.a.559.16		16	28.27	even	2
2016.2.p.g.559.1		16	24.5	odd	2
2016.2.p.g.559.2		16	84.83	odd	2
2016.2.p.g.559.15		16	168.125	even	2
2016.2.p.g.559.16		16	12.11	even	2

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.185533 - 1.40199i) q^{2} +1.00000i q^{3} +(-1.93115 + 0.520231i) q^{4} -3.84444 q^{5} +(1.40199 - 0.185533i) q^{6} +(-1.62140 - 2.09071i) q^{7} +(1.08765 + 2.61094i) q^{8} -1.00000 q^{9} +(0.713272 + 5.38987i) q^{10} -4.54637 q^{11} +(-0.520231 - 1.93115i) q^{12} +1.81625 q^{13} +(-2.63033 + 2.66108i) q^{14} -3.84444i q^{15} +(3.45872 - 2.00929i) q^{16} -3.49124i q^{17} +(0.185533 + 1.40199i) q^{18} +1.68700i q^{19} +(7.42422 - 2.00000i) q^{20} +(2.09071 - 1.62140i) q^{21} +(0.843502 + 6.37397i) q^{22} +5.00632i q^{23} +(-2.61094 + 1.08765i) q^{24} +9.77975 q^{25} +(-0.336975 - 2.54637i) q^{26} -1.00000i q^{27} +(4.21882 + 3.19398i) q^{28} -1.81625i q^{29} +(-5.38987 + 0.713272i) q^{30} -5.34329 q^{31} +(-3.45872 - 4.47630i) q^{32} -4.54637i q^{33} +(-4.89469 + 0.647741i) q^{34} +(6.23338 + 8.03761i) q^{35} +(1.93115 - 0.520231i) q^{36} -1.42654i q^{37} +(2.36516 - 0.312995i) q^{38} +1.81625i q^{39} +(-4.18142 - 10.0376i) q^{40} -8.97551i q^{41} +(-2.66108 - 2.63033i) q^{42} -8.03761 q^{43} +(8.77975 - 2.36516i) q^{44} +3.84444 q^{45} +(7.01881 - 0.928837i) q^{46} -4.83580 q^{47} +(2.00929 + 3.45872i) q^{48} +(-1.74213 + 6.77975i) q^{49} +(-1.81447 - 13.7111i) q^{50} +3.49124 q^{51} +(-3.50747 + 0.944872i) q^{52} +5.87263i q^{53} +(-1.40199 + 0.185533i) q^{54} +17.4783 q^{55} +(3.69520 - 6.50734i) q^{56} -1.68700 q^{57} +(-2.54637 + 0.336975i) q^{58} -8.46675i q^{59} +(2.00000 + 7.42422i) q^{60} -3.01955 q^{61} +(0.991357 + 7.49124i) q^{62} +(1.62140 + 2.09071i) q^{63} +(-5.63402 + 5.67959i) q^{64} -6.98249 q^{65} +(-6.37397 + 0.843502i) q^{66} -4.42914 q^{67} +(1.81625 + 6.74213i) q^{68} -5.00632 q^{69} +(10.1122 - 10.2304i) q^{70} +1.47928i q^{71} +(-1.08765 - 2.61094i) q^{72} -6.98249i q^{73} +(-2.00000 + 0.264671i) q^{74} +9.77975i q^{75} +(-0.877633 - 3.25787i) q^{76} +(7.37148 + 9.50514i) q^{77} +(2.54637 - 0.336975i) q^{78} -2.97813i q^{79} +(-13.2968 + 7.72462i) q^{80} +1.00000 q^{81} +(-12.5836 + 1.66525i) q^{82} +10.5770i q^{83} +(-3.19398 + 4.21882i) q^{84} +13.4219i q^{85} +(1.49124 + 11.2687i) q^{86} +1.81625 q^{87} +(-4.94487 - 11.8703i) q^{88} +15.9580i q^{89} +(-0.713272 - 5.38987i) q^{90} +(-2.94487 - 3.79726i) q^{91} +(-2.60444 - 9.66797i) q^{92} -5.34329i q^{93} +(0.897201 + 6.77975i) q^{94} -6.48559i q^{95} +(4.47630 - 3.45872i) q^{96} +11.6085i q^{97} +(9.82836 + 1.18459i) q^{98} +4.54637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 2 q^{4} - 10 q^{8} - 16 q^{9} - 8 q^{11} - 14 q^{14} + 18 q^{16} - 2 q^{18} + 8 q^{22} + 16 q^{25} - 10 q^{28} - 16 q^{30} - 18 q^{32} + 24 q^{35} - 2 q^{36} - 4 q^{42} - 8 q^{43} + 52 q^{46}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 2 * q^4 - 10 * q^8 - 16 * q^9 - 8 * q^11 - 14 * q^14 + 18 * q^16 - 2 * q^18 + 8 * q^22 + 16 * q^25 - 10 * q^28 - 16 * q^30 - 18 * q^32 + 24 * q^35 - 2 * q^36 - 4 * q^42 - 8 * q^43 + 52 * q^46 - 8 * q^49 - 34 * q^50 + 50 * q^56 - 16 * q^57 + 24 * q^58 + 32 * q^60 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 10 * q^72 - 32 * q^74 - 24 * q^78 + 16 * q^81 + 8 * q^84 - 32 * q^86 - 88 * q^88 - 56 * q^91 + 44 * q^92 + 66 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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