LMFDB - Embedded newform 672.2.bb.a.367.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.8
Character	$\chi$	$=$	672.367
Dual form			672.2.bb.a.271.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{3} +(2.08776 + 3.61611i) q^{5} +(2.39694 + 1.12013i) q^{7} +(0.500000 + 0.866025i) q^{9} +(0.855485 - 1.48174i) q^{11} -1.54062 q^{13} -4.17553i q^{15} +(2.02094 + 1.16679i) q^{17} +(-6.09693 + 3.52006i) q^{19} +(-1.51575 - 2.16853i) q^{21} +(0.406066 - 0.234442i) q^{23} +(-6.21752 + 10.7691i) q^{25} -1.00000i q^{27} -3.33885i q^{29} +(-1.58126 + 2.73883i) q^{31} +(-1.48174 + 0.855485i) q^{33} +(0.953738 + 11.0062i) q^{35} +(7.74648 - 4.47243i) q^{37} +(1.33422 + 0.770311i) q^{39} -5.31411i q^{41} +3.42772 q^{43} +(-2.08776 + 3.61611i) q^{45} +(2.95047 + 5.11037i) q^{47} +(4.49063 + 5.36975i) q^{49} +(-1.16679 - 2.02094i) q^{51} +(-1.35437 - 0.781947i) q^{53} +7.14421 q^{55} +7.04013 q^{57} +(5.26742 + 3.04114i) q^{59} +(4.55959 + 7.89744i) q^{61} +(0.228411 + 2.63587i) q^{63} +(-3.21646 - 5.57107i) q^{65} +(-3.73658 + 6.47195i) q^{67} -0.468884 q^{69} -3.49263i q^{71} +(-12.5811 - 7.26372i) q^{73} +(10.7691 - 6.21752i) q^{75} +(3.71029 - 2.59340i) q^{77} +(1.46108 - 0.843557i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.72601i q^{83} +9.74391i q^{85} +(-1.66943 + 2.89153i) q^{87} +(1.83829 - 1.06134i) q^{89} +(-3.69278 - 1.72569i) q^{91} +(2.73883 - 1.58126i) q^{93} +(-25.4579 - 14.6981i) q^{95} -1.95202i q^{97} +1.71097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	2.08776	+	3.61611i	0.933677	+	1.61718i	0.776977	+	0.629529i	$0.216752\pi$
$5$	2.08776	+	3.61611i	0.933677	+	1.61718i	0.156700	+	0.987646i	$0.449915\pi$
$6$		0			0
$7$	2.39694	+	1.12013i	0.905958	+	0.423368i
$7$	2.39694	+	1.12013i	0.905958	+	0.423368i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	0.855485	−	1.48174i	0.257939	−	0.446763i	−0.707751	−	0.706462i	$-0.750290\pi$
$11$	0.855485	−	1.48174i	0.257939	−	0.446763i	0.965690	+	0.259699i	$0.0836235\pi$
$12$		0			0
$13$	−1.54062			−0.427292			−0.213646	−	0.976911i	$-0.568534\pi$
$13$	−1.54062			−0.427292			−0.213646	+	0.976911i	$0.568534\pi$
$14$		0			0
$15$		−	4.17553i		−	1.07812i
$16$		0			0
$17$	2.02094	+	1.16679i	0.490149	+	0.282988i	0.724636	−	0.689132i	$-0.242008\pi$
$17$	2.02094	+	1.16679i	0.490149	+	0.282988i	−0.234487	+	0.972119i	$0.575341\pi$
$18$		0			0
$19$	−6.09693	+	3.52006i	−1.39873	+	0.807558i	−0.994260	−	0.106992i	$-0.965878\pi$
$19$	−6.09693	+	3.52006i	−1.39873	+	0.807558i	−0.404472	+	0.914551i	$0.632545\pi$
$20$		0			0
$21$	−1.51575	−	2.16853i	−0.330763	−	0.473212i
$22$		0			0
$23$	0.406066	−	0.234442i	0.0846705	−	0.0488846i	−0.457067	−	0.889432i	$-0.651100\pi$
$23$	0.406066	−	0.234442i	0.0846705	−	0.0488846i	0.541737	+	0.840548i	$0.317767\pi$
$24$		0			0
$25$	−6.21752	+	10.7691i	−1.24350	+	2.15381i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	3.33885i		−	0.620009i	−0.950735	−	0.310005i	$-0.899669\pi$
$29$		−	3.33885i		−	0.620009i	0.950735	−	0.310005i	$-0.100331\pi$
$30$		0			0
$31$	−1.58126	+	2.73883i	−0.284003	+	0.491908i	−0.972367	−	0.233458i	$-0.924996\pi$
$31$	−1.58126	+	2.73883i	−0.284003	+	0.491908i	0.688364	+	0.725366i	$0.258329\pi$
$32$		0			0
$33$	−1.48174	+	0.855485i	−0.257939	+	0.148921i
$34$		0			0
$35$	0.953738	+	11.0062i	0.161211	+	1.86038i
$36$		0			0
$37$	7.74648	−	4.47243i	1.27351	−	0.735263i	0.297865	−	0.954608i	$-0.403725\pi$
$37$	7.74648	−	4.47243i	1.27351	−	0.735263i	0.975647	+	0.219345i	$0.0703920\pi$
$38$		0			0
$39$	1.33422	+	0.770311i	0.213646	+	0.123349i
$40$		0			0
$41$		−	5.31411i		−	0.829925i	−0.909838	−	0.414963i	$-0.863795\pi$
$41$		−	5.31411i		−	0.829925i	0.909838	−	0.414963i	$-0.136205\pi$
$42$		0			0
$43$	3.42772			0.522722			0.261361	−	0.965241i	$-0.415829\pi$
$43$	3.42772			0.522722			0.261361	+	0.965241i	$0.415829\pi$
$44$		0			0
$45$	−2.08776	+	3.61611i	−0.311226	+	0.539058i
$46$		0			0
$47$	2.95047	+	5.11037i	0.430371	+	0.745424i	0.996905	−	0.0786139i	$-0.0250494\pi$
$47$	2.95047	+	5.11037i	0.430371	+	0.745424i	−0.566534	+	0.824038i	$0.691716\pi$
$48$		0			0
$49$	4.49063	+	5.36975i	0.641519	+	0.767107i
$50$		0			0
$51$	−1.16679	−	2.02094i	−0.163383	−	0.282988i
$52$		0			0
$53$	−1.35437	−	0.781947i	−0.186037	−	0.107409i	0.404089	−	0.914720i	$-0.367589\pi$
$53$	−1.35437	−	0.781947i	−0.186037	−	0.107409i	−0.590126	+	0.807311i	$0.700922\pi$
$54$		0			0
$55$	7.14421			0.963325
$56$		0			0
$57$	7.04013			0.932488
$58$		0			0
$59$	5.26742	+	3.04114i	0.685759	+	0.395923i	0.802021	−	0.597295i	$-0.203758\pi$
$59$	5.26742	+	3.04114i	0.685759	+	0.395923i	−0.116262	+	0.993219i	$0.537091\pi$
$60$		0			0
$61$	4.55959	+	7.89744i	0.583795	+	1.01116i	0.995024	+	0.0996311i	$0.0317663\pi$
$61$	4.55959	+	7.89744i	0.583795	+	1.01116i	−0.411229	+	0.911532i	$0.634900\pi$
$62$		0			0
$63$	0.228411	+	2.63587i	0.0287771	+	0.332089i
$64$		0			0
$65$	−3.21646	−	5.57107i	−0.398952	−	0.691006i
$66$		0			0
$67$	−3.73658	+	6.47195i	−0.456496	+	0.790675i	−0.998773	−	0.0495251i	$-0.984229\pi$
$67$	−3.73658	+	6.47195i	−0.456496	+	0.790675i	0.542276	+	0.840200i	$0.317563\pi$
$68$		0			0
$69$	−0.468884			−0.0564470
$70$		0			0
$71$		−	3.49263i		−	0.414499i	−0.978288	−	0.207249i	$-0.933549\pi$
$71$		−	3.49263i		−	0.414499i	0.978288	−	0.207249i	$-0.0664512\pi$
$72$		0			0
$73$	−12.5811	−	7.26372i	−1.47251	−	0.850154i	−0.472988	−	0.881069i	$-0.656824\pi$
$73$	−12.5811	−	7.26372i	−1.47251	−	0.850154i	−0.999522	+	0.0309152i	$0.990158\pi$
$74$		0			0
$75$	10.7691	−	6.21752i	1.24350	−	0.717937i
$76$		0			0
$77$	3.71029	−	2.59340i	0.422826	−	0.295545i
$78$		0			0
$79$	1.46108	−	0.843557i	0.164385	−	0.0949075i	−0.415551	−	0.909570i	$-0.636411\pi$
$79$	1.46108	−	0.843557i	0.164385	−	0.0949075i	0.579935	+	0.814662i	$0.303078\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	2.72601i		−	0.299219i	−0.988745	−	0.149609i	$-0.952198\pi$
$83$		−	2.72601i		−	0.299219i	0.988745	−	0.149609i	$-0.0478016\pi$
$84$		0			0
$85$			9.74391i			1.05688i
$86$		0			0
$87$	−1.66943	+	2.89153i	−0.178981	+	0.310005i
$88$		0			0
$89$	1.83829	−	1.06134i	0.194858	−	0.112501i	−0.399397	−	0.916778i	$-0.630780\pi$
$89$	1.83829	−	1.06134i	0.194858	−	0.112501i	0.594255	+	0.804277i	$0.297447\pi$
$90$		0			0
$91$	−3.69278	−	1.72569i	−0.387108	−	0.180902i
$92$		0			0
$93$	2.73883	−	1.58126i	0.284003	−	0.163969i
$94$		0			0
$95$	−25.4579	−	14.6981i	−2.61193	−	1.50800i
$96$		0			0
$97$		−	1.95202i		−	0.198198i	−0.995078	−	0.0990990i	$-0.968404\pi$
$97$		−	1.95202i		−	0.198198i	0.995078	−	0.0990990i	$-0.0315960\pi$
$98$		0			0
$99$	1.71097			0.171959
$100$		0			0
$101$	6.89045	−	11.9346i	0.685625	−	1.18754i	−0.287615	−	0.957746i	$-0.592862\pi$
$101$	6.89045	−	11.9346i	0.685625	−	1.18754i	0.973240	−	0.229792i	$-0.0738044\pi$
$102$		0			0
$103$	3.84129	+	6.65331i	0.378494	+	0.655570i	0.990843	−	0.135017i	$-0.0431089\pi$
$103$	3.84129	+	6.65331i	0.378494	+	0.655570i	−0.612350	+	0.790587i	$0.709776\pi$
$104$		0			0
$105$	4.67712	−	10.0085i	0.456440	−	0.976728i
$106$		0			0
$107$	−7.20414	−	12.4779i	−0.696450	−	1.20629i	−0.969689	−	0.244341i	$-0.921428\pi$
$107$	−7.20414	−	12.4779i	−0.696450	−	1.20629i	0.273239	−	0.961946i	$-0.411905\pi$
$108$		0			0
$109$	−2.92380	−	1.68806i	−0.280050	−	0.161687i	0.353396	−	0.935474i	$-0.385027\pi$
$109$	−2.92380	−	1.68806i	−0.280050	−	0.161687i	−0.633446	+	0.773787i	$0.718360\pi$
$110$		0			0
$111$	−8.94486			−0.849009
$112$		0			0
$113$	−10.7090			−1.00742			−0.503710	−	0.863873i	$-0.668032\pi$
$113$	−10.7090			−1.00742			−0.503710	+	0.863873i	$0.668032\pi$
$114$		0			0
$115$	1.69554	+	0.978920i	0.158110	+	0.0912847i
$116$		0			0
$117$	−0.770311	−	1.33422i	−0.0712153	−	0.123349i
$118$		0			0
$119$	3.53711	+	5.06042i	0.324246	+	0.463888i
$120$		0			0
$121$	4.03629	+	6.99106i	0.366935	+	0.635551i
$122$		0			0
$123$	−2.65706	+	4.60216i	−0.239579	+	0.414963i
$124$		0			0
$125$	−31.0452			−2.77677
$126$		0			0
$127$		−	9.49738i		−	0.842757i	−0.906885	−	0.421378i	$-0.861546\pi$
$127$		−	9.49738i		−	0.842757i	0.906885	−	0.421378i	$-0.138454\pi$
$128$		0			0
$129$	−2.96849	−	1.71386i	−0.261361	−	0.150897i
$130$		0			0
$131$	11.8364	−	6.83375i	1.03415	−	0.597068i	0.115981	−	0.993251i	$-0.462999\pi$
$131$	11.8364	−	6.83375i	1.03415	−	0.597068i	0.918171	+	0.396184i	$0.129666\pi$
$132$		0			0
$133$	−18.5569	+	1.60805i	−1.60909	+	0.139435i
$134$		0			0
$135$	3.61611	−	2.08776i	0.311226	−	0.179686i
$136$		0			0
$137$	5.99460	−	10.3829i	0.512153	−	0.887075i	−0.487748	−	0.872985i	$-0.662181\pi$
$137$	5.99460	−	10.3829i	0.512153	−	0.887075i	0.999901	−	0.0140902i	$-0.00448520\pi$
$138$		0			0
$139$			6.64909i			0.563968i	0.959419	+	0.281984i	$0.0909925\pi$
$139$			6.64909i			0.563968i	−0.959419	+	0.281984i	$0.909007\pi$
$140$		0			0
$141$		−	5.90095i		−	0.496950i
$142$		0			0
$143$	−1.31798	+	2.28281i	−0.110215	+	0.190898i
$144$		0			0
$145$	12.0737	−	6.97073i	1.00266	−	0.578888i
$146$		0			0
$147$	−1.20413	−	6.89566i	−0.0993147	−	0.568744i
$148$		0			0
$149$	7.03123	−	4.05948i	0.576021	−	0.332566i	−0.183530	−	0.983014i	$-0.558752\pi$
$149$	7.03123	−	4.05948i	0.576021	−	0.332566i	0.759550	+	0.650448i	$0.225419\pi$
$150$		0			0
$151$	1.07044	+	0.618020i	0.0871113	+	0.0502937i	0.542923	−	0.839783i	$-0.317318\pi$
$151$	1.07044	+	0.618020i	0.0871113	+	0.0502937i	−0.455812	+	0.890076i	$0.650651\pi$
$152$		0			0
$153$			2.33358i			0.188658i
$154$		0			0
$155$	−13.2052			−1.06067
$156$		0			0
$157$	−4.80286	+	8.31880i	−0.383310	+	0.663913i	−0.991533	−	0.129854i	$-0.958549\pi$
$157$	−4.80286	+	8.31880i	−0.383310	+	0.663913i	0.608223	+	0.793766i	$0.291883\pi$
$158$		0			0
$159$	0.781947	+	1.35437i	0.0620124	+	0.107409i
$160$		0			0
$161$	1.23592	−	0.107099i	0.0974041	−	0.00844055i
$162$		0			0
$163$	−9.70461	−	16.8089i	−0.760123	−	1.31657i	−0.942787	−	0.333397i	$-0.891805\pi$
$163$	−9.70461	−	16.8089i	−0.760123	−	1.31657i	0.182663	−	0.983176i	$-0.441528\pi$
$164$		0			0
$165$	−6.18706	−	3.57210i	−0.481662	−	0.278088i
$166$		0			0
$167$	17.7482			1.37340			0.686699	−	0.726942i	$-0.259059\pi$
$167$	17.7482			1.37340			0.686699	+	0.726942i	$0.259059\pi$
$168$		0			0
$169$	−10.6265			−0.817422
$170$		0			0
$171$	−6.09693	−	3.52006i	−0.466244	−	0.269186i
$172$		0			0
$173$	3.57075	+	6.18472i	0.271479	+	0.470216i	0.969241	−	0.246114i	$-0.0791539\pi$
$173$	3.57075	+	6.18472i	0.271479	+	0.470216i	−0.697762	+	0.716330i	$0.745821\pi$
$174$		0			0
$175$	−26.9657	+	18.8484i	−2.03842	+	1.42480i
$176$		0			0
$177$	−3.04114	−	5.26742i	−0.228586	−	0.395923i
$178$		0			0
$179$	11.9581	−	20.7121i	0.893791	−	1.54809i	0.0584980	−	0.998288i	$-0.481369\pi$
$179$	11.9581	−	20.7121i	0.893791	−	1.54809i	0.835293	−	0.549805i	$-0.185298\pi$
$180$		0			0
$181$	20.5572			1.52800			0.764002	−	0.645214i	$-0.223232\pi$
$181$	20.5572			1.52800			0.764002	+	0.645214i	$0.223232\pi$
$182$		0			0
$183$		−	9.11917i		−	0.674109i
$184$		0			0
$185$	32.3456	+	18.6748i	2.37810	+	1.37300i
$186$		0			0
$187$	3.45776	−	1.99634i	0.252857	−	0.145987i
$188$		0			0
$189$	1.12013	−	2.39694i	0.0814772	−	0.174352i
$190$		0			0
$191$	1.74523	−	1.00761i	0.126280	−	0.0729079i	−0.435529	−	0.900175i	$-0.643439\pi$
$191$	1.74523	−	1.00761i	0.126280	−	0.0729079i	0.561809	+	0.827267i	$0.310105\pi$
$192$		0			0
$193$	1.78535	−	3.09232i	0.128512	−	0.222590i	−0.794588	−	0.607149i	$-0.792313\pi$
$193$	1.78535	−	3.09232i	0.128512	−	0.222590i	0.923100	+	0.384559i	$0.125646\pi$
$194$		0			0
$195$			6.43291i			0.460671i
$196$		0			0
$197$			17.5393i			1.24962i	0.780775	+	0.624812i	$0.214824\pi$
$197$			17.5393i			1.24962i	−0.780775	+	0.624812i	$0.785176\pi$
$198$		0			0
$199$	8.85336	−	15.3345i	0.627598	−	1.08703i	−0.360434	−	0.932785i	$-0.617371\pi$
$199$	8.85336	−	15.3345i	0.627598	−	1.08703i	0.988032	−	0.154247i	$-0.0492952\pi$
$200$		0			0
$201$	6.47195	−	3.73658i	0.456496	−	0.263558i
$202$		0			0
$203$	3.73994	−	8.00302i	0.262492	−	0.561702i
$204$		0			0
$205$	19.2164	−	11.0946i	1.34213	−	0.774882i
$206$		0			0
$207$	0.406066	+	0.234442i	0.0282235	+	0.0162949i
$208$		0			0
$209$			12.0455i			0.833201i
$210$		0			0
$211$	4.23050			0.291240			0.145620	−	0.989341i	$-0.453482\pi$
$211$	4.23050			0.291240			0.145620	+	0.989341i	$0.453482\pi$
$212$		0			0
$213$	−1.74631	+	3.02471i	−0.119656	+	0.207249i
$214$		0			0
$215$	7.15626	+	12.3950i	0.488053	+	0.845333i
$216$		0			0
$217$	−6.85803	+	4.79359i	−0.465553	+	0.325410i
$218$		0			0
$219$	7.26372	+	12.5811i	0.490837	+	0.850154i
$220$		0			0
$221$	−3.11350	−	1.79758i	−0.209437	−	0.120918i
$222$		0			0
$223$	1.43532			0.0961162			0.0480581	−	0.998845i	$-0.484697\pi$
$223$	1.43532			0.0961162			0.0480581	+	0.998845i	$0.484697\pi$
$224$		0			0
$225$	−12.4350			−0.829003
$226$		0			0
$227$	−13.8688	−	8.00718i	−0.920508	−	0.531455i	−0.0367106	−	0.999326i	$-0.511688\pi$
$227$	−13.8688	−	8.00718i	−0.920508	−	0.531455i	−0.883797	+	0.467871i	$0.845021\pi$
$228$		0			0
$229$	−8.12499	−	14.0729i	−0.536914	−	0.929963i	−0.999068	−	0.0431631i	$-0.986256\pi$
$229$	−8.12499	−	14.0729i	−0.536914	−	0.929963i	0.462154	−	0.886800i	$-0.347077\pi$
$230$		0			0
$231$	−4.50990	+	0.390805i	−0.296730	+	0.0257131i
$232$		0			0
$233$	−5.93054	−	10.2720i	−0.388522	−	0.672941i	0.603729	−	0.797190i	$-0.293681\pi$
$233$	−5.93054	−	10.2720i	−0.388522	−	0.672941i	−0.992251	+	0.124249i	$0.960348\pi$
$234$		0			0
$235$	−12.3198	+	21.3385i	−0.803654	+	1.39197i
$236$		0			0
$237$	−1.68711			−0.109590
$238$		0			0
$239$		−	0.846585i		−	0.0547610i	−0.999625	−	0.0273805i	$-0.991283\pi$
$239$		−	0.846585i		−	0.0547610i	0.999625	−	0.0273805i	$-0.00871657\pi$
$240$		0			0
$241$	−0.761425	−	0.439609i	−0.0490477	−	0.0283177i	0.475276	−	0.879837i	$-0.342348\pi$
$241$	−0.761425	−	0.439609i	−0.0490477	−	0.0283177i	−0.524323	+	0.851519i	$0.675682\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−10.0422	+	27.4494i	−0.641575	+	1.75368i
$246$		0			0
$247$	9.39307	−	5.42309i	0.597667	−	0.345063i
$248$		0			0
$249$	−1.36301	+	2.36080i	−0.0863771	+	0.149609i
$250$		0			0
$251$			18.1441i			1.14524i	0.819820	+	0.572622i	$0.194074\pi$
$251$			18.1441i			1.14524i	−0.819820	+	0.572622i	$0.805926\pi$
$252$		0			0
$253$		−	0.802247i		−	0.0504368i
$254$		0			0
$255$	4.87196	−	8.43848i	0.305094	−	0.528438i
$256$		0			0
$257$	15.8902	−	9.17421i	0.991203	−	0.572271i	0.0855695	−	0.996332i	$-0.472729\pi$
$257$	15.8902	−	9.17421i	0.991203	−	0.572271i	0.905634	+	0.424061i	$0.139396\pi$
$258$		0			0
$259$	23.5775	−	2.04311i	1.46504	−	0.126953i
$260$		0			0
$261$	2.89153	−	1.66943i	0.178981	−	0.103335i
$262$		0			0
$263$	3.02044	+	1.74385i	0.186248	+	0.107531i	0.590225	−	0.807239i	$-0.299039\pi$
$263$	3.02044	+	1.74385i	0.186248	+	0.107531i	−0.403977	+	0.914769i	$0.632372\pi$
$264$		0			0
$265$		−	6.53008i		−	0.401140i
$266$		0			0
$267$	−2.12267			−0.129905
$268$		0			0
$269$	7.35605	−	12.7410i	0.448506	−	0.776835i	−0.549783	−	0.835308i	$-0.685290\pi$
$269$	7.35605	−	12.7410i	0.448506	−	0.776835i	0.998289	+	0.0584722i	$0.0186229\pi$
$270$		0			0
$271$	−9.95139	−	17.2363i	−0.604504	−	1.04703i	−0.992130	−	0.125215i	$-0.960038\pi$
$271$	−9.95139	−	17.2363i	−0.604504	−	1.04703i	0.387626	−	0.921817i	$-0.373295\pi$
$272$		0			0
$273$	2.33519	+	3.34088i	0.141332	+	0.202199i
$274$		0			0
$275$	10.6380	+	18.4255i	0.641495	+	1.11110i
$276$		0			0
$277$	−22.9034	−	13.2233i	−1.37613	−	0.794510i	−0.384440	−	0.923150i	$-0.625605\pi$
$277$	−22.9034	−	13.2233i	−1.37613	−	0.794510i	−0.991691	+	0.128640i	$0.958939\pi$
$278$		0			0
$279$	−3.16253			−0.189336
$280$		0			0
$281$	−20.2837			−1.21003			−0.605013	−	0.796216i	$-0.706832\pi$
$281$	−20.2837			−1.21003			−0.605013	+	0.796216i	$0.706832\pi$
$282$		0			0
$283$	−5.70426	−	3.29336i	−0.339083	−	0.195770i	0.320783	−	0.947153i	$-0.396054\pi$
$283$	−5.70426	−	3.29336i	−0.339083	−	0.195770i	−0.659866	+	0.751383i	$0.729387\pi$
$284$		0			0
$285$	14.6981	+	25.4579i	0.870642	+	1.50800i
$286$		0			0
$287$	5.95248	−	12.7376i	0.351364	−	0.751877i
$288$		0			0
$289$	−5.77721	−	10.0064i	−0.339836	−	0.588613i
$290$		0			0
$291$	−0.976012	+	1.69050i	−0.0572148	+	0.0990990i
$292$		0			0
$293$	12.9438			0.756187			0.378094	−	0.925767i	$-0.376580\pi$
$293$	12.9438			0.756187			0.378094	+	0.925767i	$0.376580\pi$
$294$		0			0
$295$			25.3968i			1.47866i
$296$		0			0
$297$	−1.48174	−	0.855485i	−0.0859795	−	0.0496403i
$298$		0			0
$299$	−0.625594	+	0.361187i	−0.0361790	+	0.0208880i
$300$		0			0
$301$	8.21603	+	3.83948i	0.473564	+	0.221304i
$302$		0			0
$303$	−11.9346	+	6.89045i	−0.685625	+	0.395846i
$304$		0			0
$305$	−19.0387	+	32.9760i	−1.09015	+	1.88820i
$306$		0			0
$307$			11.8773i			0.677871i	0.940810	+	0.338936i	$0.110067\pi$
$307$			11.8773i			0.677871i	−0.940810	+	0.338936i	$0.889933\pi$
$308$		0			0
$309$		−	7.68258i		−	0.437047i
$310$		0			0
$311$	−5.91849	+	10.2511i	−0.335607	+	0.581288i	−0.983601	−	0.180357i	$-0.942275\pi$
$311$	−5.91849	+	10.2511i	−0.335607	+	0.581288i	0.647994	+	0.761645i	$0.275608\pi$
$312$		0			0
$313$	−12.8383	+	7.41217i	−0.725661	+	0.418961i	−0.816833	−	0.576875i	$-0.804272\pi$
$313$	−12.8383	+	7.41217i	−0.725661	+	0.418961i	0.0911716	+	0.995835i	$0.470939\pi$
$314$		0			0
$315$	−9.05475	+	6.32904i	−0.510177	+	0.356601i
$316$		0			0
$317$	−5.87478	+	3.39181i	−0.329961	+	0.190503i	−0.655824	−	0.754914i	$-0.727678\pi$
$317$	−5.87478	+	3.39181i	−0.329961	+	0.190503i	0.325863	+	0.945417i	$0.394345\pi$
$318$		0			0
$319$	−4.94732	−	2.85634i	−0.276997	−	0.159924i
$320$		0			0
$321$			14.4083i			0.804191i
$322$		0			0
$323$	−16.4287			−0.914116
$324$		0			0
$325$	9.57885	−	16.5911i	0.531339	−	0.920306i
$326$		0			0
$327$	1.68806	+	2.92380i	0.0933499	+	0.161687i
$328$		0			0
$329$	1.34784	+	15.5542i	0.0743090	+	0.857528i
$330$		0			0
$331$	−2.37285	−	4.10989i	−0.130424	−	0.225900i	0.793416	−	0.608679i	$-0.208300\pi$
$331$	−2.37285	−	4.10989i	−0.130424	−	0.225900i	−0.923840	+	0.382779i	$0.874967\pi$
$332$		0			0
$333$	7.74648	+	4.47243i	0.424504	+	0.245088i
$334$		0			0
$335$	−31.2044			−1.70488
$336$		0			0
$337$	16.5173			0.899754			0.449877	−	0.893090i	$-0.351468\pi$
$337$	16.5173			0.899754			0.449877	+	0.893090i	$0.351468\pi$
$338$		0			0
$339$	9.27429	+	5.35451i	0.503710	+	0.290817i
$340$		0			0
$341$	2.70549	+	4.68605i	0.146511	+	0.253764i
$342$		0			0
$343$	4.74897	+	17.9010i	0.256420	+	0.966565i
$344$		0			0
$345$	−0.978920	−	1.69554i	−0.0527033	−	0.0912847i
$346$		0			0
$347$	−9.54986	+	16.5408i	−0.512663	+	0.887959i	0.487229	+	0.873274i	$0.338008\pi$
$347$	−9.54986	+	16.5408i	−0.512663	+	0.887959i	−0.999892	+	0.0146846i	$0.995326\pi$
$348$		0			0
$349$	−2.49767			−0.133697			−0.0668485	−	0.997763i	$-0.521294\pi$
$349$	−2.49767			−0.133697			−0.0668485	+	0.997763i	$0.521294\pi$
$350$		0			0
$351$			1.54062i			0.0822323i
$352$		0			0
$353$	−22.3071	−	12.8790i	−1.18729	−	0.685481i	−0.229599	−	0.973285i	$-0.573741\pi$
$353$	−22.3071	−	12.8790i	−1.18729	−	0.685481i	−0.957689	+	0.287805i	$0.907075\pi$
$354$		0			0
$355$	12.6297	−	7.29179i	0.670317	−	0.387008i
$356$		0			0
$357$	−0.533015	−	6.15101i	−0.0282102	−	0.325546i
$358$		0			0
$359$	28.7697	−	16.6102i	1.51840	−	0.876651i	0.518639	−	0.854993i	$-0.326439\pi$
$359$	28.7697	−	16.6102i	1.51840	−	0.876651i	0.999765	−	0.0216582i	$-0.00689457\pi$
$360$		0			0
$361$	15.2817	−	26.4687i	0.804300	−	1.39309i
$362$		0			0
$363$		−	8.07258i		−	0.423701i
$364$		0			0
$365$		−	60.6597i		−	3.17507i
$366$		0			0
$367$	2.17584	−	3.76866i	0.113578	−	0.196722i	−0.803633	−	0.595126i	$-0.797102\pi$
$367$	2.17584	−	3.76866i	0.113578	−	0.196722i	0.917210	+	0.398403i	$0.130436\pi$
$368$		0			0
$369$	4.60216	−	2.65706i	0.239579	−	0.138321i
$370$		0			0
$371$	−2.37047	−	3.39135i	−0.123068	−	0.176070i
$372$		0			0
$373$	−11.0943	+	6.40533i	−0.574444	+	0.331655i	−0.758922	−	0.651181i	$-0.774274\pi$
$373$	−11.0943	+	6.40533i	−0.574444	+	0.331655i	0.184479	+	0.982837i	$0.440940\pi$
$374$		0			0
$375$	26.8859	+	15.5226i	1.38838	+	0.801584i
$376$		0			0
$377$			5.14391i			0.264925i
$378$		0			0
$379$	24.0807			1.23694			0.618472	−	0.785807i	$-0.287752\pi$
$379$	24.0807			1.23694			0.618472	+	0.785807i	$0.287752\pi$
$380$		0			0
$381$	−4.74869	+	8.22498i	−0.243283	+	0.421378i
$382$		0			0
$383$	8.78233	+	15.2114i	0.448756	+	0.777268i	0.998305	−	0.0581930i	$-0.0185339\pi$
$383$	8.78233	+	15.2114i	0.448756	+	0.777268i	−0.549549	+	0.835461i	$0.685201\pi$
$384$		0			0
$385$	17.1242	+	8.00242i	0.872731	+	0.407841i
$386$		0			0
$387$	1.71386	+	2.96849i	0.0871203	+	0.150897i
$388$		0			0
$389$	23.9022	+	13.7999i	1.21189	+	0.699685i	0.963171	−	0.268890i	$-0.0866570\pi$
$389$	23.9022	+	13.7999i	1.21189	+	0.699685i	0.248719	+	0.968576i	$0.419990\pi$
$390$		0			0
$391$	1.09418			0.0553349
$392$		0			0
$393$	−13.6675			−0.689435
$394$		0			0
$395$	6.10079	+	3.52229i	0.306964	+	0.177226i
$396$		0			0
$397$	8.65850	+	14.9970i	0.434558	+	0.752676i	0.997259	−	0.0739841i	$-0.0235714\pi$
$397$	8.65850	+	14.9970i	0.434558	+	0.752676i	−0.562702	+	0.826660i	$0.690238\pi$
$398$		0			0
$399$	16.8748	+	7.88583i	0.844794	+	0.394786i
$400$		0			0
$401$	−3.87616	−	6.71371i	−0.193566	−	0.335266i	0.752863	−	0.658177i	$-0.228672\pi$
$401$	−3.87616	−	6.71371i	−0.193566	−	0.335266i	−0.946430	+	0.322910i	$0.895339\pi$
$402$		0			0
$403$	2.43613	−	4.21950i	0.121352	−	0.210188i
$404$		0			0
$405$	−4.17553			−0.207484
$406$		0			0
$407$		−	15.3044i		−	0.758611i
$408$		0			0
$409$	−4.01694	−	2.31918i	−0.198625	−	0.114676i	0.397389	−	0.917650i	$-0.369916\pi$
$409$	−4.01694	−	2.31918i	−0.198625	−	0.114676i	−0.596014	+	0.802974i	$0.703250\pi$
$410$		0			0
$411$	−10.3829	+	5.99460i	−0.512153	+	0.295692i
$412$		0			0
$413$	9.21921	+	13.1896i	0.453648	+	0.649018i
$414$		0			0
$415$	9.85758	−	5.69128i	0.483889	−	0.279374i
$416$		0			0
$417$	3.32454	−	5.75828i	0.162804	−	0.281984i
$418$		0			0
$419$			14.2419i			0.695760i	0.937539	+	0.347880i	$0.113098\pi$
$419$			14.2419i			0.695760i	−0.937539	+	0.347880i	$0.886902\pi$
$420$		0			0
$421$			20.0126i			0.975356i	0.873024	+	0.487678i	$0.162156\pi$
$421$			20.0126i			0.975356i	−0.873024	+	0.487678i	$0.837844\pi$
$422$		0			0
$423$	−2.95047	+	5.11037i	−0.143457	+	0.248475i
$424$		0			0
$425$	−25.1304	+	14.5091i	−1.21900	+	0.703793i
$426$		0			0
$427$	2.08292	+	24.0370i	0.100800	+	1.16323i
$428$		0			0
$429$	2.28281	−	1.31798i	0.110215	−	0.0636327i
$430$		0			0
$431$	12.1099	+	6.99165i	0.583313	+	0.336776i	0.762449	−	0.647049i	$-0.223997\pi$
$431$	12.1099	+	6.99165i	0.583313	+	0.336776i	−0.179136	+	0.983824i	$0.557330\pi$
$432$		0			0
$433$		−	0.984888i		−	0.0473307i	−0.999720	−	0.0236653i	$-0.992466\pi$
$433$		−	0.984888i		−	0.0473307i	0.999720	−	0.0236653i	$-0.00753362\pi$
$434$		0			0
$435$	−13.9415			−0.668442
$436$		0			0
$437$	−1.65050	+	2.85875i	−0.0789542	+	0.136753i
$438$		0			0
$439$	3.43693	+	5.95294i	0.164036	+	0.284118i	0.936312	−	0.351168i	$-0.114215\pi$
$439$	3.43693	+	5.95294i	0.164036	+	0.284118i	−0.772277	+	0.635286i	$0.780882\pi$
$440$		0			0
$441$	−2.40502	+	6.57388i	−0.114525	+	0.313042i
$442$		0			0
$443$	1.70483	+	2.95285i	0.0809989	+	0.140294i	0.903679	−	0.428210i	$-0.140856\pi$
$443$	1.70483	+	2.95285i	0.0809989	+	0.140294i	−0.822680	+	0.568504i	$0.807522\pi$
$444$		0			0
$445$	7.67582	+	4.43164i	0.363869	+	0.210080i
$446$		0			0
$447$	−8.11897			−0.384014
$448$		0			0
$449$	32.9924			1.55701			0.778503	−	0.627641i	$-0.215979\pi$
$449$	32.9924			1.55701			0.778503	+	0.627641i	$0.215979\pi$
$450$		0			0
$451$	−7.87416	−	4.54615i	−0.370780	−	0.214070i
$452$		0			0
$453$	−0.618020	−	1.07044i	−0.0290371	−	0.0502937i
$454$		0			0
$455$	−1.46935	−	16.9563i	−0.0688842	−	0.794926i
$456$		0			0
$457$	11.4224	+	19.7842i	0.534319	+	0.925467i	0.999196	+	0.0400919i	$0.0127651\pi$
$457$	11.4224	+	19.7842i	0.534319	+	0.925467i	−0.464877	+	0.885375i	$0.653902\pi$
$458$		0			0
$459$	1.16679	−	2.02094i	0.0544610	−	0.0943292i
$460$		0			0
$461$	−15.8743			−0.739338			−0.369669	−	0.929164i	$-0.620529\pi$
$461$	−15.8743			−0.739338			−0.369669	+	0.929164i	$0.620529\pi$
$462$		0			0
$463$			2.72059i			0.126436i	0.998000	+	0.0632182i	$0.0201364\pi$
$463$			2.72059i			0.126436i	−0.998000	+	0.0632182i	$0.979864\pi$
$464$		0			0
$465$	11.4361	+	6.60261i	0.530334	+	0.306189i
$466$		0			0
$467$	−20.7726	+	11.9931i	−0.961240	+	0.554972i	−0.896555	−	0.442933i	$-0.853938\pi$
$467$	−20.7726	+	11.9931i	−0.961240	+	0.554972i	−0.0646858	+	0.997906i	$0.520605\pi$
$468$		0			0
$469$	−16.2058	+	11.3274i	−0.748313	+	0.523052i
$470$		0			0
$471$	8.31880	−	4.80286i	0.383310	−	0.221304i
$472$		0			0
$473$	2.93236	−	5.07900i	0.134830	−	0.233533i
$474$		0			0
$475$		−	87.5443i		−	4.01681i
$476$		0			0
$477$		−	1.56389i		−	0.0716058i
$478$		0			0
$479$	−9.87511	+	17.1042i	−0.451205	+	0.781511i	−0.998461	−	0.0554547i	$-0.982339\pi$
$479$	−9.87511	+	17.1042i	−0.451205	+	0.781511i	0.547256	+	0.836965i	$0.315672\pi$
$480$		0			0
$481$	−11.9344	+	6.89033i	−0.544162	+	0.314172i
$482$		0			0
$483$	−1.12389	−	0.525210i	−0.0511386	−	0.0238979i
$484$		0			0
$485$	7.05874	−	4.07536i	0.320521	−	0.185053i
$486$		0			0
$487$	−32.1435	−	18.5581i	−1.45656	−	0.840946i	−0.457721	−	0.889096i	$-0.651334\pi$
$487$	−32.1435	−	18.5581i	−1.45656	−	0.840946i	−0.998840	+	0.0481495i	$0.984668\pi$
$488$		0			0
$489$			19.4092i			0.877715i
$490$		0			0
$491$	20.5746			0.928517			0.464259	−	0.885700i	$-0.346321\pi$
$491$	20.5746			0.928517			0.464259	+	0.885700i	$0.346321\pi$
$492$		0			0
$493$	3.89573	−	6.74761i	0.175455	−	0.303897i
$494$		0			0
$495$	3.57210	+	6.18706i	0.160554	+	0.278088i
$496$		0			0
$497$	3.91219	−	8.37162i	0.175486	−	0.375518i
$498$		0			0
$499$	0.517579	+	0.896473i	0.0231700	+	0.0401316i	0.877378	−	0.479800i	$-0.159291\pi$
$499$	0.517579	+	0.896473i	0.0231700	+	0.0401316i	−0.854208	+	0.519932i	$0.825957\pi$
$500$		0			0
$501$	−15.3704	−	8.87410i	−0.686699	−	0.396466i
$502$		0			0
$503$	−19.7898			−0.882382			−0.441191	−	0.897413i	$-0.645444\pi$
$503$	−19.7898			−0.882382			−0.441191	+	0.897413i	$0.645444\pi$
$504$		0			0
$505$	57.5425			2.56061
$506$		0			0
$507$	9.20280	+	5.31324i	0.408711	+	0.235969i
$508$		0			0
$509$	−2.11849	−	3.66933i	−0.0939004	−	0.162640i	0.815249	−	0.579111i	$-0.196600\pi$
$509$	−2.11849	−	3.66933i	−0.0939004	−	0.162640i	−0.909149	+	0.416471i	$0.863267\pi$
$510$		0			0
$511$	−22.0199	−	31.5031i	−0.974104	−	1.39362i
$512$		0			0
$513$	3.52006	+	6.09693i	0.155415	+	0.269186i
$514$		0			0
$515$	−16.0394	+	27.7811i	−0.706781	+	1.22418i
$516$		0			0
$517$	10.0963			0.444037
$518$		0			0
$519$		−	7.14150i		−	0.313477i
$520$		0			0
$521$	−33.6570	−	19.4319i	−1.47454	−	0.851326i	−0.474952	−	0.880012i	$-0.657535\pi$
$521$	−33.6570	−	19.4319i	−1.47454	−	0.851326i	−0.999588	+	0.0286855i	$0.990868\pi$
$522$		0			0
$523$	−14.8181	+	8.55526i	−0.647952	+	0.374095i	−0.787671	−	0.616096i	$-0.788713\pi$
$523$	−14.8181	+	8.55526i	−0.647952	+	0.374095i	0.139719	+	0.990191i	$0.455380\pi$
$524$		0			0
$525$	32.7772	−	2.84030i	1.43051	−	0.123961i
$526$		0			0
$527$	−6.39126	+	3.69000i	−0.278408	+	0.160739i
$528$		0			0
$529$	−11.3901	+	19.7282i	−0.495221	+	0.857747i
$530$		0			0
$531$			6.08229i			0.263949i
$532$		0			0
$533$			8.18704i			0.354620i
$534$		0			0
$535$	30.0811	−	52.1019i	1.30052	−	2.25256i
$536$		0			0
$537$	−20.7121	+	11.9581i	−0.893791	+	0.516031i
$538$		0			0
$539$	11.7983	−	2.06023i	0.508187	−	0.0887402i
$540$		0			0
$541$	−37.6652	+	21.7460i	−1.61935	+	0.934935i	−0.632268	+	0.774750i	$0.717876\pi$
$541$	−37.6652	+	21.7460i	−1.61935	+	0.934935i	−0.987087	+	0.160185i	$0.948791\pi$
$542$		0			0
$543$	−17.8030	−	10.2786i	−0.764002	−	0.441097i
$544$		0			0
$545$		−	14.0971i		−	0.603852i
$546$		0			0
$547$	−10.8290			−0.463016			−0.231508	−	0.972833i	$-0.574366\pi$
$547$	−10.8290			−0.463016			−0.231508	+	0.972833i	$0.574366\pi$
$548$		0			0
$549$	−4.55959	+	7.89744i	−0.194598	+	0.337054i
$550$		0			0
$551$	11.7530	+	20.3567i	0.500693	+	0.867226i
$552$		0			0
$553$	4.44702	−	0.385356i	0.189106	−	0.0163870i
$554$		0			0
$555$	−18.6748	−	32.3456i	−0.792699	−	1.37300i
$556$		0			0
$557$	7.04197	+	4.06568i	0.298378	+	0.172269i	0.641714	−	0.766944i	$-0.278224\pi$
$557$	7.04197	+	4.06568i	0.298378	+	0.172269i	−0.343336	+	0.939213i	$0.611557\pi$
$558$		0			0
$559$	−5.28082			−0.223355
$560$		0			0
$561$	−3.99268			−0.168571
$562$		0			0
$563$	−19.6081	−	11.3207i	−0.826381	−	0.477111i	0.0262311	−	0.999656i	$-0.491649\pi$
$563$	−19.6081	−	11.3207i	−0.826381	−	0.477111i	−0.852612	+	0.522545i	$0.824983\pi$
$564$		0			0
$565$	−22.3579	−	38.7251i	−0.940605	−	1.62918i
$566$		0			0
$567$	−2.16853	+	1.51575i	−0.0910696	+	0.0636554i
$568$		0			0
$569$	10.1485	+	17.5778i	0.425449	+	0.736900i	0.996462	−	0.0840413i	$-0.0267828\pi$
$569$	10.1485	+	17.5778i	0.425449	+	0.736900i	−0.571013	+	0.820941i	$0.693449\pi$
$570$		0			0
$571$	18.3819	−	31.8383i	0.769257	−	1.33239i	−0.168710	−	0.985666i	$-0.553960\pi$
$571$	18.3819	−	31.8383i	0.769257	−	1.33239i	0.937967	−	0.346726i	$-0.112707\pi$
$572$		0			0
$573$	−2.01521			−0.0841868
$574$		0			0
$575$			5.83059i			0.243153i
$576$		0			0
$577$	1.39915	+	0.807801i	0.0582475	+	0.0336292i	0.528841	−	0.848721i	$-0.322627\pi$
$577$	1.39915	+	0.807801i	0.0582475	+	0.0336292i	−0.470593	+	0.882350i	$0.655960\pi$
$578$		0			0
$579$	−3.09232	+	1.78535i	−0.128512	+	0.0741967i
$580$		0			0
$581$	3.05348	−	6.53409i	0.126680	−	0.271080i
$582$		0			0
$583$	−2.31729	+	1.33789i	−0.0959723	+	0.0554097i
$584$		0			0
$585$	3.21646	−	5.57107i	0.132984	−	0.230335i
$586$		0			0
$587$		−	3.68747i		−	0.152198i	−0.997100	−	0.0760991i	$-0.975753\pi$
$587$		−	3.68747i		−	0.152198i	0.997100	−	0.0760991i	$-0.0242465\pi$
$588$		0			0
$589$		−	22.2646i		−	0.917396i
$590$		0			0
$591$	8.76965	−	15.1895i	0.360735	−	0.624812i
$592$		0			0
$593$	32.3781	−	18.6935i	1.32961	−	0.767650i	0.344370	−	0.938834i	$-0.388092\pi$
$593$	32.3781	−	18.6935i	1.32961	−	0.767650i	0.985239	+	0.171184i	$0.0547591\pi$
$594$		0			0
$595$	−10.9144	+	23.3556i	−0.447447	+	0.957485i
$596$		0			0
$597$	−15.3345	+	8.85336i	−0.627598	+	0.362344i
$598$		0			0
$599$	8.61435	+	4.97350i	0.351973	+	0.203212i	0.665554	−	0.746350i	$-0.268195\pi$
$599$	8.61435	+	4.97350i	0.351973	+	0.203212i	−0.313581	+	0.949561i	$0.601529\pi$
$600$		0			0
$601$		−	35.9296i		−	1.46560i	−0.680445	−	0.732799i	$-0.738214\pi$
$601$		−	35.9296i		−	1.46560i	0.680445	−	0.732799i	$-0.261786\pi$
$602$		0			0
$603$	−7.47317			−0.304331
$604$		0			0
$605$	−16.8536	+	29.1914i	−0.685198	+	1.18680i
$606$		0			0
$607$	−14.9355	−	25.8690i	−0.606212	−	1.04999i	−0.991859	−	0.127344i	$-0.959355\pi$
$607$	−14.9355	−	25.8690i	−0.606212	−	1.04999i	0.385646	−	0.922647i	$-0.373978\pi$
$608$		0			0
$609$	−7.24039	+	5.06085i	−0.293395	+	0.205076i
$610$		0			0
$611$	−4.54557	−	7.87315i	−0.183894	−	0.318514i
$612$		0			0
$613$	−32.8160	−	18.9463i	−1.32542	−	0.765234i	−0.340836	−	0.940123i	$-0.610710\pi$
$613$	−32.8160	−	18.9463i	−1.32542	−	0.765234i	−0.984588	+	0.174889i	$0.944043\pi$
$614$		0			0
$615$	−22.1892			−0.894756
$616$		0			0
$617$	39.0332			1.57142			0.785709	−	0.618597i	$-0.212298\pi$
$617$	39.0332			1.57142			0.785709	+	0.618597i	$0.212298\pi$
$618$		0			0
$619$	21.5338	+	12.4325i	0.865517	+	0.499706i	0.865856	−	0.500294i	$-0.166775\pi$
$619$	21.5338	+	12.4325i	0.865517	+	0.499706i	−0.000339137		1.00000i	$0.500108\pi$
$620$		0			0
$621$	−0.234442	−	0.406066i	−0.00940784	−	0.0162949i
$622$		0			0
$623$	5.59509	−	0.484842i	0.224163	−	0.0194248i
$624$		0			0
$625$	−33.7275	−	58.4177i	−1.34910	−	2.33671i
$626$		0			0
$627$	6.02273	−	10.4317i	0.240525	−	0.416601i
$628$		0			0
$629$	20.8735			0.832281
$630$		0			0
$631$			43.3823i			1.72702i	0.504330	+	0.863511i	$0.331740\pi$
$631$			43.3823i			1.72702i	−0.504330	+	0.863511i	$0.668260\pi$
$632$		0			0
$633$	−3.66372	−	2.11525i	−0.145620	−	0.0840736i
$634$		0			0
$635$	34.3436	−	19.8283i	1.36289	−	0.786862i
$636$		0			0
$637$	−6.91837	−	8.27276i	−0.274116	−	0.327779i
$638$		0			0
$639$	3.02471	−	1.74631i	0.119656	−	0.0690831i
$640$		0			0
$641$	−3.32559	+	5.76010i	−0.131353	+	0.227510i	−0.924198	−	0.381913i	$-0.875265\pi$
$641$	−3.32559	+	5.76010i	−0.131353	+	0.227510i	0.792845	+	0.609423i	$0.208599\pi$
$642$		0			0
$643$		−	18.1066i		−	0.714055i	−0.934094	−	0.357027i	$-0.883790\pi$
$643$		−	18.1066i		−	0.714055i	0.934094	−	0.357027i	$-0.116210\pi$
$644$		0			0
$645$		−	14.3125i		−	0.563555i
$646$		0			0
$647$	−24.6421	+	42.6815i	−0.968783	+	1.67798i	−0.269694	+	0.962946i	$0.586923\pi$
$647$	−24.6421	+	42.6815i	−0.968783	+	1.67798i	−0.699089	+	0.715035i	$0.746411\pi$
$648$		0			0
$649$	9.01239	−	5.20331i	0.353767	−	0.204248i
$650$		0			0
$651$	8.33602	−	0.722357i	0.326714	−	0.0283114i
$652$		0			0
$653$	−22.1087	+	12.7645i	−0.865181	+	0.499512i	−0.865744	−	0.500488i	$-0.833154\pi$
$653$	−22.1087	+	12.7645i	−0.865181	+	0.499512i	0.000563051		1.00000i	$0.499821\pi$
$654$		0			0
$655$	49.4233	+	28.5345i	1.93113	+	1.11494i
$656$		0			0
$657$		−	14.5274i		−	0.566769i
$658$		0			0
$659$	12.0942			0.471125			0.235562	−	0.971859i	$-0.424307\pi$
$659$	12.0942			0.471125			0.235562	+	0.971859i	$0.424307\pi$
$660$		0			0
$661$	−5.42541	+	9.39708i	−0.211024	+	0.365504i	−0.952035	−	0.305988i	$-0.901013\pi$
$661$	−5.42541	+	9.39708i	−0.211024	+	0.365504i	0.741011	+	0.671493i	$0.234346\pi$
$662$		0			0
$663$	1.79758	+	3.11350i	0.0698122	+	0.120918i
$664$		0			0
$665$	−44.5573	−	63.7466i	−1.72786	−	2.47199i
$666$		0			0
$667$	−0.782767	−	1.35579i	−0.0303089	−	0.0524965i
$668$		0			0
$669$	−1.24302	−	0.717661i	−0.0480581	−	0.0277464i
$670$		0			0
$671$	15.6026			0.602333
$672$		0			0
$673$	−48.1931			−1.85771			−0.928854	−	0.370446i	$-0.879205\pi$
$673$	−48.1931			−1.85771			−0.928854	+	0.370446i	$0.879205\pi$
$674$		0			0
$675$	10.7691	+	6.21752i	0.414501	+	0.239312i
$676$		0			0
$677$	2.56093	+	4.43567i	0.0984246	+	0.170476i	0.911033	−	0.412334i	$-0.135286\pi$
$677$	2.56093	+	4.43567i	0.0984246	+	0.170476i	−0.812608	+	0.582810i	$0.801953\pi$
$678$		0			0
$679$	2.18651	−	4.67888i	0.0839107	−	0.179559i
$680$		0			0
$681$	8.00718	+	13.8688i	0.306836	+	0.531455i
$682$		0			0
$683$	11.7191	−	20.2980i	0.448418	−	0.776682i	−0.549866	−	0.835253i	$-0.685321\pi$
$683$	11.7191	−	20.2980i	0.448418	−	0.776682i	0.998283	+	0.0585709i	$0.0186544\pi$
$684$		0			0
$685$	50.0612			1.91274
$686$		0			0
$687$			16.2500i			0.619975i
$688$		0			0
$689$	2.08658	+	1.20468i	0.0794922	+	0.0458948i
$690$		0			0
$691$	−11.9534	+	6.90129i	−0.454728	+	0.262537i	−0.709825	−	0.704378i	$-0.751226\pi$
$691$	−11.9534	+	6.90129i	−0.454728	+	0.262537i	0.255097	+	0.966915i	$0.417893\pi$
$692$		0			0
$693$	4.10109	+	1.91650i	0.155788	+	0.0728020i
$694$		0			0
$695$	−24.0439	+	13.8817i	−0.912035	+	0.526564i
$696$		0			0
$697$	6.20044	−	10.7395i	0.234859	−	0.406787i
$698$		0			0
$699$			11.8611i			0.448627i
$700$		0			0
$701$		−	11.8718i		−	0.448393i	−0.974544	−	0.224196i	$-0.928024\pi$
$701$		−	11.8718i		−	0.448393i	0.974544	−	0.224196i	$-0.0719757\pi$
$702$		0			0
$703$	−31.4865	+	54.5362i	−1.18754	+	2.05687i
$704$		0			0
$705$	21.3385	−	12.3198i	0.803654	−	0.463990i
$706$		0			0
$707$	29.8843	−	20.8883i	1.12391	−	0.785587i
$708$		0			0
$709$	27.1241	−	15.6601i	1.01867	−	0.588127i	0.104949	−	0.994478i	$-0.466532\pi$
$709$	27.1241	−	15.6601i	1.01867	−	0.588127i	0.913717	+	0.406350i	$0.133199\pi$
$710$		0			0
$711$	1.46108	+	0.843557i	0.0547949	+	0.0316358i
$712$		0			0
$713$			1.48286i			0.0555335i
$714$		0			0
$715$	−11.0065			−0.411621
$716$		0			0
$717$	−0.423292	+	0.733164i	−0.0158081	+	0.0273805i
$718$		0			0
$719$	−12.6273	−	21.8712i	−0.470920	−	0.815657i	0.528527	−	0.848917i	$-0.322745\pi$
$719$	−12.6273	−	21.8712i	−0.470920	−	0.815657i	−0.999447	+	0.0332594i	$0.989411\pi$
$720$		0			0
$721$	1.75479	+	20.2503i	0.0653518	+	0.754161i
$722$		0			0
$723$	0.439609	+	0.761425i	0.0163492	+	0.0283177i
$724$		0			0
$725$	35.9563	+	20.7594i	1.33538	+	0.770984i
$726$		0			0
$727$	−17.9342			−0.665144			−0.332572	−	0.943078i	$-0.607916\pi$
$727$	−17.9342			−0.665144			−0.332572	+	0.943078i	$0.607916\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	6.92720	+	3.99942i	0.256212	+	0.147924i
$732$		0			0
$733$	−6.16779	−	10.6829i	−0.227813	−	0.394583i	0.729347	−	0.684144i	$-0.239824\pi$
$733$	−6.16779	−	10.6829i	−0.227813	−	0.394583i	−0.957160	+	0.289561i	$0.906491\pi$
$734$		0			0
$735$	22.4215	−	18.7508i	0.827031	−	0.691632i
$736$		0			0
$737$	6.39319	+	11.0733i	0.235496	+	0.407891i
$738$		0			0
$739$	21.7463	−	37.6656i	0.799949	−	1.38555i	−0.119699	−	0.992810i	$-0.538193\pi$
$739$	21.7463	−	37.6656i	0.799949	−	1.38555i	0.919648	−	0.392743i	$-0.128474\pi$
$740$		0			0
$741$	−10.8462			−0.398444
$742$		0			0
$743$		−	32.8397i		−	1.20477i	−0.798205	−	0.602386i	$-0.794217\pi$
$743$		−	32.8397i		−	1.20477i	0.798205	−	0.602386i	$-0.205783\pi$
$744$		0			0
$745$	29.3591	+	16.9505i	1.07563	+	0.621018i
$746$		0			0
$747$	2.36080	−	1.36301i	0.0863771	−	0.0498698i
$748$		0			0
$749$	−3.29101	−	37.9784i	−0.120251	−	1.38770i
$750$		0			0
$751$	−7.62670	+	4.40328i	−0.278302	+	0.160678i	−0.632655	−	0.774434i	$-0.718035\pi$
$751$	−7.62670	+	4.40328i	−0.278302	+	0.160678i	0.354352	+	0.935112i	$0.384701\pi$
$752$		0			0
$753$	9.07203	−	15.7132i	0.330603	−	0.572622i
$754$		0			0
$755$			5.16112i			0.187832i
$756$		0			0
$757$			16.9328i			0.615433i	0.951478	+	0.307717i	$0.0995649\pi$
$757$			16.9328i			0.615433i	−0.951478	+	0.307717i	$0.900435\pi$
$758$		0			0
$759$	−0.401124	+	0.694766i	−0.0145599	+	0.0252184i
$760$		0			0
$761$	10.9108	−	6.29937i	0.395517	−	0.228352i	−0.289031	−	0.957320i	$-0.593333\pi$
$761$	10.9108	−	6.29937i	0.395517	−	0.228352i	0.684548	+	0.728968i	$0.260000\pi$
$762$		0			0
$763$	−5.11734	−	7.32121i	−0.185260	−	0.265045i
$764$		0			0
$765$	−8.43848	+	4.87196i	−0.305094	+	0.176146i
$766$		0			0
$767$	−8.11510	−	4.68526i	−0.293019	−	0.169175i
$768$		0			0
$769$			16.0445i			0.578581i	0.957241	+	0.289291i	$0.0934194\pi$
$769$			16.0445i			0.578581i	−0.957241	+	0.289291i	$0.906581\pi$
$770$		0			0
$771$	−18.3484			−0.660802
$772$		0			0
$773$	−9.15671	+	15.8599i	−0.329344	+	0.570440i	−0.982382	−	0.186885i	$-0.940161\pi$
$773$	−9.15671	+	15.8599i	−0.329344	+	0.570440i	0.653038	+	0.757325i	$0.273494\pi$
$774$		0			0
$775$	−19.6631	−	34.0574i	−0.706318	−	1.22338i
$776$		0			0
$777$	−21.4403	−	10.0194i	−0.769166	−	0.359443i
$778$		0			0
$779$	18.7060	+	32.3998i	0.670213	+	1.16084i
$780$		0			0
$781$	−5.17518	−	2.98789i	−0.185183	−	0.106915i
$782$		0			0
$783$	−3.33885			−0.119321
$784$		0			0
$785$	−40.1090			−1.43155
$786$		0			0
$787$	−3.88976	−	2.24576i	−0.138655	−	0.0800526i	0.429068	−	0.903272i	$-0.358842\pi$
$787$	−3.88976	−	2.24576i	−0.138655	−	0.0800526i	−0.567723	+	0.823220i	$0.692175\pi$
$788$		0			0
$789$	−1.74385	−	3.02044i	−0.0620828	−	0.107531i
$790$		0			0
$791$	−25.6689	−	11.9955i	−0.912680	−	0.426510i
$792$		0			0
$793$	−7.02460	−	12.1670i	−0.249451	−	0.432062i
$794$		0			0
$795$	−3.26504	+	5.65522i	−0.115799	+	0.200570i
$796$		0			0
$797$	−31.7698			−1.12534			−0.562672	−	0.826680i	$-0.690227\pi$
$797$	−31.7698			−1.12534			−0.562672	+	0.826680i	$0.690227\pi$
$798$		0			0
$799$			13.7703i			0.487159i
$800$		0			0
$801$	1.83829	+	1.06134i	0.0649527	+	0.0375004i
$802$		0			0
$803$	−21.5259	+	12.4280i	−0.759634	+	0.438575i
$804$		0			0
$805$	2.96759	+	4.24563i	0.104594	+	0.149639i
$806$		0			0
$807$	−12.7410	+	7.35605i	−0.448506	+	0.258945i
$808$		0			0
$809$	−12.5784	+	21.7864i	−0.442232	+	0.765969i	−0.997855	−	0.0654659i	$-0.979147\pi$
$809$	−12.5784	+	21.7864i	−0.442232	+	0.765969i	0.555623	+	0.831435i	$0.312480\pi$
$810$		0			0
$811$			48.0042i			1.68565i	0.538184	+	0.842827i	$0.319110\pi$
$811$			48.0042i			1.68565i	−0.538184	+	0.842827i	$0.680890\pi$
$812$		0			0
$813$			19.9028i			0.698021i
$814$		0			0
$815$	40.5219	−	70.1859i	1.41942	−	2.45851i
$816$		0			0
$817$	−20.8985	+	12.0658i	−0.731148	+	0.422128i
$818$		0			0
$819$	−0.351896	−	4.06089i	−0.0122962	−	0.141899i
$820$		0			0
$821$	−14.5854	+	8.42089i	−0.509034	+	0.293891i	−0.732437	−	0.680835i	$-0.761617\pi$
$821$	−14.5854	+	8.42089i	−0.509034	+	0.293891i	0.223402	+	0.974726i	$0.428284\pi$
$822$		0			0
$823$	−17.1163	−	9.88209i	−0.596636	−	0.344468i	0.171081	−	0.985257i	$-0.445274\pi$
$823$	−17.1163	−	9.88209i	−0.596636	−	0.344468i	−0.767717	+	0.640789i	$0.778607\pi$
$824$		0			0
$825$		−	21.2760i		−	0.740735i
$826$		0			0
$827$	−49.1702			−1.70981			−0.854907	−	0.518781i	$-0.826386\pi$
$827$	−49.1702			−1.70981			−0.854907	+	0.518781i	$0.826386\pi$
$828$		0			0
$829$	−7.96007	+	13.7872i	−0.276465	+	0.478851i	−0.970504	−	0.241087i	$-0.922496\pi$
$829$	−7.96007	+	13.7872i	−0.276465	+	0.478851i	0.694039	+	0.719937i	$0.255829\pi$
$830$		0			0
$831$	13.2233	+	22.9034i	0.458710	+	0.794510i
$832$		0			0
$833$	2.80992	+	16.0915i	0.0973580	+	0.557539i
$834$		0			0
$835$	37.0541	+	64.1795i	1.28231	+	2.22102i
$836$		0			0
$837$	2.73883	+	1.58126i	0.0946678	+	0.0546565i
$838$		0			0
$839$	38.3305			1.32332			0.661658	−	0.749806i	$-0.269853\pi$
$839$	38.3305			1.32332			0.661658	+	0.749806i	$0.269853\pi$
$840$		0			0
$841$	17.8521			0.615589
$842$		0			0
$843$	17.5662	+	10.1419i	0.605013	+	0.349304i
$844$		0			0
$845$	−22.1856	−	38.4266i	−0.763207	−	1.32191i
$846$		0			0
$847$	1.84387	+	21.2783i	0.0633561	+	0.731131i
$848$		0			0
$849$	3.29336	+	5.70426i	0.113028	+	0.195770i
$850$		0			0
$851$	2.09705	−	3.63220i	0.0718860	−	0.124510i
$852$		0			0
$853$	22.5158			0.770927			0.385463	−	0.922723i	$-0.374042\pi$
$853$	22.5158			0.770927			0.385463	+	0.922723i	$0.374042\pi$
$854$		0			0
$855$		−	29.3963i		−	1.00533i
$856$		0			0
$857$	−11.1913	−	6.46129i	−0.382287	−	0.220713i	0.296526	−	0.955025i	$-0.404172\pi$
$857$	−11.1913	−	6.46129i	−0.382287	−	0.220713i	−0.678813	+	0.734311i	$0.737505\pi$
$858$		0			0
$859$	−20.1418	+	11.6289i	−0.687229	+	0.396772i	−0.802573	−	0.596554i	$-0.796536\pi$
$859$	−20.1418	+	11.6289i	−0.687229	+	0.396772i	0.115344	+	0.993326i	$0.463203\pi$
$860$		0			0
$861$	−11.5238	+	8.05485i	−0.392730	+	0.274509i
$862$		0			0
$863$	−7.69412	+	4.44220i	−0.261911	+	0.151214i	−0.625206	−	0.780460i	$-0.714985\pi$
$863$	−7.69412	+	4.44220i	−0.261911	+	0.151214i	0.363295	+	0.931674i	$0.381652\pi$
$864$		0			0
$865$	−14.9098	+	25.8245i	−0.506947	+	0.878059i
$866$		0			0
$867$			11.5544i			0.392409i
$868$		0			0
$869$		−	2.88660i		−	0.0979212i
$870$		0			0
$871$	5.75667	−	9.97084i	0.195057	−	0.337849i
$872$		0			0
$873$	1.69050	−	0.976012i	0.0572148	−	0.0330330i
$874$		0			0
$875$	−74.4135	−	34.7746i	−2.51564	−	1.17560i
$876$		0			0
$877$	40.2134	−	23.2172i	1.35791	−	0.783990i	0.368569	−	0.929600i	$-0.379848\pi$
$877$	40.2134	−	23.2172i	1.35791	−	0.783990i	0.989342	+	0.145610i	$0.0465145\pi$
$878$		0			0
$879$	−11.2097	−	6.47192i	−0.378094	−	0.218292i
$880$		0			0
$881$			27.1901i			0.916058i	0.888937	+	0.458029i	$0.151444\pi$
$881$			27.1901i			0.916058i	−0.888937	+	0.458029i	$0.848556\pi$
$882$		0			0
$883$	21.7975			0.733543			0.366772	−	0.930311i	$-0.380463\pi$
$883$	21.7975			0.733543			0.366772	+	0.930311i	$0.380463\pi$
$884$		0			0
$885$	12.6984	−	21.9942i	0.426852	−	0.739329i
$886$		0			0
$887$	−21.1661	−	36.6607i	−0.710688	−	1.23095i	−0.964599	−	0.263720i	$-0.915051\pi$
$887$	−21.1661	−	36.6607i	−0.710688	−	1.23095i	0.253911	−	0.967227i	$-0.418283\pi$
$888$		0			0
$889$	10.6383	−	22.7646i	0.356796	−	0.763502i
$890$		0			0
$891$	0.855485	+	1.48174i	0.0286598	+	0.0496403i
$892$		0			0
$893$	−35.9777	−	20.7717i	−1.20395	−	0.695099i
$894$		0			0
$895$	99.8629			3.33805
$896$		0			0
$897$	0.722374			0.0241194
$898$		0			0
$899$	9.14454	+	5.27960i	0.304987	+	0.176085i
$900$		0			0
$901$	−1.82473	−	3.16053i	−0.0607906	−	0.105292i
$902$		0			0
$903$	−5.19555	−	7.43310i	−0.172897	−	0.247358i
$904$		0			0
$905$	42.9186	+	74.3371i	1.42666	+	2.47105i
$906$		0			0
$907$	−22.5605	+	39.0760i	−0.749109	+	1.29750i	0.199141	+	0.979971i	$0.436185\pi$
$907$	−22.5605	+	39.0760i	−0.749109	+	1.29750i	−0.948250	+	0.317525i	$0.897148\pi$
$908$		0			0
$909$	13.7809			0.457083
$910$		0			0
$911$			36.2714i			1.20173i	0.799352	+	0.600863i	$0.205176\pi$
$911$			36.2714i			1.20173i	−0.799352	+	0.600863i	$0.794824\pi$
$912$		0			0
$913$	−4.03926	−	2.33207i	−0.133680	−	0.0771801i
$914$		0			0
$915$	32.9760	−	19.0387i	1.09015	−	0.629400i
$916$		0			0
$917$	36.0258	−	3.12181i	1.18968	−	0.103091i
$918$		0			0
$919$	−37.7905	+	21.8183i	−1.24659	+	0.719721i	−0.970428	−	0.241390i	$-0.922397\pi$
$919$	−37.7905	+	21.8183i	−1.24659	+	0.719721i	−0.276164	+	0.961110i	$0.589063\pi$
$920$		0			0
$921$	5.93863	−	10.2860i	0.195685	−	0.338936i
$922$		0			0
$923$			5.38082i			0.177112i
$924$		0			0
$925$			111.230i			3.65721i
$926$		0			0
$927$	−3.84129	+	6.65331i	−0.126165	+	0.218523i
$928$		0			0
$929$	10.2075	−	5.89332i	0.334898	−	0.193354i	−0.323115	−	0.946360i	$-0.604730\pi$
$929$	10.2075	−	5.89332i	0.334898	−	0.193354i	0.658014	+	0.753006i	$0.271397\pi$
$930$		0			0
$931$	−46.2809	−	16.9317i	−1.51680	−	0.554913i
$932$		0			0
$933$	10.2511	−	5.91849i	0.335607	−	0.193763i
$934$		0			0
$935$	14.4380	+	8.33578i	0.472173	+	0.272609i
$936$		0			0
$937$			35.0529i			1.14513i	0.819860	+	0.572565i	$0.194051\pi$
$937$			35.0529i			1.14513i	−0.819860	+	0.572565i	$0.805949\pi$
$938$		0			0
$939$	14.8243			0.483774
$940$		0			0
$941$	14.2985	−	24.7658i	0.466119	−	0.807342i	−0.533132	−	0.846032i	$-0.678985\pi$
$941$	14.2985	−	24.7658i	0.466119	−	0.807342i	0.999251	+	0.0386903i	$0.0123186\pi$
$942$		0			0
$943$	−1.24585	−	2.15788i	−0.0405705	−	0.0702702i
$944$		0			0
$945$	11.0062	−	0.953738i	0.358031	−	0.0310251i
$946$		0			0
$947$	−25.7444	−	44.5906i	−0.836580	−	1.44900i	−0.892738	−	0.450577i	$-0.851218\pi$
$947$	−25.7444	−	44.5906i	−0.836580	−	1.44900i	0.0561576	−	0.998422i	$-0.482115\pi$
$948$		0			0
$949$	19.3828	+	11.1906i	0.629191	+	0.363264i
$950$		0			0
$951$	6.78361			0.219974
$952$		0			0
$953$	−11.8761			−0.384706			−0.192353	−	0.981326i	$-0.561612\pi$
$953$	−11.8761			−0.384706			−0.192353	+	0.981326i	$0.561612\pi$
$954$		0			0
$955$	7.28724	+	4.20729i	0.235810	+	0.136145i
$956$		0			0
$957$	2.85634	+	4.94732i	0.0923323	+	0.159924i
$958$		0			0
$959$	25.9989	−	18.1726i	0.839548	−	0.586823i
$960$		0			0
$961$	10.4992	+	18.1852i	0.338684	+	0.586618i
$962$		0			0
$963$	7.20414	−	12.4779i	0.232150	−	0.402096i
$964$		0			0
$965$	14.9096			0.479956
$966$		0			0
$967$			59.2193i			1.90437i	0.305530	+	0.952183i	$0.401167\pi$
$967$			59.2193i			1.90437i	−0.305530	+	0.952183i	$0.598833\pi$
$968$		0			0
$969$	14.2276	+	8.21434i	0.457058	+	0.263883i
$970$		0			0
$971$	4.53638	−	2.61908i	0.145579	−	0.0840503i	−0.425441	−	0.904986i	$-0.639881\pi$
$971$	4.53638	−	2.61908i	0.145579	−	0.0840503i	0.571020	+	0.820936i	$0.306548\pi$
$972$		0			0
$973$	−7.44782	+	15.9375i	−0.238766	+	0.510931i
$974$		0			0
$975$	−16.5911	+	9.57885i	−0.531339	+	0.306769i
$976$		0			0
$977$	26.6049	−	46.0810i	0.851165	−	1.47426i	−0.0289924	−	0.999580i	$-0.509230\pi$
$977$	26.6049	−	46.0810i	0.851165	−	1.47426i	0.880158	−	0.474682i	$-0.157437\pi$
$978$		0			0
$979$		−	3.63183i		−	0.116074i
$980$		0			0
$981$		−	3.37612i		−	0.107791i
$982$		0			0
$983$	−13.9737	+	24.2032i	−0.445693	+	0.771963i	−0.998100	−	0.0616113i	$-0.980376\pi$
$983$	−13.9737	+	24.2032i	−0.445693	+	0.771963i	0.552407	+	0.833574i	$0.313709\pi$
$984$		0			0
$985$	−63.4241	+	36.6179i	−2.02086	+	1.16674i
$986$		0			0
$987$	6.60981	−	14.1442i	0.210393	−	0.450215i
$988$		0			0
$989$	1.39188	−	0.803601i	0.0442592	−	0.0255530i
$990$		0			0
$991$	18.7980	+	10.8530i	0.597139	+	0.344758i	0.767915	−	0.640552i	$-0.221294\pi$
$991$	18.7980	+	10.8530i	0.597139	+	0.344758i	−0.170776	+	0.985310i	$0.554628\pi$
$992$		0			0
$993$			4.74570i			0.150600i
$994$		0			0
$995$	73.9349			2.34389
$996$		0			0
$997$	16.8274	−	29.1458i	0.532928	−	0.923058i	−0.466333	−	0.884609i	$-0.654425\pi$
$997$	16.8274	−	29.1458i	0.532928	−	0.923058i	0.999261	−	0.0384485i	$-0.0122416\pi$
$998$		0			0
$999$	−4.47243	−	7.74648i	−0.141501	−	0.245088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bb.a.367.8		32
3.2	odd	2		2016.2.bs.c.1711.1		32
4.3	odd	2		168.2.t.a.115.1	yes	32
7.3	odd	6		4704.2.p.a.3919.23		32
7.4	even	3		4704.2.p.a.3919.6		32
7.5	odd	6	inner	672.2.bb.a.271.1		32
8.3	odd	2	inner	672.2.bb.a.367.1		32
8.5	even	2		168.2.t.a.115.12	yes	32
12.11	even	2		504.2.bk.c.451.16		32
21.5	even	6		2016.2.bs.c.271.16		32
24.5	odd	2		504.2.bk.c.451.5		32
24.11	even	2		2016.2.bs.c.1711.16		32
28.3	even	6		1176.2.p.a.979.17		32
28.11	odd	6		1176.2.p.a.979.18		32
28.19	even	6		168.2.t.a.19.12	yes	32
56.3	even	6		4704.2.p.a.3919.5		32
56.5	odd	6		168.2.t.a.19.1	✓	32
56.11	odd	6		4704.2.p.a.3919.24		32
56.19	even	6	inner	672.2.bb.a.271.8		32
56.45	odd	6		1176.2.p.a.979.20		32
56.53	even	6		1176.2.p.a.979.19		32
84.47	odd	6		504.2.bk.c.19.5		32
168.5	even	6		504.2.bk.c.19.16		32
168.131	odd	6		2016.2.bs.c.271.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.1	✓	32	56.5	odd	6
168.2.t.a.19.12	yes	32	28.19	even	6
168.2.t.a.115.1	yes	32	4.3	odd	2
168.2.t.a.115.12	yes	32	8.5	even	2
504.2.bk.c.19.5		32	84.47	odd	6
504.2.bk.c.19.16		32	168.5	even	6
504.2.bk.c.451.5		32	24.5	odd	2
504.2.bk.c.451.16		32	12.11	even	2
672.2.bb.a.271.1		32	7.5	odd	6	inner
672.2.bb.a.271.8		32	56.19	even	6	inner
672.2.bb.a.367.1		32	8.3	odd	2	inner
672.2.bb.a.367.8		32	1.1	even	1	trivial
1176.2.p.a.979.17		32	28.3	even	6
1176.2.p.a.979.18		32	28.11	odd	6
1176.2.p.a.979.19		32	56.53	even	6
1176.2.p.a.979.20		32	56.45	odd	6
2016.2.bs.c.271.1		32	168.131	odd	6
2016.2.bs.c.271.16		32	21.5	even	6
2016.2.bs.c.1711.1		32	3.2	odd	2
2016.2.bs.c.1711.16		32	24.11	even	2
4704.2.p.a.3919.5		32	56.3	even	6
4704.2.p.a.3919.6		32	7.4	even	3
4704.2.p.a.3919.23		32	7.3	odd	6
4704.2.p.a.3919.24		32	56.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(2.08776 + 3.61611i) q^{5} +(2.39694 + 1.12013i) q^{7} +(0.500000 + 0.866025i) q^{9} +(0.855485 - 1.48174i) q^{11} -1.54062 q^{13} -4.17553i q^{15} +(2.02094 + 1.16679i) q^{17} +(-6.09693 + 3.52006i) q^{19} +(-1.51575 - 2.16853i) q^{21} +(0.406066 - 0.234442i) q^{23} +(-6.21752 + 10.7691i) q^{25} -1.00000i q^{27} -3.33885i q^{29} +(-1.58126 + 2.73883i) q^{31} +(-1.48174 + 0.855485i) q^{33} +(0.953738 + 11.0062i) q^{35} +(7.74648 - 4.47243i) q^{37} +(1.33422 + 0.770311i) q^{39} -5.31411i q^{41} +3.42772 q^{43} +(-2.08776 + 3.61611i) q^{45} +(2.95047 + 5.11037i) q^{47} +(4.49063 + 5.36975i) q^{49} +(-1.16679 - 2.02094i) q^{51} +(-1.35437 - 0.781947i) q^{53} +7.14421 q^{55} +7.04013 q^{57} +(5.26742 + 3.04114i) q^{59} +(4.55959 + 7.89744i) q^{61} +(0.228411 + 2.63587i) q^{63} +(-3.21646 - 5.57107i) q^{65} +(-3.73658 + 6.47195i) q^{67} -0.468884 q^{69} -3.49263i q^{71} +(-12.5811 - 7.26372i) q^{73} +(10.7691 - 6.21752i) q^{75} +(3.71029 - 2.59340i) q^{77} +(1.46108 - 0.843557i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.72601i q^{83} +9.74391i q^{85} +(-1.66943 + 2.89153i) q^{87} +(1.83829 - 1.06134i) q^{89} +(-3.69278 - 1.72569i) q^{91} +(2.73883 - 1.58126i) q^{93} +(-25.4579 - 14.6981i) q^{95} -1.95202i q^{97} +1.71097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more