LMFDB - Embedded newform 504.2.bk.c.451.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(19,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
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			451.5
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.c.19.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.647235 + 1.25741i) q^{2} +(-1.16217 - 1.62768i) q^{4} +(2.08776 + 3.61611i) q^{5} +(2.39694 + 1.12013i) q^{7} +(2.79887 - 0.407838i) q^{8} +(-5.89822 + 0.284706i) q^{10} +(0.855485 - 1.48174i) q^{11} +1.54062 q^{13} +(-2.95984 + 2.28896i) q^{14} +(-1.29871 + 3.78330i) q^{16} +(-2.02094 - 1.16679i) q^{17} +(6.09693 - 3.52006i) q^{19} +(3.45954 - 7.60077i) q^{20} +(1.30946 + 2.03473i) q^{22} +(-0.406066 + 0.234442i) q^{23} +(-6.21752 + 10.7691i) q^{25} +(-0.997145 + 1.93720i) q^{26} +(-0.962447 - 5.20324i) q^{28} -3.33885i q^{29} +(-1.58126 + 2.73883i) q^{31} +(-3.91660 - 4.08169i) q^{32} +(2.77516 - 1.78596i) q^{34} +(0.953738 + 11.0062i) q^{35} +(-7.74648 + 4.47243i) q^{37} +(0.480026 + 9.94467i) q^{38} +(7.31817 + 9.26956i) q^{40} +5.31411i q^{41} -3.42772 q^{43} +(-3.40603 + 0.329584i) q^{44} +(-0.0319706 - 0.662331i) q^{46} +(-2.95047 - 5.11037i) q^{47} +(4.49063 + 5.36975i) q^{49} +(-9.51696 - 14.7881i) q^{50} +(-1.79047 - 2.50765i) q^{52} +(-1.35437 - 0.781947i) q^{53} +7.14421 q^{55} +(7.16555 + 2.15753i) q^{56} +(4.19831 + 2.16102i) q^{58} +(5.26742 + 3.04114i) q^{59} +(-4.55959 - 7.89744i) q^{61} +(-2.42039 - 3.76097i) q^{62} +(7.66734 - 2.28297i) q^{64} +(3.21646 + 5.57107i) q^{65} +(3.73658 - 6.47195i) q^{67} +(0.449517 + 4.64545i) q^{68} +(-14.4566 - 5.92433i) q^{70} +3.49263i q^{71} +(-12.5811 - 7.26372i) q^{73} +(-0.609899 - 12.6352i) q^{74} +(-12.8152 - 5.83295i) q^{76} +(3.71029 - 2.59340i) q^{77} +(1.46108 - 0.843557i) q^{79} +(-16.3922 + 3.20237i) q^{80} +(-6.68203 - 3.43948i) q^{82} -2.72601i q^{83} -9.74391i q^{85} +(2.21854 - 4.31005i) q^{86} +(1.79008 - 4.49611i) q^{88} +(-1.83829 + 1.06134i) q^{89} +(3.69278 + 1.72569i) q^{91} +(0.853516 + 0.388484i) q^{92} +(8.33550 - 0.402352i) q^{94} +(25.4579 + 14.6981i) q^{95} -1.95202i q^{97} +(-9.65849 + 2.17109i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.647235	+	1.25741i	−0.457664	+	0.889125i
$2$	−0.647235	+	1.25741i	−0.457664	+	0.889125i
$3$		0			0
$3$		0			0
$4$	−1.16217	−	1.62768i	−0.581087	−	0.813842i
$5$	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
$8$	2.79887	−	0.407838i	0.989550	−	0.144192i
$9$		0			0
$10$	−5.89822	+	0.284706i	−1.86518	+	0.0900318i
$11$	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	$-0.431466\pi$
$13$	1.54062			0.427292			0.213646	+	0.976911i	$0.431466\pi$
$14$	−2.95984	+	2.28896i	−0.791052	+	0.611749i
$15$		0			0
$16$	−1.29871	+	3.78330i	−0.324676	+	0.945825i
$17$	−2.02094	−	1.16679i	−0.490149	−	0.282988i	0.234487	−	0.972119i	$-0.424659\pi$
$17$	−2.02094	−	1.16679i	−0.490149	−	0.282988i	−0.724636	+	0.689132i	$0.757992\pi$
$18$		0			0
$19$	6.09693	−	3.52006i	1.39873	−	0.807558i	0.404472	−	0.914551i	$-0.367455\pi$
$19$	6.09693	−	3.52006i	1.39873	−	0.807558i	0.994260	+	0.106992i	$0.0341221\pi$
$20$	3.45954	−	7.60077i	0.773578	−	1.69958i
$21$		0			0
$22$	1.30946	+	2.03473i	0.279179	+	0.433807i
$23$	−0.406066	+	0.234442i	−0.0846705	+	0.0488846i	−0.541737	−	0.840548i	$-0.682233\pi$
$23$	−0.406066	+	0.234442i	−0.0846705	+	0.0488846i	0.457067	+	0.889432i	$0.348900\pi$
$24$		0			0
$25$	−6.21752	+	10.7691i	−1.24350	+	2.15381i
$26$	−0.997145	+	1.93720i	−0.195556	+	0.379916i
$27$		0			0
$28$	−0.962447	−	5.20324i	−0.181885	−	0.983320i
$29$		−	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	$0.258329\pi$
$32$	−3.91660	−	4.08169i	−0.692364	−	0.721548i
$33$		0			0
$34$	2.77516	−	1.78596i	0.475935	−	0.306290i
$35$	0.953738	+	11.0062i	0.161211	+	1.86038i
$36$		0			0
$37$	−7.74648	+	4.47243i	−1.27351	+	0.735263i	−0.975647	−	0.219345i	$-0.929608\pi$
$37$	−7.74648	+	4.47243i	−1.27351	+	0.735263i	−0.297865	+	0.954608i	$0.596275\pi$
$38$	0.480026	+	9.94467i	0.0778705	+	1.61324i
$39$		0			0
$40$	7.31817	+	9.26956i	1.15710	+	1.46565i
$41$			5.31411i			0.829925i	0.909838	+	0.414963i	$0.136205\pi$
$41$			5.31411i			0.829925i	−0.909838	+	0.414963i	$0.863795\pi$
$42$		0			0
$43$	−3.42772			−0.522722			−0.261361	−	0.965241i	$-0.584171\pi$
$43$	−3.42772			−0.522722			−0.261361	+	0.965241i	$0.584171\pi$
$44$	−3.40603	+	0.329584i	−0.513479	+	0.0496867i
$45$		0			0
$46$	−0.0319706	−	0.662331i	−0.00471380	−	0.0976554i
$47$	−2.95047	−	5.11037i	−0.430371	−	0.745424i	0.566534	−	0.824038i	$-0.308284\pi$
$47$	−2.95047	−	5.11037i	−0.430371	−	0.745424i	−0.996905	+	0.0786139i	$0.974951\pi$
$48$		0			0
$49$	4.49063	+	5.36975i	0.641519	+	0.767107i
$50$	−9.51696	−	14.7881i	−1.34590	−	2.09135i
$51$		0			0
$52$	−1.79047	−	2.50765i	−0.248294	−	0.347748i
$53$	−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
$56$	7.16555	+	2.15753i	0.957537	+	0.288311i
$57$		0			0
$58$	4.19831	+	2.16102i	0.551266	+	0.283756i
$59$	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	$-0.968234\pi$
$61$	−4.55959	−	7.89744i	−0.583795	−	1.01116i	0.411229	−	0.911532i	$-0.365100\pi$
$62$	−2.42039	−	3.76097i	−0.307390	−	0.477643i
$63$		0			0
$64$	7.66734	−	2.28297i	0.958417	−	0.285371i
$65$	3.21646	+	5.57107i	0.398952	+	0.691006i
$66$		0			0
$67$	3.73658	−	6.47195i	0.456496	−	0.790675i	−0.542276	−	0.840200i	$-0.682437\pi$
$67$	3.73658	−	6.47195i	0.456496	−	0.790675i	0.998773	+	0.0495251i	$0.0157708\pi$
$68$	0.449517	+	4.64545i	0.0545119	+	0.563344i
$69$		0			0
$70$	−14.4566	−	5.92433i	−1.72789	−	0.708093i
$71$			3.49263i			0.414499i	0.978288	+	0.207249i	$0.0664512\pi$
$71$			3.49263i			0.414499i	−0.978288	+	0.207249i	$0.933549\pi$
$72$		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	$0.990158\pi$
$74$	−0.609899	−	12.6352i	−0.0708993	−	1.46882i
$75$		0			0
$76$	−12.8152	−	5.83295i	−1.47001	−	0.669085i
$77$	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	$0.303078\pi$
$80$	−16.3922	+	3.20237i	−1.83271	+	0.358036i
$81$		0			0
$82$	−6.68203	−	3.43948i	−0.737907	−	0.379827i
$83$		−	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
$86$	2.21854	−	4.31005i	0.239231	−	0.464765i
$87$		0			0
$88$	1.79008	−	4.49611i	0.190823	−	0.479287i
$89$	−1.83829	+	1.06134i	−0.194858	+	0.112501i	−0.594255	−	0.804277i	$-0.702553\pi$
$89$	−1.83829	+	1.06134i	−0.194858	+	0.112501i	0.399397	+	0.916778i	$0.369220\pi$
$90$		0			0
$91$	3.69278	+	1.72569i	0.387108	+	0.180902i
$92$	0.853516	+	0.388484i	0.0889852	+	0.0405022i
$93$		0			0
$94$	8.33550	−	0.402352i	0.859741	−	0.0414995i
$95$	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	$-0.0315960\pi$
$98$	−9.65849	+	2.17109i	−0.975655	+	0.219313i
$99$		0			0
$100$	24.7545	−	2.39536i	2.47545	−	0.239536i
$101$	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	$0.709776\pi$
$104$	4.31200	−	0.628324i	0.422826	−	0.0616123i
$105$		0			0
$106$	1.85983	−	1.19690i	0.180642	−	0.116253i
$107$	−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	0.633446	−	0.773787i	$-0.281640\pi$
$109$	2.92380	+	1.68806i	0.280050	+	0.161687i	−0.353396	+	0.935474i	$0.614973\pi$
$110$	−4.62398	+	8.98322i	−0.440879	+	0.856516i
$111$		0			0
$112$	−7.35069	+	7.61363i	−0.694575	+	0.719420i
$113$	10.7090			1.00742			0.503710	−	0.863873i	$-0.331968\pi$
$113$	10.7090			1.00742			0.503710	+	0.863873i	$0.331968\pi$
$114$		0			0
$115$	−1.69554	−	0.978920i	−0.158110	−	0.0912847i
$116$	−5.43459	+	3.88032i	−0.504589	+	0.360279i
$117$		0			0
$118$	−7.23323	+	4.65498i	−0.665873	+	0.428526i
$119$	−3.53711	−	5.06042i	−0.324246	−	0.463888i
$120$		0			0
$121$	4.03629	+	6.99106i	0.366935	+	0.635551i
$122$	12.8815	−	0.621785i	1.16623	−	0.0562937i
$123$		0			0
$124$	6.29565	−	0.609198i	0.565366	−	0.0547076i
$125$	−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	$-0.138454\pi$
$128$	−2.09193	+	11.1186i	−0.184903	+	0.982757i
$129$		0			0
$130$	−9.08693	+	0.438624i	−0.796977	+	0.0384699i
$131$	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
$134$	5.71947	+	8.88730i	0.494087	+	0.767746i
$135$		0			0
$136$	−6.13220	−	2.44147i	−0.525832	−	0.209355i
$137$	−5.99460	+	10.3829i	−0.512153	+	0.887075i	0.487748	+	0.872985i	$0.337819\pi$
$137$	−5.99460	+	10.3829i	−0.512153	+	0.887075i	−0.999901	+	0.0140902i	$0.995515\pi$
$138$		0			0
$139$		−	6.64909i		−	0.563968i	−0.959419	−	0.281984i	$-0.909007\pi$
$139$		−	6.64909i		−	0.563968i	0.959419	−	0.281984i	$-0.0909925\pi$
$140$	16.8061	−	14.3435i	1.42038	−	1.21224i
$141$		0			0
$142$	−4.39168	−	2.26055i	−0.368541	−	0.189701i
$143$	1.31798	−	2.28281i	0.110215	−	0.190898i
$144$		0			0
$145$	12.0737	−	6.97073i	1.00266	−	0.578888i
$146$	17.2764	−	11.1183i	1.42981	−	0.920160i
$147$		0			0
$148$	16.2824	+	7.41107i	1.33841	+	0.609186i
$149$	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	$0.650651\pi$
$152$	15.6289	−	12.3388i	1.26767	−	1.00081i
$153$		0			0
$154$	0.859544	+	6.34390i	0.0692640	+	0.511206i
$155$	−13.2052			−1.06067
$156$		0			0
$157$	4.80286	−	8.31880i	0.383310	−	0.663913i	−0.608223	−	0.793766i	$-0.708117\pi$
$157$	4.80286	−	8.31880i	0.383310	−	0.663913i	0.991533	+	0.129854i	$0.0414507\pi$
$158$	0.115035	+	2.38316i	0.00915167	+	0.189594i
$159$		0			0
$160$	6.58293	−	22.6845i	0.520426	−	1.79337i
$161$	−1.23592	+	0.107099i	−0.0974041	+	0.00844055i
$162$		0			0
$163$	9.70461	+	16.8089i	0.760123	+	1.31657i	0.942787	+	0.333397i	$0.108195\pi$
$163$	9.70461	+	16.8089i	0.760123	+	1.31657i	−0.182663	+	0.983176i	$0.558472\pi$
$164$	8.64969	−	6.17592i	0.675428	−	0.482258i
$165$		0			0
$166$	3.42773	+	1.76437i	0.266043	+	0.136942i
$167$	−17.7482			−1.37340			−0.686699	−	0.726942i	$-0.740941\pi$
$167$	−17.7482			−1.37340			−0.686699	+	0.726942i	$0.740941\pi$
$168$		0			0
$169$	−10.6265			−0.817422
$170$	12.2521	+	6.30660i	0.939695	+	0.483694i
$171$		0			0
$172$	3.98360	+	5.57924i	0.303747	+	0.425413i
$173$	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
$176$	4.49486	+	5.16091i	0.338813	+	0.389018i
$177$		0			0
$178$	−0.144733	−	2.99842i	−0.0108482	−	0.224741i
$179$	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	$-0.776768\pi$
$181$	−20.5572			−1.52800			−0.764002	+	0.645214i	$0.776768\pi$
$182$	−4.56000	+	3.52642i	−0.338010	+	0.261395i
$183$		0			0
$184$	−1.04091	+	0.821782i	−0.0767369	+	0.0605826i
$185$	−32.3456	−	18.6748i	−2.37810	−	1.37300i
$186$		0			0
$187$	−3.45776	+	1.99634i	−0.252857	+	0.145987i
$188$	−4.88910	+	10.7416i	−0.356575	+	0.783410i
$189$		0			0
$190$	−34.9589	+	22.4979i	−2.53618	+	1.63217i
$191$	−1.74523	+	1.00761i	−0.126280	+	0.0729079i	−0.561809	−	0.827267i	$-0.689895\pi$
$191$	−1.74523	+	1.00761i	−0.126280	+	0.0729079i	0.435529	+	0.900175i	$0.356561\pi$
$192$		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	$0.125646\pi$
$194$	2.45450	+	1.26342i	0.176223	+	0.0907081i
$195$		0			0
$196$	3.52136	−	13.5499i	0.251526	−	0.967851i
$197$			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	$-0.0492952\pi$
$200$	−13.0100	+	32.6769i	−0.919945	+	2.31061i
$201$		0			0
$202$	10.5470	+	16.3886i	0.742083	+	1.15310i
$203$	3.73994	−	8.00302i	0.262492	−	0.561702i
$204$		0			0
$205$	−19.2164	+	11.0946i	−1.34213	+	0.774882i
$206$	−10.8522	+	0.523831i	−0.756107	+	0.0364971i
$207$		0			0
$208$	−2.00082	+	5.82864i	−0.138732	+	0.404143i
$209$		−	12.0455i		−	0.833201i
$210$		0			0
$211$	−4.23050			−0.291240			−0.145620	−	0.989341i	$-0.546518\pi$
$211$	−4.23050			−0.291240			−0.145620	+	0.989341i	$0.546518\pi$
$212$	0.301253	+	3.11325i	0.0206901	+	0.213819i
$213$		0			0
$214$	20.3527	−	0.982418i	1.39128	−	0.0671567i
$215$	−7.15626	−	12.3950i	−0.488053	−	0.845333i
$216$		0			0
$217$	−6.85803	+	4.79359i	−0.465553	+	0.325410i
$218$	−4.01498	+	2.58386i	−0.271928	+	0.175001i
$219$		0			0
$220$	−8.30281	−	11.6285i	−0.559775	−	0.783994i
$221$	−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	$0.484697\pi$
$224$	−4.81584	−	14.1707i	−0.321772	−	0.946817i
$225$		0			0
$226$	−6.93126	+	13.4657i	−0.461060	+	0.895723i
$227$	−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	$0.0137435\pi$
$229$	8.12499	+	14.0729i	0.536914	+	0.929963i	−0.462154	+	0.886800i	$0.652923\pi$
$230$	2.32832	−	1.49840i	0.153525	−	0.0988016i
$231$		0			0
$232$	−1.36171	−	9.34501i	−0.0894006	−	0.613530i
$233$	5.93054	+	10.2720i	0.388522	+	0.672941i	0.992251	−	0.124249i	$-0.0396522\pi$
$233$	5.93054	+	10.2720i	0.388522	+	0.672941i	−0.603729	+	0.797190i	$0.706319\pi$
$234$		0			0
$235$	12.3198	−	21.3385i	0.803654	−	1.39197i
$236$	−1.17163	−	12.1080i	−0.0762667	−	0.788165i
$237$		0			0
$238$	8.65238	−	1.17232i	0.560851	−	0.0759904i
$239$			0.846585i			0.0547610i	0.999625	+	0.0273805i	$0.00871657\pi$
$239$			0.846585i			0.0547610i	−0.999625	+	0.0273805i	$0.991283\pi$
$240$		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	$0.675682\pi$
$242$	−11.4031	+	0.550423i	−0.733017	+	0.0353825i
$243$		0			0
$244$	−7.55549	+	16.5998i	−0.483691	+	1.06269i
$245$	−10.0422	+	27.4494i	−0.641575	+	1.75368i
$246$		0			0
$247$	9.39307	−	5.42309i	0.597667	−	0.345063i
$248$	−3.30875	+	8.31052i	−0.210106	+	0.527719i
$249$		0			0
$250$	20.0936	−	39.0367i	1.27083	−	2.46889i
$251$			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
$254$	11.9421	+	6.14704i	0.749316	+	0.385700i
$255$		0			0
$256$	−12.6267	−	9.82679i	−0.789170	−	0.614174i
$257$	−15.8902	+	9.17421i	−0.991203	+	0.572271i	−0.905634	−	0.424061i	$-0.860604\pi$
$257$	−15.8902	+	9.17421i	−0.991203	+	0.572271i	−0.0855695	+	0.996332i	$0.527271\pi$
$258$		0			0
$259$	−23.5775	+	2.04311i	−1.46504	+	0.126953i
$260$	5.32985	−	11.7099i	0.330543	−	0.726218i
$261$		0			0
$262$	0.931910	+	19.3063i	0.0575736	+	1.19275i
$263$	−3.02044	−	1.74385i	−0.186248	−	0.107531i	0.403977	−	0.914769i	$-0.367628\pi$
$263$	−3.02044	−	1.74385i	−0.186248	−	0.107531i	−0.590225	+	0.807239i	$0.700961\pi$
$264$		0			0
$265$		−	6.53008i		−	0.401140i
$266$	−9.98869	+	24.3744i	−0.612446	+	1.49449i
$267$		0			0
$268$	−14.8769	+	1.43956i	−0.908748	+	0.0879349i
$269$	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	$-0.373295\pi$
$272$	7.03891	−	6.13049i	0.426797	−	0.371716i
$273$		0			0
$274$	−9.17573	−	14.2579i	−0.554326	−	0.861350i
$275$	10.6380	+	18.4255i	0.641495	+	1.11110i
$276$		0			0
$277$	22.9034	+	13.2233i	1.37613	+	0.794510i	0.991691	−	0.128640i	$-0.0410613\pi$
$277$	22.9034	+	13.2233i	1.37613	+	0.794510i	0.384440	+	0.923150i	$0.374395\pi$
$278$	8.36065	+	4.30352i	0.501438	+	0.258108i
$279$		0			0
$280$	7.15812	+	30.4158i	0.427779	+	1.81769i
$281$	20.2837			1.21003			0.605013	−	0.796216i	$-0.293168\pi$
$281$	20.2837			1.21003			0.605013	+	0.796216i	$0.293168\pi$
$282$		0			0
$283$	5.70426	+	3.29336i	0.339083	+	0.195770i	0.659866	−	0.751383i	$-0.270613\pi$
$283$	5.70426	+	3.29336i	0.339083	+	0.195770i	−0.320783	+	0.947153i	$0.603946\pi$
$284$	5.68489	−	4.05904i	0.337336	−	0.240860i
$285$		0			0
$286$	2.01739	+	3.13476i	0.119291	+	0.185362i
$287$	−5.95248	+	12.7376i	−0.351364	+	0.751877i
$288$		0			0
$289$	−5.77721	−	10.0064i	−0.339836	−	0.588613i
$290$	0.950589	+	19.6933i	0.0558205	+	1.15643i
$291$		0			0
$292$	2.79842	+	28.9198i	0.163765	+	1.69240i
$293$	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
$296$	−19.8573	+	15.6771i	−1.15418	+	0.911210i
$297$		0			0
$298$	0.553586	+	11.4686i	0.0320684	+	0.664358i
$299$	−0.625594	+	0.361187i	−0.0361790	+	0.0208880i
$300$		0			0
$301$	−8.21603	−	3.83948i	−0.473564	−	0.221304i
$302$	−1.46993	+	0.945983i	−0.0845851	+	0.0544352i
$303$		0			0
$304$	5.39934	+	27.6380i	0.309674	+	1.58515i
$305$	19.0387	−	32.9760i	1.09015	−	1.88820i
$306$		0			0
$307$		−	11.8773i		−	0.677871i	−0.940810	−	0.338936i	$-0.889933\pi$
$307$		−	11.8773i		−	0.677871i	0.940810	−	0.338936i	$-0.110067\pi$
$308$	−8.53323	−	3.02519i	−0.486226	−	0.172376i
$309$		0			0
$310$	8.54688	−	16.6044i	0.485430	−	0.943067i
$311$	5.91849	−	10.2511i	0.335607	−	0.581288i	−0.647994	−	0.761645i	$-0.724392\pi$
$311$	5.91849	−	10.2511i	0.335607	−	0.581288i	0.983601	+	0.180357i	$0.0577253\pi$
$312$		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	$0.470939\pi$
$314$	7.35159	+	11.4234i	0.414874	+	0.644660i
$315$		0			0
$316$	−3.07107	−	1.39782i	−0.172761	−	0.0786336i
$317$	−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
$320$	24.2631	+	22.9597i	1.35635	+	1.28348i
$321$		0			0
$322$	0.665263	−	1.62338i	0.0370737	−	0.0904674i
$323$	−16.4287			−0.914116
$324$		0			0
$325$	−9.57885	+	16.5911i	−0.531339	+	0.920306i
$326$	−27.4168	+	1.32340i	−1.51848	+	0.0732966i
$327$		0			0
$328$	2.16730	+	14.8735i	0.119669	+	0.821252i
$329$	−1.34784	−	15.5542i	−0.0743090	−	0.857528i
$330$		0			0
$331$	2.37285	+	4.10989i	0.130424	+	0.225900i	0.923840	−	0.382779i	$-0.125033\pi$
$331$	2.37285	+	4.10989i	0.130424	+	0.225900i	−0.793416	+	0.608679i	$0.791700\pi$
$332$	−4.43709	+	3.16810i	−0.243517	+	0.173872i
$333$		0			0
$334$	11.4873	−	22.3168i	0.628555	−	1.22112i
$335$	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	$0.351468\pi$
$338$	6.87783	−	13.3619i	0.374105	−	0.726790i
$339$		0			0
$340$	−15.8600	+	11.3241i	−0.860130	+	0.614137i
$341$	2.70549	+	4.68605i	0.146511	+	0.253764i
$342$		0			0
$343$	4.74897	+	17.9010i	0.256420	+	0.966565i
$344$	−9.59373	+	1.39795i	−0.517259	+	0.0753726i
$345$		0			0
$346$	−10.0879	+	0.486938i	−0.542327	+	0.0261780i
$347$	−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	$-0.478706\pi$
$349$	2.49767			0.133697			0.0668485	+	0.997763i	$0.478706\pi$
$350$	−6.24702	−	46.1064i	−0.333917	−	2.46449i
$351$		0			0
$352$	−9.39862	+	2.31157i	−0.500948	+	0.123207i
$353$	22.3071	+	12.8790i	1.18729	+	0.685481i	0.957689	−	0.287805i	$-0.0929254\pi$
$353$	22.3071	+	12.8790i	1.18729	+	0.685481i	0.229599	+	0.973285i	$0.426259\pi$
$354$		0			0
$355$	−12.6297	+	7.29179i	−0.670317	+	0.387008i
$356$	3.86393	+	1.75869i	0.204788	+	0.0932105i
$357$		0			0
$358$	18.3039	+	28.4419i	0.967391	+	1.50320i
$359$	−28.7697	+	16.6102i	−1.51840	+	0.876651i	−0.518639	+	0.854993i	$0.673561\pi$
$359$	−28.7697	+	16.6102i	−1.51840	+	0.876651i	−0.999765	+	0.0216582i	$0.993105\pi$
$360$		0			0
$361$	15.2817	−	26.4687i	0.804300	−	1.39309i
$362$	13.3053	−	25.8489i	0.699313	−	1.35859i
$363$		0			0
$364$	−1.48277	−	8.01623i	−0.0777182	−	0.420164i
$365$		−	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	$0.130436\pi$
$368$	−0.359605	−	1.84074i	−0.0187457	−	0.0959552i
$369$		0			0
$370$	44.4171	−	28.5849i	2.30914	−	1.48606i
$371$	−2.37047	−	3.39135i	−0.123068	−	0.176070i
$372$		0			0
$373$	11.0943	−	6.40533i	0.574444	−	0.331655i	−0.184479	−	0.982837i	$-0.559060\pi$
$373$	11.0943	−	6.40533i	0.574444	−	0.331655i	0.758922	+	0.651181i	$0.225726\pi$
$374$	−0.272238	−	5.63994i	−0.0140771	−	0.291634i
$375$		0			0
$376$	−10.3422	−	13.0999i	−0.533358	−	0.675578i
$377$		−	5.14391i		−	0.264925i
$378$		0			0
$379$	−24.0807			−1.23694			−0.618472	−	0.785807i	$-0.712248\pi$
$379$	−24.0807			−1.23694			−0.618472	+	0.785807i	$0.712248\pi$
$380$	−5.66260	−	58.5192i	−0.290485	−	3.00197i
$381$		0			0
$382$	−0.137406	−	2.84663i	−0.00703030	−	0.145646i
$383$	−8.78233	−	15.2114i	−0.448756	−	0.777268i	0.549549	−	0.835461i	$-0.314799\pi$
$383$	−8.78233	−	15.2114i	−0.448756	−	0.777268i	−0.998305	+	0.0581930i	$0.981466\pi$
$384$		0			0
$385$	17.1242	+	8.00242i	0.872731	+	0.407841i
$386$	2.73278	+	4.24638i	0.139095	+	0.216135i
$387$		0			0
$388$	−3.17728	+	2.26859i	−0.161302	+	0.115170i
$389$	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
$392$	14.7587	+	13.1978i	0.745426	+	0.666588i
$393$		0			0
$394$	−22.0541	−	11.3521i	−1.11107	−	0.571908i
$395$	6.10079	+	3.52229i	0.306964	+	0.177226i
$396$		0			0
$397$	−8.65850	−	14.9970i	−0.434558	−	0.752676i	0.562702	−	0.826660i	$-0.309762\pi$
$397$	−8.65850	−	14.9970i	−0.434558	−	0.752676i	−0.997259	+	0.0739841i	$0.976429\pi$
$398$	13.5516	+	21.0573i	0.679278	+	1.05551i
$399$		0			0
$400$	−32.6679	−	37.5086i	−1.63339	−	1.87543i
$401$	3.87616	+	6.71371i	0.193566	+	0.335266i	0.946430	−	0.322910i	$-0.104661\pi$
$401$	3.87616	+	6.71371i	0.193566	+	0.335266i	−0.752863	+	0.658177i	$0.771328\pi$
$402$		0			0
$403$	−2.43613	+	4.21950i	−0.121352	+	0.210188i
$404$	−27.4337	+	2.65462i	−1.36488	+	0.132072i
$405$		0			0
$406$	7.64248	+	9.88248i	0.379290	+	0.490459i
$407$			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	$0.703250\pi$
$410$	−1.51296	−	31.3438i	−0.0747196	−	1.54796i
$411$		0			0
$412$	6.36524	−	13.9847i	0.313593	−	0.688977i
$413$	9.21921	+	13.1896i	0.453648	+	0.649018i
$414$		0			0
$415$	9.85758	−	5.69128i	0.483889	−	0.279374i
$416$	−6.03401	−	6.28835i	−0.295841	−	0.308312i
$417$		0			0
$418$	15.1461	+	7.79624i	0.740820	+	0.381327i
$419$			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	$-0.837844\pi$
$421$		−	20.0126i		−	0.975356i	0.873024	−	0.487678i	$-0.162156\pi$
$422$	2.73813	−	5.31948i	0.133290	−	0.258948i
$423$		0			0
$424$	−4.10962	−	1.63620i	−0.199581	−	0.0794610i
$425$	25.1304	−	14.5091i	1.21900	−	0.703793i
$426$		0			0
$427$	−2.08292	−	24.0370i	−0.100800	−	1.16323i
$428$	−11.9377	+	26.2276i	−0.577029	+	1.26776i
$429$		0			0
$430$	20.2174	−	0.975890i	0.974971	−	0.0470616i
$431$	−12.1099	−	6.99165i	−0.583313	−	0.336776i	0.179136	−	0.983824i	$-0.442670\pi$
$431$	−12.1099	−	6.99165i	−0.583313	−	0.336776i	−0.762449	+	0.647049i	$0.776003\pi$
$432$		0			0
$433$		−	0.984888i		−	0.0473307i	−0.999720	−	0.0236653i	$-0.992466\pi$
$433$		−	0.984888i		−	0.0473307i	0.999720	−	0.0236653i	$-0.00753362\pi$
$434$	−1.58876	−	11.7259i	−0.0762632	−	0.562864i
$435$		0			0
$436$	−0.650342	−	6.72084i	−0.0311457	−	0.321870i
$437$	−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	$0.780882\pi$
$440$	19.9957	−	2.91368i	0.953258	−	0.138904i
$441$		0			0
$442$	4.27547	−	2.75150i	0.203363	−	0.130875i
$443$	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
$446$	−0.928990	+	1.80479i	−0.0439890	+	0.0854593i
$447$		0			0
$448$	20.9354	+	3.11625i	0.989102	+	0.147229i
$449$	−32.9924			−1.55701			−0.778503	−	0.627641i	$-0.784021\pi$
$449$	−32.9924			−1.55701			−0.778503	+	0.627641i	$0.784021\pi$
$450$		0			0
$451$	7.87416	+	4.54615i	0.370780	+	0.214070i
$452$	−12.4457	−	17.4309i	−0.585399	−	0.819881i
$453$		0			0
$454$	19.0447	−	12.2563i	0.893814	−	0.575218i
$455$	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	$0.653902\pi$
$458$	−22.9542	+	1.10799i	−1.07258	+	0.0517731i
$459$		0			0
$460$	0.377139	+	3.89747i	0.0175842	+	0.181721i
$461$	−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	$0.979864\pi$
$464$	12.6319	+	4.33619i	0.586420	+	0.201302i
$465$		0			0
$466$	−16.7546	+	0.808739i	−0.776141	+	0.0374641i
$467$	−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
$470$	18.8575	+	29.3021i	0.869832	+	1.35160i
$471$		0			0
$472$	15.9831	+	6.36351i	0.735682	+	0.292904i
$473$	−2.93236	+	5.07900i	−0.134830	+	0.233533i
$474$		0			0
$475$			87.5443i			4.01681i
$476$	−4.12603	+	11.6384i	−0.189116	+	0.533445i
$477$		0			0
$478$	−1.06451	−	0.547939i	−0.0486894	−	0.0250622i
$479$	9.87511	−	17.1042i	0.451205	−	0.781511i	−0.547256	−	0.836965i	$-0.684328\pi$
$479$	9.87511	−	17.1042i	0.451205	−	0.781511i	0.998461	+	0.0554547i	$0.0176608\pi$
$480$		0			0
$481$	−11.9344	+	6.89033i	−0.544162	+	0.314172i
$482$	1.04559	−	0.672895i	0.0476253	−	0.0306495i
$483$		0			0
$484$	6.68836	−	14.6946i	0.304016	−	0.667937i
$485$	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	$0.984668\pi$
$488$	−15.9826	−	20.2443i	−0.723497	−	0.916417i
$489$		0			0
$490$	−28.0155	−	30.3935i	−1.26561	−	1.37304i
$491$	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
$494$	0.739539	+	15.3210i	0.0332734	+	0.689323i
$495$		0			0
$496$	−8.30821	−	9.53933i	−0.373050	−	0.428328i
$497$	−3.91219	+	8.37162i	−0.175486	+	0.375518i
$498$		0			0
$499$	−0.517579	−	0.896473i	−0.0231700	−	0.0401316i	0.854208	−	0.519932i	$-0.174043\pi$
$499$	−0.517579	−	0.896473i	−0.0231700	−	0.0401316i	−0.877378	+	0.479800i	$0.840709\pi$
$500$	36.0799	+	50.5318i	1.61354	+	2.25985i
$501$		0			0
$502$	−22.8146	−	11.7435i	−1.01826	−	0.524137i
$503$	19.7898			0.882382			0.441191	−	0.897413i	$-0.354556\pi$
$503$	19.7898			0.882382			0.441191	+	0.897413i	$0.354556\pi$
$504$		0			0
$505$	57.5425			2.56061
$506$	−1.00876	−	0.519243i	−0.0448447	−	0.0230831i
$507$		0			0
$508$	−15.4587	+	11.0376i	−0.685870	+	0.489715i
$509$	−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
$512$	20.5288	−	9.51676i	0.907253	−	0.420586i
$513$		0			0
$514$	−1.25107	−	25.9184i	−0.0551825	−	1.14321i
$515$	−16.0394	+	27.7811i	−0.706781	+	1.22418i
$516$		0			0
$517$	−10.0963			−0.444037
$518$	12.6912	−	30.9690i	0.557618	−	1.36070i
$519$		0			0
$520$	11.2745	+	14.2809i	0.494421	+	0.626259i
$521$	33.6570	+	19.4319i	1.47454	+	0.851326i	0.999588	−	0.0286855i	$-0.00913212\pi$
$521$	33.6570	+	19.4319i	1.47454	+	0.851326i	0.474952	+	0.880012i	$0.342465\pi$
$522$		0			0
$523$	14.8181	−	8.55526i	0.647952	−	0.374095i	−0.139719	−	0.990191i	$-0.544620\pi$
$523$	14.8181	−	8.55526i	0.647952	−	0.374095i	0.787671	+	0.616096i	$0.211287\pi$
$524$	−24.8791	−	11.3239i	−1.08685	−	0.494688i
$525$		0			0
$526$	4.14768	−	2.66926i	0.180847	−	0.116385i
$527$	6.39126	−	3.69000i	0.278408	−	0.160739i
$528$		0			0
$529$	−11.3901	+	19.7282i	−0.495221	+	0.857747i
$530$	8.21101	+	4.22650i	0.356663	+	0.183587i
$531$		0			0
$532$	−24.1837	−	28.3359i	−1.04850	−	1.22852i
$533$			8.18704i			0.354620i
$534$		0			0
$535$	30.0811	−	52.1019i	1.30052	−	2.25256i
$536$	7.81870	−	19.6381i	0.337717	−	0.848236i
$537$		0			0
$538$	11.2597	+	17.4960i	0.485439	+	0.754308i
$539$	11.7983	−	2.06023i	0.508187	−	0.0887402i
$540$		0			0
$541$	37.6652	−	21.7460i	1.61935	−	0.934935i	0.632268	−	0.774750i	$-0.282124\pi$
$541$	37.6652	−	21.7460i	1.61935	−	0.934935i	0.987087	−	0.160185i	$-0.0512092\pi$
$542$	28.1140	−	1.35706i	1.20760	−	0.0582906i
$543$		0			0
$544$	3.15273	+	12.8187i	0.135172	+	0.549597i
$545$			14.0971i			0.603852i
$546$		0			0
$547$	10.8290			0.463016			0.231508	−	0.972833i	$-0.425634\pi$
$547$	10.8290			0.463016			0.231508	+	0.972833i	$0.425634\pi$
$548$	23.8669	−	2.30948i	1.01954	−	0.0986560i
$549$		0			0
$550$	−30.0538	+	1.45069i	−1.28150	+	0.0618576i
$551$	−11.7530	−	20.3567i	−0.500693	−	0.867226i
$552$		0			0
$553$	4.44702	−	0.385356i	0.189106	−	0.0163870i
$554$	−31.4510	+	20.2404i	−1.33622	+	0.859934i
$555$		0			0
$556$	−10.8226	+	7.72739i	−0.458981	+	0.327714i
$557$	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
$560$	−42.8783	−	10.6855i	−1.81194	−	0.451544i
$561$		0			0
$562$	−13.1283	+	25.5050i	−0.553786	+	1.07586i
$563$	−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
$566$	−7.83310	+	5.04103i	−0.329250	+	0.211890i
$567$		0			0
$568$	1.42443	+	9.77541i	0.0597676	+	0.410167i
$569$	−10.1485	−	17.5778i	−0.425449	−	0.736900i	0.571013	−	0.820941i	$-0.306551\pi$
$569$	−10.1485	−	17.5778i	−0.425449	−	0.736900i	−0.996462	+	0.0840413i	$0.973217\pi$
$570$		0			0
$571$	−18.3819	+	31.8383i	−0.769257	+	1.33239i	0.168710	+	0.985666i	$0.446040\pi$
$571$	−18.3819	+	31.8383i	−0.769257	+	1.33239i	−0.937967	+	0.346726i	$0.887293\pi$
$572$	−5.24741	+	0.507765i	−0.219405	+	0.0212307i
$573$		0			0
$574$	−12.1638	−	15.7289i	−0.507706	−	0.656514i
$575$		−	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	$0.655960\pi$
$578$	16.3214	−	0.787830i	0.678881	−	0.0327694i
$579$		0			0
$580$	−25.3778	−	11.5509i	−1.05376	−	0.479625i
$581$	3.05348	−	6.53409i	0.126680	−	0.271080i
$582$		0			0
$583$	−2.31729	+	1.33789i	−0.0959723	+	0.0554097i
$584$	−38.1753	−	15.1991i	−1.57971	−	0.628945i
$585$		0			0
$586$	−8.37771	+	16.2758i	−0.346080	+	0.672345i
$587$		−	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
$590$	−31.9342	−	16.4377i	−1.31471	−	0.676729i
$591$		0			0
$592$	−6.86015	−	35.1156i	−0.281951	−	1.44324i
$593$	−32.3781	+	18.6935i	−1.32961	+	0.767650i	−0.985239	−	0.171184i	$-0.945241\pi$
$593$	−32.3781	+	18.6935i	−1.32961	+	0.767650i	−0.344370	+	0.938834i	$0.611908\pi$
$594$		0			0
$595$	10.9144	−	23.3556i	0.447447	−	0.957485i
$596$	−14.7791	−	6.72679i	−0.605374	−	0.275540i
$597$		0			0
$598$	−0.0492546	−	1.02040i	−0.00201417	−	0.0417274i
$599$	−8.61435	−	4.97350i	−0.351973	−	0.203212i	0.313581	−	0.949561i	$-0.398471\pi$
$599$	−8.61435	−	4.97350i	−0.351973	−	0.203212i	−0.665554	+	0.746350i	$0.731805\pi$
$600$		0			0
$601$		−	35.9296i		−	1.46560i	−0.680445	−	0.732799i	$-0.738214\pi$
$601$		−	35.9296i		−	1.46560i	0.680445	−	0.732799i	$-0.261786\pi$
$602$	10.1455	−	7.84589i	0.413500	−	0.319775i
$603$		0			0
$604$	−0.238098	−	2.46059i	−0.00968808	−	0.100120i
$605$	−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	$-0.373978\pi$
$608$	−38.2471	−	11.0991i	−1.55112	−	0.450128i
$609$		0			0
$610$	29.1419	+	45.2827i	1.17992	+	1.83344i
$611$	−4.54557	−	7.87315i	−0.183894	−	0.318514i
$612$		0			0
$613$	32.8160	+	18.9463i	1.32542	+	0.765234i	0.984588	−	0.174889i	$-0.0559566\pi$
$613$	32.8160	+	18.9463i	1.32542	+	0.765234i	0.340836	+	0.940123i	$0.389290\pi$
$614$	14.9346	+	7.68738i	0.602712	+	0.310238i
$615$		0			0
$616$	9.32692	−	8.77178i	0.375792	−	0.353425i
$617$	−39.0332			−1.57142			−0.785709	−	0.618597i	$-0.787702\pi$
$617$	−39.0332			−1.57142			−0.785709	+	0.618597i	$0.787702\pi$
$618$		0			0
$619$	−21.5338	−	12.4325i	−0.865517	−	0.499706i	0.000339137	−	1.00000i	$-0.499892\pi$
$619$	−21.5338	−	12.4325i	−0.865517	−	0.499706i	−0.865856	+	0.500294i	$0.833225\pi$
$620$	15.3468	+	21.4939i	0.616341	+	0.863216i
$621$		0			0
$622$	9.05924	+	14.0769i	0.363242	+	0.564431i
$623$	−5.59509	+	0.484842i	−0.224163	+	0.0194248i
$624$		0			0
$625$	−33.7275	−	58.4177i	−1.34910	−	2.33671i
$626$	−1.01079	−	20.9404i	−0.0403992	−	0.836947i
$627$		0			0
$628$	−19.1221	+	1.85035i	−0.763056	+	0.0738371i
$629$	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	$0.668260\pi$
$632$	3.74535	−	2.95689i	0.148982	−	0.117619i
$633$		0			0
$634$	−0.462536	−	9.58232i	−0.0183696	−	0.380563i
$635$	34.3436	−	19.8283i	1.36289	−	0.786862i
$636$		0			0
$637$	6.91837	+	8.27276i	0.274116	+	0.327779i
$638$	6.79368	−	4.37210i	0.268964	−	0.173093i
$639$		0			0
$640$	−44.5737	+	15.6484i	−1.76193	+	0.618557i
$641$	3.32559	−	5.76010i	0.131353	−	0.227510i	−0.792845	−	0.609423i	$-0.791401\pi$
$641$	3.32559	−	5.76010i	0.131353	−	0.227510i	0.924198	+	0.381913i	$0.124735\pi$
$642$		0			0
$643$			18.1066i			0.714055i	0.934094	+	0.357027i	$0.116210\pi$
$643$			18.1066i			0.714055i	−0.934094	+	0.357027i	$0.883790\pi$
$644$	1.61068	+	1.88722i	0.0634695	+	0.0743668i
$645$		0			0
$646$	10.6332	−	20.6576i	0.418358	−	0.812763i
$647$	24.6421	−	42.6815i	0.968783	−	1.67798i	0.269694	−	0.962946i	$-0.413077\pi$
$647$	24.6421	−	42.6815i	0.968783	−	1.67798i	0.699089	−	0.715035i	$-0.253589\pi$
$648$		0			0
$649$	9.01239	−	5.20331i	0.353767	−	0.204248i
$650$	−14.6620	−	22.7829i	−0.575092	−	0.893618i
$651$		0			0
$652$	16.0811	−	35.3308i	0.629784	−	1.38366i
$653$	−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
$656$	−20.1049	−	6.90147i	−0.784964	−	0.269457i
$657$		0			0
$658$	20.4304	+	8.37240i	0.796458	+	0.326390i
$659$	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	−0.741011	−	0.671493i	$-0.765654\pi$
$661$	5.42541	−	9.39708i	0.211024	−	0.365504i	0.952035	+	0.305988i	$0.0989869\pi$
$662$	−6.70362	+	0.323582i	−0.260544	+	0.0125764i
$663$		0			0
$664$	−1.11177	−	7.62976i	−0.0431451	−	0.296092i
$665$	44.5573	+	63.7466i	1.72786	+	2.47199i
$666$		0			0
$667$	0.782767	+	1.35579i	0.0303089	+	0.0524965i
$668$	20.6265	+	28.8885i	0.798063	+	1.11773i
$669$		0			0
$670$	−20.1966	+	39.2368i	−0.780263	+	1.51585i
$671$	−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	$0.879205\pi$
$674$	−10.6906	+	20.7691i	−0.411785	+	0.799994i
$675$		0			0
$676$	12.3498	+	17.2965i	0.474993	+	0.665252i
$677$	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
$680$	−3.97394	−	27.2719i	−0.152394	−	1.04583i
$681$		0			0
$682$	−7.64340	+	0.368945i	−0.292681	+	0.0141276i
$683$	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
$686$	−25.5827	−	5.61476i	−0.976752	−	0.214373i
$687$		0			0
$688$	4.45160	−	12.9681i	0.169715	−	0.494404i
$689$	−2.08658	−	1.20468i	−0.0794922	−	0.0458948i
$690$		0			0
$691$	11.9534	−	6.90129i	0.454728	−	0.262537i	−0.255097	−	0.966915i	$-0.582107\pi$
$691$	11.9534	−	6.90129i	0.454728	−	0.262537i	0.709825	+	0.704378i	$0.248774\pi$
$692$	5.91694	−	12.9998i	0.224928	−	0.494177i
$693$		0			0
$694$	−14.6177	−	22.7139i	−0.554879	−	0.862209i
$695$	24.0439	−	13.8817i	0.912035	−	0.526564i
$696$		0			0
$697$	6.20044	−	10.7395i	0.234859	−	0.406787i
$698$	−1.61658	+	3.14060i	−0.0611884	+	0.118873i
$699$		0			0
$700$	62.0180	+	21.9866i	2.34406	+	0.831015i
$701$		−	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
$704$	3.17652	−	13.3141i	0.119719	−	0.501793i
$705$		0			0
$706$	−30.6322	+	19.7135i	−1.15286	+	0.741927i
$707$	29.8843	−	20.8883i	1.12391	−	0.785587i
$708$		0			0
$709$	−27.1241	+	15.6601i	−1.01867	+	0.588127i	−0.913717	−	0.406350i	$-0.866801\pi$
$709$	−27.1241	+	15.6601i	−1.01867	+	0.588127i	−0.104949	+	0.994478i	$0.533468\pi$
$710$	−0.994371	−	20.6003i	−0.0373181	−	0.773116i
$711$		0			0
$712$	−4.71227	+	3.72026i	−0.176600	+	0.139423i
$713$		−	1.48286i		−	0.0555335i
$714$		0			0
$715$	11.0065			0.411621
$716$	−47.6101	+	4.60698i	−1.77927	+	0.172171i
$717$		0			0
$718$	−2.26511	−	46.9260i	−0.0845330	−	1.75126i
$719$	12.6273	+	21.8712i	0.470920	+	0.815657i	0.999447	−	0.0332594i	$-0.0105888\pi$
$719$	12.6273	+	21.8712i	0.470920	+	0.815657i	−0.528527	+	0.848917i	$0.677255\pi$
$720$		0			0
$721$	1.75479	+	20.2503i	0.0653518	+	0.754161i
$722$	23.3912	+	36.3469i	0.870530	+	1.35269i
$723$		0			0
$724$	23.8910	+	33.4606i	0.887903	+	1.24355i
$725$	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	$0.607916\pi$
$728$	11.0394	+	3.32393i	0.409148	+	0.123193i
$729$		0			0
$730$	76.2743	+	39.2611i	2.82304	+	1.45312i
$731$	6.92720	+	3.99942i	0.256212	+	0.147924i
$732$		0			0
$733$	6.16779	+	10.6829i	0.227813	+	0.394583i	0.957160	−	0.289561i	$-0.0935093\pi$
$733$	6.16779	+	10.6829i	0.227813	+	0.394583i	−0.729347	+	0.684144i	$0.760176\pi$
$734$	3.33048	+	5.17513i	0.122930	+	0.191018i
$735$		0			0
$736$	2.54732	+	0.739219i	0.0938954	+	0.0272480i
$737$	−6.39319	−	11.0733i	−0.235496	−	0.407891i
$738$		0			0
$739$	−21.7463	+	37.6656i	−0.799949	+	1.38555i	0.119699	+	0.992810i	$0.461807\pi$
$739$	−21.7463	+	37.6656i	−0.799949	+	1.38555i	−0.919648	+	0.392743i	$0.871526\pi$
$740$	7.19464	+	74.3518i	0.264480	+	2.73322i
$741$		0			0
$742$	5.79857	−	0.785656i	0.212872	−	0.0288424i
$743$			32.8397i			1.20477i	0.798205	+	0.602386i	$0.205783\pi$
$743$			32.8397i			1.20477i	−0.798205	+	0.602386i	$0.794217\pi$
$744$		0			0
$745$	29.3591	+	16.9505i	1.07563	+	0.621018i
$746$	0.873485	+	18.0959i	0.0319806	+	0.662539i
$747$		0			0
$748$	7.26793	+	3.30805i	0.265742	+	0.120954i
$749$	−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	$0.384701\pi$
$752$	23.1659	−	4.52566i	0.844772	−	0.165034i
$753$		0			0
$754$	6.46802	+	3.32932i	0.235551	+	0.121247i
$755$			5.16112i			0.187832i
$756$		0			0
$757$		−	16.9328i		−	0.615433i	−0.951478	−	0.307717i	$-0.900435\pi$
$757$		−	16.9328i		−	0.615433i	0.951478	−	0.307717i	$-0.0995649\pi$
$758$	15.5859	−	30.2794i	0.566105	−	1.09980i
$759$		0			0
$760$	77.2478	+	30.7554i	2.80207	+	1.11562i
$761$	−10.9108	+	6.29937i	−0.395517	+	0.228352i	−0.684548	−	0.728968i	$-0.740000\pi$
$761$	−10.9108	+	6.29937i	−0.395517	+	0.228352i	0.289031	+	0.957320i	$0.406667\pi$
$762$		0			0
$763$	5.11734	+	7.32121i	0.185260	+	0.265045i
$764$	3.66832	+	1.66966i	0.132715	+	0.0604063i
$765$		0			0
$766$	24.8113	−	1.19763i	0.896468	−	0.0432723i
$767$	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	$0.906581\pi$
$770$	−21.1457	+	16.3528i	−0.762040	+	0.589313i
$771$		0			0
$772$	−7.10820	+	0.687825i	−0.255830	+	0.0247554i
$773$	−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
$776$	−0.796109	−	5.46346i	−0.0285787	−	0.196127i
$777$		0			0
$778$	−32.8226	+	21.1231i	−1.17675	+	0.757301i
$779$	18.7060	+	32.3998i	0.670213	+	1.16084i
$780$		0			0
$781$	5.17518	+	2.98789i	0.185183	+	0.106915i
$782$	−0.708190	+	1.37583i	−0.0253248	+	0.0491997i
$783$		0			0
$784$	−26.1474	+	10.0157i	−0.933835	+	0.357703i
$785$	40.1090			1.43155
$786$		0			0
$787$	3.88976	+	2.24576i	0.138655	+	0.0800526i	0.567723	−	0.823220i	$-0.307825\pi$
$787$	3.88976	+	2.24576i	0.138655	+	0.0800526i	−0.429068	+	0.903272i	$0.641158\pi$
$788$	28.5484	−	20.3837i	1.01700	−	0.726140i
$789$		0			0
$790$	−8.37763	+	5.39146i	−0.298063	+	0.191820i
$791$	25.6689	+	11.9955i	0.912680	+	0.426510i
$792$		0			0
$793$	−7.02460	−	12.1670i	−0.249451	−	0.432062i
$794$	24.4615	−	1.18075i	0.868104	−	0.0419032i
$795$		0			0
$796$	−35.2488	+	3.41085i	−1.24936	+	0.120894i
$797$	−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
$800$	68.3076	−	16.8001i	2.41504	−	0.593974i
$801$		0			0
$802$	−10.9507	+	0.528587i	−0.386682	+	0.0186650i
$803$	−21.5259	+	12.4280i	−0.759634	+	0.438575i
$804$		0			0
$805$	−2.96759	−	4.24563i	−0.104594	−	0.149639i
$806$	−3.72890	−	5.79423i	−0.131345	−	0.204093i
$807$		0			0
$808$	14.4181	−	36.2136i	0.507226	−	1.27399i
$809$	12.5784	−	21.7864i	0.442232	−	0.765969i	−0.555623	−	0.831435i	$-0.687520\pi$
$809$	12.5784	−	21.7864i	0.442232	−	0.765969i	0.997855	+	0.0654659i	$0.0208534\pi$
$810$		0			0
$811$		−	48.0042i		−	1.68565i	−0.538184	−	0.842827i	$-0.680890\pi$
$811$		−	48.0042i		−	1.68565i	0.538184	−	0.842827i	$-0.319110\pi$
$812$	−17.3728	+	3.21347i	−0.609667	+	0.112771i
$813$		0			0
$814$	−19.2439	−	9.90554i	−0.674500	−	0.347189i
$815$	−40.5219	+	70.1859i	−1.41942	+	2.45851i
$816$		0			0
$817$	−20.8985	+	12.0658i	−0.731148	+	0.422128i
$818$	5.51607	−	3.54989i	0.192865	−	0.124119i
$819$		0			0
$820$	40.3914	+	18.3844i	1.41053	+	0.642011i
$821$	−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	$0.778607\pi$
$824$	13.4647	+	17.0551i	0.469066	+	0.594143i
$825$		0			0
$826$	−22.5518	+	3.05557i	−0.784677	+	0.106317i
$827$	−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	−0.694039	−	0.719937i	$-0.744171\pi$
$829$	7.96007	−	13.7872i	0.276465	−	0.478851i	0.970504	+	0.241087i	$0.0775038\pi$
$830$	0.776111	+	16.0786i	0.0269392	+	0.558098i
$831$		0			0
$832$	11.8125	−	3.51719i	0.409524	−	0.121937i
$833$	−2.80992	−	16.0915i	−0.0973580	−	0.557539i
$834$		0			0
$835$	−37.0541	−	64.1795i	−1.28231	−	2.22102i
$836$	−19.6062	+	13.9989i	−0.678094	+	0.484162i
$837$		0			0
$838$	−17.9079	−	9.21783i	−0.618618	−	0.318425i
$839$	−38.3305			−1.32332			−0.661658	−	0.749806i	$-0.730147\pi$
$839$	−38.3305			−1.32332			−0.661658	+	0.749806i	$0.730147\pi$
$840$		0			0
$841$	17.8521			0.615589
$842$	25.1641	+	12.9529i	0.867213	+	0.446385i
$843$		0			0
$844$	4.91657	+	6.88591i	0.169235	+	0.237023i
$845$	−22.1856	−	38.4266i	−0.763207	−	1.32191i
$846$		0			0
$847$	1.84387	+	21.2783i	0.0633561	+	0.731131i
$848$	4.71727	−	4.10848i	0.161992	−	0.141086i
$849$		0			0
$850$	1.97858	+	40.9901i	0.0678647	+	1.40595i
$851$	2.09705	−	3.63220i	0.0718860	−	0.124510i
$852$		0			0
$853$	−22.5158			−0.770927			−0.385463	−	0.922723i	$-0.625958\pi$
$853$	−22.5158			−0.770927			−0.385463	+	0.922723i	$0.625958\pi$
$854$	31.5726	+	12.9385i	1.08039	+	0.442746i
$855$		0			0
$856$	−25.2524	−	31.9860i	−0.863109	−	1.09326i
$857$	11.1913	+	6.46129i	0.382287	+	0.220713i	0.678813	−	0.734311i	$-0.262495\pi$
$857$	11.1913	+	6.46129i	0.382287	+	0.220713i	−0.296526	+	0.955025i	$0.595828\pi$
$858$		0			0
$859$	20.1418	−	11.6289i	0.687229	−	0.396772i	−0.115344	−	0.993326i	$-0.536797\pi$
$859$	20.1418	−	11.6289i	0.687229	−	0.396772i	0.802573	+	0.596554i	$0.203464\pi$
$860$	−11.8583	+	26.0533i	−0.404366	+	0.888410i
$861$		0			0
$862$	16.6293	−	10.7019i	0.566397	−	0.364508i
$863$	7.69412	−	4.44220i	0.261911	−	0.151214i	−0.363295	−	0.931674i	$-0.618348\pi$
$863$	7.69412	−	4.44220i	0.261911	−	0.151214i	0.625206	+	0.780460i	$0.285015\pi$
$864$		0			0
$865$	−14.9098	+	25.8245i	−0.506947	+	0.878059i
$866$	1.23841	+	0.637454i	0.0420829	+	0.0216616i
$867$		0			0
$868$	15.7727	+	5.59171i	0.535359	+	0.189795i
$869$		−	2.88660i		−	0.0979212i
$870$		0			0
$871$	5.75667	−	9.97084i	0.195057	−	0.337849i
$872$	8.87180	+	3.53222i	0.300437	+	0.119616i
$873$		0			0
$874$	−2.52637	−	3.92565i	−0.0854558	−	0.132787i
$875$	−74.4135	−	34.7746i	−2.51564	−	1.17560i
$876$		0			0
$877$	−40.2134	+	23.2172i	−1.35791	+	0.783990i	−0.989342	−	0.145610i	$-0.953485\pi$
$877$	−40.2134	+	23.2172i	−1.35791	+	0.783990i	−0.368569	+	0.929600i	$0.620152\pi$
$878$	−9.70981	+	0.468690i	−0.327690	+	0.0158175i
$879$		0			0
$880$	−9.27822	+	27.0287i	−0.312769	+	0.911137i
$881$		−	27.1901i		−	0.916058i	−0.888937	−	0.458029i	$-0.848556\pi$
$881$		−	27.1901i		−	0.916058i	0.888937	−	0.458029i	$-0.151444\pi$
$882$		0			0
$883$	−21.7975			−0.733543			−0.366772	−	0.930311i	$-0.619537\pi$
$883$	−21.7975			−0.733543			−0.366772	+	0.930311i	$0.619537\pi$
$884$	0.692536	+	7.15689i	0.0232925	+	0.240712i
$885$		0			0
$886$	−4.81638	+	0.232485i	−0.161809	+	0.00781049i
$887$	21.1661	+	36.6607i	0.710688	+	1.23095i	0.964599	+	0.263720i	$0.0849495\pi$
$887$	21.1661	+	36.6607i	0.710688	+	1.23095i	−0.253911	+	0.967227i	$0.581717\pi$
$888$		0			0
$889$	10.6383	−	22.7646i	0.356796	−	0.763502i
$890$	10.5405	−	6.78336i	0.353317	−	0.227379i
$891$		0			0
$892$	−1.66809	−	2.33625i	−0.0558519	−	0.0782234i
$893$	−35.9777	−	20.7717i	−1.20395	−	0.695099i
$894$		0			0
$895$	99.8629			3.33805
$896$	−17.4685	+	24.3074i	−0.583582	+	0.812054i
$897$		0			0
$898$	21.3538	−	41.4850i	0.712586	−	1.38437i
$899$	9.14454	+	5.27960i	0.304987	+	0.176085i
$900$		0			0
$901$	1.82473	+	3.16053i	0.0607906	+	0.105292i
$902$	−10.8128	+	6.95864i	−0.360027	+	0.231697i
$903$		0			0
$904$	29.9732	−	4.36755i	0.996892	−	0.145262i
$905$	−42.9186	−	74.3371i	−1.42666	−	2.47105i
$906$		0			0
$907$	22.5605	−	39.0760i	0.749109	−	1.29750i	−0.199141	−	0.979971i	$-0.563815\pi$
$907$	22.5605	−	39.0760i	0.749109	−	1.29750i	0.948250	−	0.317525i	$-0.102852\pi$
$908$	3.08485	+	31.8798i	0.102374	+	1.05797i
$909$		0			0
$910$	−22.2721	−	9.12716i	−0.738314	−	0.302562i
$911$		−	36.2714i		−	1.20173i	−0.799352	−	0.600863i	$-0.794824\pi$
$911$		−	36.2714i		−	1.20173i	0.799352	−	0.600863i	$-0.205176\pi$
$912$		0			0
$913$	−4.03926	−	2.33207i	−0.133680	−	0.0771801i
$914$	−32.2699	+	1.55766i	−1.06739	+	0.0515228i
$915$		0			0
$916$	13.4636	−	29.5801i	0.444849	−	0.977352i
$917$	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	$0.589063\pi$
$920$	−5.14483	−	2.04836i	−0.169620	−	0.0675325i
$921$		0			0
$922$	10.2744	−	19.9605i	0.338369	−	0.657364i
$923$			5.38082i			0.177112i
$924$		0			0
$925$		−	111.230i		−	3.65721i
$926$	−3.42090	−	1.76086i	−0.112418	−	0.0578654i
$927$		0			0
$928$	−13.6282	+	13.0770i	−0.447367	+	0.429272i
$929$	−10.2075	+	5.89332i	−0.334898	+	0.193354i	−0.658014	−	0.753006i	$-0.728603\pi$
$929$	−10.2075	+	5.89332i	−0.334898	+	0.193354i	0.323115	+	0.946360i	$0.395270\pi$
$930$		0			0
$931$	46.2809	+	16.9317i	1.51680	+	0.554913i
$932$	9.82724	−	21.5909i	0.321902	−	0.707233i
$933$		0			0
$934$	−1.63548	−	33.8820i	−0.0535144	−	1.10865i
$935$	−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	$0.805949\pi$
$938$	3.75431	+	27.7089i	0.122583	+	0.904726i
$939$		0			0
$940$	−49.0501	+	4.74632i	−1.59984	+	0.154808i
$941$	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
$944$	−18.3464	+	15.9787i	−0.597124	+	0.520061i
$945$		0			0
$946$	−4.48847	−	6.97449i	−0.145933	−	0.226760i
$947$	−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
$950$	−110.079	−	56.6617i	−3.57144	−	1.83835i
$951$		0			0
$952$	−11.9637	−	12.7209i	−0.387747	−	0.412287i
$953$	11.8761			0.384706			0.192353	−	0.981326i	$-0.438388\pi$
$953$	11.8761			0.384706			0.192353	+	0.981326i	$0.438388\pi$
$954$		0			0
$955$	−7.28724	−	4.20729i	−0.235810	−	0.136145i
$956$	1.37797	−	0.983878i	0.0445668	−	0.0318209i
$957$		0			0
$958$	15.1155	+	23.4875i	0.488360	+	0.758848i
$959$	−25.9989	+	18.1726i	−0.839548	+	0.586823i
$960$		0			0
$961$	10.4992	+	18.1852i	0.338684	+	0.586618i
$962$	−0.939624	−	19.4661i	−0.0302947	−	0.627613i
$963$		0			0
$964$	0.169364	+	1.75026i	0.00545484	+	0.0563721i
$965$	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	$0.598833\pi$
$968$	14.1483	+	17.9209i	0.454742	+	0.576000i
$969$		0			0
$970$	0.555752	+	11.5135i	0.0178441	+	0.369675i
$971$	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
$974$	44.1396	−	28.4062i	1.41432	−	0.910194i
$975$		0			0
$976$	35.7999	−	6.99384i	1.14593	−	0.223867i
$977$	−26.6049	+	46.0810i	−0.851165	+	1.47426i	0.0289924	+	0.999580i	$0.490770\pi$
$977$	−26.6049	+	46.0810i	−0.851165	+	1.47426i	−0.880158	+	0.474682i	$0.842563\pi$
$978$		0			0
$979$			3.63183i			0.116074i
$980$	56.3498	−	15.5554i	1.80003	−	0.496899i
$981$		0			0
$982$	−13.3166	+	25.8707i	−0.424949	+	0.825568i
$983$	13.9737	−	24.2032i	0.445693	−	0.771963i	−0.552407	−	0.833574i	$-0.686291\pi$
$983$	13.9737	−	24.2032i	0.445693	−	0.771963i	0.998100	+	0.0616113i	$0.0196239\pi$
$984$		0			0
$985$	−63.4241	+	36.6179i	−2.02086	+	1.16674i
$986$	−5.96307	−	9.26583i	−0.189903	−	0.295084i
$987$		0			0
$988$	−19.7434	−	8.98637i	−0.628123	−	0.285894i
$989$	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	$0.554628\pi$
$992$	17.3722	−	4.27267i	0.551569	−	0.135657i
$993$		0			0
$994$	−7.99448	−	10.3376i	−0.253569	−	0.327890i
$995$	73.9349			2.34389
$996$		0			0
$997$	−16.8274	+	29.1458i	−0.532928	+	0.923058i	0.466333	+	0.884609i	$0.345575\pi$
$997$	−16.8274	+	29.1458i	−0.532928	+	0.923058i	−0.999261	+	0.0384485i	$0.987758\pi$
$998$	1.46223	−	0.0705815i	0.0462861	−	0.00223422i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.1	✓	32	21.5	even	6
168.2.t.a.19.12	yes	32	168.131	odd	6
168.2.t.a.115.1	yes	32	24.11	even	2
168.2.t.a.115.12	yes	32	3.2	odd	2
504.2.bk.c.19.5		32	56.19	even	6	inner
504.2.bk.c.19.16		32	7.5	odd	6	inner
504.2.bk.c.451.5		32	1.1	even	1	trivial
504.2.bk.c.451.16		32	8.3	odd	2	inner
672.2.bb.a.271.1		32	168.5	even	6
672.2.bb.a.271.8		32	84.47	odd	6
672.2.bb.a.367.1		32	12.11	even	2
672.2.bb.a.367.8		32	24.5	odd	2
1176.2.p.a.979.17		32	168.59	odd	6
1176.2.p.a.979.18		32	168.11	even	6
1176.2.p.a.979.19		32	21.11	odd	6
1176.2.p.a.979.20		32	21.17	even	6
2016.2.bs.c.271.1		32	28.19	even	6
2016.2.bs.c.271.16		32	56.5	odd	6
2016.2.bs.c.1711.1		32	8.5	even	2
2016.2.bs.c.1711.16		32	4.3	odd	2
4704.2.p.a.3919.5		32	84.59	odd	6
4704.2.p.a.3919.6		32	168.53	odd	6
4704.2.p.a.3919.23		32	168.101	even	6
4704.2.p.a.3919.24		32	84.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647235 + 1.25741i) q^{2} +(-1.16217 - 1.62768i) q^{4} +(2.08776 + 3.61611i) q^{5} +(2.39694 + 1.12013i) q^{7} +(2.79887 - 0.407838i) q^{8} +(-5.89822 + 0.284706i) q^{10} +(0.855485 - 1.48174i) q^{11} +1.54062 q^{13} +(-2.95984 + 2.28896i) q^{14} +(-1.29871 + 3.78330i) q^{16} +(-2.02094 - 1.16679i) q^{17} +(6.09693 - 3.52006i) q^{19} +(3.45954 - 7.60077i) q^{20} +(1.30946 + 2.03473i) q^{22} +(-0.406066 + 0.234442i) q^{23} +(-6.21752 + 10.7691i) q^{25} +(-0.997145 + 1.93720i) q^{26} +(-0.962447 - 5.20324i) q^{28} -3.33885i q^{29} +(-1.58126 + 2.73883i) q^{31} +(-3.91660 - 4.08169i) q^{32} +(2.77516 - 1.78596i) q^{34} +(0.953738 + 11.0062i) q^{35} +(-7.74648 + 4.47243i) q^{37} +(0.480026 + 9.94467i) q^{38} +(7.31817 + 9.26956i) q^{40} +5.31411i q^{41} -3.42772 q^{43} +(-3.40603 + 0.329584i) q^{44} +(-0.0319706 - 0.662331i) q^{46} +(-2.95047 - 5.11037i) q^{47} +(4.49063 + 5.36975i) q^{49} +(-9.51696 - 14.7881i) q^{50} +(-1.79047 - 2.50765i) q^{52} +(-1.35437 - 0.781947i) q^{53} +7.14421 q^{55} +(7.16555 + 2.15753i) q^{56} +(4.19831 + 2.16102i) q^{58} +(5.26742 + 3.04114i) q^{59} +(-4.55959 - 7.89744i) q^{61} +(-2.42039 - 3.76097i) q^{62} +(7.66734 - 2.28297i) q^{64} +(3.21646 + 5.57107i) q^{65} +(3.73658 - 6.47195i) q^{67} +(0.449517 + 4.64545i) q^{68} +(-14.4566 - 5.92433i) q^{70} +3.49263i q^{71} +(-12.5811 - 7.26372i) q^{73} +(-0.609899 - 12.6352i) q^{74} +(-12.8152 - 5.83295i) q^{76} +(3.71029 - 2.59340i) q^{77} +(1.46108 - 0.843557i) q^{79} +(-16.3922 + 3.20237i) q^{80} +(-6.68203 - 3.43948i) q^{82} -2.72601i q^{83} -9.74391i q^{85} +(2.21854 - 4.31005i) q^{86} +(1.79008 - 4.49611i) q^{88} +(-1.83829 + 1.06134i) q^{89} +(3.69278 + 1.72569i) q^{91} +(0.853516 + 0.388484i) q^{92} +(8.33550 - 0.402352i) q^{94} +(25.4579 + 14.6981i) q^{95} -1.95202i q^{97} +(-9.65849 + 2.17109i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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