LMFDB - Embedded newform 504.2.bk.c.451.16

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			451.16
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.c.19.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41257 + 0.0681843i) q^{2} +(1.99070 + 0.192630i) q^{4} +(-2.08776 - 3.61611i) q^{5} +(-2.39694 - 1.12013i) q^{7} +(2.79887 + 0.407838i) q^{8} +(-2.70255 - 5.25036i) q^{10} +(0.855485 - 1.48174i) q^{11} -1.54062 q^{13} +(-3.30947 - 1.74569i) q^{14} +(3.92579 + 0.766938i) q^{16} +(-2.02094 - 1.16679i) q^{17} +(6.09693 - 3.52006i) q^{19} +(-3.45954 - 7.60077i) q^{20} +(1.30946 - 2.03473i) q^{22} +(0.406066 - 0.234442i) q^{23} +(-6.21752 + 10.7691i) q^{25} +(-2.17624 - 0.105046i) q^{26} +(-4.55582 - 2.69156i) q^{28} +3.33885i q^{29} +(1.58126 - 2.73883i) q^{31} +(5.49315 + 1.35103i) q^{32} +(-2.77516 - 1.78596i) q^{34} +(0.953738 + 11.0062i) q^{35} +(7.74648 - 4.47243i) q^{37} +(8.85235 - 4.55662i) q^{38} +(-4.36859 - 10.9725i) q^{40} +5.31411i q^{41} -3.42772 q^{43} +(1.98844 - 2.78492i) q^{44} +(0.589581 - 0.303478i) q^{46} +(2.95047 + 5.11037i) q^{47} +(4.49063 + 5.36975i) q^{49} +(-9.51696 + 14.7881i) q^{50} +(-3.06692 - 0.296770i) q^{52} +(1.35437 + 0.781947i) q^{53} -7.14421 q^{55} +(-6.25189 - 4.11265i) q^{56} +(-0.227657 + 4.71636i) q^{58} +(5.26742 + 3.04114i) q^{59} +(4.55959 + 7.89744i) q^{61} +(2.42039 - 3.76097i) q^{62} +(7.66734 + 2.28297i) q^{64} +(3.21646 + 5.57107i) q^{65} +(3.73658 - 6.47195i) q^{67} +(-3.79832 - 2.71202i) q^{68} +(0.596773 + 15.6120i) q^{70} -3.49263i q^{71} +(-12.5811 - 7.26372i) q^{73} +(11.2474 - 5.78943i) q^{74} +(12.8152 - 5.83295i) q^{76} +(-3.71029 + 2.59340i) q^{77} +(-1.46108 + 0.843557i) q^{79} +(-5.42278 - 15.7973i) q^{80} +(-0.362339 + 7.50655i) q^{82} -2.72601i q^{83} +9.74391i q^{85} +(-4.84189 - 0.233717i) q^{86} +(2.99870 - 3.79831i) q^{88} +(-1.83829 + 1.06134i) q^{89} +(3.69278 + 1.72569i) q^{91} +(0.853516 - 0.388484i) q^{92} +(3.81930 + 7.41993i) q^{94} +(-25.4579 - 14.6981i) q^{95} -1.95202i q^{97} +(5.97720 + 7.89133i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.41257	+	0.0681843i	0.998837	+	0.0482136i
$2$	1.41257	+	0.0681843i	0.998837	+	0.0482136i
$3$		0			0
$3$		0			0
$4$	1.99070	+	0.192630i	0.995351	+	0.0963150i
$5$	−2.08776	−	3.61611i	−0.933677	−	1.61718i	−0.776977	−	0.629529i	$-0.783248\pi$
$5$	−2.08776	−	3.61611i	−0.933677	−	1.61718i	−0.156700	−	0.987646i	$-0.550085\pi$
$6$		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
$10$	−2.70255	−	5.25036i	−0.854621	−	1.66031i
$11$	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	$0.568534\pi$
$14$	−3.30947	−	1.74569i	−0.884492	−	0.466555i
$15$		0			0
$16$	3.92579	+	0.766938i	0.981447	+	0.191735i
$17$	−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	−0.457067	−	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
$26$	−2.17624	−	0.105046i	−0.426795	−	0.0206013i
$27$		0			0
$28$	−4.55582	−	2.69156i	−0.860969	−	0.508657i
$29$			3.33885i			0.620009i	0.950735	+	0.310005i	$0.100331\pi$
$29$			3.33885i			0.620009i	−0.950735	+	0.310005i	$0.899669\pi$
$30$		0			0
$31$	1.58126	−	2.73883i	0.284003	−	0.491908i	−0.688364	−	0.725366i	$-0.741671\pi$
$31$	1.58126	−	2.73883i	0.284003	−	0.491908i	0.972367	+	0.233458i	$0.0750040\pi$
$32$	5.49315	+	1.35103i	0.971061	+	0.238831i
$33$		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	0.297865	−	0.954608i	$-0.403725\pi$
$37$	7.74648	−	4.47243i	1.27351	−	0.735263i	0.975647	+	0.219345i	$0.0703920\pi$
$38$	8.85235	−	4.55662i	1.43604	−	0.739181i
$39$		0			0
$40$	−4.36859	−	10.9725i	−0.690735	−	1.73490i
$41$			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	$0.584171\pi$
$44$	1.98844	−	2.78492i	0.299769	−	0.419842i
$45$		0			0
$46$	0.589581	−	0.303478i	0.0869290	−	0.0447454i
$47$	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
$50$	−9.51696	+	14.7881i	−1.34590	+	2.09135i
$51$		0			0
$52$	−3.06692	−	0.296770i	−0.425305	−	0.0411546i
$53$	1.35437	+	0.781947i	0.186037	+	0.107409i	0.590126	−	0.807311i	$-0.299078\pi$
$53$	1.35437	+	0.781947i	0.186037	+	0.107409i	−0.404089	+	0.914720i	$0.632411\pi$
$54$		0			0
$55$	−7.14421			−0.963325
$56$	−6.25189	−	4.11265i	−0.835444	−	0.549576i
$57$		0			0
$58$	−0.227657	+	4.71636i	−0.0298929	+	0.619288i
$59$	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	$0.634900\pi$
$62$	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	$0.0157708\pi$
$68$	−3.79832	−	2.71202i	−0.460614	−	0.328881i
$69$		0			0
$70$	0.596773	+	15.6120i	0.0713281	+	1.86599i
$71$		−	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	$0.990158\pi$
$74$	11.2474	−	5.78943i	1.30748	−	0.673007i
$75$		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	−0.579935	−	0.814662i	$-0.696922\pi$
$79$	−1.46108	+	0.843557i	−0.164385	+	0.0949075i	0.415551	+	0.909570i	$0.363589\pi$
$80$	−5.42278	−	15.7973i	−0.606286	−	1.76619i
$81$		0			0
$82$	−0.362339	+	7.50655i	−0.0400137	+	0.828960i
$83$		−	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
$86$	−4.84189	−	0.233717i	−0.522114	−	0.0252023i
$87$		0			0
$88$	2.99870	−	3.79831i	0.319663	−	0.404901i
$89$	−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
$94$	3.81930	+	7.41993i	0.393931	+	0.765307i
$95$	−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	$-0.0315960\pi$
$98$	5.97720	+	7.89133i	0.603788	+	0.797145i
$99$		0			0
$100$	−14.4517	+	20.2403i	−1.44517	+	2.02403i
$101$	−6.89045	+	11.9346i	−0.685625	+	1.18754i	0.287615	+	0.957746i	$0.407138\pi$
$101$	−6.89045	+	11.9346i	−0.685625	+	1.18754i	−0.973240	+	0.229792i	$0.926196\pi$
$102$		0			0
$103$	−3.84129	−	6.65331i	−0.378494	−	0.655570i	0.612350	−	0.790587i	$-0.290224\pi$
$103$	−3.84129	−	6.65331i	−0.378494	−	0.655570i	−0.990843	+	0.135017i	$0.956891\pi$
$104$	−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	0.353396	−	0.935474i	$-0.385027\pi$
$109$	−2.92380	−	1.68806i	−0.280050	−	0.161687i	−0.633446	+	0.773787i	$0.718360\pi$
$110$	−10.0917	−	0.487123i	−0.962204	−	0.0464453i
$111$		0			0
$112$	−8.55080	−	6.23568i	−0.807975	−	0.589217i
$113$	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
$116$	−0.643163	+	6.64666i	−0.0597162	+	0.617127i
$117$		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
$122$	5.90225	+	11.4666i	0.534365	+	1.03813i
$123$		0			0
$124$	3.67540	−	5.14759i	0.330061	−	0.462267i
$125$	31.0452			2.77677
$126$		0			0
$127$			9.49738i			0.842757i	0.906885	+	0.421378i	$0.138454\pi$
$127$			9.49738i			0.842757i	−0.906885	+	0.421378i	$0.861546\pi$
$128$	10.6750	+	3.74764i	0.943544	+	0.331248i
$129$		0			0
$130$	4.16361	+	8.08883i	0.365173	+	0.709437i
$131$	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
$136$	−5.18048	−	4.08990i	−0.444222	−	0.350706i
$137$	−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	$-0.0909925\pi$
$140$	−0.221510	+	22.0937i	−0.0187210	+	1.86726i
$141$		0			0
$142$	0.238143	−	4.93358i	0.0199845	−	0.414017i
$143$	−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	−0.759550	−	0.650448i	$-0.774581\pi$
$149$	−7.03123	+	4.05948i	−0.576021	+	0.332566i	0.183530	+	0.983014i	$0.441248\pi$
$150$		0			0
$151$	−1.07044	−	0.618020i	−0.0871113	−	0.0502937i	0.455812	−	0.890076i	$-0.349349\pi$
$151$	−1.07044	−	0.618020i	−0.0871113	−	0.0502937i	−0.542923	+	0.839783i	$0.682682\pi$
$152$	18.5001	−	7.36564i	1.50056	−	0.597432i
$153$		0			0
$154$	−5.41786	+	3.41037i	−0.436584	+	0.274815i
$155$	−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	$0.291883\pi$
$158$	−2.12140	+	1.09196i	−0.168769	+	0.0868716i
$159$		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	$0.558472\pi$
$164$	−1.02366	+	10.5788i	−0.0799343	+	0.826067i
$165$		0			0
$166$	0.185871	−	3.85068i	0.0144264	−	0.298871i
$167$	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
$170$	−0.664382	+	13.7639i	−0.0509558	+	1.05565i
$171$		0			0
$172$	−6.82356	−	0.660281i	−0.520292	−	0.0503460i
$173$	−3.57075	−	6.18472i	−0.271479	−	0.470216i	0.697762	−	0.716330i	$-0.254179\pi$
$173$	−3.57075	−	6.18472i	−0.271479	−	0.470216i	−0.969241	+	0.246114i	$0.920846\pi$
$174$		0			0
$175$	26.9657	−	18.8484i	2.03842	−	1.42480i
$176$	4.49486	−	5.16091i	0.338813	−	0.389018i
$177$		0			0
$178$	−2.66907	+	1.37387i	−0.200055	+	0.102976i
$179$	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	$0.223232\pi$
$182$	5.09864	+	2.68945i	0.377936	+	0.199355i
$183$		0			0
$184$	1.23214	−	0.490564i	0.0908345	−	0.0361648i
$185$	−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	−0.435529	−	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	$0.125646\pi$
$194$	0.133097	−	2.75737i	0.00955584	−	0.197967i
$195$		0			0
$196$	7.90514	+	11.5546i	0.564653	+	0.825329i
$197$		−	17.5393i		−	1.24962i	−0.780775	−	0.624812i	$-0.785176\pi$
$197$		−	17.5393i		−	1.24962i	0.780775	−	0.624812i	$-0.214824\pi$
$198$		0			0
$199$	−8.85336	+	15.3345i	−0.627598	+	1.08703i	0.360434	+	0.932785i	$0.382629\pi$
$199$	−8.85336	+	15.3345i	−0.627598	+	1.08703i	−0.988032	+	0.154247i	$0.950705\pi$
$200$	−21.7941	+	27.6054i	−1.54107	+	1.95200i
$201$		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
$206$	−4.97244	−	9.66017i	−0.346446	−	0.673056i
$207$		0			0
$208$	−6.04816	−	1.18156i	−0.419364	−	0.0819266i
$209$		−	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	$0.546518\pi$
$212$	2.54552	+	1.81752i	0.174827	+	0.124827i
$213$		0			0
$214$	−9.32554	−	18.1171i	−0.637481	−	1.23846i
$215$	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
$220$	−14.2220	−	1.37619i	−0.958846	−	0.0927827i
$221$	3.11350	+	1.79758i	0.209437	+	0.120918i
$222$		0			0
$223$	−1.43532			−0.0961162			−0.0480581	−	0.998845i	$-0.515303\pi$
$223$	−1.43532			−0.0961162			−0.0480581	+	0.998845i	$0.515303\pi$
$224$	−11.6534	−	9.39136i	−0.778627	−	0.627487i
$225$		0			0
$226$	15.1272	+	0.730187i	1.00625	+	0.0485713i
$227$	−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	$-0.347077\pi$
$230$	−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
$236$	9.90004	+	7.06867i	0.644438	+	0.460131i
$237$		0			0
$238$	4.65137	+	7.38937i	0.301504	+	0.478982i
$239$		−	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	$0.675682\pi$
$242$	5.22486	+	10.1506i	0.335867	+	0.652503i
$243$		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
$248$	5.54275	−	7.02072i	0.351965	−	0.445816i
$249$		0			0
$250$	43.8535	+	2.11680i	2.77354	+	0.133878i
$251$			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
$254$	−0.647573	+	13.4157i	−0.0406323	+	0.841776i
$255$		0			0
$256$	14.8236	+	6.02167i	0.926476	+	0.376354i
$257$	−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
$262$	17.1857	−	8.84609i	1.06174	−	0.546513i
$263$	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
$266$	−26.3225	+	1.00619i	−1.61394	+	0.0616933i
$267$		0			0
$268$	8.68512	−	12.1640i	0.530528	−	0.743032i
$269$	−7.35605	+	12.7410i	−0.448506	+	0.776835i	−0.998289	−	0.0584722i	$-0.981377\pi$
$269$	−7.35605	+	12.7410i	−0.448506	+	0.776835i	0.549783	+	0.835308i	$0.314710\pi$
$270$		0			0
$271$	9.95139	+	17.2363i	0.604504	+	1.04703i	0.992130	+	0.125215i	$0.0399619\pi$
$271$	9.95139	+	17.2363i	0.604504	+	1.04703i	−0.387626	+	0.921817i	$0.626705\pi$
$272$	−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	−0.384440	−	0.923150i	$-0.625605\pi$
$277$	−22.9034	−	13.2233i	−1.37613	−	0.794510i	−0.991691	+	0.128640i	$0.958939\pi$
$278$	0.453363	−	9.39229i	0.0271909	−	0.563312i
$279$		0			0
$280$	−1.81934	+	31.1938i	−0.108726	+	1.86419i
$281$	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	$0.603946\pi$
$284$	0.672785	−	6.95278i	0.0399225	−	0.412572i
$285$		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
$290$	17.5302	−	9.02341i	1.02941	−	0.529873i
$291$		0			0
$292$	−23.6461	−	16.8834i	−1.38378	−	0.988026i
$293$	−12.9438			−0.756187			−0.378094	−	0.925767i	$-0.623420\pi$
$293$	−12.9438			−0.756187			−0.378094	+	0.925767i	$0.623420\pi$
$294$		0			0
$295$		−	25.3968i		−	1.47866i
$296$	23.5054	−	9.35844i	1.36622	−	0.543948i
$297$		0			0
$298$	−10.2089	+	5.25488i	−0.591385	+	0.304407i
$299$	−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
$304$	26.6349	−	9.14305i	1.52762	−	0.524390i
$305$	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	$-0.110067\pi$
$308$	−7.88564	+	4.44797i	−0.449326	+	0.253447i
$309$		0			0
$310$	−18.6533	−	0.900389i	−1.05944	−	0.0511386i
$311$	−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	$0.470939\pi$
$314$	−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	−0.325863	−	0.945417i	$-0.605655\pi$
$317$	5.87478	−	3.39181i	0.329961	−	0.190503i	0.655824	+	0.754914i	$0.272322\pi$
$318$		0			0
$319$	4.94732	+	2.85634i	0.276997	+	0.159924i
$320$	−7.75211	−	32.4923i	−0.433356	−	1.81637i
$321$		0			0
$322$	−1.75312	+	0.0670137i	−0.0976978	+	0.00373453i
$323$	−16.4287			−0.914116
$324$		0			0
$325$	9.57885	−	16.5911i	0.531339	−	0.920306i
$326$	12.5623	+	24.4054i	0.695763	+	1.35169i
$327$		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	$0.791700\pi$
$332$	0.525112	−	5.42668i	0.0288193	−	0.297828i
$333$		0			0
$334$	25.0706	+	1.21015i	1.37180	+	0.0662164i
$335$	−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	$0.351468\pi$
$338$	−15.0106	−	0.724559i	−0.816471	−	0.0394108i
$339$		0			0
$340$	−1.87697	+	19.3972i	−0.101793	+	1.05196i
$341$	−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
$346$	−4.62223	−	8.97981i	−0.248493	−	0.482758i
$347$	−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	$0.521294\pi$
$350$	39.3761	−	24.7860i	2.10474	−	1.32487i
$351$		0			0
$352$	6.70119	−	6.98366i	0.357175	−	0.372230i
$353$	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	$-0.326439\pi$
$359$	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
$362$	29.0384	+	1.40168i	1.52623	+	0.0736705i
$363$		0			0
$364$	7.01880	+	4.14668i	0.367885	+	0.217345i
$365$			60.6597i			3.17507i
$366$		0			0
$367$	−2.17584	+	3.76866i	−0.113578	+	0.196722i	−0.917210	−	0.398403i	$-0.869564\pi$
$367$	−2.17584	+	3.76866i	−0.113578	+	0.196722i	0.803633	+	0.595126i	$0.202898\pi$
$368$	1.77393	−	0.608943i	0.0924725	−	0.0317433i
$369$		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	−0.758922	−	0.651181i	$-0.774274\pi$
$373$	−11.0943	+	6.40533i	−0.574444	+	0.331655i	0.184479	+	0.982837i	$0.440940\pi$
$374$	−5.02045	+	2.58420i	−0.259601	+	0.133626i
$375$		0			0
$376$	6.17379	+	15.5066i	0.318389	+	0.799691i
$377$		−	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	$0.712248\pi$
$380$	−47.8478	−	34.1635i	−2.45454	−	1.75255i
$381$		0			0
$382$	2.53396	−	1.30432i	0.129648	−	0.0667347i
$383$	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
$386$	2.73278	−	4.24638i	0.139095	−	0.216135i
$387$		0			0
$388$	0.376018	−	3.88590i	0.0190894	−	0.197277i
$389$	−23.9022	−	13.7999i	−1.21189	−	0.699685i	−0.248719	−	0.968576i	$-0.580010\pi$
$389$	−23.9022	−	13.7999i	−1.21189	−	0.699685i	−0.963171	+	0.268890i	$0.913343\pi$
$390$		0			0
$391$	−1.09418			−0.0553349
$392$	10.3787	+	16.8607i	0.524204	+	0.851593i
$393$		0			0
$394$	1.19591	−	24.7755i	0.0602488	−	1.24817i
$395$	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	$0.690238\pi$
$398$	−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
$404$	−16.0158	+	22.4309i	−0.796815	+	1.11598i
$405$		0			0
$406$	5.82860	−	11.0498i	0.289268	−	0.548393i
$407$		−	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	$0.703250\pi$
$410$	27.9010	−	14.3617i	1.37793	−	0.709271i
$411$		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
$416$	−8.46287	−	2.08143i	−0.414927	−	0.102050i
$417$		0			0
$418$	0.821311	−	17.0150i	0.0401716	−	0.832232i
$419$			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	$0.837844\pi$
$422$	−5.97587	−	0.288454i	−0.290901	−	0.0140417i
$423$		0			0
$424$	3.47180	+	2.74093i	0.168606	+	0.133111i
$425$	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
$430$	9.26357	+	17.9968i	0.446729	+	0.867881i
$431$	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	$-0.00753362\pi$
$434$	−10.0143	+	6.30367i	−0.480701	+	0.302586i
$435$		0			0
$436$	−5.49525	−	3.92363i	−0.263175	−	0.187908i
$437$	1.65050	−	2.85875i	0.0789542	−	0.136753i
$438$		0			0
$439$	−3.43693	−	5.95294i	−0.164036	−	0.284118i	0.772277	−	0.635286i	$-0.219118\pi$
$439$	−3.43693	−	5.95294i	−0.164036	−	0.284118i	−0.936312	+	0.351168i	$0.885785\pi$
$440$	−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
$446$	−2.02749	−	0.0978664i	−0.0960044	−	0.00463411i
$447$		0			0
$448$	−15.8209	−	14.0605i	−0.747468	−	0.664297i
$449$	−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
$452$	21.3185	+	2.06288i	1.00274	+	0.0970297i
$453$		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	$0.653902\pi$
$458$	−10.5176	−	20.4329i	−0.491453	−	0.954768i
$459$		0			0
$460$	−3.18674	−	2.27535i	−0.148583	−	0.106089i
$461$	15.8743			0.739338			0.369669	−	0.929164i	$-0.379471\pi$
$461$	15.8743			0.739338			0.369669	+	0.929164i	$0.379471\pi$
$462$		0			0
$463$		−	2.72059i		−	0.126436i	−0.998000	−	0.0632182i	$-0.979864\pi$
$463$		−	2.72059i		−	0.126436i	0.998000	−	0.0632182i	$-0.0201364\pi$
$464$	−2.56069	+	13.1076i	−0.118877	+	0.608506i
$465$		0			0
$466$	7.67691	+	14.9143i	0.355626	+	0.690890i
$467$	−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
$472$	13.5025	+	10.6600i	0.621504	+	0.490667i
$473$	−2.93236	+	5.07900i	−0.134830	+	0.233533i
$474$		0			0
$475$			87.5443i			4.01681i
$476$	6.06654	+	10.7551i	0.278060	+	0.492961i
$477$		0			0
$478$	0.0577238	−	1.19586i	0.00264022	−	0.0546973i
$479$	−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
$482$	−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	0.998840	−	0.0481495i	$-0.0153324\pi$
$487$	32.1435	+	18.5581i	1.45656	+	0.840946i	0.457721	+	0.889096i	$0.348666\pi$
$488$	9.54081	+	23.9635i	0.431892	+	1.08478i
$489$		0			0
$490$	16.0570	−	38.0895i	0.725381	−	1.72071i
$491$	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
$494$	−13.6381	+	7.02003i	−0.613608	+	0.315846i
$495$		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	$0.840709\pi$
$500$	61.8018	+	5.98024i	2.76386	+	0.267445i
$501$		0			0
$502$	−1.23714	+	25.6297i	−0.0552163	+	1.14391i
$503$	−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
$506$	0.0547007	−	1.13323i	0.00243174	−	0.0503782i
$507$		0			0
$508$	−1.82948	+	18.9065i	−0.0811701	+	0.838838i
$509$	2.11849	+	3.66933i	0.0939004	+	0.162640i	0.909149	−	0.416471i	$-0.136733\pi$
$509$	2.11849	+	3.66933i	0.0939004	+	0.162640i	−0.815249	+	0.579111i	$0.803400\pi$
$510$		0			0
$511$	22.0199	+	31.5031i	0.974104	+	1.39362i
$512$	20.5288	+	9.51676i	0.907253	+	0.420586i
$513$		0			0
$514$	−23.0715	+	11.8757i	−1.01764	+	0.523816i
$515$	−16.0394	+	27.7811i	−0.706781	+	1.22418i
$516$		0			0
$517$	10.0963			0.444037
$518$	−33.4442	+	1.27841i	−1.46945	+	0.0561703i
$519$		0			0
$520$	6.73035	+	16.9045i	0.295145	+	0.741310i
$521$	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
$530$	0.445249	−	9.22419i	0.0193404	−	0.400673i
$531$		0			0
$532$	−37.2510	−	0.373475i	−1.61503	−	0.0161922i
$533$		−	8.18704i		−	0.354620i
$534$		0			0
$535$	−30.0811	+	52.1019i	−1.30052	+	2.25256i
$536$	13.0977	−	16.5902i	0.565735	−	0.716589i
$537$		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	$0.717876\pi$
$541$	−37.6652	+	21.7460i	−1.61935	+	0.934935i	−0.987087	+	0.160185i	$0.948791\pi$
$542$	12.8818	+	25.0260i	0.553320	+	1.07496i
$543$		0			0
$544$	−9.52494	−	9.13969i	−0.408379	−	0.391861i
$545$			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	$0.425634\pi$
$548$	−13.9335	+	19.5146i	−0.595210	+	0.833623i
$549$		0			0
$550$	13.7706	+	26.7527i	0.587179	+	1.14074i
$551$	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
$556$	1.28081	−	13.2363i	0.0543186	−	0.561346i
$557$	−7.04197	−	4.06568i	−0.298378	−	0.172269i	0.343336	−	0.939213i	$-0.388443\pi$
$557$	−7.04197	−	4.06568i	−0.298378	−	0.172269i	−0.641714	+	0.766944i	$0.721776\pi$
$558$		0			0
$559$	5.28082			0.223355
$560$	−4.69687	+	43.9393i	−0.198479	+	1.85678i
$561$		0			0
$562$	28.6522	+	1.38303i	1.20862	+	0.0583397i
$563$	−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	$0.887293\pi$
$572$	−3.06344	+	4.29051i	−0.128089	+	0.179395i
$573$		0			0
$574$	9.27679	−	17.5869i	0.387206	−	0.734062i
$575$			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	$0.655960\pi$
$578$	−7.47843	−	14.5287i	−0.311062	−	0.604313i
$579$		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
$584$	−32.2505	−	25.4613i	−1.33454	−	1.05359i
$585$		0			0
$586$	−18.2841	−	0.882567i	−0.755308	−	0.0364585i
$587$		−	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
$590$	1.73166	−	35.8747i	0.0712914	−	1.47694i
$591$		0			0
$592$	33.8411	−	11.6167i	1.39086	−	0.477445i
$593$	−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
$598$	−0.908322	+	0.467546i	−0.0371440	+	0.0191194i
$599$	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	$-0.261786\pi$
$602$	11.3439	+	5.98373i	0.462343	+	0.243879i
$603$		0			0
$604$	−2.01188	−	1.43649i	−0.0818622	−	0.0584500i
$605$	16.8536	−	29.1914i	0.685198	−	1.18680i
$606$		0			0
$607$	14.9355	+	25.8690i	0.606212	+	1.04999i	0.991859	+	0.127344i	$0.0406451\pi$
$607$	14.9355	+	25.8690i	0.606212	+	1.04999i	−0.385646	+	0.922647i	$0.626022\pi$
$608$	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	−0.340836	−	0.940123i	$-0.610710\pi$
$613$	−32.8160	−	18.9463i	−1.32542	−	0.765234i	−0.984588	+	0.174889i	$0.944043\pi$
$614$	0.809843	−	16.7775i	0.0326826	−	0.677083i
$615$		0			0
$616$	−11.4423	+	5.74539i	−0.461023	+	0.231488i
$617$	−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	$0.833225\pi$
$620$	−26.2877	−	2.54372i	−1.05574	−	0.102158i
$621$		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
$626$	−18.6403	+	9.59483i	−0.745017	+	0.383487i
$627$		0			0
$628$	−11.1635	+	15.6351i	−0.445473	+	0.623908i
$629$	−20.8735			−0.832281
$630$		0			0
$631$		−	43.3823i		−	1.72702i	−0.504330	−	0.863511i	$-0.668260\pi$
$631$		−	43.3823i		−	1.72702i	0.504330	−	0.863511i	$-0.331740\pi$
$632$	−4.43341	+	1.76512i	−0.176352	+	0.0702127i
$633$		0			0
$634$	8.52980	−	4.39059i	0.338762	−	0.174373i
$635$	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
$640$	−8.73493	−	46.4261i	−0.345278	−	1.83515i
$641$	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	$0.883790\pi$
$644$	−2.48098	−	0.0248741i	−0.0977642	−	0.000980176i
$645$		0			0
$646$	−23.2066	−	1.12018i	−0.913053	−	0.0440728i
$647$	−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
$650$	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	−0.000563051	−	1.00000i	$-0.500179\pi$
$653$	22.1087	−	12.7645i	0.865181	−	0.499512i	0.865744	+	0.500488i	$0.166846\pi$
$654$		0			0
$655$	−49.4233	−	28.5345i	−1.93113	−	1.11494i
$656$	−4.07560	+	20.8621i	−0.159125	+	0.814527i
$657$		0			0
$658$	−0.843373	−	22.0632i	−0.0328781	−	0.860114i
$659$	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	$0.234346\pi$
$662$	3.07158	+	5.96730i	0.119380	+	0.231926i
$663$		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
$668$	35.3314	+	3.41884i	1.36701	+	0.132279i
$669$		0			0
$670$	−44.0784	−	2.12765i	−1.70290	−	0.0821984i
$671$	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	$0.879205\pi$
$674$	23.3318	+	1.12622i	0.898708	+	0.0433804i
$675$		0			0
$676$	−21.1542	−	2.04698i	−0.813621	−	0.0787300i
$677$	−2.56093	−	4.43567i	−0.0984246	−	0.170476i	0.812608	−	0.582810i	$-0.198047\pi$
$677$	−2.56093	−	4.43567i	−0.0984246	−	0.170476i	−0.911033	+	0.412334i	$0.864714\pi$
$678$		0			0
$679$	−2.18651	+	4.67888i	−0.0839107	+	0.179559i
$680$	−3.97394	+	27.2719i	−0.152394	+	1.04583i
$681$		0			0
$682$	−3.50218	−	6.80385i	−0.134105	−	0.260533i
$683$	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
$686$	−5.48768	−	25.6103i	−0.209521	−	0.977804i
$687$		0			0
$688$	−13.4565	−	2.62885i	−0.513024	−	0.100224i
$689$	−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
$698$	−3.52813	−	0.170302i	−0.133542	−	0.00644601i
$699$		0			0
$700$	57.3115	−	32.3271i	2.16617	−	1.22185i
$701$			11.8718i			0.448393i	0.974544	+	0.224196i	$0.0719757\pi$
$701$			11.8718i			0.448393i	−0.974544	+	0.224196i	$0.928024\pi$
$702$		0			0
$703$	31.4865	−	54.5362i	1.18754	−	2.05687i
$704$	9.94207	−	9.40798i	0.374706	−	0.354577i
$705$		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	0.104949	−	0.994478i	$-0.466532\pi$
$709$	27.1241	−	15.6601i	1.01867	−	0.588127i	0.913717	+	0.406350i	$0.133199\pi$
$710$	−18.3376	+	9.43900i	−0.688197	+	0.354239i
$711$		0			0
$712$	−5.57798	+	2.22082i	−0.209043	+	0.0832286i
$713$		−	1.48286i		−	0.0555335i
$714$		0			0
$715$	11.0065			0.411621
$716$	27.7948	−	38.9280i	1.03874	−	1.45481i
$717$		0			0
$718$	41.7717	−	21.5014i	1.55891	−	0.802424i
$719$	−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
$722$	23.3912	−	36.3469i	0.870530	−	1.35269i
$723$		0			0
$724$	40.9232	+	3.95993i	1.52090	+	0.147170i
$725$	−35.9563	−	20.7594i	−1.33538	−	0.770984i
$726$		0			0
$727$	17.9342			0.665144			0.332572	−	0.943078i	$-0.392084\pi$
$727$	17.9342			0.665144			0.332572	+	0.943078i	$0.392084\pi$
$728$	9.63180	+	6.33604i	0.356978	+	0.234829i
$729$		0			0
$730$	−4.13604	+	85.6860i	−0.153082	+	3.17138i
$731$	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	$0.906491\pi$
$734$	−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	$0.871526\pi$
$740$	−60.7932	−	43.4066i	−2.23480	−	1.59566i
$741$		0			0
$742$	−3.11721	−	4.95214i	−0.114436	−	0.181799i
$743$		−	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
$746$	−16.1083	+	8.29150i	−0.589766	+	0.303574i
$747$		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	−0.354352	−	0.935112i	$-0.615299\pi$
$751$	7.62670	−	4.40328i	0.278302	−	0.160678i	0.632655	+	0.774434i	$0.281965\pi$
$752$	7.66360	+	22.3251i	0.279463	+	0.814111i
$753$		0			0
$754$	0.350734	−	7.26613i	0.0127730	−	0.264617i
$755$			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	$0.900435\pi$
$758$	−34.0157	−	1.64193i	−1.23551	−	0.0596375i
$759$		0			0
$760$	−65.2589	−	51.5208i	−2.36719	−	1.86886i
$761$	−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
$766$	11.3685	+	22.0860i	0.410759	+	0.798000i
$767$	−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	$0.906581\pi$
$770$	23.6435	+	12.4716i	0.852053	+	0.449444i
$771$		0			0
$772$	4.14978	−	5.81197i	0.149354	−	0.209177i
$773$	9.15671	−	15.8599i	0.329344	−	0.570440i	−0.653038	−	0.757325i	$-0.726506\pi$
$773$	9.15671	−	15.8599i	0.329344	−	0.570440i	0.982382	+	0.186885i	$0.0598391\pi$
$774$		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
$782$	−1.54560	−	0.0746057i	−0.0552706	−	0.00266789i
$783$		0			0
$784$	13.5110	+	24.5245i	0.482536	+	0.875876i
$785$	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	$0.641158\pi$
$788$	3.37860	−	34.9155i	0.120358	−	1.24381i
$789$		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
$794$	11.2082	+	21.7746i	0.397763	+	0.772752i
$795$		0			0
$796$	−20.5783	+	28.8209i	−0.729378	+	1.02153i
$797$	31.7698			1.12534			0.562672	−	0.826680i	$-0.309773\pi$
$797$	31.7698			1.12534			0.562672	+	0.826680i	$0.309773\pi$
$798$		0			0
$799$		−	13.7703i		−	0.487159i
$800$	−48.7031	+	50.7560i	−1.72191	+	1.79450i
$801$		0			0
$802$	5.01757	+	9.74786i	0.177177	+	0.344209i
$803$	−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
$808$	−24.1528	+	30.5932i	−0.849694	+	1.07627i
$809$	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	$-0.319110\pi$
$812$	8.98672	−	15.2112i	0.315372	−	0.533809i
$813$		0			0
$814$	1.04352	−	21.6185i	0.0365753	−	0.757728i
$815$	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	−0.223402	−	0.974726i	$-0.571716\pi$
$821$	14.5854	−	8.42089i	0.509034	−	0.293891i	0.732437	+	0.680835i	$0.238383\pi$
$822$		0			0
$823$	17.1163	+	9.88209i	0.596636	+	0.344468i	0.767717	−	0.640789i	$-0.221393\pi$
$823$	17.1163	+	9.88209i	0.596636	+	0.344468i	−0.171081	+	0.985257i	$0.554726\pi$
$824$	−8.03780	−	20.1884i	−0.280010	−	0.703295i
$825$		0			0
$826$	−12.1234	−	19.2598i	−0.421829	−	0.670135i
$827$	−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	$0.255829\pi$
$830$	−14.3126	+	7.36719i	−0.496796	+	0.255719i
$831$		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
$836$	2.32032	−	23.9789i	0.0802498	−	0.829328i
$837$		0			0
$838$	−0.971071	+	20.1176i	−0.0335451	+	0.694951i
$839$	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
$842$	−1.36455	+	28.2692i	−0.0470254	+	0.974221i
$843$		0			0
$844$	−8.42166	−	0.814921i	−0.289886	−	0.0280507i
$845$	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
$850$	36.4877	−	18.7815i	1.25152	−	0.644202i
$851$	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	$0.374042\pi$
$854$	−1.30333	−	34.0959i	−0.0445989	−	1.16674i
$855$		0			0
$856$	−15.0745	−	37.8622i	−0.515234	−	1.29410i
$857$	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	−0.625206	−	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
$866$	0.0671539	−	1.39122i	0.00228198	−	0.0472756i
$867$		0			0
$868$	−14.5757	+	8.22154i	−0.494731	+	0.279057i
$869$			2.88660i			0.0979212i
$870$		0			0
$871$	−5.75667	+	9.97084i	−0.195057	+	0.337849i
$872$	−7.49489	−	5.91709i	−0.253809	−	0.200378i
$873$		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	0.368569	−	0.929600i	$-0.379848\pi$
$877$	40.2134	−	23.2172i	1.35791	−	0.783990i	0.989342	+	0.145610i	$0.0465145\pi$
$878$	−4.44901	−	8.64329i	−0.150147	−	0.291697i
$879$		0			0
$880$	−28.0466	−	5.47916i	−0.945452	−	0.184703i
$881$		−	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	$0.619537\pi$
$884$	5.85178	+	4.17820i	0.196817	+	0.140528i
$885$		0			0
$886$	2.20685	+	4.28735i	0.0741406	+	0.144036i
$887$	−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
$890$	10.5405	+	6.78336i	0.353317	+	0.227379i
$891$		0			0
$892$	−2.85730	−	0.276486i	−0.0956694	−	0.00925744i
$893$	35.9777	+	20.7717i	1.20395	+	0.695099i
$894$		0			0
$895$	−99.8629			−3.33805
$896$	−21.3894	−	20.9402i	−0.714571	−	0.699563i
$897$		0			0
$898$	−46.6040	−	2.24956i	−1.55520	−	0.0750689i
$899$	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	$-0.102852\pi$
$908$	−26.0663	−	18.6115i	−0.865041	−	0.617643i
$909$		0			0
$910$	−0.919403	−	24.0522i	−0.0304779	−	0.797322i
$911$			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
$914$	14.7860	+	28.7254i	0.489077	+	0.950152i
$915$		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	0.276164	−	0.961110i	$-0.410937\pi$
$919$	37.7905	−	21.8183i	1.24659	−	0.719721i	0.970428	+	0.241390i	$0.0776032\pi$
$920$	−4.34635	−	3.43137i	−0.143295	−	0.113129i
$921$		0			0
$922$	22.4235	+	1.08238i	0.738478	+	0.0356461i
$923$			5.38082i			0.177112i
$924$		0			0
$925$			111.230i			3.65721i
$926$	0.185501	−	3.84302i	0.00609595	−	0.126289i
$927$		0			0
$928$	−4.51089	+	18.3408i	−0.148077	+	0.602067i
$929$	−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
$934$	−30.1604	+	15.5247i	−0.986880	+	0.507982i
$935$	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	$0.805949\pi$
$938$	−23.6641	+	14.8958i	−0.772661	+	0.486365i
$939$		0			0
$940$	28.6355	−	40.1054i	0.933986	−	1.30809i
$941$	−14.2985	+	24.7658i	−0.466119	+	0.807342i	−0.999251	−	0.0386903i	$-0.987681\pi$
$941$	−14.2985	+	24.7658i	−0.466119	+	0.807342i	0.533132	+	0.846032i	$0.321015\pi$
$942$		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
$950$	−5.96915	+	123.662i	−0.193665	+	4.01213i
$951$		0			0
$952$	7.83608	+	15.6060i	0.253969	+	0.505794i
$953$	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
$956$	0.163078	−	1.68530i	0.00527431	−	0.0545064i
$957$		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
$962$	−17.3280	+	8.91932i	−0.558676	+	0.287571i
$963$		0			0
$964$	−1.43109	−	1.02180i	−0.0460922	−	0.0329101i
$965$	−14.9096			−0.479956
$966$		0			0
$967$		−	59.2193i		−	1.90437i	−0.305530	−	0.952183i	$-0.598833\pi$
$967$		−	59.2193i		−	1.90437i	0.305530	−	0.952183i	$-0.401167\pi$
$968$	8.44583	+	21.2132i	0.271459	+	0.681818i
$969$		0			0
$970$	−10.2488	+	5.27544i	−0.329070	+	0.169384i
$971$	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
$976$	11.8431	+	34.5006i	0.379089	+	1.10434i
$977$	−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
$980$	25.2787	−	52.7092i	0.807498	−	1.68373i
$981$		0			0
$982$	29.0630	+	1.40286i	0.927438	+	0.0447672i
$983$	−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
$986$	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	0.170776	−	0.985310i	$-0.445372\pi$
$991$	−18.7980	−	10.8530i	−0.597139	−	0.344758i	−0.767915	+	0.640552i	$0.778706\pi$
$992$	12.3864	−	12.9085i	0.393267	−	0.409844i
$993$		0			0
$994$	−6.09705	+	11.5587i	−0.193387	+	0.366621i
$995$	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	$-0.0122416\pi$
$998$	−0.669990	−	1.30162i	−0.0212082	−	0.0412021i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.41257 + 0.0681843i) q^{2} +(1.99070 + 0.192630i) q^{4} +(-2.08776 - 3.61611i) q^{5} +(-2.39694 - 1.12013i) q^{7} +(2.79887 + 0.407838i) q^{8} +(-2.70255 - 5.25036i) q^{10} +(0.855485 - 1.48174i) q^{11} -1.54062 q^{13} +(-3.30947 - 1.74569i) q^{14} +(3.92579 + 0.766938i) q^{16} +(-2.02094 - 1.16679i) q^{17} +(6.09693 - 3.52006i) q^{19} +(-3.45954 - 7.60077i) q^{20} +(1.30946 - 2.03473i) q^{22} +(0.406066 - 0.234442i) q^{23} +(-6.21752 + 10.7691i) q^{25} +(-2.17624 - 0.105046i) q^{26} +(-4.55582 - 2.69156i) q^{28} +3.33885i q^{29} +(1.58126 - 2.73883i) q^{31} +(5.49315 + 1.35103i) q^{32} +(-2.77516 - 1.78596i) q^{34} +(0.953738 + 11.0062i) q^{35} +(7.74648 - 4.47243i) q^{37} +(8.85235 - 4.55662i) q^{38} +(-4.36859 - 10.9725i) q^{40} +5.31411i q^{41} -3.42772 q^{43} +(1.98844 - 2.78492i) q^{44} +(0.589581 - 0.303478i) q^{46} +(2.95047 + 5.11037i) q^{47} +(4.49063 + 5.36975i) q^{49} +(-9.51696 + 14.7881i) q^{50} +(-3.06692 - 0.296770i) q^{52} +(1.35437 + 0.781947i) q^{53} -7.14421 q^{55} +(-6.25189 - 4.11265i) q^{56} +(-0.227657 + 4.71636i) q^{58} +(5.26742 + 3.04114i) q^{59} +(4.55959 + 7.89744i) q^{61} +(2.42039 - 3.76097i) q^{62} +(7.66734 + 2.28297i) q^{64} +(3.21646 + 5.57107i) q^{65} +(3.73658 - 6.47195i) q^{67} +(-3.79832 - 2.71202i) q^{68} +(0.596773 + 15.6120i) q^{70} -3.49263i q^{71} +(-12.5811 - 7.26372i) q^{73} +(11.2474 - 5.78943i) q^{74} +(12.8152 - 5.83295i) q^{76} +(-3.71029 + 2.59340i) q^{77} +(-1.46108 + 0.843557i) q^{79} +(-5.42278 - 15.7973i) q^{80} +(-0.362339 + 7.50655i) q^{82} -2.72601i q^{83} +9.74391i q^{85} +(-4.84189 - 0.233717i) q^{86} +(2.99870 - 3.79831i) q^{88} +(-1.83829 + 1.06134i) q^{89} +(3.69278 + 1.72569i) q^{91} +(0.853516 - 0.388484i) q^{92} +(3.81930 + 7.41993i) q^{94} +(-25.4579 - 14.6981i) q^{95} -1.95202i q^{97} +(5.97720 + 7.89133i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) \) 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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