LMFDB - Embedded newform 504.2.bk.c.451.10

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)

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);

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")

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			451.10
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.c.19.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.647418 + 1.25732i) q^{2} +(-1.16170 + 1.62802i) q^{4} +(1.61398 + 2.79550i) q^{5} +(-1.82725 + 1.91341i) q^{7} +(-2.79905 - 0.406616i) q^{8} +(-2.46991 + 3.83914i) q^{10} +(1.10660 - 1.91668i) q^{11} -5.08369 q^{13} +(-3.58876 - 1.05866i) q^{14} +(-1.30091 - 3.78254i) q^{16} +(2.73597 + 1.57961i) q^{17} +(2.93566 - 1.69490i) q^{19} +(-6.42609 - 0.619932i) q^{20} +(3.12631 + 0.150450i) q^{22} +(2.65351 - 1.53200i) q^{23} +(-2.70987 + 4.69363i) q^{25} +(-3.29127 - 6.39182i) q^{26} +(-0.992355 - 5.19762i) q^{28} +9.88340i q^{29} +(1.01402 - 1.75634i) q^{31} +(3.91363 - 4.08454i) q^{32} +(-0.214760 + 4.46266i) q^{34} +(-8.29809 - 2.01987i) q^{35} +(0.798374 - 0.460941i) q^{37} +(4.03163 + 2.59375i) q^{38} +(-3.38092 - 8.48100i) q^{40} +5.96303i q^{41} -6.68790 q^{43} +(1.83487 + 4.02817i) q^{44} +(3.64414 + 2.34446i) q^{46} +(1.06113 + 1.83793i) q^{47} +(-0.322287 - 6.99258i) q^{49} +(-7.65581 - 0.368427i) q^{50} +(5.90572 - 8.27636i) q^{52} +(-3.12560 - 1.80457i) q^{53} +7.14411 q^{55} +(5.89259 - 4.61274i) q^{56} +(-12.4266 + 6.39869i) q^{58} +(10.6351 + 6.14015i) q^{59} +(6.34115 + 10.9832i) q^{61} +(2.86477 + 0.137864i) q^{62} +(7.66933 + 2.27627i) q^{64} +(-8.20498 - 14.2114i) q^{65} +(-4.40720 + 7.63350i) q^{67} +(-5.75002 + 2.61918i) q^{68} +(-2.83271 - 11.7410i) q^{70} -11.7036i q^{71} +(7.82068 + 4.51527i) q^{73} +(1.09643 + 0.705388i) q^{74} +(-0.651014 + 6.74828i) q^{76} +(1.64537 + 5.61964i) q^{77} +(9.60105 - 5.54317i) q^{79} +(8.47445 - 9.74164i) q^{80} +(-7.49743 + 3.86057i) q^{82} +3.57322i q^{83} +10.1979i q^{85} +(-4.32987 - 8.40882i) q^{86} +(-3.87677 + 4.91493i) q^{88} +(6.32253 - 3.65032i) q^{89} +(9.28920 - 9.72719i) q^{91} +(-0.588444 + 6.09969i) q^{92} +(-1.62387 + 2.52409i) q^{94} +(9.47619 + 5.47108i) q^{95} -15.2238i q^{97} +(8.58324 - 4.93234i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.647418	+	1.25732i	0.457794	+	0.889058i
$2$	0.647418	+	1.25732i	0.457794	+	0.889058i
$3$		0			0
$3$		0			0
$4$	−1.16170	+	1.62802i	−0.580850	+	0.814011i
$5$	1.61398	+	2.79550i	0.721794	+	1.25018i	0.960280	+	0.279038i	$0.0900156\pi$
$5$	1.61398	+	2.79550i	0.721794	+	1.25018i	−0.238486	+	0.971146i	$0.576651\pi$
$6$		0			0
$7$	−1.82725	+	1.91341i	−0.690637	+	0.723202i
$7$	−1.82725	+	1.91341i	−0.690637	+	0.723202i
$8$	−2.79905	−	0.406616i	−0.989613	−	0.143760i
$9$		0			0
$10$	−2.46991	+	3.83914i	−0.781054	+	1.21404i
$11$	1.10660	−	1.91668i	0.333652	−	0.577902i	−0.649573	−	0.760299i	$-0.725052\pi$
$11$	1.10660	−	1.91668i	0.333652	−	0.577902i	0.983225	+	0.182397i	$0.0583857\pi$
$12$		0			0
$13$	−5.08369			−1.40996			−0.704981	−	0.709226i	$-0.749045\pi$
$13$	−5.08369			−1.40996			−0.704981	+	0.709226i	$0.749045\pi$
$14$	−3.58876	−	1.05866i	−0.959138	−	0.282940i
$15$		0			0
$16$	−1.30091	−	3.78254i	−0.325227	−	0.945636i
$17$	2.73597	+	1.57961i	0.663571	+	0.383113i	0.793636	−	0.608393i	$-0.208185\pi$
$17$	2.73597	+	1.57961i	0.663571	+	0.383113i	−0.130065	+	0.991505i	$0.541519\pi$
$18$		0			0
$19$	2.93566	−	1.69490i	0.673486	−	0.388838i	−0.123910	−	0.992293i	$-0.539543\pi$
$19$	2.93566	−	1.69490i	0.673486	−	0.388838i	0.797396	+	0.603456i	$0.206210\pi$
$20$	−6.42609	−	0.619932i	−1.43692	−	0.138621i
$21$		0			0
$22$	3.12631	+	0.150450i	0.666532	+	0.0320761i
$23$	2.65351	−	1.53200i	0.553294	−	0.319445i	−0.197155	−	0.980372i	$-0.563170\pi$
$23$	2.65351	−	1.53200i	0.553294	−	0.319445i	0.750450	+	0.660928i	$0.229837\pi$
$24$		0			0
$25$	−2.70987	+	4.69363i	−0.541974	+	0.938726i
$26$	−3.29127	−	6.39182i	−0.645472	−	1.25354i
$27$		0			0
$28$	−0.992355	−	5.19762i	−0.187538	−	0.982257i
$29$			9.88340i			1.83530i	0.397387	+	0.917651i	$0.369917\pi$
$29$			9.88340i			1.83530i	−0.397387	+	0.917651i	$0.630083\pi$
$30$		0			0
$31$	1.01402	−	1.75634i	0.182124	−	0.315448i	−0.760480	−	0.649362i	$-0.775036\pi$
$31$	1.01402	−	1.75634i	0.182124	−	0.315448i	0.942604	+	0.333914i	$0.108369\pi$
$32$	3.91363	−	4.08454i	0.691839	−	0.722052i
$33$		0			0
$34$	−0.214760	+	4.46266i	−0.0368311	+	0.765340i
$35$	−8.29809	−	2.01987i	−1.40263	−	0.341421i
$36$		0			0
$37$	0.798374	−	0.460941i	0.131252	−	0.0757783i	−0.432936	−	0.901424i	$-0.642523\pi$
$37$	0.798374	−	0.460941i	0.131252	−	0.0757783i	0.564188	+	0.825646i	$0.309189\pi$
$38$	4.03163	+	2.59375i	0.654017	+	0.420761i
$39$		0			0
$40$	−3.38092	−	8.48100i	−0.534570	−	1.34096i
$41$			5.96303i			0.931269i	0.884977	+	0.465635i	$0.154174\pi$
$41$			5.96303i			0.931269i	−0.884977	+	0.465635i	$0.845826\pi$
$42$		0			0
$43$	−6.68790			−1.01990			−0.509948	−	0.860205i	$-0.670335\pi$
$43$	−6.68790			−1.01990			−0.509948	+	0.860205i	$0.670335\pi$
$44$	1.83487	+	4.02817i	0.276617	+	0.607270i
$45$		0			0
$46$	3.64414	+	2.34446i	0.537300	+	0.345671i
$47$	1.06113	+	1.83793i	0.154782	+	0.268090i	0.932980	−	0.359929i	$-0.117199\pi$
$47$	1.06113	+	1.83793i	0.154782	+	0.268090i	−0.778198	+	0.628019i	$0.783866\pi$
$48$		0			0
$49$	−0.322287	−	6.99258i	−0.0460410	−	0.998940i
$50$	−7.65581	−	0.368427i	−1.08269	−	0.0521034i
$51$		0			0
$52$	5.90572	−	8.27636i	0.818976	−	1.14772i
$53$	−3.12560	−	1.80457i	−0.429334	−	0.247876i	0.269729	−	0.962936i	$-0.413066\pi$
$53$	−3.12560	−	1.80457i	−0.429334	−	0.247876i	−0.699063	+	0.715060i	$0.746399\pi$
$54$		0			0
$55$	7.14411			0.963311
$56$	5.89259	−	4.61274i	0.787431	−	0.616403i
$57$		0			0
$58$	−12.4266	+	6.39869i	−1.63169	+	0.840190i
$59$	10.6351	+	6.14015i	1.38457	+	0.799379i	0.992696	−	0.120642i	$-0.0384952\pi$
$59$	10.6351	+	6.14015i	1.38457	+	0.799379i	0.391869	+	0.920021i	$0.371828\pi$
$60$		0			0
$61$	6.34115	+	10.9832i	0.811901	+	1.40625i	0.911532	+	0.411230i	$0.134901\pi$
$61$	6.34115	+	10.9832i	0.811901	+	1.40625i	−0.0996301	+	0.995025i	$0.531766\pi$
$62$	2.86477	+	0.137864i	0.363827	+	0.0175087i
$63$		0			0
$64$	7.66933	+	2.27627i	0.958666	+	0.284534i
$65$	−8.20498	−	14.2114i	−1.01770	−	1.76271i
$66$		0			0
$67$	−4.40720	+	7.63350i	−0.538425	+	0.932580i	0.460564	+	0.887627i	$0.347647\pi$
$67$	−4.40720	+	7.63350i	−0.538425	+	0.932580i	−0.998989	+	0.0449534i	$0.985686\pi$
$68$	−5.75002	+	2.61918i	−0.697293	+	0.317623i
$69$		0			0
$70$	−2.83271	−	11.7410i	−0.338574	−	1.40332i
$71$		−	11.7036i		−	1.38896i	−0.719512	−	0.694480i	$-0.755634\pi$
$71$		−	11.7036i		−	1.38896i	0.719512	−	0.694480i	$-0.244366\pi$
$72$		0			0
$73$	7.82068	+	4.51527i	0.915342	+	0.528473i	0.882146	−	0.470976i	$-0.156098\pi$
$73$	7.82068	+	4.51527i	0.915342	+	0.528473i	0.0331957	+	0.999449i	$0.489432\pi$
$74$	1.09643	+	0.705388i	0.127458	+	0.0819997i
$75$		0			0
$76$	−0.651014	+	6.74828i	−0.0746764	+	0.774081i
$77$	1.64537	+	5.61964i	0.187507	+	0.640418i
$78$		0			0
$79$	9.60105	−	5.54317i	1.08020	−	0.623655i	0.149252	−	0.988799i	$-0.452313\pi$
$79$	9.60105	−	5.54317i	1.08020	−	0.623655i	0.930951	+	0.365144i	$0.118980\pi$
$80$	8.47445	−	9.74164i	0.947472	−	1.08915i
$81$		0			0
$82$	−7.49743	+	3.86057i	−0.827953	+	0.426329i
$83$			3.57322i			0.392212i	0.980583	+	0.196106i	$0.0628297\pi$
$83$			3.57322i			0.392212i	−0.980583	+	0.196106i	$0.937170\pi$
$84$		0			0
$85$			10.1979i			1.10611i
$86$	−4.32987	−	8.40882i	−0.466902	−	0.906746i
$87$		0			0
$88$	−3.87677	+	4.91493i	−0.413265	+	0.523933i
$89$	6.32253	−	3.65032i	0.670187	−	0.386933i	−0.125960	−	0.992035i	$-0.540201\pi$
$89$	6.32253	−	3.65032i	0.670187	−	0.386933i	0.796147	+	0.605103i	$0.206868\pi$
$90$		0			0
$91$	9.28920	−	9.72719i	0.973772	−	1.01969i
$92$	−0.588444	+	6.09969i	−0.0613495	+	0.635937i
$93$		0			0
$94$	−1.62387	+	2.52409i	−0.167489	+	0.260340i
$95$	9.47619	+	5.47108i	0.972237	+	0.561321i
$96$		0			0
$97$		−	15.2238i		−	1.54574i	−0.634566	−	0.772869i	$-0.718821\pi$
$97$		−	15.2238i		−	1.54574i	0.634566	−	0.772869i	$-0.281179\pi$
$98$	8.58324	−	4.93234i	0.867038	−	0.498241i
$99$		0			0
$100$	−4.49328	−	9.86431i	−0.449328	−	0.986431i
$101$	4.92124	−	8.52383i	0.489681	−	0.848153i	−0.510248	−	0.860027i	$-0.670446\pi$
$101$	4.92124	−	8.52383i	0.489681	−	0.848153i	0.999929	+	0.0118744i	$0.00377982\pi$
$102$		0			0
$103$	−0.992258	−	1.71864i	−0.0977701	−	0.169343i	0.812991	−	0.582276i	$-0.197838\pi$
$103$	−0.992258	−	1.71864i	−0.0977701	−	0.169343i	−0.910761	+	0.412933i	$0.864504\pi$
$104$	14.2295	+	2.06711i	1.39532	+	0.202697i
$105$		0			0
$106$	0.245344	−	5.09818i	0.0238299	−	0.495179i
$107$	−1.61805	−	2.80255i	−0.156423	−	0.270933i	0.777153	−	0.629311i	$-0.216663\pi$
$107$	−1.61805	−	2.80255i	−0.156423	−	0.270933i	−0.933576	+	0.358379i	$0.883330\pi$
$108$		0			0
$109$	−3.62997	−	2.09576i	−0.347688	−	0.200738i	0.315979	−	0.948766i	$-0.397667\pi$
$109$	−3.62997	−	2.09576i	−0.347688	−	0.200738i	−0.663666	+	0.748029i	$0.731001\pi$
$110$	4.62523	+	8.98242i	0.440998	+	0.856440i
$111$		0			0
$112$	9.61465	+	4.42249i	0.908499	+	0.417886i
$113$	2.84651			0.267777			0.133889	−	0.990996i	$-0.457254\pi$
$113$	2.84651			0.267777			0.133889	+	0.990996i	$0.457254\pi$
$114$		0			0
$115$	8.56542	+	4.94525i	0.798729	+	0.461147i
$116$	−16.0904	−	11.4815i	−1.49396	−	1.06603i
$117$		0			0
$118$	−0.834798	+	17.3469i	−0.0768494	+	1.59691i
$119$	−8.02177	+	2.34868i	−0.735354	+	0.215304i
$120$		0			0
$121$	3.05088	+	5.28429i	0.277353	+	0.480390i
$122$	−9.70400	+	15.0836i	−0.878559	+	1.36560i
$123$		0			0
$124$	1.68137	+	3.69119i	0.150991	+	0.331479i
$125$	−1.35490			−0.121186
$126$		0			0
$127$		−	21.0058i		−	1.86396i	−0.362506	−	0.931981i	$-0.618079\pi$
$127$		−	21.0058i		−	1.86396i	0.362506	−	0.931981i	$-0.381921\pi$
$128$	2.10326	+	11.1165i	0.185904	+	0.982568i
$129$		0			0
$130$	12.5563	−	19.5170i	1.10126	−	1.71176i
$131$	0.494446	−	0.285468i	0.0431999	−	0.0249415i	−0.478245	−	0.878227i	$-0.658727\pi$
$131$	0.494446	−	0.285468i	0.0431999	−	0.0249415i	0.521444	+	0.853285i	$0.325393\pi$
$132$		0			0
$133$	−2.12115	+	8.71414i	−0.183927	+	0.755612i
$134$	−12.4510	−	0.599191i	−1.07561	−	0.0517623i
$135$		0			0
$136$	−7.01582	−	5.53390i	−0.601602	−	0.474528i
$137$	−6.57813	+	11.3937i	−0.562008	+	0.973426i	0.435313	+	0.900279i	$0.356638\pi$
$137$	−6.57813	+	11.3937i	−0.562008	+	0.973426i	−0.997321	+	0.0731470i	$0.976696\pi$
$138$		0			0
$139$			9.54821i			0.809869i	0.914346	+	0.404934i	$0.132706\pi$
$139$			9.54821i			0.809869i	−0.914346	+	0.404934i	$0.867294\pi$
$140$	12.9283	−	11.1630i	1.09264	−	0.943444i
$141$		0			0
$142$	14.7151	−	7.57711i	1.23487	−	0.635857i
$143$	−5.62560	+	9.74383i	−0.470436	+	0.814820i
$144$		0			0
$145$	−27.6290	+	15.9516i	−2.29447	+	1.32471i
$146$	−0.613885	+	12.7564i	−0.0508055	+	1.05572i
$147$		0			0
$148$	−0.177048	+	1.83524i	−0.0145533	+	0.150856i
$149$	−9.17651	+	5.29806i	−0.751769	+	0.434034i	−0.826333	−	0.563182i	$-0.809577\pi$
$149$	−9.17651	+	5.29806i	−0.751769	+	0.434034i	0.0745636	+	0.997216i	$0.476244\pi$
$150$		0			0
$151$	1.05318	+	0.608052i	0.0857063	+	0.0494826i	0.542241	−	0.840223i	$-0.317576\pi$
$151$	1.05318	+	0.608052i	0.0857063	+	0.0494826i	−0.456534	+	0.889706i	$0.650909\pi$
$152$	−8.90622	+	3.55043i	−0.722390	+	0.287978i
$153$		0			0
$154$	−6.00044	+	5.70701i	−0.483529	+	0.459884i
$155$	6.54645			0.525824
$156$		0			0
$157$	−1.81252	+	3.13938i	−0.144655	+	0.250550i	−0.929244	−	0.369466i	$-0.879541\pi$
$157$	−1.81252	+	3.13938i	−0.144655	+	0.250550i	0.784589	+	0.620016i	$0.212874\pi$
$158$	13.1854	+	8.48283i	1.04898	+	0.674858i
$159$		0			0
$160$	17.7349	+	4.34817i	1.40206	+	0.343753i
$161$	−1.91728	+	7.87661i	−0.151103	+	0.620764i
$162$		0			0
$163$	−9.91572	−	17.1745i	−0.776659	−	1.34521i	−0.933857	−	0.357646i	$-0.883580\pi$
$163$	−9.91572	−	17.1745i	−0.776659	−	1.34521i	0.157198	−	0.987567i	$-0.449754\pi$
$164$	−9.70794	−	6.92725i	−0.758063	−	0.540927i
$165$		0			0
$166$	−4.49268	+	2.31337i	−0.348700	+	0.179552i
$167$	12.3971			0.959317			0.479659	−	0.877455i	$-0.340760\pi$
$167$	12.3971			0.959317			0.479659	+	0.877455i	$0.340760\pi$
$168$		0			0
$169$	12.8439			0.987994
$170$	−12.8220	+	6.60229i	−0.983400	+	0.506372i
$171$		0			0
$172$	7.76933	−	10.8880i	0.592406	−	0.830206i
$173$	−0.519326	−	0.899499i	−0.0394836	−	0.0683876i	0.845608	−	0.533804i	$-0.179238\pi$
$173$	−0.519326	−	0.899499i	−0.0394836	−	0.0683876i	−0.885092	+	0.465416i	$0.845905\pi$
$174$		0			0
$175$	−4.02923	−	13.7615i	−0.304581	−	1.04028i
$176$	−8.68952	−	1.69232i	−0.654997	−	0.127564i
$177$		0			0
$178$	8.68293	+	5.58616i	0.650813	+	0.418700i
$179$	−1.26304	+	2.18764i	−0.0944038	+	0.163512i	−0.909360	−	0.416011i	$-0.863428\pi$
$179$	−1.26304	+	2.18764i	−0.0944038	+	0.163512i	0.814956	+	0.579523i	$0.196761\pi$
$180$		0			0
$181$	8.29867			0.616835			0.308418	−	0.951251i	$-0.400201\pi$
$181$	8.29867			0.616835			0.308418	+	0.951251i	$0.400201\pi$
$182$	18.2442	+	5.38192i	1.35235	+	0.398934i
$183$		0			0
$184$	−8.05022	+	3.20919i	−0.593470	+	0.236585i
$185$	2.57712	+	1.48790i	0.189474	+	0.109393i
$186$		0			0
$187$	6.05524	−	3.49599i	0.442803	−	0.255652i
$188$	−4.22491	−	0.407581i	−0.308133	−	0.0297259i
$189$		0			0
$190$	−0.743834	+	15.4567i	−0.0539634	+	1.12134i
$191$	5.26146	−	3.03771i	0.380706	−	0.219801i	−0.297419	−	0.954747i	$-0.596126\pi$
$191$	5.26146	−	3.03771i	0.380706	−	0.219801i	0.678125	+	0.734946i	$0.262793\pi$
$192$		0			0
$193$	4.59340	−	7.95599i	0.330640	−	0.572685i	−0.651998	−	0.758221i	$-0.726069\pi$
$193$	4.59340	−	7.95599i	0.330640	−	0.572685i	0.982637	+	0.185536i	$0.0594021\pi$
$194$	19.1411	−	9.85613i	1.37425	−	0.707629i
$195$		0			0
$196$	11.7585	+	7.59858i	0.839890	+	0.542756i
$197$		−	20.2764i		−	1.44463i	−0.691563	−	0.722316i	$-0.743078\pi$
$197$		−	20.2764i		−	1.44463i	0.691563	−	0.722316i	$-0.256922\pi$
$198$		0			0
$199$	1.64355	−	2.84672i	0.116508	−	0.201799i	−0.801873	−	0.597494i	$-0.796163\pi$
$199$	1.64355	−	2.84672i	0.116508	−	0.201799i	0.918382	+	0.395696i	$0.129496\pi$
$200$	9.49355	−	12.0358i	0.671296	−	0.851061i
$201$		0			0
$202$	13.9033	+	0.669078i	0.978230	+	0.0470762i
$203$	−18.9110	−	18.0595i	−1.32729	−	1.26753i
$204$		0			0
$205$	−16.6696	+	9.62422i	−1.16426	+	0.672185i
$206$	1.51847	−	2.36026i	0.105797	−	0.164447i
$207$		0			0
$208$	6.61342	+	19.2293i	0.458558	+	1.33331i
$209$		−	7.50230i		−	0.518945i
$210$		0			0
$211$	−21.6901			−1.49320			−0.746602	−	0.665271i	$-0.768316\pi$
$211$	−21.6901			−1.49320			−0.746602	+	0.665271i	$0.768316\pi$
$212$	6.56888	−	2.99218i	0.451153	−	0.205504i
$213$		0			0
$214$	2.47614	−	3.84883i	0.169265	−	0.263101i
$215$	−10.7941	−	18.6960i	−0.736154	−	1.27506i
$216$		0			0
$217$	1.50772	+	5.14952i	0.102351	+	0.349572i
$218$	0.284934	−	5.92086i	0.0192982	−	0.401011i
$219$		0			0
$220$	−8.29931	+	11.6308i	−0.559539	+	0.784146i
$221$	−13.9088	−	8.03027i	−0.935610	−	0.540175i
$222$		0			0
$223$	−19.3266			−1.29420			−0.647102	−	0.762404i	$-0.724019\pi$
$223$	−19.3266			−1.29420			−0.647102	+	0.762404i	$0.724019\pi$
$224$	0.664217	+	14.9519i	0.0443799	+	0.999015i
$225$		0			0
$226$	1.84288	+	3.57897i	0.122587	+	0.238070i
$227$	0.466841	+	0.269531i	0.0309853	+	0.0178894i	0.515413	−	0.856942i	$-0.327639\pi$
$227$	0.466841	+	0.269531i	0.0309853	+	0.0178894i	−0.484427	+	0.874832i	$0.660972\pi$
$228$		0			0
$229$	−11.4311	−	19.7993i	−0.755392	−	1.30838i	−0.945179	−	0.326551i	$-0.894113\pi$
$229$	−11.4311	−	19.7993i	−0.755392	−	1.30838i	0.189788	−	0.981825i	$-0.439220\pi$
$230$	−0.672343	+	13.9711i	−0.0443330	+	0.921227i
$231$		0			0
$232$	4.01875	−	27.6641i	0.263844	−	1.81624i
$233$	−1.50245	−	2.60232i	−0.0984287	−	0.170484i	0.812606	−	0.582814i	$-0.198048\pi$
$233$	−1.50245	−	2.60232i	−0.0984287	−	0.170484i	−0.911034	+	0.412330i	$0.864715\pi$
$234$		0			0
$235$	−3.42529	+	5.93277i	−0.223441	+	0.387011i
$236$	−22.3510	+	10.1811i	−1.45493	+	0.662732i
$237$		0			0
$238$	−8.14648	−	8.56534i	−0.528058	−	0.555208i
$239$			11.2699i			0.728988i	0.931206	+	0.364494i	$0.118758\pi$
$239$			11.2699i			0.728988i	−0.931206	+	0.364494i	$0.881242\pi$
$240$		0			0
$241$	9.76276	+	5.63653i	0.628875	+	0.363081i	0.780316	−	0.625385i	$-0.215058\pi$
$241$	9.76276	+	5.63653i	0.628875	+	0.363081i	−0.151441	+	0.988466i	$0.548392\pi$
$242$	−4.66883	+	7.25708i	−0.300124	+	0.466503i
$243$		0			0
$244$	−25.2474	−	2.43564i	−1.61630	−	0.155926i
$245$	19.0276	−	12.1868i	1.21563	−	0.778588i
$246$		0			0
$247$	−14.9240	+	8.61637i	−0.949590	+	0.548246i
$248$	−3.55245	+	4.50376i	−0.225581	+	0.285989i
$249$		0			0
$250$	−0.877184	−	1.70353i	−0.0554780	−	0.107741i
$251$		−	3.26625i		−	0.206164i	−0.994673	−	0.103082i	$-0.967130\pi$
$251$		−	3.26625i		−	0.206164i	0.994673	−	0.103082i	$-0.0328704\pi$
$252$		0			0
$253$		−	6.78124i		−	0.426333i
$254$	26.4110	−	13.5995i	1.65717	−	0.853311i
$255$		0			0
$256$	−12.6153	+	9.84149i	−0.788455	+	0.615093i
$257$	10.4533	−	6.03522i	0.652059	−	0.376467i	−0.137185	−	0.990545i	$-0.543806\pi$
$257$	10.4533	−	6.03522i	0.652059	−	0.376467i	0.789245	+	0.614079i	$0.210472\pi$
$258$		0			0
$259$	−0.576861	+	2.36987i	−0.0358444	+	0.147257i
$260$	32.6683	+	3.15154i	2.02600	+	0.195450i
$261$		0			0
$262$	0.679038	+	0.436858i	0.0419511	+	0.0269892i
$263$	−14.1861	−	8.19034i	−0.874752	−	0.505038i	−0.00582745	−	0.999983i	$-0.501855\pi$
$263$	−14.1861	−	8.19034i	−0.874752	−	0.505038i	−0.868924	+	0.494945i	$0.835188\pi$
$264$		0			0
$265$		−	11.6501i		−	0.715663i
$266$	−12.3297	+	2.97474i	−0.755984	+	0.182393i
$267$		0			0
$268$	−7.30765	−	16.0428i	−0.446386	−	0.979973i
$269$	−3.73572	+	6.47046i	−0.227771	+	0.394511i	−0.957147	−	0.289602i	$-0.906477\pi$
$269$	−3.73572	+	6.47046i	−0.227771	+	0.394511i	0.729376	+	0.684113i	$0.239810\pi$
$270$		0			0
$271$	−4.48617	−	7.77027i	−0.272515	−	0.472011i	0.696990	−	0.717081i	$-0.254522\pi$
$271$	−4.48617	−	7.77027i	−0.272515	−	0.472011i	−0.969505	+	0.245070i	$0.921189\pi$
$272$	2.41571	−	12.4039i	0.146474	−	0.752095i
$273$		0			0
$274$	−18.5843	−	0.894345i	−1.12272	−	0.0540294i
$275$	5.99747	+	10.3879i	0.361661	+	0.626415i
$276$		0			0
$277$	−5.31638	−	3.06942i	−0.319430	−	0.184423i	0.331708	−	0.943382i	$-0.392375\pi$
$277$	−5.31638	−	3.06942i	−0.319430	−	0.184423i	−0.651139	+	0.758959i	$0.725708\pi$
$278$	−12.0051	+	6.18169i	−0.720021	+	0.370753i
$279$		0			0
$280$	22.4054	+	9.02785i	1.33898	+	0.539517i
$281$	19.2936			1.15096			0.575480	−	0.817816i	$-0.304815\pi$
$281$	19.2936			1.15096			0.575480	+	0.817816i	$0.304815\pi$
$282$		0			0
$283$	19.3500	+	11.1718i	1.15024	+	0.664092i	0.948946	−	0.315439i	$-0.102152\pi$
$283$	19.3500	+	11.1718i	1.15024	+	0.664092i	0.201295	+	0.979531i	$0.435485\pi$
$284$	19.0537	+	13.5960i	1.13063	+	0.806777i
$285$		0			0
$286$	−15.8932	−	0.764842i	−0.939785	−	0.0452260i
$287$	−11.4097	−	10.8960i	−0.673495	−	0.643169i
$288$		0			0
$289$	−3.50964	−	6.07887i	−0.206449	−	0.357581i
$290$	−37.9438	−	24.4111i	−2.22814	−	1.43347i
$291$		0			0
$292$	−16.4362	+	7.48685i	−0.961859	+	0.438135i
$293$	−14.0707			−0.822018			−0.411009	−	0.911631i	$-0.634824\pi$
$293$	−14.0707			−0.822018			−0.411009	+	0.911631i	$0.634824\pi$
$294$		0			0
$295$			39.6403i			2.30795i
$296$	−2.42211	+	0.965565i	−0.140782	+	0.0561223i
$297$		0			0
$298$	−12.6024	−	8.10774i	−0.730037	−	0.469669i
$299$	−13.4896	+	7.78823i	−0.780124	+	0.450405i
$300$		0			0
$301$	12.2205	−	12.7967i	0.704377	−	0.737590i
$302$	−0.0826691	+	1.71784i	−0.00475707	+	0.0988507i
$303$		0			0
$304$	−10.2301	−	8.89934i	−0.586735	−	0.510412i
$305$	−20.4690	+	35.4533i	−1.17205	+	2.03005i
$306$		0			0
$307$			9.61787i			0.548921i	0.961598	+	0.274460i	$0.0884992\pi$
$307$			9.61787i			0.548921i	−0.961598	+	0.274460i	$0.911501\pi$
$308$	−11.0603	−	3.84964i	−0.630220	−	0.219354i
$309$		0			0
$310$	4.23829	+	8.23098i	0.240719	+	0.467488i
$311$	10.8485	−	18.7902i	0.615162	−	1.06549i	−0.375194	−	0.926946i	$-0.622424\pi$
$311$	10.8485	−	18.7902i	0.615162	−	1.06549i	0.990356	−	0.138546i	$-0.0442428\pi$
$312$		0			0
$313$	−9.46514	+	5.46470i	−0.535001	+	0.308883i	−0.743051	−	0.669235i	$-0.766622\pi$
$313$	−9.46514	+	5.46470i	−0.535001	+	0.308883i	0.208049	+	0.978118i	$0.433289\pi$
$314$	−5.12065	−	0.246425i	−0.288975	−	0.0139066i
$315$		0			0
$316$	−2.12914	+	22.0702i	−0.119773	+	1.24155i
$317$	−6.14253	+	3.54639i	−0.344999	+	0.199185i	−0.662480	−	0.749079i	$-0.730496\pi$
$317$	−6.14253	+	3.54639i	−0.344999	+	0.199185i	0.317482	+	0.948264i	$0.397163\pi$
$318$		0			0
$319$	18.9433	+	10.9369i	1.06062	+	0.612352i
$320$	6.01484	+	25.1134i	0.336240	+	1.40388i
$321$		0			0
$322$	−11.1447	+	2.68883i	−0.621069	+	0.149843i
$323$	10.7092			0.595874
$324$		0			0
$325$	13.7761	−	23.8610i	0.764163	−	1.32357i
$326$	15.1742	−	23.5863i	0.840423	−	1.30633i
$327$		0			0
$328$	2.42466	−	16.6908i	0.133880	−	0.921595i
$329$	−5.45567	−	1.32799i	−0.300781	−	0.0732144i
$330$		0			0
$331$	−5.86202	−	10.1533i	−0.322206	−	0.558077i	0.658737	−	0.752373i	$-0.271091\pi$
$331$	−5.86202	−	10.1533i	−0.322206	−	0.558077i	−0.980943	+	0.194297i	$0.937758\pi$
$332$	−5.81729	−	4.15101i	−0.319265	−	0.227816i
$333$		0			0
$334$	8.02611	+	15.5871i	0.439169	+	0.852889i
$335$	−28.4526			−1.55453
$336$		0			0
$337$	23.5287			1.28169			0.640846	−	0.767670i	$-0.278584\pi$
$337$	23.5287			1.28169			0.640846	+	0.767670i	$0.278584\pi$
$338$	8.31539	+	16.1489i	0.452298	+	0.878385i
$339$		0			0
$340$	−16.6024	−	11.8469i	−0.900389	−	0.642486i
$341$	−2.24423	−	3.88712i	−0.121532	−	0.210499i
$342$		0			0
$343$	13.9686	+	12.1605i	0.754232	+	0.656608i
$344$	18.7197	+	2.71940i	1.00930	+	0.146620i
$345$		0			0
$346$	0.794735	−	1.23531i	0.0427252	−	0.0664107i
$347$	−5.17132	+	8.95699i	−0.277611	+	0.480837i	−0.970791	−	0.239928i	$-0.922876\pi$
$347$	−5.17132	+	8.95699i	−0.277611	+	0.480837i	0.693179	+	0.720765i	$0.256209\pi$
$348$		0			0
$349$	−0.830301			−0.0444450			−0.0222225	−	0.999753i	$-0.507074\pi$
$349$	−0.830301			−0.0444450			−0.0222225	+	0.999753i	$0.507074\pi$
$350$	14.6941	−	13.9755i	0.785430	−	0.747022i
$351$		0			0
$352$	−3.49796	−	12.0211i	−0.186442	−	0.640729i
$353$	4.21179	+	2.43168i	0.224171	+	0.129425i	0.607880	−	0.794029i	$-0.292020\pi$
$353$	4.21179	+	2.43168i	0.224171	+	0.129425i	−0.383709	+	0.923454i	$0.625353\pi$
$354$		0			0
$355$	32.7173	−	18.8894i	1.73646	−	1.00254i
$356$	−1.40209	+	14.5338i	−0.0743106	+	0.770289i
$357$		0			0
$358$	−3.56828	−	0.171719i	−0.188589	−	0.00907564i
$359$	−16.3080	+	9.41543i	−0.860704	+	0.496928i	−0.864248	−	0.503066i	$-0.832205\pi$
$359$	−16.3080	+	9.41543i	−0.860704	+	0.496928i	0.00354407	+	0.999994i	$0.498872\pi$
$360$		0			0
$361$	−3.75460	+	6.50317i	−0.197611	+	0.342272i
$362$	5.37271	+	10.4341i	0.282383	+	0.548403i
$363$		0			0
$364$	5.04483	+	26.4231i	0.264421	+	1.38495i
$365$			29.1503i			1.52579i
$366$		0			0
$367$	−10.7270	+	18.5796i	−0.559943	+	0.969850i	0.437557	+	0.899190i	$0.355844\pi$
$367$	−10.7270	+	18.5796i	−0.559943	+	0.969850i	−0.997501	+	0.0706593i	$0.977490\pi$
$368$	−9.24684	−	8.04401i	−0.482025	−	0.419323i
$369$		0			0
$370$	−0.202291	+	4.20355i	−0.0105166	+	0.218532i
$371$	9.16414	−	2.68316i	0.475779	−	0.139303i
$372$		0			0
$373$	14.1525	−	8.17098i	0.732791	−	0.423077i	−0.0866513	−	0.996239i	$-0.527617\pi$
$373$	14.1525	−	8.17098i	0.732791	−	0.423077i	0.819442	+	0.573162i	$0.194283\pi$
$374$	8.31585	+	5.34999i	0.430002	+	0.276642i
$375$		0			0
$376$	−2.22282	−	5.57593i	−0.114633	−	0.287557i
$377$		−	50.2442i		−	2.58771i
$378$		0			0
$379$	−4.31636			−0.221717			−0.110858	−	0.993836i	$-0.535360\pi$
$379$	−4.31636			−0.221717			−0.110858	+	0.993836i	$0.535360\pi$
$380$	−19.9155	+	9.07169i	−1.02165	+	0.465368i
$381$		0			0
$382$	7.22573	+	4.64867i	0.369700	+	0.237846i
$383$	10.0948	+	17.4848i	0.515823	+	0.893431i	0.999831	+	0.0183677i	$0.00584695\pi$
$383$	10.0948	+	17.4848i	0.515823	+	0.893431i	−0.484009	+	0.875063i	$0.660820\pi$
$384$		0			0
$385$	−13.0541	+	13.6696i	−0.665298	+	0.696668i
$386$	12.9771	+	0.624506i	0.660515	+	0.0317865i
$387$		0			0
$388$	24.7846	+	17.6854i	1.25825	+	0.897842i
$389$	29.2383	+	16.8807i	1.48244	+	0.855886i	0.999801	−	0.0199339i	$-0.00634559\pi$
$389$	29.2383	+	16.8807i	1.48244	+	0.855886i	0.482637	+	0.875820i	$0.339679\pi$
$390$		0			0
$391$	9.67989			0.489533
$392$	−1.94119	+	19.7036i	−0.0980451	+	0.995182i
$393$		0			0
$394$	25.4939	−	13.1273i	1.28436	−	0.661343i
$395$	30.9918	+	17.8931i	1.55937	+	0.900302i
$396$		0			0
$397$	−0.0441158	−	0.0764109i	−0.00221411	−	0.00383495i	0.864916	−	0.501916i	$-0.167371\pi$
$397$	−0.0441158	−	0.0764109i	−0.00221411	−	0.00383495i	−0.867130	+	0.498081i	$0.834038\pi$
$398$	4.64330	+	0.223453i	0.232748	+	0.0112007i
$399$		0			0
$400$	21.2792	+	4.14421i	1.06396	+	0.207211i
$401$	−12.6037	−	21.8303i	−0.629400	−	1.09015i	−0.987672	−	0.156536i	$-0.949967\pi$
$401$	−12.6037	−	21.8303i	−0.629400	−	1.09015i	0.358272	−	0.933617i	$-0.383366\pi$
$402$		0			0
$403$	−5.15498	+	8.92869i	−0.256788	+	0.444770i
$404$	8.15998	+	17.9140i	0.405974	+	0.891255i
$405$		0			0
$406$	10.4632	−	35.4692i	0.519279	−	1.76031i
$407$		−	2.04031i		−	0.101134i
$408$		0			0
$409$	−26.9181	−	15.5412i	−1.33102	−	0.768462i	−0.345560	−	0.938397i	$-0.612311\pi$
$409$	−26.9181	−	15.5412i	−1.33102	−	0.768462i	−0.985455	+	0.169935i	$0.945644\pi$
$410$	−22.8929	−	14.7281i	−1.13060	−	0.727371i
$411$		0			0
$412$	3.95069	+	0.381127i	0.194637	+	0.0187768i
$413$	−31.1816	+	9.12962i	−1.53434	+	0.449239i
$414$		0			0
$415$	−9.98894	+	5.76712i	−0.490338	+	0.283097i
$416$	−19.8957	+	20.7646i	−0.975467	+	1.01807i
$417$		0			0
$418$	9.43278	−	4.85713i	0.461373	−	0.237570i
$419$		−	22.7655i		−	1.11217i	−0.831126	−	0.556085i	$-0.812303\pi$
$419$		−	22.7655i		−	1.11217i	0.831126	−	0.556085i	$-0.187697\pi$
$420$		0			0
$421$		−	24.0207i		−	1.17070i	−0.810781	−	0.585349i	$-0.800958\pi$
$421$		−	24.0207i		−	1.17070i	0.810781	−	0.585349i	$-0.199042\pi$
$422$	−14.0425	−	27.2713i	−0.683580	−	1.32755i
$423$		0			0
$424$	8.01494	+	6.32198i	0.389240	+	0.307023i
$425$	−14.8283	+	8.56109i	−0.719276	+	0.415274i
$426$		0			0
$427$	−32.6023	−	7.93586i	−1.57773	−	0.384043i
$428$	6.44230	+	0.621496i	0.311400	+	0.0300411i
$429$		0			0
$430$	16.5185	−	25.6758i	0.796593	−	1.23820i
$431$	28.2391	+	16.3039i	1.36023	+	0.785330i	0.989654	−	0.143471i	$-0.0458265\pi$
$431$	28.2391	+	16.3039i	1.36023	+	0.785330i	0.370577	+	0.928802i	$0.379160\pi$
$432$		0			0
$433$		−	18.4752i		−	0.887861i	−0.896061	−	0.443931i	$-0.853584\pi$
$433$		−	18.4752i		−	0.887861i	0.896061	−	0.443931i	$-0.146416\pi$
$434$	−5.49846	+	5.22958i	−0.263935	+	0.251028i
$435$		0			0
$436$	7.62888	−	3.47502i	0.365357	−	0.166423i
$437$	5.19319	−	8.99487i	0.248424	−	0.430283i
$438$		0			0
$439$	11.2138	+	19.4229i	0.535206	+	0.927004i	0.999153	+	0.0411413i	$0.0130994\pi$
$439$	11.2138	+	19.4229i	0.535206	+	0.927004i	−0.463947	+	0.885863i	$0.653567\pi$
$440$	−19.9967	−	2.90491i	−0.953305	−	0.138486i
$441$		0			0
$442$	1.09177	−	22.6868i	0.0519304	−	1.07910i
$443$	4.52168	+	7.83178i	0.214832	+	0.372099i	0.953220	−	0.302276i	$-0.0977464\pi$
$443$	4.52168	+	7.83178i	0.214832	+	0.372099i	−0.738389	+	0.674375i	$0.764413\pi$
$444$		0			0
$445$	20.4089	+	11.7831i	0.967474	+	0.558571i
$446$	−12.5124	−	24.2997i	−0.592478	−	1.15062i
$447$		0			0
$448$	−18.3693	+	10.5153i	−0.867866	+	0.496799i
$449$	−5.65664			−0.266954			−0.133477	−	0.991052i	$-0.542614\pi$
$449$	−5.65664			−0.266954			−0.133477	+	0.991052i	$0.542614\pi$
$450$		0			0
$451$	11.4292	+	6.59867i	0.538182	+	0.310719i
$452$	−3.30679	+	4.63418i	−0.155538	+	0.217974i
$453$		0			0
$454$	−0.0366447	+	0.761467i	−0.00171982	+	0.0357374i
$455$	42.1849	+	10.2684i	1.97766	+	0.481391i
$456$		0			0
$457$	−4.68971	−	8.12282i	−0.219376	−	0.379970i	0.735242	−	0.677805i	$-0.237069\pi$
$457$	−4.68971	−	8.12282i	−0.219376	−	0.379970i	−0.954617	+	0.297835i	$0.903735\pi$
$458$	17.4933	−	27.1910i	0.817410	−	1.27055i
$459$		0			0
$460$	−18.0014	+	8.19979i	−0.839320	+	0.382317i
$461$	31.7960			1.48089			0.740444	−	0.672118i	$-0.234615\pi$
$461$	31.7960			1.48089			0.740444	+	0.672118i	$0.234615\pi$
$462$		0			0
$463$			8.87505i			0.412458i	0.978504	+	0.206229i	$0.0661193\pi$
$463$			8.87505i			0.412458i	−0.978504	+	0.206229i	$0.933881\pi$
$464$	37.3844	−	12.8574i	1.73553	−	0.596890i
$465$		0			0
$466$	2.29923	−	3.57384i	0.106510	−	0.165555i
$467$	−2.70998	+	1.56461i	−0.125403	+	0.0724015i	−0.561389	−	0.827552i	$-0.689733\pi$
$467$	−2.70998	+	1.56461i	−0.125403	+	0.0724015i	0.435986	+	0.899953i	$0.356400\pi$
$468$		0			0
$469$	−6.55294	−	22.3811i	−0.302587	−	1.03346i
$470$	−9.67698	−	0.465693i	−0.446366	−	0.0214808i
$471$		0			0
$472$	−27.2713	−	21.5109i	−1.25526	−	0.990121i
$473$	−7.40081	+	12.8186i	−0.340290	+	0.589399i
$474$		0			0
$475$			18.3719i			0.842959i
$476$	5.49518	−	15.7881i	0.251871	−	0.723645i
$477$		0			0
$478$	−14.1698	+	7.29632i	−0.648113	+	0.333726i
$479$	−8.19517	+	14.1945i	−0.374447	+	0.648561i	−0.990244	−	0.139344i	$-0.955501\pi$
$479$	−8.19517	+	14.1945i	−0.374447	+	0.648561i	0.615797	+	0.787905i	$0.288834\pi$
$480$		0			0
$481$	−4.05869	+	2.34328i	−0.185060	+	0.106845i
$482$	−0.766328	+	15.9241i	−0.0349053	+	0.725323i
$483$		0			0
$484$	−12.1471	−	1.17185i	−0.552143	−	0.0532658i
$485$	42.5580	−	24.5708i	1.93246	−	1.11570i
$486$		0			0
$487$	−25.4297	−	14.6819i	−1.15233	−	0.665299i	−0.202877	−	0.979204i	$-0.565029\pi$
$487$	−25.4297	−	14.6819i	−1.15233	−	0.665299i	−0.949454	+	0.313905i	$0.898363\pi$
$488$	−13.2832	−	33.3209i	−0.601304	−	1.50837i
$489$		0			0
$490$	27.6415	+	16.0337i	1.24872	+	0.724330i
$491$	−33.8967			−1.52974			−0.764869	−	0.644186i	$-0.777196\pi$
$491$	−33.8967			−1.52974			−0.764869	+	0.644186i	$0.777196\pi$
$492$		0			0
$493$	−15.6120	+	27.0407i	−0.703128	+	1.21785i
$494$	−20.4956	−	13.1858i	−0.922140	−	0.593258i
$495$		0			0
$496$	−7.96258	−	1.55075i	−0.357530	−	0.0696307i
$497$	22.3938	+	21.3854i	1.00450	+	0.959267i
$498$		0			0
$499$	4.44527	+	7.69943i	0.198997	+	0.344674i	0.948204	−	0.317663i	$-0.102898\pi$
$499$	4.44527	+	7.69943i	0.198997	+	0.344674i	−0.749206	+	0.662337i	$0.769565\pi$
$500$	1.57398	−	2.20580i	0.0703906	−	0.0986463i
$501$		0			0
$502$	4.10672	−	2.11463i	0.183292	−	0.0943805i
$503$	1.51626			0.0676065			0.0338032	−	0.999429i	$-0.489238\pi$
$503$	1.51626			0.0676065			0.0338032	+	0.999429i	$0.489238\pi$
$504$		0			0
$505$	31.7711			1.41380
$506$	8.52618	−	4.39030i	0.379035	−	0.195173i
$507$		0			0
$508$	34.1979	+	24.4024i	1.51729	+	1.08268i
$509$	−3.71720	−	6.43837i	−0.164762	−	0.285376i	0.771809	−	0.635855i	$-0.219352\pi$
$509$	−3.71720	−	6.43837i	−0.164762	−	0.285376i	−0.936571	+	0.350479i	$0.886019\pi$
$510$		0			0
$511$	−22.9299	+	6.71363i	−1.01436	+	0.296994i
$512$	−20.5412	−	9.48986i	−0.907803	−	0.419397i
$513$		0			0
$514$	14.3559	+	9.23582i	0.633210	+	0.407375i
$515$	3.20297	−	5.54771i	0.141140	−	0.244461i
$516$		0			0
$517$	4.69698			0.206573
$518$	−3.35316	+	0.809001i	−0.147329	+	0.0355455i
$519$		0			0
$520$	17.1875	+	43.1148i	0.753723	+	1.89071i
$521$	11.7724	+	6.79678i	0.515757	+	0.297772i	0.735197	−	0.677854i	$-0.237090\pi$
$521$	11.7724	+	6.79678i	0.515757	+	0.297772i	−0.219440	+	0.975626i	$0.570423\pi$
$522$		0			0
$523$	3.38679	−	1.95536i	0.148094	−	0.0855020i	−0.424122	−	0.905605i	$-0.639417\pi$
$523$	3.38679	−	1.95536i	0.148094	−	0.0855020i	0.572216	+	0.820103i	$0.306084\pi$
$524$	−0.109649	+	1.13660i	−0.00479002	+	0.0496524i
$525$		0			0
$526$	1.11354	−	23.1390i	0.0485525	−	1.00891i
$527$	5.54868	−	3.20353i	0.241704	−	0.139548i
$528$		0			0
$529$	−6.80594	+	11.7882i	−0.295910	+	0.512532i
$530$	14.6479	−	7.54251i	0.636266	−	0.327626i
$531$		0			0
$532$	−11.7227	−	13.5765i	−0.508243	−	0.588615i
$533$		−	30.3142i		−	1.31305i
$534$		0			0
$535$	5.22301	−	9.04652i	0.225811	−	0.391115i
$536$	15.4399	−	19.5745i	0.666900	−	0.845489i
$537$		0			0
$538$	−10.5540	−	0.507899i	−0.455015	−	0.0218971i
$539$	−13.7592	−	7.12025i	−0.592650	−	0.306691i
$540$		0			0
$541$	29.3866	−	16.9663i	1.26343	−	0.729440i	0.289691	−	0.957120i	$-0.406447\pi$
$541$	29.3866	−	16.9663i	1.26343	−	0.729440i	0.973736	+	0.227680i	$0.0731140\pi$
$542$	6.86528	−	10.6712i	0.294889	−	0.458366i
$543$		0			0
$544$	17.1596	−	4.99317i	0.735711	−	0.214080i
$545$		−	13.5301i		−	0.579565i
$546$		0			0
$547$	19.9416			0.852640			0.426320	−	0.904572i	$-0.359810\pi$
$547$	19.9416			0.852640			0.426320	+	0.904572i	$0.359810\pi$
$548$	−10.9073	−	23.9453i	−0.465937	−	1.02289i
$549$		0			0
$550$	−9.17805	+	14.2661i	−0.391353	+	0.608307i
$551$	16.7514	+	29.0143i	0.713634	+	1.23605i
$552$		0			0
$553$	−6.93720	+	28.4995i	−0.295000	+	1.21192i
$554$	0.417310	−	8.67158i	0.0177298	−	0.368420i
$555$		0			0
$556$	−15.5447	−	11.0922i	−0.659242	−	0.470412i
$557$	29.5999	+	17.0895i	1.25419	+	0.724107i	0.971939	−	0.235234i	$-0.0755857\pi$
$557$	29.5999	+	17.0895i	1.25419	+	0.724107i	0.282251	+	0.959341i	$0.408919\pi$
$558$		0			0
$559$	33.9992			1.43801
$560$	3.15480	+	34.0156i	0.133314	+	1.43742i
$561$		0			0
$562$	12.4910	+	24.2582i	0.526902	+	1.02327i
$563$	−1.95583	−	1.12920i	−0.0824283	−	0.0475900i	0.458219	−	0.888839i	$-0.348487\pi$
$563$	−1.95583	−	1.12920i	−0.0824283	−	0.0475900i	−0.540648	+	0.841249i	$0.681821\pi$
$564$		0			0
$565$	4.59422	+	7.95742i	0.193280	+	0.334771i
$566$	−1.51888	+	31.5620i	−0.0638434	+	1.32665i
$567$		0			0
$568$	−4.75886	+	32.7589i	−0.199677	+	1.37453i
$569$	14.5803	+	25.2538i	0.611236	+	1.05869i	0.991032	+	0.133622i	$0.0426609\pi$
$569$	14.5803	+	25.2538i	0.611236	+	1.05869i	−0.379796	+	0.925070i	$0.624006\pi$
$570$		0			0
$571$	13.1289	−	22.7399i	0.549427	−	0.951636i	−0.448886	−	0.893589i	$-0.648179\pi$
$571$	13.1289	−	22.7399i	0.549427	−	0.951636i	0.998314	−	0.0580474i	$-0.0184874\pi$
$572$	−9.32790	−	20.4780i	−0.390019	−	0.856228i
$573$		0			0
$574$	6.31284	−	21.3999i	0.263493	−	0.893215i
$575$			16.6061i			0.692522i
$576$		0			0
$577$	0.0467698	+	0.0270026i	0.00194705	+	0.00112413i	0.500973	−	0.865463i	$-0.332976\pi$
$577$	0.0467698	+	0.0270026i	0.00194705	+	0.00112413i	−0.499026	+	0.866587i	$0.666309\pi$
$578$	5.37087	−	8.34830i	0.223399	−	0.347244i
$579$		0			0
$580$	6.12703	−	63.5116i	0.254411	−	2.63718i
$581$	−6.83705	−	6.52919i	−0.283649	−	0.270876i
$582$		0			0
$583$	−6.91756	+	3.99386i	−0.286496	+	0.165409i
$584$	−20.0545	−	15.8185i	−0.829860	−	0.654573i
$585$		0			0
$586$	−9.10962	−	17.6913i	−0.376315	−	0.730822i
$587$		−	4.75946i		−	0.196444i	−0.995165	−	0.0982219i	$-0.968685\pi$
$587$		−	4.75946i		−	0.196444i	0.995165	−	0.0982219i	$-0.0313155\pi$
$588$		0			0
$589$		−	6.87468i		−	0.283266i
$590$	−49.8405	+	25.6639i	−2.05190	+	1.05656i
$591$		0			0
$592$	−2.78214	−	2.42024i	−0.114345	−	0.0994713i
$593$	10.2802	−	5.93527i	0.422157	−	0.243732i	−0.273843	−	0.961774i	$-0.588295\pi$
$593$	10.2802	−	5.93527i	0.422157	−	0.243732i	0.696000	+	0.718042i	$0.254962\pi$
$594$		0			0
$595$	−19.5127	−	18.6341i	−0.799944	−	0.763923i
$596$	2.03499	−	21.0943i	0.0833565	−	0.864057i
$597$		0			0
$598$	−18.5257	−	11.9185i	−0.757572	−	0.487383i
$599$	−25.6580	−	14.8136i	−1.04836	−	0.605269i	−0.126167	−	0.992009i	$-0.540268\pi$
$599$	−25.6580	−	14.8136i	−1.04836	−	0.605269i	−0.922189	+	0.386740i	$0.873601\pi$
$600$		0			0
$601$		−	26.4608i		−	1.07936i	−0.841870	−	0.539680i	$-0.818545\pi$
$601$		−	26.4608i		−	1.07936i	0.841870	−	0.539680i	$-0.181455\pi$
$602$	24.0013	+	7.08023i	0.978220	+	0.288569i
$603$		0			0
$604$	−2.21340	+	1.00822i	−0.0900618	+	0.0410239i
$605$	−9.84814	+	17.0575i	−0.400384	+	0.693485i
$606$		0			0
$607$	−7.69208	−	13.3231i	−0.312212	−	0.540767i	0.666629	−	0.745390i	$-0.267737\pi$
$607$	−7.69208	−	13.3231i	−0.312212	−	0.540767i	−0.978841	+	0.204623i	$0.934403\pi$
$608$	4.56618	−	18.6241i	0.185183	−	0.755305i
$609$		0			0
$610$	−57.8282	−	2.78291i	−2.34139	−	0.112677i
$611$	−5.39446	−	9.34348i	−0.218237	−	0.377997i
$612$		0			0
$613$	16.8302	+	9.71692i	0.679765	+	0.392463i	0.799767	−	0.600311i	$-0.204957\pi$
$613$	16.8302	+	9.71692i	0.679765	+	0.392463i	−0.120001	+	0.992774i	$0.538290\pi$
$614$	−12.0927	+	6.22678i	−0.488023	+	0.251292i
$615$		0			0
$616$	−2.32043	−	16.3987i	−0.0934928	−	0.660721i
$617$	0.173969			0.00700371			0.00350186	−	0.999994i	$-0.498885\pi$
$617$	0.173969			0.00700371			0.00350186	+	0.999994i	$0.498885\pi$
$618$		0			0
$619$	−32.8798	−	18.9832i	−1.32155	−	0.762998i	−0.337575	−	0.941299i	$-0.609607\pi$
$619$	−32.8798	−	18.9832i	−1.32155	−	0.762998i	−0.983976	+	0.178300i	$0.942940\pi$
$620$	−7.60501	+	10.6578i	−0.305425	+	0.428026i
$621$		0			0
$622$	30.6487	+	1.47493i	1.22890	+	0.0591394i
$623$	−4.56831	+	18.7677i	−0.183026	+	0.751910i
$624$		0			0
$625$	11.3626	+	19.6805i	0.454503	+	0.787222i
$626$	−12.9988	−	8.36275i	−0.519535	−	0.334243i
$627$		0			0
$628$	−3.00537	−	6.59783i	−0.119927	−	0.263282i
$629$	2.91244			0.116127
$630$		0			0
$631$		−	26.0140i		−	1.03560i	−0.855501	−	0.517801i	$-0.826751\pi$
$631$		−	26.0140i		−	1.03560i	0.855501	−	0.517801i	$-0.173249\pi$
$632$	−29.1277	+	11.6117i	−1.15864	+	0.461887i
$633$		0			0
$634$	−8.43572	−	5.42711i	−0.335025	−	0.215538i
$635$	58.7216	−	33.9030i	2.33030	−	1.34540i
$636$		0			0
$637$	1.63841	+	35.5481i	0.0649161	+	1.40847i
$638$	−1.48696	+	30.8986i	−0.0588693	+	1.22329i
$639$		0			0
$640$	−27.6815	+	23.8215i	−1.09421	+	0.941626i
$641$	12.4573	−	21.5767i	0.492035	−	0.852230i	−0.507923	−	0.861403i	$-0.669587\pi$
$641$	12.4573	−	21.5767i	0.492035	−	0.852230i	0.999958	+	0.00917289i	$0.00291986\pi$
$642$		0			0
$643$			4.80941i			0.189665i	0.995493	+	0.0948323i	$0.0302315\pi$
$643$			4.80941i			0.189665i	−0.995493	+	0.0948323i	$0.969769\pi$
$644$	−10.5960	−	12.2716i	−0.417540	−	0.483570i
$645$		0			0
$646$	6.93331	+	13.4648i	0.272788	+	0.529767i
$647$	−4.27034	+	7.39644i	−0.167884	+	0.290784i	−0.937676	−	0.347511i	$-0.887027\pi$
$647$	−4.27034	+	7.39644i	−0.167884	+	0.290784i	0.769792	+	0.638295i	$0.220360\pi$
$648$		0			0
$649$	23.5374	−	13.5893i	0.923925	−	0.533428i
$650$	38.9198	+	1.87297i	1.52656	+	0.0734638i
$651$		0			0
$652$	39.4796	+	3.80864i	1.54614	+	0.149158i
$653$	−24.1955	+	13.9693i	−0.946845	+	0.546661i	−0.892099	−	0.451839i	$-0.850768\pi$
$653$	−24.1955	+	13.9693i	−0.946845	+	0.546661i	−0.0547454	+	0.998500i	$0.517435\pi$
$654$		0			0
$655$	1.59605	+	0.921481i	0.0623629	+	0.0360052i
$656$	22.5554	−	7.75736i	0.880641	−	0.302874i
$657$		0			0
$658$	−1.86240	−	7.71928i	−0.0726038	−	0.300929i
$659$	−28.0553			−1.09288			−0.546439	−	0.837499i	$-0.684017\pi$
$659$	−28.0553			−1.09288			−0.546439	+	0.837499i	$0.684017\pi$
$660$		0			0
$661$	4.47127	−	7.74447i	0.173912	−	0.301225i	−0.765872	−	0.642993i	$-0.777692\pi$
$661$	4.47127	−	7.74447i	0.173912	−	0.301225i	0.939784	+	0.341768i	$0.111026\pi$
$662$	8.97077	−	13.9439i	0.348659	−	0.541944i
$663$		0			0
$664$	1.45293	−	10.0016i	0.0563846	−	0.388138i
$665$	−27.7838	+	8.13480i	−1.07741	+	0.315454i
$666$		0			0
$667$	15.1414	+	26.2257i	0.586277	+	1.01546i
$668$	−14.4017	+	20.1828i	−0.557219	+	0.780895i
$669$		0			0
$670$	−18.4207	−	35.7739i	−0.711654	−	1.38207i
$671$	28.0684			1.08357
$672$		0			0
$673$	45.4881			1.75344			0.876720	−	0.481002i	$-0.159727\pi$
$673$	45.4881			1.75344			0.876720	+	0.481002i	$0.159727\pi$
$674$	15.2329	+	29.5831i	0.586750	+	1.13950i
$675$		0			0
$676$	−14.9208	+	20.9102i	−0.573876	+	0.804238i
$677$	−5.48447	−	9.49939i	−0.210785	−	0.365091i	0.741175	−	0.671312i	$-0.234269\pi$
$677$	−5.48447	−	9.49939i	−0.210785	−	0.365091i	−0.951961	+	0.306221i	$0.900935\pi$
$678$		0			0
$679$	29.1293	+	27.8177i	1.11788	+	1.06754i
$680$	4.14661	−	28.5443i	0.159015	−	1.09462i
$681$		0			0
$682$	3.43439	−	5.33830i	0.131510	−	0.204414i
$683$	−14.1037	+	24.4283i	−0.539663	+	0.934723i	0.459259	+	0.888302i	$0.348115\pi$
$683$	−14.1037	+	24.4283i	−0.539663	+	0.934723i	−0.998922	+	0.0464211i	$0.985218\pi$
$684$		0			0
$685$	−42.4679			−1.62262
$686$	−6.24617	+	25.4359i	−0.238480	+	0.971147i
$687$		0			0
$688$	8.70035	+	25.2973i	0.331698	+	0.964450i
$689$	15.8896	+	9.17386i	0.605345	+	0.349496i
$690$		0			0
$691$	8.22050	−	4.74611i	0.312723	−	0.180550i	−0.335422	−	0.942068i	$-0.608879\pi$
$691$	8.22050	−	4.74611i	0.312723	−	0.180550i	0.648144	+	0.761518i	$0.275545\pi$
$692$	2.06770	+	0.199474i	0.0786023	+	0.00758285i
$693$		0			0
$694$	−14.6098	−	0.703079i	−0.554581	−	0.0266885i
$695$	−26.6920	+	15.4106i	−1.01249	+	0.584559i
$696$		0			0
$697$	−9.41929	+	16.3147i	−0.356781	+	0.617963i
$698$	−0.537552	−	1.04395i	−0.0203466	−	0.0395142i
$699$		0			0
$700$	27.0848	+	9.42711i	1.02371	+	0.356311i
$701$		−	14.3589i		−	0.542328i	−0.962533	−	0.271164i	$-0.912591\pi$
$701$		−	14.3589i		−	0.542328i	0.962533	−	0.271164i	$-0.0874085\pi$
$702$		0			0
$703$	1.56250	−	2.70633i	0.0589309	−	0.102071i
$704$	12.8497	−	12.1808i	0.484293	−	0.459079i
$705$		0			0
$706$	−0.330605	+	6.86988i	−0.0124425	+	0.258551i
$707$	7.31725	+	24.9915i	0.275193	+	0.939904i
$708$		0			0
$709$	−8.90161	+	5.13935i	−0.334307	+	0.193012i	−0.657752	−	0.753235i	$-0.728492\pi$
$709$	−8.90161	+	5.13935i	−0.334307	+	0.193012i	0.323445	+	0.946247i	$0.395159\pi$
$710$	44.9317	+	28.9068i	1.68626	+	1.08485i
$711$		0			0
$712$	−19.1813	+	7.64656i	−0.718851	+	0.286567i
$713$		−	6.21394i		−	0.232714i
$714$		0			0
$715$	−36.3184			−1.35823
$716$	−2.09426	−	4.59764i	−0.0782662	−	0.171822i
$717$		0			0
$718$	−22.3963	−	14.4086i	−0.835823	−	0.537726i
$719$	−7.39467	−	12.8079i	−0.275775	−	0.477656i	0.694556	−	0.719439i	$-0.255601\pi$
$719$	−7.39467	−	12.8079i	−0.275775	−	0.477656i	−0.970330	+	0.241783i	$0.922268\pi$
$720$		0			0
$721$	5.10158	+	1.24180i	0.189993	+	0.0462469i
$722$	−10.6074	−	0.510466i	−0.394765	−	0.0189976i
$723$		0			0
$724$	−9.64056	+	13.5104i	−0.358289	+	0.502111i
$725$	−46.3890	−	26.7827i	−1.72285	−	0.994685i
$726$		0			0
$727$	−43.5679			−1.61585			−0.807923	−	0.589289i	$-0.799408\pi$
$727$	−43.5679			−1.61585			−0.807923	+	0.589289i	$0.799408\pi$
$728$	−29.9561	+	23.4497i	−1.11025	+	0.869105i
$729$		0			0
$730$	−36.6512	+	18.8724i	−1.35652	+	0.698499i
$731$	−18.2979	−	10.5643i	−0.676773	−	0.390735i
$732$		0			0
$733$	11.3412	+	19.6435i	0.418896	+	0.725549i	0.995829	−	0.0912424i	$-0.0290838\pi$
$733$	11.3412	+	19.6435i	0.418896	+	0.725549i	−0.576933	+	0.816792i	$0.695750\pi$
$734$	−30.3054	−	1.45841i	−1.11859	−	0.0538309i
$735$		0			0
$736$	4.12731	−	16.8341i	0.152135	−	0.620511i
$737$	9.75399	+	16.8944i	0.359293	+	0.622314i
$738$		0			0
$739$	−2.32595	+	4.02866i	−0.0855615	+	0.148197i	−0.905630	−	0.424068i	$-0.860602\pi$
$739$	−2.32595	+	4.02866i	−0.0855615	+	0.148197i	0.820069	+	0.572265i	$0.193935\pi$
$740$	−5.41617	+	2.46711i	−0.199103	+	0.0906929i
$741$		0			0
$742$	9.30662	+	9.78512i	0.341657	+	0.359223i
$743$			28.3209i			1.03899i	0.854473	+	0.519496i	$0.173880\pi$
$743$			28.3209i			1.03899i	−0.854473	+	0.519496i	$0.826120\pi$
$744$		0			0
$745$	−29.6214	−	17.1019i	−1.08525	−	0.626567i
$746$	19.4361	+	12.5042i	0.711607	+	0.457812i
$747$		0			0
$748$	−1.34281	+	13.9194i	−0.0490982	+	0.508942i
$749$	8.31902	+	2.02497i	0.303971	+	0.0739908i
$750$		0			0
$751$	28.5823	−	16.5020i	1.04298	−	0.602166i	0.122306	−	0.992492i	$-0.460971\pi$
$751$	28.5823	−	16.5020i	1.04298	−	0.602166i	0.920677	+	0.390326i	$0.127638\pi$
$752$	5.57162	−	6.40475i	0.203176	−	0.233557i
$753$		0			0
$754$	63.1729	−	32.5290i	2.30062	−	1.18464i
$755$			3.92554i			0.142865i
$756$		0			0
$757$			19.0350i			0.691838i	0.938264	+	0.345919i	$0.112433\pi$
$757$			19.0350i			0.691838i	−0.938264	+	0.345919i	$0.887567\pi$
$758$	−2.79449	−	5.42704i	−0.101500	−	0.197119i
$759$		0			0
$760$	−24.2997	−	19.1670i	−0.881442	−	0.695260i
$761$	−43.2756	+	24.9852i	−1.56874	+	0.905712i	−0.572424	+	0.819958i	$0.693997\pi$
$761$	−43.2756	+	24.9852i	−1.56874	+	0.905712i	−0.996316	+	0.0857544i	$0.972670\pi$
$762$		0			0
$763$	10.6429	−	3.11613i	0.385300	−	0.112811i
$764$	−1.16679	+	12.0947i	−0.0422128	+	0.437570i
$765$		0			0
$766$	−15.4484	+	24.0124i	−0.558172	+	0.867603i
$767$	−54.0653	−	31.2146i	−1.95219	−	1.12709i
$768$		0			0
$769$			24.2908i			0.875949i	0.898987	+	0.437974i	$0.144304\pi$
$769$			24.2908i			0.875949i	−0.898987	+	0.437974i	$0.855696\pi$
$770$	−25.6385	−	7.56320i	−0.923948	−	0.272559i
$771$		0			0
$772$	7.61639	+	16.7206i	0.274120	+	0.601788i
$773$	−8.01612	+	13.8843i	−0.288320	+	0.499385i	−0.973409	−	0.229075i	$-0.926430\pi$
$773$	−8.01612	+	13.8843i	−0.288320	+	0.499385i	0.685089	+	0.728459i	$0.259763\pi$
$774$		0			0
$775$	5.49574	+	9.51890i	0.197413	+	0.341929i
$776$	−6.19021	+	42.6120i	−0.222216	+	1.52968i
$777$		0			0
$778$	−2.29506	+	47.6907i	−0.0822818	+	1.70979i
$779$	10.1068	+	17.5054i	0.362112	+	0.627197i
$780$		0			0
$781$	−22.4321	−	12.9512i	−0.802682	−	0.463429i
$782$	6.26694	+	12.1707i	0.224105	+	0.435224i
$783$		0			0
$784$	−26.0305	+	10.3158i	−0.929659	+	0.368420i
$785$	−11.7015			−0.417644
$786$		0			0
$787$	−8.71618	−	5.03229i	−0.310698	−	0.179382i	0.336541	−	0.941669i	$-0.390743\pi$
$787$	−8.71618	−	5.03229i	−0.310698	−	0.179382i	−0.647239	+	0.762287i	$0.724076\pi$
$788$	33.0104	+	23.5551i	1.17595	+	0.839114i
$789$		0			0
$790$	−2.43270	+	50.5510i	−0.0865517	+	1.79852i
$791$	−5.20130	+	5.44655i	−0.184937	+	0.193657i
$792$		0			0
$793$	−32.2365	−	55.8352i	−1.14475	−	1.98277i
$794$	0.0675114	−	0.104937i	0.00239589	−	0.00372409i
$795$		0			0
$796$	2.72520	+	5.98277i	0.0965923	+	0.212054i
$797$	−53.0872			−1.88045			−0.940223	−	0.340560i	$-0.889383\pi$
$797$	−53.0872			−1.88045			−0.940223	+	0.340560i	$0.889383\pi$
$798$		0			0
$799$			6.70471i			0.237196i
$800$	8.56591	+	29.4377i	0.302851	+	1.04078i
$801$		0			0
$802$	19.2878	−	29.9802i	0.681074	−	1.05864i
$803$	17.3087	−	9.99318i	0.610811	−	0.352652i
$804$		0			0
$805$	−25.1135	+	7.35295i	−0.885134	+	0.259157i
$806$	−14.5636	−	0.700857i	−0.512982	−	0.0246866i
$807$		0			0
$808$	−17.2407	+	21.8575i	−0.606525	+	0.768946i
$809$	26.9529	−	46.6838i	0.947614	−	1.64132i	0.197183	−	0.980367i	$-0.436821\pi$
$809$	26.9529	−	46.6838i	0.947614	−	1.64132i	0.750431	−	0.660949i	$-0.229846\pi$
$810$		0			0
$811$			48.2050i			1.69271i	0.532621	+	0.846354i	$0.321207\pi$
$811$			48.2050i			1.69271i	−0.532621	+	0.846354i	$0.678793\pi$
$812$	51.3702	−	9.80785i	1.80274	−	0.344188i
$813$		0			0
$814$	2.56531	−	1.32093i	0.0899142	−	0.0462986i
$815$	32.0076	−	55.4387i	1.12118	−	1.94193i
$816$		0			0
$817$	−19.6334	+	11.3353i	−0.686885	+	0.396574i
$818$	2.11294	−	43.9063i	0.0738771	−	1.53515i
$819$		0			0
$820$	3.69667	−	38.3190i	0.129093	−	1.33816i
$821$	22.4271	−	12.9483i	0.782712	−	0.451899i	−0.0546787	−	0.998504i	$-0.517413\pi$
$821$	22.4271	−	12.9483i	0.782712	−	0.451899i	0.837390	+	0.546605i	$0.184080\pi$
$822$		0			0
$823$	−48.1100	−	27.7763i	−1.67701	−	0.968221i	−0.963552	−	0.267522i	$-0.913795\pi$
$823$	−48.1100	−	27.7763i	−1.67701	−	0.968221i	−0.713457	−	0.700699i	$-0.752871\pi$
$824$	2.07855	+	5.21403i	0.0724098	+	0.181639i
$825$		0			0
$826$	−31.6663	−	33.2945i	−1.10181	−	1.15846i
$827$	−23.2870			−0.809770			−0.404885	−	0.914368i	$-0.632688\pi$
$827$	−23.2870			−0.809770			−0.404885	+	0.914368i	$0.632688\pi$
$828$		0			0
$829$	−2.58838	+	4.48320i	−0.0898980	+	0.155708i	−0.907468	−	0.420122i	$-0.861987\pi$
$829$	−2.58838	+	4.48320i	−0.0898980	+	0.155708i	0.817570	+	0.575829i	$0.195321\pi$
$830$	−13.7181	−	8.82554i	−0.476163	−	0.306339i
$831$		0			0
$832$	−38.9885	−	11.5719i	−1.35168	−	0.401182i
$833$	10.1638	−	19.6406i	0.352155	−	0.680506i
$834$		0			0
$835$	20.0087	+	34.6561i	0.692430	+	1.19932i
$836$	12.2139	+	8.71542i	0.422427	+	0.301429i
$837$		0			0
$838$	28.6235	−	14.7388i	0.988783	−	0.509144i
$839$	−12.7298			−0.439480			−0.219740	−	0.975558i	$-0.570521\pi$
$839$	−12.7298			−0.439480			−0.219740	+	0.975558i	$0.570521\pi$
$840$		0			0
$841$	−68.6816			−2.36833
$842$	30.2017	−	15.5514i	1.04082	−	0.535938i
$843$		0			0
$844$	25.1973	−	35.3119i	0.867328	−	1.21548i
$845$	20.7298	+	35.9052i	0.713128	+	1.23517i
$846$		0			0
$847$	−15.6858	−	3.81814i	−0.538969	−	0.131193i
$848$	−2.75973	+	14.1703i	−0.0947695	+	0.486610i
$849$		0			0
$850$	−20.3641	−	13.1012i	−0.698483	−	0.449368i
$851$	1.41233	−	2.44622i	0.0484139	−	0.0838554i
$852$		0			0
$853$	47.2928			1.61927			0.809637	−	0.586930i	$-0.199664\pi$
$853$	47.2928			1.61927			0.809637	+	0.586930i	$0.199664\pi$
$854$	−11.1294	−	46.1293i	−0.380840	−	1.57851i
$855$		0			0
$856$	3.38945	+	8.50239i	0.115849	+	0.290606i
$857$	−45.2524	−	26.1265i	−1.54579	−	0.892463i	−0.998456	−	0.0555505i	$-0.982309\pi$
$857$	−45.2524	−	26.1265i	−1.54579	−	0.892463i	−0.547336	−	0.836913i	$-0.684358\pi$
$858$		0			0
$859$	43.7066	−	25.2340i	1.49125	−	0.860973i	0.491299	−	0.870991i	$-0.336522\pi$
$859$	43.7066	−	25.2340i	1.49125	−	0.860973i	0.999950	+	0.0100178i	$0.00318880\pi$
$860$	42.9770	+	4.14604i	1.46551	+	0.141379i
$861$		0			0
$862$	−2.21663	+	46.0610i	−0.0754988	+	1.56884i
$863$	23.1918	−	13.3898i	0.789457	−	0.455793i	−0.0503147	−	0.998733i	$-0.516022\pi$
$863$	23.1918	−	13.3898i	0.789457	−	0.455793i	0.839771	+	0.542940i	$0.182689\pi$
$864$		0			0
$865$	1.67636	−	2.90355i	0.0569981	−	0.0987236i
$866$	23.2292	−	11.9612i	0.789360	−	0.406457i
$867$		0			0
$868$	−10.1350	−	3.52759i	−0.344006	−	0.119734i
$869$		−	24.5362i		−	0.832335i
$870$		0			0
$871$	22.4049	−	38.8063i	0.759160	−	1.31490i
$872$	9.30828	+	7.34214i	0.315218	+	0.248636i
$873$		0			0
$874$	14.6716	+	0.706053i	0.496274	+	0.0238826i
$875$	2.47574	−	2.59247i	0.0836952	−	0.0876416i
$876$		0			0
$877$	−22.4411	+	12.9564i	−0.757783	+	0.437506i	−0.828499	−	0.559990i	$-0.810805\pi$
$877$	−22.4411	+	12.9564i	−0.757783	+	0.437506i	0.0707159	+	0.997496i	$0.477472\pi$
$878$	−17.1607	+	26.6741i	−0.579147	+	0.900206i
$879$		0			0
$880$	−9.29383	−	27.0229i	−0.313295	−	0.910942i
$881$			10.0120i			0.337313i	0.985675	+	0.168657i	$0.0539429\pi$
$881$			10.0120i			0.337313i	−0.985675	+	0.168657i	$0.946057\pi$
$882$		0			0
$883$	−23.6231			−0.794981			−0.397491	−	0.917606i	$-0.630119\pi$
$883$	−23.6231			−0.794981			−0.397491	+	0.917606i	$0.630119\pi$
$884$	29.2314	−	13.3151i	0.983157	−	0.447836i
$885$		0			0
$886$	−6.91962	+	10.7556i	−0.232469	+	0.361342i
$887$	−9.08123	−	15.7291i	−0.304918	−	0.528133i	0.672325	−	0.740256i	$-0.265296\pi$
$887$	−9.08123	−	15.7291i	−0.304918	−	0.528133i	−0.977243	+	0.212123i	$0.931962\pi$
$888$		0			0
$889$	40.1927	+	38.3829i	1.34802	+	1.28732i
$890$	−1.60200	+	33.2891i	−0.0536990	+	1.11585i
$891$		0			0
$892$	22.4517	−	31.4641i	0.751738	−	1.05350i
$893$	6.23023	+	3.59703i	0.208487	+	0.120370i
$894$		0			0
$895$	−8.15407			−0.272560
$896$	−25.1136	−	16.2882i	−0.838987	−	0.544152i
$897$		0			0
$898$	−3.66221	−	7.11220i	−0.122210	−	0.237337i
$899$	17.3586	+	10.0220i	0.578942	+	0.334252i
$900$		0			0
$901$	−5.70104	−	9.87449i	−0.189929	−	0.328967i
$902$	−0.897138	+	18.6423i	−0.0298714	+	0.620721i
$903$		0			0
$904$	−7.96752	−	1.15744i	−0.264996	−	0.0384958i
$905$	13.3939	+	23.1989i	0.445228	+	0.771158i
$906$		0			0
$907$	27.7185	−	48.0098i	0.920377	−	1.59414i	0.121546	−	0.992586i	$-0.461215\pi$
$907$	27.7185	−	48.0098i	0.920377	−	1.59414i	0.798832	−	0.601554i	$-0.205452\pi$
$908$	−0.981131	+	0.446913i	−0.0325600	+	0.0148313i
$909$		0			0
$910$	14.4006	+	59.6878i	0.477376	+	1.97863i
$911$		−	18.4722i		−	0.612012i	−0.952030	−	0.306006i	$-0.901007\pi$
$911$		−	18.4722i		−	0.612012i	0.952030	−	0.306006i	$-0.0989928\pi$
$912$		0			0
$913$	6.84874	+	3.95412i	0.226660	+	0.130862i
$914$	7.17677	−	11.1553i	0.237386	−	0.368985i
$915$		0			0
$916$	45.5133	+	4.39071i	1.50380	+	0.145073i
$917$	−0.357259	+	1.46770i	−0.0117977	+	0.0484678i
$918$		0			0
$919$	−0.144308	+	0.0833164i	−0.00476029	+	0.00274835i	−0.502378	−	0.864648i	$-0.667541\pi$
$919$	−0.144308	+	0.0833164i	−0.00476029	+	0.00274835i	0.497618	+	0.867396i	$0.334208\pi$
$920$	−21.9642	−	17.3248i	−0.724138	−	0.571182i
$921$		0			0
$922$	20.5853	+	39.9777i	0.677941	+	1.31660i
$923$			59.4974i			1.95838i
$924$		0			0
$925$			4.99636i			0.164279i
$926$	−11.1588	+	5.74587i	−0.366700	+	0.188821i
$927$		0			0
$928$	40.3692	+	38.6800i	1.32518	+	1.26973i
$929$	−14.0194	+	8.09409i	−0.459961	+	0.265559i	−0.712028	−	0.702151i	$-0.752223\pi$
$929$	−14.0194	+	8.09409i	−0.459961	+	0.265559i	0.252067	+	0.967710i	$0.418890\pi$
$930$		0			0
$931$	−12.7979	−	19.9816i	−0.419433	−	0.654870i
$932$	5.98202	+	0.577092i	0.195948	+	0.0189033i
$933$		0			0
$934$	−3.72170	−	2.39435i	−0.121778	−	0.0783457i
$935$	19.5461	+	11.2849i	0.639225	+	0.369057i
$936$		0			0
$937$		−	19.5153i		−	0.637538i	−0.947832	−	0.318769i	$-0.896730\pi$
$937$		−	19.5153i		−	0.637538i	0.947832	−	0.318769i	$-0.103270\pi$
$938$	23.8977	−	22.7291i	0.780288	−	0.742131i
$939$		0			0
$940$	−5.67953	−	12.4685i	−0.185246	−	0.406679i
$941$	−12.3201	+	21.3390i	−0.401624	+	0.695633i	−0.993922	−	0.110086i	$-0.964887\pi$
$941$	−12.3201	+	21.3390i	−0.401624	+	0.695633i	0.592298	+	0.805719i	$0.298221\pi$
$942$		0			0
$943$	9.13538	+	15.8229i	0.297489	+	0.515266i
$944$	9.39015	−	48.2153i	0.305623	−	1.56927i
$945$		0			0
$946$	−20.9085	−	1.00619i	−0.679793	−	0.0327142i
$947$	−4.30769	−	7.46115i	−0.139981	−	0.242455i	0.787508	−	0.616304i	$-0.211371\pi$
$947$	−4.30769	−	7.46115i	−0.139981	−	0.242455i	−0.927489	+	0.373850i	$0.878038\pi$
$948$		0			0
$949$	−39.7579	−	22.9543i	−1.29060	−	0.745127i
$950$	−23.0993	+	11.8943i	−0.749440	+	0.385901i
$951$		0			0
$952$	23.4083	−	3.31230i	0.758668	−	0.107352i
$953$	27.4982			0.890755			0.445378	−	0.895343i	$-0.353069\pi$
$953$	27.4982			0.890755			0.445378	+	0.895343i	$0.353069\pi$
$954$		0			0
$955$	16.9838	+	9.80560i	0.549583	+	0.317302i
$956$	−18.3476	−	13.0922i	−0.593404	−	0.423432i
$957$		0			0
$958$	−23.1526	−	1.11419i	−0.748028	−	0.0359980i
$959$	−9.78084	−	33.4058i	−0.315840	−	1.07873i
$960$		0			0
$961$	13.4435	+	23.2849i	0.433662	+	0.751124i
$962$	−5.57392	−	3.58598i	−0.179710	−	0.115617i
$963$		0			0
$964$	−20.5178	+	9.34603i	−0.660834	+	0.301015i
$965$	29.6546			0.954616
$966$		0			0
$967$		−	21.2591i		−	0.683647i	−0.939764	−	0.341823i	$-0.888956\pi$
$967$		−	21.2591i		−	0.683647i	0.939764	−	0.341823i	$-0.111044\pi$
$968$	−6.39090	−	16.0315i	−0.205411	−	0.515272i
$969$		0			0
$970$	58.4462	+	37.6013i	1.87659	+	1.20730i
$971$	27.3347	−	15.7817i	0.877213	−	0.506459i	0.00747434	−	0.999972i	$-0.497621\pi$
$971$	27.3347	−	15.7817i	0.877213	−	0.506459i	0.869738	+	0.493513i	$0.164287\pi$
$972$		0			0
$973$	−18.2697	−	17.4470i	−0.585698	−	0.559325i
$974$	1.99611	−	41.4786i	0.0639594	−	1.32906i
$975$		0			0
$976$	33.2952	−	38.2738i	1.06575	−	1.22512i
$977$	−9.75712	+	16.8998i	−0.312158	+	0.540673i	−0.978829	−	0.204678i	$-0.934385\pi$
$977$	−9.75712	+	16.8998i	−0.312158	+	0.540673i	0.666671	+	0.745352i	$0.267718\pi$
$978$		0			0
$979$		−	16.1577i		−	0.516403i
$980$	−2.26388	+	45.1347i	−0.0723168	+	1.44178i
$981$		0			0
$982$	−21.9454	−	42.6190i	−0.700305	−	1.36003i
$983$	11.2401	−	19.4684i	0.358503	−	0.620946i	−0.629208	−	0.777237i	$-0.716620\pi$
$983$	11.2401	−	19.4684i	0.358503	−	0.620946i	0.987711	+	0.156291i	$0.0499538\pi$
$984$		0			0
$985$	56.6825	−	32.7257i	1.80606	−	1.04273i
$986$	−44.1063	−	2.12256i	−1.40463	−	0.0675961i
$987$		0			0
$988$	3.30955	−	34.3062i	0.105291	−	1.09143i
$989$	−17.7464	+	10.2459i	−0.564302	+	0.325800i
$990$		0			0
$991$	38.9073	+	22.4631i	1.23593	+	0.713565i	0.968260	−	0.249945i	$-0.0804125\pi$
$991$	38.9073	+	22.4631i	1.23593	+	0.713565i	0.267671	+	0.963510i	$0.413746\pi$
$992$	−3.20533	−	11.0155i	−0.101769	−	0.349742i
$993$		0			0
$994$	−12.3901	+	42.0014i	−0.392992	+	1.33220i
$995$	10.6107			0.336381
$996$		0			0
$997$	−14.5890	+	25.2688i	−0.462037	+	0.800272i	−0.999062	−	0.0432942i	$-0.986215\pi$
$997$	−14.5890	+	25.2688i	−0.462037	+	0.800272i	0.537025	+	0.843566i	$0.319548\pi$
$998$	−6.80268	+	10.5739i	−0.215335	+	0.334710i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.451.10		32
3.2	odd	2		168.2.t.a.115.7	yes	32
4.3	odd	2		2016.2.bs.c.1711.15		32
7.5	odd	6	inner	504.2.bk.c.19.12		32
8.3	odd	2	inner	504.2.bk.c.451.12		32
8.5	even	2		2016.2.bs.c.1711.2		32
12.11	even	2		672.2.bb.a.367.9		32
21.5	even	6		168.2.t.a.19.5	✓	32
21.11	odd	6		1176.2.p.a.979.32		32
21.17	even	6		1176.2.p.a.979.31		32
24.5	odd	2		672.2.bb.a.367.16		32
24.11	even	2		168.2.t.a.115.5	yes	32
28.19	even	6		2016.2.bs.c.271.2		32
56.5	odd	6		2016.2.bs.c.271.15		32
56.19	even	6	inner	504.2.bk.c.19.10		32
84.11	even	6		4704.2.p.a.3919.9		32
84.47	odd	6		672.2.bb.a.271.16		32
84.59	odd	6		4704.2.p.a.3919.20		32
168.5	even	6		672.2.bb.a.271.9		32
168.11	even	6		1176.2.p.a.979.29		32
168.53	odd	6		4704.2.p.a.3919.19		32
168.59	odd	6		1176.2.p.a.979.30		32
168.101	even	6		4704.2.p.a.3919.10		32
168.131	odd	6		168.2.t.a.19.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.5	✓	32	21.5	even	6
168.2.t.a.19.7	yes	32	168.131	odd	6
168.2.t.a.115.5	yes	32	24.11	even	2
168.2.t.a.115.7	yes	32	3.2	odd	2
504.2.bk.c.19.10		32	56.19	even	6	inner
504.2.bk.c.19.12		32	7.5	odd	6	inner
504.2.bk.c.451.10		32	1.1	even	1	trivial
504.2.bk.c.451.12		32	8.3	odd	2	inner
672.2.bb.a.271.9		32	168.5	even	6
672.2.bb.a.271.16		32	84.47	odd	6
672.2.bb.a.367.9		32	12.11	even	2
672.2.bb.a.367.16		32	24.5	odd	2
1176.2.p.a.979.29		32	168.11	even	6
1176.2.p.a.979.30		32	168.59	odd	6
1176.2.p.a.979.31		32	21.17	even	6
1176.2.p.a.979.32		32	21.11	odd	6
2016.2.bs.c.271.2		32	28.19	even	6
2016.2.bs.c.271.15		32	56.5	odd	6
2016.2.bs.c.1711.2		32	8.5	even	2
2016.2.bs.c.1711.15		32	4.3	odd	2
4704.2.p.a.3919.9		32	84.11	even	6
4704.2.p.a.3919.10		32	168.101	even	6
4704.2.p.a.3919.19		32	168.53	odd	6
4704.2.p.a.3919.20		32	84.59	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)

\(f(q)\)	\(=\)	\(q+(0.647418 + 1.25732i) q^{2} +(-1.16170 + 1.62802i) q^{4} +(1.61398 + 2.79550i) q^{5} +(-1.82725 + 1.91341i) q^{7} +(-2.79905 - 0.406616i) q^{8} +(-2.46991 + 3.83914i) q^{10} +(1.10660 - 1.91668i) q^{11} -5.08369 q^{13} +(-3.58876 - 1.05866i) q^{14} +(-1.30091 - 3.78254i) q^{16} +(2.73597 + 1.57961i) q^{17} +(2.93566 - 1.69490i) q^{19} +(-6.42609 - 0.619932i) q^{20} +(3.12631 + 0.150450i) q^{22} +(2.65351 - 1.53200i) q^{23} +(-2.70987 + 4.69363i) q^{25} +(-3.29127 - 6.39182i) q^{26} +(-0.992355 - 5.19762i) q^{28} +9.88340i q^{29} +(1.01402 - 1.75634i) q^{31} +(3.91363 - 4.08454i) q^{32} +(-0.214760 + 4.46266i) q^{34} +(-8.29809 - 2.01987i) q^{35} +(0.798374 - 0.460941i) q^{37} +(4.03163 + 2.59375i) q^{38} +(-3.38092 - 8.48100i) q^{40} +5.96303i q^{41} -6.68790 q^{43} +(1.83487 + 4.02817i) q^{44} +(3.64414 + 2.34446i) q^{46} +(1.06113 + 1.83793i) q^{47} +(-0.322287 - 6.99258i) q^{49} +(-7.65581 - 0.368427i) q^{50} +(5.90572 - 8.27636i) q^{52} +(-3.12560 - 1.80457i) q^{53} +7.14411 q^{55} +(5.89259 - 4.61274i) q^{56} +(-12.4266 + 6.39869i) q^{58} +(10.6351 + 6.14015i) q^{59} +(6.34115 + 10.9832i) q^{61} +(2.86477 + 0.137864i) q^{62} +(7.66933 + 2.27627i) q^{64} +(-8.20498 - 14.2114i) q^{65} +(-4.40720 + 7.63350i) q^{67} +(-5.75002 + 2.61918i) q^{68} +(-2.83271 - 11.7410i) q^{70} -11.7036i q^{71} +(7.82068 + 4.51527i) q^{73} +(1.09643 + 0.705388i) q^{74} +(-0.651014 + 6.74828i) q^{76} +(1.64537 + 5.61964i) q^{77} +(9.60105 - 5.54317i) q^{79} +(8.47445 - 9.74164i) q^{80} +(-7.49743 + 3.86057i) q^{82} +3.57322i q^{83} +10.1979i q^{85} +(-4.32987 - 8.40882i) q^{86} +(-3.87677 + 4.91493i) q^{88} +(6.32253 - 3.65032i) q^{89} +(9.28920 - 9.72719i) q^{91} +(-0.588444 + 6.09969i) q^{92} +(-1.62387 + 2.52409i) q^{94} +(9.47619 + 5.47108i) q^{95} -15.2238i q^{97} +(8.58324 - 4.93234i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44}+ \cdots - 60 q^{98}+O(q^{100}) \) 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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