LMFDB - Embedded newform 504.2.ch.b.269.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("504.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.7
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.937852 - 1.05851i) q^{2} +(-0.240867 + 1.98544i) q^{4} +(-0.331990 + 0.191675i) q^{5} +(-2.03027 + 1.69647i) q^{7} +(2.32750 - 1.60709i) q^{8} +O(q^{10})$	\(q+(-0.937852 - 1.05851i) q^{2} +(-0.240867 + 1.98544i) q^{4} +(-0.331990 + 0.191675i) q^{5} +(-2.03027 + 1.69647i) q^{7} +(2.32750 - 1.60709i) q^{8} +(0.514246 + 0.171651i) q^{10} +(2.28107 - 3.95093i) q^{11} -2.84195 q^{13} +(3.69981 + 0.558007i) q^{14} +(-3.88397 - 0.956454i) q^{16} +(-2.46500 + 4.26950i) q^{17} +(4.18535 + 7.24924i) q^{19} +(-0.300594 - 0.705316i) q^{20} +(-6.32139 + 1.29086i) q^{22} +(-5.41792 + 3.12804i) q^{23} +(-2.42652 + 4.20286i) q^{25} +(2.66533 + 3.00822i) q^{26} +(-2.87923 - 4.43960i) q^{28} -0.292746 q^{29} +(4.93966 + 2.85191i) q^{31} +(2.63017 + 5.00821i) q^{32} +(6.83109 - 1.39495i) q^{34} +(0.348858 - 0.952363i) q^{35} +(-6.12469 + 3.53609i) q^{37} +(3.74812 - 11.2289i) q^{38} +(-0.464668 + 0.979662i) q^{40} -4.92280 q^{41} -4.35631i q^{43} +(7.29492 + 5.48059i) q^{44} +(8.39226 + 2.80126i) q^{46} +(4.73214 + 8.19631i) q^{47} +(1.24396 - 6.88858i) q^{49} +(6.72447 - 1.37317i) q^{50} +(0.684532 - 5.64254i) q^{52} +(-2.33050 + 4.03655i) q^{53} +1.74890i q^{55} +(-1.99905 + 7.21137i) q^{56} +(0.274553 + 0.309873i) q^{58} +(-5.72506 - 3.30537i) q^{59} +(-1.40098 - 2.42656i) q^{61} +(-1.61390 - 7.90332i) q^{62} +(2.83450 - 7.48102i) q^{64} +(0.943501 - 0.544730i) q^{65} +(7.81560 + 4.51234i) q^{67} +(-7.88311 - 5.92249i) q^{68} +(-1.33526 + 0.523908i) q^{70} -4.37059i q^{71} +(10.9929 + 6.34673i) q^{73} +(9.48703 + 3.16669i) q^{74} +(-15.4011 + 6.56367i) q^{76} +(2.07147 + 11.8912i) q^{77} +(-0.0352186 - 0.0610004i) q^{79} +(1.47277 - 0.426925i) q^{80} +(4.61686 + 5.21081i) q^{82} -6.48166i q^{83} -1.88991i q^{85} +(-4.61118 + 4.08558i) q^{86} +(-1.04032 - 12.8617i) q^{88} +(1.63404 + 2.83024i) q^{89} +(5.76992 - 4.82130i) q^{91} +(-4.90555 - 11.5104i) q^{92} +(4.23779 - 12.6959i) q^{94} +(-2.77899 - 1.60445i) q^{95} +0.349243i q^{97} +(-8.45825 + 5.14373i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) $ 56 * q - 8 * q^4 - 20 * q^7	$ 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) $ 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Display 100 coefficients 10 coefficients

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 $

$2$	−0.937852	−	1.05851i	−0.663162	−	0.748476i
$2$	−0.937852	−	1.05851i	−0.663162	−	0.748476i
$3$		0			0
$3$		0			0
$4$	−0.240867	+	1.98544i	−0.120433	+	0.992721i
$5$	−0.331990	+	0.191675i	−0.148471	+	0.0857195i	−0.572395	−	0.819978i	$-0.693986\pi$
$5$	−0.331990	+	0.191675i	−0.148471	+	0.0857195i	0.423924	+	0.905698i	$0.360652\pi$
$6$		0			0
$7$	−2.03027	+	1.69647i	−0.767368	+	0.641206i
$7$	−2.03027	+	1.69647i	−0.767368	+	0.641206i
$8$	2.32750	−	1.60709i	0.822895	−	0.568193i
$9$		0			0
$10$	0.514246	+	0.171651i	0.162619	+	0.0542808i
$11$	2.28107	−	3.95093i	0.687769	−	1.19125i	−0.284789	−	0.958590i	$-0.591923\pi$
$11$	2.28107	−	3.95093i	0.687769	−	1.19125i	0.972558	−	0.232661i	$-0.0747432\pi$
$12$		0			0
$13$	−2.84195			−0.788216			−0.394108	−	0.919064i	$-0.628946\pi$
$13$	−2.84195			−0.788216			−0.394108	+	0.919064i	$0.628946\pi$
$14$	3.69981	+	0.558007i	0.988817	+	0.149134i
$15$		0			0
$16$	−3.88397	−	0.956454i	−0.970992	−	0.239114i
$17$	−2.46500	+	4.26950i	−0.597850	+	1.03551i	0.395288	+	0.918557i	$0.370645\pi$
$17$	−2.46500	+	4.26950i	−0.597850	+	1.03551i	−0.993138	+	0.116949i	$0.962689\pi$
$18$		0			0
$19$	4.18535	+	7.24924i	0.960185	+	1.66309i	0.722030	+	0.691861i	$0.243209\pi$
$19$	4.18535	+	7.24924i	0.960185	+	1.66309i	0.238154	+	0.971227i	$0.423458\pi$
$20$	−0.300594	−	0.705316i	−0.0672148	−	0.157713i
$21$		0			0
$22$	−6.32139	+	1.29086i	−1.34773	+	0.275213i
$23$	−5.41792	+	3.12804i	−1.12971	+	0.652241i	−0.943863	−	0.330337i	$-0.892838\pi$
$23$	−5.41792	+	3.12804i	−1.12971	+	0.652241i	−0.185852	+	0.982578i	$0.559504\pi$
$24$		0			0
$25$	−2.42652	+	4.20286i	−0.485304	+	0.840572i
$26$	2.66533	+	3.00822i	0.522715	+	0.589961i
$27$		0			0
$28$	−2.87923	−	4.43960i	−0.544123	−	0.839006i
$29$	−0.292746			−0.0543616			−0.0271808	−	0.999631i	$-0.508653\pi$
$29$	−0.292746			−0.0543616			−0.0271808	+	0.999631i	$0.508653\pi$
$30$		0			0
$31$	4.93966	+	2.85191i	0.887188	+	0.512218i	0.873022	−	0.487681i	$-0.162157\pi$
$31$	4.93966	+	2.85191i	0.887188	+	0.512218i	0.0141665	+	0.999900i	$0.495490\pi$
$32$	2.63017	+	5.00821i	0.464954	+	0.885335i
$33$		0			0
$34$	6.83109	−	1.39495i	1.17152	−	0.239232i
$35$	0.348858	−	0.952363i	0.0589677	−	0.160979i
$36$		0			0
$37$	−6.12469	+	3.53609i	−1.00689	+	0.581330i	−0.910281	−	0.413992i	$-0.864134\pi$
$37$	−6.12469	+	3.53609i	−1.00689	+	0.581330i	−0.0966129	+	0.995322i	$0.530801\pi$
$38$	3.74812	−	11.2289i	0.608025	−	1.82157i
$39$		0			0
$40$	−0.464668	+	0.979662i	−0.0734704	+	0.154898i
$41$	−4.92280			−0.768812			−0.384406	−	0.923164i	$-0.625594\pi$
$41$	−4.92280			−0.768812			−0.384406	+	0.923164i	$0.625594\pi$
$42$		0			0
$43$		−	4.35631i		−	0.664332i	−0.943221	−	0.332166i	$-0.892221\pi$
$43$		−	4.35631i		−	0.664332i	0.943221	−	0.332166i	$-0.107779\pi$
$44$	7.29492	+	5.48059i	1.09975	+	0.826230i
$45$		0			0
$46$	8.39226	+	2.80126i	1.23737	+	0.413023i
$47$	4.73214	+	8.19631i	0.690253	+	1.19555i	0.971755	+	0.235993i	$0.0758343\pi$
$47$	4.73214	+	8.19631i	0.690253	+	1.19555i	−0.281501	+	0.959561i	$0.590832\pi$
$48$		0			0
$49$	1.24396	−	6.88858i	0.177709	−	0.984083i
$50$	6.72447	−	1.37317i	0.950983	−	0.194196i
$51$		0			0
$52$	0.684532	−	5.64254i	0.0949275	−	0.782479i
$53$	−2.33050	+	4.03655i	−0.320119	+	0.554462i	−0.980512	−	0.196458i	$-0.937056\pi$
$53$	−2.33050	+	4.03655i	−0.320119	+	0.554462i	0.660393	+	0.750920i	$0.270390\pi$
$54$		0			0
$55$			1.74890i			0.235821i
$56$	−1.99905	+	7.21137i	−0.267135	+	0.963659i
$57$		0			0
$58$	0.274553	+	0.309873i	0.0360505	+	0.0406884i
$59$	−5.72506	−	3.30537i	−0.745340	−	0.430322i	0.0786677	−	0.996901i	$-0.474933\pi$
$59$	−5.72506	−	3.30537i	−0.745340	−	0.430322i	−0.824008	+	0.566579i	$0.808267\pi$
$60$		0			0
$61$	−1.40098	−	2.42656i	−0.179376	−	0.310689i	0.762291	−	0.647235i	$-0.224075\pi$
$61$	−1.40098	−	2.42656i	−0.179376	−	0.310689i	−0.941667	+	0.336546i	$0.890741\pi$
$62$	−1.61390	−	7.90332i	−0.204966	−	1.00372i
$63$		0			0
$64$	2.83450	−	7.48102i	0.354313	−	0.935127i
$65$	0.943501	−	0.544730i	0.117027	−	0.0675655i
$66$		0			0
$67$	7.81560	+	4.51234i	0.954827	+	0.551270i	0.894577	−	0.446913i	$-0.147477\pi$
$67$	7.81560	+	4.51234i	0.954827	+	0.551270i	0.0602503	+	0.998183i	$0.480810\pi$
$68$	−7.88311	−	5.92249i	−0.955968	−	0.718208i
$69$		0			0
$70$	−1.33526	+	0.523908i	−0.159594	+	0.0626190i
$71$		−	4.37059i		−	0.518694i	−0.965784	−	0.259347i	$-0.916493\pi$
$71$		−	4.37059i		−	0.518694i	0.965784	−	0.259347i	$-0.0835073\pi$
$72$		0			0
$73$	10.9929	+	6.34673i	1.28662	+	0.742829i	0.978049	−	0.208374i	$-0.0668171\pi$
$73$	10.9929	+	6.34673i	1.28662	+	0.742829i	0.308568	+	0.951202i	$0.400150\pi$
$74$	9.48703	+	3.16669i	1.10285	+	0.368120i
$75$		0			0
$76$	−15.4011	+	6.56367i	−1.76662	+	0.752905i
$77$	2.07147	+	11.8912i	0.236066	+	1.35513i
$78$		0			0
$79$	−0.0352186	−	0.0610004i	−0.00396240	−	0.00686308i	0.864037	−	0.503428i	$-0.167928\pi$
$79$	−0.0352186	−	0.0610004i	−0.00396240	−	0.00686308i	−0.868000	+	0.496565i	$0.834595\pi$
$80$	1.47277	−	0.426925i	0.164660	−	0.0477316i
$81$		0			0
$82$	4.61686	+	5.21081i	0.509847	+	0.575438i
$83$		−	6.48166i		−	0.711454i	−0.934590	−	0.355727i	$-0.884233\pi$
$83$		−	6.48166i		−	0.711454i	0.934590	−	0.355727i	$-0.115767\pi$
$84$		0			0
$85$		−	1.88991i		−	0.204990i
$86$	−4.61118	+	4.08558i	−0.497236	+	0.440559i
$87$		0			0
$88$	−1.04032	−	12.8617i	−0.110899	−	1.37106i
$89$	1.63404	+	2.83024i	0.173208	+	0.300004i	0.939540	−	0.342441i	$-0.111254\pi$
$89$	1.63404	+	2.83024i	0.173208	+	0.300004i	−0.766332	+	0.642445i	$0.777920\pi$
$90$		0			0
$91$	5.76992	−	4.82130i	0.604852	−	0.505409i
$92$	−4.90555	−	11.5104i	−0.511438	−	1.20004i
$93$		0			0
$94$	4.23779	−	12.6959i	0.437094	−	1.30948i
$95$	−2.77899	−	1.60445i	−0.285118	−	0.164613i
$96$		0			0
$97$			0.349243i			0.0354602i	0.999843	+	0.0177301i	$0.00564396\pi$
$97$			0.349243i			0.0354602i	−0.999843	+	0.0177301i	$0.994356\pi$
$98$	−8.45825	+	5.14373i	−0.854412	+	0.519595i
$99$		0			0
$100$	−7.76007	−	5.83005i	−0.776007	−	0.583005i
$101$	−13.3130	−	7.68628i	−1.32470	−	0.764814i	−0.340222	−	0.940345i	$-0.610502\pi$
$101$	−13.3130	−	7.68628i	−1.32470	−	0.764814i	−0.984474	+	0.175531i	$0.943836\pi$
$102$		0			0
$103$	2.06085	−	1.18983i	0.203062	−	0.117238i	−0.395021	−	0.918672i	$-0.629263\pi$
$103$	2.06085	−	1.18983i	0.203062	−	0.117238i	0.598083	+	0.801434i	$0.295929\pi$
$104$	−6.61464	+	4.56728i	−0.648619	+	0.447859i
$105$		0			0
$106$	6.45837	−	1.31884i	0.627292	−	0.128097i
$107$	−0.412090	−	0.713762i	−0.0398383	−	0.0690019i	0.845419	−	0.534104i	$-0.179351\pi$
$107$	−0.412090	−	0.713762i	−0.0398383	−	0.0690019i	−0.885257	+	0.465102i	$0.846018\pi$
$108$		0			0
$109$	−14.1259	−	8.15558i	−1.35301	−	0.781163i	−0.364343	−	0.931265i	$-0.618706\pi$
$109$	−14.1259	−	8.15558i	−1.35301	−	0.781163i	−0.988670	+	0.150102i	$0.952040\pi$
$110$	1.85121	−	1.64021i	0.176506	−	0.156387i
$111$		0			0
$112$	9.50808	−	4.64719i	0.898429	−	0.439118i
$113$			3.02323i			0.284401i	0.989838	+	0.142201i	$0.0454178\pi$
$113$			3.02323i			0.284401i	−0.989838	+	0.142201i	$0.954582\pi$
$114$		0			0
$115$	1.19913	−	2.07696i	0.111820	−	0.193677i
$116$	0.0705128	−	0.581231i	0.00654695	−	0.0539659i
$117$		0			0
$118$	1.87052	+	9.15996i	0.172195	+	0.843242i
$119$	−2.23849	−	12.8500i	−0.205202	−	1.17796i
$120$		0			0
$121$	−4.90658	−	8.49845i	−0.446053	−	0.772586i
$122$	−1.25462	+	3.75869i	−0.113588	+	0.340296i
$123$		0			0
$124$	−6.85211	+	9.12047i	−0.615337	+	0.819043i
$125$		−	3.77716i		−	0.337839i
$126$		0			0
$127$	2.89959			0.257297			0.128649	−	0.991690i	$-0.458936\pi$
$127$	2.89959			0.257297			0.128649	+	0.991690i	$0.458936\pi$
$128$	−10.5770	+	4.01575i	−0.934887	+	0.354946i
$129$		0			0
$130$	−1.46146	−	0.487824i	−0.128179	−	0.0427850i
$131$	10.5535	−	6.09304i	0.922059	−	0.532351i	0.0377678	−	0.999287i	$-0.487975\pi$
$131$	10.5535	−	6.09304i	0.922059	−	0.532351i	0.884291	+	0.466935i	$0.154642\pi$
$132$		0			0
$133$	−20.7955	−	7.61755i	−1.80320	−	0.660525i
$134$	−2.55354	−	12.5048i	−0.220593	−	1.08025i
$135$		0			0
$136$	1.12421	+	13.8987i	0.0963999	+	1.19181i
$137$	−15.9155	−	9.18879i	−1.35975	−	0.785051i	−0.370159	−	0.928968i	$-0.620697\pi$
$137$	−15.9155	−	9.18879i	−1.35975	−	0.785051i	−0.989590	+	0.143917i	$0.954030\pi$
$138$		0			0
$139$	6.40327			0.543118			0.271559	−	0.962422i	$-0.412461\pi$
$139$	6.40327			0.543118			0.271559	+	0.962422i	$0.412461\pi$
$140$	1.80683	+	0.922030i	0.152705	+	0.0779257i
$141$		0			0
$142$	−4.62629	+	4.09897i	−0.388230	+	0.343978i
$143$	−6.48270	+	11.2284i	−0.542111	+	0.938963i
$144$		0			0
$145$	0.0971889	−	0.0561120i	0.00807110	−	0.00465985i
$146$	−3.59163	−	17.5883i	−0.297245	−	1.45562i
$147$		0			0
$148$	−5.54548	−	13.0120i	−0.455835	−	1.06958i
$149$	9.21714	+	15.9646i	0.755098	+	1.30787i	0.945326	+	0.326128i	$0.105744\pi$
$149$	9.21714	+	15.9646i	0.755098	+	1.30787i	−0.190228	+	0.981740i	$0.560923\pi$
$150$		0			0
$151$	−7.38424	+	12.7899i	−0.600921	+	1.04083i	0.391761	+	0.920067i	$0.371866\pi$
$151$	−7.38424	+	12.7899i	−0.600921	+	1.04083i	−0.992682	+	0.120758i	$0.961467\pi$
$152$	21.3916	+	10.1463i	1.73509	+	0.822977i
$153$		0			0
$154$	10.6442	−	13.3449i	0.857733	−	1.07536i
$155$	−2.18656			−0.175628
$156$		0			0
$157$	3.02939	−	5.24706i	0.241772	−	0.418761i	−0.719447	−	0.694547i	$-0.755605\pi$
$157$	3.02939	−	5.24706i	0.241772	−	0.418761i	0.961219	+	0.275786i	$0.0889381\pi$
$158$	−0.0315394	+	0.0944885i	−0.00250914	+	0.00751710i
$159$		0			0
$160$	−1.83314	−	1.15854i	−0.144922	−	0.0915906i
$161$	5.69319	−	15.5421i	0.448686	−	1.22489i
$162$		0			0
$163$	−3.88592	+	2.24354i	−0.304369	+	0.175727i	−0.644404	−	0.764685i	$-0.722894\pi$
$163$	−3.88592	+	2.24354i	−0.304369	+	0.175727i	0.340035	+	0.940413i	$0.389561\pi$
$164$	1.18574	−	9.77394i	0.0925906	−	0.763216i
$165$		0			0
$166$	−6.86087	+	6.07883i	−0.532507	+	0.471809i
$167$	15.9351			1.23309			0.616546	−	0.787319i	$-0.288532\pi$
$167$	15.9351			1.23309			0.616546	+	0.787319i	$0.288532\pi$
$168$		0			0
$169$	−4.92330			−0.378715
$170$	−2.00048	+	1.77246i	−0.153430	+	0.135941i
$171$		0			0
$172$	8.64921	+	1.04929i	0.659496	+	0.0800077i
$173$	−16.5050	+	9.52916i	−1.25485	+	0.724488i	−0.972069	−	0.234696i	$-0.924591\pi$
$173$	−16.5050	+	9.52916i	−1.25485	+	0.724488i	−0.282782	+	0.959184i	$0.591257\pi$
$174$		0			0
$175$	−2.20355	−	12.6494i	−0.166573	−	0.956208i
$176$	−12.6385	+	13.1636i	−0.952662	+	0.992240i
$177$		0			0
$178$	1.46333	−	4.38398i	0.109681	−	0.328593i
$179$	1.74852	−	3.02853i	0.130691	−	0.226363i	−0.793252	−	0.608893i	$-0.791614\pi$
$179$	1.74852	−	3.02853i	0.130691	−	0.226363i	0.923943	+	0.382530i	$0.124947\pi$
$180$		0			0
$181$	21.3086			1.58386			0.791929	−	0.610613i	$-0.209077\pi$
$181$	21.3086			1.58386			0.791929	+	0.610613i	$0.209077\pi$
$182$	−10.5147	−	1.58583i	−0.779401	−	0.117549i
$183$		0			0
$184$	−7.58316	+	15.9876i	−0.559038	+	1.17862i
$185$	1.35556	−	2.34790i	0.0996627	−	0.172621i
$186$		0			0
$187$	11.2457	+	19.4781i	0.822365	+	1.42438i
$188$	−17.4131	+	7.42118i	−1.26998	+	0.541245i
$189$		0			0
$190$	0.907962	+	4.44631i	0.0658705	+	0.322569i
$191$	17.2191	−	9.94147i	1.24593	−	0.719340i	0.275637	−	0.961262i	$-0.411111\pi$
$191$	17.2191	−	9.94147i	1.24593	−	0.719340i	0.970296	+	0.241922i	$0.0777778\pi$
$192$		0			0
$193$	5.21260	−	9.02849i	0.375211	−	0.649885i	−0.615147	−	0.788412i	$-0.710903\pi$
$193$	5.21260	−	9.02849i	0.375211	−	0.649885i	0.990359	+	0.138527i	$0.0442368\pi$
$194$	0.369675	−	0.327538i	0.0265411	−	0.0235158i
$195$		0			0
$196$	13.3773	+	4.12904i	0.955518	+	0.294932i
$197$	16.0387			1.14271			0.571355	−	0.820703i	$-0.306418\pi$
$197$	16.0387			1.14271			0.571355	+	0.820703i	$0.306418\pi$
$198$		0			0
$199$	2.00128	+	1.15544i	0.141867	+	0.0819069i	0.569253	−	0.822162i	$-0.307232\pi$
$199$	2.00128	+	1.15544i	0.141867	+	0.0819069i	−0.427387	+	0.904069i	$0.640566\pi$
$200$	1.10666	+	13.6818i	0.0782526	+	0.967449i
$201$		0			0
$202$	4.34969	+	21.3005i	0.306043	+	1.49870i
$203$	0.594353	−	0.496636i	0.0417154	−	0.0348570i
$204$		0			0
$205$	1.63432	−	0.943576i	0.114146	−	0.0659022i
$206$	−3.19222	−	1.06554i	−0.222413	−	0.0742394i
$207$		0			0
$208$	11.0381	+	2.71820i	0.765351	+	0.188473i
$209$	38.1883			2.64154
$210$		0			0
$211$		−	12.7274i		−	0.876193i	−0.898928	−	0.438096i	$-0.855653\pi$
$211$		−	12.7274i		−	0.876193i	0.898928	−	0.438096i	$-0.144347\pi$
$212$	−7.45299	−	5.59935i	−0.511874	−	0.384565i
$213$		0			0
$214$	−0.369040	+	1.10560i	−0.0252271	+	0.0755774i
$215$	0.834995	+	1.44625i	0.0569462	+	0.0986337i
$216$		0			0
$217$	−14.8670	+	2.58985i	−1.00924	+	0.175811i
$218$	4.61526	+	22.6010i	0.312585	+	1.53074i
$219$		0			0
$220$	−3.47233	−	0.421251i	−0.234105	−	0.0284007i
$221$	7.00541	−	12.1337i	0.471235	−	0.816202i
$222$		0			0
$223$		−	11.4933i		−	0.769649i	−0.922990	−	0.384824i	$-0.874262\pi$
$223$		−	11.4933i		−	0.769649i	0.922990	−	0.384824i	$-0.125738\pi$
$224$	−13.8362	−	5.70598i	−0.924473	−	0.381247i
$225$		0			0
$226$	3.20010	−	2.83534i	0.212868	−	0.188604i
$227$	1.51766	+	0.876221i	0.100731	+	0.0581568i	0.549519	−	0.835481i	$-0.314811\pi$
$227$	1.51766	+	0.876221i	0.100731	+	0.0581568i	−0.448788	+	0.893638i	$0.648144\pi$
$228$		0			0
$229$	2.91170	+	5.04322i	0.192411	+	0.333265i	0.946049	−	0.324025i	$-0.105036\pi$
$229$	2.91170	+	5.04322i	0.192411	+	0.333265i	−0.753638	+	0.657290i	$0.771703\pi$
$230$	−3.32308	+	0.678591i	−0.219117	+	0.0447450i
$231$		0			0
$232$	−0.681367	+	0.470470i	−0.0447339	+	0.0308879i
$233$	−7.44335	+	4.29742i	−0.487630	+	0.281533i	−0.723591	−	0.690229i	$-0.757510\pi$
$233$	−7.44335	+	4.29742i	−0.487630	+	0.281533i	0.235961	+	0.971763i	$0.424176\pi$
$234$		0			0
$235$	−3.14205	−	1.81406i	−0.204965	−	0.118336i
$236$	7.94160	−	10.5706i	0.516954	−	0.688090i
$237$		0			0
$238$	−11.5024	+	14.4209i	−0.745593	+	0.934766i
$239$		−	2.17800i		−	0.140883i	−0.997516	−	0.0704417i	$-0.977559\pi$
$239$		−	2.17800i		−	0.140883i	0.997516	−	0.0704417i	$-0.0224409\pi$
$240$		0			0
$241$	−5.08185	−	2.93401i	−0.327351	−	0.188996i	0.327314	−	0.944916i	$-0.393857\pi$
$241$	−5.08185	−	2.93401i	−0.327351	−	0.188996i	−0.654664	+	0.755920i	$0.727190\pi$
$242$	−4.39401	+	13.1639i	−0.282457	+	0.846210i
$243$		0			0
$244$	5.15524	−	2.19708i	0.330031	−	0.140654i
$245$	0.907384	+	2.52538i	0.0579706	+	0.161340i
$246$		0			0
$247$	−11.8946	−	20.6020i	−0.756833	−	1.31087i
$248$	16.0803	−	1.30067i	1.02110	−	0.0825924i
$249$		0			0
$250$	−3.99814	+	3.54242i	−0.252865	+	0.224042i
$251$			29.5645i			1.86609i	0.359755	+	0.933047i	$0.382860\pi$
$251$			29.5645i			1.86609i	−0.359755	+	0.933047i	$0.617140\pi$
$252$		0			0
$253$			28.5411i			1.79437i
$254$	−2.71939	−	3.06923i	−0.170630	−	0.192581i
$255$		0			0
$256$	14.1704	+	7.42967i	0.885649	+	0.464354i
$257$	10.4608	+	18.1187i	0.652530	+	1.13021i	0.982507	+	0.186226i	$0.0596255\pi$
$257$	10.4608	+	18.1187i	0.652530	+	1.13021i	−0.329977	+	0.943989i	$0.607041\pi$
$258$		0			0
$259$	6.43587	−	17.5696i	0.399906	−	1.09172i
$260$	0.854273	+	2.00447i	0.0529798	+	0.124312i
$261$		0			0
$262$	−16.3471	−	5.45651i	−1.00993	−	0.337105i
$263$	−10.3508	−	5.97604i	−0.638258	−	0.368498i	0.145685	−	0.989331i	$-0.453461\pi$
$263$	−10.3508	−	5.97604i	−0.638258	−	0.368498i	−0.783943	+	0.620833i	$0.786795\pi$
$264$		0			0
$265$		−	1.78679i		−	0.109762i
$266$	11.4399	+	29.1563i	0.701425	+	1.78769i
$267$		0			0
$268$	−10.8415	+	14.4306i	−0.662250	+	0.881486i
$269$	14.0600	+	8.11753i	0.857251	+	0.494934i	0.863091	−	0.505049i	$-0.168525\pi$
$269$	14.0600	+	8.11753i	0.857251	+	0.494934i	−0.00583949	+	0.999983i	$0.501859\pi$
$270$		0			0
$271$	−22.0735	+	12.7441i	−1.34087	+	0.774151i	−0.986935	−	0.161119i	$-0.948490\pi$
$271$	−22.0735	+	12.7441i	−1.34087	+	0.774151i	−0.353934	+	0.935270i	$0.615156\pi$
$272$	13.6575	−	14.2249i	0.828110	−	0.862514i
$273$		0			0
$274$	5.19996	+	25.4643i	0.314141	+	1.53836i
$275$	11.0701	+	19.1741i	0.667555	+	1.15624i
$276$		0			0
$277$	9.51680	+	5.49453i	0.571809	+	0.330134i	0.757872	−	0.652404i	$-0.226239\pi$
$277$	9.51680	+	5.49453i	0.571809	+	0.330134i	−0.186062	+	0.982538i	$0.559573\pi$
$278$	−6.00532	−	6.77789i	−0.360175	−	0.406511i
$279$		0			0
$280$	−0.718570	−	2.77727i	−0.0429428	−	0.165974i
$281$		−	6.71345i		−	0.400491i	−0.979746	−	0.200245i	$-0.935826\pi$
$281$		−	6.71345i		−	0.400491i	0.979746	−	0.200245i	$-0.0641740\pi$
$282$		0			0
$283$	−7.07673	+	12.2573i	−0.420668	+	0.728619i	−0.996005	−	0.0892979i	$-0.971538\pi$
$283$	−7.07673	+	12.2573i	−0.420668	+	0.728619i	0.575337	+	0.817917i	$0.304871\pi$
$284$	8.67756	+	1.05273i	0.514918	+	0.0624680i
$285$		0			0
$286$	17.9651	−	3.66858i	1.06230	−	0.216927i
$287$	9.99460	−	8.35140i	0.589962	−	0.492967i
$288$		0			0
$289$	−3.65242	−	6.32618i	−0.214848	−	0.372128i
$290$	−0.150544	−	0.0502502i	−0.00884023	−	0.00295079i
$291$		0			0
$292$	−15.2489	+	20.2970i	−0.892373	+	1.18779i
$293$		−	7.73971i		−	0.452159i	−0.974109	−	0.226079i	$-0.927409\pi$
$293$		−	7.73971i		−	0.452159i	0.974109	−	0.226079i	$-0.0725909\pi$
$294$		0			0
$295$	2.53422			0.147548
$296$	−8.57239	+	18.0732i	−0.498260	+	1.05048i
$297$		0			0
$298$	8.25425	−	24.7288i	0.478156	−	1.43250i
$299$	15.3975	−	8.88974i	0.890459	−	0.514107i
$300$		0			0
$301$	7.39037	+	8.84447i	0.425974	+	0.509787i
$302$	20.4635	−	4.17876i	1.17754	−	0.240460i
$303$		0			0
$304$	−9.32219	−	32.1589i	−0.534664	−	1.84444i
$305$	0.930220	+	0.537063i	0.0532643	+	0.0307521i
$306$		0			0
$307$	−24.8919			−1.42066			−0.710329	−	0.703870i	$-0.751454\pi$
$307$	−24.8919			−1.42066			−0.710329	+	0.703870i	$0.751454\pi$
$308$	−24.1083	+	1.24858i	−1.37370	+	0.0711444i
$309$		0			0
$310$	2.05067	+	2.31448i	0.116470	+	0.131454i
$311$	−4.24421	+	7.35119i	−0.240667	+	0.416848i	−0.960904	−	0.276880i	$-0.910700\pi$
$311$	−4.24421	+	7.35119i	−0.240667	+	0.416848i	0.720237	+	0.693728i	$0.244033\pi$
$312$		0			0
$313$	6.06343	−	3.50072i	0.342725	−	0.197873i	−0.318751	−	0.947838i	$-0.603263\pi$
$313$	6.06343	−	3.50072i	0.342725	−	0.197873i	0.661477	+	0.749966i	$0.269930\pi$
$314$	−8.39517	+	1.71434i	−0.473767	+	0.0967458i
$315$		0			0
$316$	0.129596	−	0.0552316i	0.00729034	−	0.00310702i
$317$	−12.5953	−	21.8157i	−0.707422	−	1.22529i	−0.965810	−	0.259250i	$-0.916525\pi$
$317$	−12.5953	−	21.8157i	−0.707422	−	1.22529i	0.258388	−	0.966041i	$-0.416809\pi$
$318$		0			0
$319$	−0.667775	+	1.15662i	−0.0373882	+	0.0647583i
$320$	0.492894	+	3.02693i	0.0275536	+	0.169210i
$321$		0			0
$322$	−21.7908	+	8.54993i	−1.21435	+	0.476469i
$323$	−41.2675			−2.29618
$324$		0			0
$325$	6.89606	−	11.9443i	0.382525	−	0.662552i
$326$	6.01922	+	2.00916i	0.333374	+	0.111277i
$327$		0			0
$328$	−11.4578	+	7.91140i	−0.632652	+	0.436834i
$329$	−23.5123	−	8.61274i	−1.29628	−	0.474836i
$330$		0			0
$331$	−17.8109	+	10.2831i	−0.978974	+	0.565211i	−0.901960	−	0.431819i	$-0.857872\pi$
$331$	−17.8109	+	10.2831i	−0.978974	+	0.565211i	−0.0770138	+	0.997030i	$0.524539\pi$
$332$	12.8690	+	1.56121i	0.706276	+	0.0856828i
$333$		0			0
$334$	−14.9447	−	16.8673i	−0.817739	−	0.922940i
$335$	−3.45960			−0.189018
$336$		0			0
$337$	9.77045			0.532230			0.266115	−	0.963941i	$-0.414260\pi$
$337$	9.77045			0.532230			0.266115	+	0.963941i	$0.414260\pi$
$338$	4.61733	+	5.21134i	0.251150	+	0.283460i
$339$		0			0
$340$	3.75231	+	0.455216i	0.203497	+	0.0246876i
$341$	22.5354	−	13.0108i	1.22036	−	0.704576i
$342$		0			0
$343$	9.16072	+	16.0960i	0.494632	+	0.869102i
$344$	−7.00100	−	10.1393i	−0.377469	−	0.546675i
$345$		0			0
$346$	25.5659	+	8.53367i	1.37443	+	0.458773i
$347$	9.63809	−	16.6937i	0.517400	−	0.896163i	−0.482396	−	0.875953i	$-0.660233\pi$
$347$	9.63809	−	16.6937i	0.517400	−	0.896163i	0.999796	−	0.0202097i	$-0.00643338\pi$
$348$		0			0
$349$	30.5766			1.63673			0.818363	−	0.574702i	$-0.194882\pi$
$349$	30.5766			1.63673			0.818363	+	0.574702i	$0.194882\pi$
$350$	−11.3229	+	14.1958i	−0.605235	+	0.758797i
$351$		0			0
$352$	25.7867	+	1.03245i	1.37444	+	0.0550297i
$353$	−4.59814	+	7.96421i	−0.244734	+	0.423892i	−0.962057	−	0.272849i	$-0.912034\pi$
$353$	−4.59814	+	7.96421i	−0.244734	+	0.423892i	0.717323	+	0.696741i	$0.245367\pi$
$354$		0			0
$355$	0.837731	+	1.45099i	0.0444622	+	0.0770107i
$356$	−6.01286	+	2.56258i	−0.318681	+	0.135816i
$357$		0			0
$358$	−4.84557	+	0.989492i	−0.256096	+	0.0522963i
$359$	0.890104	−	0.513902i	0.0469779	−	0.0271227i	−0.476327	−	0.879268i	$-0.658032\pi$
$359$	0.890104	−	0.513902i	0.0469779	−	0.0271227i	0.523305	+	0.852145i	$0.324699\pi$
$360$		0			0
$361$	−25.5343	+	44.2267i	−1.34391	+	2.32772i
$362$	−19.9843	−	22.5553i	−1.05035	−	1.18548i
$363$		0			0
$364$	8.18263	+	12.6171i	0.428886	+	0.661318i
$365$	−4.86603			−0.254700
$366$		0			0
$367$	22.9698	+	13.2616i	1.19902	+	0.692252i	0.960336	−	0.278846i	$-0.0899520\pi$
$367$	22.9698	+	13.2616i	1.19902	+	0.692252i	0.238680	+	0.971098i	$0.423285\pi$
$368$	24.0349	−	6.96720i	1.25290	−	0.363191i
$369$		0			0
$370$	−3.75658	+	0.767114i	−0.195295	+	0.0398804i
$371$	−2.11635	−	12.1489i	−0.109876	−	0.630739i
$372$		0			0
$373$	4.48008	−	2.58657i	0.231970	−	0.133928i	−0.379511	−	0.925187i	$-0.623908\pi$
$373$	4.48008	−	2.58657i	0.231970	−	0.133928i	0.611480	+	0.791260i	$0.290574\pi$
$374$	10.0709	−	30.1712i	0.520752	−	1.56011i
$375$		0			0
$376$	24.1863	+	11.4719i	1.24731	+	0.591618i
$377$	0.831971			0.0428487
$378$		0			0
$379$		−	28.2132i		−	1.44921i	−0.689163	−	0.724606i	$-0.742022\pi$
$379$		−	28.2132i		−	1.44921i	0.689163	−	0.724606i	$-0.257978\pi$
$380$	3.85491	−	5.13107i	0.197753	−	0.263218i
$381$		0			0
$382$	−26.6721	−	8.90291i	−1.36466	−	0.455513i
$383$	−1.84904	−	3.20262i	−0.0944813	−	0.163646i	0.814911	−	0.579587i	$-0.196786\pi$
$383$	−1.84904	−	3.20262i	−0.0944813	−	0.163646i	−0.909392	+	0.415940i	$0.863453\pi$
$384$		0			0
$385$	−2.96695	−	3.55072i	−0.151210	−	0.180962i
$386$	−14.4454	+	2.94982i	−0.735249	+	0.150142i
$387$		0			0
$388$	−0.693401	−	0.0841209i	−0.0352021	−	0.00427059i
$389$	−3.23187	+	5.59776i	−0.163862	+	0.283818i	−0.936251	−	0.351333i	$-0.885729\pi$
$389$	−3.23187	+	5.59776i	−0.163862	+	0.283818i	0.772388	+	0.635151i	$0.219062\pi$
$390$		0			0
$391$		−	30.8424i		−	1.55977i
$392$	−8.17528	−	18.0323i	−0.412914	−	0.910770i
$393$		0			0
$394$	−15.0419	−	16.9770i	−0.757801	−	0.855291i
$395$	0.0233845	+	0.0135010i	0.00117660	+	0.000679311i
$396$		0			0
$397$	−14.7284	−	25.5104i	−0.739198	−	1.28033i	−0.952857	−	0.303421i	$-0.901871\pi$
$397$	−14.7284	−	25.5104i	−0.739198	−	1.28033i	0.213658	−	0.976908i	$-0.431462\pi$
$398$	−0.653865	−	3.20199i	−0.0327753	−	0.160501i
$399$		0			0
$400$	13.4444	−	14.0029i	0.672219	−	0.700145i
$401$	17.7242	−	10.2331i	0.885105	−	0.511016i	0.0127669	−	0.999918i	$-0.495936\pi$
$401$	17.7242	−	10.2331i	0.885105	−	0.511016i	0.872338	+	0.488903i	$0.162603\pi$
$402$		0			0
$403$	−14.0383	−	8.10500i	−0.699296	−	0.403739i
$404$	18.4673	−	24.5809i	0.918785	−	1.22295i
$405$		0			0
$406$	−1.08311	−	0.163354i	−0.0537537	−	0.00810714i
$407$			32.2643i			1.59928i
$408$		0			0
$409$	11.5317	+	6.65785i	0.570207	+	0.329209i	0.757232	−	0.653146i	$-0.226551\pi$
$409$	11.5317	+	6.65785i	0.570207	+	0.329209i	−0.187025	+	0.982355i	$0.559884\pi$
$410$	−2.53153	−	0.845003i	−0.125023	−	0.0417317i
$411$		0			0
$412$	1.86596	+	4.37830i	0.0919291	+	0.215703i
$413$	17.2309	−	3.00164i	0.847876	−	0.147701i
$414$		0			0
$415$	1.24237	+	2.15185i	0.0609855	+	0.105630i
$416$	−7.47483	−	14.2331i	−0.366484	−	0.697835i
$417$		0			0
$418$	−35.8150	−	40.4225i	−1.75177	−	1.97713i
$419$			35.6073i			1.73953i	0.493467	+	0.869764i	$0.335729\pi$
$419$			35.6073i			1.73953i	−0.493467	+	0.869764i	$0.664271\pi$
$420$		0			0
$421$			16.1350i			0.786370i	0.919459	+	0.393185i	$0.128627\pi$
$421$			16.1350i			0.786370i	−0.919459	+	0.393185i	$0.871373\pi$
$422$	−13.4721	+	11.9365i	−0.655809	+	0.581057i
$423$		0			0
$424$	1.06287	+	13.1404i	0.0516174	+	0.638154i
$425$	−11.9627	−	20.7201i	−0.580278	−	1.00507i
$426$		0			0
$427$	6.96095	+	2.54985i	0.336864	+	0.123396i
$428$	1.51639	−	0.646261i	0.0732976	−	0.0312382i
$429$		0			0
$430$	0.747765	−	2.24022i	0.0360604	−	0.108033i
$431$	−27.7465	−	16.0194i	−1.33650	−	0.771629i	−0.350213	−	0.936670i	$-0.613891\pi$
$431$	−27.7465	−	16.0194i	−1.33650	−	0.771629i	−0.986287	+	0.165041i	$0.947224\pi$
$432$		0			0
$433$		−	25.4744i		−	1.22422i	−0.790771	−	0.612112i	$-0.790320\pi$
$433$		−	25.4744i		−	1.22422i	0.790771	−	0.612112i	$-0.209680\pi$
$434$	16.6844	+	13.3079i	0.800878	+	0.638800i
$435$		0			0
$436$	19.5949	−	26.0817i	0.938425	−	1.24909i
$437$	−45.3518	−	26.1839i	−2.16947	−	1.25254i
$438$		0			0
$439$	18.7443	−	10.8220i	0.894615	−	0.516506i	0.0191655	−	0.999816i	$-0.493899\pi$
$439$	18.7443	−	10.8220i	0.894615	−	0.516506i	0.875449	+	0.483310i	$0.160566\pi$
$440$	2.81064	+	4.07055i	0.133992	+	0.194056i
$441$		0			0
$442$	−19.4136	+	3.96438i	−0.923413	+	0.188566i
$443$	7.35423	+	12.7379i	0.349410	+	0.605196i	0.986145	−	0.165887i	$-0.0530487\pi$
$443$	7.35423	+	12.7379i	0.349410	+	0.605196i	−0.636735	+	0.771083i	$0.719715\pi$
$444$		0			0
$445$	−1.08497	−	0.626407i	−0.0514325	−	0.0296945i
$446$	−12.1657	+	10.7790i	−0.576064	+	0.510401i
$447$		0			0
$448$	6.93654	+	19.9971i	0.327721	+	0.944775i
$449$			25.7754i			1.21642i	0.793778	+	0.608208i	$0.208111\pi$
$449$			25.7754i			1.21642i	−0.793778	+	0.608208i	$0.791889\pi$
$450$		0			0
$451$	−11.2293	+	19.4497i	−0.528765	+	0.915849i
$452$	−6.00245	−	0.728195i	−0.282331	−	0.0342514i
$453$		0			0
$454$	−0.495855	−	2.42822i	−0.0232716	−	0.113962i
$455$	−0.991437	+	2.70657i	−0.0464793	+	0.126886i
$456$		0			0
$457$	16.5498	+	28.6651i	0.774168	+	1.34090i	0.935261	+	0.353960i	$0.115165\pi$
$457$	16.5498	+	28.6651i	0.774168	+	1.34090i	−0.161092	+	0.986939i	$0.551502\pi$
$458$	2.60753	−	7.81185i	0.121842	−	0.365024i
$459$		0			0
$460$	3.83485	+	2.88108i	0.178801	+	0.134331i
$461$		−	8.24676i		−	0.384090i	−0.981386	−	0.192045i	$-0.938488\pi$
$461$		−	8.24676i		−	0.384090i	0.981386	−	0.192045i	$-0.0615120\pi$
$462$		0			0
$463$	16.2797			0.756582			0.378291	−	0.925687i	$-0.376512\pi$
$463$	16.2797			0.756582			0.378291	+	0.925687i	$0.376512\pi$
$464$	1.13702	+	0.279998i	0.0527847	+	0.0129986i
$465$		0			0
$466$	11.5296	+	3.84848i	0.534098	+	0.178277i
$467$	−24.2507	+	14.0011i	−1.12219	+	0.647895i	−0.941959	−	0.335729i	$-0.891017\pi$
$467$	−24.2507	+	14.0011i	−1.12219	+	0.647895i	−0.180229	+	0.983625i	$0.557684\pi$
$468$		0			0
$469$	−23.5228	+	4.09770i	−1.08618	+	0.189214i
$470$	1.02658	+	5.02720i	0.0473527	+	0.231887i
$471$		0			0
$472$	−18.6371	+	1.50747i	−0.857843	+	0.0693871i
$473$	−17.2115	−	9.93707i	−0.791386	−	0.456907i
$474$		0			0
$475$	−40.6233			−1.86393
$476$	26.0522	−	1.34925i	1.19410	−	0.0618429i
$477$		0			0
$478$	−2.30543	+	2.04265i	−0.105448	+	0.0934284i
$479$	−5.42512	+	9.39658i	−0.247880	+	0.429341i	−0.962937	−	0.269725i	$-0.913067\pi$
$479$	−5.42512	+	9.39658i	−0.247880	+	0.429341i	0.715057	+	0.699066i	$0.246400\pi$
$480$		0			0
$481$	17.4061	−	10.0494i	0.793650	−	0.458214i
$482$	1.66036	+	8.13083i	0.0756274	+	0.370349i
$483$		0			0
$484$	18.0550	−	7.69475i	0.820683	−	0.349761i
$485$	−0.0669409	−	0.115945i	−0.00303963	−	0.00526480i
$486$		0			0
$487$	−5.75857	+	9.97414i	−0.260946	+	0.451971i	−0.966494	−	0.256691i	$-0.917368\pi$
$487$	−5.75857	+	9.97414i	−0.260946	+	0.451971i	0.705548	+	0.708662i	$0.250701\pi$
$488$	−7.16048	−	3.39632i	−0.324140	−	0.153744i
$489$		0			0
$490$	1.82213	−	3.32890i	0.0823156	−	0.150384i
$491$	−5.61613			−0.253452			−0.126726	−	0.991938i	$-0.540447\pi$
$491$	−5.61613			−0.253452			−0.126726	+	0.991938i	$0.540447\pi$
$492$		0			0
$493$	0.721619	−	1.24988i	0.0325001	−	0.0562918i
$494$	−10.6520	+	31.9121i	−0.479255	+	1.43579i
$495$		0			0
$496$	−16.4577	−	15.8013i	−0.738974	−	0.709498i
$497$	7.41459	+	8.87346i	0.332590	+	0.398029i
$498$		0			0
$499$	12.5584	−	7.25061i	0.562193	−	0.324582i	−0.191832	−	0.981428i	$-0.561443\pi$
$499$	12.5584	−	7.25061i	0.562193	−	0.324582i	0.754025	+	0.656846i	$0.228110\pi$
$500$	7.49933	+	0.909791i	0.335380	+	0.0406871i
$501$		0			0
$502$	31.2942	−	27.7271i	1.39673	−	1.23752i
$503$	10.8393			0.483301			0.241651	−	0.970363i	$-0.422311\pi$
$503$	10.8393			0.483301			0.241651	+	0.970363i	$0.422311\pi$
$504$		0			0
$505$	5.89306			0.262238
$506$	30.2109	−	26.7674i	1.34304	−	1.18995i
$507$		0			0
$508$	−0.698415	+	5.75697i	−0.0309871	+	0.255424i
$509$	−21.6861	+	12.5205i	−0.961218	+	0.554959i	−0.896548	−	0.442947i	$-0.853933\pi$
$509$	−21.6861	+	12.5205i	−0.961218	+	0.554959i	−0.0646702	+	0.997907i	$0.520600\pi$
$510$		0			0
$511$	−33.0855	+	5.76353i	−1.46362	+	0.254964i
$512$	−5.42539	−	21.9674i	−0.239770	−	0.970830i
$513$		0			0
$514$	9.36803	−	28.0655i	0.413206	−	1.23792i
$515$	−0.456122	+	0.790027i	−0.0200992	+	0.0348127i
$516$		0			0
$517$	43.1774			1.89894
$518$	−24.6334	+	9.66527i	−1.08233	+	0.424668i
$519$		0			0
$520$	1.32056	−	2.78415i	0.0579106	−	0.122093i
$521$	−16.8507	+	29.1862i	−0.738240	+	1.27867i	0.215047	+	0.976604i	$0.431010\pi$
$521$	−16.8507	+	29.1862i	−0.738240	+	1.27867i	−0.953287	+	0.302066i	$0.902324\pi$
$522$		0			0
$523$	−9.74207	−	16.8738i	−0.425991	−	0.737838i	0.570522	−	0.821283i	$-0.306741\pi$
$523$	−9.74207	−	16.8738i	−0.425991	−	0.737838i	−0.996512	+	0.0834448i	$0.973408\pi$
$524$	9.55540	+	22.4209i	0.417430	+	0.979461i
$525$		0			0
$526$	3.38186	+	16.5610i	0.147456	+	0.722095i
$527$	−24.3525	+	14.0599i	−1.06081	+	0.612459i
$528$		0			0
$529$	8.06926	−	13.9764i	0.350837	−	0.607668i
$530$	−1.89133	+	1.67575i	−0.0821541	+	0.0727898i
$531$		0			0
$532$	20.1331	−	39.4535i	0.872883	−	1.71052i
$533$	13.9904			0.605990
$534$		0			0
$535$	0.273620	+	0.157975i	0.0118296	+	0.00682984i
$536$	25.4425	−	2.05793i	1.09895	−	0.0888892i
$537$		0			0
$538$	−4.59373	−	22.4956i	−0.198050	−	0.969854i
$539$	−24.3788	−	20.6282i	−1.05007	−	0.888518i
$540$		0			0
$541$	33.3111	−	19.2322i	1.43216	−	0.826856i	0.434872	−	0.900492i	$-0.356794\pi$
$541$	33.3111	−	19.2322i	1.43216	−	0.826856i	0.997285	+	0.0736362i	$0.0234604\pi$
$542$	34.1914	+	11.4128i	1.46865	+	0.490221i
$543$		0			0
$544$	−27.8659	−	1.11569i	−1.19474	−	0.0478350i
$545$	6.25287			0.267844
$546$		0			0
$547$		−	11.2961i		−	0.482985i	−0.970403	−	0.241493i	$-0.922363\pi$
$547$		−	11.2961i		−	0.482985i	0.970403	−	0.241493i	$-0.0776370\pi$
$548$	22.0773	−	29.3859i	0.943096	−	1.25531i
$549$		0			0
$550$	9.91368	−	29.7002i	0.422721	−	1.26642i
$551$	−1.22524	−	2.12219i	−0.0521972	−	0.0904082i
$552$		0			0
$553$	0.174989	+	0.0640997i	0.00744128	+	0.00272580i
$554$	−3.10937	−	15.2266i	−0.132104	−	0.646918i
$555$		0			0
$556$	−1.54233	+	12.7133i	−0.0654095	+	0.539165i
$557$	10.9385	−	18.9460i	0.463477	−	0.802766i	−0.535654	−	0.844438i	$-0.679935\pi$
$557$	10.9385	−	18.9460i	0.463477	−	0.802766i	0.999131	+	0.0416711i	$0.0132682\pi$
$558$		0			0
$559$			12.3804i			0.523637i
$560$	−2.26584	+	3.36528i	−0.0957493	+	0.142209i
$561$		0			0
$562$	−7.10622	+	6.29623i	−0.299758	+	0.265590i
$563$	12.5783	+	7.26211i	0.530114	+	0.306061i	0.741063	−	0.671436i	$-0.234322\pi$
$563$	12.5783	+	7.26211i	0.530114	+	0.306061i	−0.210949	+	0.977497i	$0.567655\pi$
$564$		0			0
$565$	−0.579476	−	1.00368i	−0.0243788	−	0.0422252i
$566$	19.6113	−	4.00474i	0.824325	−	0.168332i
$567$		0			0
$568$	−7.02395	−	10.1725i	−0.294718	−	0.426830i
$569$	−8.24719	+	4.76152i	−0.345740	+	0.199613i	−0.662807	−	0.748790i	$-0.730635\pi$
$569$	−8.24719	+	4.76152i	−0.345740	+	0.199613i	0.317067	+	0.948403i	$0.397302\pi$
$570$		0			0
$571$	−6.63806	−	3.83248i	−0.277794	−	0.160384i	0.354630	−	0.935007i	$-0.384607\pi$
$571$	−6.63806	−	3.83248i	−0.277794	−	0.160384i	−0.632424	+	0.774622i	$0.717940\pi$
$572$	−20.7318	−	15.5756i	−0.866841	−	0.651247i
$573$		0			0
$574$	−18.2135	−	2.74696i	−0.760215	−	0.114656i
$575$		−	30.3610i		−	1.26614i
$576$		0			0
$577$	26.5704	+	15.3405i	1.10614	+	0.638631i	0.937827	−	0.347102i	$-0.112834\pi$
$577$	26.5704	+	15.3405i	1.10614	+	0.638631i	0.168315	+	0.985733i	$0.446168\pi$
$578$	−3.27086	+	9.79913i	−0.136050	+	0.407590i
$579$		0			0
$580$	0.0879977	+	0.206478i	0.00365390	+	0.00857355i
$581$	10.9960	+	13.1595i	0.456189	+	0.545947i
$582$		0			0
$583$	10.6321	+	18.4153i	0.440336	+	0.762684i
$584$	35.7857	−	2.89454i	1.48082	−	0.119777i
$585$		0			0
$586$	−8.19253	+	7.25871i	−0.338430	+	0.299854i
$587$			12.2533i			0.505748i	0.967499	+	0.252874i	$0.0813758\pi$
$587$			12.2533i			0.505748i	−0.967499	+	0.252874i	$0.918624\pi$
$588$		0			0
$589$			47.7450i			1.96730i
$590$	−2.37672	−	2.68249i	−0.0978482	−	0.110436i
$591$		0			0
$592$	27.1702	−	7.87608i	1.11669	−	0.323705i
$593$	5.04004	+	8.72961i	0.206970	+	0.358482i	0.950759	−	0.309933i	$-0.100306\pi$
$593$	5.04004	+	8.72961i	0.206970	+	0.358482i	−0.743789	+	0.668415i	$0.766973\pi$
$594$		0			0
$595$	3.20618	+	3.83702i	0.131441	+	0.157302i
$596$	−33.9168	+	14.4548i	−1.38929	+	0.592091i
$597$		0			0
$598$	−23.8504	−	7.96105i	−0.975315	−	0.325552i
$599$	8.63004	+	4.98256i	0.352614	+	0.203582i	0.665836	−	0.746098i	$-0.268075\pi$
$599$	8.63004	+	4.98256i	0.352614	+	0.203582i	−0.313222	+	0.949680i	$0.601408\pi$
$600$		0			0
$601$			36.9998i			1.50925i	0.656154	+	0.754627i	$0.272182\pi$
$601$			36.9998i			1.50925i	−0.656154	+	0.754627i	$0.727818\pi$
$602$	2.43085	−	16.1176i	0.0990741	−	0.656902i
$603$		0			0
$604$	−23.6149	−	17.7416i	−0.960878	−	0.721897i
$605$	3.25788	+	1.88094i	0.132451	+	0.0764709i
$606$		0			0
$607$	28.8906	−	16.6800i	1.17263	−	0.677021i	0.218335	−	0.975874i	$-0.429937\pi$
$607$	28.8906	−	16.6800i	1.17263	−	0.677021i	0.954299	+	0.298853i	$0.0966041\pi$
$608$	−25.2975	+	40.0279i	−1.02595	+	1.62334i
$609$		0			0
$610$	−0.303925	−	1.48833i	−0.0123056	−	0.0602607i
$611$	−13.4485	−	23.2935i	−0.544069	−	0.942355i
$612$		0			0
$613$	−6.37477	−	3.68047i	−0.257474	−	0.148653i	0.365708	−	0.930730i	$-0.380827\pi$
$613$	−6.37477	−	3.68047i	−0.257474	−	0.148653i	−0.623182	+	0.782077i	$0.714160\pi$
$614$	23.3450	+	26.3483i	0.942126	+	1.06333i
$615$		0			0
$616$	23.9316	+	24.3478i	0.964233	+	0.981000i
$617$			16.0597i			0.646540i	0.946307	+	0.323270i	$0.104782\pi$
$617$			16.0597i			0.646540i	−0.946307	+	0.323270i	$0.895218\pi$
$618$		0			0
$619$	0.283019	−	0.490203i	0.0113755	−	0.0197029i	−0.860282	−	0.509819i	$-0.829712\pi$
$619$	0.283019	−	0.490203i	0.0113755	−	0.0197029i	0.871657	+	0.490116i	$0.163046\pi$
$620$	0.526669	−	4.34128i	0.0211515	−	0.174350i
$621$		0			0
$622$	11.7617	−	2.40181i	0.471602	−	0.0963038i
$623$	−8.11895	−	2.97403i	−0.325279	−	0.119152i
$624$		0			0
$625$	−11.4086	−	19.7603i	−0.456345	−	0.790413i
$626$	−9.39213	−	3.13501i	−0.375385	−	0.125300i
$627$		0			0
$628$	9.68806	+	7.27853i	0.386596	+	0.290445i
$629$		−	34.8658i		−	1.39019i
$630$		0			0
$631$	32.2928			1.28556			0.642779	−	0.766052i	$-0.277781\pi$
$631$	32.2928			1.28556			0.642779	+	0.766052i	$0.277781\pi$
$632$	−0.180005	−	0.0853788i	−0.00716020	−	0.00339619i
$633$		0			0
$634$	−11.2795	+	33.7921i	−0.447966	+	1.34206i
$635$	−0.962636	+	0.555778i	−0.0382010	+	0.0220554i
$636$		0			0
$637$	−3.53528	+	19.5770i	−0.140073	+	0.775670i
$638$	1.85056	−	0.377896i	0.0732645	−	0.0149610i
$639$		0			0
$640$	2.74176	−	3.36054i	0.108377	−	0.132837i
$641$	7.35118	+	4.24421i	0.290354	+	0.167636i	0.638102	−	0.769952i	$-0.279720\pi$
$641$	7.35118	+	4.24421i	0.290354	+	0.167636i	−0.347747	+	0.937588i	$0.613053\pi$
$642$		0			0
$643$	−29.1690			−1.15031			−0.575156	−	0.818044i	$-0.695058\pi$
$643$	−29.1690			−1.15031			−0.575156	+	0.818044i	$0.695058\pi$
$644$	29.4867	+	15.0471i	1.16194	+	0.592938i
$645$		0			0
$646$	38.7028	+	43.6818i	1.52274	+	1.71864i
$647$	−4.70856	+	8.15546i	−0.185113	+	0.320624i	−0.943614	−	0.331046i	$-0.892598\pi$
$647$	−4.70856	+	8.15546i	−0.185113	+	0.320624i	0.758502	+	0.651671i	$0.225932\pi$
$648$		0			0
$649$	−26.1186	+	15.0796i	−1.02524	+	0.591925i
$650$	−19.1106	+	3.90250i	−0.749580	+	0.153069i
$651$		0			0
$652$	−3.51843	−	8.25567i	−0.137792	−	0.323317i
$653$	−6.88850	−	11.9312i	−0.269568	−	0.466905i	0.699182	−	0.714943i	$-0.253548\pi$
$653$	−6.88850	−	11.9312i	−0.269568	−	0.466905i	−0.968750	+	0.248038i	$0.920214\pi$
$654$		0			0
$655$	−2.33576	+	4.04566i	−0.0912658	+	0.158077i
$656$	19.1200	+	4.70843i	0.746510	+	0.183833i
$657$		0			0
$658$	12.9344	+	32.9654i	0.504237	+	1.28512i
$659$	3.86377			0.150511			0.0752555	−	0.997164i	$-0.476023\pi$
$659$	3.86377			0.150511			0.0752555	+	0.997164i	$0.476023\pi$
$660$		0			0
$661$	−1.46098	+	2.53049i	−0.0568255	+	0.0984247i	−0.893039	−	0.449980i	$-0.851431\pi$
$661$	−1.46098	+	2.53049i	−0.0568255	+	0.0984247i	0.836213	+	0.548404i	$0.184765\pi$
$662$	27.5887	+	9.20886i	1.07226	+	0.357913i
$663$		0			0
$664$	−10.4166	−	15.0860i	−0.404243	−	0.585452i
$665$	8.36399	−	1.45702i	0.324342	−	0.0565008i
$666$		0			0
$667$	1.58608	−	0.915722i	0.0614131	−	0.0354569i
$668$	−3.83822	+	31.6381i	−0.148505	+	1.22412i
$669$		0			0
$670$	3.24460	+	3.66201i	0.125350	+	0.141476i
$671$	−12.7829			−0.493479
$672$		0			0
$673$	−38.7127			−1.49227			−0.746133	−	0.665797i	$-0.768092\pi$
$673$	−38.7127			−1.49227			−0.746133	+	0.665797i	$0.768092\pi$
$674$	−9.16323	−	10.3421i	−0.352955	−	0.398362i
$675$		0			0
$676$	1.18586	−	9.77493i	0.0456100	−	0.375959i
$677$	−39.7095	+	22.9263i	−1.52616	+	0.881130i	−0.526644	+	0.850086i	$0.676550\pi$
$677$	−39.7095	+	22.9263i	−1.52616	+	0.881130i	−0.999518	+	0.0310437i	$0.990117\pi$
$678$		0			0
$679$	−0.592480	−	0.709055i	−0.0227373	−	0.0272110i
$680$	−3.03726	−	4.39876i	−0.116474	−	0.168685i
$681$		0			0
$682$	−34.9069	−	11.6516i	−1.33666	−	0.446164i
$683$	−19.9744	+	34.5968i	−0.764301	+	1.32381i	0.176315	+	0.984334i	$0.443582\pi$
$683$	−19.9744	+	34.5968i	−0.764301	+	1.32381i	−0.940615	+	0.339474i	$0.889751\pi$
$684$		0			0
$685$	7.04503			0.269177
$686$	8.44630	−	24.7923i	0.322481	−	0.946576i
$687$		0			0
$688$	−4.16661	+	16.9198i	−0.158851	+	0.645060i
$689$	6.62318	−	11.4717i	0.252323	−	0.437036i
$690$		0			0
$691$	13.9816	+	24.2169i	0.531886	+	0.921253i	0.999307	+	0.0372183i	$0.0118497\pi$
$691$	13.9816	+	24.2169i	0.531886	+	0.921253i	−0.467422	+	0.884035i	$0.654817\pi$
$692$	−14.9441	−	35.0650i	−0.568089	−	1.33297i
$693$		0			0
$694$	−26.7094	+	5.45422i	−1.01388	+	0.207039i
$695$	−2.12582	+	1.22734i	−0.0806370	+	0.0465558i
$696$		0			0
$697$	12.1347	−	21.0179i	0.459634	−	0.796110i
$698$	−28.6763	−	32.3654i	−1.08541	−	1.22505i
$699$		0			0
$700$	25.6455	−	1.32819i	0.969310	−	0.0502010i
$701$	47.3436			1.78814			0.894072	−	0.447923i	$-0.147836\pi$
$701$	47.3436			1.78814			0.894072	+	0.447923i	$0.147836\pi$
$702$		0			0
$703$	−51.2680	−	29.5996i	−1.93361	−	1.11637i
$704$	−23.0913	−	28.2637i	−0.870286	−	1.06523i
$705$		0			0
$706$	12.7425	−	2.60210i	0.479572	−	0.0979313i
$707$	40.0686	−	6.98000i	1.50693	−	0.262510i
$708$		0			0
$709$	−8.16943	+	4.71662i	−0.306810	+	0.177137i	−0.645498	−	0.763762i	$-0.723350\pi$
$709$	−8.16943	+	4.71662i	−0.306810	+	0.177137i	0.338688	+	0.940899i	$0.390017\pi$
$710$	0.750216	−	2.24756i	0.0281551	−	0.0843494i
$711$		0			0
$712$	8.35167	+	3.96132i	0.312992	+	0.148457i
$713$	−35.6836			−1.33636
$714$		0			0
$715$		−	4.97028i		−	0.185878i
$716$	5.59181	+	4.20106i	0.208976	+	0.157001i
$717$		0			0
$718$	−1.37875	−	0.460216i	−0.0514547	−	0.0171751i
$719$	22.0452	+	38.1835i	0.822148	+	1.42400i	0.904079	+	0.427364i	$0.140558\pi$
$719$	22.0452	+	38.1835i	0.822148	+	1.42400i	−0.0819312	+	0.996638i	$0.526109\pi$
$720$		0			0
$721$	−2.16556	+	5.91186i	−0.0806497	+	0.220169i
$722$	70.7615	−	14.4499i	2.63347	−	0.537770i
$723$		0			0
$724$	−5.13254	+	42.3071i	−0.190749	+	1.57233i
$725$	0.710355	−	1.23037i	0.0263819	−	0.0456948i
$726$		0			0
$727$			0.998475i			0.0370314i	0.999829	+	0.0185157i	$0.00589406\pi$
$727$			0.998475i			0.0370314i	−0.999829	+	0.0185157i	$0.994106\pi$
$728$	5.68121	−	20.4944i	0.210560	−	0.759572i
$729$		0			0
$730$	4.56362	+	5.15072i	0.168907	+	0.190637i
$731$	18.5993	+	10.7383i	0.687919	+	0.397170i
$732$		0			0
$733$	−21.6087	−	37.4274i	−0.798136	−	1.38241i	−0.920829	−	0.389967i	$-0.872486\pi$
$733$	−21.6087	−	37.4274i	−0.798136	−	1.38241i	0.122693	−	0.992445i	$-0.460847\pi$
$734$	−7.50479	−	36.7511i	−0.277007	−	1.35651i
$735$		0			0
$736$	−29.9160	−	18.9068i	−1.10272	−	0.696914i
$737$	35.6559	−	20.5859i	1.31340	−	0.758293i
$738$		0			0
$739$	20.3992	+	11.7775i	0.750398	+	0.433243i	0.825838	−	0.563908i	$-0.190703\pi$
$739$	20.3992	+	11.7775i	0.750398	+	0.433243i	−0.0754395	+	0.997150i	$0.524036\pi$
$740$	4.33511	+	3.25692i	0.159362	+	0.119727i
$741$		0			0
$742$	−10.8748	+	13.6340i	−0.399228	+	0.500521i
$743$		−	0.745461i		−	0.0273483i	−0.999907	−	0.0136742i	$-0.995647\pi$
$743$		−	0.745461i		−	0.0273483i	0.999907	−	0.0136742i	$-0.00435275\pi$
$744$		0			0
$745$	−6.12000	−	3.53339i	−0.224220	−	0.129453i
$746$	−6.93955	−	2.31636i	−0.254075	−	0.0848080i
$747$		0			0
$748$	−41.3813	+	17.6360i	−1.51305	+	0.644837i
$749$	2.04753	+	0.750026i	0.0748151	+	0.0274053i
$750$		0			0
$751$	10.2168	+	17.6961i	0.372817	+	0.645738i	0.989998	−	0.141083i	$-0.0450585\pi$
$751$	10.2168	+	17.6961i	0.372817	+	0.645738i	−0.617180	+	0.786822i	$0.711725\pi$
$752$	−10.5401	−	36.3603i	−0.384357	−	1.32592i
$753$		0			0
$754$	−0.780266	−	0.880646i	−0.0284156	−	0.0320712i
$755$		−	5.66148i		−	0.206042i
$756$		0			0
$757$			12.6416i			0.459465i	0.973254	+	0.229733i	$0.0737852\pi$
$757$			12.6416i			0.459465i	−0.973254	+	0.229733i	$0.926215\pi$
$758$	−29.8638	+	26.4598i	−1.08470	+	0.961062i
$759$		0			0
$760$	−9.04660	+	0.731739i	−0.328155	+	0.0265429i
$761$	−20.0783	−	34.7767i	−0.727839	−	1.26065i	−0.957795	−	0.287452i	$-0.907192\pi$
$761$	−20.0783	−	34.7767i	−0.727839	−	1.26065i	0.229956	−	0.973201i	$-0.426142\pi$
$762$		0			0
$763$	42.5150	−	7.40617i	1.53915	−	0.268121i
$764$	15.5907	+	36.5822i	0.564052	+	1.32350i
$765$		0			0
$766$	−1.65587	+	4.96080i	−0.0598291	+	0.179241i
$767$	16.2704	+	9.39370i	0.587489	+	0.339187i
$768$		0			0
$769$		−	9.78731i		−	0.352939i	−0.984306	−	0.176470i	$-0.943532\pi$
$769$		−	9.78731i		−	0.352939i	0.984306	−	0.176470i	$-0.0564678\pi$
$770$	−0.975895	+	6.47059i	−0.0351688	+	0.233184i
$771$		0			0
$772$	16.6700	+	12.5240i	0.599967	+	0.450748i
$773$	36.3366	+	20.9789i	1.30694	+	0.754560i	0.981584	−	0.191033i	$-0.0611839\pi$
$773$	36.3366	+	20.9789i	1.30694	+	0.754560i	0.325352	+	0.945593i	$0.394517\pi$
$774$		0			0
$775$	−23.9724	+	13.8404i	−0.861113	+	0.497164i
$776$	0.561265	+	0.812862i	0.0201482	+	0.0291800i
$777$		0			0
$778$	8.95628	−	1.82892i	0.321098	−	0.0655701i
$779$	−20.6036	−	35.6865i	−0.738202	−	1.27860i
$780$		0			0
$781$	−17.2679	−	9.96963i	−0.617894	−	0.356741i
$782$	−32.6469	+	28.9256i	−1.16745	+	1.03438i
$783$		0			0
$784$	−11.4201	+	25.5652i	−0.407861	+	0.913044i
$785$			2.32263i			0.0828983i
$786$		0			0
$787$	−15.7140	+	27.2175i	−0.560145	+	0.970200i	0.437338	+	0.899297i	$0.355921\pi$
$787$	−15.7140	+	27.2175i	−0.560145	+	0.970200i	−0.997483	+	0.0709026i	$0.977412\pi$
$788$	−3.86319	+	31.8439i	−0.137620	+	1.13439i
$789$		0			0
$790$	−0.00764026	−	0.0374146i	−0.000271828	−	0.00133115i
$791$	−5.12883	−	6.13796i	−0.182360	−	0.218241i
$792$		0			0
$793$	3.98151	+	6.89617i	0.141387	+	0.244890i
$794$	−13.1898	+	39.5151i	−0.468088	+	1.40234i
$795$		0			0
$796$	−2.77610	+	3.69512i	−0.0983962	+	0.130970i
$797$			1.25772i			0.0445507i	0.999752	+	0.0222754i	$0.00709105\pi$
$797$			1.25772i			0.0445507i	−0.999752	+	0.0222754i	$0.992909\pi$
$798$		0			0
$799$	−46.6588			−1.65067
$800$	−27.4310	−	1.09828i	−0.969832	−	0.0388301i
$801$		0			0
$802$	−27.4545	−	9.16406i	−0.969451	−	0.323594i
$803$	50.1510	−	28.9547i	1.76979	−	1.02179i
$804$		0			0
$805$	1.08894	+	6.25107i	0.0383802	+	0.220321i
$806$	4.58664	+	22.4609i	0.161557	+	0.791151i
$807$		0			0
$808$	−43.3386	+	3.50547i	−1.52465	+	0.123322i
$809$	−24.5857	−	14.1945i	−0.864386	−	0.499053i	0.00109260	−	0.999999i	$-0.499652\pi$
$809$	−24.5857	−	14.1945i	−0.864386	−	0.499053i	−0.865479	+	0.500946i	$0.832986\pi$
$810$		0			0
$811$	4.97465			0.174684			0.0873418	−	0.996178i	$-0.472163\pi$
$811$	4.97465			0.174684			0.0873418	+	0.996178i	$0.472163\pi$
$812$	0.842883	+	1.29968i	0.0295794	+	0.0456097i
$813$		0			0
$814$	34.1520	−	30.2592i	1.19703	−	1.06058i
$815$	0.860059	−	1.48967i	0.0301265	−	0.0521807i
$816$		0			0
$817$	31.5799	−	18.2327i	1.10484	−	0.637881i
$818$	−3.76769	−	18.4505i	−0.131734	−	0.645106i
$819$		0			0
$820$	1.47976	+	3.47213i	0.0516756	+	0.121252i
$821$	−5.02868	−	8.70993i	−0.175502	−	0.303979i	0.764833	−	0.644229i	$-0.222822\pi$
$821$	−5.02868	−	8.70993i	−0.175502	−	0.303979i	−0.940335	+	0.340250i	$0.889488\pi$
$822$		0			0
$823$	2.27031	−	3.93230i	0.0791382	−	0.137071i	−0.823740	−	0.566967i	$-0.808117\pi$
$823$	2.27031	−	3.93230i	0.0791382	−	0.137071i	0.902878	+	0.429896i	$0.141450\pi$
$824$	2.88446	−	6.08132i	0.100485	−	0.211853i
$825$		0			0
$826$	−19.3373	−	15.4239i	−0.672829	−	0.536665i
$827$	−19.2538			−0.669520			−0.334760	−	0.942303i	$-0.608655\pi$
$827$	−19.2538			−0.669520			−0.334760	+	0.942303i	$0.608655\pi$
$828$		0			0
$829$	−17.0503	+	29.5321i	−0.592183	+	1.02569i	0.401755	+	0.915747i	$0.368400\pi$
$829$	−17.0503	+	29.5321i	−0.592183	+	1.02569i	−0.993938	+	0.109943i	$0.964933\pi$
$830$	1.11258	−	3.33317i	0.0386183	−	0.115696i
$831$		0			0
$832$	−8.05553	+	21.2607i	−0.279275	+	0.737082i
$833$	26.3444	+	22.2914i	0.912781	+	0.772352i
$834$		0			0
$835$	−5.29028	+	3.05435i	−0.183078	+	0.105700i
$836$	−9.19830	+	75.8207i	−0.318130	+	2.62232i
$837$		0			0
$838$	37.6905	−	33.3943i	1.30200	−	1.15359i
$839$	12.0599			0.416355			0.208178	−	0.978091i	$-0.433247\pi$
$839$	12.0599			0.416355			0.208178	+	0.978091i	$0.433247\pi$
$840$		0			0
$841$	−28.9143			−0.997045
$842$	17.0789	−	15.1322i	0.588579	−	0.521490i
$843$		0			0
$844$	25.2696	+	3.06561i	0.869815	+	0.105523i
$845$	1.63449	−	0.943672i	0.0562281	−	0.0324633i
$846$		0			0
$847$	24.3791	+	8.93023i	0.837674	+	0.306846i
$848$	12.9124	−	13.4488i	0.443412	−	0.461833i
$849$		0			0
$850$	−10.7130	+	32.0950i	−0.367454	+	1.10085i
$851$	22.1221	−	38.3166i	0.758335	−	1.31348i
$852$		0			0
$853$	−28.7232			−0.983464			−0.491732	−	0.870747i	$-0.663636\pi$
$853$	−28.7232			−0.983464			−0.491732	+	0.870747i	$0.663636\pi$
$854$	−3.82931	−	9.75958i	−0.131036	−	0.333966i
$855$		0			0
$856$	−2.10622	−	0.999012i	−0.0719892	−	0.0341455i
$857$	−7.96109	+	13.7890i	−0.271946	+	0.471024i	−0.969360	−	0.245644i	$-0.921000\pi$
$857$	−7.96109	+	13.7890i	−0.271946	+	0.471024i	0.697414	+	0.716668i	$0.254334\pi$
$858$		0			0
$859$	18.1568	+	31.4484i	0.619501	+	1.07301i	0.989577	+	0.144006i	$0.0459984\pi$
$859$	18.1568	+	31.4484i	0.619501	+	1.07301i	−0.370076	+	0.929002i	$0.620668\pi$
$860$	−3.07258	+	1.30948i	−0.104774	+	0.0446529i
$861$		0			0
$862$	9.06543	+	44.3936i	0.308770	+	1.51205i
$863$	26.8218	−	15.4856i	0.913025	−	0.527135i	0.0316219	−	0.999500i	$-0.489933\pi$
$863$	26.8218	−	15.4856i	0.913025	−	0.527135i	0.881403	+	0.472365i	$0.156599\pi$
$864$		0			0
$865$	3.65300	−	6.32717i	0.124206	−	0.215130i
$866$	−26.9648	+	23.8913i	−0.916302	+	0.811858i
$867$		0			0
$868$	−1.56104	−	30.1414i	−0.0529850	−	1.02307i
$869$	−0.321345			−0.0109009
$870$		0			0
$871$	−22.2116	−	12.8239i	−0.752610	−	0.434520i
$872$	−45.9847	+	3.71950i	−1.55724	+	0.125958i
$873$		0			0
$874$	14.8175	+	72.5617i	0.501210	+	2.45444i
$875$	6.40784	+	7.66863i	0.216625	+	0.259247i
$876$		0			0
$877$	32.7909	−	18.9318i	1.10727	−	0.639282i	0.169148	−	0.985591i	$-0.445898\pi$
$877$	32.7909	−	18.9318i	1.10727	−	0.639282i	0.938121	+	0.346309i	$0.112565\pi$
$878$	−29.0345	−	9.69146i	−0.979867	−	0.327071i
$879$		0			0
$880$	1.67274	−	6.79265i	0.0563880	−	0.228980i
$881$	23.9503			0.806906			0.403453	−	0.915000i	$-0.367810\pi$
$881$	23.9503			0.806906			0.403453	+	0.915000i	$0.367810\pi$
$882$		0			0
$883$		−	10.2002i		−	0.343263i	−0.985161	−	0.171631i	$-0.945096\pi$
$883$		−	10.2002i		−	0.343263i	0.985161	−	0.171631i	$-0.0549038\pi$
$884$	22.4034	+	16.8314i	0.753509	+	0.566103i
$885$		0			0
$886$	6.58595	−	19.7308i	0.221259	−	0.662868i
$887$	−13.8743	−	24.0310i	−0.465854	−	0.806883i	0.533386	−	0.845872i	$-0.320919\pi$
$887$	−13.8743	−	24.0310i	−0.465854	−	0.806883i	−0.999240	+	0.0389894i	$0.987586\pi$
$888$		0			0
$889$	−5.88694	+	4.91908i	−0.197442	+	0.164981i
$890$	0.354485	+	1.73592i	0.0118824	+	0.0581882i
$891$		0			0
$892$	22.8193	+	2.76835i	0.764047	+	0.0926913i
$893$	−39.6113	+	68.6088i	−1.32554	+	2.29591i
$894$		0			0
$895$			1.34059i			0.0448109i
$896$	14.6616	−	26.0967i	0.489809	−	0.871830i
$897$		0			0
$898$	27.2834	−	24.1735i	0.910458	−	0.806680i
$899$	−1.44607	−	0.834886i	−0.0482290	−	0.0278450i
$900$		0			0
$901$	−11.4894	−	19.9002i	−0.382766	−	0.662970i
$902$	31.1190	−	6.35467i	1.03615	−	0.211587i
$903$		0			0
$904$	4.85861	+	7.03656i	0.161595	+	0.234033i
$905$	−7.07426	+	4.08432i	−0.235156	+	0.135767i
$906$		0			0
$907$	21.5836	+	12.4613i	0.716673	+	0.413771i	0.813527	−	0.581527i	$-0.197545\pi$
$907$	21.5836	+	12.4613i	0.716673	+	0.413771i	−0.0968542	+	0.995299i	$0.530878\pi$
$908$	−2.10524	+	2.80217i	−0.0698648	+	0.0929934i
$909$		0			0
$910$	3.79474	−	1.48892i	0.125794	−	0.0493573i
$911$		−	27.2411i		−	0.902538i	−0.892388	−	0.451269i	$-0.850971\pi$
$911$		−	27.2411i		−	0.902538i	0.892388	−	0.451269i	$-0.149029\pi$
$912$		0			0
$913$	−25.6086	−	14.7851i	−0.847521	−	0.489316i
$914$	14.8209	−	44.4018i	0.490232	−	1.46868i
$915$		0			0
$916$	−10.7144	+	4.56628i	−0.354012	+	0.150874i
$917$	−11.0896	+	30.2741i	−0.366212	+	0.999740i
$918$		0			0
$919$	0.106387	+	0.184268i	0.00350938	+	0.00607843i	0.867775	−	0.496958i	$-0.165550\pi$
$919$	0.106387	+	0.184268i	0.00350938	+	0.00607843i	−0.864265	+	0.503036i	$0.832216\pi$
$920$	−0.546886	−	6.76123i	−0.0180303	−	0.222911i
$921$		0			0
$922$	−8.72924	+	7.73425i	−0.287482	+	0.254714i
$923$			12.4210i			0.408843i
$924$		0			0
$925$		−	34.3216i		−	1.12849i
$926$	−15.2680	−	17.2322i	−0.501736	−	0.566284i
$927$		0			0
$928$	−0.769974	−	1.46613i	−0.0252756	−	0.0481282i
$929$	8.81604	+	15.2698i	0.289245	+	0.500987i	0.973630	−	0.228134i	$-0.0732625\pi$
$929$	8.81604	+	15.2698i	0.289245	+	0.500987i	−0.684385	+	0.729121i	$0.739929\pi$
$930$		0			0
$931$	55.1434	−	19.8133i	1.80725	−	0.649356i
$932$	−6.73942	−	15.8134i	−0.220757	−	0.517987i
$933$		0			0
$934$	37.5638	+	12.5385i	1.22913	+	0.410271i
$935$	−7.46691	−	4.31102i	−0.244194	−	0.140985i
$936$		0			0
$937$		−	5.18135i		−	0.169267i	−0.996412	−	0.0846337i	$-0.973028\pi$
$937$		−	5.18135i		−	0.169267i	0.996412	−	0.0846337i	$-0.0269720\pi$
$938$	26.3984	+	21.0560i	0.861937	+	0.687502i
$939$		0			0
$940$	4.35853	−	5.80141i	0.142160	−	0.189221i
$941$	−17.0687	−	9.85464i	−0.556425	−	0.321252i	0.195284	−	0.980747i	$-0.437437\pi$
$941$	−17.0687	−	9.85464i	−0.556425	−	0.321252i	−0.751709	+	0.659495i	$0.770770\pi$
$942$		0			0
$943$	26.6714	−	15.3987i	0.868539	−	0.501451i
$944$	19.0745	+	18.3137i	0.620823	+	0.596060i
$945$		0			0
$946$	5.62341	+	27.5380i	0.182833	+	0.895336i
$947$	18.8273	+	32.6098i	0.611804	+	1.05968i	0.990936	+	0.134333i	$0.0428893\pi$
$947$	18.8273	+	32.6098i	0.611804	+	1.05968i	−0.379132	+	0.925343i	$0.623777\pi$
$948$		0			0
$949$	−31.2412	−	18.0371i	−1.01413	−	0.585509i
$950$	38.0987	+	43.0000i	1.23608	+	1.39511i
$951$		0			0
$952$	−25.8613	−	26.3109i	−0.838168	−	0.852743i
$953$		−	42.9398i		−	1.39096i	−0.718547	−	0.695478i	$-0.755192\pi$
$953$		−	42.9398i		−	1.39096i	0.718547	−	0.695478i	$-0.244808\pi$
$954$		0			0
$955$	−3.81106	+	6.60094i	−0.123323	+	0.213602i
$956$	4.32430	+	0.524609i	0.139858	+	0.0169671i
$957$		0			0
$958$	15.0343	−	3.07009i	0.485736	−	0.0991900i
$959$	47.9011	−	8.34444i	1.54681	−	0.269456i
$960$		0			0
$961$	0.766797	+	1.32813i	0.0247354	+	0.0428430i
$962$	−26.9617	−	8.99958i	−0.869280	−	0.290158i
$963$		0			0
$964$	7.04935	−	9.38302i	0.227044	−	0.302207i
$965$			3.99650i			0.128652i
$966$		0			0
$967$	−22.4334			−0.721408			−0.360704	−	0.932680i	$-0.617464\pi$
$967$	−22.4334			−0.721408			−0.360704	+	0.932680i	$0.617464\pi$
$968$	−25.0779	−	11.8948i	−0.806033	−	0.382313i
$969$		0			0
$970$	−0.0599478	+	0.179597i	−0.00192481	+	0.00576650i
$971$	−7.50553	+	4.33332i	−0.240864	+	0.139063i	−0.615574	−	0.788079i	$-0.711076\pi$
$971$	−7.50553	+	4.33332i	−0.240864	+	0.139063i	0.374710	+	0.927142i	$0.377742\pi$
$972$		0			0
$973$	−13.0003	+	10.8630i	−0.416772	+	0.348251i
$974$	15.9584	−	3.25879i	0.511339	−	0.104418i
$975$		0			0
$976$	3.12045	+	10.7646i	0.0998831	+	0.344568i
$977$	48.7155	+	28.1259i	1.55855	+	0.899828i	0.997396	+	0.0721142i	$0.0229746\pi$
$977$	48.7155	+	28.1259i	1.55855	+	0.899828i	0.561151	+	0.827714i	$0.310359\pi$
$978$		0			0
$979$	14.9094			0.476507
$980$	−5.23255	+	1.19328i	−0.167148	+	0.0381179i
$981$		0			0
$982$	5.26710	+	5.94470i	0.168080	+	0.189703i
$983$	10.2462	−	17.7469i	0.326802	−	0.566038i	−0.655073	−	0.755565i	$-0.727362\pi$
$983$	10.2462	−	17.7469i	0.326802	−	0.566038i	0.981875	+	0.189527i	$0.0606955\pi$
$984$		0			0
$985$	−5.32469	+	3.07421i	−0.169659	+	0.0979525i
$986$	−1.99978	+	0.408366i	−0.0636858	+	0.0130050i
$987$		0			0
$988$	43.7691	−	18.6536i	1.39248	−	0.593451i
$989$	13.6267	+	23.6022i	0.433304	+	0.750505i
$990$		0			0
$991$	13.1943	−	22.8533i	0.419132	−	0.725958i	−0.576720	−	0.816942i	$-0.695668\pi$
$991$	13.1943	−	22.8533i	0.419132	−	0.725958i	0.995852	+	0.0909835i	$0.0290011\pi$
$992$	−1.29082	+	32.2399i	−0.0409835	+	1.02362i
$993$		0			0
$994$	2.43882	−	16.1704i	0.0773546	−	0.512893i
$995$	−0.885873			−0.0280841
$996$		0			0
$997$	19.5633	−	33.8847i	0.619577	−	1.07314i	−0.369986	−	0.929038i	$-0.620637\pi$
$997$	19.5633	−	33.8847i	0.619577	−	1.07314i	0.989563	−	0.144102i	$-0.0460293\pi$
$998$	−19.4528	−	6.49316i	−0.615767	−	0.205537i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.269.7	✓	56
3.2	odd	2	inner	504.2.ch.b.269.22	yes	56
4.3	odd	2		2016.2.cp.b.17.13		56
7.5	odd	6	inner	504.2.ch.b.341.11	yes	56
8.3	odd	2		2016.2.cp.b.17.16		56
8.5	even	2	inner	504.2.ch.b.269.18	yes	56
12.11	even	2		2016.2.cp.b.17.15		56
21.5	even	6	inner	504.2.ch.b.341.18	yes	56
24.5	odd	2	inner	504.2.ch.b.269.11	yes	56
24.11	even	2		2016.2.cp.b.17.14		56
28.19	even	6		2016.2.cp.b.593.14		56
56.5	odd	6	inner	504.2.ch.b.341.22	yes	56
56.19	even	6		2016.2.cp.b.593.15		56
84.47	odd	6		2016.2.cp.b.593.16		56
168.5	even	6	inner	504.2.ch.b.341.7	yes	56
168.131	odd	6		2016.2.cp.b.593.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.7	✓	56	1.1	even	1	trivial
504.2.ch.b.269.11	yes	56	24.5	odd	2	inner
504.2.ch.b.269.18	yes	56	8.5	even	2	inner
504.2.ch.b.269.22	yes	56	3.2	odd	2	inner
504.2.ch.b.341.7	yes	56	168.5	even	6	inner
504.2.ch.b.341.11	yes	56	7.5	odd	6	inner
504.2.ch.b.341.18	yes	56	21.5	even	6	inner
504.2.ch.b.341.22	yes	56	56.5	odd	6	inner
2016.2.cp.b.17.13		56	4.3	odd	2
2016.2.cp.b.17.14		56	24.11	even	2
2016.2.cp.b.17.15		56	12.11	even	2
2016.2.cp.b.17.16		56	8.3	odd	2
2016.2.cp.b.593.13		56	168.131	odd	6
2016.2.cp.b.593.14		56	28.19	even	6
2016.2.cp.b.593.15		56	56.19	even	6
2016.2.cp.b.593.16		56	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.937852 - 1.05851i) q^{2} +(-0.240867 + 1.98544i) q^{4} +(-0.331990 + 0.191675i) q^{5} +(-2.03027 + 1.69647i) q^{7} +(2.32750 - 1.60709i) q^{8} +O(q^{10})\)	\(q+(-0.937852 - 1.05851i) q^{2} +(-0.240867 + 1.98544i) q^{4} +(-0.331990 + 0.191675i) q^{5} +(-2.03027 + 1.69647i) q^{7} +(2.32750 - 1.60709i) q^{8} +(0.514246 + 0.171651i) q^{10} +(2.28107 - 3.95093i) q^{11} -2.84195 q^{13} +(3.69981 + 0.558007i) q^{14} +(-3.88397 - 0.956454i) q^{16} +(-2.46500 + 4.26950i) q^{17} +(4.18535 + 7.24924i) q^{19} +(-0.300594 - 0.705316i) q^{20} +(-6.32139 + 1.29086i) q^{22} +(-5.41792 + 3.12804i) q^{23} +(-2.42652 + 4.20286i) q^{25} +(2.66533 + 3.00822i) q^{26} +(-2.87923 - 4.43960i) q^{28} -0.292746 q^{29} +(4.93966 + 2.85191i) q^{31} +(2.63017 + 5.00821i) q^{32} +(6.83109 - 1.39495i) q^{34} +(0.348858 - 0.952363i) q^{35} +(-6.12469 + 3.53609i) q^{37} +(3.74812 - 11.2289i) q^{38} +(-0.464668 + 0.979662i) q^{40} -4.92280 q^{41} -4.35631i q^{43} +(7.29492 + 5.48059i) q^{44} +(8.39226 + 2.80126i) q^{46} +(4.73214 + 8.19631i) q^{47} +(1.24396 - 6.88858i) q^{49} +(6.72447 - 1.37317i) q^{50} +(0.684532 - 5.64254i) q^{52} +(-2.33050 + 4.03655i) q^{53} +1.74890i q^{55} +(-1.99905 + 7.21137i) q^{56} +(0.274553 + 0.309873i) q^{58} +(-5.72506 - 3.30537i) q^{59} +(-1.40098 - 2.42656i) q^{61} +(-1.61390 - 7.90332i) q^{62} +(2.83450 - 7.48102i) q^{64} +(0.943501 - 0.544730i) q^{65} +(7.81560 + 4.51234i) q^{67} +(-7.88311 - 5.92249i) q^{68} +(-1.33526 + 0.523908i) q^{70} -4.37059i q^{71} +(10.9929 + 6.34673i) q^{73} +(9.48703 + 3.16669i) q^{74} +(-15.4011 + 6.56367i) q^{76} +(2.07147 + 11.8912i) q^{77} +(-0.0352186 - 0.0610004i) q^{79} +(1.47277 - 0.426925i) q^{80} +(4.61686 + 5.21081i) q^{82} -6.48166i q^{83} -1.88991i q^{85} +(-4.61118 + 4.08558i) q^{86} +(-1.04032 - 12.8617i) q^{88} +(1.63404 + 2.83024i) q^{89} +(5.76992 - 4.82130i) q^{91} +(-4.90555 - 11.5104i) q^{92} +(4.23779 - 12.6959i) q^{94} +(-2.77899 - 1.60445i) q^{95} +0.349243i q^{97} +(-8.45825 + 5.14373i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 56 * q - 8 * q^4 - 20 * q^7	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

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