LMFDB - Embedded newform 945.2.p.b.622.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(433,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("945.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.p (of order $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			622.20
Character	$\chi$	$=$	945.622
Dual form			945.2.p.b.433.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27393 + 1.27393i) q^{2} +1.24581i q^{4} +(2.23606 + 0.00600881i) q^{5} +(-1.54853 - 2.14524i) q^{7} +(0.960789 - 0.960789i) q^{8} +O(q^{10})$	\(q+(1.27393 + 1.27393i) q^{2} +1.24581i q^{4} +(2.23606 + 0.00600881i) q^{5} +(-1.54853 - 2.14524i) q^{7} +(0.960789 - 0.960789i) q^{8} +(2.84093 + 2.85624i) q^{10} +4.95168 q^{11} +(-4.34673 - 4.34673i) q^{13} +(0.760171 - 4.70561i) q^{14} +4.93958 q^{16} +(-2.81538 + 2.81538i) q^{17} +2.64901 q^{19} +(-0.00748582 + 2.78570i) q^{20} +(6.30811 + 6.30811i) q^{22} +(0.761826 - 0.761826i) q^{23} +(4.99993 + 0.0268721i) q^{25} -11.0749i q^{26} +(2.67256 - 1.92917i) q^{28} -3.25945i q^{29} +0.0115464i q^{31} +(4.37111 + 4.37111i) q^{32} -7.17322 q^{34} +(-3.44971 - 4.80619i) q^{35} +(4.56825 + 4.56825i) q^{37} +(3.37466 + 3.37466i) q^{38} +(2.15416 - 2.14261i) q^{40} -2.77822i q^{41} +(-6.37466 + 6.37466i) q^{43} +6.16885i q^{44} +1.94103 q^{46} +(-8.38024 + 8.38024i) q^{47} +(-2.20412 + 6.64393i) q^{49} +(6.33534 + 6.40380i) q^{50} +(5.41519 - 5.41519i) q^{52} +(3.87019 - 3.87019i) q^{53} +(11.0723 + 0.0297537i) q^{55} +(-3.54893 - 0.573315i) q^{56} +(4.15232 - 4.15232i) q^{58} +4.06308 q^{59} +11.4059i q^{61} +(-0.0147093 + 0.0147093i) q^{62} +1.25785i q^{64} +(-9.69342 - 9.74566i) q^{65} +(-0.909987 - 0.909987i) q^{67} +(-3.50743 - 3.50743i) q^{68} +(1.72806 - 10.5175i) q^{70} -4.59015 q^{71} +(-0.162169 - 0.162169i) q^{73} +11.6393i q^{74} +3.30016i q^{76} +(-7.66783 - 10.6226i) q^{77} +5.38899i q^{79} +(11.0452 + 0.0296810i) q^{80} +(3.53926 - 3.53926i) q^{82} +(3.38215 + 3.38215i) q^{83} +(-6.31228 + 6.27845i) q^{85} -16.2418 q^{86} +(4.75752 - 4.75752i) q^{88} +0.0829077 q^{89} +(-2.59375 + 16.0558i) q^{91} +(0.949089 + 0.949089i) q^{92} -21.3517 q^{94} +(5.92335 + 0.0159174i) q^{95} +(1.06919 - 1.06919i) q^{97} +(-11.2718 + 5.65603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{7}+O(q^{10}) $ 48 * q - 8 * q^7	$ 48 q - 8 q^{7} + 40 q^{16} + 8 q^{22} - 48 q^{25} - 20 q^{28} - 24 q^{37} - 40 q^{43} + 40 q^{46} - 80 q^{58} - 64 q^{67} - 4 q^{70} - 8 q^{85} - 48 q^{88} + 48 q^{91}+O(q^{100}) $ 48 * q - 8 * q^7 + 40 * q^16 + 8 * q^22 - 48 * q^25 - 20 * q^28 - 24 * q^37 - 40 * q^43 + 40 * q^46 - 80 * q^58 - 64 * q^67 - 4 * q^70 - 8 * q^85 - 48 * q^88 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.27393	+	1.27393i	0.900806	+	0.900806i	0.995506	−	0.0946995i	$-0.0301890\pi$
$2$	1.27393	+	1.27393i	0.900806	+	0.900806i	−0.0946995	+	0.995506i	$0.530189\pi$
$3$		0			0
$3$		0			0
$4$			1.24581i			0.622904i
$5$	2.23606	+	0.00600881i	0.999996	+	0.00268722i
$5$	2.23606	+	0.00600881i	0.999996	+	0.00268722i
$6$		0			0
$7$	−1.54853	−	2.14524i	−0.585289	−	0.810825i
$7$	−1.54853	−	2.14524i	−0.585289	−	0.810825i
$8$	0.960789	−	0.960789i	0.339690	−	0.339690i
$9$		0			0
$10$	2.84093	+	2.85624i	0.898382	+	0.903224i
$11$	4.95168			1.49299			0.746495	−	0.665392i	$-0.231735\pi$
$11$	4.95168			1.49299			0.746495	+	0.665392i	$0.231735\pi$
$12$		0			0
$13$	−4.34673	−	4.34673i	−1.20557	−	1.20557i	−0.972449	−	0.233116i	$-0.925108\pi$
$13$	−4.34673	−	4.34673i	−1.20557	−	1.20557i	−0.233116	−	0.972449i	$-0.574892\pi$
$14$	0.760171	−	4.70561i	0.203164	−	1.25763i
$15$		0			0
$16$	4.93958			1.23489
$17$	−2.81538	+	2.81538i	−0.682831	+	0.682831i	−0.960637	−	0.277806i	$-0.910393\pi$
$17$	−2.81538	+	2.81538i	−0.682831	+	0.682831i	0.277806	+	0.960637i	$0.410393\pi$
$18$		0			0
$19$	2.64901			0.607725			0.303863	−	0.952716i	$-0.401724\pi$
$19$	2.64901			0.607725			0.303863	+	0.952716i	$0.401724\pi$
$20$	−0.00748582	+	2.78570i	−0.00167388	+	0.622902i
$21$		0			0
$22$	6.30811	+	6.30811i	1.34489	+	1.34489i
$23$	0.761826	−	0.761826i	0.158852	−	0.158852i	−0.623206	−	0.782058i	$-0.714170\pi$
$23$	0.761826	−	0.761826i	0.158852	−	0.158852i	0.782058	+	0.623206i	$0.214170\pi$
$24$		0			0
$25$	4.99993	+	0.0268721i	0.999986	+	0.00537442i
$26$		−	11.0749i		−	2.17196i
$27$		0			0
$28$	2.67256	−	1.92917i	0.505066	−	0.364579i
$29$		−	3.25945i		−	0.605264i	−0.953107	−	0.302632i	$-0.902135\pi$
$29$		−	3.25945i		−	0.605264i	0.953107	−	0.302632i	$-0.0978654\pi$
$30$		0			0
$31$			0.0115464i			0.00207379i	0.999999	+	0.00103690i	$0.000330055\pi$
$31$			0.0115464i			0.00207379i	−0.999999	+	0.00103690i	$0.999670\pi$
$32$	4.37111	+	4.37111i	0.772711	+	0.772711i
$33$		0			0
$34$	−7.17322			−1.23020
$35$	−3.44971	−	4.80619i	−0.583108	−	0.812395i
$36$		0			0
$37$	4.56825	+	4.56825i	0.751016	+	0.751016i	0.974669	−	0.223653i	$-0.0717982\pi$
$37$	4.56825	+	4.56825i	0.751016	+	0.751016i	−0.223653	+	0.974669i	$0.571798\pi$
$38$	3.37466	+	3.37466i	0.547443	+	0.547443i
$39$		0			0
$40$	2.15416	−	2.14261i	0.340602	−	0.338776i
$41$		−	2.77822i		−	0.433885i	−0.976184	−	0.216942i	$-0.930392\pi$
$41$		−	2.77822i		−	0.433885i	0.976184	−	0.216942i	$-0.0696083\pi$
$42$		0			0
$43$	−6.37466	+	6.37466i	−0.972126	+	0.972126i	−0.999622	−	0.0274955i	$-0.991247\pi$
$43$	−6.37466	+	6.37466i	−0.972126	+	0.972126i	0.0274955	+	0.999622i	$0.491247\pi$
$44$			6.16885i			0.929989i
$45$		0			0
$46$	1.94103			0.286189
$47$	−8.38024	+	8.38024i	−1.22238	+	1.22238i	−0.255601	+	0.966782i	$0.582273\pi$
$47$	−8.38024	+	8.38024i	−1.22238	+	1.22238i	−0.966782	+	0.255601i	$0.917727\pi$
$48$		0			0
$49$	−2.20412	+	6.64393i	−0.314874	+	0.949133i
$50$	6.33534	+	6.40380i	0.895952	+	0.905635i
$51$		0			0
$52$	5.41519	−	5.41519i	0.750952	−	0.750952i
$53$	3.87019	−	3.87019i	0.531612	−	0.531612i	−0.389440	−	0.921052i	$-0.627331\pi$
$53$	3.87019	−	3.87019i	0.531612	−	0.531612i	0.921052	+	0.389440i	$0.127331\pi$
$54$		0			0
$55$	11.0723	+	0.0297537i	1.49298	+	0.00401199i
$56$	−3.54893	−	0.573315i	−0.474246	−	0.0766124i
$57$		0			0
$58$	4.15232	−	4.15232i	0.545226	−	0.545226i
$59$	4.06308			0.528968			0.264484	−	0.964390i	$-0.414798\pi$
$59$	4.06308			0.528968			0.264484	+	0.964390i	$0.414798\pi$
$60$		0			0
$61$			11.4059i			1.46038i	0.683246	+	0.730188i	$0.260568\pi$
$61$			11.4059i			1.46038i	−0.683246	+	0.730188i	$0.739432\pi$
$62$	−0.0147093	+	0.0147093i	−0.00186809	+	0.00186809i
$63$		0			0
$64$			1.25785i			0.157231i
$65$	−9.69342	−	9.74566i	−1.20232	−	1.20880i
$66$		0			0
$67$	−0.909987	−	0.909987i	−0.111173	−	0.111173i	0.649332	−	0.760505i	$-0.275048\pi$
$67$	−0.909987	−	0.909987i	−0.111173	−	0.111173i	−0.760505	+	0.649332i	$0.775048\pi$
$68$	−3.50743	−	3.50743i	−0.425338	−	0.425338i
$69$		0			0
$70$	1.72806	−	10.5175i	0.206543	−	1.25708i
$71$	−4.59015			−0.544750			−0.272375	−	0.962191i	$-0.587809\pi$
$71$	−4.59015			−0.544750			−0.272375	+	0.962191i	$0.587809\pi$
$72$		0			0
$73$	−0.162169	−	0.162169i	−0.0189805	−	0.0189805i	0.697553	−	0.716533i	$-0.254272\pi$
$73$	−0.162169	−	0.162169i	−0.0189805	−	0.0189805i	−0.716533	+	0.697553i	$0.754272\pi$
$74$			11.6393i			1.35304i
$75$		0			0
$76$			3.30016i			0.378554i
$77$	−7.66783	−	10.6226i	−0.873830	−	1.21055i
$78$		0			0
$79$			5.38899i			0.606309i	0.952941	+	0.303154i	$0.0980398\pi$
$79$			5.38899i			0.606309i	−0.952941	+	0.303154i	$0.901960\pi$
$80$	11.0452	+	0.0296810i	1.23489	+	0.00331843i
$81$		0			0
$82$	3.53926	−	3.53926i	0.390846	−	0.390846i
$83$	3.38215	+	3.38215i	0.371239	+	0.371239i	0.867928	−	0.496689i	$-0.165451\pi$
$83$	3.38215	+	3.38215i	0.371239	+	0.371239i	−0.496689	+	0.867928i	$0.665451\pi$
$84$		0			0
$85$	−6.31228	+	6.27845i	−0.684663	+	0.680993i
$86$	−16.2418			−1.75140
$87$		0			0
$88$	4.75752	−	4.75752i	0.507154	−	0.507154i
$89$	0.0829077			0.00878820			0.00439410	−	0.999990i	$-0.498601\pi$
$89$	0.0829077			0.00878820			0.00439410	+	0.999990i	$0.498601\pi$
$90$		0			0
$91$	−2.59375	+	16.0558i	−0.271898	+	1.68311i
$92$	0.949089	+	0.949089i	0.0989494	+	0.0989494i
$93$		0			0
$94$	−21.3517			−2.20226
$95$	5.92335	+	0.0159174i	0.607723	+	0.00163309i
$96$		0			0
$97$	1.06919	−	1.06919i	0.108560	−	0.108560i	−0.650741	−	0.759300i	$-0.725541\pi$
$97$	1.06919	−	1.06919i	0.108560	−	0.108560i	0.759300	+	0.650741i	$0.225541\pi$
$98$	−11.2718	+	5.65603i	−1.13863	+	0.571345i
$99$		0			0
$100$	−0.0334775	+	6.22895i	−0.00334775	+	0.622895i
$101$			11.8763i			1.18173i	0.806770	+	0.590866i	$0.201214\pi$
$101$			11.8763i			1.18173i	−0.806770	+	0.590866i	$0.798786\pi$
$102$		0			0
$103$	−10.5772	−	10.5772i	−1.04220	−	1.04220i	−0.999069	−	0.0431295i	$-0.986267\pi$
$103$	−10.5772	−	10.5772i	−1.04220	−	1.04220i	−0.0431295	−	0.999069i	$-0.513733\pi$
$104$	−8.35258			−0.819037
$105$		0			0
$106$	9.86073			0.957758
$107$	−8.56550	−	8.56550i	−0.828058	−	0.828058i	0.159190	−	0.987248i	$-0.449112\pi$
$107$	−8.56550	−	8.56550i	−0.828058	−	0.828058i	−0.987248	+	0.159190i	$0.949112\pi$
$108$		0			0
$109$		−	8.76608i		−	0.839639i	−0.907608	−	0.419819i	$-0.862093\pi$
$109$		−	8.76608i		−	0.839639i	0.907608	−	0.419819i	$-0.137907\pi$
$110$	14.0674	+	14.1432i	1.34128	+	1.34850i
$111$		0			0
$112$	−7.64908	−	10.5966i	−0.722770	−	1.00128i
$113$	−12.4032	+	12.4032i	−1.16680	+	1.16680i	−0.183844	+	0.982955i	$0.558854\pi$
$113$	−12.4032	+	12.4032i	−1.16680	+	1.16680i	−0.982955	+	0.183844i	$0.941146\pi$
$114$		0			0
$115$	1.70807	−	1.69891i	0.159278	−	0.158424i
$116$	4.06065			0.377022
$117$		0			0
$118$	5.17609	+	5.17609i	0.476498	+	0.476498i
$119$	10.3994	+	1.67997i	0.953309	+	0.154003i
$120$		0			0
$121$	13.5192			1.22902
$122$	−14.5304	+	14.5304i	−1.31552	+	1.31552i
$123$		0			0
$124$	−0.0143846			−0.00129177
$125$	11.1800	+	0.0901312i	0.999968	+	0.00806158i
$126$		0			0
$127$	4.23766	+	4.23766i	0.376031	+	0.376031i	0.869668	−	0.493637i	$-0.164333\pi$
$127$	4.23766	+	4.23766i	0.376031	+	0.376031i	−0.493637	+	0.869668i	$0.664333\pi$
$128$	7.13981	−	7.13981i	0.631076	−	0.631076i
$129$		0			0
$130$	0.0665468	−	24.7641i	0.00583654	−	2.17195i
$131$		−	15.8185i		−	1.38207i	−0.722821	−	0.691035i	$-0.757155\pi$
$131$		−	15.8185i		−	1.38207i	0.722821	−	0.691035i	$-0.242845\pi$
$132$		0			0
$133$	−4.10207	−	5.68277i	−0.355695	−	0.492759i
$134$		−	2.31852i		−	0.200290i
$135$		0			0
$136$			5.40998i			0.463902i
$137$	12.1165	+	12.1165i	1.03518	+	1.03518i	0.999358	+	0.0358235i	$0.0114054\pi$
$137$	12.1165	+	12.1165i	1.03518	+	1.03518i	0.0358235	+	0.999358i	$0.488595\pi$
$138$		0			0
$139$	12.8985			1.09403			0.547017	−	0.837122i	$-0.315763\pi$
$139$	12.8985			1.09403			0.547017	+	0.837122i	$0.315763\pi$
$140$	5.98760	−	4.29768i	0.506044	−	0.363220i
$141$		0			0
$142$	−5.84754	−	5.84754i	−0.490715	−	0.490715i
$143$	−21.5236	−	21.5236i	−1.79990	−	1.79990i
$144$		0			0
$145$	0.0195854	−	7.28832i	0.00162648	−	0.605262i
$146$		−	0.413185i		−	0.0341954i
$147$		0			0
$148$	−5.69117	+	5.69117i	−0.467811	+	0.467811i
$149$		−	17.9605i		−	1.47138i	−0.677318	−	0.735691i	$-0.736858\pi$
$149$		−	17.9605i		−	1.47138i	0.677318	−	0.735691i	$-0.263142\pi$
$150$		0			0
$151$	−21.5659			−1.75501			−0.877504	−	0.479570i	$-0.840793\pi$
$151$	−21.5659			−1.75501			−0.877504	+	0.479570i	$0.840793\pi$
$152$	2.54514	−	2.54514i	0.206438	−	0.206438i
$153$		0			0
$154$	3.76413	−	23.3007i	0.303322	−	1.87763i
$155$	−6.93801e−5		0.0258184i	−5.57274e−6		0.00207379i
$156$		0			0
$157$	12.6979	−	12.6979i	1.01340	−	1.01340i	0.0134919	−	0.999909i	$-0.495705\pi$
$157$	12.6979	−	12.6979i	1.01340	−	1.01340i	0.999909	−	0.0134919i	$-0.00429473\pi$
$158$	−6.86521	+	6.86521i	−0.546167	+	0.546167i
$159$		0			0
$160$	9.74780	+	9.80033i	0.770631	+	0.774784i
$161$	−2.81401	−	0.454591i	−0.221775	−	0.0358268i
$162$		0			0
$163$	−7.12682	+	7.12682i	−0.558216	+	0.558216i	−0.928799	−	0.370583i	$-0.879158\pi$
$163$	−7.12682	+	7.12682i	−0.558216	+	0.558216i	0.370583	+	0.928799i	$0.379158\pi$
$164$	3.46113			0.270269
$165$		0			0
$166$			8.61726i			0.668829i
$167$	−6.04165	+	6.04165i	−0.467517	+	0.467517i	−0.901109	−	0.433592i	$-0.857246\pi$
$167$	−6.04165	+	6.04165i	−0.467517	+	0.467517i	0.433592	+	0.901109i	$0.357246\pi$
$168$		0			0
$169$			24.7881i			1.90677i
$170$	−16.0397	−	0.0431025i	−1.23019	−	0.00330581i
$171$		0			0
$172$	−7.94160	−	7.94160i	−0.605542	−	0.605542i
$173$	−5.16071	−	5.16071i	−0.392362	−	0.392362i	0.483167	−	0.875528i	$-0.339487\pi$
$173$	−5.16071	−	5.16071i	−0.392362	−	0.392362i	−0.875528	+	0.483167i	$0.839487\pi$
$174$		0			0
$175$	−7.68488	−	10.7677i	−0.580923	−	0.813959i
$176$	24.4592			1.84368
$177$		0			0
$178$	0.105619	+	0.105619i	0.00791647	+	0.00791647i
$179$			4.39981i			0.328857i	0.986389	+	0.164429i	$0.0525780\pi$
$179$			4.39981i			0.328857i	−0.986389	+	0.164429i	$0.947422\pi$
$180$		0			0
$181$			1.55581i			0.115642i	0.998327	+	0.0578211i	$0.0184153\pi$
$181$			1.55581i			0.115642i	−0.998327	+	0.0578211i	$0.981585\pi$
$182$	−23.7583	+	17.1498i	−1.76108	+	1.27122i
$183$		0			0
$184$		−	1.46391i		−	0.107921i
$185$	10.1874	+	10.2423i	0.748995	+	0.753031i
$186$		0			0
$187$	−13.9409	+	13.9409i	−1.01946	+	1.01946i
$188$	−10.4402	−	10.4402i	−0.761428	−	0.761428i
$189$		0			0
$190$	7.52567	+	7.56623i	0.545969	+	0.548912i
$191$	−14.0564			−1.01709			−0.508544	−	0.861036i	$-0.669816\pi$
$191$	−14.0564			−1.01709			−0.508544	+	0.861036i	$0.669816\pi$
$192$		0			0
$193$	−9.90465	+	9.90465i	−0.712952	+	0.712952i	−0.967152	−	0.254200i	$-0.918188\pi$
$193$	−9.90465	+	9.90465i	−0.712952	+	0.712952i	0.254200	+	0.967152i	$0.418188\pi$
$194$	2.72415			0.195582
$195$		0			0
$196$	−8.27707	−	2.74591i	−0.591219	−	0.196136i
$197$	10.2120	+	10.2120i	0.727574	+	0.727574i	0.970136	−	0.242562i	$-0.0779878\pi$
$197$	10.2120	+	10.2120i	0.727574	+	0.727574i	−0.242562	+	0.970136i	$0.577988\pi$
$198$		0			0
$199$	−16.1480			−1.14470			−0.572352	−	0.820008i	$-0.693969\pi$
$199$	−16.1480			−1.14470			−0.572352	+	0.820008i	$0.693969\pi$
$200$	4.82969	−	4.77806i	0.341511	−	0.337860i
$201$		0			0
$202$	−15.1295	+	15.1295i	−1.06451	+	1.06451i
$203$	−6.99230	+	5.04735i	−0.490763	+	0.354254i
$204$		0			0
$205$	0.0166938	−	6.21226i	0.00116594	−	0.433883i
$206$		−	26.9492i		−	1.87764i
$207$		0			0
$208$	−21.4710	−	21.4710i	−1.48875	−	1.48875i
$209$	13.1171			0.907327
$210$		0			0
$211$	−14.2802			−0.983088			−0.491544	−	0.870853i	$-0.663567\pi$
$211$	−14.2802			−0.983088			−0.491544	+	0.870853i	$0.663567\pi$
$212$	4.82152	+	4.82152i	0.331143	+	0.331143i
$213$		0			0
$214$		−	21.8237i		−	1.49184i
$215$	−14.2924	+	14.2158i	−0.974735	+	0.969511i
$216$		0			0
$217$	0.0247698	−	0.0178799i	0.00168148	−	0.00121377i
$218$	11.1674	−	11.1674i	0.756352	−	0.756352i
$219$		0			0
$220$	−0.0370674	+	13.7939i	−0.00249909	+	0.929986i
$221$	24.4754			1.64639
$222$		0			0
$223$	−14.6219	−	14.6219i	−0.979157	−	0.979157i	0.0206300	−	0.999787i	$-0.493433\pi$
$223$	−14.6219	−	14.6219i	−0.979157	−	0.979157i	−0.999787	+	0.0206300i	$0.993433\pi$
$224$	2.60830	−	16.1459i	0.174274	−	1.07879i
$225$		0			0
$226$	−31.6018			−2.10212
$227$	18.6285	−	18.6285i	1.23642	−	1.23642i	0.274959	−	0.961456i	$-0.411336\pi$
$227$	18.6285	−	18.6285i	1.23642	−	1.23642i	0.961456	−	0.274959i	$-0.0886644\pi$
$228$		0			0
$229$	20.9089			1.38170			0.690851	−	0.722997i	$-0.257236\pi$
$229$	20.9089			1.38170			0.690851	+	0.722997i	$0.257236\pi$
$230$	4.34026	+	0.0116633i	0.286188	+	0.000769053i
$231$		0			0
$232$	−3.13164	−	3.13164i	−0.205602	−	0.205602i
$233$	11.0583	−	11.0583i	0.724451	−	0.724451i	−0.245058	−	0.969509i	$-0.578807\pi$
$233$	11.0583	−	11.0583i	0.724451	−	0.724451i	0.969509	+	0.245058i	$0.0788069\pi$
$234$		0			0
$235$	−18.7891	+	18.6884i	−1.22566	+	1.21909i
$236$			5.06182i			0.329496i
$237$		0			0
$238$	11.1079	+	15.3883i	0.720020	+	0.997474i
$239$		−	3.39359i		−	0.219513i	−0.993958	−	0.109757i	$-0.964993\pi$
$239$		−	3.39359i		−	0.219513i	0.993958	−	0.109757i	$-0.0350071\pi$
$240$		0			0
$241$			25.3767i			1.63466i	0.576173	+	0.817328i	$0.304545\pi$
$241$			25.3767i			1.63466i	−0.576173	+	0.817328i	$0.695455\pi$
$242$	17.2225	+	17.2225i	1.10711	+	1.10711i
$243$		0			0
$244$	−14.2096			−0.909675
$245$	−4.96846	+	14.8430i	−0.317423	+	0.948284i
$246$		0			0
$247$	−11.5145	−	11.5145i	−0.732652	−	0.732652i
$248$	0.0110937	+	0.0110937i	0.000704447	+	0.000704447i
$249$		0			0
$250$	14.1277	+	14.3574i	0.893515	+	0.908039i
$251$		−	2.92236i		−	0.184458i	−0.995738	−	0.0922288i	$-0.970601\pi$
$251$		−	2.92236i		−	0.184458i	0.995738	−	0.0922288i	$-0.0293991\pi$
$252$		0			0
$253$	3.77232	−	3.77232i	0.237164	−	0.237164i
$254$			10.7970i			0.677463i
$255$		0			0
$256$	20.7070			1.29419
$257$	5.50980	−	5.50980i	0.343692	−	0.343692i	−0.514061	−	0.857753i	$-0.671860\pi$
$257$	5.50980	−	5.50980i	0.343692	−	0.343692i	0.857753	+	0.514061i	$0.171860\pi$
$258$		0			0
$259$	2.72593	−	16.8741i	0.169381	−	1.04850i
$260$	12.1412	−	12.0761i	0.752967	−	0.748931i
$261$		0			0
$262$	20.1517	−	20.1517i	1.24498	−	1.24498i
$263$	15.0223	−	15.0223i	0.926312	−	0.926312i	−0.0711533	−	0.997465i	$-0.522668\pi$
$263$	15.0223	−	15.0223i	0.926312	−	0.926312i	0.997465	+	0.0711533i	$0.0226680\pi$
$264$		0			0
$265$	8.67724	−	8.63073i	0.533038	−	0.530181i
$266$	2.01370	−	12.4652i	0.123468	−	0.764292i
$267$		0			0
$268$	1.13367	−	1.13367i	0.0692499	−	0.0692499i
$269$	−3.49131			−0.212869			−0.106434	−	0.994320i	$-0.533943\pi$
$269$	−3.49131			−0.212869			−0.106434	+	0.994320i	$0.533943\pi$
$270$		0			0
$271$		−	17.8124i		−	1.08202i	−0.841015	−	0.541012i	$-0.818041\pi$
$271$		−	17.8124i		−	1.08202i	0.841015	−	0.541012i	$-0.181959\pi$
$272$	−13.9068	+	13.9068i	−0.843224	+	0.843224i
$273$		0			0
$274$			30.8712i			1.86500i
$275$	24.7581	+	0.133062i	1.49297	+	0.00802395i
$276$		0			0
$277$	−3.99518	−	3.99518i	−0.240047	−	0.240047i	0.576822	−	0.816870i	$-0.304292\pi$
$277$	−3.99518	−	3.99518i	−0.240047	−	0.240047i	−0.816870	+	0.576822i	$0.804292\pi$
$278$	16.4318	+	16.4318i	0.985512	+	0.985512i
$279$		0			0
$280$	−7.93218	−	1.30329i	−0.474039	−	0.0778865i
$281$	−2.48535			−0.148263			−0.0741316	−	0.997248i	$-0.523619\pi$
$281$	−2.48535			−0.148263			−0.0741316	+	0.997248i	$0.523619\pi$
$282$		0			0
$283$	18.5528	+	18.5528i	1.10285	+	1.10285i	0.994066	+	0.108781i	$0.0346946\pi$
$283$	18.5528	+	18.5528i	1.10285	+	1.10285i	0.108781	+	0.994066i	$0.465305\pi$
$284$		−	5.71844i		−	0.339327i
$285$		0			0
$286$		−	54.8393i		−	3.24271i
$287$	−5.95994	+	4.30215i	−0.351804	+	0.253948i
$288$		0			0
$289$			1.14723i			0.0674843i
$290$	9.30978	−	9.25988i	0.546689	−	0.543759i
$291$		0			0
$292$	0.202032	−	0.202032i	0.0118230	−	0.0118230i
$293$	−17.9263	−	17.9263i	−1.04727	−	1.04727i	−0.998826	−	0.0484424i	$-0.984574\pi$
$293$	−17.9263	−	17.9263i	−1.04727	−	1.04727i	−0.0484424	−	0.998826i	$-0.515426\pi$
$294$		0			0
$295$	9.08529	+	0.0244143i	0.528966	+	0.00142145i
$296$	8.77825			0.510226
$297$		0			0
$298$	22.8805	−	22.8805i	1.32543	−	1.32543i
$299$	−6.62290			−0.383012
$300$		0			0
$301$	23.5465	+	3.80384i	1.35720	+	0.219250i
$302$	−27.4735	−	27.4735i	−1.58092	−	1.58092i
$303$		0			0
$304$	13.0850			0.750476
$305$	−0.0685359	+	25.5043i	−0.00392435	+	1.46037i
$306$		0			0
$307$	−24.0052	+	24.0052i	−1.37005	+	1.37005i	−0.509697	+	0.860354i	$0.670243\pi$
$307$	−24.0052	+	24.0052i	−1.37005	+	1.37005i	−0.860354	+	0.509697i	$0.829757\pi$
$308$	13.2337	−	9.55264i	0.754058	−	0.544312i
$309$		0			0
$310$	−0.0329793	+	0.0328026i	−0.00187310	+	0.00186306i
$311$			17.5199i			0.993464i	0.867904	+	0.496732i	$0.165467\pi$
$311$			17.5199i			0.993464i	−0.867904	+	0.496732i	$0.834533\pi$
$312$		0			0
$313$	23.6065	+	23.6065i	1.33432	+	1.33432i	0.901462	+	0.432858i	$0.142495\pi$
$313$	23.6065	+	23.6065i	1.33432	+	1.33432i	0.432858	+	0.901462i	$0.357505\pi$
$314$	32.3525			1.82576
$315$		0			0
$316$	−6.71365			−0.377672
$317$	8.08890	+	8.08890i	0.454318	+	0.454318i	0.896785	−	0.442467i	$-0.145897\pi$
$317$	8.08890	+	8.08890i	0.454318	+	0.454318i	−0.442467	+	0.896785i	$0.645897\pi$
$318$		0			0
$319$		−	16.1398i		−	0.903653i
$320$	−0.00755816	+	2.81262i	−0.000422514	+	0.157230i
$321$		0			0
$322$	−3.00574	−	4.16398i	−0.167503	−	0.232049i
$323$	−7.45798	+	7.45798i	−0.414973	+	0.414973i
$324$		0			0
$325$	−21.6165	−	21.8501i	−1.19907	−	1.21203i
$326$	−18.1582			−1.00569
$327$		0			0
$328$	−2.66928	−	2.66928i	−0.147386	−	0.147386i
$329$	30.9547	+	5.00059i	1.70659	+	0.275692i
$330$		0			0
$331$	−0.858481			−0.0471864			−0.0235932	−	0.999722i	$-0.507511\pi$
$331$	−0.858481			−0.0471864			−0.0235932	+	0.999722i	$0.507511\pi$
$332$	−4.21351	+	4.21351i	−0.231246	+	0.231246i
$333$		0			0
$334$	−15.3933			−0.842284
$335$	−2.02932	−	2.04025i	−0.110873	−	0.111471i
$336$		0			0
$337$	13.4198	+	13.4198i	0.731025	+	0.731025i	0.970823	−	0.239797i	$-0.0770810\pi$
$337$	13.4198	+	13.4198i	0.731025	+	0.731025i	−0.239797	+	0.970823i	$0.577081\pi$
$338$	−31.5783	+	31.5783i	−1.71763	+	1.71763i
$339$		0			0
$340$	−7.82175	−	7.86390i	−0.424194	−	0.426480i
$341$			0.0571741i			0.00309615i
$342$		0			0
$343$	17.6660	−	5.55996i	0.953873	−	0.300210i
$344$			12.2494i			0.660444i
$345$		0			0
$346$		−	13.1488i		−	0.706884i
$347$	−14.8000	−	14.8000i	−0.794507	−	0.794507i	0.187716	−	0.982223i	$-0.439891\pi$
$347$	−14.8000	−	14.8000i	−0.794507	−	0.794507i	−0.982223	+	0.187716i	$0.939891\pi$
$348$		0			0
$349$	−5.49301			−0.294034			−0.147017	−	0.989134i	$-0.546967\pi$
$349$	−5.49301			−0.294034			−0.147017	+	0.989134i	$0.546967\pi$
$350$	3.92725	−	23.5073i	0.209920	−	1.25652i
$351$		0			0
$352$	21.6444	+	21.6444i	1.15365	+	1.15365i
$353$	−17.6516	−	17.6516i	−0.939497	−	0.939497i	0.0587739	−	0.998271i	$-0.481281\pi$
$353$	−17.6516	−	17.6516i	−0.939497	−	0.939497i	−0.998271	+	0.0587739i	$0.981281\pi$
$354$		0			0
$355$	−10.2638	−	0.0275813i	−0.544748	−	0.00146386i
$356$			0.103287i			0.00547421i
$357$		0			0
$358$	−5.60506	+	5.60506i	−0.296237	+	0.296237i
$359$			6.59975i			0.348322i	0.984717	+	0.174161i	$0.0557212\pi$
$359$			6.59975i			0.348322i	−0.984717	+	0.174161i	$0.944279\pi$
$360$		0			0
$361$	−11.9827			−0.630670
$362$	−1.98199	+	1.98199i	−0.104171	+	0.104171i
$363$		0			0
$364$	−20.0025	−	3.23131i	−1.04841	−	0.169367i
$365$	−0.361645	−	0.363594i	−0.0189294	−	0.0190314i
$366$		0			0
$367$	−9.69471	+	9.69471i	−0.506060	+	0.506060i	−0.913315	−	0.407255i	$-0.866486\pi$
$367$	−9.69471	+	9.69471i	−0.506060	+	0.506060i	0.407255	+	0.913315i	$0.366486\pi$
$368$	3.76310	−	3.76310i	0.196165	−	0.196165i
$369$		0			0
$370$	−0.0699383	+	26.0262i	−0.00363592	+	1.35304i
$371$	−14.2956	−	2.30939i	−0.742190	−	0.119898i
$372$		0			0
$373$	−17.6318	+	17.6318i	−0.912942	+	0.912942i	−0.996503	−	0.0835605i	$-0.973371\pi$
$373$	−17.6318	+	17.6318i	−0.912942	+	0.912942i	0.0835605	+	0.996503i	$0.473371\pi$
$374$	−35.5195			−1.83667
$375$		0			0
$376$			16.1033i			0.830463i
$377$	−14.1679	+	14.1679i	−0.729686	+	0.729686i
$378$		0			0
$379$			1.14283i			0.0587030i	0.999569	+	0.0293515i	$0.00934421\pi$
$379$			1.14283i			0.0587030i	−0.999569	+	0.0293515i	$0.990656\pi$
$380$	−0.0198300	+	7.37936i	−0.00101726	+	0.378553i
$381$		0			0
$382$	−17.9069	−	17.9069i	−0.916199	−	0.916199i
$383$	17.7666	+	17.7666i	0.907829	+	0.907829i	0.996097	−	0.0882676i	$-0.0281331\pi$
$383$	17.7666	+	17.7666i	0.907829	+	0.907829i	−0.0882676	+	0.996097i	$0.528133\pi$
$384$		0			0
$385$	−17.0819	−	23.7987i	−0.870574	−	1.21290i
$386$	−25.2357			−1.28446
$387$		0			0
$388$	1.33200	+	1.33200i	0.0676222	+	0.0676222i
$389$			4.93962i			0.250449i	0.992128	+	0.125224i	$0.0399651\pi$
$389$			4.93962i			0.250449i	−0.992128	+	0.125224i	$0.960035\pi$
$390$		0			0
$391$			4.28966i			0.216938i
$392$	4.26573	+	8.50111i	0.215452	+	0.429371i
$393$		0			0
$394$			26.0188i			1.31081i
$395$	−0.0323814	+	12.0501i	−0.00162929	+	0.606307i
$396$		0			0
$397$	6.68131	−	6.68131i	0.335325	−	0.335325i	−0.519279	−	0.854605i	$-0.673800\pi$
$397$	6.68131	−	6.68131i	0.335325	−	0.335325i	0.854605	+	0.519279i	$0.173800\pi$
$398$	−20.5715	−	20.5715i	−1.03116	−	1.03116i
$399$		0			0
$400$	24.6975	+	0.132737i	1.23488	+	0.00663684i
$401$	4.92198			0.245792			0.122896	−	0.992420i	$-0.460782\pi$
$401$	4.92198			0.245792			0.122896	+	0.992420i	$0.460782\pi$
$402$		0			0
$403$	0.0501890	−	0.0501890i	0.00250009	−	0.00250009i
$404$	−14.7955			−0.736106
$405$		0			0
$406$	−15.3377	−	2.47774i	−0.761197	−	0.122968i
$407$	22.6205	+	22.6205i	1.12126	+	1.12126i
$408$		0			0
$409$	13.8937			0.686998			0.343499	−	0.939153i	$-0.388388\pi$
$409$	13.8937			0.686998			0.343499	+	0.939153i	$0.388388\pi$
$410$	7.93527	−	7.89273i	0.391895	−	0.389794i
$411$		0			0
$412$	13.1771	−	13.1771i	0.649190	−	0.649190i
$413$	−6.29180	−	8.71629i	−0.309599	−	0.428900i
$414$		0			0
$415$	7.54236	+	7.58301i	0.370240	+	0.372235i
$416$		−	38.0001i		−	1.86311i
$417$		0			0
$418$	16.7103	+	16.7103i	0.817326	+	0.817326i
$419$	29.1802			1.42554			0.712772	−	0.701396i	$-0.247439\pi$
$419$	29.1802			1.42554			0.712772	+	0.701396i	$0.247439\pi$
$420$		0			0
$421$	26.1873			1.27629			0.638147	−	0.769915i	$-0.279701\pi$
$421$	26.1873			1.27629			0.638147	+	0.769915i	$0.279701\pi$
$422$	−18.1920	−	18.1920i	−0.885572	−	0.885572i
$423$		0			0
$424$		−	7.43688i		−	0.361167i
$425$	−14.1524	+	14.0011i	−0.686491	+	0.679151i
$426$		0			0
$427$	24.4684	−	17.6624i	1.18411	−	0.854742i
$428$	10.6710	−	10.6710i	0.515801	−	0.515801i
$429$		0			0
$430$	−36.3176	−	0.0975937i	−1.75139	−	0.00470639i
$431$	−21.3282			−1.02734			−0.513671	−	0.857987i	$-0.671715\pi$
$431$	−21.3282			−1.02734			−0.513671	+	0.857987i	$0.671715\pi$
$432$		0			0
$433$	1.61647	+	1.61647i	0.0776824	+	0.0776824i	0.744880	−	0.667198i	$-0.232507\pi$
$433$	1.61647	+	1.61647i	0.0776824	+	0.0776824i	−0.667198	+	0.744880i	$0.732507\pi$
$434$	0.0543329	+	0.00877724i	0.00260806	+	0.000421321i
$435$		0			0
$436$	10.9209			0.523014
$437$	2.01809	−	2.01809i	0.0965381	−	0.0965381i
$438$		0			0
$439$	23.8651			1.13902			0.569509	−	0.821985i	$-0.307133\pi$
$439$	23.8651			1.13902			0.569509	+	0.821985i	$0.307133\pi$
$440$	10.6667	−	10.6095i	0.508515	−	0.505789i
$441$		0			0
$442$	31.1800	+	31.1800i	1.48308	+	1.48308i
$443$	−4.36166	+	4.36166i	−0.207229	+	0.207229i	−0.803089	−	0.595860i	$-0.796811\pi$
$443$	−4.36166	+	4.36166i	−0.207229	+	0.207229i	0.595860	+	0.803089i	$0.296811\pi$
$444$		0			0
$445$	0.185387		0.000498177i	0.00878817		2.36158e-5i
$446$		−	37.2547i		−	1.76406i
$447$		0			0
$448$	2.69838	−	1.94781i	0.127487	−	0.0920254i
$449$			13.8543i			0.653826i	0.945054	+	0.326913i	$0.106008\pi$
$449$			13.8543i			0.653826i	−0.945054	+	0.326913i	$0.893992\pi$
$450$		0			0
$451$		−	13.7569i		−	0.647785i
$452$	−15.4521	−	15.4521i	−0.726804	−	0.726804i
$453$		0			0
$454$	47.4628			2.22754
$455$	−5.89625	+	35.8862i	−0.276420	+	1.68237i
$456$		0			0
$457$	19.8863	+	19.8863i	0.930243	+	0.930243i	0.997721	−	0.0674779i	$-0.0214952\pi$
$457$	19.8863	+	19.8863i	0.930243	+	0.930243i	−0.0674779	+	0.997721i	$0.521495\pi$
$458$	26.6366	+	26.6366i	1.24465	+	1.24465i
$459$		0			0
$460$	2.11652	+	2.12792i	0.0986831	+	0.0992149i
$461$		−	10.9860i		−	0.511667i	−0.966721	−	0.255834i	$-0.917650\pi$
$461$		−	10.9860i		−	0.511667i	0.966721	−	0.255834i	$-0.0823500\pi$
$462$		0			0
$463$	−2.15571	+	2.15571i	−0.100184	+	0.100184i	−0.755422	−	0.655238i	$-0.772568\pi$
$463$	−2.15571	+	2.15571i	−0.100184	+	0.100184i	0.655238	+	0.755422i	$0.272568\pi$
$464$		−	16.1003i		−	0.747438i
$465$		0			0
$466$	28.1750			1.30518
$467$	−4.48457	+	4.48457i	−0.207521	+	0.207521i	−0.803213	−	0.595692i	$-0.796878\pi$
$467$	−4.48457	+	4.48457i	−0.207521	+	0.207521i	0.595692	+	0.803213i	$0.296878\pi$
$468$		0			0
$469$	−0.543000	+	3.36128i	−0.0250734	+	0.155210i
$470$	−47.7437	−	0.128298i	−2.20225	−	0.00591796i
$471$		0			0
$472$	3.90376	−	3.90376i	0.179685	−	0.179685i
$473$	−31.5653	+	31.5653i	−1.45137	+	1.45137i
$474$		0			0
$475$	13.2449	+	0.0711845i	0.607716	+	0.00326617i
$476$	−2.09293	+	12.9556i	−0.0959291	+	0.593820i
$477$		0			0
$478$	4.32321	−	4.32321i	0.197739	−	0.197739i
$479$	−4.48299			−0.204833			−0.102417	−	0.994742i	$-0.532657\pi$
$479$	−4.48299			−0.204833			−0.102417	+	0.994742i	$0.532657\pi$
$480$		0			0
$481$		−	39.7139i		−	1.81080i
$482$	−32.3282	+	32.3282i	−1.47251	+	1.47251i
$483$		0			0
$484$			16.8423i			0.765560i
$485$	2.39719	−	2.38434i	0.108851	−	0.108267i
$486$		0			0
$487$	−16.2120	−	16.2120i	−0.734637	−	0.734637i	0.236898	−	0.971535i	$-0.423869\pi$
$487$	−16.2120	−	16.2120i	−0.734637	−	0.734637i	−0.971535	+	0.236898i	$0.923869\pi$
$488$	10.9587	+	10.9587i	0.496076	+	0.496076i
$489$		0			0
$490$	−25.2385	+	12.5795i	−1.14016	+	0.568283i
$491$	−13.3948			−0.604498			−0.302249	−	0.953229i	$-0.597737\pi$
$491$	−13.3948			−0.604498			−0.302249	+	0.953229i	$0.597737\pi$
$492$		0			0
$493$	9.17660	+	9.17660i	0.413293	+	0.413293i
$494$		−	29.3375i		−	1.31996i
$495$		0			0
$496$			0.0570343i			0.00256092i
$497$	7.10797	+	9.84697i	0.318836	+	0.441697i
$498$		0			0
$499$		−	4.09144i		−	0.183158i	−0.995798	−	0.0915791i	$-0.970809\pi$
$499$		−	4.09144i		−	0.183158i	0.995798	−	0.0915791i	$-0.0291914\pi$
$500$	−0.112286	+	13.9281i	−0.00502159	+	0.622884i
$501$		0			0
$502$	3.72289	−	3.72289i	0.166161	−	0.166161i
$503$	8.45254	+	8.45254i	0.376880	+	0.376880i	0.869975	−	0.493095i	$-0.164135\pi$
$503$	8.45254	+	8.45254i	0.376880	+	0.376880i	−0.493095	+	0.869975i	$0.664135\pi$
$504$		0			0
$505$	−0.0713621	+	26.5560i	−0.00317557	+	1.18173i
$506$	9.61137			0.427277
$507$		0			0
$508$	−5.27931	+	5.27931i	−0.234231	+	0.234231i
$509$	−5.06608			−0.224550			−0.112275	−	0.993677i	$-0.535814\pi$
$509$	−5.06608			−0.224550			−0.112275	+	0.993677i	$0.535814\pi$
$510$		0			0
$511$	−0.0967683	+	0.599015i	−0.00428078	+	0.0264989i
$512$	12.0997	+	12.0997i	0.534734	+	0.534734i
$513$		0			0
$514$	14.0382			0.619200
$515$	−23.5876	−	23.7147i	−1.03939	−	1.04500i
$516$		0			0
$517$	−41.4963	+	41.4963i	−1.82501	+	1.82501i
$518$	24.9691	−	18.0238i	1.09708	−	0.791919i
$519$		0			0
$520$	−18.6769	−	0.0501890i	−0.819034	−	0.00220093i
$521$			29.5983i			1.29672i	0.761332	+	0.648362i	$0.224546\pi$
$521$			29.5983i			1.29672i	−0.761332	+	0.648362i	$0.775454\pi$
$522$		0			0
$523$	−16.7746	−	16.7746i	−0.733504	−	0.733504i	0.237808	−	0.971312i	$-0.423571\pi$
$523$	−16.7746	−	16.7746i	−0.733504	−	0.733504i	−0.971312	+	0.237808i	$0.923571\pi$
$524$	19.7069			0.860898
$525$		0			0
$526$	38.2747			1.66886
$527$	−0.0325075	−	0.0325075i	−0.00141605	−	0.00141605i
$528$		0			0
$529$			21.8392i			0.949532i
$530$	22.0492	+	0.0592512i	0.957755	+	0.00257371i
$531$		0			0
$532$	7.07964	−	5.11039i	0.306941	−	0.221564i
$533$	−12.0761	+	12.0761i	−0.523076	+	0.523076i
$534$		0			0
$535$	−19.1015	−	19.2044i	−0.825830	−	0.830280i
$536$	−1.74861			−0.0755285
$537$		0			0
$538$	−4.44769	−	4.44769i	−0.191753	−	0.191753i
$539$	−10.9141	+	32.8987i	−0.470103	+	1.41705i
$540$		0			0
$541$	1.24966			0.0537271			0.0268636	−	0.999639i	$-0.491448\pi$
$541$	1.24966			0.0537271			0.0268636	+	0.999639i	$0.491448\pi$
$542$	22.6917	−	22.6917i	0.974694	−	0.974694i
$543$		0			0
$544$	−24.6127			−1.05526
$545$	0.0526737	−	19.6015i	0.00225629	−	0.839636i
$546$		0			0
$547$	1.12537	+	1.12537i	0.0481175	+	0.0481175i	0.730756	−	0.682639i	$-0.239168\pi$
$547$	1.12537	+	1.12537i	0.0481175	+	0.0481175i	−0.682639	+	0.730756i	$0.739168\pi$
$548$	−15.0948	+	15.0948i	−0.644819	+	0.644819i
$549$		0			0
$550$	31.3706	+	31.7096i	1.33765	+	1.35210i
$551$		−	8.63432i		−	0.367834i
$552$		0			0
$553$	11.5607	−	8.34501i	0.491610	−	0.354866i
$554$		−	10.1792i		−	0.432472i
$555$		0			0
$556$			16.0690i			0.681478i
$557$	−19.6989	−	19.6989i	−0.834670	−	0.834670i	0.153482	−	0.988151i	$-0.450951\pi$
$557$	−19.6989	−	19.6989i	−0.834670	−	0.834670i	−0.988151	+	0.153482i	$0.950951\pi$
$558$		0			0
$559$	55.4178			2.34392
$560$	−17.0401	−	23.7406i	−0.720077	−	1.00322i
$561$		0			0
$562$	−3.16616	−	3.16616i	−0.133557	−	0.133557i
$563$	5.12839	+	5.12839i	0.216136	+	0.216136i	0.806868	−	0.590732i	$-0.201161\pi$
$563$	5.12839	+	5.12839i	0.216136	+	0.216136i	−0.590732	+	0.806868i	$0.701161\pi$
$564$		0			0
$565$	−27.8089	+	27.6599i	−1.16993	+	1.16366i
$566$			47.2699i			1.98690i
$567$		0			0
$568$	−4.41016	+	4.41016i	−0.185046	+	0.185046i
$569$		−	27.5906i		−	1.15666i	−0.815803	−	0.578330i	$-0.803705\pi$
$569$		−	27.5906i		−	1.15666i	0.815803	−	0.578330i	$-0.196295\pi$
$570$		0			0
$571$	−0.199970			−0.00836848			−0.00418424	−	0.999991i	$-0.501332\pi$
$571$	−0.199970			−0.00836848			−0.00418424	+	0.999991i	$0.501332\pi$
$572$	26.8143	−	26.8143i	1.12116	−	1.12116i
$573$		0			0
$574$	−13.0732	−	2.11192i	−0.545665	−	0.0881499i
$575$	3.82955	−	3.78860i	0.159703	−	0.157996i
$576$		0			0
$577$	−18.7109	+	18.7109i	−0.778947	+	0.778947i	−0.979652	−	0.200705i	$-0.935677\pi$
$577$	−18.7109	+	18.7109i	−0.778947	+	0.778947i	0.200705	+	0.979652i	$0.435677\pi$
$578$	−1.46150	+	1.46150i	−0.0607902	+	0.0607902i
$579$		0			0
$580$	9.07985	+	0.0243997i	0.377020	+	0.00101314i
$581$	2.01817	−	12.4929i	0.0837278	−	0.518292i
$582$		0			0
$583$	19.1640	−	19.1640i	0.793691	−	0.793691i
$584$	−0.311621			−0.0128950
$585$		0			0
$586$		−	45.6739i		−	1.88677i
$587$	16.3260	−	16.3260i	0.673846	−	0.673846i	−0.284755	−	0.958600i	$-0.591912\pi$
$587$	16.3260	−	16.3260i	0.673846	−	0.673846i	0.958600	+	0.284755i	$0.0919122\pi$
$588$		0			0
$589$			0.0305865i			0.00126030i
$590$	11.5429	+	11.6051i	0.475216	+	0.477776i
$591$		0			0
$592$	22.5652	+	22.5652i	0.927426	+	0.927426i
$593$	−11.9633	−	11.9633i	−0.491275	−	0.491275i	0.417432	−	0.908708i	$-0.362930\pi$
$593$	−11.9633	−	11.9633i	−0.491275	−	0.491275i	−0.908708	+	0.417432i	$0.862930\pi$
$594$		0			0
$595$	23.2435	+	3.81901i	0.952892	+	0.156564i
$596$	22.3753			0.916530
$597$		0			0
$598$	−8.43712	−	8.43712i	−0.345020	−	0.345020i
$599$		−	11.1258i		−	0.454590i	−0.973826	−	0.227295i	$-0.927012\pi$
$599$		−	11.1258i		−	0.454590i	0.973826	−	0.227295i	$-0.0729881\pi$
$600$		0			0
$601$		−	39.0679i		−	1.59361i	−0.604235	−	0.796806i	$-0.706521\pi$
$601$		−	39.0679i		−	1.59361i	0.604235	−	0.796806i	$-0.293479\pi$
$602$	25.1509	+	34.8425i	1.02507	+	1.42007i
$603$		0			0
$604$		−	26.8670i		−	1.09320i
$605$	30.2297	+	0.0812342i	1.22901	+	0.00330264i
$606$		0			0
$607$	−21.7883	+	21.7883i	−0.884358	+	0.884358i	−0.993974	−	0.109616i	$-0.965038\pi$
$607$	−21.7883	+	21.7883i	−0.884358	+	0.884358i	0.109616	+	0.993974i	$0.465038\pi$
$608$	11.5791	+	11.5791i	0.469596	+	0.469596i
$609$		0			0
$610$	−32.5781	+	32.4034i	−1.31905	+	1.31198i
$611$	72.8532			2.94733
$612$		0			0
$613$	20.6019	−	20.6019i	0.832105	−	0.832105i	−0.155700	−	0.987804i	$-0.549763\pi$
$613$	20.6019	−	20.6019i	0.832105	−	0.832105i	0.987804	+	0.155700i	$0.0497633\pi$
$614$	−61.1621			−2.46830
$615$		0			0
$616$	−17.5732	−	2.83887i	−0.708044	−	0.114381i
$617$	3.68830	+	3.68830i	0.148485	+	0.148485i	0.777441	−	0.628956i	$-0.216517\pi$
$617$	3.68830	+	3.68830i	0.148485	+	0.148485i	−0.628956	+	0.777441i	$0.716517\pi$
$618$		0			0
$619$	8.96562			0.360359			0.180179	−	0.983634i	$-0.442332\pi$
$619$	8.96562			0.360359			0.180179	+	0.983634i	$0.442332\pi$
$620$	−0.0321648		8.64343e-5i	−0.00129177		3.47128e-6i
$621$		0			0
$622$	−22.3192	+	22.3192i	−0.894918	+	0.894918i
$623$	−0.128385	−	0.177857i	−0.00514364	−	0.00712569i
$624$		0			0
$625$	24.9986	+	0.268717i	0.999942	+	0.0107487i
$626$			60.1463i			2.40393i
$627$		0			0
$628$	15.8191	+	15.8191i	0.631252	+	0.631252i
$629$	−25.7228			−1.02563
$630$		0			0
$631$	−30.8194			−1.22690			−0.613451	−	0.789733i	$-0.710219\pi$
$631$	−30.8194			−1.22690			−0.613451	+	0.789733i	$0.710219\pi$
$632$	5.17768	+	5.17768i	0.205957	+	0.205957i
$633$		0			0
$634$			20.6094i			0.818505i
$635$	9.45019	+	9.50112i	0.375019	+	0.377040i
$636$		0			0
$637$	38.4601	−	19.2987i	1.52384	−	0.764641i
$638$	20.5610	−	20.5610i	0.814016	−	0.814016i
$639$		0			0
$640$	16.0079	−	15.9221i	0.632770	−	0.629378i
$641$	−3.05995			−0.120861			−0.0604303	−	0.998172i	$-0.519247\pi$
$641$	−3.05995			−0.120861			−0.0604303	+	0.998172i	$0.519247\pi$
$642$		0			0
$643$	−11.1123	−	11.1123i	−0.438225	−	0.438225i	0.453189	−	0.891414i	$-0.350286\pi$
$643$	−11.1123	−	11.1123i	−0.438225	−	0.438225i	−0.891414	+	0.453189i	$0.850286\pi$
$644$	0.566333	−	3.50572i	0.0223167	−	0.138145i
$645$		0			0
$646$	−19.0019			−0.747621
$647$	17.2685	−	17.2685i	0.678896	−	0.678896i	−0.280854	−	0.959750i	$-0.590618\pi$
$647$	17.2685	−	17.2685i	0.678896	−	0.678896i	0.959750	+	0.280854i	$0.0906178\pi$
$648$		0			0
$649$	20.1191			0.789743
$650$	0.297605	−	55.3736i	0.0116730	−	2.17193i
$651$		0			0
$652$	−8.87866	−	8.87866i	−0.347715	−	0.347715i
$653$	21.9068	−	21.9068i	0.857278	−	0.857278i	−0.133739	−	0.991017i	$-0.542698\pi$
$653$	21.9068	−	21.9068i	0.857278	−	0.857278i	0.991017	+	0.133739i	$0.0426984\pi$
$654$		0			0
$655$	0.0950505	−	35.3712i	0.00371393	−	1.38207i
$656$		−	13.7232i		−	0.535802i
$657$		0			0
$658$	33.0637	+	45.8046i	1.28896	+	1.78565i
$659$			12.6376i			0.492290i	0.969233	+	0.246145i	$0.0791639\pi$
$659$			12.6376i			0.492290i	−0.969233	+	0.246145i	$0.920836\pi$
$660$		0			0
$661$			4.36906i			0.169937i	0.996384	+	0.0849685i	$0.0270790\pi$
$661$			4.36906i			0.169937i	−0.996384	+	0.0849685i	$0.972921\pi$
$662$	−1.09365	−	1.09365i	−0.0425058	−	0.0425058i
$663$		0			0
$664$	6.49906			0.252213
$665$	−9.13833	−	12.7317i	−0.354369	−	0.493713i
$666$		0			0
$667$	−2.48313	−	2.48313i	−0.0961472	−	0.0961472i
$668$	−7.52673	−	7.52673i	−0.291218	−	0.291218i
$669$		0			0
$670$	0.0139316	−	5.18436i	0.000538223	−	0.200289i
$671$			56.4784i			2.18033i
$672$		0			0
$673$	4.73121	−	4.73121i	0.182375	−	0.182375i	−0.610015	−	0.792390i	$-0.708837\pi$
$673$	4.73121	−	4.73121i	0.182375	−	0.182375i	0.792390	+	0.610015i	$0.208837\pi$
$674$			34.1920i			1.31702i
$675$		0			0
$676$	−30.8812			−1.18774
$677$	17.5665	−	17.5665i	0.675134	−	0.675134i	−0.283761	−	0.958895i	$-0.591582\pi$
$677$	17.5665	−	17.5665i	0.675134	−	0.675134i	0.958895	+	0.283761i	$0.0915821\pi$
$678$		0			0
$679$	−3.94933	−	0.637997i	−0.151561	−	0.0244841i
$680$	−0.0325075	+	12.0970i	−0.00124661	+	0.463900i
$681$		0			0
$682$	−0.0728360	+	0.0728360i	−0.00278903	+	0.00278903i
$683$	21.4653	−	21.4653i	0.821348	−	0.821348i	−0.164953	−	0.986301i	$-0.552747\pi$
$683$	21.4653	−	21.4653i	0.821348	−	0.821348i	0.986301	+	0.164953i	$0.0527473\pi$
$684$		0			0
$685$	27.0204	+	27.1660i	1.03240	+	1.03796i
$686$	29.5883	+	15.4223i	1.12969	+	0.588824i
$687$		0			0
$688$	−31.4881	+	31.4881i	−1.20047	+	1.20047i
$689$	−33.6453			−1.28179
$690$		0			0
$691$		−	6.81724i		−	0.259340i	−0.991557	−	0.129670i	$-0.958608\pi$
$691$		−	6.81724i		−	0.259340i	0.991557	−	0.129670i	$-0.0413918\pi$
$692$	6.42926	−	6.42926i	0.244404	−	0.244404i
$693$		0			0
$694$		−	37.7085i		−	1.43139i
$695$	28.8417	+	0.0775044i	1.09403	+	0.00293991i
$696$		0			0
$697$	7.82175	+	7.82175i	0.296270	+	0.296270i
$698$	−6.99772	−	6.99772i	−0.264868	−	0.264868i
$699$		0			0
$700$	13.4144	−	9.57389i	0.507018	−	0.361859i
$701$	−11.9256			−0.450423			−0.225211	−	0.974310i	$-0.572307\pi$
$701$	−11.9256			−0.450423			−0.225211	+	0.974310i	$0.572307\pi$
$702$		0			0
$703$	12.1014	+	12.1014i	0.456411	+	0.456411i
$704$			6.22846i			0.234744i
$705$		0			0
$706$		−	44.9738i		−	1.69261i
$707$	25.4774	−	18.3907i	0.958177	−	0.691654i
$708$		0			0
$709$		−	24.8299i		−	0.932507i	−0.884651	−	0.466254i	$-0.845603\pi$
$709$		−	24.8299i		−	0.932507i	0.884651	−	0.466254i	$-0.154397\pi$
$710$	−13.0403	−	13.1106i	−0.489394	−	0.492031i
$711$		0			0
$712$	0.0796569	−	0.0796569i	0.00298527	−	0.00298527i
$713$	0.00879634	+	0.00879634i	0.000329426	+	0.000329426i
$714$		0			0
$715$	−47.9988	−	48.2574i	−1.79505	−	1.80473i
$716$	−5.48132			−0.204847
$717$		0			0
$718$	−8.40764	+	8.40764i	−0.313770	+	0.313770i
$719$	19.4060			0.723721			0.361861	−	0.932232i	$-0.382142\pi$
$719$	19.4060			0.723721			0.361861	+	0.932232i	$0.382142\pi$
$720$		0			0
$721$	−6.31152	+	39.0696i	−0.235053	+	1.45503i
$722$	−15.2652	−	15.2652i	−0.568112	−	0.568112i
$723$		0			0
$724$	−1.93824			−0.0720340
$725$	0.0875882	−	16.2970i	0.00325295	−	0.605256i
$726$		0			0
$727$	−28.1710	+	28.1710i	−1.04481	+	1.04481i	−0.0458576	+	0.998948i	$0.514602\pi$
$727$	−28.1710	+	28.1710i	−1.04481	+	1.04481i	−0.998948	+	0.0458576i	$0.985398\pi$
$728$	12.9342	+	17.9183i	0.479373	+	0.664096i
$729$		0			0
$730$	0.00248275	−	0.923907i	9.18907e−5	−	0.0341953i
$731$		−	35.8942i		−	1.32760i
$732$		0			0
$733$	−15.6884	−	15.6884i	−0.579464	−	0.579464i	0.355292	−	0.934755i	$-0.384382\pi$
$733$	−15.6884	−	15.6884i	−0.579464	−	0.579464i	−0.934755	+	0.355292i	$0.884382\pi$
$734$	−24.7008			−0.911724
$735$		0			0
$736$	6.66005			0.245493
$737$	−4.50597	−	4.50597i	−0.165979	−	0.165979i
$738$		0			0
$739$		−	1.66024i		−	0.0610728i	−0.999534	−	0.0305364i	$-0.990278\pi$
$739$		−	1.66024i		−	0.0610728i	0.999534	−	0.0305364i	$-0.00972155\pi$
$740$	−12.7600	+	12.6916i	−0.469067	+	0.466552i
$741$		0			0
$742$	−15.2696	−	21.1536i	−0.560565	−	0.776574i
$743$	13.3520	−	13.3520i	0.489837	−	0.489837i	−0.418418	−	0.908255i	$-0.637415\pi$
$743$	13.3520	−	13.3520i	0.489837	−	0.489837i	0.908255	+	0.418418i	$0.137415\pi$
$744$		0			0
$745$	0.107921	−	40.1607i	0.00395393	−	1.47138i
$746$	−44.9236			−1.64477
$747$		0			0
$748$	−17.3677	−	17.3677i	−0.635025	−	0.635025i
$749$	−5.11114	+	31.6390i	−0.186757	+	1.15606i
$750$		0			0
$751$	42.2631			1.54220			0.771101	−	0.636712i	$-0.219706\pi$
$751$	42.2631			1.54220			0.771101	+	0.636712i	$0.219706\pi$
$752$	−41.3948	+	41.3948i	−1.50951	+	1.50951i
$753$		0			0
$754$	−36.0980			−1.31461
$755$	−48.2226	−	0.129585i	−1.75500	−	0.00471609i
$756$		0			0
$757$	5.33172	+	5.33172i	0.193785	+	0.193785i	0.797329	−	0.603545i	$-0.206245\pi$
$757$	5.33172	+	5.33172i	0.193785	+	0.193785i	−0.603545	+	0.797329i	$0.706245\pi$
$758$	−1.45588	+	1.45588i	−0.0528800	+	0.0528800i
$759$		0			0
$760$	5.70638	−	5.67580i	0.206992	−	0.205883i
$761$		−	41.7351i		−	1.51290i	−0.654054	−	0.756448i	$-0.726933\pi$
$761$		−	41.7351i		−	1.51290i	0.654054	−	0.756448i	$-0.273067\pi$
$762$		0			0
$763$	−18.8054	+	13.5745i	−0.680800	+	0.491431i
$764$		−	17.5116i		−	0.633548i
$765$		0			0
$766$			45.2668i			1.63556i
$767$	−17.6611	−	17.6611i	−0.637705	−	0.637705i
$768$		0			0
$769$	−26.9492			−0.971812			−0.485906	−	0.874011i	$-0.661510\pi$
$769$	−26.9492			−0.971812			−0.485906	+	0.874011i	$0.661510\pi$
$770$	8.55683	−	52.0792i	0.308367	−	1.87680i
$771$		0			0
$772$	−12.3393	−	12.3393i	−0.444101	−	0.444101i
$773$	10.7662	+	10.7662i	0.387232	+	0.387232i	0.873699	−	0.486467i	$-0.161715\pi$
$773$	10.7662	+	10.7662i	0.387232	+	0.387232i	−0.486467	+	0.873699i	$0.661715\pi$
$774$		0			0
$775$	−0.000310276		0.0577311i	−1.11454e−5		0.00207376i
$776$		−	2.05453i		−	0.0737532i
$777$		0			0
$778$	−6.29274	+	6.29274i	−0.225606	+	0.225606i
$779$		−	7.35953i		−	0.263682i
$780$		0			0
$781$	−22.7290			−0.813306
$782$	−5.46474	+	5.46474i	−0.195419	+	0.195419i
$783$		0			0
$784$	−10.8874	+	32.8182i	−0.388836	+	1.17208i
$785$	28.4695	−	28.3169i	1.01612	−	1.01067i
$786$		0			0
$787$	17.3124	−	17.3124i	0.617120	−	0.617120i	−0.327672	−	0.944792i	$-0.606264\pi$
$787$	17.3124	−	17.3124i	0.617120	−	0.617120i	0.944792	+	0.327672i	$0.106264\pi$
$788$	−12.7222	+	12.7222i	−0.453209	+	0.453209i
$789$		0			0
$790$	−15.3923	+	15.3098i	−0.547633	+	0.544697i
$791$	45.8147	+	7.40117i	1.62898	+	0.263155i
$792$		0			0
$793$	49.5784	−	49.5784i	1.76058	−	1.76058i
$794$	17.0231			0.604126
$795$		0			0
$796$		−	20.1174i		−	0.713041i
$797$	21.2972	−	21.2972i	0.754384	−	0.754384i	−0.220910	−	0.975294i	$-0.570903\pi$
$797$	21.2972	−	21.2972i	0.754384	−	0.754384i	0.975294	+	0.220910i	$0.0709028\pi$
$798$		0			0
$799$		−	47.1872i		−	1.66936i
$800$	21.7378	+	21.9727i	0.768547	+	0.776852i
$801$		0			0
$802$	6.27027	+	6.27027i	0.221411	+	0.221411i
$803$	−0.803010	−	0.803010i	−0.0283376	−	0.0283376i
$804$		0			0
$805$	−6.28956	−	1.03340i	−0.221678	−	0.0364226i
$806$	0.127875			0.00450420
$807$		0			0
$808$	11.4106	+	11.4106i	0.401423	+	0.401423i
$809$		−	44.5259i		−	1.56545i	−0.622370	−	0.782724i	$-0.713830\pi$
$809$		−	44.5259i		−	1.56545i	0.622370	−	0.782724i	$-0.286170\pi$
$810$		0			0
$811$			0.427478i			0.0150108i	0.999972	+	0.00750539i	$0.00238906\pi$
$811$			0.427478i			0.0150108i	−0.999972	+	0.00750539i	$0.997611\pi$
$812$	−6.28803	−	8.71107i	−0.220667	−	0.305699i
$813$		0			0
$814$			57.6341i			2.02007i
$815$	−15.9788	+	15.8932i	−0.559714	+	0.556714i
$816$		0			0
$817$	−16.8865	+	16.8865i	−0.590786	+	0.590786i
$818$	17.6996	+	17.6996i	0.618852	+	0.618852i
$819$		0			0
$820$	7.73928	+	0.0207972i	0.270268	+	0.000726271i
$821$	−1.74771			−0.0609953			−0.0304977	−	0.999535i	$-0.509709\pi$
$821$	−1.74771			−0.0609953			−0.0304977	+	0.999535i	$0.509709\pi$
$822$		0			0
$823$	−11.7544	+	11.7544i	−0.409732	+	0.409732i	−0.881645	−	0.471913i	$-0.843564\pi$
$823$	−11.7544	+	11.7544i	−0.409732	+	0.409732i	0.471913	+	0.881645i	$0.343564\pi$
$824$	−20.3249			−0.708050
$825$		0			0
$826$	3.08864	−	19.1193i	0.107467	−	0.665245i
$827$	−23.1570	−	23.1570i	−0.805246	−	0.805246i	0.178664	−	0.983910i	$-0.442823\pi$
$827$	−23.1570	−	23.1570i	−0.805246	−	0.805246i	−0.983910	+	0.178664i	$0.942823\pi$
$828$		0			0
$829$	11.0554			0.383970			0.191985	−	0.981398i	$-0.438508\pi$
$829$	11.0554			0.383970			0.191985	+	0.981398i	$0.438508\pi$
$830$	−0.0517794	+	19.2687i	−0.00179729	+	0.668827i
$831$		0			0
$832$	5.46751	−	5.46751i	0.189552	−	0.189552i
$833$	−12.4998	−	24.9107i	−0.433092	−	0.863103i
$834$		0			0
$835$	−13.5458	+	13.4732i	−0.468771	+	0.466259i
$836$			16.3414i			0.565178i
$837$		0			0
$838$	37.1736	+	37.1736i	1.28414	+	1.28414i
$839$	14.6537			0.505901			0.252950	−	0.967479i	$-0.418599\pi$
$839$	14.6537			0.505901			0.252950	+	0.967479i	$0.418599\pi$
$840$		0			0
$841$	18.3760			0.633655
$842$	33.3609	+	33.3609i	1.14969	+	1.14969i
$843$		0			0
$844$		−	17.7904i		−	0.612370i
$845$	−0.148947	+	55.4276i	−0.00512392	+	1.90677i
$846$		0			0
$847$	−20.9348	−	29.0019i	−0.719330	−	0.996517i
$848$	19.1171	−	19.1171i	0.656484	−	0.656484i
$849$		0			0
$850$	−35.8656	−	0.192759i	−1.23018	−	0.00661160i
$851$	6.96042			0.238600
$852$		0			0
$853$	−29.2935	−	29.2935i	−1.00299	−	1.00299i	−0.999996	−	0.00299587i	$-0.999046\pi$
$853$	−29.2935	−	29.2935i	−1.00299	−	1.00299i	−0.00299587	−	0.999996i	$-0.500954\pi$
$854$	53.6718	+	8.67044i	1.83661	+	0.296696i
$855$		0			0
$856$	−16.4593			−0.562567
$857$	−6.59919	+	6.59919i	−0.225424	+	0.225424i	−0.810778	−	0.585354i	$-0.800956\pi$
$857$	−6.59919	+	6.59919i	−0.225424	+	0.225424i	0.585354	+	0.810778i	$0.300956\pi$
$858$		0			0
$859$	−7.97061			−0.271954			−0.135977	−	0.990712i	$-0.543417\pi$
$859$	−7.97061			−0.271954			−0.135977	+	0.990712i	$0.543417\pi$
$860$	−17.7102	−	17.8056i	−0.603912	−	0.607167i
$861$		0			0
$862$	−27.1706	−	27.1706i	−0.925436	−	0.925436i
$863$	−6.31897	+	6.31897i	−0.215100	+	0.215100i	−0.806430	−	0.591330i	$-0.798603\pi$
$863$	−6.31897	+	6.31897i	−0.215100	+	0.215100i	0.591330	+	0.806430i	$0.298603\pi$
$864$		0			0
$865$	−11.5087	−	11.5707i	−0.391306	−	0.393415i
$866$			4.11854i			0.139954i
$867$		0			0
$868$	0.0222750	+	0.0308584i	0.000756061	+	0.00104740i
$869$			26.6846i			0.905212i
$870$		0			0
$871$			7.91093i			0.268052i
$872$	−8.42236	−	8.42236i	−0.285217	−	0.285217i
$873$		0			0
$874$	5.14181			0.173924
$875$	−17.1192	−	24.1233i	−0.578733	−	0.815517i
$876$		0			0
$877$	−11.7906	−	11.7906i	−0.398141	−	0.398141i	0.479436	−	0.877577i	$-0.340841\pi$
$877$	−11.7906	−	11.7906i	−0.398141	−	0.398141i	−0.877577	+	0.479436i	$0.840841\pi$
$878$	30.4025	+	30.4025i	1.02603	+	1.02603i
$879$		0			0
$880$	54.6923	+	0.146971i	1.84368	+	0.00495439i
$881$		−	12.4161i		−	0.418309i	−0.977883	−	0.209155i	$-0.932929\pi$
$881$		−	12.4161i		−	0.418309i	0.977883	−	0.209155i	$-0.0670712\pi$
$882$		0			0
$883$	−11.6626	+	11.6626i	−0.392478	+	0.392478i	−0.875570	−	0.483092i	$-0.839514\pi$
$883$	−11.6626	+	11.6626i	−0.392478	+	0.392478i	0.483092	+	0.875570i	$0.339514\pi$
$884$			30.4917i			1.02555i
$885$		0			0
$886$	−11.1129			−0.373346
$887$	33.0157	−	33.0157i	1.10856	−	1.10856i	0.115220	−	0.993340i	$-0.463243\pi$
$887$	33.0157	−	33.0157i	1.10856	−	1.10856i	0.993340	−	0.115220i	$-0.0367573\pi$
$888$		0			0
$889$	2.52866	−	15.6529i	0.0848086	−	0.524982i
$890$	0.235535	+	0.236805i	0.00789517	+	0.00793771i
$891$		0			0
$892$	18.2161	−	18.2161i	0.609921	−	0.609921i
$893$	−22.1994	+	22.1994i	−0.742873	+	0.742873i
$894$		0			0
$895$	−0.0264376	+	9.83824i	−0.000883712	+	0.328856i
$896$	−26.3728	−	4.26041i	−0.881054	−	0.142330i
$897$		0			0
$898$	−17.6495	+	17.6495i	−0.588970	+	0.588970i
$899$	0.0376349			0.00125519
$900$		0			0
$901$			21.7921i			0.726002i
$902$	17.5253	−	17.5253i	0.583529	−	0.583529i
$903$		0			0
$904$			23.8338i			0.792701i
$905$	−0.00934854	+	3.47888i	−0.000310756	+	0.115642i
$906$		0			0
$907$	−33.8228	−	33.8228i	−1.12307	−	1.12307i	−0.991278	−	0.131791i	$-0.957927\pi$
$907$	−33.8228	−	33.8228i	−1.12307	−	1.12307i	−0.131791	−	0.991278i	$-0.542073\pi$
$908$	23.2075	+	23.2075i	0.770168	+	0.770168i
$909$		0			0
$910$	−53.2280	+	38.2051i	−1.76449	+	1.26649i
$911$	−37.5578			−1.24435			−0.622173	−	0.782879i	$-0.713750\pi$
$911$	−37.5578			−1.24435			−0.622173	+	0.782879i	$0.713750\pi$
$912$		0			0
$913$	16.7473	+	16.7473i	0.554256	+	0.554256i
$914$			50.6677i			1.67594i
$915$		0			0
$916$			26.0485i			0.860668i
$917$	−33.9345	+	24.4954i	−1.12062	+	0.808911i
$918$		0			0
$919$		−	21.8786i		−	0.721710i	−0.932622	−	0.360855i	$-0.882485\pi$
$919$		−	21.8786i		−	0.721710i	0.932622	−	0.360855i	$-0.117515\pi$
$920$	0.00879634	−	3.27339i	0.000290007	−	0.107920i
$921$		0			0
$922$	13.9954	−	13.9954i	0.460913	−	0.460913i
$923$	19.9521	+	19.9521i	0.656732	+	0.656732i
$924$		0			0
$925$	22.7182	+	22.9637i	0.746969	+	0.755041i
$926$	−5.49245			−0.180493
$927$		0			0
$928$	14.2474	−	14.2474i	0.467694	−	0.467694i
$929$	−13.4361			−0.440825			−0.220413	−	0.975407i	$-0.570740\pi$
$929$	−13.4361			−0.440825			−0.220413	+	0.975407i	$0.570740\pi$
$930$		0			0
$931$	−5.83873	+	17.5999i	−0.191357	+	0.576812i
$932$	13.7765	+	13.7765i	0.451264	+	0.451264i
$933$		0			0
$934$	−11.4261			−0.373873
$935$	−31.2564	+	31.0889i	−1.02219	+	1.01672i
$936$		0			0
$937$	30.7453	−	30.7453i	1.00440	−	1.00440i	0.00441428	−	0.999990i	$-0.498595\pi$
$937$	30.7453	−	30.7453i	1.00440	−	1.00440i	0.999990	−	0.00441428i	$-0.00140511\pi$
$938$	−4.97379	+	3.59030i	−0.162400	+	0.117227i
$939$		0			0
$940$	−23.2821	−	23.4076i	−0.759379	−	0.763471i
$941$			13.5188i			0.440699i	0.975421	+	0.220349i	$0.0707197\pi$
$941$			13.5188i			0.440699i	−0.975421	+	0.220349i	$0.929280\pi$
$942$		0			0
$943$	−2.11652	−	2.11652i	−0.0689233	−	0.0689233i
$944$	20.0699			0.653220
$945$		0			0
$946$	−80.4241			−2.61481
$947$	17.9562	+	17.9562i	0.583497	+	0.583497i	0.935862	−	0.352366i	$-0.114623\pi$
$947$	17.9562	+	17.9562i	0.583497	+	0.583497i	−0.352366	+	0.935862i	$0.614623\pi$
$948$		0			0
$949$			1.40981i			0.0457644i
$950$	16.7824	+	16.9638i	0.544492	+	0.550377i
$951$		0			0
$952$	11.6057	−	8.37751i	0.376143	−	0.271517i
$953$	−10.7481	+	10.7481i	−0.348166	+	0.348166i	−0.859426	−	0.511260i	$-0.829179\pi$
$953$	−10.7481	+	10.7481i	−0.348166	+	0.348166i	0.511260	+	0.859426i	$0.329179\pi$
$954$		0			0
$955$	−31.4310	−	0.0844624i	−1.01708	−	0.00273314i
$956$	4.22777			0.136736
$957$		0			0
$958$	−5.71103	−	5.71103i	−0.184515	−	0.184515i
$959$	7.23006	−	44.7555i	0.233471	−	1.44523i
$960$		0			0
$961$	30.9999			0.999996
$962$	50.5928	−	50.5928i	1.63118	−	1.63118i
$963$		0			0
$964$	−31.6145			−1.01823
$965$	−22.2069	+	22.0879i	−0.714866	+	0.711034i
$966$		0			0
$967$	−22.1602	−	22.1602i	−0.712623	−	0.712623i	0.254461	−	0.967083i	$-0.418102\pi$
$967$	−22.1602	−	22.1602i	−0.712623	−	0.712623i	−0.967083	+	0.254461i	$0.918102\pi$
$968$	12.9891	−	12.9891i	0.417485	−	0.417485i
$969$		0			0
$970$	6.09135	+	0.0163689i	0.195582	+	0.000525573i
$971$			6.06677i			0.194692i	0.995251	+	0.0973460i	$0.0310353\pi$
$971$			6.06677i			0.194692i	−0.995251	+	0.0973460i	$0.968965\pi$
$972$		0			0
$973$	−19.9736	−	27.6703i	−0.640325	−	0.887069i
$974$		−	41.3060i		−	1.32353i
$975$		0			0
$976$			56.3404i			1.80341i
$977$	−33.6299	−	33.6299i	−1.07592	−	1.07592i	−0.996871	−	0.0790454i	$-0.974813\pi$
$977$	−33.6299	−	33.6299i	−1.07592	−	1.07592i	−0.0790454	−	0.996871i	$-0.525187\pi$
$978$		0			0
$979$	0.410533			0.0131207
$980$	−18.4915	−	6.18975i	−0.590690	−	0.197724i
$981$		0			0
$982$	−17.0640	−	17.0640i	−0.544535	−	0.544535i
$983$	−13.1292	−	13.1292i	−0.418757	−	0.418757i	0.466018	−	0.884775i	$-0.345688\pi$
$983$	−13.1292	−	13.1292i	−0.418757	−	0.418757i	−0.884775	+	0.466018i	$0.845688\pi$
$984$		0			0
$985$	22.7732	+	22.8960i	0.725616	+	0.729526i
$986$			23.3807i			0.744594i
$987$		0			0
$988$	14.3449	−	14.3449i	0.456372	−	0.456372i
$989$			9.71276i			0.308848i
$990$		0			0
$991$	0.00665564			0.000211423			0.000105712	−	1.00000i	$-0.499966\pi$
$991$	0.00665564			0.000211423			0.000105712		1.00000i	$0.499966\pi$
$992$	−0.0504706	+	0.0504706i	−0.00160244	+	0.00160244i
$993$		0			0
$994$	−3.48930	+	21.5995i	−0.110674	+	0.685093i
$995$	−36.1080	−	0.0970305i	−1.14470	−	0.00307607i
$996$		0			0
$997$	29.8257	−	29.8257i	0.944590	−	0.944590i	−0.0539539	−	0.998543i	$-0.517182\pi$
$997$	29.8257	−	29.8257i	0.944590	−	0.944590i	0.998543	+	0.0539539i	$0.0171824\pi$
$998$	5.21222	−	5.21222i	0.164990	−	0.164990i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.p.b.622.20	yes	48
3.2	odd	2	inner	945.2.p.b.622.5	yes	48
5.3	odd	4	inner	945.2.p.b.433.19	yes	48
7.6	odd	2	inner	945.2.p.b.622.19	yes	48
15.8	even	4	inner	945.2.p.b.433.6	yes	48
21.20	even	2	inner	945.2.p.b.622.6	yes	48
35.13	even	4	inner	945.2.p.b.433.20	yes	48
105.83	odd	4	inner	945.2.p.b.433.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.p.b.433.5	✓	48	105.83	odd	4	inner
945.2.p.b.433.6	yes	48	15.8	even	4	inner
945.2.p.b.433.19	yes	48	5.3	odd	4	inner
945.2.p.b.433.20	yes	48	35.13	even	4	inner
945.2.p.b.622.5	yes	48	3.2	odd	2	inner
945.2.p.b.622.6	yes	48	21.20	even	2	inner
945.2.p.b.622.19	yes	48	7.6	odd	2	inner
945.2.p.b.622.20	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27393 + 1.27393i) q^{2} +1.24581i q^{4} +(2.23606 + 0.00600881i) q^{5} +(-1.54853 - 2.14524i) q^{7} +(0.960789 - 0.960789i) q^{8} +O(q^{10})\)	\(q+(1.27393 + 1.27393i) q^{2} +1.24581i q^{4} +(2.23606 + 0.00600881i) q^{5} +(-1.54853 - 2.14524i) q^{7} +(0.960789 - 0.960789i) q^{8} +(2.84093 + 2.85624i) q^{10} +4.95168 q^{11} +(-4.34673 - 4.34673i) q^{13} +(0.760171 - 4.70561i) q^{14} +4.93958 q^{16} +(-2.81538 + 2.81538i) q^{17} +2.64901 q^{19} +(-0.00748582 + 2.78570i) q^{20} +(6.30811 + 6.30811i) q^{22} +(0.761826 - 0.761826i) q^{23} +(4.99993 + 0.0268721i) q^{25} -11.0749i q^{26} +(2.67256 - 1.92917i) q^{28} -3.25945i q^{29} +0.0115464i q^{31} +(4.37111 + 4.37111i) q^{32} -7.17322 q^{34} +(-3.44971 - 4.80619i) q^{35} +(4.56825 + 4.56825i) q^{37} +(3.37466 + 3.37466i) q^{38} +(2.15416 - 2.14261i) q^{40} -2.77822i q^{41} +(-6.37466 + 6.37466i) q^{43} +6.16885i q^{44} +1.94103 q^{46} +(-8.38024 + 8.38024i) q^{47} +(-2.20412 + 6.64393i) q^{49} +(6.33534 + 6.40380i) q^{50} +(5.41519 - 5.41519i) q^{52} +(3.87019 - 3.87019i) q^{53} +(11.0723 + 0.0297537i) q^{55} +(-3.54893 - 0.573315i) q^{56} +(4.15232 - 4.15232i) q^{58} +4.06308 q^{59} +11.4059i q^{61} +(-0.0147093 + 0.0147093i) q^{62} +1.25785i q^{64} +(-9.69342 - 9.74566i) q^{65} +(-0.909987 - 0.909987i) q^{67} +(-3.50743 - 3.50743i) q^{68} +(1.72806 - 10.5175i) q^{70} -4.59015 q^{71} +(-0.162169 - 0.162169i) q^{73} +11.6393i q^{74} +3.30016i q^{76} +(-7.66783 - 10.6226i) q^{77} +5.38899i q^{79} +(11.0452 + 0.0296810i) q^{80} +(3.53926 - 3.53926i) q^{82} +(3.38215 + 3.38215i) q^{83} +(-6.31228 + 6.27845i) q^{85} -16.2418 q^{86} +(4.75752 - 4.75752i) q^{88} +0.0829077 q^{89} +(-2.59375 + 16.0558i) q^{91} +(0.949089 + 0.949089i) q^{92} -21.3517 q^{94} +(5.92335 + 0.0159174i) q^{95} +(1.06919 - 1.06919i) q^{97} +(-11.2718 + 5.65603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{7}+O(q^{10}) \) 48 * q - 8 * q^7	\( 48 q - 8 q^{7} + 40 q^{16} + 8 q^{22} - 48 q^{25} - 20 q^{28} - 24 q^{37} - 40 q^{43} + 40 q^{46} - 80 q^{58} - 64 q^{67} - 4 q^{70} - 8 q^{85} - 48 q^{88} + 48 q^{91}+O(q^{100}) \) 48 * q - 8 * q^7 + 40 * q^16 + 8 * q^22 - 48 * q^25 - 20 * q^28 - 24 * q^37 - 40 * q^43 + 40 * q^46 - 80 * q^58 - 64 * q^67 - 4 * q^70 - 8 * q^85 - 48 * q^88 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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