LMFDB - Embedded newform 936.2.w.j.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(307,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Character	$\chi$	$=$	936.307
Dual form			936.2.w.j.811.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41280 - 0.0632999i) q^{2} +(1.99199 + 0.178860i) q^{4} +(1.61967 - 1.61967i) q^{5} +(2.08158 + 2.08158i) q^{7} +(-2.80295 - 0.378785i) q^{8} +(-2.39080 + 2.18574i) q^{10} +(0.0673682 - 0.0673682i) q^{11} +(-1.04130 + 3.45191i) q^{13} +(-2.80909 - 3.07262i) q^{14} +(3.93602 + 0.712572i) q^{16} +7.18195i q^{17} +(2.30579 + 2.30579i) q^{19} +(3.51606 - 2.93668i) q^{20} +(-0.0994420 + 0.0909132i) q^{22} -2.00453 q^{23} -0.246692i q^{25} +(1.68965 - 4.81093i) q^{26} +(3.77418 + 4.51880i) q^{28} +4.37007i q^{29} +(-2.08158 + 2.08158i) q^{31} +(-5.51569 - 1.25587i) q^{32} +(0.454617 - 10.1466i) q^{34} +6.74298 q^{35} +(-6.43362 - 6.43362i) q^{37} +(-3.11165 - 3.40356i) q^{38} +(-5.15337 + 3.92636i) q^{40} +(7.94353 + 7.94353i) q^{41} -10.4665i q^{43} +(0.146246 - 0.122147i) q^{44} +(2.83200 + 0.126887i) q^{46} +(-5.31365 - 5.31365i) q^{47} +1.66599i q^{49} +(-0.0156156 + 0.348525i) q^{50} +(-2.69166 + 6.68991i) q^{52} +1.41118i q^{53} -0.218229i q^{55} +(-5.04610 - 6.62305i) q^{56} +(0.276625 - 6.17401i) q^{58} +(3.96350 - 3.96350i) q^{59} +1.94041i q^{61} +(3.07262 - 2.80909i) q^{62} +(7.71304 + 2.12343i) q^{64} +(3.90441 + 7.27754i) q^{65} +(8.16072 + 8.16072i) q^{67} +(-1.28456 + 14.3063i) q^{68} +(-9.52646 - 0.426830i) q^{70} +(-0.00829610 + 0.00829610i) q^{71} +(0.419298 - 0.419298i) q^{73} +(8.68214 + 9.49664i) q^{74} +(4.18068 + 5.00551i) q^{76} +0.280465 q^{77} -8.46664i q^{79} +(7.52920 - 5.22093i) q^{80} +(-10.7198 - 11.7254i) q^{82} +(3.35193 + 3.35193i) q^{83} +(11.6324 + 11.6324i) q^{85} +(-0.662529 + 14.7870i) q^{86} +(-0.214348 + 0.163312i) q^{88} +(-1.90441 + 1.90441i) q^{89} +(-9.35300 + 5.01789i) q^{91} +(-3.99300 - 0.358530i) q^{92} +(7.17075 + 7.84346i) q^{94} +7.46925 q^{95} +(8.76265 + 8.76265i) q^{97} +(0.105457 - 2.35370i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) $ 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.41280	−	0.0632999i	−0.998998	−	0.0447598i
$2$	−1.41280	−	0.0632999i	−0.998998	−	0.0447598i
$3$		0			0
$3$		0			0
$4$	1.99199	+	0.178860i	0.995993	+	0.0894299i
$5$	1.61967	−	1.61967i	0.724341	−	0.724341i	−0.245146	−	0.969486i	$-0.578836\pi$
$5$	1.61967	−	1.61967i	0.724341	−	0.724341i	0.969486	+	0.245146i	$0.0788358\pi$
$6$		0			0
$7$	2.08158	+	2.08158i	0.786765	+	0.786765i	0.980962	−	0.194197i	$-0.0622102\pi$
$7$	2.08158	+	2.08158i	0.786765	+	0.786765i	−0.194197	+	0.980962i	$0.562210\pi$
$8$	−2.80295	−	0.378785i	−0.990992	−	0.133921i
$9$		0			0
$10$	−2.39080	+	2.18574i	−0.756036	+	0.691193i
$11$	0.0673682	−	0.0673682i	0.0203123	−	0.0203123i	−0.696878	−	0.717190i	$-0.745428\pi$
$11$	0.0673682	−	0.0673682i	0.0203123	−	0.0203123i	0.717190	+	0.696878i	$0.245428\pi$
$12$		0			0
$13$	−1.04130	+	3.45191i	−0.288804	+	0.957388i
$13$	−1.04130	+	3.45191i	−0.288804	+	0.957388i
$14$	−2.80909	−	3.07262i	−0.750761	−	0.821192i
$15$		0			0
$16$	3.93602	+	0.712572i	0.984005	+	0.178143i
$17$			7.18195i			1.74188i	0.491391	+	0.870939i	$0.336489\pi$
$17$			7.18195i			1.74188i	−0.491391	+	0.870939i	$0.663511\pi$
$18$		0			0
$19$	2.30579	+	2.30579i	0.528984	+	0.528984i	0.920269	−	0.391285i	$-0.127969\pi$
$19$	2.30579	+	2.30579i	0.528984	+	0.528984i	−0.391285	+	0.920269i	$0.627969\pi$
$20$	3.51606	−	2.93668i	0.786216	−	0.656661i
$21$		0			0
$22$	−0.0994420	+	0.0909132i	−0.0212011	+	0.0193828i
$23$	−2.00453			−0.417974			−0.208987	−	0.977918i	$-0.567017\pi$
$23$	−2.00453			−0.417974			−0.208987	+	0.977918i	$0.567017\pi$
$24$		0			0
$25$		−	0.246692i		−	0.0493384i
$26$	1.68965	−	4.81093i	0.331367	−	0.943502i
$27$		0			0
$28$	3.77418	+	4.51880i	0.713252	+	0.853973i
$29$			4.37007i			0.811501i	0.913984	+	0.405750i	$0.132990\pi$
$29$			4.37007i			0.811501i	−0.913984	+	0.405750i	$0.867010\pi$
$30$		0			0
$31$	−2.08158	+	2.08158i	−0.373864	+	0.373864i	−0.868882	−	0.495019i	$-0.835161\pi$
$31$	−2.08158	+	2.08158i	−0.373864	+	0.373864i	0.495019	+	0.868882i	$0.335161\pi$
$32$	−5.51569	−	1.25587i	−0.975045	−	0.222008i
$33$		0			0
$34$	0.454617	−	10.1466i	0.0779661	−	1.74013i
$35$	6.74298			1.13977
$36$		0			0
$37$	−6.43362	−	6.43362i	−1.05768	−	1.05768i	−0.998231	−	0.0594489i	$-0.981066\pi$
$37$	−6.43362	−	6.43362i	−1.05768	−	1.05768i	−0.0594489	−	0.998231i	$-0.518934\pi$
$38$	−3.11165	−	3.40356i	−0.504777	−	0.552131i
$39$		0			0
$40$	−5.15337	+	3.92636i	−0.814820	+	0.620812i
$41$	7.94353	+	7.94353i	1.24057	+	1.24057i	0.959764	+	0.280806i	$0.0906019\pi$
$41$	7.94353	+	7.94353i	1.24057	+	1.24057i	0.280806	+	0.959764i	$0.409398\pi$
$42$		0			0
$43$		−	10.4665i		−	1.59613i	−0.602573	−	0.798064i	$-0.705858\pi$
$43$		−	10.4665i		−	1.59613i	0.602573	−	0.798064i	$-0.294142\pi$
$44$	0.146246	−	0.122147i	0.0220474	−	0.0184144i
$45$		0			0
$46$	2.83200	+	0.126887i	0.417555	+	0.0187084i
$47$	−5.31365	−	5.31365i	−0.775076	−	0.775076i	0.203913	−	0.978989i	$-0.434634\pi$
$47$	−5.31365	−	5.31365i	−0.775076	−	0.775076i	−0.978989	+	0.203913i	$0.934634\pi$
$48$		0			0
$49$			1.66599i			0.237998i
$50$	−0.0156156	+	0.348525i	−0.00220837	+	0.0492889i
$51$		0			0
$52$	−2.69166	+	6.68991i	−0.373266	+	0.927724i
$53$			1.41118i			0.193841i	0.995292	+	0.0969204i	$0.0308992\pi$
$53$			1.41118i			0.193841i	−0.995292	+	0.0969204i	$0.969101\pi$
$54$		0			0
$55$		−	0.218229i		−	0.0294260i
$56$	−5.04610	−	6.62305i	−0.674314	−	0.885042i
$57$		0			0
$58$	0.276625	−	6.17401i	0.0363226	−	0.810687i
$59$	3.96350	−	3.96350i	0.516004	−	0.516004i	−0.400356	−	0.916360i	$-0.631113\pi$
$59$	3.96350	−	3.96350i	0.516004	−	0.516004i	0.916360	+	0.400356i	$0.131113\pi$
$60$		0			0
$61$			1.94041i			0.248444i	0.992254	+	0.124222i	$0.0396434\pi$
$61$			1.94041i			0.248444i	−0.992254	+	0.124222i	$0.960357\pi$
$62$	3.07262	−	2.80909i	0.390223	−	0.356755i
$63$		0			0
$64$	7.71304	+	2.12343i	0.964131	+	0.265429i
$65$	3.90441	+	7.27754i	0.484282	+	0.902668i
$66$		0			0
$67$	8.16072	+	8.16072i	0.996991	+	0.996991i	0.999995	−	0.00300457i	$-0.000956387\pi$
$67$	8.16072	+	8.16072i	0.996991	+	0.996991i	−0.00300457	+	0.999995i	$0.500956\pi$
$68$	−1.28456	+	14.3063i	−0.155776	+	1.73490i
$69$		0			0
$70$	−9.52646	−	0.426830i	−1.13863	−	0.0510159i
$71$	−0.00829610	+	0.00829610i	−0.000984566	+	0.000984566i	−0.707599	−	0.706614i	$-0.750222\pi$
$71$	−0.00829610	+	0.00829610i	−0.000984566	+	0.000984566i	0.706614	+	0.707599i	$0.250222\pi$
$72$		0			0
$73$	0.419298	−	0.419298i	0.0490751	−	0.0490751i	−0.682143	−	0.731218i	$-0.738952\pi$
$73$	0.419298	−	0.419298i	0.0490751	−	0.0490751i	0.731218	+	0.682143i	$0.238952\pi$
$74$	8.68214	+	9.49664i	1.00928	+	1.10396i
$75$		0			0
$76$	4.18068	+	5.00551i	0.479557	+	0.574171i
$77$	0.280465			0.0319620
$78$		0			0
$79$		−	8.46664i		−	0.952571i	−0.879291	−	0.476286i	$-0.841983\pi$
$79$		−	8.46664i		−	0.952571i	0.879291	−	0.476286i	$-0.158017\pi$
$80$	7.52920	−	5.22093i	0.841791	−	0.583718i
$81$		0			0
$82$	−10.7198	−	11.7254i	−1.18380	−	1.29486i
$83$	3.35193	+	3.35193i	0.367922	+	0.367922i	0.866719	−	0.498797i	$-0.166225\pi$
$83$	3.35193	+	3.35193i	0.367922	+	0.367922i	−0.498797	+	0.866719i	$0.666225\pi$
$84$		0			0
$85$	11.6324	+	11.6324i	1.26171	+	1.26171i
$86$	−0.662529	+	14.7870i	−0.0714423	+	1.59453i
$87$		0			0
$88$	−0.214348	+	0.163312i	−0.0228496	+	0.0174091i
$89$	−1.90441	+	1.90441i	−0.201867	+	0.201867i	−0.800799	−	0.598933i	$-0.795592\pi$
$89$	−1.90441	+	1.90441i	−0.201867	+	0.201867i	0.598933	+	0.800799i	$0.295592\pi$
$90$		0			0
$91$	−9.35300	+	5.01789i	−0.980461	+	0.526018i
$92$	−3.99300	−	0.358530i	−0.416299	−	0.0373794i
$93$		0			0
$94$	7.17075	+	7.84346i	0.739607	+	0.808991i
$95$	7.46925			0.766329
$96$		0			0
$97$	8.76265	+	8.76265i	0.889712	+	0.889712i	0.994495	−	0.104783i	$-0.0334147\pi$
$97$	8.76265	+	8.76265i	0.889712	+	0.889712i	−0.104783	+	0.994495i	$0.533415\pi$
$98$	0.105457	−	2.35370i	0.0106528	−	0.237760i
$99$		0			0
$100$	0.0441232	−	0.491407i	0.00441232	−	0.0491407i
$101$	10.5683			1.05159			0.525793	−	0.850613i	$-0.323769\pi$
$101$	10.5683			1.05159			0.525793	+	0.850613i	$0.323769\pi$
$102$		0			0
$103$	3.52228			0.347061			0.173530	−	0.984829i	$-0.444482\pi$
$103$	3.52228			0.347061			0.173530	+	0.984829i	$0.444482\pi$
$104$	4.22624	−	9.28110i	0.414417	−	0.910087i
$105$		0			0
$106$	0.0893277	−	1.99371i	0.00867627	−	0.193646i
$107$	−11.8314			−1.14378			−0.571892	−	0.820329i	$-0.693790\pi$
$107$	−11.8314			−1.14378			−0.571892	+	0.820329i	$0.693790\pi$
$108$		0			0
$109$	12.9904	−	12.9904i	1.24425	−	1.24425i	0.286033	−	0.958220i	$-0.407663\pi$
$109$	12.9904	−	12.9904i	1.24425	−	1.24425i	0.958220	−	0.286033i	$-0.0923367\pi$
$110$	−0.0138139	+	0.308313i	−0.00131710	+	0.0293965i
$111$		0			0
$112$	6.70988	+	9.67643i	0.634024	+	0.914337i
$113$	−12.7051			−1.19520			−0.597598	−	0.801796i	$-0.703878\pi$
$113$	−12.7051			−1.19520			−0.597598	+	0.801796i	$0.703878\pi$
$114$		0			0
$115$	−3.24669	+	3.24669i	−0.302756	+	0.302756i
$116$	−0.781629	+	8.70511i	−0.0725724	+	0.808249i
$117$		0			0
$118$	−5.85051	+	5.34873i	−0.538583	+	0.492391i
$119$	−14.9498	+	14.9498i	−1.37045	+	1.37045i
$120$		0			0
$121$			10.9909i			0.999175i
$122$	0.122828	−	2.74140i	0.0111203	−	0.248195i
$123$		0			0
$124$	−4.51880	+	3.77418i	−0.405800	+	0.338931i
$125$	7.69881	+	7.69881i	0.688603	+	0.688603i
$126$		0			0
$127$	−18.5476			−1.64583			−0.822916	−	0.568164i	$-0.807654\pi$
$127$	−18.5476			−1.64583			−0.822916	+	0.568164i	$0.807654\pi$
$128$	−10.7625	−	3.48821i	−0.951284	−	0.308317i
$129$		0			0
$130$	−5.05547	−	10.5288i	−0.443394	−	0.923439i
$131$	5.20053			0.454372			0.227186	−	0.973851i	$-0.427047\pi$
$131$	5.20053			0.454372			0.227186	+	0.973851i	$0.427047\pi$
$132$		0			0
$133$			9.59938i			0.832372i
$134$	−11.0129	−	12.0460i	−0.951367	−	1.04062i
$135$		0			0
$136$	2.72041	−	20.1306i	0.233274	−	1.72619i
$137$	15.0286	−	15.0286i	1.28398	−	1.28398i	0.345598	−	0.938383i	$-0.387676\pi$
$137$	15.0286	−	15.0286i	1.28398	−	1.28398i	0.938383	−	0.345598i	$-0.112324\pi$
$138$		0			0
$139$	6.12441			0.519466			0.259733	−	0.965681i	$-0.416366\pi$
$139$	6.12441			0.519466			0.259733	+	0.965681i	$0.416366\pi$
$140$	13.4319	+	1.20605i	1.13520	+	0.101930i
$141$		0			0
$142$	0.0122458	−	0.0111956i	0.00102765	−	0.000939510i
$143$	0.162399	+	0.302700i	0.0135805	+	0.0253130i
$144$		0			0
$145$	7.07808	+	7.07808i	0.587803	+	0.587803i
$146$	−0.618924	+	0.565841i	−0.0512225	+	0.0468293i
$147$		0			0
$148$	−11.6650	−	13.9664i	−0.958854	−	1.14803i
$149$	13.2521	−	13.2521i	1.08565	−	1.08565i	0.0896836	−	0.995970i	$-0.471414\pi$
$149$	13.2521	−	13.2521i	1.08565	−	1.08565i	0.995970	−	0.0896836i	$-0.0285856\pi$
$150$		0			0
$151$	2.61081	+	2.61081i	0.212465	+	0.212465i	0.805314	−	0.592849i	$-0.201997\pi$
$151$	2.61081	+	2.61081i	0.212465	+	0.212465i	−0.592849	+	0.805314i	$0.701997\pi$
$152$	−5.58961	−	7.33640i	−0.453377	−	0.595061i
$153$		0			0
$154$	−0.396240	−	0.0177534i	−0.0319300	−	0.00143061i
$155$			6.74298i			0.541609i
$156$		0			0
$157$		−	1.36321i		−	0.108796i	−0.998519	−	0.0543978i	$-0.982676\pi$
$157$		−	1.36321i		−	0.108796i	0.998519	−	0.0543978i	$-0.0173239\pi$
$158$	−0.535937	+	11.9616i	−0.0426369	+	0.951617i
$159$		0			0
$160$	−10.9677	+	6.89952i	−0.867074	+	0.545455i
$161$	−4.17261	−	4.17261i	−0.328847	−	0.328847i
$162$		0			0
$163$	13.7263	−	13.7263i	1.07513	−	1.07513i	0.0781913	−	0.996938i	$-0.475086\pi$
$163$	13.7263	−	13.7263i	1.07513	−	1.07513i	0.996938	−	0.0781913i	$-0.0249145\pi$
$164$	14.4026	+	17.2442i	1.12466	+	1.34654i
$165$		0			0
$166$	−4.52342	−	4.94777i	−0.351085	−	0.384021i
$167$	3.15502	+	3.15502i	0.244142	+	0.244142i	0.818561	−	0.574419i	$-0.194772\pi$
$167$	3.15502	+	3.15502i	0.244142	+	0.244142i	−0.574419	+	0.818561i	$0.694772\pi$
$168$		0			0
$169$	−10.8314	−	7.18895i	−0.833184	−	0.552996i
$170$	−15.6979	−	17.1706i	−1.20397	−	1.31692i
$171$		0			0
$172$	1.87204	−	20.8491i	0.142741	−	1.58973i
$173$	−2.52229			−0.191766			−0.0958830	−	0.995393i	$-0.530567\pi$
$173$	−2.52229			−0.191766			−0.0958830	+	0.995393i	$0.530567\pi$
$174$		0			0
$175$	0.513510	−	0.513510i	0.0388177	−	0.0388177i
$176$	0.313167	−	0.217158i	0.0236059	−	0.0163689i
$177$		0			0
$178$	2.81109	−	2.56999i	0.210700	−	0.192629i
$179$		−	12.1739i		−	0.909917i	−0.890513	−	0.454958i	$-0.849654\pi$
$179$		−	12.1739i		−	0.909917i	0.890513	−	0.454958i	$-0.150346\pi$
$180$		0			0
$181$	1.13958			0.0847044			0.0423522	−	0.999103i	$-0.486515\pi$
$181$	1.13958			0.0847044			0.0423522	+	0.999103i	$0.486515\pi$
$182$	13.5315	−	6.49722i	1.00302	−	0.481606i
$183$		0			0
$184$	5.61860	+	0.759287i	0.414209	+	0.0559754i
$185$	−20.8407			−1.53224
$186$		0			0
$187$	0.483835	+	0.483835i	0.0353815	+	0.0353815i
$188$	−9.63432	−	11.5351i	−0.702655	−	0.841285i
$189$		0			0
$190$	−10.5525	−	0.472803i	−0.765561	−	0.0343007i
$191$		−	22.4304i		−	1.62301i	−0.584347	−	0.811504i	$-0.698649\pi$
$191$		−	22.4304i		−	1.62301i	0.584347	−	0.811504i	$-0.301351\pi$
$192$		0			0
$193$	−3.57371	+	3.57371i	−0.257241	+	0.257241i	−0.823931	−	0.566690i	$-0.808224\pi$
$193$	−3.57371	+	3.57371i	−0.257241	+	0.257241i	0.566690	+	0.823931i	$0.308224\pi$
$194$	−11.8252	−	12.9345i	−0.848997	−	0.928644i
$195$		0			0
$196$	−0.297978	+	3.31863i	−0.0212842	+	0.237045i
$197$	−2.26114	+	2.26114i	−0.161099	+	0.161099i	−0.783054	−	0.621954i	$-0.786339\pi$
$197$	−2.26114	+	2.26114i	−0.161099	+	0.161099i	0.621954	+	0.783054i	$0.286339\pi$
$198$		0			0
$199$	−26.4375			−1.87410			−0.937051	−	0.349193i	$-0.886456\pi$
$199$	−26.4375			−1.87410			−0.937051	+	0.349193i	$0.886456\pi$
$200$	−0.0934431	+	0.691464i	−0.00660743	+	0.0488939i
$201$		0			0
$202$	−14.9309	−	0.668972i	−1.05053	−	0.0470687i
$203$	−9.09666	+	9.09666i	−0.638460	+	0.638460i
$204$		0			0
$205$	25.7319			1.79719
$206$	−4.97627	−	0.222960i	−0.346713	−	0.0155344i
$207$		0			0
$208$	−6.55831	+	12.8448i	−0.454737	+	0.890626i
$209$	0.310674			0.0214897
$210$		0			0
$211$	−2.28566			−0.157351			−0.0786755	−	0.996900i	$-0.525069\pi$
$211$	−2.28566			−0.157351			−0.0786755	+	0.996900i	$0.525069\pi$
$212$	−0.252404	+	2.81105i	−0.0173351	+	0.193064i
$213$		0			0
$214$	16.7153	+	0.748926i	1.14264	+	0.0511955i
$215$	−16.9523	−	16.9523i	−1.15614	−	1.15614i
$216$		0			0
$217$	−8.66599			−0.588286
$218$	−19.1751	+	17.5305i	−1.29870	+	1.18731i
$219$		0			0
$220$	0.0390324	−	0.434710i	0.00263157	−	0.0293081i
$221$	−24.7915	−	7.47856i	−1.66765	−	0.503062i
$222$		0			0
$223$	6.65855	−	6.65855i	0.445889	−	0.445889i	−0.448096	−	0.893985i	$-0.647898\pi$
$223$	6.65855	−	6.65855i	0.445889	−	0.445889i	0.893985	+	0.448096i	$0.147898\pi$
$224$	−8.86717	−	14.0956i	−0.592463	−	0.941800i
$225$		0			0
$226$	17.9497	+	0.804232i	1.19400	+	0.0534967i
$227$	7.86789	+	7.86789i	0.522210	+	0.522210i	0.918238	−	0.396028i	$-0.129612\pi$
$227$	7.86789	+	7.86789i	0.522210	+	0.522210i	−0.396028	+	0.918238i	$0.629612\pi$
$228$		0			0
$229$	−3.64543	−	3.64543i	−0.240897	−	0.240897i	0.576324	−	0.817221i	$-0.304487\pi$
$229$	−3.64543	−	3.64543i	−0.240897	−	0.240897i	−0.817221	+	0.576324i	$0.804487\pi$
$230$	4.79243	−	4.38140i	0.316003	−	0.288901i
$231$		0			0
$232$	1.65531	−	12.2491i	0.108677	−	0.804191i
$233$			3.31543i			0.217201i	0.994085	+	0.108601i	$0.0346370\pi$
$233$			3.31543i			0.217201i	−0.994085	+	0.108601i	$0.965363\pi$
$234$		0			0
$235$	−17.2128			−1.12284
$236$	8.60416	−	7.18633i	0.560083	−	0.467791i
$237$		0			0
$238$	22.0674	−	20.1747i	1.43042	−	1.30773i
$239$	7.48888	−	7.48888i	0.484415	−	0.484415i	−0.422123	−	0.906538i	$-0.638715\pi$
$239$	7.48888	−	7.48888i	0.484415	−	0.484415i	0.906538	+	0.422123i	$0.138715\pi$
$240$		0			0
$241$	−9.02754	+	9.02754i	−0.581515	+	0.581515i	−0.935319	−	0.353804i	$-0.884888\pi$
$241$	−9.02754	+	9.02754i	−0.581515	+	0.581515i	0.353804	+	0.935319i	$0.384888\pi$
$242$	0.695724	−	15.5279i	0.0447229	−	0.998173i
$243$		0			0
$244$	−0.347061	+	3.86526i	−0.0222183	+	0.247448i
$245$	2.69836	+	2.69836i	0.172392	+	0.172392i
$246$		0			0
$247$	−10.3604	+	5.55836i	−0.659216	+	0.353670i
$248$	6.62305	−	5.04610i	0.420564	−	0.320428i
$249$		0			0
$250$	−10.3895	−	11.3642i	−0.657091	−	0.718734i
$251$		−	18.4986i		−	1.16762i	−0.811889	−	0.583812i	$-0.801561\pi$
$251$		−	18.4986i		−	1.16762i	0.811889	−	0.583812i	$-0.198439\pi$
$252$		0			0
$253$	−0.135042	+	0.135042i	−0.00849001	+	0.00849001i
$254$	26.2039	+	1.17406i	1.64418	+	0.0736671i
$255$		0			0
$256$	14.9845	+	5.60939i	0.936530	+	0.350587i
$257$			17.6933i			1.10368i	0.833950	+	0.551840i	$0.186074\pi$
$257$			17.6933i			1.10368i	−0.833950	+	0.551840i	$0.813926\pi$
$258$		0			0
$259$		−	26.7842i		−	1.66429i
$260$	6.47587	+	15.1951i	0.401616	+	0.942360i
$261$		0			0
$262$	−7.34728	−	0.329193i	−0.453917	−	0.0203376i
$263$			18.2366i			1.12452i	0.826962	+	0.562258i	$0.190067\pi$
$263$			18.2366i			1.12452i	−0.826962	+	0.562258i	$0.809933\pi$
$264$		0			0
$265$	2.28566	+	2.28566i	0.140407	+	0.140407i
$266$	0.607640	−	13.5620i	0.0372568	−	0.831538i
$267$		0			0
$268$	14.7964	+	17.7157i	0.903835	+	1.08216i
$269$		−	6.68357i		−	0.407504i	−0.979023	−	0.203752i	$-0.934686\pi$
$269$		−	6.68357i		−	0.407504i	0.979023	−	0.203752i	$-0.0653137\pi$
$270$		0			0
$271$	−5.65140	−	5.65140i	−0.343298	−	0.343298i	0.514308	−	0.857606i	$-0.328049\pi$
$271$	−5.65140	−	5.65140i	−0.343298	−	0.343298i	−0.857606	+	0.514308i	$0.828049\pi$
$272$	−5.11766	+	28.2683i	−0.310303	+	1.71402i
$273$		0			0
$274$	−22.1837	+	20.2811i	−1.34016	+	1.22522i
$275$	−0.0166192	−	0.0166192i	−0.00100218	−	0.00100218i
$276$		0			0
$277$	−24.3573			−1.46349			−0.731745	−	0.681579i	$-0.761294\pi$
$277$	−24.3573			−1.46349			−0.731745	+	0.681579i	$0.761294\pi$
$278$	−8.65254	−	0.387674i	−0.518945	−	0.0232512i
$279$		0			0
$280$	−18.9002	−	2.55414i	−1.12950	−	0.152639i
$281$	7.19722	−	7.19722i	0.429350	−	0.429350i	−0.459057	−	0.888407i	$-0.651813\pi$
$281$	7.19722	−	7.19722i	0.429350	−	0.429350i	0.888407	+	0.459057i	$0.151813\pi$
$282$		0			0
$283$		−	14.0053i		−	0.832529i	−0.909244	−	0.416264i	$-0.863339\pi$
$283$		−	14.0053i		−	0.832529i	0.909244	−	0.416264i	$-0.136661\pi$
$284$	−0.0180096	+	0.0150419i	−0.00106867	+	0.000892571i
$285$		0			0
$286$	−0.210275	−	0.437933i	−0.0124338	−	0.0258955i
$287$			33.0703i			1.95208i
$288$		0			0
$289$	−34.5804			−2.03414
$290$	−9.55185	−	10.4479i	−0.560904	−	0.613524i
$291$		0			0
$292$	0.910231	−	0.760240i	0.0532672	−	0.0444897i
$293$	−10.4354	−	10.4354i	−0.609643	−	0.609643i	0.333210	−	0.942853i	$-0.391868\pi$
$293$	−10.4354	−	10.4354i	−0.609643	−	0.609643i	−0.942853	+	0.333210i	$0.891868\pi$
$294$		0			0
$295$		−	12.8392i		−	0.747526i
$296$	15.5961	+	20.4701i	0.906507	+	1.18980i
$297$		0			0
$298$	−19.5614	+	17.8837i	−1.13316	+	1.03597i
$299$	2.08732	−	6.91947i	0.120713	−	0.400163i
$300$		0			0
$301$	21.7869	−	21.7869i	1.25578	−	1.25578i
$302$	−3.52328	−	3.85381i	−0.202742	−	0.221762i
$303$		0			0
$304$	7.43258	+	10.7187i	0.426288	+	0.614757i
$305$	3.14283	+	3.14283i	0.179958	+	0.179958i
$306$		0			0
$307$	9.49598	−	9.49598i	0.541964	−	0.541964i	−0.382140	−	0.924104i	$-0.624813\pi$
$307$	9.49598	−	9.49598i	0.541964	−	0.541964i	0.924104	+	0.382140i	$0.124813\pi$
$308$	0.558683	+	0.0501640i	0.0318339	+	0.00285836i
$309$		0			0
$310$	0.426830	−	9.52646i	0.0242423	−	0.541066i
$311$	19.3516			1.09733			0.548664	−	0.836043i	$-0.315136\pi$
$311$	19.3516			1.09733			0.548664	+	0.836043i	$0.315136\pi$
$312$		0			0
$313$	10.1200			0.572016			0.286008	−	0.958227i	$-0.407672\pi$
$313$	10.1200			0.572016			0.286008	+	0.958227i	$0.407672\pi$
$314$	−0.0862908	+	1.92593i	−0.00486967	+	0.108687i
$315$		0			0
$316$	1.51434	−	16.8654i	0.0851883	−	0.948755i
$317$	−18.1488	+	18.1488i	−1.01934	+	1.01934i	−0.0195277	+	0.999809i	$0.506216\pi$
$317$	−18.1488	+	18.1488i	−1.01934	+	1.01934i	−0.999809	+	0.0195277i	$0.993784\pi$
$318$		0			0
$319$	0.294404	+	0.294404i	0.0164834	+	0.0164834i
$320$	15.9319	−	9.05336i	0.890619	−	0.506098i
$321$		0			0
$322$	5.63092	+	6.15917i	0.313799	+	0.343237i
$323$	−16.5600	+	16.5600i	−0.921426	+	0.921426i
$324$		0			0
$325$	0.851558	+	0.256880i	0.0472360	+	0.0142491i
$326$	−20.2614	+	18.5236i	−1.12217	+	1.02593i
$327$		0			0
$328$	−19.2564	−	25.2742i	−1.06326	−	1.39553i
$329$		−	22.1216i		−	1.21960i
$330$		0			0
$331$	−22.5976	−	22.5976i	−1.24208	−	1.24208i	−0.959138	−	0.282939i	$-0.908691\pi$
$331$	−22.5976	−	22.5976i	−1.24208	−	1.24208i	−0.282939	−	0.959138i	$-0.591309\pi$
$332$	6.07747	+	7.27652i	0.333545	+	0.399351i
$333$		0			0
$334$	−4.25768	−	4.65711i	−0.232970	−	0.254825i
$335$	26.4354			1.44432
$336$		0			0
$337$			8.65894i			0.471683i	0.971792	+	0.235841i	$0.0757846\pi$
$337$			8.65894i			0.471683i	−0.971792	+	0.235841i	$0.924215\pi$
$338$	14.8475	+	10.8421i	0.807597	+	0.589735i
$339$		0			0
$340$	21.0910	+	25.2522i	1.14382	+	1.36949i
$341$			0.280465i			0.0151881i
$342$		0			0
$343$	11.1032	−	11.1032i	0.599516	−	0.599516i
$344$	−3.96456	+	29.3371i	−0.213754	+	1.58175i
$345$		0			0
$346$	3.56348	+	0.159661i	0.191574	+	0.00858341i
$347$	16.6635			0.894546			0.447273	−	0.894397i	$-0.352395\pi$
$347$	16.6635			0.894546			0.447273	+	0.894397i	$0.352395\pi$
$348$		0			0
$349$	3.99002	+	3.99002i	0.213581	+	0.213581i	0.805787	−	0.592206i	$-0.201743\pi$
$349$	3.99002	+	3.99002i	0.213581	+	0.213581i	−0.592206	+	0.805787i	$0.701743\pi$
$350$	−0.757990	+	0.692980i	−0.0405163	+	0.0370413i
$351$		0			0
$352$	−0.456188	+	0.286976i	−0.0243149	+	0.0152959i
$353$	6.09559	+	6.09559i	0.324436	+	0.324436i	0.850466	−	0.526030i	$-0.176320\pi$
$353$	6.09559	+	6.09559i	0.324436	+	0.324436i	−0.526030	+	0.850466i	$0.676320\pi$
$354$		0			0
$355$			0.0268740i			0.00142632i
$356$	−4.13418	+	3.45293i	−0.219111	+	0.183005i
$357$		0			0
$358$	−0.770604	+	17.1992i	−0.0407277	+	0.909005i
$359$	−20.6821	−	20.6821i	−1.09156	−	1.09156i	−0.995362	−	0.0961965i	$-0.969332\pi$
$359$	−20.6821	−	20.6821i	−1.09156	−	1.09156i	−0.0961965	−	0.995362i	$-0.530668\pi$
$360$		0			0
$361$		−	8.36669i		−	0.440352i
$362$	−1.61000	−	0.0721353i	−0.0846195	−	0.00379135i
$363$		0			0
$364$	−19.5285	+	8.32270i	−1.02357	+	0.436228i
$365$		−	1.35825i		−	0.0710941i
$366$		0			0
$367$			30.1227i			1.57239i	0.617977	+	0.786196i	$0.287953\pi$
$367$			30.1227i			1.57239i	−0.617977	+	0.786196i	$0.712047\pi$
$368$	−7.88988	−	1.42837i	−0.411288	−	0.0744592i
$369$		0			0
$370$	29.4437	+	1.31922i	1.53071	+	0.0685828i
$371$	−2.93749	+	2.93749i	−0.152507	+	0.152507i
$372$		0			0
$373$			8.59939i			0.445259i	0.974903	+	0.222630i	$0.0714641\pi$
$373$			8.59939i			0.445259i	−0.974903	+	0.222630i	$0.928536\pi$
$374$	−0.652934	−	0.714187i	−0.0337624	−	0.0369297i
$375$		0			0
$376$	12.8812	+	16.9066i	0.664295	+	0.871893i
$377$	−15.0851	−	4.55055i	−0.776921	−	0.234365i
$378$		0			0
$379$	11.5751	+	11.5751i	0.594571	+	0.594571i	0.938863	−	0.344292i	$-0.111881\pi$
$379$	11.5751	+	11.5751i	0.594571	+	0.594571i	−0.344292	+	0.938863i	$0.611881\pi$
$380$	14.8786	+	1.33595i	0.763258	+	0.0685327i
$381$		0			0
$382$	−1.41984	+	31.6896i	−0.0726455	+	1.62138i
$383$	2.01486	−	2.01486i	0.102954	−	0.102954i	−0.653753	−	0.756708i	$-0.726807\pi$
$383$	2.01486	−	2.01486i	0.102954	−	0.102954i	0.756708	+	0.653753i	$0.226807\pi$
$384$		0			0
$385$	0.454263	−	0.454263i	0.0231514	−	0.0231514i
$386$	5.27513	−	4.82270i	0.268497	−	0.245469i
$387$		0			0
$388$	15.8878	+	19.0224i	0.806581	+	0.965714i
$389$	25.8294			1.30960			0.654801	−	0.755801i	$-0.272752\pi$
$389$	25.8294			1.30960			0.654801	+	0.755801i	$0.272752\pi$
$390$		0			0
$391$		−	14.3965i		−	0.728060i
$392$	0.631052	−	4.66968i	0.0318729	−	0.235855i
$393$		0			0
$394$	3.33766	−	3.05140i	0.168149	−	0.153727i
$395$	−13.7132	−	13.7132i	−0.689986	−	0.689986i
$396$		0			0
$397$	11.0841	+	11.0841i	0.556297	+	0.556297i	0.928251	−	0.371954i	$-0.121312\pi$
$397$	11.0841	+	11.0841i	0.556297	+	0.556297i	−0.371954	+	0.928251i	$0.621312\pi$
$398$	37.3507	+	1.67349i	1.87222	+	0.0838844i
$399$		0			0
$400$	0.175786	−	0.970983i	0.00878928	−	0.0485492i
$401$	25.0265	−	25.0265i	1.24977	−	1.24977i	0.293942	−	0.955823i	$-0.405033\pi$
$401$	25.0265	−	25.0265i	1.24977	−	1.24977i	0.955823	−	0.293942i	$-0.0949673\pi$
$402$		0			0
$403$	−5.01789	−	9.35300i	−0.249959	−	0.465906i
$404$	21.0519	+	1.89024i	1.04737	+	0.0940431i
$405$		0			0
$406$	13.4275	−	12.2759i	0.666398	−	0.609243i
$407$	−0.866843			−0.0429678
$408$		0			0
$409$	24.7440	+	24.7440i	1.22351	+	1.22351i	0.966374	+	0.257139i	$0.0827798\pi$
$409$	24.7440	+	24.7440i	1.22351	+	1.22351i	0.257139	+	0.966374i	$0.417220\pi$
$410$	−36.3539	−	1.62882i	−1.79539	−	0.0804419i
$411$		0			0
$412$	7.01634	+	0.629995i	0.345670	+	0.0310376i
$413$	16.5007			0.811948
$414$		0			0
$415$	10.8581			0.533002
$416$	10.0786	−	17.7319i	0.494145	−	0.869379i
$417$		0			0
$418$	−0.438919	−	0.0196656i	−0.0214682	−	0.000961876i
$419$	−15.6568			−0.764883			−0.382441	−	0.923980i	$-0.624917\pi$
$419$	−15.6568			−0.764883			−0.382441	+	0.923980i	$0.624917\pi$
$420$		0			0
$421$	5.24431	−	5.24431i	0.255592	−	0.255592i	−0.567667	−	0.823259i	$-0.692154\pi$
$421$	5.24431	−	5.24431i	0.255592	−	0.255592i	0.823259	+	0.567667i	$0.192154\pi$
$422$	3.22916	+	0.144682i	0.157193	+	0.00704300i
$423$		0			0
$424$	0.534534	−	3.95547i	0.0259593	−	0.192095i
$425$	1.77173			0.0859414
$426$		0			0
$427$	−4.03912	+	4.03912i	−0.195467	+	0.195467i
$428$	−23.5680	−	2.11616i	−1.13920	−	0.102288i
$429$		0			0
$430$	22.8771	+	25.0233i	1.10323	+	1.20673i
$431$	16.9631	−	16.9631i	0.817084	−	0.817084i	−0.168600	−	0.985684i	$-0.553925\pi$
$431$	16.9631	−	16.9631i	0.817084	−	0.817084i	0.985684	+	0.168600i	$0.0539248\pi$
$432$		0			0
$433$		−	21.6657i		−	1.04119i	−0.853805	−	0.520593i	$-0.825711\pi$
$433$		−	21.6657i		−	1.04119i	0.853805	−	0.520593i	$-0.174289\pi$
$434$	12.2433	+	0.548556i	0.587696	+	0.0263315i
$435$		0			0
$436$	28.2001	−	23.5532i	1.35054	−	1.12799i
$437$	−4.62203	−	4.62203i	−0.221102	−	0.221102i
$438$		0			0
$439$	−26.9953			−1.28842			−0.644208	−	0.764850i	$-0.722813\pi$
$439$	−26.9953			−1.28842			−0.644208	+	0.764850i	$0.722813\pi$
$440$	−0.0826619	+	0.611685i	−0.00394075	+	0.0291610i
$441$		0			0
$442$	34.5519	+	12.1350i	1.64347	+	0.577202i
$443$	3.69391			0.175503			0.0877515	−	0.996142i	$-0.472032\pi$
$443$	3.69391			0.175503			0.0877515	+	0.996142i	$0.472032\pi$
$444$		0			0
$445$			6.16904i			0.292441i
$446$	−9.82865	+	8.98568i	−0.465400	+	0.425484i
$447$		0			0
$448$	11.6353	+	20.4755i	0.549714	+	0.967374i
$449$	−15.9641	+	15.9641i	−0.753391	+	0.753391i	−0.975111	−	0.221719i	$-0.928833\pi$
$449$	−15.9641	+	15.9641i	−0.753391	+	0.753391i	0.221719	+	0.975111i	$0.428833\pi$
$450$		0			0
$451$	1.07028			0.0503977
$452$	−25.3084	−	2.27243i	−1.19041	−	0.106886i
$453$		0			0
$454$	−10.6177	−	11.6138i	−0.498313	−	0.545061i
$455$	−7.02146	+	23.2762i	−0.329171	+	1.09120i
$456$		0			0
$457$	−9.99072	−	9.99072i	−0.467346	−	0.467346i	0.433708	−	0.901054i	$-0.357205\pi$
$457$	−9.99072	−	9.99072i	−0.467346	−	0.467346i	−0.901054	+	0.433708i	$0.857205\pi$
$458$	4.91949	+	5.38100i	0.229873	+	0.251438i
$459$		0			0
$460$	−7.04807	+	5.88666i	−0.328618	+	0.274467i
$461$	−9.80788	+	9.80788i	−0.456798	+	0.456798i	−0.897603	−	0.440805i	$-0.854693\pi$
$461$	−9.80788	+	9.80788i	−0.456798	+	0.456798i	0.440805	+	0.897603i	$0.354693\pi$
$462$		0			0
$463$	16.5192	+	16.5192i	0.767714	+	0.767714i	0.977704	−	0.209990i	$-0.0673431\pi$
$463$	16.5192	+	16.5192i	0.767714	+	0.767714i	−0.209990	+	0.977704i	$0.567343\pi$
$464$	−3.11399	+	17.2007i	−0.144563	+	0.798521i
$465$		0			0
$466$	0.209867	−	4.68403i	0.00972188	−	0.216984i
$467$		−	13.7056i		−	0.634220i	−0.948389	−	0.317110i	$-0.897288\pi$
$467$		−	13.7056i		−	0.634220i	0.948389	−	0.317110i	$-0.102712\pi$
$468$		0			0
$469$			33.9745i			1.56880i
$470$	24.3181	+	1.08957i	1.12171	+	0.0502580i
$471$		0			0
$472$	−12.6108	+	9.60818i	−0.580460	+	0.442252i
$473$	−0.705110	−	0.705110i	−0.0324210	−	0.0324210i
$474$		0			0
$475$	0.568819	−	0.568819i	0.0260992	−	0.0260992i
$476$	−32.4538	+	27.1059i	−1.48752	+	1.24240i
$477$		0			0
$478$	−11.0543	+	10.1062i	−0.505612	+	0.462248i
$479$	7.17788	+	7.17788i	0.327966	+	0.327966i	0.851813	−	0.523847i	$-0.175504\pi$
$479$	7.17788	+	7.17788i	0.327966	+	0.327966i	−0.523847	+	0.851813i	$0.675504\pi$
$480$		0			0
$481$	28.9076	−	15.5090i	1.31807	−	0.707148i
$482$	13.3255	−	12.1826i	0.606961	−	0.554904i
$483$		0			0
$484$	−1.96583	+	21.8938i	−0.0893561	+	0.995171i
$485$	28.3853			1.28891
$486$		0			0
$487$	−0.384275	+	0.384275i	−0.0174132	+	0.0174132i	−0.715760	−	0.698347i	$-0.753919\pi$
$487$	−0.384275	+	0.384275i	−0.0174132	+	0.0174132i	0.698347	+	0.715760i	$0.253919\pi$
$488$	0.734997	−	5.43886i	0.0332717	−	0.246206i
$489$		0			0
$490$	−3.64143	−	3.98304i	−0.164503	−	0.179935i
$491$		−	2.72036i		−	0.122768i	−0.998114	−	0.0613840i	$-0.980449\pi$
$491$		−	2.72036i		−	0.122768i	0.998114	−	0.0613840i	$-0.0195514\pi$
$492$		0			0
$493$	−31.3856			−1.41354
$494$	14.9890	−	7.19702i	0.674385	−	0.323809i
$495$		0			0
$496$	−9.67643	+	6.70988i	−0.434485	+	0.301282i
$497$	−0.0345381			−0.00154924
$498$		0			0
$499$	29.4023	+	29.4023i	1.31623	+	1.31623i	0.916736	+	0.399493i	$0.130814\pi$
$499$	29.4023	+	29.4023i	1.31623	+	1.31623i	0.399493	+	0.916736i	$0.369186\pi$
$500$	13.9589	+	16.7129i	0.624262	+	0.747425i
$501$		0			0
$502$	−1.17096	+	26.1348i	−0.0522626	+	1.16645i
$503$		−	8.72354i		−	0.388963i	−0.980906	−	0.194482i	$-0.937698\pi$
$503$		−	8.72354i		−	0.388963i	0.980906	−	0.194482i	$-0.0623025\pi$
$504$		0			0
$505$	17.1172	−	17.1172i	0.761706	−	0.761706i
$506$	0.199335	−	0.182239i	0.00886151	−	0.00810149i
$507$		0			0
$508$	−36.9465	−	3.31741i	−1.63924	−	0.147186i
$509$	−29.8098	+	29.8098i	−1.32130	+	1.32130i	−0.408572	+	0.912726i	$0.633973\pi$
$509$	−29.8098	+	29.8098i	−1.32130	+	1.32130i	−0.912726	+	0.408572i	$0.866027\pi$
$510$		0			0
$511$	1.74561			0.0772211
$512$	−20.8149	−	8.87345i	−0.919899	−	0.392155i
$513$		0			0
$514$	1.11999	−	24.9971i	0.0494004	−	1.10257i
$515$	5.70495	−	5.70495i	0.251390	−	0.251390i
$516$		0			0
$517$	−0.715943			−0.0314871
$518$	−1.69544	+	37.8407i	−0.0744933	+	1.66262i
$519$		0			0
$520$	−8.18724	−	21.8775i	−0.359034	−	0.959392i
$521$	−23.2436			−1.01832			−0.509161	−	0.860671i	$-0.670044\pi$
$521$	−23.2436			−1.01832			−0.509161	+	0.860671i	$0.670044\pi$
$522$		0			0
$523$	15.0188			0.656728			0.328364	−	0.944551i	$-0.393503\pi$
$523$	15.0188			0.656728			0.328364	+	0.944551i	$0.393503\pi$
$524$	10.3594	+	0.930164i	0.452551	+	0.0406344i
$525$		0			0
$526$	1.15437	−	25.7646i	0.0503331	−	1.12339i
$527$	−14.9498	−	14.9498i	−0.651225	−	0.651225i
$528$		0			0
$529$	−18.9818			−0.825298
$530$	−3.08448	−	3.37385i	−0.133981	−	0.146551i
$531$		0			0
$532$	−1.71694	+	19.1218i	−0.0744389	+	0.829037i
$533$	−35.6920	+	19.1488i	−1.54599	+	0.829425i
$534$		0			0
$535$	−19.1630	+	19.1630i	−0.828489	+	0.828489i
$536$	−19.7829	−	25.9652i	−0.854492	−	1.12153i
$537$		0			0
$538$	−0.423069	+	9.44252i	−0.0182398	+	0.407096i
$539$	0.112235	+	0.112235i	0.00483429	+	0.00483429i
$540$		0			0
$541$	−7.84233	−	7.84233i	−0.337168	−	0.337168i	0.518132	−	0.855300i	$-0.326627\pi$
$541$	−7.84233	−	7.84233i	−0.337168	−	0.337168i	−0.855300	+	0.518132i	$0.826627\pi$
$542$	7.62655	+	8.34201i	0.327588	+	0.358320i
$543$		0			0
$544$	9.01958	−	39.6134i	0.386712	−	1.69841i
$545$		−	42.0804i		−	1.80253i
$546$		0			0
$547$	−24.3317			−1.04035			−0.520175	−	0.854060i	$-0.674133\pi$
$547$	−24.3317			−1.04035			−0.520175	+	0.854060i	$0.674133\pi$
$548$	32.6248	−	27.2488i	1.39366	−	1.16401i
$549$		0			0
$550$	0.0224275	+	0.0245315i	0.000956313	+	0.00104603i
$551$	−10.0764	+	10.0764i	−0.429271	+	0.429271i
$552$		0			0
$553$	17.6240	−	17.6240i	0.749450	−	0.749450i
$554$	34.4119	+	1.54182i	1.46202	+	0.0655055i
$555$		0			0
$556$	12.1997	+	1.09541i	0.517384	+	0.0464557i
$557$	−14.8145	−	14.8145i	−0.627710	−	0.627710i	0.319781	−	0.947491i	$-0.396391\pi$
$557$	−14.8145	−	14.8145i	−0.627710	−	0.627710i	−0.947491	+	0.319781i	$0.896391\pi$
$558$		0			0
$559$	36.1295	+	10.8988i	1.52811	+	0.460969i
$560$	26.5405	+	4.80486i	1.12154	+	0.203042i
$561$		0			0
$562$	−10.6238	+	9.71262i	−0.448137	+	0.409702i
$563$		−	35.1602i		−	1.48183i	−0.671601	−	0.740913i	$-0.734393\pi$
$563$		−	35.1602i		−	1.48183i	0.671601	−	0.740913i	$-0.265607\pi$
$564$		0			0
$565$	−20.5781	+	20.5781i	−0.865729	+	0.865729i
$566$	−0.886534	+	19.7866i	−0.0372638	+	0.831694i
$567$		0			0
$568$	0.0263960	−	0.0201111i	0.00110755	−	0.000843843i
$569$			18.2323i			0.764337i	0.924093	+	0.382168i	$0.124823\pi$
$569$			18.2323i			0.764337i	−0.924093	+	0.382168i	$0.875177\pi$
$570$		0			0
$571$			33.5099i			1.40235i	0.712990	+	0.701174i	$0.247340\pi$
$571$			33.5099i			1.40235i	−0.712990	+	0.701174i	$0.752660\pi$
$572$	0.269355	+	0.632020i	0.0112623	+	0.0264261i
$573$		0			0
$574$	2.09334	−	46.7215i	0.0873745	−	1.95012i
$575$			0.494502i			0.0206222i
$576$		0			0
$577$	−4.19353	−	4.19353i	−0.174579	−	0.174579i	0.614409	−	0.788988i	$-0.289395\pi$
$577$	−4.19353	−	4.19353i	−0.174579	−	0.174579i	−0.788988	+	0.614409i	$0.789395\pi$
$578$	48.8550	+	2.18893i	2.03210	+	0.0910477i
$579$		0			0
$580$	12.8335	+	15.3654i	0.532881	+	0.638015i
$581$			13.9546i			0.578936i
$582$		0			0
$583$	0.0950688	+	0.0950688i	0.00393735	+	0.00393735i
$584$	−1.33409	+	1.01645i	−0.0552052	+	0.0420608i
$585$		0			0
$586$	14.0825	+	15.4037i	0.581744	+	0.636319i
$587$	−13.2081	−	13.2081i	−0.545157	−	0.545157i	0.379879	−	0.925036i	$-0.375966\pi$
$587$	−13.2081	−	13.2081i	−0.545157	−	0.545157i	−0.925036	+	0.379879i	$0.875966\pi$
$588$		0			0
$589$	−9.59938			−0.395536
$590$	−0.812718	+	18.1391i	−0.0334591	+	0.746776i
$591$		0			0
$592$	−20.7384	−	29.9073i	−0.852344	−	1.22918i
$593$	0.911200	−	0.911200i	0.0374185	−	0.0374185i	−0.688150	−	0.725568i	$-0.741577\pi$
$593$	0.911200	−	0.911200i	0.0374185	−	0.0374185i	0.725568	+	0.688150i	$0.241577\pi$
$594$		0			0
$595$			48.4277i			1.98534i
$596$	28.7683	−	24.0277i	1.17839	−	0.984214i
$597$		0			0
$598$	−3.38696	+	9.64368i	−0.138503	+	0.394359i
$599$			25.5885i			1.04552i	0.852481	+	0.522758i	$0.175097\pi$
$599$			25.5885i			1.04552i	−0.852481	+	0.522758i	$0.824903\pi$
$600$		0			0
$601$	9.95824			0.406205			0.203103	−	0.979157i	$-0.434897\pi$
$601$	9.95824			0.406205			0.203103	+	0.979157i	$0.434897\pi$
$602$	−32.1596	+	29.4014i	−1.31073	+	1.19831i
$603$		0			0
$604$	4.73373	+	5.66767i	0.192613	+	0.230614i
$605$	17.8017	+	17.8017i	0.723743	+	0.723743i
$606$		0			0
$607$		−	41.0894i		−	1.66777i	−0.551941	−	0.833883i	$-0.686113\pi$
$607$		−	41.0894i		−	1.66777i	0.551941	−	0.833883i	$-0.313887\pi$
$608$	−9.82223	−	15.6138i	−0.398344	−	0.633222i
$609$		0			0
$610$	−4.24123	−	4.63912i	−0.171723	−	0.187832i
$611$	23.8754	−	12.8092i	0.965894	−	0.518203i
$612$		0			0
$613$	−7.07976	+	7.07976i	−0.285949	+	0.285949i	−0.835476	−	0.549527i	$-0.814808\pi$
$613$	−7.07976	+	7.07976i	−0.285949	+	0.285949i	0.549527	+	0.835476i	$0.314808\pi$
$614$	−14.0170	+	12.8148i	−0.565679	+	0.517163i
$615$		0			0
$616$	−0.786130	−	0.106236i	−0.0316741	−	0.00428037i
$617$	−2.05439	−	2.05439i	−0.0827067	−	0.0827067i	0.664543	−	0.747250i	$-0.268626\pi$
$617$	−2.05439	−	2.05439i	−0.0827067	−	0.0827067i	−0.747250	+	0.664543i	$0.768626\pi$
$618$		0			0
$619$	−16.6627	+	16.6627i	−0.669730	+	0.669730i	−0.957653	−	0.287923i	$-0.907035\pi$
$619$	−16.6627	+	16.6627i	−0.669730	+	0.669730i	0.287923	+	0.957653i	$0.407035\pi$
$620$	−1.20605	+	13.4319i	−0.0484360	+	0.539439i
$621$		0			0
$622$	−27.3399	−	1.22495i	−1.09623	−	0.0491162i
$623$	−7.92838			−0.317644
$624$		0			0
$625$	26.1726			1.04690
$626$	−14.2975	−	0.640595i	−0.571443	−	0.0256033i
$627$		0			0
$628$	0.243823	−	2.71549i	0.00972958	−	0.108360i
$629$	46.2059	−	46.2059i	1.84235	−	1.84235i
$630$		0			0
$631$	32.6063	+	32.6063i	1.29804	+	1.29804i	0.929688	+	0.368349i	$0.120077\pi$
$631$	32.6063	+	32.6063i	1.29804	+	1.29804i	0.368349	+	0.929688i	$0.379923\pi$
$632$	−3.20703	+	23.7316i	−0.127569	+	0.943991i
$633$		0			0
$634$	26.7893	−	24.4917i	1.06394	−	0.972690i
$635$	−30.0410	+	30.0410i	−1.19214	+	1.19214i
$636$		0			0
$637$	−5.75085	−	1.73479i	−0.227857	−	0.0687350i
$638$	−0.397297	−	0.434568i	−0.0157291	−	0.0172047i
$639$		0			0
$640$	−23.0816	+	11.7821i	−0.912380	+	0.465727i
$641$			2.93313i			0.115852i	0.998321	+	0.0579259i	$0.0184487\pi$
$641$			2.93313i			0.115852i	−0.998321	+	0.0579259i	$0.981551\pi$
$642$		0			0
$643$	19.2248	+	19.2248i	0.758153	+	0.758153i	0.975986	−	0.217833i	$-0.0698989\pi$
$643$	19.2248	+	19.2248i	0.758153	+	0.758153i	−0.217833	+	0.975986i	$0.569899\pi$
$644$	−7.56546	−	9.05808i	−0.298121	−	0.356939i
$645$		0			0
$646$	24.4442	−	22.3477i	0.961745	−	0.879259i
$647$	−45.3264			−1.78197			−0.890983	−	0.454037i	$-0.849983\pi$
$647$	−45.3264			−1.78197			−0.890983	+	0.454037i	$0.849983\pi$
$648$		0			0
$649$		−	0.534029i		−	0.0209625i
$650$	−1.18682	−	0.416823i	−0.0465508	−	0.0163491i
$651$		0			0
$652$	29.7978	−	24.8876i	1.16697	−	0.974673i
$653$		−	2.67450i		−	0.104661i	−0.998630	−	0.0523307i	$-0.983335\pi$
$653$		−	2.67450i		−	0.104661i	0.998630	−	0.0523307i	$-0.0166650\pi$
$654$		0			0
$655$	8.42316	−	8.42316i	0.329120	−	0.329120i
$656$	25.6055	+	36.9262i	0.999728	+	1.44173i
$657$		0			0
$658$	−1.40030	+	31.2534i	−0.0545893	+	1.21838i
$659$	−37.5991			−1.46465			−0.732326	−	0.680954i	$-0.761565\pi$
$659$	−37.5991			−1.46465			−0.732326	+	0.680954i	$0.761565\pi$
$660$		0			0
$661$	−29.7860	−	29.7860i	−1.15854	−	1.15854i	−0.984789	−	0.173752i	$-0.944411\pi$
$661$	−29.7860	−	29.7860i	−1.15854	−	1.15854i	−0.173752	−	0.984789i	$-0.555589\pi$
$662$	30.4954	+	33.3562i	1.18524	+	1.29643i
$663$		0			0
$664$	−8.12563	−	10.6649i	−0.315335	−	0.413880i
$665$	15.5479	+	15.5479i	0.602921	+	0.602921i
$666$		0			0
$667$		−	8.75994i		−	0.339186i
$668$	5.72044	+	6.84905i	0.221331	+	0.264998i
$669$		0			0
$670$	−37.3479	−	1.67336i	−1.44287	−	0.0646475i
$671$	0.130722	+	0.130722i	0.00504646	+	0.00504646i
$672$		0			0
$673$		−	26.8225i		−	1.03393i	−0.856006	−	0.516965i	$-0.827062\pi$
$673$		−	26.8225i		−	1.03393i	0.856006	−	0.516965i	$-0.172938\pi$
$674$	0.548110	−	12.2333i	0.0211124	−	0.471210i
$675$		0			0
$676$	−20.2902	−	16.2576i	−0.780391	−	0.625292i
$677$		−	27.6382i		−	1.06222i	−0.847302	−	0.531112i	$-0.821774\pi$
$677$		−	27.6382i		−	1.06222i	0.847302	−	0.531112i	$-0.178226\pi$
$678$		0			0
$679$			36.4804i			1.39999i
$680$	−28.1989	−	37.0113i	−1.08138	−	1.41932i
$681$		0			0
$682$	0.0177534	−	0.396240i	0.000679814	−	0.0151728i
$683$	0.401585	−	0.401585i	0.0153662	−	0.0153662i	−0.699382	−	0.714748i	$-0.746541\pi$
$683$	0.401585	−	0.401585i	0.0153662	−	0.0153662i	0.714748	+	0.699382i	$0.246541\pi$
$684$		0			0
$685$		−	48.6829i		−	1.86008i
$686$	−16.3894	+	14.9837i	−0.625750	+	0.572081i
$687$		0			0
$688$	7.45814	−	41.1964i	0.284339	−	1.57060i
$689$	−4.87127	−	1.46946i	−0.185581	−	0.0559820i
$690$		0			0
$691$	−25.8040	−	25.8040i	−0.981632	−	0.981632i	0.0182023	−	0.999834i	$-0.494206\pi$
$691$	−25.8040	−	25.8040i	−0.981632	−	0.981632i	−0.999834	+	0.0182023i	$0.994206\pi$
$692$	−5.02436	−	0.451136i	−0.190998	−	0.0171496i
$693$		0			0
$694$	−23.5422	−	1.05480i	−0.893650	−	0.0400397i
$695$	9.91955	−	9.91955i	0.376270	−	0.376270i
$696$		0			0
$697$	−57.0500	+	57.0500i	−2.16092	+	2.16092i
$698$	−5.38452	−	5.88965i	−0.203807	−	0.222927i
$699$		0			0
$700$	1.11475	−	0.931058i	0.0421336	−	0.0351907i
$701$	42.4434			1.60307			0.801533	−	0.597951i	$-0.204018\pi$
$701$	42.4434			1.60307			0.801533	+	0.597951i	$0.204018\pi$
$702$		0			0
$703$		−	29.6691i		−	1.11899i
$704$	0.662666	−	0.376563i	0.0249752	−	0.0141922i
$705$		0			0
$706$	−8.22598	−	8.99768i	−0.309589	−	0.338632i
$707$	21.9988	+	21.9988i	0.827350	+	0.827350i
$708$		0			0
$709$	−21.9848	−	21.9848i	−0.825657	−	0.825657i	0.161256	−	0.986913i	$-0.448446\pi$
$709$	−21.9848	−	21.9848i	−0.825657	−	0.825657i	−0.986913	+	0.161256i	$0.948446\pi$
$710$	0.00170112	−	0.0379674i	6.38419e−5	−	0.00142489i
$711$		0			0
$712$	6.05932	−	4.61660i	0.227083	−	0.173014i
$713$	4.17261	−	4.17261i	0.156265	−	0.156265i
$714$		0			0
$715$	0.753308	+	0.227242i	0.0281721	+	0.00849837i
$716$	2.17741	−	24.2502i	0.0813737	−	0.906271i
$717$		0			0
$718$	27.9104	+	30.5287i	1.04161	+	1.13932i
$719$	−4.55035			−0.169699			−0.0848497	−	0.996394i	$-0.527041\pi$
$719$	−4.55035			−0.169699			−0.0848497	+	0.996394i	$0.527041\pi$
$720$		0			0
$721$	7.33193	+	7.33193i	0.273055	+	0.273055i
$722$	−0.529611	+	11.8204i	−0.0197101	+	0.439911i
$723$		0			0
$724$	2.27003	+	0.203825i	0.0843650	+	0.00757510i
$725$	1.07806			0.0400381
$726$		0			0
$727$	35.3567			1.31131			0.655653	−	0.755062i	$-0.272393\pi$
$727$	35.3567			1.31131			0.655653	+	0.755062i	$0.272393\pi$
$728$	28.1167	−	10.5221i	1.04207	−	0.389976i
$729$		0			0
$730$	−0.0859772	+	1.91893i	−0.00318216	+	0.0710229i
$731$	75.1699			2.78026
$732$		0			0
$733$	10.2364	−	10.2364i	0.378089	−	0.378089i	−0.492323	−	0.870412i	$-0.663852\pi$
$733$	10.2364	−	10.2364i	0.378089	−	0.378089i	0.870412	+	0.492323i	$0.163852\pi$
$734$	1.90676	−	42.5572i	0.0703800	−	1.57082i
$735$		0			0
$736$	11.0564	+	2.51743i	0.407543	+	0.0927937i
$737$	1.09955			0.0405023
$738$		0			0
$739$	−15.9995	+	15.9995i	−0.588550	+	0.588550i	−0.937239	−	0.348688i	$-0.886627\pi$
$739$	−15.9995	+	15.9995i	−0.588550	+	0.588550i	0.348688	+	0.937239i	$0.386627\pi$
$740$	−41.5145	−	3.72757i	−1.52610	−	0.137028i
$741$		0			0
$742$	4.33602	−	3.96414i	0.159180	−	0.145528i
$743$	4.22277	−	4.22277i	0.154918	−	0.154918i	−0.625392	−	0.780311i	$-0.715061\pi$
$743$	4.22277	−	4.22277i	0.154918	−	0.154918i	0.780311	+	0.625392i	$0.215061\pi$
$744$		0			0
$745$		−	42.9282i		−	1.57277i
$746$	0.544340	−	12.1492i	0.0199297	−	0.444813i
$747$		0			0
$748$	0.877255	+	1.05033i	0.0320756	+	0.0384039i
$749$	−24.6280	−	24.6280i	−0.899889	−	0.899889i
$750$		0			0
$751$	39.7818			1.45166			0.725828	−	0.687876i	$-0.241457\pi$
$751$	39.7818			1.45166			0.725828	+	0.687876i	$0.241457\pi$
$752$	−17.1283	−	24.7010i	−0.624604	−	0.900752i
$753$		0			0
$754$	21.0241	+	7.38388i	0.765652	+	0.268905i
$755$	8.45732			0.307794
$756$		0			0
$757$			0.790942i			0.0287473i	0.999897	+	0.0143736i	$0.00457543\pi$
$757$			0.790942i			0.0287473i	−0.999897	+	0.0143736i	$0.995425\pi$
$758$	−15.6205	−	17.0859i	−0.567362	−	0.620588i
$759$		0			0
$760$	−20.9359	−	2.82924i	−0.759426	−	0.102627i
$761$	−2.96895	+	2.96895i	−0.107624	+	0.107624i	−0.758868	−	0.651244i	$-0.774247\pi$
$761$	−2.96895	+	2.96895i	−0.107624	+	0.107624i	0.651244	+	0.758868i	$0.274247\pi$
$762$		0			0
$763$	54.0812			1.95787
$764$	4.01190	−	44.6811i	0.145145	−	1.61650i
$765$		0			0
$766$	−2.97412	+	2.71904i	−0.107459	+	0.0982430i
$767$	9.55447	+	17.8089i	0.344992	+	0.643041i
$768$		0			0
$769$	−20.0249	−	20.0249i	−0.722117	−	0.722117i	0.246919	−	0.969036i	$-0.420582\pi$
$769$	−20.0249	−	20.0249i	−0.722117	−	0.722117i	−0.969036	+	0.246919i	$0.920582\pi$
$770$	−0.670535	+	0.613026i	−0.0241644	+	0.0220919i
$771$		0			0
$772$	−7.75796	+	6.47958i	−0.279215	+	0.233205i
$773$	−12.6302	+	12.6302i	−0.454278	+	0.454278i	−0.896772	−	0.442494i	$-0.854094\pi$
$773$	−12.6302	+	12.6302i	−0.454278	+	0.454278i	0.442494	+	0.896772i	$0.354094\pi$
$774$		0			0
$775$	0.513510	+	0.513510i	0.0184458	+	0.0184458i
$776$	−21.2421	−	27.8804i	−0.762547	−	1.00085i
$777$		0			0
$778$	−36.4917	−	1.63500i	−1.30829	−	0.0586175i
$779$			36.6322i			1.31248i
$780$		0			0
$781$			0.00111779i			3.99976e-5i
$782$	−0.911294	+	20.3393i	−0.0325878	+	0.727330i
$783$		0			0
$784$	−1.18714	+	6.55737i	−0.0423978	+	0.234192i
$785$	−2.20795	−	2.20795i	−0.0788051	−	0.0788051i
$786$		0			0
$787$	−26.5637	+	26.5637i	−0.946895	+	0.946895i	−0.998659	−	0.0517643i	$-0.983516\pi$
$787$	−26.5637	+	26.5637i	−0.946895	+	0.946895i	0.0517643	+	0.998659i	$0.483516\pi$
$788$	−4.90858	+	4.09973i	−0.174861	+	0.146047i
$789$		0			0
$790$	18.5059	+	20.2420i	0.658411	+	0.720178i
$791$	−26.4468	−	26.4468i	−0.940339	−	0.940339i
$792$		0			0
$793$	−6.69811	−	2.02054i	−0.237857	−	0.0717516i
$794$	−14.9580	−	16.3613i	−0.530840	−	0.580640i
$795$		0			0
$796$	−52.6631	−	4.72860i	−1.86659	−	0.167601i
$797$	−10.2872			−0.364393			−0.182196	−	0.983262i	$-0.558321\pi$
$797$	−10.2872			−0.364393			−0.182196	+	0.983262i	$0.558321\pi$
$798$		0			0
$799$	38.1624	−	38.1624i	1.35009	−	1.35009i
$800$	−0.309813	+	1.36067i	−0.0109535	+	0.0481071i
$801$		0			0
$802$	−36.9416	+	33.7732i	−1.30445	+	1.19257i
$803$		−	0.0564947i		−	0.00199365i
$804$		0			0
$805$	−13.5165			−0.476395
$806$	6.49722	+	13.5315i	0.228855	+	0.476627i
$807$		0			0
$808$	−29.6224	−	4.00311i	−1.04211	−	0.140829i
$809$	1.64479			0.0578278			0.0289139	−	0.999582i	$-0.490795\pi$
$809$	1.64479			0.0578278			0.0289139	+	0.999582i	$0.490795\pi$
$810$		0			0
$811$	−13.0418	−	13.0418i	−0.457958	−	0.457958i	0.440026	−	0.897985i	$-0.354969\pi$
$811$	−13.0418	−	13.0418i	−0.457958	−	0.457958i	−0.897985	+	0.440026i	$0.854969\pi$
$812$	−19.7475	+	16.4934i	−0.693000	+	0.578805i
$813$		0			0
$814$	1.22467	+	0.0548711i	0.0429248	+	0.00192323i
$815$		−	44.4644i		−	1.55752i
$816$		0			0
$817$	24.1335	−	24.1335i	0.844326	−	0.844326i
$818$	−33.3920	−	36.5246i	−1.16752	−	1.27705i
$819$		0			0
$820$	51.2575	+	4.60239i	1.78999	+	0.160723i
$821$	9.46652	−	9.46652i	0.330384	−	0.330384i	−0.522348	−	0.852732i	$-0.674944\pi$
$821$	9.46652	−	9.46652i	0.330384	−	0.330384i	0.852732	+	0.522348i	$0.174944\pi$
$822$		0			0
$823$	−9.44005			−0.329059			−0.164530	−	0.986372i	$-0.552611\pi$
$823$	−9.44005			−0.329059			−0.164530	+	0.986372i	$0.552611\pi$
$824$	−9.87278	−	1.33419i	−0.343935	−	0.0464786i
$825$		0			0
$826$	−23.3122	−	1.04450i	−0.811134	−	0.0363426i
$827$	−15.1241	+	15.1241i	−0.525916	+	0.525916i	−0.919352	−	0.393436i	$-0.871286\pi$
$827$	−15.1241	+	15.1241i	−0.525916	+	0.525916i	0.393436	+	0.919352i	$0.371286\pi$
$828$		0			0
$829$	30.8994			1.07318			0.536590	−	0.843843i	$-0.319712\pi$
$829$	30.8994			1.07318			0.536590	+	0.843843i	$0.319712\pi$
$830$	−15.3402	−	0.687315i	−0.532468	−	0.0238570i
$831$		0			0
$832$	−15.3615	+	24.4136i	−0.532563	+	0.846390i
$833$	−11.9651			−0.414564
$834$		0			0
$835$	10.2202			0.353684
$836$	0.618858	+	0.0555670i	0.0214036	+	0.00192182i
$837$		0			0
$838$	22.1198	+	0.991071i	0.764116	+	0.0342360i
$839$	39.8024	+	39.8024i	1.37413	+	1.37413i	0.854222	+	0.519909i	$0.174034\pi$
$839$	39.8024	+	39.8024i	1.37413	+	1.37413i	0.519909	+	0.854222i	$0.325966\pi$
$840$		0			0
$841$	9.90253			0.341466
$842$	−7.74110	+	7.07718i	−0.266776	+	0.243896i
$843$		0			0
$844$	−4.55299	−	0.408812i	−0.156720	−	0.0140719i
$845$	−29.1871	+	5.89958i	−1.00407	+	0.202952i
$846$		0			0
$847$	−22.8785	+	22.8785i	−0.786116	+	0.786116i
$848$	−1.00557	+	5.55444i	−0.0345314	+	0.190740i
$849$		0			0
$850$	−2.50309	−	0.112150i	−0.0858553	−	0.00384672i
$851$	12.8964	+	12.8964i	0.442083	+	0.442083i
$852$		0			0
$853$	−5.81918	−	5.81918i	−0.199245	−	0.199245i	0.600431	−	0.799676i	$-0.294996\pi$
$853$	−5.81918	−	5.81918i	−0.199245	−	0.199245i	−0.799676	+	0.600431i	$0.794996\pi$
$854$	5.96213	−	5.45078i	0.204020	−	0.186522i
$855$		0			0
$856$	33.1628	+	4.48155i	1.13348	+	0.153176i
$857$			27.8183i			0.950256i	0.879917	+	0.475128i	$0.157598\pi$
$857$			27.8183i			0.950256i	−0.879917	+	0.475128i	$0.842402\pi$
$858$		0			0
$859$	−10.0327			−0.342311			−0.171155	−	0.985244i	$-0.554750\pi$
$859$	−10.0327			−0.342311			−0.171155	+	0.985244i	$0.554750\pi$
$860$	−30.7367	−	36.8009i	−1.04811	−	1.25490i
$861$		0			0
$862$	−25.0392	+	22.8916i	−0.852838	+	0.779693i
$863$	32.0055	−	32.0055i	1.08948	−	1.08948i	0.0938995	−	0.995582i	$-0.470067\pi$
$863$	32.0055	−	32.0055i	1.08948	−	1.08948i	0.995582	−	0.0938995i	$-0.0299332\pi$
$864$		0			0
$865$	−4.08529	+	4.08529i	−0.138904	+	0.138904i
$866$	−1.37143	+	30.6092i	−0.0466032	+	1.04014i
$867$		0			0
$868$	−17.2625	−	1.55000i	−0.585929	−	0.0526103i
$869$	−0.570383	−	0.570383i	−0.0193489	−	0.0193489i
$870$		0			0
$871$	−36.6678	+	19.6723i	−1.24244	+	0.666572i
$872$	−41.3319	+	31.4908i	−1.39968	+	1.06641i
$873$		0			0
$874$	6.23741	+	6.82256i	0.210984	+	0.230776i
$875$			32.0515i			1.08354i
$876$		0			0
$877$	−20.8160	+	20.8160i	−0.702906	+	0.702906i	−0.965033	−	0.262127i	$-0.915576\pi$
$877$	−20.8160	+	20.8160i	−0.702906	+	0.702906i	0.262127	+	0.965033i	$0.415576\pi$
$878$	38.1389	+	1.70880i	1.28713	+	0.0576692i
$879$		0			0
$880$	0.155504	−	0.858954i	0.00524204	−	0.0289553i
$881$		−	13.7757i		−	0.464116i	−0.972702	−	0.232058i	$-0.925454\pi$
$881$		−	13.7757i		−	0.464116i	0.972702	−	0.232058i	$-0.0745459\pi$
$882$		0			0
$883$		−	38.8765i		−	1.30830i	−0.756366	−	0.654149i	$-0.773027\pi$
$883$		−	38.8765i		−	1.30830i	0.756366	−	0.654149i	$-0.226973\pi$
$884$	−48.0466	−	19.3314i	−1.61598	−	0.650184i
$885$		0			0
$886$	−5.21874	−	0.233824i	−0.175327	−	0.00785547i
$887$			51.7991i			1.73924i	0.493718	+	0.869622i	$0.335637\pi$
$887$			51.7991i			1.73924i	−0.493718	+	0.869622i	$0.664363\pi$
$888$		0			0
$889$	−38.6084	−	38.6084i	−1.29488	−	1.29488i
$890$	0.390500	−	8.71560i	0.0130896	−	0.292148i
$891$		0			0
$892$	14.4547	−	12.0728i	0.483978	−	0.404227i
$893$		−	24.5043i		−	0.820005i
$894$		0			0
$895$	−19.7177	−	19.7177i	−0.659090	−	0.659090i
$896$	−15.1422	−	29.6642i	−0.505864	−	0.991010i
$897$		0			0
$898$	23.5645	−	21.5435i	0.786358	−	0.718914i
$899$	−9.09666	−	9.09666i	−0.303391	−	0.303391i
$900$		0			0
$901$	−10.1350			−0.337647
$902$	−1.51209	−	0.0677488i	−0.0503472	−	0.00225579i
$903$		0			0
$904$	35.6118	+	4.81250i	1.18443	+	0.160061i
$905$	1.84575	−	1.84575i	0.0613548	−	0.0613548i
$906$		0			0
$907$			53.4908i			1.77613i	0.459714	+	0.888067i	$0.347952\pi$
$907$			53.4908i			1.77613i	−0.459714	+	0.888067i	$0.652048\pi$
$908$	14.2655	+	17.0800i	0.473416	+	0.566819i
$909$		0			0
$910$	11.3933	−	32.4400i	0.377683	−	1.07538i
$911$		−	8.34775i		−	0.276573i	−0.990392	−	0.138287i	$-0.955840\pi$
$911$		−	8.34775i		−	0.276573i	0.990392	−	0.138287i	$-0.0441595\pi$
$912$		0			0
$913$	0.451627			0.0149467
$914$	13.4824	+	14.7473i	0.445959	+	0.487796i
$915$		0			0
$916$	−6.60962	−	7.91366i	−0.218388	−	0.261475i
$917$	10.8253	+	10.8253i	0.357484	+	0.357484i
$918$		0			0
$919$		−	0.682347i		−	0.0225085i	−0.999937	−	0.0112543i	$-0.996418\pi$
$919$		−	0.682347i		−	0.0225085i	0.999937	−	0.0112543i	$-0.00358242\pi$
$920$	10.3301	−	7.87051i	0.340574	−	0.259483i
$921$		0			0
$922$	14.4774	−	13.2357i	0.476787	−	0.435894i
$923$	−0.0199987	−	0.0372761i	−0.000658265	−	0.00122696i
$924$		0			0
$925$	−1.58712	+	1.58712i	−0.0521842	+	0.0521842i
$926$	−22.2926	−	24.3840i	−0.732581	−	0.801307i
$927$		0			0
$928$	5.48823	−	24.1039i	0.180160	−	0.791250i
$929$	−11.6044	−	11.6044i	−0.380728	−	0.380728i	0.490636	−	0.871364i	$-0.336764\pi$
$929$	−11.6044	−	11.6044i	−0.380728	−	0.380728i	−0.871364	+	0.490636i	$0.836764\pi$
$930$		0			0
$931$	−3.84142	+	3.84142i	−0.125897	+	0.125897i
$932$	−0.592997	+	6.60430i	−0.0194243	+	0.216331i
$933$		0			0
$934$	−0.867563	+	19.3632i	−0.0283875	+	0.633584i
$935$	1.56731			0.0512566
$936$		0			0
$937$	−5.73855			−0.187470			−0.0937352	−	0.995597i	$-0.529881\pi$
$937$	−5.73855			−0.187470			−0.0937352	+	0.995597i	$0.529881\pi$
$938$	2.15058	−	47.9990i	0.0702189	−	1.56722i
$939$		0			0
$940$	−34.2876	−	3.07867i	−1.11834	−	0.100415i
$941$	−0.617212	+	0.617212i	−0.0201205	+	0.0201205i	−0.717095	−	0.696975i	$-0.754529\pi$
$941$	−0.617212	+	0.617212i	−0.0201205	+	0.0201205i	0.696975	+	0.717095i	$0.254529\pi$
$942$		0			0
$943$	−15.9231	−	15.9231i	−0.518526	−	0.518526i
$944$	18.4247	−	12.7761i	0.599673	−	0.415828i
$945$		0			0
$946$	0.951544	+	1.04081i	0.0309374	+	0.0338397i
$947$	2.57671	−	2.57671i	0.0837319	−	0.0837319i	−0.664000	−	0.747732i	$-0.731143\pi$
$947$	2.57671	−	2.57671i	0.0837319	−	0.0837319i	0.747732	+	0.664000i	$0.231143\pi$
$948$		0			0
$949$	1.01076	+	1.88399i	0.0328108	+	0.0611570i
$950$	−0.839631	+	0.767619i	−0.0272412	+	0.0249048i
$951$		0			0
$952$	47.5664	−	36.2408i	1.54164	−	1.17457i
$953$			44.1686i			1.43076i	0.698736	+	0.715380i	$0.253746\pi$
$953$			44.1686i			1.43076i	−0.698736	+	0.715380i	$0.746254\pi$
$954$		0			0
$955$	−36.3300	−	36.3300i	−1.17561	−	1.17561i
$956$	16.2572	−	13.5783i	0.525796	−	0.439153i
$957$		0			0
$958$	−9.68653	−	10.5952i	−0.312958	−	0.342317i
$959$	62.5667			2.02038
$960$		0			0
$961$			22.3340i			0.720452i
$962$	−41.8223	+	20.0812i	−1.34840	+	0.647442i
$963$		0			0
$964$	−19.5974	+	16.3681i	−0.631190	+	0.527180i
$965$			11.5765i			0.372660i
$966$		0			0
$967$	23.3487	−	23.3487i	0.750844	−	0.750844i	−0.223792	−	0.974637i	$-0.571844\pi$
$967$	23.3487	−	23.3487i	0.750844	−	0.750844i	0.974637	+	0.223792i	$0.0718438\pi$
$968$	4.16319	−	30.8070i	0.133810	−	0.990174i
$969$		0			0
$970$	−40.1026	−	1.79679i	−1.28762	−	0.0576913i
$971$	−15.8294			−0.507990			−0.253995	−	0.967205i	$-0.581745\pi$
$971$	−15.8294			−0.507990			−0.253995	+	0.967205i	$0.581745\pi$
$972$		0			0
$973$	12.7485	+	12.7485i	0.408697	+	0.408697i
$974$	0.567227	−	0.518578i	0.0181751	−	0.0166163i
$975$		0			0
$976$	−1.38268	+	7.63748i	−0.0442585	+	0.244470i
$977$	19.1168	+	19.1168i	0.611602	+	0.611602i	0.943363	−	0.331761i	$-0.107643\pi$
$977$	19.1168	+	19.1168i	0.611602	+	0.611602i	−0.331761	+	0.943363i	$0.607643\pi$
$978$		0			0
$979$			0.256593i			0.00820076i
$980$	4.89247	+	5.85773i	0.156284	+	0.187118i
$981$		0			0
$982$	−0.172198	+	3.84331i	−0.00549507	+	0.122645i
$983$	−20.0123	−	20.0123i	−0.638293	−	0.638293i	0.311841	−	0.950134i	$-0.399054\pi$
$983$	−20.0123	−	20.0123i	−0.638293	−	0.638293i	−0.950134	+	0.311841i	$0.899054\pi$
$984$		0			0
$985$			7.32462i			0.233382i
$986$	44.3414	+	1.98670i	1.41212	+	0.0632696i
$987$		0			0
$988$	−21.6319	+	9.21912i	−0.688203	+	0.293299i
$989$			20.9805i			0.667140i
$990$		0			0
$991$			36.3170i			1.15365i	0.816868	+	0.576824i	$0.195708\pi$
$991$			36.3170i			1.15365i	−0.816868	+	0.576824i	$0.804292\pi$
$992$	14.0956	−	8.86717i	0.447535	−	0.281533i
$993$		0			0
$994$	0.0487953	+	0.00218626i	0.00154769	+	6.93438e-5i
$995$	−42.8201	+	42.8201i	−1.35749	+	1.35749i
$996$		0			0
$997$		−	27.1788i		−	0.860762i	−0.902647	−	0.430381i	$-0.858379\pi$
$997$		−	27.1788i		−	0.860762i	0.902647	−	0.430381i	$-0.141621\pi$
$998$	−39.6783	−	43.4007i	−1.25600	−	1.37382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.j.307.1		24
3.2	odd	2		312.2.t.e.307.12	yes	24
8.3	odd	2	inner	936.2.w.j.307.6		24
12.11	even	2		1248.2.bb.f.463.4		24
13.5	odd	4	inner	936.2.w.j.811.6		24
24.5	odd	2		1248.2.bb.f.463.9		24
24.11	even	2		312.2.t.e.307.7	yes	24
39.5	even	4		312.2.t.e.187.7	✓	24
104.83	even	4	inner	936.2.w.j.811.1		24
156.83	odd	4		1248.2.bb.f.655.9		24
312.5	even	4		1248.2.bb.f.655.4		24
312.83	odd	4		312.2.t.e.187.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.7	✓	24	39.5	even	4
312.2.t.e.187.12	yes	24	312.83	odd	4
312.2.t.e.307.7	yes	24	24.11	even	2
312.2.t.e.307.12	yes	24	3.2	odd	2
936.2.w.j.307.1		24	1.1	even	1	trivial
936.2.w.j.307.6		24	8.3	odd	2	inner
936.2.w.j.811.1		24	104.83	even	4	inner
936.2.w.j.811.6		24	13.5	odd	4	inner
1248.2.bb.f.463.4		24	12.11	even	2
1248.2.bb.f.463.9		24	24.5	odd	2
1248.2.bb.f.655.4		24	312.5	even	4
1248.2.bb.f.655.9		24	156.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41280 - 0.0632999i) q^{2} +(1.99199 + 0.178860i) q^{4} +(1.61967 - 1.61967i) q^{5} +(2.08158 + 2.08158i) q^{7} +(-2.80295 - 0.378785i) q^{8} +(-2.39080 + 2.18574i) q^{10} +(0.0673682 - 0.0673682i) q^{11} +(-1.04130 + 3.45191i) q^{13} +(-2.80909 - 3.07262i) q^{14} +(3.93602 + 0.712572i) q^{16} +7.18195i q^{17} +(2.30579 + 2.30579i) q^{19} +(3.51606 - 2.93668i) q^{20} +(-0.0994420 + 0.0909132i) q^{22} -2.00453 q^{23} -0.246692i q^{25} +(1.68965 - 4.81093i) q^{26} +(3.77418 + 4.51880i) q^{28} +4.37007i q^{29} +(-2.08158 + 2.08158i) q^{31} +(-5.51569 - 1.25587i) q^{32} +(0.454617 - 10.1466i) q^{34} +6.74298 q^{35} +(-6.43362 - 6.43362i) q^{37} +(-3.11165 - 3.40356i) q^{38} +(-5.15337 + 3.92636i) q^{40} +(7.94353 + 7.94353i) q^{41} -10.4665i q^{43} +(0.146246 - 0.122147i) q^{44} +(2.83200 + 0.126887i) q^{46} +(-5.31365 - 5.31365i) q^{47} +1.66599i q^{49} +(-0.0156156 + 0.348525i) q^{50} +(-2.69166 + 6.68991i) q^{52} +1.41118i q^{53} -0.218229i q^{55} +(-5.04610 - 6.62305i) q^{56} +(0.276625 - 6.17401i) q^{58} +(3.96350 - 3.96350i) q^{59} +1.94041i q^{61} +(3.07262 - 2.80909i) q^{62} +(7.71304 + 2.12343i) q^{64} +(3.90441 + 7.27754i) q^{65} +(8.16072 + 8.16072i) q^{67} +(-1.28456 + 14.3063i) q^{68} +(-9.52646 - 0.426830i) q^{70} +(-0.00829610 + 0.00829610i) q^{71} +(0.419298 - 0.419298i) q^{73} +(8.68214 + 9.49664i) q^{74} +(4.18068 + 5.00551i) q^{76} +0.280465 q^{77} -8.46664i q^{79} +(7.52920 - 5.22093i) q^{80} +(-10.7198 - 11.7254i) q^{82} +(3.35193 + 3.35193i) q^{83} +(11.6324 + 11.6324i) q^{85} +(-0.662529 + 14.7870i) q^{86} +(-0.214348 + 0.163312i) q^{88} +(-1.90441 + 1.90441i) q^{89} +(-9.35300 + 5.01789i) q^{91} +(-3.99300 - 0.358530i) q^{92} +(7.17075 + 7.84346i) q^{94} +7.46925 q^{95} +(8.76265 + 8.76265i) q^{97} +(0.105457 - 2.35370i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{8} - 8 q^{11} - 36 q^{14} + 28 q^{16} + 20 q^{19} + 20 q^{20} + 20 q^{22} - 12 q^{26} - 16 q^{28} + 30 q^{32} + 16 q^{34} - 16 q^{35} + 36 q^{40} + 12 q^{41} + 32 q^{44} - 44 q^{46} + 36 q^{50}+ \cdots - 68 q^{98}+O(q^{100}) \) 24 * q + 6 * q^8 - 8 * q^11 - 36 * q^14 + 28 * q^16 + 20 * q^19 + 20 * q^20 + 20 * q^22 - 12 * q^26 - 16 * q^28 + 30 * q^32 + 16 * q^34 - 16 * q^35 + 36 * q^40 + 12 * q^41 + 32 * q^44 - 44 * q^46 + 36 * q^50 + 4 * q^52 + 32 * q^58 + 16 * q^59 + 76 * q^65 + 28 * q^67 - 32 * q^68 - 40 * q^70 - 8 * q^73 + 32 * q^74 - 36 * q^76 + 32 * q^80 + 72 * q^83 - 4 * q^86 - 28 * q^89 - 4 * q^91 - 32 * q^92 + 28 * q^94 + 24 * q^97 - 68 * q^98

Introduction

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