LMFDB - Embedded newform 1248.2.bb.f.655.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1248,2,Mod(463,1248)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1248, 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("1248.463"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.bb (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.96533017226$
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			655.4
Character	$\chi$	$=$	1248.655
Dual form			1248.2.bb.f.463.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-1.61967 - 1.61967i) q^{5} +(-2.08158 + 2.08158i) q^{7} +1.00000 q^{9} +(0.0673682 + 0.0673682i) q^{11} +(-1.04130 - 3.45191i) q^{13} +(-1.61967 - 1.61967i) q^{15} +7.18195i q^{17} +(-2.30579 + 2.30579i) q^{19} +(-2.08158 + 2.08158i) q^{21} -2.00453 q^{23} +0.246692i q^{25} +1.00000 q^{27} +4.37007i q^{29} +(2.08158 + 2.08158i) q^{31} +(0.0673682 + 0.0673682i) q^{33} +6.74298 q^{35} +(-6.43362 + 6.43362i) q^{37} +(-1.04130 - 3.45191i) q^{39} +(-7.94353 + 7.94353i) q^{41} -10.4665i q^{43} +(-1.61967 - 1.61967i) q^{45} +(-5.31365 + 5.31365i) q^{47} -1.66599i q^{49} +7.18195i q^{51} +1.41118i q^{53} -0.218229i q^{55} +(-2.30579 + 2.30579i) q^{57} +(3.96350 + 3.96350i) q^{59} -1.94041i q^{61} +(-2.08158 + 2.08158i) q^{63} +(-3.90441 + 7.27754i) q^{65} +(-8.16072 + 8.16072i) q^{67} -2.00453 q^{69} +(-0.00829610 - 0.00829610i) q^{71} +(0.419298 + 0.419298i) q^{73} +0.246692i q^{75} -0.280465 q^{77} -8.46664i q^{79} +1.00000 q^{81} +(3.35193 - 3.35193i) q^{83} +(11.6324 - 11.6324i) q^{85} +4.37007i q^{87} +(1.90441 + 1.90441i) q^{89} +(9.35300 + 5.01789i) q^{91} +(2.08158 + 2.08158i) q^{93} +7.46925 q^{95} +(8.76265 - 8.76265i) q^{97} +(0.0673682 + 0.0673682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.61967	−	1.61967i	−0.724341	−	0.724341i	0.245146	−	0.969486i	$-0.421164\pi$
$5$	−1.61967	−	1.61967i	−0.724341	−	0.724341i	−0.969486	+	0.245146i	$0.921164\pi$
$6$		0			0
$7$	−2.08158	+	2.08158i	−0.786765	+	0.786765i	−0.980962	−	0.194197i	$-0.937790\pi$
$7$	−2.08158	+	2.08158i	−0.786765	+	0.786765i	0.194197	+	0.980962i	$0.437790\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	0.0673682	+	0.0673682i	0.0203123	+	0.0203123i	0.717190	−	0.696878i	$-0.245428\pi$
$11$	0.0673682	+	0.0673682i	0.0203123	+	0.0203123i	−0.696878	+	0.717190i	$0.745428\pi$
$12$		0			0
$13$	−1.04130	−	3.45191i	−0.288804	−	0.957388i
$13$	−1.04130	−	3.45191i	−0.288804	−	0.957388i
$14$		0			0
$15$	−1.61967	−	1.61967i	−0.418198	−	0.418198i
$16$		0			0
$17$			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	$-0.872031\pi$
$19$	−2.30579	+	2.30579i	−0.528984	+	0.528984i	0.391285	+	0.920269i	$0.372031\pi$
$20$		0			0
$21$	−2.08158	+	2.08158i	−0.454239	+	0.454239i
$22$		0			0
$23$	−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
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$			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	$-0.164839\pi$
$31$	2.08158	+	2.08158i	0.373864	+	0.373864i	−0.495019	+	0.868882i	$0.664839\pi$
$32$		0			0
$33$	0.0673682	+	0.0673682i	0.0117273	+	0.0117273i
$34$		0			0
$35$	6.74298			1.13977
$36$		0			0
$37$	−6.43362	+	6.43362i	−1.05768	+	1.05768i	−0.0594489	+	0.998231i	$0.518934\pi$
$37$	−6.43362	+	6.43362i	−1.05768	+	1.05768i	−0.998231	+	0.0594489i	$0.981066\pi$
$38$		0			0
$39$	−1.04130	−	3.45191i	−0.166741	−	0.552748i
$40$		0			0
$41$	−7.94353	+	7.94353i	−1.24057	+	1.24057i	−0.280806	+	0.959764i	$0.590602\pi$
$41$	−7.94353	+	7.94353i	−1.24057	+	1.24057i	−0.959764	+	0.280806i	$0.909398\pi$
$42$		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			0
$45$	−1.61967	−	1.61967i	−0.241447	−	0.241447i
$46$		0			0
$47$	−5.31365	+	5.31365i	−0.775076	+	0.775076i	−0.978989	−	0.203913i	$-0.934634\pi$
$47$	−5.31365	+	5.31365i	−0.775076	+	0.775076i	0.203913	+	0.978989i	$0.434634\pi$
$48$		0			0
$49$		−	1.66599i		−	0.237998i
$50$		0			0
$51$			7.18195i			1.00567i
$52$		0			0
$53$			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
$56$		0			0
$57$	−2.30579	+	2.30579i	−0.305409	+	0.305409i
$58$		0			0
$59$	3.96350	+	3.96350i	0.516004	+	0.516004i	0.916360	−	0.400356i	$-0.131113\pi$
$59$	3.96350	+	3.96350i	0.516004	+	0.516004i	−0.400356	+	0.916360i	$0.631113\pi$
$60$		0			0
$61$		−	1.94041i		−	0.248444i	−0.992254	−	0.124222i	$-0.960357\pi$
$61$		−	1.94041i		−	0.248444i	0.992254	−	0.124222i	$-0.0396434\pi$
$62$		0			0
$63$	−2.08158	+	2.08158i	−0.262255	+	0.262255i
$64$		0			0
$65$	−3.90441	+	7.27754i	−0.484282	+	0.902668i
$66$		0			0
$67$	−8.16072	+	8.16072i	−0.996991	+	0.996991i	−0.999995	−	0.00300457i	$-0.999044\pi$
$67$	−8.16072	+	8.16072i	−0.996991	+	0.996991i	0.00300457	+	0.999995i	$0.499044\pi$
$68$		0			0
$69$	−2.00453			−0.241317
$70$		0			0
$71$	−0.00829610	−	0.00829610i	−0.000984566	−	0.000984566i	0.706614	−	0.707599i	$-0.250222\pi$
$71$	−0.00829610	−	0.00829610i	−0.000984566	−	0.000984566i	−0.707599	+	0.706614i	$0.750222\pi$
$72$		0			0
$73$	0.419298	+	0.419298i	0.0490751	+	0.0490751i	0.731218	−	0.682143i	$-0.238952\pi$
$73$	0.419298	+	0.419298i	0.0490751	+	0.0490751i	−0.682143	+	0.731218i	$0.738952\pi$
$74$		0			0
$75$			0.246692i			0.0284855i
$76$		0			0
$77$	−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	$-0.158017\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	3.35193	−	3.35193i	0.367922	−	0.367922i	−0.498797	−	0.866719i	$-0.666225\pi$
$83$	3.35193	−	3.35193i	0.367922	−	0.367922i	0.866719	+	0.498797i	$0.166225\pi$
$84$		0			0
$85$	11.6324	−	11.6324i	1.26171	−	1.26171i
$86$		0			0
$87$			4.37007i			0.468520i
$88$		0			0
$89$	1.90441	+	1.90441i	0.201867	+	0.201867i	0.800799	−	0.598933i	$-0.204408\pi$
$89$	1.90441	+	1.90441i	0.201867	+	0.201867i	−0.598933	+	0.800799i	$0.704408\pi$
$90$		0			0
$91$	9.35300	+	5.01789i	0.980461	+	0.526018i
$92$		0			0
$93$	2.08158	+	2.08158i	0.215850	+	0.215850i
$94$		0			0
$95$	7.46925			0.766329
$96$		0			0
$97$	8.76265	−	8.76265i	0.889712	−	0.889712i	−0.104783	−	0.994495i	$-0.533415\pi$
$97$	8.76265	−	8.76265i	0.889712	−	0.889712i	0.994495	+	0.104783i	$0.0334147\pi$
$98$		0			0
$99$	0.0673682	+	0.0673682i	0.00677076	+	0.00677076i
$100$		0			0
$101$	−10.5683			−1.05159			−0.525793	−	0.850613i	$-0.676231\pi$
$101$	−10.5683			−1.05159			−0.525793	+	0.850613i	$0.676231\pi$
$102$		0			0
$103$	−3.52228			−0.347061			−0.173530	−	0.984829i	$-0.555518\pi$
$103$	−3.52228			−0.347061			−0.173530	+	0.984829i	$0.555518\pi$
$104$		0			0
$105$	6.74298			0.658047
$106$		0			0
$107$	−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	0.958220	+	0.286033i	$0.0923367\pi$
$109$	12.9904	+	12.9904i	1.24425	+	1.24425i	0.286033	+	0.958220i	$0.407663\pi$
$110$		0			0
$111$	−6.43362	+	6.43362i	−0.610652	+	0.610652i
$112$		0			0
$113$	12.7051			1.19520			0.597598	−	0.801796i	$-0.296122\pi$
$113$	12.7051			1.19520			0.597598	+	0.801796i	$0.296122\pi$
$114$		0			0
$115$	3.24669	+	3.24669i	0.302756	+	0.302756i
$116$		0			0
$117$	−1.04130	−	3.45191i	−0.0962681	−	0.319129i
$118$		0			0
$119$	−14.9498	−	14.9498i	−1.37045	−	1.37045i
$120$		0			0
$121$		−	10.9909i		−	0.999175i
$122$		0			0
$123$	−7.94353	+	7.94353i	−0.716244	+	0.716244i
$124$		0			0
$125$	−7.69881	+	7.69881i	−0.688603	+	0.688603i
$126$		0			0
$127$	18.5476			1.64583			0.822916	−	0.568164i	$-0.192346\pi$
$127$	18.5476			1.64583			0.822916	+	0.568164i	$0.192346\pi$
$128$		0			0
$129$		−	10.4665i		−	0.921525i
$130$		0			0
$131$	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
$134$		0			0
$135$	−1.61967	−	1.61967i	−0.139399	−	0.139399i
$136$		0			0
$137$	−15.0286	−	15.0286i	−1.28398	−	1.28398i	−0.938383	−	0.345598i	$-0.887676\pi$
$137$	−15.0286	−	15.0286i	−1.28398	−	1.28398i	−0.345598	−	0.938383i	$-0.612324\pi$
$138$		0			0
$139$	−6.12441			−0.519466			−0.259733	−	0.965681i	$-0.583634\pi$
$139$	−6.12441			−0.519466			−0.259733	+	0.965681i	$0.583634\pi$
$140$		0			0
$141$	−5.31365	+	5.31365i	−0.447490	+	0.447490i
$142$		0			0
$143$	0.162399	−	0.302700i	0.0135805	−	0.0253130i
$144$		0			0
$145$	7.07808	−	7.07808i	0.587803	−	0.587803i
$146$		0			0
$147$		−	1.66599i		−	0.137408i
$148$		0			0
$149$	−13.2521	−	13.2521i	−1.08565	−	1.08565i	−0.995970	−	0.0896836i	$-0.971414\pi$
$149$	−13.2521	−	13.2521i	−1.08565	−	1.08565i	−0.0896836	−	0.995970i	$-0.528586\pi$
$150$		0			0
$151$	−2.61081	+	2.61081i	−0.212465	+	0.212465i	−0.805314	−	0.592849i	$-0.798003\pi$
$151$	−2.61081	+	2.61081i	−0.212465	+	0.212465i	0.592849	+	0.805314i	$0.298003\pi$
$152$		0			0
$153$			7.18195i			0.580626i
$154$		0			0
$155$		−	6.74298i		−	0.541609i
$156$		0			0
$157$			1.36321i			0.108796i	0.998519	+	0.0543978i	$0.0173239\pi$
$157$			1.36321i			0.108796i	−0.998519	+	0.0543978i	$0.982676\pi$
$158$		0			0
$159$			1.41118i			0.111914i
$160$		0			0
$161$	4.17261	−	4.17261i	0.328847	−	0.328847i
$162$		0			0
$163$	−13.7263	−	13.7263i	−1.07513	−	1.07513i	−0.996938	−	0.0781913i	$-0.975086\pi$
$163$	−13.7263	−	13.7263i	−1.07513	−	1.07513i	−0.0781913	−	0.996938i	$-0.524914\pi$
$164$		0			0
$165$		−	0.218229i		−	0.0169891i
$166$		0			0
$167$	3.15502	−	3.15502i	0.244142	−	0.244142i	−0.574419	−	0.818561i	$-0.694772\pi$
$167$	3.15502	−	3.15502i	0.244142	−	0.244142i	0.818561	+	0.574419i	$0.194772\pi$
$168$		0			0
$169$	−10.8314	+	7.18895i	−0.833184	+	0.552996i
$170$		0			0
$171$	−2.30579	+	2.30579i	−0.176328	+	0.176328i
$172$		0			0
$173$	2.52229			0.191766			0.0958830	−	0.995393i	$-0.469433\pi$
$173$	2.52229			0.191766			0.0958830	+	0.995393i	$0.469433\pi$
$174$		0			0
$175$	−0.513510	−	0.513510i	−0.0388177	−	0.0388177i
$176$		0			0
$177$	3.96350	+	3.96350i	0.297915	+	0.297915i
$178$		0			0
$179$			12.1739i			0.909917i	0.890513	+	0.454958i	$0.150346\pi$
$179$			12.1739i			0.909917i	−0.890513	+	0.454958i	$0.849654\pi$
$180$		0			0
$181$	1.13958			0.0847044			0.0423522	−	0.999103i	$-0.486515\pi$
$181$	1.13958			0.0847044			0.0423522	+	0.999103i	$0.486515\pi$
$182$		0			0
$183$		−	1.94041i		−	0.143439i
$184$		0			0
$185$	20.8407			1.53224
$186$		0			0
$187$	−0.483835	+	0.483835i	−0.0353815	+	0.0353815i
$188$		0			0
$189$	−2.08158	+	2.08158i	−0.151413	+	0.151413i
$190$		0			0
$191$			22.4304i			1.62301i	0.584347	+	0.811504i	$0.301351\pi$
$191$			22.4304i			1.62301i	−0.584347	+	0.811504i	$0.698649\pi$
$192$		0			0
$193$	−3.57371	−	3.57371i	−0.257241	−	0.257241i	0.566690	−	0.823931i	$-0.308224\pi$
$193$	−3.57371	−	3.57371i	−0.257241	−	0.257241i	−0.823931	+	0.566690i	$0.808224\pi$
$194$		0			0
$195$	−3.90441	+	7.27754i	−0.279601	+	0.521155i
$196$		0			0
$197$	2.26114	+	2.26114i	0.161099	+	0.161099i	0.783054	−	0.621954i	$-0.213661\pi$
$197$	2.26114	+	2.26114i	0.161099	+	0.161099i	−0.621954	+	0.783054i	$0.713661\pi$
$198$		0			0
$199$	26.4375			1.87410			0.937051	−	0.349193i	$-0.113544\pi$
$199$	26.4375			1.87410			0.937051	+	0.349193i	$0.113544\pi$
$200$		0			0
$201$	−8.16072	+	8.16072i	−0.575613	+	0.575613i
$202$		0			0
$203$	−9.09666	−	9.09666i	−0.638460	−	0.638460i
$204$		0			0
$205$	25.7319			1.79719
$206$		0			0
$207$	−2.00453			−0.139325
$208$		0			0
$209$	−0.310674			−0.0214897
$210$		0			0
$211$	2.28566			0.157351			0.0786755	−	0.996900i	$-0.474931\pi$
$211$	2.28566			0.157351			0.0786755	+	0.996900i	$0.474931\pi$
$212$		0			0
$213$	−0.00829610	−	0.00829610i	−0.000568439	−	0.000568439i
$214$		0			0
$215$	−16.9523	+	16.9523i	−1.15614	+	1.15614i
$216$		0			0
$217$	−8.66599			−0.588286
$218$		0			0
$219$	0.419298	+	0.419298i	0.0283335	+	0.0283335i
$220$		0			0
$221$	24.7915	−	7.47856i	1.66765	−	0.503062i
$222$		0			0
$223$	−6.65855	−	6.65855i	−0.445889	−	0.445889i	0.448096	−	0.893985i	$-0.352102\pi$
$223$	−6.65855	−	6.65855i	−0.445889	−	0.445889i	−0.893985	+	0.448096i	$0.852102\pi$
$224$		0			0
$225$			0.246692i			0.0164461i
$226$		0			0
$227$	7.86789	−	7.86789i	0.522210	−	0.522210i	−0.396028	−	0.918238i	$-0.629612\pi$
$227$	7.86789	−	7.86789i	0.522210	−	0.522210i	0.918238	+	0.396028i	$0.129612\pi$
$228$		0			0
$229$	−3.64543	+	3.64543i	−0.240897	+	0.240897i	−0.817221	−	0.576324i	$-0.804487\pi$
$229$	−3.64543	+	3.64543i	−0.240897	+	0.240897i	0.576324	+	0.817221i	$0.304487\pi$
$230$		0			0
$231$	−0.280465			−0.0184533
$232$		0			0
$233$			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
$236$		0			0
$237$		−	8.46664i		−	0.549967i
$238$		0			0
$239$	7.48888	+	7.48888i	0.484415	+	0.484415i	0.906538	−	0.422123i	$-0.138715\pi$
$239$	7.48888	+	7.48888i	0.484415	+	0.484415i	−0.422123	+	0.906538i	$0.638715\pi$
$240$		0			0
$241$	−9.02754	−	9.02754i	−0.581515	−	0.581515i	0.353804	−	0.935319i	$-0.384888\pi$
$241$	−9.02754	−	9.02754i	−0.581515	−	0.581515i	−0.935319	+	0.353804i	$0.884888\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−2.69836	+	2.69836i	−0.172392	+	0.172392i
$246$		0			0
$247$	10.3604	+	5.55836i	0.659216	+	0.353670i
$248$		0			0
$249$	3.35193	−	3.35193i	0.212420	−	0.212420i
$250$		0			0
$251$			18.4986i			1.16762i	0.811889	+	0.583812i	$0.198439\pi$
$251$			18.4986i			1.16762i	−0.811889	+	0.583812i	$0.801561\pi$
$252$		0			0
$253$	−0.135042	−	0.135042i	−0.00849001	−	0.00849001i
$254$		0			0
$255$	11.6324	−	11.6324i	0.728450	−	0.728450i
$256$		0			0
$257$			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
$260$		0			0
$261$			4.37007i			0.270500i
$262$		0			0
$263$		−	18.2366i		−	1.12452i	−0.826962	−	0.562258i	$-0.809933\pi$
$263$		−	18.2366i		−	1.12452i	0.826962	−	0.562258i	$-0.190067\pi$
$264$		0			0
$265$	2.28566	−	2.28566i	0.140407	−	0.140407i
$266$		0			0
$267$	1.90441	+	1.90441i	0.116548	+	0.116548i
$268$		0			0
$269$		−	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	$-0.671951\pi$
$271$	5.65140	−	5.65140i	0.343298	−	0.343298i	0.857606	+	0.514308i	$0.171951\pi$
$272$		0			0
$273$	9.35300	+	5.01789i	0.566069	+	0.303697i
$274$		0			0
$275$	−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	$0.761294\pi$
$278$		0			0
$279$	2.08158	+	2.08158i	0.124621	+	0.124621i
$280$		0			0
$281$	−7.19722	−	7.19722i	−0.429350	−	0.429350i	0.459057	−	0.888407i	$-0.348187\pi$
$281$	−7.19722	−	7.19722i	−0.429350	−	0.429350i	−0.888407	+	0.459057i	$0.848187\pi$
$282$		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			0
$285$	7.46925			0.442440
$286$		0			0
$287$		−	33.0703i		−	1.95208i
$288$		0			0
$289$	−34.5804			−2.03414
$290$		0			0
$291$	8.76265	−	8.76265i	0.513676	−	0.513676i
$292$		0			0
$293$	10.4354	−	10.4354i	0.609643	−	0.609643i	−0.333210	−	0.942853i	$-0.608132\pi$
$293$	10.4354	−	10.4354i	0.609643	−	0.609643i	0.942853	+	0.333210i	$0.108132\pi$
$294$		0			0
$295$		−	12.8392i		−	0.747526i
$296$		0			0
$297$	0.0673682	+	0.0673682i	0.00390910	+	0.00390910i
$298$		0			0
$299$	2.08732	+	6.91947i	0.120713	+	0.400163i
$300$		0			0
$301$	21.7869	+	21.7869i	1.25578	+	1.25578i
$302$		0			0
$303$	−10.5683			−0.607133
$304$		0			0
$305$	−3.14283	+	3.14283i	−0.179958	+	0.179958i
$306$		0			0
$307$	−9.49598	−	9.49598i	−0.541964	−	0.541964i	0.382140	−	0.924104i	$-0.375187\pi$
$307$	−9.49598	−	9.49598i	−0.541964	−	0.541964i	−0.924104	+	0.382140i	$0.875187\pi$
$308$		0			0
$309$	−3.52228			−0.200376
$310$		0			0
$311$	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			0
$315$	6.74298			0.379924
$316$		0			0
$317$	18.1488	+	18.1488i	1.01934	+	1.01934i	0.999809	+	0.0195277i	$0.00621626\pi$
$317$	18.1488	+	18.1488i	1.01934	+	1.01934i	0.0195277	+	0.999809i	$0.493784\pi$
$318$		0			0
$319$	−0.294404	+	0.294404i	−0.0164834	+	0.0164834i
$320$		0			0
$321$	−11.8314			−0.660364
$322$		0			0
$323$	−16.5600	−	16.5600i	−0.921426	−	0.921426i
$324$		0			0
$325$	0.851558	−	0.256880i	0.0472360	−	0.0142491i
$326$		0			0
$327$	12.9904	+	12.9904i	0.718370	+	0.718370i
$328$		0			0
$329$		−	22.1216i		−	1.21960i
$330$		0			0
$331$	22.5976	−	22.5976i	1.24208	−	1.24208i	0.282939	−	0.959138i	$-0.408691\pi$
$331$	22.5976	−	22.5976i	1.24208	−	1.24208i	0.959138	−	0.282939i	$-0.0913095\pi$
$332$		0			0
$333$	−6.43362	+	6.43362i	−0.352560	+	0.352560i
$334$		0			0
$335$	26.4354			1.44432
$336$		0			0
$337$		−	8.65894i		−	0.471683i	−0.971792	−	0.235841i	$-0.924215\pi$
$337$		−	8.65894i		−	0.471683i	0.971792	−	0.235841i	$-0.0757846\pi$
$338$		0			0
$339$	12.7051			0.690047
$340$		0			0
$341$			0.280465i			0.0151881i
$342$		0			0
$343$	−11.1032	−	11.1032i	−0.599516	−	0.599516i
$344$		0			0
$345$	3.24669	+	3.24669i	0.174796	+	0.174796i
$346$		0			0
$347$	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	−0.592206	−	0.805787i	$-0.701743\pi$
$349$	3.99002	−	3.99002i	0.213581	−	0.213581i	0.805787	+	0.592206i	$0.201743\pi$
$350$		0			0
$351$	−1.04130	−	3.45191i	−0.0555804	−	0.184249i
$352$		0			0
$353$	−6.09559	+	6.09559i	−0.324436	+	0.324436i	−0.850466	−	0.526030i	$-0.823680\pi$
$353$	−6.09559	+	6.09559i	−0.324436	+	0.324436i	0.526030	+	0.850466i	$0.323680\pi$
$354$		0			0
$355$			0.0268740i			0.00142632i
$356$		0			0
$357$	−14.9498	−	14.9498i	−0.791229	−	0.791229i
$358$		0			0
$359$	−20.6821	+	20.6821i	−1.09156	+	1.09156i	−0.0961965	+	0.995362i	$0.530668\pi$
$359$	−20.6821	+	20.6821i	−1.09156	+	1.09156i	−0.995362	+	0.0961965i	$0.969332\pi$
$360$		0			0
$361$			8.36669i			0.440352i
$362$		0			0
$363$		−	10.9909i		−	0.576874i
$364$		0			0
$365$		−	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	$0.712047\pi$
$368$		0			0
$369$	−7.94353	+	7.94353i	−0.413524	+	0.413524i
$370$		0			0
$371$	−2.93749	−	2.93749i	−0.152507	−	0.152507i
$372$		0			0
$373$		−	8.59939i		−	0.445259i	−0.974903	−	0.222630i	$-0.928536\pi$
$373$		−	8.59939i		−	0.445259i	0.974903	−	0.222630i	$-0.0714641\pi$
$374$		0			0
$375$	−7.69881	+	7.69881i	−0.397565	+	0.397565i
$376$		0			0
$377$	15.0851	−	4.55055i	0.776921	−	0.234365i
$378$		0			0
$379$	−11.5751	+	11.5751i	−0.594571	+	0.594571i	−0.938863	−	0.344292i	$-0.888119\pi$
$379$	−11.5751	+	11.5751i	−0.594571	+	0.594571i	0.344292	+	0.938863i	$0.388119\pi$
$380$		0			0
$381$	18.5476			0.950221
$382$		0			0
$383$	2.01486	+	2.01486i	0.102954	+	0.102954i	0.756708	−	0.653753i	$-0.226807\pi$
$383$	2.01486	+	2.01486i	0.102954	+	0.102954i	−0.653753	+	0.756708i	$0.726807\pi$
$384$		0			0
$385$	0.454263	+	0.454263i	0.0231514	+	0.0231514i
$386$		0			0
$387$		−	10.4665i		−	0.532043i
$388$		0			0
$389$	−25.8294			−1.30960			−0.654801	−	0.755801i	$-0.727248\pi$
$389$	−25.8294			−1.30960			−0.654801	+	0.755801i	$0.727248\pi$
$390$		0			0
$391$		−	14.3965i		−	0.728060i
$392$		0			0
$393$	5.20053			0.262332
$394$		0			0
$395$	−13.7132	+	13.7132i	−0.689986	+	0.689986i
$396$		0			0
$397$	11.0841	−	11.0841i	0.556297	−	0.556297i	−0.371954	−	0.928251i	$-0.621312\pi$
$397$	11.0841	−	11.0841i	0.556297	−	0.556297i	0.928251	+	0.371954i	$0.121312\pi$
$398$		0			0
$399$		−	9.59938i		−	0.480570i
$400$		0			0
$401$	−25.0265	−	25.0265i	−1.24977	−	1.24977i	−0.955823	−	0.293942i	$-0.905033\pi$
$401$	−25.0265	−	25.0265i	−1.24977	−	1.24977i	−0.293942	−	0.955823i	$-0.594967\pi$
$402$		0			0
$403$	5.01789	−	9.35300i	0.249959	−	0.465906i
$404$		0			0
$405$	−1.61967	−	1.61967i	−0.0804823	−	0.0804823i
$406$		0			0
$407$	−0.866843			−0.0429678
$408$		0			0
$409$	24.7440	−	24.7440i	1.22351	−	1.22351i	0.257139	−	0.966374i	$-0.417220\pi$
$409$	24.7440	−	24.7440i	1.22351	−	1.22351i	0.966374	−	0.257139i	$-0.0827798\pi$
$410$		0			0
$411$	−15.0286	−	15.0286i	−0.741307	−	0.741307i
$412$		0			0
$413$	−16.5007			−0.811948
$414$		0			0
$415$	−10.8581			−0.533002
$416$		0			0
$417$	−6.12441			−0.299914
$418$		0			0
$419$	−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	0.823259	−	0.567667i	$-0.192154\pi$
$421$	5.24431	+	5.24431i	0.255592	+	0.255592i	−0.567667	+	0.823259i	$0.692154\pi$
$422$		0			0
$423$	−5.31365	+	5.31365i	−0.258359	+	0.258359i
$424$		0			0
$425$	−1.77173			−0.0859414
$426$		0			0
$427$	4.03912	+	4.03912i	0.195467	+	0.195467i
$428$		0			0
$429$	0.162399	−	0.302700i	0.00784069	−	0.0146145i
$430$		0			0
$431$	16.9631	+	16.9631i	0.817084	+	0.817084i	0.985684	−	0.168600i	$-0.0539248\pi$
$431$	16.9631	+	16.9631i	0.817084	+	0.817084i	−0.168600	+	0.985684i	$0.553925\pi$
$432$		0			0
$433$			21.6657i			1.04119i	0.853805	+	0.520593i	$0.174289\pi$
$433$			21.6657i			1.04119i	−0.853805	+	0.520593i	$0.825711\pi$
$434$		0			0
$435$	7.07808	−	7.07808i	0.339368	−	0.339368i
$436$		0			0
$437$	4.62203	−	4.62203i	0.221102	−	0.221102i
$438$		0			0
$439$	26.9953			1.28842			0.644208	−	0.764850i	$-0.277187\pi$
$439$	26.9953			1.28842			0.644208	+	0.764850i	$0.277187\pi$
$440$		0			0
$441$		−	1.66599i		−	0.0793328i
$442$		0			0
$443$	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
$446$		0			0
$447$	−13.2521	−	13.2521i	−0.626803	−	0.626803i
$448$		0			0
$449$	15.9641	+	15.9641i	0.753391	+	0.753391i	0.975111	−	0.221719i	$-0.0711669\pi$
$449$	15.9641	+	15.9641i	0.753391	+	0.753391i	−0.221719	+	0.975111i	$0.571167\pi$
$450$		0			0
$451$	−1.07028			−0.0503977
$452$		0			0
$453$	−2.61081	+	2.61081i	−0.122667	+	0.122667i
$454$		0			0
$455$	−7.02146	−	23.2762i	−0.329171	−	1.09120i
$456$		0			0
$457$	−9.99072	+	9.99072i	−0.467346	+	0.467346i	−0.901054	−	0.433708i	$-0.857205\pi$
$457$	−9.99072	+	9.99072i	−0.467346	+	0.467346i	0.433708	+	0.901054i	$0.357205\pi$
$458$		0			0
$459$			7.18195i			0.335225i
$460$		0			0
$461$	9.80788	+	9.80788i	0.456798	+	0.456798i	0.897603	−	0.440805i	$-0.145307\pi$
$461$	9.80788	+	9.80788i	0.456798	+	0.456798i	−0.440805	+	0.897603i	$0.645307\pi$
$462$		0			0
$463$	−16.5192	+	16.5192i	−0.767714	+	0.767714i	−0.977704	−	0.209990i	$-0.932657\pi$
$463$	−16.5192	+	16.5192i	−0.767714	+	0.767714i	0.209990	+	0.977704i	$0.432657\pi$
$464$		0			0
$465$		−	6.74298i		−	0.312698i
$466$		0			0
$467$			13.7056i			0.634220i	0.948389	+	0.317110i	$0.102712\pi$
$467$			13.7056i			0.634220i	−0.948389	+	0.317110i	$0.897288\pi$
$468$		0			0
$469$		−	33.9745i		−	1.56880i
$470$		0			0
$471$			1.36321i			0.0628132i
$472$		0			0
$473$	0.705110	−	0.705110i	0.0324210	−	0.0324210i
$474$		0			0
$475$	−0.568819	−	0.568819i	−0.0260992	−	0.0260992i
$476$		0			0
$477$			1.41118i			0.0646136i
$478$		0			0
$479$	7.17788	−	7.17788i	0.327966	−	0.327966i	−0.523847	−	0.851813i	$-0.675504\pi$
$479$	7.17788	−	7.17788i	0.327966	−	0.327966i	0.851813	+	0.523847i	$0.175504\pi$
$480$		0			0
$481$	28.9076	+	15.5090i	1.31807	+	0.707148i
$482$		0			0
$483$	4.17261	−	4.17261i	0.189860	−	0.189860i
$484$		0			0
$485$	−28.3853			−1.28891
$486$		0			0
$487$	0.384275	+	0.384275i	0.0174132	+	0.0174132i	0.715760	−	0.698347i	$-0.246081\pi$
$487$	0.384275	+	0.384275i	0.0174132	+	0.0174132i	−0.698347	+	0.715760i	$0.746081\pi$
$488$		0			0
$489$	−13.7263	−	13.7263i	−0.620726	−	0.620726i
$490$		0			0
$491$			2.72036i			0.122768i	0.998114	+	0.0613840i	$0.0195514\pi$
$491$			2.72036i			0.122768i	−0.998114	+	0.0613840i	$0.980449\pi$
$492$		0			0
$493$	−31.3856			−1.41354
$494$		0			0
$495$		−	0.218229i		−	0.00980868i
$496$		0			0
$497$	0.0345381			0.00154924
$498$		0			0
$499$	−29.4023	+	29.4023i	−1.31623	+	1.31623i	−0.399493	+	0.916736i	$0.630814\pi$
$499$	−29.4023	+	29.4023i	−1.31623	+	1.31623i	−0.916736	+	0.399493i	$0.869186\pi$
$500$		0			0
$501$	3.15502	−	3.15502i	0.140956	−	0.140956i
$502$		0			0
$503$			8.72354i			0.388963i	0.980906	+	0.194482i	$0.0623025\pi$
$503$			8.72354i			0.388963i	−0.980906	+	0.194482i	$0.937698\pi$
$504$		0			0
$505$	17.1172	+	17.1172i	0.761706	+	0.761706i
$506$		0			0
$507$	−10.8314	+	7.18895i	−0.481039	+	0.319272i
$508$		0			0
$509$	29.8098	+	29.8098i	1.32130	+	1.32130i	0.912726	+	0.408572i	$0.133973\pi$
$509$	29.8098	+	29.8098i	1.32130	+	1.32130i	0.408572	+	0.912726i	$0.366027\pi$
$510$		0			0
$511$	−1.74561			−0.0772211
$512$		0			0
$513$	−2.30579	+	2.30579i	−0.101803	+	0.101803i
$514$		0			0
$515$	5.70495	+	5.70495i	0.251390	+	0.251390i
$516$		0			0
$517$	−0.715943			−0.0314871
$518$		0			0
$519$	2.52229			0.110716
$520$		0			0
$521$	23.2436			1.01832			0.509161	−	0.860671i	$-0.329956\pi$
$521$	23.2436			1.01832			0.509161	+	0.860671i	$0.329956\pi$
$522$		0			0
$523$	−15.0188			−0.656728			−0.328364	−	0.944551i	$-0.606497\pi$
$523$	−15.0188			−0.656728			−0.328364	+	0.944551i	$0.606497\pi$
$524$		0			0
$525$	−0.513510	−	0.513510i	−0.0224114	−	0.0224114i
$526$		0			0
$527$	−14.9498	+	14.9498i	−0.651225	+	0.651225i
$528$		0			0
$529$	−18.9818			−0.825298
$530$		0			0
$531$	3.96350	+	3.96350i	0.172001	+	0.172001i
$532$		0			0
$533$	35.6920	+	19.1488i	1.54599	+	0.829425i
$534$		0			0
$535$	19.1630	+	19.1630i	0.828489	+	0.828489i
$536$		0			0
$537$			12.1739i			0.525341i
$538$		0			0
$539$	0.112235	−	0.112235i	0.00483429	−	0.00483429i
$540$		0			0
$541$	−7.84233	+	7.84233i	−0.337168	+	0.337168i	−0.855300	−	0.518132i	$-0.826627\pi$
$541$	−7.84233	+	7.84233i	−0.337168	+	0.337168i	0.518132	+	0.855300i	$0.326627\pi$
$542$		0			0
$543$	1.13958			0.0489041
$544$		0			0
$545$		−	42.0804i		−	1.80253i
$546$		0			0
$547$	24.3317			1.04035			0.520175	−	0.854060i	$-0.325867\pi$
$547$	24.3317			1.04035			0.520175	+	0.854060i	$0.325867\pi$
$548$		0			0
$549$		−	1.94041i		−	0.0828145i
$550$		0			0
$551$	−10.0764	−	10.0764i	−0.429271	−	0.429271i
$552$		0			0
$553$	17.6240	+	17.6240i	0.749450	+	0.749450i
$554$		0			0
$555$	20.8407			0.884640
$556$		0			0
$557$	14.8145	−	14.8145i	0.627710	−	0.627710i	−0.319781	−	0.947491i	$-0.603609\pi$
$557$	14.8145	−	14.8145i	0.627710	−	0.627710i	0.947491	+	0.319781i	$0.103609\pi$
$558$		0			0
$559$	−36.1295	+	10.8988i	−1.52811	+	0.460969i
$560$		0			0
$561$	−0.483835	+	0.483835i	−0.0204275	+	0.0204275i
$562$		0			0
$563$			35.1602i			1.48183i	0.671601	+	0.740913i	$0.265607\pi$
$563$			35.1602i			1.48183i	−0.671601	+	0.740913i	$0.734393\pi$
$564$		0			0
$565$	−20.5781	−	20.5781i	−0.865729	−	0.865729i
$566$		0			0
$567$	−2.08158	+	2.08158i	−0.0874183	+	0.0874183i
$568$		0			0
$569$			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			0
$573$			22.4304i			0.937044i
$574$		0			0
$575$		−	0.494502i		−	0.0206222i
$576$		0			0
$577$	−4.19353	+	4.19353i	−0.174579	+	0.174579i	−0.788988	−	0.614409i	$-0.789395\pi$
$577$	−4.19353	+	4.19353i	−0.174579	+	0.174579i	0.614409	+	0.788988i	$0.289395\pi$
$578$		0			0
$579$	−3.57371	−	3.57371i	−0.148518	−	0.148518i
$580$		0			0
$581$			13.9546i			0.578936i
$582$		0			0
$583$	−0.0950688	+	0.0950688i	−0.00393735	+	0.00393735i
$584$		0			0
$585$	−3.90441	+	7.27754i	−0.161427	+	0.300889i
$586$		0			0
$587$	−13.2081	+	13.2081i	−0.545157	+	0.545157i	−0.925036	−	0.379879i	$-0.875966\pi$
$587$	−13.2081	+	13.2081i	−0.545157	+	0.545157i	0.379879	+	0.925036i	$0.375966\pi$
$588$		0			0
$589$	−9.59938			−0.395536
$590$		0			0
$591$	2.26114	+	2.26114i	0.0930108	+	0.0930108i
$592$		0			0
$593$	−0.911200	−	0.911200i	−0.0374185	−	0.0374185i	0.688150	−	0.725568i	$-0.258423\pi$
$593$	−0.911200	−	0.911200i	−0.0374185	−	0.0374185i	−0.725568	+	0.688150i	$0.758423\pi$
$594$		0			0
$595$			48.4277i			1.98534i
$596$		0			0
$597$	26.4375			1.08201
$598$		0			0
$599$		−	25.5885i		−	1.04552i	−0.852481	−	0.522758i	$-0.824903\pi$
$599$		−	25.5885i		−	1.04552i	0.852481	−	0.522758i	$-0.175097\pi$
$600$		0			0
$601$	9.95824			0.406205			0.203103	−	0.979157i	$-0.434897\pi$
$601$	9.95824			0.406205			0.203103	+	0.979157i	$0.434897\pi$
$602$		0			0
$603$	−8.16072	+	8.16072i	−0.332330	+	0.332330i
$604$		0			0
$605$	−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	$-0.313887\pi$
$608$		0			0
$609$	−9.09666	−	9.09666i	−0.368615	−	0.368615i
$610$		0			0
$611$	23.8754	+	12.8092i	0.965894	+	0.518203i
$612$		0			0
$613$	−7.07976	−	7.07976i	−0.285949	−	0.285949i	0.549527	−	0.835476i	$-0.314808\pi$
$613$	−7.07976	−	7.07976i	−0.285949	−	0.285949i	−0.835476	+	0.549527i	$0.814808\pi$
$614$		0			0
$615$	25.7319			1.03761
$616$		0			0
$617$	2.05439	−	2.05439i	0.0827067	−	0.0827067i	−0.664543	−	0.747250i	$-0.731374\pi$
$617$	2.05439	−	2.05439i	0.0827067	−	0.0827067i	0.747250	+	0.664543i	$0.231374\pi$
$618$		0			0
$619$	16.6627	+	16.6627i	0.669730	+	0.669730i	0.957653	−	0.287923i	$-0.0929649\pi$
$619$	16.6627	+	16.6627i	0.669730	+	0.669730i	−0.287923	+	0.957653i	$0.592965\pi$
$620$		0			0
$621$	−2.00453			−0.0804392
$622$		0			0
$623$	−7.92838			−0.317644
$624$		0			0
$625$	26.1726			1.04690
$626$		0			0
$627$	−0.310674			−0.0124071
$628$		0			0
$629$	−46.2059	−	46.2059i	−1.84235	−	1.84235i
$630$		0			0
$631$	−32.6063	+	32.6063i	−1.29804	+	1.29804i	−0.368349	+	0.929688i	$0.620077\pi$
$631$	−32.6063	+	32.6063i	−1.29804	+	1.29804i	−0.929688	+	0.368349i	$0.879923\pi$
$632$		0			0
$633$	2.28566			0.0908466
$634$		0			0
$635$	−30.0410	−	30.0410i	−1.19214	−	1.19214i
$636$		0			0
$637$	−5.75085	+	1.73479i	−0.227857	+	0.0687350i
$638$		0			0
$639$	−0.00829610	−	0.00829610i	−0.000328189	−	0.000328189i
$640$		0			0
$641$			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	$-0.930101\pi$
$643$	−19.2248	+	19.2248i	−0.758153	+	0.758153i	0.217833	+	0.975986i	$0.430101\pi$
$644$		0			0
$645$	−16.9523	+	16.9523i	−0.667498	+	0.667498i
$646$		0			0
$647$	−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
$650$		0			0
$651$	−8.66599			−0.339647
$652$		0			0
$653$		−	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
$656$		0			0
$657$	0.419298	+	0.419298i	0.0163584	+	0.0163584i
$658$		0			0
$659$	−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	−0.173752	+	0.984789i	$0.555589\pi$
$661$	−29.7860	+	29.7860i	−1.15854	+	1.15854i	−0.984789	+	0.173752i	$0.944411\pi$
$662$		0			0
$663$	24.7915	−	7.47856i	0.962820	−	0.290443i
$664$		0			0
$665$	−15.5479	+	15.5479i	−0.602921	+	0.602921i
$666$		0			0
$667$		−	8.75994i		−	0.339186i
$668$		0			0
$669$	−6.65855	−	6.65855i	−0.257434	−	0.257434i
$670$		0			0
$671$	0.130722	−	0.130722i	0.00504646	−	0.00504646i
$672$		0			0
$673$			26.8225i			1.03393i	0.856006	+	0.516965i	$0.172938\pi$
$673$			26.8225i			1.03393i	−0.856006	+	0.516965i	$0.827062\pi$
$674$		0			0
$675$			0.246692i			0.00949517i
$676$		0			0
$677$		−	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
$680$		0			0
$681$	7.86789	−	7.86789i	0.301498	−	0.301498i
$682$		0			0
$683$	0.401585	+	0.401585i	0.0153662	+	0.0153662i	0.714748	−	0.699382i	$-0.246541\pi$
$683$	0.401585	+	0.401585i	0.0153662	+	0.0153662i	−0.699382	+	0.714748i	$0.746541\pi$
$684$		0			0
$685$			48.6829i			1.86008i
$686$		0			0
$687$	−3.64543	+	3.64543i	−0.139082	+	0.139082i
$688$		0			0
$689$	4.87127	−	1.46946i	0.185581	−	0.0559820i
$690$		0			0
$691$	25.8040	−	25.8040i	0.981632	−	0.981632i	−0.0182023	−	0.999834i	$-0.505794\pi$
$691$	25.8040	−	25.8040i	0.981632	−	0.981632i	0.999834	+	0.0182023i	$0.00579429\pi$
$692$		0			0
$693$	−0.280465			−0.0106540
$694$		0			0
$695$	9.91955	+	9.91955i	0.376270	+	0.376270i
$696$		0			0
$697$	−57.0500	−	57.0500i	−2.16092	−	2.16092i
$698$		0			0
$699$			3.31543i			0.125401i
$700$		0			0
$701$	−42.4434			−1.60307			−0.801533	−	0.597951i	$-0.795982\pi$
$701$	−42.4434			−1.60307			−0.801533	+	0.597951i	$0.795982\pi$
$702$		0			0
$703$		−	29.6691i		−	1.11899i
$704$		0			0
$705$	17.2128			0.648271
$706$		0			0
$707$	21.9988	−	21.9988i	0.827350	−	0.827350i
$708$		0			0
$709$	−21.9848	+	21.9848i	−0.825657	+	0.825657i	−0.986913	−	0.161256i	$-0.948446\pi$
$709$	−21.9848	+	21.9848i	−0.825657	+	0.825657i	0.161256	+	0.986913i	$0.448446\pi$
$710$		0			0
$711$		−	8.46664i		−	0.317524i
$712$		0			0
$713$	−4.17261	−	4.17261i	−0.156265	−	0.156265i
$714$		0			0
$715$	−0.753308	+	0.227242i	−0.0281721	+	0.00849837i
$716$		0			0
$717$	7.48888	+	7.48888i	0.279677	+	0.279677i
$718$		0			0
$719$	−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			0
$723$	−9.02754	−	9.02754i	−0.335738	−	0.335738i
$724$		0			0
$725$	−1.07806			−0.0400381
$726$		0			0
$727$	−35.3567			−1.31131			−0.655653	−	0.755062i	$-0.727607\pi$
$727$	−35.3567			−1.31131			−0.655653	+	0.755062i	$0.727607\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	75.1699			2.78026
$732$		0			0
$733$	10.2364	+	10.2364i	0.378089	+	0.378089i	0.870412	−	0.492323i	$-0.163852\pi$
$733$	10.2364	+	10.2364i	0.378089	+	0.378089i	−0.492323	+	0.870412i	$0.663852\pi$
$734$		0			0
$735$	−2.69836	+	2.69836i	−0.0995305	+	0.0995305i
$736$		0			0
$737$	−1.09955			−0.0405023
$738$		0			0
$739$	15.9995	+	15.9995i	0.588550	+	0.588550i	0.937239	−	0.348688i	$-0.113373\pi$
$739$	15.9995	+	15.9995i	0.588550	+	0.588550i	−0.348688	+	0.937239i	$0.613373\pi$
$740$		0			0
$741$	10.3604	+	5.55836i	0.380598	+	0.204191i
$742$		0			0
$743$	4.22277	+	4.22277i	0.154918	+	0.154918i	0.780311	−	0.625392i	$-0.215061\pi$
$743$	4.22277	+	4.22277i	0.154918	+	0.154918i	−0.625392	+	0.780311i	$0.715061\pi$
$744$		0			0
$745$			42.9282i			1.57277i
$746$		0			0
$747$	3.35193	−	3.35193i	0.122641	−	0.122641i
$748$		0			0
$749$	24.6280	−	24.6280i	0.899889	−	0.899889i
$750$		0			0
$751$	−39.7818			−1.45166			−0.725828	−	0.687876i	$-0.758543\pi$
$751$	−39.7818			−1.45166			−0.725828	+	0.687876i	$0.758543\pi$
$752$		0			0
$753$			18.4986i			0.674128i
$754$		0			0
$755$	8.45732			0.307794
$756$		0			0
$757$		−	0.790942i		−	0.0287473i	−0.999897	−	0.0143736i	$-0.995425\pi$
$757$		−	0.790942i		−	0.0287473i	0.999897	−	0.0143736i	$-0.00457543\pi$
$758$		0			0
$759$	−0.135042	−	0.135042i	−0.00490171	−	0.00490171i
$760$		0			0
$761$	2.96895	+	2.96895i	0.107624	+	0.107624i	0.758868	−	0.651244i	$-0.225753\pi$
$761$	2.96895	+	2.96895i	0.107624	+	0.107624i	−0.651244	+	0.758868i	$0.725753\pi$
$762$		0			0
$763$	−54.0812			−1.95787
$764$		0			0
$765$	11.6324	−	11.6324i	0.420571	−	0.420571i
$766$		0			0
$767$	9.55447	−	17.8089i	0.344992	−	0.643041i
$768$		0			0
$769$	−20.0249	+	20.0249i	−0.722117	+	0.722117i	−0.969036	−	0.246919i	$-0.920582\pi$
$769$	−20.0249	+	20.0249i	−0.722117	+	0.722117i	0.246919	+	0.969036i	$0.420582\pi$
$770$		0			0
$771$			17.6933i			0.637210i
$772$		0			0
$773$	12.6302	+	12.6302i	0.454278	+	0.454278i	0.896772	−	0.442494i	$-0.145906\pi$
$773$	12.6302	+	12.6302i	0.454278	+	0.454278i	−0.442494	+	0.896772i	$0.645906\pi$
$774$		0			0
$775$	−0.513510	+	0.513510i	−0.0184458	+	0.0184458i
$776$		0			0
$777$		−	26.7842i		−	0.960879i
$778$		0			0
$779$		−	36.6322i		−	1.31248i
$780$		0			0
$781$		−	0.00111779i		−	3.99976e-5i
$782$		0			0
$783$			4.37007i			0.156173i
$784$		0			0
$785$	2.20795	−	2.20795i	0.0788051	−	0.0788051i
$786$		0			0
$787$	26.5637	+	26.5637i	0.946895	+	0.946895i	0.998659	−	0.0517643i	$-0.0164844\pi$
$787$	26.5637	+	26.5637i	0.946895	+	0.946895i	−0.0517643	+	0.998659i	$0.516484\pi$
$788$		0			0
$789$		−	18.2366i		−	0.649239i
$790$		0			0
$791$	−26.4468	+	26.4468i	−0.940339	+	0.940339i
$792$		0			0
$793$	−6.69811	+	2.02054i	−0.237857	+	0.0717516i
$794$		0			0
$795$	2.28566	−	2.28566i	0.0810638	−	0.0810638i
$796$		0			0
$797$	10.2872			0.364393			0.182196	−	0.983262i	$-0.441679\pi$
$797$	10.2872			0.364393			0.182196	+	0.983262i	$0.441679\pi$
$798$		0			0
$799$	−38.1624	−	38.1624i	−1.35009	−	1.35009i
$800$		0			0
$801$	1.90441	+	1.90441i	0.0672890	+	0.0672890i
$802$		0			0
$803$			0.0564947i			0.00199365i
$804$		0			0
$805$	−13.5165			−0.476395
$806$		0			0
$807$		−	6.68357i		−	0.235273i
$808$		0			0
$809$	−1.64479			−0.0578278			−0.0289139	−	0.999582i	$-0.509205\pi$
$809$	−1.64479			−0.0578278			−0.0289139	+	0.999582i	$0.509205\pi$
$810$		0			0
$811$	13.0418	−	13.0418i	0.457958	−	0.457958i	−0.440026	−	0.897985i	$-0.645031\pi$
$811$	13.0418	−	13.0418i	0.457958	−	0.457958i	0.897985	+	0.440026i	$0.145031\pi$
$812$		0			0
$813$	5.65140	−	5.65140i	0.198203	−	0.198203i
$814$		0			0
$815$			44.4644i			1.55752i
$816$		0			0
$817$	24.1335	+	24.1335i	0.844326	+	0.844326i
$818$		0			0
$819$	9.35300	+	5.01789i	0.326820	+	0.175339i
$820$		0			0
$821$	−9.46652	−	9.46652i	−0.330384	−	0.330384i	0.522348	−	0.852732i	$-0.325056\pi$
$821$	−9.46652	−	9.46652i	−0.330384	−	0.330384i	−0.852732	+	0.522348i	$0.825056\pi$
$822$		0			0
$823$	9.44005			0.329059			0.164530	−	0.986372i	$-0.447389\pi$
$823$	9.44005			0.329059			0.164530	+	0.986372i	$0.447389\pi$
$824$		0			0
$825$	−0.0166192	+	0.0166192i	−0.000578606	+	0.000578606i
$826$		0			0
$827$	−15.1241	−	15.1241i	−0.525916	−	0.525916i	0.393436	−	0.919352i	$-0.371286\pi$
$827$	−15.1241	−	15.1241i	−0.525916	−	0.525916i	−0.919352	+	0.393436i	$0.871286\pi$
$828$		0			0
$829$	30.8994			1.07318			0.536590	−	0.843843i	$-0.319712\pi$
$829$	30.8994			1.07318			0.536590	+	0.843843i	$0.319712\pi$
$830$		0			0
$831$	−24.3573			−0.844946
$832$		0			0
$833$	11.9651			0.414564
$834$		0			0
$835$	−10.2202			−0.353684
$836$		0			0
$837$	2.08158	+	2.08158i	0.0719501	+	0.0719501i
$838$		0			0
$839$	39.8024	−	39.8024i	1.37413	−	1.37413i	0.519909	−	0.854222i	$-0.325966\pi$
$839$	39.8024	−	39.8024i	1.37413	−	1.37413i	0.854222	−	0.519909i	$-0.174034\pi$
$840$		0			0
$841$	9.90253			0.341466
$842$		0			0
$843$	−7.19722	−	7.19722i	−0.247885	−	0.247885i
$844$		0			0
$845$	29.1871	+	5.89958i	1.00407	+	0.202952i
$846$		0			0
$847$	22.8785	+	22.8785i	0.786116	+	0.786116i
$848$		0			0
$849$		−	14.0053i		−	0.480661i
$850$		0			0
$851$	12.8964	−	12.8964i	0.442083	−	0.442083i
$852$		0			0
$853$	−5.81918	+	5.81918i	−0.199245	+	0.199245i	−0.799676	−	0.600431i	$-0.794996\pi$
$853$	−5.81918	+	5.81918i	−0.199245	+	0.199245i	0.600431	+	0.799676i	$0.294996\pi$
$854$		0			0
$855$	7.46925			0.255443
$856$		0			0
$857$			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	$-0.445250\pi$
$859$	10.0327			0.342311			0.171155	+	0.985244i	$0.445250\pi$
$860$		0			0
$861$		−	33.0703i		−	1.12703i
$862$		0			0
$863$	32.0055	+	32.0055i	1.08948	+	1.08948i	0.995582	+	0.0938995i	$0.0299332\pi$
$863$	32.0055	+	32.0055i	1.08948	+	1.08948i	0.0938995	+	0.995582i	$0.470067\pi$
$864$		0			0
$865$	−4.08529	−	4.08529i	−0.138904	−	0.138904i
$866$		0			0
$867$	−34.5804			−1.17441
$868$		0			0
$869$	0.570383	−	0.570383i	0.0193489	−	0.0193489i
$870$		0			0
$871$	36.6678	+	19.6723i	1.24244	+	0.666572i
$872$		0			0
$873$	8.76265	−	8.76265i	0.296571	−	0.296571i
$874$		0			0
$875$		−	32.0515i		−	1.08354i
$876$		0			0
$877$	−20.8160	−	20.8160i	−0.702906	−	0.702906i	0.262127	−	0.965033i	$-0.415576\pi$
$877$	−20.8160	−	20.8160i	−0.702906	−	0.702906i	−0.965033	+	0.262127i	$0.915576\pi$
$878$		0			0
$879$	10.4354	−	10.4354i	0.351977	−	0.351977i
$880$		0			0
$881$		−	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	$-0.226973\pi$
$884$		0			0
$885$		−	12.8392i		−	0.431584i
$886$		0			0
$887$		−	51.7991i		−	1.73924i	−0.493718	−	0.869622i	$-0.664363\pi$
$887$		−	51.7991i		−	1.73924i	0.493718	−	0.869622i	$-0.335637\pi$
$888$		0			0
$889$	−38.6084	+	38.6084i	−1.29488	+	1.29488i
$890$		0			0
$891$	0.0673682	+	0.0673682i	0.00225692	+	0.00225692i
$892$		0			0
$893$		−	24.5043i		−	0.820005i
$894$		0			0
$895$	19.7177	−	19.7177i	0.659090	−	0.659090i
$896$		0			0
$897$	2.08732	+	6.91947i	0.0696935	+	0.231034i
$898$		0			0
$899$	−9.09666	+	9.09666i	−0.303391	+	0.303391i
$900$		0			0
$901$	−10.1350			−0.337647
$902$		0			0
$903$	21.7869	+	21.7869i	0.725023	+	0.725023i
$904$		0			0
$905$	−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	$0.652048\pi$
$908$		0			0
$909$	−10.5683			−0.350528
$910$		0			0
$911$			8.34775i			0.276573i	0.990392	+	0.138287i	$0.0441595\pi$
$911$			8.34775i			0.276573i	−0.990392	+	0.138287i	$0.955840\pi$
$912$		0			0
$913$	0.451627			0.0149467
$914$		0			0
$915$	−3.14283	+	3.14283i	−0.103899	+	0.103899i
$916$		0			0
$917$	−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	$-0.00358242\pi$
$920$		0			0
$921$	−9.49598	−	9.49598i	−0.312903	−	0.312903i
$922$		0			0
$923$	−0.0199987	+	0.0372761i	−0.000658265	+	0.00122696i
$924$		0			0
$925$	−1.58712	−	1.58712i	−0.0521842	−	0.0521842i
$926$		0			0
$927$	−3.52228			−0.115687
$928$		0			0
$929$	11.6044	−	11.6044i	0.380728	−	0.380728i	−0.490636	−	0.871364i	$-0.663236\pi$
$929$	11.6044	−	11.6044i	0.380728	−	0.380728i	0.871364	+	0.490636i	$0.163236\pi$
$930$		0			0
$931$	3.84142	+	3.84142i	0.125897	+	0.125897i
$932$		0			0
$933$	19.3516			0.633543
$934$		0			0
$935$	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	$0.529881\pi$
$938$		0			0
$939$	10.1200			0.330254
$940$		0			0
$941$	0.617212	+	0.617212i	0.0201205	+	0.0201205i	0.717095	−	0.696975i	$-0.245471\pi$
$941$	0.617212	+	0.617212i	0.0201205	+	0.0201205i	−0.696975	+	0.717095i	$0.745471\pi$
$942$		0			0
$943$	15.9231	−	15.9231i	0.518526	−	0.518526i
$944$		0			0
$945$	6.74298			0.219349
$946$		0			0
$947$	2.57671	+	2.57671i	0.0837319	+	0.0837319i	0.747732	−	0.664000i	$-0.231143\pi$
$947$	2.57671	+	2.57671i	0.0837319	+	0.0837319i	−0.664000	+	0.747732i	$0.731143\pi$
$948$		0			0
$949$	1.01076	−	1.88399i	0.0328108	−	0.0611570i
$950$		0			0
$951$	18.1488	+	18.1488i	0.588515	+	0.588515i
$952$		0			0
$953$			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
$956$		0			0
$957$	−0.294404	+	0.294404i	−0.00951672	+	0.00951672i
$958$		0			0
$959$	62.5667			2.02038
$960$		0			0
$961$		−	22.3340i		−	0.720452i
$962$		0			0
$963$	−11.8314			−0.381261
$964$		0			0
$965$			11.5765i			0.372660i
$966$		0			0
$967$	−23.3487	−	23.3487i	−0.750844	−	0.750844i	0.223792	−	0.974637i	$-0.428156\pi$
$967$	−23.3487	−	23.3487i	−0.750844	−	0.750844i	−0.974637	+	0.223792i	$0.928156\pi$
$968$		0			0
$969$	−16.5600	−	16.5600i	−0.531985	−	0.531985i
$970$		0			0
$971$	−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			0
$975$	0.851558	−	0.256880i	0.0272717	−	0.00822674i
$976$		0			0
$977$	−19.1168	+	19.1168i	−0.611602	+	0.611602i	−0.943363	−	0.331761i	$-0.892357\pi$
$977$	−19.1168	+	19.1168i	−0.611602	+	0.611602i	0.331761	+	0.943363i	$0.392357\pi$
$978$		0			0
$979$			0.256593i			0.00820076i
$980$		0			0
$981$	12.9904	+	12.9904i	0.414751	+	0.414751i
$982$		0			0
$983$	−20.0123	+	20.0123i	−0.638293	+	0.638293i	−0.950134	−	0.311841i	$-0.899054\pi$
$983$	−20.0123	+	20.0123i	−0.638293	+	0.638293i	0.311841	+	0.950134i	$0.399054\pi$
$984$		0			0
$985$		−	7.32462i		−	0.233382i
$986$		0			0
$987$		−	22.1216i		−	0.704139i
$988$		0			0
$989$			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	$0.804292\pi$
$992$		0			0
$993$	22.5976	−	22.5976i	0.717114	−	0.717114i
$994$		0			0
$995$	−42.8201	−	42.8201i	−1.35749	−	1.35749i
$996$		0			0
$997$			27.1788i			0.860762i	0.902647	+	0.430381i	$0.141621\pi$
$997$			27.1788i			0.860762i	−0.902647	+	0.430381i	$0.858379\pi$
$998$		0			0
$999$	−6.43362	+	6.43362i	−0.203551	+	0.203551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.bb.f.655.4		24
4.3	odd	2		312.2.t.e.187.12	yes	24
8.3	odd	2	inner	1248.2.bb.f.655.9		24
8.5	even	2		312.2.t.e.187.7	✓	24
12.11	even	2		936.2.w.j.811.1		24
13.8	odd	4	inner	1248.2.bb.f.463.9		24
24.5	odd	2		936.2.w.j.811.6		24
52.47	even	4		312.2.t.e.307.7	yes	24
104.21	odd	4		312.2.t.e.307.12	yes	24
104.99	even	4	inner	1248.2.bb.f.463.4		24
156.47	odd	4		936.2.w.j.307.6		24
312.125	even	4		936.2.w.j.307.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.7	✓	24	8.5	even	2
312.2.t.e.187.12	yes	24	4.3	odd	2
312.2.t.e.307.7	yes	24	52.47	even	4
312.2.t.e.307.12	yes	24	104.21	odd	4
936.2.w.j.307.1		24	312.125	even	4
936.2.w.j.307.6		24	156.47	odd	4
936.2.w.j.811.1		24	12.11	even	2
936.2.w.j.811.6		24	24.5	odd	2
1248.2.bb.f.463.4		24	104.99	even	4	inner
1248.2.bb.f.463.9		24	13.8	odd	4	inner
1248.2.bb.f.655.4		24	1.1	even	1	trivial
1248.2.bb.f.655.9		24	8.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-1.61967 - 1.61967i) q^{5} +(-2.08158 + 2.08158i) q^{7} +1.00000 q^{9} +(0.0673682 + 0.0673682i) q^{11} +(-1.04130 - 3.45191i) q^{13} +(-1.61967 - 1.61967i) q^{15} +7.18195i q^{17} +(-2.30579 + 2.30579i) q^{19} +(-2.08158 + 2.08158i) q^{21} -2.00453 q^{23} +0.246692i q^{25} +1.00000 q^{27} +4.37007i q^{29} +(2.08158 + 2.08158i) q^{31} +(0.0673682 + 0.0673682i) q^{33} +6.74298 q^{35} +(-6.43362 + 6.43362i) q^{37} +(-1.04130 - 3.45191i) q^{39} +(-7.94353 + 7.94353i) q^{41} -10.4665i q^{43} +(-1.61967 - 1.61967i) q^{45} +(-5.31365 + 5.31365i) q^{47} -1.66599i q^{49} +7.18195i q^{51} +1.41118i q^{53} -0.218229i q^{55} +(-2.30579 + 2.30579i) q^{57} +(3.96350 + 3.96350i) q^{59} -1.94041i q^{61} +(-2.08158 + 2.08158i) q^{63} +(-3.90441 + 7.27754i) q^{65} +(-8.16072 + 8.16072i) q^{67} -2.00453 q^{69} +(-0.00829610 - 0.00829610i) q^{71} +(0.419298 + 0.419298i) q^{73} +0.246692i q^{75} -0.280465 q^{77} -8.46664i q^{79} +1.00000 q^{81} +(3.35193 - 3.35193i) q^{83} +(11.6324 - 11.6324i) q^{85} +4.37007i q^{87} +(1.90441 + 1.90441i) q^{89} +(9.35300 + 5.01789i) q^{91} +(2.08158 + 2.08158i) q^{93} +7.46925 q^{95} +(8.76265 - 8.76265i) q^{97} +(0.0673682 + 0.0673682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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