LMFDB - Embedded newform 312.2.t.e.307.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(187,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.187"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.t (of order $4$, degree $2$, 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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.7
Character	$\chi$	$=$	312.307
Dual form			312.2.t.e.187.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0632999 + 1.41280i) q^{2} -1.00000 q^{3} +(-1.99199 + 0.178860i) q^{4} +(1.61967 - 1.61967i) q^{5} +(-0.0632999 - 1.41280i) q^{6} +(-2.08158 - 2.08158i) q^{7} +(-0.378785 - 2.80295i) q^{8} +1.00000 q^{9} +(2.39080 + 2.18574i) q^{10} +(-0.0673682 + 0.0673682i) q^{11} +(1.99199 - 0.178860i) q^{12} +(1.04130 - 3.45191i) q^{13} +(2.80909 - 3.07262i) q^{14} +(-1.61967 + 1.61967i) q^{15} +(3.93602 - 0.712572i) q^{16} -7.18195i q^{17} +(0.0632999 + 1.41280i) q^{18} +(2.30579 + 2.30579i) q^{19} +(-2.93668 + 3.51606i) q^{20} +(2.08158 + 2.08158i) q^{21} +(-0.0994420 - 0.0909132i) q^{22} -2.00453 q^{23} +(0.378785 + 2.80295i) q^{24} -0.246692i q^{25} +(4.94276 + 1.25264i) q^{26} -1.00000 q^{27} +(4.51880 + 3.77418i) q^{28} +4.37007i q^{29} +(-2.39080 - 2.18574i) q^{30} +(2.08158 - 2.08158i) q^{31} +(1.25587 + 5.51569i) q^{32} +(0.0673682 - 0.0673682i) q^{33} +(10.1466 - 0.454617i) q^{34} -6.74298 q^{35} +(-1.99199 + 0.178860i) q^{36} +(6.43362 + 6.43362i) q^{37} +(-3.11165 + 3.40356i) q^{38} +(-1.04130 + 3.45191i) q^{39} +(-5.15337 - 3.92636i) q^{40} +(-7.94353 - 7.94353i) q^{41} +(-2.80909 + 3.07262i) q^{42} -10.4665i q^{43} +(0.122147 - 0.146246i) q^{44} +(1.61967 - 1.61967i) q^{45} +(-0.126887 - 2.83200i) q^{46} +(-5.31365 - 5.31365i) q^{47} +(-3.93602 + 0.712572i) q^{48} +1.66599i q^{49} +(0.348525 - 0.0156156i) q^{50} +7.18195i q^{51} +(-1.45685 + 7.06241i) q^{52} +1.41118i q^{53} +(-0.0632999 - 1.41280i) q^{54} +0.218229i q^{55} +(-5.04610 + 6.62305i) q^{56} +(-2.30579 - 2.30579i) q^{57} +(-6.17401 + 0.276625i) q^{58} +(-3.96350 + 3.96350i) q^{59} +(2.93668 - 3.51606i) q^{60} -1.94041i q^{61} +(3.07262 + 2.80909i) q^{62} +(-2.08158 - 2.08158i) q^{63} +(-7.71304 + 2.12343i) q^{64} +(-3.90441 - 7.27754i) q^{65} +(0.0994420 + 0.0909132i) q^{66} +(8.16072 + 8.16072i) q^{67} +(1.28456 + 14.3063i) q^{68} +2.00453 q^{69} +(-0.426830 - 9.52646i) q^{70} +(-0.00829610 + 0.00829610i) q^{71} +(-0.378785 - 2.80295i) q^{72} +(0.419298 - 0.419298i) q^{73} +(-8.68214 + 9.49664i) q^{74} +0.246692i q^{75} +(-5.00551 - 4.18068i) q^{76} +0.280465 q^{77} +(-4.94276 - 1.25264i) q^{78} +8.46664i q^{79} +(5.22093 - 7.52920i) q^{80} +1.00000 q^{81} +(10.7198 - 11.7254i) q^{82} +(-3.35193 - 3.35193i) q^{83} +(-4.51880 - 3.77418i) q^{84} +(-11.6324 - 11.6324i) q^{85} +(14.7870 - 0.662529i) q^{86} -4.37007i q^{87} +(0.214348 + 0.163312i) q^{88} +(1.90441 - 1.90441i) q^{89} +(2.39080 + 2.18574i) q^{90} +(-9.35300 + 5.01789i) q^{91} +(3.99300 - 0.358530i) q^{92} +(-2.08158 + 2.08158i) q^{93} +(7.17075 - 7.84346i) q^{94} +7.46925 q^{95} +(-1.25587 - 5.51569i) q^{96} +(8.76265 + 8.76265i) q^{97} +(-2.35370 + 0.105457i) q^{98} +(-0.0673682 + 0.0673682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} - 6 q^{8} + 24 q^{9} + 8 q^{11} + 36 q^{14} + 28 q^{16} + 20 q^{19} - 20 q^{20} + 20 q^{22} + 6 q^{24} + 12 q^{26} - 24 q^{27} - 16 q^{28} - 30 q^{32} - 8 q^{33} + 16 q^{34} + 16 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q - 24 * q^3 - 6 * q^8 + 24 * q^9 + 8 * q^11 + 36 * q^14 + 28 * q^16 + 20 * q^19 - 20 * q^20 + 20 * q^22 + 6 * q^24 + 12 * q^26 - 24 * q^27 - 16 * q^28 - 30 * q^32 - 8 * q^33 + 16 * q^34 + 16 * q^35 + 36 * q^40 - 12 * q^41 - 36 * q^42 - 32 * q^44 - 44 * q^46 - 28 * q^48 - 36 * q^50 + 4 * q^52 - 20 * q^57 + 32 * q^58 - 16 * q^59 + 20 * q^60 - 76 * q^65 - 20 * q^66 + 28 * q^67 + 32 * q^68 - 40 * q^70 - 6 * q^72 - 8 * q^73 - 32 * q^74 - 36 * q^76 - 12 * q^78 - 32 * q^80 + 24 * q^81 - 72 * q^83 + 16 * q^84 + 4 * q^86 + 28 * q^89 - 4 * q^91 + 32 * q^92 + 28 * q^94 + 30 * q^96 + 24 * q^97 + 68 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.0632999	+	1.41280i	0.0447598	+	0.998998i
$2$	0.0632999	+	1.41280i	0.0447598	+	0.998998i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−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	$0.0788358\pi$
$6$	−0.0632999	−	1.41280i	−0.0258421	−	0.576772i
$7$	−2.08158	−	2.08158i	−0.786765	−	0.786765i	0.194197	−	0.980962i	$-0.437790\pi$
$7$	−2.08158	−	2.08158i	−0.786765	−	0.786765i	−0.980962	+	0.194197i	$0.937790\pi$
$8$	−0.378785	−	2.80295i	−0.133921	−	0.990992i
$9$	1.00000			0.333333
$10$	2.39080	+	2.18574i	0.756036	+	0.691193i
$11$	−0.0673682	+	0.0673682i	−0.0203123	+	0.0203123i	−0.717190	−	0.696878i	$-0.754572\pi$
$11$	−0.0673682	+	0.0673682i	−0.0203123	+	0.0203123i	0.696878	+	0.717190i	$0.254572\pi$
$12$	1.99199	−	0.178860i	0.575037	−	0.0516323i
$13$	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
$15$	−1.61967	+	1.61967i	−0.418198	+	0.418198i
$16$	3.93602	−	0.712572i	0.984005	−	0.178143i
$17$		−	7.18195i		−	1.74188i	−0.491391	−	0.870939i	$-0.663511\pi$
$17$		−	7.18195i		−	1.74188i	0.491391	−	0.870939i	$-0.336489\pi$
$18$	0.0632999	+	1.41280i	0.0149199	+	0.332999i
$19$	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	$0.627969\pi$
$20$	−2.93668	+	3.51606i	−0.656661	+	0.786216i
$21$	2.08158	+	2.08158i	0.454239	+	0.454239i
$22$	−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	$0.567017\pi$
$24$	0.378785	+	2.80295i	0.0773191	+	0.572150i
$25$		−	0.246692i		−	0.0493384i
$26$	4.94276	+	1.25264i	0.969355	+	0.245662i
$27$	−1.00000			−0.192450
$28$	4.51880	+	3.77418i	0.853973	+	0.713252i
$29$			4.37007i			0.811501i	0.913984	+	0.405750i	$0.132990\pi$
$29$			4.37007i			0.811501i	−0.913984	+	0.405750i	$0.867010\pi$
$30$	−2.39080	−	2.18574i	−0.436498	−	0.399061i
$31$	2.08158	−	2.08158i	0.373864	−	0.373864i	−0.495019	−	0.868882i	$-0.664839\pi$
$31$	2.08158	−	2.08158i	0.373864	−	0.373864i	0.868882	+	0.495019i	$0.164839\pi$
$32$	1.25587	+	5.51569i	0.222008	+	0.975045i
$33$	0.0673682	−	0.0673682i	0.0117273	−	0.0117273i
$34$	10.1466	−	0.454617i	1.74013	−	0.0779661i
$35$	−6.74298			−1.13977
$36$	−1.99199	+	0.178860i	−0.331998	+	0.0298100i
$37$	6.43362	+	6.43362i	1.05768	+	1.05768i	0.998231	+	0.0594489i	$0.0189343\pi$
$37$	6.43362	+	6.43362i	1.05768	+	1.05768i	0.0594489	+	0.998231i	$0.481066\pi$
$38$	−3.11165	+	3.40356i	−0.504777	+	0.552131i
$39$	−1.04130	+	3.45191i	−0.166741	+	0.552748i
$40$	−5.15337	−	3.92636i	−0.814820	−	0.620812i
$41$	−7.94353	−	7.94353i	−1.24057	−	1.24057i	−0.959764	−	0.280806i	$-0.909398\pi$
$41$	−7.94353	−	7.94353i	−1.24057	−	1.24057i	−0.280806	−	0.959764i	$-0.590602\pi$
$42$	−2.80909	+	3.07262i	−0.433452	+	0.474115i
$43$		−	10.4665i		−	1.59613i	−0.602573	−	0.798064i	$-0.705858\pi$
$43$		−	10.4665i		−	1.59613i	0.602573	−	0.798064i	$-0.294142\pi$
$44$	0.122147	−	0.146246i	0.0184144	−	0.0220474i
$45$	1.61967	−	1.61967i	0.241447	−	0.241447i
$46$	−0.126887	−	2.83200i	−0.0187084	−	0.417555i
$47$	−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	$0.934634\pi$
$48$	−3.93602	+	0.712572i	−0.568115	+	0.102851i
$49$			1.66599i			0.237998i
$50$	0.348525	−	0.0156156i	0.0492889	−	0.00220837i
$51$			7.18195i			1.00567i
$52$	−1.45685	+	7.06241i	−0.202028	+	0.979380i
$53$			1.41118i			0.193841i	0.995292	+	0.0969204i	$0.0308992\pi$
$53$			1.41118i			0.193841i	−0.995292	+	0.0969204i	$0.969101\pi$
$54$	−0.0632999	−	1.41280i	−0.00861402	−	0.192257i
$55$			0.218229i			0.0294260i
$56$	−5.04610	+	6.62305i	−0.674314	+	0.885042i
$57$	−2.30579	−	2.30579i	−0.305409	−	0.305409i
$58$	−6.17401	+	0.276625i	−0.810687	+	0.0363226i
$59$	−3.96350	+	3.96350i	−0.516004	+	0.516004i	−0.916360	−	0.400356i	$-0.868887\pi$
$59$	−3.96350	+	3.96350i	−0.516004	+	0.516004i	0.400356	+	0.916360i	$0.368887\pi$
$60$	2.93668	−	3.51606i	0.379123	−	0.453922i
$61$		−	1.94041i		−	0.248444i	−0.992254	−	0.124222i	$-0.960357\pi$
$61$		−	1.94041i		−	0.248444i	0.992254	−	0.124222i	$-0.0396434\pi$
$62$	3.07262	+	2.80909i	0.390223	+	0.356755i
$63$	−2.08158	−	2.08158i	−0.262255	−	0.262255i
$64$	−7.71304	+	2.12343i	−0.964131	+	0.265429i
$65$	−3.90441	−	7.27754i	−0.484282	−	0.902668i
$66$	0.0994420	+	0.0909132i	0.0122405	+	0.0111906i
$67$	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
$69$	2.00453			0.241317
$70$	−0.426830	−	9.52646i	−0.0510159	−	1.13863i
$71$	−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	$0.250222\pi$
$72$	−0.378785	−	2.80295i	−0.0446402	−	0.330331i
$73$	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
$75$			0.246692i			0.0284855i
$76$	−5.00551	−	4.18068i	−0.574171	−	0.479557i
$77$	0.280465			0.0319620
$78$	−4.94276	−	1.25264i	−0.559658	−	0.141833i
$79$			8.46664i			0.952571i	0.879291	+	0.476286i	$0.158017\pi$
$79$			8.46664i			0.952571i	−0.879291	+	0.476286i	$0.841983\pi$
$80$	5.22093	−	7.52920i	0.583718	−	0.841791i
$81$	1.00000			0.111111
$82$	10.7198	−	11.7254i	1.18380	−	1.29486i
$83$	−3.35193	−	3.35193i	−0.367922	−	0.367922i	0.498797	−	0.866719i	$-0.333775\pi$
$83$	−3.35193	−	3.35193i	−0.367922	−	0.367922i	−0.866719	+	0.498797i	$0.833775\pi$
$84$	−4.51880	−	3.77418i	−0.493041	−	0.411796i
$85$	−11.6324	−	11.6324i	−1.26171	−	1.26171i
$86$	14.7870	−	0.662529i	1.59453	−	0.0714423i
$87$		−	4.37007i		−	0.468520i
$88$	0.214348	+	0.163312i	0.0228496	+	0.0174091i
$89$	1.90441	−	1.90441i	0.201867	−	0.201867i	−0.598933	−	0.800799i	$-0.704408\pi$
$89$	1.90441	−	1.90441i	0.201867	−	0.201867i	0.800799	+	0.598933i	$0.204408\pi$
$90$	2.39080	+	2.18574i	0.252012	+	0.230398i
$91$	−9.35300	+	5.01789i	−0.980461	+	0.526018i
$92$	3.99300	−	0.358530i	0.416299	−	0.0373794i
$93$	−2.08158	+	2.08158i	−0.215850	+	0.215850i
$94$	7.17075	−	7.84346i	0.739607	−	0.808991i
$95$	7.46925			0.766329
$96$	−1.25587	−	5.51569i	−0.128177	−	0.562942i
$97$	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	$0.533415\pi$
$98$	−2.35370	+	0.105457i	−0.237760	+	0.0106528i
$99$	−0.0673682	+	0.0673682i	−0.00677076	+	0.00677076i
$100$	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	$0.323769\pi$
$102$	−10.1466	+	0.454617i	−1.00467	+	0.0450137i
$103$	−3.52228			−0.347061			−0.173530	−	0.984829i	$-0.555518\pi$
$103$	−3.52228			−0.347061			−0.173530	+	0.984829i	$0.555518\pi$
$104$	−10.0700	−	1.61118i	−0.987441	−	0.157989i
$105$	6.74298			0.658047
$106$	−1.99371	+	0.0893277i	−0.193646	+	0.00867627i
$107$	11.8314			1.14378			0.571892	−	0.820329i	$-0.306210\pi$
$107$	11.8314			1.14378			0.571892	+	0.820329i	$0.306210\pi$
$108$	1.99199	−	0.178860i	0.191679	−	0.0172108i
$109$	−12.9904	+	12.9904i	−1.24425	+	1.24425i	−0.286033	+	0.958220i	$0.592337\pi$
$109$	−12.9904	+	12.9904i	−1.24425	+	1.24425i	−0.958220	+	0.286033i	$0.907663\pi$
$110$	−0.308313	+	0.0138139i	−0.0293965	+	0.00131710i
$111$	−6.43362	−	6.43362i	−0.610652	−	0.610652i
$112$	−9.67643	−	6.70988i	−0.914337	−	0.634024i
$113$	12.7051			1.19520			0.597598	−	0.801796i	$-0.296122\pi$
$113$	12.7051			1.19520			0.597598	+	0.801796i	$0.296122\pi$
$114$	3.11165	−	3.40356i	0.291433	−	0.318773i
$115$	−3.24669	+	3.24669i	−0.302756	+	0.302756i
$116$	−0.781629	−	8.70511i	−0.0725724	−	0.808249i
$117$	1.04130	−	3.45191i	0.0962681	−	0.319129i
$118$	−5.85051	−	5.34873i	−0.538583	−	0.492391i
$119$	−14.9498	+	14.9498i	−1.37045	+	1.37045i
$120$	5.15337	+	3.92636i	0.470436	+	0.358426i
$121$			10.9909i			0.999175i
$122$	2.74140	−	0.122828i	0.248195	−	0.0111203i
$123$	7.94353	+	7.94353i	0.716244	+	0.716244i
$124$	−3.77418	+	4.51880i	−0.338931	+	0.405800i
$125$	7.69881	+	7.69881i	0.688603	+	0.688603i
$126$	2.80909	−	3.07262i	0.250254	−	0.273731i
$127$	18.5476			1.64583			0.822916	−	0.568164i	$-0.192346\pi$
$127$	18.5476			1.64583			0.822916	+	0.568164i	$0.192346\pi$
$128$	−3.48821	−	10.7625i	−0.308317	−	0.951284i
$129$			10.4665i			0.921525i
$130$	10.0345	−	5.97680i	0.880087	−	0.524200i
$131$	−5.20053			−0.454372			−0.227186	−	0.973851i	$-0.572953\pi$
$131$	−5.20053			−0.454372			−0.227186	+	0.973851i	$0.572953\pi$
$132$	−0.122147	+	0.146246i	−0.0106315	+	0.0127291i
$133$		−	9.59938i		−	0.832372i
$134$	−11.0129	+	12.0460i	−0.951367	+	1.04062i
$135$	−1.61967	+	1.61967i	−0.139399	+	0.139399i
$136$	−20.1306	+	2.72041i	−1.72619	+	0.233274i
$137$	−15.0286	+	15.0286i	−1.28398	+	1.28398i	−0.345598	+	0.938383i	$0.612324\pi$
$137$	−15.0286	+	15.0286i	−1.28398	+	1.28398i	−0.938383	+	0.345598i	$0.887676\pi$
$138$	0.126887	+	2.83200i	0.0108013	+	0.241076i
$139$	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
$141$	5.31365	+	5.31365i	0.447490	+	0.447490i
$142$	−0.0122458	−	0.0111956i	−0.00102765	−	0.000939510i
$143$	0.162399	+	0.302700i	0.0135805	+	0.0253130i
$144$	3.93602	−	0.712572i	0.328002	−	0.0593810i
$145$	7.07808	+	7.07808i	0.587803	+	0.587803i
$146$	0.618924	+	0.565841i	0.0512225	+	0.0468293i
$147$		−	1.66599i		−	0.137408i
$148$	−13.9664	−	11.6650i	−1.14803	−	0.958854i
$149$	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	$-0.0285856\pi$
$150$	−0.348525	+	0.0156156i	−0.0284570	+	0.00127501i
$151$	−2.61081	−	2.61081i	−0.212465	−	0.212465i	0.592849	−	0.805314i	$-0.298003\pi$
$151$	−2.61081	−	2.61081i	−0.212465	−	0.212465i	−0.805314	+	0.592849i	$0.798003\pi$
$152$	5.58961	−	7.33640i	0.453377	−	0.595061i
$153$		−	7.18195i		−	0.580626i
$154$	0.0177534	+	0.396240i	0.00143061	+	0.0319300i
$155$		−	6.74298i		−	0.541609i
$156$	1.45685	−	7.06241i	0.116641	−	0.565445i
$157$			1.36321i			0.108796i	0.998519	+	0.0543978i	$0.0173239\pi$
$157$			1.36321i			0.108796i	−0.998519	+	0.0543978i	$0.982676\pi$
$158$	−11.9616	+	0.535937i	−0.951617	+	0.0426369i
$159$		−	1.41118i		−	0.111914i
$160$	10.9677	+	6.89952i	0.867074	+	0.545455i
$161$	4.17261	+	4.17261i	0.328847	+	0.328847i
$162$	0.0632999	+	1.41280i	0.00497331	+	0.111000i
$163$	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	$-0.0249145\pi$
$164$	17.2442	+	14.4026i	1.34654	+	1.12466i
$165$		−	0.218229i		−	0.0169891i
$166$	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	$0.694772\pi$
$168$	5.04610	−	6.62305i	0.389315	−	0.510979i
$169$	−10.8314	−	7.18895i	−0.833184	−	0.552996i
$170$	15.6979	−	17.1706i	1.20397	−	1.31692i
$171$	2.30579	+	2.30579i	0.176328	+	0.176328i
$172$	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	$0.530567\pi$
$174$	6.17401	−	0.276625i	0.468051	−	0.0209709i
$175$	−0.513510	+	0.513510i	−0.0388177	+	0.0388177i
$176$	−0.217158	+	0.313167i	−0.0163689	+	0.0236059i
$177$	3.96350	−	3.96350i	0.297915	−	0.297915i
$178$	2.81109	+	2.56999i	0.210700	+	0.192629i
$179$			12.1739i			0.909917i	0.890513	+	0.454958i	$0.150346\pi$
$179$			12.1739i			0.909917i	−0.890513	+	0.454958i	$0.849654\pi$
$180$	−2.93668	+	3.51606i	−0.218887	+	0.262072i
$181$	−1.13958			−0.0847044			−0.0423522	−	0.999103i	$-0.513485\pi$
$181$	−1.13958			−0.0847044			−0.0423522	+	0.999103i	$0.513485\pi$
$182$	−7.68131	−	12.8962i	−0.569376	−	0.955934i
$183$			1.94041i			0.143439i
$184$	0.759287	+	5.61860i	0.0559754	+	0.414209i
$185$	20.8407			1.53224
$186$	−3.07262	−	2.80909i	−0.225295	−	0.205973i
$187$	0.483835	+	0.483835i	0.0353815	+	0.0353815i
$188$	11.5351	+	9.63432i	0.841285	+	0.702655i
$189$	2.08158	+	2.08158i	0.151413	+	0.151413i
$190$	0.472803	+	10.5525i	0.0343007	+	0.765561i
$191$		−	22.4304i		−	1.62301i	−0.584347	−	0.811504i	$-0.698649\pi$
$191$		−	22.4304i		−	1.62301i	0.584347	−	0.811504i	$-0.301351\pi$
$192$	7.71304	−	2.12343i	0.556641	−	0.153245i
$193$	−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
$195$	3.90441	+	7.27754i	0.279601	+	0.521155i
$196$	−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	$0.286339\pi$
$198$	−0.0994420	−	0.0909132i	−0.00706704	−	0.00646092i
$199$	26.4375			1.87410			0.937051	−	0.349193i	$-0.113544\pi$
$199$	26.4375			1.87410			0.937051	+	0.349193i	$0.113544\pi$
$200$	−0.691464	+	0.0934431i	−0.0488939	+	0.00660743i
$201$	−8.16072	−	8.16072i	−0.575613	−	0.575613i
$202$	0.668972	+	14.9309i	0.0470687	+	1.05053i
$203$	9.09666	−	9.09666i	0.638460	−	0.638460i
$204$	−1.28456	−	14.3063i	−0.0899373	−	1.00164i
$205$	−25.7319			−1.79719
$206$	−0.222960	−	4.97627i	−0.0155344	−	0.346713i
$207$	−2.00453			−0.139325
$208$	1.63884	−	14.3288i	0.113633	−	0.993523i
$209$	−0.310674			−0.0214897
$210$	0.426830	+	9.52646i	0.0294541	+	0.657388i
$211$	−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
$213$	0.00829610	−	0.00829610i	0.000568439	−	0.000568439i
$214$	0.748926	+	16.7153i	0.0511955	+	1.14264i
$215$	−16.9523	−	16.9523i	−1.15614	−	1.15614i
$216$	0.378785	+	2.80295i	0.0257730	+	0.190717i
$217$	−8.66599			−0.588286
$218$	−19.1751	−	17.5305i	−1.29870	−	1.18731i
$219$	−0.419298	+	0.419298i	−0.0283335	+	0.0283335i
$220$	−0.0390324	−	0.434710i	−0.00263157	−	0.0293081i
$221$	−24.7915	−	7.47856i	−1.66765	−	0.503062i
$222$	8.68214	−	9.49664i	0.582707	−	0.637373i
$223$	−6.65855	+	6.65855i	−0.445889	+	0.445889i	−0.893985	−	0.448096i	$-0.852102\pi$
$223$	−6.65855	+	6.65855i	−0.445889	+	0.445889i	0.448096	+	0.893985i	$0.352102\pi$
$224$	8.86717	−	14.0956i	0.592463	−	0.941800i
$225$		−	0.246692i		−	0.0164461i
$226$	0.804232	+	17.9497i	0.0534967	+	1.19400i
$227$	−7.86789	−	7.86789i	−0.522210	−	0.522210i	0.396028	−	0.918238i	$-0.370388\pi$
$227$	−7.86789	−	7.86789i	−0.522210	−	0.522210i	−0.918238	+	0.396028i	$0.870388\pi$
$228$	5.00551	+	4.18068i	0.331498	+	0.276873i
$229$	3.64543	+	3.64543i	0.240897	+	0.240897i	0.817221	−	0.576324i	$-0.195513\pi$
$229$	3.64543	+	3.64543i	0.240897	+	0.240897i	−0.576324	+	0.817221i	$0.695513\pi$
$230$	−4.79243	−	4.38140i	−0.316003	−	0.288901i
$231$	−0.280465			−0.0184533
$232$	12.2491	−	1.65531i	0.804191	−	0.108677i
$233$		−	3.31543i		−	0.217201i	−0.994085	−	0.108601i	$-0.965363\pi$
$233$		−	3.31543i		−	0.217201i	0.994085	−	0.108601i	$-0.0346370\pi$
$234$	4.94276	+	1.25264i	0.323118	+	0.0818875i
$235$	−17.2128			−1.12284
$236$	7.18633	−	8.60416i	0.467791	−	0.560083i
$237$		−	8.46664i		−	0.549967i
$238$	−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	$0.138715\pi$
$240$	−5.22093	+	7.52920i	−0.337010	+	0.486008i
$241$	−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	$0.384888\pi$
$242$	−15.5279	+	0.695724i	−0.998173	+	0.0447229i
$243$	−1.00000			−0.0641500
$244$	0.347061	+	3.86526i	0.0222183	+	0.247448i
$245$	2.69836	+	2.69836i	0.172392	+	0.172392i
$246$	−10.7198	+	11.7254i	−0.683467	+	0.747585i
$247$	10.3604	−	5.55836i	0.659216	−	0.353670i
$248$	−6.62305	−	5.04610i	−0.420564	−	0.320428i
$249$	3.35193	+	3.35193i	0.212420	+	0.212420i
$250$	−10.3895	+	11.3642i	−0.657091	+	0.718734i
$251$			18.4986i			1.16762i	0.811889	+	0.583812i	$0.198439\pi$
$251$			18.4986i			1.16762i	−0.811889	+	0.583812i	$0.801561\pi$
$252$	4.51880	+	3.77418i	0.284658	+	0.237751i
$253$	0.135042	−	0.135042i	0.00849001	−	0.00849001i
$254$	1.17406	+	26.2039i	0.0736671	+	1.64418i
$255$	11.6324	+	11.6324i	0.728450	+	0.728450i
$256$	14.9845	−	5.60939i	0.936530	−	0.350587i
$257$		−	17.6933i		−	1.10368i	−0.833950	−	0.551840i	$-0.813926\pi$
$257$		−	17.6933i		−	1.10368i	0.833950	−	0.551840i	$-0.186074\pi$
$258$	−14.7870	+	0.662529i	−0.920601	+	0.0412473i
$259$		−	26.7842i		−	1.66429i
$260$	9.07919	+	13.7984i	0.563067	+	0.855742i
$261$			4.37007i			0.270500i
$262$	−0.329193	−	7.34728i	−0.0203376	−	0.453917i
$263$			18.2366i			1.12452i	0.826962	+	0.562258i	$0.190067\pi$
$263$			18.2366i			1.12452i	−0.826962	+	0.562258i	$0.809933\pi$
$264$	−0.214348	−	0.163312i	−0.0131922	−	0.0100511i
$265$	2.28566	+	2.28566i	0.140407	+	0.140407i
$266$	13.5620	−	0.607640i	0.831538	−	0.0372568i
$267$	−1.90441	+	1.90441i	−0.116548	+	0.116548i
$268$	−17.7157	−	14.7964i	−1.08216	−	0.903835i
$269$		−	6.68357i		−	0.407504i	−0.979023	−	0.203752i	$-0.934686\pi$
$269$		−	6.68357i		−	0.407504i	0.979023	−	0.203752i	$-0.0653137\pi$
$270$	−2.39080	−	2.18574i	−0.145499	−	0.133020i
$271$	5.65140	+	5.65140i	0.343298	+	0.343298i	0.857606	−	0.514308i	$-0.171951\pi$
$271$	5.65140	+	5.65140i	0.343298	+	0.343298i	−0.514308	+	0.857606i	$0.671951\pi$
$272$	−5.11766	−	28.2683i	−0.310303	−	1.71402i
$273$	9.35300	−	5.01789i	0.566069	−	0.303697i
$274$	−22.1837	−	20.2811i	−1.34016	−	1.22522i
$275$	0.0166192	+	0.0166192i	0.00100218	+	0.00100218i
$276$	−3.99300	+	0.358530i	−0.240351	+	0.0215810i
$277$	24.3573			1.46349			0.731745	−	0.681579i	$-0.238706\pi$
$277$	24.3573			1.46349			0.731745	+	0.681579i	$0.238706\pi$
$278$	0.387674	+	8.65254i	0.0232512	+	0.518945i
$279$	2.08158	−	2.08158i	0.124621	−	0.124621i
$280$	2.55414	+	18.9002i	0.152639	+	1.12950i
$281$	−7.19722	+	7.19722i	−0.429350	+	0.429350i	−0.888407	−	0.459057i	$-0.848187\pi$
$281$	−7.19722	+	7.19722i	−0.429350	+	0.429350i	0.459057	+	0.888407i	$0.348187\pi$
$282$	−7.17075	+	7.84346i	−0.427012	+	0.467071i
$283$		−	14.0053i		−	0.832529i	−0.909244	−	0.416264i	$-0.863339\pi$
$283$		−	14.0053i		−	0.832529i	0.909244	−	0.416264i	$-0.136661\pi$
$284$	0.0150419	−	0.0180096i	0.000892571	−	0.00106867i
$285$	−7.46925			−0.442440
$286$	−0.417373	+	0.248597i	−0.0246798	+	0.0146999i
$287$			33.0703i			1.95208i
$288$	1.25587	+	5.51569i	0.0740028	+	0.325015i
$289$	−34.5804			−2.03414
$290$	−9.55185	+	10.4479i	−0.560904	+	0.613524i
$291$	−8.76265	−	8.76265i	−0.513676	−	0.513676i
$292$	−0.760240	+	0.910231i	−0.0444897	+	0.0532672i
$293$	−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	$0.891868\pi$
$294$	2.35370	−	0.105457i	0.137271	−	0.00615037i
$295$			12.8392i			0.747526i
$296$	15.5961	−	20.4701i	0.906507	−	1.18980i
$297$	0.0673682	−	0.0673682i	0.00390910	−	0.00390910i
$298$	19.5614	+	17.8837i	1.13316	+	1.03597i
$299$	−2.08732	+	6.91947i	−0.120713	+	0.400163i
$300$	−0.0441232	−	0.491407i	−0.00254746	−	0.0283714i
$301$	−21.7869	+	21.7869i	−1.25578	+	1.25578i
$302$	3.52328	−	3.85381i	0.202742	−	0.221762i
$303$	−10.5683			−0.607133
$304$	10.7187	+	7.43258i	0.614757	+	0.426288i
$305$	−3.14283	−	3.14283i	−0.179958	−	0.179958i
$306$	10.1466	−	0.454617i	0.580044	−	0.0259887i
$307$	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
$309$	3.52228			0.200376
$310$	9.52646	−	0.426830i	0.541066	−	0.0242423i
$311$	19.3516			1.09733			0.548664	−	0.836043i	$-0.315136\pi$
$311$	19.3516			1.09733			0.548664	+	0.836043i	$0.315136\pi$
$312$	10.0700	+	1.61118i	0.570099	+	0.0912149i
$313$	10.1200			0.572016			0.286008	−	0.958227i	$-0.407672\pi$
$313$	10.1200			0.572016			0.286008	+	0.958227i	$0.407672\pi$
$314$	−1.92593	+	0.0862908i	−0.108687	+	0.00486967i
$315$	−6.74298			−0.379924
$316$	−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	$0.993784\pi$
$318$	1.99371	−	0.0893277i	0.111802	−	0.00500925i
$319$	−0.294404	−	0.294404i	−0.0164834	−	0.0164834i
$320$	−9.05336	+	15.9319i	−0.506098	+	0.890619i
$321$	−11.8314			−0.660364
$322$	−5.63092	+	6.15917i	−0.313799	+	0.343237i
$323$	16.5600	−	16.5600i	0.921426	−	0.921426i
$324$	−1.99199	+	0.178860i	−0.110666	+	0.00993665i
$325$	−0.851558	−	0.256880i	−0.0472360	−	0.0142491i
$326$	20.2614	+	18.5236i	1.12217	+	1.02593i
$327$	12.9904	−	12.9904i	0.718370	−	0.718370i
$328$	−19.2564	+	25.2742i	−1.06326	+	1.39553i
$329$			22.1216i			1.21960i
$330$	0.308313	−	0.0138139i	0.0169721	−	0.000760430i
$331$	−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	$-0.591309\pi$
$332$	7.27652	+	6.07747i	0.399351	+	0.333545i
$333$	6.43362	+	6.43362i	0.352560	+	0.352560i
$334$	−4.25768	+	4.65711i	−0.232970	+	0.254825i
$335$	26.4354			1.44432
$336$	9.67643	+	6.70988i	0.527893	+	0.366054i
$337$			8.65894i			0.471683i	0.971792	+	0.235841i	$0.0757846\pi$
$337$			8.65894i			0.471683i	−0.971792	+	0.235841i	$0.924215\pi$
$338$	9.47089	−	15.7576i	0.515148	−	0.857101i
$339$	−12.7051			−0.690047
$340$	25.2522	+	21.0910i	1.36949	+	1.14382i
$341$			0.280465i			0.0151881i
$342$	−3.11165	+	3.40356i	−0.168259	+	0.184044i
$343$	−11.1032	+	11.1032i	−0.599516	+	0.599516i
$344$	−29.3371	+	3.96456i	−1.58175	+	0.213754i
$345$	3.24669	−	3.24669i	0.174796	−	0.174796i
$346$	−0.159661	−	3.56348i	−0.00858341	−	0.191574i
$347$	−16.6635			−0.894546			−0.447273	−	0.894397i	$-0.647605\pi$
$347$	−16.6635			−0.894546			−0.447273	+	0.894397i	$0.647605\pi$
$348$	0.781629	+	8.70511i	0.0418997	+	0.466643i
$349$	−3.99002	−	3.99002i	−0.213581	−	0.213581i	0.592206	−	0.805787i	$-0.298257\pi$
$349$	−3.99002	−	3.99002i	−0.213581	−	0.213581i	−0.805787	+	0.592206i	$0.798257\pi$
$350$	−0.757990	−	0.692980i	−0.0405163	−	0.0370413i
$351$	−1.04130	+	3.45191i	−0.0555804	+	0.184249i
$352$	−0.456188	−	0.286976i	−0.0243149	−	0.0152959i
$353$	−6.09559	−	6.09559i	−0.324436	−	0.324436i	0.526030	−	0.850466i	$-0.323680\pi$
$353$	−6.09559	−	6.09559i	−0.324436	−	0.324436i	−0.850466	+	0.526030i	$0.823680\pi$
$354$	5.85051	+	5.34873i	0.310951	+	0.284282i
$355$			0.0268740i			0.00142632i
$356$	−3.45293	+	4.13418i	−0.183005	+	0.219111i
$357$	14.9498	−	14.9498i	0.791229	−	0.791229i
$358$	−17.1992	+	0.770604i	−0.909005	+	0.0407277i
$359$	−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	$-0.530668\pi$
$360$	−5.15337	−	3.92636i	−0.271607	−	0.206937i
$361$		−	8.36669i		−	0.440352i
$362$	−0.0721353	−	1.61000i	−0.00379135	−	0.0846195i
$363$		−	10.9909i		−	0.576874i
$364$	17.7335	−	11.6685i	0.929490	−	0.611593i
$365$		−	1.35825i		−	0.0710941i
$366$	−2.74140	+	0.122828i	−0.143295	+	0.00642030i
$367$		−	30.1227i		−	1.57239i	−0.617977	−	0.786196i	$-0.712047\pi$
$367$		−	30.1227i		−	1.57239i	0.617977	−	0.786196i	$-0.287953\pi$
$368$	−7.88988	+	1.42837i	−0.411288	+	0.0744592i
$369$	−7.94353	−	7.94353i	−0.413524	−	0.413524i
$370$	1.31922	+	29.4437i	0.0685828	+	1.53071i
$371$	2.93749	−	2.93749i	0.152507	−	0.152507i
$372$	3.77418	−	4.51880i	0.195682	−	0.234289i
$373$		−	8.59939i		−	0.445259i	−0.974903	−	0.222630i	$-0.928536\pi$
$373$		−	8.59939i		−	0.445259i	0.974903	−	0.222630i	$-0.0714641\pi$
$374$	−0.652934	+	0.714187i	−0.0337624	+	0.0369297i
$375$	−7.69881	−	7.69881i	−0.397565	−	0.397565i
$376$	−12.8812	+	16.9066i	−0.664295	+	0.871893i
$377$	15.0851	+	4.55055i	0.776921	+	0.234365i
$378$	−2.80909	+	3.07262i	−0.144484	+	0.158038i
$379$	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
$381$	−18.5476			−0.950221
$382$	31.6896	−	1.41984i	1.62138	−	0.0726455i
$383$	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	$0.226807\pi$
$384$	3.48821	+	10.7625i	0.178007	+	0.549224i
$385$	0.454263	−	0.454263i	0.0231514	−	0.0231514i
$386$	−5.27513	−	4.82270i	−0.268497	−	0.245469i
$387$		−	10.4665i		−	0.532043i
$388$	−19.0224	−	15.8878i	−0.965714	−	0.806581i
$389$	25.8294			1.30960			0.654801	−	0.755801i	$-0.272752\pi$
$389$	25.8294			1.30960			0.654801	+	0.755801i	$0.272752\pi$
$390$	−10.0345	+	5.97680i	−0.508118	+	0.302647i
$391$			14.3965i			0.728060i
$392$	4.66968	−	0.631052i	0.235855	−	0.0318729i
$393$	5.20053			0.262332
$394$	−3.33766	−	3.05140i	−0.168149	−	0.153727i
$395$	13.7132	+	13.7132i	0.689986	+	0.689986i
$396$	0.122147	−	0.146246i	0.00613813	−	0.00734914i
$397$	−11.0841	−	11.0841i	−0.556297	−	0.556297i	0.371954	−	0.928251i	$-0.378688\pi$
$397$	−11.0841	−	11.0841i	−0.556297	−	0.556297i	−0.928251	+	0.371954i	$0.878688\pi$
$398$	1.67349	+	37.3507i	0.0838844	+	1.87222i
$399$			9.59938i			0.480570i
$400$	−0.175786	−	0.970983i	−0.00878928	−	0.0485492i
$401$	−25.0265	+	25.0265i	−1.24977	+	1.24977i	−0.293942	+	0.955823i	$0.594967\pi$
$401$	−25.0265	+	25.0265i	−1.24977	+	1.24977i	−0.955823	+	0.293942i	$0.905033\pi$
$402$	11.0129	−	12.0460i	0.549272	−	0.600800i
$403$	−5.01789	−	9.35300i	−0.249959	−	0.465906i
$404$	−21.0519	+	1.89024i	−1.04737	+	0.0940431i
$405$	1.61967	−	1.61967i	0.0804823	−	0.0804823i
$406$	13.4275	+	12.2759i	0.666398	+	0.609243i
$407$	−0.866843			−0.0429678
$408$	20.1306	−	2.72041i	0.996615	−	0.134681i
$409$	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	$0.417220\pi$
$410$	−1.62882	−	36.3539i	−0.0804419	−	1.79539i
$411$	15.0286	−	15.0286i	0.741307	−	0.741307i
$412$	7.01634	−	0.629995i	0.345670	−	0.0310376i
$413$	16.5007			0.811948
$414$	−0.126887	−	2.83200i	−0.00623614	−	0.139185i
$415$	−10.8581			−0.533002
$416$	20.3474	+	1.40833i	0.997613	+	0.0690491i
$417$	−6.12441			−0.299914
$418$	−0.0196656	−	0.438919i	−0.000961876	−	0.0214682i
$419$	15.6568			0.764883			0.382441	−	0.923980i	$-0.375083\pi$
$419$	15.6568			0.764883			0.382441	+	0.923980i	$0.375083\pi$
$420$	−13.4319	+	1.20605i	−0.655411	+	0.0588491i
$421$	−5.24431	+	5.24431i	−0.255592	+	0.255592i	−0.823259	−	0.567667i	$-0.807846\pi$
$421$	−5.24431	+	5.24431i	−0.255592	+	0.255592i	0.567667	+	0.823259i	$0.307846\pi$
$422$	−0.144682	−	3.22916i	−0.00704300	−	0.157193i
$423$	−5.31365	−	5.31365i	−0.258359	−	0.258359i
$424$	3.95547	−	0.534534i	0.192095	−	0.0259593i
$425$	−1.77173			−0.0859414
$426$	0.0122458	+	0.0111956i	0.000593313	+	0.000542426i
$427$	−4.03912	+	4.03912i	−0.195467	+	0.195467i
$428$	−23.5680	+	2.11616i	−1.13920	+	0.102288i
$429$	−0.162399	−	0.302700i	−0.00784069	−	0.0146145i
$430$	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	$0.0539248\pi$
$432$	−3.93602	+	0.712572i	−0.189372	+	0.0342836i
$433$		−	21.6657i		−	1.04119i	−0.853805	−	0.520593i	$-0.825711\pi$
$433$		−	21.6657i		−	1.04119i	0.853805	−	0.520593i	$-0.174289\pi$
$434$	−0.548556	−	12.2433i	−0.0263315	−	0.587696i
$435$	−7.07808	−	7.07808i	−0.339368	−	0.339368i
$436$	23.5532	−	28.2001i	1.12799	−	1.35054i
$437$	−4.62203	−	4.62203i	−0.221102	−	0.221102i
$438$	−0.618924	−	0.565841i	−0.0295733	−	0.0270369i
$439$	26.9953			1.28842			0.644208	−	0.764850i	$-0.277187\pi$
$439$	26.9953			1.28842			0.644208	+	0.764850i	$0.277187\pi$
$440$	0.611685	−	0.0826619i	0.0291610	−	0.00394075i
$441$			1.66599i			0.0793328i
$442$	8.99638	−	35.4987i	0.427914	−	1.68850i
$443$	−3.69391			−0.175503			−0.0877515	−	0.996142i	$-0.527968\pi$
$443$	−3.69391			−0.175503			−0.0877515	+	0.996142i	$0.527968\pi$
$444$	13.9664	+	11.6650i	0.662816	+	0.553595i
$445$		−	6.16904i		−	0.292441i
$446$	−9.82865	−	8.98568i	−0.465400	−	0.425484i
$447$	−13.2521	+	13.2521i	−0.626803	+	0.626803i
$448$	20.4755	+	11.6353i	0.967374	+	0.549714i
$449$	15.9641	−	15.9641i	0.753391	−	0.753391i	−0.221719	−	0.975111i	$-0.571167\pi$
$449$	15.9641	−	15.9641i	0.753391	−	0.753391i	0.975111	+	0.221719i	$0.0711669\pi$
$450$	0.348525	−	0.0156156i	0.0164296	−	0.000736125i
$451$	1.07028			0.0503977
$452$	−25.3084	+	2.27243i	−1.19041	+	0.106886i
$453$	2.61081	+	2.61081i	0.122667	+	0.122667i
$454$	10.6177	−	11.6138i	0.498313	−	0.545061i
$455$	−7.02146	+	23.2762i	−0.329171	+	1.09120i
$456$	−5.58961	+	7.33640i	−0.261757	+	0.343558i
$457$	−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
$459$			7.18195i			0.335225i
$460$	5.88666	−	7.04807i	0.274467	−	0.328618i
$461$	−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	$0.354693\pi$
$462$	−0.0177534	−	0.396240i	−0.000825964	−	0.0184348i
$463$	−16.5192	−	16.5192i	−0.767714	−	0.767714i	0.209990	−	0.977704i	$-0.432657\pi$
$463$	−16.5192	−	16.5192i	−0.767714	−	0.767714i	−0.977704	+	0.209990i	$0.932657\pi$
$464$	3.11399	+	17.2007i	0.144563	+	0.798521i
$465$			6.74298i			0.312698i
$466$	4.68403	−	0.209867i	0.216984	−	0.00972188i
$467$			13.7056i			0.634220i	0.948389	+	0.317110i	$0.102712\pi$
$467$			13.7056i			0.634220i	−0.948389	+	0.317110i	$0.897288\pi$
$468$	−1.45685	+	7.06241i	−0.0673427	+	0.326460i
$469$		−	33.9745i		−	1.56880i
$470$	−1.08957	−	24.3181i	−0.0502580	−	1.12171i
$471$		−	1.36321i		−	0.0628132i
$472$	12.6108	+	9.60818i	0.580460	+	0.442252i
$473$	0.705110	+	0.705110i	0.0324210	+	0.0324210i
$474$	11.9616	−	0.535937i	0.549416	−	0.0246164i
$475$	0.568819	−	0.568819i	0.0260992	−	0.0260992i
$476$	27.1059	−	32.4538i	1.24240	−	1.48752i
$477$			1.41118i			0.0646136i
$478$	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	$0.675504\pi$
$480$	−10.9677	−	6.89952i	−0.500605	−	0.314918i
$481$	28.9076	−	15.5090i	1.31807	−	0.707148i
$482$	−13.3255	−	12.1826i	−0.606961	−	0.554904i
$483$	−4.17261	−	4.17261i	−0.189860	−	0.189860i
$484$	−1.96583	−	21.8938i	−0.0893561	−	0.995171i
$485$	28.3853			1.28891
$486$	−0.0632999	−	1.41280i	−0.00287134	−	0.0640857i
$487$	0.384275	−	0.384275i	0.0174132	−	0.0174132i	−0.698347	−	0.715760i	$-0.746081\pi$
$487$	0.384275	−	0.384275i	0.0174132	−	0.0174132i	0.715760	+	0.698347i	$0.246081\pi$
$488$	−5.43886	+	0.734997i	−0.246206	+	0.0332717i
$489$	−13.7263	+	13.7263i	−0.620726	+	0.620726i
$490$	−3.64143	+	3.98304i	−0.164503	+	0.179935i
$491$			2.72036i			0.122768i	0.998114	+	0.0613840i	$0.0195514\pi$
$491$			2.72036i			0.122768i	−0.998114	+	0.0613840i	$0.980449\pi$
$492$	−17.2442	−	14.4026i	−0.777428	−	0.649320i
$493$	31.3856			1.41354
$494$	8.50864	+	14.2853i	0.382822	+	0.642725i
$495$			0.218229i			0.00980868i
$496$	6.70988	−	9.67643i	0.301282	−	0.434485i
$497$	0.0345381			0.00154924
$498$	−4.52342	+	4.94777i	−0.202699	+	0.221715i
$499$	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	$0.369186\pi$
$500$	−16.7129	−	13.9589i	−0.747425	−	0.624262i
$501$	−3.15502	−	3.15502i	−0.140956	−	0.140956i
$502$	−26.1348	+	1.17096i	−1.16645	+	0.0522626i
$503$		−	8.72354i		−	0.388963i	−0.980906	−	0.194482i	$-0.937698\pi$
$503$		−	8.72354i		−	0.388963i	0.980906	−	0.194482i	$-0.0623025\pi$
$504$	−5.04610	+	6.62305i	−0.224771	+	0.295014i
$505$	17.1172	−	17.1172i	0.761706	−	0.761706i
$506$	0.199335	+	0.182239i	0.00886151	+	0.00810149i
$507$	10.8314	+	7.18895i	0.481039	+	0.319272i
$508$	−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	$0.866027\pi$
$510$	−15.6979	+	17.1706i	−0.695115	+	0.760326i
$511$	−1.74561			−0.0772211
$512$	8.87345	+	20.8149i	0.392155	+	0.919899i
$513$	−2.30579	−	2.30579i	−0.101803	−	0.101803i
$514$	24.9971	−	1.11999i	1.10257	−	0.0494004i
$515$	−5.70495	+	5.70495i	−0.251390	+	0.251390i
$516$	−1.87204	−	20.8491i	−0.0824118	−	0.917832i
$517$	0.715943			0.0314871
$518$	37.8407	−	1.69544i	1.66262	−	0.0744933i
$519$	2.52229			0.110716
$520$	−18.9196	+	13.7005i	−0.829681	+	0.600806i
$521$	23.2436			1.01832			0.509161	−	0.860671i	$-0.329956\pi$
$521$	23.2436			1.01832			0.509161	+	0.860671i	$0.329956\pi$
$522$	−6.17401	+	0.276625i	−0.270229	+	0.0121075i
$523$	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
$525$	0.513510	−	0.513510i	0.0224114	−	0.0224114i
$526$	−25.7646	+	1.15437i	−1.12339	+	0.0503331i
$527$	−14.9498	−	14.9498i	−0.651225	−	0.651225i
$528$	0.217158	−	0.313167i	0.00945058	−	0.0136289i
$529$	−18.9818			−0.825298
$530$	−3.08448	+	3.37385i	−0.133981	+	0.146551i
$531$	−3.96350	+	3.96350i	−0.172001	+	0.172001i
$532$	1.71694	+	19.1218i	0.0744389	+	0.829037i
$533$	−35.6920	+	19.1488i	−1.54599	+	0.829425i
$534$	−2.81109	−	2.56999i	−0.121648	−	0.111214i
$535$	19.1630	−	19.1630i	0.828489	−	0.828489i
$536$	19.7829	−	25.9652i	0.854492	−	1.12153i
$537$		−	12.1739i		−	0.525341i
$538$	9.44252	−	0.423069i	0.407096	−	0.0182398i
$539$	−0.112235	−	0.112235i	−0.00483429	−	0.00483429i
$540$	2.93668	−	3.51606i	0.126374	−	0.151307i
$541$	7.84233	+	7.84233i	0.337168	+	0.337168i	0.855300	−	0.518132i	$-0.173373\pi$
$541$	7.84233	+	7.84233i	0.337168	+	0.337168i	−0.518132	+	0.855300i	$0.673373\pi$
$542$	−7.62655	+	8.34201i	−0.327588	+	0.358320i
$543$	1.13958			0.0489041
$544$	39.6134	−	9.01958i	1.69841	−	0.386712i
$545$			42.0804i			1.80253i
$546$	7.68131	+	12.8962i	0.328730	+	0.551909i
$547$	−24.3317			−1.04035			−0.520175	−	0.854060i	$-0.674133\pi$
$547$	−24.3317			−1.04035			−0.520175	+	0.854060i	$0.674133\pi$
$548$	27.2488	−	32.6248i	1.16401	−	1.39366i
$549$		−	1.94041i		−	0.0828145i
$550$	−0.0224275	+	0.0245315i	−0.000956313	+	0.00104603i
$551$	−10.0764	+	10.0764i	−0.429271	+	0.429271i
$552$	−0.759287	−	5.61860i	−0.0323174	−	0.239144i
$553$	17.6240	−	17.6240i	0.749450	−	0.749450i
$554$	1.54182	+	34.4119i	0.0655055	+	1.46202i
$555$	−20.8407			−0.884640
$556$	−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	$0.896391\pi$
$558$	3.07262	+	2.80909i	0.130074	+	0.118918i
$559$	−36.1295	−	10.8988i	−1.52811	−	0.460969i
$560$	−26.5405	+	4.80486i	−1.12154	+	0.203042i
$561$	−0.483835	−	0.483835i	−0.0204275	−	0.0204275i
$562$	−10.6238	−	9.71262i	−0.448137	−	0.409702i
$563$			35.1602i			1.48183i	0.671601	+	0.740913i	$0.265607\pi$
$563$			35.1602i			1.48183i	−0.671601	+	0.740913i	$0.734393\pi$
$564$	−11.5351	−	9.63432i	−0.485716	−	0.405678i
$565$	20.5781	−	20.5781i	0.865729	−	0.865729i
$566$	19.7866	−	0.886534i	0.831694	−	0.0372638i
$567$	−2.08158	−	2.08158i	−0.0874183	−	0.0874183i
$568$	0.0263960	+	0.0201111i	0.00110755	+	0.000843843i
$569$		−	18.2323i		−	0.764337i	−0.924093	−	0.382168i	$-0.875177\pi$
$569$		−	18.2323i		−	0.764337i	0.924093	−	0.382168i	$-0.124823\pi$
$570$	−0.472803	−	10.5525i	−0.0198035	−	0.441997i
$571$			33.5099i			1.40235i	0.712990	+	0.701174i	$0.247340\pi$
$571$			33.5099i			1.40235i	−0.712990	+	0.701174i	$0.752660\pi$
$572$	−0.377637	−	0.573927i	−0.0157898	−	0.0239971i
$573$			22.4304i			0.937044i
$574$	−46.7215	+	2.09334i	−1.95012	+	0.0873745i
$575$			0.494502i			0.0206222i
$576$	−7.71304	+	2.12343i	−0.321377	+	0.0884762i
$577$	−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	$0.789395\pi$
$578$	−2.18893	−	48.8550i	−0.0910477	−	2.03210i
$579$	3.57371	−	3.57371i	0.148518	−	0.148518i
$580$	−15.3654	−	12.8335i	−0.638015	−	0.532881i
$581$			13.9546i			0.578936i
$582$	11.8252	−	12.9345i	0.490169	−	0.536153i
$583$	−0.0950688	−	0.0950688i	−0.00393735	−	0.00393735i
$584$	−1.33409	−	1.01645i	−0.0552052	−	0.0420608i
$585$	−3.90441	−	7.27754i	−0.161427	−	0.300889i
$586$	14.0825	−	15.4037i	0.581744	−	0.636319i
$587$	13.2081	+	13.2081i	0.545157	+	0.545157i	0.925036	−	0.379879i	$-0.124034\pi$
$587$	13.2081	+	13.2081i	0.545157	+	0.545157i	−0.379879	+	0.925036i	$0.624034\pi$
$588$	0.297978	+	3.31863i	0.0122884	+	0.136858i
$589$	9.59938			0.395536
$590$	−18.1391	+	0.812718i	−0.746776	+	0.0334591i
$591$	2.26114	−	2.26114i	0.0930108	−	0.0930108i
$592$	29.9073	+	20.7384i	1.22918	+	0.852344i
$593$	−0.911200	+	0.911200i	−0.0374185	+	0.0374185i	−0.725568	−	0.688150i	$-0.758423\pi$
$593$	−0.911200	+	0.911200i	−0.0374185	+	0.0374185i	0.688150	+	0.725568i	$0.258423\pi$
$594$	0.0994420	+	0.0909132i	0.00408015	+	0.00373021i
$595$			48.4277i			1.98534i
$596$	−24.0277	+	28.7683i	−0.984214	+	1.17839i
$597$	−26.4375			−1.08201
$598$	−9.90793	−	2.51095i	−0.405165	−	0.102681i
$599$			25.5885i			1.04552i	0.852481	+	0.522758i	$0.175097\pi$
$599$			25.5885i			1.04552i	−0.852481	+	0.522758i	$0.824903\pi$
$600$	0.691464	−	0.0934431i	0.0282289	−	0.00381480i
$601$	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
$603$	8.16072	+	8.16072i	0.332330	+	0.332330i
$604$	5.66767	+	4.73373i	0.230614	+	0.192613i
$605$	17.8017	+	17.8017i	0.723743	+	0.723743i
$606$	−0.668972	−	14.9309i	−0.0271751	−	0.606524i
$607$			41.0894i			1.66777i	0.551941	+	0.833883i	$0.313887\pi$
$607$			41.0894i			1.66777i	−0.551941	+	0.833883i	$0.686113\pi$
$608$	−9.82223	+	15.6138i	−0.398344	+	0.633222i
$609$	−9.09666	+	9.09666i	−0.368615	+	0.368615i
$610$	4.24123	−	4.63912i	0.171723	−	0.187832i
$611$	−23.8754	+	12.8092i	−0.965894	+	0.518203i
$612$	1.28456	+	14.3063i	0.0519253	+	0.578300i
$613$	7.07976	−	7.07976i	0.285949	−	0.285949i	−0.549527	−	0.835476i	$-0.685192\pi$
$613$	7.07976	−	7.07976i	0.285949	−	0.285949i	0.835476	+	0.549527i	$0.185192\pi$
$614$	14.0170	+	12.8148i	0.565679	+	0.517163i
$615$	25.7319			1.03761
$616$	−0.106236	−	0.786130i	−0.00428037	−	0.0316741i
$617$	2.05439	+	2.05439i	0.0827067	+	0.0827067i	0.747250	−	0.664543i	$-0.231374\pi$
$617$	2.05439	+	2.05439i	0.0827067	+	0.0827067i	−0.664543	+	0.747250i	$0.731374\pi$
$618$	0.222960	+	4.97627i	0.00896877	+	0.200175i
$619$	−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
$621$	2.00453			0.0804392
$622$	1.22495	+	27.3399i	0.0491162	+	1.09623i
$623$	−7.92838			−0.317644
$624$	−1.63884	+	14.3288i	−0.0656059	+	0.573611i
$625$	26.1726			1.04690
$626$	0.640595	+	14.2975i	0.0256033	+	0.571443i
$627$	0.310674			0.0124071
$628$	−0.243823	−	2.71549i	−0.00972958	−	0.108360i
$629$	46.2059	−	46.2059i	1.84235	−	1.84235i
$630$	−0.426830	−	9.52646i	−0.0170053	−	0.379543i
$631$	−32.6063	−	32.6063i	−1.29804	−	1.29804i	−0.929688	−	0.368349i	$-0.879923\pi$
$631$	−32.6063	−	32.6063i	−1.29804	−	1.29804i	−0.368349	−	0.929688i	$-0.620077\pi$
$632$	23.7316	−	3.20703i	0.943991	−	0.127569i
$633$	2.28566			0.0908466
$634$	−26.7893	−	24.4917i	−1.06394	−	0.972690i
$635$	30.0410	−	30.0410i	1.19214	−	1.19214i
$636$	0.252404	+	2.81105i	0.0100085	+	0.111466i
$637$	5.75085	+	1.73479i	0.227857	+	0.0687350i
$638$	0.397297	−	0.434568i	0.0157291	−	0.0172047i
$639$	−0.00829610	+	0.00829610i	−0.000328189	+	0.000328189i
$640$	−23.0816	−	11.7821i	−0.912380	−	0.465727i
$641$		−	2.93313i		−	0.115852i	−0.998321	−	0.0579259i	$-0.981551\pi$
$641$		−	2.93313i		−	0.115852i	0.998321	−	0.0579259i	$-0.0184487\pi$
$642$	−0.748926	−	16.7153i	−0.0295577	−	0.659702i
$643$	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	$0.569899\pi$
$644$	−9.05808	−	7.56546i	−0.356939	−	0.298121i
$645$	16.9523	+	16.9523i	0.667498	+	0.667498i
$646$	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	$0.849983\pi$
$648$	−0.378785	−	2.80295i	−0.0148801	−	0.110110i
$649$		−	0.534029i		−	0.0209625i
$650$	0.309015	−	1.21934i	0.0121206	−	0.0478264i
$651$	8.66599			0.339647
$652$	−24.8876	+	29.7978i	−0.974673	+	1.16697i
$653$		−	2.67450i		−	0.104661i	−0.998630	−	0.0523307i	$-0.983335\pi$
$653$		−	2.67450i		−	0.104661i	0.998630	−	0.0523307i	$-0.0166650\pi$
$654$	19.1751	+	17.5305i	0.749804	+	0.685496i
$655$	−8.42316	+	8.42316i	−0.329120	+	0.329120i
$656$	−36.9262	−	25.6055i	−1.44173	−	0.999728i
$657$	0.419298	−	0.419298i	0.0163584	−	0.0163584i
$658$	−31.2534	+	1.40030i	−1.21838	+	0.0545893i
$659$	37.5991			1.46465			0.732326	−	0.680954i	$-0.238435\pi$
$659$	37.5991			1.46465			0.732326	+	0.680954i	$0.238435\pi$
$660$	0.0390324	+	0.434710i	0.00151933	+	0.0169211i
$661$	29.7860	+	29.7860i	1.15854	+	1.15854i	0.984789	+	0.173752i	$0.0555892\pi$
$661$	29.7860	+	29.7860i	1.15854	+	1.15854i	0.173752	+	0.984789i	$0.444411\pi$
$662$	30.4954	−	33.3562i	1.18524	−	1.29643i
$663$	24.7915	+	7.47856i	0.962820	+	0.290443i
$664$	−8.12563	+	10.6649i	−0.315335	+	0.413880i
$665$	−15.5479	−	15.5479i	−0.602921	−	0.602921i
$666$	−8.68214	+	9.49664i	−0.336426	+	0.367987i
$667$		−	8.75994i		−	0.339186i
$668$	−6.84905	−	5.72044i	−0.264998	−	0.221331i
$669$	6.65855	−	6.65855i	0.257434	−	0.257434i
$670$	1.67336	+	37.3479i	0.0646475	+	1.44287i
$671$	0.130722	+	0.130722i	0.00504646	+	0.00504646i
$672$	−8.86717	+	14.0956i	−0.342059	+	0.543748i
$673$		−	26.8225i		−	1.03393i	−0.856006	−	0.516965i	$-0.827062\pi$
$673$		−	26.8225i		−	1.03393i	0.856006	−	0.516965i	$-0.172938\pi$
$674$	−12.2333	+	0.548110i	−0.471210	+	0.0211124i
$675$			0.246692i			0.00949517i
$676$	22.8618	+	12.3830i	0.879300	+	0.476269i
$677$		−	27.6382i		−	1.06222i	−0.847302	−	0.531112i	$-0.821774\pi$
$677$		−	27.6382i		−	1.06222i	0.847302	−	0.531112i	$-0.178226\pi$
$678$	−0.804232	−	17.9497i	−0.0308864	−	0.689355i
$679$		−	36.4804i		−	1.39999i
$680$	−28.1989	+	37.0113i	−1.08138	+	1.41932i
$681$	7.86789	+	7.86789i	0.301498	+	0.301498i
$682$	−0.396240	+	0.0177534i	−0.0151728	+	0.000679814i
$683$	−0.401585	+	0.401585i	−0.0153662	+	0.0153662i	−0.714748	−	0.699382i	$-0.753459\pi$
$683$	−0.401585	+	0.401585i	−0.0153662	+	0.0153662i	0.699382	+	0.714748i	$0.253459\pi$
$684$	−5.00551	−	4.18068i	−0.191390	−	0.159852i
$685$			48.6829i			1.86008i
$686$	−16.3894	−	14.9837i	−0.625750	−	0.572081i
$687$	−3.64543	−	3.64543i	−0.139082	−	0.139082i
$688$	−7.45814	−	41.1964i	−0.284339	−	1.57060i
$689$	4.87127	+	1.46946i	0.185581	+	0.0559820i
$690$	4.79243	+	4.38140i	0.182445	+	0.166797i
$691$	−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
$693$	0.280465			0.0106540
$694$	−1.05480	−	23.5422i	−0.0400397	−	0.893650i
$695$	9.91955	−	9.91955i	0.376270	−	0.376270i
$696$	−12.2491	+	1.65531i	−0.464300	+	0.0627445i
$697$	−57.0500	+	57.0500i	−2.16092	+	2.16092i
$698$	5.38452	−	5.88965i	0.203807	−	0.222927i
$699$			3.31543i			0.125401i
$700$	0.931058	−	1.11475i	0.0351907	−	0.0421336i
$701$	42.4434			1.60307			0.801533	−	0.597951i	$-0.204018\pi$
$701$	42.4434			1.60307			0.801533	+	0.597951i	$0.204018\pi$
$702$	−4.94276	−	1.25264i	−0.186553	−	0.0472778i
$703$			29.6691i			1.11899i
$704$	0.376563	−	0.662666i	0.0141922	−	0.0249752i
$705$	17.2128			0.648271
$706$	8.22598	−	8.99768i	0.309589	−	0.338632i
$707$	−21.9988	−	21.9988i	−0.827350	−	0.827350i
$708$	−7.18633	+	8.60416i	−0.270079	+	0.323364i
$709$	21.9848	+	21.9848i	0.825657	+	0.825657i	0.986913	−	0.161256i	$-0.0515544\pi$
$709$	21.9848	+	21.9848i	0.825657	+	0.825657i	−0.161256	+	0.986913i	$0.551554\pi$
$710$	−0.0379674	+	0.00170112i	−0.00142489	+	6.38419e-5i
$711$			8.46664i			0.317524i
$712$	−6.05932	−	4.61660i	−0.227083	−	0.173014i
$713$	−4.17261	+	4.17261i	−0.156265	+	0.156265i
$714$	22.0674	+	20.1747i	0.825851	+	0.755021i
$715$	0.753308	+	0.227242i	0.0281721	+	0.00849837i
$716$	−2.17741	−	24.2502i	−0.0813737	−	0.906271i
$717$	−7.48888	+	7.48888i	−0.279677	+	0.279677i
$718$	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	$0.527041\pi$
$720$	5.22093	−	7.52920i	0.194573	−	0.280597i
$721$	7.33193	+	7.33193i	0.273055	+	0.273055i
$722$	11.8204	−	0.529611i	0.439911	−	0.0197101i
$723$	9.02754	−	9.02754i	0.335738	−	0.335738i
$724$	2.27003	−	0.203825i	0.0843650	−	0.00757510i
$725$	1.07806			0.0400381
$726$	15.5279	−	0.695724i	0.576296	−	0.0258207i
$727$	−35.3567			−1.31131			−0.655653	−	0.755062i	$-0.727607\pi$
$727$	−35.3567			−1.31131			−0.655653	+	0.755062i	$0.727607\pi$
$728$	17.6077	+	24.3153i	0.652584	+	0.901184i
$729$	1.00000			0.0370370
$730$	1.91893	−	0.0859772i	0.0710229	−	0.00318216i
$731$	−75.1699			−2.78026
$732$	−0.347061	−	3.86526i	−0.0128277	−	0.142864i
$733$	−10.2364	+	10.2364i	−0.378089	+	0.378089i	−0.870412	−	0.492323i	$-0.836148\pi$
$733$	−10.2364	+	10.2364i	−0.378089	+	0.378089i	0.492323	+	0.870412i	$0.336148\pi$
$734$	42.5572	−	1.90676i	1.57082	−	0.0703800i
$735$	−2.69836	−	2.69836i	−0.0995305	−	0.0995305i
$736$	−2.51743	−	11.0564i	−0.0927937	−	0.407543i
$737$	−1.09955			−0.0405023
$738$	10.7198	−	11.7254i	0.394600	−	0.431618i
$739$	−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
$741$	−10.3604	+	5.55836i	−0.380598	+	0.204191i
$742$	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	$0.215061\pi$
$744$	6.62305	+	5.04610i	0.242813	+	0.184999i
$745$		−	42.9282i		−	1.57277i
$746$	12.1492	−	0.544340i	0.444813	−	0.0199297i
$747$	−3.35193	−	3.35193i	−0.122641	−	0.122641i
$748$	−1.05033	−	0.877255i	−0.0384039	−	0.0320756i
$749$	−24.6280	−	24.6280i	−0.899889	−	0.899889i
$750$	10.3895	−	11.3642i	0.379372	−	0.414961i
$751$	−39.7818			−1.45166			−0.725828	−	0.687876i	$-0.758543\pi$
$751$	−39.7818			−1.45166			−0.725828	+	0.687876i	$0.758543\pi$
$752$	−24.7010	−	17.1283i	−0.900752	−	0.624604i
$753$		−	18.4986i		−	0.674128i
$754$	−5.47411	+	21.6002i	−0.199355	+	0.786633i
$755$	−8.45732			−0.307794
$756$	−4.51880	−	3.77418i	−0.164347	−	0.137265i
$757$		−	0.790942i		−	0.0287473i	−0.999897	−	0.0143736i	$-0.995425\pi$
$757$		−	0.790942i		−	0.0287473i	0.999897	−	0.0143736i	$-0.00457543\pi$
$758$	−15.6205	+	17.0859i	−0.567362	+	0.620588i
$759$	−0.135042	+	0.135042i	−0.00490171	+	0.00490171i
$760$	−2.82924	−	20.9359i	−0.102627	−	0.759426i
$761$	2.96895	−	2.96895i	0.107624	−	0.107624i	−0.651244	−	0.758868i	$-0.725753\pi$
$761$	2.96895	−	2.96895i	0.107624	−	0.107624i	0.758868	+	0.651244i	$0.225753\pi$
$762$	−1.17406	−	26.2039i	−0.0425317	−	0.949269i
$763$	54.0812			1.95787
$764$	4.01190	+	44.6811i	0.145145	+	1.61650i
$765$	−11.6324	−	11.6324i	−0.420571	−	0.420571i
$766$	2.97412	+	2.71904i	0.107459	+	0.0982430i
$767$	9.55447	+	17.8089i	0.344992	+	0.643041i
$768$	−14.9845	+	5.60939i	−0.540706	+	0.202412i
$769$	−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
$771$			17.6933i			0.637210i
$772$	6.47958	−	7.75796i	0.233205	−	0.279215i
$773$	−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	$0.354094\pi$
$774$	14.7870	−	0.662529i	0.531509	−	0.0238141i
$775$	−0.513510	−	0.513510i	−0.0184458	−	0.0184458i
$776$	21.2421	−	27.8804i	0.762547	−	1.00085i
$777$			26.7842i			0.960879i
$778$	1.63500	+	36.4917i	0.0586175	+	1.30829i
$779$		−	36.6322i		−	1.31248i
$780$	−9.07919	−	13.7984i	−0.325087	−	0.494063i
$781$		−	0.00111779i		−	3.99976e-5i
$782$	−20.3393	+	0.911294i	−0.727330	+	0.0325878i
$783$		−	4.37007i		−	0.156173i
$784$	1.18714	+	6.55737i	0.0423978	+	0.234192i
$785$	2.20795	+	2.20795i	0.0788051	+	0.0788051i
$786$	0.329193	+	7.34728i	0.0117419	+	0.262069i
$787$	−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	$0.483516\pi$
$788$	4.09973	−	4.90858i	0.146047	−	0.174861i
$789$		−	18.2366i		−	0.649239i
$790$	−18.5059	+	20.2420i	−0.658411	+	0.720178i
$791$	−26.4468	−	26.4468i	−0.940339	−	0.940339i
$792$	0.214348	+	0.163312i	0.00761652	+	0.00580303i
$793$	−6.69811	−	2.02054i	−0.237857	−	0.0717516i
$794$	14.9580	−	16.3613i	0.530840	−	0.580640i
$795$	−2.28566	−	2.28566i	−0.0810638	−	0.0810638i
$796$	−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	$0.558321\pi$
$798$	−13.5620	+	0.607640i	−0.480089	+	0.0215102i
$799$	−38.1624	+	38.1624i	−1.35009	+	1.35009i
$800$	1.36067	−	0.309813i	0.0481071	−	0.0109535i
$801$	1.90441	−	1.90441i	0.0672890	−	0.0672890i
$802$	−36.9416	−	33.7732i	−1.30445	−	1.19257i
$803$			0.0564947i			0.00199365i
$804$	17.7157	+	14.7964i	0.624784	+	0.521830i
$805$	13.5165			0.476395
$806$	12.8962	−	7.68131i	0.454251	−	0.270562i
$807$			6.68357i			0.235273i
$808$	−4.00311	−	29.6224i	−0.140829	−	1.04211i
$809$	−1.64479			−0.0578278			−0.0289139	−	0.999582i	$-0.509205\pi$
$809$	−1.64479			−0.0578278			−0.0289139	+	0.999582i	$0.509205\pi$
$810$	2.39080	+	2.18574i	0.0840040	+	0.0767992i
$811$	−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	$0.854969\pi$
$812$	−16.4934	+	19.7475i	−0.578805	+	0.693000i
$813$	−5.65140	−	5.65140i	−0.198203	−	0.198203i
$814$	−0.0548711	−	1.22467i	−0.00192323	−	0.0429248i
$815$		−	44.4644i		−	1.55752i
$816$	5.11766	+	28.2683i	0.179154	+	0.989588i
$817$	24.1335	−	24.1335i	0.844326	−	0.844326i
$818$	−33.3920	+	36.5246i	−1.16752	+	1.27705i
$819$	−9.35300	+	5.01789i	−0.326820	+	0.175339i
$820$	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	$0.174944\pi$
$822$	22.1837	+	20.2811i	0.773744	+	0.707383i
$823$	9.44005			0.329059			0.164530	−	0.986372i	$-0.447389\pi$
$823$	9.44005			0.329059			0.164530	+	0.986372i	$0.447389\pi$
$824$	1.33419	+	9.87278i	0.0464786	+	0.343935i
$825$	−0.0166192	−	0.0166192i	−0.000578606	−	0.000578606i
$826$	1.04450	+	23.3122i	0.0363426	+	0.811134i
$827$	15.1241	−	15.1241i	0.525916	−	0.525916i	−0.393436	−	0.919352i	$-0.628714\pi$
$827$	15.1241	−	15.1241i	0.525916	−	0.525916i	0.919352	+	0.393436i	$0.128714\pi$
$828$	3.99300	−	0.358530i	0.138766	−	0.0124598i
$829$	−30.8994			−1.07318			−0.536590	−	0.843843i	$-0.680288\pi$
$829$	−30.8994			−1.07318			−0.536590	+	0.843843i	$0.680288\pi$
$830$	−0.687315	−	15.3402i	−0.0238570	−	0.532468i
$831$	−24.3573			−0.844946
$832$	−0.701696	+	28.8359i	−0.0243269	+	0.999704i
$833$	11.9651			0.414564
$834$	−0.387674	−	8.65254i	−0.0134241	−	0.299613i
$835$	10.2202			0.353684
$836$	0.618858	−	0.0555670i	0.0214036	−	0.00192182i
$837$	−2.08158	+	2.08158i	−0.0719501	+	0.0719501i
$838$	0.991071	+	22.1198i	0.0342360	+	0.764116i
$839$	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	$0.325966\pi$
$840$	−2.55414	−	18.9002i	−0.0881261	−	0.652120i
$841$	9.90253			0.341466
$842$	−7.74110	−	7.07718i	−0.266776	−	0.243896i
$843$	7.19722	−	7.19722i	0.247885	−	0.247885i
$844$	4.55299	−	0.408812i	0.156720	−	0.0140719i
$845$	−29.1871	+	5.89958i	−1.00407	+	0.202952i
$846$	7.17075	−	7.84346i	0.246536	−	0.269664i
$847$	22.8785	−	22.8785i	0.786116	−	0.786116i
$848$	1.00557	+	5.55444i	0.0345314	+	0.190740i
$849$			14.0053i			0.480661i
$850$	−0.112150	−	2.50309i	−0.00384672	−	0.0858553i
$851$	−12.8964	−	12.8964i	−0.442083	−	0.442083i
$852$	−0.0150419	+	0.0180096i	−0.000515326	+	0.000616997i
$853$	5.81918	+	5.81918i	0.199245	+	0.199245i	0.799676	−	0.600431i	$-0.205004\pi$
$853$	5.81918	+	5.81918i	0.199245	+	0.199245i	−0.600431	+	0.799676i	$0.705004\pi$
$854$	−5.96213	−	5.45078i	−0.204020	−	0.186522i
$855$	7.46925			0.255443
$856$	−4.48155	−	33.1628i	−0.153176	−	1.13348i
$857$		−	27.8183i		−	0.950256i	−0.879917	−	0.475128i	$-0.842402\pi$
$857$		−	27.8183i		−	0.950256i	0.879917	−	0.475128i	$-0.157598\pi$
$858$	0.417373	−	0.248597i	0.0142489	−	0.00848697i
$859$	−10.0327			−0.342311			−0.171155	−	0.985244i	$-0.554750\pi$
$859$	−10.0327			−0.342311			−0.171155	+	0.985244i	$0.554750\pi$
$860$	36.8009	+	30.7367i	1.25490	+	1.04811i
$861$		−	33.0703i		−	1.12703i
$862$	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	$-0.0299332\pi$
$864$	−1.25587	−	5.51569i	−0.0427255	−	0.187647i
$865$	−4.08529	+	4.08529i	−0.138904	+	0.138904i
$866$	30.6092	−	1.37143i	1.04014	−	0.0466032i
$867$	34.5804			1.17441
$868$	17.2625	−	1.55000i	0.585929	−	0.0526103i
$869$	−0.570383	−	0.570383i	−0.0193489	−	0.0193489i
$870$	9.55185	−	10.4479i	0.323838	−	0.354218i
$871$	36.6678	−	19.6723i	1.24244	−	0.666572i
$872$	41.3319	+	31.4908i	1.39968	+	1.06641i
$873$	8.76265	+	8.76265i	0.296571	+	0.296571i
$874$	6.23741	−	6.82256i	0.210984	−	0.230776i
$875$		−	32.0515i		−	1.08354i
$876$	0.760240	−	0.910231i	0.0256861	−	0.0307538i
$877$	20.8160	−	20.8160i	0.702906	−	0.702906i	−0.262127	−	0.965033i	$-0.584424\pi$
$877$	20.8160	−	20.8160i	0.702906	−	0.702906i	0.965033	+	0.262127i	$0.0844240\pi$
$878$	1.70880	+	38.1389i	0.0576692	+	1.28713i
$879$	10.4354	+	10.4354i	0.351977	+	0.351977i
$880$	0.155504	+	0.858954i	0.00524204	+	0.0289553i
$881$			13.7757i			0.464116i	0.972702	+	0.232058i	$0.0745459\pi$
$881$			13.7757i			0.464116i	−0.972702	+	0.232058i	$0.925454\pi$
$882$	−2.35370	+	0.105457i	−0.0792533	+	0.00355092i
$883$		−	38.8765i		−	1.30830i	−0.756366	−	0.654149i	$-0.773027\pi$
$883$		−	38.8765i		−	1.30830i	0.756366	−	0.654149i	$-0.226973\pi$
$884$	50.7218	+	10.4630i	1.70596	+	0.351908i
$885$		−	12.8392i		−	0.431584i
$886$	−0.233824	−	5.21874i	−0.00785547	−	0.175327i
$887$			51.7991i			1.73924i	0.493718	+	0.869622i	$0.335637\pi$
$887$			51.7991i			1.73924i	−0.493718	+	0.869622i	$0.664363\pi$
$888$	−15.5961	+	20.4701i	−0.523372	+	0.686930i
$889$	−38.6084	−	38.6084i	−1.29488	−	1.29488i
$890$	8.71560	−	0.390500i	0.292148	−	0.0130896i
$891$	−0.0673682	+	0.0673682i	−0.00225692	+	0.00225692i
$892$	12.0728	−	14.4547i	0.404227	−	0.483978i
$893$		−	24.5043i		−	0.820005i
$894$	−19.5614	−	17.8837i	−0.654230	−	0.598119i
$895$	19.7177	+	19.7177i	0.659090	+	0.659090i
$896$	−15.1422	+	29.6642i	−0.505864	+	0.991010i
$897$	2.08732	−	6.91947i	0.0696935	−	0.231034i
$898$	23.5645	+	21.5435i	0.786358	+	0.718914i
$899$	9.09666	+	9.09666i	0.303391	+	0.303391i
$900$	0.0441232	+	0.491407i	0.00147077	+	0.0163802i
$901$	10.1350			0.337647
$902$	0.0677488	+	1.51209i	0.00225579	+	0.0503472i
$903$	21.7869	−	21.7869i	0.725023	−	0.725023i
$904$	−4.81250	−	35.6118i	−0.160061	−	1.18443i
$905$	−1.84575	+	1.84575i	−0.0613548	+	0.0613548i
$906$	−3.52328	+	3.85381i	−0.117053	+	0.128034i
$907$			53.4908i			1.77613i	0.459714	+	0.888067i	$0.347952\pi$
$907$			53.4908i			1.77613i	−0.459714	+	0.888067i	$0.652048\pi$
$908$	17.0800	+	14.2655i	0.566819	+	0.473416i
$909$	10.5683			0.350528
$910$	−33.3289	−	8.44651i	−1.10484	−	0.279999i
$911$		−	8.34775i		−	0.276573i	−0.990392	−	0.138287i	$-0.955840\pi$
$911$		−	8.34775i		−	0.276573i	0.990392	−	0.138287i	$-0.0441595\pi$
$912$	−10.7187	−	7.43258i	−0.354930	−	0.246117i
$913$	0.451627			0.0149467
$914$	13.4824	−	14.7473i	0.445959	−	0.487796i
$915$	3.14283	+	3.14283i	0.103899	+	0.103899i
$916$	−7.91366	−	6.60962i	−0.261475	−	0.218388i
$917$	10.8253	+	10.8253i	0.357484	+	0.357484i
$918$	−10.1466	+	0.454617i	−0.334889	+	0.0150046i
$919$			0.682347i			0.0225085i	0.999937	+	0.0112543i	$0.00358242\pi$
$919$			0.682347i			0.0225085i	−0.999937	+	0.0112543i	$0.996418\pi$
$920$	10.3301	+	7.87051i	0.340574	+	0.259483i
$921$	−9.49598	+	9.49598i	−0.312903	+	0.312903i
$922$	−14.4774	−	13.2357i	−0.476787	−	0.435894i
$923$	0.0199987	+	0.0372761i	0.000658265	+	0.00122696i
$924$	0.558683	−	0.0501640i	0.0183793	−	0.00165027i
$925$	1.58712	−	1.58712i	0.0521842	−	0.0521842i
$926$	22.2926	−	24.3840i	0.732581	−	0.801307i
$927$	−3.52228			−0.115687
$928$	−24.1039	+	5.48823i	−0.791250	+	0.180160i
$929$	11.6044	+	11.6044i	0.380728	+	0.380728i	0.871364	−	0.490636i	$-0.163236\pi$
$929$	11.6044	+	11.6044i	0.380728	+	0.380728i	−0.490636	+	0.871364i	$0.663236\pi$
$930$	−9.52646	+	0.426830i	−0.312385	+	0.0139963i
$931$	−3.84142	+	3.84142i	−0.125897	+	0.125897i
$932$	0.592997	+	6.60430i	0.0194243	+	0.216331i
$933$	−19.3516			−0.633543
$934$	−19.3632	+	0.867563i	−0.633584	+	0.0283875i
$935$	1.56731			0.0512566
$936$	−10.0700	−	1.61118i	−0.329147	−	0.0526629i
$937$	−5.73855			−0.187470			−0.0937352	−	0.995597i	$-0.529881\pi$
$937$	−5.73855			−0.187470			−0.0937352	+	0.995597i	$0.529881\pi$
$938$	47.9990	−	2.15058i	1.56722	−	0.0702189i
$939$	−10.1200			−0.330254
$940$	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	$0.254529\pi$
$942$	1.92593	−	0.0862908i	0.0627503	−	0.00281151i
$943$	15.9231	+	15.9231i	0.518526	+	0.518526i
$944$	−12.7761	+	18.4247i	−0.415828	+	0.599673i
$945$	6.74298			0.219349
$946$	−0.951544	+	1.04081i	−0.0309374	+	0.0338397i
$947$	−2.57671	+	2.57671i	−0.0837319	+	0.0837319i	−0.747732	−	0.664000i	$-0.768857\pi$
$947$	−2.57671	+	2.57671i	−0.0837319	+	0.0837319i	0.664000	+	0.747732i	$0.268857\pi$
$948$	1.51434	+	16.8654i	0.0491835	+	0.547764i
$949$	−1.01076	−	1.88399i	−0.0328108	−	0.0611570i
$950$	0.839631	+	0.767619i	0.0272412	+	0.0249048i
$951$	18.1488	−	18.1488i	0.588515	−	0.588515i
$952$	47.5664	+	36.2408i	1.54164	+	1.17457i
$953$		−	44.1686i		−	1.43076i	−0.698736	−	0.715380i	$-0.746254\pi$
$953$		−	44.1686i		−	1.43076i	0.698736	−	0.715380i	$-0.253746\pi$
$954$	−1.99371	+	0.0893277i	−0.0645488	+	0.00289209i
$955$	−36.3300	−	36.3300i	−1.17561	−	1.17561i
$956$	−13.5783	+	16.2572i	−0.439153	+	0.525796i
$957$	0.294404	+	0.294404i	0.00951672	+	0.00951672i
$958$	−9.68653	+	10.5952i	−0.312958	+	0.342317i
$959$	62.5667			2.02038
$960$	9.05336	−	15.9319i	0.292196	−	0.514199i
$961$			22.3340i			0.720452i
$962$	23.7409	+	39.8588i	0.765436	+	1.28510i
$963$	11.8314			0.381261
$964$	16.3681	−	19.5974i	0.527180	−	0.631190i
$965$			11.5765i			0.372660i
$966$	5.63092	−	6.15917i	0.181172	−	0.198168i
$967$	−23.3487	+	23.3487i	−0.750844	+	0.750844i	−0.974637	−	0.223792i	$-0.928156\pi$
$967$	−23.3487	+	23.3487i	−0.750844	+	0.750844i	0.223792	+	0.974637i	$0.428156\pi$
$968$	30.8070	−	4.16319i	0.990174	−	0.133810i
$969$	−16.5600	+	16.5600i	−0.531985	+	0.531985i
$970$	1.79679	+	40.1026i	0.0576913	+	1.28762i
$971$	15.8294			0.507990			0.253995	−	0.967205i	$-0.418255\pi$
$971$	15.8294			0.507990			0.253995	+	0.967205i	$0.418255\pi$
$972$	1.99199	−	0.178860i	0.0638930	−	0.00573693i
$973$	−12.7485	−	12.7485i	−0.408697	−	0.408697i
$974$	0.567227	+	0.518578i	0.0181751	+	0.0166163i
$975$	0.851558	+	0.256880i	0.0272717	+	0.00822674i
$976$	−1.38268	−	7.63748i	−0.0442585	−	0.244470i
$977$	−19.1168	−	19.1168i	−0.611602	−	0.611602i	0.331761	−	0.943363i	$-0.392357\pi$
$977$	−19.1168	−	19.1168i	−0.611602	−	0.611602i	−0.943363	+	0.331761i	$0.892357\pi$
$978$	−20.2614	−	18.5236i	−0.647888	−	0.592321i
$979$			0.256593i			0.00820076i
$980$	−5.85773	−	4.89247i	−0.187118	−	0.156284i
$981$	−12.9904	+	12.9904i	−0.414751	+	0.414751i
$982$	−3.84331	+	0.172198i	−0.122645	+	0.00549507i
$983$	−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	$0.899054\pi$
$984$	19.2564	−	25.2742i	0.613872	−	0.805712i
$985$			7.32462i			0.233382i
$986$	1.98670	+	44.3414i	0.0632696	+	1.41212i
$987$		−	22.1216i		−	0.704139i
$988$	−19.6436	+	12.9252i	−0.624946	+	0.411206i
$989$			20.9805i			0.667140i
$990$	−0.308313	+	0.0138139i	−0.00979885	+	0.000439034i
$991$		−	36.3170i		−	1.15365i	−0.816868	−	0.576824i	$-0.804292\pi$
$991$		−	36.3170i		−	1.15365i	0.816868	−	0.576824i	$-0.195708\pi$
$992$	14.0956	+	8.86717i	0.447535	+	0.281533i
$993$	22.5976	+	22.5976i	0.717114	+	0.717114i
$994$	0.00218626	+	0.0487953i	6.93438e−5	+	0.00154769i
$995$	42.8201	−	42.8201i	1.35749	−	1.35749i
$996$	−7.27652	−	6.07747i	−0.230565	−	0.192572i
$997$			27.1788i			0.860762i	0.902647	+	0.430381i	$0.141621\pi$
$997$			27.1788i			0.860762i	−0.902647	+	0.430381i	$0.858379\pi$
$998$	−39.6783	+	43.4007i	−1.25600	+	1.37382i
$999$	−6.43362	−	6.43362i	−0.203551	−	0.203551i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.7	✓	24	104.83	even	4	inner
312.2.t.e.187.12	yes	24	13.5	odd	4	inner
312.2.t.e.307.7	yes	24	1.1	even	1	trivial
312.2.t.e.307.12	yes	24	8.3	odd	2	inner
936.2.w.j.307.1		24	24.11	even	2
936.2.w.j.307.6		24	3.2	odd	2
936.2.w.j.811.1		24	39.5	even	4
936.2.w.j.811.6		24	312.83	odd	4
1248.2.bb.f.463.4		24	8.5	even	2
1248.2.bb.f.463.9		24	4.3	odd	2
1248.2.bb.f.655.4		24	52.31	even	4
1248.2.bb.f.655.9		24	104.5	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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0632999 + 1.41280i) q^{2} -1.00000 q^{3} +(-1.99199 + 0.178860i) q^{4} +(1.61967 - 1.61967i) q^{5} +(-0.0632999 - 1.41280i) q^{6} +(-2.08158 - 2.08158i) q^{7} +(-0.378785 - 2.80295i) q^{8} +1.00000 q^{9} +(2.39080 + 2.18574i) q^{10} +(-0.0673682 + 0.0673682i) q^{11} +(1.99199 - 0.178860i) q^{12} +(1.04130 - 3.45191i) q^{13} +(2.80909 - 3.07262i) q^{14} +(-1.61967 + 1.61967i) q^{15} +(3.93602 - 0.712572i) q^{16} -7.18195i q^{17} +(0.0632999 + 1.41280i) q^{18} +(2.30579 + 2.30579i) q^{19} +(-2.93668 + 3.51606i) q^{20} +(2.08158 + 2.08158i) q^{21} +(-0.0994420 - 0.0909132i) q^{22} -2.00453 q^{23} +(0.378785 + 2.80295i) q^{24} -0.246692i q^{25} +(4.94276 + 1.25264i) q^{26} -1.00000 q^{27} +(4.51880 + 3.77418i) q^{28} +4.37007i q^{29} +(-2.39080 - 2.18574i) q^{30} +(2.08158 - 2.08158i) q^{31} +(1.25587 + 5.51569i) q^{32} +(0.0673682 - 0.0673682i) q^{33} +(10.1466 - 0.454617i) q^{34} -6.74298 q^{35} +(-1.99199 + 0.178860i) q^{36} +(6.43362 + 6.43362i) q^{37} +(-3.11165 + 3.40356i) q^{38} +(-1.04130 + 3.45191i) q^{39} +(-5.15337 - 3.92636i) q^{40} +(-7.94353 - 7.94353i) q^{41} +(-2.80909 + 3.07262i) q^{42} -10.4665i q^{43} +(0.122147 - 0.146246i) q^{44} +(1.61967 - 1.61967i) q^{45} +(-0.126887 - 2.83200i) q^{46} +(-5.31365 - 5.31365i) q^{47} +(-3.93602 + 0.712572i) q^{48} +1.66599i q^{49} +(0.348525 - 0.0156156i) q^{50} +7.18195i q^{51} +(-1.45685 + 7.06241i) q^{52} +1.41118i q^{53} +(-0.0632999 - 1.41280i) q^{54} +0.218229i q^{55} +(-5.04610 + 6.62305i) q^{56} +(-2.30579 - 2.30579i) q^{57} +(-6.17401 + 0.276625i) q^{58} +(-3.96350 + 3.96350i) q^{59} +(2.93668 - 3.51606i) q^{60} -1.94041i q^{61} +(3.07262 + 2.80909i) q^{62} +(-2.08158 - 2.08158i) q^{63} +(-7.71304 + 2.12343i) q^{64} +(-3.90441 - 7.27754i) q^{65} +(0.0994420 + 0.0909132i) q^{66} +(8.16072 + 8.16072i) q^{67} +(1.28456 + 14.3063i) q^{68} +2.00453 q^{69} +(-0.426830 - 9.52646i) q^{70} +(-0.00829610 + 0.00829610i) q^{71} +(-0.378785 - 2.80295i) q^{72} +(0.419298 - 0.419298i) q^{73} +(-8.68214 + 9.49664i) q^{74} +0.246692i q^{75} +(-5.00551 - 4.18068i) q^{76} +0.280465 q^{77} +(-4.94276 - 1.25264i) q^{78} +8.46664i q^{79} +(5.22093 - 7.52920i) q^{80} +1.00000 q^{81} +(10.7198 - 11.7254i) q^{82} +(-3.35193 - 3.35193i) q^{83} +(-4.51880 - 3.77418i) q^{84} +(-11.6324 - 11.6324i) q^{85} +(14.7870 - 0.662529i) q^{86} -4.37007i q^{87} +(0.214348 + 0.163312i) q^{88} +(1.90441 - 1.90441i) q^{89} +(2.39080 + 2.18574i) q^{90} +(-9.35300 + 5.01789i) q^{91} +(3.99300 - 0.358530i) q^{92} +(-2.08158 + 2.08158i) q^{93} +(7.17075 - 7.84346i) q^{94} +7.46925 q^{95} +(-1.25587 - 5.51569i) q^{96} +(8.76265 + 8.76265i) q^{97} +(-2.35370 + 0.105457i) q^{98} +(-0.0673682 + 0.0673682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} - 6 q^{8} + 24 q^{9} + 8 q^{11} + 36 q^{14} + 28 q^{16} + 20 q^{19} - 20 q^{20} + 20 q^{22} + 6 q^{24} + 12 q^{26} - 24 q^{27} - 16 q^{28} - 30 q^{32} - 8 q^{33} + 16 q^{34} + 16 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q - 24 * q^3 - 6 * q^8 + 24 * q^9 + 8 * q^11 + 36 * q^14 + 28 * q^16 + 20 * q^19 - 20 * q^20 + 20 * q^22 + 6 * q^24 + 12 * q^26 - 24 * q^27 - 16 * q^28 - 30 * q^32 - 8 * q^33 + 16 * q^34 + 16 * q^35 + 36 * q^40 - 12 * q^41 - 36 * q^42 - 32 * q^44 - 44 * q^46 - 28 * q^48 - 36 * q^50 + 4 * q^52 - 20 * q^57 + 32 * q^58 - 16 * q^59 + 20 * q^60 - 76 * q^65 - 20 * q^66 + 28 * q^67 + 32 * q^68 - 40 * q^70 - 6 * q^72 - 8 * q^73 - 32 * q^74 - 36 * q^76 - 12 * q^78 - 32 * q^80 + 24 * q^81 - 72 * q^83 + 16 * q^84 + 4 * q^86 + 28 * q^89 - 4 * q^91 + 32 * q^92 + 28 * q^94 + 30 * q^96 + 24 * q^97 + 68 * q^98 + 8 * q^99

Introduction

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