LMFDB - Embedded newform 312.2.t.e.187.12

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			187.12
Character	$\chi$	$=$	312.187
Dual form			312.2.t.e.307.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41280 - 0.0632999i) q^{2} -1.00000 q^{3} +(1.99199 - 0.178860i) q^{4} +(-1.61967 - 1.61967i) q^{5} +(-1.41280 + 0.0632999i) q^{6} +(2.08158 - 2.08158i) q^{7} +(2.80295 - 0.378785i) 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} +(1.41280 - 0.0632999i) q^{18} +(2.30579 - 2.30579i) q^{19} +(-3.51606 - 2.93668i) q^{20} +(-2.08158 + 2.08158i) q^{21} +(-0.0994420 - 0.0909132i) q^{22} +2.00453 q^{23} +(-2.80295 + 0.378785i) q^{24} +0.246692i q^{25} +(-1.68965 - 4.81093i) q^{26} -1.00000 q^{27} +(3.77418 - 4.51880i) q^{28} +4.37007i q^{29} +(2.39080 + 2.18574i) q^{30} +(-2.08158 - 2.08158i) q^{31} +(5.51569 - 1.25587i) q^{32} +(0.0673682 + 0.0673682i) q^{33} +(0.454617 + 10.1466i) 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} +(-0.146246 - 0.122147i) q^{44} +(-1.61967 - 1.61967i) q^{45} +(2.83200 - 0.126887i) q^{46} +(5.31365 - 5.31365i) q^{47} +(-3.93602 + 0.712572i) q^{48} -1.66599i q^{49} +(0.0156156 + 0.348525i) q^{50} -7.18195i q^{51} +(-2.69166 - 6.68991i) q^{52} +1.41118i q^{53} +(-1.41280 + 0.0632999i) q^{54} +0.218229i q^{55} +(5.04610 - 6.62305i) q^{56} +(-2.30579 + 2.30579i) q^{57} +(0.276625 + 6.17401i) q^{58} +(-3.96350 - 3.96350i) q^{59} +(3.51606 + 2.93668i) 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} +(-9.52646 + 0.426830i) q^{70} +(0.00829610 + 0.00829610i) q^{71} +(2.80295 - 0.378785i) q^{72} +(0.419298 + 0.419298i) q^{73} +(-8.68214 + 9.49664i) q^{74} -0.246692i q^{75} +(4.18068 - 5.00551i) q^{76} -0.280465 q^{77} +(1.68965 + 4.81093i) q^{78} +8.46664i q^{79} +(-7.52920 - 5.22093i) q^{80} +1.00000 q^{81} +(-10.7198 + 11.7254i) q^{82} +(-3.35193 + 3.35193i) q^{83} +(-3.77418 + 4.51880i) q^{84} +(11.6324 - 11.6324i) q^{85} +(0.662529 + 14.7870i) 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} +(-5.51569 + 1.25587i) q^{96} +(8.76265 - 8.76265i) q^{97} +(-0.105457 - 2.35370i) 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 $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.41280	−	0.0632999i	0.998998	−	0.0447598i
$2$	1.41280	−	0.0632999i	0.998998	−	0.0447598i
$3$	−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	$-0.421164\pi$
$5$	−1.61967	−	1.61967i	−0.724341	−	0.724341i	−0.969486	+	0.245146i	$0.921164\pi$
$6$	−1.41280	+	0.0632999i	−0.576772	+	0.0258421i
$7$	2.08158	−	2.08158i	0.786765	−	0.786765i	−0.194197	−	0.980962i	$-0.562210\pi$
$7$	2.08158	−	2.08158i	0.786765	−	0.786765i	0.980962	+	0.194197i	$0.0622102\pi$
$8$	2.80295	−	0.378785i	0.990992	−	0.133921i
$9$	1.00000			0.333333
$10$	−2.39080	−	2.18574i	−0.756036	−	0.691193i
$11$	−0.0673682	−	0.0673682i	−0.0203123	−	0.0203123i	0.696878	−	0.717190i	$-0.254572\pi$
$11$	−0.0673682	−	0.0673682i	−0.0203123	−	0.0203123i	−0.717190	+	0.696878i	$0.754572\pi$
$12$	−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	$0.336489\pi$
$17$			7.18195i			1.74188i	−0.491391	+	0.870939i	$0.663511\pi$
$18$	1.41280	−	0.0632999i	0.332999	−	0.0149199i
$19$	2.30579	−	2.30579i	0.528984	−	0.528984i	−0.391285	−	0.920269i	$-0.627969\pi$
$19$	2.30579	−	2.30579i	0.528984	−	0.528984i	0.920269	+	0.391285i	$0.127969\pi$
$20$	−3.51606	−	2.93668i	−0.786216	−	0.656661i
$21$	−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	$-0.432983\pi$
$23$	2.00453			0.417974			0.208987	+	0.977918i	$0.432983\pi$
$24$	−2.80295	+	0.378785i	−0.572150	+	0.0773191i
$25$			0.246692i			0.0493384i
$26$	−1.68965	−	4.81093i	−0.331367	−	0.943502i
$27$	−1.00000			−0.192450
$28$	3.77418	−	4.51880i	0.713252	−	0.853973i
$29$			4.37007i			0.811501i	0.913984	+	0.405750i	$0.132990\pi$
$29$			4.37007i			0.811501i	−0.913984	+	0.405750i	$0.867010\pi$
$30$	2.39080	+	2.18574i	0.436498	+	0.399061i
$31$	−2.08158	−	2.08158i	−0.373864	−	0.373864i	0.495019	−	0.868882i	$-0.335161\pi$
$31$	−2.08158	−	2.08158i	−0.373864	−	0.373864i	−0.868882	+	0.495019i	$0.835161\pi$
$32$	5.51569	−	1.25587i	0.975045	−	0.222008i
$33$	0.0673682	+	0.0673682i	0.0117273	+	0.0117273i
$34$	0.454617	+	10.1466i	0.0779661	+	1.74013i
$35$	−6.74298			−1.13977
$36$	1.99199	−	0.178860i	0.331998	−	0.0298100i
$37$	−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	$0.981066\pi$
$38$	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	−0.280806	+	0.959764i	$0.590602\pi$
$41$	−7.94353	+	7.94353i	−1.24057	+	1.24057i	−0.959764	+	0.280806i	$0.909398\pi$
$42$	−2.80909	+	3.07262i	−0.433452	+	0.474115i
$43$			10.4665i			1.59613i	0.602573	+	0.798064i	$0.294142\pi$
$43$			10.4665i			1.59613i	−0.602573	+	0.798064i	$0.705858\pi$
$44$	−0.146246	−	0.122147i	−0.0220474	−	0.0184144i
$45$	−1.61967	−	1.61967i	−0.241447	−	0.241447i
$46$	2.83200	−	0.126887i	0.417555	−	0.0187084i
$47$	5.31365	−	5.31365i	0.775076	−	0.775076i	−0.203913	−	0.978989i	$-0.565366\pi$
$47$	5.31365	−	5.31365i	0.775076	−	0.775076i	0.978989	+	0.203913i	$0.0653661\pi$
$48$	−3.93602	+	0.712572i	−0.568115	+	0.102851i
$49$		−	1.66599i		−	0.237998i
$50$	0.0156156	+	0.348525i	0.00220837	+	0.0492889i
$51$		−	7.18195i		−	1.00567i
$52$	−2.69166	−	6.68991i	−0.373266	−	0.927724i
$53$			1.41118i			0.193841i	0.995292	+	0.0969204i	$0.0308992\pi$
$53$			1.41118i			0.193841i	−0.995292	+	0.0969204i	$0.969101\pi$
$54$	−1.41280	+	0.0632999i	−0.192257	+	0.00861402i
$55$			0.218229i			0.0294260i
$56$	5.04610	−	6.62305i	0.674314	−	0.885042i
$57$	−2.30579	+	2.30579i	−0.305409	+	0.305409i
$58$	0.276625	+	6.17401i	0.0363226	+	0.810687i
$59$	−3.96350	−	3.96350i	−0.516004	−	0.516004i	0.400356	−	0.916360i	$-0.368887\pi$
$59$	−3.96350	−	3.96350i	−0.516004	−	0.516004i	−0.916360	+	0.400356i	$0.868887\pi$
$60$	3.51606	+	2.93668i	0.453922	+	0.379123i
$61$		−	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	−0.00300457	−	0.999995i	$-0.500956\pi$
$67$	8.16072	−	8.16072i	0.996991	−	0.996991i	0.999995	+	0.00300457i	$0.000956387\pi$
$68$	1.28456	+	14.3063i	0.155776	+	1.73490i
$69$	−2.00453			−0.241317
$70$	−9.52646	+	0.426830i	−1.13863	+	0.0510159i
$71$	0.00829610	+	0.00829610i	0.000984566	+	0.000984566i	0.707599	−	0.706614i	$-0.249778\pi$
$71$	0.00829610	+	0.00829610i	0.000984566	+	0.000984566i	−0.706614	+	0.707599i	$0.749778\pi$
$72$	2.80295	−	0.378785i	0.330331	−	0.0446402i
$73$	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	$0.738952\pi$
$74$	−8.68214	+	9.49664i	−1.00928	+	1.10396i
$75$		−	0.246692i		−	0.0284855i
$76$	4.18068	−	5.00551i	0.479557	−	0.574171i
$77$	−0.280465			−0.0319620
$78$	1.68965	+	4.81093i	0.191315	+	0.544731i
$79$			8.46664i			0.952571i	0.879291	+	0.476286i	$0.158017\pi$
$79$			8.46664i			0.952571i	−0.879291	+	0.476286i	$0.841983\pi$
$80$	−7.52920	−	5.22093i	−0.841791	−	0.583718i
$81$	1.00000			0.111111
$82$	−10.7198	+	11.7254i	−1.18380	+	1.29486i
$83$	−3.35193	+	3.35193i	−0.367922	+	0.367922i	−0.866719	−	0.498797i	$-0.833775\pi$
$83$	−3.35193	+	3.35193i	−0.367922	+	0.367922i	0.498797	+	0.866719i	$0.333775\pi$
$84$	−3.77418	+	4.51880i	−0.411796	+	0.493041i
$85$	11.6324	−	11.6324i	1.26171	−	1.26171i
$86$	0.662529	+	14.7870i	0.0714423	+	1.59453i
$87$		−	4.37007i		−	0.468520i
$88$	−0.214348	−	0.163312i	−0.0228496	−	0.0174091i
$89$	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	$0.704408\pi$
$90$	−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
$96$	−5.51569	+	1.25587i	−0.562942	+	0.128177i
$97$	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	$0.0334147\pi$
$98$	−0.105457	−	2.35370i	−0.0106528	−	0.237760i
$99$	−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	$-0.676231\pi$
$101$	−10.5683			−1.05159			−0.525793	+	0.850613i	$0.676231\pi$
$102$	−0.454617	−	10.1466i	−0.0450137	−	1.00467i
$103$	3.52228			0.347061			0.173530	−	0.984829i	$-0.444482\pi$
$103$	3.52228			0.347061			0.173530	+	0.984829i	$0.444482\pi$
$104$	−4.22624	−	9.28110i	−0.414417	−	0.910087i
$105$	6.74298			0.658047
$106$	0.0893277	+	1.99371i	0.00867627	+	0.193646i
$107$	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	0.958220	+	0.286033i	$0.0923367\pi$
$109$	12.9904	+	12.9904i	1.24425	+	1.24425i	0.286033	+	0.958220i	$0.407663\pi$
$110$	0.0138139	+	0.308313i	0.00131710	+	0.0293965i
$111$	6.43362	−	6.43362i	0.610652	−	0.610652i
$112$	6.70988	−	9.67643i	0.634024	−	0.914337i
$113$	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
$122$	−0.122828	−	2.74140i	−0.0111203	−	0.248195i
$123$	7.94353	−	7.94353i	0.716244	−	0.716244i
$124$	−4.51880	−	3.77418i	−0.405800	−	0.338931i
$125$	−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	$-0.807654\pi$
$127$	−18.5476			−1.64583			−0.822916	+	0.568164i	$0.807654\pi$
$128$	10.7625	−	3.48821i	0.951284	−	0.308317i
$129$		−	10.4665i		−	0.921525i
$130$	−5.05547	+	10.5288i	−0.443394	+	0.923439i
$131$	−5.20053			−0.454372			−0.227186	−	0.973851i	$-0.572953\pi$
$131$	−5.20053			−0.454372			−0.227186	+	0.973851i	$0.572953\pi$
$132$	0.146246	+	0.122147i	0.0127291	+	0.0106315i
$133$		−	9.59938i		−	0.832372i
$134$	11.0129	−	12.0460i	0.951367	−	1.04062i
$135$	1.61967	+	1.61967i	0.139399	+	0.139399i
$136$	2.72041	+	20.1306i	0.233274	+	1.72619i
$137$	−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	$-0.612324\pi$
$138$	−2.83200	+	0.126887i	−0.241076	+	0.0108013i
$139$	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
$148$	−11.6650	+	13.9664i	−0.958854	+	1.14803i
$149$	−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	$-0.528586\pi$
$150$	−0.0156156	−	0.348525i	−0.00127501	−	0.0284570i
$151$	2.61081	−	2.61081i	0.212465	−	0.212465i	−0.592849	−	0.805314i	$-0.701997\pi$
$151$	2.61081	−	2.61081i	0.212465	−	0.212465i	0.805314	+	0.592849i	$0.201997\pi$
$152$	5.58961	−	7.33640i	0.453377	−	0.595061i
$153$			7.18195i			0.580626i
$154$	−0.396240	+	0.0177534i	−0.0319300	+	0.00143061i
$155$			6.74298i			0.541609i
$156$	2.69166	+	6.68991i	0.215505	+	0.535622i
$157$			1.36321i			0.108796i	0.998519	+	0.0543978i	$0.0173239\pi$
$157$			1.36321i			0.108796i	−0.998519	+	0.0543978i	$0.982676\pi$
$158$	0.535937	+	11.9616i	0.0426369	+	0.951617i
$159$		−	1.41118i		−	0.111914i
$160$	−10.9677	−	6.89952i	−0.867074	−	0.545455i
$161$	4.17261	−	4.17261i	0.328847	−	0.328847i
$162$	1.41280	−	0.0632999i	0.111000	−	0.00497331i
$163$	13.7263	+	13.7263i	1.07513	+	1.07513i	0.996938	+	0.0781913i	$0.0249145\pi$
$163$	13.7263	+	13.7263i	1.07513	+	1.07513i	0.0781913	+	0.996938i	$0.475086\pi$
$164$	−14.4026	+	17.2442i	−1.12466	+	1.34654i
$165$		−	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	$-0.805228\pi$
$167$	−3.15502	+	3.15502i	−0.244142	+	0.244142i	0.574419	+	0.818561i	$0.305228\pi$
$168$	−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	$-0.469433\pi$
$173$	2.52229			0.191766			0.0958830	+	0.995393i	$0.469433\pi$
$174$	−0.276625	−	6.17401i	−0.0209709	−	0.468051i
$175$	0.513510	+	0.513510i	0.0388177	+	0.0388177i
$176$	−0.313167	−	0.217158i	−0.0236059	−	0.0163689i
$177$	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	$-0.849654\pi$
$179$		−	12.1739i		−	0.909917i	0.890513	−	0.454958i	$-0.150346\pi$
$180$	−3.51606	−	2.93668i	−0.262072	−	0.218887i
$181$	1.13958			0.0847044			0.0423522	−	0.999103i	$-0.486515\pi$
$181$	1.13958			0.0847044			0.0423522	+	0.999103i	$0.486515\pi$
$182$	−13.5315	−	6.49722i	−1.00302	−	0.481606i
$183$			1.94041i			0.143439i
$184$	5.61860	−	0.759287i	0.414209	−	0.0559754i
$185$	20.8407			1.53224
$186$	3.07262	+	2.80909i	0.225295	+	0.205973i
$187$	0.483835	−	0.483835i	0.0353815	−	0.0353815i
$188$	9.63432	−	11.5351i	0.702655	−	0.841285i
$189$	−2.08158	+	2.08158i	−0.151413	+	0.151413i
$190$	−10.5525	+	0.472803i	−0.765561	+	0.0343007i
$191$		−	22.4304i		−	1.62301i	−0.584347	−	0.811504i	$-0.698649\pi$
$191$		−	22.4304i		−	1.62301i	0.584347	−	0.811504i	$-0.301351\pi$
$192$	−7.71304	+	2.12343i	−0.556641	+	0.153245i
$193$	−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	$0.808224\pi$
$194$	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	$-0.213661\pi$
$197$	2.26114	+	2.26114i	0.161099	+	0.161099i	−0.621954	+	0.783054i	$0.713661\pi$
$198$	−0.0994420	−	0.0909132i	−0.00706704	−	0.00646092i
$199$	−26.4375			−1.87410			−0.937051	−	0.349193i	$-0.886456\pi$
$199$	−26.4375			−1.87410			−0.937051	+	0.349193i	$0.886456\pi$
$200$	0.0934431	+	0.691464i	0.00660743	+	0.0488939i
$201$	−8.16072	+	8.16072i	−0.575613	+	0.575613i
$202$	−14.9309	+	0.668972i	−1.05053	+	0.0470687i
$203$	9.09666	+	9.09666i	0.638460	+	0.638460i
$204$	−1.28456	−	14.3063i	−0.0899373	−	1.00164i
$205$	25.7319			1.79719
$206$	4.97627	−	0.222960i	0.346713	−	0.0155344i
$207$	2.00453			0.139325
$208$	−6.55831	−	12.8448i	−0.454737	−	0.890626i
$209$	−0.310674			−0.0214897
$210$	9.52646	−	0.426830i	0.657388	−	0.0294541i
$211$	−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
$214$	16.7153	−	0.748926i	1.14264	−	0.0511955i
$215$	16.9523	−	16.9523i	1.15614	−	1.15614i
$216$	−2.80295	+	0.378785i	−0.190717	+	0.0257730i
$217$	−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	$-0.147898\pi$
$223$	6.65855	+	6.65855i	0.445889	+	0.445889i	−0.448096	+	0.893985i	$0.647898\pi$
$224$	8.86717	−	14.0956i	0.592463	−	0.941800i
$225$			0.246692i			0.0164461i
$226$	17.9497	−	0.804232i	1.19400	−	0.0534967i
$227$	−7.86789	+	7.86789i	−0.522210	+	0.522210i	−0.918238	−	0.396028i	$-0.870388\pi$
$227$	−7.86789	+	7.86789i	−0.522210	+	0.522210i	0.396028	+	0.918238i	$0.370388\pi$
$228$	−4.18068	+	5.00551i	−0.276873	+	0.331498i
$229$	−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	$0.304487\pi$
$230$	−4.79243	−	4.38140i	−0.316003	−	0.288901i
$231$	0.280465			0.0184533
$232$	1.65531	+	12.2491i	0.108677	+	0.804191i
$233$			3.31543i			0.217201i	0.994085	+	0.108601i	$0.0346370\pi$
$233$			3.31543i			0.217201i	−0.994085	+	0.108601i	$0.965363\pi$
$234$	−1.68965	−	4.81093i	−0.110456	−	0.314501i
$235$	−17.2128			−1.12284
$236$	−8.60416	−	7.18633i	−0.560083	−	0.467791i
$237$		−	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	$-0.361285\pi$
$239$	−7.48888	−	7.48888i	−0.484415	−	0.484415i	−0.906538	+	0.422123i	$0.861285\pi$
$240$	7.52920	+	5.22093i	0.486008	+	0.337010i
$241$	−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	$0.884888\pi$
$242$	−0.695724	−	15.5279i	−0.0447229	−	0.998173i
$243$	−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	$-0.801561\pi$
$251$		−	18.4986i		−	1.16762i	0.811889	−	0.583812i	$-0.198439\pi$
$252$	3.77418	−	4.51880i	0.237751	−	0.284658i
$253$	−0.135042	−	0.135042i	−0.00849001	−	0.00849001i
$254$	−26.2039	+	1.17406i	−1.64418	+	0.0736671i
$255$	−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	$0.186074\pi$
$257$			17.6933i			1.10368i	−0.833950	+	0.551840i	$0.813926\pi$
$258$	−0.662529	−	14.7870i	−0.0412473	−	0.920601i
$259$			26.7842i			1.66429i
$260$	−6.47587	+	15.1951i	−0.401616	+	0.942360i
$261$			4.37007i			0.270500i
$262$	−7.34728	+	0.329193i	−0.453917	+	0.0203376i
$263$			18.2366i			1.12452i	0.826962	+	0.562258i	$0.190067\pi$
$263$			18.2366i			1.12452i	−0.826962	+	0.562258i	$0.809933\pi$
$264$	0.214348	+	0.163312i	0.0131922	+	0.0100511i
$265$	2.28566	−	2.28566i	0.140407	−	0.140407i
$266$	−0.607640	−	13.5620i	−0.0372568	−	0.831538i
$267$	−1.90441	−	1.90441i	−0.116548	−	0.116548i
$268$	14.7964	−	17.7157i	0.903835	−	1.08216i
$269$		−	6.68357i		−	0.407504i	−0.979023	−	0.203752i	$-0.934686\pi$
$269$		−	6.68357i		−	0.407504i	0.979023	−	0.203752i	$-0.0653137\pi$
$270$	2.39080	+	2.18574i	0.145499	+	0.133020i
$271$	−5.65140	+	5.65140i	−0.343298	+	0.343298i	−0.857606	−	0.514308i	$-0.828049\pi$
$271$	−5.65140	+	5.65140i	−0.343298	+	0.343298i	0.514308	+	0.857606i	$0.328049\pi$
$272$	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	$-0.761294\pi$
$277$	−24.3573			−1.46349			−0.731745	+	0.681579i	$0.761294\pi$
$278$	8.65254	−	0.387674i	0.518945	−	0.0232512i
$279$	−2.08158	−	2.08158i	−0.124621	−	0.124621i
$280$	−18.9002	+	2.55414i	−1.12950	+	0.152639i
$281$	−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	$0.848187\pi$
$282$	−7.17075	+	7.84346i	−0.427012	+	0.467071i
$283$			14.0053i			0.832529i	0.909244	+	0.416264i	$0.136661\pi$
$283$			14.0053i			0.832529i	−0.909244	+	0.416264i	$0.863339\pi$
$284$	0.0180096	+	0.0150419i	0.00106867	+	0.000892571i
$285$	7.46925			0.442440
$286$	−0.210275	+	0.437933i	−0.0124338	+	0.0258955i
$287$			33.0703i			1.95208i
$288$	5.51569	−	1.25587i	0.325015	−	0.0740028i
$289$	−34.5804			−2.03414
$290$	9.55185	−	10.4479i	0.560904	−	0.613524i
$291$	−8.76265	+	8.76265i	−0.513676	+	0.513676i
$292$	0.910231	+	0.760240i	0.0532672	+	0.0444897i
$293$	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	$0.108132\pi$
$294$	0.105457	+	2.35370i	0.00615037	+	0.137271i
$295$			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
$304$	7.43258	−	10.7187i	0.426288	−	0.614757i
$305$	−3.14283	+	3.14283i	−0.179958	+	0.179958i
$306$	0.454617	+	10.1466i	0.0259887	+	0.580044i
$307$	9.49598	+	9.49598i	0.541964	+	0.541964i	0.924104	−	0.382140i	$-0.124813\pi$
$307$	9.49598	+	9.49598i	0.541964	+	0.541964i	−0.382140	+	0.924104i	$0.624813\pi$
$308$	−0.558683	+	0.0501640i	−0.0318339	+	0.00285836i
$309$	−3.52228			−0.200376
$310$	0.426830	+	9.52646i	0.0242423	+	0.541066i
$311$	−19.3516			−1.09733			−0.548664	−	0.836043i	$-0.684864\pi$
$311$	−19.3516			−1.09733			−0.548664	+	0.836043i	$0.684864\pi$
$312$	4.22624	+	9.28110i	0.239264	+	0.525439i
$313$	10.1200			0.572016			0.286008	−	0.958227i	$-0.407672\pi$
$313$	10.1200			0.572016			0.286008	+	0.958227i	$0.407672\pi$
$314$	0.0862908	+	1.92593i	0.00486967	+	0.108687i
$315$	−6.74298			−0.379924
$316$	1.51434	+	16.8654i	0.0851883	+	0.948755i
$317$	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	$0.493784\pi$
$318$	−0.0893277	−	1.99371i	−0.00500925	−	0.111802i
$319$	0.294404	−	0.294404i	0.0164834	−	0.0164834i
$320$	−15.9319	−	9.05336i	−0.890619	−	0.506098i
$321$	−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
$330$	−0.0138139	−	0.308313i	−0.000760430	−	0.0169721i
$331$	−22.5976	+	22.5976i	−1.24208	+	1.24208i	−0.282939	+	0.959138i	$0.591309\pi$
$331$	−22.5976	+	22.5976i	−1.24208	+	1.24208i	−0.959138	+	0.282939i	$0.908691\pi$
$332$	−6.07747	+	7.27652i	−0.333545	+	0.399351i
$333$	−6.43362	+	6.43362i	−0.352560	+	0.352560i
$334$	−4.25768	+	4.65711i	−0.232970	+	0.254825i
$335$	−26.4354			−1.44432
$336$	−6.70988	+	9.67643i	−0.366054	+	0.527893i
$337$		−	8.65894i		−	0.471683i	−0.971792	−	0.235841i	$-0.924215\pi$
$337$		−	8.65894i		−	0.471683i	0.971792	−	0.235841i	$-0.0757846\pi$
$338$	−14.8475	+	10.8421i	−0.807597	+	0.589735i
$339$	−12.7051			−0.690047
$340$	21.0910	−	25.2522i	1.14382	−	1.36949i
$341$			0.280465i			0.0151881i
$342$	3.11165	−	3.40356i	0.168259	−	0.184044i
$343$	11.1032	+	11.1032i	0.599516	+	0.599516i
$344$	3.96456	+	29.3371i	0.213754	+	1.58175i
$345$	3.24669	+	3.24669i	0.174796	+	0.174796i
$346$	3.56348	−	0.159661i	0.191574	−	0.00858341i
$347$	−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	$-0.701743\pi$
$349$	3.99002	−	3.99002i	0.213581	−	0.213581i	0.805787	+	0.592206i	$0.201743\pi$
$350$	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	−0.850466	−	0.526030i	$-0.823680\pi$
$353$	−6.09559	+	6.09559i	−0.324436	+	0.324436i	0.526030	+	0.850466i	$0.323680\pi$
$354$	5.85051	+	5.34873i	0.310951	+	0.284282i
$355$		−	0.0268740i		−	0.00142632i
$356$	4.13418	+	3.45293i	0.219111	+	0.183005i
$357$	−14.9498	−	14.9498i	−0.791229	−	0.791229i
$358$	−0.770604	−	17.1992i	−0.0407277	−	0.909005i
$359$	20.6821	−	20.6821i	1.09156	−	1.09156i	0.0961965	−	0.995362i	$-0.469332\pi$
$359$	20.6821	−	20.6821i	1.09156	−	1.09156i	0.995362	−	0.0961965i	$-0.0306677\pi$
$360$	−5.15337	−	3.92636i	−0.271607	−	0.206937i
$361$			8.36669i			0.440352i
$362$	1.61000	−	0.0721353i	0.0846195	−	0.00379135i
$363$			10.9909i			0.576874i
$364$	−19.5285	−	8.32270i	−1.02357	−	0.436228i
$365$		−	1.35825i		−	0.0710941i
$366$	0.122828	+	2.74140i	0.00642030	+	0.143295i
$367$		−	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
$370$	29.4437	−	1.31922i	1.53071	−	0.0685828i
$371$	2.93749	+	2.93749i	0.152507	+	0.152507i
$372$	4.51880	+	3.77418i	0.234289	+	0.195682i
$373$		−	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	−0.344292	−	0.938863i	$-0.611881\pi$
$379$	11.5751	−	11.5751i	0.594571	−	0.594571i	0.938863	+	0.344292i	$0.111881\pi$
$380$	−14.8786	+	1.33595i	−0.763258	+	0.0685327i
$381$	18.5476			0.950221
$382$	−1.41984	−	31.6896i	−0.0726455	−	1.62138i
$383$	−2.01486	−	2.01486i	−0.102954	−	0.102954i	0.653753	−	0.756708i	$-0.273193\pi$
$383$	−2.01486	−	2.01486i	−0.102954	−	0.102954i	−0.756708	+	0.653753i	$0.773193\pi$
$384$	−10.7625	+	3.48821i	−0.549224	+	0.178007i
$385$	0.454263	+	0.454263i	0.0231514	+	0.0231514i
$386$	−5.27513	−	4.82270i	−0.268497	−	0.245469i
$387$			10.4665i			0.532043i
$388$	15.8878	−	19.0224i	0.806581	−	0.965714i
$389$	−25.8294			−1.30960			−0.654801	−	0.755801i	$-0.727248\pi$
$389$	−25.8294			−1.30960			−0.654801	+	0.755801i	$0.727248\pi$
$390$	5.05547	−	10.5288i	0.255993	−	0.533148i
$391$			14.3965i			0.728060i
$392$	−0.631052	−	4.66968i	−0.0318729	−	0.235855i
$393$	5.20053			0.262332
$394$	3.33766	+	3.05140i	0.168149	+	0.153727i
$395$	13.7132	−	13.7132i	0.689986	−	0.689986i
$396$	−0.146246	−	0.122147i	−0.00734914	−	0.00613813i
$397$	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	$0.121312\pi$
$398$	−37.3507	+	1.67349i	−1.87222	+	0.0838844i
$399$			9.59938i			0.480570i
$400$	0.175786	+	0.970983i	0.00878928	+	0.0485492i
$401$	−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	$-0.594967\pi$
$402$	−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
$408$	−2.72041	−	20.1306i	−0.134681	−	0.996615i
$409$	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	$-0.0827798\pi$
$410$	36.3539	−	1.62882i	1.79539	−	0.0804419i
$411$	15.0286	+	15.0286i	0.741307	+	0.741307i
$412$	7.01634	−	0.629995i	0.345670	−	0.0310376i
$413$	−16.5007			−0.811948
$414$	2.83200	−	0.126887i	0.139185	−	0.00623614i
$415$	10.8581			0.533002
$416$	−10.0786	−	17.7319i	−0.494145	−	0.869379i
$417$	−6.12441			−0.299914
$418$	−0.438919	+	0.0196656i	−0.0214682	+	0.000961876i
$419$	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	$-0.192154\pi$
$421$	5.24431	+	5.24431i	0.255592	+	0.255592i	−0.567667	+	0.823259i	$0.692154\pi$
$422$	−3.22916	+	0.144682i	−0.157193	+	0.00704300i
$423$	5.31365	−	5.31365i	0.258359	−	0.258359i
$424$	0.534534	+	3.95547i	0.0259593	+	0.192095i
$425$	−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	$-0.446075\pi$
$431$	−16.9631	−	16.9631i	−0.817084	−	0.817084i	−0.985684	+	0.168600i	$0.946075\pi$
$432$	−3.93602	+	0.712572i	−0.189372	+	0.0342836i
$433$			21.6657i			1.04119i	0.853805	+	0.520593i	$0.174289\pi$
$433$			21.6657i			1.04119i	−0.853805	+	0.520593i	$0.825711\pi$
$434$	−12.2433	+	0.548556i	−0.587696	+	0.0263315i
$435$	−7.07808	+	7.07808i	−0.339368	+	0.339368i
$436$	28.2001	+	23.5532i	1.35054	+	1.12799i
$437$	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	$-0.722813\pi$
$439$	−26.9953			−1.28842			−0.644208	+	0.764850i	$0.722813\pi$
$440$	0.0826619	+	0.611685i	0.00394075	+	0.0291610i
$441$		−	1.66599i		−	0.0793328i
$442$	34.5519	−	12.1350i	1.64347	−	0.577202i
$443$	−3.69391			−0.175503			−0.0877515	−	0.996142i	$-0.527968\pi$
$443$	−3.69391			−0.175503			−0.0877515	+	0.996142i	$0.527968\pi$
$444$	11.6650	−	13.9664i	0.553595	−	0.662816i
$445$		−	6.16904i		−	0.292441i
$446$	9.82865	+	8.98568i	0.465400	+	0.425484i
$447$	13.2521	+	13.2521i	0.626803	+	0.626803i
$448$	11.6353	−	20.4755i	0.549714	−	0.967374i
$449$	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	$0.571167\pi$
$450$	0.0156156	+	0.348525i	0.000736125	+	0.0164296i
$451$	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	−0.901054	−	0.433708i	$-0.857205\pi$
$457$	−9.99072	+	9.99072i	−0.467346	+	0.467346i	0.433708	+	0.901054i	$0.357205\pi$
$458$	−4.91949	+	5.38100i	−0.229873	+	0.251438i
$459$		−	7.18195i		−	0.335225i
$460$	−7.04807	−	5.88666i	−0.328618	−	0.274467i
$461$	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	$0.645307\pi$
$462$	0.396240	−	0.0177534i	0.0184348	−	0.000825964i
$463$	16.5192	−	16.5192i	0.767714	−	0.767714i	−0.209990	−	0.977704i	$-0.567343\pi$
$463$	16.5192	−	16.5192i	0.767714	−	0.767714i	0.977704	+	0.209990i	$0.0673431\pi$
$464$	3.11399	+	17.2007i	0.144563	+	0.798521i
$465$		−	6.74298i		−	0.312698i
$466$	0.209867	+	4.68403i	0.00972188	+	0.216984i
$467$		−	13.7056i		−	0.634220i	−0.948389	−	0.317110i	$-0.897288\pi$
$467$		−	13.7056i		−	0.634220i	0.948389	−	0.317110i	$-0.102712\pi$
$468$	−2.69166	−	6.68991i	−0.124422	−	0.309241i
$469$		−	33.9745i		−	1.56880i
$470$	−24.3181	+	1.08957i	−1.12171	+	0.0502580i
$471$		−	1.36321i		−	0.0628132i
$472$	−12.6108	−	9.60818i	−0.580460	−	0.442252i
$473$	0.705110	−	0.705110i	0.0324210	−	0.0324210i
$474$	−0.535937	−	11.9616i	−0.0246164	−	0.549416i
$475$	0.568819	+	0.568819i	0.0260992	+	0.0260992i
$476$	32.4538	+	27.1059i	1.48752	+	1.24240i
$477$			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	$-0.824496\pi$
$479$	−7.17788	+	7.17788i	−0.327966	+	0.327966i	0.523847	+	0.851813i	$0.324496\pi$
$480$	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
$486$	−1.41280	+	0.0632999i	−0.0640857	+	0.00287134i
$487$	−0.384275	−	0.384275i	−0.0174132	−	0.0174132i	0.698347	−	0.715760i	$-0.253919\pi$
$487$	−0.384275	−	0.384275i	−0.0174132	−	0.0174132i	−0.715760	+	0.698347i	$0.753919\pi$
$488$	−0.734997	−	5.43886i	−0.0332717	−	0.246206i
$489$	−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	$-0.980449\pi$
$491$		−	2.72036i		−	0.122768i	0.998114	−	0.0613840i	$-0.0195514\pi$
$492$	14.4026	−	17.2442i	0.649320	−	0.777428i
$493$	−31.3856			−1.41354
$494$	−14.9890	−	7.19702i	−0.674385	−	0.323809i
$495$			0.218229i			0.00980868i
$496$	−9.67643	−	6.70988i	−0.434485	−	0.301282i
$497$	0.0345381			0.00154924
$498$	4.52342	−	4.94777i	0.202699	−	0.221715i
$499$	29.4023	−	29.4023i	1.31623	−	1.31623i	0.399493	−	0.916736i	$-0.369186\pi$
$499$	29.4023	−	29.4023i	1.31623	−	1.31623i	0.916736	−	0.399493i	$-0.130814\pi$
$500$	−13.9589	+	16.7129i	−0.624262	+	0.747425i
$501$	3.15502	−	3.15502i	0.140956	−	0.140956i
$502$	−1.17096	−	26.1348i	−0.0522626	−	1.16645i
$503$		−	8.72354i		−	0.388963i	−0.980906	−	0.194482i	$-0.937698\pi$
$503$		−	8.72354i		−	0.388963i	0.980906	−	0.194482i	$-0.0623025\pi$
$504$	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	0.912726	+	0.408572i	$0.133973\pi$
$509$	29.8098	+	29.8098i	1.32130	+	1.32130i	0.408572	+	0.912726i	$0.366027\pi$
$510$	−15.6979	+	17.1706i	−0.695115	+	0.760326i
$511$	1.74561			0.0772211
$512$	20.8149	−	8.87345i	0.919899	−	0.392155i
$513$	−2.30579	+	2.30579i	−0.101803	+	0.101803i
$514$	1.11999	+	24.9971i	0.0494004	+	1.10257i
$515$	−5.70495	−	5.70495i	−0.251390	−	0.251390i
$516$	−1.87204	−	20.8491i	−0.0824118	−	0.917832i
$517$	−0.715943			−0.0314871
$518$	1.69544	+	37.8407i	0.0744933	+	1.66262i
$519$	−2.52229			−0.110716
$520$	−8.18724	+	21.8775i	−0.359034	+	0.959392i
$521$	23.2436			1.01832			0.509161	−	0.860671i	$-0.329956\pi$
$521$	23.2436			1.01832			0.509161	+	0.860671i	$0.329956\pi$
$522$	0.276625	+	6.17401i	0.0121075	+	0.270229i
$523$	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
$526$	1.15437	+	25.7646i	0.0503331	+	1.12339i
$527$	14.9498	−	14.9498i	0.651225	−	0.651225i
$528$	0.313167	+	0.217158i	0.0136289	+	0.00945058i
$529$	−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
$538$	−0.423069	−	9.44252i	−0.0182398	−	0.407096i
$539$	−0.112235	+	0.112235i	−0.00483429	+	0.00483429i
$540$	3.51606	+	2.93668i	0.151307	+	0.126374i
$541$	−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	$0.326627\pi$
$542$	−7.62655	+	8.34201i	−0.327588	+	0.358320i
$543$	−1.13958			−0.0489041
$544$	9.01958	+	39.6134i	0.386712	+	1.69841i
$545$		−	42.0804i		−	1.80253i
$546$	13.5315	+	6.49722i	0.579095	+	0.278055i
$547$	−24.3317			−1.04035			−0.520175	−	0.854060i	$-0.674133\pi$
$547$	−24.3317			−1.04035			−0.520175	+	0.854060i	$0.674133\pi$
$548$	−32.6248	−	27.2488i	−1.39366	−	1.16401i
$549$		−	1.94041i		−	0.0828145i
$550$	0.0224275	−	0.0245315i	0.000956313	−	0.00104603i
$551$	10.0764	+	10.0764i	0.429271	+	0.429271i
$552$	−5.61860	+	0.759287i	−0.239144	+	0.0323174i
$553$	17.6240	+	17.6240i	0.749450	+	0.749450i
$554$	−34.4119	+	1.54182i	−1.46202	+	0.0655055i
$555$	−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	$-0.603609\pi$
$557$	14.8145	−	14.8145i	0.627710	−	0.627710i	0.947491	+	0.319781i	$0.103609\pi$
$558$	−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	$-0.734393\pi$
$563$		−	35.1602i		−	1.48183i	0.671601	−	0.740913i	$-0.265607\pi$
$564$	−9.63432	+	11.5351i	−0.405678	+	0.485716i
$565$	−20.5781	−	20.5781i	−0.865729	−	0.865729i
$566$	0.886534	+	19.7866i	0.0372638	+	0.831694i
$567$	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	$0.124823\pi$
$569$			18.2323i			0.764337i	−0.924093	+	0.382168i	$0.875177\pi$
$570$	10.5525	−	0.472803i	0.441997	−	0.0198035i
$571$		−	33.5099i		−	1.40235i	−0.712990	−	0.701174i	$-0.752660\pi$
$571$		−	33.5099i		−	1.40235i	0.712990	−	0.701174i	$-0.247340\pi$
$572$	−0.269355	+	0.632020i	−0.0112623	+	0.0264261i
$573$			22.4304i			0.937044i
$574$	2.09334	+	46.7215i	0.0873745	+	1.95012i
$575$			0.494502i			0.0206222i
$576$	7.71304	−	2.12343i	0.321377	−	0.0884762i
$577$	−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	$0.289395\pi$
$578$	−48.8550	+	2.18893i	−2.03210	+	0.0910477i
$579$	3.57371	+	3.57371i	0.148518	+	0.148518i
$580$	12.8335	−	15.3654i	0.532881	−	0.638015i
$581$			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	−0.379879	−	0.925036i	$-0.624034\pi$
$587$	13.2081	−	13.2081i	0.545157	−	0.545157i	0.925036	+	0.379879i	$0.124034\pi$
$588$	0.297978	+	3.31863i	0.0122884	+	0.136858i
$589$	−9.59938			−0.395536
$590$	0.812718	+	18.1391i	0.0334591	+	0.746776i
$591$	−2.26114	−	2.26114i	−0.0930108	−	0.0930108i
$592$	−20.7384	+	29.9073i	−0.852344	+	1.22918i
$593$	−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	$0.758423\pi$
$594$	0.0994420	+	0.0909132i	0.00408015	+	0.00373021i
$595$		−	48.4277i		−	1.98534i
$596$	−28.7683	−	24.0277i	−1.17839	−	0.984214i
$597$	26.4375			1.08201
$598$	−3.38696	−	9.64368i	−0.138503	−	0.394359i
$599$			25.5885i			1.04552i	0.852481	+	0.522758i	$0.175097\pi$
$599$			25.5885i			1.04552i	−0.852481	+	0.522758i	$0.824903\pi$
$600$	−0.0934431	−	0.691464i	−0.00381480	−	0.0282289i
$601$	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
$604$	4.73373	−	5.66767i	0.192613	−	0.230614i
$605$	−17.8017	+	17.8017i	−0.723743	+	0.723743i
$606$	14.9309	−	0.668972i	0.606524	−	0.0271751i
$607$			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	$-0.314808\pi$
$613$	−7.07976	−	7.07976i	−0.285949	−	0.285949i	−0.835476	+	0.549527i	$0.814808\pi$
$614$	14.0170	+	12.8148i	0.565679	+	0.517163i
$615$	−25.7319			−1.03761
$616$	−0.786130	+	0.106236i	−0.0316741	+	0.00428037i
$617$	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	$0.231374\pi$
$618$	−4.97627	+	0.222960i	−0.200175	+	0.00896877i
$619$	−16.6627	−	16.6627i	−0.669730	−	0.669730i	0.287923	−	0.957653i	$-0.407035\pi$
$619$	−16.6627	−	16.6627i	−0.669730	−	0.669730i	−0.957653	+	0.287923i	$0.907035\pi$
$620$	1.20605	+	13.4319i	0.0484360	+	0.539439i
$621$	−2.00453			−0.0804392
$622$	−27.3399	+	1.22495i	−1.09623	+	0.0491162i
$623$	7.92838			0.317644
$624$	6.55831	+	12.8448i	0.262542	+	0.514203i
$625$	26.1726			1.04690
$626$	14.2975	−	0.640595i	0.571443	−	0.0256033i
$627$	0.310674			0.0124071
$628$	0.243823	+	2.71549i	0.00972958	+	0.108360i
$629$	−46.2059	−	46.2059i	−1.84235	−	1.84235i
$630$	−9.52646	+	0.426830i	−0.379543	+	0.0170053i
$631$	32.6063	−	32.6063i	1.29804	−	1.29804i	0.368349	−	0.929688i	$-0.379923\pi$
$631$	32.6063	−	32.6063i	1.29804	−	1.29804i	0.929688	−	0.368349i	$-0.120077\pi$
$632$	3.20703	+	23.7316i	0.127569	+	0.943991i
$633$	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	$0.0184487\pi$
$641$			2.93313i			0.115852i	−0.998321	+	0.0579259i	$0.981551\pi$
$642$	−16.7153	+	0.748926i	−0.659702	+	0.0295577i
$643$	19.2248	−	19.2248i	0.758153	−	0.758153i	−0.217833	−	0.975986i	$-0.569899\pi$
$643$	19.2248	−	19.2248i	0.758153	−	0.758153i	0.975986	+	0.217833i	$0.0698989\pi$
$644$	7.56546	−	9.05808i	0.298121	−	0.356939i
$645$	−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	$-0.150017\pi$
$647$	45.3264			1.78197			0.890983	+	0.454037i	$0.150017\pi$
$648$	2.80295	−	0.378785i	0.110110	−	0.0148801i
$649$			0.534029i			0.0209625i
$650$	1.18682	−	0.416823i	0.0465508	−	0.0163491i
$651$	8.66599			0.339647
$652$	29.7978	+	24.8876i	1.16697	+	0.974673i
$653$		−	2.67450i		−	0.104661i	−0.998630	−	0.0523307i	$-0.983335\pi$
$653$		−	2.67450i		−	0.104661i	0.998630	−	0.0523307i	$-0.0166650\pi$
$654$	−19.1751	−	17.5305i	−0.749804	−	0.685496i
$655$	8.42316	+	8.42316i	0.329120	+	0.329120i
$656$	−25.6055	+	36.9262i	−0.999728	+	1.44173i
$657$	0.419298	+	0.419298i	0.0163584	+	0.0163584i
$658$	−1.40030	−	31.2534i	−0.0545893	−	1.21838i
$659$	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	−0.173752	+	0.984789i	$0.555589\pi$
$661$	−29.7860	+	29.7860i	−1.15854	+	1.15854i	−0.984789	+	0.173752i	$0.944411\pi$
$662$	−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
$668$	−5.72044	+	6.84905i	−0.221331	+	0.264998i
$669$	−6.65855	−	6.65855i	−0.257434	−	0.257434i
$670$	−37.3479	+	1.67336i	−1.44287	+	0.0646475i
$671$	−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	$0.172938\pi$
$673$			26.8225i			1.03393i	−0.856006	+	0.516965i	$0.827062\pi$
$674$	−0.548110	−	12.2333i	−0.0211124	−	0.471210i
$675$		−	0.246692i		−	0.00949517i
$676$	−20.2902	+	16.2576i	−0.780391	+	0.625292i
$677$		−	27.6382i		−	1.06222i	−0.847302	−	0.531112i	$-0.821774\pi$
$677$		−	27.6382i		−	1.06222i	0.847302	−	0.531112i	$-0.178226\pi$
$678$	−17.9497	+	0.804232i	−0.689355	+	0.0308864i
$679$		−	36.4804i		−	1.39999i
$680$	28.1989	−	37.0113i	1.08138	−	1.41932i
$681$	7.86789	−	7.86789i	0.301498	−	0.301498i
$682$	0.0177534	+	0.396240i	0.000679814	+	0.0151728i
$683$	−0.401585	−	0.401585i	−0.0153662	−	0.0153662i	0.699382	−	0.714748i	$-0.253459\pi$
$683$	−0.401585	−	0.401585i	−0.0153662	−	0.0153662i	−0.714748	+	0.699382i	$0.753459\pi$
$684$	4.18068	−	5.00551i	0.159852	−	0.191390i
$685$			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	−0.999834	−	0.0182023i	$-0.994206\pi$
$691$	−25.8040	+	25.8040i	−0.981632	+	0.981632i	0.0182023	+	0.999834i	$0.494206\pi$
$692$	5.02436	−	0.451136i	0.190998	−	0.0171496i
$693$	−0.280465			−0.0106540
$694$	−23.5422	+	1.05480i	−0.893650	+	0.0400397i
$695$	−9.91955	−	9.91955i	−0.376270	−	0.376270i
$696$	−1.65531	−	12.2491i	−0.0627445	−	0.464300i
$697$	−57.0500	−	57.0500i	−2.16092	−	2.16092i
$698$	5.38452	−	5.88965i	0.203807	−	0.222927i
$699$		−	3.31543i		−	0.125401i
$700$	1.11475	+	0.931058i	0.0421336	+	0.0351907i
$701$	−42.4434			−1.60307			−0.801533	−	0.597951i	$-0.795982\pi$
$701$	−42.4434			−1.60307			−0.801533	+	0.597951i	$0.795982\pi$
$702$	1.68965	+	4.81093i	0.0637717	+	0.181577i
$703$			29.6691i			1.11899i
$704$	−0.662666	−	0.376563i	−0.0249752	−	0.0141922i
$705$	17.2128			0.648271
$706$	−8.22598	+	8.99768i	−0.309589	+	0.338632i
$707$	−21.9988	+	21.9988i	−0.827350	+	0.827350i
$708$	8.60416	+	7.18633i	0.323364	+	0.270079i
$709$	−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	$0.448446\pi$
$710$	−0.00170112	−	0.0379674i	−6.38419e−5	−	0.00142489i
$711$			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	$-0.472959\pi$
$719$	4.55035			0.169699			0.0848497	+	0.996394i	$0.472959\pi$
$720$	−7.52920	−	5.22093i	−0.280597	−	0.194573i
$721$	7.33193	−	7.33193i	0.273055	−	0.273055i
$722$	0.529611	+	11.8204i	0.0197101	+	0.439911i
$723$	9.02754	+	9.02754i	0.335738	+	0.335738i
$724$	2.27003	−	0.203825i	0.0843650	−	0.00757510i
$725$	−1.07806			−0.0400381
$726$	0.695724	+	15.5279i	0.0258207	+	0.576296i
$727$	35.3567			1.31131			0.655653	−	0.755062i	$-0.272393\pi$
$727$	35.3567			1.31131			0.655653	+	0.755062i	$0.272393\pi$
$728$	−28.1167	−	10.5221i	−1.04207	−	0.389976i
$729$	1.00000			0.0370370
$730$	−0.0859772	−	1.91893i	−0.00318216	−	0.0710229i
$731$	−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	$-0.163852\pi$
$733$	10.2364	+	10.2364i	0.378089	+	0.378089i	−0.492323	+	0.870412i	$0.663852\pi$
$734$	−1.90676	−	42.5572i	−0.0703800	−	1.57082i
$735$	2.69836	−	2.69836i	0.0995305	−	0.0995305i
$736$	11.0564	−	2.51743i	0.407543	−	0.0927937i
$737$	−1.09955			−0.0405023
$738$	−10.7198	+	11.7254i	−0.394600	+	0.431618i
$739$	−15.9995	−	15.9995i	−0.588550	−	0.588550i	0.348688	−	0.937239i	$-0.386627\pi$
$739$	−15.9995	−	15.9995i	−0.588550	−	0.588550i	−0.937239	+	0.348688i	$0.886627\pi$
$740$	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	$-0.284939\pi$
$743$	−4.22277	−	4.22277i	−0.154918	−	0.154918i	−0.780311	+	0.625392i	$0.784939\pi$
$744$	6.62305	+	5.04610i	0.242813	+	0.184999i
$745$			42.9282i			1.57277i
$746$	−0.544340	−	12.1492i	−0.0199297	−	0.444813i
$747$	−3.35193	+	3.35193i	−0.122641	+	0.122641i
$748$	0.877255	−	1.05033i	0.0320756	−	0.0384039i
$749$	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	$-0.241457\pi$
$751$	39.7818			1.45166			0.725828	+	0.687876i	$0.241457\pi$
$752$	17.1283	−	24.7010i	0.624604	−	0.900752i
$753$			18.4986i			0.674128i
$754$	21.0241	−	7.38388i	0.765652	−	0.268905i
$755$	−8.45732			−0.307794
$756$	−3.77418	+	4.51880i	−0.137265	+	0.164347i
$757$		−	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
$760$	−20.9359	+	2.82924i	−0.759426	+	0.102627i
$761$	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	$0.725753\pi$
$762$	26.2039	−	1.17406i	0.949269	−	0.0425317i
$763$	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	−0.969036	−	0.246919i	$-0.920582\pi$
$769$	−20.0249	+	20.0249i	−0.722117	+	0.722117i	0.246919	+	0.969036i	$0.420582\pi$
$770$	0.670535	+	0.613026i	0.0241644	+	0.0220919i
$771$		−	17.6933i		−	0.637210i
$772$	−7.75796	−	6.47958i	−0.279215	−	0.233205i
$773$	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	$0.645906\pi$
$774$	0.662529	+	14.7870i	0.0238141	+	0.531509i
$775$	0.513510	−	0.513510i	0.0184458	−	0.0184458i
$776$	21.2421	−	27.8804i	0.762547	−	1.00085i
$777$		−	26.7842i		−	0.960879i
$778$	−36.4917	+	1.63500i	−1.30829	+	0.0586175i
$779$			36.6322i			1.31248i
$780$	6.47587	−	15.1951i	0.231873	−	0.544072i
$781$		−	0.00111779i		−	3.99976e-5i
$782$	0.911294	+	20.3393i	0.0325878	+	0.727330i
$783$		−	4.37007i		−	0.156173i
$784$	−1.18714	−	6.55737i	−0.0423978	−	0.234192i
$785$	2.20795	−	2.20795i	0.0788051	−	0.0788051i
$786$	7.34728	−	0.329193i	0.262069	−	0.0117419i
$787$	−26.5637	−	26.5637i	−0.946895	−	0.946895i	0.0517643	−	0.998659i	$-0.483516\pi$
$787$	−26.5637	−	26.5637i	−0.946895	−	0.946895i	−0.998659	+	0.0517643i	$0.983516\pi$
$788$	4.90858	+	4.09973i	0.174861	+	0.146047i
$789$		−	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	$-0.441679\pi$
$797$	10.2872			0.364393			0.182196	+	0.983262i	$0.441679\pi$
$798$	0.607640	+	13.5620i	0.0215102	+	0.480089i
$799$	38.1624	+	38.1624i	1.35009	+	1.35009i
$800$	0.309813	+	1.36067i	0.0109535	+	0.0481071i
$801$	1.90441	+	1.90441i	0.0672890	+	0.0672890i
$802$	−36.9416	−	33.7732i	−1.30445	−	1.19257i
$803$		−	0.0564947i		−	0.00199365i
$804$	−14.7964	+	17.7157i	−0.521830	+	0.624784i
$805$	−13.5165			−0.476395
$806$	−6.49722	+	13.5315i	−0.228855	+	0.476627i
$807$			6.68357i			0.235273i
$808$	−29.6224	+	4.00311i	−1.04211	+	0.140829i
$809$	−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	−0.897985	−	0.440026i	$-0.854969\pi$
$811$	−13.0418	+	13.0418i	−0.457958	+	0.457958i	0.440026	+	0.897985i	$0.354969\pi$
$812$	19.7475	+	16.4934i	0.693000	+	0.578805i
$813$	5.65140	−	5.65140i	0.198203	−	0.198203i
$814$	1.22467	−	0.0548711i	0.0429248	−	0.00192323i
$815$		−	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	$-0.325056\pi$
$821$	−9.46652	−	9.46652i	−0.330384	−	0.330384i	−0.852732	+	0.522348i	$0.825056\pi$
$822$	22.1837	+	20.2811i	0.773744	+	0.707383i
$823$	−9.44005			−0.329059			−0.164530	−	0.986372i	$-0.552611\pi$
$823$	−9.44005			−0.329059			−0.164530	+	0.986372i	$0.552611\pi$
$824$	9.87278	−	1.33419i	0.343935	−	0.0464786i
$825$	−0.0166192	+	0.0166192i	−0.000578606	+	0.000578606i
$826$	−23.3122	+	1.04450i	−0.811134	+	0.0363426i
$827$	15.1241	+	15.1241i	0.525916	+	0.525916i	0.919352	−	0.393436i	$-0.128714\pi$
$827$	15.1241	+	15.1241i	0.525916	+	0.525916i	−0.393436	+	0.919352i	$0.628714\pi$
$828$	3.99300	−	0.358530i	0.138766	−	0.0124598i
$829$	30.8994			1.07318			0.536590	−	0.843843i	$-0.319712\pi$
$829$	30.8994			1.07318			0.536590	+	0.843843i	$0.319712\pi$
$830$	15.3402	−	0.687315i	0.532468	−	0.0238570i
$831$	24.3573			0.844946
$832$	−15.3615	−	24.4136i	−0.532563	−	0.846390i
$833$	11.9651			0.414564
$834$	−8.65254	+	0.387674i	−0.299613	+	0.0134241i
$835$	10.2202			0.353684
$836$	−0.618858	+	0.0555670i	−0.0214036	+	0.00192182i
$837$	2.08158	+	2.08158i	0.0719501	+	0.0719501i
$838$	22.1198	−	0.991071i	0.764116	−	0.0342360i
$839$	−39.8024	+	39.8024i	−1.37413	+	1.37413i	−0.519909	+	0.854222i	$0.674034\pi$
$839$	−39.8024	+	39.8024i	−1.37413	+	1.37413i	−0.854222	+	0.519909i	$0.825966\pi$
$840$	18.9002	−	2.55414i	0.652120	−	0.0881261i
$841$	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
$850$	−2.50309	+	0.112150i	−0.0858553	+	0.00384672i
$851$	−12.8964	+	12.8964i	−0.442083	+	0.442083i
$852$	−0.0180096	−	0.0150419i	−0.000616997	−	0.000515326i
$853$	−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	$0.294996\pi$
$854$	−5.96213	−	5.45078i	−0.204020	−	0.186522i
$855$	−7.46925			−0.255443
$856$	33.1628	−	4.48155i	1.13348	−	0.153176i
$857$			27.8183i			0.950256i	0.879917	+	0.475128i	$0.157598\pi$
$857$			27.8183i			0.950256i	−0.879917	+	0.475128i	$0.842402\pi$
$858$	0.210275	−	0.437933i	0.00717869	−	0.0149508i
$859$	−10.0327			−0.342311			−0.171155	−	0.985244i	$-0.554750\pi$
$859$	−10.0327			−0.342311			−0.171155	+	0.985244i	$0.554750\pi$
$860$	30.7367	−	36.8009i	1.04811	−	1.25490i
$861$		−	33.0703i		−	1.12703i
$862$	−25.0392	−	22.8916i	−0.852838	−	0.779693i
$863$	−32.0055	−	32.0055i	−1.08948	−	1.08948i	−0.995582	−	0.0938995i	$-0.970067\pi$
$863$	−32.0055	−	32.0055i	−1.08948	−	1.08948i	−0.0938995	−	0.995582i	$-0.529933\pi$
$864$	−5.51569	+	1.25587i	−0.187647	+	0.0427255i
$865$	−4.08529	−	4.08529i	−0.138904	−	0.138904i
$866$	1.37143	+	30.6092i	0.0466032	+	1.04014i
$867$	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
$876$	−0.910231	−	0.760240i	−0.0307538	−	0.0256861i
$877$	−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	$0.915576\pi$
$878$	−38.1389	+	1.70880i	−1.28713	+	0.0576692i
$879$	−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	$-0.925454\pi$
$881$		−	13.7757i		−	0.464116i	0.972702	−	0.232058i	$-0.0745459\pi$
$882$	−0.105457	−	2.35370i	−0.00355092	−	0.0792533i
$883$			38.8765i			1.30830i	0.756366	+	0.654149i	$0.226973\pi$
$883$			38.8765i			1.30830i	−0.756366	+	0.654149i	$0.773027\pi$
$884$	48.0466	−	19.3314i	1.61598	−	0.650184i
$885$		−	12.8392i		−	0.431584i
$886$	−5.21874	+	0.233824i	−0.175327	+	0.00785547i
$887$			51.7991i			1.73924i	0.493718	+	0.869622i	$0.335637\pi$
$887$			51.7991i			1.73924i	−0.493718	+	0.869622i	$0.664363\pi$
$888$	15.5961	−	20.4701i	0.523372	−	0.686930i
$889$	−38.6084	+	38.6084i	−1.29488	+	1.29488i
$890$	−0.390500	−	8.71560i	−0.0130896	−	0.292148i
$891$	−0.0673682	−	0.0673682i	−0.00225692	−	0.00225692i
$892$	14.4547	+	12.0728i	0.483978	+	0.404227i
$893$		−	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
$902$	1.51209	−	0.0677488i	0.0503472	−	0.00225579i
$903$	−21.7869	−	21.7869i	−0.725023	−	0.725023i
$904$	35.6118	−	4.81250i	1.18443	−	0.160061i
$905$	−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	$-0.652048\pi$
$907$		−	53.4908i		−	1.77613i	0.459714	−	0.888067i	$-0.347952\pi$
$908$	−14.2655	+	17.0800i	−0.473416	+	0.566819i
$909$	−10.5683			−0.350528
$910$	11.3933	+	32.4400i	0.377683	+	1.07538i
$911$		−	8.34775i		−	0.276573i	−0.990392	−	0.138287i	$-0.955840\pi$
$911$		−	8.34775i		−	0.276573i	0.990392	−	0.138287i	$-0.0441595\pi$
$912$	−7.43258	+	10.7187i	−0.246117	+	0.354930i
$913$	0.451627			0.0149467
$914$	−13.4824	+	14.7473i	−0.445959	+	0.487796i
$915$	3.14283	−	3.14283i	0.103899	−	0.103899i
$916$	−6.60962	+	7.91366i	−0.218388	+	0.261475i
$917$	−10.8253	+	10.8253i	−0.357484	+	0.357484i
$918$	−0.454617	−	10.1466i	−0.0150046	−	0.334889i
$919$			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
$928$	5.48823	+	24.1039i	0.180160	+	0.791250i
$929$	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	$0.163236\pi$
$930$	−0.426830	−	9.52646i	−0.0139963	−	0.312385i
$931$	−3.84142	−	3.84142i	−0.125897	−	0.125897i
$932$	0.592997	+	6.60430i	0.0194243	+	0.216331i
$933$	19.3516			0.633543
$934$	−0.867563	−	19.3632i	−0.0283875	−	0.633584i
$935$	−1.56731			−0.0512566
$936$	−4.22624	−	9.28110i	−0.138139	−	0.303362i
$937$	−5.73855			−0.187470			−0.0937352	−	0.995597i	$-0.529881\pi$
$937$	−5.73855			−0.187470			−0.0937352	+	0.995597i	$0.529881\pi$
$938$	−2.15058	−	47.9990i	−0.0702189	−	1.56722i
$939$	−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	$-0.245471\pi$
$941$	0.617212	+	0.617212i	0.0201205	+	0.0201205i	−0.696975	+	0.717095i	$0.745471\pi$
$942$	−0.0862908	−	1.92593i	−0.00281151	−	0.0627503i
$943$	−15.9231	+	15.9231i	−0.518526	+	0.518526i
$944$	−18.4247	−	12.7761i	−0.599673	−	0.415828i
$945$	6.74298			0.219349
$946$	0.951544	−	1.04081i	0.0309374	−	0.0338397i
$947$	−2.57671	−	2.57671i	−0.0837319	−	0.0837319i	0.664000	−	0.747732i	$-0.268857\pi$
$947$	−2.57671	−	2.57671i	−0.0837319	−	0.0837319i	−0.747732	+	0.664000i	$0.768857\pi$
$948$	−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	$0.253746\pi$
$953$			44.1686i			1.43076i	−0.698736	+	0.715380i	$0.746254\pi$
$954$	0.0893277	+	1.99371i	0.00289209	+	0.0645488i
$955$	−36.3300	+	36.3300i	−1.17561	+	1.17561i
$956$	−16.2572	−	13.5783i	−0.525796	−	0.439153i
$957$	−0.294404	+	0.294404i	−0.00951672	+	0.00951672i
$958$	−9.68653	+	10.5952i	−0.312958	+	0.342317i
$959$	−62.5667			−2.02038
$960$	15.9319	+	9.05336i	0.514199	+	0.292196i
$961$		−	22.3340i		−	0.720452i
$962$	41.8223	+	20.0812i	1.34840	+	0.647442i
$963$	11.8314			0.381261
$964$	−19.5974	−	16.3681i	−0.631190	−	0.527180i
$965$			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	$-0.0718438\pi$
$967$	23.3487	+	23.3487i	0.750844	+	0.750844i	−0.223792	+	0.974637i	$0.571844\pi$
$968$	−4.16319	−	30.8070i	−0.133810	−	0.990174i
$969$	−16.5600	−	16.5600i	−0.531985	−	0.531985i
$970$	−40.1026	+	1.79679i	−1.28762	+	0.0576913i
$971$	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	−0.943363	−	0.331761i	$-0.892357\pi$
$977$	−19.1168	+	19.1168i	−0.611602	+	0.611602i	0.331761	+	0.943363i	$0.392357\pi$
$978$	−20.2614	−	18.5236i	−0.647888	−	0.592321i
$979$		−	0.256593i		−	0.00820076i
$980$	−4.89247	+	5.85773i	−0.156284	+	0.187118i
$981$	12.9904	+	12.9904i	0.414751	+	0.414751i
$982$	−0.172198	−	3.84331i	−0.00549507	−	0.122645i
$983$	20.0123	−	20.0123i	0.638293	−	0.638293i	−0.311841	−	0.950134i	$-0.600946\pi$
$983$	20.0123	−	20.0123i	0.638293	−	0.638293i	0.950134	+	0.311841i	$0.100946\pi$
$984$	19.2564	−	25.2742i	0.613872	−	0.805712i
$985$		−	7.32462i		−	0.233382i
$986$	−44.3414	+	1.98670i	−1.41212	+	0.0632696i
$987$			22.1216i			0.704139i
$988$	−21.6319	−	9.21912i	−0.688203	−	0.293299i
$989$			20.9805i			0.667140i
$990$	0.0138139	+	0.308313i	0.000439034	+	0.00979885i
$991$		−	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
$994$	0.0487953	−	0.00218626i	0.00154769	−	6.93438e-5i
$995$	42.8201	+	42.8201i	1.35749	+	1.35749i
$996$	6.07747	−	7.27652i	0.192572	−	0.230565i
$997$			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.187.12	yes	24
3.2	odd	2		936.2.w.j.811.1		24
4.3	odd	2		1248.2.bb.f.655.4		24
8.3	odd	2	inner	312.2.t.e.187.7	✓	24
8.5	even	2		1248.2.bb.f.655.9		24
13.8	odd	4	inner	312.2.t.e.307.7	yes	24
24.11	even	2		936.2.w.j.811.6		24
39.8	even	4		936.2.w.j.307.6		24
52.47	even	4		1248.2.bb.f.463.9		24
104.21	odd	4		1248.2.bb.f.463.4		24
104.99	even	4	inner	312.2.t.e.307.12	yes	24
312.203	odd	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	8.3	odd	2	inner
312.2.t.e.187.12	yes	24	1.1	even	1	trivial
312.2.t.e.307.7	yes	24	13.8	odd	4	inner
312.2.t.e.307.12	yes	24	104.99	even	4	inner
936.2.w.j.307.1		24	312.203	odd	4
936.2.w.j.307.6		24	39.8	even	4
936.2.w.j.811.1		24	3.2	odd	2
936.2.w.j.811.6		24	24.11	even	2
1248.2.bb.f.463.4		24	104.21	odd	4
1248.2.bb.f.463.9		24	52.47	even	4
1248.2.bb.f.655.4		24	4.3	odd	2
1248.2.bb.f.655.9		24	8.5	even	2

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+(1.41280 - 0.0632999i) q^{2} -1.00000 q^{3} +(1.99199 - 0.178860i) q^{4} +(-1.61967 - 1.61967i) q^{5} +(-1.41280 + 0.0632999i) q^{6} +(2.08158 - 2.08158i) q^{7} +(2.80295 - 0.378785i) 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} +(1.41280 - 0.0632999i) q^{18} +(2.30579 - 2.30579i) q^{19} +(-3.51606 - 2.93668i) q^{20} +(-2.08158 + 2.08158i) q^{21} +(-0.0994420 - 0.0909132i) q^{22} +2.00453 q^{23} +(-2.80295 + 0.378785i) q^{24} +0.246692i q^{25} +(-1.68965 - 4.81093i) q^{26} -1.00000 q^{27} +(3.77418 - 4.51880i) q^{28} +4.37007i q^{29} +(2.39080 + 2.18574i) q^{30} +(-2.08158 - 2.08158i) q^{31} +(5.51569 - 1.25587i) q^{32} +(0.0673682 + 0.0673682i) q^{33} +(0.454617 + 10.1466i) 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} +(-0.146246 - 0.122147i) q^{44} +(-1.61967 - 1.61967i) q^{45} +(2.83200 - 0.126887i) q^{46} +(5.31365 - 5.31365i) q^{47} +(-3.93602 + 0.712572i) q^{48} -1.66599i q^{49} +(0.0156156 + 0.348525i) q^{50} -7.18195i q^{51} +(-2.69166 - 6.68991i) q^{52} +1.41118i q^{53} +(-1.41280 + 0.0632999i) q^{54} +0.218229i q^{55} +(5.04610 - 6.62305i) q^{56} +(-2.30579 + 2.30579i) q^{57} +(0.276625 + 6.17401i) q^{58} +(-3.96350 - 3.96350i) q^{59} +(3.51606 + 2.93668i) 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} +(-9.52646 + 0.426830i) q^{70} +(0.00829610 + 0.00829610i) q^{71} +(2.80295 - 0.378785i) q^{72} +(0.419298 + 0.419298i) q^{73} +(-8.68214 + 9.49664i) q^{74} -0.246692i q^{75} +(4.18068 - 5.00551i) q^{76} -0.280465 q^{77} +(1.68965 + 4.81093i) q^{78} +8.46664i q^{79} +(-7.52920 - 5.22093i) q^{80} +1.00000 q^{81} +(-10.7198 + 11.7254i) q^{82} +(-3.35193 + 3.35193i) q^{83} +(-3.77418 + 4.51880i) q^{84} +(11.6324 - 11.6324i) q^{85} +(0.662529 + 14.7870i) 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} +(-5.51569 + 1.25587i) q^{96} +(8.76265 - 8.76265i) q^{97} +(-0.105457 - 2.35370i) 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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