LMFDB - Embedded newform 336.2.s.d.155.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.16
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.720078 - 1.21716i) q^{2} +(-1.68530 + 0.399703i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(-2.09830 + 2.09830i) q^{5} +(-0.727043 + 2.33910i) q^{6} +1.00000 q^{7} +(-2.82699 - 0.0901270i) q^{8} +(2.68048 - 1.34724i) q^{9} +O(q^{10})$	\(q+(0.720078 - 1.21716i) q^{2} +(-1.68530 + 0.399703i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(-2.09830 + 2.09830i) q^{5} +(-0.727043 + 2.33910i) q^{6} +1.00000 q^{7} +(-2.82699 - 0.0901270i) q^{8} +(2.68048 - 1.34724i) q^{9} +(1.04303 + 4.06491i) q^{10} +(3.61163 + 3.61163i) q^{11} +(2.32355 + 2.56927i) q^{12} +(-2.99334 + 2.99334i) q^{13} +(0.720078 - 1.21716i) q^{14} +(2.69756 - 4.37495i) q^{15} +(-2.14535 + 3.37601i) q^{16} +2.25059i q^{17} +(0.290340 - 4.23269i) q^{18} +(2.89997 + 2.89997i) q^{19} +(5.69872 + 1.65750i) q^{20} +(-1.68530 + 0.399703i) q^{21} +(6.99660 - 1.79529i) q^{22} +6.47555i q^{23} +(4.80035 - 0.978065i) q^{24} -3.80569i q^{25} +(1.48795 + 5.79882i) q^{26} +(-3.97891 + 3.34190i) q^{27} +(-0.962977 - 1.75291i) q^{28} +(-7.29274 - 7.29274i) q^{29} +(-3.38258 - 6.43368i) q^{30} -6.92839i q^{31} +(2.56434 + 5.04224i) q^{32} +(-7.53026 - 4.64311i) q^{33} +(2.73933 + 1.62060i) q^{34} +(-2.09830 + 2.09830i) q^{35} +(-4.94282 - 3.40126i) q^{36} +(2.12931 + 2.12931i) q^{37} +(5.61794 - 1.44154i) q^{38} +(3.84823 - 6.24112i) q^{39} +(6.12098 - 5.74275i) q^{40} -7.93197 q^{41} +(-0.727043 + 2.33910i) q^{42} +(-0.598329 + 0.598329i) q^{43} +(2.85293 - 9.80876i) q^{44} +(-2.79753 + 8.45134i) q^{45} +(7.88180 + 4.66290i) q^{46} +2.35501 q^{47} +(2.26616 - 6.54710i) q^{48} +1.00000 q^{49} +(-4.63215 - 2.74039i) q^{50} +(-0.899566 - 3.79292i) q^{51} +(8.12955 + 2.36452i) q^{52} +(-2.98611 + 2.98611i) q^{53} +(1.20251 + 7.24941i) q^{54} -15.1565 q^{55} +(-2.82699 - 0.0901270i) q^{56} +(-6.04644 - 3.72819i) q^{57} +(-14.1278 + 3.62512i) q^{58} +(1.85127 + 1.85127i) q^{59} +(-10.2666 - 0.515596i) q^{60} +(3.40305 - 3.40305i) q^{61} +(-8.43299 - 4.98898i) q^{62} +(2.68048 - 1.34724i) q^{63} +(7.98375 + 0.509577i) q^{64} -12.5618i q^{65} +(-11.0738 + 5.82217i) q^{66} +(7.71856 + 7.71856i) q^{67} +(3.94507 - 2.16726i) q^{68} +(-2.58829 - 10.9132i) q^{69} +(1.04303 + 4.06491i) q^{70} +8.99213i q^{71} +(-7.69910 + 3.56705i) q^{72} +9.70182i q^{73} +(4.12498 - 1.05845i) q^{74} +(1.52115 + 6.41374i) q^{75} +(2.29077 - 7.87597i) q^{76} +(3.61163 + 3.61163i) q^{77} +(-4.82544 - 9.17801i) q^{78} -5.37445i q^{79} +(-2.58229 - 11.5855i) q^{80} +(5.36990 - 7.22248i) q^{81} +(-5.71164 + 9.65451i) q^{82} +(4.46497 - 4.46497i) q^{83} +(2.32355 + 2.56927i) q^{84} +(-4.72240 - 4.72240i) q^{85} +(0.297421 + 1.15911i) q^{86} +(15.2054 + 9.37553i) q^{87} +(-9.88454 - 10.5356i) q^{88} +4.75435 q^{89} +(8.27223 + 9.49067i) q^{90} +(-2.99334 + 2.99334i) q^{91} +(11.3510 - 6.23580i) q^{92} +(2.76930 + 11.6764i) q^{93} +(1.69579 - 2.86644i) q^{94} -12.1700 q^{95} +(-6.33708 - 7.47271i) q^{96} +3.98867 q^{97} +(0.720078 - 1.21716i) q^{98} +(14.5466 + 4.81516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) $ 48 * q + 6 * q^6 + 48 * q^7	$ 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) $ 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.720078	−	1.21716i	0.509172	−	0.860665i
$2$	0.720078	−	1.21716i	0.509172	−	0.860665i
$3$	−1.68530	+	0.399703i	−0.973009	+	0.230768i
$3$	−1.68530	+	0.399703i	−0.973009	+	0.230768i
$4$	−0.962977	−	1.75291i	−0.481488	−	0.876453i
$5$	−2.09830	+	2.09830i	−0.938387	+	0.938387i	−0.998209	−	0.0598225i	$-0.980947\pi$
$5$	−2.09830	+	2.09830i	−0.938387	+	0.938387i	0.0598225	+	0.998209i	$0.480947\pi$
$6$	−0.727043	+	2.33910i	−0.296814	+	0.954935i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.82699	−	0.0901270i	−0.999492	−	0.0318647i
$9$	2.68048	−	1.34724i	0.893492	−	0.449079i
$10$	1.04303	+	4.06491i	0.329837	+	1.28544i
$11$	3.61163	+	3.61163i	1.08895	+	1.08895i	0.995637	+	0.0933108i	$0.0297450\pi$
$11$	3.61163	+	3.61163i	1.08895	+	1.08895i	0.0933108	+	0.995637i	$0.470255\pi$
$12$	2.32355	+	2.56927i	0.670750	+	0.741684i
$13$	−2.99334	+	2.99334i	−0.830202	+	0.830202i	−0.987544	−	0.157342i	$-0.949708\pi$
$13$	−2.99334	+	2.99334i	−0.830202	+	0.830202i	0.157342	+	0.987544i	$0.449708\pi$
$14$	0.720078	−	1.21716i	0.192449	−	0.325301i
$15$	2.69756	−	4.37495i	0.696508	−	1.12961i
$16$	−2.14535	+	3.37601i	−0.536338	+	0.844003i
$17$			2.25059i			0.545848i	0.962036	+	0.272924i	$0.0879907\pi$
$17$			2.25059i			0.545848i	−0.962036	+	0.272924i	$0.912009\pi$
$18$	0.290340	−	4.23269i	0.0684338	−	0.997656i
$19$	2.89997	+	2.89997i	0.665298	+	0.665298i	0.956624	−	0.291326i	$-0.0940963\pi$
$19$	2.89997	+	2.89997i	0.665298	+	0.665298i	−0.291326	+	0.956624i	$0.594096\pi$
$20$	5.69872	+	1.65750i	1.27427	+	0.370629i
$21$	−1.68530	+	0.399703i	−0.367763	+	0.0872223i
$22$	6.99660	−	1.79529i	1.49168	−	0.382758i
$23$			6.47555i			1.35025i	0.737706	+	0.675123i	$0.235909\pi$
$23$			6.47555i			1.35025i	−0.737706	+	0.675123i	$0.764091\pi$
$24$	4.80035	−	0.978065i	0.979868	−	0.199647i
$25$		−	3.80569i		−	0.761138i
$26$	1.48795	+	5.79882i	0.291810	+	1.13724i
$27$	−3.97891	+	3.34190i	−0.765742	+	0.643148i
$28$	−0.962977	−	1.75291i	−0.181985	−	0.331268i
$29$	−7.29274	−	7.29274i	−1.35423	−	1.35423i	−0.880871	−	0.473357i	$-0.843042\pi$
$29$	−7.29274	−	7.29274i	−1.35423	−	1.35423i	−0.473357	−	0.880871i	$-0.656958\pi$
$30$	−3.38258	−	6.43368i	−0.617572	−	1.17462i
$31$		−	6.92839i		−	1.24438i	−0.782868	−	0.622188i	$-0.786244\pi$
$31$		−	6.92839i		−	1.24438i	0.782868	−	0.622188i	$-0.213756\pi$
$32$	2.56434	+	5.04224i	0.453316	+	0.891350i
$33$	−7.53026	−	4.64311i	−1.31085	−	0.808261i
$34$	2.73933	+	1.62060i	0.469792	+	0.277930i
$35$	−2.09830	+	2.09830i	−0.354677	+	0.354677i
$36$	−4.94282	−	3.40126i	−0.823803	−	0.566877i
$37$	2.12931	+	2.12931i	0.350056	+	0.350056i	0.860130	−	0.510074i	$-0.170382\pi$
$37$	2.12931	+	2.12931i	0.350056	+	0.350056i	−0.510074	+	0.860130i	$0.670382\pi$
$38$	5.61794	−	1.44154i	0.911350	−	0.233848i
$39$	3.84823	−	6.24112i	0.616209	−	0.999379i
$40$	6.12098	−	5.74275i	0.967811	−	0.908009i
$41$	−7.93197			−1.23877			−0.619383	−	0.785089i	$-0.712617\pi$
$41$	−7.93197			−1.23877			−0.619383	+	0.785089i	$0.712617\pi$
$42$	−0.727043	+	2.33910i	−0.112185	+	0.360932i
$43$	−0.598329	+	0.598329i	−0.0912444	+	0.0912444i	−0.751256	−	0.660011i	$-0.770551\pi$
$43$	−0.598329	+	0.598329i	−0.0912444	+	0.0912444i	0.660011	+	0.751256i	$0.270551\pi$
$44$	2.85293	−	9.80876i	0.430095	−	1.47873i
$45$	−2.79753	+	8.45134i	−0.417031	+	1.25985i
$46$	7.88180	+	4.66290i	1.16211	+	0.687507i
$47$	2.35501			0.343514			0.171757	−	0.985139i	$-0.445056\pi$
$47$	2.35501			0.343514			0.171757	+	0.985139i	$0.445056\pi$
$48$	2.26616	−	6.54710i	0.327092	−	0.944992i
$49$	1.00000			0.142857
$50$	−4.63215	−	2.74039i	−0.655085	−	0.387550i
$51$	−0.899566	−	3.79292i	−0.125964	−	0.531115i
$52$	8.12955	+	2.36452i	1.12737	+	0.327900i
$53$	−2.98611	+	2.98611i	−0.410174	+	0.410174i	−0.881799	−	0.471625i	$-0.843668\pi$
$53$	−2.98611	+	2.98611i	−0.410174	+	0.410174i	0.471625	+	0.881799i	$0.343668\pi$
$54$	1.20251	+	7.24941i	0.163641	+	0.986520i
$55$	−15.1565			−2.04371
$56$	−2.82699	−	0.0901270i	−0.377773	−	0.0120437i
$57$	−6.04644	−	3.72819i	−0.800871	−	0.493811i
$58$	−14.1278	+	3.62512i	−1.85507	+	0.476002i
$59$	1.85127	+	1.85127i	0.241015	+	0.241015i	0.817270	−	0.576255i	$-0.195486\pi$
$59$	1.85127	+	1.85127i	0.241015	+	0.241015i	−0.576255	+	0.817270i	$0.695486\pi$
$60$	−10.2666	−	0.515596i	−1.32541	−	0.0665632i
$61$	3.40305	−	3.40305i	0.435716	−	0.435716i	−0.454851	−	0.890567i	$-0.650308\pi$
$61$	3.40305	−	3.40305i	0.435716	−	0.435716i	0.890567	+	0.454851i	$0.150308\pi$
$62$	−8.43299	−	4.98898i	−1.07099	−	0.633601i
$63$	2.68048	−	1.34724i	0.337708	−	0.169736i
$64$	7.98375	+	0.509577i	0.997969	+	0.0636971i
$65$		−	12.5618i		−	1.55810i
$66$	−11.0738	+	5.82217i	−1.36309	+	0.716660i
$67$	7.71856	+	7.71856i	0.942972	+	0.942972i	0.998459	−	0.0554878i	$-0.0176714\pi$
$67$	7.71856	+	7.71856i	0.942972	+	0.942972i	−0.0554878	+	0.998459i	$0.517671\pi$
$68$	3.94507	−	2.16726i	0.478410	−	0.262819i
$69$	−2.58829	−	10.9132i	−0.311594	−	1.31380i
$70$	1.04303	+	4.06491i	0.124666	+	0.485849i
$71$			8.99213i			1.06717i	0.845747	+	0.533585i	$0.179155\pi$
$71$			8.99213i			1.06717i	−0.845747	+	0.533585i	$0.820845\pi$
$72$	−7.69910	+	3.56705i	−0.907348	+	0.420381i
$73$			9.70182i			1.13551i	0.823197	+	0.567756i	$0.192188\pi$
$73$			9.70182i			1.13551i	−0.823197	+	0.567756i	$0.807812\pi$
$74$	4.12498	−	1.05845i	0.479519	−	0.123042i
$75$	1.52115	+	6.41374i	0.175647	+	0.740594i
$76$	2.29077	−	7.87597i	0.262769	−	0.903436i
$77$	3.61163	+	3.61163i	0.411584	+	0.411584i
$78$	−4.82544	−	9.17801i	−0.546374	−	1.03921i
$79$		−	5.37445i		−	0.604673i	−0.953201	−	0.302336i	$-0.902233\pi$
$79$		−	5.37445i		−	0.604673i	0.953201	−	0.302336i	$-0.0977666\pi$
$80$	−2.58229	−	11.5855i	−0.288709	−	1.29529i
$81$	5.36990	−	7.22248i	0.596655	−	0.802498i
$82$	−5.71164	+	9.65451i	−0.630745	+	1.06616i
$83$	4.46497	−	4.46497i	0.490094	−	0.490094i	−0.418242	−	0.908336i	$-0.637354\pi$
$83$	4.46497	−	4.46497i	0.490094	−	0.490094i	0.908336	+	0.418242i	$0.137354\pi$
$84$	2.32355	+	2.56927i	0.253520	+	0.280330i
$85$	−4.72240	−	4.72240i	−0.512216	−	0.512216i
$86$	0.297421	+	1.15911i	0.0320718	+	0.124990i
$87$	15.2054	+	9.37553i	1.63019	+	1.00516i
$88$	−9.88454	−	10.5356i	−1.05370	−	1.12309i
$89$	4.75435			0.503960			0.251980	−	0.967732i	$-0.418918\pi$
$89$	4.75435			0.503960			0.251980	+	0.967732i	$0.418918\pi$
$90$	8.27223	+	9.49067i	0.871969	+	1.00040i
$91$	−2.99334	+	2.99334i	−0.313787	+	0.313787i
$92$	11.3510	−	6.23580i	1.18343	−	0.650127i
$93$	2.76930	+	11.6764i	0.287163	+	1.21079i
$94$	1.69579	−	2.86644i	0.174908	−	0.295650i
$95$	−12.1700			−1.24861
$96$	−6.33708	−	7.47271i	−0.646776	−	0.762680i
$97$	3.98867			0.404988			0.202494	−	0.979284i	$-0.435095\pi$
$97$	3.98867			0.404988			0.202494	+	0.979284i	$0.435095\pi$
$98$	0.720078	−	1.21716i	0.0727388	−	0.122952i
$99$	14.5466	+	4.81516i	1.46199	+	0.483942i
$100$	−6.67102	+	3.66479i	−0.667102	+	0.366479i
$101$	3.58534	−	3.58534i	0.356754	−	0.356754i	−0.505861	−	0.862615i	$-0.668825\pi$
$101$	3.58534	−	3.58534i	0.356754	−	0.356754i	0.862615	+	0.505861i	$0.168825\pi$
$102$	−5.26436	−	1.63627i	−0.521249	−	0.162015i
$103$	8.12614			0.800692			0.400346	−	0.916364i	$-0.368890\pi$
$103$	8.12614			0.800692			0.400346	+	0.916364i	$0.368890\pi$
$104$	8.73192	−	8.19236i	0.856235	−	0.803327i
$105$	2.69756	−	4.37495i	0.263255	−	0.426952i
$106$	1.48436	+	5.78482i	0.144173	+	0.561872i
$107$	−13.2844	−	13.2844i	−1.28426	−	1.28426i	−0.938222	−	0.346034i	$-0.887528\pi$
$107$	−13.2844	−	13.2844i	−1.28426	−	1.28426i	−0.346034	−	0.938222i	$-0.612472\pi$
$108$	9.68962	+	3.75649i	0.932384	+	0.361468i
$109$	−7.91670	+	7.91670i	−0.758282	+	0.758282i	−0.976010	−	0.217727i	$-0.930136\pi$
$109$	−7.91670	+	7.91670i	−0.758282	+	0.758282i	0.217727	+	0.976010i	$0.430136\pi$
$110$	−10.9139	+	18.4480i	−1.04060	+	1.75895i
$111$	−4.43961	−	2.73743i	−0.421389	−	0.259825i
$112$	−2.14535	+	3.37601i	−0.202717	+	0.319003i
$113$		−	3.91465i		−	0.368259i	−0.982902	−	0.184130i	$-0.941053\pi$
$113$		−	3.91465i		−	0.368259i	0.982902	−	0.184130i	$-0.0589466\pi$
$114$	−8.89173	+	4.67493i	−0.832787	+	0.437847i
$115$	−13.5876	−	13.5876i	−1.26705	−	1.26705i
$116$	−5.76074	+	19.8062i	−0.534871	+	1.83896i
$117$	−3.99083	+	12.0563i	−0.368952	+	1.11461i
$118$	3.58636	−	0.920242i	0.330151	−	0.0847152i
$119$			2.25059i			0.206311i
$120$	−8.02029	+	12.1248i	−0.732149	+	1.10684i
$121$			15.0878i			1.37161i
$122$	−1.69161	−	6.59253i	−0.153151	−	0.596860i
$123$	13.3678	−	3.17043i	1.20533	−	0.285868i
$124$	−12.1448	+	6.67188i	−1.09064	+	0.599152i
$125$	−2.50601	−	2.50601i	−0.224144	−	0.224144i
$126$	0.290340	−	4.23269i	0.0258655	−	0.377078i
$127$		−	4.24068i		−	0.376299i	−0.982140	−	0.188150i	$-0.939751\pi$
$127$		−	4.24068i		−	0.376299i	0.982140	−	0.188150i	$-0.0602490\pi$
$128$	6.36916	−	9.35060i	0.562960	−	0.826484i
$129$	0.769211	−	1.24752i	0.0677252	−	0.109838i
$130$	−15.2898	−	9.04548i	−1.34100	−	0.793341i
$131$	8.30320	−	8.30320i	0.725454	−	0.725454i	−0.244256	−	0.969711i	$-0.578544\pi$
$131$	8.30320	−	8.30320i	0.725454	−	0.725454i	0.969711	+	0.244256i	$0.0785439\pi$
$132$	−0.887455	+	17.6710i	−0.0772430	+	1.53807i
$133$	2.89997	+	2.89997i	0.251459	+	0.251459i
$134$	14.9527	−	3.83679i	1.29172	−	0.331448i
$135$	1.33665	−	15.3612i	0.115040	−	1.32208i
$136$	0.202839	−	6.36239i	0.0173933	−	0.545570i
$137$	5.65752			0.483355			0.241677	−	0.970357i	$-0.422302\pi$
$137$	5.65752			0.483355			0.241677	+	0.970357i	$0.422302\pi$
$138$	−15.1470	−	4.70800i	−1.28940	−	0.400772i
$139$	3.31656	−	3.31656i	0.281307	−	0.281307i	−0.552323	−	0.833630i	$-0.686259\pi$
$139$	3.31656	−	3.31656i	0.281307	−	0.281307i	0.833630	+	0.552323i	$0.186259\pi$
$140$	5.69872	+	1.65750i	0.481630	+	0.140085i
$141$	−3.96890	+	0.941305i	−0.334242	+	0.0792722i
$142$	10.9449	+	6.47503i	0.918475	+	0.543372i
$143$	−21.6217			−1.80809
$144$	−1.20227	+	11.9396i	−0.100189	+	0.994968i
$145$	30.6047			2.54158
$146$	11.8087	+	6.98606i	0.977295	+	0.578171i
$147$	−1.68530	+	0.399703i	−0.139001	+	0.0329669i
$148$	1.68200	−	5.78294i	0.138259	−	0.475355i
$149$	−3.14768	+	3.14768i	−0.257868	+	0.257868i	−0.824187	−	0.566318i	$-0.808367\pi$
$149$	−3.14768	+	3.14768i	−0.257868	+	0.257868i	0.566318	+	0.824187i	$0.308367\pi$
$150$	8.90191	+	2.76690i	0.726838	+	0.225917i
$151$	−0.0917754			−0.00746858			−0.00373429	−	0.999993i	$-0.501189\pi$
$151$	−0.0917754			−0.00746858			−0.00373429	+	0.999993i	$0.501189\pi$
$152$	−7.93682	−	8.45955i	−0.643761	−	0.686160i
$153$	3.03208	+	6.03264i	0.245129	+	0.487710i
$154$	6.99660	−	1.79529i	0.563802	−	0.144669i
$155$	14.5378	+	14.5378i	1.16771	+	1.16771i
$156$	−14.6458	−	0.735527i	−1.17261	−	0.0588893i
$157$	6.75829	−	6.75829i	0.539370	−	0.539370i	−0.383974	−	0.923344i	$-0.625445\pi$
$157$	6.75829	−	6.75829i	0.539370	−	0.539370i	0.923344	+	0.383974i	$0.125445\pi$
$158$	−6.54159	−	3.87002i	−0.520421	−	0.307882i
$159$	3.83894	−	6.22606i	0.304448	−	0.493758i
$160$	−15.9609	−	5.19936i	−1.26182	−	0.411045i
$161$			6.47555i			0.510345i
$162$	−4.92420	−	11.7368i	−0.386882	−	0.922129i
$163$	7.90181	+	7.90181i	0.618917	+	0.618917i	0.945254	−	0.326336i	$-0.105814\pi$
$163$	7.90181	+	7.90181i	0.618917	+	0.618917i	−0.326336	+	0.945254i	$0.605814\pi$
$164$	7.63830	+	13.9040i	0.596451	+	1.08572i
$165$	25.5433	−	6.05811i	1.98855	−	0.471623i
$166$	−2.21947	−	8.64972i	−0.172265	−	0.671348i
$167$		−	5.79819i		−	0.448677i	−0.974511	−	0.224339i	$-0.927978\pi$
$167$		−	5.79819i		−	0.448677i	0.974511	−	0.224339i	$-0.0720222\pi$
$168$	4.80035	−	0.978065i	0.370355	−	0.0754593i
$169$		−	4.92013i		−	0.378472i
$170$	−9.14843	+	2.34744i	−0.701652	+	0.180040i
$171$	11.6802	+	3.86635i	0.893211	+	0.295667i
$172$	1.62499	+	0.472637i	0.123904	+	0.0360383i
$173$	7.92007	+	7.92007i	0.602152	+	0.602152i	0.940883	−	0.338731i	$-0.109998\pi$
$173$	7.92007	+	7.92007i	0.602152	+	0.602152i	−0.338731	+	0.940883i	$0.609998\pi$
$174$	22.3606	−	11.7563i	1.69515	−	0.891246i
$175$		−	3.80569i		−	0.287683i
$176$	−19.9411	+	4.44469i	−1.50312	+	0.335031i
$177$	−3.85991	−	2.37999i	−0.290128	−	0.178891i
$178$	3.42350	−	5.78682i	0.256602	−	0.433741i
$179$	3.91011	−	3.91011i	0.292256	−	0.292256i	−0.545715	−	0.837971i	$-0.683742\pi$
$179$	3.91011	−	3.91011i	0.292256	−	0.292256i	0.837971	+	0.545715i	$0.183742\pi$
$180$	17.5083	−	3.23464i	1.30499	−	0.241096i
$181$	−15.3477	−	15.3477i	−1.14078	−	1.14078i	−0.988307	−	0.152476i	$-0.951275\pi$
$181$	−15.3477	−	15.3477i	−1.14078	−	1.14078i	−0.152476	−	0.988307i	$-0.548725\pi$
$182$	1.48795	+	5.79882i	0.110294	+	0.429837i
$183$	−4.37495	+	7.09537i	−0.323406	+	0.524505i
$184$	0.583622	−	18.3063i	0.0430252	−	1.34956i
$185$	−8.93583			−0.656975
$186$	16.2062	+	5.03724i	1.18830	+	0.369348i
$187$	−8.12829	+	8.12829i	−0.594400	+	0.594400i
$188$	−2.26782	−	4.12811i	−0.165398	−	0.301074i
$189$	−3.97891	+	3.34190i	−0.289423	+	0.243087i
$190$	−8.76333	+	14.8129i	−0.635759	+	1.07464i
$191$	−6.06029			−0.438507			−0.219254	−	0.975668i	$-0.570362\pi$
$191$	−6.06029			−0.438507			−0.219254	+	0.975668i	$0.570362\pi$
$192$	−13.6587	+	2.33234i	−0.985732	+	0.168322i
$193$	22.6239			1.62851			0.814253	−	0.580510i	$-0.197147\pi$
$193$	22.6239			1.62851			0.814253	+	0.580510i	$0.197147\pi$
$194$	2.87215	−	4.85486i	0.206208	−	0.348559i
$195$	5.02099	+	21.1704i	0.359561	+	1.51605i
$196$	−0.962977	−	1.75291i	−0.0687840	−	0.125208i
$197$	−9.86233	+	9.86233i	−0.702662	+	0.702662i	−0.964981	−	0.262319i	$-0.915513\pi$
$197$	−9.86233	+	9.86233i	−0.702662	+	0.702662i	0.262319	+	0.964981i	$0.415513\pi$
$198$	16.3355	−	14.2383i	1.16092	−	1.01187i
$199$	−5.72177			−0.405605			−0.202803	−	0.979220i	$-0.565005\pi$
$199$	−5.72177			−0.405605			−0.202803	+	0.979220i	$0.565005\pi$
$200$	−0.342996	+	10.7587i	−0.0242535	+	0.760752i
$201$	−16.0932	−	9.92296i	−1.13513	−	0.699911i
$202$	−1.78222	−	6.94567i	−0.125397	−	0.488695i
$203$	−7.29274	−	7.29274i	−0.511850	−	0.511850i
$204$	−5.78236	+	5.22934i	−0.404846	+	0.366127i
$205$	16.6436	−	16.6436i	1.16244	−	1.16244i
$206$	5.85145	−	9.89085i	0.407690	−	0.689128i
$207$	8.72411	+	17.3575i	0.606367	+	1.20643i
$208$	−3.68378	−	16.5273i	−0.255424	−	1.14596i
$209$			20.9472i			1.44895i
$210$	−3.38258	−	6.43368i	−0.233420	−	0.443966i
$211$	0.226128	+	0.226128i	0.0155673	+	0.0155673i	0.714848	−	0.699280i	$-0.246496\pi$
$211$	0.226128	+	0.226128i	0.0155673	+	0.0155673i	−0.699280	+	0.714848i	$0.746496\pi$
$212$	8.10993	+	2.35882i	0.556992	+	0.162004i
$213$	−3.59418	−	15.1544i	−0.246269	−	1.03837i
$214$	−25.7352	+	6.60352i	−1.75922	+	0.451407i
$215$		−	2.51094i		−	0.171245i
$216$	11.5495	−	9.08890i	0.785847	−	0.618421i
$217$		−	6.92839i		−	0.470330i
$218$	3.93529	+	15.3366i	0.266531	+	1.03872i
$219$	−3.87784	−	16.3505i	−0.262040	−	1.10486i
$220$	14.5954	+	26.5680i	0.984021	+	1.79121i
$221$	−6.73677	−	6.73677i	−0.453164	−	0.453164i
$222$	−6.52877	+	3.43257i	−0.438182	+	0.230379i
$223$			11.7968i			0.789970i	0.918687	+	0.394985i	$0.129250\pi$
$223$			11.7968i			0.789970i	−0.918687	+	0.394985i	$0.870750\pi$
$224$	2.56434	+	5.04224i	0.171337	+	0.336899i
$225$	−5.12718	−	10.2011i	−0.341812	−	0.680071i
$226$	−4.76477	−	2.81885i	−0.316948	−	0.187507i
$227$	2.92552	−	2.92552i	0.194173	−	0.194173i	−0.603323	−	0.797497i	$-0.706157\pi$
$227$	2.92552	−	2.92552i	0.194173	−	0.194173i	0.797497	+	0.603323i	$0.206157\pi$
$228$	−0.712584	+	14.1890i	−0.0471920	+	0.939690i
$229$	6.48834	+	6.48834i	0.428762	+	0.428762i	0.888206	−	0.459445i	$-0.151952\pi$
$229$	6.48834	+	6.48834i	0.428762	+	0.428762i	−0.459445	+	0.888206i	$0.651952\pi$
$230$	−26.3225	+	6.75422i	−1.73565	+	0.445360i
$231$	−7.53026	−	4.64311i	−0.495455	−	0.305494i
$232$	19.9592	+	21.2738i	1.31039	+	1.39669i
$233$	16.5738			1.08579			0.542894	−	0.839801i	$-0.317328\pi$
$233$	16.5738			1.08579			0.542894	+	0.839801i	$0.317328\pi$
$234$	11.8008	+	13.5390i	0.771442	+	0.885070i
$235$	−4.94151	+	4.94151i	−0.322349	+	0.322349i
$236$	1.46237	−	5.02783i	0.0951923	−	0.327284i
$237$	2.14818	+	9.05756i	0.139539	+	0.588352i
$238$	2.73933	+	1.62060i	0.177565	+	0.105048i
$239$	21.1325			1.36695			0.683473	−	0.729976i	$-0.260469\pi$
$239$	21.1325			1.36695			0.683473	+	0.729976i	$0.260469\pi$
$240$	8.98268	+	18.4928i	0.579829	+	1.19371i
$241$	−21.1524			−1.36254			−0.681272	−	0.732030i	$-0.738573\pi$
$241$	−21.1524			−1.36254			−0.681272	+	0.732030i	$0.738573\pi$
$242$	18.3643	+	10.8644i	1.18050	+	0.698387i
$243$	−6.16305	+	14.3184i	−0.395360	+	0.918526i
$244$	−9.24228	−	2.68817i	−0.591676	−	0.172092i
$245$	−2.09830	+	2.09830i	−0.134055	+	0.134055i
$246$	5.76689	−	18.5537i	0.367683	−	1.18294i
$247$	−17.3612			−1.10466
$248$	−0.624435	+	19.5865i	−0.0396517	+	1.24374i
$249$	−5.74015	+	9.30947i	−0.363767	+	0.589963i
$250$	−4.85475	+	1.24570i	−0.307041	+	0.0787853i
$251$	14.5103	+	14.5103i	0.915885	+	0.915885i	0.996727	−	0.0808422i	$-0.0257610\pi$
$251$	14.5103	+	14.5103i	0.915885	+	0.915885i	−0.0808422	+	0.996727i	$0.525761\pi$
$252$	−4.94282	−	3.40126i	−0.311368	−	0.214259i
$253$	−23.3873	+	23.3873i	−1.47035	+	1.47035i
$254$	−5.16160	−	3.05362i	−0.323867	−	0.191601i
$255$	9.84622	+	6.07111i	0.616594	+	0.380187i
$256$	−6.79493	−	14.4855i	−0.424683	−	0.905342i
$257$			2.67255i			0.166709i	0.996520	+	0.0833547i	$0.0265634\pi$
$257$			2.67255i			0.166709i	−0.996520	+	0.0833547i	$0.973437\pi$
$258$	−0.964543	−	1.83457i	−0.0600498	−	0.114215i
$259$	2.12931	+	2.12931i	0.132309	+	0.132309i
$260$	−22.0197	+	12.0967i	−1.36560	+	0.750208i
$261$	−29.3731	−	9.72295i	−1.81815	−	0.601835i
$262$	−4.12741	−	16.0853i	−0.254992	−	0.993754i
$263$		−	11.9867i		−	0.739133i	−0.929204	−	0.369567i	$-0.879506\pi$
$263$		−	11.9867i		−	0.739133i	0.929204	−	0.369567i	$-0.120494\pi$
$264$	20.8695	+	13.8047i	1.28443	+	0.849620i
$265$		−	12.5315i		−	0.769804i
$266$	5.61794	−	1.44154i	0.344458	−	0.0883862i
$267$	−8.01251	+	1.90033i	−0.490357	+	0.116298i
$268$	6.09711	−	20.9627i	0.372440	−	1.28050i
$269$	8.31377	+	8.31377i	0.506900	+	0.506900i	0.913573	−	0.406674i	$-0.133311\pi$
$269$	8.31377	+	8.31377i	0.506900	+	0.506900i	−0.406674	+	0.913573i	$0.633311\pi$
$270$	−17.7346	−	12.6882i	−1.07930	−	0.772179i
$271$			17.6492i			1.07211i	0.844182	+	0.536057i	$0.180087\pi$
$271$			17.6492i			1.07211i	−0.844182	+	0.536057i	$0.819913\pi$
$272$	−7.59801	−	4.82830i	−0.460697	−	0.292759i
$273$	3.84823	−	6.24112i	0.232905	−	0.377730i
$274$	4.07386	−	6.88613i	0.246111	−	0.416007i
$275$	13.7448	−	13.7448i	0.828840	−	0.828840i
$276$	−16.6374	+	15.0462i	−1.00145	+	0.905677i
$277$	2.30360	+	2.30360i	0.138410	+	0.138410i	0.772917	−	0.634507i	$-0.218797\pi$
$277$	2.30360	+	2.30360i	0.138410	+	0.138410i	−0.634507	+	0.772917i	$0.718797\pi$
$278$	−1.64862	−	6.42498i	−0.0988775	−	0.385345i
$279$	−9.33419	−	18.5714i	−0.558823	−	1.11184i
$280$	6.12098	−	5.74275i	0.365798	−	0.343195i
$281$	13.2238			0.788866			0.394433	−	0.918925i	$-0.370941\pi$
$281$	13.2238			0.788866			0.394433	+	0.918925i	$0.370941\pi$
$282$	−1.71220	+	5.50862i	−0.101960	+	0.328034i
$283$	−14.5633	+	14.5633i	−0.865698	+	0.865698i	−0.991993	−	0.126294i	$-0.959692\pi$
$283$	−14.5633	+	14.5633i	−0.865698	+	0.865698i	0.126294	+	0.991993i	$0.459692\pi$
$284$	15.7623	−	8.65921i	0.935323	−	0.513830i
$285$	20.5101	−	4.86438i	1.21491	−	0.288141i
$286$	−15.5693	+	26.3171i	−0.920630	+	1.55616i
$287$	−7.93197			−0.468210
$288$	13.6668	+	10.0608i	0.805321	+	0.592839i
$289$	11.9349			0.702050
$290$	22.0377	−	37.2509i	1.29410	−	2.18745i
$291$	−6.72210	+	1.59428i	−0.394057	+	0.0934584i
$292$	17.0064	−	9.34262i	0.995222	−	0.546736i
$293$	−5.85524	+	5.85524i	−0.342066	+	0.342066i	−0.857144	−	0.515077i	$-0.827763\pi$
$293$	−5.85524	+	5.85524i	−0.342066	+	0.342066i	0.515077	+	0.857144i	$0.327763\pi$
$294$	−0.727043	+	2.33910i	−0.0424020	+	0.136419i
$295$	−7.76903			−0.452331
$296$	−5.82762	−	6.21144i	−0.338724	−	0.361032i
$297$	−26.4401	−	2.30067i	−1.53421	−	0.133498i
$298$	1.56467	+	6.09782i	0.0906389	+	0.353237i
$299$	−19.3835	−	19.3835i	−1.12098	−	1.12098i
$300$	9.77784	−	8.84270i	0.564524	−	0.510534i
$301$	−0.598329	+	0.598329i	−0.0344871	+	0.0344871i
$302$	−0.0660854	+	0.111706i	−0.00380279	+	0.00642794i
$303$	−4.60930	+	7.47544i	−0.264797	+	0.429453i
$304$	−16.0118	+	3.56888i	−0.918339	+	0.204689i
$305$			14.2812i			0.817740i
$306$	9.52605	+	0.653436i	0.544568	+	0.0373544i
$307$	−18.3228	−	18.3228i	−1.04574	−	1.04574i	−0.998903	−	0.0468343i	$-0.985087\pi$
$307$	−18.3228	−	18.3228i	−1.04574	−	1.04574i	−0.0468343	−	0.998903i	$-0.514913\pi$
$308$	2.85293	−	9.80876i	0.162561	−	0.558906i
$309$	−13.6950	+	3.24804i	−0.779081	+	0.184775i
$310$	28.1633	−	7.22655i	1.59957	−	0.410440i
$311$		−	0.512912i		−	0.0290845i	−0.999894	−	0.0145423i	$-0.995371\pi$
$311$		−	0.512912i		−	0.0290845i	0.999894	−	0.0145423i	$-0.00462911\pi$
$312$	−11.4414	+	17.2968i	−0.647741	+	0.979236i
$313$		−	21.7538i		−	1.22960i	−0.788684	−	0.614799i	$-0.789237\pi$
$313$		−	21.7538i		−	1.22960i	0.788684	−	0.614799i	$-0.210763\pi$
$314$	−3.35945	−	13.0924i	−0.189585	−	0.738849i
$315$	−2.79753	+	8.45134i	−0.157623	+	0.476179i
$316$	−9.42090	+	5.17547i	−0.529967	+	0.291143i
$317$	−16.7391	−	16.7391i	−0.940160	−	0.940160i	0.0581479	−	0.998308i	$-0.481480\pi$
$317$	−16.7391	−	16.7391i	−0.940160	−	0.940160i	−0.998308	+	0.0581479i	$0.981480\pi$
$318$	−4.81380	−	9.15587i	−0.269944	−	0.513435i
$319$		−	52.6774i		−	2.94937i
$320$	−17.8215	+	15.6830i	−0.996253	+	0.876708i
$321$	27.6981	+	17.0785i	1.54596	+	0.953227i
$322$	7.88180	+	4.66290i	0.439236	+	0.259853i
$323$	−6.52663	+	6.52663i	−0.363152	+	0.363152i
$324$	−17.8314	−	2.45784i	−0.990634	−	0.136547i
$325$	11.3917	+	11.3917i	0.631899	+	0.631899i
$326$	15.3077	−	3.92788i	0.847815	−	0.217545i
$327$	10.1777	−	16.5063i	0.562828	−	0.912803i
$328$	22.4236	+	0.714885i	1.23814	+	0.0394729i
$329$	2.35501			0.129836
$330$	11.0195	−	35.4527i	0.606601	−	1.95161i
$331$	−9.17188	+	9.17188i	−0.504132	+	0.504132i	−0.912719	−	0.408587i	$-0.866022\pi$
$331$	−9.17188	+	9.17188i	−0.504132	+	0.504132i	0.408587	+	0.912719i	$0.366022\pi$
$332$	−12.1263	−	3.52700i	−0.665518	−	0.193569i
$333$	8.57623	+	2.83887i	0.469975	+	0.155569i
$334$	−7.05735	−	4.17514i	−0.386161	−	0.228454i
$335$	−32.3916			−1.76974
$336$	2.26616	−	6.54710i	0.123629	−	0.357174i
$337$	−14.8896			−0.811087			−0.405543	−	0.914076i	$-0.632918\pi$
$337$	−14.8896			−0.811087			−0.405543	+	0.914076i	$0.632918\pi$
$338$	−5.98861	−	3.54288i	−0.325737	−	0.192707i
$339$	1.56470	+	6.59736i	0.0849827	+	0.358320i
$340$	−3.73036	+	12.8255i	−0.202307	+	0.695559i
$341$	25.0228	−	25.0228i	1.35506	−	1.35506i
$342$	13.1167	−	11.4327i	0.709268	−	0.618210i
$343$	1.00000			0.0539949
$344$	1.74540	−	1.63755i	0.0941055	−	0.0882906i
$345$	28.3302	+	17.4682i	1.52525	+	0.940457i
$346$	15.3431	−	3.93696i	0.824850	−	0.211652i
$347$	−11.3244	−	11.3244i	−0.607923	−	0.607923i	0.334480	−	0.942403i	$-0.391439\pi$
$347$	−11.3244	−	11.3244i	−0.607923	−	0.607923i	−0.942403	+	0.334480i	$0.891439\pi$
$348$	1.79198	−	35.6820i	0.0960603	−	1.91276i
$349$	19.2893	−	19.2893i	1.03253	−	1.03253i	0.0330793	−	0.999453i	$-0.489469\pi$
$349$	19.2893	−	19.2893i	1.03253	−	1.03253i	0.999453	−	0.0330793i	$-0.0105314\pi$
$350$	−4.63215	−	2.74039i	−0.247599	−	0.146480i
$351$	1.90681	−	21.9136i	0.101778	−	1.16966i
$352$	−8.94924	+	27.4722i	−0.476996	+	1.46427i
$353$		−	4.63801i		−	0.246856i	−0.992354	−	0.123428i	$-0.960611\pi$
$353$		−	4.63801i		−	0.246856i	0.992354	−	0.123428i	$-0.0393889\pi$
$354$	−5.67627	+	2.98436i	−0.301690	+	0.158617i
$355$	−18.8681	−	18.8681i	−1.00142	−	1.00142i
$356$	−4.57833	−	8.33392i	−0.242651	−	0.441697i
$357$	−0.899566	−	3.79292i	−0.0476101	−	0.200742i
$358$	−1.94366	−	7.57484i	−0.102726	−	0.400342i
$359$			33.1630i			1.75027i	0.483876	+	0.875137i	$0.339229\pi$
$359$			33.1630i			1.75027i	−0.483876	+	0.875137i	$0.660771\pi$
$360$	8.67027	−	23.6397i	0.456964	−	1.24592i
$361$		−	2.18037i		−	0.114756i
$362$	−29.7321	+	7.62912i	−1.56269	+	0.400978i
$363$	−6.03062	−	25.4274i	−0.316525	−	1.33459i
$364$	8.12955	+	2.36452i	0.426104	+	0.123935i
$365$	−20.3573	−	20.3573i	−1.06555	−	1.06555i
$366$	5.48592	+	10.4343i	0.286754	+	0.545407i
$367$			24.4874i			1.27823i	0.769110	+	0.639116i	$0.220700\pi$
$367$			24.4874i			1.27823i	−0.769110	+	0.639116i	$0.779300\pi$
$368$	−21.8615	−	13.8923i	−1.13961	−	0.724188i
$369$	−21.2615	+	10.6863i	−1.10683	+	0.556304i
$370$	−6.43449	+	10.8764i	−0.334513	+	0.565435i
$371$	−2.98611	+	2.98611i	−0.155031	+	0.155031i
$372$	17.8009	−	16.0984i	0.922933	−	0.834665i
$373$	4.06668	+	4.06668i	0.210565	+	0.210565i	0.804507	−	0.593943i	$-0.202429\pi$
$373$	4.06668	+	4.06668i	0.210565	+	0.210565i	−0.593943	+	0.804507i	$0.702429\pi$
$374$	4.04046	+	15.7465i	0.208927	+	0.814230i
$375$	5.22504	+	3.22172i	0.269820	+	0.166369i
$376$	−6.65760	−	0.212250i	−0.343339	−	0.0109460i
$377$	43.6592			2.24857
$378$	1.20251	+	7.24941i	0.0618504	+	0.372870i
$379$	21.7895	−	21.7895i	1.11925	−	1.11925i	0.127401	−	0.991851i	$-0.459336\pi$
$379$	21.7895	−	21.7895i	1.11925	−	1.11925i	0.991851	−	0.127401i	$-0.0406636\pi$
$380$	11.7194	+	21.3328i	0.601193	+	1.09435i
$381$	1.69501	+	7.14681i	0.0868380	+	0.366142i
$382$	−4.36388	+	7.37637i	−0.223276	+	0.377408i
$383$	3.46713			0.177162			0.0885811	−	0.996069i	$-0.471767\pi$
$383$	3.46713			0.177162			0.0885811	+	0.996069i	$0.471767\pi$
$384$	−6.99649	+	18.3043i	−0.357038	+	0.934090i
$385$	−15.1565			−0.772449
$386$	16.2910	−	27.5370i	0.829190	−	1.40160i
$387$	−0.797715	+	2.40990i	−0.0405501	+	0.122502i
$388$	−3.84099	−	6.99176i	−0.194997	−	0.354953i
$389$	12.7879	−	12.7879i	0.648370	−	0.648370i	−0.304229	−	0.952599i	$-0.598399\pi$
$389$	12.7879	−	12.7879i	0.648370	−	0.648370i	0.952599	+	0.304229i	$0.0983988\pi$
$390$	29.3834	+	9.13298i	1.48789	+	0.462466i
$391$	−14.5738			−0.737028
$392$	−2.82699	−	0.0901270i	−0.142785	−	0.00455210i
$393$	−10.6746	+	17.3122i	−0.538461	+	0.873285i
$394$	4.90243	+	19.1057i	0.246981	+	0.962532i
$395$	11.2772	+	11.2772i	0.567417	+	0.567417i
$396$	−5.56753	−	30.1357i	−0.279779	−	1.51438i
$397$	−18.8937	+	18.8937i	−0.948249	+	0.948249i	−0.998725	−	0.0504763i	$-0.983926\pi$
$397$	−18.8937	+	18.8937i	−0.948249	+	0.948249i	0.0504763	+	0.998725i	$0.483926\pi$
$398$	−4.12012	+	6.96433i	−0.206523	+	0.349090i
$399$	−6.04644	−	3.72819i	−0.302701	−	0.186643i
$400$	12.8481	+	8.16455i	0.642403	+	0.408227i
$401$			26.1774i			1.30724i	0.756823	+	0.653620i	$0.226750\pi$
$401$			26.1774i			1.30724i	−0.756823	+	0.653620i	$0.773250\pi$
$402$	−23.6662	+	12.4428i	−1.18036	+	0.620590i
$403$	20.7390	+	20.7390i	1.03308	+	1.03308i
$404$	−9.73735	−	2.83216i	−0.484451	−	0.140905i
$405$	3.88727	+	26.4225i	0.193160	+	1.31295i
$406$	−14.1278	+	3.62512i	−0.701151	+	0.179912i
$407$			15.3805i			0.762385i
$408$	2.20122	+	10.8036i	0.108977	+	0.534859i
$409$		−	21.0959i		−	1.04312i	−0.853213	−	0.521562i	$-0.825350\pi$
$409$		−	21.0959i		−	1.04312i	0.853213	−	0.521562i	$-0.174650\pi$
$410$	−8.27332	−	32.2427i	−0.408590	−	1.59235i
$411$	−9.53463	+	2.26133i	−0.470309	+	0.111543i
$412$	−7.82528	−	14.2444i	−0.385524	−	0.701769i
$413$	1.85127	+	1.85127i	0.0910951	+	0.0910951i
$414$	27.4090	+	1.88011i	1.34708	+	0.0924024i
$415$			18.7376i			0.919794i
$416$	−22.7691	−	7.41717i	−1.11634	−	0.363657i
$417$	−4.26376	+	6.91504i	−0.208797	+	0.338631i
$418$	25.4962	+	15.0836i	1.24706	+	0.737765i
$419$	5.35115	−	5.35115i	0.261421	−	0.261421i	−0.564210	−	0.825631i	$-0.690819\pi$
$419$	5.35115	−	5.35115i	0.261421	−	0.261421i	0.825631	+	0.564210i	$0.190819\pi$
$420$	−10.2666	−	0.515596i	−0.500957	−	0.0251585i
$421$	13.4238	+	13.4238i	0.654236	+	0.654236i	0.954010	−	0.299774i	$-0.0969113\pi$
$421$	13.4238	+	13.4238i	0.654236	+	0.654236i	−0.299774	+	0.954010i	$0.596911\pi$
$422$	0.438064	−	0.112405i	0.0213246	−	0.00547180i
$423$	6.31255	−	3.17276i	0.306927	−	0.154265i
$424$	8.71085	−	8.17259i	0.423036	−	0.396896i
$425$	8.56504			0.415466
$426$	−21.0335	−	6.53767i	−1.01908	−	0.316751i
$427$	3.40305	−	3.40305i	0.164685	−	0.164685i
$428$	−10.4938	+	36.0790i	−0.507235	+	1.74394i
$429$	36.4390	−	8.64224i	1.75929	−	0.417251i
$430$	−3.05623	−	1.80807i	−0.147385	−	0.0871931i
$431$	8.55923			0.412284			0.206142	−	0.978522i	$-0.433909\pi$
$431$	8.55923			0.412284			0.206142	+	0.978522i	$0.433909\pi$
$432$	−2.74612	−	20.6024i	−0.132123	−	0.991233i
$433$	−20.0916			−0.965540			−0.482770	−	0.875747i	$-0.660369\pi$
$433$	−20.0916			−0.965540			−0.482770	+	0.875747i	$0.660369\pi$
$434$	−8.43299	−	4.98898i	−0.404796	−	0.239479i
$435$	−51.5780	+	12.2328i	−2.47298	+	0.586516i
$436$	21.5008	+	6.25363i	1.02970	+	0.299494i
$437$	−18.7789	+	18.7789i	−0.898316	+	0.898316i
$438$	−22.6936	−	7.05364i	−1.08434	−	0.337036i
$439$	7.32310			0.349512			0.174756	−	0.984612i	$-0.444086\pi$
$439$	7.32310			0.349512			0.174756	+	0.984612i	$0.444086\pi$
$440$	42.8474	+	1.36601i	2.04267	+	0.0651222i
$441$	2.68048	−	1.34724i	0.127642	−	0.0641542i
$442$	−13.0507	+	3.34876i	−0.620761	+	0.159284i
$443$	3.34159	+	3.34159i	0.158764	+	0.158764i	0.782019	−	0.623255i	$-0.214190\pi$
$443$	3.34159	+	3.34159i	0.158764	+	0.158764i	−0.623255	+	0.782019i	$0.714190\pi$
$444$	−0.523216	+	10.4183i	−0.0248307	+	0.494430i
$445$	−9.97603	+	9.97603i	−0.472909	+	0.472909i
$446$	14.3586	+	8.49459i	0.679900	+	0.402231i
$447$	4.04665	−	6.56293i	0.191400	−	0.310416i
$448$	7.98375	+	0.509577i	0.377197	+	0.0240752i
$449$		−	18.3198i		−	0.864565i	−0.901738	−	0.432283i	$-0.857708\pi$
$449$		−	18.3198i		−	0.864565i	0.901738	−	0.432283i	$-0.142292\pi$
$450$	−16.1083	−	1.10494i	−0.759354	−	0.0520876i
$451$	−28.6474	−	28.6474i	−1.34895	−	1.34895i
$452$	−6.86201	+	3.76972i	−0.322762	+	0.177313i
$453$	0.154669	−	0.0366829i	0.00726699	−	0.00172351i
$454$	−1.45424	−	5.66743i	−0.0682506	−	0.265986i
$455$		−	12.5618i		−	0.588907i
$456$	16.7572	+	11.0845i	0.784729	+	0.519080i
$457$			15.9691i			0.747001i	0.927630	+	0.373500i	$0.121843\pi$
$457$			15.9691i			0.747001i	−0.927630	+	0.373500i	$0.878157\pi$
$458$	12.5695	−	3.22527i	0.587334	−	0.150707i
$459$	−7.52123	−	8.95489i	−0.351061	−	0.417978i
$460$	−10.7332	+	36.9024i	−0.500440	+	1.72058i
$461$	9.28993	+	9.28993i	0.432675	+	0.432675i	0.889537	−	0.456862i	$-0.151027\pi$
$461$	9.28993	+	9.28993i	0.432675	+	0.432675i	−0.456862	+	0.889537i	$0.651027\pi$
$462$	−11.0738	+	5.82217i	−0.515200	+	0.270872i
$463$			7.87871i			0.366155i	0.983099	+	0.183077i	$0.0586059\pi$
$463$			7.87871i			0.366155i	−0.983099	+	0.183077i	$0.941394\pi$
$464$	40.2659	−	8.97489i	1.86930	−	0.416649i
$465$	−30.3114	−	18.6898i	−1.40566	−	0.866718i
$466$	11.9344	−	20.1731i	0.552853	−	0.934500i
$467$	25.6911	−	25.6911i	1.18884	−	1.18884i	0.211457	−	0.977387i	$-0.432179\pi$
$467$	25.6911	−	25.6911i	1.18884	−	1.18884i	0.977387	−	0.211457i	$-0.0678209\pi$
$468$	24.9766	−	4.61440i	1.15455	−	0.213301i
$469$	7.71856	+	7.71856i	0.356410	+	0.356410i
$470$	2.45636	+	9.57291i	0.113303	+	0.441565i
$471$	−8.68844	+	14.0911i	−0.400342	+	0.649281i
$472$	−5.06668	−	5.40038i	−0.233213	−	0.248573i
$473$	−4.32189			−0.198721
$474$	12.5714	+	3.90746i	0.577423	+	0.179475i
$475$	11.0364	−	11.0364i	0.506384	−	0.506384i
$476$	3.94507	−	2.16726i	0.180822	−	0.0993363i
$477$	−3.98120	+	12.0272i	−0.182287	+	0.550688i
$478$	15.2170	−	25.7217i	0.696010	−	1.17648i
$479$	28.8547			1.31841			0.659203	−	0.751965i	$-0.270894\pi$
$479$	28.8547			1.31841			0.659203	+	0.751965i	$0.270894\pi$
$480$	28.9770	+	2.38288i	1.32261	+	0.108763i
$481$	−12.7475			−0.581234
$482$	−15.2314	+	25.7459i	−0.693769	+	1.17269i
$483$	−2.58829	−	10.9132i	−0.117771	−	0.496570i
$484$	26.4474	−	14.5292i	1.20216	−	0.660416i
$485$	−8.36941	+	8.36941i	−0.380035	+	0.380035i
$486$	12.9900	+	17.8118i	0.589238	+	0.807960i
$487$	30.4536			1.37998			0.689991	−	0.723818i	$-0.257614\pi$
$487$	30.4536			1.37998			0.689991	+	0.723818i	$0.257614\pi$
$488$	−9.92710	+	9.31369i	−0.449379	+	0.421611i
$489$	−16.4753	−	10.1585i	−0.745038	−	0.459385i
$490$	1.04303	+	4.06491i	0.0471195	+	0.183634i
$491$	−10.8774	−	10.8774i	−0.490891	−	0.490891i	0.417696	−	0.908587i	$-0.362838\pi$
$491$	−10.8774	−	10.8774i	−0.490891	−	0.490891i	−0.908587	+	0.417696i	$0.862838\pi$
$492$	−18.4303	−	20.3794i	−0.830902	−	0.918772i
$493$	16.4129	−	16.4129i	0.739202	−	0.739202i
$494$	−12.5014	+	21.1314i	−0.562464	+	0.950746i
$495$	−40.6267	+	20.4195i	−1.82604	+	0.917787i
$496$	23.3903	+	14.8638i	1.05026	+	0.667406i
$497$			8.99213i			0.403352i
$498$	7.19780	+	13.6902i	0.322541	+	0.613474i
$499$	4.26797	+	4.26797i	0.191060	+	0.191060i	0.796154	−	0.605094i	$-0.206864\pi$
$499$	4.26797	+	4.26797i	0.191060	+	0.191060i	−0.605094	+	0.796154i	$0.706864\pi$
$500$	−1.97957	+	6.80603i	−0.0885290	+	0.304375i
$501$	2.31755	+	9.77169i	0.103541	+	0.436567i
$502$	28.1100	−	7.21290i	1.25461	−	0.321927i
$503$			22.9449i			1.02306i	0.859265	+	0.511531i	$0.170921\pi$
$503$			22.9449i			1.02306i	−0.859265	+	0.511531i	$0.829079\pi$
$504$	−7.69910	+	3.56705i	−0.342945	+	0.158889i
$505$			15.0462i			0.669547i
$506$	11.6255	+	45.3068i	0.516817	+	2.01413i
$507$	1.96659	+	8.29190i	0.0873393	+	0.368256i
$508$	−7.43350	+	4.08367i	−0.329808	+	0.181184i
$509$	11.5174	+	11.5174i	0.510499	+	0.510499i	0.914679	−	0.404180i	$-0.132443\pi$
$509$	11.5174	+	11.5174i	0.510499	+	0.510499i	−0.404180	+	0.914679i	$0.632443\pi$
$510$	14.4796	−	7.61279i	0.641166	−	0.337100i
$511$			9.70182i			0.429183i
$512$	−22.5241	−	2.16012i	−0.995433	−	0.0954647i
$513$	−21.2301	−	1.84733i	−0.937332	−	0.0815615i
$514$	3.25294	+	1.92445i	0.143481	+	0.0848837i
$515$	−17.0510	+	17.0510i	−0.751359	+	0.751359i
$516$	−2.92751	−	0.147022i	−0.128877	−	0.00647230i
$517$	8.50544	+	8.50544i	0.374069	+	0.374069i
$518$	4.12498	−	1.05845i	0.181241	−	0.0465056i
$519$	−16.5134	−	10.1820i	−0.724857	−	0.446941i
$520$	−1.13216	+	35.5121i	−0.0496485	+	1.55731i
$521$	−1.47241			−0.0645073			−0.0322536	−	0.999480i	$-0.510268\pi$
$521$	−1.47241			−0.0645073			−0.0322536	+	0.999480i	$0.510268\pi$
$522$	−32.9853	+	28.7506i	−1.44373	+	1.25838i
$523$	−26.7327	+	26.7327i	−1.16894	+	1.16894i	−0.186482	+	0.982458i	$0.559709\pi$
$523$	−26.7327	+	26.7327i	−1.16894	+	1.16894i	−0.982458	+	0.186482i	$0.940291\pi$
$524$	−22.5505	−	6.55894i	−0.985124	−	0.286528i
$525$	1.52115	+	6.41374i	0.0663882	+	0.279918i
$526$	−14.5898	−	8.63138i	−0.636146	−	0.376346i
$527$	15.5929			0.679239
$528$	31.8302	−	15.4612i	1.38523	−	0.672861i
$529$	−18.9327			−0.823162
$530$	−15.2529	−	9.02365i	−0.662543	−	0.391962i
$531$	7.45639	+	2.46818i	0.323580	+	0.107110i
$532$	2.29077	−	7.87597i	0.0993174	−	0.341467i
$533$	23.7431	−	23.7431i	1.02843	−	1.02843i
$534$	−3.45662	+	11.1209i	−0.149582	+	0.481249i
$535$	55.7494			2.41026
$536$	−21.1246	−	22.5159i	−0.912445	−	0.972540i
$537$	−5.02683	+	8.15260i	−0.216924	+	0.351811i
$538$	16.1058	−	4.13266i	0.694370	−	0.178172i
$539$	3.61163	+	3.61163i	0.155564	+	0.155564i
$540$	−28.2139	+	12.4495i	−1.21413	+	0.535740i
$541$	27.3381	−	27.3381i	1.17536	−	1.17536i	0.194443	−	0.980914i	$-0.437710\pi$
$541$	27.3381	−	27.3381i	1.17536	−	1.17536i	0.980914	−	0.194443i	$-0.0622899\pi$
$542$	21.4820	+	12.7088i	0.922731	+	0.545890i
$543$	31.9999	+	19.7309i	1.37325	+	0.846735i
$544$	−11.3480	+	5.77128i	−0.486541	+	0.247441i
$545$		−	33.2232i		−	1.42312i
$546$	−4.82544	−	9.17801i	−0.206510	−	0.392783i
$547$	24.9110	+	24.9110i	1.06512	+	1.06512i	0.997727	+	0.0673911i	$0.0214675\pi$
$547$	24.9110	+	24.9110i	1.06512	+	1.06512i	0.0673911	+	0.997727i	$0.478532\pi$
$548$	−5.44806	−	9.91710i	−0.232730	−	0.423638i
$549$	4.53707	−	13.7065i	0.193638	−	0.584980i
$550$	−6.83233	−	26.6269i	−0.291332	−	1.13538i
$551$		−	42.2974i		−	1.80193i
$552$	6.33351	+	31.0849i	0.269572	+	1.32306i
$553$		−	5.37445i		−	0.228545i
$554$	4.46263	−	1.14509i	0.189599	−	0.0486501i
$555$	15.0596	−	3.57168i	0.639243	−	0.151609i
$556$	−9.00739	−	2.61985i	−0.381998	−	0.111106i
$557$	−11.3149	−	11.3149i	−0.479426	−	0.479426i	0.425522	−	0.904948i	$-0.360091\pi$
$557$	−11.3149	−	11.3149i	−0.479426	−	0.479426i	−0.904948	+	0.425522i	$0.860091\pi$
$558$	−29.3258	−	2.01159i	−1.24146	−	0.0851573i
$559$		−	3.58200i		−	0.151503i
$560$	−2.58229	−	11.5855i	−0.109122	−	0.489575i
$561$	10.4497	−	16.9475i	0.441187	−	0.715525i
$562$	9.52216	−	16.0955i	0.401668	−	0.678949i
$563$	6.22999	−	6.22999i	0.262563	−	0.262563i	−0.563532	−	0.826094i	$-0.690558\pi$
$563$	6.22999	−	6.22999i	0.262563	−	0.262563i	0.826094	+	0.563532i	$0.190558\pi$
$564$	5.47198	+	6.05066i	0.230412	+	0.254779i
$565$	8.21410	+	8.21410i	0.345570	+	0.345570i
$566$	7.23922	+	28.2126i	0.304287	+	1.18587i
$567$	5.36990	−	7.22248i	0.225514	−	0.303316i
$568$	0.810434	−	25.4207i	0.0340050	−	1.06663i
$569$	−38.7320			−1.62373			−0.811865	−	0.583845i	$-0.801548\pi$
$569$	−38.7320			−1.62373			−0.811865	+	0.583845i	$0.801548\pi$
$570$	8.84810	−	28.4669i	0.370606	−	1.19235i
$571$	−4.01087	+	4.01087i	−0.167850	+	0.167850i	−0.786033	−	0.618184i	$-0.787869\pi$
$571$	−4.01087	+	4.01087i	−0.167850	+	0.167850i	0.618184	+	0.786033i	$0.287869\pi$
$572$	20.8212	+	37.9007i	0.870576	+	1.58471i
$573$	10.2134	−	2.42232i	0.426671	−	0.101194i
$574$	−5.71164	+	9.65451i	−0.238399	+	0.402972i
$575$	24.6439			1.02772
$576$	22.0868	−	9.39011i	0.920282	−	0.391255i
$577$	1.43905			0.0599084			0.0299542	−	0.999551i	$-0.490464\pi$
$577$	1.43905			0.0599084			0.0299542	+	0.999551i	$0.490464\pi$
$578$	8.59402	−	14.5267i	0.357464	−	0.604230i
$579$	−38.1281	+	9.04285i	−1.58455	+	0.375808i
$580$	−29.4716	−	53.6470i	−1.22374	−	2.22757i
$581$	4.46497	−	4.46497i	0.185238	−	0.185238i
$582$	−2.89993	+	9.32991i	−0.120206	+	0.386737i
$583$	−21.5695			−0.893317
$584$	0.874396	−	27.4270i	0.0361828	−	1.13494i
$585$	−16.9238	−	33.6716i	−0.699711	−	1.39215i
$586$	2.91056	+	11.3430i	0.120234	+	0.468575i
$587$	−21.5263	−	21.5263i	−0.888486	−	0.888486i	0.105892	−	0.994378i	$-0.466230\pi$
$587$	−21.5263	−	21.5263i	−0.888486	−	0.888486i	−0.994378	+	0.105892i	$0.966230\pi$
$588$	2.32355	+	2.56927i	0.0958214	+	0.105955i
$589$	20.0921	−	20.0921i	0.827881	−	0.827881i
$590$	−5.59431	+	9.45619i	−0.230314	+	0.389305i
$591$	12.6790	−	20.5630i	0.521544	−	0.845848i
$592$	−11.7567	+	2.62045i	−0.483196	+	0.107700i
$593$			25.1477i			1.03269i	0.856380	+	0.516347i	$0.172708\pi$
$593$			25.1477i			1.03269i	−0.856380	+	0.516347i	$0.827292\pi$
$594$	−21.8392	+	30.5252i	−0.896072	+	1.25247i
$595$	−4.72240	−	4.72240i	−0.193599	−	0.193599i
$596$	8.54873	+	2.48644i	0.350170	+	0.101849i
$597$	9.64290	−	2.28701i	0.394658	−	0.0936010i
$598$	−37.5505	+	9.63527i	−1.53555	+	0.394016i
$599$			18.5702i			0.758758i	0.925241	+	0.379379i	$0.123862\pi$
$599$			18.5702i			0.758758i	−0.925241	+	0.379379i	$0.876138\pi$
$600$	−3.72221	−	18.2687i	−0.151959	−	0.745815i
$601$			40.1461i			1.63759i	0.574085	+	0.818796i	$0.305358\pi$
$601$			40.1461i			1.63759i	−0.574085	+	0.818796i	$0.694642\pi$
$602$	0.297421	+	1.15911i	0.0121220	+	0.0472417i
$603$	31.0881	+	10.2907i	1.26601	+	0.419068i
$604$	0.0883776	+	0.160874i	0.00359603	+	0.00654585i
$605$	−31.6586	−	31.6586i	−1.28710	−	1.28710i
$606$	5.77978	+	10.9932i	0.234788	+	0.446567i
$607$		−	13.3778i		−	0.542987i	−0.962440	−	0.271494i	$-0.912482\pi$
$607$		−	13.3778i		−	0.542987i	0.962440	−	0.271494i	$-0.0875176\pi$
$608$	−7.18582	+	22.0588i	−0.291423	+	0.894604i
$609$	15.2054	+	9.37553i	0.616153	+	0.379916i
$610$	17.3826	+	10.2836i	0.703800	+	0.416370i
$611$	−7.04935	+	7.04935i	−0.285186	+	0.285186i
$612$	7.65483	−	11.1242i	0.309428	−	0.449671i
$613$	−6.41278	−	6.41278i	−0.259010	−	0.259010i	0.565641	−	0.824651i	$-0.308629\pi$
$613$	−6.41278	−	6.41278i	−0.259010	−	0.259010i	−0.824651	+	0.565641i	$0.808629\pi$
$614$	−35.4957	+	9.10801i	−1.43249	+	0.367569i
$615$	−21.3970	+	34.7020i	−0.862811	+	1.39932i
$616$	−9.88454	−	10.5356i	−0.398260	−	0.424490i
$617$	−12.6296			−0.508449			−0.254224	−	0.967145i	$-0.581820\pi$
$617$	−12.6296			−0.508449			−0.254224	+	0.967145i	$0.581820\pi$
$618$	−5.90806	+	19.0079i	−0.237657	+	0.764609i
$619$	−3.53002	+	3.53002i	−0.141883	+	0.141883i	−0.774481	−	0.632597i	$-0.781989\pi$
$619$	−3.53002	+	3.53002i	−0.141883	+	0.141883i	0.632597	+	0.774481i	$0.281989\pi$
$620$	11.4838	−	39.4830i	0.461202	−	1.58567i
$621$	−21.6406	−	25.7656i	−0.868407	−	1.03394i
$622$	−0.624298	−	0.369336i	−0.0250320	−	0.0148090i
$623$	4.75435			0.190479
$624$	12.8143	+	26.3811i	0.512982	+	1.05609i
$625$	29.5452			1.18181
$626$	−26.4779	−	15.6644i	−1.05827	−	0.626076i
$627$	−8.37267	−	35.3024i	−0.334372	−	1.40984i
$628$	−18.3547	−	5.33856i	−0.732433	−	0.213032i
$629$	−4.79219	+	4.79219i	−0.191077	+	0.191077i
$630$	8.27223	+	9.49067i	0.329573	+	0.378117i
$631$	49.6236			1.97548			0.987742	−	0.156094i	$-0.0498904\pi$
$631$	49.6236			1.97548			0.987742	+	0.156094i	$0.0498904\pi$
$632$	−0.484383	+	15.1935i	−0.0192677	+	0.604366i
$633$	−0.471477	−	0.290710i	−0.0187395	−	0.0115547i
$634$	−32.4276	+	8.32077i	−1.28787	+	0.330460i
$635$	8.89819	+	8.89819i	0.353114	+	0.353114i
$636$	−14.6105	−	0.733752i	−0.579344	−	0.0290952i
$637$	−2.99334	+	2.99334i	−0.118600	+	0.118600i
$638$	−64.1170	−	37.9318i	−2.53842	−	1.50173i
$639$	12.1145	+	24.1032i	0.479244	+	0.953507i
$640$	6.25595	+	32.9847i	0.247288	+	1.30384i
$641$		−	30.5266i		−	1.20573i	−0.797844	−	0.602865i	$-0.794026\pi$
$641$		−	30.5266i		−	1.20573i	0.797844	−	0.602865i	$-0.205974\pi$
$642$	40.7321	−	21.4153i	1.60757	−	0.845196i
$643$	23.0383	+	23.0383i	0.908541	+	0.908541i	0.996155	−	0.0876139i	$-0.0279242\pi$
$643$	23.0383	+	23.0383i	0.908541	+	0.908541i	−0.0876139	+	0.996155i	$0.527924\pi$
$644$	11.3510	−	6.23580i	0.447293	−	0.245725i
$645$	1.00363	+	4.23170i	0.0395179	+	0.166623i
$646$	3.24430	+	12.6437i	0.127645	+	0.497458i
$647$			16.1967i			0.636757i	0.947964	+	0.318378i	$0.103138\pi$
$647$			16.1967i			0.636757i	−0.947964	+	0.318378i	$0.896862\pi$
$648$	−15.8316	+	19.9339i	−0.621924	+	0.783078i
$649$			13.3722i			0.524906i
$650$	22.0685	−	5.66267i	0.865598	−	0.222108i
$651$	2.76930	+	11.6764i	0.108537	+	0.457635i
$652$	6.24186	−	21.4604i	0.244450	−	0.840453i
$653$	−1.12882	−	1.12882i	−0.0441741	−	0.0441741i	0.684675	−	0.728849i	$-0.259944\pi$
$653$	−1.12882	−	1.12882i	−0.0441741	−	0.0441741i	−0.728849	+	0.684675i	$0.759944\pi$
$654$	−12.7622	−	24.2738i	−0.499042	−	0.949180i
$655$			34.8452i			1.36151i
$656$	17.0169	−	26.7784i	0.664397	−	1.04552i
$657$	13.0707	+	26.0055i	0.509935	+	1.01457i
$658$	1.69579	−	2.86644i	0.0661088	−	0.111745i
$659$	26.8344	−	26.8344i	1.04532	−	1.04532i	0.0463963	−	0.998923i	$-0.485226\pi$
$659$	26.8344	−	26.8344i	1.04532	−	1.04532i	0.998923	−	0.0463963i	$-0.0147737\pi$
$660$	−35.2169	−	38.9412i	−1.37082	−	1.51578i
$661$	27.2666	+	27.2666i	1.06055	+	1.06055i	0.998045	+	0.0625040i	$0.0199086\pi$
$661$	27.2666	+	27.2666i	1.06055	+	1.06055i	0.0625040	+	0.998045i	$0.480091\pi$
$662$	4.55922	+	17.7682i	0.177199	+	0.690579i
$663$	14.0462	+	8.66077i	0.545508	+	0.336357i
$664$	−13.0248	+	12.2200i	−0.505461	+	0.474228i
$665$	−12.1700			−0.471932
$666$	9.63092	−	8.39448i	0.373191	−	0.325279i
$667$	47.2245	−	47.2245i	1.82854	−	1.82854i
$668$	−10.1637	+	5.58352i	−0.393244	+	0.216033i
$669$	−4.71520	−	19.8811i	−0.182300	−	0.768648i
$670$	−23.3245	+	39.4259i	−0.901103	+	1.52316i
$671$	24.5811			0.948944
$672$	−6.33708	−	7.47271i	−0.244458	−	0.288266i
$673$	−23.1916			−0.893972			−0.446986	−	0.894541i	$-0.647503\pi$
$673$	−23.1916			−0.893972			−0.446986	+	0.894541i	$0.647503\pi$
$674$	−10.7216	+	18.1231i	−0.412982	+	0.698074i
$675$	12.7182	+	15.1425i	0.489525	+	0.582836i
$676$	−8.62452	+	4.73797i	−0.331712	+	0.182230i
$677$	13.0898	−	13.0898i	0.503080	−	0.503080i	−0.409314	−	0.912394i	$-0.634232\pi$
$677$	13.0898	−	13.0898i	0.503080	−	0.503080i	0.912394	+	0.409314i	$0.134232\pi$
$678$	9.15678	+	2.84612i	0.351664	+	0.109305i
$679$	3.98867			0.153071
$680$	12.9246	+	13.7758i	0.495634	+	0.528278i
$681$	−3.76104	+	6.09971i	−0.144123	+	0.233742i
$682$	−12.4385	−	48.4752i	−0.476294	−	1.85621i
$683$	31.7392	+	31.7392i	1.21447	+	1.21447i	0.969541	+	0.244927i	$0.0787640\pi$
$683$	31.7392	+	31.7392i	1.21447	+	1.21447i	0.244927	+	0.969541i	$0.421236\pi$
$684$	−4.47047	−	24.1976i	−0.170933	−	0.925217i
$685$	−11.8712	+	11.8712i	−0.453574	+	0.453574i
$686$	0.720078	−	1.21716i	0.0274927	−	0.0464715i
$687$	−13.5282	−	8.34140i	−0.516134	−	0.318244i
$688$	−0.736341	−	3.30359i	−0.0280727	−	0.125948i
$689$		−	17.8769i		−	0.681055i
$690$	41.6616	−	21.9041i	1.58603	−	0.833874i
$691$	−0.300368	−	0.300368i	−0.0114266	−	0.0114266i	0.701370	−	0.712797i	$-0.252572\pi$
$691$	−0.300368	−	0.300368i	−0.0114266	−	0.0114266i	−0.712797	+	0.701370i	$0.752572\pi$
$692$	6.25629	−	21.5100i	0.237828	−	0.817687i
$693$	14.5466	+	4.81516i	0.552580	+	0.182913i
$694$	−21.9380	+	5.62918i	−0.832756	+	0.213681i
$695$			13.9183i			0.527949i
$696$	−42.1405	−	27.8750i	−1.59733	−	1.05660i
$697$		−	17.8516i		−	0.676177i
$698$	−9.58845	−	37.3680i	−0.362928	−	1.41440i
$699$	−27.9319	+	6.62461i	−1.05648	+	0.250566i
$700$	−6.67102	+	3.66479i	−0.252141	+	0.138516i
$701$	−4.04020	−	4.04020i	−0.152596	−	0.152596i	0.626680	−	0.779276i	$-0.284413\pi$
$701$	−4.04020	−	4.04020i	−0.152596	−	0.152596i	−0.779276	+	0.626680i	$0.784413\pi$
$702$	−25.2994	−	18.1004i	−0.954866	−	0.683156i
$703$			12.3498i			0.465783i
$704$	26.9940	+	30.6748i	1.01737	+	1.15610i
$705$	6.35280	−	10.3031i	0.239260	−	0.388036i
$706$	−5.64522	−	3.33973i	−0.212461	−	0.125692i
$707$	3.58534	−	3.58534i	0.134841	−	0.134841i
$708$	−0.454897	+	9.05793i	−0.0170961	+	0.340418i
$709$	−36.0983	−	36.0983i	−1.35570	−	1.35570i	−0.879142	−	0.476560i	$-0.841884\pi$
$709$	−36.0983	−	36.0983i	−1.35570	−	1.35570i	−0.476560	−	0.879142i	$-0.658116\pi$
$710$	−36.5522	+	9.37910i	−1.37178	+	0.351991i
$711$	−7.24066	−	14.4061i	−0.271546	−	0.540270i
$712$	−13.4405	−	0.428495i	−0.503704	−	0.0160585i
$713$	44.8651			1.68021
$714$	−5.26436	−	1.63627i	−0.197014	−	0.0612360i
$715$	45.3686	−	45.3686i	1.69669	−	1.69669i
$716$	−10.6194	−	3.08871i	−0.396866	−	0.115431i
$717$	−35.6146	+	8.44671i	−1.33005	+	0.315448i
$718$	40.3648	+	23.8799i	1.50640	+	0.891190i
$719$	−11.2872			−0.420942			−0.210471	−	0.977600i	$-0.567500\pi$
$719$	−11.2872			−0.420942			−0.210471	+	0.977600i	$0.567500\pi$
$720$	−22.5301	−	27.5756i	−0.839649	−	1.02768i
$721$	8.12614			0.302633
$722$	−2.65386	−	1.57003i	−0.0987665	−	0.0584306i
$723$	35.6481	−	8.45466i	1.32577	−	0.314432i
$724$	−12.1236	+	41.6825i	−0.450569	+	1.54912i
$725$	−27.7539	+	27.7539i	−1.03075	+	1.03075i
$726$	−35.2918	−	10.9695i	−1.30980	−	0.407115i
$727$	8.73834			0.324087			0.162044	−	0.986784i	$-0.448191\pi$
$727$	8.73834			0.324087			0.162044	+	0.986784i	$0.448191\pi$
$728$	8.73192	−	8.19236i	0.323626	−	0.303629i
$729$	4.66348	−	26.5942i	0.172721	−	0.984971i
$730$	−39.4370	+	10.1193i	−1.45963	+	0.374533i
$731$	−1.34659	−	1.34659i	−0.0498055	−	0.0498055i
$732$	16.6505	+	0.836202i	0.615420	+	0.0309069i
$733$	13.3426	−	13.3426i	0.492821	−	0.492821i	−0.416373	−	0.909194i	$-0.636699\pi$
$733$	13.3426	−	13.3426i	0.492821	−	0.492821i	0.909194	+	0.416373i	$0.136699\pi$
$734$	29.8052	+	17.6328i	1.10013	+	0.650840i
$735$	2.69756	−	4.37495i	0.0995012	−	0.161373i
$736$	−32.6512	+	16.6055i	−1.20354	+	0.612088i
$737$			55.7532i			2.05369i
$738$	−2.30297	+	33.5736i	−0.0847734	+	1.23586i
$739$	−23.0122	−	23.0122i	−0.846516	−	0.846516i	0.143180	−	0.989697i	$-0.454267\pi$
$739$	−23.0122	−	23.0122i	−0.846516	−	0.846516i	−0.989697	+	0.143180i	$0.954267\pi$
$740$	8.60499	+	15.6637i	0.316326	+	0.575808i
$741$	29.2588	−	6.93931i	1.07485	−	0.254922i
$742$	1.48436	+	5.78482i	0.0544925	+	0.212368i
$743$			15.1890i			0.557230i	0.960403	+	0.278615i	$0.0898753\pi$
$743$			15.1890i			0.557230i	−0.960403	+	0.278615i	$0.910125\pi$
$744$	−6.77641	−	33.2587i	−0.248435	−	1.21932i
$745$		−	13.2095i		−	0.483960i
$746$	7.87814	−	2.02149i	0.288439	−	0.0740120i
$747$	5.95286	−	17.9836i	0.217804	−	0.657986i
$748$	22.0755	+	6.42077i	0.807159	+	0.234767i
$749$	−13.2844	−	13.2844i	−0.485403	−	0.485403i
$750$	7.68380	−	4.03984i	0.280573	−	0.147514i
$751$			8.05484i			0.293925i	0.989142	+	0.146963i	$0.0469497\pi$
$751$			8.05484i			0.293925i	−0.989142	+	0.146963i	$0.953050\pi$
$752$	−5.05233	+	7.95055i	−0.184240	+	0.289927i
$753$	−30.2541	−	18.6545i	−1.10252	−	0.679806i
$754$	31.4380	−	53.1405i	1.14491	−	1.93526i
$755$	0.192572	−	0.192572i	0.00700841	−	0.00700841i
$756$	9.68962	+	3.75649i	0.352408	+	0.136622i
$757$	−21.7947	−	21.7947i	−0.792143	−	0.792143i	0.189699	−	0.981842i	$-0.439249\pi$
$757$	−21.7947	−	21.7947i	−0.792143	−	0.792143i	−0.981842	+	0.189699i	$0.939249\pi$
$758$	−10.8313	−	42.2116i	−0.393410	−	1.53319i
$759$	30.0667	−	48.7626i	1.09135	−	1.76997i
$760$	34.4044	+	1.09684i	1.24798	+	0.0397867i
$761$	39.1050			1.41755			0.708777	−	0.705432i	$-0.249247\pi$
$761$	39.1050			1.41755			0.708777	+	0.705432i	$0.249247\pi$
$762$	9.91938	+	3.08315i	0.359341	+	0.111691i
$763$	−7.91670	+	7.91670i	−0.286604	+	0.286604i
$764$	5.83592	+	10.6231i	0.211136	+	0.384331i
$765$	−19.0205	−	6.29608i	−0.687687	−	0.227635i
$766$	2.49661	−	4.22007i	0.0902060	−	0.152477i
$767$	−11.0830			−0.400182
$768$	17.2414	+	21.6964i	0.622145	+	0.782902i
$769$	−48.8509			−1.76161			−0.880804	−	0.473482i	$-0.842997\pi$
$769$	−48.8509			−1.76161			−0.880804	+	0.473482i	$0.842997\pi$
$770$	−10.9139	+	18.4480i	−0.393309	+	0.664820i
$771$	−1.06823	−	4.50406i	−0.0384713	−	0.162210i
$772$	−21.7863	−	39.6576i	−0.784107	−	1.42731i
$773$	26.3266	−	26.3266i	0.946901	−	0.946901i	−0.0517586	−	0.998660i	$-0.516483\pi$
$773$	26.3266	−	26.3266i	0.946901	−	0.946901i	0.998660	+	0.0517586i	$0.0164826\pi$
$774$	2.35883	+	2.70626i	0.0847863	+	0.0972747i
$775$	−26.3673			−0.947142
$776$	−11.2759	−	0.359487i	−0.404782	−	0.0129048i
$777$	−4.43961	−	2.73743i	−0.159270	−	0.0982048i
$778$	−6.35667	−	24.7732i	−0.227898	−	0.888161i
$779$	−23.0025	−	23.0025i	−0.824149	−	0.824149i
$780$	32.2747	−	29.1880i	1.15562	−	1.04510i
$781$	−32.4763	+	32.4763i	−1.16209	+	1.16209i
$782$	−10.4943	+	17.7387i	−0.375274	+	0.634334i
$783$	53.3887	+	4.64560i	1.90796	+	0.166020i
$784$	−2.14535	+	3.37601i	−0.0766197	+	0.120572i
$785$			28.3618i			1.01228i
$786$	13.3853	+	25.4588i	0.477437	+	0.908087i
$787$	−19.6895	−	19.6895i	−0.701856	−	0.701856i	0.262953	−	0.964809i	$-0.415304\pi$
$787$	−19.6895	−	19.6895i	−0.701856	−	0.701856i	−0.964809	+	0.262953i	$0.915304\pi$
$788$	26.7849	+	7.79053i	0.954173	+	0.277526i
$789$	4.79113	+	20.2012i	0.170569	+	0.719183i
$790$	21.8466	−	5.60574i	0.777268	−	0.199443i
$791$		−	3.91465i		−	0.139189i
$792$	−40.6892	−	14.9235i	−1.44583	−	0.530282i
$793$			20.3730i			0.723465i
$794$	9.39182	+	36.6017i	0.333303	+	1.29895i
$795$	5.00888	+	21.1193i	0.177647	+	0.749026i
$796$	5.50993	+	10.0297i	0.195294	+	0.355494i
$797$	−24.3789	−	24.3789i	−0.863543	−	0.863543i	0.128205	−	0.991748i	$-0.459079\pi$
$797$	−24.3789	−	24.3789i	−0.863543	−	0.863543i	−0.991748	+	0.128205i	$0.959079\pi$
$798$	−8.89173	+	4.67493i	−0.314764	+	0.165491i
$799$			5.30016i			0.187506i
$800$	19.1892	−	9.75910i	0.678441	−	0.345036i
$801$	12.7439	−	6.40524i	0.450284	−	0.226318i
$802$	31.8622	+	18.8498i	1.12509	+	0.665609i
$803$	−35.0394	+	35.0394i	−1.23651	+	1.23651i
$804$	−1.89661	+	37.7654i	−0.0668884	+	1.33188i
$805$	−13.5876	−	13.5876i	−0.478901	−	0.478901i
$806$	40.1765	−	10.3091i	1.41516	−	0.363122i
$807$	−17.3342	−	10.6882i	−0.610194	−	0.376241i
$808$	−10.4589	+	9.81258i	−0.367941	+	0.345205i
$809$	−31.4911			−1.10717			−0.553585	−	0.832793i	$-0.686741\pi$
$809$	−31.4911			−1.10717			−0.553585	+	0.832793i	$0.686741\pi$
$810$	34.9597	+	14.2948i	1.22836	+	0.502269i
$811$	−0.362103	+	0.362103i	−0.0127151	+	0.0127151i	−0.713436	−	0.700721i	$-0.752862\pi$
$811$	−0.362103	+	0.362103i	−0.0127151	+	0.0127151i	0.700721	+	0.713436i	$0.252862\pi$
$812$	−5.76074	+	19.8062i	−0.202162	+	0.695062i
$813$	−7.05445	−	29.7443i	−0.247410	−	1.04318i
$814$	18.7206	+	11.0752i	0.656158	+	0.388185i
$815$	−33.1607			−1.16157
$816$	14.7348	+	5.10019i	0.515822	+	0.178542i
$817$	−3.47027			−0.121409
$818$	−25.6771	−	15.1907i	−0.897780	−	0.531129i
$819$	−3.99083	+	12.0563i	−0.139451	+	0.421281i
$820$	−45.2021	−	13.1473i	−1.57853	−	0.459123i
$821$	−8.59531	+	8.59531i	−0.299979	+	0.299979i	−0.841005	−	0.541027i	$-0.818036\pi$
$821$	−8.59531	+	8.59531i	−0.299979	+	0.299979i	0.541027	+	0.841005i	$0.318036\pi$
$822$	−4.11326	+	13.2335i	−0.143467	+	0.461573i
$823$	−15.4889			−0.539910			−0.269955	−	0.962873i	$-0.587009\pi$
$823$	−15.4889			−0.539910			−0.269955	+	0.962873i	$0.587009\pi$
$824$	−22.9725	−	0.732385i	−0.800286	−	0.0255138i
$825$	−17.6702	+	28.6579i	−0.615198	+	0.997739i
$826$	3.58636	−	0.920242i	0.124785	−	0.0320193i
$827$	7.82252	+	7.82252i	0.272016	+	0.272016i	0.829911	−	0.557896i	$-0.188391\pi$
$827$	7.82252	+	7.82252i	0.272016	+	0.272016i	−0.557896	+	0.829911i	$0.688391\pi$
$828$	22.0250	−	32.0074i	0.765422	−	1.11234i
$829$	−15.7306	+	15.7306i	−0.546348	+	0.546348i	−0.925382	−	0.379035i	$-0.876256\pi$
$829$	−15.7306	+	15.7306i	−0.546348	+	0.546348i	0.379035	+	0.925382i	$0.376256\pi$
$830$	22.8068	+	13.4926i	0.791635	+	0.468333i
$831$	−4.80301	−	2.96150i	−0.166615	−	0.102733i
$832$	−25.4234	+	22.3727i	−0.881398	+	0.775635i
$833$			2.25059i			0.0779782i
$834$	5.34650	+	10.1691i	0.185134	+	0.352126i
$835$	12.1663	+	12.1663i	0.421033	+	0.421033i
$836$	36.7185	−	20.1717i	1.26994	−	0.697653i
$837$	23.1539	+	27.5674i	0.800318	+	0.952870i
$838$	−2.65998	−	10.3665i	−0.0918876	−	0.358104i
$839$		−	32.9766i		−	1.13848i	−0.822171	−	0.569240i	$-0.807238\pi$
$839$		−	32.9766i		−	1.13848i	0.822171	−	0.569240i	$-0.192762\pi$
$840$	−8.02029	+	12.1248i	−0.276726	+	0.418346i
$841$			77.3681i			2.66787i
$842$	26.0051	−	6.67279i	0.896196	−	0.229960i
$843$	−22.2861	+	5.28559i	−0.767573	+	0.182045i
$844$	0.178625	−	0.614137i	0.00614852	−	0.0211395i
$845$	10.3239	+	10.3239i	0.355153	+	0.355153i
$846$	0.683754	−	9.96805i	0.0235080	−	0.342709i
$847$			15.0878i			0.518422i
$848$	−3.67489	−	16.4874i	−0.126196	−	0.566181i
$849$	18.7225	−	30.3645i	0.642556	−	1.04211i
$850$	6.16750	−	10.4251i	0.211543	−	0.357577i
$851$	−13.7884	+	13.7884i	−0.472661	+	0.472661i
$852$	−23.1032	+	20.8936i	−0.791502	+	0.715804i
$853$	−29.7793	−	29.7793i	−1.01963	−	1.01963i	−0.999804	−	0.0198216i	$-0.993690\pi$
$853$	−29.7793	−	29.7793i	−1.01963	−	1.01963i	−0.0198216	−	0.999804i	$-0.506310\pi$
$854$	−1.69161	−	6.59253i	−0.0578857	−	0.225592i
$855$	−32.6213	+	16.3959i	−1.11563	+	0.560727i
$856$	36.3577	+	38.7523i	1.24268	+	1.32453i
$857$	−39.7919			−1.35926			−0.679632	−	0.733553i	$-0.737861\pi$
$857$	−39.7919			−1.35926			−0.679632	+	0.733553i	$0.737861\pi$
$858$	15.7199	−	50.5753i	0.536668	−	1.72661i
$859$	34.6594	−	34.6594i	1.18256	−	1.18256i	0.203486	−	0.979078i	$-0.434773\pi$
$859$	34.6594	−	34.6594i	1.18256	−	1.18256i	0.979078	−	0.203486i	$-0.0652272\pi$
$860$	−4.40145	+	2.41798i	−0.150088	+	0.0824525i
$861$	13.3678	−	3.17043i	0.455572	−	0.108048i
$862$	6.16331	−	10.4180i	0.209923	−	0.354838i
$863$	−1.85172			−0.0630334			−0.0315167	−	0.999503i	$-0.510034\pi$
$863$	−1.85172			−0.0630334			−0.0315167	+	0.999503i	$0.510034\pi$
$864$	−27.0539	−	11.4929i	−0.920393	−	0.390995i
$865$	−33.2373			−1.13010
$866$	−14.4675	+	24.4548i	−0.491626	+	0.831007i
$867$	−20.1138	+	4.77039i	−0.683101	+	0.162011i
$868$	−12.1448	+	6.67188i	−0.412222	+	0.226458i
$869$	19.4105	−	19.4105i	0.658457	−	0.658457i
$870$	−22.2509	+	71.5875i	−0.754376	+	2.42704i
$871$	−46.2085			−1.56571
$872$	23.0940	−	21.6669i	0.782060	−	0.733735i
$873$	10.6915	−	5.37369i	0.361853	−	0.181872i
$874$	9.33473	+	36.3792i	0.315752	+	1.23055i
$875$	−2.50601	−	2.50601i	−0.0847186	−	0.0847186i
$876$	−24.9266	+	22.5426i	−0.842191	+	0.761645i
$877$	−30.4193	+	30.4193i	−1.02719	+	1.02719i	−0.0275654	+	0.999620i	$0.508775\pi$
$877$	−30.4193	+	30.4193i	−1.02719	+	1.02719i	−0.999620	+	0.0275654i	$0.991225\pi$
$878$	5.27320	−	8.91341i	0.177962	−	0.300813i
$879$	7.52748	−	12.2082i	0.253895	−	0.411772i
$880$	32.5161	−	51.1687i	1.09612	−	1.72490i
$881$		−	20.2709i		−	0.682943i	−0.939892	−	0.341472i	$-0.889075\pi$
$881$		−	20.2709i		−	0.682943i	0.939892	−	0.341472i	$-0.110925\pi$
$882$	0.290340	−	4.23269i	0.00977626	−	0.142522i
$883$	8.90246	+	8.90246i	0.299592	+	0.299592i	0.840854	−	0.541262i	$-0.182053\pi$
$883$	8.90246	+	8.90246i	0.299592	+	0.299592i	−0.541262	+	0.840854i	$0.682053\pi$
$884$	−5.32156	+	18.2963i	−0.178984	+	0.615370i
$885$	13.0932	−	3.10530i	0.440122	−	0.104384i
$886$	6.47347	−	1.66106i	0.217480	−	0.0558044i
$887$			8.65599i			0.290640i	0.989385	+	0.145320i	$0.0464211\pi$
$887$			8.65599i			0.290640i	−0.989385	+	0.145320i	$0.953579\pi$
$888$	12.3040	+	8.13882i	0.412896	+	0.273121i
$889$		−	4.24068i		−	0.142228i
$890$	4.95895	+	19.3260i	0.166224	+	0.647808i
$891$	45.4790	−	6.69084i	1.52360	−	0.224152i
$892$	20.6786	−	11.3600i	0.692372	−	0.380362i
$893$	6.82946	+	6.82946i	0.228539	+	0.228539i
$894$	−5.07426	−	9.65126i	−0.169708	−	0.322786i
$895$			16.4092i			0.548497i
$896$	6.36916	−	9.35060i	0.212779	−	0.312382i
$897$	40.4147	+	24.9194i	1.34941	+	0.832034i
$898$	−22.2982	−	13.1917i	−0.744101	−	0.440212i
$899$	−50.5269	+	50.5269i	−1.68517	+	1.68517i
$900$	−12.9441	+	18.8108i	−0.431472	+	0.627028i
$901$	−6.72051	−	6.72051i	−0.223893	−	0.223893i
$902$	−55.4969	+	14.2402i	−1.84784	+	0.474147i
$903$	0.769211	−	1.24752i	0.0255977	−	0.0415148i
$904$	−0.352816	+	11.0667i	−0.0117345	+	0.368072i
$905$	64.4079			2.14099
$906$	0.0667247	−	0.214672i	0.00221678	−	0.00713201i
$907$	−13.2973	+	13.2973i	−0.441528	+	0.441528i	−0.892525	−	0.450997i	$-0.851068\pi$
$907$	−13.2973	+	13.2973i	−0.441528	+	0.441528i	0.450997	+	0.892525i	$0.351068\pi$
$908$	−7.94536	−	2.31095i	−0.263676	−	0.0766915i
$909$	4.78010	−	14.4407i	0.158546	−	0.478968i
$910$	−15.2898	−	9.04548i	−0.506852	−	0.299855i
$911$	−15.5689			−0.515821			−0.257911	−	0.966169i	$-0.583034\pi$
$911$	−15.5689			−0.515821			−0.257911	+	0.966169i	$0.583034\pi$
$912$	25.5582	−	12.4146i	0.846316	−	0.411088i
$913$	32.2516			1.06737
$914$	19.4370	+	11.4990i	0.642917	+	0.380352i
$915$	−5.70824	−	24.0681i	−0.188709	−	0.795668i
$916$	5.12533	−	17.6216i	0.169346	−	0.582233i
$917$	8.30320	−	8.30320i	0.274196	−	0.274196i
$918$	−16.3154	+	2.70635i	−0.538490	+	0.0893230i
$919$	−48.6537			−1.60494			−0.802468	−	0.596695i	$-0.796480\pi$
$919$	−48.6537			−1.60494			−0.802468	+	0.596695i	$0.796480\pi$
$920$	37.1875	+	39.6367i	1.22603	+	1.30678i
$921$	38.2031	+	23.5557i	1.25883	+	0.776188i
$922$	17.9968	−	4.61790i	0.592694	−	0.152082i
$923$	−26.9165	−	26.9165i	−0.885966	−	0.885966i
$924$	−0.887455	+	17.6710i	−0.0291951	+	0.581334i
$925$	8.10348	−	8.10348i	0.266441	−	0.266441i
$926$	9.58968	+	5.67328i	0.315136	+	0.186436i
$927$	21.7819	−	10.9478i	0.715412	−	0.359575i
$928$	18.0706	−	55.4728i	0.593198	−	1.82098i
$929$			36.2749i			1.19014i	0.803673	+	0.595071i	$0.202876\pi$
$929$			36.2749i			1.19014i	−0.803673	+	0.595071i	$0.797124\pi$
$930$	−44.5751	+	23.4358i	−1.46167	+	0.768491i
$931$	2.89997	+	2.89997i	0.0950426	+	0.0950426i
$932$	−15.9602	−	29.0524i	−0.522794	−	0.951642i
$933$	0.205012	+	0.864410i	0.00671180	+	0.0282995i
$934$	−12.7707	−	49.7700i	−0.417871	−	1.62852i
$935$		−	34.1111i		−	1.11555i
$936$	12.3686	−	33.7234i	0.404281	−	1.10228i
$937$		−	28.5931i		−	0.934097i	−0.884232	−	0.467048i	$-0.845317\pi$
$937$		−	28.5931i		−	0.934097i	0.884232	−	0.467048i	$-0.154683\pi$
$938$	14.9527	−	3.83679i	0.488223	−	0.125276i
$939$	8.69506	+	36.6617i	0.283752	+	1.19641i
$940$	13.4206	+	3.90344i	0.437731	+	0.127316i
$941$	14.9722	+	14.9722i	0.488081	+	0.488081i	0.907700	−	0.419620i	$-0.137837\pi$
$941$	14.9722	+	14.9722i	0.488081	+	0.488081i	−0.419620	+	0.907700i	$0.637837\pi$
$942$	10.8948	+	20.7219i	0.354971	+	0.675156i
$943$		−	51.3639i		−	1.67264i
$944$	−10.2215	+	2.27829i	−0.332683	+	0.0741520i
$945$	1.33665	−	15.3612i	0.0434812	−	0.499701i
$946$	−3.11210	+	5.26045i	−0.101183	+	0.171032i
$947$	6.19767	−	6.19767i	0.201397	−	0.201397i	−0.599201	−	0.800598i	$-0.704515\pi$
$947$	6.19767	−	6.19767i	0.201397	−	0.201397i	0.800598	+	0.599201i	$0.204515\pi$
$948$	13.8084	−	12.4878i	0.448476	−	0.405584i
$949$	−29.0408	−	29.0408i	−0.942705	−	0.942705i
$950$	−5.48604	−	21.3801i	−0.177991	−	0.693664i
$951$	34.9010	+	21.5197i	1.13174	+	0.697825i
$952$	0.202839	−	6.36239i	0.00657404	−	0.206206i
$953$	−31.9660			−1.03548			−0.517740	−	0.855538i	$-0.673227\pi$
$953$	−31.9660			−1.03548			−0.517740	+	0.855538i	$0.673227\pi$
$954$	11.7723	+	13.5063i	0.381143	+	0.437282i
$955$	12.7163	−	12.7163i	0.411489	−	0.411489i
$956$	−20.3501	−	37.0432i	−0.658168	−	1.19806i
$957$	21.0553	+	88.7772i	0.680621	+	2.86976i
$958$	20.7776	−	35.1209i	0.671295	−	1.13471i
$959$	5.65752			0.182691
$960$	23.7661	−	33.5539i	0.767047	−	1.08295i
$961$	−17.0026			−0.548470
$962$	−9.17916	+	15.5157i	−0.295948	+	0.500248i
$963$	−53.5060	−	17.7113i	−1.72421	−	0.570739i
$964$	20.3692	+	37.0781i	0.656049	+	1.19421i
$965$	−47.4717	+	47.4717i	−1.52817	+	1.52817i
$966$	−15.1470	−	4.70800i	−0.487346	−	0.151478i
$967$	1.04868			0.0337233			0.0168616	−	0.999858i	$-0.494633\pi$
$967$	1.04868			0.0337233			0.0168616	+	0.999858i	$0.494633\pi$
$968$	1.35982	−	42.6530i	0.0437061	−	1.37092i
$969$	8.39062	−	13.6081i	0.269546	−	0.437154i
$970$	4.16032	+	16.2136i	0.133580	+	0.520586i
$971$	40.0757	+	40.0757i	1.28609	+	1.28609i	0.937141	+	0.348950i	$0.113462\pi$
$971$	40.0757	+	40.0757i	1.28609	+	1.28609i	0.348950	+	0.937141i	$0.386538\pi$
$972$	31.0337	−	2.98506i	0.995406	−	0.0957459i
$973$	3.31656	−	3.31656i	0.106324	−	0.106324i
$974$	21.9289	−	37.0670i	0.702648	−	1.18770i
$975$	−23.7518	−	14.6452i	−0.760665	−	0.469021i
$976$	4.18800	+	18.7895i	0.134055	+	0.601437i
$977$		−	8.03217i		−	0.256972i	−0.991711	−	0.128486i	$-0.958988\pi$
$977$		−	8.03217i		−	0.256972i	0.991711	−	0.128486i	$-0.0410117\pi$
$978$	−24.2281	+	12.7382i	−0.774729	+	0.407322i
$979$	17.1710	+	17.1710i	0.548786	+	0.548786i
$980$	5.69872	+	1.65750i	0.182039	+	0.0529470i
$981$	−10.5548	+	31.8862i	−0.336990	+	1.01805i
$982$	−21.0722	+	5.40702i	−0.672441	+	0.172545i
$983$		−	11.1270i		−	0.354895i	−0.984130	−	0.177447i	$-0.943216\pi$
$983$		−	11.1270i		−	0.354895i	0.984130	−	0.177447i	$-0.0567840\pi$
$984$	−38.0763	+	7.75798i	−1.21383	+	0.247315i
$985$		−	41.3882i		−	1.31874i
$986$	−8.15865	−	31.7958i	−0.259824	−	1.01259i
$987$	−3.96890	+	0.941305i	−0.126332	+	0.0299621i
$988$	16.7184	+	30.4325i	0.531883	+	0.968186i
$989$	−3.87451	−	3.87451i	−0.123202	−	0.123202i
$990$	−4.40055	+	64.1530i	−0.139859	+	2.03892i
$991$		−	0.391696i		−	0.0124426i	−0.999981	−	0.00622132i	$-0.998020\pi$
$991$		−	0.391696i		−	0.0124426i	0.999981	−	0.00622132i	$-0.00198032\pi$
$992$	34.9346	−	17.7668i	1.10917	−	0.564095i
$993$	11.7914	−	19.1234i	0.374187	−	0.606863i
$994$	10.9449	+	6.47503i	0.347151	+	0.205375i
$995$	12.0060	−	12.0060i	0.380615	−	0.380615i
$996$	21.8462	+	1.09714i	0.692225	+	0.0347641i
$997$	31.1336	+	31.1336i	0.986010	+	0.986010i	0.999903	−	0.0138937i	$-0.00442266\pi$
$997$	31.1336	+	31.1336i	0.986010	+	0.986010i	−0.0138937	+	0.999903i	$0.504423\pi$
$998$	8.26808	−	2.12155i	0.261722	−	0.0671565i
$999$	−15.5882	−	1.35640i	−0.493190	−	0.0429147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.d.155.16	yes	48
3.2	odd	2	inner	336.2.s.d.155.9	✓	48
4.3	odd	2		1344.2.s.d.911.22		48
12.11	even	2		1344.2.s.d.911.11		48
16.3	odd	4	inner	336.2.s.d.323.9	yes	48
16.13	even	4		1344.2.s.d.239.11		48
48.29	odd	4		1344.2.s.d.239.22		48
48.35	even	4	inner	336.2.s.d.323.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.9	✓	48	3.2	odd	2	inner
336.2.s.d.155.16	yes	48	1.1	even	1	trivial
336.2.s.d.323.9	yes	48	16.3	odd	4	inner
336.2.s.d.323.16	yes	48	48.35	even	4	inner
1344.2.s.d.239.11		48	16.13	even	4
1344.2.s.d.239.22		48	48.29	odd	4
1344.2.s.d.911.11		48	12.11	even	2
1344.2.s.d.911.22		48	4.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.720078 - 1.21716i) q^{2} +(-1.68530 + 0.399703i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(-2.09830 + 2.09830i) q^{5} +(-0.727043 + 2.33910i) q^{6} +1.00000 q^{7} +(-2.82699 - 0.0901270i) q^{8} +(2.68048 - 1.34724i) q^{9} +O(q^{10})\)	\(q+(0.720078 - 1.21716i) q^{2} +(-1.68530 + 0.399703i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(-2.09830 + 2.09830i) q^{5} +(-0.727043 + 2.33910i) q^{6} +1.00000 q^{7} +(-2.82699 - 0.0901270i) q^{8} +(2.68048 - 1.34724i) q^{9} +(1.04303 + 4.06491i) q^{10} +(3.61163 + 3.61163i) q^{11} +(2.32355 + 2.56927i) q^{12} +(-2.99334 + 2.99334i) q^{13} +(0.720078 - 1.21716i) q^{14} +(2.69756 - 4.37495i) q^{15} +(-2.14535 + 3.37601i) q^{16} +2.25059i q^{17} +(0.290340 - 4.23269i) q^{18} +(2.89997 + 2.89997i) q^{19} +(5.69872 + 1.65750i) q^{20} +(-1.68530 + 0.399703i) q^{21} +(6.99660 - 1.79529i) q^{22} +6.47555i q^{23} +(4.80035 - 0.978065i) q^{24} -3.80569i q^{25} +(1.48795 + 5.79882i) q^{26} +(-3.97891 + 3.34190i) q^{27} +(-0.962977 - 1.75291i) q^{28} +(-7.29274 - 7.29274i) q^{29} +(-3.38258 - 6.43368i) q^{30} -6.92839i q^{31} +(2.56434 + 5.04224i) q^{32} +(-7.53026 - 4.64311i) q^{33} +(2.73933 + 1.62060i) q^{34} +(-2.09830 + 2.09830i) q^{35} +(-4.94282 - 3.40126i) q^{36} +(2.12931 + 2.12931i) q^{37} +(5.61794 - 1.44154i) q^{38} +(3.84823 - 6.24112i) q^{39} +(6.12098 - 5.74275i) q^{40} -7.93197 q^{41} +(-0.727043 + 2.33910i) q^{42} +(-0.598329 + 0.598329i) q^{43} +(2.85293 - 9.80876i) q^{44} +(-2.79753 + 8.45134i) q^{45} +(7.88180 + 4.66290i) q^{46} +2.35501 q^{47} +(2.26616 - 6.54710i) q^{48} +1.00000 q^{49} +(-4.63215 - 2.74039i) q^{50} +(-0.899566 - 3.79292i) q^{51} +(8.12955 + 2.36452i) q^{52} +(-2.98611 + 2.98611i) q^{53} +(1.20251 + 7.24941i) q^{54} -15.1565 q^{55} +(-2.82699 - 0.0901270i) q^{56} +(-6.04644 - 3.72819i) q^{57} +(-14.1278 + 3.62512i) q^{58} +(1.85127 + 1.85127i) q^{59} +(-10.2666 - 0.515596i) q^{60} +(3.40305 - 3.40305i) q^{61} +(-8.43299 - 4.98898i) q^{62} +(2.68048 - 1.34724i) q^{63} +(7.98375 + 0.509577i) q^{64} -12.5618i q^{65} +(-11.0738 + 5.82217i) q^{66} +(7.71856 + 7.71856i) q^{67} +(3.94507 - 2.16726i) q^{68} +(-2.58829 - 10.9132i) q^{69} +(1.04303 + 4.06491i) q^{70} +8.99213i q^{71} +(-7.69910 + 3.56705i) q^{72} +9.70182i q^{73} +(4.12498 - 1.05845i) q^{74} +(1.52115 + 6.41374i) q^{75} +(2.29077 - 7.87597i) q^{76} +(3.61163 + 3.61163i) q^{77} +(-4.82544 - 9.17801i) q^{78} -5.37445i q^{79} +(-2.58229 - 11.5855i) q^{80} +(5.36990 - 7.22248i) q^{81} +(-5.71164 + 9.65451i) q^{82} +(4.46497 - 4.46497i) q^{83} +(2.32355 + 2.56927i) q^{84} +(-4.72240 - 4.72240i) q^{85} +(0.297421 + 1.15911i) q^{86} +(15.2054 + 9.37553i) q^{87} +(-9.88454 - 10.5356i) q^{88} +4.75435 q^{89} +(8.27223 + 9.49067i) q^{90} +(-2.99334 + 2.99334i) q^{91} +(11.3510 - 6.23580i) q^{92} +(2.76930 + 11.6764i) q^{93} +(1.69579 - 2.86644i) q^{94} -12.1700 q^{95} +(-6.33708 - 7.47271i) q^{96} +3.98867 q^{97} +(0.720078 - 1.21716i) q^{98} +(14.5466 + 4.81516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) 48 * q + 6 * q^6 + 48 * q^7	\( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

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