LMFDB - Embedded newform 336.2.s.d.155.9

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			155.9
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.720078 + 1.21716i) q^{2} +(0.399703 - 1.68530i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(2.09830 - 2.09830i) q^{5} +(1.76347 + 1.70005i) q^{6} +1.00000 q^{7} +(2.82699 + 0.0901270i) q^{8} +(-2.68048 - 1.34724i) q^{9} +O(q^{10})$	\(q+(-0.720078 + 1.21716i) q^{2} +(0.399703 - 1.68530i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(2.09830 - 2.09830i) q^{5} +(1.76347 + 1.70005i) 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} +(-3.33908 + 0.922264i) 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} +(3.56996 - 2.29246i) q^{18} +(2.89997 + 2.89997i) q^{19} +(-5.69872 - 1.65750i) q^{20} +(0.399703 - 1.68530i) q^{21} +(6.99660 - 1.79529i) q^{22} -6.47555i q^{23} +(1.28185 - 4.72830i) q^{24} -3.80569i q^{25} +(-1.48795 - 5.79882i) q^{26} +(-3.34190 + 3.97891i) q^{27} +(-0.962977 - 1.75291i) q^{28} +(7.29274 + 7.29274i) q^{29} +(7.26749 - 0.133072i) 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} +(0.219654 + 5.99598i) 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} +(1.76347 + 1.70005i) q^{42} +(-0.598329 + 0.598329i) q^{43} +(-2.85293 + 9.80876i) q^{44} +(-8.45134 + 2.79753i) q^{45} +(7.88180 + 4.66290i) q^{46} -2.35501 q^{47} +(4.83209 + 4.96496i) q^{48} +1.00000 q^{49} +(4.63215 + 2.74039i) q^{50} +(-3.79292 - 0.899566i) q^{51} +(8.12955 + 2.36452i) q^{52} +(2.98611 - 2.98611i) q^{53} +(-2.43656 - 6.93276i) 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} +(-5.07119 + 8.94155i) 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} +(-0.229047 - 12.5090i) q^{66} +(7.71856 + 7.71856i) q^{67} +(-3.94507 + 2.16726i) q^{68} +(-10.9132 - 2.58829i) q^{69} +(1.04303 + 4.06491i) q^{70} -8.99213i q^{71} +(-7.45626 - 4.05021i) q^{72} +9.70182i q^{73} +(-4.12498 + 1.05845i) q^{74} +(-6.41374 - 1.52115i) q^{75} +(2.29077 - 7.87597i) q^{76} +(-3.61163 - 3.61163i) q^{77} +(-10.3675 + 0.189835i) 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} +(-3.33908 + 0.922264i) 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} +(2.68057 - 12.3011i) q^{90} +(-2.99334 + 2.99334i) q^{91} +(-11.3510 + 6.23580i) q^{92} +(-11.6764 - 2.76930i) q^{93} +(1.69579 - 2.86644i) q^{94} +12.1700 q^{95} +(-9.52266 + 2.30629i) q^{96} +3.98867 q^{97} +(-0.720078 + 1.21716i) q^{98} +(4.81516 + 14.5466i) 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
$3$	0.399703	−	1.68530i	0.230768	−	0.973009i
$3$	0.399703	−	1.68530i	0.230768	−	0.973009i
$4$	−0.962977	−	1.75291i	−0.481488	−	0.876453i
$5$	2.09830	−	2.09830i	0.938387	−	0.938387i	−0.0598225	−	0.998209i	$-0.519053\pi$
$5$	2.09830	−	2.09830i	0.938387	−	0.938387i	0.998209	+	0.0598225i	$0.0190535\pi$
$6$	1.76347	+	1.70005i	0.719934	+	0.694043i
$7$	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	$-0.970255\pi$
$11$	−3.61163	−	3.61163i	−1.08895	−	1.08895i	−0.0933108	−	0.995637i	$-0.529745\pi$
$12$	−3.33908	+	0.922264i	−0.963908	+	0.266235i
$13$	−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	$-0.912009\pi$
$17$		−	2.25059i		−	0.545848i	0.962036	−	0.272924i	$-0.0879907\pi$
$18$	3.56996	−	2.29246i	0.841448	−	0.540339i
$19$	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
$21$	0.399703	−	1.68530i	0.0872223	−	0.367763i
$22$	6.99660	−	1.79529i	1.49168	−	0.382758i
$23$		−	6.47555i		−	1.35025i	−0.737706	−	0.675123i	$-0.764091\pi$
$23$		−	6.47555i		−	1.35025i	0.737706	−	0.675123i	$-0.235909\pi$
$24$	1.28185	−	4.72830i	0.261656	−	0.965161i
$25$		−	3.80569i		−	0.761138i
$26$	−1.48795	−	5.79882i	−0.291810	−	1.13724i
$27$	−3.34190	+	3.97891i	−0.643148	+	0.765742i
$28$	−0.962977	−	1.75291i	−0.181985	−	0.331268i
$29$	7.29274	+	7.29274i	1.35423	+	1.35423i	0.880871	+	0.473357i	$0.156958\pi$
$29$	7.29274	+	7.29274i	1.35423	+	1.35423i	0.473357	+	0.880871i	$0.343042\pi$
$30$	7.26749	−	0.133072i	1.32686	−	0.0242956i
$31$		−	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
$36$	0.219654	+	5.99598i	0.0366090	+	0.999330i
$37$	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	$-0.287383\pi$
$41$	7.93197			1.23877			0.619383	+	0.785089i	$0.287383\pi$
$42$	1.76347	+	1.70005i	0.272109	+	0.262324i
$43$	−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
$45$	−8.45134	+	2.79753i	−1.25985	+	0.417031i
$46$	7.88180	+	4.66290i	1.16211	+	0.687507i
$47$	−2.35501			−0.343514			−0.171757	−	0.985139i	$-0.554944\pi$
$47$	−2.35501			−0.343514			−0.171757	+	0.985139i	$0.554944\pi$
$48$	4.83209	+	4.96496i	0.697453	+	0.716631i
$49$	1.00000			0.142857
$50$	4.63215	+	2.74039i	0.655085	+	0.387550i
$51$	−3.79292	−	0.899566i	−0.531115	−	0.125964i
$52$	8.12955	+	2.36452i	1.12737	+	0.327900i
$53$	2.98611	−	2.98611i	0.410174	−	0.410174i	−0.471625	−	0.881799i	$-0.656332\pi$
$53$	2.98611	−	2.98611i	0.410174	−	0.410174i	0.881799	+	0.471625i	$0.156332\pi$
$54$	−2.43656	−	6.93276i	−0.331574	−	0.943429i
$55$	−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	0.576255	−	0.817270i	$-0.304514\pi$
$59$	−1.85127	−	1.85127i	−0.241015	−	0.241015i	−0.817270	+	0.576255i	$0.804514\pi$
$60$	−5.07119	+	8.94155i	−0.654687	+	1.15435i
$61$	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
$66$	−0.229047	−	12.5090i	−0.0281938	−	1.53975i
$67$	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
$69$	−10.9132	−	2.58829i	−1.31380	−	0.311594i
$70$	1.04303	+	4.06491i	0.124666	+	0.485849i
$71$		−	8.99213i		−	1.06717i	−0.845747	−	0.533585i	$-0.820845\pi$
$71$		−	8.99213i		−	1.06717i	0.845747	−	0.533585i	$-0.179155\pi$
$72$	−7.45626	−	4.05021i	−0.878728	−	0.477322i
$73$			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
$75$	−6.41374	−	1.52115i	−0.740594	−	0.175647i
$76$	2.29077	−	7.87597i	0.262769	−	0.903436i
$77$	−3.61163	−	3.61163i	−0.411584	−	0.411584i
$78$	−10.3675	+	0.189835i	−1.17389	+	0.0214946i
$79$		−	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	−0.908336	−	0.418242i	$-0.862646\pi$
$83$	−4.46497	+	4.46497i	−0.490094	+	0.490094i	0.418242	+	0.908336i	$0.362646\pi$
$84$	−3.33908	+	0.922264i	−0.364323	+	0.100627i
$85$	−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	$-0.581082\pi$
$89$	−4.75435			−0.503960			−0.251980	+	0.967732i	$0.581082\pi$
$90$	2.68057	−	12.3011i	0.282557	−	1.29665i
$91$	−2.99334	+	2.99334i	−0.313787	+	0.313787i
$92$	−11.3510	+	6.23580i	−1.18343	+	0.650127i
$93$	−11.6764	−	2.76930i	−1.21079	−	0.287163i
$94$	1.69579	−	2.86644i	0.174908	−	0.295650i
$95$	12.1700			1.24861
$96$	−9.52266	+	2.30629i	−0.971902	+	0.235385i
$97$	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
$99$	4.81516	+	14.5466i	0.483942	+	1.46199i
$100$	−6.67102	+	3.66479i	−0.667102	+	0.366479i
$101$	−3.58534	+	3.58534i	−0.356754	+	0.356754i	−0.862615	−	0.505861i	$-0.831175\pi$
$101$	−3.58534	+	3.58534i	−0.356754	+	0.356754i	0.505861	+	0.862615i	$0.331175\pi$
$102$	3.82611	−	3.96884i	0.378842	−	0.392974i
$103$	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	$0.112472\pi$
$107$	13.2844	+	13.2844i	1.28426	+	1.28426i	0.346034	+	0.938222i	$0.387528\pi$
$108$	10.1928	+	2.02643i	0.980805	+	0.194993i
$109$	−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	$0.0589466\pi$
$113$			3.91465i			0.368259i	−0.982902	+	0.184130i	$0.941053\pi$
$114$	0.183914	+	10.0441i	0.0172251	+	0.940716i
$115$	−13.5876	−	13.5876i	−1.26705	−	1.26705i
$116$	5.76074	−	19.8062i	0.534871	−	1.83896i
$117$	12.0563	−	3.99083i	1.11461	−	0.368952i
$118$	3.58636	−	0.920242i	0.330151	−	0.0847152i
$119$		−	2.25059i		−	0.206311i
$120$	−7.23169	−	12.6111i	−0.660160	−	1.15123i
$121$			15.0878i			1.37161i
$122$	1.69161	+	6.59253i	0.153151	+	0.596860i
$123$	3.17043	−	13.3678i	0.285868	−	1.20533i
$124$	−12.1448	+	6.67188i	−1.09064	+	0.599152i
$125$	2.50601	+	2.50601i	0.224144	+	0.224144i
$126$	3.56996	−	2.29246i	0.318037	−	0.204229i
$127$		−	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	−0.969711	−	0.244256i	$-0.921456\pi$
$131$	−8.30320	+	8.30320i	−0.725454	+	0.725454i	0.244256	+	0.969711i	$0.421456\pi$
$132$	15.3904	+	8.72863i	1.33956	+	0.759730i
$133$	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	$-0.577698\pi$
$137$	−5.65752			−0.483355			−0.241677	+	0.970357i	$0.577698\pi$
$138$	11.0088	−	11.4194i	0.937128	−	0.972087i
$139$	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
$141$	−0.941305	+	3.96890i	−0.0792722	+	0.334242i
$142$	10.9449	+	6.47503i	0.918475	+	0.543372i
$143$	21.6217			1.80809
$144$	10.2989	−	6.15902i	0.858238	−	0.513252i
$145$	30.6047			2.54158
$146$	−11.8087	−	6.98606i	−0.977295	−	0.578171i
$147$	0.399703	−	1.68530i	0.0329669	−	0.139001i
$148$	1.68200	−	5.78294i	0.138259	−	0.475355i
$149$	3.14768	−	3.14768i	0.257868	−	0.257868i	−0.566318	−	0.824187i	$-0.691633\pi$
$149$	3.14768	−	3.14768i	0.257868	−	0.257868i	0.824187	+	0.566318i	$0.191633\pi$
$150$	6.46987	−	6.71122i	0.528263	−	0.547969i
$151$	−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
$156$	7.23433	−	12.7556i	0.579210	−	1.02127i
$157$	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
$162$	−12.6577	+	1.33530i	−0.994482	+	0.104911i
$163$	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
$165$	−6.05811	+	25.5433i	−0.471623	+	1.98855i
$166$	−2.21947	−	8.64972i	−0.172265	−	0.671348i
$167$			5.79819i			0.448677i	0.974511	+	0.224339i	$0.0720222\pi$
$167$			5.79819i			0.448677i	−0.974511	+	0.224339i	$0.927978\pi$
$168$	1.28185	−	4.72830i	0.0988967	−	0.364797i
$169$		−	4.92013i		−	0.378472i
$170$	9.14843	−	2.34744i	0.701652	−	0.180040i
$171$	−3.86635	−	11.6802i	−0.295667	−	0.893211i
$172$	1.62499	+	0.472637i	0.123904	+	0.0360383i
$173$	−7.92007	−	7.92007i	−0.602152	−	0.602152i	0.338731	−	0.940883i	$-0.390002\pi$
$173$	−7.92007	−	7.92007i	−0.602152	−	0.602152i	−0.940883	+	0.338731i	$0.890002\pi$
$174$	0.462501	+	25.2586i	0.0350621	+	1.91485i
$175$		−	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	−0.837971	−	0.545715i	$-0.816258\pi$
$179$	−3.91011	+	3.91011i	−0.292256	+	0.292256i	0.545715	+	0.837971i	$0.316258\pi$
$180$	13.0422	+	12.1204i	0.972111	+	0.903404i
$181$	−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
$186$	11.7786	−	12.2180i	0.863650	−	0.895868i
$187$	−8.12829	+	8.12829i	−0.594400	+	0.594400i
$188$	2.26782	+	4.12811i	0.165398	+	0.301074i
$189$	−3.34190	+	3.97891i	−0.243087	+	0.289423i
$190$	−8.76333	+	14.8129i	−0.635759	+	1.07464i
$191$	6.06029			0.438507			0.219254	−	0.975668i	$-0.429638\pi$
$191$	6.06029			0.438507			0.219254	+	0.975668i	$0.429638\pi$
$192$	4.04992	−	13.2513i	0.292278	−	0.956334i
$193$	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
$195$	21.1704	+	5.02099i	1.51605	+	0.359561i
$196$	−0.962977	−	1.75291i	−0.0687840	−	0.125208i
$197$	9.86233	−	9.86233i	0.702662	−	0.702662i	−0.262319	−	0.964981i	$-0.584487\pi$
$197$	9.86233	−	9.86233i	0.702662	−	0.702662i	0.964981	+	0.262319i	$0.0844874\pi$
$198$	−21.1729	−	4.61385i	−1.50469	−	0.327892i
$199$	−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
$204$	2.07564	+	7.51488i	0.145324	+	0.526147i
$205$	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
$210$	7.26749	−	0.133072i	0.501505	−	0.00918287i
$211$	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
$213$	−15.1544	−	3.59418i	−1.03837	−	0.246269i
$214$	−25.7352	+	6.60352i	−1.75922	+	0.451407i
$215$			2.51094i			0.171245i
$216$	−9.80611	+	10.9472i	−0.667222	+	0.744859i
$217$		−	6.92839i		−	0.470330i
$218$	−3.93529	−	15.3366i	−0.266531	−	1.03872i
$219$	16.3505	+	3.87784i	1.10486	+	0.262040i
$220$	14.5954	+	26.5680i	0.984021	+	1.79121i
$221$	6.73677	+	6.73677i	0.453164	+	0.453164i
$222$	0.135039	+	7.37490i	0.00906323	+	0.494971i
$223$			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	−0.797497	−	0.603323i	$-0.793843\pi$
$227$	−2.92552	+	2.92552i	−0.194173	+	0.194173i	0.603323	+	0.797497i	$0.293843\pi$
$228$	−12.3578	−	7.00868i	−0.818412	−	0.464161i
$229$	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	$-0.682672\pi$
$233$	−16.5738			−1.08579			−0.542894	+	0.839801i	$0.682672\pi$
$234$	−3.82398	+	17.5482i	−0.249982	+	1.14716i
$235$	−4.94151	+	4.94151i	−0.322349	+	0.322349i
$236$	−1.46237	+	5.02783i	−0.0951923	+	0.327284i
$237$	−9.05756	−	2.14818i	−0.588352	−	0.139539i
$238$	2.73933	+	1.62060i	0.177565	+	0.105048i
$239$	−21.1325			−1.36695			−0.683473	−	0.729976i	$-0.739531\pi$
$239$	−21.1325			−1.36695			−0.683473	+	0.729976i	$0.739531\pi$
$240$	20.5571	+	0.278803i	1.32696	+	0.0179966i
$241$	−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
$243$	14.3184	−	6.16305i	0.918526	−	0.395360i
$244$	−9.24228	−	2.68817i	−0.591676	−	0.172092i
$245$	2.09830	−	2.09830i	0.134055	−	0.134055i
$246$	13.9878	+	13.4848i	0.891829	+	0.859757i
$247$	−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	0.0808422	−	0.996727i	$-0.474239\pi$
$251$	−14.5103	−	14.5103i	−0.915885	−	0.915885i	−0.996727	+	0.0808422i	$0.974239\pi$
$252$	0.219654	+	5.99598i	0.0138369	+	0.377711i
$253$	−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	$-0.973437\pi$
$257$		−	2.67255i		−	0.166709i	0.996520	−	0.0833547i	$-0.0265634\pi$
$258$	−2.07233	+	0.0379456i	−0.129017	+	0.00236239i
$259$	2.12931	+	2.12931i	0.132309	+	0.132309i
$260$	22.0197	−	12.0967i	1.36560	−	0.750208i
$261$	−9.72295	−	29.3731i	−0.601835	−	1.81815i
$262$	−4.12741	−	16.0853i	−0.254992	−	0.993754i
$263$			11.9867i			0.739133i	0.929204	+	0.369567i	$0.120494\pi$
$263$			11.9867i			0.739133i	−0.929204	+	0.369567i	$0.879506\pi$
$264$	−21.7065	+	12.4473i	−1.33594	+	0.766081i
$265$		−	12.5315i		−	0.769804i
$266$	−5.61794	+	1.44154i	−0.344458	+	0.0883862i
$267$	−1.90033	+	8.01251i	−0.116298	+	0.490357i
$268$	6.09711	−	20.9627i	0.372440	−	1.28050i
$269$	−8.31377	−	8.31377i	−0.506900	−	0.506900i	0.406674	−	0.913573i	$-0.366689\pi$
$269$	−8.31377	−	8.31377i	−0.506900	−	0.506900i	−0.913573	+	0.406674i	$0.866689\pi$
$270$	−19.6596	−	9.43435i	−1.19645	−	0.574156i
$271$			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
$276$	5.97217	+	21.6223i	0.359482	+	1.30151i
$277$	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	$-0.629059\pi$
$281$	−13.2238			−0.788866			−0.394433	+	0.918925i	$0.629059\pi$
$282$	−4.15299	−	4.00364i	−0.247307	−	0.238413i
$283$	−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
$285$	4.86438	−	20.5101i	0.288141	−	1.21491i
$286$	−15.5693	+	26.3171i	−0.920630	+	1.55616i
$287$	7.93197			0.468210
$288$	0.0805605	+	16.9704i	0.00474707	+	0.999989i
$289$	11.9349			0.702050
$290$	−22.0377	+	37.2509i	−1.29410	+	2.18745i
$291$	1.59428	−	6.72210i	0.0934584	−	0.394057i
$292$	17.0064	−	9.34262i	0.995222	−	0.546736i
$293$	5.85524	−	5.85524i	0.342066	−	0.342066i	−0.515077	−	0.857144i	$-0.672237\pi$
$293$	5.85524	−	5.85524i	0.342066	−	0.342066i	0.857144	+	0.515077i	$0.172237\pi$
$294$	1.76347	+	1.70005i	0.102848	+	0.0991490i
$295$	−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
$300$	3.50985	+	12.7075i	0.202641	+	0.733668i
$301$	−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
$306$	−5.15939	−	8.03451i	−0.294943	−	0.459302i
$307$	−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
$309$	3.24804	−	13.6950i	0.184775	−	0.779081i
$310$	28.1633	−	7.22655i	1.59957	−	0.410440i
$311$			0.512912i			0.0290845i	0.999894	+	0.0145423i	$0.00462911\pi$
$311$			0.512912i			0.0290845i	−0.999894	+	0.0145423i	$0.995371\pi$
$312$	10.3164	+	17.9904i	0.584052	+	1.01851i
$313$		−	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
$315$	−8.45134	+	2.79753i	−0.476179	+	0.157623i
$316$	−9.42090	+	5.17547i	−0.529967	+	0.291143i
$317$	16.7391	+	16.7391i	0.940160	+	0.940160i	0.998308	−	0.0581479i	$-0.0185195\pi$
$317$	16.7391	+	16.7391i	0.940160	+	0.940160i	−0.0581479	+	0.998308i	$0.518520\pi$
$318$	10.3425	−	0.189377i	0.579977	−	0.0106198i
$319$		−	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
$324$	7.48923	−	16.3680i	0.416069	−	0.909333i
$325$	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
$330$	−26.7281	−	25.7669i	−1.47133	−	1.41842i
$331$	−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
$333$	−2.83887	−	8.57623i	−0.155569	−	0.469975i
$334$	−7.05735	−	4.17514i	−0.386161	−	0.228454i
$335$	32.3916			1.76974
$336$	4.83209	+	4.96496i	0.263612	+	0.270861i
$337$	−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
$339$	6.59736	+	1.56470i	0.358320	+	0.0849827i
$340$	−3.73036	+	12.8255i	−0.202307	+	0.695559i
$341$	−25.0228	+	25.0228i	−1.35506	+	1.35506i
$342$	17.0008	+	3.70470i	0.919300	+	0.200327i
$343$	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	0.942403	−	0.334480i	$-0.108561\pi$
$347$	11.3244	+	11.3244i	0.607923	+	0.607923i	−0.334480	+	0.942403i	$0.608561\pi$
$348$	−31.0768	−	17.6252i	−1.66589	−	0.944809i
$349$	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	$0.0393889\pi$
$353$			4.63801i			0.246856i	−0.992354	+	0.123428i	$0.960611\pi$
$354$	−0.117406	−	6.41192i	−0.00624008	−	0.340790i
$355$	−18.8681	−	18.8681i	−1.00142	−	1.00142i
$356$	4.57833	+	8.33392i	0.242651	+	0.441697i
$357$	−3.79292	−	0.899566i	−0.200742	−	0.0476101i
$358$	−1.94366	−	7.57484i	−0.102726	−	0.400342i
$359$		−	33.1630i		−	1.75027i	−0.483876	−	0.875137i	$-0.660771\pi$
$359$		−	33.1630i		−	1.75027i	0.483876	−	0.875137i	$-0.339229\pi$
$360$	−24.1440	+	7.14689i	−1.27250	+	0.376674i
$361$		−	2.18037i		−	0.114756i
$362$	29.7321	−	7.62912i	1.56269	−	0.400978i
$363$	25.4274	+	6.03062i	1.33459	+	0.316525i
$364$	8.12955	+	2.36452i	0.426104	+	0.123935i
$365$	20.3573	+	20.3573i	1.06555	+	1.06555i
$366$	11.7865	−	0.215819i	0.616092	−	0.0112810i
$367$			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
$372$	6.38980	+	23.1344i	0.331296	+	1.19946i
$373$	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
$378$	−2.43656	−	6.93276i	−0.125323	−	0.356583i
$379$	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
$381$	−7.14681	−	1.69501i	−0.366142	−	0.0868380i
$382$	−4.36388	+	7.37637i	−0.223276	+	0.377408i
$383$	−3.46713			−0.177162			−0.0885811	−	0.996069i	$-0.528233\pi$
$383$	−3.46713			−0.177162			−0.0885811	+	0.996069i	$0.528233\pi$
$384$	13.2128	+	14.4714i	0.674263	+	0.738491i
$385$	−15.1565			−0.772449
$386$	−16.2910	+	27.5370i	−0.829190	+	1.40160i
$387$	2.40990	−	0.797715i	0.122502	−	0.0405501i
$388$	−3.84099	−	6.99176i	−0.194997	−	0.354953i
$389$	−12.7879	+	12.7879i	−0.648370	+	0.648370i	−0.952599	−	0.304229i	$-0.901601\pi$
$389$	−12.7879	+	12.7879i	−0.648370	+	0.648370i	0.304229	+	0.952599i	$0.401601\pi$
$390$	−21.3557	+	22.1524i	−1.08139	+	1.12173i
$391$	−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
$396$	20.8620	−	22.4486i	1.04835	−	1.12808i
$397$	−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	$-0.773250\pi$
$401$		−	26.1774i		−	1.30724i	0.756823	−	0.653620i	$-0.226750\pi$
$402$	0.489505	+	26.7334i	0.0244143	+	1.33334i
$403$	20.7390	+	20.7390i	1.03308	+	1.03308i
$404$	9.73735	+	2.83216i	0.484451	+	0.140905i
$405$	26.4225	+	3.88727i	1.31295	+	0.193160i
$406$	−14.1278	+	3.62512i	−0.701151	+	0.179912i
$407$		−	15.3805i		−	0.762385i
$408$	−10.6415	−	2.88491i	−0.526831	−	0.142824i
$409$		−	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
$411$	−2.26133	+	9.53463i	−0.111543	+	0.470309i
$412$	−7.82528	−	14.2444i	−0.385524	−	0.701769i
$413$	−1.85127	−	1.85127i	−0.0910951	−	0.0910951i
$414$	−14.8449	−	23.1175i	−0.729589	−	1.13616i
$415$			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	−0.825631	−	0.564210i	$-0.809181\pi$
$419$	−5.35115	+	5.35115i	−0.261421	+	0.261421i	0.564210	+	0.825631i	$0.309181\pi$
$420$	−5.07119	+	8.94155i	−0.247449	+	0.436303i
$421$	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
$426$	15.2871	−	15.8574i	0.740661	−	0.768291i
$427$	3.40305	−	3.40305i	0.164685	−	0.164685i
$428$	10.4938	−	36.0790i	0.507235	−	1.74394i
$429$	8.64224	−	36.4390i	0.417251	−	1.75929i
$430$	−3.05623	−	1.80807i	−0.147385	−	0.0871931i
$431$	−8.55923			−0.412284			−0.206142	−	0.978522i	$-0.566091\pi$
$431$	−8.55923			−0.412284			−0.206142	+	0.978522i	$0.566091\pi$
$432$	−6.26332	−	19.8184i	−0.301344	−	0.953516i
$433$	−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
$435$	12.2328	−	51.5780i	0.586516	−	2.47298i
$436$	21.5008	+	6.25363i	1.02970	+	0.299494i
$437$	18.7789	−	18.7789i	0.898316	−	0.898316i
$438$	−16.4936	+	17.1089i	−0.788094	+	0.817493i
$439$	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	0.623255	−	0.782019i	$-0.285810\pi$
$443$	−3.34159	−	3.34159i	−0.158764	−	0.158764i	−0.782019	+	0.623255i	$0.785810\pi$
$444$	−9.07370	−	5.14613i	−0.430619	−	0.244225i
$445$	−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	$0.142292\pi$
$449$			18.3198i			0.864565i	−0.901738	+	0.432283i	$0.857708\pi$
$450$	−8.72441	−	13.5862i	−0.411272	−	0.640458i
$451$	−28.6474	−	28.6474i	−1.34895	−	1.34895i
$452$	6.86201	−	3.76972i	0.322762	−	0.177313i
$453$	−0.0366829	+	0.154669i	−0.00172351	+	0.00726699i
$454$	−1.45424	−	5.66743i	−0.0682506	−	0.265986i
$455$			12.5618i			0.588907i
$456$	17.4293	−	9.99462i	0.816199	−	0.468041i
$457$			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
$459$	8.95489	+	7.52123i	0.417978	+	0.351061i
$460$	−10.7332	+	36.9024i	−0.500440	+	1.72058i
$461$	−9.28993	−	9.28993i	−0.432675	−	0.432675i	0.456862	−	0.889537i	$-0.348973\pi$
$461$	−9.28993	−	9.28993i	−0.432675	−	0.432675i	−0.889537	+	0.456862i	$0.848973\pi$
$462$	−0.229047	−	12.5090i	−0.0106562	−	0.581970i
$463$			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	$0.567821\pi$
$467$	−25.6911	+	25.6911i	−1.18884	+	1.18884i	−0.977387	+	0.211457i	$0.932179\pi$
$468$	−18.6055	−	17.2905i	−0.860039	−	0.799253i
$469$	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
$474$	9.13684	−	9.47768i	0.419669	−	0.435324i
$475$	11.0364	−	11.0364i	0.506384	−	0.506384i
$476$	−3.94507	+	2.16726i	−0.180822	+	0.0993363i
$477$	−12.0272	+	3.98120i	−0.550688	+	0.182287i
$478$	15.2170	−	25.7217i	0.696010	−	1.17648i
$479$	−28.8547			−1.31841			−0.659203	−	0.751965i	$-0.729106\pi$
$479$	−28.8547			−1.31841			−0.659203	+	0.751965i	$0.729106\pi$
$480$	−15.1421	+	24.8206i	−0.691138	+	1.13290i
$481$	−12.7475			−0.581234
$482$	15.2314	−	25.7459i	0.693769	−	1.17269i
$483$	−10.9132	−	2.58829i	−0.496570	−	0.117771i
$484$	26.4474	−	14.5292i	1.20216	−	0.660416i
$485$	8.36941	−	8.36941i	0.380035	−	0.380035i
$486$	−2.80893	+	21.8657i	−0.127416	+	0.991849i
$487$	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	0.908587	−	0.417696i	$-0.137162\pi$
$491$	10.8774	+	10.8774i	0.490891	+	0.490891i	−0.417696	+	0.908587i	$0.637162\pi$
$492$	−26.4855	+	7.31537i	−1.19406	+	0.329802i
$493$	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
$498$	−15.4645	+	0.283165i	−0.692981	+	0.0126889i
$499$	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
$501$	9.77169	+	2.31755i	0.436567	+	0.103541i
$502$	28.1100	−	7.21290i	1.25461	−	0.321927i
$503$		−	22.9449i		−	1.02306i	−0.859265	−	0.511531i	$-0.829079\pi$
$503$		−	22.9449i		−	1.02306i	0.859265	−	0.511531i	$-0.170921\pi$
$504$	−7.45626	−	4.05021i	−0.332128	−	0.180411i
$505$			15.0462i			0.669547i
$506$	−11.6255	−	45.3068i	−0.516817	−	2.01413i
$507$	−8.29190	−	1.96659i	−0.368256	−	0.0873393i
$508$	−7.43350	+	4.08367i	−0.329808	+	0.181184i
$509$	−11.5174	−	11.5174i	−0.510499	−	0.510499i	0.404180	−	0.914679i	$-0.367557\pi$
$509$	−11.5174	−	11.5174i	−0.510499	−	0.510499i	−0.914679	+	0.404180i	$0.867557\pi$
$510$	−0.299491	−	16.3561i	−0.0132617	−	0.724261i
$511$			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
$516$	1.44605	−	2.54968i	0.0636588	−	0.112244i
$517$	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	$-0.489732\pi$
$521$	1.47241			0.0645073			0.0322536	+	0.999480i	$0.489732\pi$
$522$	42.7531	+	9.31646i	1.87125	+	0.407770i
$523$	−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
$525$	−6.41374	−	1.52115i	−0.279918	−	0.0663882i
$526$	−14.5898	−	8.63138i	−0.636146	−	0.376346i
$527$	−15.5929			−0.679239
$528$	0.479881	−	35.3834i	0.0208841	−	1.53986i
$529$	−18.9327			−0.823162
$530$	15.2529	+	9.02365i	0.662543	+	0.391962i
$531$	2.46818	+	7.45639i	0.107110	+	0.323580i
$532$	2.29077	−	7.87597i	0.0993174	−	0.341467i
$533$	−23.7431	+	23.7431i	−1.02843	+	1.02843i
$534$	−8.38415	−	8.08264i	−0.362818	−	0.349770i
$535$	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
$540$	25.6396	−	17.1355i	1.10335	−	0.737395i
$541$	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
$546$	−10.3675	+	0.189835i	−0.443687	+	0.00812420i
$547$	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
$549$	−13.7065	+	4.53707i	−0.584980	+	0.193638i
$550$	−6.83233	−	26.6269i	−0.291332	−	1.13538i
$551$			42.2974i			1.80193i
$552$	−30.6184	−	8.30066i	−1.30320	−	0.353300i
$553$		−	5.37445i		−	0.228545i
$554$	−4.46263	+	1.14509i	−0.189599	+	0.0486501i
$555$	3.57168	−	15.0596i	0.151609	−	0.639243i
$556$	−9.00739	−	2.61985i	−0.381998	−	0.111106i
$557$	11.3149	+	11.3149i	0.479426	+	0.479426i	0.904948	−	0.425522i	$-0.139909\pi$
$557$	11.3149	+	11.3149i	0.479426	+	0.479426i	−0.425522	+	0.904948i	$0.639909\pi$
$558$	−15.8831	−	24.7341i	−0.672384	−	1.04708i
$559$		−	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	−0.826094	−	0.563532i	$-0.809442\pi$
$563$	−6.22999	+	6.22999i	−0.262563	+	0.262563i	0.563532	+	0.826094i	$0.309442\pi$
$564$	7.86357	−	2.17194i	0.331116	−	0.0914553i
$565$	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	$-0.198452\pi$
$569$	38.7320			1.62373			0.811865	+	0.583845i	$0.198452\pi$
$570$	21.4614	+	20.6896i	0.898919	+	0.866592i
$571$	−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
$573$	2.42232	−	10.2134i	0.101194	−	0.426671i
$574$	−5.71164	+	9.65451i	−0.238399	+	0.402972i
$575$	−24.6439			−1.02772
$576$	−20.7137	−	12.1219i	−0.863072	−	0.505080i
$577$	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
$579$	9.04285	−	38.1281i	0.375808	−	1.58455i
$580$	−29.4716	−	53.6470i	−1.22374	−	2.22757i
$581$	−4.46497	+	4.46497i	−0.185238	+	0.185238i
$582$	7.03390	+	6.78094i	0.291564	+	0.281079i
$583$	−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	0.994378	−	0.105892i	$-0.0337697\pi$
$587$	21.5263	+	21.5263i	0.888486	+	0.888486i	−0.105892	+	0.994378i	$0.533770\pi$
$588$	−3.33908	+	0.922264i	−0.137701	+	0.0380335i
$589$	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	$-0.827292\pi$
$593$		−	25.1477i		−	1.03269i	0.856380	−	0.516347i	$-0.172708\pi$
$594$	−16.2386	+	33.8385i	−0.666278	+	1.38841i
$595$	−4.72240	−	4.72240i	−0.193599	−	0.193599i
$596$	−8.54873	−	2.48644i	−0.350170	−	0.101849i
$597$	−2.28701	+	9.64290i	−0.0936010	+	0.394658i
$598$	−37.5505	+	9.63527i	−1.53555	+	0.394016i
$599$		−	18.5702i		−	0.758758i	−0.925241	−	0.379379i	$-0.876138\pi$
$599$		−	18.5702i		−	0.758758i	0.925241	−	0.379379i	$-0.123862\pi$
$600$	−17.9945	−	4.87832i	−0.734621	−	0.199156i
$601$			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
$603$	−10.2907	−	31.0881i	−0.419068	−	1.26601i
$604$	0.0883776	+	0.160874i	0.00359603	+	0.00654585i
$605$	31.6586	+	31.6586i	1.28710	+	1.28710i
$606$	−12.4179	+	0.227380i	−0.504442	+	0.00923667i
$607$		−	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
$612$	13.4945	−	0.494351i	0.545482	−	0.0199829i
$613$	−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	$-0.418180\pi$
$617$	12.6296			0.508449			0.254224	+	0.967145i	$0.418180\pi$
$618$	14.3302	+	13.8149i	0.576445	+	0.555715i
$619$	−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
$621$	25.7656	+	21.6406i	1.03394	+	0.868407i
$622$	−0.624298	−	0.369336i	−0.0250320	−	0.0148090i
$623$	−4.75435			−0.190479
$624$	−29.3259	−	0.397728i	−1.17398	−	0.0159219i
$625$	29.5452			1.18181
$626$	26.4779	+	15.6644i	1.05827	+	0.626076i
$627$	−35.3024	−	8.37267i	−1.40984	−	0.334372i
$628$	−18.3547	−	5.33856i	−0.732433	−	0.213032i
$629$	4.79219	−	4.79219i	0.191077	−	0.191077i
$630$	2.68057	−	12.3011i	0.106796	−	0.490087i
$631$	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
$636$	−7.21688	+	12.7248i	−0.286168	+	0.504573i
$637$	−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	$0.205974\pi$
$641$			30.5266i			1.20573i	−0.797844	+	0.602865i	$0.794026\pi$
$642$	0.842491	+	46.0110i	0.0332505	+	1.81591i
$643$	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
$645$	4.23170	+	1.00363i	0.166623	+	0.0395179i
$646$	3.24430	+	12.6437i	0.127645	+	0.497458i
$647$		−	16.1967i		−	0.636757i	−0.947964	−	0.318378i	$-0.896862\pi$
$647$		−	16.1967i		−	0.636757i	0.947964	−	0.318378i	$-0.103138\pi$
$648$	14.5297	+	20.9019i	0.570781	+	0.821102i
$649$			13.3722i			0.524906i
$650$	−22.0685	+	5.66267i	−0.865598	+	0.222108i
$651$	−11.6764	−	2.76930i	−0.457635	−	0.108537i
$652$	6.24186	−	21.4604i	0.244450	−	0.840453i
$653$	1.12882	+	1.12882i	0.0441741	+	0.0441741i	0.728849	−	0.684675i	$-0.240056\pi$
$653$	1.12882	+	1.12882i	0.0441741	+	0.0441741i	−0.684675	+	0.728849i	$0.740056\pi$
$654$	−27.4197	+	0.502072i	−1.07219	+	0.0196326i
$655$			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	$0.514774\pi$
$659$	−26.8344	+	26.8344i	−1.04532	+	1.04532i	−0.998923	+	0.0463963i	$0.985226\pi$
$660$	50.6089	−	13.9783i	1.96995	−	0.544106i
$661$	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
$666$	12.4829	+	2.72018i	0.483702	+	0.105405i
$667$	47.2245	−	47.2245i	1.82854	−	1.82854i
$668$	10.1637	−	5.58352i	0.393244	−	0.216033i
$669$	19.8811	+	4.71520i	0.768648	+	0.182300i
$670$	−23.3245	+	39.4259i	−0.901103	+	1.52316i
$671$	−24.5811			−0.948944
$672$	−9.52266	+	2.30629i	−0.367345	+	0.0889671i
$673$	−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
$675$	15.1425	+	12.7182i	0.582836	+	0.489525i
$676$	−8.62452	+	4.73797i	−0.331712	+	0.182230i
$677$	−13.0898	+	13.0898i	−0.503080	+	0.503080i	−0.912394	−	0.409314i	$-0.865768\pi$
$677$	−13.0898	+	13.0898i	−0.503080	+	0.503080i	0.409314	+	0.912394i	$0.365768\pi$
$678$	−6.65511	+	6.90337i	−0.255588	+	0.265122i
$679$	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	$-0.921236\pi$
$683$	−31.7392	−	31.7392i	−1.21447	−	1.21447i	−0.244927	−	0.969541i	$-0.578764\pi$
$684$	−16.7512	+	18.0251i	−0.640496	+	0.689208i
$685$	−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
$690$	−0.861717	−	47.0610i	−0.0328050	−	1.79158i
$691$	−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
$693$	4.81516	+	14.5466i	0.182913	+	0.552580i
$694$	−21.9380	+	5.62918i	−0.832756	+	0.213681i
$695$		−	13.9183i		−	0.527949i
$696$	43.8305	−	25.1341i	1.66139	−	0.952706i
$697$		−	17.8516i		−	0.676177i
$698$	9.58845	+	37.3680i	0.362928	+	1.41440i
$699$	−6.62461	+	27.9319i	−0.250566	+	1.05648i
$700$	−6.67102	+	3.66479i	−0.252141	+	0.138516i
$701$	4.04020	+	4.04020i	0.152596	+	0.152596i	0.779276	−	0.626680i	$-0.215587\pi$
$701$	4.04020	+	4.04020i	0.152596	+	0.152596i	−0.626680	+	0.779276i	$0.715587\pi$
$702$	28.0455	+	13.4586i	1.05851	+	0.507963i
$703$			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
$708$	7.88890	+	4.47418i	0.296483	+	0.168150i
$709$	−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
$714$	3.82611	−	3.96884i	0.143189	−	0.148530i
$715$	45.3686	−	45.3686i	1.69669	−	1.69669i
$716$	10.6194	+	3.08871i	0.396866	+	0.115431i
$717$	−8.44671	+	35.6146i	−0.315448	+	1.33005i
$718$	40.3648	+	23.8799i	1.50640	+	0.891190i
$719$	11.2872			0.420942			0.210471	−	0.977600i	$-0.432500\pi$
$719$	11.2872			0.420942			0.210471	+	0.977600i	$0.432500\pi$
$720$	8.68661	−	34.5335i	0.323731	−	1.28699i
$721$	8.12614			0.302633
$722$	2.65386	+	1.57003i	0.0987665	+	0.0584306i
$723$	−8.45466	+	35.6481i	−0.314432	+	1.32577i
$724$	−12.1236	+	41.6825i	−0.450569	+	1.54912i
$725$	27.7539	−	27.7539i	1.03075	−	1.03075i
$726$	−25.6500	+	26.6068i	−0.951959	+	0.987472i
$727$	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
$732$	−8.22453	+	14.5016i	−0.303987	+	0.535993i
$733$	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
$738$	28.3168	−	18.1837i	1.04236	−	0.669353i
$739$	−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
$741$	−6.93931	+	29.2588i	−0.254922	+	1.07485i
$742$	1.48436	+	5.78482i	0.0544925	+	0.212368i
$743$		−	15.1890i		−	0.557230i	−0.960403	−	0.278615i	$-0.910125\pi$
$743$		−	15.1890i		−	0.557230i	0.960403	−	0.278615i	$-0.0898753\pi$
$744$	−32.7595	−	8.88114i	−1.20102	−	0.325598i
$745$		−	13.2095i		−	0.483960i
$746$	−7.87814	+	2.02149i	−0.288439	+	0.0740120i
$747$	17.9836	−	5.95286i	0.657986	−	0.217804i
$748$	22.0755	+	6.42077i	0.807159	+	0.234767i
$749$	13.2844	+	13.2844i	0.485403	+	0.485403i
$750$	0.158930	+	8.67962i	0.00580329	+	0.316935i
$751$			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
$756$	10.1928	+	2.02643i	0.370709	+	0.0737004i
$757$	−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	$-0.750753\pi$
$761$	−39.1050			−1.41755			−0.708777	+	0.705432i	$0.750753\pi$
$762$	7.20936	−	7.47831i	0.261168	−	0.270910i
$763$	−7.91670	+	7.91670i	−0.286604	+	0.286604i
$764$	−5.83592	−	10.6231i	−0.211136	−	0.384331i
$765$	6.29608	+	19.0205i	0.227635	+	0.687687i
$766$	2.49661	−	4.22007i	0.0902060	−	0.152477i
$767$	11.0830			0.400182
$768$	−27.1283	+	5.66161i	−0.978909	+	0.204296i
$769$	−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
$771$	−4.50406	−	1.06823i	−0.162210	−	0.0384713i
$772$	−21.7863	−	39.6576i	−0.784107	−	1.42731i
$773$	−26.3266	+	26.3266i	−0.946901	+	0.946901i	−0.998660	−	0.0517586i	$-0.983517\pi$
$773$	−26.3266	+	26.3266i	−0.946901	+	0.946901i	0.0517586	+	0.998660i	$0.483517\pi$
$774$	−0.764365	+	3.50766i	−0.0274745	+	0.126080i
$775$	−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
$780$	−11.5853	−	41.9449i	−0.414821	−	1.50187i
$781$	−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
$786$	−28.7583	+	0.526583i	−1.02578	+	0.0187826i
$787$	−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
$789$	20.2012	+	4.79113i	0.719183	+	0.170569i
$790$	21.8466	−	5.60574i	0.777268	−	0.199443i
$791$			3.91465i			0.139189i
$792$	12.3014	+	41.5571i	0.437110	+	1.47667i
$793$			20.3730i			0.723465i
$794$	−9.39182	−	36.6017i	−0.333303	−	1.29895i
$795$	−21.1193	−	5.00888i	−0.749026	−	0.177647i
$796$	5.50993	+	10.0297i	0.195294	+	0.355494i
$797$	24.3789	+	24.3789i	0.863543	+	0.863543i	0.991748	−	0.128205i	$-0.0409214\pi$
$797$	24.3789	+	24.3789i	0.863543	+	0.863543i	−0.128205	+	0.991748i	$0.540921\pi$
$798$	0.183914	+	10.0441i	0.00651049	+	0.355557i
$799$			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
$804$	−32.8914	−	18.6543i	−1.15999	−	0.657886i
$805$	−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	$-0.313259\pi$
$809$	31.4911			1.10717			0.553585	+	0.832793i	$0.313259\pi$
$810$	−23.7577	+	29.3614i	−0.834761	+	1.03166i
$811$	−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
$813$	29.7443	+	7.05445i	1.04318	+	0.247410i
$814$	18.7206	+	11.0752i	0.656158	+	0.388185i
$815$	33.1607			1.16157
$816$	11.1741	−	10.8750i	0.391171	−	0.380703i
$817$	−3.47027			−0.121409
$818$	25.6771	+	15.1907i	0.897780	+	0.531129i
$819$	12.0563	−	3.99083i	0.421281	−	0.139451i
$820$	−45.2021	−	13.1473i	−1.57853	−	0.459123i
$821$	8.59531	−	8.59531i	0.299979	−	0.299979i	−0.541027	−	0.841005i	$-0.681964\pi$
$821$	8.59531	−	8.59531i	0.299979	−	0.299979i	0.841005	+	0.541027i	$0.181964\pi$
$822$	−9.97688	−	9.61808i	−0.347983	−	0.335469i
$823$	−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	0.557896	−	0.829911i	$-0.311609\pi$
$827$	−7.82252	−	7.82252i	−0.272016	−	0.272016i	−0.829911	+	0.557896i	$0.811609\pi$
$828$	38.8272	−	1.42238i	1.34934	−	0.0494312i
$829$	−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
$834$	11.4870	−	0.210334i	0.397761	−	0.00728327i
$835$	12.1663	+	12.1663i	0.421033	+	0.421033i
$836$	−36.7185	+	20.1717i	−1.26994	+	0.697653i
$837$	27.5674	+	23.1539i	0.952870	+	0.800318i
$838$	−2.65998	−	10.3665i	−0.0918876	−	0.358104i
$839$			32.9766i			1.13848i	0.822171	+	0.569240i	$0.192762\pi$
$839$			32.9766i			1.13848i	−0.822171	+	0.569240i	$0.807238\pi$
$840$	−7.23169	−	12.6111i	−0.249517	−	0.435124i
$841$			77.3681i			2.66787i
$842$	−26.0051	+	6.67279i	−0.896196	+	0.229960i
$843$	−5.28559	+	22.2861i	−0.182045	+	0.767573i
$844$	0.178625	−	0.614137i	0.00614852	−	0.0211395i
$845$	−10.3239	−	10.3239i	−0.355153	−	0.355153i
$846$	−8.40730	+	5.39878i	−0.289049	+	0.185614i
$847$			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
$852$	8.29312	+	30.0254i	0.284118	+	1.02865i
$853$	−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	$-0.262139\pi$
$857$	39.7919			1.35926			0.679632	+	0.733553i	$0.262139\pi$
$858$	38.1291	+	36.7579i	1.30171	+	1.25489i
$859$	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
$861$	3.17043	−	13.3678i	0.108048	−	0.455572i
$862$	6.16331	−	10.4180i	0.209923	−	0.354838i
$863$	1.85172			0.0630334			0.0315167	−	0.999503i	$-0.489966\pi$
$863$	1.85172			0.0630334			0.0315167	+	0.999503i	$0.489966\pi$
$864$	28.6324	+	6.64734i	0.974093	+	0.226147i
$865$	−33.2373			−1.13010
$866$	14.4675	−	24.4548i	0.491626	−	0.831007i
$867$	4.77039	−	20.1138i	0.162011	−	0.683101i
$868$	−12.1448	+	6.67188i	−0.412222	+	0.226458i
$869$	−19.4105	+	19.4105i	−0.658457	+	0.658457i
$870$	53.9704	+	52.0295i	1.82977	+	1.76396i
$871$	−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
$876$	−8.94764	−	32.3951i	−0.302313	−	1.09453i
$877$	−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	$0.110925\pi$
$881$			20.2709i			0.682943i	−0.939892	+	0.341472i	$0.889075\pi$
$882$	3.56996	−	2.29246i	0.120207	−	0.0771912i
$883$	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
$885$	−3.10530	+	13.0932i	−0.104384	+	0.440122i
$886$	6.47347	−	1.66106i	0.217480	−	0.0558044i
$887$		−	8.65599i		−	0.290640i	−0.989385	−	0.145320i	$-0.953579\pi$
$887$		−	8.65599i		−	0.290640i	0.989385	−	0.145320i	$-0.0464211\pi$
$888$	12.7975	−	7.33856i	0.429454	−	0.246266i
$889$		−	4.24068i		−	0.142228i
$890$	−4.95895	−	19.3260i	−0.166224	−	0.647808i
$891$	6.69084	−	45.4790i	0.224152	−	1.52360i
$892$	20.6786	−	11.3600i	0.692372	−	0.380362i
$893$	−6.82946	−	6.82946i	−0.228539	−	0.228539i
$894$	10.9021	−	0.199624i	0.364620	−	0.00667642i
$895$			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
$900$	22.8188	−	0.835936i	0.760628	−	0.0278645i
$901$	−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
$906$	−0.161843	−	0.156023i	−0.00537688	−	0.00518351i
$907$	−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
$909$	14.4407	−	4.78010i	0.478968	−	0.158546i
$910$	−15.2898	−	9.04548i	−0.506852	−	0.299855i
$911$	15.5689			0.515821			0.257911	−	0.966169i	$-0.416966\pi$
$911$	15.5689			0.515821			0.257911	+	0.966169i	$0.416966\pi$
$912$	−0.385322	+	28.4112i	−0.0127593	+	0.940787i
$913$	32.2516			1.06737
$914$	−19.4370	−	11.4990i	−0.642917	−	0.380352i
$915$	−24.0681	−	5.70824i	−0.795668	−	0.188709i
$916$	5.12533	−	17.6216i	0.169346	−	0.582233i
$917$	−8.30320	+	8.30320i	−0.274196	+	0.274196i
$918$	−15.6028	+	5.48370i	−0.514969	+	0.180989i
$919$	−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
$924$	15.3904	+	8.72863i	0.506307	+	0.287151i
$925$	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	$-0.797124\pi$
$929$		−	36.2749i		−	1.19014i	0.803673	−	0.595071i	$-0.202876\pi$
$930$	−0.921978	−	50.3520i	−0.0302328	−	1.65111i
$931$	2.89997	+	2.89997i	0.0950426	+	0.0950426i
$932$	15.9602	+	29.0524i	0.522794	+	0.951642i
$933$	0.864410	+	0.205012i	0.0282995	+	0.00671180i
$934$	−12.7707	−	49.7700i	−0.417871	−	1.62852i
$935$			34.1111i			1.11555i
$936$	34.4427	−	10.1954i	1.12580	−	0.333248i
$937$		−	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
$939$	−36.6617	−	8.69506i	−1.19641	−	0.283752i
$940$	13.4206	+	3.90344i	0.437731	+	0.127316i
$941$	−14.9722	−	14.9722i	−0.488081	−	0.488081i	0.419620	−	0.907700i	$-0.362163\pi$
$941$	−14.9722	−	14.9722i	−0.488081	−	0.488081i	−0.907700	+	0.419620i	$0.862163\pi$
$942$	23.4075	−	0.428606i	0.762657	−	0.0139647i
$943$		−	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	−0.800598	−	0.599201i	$-0.795485\pi$
$947$	−6.19767	+	6.19767i	−0.201397	+	0.201397i	0.599201	+	0.800598i	$0.295485\pi$
$948$	4.95666	+	17.9457i	0.160985	+	0.582849i
$949$	−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	$-0.326773\pi$
$953$	31.9660			1.03548			0.517740	+	0.855538i	$0.326773\pi$
$954$	3.81476	−	17.5059i	0.123507	−	0.566773i
$955$	12.7163	−	12.7163i	0.411489	−	0.411489i
$956$	20.3501	+	37.0432i	0.658168	+	1.19806i
$957$	−88.7772	−	21.0553i	−2.86976	−	0.680621i
$958$	20.7776	−	35.1209i	0.671295	−	1.13471i
$959$	−5.65752			−0.182691
$960$	−19.3073	−	36.3032i	−0.623141	−	1.17168i
$961$	−17.0026			−0.548470
$962$	9.17916	−	15.5157i	0.295948	−	0.500248i
$963$	−17.7113	−	53.5060i	−0.570739	−	1.72421i
$964$	20.3692	+	37.0781i	0.656049	+	1.19421i
$965$	47.4717	−	47.4717i	1.52817	−	1.52817i
$966$	11.0088	−	11.4194i	0.354201	−	0.367414i
$967$	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	$-0.886538\pi$
$971$	−40.0757	−	40.0757i	−1.28609	−	1.28609i	−0.348950	−	0.937141i	$-0.613462\pi$
$972$	−24.5915	−	19.1639i	−0.788774	−	0.614684i
$973$	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	$0.0410117\pi$
$977$			8.03217i			0.256972i	−0.991711	+	0.128486i	$0.958988\pi$
$978$	0.501127	+	27.3681i	0.0160243	+	0.875134i
$979$	17.1710	+	17.1710i	0.548786	+	0.548786i
$980$	−5.69872	−	1.65750i	−0.182039	−	0.0529470i
$981$	31.8862	−	10.5548i	1.01805	−	0.336990i
$982$	−21.0722	+	5.40702i	−0.672441	+	0.172545i
$983$			11.1270i			0.354895i	0.984130	+	0.177447i	$0.0567840\pi$
$983$			11.1270i			0.354895i	−0.984130	+	0.177447i	$0.943216\pi$
$984$	10.1676	−	37.5048i	0.324130	−	1.19561i
$985$		−	41.3882i		−	1.31874i
$986$	8.15865	+	31.7958i	0.259824	+	1.01259i
$987$	−0.941305	+	3.96890i	−0.0299621	+	0.126332i
$988$	16.7184	+	30.4325i	0.531883	+	0.968186i
$989$	3.87451	+	3.87451i	0.123202	+	0.123202i
$990$	−54.1083	+	34.7458i	−1.71967	+	1.10429i
$991$		−	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
$996$	10.7910	−	19.0267i	0.341925	−	0.602885i
$997$	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.155.9	✓	48
3.2	odd	2	inner	336.2.s.d.155.16	yes	48
4.3	odd	2		1344.2.s.d.911.11		48
12.11	even	2		1344.2.s.d.911.22		48
16.3	odd	4	inner	336.2.s.d.323.16	yes	48
16.13	even	4		1344.2.s.d.239.22		48
48.29	odd	4		1344.2.s.d.239.11		48
48.35	even	4	inner	336.2.s.d.323.9	yes	48

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

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

\(f(q)\)	\(=\)	\(q+(-0.720078 + 1.21716i) q^{2} +(0.399703 - 1.68530i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(2.09830 - 2.09830i) q^{5} +(1.76347 + 1.70005i) q^{6} +1.00000 q^{7} +(2.82699 + 0.0901270i) q^{8} +(-2.68048 - 1.34724i) q^{9} +O(q^{10})\)	\(q+(-0.720078 + 1.21716i) q^{2} +(0.399703 - 1.68530i) q^{3} +(-0.962977 - 1.75291i) q^{4} +(2.09830 - 2.09830i) q^{5} +(1.76347 + 1.70005i) 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} +(-3.33908 + 0.922264i) 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} +(3.56996 - 2.29246i) q^{18} +(2.89997 + 2.89997i) q^{19} +(-5.69872 - 1.65750i) q^{20} +(0.399703 - 1.68530i) q^{21} +(6.99660 - 1.79529i) q^{22} -6.47555i q^{23} +(1.28185 - 4.72830i) q^{24} -3.80569i q^{25} +(-1.48795 - 5.79882i) q^{26} +(-3.34190 + 3.97891i) q^{27} +(-0.962977 - 1.75291i) q^{28} +(7.29274 + 7.29274i) q^{29} +(7.26749 - 0.133072i) 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} +(0.219654 + 5.99598i) 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} +(1.76347 + 1.70005i) q^{42} +(-0.598329 + 0.598329i) q^{43} +(-2.85293 + 9.80876i) q^{44} +(-8.45134 + 2.79753i) q^{45} +(7.88180 + 4.66290i) q^{46} -2.35501 q^{47} +(4.83209 + 4.96496i) q^{48} +1.00000 q^{49} +(4.63215 + 2.74039i) q^{50} +(-3.79292 - 0.899566i) q^{51} +(8.12955 + 2.36452i) q^{52} +(2.98611 - 2.98611i) q^{53} +(-2.43656 - 6.93276i) 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} +(-5.07119 + 8.94155i) 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} +(-0.229047 - 12.5090i) q^{66} +(7.71856 + 7.71856i) q^{67} +(-3.94507 + 2.16726i) q^{68} +(-10.9132 - 2.58829i) q^{69} +(1.04303 + 4.06491i) q^{70} -8.99213i q^{71} +(-7.45626 - 4.05021i) q^{72} +9.70182i q^{73} +(-4.12498 + 1.05845i) q^{74} +(-6.41374 - 1.52115i) q^{75} +(2.29077 - 7.87597i) q^{76} +(-3.61163 - 3.61163i) q^{77} +(-10.3675 + 0.189835i) 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} +(-3.33908 + 0.922264i) 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} +(2.68057 - 12.3011i) q^{90} +(-2.99334 + 2.99334i) q^{91} +(-11.3510 + 6.23580i) q^{92} +(-11.6764 - 2.76930i) q^{93} +(1.69579 - 2.86644i) q^{94} +12.1700 q^{95} +(-9.52266 + 2.30629i) q^{96} +3.98867 q^{97} +(-0.720078 + 1.21716i) q^{98} +(4.81516 + 14.5466i) 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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