LMFDB - Embedded newform 840.2.cf.a.341.73

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(101,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.73
Character	$\chi$	$=$	840.341
Dual form			840.2.cf.a.101.73

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.331098 + 1.37491i) q^{2} +(-0.303127 + 1.70532i) q^{3} +(-1.78075 + 0.910460i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.44502 + 0.147856i) q^{6} +(-2.64480 - 0.0708975i) q^{7} +(-1.84140 - 2.14691i) q^{8} +(-2.81623 - 1.03386i) q^{9} +(-0.400715 + 1.35626i) q^{10} +(-0.735536 - 1.27399i) q^{11} +(-1.01283 - 3.31273i) q^{12} +1.58306 q^{13} +(-0.778212 - 3.65983i) q^{14} +(-1.11518 + 1.32529i) q^{15} +(2.34213 - 3.24260i) q^{16} +(-2.77818 - 4.81195i) q^{17} +(0.489012 - 4.21436i) q^{18} +(-2.80571 + 4.85963i) q^{19} +(-1.99740 - 0.101893i) q^{20} +(0.922615 - 4.48874i) q^{21} +(1.50808 - 1.43311i) q^{22} +(-1.32154 - 0.762994i) q^{23} +(4.21935 - 2.48939i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.524149 + 2.17656i) q^{26} +(2.61673 - 4.48918i) q^{27} +(4.77427 - 2.28173i) q^{28} -5.28450 q^{29} +(-2.19138 - 1.09446i) q^{30} +(0.436649 - 0.252099i) q^{31} +(5.23375 + 2.14659i) q^{32} +(2.39551 - 0.868143i) q^{33} +(5.69614 - 5.41297i) q^{34} +(-2.25502 - 1.38380i) q^{35} +(5.95628 - 0.723022i) q^{36} +(-0.430562 - 0.248585i) q^{37} +(-7.61052 - 2.24858i) q^{38} +(-0.479869 + 2.69962i) q^{39} +(-0.521244 - 2.77998i) q^{40} +2.40233 q^{41} +(6.47708 - 0.217703i) q^{42} -0.257653i q^{43} +(2.46972 + 1.59897i) q^{44} +(-1.92200 - 2.30346i) q^{45} +(0.611486 - 2.06963i) q^{46} +(-5.41938 + 9.38664i) q^{47} +(4.81970 + 4.97699i) q^{48} +(6.98995 + 0.375020i) q^{49} +(-1.02516 + 0.974194i) q^{50} +(9.04805 - 3.27905i) q^{51} +(-2.81903 + 1.44131i) q^{52} +(-5.79342 - 10.0345i) q^{53} +(7.03860 + 2.11141i) q^{54} -1.47107i q^{55} +(4.71793 + 5.80871i) q^{56} +(-7.43674 - 6.25772i) q^{57} +(-1.74969 - 7.26570i) q^{58} +(-3.84363 + 2.21912i) q^{59} +(0.779227 - 3.37532i) q^{60} +(-7.65781 + 13.2637i) q^{61} +(0.491187 + 0.516882i) q^{62} +(7.37506 + 2.93401i) q^{63} +(-1.21848 + 7.90666i) q^{64} +(1.37097 + 0.791530i) q^{65} +(1.98677 + 3.00617i) q^{66} +(-6.84692 + 3.95307i) q^{67} +(9.32833 + 6.03945i) q^{68} +(1.70175 - 2.02237i) q^{69} +(1.15597 - 3.55862i) q^{70} +3.60793i q^{71} +(2.96620 + 7.94995i) q^{72} +(8.97713 - 5.18295i) q^{73} +(0.199224 - 0.674290i) q^{74} +(-1.62841 + 0.590144i) q^{75} +(0.571762 - 11.2083i) q^{76} +(1.85502 + 3.42158i) q^{77} +(-3.87062 + 0.234065i) q^{78} +(-3.01199 + 5.21691i) q^{79} +(3.64964 - 1.63711i) q^{80} +(6.86228 + 5.82316i) q^{81} +(0.795406 + 3.30298i) q^{82} -13.3919i q^{83} +(2.44387 + 8.83332i) q^{84} -5.55636i q^{85} +(0.354250 - 0.0853086i) q^{86} +(1.60188 - 9.01175i) q^{87} +(-1.38072 + 3.92505i) q^{88} +(3.02937 - 5.24701i) q^{89} +(2.53068 - 3.40524i) q^{90} +(-4.18688 - 0.112235i) q^{91} +(3.04801 + 0.155487i) q^{92} +(0.297549 + 0.821043i) q^{93} +(-14.7001 - 4.34325i) q^{94} +(-4.85963 + 2.80571i) q^{95} +(-5.24711 + 8.27453i) q^{96} -16.9823i q^{97} +(1.79874 + 9.73471i) q^{98} +(0.754316 + 4.34827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) $ 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0.331098	+	1.37491i	0.234122	+	0.972207i
$2$	0.331098	+	1.37491i	0.234122	+	0.972207i
$3$	−0.303127	+	1.70532i	−0.175011	+	0.984567i
$3$	−0.303127	+	1.70532i	−0.175011	+	0.984567i
$4$	−1.78075	+	0.910460i	−0.890374	+	0.455230i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−2.44502	+	0.147856i	−0.998177	+	0.0603619i
$7$	−2.64480	−	0.0708975i	−0.999641	−	0.0267967i
$7$	−2.64480	−	0.0708975i	−0.999641	−	0.0267967i
$8$	−1.84140	−	2.14691i	−0.651034	−	0.759049i
$9$	−2.81623	−	1.03386i	−0.938743	−	0.344619i
$10$	−0.400715	+	1.35626i	−0.126717	+	0.428885i
$11$	−0.735536	−	1.27399i	−0.221772	−	0.384121i	0.733574	−	0.679610i	$-0.237851\pi$
$11$	−0.735536	−	1.27399i	−0.221772	−	0.384121i	−0.955346	+	0.295489i	$0.904518\pi$
$12$	−1.01283	−	3.31273i	−0.292379	−	0.956302i
$13$	1.58306			0.439062			0.219531	−	0.975606i	$-0.429547\pi$
$13$	1.58306			0.439062			0.219531	+	0.975606i	$0.429547\pi$
$14$	−0.778212	−	3.65983i	−0.207986	−	0.978132i
$15$	−1.11518	+	1.32529i	−0.287937	+	0.342187i
$16$	2.34213	−	3.24260i	0.585531	−	0.810650i
$17$	−2.77818	−	4.81195i	−0.673808	−	1.16707i	−0.976816	−	0.214081i	$-0.931324\pi$
$17$	−2.77818	−	4.81195i	−0.673808	−	1.16707i	0.303008	−	0.952988i	$-0.402009\pi$
$18$	0.489012	−	4.21436i	0.115261	−	0.993335i
$19$	−2.80571	+	4.85963i	−0.643674	+	1.11488i	0.340932	+	0.940088i	$0.389257\pi$
$19$	−2.80571	+	4.85963i	−0.643674	+	1.11488i	−0.984606	+	0.174788i	$0.944076\pi$
$20$	−1.99740	−	0.101893i	−0.446633	−	0.0227839i
$21$	0.922615	−	4.48874i	0.201331	−	0.979523i
$22$	1.50808	−	1.43311i	0.321523	−	0.305540i
$23$	−1.32154	−	0.762994i	−0.275561	−	0.159095i	0.355851	−	0.934543i	$-0.384191\pi$
$23$	−1.32154	−	0.762994i	−0.275561	−	0.159095i	−0.631412	+	0.775447i	$0.717524\pi$
$24$	4.21935	−	2.48939i	0.861272	−	0.508144i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	0.524149	+	2.17656i	0.102794	+	0.426859i
$27$	2.61673	−	4.48918i	0.503591	−	0.863942i
$28$	4.77427	−	2.28173i	0.902253	−	0.431207i
$29$	−5.28450			−0.981306			−0.490653	−	0.871355i	$-0.663242\pi$
$29$	−5.28450			−0.981306			−0.490653	+	0.871355i	$0.663242\pi$
$30$	−2.19138	−	1.09446i	−0.400089	−	0.199821i
$31$	0.436649	−	0.252099i	0.0784244	−	0.0452783i	−0.460275	−	0.887776i	$-0.652249\pi$
$31$	0.436649	−	0.252099i	0.0784244	−	0.0452783i	0.538699	+	0.842498i	$0.318916\pi$
$32$	5.23375	+	2.14659i	0.925205	+	0.379467i
$33$	2.39551	−	0.868143i	0.417005	−	0.151124i
$34$	5.69614	−	5.41297i	0.976880	−	0.928317i
$35$	−2.25502	−	1.38380i	−0.381167	−	0.233905i
$36$	5.95628	−	0.723022i	0.992713	−	0.120504i
$37$	−0.430562	−	0.248585i	−0.0707840	−	0.0408672i	0.464190	−	0.885735i	$-0.346345\pi$
$37$	−0.430562	−	0.248585i	−0.0707840	−	0.0408672i	−0.534974	+	0.844868i	$0.679679\pi$
$38$	−7.61052	−	2.24858i	−1.23459	−	0.364768i
$39$	−0.479869	+	2.69962i	−0.0768405	+	0.432286i
$40$	−0.521244	−	2.77998i	−0.0824159	−	0.439554i
$41$	2.40233			0.375181			0.187590	−	0.982247i	$-0.439932\pi$
$41$	2.40233			0.375181			0.187590	+	0.982247i	$0.439932\pi$
$42$	6.47708	−	0.217703i	0.999436	−	0.0335923i
$43$		−	0.257653i		−	0.0392918i	−0.999807	−	0.0196459i	$-0.993746\pi$
$43$		−	0.257653i		−	0.0392918i	0.999807	−	0.0196459i	$-0.00625388\pi$
$44$	2.46972	+	1.59897i	0.372324	+	0.241054i
$45$	−1.92200	−	2.30346i	−0.286514	−	0.343380i
$46$	0.611486	−	2.06963i	0.0901587	−	0.305150i
$47$	−5.41938	+	9.38664i	−0.790498	+	1.36918i	0.135162	+	0.990824i	$0.456845\pi$
$47$	−5.41938	+	9.38664i	−0.790498	+	1.36918i	−0.925659	+	0.378358i	$0.876489\pi$
$48$	4.81970	+	4.97699i	0.695664	+	0.718367i
$49$	6.98995	+	0.375020i	0.998564	+	0.0535742i
$50$	−1.02516	+	0.974194i	−0.144979	+	0.137772i
$51$	9.04805	−	3.27905i	1.26698	−	0.459159i
$52$	−2.81903	+	1.44131i	−0.390929	+	0.199874i
$53$	−5.79342	−	10.0345i	−0.795788	−	1.37835i	−0.922338	−	0.386385i	$-0.873724\pi$
$53$	−5.79342	−	10.0345i	−0.795788	−	1.37835i	0.126550	−	0.991960i	$-0.459610\pi$
$54$	7.03860	+	2.11141i	0.957833	+	0.287327i
$55$		−	1.47107i		−	0.198359i
$56$	4.71793	+	5.80871i	0.630460	+	0.776222i
$57$	−7.43674	−	6.25772i	−0.985020	−	0.828855i
$58$	−1.74969	−	7.26570i	−0.229745	−	0.954033i
$59$	−3.84363	+	2.21912i	−0.500397	+	0.288905i	−0.728878	−	0.684644i	$-0.759958\pi$
$59$	−3.84363	+	2.21912i	−0.500397	+	0.288905i	0.228480	+	0.973549i	$0.426624\pi$
$60$	0.779227	−	3.37532i	0.100598	−	0.435752i
$61$	−7.65781	+	13.2637i	−0.980482	+	1.69824i	−0.319971	+	0.947427i	$0.603673\pi$
$61$	−7.65781	+	13.2637i	−0.980482	+	1.69824i	−0.660510	+	0.750817i	$0.729660\pi$
$62$	0.491187	+	0.516882i	0.0623808	+	0.0656441i
$63$	7.37506	+	2.93401i	0.929171	+	0.369651i
$64$	−1.21848	+	7.90666i	−0.152310	+	0.988333i
$65$	1.37097	+	0.791530i	0.170048	+	0.0981772i
$66$	1.98677	+	3.00617i	0.244554	+	0.370034i
$67$	−6.84692	+	3.95307i	−0.836484	+	0.482945i	−0.856068	−	0.516864i	$-0.827099\pi$
$67$	−6.84692	+	3.95307i	−0.836484	+	0.482945i	0.0195833	+	0.999808i	$0.493766\pi$
$68$	9.32833	+	6.03945i	1.13123	+	0.732391i
$69$	1.70175	−	2.02237i	0.204866	−	0.243465i
$70$	1.15597	−	3.55862i	0.138164	−	0.425336i
$71$			3.60793i			0.428182i	0.976814	+	0.214091i	$0.0686790\pi$
$71$			3.60793i			0.428182i	−0.976814	+	0.214091i	$0.931321\pi$
$72$	2.96620	+	7.94995i	0.349570	+	0.936910i
$73$	8.97713	−	5.18295i	1.05069	−	0.606618i	0.127850	−	0.991794i	$-0.459192\pi$
$73$	8.97713	−	5.18295i	1.05069	−	0.606618i	0.922843	+	0.385175i	$0.125859\pi$
$74$	0.199224	−	0.674290i	0.0231593	−	0.0783846i
$75$	−1.62841	+	0.590144i	−0.188033	+	0.0681439i
$76$	0.571762	−	11.2083i	0.0655856	−	1.28568i
$77$	1.85502	+	3.42158i	0.211399	+	0.389926i
$78$	−3.87062	+	0.234065i	−0.438261	+	0.0265026i
$79$	−3.01199	+	5.21691i	−0.338875	+	0.586949i	−0.984221	−	0.176941i	$-0.943380\pi$
$79$	−3.01199	+	5.21691i	−0.338875	+	0.586949i	0.645346	+	0.763890i	$0.276713\pi$
$80$	3.64964	−	1.63711i	0.408042	−	0.183034i
$81$	6.86228	+	5.82316i	0.762475	+	0.647018i
$82$	0.795406	+	3.30298i	0.0878380	+	0.364753i
$83$		−	13.3919i		−	1.46995i	−0.678092	−	0.734977i	$-0.737193\pi$
$83$		−	13.3919i		−	1.46995i	0.678092	−	0.734977i	$-0.262807\pi$
$84$	2.44387	+	8.83332i	0.266648	+	0.963794i
$85$		−	5.55636i		−	0.602672i
$86$	0.354250	−	0.0853086i	0.0381997	−	0.00919906i
$87$	1.60188	−	9.01175i	0.171739	−	0.966162i
$88$	−1.38072	+	3.92505i	−0.147185	+	0.418412i
$89$	3.02937	−	5.24701i	0.321112	−	0.556182i	−0.659606	−	0.751612i	$-0.729277\pi$
$89$	3.02937	−	5.24701i	0.321112	−	0.556182i	0.980718	+	0.195429i	$0.0626100\pi$
$90$	2.53068	−	3.40524i	0.266757	−	0.358944i
$91$	−4.18688	−	0.112235i	−0.438904	−	0.0117654i
$92$	3.04801	+	0.155487i	0.317777	+	0.0162106i
$93$	0.297549	+	0.821043i	0.0308544	+	0.0851382i
$94$	−14.7001	−	4.34325i	−1.51620	−	0.447972i
$95$	−4.85963	+	2.80571i	−0.498588	+	0.287860i
$96$	−5.24711	+	8.27453i	−0.535531	+	0.844515i
$97$		−	16.9823i		−	1.72429i	−0.506661	−	0.862145i	$-0.669121\pi$
$97$		−	16.9823i		−	1.72429i	0.506661	−	0.862145i	$-0.330879\pi$
$98$	1.79874	+	9.73471i	0.181700	+	0.983354i
$99$	0.754316	+	4.34827i	0.0758116	+	0.437018i
$100$	−1.67886	−	1.08694i	−0.167886	−	0.108694i
$101$	7.67901	−	4.43348i	0.764090	−	0.441148i	−0.0666722	−	0.997775i	$-0.521238\pi$
$101$	7.67901	−	4.43348i	0.764090	−	0.441148i	0.830762	+	0.556627i	$0.187905\pi$
$102$	7.50419	+	11.3546i	0.743026	+	1.12427i
$103$	−10.1609	−	5.86637i	−1.00118	−	0.578031i	−0.0925817	−	0.995705i	$-0.529512\pi$
$103$	−10.1609	−	5.86637i	−1.00118	−	0.578031i	−0.908597	+	0.417674i	$0.862845\pi$
$104$	−2.91505	−	3.39869i	−0.285844	−	0.333269i
$105$	3.04338	−	3.42606i	0.297003	−	0.334349i
$106$	11.8783	−	11.2878i	1.15373	−	1.09637i
$107$	−4.55994	+	7.89804i	−0.440826	+	0.763533i	−0.997751	−	0.0670301i	$-0.978648\pi$
$107$	−4.55994	+	7.89804i	−0.440826	+	0.763533i	0.556925	+	0.830563i	$0.311981\pi$
$108$	−0.572528	+	10.3765i	−0.0550915	+	0.998481i
$109$	−5.48653	+	3.16765i	−0.525514	+	0.303406i	−0.739188	−	0.673499i	$-0.764790\pi$
$109$	−5.48653	+	3.16765i	−0.525514	+	0.303406i	0.213674	+	0.976905i	$0.431457\pi$
$110$	2.02259	−	0.487069i	0.192846	−	0.0464402i
$111$	0.554432	−	0.658893i	0.0526244	−	0.0625394i
$112$	−6.42435	+	8.40998i	−0.607044	+	0.794668i
$113$			11.0625i			1.04068i	0.853960	+	0.520338i	$0.174194\pi$
$113$			11.0625i			1.04068i	−0.853960	+	0.520338i	$0.825806\pi$
$114$	6.14150	−	12.2968i	0.575204	−	1.15170i
$115$	−0.762994	−	1.32154i	−0.0711496	−	0.123235i
$116$	9.41036	−	4.81132i	0.873730	−	0.446720i
$117$	−4.45826	−	1.63666i	−0.412166	−	0.151309i
$118$	−4.32370	−	4.54989i	−0.398029	−	0.418851i
$119$	7.00658	+	12.9236i	0.642292	+	1.18471i
$120$	4.89876	−	0.0461979i	0.447194	−	0.00421727i
$121$	4.41797	−	7.65216i	0.401634	−	0.695651i
$122$	−20.7719	−	6.13719i	−1.88060	−	0.555635i
$123$	−0.728211	+	4.09674i	−0.0656606	+	0.369390i
$124$	−0.548035	+	0.846476i	−0.0492150	+	0.0760158i
$125$			1.00000i			0.0894427i
$126$	−1.59213	+	11.1115i	−0.141838	+	0.989890i
$127$	−10.6377			−0.943945			−0.471972	−	0.881613i	$-0.656458\pi$
$127$	−10.6377			−0.943945			−0.471972	+	0.881613i	$0.656458\pi$
$128$	−11.2744	+	0.942584i	−0.996523	+	0.0833134i
$129$	0.439381	+	0.0781018i	0.0386854	+	0.00687648i
$130$	−0.634356	+	2.14703i	−0.0556367	+	0.188307i
$131$	8.76573	+	5.06090i	0.765865	+	0.442173i	0.831398	−	0.555678i	$-0.187541\pi$
$131$	8.76573	+	5.06090i	0.765865	+	0.442173i	−0.0655323	+	0.997850i	$0.520875\pi$
$132$	−3.47539	+	3.72696i	−0.302494	+	0.324390i
$133$	7.76508	−	12.6538i	0.673318	−	1.09723i
$134$	−7.70212	−	8.10504i	−0.665361	−	0.700168i
$135$	4.51075	−	2.57937i	0.388223	−	0.221997i
$136$	−5.21510	+	14.8252i	−0.447191	+	1.27125i
$137$	−10.1637	+	5.86801i	−0.868343	+	0.501338i	−0.866797	−	0.498661i	$-0.833825\pi$
$137$	−10.1637	+	5.86801i	−0.868343	+	0.501338i	−0.00154582	+	0.999999i	$0.500492\pi$
$138$	3.34402	+	1.67014i	0.284662	+	0.142172i
$139$	−0.697482			−0.0591597			−0.0295798	−	0.999562i	$-0.509417\pi$
$139$	−0.697482			−0.0591597			−0.0295798	+	0.999562i	$0.509417\pi$
$140$	5.27551	+	0.411097i	0.445862	+	0.0347440i
$141$	−14.3645	−	12.0871i	−1.20971	−	1.01792i
$142$	−4.96057	+	1.19458i	−0.416282	+	0.100247i
$143$	−1.16440	−	2.01680i	−0.0973718	−	0.168653i
$144$	−9.94835	+	6.71047i	−0.829029	+	0.559206i
$145$	−4.57651	−	2.64225i	−0.380058	−	0.219427i
$146$	10.0984	+	10.6267i	0.835749	+	0.879469i
$147$	−2.75837	+	11.8064i	−0.227507	+	0.973777i
$148$	0.993049	+	0.0506580i	0.0816282	+	0.00416406i
$149$	−10.3136	+	17.8637i	−0.844922	+	1.46345i	0.0407675	+	0.999169i	$0.487020\pi$
$149$	−10.3136	+	17.8637i	−0.844922	+	1.46345i	−0.885689	+	0.464279i	$0.846314\pi$
$150$	−1.35056	−	2.04352i	−0.110273	−	0.166853i
$151$	1.06809	+	1.84999i	0.0869203	+	0.150550i	0.906208	−	0.422832i	$-0.138964\pi$
$151$	1.06809	+	1.84999i	0.0869203	+	0.150550i	−0.819288	+	0.573383i	$0.805631\pi$
$152$	15.5997	−	2.92492i	1.26530	−	0.237242i
$153$	2.84912	+	16.4238i	0.230337	+	1.32778i
$154$	−4.09017	+	3.68337i	−0.329595	+	0.296814i
$155$	0.504198			0.0404982
$156$	−1.60337	−	5.24425i	−0.128373	−	0.419876i
$157$	1.38285	+	2.39516i	0.110363	+	0.191155i	0.915917	−	0.401368i	$-0.131465\pi$
$157$	1.38285	+	2.39516i	0.110363	+	0.191155i	−0.805553	+	0.592523i	$0.798132\pi$
$158$	−8.17004	−	2.41390i	−0.649974	−	0.192039i
$159$	18.8682	−	6.83790i	1.49634	−	0.542281i
$160$	3.45927	+	4.47588i	0.273479	+	0.353849i
$161$	3.44113	+	2.11166i	0.271199	+	0.166422i
$162$	−5.73422	+	11.3630i	−0.450523	+	0.892765i
$163$	−3.88843	−	2.24499i	−0.304566	−	0.175841i	0.339926	−	0.940452i	$-0.389598\pi$
$163$	−3.88843	−	2.24499i	−0.304566	−	0.175841i	−0.644492	+	0.764611i	$0.722931\pi$
$164$	−4.27794	+	2.18722i	−0.334051	+	0.170793i
$165$	2.50865	+	0.445922i	0.195298	+	0.0347150i
$166$	18.4127	−	4.43404i	1.42910	−	0.344148i
$167$	−6.10705			−0.472578			−0.236289	−	0.971683i	$-0.575931\pi$
$167$	−6.10705			−0.472578			−0.236289	+	0.971683i	$0.575931\pi$
$168$	−11.3358	+	6.28480i	−0.874579	+	0.484883i
$169$	−10.4939			−0.807225
$170$	7.63949	−	1.83970i	0.585922	−	0.141099i
$171$	12.9257	−	10.7851i	0.988452	−	0.824759i
$172$	0.234583	+	0.458816i	0.0178868	+	0.0349844i
$173$	−11.2340	−	6.48593i	−0.854103	−	0.493116i	0.00793028	−	0.999969i	$-0.497476\pi$
$173$	−11.2340	−	6.48593i	−0.854103	−	0.493116i	−0.862033	+	0.506852i	$0.830809\pi$
$174$	12.9207	−	0.781344i	0.979517	−	0.0592335i
$175$	−1.26100	−	2.32591i	−0.0953228	−	0.175823i
$176$	−5.85374	−	0.598786i	−0.441242	−	0.0451352i
$177$	−2.61920	−	7.22728i	−0.196871	−	0.543236i
$178$	8.21718	+	2.42782i	0.615904	+	0.181973i
$179$	2.81245	+	4.87131i	0.210213	+	0.364099i	0.951781	−	0.306778i	$-0.0992511\pi$
$179$	2.81245	+	4.87131i	0.210213	+	0.364099i	−0.741568	+	0.670877i	$0.765918\pi$
$180$	5.51980	+	2.35198i	0.411421	+	0.175306i
$181$	−21.6254			−1.60740			−0.803700	−	0.595034i	$-0.797138\pi$
$181$	−21.6254			−1.60740			−0.803700	+	0.595034i	$0.797138\pi$
$182$	−1.23196	−	5.79374i	−0.0913187	−	0.429461i
$183$	−20.2976	−	17.0796i	−1.50044	−	1.26256i
$184$	0.795412	+	4.24222i	0.0586385	+	0.312741i
$185$	−0.248585	−	0.430562i	−0.0182763	−	0.0316556i
$186$	−1.03034	+	0.680949i	−0.0755483	+	0.0499296i
$187$	−4.08690	+	7.07872i	−0.298864	+	0.517647i
$188$	1.10439	−	21.6494i	0.0805458	−	1.57894i
$189$	−7.23901	+	11.6875i	−0.526561	+	0.850138i
$190$	−5.46661	−	5.75259i	−0.396590	−	0.417336i
$191$	15.8732	+	9.16437i	1.14854	+	0.663110i	0.948531	−	0.316683i	$-0.102569\pi$
$191$	15.8732	+	9.16437i	1.14854	+	0.663110i	0.200010	+	0.979794i	$0.435903\pi$
$192$	−13.1140	−	4.47462i	−0.946424	−	0.322928i
$193$	12.9693	+	22.4634i	0.933547	+	1.61695i	0.777204	+	0.629249i	$0.216637\pi$
$193$	12.9693	+	22.4634i	0.933547	+	1.61695i	0.156343	+	0.987703i	$0.450029\pi$
$194$	23.3491	−	5.62281i	1.67637	−	0.403694i
$195$	−1.76539	+	2.09801i	−0.126422	+	0.150241i
$196$	−12.7888	+	5.69625i	−0.913484	+	0.406875i
$197$	−9.99529			−0.712135			−0.356068	−	0.934460i	$-0.615883\pi$
$197$	−9.99529			−0.712135			−0.356068	+	0.934460i	$0.615883\pi$
$198$	−5.72872	+	2.47682i	−0.407123	+	0.176020i
$199$	−18.0771	+	10.4368i	−1.28145	+	0.739847i	−0.977114	−	0.212716i	$-0.931769\pi$
$199$	−18.0771	+	10.4368i	−1.28145	+	0.739847i	−0.304339	+	0.952564i	$0.598436\pi$
$200$	0.938581	−	2.66816i	0.0663677	−	0.188667i
$201$	−4.66576	−	12.8745i	−0.329097	−	0.908095i
$202$	8.63814	+	9.09002i	0.607777	+	0.639572i
$203$	13.9764	+	0.374658i	0.980954	+	0.0262958i
$204$	−13.1269	+	14.0771i	−0.919064	+	0.985591i
$205$	2.08048	+	1.20116i	0.145307	+	0.0838929i
$206$	4.70148	−	15.9126i	0.327568	−	1.10868i
$207$	2.93294	+	3.51505i	0.203854	+	0.244313i
$208$	3.70773	−	5.13323i	0.257085	−	0.355925i
$209$	8.25480			0.570996
$210$	5.71817	+	3.05001i	0.394591	+	0.210470i
$211$		−	10.3677i		−	0.713744i	−0.934153	−	0.356872i	$-0.883843\pi$
$211$		−	10.3677i		−	0.713744i	0.934153	−	0.356872i	$-0.116157\pi$
$212$	19.4526	+	12.5942i	1.33601	+	0.864976i
$213$	−6.15267	−	1.09366i	−0.421574	−	0.0749365i
$214$	−12.3689	−	3.65447i	−0.845519	−	0.249814i
$215$	0.128827	−	0.223134i	0.00878591	−	0.0152176i
$216$	−14.4563	+	2.64848i	−0.983629	+	0.180206i
$217$	−1.17272	+	0.635795i	−0.0796095	+	0.0431606i
$218$	−6.17181	−	6.49467i	−0.418007	−	0.439875i
$219$	6.11737	+	16.8800i	0.413373	+	1.14064i
$220$	1.33935	+	2.61961i	0.0902990	+	0.176614i
$221$	−4.39803	−	7.61761i	−0.295843	−	0.512416i
$222$	1.08949	+	0.544135i	0.0731217	+	0.0365200i
$223$			2.40508i			0.161056i	0.996752	+	0.0805281i	$0.0256607\pi$
$223$			2.40508i			0.161056i	−0.996752	+	0.0805281i	$0.974339\pi$
$224$	−13.6900	−	6.04836i	−0.914704	−	0.404123i
$225$	−0.512767	−	2.95585i	−0.0341844	−	0.197057i
$226$	−15.2100	+	3.66279i	−1.01175	+	0.243645i
$227$	8.39441	−	4.84652i	0.557157	−	0.321675i	−0.194847	−	0.980834i	$-0.562421\pi$
$227$	8.39441	−	4.84652i	0.557157	−	0.321675i	0.752004	+	0.659159i	$0.229088\pi$
$228$	18.9404	+	4.37257i	1.25436	+	0.289580i
$229$	8.99570	−	15.5810i	0.594452	−	1.02962i	−0.399171	−	0.916876i	$-0.630702\pi$
$229$	8.99570	−	15.5810i	0.594452	−	1.02962i	0.993624	−	0.112746i	$-0.0359645\pi$
$230$	1.56438	−	1.48661i	0.103152	−	0.0980241i
$231$	−6.39720	+	2.12623i	−0.420905	+	0.139896i
$232$	9.73088	+	11.3454i	0.638864	+	0.744859i
$233$	−21.6500	−	12.4996i	−1.41834	−	0.818877i	−0.422184	−	0.906510i	$-0.638736\pi$
$233$	−21.6500	−	12.4996i	−1.41834	−	0.818877i	−0.996153	+	0.0876331i	$0.972070\pi$
$234$	0.774136	−	6.67159i	0.0506068	−	0.436136i
$235$	−9.38664	+	5.41938i	−0.612317	+	0.353521i
$236$	4.82411	−	7.45116i	0.314023	−	0.485029i
$237$	−7.98349	−	6.71779i	−0.518583	−	0.436367i
$238$	−15.4489	+	13.9124i	−1.00141	+	0.901807i
$239$			7.80454i			0.504834i	0.967619	+	0.252417i	$0.0812254\pi$
$239$			7.80454i			0.504834i	−0.967619	+	0.252417i	$0.918775\pi$
$240$	1.68549	+	6.72005i	0.108798	+	0.433778i
$241$	13.1988	−	7.62031i	0.850207	−	0.490867i	−0.0105136	−	0.999945i	$-0.503347\pi$
$241$	13.1988	−	7.62031i	0.850207	−	0.490867i	0.860721	+	0.509077i	$0.170013\pi$
$242$	11.9838	+	3.54070i	0.770348	+	0.227605i
$243$	−12.0105	+	9.93721i	−0.770473	+	0.637472i
$244$	1.56055	−	30.5914i	0.0999038	−	1.95842i
$245$	5.86596	+	3.81975i	0.374763	+	0.244035i
$246$	−5.87375	+	0.355198i	−0.374496	+	0.0226466i
$247$	−4.44161	+	7.69309i	−0.282613	+	0.489500i
$248$	−1.34528	−	0.473231i	−0.0854254	−	0.0300502i
$249$	22.8375	+	4.05946i	1.44727	+	0.257258i
$250$	−1.37491	+	0.331098i	−0.0869569	+	0.0209405i
$251$		−	13.8272i		−	0.872763i	−0.899762	−	0.436382i	$-0.856260\pi$
$251$		−	13.8272i		−	0.872763i	0.899762	−	0.436382i	$-0.143740\pi$
$252$	−15.8044	+	1.48996i	−0.995586	+	0.0938589i
$253$			2.24484i			0.141132i
$254$	−3.52213	−	14.6259i	−0.220998	−	0.917710i
$255$	9.47537	+	1.68429i	0.593371	+	0.105474i
$256$	−5.02889	−	15.1891i	−0.314306	−	0.949322i
$257$	−4.26584	+	7.38865i	−0.266096	+	0.460891i	−0.967850	−	0.251528i	$-0.919067\pi$
$257$	−4.26584	+	7.38865i	−0.266096	+	0.460891i	0.701755	+	0.712419i	$0.252400\pi$
$258$	0.0380955	+	0.629968i	0.00237173	+	0.0392201i
$259$	1.12113	+	0.687984i	0.0696635	+	0.0427493i
$260$	−3.16201	−	0.161302i	−0.196100	−	0.0100035i
$261$	14.8823	+	5.46342i	0.921194	+	0.338177i
$262$	−4.05595	+	13.7277i	−0.250578	+	0.848102i
$263$	4.70164	−	2.71449i	0.289915	−	0.167383i	−0.347988	−	0.937499i	$-0.613135\pi$
$263$	4.70164	−	2.71449i	0.289915	−	0.167383i	0.637904	+	0.770116i	$0.279802\pi$
$264$	−6.27493	−	3.54436i	−0.386195	−	0.218140i
$265$		−	11.5868i		−	0.711774i
$266$	19.9689	+	6.48661i	1.22437	+	0.397720i
$267$	8.02955	+	6.75655i	0.491401	+	0.413494i
$268$	8.59353	−	13.2733i	0.524933	−	0.810794i
$269$	15.0753	−	8.70371i	0.919156	−	0.530675i	0.0357901	−	0.999359i	$-0.488605\pi$
$269$	15.0753	−	8.70371i	0.919156	−	0.530675i	0.883366	+	0.468684i	$0.155272\pi$
$270$	5.03990	+	5.34784i	0.306719	+	0.325459i
$271$	11.9864	+	6.92036i	0.728122	+	0.420382i	0.817735	−	0.575595i	$-0.195230\pi$
$271$	11.9864	+	6.92036i	0.728122	+	0.420382i	−0.0896124	+	0.995977i	$0.528563\pi$
$272$	−22.1101	−	2.26167i	−1.34062	−	0.137134i
$273$	1.46055	−	7.10595i	0.0883968	−	0.430071i
$274$	−11.4332	−	12.0313i	−0.690703	−	0.726835i
$275$	0.735536	−	1.27399i	0.0443545	−	0.0768242i
$276$	−1.18909	+	5.15070i	−0.0715749	+	0.310036i
$277$	20.9220	−	12.0793i	1.25708	−	0.725775i	0.284573	−	0.958654i	$-0.408148\pi$
$277$	20.9220	−	12.0793i	1.25708	−	0.725775i	0.972506	+	0.232879i	$0.0748147\pi$
$278$	−0.230935	−	0.958974i	−0.0138506	−	0.0575155i
$279$	−1.49034	+	0.258536i	−0.0892241	+	0.0154781i
$280$	1.18149	+	7.38946i	0.0706076	+	0.441605i
$281$			32.8316i			1.95857i	0.202491	+	0.979284i	$0.435096\pi$
$281$			32.8316i			1.95857i	−0.202491	+	0.979284i	$0.564904\pi$
$282$	11.8626	−	23.7518i	0.706410	−	1.41440i
$283$	−0.974962	−	1.68868i	−0.0579555	−	0.100382i	0.835592	−	0.549351i	$-0.185125\pi$
$283$	−0.974962	−	1.68868i	−0.0579555	−	0.100382i	−0.893548	+	0.448969i	$0.851791\pi$
$284$	−3.28487	−	6.42481i	−0.194921	−	0.381242i
$285$	−3.31154	−	9.13771i	−0.196159	−	0.541271i
$286$	2.38738	−	2.26870i	0.141169	−	0.134151i
$287$	−6.35368	−	0.170319i	−0.375046	−	0.0100536i
$288$	−12.5202	−	11.4562i	−0.737758	−	0.675066i
$289$	−6.93658	+	12.0145i	−0.408034	+	0.706735i
$290$	2.11758	−	7.16713i	0.124348	−	0.420868i
$291$	28.9602	+	5.14780i	1.69768	+	0.301769i
$292$	−11.2671	+	17.4028i	−0.659359	+	1.01842i
$293$			14.7459i			0.861467i	0.902479	+	0.430733i	$0.141745\pi$
$293$			14.7459i			0.861467i	−0.902479	+	0.430733i	$0.858255\pi$
$294$	−17.1460	+	0.116573i	−0.999977	+	0.00679865i
$295$	−4.43824			−0.258404
$296$	0.259147	+	1.38213i	0.0150626	+	0.0803344i
$297$	−7.64384	−	0.0317300i	−0.443541	−	0.00184116i
$298$	−27.9757	−	8.26561i	−1.62059	−	0.478814i
$299$	−2.09209	−	1.20787i	−0.120988	−	0.0698527i
$300$	2.36249	−	2.53350i	0.136399	−	0.146272i
$301$	−0.0182670	+	0.681442i	−0.00105289	+	0.0392777i
$302$	−2.18993	+	2.08106i	−0.126016	+	0.119752i
$303$	5.23278	+	14.4391i	0.300615	+	0.829503i
$304$	9.18651	+	20.4797i	0.526883	+	1.17459i
$305$	−13.2637	+	7.65781i	−0.759478	+	0.438485i
$306$	−21.6379	+	9.35516i	−1.23695	+	0.534799i
$307$	24.9046			1.42138			0.710691	−	0.703504i	$-0.248382\pi$
$307$	24.9046			1.42138			0.710691	+	0.703504i	$0.248382\pi$
$308$	−6.41854	−	4.40406i	−0.365730	−	0.250944i
$309$	13.0841	−	15.5492i	0.744327	−	0.884565i
$310$	0.166939	+	0.693227i	0.00948151	+	0.0393726i
$311$	−3.98354	−	6.89970i	−0.225886	−	0.391246i	0.730699	−	0.682700i	$-0.239194\pi$
$311$	−3.98354	−	6.89970i	−0.225886	−	0.391246i	−0.956585	+	0.291454i	$0.905861\pi$
$312$	6.67949	−	3.94085i	0.378152	−	0.223107i
$313$	24.7452	+	14.2866i	1.39868	+	0.807528i	0.994254	−	0.107043i	$-0.0341382\pi$
$313$	24.7452	+	14.2866i	1.39868	+	0.807528i	0.404425	+	0.914571i	$0.367472\pi$
$314$	−2.83527	+	2.69432i	−0.160004	+	0.152050i
$315$	4.91999	+	6.22846i	0.277210	+	0.350934i
$316$	0.613798	−	12.0323i	0.0345288	−	0.676870i
$317$	−5.89293	+	10.2069i	−0.330980	+	0.573274i	−0.982704	−	0.185182i	$-0.940713\pi$
$317$	−5.89293	+	10.2069i	−0.330980	+	0.573274i	0.651724	+	0.758456i	$0.274046\pi$
$318$	15.6487	+	23.6780i	0.877536	+	1.32780i
$319$	3.88694	+	6.73237i	0.217627	+	0.376940i
$320$	−5.00857	+	6.23813i	−0.279987	+	0.348722i
$321$	−12.0864	−	10.1703i	−0.674599	−	0.567649i
$322$	−1.76399	+	5.43041i	−0.0983034	+	0.302625i
$323$	31.1791			1.73485
$324$	−17.5217	−	4.12175i	−0.973430	−	0.228986i
$325$	0.791530	+	1.37097i	0.0439062	+	0.0760478i
$326$	1.79920	−	6.08955i	0.0996485	−	0.337269i
$327$	−3.73873	−	10.3165i	−0.206752	−	0.570503i
$328$	−4.42365	−	5.15759i	−0.244255	−	0.284780i
$329$	14.9987	−	24.4416i	0.826903	−	1.34751i
$330$	0.217506	+	3.59680i	0.0119733	+	0.197998i
$331$	−5.08881	−	2.93803i	−0.279706	−	0.161489i	0.353584	−	0.935403i	$-0.384963\pi$
$331$	−5.08881	−	2.93803i	−0.279706	−	0.161489i	−0.633290	+	0.773914i	$0.718296\pi$
$332$	12.1928	+	23.8476i	0.669167	+	1.30881i
$333$	0.955559	+	1.14521i	0.0523643	+	0.0627573i
$334$	−2.02203	−	8.39663i	−0.110641	−	0.459443i
$335$	−7.90614			−0.431959
$336$	−12.3943	−	13.5049i	−0.676165	−	0.736751i
$337$	8.48352			0.462127			0.231063	−	0.972939i	$-0.425780\pi$
$337$	8.48352			0.462127			0.231063	+	0.972939i	$0.425780\pi$
$338$	−3.47452	−	14.4282i	−0.188989	−	0.784790i
$339$	−18.8652	−	3.35336i	−1.02461	−	0.182129i
$340$	5.05884	+	9.89448i	0.274354	+	0.536603i
$341$	−0.642341	−	0.370856i	−0.0347847	−	0.0200830i
$342$	19.1082	+	14.2007i	1.03326	+	0.767886i
$343$	−18.4604	−	1.48742i	−0.996770	−	0.0803133i
$344$	−0.553160	+	0.474443i	−0.0298244	+	0.0255803i
$345$	2.48494	−	0.900552i	0.133785	−	0.0484841i
$346$	5.19802	−	17.5932i	0.279447	−	0.945814i
$347$	13.0330	+	22.5738i	0.699649	+	1.21183i	0.968588	+	0.248670i	$0.0799935\pi$
$347$	13.0330	+	22.5738i	0.699649	+	1.21183i	−0.268939	+	0.963157i	$0.586673\pi$
$348$	5.35230	+	17.5061i	0.286914	+	0.938426i
$349$	14.2563			0.763123			0.381562	−	0.924343i	$-0.375386\pi$
$349$	14.2563			0.763123			0.381562	+	0.924343i	$0.375386\pi$
$350$	2.78040	−	2.50387i	0.148619	−	0.133837i
$351$	4.14245	−	7.10664i	0.221107	−	0.379324i
$352$	−1.11489	−	8.24661i	−0.0594236	−	0.439546i
$353$	6.08482	+	10.5392i	0.323862	+	0.560946i	0.981281	−	0.192579i	$-0.0616853\pi$
$353$	6.08482	+	10.5392i	0.323862	+	0.560946i	−0.657419	+	0.753525i	$0.728352\pi$
$354$	9.06965	−	5.99410i	0.482046	−	0.318583i
$355$	−1.80396	+	3.12456i	−0.0957445	+	0.165834i
$356$	−0.617340	+	12.1017i	−0.0327189	+	0.641390i
$357$	−24.1628	+	8.03095i	−1.27883	+	0.425043i
$358$	−5.76641	+	5.47975i	−0.304764	+	0.289614i
$359$	−7.41150	−	4.27903i	−0.391164	−	0.225839i	0.291500	−	0.956571i	$-0.405846\pi$
$359$	−7.41150	−	4.27903i	−0.391164	−	0.225839i	−0.682664	+	0.730732i	$0.739179\pi$
$360$	−1.40617	+	8.36796i	−0.0741115	+	0.441030i
$361$	−6.24402	−	10.8150i	−0.328633	−	0.569209i
$362$	−7.16012	−	29.7329i	−0.376328	−	1.56273i
$363$	11.7102	+	9.85364i	0.614624	+	0.517182i
$364$	7.55796	−	3.61212i	0.396145	−	0.189327i
$365$	10.3659			0.542576
$366$	16.7624	−	33.5623i	0.876185	−	1.75433i
$367$	25.2674	−	14.5881i	1.31895	−	0.761494i	0.335387	−	0.942081i	$-0.391133\pi$
$367$	25.2674	−	14.5881i	1.31895	−	0.761494i	0.983559	+	0.180587i	$0.0577997\pi$
$368$	−5.56931	+	2.49821i	−0.290320	+	0.130228i
$369$	−6.76550	−	2.48367i	−0.352198	−	0.129294i
$370$	0.509678	−	0.484340i	0.0264969	−	0.0251797i
$371$	14.6110	+	26.9500i	0.758567	+	1.39917i
$372$	−1.27739	−	1.19116i	−0.0662295	−	0.0617590i
$373$	11.1475	+	6.43599i	0.577193	+	0.333243i	0.760017	−	0.649903i	$-0.225190\pi$
$373$	11.1475	+	6.43599i	0.577193	+	0.333243i	−0.182824	+	0.983146i	$0.558524\pi$
$374$	−11.0858	−	3.27536i	−0.573231	−	0.169365i
$375$	−1.70532	−	0.303127i	−0.0880623	−	0.0156534i
$376$	30.1316	−	5.64963i	1.55392	−	0.291358i
$377$	−8.36568			−0.430854
$378$	−18.4660	−	6.08328i	−0.949789	−	0.312890i
$379$		−	1.38872i		−	0.0713338i	−0.999364	−	0.0356669i	$-0.988644\pi$
$379$		−	1.38872i		−	0.0713338i	0.999364	−	0.0356669i	$-0.0113555\pi$
$380$	6.09929	−	9.42076i	0.312887	−	0.483275i
$381$	3.22458	−	18.1407i	0.165200	−	0.929376i
$382$	−7.34460	+	24.8584i	−0.375782	+	1.27187i
$383$	4.01414	−	6.95269i	0.205113	−	0.355266i	−0.745056	−	0.667002i	$-0.767577\pi$
$383$	4.01414	−	6.95269i	0.205113	−	0.355266i	0.950169	+	0.311736i	$0.100911\pi$
$384$	1.81016	−	19.5121i	0.0923746	−	0.995724i
$385$	−0.104295	+	3.89069i	−0.00531538	+	0.198288i
$386$	−26.5910	+	25.2691i	−1.35345	+	1.28617i
$387$	−0.266377	+	0.725610i	−0.0135407	+	0.0368848i
$388$	15.4617	+	30.2412i	0.784948	+	1.53526i
$389$	−3.02937	−	5.24702i	−0.153595	−	0.266034i	0.778952	−	0.627084i	$-0.215752\pi$
$389$	−3.02937	−	5.24702i	−0.153595	−	0.266034i	−0.932547	+	0.361050i	$0.882418\pi$
$390$	−3.46909	−	1.73260i	−0.175664	−	0.0877338i
$391$			8.47894i			0.428799i
$392$	−12.0662	−	15.6974i	−0.609433	−	0.792837i
$393$	−11.2876	+	13.4143i	−0.569383	+	0.676661i
$394$	−3.30942	−	13.7426i	−0.166726	−	0.692343i
$395$	−5.21691	+	3.01199i	−0.262491	+	0.151550i
$396$	−5.30217	−	7.05640i	−0.266444	−	0.354597i
$397$	−16.3278	+	28.2806i	−0.819469	+	1.41936i	0.0866048	+	0.996243i	$0.472398\pi$
$397$	−16.3278	+	28.2806i	−0.819469	+	1.41936i	−0.906074	+	0.423119i	$0.860935\pi$
$398$	−20.3350	−	21.3988i	−1.01930	−	1.07262i
$399$	19.2250	+	17.0777i	0.962456	+	0.854953i
$400$	3.97924	+	0.407041i	0.198962	+	0.0203521i
$401$	0.464438	+	0.268144i	0.0231929	+	0.0133905i	0.511552	−	0.859253i	$-0.329071\pi$
$401$	0.464438	+	0.268144i	0.0231929	+	0.0133905i	−0.488359	+	0.872643i	$0.662404\pi$
$402$	16.1564	−	10.6777i	0.805808	−	0.532556i
$403$	0.691241	−	0.399088i	0.0344332	−	0.0198800i
$404$	−9.63788	+	14.8863i	−0.479502	+	0.740623i
$405$	3.03133	+	8.47414i	0.150628	+	0.421083i
$406$	4.11246	+	19.3404i	0.204098	+	0.959847i
$407$			0.731373i			0.0362528i
$408$	−23.7009	−	13.3873i	−1.17337	−	0.662772i
$409$	−25.6969	+	14.8361i	−1.27063	+	0.733598i	−0.975106	−	0.221737i	$-0.928827\pi$
$409$	−25.6969	+	14.8361i	−1.27063	+	0.733598i	−0.295523	+	0.955336i	$0.595494\pi$
$410$	−0.962648	+	3.25817i	−0.0475418	+	0.160909i
$411$	−6.92594	−	19.1111i	−0.341631	−	0.942681i
$412$	23.4350	+	1.19548i	1.15456	+	0.0588970i
$413$	10.3230	−	5.59662i	0.507959	−	0.275392i
$414$	−3.86179	+	5.19636i	−0.189796	+	0.255387i
$415$	6.69596	−	11.5977i	0.328692	−	0.569311i
$416$	8.28534	+	3.39818i	0.406222	+	0.166610i
$417$	0.211426	−	1.18943i	0.0103536	−	0.0582466i
$418$	2.73315	+	11.3496i	0.133683	+	0.555127i
$419$		−	28.9694i		−	1.41525i	−0.706589	−	0.707624i	$-0.749767\pi$
$419$		−	28.9694i		−	1.41525i	0.706589	−	0.707624i	$-0.250233\pi$
$420$	−2.30020	+	8.87181i	−0.112238	+	0.432900i
$421$		−	6.53258i		−	0.318379i	−0.987248	−	0.159189i	$-0.949112\pi$
$421$		−	6.53258i		−	0.318379i	0.987248	−	0.159189i	$-0.0508880\pi$
$422$	14.2547	−	3.43274i	0.693907	−	0.167103i
$423$	24.9667	−	20.8320i	1.21392	−	1.01289i
$424$	−10.8752	+	30.9155i	−0.528146	+	1.50139i
$425$	2.77818	−	4.81195i	0.134762	−	0.233414i
$426$	−0.533453	−	8.82147i	−0.0258459	−	0.427402i
$427$	21.1937	−	34.5370i	1.02564	−	1.67136i
$428$	0.929248	−	18.2161i	0.0449169	−	0.880507i
$429$	3.79224	−	1.37432i	0.183091	−	0.0663530i
$430$	0.349444	+	0.103246i	0.0168517	+	0.00497894i
$431$	−9.31568	+	5.37841i	−0.448721	+	0.259069i	−0.707290	−	0.706924i	$-0.750082\pi$
$431$	−9.31568	+	5.37841i	−0.448721	+	0.259069i	0.258569	+	0.965993i	$0.416749\pi$
$432$	−8.42788	−	18.9992i	−0.405487	−	0.914101i
$433$		−	11.7672i		−	0.565497i	−0.959194	−	0.282748i	$-0.908754\pi$
$433$		−	11.7672i		−	0.565497i	0.959194	−	0.282748i	$-0.0912462\pi$
$434$	−1.26245	−	1.40187i	−0.0605994	−	0.0672921i
$435$	5.89314	−	7.00347i	0.282555	−	0.335791i
$436$	6.88610	−	10.6360i	0.329785	−	0.509374i
$437$	7.41574	−	4.28148i	0.354743	−	0.204811i
$438$	−21.1830	+	13.9997i	−1.01216	+	0.668934i
$439$	25.8121	+	14.9026i	1.23194	+	0.711262i	0.967434	−	0.253122i	$-0.0814573\pi$
$439$	25.8121	+	14.9026i	1.23194	+	0.711262i	0.264507	+	0.964384i	$0.414791\pi$
$440$	−3.15826	+	2.70883i	−0.150564	+	0.129139i
$441$	−19.2976	−	8.28275i	−0.918932	−	0.394417i
$442$	9.01734	−	8.56906i	0.428911	−	0.407589i
$443$	−14.3028	+	24.7731i	−0.679546	+	1.17701i	0.295572	+	0.955320i	$0.404490\pi$
$443$	−14.3028	+	24.7731i	−0.679546	+	1.17701i	−0.975118	+	0.221687i	$0.928844\pi$
$444$	−0.387408	+	1.67811i	−0.0183856	+	0.0796396i
$445$	5.24701	−	3.02937i	0.248732	−	0.143606i
$446$	−3.30677	+	0.796318i	−0.156580	+	0.0377068i
$447$	−27.3369	−	23.0029i	−1.29299	−	1.08800i
$448$	3.78320	−	20.8252i	0.178739	−	0.983896i
$449$		−	13.3090i		−	0.628089i	−0.949408	−	0.314045i	$-0.898316\pi$
$449$		−	13.3090i		−	0.628089i	0.949408	−	0.314045i	$-0.101684\pi$
$450$	3.89425	−	1.68369i	0.183577	−	0.0793697i
$451$	−1.76700	−	3.06053i	−0.0832047	−	0.144115i
$452$	−10.0720	−	19.6996i	−0.473747	−	0.926591i
$453$	−3.47860	+	1.26066i	−0.163439	+	0.0592309i
$454$	9.44289	+	9.93688i	0.443177	+	0.466361i
$455$	−3.56983	−	2.19064i	−0.167356	−	0.102699i
$456$	0.259236	+	27.4890i	0.0121398	+	1.28729i
$457$	20.7718	−	35.9778i	0.971662	−	1.68297i	0.281125	−	0.959671i	$-0.409292\pi$
$457$	20.7718	−	35.9778i	0.971662	−	1.68297i	0.690537	−	0.723297i	$-0.257374\pi$
$458$	24.4009	+	7.20942i	1.14018	+	0.336874i
$459$	−28.8715	−	0.119847i	−1.34760	−	0.00559398i
$460$	2.56191	+	1.65866i	0.119450	+	0.0773355i
$461$			1.91633i			0.0892525i	0.999004	+	0.0446262i	$0.0142097\pi$
$461$			1.91633i			0.0892525i	−0.999004	+	0.0446262i	$0.985790\pi$
$462$	−5.04148	−	8.09158i	−0.234551	−	0.376454i
$463$	7.93638			0.368835			0.184417	−	0.982848i	$-0.440960\pi$
$463$	7.93638			0.368835			0.184417	+	0.982848i	$0.440960\pi$
$464$	−12.3770	+	17.1355i	−0.574586	+	0.795496i
$465$	−0.152836	+	0.859819i	−0.00708761	+	0.0398732i
$466$	10.0176	−	33.9053i	0.464055	−	1.57063i
$467$	−24.2364	−	13.9929i	−1.12153	−	0.647513i	−0.179736	−	0.983715i	$-0.557524\pi$
$467$	−24.2364	−	13.9929i	−1.12153	−	0.647513i	−0.941790	+	0.336201i	$0.890858\pi$
$468$	9.42915	−	1.14459i	0.435862	−	0.0529086i
$469$	18.3890	−	9.96966i	0.849125	−	0.460356i
$470$	−10.5591	−	11.1114i	−0.487053	−	0.512532i
$471$	−4.50370	+	1.63216i	−0.207519	+	0.0752059i
$472$	11.8419	+	4.16565i	0.545068	+	0.191739i
$473$	−0.328246	+	0.189513i	−0.0150928	+	0.00871383i
$474$	6.59303	−	13.2008i	0.302828	−	0.606334i
$475$	−5.61142			−0.257470
$476$	−24.2434	−	16.6345i	−1.11119	−	0.762441i
$477$	5.94135	+	34.2490i	0.272036	+	1.56816i
$478$	−10.7305	+	2.58407i	−0.490803	+	0.118193i
$479$	16.4157	+	28.4329i	0.750054	+	1.29913i	0.947796	+	0.318877i	$0.103306\pi$
$479$	16.4157	+	28.4329i	0.750054	+	1.29913i	−0.197743	+	0.980254i	$0.563361\pi$
$480$	−8.68140	+	4.54239i	−0.396250	+	0.207331i
$481$	−0.681606	−	0.393525i	−0.0310786	−	0.0179432i
$482$	14.8473	+	15.6240i	0.676277	+	0.711655i
$483$	−4.64416	+	5.22812i	−0.211317	+	0.237888i
$484$	−0.900318	+	17.6490i	−0.0409235	+	0.802225i
$485$	8.49114	−	14.7071i	0.385563	−	0.667815i
$486$	−17.6394	−	13.2231i	−0.800140	−	0.599813i
$487$	−17.4947	−	30.3017i	−0.792761	−	1.37310i	−0.924251	−	0.381785i	$-0.875310\pi$
$487$	−17.4947	−	30.3017i	−0.792761	−	1.37310i	0.131491	−	0.991317i	$-0.458024\pi$
$488$	42.5771	−	7.98317i	1.92738	−	0.361381i
$489$	5.00711	−	5.95050i	0.226429	−	0.269091i
$490$	−3.30960	+	9.32987i	−0.149512	+	0.421481i
$491$	−33.0134			−1.48987			−0.744937	−	0.667135i	$-0.767520\pi$
$491$	−33.0134			−1.48987			−0.744937	+	0.667135i	$0.767520\pi$
$492$	−2.43315	−	7.95826i	−0.109695	−	0.358786i
$493$	14.6813	+	25.4287i	0.661212	+	1.14525i
$494$	−12.0479	−	3.55964i	−0.542061	−	0.160156i
$495$	−1.52088	+	4.14287i	−0.0683584	+	0.186208i
$496$	0.205229	−	2.00632i	0.00921507	−	0.0900866i
$497$	0.255793	−	9.54225i	0.0114739	−	0.428029i
$498$	1.98007	+	32.7436i	0.0887292	+	1.46727i
$499$	30.1483	+	17.4061i	1.34962	+	0.779206i	0.988196	−	0.153195i	$-0.0489561\pi$
$499$	30.1483	+	17.4061i	1.34962	+	0.779206i	0.361428	+	0.932400i	$0.382289\pi$
$500$	−0.910460	−	1.78075i	−0.0407170	−	0.0796375i
$501$	1.85121	−	10.4145i	0.0827061	−	0.465284i
$502$	19.0111	−	4.57815i	0.848507	−	0.204333i
$503$	7.82401			0.348855			0.174428	−	0.984670i	$-0.444193\pi$
$503$	7.82401			0.348855			0.174428	+	0.984670i	$0.444193\pi$
$504$	−7.28138	−	21.2363i	−0.324339	−	0.945941i
$505$	8.86696			0.394574
$506$	−3.08645	+	0.743262i	−0.137209	+	0.0330420i
$507$	3.18099	−	17.8955i	0.141273	−	0.794766i
$508$	18.9431	−	9.68521i	0.840464	−	0.429712i
$509$	26.6916	+	15.4104i	1.18308	+	0.683054i	0.956726	−	0.290990i	$-0.0939846\pi$
$509$	26.6916	+	15.4104i	1.18308	+	0.683054i	0.226359	+	0.974044i	$0.427318\pi$
$510$	0.821540	+	13.5854i	0.0363784	+	0.601573i
$511$	−24.1102	+	13.0714i	−1.06657	+	0.578245i
$512$	19.2186	−	11.9434i	0.849352	−	0.527827i
$513$	14.4740	+	25.3117i	0.639041	+	1.11754i
$514$	−11.5711	−	3.41877i	−0.510380	−	0.150795i
$515$	−5.86637	−	10.1609i	−0.258503	−	0.447741i
$516$	−0.853536	+	0.260959i	−0.0375748	+	0.0114881i
$517$	15.9446			0.701242
$518$	−0.574712	+	1.76924i	−0.0252514	+	0.0777359i
$519$	14.4659	−	17.1914i	0.634983	−	0.754620i
$520$	−0.825160	−	4.40088i	−0.0361857	−	0.192991i
$521$	2.96129	+	5.12911i	0.129737	+	0.224710i	0.923574	−	0.383419i	$-0.125253\pi$
$521$	2.96129	+	5.12911i	0.129737	+	0.224710i	−0.793838	+	0.608129i	$0.791920\pi$
$522$	−2.58418	+	22.2708i	−0.113107	+	0.974766i
$523$	10.9378	−	18.9448i	0.478275	−	0.828396i	−0.521415	−	0.853303i	$-0.674596\pi$
$523$	10.9378	−	18.9448i	0.478275	−	0.828396i	0.999690	+	0.0249070i	$0.00792895\pi$
$524$	−20.2173	−	1.03134i	−0.883197	−	0.0450541i
$525$	4.34867	−	1.44536i	0.189792	−	0.0630808i
$526$	5.28888	+	5.56556i	0.230606	+	0.242670i
$527$	−2.42618	−	1.40075i	−0.105686	−	0.0610178i
$528$	2.79555	−	9.80099i	0.121661	−	0.426533i
$529$	−10.3357	−	17.9019i	−0.449377	−	0.778344i
$530$	15.9309	−	3.83639i	0.691992	−	0.166642i
$531$	13.1188	−	2.27578i	0.569307	−	0.0987604i
$532$	−2.30684	+	29.6031i	−0.100014	+	1.28346i
$533$	3.80303			0.164727
$534$	−6.63107	+	13.2770i	−0.286954	+	0.574551i
$535$	−7.89804	+	4.55994i	−0.341462	+	0.197143i
$536$	21.0948	+	7.42056i	0.911158	+	0.320519i
$537$	−9.15967	+	3.31950i	−0.395269	+	0.143247i
$538$	16.9582	+	17.8453i	0.731120	+	0.769367i
$539$	−4.66359	−	9.18093i	−0.200875	−	0.395451i
$540$	−5.68408	+	8.70007i	−0.244604	+	0.374391i
$541$	18.9551	+	10.9437i	0.814943	+	0.470508i	0.848670	−	0.528923i	$-0.177404\pi$
$541$	18.9551	+	10.9437i	0.814943	+	0.470508i	−0.0337264	+	0.999431i	$0.510737\pi$
$542$	−5.54618	+	18.7715i	−0.238229	+	0.806306i
$543$	6.55524	−	36.8781i	0.281312	−	1.58259i
$544$	−4.21102	−	31.1482i	−0.180546	−	1.33547i
$545$	−6.33530			−0.271374
$546$	10.2536	−	0.344637i	0.438814	−	0.0147491i
$547$		−	36.9373i		−	1.57933i	−0.613541	−	0.789663i	$-0.710255\pi$
$547$		−	36.9373i		−	1.57933i	0.613541	−	0.789663i	$-0.289745\pi$
$548$	12.7564	−	19.7031i	0.544926	−	0.841674i
$549$	35.2789	−	29.4365i	1.50567	−	1.25632i
$550$	1.99515	+	0.589480i	0.0850734	+	0.0251355i
$551$	14.8268	−	25.6807i	0.631642	−	1.09404i
$552$	−7.47545	+	0.0704975i	−0.318176	+	0.00300057i
$553$	8.33597	−	13.5842i	0.354482	−	0.577657i
$554$	23.5352	+	24.7664i	0.999913	+	1.05222i
$555$	0.809599	−	0.293402i	0.0343656	−	0.0124542i
$556$	1.24204	−	0.635030i	0.0526742	−	0.0269313i
$557$	2.68615	+	4.65254i	0.113816	+	0.197135i	0.917306	−	0.398184i	$-0.130359\pi$
$557$	2.68615	+	4.65254i	0.113816	+	0.197135i	−0.803490	+	0.595318i	$0.797026\pi$
$558$	−0.848911	−	1.96348i	−0.0359373	−	0.0831206i
$559$		−	0.407881i		−	0.0172515i
$560$	−9.76864	+	4.07108i	−0.412800	+	0.172035i
$561$	−10.8326	−	9.11523i	−0.457354	−	0.384845i
$562$	−45.1404	+	10.8705i	−1.90413	+	0.458544i
$563$	−0.425627	+	0.245736i	−0.0179380	+	0.0103565i	−0.508942	−	0.860801i	$-0.669963\pi$
$563$	−0.425627	+	0.245736i	−0.0179380	+	0.0103565i	0.491004	+	0.871157i	$0.336630\pi$
$564$	36.5843	+	8.44585i	1.54048	+	0.355634i
$565$	−5.53127	+	9.58044i	−0.232702	+	0.403052i
$566$	1.99898	−	1.89960i	0.0840233	−	0.0798463i
$567$	−17.7365	−	15.8876i	−0.744863	−	0.667217i
$568$	7.74591	−	6.64365i	0.325011	−	0.278761i
$569$	−7.08363	−	4.08974i	−0.296961	−	0.171451i	0.344116	−	0.938927i	$-0.388179\pi$
$569$	−7.08363	−	4.08974i	−0.296961	−	0.171451i	−0.641077	+	0.767477i	$0.721512\pi$
$570$	11.4671	−	7.57855i	0.480303	−	0.317431i
$571$	−19.9812	+	11.5362i	−0.836188	+	0.482773i	−0.855967	−	0.517031i	$-0.827037\pi$
$571$	−19.9812	+	11.5362i	−0.836188	+	0.482773i	0.0197790	+	0.999804i	$0.493704\pi$
$572$	3.90971	+	2.53127i	0.163473	+	0.105838i
$573$	−20.4398	+	24.2908i	−0.853883	+	1.01476i
$574$	−1.86952	−	8.79212i	−0.0780322	−	0.366976i
$575$		−	1.52599i		−	0.0636381i
$576$	11.6059	−	21.0072i	0.483578	−	0.875301i
$577$	−24.5113	+	14.1516i	−1.02042	+	0.589138i	−0.914225	−	0.405208i	$-0.867199\pi$
$577$	−24.5113	+	14.1516i	−1.02042	+	0.589138i	−0.106192	+	0.994346i	$0.533866\pi$
$578$	−18.8155	−	5.55918i	−0.782623	−	0.231231i
$579$	−42.2386	+	15.3074i	−1.75538	+	0.636156i
$580$	10.5553	+	0.538451i	0.438284	+	0.0223580i
$581$	−0.949454	+	35.4190i	−0.0393900	+	1.46943i
$582$	2.51093	+	41.5221i	0.104081	+	1.72115i
$583$	−8.52254	+	14.7615i	−0.352967	+	0.611358i
$584$	−27.6578	−	9.72923i	−1.14449	−	0.402599i
$585$	−3.04264	−	3.64652i	−0.125797	−	0.150765i
$586$	−20.2743	+	4.88235i	−0.837524	+	0.201688i
$587$		−	16.1519i		−	0.666662i	−0.942810	−	0.333331i	$-0.891827\pi$
$587$		−	16.1519i		−	0.666662i	0.942810	−	0.333331i	$-0.108173\pi$
$588$	−5.83730	−	23.5356i	−0.240726	−	0.970593i
$589$			2.82927i			0.116578i
$590$	−1.46949	−	6.10217i	−0.0604981	−	0.251222i
$591$	3.02985	−	17.0452i	0.124631	−	0.701144i
$592$	−1.81449	+	0.813923i	−0.0745752	+	0.0334520i
$593$	−6.22547	+	10.7828i	−0.255650	+	0.442798i	−0.965072	−	0.261986i	$-0.915623\pi$
$593$	−6.22547	+	10.7828i	−0.255650	+	0.442798i	0.709422	+	0.704784i	$0.248956\pi$
$594$	−2.48724	−	10.5201i	−0.102053	−	0.431645i
$595$	−0.393932	+	14.6955i	−0.0161496	+	0.602456i
$596$	2.10176	−	41.2008i	0.0860913	−	1.68765i
$597$	−12.3185	−	33.9910i	−0.504161	−	1.39116i
$598$	0.968020	−	3.27635i	0.0395853	−	0.133980i
$599$	−15.3718	+	8.87490i	−0.628073	+	0.362618i	−0.780006	−	0.625773i	$-0.784784\pi$
$599$	−15.3718	+	8.87490i	−0.628073	+	0.362618i	0.151932	+	0.988391i	$0.451450\pi$
$600$	4.26555	+	2.40937i	0.174140	+	0.0983622i
$601$			23.7047i			0.966933i	0.875363	+	0.483466i	$0.160622\pi$
$601$			23.7047i			0.966933i	−0.875363	+	0.483466i	$0.839378\pi$
$602$	−0.942968	+	0.200509i	−0.0384325	+	0.00817213i
$603$	23.3694	−	4.05401i	0.951676	−	0.165092i
$604$	−3.58635	−	2.32192i	−0.145927	−	0.0944774i
$605$	7.65216	−	4.41797i	0.311104	−	0.179616i
$606$	−18.1198	+	11.9753i	−0.736068	+	0.486465i
$607$	−18.4365	−	10.6443i	−0.748313	−	0.432039i	0.0767711	−	0.997049i	$-0.475539\pi$
$607$	−18.4365	−	10.6443i	−0.748313	−	0.432039i	−0.825084	+	0.565010i	$0.808872\pi$
$608$	−25.1160	+	19.4114i	−1.01859	+	0.787236i
$609$	−4.87555	+	23.7207i	−0.197567	+	0.961213i
$610$	−14.9204	−	15.7009i	−0.604108	−	0.635711i
$611$	−8.57920	+	14.8596i	−0.347077	+	0.601156i
$612$	−20.0268	−	26.6526i	−0.809534	−	1.07737i
$613$	−12.7964	+	7.38799i	−0.516841	+	0.298398i	−0.735641	−	0.677372i	$-0.763119\pi$
$613$	−12.7964	+	7.38799i	−0.516841	+	0.298398i	0.218801	+	0.975770i	$0.429786\pi$
$614$	8.24588	+	34.2416i	0.332777	+	1.38188i
$615$	−2.67902	+	3.18377i	−0.108028	+	0.128382i
$616$	3.93001	−	10.2831i	0.158344	−	0.414317i
$617$			30.4468i			1.22574i	0.790183	+	0.612871i	$0.209985\pi$
$617$			30.4468i			1.22574i	−0.790183	+	0.612871i	$0.790015\pi$
$618$	25.7109	+	12.8411i	1.03424	+	0.516544i
$619$	−16.2068	−	28.0710i	−0.651407	−	1.12827i	−0.982782	−	0.184771i	$-0.940846\pi$
$619$	−16.2068	−	28.0710i	−0.651407	−	1.12827i	0.331374	−	0.943499i	$-0.392488\pi$
$620$	−0.897850	+	0.459052i	−0.0360585	+	0.0184360i
$621$	−6.88335	+	3.93610i	−0.276219	+	0.157950i
$622$	8.16751	−	7.76149i	0.327487	−	0.311207i
$623$	−8.38407	+	13.6625i	−0.335901	+	0.547378i
$624$	7.62988	+	7.87888i	0.305440	+	0.315408i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−11.4497	+	38.7526i	−0.457623	+	1.54887i
$627$	−2.50226	+	14.0771i	−0.0999305	+	0.562184i
$628$	−4.64320	−	3.00615i	−0.185284	−	0.119959i
$629$			2.76246i			0.110146i
$630$	−6.93457	+	8.82677i	−0.276280	+	0.351667i
$631$	−8.40055			−0.334421			−0.167210	−	0.985921i	$-0.553476\pi$
$631$	−8.40055			−0.334421			−0.167210	+	0.985921i	$0.553476\pi$
$632$	16.7465	−	3.13996i	0.666142	−	0.124901i
$633$	17.6803	+	3.14274i	0.702729	+	0.124913i
$634$	−15.9846	−	4.72277i	−0.634831	−	0.187565i
$635$	−9.21253	−	5.31886i	−0.365588	−	0.211072i
$636$	−27.3738	+	29.3553i	−1.08544	+	1.16401i
$637$	11.0655	+	0.593679i	0.438431	+	0.0235224i
$638$	−7.96944	+	7.57326i	−0.315513	+	0.299828i
$639$	3.73009	−	10.1607i	0.147560	−	0.401953i
$640$	−10.2352	−	4.82089i	−0.404581	−	0.190562i
$641$	30.8062	−	17.7860i	1.21677	−	0.702504i	0.252547	−	0.967585i	$-0.418732\pi$
$641$	30.8062	−	17.7860i	1.21677	−	0.702504i	0.964226	+	0.265081i	$0.0853986\pi$
$642$	9.98138	−	19.9851i	0.393934	−	0.788749i
$643$	−35.4168			−1.39670			−0.698351	−	0.715756i	$-0.746082\pi$
$643$	−35.4168			−1.39670			−0.698351	+	0.715756i	$0.746082\pi$
$644$	−8.05037	−	0.627329i	−0.317229	−	0.0247202i
$645$	0.341464	+	0.287329i	0.0134451	+	0.0113136i
$646$	10.3233	+	42.8684i	0.406166	+	1.68663i
$647$	−18.0279	−	31.2253i	−0.708750	−	1.22759i	−0.965321	−	0.261066i	$-0.915926\pi$
$647$	−18.0279	−	31.2253i	−0.708750	−	1.22759i	0.256570	−	0.966526i	$-0.417407\pi$
$648$	−0.134386	−	25.4555i	−0.00527919	−	0.999986i
$649$	5.65425	+	3.26448i	0.221949	+	0.128142i
$650$	−1.62289	+	1.54221i	−0.0636548	+	0.0604904i
$651$	−0.728749	−	2.19259i	−0.0285619	−	0.0859345i
$652$	8.96829	+	0.457495i	0.351225	+	0.0179169i
$653$	−6.06477	+	10.5045i	−0.237333	+	0.411073i	−0.959948	−	0.280178i	$-0.909607\pi$
$653$	−6.06477	+	10.5045i	−0.237333	+	0.411073i	0.722615	+	0.691251i	$0.242940\pi$
$654$	12.9463	−	8.55619i	0.506242	−	0.334573i
$655$	5.06090	+	8.76573i	0.197746	+	0.342505i
$656$	5.62655	−	7.78978i	0.219680	−	0.304140i
$657$	−30.6401	+	5.31528i	−1.19538	+	0.207369i
$658$	38.5710	+	12.5292i	1.50365	+	0.488440i
$659$	−6.15679			−0.239834			−0.119917	−	0.992784i	$-0.538263\pi$
$659$	−6.15679			−0.239834			−0.119917	+	0.992784i	$0.538263\pi$
$660$	−4.87326	+	1.48995i	−0.189691	+	0.0579961i
$661$	18.7652	+	32.5024i	0.729883	+	1.26420i	0.956932	+	0.290312i	$0.0937590\pi$
$661$	18.7652	+	32.5024i	0.729883	+	1.26420i	−0.227049	+	0.973883i	$0.572908\pi$
$662$	2.35462	−	7.96943i	0.0915150	−	0.309741i
$663$	14.3236	−	5.19094i	0.556283	−	0.201599i
$664$	−28.7513	+	24.6599i	−1.11577	+	0.956990i
$665$	13.0517	−	7.07601i	0.506122	−	0.274396i
$666$	−1.25818	+	1.69298i	−0.0487534	+	0.0656018i
$667$	6.98370	+	4.03204i	0.270410	+	0.156121i
$668$	10.8751	−	5.56022i	0.420771	−	0.215131i
$669$	−4.10143	−	0.729046i	−0.158570	−	0.0281865i
$670$	−2.61771	−	10.8702i	−0.101131	−	0.419953i
$671$	22.5304			0.869775
$672$	14.4642	−	21.5125i	0.557969	−	0.829862i
$673$	7.24538			0.279289			0.139644	−	0.990202i	$-0.455404\pi$
$673$	7.24538			0.279289			0.139644	+	0.990202i	$0.455404\pi$
$674$	2.80888	+	11.6641i	0.108194	+	0.449283i
$675$	5.19611	+	0.0215693i	0.199998	+	0.000830204i
$676$	18.6870	−	9.55429i	0.718732	−	0.367473i
$677$	5.99640	+	3.46202i	0.230460	+	0.133056i	0.610784	−	0.791797i	$-0.290854\pi$
$677$	5.99640	+	3.46202i	0.230460	+	0.133056i	−0.380324	+	0.924853i	$0.624188\pi$
$678$	−1.63566	−	27.0482i	−0.0628172	−	1.03878i
$679$	−1.20400	+	44.9148i	−0.0462054	+	1.72367i
$680$	−11.9290	+	10.2315i	−0.457457	+	0.392360i
$681$	5.72028	+	15.7843i	0.219202	+	0.604854i
$682$	0.297215	−	1.00595i	0.0113809	−	0.0385198i
$683$	0.187389	+	0.324567i	0.00717025	+	0.0124192i	0.869588	−	0.493778i	$-0.164384\pi$
$683$	0.187389	+	0.324567i	0.00717025	+	0.0124192i	−0.862418	+	0.506197i	$0.831051\pi$
$684$	−13.1980	+	30.9739i	−0.504637	+	1.18432i
$685$	−11.7360			−0.448410
$686$	−4.06715	−	25.8739i	−0.155284	−	0.987870i
$687$	23.8437	+	20.0636i	0.909696	+	0.765473i
$688$	−0.835466	−	0.603456i	−0.0318519	−	0.0230066i
$689$	−9.17134	−	15.8852i	−0.349400	−	0.605179i
$690$	2.06094	+	3.11839i	0.0784585	+	0.118715i
$691$	12.7306	−	22.0500i	0.484294	−	0.838821i	−0.515544	−	0.856863i	$-0.672410\pi$
$691$	12.7306	−	22.0500i	0.484294	−	0.838821i	0.999837	+	0.0180422i	$0.00574333\pi$
$692$	25.9100	+	1.32174i	0.984952	+	0.0502449i
$693$	−1.68673	−	11.5538i	−0.0640738	−	0.438892i
$694$	−26.7218	+	25.3934i	−1.01434	+	0.963919i
$695$	−0.604037	−	0.348741i	−0.0229124	−	0.0132285i
$696$	−22.2972	+	13.1552i	−0.845172	+	0.498645i
$697$	−6.67410	−	11.5599i	−0.252800	−	0.437862i
$698$	4.72024	+	19.6011i	0.178664	+	0.741914i
$699$	27.8785	−	33.1311i	1.05446	−	1.25313i
$700$	4.36318	+	2.99377i	0.164913	+	0.113154i
$701$	−36.9898			−1.39709			−0.698544	−	0.715568i	$-0.746168\pi$
$701$	−36.9898			−1.39709			−0.698544	+	0.715568i	$0.746168\pi$
$702$	11.1425	+	3.34249i	0.420548	+	0.126154i
$703$	2.41607	−	1.39492i	0.0911236	−	0.0526103i
$704$	10.9692	−	4.26331i	0.413417	−	0.160679i
$705$	−6.39642	−	17.6500i	−0.240903	−	0.664737i
$706$	−12.4758	+	11.8556i	−0.469532	+	0.446191i
$707$	−20.6238	+	11.1812i	−0.775637	+	0.420514i
$708$	11.2443	+	10.4853i	0.422586	+	0.394062i
$709$	−10.7817	−	6.22482i	−0.404916	−	0.233778i	0.283687	−	0.958917i	$-0.408442\pi$
$709$	−10.7817	−	6.22482i	−0.404916	−	0.233778i	−0.688603	+	0.725139i	$0.741776\pi$
$710$	−4.89327	−	1.44575i	−0.183641	−	0.0542581i
$711$	13.8760	−	11.5781i	0.520390	−	0.434211i
$712$	−16.8432	+	3.15807i	−0.631224	+	0.118354i
$713$	−0.769401			−0.0288143
$714$	−19.0421	−	30.5626i	−0.712632	−	1.14378i
$715$		−	2.32879i		−	0.0870920i
$716$	−9.44340	−	6.11395i	−0.352916	−	0.228489i
$717$	−13.3092	−	2.36577i	−0.497042	−	0.0883513i
$718$	3.42934	−	11.6069i	0.127982	−	0.433166i
$719$	−24.7488	+	42.8661i	−0.922974	+	1.59864i	−0.128186	+	0.991750i	$0.540915\pi$
$719$	−24.7488	+	42.8661i	−0.922974	+	1.59864i	−0.794788	+	0.606887i	$0.792418\pi$
$720$	−11.9708	+	0.837265i	−0.446124	+	0.0312030i
$721$	26.4575	+	16.2358i	0.985330	+	0.604651i
$722$	12.8022	−	12.1658i	0.476449	−	0.452763i
$723$	8.99415	+	24.8180i	0.334496	+	0.922993i
$724$	38.5093	−	19.6890i	1.43119	−	0.731737i
$725$	−2.64225	−	4.57651i	−0.0981306	−	0.169967i
$726$	−9.67063	+	19.3629i	−0.358911	+	0.718626i
$727$			25.7928i			0.956601i	0.878196	+	0.478300i	$0.158747\pi$
$727$			25.7928i			0.956601i	−0.878196	+	0.478300i	$0.841253\pi$
$728$	7.46877	+	9.19554i	0.276811	+	0.340809i
$729$	−13.3054	−	23.4940i	−0.492793	−	0.870147i
$730$	3.43213	+	14.2522i	0.127029	+	0.527496i
$731$	−1.23981	+	0.715807i	−0.0458562	+	0.0264751i
$732$	51.6951	+	11.9343i	1.91071	+	0.441106i
$733$	−16.5408	+	28.6495i	−0.610949	+	1.05819i	0.380132	+	0.924932i	$0.375878\pi$
$733$	−16.5408	+	28.6495i	−0.610949	+	1.05819i	−0.991081	+	0.133262i	$0.957455\pi$
$734$	28.4233	+	29.9102i	1.04912	+	1.10401i
$735$	−8.29203	+	8.84547i	−0.305856	+	0.326270i
$736$	−5.27880	−	6.83014i	−0.194579	−	0.251762i
$737$	10.0723	+	5.81525i	0.371018	+	0.214207i
$738$	1.17477	−	10.1243i	0.0432438	−	0.372680i
$739$	−34.5398	+	19.9416i	−1.27057	+	0.733563i	−0.975095	−	0.221788i	$-0.928811\pi$
$739$	−34.5398	+	19.9416i	−1.27057	+	0.733563i	−0.295473	+	0.955351i	$0.595477\pi$
$740$	0.834677	+	0.540396i	0.0306833	+	0.0198653i
$741$	−11.7728	−	9.90635i	−0.432485	−	0.363919i
$742$	−32.2161	+	29.0119i	−1.18269	+	1.06506i
$743$		−	28.6559i		−	1.05128i	−0.850706	−	0.525642i	$-0.823825\pi$
$743$		−	28.6559i		−	1.05128i	0.850706	−	0.525642i	$-0.176175\pi$
$744$	1.21480	−	2.15068i	0.0445368	−	0.0788479i
$745$	−17.8637	+	10.3136i	−0.654474	+	0.377860i
$746$	−5.15799	+	17.4577i	−0.188847	+	0.639171i
$747$	−13.8453	+	37.7147i	−0.506575	+	1.37991i
$748$	0.832850	−	16.3264i	0.0304520	−	0.596951i
$749$	12.6201	−	20.5655i	0.461128	−	0.751446i
$750$	−0.147856	−	2.44502i	−0.00539893	−	0.0892796i
$751$	6.99268	−	12.1117i	0.255166	−	0.441961i	−0.709774	−	0.704429i	$-0.751203\pi$
$751$	6.99268	−	12.1117i	0.255166	−	0.441961i	0.964941	+	0.262468i	$0.0845364\pi$
$752$	17.7442	+	39.5576i	0.647066	+	1.44252i
$753$	23.5797	+	4.19139i	0.859293	+	0.152743i
$754$	−2.76986	−	11.5020i	−0.100872	−	0.418880i
$755$			2.13619i			0.0777439i
$756$	2.24989	−	27.4032i	0.0818278	−	0.996646i
$757$		−	20.8260i		−	0.756933i	−0.925615	−	0.378467i	$-0.876451\pi$
$757$		−	20.8260i		−	0.756933i	0.925615	−	0.378467i	$-0.123549\pi$
$758$	1.90937	−	0.459803i	0.0693513	−	0.0167008i
$759$	−3.82816	−	0.680472i	−0.138954	−	0.0246996i
$760$	14.9722	+	5.26677i	0.543097	+	0.191046i
$761$	−10.6790	+	18.4965i	−0.387112	+	0.670498i	−0.992060	−	0.125767i	$-0.959861\pi$
$761$	−10.6790	+	18.4965i	−0.387112	+	0.670498i	0.604947	+	0.796265i	$0.293194\pi$
$762$	26.0095	−	1.57285i	0.942223	−	0.0569783i
$763$	14.7354	−	7.98882i	0.533456	−	0.289215i
$764$	−36.6099	−	1.86756i	−1.32450	−	0.0675660i
$765$	−5.74449	+	15.6480i	−0.207692	+	0.565754i
$766$	10.8884	+	3.21705i	0.393413	+	0.116237i
$767$	−6.08469	+	3.51300i	−0.219706	+	0.126847i
$768$	27.4267	−	3.97162i	0.989677	−	0.143314i
$769$		−	20.6278i		−	0.743856i	−0.928262	−	0.371928i	$-0.878697\pi$
$769$		−	20.6278i		−	0.743856i	0.928262	−	0.371928i	$-0.121303\pi$
$770$	−5.38388	+	1.14480i	−0.194021	+	0.0412559i
$771$	−11.3069	−	9.51431i	−0.407208	−	0.342650i
$772$	−43.5470	−	28.1937i	−1.56729	−	1.01471i
$773$	7.19484	−	4.15394i	0.258780	−	0.149407i	−0.364998	−	0.931008i	$-0.618930\pi$
$773$	7.19484	−	4.15394i	0.258780	−	0.149407i	0.623778	+	0.781602i	$0.285597\pi$
$774$	−1.08584	−	0.125996i	−0.0390299	−	0.00452882i
$775$	0.436649	+	0.252099i	0.0156849	+	0.00905567i
$776$	−36.4595	+	31.2712i	−1.30882	+	1.12257i
$777$	−1.51308	+	1.70333i	−0.0542813	+	0.0611067i
$778$	6.21115	−	5.90238i	0.222681	−	0.211611i
$779$	−6.74023	+	11.6744i	−0.241494	+	0.418280i
$780$	1.23356	−	5.34334i	0.0441686	−	0.191322i
$781$	4.59645	−	2.65376i	0.164474	−	0.0949590i
$782$	−11.6578	+	2.80736i	−0.416881	+	0.100391i
$783$	−13.8281	+	23.7230i	−0.494177	+	0.847792i
$784$	17.5874	−	21.7873i	0.628120	−	0.778116i
$785$			2.76570i			0.0987119i
$786$	−22.1807	−	11.0779i	−0.791159	−	0.395137i
$787$	−23.7585	−	41.1509i	−0.846899	−	1.46687i	−0.883962	−	0.467559i	$-0.845134\pi$
$787$	−23.7585	−	41.1509i	−0.846899	−	1.46687i	0.0370629	−	0.999313i	$-0.488200\pi$
$788$	17.7991	−	9.10031i	0.634066	−	0.324185i
$789$	3.20388	+	8.84063i	0.114061	+	0.314735i
$790$	−5.86852	−	6.17552i	−0.208793	−	0.219715i
$791$	0.784307	−	29.2582i	0.0278867	−	1.04030i
$792$	7.94637	−	9.62637i	0.282362	−	0.342058i
$793$	−12.1228	+	20.9973i	−0.430492	+	0.745634i
$794$	−44.2893	−	13.0856i	−1.57177	−	0.464390i
$795$	19.7593	+	3.51229i	0.700789	+	0.124568i
$796$	22.6885	−	35.0439i	0.804172	−	1.24210i
$797$		−	23.1123i		−	0.818681i	−0.912382	−	0.409341i	$-0.865759\pi$
$797$		−	23.1123i		−	0.818681i	0.912382	−	0.409341i	$-0.134241\pi$
$798$	−17.1149	+	32.0871i	−0.605860	+	1.13587i
$799$	60.2240			2.13057
$800$	0.757874	+	5.60586i	0.0267949	+	0.198197i
$801$	−13.9560	+	11.6449i	−0.493113	+	0.411451i
$802$	−0.214898	+	0.727342i	−0.00758832	+	0.0256833i
$803$	−13.2060	−	7.62449i	−0.466029	−	0.269062i
$804$	20.0302	+	18.6782i	0.706412	+	0.658729i
$805$	1.92427	+	3.54932i	0.0678217	+	0.125097i
$806$	0.777579	+	0.818256i	0.0273890	+	0.0288218i
$807$	10.2729	+	28.3465i	0.361623	+	0.997844i
$808$	−23.6584	−	8.32236i	−0.832301	−	0.292780i
$809$	40.9428	−	23.6383i	1.43947	−	0.831080i	0.441660	−	0.897183i	$-0.354390\pi$
$809$	40.9428	−	23.6383i	1.43947	−	0.831080i	0.997813	+	0.0661027i	$0.0210565\pi$
$810$	−10.6475	+	6.97357i	−0.374115	+	0.245026i
$811$	−10.6244			−0.373074			−0.186537	−	0.982448i	$-0.559726\pi$
$811$	−10.6244			−0.373074			−0.186537	+	0.982448i	$0.559726\pi$
$812$	−25.2296	+	12.0578i	−0.885387	+	0.423147i
$813$	−15.4348	+	18.3429i	−0.541323	+	0.643314i
$814$	−1.00557	+	0.242156i	−0.0352452	+	0.00848758i
$815$	−2.24499	−	3.88843i	−0.0786385	−	0.136206i
$816$	10.5590	−	37.0192i	0.369640	−	1.29593i
$817$	1.25210	+	0.722901i	0.0438055	+	0.0252911i
$818$	−28.9065	−	30.4187i	−1.01069	−	1.06356i
$819$	11.6752	+	4.64472i	0.407964	+	0.162300i
$820$	−4.79842	−	0.244779i	−0.167568	−	0.00854807i
$821$	−10.7148	+	18.5585i	−0.373948	+	0.647697i	−0.990169	−	0.139876i	$-0.955329\pi$
$821$	−10.7148	+	18.5585i	−0.373948	+	0.647697i	0.616221	+	0.787573i	$0.288663\pi$
$822$	23.9829	−	15.8502i	0.836498	−	0.552839i
$823$	0.539744	+	0.934864i	0.0188143	+	0.0325873i	0.875279	−	0.483618i	$-0.160678\pi$
$823$	0.539744	+	0.934864i	0.0188143	+	0.0325873i	−0.856465	+	0.516205i	$0.827344\pi$
$824$	6.11562	+	32.6168i	0.213048	+	1.13626i
$825$	1.94959	+	1.64050i	0.0678760	+	0.0571150i
$826$	11.1128	+	12.3401i	0.386662	+	0.429367i
$827$	0.330867			0.0115054			0.00575268	−	0.999983i	$-0.498169\pi$
$827$	0.330867			0.0115054			0.00575268	+	0.999983i	$0.498169\pi$
$828$	−8.42315	−	3.58910i	−0.292725	−	0.124730i
$829$	12.3113	+	21.3239i	0.427591	+	0.740609i	0.996658	−	0.0816820i	$-0.0260292\pi$
$829$	12.3113	+	21.3239i	0.427591	+	0.740609i	−0.569068	+	0.822291i	$0.692696\pi$
$830$	18.1629	+	5.36634i	0.630442	+	0.186268i
$831$	14.2570	+	39.3402i	0.494572	+	1.36470i
$832$	−1.92893	+	12.5167i	−0.0668735	+	0.433939i
$833$	−17.6148	−	34.6771i	−0.610315	−	1.20149i
$834$	1.70536	−	0.103127i	0.0590518	−	0.00357099i
$835$	−5.28886	−	3.05352i	−0.183029	−	0.105672i
$836$	−14.6997	+	7.51566i	−0.508400	+	0.259935i
$837$	0.0108752	−	2.61987i	0.000375903	−	0.0905559i
$838$	39.8303	−	9.59173i	1.37592	−	0.331341i
$839$	31.3993			1.08402			0.542012	−	0.840371i	$-0.317663\pi$
$839$	31.3993			1.08402			0.542012	+	0.840371i	$0.317663\pi$
$840$	−12.9595	−	0.225126i	−0.447146	−	0.00776758i
$841$	−1.07409			−0.0370376
$842$	8.98170	−	2.16293i	0.309530	−	0.0745394i
$843$	−55.9883	−	9.95215i	−1.92834	−	0.342770i
$844$	9.43940	+	18.4623i	0.324918	+	0.635499i
$845$	−9.08800	−	5.24696i	−0.312637	−	0.180501i
$846$	36.9086	+	27.4294i	1.26894	+	0.943043i
$847$	−12.2272	+	19.9252i	−0.420131	+	0.684638i
$848$	−46.1068	−	4.71632i	−1.58331	−	0.161959i
$849$	3.17528	−	1.15074i	0.108975	−	0.0394931i
$850$	7.53584	+	2.22652i	0.258477	+	0.0763689i
$851$	0.379338	+	0.657033i	0.0130035	+	0.0225228i
$852$	11.9521	−	3.65422i	0.409472	−	0.125192i
$853$	−18.6873			−0.639841			−0.319920	−	0.947444i	$-0.603656\pi$
$853$	−18.6873			−0.639841			−0.319920	+	0.947444i	$0.603656\pi$
$854$	54.5024	+	17.7043i	1.86503	+	0.605830i
$855$	16.5865	−	2.87735i	0.567248	−	0.0984033i
$856$	25.3531	−	4.75368i	0.866551	−	0.162477i
$857$	26.9989	+	46.7635i	0.922266	+	1.59741i	0.795900	+	0.605428i	$0.206998\pi$
$857$	26.9989	+	46.7635i	0.922266	+	1.59741i	0.126367	+	0.991984i	$0.459668\pi$
$858$	3.14517	+	4.75895i	0.107374	+	0.162468i
$859$	10.5039	−	18.1932i	0.358388	−	0.620745i	−0.629304	−	0.777159i	$-0.716660\pi$
$859$	10.5039	−	18.1932i	0.358388	−	0.620745i	0.987692	+	0.156414i	$0.0499933\pi$
$860$	−0.0262530	+	0.514637i	−0.000895219	+	0.0175490i
$861$	2.21642	−	10.7834i	0.0755355	−	0.367498i
$862$	−10.4792	−	11.0274i	−0.356924	−	0.375596i
$863$	−6.39202	−	3.69044i	−0.217587	−	0.125624i	0.387245	−	0.921977i	$-0.373427\pi$
$863$	−6.39202	−	3.69044i	−0.217587	−	0.125624i	−0.604832	+	0.796353i	$0.706760\pi$
$864$	23.3318	−	17.8782i	0.793762	−	0.608228i
$865$	−6.48593	−	11.2340i	−0.220528	−	0.381966i
$866$	16.1789	−	3.89611i	0.549780	−	0.132395i
$867$	−18.3859	−	15.4710i	−0.624418	−	0.525423i
$868$	1.50946	−	2.19991i	0.0512343	−	0.0746697i
$869$	8.86169			0.300612
$870$	11.5803	+	5.78370i	0.392610	+	0.196086i
$871$	−10.8391	+	6.25795i	−0.367269	+	0.212043i
$872$	16.9036	+	5.94619i	0.572427	+	0.201363i
$873$	−17.5573	+	47.8260i	−0.594224	+	1.61866i
$874$	8.34199	+	8.77838i	0.282172	+	0.296933i
$875$	0.0708975	−	2.64480i	0.00239677	−	0.0894106i
$876$	−26.2620	−	24.4893i	−0.887311	−	0.827418i
$877$	−5.16655	−	2.98291i	−0.174462	−	0.100726i	0.410226	−	0.911984i	$-0.365450\pi$
$877$	−5.16655	−	2.98291i	−0.174462	−	0.100726i	−0.584688	+	0.811258i	$0.698783\pi$
$878$	−11.9434	+	40.4234i	−0.403070	+	1.36422i
$879$	−25.1465	−	4.46990i	−0.848172	−	0.150766i
$880$	−4.77009	−	3.44543i	−0.160800	−	0.116146i
$881$	−6.16710			−0.207775			−0.103887	−	0.994589i	$-0.533128\pi$
$881$	−6.16710			−0.207775			−0.103887	+	0.994589i	$0.533128\pi$
$882$	4.99864	−	29.2748i	0.168313	−	0.985734i
$883$		−	33.1527i		−	1.11568i	−0.829950	−	0.557839i	$-0.811631\pi$
$883$		−	33.1527i		−	1.11568i	0.829950	−	0.557839i	$-0.188369\pi$
$884$	14.7673	+	9.56081i	0.496678	+	0.321565i
$885$	1.34535	−	7.56861i	0.0452235	−	0.254416i
$886$	−38.7964	−	11.4627i	−1.30339	−	0.385096i
$887$	27.6596	−	47.9079i	0.928719	−	1.60859i	0.143252	−	0.989686i	$-0.454244\pi$
$887$	27.6596	−	47.9079i	0.928719	−	1.60859i	0.785467	−	0.618903i	$-0.212423\pi$
$888$	−2.43552	+	0.0229682i	−0.0817307	+	0.000770763i
$889$	28.1346	+	0.754188i	0.943606	+	0.0252946i
$890$	5.90238	+	6.21115i	0.197848	+	0.208198i
$891$	2.37117	−	13.0256i	0.0794371	−	0.436373i
$892$	−2.18973	−	4.28284i	−0.0733176	−	0.143400i
$893$	−30.4104	−	52.6724i	−1.01765	−	1.76261i
$894$	22.5757	−	45.2020i	0.755045	−	1.51178i
$895$			5.62490i			0.188020i
$896$	29.8853	−	1.69362i	0.998398	−	0.0565799i
$897$	2.69397	−	3.20154i	0.0899489	−	0.106896i
$898$	18.2986	−	4.40658i	0.610633	−	0.147049i
$899$	−2.30747	+	1.33222i	−0.0769584	+	0.0444319i
$900$	3.60429	+	4.79678i	0.120143	+	0.159893i
$901$	−32.1904	+	55.7553i	−1.07242	+	1.85748i
$902$	3.62290	−	3.44280i	0.120629	−	0.114633i
$903$	−1.15654	−	0.237715i	−0.0384872	−	0.00791065i
$904$	23.7503	−	20.3706i	0.789924	−	0.677515i
$905$	−18.7281	−	10.8127i	−0.622544	−	0.359426i
$906$	−2.88505	−	4.36535i	−0.0958493	−	0.145029i
$907$	−26.3055	+	15.1875i	−0.873460	+	0.504292i	−0.868496	−	0.495695i	$-0.834913\pi$
$907$	−26.3055	+	15.1875i	−0.873460	+	0.504292i	−0.00496351	+	0.999988i	$0.501580\pi$
$908$	−10.5358	+	16.2732i	−0.349642	+	0.540045i
$909$	−26.2094	+	4.54668i	−0.869312	+	0.150804i
$910$	1.82996	−	5.63350i	0.0606627	−	0.186749i
$911$			27.1919i			0.900908i	0.892800	+	0.450454i	$0.148738\pi$
$911$			27.1919i			0.900908i	−0.892800	+	0.450454i	$0.851262\pi$
$912$	−37.7090	+	9.45799i	−1.24867	+	0.313185i
$913$	−17.0611	+	9.85023i	−0.564640	+	0.325995i
$914$	56.3436	+	16.6471i	1.86368	+	0.550637i
$915$	−9.03841	−	24.9402i	−0.298801	−	0.824496i
$916$	−1.83319	+	35.9361i	−0.0605703	+	1.18736i
$917$	−22.8248	−	14.0065i	−0.753742	−	0.462537i
$918$	−9.39451	−	39.7353i	−0.310065	−	1.31146i
$919$	2.13532	−	3.69848i	0.0704376	−	0.122002i	−0.828656	−	0.559759i	$-0.810894\pi$
$919$	2.13532	−	3.69848i	0.0704376	−	0.122002i	0.899093	+	0.437757i	$0.144227\pi$
$920$	−1.43226	+	4.07158i	−0.0472203	+	0.134236i
$921$	−7.54928	+	42.4704i	−0.248757	+	1.39945i
$922$	−2.63478	+	0.634494i	−0.0867719	+	0.0208960i
$923$			5.71157i			0.187999i
$924$	9.45596	−	9.61068i	0.311078	−	0.316168i
$925$		−	0.497170i		−	0.0163469i
$926$	2.62772	+	10.9118i	0.0863523	+	0.358584i
$927$	22.5503	+	27.0259i	0.740648	+	0.887647i
$928$	−27.6577	−	11.3437i	−0.907910	−	0.372374i
$929$	−10.0716	+	17.4445i	−0.330438	+	0.572335i	−0.982598	−	0.185747i	$-0.940530\pi$
$929$	−10.0716	+	17.4445i	−0.330438	+	0.572335i	0.652160	+	0.758081i	$0.273863\pi$
$930$	−1.23278	+	0.0745487i	−0.0404243	+	0.00244455i
$931$	−21.4342	+	32.9164i	−0.702478	+	1.07879i
$932$	49.9335	+	2.54724i	1.63563	+	0.0834375i
$933$	12.9737	−	4.70173i	0.424740	−	0.153928i
$934$	11.2143	−	37.9558i	0.366944	−	1.24195i
$935$	−7.07872	+	4.08690i	−0.231499	+	0.133656i
$936$	4.69568	+	12.5852i	0.153483	+	0.411362i
$937$			16.7110i			0.545926i	0.962025	+	0.272963i	$0.0880036\pi$
$937$			16.7110i			0.545926i	−0.962025	+	0.272963i	$0.911996\pi$
$938$	19.7959	+	21.9823i	0.646360	+	0.717746i
$939$	−31.8642	+	37.8677i	−1.03985	+	1.23577i
$940$	11.7811	−	18.1967i	0.384257	−	0.593511i
$941$	16.1422	−	9.31972i	0.526221	−	0.303814i	−0.213255	−	0.976997i	$-0.568407\pi$
$941$	16.1422	−	9.31972i	0.526221	−	0.303814i	0.739476	+	0.673183i	$0.235073\pi$
$942$	−3.73523	−	5.65177i	−0.121701	−	0.184145i
$943$	−3.17478	−	1.83296i	−0.103385	−	0.0596894i
$944$	−1.80654	+	17.6608i	−0.0587980	+	0.574810i
$945$	−12.1129	+	6.50213i	−0.394033	+	0.211514i
$946$	−0.369245	−	0.388561i	−0.0120052	−	0.0126332i
$947$	0.965283	−	1.67192i	0.0313675	−	0.0543301i	−0.849916	−	0.526919i	$-0.823347\pi$
$947$	0.965283	−	1.67192i	0.0313675	−	0.0543301i	0.881283	+	0.472589i	$0.156680\pi$
$948$	20.3329	+	4.69404i	0.660380	+	0.152455i
$949$	14.2113	−	8.20492i	0.461320	−	0.266343i
$950$	−1.85793	−	7.71519i	−0.0602793	−	0.250314i
$951$	−15.6196	−	13.1433i	−0.506501	−	0.426201i
$952$	14.8440	−	38.8401i	0.481096	−	1.25881i
$953$			42.6606i			1.38191i	0.722897	+	0.690956i	$0.242810\pi$
$953$			42.6606i			1.38191i	−0.722897	+	0.690956i	$0.757190\pi$
$954$	−45.1221	+	19.5086i	−1.46088	+	0.631614i
$955$	9.16437	+	15.8732i	0.296552	+	0.513643i
$956$	−7.10572	−	13.8979i	−0.229815	−	0.449491i
$957$	−12.6591	+	4.58770i	−0.409210	+	0.148299i
$958$	−33.6574	+	31.9842i	−1.08742	+	1.03336i
$959$	27.2970	−	14.7991i	0.881466	−	0.477889i
$960$	−9.11977	−	10.4322i	−0.294339	−	0.336696i
$961$	−15.3729	+	26.6266i	−0.495900	+	0.858924i
$962$	0.315383	−	1.06744i	0.0101684	−	0.0344157i
$963$	21.0073	−	17.5284i	0.676950	−	0.564843i
$964$	−16.5657	+	25.5868i	−0.533545	+	0.824095i
$965$			25.9385i			0.834990i
$966$	−8.72586	−	4.65427i	−0.280750	−	0.149749i
$967$	33.0187			1.06181			0.530905	−	0.847432i	$-0.321852\pi$
$967$	33.0187			1.06181			0.530905	+	0.847432i	$0.321852\pi$
$968$	−24.5638	+	4.60568i	−0.789510	+	0.148032i
$969$	−9.45123	+	53.1703i	−0.303617	+	1.70808i
$970$	23.0323	+	6.80506i	0.739523	+	0.218497i
$971$	13.4749	+	7.77976i	0.432431	+	0.249664i	0.700382	−	0.713768i	$-0.253013\pi$
$971$	13.4749	+	7.77976i	0.432431	+	0.249664i	−0.267951	+	0.963433i	$0.586346\pi$
$972$	12.3402	−	28.6307i	0.395813	−	0.918331i
$973$	1.84470	+	0.0494498i	0.0591384	+	0.00158529i
$974$	35.8696	−	34.0865i	1.14934	−	1.09220i
$975$	−2.57788	+	0.934233i	−0.0825581	+	0.0299194i
$976$	25.0733	+	55.8965i	0.802578	+	1.78920i
$977$	−14.1606	+	8.17565i	−0.453039	+	0.261562i	−0.709113	−	0.705095i	$-0.750904\pi$
$977$	−14.1606	+	8.17565i	−0.453039	+	0.261562i	0.256074	+	0.966657i	$0.417571\pi$
$978$	9.83925	+	4.91412i	0.314624	+	0.157136i
$979$	−8.91282			−0.284855
$980$	−13.9235	−	1.46129i	−0.444771	−	0.0466792i
$981$	18.7262	−	3.24853i	0.597882	−	0.103718i
$982$	−10.9307	−	45.3904i	−0.348812	−	1.44847i
$983$	−26.2863	−	45.5291i	−0.838401	−	1.45215i	−0.891231	−	0.453550i	$-0.850157\pi$
$983$	−26.2863	−	45.5291i	−0.838401	−	1.45215i	0.0528295	−	0.998604i	$-0.483176\pi$
$984$	10.1363	−	5.98033i	0.323132	−	0.190646i
$985$	−8.65618	−	4.99765i	−0.275809	−	0.159238i
$986$	−30.1012	+	28.6048i	−0.958619	+	0.910964i
$987$	37.1342	+	32.9864i	1.18199	+	1.04997i
$988$	0.905134	−	17.7434i	0.0287962	−	0.564492i
$989$	−0.196588	+	0.340500i	−0.00625113	+	0.0108273i
$990$	−6.19963	−	0.719372i	−0.197037	−	0.0228631i
$991$	−22.9752	−	39.7941i	−0.729830	−	1.26410i	−0.956955	−	0.290237i	$-0.906266\pi$
$991$	−22.9752	−	39.7941i	−0.729830	−	1.26410i	0.227125	−	0.973866i	$-0.427067\pi$
$992$	2.82646	−	0.382119i	0.0897403	−	0.0121323i
$993$	6.55283	−	7.78745i	0.207948	−	0.247127i
$994$	13.2044	−	2.80773i	0.418819	−	0.0890558i
$995$	−20.8737			−0.661740
$996$	−44.3638	+	13.5638i	−1.40572	+	0.429784i
$997$	1.39446	+	2.41527i	0.0441629	+	0.0764923i	0.887262	−	0.461266i	$-0.152605\pi$
$997$	1.39446	+	2.41527i	0.0441629	+	0.0764923i	−0.843099	+	0.537758i	$0.819271\pi$
$998$	−13.9498	+	47.2143i	−0.441573	+	1.49454i
$999$	−2.24261	+	1.28239i	−0.0709530	+	0.0405730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cf.a.341.73	yes	256
3.2	odd	2	inner	840.2.cf.a.341.56	yes	256
7.3	odd	6	inner	840.2.cf.a.101.13	✓	256
8.5	even	2	inner	840.2.cf.a.341.116	yes	256
21.17	even	6	inner	840.2.cf.a.101.116	yes	256
24.5	odd	2	inner	840.2.cf.a.341.13	yes	256
56.45	odd	6	inner	840.2.cf.a.101.56	yes	256
168.101	even	6	inner	840.2.cf.a.101.73	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.13	✓	256	7.3	odd	6	inner
840.2.cf.a.101.56	yes	256	56.45	odd	6	inner
840.2.cf.a.101.73	yes	256	168.101	even	6	inner
840.2.cf.a.101.116	yes	256	21.17	even	6	inner
840.2.cf.a.341.13	yes	256	24.5	odd	2	inner
840.2.cf.a.341.56	yes	256	3.2	odd	2	inner
840.2.cf.a.341.73	yes	256	1.1	even	1	trivial
840.2.cf.a.341.116	yes	256	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.331098 + 1.37491i) q^{2} +(-0.303127 + 1.70532i) q^{3} +(-1.78075 + 0.910460i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.44502 + 0.147856i) q^{6} +(-2.64480 - 0.0708975i) q^{7} +(-1.84140 - 2.14691i) q^{8} +(-2.81623 - 1.03386i) q^{9} +(-0.400715 + 1.35626i) q^{10} +(-0.735536 - 1.27399i) q^{11} +(-1.01283 - 3.31273i) q^{12} +1.58306 q^{13} +(-0.778212 - 3.65983i) q^{14} +(-1.11518 + 1.32529i) q^{15} +(2.34213 - 3.24260i) q^{16} +(-2.77818 - 4.81195i) q^{17} +(0.489012 - 4.21436i) q^{18} +(-2.80571 + 4.85963i) q^{19} +(-1.99740 - 0.101893i) q^{20} +(0.922615 - 4.48874i) q^{21} +(1.50808 - 1.43311i) q^{22} +(-1.32154 - 0.762994i) q^{23} +(4.21935 - 2.48939i) q^{24} +(0.500000 + 0.866025i) q^{25} +(0.524149 + 2.17656i) q^{26} +(2.61673 - 4.48918i) q^{27} +(4.77427 - 2.28173i) q^{28} -5.28450 q^{29} +(-2.19138 - 1.09446i) q^{30} +(0.436649 - 0.252099i) q^{31} +(5.23375 + 2.14659i) q^{32} +(2.39551 - 0.868143i) q^{33} +(5.69614 - 5.41297i) q^{34} +(-2.25502 - 1.38380i) q^{35} +(5.95628 - 0.723022i) q^{36} +(-0.430562 - 0.248585i) q^{37} +(-7.61052 - 2.24858i) q^{38} +(-0.479869 + 2.69962i) q^{39} +(-0.521244 - 2.77998i) q^{40} +2.40233 q^{41} +(6.47708 - 0.217703i) q^{42} -0.257653i q^{43} +(2.46972 + 1.59897i) q^{44} +(-1.92200 - 2.30346i) q^{45} +(0.611486 - 2.06963i) q^{46} +(-5.41938 + 9.38664i) q^{47} +(4.81970 + 4.97699i) q^{48} +(6.98995 + 0.375020i) q^{49} +(-1.02516 + 0.974194i) q^{50} +(9.04805 - 3.27905i) q^{51} +(-2.81903 + 1.44131i) q^{52} +(-5.79342 - 10.0345i) q^{53} +(7.03860 + 2.11141i) q^{54} -1.47107i q^{55} +(4.71793 + 5.80871i) q^{56} +(-7.43674 - 6.25772i) q^{57} +(-1.74969 - 7.26570i) q^{58} +(-3.84363 + 2.21912i) q^{59} +(0.779227 - 3.37532i) q^{60} +(-7.65781 + 13.2637i) q^{61} +(0.491187 + 0.516882i) q^{62} +(7.37506 + 2.93401i) q^{63} +(-1.21848 + 7.90666i) q^{64} +(1.37097 + 0.791530i) q^{65} +(1.98677 + 3.00617i) q^{66} +(-6.84692 + 3.95307i) q^{67} +(9.32833 + 6.03945i) q^{68} +(1.70175 - 2.02237i) q^{69} +(1.15597 - 3.55862i) q^{70} +3.60793i q^{71} +(2.96620 + 7.94995i) q^{72} +(8.97713 - 5.18295i) q^{73} +(0.199224 - 0.674290i) q^{74} +(-1.62841 + 0.590144i) q^{75} +(0.571762 - 11.2083i) q^{76} +(1.85502 + 3.42158i) q^{77} +(-3.87062 + 0.234065i) q^{78} +(-3.01199 + 5.21691i) q^{79} +(3.64964 - 1.63711i) q^{80} +(6.86228 + 5.82316i) q^{81} +(0.795406 + 3.30298i) q^{82} -13.3919i q^{83} +(2.44387 + 8.83332i) q^{84} -5.55636i q^{85} +(0.354250 - 0.0853086i) q^{86} +(1.60188 - 9.01175i) q^{87} +(-1.38072 + 3.92505i) q^{88} +(3.02937 - 5.24701i) q^{89} +(2.53068 - 3.40524i) q^{90} +(-4.18688 - 0.112235i) q^{91} +(3.04801 + 0.155487i) q^{92} +(0.297549 + 0.821043i) q^{93} +(-14.7001 - 4.34325i) q^{94} +(-4.85963 + 2.80571i) q^{95} +(-5.24711 + 8.27453i) q^{96} -16.9823i q^{97} +(1.79874 + 9.73471i) q^{98} +(0.754316 + 4.34827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) \) 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more