LMFDB - Embedded newform 961.2.d.h.374.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.2
Root			$-1.14412 + 0.831254i$ of defining polynomial
Character	$\chi$	$=$	961.374
Dual form			961.2.d.h.388.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.11803 - 1.53884i) q^{2} +(0.707107 - 0.513743i) q^{3} +(1.50000 + 4.61653i) q^{4} +2.23607 q^{5} -2.28825 q^{6} +(-0.309017 - 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.690983 + 2.12663i) q^{9} +(-4.73607 - 3.44095i) q^{10} +(1.31105 + 4.03499i) q^{11} +(3.43237 + 2.49376i) q^{12} +(2.12132 - 1.54123i) q^{13} +(-0.809017 + 2.48990i) q^{14} +(1.58114 - 1.14876i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(1.14412 - 3.52125i) q^{17} +(4.73607 - 3.44095i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(3.35410 + 10.3229i) q^{20} +(-0.707107 - 0.513743i) q^{21} +(3.43237 - 10.5637i) q^{22} +(-0.810272 + 2.49376i) q^{23} +(-2.01815 - 6.21124i) q^{24} -6.86474 q^{26} +(1.41421 + 4.35250i) q^{27} +(3.92705 - 2.85317i) q^{28} +(0.437016 + 0.317511i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(3.00000 + 2.17963i) q^{33} +(-7.84193 + 5.69750i) q^{34} +(-0.690983 - 2.12663i) q^{35} -10.8541 q^{36} +4.24264 q^{37} +(0.809017 + 2.48990i) q^{38} +(0.708204 - 2.17963i) q^{39} +(5.16312 - 15.8904i) q^{40} +(1.19098 + 0.865300i) q^{41} +(0.707107 + 2.17625i) q^{42} +(7.84193 + 5.69750i) q^{43} +(-16.6611 + 12.1050i) q^{44} +(-1.54508 + 4.75528i) q^{45} +(5.55369 - 4.03499i) q^{46} +(7.85410 - 5.70634i) q^{47} +(-2.66150 + 8.19126i) q^{48} +(4.85410 - 3.52671i) q^{49} +(-1.00000 - 3.07768i) q^{51} +(10.2971 + 7.48128i) q^{52} +(-4.24264 + 13.0575i) q^{53} +(3.70246 - 11.3950i) q^{54} +(2.93159 + 9.02251i) q^{55} -7.47214 q^{56} -0.874032 q^{57} +(-0.437016 - 1.34500i) q^{58} +(-9.66312 + 7.02067i) q^{59} +(7.67501 + 5.57622i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(-7.04508 - 5.11855i) q^{64} +(4.74342 - 3.44629i) q^{65} +(-3.00000 - 9.23305i) q^{66} +6.00000 q^{67} +17.9721 q^{68} +(0.708204 + 2.17963i) q^{69} +(-1.80902 + 5.56758i) q^{70} +(-0.454915 + 1.40008i) q^{71} +(13.5172 + 9.82084i) q^{72} +(1.31105 + 4.03499i) q^{73} +(-8.98606 - 6.52875i) q^{74} +(1.50000 - 4.61653i) q^{76} +(3.43237 - 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(-0.500776 + 1.54123i) q^{79} +(-17.8262 + 12.9515i) q^{80} +(-2.19098 - 1.59184i) q^{81} +(-1.19098 - 3.66547i) q^{82} +(2.55834 + 1.85874i) q^{83} +(1.31105 - 4.03499i) q^{84} +(2.55834 - 7.87375i) q^{85} +(-7.84193 - 24.1350i) q^{86} +0.472136 q^{87} +31.7016 q^{88} +(-4.74342 - 14.5987i) q^{89} +(10.5902 - 7.69421i) q^{90} +(-2.12132 - 1.54123i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(-1.80902 - 1.31433i) q^{95} +(7.67501 - 5.57622i) q^{96} +(-2.16312 - 6.65740i) q^{97} -15.7082 q^{98} -9.48683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 12 q^{4} + 2 q^{7} + 14 q^{8} - 10 q^{9} - 20 q^{10} - 2 q^{14} - 28 q^{16} + 20 q^{18} - 2 q^{19} + 18 q^{28} + 60 q^{32} + 24 q^{33} - 10 q^{35} - 60 q^{36} + 2 q^{38} - 48 q^{39} + 10 q^{40}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 12 * q^4 + 2 * q^7 + 14 * q^8 - 10 * q^9 - 20 * q^10 - 2 * q^14 - 28 * q^16 + 20 * q^18 - 2 * q^19 + 18 * q^28 + 60 * q^32 + 24 * q^33 - 10 * q^35 - 60 * q^36 + 2 * q^38 - 48 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^45 + 36 * q^47 + 12 * q^49 - 8 * q^51 - 24 * q^56 - 46 * q^59 - 34 * q^64 - 24 * q^66 + 48 * q^67 - 48 * q^69 - 10 * q^70 - 26 * q^71 + 50 * q^72 + 12 * q^76 - 12 * q^78 - 80 * q^80 - 22 * q^81 - 14 * q^82 - 32 * q^87 + 40 * q^90 - 96 * q^94 - 10 * q^95 + 14 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.971295	−	0.237877i	$-0.923549\pi$
$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.526381	−	0.850249i	$-0.676451\pi$
$3$	0.707107	−	0.513743i	0.408248	−	0.296610i	−0.364644	−	0.931147i	$-0.618809\pi$
$3$	0.707107	−	0.513743i	0.408248	−	0.296610i	0.772892	+	0.634537i	$0.218809\pi$
$4$	1.50000	+	4.61653i	0.750000	+	2.30826i
$5$	2.23607			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$6$	−2.28825			−0.934172
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i	0.875520	−	0.483181i	$-0.160519\pi$
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i	−0.992318	+	0.123716i	$0.960519\pi$
$8$	2.30902	−	7.10642i	0.816361	−	2.51250i
$9$	−0.690983	+	2.12663i	−0.230328	+	0.708876i
$10$	−4.73607	−	3.44095i	−1.49768	−	1.08813i
$11$	1.31105	+	4.03499i	0.395296	+	1.21660i	0.928731	+	0.370755i	$0.120901\pi$
$11$	1.31105	+	4.03499i	0.395296	+	1.21660i	−0.533435	+	0.845841i	$0.679099\pi$
$12$	3.43237	+	2.49376i	0.990839	+	0.719887i
$13$	2.12132	−	1.54123i	0.588348	−	0.427460i	−0.253376	−	0.967368i	$-0.581541\pi$
$13$	2.12132	−	1.54123i	0.588348	−	0.427460i	0.841724	+	0.539908i	$0.181541\pi$
$14$	−0.809017	+	2.48990i	−0.216219	+	0.665453i
$15$	1.58114	−	1.14876i	0.408248	−	0.296610i
$16$	−7.97214	+	5.79210i	−1.99303	+	1.44802i
$17$	1.14412	−	3.52125i	0.277491	−	0.854028i	−0.711059	−	0.703132i	$-0.751784\pi$
$17$	1.14412	−	3.52125i	0.277491	−	0.854028i	0.988550	−	0.150896i	$-0.0482158\pi$
$18$	4.73607	−	3.44095i	1.11630	−	0.811041i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	0.491105	−	0.871100i	$-0.336593\pi$
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	−0.676706	+	0.736253i	$0.736593\pi$
$20$	3.35410	+	10.3229i	0.750000	+	2.30826i
$21$	−0.707107	−	0.513743i	−0.154303	−	0.112108i
$22$	3.43237	−	10.5637i	0.731783	−	2.25220i
$23$	−0.810272	+	2.49376i	−0.168953	+	0.519985i	−0.999306	−	0.0372534i	$-0.988139\pi$
$23$	−0.810272	+	2.49376i	−0.168953	+	0.519985i	0.830352	+	0.557239i	$0.188139\pi$
$24$	−2.01815	−	6.21124i	−0.411954	−	1.26786i
$25$		0			0
$26$	−6.86474			−1.34629
$27$	1.41421	+	4.35250i	0.272166	+	0.837639i
$28$	3.92705	−	2.85317i	0.742143	−	0.539198i
$29$	0.437016	+	0.317511i	0.0811518	+	0.0589603i	0.627621	−	0.778519i	$-0.284029\pi$
$29$	0.437016	+	0.317511i	0.0811518	+	0.0589603i	−0.546470	+	0.837479i	$0.684029\pi$
$30$	−5.11667			−0.934172
$31$		0			0
$31$		0			0
$32$	10.8541			1.91875
$33$	3.00000	+	2.17963i	0.522233	+	0.379424i
$34$	−7.84193	+	5.69750i	−1.34488	+	0.977113i
$35$	−0.690983	−	2.12663i	−0.116797	−	0.359466i
$36$	−10.8541			−1.80902
$37$	4.24264			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$37$	4.24264			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$38$	0.809017	+	2.48990i	0.131240	+	0.403915i
$39$	0.708204	−	2.17963i	0.113403	−	0.349020i
$40$	5.16312	−	15.8904i	0.816361	−	2.51250i
$41$	1.19098	+	0.865300i	0.186000	+	0.135137i	0.676889	−	0.736085i	$-0.263328\pi$
$41$	1.19098	+	0.865300i	0.186000	+	0.135137i	−0.490889	+	0.871222i	$0.663328\pi$
$42$	0.707107	+	2.17625i	0.109109	+	0.335803i
$43$	7.84193	+	5.69750i	1.19588	+	0.868860i	0.993874	−	0.110523i	$-0.0352526\pi$
$43$	7.84193	+	5.69750i	1.19588	+	0.868860i	0.202010	+	0.979383i	$0.435253\pi$
$44$	−16.6611	+	12.1050i	−2.51175	+	1.82489i
$45$	−1.54508	+	4.75528i	−0.230328	+	0.708876i
$46$	5.55369	−	4.03499i	0.818847	−	0.594927i
$47$	7.85410	−	5.70634i	1.14564	−	0.832355i	0.157744	−	0.987480i	$-0.449578\pi$
$47$	7.85410	−	5.70634i	1.14564	−	0.832355i	0.987895	+	0.155125i	$0.0495780\pi$
$48$	−2.66150	+	8.19126i	−0.384155	+	1.18231i
$49$	4.85410	−	3.52671i	0.693443	−	0.503816i
$50$		0			0
$51$	−1.00000	−	3.07768i	−0.140028	−	0.430962i
$52$	10.2971	+	7.48128i	1.42795	+	1.03747i
$53$	−4.24264	+	13.0575i	−0.582772	+	1.79359i	0.0252695	+	0.999681i	$0.491956\pi$
$53$	−4.24264	+	13.0575i	−0.582772	+	1.79359i	−0.608041	+	0.793906i	$0.708044\pi$
$54$	3.70246	−	11.3950i	0.503841	−	1.55066i
$55$	2.93159	+	9.02251i	0.395296	+	1.21660i
$56$	−7.47214			−0.998506
$57$	−0.874032			−0.115768
$58$	−0.437016	−	1.34500i	−0.0573830	−	0.176607i
$59$	−9.66312	+	7.02067i	−1.25803	+	0.914013i	−0.998659	−	0.0517646i	$-0.983515\pi$
$59$	−9.66312	+	7.02067i	−1.25803	+	0.914013i	−0.259372	+	0.965778i	$0.583515\pi$
$60$	7.67501	+	5.57622i	0.990839	+	0.719887i
$61$	13.9358			1.78430			0.892148	−	0.451742i	$-0.149197\pi$
$61$	13.9358			1.78430			0.892148	+	0.451742i	$0.149197\pi$
$62$		0			0
$63$	2.23607			0.281718
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	4.74342	−	3.44629i	0.588348	−	0.427460i
$66$	−3.00000	−	9.23305i	−0.369274	−	1.13651i
$67$	6.00000			0.733017			0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000			0.733017			0.366508	+	0.930415i	$0.380553\pi$
$68$	17.9721			2.17944
$69$	0.708204	+	2.17963i	0.0852577	+	0.262396i
$70$	−1.80902	+	5.56758i	−0.216219	+	0.665453i
$71$	−0.454915	+	1.40008i	−0.0539885	+	0.166159i	−0.974415	−	0.224756i	$-0.927842\pi$
$71$	−0.454915	+	1.40008i	−0.0539885	+	0.166159i	0.920427	+	0.390915i	$0.127842\pi$
$72$	13.5172	+	9.82084i	1.59302	+	1.15740i
$73$	1.31105	+	4.03499i	0.153447	+	0.472260i	0.998000	−	0.0632110i	$-0.0201341\pi$
$73$	1.31105	+	4.03499i	0.153447	+	0.472260i	−0.844554	+	0.535471i	$0.820134\pi$
$74$	−8.98606	−	6.52875i	−1.04461	−	0.758952i
$75$		0			0
$76$	1.50000	−	4.61653i	0.172062	−	0.529552i
$77$	3.43237	−	2.49376i	0.391155	−	0.284191i
$78$	−4.85410	+	3.52671i	−0.549619	+	0.399321i
$79$	−0.500776	+	1.54123i	−0.0563417	+	0.173402i	−0.975267	−	0.221029i	$-0.929058\pi$
$79$	−0.500776	+	1.54123i	−0.0563417	+	0.173402i	0.918925	+	0.394431i	$0.129058\pi$
$80$	−17.8262	+	12.9515i	−1.99303	+	1.44802i
$81$	−2.19098	−	1.59184i	−0.243443	−	0.176871i
$82$	−1.19098	−	3.66547i	−0.131522	−	0.404783i
$83$	2.55834	+	1.85874i	0.280814	+	0.204023i	0.719272	−	0.694728i	$-0.244475\pi$
$83$	2.55834	+	1.85874i	0.280814	+	0.204023i	−0.438458	+	0.898751i	$0.644475\pi$
$84$	1.31105	−	4.03499i	0.143047	−	0.440254i
$85$	2.55834	−	7.87375i	0.277491	−	0.854028i
$86$	−7.84193	−	24.1350i	−0.845618	−	2.60254i
$87$	0.472136			0.0506183
$88$	31.7016			3.37940
$89$	−4.74342	−	14.5987i	−0.502801	−	1.54746i	−0.804436	−	0.594039i	$-0.797532\pi$
$89$	−4.74342	−	14.5987i	−0.502801	−	1.54746i	0.301635	−	0.953424i	$-0.402468\pi$
$90$	10.5902	−	7.69421i	1.11630	−	0.811041i
$91$	−2.12132	−	1.54123i	−0.222375	−	0.161565i
$92$	−12.7279			−1.32698
$93$		0			0
$94$	−25.4164			−2.62150
$95$	−1.80902	−	1.31433i	−0.185601	−	0.134847i
$96$	7.67501	−	5.57622i	0.783327	−	0.569121i
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	−0.998792	−	0.0491321i	$-0.984354\pi$
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	0.779161	−	0.626824i	$-0.215646\pi$
$98$	−15.7082			−1.58677
$99$	−9.48683			−0.953463
$100$		0			0
$101$	0.690983	−	2.12663i	0.0687554	−	0.211607i	−0.910775	−	0.412902i	$-0.864515\pi$
$101$	0.690983	−	2.12663i	0.0687554	−	0.211607i	0.979531	+	0.201295i	$0.0645150\pi$
$102$	−2.61803	+	8.05748i	−0.259224	+	0.797809i
$103$	−8.66312	−	6.29412i	−0.853602	−	0.620179i	0.0725345	−	0.997366i	$-0.476891\pi$
$103$	−8.66312	−	6.29412i	−0.853602	−	0.620179i	−0.926137	+	0.377187i	$0.876891\pi$
$104$	−6.05446	−	18.6337i	−0.593689	−	1.82719i
$105$	−1.58114	−	1.14876i	−0.154303	−	0.112108i
$106$	29.0795	−	21.1275i	2.82445	−	2.05208i
$107$	0.454915	−	1.40008i	0.0439783	−	0.135351i	−0.926656	−	0.375909i	$-0.877330\pi$
$107$	0.454915	−	1.40008i	0.0439783	−	0.135351i	0.970635	+	0.240558i	$0.0773304\pi$
$108$	−17.9721	+	13.0575i	−1.72937	+	1.25646i
$109$	1.04508	−	0.759299i	0.100101	−	0.0727276i	−0.536609	−	0.843831i	$-0.680295\pi$
$109$	1.04508	−	0.759299i	0.100101	−	0.0727276i	0.636710	+	0.771103i	$0.280295\pi$
$110$	7.67501	−	23.6212i	0.731783	−	2.25220i
$111$	3.00000	−	2.17963i	0.284747	−	0.206881i
$112$	7.97214	+	5.79210i	0.753296	+	0.547302i
$113$	−3.01722	−	9.28605i	−0.283836	−	0.873558i	−0.986745	−	0.162278i	$-0.948116\pi$
$113$	−3.01722	−	9.28605i	−0.283836	−	0.873558i	0.702909	−	0.711280i	$-0.251884\pi$
$114$	1.85123	+	1.34500i	0.173384	+	0.125971i
$115$	−1.81182	+	5.57622i	−0.168953	+	0.519985i
$116$	−0.810272	+	2.49376i	−0.0752319	+	0.231540i
$117$	1.81182	+	5.57622i	0.167503	+	0.515522i
$118$	31.2705			2.87868
$119$	−3.70246			−0.339404
$120$	−4.51273	−	13.8888i	−0.411954	−	1.26786i
$121$	−5.66312	+	4.11450i	−0.514829	+	0.374045i
$122$	−29.5165	−	21.4450i	−2.67230	−	1.94154i
$123$	1.28669			0.116017
$124$		0			0
$125$	−11.1803			−1.00000
$126$	−4.73607	−	3.44095i	−0.421922	−	0.306545i
$127$	7.67501	−	5.57622i	0.681047	−	0.494810i	−0.192658	−	0.981266i	$-0.561711\pi$
$127$	7.67501	−	5.57622i	0.681047	−	0.494810i	0.873705	+	0.486456i	$0.161711\pi$
$128$	0.336881	+	1.03681i	0.0297764	+	0.0916422i
$129$	8.47214			0.745930
$130$	−15.3500			−1.34629
$131$	2.29180	+	7.05342i	0.200235	+	0.616260i	0.999875	+	0.0157812i	$0.00502351\pi$
$131$	2.29180	+	7.05342i	0.200235	+	0.616260i	−0.799640	+	0.600479i	$0.794976\pi$
$132$	−5.56231	+	17.1190i	−0.484137	+	1.49002i
$133$	−0.309017	+	0.951057i	−0.0267952	+	0.0824671i
$134$	−12.7082	−	9.23305i	−1.09782	−	0.797614i
$135$	3.16228	+	9.73249i	0.272166	+	0.837639i
$136$	−22.3817	−	16.2612i	−1.91921	−	1.39439i
$137$	2.12132	−	1.54123i	0.181237	−	0.131676i	−0.493468	−	0.869764i	$-0.664271\pi$
$137$	2.12132	−	1.54123i	0.181237	−	0.131676i	0.674705	+	0.738088i	$0.264271\pi$
$138$	1.85410	−	5.70634i	0.157832	−	0.485756i
$139$	14.5397	−	10.5637i	1.23325	−	0.896005i	0.236116	−	0.971725i	$-0.424125\pi$
$139$	14.5397	−	10.5637i	1.23325	−	0.896005i	0.997129	+	0.0757198i	$0.0241255\pi$
$140$	8.78115	−	6.37988i	0.742143	−	0.539198i
$141$	2.62210	−	8.06998i	0.220820	−	0.679615i
$142$	3.11803	−	2.26538i	0.261660	−	0.190107i
$143$	9.00000	+	6.53888i	0.752618	+	0.546809i
$144$	−6.80902	−	20.9560i	−0.567418	−	1.74633i
$145$	0.977198	+	0.709976i	0.0811518	+	0.0589603i
$146$	3.43237	−	10.5637i	0.284065	−	0.874262i
$147$	1.62054	−	4.98752i	0.133660	−	0.411364i
$148$	6.36396	+	19.5863i	0.523114	+	1.60998i
$149$	−13.4164			−1.09911			−0.549557	−	0.835456i	$-0.685204\pi$
$149$	−13.4164			−1.09911			−0.549557	+	0.835456i	$0.685204\pi$
$150$		0			0
$151$	3.86938	+	11.9087i	0.314886	+	0.969120i	0.975801	+	0.218659i	$0.0701683\pi$
$151$	3.86938	+	11.9087i	0.314886	+	0.969120i	−0.660915	+	0.750461i	$0.729832\pi$
$152$	−6.04508	+	4.39201i	−0.490321	+	0.356239i
$153$	6.69781	+	4.86624i	0.541486	+	0.393413i
$154$	−11.1074			−0.895058
$155$		0			0
$156$	11.1246			0.890682
$157$	−7.04508	−	5.11855i	−0.562259	−	0.408505i	0.270026	−	0.962853i	$-0.412968\pi$
$157$	−7.04508	−	5.11855i	−0.562259	−	0.408505i	−0.832285	+	0.554348i	$0.812968\pi$
$158$	3.43237	−	2.49376i	0.273065	−	0.198393i
$159$	3.70820	+	11.4127i	0.294080	+	0.905084i
$160$	24.2705			1.91875
$161$	2.62210			0.206650
$162$	2.19098	+	6.74315i	0.172140	+	0.529792i
$163$	4.45492	−	13.7108i	0.348936	−	1.07391i	−0.610507	−	0.792011i	$-0.709034\pi$
$163$	4.45492	−	13.7108i	0.348936	−	1.07391i	0.959443	−	0.281903i	$-0.0909657\pi$
$164$	−2.20820	+	6.79615i	−0.172432	+	0.530690i
$165$	6.70820	+	4.87380i	0.522233	+	0.379424i
$166$	−2.55834	−	7.87375i	−0.198565	−	0.611121i
$167$	0.874032	+	0.635021i	0.0676346	+	0.0491394i	0.621089	−	0.783740i	$-0.286691\pi$
$167$	0.874032	+	0.635021i	0.0676346	+	0.0491394i	−0.553454	+	0.832880i	$0.686691\pi$
$168$	−5.28360	+	3.83876i	−0.407638	+	0.296167i
$169$	−1.89261	+	5.82485i	−0.145585	+	0.448066i
$170$	−17.5351	+	12.7400i	−1.34488	+	0.977113i
$171$	1.80902	−	1.31433i	0.138339	−	0.100509i
$172$	−14.5397	+	44.7487i	−1.10865	+	3.41206i
$173$	−14.5623	+	10.5801i	−1.10715	+	0.804393i	−0.982213	−	0.187772i	$-0.939873\pi$
$173$	−14.5623	+	10.5801i	−1.10715	+	0.804393i	−0.124939	+	0.992164i	$0.539873\pi$
$174$	−1.00000	−	0.726543i	−0.0758098	−	0.0550790i
$175$		0			0
$176$	−33.8229	−	24.5738i	−2.54950	−	1.85232i
$177$	−3.22604	+	9.92872i	−0.242484	+	0.746288i
$178$	−12.4184	+	38.2200i	−0.930800	+	2.86471i
$179$	4.10007	+	12.6187i	0.306454	+	0.943167i	0.979131	+	0.203231i	$0.0651443\pi$
$179$	4.10007	+	12.6187i	0.306454	+	0.943167i	−0.672677	+	0.739936i	$0.734856\pi$
$180$	−24.2705			−1.80902
$181$	8.69161			0.646042			0.323021	−	0.946392i	$-0.395301\pi$
$181$	8.69161			0.646042			0.323021	+	0.946392i	$0.395301\pi$
$182$	2.12132	+	6.52875i	0.157243	+	0.483943i
$183$	9.85410	−	7.15942i	0.728436	−	0.529240i
$184$	15.8508	+	11.5163i	1.16854	+	0.848991i
$185$	9.48683			0.697486
$186$		0			0
$187$	15.7082			1.14870
$188$	38.1246	+	27.6992i	2.78052	+	2.02017i
$189$	3.70246	−	2.68999i	0.269314	−	0.195668i
$190$	1.80902	+	5.56758i	0.131240	+	0.403915i
$191$	9.76393			0.706493			0.353247	−	0.935530i	$-0.385078\pi$
$191$	9.76393			0.706493			0.353247	+	0.935530i	$0.385078\pi$
$192$	−7.61125			−0.549295
$193$	−6.39919	−	19.6947i	−0.460624	−	1.41765i	−0.864404	−	0.502798i	$-0.832304\pi$
$193$	−6.39919	−	19.6947i	−0.460624	−	1.41765i	0.403781	−	0.914856i	$-0.367696\pi$
$194$	−5.66312	+	17.4293i	−0.406588	+	1.25135i
$195$	1.58359	−	4.87380i	0.113403	−	0.349020i
$196$	23.5623	+	17.1190i	1.68302	+	1.22279i
$197$	−0.333851	−	1.02749i	−0.0237859	−	0.0732054i	0.938459	−	0.345391i	$-0.112254\pi$
$197$	−0.333851	−	1.02749i	−0.0237859	−	0.0732054i	−0.962245	+	0.272185i	$0.912254\pi$
$198$	20.0934	+	14.5987i	1.42798	+	1.03749i
$199$	−18.7824	+	13.6462i	−1.33145	+	0.967354i	−0.331736	+	0.943372i	$0.607634\pi$
$199$	−18.7824	+	13.6462i	−1.33145	+	0.967354i	−0.999712	+	0.0239813i	$0.992366\pi$
$200$		0			0
$201$	4.24264	−	3.08246i	0.299253	−	0.217420i
$202$	−4.73607	+	3.44095i	−0.333229	+	0.242105i
$203$	0.166925	−	0.513743i	0.0117159	−	0.0360577i
$204$	12.7082	−	9.23305i	0.889752	−	0.646443i
$205$	2.66312	+	1.93487i	0.186000	+	0.135137i
$206$	8.66312	+	26.6623i	0.603588	+	1.85765i
$207$	−4.74342	−	3.44629i	−0.329690	−	0.239534i
$208$	−7.98451	+	24.5738i	−0.553626	+	1.70389i
$209$	1.31105	−	4.03499i	0.0906871	−	0.279106i
$210$	1.58114	+	4.86624i	0.109109	+	0.335803i
$211$	−5.00000			−0.344214			−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000			−0.344214			−0.172107	+	0.985078i	$0.555058\pi$
$212$	−66.6443			−4.57715
$213$	0.397610	+	1.22372i	0.0272438	+	0.0838478i
$214$	−3.11803	+	2.26538i	−0.213144	+	0.154858i
$215$	17.5351	+	12.7400i	1.19588	+	0.868860i
$216$	34.1962			2.32675
$217$		0			0
$218$	−3.38197			−0.229056
$219$	3.00000	+	2.17963i	0.202721	+	0.147286i
$220$	−37.2553	+	27.0675i	−2.51175	+	1.82489i
$221$	−3.00000	−	9.23305i	−0.201802	−	0.621082i
$222$	−9.70820			−0.651572
$223$	16.1452			1.08117			0.540583	−	0.841291i	$-0.318204\pi$
$223$	16.1452			1.08117			0.540583	+	0.841291i	$0.318204\pi$
$224$	−3.35410	−	10.3229i	−0.224105	−	0.689725i
$225$		0			0
$226$	−7.89919	+	24.3112i	−0.525446	+	1.61716i
$227$	−1.85410	−	1.34708i	−0.123061	−	0.0894091i	0.524552	−	0.851378i	$-0.324233\pi$
$227$	−1.85410	−	1.34708i	−0.123061	−	0.0894091i	−0.647613	+	0.761969i	$0.724233\pi$
$228$	−1.31105	−	4.03499i	−0.0868263	−	0.267224i
$229$	−3.43237	−	2.49376i	−0.226817	−	0.164792i	0.468573	−	0.883425i	$-0.344768\pi$
$229$	−3.43237	−	2.49376i	−0.226817	−	0.164792i	−0.695390	+	0.718632i	$0.744768\pi$
$230$	12.4184	−	9.02251i	0.818847	−	0.594927i
$231$	1.14590	−	3.52671i	0.0753946	−	0.232041i
$232$	3.26544	−	2.37248i	0.214387	−	0.155761i
$233$	10.8992	−	7.91872i	0.714029	−	0.518773i	−0.170442	−	0.985368i	$-0.554519\pi$
$233$	10.8992	−	7.91872i	0.714029	−	0.518773i	0.884471	+	0.466595i	$0.154519\pi$
$234$	4.74342	−	14.5987i	0.310087	−	0.954349i
$235$	17.5623	−	12.7598i	1.14564	−	0.832355i
$236$	−46.9058	−	34.0790i	−3.05331	−	2.21836i
$237$	0.437694	+	1.34708i	0.0284313	+	0.0875025i
$238$	7.84193	+	5.69750i	0.508317	+	0.369314i
$239$	3.74186	−	11.5163i	0.242041	−	0.744926i	−0.754068	−	0.656796i	$-0.771911\pi$
$239$	3.74186	−	11.5163i	0.242041	−	0.744926i	0.996109	−	0.0881295i	$-0.0280889\pi$
$240$	−5.95130	+	18.3162i	−0.384155	+	1.18231i
$241$	−7.17423	−	22.0800i	−0.462133	−	1.42230i	−0.862553	−	0.505967i	$-0.831136\pi$
$241$	−7.17423	−	22.0800i	−0.462133	−	1.42230i	0.400420	−	0.916332i	$-0.368864\pi$
$242$	18.3262			1.17806
$243$	−16.0965			−1.03259
$244$	20.9037	+	64.3350i	1.33822	+	4.11863i
$245$	10.8541	−	7.88597i	0.693443	−	0.503816i
$246$	−2.72526	−	1.98002i	−0.173756	−	0.126241i
$247$	−2.62210			−0.166840
$248$		0			0
$249$	2.76393			0.175157
$250$	23.6803	+	17.2048i	1.49768	+	1.08813i
$251$	−8.92230	+	6.48243i	−0.563170	+	0.409167i	−0.832618	−	0.553848i	$-0.813159\pi$
$251$	−8.92230	+	6.48243i	−0.563170	+	0.409167i	0.269447	+	0.963015i	$0.413159\pi$
$252$	3.35410	+	10.3229i	0.211289	+	0.650279i
$253$	−11.1246			−0.699398
$254$	−24.8369			−1.55840
$255$	−2.23607	−	6.88191i	−0.140028	−	0.430962i
$256$	−4.50000	+	13.8496i	−0.281250	+	0.865598i
$257$	1.87132	−	5.75934i	0.116730	−	0.359258i	−0.875574	−	0.483084i	$-0.839517\pi$
$257$	1.87132	−	5.75934i	0.116730	−	0.359258i	0.992304	+	0.123826i	$0.0395166\pi$
$258$	−17.9443	−	13.0373i	−1.11716	−	0.811665i
$259$	−1.31105	−	4.03499i	−0.0814646	−	0.250722i
$260$	23.0250	+	16.7287i	1.42795	+	1.03747i
$261$	−0.977198	+	0.709976i	−0.0604870	+	0.0439464i
$262$	6.00000	−	18.4661i	0.370681	−	1.14084i
$263$	−14.9768	+	10.8813i	−0.923507	+	0.670967i	−0.944394	−	0.328815i	$-0.893351\pi$
$263$	−14.9768	+	10.8813i	−0.923507	+	0.670967i	0.0208877	+	0.999782i	$0.493351\pi$
$264$	22.4164	−	16.2865i	1.37963	−	1.00236i
$265$	−9.48683	+	29.1975i	−0.582772	+	1.79359i
$266$	2.11803	−	1.53884i	0.129865	−	0.0943524i
$267$	−10.8541	−	7.88597i	−0.664260	−	0.482613i
$268$	9.00000	+	27.6992i	0.549762	+	1.69199i
$269$	−1.74806	−	1.27004i	−0.106581	−	0.0774359i	0.533218	−	0.845978i	$-0.320983\pi$
$269$	−1.74806	−	1.27004i	−0.106581	−	0.0774359i	−0.639799	+	0.768542i	$0.720983\pi$
$270$	8.27895	−	25.4800i	0.503841	−	1.55066i
$271$	−5.74497	+	17.6812i	−0.348982	+	1.07406i	0.610435	+	0.792066i	$0.290994\pi$
$271$	−5.74497	+	17.6812i	−0.348982	+	1.07406i	−0.959417	+	0.281990i	$0.909006\pi$
$272$	11.2743	+	34.6987i	0.683605	+	2.10392i
$273$	−2.29180			−0.138706
$274$	−6.86474			−0.414714
$275$		0			0
$276$	−9.00000	+	6.53888i	−0.541736	+	0.393594i
$277$	−8.17578	−	5.94006i	−0.491235	−	0.356903i	0.314424	−	0.949283i	$-0.398189\pi$
$277$	−8.17578	−	5.94006i	−0.491235	−	0.356903i	−0.805659	+	0.592379i	$0.798189\pi$
$278$	−47.0516			−2.82197
$279$		0			0
$280$	−16.7082			−0.998506
$281$	−10.8090	−	7.85321i	−0.644812	−	0.468483i	0.216688	−	0.976241i	$-0.430475\pi$
$281$	−10.8090	−	7.85321i	−0.644812	−	0.468483i	−0.861500	+	0.507758i	$0.830475\pi$
$282$	−17.9721	+	13.0575i	−1.07022	+	0.777563i
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	0.886961	+	0.461844i	$0.152812\pi$
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	−0.446101	+	0.894982i	$0.647188\pi$
$284$	−7.14590			−0.424031
$285$	−1.95440			−0.115768
$286$	−9.00000	−	27.6992i	−0.532181	−	1.63789i
$287$	0.454915	−	1.40008i	0.0268528	−	0.0826444i
$288$	−7.50000	+	23.0826i	−0.441942	+	1.36016i
$289$	2.66312	+	1.93487i	0.156654	+	0.113816i
$290$	−0.977198	−	3.00750i	−0.0573830	−	0.176607i
$291$	−4.94975	−	3.59620i	−0.290159	−	0.210813i
$292$	−16.6611	+	12.1050i	−0.975015	+	0.708390i
$293$	−0.708204	+	2.17963i	−0.0413737	+	0.127335i	−0.969610	−	0.244656i	$-0.921325\pi$
$293$	−0.708204	+	2.17963i	−0.0413737	+	0.127335i	0.928236	+	0.371991i	$0.121325\pi$
$294$	−11.1074	+	8.06998i	−0.647795	+	0.470651i
$295$	−21.6074	+	15.6987i	−1.25803	+	0.914013i
$296$	9.79633	−	30.1500i	0.569400	−	1.75243i
$297$	−15.7082	+	11.4127i	−0.911482	+	0.662231i
$298$	28.4164	+	20.6457i	1.64612	+	1.19597i
$299$	2.12461	+	6.53888i	0.122869	+	0.378153i
$300$		0			0
$301$	2.99535	−	9.21875i	0.172649	−	0.531360i
$302$	10.1302	−	31.1775i	0.582926	−	1.79406i
$303$	−0.603941	−	1.85874i	−0.0346955	−	0.106782i
$304$	9.85410			0.565172
$305$	31.1614			1.78430
$306$	−6.69781	−	20.6137i	−0.382888	−	1.17841i
$307$	−19.5172	+	14.1801i	−1.11391	+	0.809301i	−0.983274	−	0.182130i	$-0.941701\pi$
$307$	−19.5172	+	14.1801i	−1.11391	+	0.809301i	−0.130632	+	0.991431i	$0.541701\pi$
$308$	16.6611	+	12.1050i	0.949352	+	0.689745i
$309$	−9.35931			−0.532433
$310$		0			0
$311$	25.4721			1.44439			0.722196	−	0.691688i	$-0.243133\pi$
$311$	25.4721			1.44439			0.722196	+	0.691688i	$0.243133\pi$
$312$	−13.8541	−	10.0656i	−0.784334	−	0.569852i
$313$	9.31991	−	6.77131i	0.526792	−	0.382737i	−0.292364	−	0.956307i	$-0.594442\pi$
$313$	9.31991	−	6.77131i	0.526792	−	0.382737i	0.819157	+	0.573570i	$0.194442\pi$
$314$	7.04508	+	21.6825i	0.397577	+	1.22362i
$315$	5.00000			0.281718
$316$	−7.86629			−0.442513
$317$	8.10739	+	24.9520i	0.455356	+	1.40144i	0.870716	+	0.491786i	$0.163656\pi$
$317$	8.10739	+	24.9520i	0.455356	+	1.40144i	−0.415360	+	0.909657i	$0.636344\pi$
$318$	9.70820	−	29.8788i	0.544409	−	1.67552i
$319$	−0.708204	+	2.17963i	−0.0396518	+	0.122036i
$320$	−15.7533	−	11.4454i	−0.880636	−	0.639819i
$321$	−0.397610	−	1.22372i	−0.0221924	−	0.0683013i
$322$	−5.55369	−	4.03499i	−0.309495	−	0.224861i
$323$	−2.99535	+	2.17625i	−0.166666	+	0.121090i
$324$	4.06231	−	12.5025i	0.225684	−	0.694583i
$325$		0			0
$326$	−30.5344	+	22.1846i	−1.69115	+	1.22869i
$327$	0.348902	−	1.07381i	0.0192943	−	0.0593819i
$328$	8.89919	−	6.46564i	0.491375	−	0.357005i
$329$	−7.85410	−	5.70634i	−0.433011	−	0.314601i
$330$	−6.70820	−	20.6457i	−0.369274	−	1.13651i
$331$	−25.3133	−	18.3912i	−1.39134	−	1.01087i	−0.995717	−	0.0924587i	$-0.970527\pi$
$331$	−25.3133	−	18.3912i	−1.39134	−	1.01087i	−0.395627	−	0.918411i	$-0.629473\pi$
$332$	−4.74342	+	14.5987i	−0.260329	+	0.801210i
$333$	−2.93159	+	9.02251i	−0.160650	+	0.494431i
$334$	−0.874032	−	2.68999i	−0.0478249	−	0.147190i
$335$	13.4164			0.733017
$336$	8.61280			0.469867
$337$	−4.74342	−	14.5987i	−0.258390	−	0.795244i	−0.993143	−	0.116908i	$-0.962702\pi$
$337$	−4.74342	−	14.5987i	−0.258390	−	0.795244i	0.734752	−	0.678335i	$-0.237298\pi$
$338$	12.9721	−	9.42481i	0.705591	−	0.512642i
$339$	−6.90414	−	5.01615i	−0.374982	−	0.272440i
$340$	40.1869			2.17944
$341$		0			0
$342$	−5.85410			−0.316554
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$	58.5960	−	42.5725i	3.15928	−	2.29535i
$345$	1.58359	+	4.87380i	0.0852577	+	0.262396i
$346$	47.1246			2.53343
$347$	−21.5958			−1.15932			−0.579661	−	0.814858i	$-0.696815\pi$
$347$	−21.5958			−1.15932			−0.579661	+	0.814858i	$0.696815\pi$
$348$	0.708204	+	2.17963i	0.0379637	+	0.116840i
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	−0.889090	−	0.457733i	$-0.848662\pi$
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	0.988337	+	0.152280i	$0.0486615\pi$
$350$		0			0
$351$	9.70820	+	7.05342i	0.518186	+	0.376484i
$352$	14.2302	+	43.7962i	0.758475	+	2.33435i
$353$	−7.73877	−	5.62254i	−0.411893	−	0.299258i	0.362475	−	0.931994i	$-0.381932\pi$
$353$	−7.73877	−	5.62254i	−0.411893	−	0.299258i	−0.774368	+	0.632736i	$0.781932\pi$
$354$	22.1116	−	16.0650i	1.17522	−	0.853846i
$355$	−1.01722	+	3.13068i	−0.0539885	+	0.166159i
$356$	60.2803	−	43.7962i	3.19485	−	2.32119i
$357$	−2.61803	+	1.90211i	−0.138561	+	0.100670i
$358$	10.7341	−	33.0362i	0.567316	−	1.74602i
$359$	−11.5172	+	8.36775i	−0.607856	+	0.441633i	−0.848659	−	0.528941i	$-0.822589\pi$
$359$	−11.5172	+	8.36775i	−0.607856	+	0.441633i	0.240803	+	0.970574i	$0.422589\pi$
$360$	30.2254	+	21.9601i	1.59302	+	1.15740i
$361$	−5.56231	−	17.1190i	−0.292753	−	0.901001i
$362$	−18.4091	−	13.3750i	−0.967562	−	0.702975i
$363$	−1.89064	+	5.81878i	−0.0992326	+	0.305407i
$364$	3.93314	−	12.1050i	0.206153	−	0.634473i
$365$	2.93159	+	9.02251i	0.153447	+	0.472260i
$366$	−31.8885			−1.66684
$367$	6.65841			0.347566			0.173783	−	0.984784i	$-0.444401\pi$
$367$	6.65841			0.347566			0.173783	+	0.984784i	$0.444401\pi$
$368$	−7.98451	−	24.5738i	−0.416221	−	1.28100i
$369$	−2.66312	+	1.93487i	−0.138636	+	0.100725i
$370$	−20.0934	−	14.5987i	−1.04461	−	0.758952i
$371$	13.7295			0.712799
$372$		0			0
$373$	−9.29180			−0.481111			−0.240555	−	0.970635i	$-0.577330\pi$
$373$	−9.29180			−0.481111			−0.240555	+	0.970635i	$0.577330\pi$
$374$	−33.2705	−	24.1724i	−1.72038	−	1.24993i
$375$	−7.90569	+	5.74382i	−0.408248	+	0.296610i
$376$	−22.4164	−	68.9906i	−1.15604	−	3.55792i
$377$	1.41641			0.0729487
$378$	−11.9814			−0.616257
$379$	2.29180	+	7.05342i	0.117722	+	0.362310i	0.992505	−	0.122204i	$-0.0389963\pi$
$379$	2.29180	+	7.05342i	0.117722	+	0.362310i	−0.874783	+	0.484514i	$0.838996\pi$
$380$	3.35410	−	10.3229i	0.172062	−	0.529552i
$381$	2.56231	−	7.88597i	0.131271	−	0.404010i
$382$	−20.6803	−	15.0251i	−1.05810	−	0.768753i
$383$	−1.97875	−	6.08996i	−0.101109	−	0.311183i	0.887688	−	0.460445i	$-0.152310\pi$
$383$	−1.97875	−	6.08996i	−0.101109	−	0.311183i	−0.988798	+	0.149262i	$0.952310\pi$
$384$	0.770867	+	0.560067i	0.0393381	+	0.0285808i
$385$	7.67501	−	5.57622i	0.391155	−	0.284191i
$386$	−16.7533	+	51.5613i	−0.852720	+	2.62440i
$387$	−17.5351	+	12.7400i	−0.891359	+	0.647610i
$388$	27.4894	−	19.9722i	1.39556	−	1.01393i
$389$	−5.19548	+	15.9901i	−0.263422	+	0.810728i	0.728631	+	0.684906i	$0.240157\pi$
$389$	−5.19548	+	15.9901i	−0.263422	+	0.810728i	−0.992053	+	0.125822i	$0.959843\pi$
$390$	−10.8541	+	7.88597i	−0.549619	+	0.399321i
$391$	7.85410	+	5.70634i	0.397199	+	0.288582i
$392$	−13.8541	−	42.6385i	−0.699738	−	2.15357i
$393$	5.24419	+	3.81013i	0.264535	+	0.192196i
$394$	−0.874032	+	2.68999i	−0.0440331	+	0.135520i
$395$	−1.11977	+	3.44629i	−0.0563417	+	0.173402i
$396$	−14.2302	−	43.7962i	−0.715097	−	2.20084i
$397$	14.7082			0.738184			0.369092	−	0.929393i	$-0.379669\pi$
$397$	14.7082			0.738184			0.369092	+	0.929393i	$0.379669\pi$
$398$	60.7811			3.04668
$399$	0.270091	+	0.831254i	0.0135215	+	0.0416147i
$400$		0			0
$401$	0.437016	+	0.317511i	0.0218235	+	0.0158557i	0.598644	−	0.801016i	$-0.295707\pi$
$401$	0.437016	+	0.317511i	0.0218235	+	0.0158557i	−0.576820	+	0.816871i	$0.695707\pi$
$402$	−13.7295			−0.684764
$403$		0			0
$404$	10.8541			0.540012
$405$	−4.89919	−	3.55947i	−0.243443	−	0.176871i
$406$	−1.14412	+	0.831254i	−0.0567819	+	0.0412544i
$407$	5.56231	+	17.1190i	0.275713	+	0.848558i
$408$	−24.1803			−1.19711
$409$	30.0810			1.48741			0.743706	−	0.668507i	$-0.233066\pi$
$409$	30.0810			1.48741			0.743706	+	0.668507i	$0.233066\pi$
$410$	−2.66312	−	8.19624i	−0.131522	−	0.404783i
$411$	0.708204	−	2.17963i	0.0349331	−	0.107513i
$412$	16.0623	−	49.4347i	0.791333	−	2.43547i
$413$	9.66312	+	7.02067i	0.475491	+	0.345464i
$414$	4.74342	+	14.5987i	0.233126	+	0.717489i
$415$	5.72061	+	4.15627i	0.280814	+	0.204023i
$416$	23.0250	−	16.7287i	1.12889	−	0.820190i
$417$	4.85410	−	14.9394i	0.237706	−	0.731585i
$418$	−8.98606	+	6.52875i	−0.439522	+	0.319332i
$419$	−24.7533	+	17.9843i	−1.20928	+	0.878591i	−0.995165	−	0.0982177i	$-0.968686\pi$
$419$	−24.7533	+	17.9843i	−1.20928	+	0.878591i	−0.214112	+	0.976809i	$0.568686\pi$
$420$	2.93159	−	9.02251i	0.143047	−	0.440254i
$421$	−21.3713	+	15.5272i	−1.04157	+	0.756748i	−0.970592	−	0.240729i	$-0.922613\pi$
$421$	−21.3713	+	15.5272i	−1.04157	+	0.756748i	−0.0709823	+	0.997478i	$0.522613\pi$
$422$	10.5902	+	7.69421i	0.515521	+	0.374548i
$423$	6.70820	+	20.6457i	0.326164	+	1.00383i
$424$	82.9958	+	60.3000i	4.03063	+	2.92843i
$425$		0			0
$426$	1.04096	−	3.20374i	0.0504345	−	0.155222i
$427$	−4.30640	−	13.2537i	−0.208401	−	0.641393i
$428$	7.14590			0.345410
$429$	9.72327			0.469444
$430$	−17.5351	−	53.9675i	−0.845618	−	2.60254i
$431$	29.0344	−	21.0948i	1.39854	−	1.01610i	0.403673	−	0.914903i	$-0.367733\pi$
$431$	29.0344	−	21.0948i	1.39854	−	1.01610i	0.994867	−	0.101195i	$-0.0322668\pi$
$432$	−36.4844	−	26.5075i	−1.75536	−	1.27534i
$433$	−25.8384			−1.24171			−0.620857	−	0.783924i	$-0.713215\pi$
$433$	−25.8384			−1.24171			−0.620857	+	0.783924i	$0.713215\pi$
$434$		0			0
$435$	1.05573			0.0506183
$436$	5.07295	+	3.68571i	0.242950	+	0.176514i
$437$	2.12132	−	1.54123i	0.101477	−	0.0737270i
$438$	−3.00000	−	9.23305i	−0.143346	−	0.441172i
$439$	−25.0000			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$440$	70.8869			3.37940
$441$	4.14590	+	12.7598i	0.197424	+	0.607608i
$442$	−7.85410	+	24.1724i	−0.373582	+	1.14977i
$443$	1.87132	−	5.75934i	0.0889092	−	0.273634i	−0.896709	−	0.442620i	$-0.854049\pi$
$443$	1.87132	−	5.75934i	0.0889092	−	0.273634i	0.985619	+	0.168985i	$0.0540491\pi$
$444$	14.5623	+	10.5801i	0.691096	+	0.502111i
$445$	−10.6066	−	32.6438i	−0.502801	−	1.54746i
$446$	−34.1962	−	24.8450i	−1.61924	−	1.17644i
$447$	−9.48683	+	6.89259i	−0.448712	+	0.326008i
$448$	−2.69098	+	8.28199i	−0.127137	+	0.391287i
$449$	−27.2677	+	19.8111i	−1.28684	+	0.934945i	−0.999737	−	0.0229547i	$-0.992693\pi$
$449$	−27.2677	+	19.8111i	−1.28684	+	0.934945i	−0.287104	+	0.957899i	$0.592693\pi$
$450$		0			0
$451$	−1.93004	+	5.94006i	−0.0908821	+	0.279706i
$452$	38.3435	−	27.8582i	1.80352	−	1.31034i
$453$	8.85410	+	6.43288i	0.416002	+	0.302243i
$454$	1.85410	+	5.70634i	0.0870173	+	0.267812i
$455$	−4.74342	−	3.44629i	−0.222375	−	0.161565i
$456$	−2.01815	+	6.21124i	−0.0945088	+	0.290868i
$457$	3.49613	−	10.7600i	0.163542	−	0.503330i	−0.835384	−	0.549667i	$-0.814755\pi$
$457$	3.49613	−	10.7600i	0.163542	−	0.503330i	0.998926	+	0.0463365i	$0.0147546\pi$
$458$	3.43237	+	10.5637i	0.160384	+	0.493611i
$459$	16.9443			0.790891
$460$	−28.4605			−1.32698
$461$	1.59619	+	4.91257i	0.0743420	+	0.228801i	0.981322	−	0.192373i	$-0.0616182\pi$
$461$	1.59619	+	4.91257i	0.0743420	+	0.228801i	−0.906980	+	0.421174i	$0.861618\pi$
$462$	−7.85410	+	5.70634i	−0.365406	+	0.265483i
$463$	3.09852	+	2.25121i	0.144000	+	0.104622i	0.657453	−	0.753496i	$-0.271634\pi$
$463$	3.09852	+	2.25121i	0.144000	+	0.104622i	−0.513453	+	0.858118i	$0.671634\pi$
$464$	−5.32300			−0.247114
$465$		0			0
$466$	−35.2705			−1.63387
$467$	12.6631	+	9.20029i	0.585979	+	0.425739i	0.840875	−	0.541230i	$-0.182041\pi$
$467$	12.6631	+	9.20029i	0.585979	+	0.425739i	−0.254895	+	0.966969i	$0.582041\pi$
$468$	−23.0250	+	16.7287i	−1.06433	+	0.773283i
$469$	−1.85410	−	5.70634i	−0.0856145	−	0.263494i
$470$	−56.8328			−2.62150
$471$	−7.61125			−0.350708
$472$	27.5795	+	84.8811i	1.26945	+	3.90697i
$473$	−12.7082	+	39.1118i	−0.584324	+	1.79836i
$474$	1.14590	−	3.52671i	0.0526328	−	0.161987i
$475$		0			0
$476$	−5.55369	−	17.0925i	−0.254553	−	0.783433i
$477$	−24.8369	−	18.0450i	−1.13720	−	0.826225i
$478$	−25.6471	+	18.6337i	−1.17307	+	0.852287i
$479$	5.10739	−	15.7189i	0.233363	−	0.718216i	−0.763972	−	0.645250i	$-0.776753\pi$
$479$	5.10739	−	15.7189i	0.233363	−	0.718216i	0.997334	−	0.0729667i	$-0.0232467\pi$
$480$	17.1618	−	12.4688i	0.783327	−	0.569121i
$481$	9.00000	−	6.53888i	0.410365	−	0.298147i
$482$	−18.7824	+	57.8062i	−0.855514	+	2.63300i
$483$	1.85410	−	1.34708i	0.0843646	−	0.0612944i
$484$	−27.4894	−	19.9722i	−1.24952	−	0.907827i
$485$	−4.83688	−	14.8864i	−0.219631	−	0.675956i
$486$	34.0930	+	24.7700i	1.54649	+	1.12359i
$487$	8.67656	−	26.7037i	0.393172	−	1.21006i	−0.537203	−	0.843453i	$-0.680519\pi$
$487$	8.67656	−	26.7037i	0.393172	−	1.21006i	0.930376	−	0.366608i	$-0.119481\pi$
$488$	32.1780	−	99.0337i	1.45663	−	4.48305i
$489$	−3.89374	−	11.9837i	−0.176081	−	0.541921i
$490$	−35.1246			−1.58677
$491$	−15.8902			−0.717115			−0.358557	−	0.933508i	$-0.616731\pi$
$491$	−15.8902			−0.717115			−0.358557	+	0.933508i	$0.616731\pi$
$492$	1.93004	+	5.94006i	0.0870130	+	0.267798i
$493$	1.61803	−	1.17557i	0.0728726	−	0.0529450i
$494$	5.55369	+	4.03499i	0.249872	+	0.181543i
$495$	−21.2132			−0.953463
$496$		0			0
$497$	1.47214			0.0660343
$498$	−5.85410	−	4.25325i	−0.262329	−	0.190593i
$499$	−14.8736	+	10.8063i	−0.665834	+	0.483756i	−0.868628	−	0.495465i	$-0.834998\pi$
$499$	−14.8736	+	10.8063i	−0.665834	+	0.483756i	0.202794	+	0.979221i	$0.434998\pi$
$500$	−16.7705	−	51.6143i	−0.750000	−	2.30826i
$501$	0.944272			0.0421870
$502$	28.8732			1.28867
$503$	−10.1631	−	31.2789i	−0.453151	−	1.39466i	−0.873292	−	0.487197i	$-0.838019\pi$
$503$	−10.1631	−	31.2789i	−0.453151	−	1.39466i	0.420141	−	0.907459i	$-0.361981\pi$
$504$	5.16312	−	15.8904i	0.229984	−	0.707817i
$505$	1.54508	−	4.75528i	0.0687554	−	0.211607i
$506$	23.5623	+	17.1190i	1.04747	+	0.761033i
$507$	1.65420	+	5.09111i	0.0734656	+	0.226104i
$508$	37.2553	+	27.0675i	1.65294	+	1.20093i
$509$	6.42772	−	4.67001i	0.284904	−	0.206995i	−0.436150	−	0.899874i	$-0.643658\pi$
$509$	6.42772	−	4.67001i	0.284904	−	0.206995i	0.721053	+	0.692879i	$0.243658\pi$
$510$	−5.85410	+	18.0171i	−0.259224	+	0.797809i
$511$	3.43237	−	2.49376i	0.151839	−	0.110318i
$512$	32.6074	−	23.6907i	1.44106	−	1.04699i
$513$	1.41421	−	4.35250i	0.0624391	−	0.192168i
$514$	−12.8262	+	9.31881i	−0.565741	+	0.411035i
$515$	−19.3713	−	14.0741i	−0.853602	−	0.620179i
$516$	12.7082	+	39.1118i	0.559447	+	1.72180i
$517$	33.3221	+	24.2099i	1.46551	+	1.06475i
$518$	−3.43237	+	10.5637i	−0.150810	+	0.464144i
$519$	−4.86163	+	14.9626i	−0.213402	+	0.656784i
$520$	−13.5382	−	41.6663i	−0.593689	−	1.82719i
$521$	−13.4164			−0.587784			−0.293892	−	0.955839i	$-0.594951\pi$
$521$	−13.4164			−0.587784			−0.293892	+	0.955839i	$0.594951\pi$
$522$	3.16228			0.138409
$523$	0.191279	+	0.588697i	0.00836406	+	0.0257419i	0.955151	−	0.296118i	$-0.0956921\pi$
$523$	0.191279	+	0.588697i	0.00836406	+	0.0257419i	−0.946787	+	0.321860i	$0.895692\pi$
$524$	−29.1246	+	21.1603i	−1.27231	+	0.924391i
$525$		0			0
$526$	48.4658			2.11321
$527$		0			0
$528$	−36.5410			−1.59024
$529$	13.0451	+	9.47781i	0.567178	+	0.412079i
$530$	65.0237	−	47.2425i	2.82445	−	2.05208i
$531$	−8.25329	−	25.4010i	−0.358162	−	1.10231i
$532$	−4.85410			−0.210452
$533$	3.86008			0.167199
$534$	10.8541	+	33.4055i	0.469703	+	1.44560i
$535$	1.01722	−	3.13068i	0.0439783	−	0.135351i
$536$	13.8541	−	42.6385i	0.598406	−	1.84170i
$537$	9.38197	+	6.81640i	0.404862	+	0.294149i
$538$	1.74806	+	5.37999i	0.0753644	+	0.231948i
$539$	20.5942	+	14.9626i	0.887055	+	0.644484i
$540$	−40.1869	+	29.1975i	−1.72937	+	1.25646i
$541$	7.98278	−	24.5685i	0.343206	−	1.05628i	−0.619330	−	0.785130i	$-0.712596\pi$
$541$	7.98278	−	24.5685i	0.343206	−	1.05628i	0.962537	−	0.271151i	$-0.0874041\pi$
$542$	39.3766	−	28.6088i	1.69137	−	1.22885i
$543$	6.14590	−	4.46526i	0.263746	−	0.191622i
$544$	12.4184	−	38.2200i	0.532436	−	1.63867i
$545$	2.33688	−	1.69784i	0.100101	−	0.0727276i
$546$	4.85410	+	3.52671i	0.207736	+	0.150929i
$547$	0.746711	+	2.29814i	0.0319271	+	0.0982614i	0.965750	−	0.259474i	$-0.0835491\pi$
$547$	0.746711	+	2.29814i	0.0319271	+	0.0982614i	−0.933823	+	0.357735i	$0.883549\pi$
$548$	10.2971	+	7.48128i	0.439871	+	0.319585i
$549$	−9.62940	+	29.6363i	−0.410973	+	1.26484i
$550$		0			0
$551$	−0.166925	−	0.513743i	−0.00711126	−	0.0218862i
$552$	17.1246			0.728872
$553$	1.62054			0.0689126
$554$	8.17578	+	25.1625i	0.347356	+	1.06905i
$555$	6.70820	−	4.87380i	0.284747	−	0.206881i
$556$	70.5774	+	51.2775i	2.99315	+	2.17465i
$557$	−10.6460			−0.451086			−0.225543	−	0.974233i	$-0.572416\pi$
$557$	−10.6460			−0.451086			−0.225543	+	0.974233i	$0.572416\pi$
$558$		0			0
$559$	25.4164			1.07500
$560$	17.8262	+	12.9515i	0.753296	+	0.547302i
$561$	11.1074	−	8.06998i	0.468954	−	0.340715i
$562$	10.8090	+	33.2667i	0.455951	+	1.40327i
$563$	9.76393			0.411501			0.205750	−	0.978605i	$-0.434037\pi$
$563$	9.76393			0.411501			0.205750	+	0.978605i	$0.434037\pi$
$564$	41.1884			1.73435
$565$	−6.74671	−	20.7642i	−0.283836	−	0.873558i
$566$	19.4164	−	59.7576i	0.816132	−	2.51180i
$567$	−0.836881	+	2.57565i	−0.0351457	+	0.108167i
$568$	8.89919	+	6.46564i	0.373402	+	0.271292i
$569$	−3.62365	−	11.1524i	−0.151911	−	0.467535i	0.845924	−	0.533304i	$-0.179050\pi$
$569$	−3.62365	−	11.1524i	−0.151911	−	0.467535i	−0.997835	+	0.0657694i	$0.979050\pi$
$570$	4.13948	+	3.00750i	0.173384	+	0.125971i
$571$	2.12132	−	1.54123i	0.0887745	−	0.0644984i	−0.542513	−	0.840048i	$-0.682527\pi$
$571$	2.12132	−	1.54123i	0.0887745	−	0.0644984i	0.631287	+	0.775549i	$0.282527\pi$
$572$	−16.6869	+	51.3571i	−0.697715	+	2.14735i
$573$	6.90414	−	5.01615i	0.288425	−	0.209553i
$574$	−3.11803	+	2.26538i	−0.130144	+	0.0945553i
$575$		0			0
$576$	15.7533	−	11.4454i	0.656387	−	0.476893i
$577$	24.2705	+	17.6336i	1.01039	+	0.734095i	0.964292	−	0.264842i	$-0.0853198\pi$
$577$	24.2705	+	17.6336i	1.01039	+	0.734095i	0.0461028	+	0.998937i	$0.485320\pi$
$578$	−2.66312	−	8.19624i	−0.110771	−	0.340919i
$579$	−14.6429	−	10.6387i	−0.608539	−	0.442129i
$580$	−1.81182	+	5.57622i	−0.0752319	+	0.231540i
$581$	0.977198	−	3.00750i	0.0405410	−	0.124772i
$582$	4.94975	+	15.2338i	0.205174	+	0.631460i
$583$	−58.2492			−2.41244
$584$	31.7016			1.31182
$585$	4.05136	+	12.4688i	0.167503	+	0.515522i
$586$	4.85410	−	3.52671i	0.200521	−	0.145687i
$587$	12.7279	+	9.24738i	0.525338	+	0.381680i	0.818611	−	0.574349i	$-0.194745\pi$
$587$	12.7279	+	9.24738i	0.525338	+	0.381680i	−0.293273	+	0.956029i	$0.594745\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	69.9230			2.87868
$591$	−0.763932	−	0.555029i	−0.0314240	−	0.0228308i
$592$	−33.8229	+	24.5738i	−1.39011	+	1.00998i
$593$	1.60081	+	4.92680i	0.0657375	+	0.202319i	0.978530	−	0.206104i	$-0.0660786\pi$
$593$	1.60081	+	4.92680i	0.0657375	+	0.202319i	−0.912793	+	0.408424i	$0.866079\pi$
$594$	50.8328			2.08570
$595$	−8.27895			−0.339404
$596$	−20.1246	−	61.9372i	−0.824336	−	2.53705i
$597$	−6.27051	+	19.2986i	−0.256635	+	0.789841i
$598$	5.56231	−	17.1190i	0.227460	−	0.700049i
$599$	−4.89919	−	3.55947i	−0.200175	−	0.145436i	0.483182	−	0.875520i	$-0.339481\pi$
$599$	−4.89919	−	3.55947i	−0.200175	−	0.145436i	−0.683357	+	0.730084i	$0.739481\pi$
$600$		0			0
$601$	−14.7067	−	10.6850i	−0.599898	−	0.435851i	0.245945	−	0.969284i	$-0.420902\pi$
$601$	−14.7067	−	10.6850i	−0.599898	−	0.435851i	−0.845843	+	0.533433i	$0.820902\pi$
$602$	−20.5305	+	14.9162i	−0.836759	+	0.607941i
$603$	−4.14590	+	12.7598i	−0.168834	+	0.519618i
$604$	−49.1729	+	35.7262i	−2.00082	+	1.45368i
$605$	−12.6631	+	9.20029i	−0.514829	+	0.374045i
$606$	−1.58114	+	4.86624i	−0.0642294	+	0.197678i
$607$	−12.2361	+	8.89002i	−0.496647	+	0.360835i	−0.807735	−	0.589546i	$-0.799307\pi$
$607$	−12.2361	+	8.89002i	−0.496647	+	0.360835i	0.311088	+	0.950381i	$0.399307\pi$
$608$	−8.78115	−	6.37988i	−0.356123	−	0.258738i
$609$	−0.145898	−	0.449028i	−0.00591209	−	0.0181955i
$610$	−66.0009	−	47.9525i	−2.67230	−	1.94154i
$611$	7.86629	−	24.2099i	0.318236	−	0.979430i
$612$	−12.4184	+	38.2200i	−0.501985	+	1.54495i
$613$	0.181977	+	0.560067i	0.00734998	+	0.0226209i	0.954664	−	0.297685i	$-0.0962144\pi$
$613$	0.181977	+	0.560067i	0.00734998	+	0.0226209i	−0.947314	+	0.320306i	$0.896214\pi$
$614$	63.1591			2.54889
$615$	2.87714			0.116017
$616$	−9.79633	−	30.1500i	−0.394705	−	1.21478i
$617$	5.56231	−	4.04125i	0.223930	−	0.162695i	−0.470164	−	0.882579i	$-0.655805\pi$
$617$	5.56231	−	4.04125i	0.223930	−	0.162695i	0.694094	+	0.719884i	$0.255805\pi$
$618$	19.8233	+	14.4025i	0.797412	+	0.579354i
$619$	25.8384			1.03853			0.519267	−	0.854612i	$-0.326205\pi$
$619$	25.8384			1.03853			0.519267	+	0.854612i	$0.326205\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	−53.9508	−	39.1976i	−2.16323	−	1.57168i
$623$	−12.4184	+	9.02251i	−0.497534	+	0.361479i
$624$	6.97871	+	21.4783i	0.279372	+	0.859819i
$625$	−25.0000			−1.00000
$626$	−30.1599			−1.20543
$627$	−1.14590	−	3.52671i	−0.0457628	−	0.140843i
$628$	13.0623	−	40.2016i	0.521243	−	1.60422i
$629$	4.85410	−	14.9394i	0.193546	−	0.595672i
$630$	−10.5902	−	7.69421i	−0.421922	−	0.306545i
$631$	−7.30175	−	22.4725i	−0.290678	−	0.894615i	−0.984639	−	0.174603i	$-0.944136\pi$
$631$	−7.30175	−	22.4725i	−0.290678	−	0.894615i	0.693961	−	0.720013i	$-0.255864\pi$
$632$	9.79633	+	7.11745i	0.389677	+	0.283117i
$633$	−3.53553	+	2.56872i	−0.140525	+	0.102097i
$634$	21.2254	−	65.3251i	0.842969	−	2.59439i
$635$	17.1618	−	12.4688i	0.681047	−	0.494810i
$636$	−47.1246	+	34.2380i	−1.86861	+	1.35763i
$637$	4.86163	−	14.9626i	0.192625	−	0.592839i
$638$	4.85410	−	3.52671i	0.192176	−	0.139624i
$639$	−2.66312	−	1.93487i	−0.105351	−	0.0765422i
$640$	0.753289	+	2.31838i	0.0297764	+	0.0916422i
$641$	6.86474	+	4.98752i	0.271141	+	0.196995i	0.715044	−	0.699079i	$-0.246407\pi$
$641$	6.86474	+	4.98752i	0.271141	+	0.196995i	−0.443903	+	0.896075i	$0.646407\pi$
$642$	−1.04096	+	3.20374i	−0.0410833	+	0.126441i
$643$	−1.43857	+	4.42746i	−0.0567316	+	0.174602i	−0.975407	−	0.220411i	$-0.929260\pi$
$643$	−1.43857	+	4.42746i	−0.0567316	+	0.174602i	0.918675	+	0.395013i	$0.129260\pi$
$644$	3.93314	+	12.1050i	0.154988	+	0.477003i
$645$	18.9443			0.745930
$646$	9.69316			0.381372
$647$	9.82068	+	30.2250i	0.386091	+	1.18827i	0.935686	+	0.352834i	$0.114782\pi$
$647$	9.82068	+	30.2250i	0.386091	+	1.18827i	−0.549595	+	0.835431i	$0.685218\pi$
$648$	−16.3713	+	11.8945i	−0.643126	+	0.467259i
$649$	−40.9971	−	29.7862i	−1.60928	−	1.16921i
$650$		0			0
$651$		0			0
$652$	69.9787			2.74058
$653$	−19.9443	−	14.4904i	−0.780480	−	0.567052i	0.124643	−	0.992202i	$-0.460221\pi$
$653$	−19.9443	−	14.4904i	−0.780480	−	0.567052i	−0.905123	+	0.425150i	$0.860221\pi$
$654$	−2.39141	+	1.73746i	−0.0935116	+	0.0679401i
$655$	5.12461	+	15.7719i	0.200235	+	0.616260i
$656$	−14.5066			−0.566387
$657$	−9.48683			−0.370117
$658$	7.85410	+	24.1724i	0.306185	+	0.942340i
$659$	7.66970	−	23.6049i	0.298769	−	0.919516i	−0.683160	−	0.730268i	$-0.739395\pi$
$659$	7.66970	−	23.6049i	0.298769	−	0.919516i	0.981929	−	0.189248i	$-0.0606050\pi$
$660$	−12.4377	+	38.2793i	−0.484137	+	1.49002i
$661$	−6.33688	−	4.60401i	−0.246476	−	0.179075i	0.457688	−	0.889113i	$-0.348678\pi$
$661$	−6.33688	−	4.60401i	−0.246476	−	0.179075i	−0.704164	+	0.710038i	$0.748678\pi$
$662$	25.3133	+	77.9062i	0.983828	+	3.02791i
$663$	−6.86474	−	4.98752i	−0.266604	−	0.193699i
$664$	19.1162	−	13.8888i	0.741854	−	0.538988i
$665$	−0.690983	+	2.12663i	−0.0267952	+	0.0824671i
$666$	20.0934	−	14.5987i	0.778605	−	0.565689i
$667$	−1.14590	+	0.832544i	−0.0443693	+	0.0322362i
$668$	−1.62054	+	4.98752i	−0.0627008	+	0.192973i
$669$	11.4164	−	8.29451i	0.441384	−	0.320684i
$670$	−28.4164	−	20.6457i	−1.09782	−	0.797614i
$671$	18.2705	+	56.2308i	0.705325	+	2.17077i
$672$	−7.67501	−	5.57622i	−0.296070	−	0.215107i
$673$	12.3547	−	38.0238i	0.476237	−	1.46571i	−0.368044	−	0.929808i	$-0.619973\pi$
$673$	12.3547	−	38.0238i	0.476237	−	1.46571i	0.844282	−	0.535900i	$-0.180027\pi$
$674$	−12.4184	+	38.2200i	−0.478340	+	1.47218i
$675$		0			0
$676$	−29.7295			−1.14344
$677$	−21.2132			−0.815290			−0.407645	−	0.913141i	$-0.633650\pi$
$677$	−21.2132			−0.815290			−0.407645	+	0.913141i	$0.633650\pi$
$678$	6.90414	+	21.2488i	0.265152	+	0.816054i
$679$	−5.66312	+	4.11450i	−0.217331	+	0.157900i
$680$	−50.0470	−	36.3612i	−1.91921	−	1.39439i
$681$	−2.00310			−0.0767591
$682$		0			0
$683$	−41.1803			−1.57572			−0.787861	−	0.615853i	$-0.788811\pi$
$683$	−41.1803			−1.57572			−0.787861	+	0.615853i	$0.788811\pi$
$684$	8.78115	+	6.37988i	0.335756	+	0.243941i
$685$	4.74342	−	3.44629i	0.181237	−	0.131676i
$686$	10.5172	+	32.3687i	0.401549	+	1.23584i
$687$	−3.70820			−0.141477
$688$	−95.5174			−3.64157
$689$	11.1246	+	34.2380i	0.423814	+	1.30437i
$690$	4.14590	−	12.7598i	0.157832	−	0.485756i
$691$	−14.9615	+	46.0467i	−0.569162	+	1.75170i	0.0860870	+	0.996288i	$0.472564\pi$
$691$	−14.9615	+	46.0467i	−0.569162	+	1.75170i	−0.655249	+	0.755413i	$0.727436\pi$
$692$	−70.6869	−	51.3571i	−2.68711	−	1.95230i
$693$	2.93159	+	9.02251i	0.111362	+	0.342737i
$694$	45.7406	+	33.2325i	1.73629	+	1.26149i
$695$	32.5119	−	23.6212i	1.23325	−	0.896005i
$696$	1.09017	−	3.35520i	0.0413228	−	0.127178i
$697$	4.40957	−	3.20374i	0.167024	−	0.121350i
$698$	−12.7082	+	9.23305i	−0.481013	+	0.349476i
$699$	3.63870	−	11.1988i	0.137628	−	0.423576i
$700$		0			0
$701$	2.95492	+	2.14687i	0.111606	+	0.0810862i	0.642188	−	0.766547i	$-0.278027\pi$
$701$	2.95492	+	2.14687i	0.111606	+	0.0810862i	−0.530583	+	0.847633i	$0.678027\pi$
$702$	−9.70820	−	29.8788i	−0.366413	−	1.12770i
$703$	−3.43237	−	2.49376i	−0.129454	−	0.0940540i
$704$	11.4169	−	35.1375i	0.430290	−	1.32430i
$705$	5.86319	−	18.0450i	0.220820	−	0.679615i
$706$	7.73877	+	23.8175i	0.291252	+	0.896383i
$707$	−2.23607			−0.0840960
$708$	−50.6753			−1.90449
$709$	−12.7279	−	39.1725i	−0.478007	−	1.47115i	−0.841859	−	0.539698i	$-0.818538\pi$
$709$	−12.7279	−	39.1725i	−0.478007	−	1.47115i	0.363852	−	0.931457i	$-0.381462\pi$
$710$	6.97214	−	5.06555i	0.261660	−	0.190107i
$711$	−2.93159	−	2.12993i	−0.109943	−	0.0798785i
$712$	−114.697			−4.29847
$713$		0			0
$714$	8.47214			0.317062
$715$	20.1246	+	14.6214i	0.752618	+	0.546809i
$716$	−52.1045	+	37.8561i	−1.94724	+	1.41475i
$717$	−3.27051	−	10.0656i	−0.122139	−	0.375907i
$718$	37.2705			1.39092
$719$	−37.5648			−1.40093			−0.700465	−	0.713687i	$-0.747024\pi$
$719$	−37.5648			−1.40093			−0.700465	+	0.713687i	$0.747024\pi$
$720$	−15.2254	−	46.8590i	−0.567418	−	1.74633i
$721$	−3.30902	+	10.1841i	−0.123234	+	0.379276i
$722$	−14.5623	+	44.8182i	−0.541953	+	1.66796i
$723$	−16.4164	−	11.9272i	−0.610533	−	0.443578i
$724$	13.0374	+	40.1250i	0.484532	+	1.49124i
$725$		0			0
$726$	12.9586	−	9.41498i	0.480939	−	0.349423i
$727$	−9.39919	+	28.9277i	−0.348597	+	1.07287i	0.611034	+	0.791605i	$0.290754\pi$
$727$	−9.39919	+	28.9277i	−0.348597	+	1.07287i	−0.959630	+	0.281265i	$0.909246\pi$
$728$	−15.8508	+	11.5163i	−0.587470	+	0.426822i
$729$	−4.80902	+	3.49396i	−0.178112	+	0.129406i
$730$	7.67501	−	23.6212i	0.284065	−	0.874262i
$731$	29.0344	−	21.0948i	1.07388	−	0.780218i
$732$	47.8328	+	34.7526i	1.76795	+	1.28449i
$733$	−4.45492	−	13.7108i	−0.164546	−	0.506421i	0.834457	−	0.551074i	$-0.185782\pi$
$733$	−4.45492	−	13.7108i	−0.164546	−	0.506421i	−0.999003	+	0.0446532i	$0.985782\pi$
$734$	−14.1027	−	10.2462i	−0.520541	−	0.378195i
$735$	3.62365	−	11.1524i	0.133660	−	0.411364i
$736$	−8.79478	+	27.0675i	−0.324180	+	0.997723i
$737$	7.86629	+	24.2099i	0.289758	+	0.891785i
$738$	8.61803			0.317234
$739$	−35.1490			−1.29298			−0.646489	−	0.762924i	$-0.723763\pi$
$739$	−35.1490			−1.29298			−0.646489	+	0.762924i	$0.723763\pi$
$740$	14.2302	+	43.7962i	0.523114	+	1.60998i
$741$	−1.85410	+	1.34708i	−0.0681121	+	0.0494864i
$742$	−29.0795	−	21.1275i	−1.06754	−	0.775614i
$743$	−36.4844			−1.33848			−0.669242	−	0.743045i	$-0.733381\pi$
$743$	−36.4844			−1.33848			−0.669242	+	0.743045i	$0.733381\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	19.6803	+	14.2986i	0.720548	+	0.523509i
$747$	−5.72061	+	4.15627i	−0.209306	+	0.152070i
$748$	23.5623	+	72.5173i	0.861523	+	2.65150i
$749$	−1.47214			−0.0537907
$750$	25.5834			0.934172
$751$	−11.6008	−	35.7036i	−0.423320	−	1.30284i	−0.904594	−	0.426274i	$-0.859826\pi$
$751$	−11.6008	−	35.7036i	−0.423320	−	1.30284i	0.481274	−	0.876570i	$-0.340174\pi$
$752$	−29.5623	+	90.9834i	−1.07803	+	3.31782i
$753$	−2.97871	+	9.16754i	−0.108550	+	0.334084i
$754$	−3.00000	−	2.17963i	−0.109254	−	0.0793774i
$755$	8.65221	+	26.6288i	0.314886	+	0.969120i
$756$	17.9721	+	13.0575i	0.653639	+	0.474897i
$757$	−7.50808	+	5.45494i	−0.272886	+	0.198263i	−0.715809	−	0.698297i	$-0.753942\pi$
$757$	−7.50808	+	5.45494i	−0.272886	+	0.198263i	0.442923	+	0.896560i	$0.353942\pi$
$758$	6.00000	−	18.4661i	0.217930	−	0.670719i
$759$	−7.86629	+	5.71519i	−0.285528	+	0.207448i
$760$	−13.5172	+	9.82084i	−0.490321	+	0.356239i
$761$	12.4184	−	38.2200i	0.450168	−	1.38547i	−0.426548	−	0.904465i	$-0.640271\pi$
$761$	12.4184	−	38.2200i	0.450168	−	1.38547i	0.876716	−	0.481009i	$-0.159729\pi$
$762$	−17.5623	+	12.7598i	−0.636215	+	0.462237i
$763$	−1.04508	−	0.759299i	−0.0378346	−	0.0274885i
$764$	14.6459	+	45.0754i	0.529870	+	1.63077i
$765$	14.9768	+	10.8813i	0.541486	+	0.393413i
$766$	−5.18043	+	15.9437i	−0.187177	+	0.576070i
$767$	−9.67811	+	29.7862i	−0.349456	+	1.07552i
$768$	3.93314	+	12.1050i	0.141925	+	0.436801i
$769$	54.1246			1.95178			0.975892	−	0.218255i	$-0.0700365\pi$
$769$	54.1246			1.95178			0.975892	+	0.218255i	$0.0700365\pi$
$770$	−24.8369			−0.895058
$771$	−1.63560	−	5.03385i	−0.0589046	−	0.181290i
$772$	81.3222	−	59.0840i	2.92685	−	2.12648i
$773$	9.04982	+	6.57508i	0.325499	+	0.236489i	0.738518	−	0.674233i	$-0.235526\pi$
$773$	9.04982	+	6.57508i	0.325499	+	0.236489i	−0.413019	+	0.910722i	$0.635526\pi$
$774$	56.7448			2.03965
$775$		0			0
$776$	−52.3050			−1.87764
$777$	−3.00000	−	2.17963i	−0.107624	−	0.0781937i
$778$	35.6104	−	25.8725i	1.27669	−	0.927572i
$779$	−0.454915	−	1.40008i	−0.0162990	−	0.0501632i
$780$	24.8754			0.890682
$781$	−6.24574			−0.223490
$782$	−7.85410	−	24.1724i	−0.280862	−	0.864405i
$783$	−0.763932	+	2.35114i	−0.0273007	+	0.0840229i
$784$	−18.2705	+	56.2308i	−0.652518	+	2.00824i
$785$	−15.7533	−	11.4454i	−0.562259	−	0.408505i
$786$	−5.24419	−	16.1400i	−0.187054	−	0.575693i
$787$	30.3905	+	22.0800i	1.08331	+	0.787068i	0.978256	−	0.207399i	$-0.0664999\pi$
$787$	30.3905	+	22.0800i	1.08331	+	0.787068i	0.105049	+	0.994467i	$0.466500\pi$
$788$	4.24264	−	3.08246i	0.151138	−	0.109808i
$789$	−5.00000	+	15.3884i	−0.178005	+	0.547842i
$790$	7.67501	−	5.57622i	0.273065	−	0.198393i
$791$	−7.89919	+	5.73910i	−0.280863	+	0.204059i
$792$	−21.9053	+	67.4175i	−0.778369	+	2.39557i
$793$	29.5623	−	21.4783i	1.04979	−	0.762716i
$794$	−31.1525	−	22.6336i	−1.10556	−	0.803236i
$795$	8.29180	+	25.5195i	0.294080	+	0.905084i
$796$	−91.1716	−	66.2401i	−3.23149	−	2.34782i
$797$	−4.24264	+	13.0575i	−0.150282	+	0.462521i	−0.997652	−	0.0684818i	$-0.978184\pi$
$797$	−4.24264	+	13.0575i	−0.150282	+	0.462521i	0.847370	+	0.531002i	$0.178184\pi$
$798$	0.707107	−	2.17625i	0.0250313	−	0.0770384i
$799$	−11.1074	−	34.1850i	−0.392951	−	1.20938i
$800$		0			0
$801$	34.3237			1.21277
$802$	−0.437016	−	1.34500i	−0.0154316	−	0.0474935i
$803$	−14.5623	+	10.5801i	−0.513893	+	0.373365i
$804$	20.5942	+	14.9626i	0.726302	+	0.527689i
$805$	5.86319			0.206650
$806$		0			0
$807$	−1.88854			−0.0664799
$808$	−13.5172	−	9.82084i	−0.475534	−	0.345496i
$809$	−38.4388	+	27.9274i	−1.35144	+	0.981876i	−0.352498	+	0.935813i	$0.614668\pi$
$809$	−38.4388	+	27.9274i	−1.35144	+	0.981876i	−0.998939	+	0.0460634i	$0.985332\pi$
$810$	4.89919	+	15.0781i	0.172140	+	0.529792i
$811$	−16.5836			−0.582329			−0.291164	−	0.956673i	$-0.594043\pi$
$811$	−16.5836			−0.582329			−0.291164	+	0.956673i	$0.594043\pi$
$812$	2.62210			0.0920175
$813$	5.02129	+	15.4539i	0.176104	+	0.541993i
$814$	14.5623	−	44.8182i	0.510409	−	1.57088i
$815$	9.96149	−	30.6583i	0.348936	−	1.07391i
$816$	25.7984	+	18.7436i	0.903124	+	0.656158i
$817$	−2.99535	−	9.21875i	−0.104794	−	0.322523i
$818$	−63.7127	−	46.2900i	−2.22766	−	1.61849i
$819$	4.74342	−	3.44629i	0.165748	−	0.120423i
$820$	−4.93769	+	15.1967i	−0.172432	+	0.530690i
$821$	−19.2832	+	14.0100i	−0.672987	+	0.488954i	−0.871024	−	0.491241i	$-0.836543\pi$
$821$	−19.2832	+	14.0100i	−0.672987	+	0.488954i	0.198037	+	0.980195i	$0.436543\pi$
$822$	−4.85410	+	3.52671i	−0.169306	+	0.123008i
$823$	−4.17888	+	12.8613i	−0.145667	+	0.448316i	−0.997096	−	0.0761533i	$-0.975736\pi$
$823$	−4.17888	+	12.8613i	−0.145667	+	0.448316i	0.851429	+	0.524469i	$0.175736\pi$
$824$	−64.7320	+	47.0306i	−2.25505	+	1.63839i
$825$		0			0
$826$	−9.66312	−	29.7400i	−0.336223	−	1.03479i
$827$	14.8492	+	10.7886i	0.516359	+	0.375157i	0.815230	−	0.579137i	$-0.196610\pi$
$827$	14.8492	+	10.7886i	0.516359	+	0.375157i	−0.298872	+	0.954293i	$0.596610\pi$
$828$	8.79478	−	27.0675i	0.305640	−	0.940662i
$829$	15.7870	−	48.5875i	0.548306	−	1.68751i	−0.164690	−	0.986345i	$-0.552662\pi$
$829$	15.7870	−	48.5875i	0.548306	−	1.68751i	0.712996	−	0.701168i	$-0.247338\pi$
$830$	−5.72061	−	17.6062i	−0.198565	−	0.611121i
$831$	−8.83282			−0.306407
$832$	−22.8337			−0.791618
$833$	−6.86474	−	21.1275i	−0.237849	−	0.732024i
$834$	−33.2705	+	24.1724i	−1.15206	+	0.837023i
$835$	1.95440	+	1.41995i	0.0676346	+	0.0491394i
$836$	20.5942			0.712266
$837$		0			0
$838$	80.1033			2.76712
$839$	15.7082	+	11.4127i	0.542307	+	0.394009i	0.824941	−	0.565218i	$-0.191208\pi$
$839$	15.7082	+	11.4127i	0.542307	+	0.394009i	−0.282634	+	0.959228i	$0.591208\pi$
$840$	−11.8145	+	8.58373i	−0.407638	+	0.296167i
$841$	−8.87132	−	27.3031i	−0.305908	−	0.941487i
$842$	69.1591			2.38338
$843$	−11.6777			−0.402200
$844$	−7.50000	−	23.0826i	−0.258161	−	0.794537i
$845$	−4.23200	+	13.0248i	−0.145585	+	0.448066i
$846$	17.5623	−	54.0512i	0.603805	−	1.85832i
$847$	5.66312	+	4.11450i	0.194587	+	0.141376i
$848$	−41.8074	−	128.670i	−1.43567	−	4.41855i
$849$	16.9706	+	12.3298i	0.582428	+	0.423159i
$850$		0			0
$851$	−3.43769	+	10.5801i	−0.117843	+	0.362682i
$852$	−5.05291	+	3.67116i	−0.173110	+	0.125772i
$853$	26.1246	−	18.9806i	0.894490	−	0.649885i	−0.0425551	−	0.999094i	$-0.513550\pi$
$853$	26.1246	−	18.9806i	0.894490	−	0.649885i	0.937045	+	0.349209i	$0.113550\pi$
$854$	−11.2743	+	34.6987i	−0.385799	+	1.18737i
$855$	4.04508	−	2.93893i	0.138339	−	0.100509i
$856$	−8.89919	−	6.46564i	−0.304168	−	0.220991i
$857$	−1.85410	−	5.70634i	−0.0633349	−	0.194925i	0.914382	−	0.404853i	$-0.132677\pi$
$857$	−1.85410	−	5.70634i	−0.0633349	−	0.194925i	−0.977717	+	0.209928i	$0.932677\pi$
$858$	−20.5942	−	14.9626i	−0.703075	−	0.510814i
$859$	−12.8554	+	39.5650i	−0.438622	+	1.34994i	0.450707	+	0.892672i	$0.351172\pi$
$859$	−12.8554	+	39.5650i	−0.438622	+	1.34994i	−0.889329	+	0.457268i	$0.848828\pi$
$860$	−32.5119	+	100.061i	−1.10865	+	3.41206i
$861$	−0.397610	−	1.22372i	−0.0135505	−	0.0417042i
$862$	−93.9574			−3.20020
$863$	−31.0826			−1.05806			−0.529032	−	0.848602i	$-0.677445\pi$
$863$	−31.0826			−1.05806			−0.529032	+	0.848602i	$0.677445\pi$
$864$	15.3500	+	47.2425i	0.522218	+	1.60722i
$865$	−32.5623	+	23.6579i	−1.10715	+	0.804393i
$866$	54.7266	+	39.7612i	1.85969	+	1.35114i
$867$	2.87714			0.0977126
$868$		0			0
$869$	−6.87539			−0.233232
$870$	−2.23607	−	1.62460i	−0.0758098	−	0.0550790i
$871$	12.7279	−	9.24738i	0.431269	−	0.313335i
$872$	−2.98278	−	9.18005i	−0.101010	−	0.310876i
$873$	15.6525			0.529756
$874$	−6.86474			−0.232203
$875$	3.45492	+	10.6331i	0.116797	+	0.359466i
$876$	−5.56231	+	17.1190i	−0.187933	+	0.578398i
$877$	−8.87132	+	27.3031i	−0.299563	+	0.921961i	0.682087	+	0.731271i	$0.261073\pi$
$877$	−8.87132	+	27.3031i	−0.299563	+	0.921961i	−0.981650	+	0.190690i	$0.938927\pi$
$878$	52.9508	+	38.4710i	1.78700	+	1.29833i
$879$	0.618993	+	1.90506i	0.0208781	+	0.0642562i
$880$	−75.6303	−	54.9486i	−2.54950	−	1.85232i
$881$	−5.86319	+	4.25985i	−0.197536	+	0.143518i	−0.682156	−	0.731206i	$-0.738958\pi$
$881$	−5.86319	+	4.25985i	−0.197536	+	0.143518i	0.484621	+	0.874724i	$0.338958\pi$
$882$	10.8541	−	33.4055i	0.365477	−	1.12482i
$883$	27.4589	−	19.9501i	0.924067	−	0.671374i	−0.0204659	−	0.999791i	$-0.506515\pi$
$883$	27.4589	−	19.9501i	0.924067	−	0.671374i	0.944533	+	0.328416i	$0.106515\pi$
$884$	38.1246	−	27.6992i	1.28227	−	0.931623i
$885$	−7.21364	+	22.2013i	−0.242484	+	0.746288i
$886$	−12.8262	+	9.31881i	−0.430906	+	0.313071i
$887$	−20.5172	−	14.9066i	−0.688901	−	0.500516i	0.187398	−	0.982284i	$-0.439995\pi$
$887$	−20.5172	−	14.9066i	−0.688901	−	0.500516i	−0.876299	+	0.481768i	$0.839995\pi$
$888$	−8.56231	−	26.3521i	−0.287332	−	0.884317i
$889$	−7.67501	−	5.57622i	−0.257412	−	0.187020i
$890$	−27.7684	+	85.4625i	−0.930800	+	2.86471i
$891$	3.55059	−	10.9276i	0.118949	−	0.366088i
$892$	24.2179	+	74.5349i	0.810874	+	2.49561i
$893$	−9.70820			−0.324873
$894$	30.7000			1.02676
$895$	9.16803	+	28.2163i	0.306454	+	0.943167i
$896$	0.881966	−	0.640786i	0.0294644	−	0.0214072i
$897$	4.86163	+	3.53218i	0.162325	+	0.117936i
$898$	88.2400			2.94461
$899$		0			0
$900$		0			0
$901$	41.1246	+	29.8788i	1.37006	+	0.995406i
$902$	13.2287	−	9.61121i	0.440467	−	0.320018i
$903$	−2.61803	−	8.05748i	−0.0871227	−	0.268136i
$904$	−72.9574			−2.42653
$905$	19.4350			0.646042
$906$	−8.85410	−	27.2501i	−0.294158	−	0.905325i
$907$	3.56637	−	10.9762i	0.118419	−	0.364457i	−0.874225	−	0.485520i	$-0.838630\pi$
$907$	3.56637	−	10.9762i	0.118419	−	0.364457i	0.992645	+	0.121063i	$0.0386302\pi$
$908$	3.43769	−	10.5801i	0.114084	−	0.351114i
$909$	4.04508	+	2.93893i	0.134167	+	0.0974780i
$910$	4.74342	+	14.5987i	0.157243	+	0.483943i
$911$	21.7777	+	15.8225i	0.721529	+	0.524221i	0.886872	−	0.462015i	$-0.152873\pi$
$911$	21.7777	+	15.8225i	0.721529	+	0.524221i	−0.165344	+	0.986236i	$0.552873\pi$
$912$	6.96790	−	5.06248i	0.230730	−	0.167635i
$913$	−4.14590	+	12.7598i	−0.137209	+	0.422286i
$914$	−23.9628	+	17.4100i	−0.792620	+	0.575872i
$915$	22.0344	−	16.0090i	0.728436	−	0.529240i
$916$	6.36396	−	19.5863i	0.210271	−	0.647148i
$917$	6.00000	−	4.35926i	0.198137	−	0.143955i
$918$	−35.8885	−	26.0746i	−1.18450	−	0.860588i
$919$	−13.1459	−	40.4589i	−0.433643	−	1.33462i	−0.894471	−	0.447127i	$-0.852447\pi$
$919$	−13.1459	−	40.4589i	−0.433643	−	1.33462i	0.460827	−	0.887490i	$-0.347553\pi$
$920$	35.4435	+	25.7512i	1.16854	+	0.848991i
$921$	−6.51583	+	20.0537i	−0.214704	+	0.660791i
$922$	4.17888	−	12.8613i	0.137624	−	0.423563i
$923$	1.19283	+	3.67116i	0.0392625	+	0.120838i
$924$	18.0000			0.592157
$925$		0			0
$926$	−3.09852	−	9.53626i	−0.101824	−	0.313381i
$927$	19.3713	−	14.0741i	0.636238	−	0.462254i
$928$	4.74342	+	3.44629i	0.155710	+	0.113130i
$929$	10.6460			0.349284			0.174642	−	0.984632i	$-0.444123\pi$
$929$	10.6460			0.349284			0.174642	+	0.984632i	$0.444123\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	52.9058	+	38.4383i	1.73299	+	1.25909i
$933$	18.0115	−	13.0861i	0.589671	−	0.428421i
$934$	−12.6631	−	38.9731i	−0.414350	−	1.27524i
$935$	35.1246			1.14870
$936$	43.8105			1.43199
$937$	7.49342	+	23.0624i	0.244799	+	0.753415i	0.995669	+	0.0929651i	$0.0296345\pi$
$937$	7.49342	+	23.0624i	0.244799	+	0.753415i	−0.750870	+	0.660450i	$0.770366\pi$
$938$	−4.85410	+	14.9394i	−0.158492	+	0.487788i
$939$	3.11146	−	9.57608i	0.101539	−	0.312503i
$940$	85.2492	+	61.9372i	2.78052	+	2.02017i
$941$	7.89064	+	24.2849i	0.257228	+	0.791665i	0.993383	+	0.114852i	$0.0366394\pi$
$941$	7.89064	+	24.2849i	0.257228	+	0.791665i	−0.736155	+	0.676813i	$0.763361\pi$
$942$	16.1209	+	11.7125i	0.525247	+	0.381614i
$943$	−3.12287	+	2.26890i	−0.101695	+	0.0738855i
$944$	36.3713	−	111.939i	1.18379	−	3.64332i
$945$	8.27895	−	6.01501i	0.269314	−	0.195668i
$946$	87.1033	−	63.2843i	2.83197	−	2.05755i
$947$	12.4184	−	38.2200i	0.403545	−	1.24198i	−0.518560	−	0.855041i	$-0.673532\pi$
$947$	12.4184	−	38.2200i	0.403545	−	1.24198i	0.922104	−	0.386941i	$-0.126468\pi$
$948$	−5.56231	+	4.04125i	−0.180655	+	0.131254i
$949$	9.00000	+	6.53888i	0.292152	+	0.212261i
$950$		0			0
$951$	18.5517	+	13.4786i	0.601580	+	0.437074i
$952$	−8.54904	+	26.3112i	−0.277076	+	0.852752i
$953$	5.76932	−	17.7561i	0.186887	−	0.575178i	−0.813089	−	0.582139i	$-0.802216\pi$
$953$	5.76932	−	17.7561i	0.186887	−	0.575178i	0.999976	+	0.00696122i	$0.00221584\pi$
$954$	24.8369	+	76.4400i	0.804123	+	2.47484i
$955$	21.8328			0.706493
$956$	58.7780			1.90102
$957$	0.618993	+	1.90506i	0.0200092	+	0.0615820i
$958$	−35.0066	+	25.4338i	−1.13101	+	0.821728i
$959$	−2.12132	−	1.54123i	−0.0685010	−	0.0497689i
$960$	−17.0193			−0.549295
$961$		0			0
$962$	−29.1246			−0.939015
$963$	2.66312	+	1.93487i	0.0858178	+	0.0623503i
$964$	91.1716	−	66.2401i	2.93644	−	2.13345i
$965$	−14.3090	−	44.0386i	−0.460624	−	1.41765i
$966$	−6.00000			−0.193047
$967$	44.0168			1.41549			0.707743	−	0.706470i	$-0.249713\pi$
$967$	44.0168			1.41549			0.707743	+	0.706470i	$0.249713\pi$
$968$	16.1631	+	49.7450i	0.519502	+	1.59886i
$969$	−1.00000	+	3.07768i	−0.0321246	+	0.0988694i
$970$	−12.6631	+	38.9731i	−0.406588	+	1.25135i
$971$	−43.5967	−	31.6749i	−1.39909	−	1.01650i	−0.994798	−	0.101864i	$-0.967519\pi$
$971$	−43.5967	−	31.6749i	−1.39909	−	1.01650i	−0.404288	−	0.914632i	$-0.632481\pi$
$972$	−24.1448	−	74.3100i	−0.774445	−	2.38350i
$973$	−14.5397	−	10.5637i	−0.466123	−	0.338658i
$974$	−59.4700	+	43.2075i	−1.90554	+	1.38446i
$975$		0			0
$976$	−111.098	+	80.7175i	−3.55616	+	2.58370i
$977$	34.3713	−	24.9722i	1.09964	−	0.798932i	0.118636	−	0.992938i	$-0.462148\pi$
$977$	34.3713	−	24.9722i	1.09964	−	0.798932i	0.981000	+	0.194006i	$0.0621480\pi$
$978$	−10.1939	+	31.3737i	−0.325966	+	1.00322i
$979$	52.6869	−	38.2793i	1.68388	−	1.22341i
$980$	52.6869	+	38.2793i	1.68302	+	1.22279i
$981$	0.892609	+	2.74717i	0.0284988	+	0.0877103i
$982$	33.6560	+	24.4525i	1.07401	+	0.780311i
$983$	16.6611	−	51.2775i	0.531405	−	1.63550i	−0.219885	−	0.975526i	$-0.570568\pi$
$983$	16.6611	−	51.2775i	0.531405	−	1.63550i	0.751290	−	0.659972i	$-0.229432\pi$
$984$	2.97100	−	9.14379i	0.0947120	−	0.291493i
$985$	−0.746512	−	2.29753i	−0.0237859	−	0.0732054i
$986$	−5.23607			−0.166750
$987$	−8.48528			−0.270089
$988$	−3.93314	−	12.1050i	−0.125130	−	0.385111i
$989$	−20.5623	+	14.9394i	−0.653843	+	0.475045i
$990$	44.9303	+	32.6438i	1.42798	+	1.03749i
$991$	−13.9358			−0.442685			−0.221343	−	0.975196i	$-0.571044\pi$
$991$	−13.9358			−0.442685			−0.221343	+	0.975196i	$0.571044\pi$
$992$		0			0
$993$	−27.3475			−0.867847
$994$	−3.11803	−	2.26538i	−0.0988980	−	0.0718536i
$995$	−41.9987	+	30.5138i	−1.33145	+	0.967354i
$996$	4.14590	+	12.7598i	0.131368	+	0.404309i
$997$	−58.6656			−1.85796			−0.928980	−	0.370131i	$-0.879313\pi$
$997$	−58.6656			−1.85796			−0.928980	+	0.370131i	$0.879313\pi$
$998$	48.1320			1.52359
$999$	6.00000	+	18.4661i	0.189832	+	0.584242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.h.374.2		8
31.2	even	5		961.2.d.j.628.1		8
31.3	odd	30		961.2.g.i.235.2		16
31.4	even	5		961.2.a.h.1.3	✓	4
31.5	even	3		961.2.g.i.732.1		16
31.6	odd	6		961.2.g.i.816.1		16
31.7	even	15		961.2.c.h.439.4		8
31.8	even	5		961.2.d.j.531.1		8
31.9	even	15		961.2.g.p.844.2		16
31.10	even	15		961.2.g.p.448.1		16
31.11	odd	30		961.2.c.h.521.3		8
31.12	odd	30		961.2.g.p.846.1		16
31.13	odd	30		961.2.g.i.338.1		16
31.14	even	15		961.2.g.p.547.1		16
31.15	odd	10	inner	961.2.d.h.388.1		8
31.16	even	5	inner	961.2.d.h.388.2		8
31.17	odd	30		961.2.g.p.547.2		16
31.18	even	15		961.2.g.i.338.2		16
31.19	even	15		961.2.g.p.846.2		16
31.20	even	15		961.2.c.h.521.4		8
31.21	odd	30		961.2.g.p.448.2		16
31.22	odd	30		961.2.g.p.844.1		16
31.23	odd	10		961.2.d.j.531.2		8
31.24	odd	30		961.2.c.h.439.3		8
31.25	even	3		961.2.g.i.816.2		16
31.26	odd	6		961.2.g.i.732.2		16
31.27	odd	10		961.2.a.h.1.4	yes	4
31.28	even	15		961.2.g.i.235.1		16
31.29	odd	10		961.2.d.j.628.2		8
31.30	odd	2	inner	961.2.d.h.374.1		8
93.35	odd	10		8649.2.a.r.1.1		4
93.89	even	10		8649.2.a.r.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.3	✓	4	31.4	even	5
961.2.a.h.1.4	yes	4	31.27	odd	10
961.2.c.h.439.3		8	31.24	odd	30
961.2.c.h.439.4		8	31.7	even	15
961.2.c.h.521.3		8	31.11	odd	30
961.2.c.h.521.4		8	31.20	even	15
961.2.d.h.374.1		8	31.30	odd	2	inner
961.2.d.h.374.2		8	1.1	even	1	trivial
961.2.d.h.388.1		8	31.15	odd	10	inner
961.2.d.h.388.2		8	31.16	even	5	inner
961.2.d.j.531.1		8	31.8	even	5
961.2.d.j.531.2		8	31.23	odd	10
961.2.d.j.628.1		8	31.2	even	5
961.2.d.j.628.2		8	31.29	odd	10
961.2.g.i.235.1		16	31.28	even	15
961.2.g.i.235.2		16	31.3	odd	30
961.2.g.i.338.1		16	31.13	odd	30
961.2.g.i.338.2		16	31.18	even	15
961.2.g.i.732.1		16	31.5	even	3
961.2.g.i.732.2		16	31.26	odd	6
961.2.g.i.816.1		16	31.6	odd	6
961.2.g.i.816.2		16	31.25	even	3
961.2.g.p.448.1		16	31.10	even	15
961.2.g.p.448.2		16	31.21	odd	30
961.2.g.p.547.1		16	31.14	even	15
961.2.g.p.547.2		16	31.17	odd	30
961.2.g.p.844.1		16	31.22	odd	30
961.2.g.p.844.2		16	31.9	even	15
961.2.g.p.846.1		16	31.12	odd	30
961.2.g.p.846.2		16	31.19	even	15
8649.2.a.r.1.1		4	93.35	odd	10
8649.2.a.r.1.2		4	93.89	even	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.11803 - 1.53884i) q^{2} +(0.707107 - 0.513743i) q^{3} +(1.50000 + 4.61653i) q^{4} +2.23607 q^{5} -2.28825 q^{6} +(-0.309017 - 0.951057i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-0.690983 + 2.12663i) q^{9} +(-4.73607 - 3.44095i) q^{10} +(1.31105 + 4.03499i) q^{11} +(3.43237 + 2.49376i) q^{12} +(2.12132 - 1.54123i) q^{13} +(-0.809017 + 2.48990i) q^{14} +(1.58114 - 1.14876i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(1.14412 - 3.52125i) q^{17} +(4.73607 - 3.44095i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(3.35410 + 10.3229i) q^{20} +(-0.707107 - 0.513743i) q^{21} +(3.43237 - 10.5637i) q^{22} +(-0.810272 + 2.49376i) q^{23} +(-2.01815 - 6.21124i) q^{24} -6.86474 q^{26} +(1.41421 + 4.35250i) q^{27} +(3.92705 - 2.85317i) q^{28} +(0.437016 + 0.317511i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(3.00000 + 2.17963i) q^{33} +(-7.84193 + 5.69750i) q^{34} +(-0.690983 - 2.12663i) q^{35} -10.8541 q^{36} +4.24264 q^{37} +(0.809017 + 2.48990i) q^{38} +(0.708204 - 2.17963i) q^{39} +(5.16312 - 15.8904i) q^{40} +(1.19098 + 0.865300i) q^{41} +(0.707107 + 2.17625i) q^{42} +(7.84193 + 5.69750i) q^{43} +(-16.6611 + 12.1050i) q^{44} +(-1.54508 + 4.75528i) q^{45} +(5.55369 - 4.03499i) q^{46} +(7.85410 - 5.70634i) q^{47} +(-2.66150 + 8.19126i) q^{48} +(4.85410 - 3.52671i) q^{49} +(-1.00000 - 3.07768i) q^{51} +(10.2971 + 7.48128i) q^{52} +(-4.24264 + 13.0575i) q^{53} +(3.70246 - 11.3950i) q^{54} +(2.93159 + 9.02251i) q^{55} -7.47214 q^{56} -0.874032 q^{57} +(-0.437016 - 1.34500i) q^{58} +(-9.66312 + 7.02067i) q^{59} +(7.67501 + 5.57622i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(-7.04508 - 5.11855i) q^{64} +(4.74342 - 3.44629i) q^{65} +(-3.00000 - 9.23305i) q^{66} +6.00000 q^{67} +17.9721 q^{68} +(0.708204 + 2.17963i) q^{69} +(-1.80902 + 5.56758i) q^{70} +(-0.454915 + 1.40008i) q^{71} +(13.5172 + 9.82084i) q^{72} +(1.31105 + 4.03499i) q^{73} +(-8.98606 - 6.52875i) q^{74} +(1.50000 - 4.61653i) q^{76} +(3.43237 - 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(-0.500776 + 1.54123i) q^{79} +(-17.8262 + 12.9515i) q^{80} +(-2.19098 - 1.59184i) q^{81} +(-1.19098 - 3.66547i) q^{82} +(2.55834 + 1.85874i) q^{83} +(1.31105 - 4.03499i) q^{84} +(2.55834 - 7.87375i) q^{85} +(-7.84193 - 24.1350i) q^{86} +0.472136 q^{87} +31.7016 q^{88} +(-4.74342 - 14.5987i) q^{89} +(10.5902 - 7.69421i) q^{90} +(-2.12132 - 1.54123i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(-1.80902 - 1.31433i) q^{95} +(7.67501 - 5.57622i) q^{96} +(-2.16312 - 6.65740i) q^{97} -15.7082 q^{98} -9.48683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 12 q^{4} + 2 q^{7} + 14 q^{8} - 10 q^{9} - 20 q^{10} - 2 q^{14} - 28 q^{16} + 20 q^{18} - 2 q^{19} + 18 q^{28} + 60 q^{32} + 24 q^{33} - 10 q^{35} - 60 q^{36} + 2 q^{38} - 48 q^{39} + 10 q^{40}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 12 * q^4 + 2 * q^7 + 14 * q^8 - 10 * q^9 - 20 * q^10 - 2 * q^14 - 28 * q^16 + 20 * q^18 - 2 * q^19 + 18 * q^28 + 60 * q^32 + 24 * q^33 - 10 * q^35 - 60 * q^36 + 2 * q^38 - 48 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^45 + 36 * q^47 + 12 * q^49 - 8 * q^51 - 24 * q^56 - 46 * q^59 - 34 * q^64 - 24 * q^66 + 48 * q^67 - 48 * q^69 - 10 * q^70 - 26 * q^71 + 50 * q^72 + 12 * q^76 - 12 * q^78 - 80 * q^80 - 22 * q^81 - 14 * q^82 - 32 * q^87 + 40 * q^90 - 96 * q^94 - 10 * q^95 + 14 * q^97 - 72 * q^98

Introduction

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