LMFDB - Embedded newform 637.2.e.i.79.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(79,637)] 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("637.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-1,-2,-3,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.235342 - 0.407624i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.i.508.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.235342 + 0.407624i) q^{2} +(1.12457 + 1.94781i) q^{3} +(0.889229 + 1.54019i) q^{4} +(0.264658 - 0.458402i) q^{5} -1.05863 q^{6} -1.77846 q^{8} +(-1.02932 + 1.78283i) q^{9} +(0.124570 + 0.215762i) q^{10} +(1.12457 + 1.94781i) q^{11} +(-2.00000 + 3.46410i) q^{12} -1.00000 q^{13} +1.19051 q^{15} +(-1.35991 + 2.35544i) q^{16} +(-0.653887 - 1.13257i) q^{17} +(-0.484482 - 0.839148i) q^{18} +(-0.735342 + 1.27365i) q^{19} +0.941367 q^{20} -1.05863 q^{22} +(-2.91855 + 5.05507i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(2.35991 + 4.08749i) q^{25} +(0.235342 - 0.407624i) q^{26} +2.11727 q^{27} +5.22154 q^{29} +(-0.280176 + 0.485279i) q^{30} +(-3.51380 - 6.08608i) q^{31} +(-2.41855 - 4.18904i) q^{32} +(-2.52932 + 4.38090i) q^{33} +0.615547 q^{34} -3.66119 q^{36} +(1.18320 - 2.04937i) q^{37} +(-0.346113 - 0.599486i) q^{38} +(-1.12457 - 1.94781i) q^{39} +(-0.470683 + 0.815248i) q^{40} -6.49828 q^{41} +11.3940 q^{43} +(-2.00000 + 3.46410i) q^{44} +(0.544834 + 0.943681i) q^{45} +(-1.37371 - 2.37934i) q^{46} +(4.29226 - 7.43441i) q^{47} -6.11727 q^{48} -2.22154 q^{50} +(1.47068 - 2.54730i) q^{51} +(-0.889229 - 1.54019i) q^{52} +(-5.63837 - 9.76594i) q^{53} +(-0.498281 + 0.863048i) q^{54} +1.19051 q^{55} -3.30777 q^{57} +(-1.22885 + 2.12843i) q^{58} +(-6.08623 - 10.5417i) q^{59} +(1.05863 + 1.83361i) q^{60} +(-1.00000 + 1.73205i) q^{61} +3.30777 q^{62} -3.16291 q^{64} +(-0.264658 + 0.458402i) q^{65} +(-1.19051 - 2.06202i) q^{66} +(7.96896 + 13.8027i) q^{67} +(1.16291 - 2.01422i) q^{68} -13.1284 q^{69} +1.19051 q^{71} +(1.83060 - 3.17068i) q^{72} +(3.82157 + 6.61916i) q^{73} +(0.556914 + 0.964604i) q^{74} +(-5.30777 + 9.19333i) q^{75} -2.61555 q^{76} +1.05863 q^{78} +(0.669405 - 1.15944i) q^{79} +(0.719824 + 1.24677i) q^{80} +(5.46896 + 9.47252i) q^{81} +(1.52932 - 2.64885i) q^{82} +16.3500 q^{83} -0.692226 q^{85} +(-2.68148 + 4.64447i) q^{86} +(5.87199 + 10.1706i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.45517 - 5.98452i) q^{89} -0.512889 q^{90} -10.3810 q^{92} +(7.90303 - 13.6884i) q^{93} +(2.02029 + 3.49925i) q^{94} +(0.389229 + 0.674164i) q^{95} +(5.43965 - 9.42175i) q^{96} +3.47068 q^{97} -4.63016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23}+ \cdots + 28 q^{99}+O(q^{100}) $ 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9 - 8 * q^10 - 2 * q^11 - 12 * q^12 - 6 * q^13 - 12 * q^15 + q^16 + 4 * q^17 + 15 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 + 5 * q^25 + q^26 + 16 * q^27 + 48 * q^29 - 20 * q^30 - 4 * q^31 - 7 * q^32 - 16 * q^33 - 28 * q^34 - 2 * q^36 - 10 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 + 20 * q^43 - 12 * q^44 + 22 * q^45 + 18 * q^46 - 8 * q^47 - 40 * q^48 - 30 * q^50 + 8 * q^51 + 3 * q^52 - 8 * q^53 + 32 * q^54 - 12 * q^55 - 4 * q^57 - 12 * q^58 - 4 * q^59 + 8 * q^60 - 6 * q^61 + 4 * q^62 - 34 * q^64 - 2 * q^65 + 12 * q^66 + 12 * q^67 + 22 * q^68 + 12 * q^69 - 12 * q^71 + q^72 - 10 * q^73 - 30 * q^74 - 16 * q^75 + 16 * q^76 + 8 * q^78 + 14 * q^79 - 14 * q^80 - 3 * q^81 + 10 * q^82 + 24 * q^83 - 20 * q^85 + 26 * q^86 - 26 * q^87 - 12 * q^88 + 2 * q^89 + 56 * q^90 - 24 * q^92 + 22 * q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 20 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.235342	+	0.407624i	−0.166412	+	0.288234i	−0.937156	−	0.348911i	$-0.886551\pi$
$2$	−0.235342	+	0.407624i	−0.166412	+	0.288234i	0.770744	+	0.637145i	$0.219885\pi$
$3$	1.12457	+	1.94781i	0.649271	+	1.12457i	0.983297	+	0.182007i	$0.0582592\pi$
$3$	1.12457	+	1.94781i	0.649271	+	1.12457i	−0.334026	+	0.942564i	$0.608407\pi$
$4$	0.889229	+	1.54019i	0.444614	+	0.770095i
$5$	0.264658	−	0.458402i	0.118359	−	0.205003i	−0.800759	−	0.598987i	$-0.795570\pi$
$5$	0.264658	−	0.458402i	0.118359	−	0.205003i	0.919117	+	0.393984i	$0.128903\pi$
$6$	−1.05863			−0.432185
$7$		0			0
$7$		0			0
$8$	−1.77846			−0.628780
$9$	−1.02932	+	1.78283i	−0.343106	+	0.594276i
$10$	0.124570	+	0.215762i	0.0393926	+	0.0682299i
$11$	1.12457	+	1.94781i	0.339071	+	0.587288i	0.984258	−	0.176737i	$-0.0565541\pi$
$11$	1.12457	+	1.94781i	0.339071	+	0.587288i	−0.645187	+	0.764024i	$0.723221\pi$
$12$	−2.00000	+	3.46410i	−0.577350	+	1.00000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	1.19051			0.307388
$16$	−1.35991	+	2.35544i	−0.339978	+	0.588859i
$17$	−0.653887	−	1.13257i	−0.158591	−	0.274687i	0.775770	−	0.631016i	$-0.217362\pi$
$17$	−0.653887	−	1.13257i	−0.158591	−	0.274687i	−0.934361	+	0.356328i	$0.884028\pi$
$18$	−0.484482	−	0.839148i	−0.114194	−	0.197789i
$19$	−0.735342	+	1.27365i	−0.168699	+	0.292195i	−0.937963	−	0.346736i	$-0.887290\pi$
$19$	−0.735342	+	1.27365i	−0.168699	+	0.292195i	0.769264	+	0.638931i	$0.220623\pi$
$20$	0.941367			0.210496
$21$		0			0
$22$	−1.05863			−0.225701
$23$	−2.91855	+	5.05507i	−0.608559	+	1.05405i	0.382919	+	0.923782i	$0.374919\pi$
$23$	−2.91855	+	5.05507i	−0.608559	+	1.05405i	−0.991478	+	0.130273i	$0.958415\pi$
$24$	−2.00000	−	3.46410i	−0.408248	−	0.707107i
$25$	2.35991	+	4.08749i	0.471982	+	0.817497i
$26$	0.235342	−	0.407624i	0.0461543	−	0.0799416i
$27$	2.11727			0.407468
$28$		0			0
$29$	5.22154			0.969616			0.484808	−	0.874621i	$-0.338889\pi$
$29$	5.22154			0.969616			0.484808	+	0.874621i	$0.338889\pi$
$30$	−0.280176	+	0.485279i	−0.0511529	+	0.0885994i
$31$	−3.51380	−	6.08608i	−0.631097	−	1.09309i	−0.987328	−	0.158694i	$-0.949272\pi$
$31$	−3.51380	−	6.08608i	−0.631097	−	1.09309i	0.356231	−	0.934398i	$-0.384062\pi$
$32$	−2.41855	−	4.18904i	−0.427542	−	0.740525i
$33$	−2.52932	+	4.38090i	−0.440298	+	0.762618i
$34$	0.615547			0.105566
$35$		0			0
$36$	−3.66119			−0.610198
$37$	1.18320	−	2.04937i	0.194517	−	0.336914i	−0.752225	−	0.658907i	$-0.771019\pi$
$37$	1.18320	−	2.04937i	0.194517	−	0.336914i	0.946742	+	0.321992i	$0.104353\pi$
$38$	−0.346113	−	0.599486i	−0.0561470	−	0.0972494i
$39$	−1.12457	−	1.94781i	−0.180075	−	0.311900i
$40$	−0.470683	+	0.815248i	−0.0744216	+	0.128902i
$41$	−6.49828			−1.01486			−0.507431	−	0.861693i	$-0.669405\pi$
$41$	−6.49828			−1.01486			−0.507431	+	0.861693i	$0.669405\pi$
$42$		0			0
$43$	11.3940			1.73757			0.868785	−	0.495190i	$-0.164902\pi$
$43$	11.3940			1.73757			0.868785	+	0.495190i	$0.164902\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$	0.544834	+	0.943681i	0.0812191	+	0.140676i
$46$	−1.37371	−	2.37934i	−0.202543	−	0.350814i
$47$	4.29226	−	7.43441i	0.626090	−	1.08442i	−0.362239	−	0.932085i	$-0.617988\pi$
$47$	4.29226	−	7.43441i	0.626090	−	1.08442i	0.988329	−	0.152334i	$-0.0486790\pi$
$48$	−6.11727			−0.882951
$49$		0			0
$50$	−2.22154			−0.314174
$51$	1.47068	−	2.54730i	0.205937	−	0.356693i
$52$	−0.889229	−	1.54019i	−0.123314	−	0.213586i
$53$	−5.63837	−	9.76594i	−0.774490	−	1.34146i	−0.935081	−	0.354434i	$-0.884673\pi$
$53$	−5.63837	−	9.76594i	−0.774490	−	1.34146i	0.160591	−	0.987021i	$-0.448660\pi$
$54$	−0.498281	+	0.863048i	−0.0678075	+	0.117446i
$55$	1.19051			0.160528
$56$		0			0
$57$	−3.30777			−0.438125
$58$	−1.22885	+	2.12843i	−0.161355	+	0.279476i
$59$	−6.08623	−	10.5417i	−0.792360	−	1.37241i	−0.924502	−	0.381177i	$-0.875519\pi$
$59$	−6.08623	−	10.5417i	−0.792360	−	1.37241i	0.132142	−	0.991231i	$-0.457814\pi$
$60$	1.05863	+	1.83361i	0.136669	+	0.236718i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	3.30777			0.420088
$63$		0			0
$64$	−3.16291			−0.395364
$65$	−0.264658	+	0.458402i	−0.0328268	+	0.0568577i
$66$	−1.19051	−	2.06202i	−0.146541	−	0.253817i
$67$	7.96896	+	13.8027i	0.973564	+	1.68626i	0.684595	+	0.728924i	$0.259979\pi$
$67$	7.96896	+	13.8027i	0.973564	+	1.68626i	0.288969	+	0.957338i	$0.406687\pi$
$68$	1.16291	−	2.01422i	0.141024	−	0.244260i
$69$	−13.1284			−1.58048
$70$		0			0
$71$	1.19051			0.141287			0.0706436	−	0.997502i	$-0.477495\pi$
$71$	1.19051			0.141287			0.0706436	+	0.997502i	$0.477495\pi$
$72$	1.83060	−	3.17068i	0.215738	−	0.373669i
$73$	3.82157	+	6.61916i	0.447281	+	0.774714i	0.998208	−	0.0598398i	$-0.0190590\pi$
$73$	3.82157	+	6.61916i	0.447281	+	0.774714i	−0.550927	+	0.834554i	$0.685726\pi$
$74$	0.556914	+	0.964604i	0.0647400	+	0.112133i
$75$	−5.30777	+	9.19333i	−0.612889	+	1.06155i
$76$	−2.61555			−0.300024
$77$		0			0
$78$	1.05863			0.119867
$79$	0.669405	−	1.15944i	0.0753139	−	0.130448i	−0.825909	−	0.563804i	$-0.809337\pi$
$79$	0.669405	−	1.15944i	0.0753139	−	0.130448i	0.901223	+	0.433356i	$0.142671\pi$
$80$	0.719824	+	1.24677i	0.0804788	+	0.139393i
$81$	5.46896	+	9.47252i	0.607663	+	1.05250i
$82$	1.52932	−	2.64885i	0.168885	−	0.292517i
$83$	16.3500			1.79464			0.897322	−	0.441377i	$-0.145510\pi$
$83$	16.3500			1.79464			0.897322	+	0.441377i	$0.145510\pi$
$84$		0			0
$85$	−0.692226			−0.0750825
$86$	−2.68148	+	4.64447i	−0.289152	+	0.500826i
$87$	5.87199	+	10.1706i	0.629544	+	1.09040i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	3.45517	−	5.98452i	0.366247	−	0.634358i	−0.622729	−	0.782438i	$-0.713976\pi$
$89$	3.45517	−	5.98452i	0.366247	−	0.634358i	0.988975	+	0.148080i	$0.0473093\pi$
$90$	−0.512889			−0.0540632
$91$		0			0
$92$	−10.3810			−1.08230
$93$	7.90303	−	13.6884i	0.819506	−	1.41943i
$94$	2.02029	+	3.49925i	0.208377	+	0.360920i
$95$	0.389229	+	0.674164i	0.0399340	+	0.0691677i
$96$	5.43965	−	9.42175i	0.555182	−	0.961603i
$97$	3.47068			0.352395			0.176197	−	0.984355i	$-0.443620\pi$
$97$	3.47068			0.352395			0.176197	+	0.984355i	$0.443620\pi$
$98$		0			0
$99$	−4.63016			−0.465348
$100$	−4.19700	+	7.26942i	−0.419700	+	0.726942i
$101$	3.87543	+	6.71244i	0.385620	+	0.667913i	0.991855	−	0.127372i	$-0.0406544\pi$
$101$	3.87543	+	6.71244i	0.385620	+	0.667913i	−0.606235	+	0.795285i	$0.707321\pi$
$102$	0.692226	+	1.19897i	0.0685406	+	0.118716i
$103$	−8.49828	+	14.7195i	−0.837361	+	1.45035i	0.0547334	+	0.998501i	$0.482569\pi$
$103$	−8.49828	+	14.7195i	−0.837361	+	1.45035i	−0.892094	+	0.451850i	$0.850764\pi$
$104$	1.77846			0.174392
$105$		0			0
$106$	5.30777			0.515537
$107$	2.77846	−	4.81243i	0.268604	−	0.465235i	−0.699898	−	0.714243i	$-0.746771\pi$
$107$	2.77846	−	4.81243i	0.268604	−	0.465235i	0.968501	+	0.249008i	$0.0801045\pi$
$108$	1.88273	+	3.26099i	0.181166	+	0.313789i
$109$	−3.96166	−	6.86180i	−0.379458	−	0.657241i	0.611525	−	0.791225i	$-0.290556\pi$
$109$	−3.96166	−	6.86180i	−0.379458	−	0.657241i	−0.990984	+	0.133984i	$0.957223\pi$
$110$	−0.280176	+	0.485279i	−0.0267137	+	0.0462696i
$111$	5.32238			0.505178
$112$		0			0
$113$	−9.89229			−0.930588			−0.465294	−	0.885156i	$-0.654051\pi$
$113$	−9.89229			−0.930588			−0.465294	+	0.885156i	$0.654051\pi$
$114$	0.778457	−	1.34833i	0.0729092	−	0.126282i
$115$	1.54483	+	2.67573i	0.144057	+	0.249513i
$116$	4.64315	+	8.04216i	0.431105	+	0.746696i
$117$	1.02932	−	1.78283i	0.0951604	−	0.164823i
$118$	5.72938			0.527432
$119$		0			0
$120$	−2.11727			−0.193279
$121$	2.97068	−	5.14537i	0.270062	−	0.467761i
$122$	−0.470683	−	0.815248i	−0.0426137	−	0.0738090i
$123$	−7.30777	−	12.6574i	−0.658920	−	1.14128i
$124$	6.24914	−	10.8238i	0.561189	−	0.972009i
$125$	5.14486			0.460171
$126$		0			0
$127$	0.824101			0.0731271			0.0365635	−	0.999331i	$-0.488359\pi$
$127$	0.824101			0.0731271			0.0365635	+	0.999331i	$0.488359\pi$
$128$	5.58145	−	9.66736i	0.493336	−	0.854482i
$129$	12.8134	+	22.1934i	1.12815	+	1.95402i
$130$	−0.124570	−	0.215762i	−0.0109255	−	0.0189236i
$131$	5.30777	−	9.19333i	0.463742	−	0.803225i	−0.535401	−	0.844598i	$-0.679840\pi$
$131$	5.30777	−	9.19333i	0.463742	−	0.803225i	0.999144	+	0.0413724i	$0.0131730\pi$
$132$	−8.99656			−0.783050
$133$		0			0
$134$	−7.50172			−0.648050
$135$	0.560352	−	0.970558i	0.0482274	−	0.0835324i
$136$	1.16291	+	2.01422i	0.0997187	+	0.172718i
$137$	−5.68148	−	9.84062i	−0.485402	−	0.840741i	0.514457	−	0.857516i	$-0.327993\pi$
$137$	−5.68148	−	9.84062i	−0.485402	−	0.840741i	−0.999859	+	0.0167751i	$0.994660\pi$
$138$	3.08967	−	5.35146i	0.263010	−	0.455547i
$139$	13.9233			1.18096			0.590480	−	0.807052i	$-0.298938\pi$
$139$	13.9233			1.18096			0.590480	+	0.807052i	$0.298938\pi$
$140$		0			0
$141$	19.3078			1.62601
$142$	−0.280176	+	0.485279i	−0.0235119	+	0.0407237i
$143$	−1.12457	−	1.94781i	−0.0940413	−	0.162884i
$144$	−2.79956	−	4.84898i	−0.233297	−	0.404082i
$145$	1.38192	−	2.39356i	0.114763	−	0.198775i
$146$	−3.59750			−0.297731
$147$		0			0
$148$	4.20855			0.345941
$149$	−4.65389	+	8.06077i	−0.381261	+	0.660364i	−0.991243	−	0.132052i	$-0.957844\pi$
$149$	−4.65389	+	8.06077i	−0.381261	+	0.660364i	0.609982	+	0.792416i	$0.291177\pi$
$150$	−2.49828	−	4.32715i	−0.203984	−	0.353310i
$151$	−3.53662	−	6.12561i	−0.287806	−	0.498495i	0.685480	−	0.728092i	$-0.259593\pi$
$151$	−3.53662	−	6.12561i	−0.287806	−	0.498495i	−0.973286	+	0.229597i	$0.926259\pi$
$152$	1.30777	−	2.26513i	0.106074	−	0.183726i
$153$	2.69223			0.217654
$154$		0			0
$155$	−3.71982			−0.298783
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−3.02029	−	5.23130i	−0.241046	−	0.417503i	0.719967	−	0.694009i	$-0.244157\pi$
$157$	−3.02029	−	5.23130i	−0.241046	−	0.417503i	−0.961012	+	0.276505i	$0.910824\pi$
$158$	0.315078	+	0.545730i	0.0250662	+	0.0434160i
$159$	12.6815	−	21.9650i	1.00571	−	1.74194i
$160$	−2.56035			−0.202414
$161$		0			0
$162$	−5.14830			−0.404489
$163$	−3.19051	+	5.52612i	−0.249900	+	0.432839i	−0.963498	−	0.267716i	$-0.913731\pi$
$163$	−3.19051	+	5.52612i	−0.249900	+	0.432839i	0.713598	+	0.700555i	$0.247064\pi$
$164$	−5.77846	−	10.0086i	−0.451222	−	0.781539i
$165$	1.33881	+	2.31889i	0.104226	+	0.180525i
$166$	−3.84783	+	6.66464i	−0.298650	+	0.517276i
$167$	16.5845			1.28335			0.641674	−	0.766977i	$-0.278240\pi$
$167$	16.5845			1.28335			0.641674	+	0.766977i	$0.278240\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	0.162910	−	0.282168i	0.0124946	−	0.0216413i
$171$	−1.51380	−	2.62198i	−0.115763	−	0.200508i
$172$	10.1319	+	17.5489i	0.772548	+	1.33809i
$173$	−11.6504	+	20.1792i	−0.885767	+	1.53419i	−0.0409355	+	0.999162i	$0.513034\pi$
$173$	−11.6504	+	20.1792i	−0.885767	+	1.53419i	−0.844832	+	0.535032i	$0.820300\pi$
$174$	−5.52770			−0.419054
$175$		0			0
$176$	−6.11727			−0.461106
$177$	13.6888	−	23.7097i	1.02891	−	1.78213i
$178$	1.62629	+	2.81682i	0.121896	+	0.211129i
$179$	−10.5211	−	18.2231i	−0.786384	−	1.36206i	−0.928169	−	0.372160i	$-0.878617\pi$
$179$	−10.5211	−	18.2231i	−0.786384	−	1.36206i	0.141785	−	0.989898i	$-0.454716\pi$
$180$	−0.968964	+	1.67830i	−0.0722223	+	0.125093i
$181$	−16.7474			−1.24483			−0.622413	−	0.782689i	$-0.713848\pi$
$181$	−16.7474			−1.24483			−0.622413	+	0.782689i	$0.713848\pi$
$182$		0			0
$183$	−4.49828			−0.332523
$184$	5.19051	−	8.99022i	0.382649	−	0.662768i
$185$	−0.626289	−	1.08476i	−0.0460457	−	0.0797535i
$186$	3.71982	+	6.44292i	0.272751	+	0.472418i
$187$	1.47068	−	2.54730i	0.107547	−	0.186277i
$188$	15.2672			1.11347
$189$		0			0
$190$	−0.366407			−0.0265819
$191$	3.71982	−	6.44292i	0.269157	−	0.466194i	−0.699487	−	0.714645i	$-0.746588\pi$
$191$	3.71982	−	6.44292i	0.269157	−	0.466194i	0.968644	+	0.248451i	$0.0799216\pi$
$192$	−3.55691	−	6.16076i	−0.256698	−	0.444614i
$193$	0.750859	+	1.30053i	0.0540480	+	0.0936140i	0.891784	−	0.452462i	$-0.149454\pi$
$193$	0.750859	+	1.30053i	0.0540480	+	0.0936140i	−0.837736	+	0.546076i	$0.816121\pi$
$194$	−0.816797	+	1.41473i	−0.0586426	+	0.101572i
$195$	−1.19051			−0.0852540
$196$		0			0
$197$	23.9931			1.70944			0.854720	−	0.519090i	$-0.173729\pi$
$197$	23.9931			1.70944			0.854720	+	0.519090i	$0.173729\pi$
$198$	1.08967	−	1.88736i	0.0774394	−	0.134129i
$199$	−1.00730	−	1.74470i	−0.0714059	−	0.123679i	0.828112	−	0.560563i	$-0.189415\pi$
$199$	−1.00730	−	1.74470i	−0.0714059	−	0.123679i	−0.899518	+	0.436884i	$0.856082\pi$
$200$	−4.19700	−	7.26942i	−0.296773	−	0.514026i
$201$	−17.9233	+	31.0441i	−1.26421	+	2.18968i
$202$	−3.64820			−0.256687
$203$		0			0
$204$	5.23109			0.366250
$205$	−1.71982	+	2.97882i	−0.120118	+	0.208050i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	−6.00821	−	10.4065i	−0.417600	−	0.723304i
$208$	1.35991	−	2.35544i	0.0942929	−	0.163320i
$209$	−3.30777			−0.228803
$210$		0			0
$211$	10.1008			0.695370			0.347685	−	0.937611i	$-0.386968\pi$
$211$	10.1008			0.695370			0.347685	+	0.937611i	$0.386968\pi$
$212$	10.0276	−	17.3683i	0.688698	−	1.19286i
$213$	1.33881	+	2.31889i	0.0917337	+	0.158887i
$214$	1.30777	+	2.26513i	0.0893976	+	0.154841i
$215$	3.01552	−	5.22303i	0.205657	−	0.356208i
$216$	−3.76547			−0.256208
$217$		0			0
$218$	3.72938			0.252585
$219$	−8.59525	+	14.8874i	−0.580813	+	1.00600i
$220$	1.05863	+	1.83361i	0.0713730	+	0.123622i
$221$	0.653887	+	1.13257i	0.0439852	+	0.0761846i
$222$	−1.25258	+	2.16953i	−0.0840676	+	0.145609i
$223$	−10.1414			−0.679120			−0.339560	−	0.940584i	$-0.610278\pi$
$223$	−10.1414			−0.679120			−0.339560	+	0.940584i	$0.610278\pi$
$224$		0			0
$225$	−9.71639			−0.647759
$226$	2.32807	−	4.03233i	0.154861	−	0.268227i
$227$	−2.69223	−	4.66307i	−0.178689	−	0.309499i	0.762743	−	0.646702i	$-0.223852\pi$
$227$	−2.69223	−	4.66307i	−0.178689	−	0.309499i	−0.941432	+	0.337203i	$0.890519\pi$
$228$	−2.94137	−	5.09460i	−0.194797	−	0.337398i
$229$	1.66119	−	2.87727i	0.109775	−	0.190135i	−0.805904	−	0.592046i	$-0.798320\pi$
$229$	1.66119	−	2.87727i	0.109775	−	0.190135i	0.915679	+	0.401911i	$0.131654\pi$
$230$	−1.45426			−0.0958908
$231$		0			0
$232$	−9.28629			−0.609675
$233$	−6.85991	+	11.8817i	−0.449408	+	0.778397i	−0.998348	−	0.0574648i	$-0.981698\pi$
$233$	−6.85991	+	11.8817i	−0.449408	+	0.778397i	0.548940	+	0.835862i	$0.315032\pi$
$234$	0.484482	+	0.839148i	0.0316716	+	0.0548568i
$235$	−2.27196	−	3.93515i	−0.148206	−	0.256701i
$236$	10.8241	−	18.7479i	0.704589	−	1.22038i
$237$	3.01117			0.195597
$238$		0			0
$239$	−3.50172			−0.226507			−0.113254	−	0.993566i	$-0.536127\pi$
$239$	−3.50172			−0.226507			−0.113254	+	0.993566i	$0.536127\pi$
$240$	−1.61899	+	2.80416i	−0.104505	+	0.181008i
$241$	0.793975	+	1.37520i	0.0511444	+	0.0885847i	0.890464	−	0.455053i	$-0.150380\pi$
$241$	0.793975	+	1.37520i	0.0511444	+	0.0885847i	−0.839320	+	0.543638i	$0.817046\pi$
$242$	1.39825	+	2.42184i	0.0898830	+	0.155682i
$243$	−9.12457	+	15.8042i	−0.585341	+	1.01384i
$244$	−3.55691			−0.227708
$245$		0			0
$246$	6.87930			0.438608
$247$	0.735342	−	1.27365i	0.0467887	−	0.0810404i
$248$	6.24914	+	10.8238i	0.396821	+	0.687314i
$249$	18.3867	+	31.8467i	1.16521	+	2.01820i
$250$	−1.21080	+	2.09717i	−0.0765778	+	0.132637i
$251$	4.92676			0.310974			0.155487	−	0.987838i	$-0.450305\pi$
$251$	4.92676			0.310974			0.155487	+	0.987838i	$0.450305\pi$
$252$		0			0
$253$	−13.1284			−0.825378
$254$	−0.193945	+	0.335923i	−0.0121692	+	0.0210777i
$255$	−0.778457	−	1.34833i	−0.0487489	−	0.0844355i
$256$	−0.535811	−	0.928053i	−0.0334882	−	0.0580033i
$257$	−4.00730	+	6.94085i	−0.249969	+	0.432959i	−0.963517	−	0.267648i	$-0.913754\pi$
$257$	−4.00730	+	6.94085i	−0.249969	+	0.432959i	0.713548	+	0.700606i	$0.247087\pi$
$258$	−12.0621			−0.750952
$259$		0			0
$260$	−0.941367			−0.0583811
$261$	−5.37462	+	9.30912i	−0.332681	+	0.576220i
$262$	2.49828	+	4.32715i	0.154344	+	0.267332i
$263$	−0.801279	−	1.38786i	−0.0494090	−	0.0855788i	0.840263	−	0.542179i	$-0.182400\pi$
$263$	−0.801279	−	1.38786i	−0.0494090	−	0.0855788i	−0.889672	+	0.456600i	$0.849067\pi$
$264$	4.49828	−	7.79125i	0.276850	−	0.479518i
$265$	−5.96896			−0.366671
$266$		0			0
$267$	15.5423			0.951174
$268$	−14.1725	+	24.5474i	−0.865721	+	1.49947i
$269$	−5.91033	−	10.2370i	−0.360359	−	0.624161i	0.627661	−	0.778487i	$-0.284013\pi$
$269$	−5.91033	−	10.2370i	−0.360359	−	0.624161i	−0.988020	+	0.154327i	$0.950679\pi$
$270$	0.263748	+	0.456826i	0.0160512	+	0.0278015i
$271$	10.9414	−	18.9510i	0.664641	−	1.15119i	−0.314742	−	0.949177i	$-0.601918\pi$
$271$	10.9414	−	18.9510i	0.664641	−	1.15119i	0.979383	−	0.202014i	$-0.0647487\pi$
$272$	3.55691			0.215670
$273$		0			0
$274$	5.34836			0.323106
$275$	−5.30777	+	9.19333i	−0.320071	+	0.554379i
$276$	−11.6742	−	20.2203i	−0.702703	−	1.21712i
$277$	5.10905	+	8.84914i	0.306973	+	0.531693i	0.977699	−	0.210012i	$-0.0673505\pi$
$277$	5.10905	+	8.84914i	0.306973	+	0.531693i	−0.670725	+	0.741706i	$0.734017\pi$
$278$	−3.27674	+	5.67548i	−0.196526	+	0.340392i
$279$	14.4672			0.866131
$280$		0			0
$281$	1.54231			0.0920063			0.0460031	−	0.998941i	$-0.485352\pi$
$281$	1.54231			0.0920063			0.0460031	+	0.998941i	$0.485352\pi$
$282$	−4.54392	+	7.87031i	−0.270587	+	0.468670i
$283$	7.92332	+	13.7236i	0.470993	+	0.815783i	0.999449	−	0.0331771i	$-0.0105625\pi$
$283$	7.92332	+	13.7236i	0.470993	+	0.815783i	−0.528457	+	0.848960i	$0.677229\pi$
$284$	1.05863	+	1.83361i	0.0628183	+	0.108805i
$285$	−0.875430	+	1.51629i	−0.0518560	+	0.0898172i
$286$	1.05863			0.0625983
$287$		0			0
$288$	9.95779			0.586769
$289$	7.64486	−	13.2413i	0.449698	−	0.778900i
$290$	0.650449	+	1.12661i	0.0381957	+	0.0661569i
$291$	3.90303	+	6.76024i	0.228800	+	0.396292i
$292$	−6.79650	+	11.7719i	−0.397735	+	0.688898i
$293$	−11.0828			−0.647464			−0.323732	−	0.946149i	$-0.604938\pi$
$293$	−11.0828			−0.647464			−0.323732	+	0.946149i	$0.604938\pi$
$294$		0			0
$295$	−6.44309			−0.375131
$296$	−2.10428	+	3.64471i	−0.122309	+	0.211845i
$297$	2.38101	+	4.12404i	0.138160	+	0.239301i
$298$	−2.19051	−	3.79407i	−0.126893	−	0.219785i
$299$	2.91855	−	5.05507i	0.168784	−	0.292342i
$300$	−18.8793			−1.09000
$301$		0			0
$302$	3.32926			0.191577
$303$	−8.71639	+	15.0972i	−0.500743	+	0.867313i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	0.529317	+	0.916803i	0.0303086	+	0.0524960i
$306$	−0.633593	+	1.09742i	−0.0362201	+	0.0627351i
$307$	−20.4121			−1.16498			−0.582489	−	0.812839i	$-0.697921\pi$
$307$	−20.4121			−1.16498			−0.582489	+	0.812839i	$0.697921\pi$
$308$		0			0
$309$	−38.2277			−2.17470
$310$	0.875430	−	1.51629i	0.0497211	−	0.0861194i
$311$	−0.961661	−	1.66564i	−0.0545308	−	0.0944501i	0.837471	−	0.546481i	$-0.184033\pi$
$311$	−0.961661	−	1.66564i	−0.0545308	−	0.0944501i	−0.892002	+	0.452031i	$0.850700\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	−7.18320	+	12.4417i	−0.406019	+	0.703245i	−0.994439	−	0.105310i	$-0.966417\pi$
$313$	−7.18320	+	12.4417i	−0.406019	+	0.703245i	0.588421	+	0.808555i	$0.299750\pi$
$314$	2.84320			0.160451
$315$		0			0
$316$	2.38101			0.133943
$317$	−7.77846	+	13.4727i	−0.436882	+	0.756701i	−0.997447	−	0.0714089i	$-0.977250\pi$
$317$	−7.77846	+	13.4727i	−0.436882	+	0.756701i	0.560565	+	0.828110i	$0.310584\pi$
$318$	5.96896	+	10.3385i	0.334723	+	0.579757i
$319$	5.87199	+	10.1706i	0.328768	+	0.569444i
$320$	−0.837090	+	1.44988i	−0.0467948	+	0.0810509i
$321$	12.4983			0.697586
$322$		0			0
$323$	1.92332			0.107016
$324$	−9.72632	+	16.8465i	−0.540351	+	0.935915i
$325$	−2.35991	−	4.08749i	−0.130904	−	0.226733i
$326$	−1.50172	−	2.60105i	−0.0831725	−	0.144059i
$327$	8.91033	−	15.4331i	0.492742	−	0.853455i
$328$	11.5569			0.638124
$329$		0			0
$330$	−1.26031			−0.0693778
$331$	−15.7750	+	27.3231i	−0.867073	+	1.50182i	−0.00209996	+	0.999998i	$0.500668\pi$
$331$	−15.7750	+	27.3231i	−0.867073	+	1.50182i	−0.864974	+	0.501818i	$0.832665\pi$
$332$	14.5389	+	25.1821i	0.797924	+	1.38205i
$333$	2.43578	+	4.21890i	0.133480	+	0.231194i
$334$	−3.90303	+	6.76024i	−0.213564	+	0.369904i
$335$	8.43621			0.460919
$336$		0			0
$337$	−8.42666			−0.459029			−0.229515	−	0.973305i	$-0.573714\pi$
$337$	−8.42666			−0.459029			−0.229515	+	0.973305i	$0.573714\pi$
$338$	−0.235342	+	0.407624i	−0.0128009	+	0.0221718i
$339$	−11.1246	−	19.2683i	−0.604204	−	1.04651i
$340$	−0.615547	−	1.06616i	−0.0333827	−	0.0578206i
$341$	7.90303	−	13.6884i	0.427973	−	0.741271i
$342$	1.42504			0.0770573
$343$		0			0
$344$	−20.2637			−1.09255
$345$	−3.47455	+	6.01810i	−0.187063	+	0.324003i
$346$	−5.48367	−	9.49800i	−0.294804	−	0.510616i
$347$	−9.67418	−	16.7562i	−0.519337	−	0.899518i	−0.999747	−	0.0224745i	$-0.992846\pi$
$347$	−9.67418	−	16.7562i	−0.519337	−	0.899518i	0.480410	−	0.877044i	$-0.340488\pi$
$348$	−10.4431	+	18.0880i	−0.559808	+	0.969616i
$349$	−27.2553			−1.45894			−0.729470	−	0.684013i	$-0.760233\pi$
$349$	−27.2553			−1.45894			−0.729470	+	0.684013i	$0.760233\pi$
$350$		0			0
$351$	−2.11727			−0.113011
$352$	5.43965	−	9.42175i	0.289934	−	0.502181i
$353$	−12.8371	−	22.2345i	−0.683249	−	1.18342i	−0.973984	−	0.226619i	$-0.927233\pi$
$353$	−12.8371	−	22.2345i	−0.683249	−	1.18342i	0.290734	−	0.956804i	$-0.406100\pi$
$354$	6.44309	+	11.1598i	0.342446	+	0.593134i
$355$	0.315078	−	0.545730i	0.0167226	−	0.0289644i
$356$	12.2897			0.651354
$357$		0			0
$358$	9.90422			0.523454
$359$	11.7091	−	20.2807i	0.617982	−	1.07038i	−0.371872	−	0.928284i	$-0.621284\pi$
$359$	11.7091	−	20.2807i	0.617982	−	1.07038i	0.989854	−	0.142092i	$-0.0453828\pi$
$360$	−0.968964	−	1.67830i	−0.0510689	−	0.0884540i
$361$	8.41855	+	14.5813i	0.443081	+	0.767439i
$362$	3.94137	−	6.82665i	0.207154	−	0.358801i
$363$	13.3630			0.701374
$364$		0			0
$365$	4.04564			0.211759
$366$	1.05863	−	1.83361i	0.0553356	−	0.0958441i
$367$	−7.34268	−	12.7179i	−0.383285	−	0.663868i	0.608245	−	0.793749i	$-0.291874\pi$
$367$	−7.34268	−	12.7179i	−0.383285	−	0.663868i	−0.991530	+	0.129881i	$0.958540\pi$
$368$	−7.93793	−	13.7489i	−0.413793	−	0.716711i
$369$	6.68879	−	11.5853i	0.348204	−	0.603108i
$370$	0.589568			0.0306502
$371$		0			0
$372$	28.1104			1.45746
$373$	11.8337	−	20.4965i	0.612723	−	1.06127i	−0.378056	−	0.925783i	$-0.623407\pi$
$373$	11.8337	−	20.4965i	0.612723	−	1.06127i	0.990779	−	0.135485i	$-0.0432593\pi$
$374$	0.692226	+	1.19897i	0.0357942	+	0.0619973i
$375$	5.78576	+	10.0212i	0.298775	+	0.517494i
$376$	−7.63359	+	13.2218i	−0.393673	+	0.681861i
$377$	−5.22154			−0.268923
$378$		0			0
$379$	−32.7405			−1.68177			−0.840884	−	0.541215i	$-0.817965\pi$
$379$	−32.7405			−1.68177			−0.840884	+	0.541215i	$0.817965\pi$
$380$	−0.692226	+	1.19897i	−0.0355105	+	0.0615059i
$381$	0.926759	+	1.60519i	0.0474793	+	0.0822366i
$382$	1.75086	+	3.03258i	0.0895818	+	0.155160i
$383$	−11.3078	+	19.5856i	−0.577800	+	1.00078i	0.417931	+	0.908479i	$0.362755\pi$
$383$	−11.3078	+	19.5856i	−0.577800	+	1.00078i	−0.995731	+	0.0923006i	$0.970578\pi$
$384$	25.1070			1.28123
$385$		0			0
$386$	−0.706834			−0.0359769
$387$	−11.7280	+	20.3136i	−0.596170	+	1.03260i
$388$	3.08623	+	5.34551i	0.156680	+	0.271377i
$389$	−19.0242	−	32.9508i	−0.964563	−	1.67067i	−0.710784	−	0.703410i	$-0.751660\pi$
$389$	−19.0242	−	32.9508i	−0.964563	−	1.67067i	−0.253779	−	0.967262i	$-0.581674\pi$
$390$	0.280176	−	0.485279i	0.0141873	−	0.0245731i
$391$	7.63359			0.386047
$392$		0			0
$393$	23.8759			1.20438
$394$	−5.64658	+	9.78017i	−0.284471	+	0.492718i
$395$	−0.354327	−	0.613712i	−0.0178281	−	0.0308792i
$396$	−4.11727	−	7.13131i	−0.206900	−	0.358362i
$397$	−5.85261	+	10.1370i	−0.293734	+	0.508762i	−0.974690	−	0.223563i	$-0.928231\pi$
$397$	−5.85261	+	10.1370i	−0.293734	+	0.508762i	0.680956	+	0.732325i	$0.261565\pi$
$398$	0.948243			0.0475311
$399$		0			0
$400$	−12.8371			−0.641855
$401$	−1.77846	+	3.08038i	−0.0888119	+	0.153827i	−0.907009	−	0.421111i	$-0.861640\pi$
$401$	−1.77846	+	3.08038i	−0.0888119	+	0.153827i	0.818197	+	0.574938i	$0.194974\pi$
$402$	−8.43621	−	14.6119i	−0.420760	−	0.728778i
$403$	3.51380	+	6.08608i	0.175035	+	0.303169i
$404$	−6.89229	+	11.9378i	−0.342904	+	0.593927i
$405$	5.78963			0.287689
$406$		0			0
$407$	5.32238			0.263821
$408$	−2.61555	+	4.53026i	−0.129489	+	0.224281i
$409$	2.63107	+	4.55714i	0.130098	+	0.225336i	0.923714	−	0.383083i	$-0.125138\pi$
$409$	2.63107	+	4.55714i	0.130098	+	0.225336i	−0.793616	+	0.608419i	$0.791804\pi$
$410$	−0.809493	−	1.40208i	−0.0399780	−	0.0692439i
$411$	12.7785	−	22.1329i	0.630315	−	1.09174i
$412$	−30.2277			−1.48921
$413$		0			0
$414$	5.65593			0.277974
$415$	4.32716	−	7.49486i	0.212412	−	0.367908i
$416$	2.41855	+	4.18904i	0.118579	+	0.205385i
$417$	15.6578	+	27.1200i	0.766763	+	1.32807i
$418$	0.778457	−	1.34833i	0.0380756	−	0.0659488i
$419$	−26.0337			−1.27183			−0.635915	−	0.771759i	$-0.719377\pi$
$419$	−26.0337			−1.27183			−0.635915	+	0.771759i	$0.719377\pi$
$420$		0			0
$421$	22.2423			1.08402			0.542011	−	0.840372i	$-0.317663\pi$
$421$	22.2423			1.08402			0.542011	+	0.840372i	$0.317663\pi$
$422$	−2.37715	+	4.11734i	−0.115718	+	0.200429i
$423$	8.83618	+	15.3047i	0.429630	+	0.744141i
$424$	10.0276	+	17.3683i	0.486983	+	0.843480i
$425$	3.08623	−	5.34551i	0.149704	−	0.259295i
$426$	−1.26031			−0.0610622
$427$		0			0
$428$	9.88273			0.477700
$429$	2.52932	−	4.38090i	0.122117	−	0.211512i
$430$	1.41935	+	2.45839i	0.0684473	+	0.118554i
$431$	−13.8371	−	23.9665i	−0.666509	−	1.15443i	−0.978874	−	0.204465i	$-0.934454\pi$
$431$	−13.8371	−	23.9665i	−0.666509	−	1.15443i	0.312365	−	0.949962i	$-0.398879\pi$
$432$	−2.87930	+	4.98709i	−0.138530	+	0.239941i
$433$	12.7880			0.614552			0.307276	−	0.951620i	$-0.400582\pi$
$433$	12.7880			0.614552			0.307276	+	0.951620i	$0.400582\pi$
$434$		0			0
$435$	6.21629			0.298048
$436$	7.04564	−	12.2034i	0.337425	−	0.584437i
$437$	−4.29226	−	7.43441i	−0.205326	−	0.355636i
$438$	−4.04564	−	7.00726i	−0.193308	−	0.334820i
$439$	−9.08279	+	15.7319i	−0.433498	+	0.750841i	−0.997172	−	0.0751569i	$-0.976054\pi$
$439$	−9.08279	+	15.7319i	−0.433498	+	0.750841i	0.563674	+	0.825998i	$0.309388\pi$
$440$	−2.11727			−0.100937
$441$		0			0
$442$	−0.615547			−0.0292786
$443$	−0.0538572	+	0.0932834i	−0.00255883	+	0.00443203i	−0.867302	−	0.497782i	$-0.834148\pi$
$443$	−0.0538572	+	0.0932834i	−0.00255883	+	0.00443203i	0.864743	+	0.502214i	$0.167481\pi$
$444$	4.73281	+	8.19747i	0.224609	+	0.389035i
$445$	−1.82888	−	3.16771i	−0.0866971	−	0.150164i
$446$	2.38670	−	4.13389i	0.113014	−	0.195745i
$447$	−20.9345			−0.990167
$448$		0			0
$449$	−22.1725			−1.04638			−0.523192	−	0.852215i	$-0.675259\pi$
$449$	−22.1725			−1.04638			−0.523192	+	0.852215i	$0.675259\pi$
$450$	2.28667	−	3.96063i	0.107795	−	0.186706i
$451$	−7.30777	−	12.6574i	−0.344110	−	0.596015i
$452$	−8.79650	−	15.2360i	−0.413753	−	0.716641i
$453$	7.95436	−	13.7773i	0.373728	−	0.647316i
$454$	2.53437			0.118944
$455$		0			0
$456$	5.88273			0.275484
$457$	−2.17977	+	3.77546i	−0.101965	+	0.176609i	−0.912494	−	0.409090i	$-0.865846\pi$
$457$	−2.17977	+	3.77546i	−0.101965	+	0.176609i	0.810529	+	0.585698i	$0.199180\pi$
$458$	0.781895	+	1.35428i	0.0365356	+	0.0632814i
$459$	−1.38445	−	2.39794i	−0.0646207	−	0.111926i
$460$	−2.74742	+	4.75867i	−0.128099	+	0.221874i
$461$	−32.3810			−1.50813			−0.754067	−	0.656797i	$-0.771911\pi$
$461$	−32.3810			−1.50813			−0.754067	+	0.656797i	$0.771911\pi$
$462$		0			0
$463$	8.36641			0.388820			0.194410	−	0.980920i	$-0.437721\pi$
$463$	8.36641			0.388820			0.194410	+	0.980920i	$0.437721\pi$
$464$	−7.10084	+	12.2990i	−0.329648	+	0.570967i
$465$	−4.18320	−	7.24552i	−0.193991	−	0.336003i
$466$	−3.22885	−	5.59253i	−0.149573	−	0.259069i
$467$	−9.77115	+	16.9241i	−0.452155	+	0.783156i	−0.998520	−	0.0543919i	$-0.982678\pi$
$467$	−9.77115	+	16.9241i	−0.452155	+	0.783156i	0.546365	+	0.837547i	$0.316011\pi$
$468$	3.66119			0.169239
$469$		0			0
$470$	2.13875			0.0986532
$471$	6.79307	−	11.7659i	0.313008	−	0.542146i
$472$	10.8241	+	18.7479i	0.498220	+	0.862942i
$473$	12.8134	+	22.1934i	0.589159	+	1.02045i
$474$	−0.708654	+	1.22742i	−0.0325496	+	0.0563775i
$475$	−6.94137			−0.318492
$476$		0			0
$477$	23.2147			1.06293
$478$	0.824101	−	1.42738i	0.0376935	−	0.0652870i
$479$	−14.2612	−	24.7012i	−0.651612	−	1.12862i	−0.982732	−	0.185036i	$-0.940760\pi$
$479$	−14.2612	−	24.7012i	−0.651612	−	1.12862i	0.331120	−	0.943589i	$-0.392574\pi$
$480$	−2.87930	−	4.98709i	−0.131421	−	0.227628i
$481$	−1.18320	+	2.04937i	−0.0539494	+	0.0934432i
$482$	−0.747422			−0.0340441
$483$		0			0
$484$	10.5665			0.480294
$485$	0.918545	−	1.59097i	0.0417090	−	0.0722421i
$486$	−4.29478	−	7.43878i	−0.194815	−	0.337430i
$487$	−12.4121	−	21.4983i	−0.562444	−	0.974181i	−0.997282	−	0.0736727i	$-0.976528\pi$
$487$	−12.4121	−	21.4983i	−0.562444	−	0.974181i	0.434839	−	0.900508i	$-0.356805\pi$
$488$	1.77846	−	3.08038i	0.0805070	−	0.139442i
$489$	−14.3518			−0.649011
$490$		0			0
$491$	29.1690			1.31638			0.658190	−	0.752852i	$-0.271322\pi$
$491$	29.1690			1.31638			0.658190	+	0.752852i	$0.271322\pi$
$492$	12.9966	−	22.5107i	0.585930	−	1.01486i
$493$	−3.41430	−	5.91374i	−0.153772	−	0.266341i
$494$	0.346113	+	0.599486i	0.0155724	+	0.0269721i
$495$	−1.22541	+	2.12247i	−0.0550780	+	0.0953980i
$496$	19.1138			0.858236
$497$		0			0
$498$	−17.3086			−0.775618
$499$	16.6504	−	28.8394i	0.745376	−	1.29103i	−0.204642	−	0.978837i	$-0.565603\pi$
$499$	16.6504	−	28.8394i	0.745376	−	1.29103i	0.950019	−	0.312193i	$-0.101064\pi$
$500$	4.57496	+	7.92406i	0.204598	+	0.354375i
$501$	18.6504	+	32.3035i	0.833241	+	1.44322i
$502$	−1.15947	+	2.00826i	−0.0517498	+	0.0896332i
$503$	12.3258			0.549581			0.274791	−	0.961504i	$-0.411391\pi$
$503$	12.3258			0.549581			0.274791	+	0.961504i	$0.411391\pi$
$504$		0			0
$505$	4.10266			0.182566
$506$	3.08967	−	5.35146i	0.137353	−	0.237902i
$507$	1.12457	+	1.94781i	0.0499439	+	0.0865054i
$508$	0.732814	+	1.26927i	0.0325134	+	0.0563148i
$509$	11.8526	−	20.5293i	0.525358	−	0.909946i	−0.474206	−	0.880414i	$-0.657265\pi$
$509$	11.8526	−	20.5293i	0.525358	−	0.909946i	0.999564	−	0.0295323i	$-0.00940178\pi$
$510$	0.732814			0.0324495
$511$		0			0
$512$	22.8302			1.00896
$513$	−1.55691	+	2.69665i	−0.0687394	+	0.119060i
$514$	−1.88617	−	3.26694i	−0.0831955	−	0.144099i
$515$	4.49828	+	7.79125i	0.198218	+	0.343324i
$516$	−22.7880	+	39.4700i	−1.00319	+	1.73757i
$517$	19.3078			0.849155
$518$		0			0
$519$	−52.4070			−2.30041
$520$	0.470683	−	0.815248i	0.0206408	−	0.0357510i
$521$	21.9509	+	38.0201i	0.961687	+	1.66569i	0.718264	+	0.695771i	$0.244937\pi$
$521$	21.9509	+	38.0201i	0.961687	+	1.66569i	0.243424	+	0.969920i	$0.421730\pi$
$522$	−2.52974	−	4.38165i	−0.110724	−	0.191779i
$523$	18.7164	−	32.4177i	0.818410	−	1.41753i	−0.0884425	−	0.996081i	$-0.528189\pi$
$523$	18.7164	−	32.4177i	0.818410	−	1.41753i	0.906853	−	0.421447i	$-0.138478\pi$
$524$	18.8793			0.824746
$525$		0			0
$526$	0.754297			0.0328889
$527$	−4.59525	+	7.95921i	−0.200172	+	0.346709i
$528$	−6.87930	−	11.9153i	−0.299383	−	0.518546i
$529$	−5.53581	−	9.58831i	−0.240687	−	0.416883i
$530$	1.40475	−	2.43309i	0.0610183	−	0.105687i
$531$	25.0586			1.08745
$532$		0			0
$533$	6.49828			0.281472
$534$	−3.65775	+	6.33541i	−0.158286	+	0.274160i
$535$	−1.47068	−	2.54730i	−0.0635832	−	0.110129i
$536$	−14.1725	−	24.5474i	−0.612157	−	1.06029i
$537$	23.6634	−	40.9863i	1.02115	−	1.76869i
$538$	5.56379			0.239872
$539$		0			0
$540$	1.99312			0.0857704
$541$	17.4875	−	30.2893i	0.751848	−	1.30224i	−0.195078	−	0.980788i	$-0.562496\pi$
$541$	17.4875	−	30.2893i	0.751848	−	1.30224i	0.946926	−	0.321451i	$-0.104171\pi$
$542$	5.14992	+	8.91992i	0.221208	+	0.383144i
$543$	−18.8337	−	32.6208i	−0.808229	−	1.39989i
$544$	−3.16291	+	5.47832i	−0.135609	+	0.234881i
$545$	−4.19395			−0.179649
$546$		0			0
$547$	6.50783			0.278255			0.139127	−	0.990274i	$-0.455570\pi$
$547$	6.50783			0.278255			0.139127	+	0.990274i	$0.455570\pi$
$548$	10.1043	−	17.5011i	0.431633	−	0.747611i
$549$	−2.05863	−	3.56566i	−0.0878603	−	0.152179i
$550$	−2.49828	−	4.32715i	−0.106527	−	0.184510i
$551$	−3.83962	+	6.65041i	−0.163573	+	0.283317i
$552$	23.3484			0.993772
$553$		0			0
$554$	−4.80949			−0.204336
$555$	1.40861	−	2.43979i	0.0597923	−	0.103563i
$556$	12.3810	+	21.4445i	0.525072	+	0.909451i
$557$	21.7164	+	37.6139i	0.920153	+	1.59375i	0.799177	+	0.601096i	$0.205269\pi$
$557$	21.7164	+	37.6139i	0.920153	+	1.59375i	0.120976	+	0.992655i	$0.461398\pi$
$558$	−3.40475	+	5.89719i	−0.144134	+	0.249648i
$559$	−11.3940			−0.481915
$560$		0			0
$561$	6.61555			0.279309
$562$	−0.362969	+	0.628681i	−0.0153109	+	0.0265193i
$563$	−16.9414	−	29.3433i	−0.713993	−	1.23667i	−0.963346	−	0.268260i	$-0.913551\pi$
$563$	−16.9414	−	29.3433i	−0.713993	−	1.23667i	0.249353	−	0.968413i	$-0.419782\pi$
$564$	17.1690	+	29.7376i	0.722946	+	1.25218i
$565$	−2.61808	+	4.53464i	−0.110143	+	0.190774i
$566$	−7.45875			−0.313515
$567$		0			0
$568$	−2.11727			−0.0888385
$569$	−9.60733	+	16.6404i	−0.402760	+	0.697601i	−0.994058	−	0.108852i	$-0.965283\pi$
$569$	−9.60733	+	16.6404i	−0.402760	+	0.697601i	0.591298	+	0.806453i	$0.298616\pi$
$570$	−0.412050	−	0.713692i	−0.0172589	−	0.0298933i
$571$	−10.4134	−	18.0365i	−0.435787	−	0.754805i	0.561573	−	0.827427i	$-0.310196\pi$
$571$	−10.4134	−	18.0365i	−0.435787	−	0.754805i	−0.997359	+	0.0726226i	$0.976863\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	16.7328			0.699023
$574$		0			0
$575$	−27.5500			−1.14892
$576$	3.25564	−	5.63893i	0.135651	−	0.234955i
$577$	14.3224	+	24.8071i	0.596249	+	1.03273i	0.993369	+	0.114966i	$0.0366761\pi$
$577$	14.3224	+	24.8071i	0.596249	+	1.03273i	−0.397121	+	0.917766i	$0.629991\pi$
$578$	3.59831	+	6.23246i	0.149670	+	0.259236i
$579$	−1.68879	+	2.92507i	−0.0701837	+	0.121562i
$580$	4.91539			0.204100
$581$		0			0
$582$	−3.67418			−0.152300
$583$	12.6815	−	21.9650i	0.525213	−	0.909696i
$584$	−6.79650	−	11.7719i	−0.281241	−	0.487124i
$585$	−0.544834	−	0.943681i	−0.0225261	−	0.0390164i
$586$	2.60824	−	4.51761i	0.107746	−	0.186621i
$587$	4.32076			0.178337			0.0891685	−	0.996017i	$-0.471579\pi$
$587$	4.32076			0.178337			0.0891685	+	0.996017i	$0.471579\pi$
$588$		0			0
$589$	10.3354			0.425862
$590$	1.51633	−	2.62636i	0.0624262	−	0.108125i
$591$	26.9820	+	46.7341i	1.10989	+	1.92238i
$592$	3.21811	+	5.57392i	0.132263	+	0.229087i
$593$	−7.98448	+	13.8295i	−0.327883	+	0.567911i	−0.982092	−	0.188404i	$-0.939669\pi$
$593$	−7.98448	+	13.8295i	−0.327883	+	0.567911i	0.654208	+	0.756314i	$0.273002\pi$
$594$	−2.24141			−0.0919661
$595$		0			0
$596$	−16.5535			−0.678057
$597$	2.26557	−	3.92408i	0.0927235	−	0.160602i
$598$	1.37371	+	2.37934i	0.0561752	+	0.0972983i
$599$	8.43487	+	14.6096i	0.344640	+	0.596933i	0.985288	−	0.170901i	$-0.0546678\pi$
$599$	8.43487	+	14.6096i	0.344640	+	0.596933i	−0.640649	+	0.767834i	$0.721334\pi$
$600$	9.43965	−	16.3499i	0.385372	−	0.667484i
$601$	15.3415			0.625792			0.312896	−	0.949787i	$-0.398701\pi$
$601$	15.3415			0.625792			0.312896	+	0.949787i	$0.398701\pi$
$602$		0			0
$603$	−32.8103			−1.33614
$604$	6.28973	−	10.8941i	0.255925	−	0.443276i
$605$	−1.57243	−	2.72353i	−0.0639285	−	0.110727i
$606$	−4.10266	−	7.10601i	−0.166659	−	0.288662i
$607$	17.9176	−	31.0343i	0.727254	−	1.25964i	−0.230785	−	0.973005i	$-0.574129\pi$
$607$	17.9176	−	31.0343i	0.727254	−	1.25964i	0.958039	−	0.286637i	$-0.0925373\pi$
$608$	7.11383			0.288504
$609$		0			0
$610$	−0.498281			−0.0201748
$611$	−4.29226	+	7.43441i	−0.173646	+	0.300764i
$612$	2.39400	+	4.14654i	0.0967719	+	0.167614i
$613$	−9.83365	−	17.0324i	−0.397177	−	0.687932i	0.596199	−	0.802837i	$-0.296677\pi$
$613$	−9.83365	−	17.0324i	−0.397177	−	0.687932i	−0.993376	+	0.114905i	$0.963344\pi$
$614$	4.80381	−	8.32044i	0.193866	−	0.335786i
$615$	−7.73625			−0.311956
$616$		0			0
$617$	−41.4588			−1.66907			−0.834533	−	0.550958i	$-0.814263\pi$
$617$	−41.4588			−1.66907			−0.834533	+	0.550958i	$0.814263\pi$
$618$	8.99656	−	15.5825i	0.361895	−	0.626820i
$619$	5.43965	+	9.42175i	0.218638	+	0.378692i	0.954392	−	0.298557i	$-0.0965053\pi$
$619$	5.43965	+	9.42175i	0.218638	+	0.378692i	−0.735754	+	0.677249i	$0.763172\pi$
$620$	−3.30777	−	5.72923i	−0.132843	−	0.230091i
$621$	−6.17934	+	10.7029i	−0.247968	+	0.429494i
$622$	0.905275			0.0362982
$623$		0			0
$624$	6.11727			0.244887
$625$	−10.4379	+	18.0790i	−0.417517	+	0.723161i
$626$	−3.38101	−	5.85609i	−0.135133	−	0.234056i
$627$	−3.71982	−	6.44292i	−0.148555	−	0.257306i
$628$	5.37146	−	9.30365i	0.214345	−	0.371256i
$629$	−3.09472			−0.123395
$630$		0			0
$631$	−31.4396			−1.25159			−0.625796	−	0.779987i	$-0.715226\pi$
$631$	−31.4396			−1.25159			−0.625796	+	0.779987i	$0.715226\pi$
$632$	−1.19051	+	2.06202i	−0.0473558	+	0.0820227i
$633$	11.3591	+	19.6745i	0.451484	+	0.781993i
$634$	−3.66119	−	6.34137i	−0.145404	−	0.251848i
$635$	0.218105	−	0.377769i	0.00865523	−	0.0149913i
$636$	45.1070			1.78861
$637$		0			0
$638$	−5.52770			−0.218844
$639$	−1.22541	+	2.12247i	−0.0484764	+	0.0839636i
$640$	−2.95436	−	5.11710i	−0.116781	−	0.202271i
$641$	−1.52110	−	2.63463i	−0.0600799	−	0.104062i	0.834421	−	0.551128i	$-0.185802\pi$
$641$	−1.52110	−	2.63463i	−0.0600799	−	0.104062i	−0.894501	+	0.447066i	$0.852469\pi$
$642$	−2.94137	+	5.09460i	−0.116086	+	0.201068i
$643$	−8.02922			−0.316641			−0.158321	−	0.987388i	$-0.550608\pi$
$643$	−8.02922			−0.316641			−0.158321	+	0.987388i	$0.550608\pi$
$644$		0			0
$645$	13.5646			0.534107
$646$	−0.452638	+	0.783991i	−0.0178088	+	0.0308457i
$647$	3.53662	+	6.12561i	0.139039	+	0.240822i	0.927133	−	0.374732i	$-0.122265\pi$
$647$	3.53662	+	6.12561i	0.139039	+	0.240822i	−0.788094	+	0.615555i	$0.788932\pi$
$648$	−9.72632	−	16.8465i	−0.382086	−	0.661792i
$649$	13.6888	−	23.7097i	0.537332	−	0.930686i
$650$	2.22154			0.0871361
$651$		0			0
$652$	−11.3484			−0.444436
$653$	7.87930	−	13.6473i	0.308341	−	0.534062i	−0.669659	−	0.742669i	$-0.733560\pi$
$653$	7.87930	−	13.6473i	0.308341	−	0.534062i	0.978000	+	0.208607i	$0.0668930\pi$
$654$	4.19395	+	7.26413i	0.163996	+	0.284050i
$655$	−2.80949	−	4.86618i	−0.109776	−	0.190138i
$656$	8.83709	−	15.3063i	0.345030	−	0.597610i
$657$	−15.7344			−0.613859
$658$		0			0
$659$	−12.2181			−0.475950			−0.237975	−	0.971271i	$-0.576484\pi$
$659$	−12.2181			−0.475950			−0.237975	+	0.971271i	$0.576484\pi$
$660$	−2.38101	+	4.12404i	−0.0926809	+	0.160528i
$661$	1.86722	+	3.23411i	0.0726263	+	0.125792i	0.900052	−	0.435783i	$-0.143529\pi$
$661$	1.86722	+	3.23411i	0.0726263	+	0.125792i	−0.827425	+	0.561576i	$0.810195\pi$
$662$	−7.42504	−	12.8605i	−0.288582	−	0.499839i
$663$	−1.47068	+	2.54730i	−0.0571166	+	0.0989289i
$664$	−29.0777			−1.12844
$665$		0			0
$666$	−2.29296			−0.0888506
$667$	−15.2393	+	26.3953i	−0.590068	+	1.02203i
$668$	14.7474	+	25.5433i	0.570595	+	0.988299i
$669$	−11.4047	−	19.7536i	−0.440933	−	0.763718i
$670$	−1.98539	+	3.43880i	−0.0767024	+	0.132852i
$671$	−4.49828			−0.173654
$672$		0			0
$673$	−5.65775			−0.218090			−0.109045	−	0.994037i	$-0.534779\pi$
$673$	−5.65775			−0.218090			−0.109045	+	0.994037i	$0.534779\pi$
$674$	1.98314	−	3.43491i	0.0763879	−	0.132308i
$675$	4.99656	+	8.65430i	0.192318	+	0.333104i
$676$	0.889229	+	1.54019i	0.0342011	+	0.0592380i
$677$	4.69953	−	8.13983i	0.180618	−	0.312839i	−0.761473	−	0.648196i	$-0.775524\pi$
$677$	4.69953	−	8.13983i	0.180618	−	0.312839i	0.942091	+	0.335357i	$0.108857\pi$
$678$	10.4723			0.402186
$679$		0			0
$680$	1.23109			0.0472103
$681$	6.05520	−	10.4879i	0.232036	−	0.401897i
$682$	3.71982	+	6.44292i	0.142439	+	0.246712i
$683$	10.3664	+	17.9551i	0.396660	+	0.687034i	0.993311	−	0.115466i	$-0.0368360\pi$
$683$	10.3664	+	17.9551i	0.396660	+	0.687034i	−0.596652	+	0.802500i	$0.703503\pi$
$684$	2.69223	−	4.66307i	0.102940	−	0.178297i
$685$	−6.01461			−0.229806
$686$		0			0
$687$	7.47250			0.285094
$688$	−15.4948	+	26.8379i	−0.590735	+	1.02318i
$689$	5.63837	+	9.76594i	0.214805	+	0.372053i
$690$	−1.63541	−	2.83262i	−0.0622591	−	0.107836i
$691$	8.04312	−	13.9311i	0.305975	−	0.529963i	−0.671503	−	0.741002i	$-0.734351\pi$
$691$	8.04312	−	13.9311i	0.305975	−	0.529963i	0.977478	+	0.211038i	$0.0676844\pi$
$692$	−41.4396			−1.57530
$693$		0			0
$694$	9.10695			0.345695
$695$	3.68492	−	6.38247i	0.139777	−	0.242101i
$696$	−10.4431	−	18.0880i	−0.395844	−	0.685622i
$697$	4.24914	+	7.35973i	0.160948	+	0.278770i
$698$	6.41430	−	11.1099i	0.242785	−	0.420516i
$699$	−30.8578			−1.16715
$700$		0			0
$701$	−6.98013			−0.263636			−0.131818	−	0.991274i	$-0.542081\pi$
$701$	−6.98013			−0.263636			−0.131818	+	0.991274i	$0.542081\pi$
$702$	0.498281	−	0.863048i	0.0188064	−	0.0325737i
$703$	1.74012	+	3.01397i	0.0656298	+	0.113674i
$704$	−3.55691	−	6.16076i	−0.134056	−	0.232192i
$705$	5.10996	−	8.85071i	0.192452	−	0.333337i
$706$	12.0844			0.454803
$707$		0			0
$708$	48.6898			1.82988
$709$	−4.19619	+	7.26802i	−0.157591	+	0.272956i	−0.934000	−	0.357274i	$-0.883706\pi$
$709$	−4.19619	+	7.26802i	−0.157591	+	0.272956i	0.776408	+	0.630230i	$0.217040\pi$
$710$	0.148302	+	0.256866i	0.00556567	+	0.00964002i
$711$	1.37806	+	2.38687i	0.0516812	+	0.0895145i
$712$	−6.14486	+	10.6432i	−0.230289	+	0.398871i
$713$	41.0207			1.53624
$714$		0			0
$715$	−1.19051			−0.0445225
$716$	18.7113	−	32.4090i	0.699275	−	1.21118i
$717$	−3.93793	−	6.82069i	−0.147065	−	0.254723i
$718$	5.51127	+	9.54580i	0.205679	+	0.356246i
$719$	−2.58065	+	4.46981i	−0.0962418	+	0.166696i	−0.910126	−	0.414331i	$-0.864016\pi$
$719$	−2.58065	+	4.46981i	−0.0962418	+	0.166696i	0.813884	+	0.581027i	$0.197349\pi$
$720$	−2.96371			−0.110451
$721$		0			0
$722$	−7.92494			−0.294936
$723$	−1.78576	+	3.09303i	−0.0664132	+	0.115031i
$724$	−14.8923	−	25.7942i	−0.553467	−	0.958634i
$725$	12.3224	+	21.3430i	0.457642	+	0.792659i
$726$	−3.14486	+	5.44706i	−0.116717	+	0.202160i
$727$	40.4362			1.49970			0.749848	−	0.661610i	$-0.230127\pi$
$727$	40.4362			1.49970			0.749848	+	0.661610i	$0.230127\pi$
$728$		0			0
$729$	−8.23109			−0.304855
$730$	−0.952109	+	1.64910i	−0.0352391	+	0.0610359i
$731$	−7.45039	−	12.9045i	−0.275563	−	0.477288i
$732$	−4.00000	−	6.92820i	−0.147844	−	0.256074i
$733$	−19.5656	+	33.8885i	−0.722670	+	1.25170i	0.237255	+	0.971447i	$0.423752\pi$
$733$	−19.5656	+	33.8885i	−0.722670	+	1.25170i	−0.959926	+	0.280254i	$0.909581\pi$
$734$	6.91215			0.255132
$735$		0			0
$736$	28.2345			1.04074
$737$	−17.9233	+	31.0441i	−0.660214	+	1.14352i
$738$	3.14830	+	5.45302i	0.115891	+	0.200728i
$739$	3.56766	+	6.17936i	0.131238	+	0.227311i	0.924154	−	0.382020i	$-0.124771\pi$
$739$	3.56766	+	6.17936i	0.131238	+	0.227311i	−0.792916	+	0.609331i	$0.791438\pi$
$740$	1.11383	−	1.92921i	0.0409451	−	0.0709191i
$741$	3.30777			0.121514
$742$		0			0
$743$	13.8827			0.509308			0.254654	−	0.967032i	$-0.418038\pi$
$743$	13.8827			0.509308			0.254654	+	0.967032i	$0.418038\pi$
$744$	−14.0552	+	24.3443i	−0.515288	+	0.892506i
$745$	2.46338	+	4.26670i	0.0902512	+	0.156320i
$746$	5.56990	+	9.64736i	0.203929	+	0.353215i
$747$	−16.8293	+	29.1492i	−0.615752	+	1.06651i
$748$	5.23109			0.191268
$749$		0			0
$750$	−5.44652			−0.198879
$751$	18.6625	−	32.3244i	0.681005	−	1.17954i	−0.293669	−	0.955907i	$-0.594876\pi$
$751$	18.6625	−	32.3244i	0.681005	−	1.17954i	0.974674	−	0.223629i	$-0.0717903\pi$
$752$	11.6742	+	20.2203i	0.425714	+	0.737358i
$753$	5.54049	+	9.59640i	0.201907	+	0.349712i
$754$	1.22885	−	2.12843i	0.0447520	−	0.0775127i
$755$	−3.74398			−0.136258
$756$		0			0
$757$	−7.10428			−0.258209			−0.129105	−	0.991631i	$-0.541210\pi$
$757$	−7.10428			−0.258209			−0.129105	+	0.991631i	$0.541210\pi$
$758$	7.70522	−	13.3458i	0.279866	−	0.484742i
$759$	−14.7638	−	25.5717i	−0.535894	−	0.928195i
$760$	−0.692226	−	1.19897i	−0.0251097	−	0.0434913i
$761$	−12.9810	+	22.4838i	−0.470562	+	0.815038i	−0.999433	−	0.0336643i	$-0.989282\pi$
$761$	−12.9810	+	22.4838i	−0.470562	+	0.815038i	0.528871	+	0.848702i	$0.322616\pi$
$762$	−0.872420			−0.0316044
$763$		0			0
$764$	13.2311			0.478684
$765$	0.712520	−	1.23412i	0.0257612	−	0.0446197i
$766$	−5.32238	−	9.21864i	−0.192305	−	0.333083i
$767$	6.08623	+	10.5417i	0.219761	+	0.380637i
$768$	1.20512	−	2.08732i	0.0434859	−	0.0753197i
$769$	21.4638			0.774005			0.387002	−	0.922079i	$-0.373511\pi$
$769$	21.4638			0.774005			0.387002	+	0.922079i	$0.373511\pi$
$770$		0			0
$771$	−18.0260			−0.649190
$772$	−1.33537	+	2.31293i	−0.0480611	+	0.0832442i
$773$	−20.2457	−	35.0666i	−0.728187	−	1.26126i	−0.957649	−	0.287940i	$-0.907030\pi$
$773$	−20.2457	−	35.0666i	−0.728187	−	1.26126i	0.229461	−	0.973318i	$-0.426304\pi$
$774$	−5.52019	−	9.56125i	−0.198419	−	0.343672i
$775$	16.5845	−	28.7252i	0.595733	−	1.03184i
$776$	−6.17246			−0.221578
$777$		0			0
$778$	17.9087			0.642058
$779$	4.77846	−	8.27653i	0.171206	−	0.296537i
$780$	−1.05863	−	1.83361i	−0.0379051	−	0.0656536i
$781$	1.33881	+	2.31889i	0.0479064	+	0.0829762i
$782$	−1.79650	+	3.11163i	−0.0642428	+	0.111272i
$783$	11.0554			0.395088
$784$		0			0
$785$	−3.19738			−0.114119
$786$	−5.61899	+	9.73237i	−0.200423	+	0.347142i
$787$	−2.51036	−	4.34807i	−0.0894847	−	0.154992i	0.817809	−	0.575490i	$-0.195189\pi$
$787$	−2.51036	−	4.34807i	−0.0894847	−	0.154992i	−0.907293	+	0.420498i	$0.861855\pi$
$788$	21.3354	+	36.9539i	0.760041	+	1.31643i
$789$	1.80219	−	3.12148i	0.0641596	−	0.111128i
$790$	0.333552			0.0118672
$791$		0			0
$792$	8.23453			0.292601
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$	−2.75473	−	4.77132i	−0.0977616	−	0.169328i
$795$	−6.71252	−	11.6264i	−0.238069	−	0.412347i
$796$	1.79145	−	3.10288i	0.0634962	−	0.109979i
$797$	−19.7002			−0.697815			−0.348908	−	0.937157i	$-0.613447\pi$
$797$	−19.7002			−0.697815			−0.348908	+	0.937157i	$0.613447\pi$
$798$		0			0
$799$	−11.2266			−0.397169
$800$	11.4151	−	19.7715i	0.403585	−	0.699030i
$801$	7.11292	+	12.3199i	0.251323	+	0.435304i
$802$	−0.837090	−	1.44988i	−0.0295587	−	0.0511971i
$803$	−8.59525	+	14.8874i	−0.303320	+	0.525366i
$804$	−63.7517			−2.24835
$805$		0			0
$806$	−3.30777			−0.116511
$807$	13.2932	−	23.0244i	0.467942	−	0.810499i
$808$	−6.89229	−	11.9378i	−0.242470	−	0.419970i
$809$	1.28839	+	2.23156i	0.0452974	+	0.0784574i	0.887785	−	0.460258i	$-0.152243\pi$
$809$	1.28839	+	2.23156i	0.0452974	+	0.0784574i	−0.842488	+	0.538715i	$0.818910\pi$
$810$	−1.36254	+	2.35999i	−0.0478748	+	0.0829216i
$811$	−41.2311			−1.44782			−0.723910	−	0.689895i	$-0.757657\pi$
$811$	−41.2311			−1.44782			−0.723910	+	0.689895i	$0.757657\pi$
$812$		0			0
$813$	49.2173			1.72613
$814$	−1.25258	+	2.16953i	−0.0439028	+	0.0760420i
$815$	1.68879	+	2.92507i	0.0591557	+	0.102461i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	−8.37849	+	14.5120i	−0.293126	+	0.507709i
$818$	−2.47680			−0.0865992
$819$		0			0
$820$	−6.11727			−0.213624
$821$	−2.63359	+	4.56152i	−0.0919130	+	0.159198i	−0.908316	−	0.418284i	$-0.862632\pi$
$821$	−2.63359	+	4.56152i	−0.0919130	+	0.159198i	0.816403	+	0.577483i	$0.195965\pi$
$822$	6.01461	+	10.4176i	0.209784	+	0.363356i
$823$	−18.0096	−	31.1935i	−0.627774	−	1.08734i	−0.987998	−	0.154470i	$-0.950633\pi$
$823$	−18.0096	−	31.1935i	−0.627774	−	1.08734i	0.360224	−	0.932866i	$-0.382700\pi$
$824$	15.1138	−	26.1779i	0.526515	−	0.911951i
$825$	−23.8759			−0.831251
$826$		0			0
$827$	−16.3157			−0.567353			−0.283676	−	0.958920i	$-0.591554\pi$
$827$	−16.3157			−0.567353			−0.283676	+	0.958920i	$0.591554\pi$
$828$	10.6854	−	18.5076i	0.371342	−	0.643183i
$829$	−15.1978	−	26.3234i	−0.527842	−	0.914249i	−0.999473	−	0.0324531i	$-0.989668\pi$
$829$	−15.1978	−	26.3234i	−0.527842	−	0.914249i	0.471631	−	0.881796i	$-0.343665\pi$
$830$	2.03672	+	3.52770i	0.0706956	+	0.122448i
$831$	−11.4910	+	19.9030i	−0.398618	+	0.690426i
$832$	3.16291			0.109654
$833$		0			0
$834$	−14.7397			−0.510394
$835$	4.38923	−	7.60237i	0.151896	−	0.263091i
$836$	−2.94137	−	5.09460i	−0.101729	−	0.176200i
$837$	−7.43965	−	12.8858i	−0.257152	−	0.445400i
$838$	6.12682	−	10.6120i	0.211647	−	0.366584i
$839$	−29.8398			−1.03018			−0.515092	−	0.857135i	$-0.672242\pi$
$839$	−29.8398			−1.03018			−0.515092	+	0.857135i	$0.672242\pi$
$840$		0			0
$841$	−1.73549			−0.0598445
$842$	−5.23453	+	9.06648i	−0.180394	+	0.312451i
$843$	1.73443	+	3.00412i	0.0597370	+	0.103468i
$844$	8.98195	+	15.5572i	0.309172	+	0.535501i
$845$	0.264658	−	0.458402i	0.00910452	−	0.0157695i
$846$	−8.31809			−0.285982
$847$		0			0
$848$	30.6707			1.05324
$849$	−17.8207	+	30.8663i	−0.611604	+	1.05933i
$850$	1.45264	+	2.51604i	0.0498251	+	0.0862995i
$851$	6.90647	+	11.9623i	0.236751	+	0.410064i
$852$	−2.38101	+	4.12404i	−0.0815722	+	0.141287i
$853$	0.203497			0.00696761			0.00348380	−	0.999994i	$-0.498891\pi$
$853$	0.203497			0.00696761			0.00348380	+	0.999994i	$0.498891\pi$
$854$		0			0
$855$	−1.60256			−0.0548063
$856$	−4.94137	+	8.55870i	−0.168892	+	0.292530i
$857$	−6.30777	−	10.9254i	−0.215469	−	0.373204i	0.737948	−	0.674857i	$-0.235795\pi$
$857$	−6.30777	−	10.9254i	−0.215469	−	0.373204i	−0.953418	+	0.301653i	$0.902462\pi$
$858$	1.19051	+	2.06202i	0.0406433	+	0.0703962i
$859$	−13.9836	+	24.2203i	−0.477113	+	0.826385i	−0.999656	−	0.0262286i	$-0.991650\pi$
$859$	−13.9836	+	24.2203i	−0.477113	+	0.826385i	0.522543	+	0.852613i	$0.324984\pi$
$860$	10.7259			0.365751
$861$		0			0
$862$	13.0258			0.443660
$863$	1.38445	−	2.39794i	0.0471273	−	0.0816269i	−0.841499	−	0.540258i	$-0.818327\pi$
$863$	1.38445	−	2.39794i	0.0471273	−	0.0816269i	0.888627	+	0.458631i	$0.151660\pi$
$864$	−5.12070	−	8.86932i	−0.174210	−	0.301740i
$865$	6.16678	+	10.6812i	0.209677	+	0.363171i
$866$	−3.00955	+	5.21270i	−0.102269	+	0.177135i
$867$	34.3887			1.16790
$868$		0			0
$869$	3.01117			0.102147
$870$	−1.46295	+	2.53391i	−0.0495987	+	0.0859075i
$871$	−7.96896	−	13.8027i	−0.270018	−	0.467685i
$872$	7.04564	+	12.2034i	0.238596	+	0.413260i
$873$	−3.57243	+	6.18763i	−0.120909	+	0.209420i
$874$	4.04059			0.136675
$875$		0			0
$876$	−30.5726			−1.03295
$877$	−3.35567	+	5.81218i	−0.113313	+	0.196263i	−0.917104	−	0.398648i	$-0.869480\pi$
$877$	−3.35567	+	5.81218i	−0.113313	+	0.196263i	0.803791	+	0.594911i	$0.202813\pi$
$878$	−4.27512	−	7.40473i	−0.144278	−	0.249897i
$879$	−12.4634	−	21.5872i	−0.420379	−	0.728118i
$880$	−1.61899	+	2.80416i	−0.0545760	+	0.0945284i
$881$	18.3741			0.619040			0.309520	−	0.950893i	$-0.399832\pi$
$881$	18.3741			0.619040			0.309520	+	0.950893i	$0.399832\pi$
$882$		0			0
$883$	9.93105			0.334207			0.167103	−	0.985939i	$-0.446559\pi$
$883$	9.93105			0.334207			0.167103	+	0.985939i	$0.446559\pi$
$884$	−1.16291	+	2.01422i	−0.0391129	+	0.0677455i
$885$	−7.24570	−	12.5499i	−0.243562	−	0.421861i
$886$	−0.0253497	−	0.0439070i	−0.000851640	−	0.00147508i
$887$	−25.6888	+	44.4943i	−0.862545	+	1.49397i	0.00691915	+	0.999976i	$0.497798\pi$
$887$	−25.6888	+	44.4943i	−0.862545	+	1.49397i	−0.869464	+	0.493996i	$0.835536\pi$
$888$	−9.46563			−0.317646
$889$		0			0
$890$	1.72164			0.0577096
$891$	−12.3005	+	21.3050i	−0.412081	+	0.713746i
$892$	−9.01805	−	15.6197i	−0.301947	−	0.522987i
$893$	6.31255	+	10.9337i	0.211241	+	0.365881i
$894$	4.92676	−	8.53340i	0.164775	−	0.285399i
$895$	−11.1380			−0.372302
$896$		0			0
$897$	13.1284			0.438346
$898$	5.21811	−	9.03802i	0.174130	−	0.301603i
$899$	−18.3475	−	31.7787i	−0.611922	−	1.05988i
$900$	−8.64009	−	14.9651i	−0.288003	−	0.498836i
$901$	−7.37371	+	12.7716i	−0.245654	+	0.425485i
$902$	6.87930			0.229055
$903$		0			0
$904$	17.5930			0.585135
$905$	−4.43234	+	7.67704i	−0.147336	+	0.255194i
$906$	3.74398	+	6.48477i	0.124386	+	0.215442i
$907$	−2.17112	−	3.76050i	−0.0720910	−	0.124865i	0.827727	−	0.561132i	$-0.189634\pi$
$907$	−2.17112	−	3.76050i	−0.0720910	−	0.124865i	−0.899818	+	0.436266i	$0.856301\pi$
$908$	4.78801	−	8.29307i	0.158896	−	0.275215i
$909$	−15.9562			−0.529233
$910$		0			0
$911$	31.4853			1.04315			0.521577	−	0.853204i	$-0.325344\pi$
$911$	31.4853			1.04315			0.521577	+	0.853204i	$0.325344\pi$
$912$	4.49828	−	7.79125i	0.148953	−	0.257994i
$913$	18.3867	+	31.8467i	0.608511	+	1.05397i
$914$	−1.02598	−	1.77705i	−0.0339364	−	0.0587795i
$915$	−1.19051	+	2.06202i	−0.0393570	+	0.0681683i
$916$	5.90871			0.195229
$917$		0			0
$918$	1.30328			0.0430146
$919$	−21.7294	+	37.6364i	−0.716786	+	1.24151i	0.245481	+	0.969401i	$0.421054\pi$
$919$	−21.7294	+	37.6364i	−0.716786	+	1.24151i	−0.962267	+	0.272108i	$0.912279\pi$
$920$	−2.74742	−	4.75867i	−0.0905798	−	0.156889i
$921$	−22.9548	−	39.7589i	−0.756386	−	1.31010i
$922$	7.62060	−	13.1993i	0.250971	−	0.434695i
$923$	−1.19051			−0.0391860
$924$		0			0
$925$	11.1690			0.367235
$926$	−1.96896	+	3.41035i	−0.0647042	+	0.112071i
$927$	−17.4948	−	30.3020i	−0.574606	−	0.995247i
$928$	−12.6285	−	21.8733i	−0.414552	−	0.718025i
$929$	2.20259	−	3.81499i	0.0722645	−	0.125166i	−0.827629	−	0.561276i	$-0.810311\pi$
$929$	2.20259	−	3.81499i	0.0722645	−	0.125166i	0.899893	+	0.436110i	$0.143644\pi$
$930$	3.93793			0.129130
$931$		0			0
$932$	−24.4001			−0.799252
$933$	2.16291	−	3.74627i	0.0708105	−	0.122647i
$934$	−4.59912	−	7.96591i	−0.150488	−	0.260653i
$935$	−0.778457	−	1.34833i	−0.0254583	−	0.0440950i
$936$	−1.83060	+	3.17068i	−0.0598349	+	0.103637i
$937$	34.0990			1.11397			0.556983	−	0.830524i	$-0.311959\pi$
$937$	34.0990			1.11397			0.556983	+	0.830524i	$0.311959\pi$
$938$		0			0
$939$	−32.3121			−1.05446
$940$	4.04059	−	6.99850i	0.131789	−	0.228266i
$941$	22.2336	+	38.5098i	0.724795	+	1.25538i	0.959058	+	0.283209i	$0.0913991\pi$
$941$	22.2336	+	38.5098i	0.724795	+	1.25538i	−0.234263	+	0.972173i	$0.575268\pi$
$942$	3.19738	+	5.53803i	0.104176	+	0.180439i
$943$	18.9655	−	32.8493i	0.617603	−	1.06972i
$944$	33.1070			1.07754
$945$		0			0
$946$	−12.0621			−0.392172
$947$	−28.9655	+	50.1698i	−0.941253	+	1.63030i	−0.178168	+	0.984000i	$0.557017\pi$
$947$	−28.9655	+	50.1698i	−0.941253	+	1.63030i	−0.763085	+	0.646298i	$0.776316\pi$
$948$	2.67762	+	4.63777i	0.0869650	+	0.150628i
$949$	−3.82157	−	6.61916i	−0.124053	−	0.214867i
$950$	1.63359	−	2.82947i	0.0530008	−	0.0918000i
$951$	−34.9897			−1.13462
$952$		0			0
$953$	35.3060			1.14367			0.571836	−	0.820368i	$-0.306231\pi$
$953$	35.3060			1.14367			0.571836	+	0.820368i	$0.306231\pi$
$954$	−5.46338	+	9.46285i	−0.176883	+	0.306371i
$955$	−1.96896	−	3.41035i	−0.0637142	−	0.110356i
$956$	−3.11383	−	5.39331i	−0.100708	−	0.174432i
$957$	−13.2069	+	22.8751i	−0.426920	+	0.739446i
$958$	13.4250			0.433743
$959$		0			0
$960$	−3.76547			−0.121530
$961$	−9.19356	+	15.9237i	−0.296567	+	0.513668i
$962$	−0.556914	−	0.964604i	−0.0179556	−	0.0311001i
$963$	5.71982	+	9.90703i	0.184319	+	0.319249i
$964$	−1.41205	+	2.44574i	−0.0454791	+	0.0787721i
$965$	0.794885			0.0255882
$966$		0			0
$967$	23.7148			0.762616			0.381308	−	0.924448i	$-0.375474\pi$
$967$	23.7148			0.762616			0.381308	+	0.924448i	$0.375474\pi$
$968$	−5.28323	+	9.15083i	−0.169810	+	0.294119i
$969$	2.16291	+	3.74627i	0.0694827	+	0.120348i
$970$	0.432344	+	0.748842i	0.0138817	+	0.0240439i
$971$	−11.9690	+	20.7309i	−0.384102	+	0.665285i	−0.991644	−	0.129003i	$-0.958822\pi$
$971$	−11.9690	+	20.7309i	−0.384102	+	0.665285i	0.607542	+	0.794288i	$0.292156\pi$
$972$	−32.4553			−1.04100
$973$		0			0
$974$	11.6843			0.374389
$975$	5.30777	−	9.19333i	0.169985	−	0.294422i
$976$	−2.71982	−	4.71087i	−0.0870594	−	0.150791i
$977$	8.09353	+	14.0184i	0.258935	+	0.448489i	0.965957	−	0.258703i	$-0.0832951\pi$
$977$	8.09353	+	14.0184i	0.258935	+	0.448489i	−0.707022	+	0.707192i	$0.749962\pi$
$978$	3.37758	−	5.85013i	0.108003	−	0.187067i
$979$	15.5423			0.496734
$980$		0			0
$981$	16.3112			0.520777
$982$	−6.86469	+	11.8900i	−0.219061	+	0.379425i
$983$	22.8622	+	39.5984i	0.729190	+	1.26299i	0.957226	+	0.289341i	$0.0934361\pi$
$983$	22.8622	+	39.5984i	0.729190	+	1.26299i	−0.228036	+	0.973653i	$0.573231\pi$
$984$	12.9966	+	22.5107i	0.414315	+	0.717615i
$985$	6.34998	−	10.9985i	0.202327	−	0.350441i
$986$	3.21411			0.102358
$987$		0			0
$988$	2.61555			0.0832116
$989$	−33.2539	+	57.5975i	−1.05741	+	1.83149i
$990$	−0.576780	−	0.999012i	−0.0183313	−	0.0317507i
$991$	2.70178	+	4.67962i	0.0858248	+	0.148653i	0.905742	−	0.423829i	$-0.139314\pi$
$991$	2.70178	+	4.67962i	0.0858248	+	0.148653i	−0.819918	+	0.572482i	$0.805981\pi$
$992$	−16.9966	+	29.4389i	−0.539641	+	0.934686i
$993$	−70.9605			−2.25186
$994$		0			0
$995$	−1.06637			−0.0338061
$996$	−32.7000	+	56.6380i	−1.03614	+	1.79464i
$997$	3.02416	+	5.23800i	0.0957761	+	0.165889i	0.909932	−	0.414757i	$-0.136133\pi$
$997$	3.02416	+	5.23800i	0.0957761	+	0.165889i	−0.814156	+	0.580646i	$0.802800\pi$
$998$	7.83709	+	13.5742i	0.248079	+	0.429685i
$999$	2.50516	−	4.33906i	0.0792597	−	0.137282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.i.79.2		6
7.2	even	3		637.2.a.j.1.2		3
7.3	odd	6		637.2.e.j.508.2		6
7.4	even	3	inner	637.2.e.i.508.2		6
7.5	odd	6		91.2.a.d.1.2	✓	3
7.6	odd	2		637.2.e.j.79.2		6
21.2	odd	6		5733.2.a.x.1.2		3
21.5	even	6		819.2.a.i.1.2		3
28.19	even	6		1456.2.a.t.1.1		3
35.19	odd	6		2275.2.a.m.1.2		3
56.5	odd	6		5824.2.a.by.1.1		3
56.19	even	6		5824.2.a.bs.1.3		3
91.5	even	12		1183.2.c.f.337.3		6
91.12	odd	6		1183.2.a.i.1.2		3
91.47	even	12		1183.2.c.f.337.4		6
91.51	even	6		8281.2.a.bg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.d.1.2	✓	3	7.5	odd	6
637.2.a.j.1.2		3	7.2	even	3
637.2.e.i.79.2		6	1.1	even	1	trivial
637.2.e.i.508.2		6	7.4	even	3	inner
637.2.e.j.79.2		6	7.6	odd	2
637.2.e.j.508.2		6	7.3	odd	6
819.2.a.i.1.2		3	21.5	even	6
1183.2.a.i.1.2		3	91.12	odd	6
1183.2.c.f.337.3		6	91.5	even	12
1183.2.c.f.337.4		6	91.47	even	12
1456.2.a.t.1.1		3	28.19	even	6
2275.2.a.m.1.2		3	35.19	odd	6
5733.2.a.x.1.2		3	21.2	odd	6
5824.2.a.bs.1.3		3	56.19	even	6
5824.2.a.by.1.1		3	56.5	odd	6
8281.2.a.bg.1.2		3	91.51	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.235342 + 0.407624i) q^{2} +(1.12457 + 1.94781i) q^{3} +(0.889229 + 1.54019i) q^{4} +(0.264658 - 0.458402i) q^{5} -1.05863 q^{6} -1.77846 q^{8} +(-1.02932 + 1.78283i) q^{9} +(0.124570 + 0.215762i) q^{10} +(1.12457 + 1.94781i) q^{11} +(-2.00000 + 3.46410i) q^{12} -1.00000 q^{13} +1.19051 q^{15} +(-1.35991 + 2.35544i) q^{16} +(-0.653887 - 1.13257i) q^{17} +(-0.484482 - 0.839148i) q^{18} +(-0.735342 + 1.27365i) q^{19} +0.941367 q^{20} -1.05863 q^{22} +(-2.91855 + 5.05507i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(2.35991 + 4.08749i) q^{25} +(0.235342 - 0.407624i) q^{26} +2.11727 q^{27} +5.22154 q^{29} +(-0.280176 + 0.485279i) q^{30} +(-3.51380 - 6.08608i) q^{31} +(-2.41855 - 4.18904i) q^{32} +(-2.52932 + 4.38090i) q^{33} +0.615547 q^{34} -3.66119 q^{36} +(1.18320 - 2.04937i) q^{37} +(-0.346113 - 0.599486i) q^{38} +(-1.12457 - 1.94781i) q^{39} +(-0.470683 + 0.815248i) q^{40} -6.49828 q^{41} +11.3940 q^{43} +(-2.00000 + 3.46410i) q^{44} +(0.544834 + 0.943681i) q^{45} +(-1.37371 - 2.37934i) q^{46} +(4.29226 - 7.43441i) q^{47} -6.11727 q^{48} -2.22154 q^{50} +(1.47068 - 2.54730i) q^{51} +(-0.889229 - 1.54019i) q^{52} +(-5.63837 - 9.76594i) q^{53} +(-0.498281 + 0.863048i) q^{54} +1.19051 q^{55} -3.30777 q^{57} +(-1.22885 + 2.12843i) q^{58} +(-6.08623 - 10.5417i) q^{59} +(1.05863 + 1.83361i) q^{60} +(-1.00000 + 1.73205i) q^{61} +3.30777 q^{62} -3.16291 q^{64} +(-0.264658 + 0.458402i) q^{65} +(-1.19051 - 2.06202i) q^{66} +(7.96896 + 13.8027i) q^{67} +(1.16291 - 2.01422i) q^{68} -13.1284 q^{69} +1.19051 q^{71} +(1.83060 - 3.17068i) q^{72} +(3.82157 + 6.61916i) q^{73} +(0.556914 + 0.964604i) q^{74} +(-5.30777 + 9.19333i) q^{75} -2.61555 q^{76} +1.05863 q^{78} +(0.669405 - 1.15944i) q^{79} +(0.719824 + 1.24677i) q^{80} +(5.46896 + 9.47252i) q^{81} +(1.52932 - 2.64885i) q^{82} +16.3500 q^{83} -0.692226 q^{85} +(-2.68148 + 4.64447i) q^{86} +(5.87199 + 10.1706i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(3.45517 - 5.98452i) q^{89} -0.512889 q^{90} -10.3810 q^{92} +(7.90303 - 13.6884i) q^{93} +(2.02029 + 3.49925i) q^{94} +(0.389229 + 0.674164i) q^{95} +(5.43965 - 9.42175i) q^{96} +3.47068 q^{97} -4.63016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23}+ \cdots + 28 q^{99}+O(q^{100}) \) 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9 - 8 * q^10 - 2 * q^11 - 12 * q^12 - 6 * q^13 - 12 * q^15 + q^16 + 4 * q^17 + 15 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 + 5 * q^25 + q^26 + 16 * q^27 + 48 * q^29 - 20 * q^30 - 4 * q^31 - 7 * q^32 - 16 * q^33 - 28 * q^34 - 2 * q^36 - 10 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 + 20 * q^43 - 12 * q^44 + 22 * q^45 + 18 * q^46 - 8 * q^47 - 40 * q^48 - 30 * q^50 + 8 * q^51 + 3 * q^52 - 8 * q^53 + 32 * q^54 - 12 * q^55 - 4 * q^57 - 12 * q^58 - 4 * q^59 + 8 * q^60 - 6 * q^61 + 4 * q^62 - 34 * q^64 - 2 * q^65 + 12 * q^66 + 12 * q^67 + 22 * q^68 + 12 * q^69 - 12 * q^71 + q^72 - 10 * q^73 - 30 * q^74 - 16 * q^75 + 16 * q^76 + 8 * q^78 + 14 * q^79 - 14 * q^80 - 3 * q^81 + 10 * q^82 + 24 * q^83 - 20 * q^85 + 26 * q^86 - 26 * q^87 - 12 * q^88 + 2 * q^89 + 56 * q^90 - 24 * q^92 + 22 * q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 20 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more