LMFDB - Embedded newform 2214.2.i.b.901.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2214,2,Mod(901,2214)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2214, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2214.901"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2214 = 2 \cdot 3^{3} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2214.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$17.6788790075$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 738)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.5
Character	$\chi$	$=$	2214.901
Dual form			2214.2.i.b.1639.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.13494 + 1.96578i) q^{5} +(-4.05054 + 2.33858i) q^{7} -1.00000 q^{8} -2.26989 q^{10} +(-1.57221 + 0.907717i) q^{11} +(-0.198711 - 0.114726i) q^{13} +(-4.05054 - 2.33858i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.87362i q^{17} +2.36579i q^{19} +(-1.13494 - 1.96578i) q^{20} +(-1.57221 - 0.907717i) q^{22} +(0.946744 - 1.63981i) q^{23} +(-0.0761995 - 0.131981i) q^{25} -0.229452i q^{26} -4.67716i q^{28} +(-6.44774 + 3.72261i) q^{29} +(-0.460392 + 0.797423i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.22067 - 2.43681i) q^{34} -10.6166i q^{35} +3.19279 q^{37} +(-2.04884 + 1.18290i) q^{38} +(1.13494 - 1.96578i) q^{40} +(0.775456 - 6.35599i) q^{41} +(0.638021 + 1.10508i) q^{43} -1.81543i q^{44} +1.89349 q^{46} +(2.19645 - 1.26812i) q^{47} +(7.43793 - 12.8829i) q^{49} +(0.0761995 - 0.131981i) q^{50} +(0.198711 - 0.114726i) q^{52} +2.66180i q^{53} -4.12083i q^{55} +(4.05054 - 2.33858i) q^{56} +(-6.44774 - 3.72261i) q^{58} +(-3.32786 + 5.76402i) q^{59} +(2.29239 + 3.97053i) q^{61} -0.920785 q^{62} +1.00000 q^{64} +(0.451052 - 0.260415i) q^{65} +(0.268210 + 0.154851i) q^{67} +(4.22067 + 2.43681i) q^{68} +(9.19428 - 5.30832i) q^{70} -11.0540i q^{71} +14.4770 q^{73} +(1.59640 + 2.76504i) q^{74} +(-2.04884 - 1.18290i) q^{76} +(4.24554 - 7.35349i) q^{77} +(8.28272 - 4.78203i) q^{79} +2.26989 q^{80} +(5.89218 - 2.50643i) q^{82} +(-0.426481 - 0.738686i) q^{83} +(9.58047 + 5.53128i) q^{85} +(-0.638021 + 1.10508i) q^{86} +(1.57221 - 0.907717i) q^{88} -11.1698i q^{89} +1.07318 q^{91} +(0.946744 + 1.63981i) q^{92} +(2.19645 + 1.26812i) q^{94} +(-4.65063 - 2.68504i) q^{95} +(-7.13300 + 4.11824i) q^{97} +14.8759 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2214\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.13494	+	1.96578i	−0.507563	+	0.879124i	0.492399	+	0.870370i	$0.336120\pi$
$5$	−1.13494	+	1.96578i	−0.507563	+	0.879124i	−0.999962	+	0.00875484i	$0.997213\pi$
$6$		0			0
$7$	−4.05054	+	2.33858i	−1.53096	+	0.883901i	−0.531643	+	0.846968i	$0.678425\pi$
$7$	−4.05054	+	2.33858i	−1.53096	+	0.883901i	−0.999318	+	0.0369322i	$0.988241\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.26989			−0.717802
$11$	−1.57221	+	0.907717i	−0.474040	+	0.273687i	−0.717929	−	0.696116i	$-0.754910\pi$
$11$	−1.57221	+	0.907717i	−0.474040	+	0.273687i	0.243890	+	0.969803i	$0.421577\pi$
$12$		0			0
$13$	−0.198711	−	0.114726i	−0.0551125	−	0.0318192i	0.472191	−	0.881497i	$-0.343463\pi$
$13$	−0.198711	−	0.114726i	−0.0551125	−	0.0318192i	−0.527303	+	0.849677i	$0.676797\pi$
$14$	−4.05054	−	2.33858i	−1.08255	−	0.625012i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	4.87362i		−	1.18203i	−0.806662	−	0.591013i	$-0.798728\pi$
$17$		−	4.87362i		−	1.18203i	0.806662	−	0.591013i	$-0.201272\pi$
$18$		0			0
$19$			2.36579i			0.542750i	0.962474	+	0.271375i	$0.0874783\pi$
$19$			2.36579i			0.542750i	−0.962474	+	0.271375i	$0.912522\pi$
$20$	−1.13494	−	1.96578i	−0.253781	−	0.439562i
$21$		0			0
$22$	−1.57221	−	0.907717i	−0.335197	−	0.193526i
$23$	0.946744	−	1.63981i	0.197410	−	0.341924i	−0.750278	−	0.661122i	$-0.770080\pi$
$23$	0.946744	−	1.63981i	0.197410	−	0.341924i	0.947688	+	0.319199i	$0.103414\pi$
$24$		0			0
$25$	−0.0761995	−	0.131981i	−0.0152399	−	0.0263963i
$26$		−	0.229452i		−	0.0449992i
$27$		0			0
$28$		−	4.67716i		−	0.883901i
$29$	−6.44774	+	3.72261i	−1.19732	+	0.691271i	−0.959956	−	0.280151i	$-0.909615\pi$
$29$	−6.44774	+	3.72261i	−1.19732	+	0.691271i	−0.237360	+	0.971422i	$0.576282\pi$
$30$		0			0
$31$	−0.460392	+	0.797423i	−0.0826889	+	0.143221i	−0.904404	−	0.426677i	$-0.859684\pi$
$31$	−0.460392	+	0.797423i	−0.0826889	+	0.143221i	0.821715	+	0.569898i	$0.193017\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	4.22067	−	2.43681i	0.723840	−	0.417909i
$35$		−	10.6166i		−	1.79454i
$36$		0			0
$37$	3.19279			0.524892			0.262446	−	0.964947i	$-0.415471\pi$
$37$	3.19279			0.524892			0.262446	+	0.964947i	$0.415471\pi$
$38$	−2.04884	+	1.18290i	−0.332365	+	0.191891i
$39$		0			0
$40$	1.13494	−	1.96578i	0.179451	−	0.310817i
$41$	0.775456	−	6.35599i	0.121106	−	0.992640i
$41$	0.775456	−	6.35599i	0.121106	−	0.992640i
$42$		0			0
$43$	0.638021	+	1.10508i	0.0972973	+	0.168524i	0.910565	−	0.413366i	$-0.135647\pi$
$43$	0.638021	+	1.10508i	0.0972973	+	0.168524i	−0.813268	+	0.581890i	$0.802314\pi$
$44$		−	1.81543i		−	0.273687i
$45$		0			0
$46$	1.89349			0.279180
$47$	2.19645	−	1.26812i	0.320385	−	0.184975i	−0.331179	−	0.943568i	$-0.607446\pi$
$47$	2.19645	−	1.26812i	0.320385	−	0.184975i	0.651564	+	0.758593i	$0.274113\pi$
$48$		0			0
$49$	7.43793	−	12.8829i	1.06256	−	1.84041i
$50$	0.0761995	−	0.131981i	0.0107762	−	0.0186650i
$51$		0			0
$52$	0.198711	−	0.114726i	0.0275563	−	0.0159096i
$53$			2.66180i			0.365626i	0.983148	+	0.182813i	$0.0585203\pi$
$53$			2.66180i			0.365626i	−0.983148	+	0.182813i	$0.941480\pi$
$54$		0			0
$55$		−	4.12083i		−	0.555653i
$56$	4.05054	−	2.33858i	0.541276	−	0.312506i
$57$		0			0
$58$	−6.44774	−	3.72261i	−0.846630	−	0.488802i
$59$	−3.32786	+	5.76402i	−0.433251	+	0.750412i	−0.997151	−	0.0754307i	$-0.975967\pi$
$59$	−3.32786	+	5.76402i	−0.433251	+	0.750412i	0.563900	+	0.825843i	$0.309300\pi$
$60$		0			0
$61$	2.29239	+	3.97053i	0.293510	+	0.508375i	0.974637	−	0.223791i	$-0.0718432\pi$
$61$	2.29239	+	3.97053i	0.293510	+	0.508375i	−0.681127	+	0.732165i	$0.738510\pi$
$62$	−0.920785			−0.116940
$63$		0			0
$64$	1.00000			0.125000
$65$	0.451052	−	0.260415i	0.0559462	−	0.0323005i
$66$		0			0
$67$	0.268210	+	0.154851i	0.0327671	+	0.0189181i	0.516294	−	0.856411i	$-0.327311\pi$
$67$	0.268210	+	0.154851i	0.0327671	+	0.0189181i	−0.483527	+	0.875329i	$0.660644\pi$
$68$	4.22067	+	2.43681i	0.511832	+	0.295506i
$69$		0			0
$70$	9.19428	−	5.30832i	1.09893	−	0.634466i
$71$		−	11.0540i		−	1.31187i	−0.754818	−	0.655935i	$-0.772275\pi$
$71$		−	11.0540i		−	1.31187i	0.754818	−	0.655935i	$-0.227725\pi$
$72$		0			0
$73$	14.4770			1.69440			0.847200	−	0.531274i	$-0.178287\pi$
$73$	14.4770			1.69440			0.847200	+	0.531274i	$0.178287\pi$
$74$	1.59640	+	2.76504i	0.185577	+	0.321429i
$75$		0			0
$76$	−2.04884	−	1.18290i	−0.235018	−	0.135687i
$77$	4.24554	−	7.35349i	0.483824	−	0.838008i
$78$		0			0
$79$	8.28272	−	4.78203i	0.931879	−	0.538021i	0.0444736	−	0.999011i	$-0.485839\pi$
$79$	8.28272	−	4.78203i	0.931879	−	0.538021i	0.887405	+	0.460990i	$0.152506\pi$
$80$	2.26989			0.253781
$81$		0			0
$82$	5.89218	−	2.50643i	0.650683	−	0.276789i
$83$	−0.426481	−	0.738686i	−0.0468124	−	0.0810814i	0.841670	−	0.539993i	$-0.181573\pi$
$83$	−0.426481	−	0.738686i	−0.0468124	−	0.0810814i	−0.888482	+	0.458911i	$0.848240\pi$
$84$		0			0
$85$	9.58047	+	5.53128i	1.03915	+	0.599952i
$86$	−0.638021	+	1.10508i	−0.0687996	+	0.119164i
$87$		0			0
$88$	1.57221	−	0.907717i	0.167598	−	0.0967629i
$89$		−	11.1698i		−	1.18399i	−0.805941	−	0.591996i	$-0.798340\pi$
$89$		−	11.1698i		−	1.18399i	0.805941	−	0.591996i	$-0.201660\pi$
$90$		0			0
$91$	1.07318			0.112500
$92$	0.946744	+	1.63981i	0.0987049	+	0.170962i
$93$		0			0
$94$	2.19645	+	1.26812i	0.226547	+	0.130797i
$95$	−4.65063	−	2.68504i	−0.477145	−	0.275480i
$96$		0			0
$97$	−7.13300	+	4.11824i	−0.724247	+	0.418144i	−0.816314	−	0.577609i	$-0.803986\pi$
$97$	−7.13300	+	4.11824i	−0.724247	+	0.418144i	0.0920670	+	0.995753i	$0.470653\pi$
$98$	14.8759			1.50269
$99$		0			0
$100$	0.152399			0.0152399
$101$	−10.8456	+	6.26169i	−1.07917	+	0.623062i	−0.930674	−	0.365850i	$-0.880778\pi$
$101$	−10.8456	+	6.26169i	−1.07917	+	0.623062i	−0.148501	+	0.988912i	$0.547445\pi$
$102$		0			0
$103$	−5.50767	+	9.53956i	−0.542687	+	0.939961i	0.456062	+	0.889948i	$0.349260\pi$
$103$	−5.50767	+	9.53956i	−0.542687	+	0.939961i	−0.998749	+	0.0500128i	$0.984074\pi$
$104$	0.198711	+	0.114726i	0.0194852	+	0.0112498i
$105$		0			0
$106$	−2.30518	+	1.33090i	−0.223899	+	0.129268i
$107$	−14.8306			−1.43373			−0.716864	−	0.697213i	$-0.754423\pi$
$107$	−14.8306			−1.43373			−0.716864	+	0.697213i	$0.754423\pi$
$108$		0			0
$109$		−	12.9298i		−	1.23845i	−0.785212	−	0.619227i	$-0.787446\pi$
$109$		−	12.9298i		−	1.23845i	0.785212	−	0.619227i	$-0.212554\pi$
$110$	3.56875	−	2.06042i	0.340267	−	0.196453i
$111$		0			0
$112$	4.05054	+	2.33858i	0.382740	+	0.220975i
$113$	6.85832	−	11.8790i	0.645177	−	1.11748i	−0.339084	−	0.940756i	$-0.610117\pi$
$113$	6.85832	−	11.8790i	0.645177	−	1.11748i	0.984261	−	0.176722i	$-0.0565495\pi$
$114$		0			0
$115$	2.14900	+	3.72219i	0.200396	+	0.347096i
$116$		−	7.44521i		−	0.691271i
$117$		0			0
$118$	−6.65572			−0.612709
$119$	11.3973	+	19.7408i	1.04479	+	1.80963i
$120$		0			0
$121$	−3.85210	+	6.67203i	−0.350191	+	0.606549i
$122$	−2.29239	+	3.97053i	−0.207543	+	0.359475i
$123$		0			0
$124$	−0.460392	−	0.797423i	−0.0413444	−	0.0716107i
$125$	−11.0035			−0.984185
$126$		0			0
$127$	−19.9207			−1.76768			−0.883838	−	0.467793i	$-0.845049\pi$
$127$	−19.9207			−1.76768			−0.883838	+	0.467793i	$0.845049\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	0.451052	+	0.260415i	0.0395599	+	0.0228399i
$131$	11.0328	−	19.1093i	0.963937	−	1.66959i	0.251494	−	0.967859i	$-0.419078\pi$
$131$	11.0328	−	19.1093i	0.963937	−	1.66959i	0.712443	−	0.701730i	$-0.247589\pi$
$132$		0			0
$133$	−5.53260	−	9.58274i	−0.479737	−	0.830929i
$134$			0.309702i			0.0267542i
$135$		0			0
$136$			4.87362i			0.417909i
$137$	17.9752	−	10.3780i	1.53572	−	0.886651i	0.536642	−	0.843810i	$-0.319692\pi$
$137$	17.9752	−	10.3780i	1.53572	−	0.886651i	0.999082	−	0.0428410i	$-0.0136409\pi$
$138$		0			0
$139$	−8.74795	+	15.1519i	−0.741992	+	1.28517i	0.209596	+	0.977788i	$0.432785\pi$
$139$	−8.74795	+	15.1519i	−0.741992	+	1.28517i	−0.951587	+	0.307379i	$0.900548\pi$
$140$	9.19428	+	5.30832i	0.777059	+	0.448635i
$141$		0			0
$142$	9.57305	−	5.52700i	0.803353	−	0.463816i
$143$	0.416554			0.0348340
$144$		0			0
$145$		−	16.8998i		−	1.40345i
$146$	7.23848	+	12.5374i	0.599061	+	1.03760i
$147$		0			0
$148$	−1.59640	+	2.76504i	−0.131223	+	0.227285i
$149$	−7.52980	−	4.34733i	−0.616866	−	0.356148i	0.158782	−	0.987314i	$-0.449243\pi$
$149$	−7.52980	−	4.34733i	−0.616866	−	0.356148i	−0.775648	+	0.631166i	$0.782577\pi$
$150$		0			0
$151$	2.51055	−	1.44947i	0.204306	−	0.117956i	−0.394357	−	0.918957i	$-0.629033\pi$
$151$	2.51055	−	1.44947i	0.204306	−	0.117956i	0.598662	+	0.801002i	$0.295699\pi$
$152$		−	2.36579i		−	0.191891i
$153$		0			0
$154$	8.49108			0.684230
$155$	−1.04504	−	1.81006i	−0.0839396	−	0.145388i
$156$		0			0
$157$	−12.0274	−	6.94403i	−0.959892	−	0.554194i	−0.0637520	−	0.997966i	$-0.520307\pi$
$157$	−12.0274	−	6.94403i	−0.959892	−	0.554194i	−0.896140	+	0.443772i	$0.853640\pi$
$158$	8.28272	+	4.78203i	0.658938	+	0.380438i
$159$		0			0
$160$	1.13494	+	1.96578i	0.0897253	+	0.155409i
$161$			8.85615i			0.697963i
$162$		0			0
$163$	−12.3060			−0.963881			−0.481940	−	0.876204i	$-0.660068\pi$
$163$	−12.3060			−0.963881			−0.481940	+	0.876204i	$0.660068\pi$
$164$	5.11672	+	3.84956i	0.399549	+	0.300600i
$165$		0			0
$166$	0.426481	−	0.738686i	0.0331013	−	0.0573332i
$167$	−11.9934	−	6.92439i	−0.928076	−	0.535825i	−0.0418736	−	0.999123i	$-0.513333\pi$
$167$	−11.9934	−	6.92439i	−0.928076	−	0.535825i	−0.886203	+	0.463298i	$0.846666\pi$
$168$		0			0
$169$	−6.47368	−	11.2127i	−0.497975	−	0.862518i
$170$			11.0626i			0.848460i
$171$		0			0
$172$	−1.27604			−0.0972973
$173$	−3.53125	−	6.11630i	−0.268476	−	0.465013i	0.699993	−	0.714150i	$-0.253187\pi$
$173$	−3.53125	−	6.11630i	−0.268476	−	0.465013i	−0.968468	+	0.249137i	$0.919853\pi$
$174$		0			0
$175$	0.617298	+	0.356397i	0.0466634	+	0.0269411i
$176$	1.57221	+	0.907717i	0.118510	+	0.0684217i
$177$		0			0
$178$	9.67329	−	5.58488i	0.725044	−	0.418604i
$179$		−	0.495257i		−	0.0370172i	−0.999829	−	0.0185086i	$-0.994108\pi$
$179$		−	0.495257i		−	0.0370172i	0.999829	−	0.0185086i	$-0.00589181\pi$
$180$		0			0
$181$			12.1145i			0.900466i	0.892911	+	0.450233i	$0.148659\pi$
$181$			12.1145i			0.900466i	−0.892911	+	0.450233i	$0.851341\pi$
$182$	0.536592	+	0.929404i	0.0397748	+	0.0688920i
$183$		0			0
$184$	−0.946744	+	1.63981i	−0.0697949	+	0.120888i
$185$	−3.62364	+	6.27633i	−0.266416	+	0.461445i
$186$		0			0
$187$	4.42386	+	7.66235i	0.323505	+	0.560327i
$188$			2.53624i			0.184975i
$189$		0			0
$190$		−	5.37008i		−	0.389587i
$191$	−20.2474	+	11.6898i	−1.46505	+	0.845847i	−0.999238	−	0.0390358i	$-0.987571\pi$
$191$	−20.2474	+	11.6898i	−1.46505	+	0.845847i	−0.465813	+	0.884883i	$0.654238\pi$
$192$		0			0
$193$	5.47675	+	3.16200i	0.394225	+	0.227606i	0.683989	−	0.729492i	$-0.260244\pi$
$193$	5.47675	+	3.16200i	0.394225	+	0.227606i	−0.289764	+	0.957098i	$0.593577\pi$
$194$	−7.13300	−	4.11824i	−0.512120	−	0.295672i
$195$		0			0
$196$	7.43793	+	12.8829i	0.531280	+	0.920205i
$197$	10.3632			0.738351			0.369175	−	0.929360i	$-0.379640\pi$
$197$	10.3632			0.738351			0.369175	+	0.929360i	$0.379640\pi$
$198$		0			0
$199$			13.3331i			0.945160i	0.881288	+	0.472580i	$0.156677\pi$
$199$			13.3331i			0.945160i	−0.881288	+	0.472580i	$0.843323\pi$
$200$	0.0761995	+	0.131981i	0.00538812	+	0.00933249i
$201$		0			0
$202$	−10.8456	−	6.26169i	−0.763092	−	0.440571i
$203$	17.4112	−	30.1571i	1.22203	−	2.11662i
$204$		0			0
$205$	11.6144	+	8.73808i	0.811185	+	0.610294i
$206$	−11.0153			−0.767475
$207$		0			0
$208$			0.229452i			0.0159096i
$209$	−2.14747	−	3.71952i	−0.148543	−	0.257285i
$210$		0			0
$211$	3.05349	+	1.76293i	0.210211	+	0.121365i	0.601409	−	0.798941i	$-0.294606\pi$
$211$	3.05349	+	1.76293i	0.210211	+	0.121365i	−0.391198	+	0.920306i	$0.627939\pi$
$212$	−2.30518	−	1.33090i	−0.158321	−	0.0914065i
$213$		0			0
$214$	−7.41530	−	12.8437i	−0.506900	−	0.877976i
$215$	−2.89647			−0.197538
$216$		0			0
$217$		−	4.30666i		−	0.292355i
$218$	11.1976	−	6.46492i	0.758395	−	0.437859i
$219$		0			0
$220$	3.56875	+	2.06042i	0.240605	+	0.138913i
$221$	−0.559130	+	0.968442i	−0.0376112	+	0.0651444i
$222$		0			0
$223$	10.8103	+	18.7239i	0.723909	+	1.25385i	0.959421	+	0.281976i	$0.0909898\pi$
$223$	10.8103	+	18.7239i	0.723909	+	1.25385i	−0.235512	+	0.971871i	$0.575677\pi$
$224$			4.67716i			0.312506i
$225$		0			0
$226$	13.7166			0.912417
$227$	−4.54274	+	2.62275i	−0.301513	+	0.174078i	−0.643122	−	0.765764i	$-0.722361\pi$
$227$	−4.54274	+	2.62275i	−0.301513	+	0.174078i	0.341610	+	0.939842i	$0.389028\pi$
$228$		0			0
$229$	−6.66016	−	3.84524i	−0.440116	−	0.254101i	0.263531	−	0.964651i	$-0.415113\pi$
$229$	−6.66016	−	3.84524i	−0.440116	−	0.254101i	−0.703647	+	0.710550i	$0.748446\pi$
$230$	−2.14900	+	3.72219i	−0.141701	+	0.245434i
$231$		0			0
$232$	6.44774	−	3.72261i	0.423315	−	0.244401i
$233$			11.2106i			0.734433i	0.930136	+	0.367216i	$0.119689\pi$
$233$			11.2106i			0.734433i	−0.930136	+	0.367216i	$0.880311\pi$
$234$		0			0
$235$			5.75699i			0.375545i
$236$	−3.32786	−	5.76402i	−0.216625	−	0.375206i
$237$		0			0
$238$	−11.3973	+	19.7408i	−0.738780	+	1.27960i
$239$	7.06868	+	4.08110i	0.457235	+	0.263985i	0.710881	−	0.703313i	$-0.248297\pi$
$239$	7.06868	+	4.08110i	0.457235	+	0.263985i	−0.253646	+	0.967297i	$0.581630\pi$
$240$		0			0
$241$	−8.85183	−	15.3318i	−0.570196	−	0.987609i	−0.996545	−	0.0830502i	$-0.973534\pi$
$241$	−8.85183	−	15.3318i	−0.570196	−	0.987609i	0.426349	−	0.904559i	$-0.359800\pi$
$242$	−7.70420			−0.495245
$243$		0			0
$244$	−4.58478			−0.293510
$245$	16.8833	+	29.2427i	1.07863	+	1.86825i
$246$		0			0
$247$	0.271418	−	0.470109i	0.0172699	−	0.0299123i
$248$	0.460392	−	0.797423i	0.0292349	−	0.0506364i
$249$		0			0
$250$	−5.50176	−	9.52933i	−0.347962	−	0.602688i
$251$	−11.8754			−0.749570			−0.374785	−	0.927112i	$-0.622283\pi$
$251$	−11.8754			−0.749570			−0.374785	+	0.927112i	$0.622283\pi$
$252$		0			0
$253$			3.43750i			0.216114i
$254$	−9.96035	−	17.2518i	−0.624968	−	1.08248i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−26.4839	−	15.2905i	−1.65202	−	0.953793i	−0.976241	−	0.216685i	$-0.930475\pi$
$257$	−26.4839	−	15.2905i	−1.65202	−	0.953793i	−0.675776	−	0.737107i	$-0.736191\pi$
$258$		0			0
$259$	−12.9325	+	7.46661i	−0.803589	+	0.463952i
$260$			0.520830i			0.0323005i
$261$		0			0
$262$	22.0655			1.36321
$263$	−7.67620	+	4.43186i	−0.473335	+	0.273280i	−0.717635	−	0.696420i	$-0.754775\pi$
$263$	−7.67620	+	4.43186i	−0.473335	+	0.273280i	0.244300	+	0.969700i	$0.421442\pi$
$264$		0			0
$265$	−5.23251	−	3.02099i	−0.321431	−	0.185578i
$266$	5.53260	−	9.58274i	0.339225	−	0.587555i
$267$		0			0
$268$	−0.268210	+	0.154851i	−0.0163835	+	0.00945903i
$269$	−9.90420			−0.603870			−0.301935	−	0.953329i	$-0.597633\pi$
$269$	−9.90420			−0.603870			−0.301935	+	0.953329i	$0.597633\pi$
$270$		0			0
$271$	23.5691			1.43172			0.715860	−	0.698244i	$-0.246035\pi$
$271$	23.5691			1.43172			0.715860	+	0.698244i	$0.246035\pi$
$272$	−4.22067	+	2.43681i	−0.255916	+	0.147753i
$273$		0			0
$274$	17.9752	+	10.3780i	1.08592	+	0.626957i
$275$	0.239603	+	0.138335i	0.0144486	+	0.00834192i
$276$		0			0
$277$	−6.55204	−	11.3485i	−0.393674	−	0.681864i	0.599257	−	0.800557i	$-0.295463\pi$
$277$	−6.55204	−	11.3485i	−0.393674	−	0.681864i	−0.992931	+	0.118693i	$0.962129\pi$
$278$	−17.4959			−1.04933
$279$		0			0
$280$			10.6166i			0.634466i
$281$	−5.76890	+	3.33068i	−0.344144	+	0.198691i	−0.662103	−	0.749413i	$-0.730336\pi$
$281$	−5.76890	+	3.33068i	−0.344144	+	0.198691i	0.317959	+	0.948104i	$0.397002\pi$
$282$		0			0
$283$	8.23872	−	14.2699i	0.489741	−	0.848256i	−0.510189	−	0.860062i	$-0.670425\pi$
$283$	8.23872	−	14.2699i	0.489741	−	0.848256i	0.999930	+	0.0118060i	$0.00375806\pi$
$284$	9.57305	+	5.52700i	0.568056	+	0.327967i
$285$		0			0
$286$	0.208277	+	0.360747i	0.0123157	+	0.0213314i
$287$	11.7230	+	27.5587i	0.691986	+	1.62674i
$288$		0			0
$289$	−6.75213			−0.397184
$290$	14.6357	−	8.44990i	0.859436	−	0.496195i
$291$		0			0
$292$	−7.23848	+	12.5374i	−0.423600	+	0.733697i
$293$	17.3990	+	10.0453i	1.01646	+	0.586855i	0.913077	−	0.407787i	$-0.133699\pi$
$293$	17.3990	+	10.0453i	1.01646	+	0.586855i	0.103385	+	0.994641i	$0.467033\pi$
$294$		0			0
$295$	−7.55388	−	13.0837i	−0.439804	−	0.761762i
$296$	−3.19279			−0.185577
$297$		0			0
$298$		−	8.69467i		−	0.503669i
$299$	−0.376257	+	0.217232i	−0.0217595	+	0.0125629i
$300$		0			0
$301$	−5.16866	−	2.98413i	−0.297917	−	0.172002i
$302$	2.51055	+	1.44947i	0.144466	+	0.0834074i
$303$		0			0
$304$	2.04884	−	1.18290i	0.117509	−	0.0678437i
$305$	−10.4069			−0.595900
$306$		0			0
$307$	−3.85257			−0.219878			−0.109939	−	0.993938i	$-0.535065\pi$
$307$	−3.85257			−0.219878			−0.109939	+	0.993938i	$0.535065\pi$
$308$	4.24554	+	7.35349i	0.241912	+	0.419004i
$309$		0			0
$310$	1.04504	−	1.81006i	0.0593543	−	0.102805i
$311$	12.8184	+	7.40068i	0.726862	+	0.419654i	0.817273	−	0.576250i	$-0.195485\pi$
$311$	12.8184	+	7.40068i	0.726862	+	0.419654i	−0.0904109	+	0.995905i	$0.528818\pi$
$312$		0			0
$313$	−17.7169	+	10.2288i	−1.00142	+	0.578168i	−0.908667	−	0.417521i	$-0.862899\pi$
$313$	−17.7169	+	10.2288i	−1.00142	+	0.578168i	−0.0927496	+	0.995689i	$0.529566\pi$
$314$		−	13.8881i		−	0.783748i
$315$		0			0
$316$			9.56406i			0.538021i
$317$	4.00247	−	2.31083i	0.224801	−	0.129789i	−0.383370	−	0.923595i	$-0.625237\pi$
$317$	4.00247	−	2.31083i	0.224801	−	0.129789i	0.608171	+	0.793806i	$0.291903\pi$
$318$		0			0
$319$	6.75814	−	11.7054i	0.378383	−	0.655379i
$320$	−1.13494	+	1.96578i	−0.0634453	+	0.109891i
$321$		0			0
$322$	−7.66965	+	4.42808i	−0.427413	+	0.246767i
$323$	11.5300			0.641544
$324$		0			0
$325$			0.0349682i			0.00193969i
$326$	−6.15300	−	10.6573i	−0.340783	−	0.590254i
$327$		0			0
$328$	−0.775456	+	6.35599i	−0.0428174	+	0.350951i
$329$	−5.93121	+	10.2732i	−0.326998	+	0.566378i
$330$		0			0
$331$	12.4712	−	7.20025i	0.685479	−	0.395761i	−0.116437	−	0.993198i	$-0.537147\pi$
$331$	12.4712	−	7.20025i	0.685479	−	0.395761i	0.801916	+	0.597437i	$0.203814\pi$
$332$	0.852962			0.0468124
$333$		0			0
$334$		−	13.8488i		−	0.757771i
$335$	−0.608807	+	0.351495i	−0.0332627	+	0.0192042i
$336$		0			0
$337$	15.4958	−	26.8395i	0.844111	−	1.46204i	−0.0422807	−	0.999106i	$-0.513462\pi$
$337$	15.4958	−	26.8395i	0.844111	−	1.46204i	0.886391	−	0.462937i	$-0.153204\pi$
$338$	6.47368	−	11.2127i	0.352122	−	0.609892i
$339$		0			0
$340$	−9.58047	+	5.53128i	−0.519574	+	0.299976i
$341$		−	1.67162i		−	0.0905235i
$342$		0			0
$343$			36.8366i			1.98899i
$344$	−0.638021	−	1.10508i	−0.0343998	−	0.0595822i
$345$		0			0
$346$	3.53125	−	6.11630i	0.189841	−	0.328814i
$347$	27.0689	+	15.6283i	1.45314	+	0.838969i	0.998658	−	0.0517890i	$-0.0164923\pi$
$347$	27.0689	+	15.6283i	1.45314	+	0.838969i	0.454478	+	0.890758i	$0.349826\pi$
$348$		0			0
$349$	−15.9676	−	27.6567i	−0.854725	−	1.48043i	−0.876900	−	0.480673i	$-0.840392\pi$
$349$	−15.9676	−	27.6567i	−0.854725	−	1.48043i	0.0221745	−	0.999754i	$-0.492941\pi$
$350$			0.712795i			0.0381005i
$351$		0			0
$352$			1.81543i			0.0967629i
$353$	0.174178	+	0.301685i	0.00927056	+	0.0160571i	0.870623	−	0.491950i	$-0.163716\pi$
$353$	0.174178	+	0.301685i	0.00927056	+	0.0160571i	−0.861353	+	0.508007i	$0.830382\pi$
$354$		0			0
$355$	21.7298	+	12.5457i	1.15330	+	0.665856i
$356$	9.67329	+	5.58488i	0.512684	+	0.295998i
$357$		0			0
$358$	0.428905	−	0.247629i	0.0226683	−	0.0130876i
$359$	−16.4128			−0.866236			−0.433118	−	0.901337i	$-0.642587\pi$
$359$	−16.4128			−0.866236			−0.433118	+	0.901337i	$0.642587\pi$
$360$		0			0
$361$	13.4030			0.705423
$362$	−10.4915	+	6.05727i	−0.551421	+	0.318363i
$363$		0			0
$364$	−0.536592	+	0.929404i	−0.0281251	+	0.0487140i
$365$	−16.4305	+	28.4585i	−0.860014	+	1.48959i
$366$		0			0
$367$	−0.716065	−	1.24026i	−0.0373783	−	0.0647411i	0.846731	−	0.532021i	$-0.178567\pi$
$367$	−0.716065	−	1.24026i	−0.0373783	−	0.0647411i	−0.884109	+	0.467280i	$0.845234\pi$
$368$	−1.89349			−0.0987049
$369$		0			0
$370$	−7.24729			−0.376769
$371$	−6.22483	−	10.7817i	−0.323177	−	0.559759i
$372$		0			0
$373$	−1.38459	+	2.39818i	−0.0716915	+	0.124173i	−0.899643	−	0.436627i	$-0.856173\pi$
$373$	−1.38459	+	2.39818i	−0.0716915	+	0.124173i	0.827951	+	0.560800i	$0.189506\pi$
$374$	−4.42386	+	7.66235i	−0.228752	+	0.396211i
$375$		0			0
$376$	−2.19645	+	1.26812i	−0.113273	+	0.0653984i
$377$	1.70832			0.0879828
$378$		0			0
$379$	−31.8314			−1.63507			−0.817535	−	0.575879i	$-0.804660\pi$
$379$	−31.8314			−1.63507			−0.817535	+	0.575879i	$0.804660\pi$
$380$	4.65063	−	2.68504i	0.238572	−	0.137740i
$381$		0			0
$382$	−20.2474	−	11.6898i	−1.03595	−	0.598104i
$383$	−8.07725	−	4.66340i	−0.412728	−	0.238289i	0.279233	−	0.960223i	$-0.409920\pi$
$383$	−8.07725	−	4.66340i	−0.412728	−	0.238289i	−0.691961	+	0.721935i	$0.743253\pi$
$384$		0			0
$385$	9.63690	+	16.6916i	0.491142	+	0.850683i
$386$			6.32401i			0.321883i
$387$		0			0
$388$		−	8.23648i		−	0.418144i
$389$	3.56411	+	6.17321i	0.180707	+	0.312994i	0.942122	−	0.335271i	$-0.108828\pi$
$389$	3.56411	+	6.17321i	0.180707	+	0.312994i	−0.761414	+	0.648266i	$0.775495\pi$
$390$		0			0
$391$	−7.99180	−	4.61407i	−0.404163	−	0.233343i
$392$	−7.43793	+	12.8829i	−0.375672	+	0.650683i
$393$		0			0
$394$	5.18162	+	8.97484i	0.261046	+	0.452146i
$395$			21.7094i			1.09232i
$396$		0			0
$397$			31.2555i			1.56867i	0.620339	+	0.784334i	$0.286995\pi$
$397$			31.2555i			1.56867i	−0.620339	+	0.784334i	$0.713005\pi$
$398$	−11.5468	+	6.66656i	−0.578790	+	0.334164i
$399$		0			0
$400$	−0.0761995	+	0.131981i	−0.00380997	+	0.00659907i
$401$	−7.03829	+	12.1907i	−0.351475	+	0.608773i	−0.986508	−	0.163712i	$-0.947653\pi$
$401$	−7.03829	+	12.1907i	−0.351475	+	0.608773i	0.635033	+	0.772485i	$0.280987\pi$
$402$		0			0
$403$	0.182970	−	0.105638i	0.00911439	−	0.00526220i
$404$		−	12.5234i		−	0.623062i
$405$		0			0
$406$	34.8225			1.72821
$407$	−5.01974	+	2.89815i	−0.248820	+	0.143656i
$408$		0			0
$409$	−6.18056	+	10.7050i	−0.305609	+	0.529330i	−0.977397	−	0.211413i	$-0.932193\pi$
$409$	−6.18056	+	10.7050i	−0.305609	+	0.529330i	0.671788	+	0.740744i	$0.265527\pi$
$410$	−1.76020	+	14.4274i	−0.0869301	+	0.712519i
$411$		0			0
$412$	−5.50767	−	9.53956i	−0.271343	−	0.469980i
$413$		−	31.1299i		−	1.53180i
$414$		0			0
$415$	1.93613			0.0950408
$416$	−0.198711	+	0.114726i	−0.00974261	+	0.00562490i
$417$		0			0
$418$	2.14747	−	3.71952i	0.105036	−	0.181928i
$419$	2.41507	−	4.18302i	0.117984	−	0.204354i	−0.800985	−	0.598685i	$-0.795690\pi$
$419$	2.41507	−	4.18302i	0.117984	−	0.204354i	0.918969	+	0.394331i	$0.129024\pi$
$420$		0			0
$421$	−6.14525	+	3.54796i	−0.299501	+	0.172917i	−0.642219	−	0.766521i	$-0.721986\pi$
$421$	−6.14525	+	3.54796i	−0.299501	+	0.172917i	0.342718	+	0.939438i	$0.388653\pi$
$422$			3.52587i			0.171637i
$423$		0			0
$424$		−	2.66180i		−	0.129268i
$425$	−0.643226	+	0.371367i	−0.0312011	+	0.0180139i
$426$		0			0
$427$	−18.5708	−	10.7219i	−0.898705	−	0.518868i
$428$	7.41530	−	12.8437i	0.358432	−	0.620823i
$429$		0			0
$430$	−1.44824	−	2.50842i	−0.0698402	−	0.120967i
$431$	4.65150			0.224055			0.112027	−	0.993705i	$-0.464266\pi$
$431$	4.65150			0.224055			0.112027	+	0.993705i	$0.464266\pi$
$432$		0			0
$433$	19.0392			0.914967			0.457483	−	0.889218i	$-0.348751\pi$
$433$	19.0392			0.914967			0.457483	+	0.889218i	$0.348751\pi$
$434$	3.72968	−	2.15333i	0.179030	−	0.103363i
$435$		0			0
$436$	11.1976	+	6.46492i	0.536266	+	0.309613i
$437$	3.87945	+	2.23980i	0.185579	+	0.107144i
$438$		0			0
$439$	30.9160	−	17.8493i	1.47554	−	0.851902i	0.475919	−	0.879489i	$-0.342116\pi$
$439$	30.9160	−	17.8493i	1.47554	−	0.851902i	0.999619	+	0.0275867i	$0.00878225\pi$
$440$			4.12083i			0.196453i
$441$		0			0
$442$	−1.11826			−0.0531902
$443$	16.1081	+	27.9000i	0.765318	+	1.32557i	0.940078	+	0.340959i	$0.110752\pi$
$443$	16.1081	+	27.9000i	0.765318	+	1.32557i	−0.174760	+	0.984611i	$0.555915\pi$
$444$		0			0
$445$	21.9573	+	12.6771i	1.04088	+	0.600950i
$446$	−10.8103	+	18.7239i	−0.511881	+	0.886604i
$447$		0			0
$448$	−4.05054	+	2.33858i	−0.191370	+	0.110488i
$449$	5.88404			0.277685			0.138843	−	0.990314i	$-0.455662\pi$
$449$	5.88404			0.277685			0.138843	+	0.990314i	$0.455662\pi$
$450$		0			0
$451$	4.55026	+	10.6969i	0.214263	+	0.503695i
$452$	6.85832	+	11.8790i	0.322588	+	0.558739i
$453$		0			0
$454$	−4.54274	−	2.62275i	−0.213202	−	0.123092i
$455$	−1.21800	+	2.10964i	−0.0571009	+	0.0989017i
$456$		0			0
$457$	−11.2356	+	6.48687i	−0.525579	+	0.303443i	−0.739214	−	0.673470i	$-0.764803\pi$
$457$	−11.2356	+	6.48687i	−0.525579	+	0.303443i	0.213635	+	0.976913i	$0.431470\pi$
$458$		−	7.69049i		−	0.359353i
$459$		0			0
$460$	−4.29801			−0.200396
$461$	−16.9376	−	29.3368i	−0.788863	−	1.36635i	−0.926664	−	0.375891i	$-0.877337\pi$
$461$	−16.9376	−	29.3368i	−0.788863	−	1.36635i	0.137800	−	0.990460i	$-0.455997\pi$
$462$		0			0
$463$	25.9941	+	15.0077i	1.20805	+	0.697468i	0.962333	−	0.271874i	$-0.0876434\pi$
$463$	25.9941	+	15.0077i	1.20805	+	0.697468i	0.245717	+	0.969342i	$0.420977\pi$
$464$	6.44774	+	3.72261i	0.299329	+	0.172818i
$465$		0			0
$466$	−9.70869	+	5.60531i	−0.449746	+	0.259661i
$467$	−13.0504			−0.603900			−0.301950	−	0.953324i	$-0.597638\pi$
$467$	−13.0504			−0.603900			−0.301950	+	0.953324i	$0.597638\pi$
$468$		0			0
$469$	−1.44853			−0.0668868
$470$	−4.98570	+	2.87850i	−0.229973	+	0.132775i
$471$		0			0
$472$	3.32786	−	5.76402i	0.153177	−	0.265311i
$473$	−2.00621	−	1.15828i	−0.0922455	−	0.0532580i
$474$		0			0
$475$	0.312240	−	0.180272i	0.0143266	−	0.00827145i
$476$	−22.7947			−1.04479
$477$		0			0
$478$			8.16220i			0.373331i
$479$	2.68307	−	1.54907i	0.122593	−	0.0707790i	−0.437450	−	0.899243i	$-0.644118\pi$
$479$	2.68307	−	1.54907i	0.122593	−	0.0707790i	0.560042	+	0.828464i	$0.310785\pi$
$480$		0			0
$481$	−0.634443	−	0.366296i	−0.0289281	−	0.0167017i
$482$	8.85183	−	15.3318i	0.403190	−	0.698345i
$483$		0			0
$484$	−3.85210	−	6.67203i	−0.175096	−	0.303274i
$485$		−	18.6959i		−	0.848937i
$486$		0			0
$487$	−25.3738			−1.14980			−0.574898	−	0.818225i	$-0.694958\pi$
$487$	−25.3738			−1.14980			−0.574898	+	0.818225i	$0.694958\pi$
$488$	−2.29239	−	3.97053i	−0.103772	−	0.179738i
$489$		0			0
$490$	−16.8833	+	29.2427i	−0.762708	+	1.32105i
$491$	−6.22441	+	10.7810i	−0.280904	+	0.486539i	−0.971608	−	0.236598i	$-0.923967\pi$
$491$	−6.22441	+	10.7810i	−0.280904	+	0.486539i	0.690704	+	0.723138i	$0.257301\pi$
$492$		0			0
$493$	18.1425	+	31.4238i	0.817099	+	1.41526i
$494$	0.542835			0.0244233
$495$		0			0
$496$	0.920785			0.0413444
$497$	25.8507	+	44.7747i	1.15956	+	2.00842i
$498$		0			0
$499$	−30.8418	−	17.8065i	−1.38067	−	0.797130i	−0.388431	−	0.921478i	$-0.626983\pi$
$499$	−30.8418	−	17.8065i	−1.38067	−	0.797130i	−0.992239	+	0.124347i	$0.960316\pi$
$500$	5.50176	−	9.52933i	0.246046	−	0.426164i
$501$		0			0
$502$	−5.93771	−	10.2844i	−0.265013	−	0.459016i
$503$			7.82992i			0.349119i	0.984647	+	0.174559i	$0.0558501\pi$
$503$			7.82992i			0.349119i	−0.984647	+	0.174559i	$0.944150\pi$
$504$		0			0
$505$		−	28.4267i		−	1.26497i
$506$	−2.97696	+	1.71875i	−0.132342	+	0.0764078i
$507$		0			0
$508$	9.96035	−	17.2518i	0.441919	−	0.765426i
$509$	13.0841	+	7.55408i	0.579941	+	0.334829i	0.761110	−	0.648623i	$-0.224655\pi$
$509$	13.0841	+	7.55408i	0.579941	+	0.334829i	−0.181169	+	0.983452i	$0.557988\pi$
$510$		0			0
$511$	−58.6395	+	33.8555i	−2.59406	+	1.49768i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		−	30.5809i		−	1.34887i
$515$	−12.5018	−	21.6538i	−0.550895	−	0.954178i
$516$		0			0
$517$	−2.30219	+	3.98751i	−0.101250	+	0.175370i
$518$	−12.9325	−	7.46661i	−0.568223	−	0.328064i
$519$		0			0
$520$	−0.451052	+	0.260415i	−0.0197800	+	0.0114200i
$521$		−	23.1947i		−	1.01618i	−0.861305	−	0.508089i	$-0.830352\pi$
$521$		−	23.1947i		−	1.01618i	0.861305	−	0.508089i	$-0.169648\pi$
$522$		0			0
$523$	−41.0169			−1.79354			−0.896771	−	0.442495i	$-0.854093\pi$
$523$	−41.0169			−1.79354			−0.896771	+	0.442495i	$0.854093\pi$
$524$	11.0328	+	19.1093i	0.481969	+	0.834794i
$525$		0			0
$526$	−7.67620	−	4.43186i	−0.334698	−	0.193238i
$527$	3.88633	+	2.24377i	0.169291	+	0.0977404i
$528$		0			0
$529$	9.70735	+	16.8136i	0.422059	+	0.731027i
$530$		−	6.04199i		−	0.262447i
$531$		0			0
$532$	11.0652			0.479737
$533$	−0.883289	+	1.17404i	−0.0382595	+	0.0508534i
$534$		0			0
$535$	16.8319	−	29.1537i	0.727707	−	1.26043i
$536$	−0.268210	−	0.154851i	−0.0115849	−	0.00668855i
$537$		0			0
$538$	−4.95210	−	8.57729i	−0.213500	−	0.369793i
$539$			27.0061i			1.16324i
$540$		0			0
$541$	−39.2083			−1.68570			−0.842849	−	0.538150i	$-0.819123\pi$
$541$	−39.2083			−1.68570			−0.842849	+	0.538150i	$0.819123\pi$
$542$	11.7845	+	20.4114i	0.506190	+	0.876746i
$543$		0			0
$544$	−4.22067	−	2.43681i	−0.180960	−	0.104477i
$545$	25.4172	+	14.6746i	1.08875	+	0.628593i
$546$		0			0
$547$	27.8247	−	16.0646i	1.18970	−	0.686872i	0.231460	−	0.972844i	$-0.425650\pi$
$547$	27.8247	−	16.0646i	1.18970	−	0.686872i	0.958238	+	0.285972i	$0.0923165\pi$
$548$			20.7560i			0.886651i
$549$		0			0
$550$			0.276670i			0.0117973i
$551$	−8.80691	−	15.2540i	−0.375187	−	0.649843i
$552$		0			0
$553$	−22.3663	+	38.7396i	−0.951113	+	1.64738i
$554$	6.55204	−	11.3485i	0.278370	−	0.482150i
$555$		0			0
$556$	−8.74795	−	15.1519i	−0.370996	−	0.642584i
$557$			21.6738i			0.918347i	0.888347	+	0.459174i	$0.151854\pi$
$557$			21.6738i			0.918347i	−0.888347	+	0.459174i	$0.848146\pi$
$558$		0			0
$559$		−	0.292790i		−	0.0123837i
$560$	−9.19428	+	5.30832i	−0.388529	+	0.224318i
$561$		0			0
$562$	−5.76890	−	3.33068i	−0.243346	−	0.140496i
$563$	1.76970	+	1.02174i	0.0745840	+	0.0430611i	0.536828	−	0.843692i	$-0.319622\pi$
$563$	1.76970	+	1.02174i	0.0745840	+	0.0430611i	−0.462244	+	0.886753i	$0.652956\pi$
$564$		0			0
$565$	15.5676	+	26.9639i	0.654935	+	1.13438i
$566$	16.4774			0.692598
$567$		0			0
$568$			11.0540i			0.463816i
$569$	−19.7330	−	34.1785i	−0.827249	−	1.43284i	−0.900188	−	0.435501i	$-0.856571\pi$
$569$	−19.7330	−	34.1785i	−0.827249	−	1.43284i	0.0729396	−	0.997336i	$-0.476762\pi$
$570$		0			0
$571$	−17.6743	−	10.2043i	−0.739647	−	0.427035i	0.0822941	−	0.996608i	$-0.473775\pi$
$571$	−17.6743	−	10.2043i	−0.739647	−	0.427035i	−0.821941	+	0.569573i	$0.807109\pi$
$572$	−0.208277	+	0.360747i	−0.00870851	+	0.0150836i
$573$		0			0
$574$	−18.0050	+	23.9318i	−0.751515	+	0.998892i
$575$	−0.288566			−0.0120340
$576$		0			0
$577$		−	34.5880i		−	1.43992i	−0.694018	−	0.719958i	$-0.744161\pi$
$577$		−	34.5880i		−	1.43992i	0.694018	−	0.719958i	$-0.255839\pi$
$578$	−3.37606	−	5.84751i	−0.140426	−	0.243224i
$579$		0			0
$580$	14.6357	+	8.44990i	0.607713	+	0.350863i
$581$	3.45496	+	1.99472i	0.143336	+	0.0827549i
$582$		0			0
$583$	−2.41616	−	4.18491i	−0.100067	−	0.173321i
$584$	−14.4770			−0.599061
$585$		0			0
$586$			20.0907i			0.829938i
$587$	−13.3335	+	7.69810i	−0.550332	+	0.317735i	−0.749256	−	0.662280i	$-0.769589\pi$
$587$	−13.3335	+	7.69810i	−0.550332	+	0.317735i	0.198924	+	0.980015i	$0.436255\pi$
$588$		0			0
$589$	−1.88654	−	1.08919i	−0.0777334	−	0.0448794i
$590$	7.55388	−	13.0837i	0.310988	−	0.538647i
$591$		0			0
$592$	−1.59640	−	2.76504i	−0.0656115	−	0.113642i
$593$		−	29.4528i		−	1.20948i	−0.796423	−	0.604740i	$-0.793277\pi$
$593$		−	29.4528i		−	1.20948i	0.796423	−	0.604740i	$-0.206723\pi$
$594$		0			0
$595$	−51.7414			−2.12119
$596$	7.52980	−	4.34733i	0.308433	−	0.178074i
$597$		0			0
$598$	−0.376257	−	0.217232i	−0.0153863	−	0.00888328i
$599$	−9.85804	+	17.0746i	−0.402789	+	0.697651i	−0.994061	−	0.108821i	$-0.965292\pi$
$599$	−9.85804	+	17.0746i	−0.402789	+	0.697651i	0.591273	+	0.806472i	$0.298626\pi$
$600$		0			0
$601$	−34.2325	+	19.7641i	−1.39637	+	0.806196i	−0.994011	−	0.109284i	$-0.965144\pi$
$601$	−34.2325	+	19.7641i	−1.39637	+	0.806196i	−0.402362	+	0.915481i	$0.631811\pi$
$602$		−	5.96826i		−	0.243248i
$603$		0			0
$604$			2.89893i			0.117956i
$605$	−8.74384	−	15.1448i	−0.355488	−	0.615723i
$606$		0			0
$607$	6.48249	−	11.2280i	0.263116	−	0.455730i	−0.703952	−	0.710247i	$-0.748583\pi$
$607$	6.48249	−	11.2280i	0.263116	−	0.455730i	0.967068	+	0.254517i	$0.0819165\pi$
$608$	2.04884	+	1.18290i	0.0830912	+	0.0479728i
$609$		0			0
$610$	−5.20347	−	9.01267i	−0.210682	−	0.364912i
$611$	−0.581946			−0.0235430
$612$		0			0
$613$	27.3903			1.10629			0.553143	−	0.833087i	$-0.313428\pi$
$613$	27.3903			1.10629			0.553143	+	0.833087i	$0.313428\pi$
$614$	−1.92628	−	3.33642i	−0.0777385	−	0.134647i
$615$		0			0
$616$	−4.24554	+	7.35349i	−0.171058	+	0.296280i
$617$	14.5863	−	25.2642i	0.587223	−	1.01710i	−0.407371	−	0.913263i	$-0.633554\pi$
$617$	14.5863	−	25.2642i	0.587223	−	1.01710i	0.994594	−	0.103838i	$-0.0331122\pi$
$618$		0			0
$619$	−24.6109	−	42.6274i	−0.989197	−	1.71334i	−0.621551	−	0.783374i	$-0.713497\pi$
$619$	−24.6109	−	42.6274i	−0.989197	−	1.71334i	−0.367646	−	0.929966i	$-0.619836\pi$
$620$	2.09008			0.0839396
$621$		0			0
$622$			14.8014i			0.593481i
$623$	26.1214	+	45.2436i	1.04653	+	1.81265i
$624$		0			0
$625$	12.8694	−	22.2904i	0.514775	−	0.891617i
$626$	−17.7169	−	10.2288i	−0.708109	−	0.408827i
$627$		0			0
$628$	12.0274	−	6.94403i	0.479946	−	0.277097i
$629$		−	15.5604i		−	0.620436i
$630$		0			0
$631$	−1.02312			−0.0407298			−0.0203649	−	0.999793i	$-0.506483\pi$
$631$	−1.02312			−0.0407298			−0.0203649	+	0.999793i	$0.506483\pi$
$632$	−8.28272	+	4.78203i	−0.329469	+	0.190219i
$633$		0			0
$634$	4.00247	+	2.31083i	0.158959	+	0.0917747i
$635$	22.6089	−	39.1597i	0.897206	−	1.55401i
$636$		0			0
$637$	−2.95600	+	1.70665i	−0.117121	+	0.0676198i
$638$	13.5163			0.535115
$639$		0			0
$640$	−2.26989			−0.0897253
$641$	19.7641	−	11.4108i	0.780636	−	0.450700i	−0.0560197	−	0.998430i	$-0.517841\pi$
$641$	19.7641	−	11.4108i	0.780636	−	0.450700i	0.836656	+	0.547729i	$0.184508\pi$
$642$		0			0
$643$	34.3473	+	19.8304i	1.35453	+	0.782036i	0.988880	−	0.148718i	$-0.0475147\pi$
$643$	34.3473	+	19.8304i	1.35453	+	0.782036i	0.365646	+	0.930754i	$0.380848\pi$
$644$	−7.66965	−	4.42808i	−0.302227	−	0.174491i
$645$		0			0
$646$	5.76498	+	9.98523i	0.226820	+	0.392864i
$647$	−15.9556			−0.627280			−0.313640	−	0.949542i	$-0.601549\pi$
$647$	−15.9556			−0.627280			−0.313640	+	0.949542i	$0.601549\pi$
$648$		0			0
$649$		−	12.0830i		−	0.474300i
$650$	−0.0302834	+	0.0174841i	−0.00118781	+	0.000685783i
$651$		0			0
$652$	6.15300	−	10.6573i	0.240970	−	0.417373i
$653$	26.9917	+	15.5837i	1.05627	+	0.609837i	0.924398	−	0.381430i	$-0.124568\pi$
$653$	26.9917	+	15.5837i	1.05627	+	0.609837i	0.131871	+	0.991267i	$0.457902\pi$
$654$		0			0
$655$	25.0432	+	43.3760i	0.978517	+	1.69484i
$656$	−5.89218	+	2.50643i	−0.230051	+	0.0978598i
$657$		0			0
$658$	−11.8624			−0.462445
$659$	−28.2335	+	16.3006i	−1.09982	+	0.634981i	−0.936174	−	0.351538i	$-0.885659\pi$
$659$	−28.2335	+	16.3006i	−1.09982	+	0.634981i	−0.163646	+	0.986519i	$0.552325\pi$
$660$		0			0
$661$	21.6447	−	37.4898i	0.841883	−	1.45818i	−0.0464184	−	0.998922i	$-0.514781\pi$
$661$	21.6447	−	37.4898i	0.841883	−	1.45818i	0.888301	−	0.459262i	$-0.151886\pi$
$662$	12.4712	+	7.20025i	0.484707	+	0.279846i
$663$		0			0
$664$	0.426481	+	0.738686i	0.0165507	+	0.0286666i
$665$	25.1168			0.973986
$666$		0			0
$667$			14.0974i			0.545854i
$668$	11.9934	−	6.92439i	0.464038	−	0.267913i
$669$		0			0
$670$	−0.608807	−	0.351495i	−0.0235203	−	0.0135794i
$671$	−7.20824	−	4.16168i	−0.278271	−	0.160660i
$672$		0			0
$673$	−12.3737	+	7.14393i	−0.476969	+	0.275378i	−0.719153	−	0.694852i	$-0.755470\pi$
$673$	−12.3737	+	7.14393i	−0.476969	+	0.275378i	0.242183	+	0.970231i	$0.422136\pi$
$674$	30.9916			1.19375
$675$		0			0
$676$	12.9474			0.497975
$677$	−5.76736	−	9.98936i	−0.221658	−	0.383922i	0.733654	−	0.679523i	$-0.237813\pi$
$677$	−5.76736	−	9.98936i	−0.221658	−	0.383922i	−0.955311	+	0.295601i	$0.904480\pi$
$678$		0			0
$679$	19.2617	−	33.3622i	0.739196	−	1.28032i
$680$	−9.58047	−	5.53128i	−0.367394	−	0.212115i
$681$		0			0
$682$	1.44767	−	0.835811i	0.0554341	−	0.0320049i
$683$			11.7999i			0.451512i	0.974184	+	0.225756i	$0.0724853\pi$
$683$			11.7999i			0.451512i	−0.974184	+	0.225756i	$0.927515\pi$
$684$		0			0
$685$			47.1137i			1.80012i
$686$	−31.9015	+	18.4183i	−1.21800	+	0.703215i
$687$		0			0
$688$	0.638021	−	1.10508i	0.0243243	−	0.0421310i
$689$	0.305377	−	0.528929i	0.0116339	−	0.0201506i
$690$		0			0
$691$	−37.5680	+	21.6899i	−1.42915	+	0.825122i	−0.997054	−	0.0767041i	$-0.975560\pi$
$691$	−37.5680	+	21.6899i	−1.42915	+	0.825122i	−0.432099	+	0.901826i	$0.642227\pi$
$692$	7.06249			0.268476
$693$		0			0
$694$			31.2565i			1.18648i
$695$	−19.8569	−	34.3931i	−0.753215	−	1.30461i
$696$		0			0
$697$	−30.9767	−	3.77927i	−1.17333	−	0.143150i
$698$	15.9676	−	27.6567i	0.604382	−	1.04682i
$699$		0			0
$700$	−0.617298	+	0.356397i	−0.0233317	+	0.0134706i
$701$	−21.2267			−0.801721			−0.400861	−	0.916139i	$-0.631289\pi$
$701$	−21.2267			−0.801721			−0.400861	+	0.916139i	$0.631289\pi$
$702$		0			0
$703$			7.55348i			0.284885i
$704$	−1.57221	+	0.907717i	−0.0592549	+	0.0342109i
$705$		0			0
$706$	−0.174178	+	0.301685i	−0.00655528	+	0.0113541i
$707$	29.2870	−	50.7265i	1.10145	−	1.90777i
$708$		0			0
$709$	−6.88888	+	3.97729i	−0.258717	+	0.149370i	−0.623749	−	0.781625i	$-0.714391\pi$
$709$	−6.88888	+	3.97729i	−0.258717	+	0.149370i	0.365032	+	0.930995i	$0.381058\pi$
$710$			25.0914i			0.941663i
$711$		0			0
$712$			11.1698i			0.418604i
$713$	0.871747	+	1.50991i	0.0326472	+	0.0565466i
$714$		0			0
$715$	−0.472766	+	0.818855i	−0.0176805	+	0.0306235i
$716$	0.428905	+	0.247629i	0.0160289	+	0.00925431i
$717$		0			0
$718$	−8.20642	−	14.2139i	−0.306261	−	0.530459i
$719$		−	20.2369i		−	0.754708i	−0.926069	−	0.377354i	$-0.876834\pi$
$719$		−	20.2369i		−	0.754708i	0.926069	−	0.377354i	$-0.123166\pi$
$720$		0			0
$721$		−	51.5205i		−	1.91872i
$722$	6.70152	+	11.6074i	0.249405	+	0.431981i
$723$		0			0
$724$	−10.4915	−	6.05727i	−0.389913	−	0.225117i
$725$	0.982629	+	0.567321i	0.0364939	+	0.0210698i
$726$		0			0
$727$	−5.02800	+	2.90292i	−0.186478	+	0.107663i	−0.590333	−	0.807160i	$-0.701003\pi$
$727$	−5.02800	+	2.90292i	−0.186478	+	0.107663i	0.403855	+	0.914823i	$0.367670\pi$
$728$	−1.07318			−0.0397748
$729$		0			0
$730$	−32.8611			−1.21624
$731$	5.38576	−	3.10947i	0.199199	−	0.115008i
$732$		0			0
$733$	−5.89862	+	10.2167i	−0.217870	+	0.377363i	−0.954157	−	0.299308i	$-0.903244\pi$
$733$	−5.89862	+	10.2167i	−0.217870	+	0.377363i	0.736286	+	0.676670i	$0.236578\pi$
$734$	0.716065	−	1.24026i	0.0264305	−	0.0457789i
$735$		0			0
$736$	−0.946744	−	1.63981i	−0.0348975	−	0.0604442i
$737$	−0.562244			−0.0207105
$738$		0			0
$739$	21.3593			0.785715			0.392858	−	0.919599i	$-0.371487\pi$
$739$	21.3593			0.785715			0.392858	+	0.919599i	$0.371487\pi$
$740$	−3.62364	−	6.27633i	−0.133208	−	0.230723i
$741$		0			0
$742$	6.22483	−	10.7817i	0.228521	−	0.395810i
$743$	−24.1170	+	41.7719i	−0.884768	+	1.53246i	−0.0387889	+	0.999247i	$0.512350\pi$
$743$	−24.1170	+	41.7719i	−0.884768	+	1.53246i	−0.845979	+	0.533216i	$0.820983\pi$
$744$		0			0
$745$	17.0918	−	9.86797i	0.626196	−	0.361534i
$746$	−2.76918			−0.101387
$747$		0			0
$748$	−8.84772			−0.323505
$749$	60.0720	−	34.6826i	2.19498	−	1.26727i
$750$		0			0
$751$	3.17639	+	1.83389i	0.115908	+	0.0669196i	0.556833	−	0.830624i	$-0.312016\pi$
$751$	3.17639	+	1.83389i	0.115908	+	0.0669196i	−0.440925	+	0.897544i	$0.645350\pi$
$752$	−2.19645	−	1.26812i	−0.0800963	−	0.0462436i
$753$		0			0
$754$	0.854159	+	1.47945i	0.0311066	+	0.0538783i
$755$			6.58026i			0.239480i
$756$		0			0
$757$			9.69425i			0.352343i	0.984359	+	0.176172i	$0.0563714\pi$
$757$			9.69425i			0.352343i	−0.984359	+	0.176172i	$0.943629\pi$
$758$	−15.9157	−	27.5668i	−0.578084	−	1.00127i
$759$		0			0
$760$	4.65063	+	2.68504i	0.168696	+	0.0973967i
$761$	−9.60700	+	16.6398i	−0.348254	+	0.603193i	−0.985939	−	0.167104i	$-0.946559\pi$
$761$	−9.60700	+	16.6398i	−0.348254	+	0.603193i	0.637686	+	0.770297i	$0.279892\pi$
$762$		0			0
$763$	30.2375	+	52.3728i	1.09467	+	1.89602i
$764$		−	23.3797i		−	0.845847i
$765$		0			0
$766$		−	9.32680i		−	0.336991i
$767$	1.32257	−	0.763584i	0.0477551	−	0.0275714i
$768$		0			0
$769$	−7.64231	+	13.2369i	−0.275589	+	0.477334i	−0.970283	−	0.241971i	$-0.922206\pi$
$769$	−7.64231	+	13.2369i	−0.275589	+	0.477334i	0.694695	+	0.719305i	$0.255539\pi$
$770$	−9.63690	+	16.6916i	−0.347290	+	0.601524i
$771$		0			0
$772$	−5.47675	+	3.16200i	−0.197113	+	0.113803i
$773$		−	16.7443i		−	0.602252i	−0.953584	−	0.301126i	$-0.902638\pi$
$773$		−	16.7443i		−	0.602252i	0.953584	−	0.301126i	$-0.0973625\pi$
$774$		0			0
$775$	0.140327			0.00504068
$776$	7.13300	−	4.11824i	0.256060	−	0.147836i
$777$		0			0
$778$	−3.56411	+	6.17321i	−0.127779	+	0.221320i
$779$	15.0370	+	1.83457i	0.538755	+	0.0657302i
$780$		0			0
$781$	10.0339	+	17.3792i	0.359041	+	0.621878i
$782$		−	9.22813i		−	0.329997i
$783$		0			0
$784$	−14.8759			−0.531280
$785$	27.3009	−	15.7622i	0.974411	−	0.562576i
$786$		0			0
$787$	−4.27699	+	7.40796i	−0.152458	+	0.264065i	−0.932131	−	0.362122i	$-0.882052\pi$
$787$	−4.27699	+	7.40796i	−0.152458	+	0.264065i	0.779672	+	0.626188i	$0.215386\pi$
$788$	−5.18162	+	8.97484i	−0.184588	+	0.319715i
$789$		0			0
$790$	−18.8009	+	10.8547i	−0.668905	+	0.386192i
$791$			64.1550i			2.28109i
$792$		0			0
$793$		−	1.05199i		−	0.0373571i
$794$	−27.0680	+	15.6277i	−0.960609	+	0.554608i
$795$		0			0
$796$	−11.5468	−	6.66656i	−0.409266	−	0.236290i
$797$	−13.5350	+	23.4433i	−0.479434	+	0.830404i	−0.999722	−	0.0235872i	$-0.992491\pi$
$797$	−13.5350	+	23.4433i	−0.479434	+	0.830404i	0.520288	+	0.853991i	$0.325825\pi$
$798$		0			0
$799$	−6.18034	−	10.7047i	−0.218645	−	0.378704i
$800$	−0.152399			−0.00538812
$801$		0			0
$802$	−14.0766			−0.497061
$803$	−22.7608	+	13.1410i	−0.803212	+	0.463735i
$804$		0			0
$805$	−17.4093	−	10.0512i	−0.613596	−	0.354260i
$806$	0.182970	+	0.105638i	0.00644485	+	0.00372093i
$807$		0			0
$808$	10.8456	−	6.26169i	0.381546	−	0.220286i
$809$		−	24.2145i		−	0.851335i	−0.904880	−	0.425668i	$-0.860039\pi$
$809$		−	24.2145i		−	0.851335i	0.904880	−	0.425668i	$-0.139961\pi$
$810$		0			0
$811$	2.43950			0.0856624			0.0428312	−	0.999082i	$-0.486362\pi$
$811$	2.43950			0.0856624			0.0428312	+	0.999082i	$0.486362\pi$
$812$	17.4112	+	30.1571i	0.611014	+	1.05831i
$813$		0			0
$814$	−5.01974	−	2.89815i	−0.175942	−	0.101580i
$815$	13.9666	−	24.1909i	0.489230	−	0.847371i
$816$		0			0
$817$	−2.61440	+	1.50942i	−0.0914663	+	0.0528081i
$818$	−12.3611			−0.432196
$819$		0			0
$820$	−13.3746	+	5.68933i	−0.467061	+	0.198680i
$821$	8.73677	+	15.1325i	0.304916	+	0.528129i	0.977243	−	0.212125i	$-0.0680384\pi$
$821$	8.73677	+	15.1325i	0.304916	+	0.528129i	−0.672327	+	0.740254i	$0.734705\pi$
$822$		0			0
$823$	15.1178	+	8.72828i	0.526974	+	0.304249i	0.739783	−	0.672845i	$-0.234928\pi$
$823$	15.1178	+	8.72828i	0.526974	+	0.304249i	−0.212809	+	0.977094i	$0.568261\pi$
$824$	5.50767	−	9.53956i	0.191869	−	0.332326i
$825$		0			0
$826$	26.9593	−	15.5649i	0.938033	−	0.541574i
$827$			5.65389i			0.196605i	0.995157	+	0.0983026i	$0.0313413\pi$
$827$			5.65389i			0.196605i	−0.995157	+	0.0983026i	$0.968659\pi$
$828$		0			0
$829$	−37.5063			−1.30265			−0.651325	−	0.758799i	$-0.725786\pi$
$829$	−37.5063			−1.30265			−0.651325	+	0.758799i	$0.725786\pi$
$830$	0.968064	+	1.67674i	0.0336020	+	0.0582004i
$831$		0			0
$832$	−0.198711	−	0.114726i	−0.00688907	−	0.00397741i
$833$	−62.7861	−	36.2496i	−2.17541	−	1.25597i
$834$		0			0
$835$	27.2237	−	15.7176i	0.942114	−	0.543930i
$836$	4.29494			0.148543
$837$		0			0
$838$	4.83014			0.166854
$839$	−41.7139	+	24.0836i	−1.44013	+	0.831457i	−0.997857	−	0.0654262i	$-0.979159\pi$
$839$	−41.7139	+	24.0836i	−1.44013	+	0.831457i	−0.442268	+	0.896883i	$0.645826\pi$
$840$		0			0
$841$	13.2156	−	22.8901i	0.455710	−	0.789313i
$842$	−6.14525	−	3.54796i	−0.211779	−	0.122271i
$843$		0			0
$844$	−3.05349	+	1.76293i	−0.105106	+	0.0606827i
$845$	29.3891			1.01101
$846$		0			0
$847$		−	36.0338i		−	1.23814i
$848$	2.30518	−	1.33090i	0.0791604	−	0.0457033i
$849$		0			0
$850$	−0.643226	−	0.371367i	−0.0220625	−	0.0127378i
$851$	3.02276	−	5.23557i	0.103619	−	0.179473i
$852$		0			0
$853$	−16.0226	−	27.7520i	−0.548605	−	0.950212i	−0.998370	−	0.0570651i	$-0.981826\pi$
$853$	−16.0226	−	27.7520i	−0.548605	−	0.950212i	0.449765	−	0.893147i	$-0.351508\pi$
$854$		−	21.4437i		−	0.733790i
$855$		0			0
$856$	14.8306			0.506900
$857$	14.0736	+	24.3762i	0.480745	+	0.832674i	0.999756	−	0.0220934i	$-0.00703312\pi$
$857$	14.0736	+	24.3762i	0.480745	+	0.832674i	−0.519011	+	0.854767i	$0.673700\pi$
$858$		0			0
$859$	10.0669	−	17.4363i	0.343477	−	0.594920i	−0.641599	−	0.767040i	$-0.721729\pi$
$859$	10.0669	−	17.4363i	0.343477	−	0.594920i	0.985076	+	0.172121i	$0.0550619\pi$
$860$	1.44824	−	2.50842i	0.0493845	−	0.0855364i
$861$		0			0
$862$	2.32575	+	4.02832i	0.0792154	+	0.137205i
$863$	6.17389			0.210162			0.105081	−	0.994464i	$-0.466490\pi$
$863$	6.17389			0.210162			0.105081	+	0.994464i	$0.466490\pi$
$864$		0			0
$865$	16.0311			0.545073
$866$	9.51961	+	16.4885i	0.323490	+	0.560301i
$867$		0			0
$868$	3.72968	+	2.15333i	0.126593	+	0.0730888i
$869$	−8.68146	+	15.0367i	−0.294498	+	0.510086i
$870$		0			0
$871$	−0.0355309	−	0.0615413i	−0.00120392	−	0.00208525i
$872$			12.9298i			0.437859i
$873$		0			0
$874$			4.47960i			0.151525i
$875$	44.5702	−	25.7326i	1.50675	−	0.869922i
$876$		0			0
$877$	11.4559	−	19.8423i	0.386840	−	0.670026i	−0.605183	−	0.796087i	$-0.706900\pi$
$877$	11.4559	−	19.8423i	0.386840	−	0.670026i	0.992023	+	0.126060i	$0.0402333\pi$
$878$	30.9160	+	17.8493i	1.04336	+	0.602386i
$879$		0			0
$880$	−3.56875	+	2.06042i	−0.120302	+	0.0694566i
$881$	−17.0002			−0.572750			−0.286375	−	0.958118i	$-0.592450\pi$
$881$	−17.0002			−0.572750			−0.286375	+	0.958118i	$0.592450\pi$
$882$		0			0
$883$			4.65006i			0.156487i	0.996934	+	0.0782434i	$0.0249311\pi$
$883$			4.65006i			0.156487i	−0.996934	+	0.0782434i	$0.975069\pi$
$884$	−0.559130	−	0.968442i	−0.0188056	−	0.0325722i
$885$		0			0
$886$	−16.1081	+	27.9000i	−0.541162	+	0.937320i
$887$	−23.2868	−	13.4446i	−0.781894	−	0.451427i	0.0552071	−	0.998475i	$-0.482418\pi$
$887$	−23.2868	−	13.4446i	−0.781894	−	0.451427i	−0.837101	+	0.547048i	$0.815751\pi$
$888$		0			0
$889$	80.6896	−	46.5862i	2.70624	−	1.56245i
$890$			25.3541i			0.849872i
$891$		0			0
$892$	−21.6205			−0.723909
$893$	3.00011	+	5.19634i	0.100395	+	0.173889i
$894$		0			0
$895$	0.973567	+	0.562089i	0.0325428	+	0.0187886i
$896$	−4.05054	−	2.33858i	−0.135319	−	0.0781265i
$897$		0			0
$898$	2.94202	+	5.09573i	0.0981766	+	0.170047i
$899$		−	6.85544i		−	0.228642i
$900$		0			0
$901$	12.9726			0.432179
$902$	−6.98862	+	9.28907i	−0.232696	+	0.309292i
$903$		0			0
$904$	−6.85832	+	11.8790i	−0.228104	+	0.395088i
$905$	−23.8145	−	13.7493i	−0.791622	−	0.457043i
$906$		0			0
$907$	9.58654	+	16.6044i	0.318316	+	0.551339i	0.980137	−	0.198323i	$-0.0635494\pi$
$907$	9.58654	+	16.6044i	0.318316	+	0.551339i	−0.661821	+	0.749662i	$0.730216\pi$
$908$		−	5.24551i		−	0.174078i
$909$		0			0
$910$	−2.43601			−0.0807529
$911$	8.05832	+	13.9574i	0.266984	+	0.462430i	0.968082	−	0.250635i	$-0.0806395\pi$
$911$	8.05832	+	13.9574i	0.266984	+	0.462430i	−0.701097	+	0.713066i	$0.747306\pi$
$912$		0			0
$913$	1.34104	+	0.774247i	0.0443818	+	0.0256239i
$914$	−11.2356	−	6.48687i	−0.371640	−	0.214567i
$915$		0			0
$916$	6.66016	−	3.84524i	0.220058	−	0.127050i
$917$			103.204i			3.40810i
$918$		0			0
$919$		−	24.3829i		−	0.804316i	−0.915570	−	0.402158i	$-0.868260\pi$
$919$		−	24.3829i		−	0.804316i	0.915570	−	0.402158i	$-0.131740\pi$
$920$	−2.14900	−	3.72219i	−0.0708506	−	0.122717i
$921$		0			0
$922$	16.9376	−	29.3368i	0.557811	−	0.966156i
$923$	−1.26818	+	2.19655i	−0.0417427	+	0.0723005i
$924$		0			0
$925$	−0.243289	−	0.421389i	−0.00799930	−	0.0138552i
$926$			30.0154i			0.986368i
$927$		0			0
$928$			7.44521i			0.244401i
$929$	27.1697	−	15.6864i	0.891409	−	0.514655i	0.0170056	−	0.999855i	$-0.494587\pi$
$929$	27.1697	−	15.6864i	0.891409	−	0.514655i	0.874403	+	0.485200i	$0.161253\pi$
$930$		0			0
$931$	30.4782	+	17.5966i	0.998882	+	0.576705i
$932$	−9.70869	−	5.60531i	−0.318019	−	0.183608i
$933$		0			0
$934$	−6.52519	−	11.3020i	−0.213511	−	0.369812i
$935$	−20.0834			−0.656796
$936$		0			0
$937$		−	59.0911i		−	1.93042i	−0.261474	−	0.965210i	$-0.584209\pi$
$937$		−	59.0911i		−	1.93042i	0.261474	−	0.965210i	$-0.415791\pi$
$938$	−0.724264	−	1.25446i	−0.0236480	−	0.0409596i
$939$		0			0
$940$	−4.98570	−	2.87850i	−0.162616	−	0.0938862i
$941$	17.3889	−	30.1185i	0.566863	−	0.981835i	−0.430011	−	0.902824i	$-0.641490\pi$
$941$	17.3889	−	30.1185i	0.566863	−	0.981835i	0.996874	−	0.0790113i	$-0.0251763\pi$
$942$		0			0
$943$	−9.68846	−	7.28910i	−0.315500	−	0.237366i
$944$	6.65572			0.216625
$945$		0			0
$946$		−	2.31657i		−	0.0753181i
$947$	−20.5561	−	35.6042i	−0.667983	−	1.15698i	−0.978467	−	0.206402i	$-0.933825\pi$
$947$	−20.5561	−	35.6042i	−0.667983	−	1.15698i	0.310484	−	0.950578i	$-0.399509\pi$
$948$		0			0
$949$	−2.87673	−	1.66088i	−0.0933827	−	0.0539145i
$950$	0.312240	+	0.180272i	0.0101304	+	0.00584880i
$951$		0			0
$952$	−11.3973	−	19.7408i	−0.369390	−	0.639802i
$953$	1.85219			0.0599983			0.0299992	−	0.999550i	$-0.490450\pi$
$953$	1.85219			0.0599983			0.0299992	+	0.999550i	$0.490450\pi$
$954$		0			0
$955$		−	53.0693i		−	1.71728i
$956$	−7.06868	+	4.08110i	−0.228617	+	0.131992i
$957$		0			0
$958$	2.68307	+	1.54907i	0.0866862	+	0.0500483i
$959$	−48.5395	+	84.0729i	−1.56742	+	2.71486i
$960$		0			0
$961$	15.0761	+	26.1125i	0.486325	+	0.842340i
$962$		−	0.732592i		−	0.0236197i
$963$		0			0
$964$	17.7037			0.570196
$965$	−12.4316	+	7.17740i	−0.400188	+	0.231049i
$966$		0			0
$967$	45.7858	+	26.4345i	1.47237	+	0.850075i	0.999517	−	0.0310652i	$-0.00988994\pi$
$967$	45.7858	+	26.4345i	1.47237	+	0.850075i	0.472855	+	0.881140i	$0.343223\pi$
$968$	3.85210	−	6.67203i	0.123811	−	0.214447i
$969$		0			0
$970$	16.1911	−	9.34795i	0.519866	−	0.300145i
$971$		−	23.0562i		−	0.739909i	−0.929050	−	0.369955i	$-0.879373\pi$
$971$		−	23.0562i		−	0.739909i	0.929050	−	0.369955i	$-0.120627\pi$
$972$		0			0
$973$		−	81.8312i		−	2.62339i
$974$	−12.6869	−	21.9744i	−0.406514	−	0.704104i
$975$		0			0
$976$	2.29239	−	3.97053i	0.0733776	−	0.127094i
$977$	−11.0633	−	6.38739i	−0.353946	−	0.204351i	0.312476	−	0.949926i	$-0.398842\pi$
$977$	−11.0633	−	6.38739i	−0.353946	−	0.204351i	−0.666422	+	0.745575i	$0.732175\pi$
$978$		0			0
$979$	10.1390	+	17.5612i	0.324043	+	0.561259i
$980$	−33.7665			−1.07863
$981$		0			0
$982$	−12.4488			−0.397258
$983$	21.4000	+	37.0660i	0.682555	+	1.18222i	0.974198	+	0.225693i	$0.0724647\pi$
$983$	21.4000	+	37.0660i	0.682555	+	1.18222i	−0.291643	+	0.956527i	$0.594202\pi$
$984$		0			0
$985$	−11.7617	+	20.3719i	−0.374759	+	0.649102i
$986$	−18.1425	+	31.4238i	−0.577776	+	1.00074i
$987$		0			0
$988$	0.271418	+	0.470109i	0.00863494	+	0.0149562i
$989$	2.41617			0.0768297
$990$		0			0
$991$			15.0658i			0.478582i	0.970948	+	0.239291i	$0.0769150\pi$
$991$			15.0658i			0.478582i	−0.970948	+	0.239291i	$0.923085\pi$
$992$	0.460392	+	0.797423i	0.0146175	+	0.0253182i
$993$		0			0
$994$	−25.8507	+	44.7747i	−0.819934	+	1.42017i
$995$	−26.2100	−	15.1324i	−0.830913	−	0.479728i
$996$		0			0
$997$	29.8675	−	17.2440i	0.945914	−	0.546124i	0.0541049	−	0.998535i	$-0.482769\pi$
$997$	29.8675	−	17.2440i	0.945914	−	0.546124i	0.891809	+	0.452411i	$0.149436\pi$
$998$		−	35.6131i		−	1.12731i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2214.2.i.b.901.5		36
3.2	odd	2		738.2.i.b.409.3	✓	36
9.2	odd	6		738.2.i.b.655.16	yes	36
9.7	even	3	inner	2214.2.i.b.1639.6		36
41.40	even	2	inner	2214.2.i.b.901.6		36
123.122	odd	2		738.2.i.b.409.16	yes	36
369.245	odd	6		738.2.i.b.655.3	yes	36
369.286	even	6	inner	2214.2.i.b.1639.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.i.b.409.3	✓	36	3.2	odd	2
738.2.i.b.409.16	yes	36	123.122	odd	2
738.2.i.b.655.3	yes	36	369.245	odd	6
738.2.i.b.655.16	yes	36	9.2	odd	6
2214.2.i.b.901.5		36	1.1	even	1	trivial
2214.2.i.b.901.6		36	41.40	even	2	inner
2214.2.i.b.1639.5		36	369.286	even	6	inner
2214.2.i.b.1639.6		36	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2214 = 2 \cdot 3^{3} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2214.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.13494 + 1.96578i) q^{5} +(-4.05054 + 2.33858i) q^{7} -1.00000 q^{8} -2.26989 q^{10} +(-1.57221 + 0.907717i) q^{11} +(-0.198711 - 0.114726i) q^{13} +(-4.05054 - 2.33858i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.87362i q^{17} +2.36579i q^{19} +(-1.13494 - 1.96578i) q^{20} +(-1.57221 - 0.907717i) q^{22} +(0.946744 - 1.63981i) q^{23} +(-0.0761995 - 0.131981i) q^{25} -0.229452i q^{26} -4.67716i q^{28} +(-6.44774 + 3.72261i) q^{29} +(-0.460392 + 0.797423i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.22067 - 2.43681i) q^{34} -10.6166i q^{35} +3.19279 q^{37} +(-2.04884 + 1.18290i) q^{38} +(1.13494 - 1.96578i) q^{40} +(0.775456 - 6.35599i) q^{41} +(0.638021 + 1.10508i) q^{43} -1.81543i q^{44} +1.89349 q^{46} +(2.19645 - 1.26812i) q^{47} +(7.43793 - 12.8829i) q^{49} +(0.0761995 - 0.131981i) q^{50} +(0.198711 - 0.114726i) q^{52} +2.66180i q^{53} -4.12083i q^{55} +(4.05054 - 2.33858i) q^{56} +(-6.44774 - 3.72261i) q^{58} +(-3.32786 + 5.76402i) q^{59} +(2.29239 + 3.97053i) q^{61} -0.920785 q^{62} +1.00000 q^{64} +(0.451052 - 0.260415i) q^{65} +(0.268210 + 0.154851i) q^{67} +(4.22067 + 2.43681i) q^{68} +(9.19428 - 5.30832i) q^{70} -11.0540i q^{71} +14.4770 q^{73} +(1.59640 + 2.76504i) q^{74} +(-2.04884 - 1.18290i) q^{76} +(4.24554 - 7.35349i) q^{77} +(8.28272 - 4.78203i) q^{79} +2.26989 q^{80} +(5.89218 - 2.50643i) q^{82} +(-0.426481 - 0.738686i) q^{83} +(9.58047 + 5.53128i) q^{85} +(-0.638021 + 1.10508i) q^{86} +(1.57221 - 0.907717i) q^{88} -11.1698i q^{89} +1.07318 q^{91} +(0.946744 + 1.63981i) q^{92} +(2.19645 + 1.26812i) q^{94} +(-4.65063 - 2.68504i) q^{95} +(-7.13300 + 4.11824i) q^{97} +14.8759 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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