LMFDB - Embedded newform 2214.2.i.b.901.6

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			901.6
Character	$\chi$	$=$	2214.901
Dual form			2214.2.i.b.1639.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.13494 + 1.96578i) q^{5} +(4.05054 - 2.33858i) q^{7} -1.00000 q^{8} -2.26989 q^{10} +(1.57221 - 0.907717i) q^{11} +(0.198711 + 0.114726i) q^{13} +(4.05054 + 2.33858i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.87362i q^{17} -2.36579i q^{19} +(-1.13494 - 1.96578i) q^{20} +(1.57221 + 0.907717i) q^{22} +(0.946744 - 1.63981i) q^{23} +(-0.0761995 - 0.131981i) q^{25} +0.229452i q^{26} +4.67716i q^{28} +(6.44774 - 3.72261i) q^{29} +(-0.460392 + 0.797423i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.22067 + 2.43681i) q^{34} +10.6166i q^{35} +3.19279 q^{37} +(2.04884 - 1.18290i) q^{38} +(1.13494 - 1.96578i) q^{40} +(5.11672 - 3.84956i) q^{41} +(0.638021 + 1.10508i) q^{43} +1.81543i q^{44} +1.89349 q^{46} +(-2.19645 + 1.26812i) q^{47} +(7.43793 - 12.8829i) q^{49} +(0.0761995 - 0.131981i) q^{50} +(-0.198711 + 0.114726i) q^{52} -2.66180i q^{53} +4.12083i q^{55} +(-4.05054 + 2.33858i) q^{56} +(6.44774 + 3.72261i) q^{58} +(-3.32786 + 5.76402i) q^{59} +(2.29239 + 3.97053i) q^{61} -0.920785 q^{62} +1.00000 q^{64} +(-0.451052 + 0.260415i) q^{65} +(-0.268210 - 0.154851i) q^{67} +(-4.22067 - 2.43681i) q^{68} +(-9.19428 + 5.30832i) q^{70} +11.0540i q^{71} +14.4770 q^{73} +(1.59640 + 2.76504i) q^{74} +(2.04884 + 1.18290i) q^{76} +(4.24554 - 7.35349i) q^{77} +(-8.28272 + 4.78203i) q^{79} +2.26989 q^{80} +(5.89218 + 2.50643i) q^{82} +(-0.426481 - 0.738686i) q^{83} +(-9.58047 - 5.53128i) q^{85} +(-0.638021 + 1.10508i) q^{86} +(-1.57221 + 0.907717i) q^{88} +11.1698i q^{89} +1.07318 q^{91} +(0.946744 + 1.63981i) q^{92} +(-2.19645 - 1.26812i) q^{94} +(4.65063 + 2.68504i) q^{95} +(7.13300 - 4.11824i) q^{97} +14.8759 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.321575\pi$
$7$	4.05054	−	2.33858i	1.53096	−	0.883901i	0.999318	−	0.0369322i	$-0.0117586\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.26989			−0.717802
$11$	1.57221	−	0.907717i	0.474040	−	0.273687i	−0.243890	−	0.969803i	$-0.578423\pi$
$11$	1.57221	−	0.907717i	0.474040	−	0.273687i	0.717929	+	0.696116i	$0.245090\pi$
$12$		0			0
$13$	0.198711	+	0.114726i	0.0551125	+	0.0318192i	0.527303	−	0.849677i	$-0.323203\pi$
$13$	0.198711	+	0.114726i	0.0551125	+	0.0318192i	−0.472191	+	0.881497i	$0.656537\pi$
$14$	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	$0.201272\pi$
$17$			4.87362i			1.18203i	−0.806662	+	0.591013i	$0.798728\pi$
$18$		0			0
$19$		−	2.36579i		−	0.542750i	−0.962474	−	0.271375i	$-0.912522\pi$
$19$		−	2.36579i		−	0.542750i	0.962474	−	0.271375i	$-0.0874783\pi$
$20$	−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	0.237360	−	0.971422i	$-0.423718\pi$
$29$	6.44774	−	3.72261i	1.19732	−	0.691271i	0.959956	+	0.280151i	$0.0903846\pi$
$30$		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
$41$	5.11672	−	3.84956i	0.799098	−	0.601201i
$41$	5.11672	−	3.84956i	0.799098	−	0.601201i
$42$		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	−0.651564	−	0.758593i	$-0.725887\pi$
$47$	−2.19645	+	1.26812i	−0.320385	+	0.184975i	0.331179	+	0.943568i	$0.392554\pi$
$48$		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	$-0.941480\pi$
$53$		−	2.66180i		−	0.365626i	0.983148	−	0.182813i	$-0.0585203\pi$
$54$		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	0.483527	−	0.875329i	$-0.339356\pi$
$67$	−0.268210	−	0.154851i	−0.0327671	−	0.0189181i	−0.516294	+	0.856411i	$0.672689\pi$
$68$	−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	$0.227725\pi$
$71$			11.0540i			1.31187i	−0.754818	+	0.655935i	$0.772275\pi$
$72$		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	−0.887405	−	0.460990i	$-0.847494\pi$
$79$	−8.28272	+	4.78203i	−0.931879	+	0.538021i	−0.0444736	+	0.999011i	$0.514161\pi$
$80$	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	$0.201660\pi$
$89$			11.1698i			1.18399i	−0.805941	+	0.591996i	$0.798340\pi$
$90$		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	−0.0920670	−	0.995753i	$-0.529347\pi$
$97$	7.13300	−	4.11824i	0.724247	−	0.418144i	0.816314	+	0.577609i	$0.196014\pi$
$98$	14.8759			1.50269
$99$		0			0
$100$	0.152399			0.0152399
$101$	10.8456	−	6.26169i	1.07917	−	0.623062i	0.148501	−	0.988912i	$-0.452555\pi$
$101$	10.8456	−	6.26169i	1.07917	−	0.623062i	0.930674	+	0.365850i	$0.119222\pi$
$102$		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	$0.212554\pi$
$109$			12.9298i			1.23845i	−0.785212	+	0.619227i	$0.787446\pi$
$110$	−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	$0.680308\pi$
$137$	−17.9752	+	10.3780i	−1.53572	+	0.886651i	−0.999082	+	0.0428410i	$0.986359\pi$
$138$		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	0.775648	−	0.631166i	$-0.217423\pi$
$149$	7.52980	+	4.34733i	0.616866	+	0.356148i	−0.158782	+	0.987314i	$0.550757\pi$
$150$		0			0
$151$	−2.51055	+	1.44947i	−0.204306	+	0.117956i	−0.598662	−	0.801002i	$-0.704301\pi$
$151$	−2.51055	+	1.44947i	−0.204306	+	0.117956i	0.394357	+	0.918957i	$0.370967\pi$
$152$			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	0.896140	−	0.443772i	$-0.146360\pi$
$157$	12.0274	+	6.94403i	0.959892	+	0.554194i	0.0637520	+	0.997966i	$0.479693\pi$
$158$	−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	$0.660068\pi$
$164$	0.775456	+	6.35599i	0.0605529	+	0.496320i
$165$		0			0
$166$	0.426481	−	0.738686i	0.0331013	−	0.0573332i
$167$	11.9934	+	6.92439i	0.928076	+	0.535825i	0.886203	−	0.463298i	$-0.153334\pi$
$167$	11.9934	+	6.92439i	0.928076	+	0.535825i	0.0418736	+	0.999123i	$0.486667\pi$
$168$		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	$0.00589181\pi$
$179$			0.495257i			0.0370172i	−0.999829	+	0.0185086i	$0.994108\pi$
$180$		0			0
$181$		−	12.1145i		−	0.900466i	−0.892911	−	0.450233i	$-0.851341\pi$
$181$		−	12.1145i		−	0.900466i	0.892911	−	0.450233i	$-0.148659\pi$
$182$	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	0.465813	−	0.884883i	$-0.345762\pi$
$191$	20.2474	−	11.6898i	1.46505	−	0.845847i	0.999238	+	0.0390358i	$0.0124286\pi$
$192$		0			0
$193$	−5.47675	−	3.16200i	−0.394225	−	0.227606i	0.289764	−	0.957098i	$-0.406423\pi$
$193$	−5.47675	−	3.16200i	−0.394225	−	0.227606i	−0.683989	+	0.729492i	$0.739756\pi$
$194$	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	$-0.843323\pi$
$199$		−	13.3331i		−	0.945160i	0.881288	−	0.472580i	$-0.156677\pi$
$200$	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
$205$	1.76020	+	14.4274i	0.122938	+	1.00765i
$206$	−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	0.391198	−	0.920306i	$-0.372061\pi$
$211$	−3.05349	−	1.76293i	−0.210211	−	0.121365i	−0.601409	+	0.798941i	$0.705394\pi$
$212$	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	−0.341610	−	0.939842i	$-0.610972\pi$
$227$	4.54274	−	2.62275i	0.301513	−	0.174078i	0.643122	+	0.765764i	$0.277639\pi$
$228$		0			0
$229$	6.66016	+	3.84524i	0.440116	+	0.254101i	0.703647	−	0.710550i	$-0.251554\pi$
$229$	6.66016	+	3.84524i	0.440116	+	0.254101i	−0.263531	+	0.964651i	$0.584887\pi$
$230$	−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	$-0.880311\pi$
$233$		−	11.2106i		−	0.734433i	0.930136	−	0.367216i	$-0.119689\pi$
$234$		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	0.253646	−	0.967297i	$-0.418370\pi$
$239$	−7.06868	−	4.08110i	−0.457235	−	0.263985i	−0.710881	+	0.703313i	$0.751703\pi$
$240$		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	$0.0695246\pi$
$257$	26.4839	+	15.2905i	1.65202	+	0.953793i	0.675776	+	0.737107i	$0.263809\pi$
$258$		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	−0.244300	−	0.969700i	$-0.578558\pi$
$263$	7.67620	−	4.43186i	0.473335	−	0.273280i	0.717635	+	0.696420i	$0.245225\pi$
$264$		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	−0.317959	−	0.948104i	$-0.602998\pi$
$281$	5.76890	−	3.33068i	0.344144	−	0.198691i	0.662103	+	0.749413i	$0.269664\pi$
$282$		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	−0.103385	−	0.994641i	$-0.532967\pi$
$293$	−17.3990	−	10.0453i	−1.01646	−	0.586855i	−0.913077	+	0.407787i	$0.866301\pi$
$294$		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	0.0904109	−	0.995905i	$-0.471182\pi$
$311$	−12.8184	−	7.40068i	−0.726862	−	0.419654i	−0.817273	+	0.576250i	$0.804515\pi$
$312$		0			0
$313$	17.7169	−	10.2288i	1.00142	−	0.578168i	0.0927496	−	0.995689i	$-0.470434\pi$
$313$	17.7169	−	10.2288i	1.00142	−	0.578168i	0.908667	+	0.417521i	$0.137101\pi$
$314$			13.8881i			0.783748i
$315$		0			0
$316$		−	9.56406i		−	0.538021i
$317$	−4.00247	+	2.31083i	−0.224801	+	0.129789i	−0.608171	−	0.793806i	$-0.708097\pi$
$317$	−4.00247	+	2.31083i	−0.224801	+	0.129789i	0.383370	+	0.923595i	$0.374763\pi$
$318$		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
$328$	−5.11672	+	3.84956i	−0.282524	+	0.212556i
$329$	−5.93121	+	10.2732i	−0.326998	+	0.566378i
$330$		0			0
$331$	−12.4712	+	7.20025i	−0.685479	+	0.395761i	−0.801916	−	0.597437i	$-0.796186\pi$
$331$	−12.4712	+	7.20025i	−0.685479	+	0.395761i	0.116437	+	0.993198i	$0.462853\pi$
$332$	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	−0.454478	−	0.890758i	$-0.650174\pi$
$347$	−27.0689	−	15.6283i	−1.45314	−	0.838969i	−0.998658	+	0.0517890i	$0.983508\pi$
$348$		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	0.691961	−	0.721935i	$-0.256747\pi$
$383$	8.07725	+	4.66340i	0.412728	+	0.238289i	−0.279233	+	0.960223i	$0.590080\pi$
$384$		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	$-0.713005\pi$
$397$		−	31.2555i		−	1.56867i	0.620339	−	0.784334i	$-0.286995\pi$
$398$	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	$0.265527\pi$
$410$	−11.6144	+	8.73808i	−0.573594	+	0.431543i
$411$		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	−0.342718	−	0.939438i	$-0.611347\pi$
$421$	6.14525	−	3.54796i	0.299501	−	0.172917i	0.642219	+	0.766521i	$0.278014\pi$
$422$		−	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	−0.999619	−	0.0275867i	$-0.991218\pi$
$439$	−30.9160	+	17.8493i	−1.47554	+	0.851902i	−0.475919	+	0.879489i	$0.657884\pi$
$440$		−	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	−0.213635	−	0.976913i	$-0.568530\pi$
$457$	11.2356	−	6.48687i	0.525579	−	0.303443i	0.739214	+	0.673470i	$0.235197\pi$
$458$			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	−0.245717	−	0.969342i	$-0.579023\pi$
$463$	−25.9941	−	15.0077i	−1.20805	−	0.697468i	−0.962333	+	0.271874i	$0.912357\pi$
$464$	−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	−0.560042	−	0.828464i	$-0.689215\pi$
$479$	−2.68307	+	1.54907i	−0.122593	+	0.0707790i	0.437450	+	0.899243i	$0.355882\pi$
$480$		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	0.992239	−	0.124347i	$-0.0396837\pi$
$499$	30.8418	+	17.8065i	1.38067	+	0.797130i	0.388431	+	0.921478i	$0.373017\pi$
$500$	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	$-0.944150\pi$
$503$		−	7.82992i		−	0.349119i	0.984647	−	0.174559i	$-0.0558501\pi$
$504$		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	0.181169	−	0.983452i	$-0.442012\pi$
$509$	−13.0841	−	7.55408i	−0.579941	−	0.334829i	−0.761110	+	0.648623i	$0.775345\pi$
$510$		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	$0.169648\pi$
$521$			23.1947i			1.01618i	−0.861305	+	0.508089i	$0.830352\pi$
$522$		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
$533$	1.45839	−	0.177930i	0.0631701	−	0.00770699i
$534$		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	−0.958238	−	0.285972i	$-0.907684\pi$
$547$	−27.8247	+	16.0646i	−1.18970	+	0.686872i	−0.231460	+	0.972844i	$0.574350\pi$
$548$		−	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	$-0.848146\pi$
$557$		−	21.6738i		−	0.918347i	0.888347	−	0.459174i	$-0.151854\pi$
$558$		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	0.462244	−	0.886753i	$-0.347044\pi$
$563$	−1.76970	−	1.02174i	−0.0745840	−	0.0430611i	−0.536828	+	0.843692i	$0.680378\pi$
$564$		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	0.821941	−	0.569573i	$-0.192891\pi$
$571$	17.6743	+	10.2043i	0.739647	+	0.427035i	−0.0822941	+	0.996608i	$0.526225\pi$
$572$	−0.208277	+	0.360747i	−0.00870851	+	0.0150836i
$573$		0			0
$574$	29.7280	−	3.62693i	1.24082	−	0.151385i
$575$	−0.288566			−0.0120340
$576$		0			0
$577$			34.5880i			1.43992i	0.694018	+	0.719958i	$0.255839\pi$
$577$			34.5880i			1.43992i	−0.694018	+	0.719958i	$0.744161\pi$
$578$	−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	−0.198924	−	0.980015i	$-0.563745\pi$
$587$	13.3335	−	7.69810i	0.550332	−	0.317735i	0.749256	+	0.662280i	$0.230411\pi$
$588$		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	$0.206723\pi$
$593$			29.4528i			1.20948i	−0.796423	+	0.604740i	$0.793277\pi$
$594$		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	0.402362	−	0.915481i	$-0.368189\pi$
$601$	34.2325	−	19.7641i	1.39637	−	0.806196i	0.994011	+	0.109284i	$0.0348559\pi$
$602$			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	−0.836656	−	0.547729i	$-0.815492\pi$
$641$	−19.7641	+	11.4108i	−0.780636	+	0.450700i	0.0560197	+	0.998430i	$0.482159\pi$
$642$		0			0
$643$	−34.3473	−	19.8304i	−1.35453	−	0.782036i	−0.365646	−	0.930754i	$-0.619152\pi$
$643$	−34.3473	−	19.8304i	−1.35453	−	0.782036i	−0.988880	+	0.148718i	$0.952485\pi$
$644$	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	−0.131871	−	0.991267i	$-0.542098\pi$
$653$	−26.9917	−	15.5837i	−1.05627	−	0.609837i	−0.924398	+	0.381430i	$0.875432\pi$
$654$		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	0.163646	−	0.986519i	$-0.447675\pi$
$659$	28.2335	−	16.3006i	1.09982	−	0.634981i	0.936174	+	0.351538i	$0.114341\pi$
$660$		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	−0.242183	−	0.970231i	$-0.577864\pi$
$673$	12.3737	−	7.14393i	0.476969	−	0.275378i	0.719153	+	0.694852i	$0.244530\pi$
$674$	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	$-0.927515\pi$
$683$		−	11.7999i		−	0.451512i	0.974184	−	0.225756i	$-0.0724853\pi$
$684$		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	0.432099	−	0.901826i	$-0.357773\pi$
$691$	37.5680	−	21.6899i	1.42915	−	0.825122i	0.997054	+	0.0767041i	$0.0244397\pi$
$692$	7.06249			0.268476
$693$		0			0
$694$		−	31.2565i		−	1.18648i
$695$	−19.8569	−	34.3931i	−0.753215	−	1.30461i
$696$		0			0
$697$	18.7613	+	24.9369i	0.710634	+	0.944554i
$698$	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	−0.365032	−	0.930995i	$-0.618942\pi$
$709$	6.88888	−	3.97729i	0.258717	−	0.149370i	0.623749	+	0.781625i	$0.285609\pi$
$710$		−	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	$0.123166\pi$
$719$			20.2369i			0.754708i	−0.926069	+	0.377354i	$0.876834\pi$
$720$		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	−0.403855	−	0.914823i	$-0.632330\pi$
$727$	5.02800	−	2.90292i	0.186478	−	0.107663i	0.590333	+	0.807160i	$0.298997\pi$
$728$	−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	0.440925	−	0.897544i	$-0.354650\pi$
$751$	−3.17639	−	1.83389i	−0.115908	−	0.0669196i	−0.556833	+	0.830624i	$0.687984\pi$
$752$	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	$-0.943629\pi$
$757$		−	9.69425i		−	0.352343i	0.984359	−	0.176172i	$-0.0563714\pi$
$758$	−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	$0.0973625\pi$
$773$			16.7443i			0.602252i	−0.953584	+	0.301126i	$0.902638\pi$
$774$		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
$779$	−9.10726	−	12.1051i	−0.326301	−	0.433710i
$780$		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	$0.139961\pi$
$809$			24.2145i			0.851335i	−0.904880	+	0.425668i	$0.860039\pi$
$810$		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	0.212809	−	0.977094i	$-0.431739\pi$
$823$	−15.1178	−	8.72828i	−0.526974	−	0.304249i	−0.739783	+	0.672845i	$0.765072\pi$
$824$	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	$-0.968659\pi$
$827$		−	5.65389i		−	0.196605i	0.995157	−	0.0983026i	$-0.0313413\pi$
$828$		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	0.442268	−	0.896883i	$-0.354174\pi$
$839$	41.7139	−	24.0836i	1.44013	−	0.831457i	0.997857	+	0.0654262i	$0.0208407\pi$
$840$		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	$-0.975069\pi$
$883$		−	4.65006i		−	0.156487i	0.996934	−	0.0782434i	$-0.0249311\pi$
$884$	−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	0.837101	−	0.547048i	$-0.184249\pi$
$887$	23.2868	+	13.4446i	0.781894	+	0.451427i	−0.0552071	+	0.998475i	$0.517582\pi$
$888$		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
$902$	11.5389	−	1.40779i	0.384203	−	0.0468742i
$903$		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	$0.131740\pi$
$919$			24.3829i			0.804316i	−0.915570	+	0.402158i	$0.868260\pi$
$920$	−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	−0.874403	−	0.485200i	$-0.838747\pi$
$929$	−27.1697	+	15.6864i	−0.891409	+	0.514655i	−0.0170056	+	0.999855i	$0.505413\pi$
$930$		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	$0.415791\pi$
$937$			59.0911i			1.93042i	−0.261474	+	0.965210i	$0.584209\pi$
$938$	−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
$943$	−1.46832	−	12.0350i	−0.0478150	−	0.391914i
$944$	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	−0.472855	−	0.881140i	$-0.656777\pi$
$967$	−45.7858	−	26.4345i	−1.47237	−	0.850075i	−0.999517	+	0.0310652i	$0.990110\pi$
$968$	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	$0.120627\pi$
$971$			23.0562i			0.739909i	−0.929050	+	0.369955i	$0.879373\pi$
$972$		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	0.666422	−	0.745575i	$-0.267825\pi$
$977$	11.0633	+	6.38739i	0.353946	+	0.204351i	−0.312476	+	0.949926i	$0.601158\pi$
$978$		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	$-0.923085\pi$
$991$		−	15.0658i		−	0.478582i	0.970948	−	0.239291i	$-0.0769150\pi$
$992$	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	−0.891809	−	0.452411i	$-0.850564\pi$
$997$	−29.8675	+	17.2440i	−0.945914	+	0.546124i	−0.0541049	+	0.998535i	$0.517231\pi$
$998$			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.901.6		36
3.2	odd	2		738.2.i.b.409.16	yes	36
9.2	odd	6		738.2.i.b.655.3	yes	36
9.7	even	3	inner	2214.2.i.b.1639.5		36
41.40	even	2	inner	2214.2.i.b.901.5		36
123.122	odd	2		738.2.i.b.409.3	✓	36
369.245	odd	6		738.2.i.b.655.16	yes	36
369.286	even	6	inner	2214.2.i.b.1639.6		36

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.13494 + 1.96578i) q^{5} +(4.05054 - 2.33858i) q^{7} -1.00000 q^{8} -2.26989 q^{10} +(1.57221 - 0.907717i) q^{11} +(0.198711 + 0.114726i) q^{13} +(4.05054 + 2.33858i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.87362i q^{17} -2.36579i q^{19} +(-1.13494 - 1.96578i) q^{20} +(1.57221 + 0.907717i) q^{22} +(0.946744 - 1.63981i) q^{23} +(-0.0761995 - 0.131981i) q^{25} +0.229452i q^{26} +4.67716i q^{28} +(6.44774 - 3.72261i) q^{29} +(-0.460392 + 0.797423i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.22067 + 2.43681i) q^{34} +10.6166i q^{35} +3.19279 q^{37} +(2.04884 - 1.18290i) q^{38} +(1.13494 - 1.96578i) q^{40} +(5.11672 - 3.84956i) q^{41} +(0.638021 + 1.10508i) q^{43} +1.81543i q^{44} +1.89349 q^{46} +(-2.19645 + 1.26812i) q^{47} +(7.43793 - 12.8829i) q^{49} +(0.0761995 - 0.131981i) q^{50} +(-0.198711 + 0.114726i) q^{52} -2.66180i q^{53} +4.12083i q^{55} +(-4.05054 + 2.33858i) q^{56} +(6.44774 + 3.72261i) q^{58} +(-3.32786 + 5.76402i) q^{59} +(2.29239 + 3.97053i) q^{61} -0.920785 q^{62} +1.00000 q^{64} +(-0.451052 + 0.260415i) q^{65} +(-0.268210 - 0.154851i) q^{67} +(-4.22067 - 2.43681i) q^{68} +(-9.19428 + 5.30832i) q^{70} +11.0540i q^{71} +14.4770 q^{73} +(1.59640 + 2.76504i) q^{74} +(2.04884 + 1.18290i) q^{76} +(4.24554 - 7.35349i) q^{77} +(-8.28272 + 4.78203i) q^{79} +2.26989 q^{80} +(5.89218 + 2.50643i) q^{82} +(-0.426481 - 0.738686i) q^{83} +(-9.58047 - 5.53128i) q^{85} +(-0.638021 + 1.10508i) q^{86} +(-1.57221 + 0.907717i) q^{88} +11.1698i q^{89} +1.07318 q^{91} +(0.946744 + 1.63981i) q^{92} +(-2.19645 - 1.26812i) q^{94} +(4.65063 + 2.68504i) q^{95} +(7.13300 - 4.11824i) q^{97} +14.8759 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) \) 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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