LMFDB - Embedded newform 738.2.ba.c.593.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,0,0,0,-4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$4$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			593.4
Character	$\chi$	$=$	738.593
Dual form			738.2.ba.c.341.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(0.411110 + 2.59565i) q^{5} +(-2.04814 + 1.74928i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.12610 - 1.54470i) q^{10} +(-3.44367 - 2.11028i) q^{11} +(2.15705 - 0.169764i) q^{13} +(2.48846 + 1.03075i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-7.35167 + 1.76498i) q^{17} +(0.291559 + 0.0229462i) q^{19} +(-2.34157 - 1.19309i) q^{20} +(-0.316883 + 4.02638i) q^{22} +(2.52027 - 7.75659i) q^{23} +(-1.81310 + 0.589111i) q^{25} +(-1.13054 - 1.84488i) q^{26} +(-0.211328 - 2.68518i) q^{28} +(-9.65226 - 2.31730i) q^{29} +(1.82426 + 2.51087i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.91020 + 5.74911i) q^{34} +(-5.38252 - 4.59711i) q^{35} +(-9.31688 - 6.76911i) q^{37} +(-0.111920 - 0.270198i) q^{38} +2.62800i q^{40} +(-6.36190 + 0.725419i) q^{41} +(6.30064 - 3.21034i) q^{43} +(3.73139 - 1.54559i) q^{44} +(-8.05535 + 1.27584i) q^{46} +(-2.06577 + 2.41870i) q^{47} +(0.0398687 - 0.251721i) q^{49} +(1.34803 + 1.34803i) q^{50} +(-1.13054 + 1.84488i) q^{52} +(-1.45943 + 6.07895i) q^{53} +(4.06182 - 9.80611i) q^{55} +(-2.29657 + 1.40734i) q^{56} +(2.31730 + 9.65226i) q^{58} +(13.6035 + 4.42003i) q^{59} +(-3.72390 + 7.30856i) q^{61} +(1.40901 - 2.76534i) q^{62} +(0.951057 + 0.309017i) q^{64} +(1.32743 + 5.52916i) q^{65} +(-7.36261 + 4.51182i) q^{67} +(2.89331 - 6.98506i) q^{68} +(-1.65244 + 6.88291i) q^{70} +(1.47588 - 2.40842i) q^{71} +(7.65081 + 7.65081i) q^{73} +(-1.80155 + 11.3745i) q^{74} +(-0.189938 + 0.222389i) q^{76} +(10.7446 - 1.70178i) q^{77} +(-7.24823 + 3.00231i) q^{79} +(2.34157 - 1.19309i) q^{80} +(3.53459 + 5.33916i) q^{82} +8.81543i q^{83} +(-7.60362 - 18.3568i) q^{85} +(-5.72086 - 4.15645i) q^{86} +(-3.07115 - 2.62301i) q^{88} +(-4.75921 - 5.57232i) q^{89} +(-4.12099 + 4.12099i) q^{91} +(4.79384 + 6.59815i) q^{92} +(3.09292 + 0.742544i) q^{94} +(0.0603026 + 0.766218i) q^{95} +(-0.338102 - 0.551732i) q^{97} +(-0.242385 + 0.0787557i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{14} + 16 q^{16} - 16 q^{17} + 4 q^{19} - 4 q^{22} + 48 q^{23} + 40 q^{25} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 40 q^{31} + 4 q^{34} - 52 q^{35} + 8 q^{37} + 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) $ 64 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^14 + 16 * q^16 - 16 * q^17 + 4 * q^19 - 4 * q^22 + 48 * q^23 + 40 * q^25 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 40 * q^31 + 4 * q^34 - 52 * q^35 + 8 * q^37 + 16 * q^38 + 12 * q^41 + 32 * q^43 - 4 * q^44 - 8 * q^47 + 48 * q^49 + 16 * q^50 - 20 * q^52 - 48 * q^53 - 36 * q^55 + 16 * q^56 - 20 * q^58 + 20 * q^59 + 24 * q^61 - 36 * q^62 + 60 * q^65 - 20 * q^67 + 12 * q^68 - 8 * q^70 - 8 * q^71 + 72 * q^73 - 12 * q^74 + 4 * q^76 - 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 - 32 * q^86 - 8 * q^88 + 84 * q^89 + 72 * q^91 + 12 * q^94 - 12 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{9}{40}\right)$

Coefficient data

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

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

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

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$		0			0
$3$		0			0
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	0.411110	+	2.59565i	0.183854	+	1.16081i	0.891088	+	0.453830i	$0.149943\pi$
$5$	0.411110	+	2.59565i	0.183854	+	1.16081i	−0.707234	+	0.706979i	$0.750057\pi$
$6$		0			0
$7$	−2.04814	+	1.74928i	−0.774125	+	0.661165i	−0.946078	−	0.323940i	$-0.894992\pi$
$7$	−2.04814	+	1.74928i	−0.774125	+	0.661165i	0.171953	+	0.985105i	$0.444992\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$		0			0
$10$	2.12610	−	1.54470i	0.672332	−	0.488478i
$11$	−3.44367	−	2.11028i	−1.03830	−	0.636274i	−0.104672	−	0.994507i	$-0.533379\pi$
$11$	−3.44367	−	2.11028i	−1.03830	−	0.636274i	−0.933632	+	0.358233i	$0.883379\pi$
$12$		0			0
$13$	2.15705	−	0.169764i	0.598259	−	0.0470840i	0.224285	−	0.974523i	$-0.427995\pi$
$13$	2.15705	−	0.169764i	0.598259	−	0.0470840i	0.373973	+	0.927439i	$0.377995\pi$
$14$	2.48846	+	1.03075i	0.665068	+	0.275480i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−7.35167	+	1.76498i	−1.78304	+	0.428071i	−0.984718	−	0.174156i	$-0.944280\pi$
$17$	−7.35167	+	1.76498i	−1.78304	+	0.428071i	−0.798325	+	0.602227i	$0.794280\pi$
$18$		0			0
$19$	0.291559	+	0.0229462i	0.0668882	+	0.00526421i	0.111859	−	0.993724i	$-0.464319\pi$
$19$	0.291559	+	0.0229462i	0.0668882	+	0.00526421i	−0.0449708	+	0.998988i	$0.514319\pi$
$20$	−2.34157	−	1.19309i	−0.523591	−	0.266783i
$21$		0			0
$22$	−0.316883	+	4.02638i	−0.0675596	+	0.858426i
$23$	2.52027	−	7.75659i	0.525512	−	1.61736i	−0.237788	−	0.971317i	$-0.576422\pi$
$23$	2.52027	−	7.75659i	0.525512	−	1.61736i	0.763300	−	0.646044i	$-0.223578\pi$
$24$		0			0
$25$	−1.81310	+	0.589111i	−0.362619	+	0.117822i
$26$	−1.13054	−	1.84488i	−0.221718	−	0.361810i
$27$		0			0
$28$	−0.211328	−	2.68518i	−0.0399373	−	0.507452i
$29$	−9.65226	−	2.31730i	−1.79238	−	0.430312i	−0.805611	−	0.592445i	$-0.798163\pi$
$29$	−9.65226	−	2.31730i	−1.79238	−	0.430312i	−0.986769	+	0.162133i	$0.948163\pi$
$30$		0			0
$31$	1.82426	+	2.51087i	0.327646	+	0.450966i	0.940782	−	0.339011i	$-0.110092\pi$
$31$	1.82426	+	2.51087i	0.327646	+	0.450966i	−0.613136	+	0.789977i	$0.710092\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	4.91020	+	5.74911i	0.842092	+	0.985963i
$35$	−5.38252	−	4.59711i	−0.909813	−	0.777053i
$36$		0			0
$37$	−9.31688	−	6.76911i	−1.53169	−	1.11283i	−0.955293	−	0.295662i	$-0.904460\pi$
$37$	−9.31688	−	6.76911i	−1.53169	−	1.11283i	−0.576393	−	0.817173i	$-0.695540\pi$
$38$	−0.111920	−	0.270198i	−0.0181558	−	0.0438319i
$39$		0			0
$40$			2.62800i			0.415524i
$41$	−6.36190	+	0.725419i	−0.993562	+	0.113291i
$41$	−6.36190	+	0.725419i	−0.993562	+	0.113291i
$42$		0			0
$43$	6.30064	−	3.21034i	0.960839	−	0.489572i	0.0980751	−	0.995179i	$-0.468731\pi$
$43$	6.30064	−	3.21034i	0.960839	−	0.489572i	0.862764	+	0.505607i	$0.168731\pi$
$44$	3.73139	−	1.54559i	0.562528	−	0.233007i
$45$		0			0
$46$	−8.05535	+	1.27584i	−1.18770	+	0.188113i
$47$	−2.06577	+	2.41870i	−0.301323	+	0.352804i	−0.890323	−	0.455329i	$-0.849522\pi$
$47$	−2.06577	+	2.41870i	−0.301323	+	0.352804i	0.589000	+	0.808133i	$0.299522\pi$
$48$		0			0
$49$	0.0398687	−	0.251721i	0.00569553	−	0.0359602i
$50$	1.34803	+	1.34803i	0.190640	+	0.190640i
$51$		0			0
$52$	−1.13054	+	1.84488i	−0.156778	+	0.255838i
$53$	−1.45943	+	6.07895i	−0.200468	+	0.835008i	0.777942	+	0.628336i	$0.216264\pi$
$53$	−1.45943	+	6.07895i	−0.200468	+	0.835008i	−0.978410	+	0.206673i	$0.933736\pi$
$54$		0			0
$55$	4.06182	−	9.80611i	0.547696	−	1.32226i
$56$	−2.29657	+	1.40734i	−0.306892	+	0.188064i
$57$		0			0
$58$	2.31730	+	9.65226i	0.304277	+	1.26740i
$59$	13.6035	+	4.42003i	1.77102	+	0.575439i	0.998244	−	0.0592414i	$-0.0188682\pi$
$59$	13.6035	+	4.42003i	1.77102	+	0.575439i	0.772775	+	0.634680i	$0.218868\pi$
$60$		0			0
$61$	−3.72390	+	7.30856i	−0.476796	+	0.935765i	0.519875	+	0.854242i	$0.325978\pi$
$61$	−3.72390	+	7.30856i	−0.476796	+	0.935765i	−0.996671	+	0.0815229i	$0.974022\pi$
$62$	1.40901	−	2.76534i	0.178944	−	0.351198i
$63$		0			0
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	1.32743	+	5.52916i	0.164648	+	0.685808i
$66$		0			0
$67$	−7.36261	+	4.51182i	−0.899486	+	0.551206i	−0.893644	−	0.448777i	$-0.851860\pi$
$67$	−7.36261	+	4.51182i	−0.899486	+	0.551206i	−0.00584265	+	0.999983i	$0.501860\pi$
$68$	2.89331	−	6.98506i	0.350865	−	0.847063i
$69$		0			0
$70$	−1.65244	+	6.88291i	−0.197504	+	0.822665i
$71$	1.47588	−	2.40842i	0.175155	−	0.285827i	−0.753000	−	0.658020i	$-0.771394\pi$
$71$	1.47588	−	2.40842i	0.175155	−	0.285827i	0.928155	+	0.372193i	$0.121394\pi$
$72$		0			0
$73$	7.65081	+	7.65081i	0.895460	+	0.895460i	0.995030	−	0.0995706i	$-0.0317469\pi$
$73$	7.65081	+	7.65081i	0.895460	+	0.895460i	−0.0995706	+	0.995030i	$0.531747\pi$
$74$	−1.80155	+	11.3745i	−0.209425	+	1.32226i
$75$		0			0
$76$	−0.189938	+	0.222389i	−0.0217874	+	0.0255097i
$77$	10.7446	−	1.70178i	1.22446	−	0.193935i
$78$		0			0
$79$	−7.24823	+	3.00231i	−0.815489	+	0.337787i	−0.751142	−	0.660141i	$-0.770497\pi$
$79$	−7.24823	+	3.00231i	−0.815489	+	0.337787i	−0.0643474	+	0.997928i	$0.520497\pi$
$80$	2.34157	−	1.19309i	0.261795	−	0.133391i
$81$		0			0
$82$	3.53459	+	5.33916i	0.390331	+	0.589612i
$83$			8.81543i			0.967619i	0.875173	+	0.483810i	$0.160747\pi$
$83$			8.81543i			0.967619i	−0.875173	+	0.483810i	$0.839253\pi$
$84$		0			0
$85$	−7.60362	−	18.3568i	−0.824728	−	1.99107i
$86$	−5.72086	−	4.15645i	−0.616897	−	0.448202i
$87$		0			0
$88$	−3.07115	−	2.62301i	−0.327386	−	0.279614i
$89$	−4.75921	−	5.57232i	−0.504476	−	0.590665i	0.448473	−	0.893796i	$-0.351968\pi$
$89$	−4.75921	−	5.57232i	−0.504476	−	0.590665i	−0.952949	+	0.303131i	$0.901968\pi$
$90$		0			0
$91$	−4.12099	+	4.12099i	−0.431997	+	0.431997i
$92$	4.79384	+	6.59815i	0.499792	+	0.687905i
$93$		0			0
$94$	3.09292	+	0.742544i	0.319010	+	0.0765876i
$95$	0.0603026	+	0.766218i	0.00618692	+	0.0786123i
$96$		0			0
$97$	−0.338102	−	0.551732i	−0.0343291	−	0.0560199i	0.835015	−	0.550227i	$-0.185459\pi$
$97$	−0.338102	−	0.551732i	−0.0343291	−	0.0560199i	−0.869344	+	0.494207i	$0.835459\pi$
$98$	−0.242385	+	0.0787557i	−0.0244846	+	0.00795553i
$99$		0			0
$100$	0.589111	−	1.81310i	0.0589111	−	0.181310i
$101$	0.0587329	−	0.746272i	0.00584414	−	0.0742569i	−0.993304	−	0.115533i	$-0.963142\pi$
$101$	0.0587329	−	0.746272i	0.00584414	−	0.0742569i	0.999148	+	0.0412762i	$0.0131424\pi$
$102$		0			0
$103$	−1.30320	−	0.664013i	−0.128408	−	0.0654272i	0.388606	−	0.921404i	$-0.372957\pi$
$103$	−1.30320	−	0.664013i	−0.128408	−	0.0654272i	−0.517014	+	0.855977i	$0.672957\pi$
$104$	2.15705	+	0.169764i	0.211516	+	0.0166467i
$105$		0			0
$106$	6.07895	−	1.45943i	0.590440	−	0.141752i
$107$	−0.0855603	−	0.263328i	−0.00827143	−	0.0254568i	0.946836	−	0.321718i	$-0.104260\pi$
$107$	−0.0855603	−	0.263328i	−0.00827143	−	0.0254568i	−0.955107	+	0.296261i	$0.904260\pi$
$108$		0			0
$109$	−4.00305	−	1.65812i	−0.383423	−	0.158819i	0.182642	−	0.983179i	$-0.441535\pi$
$109$	−4.00305	−	1.65812i	−0.383423	−	0.158819i	−0.566065	+	0.824360i	$0.691535\pi$
$110$	−10.5813	+	0.832769i	−1.00889	+	0.0794014i
$111$		0			0
$112$	2.29657	+	1.40734i	0.217006	+	0.132981i
$113$	−4.19219	+	3.04580i	−0.394368	+	0.286525i	−0.767243	−	0.641356i	$-0.778372\pi$
$113$	−4.19219	+	3.04580i	−0.394368	+	0.286525i	0.372875	+	0.927882i	$0.378372\pi$
$114$		0			0
$115$	21.1695	+	3.35292i	1.97407	+	0.312661i
$116$	7.54819	−	6.44677i	0.700832	−	0.598567i
$117$		0			0
$118$	−2.23756	−	14.1274i	−0.205984	−	1.30053i
$119$	11.9698	−	16.4751i	1.09727	−	1.51027i
$120$		0			0
$121$	2.41165	+	4.73314i	0.219241	+	0.430285i
$122$	8.20259			0.742627
$123$		0			0
$124$	−3.10361			−0.278712
$125$	3.69094	+	7.24387i	0.330127	+	0.647911i
$126$		0			0
$127$	−0.545165	+	0.750355i	−0.0483755	+	0.0665832i	−0.832519	−	0.553996i	$-0.813102\pi$
$127$	−0.545165	+	0.750355i	−0.0483755	+	0.0665832i	0.784144	+	0.620579i	$0.213102\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$		0			0
$130$	4.32387	−	3.69294i	0.379229	−	0.323892i
$131$	−12.9212	−	2.04652i	−1.12893	−	0.178805i	−0.436095	−	0.899901i	$-0.643639\pi$
$131$	−12.9212	−	2.04652i	−1.12893	−	0.178805i	−0.692836	+	0.721096i	$0.743639\pi$
$132$		0			0
$133$	−0.637293	+	0.463021i	−0.0552603	+	0.0401490i
$134$	7.36261	+	4.51182i	0.636033	+	0.389762i
$135$		0			0
$136$	−7.53727	+	0.593196i	−0.646315	+	0.0508661i
$137$	11.1562	+	4.62106i	0.953140	+	0.394804i	0.804410	−	0.594074i	$-0.202481\pi$
$137$	11.1562	+	4.62106i	0.953140	+	0.394804i	0.148730	+	0.988878i	$0.452481\pi$
$138$		0			0
$139$	−1.89325	−	5.82684i	−0.160584	−	0.494226i	0.838100	−	0.545516i	$-0.183666\pi$
$139$	−1.89325	−	5.82684i	−0.160584	−	0.494226i	−0.998684	+	0.0512908i	$0.983666\pi$
$140$	6.88291	−	1.65244i	0.581712	−	0.139657i
$141$		0			0
$142$	−2.81596	−	0.221621i	−0.236310	−	0.0185980i
$143$	−7.78642	−	3.96738i	−0.651133	−	0.331769i
$144$		0			0
$145$	2.04676	−	26.0065i	0.169974	−	2.15973i
$146$	3.34353	−	10.2903i	0.276712	−	0.851633i
$147$		0			0
$148$	10.9526	−	3.55873i	0.900302	−	0.292526i
$149$	10.3624	+	16.9098i	0.848917	+	1.38531i	0.921677	+	0.387957i	$0.126819\pi$
$149$	10.3624	+	16.9098i	0.848917	+	1.38531i	−0.0727606	+	0.997349i	$0.523181\pi$
$150$		0			0
$151$	−0.0644208	−	0.818544i	−0.00524249	−	0.0666122i	0.993740	−	0.111721i	$-0.0356364\pi$
$151$	−0.0644208	−	0.818544i	−0.00524249	−	0.0666122i	−0.998982	+	0.0451092i	$0.985636\pi$
$152$	0.284380	+	0.0682735i	0.0230662	+	0.00553771i
$153$		0			0
$154$	−6.39423	−	8.80091i	−0.515262	−	0.709197i
$155$	−5.76737	+	5.76737i	−0.463247	+	0.463247i
$156$		0			0
$157$	−1.15620	−	1.35373i	−0.0922747	−	0.108040i	0.712347	−	0.701827i	$-0.247632\pi$
$157$	−1.15620	−	1.35373i	−0.0922747	−	0.108040i	−0.804622	+	0.593787i	$0.797632\pi$
$158$	5.96571	+	5.09520i	0.474606	+	0.405352i
$159$		0			0
$160$	−2.12610	−	1.54470i	−0.168083	−	0.122119i
$161$	8.40657	+	20.2953i	0.662530	+	1.59949i
$162$		0			0
$163$		−	22.2882i		−	1.74574i	−0.487949	−	0.872872i	$-0.662255\pi$
$163$		−	22.2882i		−	1.74574i	0.487949	−	0.872872i	$-0.337745\pi$
$164$	3.15255	−	5.57328i	0.246173	−	0.435200i
$165$		0			0
$166$	7.85461	−	4.00212i	0.609636	−	0.310625i
$167$	−12.4756	+	5.16757i	−0.965392	+	0.399878i	−0.808995	−	0.587816i	$-0.799988\pi$
$167$	−12.4756	+	5.16757i	−0.965392	+	0.399878i	−0.156397	+	0.987694i	$0.549988\pi$
$168$		0			0
$169$	−8.21589	+	1.30127i	−0.631992	+	0.100098i
$170$	−12.9040	+	15.1087i	−0.989693	+	1.15878i
$171$		0			0
$172$	−1.10621	+	6.98432i	−0.0843475	+	0.532549i
$173$	−7.68491	−	7.68491i	−0.584273	−	0.584273i	0.351802	−	0.936075i	$-0.385569\pi$
$173$	−7.68491	−	7.68491i	−0.584273	−	0.584273i	−0.936075	+	0.351802i	$0.885569\pi$
$174$		0			0
$175$	2.68296	−	4.37819i	0.202813	−	0.330960i
$176$	−0.942845	+	3.92723i	−0.0710697	+	0.296026i
$177$		0			0
$178$	−2.80434	+	6.77027i	−0.210194	+	0.507453i
$179$	−5.31468	+	3.25684i	−0.397238	+	0.243428i	−0.706743	−	0.707470i	$-0.749836\pi$
$179$	−5.31468	+	3.25684i	−0.397238	+	0.243428i	0.309505	+	0.950898i	$0.399836\pi$
$180$		0			0
$181$	3.84904	+	16.0324i	0.286097	+	1.19168i	0.911474	+	0.411357i	$0.134945\pi$
$181$	3.84904	+	16.0324i	0.286097	+	1.19168i	−0.625377	+	0.780322i	$0.715055\pi$
$182$	5.54271	+	1.80094i	0.410853	+	0.133494i
$183$		0			0
$184$	3.70264	−	7.26684i	0.272962	−	0.535718i
$185$	13.7400	−	26.9662i	1.01018	−	1.98259i
$186$		0			0
$187$	29.0413	+	9.43610i	2.12371	+	0.690036i
$188$	−0.742544	−	3.09292i	−0.0541556	−	0.225574i
$189$		0			0
$190$	0.655328	−	0.401586i	0.0475425	−	0.0291341i
$191$	10.1152	−	24.4203i	0.731912	−	1.76699i	0.0957913	−	0.995401i	$-0.469462\pi$
$191$	10.1152	−	24.4203i	0.731912	−	1.76699i	0.636120	−	0.771590i	$-0.280538\pi$
$192$		0			0
$193$	3.02930	−	12.6179i	0.218054	−	0.908258i	−0.750781	−	0.660551i	$-0.770323\pi$
$193$	3.02930	−	12.6179i	0.218054	−	0.908258i	0.968835	−	0.247707i	$-0.0796772\pi$
$194$	−0.338102	+	0.551732i	−0.0242743	+	0.0396121i
$195$		0			0
$196$	0.180212	+	0.180212i	0.0128723	+	0.0128723i
$197$	2.76967	−	17.4870i	0.197331	−	1.24590i	−0.667797	−	0.744344i	$-0.732762\pi$
$197$	2.76967	−	17.4870i	0.197331	−	1.24590i	0.865127	−	0.501552i	$-0.167238\pi$
$198$		0			0
$199$	−4.69318	+	5.49500i	−0.332690	+	0.389530i	−0.901385	−	0.433018i	$-0.857449\pi$
$199$	−4.69318	+	5.49500i	−0.332690	+	0.389530i	0.568695	+	0.822549i	$0.307449\pi$
$200$	−1.88293	+	0.298227i	−0.133143	+	0.0210878i
$201$		0			0
$202$	−0.691598	+	0.286469i	−0.0486606	+	0.0201559i
$203$	23.8228	−	12.1383i	1.67203	−	0.851943i
$204$		0			0
$205$	−4.49837	−	16.2150i	−0.314180	−	1.13251i
$206$			1.46261i			0.101905i
$207$		0			0
$208$	−0.828021	−	1.99902i	−0.0574129	−	0.138607i
$209$	−0.955609	−	0.694290i	−0.0661008	−	0.0480251i
$210$		0			0
$211$	13.9118	+	11.8818i	0.957725	+	0.817974i	0.983355	−	0.181697i	$-0.0581591\pi$
$211$	13.9118	+	11.8818i	0.957725	+	0.817974i	−0.0256296	+	0.999672i	$0.508159\pi$
$212$	−4.06015	−	4.75382i	−0.278852	−	0.326494i
$213$		0			0
$214$	−0.195783	+	0.195783i	−0.0133835	+	0.0133835i
$215$	10.9232	+	15.0344i	0.744954	+	1.02534i
$216$		0			0
$217$	−8.12855	−	1.95149i	−0.551802	−	0.132476i
$218$	0.339953	+	4.31952i	0.0230245	+	0.292554i
$219$		0			0
$220$	5.54583	+	9.04997i	0.373900	+	0.610149i
$221$	−15.5583	+	5.05520i	−1.04657	+	0.340050i
$222$		0			0
$223$	−1.13493	+	3.49295i	−0.0760003	+	0.233905i	−0.981838	−	0.189719i	$-0.939242\pi$
$223$	−1.13493	+	3.49295i	−0.0760003	+	0.233905i	0.905838	+	0.423624i	$0.139242\pi$
$224$	0.211328	−	2.68518i	0.0141200	−	0.179411i
$225$		0			0
$226$	4.61705	+	2.35250i	0.307121	+	0.156486i
$227$	14.3286	+	1.12769i	0.951023	+	0.0748471i	0.544470	−	0.838780i	$-0.316731\pi$
$227$	14.3286	+	1.12769i	0.951023	+	0.0748471i	0.406553	+	0.913627i	$0.366731\pi$
$228$		0			0
$229$	1.70910	−	0.410319i	0.112941	−	0.0271147i	−0.176581	−	0.984286i	$-0.556504\pi$
$229$	1.70910	−	0.410319i	0.112941	−	0.0271147i	0.289522	+	0.957171i	$0.406504\pi$
$230$	−6.62328	−	20.3844i	−0.436726	−	1.34410i
$231$		0			0
$232$	−9.17092	−	3.79872i	−0.602100	−	0.249398i
$233$	−5.26722	+	0.414539i	−0.345067	+	0.0271574i	−0.249809	−	0.968295i	$-0.580368\pi$
$233$	−5.26722	+	0.414539i	−0.345067	+	0.0271574i	−0.0952584	+	0.995453i	$0.530368\pi$
$234$		0			0
$235$	−7.12736	−	4.36765i	−0.464938	−	0.284914i
$236$	−11.5718	+	8.40740i	−0.753259	+	0.547275i
$237$		0			0
$238$	−20.1136	−	3.18568i	−1.30377	−	0.206497i
$239$	−19.1656	+	16.3690i	−1.23972	+	1.05882i	−0.243688	+	0.969854i	$0.578357\pi$
$239$	−19.1656	+	16.3690i	−1.23972	+	1.05882i	−0.996034	+	0.0889695i	$0.971643\pi$
$240$		0			0
$241$	2.98875	+	18.8702i	0.192522	+	1.21554i	0.874814	+	0.484459i	$0.160984\pi$
$241$	2.98875	+	18.8702i	0.192522	+	1.21554i	−0.682291	+	0.731080i	$0.739016\pi$
$242$	3.12239	−	4.29760i	0.200715	−	0.276260i
$243$		0			0
$244$	−3.72390	−	7.30856i	−0.238398	−	0.467883i
$245$	0.669770			0.0427900
$246$		0			0
$247$	0.632803			0.0402643
$248$	1.40901	+	2.76534i	0.0894722	+	0.175599i
$249$		0			0
$250$	4.77868	−	6.57729i	0.302231	−	0.415985i
$251$	1.61404	+	10.1906i	0.101877	+	0.643228i	0.984798	+	0.173705i	$0.0555740\pi$
$251$	1.61404	+	10.1906i	0.101877	+	0.643228i	−0.882920	+	0.469523i	$0.844426\pi$
$252$		0			0
$253$	−25.0476	+	21.3926i	−1.57473	+	1.34494i
$254$	0.916070	+	0.145091i	0.0574794	+	0.00910384i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	13.9754	+	8.56416i	0.871764	+	0.534217i	0.884945	−	0.465696i	$-0.154196\pi$
$257$	13.9754	+	8.56416i	0.871764	+	0.534217i	−0.0131813	+	0.999913i	$0.504196\pi$
$258$		0			0
$259$	30.9233	−	2.43372i	1.92148	−	0.151224i
$260$	−5.25343	−	2.17604i	−0.325804	−	0.134952i
$261$		0			0
$262$	4.04264	+	12.4420i	0.249755	+	0.768668i
$263$	−0.123456	+	0.0296391i	−0.00761261	+	0.00182763i	−0.237250	−	0.971449i	$-0.576246\pi$
$263$	−0.123456	+	0.0296391i	−0.00761261	+	0.00182763i	0.229637	+	0.973276i	$0.426246\pi$
$264$		0			0
$265$	−16.3788	−	1.28904i	−1.00614	−	0.0791851i
$266$	0.701879	+	0.357625i	0.0430350	+	0.0219274i
$267$		0			0
$268$	0.677500	−	8.60846i	0.0413849	−	0.525845i
$269$	−3.61629	+	11.1298i	−0.220489	+	0.678595i	0.778229	+	0.627980i	$0.216118\pi$
$269$	−3.61629	+	11.1298i	−0.220489	+	0.678595i	−0.998718	+	0.0506150i	$0.983882\pi$
$270$		0			0
$271$	−17.5323	+	5.69659i	−1.06501	+	0.346043i	−0.788543	−	0.614979i	$-0.789164\pi$
$271$	−17.5323	+	5.69659i	−1.06501	+	0.346043i	−0.276469	+	0.961023i	$0.589164\pi$
$272$	3.95039	+	6.44645i	0.239528	+	0.390873i
$273$		0			0
$274$	−0.947425	−	12.0382i	−0.0572361	−	0.727253i
$275$	7.48689	+	1.79744i	0.451477	+	0.108390i
$276$		0			0
$277$	−9.95977	−	13.7084i	−0.598425	−	0.823661i	0.397138	−	0.917759i	$-0.370003\pi$
$277$	−9.95977	−	13.7084i	−0.598425	−	0.823661i	−0.995563	+	0.0940980i	$0.970003\pi$
$278$	−4.33223	+	4.33223i	−0.259830	+	0.259830i
$279$		0			0
$280$	−4.59711	−	5.38252i	−0.274730	−	0.321667i
$281$	9.55436	+	8.16020i	0.569965	+	0.486796i	0.887096	−	0.461586i	$-0.152719\pi$
$281$	9.55436	+	8.16020i	0.569965	+	0.486796i	−0.317130	+	0.948382i	$0.602719\pi$
$282$		0			0
$283$	5.66033	+	4.11247i	0.336472	+	0.244461i	0.743172	−	0.669101i	$-0.233321\pi$
$283$	5.66033	+	4.11247i	0.336472	+	0.244461i	−0.406700	+	0.913562i	$0.633321\pi$
$284$	1.08095	+	2.60965i	0.0641427	+	0.154854i
$285$		0			0
$286$			8.73890i			0.516742i
$287$	11.7611	−	12.6145i	0.694237	−	0.744610i
$288$		0			0
$289$	35.7848	−	18.2333i	2.10499	−	1.07255i
$290$	−24.1012	+	9.98305i	−1.41527	+	0.586225i
$291$		0			0
$292$	−10.6867	+	1.69260i	−0.625390	+	0.0990521i
$293$	0.958456	−	1.12221i	0.0559936	−	0.0655601i	−0.731702	−	0.681624i	$-0.761274\pi$
$293$	0.958456	−	1.12221i	0.0559936	−	0.0655601i	0.787696	+	0.616064i	$0.211274\pi$
$294$		0			0
$295$	−5.88032	+	37.1269i	−0.342366	+	2.16161i
$296$	−8.14325	−	8.14325i	−0.473317	−	0.473317i
$297$		0			0
$298$	10.3624	−	16.9098i	0.600275	−	0.979560i
$299$	4.11957	−	17.1592i	0.238241	−	0.992344i
$300$		0			0
$301$	−7.28883	+	17.5968i	−0.420121	+	1.01426i
$302$	−0.700082	+	0.429011i	−0.0402852	+	0.0246868i
$303$		0			0
$304$	−0.0682735	−	0.284380i	−0.00391576	−	0.0163103i
$305$	−20.5014	−	6.66130i	−1.17391	−	0.381425i
$306$		0			0
$307$	13.3000	−	26.1028i	0.759074	−	1.48977i	−0.109382	−	0.994000i	$-0.534887\pi$
$307$	13.3000	−	26.1028i	0.759074	−	1.48977i	0.868456	−	0.495767i	$-0.165113\pi$
$308$	−4.93874	+	9.69283i	−0.281411	+	0.552300i
$309$		0			0
$310$	7.75710	+	2.52044i	0.440574	+	0.143151i
$311$	5.49882	+	22.9042i	0.311810	+	1.29878i	0.879642	+	0.475636i	$0.157782\pi$
$311$	5.49882	+	22.9042i	0.311810	+	1.29878i	−0.567833	+	0.823144i	$0.692218\pi$
$312$		0			0
$313$	−22.4270	+	13.7433i	−1.26765	+	0.776816i	−0.983315	−	0.181909i	$-0.941772\pi$
$313$	−22.4270	+	13.7433i	−1.26765	+	0.776816i	−0.284333	+	0.958725i	$0.591772\pi$
$314$	−0.681283	+	1.64476i	−0.0384470	+	0.0928193i
$315$		0			0
$316$	1.83148	−	7.62865i	0.103029	−	0.429145i
$317$	8.00287	−	13.0595i	0.449486	−	0.733494i	−0.544992	−	0.838441i	$-0.683467\pi$
$317$	8.00287	−	13.0595i	0.449486	−	0.733494i	0.994478	+	0.104947i	$0.0334673\pi$
$318$		0			0
$319$	28.3490	+	28.3490i	1.58724	+	1.58724i
$320$	−0.411110	+	2.59565i	−0.0229818	+	0.145101i
$321$		0			0
$322$	14.2667	−	16.7042i	0.795052	−	0.930886i
$323$	−2.18395	+	0.345903i	−0.121518	+	0.0192466i
$324$		0			0
$325$	−3.81094	+	1.57854i	−0.211393	+	0.0875617i
$326$	−19.8589	+	10.1186i	−1.09988	+	0.560418i
$327$		0			0
$328$	−6.39705	−	0.278733i	−0.353218	−	0.0153905i
$329$		−	8.56745i		−	0.472339i
$330$		0			0
$331$	−0.441290	−	1.06537i	−0.0242555	−	0.0585579i	0.911288	−	0.411770i	$-0.135089\pi$
$331$	−0.441290	−	1.06537i	−0.0242555	−	0.0585579i	−0.935543	+	0.353212i	$0.885089\pi$
$332$	−7.13183	−	5.18158i	−0.391410	−	0.284376i
$333$		0			0
$334$	10.2681	+	8.76982i	0.561848	+	0.479863i
$335$	−14.7379	−	17.2559i	−0.805219	−	0.942791i
$336$		0			0
$337$	1.11484	−	1.11484i	0.0607293	−	0.0607293i	−0.676090	−	0.736819i	$-0.736327\pi$
$337$	1.11484	−	1.11484i	0.0607293	−	0.0607293i	0.736819	+	0.676090i	$0.236327\pi$
$338$	4.88938	+	6.72965i	0.265947	+	0.366045i
$339$		0			0
$340$	19.3202	+	4.63838i	1.04779	+	0.251551i
$341$	−0.983480	−	12.4963i	−0.0532585	−	0.676713i
$342$		0			0
$343$	−9.49272	−	15.4907i	−0.512559	−	0.836420i
$344$	6.72528	−	2.18518i	0.362603	−	0.117817i
$345$		0			0
$346$	−3.35843	+	10.3362i	−0.180550	+	0.555677i
$347$	−0.477686	+	6.06957i	−0.0256435	+	0.325832i	0.970694	+	0.240320i	$0.0772524\pi$
$347$	−0.477686	+	6.06957i	−0.0256435	+	0.325832i	−0.996337	+	0.0855115i	$0.972748\pi$
$348$		0			0
$349$	−9.52685	−	4.85417i	−0.509961	−	0.259838i	0.180024	−	0.983662i	$-0.442383\pi$
$349$	−9.52685	−	4.85417i	−0.509961	−	0.259838i	−0.689984	+	0.723824i	$0.742383\pi$
$350$	−5.11904	−	0.402877i	−0.273624	−	0.0215347i
$351$		0			0
$352$	3.92723	−	0.942845i	0.209322	−	0.0502538i
$353$	0.710189	+	2.18574i	0.0377995	+	0.116335i	0.968176	−	0.250271i	$-0.0805197\pi$
$353$	0.710189	+	2.18574i	0.0377995	+	0.116335i	−0.930376	+	0.366606i	$0.880520\pi$
$354$		0			0
$355$	6.85817	+	2.84075i	0.363994	+	0.150771i
$356$	7.30550	−	0.574955i	0.387191	−	0.0304726i
$357$		0			0
$358$	5.31468	+	3.25684i	0.280890	+	0.172129i
$359$	13.0904	−	9.51077i	0.690887	−	0.501959i	−0.186064	−	0.982538i	$-0.559573\pi$
$359$	13.0904	−	9.51077i	0.690887	−	0.501959i	0.876952	+	0.480579i	$0.159573\pi$
$360$		0			0
$361$	−18.6816	−	2.95887i	−0.983242	−	0.155730i
$362$	12.5376	−	10.7081i	0.658959	−	0.562804i
$363$		0			0
$364$	−0.911693	−	5.75620i	−0.0477857	−	0.301707i
$365$	−16.7135	+	23.0041i	−0.874824	+	1.20409i
$366$		0			0
$367$	−0.425604	−	0.835295i	−0.0222163	−	0.0436020i	0.879632	−	0.475656i	$-0.157789\pi$
$367$	−0.425604	−	0.835295i	−0.0222163	−	0.0436020i	−0.901848	+	0.432054i	$0.857789\pi$
$368$	−8.15576			−0.425149
$369$		0			0
$370$	−30.2649			−1.57340
$371$	−7.64467	−	15.0035i	−0.396891	−	0.778943i
$372$		0			0
$373$	−7.03781	+	9.68671i	−0.364404	+	0.501559i	−0.951369	−	0.308053i	$-0.900323\pi$
$373$	−7.03781	+	9.68671i	−0.364404	+	0.501559i	0.586965	+	0.809612i	$0.300323\pi$
$374$	−4.77686	−	30.1599i	−0.247006	−	1.55953i
$375$		0			0
$376$	−2.41870	+	2.06577i	−0.124735	+	0.106534i
$377$	−21.2138	−	3.35994i	−1.09257	−	0.173046i
$378$		0			0
$379$	−8.90444	+	6.46945i	−0.457390	+	0.332313i	−0.792507	−	0.609863i	$-0.791224\pi$
$379$	−8.90444	+	6.46945i	−0.457390	+	0.332313i	0.335116	+	0.942177i	$0.391224\pi$
$380$	−0.655328	−	0.401586i	−0.0336176	−	0.0206009i
$381$		0			0
$382$	−26.3509	+	2.07386i	−1.34823	+	0.106108i
$383$	−15.1623	−	6.28043i	−0.774757	−	0.320915i	−0.0399594	−	0.999201i	$-0.512723\pi$
$383$	−15.1623	−	6.28043i	−0.774757	−	0.320915i	−0.734798	+	0.678286i	$0.762723\pi$
$384$		0			0
$385$	8.83442	+	27.1896i	0.450244	+	1.38571i
$386$	−12.6179	+	3.02930i	−0.642236	+	0.154187i
$387$		0			0
$388$	0.645092	+	0.0507699i	0.0327496	+	0.00257745i
$389$	12.3580	+	6.29672i	0.626576	+	0.319256i	0.738289	−	0.674484i	$-0.235634\pi$
$389$	12.3580	+	6.29672i	0.626576	+	0.319256i	−0.111714	+	0.993740i	$0.535634\pi$
$390$		0			0
$391$	−4.83796	+	61.4722i	−0.244666	+	3.10878i
$392$	0.0787557	−	0.242385i	0.00397776	−	0.0122423i
$393$		0			0
$394$	−16.8384	+	5.47114i	−0.848307	+	0.275632i
$395$	−10.7728	−	17.5796i	−0.542037	−	0.884524i
$396$		0			0
$397$	−0.541457	−	6.87986i	−0.0271749	−	0.345290i	−0.995442	−	0.0953715i	$-0.969596\pi$
$397$	−0.541457	−	6.87986i	−0.0271749	−	0.345290i	0.968267	−	0.249919i	$-0.0804039\pi$
$398$	7.02674	+	1.68697i	0.352219	+	0.0845602i
$399$		0			0
$400$	1.12056	+	1.54231i	0.0560278	+	0.0771156i
$401$	−12.3904	+	12.3904i	−0.618747	+	0.618747i	−0.945210	−	0.326463i	$-0.894143\pi$
$401$	−12.3904	+	12.3904i	−0.618747	+	0.618747i	0.326463	+	0.945210i	$0.394143\pi$
$402$		0			0
$403$	4.36127	+	5.10639i	0.217250	+	0.254368i
$404$	0.569225	+	0.486164i	0.0283200	+	0.0241876i
$405$		0			0
$406$	−21.6307	−	15.7156i	−1.07351	−	0.779952i
$407$	17.7995	+	42.9718i	0.882288	+	2.13003i
$408$		0			0
$409$			30.2969i			1.49809i	0.662521	+	0.749043i	$0.269486\pi$
$409$			30.2969i			1.49809i	−0.662521	+	0.749043i	$0.730514\pi$
$410$	−12.4055	+	11.3695i	−0.612663	+	0.561502i
$411$		0			0
$412$	1.30320	−	0.664013i	0.0642040	−	0.0327136i
$413$	−35.5937	+	14.7434i	−1.75145	+	0.725474i
$414$		0			0
$415$	−22.8818	+	3.62412i	−1.12322	+	0.177901i
$416$	−1.40523	+	1.64531i	−0.0688968	+	0.0806678i
$417$		0			0
$418$	−0.184780	+	1.16665i	−0.00903788	+	0.0570629i
$419$	6.24901	+	6.24901i	0.305284	+	0.305284i	0.843077	−	0.537793i	$-0.180742\pi$
$419$	6.24901	+	6.24901i	0.305284	+	0.305284i	−0.537793	+	0.843077i	$0.680742\pi$
$420$		0			0
$421$	−9.50705	+	15.5141i	−0.463345	+	0.756111i	−0.995917	−	0.0902740i	$-0.971226\pi$
$421$	−9.50705	+	15.5141i	−0.463345	+	0.756111i	0.532572	+	0.846385i	$0.321226\pi$
$422$	4.27092	−	17.7897i	0.207905	−	0.865988i
$423$		0			0
$424$	−2.39242	+	5.77581i	−0.116186	+	0.280498i
$425$	12.2895	−	7.53103i	0.596130	−	0.365309i
$426$		0			0
$427$	−5.15763	−	21.4831i	−0.249595	−	1.03964i
$428$	0.263328	+	0.0855603i	0.0127284	+	0.00413572i
$429$		0			0
$430$	8.43678	−	16.5581i	0.406858	−	0.798503i
$431$	4.66652	−	9.15857i	0.224779	−	0.441153i	−0.750883	−	0.660435i	$-0.770372\pi$
$431$	4.66652	−	9.15857i	0.224779	−	0.441153i	0.975661	+	0.219283i	$0.0703717\pi$
$432$		0			0
$433$	−11.5578	−	3.75534i	−0.555430	−	0.180470i	0.0178336	−	0.999841i	$-0.494323\pi$
$433$	−11.5578	−	3.75534i	−0.555430	−	0.180470i	−0.573264	+	0.819371i	$0.694323\pi$
$434$	1.95149	+	8.12855i	0.0936746	+	0.390183i
$435$		0			0
$436$	3.69438	−	2.26392i	0.176929	−	0.108422i
$437$	0.912791	−	2.20367i	0.0436647	−	0.105416i
$438$		0			0
$439$	−5.38758	+	22.4409i	−0.257135	+	1.07104i	0.683048	+	0.730374i	$0.260654\pi$
$439$	−5.38758	+	22.4409i	−0.257135	+	1.07104i	−0.940183	+	0.340671i	$0.889346\pi$
$440$	5.54583	−	9.04997i	0.264387	−	0.431440i
$441$		0			0
$442$	11.5675	+	11.5675i	0.550212	+	0.550212i
$443$	6.47659	−	40.8916i	0.307712	−	1.94282i	−0.0247345	−	0.999694i	$-0.507874\pi$
$443$	6.47659	−	40.8916i	0.307712	−	1.94282i	0.332446	−	0.943122i	$-0.392126\pi$
$444$		0			0
$445$	12.5072	−	14.6441i	0.592900	−	0.694196i
$446$	3.62748	−	0.574537i	0.171766	−	0.0272051i
$447$		0			0
$448$	−2.48846	+	1.03075i	−0.117568	+	0.0486984i
$449$	15.8657	−	8.08398i	0.748749	−	0.381507i	−0.0375971	−	0.999293i	$-0.511970\pi$
$449$	15.8657	−	8.08398i	0.748749	−	0.381507i	0.786346	+	0.617786i	$0.211970\pi$
$450$		0			0
$451$	23.4391	+	10.9273i	1.10370	+	0.514546i
$452$		−	5.18183i		−	0.243733i
$453$		0			0
$454$	−5.50028	−	13.2788i	−0.258141	−	0.623207i
$455$	−12.3908	−	9.00245i	−0.580890	−	0.422041i
$456$		0			0
$457$	−0.706113	−	0.603077i	−0.0330306	−	0.0282108i	0.632780	−	0.774332i	$-0.281914\pi$
$457$	−0.706113	−	0.603077i	−0.0330306	−	0.0282108i	−0.665810	+	0.746121i	$0.731914\pi$
$458$	−1.14151	−	1.33654i	−0.0533394	−	0.0624524i
$459$		0			0
$460$	−15.1557	+	15.1557i	−0.706637	+	0.706637i
$461$	6.20725	+	8.54354i	0.289100	+	0.397912i	0.928722	−	0.370778i	$-0.120909\pi$
$461$	6.20725	+	8.54354i	0.289100	+	0.397912i	−0.639621	+	0.768690i	$0.720909\pi$
$462$		0			0
$463$	26.0545	+	6.25514i	1.21086	+	0.290701i	0.788103	−	0.615544i	$-0.211064\pi$
$463$	26.0545	+	6.25514i	1.21086	+	0.290701i	0.422754	+	0.906245i	$0.361064\pi$
$464$	0.778827	+	9.89593i	0.0361561	+	0.459407i
$465$		0			0
$466$	2.76063	+	4.50493i	0.127883	+	0.208687i
$467$	2.39740	−	0.778962i	0.110938	−	0.0360461i	−0.253022	−	0.967461i	$-0.581424\pi$
$467$	2.39740	−	0.778962i	0.110938	−	0.0360461i	0.363960	+	0.931415i	$0.381424\pi$
$468$		0			0
$469$	7.18726	−	22.1201i	0.331877	−	1.02141i
$470$	−0.655852	+	8.33340i	−0.0302522	+	0.384391i
$471$		0			0
$472$	12.7445	+	6.49366i	0.586614	+	0.298895i
$473$	−28.4720	−	2.24080i	−1.30915	−	0.103032i
$474$		0			0
$475$	−0.542142	+	0.130157i	−0.0248752	+	0.00597201i
$476$	6.29291	+	19.3676i	0.288435	+	0.887712i
$477$		0			0
$478$	23.2859	+	9.64534i	1.06507	+	0.441168i
$479$	−24.3350	+	1.91521i	−1.11190	+	0.0875081i	−0.621074	−	0.783752i	$-0.713303\pi$
$479$	−24.3350	+	1.91521i	−1.11190	+	0.0875081i	−0.490822	+	0.871260i	$0.663303\pi$
$480$		0			0
$481$	−21.2461	−	13.0197i	−0.968741	−	0.593645i
$482$	15.4566	−	11.2299i	0.704031	−	0.511508i
$483$		0			0
$484$	−5.24672	−	0.830999i	−0.238487	−	0.0377727i
$485$	1.29311	−	1.10442i	0.0587169	−	0.0501490i
$486$		0			0
$487$	−3.59456	−	22.6951i	−0.162885	−	1.02841i	−0.924721	−	0.380645i	$-0.875702\pi$
$487$	−3.59456	−	22.6951i	−0.162885	−	1.02841i	0.761836	−	0.647769i	$-0.224298\pi$
$488$	−4.82136	+	6.63603i	−0.218253	+	0.300399i
$489$		0			0
$490$	−0.304069	−	0.596769i	−0.0137364	−	0.0269593i
$491$	−34.3959			−1.55226			−0.776132	−	0.630571i	$-0.782821\pi$
$491$	−34.3959			−1.55226			−0.776132	+	0.630571i	$0.782821\pi$
$492$		0			0
$493$	75.0503			3.38009
$494$	−0.287287	−	0.563832i	−0.0129256	−	0.0253680i
$495$		0			0
$496$	1.82426	−	2.51087i	0.0819115	−	0.112742i
$497$	1.19018	+	7.51452i	0.0533870	+	0.337072i
$498$		0			0
$499$	−14.7860	+	12.6285i	−0.661913	+	0.565327i	−0.915665	−	0.401942i	$-0.868335\pi$
$499$	−14.7860	+	12.6285i	−0.661913	+	0.565327i	0.253752	+	0.967269i	$0.418335\pi$
$500$	−8.02989	−	1.27181i	−0.359108	−	0.0568771i
$501$		0			0
$502$	8.34717	−	6.06458i	0.372552	−	0.270675i
$503$	32.1033	+	19.6729i	1.43141	+	0.877171i	0.999692	−	0.0248355i	$-0.00790619\pi$
$503$	32.1033	+	19.6729i	1.43141	+	0.877171i	0.431722	+	0.902007i	$0.357906\pi$
$504$		0			0
$505$	1.96121	−	0.154350i	0.0872725	−	0.00686850i
$506$	30.4323	+	12.6055i	1.35288	+	0.560382i
$507$		0			0
$508$	−0.286610	−	0.882095i	−0.0127163	−	0.0391366i
$509$	18.2566	−	4.38301i	0.809208	−	0.194274i	0.192328	−	0.981331i	$-0.438396\pi$
$509$	18.2566	−	4.38301i	0.809208	−	0.194274i	0.616880	+	0.787057i	$0.288396\pi$
$510$		0			0
$511$	−29.0533	−	2.28655i	−1.28524	−	0.101151i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$		0			0
$514$	1.28601	−	16.3402i	0.0567233	−	0.720738i
$515$	1.18779	−	3.65563i	0.0523401	−	0.161086i
$516$		0			0
$517$	12.2180	−	3.96985i	0.537345	−	0.174594i
$518$	−16.2074	−	26.4480i	−0.712111	−	1.16206i
$519$		0			0
$520$	0.446140	+	5.66874i	0.0195645	+	0.248591i
$521$	18.7793	+	4.50851i	0.822735	+	0.197521i	0.622893	−	0.782307i	$-0.285957\pi$
$521$	18.7793	+	4.50851i	0.822735	+	0.197521i	0.199842	+	0.979828i	$0.435957\pi$
$522$		0			0
$523$	0.455406	+	0.626812i	0.0199135	+	0.0274086i	0.818858	−	0.573997i	$-0.194608\pi$
$523$	0.455406	+	0.626812i	0.0199135	+	0.0274086i	−0.798944	+	0.601405i	$0.794608\pi$
$524$	9.25056	−	9.25056i	0.404113	−	0.404113i
$525$		0			0
$526$	0.0824564	+	0.0965440i	0.00359527	+	0.00420952i
$527$	−17.8430	−	15.2393i	−0.777252	−	0.663836i
$528$		0			0
$529$	−35.2056	−	25.5783i	−1.53068	−	1.11210i
$530$	6.28728	+	15.1788i	0.273102	+	0.659327i
$531$		0			0
$532$		−	0.787738i		−	0.0341528i
$533$	−13.5998	+	2.64479i	−0.589073	+	0.114558i
$534$		0			0
$535$	0.648331	−	0.330341i	0.0280298	−	0.0142819i
$536$	−7.97777	+	3.30450i	−0.344587	+	0.142733i
$537$		0			0
$538$	11.5585	−	1.83068i	0.498321	−	0.0789263i
$539$	−0.668497	+	0.782709i	−0.0287942	+	0.0337137i
$540$		0			0
$541$	2.19238	−	13.8422i	0.0942580	−	0.595121i	−0.894670	−	0.446727i	$-0.852590\pi$
$541$	2.19238	−	13.8422i	0.0942580	−	0.595121i	0.988928	−	0.148394i	$-0.0474105\pi$
$542$	13.0352	+	13.0352i	0.559910	+	0.559910i
$543$		0			0
$544$	3.95039	−	6.44645i	0.169372	−	0.276389i
$545$	2.65820	−	11.0722i	0.113865	−	0.474280i
$546$		0			0
$547$	8.20502	−	19.8087i	0.350821	−	0.846957i	−0.645698	−	0.763593i	$-0.723433\pi$
$547$	8.20502	−	19.8087i	0.350821	−	0.846957i	0.996519	−	0.0833644i	$-0.0265666\pi$
$548$	−10.2960	+	6.30938i	−0.439822	+	0.269523i
$549$		0			0
$550$	−1.79744	−	7.48689i	−0.0766433	−	0.319242i
$551$	−2.76103	−	0.897113i	−0.117624	−	0.0382183i
$552$		0			0
$553$	9.59351	−	18.8283i	0.407958	−	0.800662i
$554$	−7.69267	+	15.0977i	−0.326830	+	0.641441i
$555$		0			0
$556$	5.82684	+	1.89325i	0.247113	+	0.0802918i
$557$	5.82587	+	24.2665i	0.246850	+	1.02820i	0.948775	+	0.315953i	$0.102324\pi$
$557$	5.82587	+	24.2665i	0.246850	+	1.02820i	−0.701925	+	0.712251i	$0.747676\pi$
$558$		0			0
$559$	13.0458	−	7.99449i	0.551779	−	0.338131i
$560$	−2.70882	+	6.53967i	−0.114469	+	0.276351i
$561$		0			0
$562$	2.93320	−	12.2176i	0.123729	−	0.515370i
$563$	9.58790	−	15.6460i	0.404082	−	0.659402i	−0.584275	−	0.811556i	$-0.698621\pi$
$563$	9.58790	−	15.6460i	0.404082	−	0.659402i	0.988357	+	0.152154i	$0.0486210\pi$
$564$		0			0
$565$	−9.62929	−	9.62929i	−0.405107	−	0.405107i
$566$	1.09450	−	6.91041i	0.0460054	−	0.290466i
$567$		0			0
$568$	1.83447	−	2.14789i	0.0769728	−	0.0901236i
$569$	−28.1368	+	4.45644i	−1.17956	+	0.186824i	−0.715262	−	0.698857i	$-0.753692\pi$
$569$	−28.1368	+	4.45644i	−1.17956	+	0.186824i	−0.464296	+	0.885680i	$0.653692\pi$
$570$		0			0
$571$	−0.515270	+	0.213432i	−0.0215634	+	0.00893184i	−0.393439	−	0.919351i	$-0.628715\pi$
$571$	−0.515270	+	0.213432i	−0.0215634	+	0.00893184i	0.371876	+	0.928283i	$0.378715\pi$
$572$	7.78642	−	3.96738i	0.325566	−	0.165884i
$573$		0			0
$574$	−16.5790	−	4.75237i	−0.691995	−	0.198360i
$575$			15.5482i			0.648404i
$576$		0			0
$577$	−6.62099	−	15.9845i	−0.275636	−	0.665443i	0.724070	−	0.689727i	$-0.242269\pi$
$577$	−6.62099	−	15.9845i	−0.275636	−	0.665443i	−0.999705	+	0.0242839i	$0.992269\pi$
$578$	−32.4920	−	23.6068i	−1.35149	−	0.981913i
$579$		0			0
$580$	19.8367	+	16.9421i	0.823673	+	0.703484i
$581$	−15.4206	−	18.0553i	−0.639756	−	0.749058i
$582$		0			0
$583$	17.8541	−	17.8541i	0.739441	−	0.739441i
$584$	6.35977	+	8.75347i	0.263169	+	0.362221i
$585$		0			0
$586$	−1.43502	−	0.344519i	−0.0592803	−	0.0142319i
$587$	−1.47584	−	18.7523i	−0.0609144	−	0.773991i	−0.949195	−	0.314689i	$-0.898100\pi$
$587$	−1.47584	−	18.7523i	−0.0609144	−	0.773991i	0.888280	−	0.459302i	$-0.151900\pi$
$588$		0			0
$589$	0.474263	+	0.773927i	0.0195417	+	0.0318891i
$590$	35.7499	−	11.6159i	1.47180	−	0.478217i
$591$		0			0
$592$	−3.55873	+	10.9526i	−0.146263	+	0.450151i
$593$	1.58282	−	20.1116i	0.0649984	−	0.825883i	−0.874872	−	0.484353i	$-0.839055\pi$
$593$	1.58282	−	20.1116i	0.0649984	−	0.825883i	0.939871	−	0.341530i	$-0.110945\pi$
$594$		0			0
$595$	47.6844	+	24.2964i	1.95487	+	0.996055i
$596$	−19.7712	−	1.55602i	−0.809859	−	0.0637373i
$597$		0			0
$598$	−17.1592	+	4.11957i	−0.701693	+	0.168462i
$599$	0.986618	+	3.03650i	0.0403121	+	0.124068i	0.969187	−	0.246325i	$-0.0792230\pi$
$599$	0.986618	+	3.03650i	0.0403121	+	0.124068i	−0.928875	+	0.370393i	$0.879223\pi$
$600$		0			0
$601$	16.3212	+	6.76046i	0.665755	+	0.275765i	0.689858	−	0.723945i	$-0.257673\pi$
$601$	16.3212	+	6.76046i	0.665755	+	0.275765i	−0.0241028	+	0.999709i	$0.507673\pi$
$602$	18.9879	−	1.49438i	0.773890	−	0.0609065i
$603$		0			0
$604$	0.700082	+	0.429011i	0.0284859	+	0.0174562i
$605$	−11.2941	+	8.20565i	−0.459171	+	0.333607i
$606$		0			0
$607$	−23.2793	−	3.68709i	−0.944880	−	0.149654i	−0.335062	−	0.942196i	$-0.608757\pi$
$607$	−23.2793	−	3.68709i	−0.944880	−	0.149654i	−0.609818	+	0.792542i	$0.708757\pi$
$608$	−0.222389	+	0.189938i	−0.00901905	+	0.00770300i
$609$		0			0
$610$	3.37217	+	21.2910i	0.136535	+	0.862049i
$611$	−4.04536	+	5.56796i	−0.163658	+	0.225256i
$612$		0			0
$613$	5.04719	+	9.90567i	0.203854	+	0.400086i	0.970187	−	0.242357i	$-0.0779206\pi$
$613$	5.04719	+	9.90567i	0.203854	+	0.400086i	−0.766333	+	0.642444i	$0.777921\pi$
$614$	−29.2959			−1.18229
$615$		0			0
$616$	10.8785			0.438308
$617$	10.5642	+	20.7333i	0.425297	+	0.834693i	0.999868	+	0.0162382i	$0.00516901\pi$
$617$	10.5642	+	20.7333i	0.425297	+	0.834693i	−0.574571	+	0.818455i	$0.694831\pi$
$618$		0			0
$619$	13.1090	−	18.0430i	0.526895	−	0.725208i	−0.459759	−	0.888044i	$-0.652064\pi$
$619$	13.1090	−	18.0430i	0.526895	−	0.725208i	0.986653	+	0.162836i	$0.0520641\pi$
$620$	−1.27593	−	8.05588i	−0.0512424	−	0.323532i
$621$		0			0
$622$	17.9114	−	15.2978i	0.718182	−	0.613386i
$623$	19.4951	+	3.08772i	0.781054	+	0.123707i
$624$		0			0
$625$	−24.9967	+	18.1612i	−0.999869	+	0.726447i
$626$	22.4270	+	13.7433i	0.896363	+	0.549292i
$627$		0			0
$628$	1.77479	−	0.139679i	0.0708219	−	0.00557380i
$629$	80.4420	+	33.3202i	3.20743	+	1.32856i
$630$		0			0
$631$	−8.78118	−	27.0257i	−0.349573	−	1.07588i	−0.959090	−	0.283102i	$-0.908636\pi$
$631$	−8.78118	−	27.0257i	−0.349573	−	1.07588i	0.609517	−	0.792773i	$-0.291364\pi$
$632$	−7.62865	+	1.83148i	−0.303452	+	0.0728523i
$633$		0			0
$634$	−15.2693	−	1.20172i	−0.606422	−	0.0477265i
$635$	−2.17178	−	1.10658i	−0.0861844	−	0.0439132i
$636$		0			0
$637$	0.0432658	−	0.549744i	0.00171425	−	0.0217816i
$638$	12.3890	−	38.1293i	0.490484	−	1.50955i
$639$		0			0
$640$	2.49938	−	0.812098i	0.0987967	−	0.0321010i
$641$	−2.28145	−	3.72300i	−0.0901120	−	0.147049i	0.804408	−	0.594077i	$-0.202483\pi$
$641$	−2.28145	−	3.72300i	−0.0901120	−	0.147049i	−0.894520	+	0.447028i	$0.852483\pi$
$642$		0			0
$643$	−3.63906	−	46.2387i	−0.143511	−	1.82348i	−0.474966	−	0.880004i	$-0.657540\pi$
$643$	−3.63906	−	46.2387i	−0.143511	−	1.82348i	0.331455	−	0.943471i	$-0.392460\pi$
$644$	−21.3605	−	5.12819i	−0.841720	−	0.202079i
$645$		0			0
$646$	1.29969	+	1.78887i	0.0511357	+	0.0703823i
$647$	−10.4124	+	10.4124i	−0.409353	+	0.409353i	−0.881513	−	0.472160i	$-0.843475\pi$
$647$	−10.4124	+	10.4124i	−0.409353	+	0.409353i	0.472160	+	0.881513i	$0.343475\pi$
$648$		0			0
$649$	−37.5182	−	43.9282i	−1.47272	−	1.72433i
$650$	3.13662	+	2.67893i	0.123028	+	0.105076i
$651$		0			0
$652$	18.0315	+	13.1007i	0.706168	+	0.513061i
$653$	5.62230	+	13.5734i	0.220017	+	0.531169i	0.994892	−	0.100946i	$-0.0321869\pi$
$653$	5.62230	+	13.5734i	0.220017	+	0.531169i	−0.774874	+	0.632115i	$0.782187\pi$
$654$		0			0
$655$		−	34.3802i		−	1.34335i
$656$	2.65585	+	5.82636i	0.103693	+	0.227481i
$657$		0			0
$658$	−7.63365	+	3.88954i	−0.297591	+	0.151630i
$659$	34.1544	−	14.1472i	1.33047	−	0.551097i	0.399678	−	0.916656i	$-0.369122\pi$
$659$	34.1544	−	14.1472i	1.33047	−	0.551097i	0.930788	+	0.365559i	$0.119122\pi$
$660$		0			0
$661$	29.2141	−	4.62706i	1.13630	−	0.179972i	0.440187	−	0.897906i	$-0.354912\pi$
$661$	29.2141	−	4.62706i	1.13630	−	0.179972i	0.696111	+	0.717934i	$0.254912\pi$
$662$	−0.748908	+	0.876859i	−0.0291071	+	0.0340801i
$663$		0			0
$664$	−1.37904	+	8.70690i	−0.0535170	+	0.337893i
$665$	−1.46384	−	1.46384i	−0.0567651	−	0.0567651i
$666$		0			0
$667$	−42.3007	+	69.0284i	−1.63789	+	2.67279i
$668$	3.15233	−	13.1304i	0.121967	−	0.508031i
$669$		0			0
$670$	−8.68424	+	20.9656i	−0.335502	+	0.809972i
$671$	28.2470	−	17.3098i	1.09046	−	0.668236i
$672$		0			0
$673$	−4.83722	−	20.1485i	−0.186461	−	0.776667i	−0.984690	−	0.174313i	$-0.944230\pi$
$673$	−4.83722	−	20.1485i	−0.186461	−	0.776667i	0.798229	−	0.602354i	$-0.205770\pi$
$674$	−1.49946	−	0.487204i	−0.0577570	−	0.0187664i
$675$		0			0
$676$	3.77643	−	7.41166i	0.145247	−	0.285064i
$677$	−1.59291	+	3.12627i	−0.0612206	+	0.120152i	−0.919589	−	0.392881i	$-0.871478\pi$
$677$	−1.59291	+	3.12627i	−0.0612206	+	0.120152i	0.858369	+	0.513033i	$0.171478\pi$
$678$		0			0
$679$	1.65761	+	0.538591i	0.0636134	+	0.0206692i
$680$	−4.63838	−	19.3202i	−0.177874	−	0.740897i
$681$		0			0
$682$	−10.6878	+	6.54949i	−0.409257	+	0.250793i
$683$	−3.66948	+	8.85892i	−0.140409	+	0.338977i	−0.978404	−	0.206700i	$-0.933728\pi$
$683$	−3.66948	+	8.85892i	−0.140409	+	0.338977i	0.837995	+	0.545677i	$0.183728\pi$
$684$		0			0
$685$	−7.40820	+	30.8574i	−0.283053	+	1.17900i
$686$	−9.49272	+	15.4907i	−0.362434	+	0.591438i
$687$		0			0
$688$	−5.00022	−	5.00022i	−0.190632	−	0.190632i
$689$	−2.11608	+	13.3604i	−0.0806161	+	0.508990i
$690$		0			0
$691$	11.8470	−	13.8711i	0.450682	−	0.527680i	−0.487825	−	0.872941i	$-0.662210\pi$
$691$	11.8470	−	13.8711i	0.450682	−	0.527680i	0.938507	+	0.345261i	$0.112210\pi$
$692$	10.7343	−	1.70015i	0.408057	−	0.0646299i
$693$		0			0
$694$	5.62489	−	2.32991i	0.213518	−	0.0884420i
$695$	14.3461	−	7.30969i	0.544178	−	0.277272i
$696$		0			0
$697$	45.4903	−	16.5617i	1.72307	−	0.627318i
$698$			10.6922i			0.404707i
$699$		0			0
$700$	1.96503	+	4.74400i	0.0742711	+	0.179306i
$701$	−27.5009	−	19.9806i	−1.03869	−	0.754656i	−0.0686641	−	0.997640i	$-0.521874\pi$
$701$	−27.5009	−	19.9806i	−1.03869	−	0.754656i	−0.970030	+	0.242984i	$0.921874\pi$
$702$		0			0
$703$	−2.56109	−	2.18738i	−0.0965935	−	0.0824986i
$704$	−2.62301	−	3.07115i	−0.0988583	−	0.115748i
$705$		0			0
$706$	1.62509	−	1.62509i	0.0611609	−	0.0611609i
$707$	1.18514	+	1.63121i	0.0445720	+	0.0613480i
$708$		0			0
$709$	28.9719	+	6.95554i	1.08806	+	0.261221i	0.737519	−	0.675326i	$-0.235997\pi$
$709$	28.9719	+	6.95554i	1.08806	+	0.261221i	0.350543	+	0.936547i	$0.385997\pi$
$710$	−0.582420	−	7.40035i	−0.0218578	−	0.277730i
$711$		0			0
$712$	−3.82892	−	6.24822i	−0.143495	−	0.234162i
$713$	24.0734	−	7.82193i	0.901557	−	0.292934i
$714$		0			0
$715$	7.09684	−	21.8418i	0.265407	−	0.816838i
$716$	0.489052	−	6.21399i	0.0182767	−	0.232228i
$717$		0			0
$718$	−14.4171	−	7.34588i	−0.538041	−	0.274146i
$719$	20.9193	+	1.64638i	0.780158	+	0.0613998i	0.462283	−	0.886733i	$-0.347031\pi$
$719$	20.9193	+	1.64638i	0.780158	+	0.0613998i	0.317876	+	0.948132i	$0.397031\pi$
$720$		0			0
$721$	3.83068	−	0.919665i	0.142662	−	0.0342501i
$722$	5.84489	+	17.9887i	0.217524	+	0.669471i
$723$		0			0
$724$	−15.2329	−	6.30967i	−0.566126	−	0.234497i
$725$	18.8656	−	1.48476i	0.700652	−	0.0551425i
$726$		0			0
$727$	−43.2632	−	26.5117i	−1.60454	−	0.983266i	−0.979195	−	0.202921i	$-0.934956\pi$
$727$	−43.2632	−	26.5117i	−1.60454	−	0.983266i	−0.625349	−	0.780345i	$-0.715044\pi$
$728$	−4.71491	+	3.42558i	−0.174746	+	0.126961i
$729$		0			0
$730$	28.0846	+	4.44817i	1.03946	+	0.164634i
$731$	−40.6541	+	34.7219i	−1.50365	+	1.28423i
$732$		0			0
$733$	0.119149	+	0.752277i	0.00440087	+	0.0277860i	0.989791	−	0.142526i	$-0.0455225\pi$
$733$	0.119149	+	0.752277i	0.00440087	+	0.0277860i	−0.985390	+	0.170312i	$0.945522\pi$
$734$	−0.551033	+	0.758432i	−0.0203390	+	0.0279942i
$735$		0			0
$736$	3.70264	+	7.26684i	0.136481	+	0.267859i
$737$	34.8756			1.28466
$738$		0			0
$739$	−43.0010			−1.58182			−0.790909	−	0.611934i	$-0.790392\pi$
$739$	−43.0010			−1.58182			−0.790909	+	0.611934i	$0.790392\pi$
$740$	13.7400	+	26.9662i	0.505091	+	0.991297i
$741$		0			0
$742$	−9.89761	+	13.6229i	−0.363353	+	0.500112i
$743$	6.92282	+	43.7090i	0.253974	+	1.60353i	0.703792	+	0.710406i	$0.251489\pi$
$743$	6.92282	+	43.7090i	0.253974	+	1.60353i	−0.449818	+	0.893120i	$0.648511\pi$
$744$		0			0
$745$	−39.6319	+	33.8488i	−1.45200	+	1.24012i
$746$	11.8260	+	1.87306i	0.432981	+	0.0685775i
$747$		0			0
$748$	−24.7040	+	17.9485i	−0.903268	+	0.656263i
$749$	0.635873	+	0.389664i	0.0232343	+	0.0142380i
$750$		0			0
$751$	−27.7937	+	2.18741i	−1.01421	+	0.0798198i	−0.574654	−	0.818397i	$-0.694863\pi$
$751$	−27.7937	+	2.18741i	−1.01421	+	0.0798198i	−0.439553	+	0.898217i	$0.644863\pi$
$752$	2.93868	+	1.21724i	0.107163	+	0.0443882i
$753$		0			0
$754$	6.63715	+	20.4270i	0.241711	+	0.743909i
$755$	2.09817	−	0.503726i	0.0763602	−	0.0183325i
$756$		0			0
$757$	26.7404	+	2.10451i	0.971895	+	0.0764898i	0.554454	−	0.832214i	$-0.312927\pi$
$757$	26.7404	+	2.10451i	0.971895	+	0.0764898i	0.417441	+	0.908704i	$0.362927\pi$
$758$	9.80685	+	4.99684i	0.356201	+	0.181493i
$759$		0			0
$760$	−0.0603026	+	0.766218i	−0.00218741	+	0.0277936i
$761$	−5.23034	+	16.0973i	−0.189600	+	0.583528i	−0.999997	−	0.00235250i	$-0.999251\pi$
$761$	−5.23034	+	16.0973i	−0.189600	+	0.583528i	0.810398	+	0.585880i	$0.199251\pi$
$762$		0			0
$763$	11.0993	−	3.60639i	0.401823	−	0.130560i
$764$	13.8109	+	22.5373i	0.499660	+	0.815370i
$765$		0			0
$766$	1.28764	+	16.3610i	0.0465242	+	0.591145i
$767$	30.0937	+	7.22486i	1.08662	+	0.260875i
$768$		0			0
$769$	23.2609	+	32.0159i	0.838810	+	1.15452i	0.986219	+	0.165447i	$0.0529066\pi$
$769$	23.2609	+	32.0159i	0.838810	+	1.15452i	−0.147409	+	0.989076i	$0.547093\pi$
$770$	20.2153	−	20.2153i	0.728510	−	0.728510i
$771$		0			0
$772$	8.42754	+	9.86738i	0.303314	+	0.355135i
$773$	−41.0554	−	35.0646i	−1.47666	−	1.26119i	−0.893685	−	0.448696i	$-0.851889\pi$
$773$	−41.0554	−	35.0646i	−1.47666	−	1.26119i	−0.582975	−	0.812490i	$-0.698111\pi$
$774$		0			0
$775$	−4.78674	−	3.47777i	−0.171945	−	0.124925i
$776$	−0.247629	−	0.597830i	−0.00888938	−	0.0214609i
$777$		0			0
$778$		−	13.8697i		−	0.497253i
$779$	−1.87151	+	0.0655209i	−0.0670539	+	0.00234753i
$780$		0			0
$781$	−10.1649	+	5.17928i	−0.363729	+	0.185329i
$782$	56.9685	−	23.5971i	2.03719	−	0.843831i
$783$		0			0
$784$	−0.251721	+	0.0398687i	−0.00899004	+	0.00142388i
$785$	3.03849	−	3.55762i	0.108448	−	0.126977i
$786$		0			0
$787$	6.93307	−	43.7737i	0.247137	−	1.56036i	−0.482108	−	0.876112i	$-0.660129\pi$
$787$	6.93307	−	43.7737i	0.247137	−	1.56036i	0.729245	−	0.684252i	$-0.239871\pi$
$788$	12.5193	+	12.5193i	0.445982	+	0.445982i
$789$		0			0
$790$	−10.7728	+	17.5796i	−0.383278	+	0.625453i
$791$	3.25824	−	13.5715i	0.115850	−	0.482549i
$792$		0			0
$793$	−6.79191	+	16.3971i	−0.241188	+	0.582279i
$794$	−5.88418	+	3.60583i	−0.208822	+	0.127966i
$795$		0			0
$796$	−1.68697	−	7.02674i	−0.0597931	−	0.249056i
$797$	−51.3119	−	16.6722i	−1.81756	−	0.590561i	−0.999889	−	0.0148760i	$-0.995265\pi$
$797$	−51.3119	−	16.6722i	−1.81756	−	0.590561i	−0.817671	−	0.575685i	$-0.804735\pi$
$798$		0			0
$799$	10.9179	−	21.4276i	0.386247	−	0.758052i
$800$	0.865489	−	1.69862i	0.0305997	−	0.0600552i
$801$		0			0
$802$	16.6651	+	5.41481i	0.588464	+	0.191203i
$803$	−10.2015	−	42.4922i	−0.360002	−	1.49952i
$804$		0			0
$805$	−49.2233	+	30.1641i	−1.73489	+	1.06314i
$806$	2.56985	−	6.20418i	0.0905192	−	0.218533i
$807$		0			0
$808$	0.174753	−	0.727897i	0.00614777	−	0.0256073i
$809$	−20.0159	+	32.6630i	−0.703722	+	1.14837i	0.278461	+	0.960447i	$0.410176\pi$
$809$	−20.0159	+	32.6630i	−0.703722	+	1.14837i	−0.982184	+	0.187923i	$0.939824\pi$
$810$		0			0
$811$	33.9812	+	33.9812i	1.19324	+	1.19324i	0.976152	+	0.217089i	$0.0696562\pi$
$811$	33.9812	+	33.9812i	1.19324	+	1.19324i	0.217089	+	0.976152i	$0.430344\pi$
$812$	−4.18258	+	26.4078i	−0.146780	+	0.926732i
$813$		0			0
$814$	30.2073	−	35.3683i	1.05877	−	1.23966i
$815$	57.8522	−	9.16290i	2.02648	−	0.320962i
$816$		0			0
$817$	1.91067	−	0.791427i	0.0668460	−	0.0276885i
$818$	26.9948	−	13.7545i	0.943850	−	0.480915i
$819$		0			0
$820$	15.7623	+	5.89169i	0.550444	+	0.205747i
$821$			7.25584i			0.253231i	0.991952	+	0.126615i	$0.0404114\pi$
$821$			7.25584i			0.253231i	−0.991952	+	0.126615i	$0.959589\pi$
$822$		0			0
$823$	−11.4364	−	27.6099i	−0.398647	−	0.962419i	−0.987987	−	0.154534i	$-0.950612\pi$
$823$	−11.4364	−	27.6099i	−0.398647	−	0.962419i	0.589340	−	0.807885i	$-0.299388\pi$
$824$	−1.18328	−	0.859703i	−0.0412215	−	0.0299492i
$825$		0			0
$826$	29.2956	+	25.0208i	1.01933	+	0.870586i
$827$	10.6942	+	12.5212i	0.371872	+	0.435406i	0.914512	−	0.404559i	$-0.132575\pi$
$827$	10.6942	+	12.5212i	0.371872	+	0.435406i	−0.542640	+	0.839966i	$0.682575\pi$
$828$		0			0
$829$	0.288732	−	0.288732i	0.0100281	−	0.0100281i	−0.702075	−	0.712103i	$-0.747743\pi$
$829$	0.288732	−	0.288732i	0.0100281	−	0.0100281i	0.712103	+	0.702075i	$0.247743\pi$
$830$	13.6172	+	18.7425i	0.472660	+	0.650561i
$831$		0			0
$832$	2.10394	+	0.505111i	0.0729410	+	0.0175116i
$833$	0.151181	+	1.92094i	0.00523812	+	0.0665566i
$834$		0			0
$835$	−18.5420	−	30.2579i	−0.641674	−	1.04712i
$836$	1.12339	−	0.365010i	0.0388531	−	0.0126241i
$837$		0			0
$838$	2.73092	−	8.40490i	0.0943380	−	0.290342i
$839$	2.80481	−	35.6385i	0.0968328	−	1.23038i	−0.736050	−	0.676928i	$-0.763311\pi$
$839$	2.80481	−	35.6385i	0.0968328	−	1.23038i	0.832882	−	0.553450i	$-0.186689\pi$
$840$		0			0
$841$	61.9571	+	31.5687i	2.13645	+	1.08858i
$842$	18.1393	+	1.42759i	0.625121	+	0.0491981i
$843$		0			0
$844$	−17.7897	+	4.27092i	−0.612346	+	0.147011i
$845$	−6.75528	−	20.7906i	−0.232389	−	0.715219i
$846$		0			0
$847$	−13.2190	−	5.47548i	−0.454210	−	0.188140i
$848$	6.23242	−	0.490502i	0.214022	−	0.0168439i
$849$		0			0
$850$	−12.2895	−	7.53103i	−0.421527	−	0.258312i
$851$	−75.9863	+	55.2072i	−2.60478	+	1.89248i
$852$		0			0
$853$	−22.4784	−	3.56023i	−0.769647	−	0.121900i	−0.240751	−	0.970587i	$-0.577394\pi$
$853$	−22.4784	−	3.56023i	−0.769647	−	0.121900i	−0.528896	+	0.848687i	$0.677394\pi$
$854$	−16.8001	+	14.3486i	−0.574886	+	0.490999i
$855$		0			0
$856$	−0.0433134	−	0.273470i	−0.00148042	−	0.00934702i
$857$	−17.6877	+	24.3450i	−0.604200	+	0.831610i	−0.996085	−	0.0884042i	$-0.971823\pi$
$857$	−17.6877	+	24.3450i	−0.604200	+	0.831610i	0.391885	+	0.920014i	$0.371823\pi$
$858$		0			0
$859$	−6.55506	−	12.8650i	−0.223656	−	0.438949i	0.751725	−	0.659477i	$-0.229222\pi$
$859$	−6.55506	−	12.8650i	−0.223656	−	0.438949i	−0.975381	+	0.220527i	$0.929222\pi$
$860$	−18.5836			−0.633696
$861$		0			0
$862$	−10.2789			−0.350101
$863$	21.4724	+	42.1419i	0.730928	+	1.43453i	0.894071	+	0.447925i	$0.147837\pi$
$863$	21.4724	+	42.1419i	0.730928	+	1.43453i	−0.163143	+	0.986602i	$0.552163\pi$
$864$		0			0
$865$	16.7880	−	23.1067i	0.570809	−	0.785651i
$866$	1.90108	+	12.0029i	0.0646012	+	0.407876i
$867$		0			0
$868$	6.35663	−	5.42908i	0.215758	−	0.184275i
$869$	31.2962	+	4.95683i	1.06165	+	0.168149i
$870$		0			0
$871$	−15.1156	+	10.9821i	−0.512173	+	0.372115i
$872$	−3.69438	−	2.26392i	−0.125108	−	0.0766660i
$873$		0			0
$874$	−2.37788	+	0.187144i	−0.0804332	+	0.00633023i
$875$	−20.2311	−	8.38000i	−0.683936	−	0.283296i
$876$		0			0
$877$	−0.716220	−	2.20430i	−0.0241850	−	0.0744339i	0.938236	−	0.345997i	$-0.112459\pi$
$877$	−0.716220	−	2.20430i	−0.0241850	−	0.0744339i	−0.962421	+	0.271563i	$0.912459\pi$
$878$	22.4409	−	5.38758i	0.757343	−	0.181822i
$879$		0			0
$880$	−10.5813	−	0.832769i	−0.356697	−	0.0280726i
$881$	−43.5494	−	22.1895i	−1.46722	−	0.747584i	−0.475951	−	0.879472i	$-0.657896\pi$
$881$	−43.5494	−	22.1895i	−1.46722	−	0.747584i	−0.991265	+	0.131888i	$0.957896\pi$
$882$		0			0
$883$	3.06152	−	38.9003i	0.103028	−	1.30910i	−0.700422	−	0.713729i	$-0.747005\pi$
$883$	3.06152	−	38.9003i	0.103028	−	1.30910i	0.803450	−	0.595372i	$-0.202995\pi$
$884$	5.05520	−	15.5583i	0.170025	−	0.523283i
$885$		0			0
$886$	−39.3749	+	12.7937i	−1.32283	+	0.429813i
$887$	−0.751098	−	1.22568i	−0.0252194	−	0.0411543i	0.839782	−	0.542924i	$-0.182683\pi$
$887$	−0.751098	−	1.22568i	−0.0252194	−	0.0411543i	−0.865002	+	0.501769i	$0.832683\pi$
$888$		0			0
$889$	−0.196005	−	2.49048i	−0.00657379	−	0.0835279i
$890$	−18.7261	−	4.49575i	−0.627702	−	0.150698i
$891$		0			0
$892$	−2.15876	−	2.97128i	−0.0722806	−	0.0994857i
$893$	−0.657793	+	0.657793i	−0.0220122	+	0.0220122i
$894$		0			0
$895$	−10.6385	−	12.4561i	−0.355607	−	0.416362i
$896$	2.04814	+	1.74928i	0.0684236	+	0.0584393i
$897$		0			0
$898$	−14.4058	−	10.4664i	−0.480726	−	0.349268i
$899$	−11.7897	−	28.4630i	−0.393210	−	0.949293i
$900$		0			0
$901$		−	47.2663i		−	1.57467i
$902$	−0.904832	−	25.8453i	−0.0301276	−	0.860554i
$903$		0			0
$904$	−4.61705	+	2.35250i	−0.153561	+	0.0782431i
$905$	−40.0321	+	16.5818i	−1.33071	+	0.551199i
$906$		0			0
$907$	7.43999	−	1.17838i	0.247041	−	0.0391274i	−0.0316860	−	0.999498i	$-0.510088\pi$
$907$	7.43999	−	1.17838i	0.247041	−	0.0391274i	0.278727	+	0.960370i	$0.410088\pi$
$908$	−9.33446	+	10.9292i	−0.309775	+	0.362700i
$909$		0			0
$910$	−2.39593	+	15.1273i	−0.0794244	+	0.501466i
$911$	20.1654	+	20.1654i	0.668111	+	0.668111i	0.957278	−	0.289168i	$-0.0933785\pi$
$911$	20.1654	+	20.1654i	0.668111	+	0.668111i	−0.289168	+	0.957278i	$0.593379\pi$
$912$		0			0
$913$	18.6030	−	30.3574i	0.615671	−	1.00468i
$914$	−0.216777	+	0.902942i	−0.00717035	+	0.0298667i
$915$		0			0
$916$	−0.672630	+	1.62387i	−0.0222243	+	0.0536543i
$917$	30.0444	−	18.4112i	0.992153	−	0.607992i
$918$		0			0
$919$	5.58281	+	23.2541i	0.184160	+	0.767081i	0.985612	+	0.169023i	$0.0540611\pi$
$919$	5.58281	+	23.2541i	0.184160	+	0.767081i	−0.801452	+	0.598059i	$0.795939\pi$
$920$	20.3844	+	6.62328i	0.672052	+	0.218363i
$921$		0			0
$922$	4.79432	−	9.40939i	0.157893	−	0.309882i
$923$	2.77470	−	5.44565i	0.0913302	−	0.179246i
$924$		0			0
$925$	20.8802	+	6.78438i	0.686536	+	0.223069i
$926$	−6.25514	−	26.0545i	−0.205557	−	0.856205i
$927$		0			0
$928$	8.46376	−	5.18660i	0.277837	−	0.170258i
$929$	10.3194	−	24.9132i	0.338569	−	0.817377i	−0.659285	−	0.751893i	$-0.729141\pi$
$929$	10.3194	−	24.9132i	0.338569	−	0.817377i	0.997854	−	0.0654839i	$-0.0208591\pi$
$930$		0			0
$931$	0.0174001	−	0.0724767i	0.000570266	−	0.00237533i
$932$	2.76063	−	4.50493i	0.0904273	−	0.147564i
$933$		0			0
$934$	−1.78246	−	1.78246i	−0.0583238	−	0.0583238i
$935$	−12.5536	+	79.2603i	−0.410547	+	2.59209i
$936$		0			0
$937$	−14.5044	+	16.9825i	−0.473839	+	0.554794i	−0.944922	−	0.327295i	$-0.893863\pi$
$937$	−14.5044	+	16.9825i	−0.473839	+	0.554794i	0.471084	+	0.882089i	$0.343863\pi$
$938$	−22.9721	+	3.63842i	−0.750066	+	0.118799i
$939$		0			0
$940$	7.72286	−	3.19891i	0.251892	−	0.104337i
$941$	1.12094	−	0.571146i	0.0365415	−	0.0186188i	−0.435624	−	0.900129i	$-0.643472\pi$
$941$	1.12094	−	0.571146i	0.0365415	−	0.0186188i	0.472166	+	0.881510i	$0.343472\pi$
$942$		0			0
$943$	−10.4069	+	51.1749i	−0.338896	+	1.66648i
$944$		−	14.3035i		−	0.465540i
$945$		0			0
$946$	10.9295	+	26.3861i	0.355348	+	0.857885i
$947$	−8.68100	−	6.30712i	−0.282095	−	0.204954i	0.437736	−	0.899104i	$-0.355780\pi$
$947$	−8.68100	−	6.30712i	−0.282095	−	0.204954i	−0.719831	+	0.694150i	$0.755780\pi$
$948$		0			0
$949$	17.8020	+	15.2044i	0.577879	+	0.493555i
$950$	0.362098	+	0.423962i	0.0117480	+	0.0137552i
$951$		0			0
$952$	14.3997	−	14.3997i	0.466698	−	0.466698i
$953$	−2.83088	−	3.89637i	−0.0917013	−	0.126216i	0.760701	−	0.649102i	$-0.224855\pi$
$953$	−2.83088	−	3.89637i	−0.0917013	−	0.126216i	−0.852402	+	0.522886i	$0.824855\pi$
$954$		0			0
$955$	67.5450	+	16.2161i	2.18570	+	0.524741i
$956$	−1.97752	−	25.1268i	−0.0639576	−	0.812659i
$957$		0			0
$958$	12.7543	+	20.8132i	0.412074	+	0.672443i
$959$	−30.9330	+	10.0508i	−0.998880	+	0.324556i
$960$		0			0
$961$	6.60295	−	20.3218i	0.212998	−	0.655542i
$962$	−1.95505	+	24.8413i	−0.0630333	+	0.800914i
$963$		0			0
$964$	−17.0231	−	8.67370i	−0.548277	−	0.279361i
$965$	33.9971	+	2.67563i	1.09440	+	0.0861315i
$966$		0			0
$967$	−14.7889	+	3.55050i	−0.475578	+	0.114176i	−0.464147	−	0.885758i	$-0.653639\pi$
$967$	−14.7889	+	3.55050i	−0.475578	+	0.114176i	−0.0114318	+	0.999935i	$0.503639\pi$
$968$	1.64154	+	5.05213i	0.0527610	+	0.162382i
$969$		0			0
$970$	−1.57110	−	0.650771i	−0.0504450	−	0.0208950i
$971$	−38.0444	+	2.99416i	−1.22090	+	0.0960873i	−0.672482	−	0.740114i	$-0.734772\pi$
$971$	−38.0444	+	2.99416i	−1.22090	+	0.0960873i	−0.548423	+	0.836201i	$0.684772\pi$
$972$		0			0
$973$	14.0704	+	8.62236i	0.451077	+	0.276420i
$974$	−18.5896	+	13.5061i	−0.595650	+	0.432765i
$975$		0			0
$976$	8.10160	+	1.28317i	0.259326	+	0.0410732i
$977$	21.8772	−	18.6849i	0.699913	−	0.597782i	−0.226626	−	0.973982i	$-0.572769\pi$
$977$	21.8772	−	18.6849i	0.699913	−	0.597782i	0.926538	+	0.376200i	$0.122769\pi$
$978$		0			0
$979$	4.62997	+	29.2325i	0.147975	+	0.934275i
$980$	−0.393681	+	0.541855i	−0.0125757	+	0.0173089i
$981$		0			0
$982$	15.6154	+	30.6469i	0.498307	+	0.977983i
$983$	−43.5889			−1.39027			−0.695135	−	0.718880i	$-0.744655\pi$
$983$	−43.5889			−1.39027			−0.695135	+	0.718880i	$0.744655\pi$
$984$		0			0
$985$	46.5287			1.48253
$986$	−34.0721	−	66.8703i	−1.08508	−	2.12958i
$987$		0			0
$988$	−0.371952	+	0.511949i	−0.0118334	+	0.0162873i
$989$	−9.02196	−	56.9624i	−0.286882	−	1.81130i
$990$		0			0
$991$	18.6784	−	15.9529i	0.593340	−	0.506761i	−0.301311	−	0.953526i	$-0.597424\pi$
$991$	18.6784	−	15.9529i	0.593340	−	0.506761i	0.894651	+	0.446765i	$0.147424\pi$
$992$	−3.06540	−	0.485512i	−0.0973265	−	0.0154150i
$993$		0			0
$994$	6.15516	−	4.47198i	0.195230	−	0.141843i
$995$	−16.1925	−	9.92278i	−0.513337	−	0.314573i
$996$		0			0
$997$	−57.0026	+	4.48620i	−1.80529	+	0.142079i	−0.935950	−	0.352134i	$-0.885456\pi$
$997$	−57.0026	+	4.48620i	−1.80529	+	0.142079i	−0.869341	+	0.494213i	$0.835456\pi$
$998$	17.9648	+	7.44125i	0.568664	+	0.235548i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.c.593.4	yes	64
3.2	odd	2		738.2.ba.d.593.1	yes	64
41.13	odd	40		738.2.ba.d.341.1	yes	64
123.95	even	40	inner	738.2.ba.c.341.4	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.c.341.4	✓	64	123.95	even	40	inner
738.2.ba.c.593.4	yes	64	1.1	even	1	trivial
738.2.ba.d.341.1	yes	64	41.13	odd	40
738.2.ba.d.593.1	yes	64	3.2	odd	2

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.587785 + 0.809017i) q^{4} +(0.411110 + 2.59565i) q^{5} +(-2.04814 + 1.74928i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.12610 - 1.54470i) q^{10} +(-3.44367 - 2.11028i) q^{11} +(2.15705 - 0.169764i) q^{13} +(2.48846 + 1.03075i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-7.35167 + 1.76498i) q^{17} +(0.291559 + 0.0229462i) q^{19} +(-2.34157 - 1.19309i) q^{20} +(-0.316883 + 4.02638i) q^{22} +(2.52027 - 7.75659i) q^{23} +(-1.81310 + 0.589111i) q^{25} +(-1.13054 - 1.84488i) q^{26} +(-0.211328 - 2.68518i) q^{28} +(-9.65226 - 2.31730i) q^{29} +(1.82426 + 2.51087i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.91020 + 5.74911i) q^{34} +(-5.38252 - 4.59711i) q^{35} +(-9.31688 - 6.76911i) q^{37} +(-0.111920 - 0.270198i) q^{38} +2.62800i q^{40} +(-6.36190 + 0.725419i) q^{41} +(6.30064 - 3.21034i) q^{43} +(3.73139 - 1.54559i) q^{44} +(-8.05535 + 1.27584i) q^{46} +(-2.06577 + 2.41870i) q^{47} +(0.0398687 - 0.251721i) q^{49} +(1.34803 + 1.34803i) q^{50} +(-1.13054 + 1.84488i) q^{52} +(-1.45943 + 6.07895i) q^{53} +(4.06182 - 9.80611i) q^{55} +(-2.29657 + 1.40734i) q^{56} +(2.31730 + 9.65226i) q^{58} +(13.6035 + 4.42003i) q^{59} +(-3.72390 + 7.30856i) q^{61} +(1.40901 - 2.76534i) q^{62} +(0.951057 + 0.309017i) q^{64} +(1.32743 + 5.52916i) q^{65} +(-7.36261 + 4.51182i) q^{67} +(2.89331 - 6.98506i) q^{68} +(-1.65244 + 6.88291i) q^{70} +(1.47588 - 2.40842i) q^{71} +(7.65081 + 7.65081i) q^{73} +(-1.80155 + 11.3745i) q^{74} +(-0.189938 + 0.222389i) q^{76} +(10.7446 - 1.70178i) q^{77} +(-7.24823 + 3.00231i) q^{79} +(2.34157 - 1.19309i) q^{80} +(3.53459 + 5.33916i) q^{82} +8.81543i q^{83} +(-7.60362 - 18.3568i) q^{85} +(-5.72086 - 4.15645i) q^{86} +(-3.07115 - 2.62301i) q^{88} +(-4.75921 - 5.57232i) q^{89} +(-4.12099 + 4.12099i) q^{91} +(4.79384 + 6.59815i) q^{92} +(3.09292 + 0.742544i) q^{94} +(0.0603026 + 0.766218i) q^{95} +(-0.338102 - 0.551732i) q^{97} +(-0.242385 + 0.0787557i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{14} + 16 q^{16} - 16 q^{17} + 4 q^{19} - 4 q^{22} + 48 q^{23} + 40 q^{25} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 40 q^{31} + 4 q^{34} - 52 q^{35} + 8 q^{37} + 16 q^{38}+ \cdots + 64 q^{97}+O(q^{100}) \) 64 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^14 + 16 * q^16 - 16 * q^17 + 4 * q^19 - 4 * q^22 + 48 * q^23 + 40 * q^25 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 40 * q^31 + 4 * q^34 - 52 * q^35 + 8 * q^37 + 16 * q^38 + 12 * q^41 + 32 * q^43 - 4 * q^44 - 8 * q^47 + 48 * q^49 + 16 * q^50 - 20 * q^52 - 48 * q^53 - 36 * q^55 + 16 * q^56 - 20 * q^58 + 20 * q^59 + 24 * q^61 - 36 * q^62 + 60 * q^65 - 20 * q^67 + 12 * q^68 - 8 * q^70 - 8 * q^71 + 72 * q^73 - 12 * q^74 + 4 * q^76 - 76 * q^77 + 44 * q^79 - 68 * q^82 - 88 * q^85 - 32 * q^86 - 8 * q^88 + 84 * q^89 + 72 * q^91 + 12 * q^94 - 12 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

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