LMFDB - Embedded newform 738.2.ba.b.179.1

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 = [48,0,0,0,4,0,4,0,0,0,8] 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:	$48$
Relative dimension:	$3$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			179.1
Character	$\chi$	$=$	738.179
Dual form			738.2.ba.b.503.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.156434 - 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-0.454725 + 0.231694i) q^{5} +(-2.47024 - 0.593051i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.157707 + 0.485372i) q^{10} +(-0.749706 - 0.877793i) q^{11} +(1.99976 - 3.26331i) q^{13} +(-0.972180 + 2.34705i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-4.13047 - 0.325075i) q^{17} +(1.92242 + 3.13710i) q^{19} +(0.504067 - 0.0798363i) q^{20} +(-0.984266 + 0.603159i) q^{22} +(-6.21581 + 4.51605i) q^{23} +(-2.78583 + 3.83437i) q^{25} +(-2.91030 - 2.48563i) q^{26} +(2.16607 + 1.32737i) q^{28} +(-9.14125 + 0.719432i) q^{29} +(-5.04650 + 1.63971i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.967221 + 4.02876i) q^{34} +(1.26069 - 0.302664i) q^{35} +(2.33070 - 7.17315i) q^{37} +(3.39921 - 1.40800i) q^{38} -0.510350i q^{40} +(-6.27492 + 1.27492i) q^{41} +(5.66299 + 0.896930i) q^{43} +(0.441760 + 1.06650i) q^{44} +(3.48808 + 6.84575i) q^{46} +(1.17903 + 4.91101i) q^{47} +(-0.486684 - 0.247978i) q^{49} +(3.35136 + 3.35136i) q^{50} +(-2.91030 + 2.48563i) q^{52} +(-0.512168 - 6.50772i) q^{53} +(0.544290 + 0.225452i) q^{55} +(1.64988 - 1.93176i) q^{56} +(-0.719432 + 9.14125i) q^{58} +(-2.09802 - 2.88767i) q^{59} +(-1.54792 - 9.77318i) q^{61} +(0.830073 + 5.24088i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(-0.153251 + 1.94724i) q^{65} +(-1.23719 + 1.44857i) q^{67} +(3.82786 + 1.58555i) q^{68} +(-0.101723 - 1.29251i) q^{70} +(8.02851 - 6.85699i) q^{71} +(8.63876 + 8.63876i) q^{73} +(-6.72023 - 3.42413i) q^{74} +(-0.858911 - 3.57762i) q^{76} +(1.33138 + 2.61297i) q^{77} +(0.430110 + 1.03838i) q^{79} +(-0.504067 - 0.0798363i) q^{80} +(0.277612 + 6.39710i) q^{82} -2.60736i q^{83} +(1.95355 - 0.809186i) q^{85} +(1.77177 - 5.45296i) q^{86} +(1.12248 - 0.269483i) q^{88} +(0.725172 - 3.02056i) q^{89} +(-6.87518 + 6.87518i) q^{91} +(7.30712 - 2.37423i) q^{92} +(5.03499 - 0.396262i) q^{94} +(-1.60102 - 0.981107i) q^{95} +(-10.0740 - 8.60401i) q^{97} +(-0.321059 + 0.441900i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{13} - 4 q^{14} + 12 q^{16} + 16 q^{17} - 4 q^{19} - 16 q^{20} + 20 q^{22} - 40 q^{25} + 20 q^{26} - 4 q^{28} - 32 q^{29} - 40 q^{31} - 4 q^{34} + 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) $ 48 * q + 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^13 - 4 * q^14 + 12 * q^16 + 16 * q^17 - 4 * q^19 - 16 * q^20 + 20 * q^22 - 40 * q^25 + 20 * q^26 - 4 * q^28 - 32 * q^29 - 40 * q^31 - 4 * q^34 + 52 * q^35 - 24 * q^37 - 16 * q^38 - 12 * q^41 + 20 * q^44 + 16 * q^46 + 8 * q^47 - 48 * q^49 + 16 * q^50 + 20 * q^52 - 64 * q^53 + 4 * q^55 - 16 * q^56 + 36 * q^58 - 20 * q^59 - 60 * q^61 + 36 * q^62 - 128 * q^65 - 12 * q^67 + 8 * q^68 + 8 * q^70 + 40 * q^71 + 8 * q^73 - 8 * q^74 + 12 * q^76 + 44 * q^77 + 36 * q^79 + 16 * q^80 + 68 * q^82 + 104 * q^85 + 16 * q^86 + 8 * q^88 + 60 * q^89 + 56 * q^91 - 12 * q^94 + 28 * q^95 + 16 * q^97

Character values

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

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{37}{40}\right)$

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 $

$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$3$		0			0
$3$		0			0
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	−0.454725	+	0.231694i	−0.203359	+	0.103617i	−0.552704	−	0.833377i	$-0.686404\pi$
$5$	−0.454725	+	0.231694i	−0.203359	+	0.103617i	0.349345	+	0.936994i	$0.386404\pi$
$6$		0			0
$7$	−2.47024	−	0.593051i	−0.933662	−	0.224152i	−0.262049	−	0.965055i	$-0.584398\pi$
$7$	−2.47024	−	0.593051i	−0.933662	−	0.224152i	−0.671613	+	0.740902i	$0.734398\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$		0			0
$10$	0.157707	+	0.485372i	0.0498713	+	0.153488i
$11$	−0.749706	−	0.877793i	−0.226045	−	0.264665i	0.635780	−	0.771870i	$-0.280678\pi$
$11$	−0.749706	−	0.877793i	−0.226045	−	0.264665i	−0.861825	+	0.507206i	$0.830678\pi$
$12$		0			0
$13$	1.99976	−	3.26331i	0.554633	−	0.905079i	−0.445320	−	0.895371i	$-0.646910\pi$
$13$	1.99976	−	3.26331i	0.554633	−	0.905079i	0.999953	−	0.00970714i	$-0.00308993\pi$
$14$	−0.972180	+	2.34705i	−0.259826	+	0.627276i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−4.13047	−	0.325075i	−1.00179	−	0.0788423i	−0.433057	−	0.901367i	$-0.642565\pi$
$17$	−4.13047	−	0.325075i	−1.00179	−	0.0788423i	−0.568730	+	0.822524i	$0.692565\pi$
$18$		0			0
$19$	1.92242	+	3.13710i	0.441033	+	0.719701i	0.993500	−	0.113834i	$-0.0363133\pi$
$19$	1.92242	+	3.13710i	0.441033	+	0.719701i	−0.552467	+	0.833535i	$0.686313\pi$
$20$	0.504067	−	0.0798363i	0.112713	−	0.0178519i
$21$		0			0
$22$	−0.984266	+	0.603159i	−0.209846	+	0.128594i
$23$	−6.21581	+	4.51605i	−1.29609	+	0.941661i	−0.999909	−	0.0134722i	$-0.995712\pi$
$23$	−6.21581	+	4.51605i	−1.29609	+	0.941661i	−0.296176	+	0.955133i	$0.595712\pi$
$24$		0			0
$25$	−2.78583	+	3.83437i	−0.557167	+	0.766874i
$26$	−2.91030	−	2.48563i	−0.570757	−	0.487472i
$27$		0			0
$28$	2.16607	+	1.32737i	0.409349	+	0.250849i
$29$	−9.14125	+	0.719432i	−1.69749	+	0.133595i	−0.889901	−	0.456153i	$-0.849227\pi$
$29$	−9.14125	+	0.719432i	−1.69749	+	0.133595i	−0.807587	+	0.589749i	$0.799227\pi$
$30$		0			0
$31$	−5.04650	+	1.63971i	−0.906378	+	0.294500i	−0.724867	−	0.688889i	$-0.758099\pi$
$31$	−5.04650	+	1.63971i	−0.906378	+	0.294500i	−0.181511	+	0.983389i	$0.558099\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−0.967221	+	4.02876i	−0.165877	+	0.690927i
$35$	1.26069	−	0.302664i	0.213095	−	0.0511595i
$36$		0			0
$37$	2.33070	−	7.17315i	0.383164	−	1.17926i	−0.554639	−	0.832091i	$-0.687144\pi$
$37$	2.33070	−	7.17315i	0.383164	−	1.17926i	0.937803	−	0.347167i	$-0.112856\pi$
$38$	3.39921	−	1.40800i	0.551425	−	0.228408i
$39$		0			0
$40$		−	0.510350i		−	0.0806934i
$41$	−6.27492	+	1.27492i	−0.979977	+	0.199109i
$41$	−6.27492	+	1.27492i	−0.979977	+	0.199109i
$42$		0			0
$43$	5.66299	+	0.896930i	0.863598	+	0.136781i	0.572492	−	0.819910i	$-0.305977\pi$
$43$	5.66299	+	0.896930i	0.863598	+	0.136781i	0.291106	+	0.956691i	$0.405977\pi$
$44$	0.441760	+	1.06650i	0.0665978	+	0.160781i
$45$		0			0
$46$	3.48808	+	6.84575i	0.514290	+	1.00935i
$47$	1.17903	+	4.91101i	0.171979	+	0.716345i	0.989989	+	0.141141i	$0.0450772\pi$
$47$	1.17903	+	4.91101i	0.171979	+	0.716345i	−0.818010	+	0.575204i	$0.804923\pi$
$48$		0			0
$49$	−0.486684	−	0.247978i	−0.0695263	−	0.0354254i
$50$	3.35136	+	3.35136i	0.473954	+	0.473954i
$51$		0			0
$52$	−2.91030	+	2.48563i	−0.403586	+	0.344695i
$53$	−0.512168	−	6.50772i	−0.0703517	−	0.893904i	−0.926287	−	0.376820i	$-0.877018\pi$
$53$	−0.512168	−	6.50772i	−0.0703517	−	0.893904i	0.855935	−	0.517084i	$-0.172982\pi$
$54$		0			0
$55$	0.544290	+	0.225452i	0.0733920	+	0.0304000i
$56$	1.64988	−	1.93176i	0.220474	−	0.258142i
$57$		0			0
$58$	−0.719432	+	9.14125i	−0.0944661	+	1.20031i
$59$	−2.09802	−	2.88767i	−0.273139	−	0.375943i	0.650308	−	0.759671i	$-0.274640\pi$
$59$	−2.09802	−	2.88767i	−0.273139	−	0.375943i	−0.923446	+	0.383728i	$0.874640\pi$
$60$		0			0
$61$	−1.54792	−	9.77318i	−0.198191	−	1.25133i	−0.863342	−	0.504619i	$-0.831633\pi$
$61$	−1.54792	−	9.77318i	−0.198191	−	1.25133i	0.665151	−	0.746709i	$-0.268367\pi$
$62$	0.830073	+	5.24088i	0.105419	+	0.665592i
$63$		0			0
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−0.153251	+	1.94724i	−0.0190085	+	0.241525i
$66$		0			0
$67$	−1.23719	+	1.44857i	−0.151147	+	0.176971i	−0.830814	−	0.556551i	$-0.812125\pi$
$67$	−1.23719	+	1.44857i	−0.151147	+	0.176971i	0.679666	+	0.733521i	$0.262125\pi$
$68$	3.82786	+	1.58555i	0.464196	+	0.192276i
$69$		0			0
$70$	−0.101723	−	1.29251i	−0.0121582	−	0.154485i
$71$	8.02851	−	6.85699i	0.952808	−	0.813775i	−0.0297827	−	0.999556i	$-0.509482\pi$
$71$	8.02851	−	6.85699i	0.952808	−	0.813775i	0.982591	+	0.185781i	$0.0594815\pi$
$72$		0			0
$73$	8.63876	+	8.63876i	1.01109	+	1.01109i	0.999938	+	0.0111528i	$0.00355011\pi$
$73$	8.63876	+	8.63876i	1.01109	+	1.01109i	0.0111528	+	0.999938i	$0.496450\pi$
$74$	−6.72023	−	3.42413i	−0.781211	−	0.398047i
$75$		0			0
$76$	−0.858911	−	3.57762i	−0.0985239	−	0.410381i
$77$	1.33138	+	2.61297i	0.151724	+	0.297776i
$78$		0			0
$79$	0.430110	+	1.03838i	0.0483912	+	0.116827i	0.946227	−	0.323504i	$-0.104861\pi$
$79$	0.430110	+	1.03838i	0.0483912	+	0.116827i	−0.897835	+	0.440331i	$0.854861\pi$
$80$	−0.504067	−	0.0798363i	−0.0563564	−	0.00892597i
$81$		0			0
$82$	0.277612	+	6.39710i	0.0306571	+	0.706442i
$83$		−	2.60736i		−	0.286195i	−0.989709	−	0.143098i	$-0.954294\pi$
$83$		−	2.60736i		−	0.286195i	0.989709	−	0.143098i	$-0.0457063\pi$
$84$		0			0
$85$	1.95355	−	0.809186i	0.211892	−	0.0877685i
$86$	1.77177	−	5.45296i	0.191055	−	0.588008i
$87$		0			0
$88$	1.12248	−	0.269483i	0.119657	−	0.0287270i
$89$	0.725172	−	3.02056i	0.0768681	−	0.320179i	−0.920667	−	0.390349i	$-0.872354\pi$
$89$	0.725172	−	3.02056i	0.0768681	−	0.320179i	0.997535	+	0.0701705i	$0.0223543\pi$
$90$		0			0
$91$	−6.87518	+	6.87518i	−0.720715	+	0.720715i
$92$	7.30712	−	2.37423i	0.761820	−	0.247530i
$93$		0			0
$94$	5.03499	−	0.396262i	0.519320	−	0.0408713i
$95$	−1.60102	−	0.981107i	−0.164261	−	0.100659i
$96$		0			0
$97$	−10.0740	−	8.60401i	−1.02286	−	0.873605i	−0.0308199	−	0.999525i	$-0.509812\pi$
$97$	−10.0740	−	8.60401i	−1.02286	−	0.873605i	−0.992040	+	0.125920i	$0.959812\pi$
$98$	−0.321059	+	0.441900i	−0.0324319	+	0.0446386i
$99$		0			0
$100$	3.83437	−	2.78583i	0.383437	−	0.278583i
$101$	−4.89602	+	3.00028i	−0.487172	+	0.298540i	−0.744309	−	0.667836i	$-0.767221\pi$
$101$	−4.89602	+	3.00028i	−0.487172	+	0.298540i	0.257137	+	0.966375i	$0.417221\pi$
$102$		0			0
$103$	1.71321	−	0.271346i	0.168808	−	0.0267366i	−0.0714582	−	0.997444i	$-0.522765\pi$
$103$	1.71321	−	0.271346i	0.168808	−	0.0267366i	0.240266	+	0.970707i	$0.422765\pi$
$104$	1.99976	+	3.26331i	0.196092	+	0.319994i
$105$		0			0
$106$	−6.50772	−	0.512168i	−0.632085	−	0.0497462i
$107$	7.43350	+	5.40075i	0.718623	+	0.522110i	0.885944	−	0.463792i	$-0.153512\pi$
$107$	7.43350	+	5.40075i	0.718623	+	0.522110i	−0.167321	+	0.985902i	$0.553512\pi$
$108$		0			0
$109$	−0.309072	+	0.746167i	−0.0296038	+	0.0714698i	−0.937990	−	0.346662i	$-0.887315\pi$
$109$	−0.309072	+	0.746167i	−0.0296038	+	0.0714698i	0.908386	+	0.418132i	$0.137315\pi$
$110$	0.307822	−	0.502320i	0.0293497	−	0.0478944i
$111$		0			0
$112$	−1.64988	−	1.93176i	−0.155899	−	0.182534i
$113$	1.80986	+	5.57016i	0.170257	+	0.523997i	0.999385	−	0.0350615i	$-0.0111627\pi$
$113$	1.80986	+	5.57016i	0.170257	+	0.523997i	−0.829128	+	0.559058i	$0.811163\pi$
$114$		0			0
$115$	1.78014	−	3.49373i	0.165999	−	0.325792i
$116$	8.91616	+	2.14058i	0.827845	+	0.198748i
$117$		0			0
$118$	−3.18032	+	1.62046i	−0.292773	+	0.149175i
$119$	10.0105	+	3.25259i	0.917657	+	0.298165i
$120$		0			0
$121$	1.51232	−	9.54840i	0.137483	−	0.868036i
$122$	−9.89501			−0.895852
$123$		0			0
$124$	5.30621			0.476511
$125$	0.777569	−	4.90938i	0.0695479	−	0.439108i
$126$		0			0
$127$	16.7151	+	5.43105i	1.48322	+	0.481928i	0.935074	−	0.354454i	$-0.115333\pi$
$127$	16.7151	+	5.43105i	1.48322	+	0.481928i	0.548148	+	0.836382i	$0.315333\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$		0			0
$130$	1.89929	+	0.455980i	0.166579	+	0.0399921i
$131$	3.34214	−	6.55932i	0.292004	−	0.573091i	−0.697671	−	0.716418i	$-0.745780\pi$
$131$	3.34214	−	6.55932i	0.292004	−	0.573091i	0.989675	+	0.143328i	$0.0457803\pi$
$132$		0			0
$133$	−2.88837	−	8.88948i	−0.250453	−	0.770816i
$134$	1.23719	+	1.44857i	0.106877	+	0.125137i
$135$		0			0
$136$	2.16484	−	3.53270i	0.185633	−	0.302926i
$137$	2.72392	−	6.57613i	0.232720	−	0.561837i	−0.763775	−	0.645482i	$-0.776656\pi$
$137$	2.72392	−	6.57613i	0.232720	−	0.561837i	0.996496	+	0.0836457i	$0.0266564\pi$
$138$		0			0
$139$	−6.76359	−	4.91404i	−0.573680	−	0.416803i	0.262760	−	0.964861i	$-0.415367\pi$
$139$	−6.76359	−	4.91404i	−0.573680	−	0.416803i	−0.836440	+	0.548058i	$0.815367\pi$
$140$	−1.29251	−	0.101723i	−0.109237	−	0.00859715i
$141$		0			0
$142$	−5.51664	−	9.00233i	−0.462946	−	0.755459i
$143$	−4.36374	+	0.691148i	−0.364914	+	0.0577967i
$144$		0			0
$145$	3.99007	−	2.44512i	0.331357	−	0.203056i
$146$	9.88380	−	7.18100i	0.817989	−	0.594304i
$147$		0			0
$148$	−4.43325	+	6.10184i	−0.364411	+	0.501568i
$149$	12.7717	+	10.9080i	1.04630	+	0.893622i	0.994469	−	0.105034i	$-0.0334952\pi$
$149$	12.7717	+	10.9080i	1.04630	+	0.893622i	0.0518280	+	0.998656i	$0.483495\pi$
$150$		0			0
$151$	−18.4114	−	11.2825i	−1.49830	−	0.918159i	−0.998651	−	0.0519306i	$-0.983463\pi$
$151$	−18.4114	−	11.2825i	−1.49830	−	0.918159i	−0.499648	−	0.866228i	$-0.666537\pi$
$152$	−3.66794	+	0.288673i	−0.297509	+	0.0234145i
$153$		0			0
$154$	2.78907	−	0.906225i	0.224750	−	0.0730257i
$155$	1.91486	−	1.91486i	0.153805	−	0.153805i
$156$		0			0
$157$	−2.00435	+	8.34871i	−0.159964	+	0.666300i	0.833535	+	0.552466i	$0.186313\pi$
$157$	−2.00435	+	8.34871i	−0.159964	+	0.666300i	−0.993500	+	0.113834i	$0.963687\pi$
$158$	1.09288	−	0.262377i	0.0869447	−	0.0208736i
$159$		0			0
$160$	−0.157707	+	0.485372i	−0.0124678	+	0.0383720i
$161$	18.0328	−	7.46942i	1.42118	−	0.588672i
$162$		0			0
$163$			4.71832i			0.369567i	0.982779	+	0.184784i	$0.0591585\pi$
$163$			4.71832i			0.369567i	−0.982779	+	0.184784i	$0.940842\pi$
$164$	6.36177	+	0.726533i	0.496771	+	0.0567327i
$165$		0			0
$166$	−2.57526	−	0.407881i	−0.199879	−	0.0316577i
$167$	−0.805984	−	1.94582i	−0.0623689	−	0.150572i	0.889622	−	0.456697i	$-0.150968\pi$
$167$	−0.805984	−	1.94582i	−0.0623689	−	0.150572i	−0.951991	+	0.306125i	$0.900968\pi$
$168$		0			0
$169$	−0.748269	−	1.46856i	−0.0575592	−	0.112966i
$170$	−0.493621	−	2.05608i	−0.0378590	−	0.157694i
$171$		0			0
$172$	−5.10866	−	2.60299i	−0.389532	−	0.198476i
$173$	−5.20524	−	5.20524i	−0.395747	−	0.395747i	0.480983	−	0.876730i	$-0.340280\pi$
$173$	−5.20524	−	5.20524i	−0.395747	−	0.395747i	−0.876730	+	0.480983i	$0.840280\pi$
$174$		0			0
$175$	9.15565	−	7.81966i	0.692102	−	0.591111i
$176$	−0.0905712	−	1.15082i	−0.00682706	−	0.0867460i
$177$		0			0
$178$	−2.86993	−	1.18876i	−0.215110	−	0.0891016i
$179$	−11.2155	+	13.1317i	−0.838287	+	0.981508i	−0.999986	−	0.00533190i	$-0.998303\pi$
$179$	−11.2155	+	13.1317i	−0.838287	+	0.981508i	0.161698	+	0.986840i	$0.448303\pi$
$180$		0			0
$181$	0.871880	−	11.0783i	0.0648063	−	0.823442i	−0.875523	−	0.483176i	$-0.839483\pi$
$181$	0.871880	−	11.0783i	0.0648063	−	0.823442i	0.940329	−	0.340266i	$-0.110517\pi$
$182$	5.71502	+	7.86606i	0.423626	+	0.583071i
$183$		0			0
$184$	−1.20191	−	7.58857i	−0.0886061	−	0.559437i
$185$	0.602149	+	3.80182i	0.0442709	+	0.279515i
$186$		0			0
$187$	2.81129	+	3.86941i	0.205582	+	0.282959i
$188$	0.396262	−	5.03499i	0.0289004	−	0.367214i
$189$		0			0
$190$	−1.21948	+	1.42783i	−0.0884706	+	0.103586i
$191$	−11.7603	−	4.87126i	−0.850943	−	0.352472i	−0.0857841	−	0.996314i	$-0.527340\pi$
$191$	−11.7603	−	4.87126i	−0.850943	−	0.352472i	−0.765159	+	0.643842i	$0.777340\pi$
$192$		0			0
$193$	−1.30078	−	16.5280i	−0.0936323	−	1.18971i	−0.846810	−	0.531895i	$-0.821480\pi$
$193$	−1.30078	−	16.5280i	−0.0936323	−	1.18971i	0.753178	−	0.657817i	$-0.228520\pi$
$194$	−10.0740	+	8.60401i	−0.723271	+	0.617732i
$195$		0			0
$196$	0.386235	+	0.386235i	0.0275882	+	0.0275882i
$197$	−16.1458	−	8.22669i	−1.15034	−	0.586128i	−0.228441	−	0.973558i	$-0.573363\pi$
$197$	−16.1458	−	8.22669i	−1.15034	−	0.586128i	−0.921899	+	0.387430i	$0.873363\pi$
$198$		0			0
$199$	−2.40924	−	10.0352i	−0.170786	−	0.711376i	−0.990373	−	0.138421i	$-0.955797\pi$
$199$	−2.40924	−	10.0352i	−0.170786	−	0.711376i	0.819587	−	0.572955i	$-0.194203\pi$
$200$	−2.15171	−	4.22296i	−0.152149	−	0.298609i
$201$		0			0
$202$	2.19744	+	5.30509i	0.154611	+	0.373265i
$203$	23.0077	+	3.64407i	1.61483	+	0.255763i
$204$		0			0
$205$	2.55797	−	2.03360i	0.178656	−	0.142033i
$206$		−	1.73457i		−	0.120853i
$207$		0			0
$208$	3.53596	−	1.46464i	0.245175	−	0.101555i
$209$	1.31248	−	4.03939i	0.0907860	−	0.279411i
$210$		0			0
$211$	−23.8174	+	5.71805i	−1.63966	+	0.393647i	−0.945356	−	0.326040i	$-0.894286\pi$
$211$	−23.8174	+	5.71805i	−1.63966	+	0.393647i	−0.694300	+	0.719686i	$0.744286\pi$
$212$	−1.52389	+	6.34747i	−0.104661	+	0.435946i
$213$		0			0
$214$	6.49711	−	6.49711i	0.444134	−	0.444134i
$215$	−2.78292	+	0.904225i	−0.189794	+	0.0616676i
$216$		0			0
$217$	13.4385	−	1.05763i	0.912264	−	0.0717967i
$218$	0.688631	+	0.421993i	0.0466400	+	0.0285810i
$219$		0			0
$220$	−0.447982	−	0.382613i	−0.0302029	−	0.0257957i
$221$	−9.32076	+	12.8289i	−0.626982	+	0.862967i
$222$		0			0
$223$	−4.77463	+	3.46897i	−0.319733	+	0.232300i	−0.736061	−	0.676915i	$-0.763317\pi$
$223$	−4.77463	+	3.46897i	−0.319733	+	0.232300i	0.416329	+	0.909214i	$0.363317\pi$
$224$	−2.16607	+	1.32737i	−0.144727	+	0.0886887i
$225$		0			0
$226$	5.78471	−	0.916208i	0.384793	−	0.0609453i
$227$	7.76404	+	12.6698i	0.515318	+	0.840922i	0.999419	−	0.0340901i	$-0.0108533\pi$
$227$	7.76404	+	12.6698i	0.515318	+	0.840922i	−0.484101	+	0.875012i	$0.660853\pi$
$228$		0			0
$229$	23.4440	+	1.84508i	1.54922	+	0.121926i	0.824000	−	0.566589i	$-0.191737\pi$
$229$	23.4440	+	1.84508i	1.54922	+	0.121926i	0.725221	+	0.688516i	$0.241737\pi$
$230$	−3.17224	−	2.30477i	−0.209171	−	0.151972i
$231$		0			0
$232$	3.50902	−	8.47153i	0.230379	−	0.556183i
$233$	1.87377	−	3.05771i	0.122755	−	0.200317i	−0.785360	−	0.619040i	$-0.787522\pi$
$233$	1.87377	−	3.05771i	0.122755	−	0.200317i	0.908114	+	0.418722i	$0.137522\pi$
$234$		0			0
$235$	−1.67399	−	1.95999i	−0.109199	−	0.127855i
$236$	1.10299	+	3.39466i	0.0717987	+	0.220974i
$237$		0			0
$238$	4.77853	−	9.37839i	0.309746	−	0.607911i
$239$	9.62785	+	2.31144i	0.622774	+	0.149515i	0.532539	−	0.846406i	$-0.321238\pi$
$239$	9.62785	+	2.31144i	0.622774	+	0.149515i	0.0902353	+	0.995920i	$0.471238\pi$
$240$		0			0
$241$	−23.3491	+	11.8970i	−1.50405	+	0.766351i	−0.995507	−	0.0946858i	$-0.969815\pi$
$241$	−23.3491	+	11.8970i	−1.50405	+	0.766351i	−0.508542	+	0.861037i	$0.669815\pi$
$242$	−9.19426	−	2.98740i	−0.591030	−	0.192037i
$243$		0			0
$244$	−1.54792	+	9.77318i	−0.0990954	+	0.625664i
$245$	0.278763			0.0178095
$246$		0			0
$247$	14.0817			0.895997
$248$	0.830073	−	5.24088i	0.0527097	−	0.332796i
$249$		0			0
$250$	−4.72730	−	1.53599i	−0.298981	−	0.0971447i
$251$	19.3010	−	9.83434i	1.21827	−	0.620738i	0.277806	−	0.960637i	$-0.410393\pi$
$251$	19.3010	−	9.83434i	1.21827	−	0.620738i	0.940462	+	0.339899i	$0.110393\pi$
$252$		0			0
$253$	8.62419	+	2.07048i	0.542198	+	0.130170i
$254$	7.97900	−	15.6597i	0.500647	−	0.982575i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−5.56862	−	6.52001i	−0.347361	−	0.406707i	0.559030	−	0.829147i	$-0.311174\pi$
$257$	−5.56862	−	6.52001i	−0.347361	−	0.406707i	−0.906391	+	0.422440i	$0.861174\pi$
$258$		0			0
$259$	−10.0114	+	16.3372i	−0.622079	+	1.01514i
$260$	0.747481	−	1.80458i	0.0463568	−	0.111915i
$261$		0			0
$262$	−5.95574	−	4.32710i	−0.367947	−	0.267329i
$263$	1.85288	+	0.145825i	0.114254	+	0.00899196i	0.135457	−	0.990783i	$-0.456750\pi$
$263$	1.85288	+	0.145825i	0.114254	+	0.00899196i	−0.0212033	+	0.999775i	$0.506750\pi$
$264$		0			0
$265$	1.74070	+	2.84056i	0.106930	+	0.174494i
$266$	−9.23188	+	1.46219i	−0.566043	+	0.0896524i
$267$		0			0
$268$	1.62427	−	0.995356i	0.0992183	−	0.0608011i
$269$	1.82728	−	1.32759i	0.111411	−	0.0809449i	−0.530685	−	0.847569i	$-0.678065\pi$
$269$	1.82728	−	1.32759i	0.111411	−	0.0809449i	0.642096	+	0.766624i	$0.278065\pi$
$270$		0			0
$271$	−15.0466	+	20.7099i	−0.914018	+	1.25804i	0.0517576	+	0.998660i	$0.483518\pi$
$271$	−15.0466	+	20.7099i	−0.914018	+	1.25804i	−0.965776	+	0.259378i	$0.916482\pi$
$272$	−3.15055	−	2.69082i	−0.191030	−	0.163155i
$273$		0			0
$274$	−6.06905	−	3.71912i	−0.366645	−	0.224680i
$275$	5.45434	−	0.429266i	0.328909	−	0.0258857i
$276$		0			0
$277$	1.10241	−	0.358196i	0.0662376	−	0.0215219i	−0.275711	−	0.961241i	$-0.588913\pi$
$277$	1.10241	−	0.358196i	0.0662376	−	0.0215219i	0.341948	+	0.939719i	$0.388913\pi$
$278$	−5.91159	+	5.91159i	−0.354554	+	0.354554i
$279$		0			0
$280$	−0.302664	+	1.26069i	−0.0180876	+	0.0753404i
$281$	−19.3259	+	4.63973i	−1.15288	+	0.276783i	−0.764443	−	0.644691i	$-0.776986\pi$
$281$	−19.3259	+	4.63973i	−1.15288	+	0.276783i	−0.388441	+	0.921474i	$0.626986\pi$
$282$		0			0
$283$	−2.91725	+	8.97836i	−0.173412	+	0.533708i	−0.999557	−	0.0297492i	$-0.990529\pi$
$283$	−2.91725	+	8.97836i	−0.173412	+	0.533708i	0.826145	+	0.563458i	$0.190529\pi$
$284$	−9.75449	+	4.04044i	−0.578823	+	0.239756i
$285$		0			0
$286$			4.41813i			0.261250i
$287$	16.2566	+	0.571990i	0.959598	+	0.0337635i
$288$		0			0
$289$	0.164410	+	0.0260400i	0.00967119	+	0.00153177i
$290$	−1.79083	−	4.32345i	−0.105161	−	0.253882i
$291$		0			0
$292$	−5.54643	−	10.8855i	−0.324580	−	0.637024i
$293$	−4.38916	−	18.2822i	−0.256418	−	1.06806i	−0.940808	−	0.338941i	$-0.889931\pi$
$293$	−4.38916	−	18.2822i	−0.256418	−	1.06806i	0.684390	−	0.729116i	$-0.260069\pi$
$294$		0			0
$295$	1.62308	+	0.827000i	0.0944993	+	0.0481498i
$296$	5.33321	+	5.33321i	0.309986	+	0.309986i
$297$		0			0
$298$	12.7717	−	10.9080i	0.739843	−	0.631886i
$299$	2.30715	+	29.3151i	0.133426	+	1.69534i
$300$		0			0
$301$	−13.4570	−	5.57408i	−0.775649	−	0.321284i
$302$	−14.0238	+	16.4198i	−0.806979	+	0.944851i
$303$		0			0
$304$	−0.288673	+	3.66794i	−0.0165565	+	0.210371i
$305$	2.96827	+	4.08547i	0.169962	+	0.233933i
$306$		0			0
$307$	4.55899	+	28.7843i	0.260195	+	1.64281i	0.678572	+	0.734534i	$0.262599\pi$
$307$	4.55899	+	28.7843i	0.260195	+	1.64281i	−0.418377	+	0.908273i	$0.637401\pi$
$308$	−0.458761	−	2.89650i	−0.0261403	−	0.165043i
$309$		0			0
$310$	−1.59174	−	2.19084i	−0.0904045	−	0.124431i
$311$	1.62732	−	20.6771i	0.0922771	−	1.17249i	−0.760187	−	0.649705i	$-0.774893\pi$
$311$	1.62732	−	20.6771i	0.0922771	−	1.17249i	0.852464	−	0.522786i	$-0.175107\pi$
$312$		0			0
$313$	14.9511	−	17.5055i	0.845088	−	0.989471i	−0.154911	−	0.987928i	$-0.549509\pi$
$313$	14.9511	−	17.5055i	0.845088	−	0.989471i	0.999999	−	0.00154212i	$-0.000490872\pi$
$314$	7.93238	+	3.28570i	0.447650	+	0.185423i
$315$		0			0
$316$	−0.0881827	−	1.12047i	−0.00496067	−	0.0630312i
$317$	14.3739	−	12.2764i	0.807316	−	0.689513i	−0.146729	−	0.989177i	$-0.546874\pi$
$317$	14.3739	−	12.2764i	0.807316	−	0.689513i	0.954045	+	0.299664i	$0.0968744\pi$
$318$		0			0
$319$	7.48477	+	7.48477i	0.419066	+	0.419066i
$320$	0.454725	+	0.231694i	0.0254199	+	0.0129521i
$321$		0			0
$322$	−4.55651	−	18.9792i	−0.253924	−	1.05767i
$323$	−6.92070	−	13.5826i	−0.385078	−	0.755758i
$324$		0			0
$325$	6.94174	+	16.7588i	0.385058	+	0.929613i
$326$	4.66023	+	0.738108i	0.258106	+	0.0408800i
$327$		0			0
$328$	1.71279	−	6.16979i	0.0945730	−	0.340670i
$329$		−	12.8306i		−	0.707373i
$330$		0			0
$331$	13.5794	−	5.62476i	0.746390	−	0.309165i	0.0231223	−	0.999733i	$-0.492639\pi$
$331$	13.5794	−	5.62476i	0.746390	−	0.309165i	0.723268	+	0.690568i	$0.242639\pi$
$332$	−0.805719	+	2.47975i	−0.0442196	+	0.136094i
$333$		0			0
$334$	−2.04795	+	0.491668i	−0.112059	+	0.0269029i
$335$	0.226959	−	0.945351i	0.0124001	−	0.0516500i
$336$		0			0
$337$	−19.3581	+	19.3581i	−1.05450	+	1.05450i	−0.0560754	+	0.998427i	$0.517859\pi$
$337$	−19.3581	+	19.3581i	−1.05450	+	1.05450i	−0.998427	+	0.0560754i	$0.982141\pi$
$338$	−1.56754	+	0.509323i	−0.0852627	+	0.0277035i
$339$		0			0
$340$	−2.10799	+	0.165902i	−0.114322	+	0.00899730i
$341$	5.22272	+	3.20049i	0.282826	+	0.173316i
$342$		0			0
$343$	14.5775	+	12.4503i	0.787109	+	0.672255i
$344$	−3.37012	+	4.63857i	−0.181704	+	0.250095i
$345$		0			0
$346$	−5.95543	+	4.32687i	−0.320166	+	0.232614i
$347$	−22.3403	+	13.6902i	−1.19929	+	0.734927i	−0.971096	−	0.238689i	$-0.923282\pi$
$347$	−22.3403	+	13.6902i	−1.19929	+	0.734927i	−0.228195	+	0.973615i	$0.573282\pi$
$348$		0			0
$349$	8.98820	−	1.42359i	0.481127	−	0.0762031i	0.0888402	−	0.996046i	$-0.471684\pi$
$349$	8.98820	−	1.42359i	0.481127	−	0.0762031i	0.392287	+	0.919843i	$0.371684\pi$
$350$	−6.29113	−	10.2662i	−0.336275	−	0.548751i
$351$		0			0
$352$	−1.15082	−	0.0905712i	−0.0613387	−	0.00482746i
$353$	12.2481	+	8.89877i	0.651901	+	0.473634i	0.863918	−	0.503632i	$-0.168003\pi$
$353$	12.2481	+	8.89877i	0.651901	+	0.473634i	−0.212017	+	0.977266i	$0.568003\pi$
$354$		0			0
$355$	−2.06204	+	4.97821i	−0.109442	+	0.264216i
$356$	−1.62308	+	2.64863i	−0.0860232	+	0.140377i
$357$		0			0
$358$	11.2155	+	13.1317i	0.592759	+	0.694031i
$359$	−2.29656	−	7.06809i	−0.121208	−	0.373040i	0.871983	−	0.489536i	$-0.162834\pi$
$359$	−2.29656	−	7.06809i	−0.121208	−	0.373040i	−0.993191	+	0.116496i	$0.962834\pi$
$360$		0			0
$361$	2.48010	−	4.86747i	0.130532	−	0.256183i
$362$	−10.8055	−	2.59417i	−0.567924	−	0.136347i
$363$		0			0
$364$	8.66324	−	4.41414i	0.454077	−	0.231364i
$365$	−5.92981	−	1.92671i	−0.310381	−	0.100849i
$366$		0			0
$367$	−4.98806	+	31.4934i	−0.260374	+	1.64394i	0.417438	+	0.908705i	$0.362928\pi$
$367$	−4.98806	+	31.4934i	−0.260374	+	1.64394i	−0.677813	+	0.735235i	$0.737072\pi$
$368$	−7.68316			−0.400512
$369$		0			0
$370$	3.84921			0.200111
$371$	−2.59423	+	16.3793i	−0.134686	+	0.850373i
$372$		0			0
$373$	−29.7351	−	9.66152i	−1.53962	−	0.500254i	−0.588352	−	0.808605i	$-0.700223\pi$
$373$	−29.7351	−	9.66152i	−1.53962	−	0.500254i	−0.951273	+	0.308351i	$0.900223\pi$
$374$	4.26155	−	2.17137i	0.220360	−	0.112279i
$375$		0			0
$376$	−4.91101	−	1.17903i	−0.253266	−	0.0608038i
$377$	−15.9326	+	31.2694i	−0.820569	+	1.61046i
$378$		0			0
$379$	8.95946	+	27.5744i	0.460217	+	1.41640i	0.864900	+	0.501945i	$0.167382\pi$
$379$	8.95946	+	27.5744i	0.460217	+	1.41640i	−0.404683	+	0.914457i	$0.632618\pi$
$380$	1.21948	+	1.42783i	0.0625581	+	0.0732462i
$381$		0			0
$382$	−6.65100	+	10.8534i	−0.340295	+	0.555310i
$383$	3.64633	−	8.80302i	0.186319	−	0.449813i	−0.802927	−	0.596078i	$-0.796725\pi$
$383$	3.64633	−	8.80302i	0.186319	−	0.449813i	0.989246	+	0.146264i	$0.0467250\pi$
$384$		0			0
$385$	−1.21082	−	0.879712i	−0.0617091	−	0.0448343i
$386$	−16.5280	−	1.30078i	−0.841253	−	0.0662080i
$387$		0			0
$388$	6.92216	+	11.2959i	0.351420	+	0.573465i
$389$	−27.0435	+	4.28327i	−1.37116	+	0.217171i	−0.798190	−	0.602405i	$-0.794209\pi$
$389$	−27.0435	+	4.28327i	−1.37116	+	0.217171i	−0.572971	+	0.819576i	$0.694209\pi$
$390$		0			0
$391$	27.1423	−	16.6328i	1.37264	−	0.841157i
$392$	0.441900	−	0.321059i	0.0223193	−	0.0162159i
$393$		0			0
$394$	−10.6512	+	14.6601i	−0.536598	+	0.738564i
$395$	−0.436168	−	0.372523i	−0.0219460	−	0.0187437i
$396$		0			0
$397$	−0.832476	−	0.510142i	−0.0417808	−	0.0256033i	0.501451	−	0.865186i	$-0.332800\pi$
$397$	−0.832476	−	0.510142i	−0.0417808	−	0.0256033i	−0.543232	+	0.839583i	$0.682800\pi$
$398$	−10.2885	+	0.809725i	−0.515717	+	0.0405878i
$399$		0			0
$400$	−4.50757	+	1.46460i	−0.225379	+	0.0732300i
$401$	−3.89680	+	3.89680i	−0.194597	+	0.194597i	−0.797679	−	0.603082i	$-0.793939\pi$
$401$	−3.89680	+	3.89680i	−0.194597	+	0.194597i	0.603082	+	0.797679i	$0.293939\pi$
$402$		0			0
$403$	−4.74091	+	19.7473i	−0.236161	+	0.983683i
$404$	5.58353	−	1.34049i	0.277791	−	0.0666917i
$405$		0			0
$406$	7.19840	−	22.1544i	0.357251	−	1.09950i
$407$	−8.04388	+	3.33188i	−0.398720	+	0.165155i
$408$		0			0
$409$			12.8222i			0.634016i	0.948423	+	0.317008i	$0.102678\pi$
$409$			12.8222i			0.634016i	−0.948423	+	0.317008i	$0.897322\pi$
$410$	−1.60841	−	2.84460i	−0.0794336	−	0.140485i
$411$		0			0
$412$	−1.71321	−	0.271346i	−0.0844040	−	0.0133683i
$413$	3.47006	+	8.37747i	0.170751	+	0.412228i
$414$		0			0
$415$	0.604110	+	1.18563i	0.0296546	+	0.0582005i
$416$	−0.893465	−	3.72155i	−0.0438057	−	0.182464i
$417$		0			0
$418$	−3.78434	−	1.92822i	−0.185098	−	0.0943123i
$419$	16.7810	+	16.7810i	0.819805	+	0.819805i	0.986080	−	0.166274i	$-0.0531737\pi$
$419$	16.7810	+	16.7810i	0.819805	+	0.819805i	−0.166274	+	0.986080i	$0.553174\pi$
$420$		0			0
$421$	−7.40253	+	6.32236i	−0.360777	+	0.308133i	−0.811298	−	0.584633i	$-0.801238\pi$
$421$	−7.40253	+	6.32236i	−0.360777	+	0.308133i	0.450520	+	0.892766i	$0.351238\pi$
$422$	1.92179	+	24.4186i	0.0935512	+	1.18868i
$423$		0			0
$424$	6.03094	+	2.49810i	0.292888	+	0.121318i
$425$	12.7533	−	14.9321i	0.618624	−	0.724316i
$426$		0			0
$427$	−1.97227	+	25.0601i	−0.0954449	+	1.21274i
$428$	−5.40075	−	7.43350i	−0.261055	−	0.359312i
$429$		0			0
$430$	0.457748	+	2.89011i	0.0220746	+	0.139373i
$431$	−1.33556	−	8.43239i	−0.0643316	−	0.406174i	−0.998749	−	0.0499951i	$-0.984079\pi$
$431$	−1.33556	−	8.43239i	−0.0643316	−	0.406174i	0.934418	−	0.356179i	$-0.115921\pi$
$432$		0			0
$433$	16.3965	+	22.5678i	0.787965	+	1.08454i	0.994358	+	0.106072i	$0.0338273\pi$
$433$	16.3965	+	22.5678i	0.787965	+	1.08454i	−0.206394	+	0.978469i	$0.566173\pi$
$434$	1.05763	−	13.4385i	0.0507680	−	0.645068i
$435$		0			0
$436$	0.524524	−	0.614138i	0.0251201	−	0.0294119i
$437$	−26.1167	−	10.8179i	−1.24933	−	0.517490i
$438$		0			0
$439$	−2.29826	−	29.2021i	−0.109690	−	1.39374i	−0.767737	−	0.640765i	$-0.778617\pi$
$439$	−2.29826	−	29.2021i	−0.109690	−	1.39374i	0.658047	−	0.752977i	$-0.271383\pi$
$440$	−0.447982	+	0.382613i	−0.0213567	+	0.0182403i
$441$		0			0
$442$	11.2129	+	11.2129i	0.533343	+	0.533343i
$443$	−31.4603	−	16.0298i	−1.49472	−	0.761599i	−0.500178	−	0.865922i	$-0.666732\pi$
$443$	−31.4603	−	16.0298i	−1.49472	−	0.761599i	−0.994543	+	0.104324i	$0.966732\pi$
$444$		0			0
$445$	0.370092	+	1.54154i	0.0175440	+	0.0730761i
$446$	2.67935	+	5.25851i	0.126871	+	0.248998i
$447$		0			0
$448$	0.972180	+	2.34705i	0.0459312	+	0.110888i
$449$	−19.7941	−	3.13507i	−0.934139	−	0.147953i	−0.329232	−	0.944249i	$-0.606790\pi$
$449$	−19.7941	−	3.13507i	−0.934139	−	0.147953i	−0.604907	+	0.796296i	$0.706790\pi$
$450$		0			0
$451$	5.82346	+	4.55226i	0.274216	+	0.214358i
$452$		−	5.85682i		−	0.275482i
$453$		0			0
$454$	13.7283	−	5.68647i	0.644303	−	0.266879i
$455$	1.53338	−	4.71926i	0.0718860	−	0.221242i
$456$		0			0
$457$	18.1440	−	4.35599i	0.848741	−	0.203765i	0.214331	−	0.976761i	$-0.431243\pi$
$457$	18.1440	−	4.35599i	0.848741	−	0.203765i	0.634410	+	0.772997i	$0.281243\pi$
$458$	5.48981	−	22.8667i	0.256522	−	1.06849i
$459$		0			0
$460$	−2.77264	+	2.77264i	−0.129275	+	0.129275i
$461$	24.1257	−	7.83891i	1.12365	−	0.365095i	0.312488	−	0.949922i	$-0.398838\pi$
$461$	24.1257	−	7.83891i	1.12365	−	0.365095i	0.811158	+	0.584827i	$0.198838\pi$
$462$		0			0
$463$	−26.2880	+	2.06891i	−1.22171	+	0.0961505i	−0.672859	−	0.739771i	$-0.734934\pi$
$463$	−26.2880	+	2.06891i	−1.22171	+	0.0961505i	−0.548849	+	0.835921i	$0.684934\pi$
$464$	−7.81830	−	4.79106i	−0.362955	−	0.222419i
$465$		0			0
$466$	−2.72694	−	2.32903i	−0.126323	−	0.107890i
$467$	−7.00444	+	9.64078i	−0.324127	+	0.446122i	−0.939722	−	0.341941i	$-0.888916\pi$
$467$	−7.00444	+	9.64078i	−0.324127	+	0.446122i	0.615595	+	0.788063i	$0.288916\pi$
$468$		0			0
$469$	3.91524	−	2.84459i	0.180789	−	0.131351i
$470$	−2.19773	+	1.34677i	−0.101374	+	0.0621218i
$471$		0			0
$472$	3.52542	−	0.558371i	0.162270	−	0.0257011i
$473$	−3.45826	−	5.64337i	−0.159011	−	0.259482i
$474$		0			0
$475$	−17.3844	−	1.36818i	−0.797649	−	0.0627763i
$476$	−8.51540	−	6.18680i	−0.390303	−	0.283572i
$477$		0			0
$478$	3.78911	−	9.14773i	0.173310	−	0.418407i
$479$	−15.3463	+	25.0429i	−0.701190	+	1.14424i	0.281604	+	0.959531i	$0.409134\pi$
$479$	−15.3463	+	25.0429i	−0.701190	+	1.14424i	−0.982794	+	0.184707i	$0.940866\pi$
$480$		0			0
$481$	−18.7474	−	21.9503i	−0.854806	−	1.00085i
$482$	8.09789	+	24.9228i	0.368849	+	1.13520i
$483$		0			0
$484$	−4.38892	+	8.61373i	−0.199496	+	0.391533i
$485$	6.57440	+	1.57837i	0.298528	+	0.0716703i
$486$		0			0
$487$	18.4688	−	9.41030i	0.836899	−	0.426421i	0.0176396	−	0.999844i	$-0.494385\pi$
$487$	18.4688	−	9.41030i	0.836899	−	0.426421i	0.819259	+	0.573423i	$0.194385\pi$
$488$	9.41071	+	3.05773i	0.426003	+	0.138417i
$489$		0			0
$490$	0.0436081	−	0.275331i	0.00197001	−	0.0124382i
$491$	31.0564			1.40156			0.700778	−	0.713379i	$-0.252836\pi$
$491$	31.0564			1.40156			0.700778	+	0.713379i	$0.252836\pi$
$492$		0			0
$493$	37.9915			1.71105
$494$	2.20286	−	13.9083i	0.0991115	−	0.625766i
$495$		0			0
$496$	−5.04650	−	1.63971i	−0.226595	−	0.0736251i
$497$	−23.8989	+	12.1771i	−1.07201	+	0.546217i
$498$		0			0
$499$	−15.2270	−	3.65567i	−0.681653	−	0.163650i	−0.122191	−	0.992507i	$-0.538992\pi$
$499$	−15.2270	−	3.65567i	−0.681653	−	0.163650i	−0.559462	+	0.828856i	$0.688992\pi$
$500$	−2.25659	+	4.42882i	−0.100918	+	0.198063i
$501$		0			0
$502$	−6.69393	−	20.6018i	−0.298765	−	0.919503i
$503$	10.1004	+	11.8261i	0.450356	+	0.527300i	0.938415	−	0.345512i	$-0.112295\pi$
$503$	10.1004	+	11.8261i	0.450356	+	0.527300i	−0.488058	+	0.872811i	$0.662295\pi$
$504$		0			0
$505$	1.53120	−	2.49868i	0.0681373	−	0.111190i
$506$	3.39411	−	8.19411i	0.150887	−	0.364273i
$507$		0			0
$508$	−14.2187	−	10.3305i	−0.630852	−	0.458341i
$509$	12.1727	+	0.958015i	0.539547	+	0.0424633i	0.345305	−	0.938490i	$-0.387775\pi$
$509$	12.1727	+	0.958015i	0.539547	+	0.0424633i	0.194242	+	0.980954i	$0.437775\pi$
$510$		0			0
$511$	−16.2166	−	26.4630i	−0.717378	−	1.17066i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$		0			0
$514$	−7.31086	+	4.48010i	−0.322468	+	0.197609i
$515$	−0.716172	+	0.520329i	−0.0315583	+	0.0229285i
$516$		0			0
$517$	3.42693	−	4.71676i	0.150716	−	0.207443i
$518$	14.5699	+	12.4439i	0.640164	+	0.546752i
$519$		0			0
$520$	−1.66543	−	1.02058i	−0.0730339	−	0.0447552i
$521$	−4.91203	+	0.386585i	−0.215200	+	0.0169366i	−0.185601	−	0.982625i	$-0.559423\pi$
$521$	−4.91203	+	0.386585i	−0.215200	+	0.0169366i	−0.0295993	+	0.999562i	$0.509423\pi$
$522$		0			0
$523$	−17.3135	+	5.62551i	−0.757068	+	0.245986i	−0.662020	−	0.749486i	$-0.730301\pi$
$523$	−17.3135	+	5.62551i	−0.757068	+	0.245986i	−0.0950482	+	0.995473i	$0.530301\pi$
$524$	−5.20551	+	5.20551i	−0.227404	+	0.227404i
$525$		0			0
$526$	0.433885	−	1.80726i	0.0189183	−	0.0788003i
$527$	21.3775	−	5.13227i	0.931217	−	0.223565i
$528$		0			0
$529$	11.1342	−	34.2675i	0.484095	−	1.48989i
$530$	3.07789	−	1.27490i	0.133695	−	0.0553783i
$531$		0			0
$532$			9.34695i			0.405242i
$533$	−8.38785	+	23.0265i	−0.363318	+	0.997389i
$534$		0			0
$535$	−4.63152	−	0.733561i	−0.200238	−	0.0317146i
$536$	−0.729009	−	1.75998i	−0.0314884	−	0.0760197i
$537$		0			0
$538$	−1.02540	−	2.01246i	−0.0442082	−	0.0867634i
$539$	0.147197	+	0.613119i	0.00634021	+	0.0264089i
$540$		0			0
$541$	−30.9025	−	15.7456i	−1.32860	−	0.676957i	−0.361746	−	0.932277i	$-0.617819\pi$
$541$	−30.9025	−	15.7456i	−1.32860	−	0.676957i	−0.966857	+	0.255320i	$0.917819\pi$
$542$	18.1011	+	18.1011i	0.777510	+	0.777510i
$543$		0			0
$544$	−3.15055	+	2.69082i	−0.135079	+	0.115368i
$545$	−0.0323394	−	0.410911i	−0.00138527	−	0.0176015i
$546$		0			0
$547$	0.331168	+	0.137174i	0.0141597	+	0.00586514i	0.389752	−	0.920920i	$-0.372561\pi$
$547$	0.331168	+	0.137174i	0.0141597	+	0.00586514i	−0.375592	+	0.926785i	$0.622561\pi$
$548$	−4.62274	+	5.41253i	−0.197474	+	0.231212i
$549$		0			0
$550$	0.429266	−	5.45434i	0.0183040	−	0.232574i
$551$	−19.8303	−	27.2940i	−0.844797	−	1.16276i
$552$		0			0
$553$	−0.446663	−	2.82012i	−0.0189940	−	0.119924i
$554$	−0.181330	−	1.14488i	−0.00770399	−	0.0486411i
$555$		0			0
$556$	4.91404	+	6.76359i	0.208402	+	0.286840i
$557$	1.76153	−	22.3823i	0.0746383	−	0.948369i	−0.839603	−	0.543200i	$-0.817213\pi$
$557$	1.76153	−	22.3823i	0.0746383	−	0.948369i	0.914242	−	0.405169i	$-0.132787\pi$
$558$		0			0
$559$	14.2516	−	16.6864i	0.602777	−	0.705761i
$560$	1.19782	+	0.496152i	0.0506170	+	0.0209663i
$561$		0			0
$562$	1.55938	+	19.8137i	0.0657783	+	0.835792i
$563$	29.4158	−	25.1234i	1.23973	−	1.05883i	0.243693	−	0.969853i	$-0.421641\pi$
$563$	29.4158	−	25.1234i	1.23973	−	1.05883i	0.996034	−	0.0889741i	$-0.0283588\pi$
$564$		0			0
$565$	−2.11356	−	2.11356i	−0.0889182	−	0.0889182i
$566$	8.41147	+	4.28586i	0.353560	+	0.180148i
$567$		0			0
$568$	2.46476	+	10.2665i	0.103419	+	0.430771i
$569$	−3.71557	−	7.29221i	−0.155765	−	0.305705i	0.799915	−	0.600113i	$-0.204878\pi$
$569$	−3.71557	−	7.29221i	−0.155765	−	0.305705i	−0.955680	+	0.294408i	$0.904878\pi$
$570$		0			0
$571$	3.99515	+	9.64513i	0.167192	+	0.403636i	0.985163	−	0.171623i	$-0.0549011\pi$
$571$	3.99515	+	9.64513i	0.167192	+	0.403636i	−0.817971	+	0.575259i	$0.804901\pi$
$572$	4.36374	+	0.691148i	0.182457	+	0.0288984i
$573$		0			0
$574$	3.10804	−	15.9670i	0.129727	−	0.666450i
$575$		−	36.4147i		−	1.51860i
$576$		0			0
$577$	28.3362	−	11.7373i	1.17965	−	0.488628i	0.295281	−	0.955410i	$-0.404587\pi$
$577$	28.3362	−	11.7373i	1.17965	−	0.488628i	0.884372	+	0.466782i	$0.154587\pi$
$578$	0.0514389	−	0.158313i	0.00213957	−	0.00658493i
$579$		0			0
$580$	−4.55037	+	1.09245i	−0.188944	+	0.0453614i
$581$	−1.54630	+	6.44080i	−0.0641513	+	0.267210i
$582$		0			0
$583$	−5.32845	+	5.32845i	−0.220682	+	0.220682i
$584$	−11.6191	+	3.77528i	−0.480802	+	0.156222i
$585$		0			0
$586$	−18.7437	+	1.47516i	−0.774296	+	0.0609384i
$587$	30.3747	+	18.6136i	1.25370	+	0.768266i	0.981032	−	0.193843i	$-0.0620954\pi$
$587$	30.3747	+	18.6136i	1.25370	+	0.768266i	0.272664	+	0.962109i	$0.412095\pi$
$588$		0			0
$589$	−14.8454	−	12.6792i	−0.611695	−	0.522437i
$590$	1.07072	−	1.47372i	0.0440810	−	0.0606723i
$591$		0			0
$592$	6.10184	−	4.43325i	0.250784	−	0.182205i
$593$	−18.5125	+	11.3445i	−0.760218	+	0.465862i	−0.847814	−	0.530294i	$-0.822082\pi$
$593$	−18.5125	+	11.3445i	−0.760218	+	0.465862i	0.0875958	+	0.996156i	$0.472082\pi$
$594$		0			0
$595$	−5.30561	+	0.840327i	−0.217509	+	0.0344500i
$596$	−8.77582	−	14.3208i	−0.359471	−	0.586604i
$597$		0			0
$598$	29.3151	+	2.30715i	1.19878	+	0.0943463i
$599$	−26.4445	−	19.2130i	−1.08049	−	0.785023i	−0.102723	−	0.994710i	$-0.532755\pi$
$599$	−26.4445	−	19.2130i	−1.08049	−	0.785023i	−0.977768	+	0.209687i	$0.932755\pi$
$600$		0			0
$601$	−2.96813	+	7.16570i	−0.121073	+	0.292295i	−0.972783	−	0.231718i	$-0.925566\pi$
$601$	−2.96813	+	7.16570i	−0.121073	+	0.292295i	0.851711	+	0.524013i	$0.175566\pi$
$602$	−7.61059	+	12.4194i	−0.310184	+	0.506175i
$603$		0			0
$604$	14.0238	+	16.4198i	0.570620	+	0.668110i
$605$	1.52462	+	4.69229i	0.0619846	+	0.190769i
$606$		0			0
$607$	11.9289	−	23.4117i	0.484178	−	0.950253i	−0.511667	−	0.859184i	$-0.670972\pi$
$607$	11.9289	−	23.4117i	0.484178	−	0.950253i	0.995845	−	0.0910687i	$-0.0290283\pi$
$608$	3.57762	+	0.858911i	0.145092	+	0.0348334i
$609$		0			0
$610$	4.49951	−	2.29261i	0.182180	−	0.0928253i
$611$	18.3839	+	5.97330i	0.743734	+	0.241654i
$612$		0			0
$613$	−1.51327	+	9.55439i	−0.0611203	+	0.385898i	0.938098	+	0.346370i	$0.112586\pi$
$613$	−1.51327	+	9.55439i	−0.0611203	+	0.385898i	−0.999218	+	0.0395288i	$0.987414\pi$
$614$	29.1431			1.17612
$615$		0			0
$616$	−2.93261			−0.118158
$617$	0.951809	−	6.00948i	0.0383184	−	0.241933i	−0.961094	−	0.276223i	$-0.910917\pi$
$617$	0.951809	−	6.00948i	0.0383184	−	0.241933i	0.999412	+	0.0342904i	$0.0109171\pi$
$618$		0			0
$619$	−39.5299	−	12.8441i	−1.58884	−	0.516246i	−0.624527	−	0.781003i	$-0.714708\pi$
$619$	−39.5299	−	12.8441i	−1.58884	−	0.516246i	−0.964315	+	0.264757i	$0.914708\pi$
$620$	−2.41287	+	1.22942i	−0.0969030	+	0.0493746i
$621$		0			0
$622$	−20.1680	−	4.84190i	−0.808662	−	0.194143i
$623$	−3.58269	+	7.03143i	−0.143538	+	0.281708i
$624$		0			0
$625$	−6.53910	−	20.1253i	−0.261564	−	0.805012i
$626$	−14.9511	−	17.5055i	−0.597567	−	0.699661i
$627$		0			0
$628$	4.48614	−	7.32072i	0.179017	−	0.292129i
$629$	−11.9587	+	28.8708i	−0.476824	+	1.15115i
$630$		0			0
$631$	−11.1550	−	8.10455i	−0.444072	−	0.322637i	0.343179	−	0.939270i	$-0.388496\pi$
$631$	−11.1550	−	8.10455i	−0.444072	−	0.322637i	−0.787251	+	0.616633i	$0.788496\pi$
$632$	−1.12047	−	0.0881827i	−0.0445698	−	0.00350772i
$633$		0			0
$634$	−9.87672	−	16.1173i	−0.392255	−	0.640102i
$635$	−8.85910	+	1.40314i	−0.351563	+	0.0556821i
$636$		0			0
$637$	−1.78248	+	1.09230i	−0.0706244	+	0.0432787i
$638$	8.56349	−	6.22174i	0.339032	−	0.246321i
$639$		0			0
$640$	0.299976	−	0.412882i	0.0118576	−	0.0163206i
$641$	20.6119	+	17.6042i	0.814120	+	0.695324i	0.955616	−	0.294614i	$-0.0951912\pi$
$641$	20.6119	+	17.6042i	0.814120	+	0.695324i	−0.141496	+	0.989939i	$0.545191\pi$
$642$		0			0
$643$	−18.5580	−	11.3723i	−0.731855	−	0.448481i	0.106006	−	0.994366i	$-0.466194\pi$
$643$	−18.5580	−	11.3723i	−0.731855	−	0.448481i	−0.837861	+	0.545884i	$0.816194\pi$
$644$	−19.4584	+	1.53141i	−0.766767	+	0.0603458i
$645$		0			0
$646$	−14.4981	+	4.71070i	−0.570418	+	0.185340i
$647$	−6.44743	+	6.44743i	−0.253475	+	0.253475i	−0.822394	−	0.568919i	$-0.807362\pi$
$647$	−6.44743	+	6.44743i	−0.253475	+	0.253475i	0.568919	+	0.822394i	$0.307362\pi$
$648$		0			0
$649$	−0.961883	+	4.00653i	−0.0377572	+	0.157270i
$650$	17.6384	−	4.23461i	0.691837	−	0.166095i
$651$		0			0
$652$	1.45804	−	4.48739i	0.0571013	−	0.175740i
$653$	37.6990	−	15.6154i	1.47527	−	0.611078i	0.507219	−	0.861817i	$-0.330673\pi$
$653$	37.6990	−	15.6154i	1.47527	−	0.611078i	0.968055	+	0.250739i	$0.0806735\pi$
$654$		0			0
$655$			3.75704i			0.146800i
$656$	−5.82589	−	2.65687i	−0.227463	−	0.103733i
$657$		0			0
$658$	−12.6726	−	2.00715i	−0.494030	−	0.0782467i
$659$	0.837963	+	2.02302i	0.0326424	+	0.0788058i	0.939360	−	0.342932i	$-0.111420\pi$
$659$	0.837963	+	2.02302i	0.0326424	+	0.0788058i	−0.906718	+	0.421738i	$0.861420\pi$
$660$		0			0
$661$	3.89423	+	7.64285i	0.151468	+	0.297273i	0.954255	−	0.298993i	$-0.0966506\pi$
$661$	3.89423	+	7.64285i	0.151468	+	0.297273i	−0.802787	+	0.596265i	$0.796651\pi$
$662$	−3.43123	−	14.2921i	−0.133359	−	0.555478i
$663$		0			0
$664$	2.32318	+	1.18372i	0.0901567	+	0.0459372i
$665$	3.37305	+	3.37305i	0.130801	+	0.130801i
$666$		0			0
$667$	53.5713	−	45.7542i	2.07429	−	1.77161i
$668$	0.165246	+	2.09965i	0.00639355	+	0.0812377i
$669$		0			0
$670$	−0.898208	−	0.372050i	−0.0347008	−	0.0143735i
$671$	−7.41835	+	8.68577i	−0.286382	+	0.335310i
$672$		0			0
$673$	−2.04734	+	26.0140i	−0.0789193	+	1.00277i	0.822201	+	0.569197i	$0.192746\pi$
$673$	−2.04734	+	26.0140i	−0.0789193	+	1.00277i	−0.901121	+	0.433568i	$0.857254\pi$
$674$	16.0915	+	22.1480i	0.619821	+	0.853110i
$675$		0			0
$676$	0.257836	+	1.62791i	0.00991677	+	0.0626120i
$677$	5.91025	+	37.3159i	0.227149	+	1.43416i	0.792781	+	0.609507i	$0.208632\pi$
$677$	5.91025	+	37.3159i	0.227149	+	1.43416i	−0.565632	+	0.824658i	$0.691368\pi$
$678$		0			0
$679$	19.7826	+	27.2284i	0.759185	+	1.04493i
$680$	−0.165902	+	2.10799i	−0.00636205	+	0.0808376i
$681$		0			0
$682$	3.97810	−	4.65775i	0.152329	−	0.178355i
$683$	3.90119	+	1.61592i	0.149275	+	0.0618316i	0.456070	−	0.889944i	$-0.349257\pi$
$683$	3.90119	+	1.61592i	0.149275	+	0.0618316i	−0.306795	+	0.951776i	$0.599257\pi$
$684$		0			0
$685$	0.285014	+	3.62145i	0.0108898	+	0.138368i
$686$	14.5775	−	12.4503i	0.556570	−	0.475356i
$687$		0			0
$688$	4.05425	+	4.05425i	0.154567	+	0.154567i
$689$	−22.2609	−	11.3425i	−0.848072	−	0.432114i
$690$		0			0
$691$	−0.366642	−	1.52717i	−0.0139477	−	0.0580965i	0.964962	−	0.262389i	$-0.0845105\pi$
$691$	−0.366642	−	1.52717i	−0.0139477	−	0.0580965i	−0.978910	+	0.204293i	$0.934510\pi$
$692$	3.34197	+	6.55898i	0.127043	+	0.249335i
$693$		0			0
$694$	10.0268	+	24.2069i	0.380613	+	0.918881i
$695$	4.21413	+	0.667452i	0.159851	+	0.0253179i
$696$		0			0
$697$	26.3328	−	3.22621i	0.997426	−	0.122201i
$698$		−	9.10024i		−	0.344449i
$699$		0			0
$700$	−11.1239	+	4.60769i	−0.420446	+	0.174154i
$701$	3.32985	−	10.2482i	0.125767	−	0.387071i	−0.868273	−	0.496086i	$-0.834770\pi$
$701$	3.32985	−	10.2482i	0.125767	−	0.387071i	0.994040	+	0.109016i	$0.0347699\pi$
$702$		0			0
$703$	26.9835	−	6.47816i	1.01770	−	0.244328i
$704$	−0.269483	+	1.12248i	−0.0101565	+	0.0423050i
$705$		0			0
$706$	10.7052	−	10.7052i	0.402897	−	0.402897i
$707$	13.8737	−	4.50782i	0.521772	−	0.169534i
$708$		0			0
$709$	2.00315	−	0.157651i	0.0752299	−	0.00592072i	−0.0407883	−	0.999168i	$-0.512987\pi$
$709$	2.00315	−	0.157651i	0.0752299	−	0.00592072i	0.116018	+	0.993247i	$0.462987\pi$
$710$	4.59434	+	2.81542i	0.172423	+	0.105661i
$711$		0			0
$712$	2.36212	+	2.01744i	0.0885240	+	0.0756067i
$713$	23.9631	−	32.9824i	0.897424	−	1.23520i
$714$		0			0
$715$	1.82417	−	1.32534i	0.0682200	−	0.0495647i
$716$	14.7245	−	9.02319i	0.550281	−	0.337212i
$717$		0			0
$718$	−7.34034	+	1.16259i	−0.273939	+	0.0433877i
$719$	22.5364	+	36.7761i	0.840466	+	1.37152i	0.926919	+	0.375260i	$0.122447\pi$
$719$	22.5364	+	36.7761i	0.840466	+	1.37152i	−0.0864533	+	0.996256i	$0.527553\pi$
$720$		0			0
$721$	−4.39297	−	0.345734i	−0.163603	−	0.0128758i
$722$	−4.41957	−	3.21101i	−0.164479	−	0.119501i
$723$		0			0
$724$	−4.25258	+	10.2666i	−0.158046	+	0.381557i
$725$	22.7074	−	37.0552i	0.843333	−	1.37619i
$726$		0			0
$727$	6.12920	+	7.17637i	0.227319	+	0.266157i	0.862330	−	0.506347i	$-0.169004\pi$
$727$	6.12920	+	7.17637i	0.227319	+	0.266157i	−0.635011	+	0.772503i	$0.719004\pi$
$728$	−3.00457	−	9.24710i	−0.111357	−	0.342720i
$729$		0			0
$730$	−2.83062	+	5.55540i	−0.104766	+	0.205615i
$731$	−23.0993	−	5.54564i	−0.854357	−	0.205113i
$732$		0			0
$733$	−2.87391	+	1.46433i	−0.106150	+	0.0540862i	−0.506259	−	0.862381i	$-0.668972\pi$
$733$	−2.87391	+	1.46433i	−0.106150	+	0.0540862i	0.400109	+	0.916467i	$0.368972\pi$
$734$	30.3253	+	9.85329i	1.11933	+	0.363692i
$735$		0			0
$736$	−1.20191	+	7.58857i	−0.0443030	+	0.279718i
$737$	2.19908			0.0810040
$738$		0			0
$739$	−29.6554			−1.09089			−0.545446	−	0.838146i	$-0.683640\pi$
$739$	−29.6554			−1.09089			−0.545446	+	0.838146i	$0.683640\pi$
$740$	0.602149	−	3.80182i	0.0221354	−	0.139758i
$741$		0			0
$742$	15.7719	+	5.12459i	0.579003	+	0.188130i
$743$	−22.7775	+	11.6057i	−0.835627	+	0.425773i	−0.818796	−	0.574085i	$-0.805358\pi$
$743$	−22.7775	+	11.6057i	−0.835627	+	0.425773i	−0.0168313	+	0.999858i	$0.505358\pi$
$744$		0			0
$745$	−8.33493	−	2.00104i	−0.305368	−	0.0733125i
$746$	−14.1942	+	27.8576i	−0.519685	+	1.01994i
$747$		0			0
$748$	−1.47798	−	4.54876i	−0.0540404	−	0.166319i
$749$	−15.1596	−	17.7496i	−0.553919	−	0.648556i
$750$		0			0
$751$	17.6875	−	28.8634i	0.645426	−	1.05324i	−0.347859	−	0.937547i	$-0.613091\pi$
$751$	17.6875	−	28.8634i	0.645426	−	1.05324i	0.993285	−	0.115693i	$-0.0369088\pi$
$752$	−1.93277	+	4.66611i	−0.0704807	+	0.170155i
$753$		0			0
$754$	28.3920	+	20.6280i	1.03398	+	0.751228i
$755$	10.9862	+	0.864635i	0.399830	+	0.0314673i
$756$		0			0
$757$	−18.1952	−	29.6919i	−0.661317	−	1.07917i	−0.990842	−	0.135024i	$-0.956889\pi$
$757$	−18.1952	−	29.6919i	−0.661317	−	1.07917i	0.329526	−	0.944147i	$-0.393111\pi$
$758$	28.6365	−	4.53557i	1.04012	−	0.164739i
$759$		0			0
$760$	1.60102	−	0.981107i	0.0580751	−	0.0355885i
$761$	33.1425	−	24.0795i	1.20142	−	0.872880i	0.206992	−	0.978343i	$-0.433632\pi$
$761$	33.1425	−	24.0795i	1.20142	−	0.872880i	0.994423	+	0.105463i	$0.0336325\pi$
$762$		0			0
$763$	1.20600	−	1.65991i	0.0436600	−	0.0600929i
$764$	9.67937	+	8.26697i	0.350187	+	0.299088i
$765$		0			0
$766$	−8.12423	−	4.97853i	−0.293540	−	0.179882i
$767$	−13.6189	+	1.07183i	−0.491750	+	0.0387015i
$768$		0			0
$769$	−13.2236	+	4.29661i	−0.476855	+	0.154940i	−0.537576	−	0.843215i	$-0.680660\pi$
$769$	−13.2236	+	4.29661i	−0.476855	+	0.154940i	0.0607210	+	0.998155i	$0.480660\pi$
$770$	−1.05830	+	1.05830i	−0.0381383	+	0.0381383i
$771$		0			0
$772$	−3.87032	+	16.1210i	−0.139296	+	0.580208i
$773$	9.77944	−	2.34784i	0.351742	−	0.0844458i	−0.0537243	−	0.998556i	$-0.517109\pi$
$773$	9.77944	−	2.34784i	0.351742	−	0.0844458i	0.405466	+	0.914110i	$0.367109\pi$
$774$		0			0
$775$	7.77147	−	23.9181i	0.279159	−	0.859164i
$776$	12.2397	−	5.06986i	0.439381	−	0.181998i
$777$		0			0
$778$			27.3806i			0.981643i
$779$	−16.0626	−	17.2341i	−0.575502	−	0.617477i
$780$		0			0
$781$	−12.0380	−	1.90664i	−0.430755	−	0.0682249i
$782$	−12.1820	−	29.4100i	−0.435629	−	1.05170i
$783$		0			0
$784$	−0.247978	−	0.486684i	−0.00885636	−	0.0173816i
$785$	−1.02292	−	4.26077i	−0.0365096	−	0.152073i
$786$		0			0
$787$	−20.7569	−	10.5762i	−0.739903	−	0.376999i	0.0430564	−	0.999073i	$-0.486290\pi$
$787$	−20.7569	−	10.5762i	−0.739903	−	0.376999i	−0.782959	+	0.622073i	$0.786290\pi$
$788$	12.8134	+	12.8134i	0.456458	+	0.456458i
$789$		0			0
$790$	−0.436168	+	0.372523i	−0.0155182	+	0.0132538i
$791$	−1.16738	−	14.8330i	−0.0415072	−	0.527399i
$792$		0			0
$793$	−34.9884	−	14.4927i	−1.24247	−	0.514649i
$794$	−0.634089	+	0.742423i	−0.0225030	+	0.0263476i
$795$		0			0
$796$	−0.809725	+	10.2885i	−0.0286999	+	0.364667i
$797$	28.2843	+	38.9300i	1.00188	+	1.37897i	0.924164	+	0.381995i	$0.124763\pi$
$797$	28.2843	+	38.9300i	1.00188	+	1.37897i	0.0777167	+	0.996975i	$0.475237\pi$
$798$		0			0
$799$	−3.27350	−	20.6681i	−0.115808	−	0.731184i
$800$	0.741428	+	4.68119i	0.0262134	+	0.165505i
$801$		0			0
$802$	3.23923	+	4.45842i	0.114381	+	0.157432i
$803$	1.10651	−	14.0596i	0.0390480	−	0.496152i
$804$		0			0
$805$	−6.46933	+	7.57462i	−0.228014	+	0.266970i
$806$	18.7625	+	7.77170i	0.660882	+	0.273746i
$807$		0			0
$808$	−0.450527	−	5.72449i	−0.0158495	−	0.201387i
$809$	9.65261	−	8.24411i	0.339368	−	0.289848i	−0.463388	−	0.886156i	$-0.653366\pi$
$809$	9.65261	−	8.24411i	0.339368	−	0.289848i	0.802756	+	0.596308i	$0.203366\pi$
$810$		0			0
$811$	−15.8759	−	15.8759i	−0.557478	−	0.557478i	0.371110	−	0.928589i	$-0.378977\pi$
$811$	−15.8759	−	15.8759i	−0.557478	−	0.557478i	−0.928589	+	0.371110i	$0.878977\pi$
$812$	−20.7556	−	10.5755i	−0.728378	−	0.371127i
$813$		0			0
$814$	2.03252	+	8.46607i	0.0712399	+	0.296735i
$815$	−1.09321	−	2.14554i	−0.0382934	−	0.0751550i
$816$		0			0
$817$	8.07288	+	19.4897i	0.282434	+	0.681857i
$818$	12.6643	+	2.00583i	0.442797	+	0.0701322i
$819$		0			0
$820$	−3.06119	+	1.14361i	−0.106901	+	0.0399367i
$821$		−	26.2045i		−	0.914543i	−0.889327	−	0.457271i	$-0.848827\pi$
$821$		−	26.2045i		−	0.914543i	0.889327	−	0.457271i	$-0.151173\pi$
$822$		0			0
$823$	46.9062	−	19.4292i	1.63505	−	0.677259i	0.639265	−	0.768987i	$-0.279239\pi$
$823$	46.9062	−	19.4292i	1.63505	−	0.677259i	0.995784	+	0.0917272i	$0.0292388\pi$
$824$	−0.536011	+	1.64967i	−0.0186728	+	0.0574691i
$825$		0			0
$826$	8.81717	−	2.11681i	0.306789	−	0.0736534i
$827$	6.06196	−	25.2499i	0.210795	−	0.878024i	−0.762227	−	0.647310i	$-0.775894\pi$
$827$	6.06196	−	25.2499i	0.210795	−	0.878024i	0.973022	−	0.230714i	$-0.0741061\pi$
$828$		0			0
$829$	−32.6794	+	32.6794i	−1.13500	+	1.13500i	−0.145670	+	0.989333i	$0.546534\pi$
$829$	−32.6794	+	32.6794i	−1.13500	+	1.13500i	−0.989333	+	0.145670i	$0.953466\pi$
$830$	1.26554	−	0.411199i	0.0439275	−	0.0142729i
$831$		0			0
$832$	−3.81550	+	0.300286i	−0.132279	+	0.0104106i
$833$	1.92962	+	1.18247i	0.0668575	+	0.0409703i
$834$		0			0
$835$	0.817336	+	0.698071i	0.0282851	+	0.0241577i
$836$	−2.49648	+	3.43611i	−0.0863426	+	0.118840i
$837$		0			0
$838$	19.1995	−	13.9493i	0.663236	−	0.481869i
$839$	−44.4330	+	27.2286i	−1.53400	+	0.940035i	−0.538770	+	0.842453i	$0.681111\pi$
$839$	−44.4330	+	27.2286i	−1.53400	+	0.940035i	−0.995227	+	0.0975821i	$0.968889\pi$
$840$		0			0
$841$	54.4020	−	8.61642i	1.87593	−	0.297118i
$842$	5.08651	+	8.30043i	0.175293	+	0.286052i
$843$		0			0
$844$	24.4186	+	1.92179i	0.840524	+	0.0661507i
$845$	0.680514	+	0.494422i	0.0234104	+	0.0170086i
$846$		0			0
$847$	−9.39847	+	22.6899i	−0.322935	+	0.779635i
$848$	3.41079	−	5.56590i	0.117127	−	0.191134i
$849$		0			0
$850$	−12.7533	−	14.9321i	−0.437433	−	0.512169i
$851$	17.9071	+	55.1124i	0.613848	+	1.88923i
$852$		0			0
$853$	11.6928	−	22.9485i	0.400355	−	0.785742i	−0.599538	−	0.800346i	$-0.704649\pi$
$853$	11.6928	−	22.9485i	0.400355	−	0.785742i	0.999893	+	0.0146047i	$0.00464897\pi$
$854$	24.4430	+	5.86825i	0.836423	+	0.200807i
$855$		0			0
$856$	−8.18684	+	4.17140i	−0.279820	+	0.142576i
$857$	−7.22479	−	2.34748i	−0.246794	−	0.0801882i	0.183008	−	0.983111i	$-0.441417\pi$
$857$	−7.22479	−	2.34748i	−0.246794	−	0.0801882i	−0.429802	+	0.902923i	$0.641417\pi$
$858$		0			0
$859$	−2.24397	+	14.1679i	−0.0765634	+	0.483402i	0.919376	+	0.393379i	$0.128694\pi$
$859$	−2.24397	+	14.1679i	−0.0765634	+	0.483402i	−0.995940	+	0.0900230i	$0.971306\pi$
$860$	2.92613			0.0997804
$861$		0			0
$862$	−8.53750			−0.290788
$863$	−8.10008	+	51.1419i	−0.275730	+	1.74089i	0.328884	+	0.944370i	$0.393328\pi$
$863$	−8.10008	+	51.1419i	−0.275730	+	1.74089i	−0.604614	+	0.796519i	$0.706672\pi$
$864$		0			0
$865$	3.57297	+	1.16093i	0.121485	+	0.0394728i
$866$	24.8550	−	12.6642i	0.844606	−	0.430348i
$867$		0			0
$868$	−13.1076	−	3.14685i	−0.444900	−	0.106811i
$869$	0.589025	−	1.15603i	0.0199813	−	0.0392155i
$870$		0			0
$871$	2.25304	+	6.93413i	0.0763412	+	0.234954i
$872$	−0.524524	−	0.614138i	−0.0177626	−	0.0207973i
$873$		0			0
$874$	−14.7703	+	24.1029i	−0.499611	+	0.815291i
$875$	−4.83230	+	11.6662i	−0.163361	+	0.394389i
$876$		0			0
$877$	16.4850	+	11.9770i	0.556658	+	0.404436i	0.830234	−	0.557414i	$-0.188207\pi$
$877$	16.4850	+	11.9770i	0.556658	+	0.404436i	−0.273576	+	0.961850i	$0.588207\pi$
$878$	−29.2021	−	2.29826i	−0.985524	−	0.0775624i
$879$		0			0
$880$	0.307822	+	0.502320i	0.0103767	+	0.0169332i
$881$	−23.7510	+	3.76179i	−0.800191	+	0.126738i	−0.543120	−	0.839655i	$-0.682757\pi$
$881$	−23.7510	+	3.76179i	−0.800191	+	0.126738i	−0.257070	+	0.966393i	$0.582757\pi$
$882$		0			0
$883$	−1.25850	+	0.771207i	−0.0423517	+	0.0259532i	−0.543513	−	0.839401i	$-0.682906\pi$
$883$	−1.25850	+	0.771207i	−0.0423517	+	0.0259532i	0.501162	+	0.865354i	$0.332906\pi$
$884$	12.8289	−	9.32076i	0.431483	−	0.313491i
$885$		0			0
$886$	−20.7539	+	28.5653i	−0.697241	+	0.959670i
$887$	−22.8593	−	19.5237i	−0.767539	−	0.655540i	0.176899	−	0.984229i	$-0.443393\pi$
$887$	−22.8593	−	19.5237i	−0.767539	−	0.655540i	−0.944438	+	0.328689i	$0.893393\pi$
$888$		0			0
$889$	−38.0693	−	23.3289i	−1.27680	−	0.782425i
$890$	1.58046	−	0.124385i	0.0529771	−	0.00416939i
$891$		0			0
$892$	5.61291	−	1.82375i	0.187934	−	0.0610635i
$893$	−13.1398	+	13.1398i	−0.439705	+	0.439705i
$894$		0			0
$895$	2.05745	−	8.56988i	0.0687728	−	0.286459i
$896$	2.47024	−	0.593051i	0.0825248	−	0.0198125i
$897$		0			0
$898$	−6.19294	+	19.0599i	−0.206661	+	0.636038i
$899$	44.9517	−	18.6196i	1.49922	−	0.620998i
$900$		0			0
$901$			27.0464i			0.901047i
$902$	5.40721	−	5.03963i	0.180040	−	0.167801i
$903$		0			0
$904$	−5.78471	−	0.916208i	−0.192397	−	0.0304726i
$905$	2.17031	+	5.23958i	0.0721434	+	0.174170i
$906$		0			0
$907$	8.66949	+	17.0148i	0.287866	+	0.564968i	0.988974	−	0.148086i	$-0.0473113\pi$
$907$	8.66949	+	17.0148i	0.287866	+	0.564968i	−0.701109	+	0.713054i	$0.747311\pi$
$908$	−3.46887	−	14.4489i	−0.115119	−	0.479503i
$909$		0			0
$910$	−4.42128	−	2.25276i	−0.146564	−	0.0746782i
$911$	−34.0498	−	34.0498i	−1.12812	−	1.12812i	−0.990482	−	0.137639i	$-0.956049\pi$
$911$	−34.0498	−	34.0498i	−1.12812	−	1.12812i	−0.137639	−	0.990482i	$-0.543951\pi$
$912$		0			0
$913$	−2.28872	+	1.95476i	−0.0757457	+	0.0646930i
$914$	−1.46401	−	18.6021i	−0.0484253	−	0.615301i
$915$		0			0
$916$	−21.7264	−	8.99936i	−0.717860	−	0.297347i
$917$	−12.1459	+	14.2210i	−0.401093	+	0.469619i
$918$		0			0
$919$	2.62961	−	33.4124i	0.0867428	−	1.10217i	−0.787380	−	0.616468i	$-0.788563\pi$
$919$	2.62961	−	33.4124i	0.0867428	−	1.10217i	0.874123	−	0.485704i	$-0.161437\pi$
$920$	2.30477	+	3.17224i	0.0759859	+	0.104586i
$921$		0			0
$922$	−3.96831	−	25.0549i	−0.130689	−	0.825141i
$923$	−6.32141	−	39.9118i	−0.208072	−	1.31371i
$924$		0			0
$925$	21.0116	+	28.9199i	0.690856	+	0.950882i
$926$	−2.06891	+	26.2880i	−0.0679887	+	0.863878i
$927$		0			0
$928$	−5.95513	+	6.97256i	−0.195487	+	0.228885i
$929$	40.3885	+	16.7295i	1.32510	+	0.548875i	0.929254	−	0.369440i	$-0.120451\pi$
$929$	40.3885	+	16.7295i	1.32510	+	0.548875i	0.395848	+	0.918316i	$0.370451\pi$
$930$		0			0
$931$	−0.157679	−	2.00350i	−0.00516770	−	0.0656619i
$932$	−2.72694	+	2.32903i	−0.0893240	+	0.0762899i
$933$		0			0
$934$	8.42635	+	8.42635i	0.275719	+	0.275719i
$935$	−2.17488	−	1.10816i	−0.0711263	−	0.0362407i
$936$		0			0
$937$	−2.76813	−	11.5301i	−0.0904310	−	0.376672i	0.908741	−	0.417361i	$-0.137045\pi$
$937$	−2.76813	−	11.5301i	−0.0904310	−	0.376672i	−0.999172	+	0.0406886i	$0.987045\pi$
$938$	−2.19709	−	4.31203i	−0.0717374	−	0.140793i
$939$		0			0
$940$	0.986387	+	2.38135i	0.0321724	+	0.0776711i
$941$	13.9834	+	2.21475i	0.455844	+	0.0721986i	0.380134	−	0.924931i	$-0.375878\pi$
$941$	13.9834	+	2.21475i	0.455844	+	0.0721986i	0.0757098	+	0.997130i	$0.475878\pi$
$942$		0			0
$943$	33.2461	−	36.2625i	1.08264	−	1.18087i
$944$		−	3.56936i		−	0.116173i
$945$		0			0
$946$	−6.11488	+	2.53287i	−0.198812	+	0.0823506i
$947$	−2.20348	+	6.78161i	−0.0716035	+	0.220373i	−0.980454	−	0.196750i	$-0.936961\pi$
$947$	−2.20348	+	6.78161i	−0.0716035	+	0.220373i	0.908850	+	0.417122i	$0.136961\pi$
$948$		0			0
$949$	45.4664	−	10.9155i	1.47590	−	0.354332i
$950$	−4.07085	+	16.9563i	−0.132076	+	0.550135i
$951$		0			0
$952$	−7.44273	+	7.44273i	−0.241220	+	0.241220i
$953$	−31.3380	+	10.1823i	−1.01514	+	0.329838i	−0.768899	−	0.639370i	$-0.779195\pi$
$953$	−31.3380	+	10.1823i	−1.01514	+	0.329838i	−0.246240	+	0.969209i	$0.579195\pi$
$954$		0			0
$955$	6.47633	−	0.509698i	0.209569	−	0.0164935i
$956$	−8.44236	−	5.17348i	−0.273045	−	0.167322i
$957$		0			0
$958$	22.3339	+	19.0749i	0.721574	+	0.616282i
$959$	−10.6287	+	14.6292i	−0.343219	+	0.472401i
$960$		0			0
$961$	−2.30099	+	1.67177i	−0.0742255	+	0.0539280i
$962$	−24.6128	+	15.0828i	−0.793549	+	0.486288i
$963$		0			0
$964$	25.8827	−	4.09942i	0.833626	−	0.132033i
$965$	4.42094	+	7.21431i	0.142315	+	0.232237i
$966$		0			0
$967$	−23.6786	−	1.86354i	−0.761452	−	0.0599276i	−0.308214	−	0.951317i	$-0.599731\pi$
$967$	−23.6786	−	1.86354i	−0.761452	−	0.0599276i	−0.453238	+	0.891390i	$0.649731\pi$
$968$	7.82111	+	5.68237i	0.251380	+	0.182638i
$969$		0			0
$970$	2.58741	−	6.24655i	0.0830766	−	0.200565i
$971$	10.9701	−	17.9016i	0.352047	−	0.574489i	−0.626775	−	0.779200i	$-0.715626\pi$
$971$	10.9701	−	17.9016i	0.352047	−	0.574489i	0.978822	+	0.204711i	$0.0656256\pi$
$972$		0			0
$973$	13.7934	+	16.1500i	0.442196	+	0.517745i
$974$	−6.40529	−	19.7135i	−0.205239	−	0.631660i
$975$		0			0
$976$	4.49224	−	8.81652i	0.143793	−	0.282210i
$977$	4.48456	+	1.07665i	0.143474	+	0.0344450i	0.304546	−	0.952498i	$-0.401495\pi$
$977$	4.48456	+	1.07665i	0.143474	+	0.0344450i	−0.161072	+	0.986943i	$0.551495\pi$
$978$		0			0
$979$	−3.19509	+	1.62798i	−0.102116	+	0.0520305i
$980$	−0.265119	−	0.0861424i	−0.00846892	−	0.00275172i
$981$		0			0
$982$	4.85830	−	30.6741i	0.155034	−	0.978849i
$983$	−25.8309			−0.823877			−0.411938	−	0.911212i	$-0.635148\pi$
$983$	−25.8309			−0.823877			−0.411938	+	0.911212i	$0.635148\pi$
$984$		0			0
$985$	9.24798			0.294665
$986$	5.94319	−	37.5238i	0.189270	−	1.19500i
$987$		0			0
$988$	−13.3925	−	4.35149i	−0.426072	−	0.138439i
$989$	−39.2506	+	19.9992i	−1.24810	+	0.635938i
$990$		0			0
$991$	−34.6952	−	8.32958i	−1.10213	−	0.264598i	−0.358727	−	0.933443i	$-0.616789\pi$
$991$	−34.6952	−	8.32958i	−1.10213	−	0.264598i	−0.743402	+	0.668845i	$0.766789\pi$
$992$	−2.40897	+	4.72786i	−0.0764848	+	0.150110i
$993$		0			0
$994$	8.28855	+	25.5095i	0.262897	+	0.809114i
$995$	3.42064	+	4.00505i	0.108441	+	0.126969i
$996$		0			0
$997$	−28.1382	+	45.9174i	−0.891147	+	1.45422i	−0.000257007		1.00000i	$0.500082\pi$
$997$	−28.1382	+	45.9174i	−0.891147	+	1.45422i	−0.890890	+	0.454219i	$0.849918\pi$
$998$	−5.99269	+	14.4676i	−0.189695	+	0.457965i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.b.179.1	yes	48
3.2	odd	2		738.2.ba.a.179.3	✓	48
41.11	odd	40		738.2.ba.a.503.3	yes	48
123.11	even	40	inner	738.2.ba.b.503.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.a.179.3	✓	48	3.2	odd	2
738.2.ba.a.503.3	yes	48	41.11	odd	40
738.2.ba.b.179.1	yes	48	1.1	even	1	trivial
738.2.ba.b.503.1	yes	48	123.11	even	40	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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.951057 - 0.309017i) q^{4} +(-0.454725 + 0.231694i) q^{5} +(-2.47024 - 0.593051i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.157707 + 0.485372i) q^{10} +(-0.749706 - 0.877793i) q^{11} +(1.99976 - 3.26331i) q^{13} +(-0.972180 + 2.34705i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-4.13047 - 0.325075i) q^{17} +(1.92242 + 3.13710i) q^{19} +(0.504067 - 0.0798363i) q^{20} +(-0.984266 + 0.603159i) q^{22} +(-6.21581 + 4.51605i) q^{23} +(-2.78583 + 3.83437i) q^{25} +(-2.91030 - 2.48563i) q^{26} +(2.16607 + 1.32737i) q^{28} +(-9.14125 + 0.719432i) q^{29} +(-5.04650 + 1.63971i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.967221 + 4.02876i) q^{34} +(1.26069 - 0.302664i) q^{35} +(2.33070 - 7.17315i) q^{37} +(3.39921 - 1.40800i) q^{38} -0.510350i q^{40} +(-6.27492 + 1.27492i) q^{41} +(5.66299 + 0.896930i) q^{43} +(0.441760 + 1.06650i) q^{44} +(3.48808 + 6.84575i) q^{46} +(1.17903 + 4.91101i) q^{47} +(-0.486684 - 0.247978i) q^{49} +(3.35136 + 3.35136i) q^{50} +(-2.91030 + 2.48563i) q^{52} +(-0.512168 - 6.50772i) q^{53} +(0.544290 + 0.225452i) q^{55} +(1.64988 - 1.93176i) q^{56} +(-0.719432 + 9.14125i) q^{58} +(-2.09802 - 2.88767i) q^{59} +(-1.54792 - 9.77318i) q^{61} +(0.830073 + 5.24088i) q^{62} +(-0.587785 - 0.809017i) q^{64} +(-0.153251 + 1.94724i) q^{65} +(-1.23719 + 1.44857i) q^{67} +(3.82786 + 1.58555i) q^{68} +(-0.101723 - 1.29251i) q^{70} +(8.02851 - 6.85699i) q^{71} +(8.63876 + 8.63876i) q^{73} +(-6.72023 - 3.42413i) q^{74} +(-0.858911 - 3.57762i) q^{76} +(1.33138 + 2.61297i) q^{77} +(0.430110 + 1.03838i) q^{79} +(-0.504067 - 0.0798363i) q^{80} +(0.277612 + 6.39710i) q^{82} -2.60736i q^{83} +(1.95355 - 0.809186i) q^{85} +(1.77177 - 5.45296i) q^{86} +(1.12248 - 0.269483i) q^{88} +(0.725172 - 3.02056i) q^{89} +(-6.87518 + 6.87518i) q^{91} +(7.30712 - 2.37423i) q^{92} +(5.03499 - 0.396262i) q^{94} +(-1.60102 - 0.981107i) q^{95} +(-10.0740 - 8.60401i) q^{97} +(-0.321059 + 0.441900i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{13} - 4 q^{14} + 12 q^{16} + 16 q^{17} - 4 q^{19} - 16 q^{20} + 20 q^{22} - 40 q^{25} + 20 q^{26} - 4 q^{28} - 32 q^{29} - 40 q^{31} - 4 q^{34} + 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) \) 48 * q + 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^13 - 4 * q^14 + 12 * q^16 + 16 * q^17 - 4 * q^19 - 16 * q^20 + 20 * q^22 - 40 * q^25 + 20 * q^26 - 4 * q^28 - 32 * q^29 - 40 * q^31 - 4 * q^34 + 52 * q^35 - 24 * q^37 - 16 * q^38 - 12 * q^41 + 20 * q^44 + 16 * q^46 + 8 * q^47 - 48 * q^49 + 16 * q^50 + 20 * q^52 - 64 * q^53 + 4 * q^55 - 16 * q^56 + 36 * q^58 - 20 * q^59 - 60 * q^61 + 36 * q^62 - 128 * q^65 - 12 * q^67 + 8 * q^68 + 8 * q^70 + 40 * q^71 + 8 * q^73 - 8 * q^74 + 12 * q^76 + 44 * q^77 + 36 * q^79 + 16 * q^80 + 68 * q^82 + 104 * q^85 + 16 * q^86 + 8 * q^88 + 60 * q^89 + 56 * q^91 - 12 * q^94 + 28 * q^95 + 16 * q^97

Introduction

L-functions

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