LMFDB - Embedded newform 738.2.ba.b.503.1

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			503.1
Character	$\chi$	$=$	738.503
Dual form			738.2.ba.b.179.1

$q$-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 $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$

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	0.349345	−	0.936994i	$-0.386404\pi$
$5$	−0.454725	−	0.231694i	−0.203359	−	0.103617i	−0.552704	+	0.833377i	$0.686404\pi$
$6$		0			0
$7$	−2.47024	+	0.593051i	−0.933662	+	0.224152i	−0.671613	−	0.740902i	$-0.734398\pi$
$7$	−2.47024	+	0.593051i	−0.933662	+	0.224152i	−0.262049	+	0.965055i	$0.584398\pi$
$8$	−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	−0.861825	−	0.507206i	$-0.830678\pi$
$11$	−0.749706	+	0.877793i	−0.226045	+	0.264665i	0.635780	+	0.771870i	$0.280678\pi$
$12$		0			0
$13$	1.99976	+	3.26331i	0.554633	+	0.905079i	0.999953	+	0.00970714i	$0.00308993\pi$
$13$	1.99976	+	3.26331i	0.554633	+	0.905079i	−0.445320	+	0.895371i	$0.646910\pi$
$14$	−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	−0.568730	−	0.822524i	$-0.692565\pi$
$17$	−4.13047	+	0.325075i	−1.00179	+	0.0788423i	−0.433057	+	0.901367i	$0.642565\pi$
$18$		0			0
$19$	1.92242	−	3.13710i	0.441033	−	0.719701i	−0.552467	−	0.833535i	$-0.686313\pi$
$19$	1.92242	−	3.13710i	0.441033	−	0.719701i	0.993500	+	0.113834i	$0.0363133\pi$
$20$	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	−0.296176	−	0.955133i	$-0.595712\pi$
$23$	−6.21581	−	4.51605i	−1.29609	−	0.941661i	−0.999909	+	0.0134722i	$0.995712\pi$
$24$		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	−0.807587	−	0.589749i	$-0.799227\pi$
$29$	−9.14125	−	0.719432i	−1.69749	−	0.133595i	−0.889901	+	0.456153i	$0.849227\pi$
$30$		0			0
$31$	−5.04650	−	1.63971i	−0.906378	−	0.294500i	−0.181511	−	0.983389i	$-0.558099\pi$
$31$	−5.04650	−	1.63971i	−0.906378	−	0.294500i	−0.724867	+	0.688889i	$0.758099\pi$
$32$	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	0.937803	+	0.347167i	$0.112856\pi$
$37$	2.33070	+	7.17315i	0.383164	+	1.17926i	−0.554639	+	0.832091i	$0.687144\pi$
$38$	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	0.291106	−	0.956691i	$-0.405977\pi$
$43$	5.66299	−	0.896930i	0.863598	−	0.136781i	0.572492	+	0.819910i	$0.305977\pi$
$44$	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	−0.818010	−	0.575204i	$-0.804923\pi$
$47$	1.17903	−	4.91101i	0.171979	−	0.716345i	0.989989	−	0.141141i	$-0.0450772\pi$
$48$		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	0.855935	+	0.517084i	$0.172982\pi$
$53$	−0.512168	+	6.50772i	−0.0703517	+	0.893904i	−0.926287	+	0.376820i	$0.877018\pi$
$54$		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	−0.923446	−	0.383728i	$-0.874640\pi$
$59$	−2.09802	+	2.88767i	−0.273139	+	0.375943i	0.650308	+	0.759671i	$0.274640\pi$
$60$		0			0
$61$	−1.54792	+	9.77318i	−0.198191	+	1.25133i	0.665151	+	0.746709i	$0.268367\pi$
$61$	−1.54792	+	9.77318i	−0.198191	+	1.25133i	−0.863342	+	0.504619i	$0.831633\pi$
$62$	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	0.679666	−	0.733521i	$-0.262125\pi$
$67$	−1.23719	−	1.44857i	−0.151147	−	0.176971i	−0.830814	+	0.556551i	$0.812125\pi$
$68$	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	0.982591	−	0.185781i	$-0.0594815\pi$
$71$	8.02851	+	6.85699i	0.952808	+	0.813775i	−0.0297827	+	0.999556i	$0.509482\pi$
$72$		0			0
$73$	8.63876	−	8.63876i	1.01109	−	1.01109i	0.0111528	−	0.999938i	$-0.496450\pi$
$73$	8.63876	−	8.63876i	1.01109	−	1.01109i	0.999938	−	0.0111528i	$-0.00355011\pi$
$74$	−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	−0.897835	−	0.440331i	$-0.854861\pi$
$79$	0.430110	−	1.03838i	0.0483912	−	0.116827i	0.946227	+	0.323504i	$0.104861\pi$
$80$	−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	$0.0457063\pi$
$83$			2.60736i			0.286195i	−0.989709	+	0.143098i	$0.954294\pi$
$84$		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	0.997535	−	0.0701705i	$-0.0223543\pi$
$89$	0.725172	+	3.02056i	0.0768681	+	0.320179i	−0.920667	+	0.390349i	$0.872354\pi$
$90$		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	−0.992040	−	0.125920i	$-0.959812\pi$
$97$	−10.0740	+	8.60401i	−1.02286	+	0.873605i	−0.0308199	+	0.999525i	$0.509812\pi$
$98$	−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	0.257137	−	0.966375i	$-0.417221\pi$
$101$	−4.89602	−	3.00028i	−0.487172	−	0.298540i	−0.744309	+	0.667836i	$0.767221\pi$
$102$		0			0
$103$	1.71321	+	0.271346i	0.168808	+	0.0267366i	0.240266	−	0.970707i	$-0.422765\pi$
$103$	1.71321	+	0.271346i	0.168808	+	0.0267366i	−0.0714582	+	0.997444i	$0.522765\pi$
$104$	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	−0.167321	−	0.985902i	$-0.553512\pi$
$107$	7.43350	−	5.40075i	0.718623	−	0.522110i	0.885944	+	0.463792i	$0.153512\pi$
$108$		0			0
$109$	−0.309072	−	0.746167i	−0.0296038	−	0.0714698i	0.908386	−	0.418132i	$-0.137315\pi$
$109$	−0.309072	−	0.746167i	−0.0296038	−	0.0714698i	−0.937990	+	0.346662i	$0.887315\pi$
$110$	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	−0.829128	−	0.559058i	$-0.811163\pi$
$113$	1.80986	−	5.57016i	0.170257	−	0.523997i	0.999385	+	0.0350615i	$0.0111627\pi$
$114$		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	0.548148	−	0.836382i	$-0.315333\pi$
$127$	16.7151	−	5.43105i	1.48322	−	0.481928i	0.935074	+	0.354454i	$0.115333\pi$
$128$	−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	0.989675	−	0.143328i	$-0.0457803\pi$
$131$	3.34214	+	6.55932i	0.292004	+	0.573091i	−0.697671	+	0.716418i	$0.745780\pi$
$132$		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	0.996496	−	0.0836457i	$-0.0266564\pi$
$137$	2.72392	+	6.57613i	0.232720	+	0.561837i	−0.763775	+	0.645482i	$0.776656\pi$
$138$		0			0
$139$	−6.76359	+	4.91404i	−0.573680	+	0.416803i	−0.836440	−	0.548058i	$-0.815367\pi$
$139$	−6.76359	+	4.91404i	−0.573680	+	0.416803i	0.262760	+	0.964861i	$0.415367\pi$
$140$	−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	0.0518280	−	0.998656i	$-0.483495\pi$
$149$	12.7717	−	10.9080i	1.04630	−	0.893622i	0.994469	+	0.105034i	$0.0334952\pi$
$150$		0			0
$151$	−18.4114	+	11.2825i	−1.49830	+	0.918159i	−0.499648	+	0.866228i	$0.666537\pi$
$151$	−18.4114	+	11.2825i	−1.49830	+	0.918159i	−0.998651	+	0.0519306i	$0.983463\pi$
$152$	−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	−0.993500	−	0.113834i	$-0.963687\pi$
$157$	−2.00435	−	8.34871i	−0.159964	−	0.666300i	0.833535	−	0.552466i	$-0.186313\pi$
$158$	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	$-0.940842\pi$
$163$		−	4.71832i		−	0.369567i	0.982779	−	0.184784i	$-0.0591585\pi$
$164$	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	−0.951991	−	0.306125i	$-0.900968\pi$
$167$	−0.805984	+	1.94582i	−0.0623689	+	0.150572i	0.889622	+	0.456697i	$0.150968\pi$
$168$		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	−0.876730	−	0.480983i	$-0.840280\pi$
$173$	−5.20524	+	5.20524i	−0.395747	+	0.395747i	0.480983	+	0.876730i	$0.340280\pi$
$174$		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	0.161698	−	0.986840i	$-0.448303\pi$
$179$	−11.2155	−	13.1317i	−0.838287	−	0.981508i	−0.999986	+	0.00533190i	$0.998303\pi$
$180$		0			0
$181$	0.871880	+	11.0783i	0.0648063	+	0.823442i	0.940329	+	0.340266i	$0.110517\pi$
$181$	0.871880	+	11.0783i	0.0648063	+	0.823442i	−0.875523	+	0.483176i	$0.839483\pi$
$182$	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	−0.765159	−	0.643842i	$-0.777340\pi$
$191$	−11.7603	+	4.87126i	−0.850943	+	0.352472i	−0.0857841	+	0.996314i	$0.527340\pi$
$192$		0			0
$193$	−1.30078	+	16.5280i	−0.0936323	+	1.18971i	0.753178	+	0.657817i	$0.228520\pi$
$193$	−1.30078	+	16.5280i	−0.0936323	+	1.18971i	−0.846810	+	0.531895i	$0.821480\pi$
$194$	−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	−0.921899	−	0.387430i	$-0.873363\pi$
$197$	−16.1458	+	8.22669i	−1.15034	+	0.586128i	−0.228441	+	0.973558i	$0.573363\pi$
$198$		0			0
$199$	−2.40924	+	10.0352i	−0.170786	+	0.711376i	0.819587	+	0.572955i	$0.194203\pi$
$199$	−2.40924	+	10.0352i	−0.170786	+	0.711376i	−0.990373	+	0.138421i	$0.955797\pi$
$200$	−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	−0.694300	−	0.719686i	$-0.744286\pi$
$211$	−23.8174	−	5.71805i	−1.63966	−	0.393647i	−0.945356	+	0.326040i	$0.894286\pi$
$212$	−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	0.416329	−	0.909214i	$-0.363317\pi$
$223$	−4.77463	−	3.46897i	−0.319733	−	0.232300i	−0.736061	+	0.676915i	$0.763317\pi$
$224$	−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	−0.484101	−	0.875012i	$-0.660853\pi$
$227$	7.76404	−	12.6698i	0.515318	−	0.840922i	0.999419	+	0.0340901i	$0.0108533\pi$
$228$		0			0
$229$	23.4440	−	1.84508i	1.54922	−	0.121926i	0.725221	−	0.688516i	$-0.241737\pi$
$229$	23.4440	−	1.84508i	1.54922	−	0.121926i	0.824000	+	0.566589i	$0.191737\pi$
$230$	−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	0.908114	−	0.418722i	$-0.137522\pi$
$233$	1.87377	+	3.05771i	0.122755	+	0.200317i	−0.785360	+	0.619040i	$0.787522\pi$
$234$		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	0.0902353	−	0.995920i	$-0.471238\pi$
$239$	9.62785	−	2.31144i	0.622774	−	0.149515i	0.532539	+	0.846406i	$0.321238\pi$
$240$		0			0
$241$	−23.3491	−	11.8970i	−1.50405	−	0.766351i	−0.508542	−	0.861037i	$-0.669815\pi$
$241$	−23.3491	−	11.8970i	−1.50405	−	0.766351i	−0.995507	+	0.0946858i	$0.969815\pi$
$242$	−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	0.940462	−	0.339899i	$-0.110393\pi$
$251$	19.3010	+	9.83434i	1.21827	+	0.620738i	0.277806	+	0.960637i	$0.410393\pi$
$252$		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	−0.906391	−	0.422440i	$-0.861174\pi$
$257$	−5.56862	+	6.52001i	−0.347361	+	0.406707i	0.559030	+	0.829147i	$0.311174\pi$
$258$		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	−0.0212033	−	0.999775i	$-0.506750\pi$
$263$	1.85288	−	0.145825i	0.114254	−	0.00899196i	0.135457	+	0.990783i	$0.456750\pi$
$264$		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	0.642096	−	0.766624i	$-0.278065\pi$
$269$	1.82728	+	1.32759i	0.111411	+	0.0809449i	−0.530685	+	0.847569i	$0.678065\pi$
$270$		0			0
$271$	−15.0466	−	20.7099i	−0.914018	−	1.25804i	−0.965776	−	0.259378i	$-0.916482\pi$
$271$	−15.0466	−	20.7099i	−0.914018	−	1.25804i	0.0517576	−	0.998660i	$-0.483518\pi$
$272$	−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	0.341948	−	0.939719i	$-0.388913\pi$
$277$	1.10241	+	0.358196i	0.0662376	+	0.0215219i	−0.275711	+	0.961241i	$0.588913\pi$
$278$	−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	−0.388441	−	0.921474i	$-0.626986\pi$
$281$	−19.3259	−	4.63973i	−1.15288	−	0.276783i	−0.764443	+	0.644691i	$0.776986\pi$
$282$		0			0
$283$	−2.91725	−	8.97836i	−0.173412	−	0.533708i	0.826145	−	0.563458i	$-0.190529\pi$
$283$	−2.91725	−	8.97836i	−0.173412	−	0.533708i	−0.999557	+	0.0297492i	$0.990529\pi$
$284$	−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	0.684390	+	0.729116i	$0.260069\pi$
$293$	−4.38916	+	18.2822i	−0.256418	+	1.06806i	−0.940808	+	0.338941i	$0.889931\pi$
$294$		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	−0.418377	−	0.908273i	$-0.637401\pi$
$307$	4.55899	−	28.7843i	0.260195	−	1.64281i	0.678572	−	0.734534i	$-0.262599\pi$
$308$	−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	0.852464	+	0.522786i	$0.175107\pi$
$311$	1.62732	+	20.6771i	0.0922771	+	1.17249i	−0.760187	+	0.649705i	$0.774893\pi$
$312$		0			0
$313$	14.9511	+	17.5055i	0.845088	+	0.989471i	0.999999	+	0.00154212i	$0.000490872\pi$
$313$	14.9511	+	17.5055i	0.845088	+	0.989471i	−0.154911	+	0.987928i	$0.549509\pi$
$314$	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	0.954045	−	0.299664i	$-0.0968744\pi$
$317$	14.3739	+	12.2764i	0.807316	+	0.689513i	−0.146729	+	0.989177i	$0.546874\pi$
$318$		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	0.723268	−	0.690568i	$-0.242639\pi$
$331$	13.5794	+	5.62476i	0.746390	+	0.309165i	0.0231223	+	0.999733i	$0.492639\pi$
$332$	−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	−0.998427	−	0.0560754i	$-0.982141\pi$
$337$	−19.3581	−	19.3581i	−1.05450	−	1.05450i	−0.0560754	−	0.998427i	$-0.517859\pi$
$338$	−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	−0.228195	−	0.973615i	$-0.573282\pi$
$347$	−22.3403	−	13.6902i	−1.19929	−	0.734927i	−0.971096	+	0.238689i	$0.923282\pi$
$348$		0			0
$349$	8.98820	+	1.42359i	0.481127	+	0.0762031i	0.392287	−	0.919843i	$-0.371684\pi$
$349$	8.98820	+	1.42359i	0.481127	+	0.0762031i	0.0888402	+	0.996046i	$0.471684\pi$
$350$	−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	−0.212017	−	0.977266i	$-0.568003\pi$
$353$	12.2481	−	8.89877i	0.651901	−	0.473634i	0.863918	+	0.503632i	$0.168003\pi$
$354$		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	−0.993191	−	0.116496i	$-0.962834\pi$
$359$	−2.29656	+	7.06809i	−0.121208	+	0.373040i	0.871983	+	0.489536i	$0.162834\pi$
$360$		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	−0.677813	−	0.735235i	$-0.737072\pi$
$367$	−4.98806	−	31.4934i	−0.260374	−	1.64394i	0.417438	−	0.908705i	$-0.362928\pi$
$368$	−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	−0.951273	−	0.308351i	$-0.900223\pi$
$373$	−29.7351	+	9.66152i	−1.53962	+	0.500254i	−0.588352	+	0.808605i	$0.700223\pi$
$374$	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	−0.404683	−	0.914457i	$-0.632618\pi$
$379$	8.95946	−	27.5744i	0.460217	−	1.41640i	0.864900	−	0.501945i	$-0.167382\pi$
$380$	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	0.989246	−	0.146264i	$-0.0467250\pi$
$383$	3.64633	+	8.80302i	0.186319	+	0.449813i	−0.802927	+	0.596078i	$0.796725\pi$
$384$		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	−0.572971	−	0.819576i	$-0.694209\pi$
$389$	−27.0435	−	4.28327i	−1.37116	−	0.217171i	−0.798190	+	0.602405i	$0.794209\pi$
$390$		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	−0.543232	−	0.839583i	$-0.682800\pi$
$397$	−0.832476	+	0.510142i	−0.0417808	+	0.0256033i	0.501451	+	0.865186i	$0.332800\pi$
$398$	−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	0.603082	−	0.797679i	$-0.293939\pi$
$401$	−3.89680	−	3.89680i	−0.194597	−	0.194597i	−0.797679	+	0.603082i	$0.793939\pi$
$402$		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	$-0.897322\pi$
$409$		−	12.8222i		−	0.634016i	0.948423	−	0.317008i	$-0.102678\pi$
$410$	−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	−0.166274	−	0.986080i	$-0.553174\pi$
$419$	16.7810	−	16.7810i	0.819805	−	0.819805i	0.986080	+	0.166274i	$0.0531737\pi$
$420$		0			0
$421$	−7.40253	−	6.32236i	−0.360777	−	0.308133i	0.450520	−	0.892766i	$-0.351238\pi$
$421$	−7.40253	−	6.32236i	−0.360777	−	0.308133i	−0.811298	+	0.584633i	$0.801238\pi$
$422$	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	0.934418	+	0.356179i	$0.115921\pi$
$431$	−1.33556	+	8.43239i	−0.0643316	+	0.406174i	−0.998749	+	0.0499951i	$0.984079\pi$
$432$		0			0
$433$	16.3965	−	22.5678i	0.787965	−	1.08454i	−0.206394	−	0.978469i	$-0.566173\pi$
$433$	16.3965	−	22.5678i	0.787965	−	1.08454i	0.994358	−	0.106072i	$-0.0338273\pi$
$434$	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	0.658047	+	0.752977i	$0.271383\pi$
$439$	−2.29826	+	29.2021i	−0.109690	+	1.39374i	−0.767737	+	0.640765i	$0.778617\pi$
$440$	−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	−0.994543	−	0.104324i	$-0.966732\pi$
$443$	−31.4603	+	16.0298i	−1.49472	+	0.761599i	−0.500178	+	0.865922i	$0.666732\pi$
$444$		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	−0.604907	−	0.796296i	$-0.706790\pi$
$449$	−19.7941	+	3.13507i	−0.934139	+	0.147953i	−0.329232	+	0.944249i	$0.606790\pi$
$450$		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	0.634410	−	0.772997i	$-0.281243\pi$
$457$	18.1440	+	4.35599i	0.848741	+	0.203765i	0.214331	+	0.976761i	$0.431243\pi$
$458$	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	0.811158	−	0.584827i	$-0.198838\pi$
$461$	24.1257	+	7.83891i	1.12365	+	0.365095i	0.312488	+	0.949922i	$0.398838\pi$
$462$		0			0
$463$	−26.2880	−	2.06891i	−1.22171	−	0.0961505i	−0.548849	−	0.835921i	$-0.684934\pi$
$463$	−26.2880	−	2.06891i	−1.22171	−	0.0961505i	−0.672859	+	0.739771i	$0.734934\pi$
$464$	−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	0.615595	−	0.788063i	$-0.288916\pi$
$467$	−7.00444	−	9.64078i	−0.324127	−	0.446122i	−0.939722	+	0.341941i	$0.888916\pi$
$468$		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	−0.982794	−	0.184707i	$-0.940866\pi$
$479$	−15.3463	−	25.0429i	−0.701190	−	1.14424i	0.281604	−	0.959531i	$-0.409134\pi$
$480$		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	0.819259	−	0.573423i	$-0.194385\pi$
$487$	18.4688	+	9.41030i	0.836899	+	0.426421i	0.0176396	+	0.999844i	$0.494385\pi$
$488$	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	−0.559462	−	0.828856i	$-0.688992\pi$
$499$	−15.2270	+	3.65567i	−0.681653	+	0.163650i	−0.122191	+	0.992507i	$0.538992\pi$
$500$	−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	−0.488058	−	0.872811i	$-0.662295\pi$
$503$	10.1004	−	11.8261i	0.450356	−	0.527300i	0.938415	+	0.345512i	$0.112295\pi$
$504$		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	0.194242	−	0.980954i	$-0.437775\pi$
$509$	12.1727	−	0.958015i	0.539547	−	0.0424633i	0.345305	+	0.938490i	$0.387775\pi$
$510$		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	−0.0295993	−	0.999562i	$-0.509423\pi$
$521$	−4.91203	−	0.386585i	−0.215200	−	0.0169366i	−0.185601	+	0.982625i	$0.559423\pi$
$522$		0			0
$523$	−17.3135	−	5.62551i	−0.757068	−	0.245986i	−0.0950482	−	0.995473i	$-0.530301\pi$
$523$	−17.3135	−	5.62551i	−0.757068	−	0.245986i	−0.662020	+	0.749486i	$0.730301\pi$
$524$	−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	−0.966857	−	0.255320i	$-0.917819\pi$
$541$	−30.9025	+	15.7456i	−1.32860	+	0.676957i	−0.361746	+	0.932277i	$0.617819\pi$
$542$	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	−0.375592	−	0.926785i	$-0.622561\pi$
$547$	0.331168	−	0.137174i	0.0141597	−	0.00586514i	0.389752	+	0.920920i	$0.372561\pi$
$548$	−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	0.914242	+	0.405169i	$0.132787\pi$
$557$	1.76153	+	22.3823i	0.0746383	+	0.948369i	−0.839603	+	0.543200i	$0.817213\pi$
$558$		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	0.996034	+	0.0889741i	$0.0283588\pi$
$563$	29.4158	+	25.1234i	1.23973	+	1.05883i	0.243693	+	0.969853i	$0.421641\pi$
$564$		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	−0.955680	−	0.294408i	$-0.904878\pi$
$569$	−3.71557	+	7.29221i	−0.155765	+	0.305705i	0.799915	+	0.600113i	$0.204878\pi$
$570$		0			0
$571$	3.99515	−	9.64513i	0.167192	−	0.403636i	−0.817971	−	0.575259i	$-0.804901\pi$
$571$	3.99515	−	9.64513i	0.167192	−	0.403636i	0.985163	+	0.171623i	$0.0549011\pi$
$572$	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	0.884372	−	0.466782i	$-0.154587\pi$
$577$	28.3362	+	11.7373i	1.17965	+	0.488628i	0.295281	+	0.955410i	$0.404587\pi$
$578$	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	0.272664	−	0.962109i	$-0.412095\pi$
$587$	30.3747	−	18.6136i	1.25370	−	0.768266i	0.981032	+	0.193843i	$0.0620954\pi$
$588$		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	0.0875958	−	0.996156i	$-0.472082\pi$
$593$	−18.5125	−	11.3445i	−0.760218	−	0.465862i	−0.847814	+	0.530294i	$0.822082\pi$
$594$		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	−0.977768	−	0.209687i	$-0.932755\pi$
$599$	−26.4445	+	19.2130i	−1.08049	+	0.785023i	−0.102723	+	0.994710i	$0.532755\pi$
$600$		0			0
$601$	−2.96813	−	7.16570i	−0.121073	−	0.292295i	0.851711	−	0.524013i	$-0.175566\pi$
$601$	−2.96813	−	7.16570i	−0.121073	−	0.292295i	−0.972783	+	0.231718i	$0.925566\pi$
$602$	−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	0.995845	+	0.0910687i	$0.0290283\pi$
$607$	11.9289	+	23.4117i	0.484178	+	0.950253i	−0.511667	+	0.859184i	$0.670972\pi$
$608$	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	−0.999218	−	0.0395288i	$-0.987414\pi$
$613$	−1.51327	−	9.55439i	−0.0611203	−	0.385898i	0.938098	−	0.346370i	$-0.112586\pi$
$614$	29.1431			1.17612
$615$		0			0
$616$	−2.93261			−0.118158
$617$	0.951809	+	6.00948i	0.0383184	+	0.241933i	0.999412	−	0.0342904i	$-0.0109171\pi$
$617$	0.951809	+	6.00948i	0.0383184	+	0.241933i	−0.961094	+	0.276223i	$0.910917\pi$
$618$		0			0
$619$	−39.5299	+	12.8441i	−1.58884	+	0.516246i	−0.964315	−	0.264757i	$-0.914708\pi$
$619$	−39.5299	+	12.8441i	−1.58884	+	0.516246i	−0.624527	+	0.781003i	$0.714708\pi$
$620$	−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	−0.787251	−	0.616633i	$-0.788496\pi$
$631$	−11.1550	+	8.10455i	−0.444072	+	0.322637i	0.343179	+	0.939270i	$0.388496\pi$
$632$	−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	−0.141496	−	0.989939i	$-0.545191\pi$
$641$	20.6119	−	17.6042i	0.814120	−	0.695324i	0.955616	+	0.294614i	$0.0951912\pi$
$642$		0			0
$643$	−18.5580	+	11.3723i	−0.731855	+	0.448481i	−0.837861	−	0.545884i	$-0.816194\pi$
$643$	−18.5580	+	11.3723i	−0.731855	+	0.448481i	0.106006	+	0.994366i	$0.466194\pi$
$644$	−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	0.568919	−	0.822394i	$-0.307362\pi$
$647$	−6.44743	−	6.44743i	−0.253475	−	0.253475i	−0.822394	+	0.568919i	$0.807362\pi$
$648$		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	0.968055	−	0.250739i	$-0.0806735\pi$
$653$	37.6990	+	15.6154i	1.47527	+	0.611078i	0.507219	+	0.861817i	$0.330673\pi$
$654$		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	−0.906718	−	0.421738i	$-0.861420\pi$
$659$	0.837963	−	2.02302i	0.0326424	−	0.0788058i	0.939360	+	0.342932i	$0.111420\pi$
$660$		0			0
$661$	3.89423	−	7.64285i	0.151468	−	0.297273i	−0.802787	−	0.596265i	$-0.796651\pi$
$661$	3.89423	−	7.64285i	0.151468	−	0.297273i	0.954255	+	0.298993i	$0.0966506\pi$
$662$	−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	−0.901121	−	0.433568i	$-0.857254\pi$
$673$	−2.04734	−	26.0140i	−0.0789193	−	1.00277i	0.822201	−	0.569197i	$-0.192746\pi$
$674$	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	−0.565632	−	0.824658i	$-0.691368\pi$
$677$	5.91025	−	37.3159i	0.227149	−	1.43416i	0.792781	−	0.609507i	$-0.208632\pi$
$678$		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	−0.306795	−	0.951776i	$-0.599257\pi$
$683$	3.90119	−	1.61592i	0.149275	−	0.0618316i	0.456070	+	0.889944i	$0.349257\pi$
$684$		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	−0.978910	−	0.204293i	$-0.934510\pi$
$691$	−0.366642	+	1.52717i	−0.0139477	+	0.0580965i	0.964962	+	0.262389i	$0.0845105\pi$
$692$	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	0.994040	−	0.109016i	$-0.0347699\pi$
$701$	3.32985	+	10.2482i	0.125767	+	0.387071i	−0.868273	+	0.496086i	$0.834770\pi$
$702$		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	0.116018	−	0.993247i	$-0.462987\pi$
$709$	2.00315	+	0.157651i	0.0752299	+	0.00592072i	−0.0407883	+	0.999168i	$0.512987\pi$
$710$	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	−0.0864533	−	0.996256i	$-0.527553\pi$
$719$	22.5364	−	36.7761i	0.840466	−	1.37152i	0.926919	−	0.375260i	$-0.122447\pi$
$720$		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	−0.635011	−	0.772503i	$-0.719004\pi$
$727$	6.12920	−	7.17637i	0.227319	−	0.266157i	0.862330	+	0.506347i	$0.169004\pi$
$728$	−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	0.400109	−	0.916467i	$-0.368972\pi$
$733$	−2.87391	−	1.46433i	−0.106150	−	0.0540862i	−0.506259	+	0.862381i	$0.668972\pi$
$734$	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	−0.0168313	−	0.999858i	$-0.505358\pi$
$743$	−22.7775	−	11.6057i	−0.835627	−	0.425773i	−0.818796	+	0.574085i	$0.805358\pi$
$744$		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	0.993285	+	0.115693i	$0.0369088\pi$
$751$	17.6875	+	28.8634i	0.645426	+	1.05324i	−0.347859	+	0.937547i	$0.613091\pi$
$752$	−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	0.329526	+	0.944147i	$0.393111\pi$
$757$	−18.1952	+	29.6919i	−0.661317	+	1.07917i	−0.990842	+	0.135024i	$0.956889\pi$
$758$	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	0.994423	−	0.105463i	$-0.0336325\pi$
$761$	33.1425	+	24.0795i	1.20142	+	0.872880i	0.206992	+	0.978343i	$0.433632\pi$
$762$		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	0.0607210	−	0.998155i	$-0.480660\pi$
$769$	−13.2236	−	4.29661i	−0.476855	−	0.154940i	−0.537576	+	0.843215i	$0.680660\pi$
$770$	−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	0.405466	−	0.914110i	$-0.367109\pi$
$773$	9.77944	+	2.34784i	0.351742	+	0.0844458i	−0.0537243	+	0.998556i	$0.517109\pi$
$774$		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	−0.782959	−	0.622073i	$-0.786290\pi$
$787$	−20.7569	+	10.5762i	−0.739903	+	0.376999i	0.0430564	+	0.999073i	$0.486290\pi$
$788$	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	0.0777167	−	0.996975i	$-0.475237\pi$
$797$	28.2843	−	38.9300i	1.00188	−	1.37897i	0.924164	−	0.381995i	$-0.124763\pi$
$798$		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	0.802756	−	0.596308i	$-0.203366\pi$
$809$	9.65261	+	8.24411i	0.339368	+	0.289848i	−0.463388	+	0.886156i	$0.653366\pi$
$810$		0			0
$811$	−15.8759	+	15.8759i	−0.557478	+	0.557478i	−0.928589	−	0.371110i	$-0.878977\pi$
$811$	−15.8759	+	15.8759i	−0.557478	+	0.557478i	0.371110	+	0.928589i	$0.378977\pi$
$812$	−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	$0.151173\pi$
$821$			26.2045i			0.914543i	−0.889327	+	0.457271i	$0.848827\pi$
$822$		0			0
$823$	46.9062	+	19.4292i	1.63505	+	0.677259i	0.995784	−	0.0917272i	$-0.0292388\pi$
$823$	46.9062	+	19.4292i	1.63505	+	0.677259i	0.639265	+	0.768987i	$0.279239\pi$
$824$	−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	0.973022	+	0.230714i	$0.0741061\pi$
$827$	6.06196	+	25.2499i	0.210795	+	0.878024i	−0.762227	+	0.647310i	$0.775894\pi$
$828$		0			0
$829$	−32.6794	−	32.6794i	−1.13500	−	1.13500i	−0.989333	−	0.145670i	$-0.953466\pi$
$829$	−32.6794	−	32.6794i	−1.13500	−	1.13500i	−0.145670	−	0.989333i	$-0.546534\pi$
$830$	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	−0.995227	−	0.0975821i	$-0.968889\pi$
$839$	−44.4330	−	27.2286i	−1.53400	−	0.940035i	−0.538770	−	0.842453i	$-0.681111\pi$
$840$		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	0.999893	−	0.0146047i	$-0.00464897\pi$
$853$	11.6928	+	22.9485i	0.400355	+	0.785742i	−0.599538	+	0.800346i	$0.704649\pi$
$854$	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	−0.429802	−	0.902923i	$-0.641417\pi$
$857$	−7.22479	+	2.34748i	−0.246794	+	0.0801882i	0.183008	+	0.983111i	$0.441417\pi$
$858$		0			0
$859$	−2.24397	−	14.1679i	−0.0765634	−	0.483402i	−0.995940	−	0.0900230i	$-0.971306\pi$
$859$	−2.24397	−	14.1679i	−0.0765634	−	0.483402i	0.919376	−	0.393379i	$-0.128694\pi$
$860$	2.92613			0.0997804
$861$		0			0
$862$	−8.53750			−0.290788
$863$	−8.10008	−	51.1419i	−0.275730	−	1.74089i	−0.604614	−	0.796519i	$-0.706672\pi$
$863$	−8.10008	−	51.1419i	−0.275730	−	1.74089i	0.328884	−	0.944370i	$-0.393328\pi$
$864$		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	−0.273576	−	0.961850i	$-0.588207\pi$
$877$	16.4850	−	11.9770i	0.556658	−	0.404436i	0.830234	+	0.557414i	$0.188207\pi$
$878$	−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	−0.257070	−	0.966393i	$-0.582757\pi$
$881$	−23.7510	−	3.76179i	−0.800191	−	0.126738i	−0.543120	+	0.839655i	$0.682757\pi$
$882$		0			0
$883$	−1.25850	−	0.771207i	−0.0423517	−	0.0259532i	0.501162	−	0.865354i	$-0.332906\pi$
$883$	−1.25850	−	0.771207i	−0.0423517	−	0.0259532i	−0.543513	+	0.839401i	$0.682906\pi$
$884$	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	−0.944438	−	0.328689i	$-0.893393\pi$
$887$	−22.8593	+	19.5237i	−0.767539	+	0.655540i	0.176899	+	0.984229i	$0.443393\pi$
$888$		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	−0.701109	−	0.713054i	$-0.747311\pi$
$907$	8.66949	−	17.0148i	0.287866	−	0.564968i	0.988974	+	0.148086i	$0.0473113\pi$
$908$	−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	−0.137639	+	0.990482i	$0.543951\pi$
$911$	−34.0498	+	34.0498i	−1.12812	+	1.12812i	−0.990482	+	0.137639i	$0.956049\pi$
$912$		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	0.874123	+	0.485704i	$0.161437\pi$
$919$	2.62961	+	33.4124i	0.0867428	+	1.10217i	−0.787380	+	0.616468i	$0.788563\pi$
$920$	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	0.395848	−	0.918316i	$-0.370451\pi$
$929$	40.3885	−	16.7295i	1.32510	−	0.548875i	0.929254	+	0.369440i	$0.120451\pi$
$930$		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	−0.999172	−	0.0406886i	$-0.987045\pi$
$937$	−2.76813	+	11.5301i	−0.0904310	+	0.376672i	0.908741	+	0.417361i	$0.137045\pi$
$938$	−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	0.0757098	−	0.997130i	$-0.475878\pi$
$941$	13.9834	−	2.21475i	0.455844	−	0.0721986i	0.380134	+	0.924931i	$0.375878\pi$
$942$		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	0.908850	−	0.417122i	$-0.136961\pi$
$947$	−2.20348	−	6.78161i	−0.0716035	−	0.220373i	−0.980454	+	0.196750i	$0.936961\pi$
$948$		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	−0.246240	−	0.969209i	$-0.579195\pi$
$953$	−31.3380	−	10.1823i	−1.01514	−	0.329838i	−0.768899	+	0.639370i	$0.779195\pi$
$954$		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	−0.453238	−	0.891390i	$-0.649731\pi$
$967$	−23.6786	+	1.86354i	−0.761452	+	0.0599276i	−0.308214	+	0.951317i	$0.599731\pi$
$968$	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	0.978822	−	0.204711i	$-0.0656256\pi$
$971$	10.9701	+	17.9016i	0.352047	+	0.574489i	−0.626775	+	0.779200i	$0.715626\pi$
$972$		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	−0.161072	−	0.986943i	$-0.551495\pi$
$977$	4.48456	−	1.07665i	0.143474	−	0.0344450i	0.304546	+	0.952498i	$0.401495\pi$
$978$		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	−0.743402	−	0.668845i	$-0.766789\pi$
$991$	−34.6952	+	8.32958i	−1.10213	+	0.264598i	−0.358727	+	0.933443i	$0.616789\pi$
$992$	−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	−0.890890	−	0.454219i	$-0.849918\pi$
$997$	−28.1382	−	45.9174i	−0.891147	−	1.45422i	−0.000257007	−	1.00000i	$-0.500082\pi$
$998$	−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.503.1	yes	48
3.2	odd	2		738.2.ba.a.503.3	yes	48
41.15	odd	40		738.2.ba.a.179.3	✓	48
123.56	even	40	inner	738.2.ba.b.179.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.a.179.3	✓	48	41.15	odd	40
738.2.ba.a.503.3	yes	48	3.2	odd	2
738.2.ba.b.179.1	yes	48	123.56	even	40	inner
738.2.ba.b.503.1	yes	48	1.1	even	1	trivial

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

Modular forms

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Database

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