LMFDB - Embedded newform 738.2.ba.a.179.3

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			179.3
Character	$\chi$	$=$	738.179
Dual form			738.2.ba.a.503.3

$q$-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	−0.349345	−	0.936994i	$-0.613596\pi$
$5$	0.454725	−	0.231694i	0.203359	−	0.103617i	0.552704	+	0.833377i	$0.313596\pi$
$6$		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	0.861825	−	0.507206i	$-0.169322\pi$
$11$	0.749706	+	0.877793i	0.226045	+	0.264665i	−0.635780	+	0.771870i	$0.719322\pi$
$12$		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	0.568730	−	0.822524i	$-0.307435\pi$
$17$	4.13047	+	0.325075i	1.00179	+	0.0788423i	0.433057	+	0.901367i	$0.357435\pi$
$18$		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	0.296176	−	0.955133i	$-0.404288\pi$
$23$	6.21581	−	4.51605i	1.29609	−	0.941661i	0.999909	+	0.0134722i	$0.00428848\pi$
$24$		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	$-0.200773\pi$
$29$	9.14125	−	0.719432i	1.69749	−	0.133595i	0.889901	+	0.456153i	$0.150773\pi$
$30$		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	$-0.954923\pi$
$47$	−1.17903	−	4.91101i	−0.171979	−	0.716345i	0.818010	−	0.575204i	$-0.195077\pi$
$48$		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	$0.122982\pi$
$53$	0.512168	+	6.50772i	0.0703517	+	0.893904i	−0.855935	+	0.517084i	$0.827018\pi$
$54$		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	$-0.125360\pi$
$59$	2.09802	+	2.88767i	0.273139	+	0.375943i	−0.650308	+	0.759671i	$0.725360\pi$
$60$		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	−0.982591	−	0.185781i	$-0.940518\pi$
$71$	−8.02851	+	6.85699i	−0.952808	+	0.813775i	0.0297827	+	0.999556i	$0.490518\pi$
$72$		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	$0.0457063\pi$
$83$			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	$-0.977646\pi$
$89$	−0.725172	+	3.02056i	−0.0768681	+	0.320179i	0.920667	+	0.390349i	$0.127646\pi$
$90$		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	−0.257137	−	0.966375i	$-0.582779\pi$
$101$	4.89602	−	3.00028i	0.487172	−	0.298540i	0.744309	+	0.667836i	$0.232779\pi$
$102$		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	0.167321	−	0.985902i	$-0.446488\pi$
$107$	−7.43350	−	5.40075i	−0.718623	−	0.522110i	−0.885944	+	0.463792i	$0.846488\pi$
$108$		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	0.829128	−	0.559058i	$-0.188837\pi$
$113$	−1.80986	−	5.57016i	−0.170257	−	0.523997i	−0.999385	+	0.0350615i	$0.988837\pi$
$114$		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	−0.989675	−	0.143328i	$-0.954220\pi$
$131$	−3.34214	+	6.55932i	−0.292004	+	0.573091i	0.697671	+	0.716418i	$0.254220\pi$
$132$		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	$-0.973344\pi$
$137$	−2.72392	+	6.57613i	−0.232720	+	0.561837i	0.763775	+	0.645482i	$0.223344\pi$
$138$		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	−0.0518280	−	0.998656i	$-0.516505\pi$
$149$	−12.7717	−	10.9080i	−1.04630	−	0.893622i	−0.994469	+	0.105034i	$0.966505\pi$
$150$		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	0.951991	−	0.306125i	$-0.0990325\pi$
$167$	0.805984	+	1.94582i	0.0623689	+	0.150572i	−0.889622	+	0.456697i	$0.849032\pi$
$168$		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	$-0.159720\pi$
$173$	5.20524	+	5.20524i	0.395747	+	0.395747i	−0.480983	+	0.876730i	$0.659720\pi$
$174$		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	$-0.551697\pi$
$179$	11.2155	−	13.1317i	0.838287	−	0.981508i	0.999986	+	0.00533190i	$0.00169721\pi$
$180$		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	0.765159	−	0.643842i	$-0.222660\pi$
$191$	11.7603	+	4.87126i	0.850943	+	0.352472i	0.0857841	+	0.996314i	$0.472660\pi$
$192$		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	0.921899	−	0.387430i	$-0.126637\pi$
$197$	16.1458	+	8.22669i	1.15034	+	0.586128i	0.228441	+	0.973558i	$0.426637\pi$
$198$		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	0.484101	−	0.875012i	$-0.339147\pi$
$227$	−7.76404	−	12.6698i	−0.515318	−	0.840922i	−0.999419	+	0.0340901i	$0.989147\pi$
$228$		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	−0.908114	−	0.418722i	$-0.862478\pi$
$233$	−1.87377	+	3.05771i	−0.122755	+	0.200317i	0.785360	+	0.619040i	$0.212478\pi$
$234$		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	$-0.528762\pi$
$239$	−9.62785	−	2.31144i	−0.622774	−	0.149515i	−0.532539	+	0.846406i	$0.678762\pi$
$240$		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	−0.940462	−	0.339899i	$-0.889607\pi$
$251$	−19.3010	+	9.83434i	−1.21827	+	0.620738i	−0.277806	+	0.960637i	$0.589607\pi$
$252$		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	$-0.138826\pi$
$257$	5.56862	+	6.52001i	0.347361	+	0.406707i	−0.559030	+	0.829147i	$0.688826\pi$
$258$		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	$-0.493250\pi$
$263$	−1.85288	−	0.145825i	−0.114254	−	0.00899196i	−0.135457	+	0.990783i	$0.543250\pi$
$264$		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	$-0.721935\pi$
$269$	−1.82728	+	1.32759i	−0.111411	+	0.0809449i	0.530685	+	0.847569i	$0.321935\pi$
$270$		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	0.388441	−	0.921474i	$-0.373014\pi$
$281$	19.3259	−	4.63973i	1.15288	−	0.276783i	0.764443	+	0.644691i	$0.223014\pi$
$282$		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	$0.110069\pi$
$293$	4.38916	+	18.2822i	0.256418	+	1.06806i	−0.684390	+	0.729116i	$0.739931\pi$
$294$		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	$0.225107\pi$
$311$	−1.62732	+	20.6771i	−0.0922771	+	1.17249i	−0.852464	+	0.522786i	$0.824893\pi$
$312$		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	−0.954045	−	0.299664i	$-0.903126\pi$
$317$	−14.3739	+	12.2764i	−0.807316	+	0.689513i	0.146729	+	0.989177i	$0.453126\pi$
$318$		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	0.228195	−	0.973615i	$-0.426718\pi$
$347$	22.3403	−	13.6902i	1.19929	−	0.734927i	0.971096	+	0.238689i	$0.0767176\pi$
$348$		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	0.212017	−	0.977266i	$-0.431997\pi$
$353$	−12.2481	−	8.89877i	−0.651901	−	0.473634i	−0.863918	+	0.503632i	$0.831997\pi$
$354$		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	$-0.0371662\pi$
$359$	2.29656	+	7.06809i	0.121208	+	0.373040i	−0.871983	+	0.489536i	$0.837166\pi$
$360$		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	−0.989246	−	0.146264i	$-0.953275\pi$
$383$	−3.64633	+	8.80302i	−0.186319	+	0.449813i	0.802927	+	0.596078i	$0.203275\pi$
$384$		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	$-0.305791\pi$
$389$	27.0435	−	4.28327i	1.37116	−	0.217171i	0.798190	+	0.602405i	$0.205791\pi$
$390$		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	−0.603082	−	0.797679i	$-0.706061\pi$
$401$	3.89680	−	3.89680i	0.194597	−	0.194597i	0.797679	+	0.603082i	$0.206061\pi$
$402$		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	0.166274	−	0.986080i	$-0.446826\pi$
$419$	−16.7810	−	16.7810i	−0.819805	−	0.819805i	−0.986080	+	0.166274i	$0.946826\pi$
$420$		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	$0.0159206\pi$
$431$	1.33556	+	8.43239i	0.0643316	+	0.406174i	−0.934418	+	0.356179i	$0.884079\pi$
$432$		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	0.994543	−	0.104324i	$-0.0332678\pi$
$443$	31.4603	+	16.0298i	1.49472	+	0.761599i	0.500178	+	0.865922i	$0.333268\pi$
$444$		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	$-0.293210\pi$
$449$	19.7941	+	3.13507i	0.934139	+	0.147953i	0.329232	+	0.944249i	$0.393210\pi$
$450$		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	−0.811158	−	0.584827i	$-0.801162\pi$
$461$	−24.1257	+	7.83891i	−1.12365	+	0.365095i	−0.312488	+	0.949922i	$0.601162\pi$
$462$		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	−0.615595	−	0.788063i	$-0.711084\pi$
$467$	7.00444	−	9.64078i	0.324127	−	0.446122i	0.939722	+	0.341941i	$0.111084\pi$
$468$		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	$-0.590866\pi$
$479$	15.3463	−	25.0429i	0.701190	−	1.14424i	0.982794	−	0.184707i	$-0.0591335\pi$
$480$		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	$-0.747164\pi$
$491$	−31.0564			−1.40156			−0.700778	+	0.713379i	$0.747164\pi$
$492$		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	0.488058	−	0.872811i	$-0.337705\pi$
$503$	−10.1004	−	11.8261i	−0.450356	−	0.527300i	−0.938415	+	0.345512i	$0.887705\pi$
$504$		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	$-0.562225\pi$
$509$	−12.1727	−	0.958015i	−0.539547	−	0.0424633i	−0.345305	+	0.938490i	$0.612225\pi$
$510$		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	$-0.490577\pi$
$521$	4.91203	−	0.386585i	0.215200	−	0.0169366i	0.185601	+	0.982625i	$0.440577\pi$
$522$		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	$0.182787\pi$
$557$	−1.76153	+	22.3823i	−0.0746383	+	0.948369i	−0.914242	+	0.405169i	$0.867213\pi$
$558$		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	$0.578359\pi$
$563$	−29.4158	+	25.1234i	−1.23973	+	1.05883i	−0.996034	+	0.0889741i	$0.971641\pi$
$564$		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	$-0.0951223\pi$
$569$	3.71557	+	7.29221i	0.155765	+	0.305705i	−0.799915	+	0.600113i	$0.795122\pi$
$570$		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	−0.272664	−	0.962109i	$-0.587905\pi$
$587$	−30.3747	−	18.6136i	−1.25370	−	0.768266i	−0.981032	+	0.193843i	$0.937905\pi$
$588$		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	$-0.527918\pi$
$593$	18.5125	−	11.3445i	0.760218	−	0.465862i	0.847814	+	0.530294i	$0.177918\pi$
$594$		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	$-0.0672446\pi$
$599$	26.4445	+	19.2130i	1.08049	+	0.785023i	0.102723	+	0.994710i	$0.467245\pi$
$600$		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	−0.999412	−	0.0342904i	$-0.989083\pi$
$617$	−0.951809	+	6.00948i	−0.0383184	+	0.241933i	0.961094	+	0.276223i	$0.0890829\pi$
$618$		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	0.141496	−	0.989939i	$-0.454809\pi$
$641$	−20.6119	−	17.6042i	−0.814120	−	0.695324i	−0.955616	+	0.294614i	$0.904809\pi$
$642$		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	−0.568919	−	0.822394i	$-0.692638\pi$
$647$	6.44743	−	6.44743i	0.253475	−	0.253475i	0.822394	+	0.568919i	$0.192638\pi$
$648$		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	$-0.919327\pi$
$653$	−37.6990	+	15.6154i	−1.47527	+	0.611078i	−0.507219	+	0.861817i	$0.669327\pi$
$654$		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	$-0.138580\pi$
$659$	−0.837963	−	2.02302i	−0.0326424	−	0.0788058i	−0.939360	+	0.342932i	$0.888580\pi$
$660$		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	$-0.791368\pi$
$677$	−5.91025	−	37.3159i	−0.227149	−	1.43416i	0.565632	−	0.824658i	$-0.308632\pi$
$678$		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	$-0.400743\pi$
$683$	−3.90119	−	1.61592i	−0.149275	−	0.0618316i	−0.456070	+	0.889944i	$0.650743\pi$
$684$		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	−0.994040	−	0.109016i	$-0.965230\pi$
$701$	−3.32985	+	10.2482i	−0.125767	+	0.387071i	0.868273	+	0.496086i	$0.165230\pi$
$702$		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	$-0.877553\pi$
$719$	−22.5364	−	36.7761i	−0.840466	−	1.37152i	0.0864533	−	0.996256i	$-0.472447\pi$
$720$		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	0.0168313	−	0.999858i	$-0.494642\pi$
$743$	22.7775	−	11.6057i	0.835627	−	0.425773i	0.818796	+	0.574085i	$0.194642\pi$
$744$		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	−0.994423	−	0.105463i	$-0.966368\pi$
$761$	−33.1425	+	24.0795i	−1.20142	+	0.872880i	−0.206992	+	0.978343i	$0.566368\pi$
$762$		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	−0.405466	−	0.914110i	$-0.632891\pi$
$773$	−9.77944	+	2.34784i	−0.351742	+	0.0844458i	0.0537243	+	0.998556i	$0.482891\pi$
$774$		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	$-0.875237\pi$
$797$	−28.2843	−	38.9300i	−1.00188	−	1.37897i	−0.0777167	−	0.996975i	$-0.524763\pi$
$798$		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	$-0.796634\pi$
$809$	−9.65261	+	8.24411i	−0.339368	+	0.289848i	0.463388	+	0.886156i	$0.346634\pi$
$810$		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	$0.151173\pi$
$821$			26.2045i			0.914543i	−0.889327	+	0.457271i	$0.848827\pi$
$822$		0			0
$823$	46.9062	−	19.4292i	1.63505	−	0.677259i	0.639265	−	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	$0.224106\pi$
$827$	−6.06196	+	25.2499i	−0.210795	+	0.878024i	−0.973022	+	0.230714i	$0.925894\pi$
$828$		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	$-0.318889\pi$
$839$	44.4330	−	27.2286i	1.53400	−	0.940035i	0.995227	−	0.0975821i	$-0.0311109\pi$
$840$		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	0.429802	−	0.902923i	$-0.358583\pi$
$857$	7.22479	+	2.34748i	0.246794	+	0.0801882i	−0.183008	+	0.983111i	$0.558583\pi$
$858$		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	$-0.606672\pi$
$863$	8.10008	−	51.1419i	0.275730	−	1.74089i	0.604614	−	0.796519i	$-0.293328\pi$
$864$		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	0.257070	−	0.966393i	$-0.417243\pi$
$881$	23.7510	−	3.76179i	0.800191	−	0.126738i	0.543120	+	0.839655i	$0.317243\pi$
$882$		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	0.944438	−	0.328689i	$-0.106607\pi$
$887$	22.8593	+	19.5237i	0.767539	+	0.655540i	−0.176899	+	0.984229i	$0.556607\pi$
$888$		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	$0.0439513\pi$
$911$	34.0498	+	34.0498i	1.12812	+	1.12812i	0.137639	+	0.990482i	$0.456049\pi$
$912$		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	−0.395848	−	0.918316i	$-0.629549\pi$
$929$	−40.3885	−	16.7295i	−1.32510	−	0.548875i	−0.929254	+	0.369440i	$0.879549\pi$
$930$		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	−0.0757098	−	0.997130i	$-0.524122\pi$
$941$	−13.9834	−	2.21475i	−0.455844	−	0.0721986i	−0.380134	+	0.924931i	$0.624122\pi$
$942$		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	$-0.863039\pi$
$947$	2.20348	−	6.78161i	0.0716035	−	0.220373i	0.980454	+	0.196750i	$0.0630386\pi$
$948$		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	$-0.420805\pi$
$953$	31.3380	−	10.1823i	1.01514	−	0.329838i	0.768899	+	0.639370i	$0.220805\pi$
$954$		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	−0.978822	−	0.204711i	$-0.934374\pi$
$971$	−10.9701	+	17.9016i	−0.352047	+	0.574489i	0.626775	+	0.779200i	$0.284374\pi$
$972$		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	$-0.448505\pi$
$977$	−4.48456	−	1.07665i	−0.143474	−	0.0344450i	−0.304546	+	0.952498i	$0.598505\pi$
$978$		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	$-0.364852\pi$
$983$	25.8309			0.823877			0.411938	+	0.911212i	$0.364852\pi$
$984$		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.a.179.3	✓	48
3.2	odd	2		738.2.ba.b.179.1	yes	48
41.11	odd	40		738.2.ba.b.503.1	yes	48
123.11	even	40	inner	738.2.ba.a.503.3	yes	48

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

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more