LMFDB - Embedded newform 891.2.bb.a.413.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(8,891)] 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("891.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(90)) chi = DirichletCharacter(H, H._module([5, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.bb (of order $90$, degree $24$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$34$ over $\Q(\zeta_{90})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			413.18
Character	$\chi$	$=$	891.413
Dual form			891.2.bb.a.233.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.302038 - 0.0424487i) q^{2} +(-1.83310 + 0.525632i) q^{4} +(-3.15888 + 1.27627i) q^{5} +(1.84008 + 1.24115i) q^{7} +(-1.08863 + 0.484688i) q^{8} +(-0.899926 + 0.519573i) q^{10} +(1.31416 + 3.04516i) q^{11} +(-1.20476 - 2.26582i) q^{13} +(0.608459 + 0.296765i) q^{14} +(2.92617 - 1.82848i) q^{16} +(-2.81623 + 0.598608i) q^{17} +(-2.67981 - 6.01896i) q^{19} +(5.11969 - 3.99994i) q^{20} +(0.526190 + 0.863968i) q^{22} +(-0.985887 + 2.70870i) q^{23} +(4.75296 - 4.58988i) q^{25} +(-0.460065 - 0.633225i) q^{26} +(-4.02544 - 1.30794i) q^{28} +(-1.94578 - 3.98943i) q^{29} +(0.190149 - 5.44515i) q^{31} +(2.63191 - 2.20844i) q^{32} +(-0.825198 + 0.300348i) q^{34} +(-7.39664 - 1.57220i) q^{35} +(0.930097 + 0.414106i) q^{37} +(-1.06490 - 1.70420i) q^{38} +(2.82025 - 2.92045i) q^{40} +(2.66661 - 5.46737i) q^{41} +(-5.75703 + 6.86096i) q^{43} +(-4.00962 - 4.89130i) q^{44} +(-0.182795 + 0.859981i) q^{46} +(1.46895 - 5.12285i) q^{47} +(-0.776804 - 1.92266i) q^{49} +(1.24074 - 1.58808i) q^{50} +(3.39944 + 3.52022i) q^{52} +(-1.93503 + 0.628729i) q^{53} +(-8.03773 - 7.94206i) q^{55} +(-2.60473 - 0.459284i) q^{56} +(-0.757044 - 1.12236i) q^{58} +(-13.9361 - 3.47466i) q^{59} +(6.83291 - 0.238610i) q^{61} +(-0.173707 - 1.65271i) q^{62} +(-3.91645 + 4.34966i) q^{64} +(6.69750 + 5.61987i) q^{65} +(-1.83491 - 10.4063i) q^{67} +(4.84778 - 2.57761i) q^{68} +(-2.30080 - 0.160888i) q^{70} +(-0.919525 - 4.32602i) q^{71} +(8.57160 - 0.900912i) q^{73} +(0.298503 + 0.0855943i) q^{74} +(8.07612 + 9.62475i) q^{76} +(-1.36133 + 7.23440i) q^{77} +(1.14946 + 8.17884i) q^{79} +(-6.90981 + 9.51053i) q^{80} +(0.573336 - 1.76455i) q^{82} +(-2.96787 - 1.57805i) q^{83} +(8.13215 - 5.48521i) q^{85} +(-1.44760 + 2.31665i) q^{86} +(-2.90658 - 2.67808i) q^{88} +(5.11538 + 2.95336i) q^{89} +(0.595372 - 5.66459i) q^{91} +(0.383446 - 5.48353i) q^{92} +(0.226222 - 1.60965i) q^{94} +(16.1470 + 15.5930i) q^{95} +(-6.84359 + 16.9385i) q^{97} +(-0.316238 - 0.547741i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) $ 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	0.302038	−	0.0424487i	0.213573	−	0.0300157i	−0.0315750	−	0.999501i	$-0.510052\pi$
$2$	0.302038	−	0.0424487i	0.213573	−	0.0300157i	0.245148	+	0.969486i	$0.421163\pi$
$3$		0			0
$3$		0			0
$4$	−1.83310	+	0.525632i	−0.916549	+	0.262816i
$5$	−3.15888	+	1.27627i	−1.41269	+	0.570766i	−0.949013	−	0.315236i	$-0.897916\pi$
$5$	−3.15888	+	1.27627i	−1.41269	+	0.570766i	−0.463681	+	0.886002i	$0.653472\pi$
$6$		0			0
$7$	1.84008	+	1.24115i	0.695485	+	0.469111i	0.855365	−	0.518026i	$-0.173333\pi$
$7$	1.84008	+	1.24115i	0.695485	+	0.469111i	−0.159880	+	0.987136i	$0.551111\pi$
$8$	−1.08863	+	0.484688i	−0.384888	+	0.171363i
$9$		0			0
$10$	−0.899926	+	0.519573i	−0.284582	+	0.164303i
$11$	1.31416	+	3.04516i	0.396235	+	0.918149i
$11$	1.31416	+	3.04516i	0.396235	+	0.918149i
$12$		0			0
$13$	−1.20476	−	2.26582i	−0.334140	−	0.628427i	0.658076	−	0.752951i	$-0.271371\pi$
$13$	−1.20476	−	2.26582i	−0.334140	−	0.628427i	−0.992217	+	0.124525i	$0.960259\pi$
$14$	0.608459	+	0.296765i	0.162618	+	0.0793139i
$15$		0			0
$16$	2.92617	−	1.82848i	0.731544	−	0.457119i
$17$	−2.81623	+	0.598608i	−0.683036	+	0.145184i	−0.536345	−	0.843999i	$-0.680196\pi$
$17$	−2.81623	+	0.598608i	−0.683036	+	0.145184i	−0.146691	+	0.989182i	$0.546862\pi$
$18$		0			0
$19$	−2.67981	−	6.01896i	−0.614792	−	1.38084i	−0.905629	−	0.424072i	$-0.860600\pi$
$19$	−2.67981	−	6.01896i	−0.614792	−	1.38084i	0.290837	−	0.956773i	$-0.406066\pi$
$20$	5.11969	−	3.99994i	1.14480	−	0.894414i
$21$		0			0
$22$	0.526190	+	0.863968i	0.112184	+	0.184199i
$23$	−0.985887	+	2.70870i	−0.205572	+	0.564804i	−0.999040	−	0.0438080i	$-0.986051\pi$
$23$	−0.985887	+	2.70870i	−0.205572	+	0.564804i	0.793468	+	0.608612i	$0.208273\pi$
$24$		0			0
$25$	4.75296	−	4.58988i	0.950593	−	0.917977i
$26$	−0.460065	−	0.633225i	−0.0902261	−	0.124186i
$27$		0			0
$28$	−4.02544	−	1.30794i	−0.760736	−	0.247178i
$29$	−1.94578	−	3.98943i	−0.361321	−	0.740819i	0.638258	−	0.769823i	$-0.279655\pi$
$29$	−1.94578	−	3.98943i	−0.361321	−	0.740819i	−0.999579	+	0.0290039i	$0.990766\pi$
$30$		0			0
$31$	0.190149	−	5.44515i	0.0341517	−	0.977978i	−0.854516	−	0.519426i	$-0.826146\pi$
$31$	0.190149	−	5.44515i	0.0341517	−	0.977978i	0.888667	−	0.458552i	$-0.151632\pi$
$32$	2.63191	−	2.20844i	0.465261	−	0.390400i
$33$		0			0
$34$	−0.825198	+	0.300348i	−0.141520	+	0.0515092i
$35$	−7.39664	−	1.57220i	−1.25026	−	0.265751i
$36$		0			0
$37$	0.930097	+	0.414106i	0.152907	+	0.0680786i	0.481763	−	0.876301i	$-0.339997\pi$
$37$	0.930097	+	0.414106i	0.152907	+	0.0680786i	−0.328856	+	0.944380i	$0.606663\pi$
$38$	−1.06490	−	1.70420i	−0.172750	−	0.276458i
$39$		0			0
$40$	2.82025	−	2.92045i	0.445921	−	0.461764i
$41$	2.66661	−	5.46737i	0.416455	−	0.853859i	−0.582697	−	0.812689i	$-0.698003\pi$
$41$	2.66661	−	5.46737i	0.416455	−	0.853859i	0.999152	−	0.0411698i	$-0.0131084\pi$
$42$		0			0
$43$	−5.75703	+	6.86096i	−0.877939	+	1.04629i	0.120624	+	0.992698i	$0.461510\pi$
$43$	−5.75703	+	6.86096i	−0.877939	+	1.04629i	−0.998563	+	0.0535888i	$0.982934\pi$
$44$	−4.00962	−	4.89130i	−0.604473	−	0.737392i
$45$		0			0
$46$	−0.182795	+	0.859981i	−0.0269516	+	0.126797i
$47$	1.46895	−	5.12285i	0.214269	−	0.747245i	−0.778546	−	0.627587i	$-0.784043\pi$
$47$	1.46895	−	5.12285i	0.214269	−	0.747245i	0.992815	−	0.119657i	$-0.0381796\pi$
$48$		0			0
$49$	−0.776804	−	1.92266i	−0.110972	−	0.274665i
$50$	1.24074	−	1.58808i	0.175467	−	0.224588i
$51$		0			0
$52$	3.39944	+	3.52022i	0.471417	+	0.488166i
$53$	−1.93503	+	0.628729i	−0.265797	+	0.0863625i	−0.438883	−	0.898544i	$-0.644626\pi$
$53$	−1.93503	+	0.628729i	−0.265797	+	0.0863625i	0.173087	+	0.984907i	$0.444626\pi$
$54$		0			0
$55$	−8.03773	−	7.94206i	−1.08381	−	1.07091i
$56$	−2.60473	−	0.459284i	−0.348072	−	0.0613745i
$57$		0			0
$58$	−0.757044	−	1.12236i	−0.0994048	−	0.147374i
$59$	−13.9361	−	3.47466i	−1.81433	−	0.452363i	−0.821325	−	0.570460i	$-0.806765\pi$
$59$	−13.9361	−	3.47466i	−1.81433	−	0.452363i	−0.993002	+	0.118097i	$0.962321\pi$
$60$		0			0
$61$	6.83291	−	0.238610i	0.874865	−	0.0305509i	0.406053	−	0.913849i	$-0.366905\pi$
$61$	6.83291	−	0.238610i	0.874865	−	0.0305509i	0.468811	+	0.883298i	$0.344682\pi$
$62$	−0.173707	−	1.65271i	−0.0220608	−	0.209895i
$63$		0			0
$64$	−3.91645	+	4.34966i	−0.489557	+	0.543708i
$65$	6.69750	+	5.61987i	0.830723	+	0.697059i
$66$		0			0
$67$	−1.83491	−	10.4063i	−0.224170	−	1.27133i	−0.864265	−	0.503037i	$-0.832216\pi$
$67$	−1.83491	−	10.4063i	−0.224170	−	1.27133i	0.640095	−	0.768296i	$-0.278895\pi$
$68$	4.84778	−	2.57761i	0.587880	−	0.312581i
$69$		0			0
$70$	−2.30080	−	0.160888i	−0.274999	−	0.0192298i
$71$	−0.919525	−	4.32602i	−0.109128	−	0.513405i	−0.998426	−	0.0560781i	$-0.982140\pi$
$71$	−0.919525	−	4.32602i	−0.109128	−	0.513405i	0.889299	−	0.457326i	$-0.151193\pi$
$72$		0			0
$73$	8.57160	−	0.900912i	1.00323	−	0.105444i	0.411357	−	0.911475i	$-0.365055\pi$
$73$	8.57160	−	0.900912i	1.00323	−	0.105444i	0.591874	+	0.806031i	$0.298388\pi$
$74$	0.298503	+	0.0855943i	0.0347002	+	0.00995014i
$75$		0			0
$76$	8.07612	+	9.62475i	0.926395	+	1.10403i
$77$	−1.36133	+	7.23440i	−0.155138	+	0.824437i
$78$		0			0
$79$	1.14946	+	8.17884i	0.129324	+	0.920192i	0.941556	+	0.336856i	$0.109364\pi$
$79$	1.14946	+	8.17884i	0.129324	+	0.920192i	−0.812232	+	0.583335i	$0.801747\pi$
$80$	−6.90981	+	9.51053i	−0.772540	+	1.06331i
$81$		0			0
$82$	0.573336	−	1.76455i	0.0633143	−	0.194862i
$83$	−2.96787	−	1.57805i	−0.325766	−	0.173213i	0.298531	−	0.954400i	$-0.403503\pi$
$83$	−2.96787	−	1.57805i	−0.325766	−	0.173213i	−0.624297	+	0.781187i	$0.714615\pi$
$84$		0			0
$85$	8.13215	−	5.48521i	0.882056	−	0.594954i
$86$	−1.44760	+	2.31665i	−0.156099	+	0.249811i
$87$		0			0
$88$	−2.90658	−	2.67808i	−0.309843	−	0.285484i
$89$	5.11538	+	2.95336i	0.542229	+	0.313056i	0.745982	−	0.665966i	$-0.231981\pi$
$89$	5.11538	+	2.95336i	0.542229	+	0.313056i	−0.203753	+	0.979022i	$0.565314\pi$
$90$		0			0
$91$	0.595372	−	5.66459i	0.0624120	−	0.593810i
$92$	0.383446	−	5.48353i	0.0399770	−	0.571698i
$93$		0			0
$94$	0.226222	−	1.60965i	0.0233330	−	0.166023i
$95$	16.1470	+	15.5930i	1.65665	+	1.59981i
$96$		0			0
$97$	−6.84359	+	16.9385i	−0.694862	+	1.71984i	−0.000724419		1.00000i	$0.500231\pi$
$97$	−6.84359	+	16.9385i	−0.694862	+	1.71984i	−0.694137	+	0.719843i	$0.744214\pi$
$98$	−0.316238	−	0.547741i	−0.0319449	−	0.0553302i
$99$		0			0
$100$	−6.30006	+	10.9120i	−0.630006	+	1.09120i
$101$	−11.7084	−	14.9861i	−1.16503	−	1.49118i	−0.837585	−	0.546307i	$-0.816033\pi$
$101$	−11.7084	−	14.9861i	−1.16503	−	1.49118i	−0.327449	−	0.944869i	$-0.606189\pi$
$102$		0			0
$103$	0.0186645	−	0.0748594i	0.00183907	−	0.00737611i	−0.969369	−	0.245608i	$-0.921012\pi$
$103$	0.0186645	−	0.0748594i	0.00183907	−	0.00737611i	0.971208	+	0.238232i	$0.0765679\pi$
$104$	2.40975	+	1.88271i	0.236296	+	0.184614i
$105$		0			0
$106$	−0.557763	+	0.272039i	−0.0541748	+	0.0264228i
$107$	7.68879	+	5.58623i	0.743304	+	0.540042i	0.893744	−	0.448577i	$-0.148069\pi$
$107$	7.68879	+	5.58623i	0.743304	+	0.540042i	−0.150440	+	0.988619i	$0.548069\pi$
$108$		0			0
$109$			9.97796i			0.955715i	0.878437	+	0.477858i	$0.158587\pi$
$109$			9.97796i			0.955715i	−0.878437	+	0.477858i	$0.841413\pi$
$110$	−2.76483	−	2.05761i	−0.263616	−	0.196186i
$111$		0			0
$112$	7.65381	+	0.267277i	0.723217	+	0.0252553i
$113$	0.678656	+	9.70524i	0.0638426	+	0.912992i	0.918908	+	0.394472i	$0.129072\pi$
$113$	0.678656	+	9.70524i	0.0638426	+	0.912992i	−0.855065	+	0.518520i	$0.826483\pi$
$114$		0			0
$115$	−0.342738	−	9.81473i	−0.0319605	−	0.915228i
$116$	5.66377	+	6.29026i	0.525868	+	0.584036i
$117$		0			0
$118$	−4.35673	−	0.457911i	−0.401070	−	0.0421541i
$119$	−5.92505	−	2.39388i	−0.543149	−	0.219446i
$120$		0			0
$121$	−7.54595	+	8.00366i	−0.685996	+	0.727606i
$122$	2.05367	−	0.362117i	0.185931	−	0.0327846i
$123$		0			0
$124$	2.51359	+	10.0814i	0.225727	+	0.905340i
$125$	−2.22743	+	5.00289i	−0.199227	+	0.447472i
$126$		0			0
$127$	−10.1294	+	9.12060i	−0.898843	+	0.809322i	−0.982324	−	0.187187i	$-0.940063\pi$
$127$	−10.1294	+	9.12060i	−0.898843	+	0.809322i	0.0834810	+	0.996509i	$0.473396\pi$
$128$	−4.84074	+	7.17669i	−0.427865	+	0.634336i
$129$		0			0
$130$	2.26146	+	1.41311i	0.198343	+	0.123938i
$131$	12.3014	+	4.47733i	1.07478	+	0.391186i	0.817960	−	0.575275i	$-0.195105\pi$
$131$	12.3014	+	4.47733i	1.07478	+	0.391186i	0.256815	+	0.966461i	$0.417327\pi$
$132$		0			0
$133$	2.53936	−	14.4014i	0.220190	−	1.24876i
$134$	−0.995947	−	3.06521i	−0.0860367	−	0.264794i
$135$		0			0
$136$	2.77569	−	2.01665i	0.238013	−	0.172927i
$137$	6.15858	−	11.5826i	0.526163	−	0.989568i	−0.468209	−	0.883618i	$-0.655101\pi$
$137$	6.15858	−	11.5826i	0.526163	−	0.989568i	0.994371	−	0.105950i	$-0.0337884\pi$
$138$		0			0
$139$	−1.11795	−	3.89874i	−0.0948230	−	0.330687i	0.899523	−	0.436873i	$-0.143914\pi$
$139$	−1.11795	−	3.89874i	−0.0948230	−	0.330687i	−0.994346	+	0.106186i	$0.966136\pi$
$140$	14.3852	−	1.00591i	1.21577	−	0.0850148i
$141$		0			0
$142$	−0.461365	−	1.26759i	−0.0387169	−	0.106374i
$143$	5.31654	−	6.64635i	0.444591	−	0.555795i
$144$		0			0
$145$	11.2381	+	10.1188i	0.933271	+	0.840321i
$146$	2.55071	−	0.635963i	0.211098	−	0.0526326i
$147$		0			0
$148$	−1.92263	−	0.270208i	−0.158039	−	0.0222109i
$149$	−13.6037	−	1.91187i	−1.11445	−	0.156626i	−0.442179	−	0.896927i	$-0.645794\pi$
$149$	−13.6037	−	1.91187i	−1.11445	−	0.156626i	−0.672276	+	0.740301i	$0.734683\pi$
$150$		0			0
$151$	−4.48939	+	1.11933i	−0.365341	+	0.0910898i	−0.420267	−	0.907401i	$-0.638063\pi$
$151$	−4.48939	+	1.11933i	−0.365341	+	0.0910898i	0.0549253	+	0.998490i	$0.482508\pi$
$152$	5.83464	+	5.25353i	0.473252	+	0.426118i
$153$		0			0
$154$	−0.104083	+	2.24285i	−0.00838722	+	0.180734i
$155$	6.34883	+	17.4433i	0.509950	+	1.40108i
$156$		0			0
$157$	8.91996	−	0.623744i	0.711890	−	0.0497802i	0.290780	−	0.956790i	$-0.406085\pi$
$157$	8.91996	−	0.623744i	0.711890	−	0.0497802i	0.421110	+	0.907010i	$0.361641\pi$
$158$	0.694362	+	2.42153i	0.0552405	+	0.192646i
$159$		0			0
$160$	−5.49534	+	10.3352i	−0.434445	+	0.817072i
$161$	−5.17602	+	3.76060i	−0.407927	+	0.296377i
$162$		0			0
$163$	−4.74287	−	14.5971i	−0.371490	−	1.14333i	−0.945816	−	0.324703i	$-0.894736\pi$
$163$	−4.74287	−	14.5971i	−0.371490	−	1.14333i	0.574326	−	0.818627i	$-0.305264\pi$
$164$	−2.01434	+	11.4239i	−0.157293	+	0.892055i
$165$		0			0
$166$	−0.963396	−	0.350647i	−0.0747740	−	0.0272155i
$167$	−8.01659	−	5.00932i	−0.620343	−	0.387633i	0.183032	−	0.983107i	$-0.441409\pi$
$167$	−8.01659	−	5.00932i	−0.620343	−	0.387633i	−0.803375	+	0.595474i	$0.796964\pi$
$168$		0			0
$169$	3.58699	−	5.31794i	0.275923	−	0.409072i
$170$	2.22338	−	2.00194i	0.170525	−	0.153542i
$171$		0			0
$172$	6.94686	−	15.6029i	0.529693	−	1.18971i
$173$	−3.84488	−	15.4210i	−0.292321	−	1.17244i	−0.919350	−	0.393440i	$-0.871285\pi$
$173$	−3.84488	−	15.4210i	−0.292321	−	1.17244i	0.627029	−	0.778996i	$-0.284271\pi$
$174$		0			0
$175$	14.4426	−	2.54661i	1.09176	−	0.192506i
$176$	9.41347	+	6.50774i	0.709567	+	0.490540i
$177$		0			0
$178$	1.67040	+	0.674887i	0.125202	+	0.0505849i
$179$	−13.2331	−	1.39086i	−0.989090	−	0.103958i	−0.403857	−	0.914822i	$-0.632331\pi$
$179$	−13.2331	−	1.39086i	−0.989090	−	0.103958i	−0.585234	+	0.810865i	$0.698997\pi$
$180$		0			0
$181$	−10.2776	−	11.4145i	−0.763931	−	0.848431i	0.228203	−	0.973614i	$-0.426715\pi$
$181$	−10.2776	−	11.4145i	−0.763931	−	0.848431i	−0.992134	+	0.125183i	$0.960048\pi$
$182$	−0.0606292	−	1.73619i	−0.00449414	−	0.128695i
$183$		0			0
$184$	−0.239612	−	3.42661i	−0.0176645	−	0.252613i
$185$	−3.46658	−	0.121056i	−0.254868	−	0.00890018i
$186$		0			0
$187$	−5.52384	−	7.78919i	−0.403943	−	0.569602i
$188$			10.1628i			0.741200i
$189$		0			0
$190$	5.53892	+	4.02426i	0.401836	+	0.291951i
$191$	3.39738	−	1.65701i	0.245826	−	0.119897i	−0.311340	−	0.950299i	$-0.600778\pi$
$191$	3.39738	−	1.65701i	0.245826	−	0.119897i	0.557166	+	0.830401i	$0.311889\pi$
$192$		0			0
$193$	−16.6747	−	13.0277i	−1.20027	−	0.937755i	−0.201146	−	0.979561i	$-0.564467\pi$
$193$	−16.6747	−	13.0277i	−1.20027	−	0.937755i	−0.999126	+	0.0418060i	$0.986689\pi$
$194$	−1.34801	+	5.40657i	−0.0967814	+	0.388169i
$195$		0			0
$196$	2.43457	+	3.11611i	0.173898	+	0.222579i
$197$	−5.44528	+	9.43151i	−0.387960	+	0.671967i	−0.992175	−	0.124855i	$-0.960154\pi$
$197$	−5.44528	+	9.43151i	−0.387960	+	0.671967i	0.604215	+	0.796822i	$0.293487\pi$
$198$		0			0
$199$	3.50306	+	6.06748i	0.248325	+	0.430112i	0.963061	−	0.269282i	$-0.0867865\pi$
$199$	3.50306	+	6.06748i	0.248325	+	0.430112i	−0.714736	+	0.699394i	$0.753453\pi$
$200$	−2.94954	+	7.30038i	−0.208564	+	0.516215i
$201$		0			0
$202$	−4.17254	−	4.02937i	−0.293579	−	0.283506i
$203$	1.37110	−	9.75587i	0.0962322	−	0.684728i
$204$		0			0
$205$	−1.44567	+	20.6741i	−0.100970	+	1.44394i
$206$	0.00245972	−	0.0234027i	0.000171377	−	0.00163054i
$207$		0			0
$208$	−7.66835	−	4.42732i	−0.531704	−	0.306980i
$209$	14.8070	−	16.0703i	1.02422	−	1.11161i
$210$		0			0
$211$	−10.4368	+	16.7024i	−0.718499	+	1.14984i	0.264171	+	0.964476i	$0.414902\pi$
$211$	−10.4368	+	16.7024i	−0.718499	+	1.14984i	−0.982670	+	0.185363i	$0.940654\pi$
$212$	3.21662	−	2.16964i	0.220918	−	0.149011i
$213$		0			0
$214$	2.55944	+	1.36088i	0.174959	+	0.0930276i
$215$	9.42933	−	29.0205i	0.643075	−	1.97918i
$216$		0			0
$217$	7.10814	−	9.78351i	0.482532	−	0.664148i
$218$	0.423551	+	3.01372i	0.0286865	+	0.204115i
$219$		0			0
$220$	18.9085	+	10.3337i	1.27481	+	0.696697i
$221$	4.74922	+	5.65991i	0.319467	+	0.380726i
$222$		0			0
$223$	−22.7733	−	6.53013i	−1.52501	−	0.437290i	−0.594665	−	0.803973i	$-0.702715\pi$
$223$	−22.7733	−	6.53013i	−1.52501	−	0.437290i	−0.930346	+	0.366683i	$0.880493\pi$
$224$	7.58394	−	0.797104i	0.506723	−	0.0532587i
$225$		0			0
$226$	0.616954	+	2.90254i	0.0410392	+	0.193074i
$227$	14.9265	+	1.04376i	0.990704	+	0.0692768i	0.555901	−	0.831249i	$-0.312374\pi$
$227$	14.9265	+	1.04376i	0.990704	+	0.0692768i	0.434803	+	0.900526i	$0.356818\pi$
$228$		0			0
$229$	−5.79529	+	3.08141i	−0.382963	+	0.203625i	−0.649780	−	0.760122i	$-0.725139\pi$
$229$	−5.79529	+	3.08141i	−0.382963	+	0.203625i	0.266817	+	0.963747i	$0.414028\pi$
$230$	−0.520142	−	2.94987i	−0.0342972	−	0.194509i
$231$		0			0
$232$	4.05185	+	3.39991i	0.266017	+	0.223215i
$233$	−0.605101	+	0.672033i	−0.0396415	+	0.0440264i	−0.762639	−	0.646824i	$-0.776097\pi$
$233$	−0.605101	+	0.672033i	−0.0396415	+	0.0440264i	0.722998	+	0.690850i	$0.242764\pi$
$234$		0			0
$235$	1.89789	+	18.0573i	0.123805	+	1.17793i
$236$	27.3727	−	0.955874i	1.78181	−	0.0622221i
$237$		0			0
$238$	−1.89121	−	0.471531i	−0.122589	−	0.0305648i
$239$	−12.7654	−	18.9256i	−0.825728	−	1.22419i	−0.972008	−	0.234949i	$-0.924508\pi$
$239$	−12.7654	−	18.9256i	−0.825728	−	1.22419i	0.146279	−	0.989243i	$-0.453270\pi$
$240$		0			0
$241$	12.0594	+	2.12641i	0.776817	+	0.136974i	0.547981	−	0.836491i	$-0.315397\pi$
$241$	12.0594	+	2.12641i	0.776817	+	0.136974i	0.228837	+	0.973465i	$0.426508\pi$
$242$	−1.93942	+	2.73773i	−0.124671	+	0.175988i
$243$		0			0
$244$	−12.4000	+	4.02900i	−0.793827	+	0.257930i
$245$	4.90766	+	5.08203i	0.313539	+	0.324679i
$246$		0			0
$247$	−10.4094	+	13.3234i	−0.662333	+	0.847747i
$248$	2.43220	+	6.01990i	0.154445	+	0.382264i
$249$		0			0
$250$	−0.460402	+	1.60561i	−0.0291184	+	0.101548i
$251$	−3.35914	+	15.8035i	−0.212027	+	0.997509i	0.735424	+	0.677607i	$0.236983\pi$
$251$	−3.35914	+	15.8035i	−0.212027	+	0.997509i	−0.947451	+	0.319901i	$0.896350\pi$
$252$		0			0
$253$	−9.54404	+	0.557495i	−0.600029	+	0.0350494i
$254$	−2.67232	+	3.18475i	−0.167676	+	0.199829i
$255$		0			0
$256$	3.97417	−	8.14825i	0.248385	−	0.509266i
$257$	−3.19806	+	3.31169i	−0.199490	+	0.206578i	−0.811630	−	0.584171i	$-0.801420\pi$
$257$	−3.19806	+	3.31169i	−0.199490	+	0.206578i	0.612141	+	0.790749i	$0.290309\pi$
$258$		0			0
$259$	1.19749	+	1.91638i	0.0744081	+	0.119078i
$260$	−15.2312	−	6.78135i	−0.944597	−	0.420562i
$261$		0			0
$262$	3.90554	+	0.830147i	0.241285	+	0.0512867i
$263$	−19.6449	+	7.15016i	−1.21136	+	0.440898i	−0.867174	−	0.498005i	$-0.834066\pi$
$263$	−19.6449	+	7.15016i	−1.21136	+	0.440898i	−0.344182	+	0.938903i	$0.611844\pi$
$264$		0			0
$265$	5.31010	−	4.45570i	0.326197	−	0.273711i
$266$	0.155662	−	4.45757i	0.00954423	−	0.273311i
$267$		0			0
$268$	8.83347	+	18.1113i	0.539590	+	1.10632i
$269$	−22.4817	−	7.30475i	−1.37073	−	0.445379i	−0.471122	−	0.882068i	$-0.656151\pi$
$269$	−22.4817	−	7.30475i	−1.37073	−	0.445379i	−0.899612	+	0.436689i	$0.856151\pi$
$270$		0			0
$271$	17.8113	+	24.5151i	1.08196	+	1.48919i	0.857347	+	0.514739i	$0.172111\pi$
$271$	17.8113	+	24.5151i	1.08196	+	1.48919i	0.224611	+	0.974449i	$0.427889\pi$
$272$	−7.14624	+	6.90104i	−0.433304	+	0.418437i
$273$		0			0
$274$	1.36846	−	3.75981i	0.0826716	−	0.227138i
$275$	20.2231	+	8.44166i	1.21950	+	0.509052i
$276$		0			0
$277$	−5.23126	+	4.08711i	−0.314316	+	0.245570i	−0.760451	−	0.649395i	$-0.775022\pi$
$277$	−5.23126	+	4.08711i	−0.314316	+	0.245570i	0.446135	+	0.894965i	$0.352800\pi$
$278$	−0.503159	−	1.13011i	−0.0301775	−	0.0677797i
$279$		0			0
$280$	8.81421	−	1.87352i	0.526750	−	0.111964i
$281$	−8.19749	+	5.12236i	−0.489021	+	0.305574i	−0.751926	−	0.659247i	$-0.770875\pi$
$281$	−8.19749	+	5.12236i	−0.489021	+	0.305574i	0.262905	+	0.964822i	$0.415319\pi$
$282$		0			0
$283$	17.8769	+	8.71915i	1.06267	+	0.518299i	0.884904	−	0.465773i	$-0.154224\pi$
$283$	17.8769	+	8.71915i	1.06267	+	0.518299i	0.177767	+	0.984073i	$0.443113\pi$
$284$	3.95948	+	7.44670i	0.234952	+	0.441880i
$285$		0			0
$286$	1.32367	−	2.23313i	0.0782702	−	0.132048i
$287$	11.6926	−	6.75073i	0.690192	−	0.398483i
$288$		0			0
$289$	−7.95745	+	3.54288i	−0.468085	+	0.208405i
$290$	3.82385	+	2.57922i	0.224544	+	0.151457i
$291$		0			0
$292$	−15.2390	+	6.15697i	−0.891797	+	0.360310i
$293$	−7.32992	+	2.10182i	−0.428219	+	0.122790i	−0.482822	−	0.875718i	$-0.660388\pi$
$293$	−7.32992	+	2.10182i	−0.428219	+	0.122790i	0.0546036	+	0.998508i	$0.482610\pi$
$294$		0			0
$295$	48.4571	−	6.81021i	2.82128	−	0.396506i
$296$	−1.21324			−0.0705182
$297$		0			0
$298$	−4.18998			−0.242719
$299$	7.32520	−	1.02949i	0.423627	−	0.0595370i
$300$		0			0
$301$	−19.1089	+	5.47938i	−1.10142	+	0.315826i
$302$	−1.30845	+	0.528649i	−0.0752930	+	0.0304203i
$303$		0			0
$304$	−18.8471	−	12.7126i	−1.08096	−	0.729115i
$305$	−21.2798	+	9.47439i	−1.21848	+	0.542502i
$306$		0			0
$307$	−23.5248	+	13.5821i	−1.34263	+	0.775169i	−0.987193	−	0.159531i	$-0.949002\pi$
$307$	−23.5248	+	13.5821i	−1.34263	+	0.775169i	−0.355439	+	0.934700i	$0.615669\pi$
$308$	−1.30719	−	13.9769i	−0.0744838	−	0.796410i
$309$		0			0
$310$	2.65803	+	4.99903i	0.150966	+	0.283926i
$311$	3.64103	+	1.77585i	0.206464	+	0.100699i	0.538702	−	0.842496i	$-0.318915\pi$
$311$	3.64103	+	1.77585i	0.206464	+	0.100699i	−0.332238	+	0.943195i	$0.607804\pi$
$312$		0			0
$313$	15.7402	−	9.83557i	0.889689	−	0.555940i	−0.00631747	−	0.999980i	$-0.502011\pi$
$313$	15.7402	−	9.83557i	0.889689	−	0.555940i	0.896007	+	0.444041i	$0.146455\pi$
$314$	2.66769	−	0.567035i	0.150546	−	0.0319996i
$315$		0			0
$316$	−6.40614	−	14.3884i	−0.360374	−	0.809412i
$317$	−8.35593	+	6.52837i	−0.469316	+	0.366670i	−0.822389	−	0.568926i	$-0.807359\pi$
$317$	−8.35593	+	6.52837i	−0.469316	+	0.366670i	0.353073	+	0.935596i	$0.385137\pi$
$318$		0			0
$319$	9.59138	−	11.1680i	0.537014	−	0.625285i
$320$	6.82026	−	18.7385i	0.381264	−	1.04751i
$321$		0			0
$322$	−1.40372	+	1.35556i	−0.0782263	+	0.0755423i
$323$	11.1500	+	15.3466i	0.620401	+	0.853909i
$324$		0			0
$325$	−16.1261	−	5.23967i	−0.894513	−	0.290645i
$326$	−2.05215	−	4.20754i	−0.113658	−	0.233034i
$327$		0			0
$328$	−0.252980	+	7.24440i	−0.0139685	+	0.400005i
$329$	9.06122	−	7.60327i	0.499561	−	0.419182i
$330$		0			0
$331$	26.0174	−	9.46955i	1.43004	−	0.520494i	0.493101	−	0.869972i	$-0.335863\pi$
$331$	26.0174	−	9.46955i	1.43004	−	0.520494i	0.936944	+	0.349479i	$0.113641\pi$
$332$	6.26987	+	1.33270i	0.344104	+	0.0731415i
$333$		0			0
$334$	−2.63395	−	1.17271i	−0.144124	−	0.0641679i
$335$	19.0775	+	30.5304i	1.04232	+	1.66806i
$336$		0			0
$337$	−2.94091	+	3.04540i	−0.160202	+	0.165894i	−0.794642	−	0.607078i	$-0.792342\pi$
$337$	−2.94091	+	3.04540i	−0.160202	+	0.165894i	0.634441	+	0.772971i	$0.281230\pi$
$338$	0.857669	−	1.75848i	0.0466510	−	0.0956488i
$339$		0			0
$340$	−12.0238	+	14.3294i	−0.652084	+	0.777123i
$341$	16.8312	−	6.57678i	0.911462	−	0.356153i
$342$		0			0
$343$	4.18720	−	19.6992i	0.226087	−	1.06366i
$344$	2.94183	−	10.2594i	0.158613	−	0.553149i
$345$		0			0
$346$	−1.81590	−	4.49451i	−0.0976234	−	0.241626i
$347$	10.4107	−	13.3251i	0.558878	−	0.715331i	−0.422726	−	0.906257i	$-0.638927\pi$
$347$	10.4107	−	13.3251i	0.558878	−	0.715331i	0.981604	+	0.190926i	$0.0611491\pi$
$348$		0			0
$349$	7.52037	+	7.78757i	0.402556	+	0.416859i	0.889760	−	0.456429i	$-0.150872\pi$
$349$	7.52037	+	7.78757i	0.402556	+	0.416859i	−0.487203	+	0.873288i	$0.661983\pi$
$350$	4.25410	−	1.38224i	0.227391	−	0.0738840i
$351$		0			0
$352$	10.1838	+	5.11234i	0.542798	+	0.272489i
$353$	23.1039	+	4.07384i	1.22970	+	0.216829i	0.750495	−	0.660876i	$-0.229815\pi$
$353$	23.1039	+	4.07384i	1.22970	+	0.216829i	0.479202	+	0.877705i	$0.340926\pi$
$354$		0			0
$355$	8.42585	+	12.4918i	0.447198	+	0.662998i
$356$	−10.9294	−	2.72500i	−0.579256	−	0.144425i
$357$		0			0
$358$	−4.05595	+	0.141637i	−0.214363	+	0.00748574i
$359$	−3.48845	−	33.1903i	−0.184113	−	1.75172i	−0.563166	−	0.826344i	$-0.690417\pi$
$359$	−3.48845	−	33.1903i	−0.184113	−	1.75172i	0.379053	−	0.925375i	$-0.376250\pi$
$360$		0			0
$361$	−16.3330	+	18.1396i	−0.859632	+	0.954718i
$362$	−3.58876	−	3.01133i	−0.188621	−	0.158272i
$363$		0			0
$364$	1.88612	+	10.6967i	0.0988593	+	0.560659i
$365$	−25.9269	+	13.7856i	−1.35707	+	0.721569i
$366$		0			0
$367$	−23.8176	−	1.66549i	−1.24327	−	0.0869379i	−0.567078	−	0.823664i	$-0.691926\pi$
$367$	−23.8176	−	1.66549i	−1.24327	−	0.0869379i	−0.676191	+	0.736726i	$0.736371\pi$
$368$	2.06792	+	9.72881i	0.107798	+	0.507149i
$369$		0			0
$370$	−1.05218	+	0.110588i	−0.0547000	+	0.00574921i
$371$	−4.34095	−	1.24475i	−0.225371	−	0.0646241i
$372$		0			0
$373$	−16.5448	−	19.7173i	−0.856658	−	1.02092i	−0.999514	−	0.0311813i	$-0.990073\pi$
$373$	−16.5448	−	19.7173i	−0.856658	−	1.02092i	0.142856	−	0.989743i	$-0.454371\pi$
$374$	−1.99905	−	2.11815i	−0.103368	−	0.109527i
$375$		0			0
$376$	0.883842	+	6.28886i	0.0455806	+	0.324323i
$377$	−6.69516	+	9.21510i	−0.344818	+	0.474602i
$378$		0			0
$379$	4.42082	−	13.6059i	0.227082	−	0.698887i	−0.770991	−	0.636846i	$-0.780239\pi$
$379$	4.42082	−	13.6059i	0.227082	−	0.698887i	0.998074	−	0.0620417i	$-0.0197612\pi$
$380$	−37.7953	−	20.0961i	−1.93886	−	1.03091i
$381$		0			0
$382$	0.955799	−	0.644695i	0.0489029	−	0.0329855i
$383$	−1.79680	+	2.87547i	−0.0918120	+	0.146930i	−0.890766	−	0.454462i	$-0.849831\pi$
$383$	−1.79680	+	2.87547i	−0.0918120	+	0.146930i	0.798954	+	0.601392i	$0.205387\pi$
$384$		0			0
$385$	−4.93278	−	24.5901i	−0.251398	−	1.25323i
$386$	−5.58940	−	3.22704i	−0.284493	−	0.164252i
$387$		0			0
$388$	3.64156	−	34.6471i	0.184872	−	1.75894i
$389$	0.385280	−	5.50976i	0.0195345	−	0.279356i	−0.977970	−	0.208747i	$-0.933061\pi$
$389$	0.385280	−	5.50976i	0.0195345	−	0.279356i	0.997504	−	0.0706087i	$-0.0224942\pi$
$390$		0			0
$391$	1.15503	−	8.21849i	0.0584126	−	0.415627i
$392$	1.77754	+	1.71655i	0.0897792	+	0.0866988i
$393$		0			0
$394$	−1.24433	+	3.07982i	−0.0626883	+	0.155159i
$395$	−14.0694	−	24.3690i	−0.707910	−	1.22614i
$396$		0			0
$397$	4.99126	−	8.64512i	0.250504	−	0.433886i	−0.713160	−	0.701001i	$-0.752737\pi$
$397$	4.99126	−	8.64512i	0.250504	−	0.433886i	0.963665	+	0.267115i	$0.0860702\pi$
$398$	1.31561	+	1.68391i	0.0659457	+	0.0844067i
$399$		0			0
$400$	5.51551	−	22.1215i	0.275775	−	1.10607i
$401$	−5.00054	−	3.90685i	−0.249715	−	0.195099i	0.483027	−	0.875606i	$-0.339537\pi$
$401$	−5.00054	−	3.90685i	−0.249715	−	0.195099i	−0.732742	+	0.680507i	$0.761760\pi$
$402$		0			0
$403$	−12.5668	+	6.12926i	−0.625999	+	0.305320i
$404$	29.3399	+	21.3167i	1.45972	+	1.06055i
$405$		0			0
$406$		−	3.00485i		−	0.149128i
$407$	−0.0387184	+	3.37649i	−0.00191920	+	0.167367i
$408$		0			0
$409$	−17.0505	−	0.595415i	−0.843091	−	0.0294414i	−0.389903	−	0.920856i	$-0.627491\pi$
$409$	−17.0505	−	0.595415i	−0.843091	−	0.0294414i	−0.453188	+	0.891415i	$0.649714\pi$
$410$	0.440939	+	6.30572i	0.0217764	+	0.311417i
$411$		0			0
$412$	0.00513458	+	0.147035i	0.000252963	+	0.00724391i
$413$	−21.3310	−	23.6905i	−1.04963	−	1.16573i
$414$		0			0
$415$	11.3892	+	1.19705i	0.559072	+	0.0587609i
$416$	−8.17476	−	3.30282i	−0.400801	−	0.161934i
$417$		0			0
$418$	3.79010	−	5.48239i	0.185380	−	0.268152i
$419$	−31.6188	+	5.57525i	−1.54468	+	0.272369i	−0.880078	−	0.474828i	$-0.842510\pi$
$419$	−31.6188	+	5.57525i	−1.54468	+	0.272369i	−0.664602	+	0.747197i	$0.731399\pi$
$420$		0			0
$421$	−4.23366	−	16.9803i	−0.206336	−	0.827569i	−0.980810	−	0.194964i	$-0.937541\pi$
$421$	−4.23366	−	16.9803i	−0.206336	−	0.827569i	0.774474	−	0.632605i	$-0.218014\pi$
$422$	−2.44332	+	5.48778i	−0.118939	+	0.267141i
$423$		0			0
$424$	1.80179	−	1.62234i	0.0875025	−	0.0787876i
$425$	−10.6379	+	15.7713i	−0.516014	+	0.765022i
$426$		0			0
$427$	12.8693	+	8.04160i	0.622787	+	0.389160i
$428$	−17.0306	−	6.19864i	−0.823206	−	0.299622i
$429$		0			0
$430$	1.61613	−	9.16556i	0.0779369	−	0.442002i
$431$	7.74707	+	23.8430i	0.373163	+	1.14848i	0.944709	+	0.327909i	$0.106344\pi$
$431$	7.74707	+	23.8430i	0.373163	+	1.14848i	−0.571546	+	0.820570i	$0.693656\pi$
$432$		0			0
$433$	3.15629	−	2.29318i	0.151682	−	0.110203i	−0.509356	−	0.860556i	$-0.670116\pi$
$433$	3.15629	−	2.29318i	0.151682	−	0.110203i	0.661038	+	0.750353i	$0.270116\pi$
$434$	1.73163	−	3.25672i	0.0831209	−	0.156328i
$435$		0			0
$436$	−5.24474	−	18.2906i	−0.251178	−	0.875960i
$437$	18.9456	−	1.32480i	0.906290	−	0.0633739i
$438$		0			0
$439$	−10.3316	−	28.3859i	−0.493101	−	1.35478i	−0.897828	−	0.440346i	$-0.854856\pi$
$439$	−10.3316	−	28.3859i	−0.493101	−	1.35478i	0.404727	−	0.914437i	$-0.367366\pi$
$440$	12.5995	+	4.75015i	0.600658	+	0.226455i
$441$		0			0
$442$	1.67470	+	1.50791i	0.0796574	+	0.0717239i
$443$	−3.14116	+	0.783178i	−0.149241	+	0.0372099i	−0.315826	−	0.948817i	$-0.602282\pi$
$443$	−3.14116	+	0.783178i	−0.149241	+	0.0372099i	0.166585	+	0.986027i	$0.446726\pi$
$444$		0			0
$445$	−19.9282	−	2.80072i	−0.944686	−	0.132767i
$446$	−7.15559	−	1.00565i	−0.338827	−	0.0476190i
$447$		0			0
$448$	−12.6052	+	3.14282i	−0.595538	+	0.148484i
$449$	12.8614	+	11.5805i	0.606968	+	0.546516i	0.914275	−	0.405094i	$-0.132761\pi$
$449$	12.8614	+	11.5805i	0.606968	+	0.546516i	−0.307307	+	0.951610i	$0.599428\pi$
$450$		0			0
$451$	20.1533	+	0.935244i	0.948984	+	0.0440389i
$452$	−6.34543	−	17.4339i	−0.298464	−	0.820023i
$453$		0			0
$454$	4.55266	−	0.318353i	0.213667	−	0.0149411i
$455$	5.34884	+	18.6536i	0.250757	+	0.874495i
$456$		0			0
$457$	9.66995	−	18.1865i	0.452341	−	0.850730i	−0.547561	−	0.836766i	$-0.684444\pi$
$457$	9.66995	−	18.1865i	0.452341	−	0.850730i	0.999902	−	0.0139647i	$-0.00444525\pi$
$458$	−1.61959	+	1.17670i	−0.0756787	+	0.0549838i
$459$		0			0
$460$	5.78721	+	17.8112i	0.269830	+	0.830452i
$461$	−3.25208	+	18.4435i	−0.151465	+	0.858998i	0.810483	+	0.585763i	$0.199205\pi$
$461$	−3.25208	+	18.4435i	−0.151465	+	0.858998i	−0.961947	+	0.273235i	$0.911906\pi$
$462$		0			0
$463$	9.69243	+	3.52776i	0.450446	+	0.163949i	0.557274	−	0.830329i	$-0.311847\pi$
$463$	9.69243	+	3.52776i	0.450446	+	0.163949i	−0.106828	+	0.994277i	$0.534070\pi$
$464$	−12.9883	−	8.11597i	−0.602965	−	0.376774i
$465$		0			0
$466$	−0.154237	+	0.228665i	−0.00714488	+	0.0105927i
$467$	11.9759	−	10.7831i	0.554177	−	0.498983i	−0.343790	−	0.939047i	$-0.611711\pi$
$467$	11.9759	−	10.7831i	0.554177	−	0.498983i	0.897967	+	0.440063i	$0.145044\pi$
$468$		0			0
$469$	9.53940	−	21.4258i	0.440488	−	0.989353i
$470$	1.33974	+	5.37342i	0.0617977	+	0.247857i
$471$		0			0
$472$	16.8554	−	2.97205i	0.775831	−	0.136800i
$473$	−28.4584	−	8.51464i	−1.30852	−	0.391504i
$474$		0			0
$475$	−40.3634	−	16.3079i	−1.85200	−	0.748256i
$476$	12.1195	+	1.27381i	0.555497	+	0.0583850i
$477$		0			0
$478$	−4.65902	−	5.17436i	−0.213098	−	0.236670i
$479$	0.761724	+	21.8129i	0.0348041	+	0.996658i	0.883687	+	0.468077i	$0.155053\pi$
$479$	0.761724	+	21.8129i	0.0348041	+	0.996658i	−0.848883	+	0.528580i	$0.822725\pi$
$480$		0			0
$481$	−0.182253	−	2.60633i	−0.00831001	−	0.118839i
$482$	3.73267	+	0.130348i	0.170019	+	0.00593718i
$483$		0			0
$484$	9.62549	−	18.6379i	0.437522	−	0.847177i
$485$		−	62.2409i		−	2.82622i
$486$		0			0
$487$	26.2512	+	19.0726i	1.18956	+	0.864263i	0.993217	−	0.116274i	$-0.0370950\pi$
$487$	26.2512	+	19.0726i	1.18956	+	0.864263i	0.196338	+	0.980536i	$0.437095\pi$
$488$	−7.32284	+	3.57159i	−0.331489	+	0.161678i
$489$		0			0
$490$	1.69803	+	1.32664i	0.0767090	+	0.0599316i
$491$	5.15606	−	20.6798i	0.232690	−	0.933268i	−0.734376	−	0.678743i	$-0.762525\pi$
$491$	5.15606	−	20.6798i	0.232690	−	0.933268i	0.967066	−	0.254526i	$-0.0819193\pi$
$492$		0			0
$493$	7.86786	+	10.0704i	0.354351	+	0.453548i
$494$	−2.57847	+	4.46604i	−0.116011	+	0.200936i
$495$		0			0
$496$	−9.39992	−	16.2811i	−0.422069	−	0.731045i
$497$	3.67724	−	9.10150i	0.164947	−	0.408258i
$498$		0			0
$499$	17.3730	+	16.7769i	0.777723	+	0.751039i	0.973272	−	0.229655i	$-0.0737599\pi$
$499$	17.3730	+	16.7769i	0.777723	+	0.751039i	−0.195549	+	0.980694i	$0.562649\pi$
$500$	1.45342	−	10.3416i	0.0649988	−	0.462490i
$501$		0			0
$502$	−0.343750	+	4.91585i	−0.0153423	+	0.219405i
$503$	−0.267072	+	2.54102i	−0.0119082	+	0.113298i	−0.998861	−	0.0477095i	$-0.984808\pi$
$503$	−0.267072	+	2.54102i	−0.0119082	+	0.113298i	0.986953	+	0.161008i	$0.0514745\pi$
$504$		0			0
$505$	56.1120	+	32.3963i	2.49695	+	1.44161i
$506$	−2.85900	+	0.573516i	−0.127098	+	0.0254959i
$507$		0			0
$508$	13.7742	−	22.0433i	0.611131	−	0.978014i
$509$	−14.8880	+	10.0421i	−0.659898	+	0.445107i	−0.842947	−	0.537997i	$-0.819181\pi$
$509$	−14.8880	+	10.0421i	−0.659898	+	0.445107i	0.183048	+	0.983104i	$0.441403\pi$
$510$		0			0
$511$	16.8906	+	8.98089i	0.747196	+	0.397291i
$512$	6.20457	−	19.0957i	0.274206	−	0.843919i
$513$		0			0
$514$	−0.825360	+	1.13601i	−0.0364051	+	0.0501073i
$515$	0.0365818	+	0.260293i	0.00161199	+	0.0114699i
$516$		0			0
$517$	17.5303	−	2.25907i	0.770983	−	0.0993536i
$518$	0.443034	+	0.527987i	0.0194658	+	0.0231984i
$519$		0			0
$520$	−10.0150	−	2.87175i	−0.439185	−	0.125934i
$521$	9.19009	−	0.965917i	0.402625	−	0.0423176i	0.0989480	−	0.995093i	$-0.468452\pi$
$521$	9.19009	−	0.965917i	0.402625	−	0.0423176i	0.303677	+	0.952775i	$0.401786\pi$
$522$		0			0
$523$	2.80020	+	13.1739i	0.122444	+	0.576055i	0.996002	+	0.0893339i	$0.0284738\pi$
$523$	2.80020	+	13.1739i	0.122444	+	0.576055i	−0.873558	+	0.486721i	$0.838193\pi$
$524$	−24.9030	−	1.74139i	−1.08789	−	0.0760730i
$525$		0			0
$526$	−5.62999	+	2.99352i	−0.245479	+	0.130524i
$527$	2.72401	+	15.4486i	0.118660	+	0.672953i
$528$		0			0
$529$	11.2539	+	9.44316i	0.489301	+	0.410572i
$530$	1.41471	−	1.57120i	0.0614512	−	0.0682484i
$531$		0			0
$532$	2.91496	+	27.7340i	0.126380	+	1.20242i
$533$	−15.6007	+	0.544789i	−0.675742	+	0.0235974i
$534$		0			0
$535$	−31.4175	−	7.83327i	−1.35830	−	0.338662i
$536$	7.04135	+	10.4392i	0.304140	+	0.450906i
$537$		0			0
$538$	−7.10041	−	1.25199i	−0.306120	−	0.0539773i
$539$	4.83394	−	4.89217i	0.208213	−	0.210721i
$540$		0			0
$541$	−39.1248	+	12.7124i	−1.68211	+	0.546549i	−0.985318	−	0.170729i	$-0.945388\pi$
$541$	−39.1248	+	12.7124i	−1.68211	+	0.546549i	−0.696787	+	0.717278i	$0.745388\pi$
$542$	6.42032	+	6.64843i	0.275776	+	0.285575i
$543$		0			0
$544$	−6.09009	+	7.79496i	−0.261110	+	0.334206i
$545$	−12.7346	−	31.5192i	−0.545490	−	1.35013i
$546$		0			0
$547$	−0.119883	+	0.418083i	−0.00512585	+	0.0178760i	−0.963783	−	0.266687i	$-0.914071\pi$
$547$	−0.119883	+	0.418083i	−0.00512585	+	0.0178760i	0.958657	+	0.284563i	$0.0918486\pi$
$548$	−5.20109	+	24.4692i	−0.222179	+	1.04527i
$549$		0			0
$550$	6.46648	+	1.69126i	0.275731	+	0.0721156i
$551$	−18.7979	+	22.4025i	−0.800818	+	0.954378i
$552$		0			0
$553$	−8.03607	+	16.4764i	−0.341728	+	0.700647i
$554$	−1.40655	+	1.45652i	−0.0597584	+	0.0618817i
$555$		0			0
$556$	4.09861	+	6.55915i	0.173820	+	0.278170i
$557$	14.3252	+	6.37797i	0.606976	+	0.270243i	0.687124	−	0.726540i	$-0.258873\pi$
$557$	14.3252	+	6.37797i	0.606976	+	0.270243i	−0.0801483	+	0.996783i	$0.525539\pi$
$558$		0			0
$559$	22.4816	+	4.77861i	0.950870	+	0.202114i
$560$	−24.5186	+	8.92404i	−1.03610	+	0.377109i
$561$		0			0
$562$	−2.25851	+	1.89512i	−0.0952697	+	0.0799408i
$563$	−0.660953	+	18.9272i	−0.0278558	+	0.797687i	0.902427	+	0.430843i	$0.141784\pi$
$563$	−0.660953	+	18.9272i	−0.0278558	+	0.797687i	−0.930283	+	0.366844i	$0.880438\pi$
$564$		0			0
$565$	−14.5303	−	29.7915i	−0.611295	−	1.25334i
$566$	5.76962	+	1.87466i	0.242515	+	0.0787979i
$567$		0			0
$568$	3.09779	+	4.26374i	0.129980	+	0.178903i
$569$	6.75833	−	6.52644i	0.283324	−	0.273603i	−0.539393	−	0.842054i	$-0.681346\pi$
$569$	6.75833	−	6.52644i	0.283324	−	0.273603i	0.822717	+	0.568451i	$0.192457\pi$
$570$		0			0
$571$	1.45212	−	3.98968i	0.0607695	−	0.166963i	−0.905592	−	0.424149i	$-0.860573\pi$
$571$	1.45212	−	3.98968i	0.0607695	−	0.166963i	0.966362	+	0.257186i	$0.0827954\pi$
$572$	−6.25220	+	14.9780i	−0.261418	+	0.626260i
$573$		0			0
$574$	3.24505	−	2.53531i	0.135446	−	0.105822i
$575$	7.74675	+	17.3995i	0.323062	+	0.725608i
$576$		0			0
$577$	−0.0135074	+	0.00287108i	−0.000562319	+	0.000119525i	−0.208193	−	0.978088i	$-0.566758\pi$
$577$	−0.0135074	+	0.00287108i	−0.000562319	+	0.000119525i	0.207631	+	0.978207i	$0.433425\pi$
$578$	−2.25306	+	1.40787i	−0.0937150	+	0.0585596i
$579$		0			0
$580$	−25.9193	−	12.6417i	−1.07624	−	0.524917i
$581$	−3.50253	−	6.58730i	−0.145309	−	0.273287i
$582$		0			0
$583$	−4.45752	−	5.06621i	−0.184612	−	0.209821i
$584$	−8.89462	+	5.13531i	−0.368062	+	0.212501i
$585$		0			0
$586$	−2.12470	+	0.945975i	−0.0877703	+	0.0390779i
$587$	−6.90595	−	4.65812i	−0.285039	−	0.192261i	0.408349	−	0.912826i	$-0.366105\pi$
$587$	−6.90595	−	4.65812i	−0.285039	−	0.192261i	−0.693387	+	0.720565i	$0.743883\pi$
$588$		0			0
$589$	−33.2837	+	13.4475i	−1.37143	+	0.554094i
$590$	14.3468	−	4.11388i	0.590649	−	0.169366i
$591$		0			0
$592$	3.47881	−	0.488915i	0.142978	−	0.0200943i
$593$	0.421935			0.0173268			0.00866341	−	0.999962i	$-0.497242\pi$
$593$	0.421935			0.0173268			0.00866341	+	0.999962i	$0.497242\pi$
$594$		0			0
$595$	21.7718			0.892556
$596$	25.9418	−	3.64588i	1.06262	−	0.149341i
$597$		0			0
$598$	2.16879	−	0.621890i	0.0886884	−	0.0254310i
$599$	13.8835	−	5.60928i	0.567263	−	0.229189i	−0.0730173	−	0.997331i	$-0.523263\pi$
$599$	13.8835	−	5.60928i	0.567263	−	0.229189i	0.640280	+	0.768142i	$0.278818\pi$
$600$		0			0
$601$	−21.3136	−	14.3762i	−0.869398	−	0.586417i	0.0414580	−	0.999140i	$-0.486800\pi$
$601$	−21.3136	−	14.3762i	−0.869398	−	0.586417i	−0.910856	+	0.412724i	$0.864578\pi$
$602$	−5.53902	+	2.46613i	−0.225753	+	0.100512i
$603$		0			0
$604$	7.64114	−	4.41161i	0.310913	−	0.179506i
$605$	13.6219	−	34.9133i	0.553810	−	1.41943i
$606$		0			0
$607$	−0.731717	−	1.37616i	−0.0296995	−	0.0558566i	0.867656	−	0.497165i	$-0.165626\pi$
$607$	−0.731717	−	1.37616i	−0.0296995	−	0.0558566i	−0.897356	+	0.441308i	$0.854515\pi$
$608$	−20.3455	−	9.92318i	−0.825121	−	0.402438i
$609$		0			0
$610$	−6.02514	+	3.76492i	−0.243951	+	0.152437i
$611$	−13.3772	+	2.84342i	−0.541184	+	0.115032i
$612$		0			0
$613$	−16.1485	−	36.2700i	−0.652230	−	1.46493i	−0.872062	−	0.489395i	$-0.837218\pi$
$613$	−16.1485	−	36.2700i	−0.652230	−	1.46493i	0.219832	−	0.975538i	$-0.429449\pi$
$614$	−6.52885	+	5.10089i	−0.263483	+	0.205855i
$615$		0			0
$616$	−2.02445	−	8.53539i	−0.0815673	−	0.343901i
$617$	−1.76882	+	4.85980i	−0.0712101	+	0.195648i	−0.970192	−	0.242338i	$-0.922086\pi$
$617$	−1.76882	+	4.85980i	−0.0712101	+	0.195648i	0.898982	+	0.437986i	$0.144308\pi$
$618$		0			0
$619$	11.7676	−	11.3639i	0.472981	−	0.456753i	−0.419554	−	0.907730i	$-0.637813\pi$
$619$	11.7676	−	11.3639i	0.472981	−	0.456753i	0.892535	+	0.450978i	$0.148925\pi$
$620$	−20.8068	−	28.6381i	−0.835620	−	1.15013i
$621$		0			0
$622$	1.17511	+	0.381816i	0.0471176	+	0.0153094i
$623$	5.74714	+	11.7834i	0.230254	+	0.472091i
$624$		0			0
$625$	−0.501830	+	14.3705i	−0.0200732	+	0.574821i
$626$	4.33663	−	3.63887i	0.173327	−	0.145438i
$627$		0			0
$628$	−16.0233	+	5.83200i	−0.639399	+	0.232722i
$629$	−2.86725	−	0.609454i	−0.114325	−	0.0243005i
$630$		0			0
$631$	11.3909	+	5.07157i	0.453466	+	0.201896i	0.620743	−	0.784014i	$-0.286831\pi$
$631$	11.3909	+	5.07157i	0.453466	+	0.201896i	−0.167277	+	0.985910i	$0.553498\pi$
$632$	−5.21552	−	8.34658i	−0.207462	−	0.332009i
$633$		0			0
$634$	−2.24669	+	2.32651i	−0.0892274	+	0.0923976i
$635$	20.3574	−	41.7388i	0.807858	−	1.65635i
$636$		0			0
$637$	−3.42054	+	4.07644i	−0.135527	+	0.161515i
$638$	2.42290	−	3.78029i	0.0959233	−	0.149663i
$639$		0			0
$640$	6.13192	−	28.8484i	0.242385	−	1.14033i
$641$	1.08016	−	3.76696i	0.0426637	−	0.148786i	−0.937047	−	0.349204i	$-0.886452\pi$
$641$	1.08016	−	3.76696i	0.0426637	−	0.148786i	0.979711	+	0.200418i	$0.0642299\pi$
$642$		0			0
$643$	11.0703	+	27.3999i	0.436569	+	1.08055i	0.971793	+	0.235835i	$0.0757826\pi$
$643$	11.0703	+	27.3999i	0.436569	+	1.08055i	−0.535224	+	0.844710i	$0.679773\pi$
$644$	7.51146	−	9.61423i	0.295993	−	0.378854i
$645$		0			0
$646$	4.01916	+	4.16196i	0.158132	+	0.163750i
$647$	20.9572	−	6.80940i	0.823911	−	0.267705i	0.133433	−	0.991058i	$-0.457400\pi$
$647$	20.9572	−	6.80940i	0.823911	−	0.267705i	0.690478	+	0.723353i	$0.257400\pi$
$648$		0			0
$649$	−7.73343	−	47.0039i	−0.303564	−	1.84507i
$650$	−5.09310	−	0.898051i	−0.199768	−	0.0352244i
$651$		0			0
$652$	16.3668	+	24.2648i	0.640975	+	0.950284i
$653$	−17.0538	−	4.25200i	−0.667369	−	0.166394i	−0.106518	−	0.994311i	$-0.533970\pi$
$653$	−17.0538	−	4.25200i	−0.667369	−	0.166394i	−0.560850	+	0.827917i	$0.689526\pi$
$654$		0			0
$655$	−44.5728	+	1.55652i	−1.74160	+	0.0608182i
$656$	−2.19398	−	20.8743i	−0.0856604	−	0.815005i
$657$		0			0
$658$	2.41408	−	2.68111i	0.0941108	−	0.104521i
$659$	−0.586973	−	0.492529i	−0.0228652	−	0.0191862i	0.631283	−	0.775552i	$-0.282528\pi$
$659$	−0.586973	−	0.492529i	−0.0228652	−	0.0191862i	−0.654149	+	0.756366i	$0.726973\pi$
$660$		0			0
$661$	1.32631	+	7.52186i	0.0515874	+	0.292567i	0.999676	−	0.0254385i	$-0.00809821\pi$
$661$	1.32631	+	7.52186i	0.0515874	+	0.292567i	−0.948089	+	0.318005i	$0.896987\pi$
$662$	7.45627	−	3.96457i	0.289796	−	0.154087i
$663$		0			0
$664$	3.99576	+	0.279411i	0.155066	+	0.0108433i
$665$	10.3586	+	48.7333i	0.401689	+	1.88980i
$666$		0			0
$667$	12.7245	−	1.33740i	0.492695	−	0.0517843i
$668$	17.3283	+	4.96880i	0.670451	+	0.192249i
$669$		0			0
$670$	7.05812	+	8.41154i	0.272679	+	0.324966i
$671$	9.70616	+	20.4937i	0.374702	+	0.791151i
$672$		0			0
$673$	−0.761714	−	5.41988i	−0.0293619	−	0.208921i	0.970062	−	0.242857i	$-0.0780846\pi$
$673$	−0.761714	−	5.41988i	−0.0293619	−	0.208921i	−0.999424	+	0.0339362i	$0.989196\pi$
$674$	−0.758993	+	1.04466i	−0.0292353	+	0.0402390i
$675$		0			0
$676$	−3.78003	+	11.6337i	−0.145386	+	0.447452i
$677$	28.7025	+	15.2614i	1.10313	+	0.586543i	0.918163	−	0.396203i	$-0.129672\pi$
$677$	28.7025	+	15.2614i	1.10313	+	0.586543i	0.184963	+	0.982745i	$0.440783\pi$
$678$		0			0
$679$	−33.6160	+	22.6742i	−1.29006	+	0.870158i
$680$	−6.19427	+	9.91290i	−0.237539	+	0.380142i
$681$		0			0
$682$	4.80449	−	2.70090i	0.183973	−	0.103423i
$683$	27.4880	+	15.8702i	1.05180	+	0.607256i	0.923152	−	0.384434i	$-0.125603\pi$
$683$	27.4880	+	15.8702i	1.05180	+	0.607256i	0.128646	+	0.991691i	$0.458937\pi$
$684$		0			0
$685$	−4.67168	+	44.4481i	−0.178496	+	1.69827i
$686$	0.428487	−	6.12765i	0.0163597	−	0.233955i
$687$		0			0
$688$	−4.30097	+	30.6030i	−0.163973	+	1.16673i
$689$	3.75583	+	3.62697i	0.143086	+	0.138176i
$690$		0			0
$691$	9.16562	−	22.6857i	0.348677	−	0.863005i	−0.646317	−	0.763069i	$-0.723692\pi$
$691$	9.16562	−	22.6857i	0.348677	−	0.863005i	0.994994	−	0.0999362i	$-0.0318639\pi$
$692$	15.1538	+	26.2472i	0.576062	+	0.997768i
$693$		0			0
$694$	2.57881	−	4.46662i	0.0978901	−	0.169551i
$695$	8.50731	+	10.8889i	0.322701	+	0.413038i
$696$		0			0
$697$	−4.23699	+	16.9936i	−0.160487	+	0.643679i
$698$	2.60201	+	2.03291i	0.0984875	+	0.0769469i
$699$		0			0
$700$	−25.1361	+	12.2597i	−0.950054	+	0.463372i
$701$	−20.4382	−	14.8492i	−0.771941	−	0.560848i	0.130608	−	0.991434i	$-0.458307\pi$
$701$	−20.4382	−	14.8492i	−0.771941	−	0.560848i	−0.902550	+	0.430586i	$0.858307\pi$
$702$		0			0
$703$		−	6.70794i		−	0.252995i
$704$	−18.3923	−	6.21005i	−0.693184	−	0.234050i
$705$		0			0
$706$	7.15119	+	0.249725i	0.269139	+	0.00939852i
$707$	−2.94445	−	42.1076i	−0.110738	−	1.58362i
$708$		0			0
$709$	−0.966298	−	27.6712i	−0.0362901	−	1.03921i	−0.871838	−	0.489794i	$-0.837072\pi$
$709$	−0.966298	−	27.6712i	−0.0362901	−	1.03921i	0.835548	−	0.549418i	$-0.185150\pi$
$710$	3.07519	+	3.41534i	0.115410	+	0.128176i
$711$		0			0
$712$	−7.00020	−	0.735751i	−0.262344	−	0.0275734i
$713$	14.5618	+	5.88336i	0.545345	+	0.220334i
$714$		0			0
$715$	−8.31178	+	27.7804i	−0.310843	+	1.03893i
$716$	24.9887	−	4.40618i	0.933872	−	0.164667i
$717$		0			0
$718$	−2.46253	−	9.87666i	−0.0919008	−	0.368594i
$719$	7.75673	−	17.4219i	0.289277	−	0.649728i	−0.709193	−	0.705014i	$-0.750941\pi$
$719$	7.75673	−	17.4219i	0.289277	−	0.649728i	0.998471	+	0.0552866i	$0.0176072\pi$
$720$		0			0
$721$	0.127256	−	0.114582i	0.00473926	−	0.00426725i
$722$	−4.16318	+	6.17218i	−0.154938	+	0.229705i
$723$		0			0
$724$	24.8397	+	15.5216i	0.923161	+	0.576855i
$725$	−27.5592	−	10.0307i	−1.02352	−	0.372532i
$726$		0			0
$727$	−8.83265	+	50.0925i	−0.327585	+	1.85783i	0.163265	+	0.986582i	$0.447797\pi$
$727$	−8.83265	+	50.0925i	−0.327585	+	1.85783i	−0.490850	+	0.871244i	$0.663314\pi$
$728$	2.09742	+	6.45519i	0.0777355	+	0.239245i
$729$		0			0
$730$	−7.24572	+	5.26432i	−0.268176	+	0.194841i
$731$	12.1061	−	22.7683i	0.447760	−	0.842115i
$732$		0			0
$733$	−6.59426	−	22.9969i	−0.243565	−	0.849411i	−0.984133	−	0.177430i	$-0.943222\pi$
$733$	−6.59426	−	22.9969i	−0.243565	−	0.849411i	0.740569	−	0.671981i	$-0.234556\pi$
$734$	−7.26452	+	0.507985i	−0.268138	+	0.0187501i
$735$		0			0
$736$	3.38723	+	9.30634i	0.124855	+	0.343036i
$737$	29.2775	−	19.2632i	1.07845	−	0.709568i
$738$		0			0
$739$	30.2672	+	27.2527i	1.11340	+	1.00251i	0.999960	+	0.00896278i	$0.00285298\pi$
$739$	30.2672	+	27.2527i	1.11340	+	1.00251i	0.113438	+	0.993545i	$0.463814\pi$
$740$	6.41821	−	1.60024i	0.235938	−	0.0588259i
$741$		0			0
$742$	−1.36397	−	0.191694i	−0.0500729	−	0.00703729i
$743$	5.72586	+	0.804718i	0.210062	+	0.0295222i	0.243419	−	0.969921i	$-0.421731\pi$
$743$	5.72586	+	0.804718i	0.210062	+	0.0295222i	−0.0333573	+	0.999443i	$0.510620\pi$
$744$		0			0
$745$	45.4124	−	11.3226i	1.66378	−	0.414827i
$746$	−5.83413	−	5.25308i	−0.213603	−	0.192329i
$747$		0			0
$748$	14.2200	+	11.3748i	0.519935	+	0.415906i
$749$	7.21464	+	19.8221i	0.263617	+	0.724282i
$750$		0			0
$751$	−21.1118	+	1.47628i	−0.770382	+	0.0538703i	−0.449537	−	0.893262i	$-0.648411\pi$
$751$	−21.1118	+	1.47628i	−0.770382	+	0.0538703i	−0.320844	+	0.947132i	$0.603967\pi$
$752$	−5.06860	−	17.6763i	−0.184833	−	0.644588i
$753$		0			0
$754$	−1.63102	+	3.06751i	−0.0593984	+	0.111712i
$755$	12.7529	−	9.26551i	0.464125	−	0.337206i
$756$		0			0
$757$	−11.9306	−	36.7185i	−0.433623	−	1.33456i	−0.894491	−	0.447087i	$-0.852462\pi$
$757$	−11.9306	−	36.7185i	−0.433623	−	1.33456i	0.460867	−	0.887469i	$-0.347538\pi$
$758$	0.757704	−	4.29715i	0.0275210	−	0.156080i
$759$		0			0
$760$	−25.1359	−	9.14870i	−0.911773	−	0.331858i
$761$	3.72143	+	2.32541i	0.134902	+	0.0842960i	0.595691	−	0.803213i	$-0.296878\pi$
$761$	3.72143	+	2.32541i	0.134902	+	0.0842960i	−0.460790	+	0.887509i	$0.652434\pi$
$762$		0			0
$763$	−12.3841	+	18.3603i	−0.448336	+	0.664686i
$764$	−5.35675	+	4.82324i	−0.193800	+	0.174499i
$765$		0			0
$766$	−0.420640	+	0.944774i	−0.0151984	+	0.0341361i
$767$	8.91670	+	35.7629i	0.321963	+	1.29132i
$768$		0			0
$769$	−23.9946	+	4.23090i	−0.865268	+	0.152570i	−0.588628	−	0.808404i	$-0.700332\pi$
$769$	−23.9946	+	4.23090i	−0.865268	+	0.152570i	−0.276639	+	0.960974i	$0.589221\pi$
$770$	−2.53370	−	7.21774i	−0.0913083	−	0.260109i
$771$		0			0
$772$	37.4142	+	15.1163i	1.34657	+	0.544048i
$773$	49.8408	+	5.23848i	1.79265	+	0.188415i	0.941614	−	0.336693i	$-0.109309\pi$
$773$	49.8408	+	5.23848i	1.79265	+	0.188415i	0.851035	+	0.525108i	$0.175975\pi$
$774$		0			0
$775$	−24.0888	−	26.7534i	−0.865297	−	0.961009i
$776$	−0.759761	−	21.7567i	−0.0272738	−	0.781020i
$777$		0			0
$778$	−0.117513	−	1.68051i	−0.00421304	−	0.0602493i
$779$	−40.0539	−	1.39871i	−1.43508	−	0.0501141i
$780$		0			0
$781$	11.9650	−	8.48520i	0.428142	−	0.303624i
$782$		−	2.53133i		−	0.0905200i
$783$		0			0
$784$	−5.78860	−	4.20566i	−0.206736	−	0.150202i
$785$	−27.3810	+	13.3546i	−0.977271	+	0.476647i
$786$		0			0
$787$	21.9370	+	17.1391i	0.781971	+	0.610942i	0.925519	−	0.378701i	$-0.123629\pi$
$787$	21.9370	+	17.1391i	0.781971	+	0.610942i	−0.143549	+	0.989643i	$0.545851\pi$
$788$	5.02423	−	20.1511i	0.178981	−	0.717853i
$789$		0			0
$790$	−5.28393	−	6.76312i	−0.187994	−	0.240621i
$791$	−10.7969	+	18.7007i	−0.383893	+	0.664921i
$792$		0			0
$793$	−8.77267	−	15.1947i	−0.311527	−	0.539580i
$794$	1.14058	−	2.82303i	0.0404776	−	0.100185i
$795$		0			0
$796$	−9.61072	−	9.28096i	−0.340643	−	0.328955i
$797$	6.13032	−	43.6195i	0.217147	−	1.54508i	−0.510951	−	0.859610i	$-0.670707\pi$
$797$	6.13032	−	43.6195i	0.217147	−	1.54508i	0.728098	−	0.685473i	$-0.240404\pi$
$798$		0			0
$799$	−1.07033	+	15.3065i	−0.0378656	+	0.541504i
$800$	2.37292	−	22.5768i	0.0838953	−	0.798211i
$801$		0			0
$802$	−1.67619	−	0.967752i	−0.0591885	−	0.0341725i
$803$	14.0079	+	24.9179i	0.494328	+	0.879334i
$804$		0			0
$805$	11.5509	−	18.4853i	0.407115	−	0.651520i
$806$	−3.53548	+	2.38471i	−0.124532	+	0.0839980i
$807$		0			0
$808$	20.0097	+	10.6394i	0.703940	+	0.374291i
$809$	−6.72556	+	20.6991i	−0.236458	+	0.727743i	0.760467	+	0.649377i	$0.224970\pi$
$809$	−6.72556	+	20.6991i	−0.236458	+	0.727743i	−0.996925	+	0.0783659i	$0.975030\pi$
$810$		0			0
$811$	−19.0123	+	26.1681i	−0.667611	+	0.918888i	−0.999703	−	0.0243591i	$-0.992245\pi$
$811$	−19.0123	+	26.1681i	−0.667611	+	0.918888i	0.332092	+	0.943247i	$0.392245\pi$
$812$	2.61465	+	18.6042i	0.0917561	+	0.652878i
$813$		0			0
$814$	0.131633	+	1.02147i	0.00461374	+	0.0358026i
$815$	33.6120	+	40.0572i	1.17738	+	1.40314i
$816$		0			0
$817$	56.7236	+	16.2652i	1.98451	+	0.569049i
$818$	−5.17516	+	0.543931i	−0.180945	+	0.0190181i
$819$		0			0
$820$	−8.21691	−	38.6575i	−0.286947	−	1.34998i
$821$	−34.4021	−	2.40563i	−1.20064	−	0.0839570i	−0.544609	−	0.838690i	$-0.683322\pi$
$821$	−34.4021	−	2.40563i	−1.20064	−	0.0839570i	−0.656032	+	0.754733i	$0.727766\pi$
$822$		0			0
$823$	28.1487	−	14.9669i	0.981201	−	0.521714i	0.100271	−	0.994960i	$-0.468029\pi$
$823$	28.1487	−	14.9669i	0.981201	−	0.521714i	0.880930	+	0.473246i	$0.156918\pi$
$824$	0.0159647	+	0.0905404i	0.000556157	+	0.00315412i
$825$		0			0
$826$	−7.44840	−	6.24995i	−0.259163	−	0.217463i
$827$	1.74959	−	1.94312i	0.0608393	−	0.0675689i	−0.711957	−	0.702223i	$-0.752191\pi$
$827$	1.74959	−	1.94312i	0.0608393	−	0.0675689i	0.772796	+	0.634654i	$0.218858\pi$
$828$		0			0
$829$	0.916289	+	8.71791i	0.0318240	+	0.302786i	0.998843	+	0.0480825i	$0.0153111\pi$
$829$	0.916289	+	8.71791i	0.0318240	+	0.302786i	−0.967019	+	0.254703i	$0.918022\pi$
$830$	3.49077	−	0.121901i	0.121167	−	0.00423123i
$831$		0			0
$832$	14.5740	+	3.63370i	0.505261	+	0.125976i
$833$	3.33858	+	4.94964i	0.115675	+	0.171495i
$834$		0			0
$835$	31.7167	+	5.59251i	1.09760	+	0.193537i
$836$	−18.6955	+	37.2415i	−0.646598	+	1.28803i
$837$		0			0
$838$	−9.31343	+	3.02612i	−0.321727	+	0.104535i
$839$	19.5785	+	20.2741i	0.675924	+	0.699940i	0.966429	−	0.256933i	$-0.0827121\pi$
$839$	19.5785	+	20.2741i	0.675924	+	0.699940i	−0.290505	+	0.956874i	$0.593823\pi$
$840$		0			0
$841$	5.72466	−	7.32724i	0.197402	−	0.252663i
$842$	−1.99952	−	4.94898i	−0.0689079	−	0.170553i
$843$		0			0
$844$	10.3524	−	36.1030i	0.356344	−	1.24272i
$845$	−4.54376	+	21.3767i	−0.156310	+	0.735381i
$846$		0			0
$847$	−23.8189	+	5.36172i	−0.818427	+	0.184231i
$848$	−4.51261	+	5.37792i	−0.154964	+	0.184679i
$849$		0			0
$850$	−2.54358	+	5.21511i	−0.0872440	+	0.178877i
$851$	−2.03866	+	2.11109i	−0.0698844	+	0.0723674i
$852$		0			0
$853$	6.39029	+	10.2266i	0.218799	+	0.350152i	0.939179	−	0.343428i	$-0.111588\pi$
$853$	6.39029	+	10.2266i	0.218799	+	0.350152i	−0.720380	+	0.693580i	$0.756032\pi$
$854$	4.22836	+	1.88259i	0.144691	+	0.0644208i
$855$		0			0
$856$	−11.0778	−	2.35466i	−0.378632	−	0.0804806i
$857$	10.8263	−	3.94045i	0.369819	−	0.134603i	−0.150424	−	0.988622i	$-0.548064\pi$
$857$	10.8263	−	3.94045i	0.369819	−	0.134603i	0.520243	+	0.854019i	$0.325842\pi$
$858$		0			0
$859$	−22.0450	+	18.4979i	−0.752164	+	0.631141i	−0.936074	−	0.351802i	$-0.885569\pi$
$859$	−22.0450	+	18.4979i	−0.752164	+	0.631141i	0.183910	+	0.982943i	$0.441125\pi$
$860$	−2.03078	+	58.1538i	−0.0692489	+	1.98303i
$861$		0			0
$862$	3.35202	+	6.87265i	0.114170	+	0.234083i
$863$	11.4124	+	3.70811i	0.388483	+	0.126226i	0.496745	−	0.867897i	$-0.334529\pi$
$863$	11.4124	+	3.70811i	0.388483	+	0.126226i	−0.108262	+	0.994122i	$0.534529\pi$
$864$		0			0
$865$	31.8269	+	43.8059i	1.08215	+	1.48945i
$866$	0.855978	−	0.826608i	0.0290873	−	0.0280893i
$867$		0			0
$868$	−7.88738	+	21.6704i	−0.267715	+	0.735541i
$869$	−23.3953	+	14.2486i	−0.793630	+	0.483351i
$870$		0			0
$871$	−21.3682	+	16.6947i	−0.724035	+	0.565678i
$872$	−4.83620	−	10.8623i	−0.163774	−	0.367843i
$873$		0			0
$874$	5.66605	−	1.20436i	0.191657	−	0.0407379i
$875$	−10.3080	+	6.44114i	−0.348474	+	0.217750i
$876$		0			0
$877$	−16.5931	−	8.09298i	−0.560308	−	0.273280i	0.136378	−	0.990657i	$-0.456454\pi$
$877$	−16.5931	−	8.09298i	−0.560308	−	0.273280i	−0.696686	+	0.717376i	$0.745343\pi$
$878$	−4.32548	−	8.13505i	−0.145978	−	0.274545i
$879$		0			0
$880$	−38.0417	−	8.54305i	−1.28238	−	0.287986i
$881$	−24.4021	+	14.0886i	−0.822129	+	0.474657i	−0.851150	−	0.524922i	$-0.824094\pi$
$881$	−24.4021	+	14.0886i	−0.822129	+	0.474657i	0.0290209	+	0.999579i	$0.490761\pi$
$882$		0			0
$883$	−17.3637	+	7.73084i	−0.584336	+	0.260163i	−0.677543	−	0.735483i	$-0.736955\pi$
$883$	−17.3637	+	7.73084i	−0.584336	+	0.260163i	0.0932062	+	0.995647i	$0.470288\pi$
$884$	−11.6808	−	7.87882i	−0.392869	−	0.264993i
$885$		0			0
$886$	−0.915504	+	0.369888i	−0.0307570	+	0.0124266i
$887$	42.2597	−	12.1178i	1.41894	−	0.406875i	0.523488	−	0.852033i	$-0.324630\pi$
$887$	42.2597	−	12.1178i	1.41894	−	0.406875i	0.895452	+	0.445158i	$0.146853\pi$
$888$		0			0
$889$	−29.9590	+	4.21047i	−1.00479	+	0.141215i
$890$	−6.13795			−0.205745
$891$		0			0
$892$	45.1781			1.51267
$893$	−34.7708	+	4.88671i	−1.16356	+	0.163528i
$894$		0			0
$895$	43.5770	−	12.4955i	1.45662	−	0.417678i
$896$	−17.8147	+	7.19761i	−0.595147	+	0.240455i
$897$		0			0
$898$	4.37621	+	2.95179i	0.146036	+	0.0985026i
$899$	−22.0930	+	9.83645i	−0.736844	+	0.328064i
$900$		0			0
$901$	5.07312	−	2.92897i	0.169010	−	0.0975781i
$902$	6.12678	−	0.573003i	0.203999	−	0.0190789i
$903$		0			0
$904$	−5.44282	−	10.2364i	−0.181025	−	0.340459i
$905$	47.0338	+	22.9399i	1.56346	+	0.762548i
$906$		0			0
$907$	−15.6006	+	9.74832i	−0.518008	+	0.323688i	−0.763604	−	0.645685i	$-0.776572\pi$
$907$	−15.6006	+	9.74832i	−0.518008	+	0.323688i	0.245596	+	0.969372i	$0.421016\pi$
$908$	−27.9103	+	5.93252i	−0.926236	+	0.196877i
$909$		0			0
$910$	2.40737	+	5.40705i	0.0798037	+	0.179242i
$911$	4.37755	−	3.42012i	0.145035	−	0.113314i	−0.540532	−	0.841324i	$-0.681777\pi$
$911$	4.37755	−	3.42012i	0.145035	−	0.113314i	0.685566	+	0.728010i	$0.259555\pi$
$912$		0			0
$913$	0.905129	−	11.1114i	0.0299554	−	0.367735i
$914$	2.14870	−	5.90350i	0.0710726	−	0.195270i
$915$		0			0
$916$	9.00364	−	8.69471i	0.297489	−	0.287281i
$917$	17.0785	+	23.5065i	0.563980	+	0.776252i
$918$		0			0
$919$	13.4610	+	4.37374i	0.444037	+	0.144276i	0.522497	−	0.852641i	$-0.325000\pi$
$919$	13.4610	+	4.37374i	0.444037	+	0.144276i	−0.0784604	+	0.996917i	$0.525000\pi$
$920$	5.13020	+	10.5185i	0.169138	+	0.346783i
$921$		0			0
$922$	−0.199351	+	5.70867i	−0.00656529	+	0.188005i
$923$	−8.69421	+	7.29530i	−0.286173	+	0.240128i
$924$		0			0
$925$	6.32141	−	2.30081i	0.207847	−	0.0756501i
$926$	3.07723	+	0.654086i	0.101124	+	0.0214946i
$927$		0			0
$928$	−13.9315	−	6.20272i	−0.457325	−	0.203614i
$929$	7.17652	+	11.4848i	0.235454	+	0.376805i	0.944583	−	0.328274i	$-0.106467\pi$
$929$	7.17652	+	11.4848i	0.235454	+	0.376805i	−0.709128	+	0.705079i	$0.750911\pi$
$930$		0			0
$931$	−9.49071	+	9.82791i	−0.311045	+	0.322097i
$932$	0.755968	−	1.54996i	0.0247625	−	0.0507708i
$933$		0			0
$934$	3.15944	−	3.76527i	0.103380	−	0.123203i
$935$	27.3903	+	17.5552i	0.895758	+	0.574117i
$936$		0			0
$937$	−1.89625	+	8.92115i	−0.0619478	+	0.291441i	−0.998206	−	0.0598709i	$-0.980931\pi$
$937$	−1.89625	+	8.92115i	−0.0619478	+	0.291441i	0.936258	+	0.351312i	$0.114264\pi$
$938$	1.97176	−	6.87635i	0.0643803	−	0.224521i
$939$		0			0
$940$	−12.9705	−	32.1031i	−0.423051	−	1.04709i
$941$	−14.9201	+	19.0969i	−0.486382	+	0.622541i	−0.967119	−	0.254324i	$-0.918147\pi$
$941$	−14.9201	+	19.0969i	−0.486382	+	0.622541i	0.480737	+	0.876865i	$0.340369\pi$
$942$		0			0
$943$	12.1805	+	12.6133i	0.396651	+	0.410744i
$944$	−47.1328	+	15.3144i	−1.53404	+	0.498441i
$945$		0			0
$946$	−8.95695	−	1.36372i	−0.291215	−	0.0443385i
$947$	−5.16006	−	0.909858i	−0.167680	−	0.0295664i	0.0891780	−	0.996016i	$-0.471576\pi$
$947$	−5.16006	−	0.909858i	−0.167680	−	0.0295664i	−0.256858	+	0.966449i	$0.582687\pi$
$948$		0			0
$949$	−12.3680	−	18.3364i	−0.401483	−	0.595224i
$950$	−12.8835	−	3.21222i	−0.417997	−	0.104218i
$951$		0			0
$952$	7.61046	−	0.265763i	0.246656	−	0.00861343i
$953$	−4.59645	−	43.7323i	−0.148894	−	1.41663i	−0.772562	−	0.634939i	$-0.781025\pi$
$953$	−4.59645	−	43.7323i	−0.148894	−	1.41663i	0.623669	−	0.781689i	$-0.285641\pi$
$954$		0			0
$955$	−8.61712	+	9.57028i	−0.278843	+	0.309687i
$956$	33.3482	+	27.9825i	1.07856	+	0.905018i
$957$		0			0
$958$	1.15600	+	6.55600i	0.0373486	+	0.211815i
$959$	25.7080	−	13.6692i	0.830155	−	0.441401i
$960$		0			0
$961$	1.31099	+	0.0916731i	0.0422899	+	0.00295720i
$962$	−0.165683	−	0.779476i	−0.00534182	−	0.0251313i
$963$		0			0
$964$	−23.2239	+	2.44093i	−0.747990	+	0.0786169i
$965$	69.3003	+	19.8715i	2.23086	+	0.639688i
$966$		0			0
$967$	9.98272	+	11.8969i	0.321023	+	0.382580i	0.902288	−	0.431134i	$-0.141887\pi$
$967$	9.98272	+	11.8969i	0.321023	+	0.382580i	−0.581265	+	0.813714i	$0.697442\pi$
$968$	4.33545	−	12.3704i	0.139347	−	0.397601i
$969$		0			0
$970$	−2.64205	−	18.7991i	−0.0848310	−	0.603604i
$971$	−11.4826	+	15.8045i	−0.368495	+	0.507190i	−0.952491	−	0.304566i	$-0.901488\pi$
$971$	−11.4826	+	15.8045i	−0.368495	+	0.507190i	0.583996	+	0.811757i	$0.301488\pi$
$972$		0			0
$973$	2.78181	−	8.56154i	0.0891808	−	0.274470i
$974$	8.73847	+	4.64632i	0.279999	+	0.148878i
$975$		0			0
$976$	19.5580	−	13.1920i	0.626036	−	0.422267i
$977$	−9.90505	+	15.8514i	−0.316891	+	0.507131i	−0.967698	−	0.252112i	$-0.918875\pi$
$977$	−9.90505	+	15.8514i	−0.316891	+	0.507131i	0.650807	+	0.759243i	$0.274431\pi$
$978$		0			0
$979$	−2.27102	+	19.4583i	−0.0725821	+	0.621891i
$980$	−11.6675	−	6.73624i	−0.372705	−	0.215181i
$981$		0			0
$982$	0.679495	−	6.46497i	0.0216836	−	0.206305i
$983$	4.26388	−	60.9763i	0.135997	−	1.94484i	−0.154558	−	0.987984i	$-0.549395\pi$
$983$	4.26388	−	60.9763i	0.135997	−	1.94484i	0.290555	−	0.956858i	$-0.406160\pi$
$984$		0			0
$985$	5.16384	−	36.7427i	0.164534	−	1.17072i
$986$	2.80387	+	2.70766i	0.0892933	+	0.0862296i
$987$		0			0
$988$	12.0782	−	29.8946i	0.384259	−	0.951074i
$989$	−12.9085	−	22.3582i	−0.410467	−	0.710950i
$990$		0			0
$991$	9.31557	−	16.1350i	0.295919	−	0.512547i	−0.679279	−	0.733880i	$-0.737708\pi$
$991$	9.31557	−	16.1350i	0.295919	−	0.512547i	0.975198	+	0.221333i	$0.0710408\pi$
$992$	−11.5248	−	14.7511i	−0.365913	−	0.468348i
$993$		0			0
$994$	0.724321	−	2.90509i	0.0229741	−	0.0921439i
$995$	−18.8095	−	14.6956i	−0.596301	−	0.465881i
$996$		0			0
$997$	−15.1879	+	7.40765i	−0.481007	+	0.234603i	−0.662889	−	0.748718i	$-0.730670\pi$
$997$	−15.1879	+	7.40765i	−0.481007	+	0.234603i	0.181882	+	0.983320i	$0.441781\pi$
$998$	5.95947	+	4.32981i	0.188644	+	0.137058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.bb.a.413.18		816
3.2	odd	2		297.2.x.a.83.17	yes	816
11.2	odd	10	inner	891.2.bb.a.332.18		816
27.13	even	9		297.2.x.a.149.17	yes	816
27.14	odd	18	inner	891.2.bb.a.314.18		816
33.2	even	10		297.2.x.a.2.17	✓	816
297.13	odd	90		297.2.x.a.68.17	yes	816
297.68	even	90	inner	891.2.bb.a.233.18		816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.2.17	✓	816	33.2	even	10
297.2.x.a.68.17	yes	816	297.13	odd	90
297.2.x.a.83.17	yes	816	3.2	odd	2
297.2.x.a.149.17	yes	816	27.13	even	9
891.2.bb.a.233.18		816	297.68	even	90	inner
891.2.bb.a.314.18		816	27.14	odd	18	inner
891.2.bb.a.332.18		816	11.2	odd	10	inner
891.2.bb.a.413.18		816	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.bb (of order \(90\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.302038 - 0.0424487i) q^{2} +(-1.83310 + 0.525632i) q^{4} +(-3.15888 + 1.27627i) q^{5} +(1.84008 + 1.24115i) q^{7} +(-1.08863 + 0.484688i) q^{8} +(-0.899926 + 0.519573i) q^{10} +(1.31416 + 3.04516i) q^{11} +(-1.20476 - 2.26582i) q^{13} +(0.608459 + 0.296765i) q^{14} +(2.92617 - 1.82848i) q^{16} +(-2.81623 + 0.598608i) q^{17} +(-2.67981 - 6.01896i) q^{19} +(5.11969 - 3.99994i) q^{20} +(0.526190 + 0.863968i) q^{22} +(-0.985887 + 2.70870i) q^{23} +(4.75296 - 4.58988i) q^{25} +(-0.460065 - 0.633225i) q^{26} +(-4.02544 - 1.30794i) q^{28} +(-1.94578 - 3.98943i) q^{29} +(0.190149 - 5.44515i) q^{31} +(2.63191 - 2.20844i) q^{32} +(-0.825198 + 0.300348i) q^{34} +(-7.39664 - 1.57220i) q^{35} +(0.930097 + 0.414106i) q^{37} +(-1.06490 - 1.70420i) q^{38} +(2.82025 - 2.92045i) q^{40} +(2.66661 - 5.46737i) q^{41} +(-5.75703 + 6.86096i) q^{43} +(-4.00962 - 4.89130i) q^{44} +(-0.182795 + 0.859981i) q^{46} +(1.46895 - 5.12285i) q^{47} +(-0.776804 - 1.92266i) q^{49} +(1.24074 - 1.58808i) q^{50} +(3.39944 + 3.52022i) q^{52} +(-1.93503 + 0.628729i) q^{53} +(-8.03773 - 7.94206i) q^{55} +(-2.60473 - 0.459284i) q^{56} +(-0.757044 - 1.12236i) q^{58} +(-13.9361 - 3.47466i) q^{59} +(6.83291 - 0.238610i) q^{61} +(-0.173707 - 1.65271i) q^{62} +(-3.91645 + 4.34966i) q^{64} +(6.69750 + 5.61987i) q^{65} +(-1.83491 - 10.4063i) q^{67} +(4.84778 - 2.57761i) q^{68} +(-2.30080 - 0.160888i) q^{70} +(-0.919525 - 4.32602i) q^{71} +(8.57160 - 0.900912i) q^{73} +(0.298503 + 0.0855943i) q^{74} +(8.07612 + 9.62475i) q^{76} +(-1.36133 + 7.23440i) q^{77} +(1.14946 + 8.17884i) q^{79} +(-6.90981 + 9.51053i) q^{80} +(0.573336 - 1.76455i) q^{82} +(-2.96787 - 1.57805i) q^{83} +(8.13215 - 5.48521i) q^{85} +(-1.44760 + 2.31665i) q^{86} +(-2.90658 - 2.67808i) q^{88} +(5.11538 + 2.95336i) q^{89} +(0.595372 - 5.66459i) q^{91} +(0.383446 - 5.48353i) q^{92} +(0.226222 - 1.60965i) q^{94} +(16.1470 + 15.5930i) q^{95} +(-6.84359 + 16.9385i) q^{97} +(-0.316238 - 0.547741i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) \) 816 * q + 30 * q^2 - 18 * q^4 + 21 * q^5 - 30 * q^7 + 45 * q^8 + 33 * q^11 - 30 * q^13 + 18 * q^14 - 30 * q^16 + 45 * q^17 - 15 * q^19 + 60 * q^20 - 15 * q^22 + 84 * q^23 - 27 * q^25 - 60 * q^28 - 60 * q^29 - 9 * q^31 - 42 * q^34 + 45 * q^35 - 9 * q^37 + 18 * q^38 - 90 * q^40 + 30 * q^41 + 108 * q^44 - 15 * q^46 + 6 * q^47 - 18 * q^49 + 105 * q^50 - 30 * q^52 - 48 * q^55 - 54 * q^56 - 18 * q^58 - 81 * q^59 - 30 * q^61 + 45 * q^62 + 51 * q^64 + 6 * q^67 + 225 * q^68 - 93 * q^70 + 27 * q^71 - 15 * q^73 + 30 * q^74 + 141 * q^77 - 30 * q^79 - 36 * q^82 - 15 * q^83 - 30 * q^85 - 93 * q^86 - 108 * q^88 - 54 * q^89 - 9 * q^91 - 276 * q^92 - 30 * q^94 - 90 * q^95 - 81 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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