LMFDB - Embedded newform 891.2.bb.a.233.22

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			233.22
Character	$\chi$	$=$	891.233
Dual form			891.2.bb.a.413.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.793594 + 0.111532i) q^{2} +(-1.30517 - 0.374252i) q^{4} +(3.10727 + 1.25542i) q^{5} +(3.54248 - 2.38943i) q^{7} +(-2.45825 - 1.09449i) q^{8} +(2.32589 + 1.34285i) q^{10} +(-2.26366 - 2.42401i) q^{11} +(2.28030 - 4.28862i) q^{13} +(3.07779 - 1.50114i) q^{14} +(0.474121 + 0.296263i) q^{16} +(-5.16306 - 1.09744i) q^{17} +(0.636201 - 1.42893i) q^{19} +(-3.58568 - 2.80144i) q^{20} +(-1.52608 - 2.17615i) q^{22} +(1.01565 + 2.79048i) q^{23} +(4.48236 + 4.32856i) q^{25} +(2.28795 - 3.14910i) q^{26} +(-5.51779 + 1.79284i) q^{28} +(-0.936240 + 1.91958i) q^{29} +(0.219193 + 6.27687i) q^{31} +(4.46590 + 3.74734i) q^{32} +(-3.97498 - 1.44677i) q^{34} +(14.0072 - 2.97732i) q^{35} +(9.67024 - 4.30547i) q^{37} +(0.664258 - 1.06303i) q^{38} +(-6.26442 - 6.48700i) q^{40} +(-2.36287 - 4.84460i) q^{41} +(-3.85110 - 4.58956i) q^{43} +(2.04728 + 4.01093i) q^{44} +(0.494786 + 2.32779i) q^{46} +(1.60291 + 5.59002i) q^{47} +(4.21753 - 10.4388i) q^{49} +(3.07440 + 3.93505i) q^{50} +(-4.58121 + 4.74398i) q^{52} +(4.45134 + 1.44633i) q^{53} +(-3.99067 - 10.3739i) q^{55} +(-11.3235 + 1.99664i) q^{56} +(-0.957089 + 1.41894i) q^{58} +(3.20015 - 0.797887i) q^{59} +(-2.32705 - 0.0812623i) q^{61} +(-0.526124 + 5.00574i) q^{62} +(2.37798 + 2.64102i) q^{64} +(12.4695 - 10.4632i) q^{65} +(-0.546612 + 3.09999i) q^{67} +(6.32796 + 3.36463i) q^{68} +(11.4481 - 0.800529i) q^{70} +(-0.585658 + 2.75530i) q^{71} +(0.245902 + 0.0258453i) q^{73} +(8.15445 - 2.33825i) q^{74} +(-1.36513 + 1.62690i) q^{76} +(-13.8110 - 3.17813i) q^{77} +(-1.58209 + 11.2571i) q^{79} +(1.10129 + 1.51579i) q^{80} +(-1.33483 - 4.10819i) q^{82} +(-4.77438 + 2.53858i) q^{83} +(-14.6653 - 9.89186i) q^{85} +(-2.54433 - 4.07177i) q^{86} +(2.91162 + 8.43638i) q^{88} +(13.5062 - 7.79783i) q^{89} +(-2.16946 - 20.6410i) q^{91} +(-0.281257 - 4.02216i) q^{92} +(0.648594 + 4.61499i) q^{94} +(3.77076 - 3.64138i) q^{95} +(4.52262 + 11.1939i) q^{97} +(4.51127 - 7.81375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.793594	+	0.111532i	0.561156	+	0.0788653i	0.414048	−	0.910255i	$-0.364115\pi$
$2$	0.793594	+	0.111532i	0.561156	+	0.0788653i	0.147108	+	0.989120i	$0.453003\pi$
$3$		0			0
$3$		0			0
$4$	−1.30517	−	0.374252i	−0.652585	−	0.187126i
$5$	3.10727	+	1.25542i	1.38961	+	0.561440i	0.942852	−	0.333212i	$-0.108133\pi$
$5$	3.10727	+	1.25542i	1.38961	+	0.561440i	0.446762	+	0.894653i	$0.352577\pi$
$6$		0			0
$7$	3.54248	−	2.38943i	1.33893	−	0.903121i	0.339633	−	0.940558i	$-0.389697\pi$
$7$	3.54248	−	2.38943i	1.33893	−	0.903121i	0.999299	+	0.0374370i	$0.0119194\pi$
$8$	−2.45825	−	1.09449i	−0.869124	−	0.386959i
$9$		0			0
$10$	2.32589	+	1.34285i	0.735512	+	0.424648i
$11$	−2.26366	−	2.42401i	−0.682521	−	0.730866i
$11$	−2.26366	−	2.42401i	−0.682521	−	0.730866i
$12$		0			0
$13$	2.28030	−	4.28862i	0.632442	−	1.18945i	−0.336388	−	0.941723i	$-0.609205\pi$
$13$	2.28030	−	4.28862i	0.632442	−	1.18945i	0.968830	−	0.247727i	$-0.0796835\pi$
$14$	3.07779	−	1.50114i	0.822575	−	0.401196i
$15$		0			0
$16$	0.474121	+	0.296263i	0.118530	+	0.0740659i
$17$	−5.16306	−	1.09744i	−1.25223	−	0.266169i	−0.466376	−	0.884586i	$-0.654441\pi$
$17$	−5.16306	−	1.09744i	−1.25223	−	0.266169i	−0.785850	+	0.618417i	$0.787774\pi$
$18$		0			0
$19$	0.636201	−	1.42893i	0.145955	−	0.327819i	−0.825743	−	0.564046i	$-0.809244\pi$
$19$	0.636201	−	1.42893i	0.145955	−	0.327819i	0.971698	+	0.236227i	$0.0759108\pi$
$20$	−3.58568	−	2.80144i	−0.801782	−	0.626421i
$21$		0			0
$22$	−1.52608	−	2.17615i	−0.325360	−	0.463957i
$23$	1.01565	+	2.79048i	0.211778	+	0.581855i	0.999412	−	0.0342882i	$-0.0109164\pi$
$23$	1.01565	+	2.79048i	0.211778	+	0.581855i	−0.787634	+	0.616143i	$0.788694\pi$
$24$		0			0
$25$	4.48236	+	4.32856i	0.896472	+	0.865713i
$26$	2.28795	−	3.14910i	0.448705	−	0.617589i
$27$		0			0
$28$	−5.51779	+	1.79284i	−1.04276	+	0.338815i
$29$	−0.936240	+	1.91958i	−0.173855	+	0.356456i	−0.967873	−	0.251438i	$-0.919097\pi$
$29$	−0.936240	+	1.91958i	−0.173855	+	0.356456i	0.794018	+	0.607894i	$0.207985\pi$
$30$		0			0
$31$	0.219193	+	6.27687i	0.0393683	+	1.12736i	0.844940	+	0.534861i	$0.179636\pi$
$31$	0.219193	+	6.27687i	0.0393683	+	1.12736i	−0.805572	+	0.592499i	$0.798142\pi$
$32$	4.46590	+	3.74734i	0.789468	+	0.662442i
$33$		0			0
$34$	−3.97498	−	1.44677i	−0.681703	−	0.248119i
$35$	14.0072	−	2.97732i	2.36765	−	0.503259i
$36$		0			0
$37$	9.67024	−	4.30547i	1.58978	−	0.707814i	0.594428	−	0.804149i	$-0.297378\pi$
$37$	9.67024	−	4.30547i	1.58978	−	0.707814i	0.995349	+	0.0963341i	$0.0307117\pi$
$38$	0.664258	−	1.06303i	0.107757	−	0.172447i
$39$		0			0
$40$	−6.26442	−	6.48700i	−0.990492	−	1.02568i
$41$	−2.36287	−	4.84460i	−0.369018	−	0.756600i	0.630794	−	0.775950i	$-0.282729\pi$
$41$	−2.36287	−	4.84460i	−0.369018	−	0.756600i	−0.999813	+	0.0193503i	$0.993840\pi$
$42$		0			0
$43$	−3.85110	−	4.58956i	−0.587287	−	0.699902i	0.387795	−	0.921746i	$-0.373237\pi$
$43$	−3.85110	−	4.58956i	−0.587287	−	0.699902i	−0.975082	+	0.221844i	$0.928792\pi$
$44$	2.04728	+	4.01093i	0.308639	+	0.604670i
$45$		0			0
$46$	0.494786	+	2.32779i	0.0729522	+	0.343213i
$47$	1.60291	+	5.59002i	0.233809	+	0.815389i	0.987427	+	0.158076i	$0.0505291\pi$
$47$	1.60291	+	5.59002i	0.233809	+	0.815389i	−0.753618	+	0.657313i	$0.771693\pi$
$48$		0			0
$49$	4.21753	−	10.4388i	0.602505	−	1.49125i
$50$	3.07440	+	3.93505i	0.434786	+	0.556500i
$51$		0			0
$52$	−4.58121	+	4.74398i	−0.635299	+	0.657872i
$53$	4.45134	+	1.44633i	0.611438	+	0.198668i	0.598335	−	0.801246i	$-0.295829\pi$
$53$	4.45134	+	1.44633i	0.611438	+	0.198668i	0.0131030	+	0.999914i	$0.495829\pi$
$54$		0			0
$55$	−3.99067	−	10.3739i	−0.538102	−	1.39882i
$56$	−11.3235	+	1.99664i	−1.51317	+	0.266812i
$57$		0			0
$58$	−0.957089	+	1.41894i	−0.125672	+	0.186316i
$59$	3.20015	−	0.797887i	0.416624	−	0.103876i	−0.0279689	−	0.999609i	$-0.508904\pi$
$59$	3.20015	−	0.797887i	0.416624	−	0.103876i	0.444593	+	0.895733i	$0.353348\pi$
$60$		0			0
$61$	−2.32705	−	0.0812623i	−0.297948	−	0.0104046i	−0.114464	−	0.993427i	$-0.536515\pi$
$61$	−2.32705	−	0.0812623i	−0.297948	−	0.0104046i	−0.183484	+	0.983023i	$0.558737\pi$
$62$	−0.526124	+	5.00574i	−0.0668179	+	0.635729i
$63$		0			0
$64$	2.37798	+	2.64102i	0.297248	+	0.330127i
$65$	12.4695	−	10.4632i	1.54666	−	1.29780i
$66$		0			0
$67$	−0.546612	+	3.09999i	−0.0667793	+	0.378724i	0.933041	+	0.359770i	$0.117145\pi$
$67$	−0.546612	+	3.09999i	−0.0667793	+	0.378724i	−0.999820	+	0.0189543i	$0.993966\pi$
$68$	6.32796	+	3.36463i	0.767378	+	0.408022i
$69$		0			0
$70$	11.4481	−	0.800529i	1.36831	−	0.0956815i
$71$	−0.585658	+	2.75530i	−0.0695048	+	0.326994i	−0.999139	−	0.0414896i	$-0.986790\pi$
$71$	−0.585658	+	2.75530i	−0.0695048	+	0.326994i	0.929634	+	0.368484i	$0.120123\pi$
$72$		0			0
$73$	0.245902	+	0.0258453i	0.0287806	+	0.00302496i	0.118908	−	0.992905i	$-0.462061\pi$
$73$	0.245902	+	0.0258453i	0.0287806	+	0.00302496i	−0.0901272	+	0.995930i	$0.528727\pi$
$74$	8.15445	−	2.33825i	0.947935	−	0.271816i
$75$		0			0
$76$	−1.36513	+	1.62690i	−0.156591	+	0.186618i
$77$	−13.8110	−	3.17813i	−1.57391	−	0.362182i
$78$		0			0
$79$	−1.58209	+	11.2571i	−0.177999	+	1.26653i	0.672321	+	0.740259i	$0.265297\pi$
$79$	−1.58209	+	11.2571i	−0.177999	+	1.26653i	−0.850320	+	0.526266i	$0.823592\pi$
$80$	1.10129	+	1.51579i	0.123128	+	0.169471i
$81$		0			0
$82$	−1.33483	−	4.10819i	−0.147407	−	0.453673i
$83$	−4.77438	+	2.53858i	−0.524056	+	0.278646i	−0.710350	−	0.703848i	$-0.751463\pi$
$83$	−4.77438	+	2.53858i	−0.524056	+	0.278646i	0.186294	+	0.982494i	$0.440352\pi$
$84$		0			0
$85$	−14.6653	−	9.89186i	−1.59067	−	1.07292i
$86$	−2.54433	−	4.07177i	−0.274362	−	0.439071i
$87$		0			0
$88$	2.91162	+	8.43638i	0.310380	+	0.899321i
$89$	13.5062	−	7.79783i	1.43166	−	0.826569i	0.434412	−	0.900714i	$-0.356956\pi$
$89$	13.5062	−	7.79783i	1.43166	−	0.826569i	0.997247	+	0.0741455i	$0.0236229\pi$
$90$		0			0
$91$	−2.16946	−	20.6410i	−0.227421	−	2.16376i
$92$	−0.281257	−	4.02216i	−0.0293231	−	0.419339i
$93$		0			0
$94$	0.648594	+	4.61499i	0.0668974	+	0.476000i
$95$	3.77076	−	3.64138i	0.386871	−	0.373597i
$96$		0			0
$97$	4.52262	+	11.1939i	0.459203	+	1.13657i	0.962216	+	0.272288i	$0.0877803\pi$
$97$	4.52262	+	11.1939i	0.459203	+	1.13657i	−0.503013	+	0.864279i	$0.667775\pi$
$98$	4.51127	−	7.81375i	0.455707	−	0.789308i
$99$		0			0
$100$	−4.23027	−	7.32705i	−0.423027	−	0.732705i
$101$	−1.42438	+	1.82312i	−0.141731	+	0.181407i	−0.853639	−	0.520866i	$-0.825609\pi$
$101$	−1.42438	+	1.82312i	−0.141731	+	0.181407i	0.711908	+	0.702273i	$0.247831\pi$
$102$		0			0
$103$	3.27116	+	13.1199i	0.322317	+	1.29274i	0.884814	+	0.465944i	$0.154285\pi$
$103$	3.27116	+	13.1199i	0.322317	+	1.29274i	−0.562497	+	0.826799i	$0.690159\pi$
$104$	−10.2994	+	8.04677i	−1.00994	+	0.789050i
$105$		0			0
$106$	3.37124	+	1.64427i	0.327444	+	0.159705i
$107$	−2.01203	+	1.46183i	−0.194511	+	0.141320i	−0.680778	−	0.732490i	$-0.738358\pi$
$107$	−2.01203	+	1.46183i	−0.194511	+	0.141320i	0.486267	+	0.873810i	$0.338358\pi$
$108$		0			0
$109$			2.16942i			0.207793i	0.994588	+	0.103896i	$0.0331311\pi$
$109$			2.16942i			0.207793i	−0.994588	+	0.103896i	$0.966869\pi$
$110$	−2.00995	−	8.67776i	−0.191641	−	0.827392i
$111$		0			0
$112$	2.38747	−	0.0833721i	0.225594	−	0.00787793i
$113$	−0.586970	+	8.39407i	−0.0552175	+	0.789647i	0.888496	+	0.458884i	$0.151751\pi$
$113$	−0.586970	+	8.39407i	−0.0552175	+	0.789647i	−0.943714	+	0.330763i	$0.892694\pi$
$114$		0			0
$115$	−0.347316	+	9.94584i	−0.0323874	+	0.927455i
$116$	1.94036	−	2.15499i	0.180158	−	0.200085i
$117$		0			0
$118$	2.62861	−	0.276278i	0.241983	−	0.0254335i
$119$	−20.9123	+	8.44912i	−1.91703	+	0.774530i
$120$		0			0
$121$	−0.751646	+	10.9743i	−0.0683315	+	0.997663i
$122$	−1.83767	−	0.324031i	−0.166375	−	0.0293364i
$123$		0			0
$124$	2.06305	−	8.27443i	0.185267	−	0.743066i
$125$	1.67826	+	3.76943i	0.150108	+	0.337148i
$126$		0			0
$127$	−2.28636	−	2.05865i	−0.202882	−	0.182676i	0.561427	−	0.827527i	$-0.310253\pi$
$127$	−2.28636	−	2.05865i	−0.202882	−	0.182676i	−0.764308	+	0.644851i	$0.776919\pi$
$128$	−4.92740	−	7.30517i	−0.435525	−	0.645692i
$129$		0			0
$130$	11.0627	−	6.91276i	0.970266	−	0.606289i
$131$	−10.8415	+	3.94597i	−0.947224	+	0.344761i	−0.769014	−	0.639231i	$-0.779253\pi$
$131$	−10.8415	+	3.94597i	−0.947224	+	0.344761i	−0.178209	+	0.983993i	$0.557030\pi$
$132$		0			0
$133$	−1.16061	−	6.58212i	−0.100637	−	0.570742i
$134$	−0.779538	+	2.39917i	−0.0673418	+	0.207257i
$135$		0			0
$136$	11.4910	+	8.34868i	0.985343	+	0.715894i
$137$	1.26767	+	2.38414i	0.108304	+	0.203691i	0.931206	−	0.364493i	$-0.118758\pi$
$137$	1.26767	+	2.38414i	0.108304	+	0.203691i	−0.822902	+	0.568183i	$0.807646\pi$
$138$		0			0
$139$	−2.22081	+	7.74490i	−0.188367	+	0.656913i	0.809221	+	0.587504i	$0.199889\pi$
$139$	−2.22081	+	7.74490i	−0.188367	+	0.656913i	−0.997588	+	0.0694096i	$0.977888\pi$
$140$	−19.3960	−	1.35630i	−1.63926	−	0.114629i
$141$		0			0
$142$	−0.772080	+	2.12127i	−0.0647915	+	0.178013i
$143$	−15.5575	+	4.18053i	−1.30098	+	0.349594i
$144$		0			0
$145$	−5.31902	+	4.78927i	−0.441721	+	0.397727i
$146$	0.192264	+	0.0479367i	0.0159118	+	0.00396727i
$147$		0			0
$148$	−14.2326	+	2.00027i	−1.16992	+	0.164421i
$149$	3.37115	−	0.473784i	0.276175	−	0.0388139i	0.000274308	−	1.00000i	$-0.499913\pi$
$149$	3.37115	−	0.473784i	0.276175	−	0.0388139i	0.275901	+	0.961186i	$0.411024\pi$
$150$		0			0
$151$	−21.5247	−	5.36671i	−1.75166	−	0.436737i	−0.771706	−	0.635979i	$-0.780596\pi$
$151$	−21.5247	−	5.36671i	−1.75166	−	0.436737i	−0.979950	+	0.199242i	$0.936152\pi$
$152$	−3.12789	+	2.81636i	−0.253705	+	0.228437i
$153$		0			0
$154$	−10.6059	−	4.06252i	−0.854645	−	0.327367i
$155$	−7.19901	+	19.7791i	−0.578239	+	1.58870i
$156$		0			0
$157$	−14.1069	−	0.986447i	−1.12585	−	0.0787271i	−0.505336	−	0.862923i	$-0.668631\pi$
$157$	−14.1069	−	0.986447i	−1.12585	−	0.0787271i	−0.620514	+	0.784196i	$0.713076\pi$
$158$	−2.51107	+	8.75714i	−0.199770	+	0.696680i
$159$		0			0
$160$	9.17230	+	17.2506i	0.725134	+	1.36378i
$161$	10.2656	+	7.45839i	0.809042	+	0.587803i
$162$		0			0
$163$	−1.54220	+	4.74641i	−0.120795	+	0.371767i	−0.993111	−	0.117174i	$-0.962617\pi$
$163$	−1.54220	+	4.74641i	−0.120795	+	0.371767i	0.872317	+	0.488941i	$0.162617\pi$
$164$	1.27085	+	7.20734i	0.0992366	+	0.562799i
$165$		0			0
$166$	−4.07205	+	1.48211i	−0.316053	+	0.115034i
$167$	7.89422	−	4.93285i	0.610873	−	0.381716i	−0.188919	−	0.981993i	$-0.560499\pi$
$167$	7.89422	−	4.93285i	0.610873	−	0.381716i	0.799792	+	0.600277i	$0.204943\pi$
$168$		0			0
$169$	−5.92301	−	8.78122i	−0.455616	−	0.675478i
$170$	−10.5350	−	9.48577i	−0.807999	−	0.727526i
$171$		0			0
$172$	3.30869	+	7.43144i	0.252285	+	0.566642i
$173$	−3.85356	+	15.4558i	−0.292981	+	1.17508i	0.625694	+	0.780069i	$0.284816\pi$
$173$	−3.85356	+	15.4558i	−0.292981	+	1.17508i	−0.918675	+	0.395014i	$0.870740\pi$
$174$		0			0
$175$	26.2215	+	4.62356i	1.98216	+	0.349508i
$176$	−0.355105	−	1.81991i	−0.0267670	−	0.137181i
$177$		0			0
$178$	11.5882	−	4.68193i	0.868572	−	0.350926i
$179$	9.71912	−	1.02152i	0.726441	−	0.0763520i	0.265913	−	0.963997i	$-0.414327\pi$
$179$	9.71912	−	1.02152i	0.726441	−	0.0763520i	0.460528	+	0.887645i	$0.347660\pi$
$180$		0			0
$181$	9.55033	−	10.6067i	0.709871	−	0.788391i	−0.275044	−	0.961432i	$-0.588692\pi$
$181$	9.55033	−	10.6067i	0.709871	−	0.788391i	0.984915	+	0.173040i	$0.0553591\pi$
$182$	0.580472	−	16.6225i	0.0430274	−	1.23214i
$183$		0			0
$184$	0.557409	−	7.97132i	0.0410927	−	0.587654i
$185$	35.4532	−	1.23805i	2.60657	−	0.0910235i
$186$		0			0
$187$	9.02723	+	14.9996i	0.660136	+	1.09688i
$188$		−	7.89583i		−	0.575863i
$189$		0			0
$190$	3.39858	−	2.46921i	0.246559	−	0.179136i
$191$	−17.9977	−	8.77809i	−1.30227	−	0.635160i	−0.348956	−	0.937139i	$-0.613464\pi$
$191$	−17.9977	−	8.77809i	−1.30227	−	0.635160i	−0.953315	+	0.301979i	$0.902353\pi$
$192$		0			0
$193$	13.2562	−	10.3569i	0.954202	−	0.745504i	−0.0128937	−	0.999917i	$-0.504104\pi$
$193$	13.2562	−	10.3569i	0.954202	−	0.745504i	0.967096	+	0.254412i	$0.0818821\pi$
$194$	2.34065	+	9.38782i	0.168049	+	0.674006i
$195$		0			0
$196$	−9.41133	+	12.0459i	−0.672238	+	0.860425i
$197$	−2.45294	−	4.24861i	−0.174765	−	0.302701i	0.765315	−	0.643656i	$-0.222583\pi$
$197$	−2.45294	−	4.24861i	−0.174765	−	0.302701i	−0.940080	+	0.340955i	$0.889250\pi$
$198$		0			0
$199$	−3.27399	+	5.67071i	−0.232087	+	0.401986i	−0.958422	−	0.285354i	$-0.907889\pi$
$199$	−3.27399	+	5.67071i	−0.232087	+	0.401986i	0.726335	+	0.687341i	$0.241222\pi$
$200$	−6.28123	−	15.5466i	−0.444150	−	1.09931i
$201$		0			0
$202$	−1.33372	+	1.28796i	−0.0938400	+	0.0906202i
$203$	1.27009	+	9.03714i	0.0891427	+	0.634283i
$204$		0			0
$205$	−1.26007	−	18.0199i	−0.0880073	−	1.25856i
$206$	1.13268	+	10.7767i	0.0789176	+	0.750850i
$207$		0			0
$208$	2.35170	−	1.35775i	0.163061	−	0.0941434i
$209$	−4.90389	+	1.69246i	−0.339209	+	0.117070i
$210$		0			0
$211$	−3.19206	−	5.10836i	−0.219750	−	0.351674i	0.719743	−	0.694240i	$-0.244259\pi$
$211$	−3.19206	−	5.10836i	−0.219750	−	0.351674i	−0.939494	+	0.342566i	$0.888704\pi$
$212$	−5.26847	−	3.55363i	−0.361840	−	0.244064i
$213$		0			0
$214$	−1.75978	+	0.935691i	−0.120296	+	0.0639625i
$215$	−6.20459	−	19.0958i	−0.423149	−	1.30232i
$216$		0			0
$217$	15.7747	+	21.7120i	1.07085	+	1.47390i
$218$	−0.241961	+	1.72164i	−0.0163877	+	0.116604i
$219$		0			0
$220$	1.32606	+	15.0332i	0.0894027	+	1.01354i
$221$	−16.4799	+	19.6399i	−1.10855	+	1.32112i
$222$		0			0
$223$	−0.981492	+	0.281438i	−0.0657256	+	0.0188465i	−0.308339	−	0.951277i	$-0.599773\pi$
$223$	−0.981492	+	0.281438i	−0.0657256	+	0.0188465i	0.242613	+	0.970123i	$0.421995\pi$
$224$	24.7744	+	2.60389i	1.65531	+	0.173980i
$225$		0			0
$226$	−1.40203	+	6.59602i	−0.0932614	+	0.438760i
$227$	11.5689	−	0.808978i	0.767856	−	0.0536937i	0.319545	−	0.947571i	$-0.396470\pi$
$227$	11.5689	−	0.808978i	0.767856	−	0.0536937i	0.448311	+	0.893877i	$0.352026\pi$
$228$		0			0
$229$	−14.6827	−	7.80694i	−0.970261	−	0.515897i	−0.0928729	−	0.995678i	$-0.529605\pi$
$229$	−14.6827	−	7.80694i	−0.970261	−	0.515897i	−0.877388	+	0.479781i	$0.840716\pi$
$230$	−1.38491	+	7.85423i	−0.0913184	+	0.517892i
$231$		0			0
$232$	4.40246	−	3.69410i	0.289036	−	0.242530i
$233$	−9.74051	−	10.8179i	−0.638122	−	0.708706i	0.334160	−	0.942516i	$-0.391547\pi$
$233$	−9.74051	−	10.8179i	−0.638122	−	0.708706i	−0.972282	+	0.233810i	$0.924881\pi$
$234$		0			0
$235$	−2.03714	+	19.3820i	−0.132888	+	1.26435i
$236$	−4.47535	−	0.156283i	−0.291321	−	0.0101731i
$237$		0			0
$238$	−17.5382	+	4.37277i	−1.13684	+	0.283445i
$239$	2.30258	−	3.41372i	0.148942	−	0.220815i	−0.747182	−	0.664619i	$-0.768594\pi$
$239$	2.30258	−	3.41372i	0.148942	−	0.220815i	0.896124	+	0.443804i	$0.146371\pi$
$240$		0			0
$241$	−15.4961	+	2.73237i	−0.998189	+	0.176008i	−0.648791	−	0.760967i	$-0.724725\pi$
$241$	−15.4961	+	2.73237i	−0.998189	+	0.176008i	−0.349398	+	0.936974i	$0.613614\pi$
$242$	−1.82049	+	8.62530i	−0.117026	+	0.554455i
$243$		0			0
$244$	3.00678	+	0.976963i	0.192490	+	0.0625437i
$245$	26.2100	−	27.1413i	1.67450	−	1.73399i
$246$		0			0
$247$	−4.67742	−	5.98682i	−0.297617	−	0.380932i
$248$	6.33111	−	15.6701i	0.402026	−	0.995049i
$249$		0			0
$250$	0.911444	+	3.17858i	0.0576448	+	0.201031i
$251$	−1.87584	−	8.82512i	−0.118402	−	0.557037i	−0.996858	−	0.0792133i	$-0.974759\pi$
$251$	−1.87584	−	8.82512i	−0.118402	−	0.557037i	0.878456	−	0.477824i	$-0.158574\pi$
$252$		0			0
$253$	4.46505	−	8.77866i	0.280716	−	0.551909i
$254$	−1.58484	−	1.88873i	−0.0994415	−	0.118510i
$255$		0			0
$256$	−6.21139	−	12.7352i	−0.388212	−	0.795953i
$257$	−2.23997	−	2.31956i	−0.139725	−	0.144690i	0.645830	−	0.763481i	$-0.276512\pi$
$257$	−2.23997	−	2.31956i	−0.139725	−	0.144690i	−0.785555	+	0.618791i	$0.787623\pi$
$258$		0			0
$259$	23.9690	−	38.3584i	1.48936	−	2.38348i
$260$	−20.1907	+	8.98950i	−1.25218	+	0.557505i
$261$		0			0
$262$	−9.04383	+	1.92233i	−0.558730	+	0.118762i
$263$	9.60627	+	3.49640i	0.592348	+	0.215597i	0.620762	−	0.783999i	$-0.286823\pi$
$263$	9.60627	+	3.49640i	0.592348	+	0.215597i	−0.0284137	+	0.999596i	$0.509046\pi$
$264$		0			0
$265$	12.0158	+	10.0824i	0.738123	+	0.619359i
$266$	−0.186930	−	5.35298i	−0.0114614	−	0.328212i
$267$		0			0
$268$	1.87360	−	3.84145i	0.114448	−	0.234654i
$269$	15.0863	−	4.90185i	0.919830	−	0.298871i	0.189433	−	0.981894i	$-0.439335\pi$
$269$	15.0863	−	4.90185i	0.919830	−	0.298871i	0.730397	+	0.683023i	$0.239335\pi$
$270$		0			0
$271$	−9.29765	+	12.7971i	−0.564792	+	0.777369i	−0.991926	−	0.126819i	$-0.959523\pi$
$271$	−9.29765	+	12.7971i	−0.564792	+	0.777369i	0.427134	+	0.904188i	$0.359523\pi$
$272$	−2.12278	−	2.04995i	−0.128713	−	0.124296i
$273$		0			0
$274$	0.740106	+	2.03343i	0.0447115	+	0.122844i
$275$	0.345924	−	20.6637i	0.0208600	−	1.24607i
$276$		0			0
$277$	−1.91573	−	1.49673i	−0.115105	−	0.0899300i	0.556465	−	0.830871i	$-0.312157\pi$
$277$	−1.91573	−	1.49673i	−0.115105	−	0.0899300i	−0.671570	+	0.740941i	$0.734380\pi$
$278$	−2.62623	+	5.89861i	−0.157511	+	0.353775i
$279$		0			0
$280$	−37.6919	−	8.01165i	−2.25252	−	0.478788i
$281$	−12.0155	−	7.50812i	−0.716785	−	0.447897i	0.121880	−	0.992545i	$-0.461108\pi$
$281$	−12.0155	−	7.50812i	−0.716785	−	0.447897i	−0.838665	+	0.544648i	$0.816663\pi$
$282$		0			0
$283$	9.93980	−	4.84796i	0.590860	−	0.288181i	−0.118584	−	0.992944i	$-0.537835\pi$
$283$	9.93980	−	4.84796i	0.590860	−	0.288181i	0.709443	+	0.704763i	$0.248946\pi$
$284$	1.79556	−	3.37696i	0.106547	−	0.200386i
$285$		0			0
$286$	−12.8126	+	1.58248i	−0.757625	+	0.0935740i
$287$	−19.9463	−	11.5160i	−1.17739	−	0.679767i
$288$		0			0
$289$	9.92254	+	4.41780i	0.583679	+	0.259871i
$290$	−4.75530	+	3.20749i	−0.279241	+	0.188350i
$291$		0			0
$292$	−0.311271	−	0.125762i	−0.0182158	−	0.00735964i
$293$	18.9301	+	5.42813i	1.10591	+	0.317115i	0.778422	−	0.627741i	$-0.216020\pi$
$293$	18.9301	+	5.42813i	1.10591	+	0.317115i	0.327488	+	0.944855i	$0.393798\pi$
$294$		0			0
$295$	10.9454	+	1.53828i	0.637267	+	0.0895620i
$296$	−28.4842			−1.65561
$297$		0			0
$298$	2.72817			0.158038
$299$	14.2833	+	2.00739i	0.826025	+	0.116090i
$300$		0			0
$301$	−24.6089	−	7.05649i	−1.41843	−	0.406729i
$302$	−16.4833	−	6.65970i	−0.948509	−	0.383223i
$303$		0			0
$304$	0.724976	−	0.489002i	0.0415802	−	0.0280462i
$305$	−7.12875	−	3.17393i	−0.408191	−	0.181738i
$306$		0			0
$307$	20.5084	+	11.8405i	1.17048	+	0.675774i	0.953792	−	0.300468i	$-0.0971427\pi$
$307$	20.5084	+	11.8405i	1.17048	+	0.675774i	0.216683	+	0.976242i	$0.430476\pi$
$308$	16.8363	+	9.31680i	0.959337	+	0.530874i
$309$		0			0
$310$	−7.91911	+	14.8937i	−0.449775	+	0.845904i
$311$	−21.3530	+	10.4146i	−1.21082	+	0.590555i	−0.929415	−	0.369035i	$-0.879688\pi$
$311$	−21.3530	+	10.4146i	−1.21082	+	0.590555i	−0.281402	+	0.959590i	$0.590799\pi$
$312$		0			0
$313$	17.7192	+	11.0722i	1.00155	+	0.625838i	0.928439	−	0.371486i	$-0.121152\pi$
$313$	17.7192	+	11.0722i	1.00155	+	0.625838i	0.0731115	+	0.997324i	$0.476707\pi$
$314$	−11.0851	−	2.35621i	−0.625568	−	0.132969i
$315$		0			0
$316$	6.27789	−	14.1004i	0.353159	−	0.793208i
$317$	10.9597	+	8.56263i	0.615556	+	0.480925i	0.874538	−	0.484957i	$-0.161165\pi$
$317$	10.9597	+	8.56263i	0.615556	+	0.480925i	−0.258982	+	0.965882i	$0.583387\pi$
$318$		0			0
$319$	6.77240	−	2.07582i	0.379182	−	0.116224i
$320$	4.07345	+	11.1917i	0.227713	+	0.625636i
$321$		0			0
$322$	7.31486	+	7.06388i	0.407641	+	0.393655i
$323$	−4.85291	+	6.67946i	−0.270023	+	0.371655i
$324$		0			0
$325$	28.7847	−	9.35272i	1.59669	−	0.518795i
$326$	−1.75326	+	3.59472i	−0.0971041	+	0.199093i
$327$		0			0
$328$	0.506190	+	14.4954i	0.0279497	+	0.800374i
$329$	19.0353	+	15.9725i	1.04945	+	0.880592i
$330$		0			0
$331$	−29.1864	−	10.6230i	−1.60423	−	0.583892i	−0.623942	−	0.781470i	$-0.714470\pi$
$331$	−29.1864	−	10.6230i	−1.60423	−	0.583892i	−0.980287	+	0.197579i	$0.936692\pi$
$332$	7.18145	−	1.52646i	0.394133	−	0.0837756i
$333$		0			0
$334$	6.81498	−	3.03422i	0.372899	−	0.166025i
$335$	−5.59026	+	8.94629i	−0.305429	+	0.488788i
$336$		0			0
$337$	−10.9669	−	11.3566i	−0.597406	−	0.618632i	0.350737	−	0.936474i	$-0.385931\pi$
$337$	−10.9669	−	11.3566i	−0.597406	−	0.618632i	−0.948144	+	0.317841i	$0.897042\pi$
$338$	−3.72107	−	7.62933i	−0.202400	−	0.414981i
$339$		0			0
$340$	15.4387	+	18.3991i	0.837278	+	0.997830i
$341$	14.7190	−	14.7401i	0.797080	−	0.798219i
$342$		0			0
$343$	−3.78334	−	17.7992i	−0.204281	−	0.961068i
$344$	4.44377	+	15.4973i	0.239592	+	0.835557i
$345$		0			0
$346$	−4.78199	+	11.8358i	−0.257081	+	0.636299i
$347$	4.59256	+	5.87821i	0.246542	+	0.315559i	0.895324	−	0.445415i	$-0.146944\pi$
$347$	4.59256	+	5.87821i	0.246542	+	0.315559i	−0.648783	+	0.760974i	$0.724722\pi$
$348$		0			0
$349$	−13.3433	+	13.8174i	−0.714251	+	0.739628i	−0.974124	−	0.226014i	$-0.927430\pi$
$349$	−13.3433	+	13.8174i	−0.714251	+	0.739628i	0.259873	+	0.965643i	$0.416319\pi$
$350$	20.2935	+	6.59377i	1.08474	+	0.352452i
$351$		0			0
$352$	−1.02572	−	19.3081i	−0.0546712	−	1.02913i
$353$	20.9219	−	3.68910i	1.11356	−	0.196351i	0.413549	−	0.910482i	$-0.364289\pi$
$353$	20.9219	−	3.68910i	1.11356	−	0.196351i	0.700012	+	0.714131i	$0.253178\pi$
$354$		0			0
$355$	−5.27886	+	7.82623i	−0.280173	+	0.415373i
$356$	−20.5463	+	5.12277i	−1.08895	+	0.271506i
$357$		0			0
$358$	7.82697	+	0.273324i	0.413668	+	0.0144456i
$359$	−1.07257	+	10.2048i	−0.0566079	+	0.538588i	0.929065	+	0.369918i	$0.120614\pi$
$359$	−1.07257	+	10.2048i	−0.0566079	+	0.538588i	−0.985672	+	0.168671i	$0.946053\pi$
$360$		0			0
$361$	11.0764	+	12.3016i	0.582968	+	0.647451i
$362$	8.76208	−	7.35226i	0.460525	−	0.386426i
$363$		0			0
$364$	−4.89342	+	27.7519i	−0.256485	+	1.45460i
$365$	0.731636	+	0.389018i	0.0382956	+	0.0203621i
$366$		0			0
$367$	−17.1252	+	1.19751i	−0.893926	+	0.0625094i	−0.509326	−	0.860574i	$-0.670105\pi$
$367$	−17.1252	+	1.19751i	−0.893926	+	0.0625094i	−0.384600	+	0.923083i	$0.625661\pi$
$368$	−0.345176	+	1.62392i	−0.0179935	+	0.0846529i
$369$		0			0
$370$	28.2736	+	2.97167i	1.46987	+	0.154490i
$371$	19.2247	−	5.51259i	0.998096	−	0.286199i
$372$		0			0
$373$	−7.09352	+	8.45373i	−0.367289	+	0.437717i	−0.917759	−	0.397137i	$-0.870004\pi$
$373$	−7.09352	+	8.45373i	−0.367289	+	0.437717i	0.550471	+	0.834854i	$0.314448\pi$
$374$	5.49102	+	12.9104i	0.283934	+	0.667580i
$375$		0			0
$376$	2.17783	−	15.4961i	0.112313	−	0.799148i
$377$	6.09743	+	8.39239i	0.314034	+	0.432230i
$378$		0			0
$379$	−3.94107	−	12.1294i	−0.202439	−	0.623044i	−0.999809	−	0.0195526i	$-0.993776\pi$
$379$	−3.94107	−	12.1294i	−0.202439	−	0.623044i	0.797370	−	0.603491i	$-0.206224\pi$
$380$	−6.28427	+	3.34141i	−0.322376	+	0.171411i
$381$		0			0
$382$	−13.3039	−	8.97357i	−0.680685	−	0.459128i
$383$	−2.53114	−	4.05068i	−0.129335	−	0.206980i	0.777042	−	0.629449i	$-0.216719\pi$
$383$	−2.53114	−	4.05068i	−0.129335	−	0.206980i	−0.906378	+	0.422469i	$0.861164\pi$
$384$		0			0
$385$	−38.9246	−	27.2139i	−1.98378	−	1.38695i
$386$	11.6752	−	6.74066i	0.594251	−	0.343091i
$387$		0			0
$388$	−1.71347	−	16.3025i	−0.0869880	−	0.827636i
$389$	1.05873	+	15.1405i	0.0536796	+	0.767654i	0.947606	+	0.319441i	$0.103495\pi$
$389$	1.05873	+	15.1405i	0.0536796	+	0.767654i	−0.893927	+	0.448213i	$0.852061\pi$
$390$		0			0
$391$	−2.18148	−	15.5220i	−0.110322	−	0.784983i
$392$	−21.7928	+	21.0451i	−1.10070	+	1.06294i
$393$		0			0
$394$	−1.47278	−	3.64526i	−0.0741975	−	0.183645i
$395$	−19.0484	+	32.9928i	−0.958428	+	1.66005i
$396$		0			0
$397$	8.39802	+	14.5458i	0.421485	+	0.730033i	0.996085	−	0.0884014i	$-0.0281758\pi$
$397$	8.39802	+	14.5458i	0.421485	+	0.730033i	−0.574600	+	0.818434i	$0.694842\pi$
$398$	−3.23069	+	4.13509i	−0.161940	+	0.207273i
$399$		0			0
$400$	0.842784	+	3.38022i	0.0421392	+	0.169011i
$401$	−4.22107	+	3.29786i	−0.210790	+	0.164687i	−0.715525	−	0.698587i	$-0.753812\pi$
$401$	−4.22107	+	3.29786i	−0.210790	+	0.164687i	0.504735	+	0.863274i	$0.331590\pi$
$402$		0			0
$403$	27.4190	+	13.3731i	1.36584	+	0.666163i
$404$	2.54137	−	1.84641i	0.126438	−	0.0918623i
$405$		0			0
$406$			7.31348i			0.362962i
$407$	−32.3267	−	13.6946i	−1.60237	−	0.678817i
$408$		0			0
$409$	21.3100	−	0.744161i	1.05371	−	0.0367964i	0.497199	−	0.867636i	$-0.334362\pi$
$409$	21.3100	−	0.744161i	1.05371	−	0.0367964i	0.556511	+	0.830840i	$0.312140\pi$
$410$	1.00981	−	14.4410i	0.0498712	−	0.713191i
$411$		0			0
$412$	0.640725	−	18.3480i	0.0315663	−	0.903940i
$413$	9.42997	−	10.4730i	0.464019	−	0.515345i
$414$		0			0
$415$	−18.0223	+	1.89422i	−0.884679	+	0.0929835i
$416$	26.2545	−	10.6075i	1.28723	−	0.520076i
$417$		0			0
$418$	−4.08046	+	0.796186i	−0.199582	+	0.0389427i
$419$	38.2083	+	6.73716i	1.86660	+	0.329132i	0.988723	−	0.149757i	$-0.0478492\pi$
$419$	38.2083	+	6.73716i	1.86660	+	0.329132i	0.877876	+	0.478889i	$0.158960\pi$
$420$		0			0
$421$	−1.76306	+	7.07123i	−0.0859261	+	0.344631i	−0.997835	−	0.0657610i	$-0.979053\pi$
$421$	−1.76306	+	7.07123i	−0.0859261	+	0.344631i	0.911909	+	0.410392i	$0.134608\pi$
$422$	−1.96345	−	4.40998i	−0.0955793	−	0.214675i
$423$		0			0
$424$	−9.35954	−	8.42736i	−0.454539	−	0.409269i
$425$	−18.3923	−	27.2678i	−0.892160	−	1.32268i
$426$		0			0
$427$	−8.43770	+	5.27246i	−0.408329	+	0.255152i
$428$	3.17314	−	1.15493i	0.153379	−	0.0558255i
$429$		0			0
$430$	−2.79413	−	15.8463i	−0.134745	−	0.764176i
$431$	4.51246	−	13.8879i	0.217358	−	0.668958i	−0.781620	−	0.623755i	$-0.785606\pi$
$431$	4.51246	−	13.8879i	0.217358	−	0.668958i	0.998978	−	0.0452032i	$-0.0143935\pi$
$432$		0			0
$433$	−30.8874	−	22.4410i	−1.48435	−	1.07845i	−0.976122	−	0.217225i	$-0.930300\pi$
$433$	−30.8874	−	22.4410i	−1.48435	−	1.07845i	−0.508231	−	0.861221i	$-0.669700\pi$
$434$	10.0971	+	18.9899i	0.484676	+	0.911543i
$435$		0			0
$436$	0.811910	−	2.83147i	0.0388834	−	0.135603i
$437$	4.63356	+	0.324010i	0.221653	+	0.0154995i
$438$		0			0
$439$	−5.33306	+	14.6525i	−0.254533	+	0.699324i	0.744948	+	0.667122i	$0.232474\pi$
$439$	−5.33306	+	14.6525i	−0.254533	+	0.699324i	−0.999481	+	0.0322016i	$0.989748\pi$
$440$	−1.54400	+	29.8694i	−0.0736073	+	1.42397i
$441$		0			0
$442$	−15.2688	+	13.7481i	−0.726263	+	0.653930i
$443$	−19.6708	−	4.90449i	−0.934590	−	0.233019i	−0.255277	−	0.966868i	$-0.582167\pi$
$443$	−19.6708	−	4.90449i	−0.934590	−	0.233019i	−0.679313	+	0.733849i	$0.737722\pi$
$444$		0			0
$445$	51.7571	−	7.27399i	2.45352	−	0.344820i
$446$	−0.810296	+	0.113880i	−0.0383686	+	0.00539236i
$447$		0			0
$448$	14.7345	+	3.67372i	0.696139	+	0.173567i
$449$	18.8135	−	16.9398i	0.887864	−	0.799437i	−0.0926880	−	0.995695i	$-0.529546\pi$
$449$	18.8135	−	16.9398i	0.887864	−	0.799437i	0.980552	+	0.196259i	$0.0628792\pi$
$450$		0			0
$451$	−6.39462	+	16.6942i	−0.301111	+	0.786098i
$452$	3.90759	−	10.7360i	0.183798	−	0.504980i
$453$		0			0
$454$	9.27126	+	0.648309i	0.435122	+	0.0304267i
$455$	19.1720	−	66.8607i	0.898798	−	3.13448i
$456$		0			0
$457$	2.03908	+	3.83496i	0.0953844	+	0.179392i	0.926072	−	0.377347i	$-0.123164\pi$
$457$	2.03908	+	3.83496i	0.0953844	+	0.179392i	−0.830688	+	0.556739i	$0.812052\pi$
$458$	−10.7814	−	7.83314i	−0.503781	−	0.366019i
$459$		0			0
$460$	4.17556	−	12.8510i	0.194686	−	0.599183i
$461$	5.97615	+	33.8924i	0.278337	+	1.57853i	0.728158	+	0.685409i	$0.240377\pi$
$461$	5.97615	+	33.8924i	0.278337	+	1.57853i	−0.449821	+	0.893119i	$0.648512\pi$
$462$		0			0
$463$	36.1448	−	13.1556i	1.67979	−	0.611394i	0.686510	−	0.727120i	$-0.259142\pi$
$463$	36.1448	−	13.1556i	1.67979	−	0.611394i	0.993281	+	0.115726i	$0.0369194\pi$
$464$	−1.01259	+	0.632737i	−0.0470083	+	0.0293741i
$465$		0			0
$466$	−6.52346	−	9.67143i	−0.302194	−	0.448020i
$467$	−12.2512	−	11.0310i	−0.566919	−	0.510456i	0.335083	−	0.942189i	$-0.391236\pi$
$467$	−12.2512	−	11.0310i	−0.566919	−	0.510456i	−0.902002	+	0.431733i	$0.857902\pi$
$468$		0			0
$469$	5.47086	+	12.2878i	0.252621	+	0.567396i
$470$	−3.77838	+	15.1543i	−0.174284	+	0.699015i
$471$		0			0
$472$	−8.74005	−	1.54111i	−0.402294	−	0.0709352i
$473$	−2.40755	+	19.7243i	−0.110699	+	0.906926i
$474$		0			0
$475$	9.03690	−	3.65114i	0.414641	−	0.167526i
$476$	30.4562	−	3.20108i	1.39596	−	0.146721i
$477$		0			0
$478$	2.20806	−	2.45229i	0.100994	−	0.112165i
$479$	0.885987	−	25.3713i	0.0404818	−	1.15925i	−0.793896	−	0.608053i	$-0.791951\pi$
$479$	0.885987	−	25.3713i	0.0404818	−	1.15925i	0.834378	−	0.551193i	$-0.185827\pi$
$480$		0			0
$481$	3.58653	−	51.2898i	0.163532	−	2.33861i
$482$	−12.6023	+	0.440083i	−0.574021	+	0.0200452i
$483$		0			0
$484$	5.08817	−	14.0420i	0.231281	−	0.638274i
$485$			40.4602i			1.83720i
$486$		0			0
$487$	−25.6524	+	18.6376i	−1.16242	+	0.844549i	−0.990082	−	0.140489i	$-0.955133\pi$
$487$	−25.6524	+	18.6376i	−1.16242	+	0.844549i	−0.172339	+	0.985038i	$0.555133\pi$
$488$	5.63154	+	2.74668i	0.254928	+	0.124337i
$489$		0			0
$490$	23.8273	−	18.6159i	1.07641	−	0.840981i
$491$	−3.39411	−	13.6130i	−0.153174	−	0.614347i	−0.996977	−	0.0776947i	$-0.975244\pi$
$491$	−3.39411	−	13.6130i	−0.153174	−	0.614347i	0.843803	−	0.536653i	$-0.180311\pi$
$492$		0			0
$493$	6.94049	−	8.88342i	0.312584	−	0.400089i
$494$	−3.04425	−	5.27279i	−0.136967	−	0.237234i
$495$		0			0
$496$	−1.75568	+	3.04093i	−0.0788326	+	0.136542i
$497$	4.50893	+	11.1600i	0.202253	+	0.500594i
$498$		0			0
$499$	21.6740	−	20.9303i	0.970260	−	0.936970i	−0.0277755	−	0.999614i	$-0.508842\pi$
$499$	21.6740	−	20.9303i	0.970260	−	0.936970i	0.998036	+	0.0626446i	$0.0199535\pi$
$500$	−0.779699	−	5.54785i	−0.0348692	−	0.248107i
$501$		0			0
$502$	−0.504367	−	7.21278i	−0.0225110	−	0.321922i
$503$	−1.84283	−	17.5333i	−0.0821676	−	0.781773i	−0.955568	−	0.294770i	$-0.904757\pi$
$503$	−1.84283	−	17.5333i	−0.0821676	−	0.781773i	0.873400	−	0.487003i	$-0.161910\pi$
$504$		0			0
$505$	−6.71472	+	3.87674i	−0.298801	+	0.172513i
$506$	4.52255	−	6.46869i	0.201052	−	0.287568i
$507$		0			0
$508$	2.21364	+	3.54256i	0.0982143	+	0.157176i
$509$	−25.9019	−	17.4711i	−1.14808	−	0.774391i	−0.170586	−	0.985343i	$-0.554566\pi$
$509$	−25.9019	−	17.4711i	−1.14808	−	0.774391i	−0.977497	+	0.210952i	$0.932344\pi$
$510$		0			0
$511$	0.932858	−	0.496009i	0.0412672	−	0.0219422i
$512$	1.93695	+	5.96132i	0.0856020	+	0.263456i
$513$		0			0
$514$	−1.51892	−	2.09062i	−0.0669967	−	0.0922131i
$515$	−6.30660	+	44.8738i	−0.277902	+	1.97738i
$516$		0			0
$517$	9.92181	−	16.5394i	0.436361	−	0.727403i
$518$	23.2999	−	27.7677i	1.02374	−	1.22004i
$519$		0			0
$520$	−42.1051	+	12.0734i	−1.84643	+	0.529455i
$521$	−2.40815	−	0.253106i	−0.105503	−	0.0110888i	0.0516299	−	0.998666i	$-0.483558\pi$
$521$	−2.40815	−	0.253106i	−0.105503	−	0.0110888i	−0.157133	+	0.987577i	$0.550225\pi$
$522$		0			0
$523$	2.49227	−	11.7252i	0.108979	−	0.512707i	−0.889468	−	0.456998i	$-0.848925\pi$
$523$	2.49227	−	11.7252i	0.108979	−	0.512707i	0.998447	−	0.0557092i	$-0.0177420\pi$
$524$	15.6268	−	1.09273i	0.682658	−	0.0477361i
$525$		0			0
$526$	7.23352	+	3.84613i	0.315397	+	0.167699i
$527$	5.75680	−	32.6484i	0.250770	−	1.42219i
$528$		0			0
$529$	10.8638	−	9.11581i	0.472339	−	0.396339i
$530$	8.41113	+	9.34150i	0.365356	+	0.405769i
$531$		0			0
$532$	−0.948582	+	9.02515i	−0.0411262	+	0.391290i
$533$	−26.1647	−	0.913692i	−1.13332	−	0.0395764i
$534$		0			0
$535$	−8.08714	+	2.01635i	−0.349637	+	0.0871744i
$536$	4.73661	−	7.02231i	0.204590	−	0.303317i
$537$		0			0
$538$	12.5191	−	2.20746i	0.539739	−	0.0951705i
$539$	−34.8507	+	13.4065i	−1.50113	+	0.577459i
$540$		0			0
$541$	38.8169	+	12.6124i	1.66887	+	0.542248i	0.982702	−	0.185196i	$-0.0592919\pi$
$541$	38.8169	+	12.6124i	1.66887	+	0.542248i	0.686167	+	0.727444i	$0.259292\pi$
$542$	−8.80585	+	9.11873i	−0.378244	+	0.391683i
$543$		0			0
$544$	−18.9452	−	24.2488i	−0.812271	−	1.03966i
$545$	−2.72353	+	6.74098i	−0.116663	+	0.288752i
$546$		0			0
$547$	1.07303	+	3.74211i	0.0458796	+	0.160001i	0.980867	−	0.194681i	$-0.0623670\pi$
$547$	1.07303	+	3.74211i	0.0458796	+	0.160001i	−0.934987	+	0.354682i	$0.884589\pi$
$548$	−0.762257	−	3.58614i	−0.0325620	−	0.153192i
$549$		0			0
$550$	2.57919	−	16.3600i	0.109977	−	0.697593i
$551$	2.14730	+	2.55906i	0.0914782	+	0.109020i
$552$		0			0
$553$	21.2936	+	43.6584i	0.905498	+	1.85655i
$554$	−1.35338	−	1.40146i	−0.0574996	−	0.0595425i
$555$		0			0
$556$	5.79708	−	9.27727i	0.245851	−	0.393444i
$557$	−18.6920	+	8.32223i	−0.792007	+	0.352624i	−0.762540	−	0.646942i	$-0.776048\pi$
$557$	−18.6920	+	8.32223i	−0.792007	+	0.352624i	−0.0294673	+	0.999566i	$0.509381\pi$
$558$		0			0
$559$	−28.4646	+	6.05033i	−1.20392	+	0.255902i
$560$	7.52317	+	2.73821i	0.317912	+	0.115710i
$561$		0			0
$562$	−8.69803	−	7.29852i	−0.366904	−	0.307869i
$563$	−1.48760	−	42.5994i	−0.0626950	−	1.79535i	−0.470621	−	0.882336i	$-0.655970\pi$
$563$	−1.48760	−	42.5994i	−0.0626950	−	1.79535i	0.407926	−	0.913015i	$-0.366252\pi$
$564$		0			0
$565$	−12.3619	+	25.3457i	−0.520071	+	1.06630i
$566$	8.42887	−	2.73871i	0.354292	−	0.115116i
$567$		0			0
$568$	4.45533	−	6.13224i	0.186942	−	0.257303i
$569$	11.8812	+	11.4735i	0.498085	+	0.480995i	0.900741	−	0.434357i	$-0.143024\pi$
$569$	11.8812	+	11.4735i	0.498085	+	0.480995i	−0.402657	+	0.915351i	$0.631913\pi$
$570$		0			0
$571$	11.1190	+	30.5493i	0.465316	+	1.27845i	0.921437	+	0.388528i	$0.127016\pi$
$571$	11.1190	+	30.5493i	0.465316	+	1.27845i	−0.456120	+	0.889918i	$0.650761\pi$
$572$	21.8698	+	0.366114i	0.914421	+	0.0153080i
$573$		0			0
$574$	−14.5448	−	11.3637i	−0.607090	−	0.474311i
$575$	−7.52625	+	16.9042i	−0.313866	+	0.704955i
$576$		0			0
$577$	−27.8201	−	5.91333i	−1.15816	−	0.246175i	−0.411521	−	0.911400i	$-0.635002\pi$
$577$	−27.8201	−	5.91333i	−1.15816	−	0.246175i	−0.746643	+	0.665225i	$0.768336\pi$
$578$	7.38175	+	4.61263i	0.307040	+	0.191860i
$579$		0			0
$580$	8.73463	−	4.26016i	0.362686	−	0.176894i
$581$	−10.8474	+	20.4009i	−0.450025	+	0.846374i
$582$		0			0
$583$	−6.57042	−	14.0641i	−0.272119	−	0.582475i
$584$	−0.576201	−	0.332670i	−0.0238434	−	0.0137660i
$585$		0			0
$586$	14.4174	+	6.41905i	0.595579	+	0.265169i
$587$	14.4303	−	9.73334i	0.595601	−	0.401738i	−0.224070	−	0.974573i	$-0.571934\pi$
$587$	14.4303	−	9.73334i	0.595601	−	0.401738i	0.819670	+	0.572835i	$0.194157\pi$
$588$		0			0
$589$	9.10867	+	3.68014i	0.375316	+	0.151638i
$590$	8.51465	+	2.44154i	0.350543	+	0.100516i
$591$		0			0
$592$	5.86041	+	0.823627i	0.240861	+	0.0338509i
$593$	35.7162			1.46669			0.733345	−	0.679856i	$-0.237958\pi$
$593$	35.7162			1.46669			0.733345	+	0.679856i	$0.237958\pi$
$594$		0			0
$595$	−75.5874			−3.09878
$596$	−4.57724	−	0.643289i	−0.187491	−	0.0263502i
$597$		0			0
$598$	11.1113	+	3.18610i	0.454373	+	0.130289i
$599$	−9.64510	−	3.89687i	−0.394088	−	0.159222i	0.169005	−	0.985615i	$-0.445944\pi$
$599$	−9.64510	−	3.89687i	−0.394088	−	0.159222i	−0.563093	+	0.826393i	$0.690389\pi$
$600$		0			0
$601$	20.7338	−	13.9851i	0.845751	−	0.570466i	−0.0581015	−	0.998311i	$-0.518505\pi$
$601$	20.7338	−	13.9851i	0.845751	−	0.570466i	0.903852	+	0.427845i	$0.140727\pi$
$602$	−18.7425	−	8.34468i	−0.763886	−	0.340104i
$603$		0			0
$604$	26.0849	+	15.0601i	1.06138	+	0.612788i
$605$	−16.1129	+	33.1565i	−0.655083	+	1.34800i
$606$		0			0
$607$	−15.3250	+	28.8222i	−0.622024	+	1.16986i	0.350392	+	0.936603i	$0.386048\pi$
$607$	−15.3250	+	28.8222i	−0.622024	+	1.16986i	−0.972416	+	0.233254i	$0.925063\pi$
$608$	8.19590	−	3.99741i	0.332388	−	0.162116i
$609$		0			0
$610$	−5.30334	−	3.31390i	−0.214726	−	0.134176i
$611$	27.6286	+	5.87265i	1.11773	+	0.237582i
$612$		0			0
$613$	−19.0640	+	42.8184i	−0.769987	+	1.72942i	−0.0903037	+	0.995914i	$0.528784\pi$
$613$	−19.0640	+	42.8184i	−0.769987	+	1.72942i	−0.679684	+	0.733505i	$0.737883\pi$
$614$	14.9547	+	11.6839i	0.603524	+	0.471525i
$615$		0			0
$616$	30.4725	+	22.9286i	1.22777	+	0.923819i
$617$	−1.00444	−	2.75968i	−0.0404373	−	0.111101i	0.917831	−	0.396972i	$-0.129939\pi$
$617$	−1.00444	−	2.75968i	−0.0404373	−	0.111101i	−0.958268	+	0.285872i	$0.907717\pi$
$618$		0			0
$619$	5.54492	+	5.35466i	0.222869	+	0.215222i	0.797707	−	0.603045i	$-0.206046\pi$
$619$	5.54492	+	5.35466i	0.222869	+	0.215222i	−0.574838	+	0.818267i	$0.694935\pi$
$620$	16.7983	−	23.1209i	0.674637	−	0.928558i
$621$		0			0
$622$	−18.1072	+	5.88338i	−0.726032	+	0.235902i
$623$	29.2132	−	59.8960i	1.17040	−	2.39968i
$624$		0			0
$625$	−0.604741	−	17.3175i	−0.0241896	−	0.692700i
$626$	12.8270	+	10.7631i	0.512669	+	0.430180i
$627$		0			0
$628$	18.0427	+	6.56700i	0.719981	+	0.262052i
$629$	−54.6530	+	11.6169i	−2.17916	+	0.463195i
$630$		0			0
$631$	26.2906	−	11.7053i	1.04661	−	0.465981i	0.189914	−	0.981801i	$-0.439179\pi$
$631$	26.2906	−	11.7053i	1.04661	−	0.465981i	0.856697	+	0.515819i	$0.172512\pi$
$632$	16.2099	−	25.9413i	0.644796	−	1.03189i
$633$		0			0
$634$	7.74252	+	8.01762i	0.307495	+	0.318420i
$635$	−4.51988	−	9.26712i	−0.179366	−	0.367754i
$636$		0			0
$637$	−35.1507	−	41.8909i	−1.39272	−	1.65978i
$638$	5.60606	−	0.892018i	0.221946	−	0.0353153i
$639$		0			0
$640$	−6.13972	−	28.8851i	−0.242694	−	1.14178i
$641$	9.63638	+	33.6061i	0.380614	+	1.32736i	0.885687	+	0.464283i	$0.153688\pi$
$641$	9.63638	+	33.6061i	0.380614	+	1.32736i	−0.505073	+	0.863077i	$0.668534\pi$
$642$		0			0
$643$	−0.411091	+	1.01749i	−0.0162118	+	0.0401257i	−0.935073	−	0.354456i	$-0.884666\pi$
$643$	−0.411091	+	1.01749i	−0.0162118	+	0.0401257i	0.918861	+	0.394582i	$0.129111\pi$
$644$	−10.6070	−	13.5764i	−0.417976	−	0.534985i
$645$		0			0
$646$	−4.59622	+	4.75953i	−0.180836	+	0.187261i
$647$	14.8983	+	4.84076i	0.585714	+	0.190310i	0.586859	−	0.809689i	$-0.300364\pi$
$647$	14.8983	+	4.84076i	0.585714	+	0.190310i	−0.00114459	+	0.999999i	$0.500364\pi$
$648$		0			0
$649$	−9.17815	−	5.95104i	−0.360274	−	0.233599i
$650$	23.8865	−	4.21184i	0.936906	−	0.165202i
$651$		0			0
$652$	3.78919	−	5.61770i	0.148396	−	0.220006i
$653$	5.11019	−	1.27411i	0.199977	−	0.0498599i	−0.140645	−	0.990060i	$-0.544918\pi$
$653$	5.11019	−	1.27411i	0.199977	−	0.0498599i	0.340623	+	0.940200i	$0.389362\pi$
$654$		0			0
$655$	−38.6412	−	1.34938i	−1.50984	−	0.0527247i
$656$	0.314993	−	2.99696i	0.0122984	−	0.117012i
$657$		0			0
$658$	13.3248	+	14.7987i	0.519456	+	0.576915i
$659$	6.90159	−	5.79112i	0.268848	−	0.225590i	−0.498390	−	0.866953i	$-0.666075\pi$
$659$	6.90159	−	5.79112i	0.268848	−	0.225590i	0.767238	+	0.641363i	$0.221631\pi$
$660$		0			0
$661$	7.14775	−	40.5369i	0.278015	−	1.57670i	−0.451203	−	0.892421i	$-0.649005\pi$
$661$	7.14775	−	40.5369i	0.278015	−	1.57670i	0.729219	−	0.684281i	$-0.239884\pi$
$662$	−21.9774	−	11.6856i	−0.854174	−	0.454172i
$663$		0			0
$664$	14.5151	−	1.01499i	0.563294	−	0.0393894i
$665$	4.65700	−	21.9095i	0.180591	−	0.849613i
$666$		0			0
$667$	−6.30743	−	0.662937i	−0.244225	−	0.0256690i
$668$	−12.1494	+	3.48379i	−0.470076	+	0.134792i
$669$		0			0
$670$	−5.43420	+	6.47623i	−0.209941	+	0.250199i
$671$	5.07068	+	5.82474i	0.195751	+	0.224862i
$672$		0			0
$673$	5.76787	−	41.0405i	0.222335	−	1.58200i	−0.484612	−	0.874729i	$-0.661039\pi$
$673$	5.76787	−	41.0405i	0.222335	−	1.58200i	0.706947	−	0.707267i	$-0.250072\pi$
$674$	−7.43666	−	10.2357i	−0.286450	−	0.394264i
$675$		0			0
$676$	4.44415	+	13.6777i	0.170929	+	0.526065i
$677$	23.3319	−	12.4058i	0.896719	−	0.476794i	0.0439209	−	0.999035i	$-0.486015\pi$
$677$	23.3319	−	12.4058i	0.896719	−	0.476794i	0.852798	+	0.522241i	$0.174904\pi$
$678$		0			0
$679$	42.7684	+	28.8476i	1.64130	+	1.10707i
$680$	25.2245	+	40.3676i	0.967315	+	1.54803i
$681$		0			0
$682$	13.3249	−	10.0560i	0.510238	−	0.385063i
$683$	−40.8468	+	23.5829i	−1.56296	+	0.902375i	−0.566005	+	0.824402i	$0.691512\pi$
$683$	−40.8468	+	23.5829i	−1.56296	+	0.902375i	−0.996955	+	0.0779734i	$0.975155\pi$
$684$		0			0
$685$	0.945899	+	8.99962i	0.0361409	+	0.343858i
$686$	−1.01725	−	14.5473i	−0.0388387	−	0.555419i
$687$		0			0
$688$	−0.466166	−	3.31695i	−0.0177724	−	0.126457i
$689$	16.3531	−	15.7921i	0.623005	−	0.601629i
$690$		0			0
$691$	13.5950	+	33.6487i	0.517177	+	1.28006i	0.929434	+	0.368990i	$0.120296\pi$
$691$	13.5950	+	33.6487i	0.517177	+	1.28006i	−0.412257	+	0.911068i	$0.635259\pi$
$692$	10.8139	−	18.7303i	0.411084	−	0.712018i
$693$		0			0
$694$	2.98902	+	5.17713i	0.113462	+	0.196521i
$695$	−16.6238	+	21.2774i	−0.630575	+	0.807099i
$696$		0			0
$697$	6.88297	+	27.6061i	0.260711	+	1.04566i
$698$	−12.1303	+	9.47720i	−0.459137	+	0.358717i
$699$		0			0
$700$	−32.4931	−	15.8480i	−1.22813	−	0.598997i
$701$	−20.3162	+	14.7606i	−0.767333	+	0.557500i	−0.901151	−	0.433506i	$-0.857276\pi$
$701$	−20.3162	+	14.7606i	−0.767333	+	0.557500i	0.133818	+	0.991006i	$0.457276\pi$
$702$		0			0
$703$		−	16.5572i		−	0.624468i
$704$	1.01890	−	11.7426i	0.0384011	−	0.442567i
$705$		0			0
$706$	17.0150	−	0.594176i	0.640367	−	0.0223621i
$707$	−0.689607	+	9.86184i	−0.0259353	+	0.370893i
$708$		0			0
$709$	0.0375991	−	1.07670i	0.00141206	−	0.0404362i	−0.998480	−	0.0551105i	$-0.982449\pi$
$709$	0.0375991	−	1.07670i	0.00141206	−	0.0404362i	0.999892	+	0.0146743i	$0.00467113\pi$
$710$	−5.06215	+	5.62209i	−0.189979	+	0.210993i
$711$		0			0
$712$	−41.7364	+	4.38667i	−1.56414	+	0.164397i
$713$	−17.2929	+	6.98677i	−0.647623	+	0.261657i
$714$		0			0
$715$	−53.5897	−	6.54114i	−2.00414	−	0.244625i
$716$	−13.0674	−	2.30414i	−0.488352	−	0.0861097i
$717$		0			0
$718$	−1.98935	+	7.97884i	−0.0742418	+	0.297768i
$719$	14.8900	+	33.4434i	0.555302	+	1.24723i	0.945237	+	0.326386i	$0.105831\pi$
$719$	14.8900	+	33.4434i	0.555302	+	1.24723i	−0.389935	+	0.920843i	$0.627502\pi$
$720$		0			0
$721$	42.9372	+	38.6608i	1.59906	+	1.43980i
$722$	7.41814	+	10.9978i	0.276074	+	0.409297i
$723$		0			0
$724$	−16.4344	+	10.2694i	−0.610780	+	0.381657i
$725$	−12.5056	+	4.55165i	−0.464445	+	0.169044i
$726$		0			0
$727$	6.01334	+	34.1033i	0.223022	+	1.26482i	0.866430	+	0.499299i	$0.166409\pi$
$727$	6.01334	+	34.1033i	0.223022	+	1.26482i	−0.643407	+	0.765524i	$0.722480\pi$
$728$	−17.2582	+	53.1152i	−0.639631	+	1.96858i
$729$		0			0
$730$	0.537234	+	0.390324i	0.0198839	+	0.0144465i
$731$	14.8467	+	27.9225i	0.549124	+	1.03275i
$732$		0			0
$733$	−0.664723	+	2.31816i	−0.0245521	+	0.0856233i	−0.972584	−	0.232552i	$-0.925292\pi$
$733$	−0.664723	+	2.31816i	−0.0245521	+	0.0856233i	0.948032	+	0.318176i	$0.103070\pi$
$734$	−13.7240	−	0.959674i	−0.506561	−	0.0354222i
$735$		0			0
$736$	−5.92107	+	16.2680i	−0.218253	+	0.599647i
$737$	8.75176	−	5.69235i	0.322375	−	0.209680i
$738$		0			0
$739$	14.8113	−	13.3362i	0.544843	−	0.490579i	−0.350129	−	0.936702i	$-0.613862\pi$
$739$	14.8113	−	13.3362i	0.544843	−	0.490579i	0.894972	+	0.446123i	$0.147196\pi$
$740$	−46.7359	−	11.6526i	−1.71804	−	0.428357i
$741$		0			0
$742$	15.8714	−	2.23058i	0.582659	−	0.0818873i
$743$	−14.1662	+	1.99093i	−0.519706	+	0.0730400i	−0.394149	−	0.919046i	$-0.628961\pi$
$743$	−14.1662	+	1.99093i	−0.519706	+	0.0730400i	−0.125557	+	0.992086i	$0.540072\pi$
$744$		0			0
$745$	11.0699	+	2.76003i	0.405569	+	0.101120i
$746$	−6.57224	+	5.91767i	−0.240627	+	0.216661i
$747$		0			0
$748$	−6.16846	−	22.9554i	−0.225541	−	0.839334i
$749$	−3.63465	+	9.98611i	−0.132807	+	0.364885i
$750$		0			0
$751$	−30.6557	−	2.14366i	−1.11864	−	0.0782231i	−0.501561	−	0.865122i	$-0.667241\pi$
$751$	−30.6557	−	2.14366i	−1.11864	−	0.0782231i	−0.617082	+	0.786899i	$0.711685\pi$
$752$	−0.896145	+	3.12523i	−0.0326791	+	0.113965i
$753$		0			0
$754$	3.90286	+	7.34021i	0.142134	+	0.267315i
$755$	−60.1457	−	43.6984i	−2.18892	−	1.59035i
$756$		0			0
$757$	9.78964	−	30.1294i	0.355810	−	1.09507i	−0.599728	−	0.800204i	$-0.704724\pi$
$757$	9.78964	−	30.1294i	0.355810	−	1.09507i	0.955538	−	0.294868i	$-0.0952756\pi$
$758$	−1.77479	−	10.0654i	−0.0644634	−	0.365590i
$759$		0			0
$760$	−13.2549	+	4.82439i	−0.480806	+	0.174999i
$761$	21.5345	−	13.4563i	0.780627	−	0.487790i	−0.0801436	−	0.996783i	$-0.525538\pi$
$761$	21.5345	−	13.4563i	0.780627	−	0.487790i	0.860770	+	0.508994i	$0.169982\pi$
$762$		0			0
$763$	5.18369	+	7.68514i	0.187662	+	0.278221i
$764$	20.2049	+	18.1926i	0.730988	+	0.658185i
$765$		0			0
$766$	−1.55692	−	3.49690i	−0.0562538	−	0.126348i
$767$	3.87547	−	15.5437i	0.139935	−	0.561249i
$768$		0			0
$769$	−19.0841	−	3.36505i	−0.688191	−	0.121347i	−0.181392	−	0.983411i	$-0.558060\pi$
$769$	−19.0841	−	3.36505i	−0.688191	−	0.121347i	−0.506799	+	0.862064i	$0.669171\pi$
$770$	−27.8551	−	25.9382i	−1.00383	−	0.934746i
$771$		0			0
$772$	−21.1777	+	8.55634i	−0.762202	+	0.307949i
$773$	20.0530	−	2.10766i	0.721256	−	0.0758071i	0.263214	−	0.964737i	$-0.415217\pi$
$773$	20.0530	−	2.10766i	0.721256	−	0.0758071i	0.458042	+	0.888930i	$0.348551\pi$
$774$		0			0
$775$	−26.1873	+	29.0840i	−0.940677	+	1.04473i
$776$	1.13378	−	32.4674i	0.0407005	−	1.16551i
$777$		0			0
$778$	−0.848457	+	12.1335i	−0.0304186	+	0.435007i
$779$	−8.42586	+	0.294238i	−0.301888	+	0.0105422i
$780$		0			0
$781$	8.00461	−	4.81744i	0.286428	−	0.172382i
$782$		−	12.5615i		−	0.449198i
$783$		0			0
$784$	5.09224	−	3.69973i	0.181866	−	0.132133i
$785$	−42.5954	−	20.7752i	−1.52030	−	0.741498i
$786$		0			0
$787$	−28.0600	+	21.9228i	−1.00023	+	0.781465i	−0.975895	−	0.218239i	$-0.929969\pi$
$787$	−28.0600	+	21.9228i	−1.00023	+	0.781465i	−0.0243341	+	0.999704i	$0.507747\pi$
$788$	1.61145	+	6.46318i	0.0574056	+	0.230241i
$789$		0			0
$790$	−18.7964	+	24.0584i	−0.668747	+	0.855958i
$791$	17.9777	+	31.1383i	0.639215	+	1.10715i
$792$		0			0
$793$	−5.65488	+	9.79453i	−0.200811	+	0.347814i
$794$	5.04229	+	12.4801i	0.178944	+	0.442903i
$795$		0			0
$796$	6.39539	−	6.17596i	0.226679	−	0.218901i
$797$	−2.20122	−	15.6625i	−0.0779713	−	0.554795i	−0.989607	−	0.143796i	$-0.954069\pi$
$797$	−2.20122	−	15.6625i	−0.0779713	−	0.554795i	0.911636	−	0.410999i	$-0.134820\pi$
$798$		0			0
$799$	−2.14121	−	30.6207i	−0.0757506	−	1.08328i
$800$	3.79719	+	36.1279i	0.134251	+	1.27731i
$801$		0			0
$802$	−3.71764	+	2.14638i	−0.131274	+	0.0757913i
$803$	−0.493990	−	0.654573i	−0.0174325	−	0.0230994i
$804$		0			0
$805$	22.5346	+	36.0628i	0.794239	+	1.27105i
$806$	20.2680	+	13.6709i	0.713910	+	0.481538i
$807$		0			0
$808$	5.49687	−	2.92274i	0.193379	−	0.102821i
$809$	−9.57125	−	29.4573i	−0.336507	−	1.03566i	−0.965975	−	0.258636i	$-0.916727\pi$
$809$	−9.57125	−	29.4573i	−0.336507	−	1.03566i	0.629468	−	0.777027i	$-0.283273\pi$
$810$		0			0
$811$	−12.8046	−	17.6240i	−0.449630	−	0.618863i	0.522688	−	0.852524i	$-0.324929\pi$
$811$	−12.8046	−	17.6240i	−0.449630	−	0.618863i	−0.972318	+	0.233661i	$0.924929\pi$
$812$	1.72449	−	12.2703i	0.0605176	−	0.430605i
$813$		0			0
$814$	−24.1269	−	14.4734i	−0.845646	−	0.507294i
$815$	−10.7508	+	12.8123i	−0.376583	+	0.448794i
$816$		0			0
$817$	−9.00824	+	2.58307i	−0.315158	+	0.0903702i
$818$	16.9945	+	1.78619i	0.594198	+	0.0624527i
$819$		0			0
$820$	−5.09936	+	23.9906i	−0.178077	+	0.837789i
$821$	25.4204	−	1.77757i	0.887177	−	0.0620375i	0.381108	−	0.924530i	$-0.375543\pi$
$821$	25.4204	−	1.77757i	0.887177	−	0.0620375i	0.506069	+	0.862493i	$0.331098\pi$
$822$		0			0
$823$	−17.0773	−	9.08015i	−0.595277	−	0.316514i	0.144355	−	0.989526i	$-0.453889\pi$
$823$	−17.0773	−	9.08015i	−0.595277	−	0.316514i	−0.739632	+	0.673012i	$0.765000\pi$
$824$	6.31820	−	35.8323i	0.220105	−	1.24828i
$825$		0			0
$826$	8.65165	−	7.25960i	0.301030	−	0.252594i
$827$	0.478091	+	0.530974i	0.0166249	+	0.0184638i	0.751400	−	0.659847i	$-0.229379\pi$
$827$	0.478091	+	0.530974i	0.0166249	+	0.0184638i	−0.734775	+	0.678311i	$0.762712\pi$
$828$		0			0
$829$	0.245297	−	2.33384i	0.00851951	−	0.0810577i	−0.989436	−	0.144970i	$-0.953691\pi$
$829$	0.245297	−	2.33384i	0.00851951	−	0.0810577i	0.997955	+	0.0639128i	$0.0203579\pi$
$830$	−14.5136	−	0.506828i	−0.503776	−	0.0175922i
$831$		0			0
$832$	16.7488	−	4.17595i	0.580661	−	0.144775i
$833$	−33.2313	+	49.2674i	−1.15140	+	1.70702i
$834$		0			0
$835$	30.7223	−	5.41716i	1.06319	−	0.187469i
$836$	7.03382	−	0.373664i	0.243270	−	0.0129235i
$837$		0			0
$838$	29.5705	+	9.60804i	1.02150	+	0.331904i
$839$	−10.7328	+	11.1141i	−0.370536	+	0.383701i	−0.878552	−	0.477646i	$-0.841490\pi$
$839$	−10.7328	+	11.1141i	−0.370536	+	0.383701i	0.508016	+	0.861347i	$0.330379\pi$
$840$		0			0
$841$	15.0460	+	19.2579i	0.518826	+	0.664067i
$842$	−2.18782	+	5.41505i	−0.0753974	+	0.186615i
$843$		0			0
$844$	2.25437	+	7.86192i	0.0775986	+	0.270618i
$845$	−7.38028	−	34.7215i	−0.253889	−	1.19446i
$846$		0			0
$847$	23.5596	+	40.6722i	0.809519	+	1.39751i
$848$	1.68198	+	2.00450i	0.0577593	+	0.0688349i
$849$		0			0
$850$	−11.5548	−	23.6909i	−0.396327	−	0.812591i
$851$	21.8359	+	22.6117i	0.748525	+	0.775121i
$852$		0			0
$853$	−15.1323	+	24.2167i	−0.518118	+	0.829163i	−0.998862	−	0.0476985i	$-0.984811\pi$
$853$	−15.1323	+	24.2167i	−0.518118	+	0.829163i	0.480743	+	0.876861i	$0.340367\pi$
$854$	−7.28416	+	3.24312i	−0.249259	+	0.110977i
$855$		0			0
$856$	6.54603	−	1.39140i	0.223739	−	0.0475572i
$857$	−48.2213	−	17.5511i	−1.64721	−	0.599535i	−0.658932	−	0.752202i	$-0.728992\pi$
$857$	−48.2213	−	17.5511i	−1.64721	−	0.599535i	−0.988278	+	0.152667i	$0.951214\pi$
$858$		0			0
$859$	−12.6431	−	10.6088i	−0.431378	−	0.361969i	0.401094	−	0.916037i	$-0.368630\pi$
$859$	−12.6431	−	10.6088i	−0.431378	−	0.361969i	−0.832471	+	0.554068i	$0.813075\pi$
$860$	0.951427	+	27.2453i	0.0324434	+	0.929057i
$861$		0			0
$862$	5.13002	−	10.5181i	0.174729	−	0.358248i
$863$	−35.8278	+	11.6412i	−1.21959	+	0.396270i	−0.846934	−	0.531699i	$-0.821554\pi$
$863$	−35.8278	+	11.6412i	−1.21959	+	0.396270i	−0.372659	+	0.927968i	$0.621554\pi$
$864$		0			0
$865$	−31.3776	+	43.1875i	−1.06687	+	1.46842i
$866$	−22.0091	−	21.2540i	−0.747901	−	0.722240i
$867$		0			0
$868$	−12.4629	−	34.2415i	−0.423018	−	1.16223i
$869$	30.8687	−	21.6474i	1.04715	−	0.734336i
$870$		0			0
$871$	12.0483	+	9.41313i	0.408240	+	0.318952i
$872$	2.37440	−	5.33299i	0.0804073	−	0.180598i
$873$		0			0
$874$	3.64103	+	0.773925i	0.123160	+	0.0261784i
$875$	14.9520	+	9.34306i	0.505470	+	0.315853i
$876$		0			0
$877$	−17.1187	+	8.34934i	−0.578057	+	0.281937i	−0.704115	−	0.710086i	$-0.748656\pi$
$877$	−17.1187	+	8.34934i	−0.578057	+	0.281937i	0.126058	+	0.992023i	$0.459767\pi$
$878$	−5.86651	+	11.0333i	−0.197985	+	0.372356i
$879$		0			0
$880$	1.18135	−	6.10077i	0.0398233	−	0.205657i
$881$	−48.0662	−	27.7510i	−1.61939	−	0.934956i	−0.987078	−	0.160242i	$-0.948772\pi$
$881$	−48.0662	−	27.7510i	−1.61939	−	0.934956i	−0.632313	−	0.774713i	$-0.717894\pi$
$882$		0			0
$883$	31.0192	+	13.8106i	1.04388	+	0.464765i	0.855755	−	0.517381i	$-0.173093\pi$
$883$	31.0192	+	13.8106i	1.04388	+	0.464765i	0.188123	+	0.982145i	$0.439760\pi$
$884$	28.8593	−	19.4658i	0.970643	−	0.654707i
$885$		0			0
$886$	−15.0637	−	6.08611i	−0.506074	−	0.204467i
$887$	−48.6214	−	13.9419i	−1.63255	−	0.468125i	−0.670702	−	0.741727i	$-0.734007\pi$
$887$	−48.6214	−	13.9419i	−1.63255	−	0.468125i	−0.961843	+	0.273602i	$0.911785\pi$
$888$		0			0
$889$	−13.0184	−	1.82962i	−0.436623	−	0.0613633i
$890$	41.8854			1.40400
$891$		0			0
$892$	1.38634			0.0464182
$893$	9.00753	+	1.26593i	0.301426	+	0.0423626i
$894$		0			0
$895$	31.4824	+	9.02742i	1.05234	+	0.301753i
$896$	−34.9104	−	14.1047i	−1.16628	−	0.471206i
$897$		0			0
$898$	16.8196	−	11.3450i	0.561278	−	0.378587i
$899$	−12.2542	−	5.45590i	−0.408699	−	0.181964i
$900$		0			0
$901$	−21.3953	−	12.3526i	−0.712780	−	0.411524i
$902$	−6.93667	+	12.5352i	−0.230966	+	0.417376i
$903$		0			0
$904$	10.6301	−	19.9923i	0.353552	−	0.664934i
$905$	42.9914	−	20.9683i	1.42908	−	0.697009i
$906$		0			0
$907$	18.4542	+	11.5315i	0.612763	+	0.382897i	0.800509	−	0.599321i	$-0.204563\pi$
$907$	18.4542	+	11.5315i	0.612763	+	0.382897i	−0.187746	+	0.982218i	$0.560118\pi$
$908$	−15.4022	−	3.27383i	−0.511139	−	0.108646i
$909$		0			0
$910$	22.6719	−	50.9220i	0.751567	−	1.68805i
$911$	−27.8417	−	21.7523i	−0.922438	−	0.720688i	0.0379718	−	0.999279i	$-0.487910\pi$
$911$	−27.8417	−	21.7523i	−0.922438	−	0.720688i	−0.960410	+	0.278591i	$0.910133\pi$
$912$		0			0
$913$	16.9611	+	5.82664i	0.561332	+	0.192834i
$914$	1.19048	+	3.27083i	0.0393777	+	0.108189i
$915$		0			0
$916$	16.2417	+	15.6844i	0.536641	+	0.518228i
$917$	−28.9771	+	39.8835i	−0.956907	+	1.31707i
$918$		0			0
$919$	37.1192	−	12.0608i	1.22445	−	0.397848i	0.375750	−	0.926721i	$-0.377385\pi$
$919$	37.1192	−	12.0608i	1.22445	−	0.397848i	0.848701	+	0.528873i	$0.177385\pi$
$920$	11.7394	−	24.0693i	0.387036	−	0.793540i
$921$		0			0
$922$	0.962534	+	27.5634i	0.0316994	+	0.907751i
$923$	10.4810	+	8.79458i	0.344986	+	0.289477i
$924$		0			0
$925$	61.9820	+	22.5596i	2.03795	+	0.741755i
$926$	30.1516	−	6.40892i	0.990843	−	0.210610i
$927$		0			0
$928$	−11.3745	+	5.06423i	−0.373385	+	0.166242i
$929$	−2.65434	+	4.24784i	−0.0870861	+	0.139367i	−0.888723	−	0.458444i	$-0.848407\pi$
$929$	−2.65434	+	4.24784i	−0.0870861	+	0.139367i	0.801637	+	0.597811i	$0.203963\pi$
$930$		0			0
$931$	−12.2331	−	12.6677i	−0.400923	−	0.415167i
$932$	8.66440	+	17.7646i	0.283812	+	0.581900i
$933$		0			0
$934$	−8.49218	−	10.1206i	−0.277873	−	0.331156i
$935$	9.21932	+	57.9406i	0.301504	+	1.89486i
$936$		0			0
$937$	−11.2227	−	52.7989i	−0.366631	−	1.72486i	−0.644817	−	0.764337i	$-0.723067\pi$
$937$	−11.2227	−	52.7989i	−0.366631	−	1.72486i	0.278186	−	0.960527i	$-0.410267\pi$
$938$	2.97116	+	10.3617i	0.0970119	+	0.338321i
$939$		0			0
$940$	9.91257	−	24.5345i	0.323313	−	0.800227i
$941$	16.1213	+	20.6344i	0.525540	+	0.672661i	0.975401	−	0.220438i	$-0.0707486\pi$
$941$	16.1213	+	20.6344i	0.525540	+	0.672661i	−0.449861	+	0.893099i	$0.648526\pi$
$942$		0			0
$943$	11.1189	−	11.5140i	0.362081	−	0.374946i
$944$	1.75364	+	0.569793i	0.0570762	+	0.0185452i
$945$		0			0
$946$	−4.11052	+	15.3846i	−0.133644	+	0.500196i
$947$	2.07383	−	0.365673i	0.0673906	−	0.0118828i	−0.139851	−	0.990173i	$-0.544662\pi$
$947$	2.07383	−	0.365673i	0.0673906	−	0.0118828i	0.207242	+	0.978290i	$0.433551\pi$
$948$		0			0
$949$	0.671571	−	0.995644i	0.0218001	−	0.0323200i
$950$	7.57885	−	1.88962i	0.245890	−	0.0613074i
$951$		0			0
$952$	60.6552	+	2.11813i	1.96585	+	0.0686489i
$953$	−1.62794	+	15.4888i	−0.0527341	+	0.501732i	0.935995	+	0.352014i	$0.114503\pi$
$953$	−1.62794	+	15.4888i	−0.0527341	+	0.501732i	−0.988729	+	0.149717i	$0.952164\pi$
$954$		0			0
$955$	−44.9037	−	49.8706i	−1.45305	−	1.61377i
$956$	−4.28285	+	3.59374i	−0.138517	+	0.116230i
$957$		0			0
$958$	3.53284	−	20.0357i	0.114141	−	0.647325i
$959$	10.1874	+	5.41676i	0.328969	+	0.174916i
$960$		0			0
$961$	−8.42662	+	0.589247i	−0.271826	+	0.0190080i
$962$	8.56672	−	40.3033i	0.276202	−	1.29943i
$963$		0			0
$964$	21.2476	+	2.23321i	0.684339	+	0.0719270i
$965$	54.1928	−	15.5395i	1.74453	−	0.500236i
$966$		0			0
$967$	10.8180	−	12.8924i	0.347884	−	0.414592i	−0.563521	−	0.826102i	$-0.690554\pi$
$967$	10.8180	−	12.8924i	0.347884	−	0.414592i	0.911406	+	0.411509i	$0.134998\pi$
$968$	13.8589	−	26.1549i	0.445443	−	0.840651i
$969$		0			0
$970$	−4.51263	+	32.1090i	−0.144892	+	1.03096i
$971$	−13.8868	−	19.1136i	−0.445649	−	0.613384i	0.525806	−	0.850604i	$-0.323764\pi$
$971$	−13.8868	−	19.1136i	−0.445649	−	0.613384i	−0.971456	+	0.237220i	$0.923764\pi$
$972$		0			0
$973$	10.6387	+	32.7426i	0.341062	+	1.04968i
$974$	−22.4363	+	11.9296i	−0.718905	+	0.382249i
$975$		0			0
$976$	−1.07923	−	0.727948i	−0.0345452	−	0.0233010i
$977$	−6.13825	−	9.82325i	−0.196380	−	0.314273i	0.735173	−	0.677880i	$-0.237101\pi$
$977$	−6.13825	−	9.82325i	−0.196380	−	0.314273i	−0.931553	+	0.363606i	$0.881545\pi$
$978$		0			0
$979$	−49.4756	−	15.0876i	−1.58125	−	0.482201i
$980$	−44.3663	+	25.6149i	−1.41723	+	0.818237i
$981$		0			0
$982$	−1.17525	−	11.1818i	−0.0375038	−	0.356825i
$983$	1.67195	+	23.9100i	0.0533269	+	0.762610i	0.948477	+	0.316846i	$0.102624\pi$
$983$	1.67195	+	23.9100i	0.0533269	+	0.762610i	−0.895150	+	0.445765i	$0.852932\pi$
$984$		0			0
$985$	−2.28815	−	16.2811i	−0.0729066	−	0.518757i
$986$	6.49872	−	6.27574i	0.206961	−	0.199860i
$987$		0			0
$988$	3.86425	+	9.56435i	0.122938	+	0.304283i
$989$	8.89570	−	15.4078i	0.282867	−	0.489940i
$990$		0			0
$991$	11.7763	+	20.3971i	0.374086	+	0.647935i	0.990190	−	0.139730i	$-0.0446233\pi$
$991$	11.7763	+	20.3971i	0.374086	+	0.647935i	−0.616104	+	0.787665i	$0.711290\pi$
$992$	−22.5427	+	28.8533i	−0.715731	+	0.916094i
$993$		0			0
$994$	2.33356	+	9.35940i	0.0740161	+	0.296862i
$995$	−17.2923	+	13.5102i	−0.548203	+	0.428303i
$996$		0			0
$997$	−26.2718	−	12.8136i	−0.832036	−	0.405811i	−0.0274329	−	0.999624i	$-0.508733\pi$
$997$	−26.2718	−	12.8136i	−0.832036	−	0.405811i	−0.804604	+	0.593812i	$0.797622\pi$
$998$	19.5348	−	14.1928i	0.618362	−	0.449266i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.bb.a.233.22		816
3.2	odd	2		297.2.x.a.68.13	yes	816
11.6	odd	10	inner	891.2.bb.a.314.22		816
27.2	odd	18	inner	891.2.bb.a.332.22		816
27.25	even	9		297.2.x.a.2.13	✓	816
33.17	even	10		297.2.x.a.149.13	yes	816
297.83	even	90	inner	891.2.bb.a.413.22		816
297.160	odd	90		297.2.x.a.83.13	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.x.a.2.13	✓	816	27.25	even	9
297.2.x.a.68.13	yes	816	3.2	odd	2
297.2.x.a.83.13	yes	816	297.160	odd	90
297.2.x.a.149.13	yes	816	33.17	even	10
891.2.bb.a.233.22		816	1.1	even	1	trivial
891.2.bb.a.314.22		816	11.6	odd	10	inner
891.2.bb.a.332.22		816	27.2	odd	18	inner
891.2.bb.a.413.22		816	297.83	even	90	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.793594 + 0.111532i) q^{2} +(-1.30517 - 0.374252i) q^{4} +(3.10727 + 1.25542i) q^{5} +(3.54248 - 2.38943i) q^{7} +(-2.45825 - 1.09449i) q^{8} +(2.32589 + 1.34285i) q^{10} +(-2.26366 - 2.42401i) q^{11} +(2.28030 - 4.28862i) q^{13} +(3.07779 - 1.50114i) q^{14} +(0.474121 + 0.296263i) q^{16} +(-5.16306 - 1.09744i) q^{17} +(0.636201 - 1.42893i) q^{19} +(-3.58568 - 2.80144i) q^{20} +(-1.52608 - 2.17615i) q^{22} +(1.01565 + 2.79048i) q^{23} +(4.48236 + 4.32856i) q^{25} +(2.28795 - 3.14910i) q^{26} +(-5.51779 + 1.79284i) q^{28} +(-0.936240 + 1.91958i) q^{29} +(0.219193 + 6.27687i) q^{31} +(4.46590 + 3.74734i) q^{32} +(-3.97498 - 1.44677i) q^{34} +(14.0072 - 2.97732i) q^{35} +(9.67024 - 4.30547i) q^{37} +(0.664258 - 1.06303i) q^{38} +(-6.26442 - 6.48700i) q^{40} +(-2.36287 - 4.84460i) q^{41} +(-3.85110 - 4.58956i) q^{43} +(2.04728 + 4.01093i) q^{44} +(0.494786 + 2.32779i) q^{46} +(1.60291 + 5.59002i) q^{47} +(4.21753 - 10.4388i) q^{49} +(3.07440 + 3.93505i) q^{50} +(-4.58121 + 4.74398i) q^{52} +(4.45134 + 1.44633i) q^{53} +(-3.99067 - 10.3739i) q^{55} +(-11.3235 + 1.99664i) q^{56} +(-0.957089 + 1.41894i) q^{58} +(3.20015 - 0.797887i) q^{59} +(-2.32705 - 0.0812623i) q^{61} +(-0.526124 + 5.00574i) q^{62} +(2.37798 + 2.64102i) q^{64} +(12.4695 - 10.4632i) q^{65} +(-0.546612 + 3.09999i) q^{67} +(6.32796 + 3.36463i) q^{68} +(11.4481 - 0.800529i) q^{70} +(-0.585658 + 2.75530i) q^{71} +(0.245902 + 0.0258453i) q^{73} +(8.15445 - 2.33825i) q^{74} +(-1.36513 + 1.62690i) q^{76} +(-13.8110 - 3.17813i) q^{77} +(-1.58209 + 11.2571i) q^{79} +(1.10129 + 1.51579i) q^{80} +(-1.33483 - 4.10819i) q^{82} +(-4.77438 + 2.53858i) q^{83} +(-14.6653 - 9.89186i) q^{85} +(-2.54433 - 4.07177i) q^{86} +(2.91162 + 8.43638i) q^{88} +(13.5062 - 7.79783i) q^{89} +(-2.16946 - 20.6410i) q^{91} +(-0.281257 - 4.02216i) q^{92} +(0.648594 + 4.61499i) q^{94} +(3.77076 - 3.64138i) q^{95} +(4.52262 + 11.1939i) q^{97} +(4.51127 - 7.81375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q + 30 q^{2} - 18 q^{4} + 21 q^{5} - 30 q^{7} + 45 q^{8} + 33 q^{11} - 30 q^{13} + 18 q^{14} - 30 q^{16} + 45 q^{17} - 15 q^{19} + 60 q^{20} - 15 q^{22} + 84 q^{23} - 27 q^{25} - 60 q^{28} - 60 q^{29}+ \cdots - 81 q^{97}+O(q^{100}) \) 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

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Representations

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Database

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