LMFDB - Embedded newform 297.2.t.a.260.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			260.9
Character	$\chi$	$=$	297.260
Dual form			297.2.t.a.8.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.205839 - 1.95843i) q^{2} +(-1.83679 - 0.390421i) q^{4} +(1.96633 - 0.206670i) q^{5} +(0.235695 + 0.212221i) q^{7} +(0.0743474 - 0.228818i) q^{8} -3.89347i q^{10} +(-0.900082 - 3.19215i) q^{11} +(0.782431 + 1.75737i) q^{13} +(0.464135 - 0.417909i) q^{14} +(-3.86377 - 1.72026i) q^{16} +(2.02504 - 1.47127i) q^{17} +(4.44962 + 1.44577i) q^{19} +(-3.69242 - 0.388089i) q^{20} +(-6.43689 + 1.10568i) q^{22} +(-4.68148 - 2.70286i) q^{23} +(-1.06699 + 0.226795i) q^{25} +(3.60274 - 1.17060i) q^{26} +(-0.350066 - 0.481825i) q^{28} +(-5.96640 + 6.62636i) q^{29} +(-0.304670 + 0.135648i) q^{31} +(-3.92374 + 6.79612i) q^{32} +(-2.46456 - 4.26874i) q^{34} +(0.507314 + 0.368585i) q^{35} +(2.37275 + 7.30257i) q^{37} +(3.74735 - 8.41668i) q^{38} +(0.0989020 - 0.465297i) q^{40} +(6.69670 + 7.43744i) q^{41} +(7.95160 - 4.59086i) q^{43} +(0.406974 + 6.21472i) q^{44} +(-6.25699 + 8.61201i) q^{46} +(1.77326 + 8.34251i) q^{47} +(-0.721185 - 6.86161i) q^{49} +(0.224534 + 2.13630i) q^{50} +(-0.751046 - 3.53339i) q^{52} +(1.05383 - 1.45047i) q^{53} +(-2.42958 - 6.09082i) q^{55} +(0.0660832 - 0.0381531i) q^{56} +(11.7492 + 13.0488i) q^{58} +(1.61495 - 7.59774i) q^{59} +(-1.00557 + 2.25856i) q^{61} +(0.202944 + 0.624596i) q^{62} +(5.65871 + 4.11130i) q^{64} +(1.90171 + 3.29387i) q^{65} +(-5.40401 + 9.36002i) q^{67} +(-4.29398 + 1.91180i) q^{68} +(0.826275 - 0.917671i) q^{70} +(-6.99647 - 9.62982i) q^{71} +(0.116476 - 0.0378454i) q^{73} +(14.7900 - 3.14371i) q^{74} +(-7.60855 - 4.39280i) q^{76} +(0.465297 - 0.943391i) q^{77} +(12.4188 + 1.30527i) q^{79} +(-7.95299 - 2.58408i) q^{80} +(15.9442 - 11.5841i) q^{82} +(0.394220 + 0.175518i) q^{83} +(3.67783 - 3.31153i) q^{85} +(-7.35413 - 16.5176i) q^{86} +(-0.797341 - 0.0313737i) q^{88} +8.15328i q^{89} +(-0.188535 + 0.580251i) q^{91} +(7.54364 + 6.79232i) q^{92} +(16.7032 - 1.75558i) q^{94} +(9.04823 + 1.92326i) q^{95} +(-0.903553 + 8.59673i) q^{97} -13.5864 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.205839	−	1.95843i	0.145550	−	1.38482i	−0.641117	−	0.767443i	$-0.721529\pi$
$2$	0.205839	−	1.95843i	0.145550	−	1.38482i	0.786667	−	0.617377i	$-0.211805\pi$
$3$		0			0
$3$		0			0
$4$	−1.83679	−	0.390421i	−0.918394	−	0.195211i
$5$	1.96633	−	0.206670i	0.879371	−	0.0924256i	0.345927	−	0.938261i	$-0.387564\pi$
$5$	1.96633	−	0.206670i	0.879371	−	0.0924256i	0.533443	+	0.845836i	$0.320898\pi$
$6$		0			0
$7$	0.235695	+	0.212221i	0.0890843	+	0.0802119i	0.712470	−	0.701703i	$-0.247577\pi$
$7$	0.235695	+	0.212221i	0.0890843	+	0.0802119i	−0.623385	+	0.781915i	$0.714243\pi$
$8$	0.0743474	−	0.228818i	0.0262858	−	0.0808993i
$9$		0			0
$10$		−	3.89347i		−	1.23122i
$11$	−0.900082	−	3.19215i	−0.271385	−	0.962471i
$11$	−0.900082	−	3.19215i	−0.271385	−	0.962471i
$12$		0			0
$13$	0.782431	+	1.75737i	0.217007	+	0.487406i	0.988943	−	0.148294i	$-0.0473781\pi$
$13$	0.782431	+	1.75737i	0.217007	+	0.487406i	−0.771936	+	0.635700i	$0.780711\pi$
$14$	0.464135	−	0.417909i	0.124045	−	0.111691i
$15$		0			0
$16$	−3.86377	−	1.72026i	−0.965943	−	0.430066i
$17$	2.02504	−	1.47127i	0.491143	−	0.356836i	−0.314481	−	0.949264i	$-0.601830\pi$
$17$	2.02504	−	1.47127i	0.491143	−	0.356836i	0.805624	+	0.592427i	$0.201830\pi$
$18$		0			0
$19$	4.44962	+	1.44577i	1.02081	+	0.331682i	0.771152	−	0.636651i	$-0.219681\pi$
$19$	4.44962	+	1.44577i	1.02081	+	0.331682i	0.249661	+	0.968333i	$0.419681\pi$
$20$	−3.69242	−	0.388089i	−0.825651	−	0.0867794i
$21$		0			0
$22$	−6.43689	+	1.10568i	−1.37235	+	0.235731i
$23$	−4.68148	−	2.70286i	−0.976157	−	0.563584i	−0.0750491	−	0.997180i	$-0.523911\pi$
$23$	−4.68148	−	2.70286i	−0.976157	−	0.563584i	−0.901108	+	0.433595i	$0.857245\pi$
$24$		0			0
$25$	−1.06699	+	0.226795i	−0.213397	+	0.0453590i
$26$	3.60274	−	1.17060i	0.706556	−	0.229574i
$27$		0			0
$28$	−0.350066	−	0.481825i	−0.0661563	−	0.0910563i
$29$	−5.96640	+	6.62636i	−1.10793	+	1.23048i	−0.137144	+	0.990551i	$0.543792\pi$
$29$	−5.96640	+	6.62636i	−1.10793	+	1.23048i	−0.970789	+	0.239933i	$0.922874\pi$
$30$		0			0
$31$	−0.304670	+	0.135648i	−0.0547203	+	0.0243631i	−0.433914	−	0.900954i	$-0.642868\pi$
$31$	−0.304670	+	0.135648i	−0.0547203	+	0.0243631i	0.379194	+	0.925317i	$0.376201\pi$
$32$	−3.92374	+	6.79612i	−0.693626	+	1.20140i
$33$		0			0
$34$	−2.46456	−	4.26874i	−0.422668	−	0.732083i
$35$	0.507314	+	0.368585i	0.0857518	+	0.0623023i
$36$		0			0
$37$	2.37275	+	7.30257i	0.390078	+	1.20054i	0.932729	+	0.360577i	$0.117420\pi$
$37$	2.37275	+	7.30257i	0.390078	+	1.20054i	−0.542652	+	0.839958i	$0.682580\pi$
$38$	3.74735	−	8.41668i	0.607900	−	1.36537i
$39$		0			0
$40$	0.0989020	−	0.465297i	0.0156378	−	0.0735700i
$41$	6.69670	+	7.43744i	1.04585	+	1.16153i	0.986578	+	0.163292i	$0.0522112\pi$
$41$	6.69670	+	7.43744i	1.04585	+	1.16153i	0.0592717	+	0.998242i	$0.481122\pi$
$42$		0			0
$43$	7.95160	−	4.59086i	1.21261	−	0.700100i	0.249281	−	0.968431i	$-0.419806\pi$
$43$	7.95160	−	4.59086i	1.21261	−	0.700100i	0.963327	+	0.268331i	$0.0864723\pi$
$44$	0.406974	+	6.21472i	0.0613536	+	0.936905i
$45$		0			0
$46$	−6.25699	+	8.61201i	−0.922543	+	1.26977i
$47$	1.77326	+	8.34251i	0.258656	+	1.21688i	0.895209	+	0.445647i	$0.147026\pi$
$47$	1.77326	+	8.34251i	0.258656	+	1.21688i	−0.636553	+	0.771233i	$0.719640\pi$
$48$		0			0
$49$	−0.721185	−	6.86161i	−0.103026	−	0.980231i
$50$	0.224534	+	2.13630i	0.0317540	+	0.302119i
$51$		0			0
$52$	−0.751046	−	3.53339i	−0.104151	−	0.489993i
$53$	1.05383	−	1.45047i	0.144754	−	0.199237i	−0.730483	−	0.682931i	$-0.760705\pi$
$53$	1.05383	−	1.45047i	0.144754	−	0.199237i	0.875238	+	0.483693i	$0.160705\pi$
$54$		0			0
$55$	−2.42958	−	6.09082i	−0.327605	−	0.821286i
$56$	0.0660832	−	0.0381531i	0.00883074	−	0.00509843i
$57$		0			0
$58$	11.7492	+	13.0488i	1.54274	+	1.71339i
$59$	1.61495	−	7.59774i	0.210249	−	0.989142i	−0.738779	−	0.673948i	$-0.764597\pi$
$59$	1.61495	−	7.59774i	0.210249	−	0.989142i	0.949027	−	0.315194i	$-0.102070\pi$
$60$		0			0
$61$	−1.00557	+	2.25856i	−0.128751	+	0.289179i	−0.966406	−	0.257021i	$-0.917259\pi$
$61$	−1.00557	+	2.25856i	−0.128751	+	0.289179i	0.837655	+	0.546199i	$0.183926\pi$
$62$	0.202944	+	0.624596i	0.0257739	+	0.0793238i
$63$		0			0
$64$	5.65871	+	4.11130i	0.707339	+	0.513912i
$65$	1.90171	+	3.29387i	0.235879	+	0.408554i
$66$		0			0
$67$	−5.40401	+	9.36002i	−0.660205	+	1.14351i	0.320357	+	0.947297i	$0.396197\pi$
$67$	−5.40401	+	9.36002i	−0.660205	+	1.14351i	−0.980562	+	0.196211i	$0.937136\pi$
$68$	−4.29398	+	1.91180i	−0.520721	+	0.231840i
$69$		0			0
$70$	0.826275	−	0.917671i	0.0987587	−	0.109683i
$71$	−6.99647	−	9.62982i	−0.830329	−	1.14285i	−0.987862	−	0.155336i	$-0.950354\pi$
$71$	−6.99647	−	9.62982i	−0.830329	−	1.14285i	0.157533	−	0.987514i	$-0.449646\pi$
$72$		0			0
$73$	0.116476	−	0.0378454i	0.0136325	−	0.00442947i	−0.302193	−	0.953247i	$-0.597719\pi$
$73$	0.116476	−	0.0378454i	0.0136325	−	0.00442947i	0.315825	+	0.948817i	$0.397719\pi$
$74$	14.7900	−	3.14371i	1.71930	−	0.365449i
$75$		0			0
$76$	−7.60855	−	4.39280i	−0.872761	−	0.503889i
$77$	0.465297	−	0.943391i	0.0530255	−	0.107509i
$78$		0			0
$79$	12.4188	+	1.30527i	1.39722	+	0.146854i	0.773007	−	0.634397i	$-0.218752\pi$
$79$	12.4188	+	1.30527i	1.39722	+	0.146854i	0.624217	+	0.781251i	$0.285418\pi$
$80$	−7.95299	−	2.58408i	−0.889171	−	0.288909i
$81$		0			0
$82$	15.9442	−	11.5841i	1.76074	−	1.27925i
$83$	0.394220	+	0.175518i	0.0432713	+	0.0192656i	0.428258	−	0.903656i	$-0.359127\pi$
$83$	0.394220	+	0.175518i	0.0432713	+	0.0192656i	−0.384987	+	0.922922i	$0.625794\pi$
$84$		0			0
$85$	3.67783	−	3.31153i	0.398916	−	0.359186i
$86$	−7.35413	−	16.5176i	−0.793016	−	1.78114i
$87$		0			0
$88$	−0.797341	−	0.0313737i	−0.0849968	−	0.00334445i
$89$			8.15328i			0.864246i	0.901815	+	0.432123i	$0.142235\pi$
$89$			8.15328i			0.864246i	−0.901815	+	0.432123i	$0.857765\pi$
$90$		0			0
$91$	−0.188535	+	0.580251i	−0.0197638	+	0.0608268i
$92$	7.54364	+	6.79232i	0.786479	+	0.708149i
$93$		0			0
$94$	16.7032	−	1.75558i	1.72281	−	0.181074i
$95$	9.04823	+	1.92326i	0.928329	+	0.197322i
$96$		0			0
$97$	−0.903553	+	8.59673i	−0.0917419	+	0.872866i	0.847773	+	0.530359i	$0.177943\pi$
$97$	−0.903553	+	8.59673i	−0.0917419	+	0.872866i	−0.939515	+	0.342507i	$0.888724\pi$
$98$	−13.5864			−1.37244
$99$		0			0
$100$	2.04837			0.204837
$101$	−0.172842	+	1.64448i	−0.0171984	+	0.163632i	−0.999750	−	0.0223582i	$-0.992883\pi$
$101$	−0.172842	+	1.64448i	−0.0171984	+	0.163632i	0.982552	+	0.185990i	$0.0595492\pi$
$102$		0			0
$103$	−6.03852	−	1.28353i	−0.594993	−	0.126470i	−0.0994345	−	0.995044i	$-0.531703\pi$
$103$	−6.03852	−	1.28353i	−0.594993	−	0.126470i	−0.495559	+	0.868574i	$0.665037\pi$
$104$	0.460289	−	0.0483783i	0.0451350	−	0.00474388i
$105$		0			0
$106$	−2.62373	−	2.36241i	−0.254839	−	0.229458i
$107$	−3.66316	+	11.2740i	−0.354131	+	1.08990i	0.602381	+	0.798209i	$0.294219\pi$
$107$	−3.66316	+	11.2740i	−0.354131	+	1.08990i	−0.956512	+	0.291694i	$0.905781\pi$
$108$		0			0
$109$			3.30028i			0.316109i	0.987430	+	0.158055i	$0.0505222\pi$
$109$			3.30028i			0.316109i	−0.987430	+	0.158055i	$0.949478\pi$
$110$	−12.4286	+	3.50444i	−1.18502	+	0.334135i
$111$		0			0
$112$	−0.545597	−	1.22543i	−0.0515540	−	0.115792i
$113$	−3.84715	+	3.46399i	−0.361910	+	0.325865i	−0.829945	−	0.557845i	$-0.811629\pi$
$113$	−3.84715	+	3.46399i	−0.361910	+	0.325865i	0.468036	+	0.883710i	$0.344962\pi$
$114$		0			0
$115$	−9.76395	−	4.34719i	−0.910493	−	0.405378i
$116$	13.5461	−	9.84181i	1.25772	−	0.913789i
$117$		0			0
$118$	−14.5472	−	4.72668i	−1.33918	−	0.435127i
$119$	0.789526	+	0.0829825i	0.0723757	+	0.00760699i
$120$		0			0
$121$	−9.37971	+	5.74640i	−0.852701	+	0.522400i
$122$	4.21624	+	2.43425i	0.381721	+	0.220387i
$123$		0			0
$124$	0.612574	−	0.130207i	0.0550107	−	0.0116929i
$125$	−11.4532	+	3.72135i	−1.02440	+	0.332848i
$126$		0			0
$127$	−2.22013	−	3.05575i	−0.197005	−	0.271154i	0.699073	−	0.715050i	$-0.253596\pi$
$127$	−2.22013	−	3.05575i	−0.197005	−	0.271154i	−0.896078	+	0.443896i	$0.853596\pi$
$128$	−1.28550	+	1.42770i	−0.113624	+	0.126192i
$129$		0			0
$130$	6.84226	−	3.04637i	0.600106	−	0.267184i
$131$	4.45993	−	7.72483i	0.389666	−	0.674921i	−0.602738	−	0.797939i	$-0.705924\pi$
$131$	4.45993	−	7.72483i	0.389666	−	0.674921i	0.992405	+	0.123017i	$0.0392571\pi$
$132$		0			0
$133$	0.741931	+	1.28506i	0.0643336	+	0.111429i
$134$	17.2186	+	12.5100i	1.48746	+	1.08070i
$135$		0			0
$136$	−0.186098	−	0.572750i	−0.0159577	−	0.0491129i
$137$	1.96181	−	4.40630i	0.167609	−	0.376455i	−0.810140	−	0.586237i	$-0.800609\pi$
$137$	1.96181	−	4.40630i	0.167609	−	0.376455i	0.977748	+	0.209782i	$0.0672754\pi$
$138$		0			0
$139$	−1.49662	+	7.04103i	−0.126941	+	0.597212i	0.867984	+	0.496593i	$0.165416\pi$
$139$	−1.49662	+	7.04103i	−0.126941	+	0.597212i	−0.994925	+	0.100619i	$0.967918\pi$
$140$	−0.787925	−	0.875080i	−0.0665918	−	0.0739577i
$141$		0			0
$142$	−20.2995	+	11.7199i	−1.70350	+	0.983514i
$143$	4.90554	−	4.07942i	0.410222	−	0.341138i
$144$		0			0
$145$	−10.3625	+	14.2627i	−0.860556	+	1.18445i
$146$	−0.0501422	−	0.235901i	−0.00414980	−	0.0195233i
$147$		0			0
$148$	−1.50716	−	14.3396i	−0.123888	−	1.17871i
$149$	−0.354951	−	3.37713i	−0.0290787	−	0.276666i	−0.999394	−	0.0348205i	$-0.988914\pi$
$149$	−0.354951	−	3.37713i	−0.0290787	−	0.276666i	0.970315	−	0.241845i	$-0.0777526\pi$
$150$		0			0
$151$	−1.76609	−	8.30882i	−0.143723	−	0.676162i	−0.989725	−	0.142983i	$-0.954330\pi$
$151$	−1.76609	−	8.30882i	−0.143723	−	0.676162i	0.846002	−	0.533179i	$-0.179003\pi$
$152$	0.661635	−	0.910663i	0.0536657	−	0.0738645i
$153$		0			0
$154$	−1.75179	−	1.10544i	−0.141163	−	0.0890788i
$155$	−0.571048	+	0.329695i	−0.0458677	+	0.0264817i
$156$		0			0
$157$	−12.3770	−	13.7461i	−0.987795	−	1.09706i	−0.995276	−	0.0970857i	$-0.969048\pi$
$157$	−12.3770	−	13.7461i	−0.987795	−	1.09706i	0.00748085	−	0.999972i	$-0.497619\pi$
$158$	5.11256	−	24.0527i	0.406733	−	1.91353i
$159$		0			0
$160$	−6.31083	+	14.1743i	−0.498915	+	1.12058i
$161$	−0.529800	−	1.63056i	−0.0417541	−	0.128506i
$162$		0			0
$163$	−15.0169	−	10.9104i	−1.17622	−	0.854572i	−0.184478	−	0.982837i	$-0.559059\pi$
$163$	−15.0169	−	10.9104i	−1.17622	−	0.854572i	−0.991740	+	0.128265i	$0.959059\pi$
$164$	−9.39669	−	16.2755i	−0.733758	−	1.27091i
$165$		0			0
$166$	0.424886	−	0.735925i	0.0329776	−	0.0571188i
$167$	−12.5097	+	5.56967i	−0.968028	+	0.430994i	−0.828972	−	0.559291i	$-0.811074\pi$
$167$	−12.5097	+	5.56967i	−0.968028	+	0.430994i	−0.139056	+	0.990284i	$0.544407\pi$
$168$		0			0
$169$	6.22255	−	6.91084i	0.478658	−	0.531603i
$170$	−5.72836	−	7.88441i	−0.439345	−	0.604707i
$171$		0			0
$172$	−16.3978	+	5.32796i	−1.25032	+	0.406253i
$173$	−12.9398	+	2.75044i	−0.983797	+	0.209112i	−0.671607	−	0.740907i	$-0.734396\pi$
$173$	−12.9398	+	2.75044i	−0.983797	+	0.209112i	−0.312189	+	0.950020i	$0.601062\pi$
$174$		0			0
$175$	−0.299614	−	0.172982i	−0.0226487	−	0.0130762i
$176$	−2.01363	+	13.8821i	−0.151783	+	1.04641i
$177$		0			0
$178$	15.9676	+	1.67827i	1.19683	+	0.125791i
$179$	5.38656	+	1.75020i	0.402611	+	0.130816i	0.503321	−	0.864100i	$-0.332111\pi$
$179$	5.38656	+	1.75020i	0.402611	+	0.130816i	−0.100710	+	0.994916i	$0.532111\pi$
$180$		0			0
$181$	8.30217	−	6.03188i	0.617096	−	0.448346i	−0.234810	−	0.972041i	$-0.575447\pi$
$181$	8.30217	−	6.03188i	0.617096	−	0.448346i	0.851906	+	0.523695i	$0.175447\pi$
$182$	1.09757	+	0.488671i	0.0813576	+	0.0362227i
$183$		0			0
$184$	−0.966518	+	0.870256i	−0.0712526	+	0.0641561i
$185$	6.17484	+	13.8689i	0.453983	+	1.01966i
$186$		0			0
$187$	−6.51923	−	5.13996i	−0.476734	−	0.375871i
$188$		−	16.0157i		−	1.16807i
$189$		0			0
$190$	5.62906	−	17.3245i	0.408375	−	1.25685i
$191$	−4.19996	−	3.78166i	−0.303899	−	0.273631i	0.503045	−	0.864260i	$-0.332213\pi$
$191$	−4.19996	−	3.78166i	−0.303899	−	0.273631i	−0.806943	+	0.590629i	$0.798880\pi$
$192$		0			0
$193$	17.8702	−	1.87823i	1.28633	−	0.135198i	0.563435	−	0.826161i	$-0.309480\pi$
$193$	17.8702	−	1.87823i	1.28633	−	0.135198i	0.722891	+	0.690962i	$0.242813\pi$
$194$	16.6501	+	3.53909i	1.19541	+	0.254092i
$195$		0			0
$196$	−1.35426	+	12.8849i	−0.0967327	+	0.920350i
$197$	−2.51065			−0.178877			−0.0894383	−	0.995992i	$-0.528507\pi$
$197$	−2.51065			−0.178877			−0.0894383	+	0.995992i	$0.528507\pi$
$198$		0			0
$199$	12.2300			0.866959			0.433479	−	0.901163i	$-0.357286\pi$
$199$	12.2300			0.866959			0.433479	+	0.901163i	$0.357286\pi$
$200$	−0.0274329	+	0.261007i	−0.00193980	+	0.0184560i
$201$		0			0
$202$	3.18502	+	0.676998i	0.224097	+	0.0476334i
$203$	−2.81250	+	0.295606i	−0.197399	+	0.0207475i
$204$		0			0
$205$	14.7050	+	13.2405i	1.02704	+	0.924755i
$206$	−3.75667	+	11.5618i	−0.261739	+	0.805551i
$207$		0			0
$208$		−	8.13606i		−	0.564134i
$209$	0.610097	−	15.5052i	0.0422013	−	1.07252i
$210$		0			0
$211$	−10.2782	−	23.0852i	−0.707580	−	1.58925i	−0.804496	−	0.593957i	$-0.797565\pi$
$211$	−10.2782	−	23.0852i	−0.707580	−	1.58925i	0.0969168	−	0.995292i	$-0.469102\pi$
$212$	−2.50195	+	2.25277i	−0.171835	+	0.154721i
$213$		0			0
$214$	21.3254	+	9.49468i	1.45777	+	0.649043i
$215$	14.6867	−	10.6705i	1.00162	−	0.727723i
$216$		0			0
$217$	−0.100596	−	0.0326858i	−0.00682893	−	0.00221885i
$218$	6.46337	+	0.679328i	0.437755	+	0.0460099i
$219$		0			0
$220$	2.08464	+	12.1361i	0.140547	+	0.818216i
$221$	4.17002	+	2.40756i	0.280506	+	0.161950i
$222$		0			0
$223$	−13.7808	+	2.92920i	−0.922832	+	0.196154i	−0.644741	−	0.764401i	$-0.723035\pi$
$223$	−13.7808	+	2.92920i	−0.922832	+	0.196154i	−0.278091	+	0.960555i	$0.589702\pi$
$224$	−2.36708	+	0.769112i	−0.158157	+	0.0513884i
$225$		0			0
$226$	5.99210	+	8.24741i	0.398588	+	0.548610i
$227$	10.4271	−	11.5805i	0.692071	−	0.768623i	−0.290022	−	0.957020i	$-0.593663\pi$
$227$	10.4271	−	11.5805i	0.692071	−	0.768623i	0.982093	+	0.188397i	$0.0603292\pi$
$228$		0			0
$229$	18.8030	−	8.37163i	1.24254	−	0.553213i	0.323068	−	0.946376i	$-0.395286\pi$
$229$	18.8030	−	8.37163i	1.24254	−	0.553213i	0.919469	+	0.393163i	$0.128619\pi$
$230$	−10.5235	+	18.2272i	−0.693898	+	1.20187i
$231$		0			0
$232$	1.07264	+	1.85787i	0.0704224	+	0.121975i
$233$	2.11851	+	1.53918i	0.138788	+	0.100835i	0.655013	−	0.755618i	$-0.272663\pi$
$233$	2.11851	+	1.53918i	0.138788	+	0.100835i	−0.516225	+	0.856453i	$0.672663\pi$
$234$		0			0
$235$	5.21096	+	16.0377i	0.339925	+	1.04618i
$236$	−5.93264	+	13.3249i	−0.386182	+	0.867379i
$237$		0			0
$238$	0.325031	−	1.52915i	0.0210686	−	0.0991201i
$239$	−14.9011	−	16.5494i	−0.963873	−	1.07049i	−0.997472	−	0.0710537i	$-0.977364\pi$
$239$	−14.9011	−	16.5494i	−0.963873	−	1.07049i	0.0335998	−	0.999435i	$-0.489303\pi$
$240$		0			0
$241$	21.2923	−	12.2931i	1.37156	−	0.791870i	0.380434	−	0.924808i	$-0.375775\pi$
$241$	21.2923	−	12.2931i	1.37156	−	0.791870i	0.991124	+	0.132938i	$0.0424412\pi$
$242$	9.32322	+	19.5523i	0.599319	+	1.25687i
$243$		0			0
$244$	2.72882	−	3.75589i	0.174695	−	0.240447i
$245$	−2.83618	−	13.3432i	−0.181197	−	0.852464i
$246$		0			0
$247$	0.940771	+	8.95084i	0.0598598	+	0.569528i
$248$	0.00838720	+	0.0797989i	0.000532588	+	0.00506724i
$249$		0			0
$250$	4.93051	+	23.1962i	0.311833	+	1.46706i
$251$	7.34629	−	10.1113i	0.463694	−	0.638220i	−0.511576	−	0.859238i	$-0.670938\pi$
$251$	7.34629	−	10.1113i	0.463694	−	0.638220i	0.975270	+	0.221018i	$0.0709381\pi$
$252$		0			0
$253$	−4.41422	+	17.3768i	−0.277519	+	1.09247i
$254$	−6.44147	+	3.71898i	−0.404174	+	0.233350i
$255$		0			0
$256$	11.8920	+	13.2074i	0.743249	+	0.825461i
$257$	−2.54992	+	11.9964i	−0.159060	+	0.748317i	0.824228	+	0.566258i	$0.191610\pi$
$257$	−2.54992	+	11.9964i	−0.159060	+	0.748317i	−0.983288	+	0.182059i	$0.941724\pi$
$258$		0			0
$259$	−0.990512	+	2.22473i	−0.0615474	+	0.138238i
$260$	−2.20705	−	6.79261i	−0.136876	−	0.421259i
$261$		0			0
$262$	−14.2105	−	10.3245i	−0.877929	−	0.637853i
$263$	4.64521	+	8.04575i	0.286436	+	0.496122i	0.972956	−	0.230989i	$-0.0741960\pi$
$263$	4.64521	+	8.04575i	0.286436	+	0.496122i	−0.686520	+	0.727111i	$0.740863\pi$
$264$		0			0
$265$	1.77241	−	3.06990i	0.108878	−	0.188583i
$266$	2.66942	−	1.18850i	0.163673	−	0.0728719i
$267$		0			0
$268$	13.5804	−	15.0825i	0.829553	−	0.921312i
$269$	−12.5983	−	17.3401i	−0.768131	−	1.05724i	−0.996494	−	0.0836659i	$-0.973337\pi$
$269$	−12.5983	−	17.3401i	−0.768131	−	1.05724i	0.228363	−	0.973576i	$-0.426663\pi$
$270$		0			0
$271$	−7.87807	+	2.55974i	−0.478559	+	0.155493i	−0.538356	−	0.842717i	$-0.680954\pi$
$271$	−7.87807	+	2.55974i	−0.478559	+	0.155493i	0.0597976	+	0.998211i	$0.480954\pi$
$272$	−10.3553	+	2.20108i	−0.627880	+	0.133460i
$273$		0			0
$274$	−8.22561	−	4.74906i	−0.496927	−	0.286901i
$275$	1.68434	+	3.20185i	0.101569	+	0.193079i
$276$		0			0
$277$	−11.4853	−	1.20716i	−0.690086	−	0.0725310i	−0.247007	−	0.969014i	$-0.579447\pi$
$277$	−11.4853	−	1.20716i	−0.690086	−	0.0725310i	−0.443079	+	0.896483i	$0.646114\pi$
$278$	13.4813	+	4.38034i	0.808555	+	0.262715i
$279$		0			0
$280$	0.122056	−	0.0886792i	0.00729427	−	0.00529959i
$281$	1.18330	+	0.526838i	0.0705896	+	0.0314285i	0.441728	−	0.897149i	$-0.354366\pi$
$281$	1.18330	+	0.526838i	0.0705896	+	0.0314285i	−0.371138	+	0.928578i	$0.621032\pi$
$282$		0			0
$283$	−4.91434	+	4.42489i	−0.292127	+	0.263033i	−0.802142	−	0.597133i	$-0.796307\pi$
$283$	−4.91434	+	4.42489i	−0.292127	+	0.263033i	0.510015	+	0.860165i	$0.329640\pi$
$284$	9.09135	+	20.4195i	0.539473	+	1.21168i
$285$		0			0
$286$	−6.97950	−	10.4469i	−0.412707	−	0.617736i
$287$			3.17415i			0.187364i
$288$		0			0
$289$	−3.31717	+	10.2092i	−0.195128	+	0.600541i
$290$	25.7995	+	23.2300i	1.51500	+	1.36411i
$291$		0			0
$292$	−0.228718	+	0.0240392i	−0.0133847	+	0.00140679i
$293$	−6.75675	−	1.43619i	−0.394733	−	0.0839032i	0.00626865	−	0.999980i	$-0.498005\pi$
$293$	−6.75675	−	1.43619i	−0.394733	−	0.0839032i	−0.401002	+	0.916077i	$0.631338\pi$
$294$		0			0
$295$	1.60530	−	15.2735i	0.0934645	−	0.889255i
$296$	1.84737			0.107376
$297$		0			0
$298$	−6.68695			−0.387365
$299$	1.08698	−	10.3419i	0.0628615	−	0.598087i
$300$		0			0
$301$	2.84843	+	0.605452i	0.164181	+	0.0348977i
$302$	−16.6358	+	1.74849i	−0.957282	+	0.100614i
$303$		0			0
$304$	−14.7052	−	13.2406i	−0.843402	−	0.759403i
$305$	−1.51052	+	4.64890i	−0.0864921	+	0.266195i
$306$		0			0
$307$		−	11.5549i		−	0.659473i	−0.944073	−	0.329737i	$-0.893040\pi$
$307$		−	11.5549i		−	0.659473i	0.944073	−	0.329737i	$-0.106960\pi$
$308$	−1.22297	+	1.55115i	−0.0696853	+	0.0883848i
$309$		0			0
$310$	0.528140	+	1.18622i	0.0299963	+	0.0673729i
$311$	5.18788	−	4.67119i	0.294178	−	0.264879i	−0.508804	−	0.860882i	$-0.669912\pi$
$311$	5.18788	−	4.67119i	0.294178	−	0.264879i	0.802982	+	0.596004i	$0.203246\pi$
$312$		0			0
$313$	−26.1993	−	11.6647i	−1.48087	−	0.659327i	−0.502199	−	0.864752i	$-0.667475\pi$
$313$	−26.1993	−	11.6647i	−1.48087	−	0.659327i	−0.978673	+	0.205426i	$0.934142\pi$
$314$	−29.4685	+	21.4101i	−1.66300	+	1.20824i
$315$		0			0
$316$	−22.3011	−	7.24607i	−1.25453	−	0.407623i
$317$	29.8418	+	3.13650i	1.67608	+	0.176163i	0.894324	−	0.447421i	$-0.147657\pi$
$317$	29.8418	+	3.13650i	1.67608	+	0.176163i	0.781757	+	0.623584i	$0.214324\pi$
$318$		0			0
$319$	26.5226	+	13.0814i	1.48498	+	0.732419i
$320$	11.9766	+	6.91469i	0.669512	+	0.386543i
$321$		0			0
$322$	−3.30239	+	0.701944i	−0.184035	+	0.0391178i
$323$	11.1378	−	3.61888i	0.619722	−	0.201360i
$324$		0			0
$325$	−1.23341	−	1.69764i	−0.0684170	−	0.0941679i
$326$	−24.4584	+	27.1638i	−1.35463	+	1.50447i
$327$		0			0
$328$	2.19970	−	0.979370i	0.121458	−	0.0540767i
$329$	−1.35251	+	2.34261i	−0.0745661	+	0.129152i
$330$		0			0
$331$	−4.26661	−	7.38998i	−0.234514	−	0.406190i	0.724617	−	0.689151i	$-0.242017\pi$
$331$	−4.26661	−	7.38998i	−0.234514	−	0.406190i	−0.959131	+	0.282961i	$0.908683\pi$
$332$	−0.655573	−	0.476302i	−0.0359792	−	0.0261404i
$333$		0			0
$334$	8.33283	+	25.6458i	0.455952	+	1.40328i
$335$	−8.69165	+	19.5218i	−0.474875	+	1.06659i
$336$		0			0
$337$	−2.48300	+	11.6816i	−0.135257	+	0.636336i	0.857326	+	0.514773i	$0.172124\pi$
$337$	−2.48300	+	11.6816i	−0.135257	+	0.636336i	−0.992584	+	0.121563i	$0.961209\pi$
$338$	−12.2536	−	13.6090i	−0.666506	−	0.740230i
$339$		0			0
$340$	−8.04828	+	4.64667i	−0.436479	+	0.252001i
$341$	0.707236	+	0.850459i	0.0382990	+	0.0460549i
$342$		0			0
$343$	2.59115	−	3.56641i	0.139909	−	0.192568i
$344$	−0.459289	−	2.16079i	−0.0247632	−	0.116502i
$345$		0			0
$346$	2.72303	+	25.9079i	0.146391	+	1.39282i
$347$	−1.50947	−	14.3616i	−0.0810326	−	0.770974i	−0.957290	−	0.289130i	$-0.906634\pi$
$347$	−1.50947	−	14.3616i	−0.0810326	−	0.770974i	0.876257	−	0.481844i	$-0.160033\pi$
$348$		0			0
$349$	6.71017	+	31.5689i	0.359187	+	1.68984i	0.672422	+	0.740168i	$0.265254\pi$
$349$	6.71017	+	31.5689i	0.359187	+	1.68984i	−0.313235	+	0.949676i	$0.601413\pi$
$350$	−0.400446	+	0.551167i	−0.0214047	+	0.0294611i
$351$		0			0
$352$	25.2259	+	6.40813i	1.34455	+	0.341554i
$353$	−5.61311	+	3.24073i	−0.298756	+	0.172487i	−0.641884	−	0.766802i	$-0.721847\pi$
$353$	−5.61311	+	3.24073i	−0.298756	+	0.172487i	0.343128	+	0.939289i	$0.388513\pi$
$354$		0			0
$355$	−15.7476	−	17.4895i	−0.835795	−	0.928245i
$356$	3.18322	−	14.9759i	0.168710	−	0.793719i
$357$		0			0
$358$	4.53642	−	10.1890i	0.239757	−	0.538503i
$359$	2.95299	+	9.08837i	0.155853	+	0.479666i	0.998246	−	0.0591972i	$-0.0188541\pi$
$359$	2.95299	+	9.08837i	0.155853	+	0.479666i	−0.842393	+	0.538863i	$0.818854\pi$
$360$		0			0
$361$	2.33755	+	1.69833i	0.123029	+	0.0893858i
$362$	−10.1041	−	17.5008i	−0.531060	−	0.919824i
$363$		0			0
$364$	0.572841	−	0.992190i	0.0300250	−	0.0520049i
$365$	0.221209	−	0.0984888i	0.0115786	−	0.00515514i
$366$		0			0
$367$	−5.39961	+	5.99687i	−0.281857	+	0.313034i	−0.867404	−	0.497604i	$-0.834213\pi$
$367$	−5.39961	+	5.99687i	−0.281857	+	0.313034i	0.585547	+	0.810639i	$0.300880\pi$
$368$	13.4386	+	18.4966i	0.700534	+	0.964202i
$369$		0			0
$370$	28.4323	−	9.23822i	1.47813	−	0.480272i
$371$	0.556202	−	0.118224i	0.0288766	−	0.00613790i
$372$		0			0
$373$	0.603037	+	0.348164i	0.0312241	+	0.0180272i	0.515531	−	0.856871i	$-0.327595\pi$
$373$	0.603037	+	0.348164i	0.0312241	+	0.0180272i	−0.484307	+	0.874898i	$0.660928\pi$
$374$	−11.4082	+	11.7095i	−0.589903	+	0.605482i
$375$		0			0
$376$	2.04075	+	0.214492i	0.105244	+	0.0110616i
$377$	−16.3133	−	5.30050i	−0.840175	−	0.272990i
$378$		0			0
$379$	2.08014	−	1.51131i	0.106850	−	0.0776308i	−0.533077	−	0.846066i	$-0.678965\pi$
$379$	2.08014	−	1.51131i	0.106850	−	0.0776308i	0.639927	+	0.768436i	$0.278965\pi$
$380$	−15.8688	−	7.06525i	−0.814052	−	0.362439i
$381$		0			0
$382$	−8.27064	+	7.44692i	−0.423163	+	0.381018i
$383$	2.53623	+	5.69646i	0.129595	+	0.291075i	0.966676	−	0.256004i	$-0.0824061\pi$
$383$	2.53623	+	5.69646i	0.129595	+	0.291075i	−0.837080	+	0.547080i	$0.815739\pi$
$384$		0			0
$385$	0.719958	−	1.95118i	0.0366924	−	0.0994415i
$386$		−	35.3842i		−	1.80101i
$387$		0			0
$388$	5.01598	−	15.4376i	0.254648	−	0.783726i
$389$	20.4196	+	18.3859i	1.03532	+	0.932203i	0.997747	−	0.0670912i	$-0.0213719\pi$
$389$	20.4196	+	18.3859i	1.03532	+	0.932203i	0.0375692	+	0.999294i	$0.488039\pi$
$390$		0			0
$391$	−13.4568	+	1.41437i	−0.680540	+	0.0715277i
$392$	−1.62368	−	0.345123i	−0.0820081	−	0.0174314i
$393$		0			0
$394$	−0.516791	+	4.91694i	−0.0260356	+	0.247712i
$395$	24.6893			1.24225
$396$		0			0
$397$	7.45945			0.374379			0.187190	−	0.982324i	$-0.440062\pi$
$397$	7.45945			0.374379			0.187190	+	0.982324i	$0.440062\pi$
$398$	2.51741	−	23.9515i	0.126186	−	1.20058i
$399$		0			0
$400$	4.51274	+	0.959212i	0.225637	+	0.0479606i
$401$	2.47498	−	0.260131i	0.123595	−	0.0129903i	−0.0425291	−	0.999095i	$-0.513542\pi$
$401$	2.47498	−	0.260131i	0.123595	−	0.0129903i	0.166124	+	0.986105i	$0.446875\pi$
$402$		0			0
$403$	−0.476766	−	0.429282i	−0.0237494	−	0.0213841i
$404$	0.959514	−	2.95308i	0.0477376	−	0.146921i
$405$		0			0
$406$			5.56894i			0.276382i
$407$	21.1753	−	14.1471i	1.04962	−	0.701245i
$408$		0			0
$409$	−12.0466	−	27.0572i	−0.595668	−	1.33789i	−0.919989	−	0.391945i	$-0.871802\pi$
$409$	−12.0466	−	27.0572i	−0.595668	−	1.33789i	0.324321	−	0.945947i	$-0.394864\pi$
$410$	28.9575	−	26.0734i	1.43011	−	1.28767i
$411$		0			0
$412$	10.5904	+	4.71514i	0.521750	+	0.232298i
$413$	1.99303	−	1.44802i	0.0980708	−	0.0712526i
$414$		0			0
$415$	0.811442	+	0.263654i	0.0398321	+	0.0129422i
$416$	−15.0133	−	1.57797i	−0.736090	−	0.0773661i
$417$		0			0
$418$	−30.2403	−	4.38641i	−1.47910	−	0.214546i
$419$	7.83379	+	4.52284i	0.382706	+	0.220955i	0.678995	−	0.734143i	$-0.262416\pi$
$419$	7.83379	+	4.52284i	0.382706	+	0.220955i	−0.296289	+	0.955098i	$0.595749\pi$
$420$		0			0
$421$	21.2588	−	4.51871i	1.03609	−	0.220228i	0.341688	−	0.939813i	$-0.389001\pi$
$421$	21.2588	−	4.51871i	1.03609	−	0.220228i	0.694404	+	0.719585i	$0.255668\pi$
$422$	−47.3264	+	15.3773i	−2.30381	+	0.748554i
$423$		0			0
$424$	−0.253544	−	0.348973i	−0.0123132	−	0.0169476i
$425$	−1.82701	+	2.02910i	−0.0886229	+	0.0984257i
$426$		0			0
$427$	−0.716322	+	0.318927i	−0.0346652	+	0.0154340i
$428$	11.1301	−	19.2778i	0.537992	−	0.931830i
$429$		0			0
$430$	−17.8744	−	30.9593i	−0.861979	−	1.49299i
$431$	−14.2119	−	10.3256i	−0.684565	−	0.497366i	0.190304	−	0.981725i	$-0.439053\pi$
$431$	−14.2119	−	10.3256i	−0.684565	−	0.497366i	−0.874869	+	0.484359i	$0.839053\pi$
$432$		0			0
$433$	−4.84981	−	14.9262i	−0.233067	−	0.717306i	−0.997372	−	0.0724515i	$-0.976918\pi$
$433$	−4.84981	−	14.9262i	−0.233067	−	0.717306i	0.764305	−	0.644855i	$-0.223082\pi$
$434$	−0.0847195	+	0.190283i	−0.00406667	+	0.00913388i
$435$		0			0
$436$	1.28850	−	6.06191i	0.0617079	−	0.290313i
$437$	−16.9231	−	18.7950i	−0.809543	−	0.899088i
$438$		0			0
$439$	10.3281	−	5.96296i	0.492936	−	0.284597i	−0.232856	−	0.972511i	$-0.574807\pi$
$439$	10.3281	−	5.96296i	0.492936	−	0.284597i	0.725792	+	0.687915i	$0.241474\pi$
$440$	−1.57432	+	0.103095i	−0.0750528	+	0.00491487i
$441$		0			0
$442$	5.57340	−	7.67113i	0.265100	−	0.364878i
$443$	−3.21054	−	15.1044i	−0.152537	−	0.717632i	−0.986227	−	0.165398i	$-0.947109\pi$
$443$	−3.21054	−	15.1044i	−0.152537	−	0.717632i	0.833689	−	0.552234i	$-0.186224\pi$
$444$		0			0
$445$	1.68504	+	16.0321i	0.0798785	+	0.759993i
$446$	2.90001	+	27.5917i	0.137319	+	1.30651i
$447$		0			0
$448$	0.461228	+	2.16991i	0.0217910	+	0.102519i
$449$	−13.6969	+	18.8521i	−0.646395	+	0.889687i	−0.998936	−	0.0461094i	$-0.985318\pi$
$449$	−13.6969	+	18.8521i	−0.646395	+	0.889687i	0.352541	+	0.935796i	$0.385318\pi$
$450$		0			0
$451$	17.7139	−	28.0712i	0.834115	−	1.32182i
$452$	8.41882	−	4.86061i	0.395988	−	0.228624i
$453$		0			0
$454$	−20.5332	−	22.8045i	−0.963673	−	1.07027i
$455$	−0.250802	+	1.17993i	−0.0117578	+	0.0553160i
$456$		0			0
$457$	0.251498	−	0.564874i	0.0117646	−	0.0264237i	−0.907568	−	0.419906i	$-0.862063\pi$
$457$	0.251498	−	0.564874i	0.0117646	−	0.0264237i	0.919332	+	0.393482i	$0.128730\pi$
$458$	−12.5249	−	38.5476i	−0.585249	−	1.80121i
$459$		0			0
$460$	16.2371	+	11.7969i	0.757058	+	0.550035i
$461$	−11.3787	−	19.7085i	−0.529959	−	0.917915i	−0.999389	−	0.0349460i	$-0.988874\pi$
$461$	−11.3787	−	19.7085i	−0.529959	−	0.917915i	0.469430	−	0.882969i	$-0.344459\pi$
$462$		0			0
$463$	−3.54426	+	6.13884i	−0.164716	+	0.285296i	−0.936554	−	0.350523i	$-0.886004\pi$
$463$	−3.54426	+	6.13884i	−0.164716	+	0.285296i	0.771839	+	0.635818i	$0.219337\pi$
$464$	34.4519	−	15.3390i	1.59939	−	0.712094i
$465$		0			0
$466$	3.45046	−	3.83212i	0.159839	−	0.177520i
$467$	3.50195	+	4.82002i	0.162051	+	0.223044i	0.882319	−	0.470652i	$-0.155981\pi$
$467$	3.50195	+	4.82002i	0.162051	+	0.223044i	−0.720268	+	0.693696i	$0.755981\pi$
$468$		0			0
$469$	−3.26009	+	1.05927i	−0.150537	+	0.0489124i
$470$	32.4813	−	6.90411i	1.49825	−	0.318463i
$471$		0			0
$472$	−1.61843	−	0.934402i	−0.0744944	−	0.0430093i
$473$	−21.8118	−	21.2506i	−1.00291	−	0.977104i
$474$		0			0
$475$	−5.07558	−	0.533465i	−0.232883	−	0.0244770i
$476$	−1.41779	−	0.460669i	−0.0649844	−	0.0211147i
$477$		0			0
$478$	−35.4780	+	25.7763i	−1.62273	+	1.17898i
$479$	−1.60986	−	0.716754i	−0.0735562	−	0.0327493i	0.369629	−	0.929180i	$-0.379485\pi$
$479$	−1.60986	−	0.716754i	−0.0735562	−	0.0327493i	−0.443185	+	0.896430i	$0.646152\pi$
$480$		0			0
$481$	−10.9768	+	9.88355i	−0.500499	+	0.450651i
$482$	−19.6924	−	44.2299i	−0.896966	−	2.01462i
$483$		0			0
$484$	19.4720	−	6.89288i	0.885093	−	0.313313i
$485$			17.0908i			0.776052i
$486$		0			0
$487$	−5.37983	+	16.5574i	−0.243783	+	0.750288i	0.752051	+	0.659105i	$0.229065\pi$
$487$	−5.37983	+	16.5574i	−0.243783	+	0.750288i	−0.995834	+	0.0911829i	$0.970935\pi$
$488$	0.442036	+	0.398011i	0.0200100	+	0.0180171i
$489$		0			0
$490$	−26.7155	+	2.80791i	−1.20688	+	0.126848i
$491$	32.8692	+	6.98657i	1.48337	+	0.315299i	0.877234	−	0.480064i	$-0.159386\pi$
$491$	32.8692	+	6.98657i	1.48337	+	0.315299i	0.606133	+	0.795363i	$0.292720\pi$
$492$		0			0
$493$	−2.33298	+	22.1968i	−0.105072	+	0.999695i
$494$	17.7233			0.797407
$495$		0			0
$496$	1.41052			0.0633344
$497$	0.394614	−	3.75450i	0.0177008	−	0.168412i
$498$		0			0
$499$	−19.0961	−	4.05900i	−0.854859	−	0.181706i	−0.240419	−	0.970669i	$-0.577285\pi$
$499$	−19.0961	−	4.05900i	−0.854859	−	0.181706i	−0.614440	+	0.788963i	$0.710618\pi$
$500$	22.4899	−	2.36378i	1.00578	−	0.105712i
$501$		0			0
$502$	−18.2901	−	16.4685i	−0.816328	−	0.735025i
$503$	−7.43631	+	22.8866i	−0.331569	+	1.02046i	0.636819	+	0.771013i	$0.280250\pi$
$503$	−7.43631	+	22.8866i	−0.331569	+	1.02046i	−0.968388	+	0.249450i	$0.919750\pi$
$504$		0			0
$505$			3.26932i			0.145483i
$506$	33.1227	+	12.2218i	1.47248	+	0.543324i
$507$		0			0
$508$	2.88488	+	6.47956i	0.127996	+	0.287484i
$509$	−13.0245	+	11.7273i	−0.577301	+	0.519804i	−0.905243	−	0.424894i	$-0.860311\pi$
$509$	−13.0245	+	11.7273i	−0.577301	+	0.519804i	0.327943	+	0.944698i	$0.393645\pi$
$510$		0			0
$511$	0.0354844	+	0.0157987i	0.00156974	+	0.000698893i
$512$	25.2051	−	18.3126i	1.11392	−	0.809309i
$513$		0			0
$514$	22.9693	+	7.46319i	1.01313	+	0.329187i
$515$	−12.1390	−	1.27586i	−0.534909	−	0.0562212i
$516$		0			0
$517$	25.0345	−	13.1694i	1.10102	−	0.579192i
$518$	4.15309	+	2.39779i	0.182476	+	0.105353i
$519$		0			0
$520$	0.895083	−	0.190256i	0.0392520	−	0.00834327i
$521$	7.32063	−	2.37862i	0.320723	−	0.104209i	−0.144231	−	0.989544i	$-0.546071\pi$
$521$	7.32063	−	2.37862i	0.320723	−	0.104209i	0.464954	+	0.885335i	$0.346071\pi$
$522$		0			0
$523$	−7.75187	−	10.6695i	−0.338966	−	0.466546i	0.605173	−	0.796094i	$-0.293104\pi$
$523$	−7.75187	−	10.6695i	−0.338966	−	0.466546i	−0.944139	+	0.329547i	$0.893104\pi$
$524$	−11.2079	+	12.4476i	−0.489619	+	0.543777i
$525$		0			0
$526$	16.7132	−	7.44120i	0.728731	−	0.324452i
$527$	−0.417392	+	0.722944i	−0.0181819	+	0.0314919i
$528$		0			0
$529$	3.11086	+	5.38816i	0.135255	+	0.234268i
$530$	−5.64736	−	4.10305i	−0.245306	−	0.178225i
$531$		0			0
$532$	−0.861054	−	2.65005i	−0.0373314	−	0.114894i
$533$	−7.83062	+	17.5879i	−0.339182	+	0.761815i
$534$		0			0
$535$	−4.87298	+	22.9256i	−0.210677	+	0.991159i
$536$	1.73996	+	1.93243i	0.0751550	+	0.0834681i
$537$		0			0
$538$	−36.5525	+	21.1036i	−1.57589	+	0.909842i
$539$	−21.2542	+	8.47815i	−0.915484	+	0.365180i
$540$		0			0
$541$	−8.36941	+	11.5195i	−0.359829	+	0.495262i	−0.950101	−	0.311942i	$-0.899021\pi$
$541$	−8.36941	+	11.5195i	−0.359829	+	0.495262i	0.590272	+	0.807204i	$0.299021\pi$
$542$	3.39146	+	15.9556i	0.145676	+	0.685350i
$543$		0			0
$544$	2.05324	+	19.5353i	0.0880320	+	0.837568i
$545$	0.682069	+	6.48945i	0.0292166	+	0.277977i
$546$		0			0
$547$	−7.86214	−	36.9885i	−0.336161	−	1.58151i	−0.743821	−	0.668379i	$-0.766988\pi$
$547$	−7.86214	−	36.9885i	−0.336161	−	1.58151i	0.407660	−	0.913134i	$-0.366345\pi$
$548$	−5.32374	+	7.32750i	−0.227419	+	0.313015i
$549$		0			0
$550$	6.61731	−	2.63960i	0.282163	−	0.112553i
$551$	−36.1284	+	20.8588i	−1.53912	+	0.888613i
$552$		0			0
$553$	2.65004	+	2.94317i	0.112691	+	0.125156i
$554$	−4.72826	+	22.2447i	−0.200885	+	0.945088i
$555$		0			0
$556$	5.49793	−	12.3486i	0.233164	−	0.523696i
$557$	4.83577	+	14.8830i	0.204898	+	0.630612i	0.999718	+	0.0237660i	$0.00756565\pi$
$557$	4.83577	+	14.8830i	0.204898	+	0.630612i	−0.794819	+	0.606846i	$0.792434\pi$
$558$		0			0
$559$	14.2894	+	10.3819i	0.604378	+	0.439106i
$560$	−1.32608	−	2.29684i	−0.0560373	−	0.0970594i
$561$		0			0
$562$	1.27535	−	2.20896i	0.0537972	−	0.0931795i
$563$	−14.7246	+	6.55580i	−0.620566	+	0.276294i	−0.692840	−	0.721091i	$-0.743641\pi$
$563$	−14.7246	+	6.55580i	−0.620566	+	0.276294i	0.0722743	+	0.997385i	$0.476974\pi$
$564$		0			0
$565$	−6.84888	+	7.60645i	−0.288135	+	0.320006i
$566$	7.65428	+	10.5352i	0.321734	+	0.442828i
$567$		0			0
$568$	−2.72364	+	0.884966i	−0.114282	+	0.0371323i
$569$	23.7313	−	5.04424i	0.994868	−	0.211466i	0.318415	−	0.947951i	$-0.396849\pi$
$569$	23.7313	−	5.04424i	0.994868	−	0.211466i	0.676453	+	0.736486i	$0.263516\pi$
$570$		0			0
$571$	14.5377	+	8.39334i	0.608384	+	0.351250i	0.772333	−	0.635218i	$-0.219090\pi$
$571$	14.5377	+	8.39334i	0.608384	+	0.351250i	−0.163949	+	0.986469i	$0.552423\pi$
$572$	−10.6031	+	5.57780i	−0.443339	+	0.233219i
$573$		0			0
$574$	6.21635	+	0.653365i	0.259465	+	0.0272709i
$575$	5.60807	+	1.82217i	0.233873	+	0.0759899i
$576$		0			0
$577$	5.58119	−	4.05497i	0.232348	−	0.168811i	−0.465519	−	0.885038i	$-0.654132\pi$
$577$	5.58119	−	4.05497i	0.232348	−	0.168811i	0.697867	+	0.716227i	$0.254132\pi$
$578$	19.3112	+	8.59790i	0.803240	+	0.357626i
$579$		0			0
$580$	24.6021	−	22.1518i	1.02155	−	0.919805i
$581$	0.0556671	+	0.125030i	0.00230946	+	0.00518714i
$582$		0			0
$583$	−5.57866	−	2.05844i	−0.231044	−	0.0852520i
$584$		−	0.0294655i		−	0.00121929i
$585$		0			0
$586$	−4.20349	+	12.9370i	−0.173644	+	0.534422i
$587$	−18.2680	−	16.4486i	−0.754003	−	0.678907i	0.199633	−	0.979871i	$-0.436025\pi$
$587$	−18.2680	−	16.4486i	−0.754003	−	0.678907i	−0.953636	+	0.300964i	$0.902692\pi$
$588$		0			0
$589$	−1.55178	+	0.163099i	−0.0639400	+	0.00672036i
$590$	−29.5816	−	6.28776i	−1.21785	−	0.258863i
$591$		0			0
$592$	3.39458	−	32.2972i	0.139516	−	1.32741i
$593$	25.3400			1.04059			0.520295	−	0.853987i	$-0.325822\pi$
$593$	25.3400			1.04059			0.520295	+	0.853987i	$0.325822\pi$
$594$		0			0
$595$	1.56962			0.0643481
$596$	−0.666535	+	6.34166i	−0.0273024	+	0.259765i
$597$		0			0
$598$	−20.0301	−	4.25754i	−0.819093	−	0.174104i
$599$	−21.6110	+	2.27140i	−0.883000	+	0.0928070i	−0.535164	−	0.844748i	$-0.679750\pi$
$599$	−21.6110	+	2.27140i	−0.883000	+	0.0928070i	−0.347836	+	0.937555i	$0.613083\pi$
$600$		0			0
$601$	13.9577	+	12.5676i	0.569346	+	0.512642i	0.902763	−	0.430138i	$-0.141535\pi$
$601$	13.9577	+	12.5676i	0.569346	+	0.512642i	−0.333417	+	0.942779i	$0.608202\pi$
$602$	1.77206	−	5.45383i	0.0722236	−	0.222281i
$603$		0			0
$604$			15.9511i			0.649040i
$605$	−17.2560	+	13.2378i	−0.701557	+	0.538195i
$606$		0			0
$607$	19.5340	+	43.8741i	0.792862	+	1.78080i	0.600774	+	0.799419i	$0.294859\pi$
$607$	19.5340	+	43.8741i	0.792862	+	1.78080i	0.192088	+	0.981378i	$0.438474\pi$
$608$	−27.2848	+	24.5673i	−1.10654	+	0.996336i
$609$		0			0
$610$	8.79362	+	3.91517i	0.356043	+	0.158521i
$611$	−13.2734	+	9.64370i	−0.536985	+	0.390142i
$612$		0			0
$613$	1.96455	+	0.638321i	0.0793474	+	0.0257815i	0.348422	−	0.937338i	$-0.386718\pi$
$613$	1.96455	+	0.638321i	0.0793474	+	0.0257815i	−0.269074	+	0.963119i	$0.586718\pi$
$614$	−22.6295	−	2.37845i	−0.913252	−	0.0959866i
$615$		0			0
$616$	−0.181271	−	0.176607i	−0.00730362	−	0.00711569i
$617$	29.9543	+	17.2941i	1.20591	+	0.696235i	0.961864	−	0.273527i	$-0.0881904\pi$
$617$	29.9543	+	17.2941i	1.20591	+	0.696235i	0.244050	+	0.969763i	$0.421524\pi$
$618$		0			0
$619$	−26.8319	+	5.70330i	−1.07847	+	0.229235i	−0.712698	−	0.701471i	$-0.752527\pi$
$619$	−26.8319	+	5.70330i	−1.07847	+	0.229235i	−0.365768	+	0.930706i	$0.619194\pi$
$620$	1.17761	−	0.382630i	0.0472941	−	0.0153668i
$621$		0			0
$622$	−8.08033	−	11.1216i	−0.323992	−	0.445936i
$623$	−1.73030	+	1.92169i	−0.0693228	+	0.0769908i
$624$		0			0
$625$	−16.7690	+	7.46605i	−0.670761	+	0.298642i
$626$	−28.2373	+	48.9085i	−1.12859	+	1.95478i
$627$		0			0
$628$	17.3672	+	30.0809i	0.693028	+	1.20036i
$629$	15.5490	+	11.2970i	0.619979	+	0.450441i
$630$		0			0
$631$	−8.09100	−	24.9015i	−0.322098	−	0.991315i	−0.972734	−	0.231925i	$-0.925498\pi$
$631$	−8.09100	−	24.9015i	−0.322098	−	0.991315i	0.650636	−	0.759390i	$-0.274502\pi$
$632$	1.22197	−	2.74460i	0.0486075	−	0.109174i
$633$		0			0
$634$	12.2852	−	57.7974i	0.487908	−	2.29543i
$635$	−4.99705	−	5.54979i	−0.198302	−	0.220237i
$636$		0			0
$637$	11.4941	−	6.63613i	0.455413	−	0.262933i
$638$	31.0784	−	49.2501i	1.23041	−	1.94983i
$639$		0			0
$640$	−2.23267	+	3.07300i	−0.0882539	+	0.121471i
$641$	−1.27122	−	5.98060i	−0.0502100	−	0.236220i	0.945886	−	0.324500i	$-0.105196\pi$
$641$	−1.27122	−	5.98060i	−0.0502100	−	0.236220i	−0.996096	+	0.0882806i	$0.971863\pi$
$642$		0			0
$643$	0.0855453	+	0.813909i	0.00337358	+	0.0320974i	0.996079	−	0.0884661i	$-0.0281965\pi$
$643$	0.0855453	+	0.813909i	0.00337358	+	0.0320974i	−0.992706	+	0.120564i	$0.961530\pi$
$644$	0.336526	+	3.20183i	0.0132610	+	0.126170i
$645$		0			0
$646$	−4.79473	−	22.5575i	−0.188646	−	0.887511i
$647$	−3.42533	+	4.71456i	−0.134664	+	0.185349i	−0.871023	−	0.491242i	$-0.836543\pi$
$647$	−3.42533	+	4.71456i	−0.134664	+	0.185349i	0.736360	+	0.676590i	$0.236543\pi$
$648$		0			0
$649$	−25.7068	+	1.68342i	−1.00908	+	0.0660800i
$650$	−3.57859	+	2.06610i	−0.140364	+	0.0810391i
$651$		0			0
$652$	23.3233	+	25.9031i	0.913410	+	1.01444i
$653$	−0.541428	+	2.54722i	−0.0211877	+	0.0996803i	−0.987471	−	0.157801i	$-0.949559\pi$
$653$	−0.541428	+	2.54722i	−0.0211877	+	0.0996803i	0.966283	+	0.257482i	$0.0828927\pi$
$654$		0			0
$655$	7.17322	−	16.1113i	0.280281	−	0.629521i
$656$	−13.0802	−	40.2567i	−0.510696	−	1.57176i
$657$		0			0
$658$	4.30944	+	3.13099i	0.168000	+	0.122059i
$659$	11.2518	+	19.4886i	0.438306	+	0.759169i	0.997559	−	0.0698283i	$-0.0222451\pi$
$659$	11.2518	+	19.4886i	0.438306	+	0.759169i	−0.559253	+	0.828997i	$0.688912\pi$
$660$		0			0
$661$	3.23287	−	5.59950i	0.125744	−	0.217795i	−0.796279	−	0.604929i	$-0.793201\pi$
$661$	3.23287	−	5.59950i	0.125744	−	0.217795i	0.922024	+	0.387134i	$0.126535\pi$
$662$	−15.3510	+	6.83471i	−0.596634	+	0.265639i
$663$		0			0
$664$	0.0694709	−	0.0771553i	0.00269599	−	0.00299420i
$665$	1.72447	+	2.37353i	0.0668720	+	0.0920414i
$666$		0			0
$667$	45.8417	−	14.8949i	1.77500	−	0.576732i
$668$	25.1521	−	5.34625i	0.973166	−	0.206853i
$669$		0			0
$670$	36.4429	+	21.0403i	1.40791	+	0.812859i
$671$	8.11477	+	1.17706i	0.313267	+	0.0454400i
$672$		0			0
$673$	−0.353467	−	0.0371509i	−0.0136252	−	0.00143206i	0.0977134	−	0.995215i	$-0.468847\pi$
$673$	−0.353467	−	0.0371509i	−0.0136252	−	0.00143206i	−0.111339	+	0.993783i	$0.535514\pi$
$674$	22.3665	+	7.26731i	0.861524	+	0.279926i
$675$		0			0
$676$	−14.1276	+	10.2643i	−0.543371	+	0.394782i
$677$	−26.7176	−	11.8955i	−1.02684	−	0.457179i	−0.176996	−	0.984212i	$-0.556638\pi$
$677$	−26.7176	−	11.8955i	−1.02684	−	0.457179i	−0.849845	+	0.527032i	$0.823305\pi$
$678$		0			0
$679$	−2.03737	+	1.83445i	−0.0781870	+	0.0703999i
$680$	−0.484300	−	1.08776i	−0.0185721	−	0.0417135i
$681$		0			0
$682$	1.81114	−	1.21002i	0.0693522	−	0.0463339i
$683$		−	26.1630i		−	1.00110i	−0.865708	−	0.500549i	$-0.833132\pi$
$683$		−	26.1630i		−	1.00110i	0.865708	−	0.500549i	$-0.166868\pi$
$684$		0			0
$685$	2.94692	−	9.06969i	0.112596	−	0.346535i
$686$	−6.45120	−	5.80869i	−0.246308	−	0.221777i
$687$		0			0
$688$	−38.6207	+	4.05920i	−1.47240	+	0.154755i
$689$	3.37356	+	0.717072i	0.128522	+	0.0273183i
$690$		0			0
$691$	−4.66483	+	44.3829i	−0.177458	+	1.68840i	0.437006	+	0.899459i	$0.356039\pi$
$691$	−4.66483	+	44.3829i	−0.177458	+	1.68840i	−0.614464	+	0.788945i	$0.710628\pi$
$692$	24.8415			0.944334
$693$		0			0
$694$	−28.4370			−1.07945
$695$	−1.48768	+	14.1543i	−0.0564308	+	0.536903i
$696$		0			0
$697$	24.5036	+	5.20840i	0.928139	+	0.197282i
$698$	63.2067	−	6.64329i	2.39241	−	0.251452i
$699$		0			0
$700$	0.482791	+	0.434707i	0.0182478	+	0.0164304i
$701$	3.87098	−	11.9137i	0.146205	−	0.449972i	−0.850959	−	0.525232i	$-0.823979\pi$
$701$	3.87098	−	11.9137i	0.146205	−	0.449972i	0.997164	+	0.0752595i	$0.0239785\pi$
$702$		0			0
$703$			35.9241i			1.35490i
$704$	8.03059	−	21.7640i	0.302664	−	0.820261i
$705$		0			0
$706$	5.19135	+	11.6600i	0.195379	+	0.438828i
$707$	−0.389731	+	0.350915i	−0.0146573	+	0.0131975i
$708$		0			0
$709$	−10.2712	−	4.57305i	−0.385744	−	0.171745i	0.204696	−	0.978826i	$-0.434379\pi$
$709$	−10.2712	−	4.57305i	−0.385744	−	0.171745i	−0.590441	+	0.807081i	$0.701046\pi$
$710$	−37.4934	+	27.2406i	−1.40710	+	1.02232i
$711$		0			0
$712$	1.86562	+	0.606176i	0.0699169	+	0.0227174i
$713$	1.79294	+	0.188446i	0.0671462	+	0.00705735i
$714$		0			0
$715$	8.80283	−	9.03532i	0.329207	−	0.337902i
$716$	−9.21066	−	5.31778i	−0.344219	−	0.198735i
$717$		0			0
$718$	18.4068	−	3.91248i	0.686935	−	0.146013i
$719$	−8.20360	+	2.66551i	−0.305942	+	0.0994067i	−0.457965	−	0.888970i	$-0.651421\pi$
$719$	−8.20360	+	2.66551i	−0.305942	+	0.0994067i	0.152022	+	0.988377i	$0.451421\pi$
$720$		0			0
$721$	−1.15086	−	1.58402i	−0.0428602	−	0.0589920i
$722$	3.80723	−	4.22835i	0.141690	−	0.157363i
$723$		0			0
$724$	−17.6043	+	7.83794i	−0.654259	+	0.291295i
$725$	4.86324	−	8.42338i	0.180616	−	0.312837i
$726$		0			0
$727$	23.7016	+	41.0524i	0.879044	+	1.52255i	0.852391	+	0.522905i	$0.175152\pi$
$727$	23.7016	+	41.0524i	0.879044	+	1.52255i	0.0266533	+	0.999645i	$0.491515\pi$
$728$	0.118755	+	0.0862803i	0.00440134	+	0.00319776i
$729$		0			0
$730$	−0.147350	−	0.453496i	−0.00545366	−	0.0167847i
$731$	9.34786	−	20.9956i	0.345743	−	0.776552i
$732$		0			0
$733$	3.21853	−	15.1420i	0.118879	−	0.559282i	−0.877883	−	0.478875i	$-0.841045\pi$
$733$	3.21853	−	15.1420i	0.118879	−	0.559282i	0.996762	−	0.0804070i	$-0.0256220\pi$
$734$	10.6330	+	11.8092i	0.392472	+	0.435884i
$735$		0			0
$736$	36.7379	−	21.2106i	1.35418	−	0.781833i
$737$	34.7427	+	8.82565i	1.27976	+	0.325097i
$738$		0			0
$739$	25.0234	−	34.4418i	0.920502	−	1.26696i	−0.0429492	−	0.999077i	$-0.513675\pi$
$739$	25.0234	−	34.4418i	0.920502	−	1.26696i	0.963451	−	0.267885i	$-0.0863246\pi$
$740$	−5.92715	−	27.8850i	−0.217886	−	1.02507i
$741$		0			0
$742$	−0.117046	−	1.11362i	−0.00429690	−	0.0408822i
$743$	5.04718	+	48.0207i	0.185163	+	1.76171i	0.554283	+	0.832328i	$0.312993\pi$
$743$	5.04718	+	48.0207i	0.185163	+	1.76171i	−0.369120	+	0.929382i	$0.620341\pi$
$744$		0			0
$745$	−1.39590	−	6.56721i	−0.0511420	−	0.240604i
$746$	0.805983	−	1.10934i	0.0295091	−	0.0406159i
$747$		0			0
$748$	9.96770	+	11.9863i	0.364455	+	0.438261i
$749$	−3.25597	+	1.87984i	−0.118971	+	0.0686877i
$750$		0			0
$751$	17.2188	+	19.1234i	0.628323	+	0.697823i	0.970305	−	0.241883i	$-0.0777651\pi$
$751$	17.2188	+	19.1234i	0.628323	+	0.697823i	−0.341983	+	0.939706i	$0.611098\pi$
$752$	7.49986	−	35.2840i	0.273492	−	1.28668i
$753$		0			0
$754$	−13.7386	+	30.8573i	−0.500329	+	1.12376i
$755$	−5.18991	−	15.9729i	−0.188880	−	0.581314i
$756$		0			0
$757$	−41.1683	−	29.9105i	−1.49629	−	1.08712i	−0.971832	−	0.235676i	$-0.924269\pi$
$757$	−41.1683	−	29.9105i	−1.49629	−	1.08712i	−0.524454	−	0.851439i	$-0.675731\pi$
$758$	−2.53162	−	4.38490i	−0.0919527	−	0.159267i
$759$		0			0
$760$	1.11279	−	1.92741i	0.0403651	−	0.0699144i
$761$	−19.4991	+	8.68155i	−0.706841	+	0.314706i	−0.728487	−	0.685060i	$-0.759776\pi$
$761$	−19.4991	+	8.68155i	−0.706841	+	0.314706i	0.0216460	+	0.999766i	$0.493109\pi$
$762$		0			0
$763$	−0.700388	+	0.777859i	−0.0253557	+	0.0281604i
$764$	6.23800	+	8.58587i	0.225683	+	0.310626i
$765$		0			0
$766$	11.6782	−	3.79447i	0.421950	−	0.137100i
$767$	14.6156	−	3.10665i	0.527740	−	0.112175i
$768$		0			0
$769$	−18.7124	−	10.8036i	−0.674786	−	0.389588i	0.123102	−	0.992394i	$-0.460716\pi$
$769$	−18.7124	−	10.8036i	−0.674786	−	0.389588i	−0.797888	+	0.602806i	$0.794049\pi$
$770$	−3.67306	−	1.81162i	−0.132368	−	0.0652862i
$771$		0			0
$772$	−33.5571	−	3.52699i	−1.20775	−	0.126939i
$773$	−9.33763	−	3.03398i	−0.335851	−	0.109125i	0.136236	−	0.990676i	$-0.456499\pi$
$773$	−9.33763	−	3.03398i	−0.335851	−	0.109125i	−0.472088	+	0.881552i	$0.656499\pi$
$774$		0			0
$775$	0.294314	−	0.213832i	0.0105721	−	0.00768106i
$776$	1.89991	+	0.845894i	0.0682027	+	0.0303658i
$777$		0			0
$778$	40.2107	−	36.2059i	1.44162	−	1.29804i
$779$	19.0450	+	42.7757i	0.682357	+	1.53260i
$780$		0			0
$781$	−24.4425	+	31.0015i	−0.874621	+	1.10932i
$782$			26.6454i			0.952837i
$783$		0			0
$784$	−9.01729	+	27.7524i	−0.322046	+	0.991155i
$785$	−27.1783	−	24.4714i	−0.970034	−	0.873423i
$786$		0			0
$787$	34.9251	−	3.67077i	1.24494	−	0.130849i	0.540950	−	0.841055i	$-0.318065\pi$
$787$	34.9251	−	3.67077i	1.24494	−	0.130849i	0.703994	+	0.710206i	$0.251398\pi$
$788$	4.61154	+	0.980212i	0.164279	+	0.0349186i
$789$		0			0
$790$	5.08202	−	48.3522i	0.180810	−	1.72029i
$791$	−1.64189			−0.0583787
$792$		0			0
$793$	−4.75591			−0.168887
$794$	1.53545	−	14.6088i	0.0544911	−	0.518448i
$795$		0			0
$796$	−22.4638	−	4.77484i	−0.796210	−	0.169240i
$797$	48.4165	−	5.08878i	1.71500	−	0.180254i	0.804553	−	0.593881i	$-0.202405\pi$
$797$	48.4165	−	5.08878i	1.71500	−	0.180254i	0.910446	+	0.413627i	$0.135738\pi$
$798$		0			0
$799$	15.8650	+	14.2849i	0.561264	+	0.505365i
$800$	2.64525	−	8.14125i	0.0935238	−	0.287837i
$801$		0			0
$802$		−	4.90063i		−	0.173047i
$803$	−0.225647	−	0.337746i	−0.00796289	−	0.0119188i
$804$		0			0
$805$	−1.37875	−	3.09672i	−0.0485946	−	0.109145i
$806$	−0.938857	+	0.845351i	−0.0330698	+	0.0297762i
$807$		0			0
$808$	0.363436	+	0.161812i	0.0127856	+	0.00569253i
$809$	1.95603	−	1.42114i	0.0687705	−	0.0499647i	−0.552869	−	0.833268i	$-0.686467\pi$
$809$	1.95603	−	1.42114i	0.0687705	−	0.0499647i	0.621639	+	0.783304i	$0.286467\pi$
$810$		0			0
$811$	22.4513	+	7.29488i	0.788373	+	0.256158i	0.675411	−	0.737441i	$-0.263966\pi$
$811$	22.4513	+	7.29488i	0.788373	+	0.256158i	0.112962	+	0.993599i	$0.463966\pi$
$812$	5.28138	+	0.555095i	0.185340	+	0.0194800i
$813$		0			0
$814$	−23.3474	−	44.3823i	−0.818326	−	1.55560i
$815$	−31.7832	−	18.3500i	−1.11332	−	0.642773i
$816$		0			0
$817$	42.0189	−	8.93140i	1.47006	−	0.312470i
$818$	−55.4693	+	18.0231i	−1.93944	+	0.630162i
$819$		0			0
$820$	−21.8407	−	30.0611i	−0.762710	−	1.04978i
$821$	23.9476	−	26.5965i	0.835778	−	0.928226i	−0.162510	−	0.986707i	$-0.551959\pi$
$821$	23.9476	−	26.5965i	0.835778	−	0.928226i	0.998289	+	0.0584813i	$0.0186258\pi$
$822$		0			0
$823$	−32.7895	+	14.5988i	−1.14297	+	0.508883i	−0.888809	−	0.458279i	$-0.848466\pi$
$823$	−32.7895	+	14.5988i	−1.14297	+	0.508883i	−0.254162	+	0.967162i	$0.581800\pi$
$824$	−0.742643	+	1.28629i	−0.0258712	+	0.0448102i
$825$		0			0
$826$	−2.42561	−	4.20128i	−0.0843978	−	0.146181i
$827$	−11.6799	−	8.48596i	−0.406151	−	0.295086i	0.365891	−	0.930658i	$-0.380764\pi$
$827$	−11.6799	−	8.48596i	−0.406151	−	0.295086i	−0.772042	+	0.635572i	$0.780764\pi$
$828$		0			0
$829$	−16.7616	−	51.5868i	−0.582153	−	1.79168i	−0.610415	−	0.792082i	$-0.708997\pi$
$829$	−16.7616	−	51.5868i	−0.582153	−	1.79168i	0.0282623	−	0.999601i	$-0.491003\pi$
$830$	0.683374	−	1.53488i	0.0237203	−	0.0532766i
$831$		0			0
$832$	−2.79751	+	13.1612i	−0.0969862	+	0.456284i
$833$	−11.5557	−	12.8340i	−0.400383	−	0.444670i
$834$		0			0
$835$	−23.4471	+	13.5372i	−0.811421	+	0.468474i
$836$	−7.17418	+	28.2416i	−0.248124	+	0.976754i
$837$		0			0
$838$	10.4702	−	14.4110i	0.361686	−	0.497819i
$839$	11.5611	+	54.3907i	0.399134	+	1.87778i	0.473905	+	0.880576i	$0.342844\pi$
$839$	11.5611	+	54.3907i	0.399134	+	1.87778i	−0.0747712	+	0.997201i	$0.523823\pi$
$840$		0			0
$841$	−5.27938	−	50.2299i	−0.182048	−	1.73207i
$842$	−4.47367	−	42.5641i	−0.154173	−	1.46686i
$843$		0			0
$844$	9.86590	+	46.4154i	0.339598	+	1.59768i
$845$	10.8073	−	14.8750i	0.371784	−	0.511717i
$846$		0			0
$847$	−3.43025	−	0.636170i	−0.117865	−	0.0218591i
$848$	−6.56695	+	3.79143i	−0.225510	+	0.130198i
$849$		0			0
$850$	3.59778	+	3.99574i	0.123403	+	0.137053i
$851$	8.62981	−	40.6001i	0.295826	−	1.39175i
$852$		0			0
$853$	6.56555	−	14.7465i	0.224800	−	0.504909i	−0.765570	−	0.643352i	$-0.777543\pi$
$853$	6.56555	−	14.7465i	0.224800	−	0.504909i	0.990370	+	0.138443i	$0.0442097\pi$
$854$	0.477149	+	1.46851i	0.0163277	+	0.0502515i
$855$		0			0
$856$	2.30735	+	1.67639i	0.0788637	+	0.0572979i
$857$	23.6770	+	41.0098i	0.808792	+	1.40087i	0.913701	+	0.406387i	$0.133211\pi$
$857$	23.6770	+	41.0098i	0.808792	+	1.40087i	−0.104909	+	0.994482i	$0.533455\pi$
$858$		0			0
$859$	4.16516	−	7.21427i	0.142114	−	0.246148i	−0.786179	−	0.617999i	$-0.787944\pi$
$859$	4.16516	−	7.21427i	0.142114	−	0.246148i	0.928292	+	0.371851i	$0.121277\pi$
$860$	−31.1424	+	13.8655i	−1.06195	+	0.472809i
$861$		0			0
$862$	−23.1473	+	25.7077i	−0.788401	+	0.875608i
$863$	3.57452	+	4.91990i	0.121678	+	0.167475i	0.865511	−	0.500890i	$-0.166994\pi$
$863$	3.57452	+	4.91990i	0.121678	+	0.167475i	−0.743833	+	0.668366i	$0.766994\pi$
$864$		0			0
$865$	−24.8756	+	8.08256i	−0.845795	+	0.274815i
$866$	−30.2302	+	6.42562i	−1.02726	+	0.218352i
$867$		0			0
$868$	0.172013	+	0.0993118i	0.00583850	+	0.00337086i
$869$	−7.01132	−	40.8176i	−0.237843	−	1.38464i
$870$		0			0
$871$	−20.6773	−	2.17327i	−0.700623	−	0.0736384i
$872$	0.755163	+	0.245367i	0.0255730	+	0.00830918i
$873$		0			0
$874$	−40.2922	+	29.2740i	−1.36290	+	0.990208i
$875$	−3.48920	−	1.55349i	−0.117956	−	0.0525176i
$876$		0			0
$877$	9.24839	−	8.32729i	0.312296	−	0.281193i	−0.498045	−	0.867151i	$-0.665949\pi$
$877$	9.24839	−	8.32729i	0.312296	−	0.281193i	0.810341	+	0.585959i	$0.199282\pi$
$878$	−9.55211	−	21.4544i	−0.322368	−	0.724050i
$879$		0			0
$880$	−1.09045	+	27.7131i	−0.0367591	+	0.934207i
$881$		−	59.2385i		−	1.99580i	−0.0647993	−	0.997898i	$-0.520641\pi$
$881$		−	59.2385i		−	1.99580i	0.0647993	−	0.997898i	$-0.479359\pi$
$882$		0			0
$883$	−13.1258	+	40.3970i	−0.441718	+	1.35947i	0.444325	+	0.895866i	$0.353444\pi$
$883$	−13.1258	+	40.3970i	−0.441718	+	1.35947i	−0.886043	+	0.463603i	$0.846556\pi$
$884$	−6.71948	−	6.05025i	−0.226001	−	0.203492i
$885$		0			0
$886$	−30.2418	+	3.17854i	−1.01599	+	0.106785i
$887$	−22.5087	−	4.78438i	−0.755769	−	0.160644i	−0.186115	−	0.982528i	$-0.559590\pi$
$887$	−22.5087	−	4.78438i	−0.755769	−	0.160644i	−0.569654	+	0.821884i	$0.692923\pi$
$888$		0			0
$889$	0.125219	−	1.19138i	0.00419973	−	0.0399577i
$890$	31.7446			1.06408
$891$		0			0
$892$	26.4561			0.885815
$893$	−4.17103	+	39.6847i	−0.139578	+	1.32800i
$894$		0			0
$895$	10.9535	+	2.32824i	0.366135	+	0.0778244i
$896$	−0.605973	+	0.0636904i	−0.0202441	+	0.00212775i
$897$		0			0
$898$	34.1012	+	30.7049i	1.13797	+	1.02464i
$899$	0.918932	−	2.82818i	0.0306481	−	0.0943251i
$900$		0			0
$901$		−	4.48773i		−	0.149508i
$902$	−51.3294	−	40.4696i	−1.70908	−	1.34749i
$903$		0			0
$904$	0.506597	+	1.13784i	0.0168492	+	0.0378439i
$905$	15.0782	−	13.5765i	0.501217	−	0.451298i
$906$		0			0
$907$	−10.3132	−	4.59175i	−0.342446	−	0.152467i	0.228306	−	0.973589i	$-0.426681\pi$
$907$	−10.3132	−	4.59175i	−0.342446	−	0.152467i	−0.570752	+	0.821123i	$0.693348\pi$
$908$	−23.6736	+	17.1999i	−0.785637	+	0.570799i
$909$		0			0
$910$	2.25919	+	0.734055i	0.0748914	+	0.0243337i
$911$	−24.3589	−	2.56022i	−0.807046	−	0.0848240i	−0.307986	−	0.951391i	$-0.599655\pi$
$911$	−24.3589	−	2.56022i	−0.807046	−	0.0848240i	−0.499061	+	0.866567i	$0.666322\pi$
$912$		0			0
$913$	0.205451	−	1.41639i	0.00679942	−	0.0468757i
$914$	−1.05450	−	0.608815i	−0.0348797	−	0.0201378i
$915$		0			0
$916$	−37.8056	+	8.03583i	−1.24913	+	0.265511i
$917$	2.69055	−	0.874214i	0.0888499	−	0.0288691i
$918$		0			0
$919$	20.6927	+	28.4811i	0.682590	+	0.939504i	0.999961	−	0.00879691i	$-0.00280018\pi$
$919$	20.6927	+	28.4811i	0.682590	+	0.939504i	−0.317371	+	0.948301i	$0.602800\pi$
$920$	−1.72064	+	1.91096i	−0.0567278	+	0.0630026i
$921$		0			0
$922$	−40.9399	+	18.2276i	−1.34828	+	0.600294i
$923$	11.4489	−	19.8301i	0.376845	−	0.652714i
$924$		0			0
$925$	−4.18788	−	7.25361i	−0.137696	−	0.238497i
$926$	11.2929	+	8.20480i	0.371109	+	0.269626i
$927$		0			0
$928$	−21.6229	−	66.5485i	−0.709807	−	2.18456i
$929$	−7.37153	+	16.5567i	−0.241852	+	0.543209i	−0.993162	−	0.116740i	$-0.962755\pi$
$929$	−7.37153	+	16.5567i	−0.241852	+	0.543209i	0.751310	+	0.659949i	$0.229422\pi$
$930$		0			0
$931$	6.71131	−	31.5742i	0.219954	−	1.03480i
$932$	−3.29032	−	3.65427i	−0.107778	−	0.119699i
$933$		0			0
$934$	10.1605	−	5.86618i	0.332462	−	0.191947i
$935$	−13.8813	−	8.75954i	−0.453966	−	0.286468i
$936$		0			0
$937$	−17.7777	+	24.4689i	−0.580772	+	0.799365i	−0.993780	−	0.111363i	$-0.964478\pi$
$937$	−17.7777	+	24.4689i	−0.580772	+	0.799365i	0.413007	+	0.910728i	$0.364478\pi$
$938$	1.40345	+	6.60270i	0.0458242	+	0.215586i
$939$		0			0
$940$	−3.30997	−	31.4923i	−0.107959	−	1.02716i
$941$	−2.73892	−	26.0591i	−0.0892862	−	0.849502i	−0.943899	−	0.330235i	$-0.892872\pi$
$941$	−2.73892	−	26.0591i	−0.0892862	−	0.849502i	0.854612	−	0.519266i	$-0.173795\pi$
$942$		0			0
$943$	−11.2482	−	52.9185i	−0.366291	−	1.72326i
$944$	−19.3099	+	26.5778i	−0.628484	+	0.865035i
$945$		0			0
$946$	−46.1076	+	38.3428i	−1.49909	+	1.24663i
$947$	28.0006	−	16.1662i	0.909897	−	0.525330i	0.0294993	−	0.999565i	$-0.490609\pi$
$947$	28.0006	−	16.1662i	0.909897	−	0.525330i	0.880398	+	0.474235i	$0.157275\pi$
$948$		0			0
$949$	0.157643	+	0.175080i	0.00511731	+	0.00568334i
$950$	−2.08951	+	9.83036i	−0.0677926	+	0.318939i
$951$		0			0
$952$	0.0776870	−	0.174488i	0.00251785	−	0.00565519i
$953$	10.9868	+	33.8138i	0.355897	+	1.09534i	0.955488	+	0.295031i	$0.0953299\pi$
$953$	10.9868	+	33.8138i	0.355897	+	1.09534i	−0.599591	+	0.800306i	$0.704670\pi$
$954$		0			0
$955$	−9.04008	−	6.56800i	−0.292530	−	0.212536i
$956$	20.9090	+	36.2154i	0.676244	+	1.17129i
$957$		0			0
$958$	−1.73509	+	3.00526i	−0.0560581	+	0.0970954i
$959$	1.39750	−	0.622205i	0.0451275	−	0.0200921i
$960$		0			0
$961$	−20.6686	+	22.9548i	−0.666730	+	0.740479i
$962$	17.0968	+	23.5317i	0.551223	+	0.758693i
$963$		0			0
$964$	−43.9090	+	14.2669i	−1.41421	+	0.459506i
$965$	34.7506	−	7.38647i	1.11866	−	0.237779i
$966$		0			0
$967$	37.9734	+	21.9240i	1.22114	+	0.705027i	0.965161	−	0.261655i	$-0.0842683\pi$
$967$	37.9734	+	21.9240i	1.22114	+	0.705027i	0.255981	+	0.966682i	$0.417602\pi$
$968$	0.617522	+	2.57347i	0.0198479	+	0.0827146i
$969$		0			0
$970$	33.4711	+	3.51795i	1.07469	+	0.112955i
$971$	−24.4501	−	7.94432i	−0.784641	−	0.254945i	−0.110820	−	0.993840i	$-0.535348\pi$
$971$	−24.4501	−	7.94432i	−0.784641	−	0.254945i	−0.673820	+	0.738895i	$0.735348\pi$
$972$		0			0
$973$	−1.84700	+	1.34192i	−0.0592120	+	0.0430200i
$974$	31.3192	+	13.9442i	1.00353	+	0.446801i
$975$		0			0
$976$	7.77063	−	6.99670i	0.248732	−	0.223959i
$977$	−6.74930	−	15.1592i	−0.215929	−	0.484985i	0.772809	−	0.634638i	$-0.218851\pi$
$977$	−6.74930	−	15.1592i	−0.215929	−	0.484985i	−0.988739	+	0.149653i	$0.952184\pi$
$978$		0			0
$979$	26.0265	−	7.33862i	0.831812	−	0.234543i
$980$			25.6159i			0.818269i
$981$		0			0
$982$	20.4485	−	62.9340i	0.652538	−	2.00830i
$983$	31.1446	+	28.0427i	0.993357	+	0.894423i	0.994411	−	0.105576i	$-0.0336687\pi$
$983$	31.1446	+	28.0427i	0.993357	+	0.894423i	−0.00105371	+	0.999999i	$0.500335\pi$
$984$		0			0
$985$	−4.93678	+	0.518876i	−0.157299	+	0.0165328i
$986$	42.9907	+	9.13796i	1.36910	+	0.291012i
$987$		0			0
$988$	1.76660	−	16.8081i	0.0562031	−	0.534737i
$989$	−49.6337			−1.57826
$990$		0			0
$991$	−21.9883			−0.698482			−0.349241	−	0.937033i	$-0.613561\pi$
$991$	−21.9883			−0.698482			−0.349241	+	0.937033i	$0.613561\pi$
$992$	0.273567	−	2.60282i	0.00868577	−	0.0826396i
$993$		0			0
$994$	−7.27170	−	1.54565i	−0.230644	−	0.0490249i
$995$	24.0482	−	2.52756i	0.762378	−	0.0801292i
$996$		0			0
$997$	−35.1693	−	31.6666i	−1.11382	−	1.00289i	−0.999956	−	0.00939598i	$-0.997009\pi$
$997$	−35.1693	−	31.6666i	−1.11382	−	1.00289i	−0.113868	−	0.993496i	$-0.536324\pi$
$998$	−11.8800	+	36.5629i	−0.376055	+	1.15738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.260.9		80
3.2	odd	2		99.2.p.a.95.2	yes	80
9.2	odd	6	inner	297.2.t.a.62.9		80
9.4	even	3		891.2.k.a.161.17		80
9.5	odd	6		891.2.k.a.161.4		80
9.7	even	3		99.2.p.a.29.2	✓	80
11.8	odd	10	inner	297.2.t.a.206.9		80
33.8	even	10		99.2.p.a.41.2	yes	80
99.41	even	30		891.2.k.a.404.17		80
99.52	odd	30		99.2.p.a.74.2	yes	80
99.74	even	30	inner	297.2.t.a.8.9		80
99.85	odd	30		891.2.k.a.404.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.2	✓	80	9.7	even	3
99.2.p.a.41.2	yes	80	33.8	even	10
99.2.p.a.74.2	yes	80	99.52	odd	30
99.2.p.a.95.2	yes	80	3.2	odd	2
297.2.t.a.8.9		80	99.74	even	30	inner
297.2.t.a.62.9		80	9.2	odd	6	inner
297.2.t.a.206.9		80	11.8	odd	10	inner
297.2.t.a.260.9		80	1.1	even	1	trivial
891.2.k.a.161.4		80	9.5	odd	6
891.2.k.a.161.17		80	9.4	even	3
891.2.k.a.404.4		80	99.85	odd	30
891.2.k.a.404.17		80	99.41	even	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.205839 - 1.95843i) q^{2} +(-1.83679 - 0.390421i) q^{4} +(1.96633 - 0.206670i) q^{5} +(0.235695 + 0.212221i) q^{7} +(0.0743474 - 0.228818i) q^{8} -3.89347i q^{10} +(-0.900082 - 3.19215i) q^{11} +(0.782431 + 1.75737i) q^{13} +(0.464135 - 0.417909i) q^{14} +(-3.86377 - 1.72026i) q^{16} +(2.02504 - 1.47127i) q^{17} +(4.44962 + 1.44577i) q^{19} +(-3.69242 - 0.388089i) q^{20} +(-6.43689 + 1.10568i) q^{22} +(-4.68148 - 2.70286i) q^{23} +(-1.06699 + 0.226795i) q^{25} +(3.60274 - 1.17060i) q^{26} +(-0.350066 - 0.481825i) q^{28} +(-5.96640 + 6.62636i) q^{29} +(-0.304670 + 0.135648i) q^{31} +(-3.92374 + 6.79612i) q^{32} +(-2.46456 - 4.26874i) q^{34} +(0.507314 + 0.368585i) q^{35} +(2.37275 + 7.30257i) q^{37} +(3.74735 - 8.41668i) q^{38} +(0.0989020 - 0.465297i) q^{40} +(6.69670 + 7.43744i) q^{41} +(7.95160 - 4.59086i) q^{43} +(0.406974 + 6.21472i) q^{44} +(-6.25699 + 8.61201i) q^{46} +(1.77326 + 8.34251i) q^{47} +(-0.721185 - 6.86161i) q^{49} +(0.224534 + 2.13630i) q^{50} +(-0.751046 - 3.53339i) q^{52} +(1.05383 - 1.45047i) q^{53} +(-2.42958 - 6.09082i) q^{55} +(0.0660832 - 0.0381531i) q^{56} +(11.7492 + 13.0488i) q^{58} +(1.61495 - 7.59774i) q^{59} +(-1.00557 + 2.25856i) q^{61} +(0.202944 + 0.624596i) q^{62} +(5.65871 + 4.11130i) q^{64} +(1.90171 + 3.29387i) q^{65} +(-5.40401 + 9.36002i) q^{67} +(-4.29398 + 1.91180i) q^{68} +(0.826275 - 0.917671i) q^{70} +(-6.99647 - 9.62982i) q^{71} +(0.116476 - 0.0378454i) q^{73} +(14.7900 - 3.14371i) q^{74} +(-7.60855 - 4.39280i) q^{76} +(0.465297 - 0.943391i) q^{77} +(12.4188 + 1.30527i) q^{79} +(-7.95299 - 2.58408i) q^{80} +(15.9442 - 11.5841i) q^{82} +(0.394220 + 0.175518i) q^{83} +(3.67783 - 3.31153i) q^{85} +(-7.35413 - 16.5176i) q^{86} +(-0.797341 - 0.0313737i) q^{88} +8.15328i q^{89} +(-0.188535 + 0.580251i) q^{91} +(7.54364 + 6.79232i) q^{92} +(16.7032 - 1.75558i) q^{94} +(9.04823 + 1.92326i) q^{95} +(-0.903553 + 8.59673i) q^{97} -13.5864 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

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