LMFDB - Embedded newform 675.2.r.a.316.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] 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("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			316.18
Character	$\chi$	$=$	675.316
Dual form			675.2.r.a.361.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.973390 - 0.433381i) q^{2} +(-0.578592 + 0.642592i) q^{4} +(2.03848 + 0.919011i) q^{5} +(-0.798426 + 1.38291i) q^{7} +(-0.943229 + 2.90296i) q^{8} +(2.38252 + 0.0111154i) q^{10} +(-4.35427 + 1.93865i) q^{11} +(0.904123 + 0.402542i) q^{13} +(-0.177851 + 1.69214i) q^{14} +(0.159189 + 1.51458i) q^{16} +(-0.0927524 + 0.285463i) q^{17} +(0.468623 - 1.44227i) q^{19} +(-1.77000 + 0.778180i) q^{20} +(-3.39823 + 3.77412i) q^{22} +(-0.597633 + 5.68610i) q^{23} +(3.31084 + 3.74678i) q^{25} +1.05452 q^{26} +(-0.426686 - 1.31321i) q^{28} +(-5.78936 - 1.23057i) q^{29} +(2.67051 - 0.567634i) q^{31} +(-2.24101 - 3.88154i) q^{32} +(0.0334298 + 0.318064i) q^{34} +(-2.89849 + 2.08529i) q^{35} +(1.92560 - 1.39903i) q^{37} +(-0.168901 - 1.60699i) q^{38} +(-4.59061 + 5.05080i) q^{40} +(10.2958 + 4.58400i) q^{41} +(3.80449 - 6.58957i) q^{43} +(1.27359 - 3.91970i) q^{44} +(1.88252 + 5.79380i) q^{46} +(5.69960 + 1.21149i) q^{47} +(2.22503 + 3.85387i) q^{49} +(4.84652 + 2.21222i) q^{50} +(-0.781789 + 0.348075i) q^{52} +(-0.598625 - 1.84238i) q^{53} +(-10.6578 - 0.0497227i) q^{55} +(-3.26145 - 3.62220i) q^{56} +(-6.16861 + 1.31118i) q^{58} +(-5.31370 - 2.36581i) q^{59} +(12.1540 - 5.41129i) q^{61} +(2.35344 - 1.70988i) q^{62} +(-6.32771 - 4.59735i) q^{64} +(1.47310 + 1.65147i) q^{65} +(1.02420 - 0.217699i) q^{67} +(-0.129770 - 0.224768i) q^{68} +(-1.91764 + 3.28595i) q^{70} +(5.09100 + 15.6685i) q^{71} +(7.42742 + 5.39634i) q^{73} +(1.26805 - 2.19633i) q^{74} +(0.655651 + 1.13562i) q^{76} +(0.795582 - 7.56945i) q^{77} +(-10.9470 - 2.32686i) q^{79} +(-1.06741 + 3.23374i) q^{80} +12.0085 q^{82} +(-3.98246 - 4.42297i) q^{83} +(-0.451418 + 0.496671i) q^{85} +(0.847457 - 8.06302i) q^{86} +(-1.52074 - 14.4689i) q^{88} +(-1.01962 - 0.740795i) q^{89} +(-1.27856 + 0.928926i) q^{91} +(-3.30805 - 3.67397i) q^{92} +(6.07297 - 1.29085i) q^{94} +(2.28075 - 2.50938i) q^{95} +(1.87620 + 0.398799i) q^{97} +(3.83602 + 2.78703i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.973390	−	0.433381i	0.688291	−	0.306447i	−0.0326268	−	0.999468i	$-0.510387\pi$
$2$	0.973390	−	0.433381i	0.688291	−	0.306447i	0.720918	+	0.693021i	$0.243721\pi$
$3$		0			0
$3$		0			0
$4$	−0.578592	+	0.642592i	−0.289296	+	0.321296i
$5$	2.03848	+	0.919011i	0.911638	+	0.410994i
$5$	2.03848	+	0.919011i	0.911638	+	0.410994i
$6$		0			0
$7$	−0.798426	+	1.38291i	−0.301777	+	0.522693i	−0.976538	−	0.215343i	$-0.930913\pi$
$7$	−0.798426	+	1.38291i	−0.301777	+	0.522693i	0.674762	+	0.738036i	$0.264246\pi$
$8$	−0.943229	+	2.90296i	−0.333482	+	1.02635i
$9$		0			0
$10$	2.38252	+	0.0111154i	0.753420	+	0.00351501i
$11$	−4.35427	+	1.93865i	−1.31286	+	0.584524i	−0.939305	−	0.343083i	$-0.888529\pi$
$11$	−4.35427	+	1.93865i	−1.31286	+	0.584524i	−0.373557	+	0.927607i	$0.621862\pi$
$12$		0			0
$13$	0.904123	+	0.402542i	0.250759	+	0.111645i	0.528267	−	0.849078i	$-0.322842\pi$
$13$	0.904123	+	0.402542i	0.250759	+	0.111645i	−0.277508	+	0.960723i	$0.589509\pi$
$14$	−0.177851	+	1.69214i	−0.0475327	+	0.452243i
$15$		0			0
$16$	0.159189	+	1.51458i	0.0397972	+	0.378645i
$17$	−0.0927524	+	0.285463i	−0.0224958	+	0.0692348i	−0.961674	−	0.274195i	$-0.911589\pi$
$17$	−0.0927524	+	0.285463i	−0.0224958	+	0.0692348i	0.939178	+	0.343430i	$0.111589\pi$
$18$		0			0
$19$	0.468623	−	1.44227i	0.107510	−	0.330880i	−0.882802	−	0.469746i	$-0.844346\pi$
$19$	0.468623	−	1.44227i	0.107510	−	0.330880i	0.990311	+	0.138866i	$0.0443456\pi$
$20$	−1.77000	+	0.778180i	−0.395784	+	0.174006i
$21$		0			0
$22$	−3.39823	+	3.77412i	−0.724506	+	0.804645i
$23$	−0.597633	+	5.68610i	−0.124615	+	1.18563i	0.736217	+	0.676745i	$0.236610\pi$
$23$	−0.597633	+	5.68610i	−0.124615	+	1.18563i	−0.860832	+	0.508889i	$0.830056\pi$
$24$		0			0
$25$	3.31084	+	3.74678i	0.662167	+	0.749356i
$26$	1.05452			0.206808
$27$		0			0
$28$	−0.426686	−	1.31321i	−0.0806361	−	0.248173i
$29$	−5.78936	−	1.23057i	−1.07506	−	0.228511i	−0.363825	−	0.931467i	$-0.618529\pi$
$29$	−5.78936	−	1.23057i	−1.07506	−	0.228511i	−0.711233	+	0.702957i	$0.751863\pi$
$30$		0			0
$31$	2.67051	−	0.567634i	0.479637	−	0.101950i	0.0382528	−	0.999268i	$-0.487821\pi$
$31$	2.67051	−	0.567634i	0.479637	−	0.101950i	0.441385	+	0.897318i	$0.354487\pi$
$32$	−2.24101	−	3.88154i	−0.396158	−	0.686166i
$33$		0			0
$34$	0.0334298	+	0.318064i	0.00573317	+	0.0545475i
$35$	−2.89849	+	2.08529i	−0.489935	+	0.352478i
$36$		0			0
$37$	1.92560	−	1.39903i	0.316567	−	0.230000i	−0.418142	−	0.908382i	$-0.637319\pi$
$37$	1.92560	−	1.39903i	0.316567	−	0.230000i	0.734709	+	0.678382i	$0.237319\pi$
$38$	−0.168901	−	1.60699i	−0.0273994	−	0.260688i
$39$		0			0
$40$	−4.59061	+	5.05080i	−0.725839	+	0.798602i
$41$	10.2958	+	4.58400i	1.60794	+	0.715901i	0.997118	−	0.0758673i	$-0.0241725\pi$
$41$	10.2958	+	4.58400i	1.60794	+	0.715901i	0.610822	+	0.791768i	$0.290839\pi$
$42$		0			0
$43$	3.80449	−	6.58957i	0.580179	−	1.00490i	−0.415278	−	0.909694i	$-0.636316\pi$
$43$	3.80449	−	6.58957i	0.580179	−	1.00490i	0.995458	−	0.0952056i	$-0.0303508\pi$
$44$	1.27359	−	3.91970i	0.192001	−	0.590918i
$45$		0			0
$46$	1.88252	+	5.79380i	0.277562	+	0.854249i
$47$	5.69960	+	1.21149i	0.831372	+	0.176714i	0.603889	−	0.797069i	$-0.293617\pi$
$47$	5.69960	+	1.21149i	0.831372	+	0.176714i	0.227483	+	0.973782i	$0.426950\pi$
$48$		0			0
$49$	2.22503	+	3.85387i	0.317862	+	0.550552i
$50$	4.84652	+	2.21222i	0.685401	+	0.312856i
$51$		0			0
$52$	−0.781789	+	0.348075i	−0.108415	+	0.0482693i
$53$	−0.598625	−	1.84238i	−0.0822275	−	0.253070i	0.901488	−	0.432805i	$-0.142476\pi$
$53$	−0.598625	−	1.84238i	−0.0822275	−	0.253070i	−0.983715	+	0.179735i	$0.942476\pi$
$54$		0			0
$55$	−10.6578	−	0.0497227i	−1.43709	−	0.00670461i
$56$	−3.26145	−	3.62220i	−0.435829	−	0.484037i
$57$		0			0
$58$	−6.16861	+	1.31118i	−0.809979	+	0.172166i
$59$	−5.31370	−	2.36581i	−0.691784	−	0.308002i	0.0305627	−	0.999533i	$-0.490270\pi$
$59$	−5.31370	−	2.36581i	−0.691784	−	0.308002i	−0.722347	+	0.691531i	$0.756937\pi$
$60$		0			0
$61$	12.1540	−	5.41129i	1.55616	−	0.692845i	0.564944	−	0.825129i	$-0.308898\pi$
$61$	12.1540	−	5.41129i	1.55616	−	0.692845i	0.991212	+	0.132284i	$0.0422311\pi$
$62$	2.35344	−	1.70988i	0.298888	−	0.217155i
$63$		0			0
$64$	−6.32771	−	4.59735i	−0.790963	−	0.574668i
$65$	1.47310	+	1.65147i	0.182716	+	0.204840i
$66$		0			0
$67$	1.02420	−	0.217699i	0.125125	−	0.0265962i	−0.144923	−	0.989443i	$-0.546294\pi$
$67$	1.02420	−	0.217699i	0.125125	−	0.0265962i	0.270049	+	0.962847i	$0.412960\pi$
$68$	−0.129770	−	0.224768i	−0.0157369	−	0.0272572i
$69$		0			0
$70$	−1.91764	+	3.28595i	−0.229202	+	0.392746i
$71$	5.09100	+	15.6685i	0.604191	+	1.85951i	0.502260	+	0.864716i	$0.332502\pi$
$71$	5.09100	+	15.6685i	0.604191	+	1.85951i	0.101930	+	0.994792i	$0.467498\pi$
$72$		0			0
$73$	7.42742	+	5.39634i	0.869314	+	0.631594i	0.930403	−	0.366539i	$-0.119457\pi$
$73$	7.42742	+	5.39634i	0.869314	+	0.631594i	−0.0610888	+	0.998132i	$0.519457\pi$
$74$	1.26805	−	2.19633i	0.147408	−	0.255318i
$75$		0			0
$76$	0.655651	+	1.13562i	0.0752084	+	0.130265i
$77$	0.795582	−	7.56945i	0.0906649	−	0.862619i
$78$		0			0
$79$	−10.9470	−	2.32686i	−1.23164	−	0.261792i	−0.454284	−	0.890857i	$-0.650105\pi$
$79$	−10.9470	−	2.32686i	−1.23164	−	0.261792i	−0.777353	+	0.629065i	$0.783438\pi$
$80$	−1.06741	+	3.23374i	−0.119340	+	0.361544i
$81$		0			0
$82$	12.0085			1.32612
$83$	−3.98246	−	4.42297i	−0.437132	−	0.485485i	0.483816	−	0.875170i	$-0.339250\pi$
$83$	−3.98246	−	4.42297i	−0.437132	−	0.485485i	−0.920948	+	0.389685i	$0.872584\pi$
$84$		0			0
$85$	−0.451418	+	0.496671i	−0.0489631	+	0.0538715i
$86$	0.847457	−	8.06302i	0.0913837	−	0.869457i
$87$		0			0
$88$	−1.52074	−	14.4689i	−0.162111	−	1.54239i
$89$	−1.01962	−	0.740795i	−0.108079	−	0.0785241i	0.532433	−	0.846472i	$-0.321278\pi$
$89$	−1.01962	−	0.740795i	−0.108079	−	0.0785241i	−0.640512	+	0.767948i	$0.721278\pi$
$90$		0			0
$91$	−1.27856	+	0.928926i	−0.134029	+	0.0973779i
$92$	−3.30805	−	3.67397i	−0.344889	−	0.383038i
$93$		0			0
$94$	6.07297	−	1.29085i	0.626379	−	0.133141i
$95$	2.28075	−	2.50938i	0.234000	−	0.257457i
$96$		0			0
$97$	1.87620	+	0.398799i	0.190499	+	0.0404919i	0.302173	−	0.953253i	$-0.402288\pi$
$97$	1.87620	+	0.398799i	0.190499	+	0.0404919i	−0.111674	+	0.993745i	$0.535621\pi$
$98$	3.83602	+	2.78703i	0.387496	+	0.281533i
$99$		0			0
$100$	−4.32327	−	0.0403405i	−0.432327	−	0.00403405i
$101$	2.94567	−	5.10205i	0.293105	−	0.507673i	−0.681437	−	0.731877i	$-0.738645\pi$
$101$	2.94567	−	5.10205i	0.293105	−	0.507673i	0.974542	+	0.224204i	$0.0719781\pi$
$102$		0			0
$103$	8.59006	−	9.54023i	0.846404	−	0.940027i	−0.152430	−	0.988314i	$-0.548710\pi$
$103$	8.59006	−	9.54023i	0.846404	−	0.940027i	0.998833	+	0.0482876i	$0.0153764\pi$
$104$	−2.02136	+	2.24495i	−0.198210	+	0.220135i
$105$		0			0
$106$	−1.38115	−	1.53392i	−0.134149	−	0.148988i
$107$	−19.9558			−1.92920			−0.964600	−	0.263716i	$-0.915052\pi$
$107$	−19.9558			−1.92920			−0.964600	+	0.263716i	$0.915052\pi$
$108$		0			0
$109$	6.54028	−	4.75180i	0.626446	−	0.455139i	−0.228721	−	0.973492i	$-0.573454\pi$
$109$	6.54028	−	4.75180i	0.626446	−	0.455139i	0.855167	+	0.518353i	$0.173454\pi$
$110$	−10.3957	+	4.57047i	−0.991191	+	0.435777i
$111$		0			0
$112$	−2.22164	−	0.989136i	−0.209925	−	0.0934646i
$113$	−11.9044	−	5.30018i	−1.11987	−	0.498599i	−0.238557	−	0.971129i	$-0.576674\pi$
$113$	−11.9044	−	5.30018i	−1.11987	−	0.498599i	−0.881315	+	0.472530i	$0.843341\pi$
$114$		0			0
$115$	−6.44386	+	11.0418i	−0.600893	+	1.02965i
$116$	4.14043	−	3.00820i	0.384429	−	0.279304i
$117$		0			0
$118$	−6.19760			−0.570535
$119$	−0.320714	−	0.356189i	−0.0293998	−	0.0326518i
$120$		0			0
$121$	7.84090	−	8.70820i	0.712809	−	0.791654i
$122$	9.48540	−	10.5346i	0.858767	−	0.953758i
$123$		0			0
$124$	−1.18038	+	2.04447i	−0.106001	+	0.183599i
$125$	3.30576	+	10.6804i	0.295676	+	0.955288i
$126$		0			0
$127$	−8.64345	−	6.27983i	−0.766982	−	0.557245i	0.134062	−	0.990973i	$-0.457198\pi$
$127$	−8.64345	−	6.27983i	−0.766982	−	0.557245i	−0.901044	+	0.433728i	$0.857198\pi$
$128$	0.616423	+	0.131025i	0.0544846	+	0.0115811i
$129$		0			0
$130$	2.14962	+	0.969114i	0.188534	+	0.0849970i
$131$	17.3455	−	3.68690i	1.51548	−	0.322126i	0.626266	−	0.779610i	$-0.284583\pi$
$131$	17.3455	−	3.68690i	1.51548	−	0.322126i	0.889218	+	0.457484i	$0.151249\pi$
$132$		0			0
$133$	1.62038	+	1.79961i	0.140505	+	0.156046i
$134$	0.902595	−	0.655773i	0.0779723	−	0.0566502i
$135$		0			0
$136$	−0.741200	−	0.538513i	−0.0635574	−	0.0461771i
$137$	−1.79963	−	17.1223i	−0.153753	−	1.46286i	−0.750734	−	0.660605i	$-0.770300\pi$
$137$	−1.79963	−	17.1223i	−0.153753	−	1.46286i	0.596981	−	0.802255i	$-0.296367\pi$
$138$		0			0
$139$	0.899749	−	8.56054i	0.0763157	−	0.726095i	−0.887731	−	0.460363i	$-0.847719\pi$
$139$	0.899749	−	8.56054i	0.0763157	−	0.726095i	0.964047	−	0.265733i	$-0.0856139\pi$
$140$	0.337057	−	3.06908i	0.0284865	−	0.259384i
$141$		0			0
$142$	11.7460	+	13.0452i	0.985699	+	1.09473i
$143$	−4.71719			−0.394471
$144$		0			0
$145$	−10.6706	−	7.82898i	−0.886147	−	0.650161i
$146$	9.56845	+	2.03384i	0.791891	+	0.168322i
$147$		0			0
$148$	−0.215132	+	2.04685i	−0.0176838	+	0.168250i
$149$	4.79551	+	8.30607i	0.392863	+	0.680460i	0.992826	−	0.119569i	$-0.0381512\pi$
$149$	4.79551	+	8.30607i	0.392863	+	0.680460i	−0.599962	+	0.800028i	$0.704818\pi$
$150$		0			0
$151$	−7.37063	+	12.7663i	−0.599814	+	1.03891i	0.393034	+	0.919524i	$0.371425\pi$
$151$	−7.37063	+	12.7663i	−0.599814	+	1.03891i	−0.992848	+	0.119384i	$0.961908\pi$
$152$	3.74484	+	2.72079i	0.303747	+	0.220685i
$153$		0			0
$154$	−2.50605	−	7.71282i	−0.201943	−	0.621517i
$155$	5.96545	+	1.29711i	0.479157	+	0.104187i
$156$		0			0
$157$	−6.76957	−	11.7252i	−0.540270	−	0.935775i	−0.998888	−	0.0471419i	$-0.984989\pi$
$157$	−6.76957	−	11.7252i	−0.540270	−	0.935775i	0.458618	−	0.888634i	$-0.348345\pi$
$158$	−11.6641	+	2.47929i	−0.927950	+	0.197242i
$159$		0			0
$160$	−1.00108	−	9.97198i	−0.0791425	−	0.788354i
$161$	−7.38623	−	5.36641i	−0.582116	−	0.422932i
$162$		0			0
$163$	2.23732	−	1.62551i	0.175240	−	0.127320i	−0.496708	−	0.867918i	$-0.665458\pi$
$163$	2.23732	−	1.62551i	0.175240	−	0.127320i	0.671948	+	0.740598i	$0.265458\pi$
$164$	−8.90273	+	3.96375i	−0.695187	+	0.309517i
$165$		0			0
$166$	−5.79333	−	2.57935i	−0.449649	−	0.200197i
$167$	2.90321	−	0.617096i	0.224657	−	0.0477524i	−0.0942076	−	0.995553i	$-0.530032\pi$
$167$	2.90321	−	0.617096i	0.224657	−	0.0477524i	0.318865	+	0.947800i	$0.396698\pi$
$168$		0			0
$169$	−8.04330	−	8.93299i	−0.618715	−	0.687153i
$170$	−0.224158	+	0.679090i	−0.0171921	+	0.0520838i
$171$		0			0
$172$	2.03315	+	6.25741i	0.155027	+	0.477123i
$173$	11.4424	−	5.09449i	0.869951	−	0.387327i	0.0773039	−	0.997008i	$-0.475369\pi$
$173$	11.4424	−	5.09449i	0.869951	−	0.387327i	0.792647	+	0.609680i	$0.208702\pi$
$174$		0			0
$175$	−7.82494	+	1.58708i	−0.591510	+	0.119972i
$176$	−3.62939	−	6.28628i	−0.273575	−	0.473846i
$177$		0			0
$178$	−1.31353	−	0.279200i	−0.0984533	−	0.0209269i
$179$	3.60018	+	11.0802i	0.269090	+	0.828174i	0.990723	+	0.135898i	$0.0433919\pi$
$179$	3.60018	+	11.0802i	0.269090	+	0.828174i	−0.721633	+	0.692276i	$0.756608\pi$
$180$		0			0
$181$	−6.84051	+	21.0529i	−0.508451	+	1.56485i	0.286440	+	0.958098i	$0.407528\pi$
$181$	−6.84051	+	21.0529i	−0.508451	+	1.56485i	−0.794891	+	0.606752i	$0.792472\pi$
$182$	−0.841955	+	1.45831i	−0.0624099	+	0.108097i
$183$		0			0
$184$	−15.9428	−	7.09820i	−1.17532	−	0.523286i
$185$	5.21104	−	1.08226i	0.383123	−	0.0795691i
$186$		0			0
$187$	−0.149542	−	1.42280i	−0.0109356	−	0.104045i
$188$	−4.07623	+	2.96156i	−0.297290	+	0.215994i
$189$		0			0
$190$	1.13254	−	3.43104i	0.0821629	−	0.248914i
$191$	1.19373	+	11.3576i	0.0863753	+	0.821806i	0.948855	+	0.315714i	$0.102244\pi$
$191$	1.19373	+	11.3576i	0.0863753	+	0.821806i	−0.862479	+	0.506092i	$0.831089\pi$
$192$		0			0
$193$	8.87230	+	15.3673i	0.638642	+	1.10616i	0.985731	+	0.168328i	$0.0538369\pi$
$193$	8.87230	+	15.3673i	0.638642	+	1.10616i	−0.347089	+	0.937832i	$0.612830\pi$
$194$	1.99911	−	0.424923i	0.143527	−	0.0305077i
$195$		0			0
$196$	−3.76385	−	0.800031i	−0.268846	−	0.0571450i
$197$	2.97775	+	9.16457i	0.212156	+	0.652948i	0.999343	+	0.0362347i	$0.0115364\pi$
$197$	2.97775	+	9.16457i	0.212156	+	0.652948i	−0.787187	+	0.616714i	$0.788464\pi$
$198$		0			0
$199$	3.11193			0.220599			0.110299	−	0.993898i	$-0.464819\pi$
$199$	3.11193			0.220599			0.110299	+	0.993898i	$0.464819\pi$
$200$	−13.9996	+	6.07716i	−0.989923	+	0.429720i
$201$		0			0
$202$	0.656153	−	6.24288i	0.0461668	−	0.439248i
$203$	6.32415	−	7.02368i	0.443868	−	0.492966i
$204$		0			0
$205$	16.7752	+	18.8064i	1.17163	+	1.31350i
$206$	4.22692	−	13.0091i	0.294504	−	0.906389i
$207$		0			0
$208$	−0.465755	+	1.43345i	−0.0322943	+	0.0993917i
$209$	0.755547	+	7.18855i	0.0522623	+	0.497242i
$210$		0			0
$211$	−0.896864	+	8.53309i	−0.0617427	+	0.587442i	0.919287	+	0.393587i	$0.128766\pi$
$211$	−0.896864	+	8.53309i	−0.0617427	+	0.587442i	−0.981030	+	0.193856i	$0.937901\pi$
$212$	1.53026	+	0.681315i	0.105099	+	0.0467929i
$213$		0			0
$214$	−19.4248	+	8.64847i	−1.32785	+	0.591197i
$215$	13.8113	−	9.93637i	0.941921	−	0.677655i
$216$		0			0
$217$	−1.34721	+	4.14630i	−0.0914549	+	0.281469i
$218$	4.30691	−	7.45979i	0.291701	−	0.505241i
$219$		0			0
$220$	6.19844	−	6.81981i	0.417899	−	0.459792i
$221$	−0.198770	+	0.220757i	−0.0133707	+	0.0148497i
$222$		0			0
$223$	−10.8831	+	4.84546i	−0.728785	+	0.324476i	−0.737372	−	0.675487i	$-0.763933\pi$
$223$	−10.8831	+	4.84546i	−0.728785	+	0.324476i	0.00858684	+	0.999963i	$0.497267\pi$
$224$	7.15712			0.478205
$225$		0			0
$226$	−13.8846			−0.923591
$227$	20.2359	−	9.00961i	1.34310	−	0.597989i	0.395804	−	0.918335i	$-0.370466\pi$
$227$	20.2359	−	9.00961i	1.34310	−	0.597989i	0.947300	+	0.320347i	$0.103799\pi$
$228$		0			0
$229$	−10.1750	+	11.3005i	−0.672386	+	0.746760i	−0.978728	−	0.205161i	$-0.934228\pi$
$229$	−10.1750	+	11.3005i	−0.672386	+	0.746760i	0.306343	+	0.951921i	$0.400895\pi$
$230$	−1.48708	+	13.5406i	−0.0980550	+	0.892842i
$231$		0			0
$232$	9.03298	−	15.6456i	0.593044	−	1.02718i
$233$	4.57150	−	14.0696i	0.299489	−	0.921732i	−0.682188	−	0.731177i	$-0.738971\pi$
$233$	4.57150	−	14.0696i	0.299489	−	0.921732i	0.981677	−	0.190555i	$-0.0610288\pi$
$234$		0			0
$235$	10.5052	+	7.70759i	0.685282	+	0.502788i
$236$	4.59471	−	2.04570i	0.299090	−	0.133164i
$237$		0			0
$238$	−0.466546	−	0.207720i	−0.0302417	−	0.0134645i
$239$	−0.530735	+	5.04960i	−0.0343304	+	0.326632i	0.963856	+	0.266425i	$0.0858426\pi$
$239$	−0.530735	+	5.04960i	−0.0343304	+	0.326632i	−0.998186	+	0.0602064i	$0.980824\pi$
$240$		0			0
$241$	−1.40061	−	13.3259i	−0.0902211	−	0.858397i	−0.942252	−	0.334905i	$-0.891296\pi$
$241$	−1.40061	−	13.3259i	−0.0902211	−	0.858397i	0.852031	−	0.523492i	$-0.175371\pi$
$242$	3.85828	−	11.8746i	0.248020	−	0.763326i
$243$		0			0
$244$	−3.55494	+	10.9410i	−0.227581	+	0.700424i
$245$	0.993945	+	9.90088i	0.0635008	+	0.632544i
$246$		0			0
$247$	1.00427	−	1.11535i	0.0639001	−	0.0709682i
$248$	−0.871082	+	8.28779i	−0.0553137	+	0.526275i
$249$		0			0
$250$	7.84650	+	8.96359i	0.496256	+	0.566907i
$251$	−25.6881			−1.62142			−0.810709	−	0.585450i	$-0.800918\pi$
$251$	−25.6881			−1.62142			−0.810709	+	0.585450i	$0.800918\pi$
$252$		0			0
$253$	−8.42108	−	25.9174i	−0.529429	−	1.62941i
$254$	−11.1350	−	2.36682i	−0.698673	−	0.148507i
$255$		0			0
$256$	15.9579	−	3.39196i	0.997370	−	0.211997i
$257$	9.78552	+	16.9490i	0.610404	+	1.05725i	0.991172	+	0.132580i	$0.0423262\pi$
$257$	9.78552	+	16.9490i	0.610404	+	1.05725i	−0.380768	+	0.924670i	$0.624340\pi$
$258$		0			0
$259$	0.397291	+	3.77997i	0.0246865	+	0.234876i
$260$	−1.91355	−	0.00892748i	−0.118673	−	0.000553659i
$261$		0			0
$262$	15.2861	−	11.1060i	0.944379	−	0.686131i
$263$	−0.779304	−	7.41458i	−0.0480540	−	0.457203i	−0.991919	−	0.126872i	$-0.959506\pi$
$263$	−0.779304	−	7.41458i	−0.0480540	−	0.457203i	0.943865	−	0.330331i	$-0.107160\pi$
$264$		0			0
$265$	0.472879	−	4.30581i	0.0290487	−	0.264504i
$266$	2.35718	+	1.04948i	0.144528	+	0.0643481i
$267$		0			0
$268$	−0.452699	+	0.784098i	−0.0276530	+	0.0478964i
$269$	1.24097	−	3.81931i	0.0756631	−	0.232867i	−0.906071	−	0.423126i	$-0.860933\pi$
$269$	1.24097	−	3.81931i	0.0756631	−	0.232867i	0.981734	+	0.190259i	$0.0609327\pi$
$270$		0			0
$271$	7.44164	+	22.9030i	0.452047	+	1.39126i	0.874567	+	0.484905i	$0.161146\pi$
$271$	7.44164	+	22.9030i	0.452047	+	1.39126i	−0.422519	+	0.906354i	$0.638854\pi$
$272$	−0.447121	−	0.0950385i	−0.0271107	−	0.00576256i
$273$		0			0
$274$	−9.17224	−	15.8868i	−0.554115	−	0.959756i
$275$	−21.6800	−	9.89595i	−1.30735	−	0.596748i
$276$		0			0
$277$	16.8715	−	7.51166i	1.01371	−	0.451332i	0.168461	−	0.985708i	$-0.446120\pi$
$277$	16.8715	−	7.51166i	1.01371	−	0.451332i	0.845246	+	0.534377i	$0.179454\pi$
$278$	−2.83417	−	8.72268i	−0.169982	−	0.523152i
$279$		0			0
$280$	−3.31956	−	10.3811i	−0.198382	−	0.620390i
$281$	4.37061	+	4.85406i	0.260729	+	0.289569i	0.859269	−	0.511524i	$-0.170919\pi$
$281$	4.37061	+	4.85406i	0.260729	+	0.289569i	−0.598540	+	0.801093i	$0.704252\pi$
$282$		0			0
$283$	24.3288	−	5.17125i	1.44620	−	0.307399i	0.583085	−	0.812411i	$-0.301845\pi$
$283$	24.3288	−	5.17125i	1.44620	−	0.307399i	0.863112	+	0.505013i	$0.168512\pi$
$284$	−13.0141	−	5.79423i	−0.772242	−	0.343824i
$285$		0			0
$286$	−4.59166	+	2.04434i	−0.271511	+	0.120884i
$287$	−14.5598	+	10.5783i	−0.859435	+	0.624416i
$288$		0			0
$289$	13.6804	+	9.93939i	0.804730	+	0.584670i
$290$	−13.7796	−	2.99620i	−0.809167	−	0.175943i
$291$		0			0
$292$	−7.76509	+	1.65052i	−0.454417	+	0.0965894i
$293$	−3.51196	−	6.08289i	−0.205171	−	0.355366i	0.745016	−	0.667046i	$-0.232442\pi$
$293$	−3.51196	−	6.08289i	−0.205171	−	0.355366i	−0.950187	+	0.311680i	$0.899108\pi$
$294$		0			0
$295$	−8.65768	−	9.70601i	−0.504070	−	0.565106i
$296$	2.24505	+	6.90956i	0.130491	+	0.401610i
$297$		0			0
$298$	8.26760	+	6.00676i	0.478929	+	0.347962i
$299$	−2.82923	+	4.90036i	−0.163618	+	0.283395i
$300$		0			0
$301$	6.07521	+	10.5226i	0.350169	+	0.606511i
$302$	−1.64182	+	15.6209i	−0.0944763	+	0.898882i
$303$		0			0
$304$	2.25904	+	0.480173i	0.129565	+	0.0275398i
$305$	29.7487	+	0.138790i	1.70341	+	0.00794708i
$306$		0			0
$307$	20.8173			1.18810			0.594052	−	0.804427i	$-0.297527\pi$
$307$	20.8173			1.18810			0.594052	+	0.804427i	$0.297527\pi$
$308$	4.40375	+	4.89086i	0.250927	+	0.278683i
$309$		0			0
$310$	6.36886	−	1.32272i	0.361727	−	0.0751253i
$311$	−0.714248	+	6.79561i	−0.0405013	+	0.385344i	0.955429	+	0.295220i	$0.0953930\pi$
$311$	−0.714248	+	6.79561i	−0.0405013	+	0.385344i	−0.995931	+	0.0901238i	$0.971274\pi$
$312$		0			0
$313$	−3.31544	−	31.5443i	−0.187400	−	1.78299i	−0.534507	−	0.845164i	$-0.679503\pi$
$313$	−3.31544	−	31.5443i	−0.187400	−	1.78299i	0.347108	−	0.937825i	$-0.387164\pi$
$314$	−11.6709	−	8.47942i	−0.658628	−	0.478522i
$315$		0			0
$316$	7.82908	−	5.68816i	0.440420	−	0.319984i
$317$	−5.22722	−	5.80542i	−0.293590	−	0.326065i	0.578246	−	0.815862i	$-0.303737\pi$
$317$	−5.22722	−	5.80542i	−0.293590	−	0.326065i	−0.871836	+	0.489797i	$0.837071\pi$
$318$		0			0
$319$	27.5941	−	5.86531i	1.54497	−	0.328394i
$320$	−8.67392	−	15.1869i	−0.484887	−	0.848971i
$321$		0			0
$322$	−9.51538	−	2.02256i	−0.530271	−	0.112713i
$323$	0.368249	+	0.267549i	0.0204899	+	0.0148868i
$324$		0			0
$325$	1.48517	+	4.72030i	0.0823825	+	0.261835i
$326$	1.47332	−	2.55186i	0.0815996	−	0.141335i
$327$		0			0
$328$	−23.0185	+	25.5646i	−1.27098	+	1.41157i
$329$	−6.22609	+	6.91477i	−0.343256	+	0.381224i
$330$		0			0
$331$	−14.3709	−	15.9605i	−0.789894	−	0.877266i	0.204941	−	0.978774i	$-0.434300\pi$
$331$	−14.3709	−	15.9605i	−0.789894	−	0.877266i	−0.994835	+	0.101508i	$0.967633\pi$
$332$	5.14639			0.282445
$333$		0			0
$334$	2.55852	−	1.85887i	0.139996	−	0.101713i
$335$	2.28787	+	0.497470i	0.125000	+	0.0271797i
$336$		0			0
$337$	−15.6867	−	6.98418i	−0.854511	−	0.380453i	−0.0677437	−	0.997703i	$-0.521580\pi$
$337$	−15.6867	−	6.98418i	−0.854511	−	0.380453i	−0.786767	+	0.617250i	$0.788247\pi$
$338$	−11.7007	−	5.20947i	−0.636432	−	0.283358i
$339$		0			0
$340$	−0.0579697	−	0.577447i	−0.00314385	−	0.0313164i
$341$	−10.5277	+	7.64880i	−0.570106	+	0.414206i
$342$		0			0
$343$	−18.2841			−0.987246
$344$	15.5408	+	17.2598i	0.837901	+	0.930584i
$345$		0			0
$346$	8.93008	−	9.91786i	0.480084	−	0.533188i
$347$	−12.4606	+	13.8389i	−0.668920	+	0.742911i	−0.978110	−	0.208089i	$-0.933276\pi$
$347$	−12.4606	+	13.8389i	−0.668920	+	0.742911i	0.309190	+	0.951000i	$0.399942\pi$
$348$		0			0
$349$	−8.55166	+	14.8119i	−0.457760	+	0.792863i	−0.998842	−	0.0481065i	$-0.984681\pi$
$349$	−8.55166	+	14.8119i	−0.457760	+	0.792863i	0.541083	+	0.840969i	$0.318015\pi$
$350$	−6.92891	+	4.93603i	−0.370366	+	0.263842i
$351$		0			0
$352$	17.2829	+	12.5568i	0.921182	+	0.669278i
$353$	−19.6474	−	4.17618i	−1.04573	−	0.222276i	−0.347148	−	0.937810i	$-0.612850\pi$
$353$	−19.6474	−	4.17618i	−1.04573	−	0.222276i	−0.698577	+	0.715535i	$0.746183\pi$
$354$		0			0
$355$	−4.02159	+	36.6187i	−0.213444	+	1.94352i
$356$	1.06597	−	0.226579i	0.0564963	−	0.0120087i
$357$		0			0
$358$	8.30633	+	9.22512i	0.439003	+	0.487563i
$359$	3.71885	−	2.70190i	0.196273	−	0.142601i	−0.485308	−	0.874343i	$-0.661293\pi$
$359$	3.71885	−	2.70190i	0.196273	−	0.142601i	0.681581	+	0.731742i	$0.261293\pi$
$360$		0			0
$361$	13.5108	+	9.81615i	0.711094	+	0.516640i
$362$	2.46546	+	23.4572i	0.129581	+	1.23289i
$363$		0			0
$364$	0.142843	−	1.35906i	0.00748700	−	0.0712340i
$365$	10.1814	+	17.8262i	0.532918	+	0.933068i
$366$		0			0
$367$	11.7878	+	13.0917i	0.615318	+	0.683380i	0.967592	−	0.252517i	$-0.0812583\pi$
$367$	11.7878	+	13.0917i	0.615318	+	0.683380i	−0.352275	+	0.935897i	$0.614592\pi$
$368$	−8.70719			−0.453894
$369$		0			0
$370$	4.60335	−	3.31183i	0.239317	−	0.172174i
$371$	3.02581	+	0.643156i	0.157092	+	0.0333910i
$372$		0			0
$373$	−1.05604	+	10.0475i	−0.0546795	+	0.520240i	0.932562	+	0.361010i	$0.117568\pi$
$373$	−1.05604	+	10.0475i	−0.0546795	+	0.520240i	−0.987241	+	0.159230i	$0.949099\pi$
$374$	−0.762176	−	1.32013i	−0.0394112	−	0.0682621i
$375$		0			0
$376$	−8.89292	+	15.4030i	−0.458618	+	0.794349i
$377$	−4.73894	−	3.44304i	−0.244068	−	0.177326i
$378$		0			0
$379$	6.82808	+	21.0147i	0.350735	+	1.07945i	0.958442	+	0.285289i	$0.0920896\pi$
$379$	6.82808	+	21.0147i	0.350735	+	1.07945i	−0.607707	+	0.794162i	$0.707910\pi$
$380$	0.292886	+	2.91750i	0.0150248	+	0.149664i
$381$		0			0
$382$	6.08413	+	10.5380i	0.311291	+	0.539172i
$383$	7.60202	−	1.61586i	0.388445	−	0.0825666i	−0.00954918	−	0.999954i	$-0.503040\pi$
$383$	7.60202	−	1.61586i	0.388445	−	0.0825666i	0.397994	+	0.917388i	$0.369706\pi$
$384$		0			0
$385$	8.57819	−	14.6991i	0.437185	−	0.749134i
$386$	15.2961	+	11.1133i	0.778551	+	0.565650i
$387$		0			0
$388$	−1.34182	+	0.974889i	−0.0681205	+	0.0494925i
$389$	11.4424	−	5.09450i	0.580154	−	0.258301i	−0.0956104	−	0.995419i	$-0.530480\pi$
$389$	11.4424	−	5.09450i	0.580154	−	0.258301i	0.675764	+	0.737118i	$0.263814\pi$
$390$		0			0
$391$	−1.56774	−	0.698001i	−0.0792839	−	0.0352995i
$392$	−13.2863	+	2.82410i	−0.671061	+	0.142638i
$393$		0			0
$394$	6.87026	+	7.63020i	0.346119	+	0.384404i
$395$	−20.1769	−	14.8037i	−1.01521	−	0.744855i
$396$		0			0
$397$	−8.80399	−	27.0959i	−0.441859	−	1.35990i	−0.885891	−	0.463893i	$-0.846452\pi$
$397$	−8.80399	−	27.0959i	−0.441859	−	1.35990i	0.444032	−	0.896011i	$-0.353548\pi$
$398$	3.02912	−	1.34865i	0.151836	−	0.0676019i
$399$		0			0
$400$	−5.14775	+	5.61097i	−0.257387	+	0.280549i
$401$	−4.38488	−	7.59484i	−0.218971	−	0.379268i	0.735523	−	0.677500i	$-0.236937\pi$
$401$	−4.38488	−	7.59484i	−0.218971	−	0.379268i	−0.954494	+	0.298232i	$0.903603\pi$
$402$		0			0
$403$	2.64297	+	0.561780i	0.131655	+	0.0279842i
$404$	1.57419	+	4.84487i	0.0783190	+	0.241041i
$405$		0			0
$406$	3.11193	−	9.57755i	0.154443	−	0.475326i
$407$	−5.67237	+	9.82484i	−0.281169	+	0.486999i
$408$		0			0
$409$	−10.5929	−	4.71627i	−0.523786	−	0.233205i	0.127772	−	0.991804i	$-0.459218\pi$
$409$	−10.5929	−	4.71627i	−0.523786	−	0.233205i	−0.651558	+	0.758599i	$0.725884\pi$
$410$	24.4791	+	11.0359i	1.20894	+	0.545026i
$411$		0			0
$412$	1.16033	+	11.0398i	0.0571654	+	0.543892i
$413$	7.51431	−	5.45947i	0.369755	−	0.268643i
$414$		0			0
$415$	−4.05343	−	12.6761i	−0.198975	−	0.622245i
$416$	−0.463667	−	4.41149i	−0.0227331	−	0.216291i
$417$		0			0
$418$	3.85082	+	6.66982i	0.188350	+	0.326232i
$419$	−28.0034	+	5.95230i	−1.36806	+	0.290789i	−0.832647	−	0.553804i	$-0.813176\pi$
$419$	−28.0034	+	5.95230i	−1.36806	+	0.290789i	−0.535408	+	0.844593i	$0.679842\pi$
$420$		0			0
$421$	13.6168	+	2.89433i	0.663640	+	0.141061i	0.527403	−	0.849615i	$-0.323166\pi$
$421$	13.6168	+	2.89433i	0.663640	+	0.141061i	0.136237	+	0.990676i	$0.456499\pi$
$422$	2.82508	+	8.69471i	0.137523	+	0.423252i
$423$		0			0
$424$	5.91300			0.287160
$425$	−1.37665	+	0.597597i	−0.0667775	+	0.0289877i
$426$		0			0
$427$	−2.22069	+	21.1284i	−0.107467	+	1.02248i
$428$	11.5463	−	12.8234i	0.558110	−	0.619844i
$429$		0			0
$430$	9.13753	−	15.6575i	0.440651	−	0.755072i
$431$	3.32930	−	10.2465i	0.160367	−	0.493559i	−0.838298	−	0.545212i	$-0.816449\pi$
$431$	3.32930	−	10.2465i	0.160367	−	0.493559i	0.998665	+	0.0516534i	$0.0164491\pi$
$432$		0			0
$433$	−3.22740	+	9.93293i	−0.155099	+	0.477346i	−0.998171	−	0.0604550i	$-0.980745\pi$
$433$	−3.22740	+	9.93293i	−0.155099	+	0.477346i	0.843072	+	0.537801i	$0.180745\pi$
$434$	0.485563	+	4.61982i	0.0233078	+	0.221759i
$435$		0			0
$436$	−0.730693	+	6.95208i	−0.0349939	+	0.332944i
$437$	7.92085	+	3.52659i	0.378906	+	0.168700i
$438$		0			0
$439$	24.0422	−	10.7043i	1.14747	−	0.510887i	0.257219	−	0.966353i	$-0.417194\pi$
$439$	24.0422	−	10.7043i	1.14747	−	0.510887i	0.890253	+	0.455466i	$0.150527\pi$
$440$	10.1970	−	30.8921i	0.486125	−	1.47272i
$441$		0			0
$442$	−0.0978092	+	0.301026i	−0.00465231	+	0.0143183i
$443$	1.09162	−	1.89074i	0.0518643	−	0.0898316i	−0.838928	−	0.544243i	$-0.816817\pi$
$443$	1.09162	−	1.89074i	0.0518643	−	0.0898316i	0.890792	+	0.454411i	$0.150150\pi$
$444$		0			0
$445$	−1.39767	−	2.44714i	−0.0662561	−	0.116005i
$446$	−8.49355	+	9.43304i	−0.402181	+	0.446668i
$447$		0			0
$448$	11.4099	−	5.08003i	0.539069	−	0.240009i
$449$	32.5364			1.53549			0.767743	−	0.640758i	$-0.221380\pi$
$449$	32.5364			1.53549			0.767743	+	0.640758i	$0.221380\pi$
$450$		0			0
$451$	−53.7176			−2.52946
$452$	10.2936	−	4.58302i	0.484172	−	0.215567i
$453$		0			0
$454$	15.7928	−	17.5397i	0.741195	−	0.823180i
$455$	−3.46001	+	0.718593i	−0.162208	+	0.0336882i
$456$		0			0
$457$	−10.4827	+	18.1566i	−0.490360	+	0.849328i	−0.999938	−	0.0110963i	$-0.996468\pi$
$457$	−10.4827	+	18.1566i	−0.490360	+	0.849328i	0.509579	+	0.860424i	$0.329801\pi$
$458$	−5.00685	+	15.4095i	−0.233955	+	0.720038i
$459$		0			0
$460$	−3.36700	−	10.5295i	−0.156987	−	0.490939i
$461$	−13.3684	+	5.95197i	−0.622626	+	0.277211i	−0.693705	−	0.720260i	$-0.744023\pi$
$461$	−13.3684	+	5.95197i	−0.622626	+	0.277211i	0.0710784	+	0.997471i	$0.477356\pi$
$462$		0			0
$463$	−24.2009	−	10.7749i	−1.12471	−	0.500753i	−0.241814	−	0.970323i	$-0.577743\pi$
$463$	−24.2009	−	10.7749i	−1.12471	−	0.500753i	−0.882896	+	0.469569i	$0.844409\pi$
$464$	0.942191	−	8.96434i	0.0437401	−	0.416159i
$465$		0			0
$466$	−1.64766	−	15.6764i	−0.0763264	−	0.726197i
$467$	6.73062	−	20.7147i	0.311456	−	0.958562i	−0.665733	−	0.746190i	$-0.731881\pi$
$467$	6.73062	−	20.7147i	0.311456	−	0.958562i	0.977189	−	0.212372i	$-0.0681189\pi$
$468$		0			0
$469$	−0.516684	+	1.59019i	−0.0238583	+	0.0734282i
$470$	13.5660	+	2.94975i	0.625751	+	0.136062i
$471$		0			0
$472$	11.8799	−	13.1940i	0.546816	−	0.607301i
$473$	−3.79094	+	36.0683i	−0.174307	+	1.65842i
$474$		0			0
$475$	6.95542	−	3.01931i	0.319136	−	0.138535i
$476$	0.414447			0.0189962
$477$		0			0
$478$	1.67179	+	5.14524i	0.0764660	+	0.235338i
$479$	6.19057	+	1.31585i	0.282854	+	0.0601225i	0.347154	−	0.937808i	$-0.387148\pi$
$479$	6.19057	+	1.31585i	0.282854	+	0.0601225i	−0.0642999	+	0.997931i	$0.520481\pi$
$480$		0			0
$481$	2.30415	−	0.489763i	0.105060	−	0.0223313i
$482$	−7.13853	−	12.3643i	−0.325151	−	0.563178i
$483$		0			0
$484$	1.05913	+	10.0770i	0.0481425	+	0.458045i
$485$	3.45810	+	2.53719i	0.157024	+	0.115208i
$486$		0			0
$487$	−18.7250	+	13.6045i	−0.848512	+	0.616480i	−0.924735	−	0.380611i	$-0.875714\pi$
$487$	−18.7250	+	13.6045i	−0.848512	+	0.616480i	0.0762233	+	0.997091i	$0.475714\pi$
$488$	4.24480	+	40.3866i	0.192153	+	1.82821i
$489$		0			0
$490$	5.25835	+	9.20666i	0.237548	+	0.415914i
$491$	−9.25616	−	4.12111i	−0.417725	−	0.185983i	0.187101	−	0.982341i	$-0.440091\pi$
$491$	−9.25616	−	4.12111i	−0.417725	−	0.185983i	−0.604826	+	0.796358i	$0.706757\pi$
$492$		0			0
$493$	0.888258	−	1.53851i	0.0400051	−	0.0692909i
$494$	0.494172	−	1.52090i	0.0222338	−	0.0684287i
$495$		0			0
$496$	1.28484	+	3.95434i	0.0576911	+	0.177555i
$497$	−25.7330	−	5.46971i	−1.15428	−	0.245350i
$498$		0			0
$499$	2.03652	+	3.52736i	0.0911674	+	0.157906i	0.908003	−	0.418965i	$-0.137607\pi$
$499$	2.03652	+	3.52736i	0.0911674	+	0.157906i	−0.816835	+	0.576871i	$0.804274\pi$
$500$	−8.77585	−	4.05537i	−0.392468	−	0.181362i
$501$		0			0
$502$	−25.0045	+	11.1327i	−1.11601	+	0.496878i
$503$	−6.77990	−	20.8664i	−0.302301	−	0.930386i	−0.980671	−	0.195666i	$-0.937313\pi$
$503$	−6.77990	−	20.8664i	−0.302301	−	0.930386i	0.678370	−	0.734721i	$-0.262687\pi$
$504$		0			0
$505$	10.6935	−	7.69334i	0.475856	−	0.342349i
$506$	−19.4291	−	21.5782i	−0.863730	−	0.959269i
$507$		0			0
$508$	9.03640	−	1.92075i	0.400925	−	0.0852193i
$509$	10.2484	+	4.56289i	0.454253	+	0.202247i	0.621092	−	0.783738i	$-0.286689\pi$
$509$	10.2484	+	4.56289i	0.454253	+	0.202247i	−0.166839	+	0.985984i	$0.553356\pi$
$510$		0			0
$511$	−13.3929	+	5.96291i	−0.592468	+	0.263784i
$512$	13.0436	−	9.47672i	0.576451	−	0.418816i
$513$		0			0
$514$	16.8705	+	12.2571i	0.744126	+	0.540639i
$515$	26.2783	−	11.5532i	1.15796	−	0.509097i
$516$		0			0
$517$	−27.1662	+	5.77436i	−1.19477	+	0.253956i
$518$	2.02489	+	3.50721i	0.0889685	+	0.154098i
$519$		0			0
$520$	−6.18364	+	2.71864i	−0.271170	+	0.119220i
$521$	0.276314	+	0.850408i	0.0121056	+	0.0372571i	0.956927	−	0.290329i	$-0.0937648\pi$
$521$	0.276314	+	0.850408i	0.0121056	+	0.0372571i	−0.944821	+	0.327586i	$0.893765\pi$
$522$		0			0
$523$	−9.65472	−	7.01456i	−0.422171	−	0.306725i	0.356340	−	0.934357i	$-0.384025\pi$
$523$	−9.65472	−	7.01456i	−0.422171	−	0.306725i	−0.778511	+	0.627631i	$0.784025\pi$
$524$	−7.66680	+	13.2793i	−0.334926	+	0.580108i
$525$		0			0
$526$	−3.97191	−	6.87955i	−0.173183	−	0.299962i
$527$	−0.0856578	+	0.814980i	−0.00373131	+	0.0355011i
$528$		0			0
$529$	−9.47718	−	2.01444i	−0.412051	−	0.0875842i
$530$	−1.40576	−	4.39617i	−0.0610623	−	0.190957i
$531$		0			0
$532$	−2.09396			−0.0907845
$533$	7.46346	+	8.28901i	0.323278	+	0.359037i
$534$		0			0
$535$	−40.6796	−	18.3396i	−1.75873	−	0.792890i
$536$	−0.334078	+	3.17854i	−0.0144300	+	0.137292i
$537$		0			0
$538$	−0.447270	−	4.25549i	−0.0192832	−	0.183467i
$539$	−17.1597	−	12.4672i	−0.739120	−	0.537002i
$540$		0			0
$541$	24.7363	−	17.9720i	1.06350	−	0.772675i	0.0887638	−	0.996053i	$-0.471708\pi$
$541$	24.7363	−	17.9720i	1.06350	−	0.772675i	0.974732	+	0.223378i	$0.0717084\pi$
$542$	17.1694	+	19.0685i	0.737487	+	0.819062i
$543$		0			0
$544$	1.31589	−	0.279702i	0.0564185	−	0.0119921i
$545$	17.6992	−	3.67587i	0.758151	−	0.157457i
$546$		0			0
$547$	−0.403221	−	0.0857073i	−0.0172405	−	0.00366458i	0.199283	−	0.979942i	$-0.436139\pi$
$547$	−0.403221	−	0.0857073i	−0.0172405	−	0.00366458i	−0.216524	+	0.976277i	$0.569472\pi$
$548$	12.0439	+	8.75042i	0.514491	+	0.373799i
$549$		0			0
$550$	−25.3918	−	0.236931i	−1.08271	−	0.0101028i
$551$	−4.48784	+	7.77317i	−0.191189	+	0.331148i
$552$		0			0
$553$	11.9582	−	13.2810i	0.508516	−	0.564765i
$554$	13.1671	−	14.6235i	0.559416	−	0.621295i
$555$		0			0
$556$	4.98034	+	5.53123i	0.211214	+	0.234576i
$557$	11.0413			0.467833			0.233917	−	0.972257i	$-0.424846\pi$
$557$	11.0413			0.467833			0.233917	+	0.972257i	$0.424846\pi$
$558$		0			0
$559$	6.09230	−	4.42632i	0.257677	−	0.187213i
$560$	−3.61974	−	4.05805i	−0.152962	−	0.171484i
$561$		0			0
$562$	6.35797	+	2.83075i	0.268195	+	0.119408i
$563$	28.1794	+	12.5463i	1.18762	+	0.528762i	0.902901	−	0.429849i	$-0.141433\pi$
$563$	28.1794	+	12.5463i	1.18762	+	0.528762i	0.284719	+	0.958611i	$0.408100\pi$
$564$		0			0
$565$	−19.3960	−	21.7446i	−0.815996	−	0.914803i
$566$	21.4403	−	15.5773i	0.901203	−	0.654762i
$567$		0			0
$568$	−50.2870			−2.11000
$569$	−4.77576	−	5.30402i	−0.200210	−	0.222356i	0.634676	−	0.772778i	$-0.281133\pi$
$569$	−4.77576	−	5.30402i	−0.200210	−	0.222356i	−0.834886	+	0.550422i	$0.814467\pi$
$570$		0			0
$571$	0.561367	−	0.623461i	0.0234925	−	0.0260910i	−0.731284	−	0.682073i	$-0.761079\pi$
$571$	0.561367	−	0.623461i	0.0234925	−	0.0260910i	0.754777	+	0.655982i	$0.227745\pi$
$572$	2.72933	−	3.03122i	0.114119	−	0.126742i
$573$		0			0
$574$	−9.58789	+	16.6067i	−0.400191	+	0.693151i
$575$	−23.2832	+	16.5866i	−0.970978	+	0.691707i
$576$		0			0
$577$	−21.7584	−	15.8084i	−0.905813	−	0.658112i	0.0341394	−	0.999417i	$-0.489131\pi$
$577$	−21.7584	−	15.8084i	−0.905813	−	0.658112i	−0.939952	+	0.341305i	$0.889131\pi$
$578$	17.6239	+	3.74608i	0.733058	+	0.155816i
$579$		0			0
$580$	11.2048	−	2.32707i	0.465253	−	0.0966261i
$581$	9.29630	−	1.97599i	0.385676	−	0.0819779i
$582$		0			0
$583$	6.17830	+	6.86170i	0.255879	+	0.284183i
$584$	−22.6711	+	16.4715i	−0.938137	+	0.681597i
$585$		0			0
$586$	−6.05471	−	4.39901i	−0.250118	−	0.181721i
$587$	0.0950816	+	0.904641i	0.00392444	+	0.0373385i	0.996309	−	0.0858408i	$-0.0273576\pi$
$587$	0.0950816	+	0.904641i	0.00392444	+	0.0373385i	−0.992384	+	0.123179i	$0.960691\pi$
$588$		0			0
$589$	0.432778	−	4.11761i	0.0178323	−	0.169663i
$590$	−12.6337	−	5.69566i	−0.520122	−	0.234487i
$591$		0			0
$592$	2.42548	+	2.69377i	0.0996867	+	0.110713i
$593$	−35.9174			−1.47495			−0.737476	−	0.675373i	$-0.763983\pi$
$593$	−35.9174			−1.47495			−0.737476	+	0.675373i	$0.763983\pi$
$594$		0			0
$595$	−0.326429	−	1.02083i	−0.0133823	−	0.0418498i
$596$	−8.11205	−	1.72427i	−0.332283	−	0.0706289i
$597$		0			0
$598$	−0.630216	+	5.99610i	−0.0257714	+	0.245199i
$599$	−21.6849	−	37.5593i	−0.886020	−	1.53463i	−0.844540	−	0.535492i	$-0.820126\pi$
$599$	−21.6849	−	37.5593i	−0.886020	−	1.53463i	−0.0414800	−	0.999139i	$-0.513207\pi$
$600$		0			0
$601$	−9.27357	+	16.0623i	−0.378277	+	0.655195i	−0.990812	−	0.135249i	$-0.956817\pi$
$601$	−9.27357	+	16.0623i	−0.378277	+	0.655195i	0.612535	+	0.790444i	$0.290150\pi$
$602$	10.4738	+	7.60968i	0.426882	+	0.310148i
$603$		0			0
$604$	−3.93893	−	12.1228i	−0.160273	−	0.493270i
$605$	23.9865	−	10.5457i	0.975189	−	0.428742i
$606$		0			0
$607$	−10.0739	−	17.4485i	−0.408886	−	0.708212i	0.585879	−	0.810398i	$-0.300749\pi$
$607$	−10.0739	−	17.4485i	−0.408886	−	0.708212i	−0.994765	+	0.102187i	$0.967416\pi$
$608$	−6.64844	+	1.41317i	−0.269630	+	0.0573116i
$609$		0			0
$610$	29.0172	−	12.7574i	1.17487	−	0.516533i
$611$	4.66547	+	3.38966i	0.188745	+	0.137131i
$612$		0			0
$613$	6.07494	−	4.41370i	0.245365	−	0.178268i	−0.458305	−	0.888795i	$-0.651543\pi$
$613$	6.07494	−	4.41370i	0.245365	−	0.178268i	0.703670	+	0.710527i	$0.251543\pi$
$614$	20.2633	−	9.02181i	0.817761	−	0.364091i
$615$		0			0
$616$	21.2234	+	9.44927i	0.855115	+	0.380722i
$617$	−9.59800	+	2.04012i	−0.386401	+	0.0821320i	−0.397016	−	0.917812i	$-0.629954\pi$
$617$	−9.59800	+	2.04012i	−0.386401	+	0.0821320i	0.0106153	+	0.999944i	$0.496621\pi$
$618$		0			0
$619$	1.03695	+	1.15165i	0.0416787	+	0.0462889i	0.763624	−	0.645662i	$-0.223418\pi$
$619$	1.03695	+	1.15165i	0.0416787	+	0.0462889i	−0.721945	+	0.691950i	$0.756752\pi$
$620$	−4.28508	+	3.08285i	−0.172093	+	0.123810i
$621$		0			0
$622$	2.24985	+	6.92432i	0.0902107	+	0.277640i
$623$	1.83854	−	0.818573i	0.0736597	−	0.0327954i
$624$		0			0
$625$	−3.07671	+	24.8100i	−0.123068	+	0.992398i
$626$	−16.8979	−	29.2681i	−0.675377	−	1.16979i
$627$		0			0
$628$	11.4514	+	2.43406i	0.456959	+	0.0971296i
$629$	0.220767	+	0.679452i	0.00880257	+	0.0270915i
$630$		0			0
$631$	3.50012	−	10.7722i	0.139337	−	0.428836i	−0.856902	−	0.515479i	$-0.827614\pi$
$631$	3.50012	−	10.7722i	0.139337	−	0.428836i	0.996239	+	0.0866429i	$0.0276139\pi$
$632$	17.0803	−	29.5840i	0.679419	−	1.17679i
$633$		0			0
$634$	−7.60409	−	3.38556i	−0.301997	−	0.134458i
$635$	−11.8483	−	20.7448i	−0.470185	−	0.823231i
$636$		0			0
$637$	0.460361	+	4.38004i	0.0182402	+	0.173543i
$638$	24.3179	−	17.6680i	0.962755	−	0.699483i
$639$		0			0
$640$	1.13616	+	0.833592i	0.0449105	+	0.0329506i
$641$	−1.91800	−	18.2485i	−0.0757564	−	0.720774i	−0.964806	−	0.262963i	$-0.915300\pi$
$641$	−1.91800	−	18.2485i	−0.0757564	−	0.720774i	0.889050	−	0.457811i	$-0.151366\pi$
$642$		0			0
$643$	6.43258	+	11.1415i	0.253676	+	0.439380i	0.964535	−	0.263955i	$-0.0850270\pi$
$643$	6.43258	+	11.1415i	0.253676	+	0.439380i	−0.710859	+	0.703334i	$0.751694\pi$
$644$	7.72202	−	1.64137i	0.304290	−	0.0646789i
$645$		0			0
$646$	0.474401	+	0.100837i	0.0186650	+	0.00396738i
$647$	−5.33164	−	16.4091i	−0.209608	−	0.645108i	−0.999493	−	0.0318523i	$-0.989859\pi$
$647$	−5.33164	−	16.4091i	−0.209608	−	0.645108i	0.789884	−	0.613256i	$-0.210141\pi$
$648$		0			0
$649$	27.7238			1.08825
$650$	3.49134	+	3.95105i	0.136942	+	0.154973i
$651$		0			0
$652$	−0.249958	+	2.37819i	−0.00978909	+	0.0931370i
$653$	18.9109	−	21.0027i	0.740041	−	0.821899i	−0.249160	−	0.968462i	$-0.580155\pi$
$653$	18.9109	−	21.0027i	0.740041	−	0.821899i	0.989201	+	0.146563i	$0.0468213\pi$
$654$		0			0
$655$	38.7468	+	8.42502i	1.51396	+	0.329193i
$656$	−5.30386	+	16.3236i	−0.207081	+	0.637329i
$657$		0			0
$658$	−3.06368	+	9.42904i	−0.119435	+	0.367582i
$659$	−2.21265	−	21.0520i	−0.0861928	−	0.820069i	−0.949157	−	0.314804i	$-0.898061\pi$
$659$	−2.21265	−	21.0520i	−0.0861928	−	0.820069i	0.862964	−	0.505266i	$-0.168605\pi$
$660$		0			0
$661$	4.60125	−	43.7780i	0.178968	−	1.70277i	−0.424540	−	0.905409i	$-0.639564\pi$
$661$	4.60125	−	43.7780i	0.178968	−	1.70277i	0.603508	−	0.797357i	$-0.293769\pi$
$662$	−20.9054	−	9.30769i	−0.812512	−	0.361754i
$663$		0			0
$664$	16.5961	−	7.38906i	0.644053	−	0.286751i
$665$	1.64925	+	5.15763i	0.0639553	+	0.200004i
$666$		0			0
$667$	10.4570	−	32.1835i	0.404898	−	1.24615i
$668$	−1.28323	+	2.22263i	−0.0496498	+	0.0859960i
$669$		0			0
$670$	2.44259	−	0.507289i	0.0943654	−	0.0195983i
$671$	−42.4311	+	47.1245i	−1.63803	+	1.81922i
$672$		0			0
$673$	8.38851	−	3.73480i	0.323353	−	0.143966i	−0.238640	−	0.971108i	$-0.576702\pi$
$673$	8.38851	−	3.73480i	0.323353	−	0.143966i	0.561993	+	0.827142i	$0.310035\pi$
$674$	−18.2961			−0.704740
$675$		0			0
$676$	10.3941			0.399771
$677$	−19.9666	+	8.88970i	−0.767379	+	0.341659i	−0.752813	−	0.658235i	$-0.771303\pi$
$677$	−19.9666	+	8.88970i	−0.767379	+	0.341659i	−0.0145662	+	0.999894i	$0.504637\pi$
$678$		0			0
$679$	−2.04951	+	2.27621i	−0.0786530	+	0.0873530i
$680$	−1.01602	−	1.77892i	−0.0389628	−	0.0682185i
$681$		0			0
$682$	−6.93269	+	12.0078i	−0.265466	+	0.459801i
$683$	1.01224	−	3.11535i	0.0387322	−	0.119206i	−0.929821	−	0.368012i	$-0.880038\pi$
$683$	1.01224	−	3.11535i	0.0387322	−	0.119206i	0.968553	+	0.248807i	$0.0800384\pi$
$684$		0			0
$685$	12.0671	−	36.5575i	0.461060	−	1.39679i
$686$	−17.7975	+	7.92397i	−0.679513	+	0.302539i
$687$		0			0
$688$	10.5861	+	4.71322i	0.403590	+	0.179690i
$689$	0.200403	−	1.90671i	0.00763476	−	0.0726399i
$690$		0			0
$691$	−1.98375	−	18.8741i	−0.0754655	−	0.718006i	−0.965197	−	0.261523i	$-0.915775\pi$
$691$	−1.98375	−	18.8741i	−0.0754655	−	0.718006i	0.889732	−	0.456484i	$-0.150891\pi$
$692$	−3.34682	+	10.3004i	−0.127227	+	0.391564i
$693$		0			0
$694$	−6.13151	+	18.8708i	−0.232749	+	0.716327i
$695$	9.70135	−	16.6236i	0.367993	−	0.630571i
$696$		0			0
$697$	−2.26352	+	2.51390i	−0.0857371	+	0.0952207i
$698$	−1.90490	+	18.1239i	−0.0721014	+	0.685999i
$699$		0			0
$700$	3.50760	−	5.94651i	0.132575	−	0.224757i
$701$	−26.6440			−1.00633			−0.503164	−	0.864191i	$-0.667831\pi$
$701$	−26.6440			−1.00633			−0.503164	+	0.864191i	$0.667831\pi$
$702$		0			0
$703$	−1.11541	−	3.43287i	−0.0420684	−	0.129473i
$704$	36.4652	+	7.75091i	1.37433	+	0.292124i
$705$		0			0
$706$	−20.9345	+	4.44976i	−0.787879	+	0.167469i
$707$	4.70380	+	8.14722i	0.176905	+	0.306408i
$708$		0			0
$709$	1.72168	+	16.3807i	0.0646592	+	0.615191i	0.978088	+	0.208192i	$0.0667580\pi$
$709$	1.72168	+	16.3807i	0.0646592	+	0.615191i	−0.913429	+	0.406999i	$0.866575\pi$
$710$	11.9553	+	37.3871i	0.448673	+	1.40311i
$711$		0			0
$712$	3.11223	−	2.26117i	0.116636	−	0.0847408i
$713$	1.63164	+	15.5240i	0.0611054	+	0.581379i
$714$		0			0
$715$	−9.61591	−	4.33515i	−0.359615	−	0.162125i
$716$	−9.20309	−	4.09748i	−0.343935	−	0.153130i
$717$		0			0
$718$	2.44894	−	4.24168i	0.0913935	−	0.158298i
$719$	8.80843	−	27.1096i	0.328499	−	1.01102i	−0.641337	−	0.767259i	$-0.721620\pi$
$719$	8.80843	−	27.1096i	0.328499	−	1.01102i	0.969836	−	0.243757i	$-0.0783800\pi$
$720$		0			0
$721$	6.33479	+	19.4965i	0.235920	+	0.726087i
$722$	17.4054	+	3.69963i	0.647762	+	0.137686i
$723$		0			0
$724$	−9.57056	−	16.5767i	−0.355687	−	0.616068i
$725$	−14.5570	−	25.7657i	−0.540632	−	0.956913i
$726$		0			0
$727$	−21.9994	+	9.79479i	−0.815914	+	0.363269i	−0.771885	−	0.635762i	$-0.780686\pi$
$727$	−21.9994	+	9.79479i	−0.815914	+	0.363269i	−0.0440291	+	0.999030i	$0.514019\pi$
$728$	−1.49066	−	4.58779i	−0.0552476	−	0.170035i
$729$		0			0
$730$	17.6360	+	12.9395i	0.652738	+	0.478911i
$731$	1.52820	+	1.69724i	0.0565225	+	0.0627746i
$732$		0			0
$733$	−1.98030	+	0.420926i	−0.0731441	+	0.0155473i	−0.244338	−	0.969690i	$-0.578571\pi$
$733$	−1.98030	+	0.420926i	−0.0731441	+	0.0155473i	0.171194	+	0.985237i	$0.445237\pi$
$734$	17.1478	+	7.63470i	0.632937	+	0.281802i
$735$		0			0
$736$	23.4101	−	10.4229i	0.862909	−	0.384192i
$737$	−4.03758	+	2.93347i	−0.148726	+	0.108056i
$738$		0			0
$739$	−32.8526	−	23.8688i	−1.20850	−	0.878028i	−0.213408	−	0.976963i	$-0.568456\pi$
$739$	−32.8526	−	23.8688i	−1.20850	−	0.878028i	−0.995094	+	0.0989355i	$0.968456\pi$
$740$	−2.31962	+	3.97476i	−0.0852709	+	0.146115i
$741$		0			0
$742$	3.22403	−	0.685288i	0.118358	−	0.0251577i
$743$	−4.58729	−	7.94543i	−0.168292	−	0.291489i	0.769528	−	0.638613i	$-0.220492\pi$
$743$	−4.58729	−	7.94543i	−0.168292	−	0.291489i	−0.937819	+	0.347124i	$0.887158\pi$
$744$		0			0
$745$	2.14221	+	21.3389i	0.0784843	+	0.781797i
$746$	3.32647	+	10.2378i	0.121791	+	0.374833i
$747$		0			0
$748$	1.00080	+	0.727124i	0.0365929	+	0.0265863i
$749$	15.9332	−	27.5972i	0.582188	−	1.00838i
$750$		0			0
$751$	−7.16746	−	12.4144i	−0.261544	−	0.453008i	0.705108	−	0.709100i	$-0.250898\pi$
$751$	−7.16746	−	12.4144i	−0.261544	−	0.453008i	−0.966652	+	0.256092i	$0.917565\pi$
$752$	−0.927582	+	8.82535i	−0.0338254	+	0.321827i
$753$		0			0
$754$	−6.10499	−	1.29766i	−0.222331	−	0.0472578i
$755$	−26.7573	+	19.2502i	−0.973798	+	0.700588i
$756$		0			0
$757$	−7.98963			−0.290388			−0.145194	−	0.989403i	$-0.546381\pi$
$757$	−7.98963			−0.290388			−0.145194	+	0.989403i	$0.546381\pi$
$758$	15.7537	+	17.4963i	0.572202	+	0.635494i
$759$		0			0
$760$	5.13337	+	8.98784i	0.186207	+	0.326023i
$761$	−0.0356082	+	0.338790i	−0.00129080	+	0.0122811i	−0.995148	−	0.0983859i	$-0.968632\pi$
$761$	−0.0356082	+	0.338790i	−0.00129080	+	0.0122811i	0.993858	+	0.110667i	$0.0352987\pi$
$762$		0			0
$763$	1.34939	+	12.8386i	0.0488513	+	0.464789i
$764$	−7.98897	−	5.80433i	−0.289031	−	0.209993i
$765$		0			0
$766$	6.69945	−	4.86744i	0.242061	−	0.175868i
$767$	−3.85190	−	4.27797i	−0.139084	−	0.154469i
$768$		0			0
$769$	1.75737	−	0.373540i	0.0633723	−	0.0134702i	−0.176116	−	0.984369i	$-0.556354\pi$
$769$	1.75737	−	0.373540i	0.0633723	−	0.0134702i	0.239489	+	0.970899i	$0.423020\pi$
$770$	1.97963	−	18.0256i	0.0713409	−	0.649596i
$771$		0			0
$772$	−15.0083	−	3.19012i	−0.540161	−	0.114815i
$773$	34.6828	+	25.1985i	1.24745	+	0.906328i	0.998071	−	0.0620773i	$-0.0197725\pi$
$773$	34.6828	+	25.1985i	1.24745	+	0.906328i	0.249382	+	0.968405i	$0.419773\pi$
$774$		0			0
$775$	10.9684	+	8.12646i	0.393997	+	0.291911i
$776$	−2.92738	+	5.07038i	−0.105087	+	0.182016i
$777$		0			0
$778$	8.93009	−	9.91787i	0.320159	−	0.355573i
$779$	11.4363	−	12.7012i	0.409746	−	0.455069i
$780$		0			0
$781$	−52.5433	−	58.3552i	−1.88015	−	2.08811i
$782$	−1.82852			−0.0653878
$783$		0			0
$784$	−5.48279	+	3.98348i	−0.195814	+	0.142267i
$785$	−3.02404	−	30.1230i	−0.107933	−	1.07514i
$786$		0			0
$787$	10.0343	+	4.46758i	0.357686	+	0.159252i	0.577709	−	0.816243i	$-0.303947\pi$
$787$	10.0343	+	4.46758i	0.357686	+	0.159252i	−0.220024	+	0.975495i	$0.570613\pi$
$788$	−7.61198	−	3.38907i	−0.271165	−	0.120731i
$789$		0			0
$790$	−26.0557	−	5.66548i	−0.927019	−	0.201569i
$791$	16.8345	−	12.2310i	0.598565	−	0.434883i
$792$		0			0
$793$	13.1670			0.467572
$794$	−20.3126	−	22.5594i	−0.720866	−	0.800603i
$795$		0			0
$796$	−1.80054	+	1.99970i	−0.0638184	+	0.0708775i
$797$	22.8733	−	25.4033i	0.810213	−	0.899832i	−0.186366	−	0.982480i	$-0.559671\pi$
$797$	22.8733	−	25.4033i	0.810213	−	0.899832i	0.996579	+	0.0826482i	$0.0263378\pi$
$798$		0			0
$799$	−0.874486	+	1.51465i	−0.0309371	+	0.0535846i
$800$	7.12367	−	21.2477i	0.251860	−	0.751221i
$801$		0			0
$802$	−7.55966	−	5.49242i	−0.266941	−	0.193944i
$803$	−42.8026	−	9.09798i	−1.51047	−	0.321061i
$804$		0			0
$805$	−10.1249	−	17.7274i	−0.356857	−	0.624807i
$806$	2.81610	−	0.598581i	0.0991929	−	0.0210841i
$807$		0			0
$808$	12.0326	+	13.3636i	0.423306	+	0.470128i
$809$	6.42510	−	4.66811i	0.225894	−	0.164122i	−0.469082	−	0.883155i	$-0.655415\pi$
$809$	6.42510	−	4.66811i	0.225894	−	0.164122i	0.694976	+	0.719033i	$0.255415\pi$
$810$		0			0
$811$	−6.94724	−	5.04746i	−0.243951	−	0.177240i	0.459091	−	0.888389i	$-0.348175\pi$
$811$	−6.94724	−	5.04746i	−0.243951	−	0.177240i	−0.703041	+	0.711149i	$0.748175\pi$
$812$	0.854254	+	8.12769i	0.0299785	+	0.285226i
$813$		0			0
$814$	−1.26353	+	12.0217i	−0.0442868	+	0.421360i
$815$	6.05460	−	1.25745i	0.212083	−	0.0440466i
$816$		0			0
$817$	−7.72109	−	8.57514i	−0.270127	−	0.300006i
$818$	−12.3550			−0.431982
$819$		0			0
$820$	−21.7908	−	0.101663i	−0.760968	−	0.00355022i
$821$	1.65706	+	0.352220i	0.0578319	+	0.0122926i	0.236737	−	0.971574i	$-0.423922\pi$
$821$	1.65706	+	0.352220i	0.0578319	+	0.0122926i	−0.178905	+	0.983866i	$0.557255\pi$
$822$		0			0
$823$	0.455648	−	4.33520i	0.0158829	−	0.151116i	−0.983706	−	0.179784i	$-0.942460\pi$
$823$	0.455648	−	4.33520i	0.0158829	−	0.151116i	0.999589	+	0.0286686i	$0.00912674\pi$
$824$	19.5925	+	33.9352i	0.682538	+	1.18219i
$825$		0			0
$826$	4.94833	−	8.57075i	0.172174	−	0.298215i
$827$	−21.8549	−	15.8785i	−0.759968	−	0.552149i	0.138933	−	0.990302i	$-0.455633\pi$
$827$	−21.8549	−	15.8785i	−0.759968	−	0.552149i	−0.898901	+	0.438153i	$0.855633\pi$
$828$		0			0
$829$	16.9452	+	52.1521i	0.588533	+	1.81132i	0.584595	+	0.811326i	$0.301254\pi$
$829$	16.9452	+	52.1521i	0.588533	+	1.81132i	0.00393824	+	0.999992i	$0.498746\pi$
$830$	−9.43915	−	10.5821i	−0.327638	−	0.367310i
$831$		0			0
$832$	−3.87040	−	6.70373i	−0.134182	−	0.232410i
$833$	−1.30651	+	0.277708i	−0.0452680	+	0.00962200i
$834$		0			0
$835$	6.48527	+	1.41014i	0.224432	+	0.0487999i
$836$	−5.05645	−	3.67373i	−0.174881	−	0.127059i
$837$		0			0
$838$	−24.6786	+	17.9301i	−0.852508	+	0.619384i
$839$	19.4076	−	8.64084i	0.670026	−	0.298315i	−0.0433873	−	0.999058i	$-0.513815\pi$
$839$	19.4076	−	8.64084i	0.670026	−	0.298315i	0.713413	+	0.700744i	$0.247148\pi$
$840$		0			0
$841$	5.50960	+	2.45303i	0.189986	+	0.0845873i
$842$	14.5088	−	3.08393i	0.500005	−	0.106279i
$843$		0			0
$844$	−4.96438	−	5.51350i	−0.170881	−	0.189782i
$845$	−8.18662	−	25.6016i	−0.281628	−	0.880723i
$846$		0			0
$847$	5.78232	+	17.7961i	0.198683	+	0.611483i
$848$	2.69514	−	1.19995i	0.0925514	−	0.0412065i
$849$		0			0
$850$	−1.08103	+	1.17831i	−0.0370791	+	0.0404157i
$851$	6.80424	+	11.7853i	0.233246	+	0.403995i
$852$		0			0
$853$	−14.2031	−	3.01897i	−0.486306	−	0.103368i	−0.0417679	−	0.999127i	$-0.513299\pi$
$853$	−14.2031	−	3.01897i	−0.486306	−	0.103368i	−0.444539	+	0.895760i	$0.646632\pi$
$854$	6.99506	+	21.5286i	0.239366	+	0.736693i
$855$		0			0
$856$	18.8229	−	57.9309i	0.643353	−	1.98004i
$857$	−27.2809	+	47.2519i	−0.931897	+	1.61409i	−0.151822	+	0.988408i	$0.548514\pi$
$857$	−27.2809	+	47.2519i	−0.931897	+	1.61409i	−0.780075	+	0.625686i	$0.784819\pi$
$858$		0			0
$859$	20.8211	+	9.27017i	0.710408	+	0.316294i	0.729936	−	0.683515i	$-0.239550\pi$
$859$	20.8211	+	9.27017i	0.710408	+	0.316294i	−0.0195281	+	0.999809i	$0.506216\pi$
$860$	−1.60607	+	14.6241i	−0.0547666	+	0.498678i
$861$		0			0
$862$	−1.19995	−	11.4167i	−0.0408704	−	0.388856i
$863$	35.8456	−	26.0434i	1.22020	−	0.886526i	0.224082	−	0.974570i	$-0.428062\pi$
$863$	35.8456	−	26.0434i	1.22020	−	0.886526i	0.996117	+	0.0880440i	$0.0280616\pi$
$864$		0			0
$865$	28.0071	+	0.130664i	0.952270	+	0.00444272i
$866$	1.16322	+	11.0673i	0.0395279	+	0.376083i
$867$		0			0
$868$	−1.88489	−	3.26472i	−0.0639773	−	0.110812i
$869$	52.1773	−	11.0906i	1.76999	−	0.376224i
$870$		0			0
$871$	1.01363	+	0.215454i	0.0343456	+	0.00730038i
$872$	7.62529	+	23.4682i	0.258225	+	0.794734i
$873$		0			0
$874$	9.23843			0.312495
$875$	−17.4096	−	3.95597i	−0.588550	−	0.133736i
$876$		0			0
$877$	1.99617	−	18.9923i	0.0674060	−	0.641325i	−0.907705	−	0.419609i	$-0.862167\pi$
$877$	1.99617	−	18.9923i	0.0674060	−	0.641325i	0.975111	−	0.221717i	$-0.0711660\pi$
$878$	18.7634	−	20.8389i	0.633235	−	0.703278i
$879$		0			0
$880$	−1.62129	−	16.1499i	−0.0546535	−	0.544414i
$881$	8.53041	−	26.2539i	0.287397	−	0.884517i	−0.698273	−	0.715832i	$-0.746048\pi$
$881$	8.53041	−	26.2539i	0.287397	−	0.884517i	0.985670	−	0.168685i	$-0.0539522\pi$
$882$		0			0
$883$	−15.3512	+	47.2463i	−0.516610	+	1.58996i	0.263722	+	0.964599i	$0.415050\pi$
$883$	−15.3512	+	47.2463i	−0.516610	+	1.58996i	−0.780333	+	0.625365i	$0.784950\pi$
$884$	−0.0268495	−	0.255456i	−0.000903047	−	0.00859192i
$885$		0			0
$886$	0.243160	−	2.31351i	0.00816911	−	0.0777239i
$887$	6.42792	+	2.86190i	0.215829	+	0.0960931i	0.511803	−	0.859103i	$-0.328978\pi$
$887$	6.42792	+	2.86190i	0.215829	+	0.0960931i	−0.295975	+	0.955196i	$0.595644\pi$
$888$		0			0
$889$	15.5856	−	6.93917i	0.522725	−	0.232732i
$890$	−2.42103	−	1.77629i	−0.0811530	−	0.0595415i
$891$		0			0
$892$	3.18321	−	9.79692i	0.106582	−	0.328025i
$893$	4.41826	−	7.65265i	0.147851	−	0.256086i
$894$		0			0
$895$	−2.84393	+	25.8954i	−0.0950620	+	0.865589i
$896$	−0.673365	+	0.747847i	−0.0224955	+	0.0249838i
$897$		0			0
$898$	31.6706	−	14.1006i	1.05686	−	0.470545i
$899$	−16.1590			−0.538934
$900$		0			0
$901$	0.581454			0.0193711
$902$	−52.2882	+	23.2802i	−1.74101	+	0.775146i
$903$		0			0
$904$	26.6148	−	29.5587i	0.885195	−	0.983108i
$905$	−33.2921	+	36.6295i	−1.10667	+	1.21761i
$906$		0			0
$907$	−24.0868	+	41.7196i	−0.799789	+	1.38528i	0.119964	+	0.992778i	$0.461722\pi$
$907$	−24.0868	+	41.7196i	−0.799789	+	1.38528i	−0.919753	+	0.392497i	$0.871611\pi$
$908$	−5.91884	+	18.2163i	−0.196424	+	0.604529i
$909$		0			0
$910$	−3.05652	+	2.19898i	−0.101323	+	0.0728953i
$911$	48.2662	−	21.4895i	1.59913	−	0.711979i	0.602827	−	0.797872i	$-0.294041\pi$
$911$	48.2662	−	21.4895i	1.59913	−	0.711979i	0.996304	+	0.0858924i	$0.0273741\pi$
$912$		0			0
$913$	25.9153	+	11.5382i	0.857672	+	0.381860i
$914$	−2.33504	+	22.2164i	−0.0772362	+	0.734854i
$915$		0			0
$916$	−1.37443	−	13.0768i	−0.0454123	−	0.432069i
$917$	−8.75044	+	26.9311i	−0.288965	+	0.889342i
$918$		0			0
$919$	−5.29882	+	16.3081i	−0.174792	+	0.537954i	−0.999624	−	0.0274237i	$-0.991270\pi$
$919$	−5.29882	+	16.3081i	−0.174792	+	0.537954i	0.824832	+	0.565378i	$0.191270\pi$
$920$	−25.9759	−	29.1212i	−0.856399	−	0.960097i
$921$		0			0
$922$	−10.4331	+	11.5872i	−0.343597	+	0.381604i
$923$	−1.70433	+	16.2156i	−0.0560986	+	0.533743i
$924$		0			0
$925$	11.6172	+	2.58284i	0.381972	+	0.0849233i
$926$	−28.2265			−0.927582
$927$		0			0
$928$	8.19752	+	25.2294i	0.269097	+	0.828195i
$929$	−38.9315	−	8.27514i	−1.27730	−	0.271499i	−0.481172	−	0.876626i	$-0.659789\pi$
$929$	−38.9315	−	8.27514i	−1.27730	−	0.271499i	−0.796129	+	0.605127i	$0.793122\pi$
$930$		0			0
$931$	6.60103	−	1.40309i	0.216340	−	0.0459845i
$932$	6.39599	+	11.0782i	0.209508	+	0.362878i
$933$		0			0
$934$	−2.42585	−	23.0804i	−0.0793762	−	0.755214i
$935$	1.00273	−	3.03778i	0.0327927	−	0.0993460i
$936$		0			0
$937$	−18.7168	+	13.5986i	−0.611453	+	0.444246i	−0.849926	−	0.526903i	$-0.823353\pi$
$937$	−18.7168	+	13.5986i	−0.611453	+	0.444246i	0.238473	+	0.971149i	$0.423353\pi$
$938$	0.186223	+	1.77180i	0.00608041	+	0.0578513i
$939$		0			0
$940$	−11.0310	+	2.29098i	−0.359793	+	0.0747237i
$941$	30.7723	+	13.7007i	1.00315	+	0.446630i	0.841523	−	0.540222i	$-0.181660\pi$
$941$	30.7723	+	13.7007i	1.00315	+	0.446630i	0.161625	+	0.986852i	$0.448326\pi$
$942$		0			0
$943$	−32.2182	+	55.8036i	−1.04917	+	1.81722i
$944$	2.73733	−	8.42463i	0.0890924	−	0.274198i
$945$		0			0
$946$	11.9413	+	36.7515i	0.388245	+	1.19489i
$947$	−40.1494	−	8.53401i	−1.30468	−	0.277318i	−0.497417	−	0.867512i	$-0.665718\pi$
$947$	−40.1494	−	8.53401i	−1.30468	−	0.277318i	−0.807262	+	0.590194i	$0.799051\pi$
$948$		0			0
$949$	4.54306	+	7.86880i	0.147474	+	0.255432i
$950$	5.46182	−	5.95331i	0.177205	−	0.193151i
$951$		0			0
$952$	1.33651	−	0.595053i	0.0433166	−	0.0192858i
$953$	18.3625	+	56.5138i	0.594818	+	1.83066i	0.555629	+	0.831430i	$0.312478\pi$
$953$	18.3625	+	56.5138i	0.594818	+	1.83066i	0.0391893	+	0.999232i	$0.487522\pi$
$954$		0			0
$955$	−8.00435	+	24.2493i	−0.259015	+	0.784689i
$956$	−2.93775	−	3.26271i	−0.0950137	−	0.105523i
$957$		0			0
$958$	6.59610	−	1.40204i	0.213110	−	0.0452980i
$959$	25.1156	+	11.1822i	0.811025	+	0.361092i
$960$		0			0
$961$	−21.5105	+	9.57709i	−0.693887	+	0.308939i
$962$	2.03059	−	1.47531i	0.0654687	−	0.0475658i
$963$		0			0
$964$	9.37349	+	6.81024i	0.301900	+	0.219343i
$965$	3.96335	+	39.4797i	0.127585	+	1.27090i
$966$		0			0
$967$	6.02838	−	1.28137i	0.193860	−	0.0412062i	−0.109958	−	0.993936i	$-0.535072\pi$
$967$	6.02838	−	1.28137i	0.193860	−	0.0412062i	0.303818	+	0.952730i	$0.401738\pi$
$968$	17.8838	+	30.9756i	0.574807	+	0.995595i
$969$		0			0
$970$	4.46566	+	0.971002i	0.143384	+	0.0311770i
$971$	13.0593	+	40.1925i	0.419094	+	1.28984i	0.908537	+	0.417804i	$0.137200\pi$
$971$	13.0593	+	40.1925i	0.419094	+	1.28984i	−0.489443	+	0.872036i	$0.662800\pi$
$972$		0			0
$973$	11.1201	+	8.07923i	0.356494	+	0.259008i
$974$	−12.3308	+	21.3576i	−0.395105	+	0.684341i
$975$		0			0
$976$	10.1306	+	17.5467i	0.324273	+	0.561657i
$977$	1.22573	−	11.6621i	0.0392147	−	0.373103i	−0.957261	−	0.289225i	$-0.906603\pi$
$977$	1.22573	−	11.6621i	0.0392147	−	0.373103i	0.996476	−	0.0838785i	$-0.0267308\pi$
$978$		0			0
$979$	5.87583	+	1.24895i	0.187792	+	0.0399165i
$980$	−6.93731	−	5.08987i	−0.221604	−	0.162590i
$981$		0			0
$982$	−10.7959			−0.344510
$983$	−3.94352	−	4.37972i	−0.125779	−	0.139692i	0.676966	−	0.736014i	$-0.263294\pi$
$983$	−3.94352	−	4.37972i	−0.125779	−	0.139692i	−0.802745	+	0.596323i	$0.796628\pi$
$984$		0			0
$985$	−2.35225	+	21.4184i	−0.0749488	+	0.682447i
$986$	0.197861	−	1.88252i	0.00630118	−	0.0599517i
$987$		0			0
$988$	0.135655	+	1.29067i	0.00431575	+	0.0410616i
$989$	35.1953	+	25.5709i	1.11914	+	0.813106i
$990$		0			0
$991$	−6.01131	+	4.36747i	−0.190956	+	0.138737i	−0.679155	−	0.733995i	$-0.737654\pi$
$991$	−6.01131	+	4.36747i	−0.190956	+	0.138737i	0.488200	+	0.872732i	$0.337654\pi$
$992$	−8.18793	−	9.09362i	−0.259967	−	0.288723i
$993$		0			0
$994$	−27.4187	+	5.82802i	−0.869668	+	0.184854i
$995$	6.34362	+	2.85990i	0.201106	+	0.0906649i
$996$		0			0
$997$	1.78229	+	0.378837i	0.0564456	+	0.0119979i	0.236048	−	0.971741i	$-0.424148\pi$
$997$	1.78229	+	0.378837i	0.0564456	+	0.0119979i	−0.179602	+	0.983739i	$0.557481\pi$
$998$	3.51103	+	2.55091i	0.111140	+	0.0807476i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.316.18		224
3.2	odd	2		225.2.q.a.16.11	✓	224
9.4	even	3	inner	675.2.r.a.91.11		224
9.5	odd	6		225.2.q.a.166.18	yes	224
25.11	even	5	inner	675.2.r.a.586.11		224
75.11	odd	10		225.2.q.a.61.18	yes	224
225.86	odd	30		225.2.q.a.211.11	yes	224
225.211	even	15	inner	675.2.r.a.361.18		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.11	✓	224	3.2	odd	2
225.2.q.a.61.18	yes	224	75.11	odd	10
225.2.q.a.166.18	yes	224	9.5	odd	6
225.2.q.a.211.11	yes	224	225.86	odd	30
675.2.r.a.91.11		224	9.4	even	3	inner
675.2.r.a.316.18		224	1.1	even	1	trivial
675.2.r.a.361.18		224	225.211	even	15	inner
675.2.r.a.586.11		224	25.11	even	5	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.973390 - 0.433381i) q^{2} +(-0.578592 + 0.642592i) q^{4} +(2.03848 + 0.919011i) q^{5} +(-0.798426 + 1.38291i) q^{7} +(-0.943229 + 2.90296i) q^{8} +(2.38252 + 0.0111154i) q^{10} +(-4.35427 + 1.93865i) q^{11} +(0.904123 + 0.402542i) q^{13} +(-0.177851 + 1.69214i) q^{14} +(0.159189 + 1.51458i) q^{16} +(-0.0927524 + 0.285463i) q^{17} +(0.468623 - 1.44227i) q^{19} +(-1.77000 + 0.778180i) q^{20} +(-3.39823 + 3.77412i) q^{22} +(-0.597633 + 5.68610i) q^{23} +(3.31084 + 3.74678i) q^{25} +1.05452 q^{26} +(-0.426686 - 1.31321i) q^{28} +(-5.78936 - 1.23057i) q^{29} +(2.67051 - 0.567634i) q^{31} +(-2.24101 - 3.88154i) q^{32} +(0.0334298 + 0.318064i) q^{34} +(-2.89849 + 2.08529i) q^{35} +(1.92560 - 1.39903i) q^{37} +(-0.168901 - 1.60699i) q^{38} +(-4.59061 + 5.05080i) q^{40} +(10.2958 + 4.58400i) q^{41} +(3.80449 - 6.58957i) q^{43} +(1.27359 - 3.91970i) q^{44} +(1.88252 + 5.79380i) q^{46} +(5.69960 + 1.21149i) q^{47} +(2.22503 + 3.85387i) q^{49} +(4.84652 + 2.21222i) q^{50} +(-0.781789 + 0.348075i) q^{52} +(-0.598625 - 1.84238i) q^{53} +(-10.6578 - 0.0497227i) q^{55} +(-3.26145 - 3.62220i) q^{56} +(-6.16861 + 1.31118i) q^{58} +(-5.31370 - 2.36581i) q^{59} +(12.1540 - 5.41129i) q^{61} +(2.35344 - 1.70988i) q^{62} +(-6.32771 - 4.59735i) q^{64} +(1.47310 + 1.65147i) q^{65} +(1.02420 - 0.217699i) q^{67} +(-0.129770 - 0.224768i) q^{68} +(-1.91764 + 3.28595i) q^{70} +(5.09100 + 15.6685i) q^{71} +(7.42742 + 5.39634i) q^{73} +(1.26805 - 2.19633i) q^{74} +(0.655651 + 1.13562i) q^{76} +(0.795582 - 7.56945i) q^{77} +(-10.9470 - 2.32686i) q^{79} +(-1.06741 + 3.23374i) q^{80} +12.0085 q^{82} +(-3.98246 - 4.42297i) q^{83} +(-0.451418 + 0.496671i) q^{85} +(0.847457 - 8.06302i) q^{86} +(-1.52074 - 14.4689i) q^{88} +(-1.01962 - 0.740795i) q^{89} +(-1.27856 + 0.928926i) q^{91} +(-3.30805 - 3.67397i) q^{92} +(6.07297 - 1.29085i) q^{94} +(2.28075 - 2.50938i) q^{95} +(1.87620 + 0.398799i) q^{97} +(3.83602 + 2.78703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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