LMFDB - Embedded newform 945.2.bv.e.73.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(73,945)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("945.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bv (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.34
Character	$\chi$	$=$	945.73
Dual form			945.2.bv.e.712.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48808 - 1.48808i) q^{2} -2.42876i q^{4} +(-0.500247 + 2.17939i) q^{5} +(-2.43052 + 1.04527i) q^{7} +(-0.638021 - 0.638021i) q^{8} +O(q^{10})$	\(q+(1.48808 - 1.48808i) q^{2} -2.42876i q^{4} +(-0.500247 + 2.17939i) q^{5} +(-2.43052 + 1.04527i) q^{7} +(-0.638021 - 0.638021i) q^{8} +(2.49870 + 3.98751i) q^{10} +(-0.0441776 - 0.0765178i) q^{11} +(5.14229 + 1.37787i) q^{13} +(-2.06136 + 5.17224i) q^{14} +2.95866 q^{16} +(3.40854 - 0.913316i) q^{17} +(2.57895 + 4.46688i) q^{19} +(5.29321 + 1.21498i) q^{20} +(-0.179604 - 0.0481248i) q^{22} +(-3.58010 + 0.959285i) q^{23} +(-4.49951 - 2.18047i) q^{25} +(9.70252 - 5.60175i) q^{26} +(2.53870 + 5.90313i) q^{28} +(0.609023 + 0.351619i) q^{29} +4.87601i q^{31} +(5.67876 - 5.67876i) q^{32} +(3.71309 - 6.43126i) q^{34} +(-1.06219 - 5.81994i) q^{35} +(8.44603 + 2.26311i) q^{37} +(10.4847 + 2.80938i) q^{38} +(1.70967 - 1.07133i) q^{40} +(2.57843 - 1.48865i) q^{41} +(2.22267 - 0.595563i) q^{43} +(-0.185843 + 0.107297i) q^{44} +(-3.89998 + 6.75496i) q^{46} +(-4.06198 - 4.06198i) q^{47} +(4.81483 - 5.08108i) q^{49} +(-9.94033 + 3.45090i) q^{50} +(3.34652 - 12.4894i) q^{52} +(-13.5481 + 3.63020i) q^{53} +(0.188862 - 0.0580025i) q^{55} +(2.21762 + 0.883819i) q^{56} +(1.42951 - 0.383036i) q^{58} -3.46294 q^{59} +1.36482i q^{61} +(7.25589 + 7.25589i) q^{62} -10.9836i q^{64} +(-5.57535 + 10.5178i) q^{65} +(-4.23347 + 4.23347i) q^{67} +(-2.21822 - 8.27851i) q^{68} +(-10.2412 - 7.07991i) q^{70} -13.4890 q^{71} +(-0.285680 - 1.06617i) q^{73} +(15.9360 - 9.20068i) q^{74} +(10.8489 - 6.26364i) q^{76} +(0.187356 + 0.139801i) q^{77} +3.55373i q^{79} +(-1.48006 + 6.44808i) q^{80} +(1.62166 - 6.05214i) q^{82} +(0.0856239 + 0.319553i) q^{83} +(0.285360 + 7.88543i) q^{85} +(2.42127 - 4.19376i) q^{86} +(-0.0206338 + 0.0770062i) q^{88} +(-5.71165 - 9.89286i) q^{89} +(-13.9387 + 2.02613i) q^{91} +(2.32987 + 8.69519i) q^{92} -12.0891 q^{94} +(-11.0252 + 3.38601i) q^{95} +(10.0857 - 2.70245i) q^{97} +(-0.396205 - 14.7259i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	$ 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) $ 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.48808	−	1.48808i	1.05223	−	1.05223i	0.0536717	−	0.998559i	$-0.482908\pi$
$2$	1.48808	−	1.48808i	1.05223	−	1.05223i	0.998559	−	0.0536717i	$-0.0170925\pi$
$3$		0			0
$3$		0			0
$4$		−	2.42876i		−	1.21438i
$5$	−0.500247	+	2.17939i	−0.223717	+	0.974654i
$5$	−0.500247	+	2.17939i	−0.223717	+	0.974654i
$6$		0			0
$7$	−2.43052	+	1.04527i	−0.918649	+	0.395074i
$7$	−2.43052	+	1.04527i	−0.918649	+	0.395074i
$8$	−0.638021	−	0.638021i	−0.225575	−	0.225575i
$9$		0			0
$10$	2.49870	+	3.98751i	0.790158	+	1.26096i
$11$	−0.0441776	−	0.0765178i	−0.0133200	−	0.0230710i	0.859289	−	0.511491i	$-0.170907\pi$
$11$	−0.0441776	−	0.0765178i	−0.0133200	−	0.0230710i	−0.872609	+	0.488420i	$0.837573\pi$
$12$		0			0
$13$	5.14229	+	1.37787i	1.42622	+	0.382153i	0.887684	−	0.460452i	$-0.152313\pi$
$13$	5.14229	+	1.37787i	1.42622	+	0.382153i	0.538531	+	0.842606i	$0.318979\pi$
$14$	−2.06136	+	5.17224i	−0.550922	+	1.38234i
$15$		0			0
$16$	2.95866			0.739665
$17$	3.40854	−	0.913316i	0.826693	−	0.221512i	0.179422	−	0.983772i	$-0.442577\pi$
$17$	3.40854	−	0.913316i	0.826693	−	0.221512i	0.647270	+	0.762260i	$0.275910\pi$
$18$		0			0
$19$	2.57895	+	4.46688i	0.591652	+	1.02477i	0.994010	+	0.109289i	$0.0348574\pi$
$19$	2.57895	+	4.46688i	0.591652	+	1.02477i	−0.402358	+	0.915482i	$0.631809\pi$
$20$	5.29321	+	1.21498i	1.18360	+	0.271677i
$21$		0			0
$22$	−0.179604	−	0.0481248i	−0.0382918	−	0.0102602i
$23$	−3.58010	+	0.959285i	−0.746503	+	0.200025i	−0.611966	−	0.790884i	$-0.709621\pi$
$23$	−3.58010	+	0.959285i	−0.746503	+	0.200025i	−0.134536	+	0.990909i	$0.542955\pi$
$24$		0			0
$25$	−4.49951	−	2.18047i	−0.899901	−	0.436094i
$26$	9.70252	−	5.60175i	1.90282	−	1.09859i
$27$		0			0
$28$	2.53870	+	5.90313i	0.479769	+	1.11559i
$29$	0.609023	+	0.351619i	0.113093	+	0.0652941i	0.555479	−	0.831530i	$-0.312535\pi$
$29$	0.609023	+	0.351619i	0.113093	+	0.0652941i	−0.442387	+	0.896824i	$0.645868\pi$
$30$		0			0
$31$			4.87601i			0.875758i	0.899034	+	0.437879i	$0.144270\pi$
$31$			4.87601i			0.875758i	−0.899034	+	0.437879i	$0.855730\pi$
$32$	5.67876	−	5.67876i	1.00387	−	1.00387i
$33$		0			0
$34$	3.71309	−	6.43126i	0.636790	−	1.10295i
$35$	−1.06219	−	5.81994i	−0.179543	−	0.983750i
$36$		0			0
$37$	8.44603	+	2.26311i	1.38852	+	0.372053i	0.874208	−	0.485551i	$-0.161381\pi$
$37$	8.44603	+	2.26311i	1.38852	+	0.372053i	0.514311	+	0.857604i	$0.328048\pi$
$38$	10.4847	+	2.80938i	1.70085	+	0.455741i
$39$		0			0
$40$	1.70967	−	1.07133i	0.270322	−	0.169392i
$41$	2.57843	−	1.48865i	0.402682	−	0.232489i	−0.284958	−	0.958540i	$-0.591980\pi$
$41$	2.57843	−	1.48865i	0.402682	−	0.232489i	0.687641	+	0.726051i	$0.258646\pi$
$42$		0			0
$43$	2.22267	−	0.595563i	0.338954	−	0.0908225i	−0.0853269	−	0.996353i	$-0.527193\pi$
$43$	2.22267	−	0.595563i	0.338954	−	0.0908225i	0.424281	+	0.905530i	$0.360527\pi$
$44$	−0.185843	+	0.107297i	−0.0280169	+	0.0161756i
$45$		0			0
$46$	−3.89998	+	6.75496i	−0.575021	+	0.995965i
$47$	−4.06198	−	4.06198i	−0.592501	−	0.592501i	0.345805	−	0.938306i	$-0.387606\pi$
$47$	−4.06198	−	4.06198i	−0.592501	−	0.592501i	−0.938306	+	0.345805i	$0.887606\pi$
$48$		0			0
$49$	4.81483	−	5.08108i	0.687833	−	0.725869i
$50$	−9.94033	+	3.45090i	−1.40577	+	0.488032i
$51$		0			0
$52$	3.34652	−	12.4894i	0.464078	−	1.73196i
$53$	−13.5481	+	3.63020i	−1.86097	+	0.498646i	−0.999951	−	0.00992346i	$-0.996841\pi$
$53$	−13.5481	+	3.63020i	−1.86097	+	0.498646i	−0.861021	+	0.508569i	$0.830175\pi$
$54$		0			0
$55$	0.188862	−	0.0580025i	0.0254662	−	0.00782105i
$56$	2.21762	+	0.883819i	0.296343	+	0.118105i
$57$		0			0
$58$	1.42951	−	0.383036i	0.187704	−	0.0502951i
$59$	−3.46294			−0.450836			−0.225418	−	0.974262i	$-0.572375\pi$
$59$	−3.46294			−0.450836			−0.225418	+	0.974262i	$0.572375\pi$
$60$		0			0
$61$			1.36482i			0.174747i	0.996176	+	0.0873735i	$0.0278474\pi$
$61$			1.36482i			0.174747i	−0.996176	+	0.0873735i	$0.972153\pi$
$62$	7.25589	+	7.25589i	0.921499	+	0.921499i
$63$		0			0
$64$		−	10.9836i		−	1.37295i
$65$	−5.57535	+	10.5178i	−0.691537	+	1.30457i
$66$		0			0
$67$	−4.23347	+	4.23347i	−0.517200	+	0.517200i	−0.916723	−	0.399523i	$-0.869176\pi$
$67$	−4.23347	+	4.23347i	−0.517200	+	0.517200i	0.399523	+	0.916723i	$0.369176\pi$
$68$	−2.21822	−	8.27851i	−0.268999	−	1.00392i
$69$		0			0
$70$	−10.2412	−	7.07991i	−1.22405	−	0.846212i
$71$	−13.4890			−1.60085			−0.800425	−	0.599433i	$-0.795393\pi$
$71$	−13.4890			−1.60085			−0.800425	+	0.599433i	$0.795393\pi$
$72$		0			0
$73$	−0.285680	−	1.06617i	−0.0334363	−	0.124786i	0.947190	−	0.320672i	$-0.103909\pi$
$73$	−0.285680	−	1.06617i	−0.0334363	−	0.124786i	−0.980627	+	0.195886i	$0.937242\pi$
$74$	15.9360	−	9.20068i	1.85253	−	1.06956i
$75$		0			0
$76$	10.8489	−	6.26364i	1.24446	−	0.718489i
$77$	0.187356	+	0.139801i	0.0213512	+	0.0159317i
$78$		0			0
$79$			3.55373i			0.399826i	0.979814	+	0.199913i	$0.0640660\pi$
$79$			3.55373i			0.399826i	−0.979814	+	0.199913i	$0.935934\pi$
$80$	−1.48006	+	6.44808i	−0.165476	+	0.720917i
$81$		0			0
$82$	1.62166	−	6.05214i	0.179083	−	0.668347i
$83$	0.0856239	+	0.319553i	0.00939845	+	0.0350755i	0.970466	−	0.241239i	$-0.0775537\pi$
$83$	0.0856239	+	0.319553i	0.00939845	+	0.0350755i	−0.961067	+	0.276314i	$0.910887\pi$
$84$		0			0
$85$	0.285360	+	7.88543i	0.0309516	+	0.855295i
$86$	2.42127	−	4.19376i	0.261092	−	0.452224i
$87$		0			0
$88$	−0.0206338	+	0.0770062i	−0.00219957	+	0.00820889i
$89$	−5.71165	−	9.89286i	−0.605434	−	1.04864i	−0.991983	−	0.126373i	$-0.959666\pi$
$89$	−5.71165	−	9.89286i	−0.605434	−	1.04864i	0.386549	−	0.922269i	$-0.373667\pi$
$90$		0			0
$91$	−13.9387	+	2.02613i	−1.46117	+	0.212396i
$92$	2.32987	+	8.69519i	0.242906	+	0.906536i
$93$		0			0
$94$	−12.0891			−1.24690
$95$	−11.0252	+	3.38601i	−1.13116	+	0.347397i
$96$		0			0
$97$	10.0857	−	2.70245i	1.02405	−	0.274393i	0.292559	−	0.956247i	$-0.405493\pi$
$97$	10.0857	−	2.70245i	1.02405	−	0.274393i	0.731488	+	0.681855i	$0.238826\pi$
$98$	−0.396205	−	14.7259i	−0.0400227	−	1.48754i
$99$		0			0
$100$	−5.29583	+	10.9282i	−0.529583	+	1.09282i
$101$	9.95214	−	5.74587i	0.990274	−	0.571735i	0.0849182	−	0.996388i	$-0.472937\pi$
$101$	9.95214	−	5.74587i	0.990274	−	0.571735i	0.905356	+	0.424653i	$0.139604\pi$
$102$		0			0
$103$	−3.38400	−	12.6293i	−0.333435	−	1.24440i	−0.905555	−	0.424228i	$-0.860545\pi$
$103$	−3.38400	−	12.6293i	−0.333435	−	1.24440i	0.572120	−	0.820170i	$-0.306121\pi$
$104$	−2.40178	−	4.16000i	−0.235514	−	0.407922i
$105$		0			0
$106$	−14.7586	+	25.5626i	−1.43348	+	2.48286i
$107$	11.6419	+	3.11943i	1.12546	+	0.301567i	0.773092	−	0.634294i	$-0.218709\pi$
$107$	11.6419	+	3.11943i	1.12546	+	0.301567i	0.352371	+	0.935860i	$0.385376\pi$
$108$		0			0
$109$	−11.5914	−	6.69232i	−1.11026	−	0.641008i	−0.171363	−	0.985208i	$-0.554817\pi$
$109$	−11.5914	−	6.69232i	−1.11026	−	0.641008i	−0.938897	+	0.344200i	$0.888150\pi$
$110$	0.194729	−	0.367354i	0.0185667	−	0.0350258i
$111$		0			0
$112$	−7.19107	+	3.09259i	−0.679492	+	0.292222i
$113$	3.86407	−	14.4209i	0.363501	−	1.35660i	−0.505941	−	0.862568i	$-0.668855\pi$
$113$	3.86407	−	14.4209i	0.363501	−	1.35660i	0.869442	−	0.494035i	$-0.164479\pi$
$114$		0			0
$115$	−0.299723	−	8.28233i	−0.0279493	−	0.772331i
$116$	0.853998	−	1.47917i	0.0792917	−	0.137337i
$117$		0			0
$118$	−5.15313	+	5.15313i	−0.474384	+	0.474384i
$119$	−7.32986	+	5.78267i	−0.671927	+	0.530096i
$120$		0			0
$121$	5.49610	−	9.51952i	0.499645	−	0.865411i
$122$	2.03096	+	2.03096i	0.183874	+	0.183874i
$123$		0			0
$124$	11.8426			1.06350
$125$	7.00297	−	8.71541i	0.626365	−	0.779530i
$126$		0			0
$127$	4.64611	−	4.64611i	0.412276	−	0.412276i	−0.470255	−	0.882531i	$-0.655838\pi$
$127$	4.64611	−	4.64611i	0.412276	−	0.412276i	0.882531	+	0.470255i	$0.155838\pi$
$128$	−4.98688	−	4.98688i	−0.440782	−	0.440782i
$129$		0			0
$130$	7.35476	+	23.9479i	0.645055	+	2.10037i
$131$	16.5971	+	9.58232i	1.45009	+	0.837211i	0.998486	−	0.0550067i	$-0.0175180\pi$
$131$	16.5971	+	9.58232i	1.45009	+	0.837211i	0.451606	+	0.892218i	$0.350851\pi$
$132$		0			0
$133$	−10.9373	−	8.16112i	−0.948382	−	0.707659i
$134$			12.5995i			1.08843i
$135$		0			0
$136$	−2.75744	−	1.59201i	−0.236448	−	0.136513i
$137$	−13.8108	−	3.70060i	−1.17994	−	0.316163i	−0.385036	−	0.922901i	$-0.625811\pi$
$137$	−13.8108	−	3.70060i	−1.17994	−	0.316163i	−0.794902	+	0.606738i	$0.792478\pi$
$138$		0			0
$139$	8.63234	+	14.9516i	0.732185	+	1.26818i	0.955947	+	0.293538i	$0.0948328\pi$
$139$	8.63234	+	14.9516i	0.732185	+	1.26818i	−0.223762	+	0.974644i	$0.571834\pi$
$140$	−14.1352	+	2.57980i	−1.19464	+	0.218033i
$141$		0			0
$142$	−20.0727	+	20.0727i	−1.68446	+	1.68446i
$143$	−0.121742	−	0.454348i	−0.0101806	−	0.0379945i
$144$		0			0
$145$	−1.07098	+	1.15140i	−0.0889400	+	0.0956188i
$146$	−2.01166	−	1.16143i	−0.166486	−	0.0961209i
$147$		0			0
$148$	5.49653	−	20.5133i	0.451812	−	1.68619i
$149$	2.44681	+	1.41266i	0.200450	+	0.115730i	0.596865	−	0.802341i	$-0.296413\pi$
$149$	2.44681	+	1.41266i	0.200450	+	0.115730i	−0.396415	+	0.918071i	$0.629746\pi$
$150$		0			0
$151$	−2.94996	−	5.10947i	−0.240064	−	0.415803i	0.720668	−	0.693280i	$-0.243835\pi$
$151$	−2.94996	−	5.10947i	−0.240064	−	0.415803i	−0.960732	+	0.277477i	$0.910502\pi$
$152$	1.20454	−	4.49539i	0.0977007	−	0.364624i
$153$		0			0
$154$	0.486835	−	0.0707663i	0.0392302	−	0.00570251i
$155$	−10.6267	−	2.43921i	−0.853561	−	0.195922i
$156$		0			0
$157$	−8.34178	−	8.34178i	−0.665747	−	0.665747i	0.290982	−	0.956729i	$-0.406018\pi$
$157$	−8.34178	−	8.34178i	−0.665747	−	0.665747i	−0.956729	+	0.290982i	$0.906018\pi$
$158$	5.28823	+	5.28823i	0.420709	+	0.420709i
$159$		0			0
$160$	9.53546	+	15.2170i	0.753844	+	1.20301i
$161$	7.69879	−	6.07372i	0.606750	−	0.478677i
$162$		0			0
$163$	2.60174	−	9.70984i	0.203784	−	0.760533i	−0.786032	−	0.618185i	$-0.787868\pi$
$163$	2.60174	−	9.70984i	0.203784	−	0.760533i	0.989817	−	0.142348i	$-0.0454652\pi$
$164$	−3.61558	−	6.26237i	−0.282329	−	0.489009i
$165$		0			0
$166$	0.602935	+	0.348105i	0.0467968	+	0.0270182i
$167$	−0.281253	+	1.04965i	−0.0217640	+	0.0812244i	−0.975954	−	0.217978i	$-0.930054\pi$
$167$	−0.281253	+	1.04965i	−0.0217640	+	0.0812244i	0.954190	+	0.299202i	$0.0967206\pi$
$168$		0			0
$169$	13.2863	+	7.67086i	1.02202	+	0.590066i
$170$	12.1588	+	11.3095i	0.932536	+	0.867400i
$171$		0			0
$172$	−1.44648	−	5.39833i	−0.110293	−	0.411619i
$173$	7.23785	−	7.23785i	0.550283	−	0.550283i	−0.376239	−	0.926523i	$-0.622783\pi$
$173$	7.23785	−	7.23785i	0.550283	−	0.550283i	0.926523	+	0.376239i	$0.122783\pi$
$174$		0			0
$175$	13.2153	+	0.596486i	0.998983	+	0.0450901i
$176$	−0.130706	−	0.226390i	−0.00985237	−	0.0170648i
$177$		0			0
$178$	−23.2207	−	6.22198i	−1.74047	−	0.466357i
$179$	−4.73666	−	2.73471i	−0.354034	−	0.204402i	0.312426	−	0.949942i	$-0.398858\pi$
$179$	−4.73666	−	2.73471i	−0.354034	−	0.204402i	−0.666461	+	0.745540i	$0.732192\pi$
$180$		0			0
$181$			17.8425i			1.32622i	0.748520	+	0.663112i	$0.230765\pi$
$181$			17.8425i			1.32622i	−0.748520	+	0.663112i	$0.769235\pi$
$182$	−17.7268	+	23.7569i	−1.31400	+	1.76098i
$183$		0			0
$184$	2.89622	+	1.67214i	0.213513	+	0.123272i
$185$	−9.15731	+	17.2751i	−0.673259	+	1.27009i
$186$		0			0
$187$	−0.220466	−	0.220466i	−0.0161221	−	0.0161221i
$188$	−9.86556	+	9.86556i	−0.719520	+	0.719520i
$189$		0			0
$190$	−11.3677	+	21.4450i	−0.824700	+	1.55578i
$191$	−0.858925			−0.0621497			−0.0310748	−	0.999517i	$-0.509893\pi$
$191$	−0.858925			−0.0621497			−0.0310748	+	0.999517i	$0.509893\pi$
$192$		0			0
$193$	−8.68815	−	8.68815i	−0.625387	−	0.625387i	0.321517	−	0.946904i	$-0.395807\pi$
$193$	−8.68815	−	8.68815i	−0.625387	−	0.625387i	−0.946904	+	0.321517i	$0.895807\pi$
$194$	10.9868	−	19.0298i	0.788809	−	1.36626i
$195$		0			0
$196$	−12.3407	−	11.6940i	−0.881479	−	0.835289i
$197$	−4.02358	+	4.02358i	−0.286668	+	0.286668i	−0.835761	−	0.549093i	$-0.814973\pi$
$197$	−4.02358	+	4.02358i	−0.286668	+	0.286668i	0.549093	+	0.835761i	$0.314973\pi$
$198$		0			0
$199$	−11.9528	+	20.7029i	−0.847314	+	1.46759i	0.0362825	+	0.999342i	$0.488448\pi$
$199$	−11.9528	+	20.7029i	−0.847314	+	1.46759i	−0.883596	+	0.468249i	$0.844885\pi$
$200$	1.47959	+	4.26197i	0.104623	+	0.301367i
$201$		0			0
$202$	6.25926	−	23.3599i	0.440400	−	1.64359i
$203$	−1.84778	−	0.218025i	−0.129689	−	0.0153024i
$204$		0			0
$205$	1.95451	+	6.36410i	0.136509	+	0.444488i
$206$	−23.8290	−	13.7577i	−1.66024	−	0.958542i
$207$		0			0
$208$	15.2143	+	4.07666i	1.05492	+	0.282665i
$209$	0.227864	−	0.394672i	0.0157617	−	0.0273000i
$210$		0			0
$211$	5.61540	+	9.72616i	0.386580	+	0.669576i	0.991987	−	0.126340i	$-0.0403229\pi$
$211$	5.61540	+	9.72616i	0.386580	+	0.669576i	−0.605407	+	0.795916i	$0.706990\pi$
$212$	8.81686	+	32.9050i	0.605544	+	2.25992i
$213$		0			0
$214$	21.9660	−	12.6821i	1.50156	−	0.866929i
$215$	0.186080	+	5.14200i	0.0126906	+	0.350682i
$216$		0			0
$217$	−5.09674	−	11.8512i	−0.345989	−	0.804514i
$218$	−27.2077	+	7.29028i	−1.84274	+	0.493760i
$219$		0			0
$220$	−0.140874	−	0.458700i	−0.00949771	−	0.0309255i
$221$	18.7862			1.26369
$222$		0			0
$223$	−6.58992	−	24.5939i	−0.441294	−	1.64693i	−0.725540	−	0.688180i	$-0.758410\pi$
$223$	−6.58992	−	24.5939i	−0.441294	−	1.64693i	0.284247	−	0.958751i	$-0.408257\pi$
$224$	−7.86650	+	19.7381i	−0.525603	+	1.31881i
$225$		0			0
$226$	−15.7094	−	27.2094i	−1.04497	−	1.80995i
$227$	1.62751	−	6.07394i	0.108022	−	0.403142i	−0.890649	−	0.454692i	$-0.849749\pi$
$227$	1.62751	−	6.07394i	0.108022	−	0.403142i	0.998670	+	0.0515499i	$0.0164161\pi$
$228$		0			0
$229$	1.71491	−	2.97031i	0.113324	−	0.196283i	−0.803784	−	0.594921i	$-0.797183\pi$
$229$	1.71491	−	2.97031i	0.113324	−	0.196283i	0.917109	+	0.398637i	$0.130517\pi$
$230$	−12.7708	−	11.8787i	−0.842079	−	0.783261i
$231$		0			0
$232$	−0.164229	−	0.612910i	−0.0107821	−	0.0402395i
$233$	2.45042	−	9.14509i	0.160532	−	0.599115i	−0.838036	−	0.545616i	$-0.816296\pi$
$233$	2.45042	−	9.14509i	0.160532	−	0.599115i	0.998568	−	0.0534991i	$-0.0170374\pi$
$234$		0			0
$235$	10.8847	−	6.82066i	0.710037	−	0.444931i
$236$			8.41063i			0.547485i
$237$		0			0
$238$	−2.30234	+	19.5125i	−0.149239	+	1.26481i
$239$	1.38131	−	0.797500i	0.0893495	−	0.0515860i	−0.454660	−	0.890665i	$-0.650239\pi$
$239$	1.38131	−	0.797500i	0.0893495	−	0.0515860i	0.544009	+	0.839079i	$0.316906\pi$
$240$		0			0
$241$	19.3522	−	11.1730i	1.24659	−	0.719716i	0.276158	−	0.961112i	$-0.410939\pi$
$241$	19.3522	−	11.1730i	1.24659	−	0.719716i	0.970427	+	0.241396i	$0.0776052\pi$
$242$	−5.98717	−	22.3444i	−0.384870	−	1.43635i
$243$		0			0
$244$	3.31481			0.212209
$245$	8.66507	+	13.0352i	0.553591	+	0.832789i
$246$		0			0
$247$	7.10694	+	26.5235i	0.452204	+	1.68765i
$248$	3.11100	−	3.11100i	0.197549	−	0.197549i
$249$		0			0
$250$	−2.54825	−	23.3902i	−0.161166	−	1.47933i
$251$			20.2602i			1.27881i	0.768869	+	0.639406i	$0.220820\pi$
$251$			20.2602i			1.27881i	−0.768869	+	0.639406i	$0.779180\pi$
$252$		0			0
$253$	0.231563	+	0.231563i	0.0145582	+	0.0145582i
$254$		−	13.8276i		−	0.867618i
$255$		0			0
$256$	7.12538			0.445336
$257$	7.76981	−	2.08191i	0.484667	−	0.129866i	−0.00820768	−	0.999966i	$-0.502613\pi$
$257$	7.76981	−	2.08191i	0.484667	−	0.129866i	0.492875	+	0.870100i	$0.335946\pi$
$258$		0			0
$259$	−22.8938	+	3.32784i	−1.42255	+	0.206782i
$260$	25.5452	+	13.5411i	1.58424	+	0.839786i
$261$		0			0
$262$	38.9570	−	10.4385i	2.40677	−	0.644892i
$263$	5.41712	−	20.2170i	0.334034	−	1.24663i	−0.570879	−	0.821034i	$-0.693397\pi$
$263$	5.41712	−	20.2170i	0.334034	−	1.24663i	0.904913	−	0.425597i	$-0.139936\pi$
$264$		0			0
$265$	−1.13423	−	31.3426i	−0.0696754	−	1.92536i
$266$	−28.4199	+	4.13112i	−1.74254	+	0.253295i
$267$		0			0
$268$	10.2821	+	10.2821i	0.628077	+	0.628077i
$269$	−3.69593	+	6.40154i	−0.225345	+	0.390309i	−0.956423	−	0.291985i	$-0.905684\pi$
$269$	−3.69593	+	6.40154i	−0.225345	+	0.390309i	0.731078	+	0.682294i	$0.239018\pi$
$270$		0			0
$271$	0.675089	−	0.389763i	0.0410087	−	0.0236764i	−0.479355	−	0.877621i	$-0.659130\pi$
$271$	0.675089	−	0.389763i	0.0410087	−	0.0236764i	0.520364	+	0.853944i	$0.325796\pi$
$272$	10.0847	−	2.70219i	0.611476	−	0.163844i
$273$		0			0
$274$	−26.0584	+	15.0448i	−1.57424	+	0.908890i
$275$	0.0319324	+	0.440620i	0.00192559	+	0.0265704i
$276$		0			0
$277$	9.21225	+	2.46841i	0.553510	+	0.148313i	0.524723	−	0.851273i	$-0.324169\pi$
$277$	9.21225	+	2.46841i	0.553510	+	0.148313i	0.0287871	+	0.999586i	$0.490836\pi$
$278$	35.0948	+	9.40363i	2.10485	+	0.563992i
$279$		0			0
$280$	−3.03555	+	4.39095i	−0.181409	+	0.262409i
$281$	−9.49861	+	16.4521i	−0.566639	+	0.981448i	0.430256	+	0.902707i	$0.358423\pi$
$281$	−9.49861	+	16.4521i	−0.566639	+	0.981448i	−0.996895	+	0.0787411i	$0.974910\pi$
$282$		0			0
$283$	15.8779	−	15.8779i	0.943844	−	0.943844i	−0.0546609	−	0.998505i	$-0.517408\pi$
$283$	15.8779	−	15.8779i	0.943844	−	0.943844i	0.998505	+	0.0546609i	$0.0174078\pi$
$284$			32.7615i			1.94404i
$285$		0			0
$286$	−0.857268	−	0.494944i	−0.0506913	−	0.0292666i
$287$	−4.71087	+	6.31335i	−0.278074	+	0.372665i
$288$		0			0
$289$	−3.93842	+	2.27385i	−0.231672	+	0.133756i
$290$	0.119677	+	3.30708i	0.00702770	+	0.194198i
$291$		0			0
$292$	−2.58947	+	0.693846i	−0.151537	+	0.0406043i
$293$	9.16886	+	2.45679i	0.535651	+	0.143527i	0.516496	−	0.856289i	$-0.327236\pi$
$293$	9.16886	+	2.45679i	0.535651	+	0.143527i	0.0191543	+	0.999817i	$0.493903\pi$
$294$		0			0
$295$	1.73233	−	7.54710i	0.100860	−	0.439409i
$296$	−3.94484	−	6.83266i	−0.229289	−	0.397140i
$297$		0			0
$298$	5.74319	−	1.53888i	0.332694	−	0.0891452i
$299$	−19.7317			−1.14111
$300$		0			0
$301$	−4.77972	+	3.77081i	−0.275499	+	0.217346i
$302$	−11.9931	−	3.21353i	−0.690123	−	0.184918i
$303$		0			0
$304$	7.63024	+	13.2160i	0.437624	+	0.757987i
$305$	−2.97447	−	0.682747i	−0.170318	−	0.0390940i
$306$		0			0
$307$	−4.02496	−	4.02496i	−0.229717	−	0.229717i	0.582858	−	0.812574i	$-0.301935\pi$
$307$	−4.02496	−	4.02496i	−0.229717	−	0.229717i	−0.812574	+	0.582858i	$0.801935\pi$
$308$	0.339541	−	0.455042i	0.0193472	−	0.0259284i
$309$		0			0
$310$	−19.4432	+	12.1837i	−1.10430	+	0.691987i
$311$		−	5.58045i		−	0.316438i	−0.987404	−	0.158219i	$-0.949425\pi$
$311$		−	5.58045i		−	0.316438i	0.987404	−	0.158219i	$-0.0505753\pi$
$312$		0			0
$313$	−22.9394	+	22.9394i	−1.29661	+	1.29661i	−0.365991	+	0.930618i	$0.619270\pi$
$313$	−22.9394	+	22.9394i	−1.29661	+	1.29661i	−0.930618	+	0.365991i	$0.880730\pi$
$314$	−24.8265			−1.40104
$315$		0			0
$316$	8.63115			0.485540
$317$	4.53390	−	4.53390i	0.254649	−	0.254649i	−0.568224	−	0.822874i	$-0.692369\pi$
$317$	4.53390	−	4.53390i	0.254649	−	0.254649i	0.822874	+	0.568224i	$0.192369\pi$
$318$		0			0
$319$		−	0.0621348i		−	0.00347888i
$320$	23.9375	+	5.49450i	1.33815	+	0.307152i
$321$		0			0
$322$	2.41822	−	20.4946i	0.134762	−	1.14212i
$323$	12.8701	+	12.8701i	0.716113	+	0.716113i
$324$		0			0
$325$	−20.1334	−	17.4124i	−1.11680	−	0.965864i
$326$	−10.5774	−	18.3206i	−0.585828	−	1.01468i
$327$		0			0
$328$	−2.59488	−	0.695297i	−0.143278	−	0.0383914i
$329$	14.1186	+	5.62686i	0.778383	+	0.310219i
$330$		0			0
$331$	−5.93070			−0.325981			−0.162990	−	0.986628i	$-0.552114\pi$
$331$	−5.93070			−0.325981			−0.162990	+	0.986628i	$0.552114\pi$
$332$	0.776116	−	0.207960i	0.0425949	−	0.0114133i
$333$		0			0
$334$	1.14344	+	1.98049i	0.0625660	+	0.108368i
$335$	−7.10861	−	11.3442i	−0.388385	−	0.619798i
$336$		0			0
$337$	9.33028	+	2.50004i	0.508253	+	0.136186i	0.503828	−	0.863804i	$-0.331925\pi$
$337$	9.33028	+	2.50004i	0.508253	+	0.136186i	0.00442531	+	0.999990i	$0.498591\pi$
$338$	31.1859	−	8.35624i	1.69629	−	0.454519i
$339$		0			0
$340$	19.1518	−	0.693070i	1.03865	−	0.0375870i
$341$	0.373102	−	0.215411i	0.0202046	−	0.0116651i
$342$		0			0
$343$	−6.39144	+	17.3824i	−0.345105	+	0.938564i
$344$	−1.79809	−	1.03813i	−0.0969467	−	0.0559722i
$345$		0			0
$346$		−	21.5410i		−	1.15805i
$347$	21.7726	−	21.7726i	1.16882	−	1.16882i	0.186329	−	0.982487i	$-0.440341\pi$
$347$	21.7726	−	21.7726i	1.16882	−	1.16882i	0.982487	−	0.186329i	$-0.0596589\pi$
$348$		0			0
$349$	−5.20858	+	9.02153i	−0.278809	+	0.482911i	−0.971089	−	0.238718i	$-0.923273\pi$
$349$	−5.20858	+	9.02153i	−0.278809	+	0.482911i	0.692280	+	0.721629i	$0.256606\pi$
$350$	20.5530	−	18.7778i	1.09861	−	1.00372i
$351$		0			0
$352$	−0.685400	−	0.183652i	−0.0365320	−	0.00978871i
$353$	−31.1229	−	8.33935i	−1.65650	−	0.443859i	−0.695081	−	0.718932i	$-0.744631\pi$
$353$	−31.1229	−	8.33935i	−1.65650	−	0.443859i	−0.961423	+	0.275072i	$0.911298\pi$
$354$		0			0
$355$	6.74784	−	29.3978i	0.358138	−	1.56027i
$356$	−24.0273	+	13.8722i	−1.27345	+	0.735225i
$357$		0			0
$358$	−11.1180	+	2.97905i	−0.587604	+	0.157448i
$359$	−6.83504	+	3.94621i	−0.360739	+	0.208273i	−0.669405	−	0.742898i	$-0.733451\pi$
$359$	−6.83504	+	3.94621i	−0.360739	+	0.208273i	0.308666	+	0.951171i	$0.400118\pi$
$360$		0			0
$361$	−3.80199	+	6.58524i	−0.200105	+	0.346591i
$362$	26.5511	+	26.5511i	1.39549	+	1.39549i
$363$		0			0
$364$	4.92097	+	33.8536i	0.257929	+	1.77441i
$365$	2.46652	−	0.0892589i	0.129103	−	0.00467203i
$366$		0			0
$367$	−2.33496	+	8.71417i	−0.121884	+	0.454876i	−0.999709	−	0.0241040i	$-0.992327\pi$
$367$	−2.33496	+	8.71417i	−0.121884	+	0.454876i	0.877826	+	0.478980i	$0.158993\pi$
$368$	−10.5923	+	2.83820i	−0.552162	+	0.147951i
$369$		0			0
$370$	12.0799	+	39.3335i	0.628005	+	2.04485i
$371$	29.1343	−	22.9846i	1.51258	−	1.19330i
$372$		0			0
$373$	3.20789	−	0.859552i	0.166098	−	0.0445059i	−0.174811	−	0.984602i	$-0.555932\pi$
$373$	3.20789	−	0.859552i	0.166098	−	0.0445059i	0.340910	+	0.940096i	$0.389265\pi$
$374$	−0.656142			−0.0339283
$375$		0			0
$376$			5.18326i			0.267306i
$377$	2.64729	+	2.64729i	0.136342	+	0.136342i
$378$		0			0
$379$		−	9.10326i		−	0.467603i	−0.972284	−	0.233802i	$-0.924883\pi$
$379$		−	9.10326i		−	0.467603i	0.972284	−	0.233802i	$-0.0751166\pi$
$380$	8.22378	+	26.7775i	0.421871	+	1.37366i
$381$		0			0
$382$	−1.27815	+	1.27815i	−0.0653958	+	0.0653958i
$383$	−5.27701	−	19.6941i	−0.269643	−	1.00632i	−0.959347	−	0.282229i	$-0.908926\pi$
$383$	−5.27701	−	19.6941i	−0.269643	−	1.00632i	0.689705	−	0.724091i	$-0.257740\pi$
$384$		0			0
$385$	−0.398405	+	0.338387i	−0.0203046	+	0.0172458i
$386$	−25.8573			−1.31610
$387$		0			0
$388$	−6.56360	−	24.4957i	−0.333216	−	1.24358i
$389$	10.4643	−	6.04159i	0.530563	−	0.306321i	−0.210682	−	0.977555i	$-0.567569\pi$
$389$	10.4643	−	6.04159i	0.530563	−	0.306321i	0.741246	+	0.671234i	$0.234235\pi$
$390$		0			0
$391$	−11.3268	+	6.53953i	−0.572821	+	0.330718i
$392$	−6.31380	+	0.169875i	−0.318895	+	0.00857997i
$393$		0			0
$394$			11.9748i			0.603282i
$395$	−7.74498	−	1.77775i	−0.389692	−	0.0894481i
$396$		0			0
$397$	−7.12359	+	26.5856i	−0.357523	+	1.33429i	0.519757	+	0.854314i	$0.326022\pi$
$397$	−7.12359	+	26.5856i	−0.357523	+	1.33429i	−0.877280	+	0.479979i	$0.840644\pi$
$398$	13.0208	+	48.5943i	0.652674	+	2.43581i
$399$		0			0
$400$	−13.3125	−	6.45127i	−0.665625	−	0.322564i
$401$	3.10574	−	5.37931i	0.155093	−	0.268630i	−0.778000	−	0.628265i	$-0.783765\pi$
$401$	3.10574	−	5.37931i	0.155093	−	0.268630i	0.933093	+	0.359635i	$0.117099\pi$
$402$		0			0
$403$	−6.71853	+	25.0739i	−0.334674	+	1.24902i
$404$	−13.9553	−	24.1713i	−0.694302	−	1.20257i
$405$		0			0
$406$	−3.07408	+	2.42520i	−0.152564	+	0.120361i
$407$	−0.199957	−	0.746251i	−0.00991151	−	0.0369903i
$408$		0			0
$409$	2.77080			0.137007			0.0685036	−	0.997651i	$-0.478178\pi$
$409$	2.77080			0.137007			0.0685036	+	0.997651i	$0.478178\pi$
$410$	12.3787	+	6.56181i	0.611343	+	0.324065i
$411$		0			0
$412$	−30.6734	+	8.21891i	−1.51117	+	0.404917i
$413$	8.41673	−	3.61970i	0.414160	−	0.178114i
$414$		0			0
$415$	−0.739264	+	0.0267527i	−0.0362891	+	0.00131324i
$416$	37.0265	−	21.3772i	1.81537	−	1.04811i
$417$		0			0
$418$	−0.248223	−	0.926381i	−0.0121410	−	0.0453108i
$419$	6.18341	+	10.7100i	0.302079	+	0.523217i	0.976607	−	0.215033i	$-0.0689859\pi$
$419$	6.18341	+	10.7100i	0.302079	+	0.523217i	−0.674527	+	0.738250i	$0.735653\pi$
$420$		0			0
$421$	5.64924	−	9.78478i	0.275327	−	0.476881i	−0.694890	−	0.719116i	$-0.744547\pi$
$421$	5.64924	−	9.78478i	0.275327	−	0.476881i	0.970218	+	0.242235i	$0.0778804\pi$
$422$	22.8294	+	6.11713i	1.11132	+	0.297777i
$423$		0			0
$424$	10.9601	+	6.32782i	0.532270	+	0.307306i
$425$	−17.3282	−	3.32276i	−0.840542	−	0.161177i
$426$		0			0
$427$	−1.42660	−	3.31721i	−0.0690380	−	0.160531i
$428$	7.57634	−	28.2753i	0.366216	−	1.36674i
$429$		0			0
$430$	7.92861	+	7.37480i	0.382351	+	0.355645i
$431$	−15.9132	+	27.5625i	−0.766513	+	1.32764i	0.172929	+	0.984934i	$0.444677\pi$
$431$	−15.9132	+	27.5625i	−0.766513	+	1.32764i	−0.939443	+	0.342706i	$0.888657\pi$
$432$		0			0
$433$	6.61149	−	6.61149i	0.317728	−	0.317728i	−0.530166	−	0.847894i	$-0.677870\pi$
$433$	6.61149	−	6.61149i	0.317728	−	0.317728i	0.847894	+	0.530166i	$0.177870\pi$
$434$	−25.2199	−	10.0512i	−1.21059	−	0.482474i
$435$		0			0
$436$	−16.2540	+	28.1528i	−0.778426	+	1.34827i
$437$	−13.5179	−	13.5179i	−0.646650	−	0.646650i
$438$		0			0
$439$	9.38697			0.448015			0.224008	−	0.974587i	$-0.428086\pi$
$439$	9.38697			0.448015			0.224008	+	0.974587i	$0.428086\pi$
$440$	−0.157505	−	0.0834912i	−0.00750875	−	0.00398029i
$441$		0			0
$442$	27.9553	−	27.9553i	1.32970	−	1.32970i
$443$	−17.9103	−	17.9103i	−0.850943	−	0.850943i	0.139307	−	0.990249i	$-0.455513\pi$
$443$	−17.9103	−	17.9103i	−0.850943	−	0.850943i	−0.990249	+	0.139307i	$0.955513\pi$
$444$		0			0
$445$	24.4177	−	7.49904i	1.15751	−	0.355489i
$446$	−46.4040	−	26.7914i	−2.19729	−	1.26861i
$447$		0			0
$448$	11.4808	+	26.6957i	0.542415	+	1.26125i
$449$		−	7.88064i		−	0.371910i	−0.982558	−	0.185955i	$-0.940462\pi$
$449$		−	7.88064i		−	0.371910i	0.982558	−	0.185955i	$-0.0595379\pi$
$450$		0			0
$451$	−0.227817	−	0.131530i	−0.0107275	−	0.00619352i
$452$	−35.0248	−	9.38487i	−1.64743	−	0.441427i
$453$		0			0
$454$	−6.61665	−	11.4604i	−0.310535	−	0.537862i
$455$	2.55706	−	31.3914i	0.119877	−	1.47165i
$456$		0			0
$457$	29.0388	−	29.0388i	1.35838	−	1.35838i	0.482461	−	0.875917i	$-0.339743\pi$
$457$	29.0388	−	29.0388i	1.35838	−	1.35838i	0.875917	−	0.482461i	$-0.160257\pi$
$458$	−1.86813	−	6.97197i	−0.0872921	−	0.325779i
$459$		0			0
$460$	−20.1157	+	0.727953i	−0.937901	+	0.0339410i
$461$	−14.4344	−	8.33373i	−0.672279	−	0.388140i	0.124661	−	0.992199i	$-0.460216\pi$
$461$	−14.4344	−	8.33373i	−0.672279	−	0.388140i	−0.796940	+	0.604059i	$0.793549\pi$
$462$		0			0
$463$	1.22034	−	4.55437i	0.0567140	−	0.211659i	−0.931754	−	0.363091i	$-0.881722\pi$
$463$	1.22034	−	4.55437i	0.0567140	−	0.211659i	0.988468	+	0.151431i	$0.0483882\pi$
$464$	1.80189	+	1.04032i	0.0836507	+	0.0482957i
$465$		0			0
$466$	−9.96219	−	17.2550i	−0.461490	−	0.799323i
$467$	−4.40276	+	16.4313i	−0.203735	+	0.760350i	0.786096	+	0.618104i	$0.212099\pi$
$467$	−4.40276	+	16.4313i	−0.203735	+	0.760350i	−0.989831	+	0.142246i	$0.954568\pi$
$468$		0			0
$469$	5.86441	−	14.7146i	0.270793	−	0.679458i
$470$	6.04754	−	26.3469i	0.278952	−	1.21529i
$471$		0			0
$472$	2.20943	+	2.20943i	0.101697	+	0.101697i
$473$	−0.143764	−	0.143764i	−0.00661025	−	0.00661025i
$474$		0			0
$475$	−1.86411	−	25.7221i	−0.0855314	−	1.18021i
$476$	14.0447	+	17.8024i	0.643737	+	0.815973i
$477$		0			0
$478$	0.868755	−	3.24224i	0.0397359	−	0.148297i
$479$	2.37092	+	4.10655i	0.108330	+	0.187633i	0.915094	−	0.403241i	$-0.132116\pi$
$479$	2.37092	+	4.10655i	0.108330	+	0.187633i	−0.806764	+	0.590874i	$0.798783\pi$
$480$		0			0
$481$	40.3137	+	23.2751i	1.83815	+	1.06125i
$482$	12.1713	−	45.4239i	0.554387	−	2.06900i
$483$		0			0
$484$	−23.1206	−	13.3487i	−1.05094	−	0.606758i
$485$	0.844365	+	23.3326i	0.0383407	+	1.05948i
$486$		0			0
$487$	−5.49403	−	20.5040i	−0.248958	−	0.929125i	−0.971352	−	0.237644i	$-0.923625\pi$
$487$	−5.49403	−	20.5040i	−0.248958	−	0.929125i	0.722394	−	0.691482i	$-0.243042\pi$
$488$	0.870783	−	0.870783i	0.0394185	−	0.0394185i
$489$		0			0
$490$	32.2917	+	6.50311i	1.45879	+	0.293780i
$491$	−9.50551	−	16.4640i	−0.428978	−	0.743011i	0.567805	−	0.823163i	$-0.307793\pi$
$491$	−9.50551	−	16.4640i	−0.428978	−	0.743011i	−0.996783	+	0.0801518i	$0.974459\pi$
$492$		0			0
$493$	2.39702	+	0.642279i	0.107956	+	0.0289268i
$494$	50.0447	+	28.8933i	2.25162	+	1.29997i
$495$		0			0
$496$			14.4265i			0.647767i
$497$	32.7852	−	14.0996i	1.47062	−	0.632454i
$498$		0			0
$499$	−36.8723	−	21.2882i	−1.65063	−	0.952992i	−0.976813	−	0.214093i	$-0.931320\pi$
$499$	−36.8723	−	21.2882i	−1.65063	−	0.952992i	−0.673817	−	0.738898i	$-0.735346\pi$
$500$	−21.1676	−	17.0085i	−0.946644	−	0.760643i
$501$		0			0
$502$	30.1488	+	30.1488i	1.34561	+	1.34561i
$503$	−7.74911	+	7.74911i	−0.345516	+	0.345516i	−0.858436	−	0.512920i	$-0.828564\pi$
$503$	−7.74911	+	7.74911i	−0.345516	+	0.345516i	0.512920	+	0.858436i	$0.328564\pi$
$504$		0			0
$505$	7.54397	+	24.5640i	0.335702	+	1.09308i
$506$	0.689167			0.0306372
$507$		0			0
$508$	−11.2843	−	11.2843i	−0.500659	−	0.500659i
$509$	2.24025	−	3.88022i	0.0992972	−	0.171988i	−0.812097	−	0.583523i	$-0.801674\pi$
$509$	2.24025	−	3.88022i	0.0992972	−	0.171988i	0.911394	+	0.411535i	$0.135007\pi$
$510$		0			0
$511$	1.80878	+	2.29274i	0.0800159	+	0.101425i
$512$	20.5769	−	20.5769i	0.909378	−	0.909378i
$513$		0			0
$514$	8.46403	−	14.6601i	0.373333	−	0.646631i
$515$	29.2170	−	1.05731i	1.28745	−	0.0465907i
$516$		0			0
$517$	−0.131366	+	0.490263i	−0.00577745	+	0.0215617i
$518$	−29.1157	+	39.0198i	−1.27927	+	1.71443i
$519$		0			0
$520$	10.2678	−	3.15339i	0.450271	−	0.138285i
$521$	−25.1653	−	14.5292i	−1.10251	−	0.636534i	−0.165631	−	0.986188i	$-0.552966\pi$
$521$	−25.1653	−	14.5292i	−1.10251	−	0.636534i	−0.936879	+	0.349653i	$0.886299\pi$
$522$		0			0
$523$	6.48593	+	1.73790i	0.283610	+	0.0759931i	0.397820	−	0.917464i	$-0.369767\pi$
$523$	6.48593	+	1.73790i	0.283610	+	0.0759931i	−0.114210	+	0.993457i	$0.536434\pi$
$524$	23.2731	−	40.3102i	1.01669	−	1.76096i
$525$		0			0
$526$	−22.0233	−	38.1455i	−0.960263	−	1.66322i
$527$	4.45334	+	16.6201i	0.193991	+	0.723983i
$528$		0			0
$529$	−8.02169	+	4.63132i	−0.348769	+	0.201362i
$530$	−48.3280	−	44.9524i	−2.09924	−	1.95261i
$531$		0			0
$532$	−19.8214	+	26.5639i	−0.859366	+	1.15169i
$533$	15.3102	−	4.10236i	0.663158	−	0.177693i
$534$		0			0
$535$	−12.6223	+	23.8117i	−0.545709	+	1.02947i
$536$	5.40208			0.233335
$537$		0			0
$538$	4.02616	+	15.0258i	0.173580	+	0.647809i
$539$	−0.601501	−	0.143950i	−0.0259085	−	0.00620038i
$540$		0			0
$541$	−12.0145	−	20.8098i	−0.516544	−	0.894681i	−0.999815	−	0.0192104i	$-0.993885\pi$
$541$	−12.0145	−	20.8098i	−0.516544	−	0.894681i	0.483271	−	0.875471i	$-0.339449\pi$
$542$	0.424587	−	1.58458i	0.0182376	−	0.0680636i
$543$		0			0
$544$	14.1698	−	24.5428i	0.607525	−	1.05226i
$545$	20.3838	−	21.9145i	0.873146	−	0.938714i
$546$		0			0
$547$	−1.65315	−	6.16965i	−0.0706837	−	0.263795i	0.921536	−	0.388292i	$-0.126935\pi$
$547$	−1.65315	−	6.16965i	−0.0706837	−	0.263795i	−0.992220	+	0.124497i	$0.960268\pi$
$548$	−8.98785	+	33.5431i	−0.383942	+	1.43289i
$549$		0			0
$550$	0.703195	+	0.608160i	0.0299844	+	0.0259320i
$551$			3.62724i			0.154526i
$552$		0			0
$553$	−3.71460	−	8.63741i	−0.157961	−	0.367300i
$554$	17.3817	−	10.0354i	0.738479	−	0.426361i
$555$		0			0
$556$	36.3139	−	20.9658i	1.54005	−	0.889149i
$557$	−5.29513	−	19.7617i	−0.224362	−	0.837329i	−0.982659	−	0.185421i	$-0.940635\pi$
$557$	−5.29513	−	19.7617i	−0.224362	−	0.837329i	0.758298	−	0.651909i	$-0.226031\pi$
$558$		0			0
$559$	12.2502			0.518130
$560$	−3.14265	−	17.2192i	−0.132801	−	0.727645i
$561$		0			0
$562$	10.3473	+	38.6166i	0.436474	+	1.62894i
$563$	−15.0600	+	15.0600i	−0.634705	+	0.634705i	−0.949245	−	0.314539i	$-0.898150\pi$
$563$	−15.0600	+	15.0600i	−0.634705	+	0.634705i	0.314539	+	0.949245i	$0.398150\pi$
$564$		0			0
$565$	29.4958	+	15.6353i	1.24090	+	0.657783i
$566$		−	47.2552i		−	1.98628i
$567$		0			0
$568$	8.60627	+	8.60627i	0.361111	+	0.361111i
$569$			28.3030i			1.18652i	0.805009	+	0.593262i	$0.202160\pi$
$569$			28.3030i			1.18652i	−0.805009	+	0.593262i	$0.797840\pi$
$570$		0			0
$571$	−40.0696			−1.67686			−0.838430	−	0.545010i	$-0.816526\pi$
$571$	−40.0696			−1.67686			−0.838430	+	0.545010i	$0.816526\pi$
$572$	−1.10350	+	0.295682i	−0.0461397	+	0.0123631i
$573$		0			0
$574$	2.38462	+	16.4049i	0.0995320	+	0.684727i
$575$	18.2004	+	3.49000i	0.759008	+	0.145543i
$576$		0			0
$577$	1.72908	−	0.463305i	0.0719825	−	0.0192876i	−0.222648	−	0.974899i	$-0.571470\pi$
$577$	1.72908	−	0.463305i	0.0719825	−	0.0192876i	0.294631	+	0.955611i	$0.404803\pi$
$578$	−2.47702	+	9.24435i	−0.103030	+	0.384514i
$579$		0			0
$580$	2.79648	+	2.60115i	0.116117	+	0.108007i
$581$	−0.542129	−	0.687179i	−0.0224913	−	0.0285090i
$582$		0			0
$583$	0.876296	+	0.876296i	0.0362925	+	0.0362925i
$584$	−0.497970	+	0.862510i	−0.0206062	+	0.0356909i
$585$		0			0
$586$	17.2999	−	9.98809i	0.714652	−	0.412604i
$587$	−6.57314	+	1.76127i	−0.271302	+	0.0726953i	−0.391905	−	0.920006i	$-0.628184\pi$
$587$	−6.57314	+	1.76127i	−0.271302	+	0.0726953i	0.120603	+	0.992701i	$0.461517\pi$
$588$		0			0
$589$	−21.7805	+	12.5750i	−0.897452	+	0.518144i
$590$	−8.65285	−	13.8085i	−0.356232	−	0.568488i
$591$		0			0
$592$	24.9889	+	6.69576i	1.02704	+	0.275194i
$593$	23.7495	+	6.36367i	0.975277	+	0.261325i	0.711054	−	0.703137i	$-0.248218\pi$
$593$	23.7495	+	6.36367i	0.975277	+	0.261325i	0.264223	+	0.964462i	$0.414885\pi$
$594$		0			0
$595$	−8.93596	−	18.8674i	−0.366339	−	0.773488i
$596$	3.43102	−	5.94269i	0.140540	−	0.243422i
$597$		0			0
$598$	−29.3623	+	29.3623i	−1.20071	+	1.20071i
$599$			23.0695i			0.942593i	0.881975	+	0.471296i	$0.156214\pi$
$599$			23.0695i			0.942593i	−0.881975	+	0.471296i	$0.843786\pi$
$600$		0			0
$601$	−17.9685	−	10.3741i	−0.732951	−	0.423169i	0.0865498	−	0.996248i	$-0.472416\pi$
$601$	−17.9685	−	10.3741i	−0.732951	−	0.423169i	−0.819501	+	0.573078i	$0.805749\pi$
$602$	−1.50133	+	12.7239i	−0.0611897	+	0.518586i
$603$		0			0
$604$	−12.4097	+	7.16472i	−0.504942	+	0.291528i
$605$	17.9974	+	16.7403i	0.731697	+	0.680589i
$606$		0			0
$607$	−30.5526	+	8.18655i	−1.24009	+	0.332282i	−0.818501	−	0.574505i	$-0.805195\pi$
$607$	−30.5526	+	8.18655i	−1.24009	+	0.332282i	−0.421591	+	0.906786i	$0.638528\pi$
$608$	40.0116	+	10.7211i	1.62268	+	0.434797i
$609$		0			0
$610$	−5.44223	+	3.41027i	−0.220350	+	0.138078i
$611$	−15.2910	−	26.4848i	−0.618608	−	1.07146i
$612$		0			0
$613$	−22.5570	+	6.04412i	−0.911067	+	0.244120i	−0.683763	−	0.729704i	$-0.739658\pi$
$613$	−22.5570	+	6.04412i	−0.911067	+	0.244120i	−0.227304	+	0.973824i	$0.572991\pi$
$614$	−11.9789			−0.483430
$615$		0			0
$616$	−0.0303414	−	0.208733i	−0.00122249	−	0.00841008i
$617$	−0.966179	−	0.258887i	−0.0388969	−	0.0104224i	0.239318	−	0.970941i	$-0.423076\pi$
$617$	−0.966179	−	0.258887i	−0.0388969	−	0.0104224i	−0.278215	+	0.960519i	$0.589743\pi$
$618$		0			0
$619$	−6.24857	−	10.8228i	−0.251151	−	0.435007i	0.712692	−	0.701477i	$-0.247476\pi$
$619$	−6.24857	−	10.8228i	−0.251151	−	0.435007i	−0.963843	+	0.266471i	$0.914142\pi$
$620$	−5.92425	+	25.8098i	−0.237924	+	1.03655i
$621$		0			0
$622$	−8.30415	−	8.30415i	−0.332966	−	0.332966i
$623$	24.2230	+	18.0746i	0.970472	+	0.724143i
$624$		0			0
$625$	15.4911	+	19.6221i	0.619644	+	0.784883i
$626$			68.2712i			2.72866i
$627$		0			0
$628$	−20.2602	+	20.2602i	−0.808468	+	0.808468i
$629$	30.8556			1.23029
$630$		0			0
$631$	26.4557			1.05318			0.526592	−	0.850118i	$-0.323470\pi$
$631$	26.4557			1.05318			0.526592	+	0.850118i	$0.323470\pi$
$632$	2.26736	−	2.26736i	0.0901906	−	0.0901906i
$633$		0			0
$634$		−	13.4936i		−	0.535899i
$635$	7.80150	+	12.4499i	0.309593	+	0.494060i
$636$		0			0
$637$	31.7604	−	19.4942i	1.25839	−	0.772388i
$638$	−0.0924615	−	0.0924615i	−0.00366058	−	0.00366058i
$639$		0			0
$640$	13.3630	−	8.37370i	0.528221	−	0.330999i
$641$	23.8544	+	41.3170i	0.942192	+	1.63193i	0.761277	+	0.648426i	$0.224573\pi$
$641$	23.8544	+	41.3170i	0.942192	+	1.63193i	0.180915	+	0.983499i	$0.442094\pi$
$642$		0			0
$643$	22.5788	+	6.04998i	0.890422	+	0.238588i	0.674898	−	0.737911i	$-0.264188\pi$
$643$	22.5788	+	6.04998i	0.890422	+	0.238588i	0.215524	+	0.976499i	$0.430854\pi$
$644$	−14.7516	−	18.6985i	−0.581294	−	0.736823i
$645$		0			0
$646$	38.3035			1.50703
$647$	7.74958	−	2.07649i	0.304667	−	0.0816354i	−0.103246	−	0.994656i	$-0.532923\pi$
$647$	7.74958	−	2.07649i	0.304667	−	0.0816354i	0.407914	+	0.913020i	$0.366256\pi$
$648$		0			0
$649$	0.152984	+	0.264977i	0.00600516	+	0.0104012i
$650$	−55.8710	+	4.04905i	−2.19144	+	0.158817i
$651$		0			0
$652$	−23.5828	−	6.31900i	−0.923575	−	0.247471i
$653$	16.7473	−	4.48742i	0.655372	−	0.175606i	0.0842153	−	0.996448i	$-0.473162\pi$
$653$	16.7473	−	4.48742i	0.655372	−	0.175606i	0.571156	+	0.820841i	$0.306495\pi$
$654$		0			0
$655$	−29.1863	+	31.3780i	−1.14040	+	1.22604i
$656$	7.62868	−	4.40442i	0.297850	−	0.171964i
$657$		0			0
$658$	29.3828	−	12.6363i	1.14546	−	0.492616i
$659$	27.0155	+	15.5974i	1.05237	+	0.607588i	0.923313	−	0.384049i	$-0.125471\pi$
$659$	27.0155	+	15.5974i	1.05237	+	0.607588i	0.129060	+	0.991637i	$0.458804\pi$
$660$		0			0
$661$			15.2408i			0.592799i	0.955064	+	0.296400i	$0.0957860\pi$
$661$			15.2408i			0.592799i	−0.955064	+	0.296400i	$0.904214\pi$
$662$	−8.82535	+	8.82535i	−0.343007	+	0.343007i
$663$		0			0
$664$	0.149252	−	0.258511i	0.00579208	−	0.0100322i
$665$	23.2576	−	19.7540i	0.901892	−	0.766028i
$666$		0			0
$667$	−2.51767	−	0.674607i	−0.0974844	−	0.0261209i
$668$	2.54934	+	0.683095i	0.0986371	+	0.0264297i
$669$		0			0
$670$	−27.4592	−	6.30285i	−1.06084	−	0.243500i
$671$	0.104433	−	0.0602944i	0.00403159	−	0.00232764i
$672$		0			0
$673$	38.5740	−	10.3359i	1.48692	−	0.398418i	0.578223	−	0.815879i	$-0.303746\pi$
$673$	38.5740	−	10.3359i	1.48692	−	0.398418i	0.908695	+	0.417461i	$0.137080\pi$
$674$	17.6044	−	10.1639i	0.678098	−	0.391500i
$675$		0			0
$676$	18.6306	−	32.2692i	0.716563	−	1.24112i
$677$	−0.290204	−	0.290204i	−0.0111534	−	0.0111534i	0.701508	−	0.712662i	$-0.252510\pi$
$677$	−0.290204	−	0.290204i	−0.0111534	−	0.0111534i	−0.712662	+	0.701508i	$0.752510\pi$
$678$		0			0
$679$	−21.6887	+	17.1106i	−0.832335	+	0.656645i
$680$	4.84901	−	5.21314i	0.185951	−	0.199915i
$681$		0			0
$682$	0.234657	−	0.875753i	0.00898549	−	0.0335343i
$683$	−29.7361	+	7.96776i	−1.13782	+	0.304878i	−0.778074	−	0.628173i	$-0.783803\pi$
$683$	−29.7361	+	7.96776i	−1.13782	+	0.304878i	−0.359746	+	0.933050i	$0.617137\pi$
$684$		0			0
$685$	14.9739	−	28.2480i	0.572123	−	1.07930i
$686$	16.3555	+	35.3774i	0.624455	+	1.35072i
$687$		0			0
$688$	6.57613	−	1.76207i	0.250713	−	0.0671782i
$689$	−74.6701			−2.84471
$690$		0			0
$691$		−	20.2512i		−	0.770393i	−0.922835	−	0.385197i	$-0.874134\pi$
$691$		−	20.2512i		−	0.770393i	0.922835	−	0.385197i	$-0.125866\pi$
$692$	−17.5790	−	17.5790i	−0.668252	−	0.668252i
$693$		0			0
$694$		−	64.7988i		−	2.45973i
$695$	−36.9038	+	11.3337i	−1.39984	+	0.429913i
$696$		0			0
$697$	7.42906	−	7.42906i	0.281396	−	0.281396i
$698$	5.67396	+	21.1755i	0.214763	+	0.801505i
$699$		0			0
$700$	1.44872	−	32.0967i	0.0547564	−	1.21314i
$701$	33.6028			1.26916			0.634581	−	0.772856i	$-0.281173\pi$
$701$	33.6028			1.26916			0.634581	+	0.772856i	$0.281173\pi$
$702$		0			0
$703$	11.6729	+	43.5638i	0.440251	+	1.64304i
$704$	−0.840438	+	0.485227i	−0.0316752	+	0.0182877i
$705$		0			0
$706$	−58.7229	+	33.9037i	−2.21007	+	1.27598i
$707$	−18.1829	+	24.3681i	−0.683837	+	0.916456i
$708$		0			0
$709$		−	5.52172i		−	0.207372i	−0.994610	−	0.103686i	$-0.966936\pi$
$709$		−	5.52172i		−	0.207372i	0.994610	−	0.103686i	$-0.0330638\pi$
$710$	−33.7050	−	53.7876i	−1.26492	−	2.01861i
$711$		0			0
$712$	−2.66770	+	9.95601i	−0.0999765	+	0.373117i
$713$	−4.67749	−	17.4566i	−0.175173	−	0.653756i
$714$		0			0
$715$	1.05110	−	0.0380376i	0.0393091	−	0.00142253i
$716$	−6.64194	+	11.5042i	−0.248221	+	0.429931i
$717$		0			0
$718$	−4.29880	+	16.0433i	−0.160430	+	0.598732i
$719$	12.7748	+	22.1267i	0.476421	+	0.825186i	0.999635	−	0.0270154i	$-0.00860032\pi$
$719$	12.7748	+	22.1267i	0.476421	+	0.825186i	−0.523214	+	0.852202i	$0.675267\pi$
$720$		0			0
$721$	21.4258	+	27.1585i	0.797940	+	1.01143i
$722$	4.14169	+	15.4570i	0.154138	+	0.575250i
$723$		0			0
$724$	43.3351			1.61054
$725$	−1.97360	−	2.91007i	−0.0732978	−	0.108077i
$726$		0			0
$727$	−22.0507	+	5.90847i	−0.817816	+	0.219133i	−0.643391	−	0.765537i	$-0.722473\pi$
$727$	−22.0507	+	5.90847i	−0.817816	+	0.219133i	−0.174425	+	0.984671i	$0.555807\pi$
$728$	10.1859	+	7.60046i	0.377514	+	0.281692i
$729$		0			0
$730$	3.53755	−	3.80320i	0.130930	−	0.140763i
$731$	7.03213	−	4.06000i	0.260093	−	0.150165i
$732$		0			0
$733$	9.97964	+	37.2445i	0.368607	+	1.37566i	0.862465	+	0.506116i	$0.168919\pi$
$733$	9.97964	+	37.2445i	0.368607	+	1.37566i	−0.493859	+	0.869542i	$0.664414\pi$
$734$	9.49278	+	16.4420i	0.350385	+	0.606884i
$735$		0			0
$736$	−14.8830	+	25.7781i	−0.548594	+	0.950193i
$737$	0.510960	+	0.136911i	0.0188215	+	0.00504320i
$738$		0			0
$739$	15.5491	+	8.97729i	0.571984	+	0.330235i	0.757941	−	0.652323i	$-0.226205\pi$
$739$	15.5491	+	8.97729i	0.571984	+	0.330235i	−0.185958	+	0.982558i	$0.559539\pi$
$740$	41.9570	+	22.2409i	1.54237	+	0.817590i
$741$		0			0
$742$	9.15122	−	77.5571i	0.335952	−	2.84721i
$743$	−8.34823	+	31.1560i	−0.306267	+	1.14300i	0.625583	+	0.780158i	$0.284861\pi$
$743$	−8.34823	+	31.1560i	−0.306267	+	1.14300i	−0.931849	+	0.362845i	$0.881805\pi$
$744$		0			0
$745$	−4.30276	+	4.62587i	−0.157641	+	0.169479i
$746$	3.49451	−	6.05267i	0.127943	−	0.221604i
$747$		0			0
$748$	−0.535458	+	0.535458i	−0.0195783	+	0.0195783i
$749$	−31.5564	+	4.58705i	−1.15305	+	0.167607i
$750$		0			0
$751$	14.0791	−	24.3856i	0.513752	−	0.889845i	−0.486121	−	0.873892i	$-0.661588\pi$
$751$	14.0791	−	24.3856i	0.513752	−	0.889845i	0.999873	−	0.0159529i	$-0.00507819\pi$
$752$	−12.0180	−	12.0180i	−0.438252	−	0.438252i
$753$		0			0
$754$	7.87874			0.286927
$755$	12.6113	−	3.87311i	0.458971	−	0.140957i
$756$		0			0
$757$	−8.49483	+	8.49483i	−0.308750	+	0.308750i	−0.844424	−	0.535675i	$-0.820057\pi$
$757$	−8.49483	+	8.49483i	−0.308750	+	0.308750i	0.535675	+	0.844424i	$0.320057\pi$
$758$	−13.5464	−	13.5464i	−0.492026	−	0.492026i
$759$		0			0
$760$	9.19465	+	4.87396i	0.333525	+	0.176797i
$761$	22.0829	+	12.7496i	0.800505	+	0.462172i	0.843648	−	0.536897i	$-0.180404\pi$
$761$	22.0829	+	12.7496i	0.800505	+	0.462172i	−0.0431425	+	0.999069i	$0.513737\pi$
$762$		0			0
$763$	35.1685	+	4.14965i	1.27318	+	0.150227i
$764$			2.08612i			0.0754732i
$765$		0			0
$766$	−37.1589	−	21.4537i	−1.34261	−	0.775154i
$767$	−17.8074	−	4.77149i	−0.642990	−	0.172289i
$768$		0			0
$769$	17.8420	+	30.9033i	0.643401	+	1.11440i	0.984668	+	0.174436i	$0.0558103\pi$
$769$	17.8420	+	30.9033i	0.643401	+	1.11440i	−0.341268	+	0.939966i	$0.610856\pi$
$770$	−0.0893101	+	1.09640i	−0.00321851	+	0.0395117i
$771$		0			0
$772$	−21.1014	+	21.1014i	−0.759455	+	0.759455i
$773$	5.62676	+	20.9993i	0.202380	+	0.755294i	0.990232	+	0.139429i	$0.0445266\pi$
$773$	5.62676	+	20.9993i	0.202380	+	0.755294i	−0.787852	+	0.615865i	$0.788807\pi$
$774$		0			0
$775$	10.6320	−	21.9396i	0.381913	−	0.788095i
$776$	−8.15911	−	4.71066i	−0.292895	−	0.169103i
$777$		0			0
$778$	6.58140	−	24.5621i	0.235955	−	0.880595i
$779$	13.2993	+	7.67834i	0.476496	+	0.275105i
$780$		0			0
$781$	0.595911	+	1.03215i	0.0213234	+	0.0369332i
$782$	−7.12383	+	26.5865i	−0.254748	+	0.950731i
$783$		0			0
$784$	14.2454	−	15.0332i	0.508766	−	0.536900i
$785$	22.3530	−	14.0071i	0.797812	−	0.499934i
$786$		0			0
$787$	12.7179	+	12.7179i	0.453346	+	0.453346i	0.896463	−	0.443118i	$-0.146128\pi$
$787$	12.7179	+	12.7179i	0.453346	+	0.453346i	−0.443118	+	0.896463i	$0.646128\pi$
$788$	9.77230	+	9.77230i	0.348124	+	0.348124i
$789$		0			0
$790$	−14.1706	+	8.87971i	−0.504166	+	0.315926i
$791$	5.68201	+	39.0892i	0.202029	+	1.38985i
$792$		0			0
$793$	−1.88055	+	7.01830i	−0.0667802	+	0.249227i
$794$	28.9610	+	50.1619i	1.02779	+	1.78018i
$795$		0			0
$796$	50.2823	+	29.0305i	1.78221	+	1.02896i
$797$	−10.5307	+	39.3012i	−0.373017	+	1.39212i	0.483203	+	0.875509i	$0.339473\pi$
$797$	−10.5307	+	39.3012i	−0.373017	+	1.39212i	−0.856220	+	0.516611i	$0.827193\pi$
$798$		0			0
$799$	−17.5553	−	10.1356i	−0.621062	−	0.358571i
$800$	−37.9340	+	13.1692i	−1.34117	+	0.465603i
$801$		0			0
$802$	−3.38324	−	12.6264i	−0.119466	−	0.445854i
$803$	−0.0689605	+	0.0689605i	−0.00243356	+	0.00243356i
$804$		0			0
$805$	9.38573	+	19.8171i	0.330804	+	0.698459i
$806$	27.3142	+	47.3096i	0.962102	+	1.66641i
$807$		0			0
$808$	−10.0157	−	2.68369i	−0.352350	−	0.0944118i
$809$	−24.7124	−	14.2677i	−0.868840	−	0.501625i	−0.00187764	−	0.999998i	$-0.500598\pi$
$809$	−24.7124	−	14.2677i	−0.868840	−	0.501625i	−0.866963	+	0.498373i	$0.833931\pi$
$810$		0			0
$811$		−	48.5126i		−	1.70351i	−0.523941	−	0.851755i	$-0.675539\pi$
$811$		−	48.5126i		−	1.70351i	0.523941	−	0.851755i	$-0.324461\pi$
$812$	−0.529530	+	4.48780i	−0.0185829	+	0.157491i
$813$		0			0
$814$	−1.40803	−	0.812927i	−0.0493515	−	0.0284931i
$815$	19.8600	+	10.5275i	0.695667	+	0.368764i
$816$		0			0
$817$	8.39247	+	8.39247i	0.293615	+	0.293615i
$818$	4.12317	−	4.12317i	0.144163	−	0.144163i
$819$		0			0
$820$	15.4568	−	4.74703i	0.539776	−	0.165774i
$821$	−5.09172			−0.177702			−0.0888512	−	0.996045i	$-0.528320\pi$
$821$	−5.09172			−0.177702			−0.0888512	+	0.996045i	$0.528320\pi$
$822$		0			0
$823$	−20.6134	−	20.6134i	−0.718537	−	0.718537i	0.249769	−	0.968306i	$-0.419645\pi$
$823$	−20.6134	−	20.6134i	−0.718537	−	0.718537i	−0.968306	+	0.249769i	$0.919645\pi$
$824$	−5.89867	+	10.2168i	−0.205490	+	0.355919i
$825$		0			0
$826$	7.13837	−	17.9112i	0.248376	−	0.623209i
$827$	19.3594	−	19.3594i	0.673191	−	0.673191i	−0.285259	−	0.958450i	$-0.592080\pi$
$827$	19.3594	−	19.3594i	0.673191	−	0.673191i	0.958450	+	0.285259i	$0.0920797\pi$
$828$		0			0
$829$	−15.8644	+	27.4780i	−0.550994	+	0.954350i	0.447209	+	0.894430i	$0.352418\pi$
$829$	−15.8644	+	27.4780i	−0.550994	+	0.954350i	−0.998203	+	0.0599208i	$0.980915\pi$
$830$	−1.06027	+	1.13989i	−0.0368026	+	0.0395663i
$831$		0			0
$832$	15.1340	−	56.4807i	0.524675	−	1.95812i
$833$	11.7709	−	21.7165i	0.407838	−	0.752434i
$834$		0			0
$835$	−2.14690	−	1.13805i	−0.0742967	−	0.0393837i
$836$	−0.958561	−	0.553425i	−0.0331525	−	0.0191406i
$837$		0			0
$838$	25.1387	+	6.73589i	0.868401	+	0.232687i
$839$	−6.71273	+	11.6268i	−0.231749	+	0.401401i	−0.958323	−	0.285687i	$-0.907778\pi$
$839$	−6.71273	+	11.6268i	−0.231749	+	0.401401i	0.726574	+	0.687088i	$0.241112\pi$
$840$		0			0
$841$	−14.2527	−	24.6864i	−0.491473	−	0.851257i
$842$	−6.15400	−	22.9670i	−0.212081	−	0.791496i
$843$		0			0
$844$	23.6225	−	13.6384i	0.813119	−	0.469454i
$845$	−23.3642	+	25.1188i	−0.803755	+	0.864112i
$846$		0			0
$847$	−3.40791	+	28.8822i	−0.117097	+	0.992406i
$848$	−40.0841	+	10.7405i	−1.37650	+	0.368831i
$849$		0			0
$850$	−30.7303	+	20.8412i	−1.05404	+	0.714848i
$851$	−32.4086			−1.11095
$852$		0			0
$853$	−10.8745	−	40.5841i	−0.372335	−	1.38957i	−0.857199	−	0.514985i	$-0.827798\pi$
$853$	−10.8745	−	40.5841i	−0.372335	−	1.38957i	0.484864	−	0.874590i	$-0.338869\pi$
$854$	−7.05917	−	2.81338i	−0.241560	−	0.0962720i
$855$		0			0
$856$	−5.43750	−	9.41803i	−0.185850	−	0.321902i
$857$	−5.55913	+	20.7470i	−0.189896	+	0.708703i	0.803633	+	0.595125i	$0.202898\pi$
$857$	−5.55913	+	20.7470i	−0.189896	+	0.708703i	−0.993529	+	0.113577i	$0.963769\pi$
$858$		0			0
$859$	1.77757	−	3.07884i	0.0606499	−	0.105049i	−0.834106	−	0.551604i	$-0.814016\pi$
$859$	1.77757	−	3.07884i	0.0606499	−	0.105049i	0.894756	+	0.446555i	$0.147349\pi$
$860$	12.4887	−	0.451943i	0.425860	−	0.0154111i
$861$		0			0
$862$	17.3351	+	64.6953i	0.590435	+	2.20353i
$863$	13.0583	−	48.7342i	0.444509	−	1.65893i	−0.272719	−	0.962094i	$-0.587923\pi$
$863$	13.0583	−	48.7342i	0.444509	−	1.65893i	0.717229	−	0.696838i	$-0.245410\pi$
$864$		0			0
$865$	12.1534	+	19.3948i	0.413228	+	0.659444i
$866$		−	19.6768i		−	0.668646i
$867$		0			0
$868$	−28.7838	+	12.3787i	−0.976984	+	0.420162i
$869$	0.271924	−	0.156995i	0.00922439	−	0.00532570i
$870$		0			0
$871$	−27.6029	+	15.9366i	−0.935289	+	0.539989i
$872$	3.12574	+	11.6654i	0.105851	+	0.395041i
$873$		0			0
$874$	−40.2314			−1.36085
$875$	−7.91090	+	28.5029i	−0.267437	+	0.963575i
$876$		0			0
$877$	11.1744	+	41.7033i	0.377331	+	1.40822i	0.849908	+	0.526931i	$0.176657\pi$
$877$	11.1744	+	41.7033i	0.377331	+	1.40822i	−0.472577	+	0.881289i	$0.656676\pi$
$878$	13.9685	−	13.9685i	0.471415	−	0.471415i
$879$		0			0
$880$	0.558779	−	0.171610i	0.0188364	−	0.00578496i
$881$		−	44.2073i		−	1.48938i	−0.667409	−	0.744691i	$-0.732597\pi$
$881$		−	44.2073i		−	1.48938i	0.667409	−	0.744691i	$-0.267403\pi$
$882$		0			0
$883$	−15.1931	−	15.1931i	−0.511288	−	0.511288i	0.403633	−	0.914921i	$-0.367747\pi$
$883$	−15.1931	−	15.1931i	−0.511288	−	0.511288i	−0.914921	+	0.403633i	$0.867747\pi$
$884$		−	45.6270i		−	1.53460i
$885$		0			0
$886$	−53.3038			−1.79078
$887$	−30.5301	+	8.18050i	−1.02510	+	0.274674i	−0.731925	−	0.681385i	$-0.761378\pi$
$887$	−30.5301	+	8.18050i	−1.02510	+	0.274674i	−0.293174	+	0.956059i	$0.594711\pi$
$888$		0			0
$889$	−6.43603	+	16.1489i	−0.215857	+	0.541616i
$890$	25.1762	−	47.4946i	0.843910	−	1.59202i
$891$		0			0
$892$	−59.7326	+	16.0053i	−2.00000	+	0.535897i
$893$	7.66872	−	28.6200i	0.256624	−	0.957733i
$894$		0			0
$895$	8.32951	−	8.95501i	0.278425	−	0.299333i
$896$	17.3333	+	6.90808i	0.579066	+	0.230783i
$897$		0			0
$898$	−11.7270	−	11.7270i	−0.391335	−	0.391335i
$899$	−1.71450	+	2.96960i	−0.0571818	+	0.0990418i
$900$		0			0
$901$	−42.8637	+	24.7474i	−1.42800	+	0.824454i
$902$	−0.534737	+	0.143282i	−0.0178048	+	0.00477078i
$903$		0			0
$904$	−11.6662	+	6.73548i	−0.388012	+	0.224019i
$905$	−38.8859	−	8.92567i	−1.29261	−	0.296699i
$906$		0			0
$907$	−15.1798	−	4.06743i	−0.504039	−	0.135057i	−0.00216486	−	0.999998i	$-0.500689\pi$
$907$	−15.1798	−	4.06743i	−0.504039	−	0.135057i	−0.501874	+	0.864941i	$0.667356\pi$
$908$	−14.7521	−	3.95282i	−0.489566	−	0.131179i
$909$		0			0
$910$	−42.9078	−	50.5180i	−1.42238	−	1.67466i
$911$	12.1778	−	21.0926i	0.403468	−	0.698828i	−0.590673	−	0.806911i	$-0.701138\pi$
$911$	12.1778	−	21.0926i	0.403468	−	0.698828i	0.994142	+	0.108083i	$0.0344712\pi$
$912$		0			0
$913$	0.0206688	−	0.0206688i	0.000684038	−	0.000684038i
$914$		−	86.4241i		−	2.85865i
$915$		0			0
$916$	−7.21415	−	4.16509i	−0.238362	−	0.137618i
$917$	−50.3555	−	5.94162i	−1.66289	−	0.196209i
$918$		0			0
$919$	−1.01486	+	0.585929i	−0.0334771	+	0.0193280i	−0.516645	−	0.856200i	$-0.672819\pi$
$919$	−1.01486	+	0.585929i	−0.0334771	+	0.0193280i	0.483168	+	0.875528i	$0.339486\pi$
$920$	−5.09307	+	5.47553i	−0.167914	+	0.180523i
$921$		0			0
$922$	−33.8808	+	9.07834i	−1.11581	+	0.298979i
$923$	−69.3644	−	18.5861i	−2.28316	−	0.611770i
$924$		0			0
$925$	−33.0683	−	28.5992i	−1.08728	−	0.940336i
$926$	−4.96130	−	8.59322i	−0.163038	−	0.282391i
$927$		0			0
$928$	5.45526	−	1.46173i	0.179078	−	0.0479837i
$929$	1.34923			0.0442668			0.0221334	−	0.999755i	$-0.492954\pi$
$929$	1.34923			0.0442668			0.0221334	+	0.999755i	$0.492954\pi$
$930$		0			0
$931$	35.1138	+	8.40338i	1.15081	+	0.275410i
$932$	−22.2112	−	5.95147i	−0.727551	−	0.194947i
$933$		0			0
$934$	17.8994	+	31.0027i	0.585687	+	1.01444i
$935$	0.590770	−	0.370195i	0.0193202	−	0.0121067i
$936$		0			0
$937$	25.3539	+	25.3539i	0.828277	+	0.828277i	0.987278	−	0.159001i	$-0.0508274\pi$
$937$	25.3539	+	25.3539i	0.828277	+	0.828277i	−0.159001	+	0.987278i	$0.550827\pi$
$938$	−13.1698	−	30.6232i	−0.430010	−	0.999884i
$939$		0			0
$940$	−16.5657	−	26.4362i	−0.540314	−	0.862252i
$941$			29.5355i			0.962829i	0.876493	+	0.481414i	$0.159877\pi$
$941$			29.5355i			0.962829i	−0.876493	+	0.481414i	$0.840123\pi$
$942$		0			0
$943$	−7.80298	+	7.80298i	−0.254100	+	0.254100i
$944$	−10.2457			−0.333468
$945$		0			0
$946$	−0.427863			−0.0139110
$947$	15.2295	−	15.2295i	0.494893	−	0.494893i	−0.414951	−	0.909844i	$-0.636201\pi$
$947$	15.2295	−	15.2295i	0.494893	−	0.494893i	0.909844	+	0.414951i	$0.136201\pi$
$948$		0			0
$949$		−	5.87620i		−	0.190749i
$950$	−41.0504	−	35.5025i	−1.33185	−	1.15185i
$951$		0			0
$952$	8.36607	+	0.987141i	0.271146	+	0.0319934i
$953$	7.79646	+	7.79646i	0.252552	+	0.252552i	0.822016	−	0.569464i	$-0.192849\pi$
$953$	7.79646	+	7.79646i	0.252552	+	0.252552i	−0.569464	+	0.822016i	$0.692849\pi$
$954$		0			0
$955$	0.429675	−	1.87194i	0.0139040	−	0.0605744i
$956$	−1.93693	−	3.35486i	−0.0626448	−	0.108504i
$957$		0			0
$958$	9.63897	+	2.58275i	0.311421	+	0.0834450i
$959$	37.4356	−	5.44164i	1.20886	−	0.175720i
$960$		0			0
$961$	7.22449			0.233048
$962$	94.6252	−	25.3547i	3.05084	−	0.817469i
$963$		0			0
$964$	−27.1365	−	47.0018i	−0.874007	−	1.51382i
$965$	23.2811	−	14.5887i	0.749445	−	0.469626i
$966$		0			0
$967$	−36.4432	−	9.76493i	−1.17193	−	0.314019i	−0.380212	−	0.924899i	$-0.624149\pi$
$967$	−36.4432	−	9.76493i	−1.17193	−	0.314019i	−0.791723	+	0.610880i	$0.790816\pi$
$968$	−9.58028	+	2.56703i	−0.307922	+	0.0825074i
$969$		0			0
$970$	35.9772	+	33.4642i	1.15516	+	1.07447i
$971$	−2.41770	+	1.39586i	−0.0775877	+	0.0447953i	−0.538292	−	0.842758i	$-0.680930\pi$
$971$	−2.41770	+	1.39586i	−0.0775877	+	0.0447953i	0.460704	+	0.887554i	$0.347597\pi$
$972$		0			0
$973$	−36.6095	−	27.3171i	−1.17365	−	0.875747i
$974$	−38.6871	−	22.3360i	−1.23962	−	0.715692i
$975$		0			0
$976$			4.03803i			0.129254i
$977$	11.2827	−	11.2827i	0.360964	−	0.360964i	−0.503204	−	0.864168i	$-0.667845\pi$
$977$	11.2827	−	11.2827i	0.360964	−	0.360964i	0.864168	+	0.503204i	$0.167845\pi$
$978$		0			0
$979$	−0.504654	+	0.874086i	−0.0161288	+	0.0279359i
$980$	31.6593	−	21.0453i	1.01132	−	0.672268i
$981$		0			0
$982$	−38.6447	−	10.3548i	−1.23320	−	0.330436i
$983$	−0.687058	−	0.184097i	−0.0219137	−	0.00587177i	0.247846	−	0.968800i	$-0.420277\pi$
$983$	−0.687058	−	0.184097i	−0.0219137	−	0.00587177i	−0.269759	+	0.962928i	$0.586944\pi$
$984$		0			0
$985$	−6.75618	−	10.7818i	−0.215270	−	0.343535i
$986$	4.52271	−	2.61119i	0.144033	−	0.0831572i
$987$		0			0
$988$	64.4190	−	17.2610i	2.04944	−	0.549146i
$989$	−7.38608	+	4.26435i	−0.234864	+	0.135599i
$990$		0			0
$991$	−22.9124	+	39.6855i	−0.727837	+	1.26065i	0.229959	+	0.973200i	$0.426141\pi$
$991$	−22.9124	+	39.6855i	−0.727837	+	1.26065i	−0.957796	+	0.287450i	$0.907192\pi$
$992$	27.6897	+	27.6897i	0.879149	+	0.879149i
$993$		0			0
$994$	27.8057	−	69.7684i	0.881943	−	2.21292i
$995$	−39.1404	−	36.4065i	−1.24083	−	1.15416i
$996$		0			0
$997$	1.95162	−	7.28356i	0.0618086	−	0.230673i	−0.928111	−	0.372304i	$-0.878568\pi$
$997$	1.95162	−	7.28356i	0.0618086	−	0.230673i	0.989920	+	0.141631i	$0.0452347\pi$
$998$	−86.5474	+	23.1903i	−2.73961	+	0.734076i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bv.e.73.34		160
3.2	odd	2		315.2.bs.e.178.7	yes	160
5.2	odd	4	inner	945.2.bv.e.262.34		160
7.5	odd	6		945.2.cj.e.208.7		160
9.4	even	3		945.2.cj.e.388.34		160
9.5	odd	6		315.2.cg.e.283.7	yes	160
15.2	even	4		315.2.bs.e.52.7	✓	160
21.5	even	6		315.2.cg.e.313.34	yes	160
35.12	even	12		945.2.cj.e.397.34		160
45.22	odd	12		945.2.cj.e.577.7		160
45.32	even	12		315.2.cg.e.157.34	yes	160
63.5	even	6		315.2.bs.e.103.7	yes	160
63.40	odd	6	inner	945.2.bv.e.523.34		160
105.47	odd	12		315.2.cg.e.187.7	yes	160
315.257	odd	12		315.2.bs.e.292.7	yes	160
315.292	even	12	inner	945.2.bv.e.712.34		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.7	✓	160	15.2	even	4
315.2.bs.e.103.7	yes	160	63.5	even	6
315.2.bs.e.178.7	yes	160	3.2	odd	2
315.2.bs.e.292.7	yes	160	315.257	odd	12
315.2.cg.e.157.34	yes	160	45.32	even	12
315.2.cg.e.187.7	yes	160	105.47	odd	12
315.2.cg.e.283.7	yes	160	9.5	odd	6
315.2.cg.e.313.34	yes	160	21.5	even	6
945.2.bv.e.73.34		160	1.1	even	1	trivial
945.2.bv.e.262.34		160	5.2	odd	4	inner
945.2.bv.e.523.34		160	63.40	odd	6	inner
945.2.bv.e.712.34		160	315.292	even	12	inner
945.2.cj.e.208.7		160	7.5	odd	6
945.2.cj.e.388.34		160	9.4	even	3
945.2.cj.e.397.34		160	35.12	even	12
945.2.cj.e.577.7		160	45.22	odd	12

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bv (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.48808 - 1.48808i) q^{2} -2.42876i q^{4} +(-0.500247 + 2.17939i) q^{5} +(-2.43052 + 1.04527i) q^{7} +(-0.638021 - 0.638021i) q^{8} +O(q^{10})\)	\(q+(1.48808 - 1.48808i) q^{2} -2.42876i q^{4} +(-0.500247 + 2.17939i) q^{5} +(-2.43052 + 1.04527i) q^{7} +(-0.638021 - 0.638021i) q^{8} +(2.49870 + 3.98751i) q^{10} +(-0.0441776 - 0.0765178i) q^{11} +(5.14229 + 1.37787i) q^{13} +(-2.06136 + 5.17224i) q^{14} +2.95866 q^{16} +(3.40854 - 0.913316i) q^{17} +(2.57895 + 4.46688i) q^{19} +(5.29321 + 1.21498i) q^{20} +(-0.179604 - 0.0481248i) q^{22} +(-3.58010 + 0.959285i) q^{23} +(-4.49951 - 2.18047i) q^{25} +(9.70252 - 5.60175i) q^{26} +(2.53870 + 5.90313i) q^{28} +(0.609023 + 0.351619i) q^{29} +4.87601i q^{31} +(5.67876 - 5.67876i) q^{32} +(3.71309 - 6.43126i) q^{34} +(-1.06219 - 5.81994i) q^{35} +(8.44603 + 2.26311i) q^{37} +(10.4847 + 2.80938i) q^{38} +(1.70967 - 1.07133i) q^{40} +(2.57843 - 1.48865i) q^{41} +(2.22267 - 0.595563i) q^{43} +(-0.185843 + 0.107297i) q^{44} +(-3.89998 + 6.75496i) q^{46} +(-4.06198 - 4.06198i) q^{47} +(4.81483 - 5.08108i) q^{49} +(-9.94033 + 3.45090i) q^{50} +(3.34652 - 12.4894i) q^{52} +(-13.5481 + 3.63020i) q^{53} +(0.188862 - 0.0580025i) q^{55} +(2.21762 + 0.883819i) q^{56} +(1.42951 - 0.383036i) q^{58} -3.46294 q^{59} +1.36482i q^{61} +(7.25589 + 7.25589i) q^{62} -10.9836i q^{64} +(-5.57535 + 10.5178i) q^{65} +(-4.23347 + 4.23347i) q^{67} +(-2.21822 - 8.27851i) q^{68} +(-10.2412 - 7.07991i) q^{70} -13.4890 q^{71} +(-0.285680 - 1.06617i) q^{73} +(15.9360 - 9.20068i) q^{74} +(10.8489 - 6.26364i) q^{76} +(0.187356 + 0.139801i) q^{77} +3.55373i q^{79} +(-1.48006 + 6.44808i) q^{80} +(1.62166 - 6.05214i) q^{82} +(0.0856239 + 0.319553i) q^{83} +(0.285360 + 7.88543i) q^{85} +(2.42127 - 4.19376i) q^{86} +(-0.0206338 + 0.0770062i) q^{88} +(-5.71165 - 9.89286i) q^{89} +(-13.9387 + 2.02613i) q^{91} +(2.32987 + 8.69519i) q^{92} -12.0891 q^{94} +(-11.0252 + 3.38601i) q^{95} +(10.0857 - 2.70245i) q^{97} +(-0.396205 - 14.7259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8}+O(q^{10}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8	\( 160 q - 4 q^{2} + 6 q^{5} + 16 q^{8} - 24 q^{10} + 16 q^{11} - 152 q^{16} + 6 q^{17} - 60 q^{20} + 8 q^{22} - 8 q^{23} + 2 q^{25} + 36 q^{26} + 22 q^{28} - 12 q^{32} + 36 q^{35} - 4 q^{37} + 18 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 44 q^{50} + 54 q^{52} - 8 q^{53} - 148 q^{56} + 28 q^{58} + 124 q^{65} - 24 q^{67} - 42 q^{68} - 34 q^{70} + 40 q^{71} + 36 q^{73} + 96 q^{76} - 58 q^{77} - 36 q^{80} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 16 q^{86} + 46 q^{88} - 48 q^{91} + 26 q^{92} - 188 q^{95} + 48 q^{97} - 102 q^{98}+O(q^{100}) \) 160 * q - 4 * q^2 + 6 * q^5 + 16 * q^8 - 24 * q^10 + 16 * q^11 - 152 * q^16 + 6 * q^17 - 60 * q^20 + 8 * q^22 - 8 * q^23 + 2 * q^25 + 36 * q^26 + 22 * q^28 - 12 * q^32 + 36 * q^35 - 4 * q^37 + 18 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 44 * q^50 + 54 * q^52 - 8 * q^53 - 148 * q^56 + 28 * q^58 + 124 * q^65 - 24 * q^67 - 42 * q^68 - 34 * q^70 + 40 * q^71 + 36 * q^73 + 96 * q^76 - 58 * q^77 - 36 * q^80 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 16 * q^86 + 46 * q^88 - 48 * q^91 + 26 * q^92 - 188 * q^95 + 48 * q^97 - 102 * q^98

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