LMFDB - Embedded newform 297.2.n.b.280.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(37,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			280.7
Character	$\chi$	$=$	297.280
Dual form			297.2.n.b.262.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.992662 - 1.10246i) q^{2} +(-0.0209894 - 0.199701i) q^{4} +(0.0483964 + 0.0537496i) q^{5} +(1.78161 + 0.793226i) q^{7} +(2.15937 + 1.56887i) q^{8} +0.107298 q^{10} +(2.15852 - 2.51810i) q^{11} +(-1.08533 - 0.230693i) q^{13} +(2.64304 - 1.17676i) q^{14} +(4.26598 - 0.906761i) q^{16} +(0.0576906 - 0.177553i) q^{17} +(-4.20255 - 3.05333i) q^{19} +(0.00971804 - 0.0107930i) q^{20} +(-0.633432 - 4.87930i) q^{22} +(-3.42420 + 5.93089i) q^{23} +(0.522096 - 4.96741i) q^{25} +(-1.33169 + 0.967532i) q^{26} +(0.121013 - 0.372440i) q^{28} +(2.95048 + 1.31364i) q^{29} +(-1.61139 - 0.342511i) q^{31} +(0.565872 - 0.980120i) q^{32} +(-0.138479 - 0.239852i) q^{34} +(0.0435881 + 0.134150i) q^{35} +(-7.75416 + 5.63373i) q^{37} +(-7.53790 + 1.60223i) q^{38} +(0.0201793 + 0.191993i) q^{40} +(-4.62566 + 2.05948i) q^{41} +(4.06266 + 7.03673i) q^{43} +(-0.548173 - 0.378204i) q^{44} +(3.13951 + 9.66242i) q^{46} +(0.907572 - 8.63497i) q^{47} +(-2.13897 - 2.37557i) q^{49} +(-4.95812 - 5.50655i) q^{50} +(-0.0232893 + 0.221583i) q^{52} +(-0.467571 - 1.43904i) q^{53} +(0.239811 - 0.00584740i) q^{55} +(2.60269 + 4.50800i) q^{56} +(4.37707 - 1.94880i) q^{58} +(-0.554654 - 5.27718i) q^{59} +(-6.92183 + 1.47128i) q^{61} +(-1.97717 + 1.43649i) q^{62} +(2.17659 + 6.69887i) q^{64} +(-0.0401262 - 0.0695006i) q^{65} +(-0.447660 + 0.775370i) q^{67} +(-0.0366685 - 0.00779413i) q^{68} +(0.191164 + 0.0851116i) q^{70} +(0.476791 - 1.46741i) q^{71} +(9.31301 - 6.76630i) q^{73} +(-1.48629 + 14.1411i) q^{74} +(-0.521545 + 0.903343i) q^{76} +(5.84306 - 2.77409i) q^{77} +(-8.87869 + 9.86078i) q^{79} +(0.255196 + 0.185411i) q^{80} +(-2.32122 + 7.14398i) q^{82} +(-17.5744 + 3.73556i) q^{83} +(0.0123354 - 0.00549209i) q^{85} +(11.7906 + 2.50616i) q^{86} +(8.61161 - 2.05107i) q^{88} +12.3990 q^{89} +(-1.75064 - 1.27192i) q^{91} +(1.25628 + 0.559331i) q^{92} +(-8.61882 - 9.57217i) q^{94} +(-0.0392728 - 0.373656i) q^{95} +(6.99476 - 7.76847i) q^{97} -4.74225 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

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

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.992662	−	1.10246i	0.701918	−	0.779559i	−0.281762	−	0.959484i	$-0.590919\pi$
$2$	0.992662	−	1.10246i	0.701918	−	0.779559i	0.983680	+	0.179925i	$0.0575857\pi$
$3$		0			0
$3$		0			0
$4$	−0.0209894	−	0.199701i	−0.0104947	−	0.0998506i
$5$	0.0483964	+	0.0537496i	0.0216435	+	0.0240376i	0.753869	−	0.657024i	$-0.228185\pi$
$5$	0.0483964	+	0.0537496i	0.0216435	+	0.0240376i	−0.732226	+	0.681062i	$0.761518\pi$
$6$		0			0
$7$	1.78161	+	0.793226i	0.673387	+	0.299811i	0.714798	−	0.699331i	$-0.246519\pi$
$7$	1.78161	+	0.793226i	0.673387	+	0.299811i	−0.0414112	+	0.999142i	$0.513185\pi$
$8$	2.15937	+	1.56887i	0.763453	+	0.554681i
$9$		0			0
$10$	0.107298			0.0339307
$11$	2.15852	−	2.51810i	0.650817	−	0.759235i
$11$	2.15852	−	2.51810i	0.650817	−	0.759235i
$12$		0			0
$13$	−1.08533	−	0.230693i	−0.301015	−	0.0639828i	0.0549280	−	0.998490i	$-0.482507\pi$
$13$	−1.08533	−	0.230693i	−0.301015	−	0.0639828i	−0.355943	+	0.934508i	$0.615840\pi$
$14$	2.64304	−	1.17676i	0.706383	−	0.314502i
$15$		0			0
$16$	4.26598	−	0.906761i	1.06649	−	0.226690i
$17$	0.0576906	−	0.177553i	0.0139920	−	0.0430630i	−0.943817	−	0.330469i	$-0.892793\pi$
$17$	0.0576906	−	0.177553i	0.0139920	−	0.0430630i	0.957809	+	0.287406i	$0.0927930\pi$
$18$		0			0
$19$	−4.20255	−	3.05333i	−0.964132	−	0.700483i	−0.0100254	−	0.999950i	$-0.503191\pi$
$19$	−4.20255	−	3.05333i	−0.964132	−	0.700483i	−0.954107	+	0.299467i	$0.903191\pi$
$20$	0.00971804	−	0.0107930i	0.00217302	−	0.00241338i
$21$		0			0
$22$	−0.633432	−	4.87930i	−0.135048	−	1.04027i
$23$	−3.42420	+	5.93089i	−0.713995	+	1.23668i	0.249351	+	0.968413i	$0.419783\pi$
$23$	−3.42420	+	5.93089i	−0.713995	+	1.23668i	−0.963346	+	0.268263i	$0.913551\pi$
$24$		0			0
$25$	0.522096	−	4.96741i	0.104419	−	0.993481i
$26$	−1.33169	+	0.967532i	−0.261166	+	0.189749i
$27$		0			0
$28$	0.121013	−	0.372440i	0.0228693	−	0.0703845i
$29$	2.95048	+	1.31364i	0.547890	+	0.243937i	0.661964	−	0.749536i	$-0.269723\pi$
$29$	2.95048	+	1.31364i	0.547890	+	0.243937i	−0.114073	+	0.993472i	$0.536390\pi$
$30$		0			0
$31$	−1.61139	−	0.342511i	−0.289413	−	0.0615167i	0.0609172	−	0.998143i	$-0.480597\pi$
$31$	−1.61139	−	0.342511i	−0.289413	−	0.0615167i	−0.350331	+	0.936626i	$0.613931\pi$
$32$	0.565872	−	0.980120i	0.100033	−	0.173262i
$33$		0			0
$34$	−0.138479	−	0.239852i	−0.0237489	−	0.0411343i
$35$	0.0435881	+	0.134150i	0.00736773	+	0.0226755i
$36$		0			0
$37$	−7.75416	+	5.63373i	−1.27478	+	0.926179i	−0.999382	−	0.0351519i	$-0.988808\pi$
$37$	−7.75416	+	5.63373i	−1.27478	+	0.926179i	−0.275395	+	0.961331i	$0.588808\pi$
$38$	−7.53790	+	1.60223i	−1.22281	+	0.259916i
$39$		0			0
$40$	0.0201793	+	0.191993i	0.00319063	+	0.0303568i
$41$	−4.62566	+	2.05948i	−0.722407	+	0.321636i	−0.734797	−	0.678287i	$-0.762723\pi$
$41$	−4.62566	+	2.05948i	−0.722407	+	0.321636i	0.0123903	+	0.999923i	$0.496056\pi$
$42$		0			0
$43$	4.06266	+	7.03673i	0.619549	+	1.07309i	0.989568	+	0.144066i	$0.0460179\pi$
$43$	4.06266	+	7.03673i	0.619549	+	1.07309i	−0.370019	+	0.929024i	$0.620649\pi$
$44$	−0.548173	−	0.378204i	−0.0826402	−	0.0570165i
$45$		0			0
$46$	3.13951	+	9.66242i	0.462896	+	1.42465i
$47$	0.907572	−	8.63497i	0.132383	−	1.25954i	−0.703525	−	0.710670i	$-0.748392\pi$
$47$	0.907572	−	8.63497i	0.132383	−	1.25954i	0.835908	−	0.548869i	$-0.184942\pi$
$48$		0			0
$49$	−2.13897	−	2.37557i	−0.305568	−	0.339367i
$50$	−4.95812	−	5.50655i	−0.701183	−	0.778743i
$51$		0			0
$52$	−0.0232893	+	0.221583i	−0.00322965	+	0.0307280i
$53$	−0.467571	−	1.43904i	−0.0642259	−	0.197667i	0.913794	−	0.406177i	$-0.133138\pi$
$53$	−0.467571	−	1.43904i	−0.0642259	−	0.197667i	−0.978020	+	0.208510i	$0.933138\pi$
$54$		0			0
$55$	0.239811	−	0.00584740i	0.0323361	−	0.000788463i
$56$	2.60269	+	4.50800i	0.347800	+	0.602406i
$57$		0			0
$58$	4.37707	−	1.94880i	0.574737	−	0.255889i
$59$	−0.554654	−	5.27718i	−0.0722098	−	0.687030i	−0.969417	−	0.245420i	$-0.921074\pi$
$59$	−0.554654	−	5.27718i	−0.0722098	−	0.687030i	0.897207	−	0.441610i	$-0.145593\pi$
$60$		0			0
$61$	−6.92183	+	1.47128i	−0.886249	+	0.188378i	−0.628477	−	0.777828i	$-0.716322\pi$
$61$	−6.92183	+	1.47128i	−0.886249	+	0.188378i	−0.257772	+	0.966206i	$0.582988\pi$
$62$	−1.97717	+	1.43649i	−0.251100	+	0.182435i
$63$		0			0
$64$	2.17659	+	6.69887i	0.272074	+	0.837359i
$65$	−0.0401262	−	0.0695006i	−0.00497704	−	0.00862049i
$66$		0			0
$67$	−0.447660	+	0.775370i	−0.0546904	+	0.0947265i	−0.892074	−	0.451888i	$-0.850751\pi$
$67$	−0.447660	+	0.775370i	−0.0546904	+	0.0947265i	0.837384	+	0.546615i	$0.184084\pi$
$68$	−0.0366685	−	0.00779413i	−0.00444671	−	0.000945177i
$69$		0			0
$70$	0.191164	+	0.0851116i	0.0228485	+	0.0101728i
$71$	0.476791	−	1.46741i	0.0565847	−	0.174150i	−0.918770	−	0.394794i	$-0.870816\pi$
$71$	0.476791	−	1.46741i	0.0565847	−	0.174150i	0.975354	+	0.220644i	$0.0708159\pi$
$72$		0			0
$73$	9.31301	−	6.76630i	1.09001	−	0.791935i	0.110605	−	0.993864i	$-0.464721\pi$
$73$	9.31301	−	6.76630i	1.09001	−	0.791935i	0.979400	+	0.201929i	$0.0647211\pi$
$74$	−1.48629	+	14.1411i	−0.172777	+	1.64387i
$75$		0			0
$76$	−0.521545	+	0.903343i	−0.0598253	+	0.103620i
$77$	5.84306	−	2.77409i	0.665878	−	0.316137i
$78$		0			0
$79$	−8.87869	+	9.86078i	−0.998930	+	1.10942i	−0.00493674	+	0.999988i	$0.501571\pi$
$79$	−8.87869	+	9.86078i	−0.998930	+	1.10942i	−0.993994	+	0.109437i	$0.965095\pi$
$80$	0.255196	+	0.185411i	0.0285318	+	0.0207295i
$81$		0			0
$82$	−2.32122	+	7.14398i	−0.256336	+	0.788921i
$83$	−17.5744	+	3.73556i	−1.92905	+	0.410031i	−0.929942	+	0.367706i	$0.880143\pi$
$83$	−17.5744	+	3.73556i	−1.92905	+	0.410031i	−0.999104	+	0.0423259i	$0.986523\pi$
$84$		0			0
$85$	0.0123354	−	0.00549209i	0.00133797	−	0.000595701i
$86$	11.7906	+	2.50616i	1.27141	+	0.270247i
$87$		0			0
$88$	8.61161	−	2.05107i	0.918001	−	0.218644i
$89$	12.3990			1.31429			0.657145	−	0.753764i	$-0.271764\pi$
$89$	12.3990			1.31429			0.657145	+	0.753764i	$0.271764\pi$
$90$		0			0
$91$	−1.75064	−	1.27192i	−0.183517	−	0.133333i
$92$	1.25628	+	0.559331i	0.130976	+	0.0583142i
$93$		0			0
$94$	−8.61882	−	9.57217i	−0.888963	−	0.987294i
$95$	−0.0392728	−	0.373656i	−0.00402931	−	0.0383363i
$96$		0			0
$97$	6.99476	−	7.76847i	0.710211	−	0.788769i	−0.274756	−	0.961514i	$-0.588597\pi$
$97$	6.99476	−	7.76847i	0.710211	−	0.788769i	0.984967	+	0.172745i	$0.0552637\pi$
$98$	−4.74225			−0.479040
$99$		0			0
$100$	−1.00296			−0.100296
$101$	2.31661	−	2.57286i	0.230511	−	0.256009i	−0.616782	−	0.787134i	$-0.711564\pi$
$101$	2.31661	−	2.57286i	0.230511	−	0.256009i	0.847293	+	0.531125i	$0.178231\pi$
$102$		0			0
$103$	1.86938	+	17.7860i	0.184196	+	1.75251i	0.562474	+	0.826815i	$0.309850\pi$
$103$	1.86938	+	17.7860i	0.184196	+	1.75251i	−0.378278	+	0.925692i	$0.623484\pi$
$104$	−1.98169	−	2.20089i	−0.194321	−	0.215815i
$105$		0			0
$106$	−2.05062	−	0.912997i	−0.199174	−	0.0886781i
$107$	−11.3281	−	8.23036i	−1.09513	−	0.795659i	−0.114872	−	0.993380i	$-0.536646\pi$
$107$	−11.3281	−	8.23036i	−1.09513	−	0.795659i	−0.980258	+	0.197722i	$0.936646\pi$
$108$		0			0
$109$	−5.00844			−0.479722			−0.239861	−	0.970807i	$-0.577102\pi$
$109$	−5.00844			−0.479722			−0.239861	+	0.970807i	$0.577102\pi$
$110$	0.231605	−	0.270187i	0.0220826	−	0.0257613i
$111$		0			0
$112$	8.31959	+	1.76838i	0.786127	+	0.167097i
$113$	10.3139	−	4.59206i	0.970252	−	0.431984i	0.140478	−	0.990084i	$-0.455136\pi$
$113$	10.3139	−	4.59206i	0.970252	−	0.431984i	0.829774	+	0.558100i	$0.188469\pi$
$114$		0			0
$115$	−0.484502	+	0.102984i	−0.0451800	+	0.00960331i
$116$	0.200406	−	0.616787i	0.0186072	−	0.0572672i
$117$		0			0
$118$	−6.36848	−	4.62697i	−0.586266	−	0.425947i
$119$	0.243622	−	0.270570i	0.0223328	−	0.0248031i
$120$		0			0
$121$	−1.68162	−	10.8707i	−0.152875	−	0.988246i
$122$	−5.24900	+	9.09154i	−0.475222	+	0.823109i
$123$		0			0
$124$	−0.0345777	+	0.328985i	−0.00310517	+	0.0295437i
$125$	0.584833	−	0.424906i	0.0523091	−	0.0380048i
$126$		0			0
$127$	6.14382	−	18.9087i	0.545176	−	1.67788i	−0.175394	−	0.984498i	$-0.556120\pi$
$127$	6.14382	−	18.9087i	0.545176	−	1.67788i	0.720570	−	0.693382i	$-0.243880\pi$
$128$	11.6137	+	5.17074i	1.02651	+	0.457033i
$129$		0			0
$130$	−0.116454	−	0.0247530i	−0.0102137	−	0.00217098i
$131$	−4.33332	+	7.50552i	−0.378604	+	0.655761i	−0.990859	−	0.134899i	$-0.956929\pi$
$131$	−4.33332	+	7.50552i	−0.378604	+	0.655761i	0.612256	+	0.790660i	$0.290262\pi$
$132$		0			0
$133$	−5.06535	−	8.77344i	−0.439221	−	0.760753i
$134$	0.410441	+	1.26321i	0.0354567	+	0.109125i
$135$		0			0
$136$	0.403134	−	0.292894i	0.0345685	−	0.0251155i
$137$	7.16590	−	1.52316i	0.612225	−	0.130132i	0.108644	−	0.994081i	$-0.465349\pi$
$137$	7.16590	−	1.52316i	0.612225	−	0.130132i	0.503580	+	0.863948i	$0.332016\pi$
$138$		0			0
$139$	0.548446	+	5.21812i	0.0465186	+	0.442595i	0.992847	+	0.119390i	$0.0380938\pi$
$139$	0.548446	+	5.21812i	0.0465186	+	0.442595i	−0.946329	+	0.323205i	$0.895240\pi$
$140$	0.0258751	−	0.0115203i	0.00218684	−	0.000973645i
$141$		0			0
$142$	−1.14448	−	1.98229i	−0.0960423	−	0.166350i
$143$	−2.92360	+	2.23500i	−0.244484	+	0.186900i
$144$		0			0
$145$	0.0721850	+	0.222162i	0.00599463	+	0.0184496i
$146$	1.78508	−	16.9839i	0.147734	−	1.40560i
$147$		0			0
$148$	1.28782	+	1.43027i	0.105858	+	0.117567i
$149$	−1.44722	−	1.60730i	−0.118561	−	0.131675i	0.680942	−	0.732337i	$-0.261570\pi$
$149$	−1.44722	−	1.60730i	−0.118561	−	0.131675i	−0.799503	+	0.600662i	$0.794904\pi$
$150$		0			0
$151$	−0.729131	+	6.93722i	−0.0593358	+	0.564543i	0.923955	+	0.382501i	$0.124937\pi$
$151$	−0.729131	+	6.93722i	−0.0593358	+	0.564543i	−0.983291	+	0.182042i	$0.941729\pi$
$152$	−4.28457	−	13.1866i	−0.347525	−	1.06957i
$153$		0			0
$154$	2.74185	−	9.19548i	0.220945	−	0.740993i
$155$	−0.0595754	−	0.103188i	−0.00478521	−	0.00828823i
$156$		0			0
$157$	16.1215	−	7.17774i	1.28663	−	0.572846i	0.354532	−	0.935044i	$-0.384640\pi$
$157$	16.1215	−	7.17774i	1.28663	−	0.572846i	0.932101	+	0.362198i	$0.117973\pi$
$158$	2.05761	+	19.5768i	0.163695	+	1.55745i
$159$		0			0
$160$	0.0800672	−	0.0170188i	0.00632987	−	0.00134546i
$161$	−10.8051	+	7.85039i	−0.851564	+	0.618697i
$162$		0			0
$163$	1.14520	+	3.52457i	0.0896991	+	0.276065i	0.985836	−	0.167712i	$-0.0536380\pi$
$163$	1.14520	+	3.52457i	0.0896991	+	0.276065i	−0.896137	+	0.443778i	$0.853638\pi$
$164$	0.508370	+	0.880522i	0.0396970	+	0.0687572i
$165$		0			0
$166$	−13.3272	+	23.0833i	−1.03439	+	1.79161i
$167$	−1.98612	−	0.422162i	−0.153690	−	0.0326679i	0.130424	−	0.991458i	$-0.458366\pi$
$167$	−1.98612	−	0.422162i	−0.153690	−	0.0326679i	−0.284114	+	0.958790i	$0.591699\pi$
$168$		0			0
$169$	−10.7514	−	4.78682i	−0.827029	−	0.368217i
$170$	0.00619009	−	0.0190511i	0.000474758	−	0.00146116i
$171$		0			0
$172$	1.31997	−	0.959014i	0.100647	−	0.0731241i
$173$	0.899395	−	8.55717i	0.0683798	−	0.650590i	−0.905628	−	0.424074i	$-0.860600\pi$
$173$	0.899395	−	8.55717i	0.0683798	−	0.650590i	0.974007	−	0.226516i	$-0.0727336\pi$
$174$		0			0
$175$	4.87045	−	8.43586i	0.368171	−	0.637691i
$176$	6.92486	−	12.6994i	0.521981	−	0.957253i
$177$		0			0
$178$	12.3080	−	13.6694i	0.922524	−	1.02457i
$179$	2.03852	+	1.48107i	0.152366	+	0.110701i	0.661357	−	0.750072i	$-0.269981\pi$
$179$	2.03852	+	1.48107i	0.152366	+	0.110701i	−0.508990	+	0.860772i	$0.669981\pi$
$180$		0			0
$181$	4.40514	−	13.5576i	0.327432	−	1.00773i	−0.642899	−	0.765951i	$-0.722269\pi$
$181$	4.40514	−	13.5576i	0.327432	−	1.00773i	0.970331	−	0.241780i	$-0.0777314\pi$
$182$	−3.14003	+	0.667435i	−0.232755	+	0.0494735i
$183$		0			0
$184$	−16.6989	+	7.43485i	−1.23106	+	0.548104i
$185$	−0.678084	−	0.144131i	−0.0498537	−	0.0105967i
$186$		0			0
$187$	−0.322571	−	0.528522i	−0.0235887	−	0.0386494i
$188$	−1.74346			−0.127155
$189$		0			0
$190$	−0.450926	−	0.327617i	−0.0327136	−	0.0237678i
$191$	15.6220	+	6.95537i	1.13037	+	0.503273i	0.884737	−	0.466090i	$-0.154338\pi$
$191$	15.6220	+	6.95537i	1.13037	+	0.503273i	0.245632	+	0.969363i	$0.421004\pi$
$192$		0			0
$193$	11.1338	+	12.3654i	0.801430	+	0.890078i	0.995866	−	0.0908374i	$-0.0289543\pi$
$193$	11.1338	+	12.3654i	0.801430	+	0.890078i	−0.194436	+	0.980915i	$0.562288\pi$
$194$	−1.62102	−	15.4229i	−0.116382	−	1.10730i
$195$		0			0
$196$	−0.429508	+	0.477017i	−0.0306792	+	0.0340727i
$197$	20.1670			1.43684			0.718421	−	0.695609i	$-0.244865\pi$
$197$	20.1670			1.43684			0.718421	+	0.695609i	$0.244865\pi$
$198$		0			0
$199$	15.9840			1.13308			0.566539	−	0.824035i	$-0.308282\pi$
$199$	15.9840			1.13308			0.566539	+	0.824035i	$0.308282\pi$
$200$	8.92064	−	9.90737i	0.630784	−	0.700557i
$201$		0			0
$202$	−0.536868	−	5.10795i	−0.0377739	−	0.359394i
$203$	4.21460	+	4.68079i	0.295807	+	0.328527i
$204$		0			0
$205$	−0.334561	−	0.148956i	−0.0233668	−	0.0104036i
$206$	21.4641	+	15.5946i	1.49547	+	1.08652i
$207$		0			0
$208$	−4.83916			−0.335535
$209$	−16.7599	+	3.99177i	−1.15930	+	0.276117i
$210$		0			0
$211$	9.59130	+	2.03869i	0.660292	+	0.140349i	0.525857	−	0.850573i	$-0.323745\pi$
$211$	9.59130	+	2.03869i	0.660292	+	0.140349i	0.134435	+	0.990922i	$0.457078\pi$
$212$	−0.277563	+	0.123579i	−0.0190631	+	0.00848745i
$213$		0			0
$214$	−20.3186	+	4.31886i	−1.38895	+	0.295231i
$215$	−0.181604	+	0.558918i	−0.0123853	+	0.0381179i
$216$		0			0
$217$	−2.59918	−	1.88841i	−0.176444	−	0.128194i
$218$	−4.97169	+	5.52162i	−0.336725	+	0.373971i
$219$		0			0
$220$	−0.00620123	−	0.0477678i	−0.000418087	−	0.00322050i
$221$	−0.103573	+	0.179395i	−0.00696711	+	0.0120674i
$222$		0			0
$223$	−1.76733	+	16.8151i	−0.118349	+	1.12602i	0.760638	+	0.649176i	$0.224886\pi$
$223$	−1.76733	+	16.8151i	−0.118349	+	1.12602i	−0.878988	+	0.476844i	$0.841781\pi$
$224$	1.78562	−	1.29733i	0.119307	−	0.0866815i
$225$		0			0
$226$	5.17567	−	15.9291i	0.344280	−	1.05959i
$227$	−2.90868	−	1.29503i	−0.193056	−	0.0859541i	0.307932	−	0.951408i	$-0.400363\pi$
$227$	−2.90868	−	1.29503i	−0.193056	−	0.0859541i	−0.500988	+	0.865454i	$0.667030\pi$
$228$		0			0
$229$	−4.71589	−	1.00239i	−0.311635	−	0.0662400i	0.0494393	−	0.998777i	$-0.484257\pi$
$229$	−4.71589	−	1.00239i	−0.311635	−	0.0662400i	−0.361074	+	0.932537i	$0.617590\pi$
$230$	−0.367410	+	0.636373i	−0.0242263	+	0.0419612i
$231$		0			0
$232$	4.31025	+	7.46557i	0.282982	+	0.490138i
$233$	6.50281	+	20.0136i	0.426013	+	1.31113i	0.902021	+	0.431693i	$0.142084\pi$
$233$	6.50281	+	20.0136i	0.426013	+	1.31113i	−0.476007	+	0.879441i	$0.657916\pi$
$234$		0			0
$235$	0.508049	−	0.369120i	0.0331415	−	0.0240787i
$236$	−1.04222	+	0.221530i	−0.0678425	+	0.0144204i
$237$		0			0
$238$	−0.0564587	−	0.537169i	−0.00365967	−	0.0348195i
$239$	−13.0571	+	5.81341i	−0.844595	+	0.376038i	−0.782969	−	0.622061i	$-0.786295\pi$
$239$	−13.0571	+	5.81341i	−0.844595	+	0.376038i	−0.0616265	+	0.998099i	$0.519629\pi$
$240$		0			0
$241$	−0.0808738	−	0.140078i	−0.00520954	−	0.00902319i	0.863409	−	0.504505i	$-0.168325\pi$
$241$	−0.0808738	−	0.140078i	−0.00520954	−	0.00902319i	−0.868618	+	0.495482i	$0.834992\pi$
$242$	−13.6538	−	8.93700i	−0.877701	−	0.574492i
$243$		0			0
$244$	0.439101	+	1.35142i	0.0281106	+	0.0865155i
$245$	0.0241675	−	0.229938i	0.00154400	−	0.0146902i
$246$		0			0
$247$	3.85676	+	4.28337i	0.245400	+	0.272544i
$248$	−2.94222	−	3.26767i	−0.186831	−	0.207497i
$249$		0			0
$250$	0.112098	−	1.06655i	0.00708973	−	0.0674542i
$251$	2.75542	+	8.48032i	0.173921	+	0.535273i	0.999583	−	0.0288924i	$-0.00919801\pi$
$251$	2.75542	+	8.48032i	0.173921	+	0.535273i	−0.825662	+	0.564165i	$0.809198\pi$
$252$		0			0
$253$	7.54337	+	21.4244i	0.474247	+	1.34694i
$254$	−14.7474	−	25.5433i	−0.925337	−	1.60273i
$255$		0			0
$256$	4.35969	−	1.94106i	0.272481	−	0.121316i
$257$	0.445260	+	4.23636i	0.0277745	+	0.264257i	0.999593	+	0.0285267i	$0.00908156\pi$
$257$	0.445260	+	4.23636i	0.0277745	+	0.264257i	−0.971818	+	0.235730i	$0.924252\pi$
$258$		0			0
$259$	−18.2837	+	3.88633i	−1.13610	+	0.241485i
$260$	−0.0130371	+	0.00947202i	−0.000808528	+	0.000587430i
$261$		0			0
$262$	3.97304	+	12.2278i	0.245455	+	0.755434i
$263$	11.6890	+	20.2459i	0.720774	+	1.24842i	0.960690	+	0.277623i	$0.0895467\pi$
$263$	11.6890	+	20.2459i	0.720774	+	1.24842i	−0.239916	+	0.970794i	$0.577120\pi$
$264$		0			0
$265$	0.0547189	−	0.0947759i	0.00336136	−	0.00582204i
$266$	−14.7006	−	3.12470i	−0.901349	−	0.191588i
$267$		0			0
$268$	0.164238	+	0.0731236i	0.0100325	+	0.00446674i
$269$	4.69356	−	14.4453i	0.286172	−	0.880746i	−0.699873	−	0.714267i	$-0.746760\pi$
$269$	4.69356	−	14.4453i	0.286172	−	0.880746i	0.986045	−	0.166479i	$-0.0532398\pi$
$270$		0			0
$271$	−12.7047	+	9.23053i	−0.771757	+	0.560715i	−0.902494	−	0.430703i	$-0.858266\pi$
$271$	−12.7047	+	9.23053i	−0.771757	+	0.560715i	0.130736	+	0.991417i	$0.458266\pi$
$272$	0.0851082	−	0.809750i	0.00516044	−	0.0490983i
$273$		0			0
$274$	5.43409	−	9.41212i	0.328286	−	0.568607i
$275$	−11.3815	−	12.0369i	−0.686328	−	0.725853i
$276$		0			0
$277$	5.00368	−	5.55715i	0.300642	−	0.333897i	−0.573829	−	0.818975i	$-0.694542\pi$
$277$	5.00368	−	5.55715i	0.300642	−	0.333897i	0.874470	+	0.485079i	$0.161209\pi$
$278$	6.29720	+	4.57519i	0.377681	+	0.274401i
$279$		0			0
$280$	−0.116342	+	0.358064i	−0.00695277	+	0.0213984i
$281$	−12.5286	+	2.66303i	−0.747391	+	0.158863i	−0.565836	−	0.824518i	$-0.691446\pi$
$281$	−12.5286	+	2.66303i	−0.747391	+	0.158863i	−0.181555	+	0.983381i	$0.558113\pi$
$282$		0			0
$283$	−5.99350	+	2.66848i	−0.356277	+	0.158625i	−0.577067	−	0.816697i	$-0.695803\pi$
$283$	−5.99350	+	2.66848i	−0.356277	+	0.158625i	0.220790	+	0.975321i	$0.429136\pi$
$284$	−0.303052	−	0.0644156i	−0.0179828	−	0.00382236i
$285$		0			0
$286$	−0.438141	+	5.44176i	−0.0259078	+	0.321778i
$287$	−9.87477			−0.582889
$288$		0			0
$289$	13.7251	+	9.97186i	0.807358	+	0.586580i
$290$	0.316581	+	0.140951i	0.0185903	+	0.00827692i
$291$		0			0
$292$	−1.54671	−	1.71780i	−0.0905145	−	0.100526i
$293$	−1.22958	−	11.6987i	−0.0718331	−	0.683446i	−0.969886	−	0.243559i	$-0.921685\pi$
$293$	−1.22958	−	11.6987i	−0.0718331	−	0.683446i	0.898053	−	0.439887i	$-0.144982\pi$
$294$		0			0
$295$	0.256803	−	0.285209i	0.0149517	−	0.0166055i
$296$	−25.5827			−1.48697
$297$		0			0
$298$	−3.20859			−0.185869
$299$	5.08459	−	5.64701i	0.294050	−	0.326575i
$300$		0			0
$301$	1.65637	+	15.7593i	0.0954717	+	0.908353i
$302$	6.92424	+	7.69015i	0.398445	+	0.442518i
$303$		0			0
$304$	−20.6966	−	9.21474i	−1.18703	−	0.528502i
$305$	−0.414072	−	0.300841i	−0.0237097	−	0.0172261i
$306$		0			0
$307$	−23.8127			−1.35906			−0.679530	−	0.733647i	$-0.737816\pi$
$307$	−23.8127			−1.35906			−0.679530	+	0.733647i	$0.737816\pi$
$308$	−0.676631	−	1.10864i	−0.0385546	−	0.0631706i
$309$		0			0
$310$	−0.172899	−	0.0367507i	−0.00981998	−	0.00208730i
$311$	−21.5120	+	9.57774i	−1.21983	+	0.543104i	−0.912726	−	0.408572i	$-0.866027\pi$
$311$	−21.5120	+	9.57774i	−1.21983	+	0.543104i	−0.307105	+	0.951676i	$0.599360\pi$
$312$		0			0
$313$	11.2007	−	2.38078i	0.633100	−	0.134569i	0.119827	−	0.992795i	$-0.461766\pi$
$313$	11.2007	−	2.38078i	0.633100	−	0.134569i	0.513273	+	0.858225i	$0.328433\pi$
$314$	8.08998	−	24.8984i	0.456544	−	1.40510i
$315$		0			0
$316$	2.15557	+	1.56611i	0.121260	+	0.0881007i
$317$	−9.84727	+	10.9365i	−0.553078	+	0.614255i	−0.953249	−	0.302185i	$-0.902284\pi$
$317$	−9.84727	+	10.9365i	−0.553078	+	0.614255i	0.400171	+	0.916440i	$0.368951\pi$
$318$		0			0
$319$	9.67652	−	4.59409i	0.541781	−	0.257219i
$320$	−0.254722	+	0.441192i	−0.0142394	+	0.0246634i
$321$		0			0
$322$	−2.07108	+	19.7050i	−0.115417	+	1.09812i
$323$	−0.784578	+	0.570029i	−0.0436551	+	0.0317173i
$324$		0			0
$325$	−1.71259	+	5.27081i	−0.0949975	+	0.292372i
$326$	5.02250	+	2.23616i	0.278171	+	0.123850i
$327$		0			0
$328$	−13.2196	−	2.80991i	−0.729929	−	0.155151i
$329$	8.46642	−	14.6643i	0.466769	−	0.808468i
$330$		0			0
$331$	−6.73090	−	11.6583i	−0.369964	−	0.640796i	0.619596	−	0.784921i	$-0.287297\pi$
$331$	−6.73090	−	11.6583i	−0.369964	−	0.640796i	−0.989559	+	0.144125i	$0.953963\pi$
$332$	1.11487	+	3.43123i	0.0611867	+	0.188313i
$333$		0			0
$334$	−2.43696	+	1.77055i	−0.133344	+	0.0968804i
$335$	−0.0633409	+	0.0134635i	−0.00346068	+	0.000735591i
$336$		0			0
$337$	−0.305702	−	2.90856i	−0.0166526	−	0.158439i	0.983035	−	0.183416i	$-0.0587155\pi$
$337$	−0.305702	−	2.90856i	−0.0166526	−	0.158439i	−0.999688	+	0.0249766i	$0.992049\pi$
$338$	−15.9498	+	7.10130i	−0.867553	+	0.386260i
$339$		0			0
$340$	−0.00135569	−	0.00234812i	−7.35226e−5	−	0.000127345i
$341$	−4.34067	+	3.31831i	−0.235061	+	0.179697i
$342$		0			0
$343$	−6.14502	−	18.9124i	−0.331800	−	1.02117i
$344$	−2.26696	+	21.5687i	−0.122226	+	1.16291i
$345$		0			0
$346$	−8.54117	−	9.48593i	−0.459176	−	0.509967i
$347$	18.0136	+	20.0061i	0.967019	+	1.07398i	0.997225	+	0.0744402i	$0.0237170\pi$
$347$	18.0136	+	20.0061i	0.967019	+	1.07398i	−0.0302060	+	0.999544i	$0.509616\pi$
$348$		0			0
$349$	0.158979	−	1.51258i	0.00850993	−	0.0809665i	−0.989443	−	0.144925i	$-0.953706\pi$
$349$	0.158979	−	1.51258i	0.00850993	−	0.0809665i	0.997953	+	0.0639586i	$0.0203725\pi$
$350$	−4.46552	−	13.7434i	−0.238692	−	0.734618i
$351$		0			0
$352$	−1.24659	−	3.54053i	−0.0664436	−	0.188711i
$353$	0.161316	+	0.279408i	0.00858599	+	0.0148714i	0.870286	−	0.492546i	$-0.163934\pi$
$353$	0.161316	+	0.279408i	0.00858599	+	0.0148714i	−0.861700	+	0.507417i	$0.830600\pi$
$354$		0			0
$355$	0.101948	−	0.0453901i	0.00541083	−	0.00240906i
$356$	−0.260248	−	2.47609i	−0.0137931	−	0.131233i
$357$		0			0
$358$	3.65639	−	0.777190i	0.193246	−	0.0410758i
$359$	−8.95215	+	6.50411i	−0.472476	+	0.343274i	−0.798406	−	0.602120i	$-0.794323\pi$
$359$	−8.95215	+	6.50411i	−0.472476	+	0.343274i	0.325929	+	0.945394i	$0.394323\pi$
$360$		0			0
$361$	2.46729	+	7.59354i	0.129857	+	0.399660i
$362$	−10.5740	−	18.3147i	−0.555756	−	0.962597i
$363$		0			0
$364$	−0.217258	+	0.376302i	−0.0113874	+	0.0197236i
$365$	0.814402	+	0.173106i	0.0426277	+	0.00906080i
$366$		0			0
$367$	13.2047	+	5.87909i	0.689278	+	0.306886i	0.721322	−	0.692600i	$-0.243535\pi$
$367$	13.2047	+	5.87909i	0.689278	+	0.306886i	−0.0320440	+	0.999486i	$0.510202\pi$
$368$	−9.22966	+	28.4060i	−0.481129	+	1.48076i
$369$		0			0
$370$	−0.832007	+	0.604489i	−0.0432540	+	0.0314259i
$371$	0.308449	−	2.93470i	0.0160139	−	0.152362i
$372$		0			0
$373$	−4.61875	+	7.99991i	−0.239150	+	0.414219i	−0.960471	−	0.278382i	$-0.910202\pi$
$373$	−4.61875	+	7.99991i	−0.239150	+	0.414219i	0.721321	+	0.692601i	$0.243535\pi$
$374$	−0.902879	−	0.169022i	−0.0466868	−	0.00873990i
$375$		0			0
$376$	15.5070	−	17.2222i	0.799711	−	0.888169i
$377$	−2.89919	−	2.10638i	−0.149316	−	0.108484i
$378$		0			0
$379$	1.54865	−	4.76624i	0.0795486	−	0.244825i	−0.903371	−	0.428859i	$-0.858916\pi$
$379$	1.54865	−	4.76624i	0.0795486	−	0.244825i	0.982920	+	0.184034i	$0.0589156\pi$
$380$	−0.0737952	+	0.0156857i	−0.00378561	+	0.000804657i
$381$		0			0
$382$	23.1754	−	10.3184i	1.18576	−	0.527933i
$383$	34.1937	+	7.26810i	1.74722	+	0.371383i	0.967129	−	0.254286i	$-0.0818404\pi$
$383$	34.1937	+	7.26810i	1.74722	+	0.371383i	0.780089	+	0.625668i	$0.215174\pi$
$384$		0			0
$385$	0.431889	+	0.179806i	0.0220111	+	0.00916378i
$386$	24.6845			1.25641
$387$		0			0
$388$	−1.69819	−	1.23381i	−0.0862125	−	0.0626370i
$389$	20.0211	+	8.91398i	1.01511	+	0.451957i	0.845740	−	0.533596i	$-0.179160\pi$
$389$	20.0211	+	8.91398i	1.01511	+	0.451957i	0.169372	+	0.985552i	$0.445826\pi$
$390$		0			0
$391$	0.855505	+	0.950135i	0.0432648	+	0.0480504i
$392$	−0.891864	−	8.48552i	−0.0450459	−	0.428583i
$393$		0			0
$394$	20.0190	−	22.2334i	1.00854	−	1.12010i
$395$	−0.959709			−0.0482882
$396$		0			0
$397$	−15.3168			−0.768726			−0.384363	−	0.923182i	$-0.625579\pi$
$397$	−15.3168			−0.768726			−0.384363	+	0.923182i	$0.625579\pi$
$398$	15.8667	−	17.6218i	0.795328	−	0.883301i
$399$		0			0
$400$	−2.27701	−	21.6643i	−0.113850	−	1.08321i
$401$	−0.144305	−	0.160267i	−0.00720624	−	0.00800334i	0.739531	−	0.673123i	$-0.235047\pi$
$401$	−0.144305	−	0.160267i	−0.00720624	−	0.00800334i	−0.746737	+	0.665119i	$0.768381\pi$
$402$		0			0
$403$	1.66986	+	0.743472i	0.0831819	+	0.0370350i
$404$	−0.562427	−	0.408627i	−0.0279818	−	0.0203299i
$405$		0			0
$406$	9.34407			0.463739
$407$	−2.55120	+	31.6862i	−0.126458	+	1.57063i
$408$		0			0
$409$	−22.2047	−	4.71975i	−1.09795	−	0.233377i	−0.376897	−	0.926255i	$-0.623009\pi$
$409$	−22.2047	−	4.71975i	−1.09795	−	0.233377i	−0.721054	+	0.692879i	$0.756342\pi$
$410$	−0.496325	+	0.220978i	−0.0245117	+	0.0109133i
$411$		0			0
$412$	3.51265	−	0.746636i	0.173056	−	0.0367841i
$413$	3.19782	−	9.84186i	0.157354	−	0.484286i
$414$		0			0
$415$	−1.05132	−	0.763832i	−0.0516075	−	0.0374950i
$416$	−0.840263	+	0.933207i	−0.0411973	+	0.0457542i
$417$		0			0
$418$	−12.2361	+	22.4396i	−0.598487	+	1.09756i
$419$	8.54073	−	14.7930i	0.417242	−	0.722684i	−0.578419	−	0.815740i	$-0.696330\pi$
$419$	8.54073	−	14.7930i	0.417242	−	0.722684i	0.995661	+	0.0930557i	$0.0296635\pi$
$420$		0			0
$421$	0.626911	−	5.96466i	0.0305538	−	0.290700i	−0.968566	−	0.248756i	$-0.919978\pi$
$421$	0.626911	−	5.96466i	0.0305538	−	0.290700i	0.999120	−	0.0419437i	$-0.0133550\pi$
$422$	11.7685	−	8.55031i	0.572881	−	0.416223i
$423$		0			0
$424$	1.24801	−	3.84098i	0.0606087	−	0.186534i
$425$	−0.851860	−	0.379272i	−0.0413213	−	0.0183974i
$426$		0			0
$427$	−13.4991	−	2.86932i	−0.653266	−	0.138856i
$428$	−1.40584	+	2.43499i	−0.0679539	+	0.117700i
$429$		0			0
$430$	0.435915	+	0.755028i	0.0210217	+	0.0364107i
$431$	1.23449	+	3.79938i	0.0594635	+	0.183010i	0.976376	−	0.216078i	$-0.0693267\pi$
$431$	1.23449	+	3.79938i	0.0594635	+	0.183010i	−0.916912	+	0.399088i	$0.869327\pi$
$432$		0			0
$433$	21.9374	−	15.9385i	1.05425	−	0.765954i	0.0812301	−	0.996695i	$-0.474115\pi$
$433$	21.9374	−	15.9385i	1.05425	−	0.765954i	0.973015	+	0.230741i	$0.0741151\pi$
$434$	−4.66201	+	0.990941i	−0.223784	+	0.0475667i
$435$		0			0
$436$	0.105124	+	1.00019i	0.00503455	+	0.0479005i
$437$	32.4994	−	14.4697i	1.55466	−	0.692177i
$438$		0			0
$439$	12.7238	+	22.0383i	0.607275	+	1.05183i	0.991688	+	0.128669i	$0.0410706\pi$
$439$	12.7238	+	22.0383i	0.607275	+	1.05183i	−0.384413	+	0.923161i	$0.625596\pi$
$440$	0.527015	+	0.363607i	0.0251244	+	0.0173343i
$441$		0			0
$442$	0.0949623	+	0.292264i	0.00451690	+	0.0139016i
$443$	1.05830	−	10.0690i	0.0502812	−	0.478394i	−0.940188	−	0.340657i	$-0.889351\pi$
$443$	1.05830	−	10.0690i	0.0502812	−	0.478394i	0.990469	−	0.137737i	$-0.0439828\pi$
$444$		0			0
$445$	0.600066	+	0.666441i	0.0284459	+	0.0315923i
$446$	16.7836	+	18.6401i	0.794727	+	0.882634i
$447$		0			0
$448$	−1.43586	+	13.6613i	−0.0678382	+	0.645437i
$449$	−5.04599	−	15.5299i	−0.238135	−	0.732904i	−0.996690	−	0.0812949i	$-0.974094\pi$
$449$	−5.04599	−	15.5299i	−0.238135	−	0.732904i	0.758555	−	0.651609i	$-0.225906\pi$
$450$		0			0
$451$	−4.79860	+	16.0933i	−0.225957	+	0.757803i
$452$	−1.13352	−	1.96332i	−0.0533164	−	0.0923467i
$453$		0			0
$454$	−4.31506	+	1.92119i	−0.202516	+	0.0901659i
$455$	−0.0163597	−	0.155652i	−0.000766955	−	0.00729709i
$456$		0			0
$457$	22.9933	−	4.88738i	1.07558	−	0.228622i	0.364124	−	0.931350i	$-0.381368\pi$
$457$	22.9933	−	4.88738i	1.07558	−	0.228622i	0.711458	+	0.702728i	$0.248035\pi$
$458$	−5.78639	+	4.20406i	−0.270380	+	0.196443i
$459$		0			0
$460$	0.0307354	+	0.0945940i	0.00143305	+	0.00441047i
$461$	−3.89658	−	6.74907i	−0.181482	−	0.314336i	0.760904	−	0.648865i	$-0.224756\pi$
$461$	−3.89658	−	6.74907i	−0.181482	−	0.314336i	−0.942385	+	0.334529i	$0.891423\pi$
$462$		0			0
$463$	14.9024	−	25.8118i	0.692575	−	1.19957i	−0.278417	−	0.960460i	$-0.589810\pi$
$463$	14.9024	−	25.8118i	0.692575	−	1.19957i	0.970991	−	0.239114i	$-0.0768571\pi$
$464$	13.7778	+	2.92857i	0.639620	+	0.135955i
$465$		0			0
$466$	28.5193	+	12.6976i	1.32113	+	0.588206i
$467$	11.1849	−	34.4236i	0.517575	−	1.59293i	−0.260972	−	0.965346i	$-0.584043\pi$
$467$	11.1849	−	34.4236i	0.517575	−	1.59293i	0.778547	−	0.627586i	$-0.215957\pi$
$468$		0			0
$469$	−1.41260	+	1.02631i	−0.0652278	+	0.0473908i
$470$	0.0973808	−	0.926516i	0.00449184	−	0.0427370i
$471$		0			0
$472$	7.08153	−	12.2656i	0.325954	−	0.564569i
$473$	26.4885	+	4.95872i	1.21794	+	0.228002i
$474$		0			0
$475$	−17.3613	+	19.2817i	−0.796591	+	0.884704i
$476$	−0.0591466	−	0.0429725i	−0.00271098	−	0.00196964i
$477$		0			0
$478$	−6.55224	+	20.1657i	−0.299693	+	0.922359i
$479$	7.31949	−	1.55581i	0.334436	−	0.0710865i	−0.0376331	−	0.999292i	$-0.511982\pi$
$479$	7.31949	−	1.55581i	0.334436	−	0.0710865i	0.372069	+	0.928205i	$0.378648\pi$
$480$		0			0
$481$	9.71546	−	4.32560i	0.442987	−	0.197231i
$482$	−0.234711	−	0.0498893i	−0.0106908	−	0.00227239i
$483$		0			0
$484$	−2.13559	+	0.563992i	−0.0970725	+	0.0256360i
$485$	0.756073			0.0343315
$486$		0			0
$487$	−6.39891	−	4.64908i	−0.289962	−	0.210670i	0.433289	−	0.901255i	$-0.357353\pi$
$487$	−6.39891	−	4.64908i	−0.289962	−	0.210670i	−0.723251	+	0.690585i	$0.757353\pi$
$488$	−17.2550	−	7.68244i	−0.781099	−	0.347768i
$489$		0			0
$490$	−0.229508	−	0.254894i	−0.0103681	−	0.0115150i
$491$	−2.15259	−	20.4806i	−0.0971452	−	0.924275i	−0.929199	−	0.369580i	$-0.879502\pi$
$491$	−2.15259	−	20.4806i	−0.0971452	−	0.924275i	0.832054	−	0.554695i	$-0.187165\pi$
$492$		0			0
$493$	0.403456	−	0.448083i	0.0181707	−	0.0201806i
$494$	8.55071			0.384715
$495$		0			0
$496$	−7.18471			−0.322603
$497$	2.01345	−	2.23616i	0.0903155	−	0.100306i
$498$		0			0
$499$	−1.52156	−	14.4767i	−0.0681143	−	0.648065i	−0.974311	−	0.225208i	$-0.927694\pi$
$499$	−1.52156	−	14.4767i	−0.0681143	−	0.648065i	0.906196	−	0.422857i	$-0.138973\pi$
$500$	−0.0971296	−	0.107873i	−0.00434377	−	0.00482424i
$501$		0			0
$502$	12.0844	+	5.38034i	0.539355	+	0.240136i
$503$	−25.7196	−	18.6864i	−1.14678	−	0.833183i	−0.158729	−	0.987322i	$-0.550740\pi$
$503$	−25.7196	−	18.6864i	−1.14678	−	0.833183i	−0.988049	+	0.154139i	$0.950740\pi$
$504$		0			0
$505$	0.250406			0.0111429
$506$	31.1076	+	12.9509i	1.38290	+	0.575737i
$507$		0			0
$508$	−3.90505	−	0.830045i	−0.173259	−	0.0368273i
$509$	−32.0323	+	14.2617i	−1.41981	+	0.632139i	−0.965901	−	0.258910i	$-0.916637\pi$
$509$	−32.0323	+	14.2617i	−1.41981	+	0.632139i	−0.453906	+	0.891049i	$0.649970\pi$
$510$		0			0
$511$	21.9594	−	4.66761i	0.971426	−	0.206483i
$512$	−5.66916	+	17.4479i	−0.250544	+	0.771095i
$513$		0			0
$514$	5.11242	+	3.71439i	0.225499	+	0.163835i
$515$	−0.865519	+	0.961257i	−0.0381393	+	0.0423580i
$516$		0			0
$517$	−19.7847	−	20.9241i	−0.870129	−	0.920239i
$518$	−13.8650	+	24.0150i	−0.609195	+	1.05516i
$519$		0			0
$520$	0.0223904	−	0.213031i	0.000981884	−	0.00934201i
$521$	−23.9643	+	17.4111i	−1.04990	+	0.762794i	−0.972193	−	0.234183i	$-0.924759\pi$
$521$	−23.9643	+	17.4111i	−1.04990	+	0.762794i	−0.0777032	+	0.996977i	$0.524759\pi$
$522$		0			0
$523$	−3.46900	+	10.6765i	−0.151689	+	0.466850i	−0.997810	−	0.0661400i	$-0.978932\pi$
$523$	−3.46900	+	10.6765i	−0.151689	+	0.466850i	0.846122	+	0.532990i	$0.178932\pi$
$524$	1.58981	+	0.707831i	0.0694514	+	0.0309217i
$525$		0			0
$526$	33.9236	+	7.21068i	1.47914	+	0.314401i
$527$	−0.153776	+	0.266347i	−0.00669857	+	0.0116023i
$528$		0			0
$529$	−11.9503	−	20.6985i	−0.519578	−	0.899936i
$530$	−0.0501696	−	0.154406i	−0.00217923	−	0.00670697i
$531$		0			0
$532$	−1.64575	+	1.19570i	−0.0713522	+	0.0518404i
$533$	5.49546	−	1.16810i	0.238035	−	0.0505958i
$534$		0			0
$535$	−0.105861	−	1.00720i	−0.00457677	−	0.0435451i
$536$	−2.18312	+	0.971988i	−0.0942965	+	0.0419835i
$537$		0			0
$538$	−11.2663	−	19.5138i	−0.485724	−	0.841299i
$539$	−10.5989	+	0.258437i	−0.456528	+	0.0111317i
$540$		0			0
$541$	1.79412	+	5.52174i	0.0771354	+	0.237398i	0.982188	−	0.187902i	$-0.0601686\pi$
$541$	1.79412	+	5.52174i	0.0771354	+	0.237398i	−0.905052	+	0.425300i	$0.860169\pi$
$542$	−2.43519	+	23.1693i	−0.104600	+	0.995206i
$543$		0			0
$544$	−0.141378	−	0.157016i	−0.00606153	−	0.00673202i
$545$	−0.242390	−	0.269202i	−0.0103829	−	0.0115313i
$546$		0			0
$547$	2.25951	−	21.4978i	0.0966095	−	0.919178i	−0.833654	−	0.552286i	$-0.813755\pi$
$547$	2.25951	−	21.4978i	0.0966095	−	0.919178i	0.930264	−	0.366891i	$-0.119578\pi$
$548$	−0.454585	−	1.39907i	−0.0194189	−	0.0597653i
$549$		0			0
$550$	−24.5682	+	0.599055i	−1.04759	+	0.0255438i
$551$	−8.38858	−	14.5294i	−0.357365	−	0.618975i
$552$		0			0
$553$	−23.6402	+	10.5253i	−1.00528	+	0.447581i
$554$	−1.15959	−	11.0327i	−0.0492661	−	0.468736i
$555$		0			0
$556$	1.03055	−	0.219051i	0.0437052	−	0.00928982i
$557$	−5.71836	+	4.15463i	−0.242295	+	0.176037i	−0.702305	−	0.711876i	$-0.747846\pi$
$557$	−5.71836	+	4.15463i	−0.242295	+	0.176037i	0.460010	+	0.887914i	$0.347846\pi$
$558$		0			0
$559$	−2.78598	−	8.57437i	−0.117835	−	0.362657i
$560$	0.307588	+	0.532758i	0.0129980	+	0.0225131i
$561$		0			0
$562$	−9.50073	+	16.4557i	−0.400764	+	0.694144i
$563$	−22.3938	−	4.75994i	−0.943785	−	0.200608i	−0.289776	−	0.957094i	$-0.593581\pi$
$563$	−22.3938	−	4.75994i	−0.943785	−	0.200608i	−0.654009	+	0.756487i	$0.726914\pi$
$564$		0			0
$565$	0.745978	+	0.332131i	0.0313835	+	0.0139728i
$566$	−3.00762	+	9.25651i	−0.126420	+	0.389080i
$567$		0			0
$568$	3.33176	−	2.42066i	0.139797	−	0.101569i
$569$	1.91977	−	18.2654i	0.0804808	−	0.765724i	−0.877632	−	0.479334i	$-0.840878\pi$
$569$	1.91977	−	18.2654i	0.0804808	−	0.765724i	0.958113	−	0.286390i	$-0.0924551\pi$
$570$		0			0
$571$	−4.04504	+	7.00621i	−0.169280	+	0.293201i	−0.938167	−	0.346184i	$-0.887477\pi$
$571$	−4.04504	+	7.00621i	−0.169280	+	0.293201i	0.768887	+	0.639384i	$0.220811\pi$
$572$	0.507697	+	0.536935i	0.0212279	+	0.0224504i
$573$		0			0
$574$	−9.80231	+	10.8866i	−0.409140	+	0.454396i
$575$	27.6734	+	20.1059i	1.15406	+	0.838473i
$576$		0			0
$577$	−0.856306	+	2.63544i	−0.0356485	+	0.109715i	−0.967297	−	0.253645i	$-0.918370\pi$
$577$	−0.856306	+	2.63544i	−0.0356485	+	0.109715i	0.931649	+	0.363360i	$0.118370\pi$
$578$	24.6180	−	5.23271i	1.02397	−	0.217652i
$579$		0			0
$580$	0.0428510	−	0.0190785i	0.00177929	−	0.000792191i
$581$	−34.2740	−	7.28517i	−1.42193	−	0.302240i
$582$		0			0
$583$	−4.63289	−	1.92879i	−0.191875	−	0.0798824i
$584$	30.7257			1.27144
$585$		0			0
$586$	−14.1180	−	10.2573i	−0.583207	−	0.423725i
$587$	−33.1947	−	14.7792i	−1.37009	−	0.610004i	−0.415957	−	0.909384i	$-0.636553\pi$
$587$	−33.1947	−	14.7792i	−1.37009	−	0.610004i	−0.954134	+	0.299380i	$0.903220\pi$
$588$		0			0
$589$	5.72614	+	6.35952i	0.235941	+	0.262039i
$590$	−0.0595133	−	0.566232i	−0.00245013	−	0.0233114i
$591$		0			0
$592$	−27.9706	+	31.0645i	−1.14959	+	1.27674i
$593$	−7.21741			−0.296384			−0.148192	−	0.988959i	$-0.547345\pi$
$593$	−7.21741			−0.296384			−0.148192	+	0.988959i	$0.547345\pi$
$594$		0			0
$595$	0.0263335			0.00107957
$596$	−0.290603	+	0.322748i	−0.0119036	+	0.0132203i
$597$		0			0
$598$	−1.17834	−	11.2111i	−0.0481859	−	0.458458i
$599$	−10.6433	−	11.8206i	−0.434875	−	0.482978i	0.485376	−	0.874305i	$-0.338683\pi$
$599$	−10.6433	−	11.8206i	−0.434875	−	0.482978i	−0.920251	+	0.391328i	$0.872016\pi$
$600$		0			0
$601$	9.72914	+	4.33169i	0.396860	+	0.176693i	0.595456	−	0.803388i	$-0.296971\pi$
$601$	9.72914	+	4.33169i	0.396860	+	0.176693i	−0.198596	+	0.980081i	$0.563638\pi$
$602$	19.0183	+	13.8176i	0.775128	+	0.563163i
$603$		0			0
$604$	1.40067			0.0569926
$605$	0.502911	−	0.616489i	0.0204463	−	0.0250638i
$606$		0			0
$607$	−16.5479	−	3.51737i	−0.671659	−	0.142766i	−0.140556	−	0.990073i	$-0.544889\pi$
$607$	−16.5479	−	3.51737i	−0.671659	−	0.142766i	−0.531103	+	0.847307i	$0.678222\pi$
$608$	−5.37074	+	2.39121i	−0.217812	+	0.0969763i
$609$		0			0
$610$	−0.742699	+	0.157866i	−0.0300710	+	0.00639179i
$611$	−2.97704	+	9.16239i	−0.120438	+	0.370671i
$612$		0			0
$613$	15.9766	+	11.6077i	0.645290	+	0.468830i	0.861663	−	0.507480i	$-0.169423\pi$
$613$	15.9766	+	11.6077i	0.645290	+	0.468830i	−0.216374	+	0.976311i	$0.569423\pi$
$614$	−23.6379	+	26.2526i	−0.953949	+	1.05947i
$615$		0			0
$616$	16.9695	+	3.17675i	0.683722	+	0.127995i
$617$	−14.2059	+	24.6053i	−0.571908	+	0.990573i	0.424462	+	0.905446i	$0.360463\pi$
$617$	−14.2059	+	24.6053i	−0.571908	+	0.990573i	−0.996370	+	0.0851276i	$0.972870\pi$
$618$		0			0
$619$	3.51868	−	33.4780i	0.141428	−	1.34559i	−0.661691	−	0.749776i	$-0.730161\pi$
$619$	3.51868	−	33.4780i	0.141428	−	1.34559i	0.803119	−	0.595819i	$-0.203172\pi$
$620$	−0.0193562	+	0.0140631i	−0.000777365	+	0.000564788i
$621$		0			0
$622$	−10.7950	+	33.2236i	−0.432840	+	1.33214i
$623$	22.0902	+	9.83520i	0.885026	+	0.394039i
$624$		0			0
$625$	−24.3770	−	5.18148i	−0.975079	−	0.207259i
$626$	8.49376	−	14.7116i	0.339479	−	0.587995i
$627$		0			0
$628$	−1.77178	−	3.06882i	−0.0707019	−	0.122459i
$629$	0.552945	+	1.70179i	0.0220474	+	0.0678548i
$630$		0			0
$631$	10.5417	−	7.65896i	0.419657	−	0.304898i	−0.357843	−	0.933782i	$-0.616488\pi$
$631$	10.5417	−	7.65896i	0.419657	−	0.304898i	0.777500	+	0.628883i	$0.216488\pi$
$632$	−34.6427	+	7.36354i	−1.37801	+	0.292906i
$633$		0			0
$634$	2.28208	+	21.7125i	0.0906328	+	0.862313i
$635$	1.31368	−	0.584886i	0.0521317	−	0.0232105i
$636$		0			0
$637$	1.77346	+	3.07172i	0.0702669	+	0.121706i
$638$	4.54071	−	15.2284i	0.179768	−	0.602897i
$639$		0			0
$640$	0.284134	+	0.874476i	0.0112314	+	0.0345667i
$641$	0.451688	−	4.29753i	0.0178406	−	0.169742i	−0.981974	−	0.189018i	$-0.939469\pi$
$641$	0.451688	−	4.29753i	0.0178406	−	0.169742i	0.999814	+	0.0192761i	$0.00613614\pi$
$642$		0			0
$643$	13.9683	+	15.5133i	0.550854	+	0.611786i	0.952697	−	0.303923i	$-0.0982966\pi$
$643$	13.9683	+	15.5133i	0.550854	+	0.611786i	−0.401842	+	0.915709i	$0.631630\pi$
$644$	1.79453	+	1.99302i	0.0707142	+	0.0785361i
$645$		0			0
$646$	−0.150385	+	1.43081i	−0.00591680	+	0.0562946i
$647$	−1.77013	−	5.44789i	−0.0695909	−	0.214179i	0.910213	−	0.414141i	$-0.135918\pi$
$647$	−1.77013	−	5.44789i	−0.0695909	−	0.214179i	−0.979804	+	0.199962i	$0.935918\pi$
$648$		0			0
$649$	−14.4857	−	9.99420i	−0.568613	−	0.392307i
$650$	4.11085	+	7.12020i	0.161241	+	0.279277i
$651$		0			0
$652$	0.679823	−	0.302677i	0.0266239	−	0.0118537i
$653$	−1.07341	−	10.2128i	−0.0420058	−	0.399658i	−0.995242	−	0.0974325i	$-0.968937\pi$
$653$	−1.07341	−	10.2128i	−0.0420058	−	0.399658i	0.953236	−	0.302226i	$-0.0977297\pi$
$654$		0			0
$655$	−0.613136	+	0.130326i	−0.0239572	+	0.00509226i
$656$	−17.8655	+	12.9800i	−0.697531	+	0.506786i
$657$		0			0
$658$	−7.76252	−	23.8906i	−0.302614	−	0.931352i
$659$	−7.65543	−	13.2596i	−0.298213	−	0.516520i	0.677514	−	0.735510i	$-0.263057\pi$
$659$	−7.65543	−	13.2596i	−0.298213	−	0.516520i	−0.975727	+	0.218990i	$0.929724\pi$
$660$		0			0
$661$	12.8232	−	22.2105i	0.498766	−	0.863889i	−0.501233	−	0.865313i	$-0.667120\pi$
$661$	12.8232	−	22.2105i	0.498766	−	0.863889i	0.999999	+	0.00142377i	$0.000453199\pi$
$662$	−19.5343	−	4.15214i	−0.759222	−	0.161378i
$663$		0			0
$664$	−43.8104	−	19.5056i	−1.70017	−	0.756966i
$665$	0.226424	−	0.696863i	0.00878036	−	0.0270232i
$666$		0			0
$667$	−17.8941	+	13.0008i	−0.692861	+	0.503393i
$668$	−0.0426187	+	0.405490i	−0.00164897	+	0.0156889i
$669$		0			0
$670$	−0.0480331	+	0.0831957i	−0.00185568	+	0.00321413i
$671$	−11.2360	+	20.6056i	−0.433763	+	0.795471i
$672$		0			0
$673$	−13.3196	+	14.7930i	−0.513434	+	0.570226i	−0.942993	−	0.332812i	$-0.892002\pi$
$673$	−13.3196	+	14.7930i	−0.513434	+	0.570226i	0.429559	+	0.903039i	$0.358669\pi$
$674$	−3.51004	−	2.55019i	−0.135202	−	0.0982297i
$675$		0			0
$676$	−0.730268	+	2.24753i	−0.0280872	+	0.0864436i
$677$	−2.34408	+	0.498250i	−0.0900903	+	0.0191493i	−0.252736	−	0.967535i	$-0.581330\pi$
$677$	−2.34408	+	0.498250i	−0.0900903	+	0.0191493i	0.162646	+	0.986684i	$0.447997\pi$
$678$		0			0
$679$	18.6241	−	8.29199i	0.714728	−	0.318217i
$680$	0.0352532	+	0.00749330i	0.00135190	+	0.000287355i
$681$		0			0
$682$	−0.650508	+	8.07939i	−0.0249093	+	0.309376i
$683$	1.75102			0.0670009			0.0335005	−	0.999439i	$-0.489334\pi$
$683$	1.75102			0.0670009			0.0335005	+	0.999439i	$0.489334\pi$
$684$		0			0
$685$	0.428673	+	0.311449i	0.0163788	+	0.0118999i
$686$	−26.9502	−	11.9990i	−1.02896	−	0.458123i
$687$		0			0
$688$	23.7118	+	26.3347i	0.904005	+	1.00400i
$689$	0.175492	+	1.66969i	0.00668570	+	0.0636102i
$690$		0			0
$691$	−17.3828	+	19.3056i	−0.661274	+	0.734419i	−0.976718	−	0.214525i	$-0.931180\pi$
$691$	−17.3828	+	19.3056i	−0.661274	+	0.734419i	0.315445	+	0.948944i	$0.397846\pi$
$692$	−1.72775			−0.0656794
$693$		0			0
$694$	39.9374			1.51600
$695$	−0.253929	+	0.282017i	−0.00963208	+	0.0106975i
$696$		0			0
$697$	0.0988099	+	0.940114i	0.00374269	+	0.0356094i
$698$	−1.50975	−	1.67675i	−0.0571449	−	0.0634658i
$699$		0			0
$700$	−1.78688	−	0.795570i	−0.0675377	−	0.0300697i
$701$	11.8682	+	8.62278i	0.448257	+	0.325678i	0.788907	−	0.614512i	$-0.210647\pi$
$701$	11.8682	+	8.62278i	0.448257	+	0.325678i	−0.340650	+	0.940190i	$0.610647\pi$
$702$		0			0
$703$	49.7890			1.87783
$704$	21.5666	+	8.97873i	0.812822	+	0.338399i
$705$		0			0
$706$	0.468169	+	0.0995124i	0.0176198	+	0.00374520i
$707$	6.16816	−	2.74624i	0.231978	−	0.103283i
$708$		0			0
$709$	−0.378481	+	0.0804487i	−0.0142142	+	0.00302132i	−0.215013	−	0.976611i	$-0.568979\pi$
$709$	−0.378481	+	0.0804487i	−0.0142142	+	0.00302132i	0.200799	+	0.979632i	$0.435646\pi$
$710$	0.0511588	−	0.157451i	0.00191996	−	0.00590902i
$711$		0			0
$712$	26.7740	+	19.4525i	1.00340	+	0.729012i
$713$	7.54910	−	8.38412i	0.282716	−	0.313988i
$714$		0			0
$715$	−0.261622	−	0.0489765i	−0.00978412	−	0.00183162i
$716$	0.252985	−	0.438182i	0.00945448	−	0.0163756i
$717$		0			0
$718$	−1.71591	+	16.3258i	−0.0640372	+	0.609273i
$719$	19.2508	−	13.9865i	0.717935	−	0.521610i	−0.167789	−	0.985823i	$-0.553663\pi$
$719$	19.2508	−	13.9865i	0.717935	−	0.521610i	0.885724	+	0.464213i	$0.153663\pi$
$720$		0			0
$721$	−10.7778	+	33.1706i	−0.401386	+	1.23534i
$722$	10.8208	+	4.81772i	0.402708	+	0.179297i
$723$		0			0
$724$	−2.79994	−	0.595145i	−0.104059	−	0.0221184i
$725$	8.06581	−	13.9704i	0.299557	−	0.518847i
$726$		0			0
$727$	21.9528	+	38.0233i	0.814184	+	1.41021i	0.909913	+	0.414800i	$0.136148\pi$
$727$	21.9528	+	38.0233i	0.814184	+	1.41021i	−0.0957289	+	0.995407i	$0.530518\pi$
$728$	−1.78481	−	5.49307i	−0.0661494	−	0.203587i
$729$		0			0
$730$	0.999269	−	0.726011i	0.0369846	−	0.0268709i
$731$	1.48377	−	0.315385i	0.0548793	−	0.0116649i
$732$		0			0
$733$	−1.71792	−	16.3449i	−0.0634527	−	0.603712i	−0.979332	−	0.202258i	$-0.935172\pi$
$733$	−1.71792	−	16.3449i	−0.0634527	−	0.603712i	0.915880	−	0.401453i	$-0.131495\pi$
$734$	19.5892	−	8.72169i	0.723052	−	0.321923i
$735$		0			0
$736$	3.87532	+	6.71225i	0.142846	+	0.247417i
$737$	0.986175	+	2.80090i	0.0363262	+	0.103172i
$738$		0			0
$739$	−1.22843	−	3.78073i	−0.0451887	−	0.139076i	0.925917	−	0.377728i	$-0.123295\pi$
$739$	−1.22843	−	3.78073i	−0.0451887	−	0.139076i	−0.971105	+	0.238652i	$0.923295\pi$
$740$	−0.0145506	+	0.138439i	−0.000534889	+	0.00508913i
$741$		0			0
$742$	−2.92921	−	3.25322i	−0.107535	−	0.119429i
$743$	10.5941	+	11.7659i	0.388658	+	0.431649i	0.905444	−	0.424466i	$-0.139538\pi$
$743$	10.5941	+	11.7659i	0.388658	+	0.431649i	−0.516786	+	0.856115i	$0.672872\pi$
$744$		0			0
$745$	0.0163516	−	0.155575i	0.000599076	−	0.00569983i
$746$	4.23474	+	13.0332i	0.155045	+	0.477179i
$747$		0			0
$748$	−0.0987759	+	0.0755111i	−0.00361160	+	0.00276096i
$749$	−13.6538	−	23.6491i	−0.498899	−	0.864118i
$750$		0			0
$751$	−35.3346	+	15.7320i	−1.28938	+	0.574068i	−0.932866	−	0.360224i	$-0.882700\pi$
$751$	−35.3346	+	15.7320i	−1.28938	+	0.574068i	−0.356511	+	0.934291i	$0.616034\pi$
$752$	−3.95818	−	37.6595i	−0.144340	−	1.37330i
$753$		0			0
$754$	−5.20012	+	1.10532i	−0.189377	+	0.0402534i
$755$	−0.408160	+	0.296546i	−0.0148545	+	0.0107924i
$756$		0			0
$757$	−3.47082	−	10.6821i	−0.126149	−	0.388247i	0.867960	−	0.496635i	$-0.165431\pi$
$757$	−3.47082	−	10.6821i	−0.126149	−	0.388247i	−0.994109	+	0.108388i	$0.965431\pi$
$758$	−3.71732	−	6.43859i	−0.135019	−	0.233860i
$759$		0			0
$760$	0.501415	−	0.868476i	0.0181882	−	0.0315029i
$761$	−36.0942	−	7.67206i	−1.30841	−	0.278112i	−0.499641	−	0.866233i	$-0.666535\pi$
$761$	−36.0942	−	7.67206i	−1.30841	−	0.278112i	−0.808773	+	0.588121i	$0.799868\pi$
$762$		0			0
$763$	−8.92311	−	3.97283i	−0.323038	−	0.143826i
$764$	1.06110	−	3.26572i	0.0383892	−	0.118150i
$765$		0			0
$766$	41.9556	−	30.4825i	1.51592	−	1.10138i
$767$	−0.615429	+	5.85542i	−0.0222219	+	0.211427i
$768$		0			0
$769$	−24.4141	+	42.2864i	−0.880393	+	1.52489i	−0.0294888	+	0.999565i	$0.509388\pi$
$769$	−24.4141	+	42.2864i	−0.880393	+	1.52489i	−0.850904	+	0.525321i	$0.823945\pi$
$770$	0.626949	−	0.297654i	0.0225937	−	0.0107267i
$771$		0			0
$772$	2.23568	−	2.48298i	0.0804640	−	0.0893643i
$773$	−6.32496	−	4.59536i	−0.227493	−	0.165283i	0.468200	−	0.883623i	$-0.344903\pi$
$773$	−6.32496	−	4.59536i	−0.227493	−	0.165283i	−0.695693	+	0.718339i	$0.744903\pi$
$774$		0			0
$775$	−2.54269	+	7.82558i	−0.0913360	+	0.281103i
$776$	27.2920	−	5.80110i	0.979727	−	0.208247i
$777$		0			0
$778$	29.7015	−	13.2240i	1.06485	−	0.474102i
$779$	25.7279	+	5.46863i	0.921796	+	0.195934i
$780$		0			0
$781$	−2.66593	−	4.36804i	−0.0953944	−	0.156301i
$782$	1.89672			0.0678264
$783$		0			0
$784$	−11.2789	−	8.19459i	−0.402817	−	0.292664i
$785$	1.16602	+	0.519146i	0.0416171	+	0.0185291i
$786$		0			0
$787$	0.616721	+	0.684938i	0.0219837	+	0.0244154i	0.754036	−	0.656833i	$-0.228104\pi$
$787$	0.616721	+	0.684938i	0.0219837	+	0.0244154i	−0.732053	+	0.681248i	$0.761438\pi$
$788$	−0.423295	−	4.02738i	−0.0150792	−	0.143469i
$789$		0			0
$790$	−0.952667	+	1.05804i	−0.0338944	+	0.0376435i
$791$	22.0180			0.782869
$792$		0			0
$793$	7.85186			0.278828
$794$	−15.2044	+	16.8861i	−0.539582	+	0.599267i
$795$		0			0
$796$	−0.335496	−	3.19203i	−0.0118913	−	0.113138i
$797$	24.5323	+	27.2459i	0.868980	+	0.965100i	0.999653	−	0.0263254i	$-0.00838059\pi$
$797$	24.5323	+	27.2459i	0.868980	+	0.965100i	−0.130673	+	0.991425i	$0.541714\pi$
$798$		0			0
$799$	−1.48081	−	0.659299i	−0.0523873	−	0.0233243i
$800$	−4.57321	−	3.32263i	−0.161688	−	0.117473i
$801$		0			0
$802$	−0.319934			−0.0112973
$803$	3.06408	−	38.0562i	0.108129	−	1.34297i
$804$		0			0
$805$	−0.944885	−	0.200841i	−0.0333028	−	0.00707873i
$806$	2.47726	−	1.10295i	0.0872578	−	0.0388497i
$807$		0			0
$808$	9.03891	−	1.92128i	0.317988	−	0.0675904i
$809$	14.1795	−	43.6399i	0.498523	−	1.53430i	−0.312869	−	0.949796i	$-0.601290\pi$
$809$	14.1795	−	43.6399i	0.498523	−	1.53430i	0.811393	−	0.584501i	$-0.198710\pi$
$810$		0			0
$811$	−35.8258	−	26.0290i	−1.25801	−	0.914001i	−0.259356	−	0.965782i	$-0.583510\pi$
$811$	−35.8258	−	26.0290i	−1.25801	−	0.914001i	−0.998658	+	0.0517807i	$0.983510\pi$
$812$	0.846297	−	0.939908i	0.0296992	−	0.0329843i
$813$		0			0
$814$	32.4004	+	34.2663i	1.13563	+	1.20103i
$815$	−0.134021	+	0.232130i	−0.00469454	+	0.00813117i
$816$		0			0
$817$	4.41195	−	41.9769i	0.154355	−	1.46858i
$818$	−27.2451	+	19.7947i	−0.952602	+	0.692106i
$819$		0			0
$820$	−0.0227245	+	0.0699387i	−0.000793573	+	0.00244237i
$821$	43.9837	+	19.5828i	1.53504	+	0.683445i	0.988113	−	0.153732i	$-0.0491294\pi$
$821$	43.9837	+	19.5828i	1.53504	+	0.683445i	0.546931	+	0.837178i	$0.315796\pi$
$822$		0			0
$823$	36.7464	+	7.81069i	1.28090	+	0.272263i	0.797597	−	0.603190i	$-0.206104\pi$
$823$	36.7464	+	7.81069i	1.28090	+	0.272263i	0.483302	+	0.875454i	$0.339437\pi$
$824$	−23.8673	+	41.3394i	−0.831457	+	1.44013i
$825$		0			0
$826$	−7.67594	−	13.2951i	−0.267080	−	0.462596i
$827$	16.6450	+	51.2279i	0.578802	+	1.78137i	0.622853	+	0.782339i	$0.285974\pi$
$827$	16.6450	+	51.2279i	0.578802	+	1.78137i	−0.0440508	+	0.999029i	$0.514026\pi$
$828$		0			0
$829$	−13.1554	+	9.55794i	−0.456905	+	0.331961i	−0.792316	−	0.610111i	$-0.791125\pi$
$829$	−13.1554	+	9.55794i	−0.456905	+	0.331961i	0.335411	+	0.942072i	$0.391125\pi$
$830$	−1.88571	+	0.400819i	−0.0654538	+	0.0139126i
$831$		0			0
$832$	−0.816932	−	7.77259i	−0.0283220	−	0.269466i
$833$	−0.545189	+	0.242734i	−0.0188897	+	0.00841023i
$834$		0			0
$835$	−0.0734297	−	0.127184i	−0.00254114	−	0.00440138i
$836$	1.14894	+	3.26318i	0.0397370	+	0.112859i
$837$		0			0
$838$	−7.83065	−	24.1003i	−0.270505	−	0.832529i
$839$	2.53174	−	24.0879i	0.0874054	−	0.831607i	−0.859725	−	0.510758i	$-0.829365\pi$
$839$	2.53174	−	24.0879i	0.0874054	−	0.831607i	0.947130	−	0.320849i	$-0.103968\pi$
$840$		0			0
$841$	−12.4251	−	13.7995i	−0.428452	−	0.475844i
$842$	−5.95350	−	6.61203i	−0.205171	−	0.227866i
$843$		0			0
$844$	0.205813	−	1.95818i	0.00708439	−	0.0674034i
$845$	−0.263038	−	0.809547i	−0.00904877	−	0.0278493i
$846$		0			0
$847$	5.62691	−	20.7013i	0.193343	−	0.711305i
$848$	−3.29951	−	5.71492i	−0.113306	−	0.196251i
$849$		0			0
$850$	−1.26374	+	0.562654i	−0.0433460	+	0.0192989i
$851$	−6.86121	−	65.2801i	−0.235199	−	2.23777i
$852$		0			0
$853$	−1.61191	+	0.342621i	−0.0551906	+	0.0117311i	−0.235424	−	0.971893i	$-0.575648\pi$
$853$	−1.61191	+	0.342621i	−0.0551906	+	0.0117311i	0.180234	+	0.983624i	$0.442315\pi$
$854$	−16.5633	+	12.0340i	−0.566786	+	0.411794i
$855$		0			0
$856$	−11.5492	−	35.5448i	−0.394744	−	1.21490i
$857$	23.3721	+	40.4817i	0.798376	+	1.38283i	0.920673	+	0.390334i	$0.127641\pi$
$857$	23.3721	+	40.4817i	0.798376	+	1.38283i	−0.122297	+	0.992494i	$0.539026\pi$
$858$		0			0
$859$	12.7932	−	22.1585i	0.436498	−	0.756037i	−0.560918	−	0.827871i	$-0.689552\pi$
$859$	12.7932	−	22.1585i	0.436498	−	0.756037i	0.997417	+	0.0718338i	$0.0228851\pi$
$860$	0.115428	+	0.0245350i	0.00393607	+	0.000836638i
$861$		0			0
$862$	5.41411	+	2.41052i	0.184405	+	0.0821026i
$863$	0.836222	−	2.57363i	0.0284653	−	0.0876073i	−0.935815	−	0.352493i	$-0.885334\pi$
$863$	0.836222	−	2.57363i	0.0284653	−	0.0876073i	0.964280	+	0.264885i	$0.0853341\pi$
$864$		0			0
$865$	0.503472	−	0.365794i	0.0171186	−	0.0124374i
$866$	4.20487	−	40.0067i	0.142887	−	1.35948i
$867$		0			0
$868$	−0.322563	+	0.558695i	−0.0109485	+	0.0189634i
$869$	5.66562	+	43.6420i	0.192193	+	1.48046i
$870$		0			0
$871$	0.664730	−	0.738257i	0.0225235	−	0.0250149i
$872$	−10.8151	−	7.85762i	−0.366245	−	0.266093i
$873$		0			0
$874$	16.3086	−	50.1928i	0.551648	−	1.69780i
$875$	1.37899	−	0.293114i	0.0466185	−	0.00990907i
$876$		0			0
$877$	−25.5977	+	11.3968i	−0.864371	+	0.384843i	−0.790527	−	0.612427i	$-0.790193\pi$
$877$	−25.5977	+	11.3968i	−0.864371	+	0.384843i	−0.0738442	+	0.997270i	$0.523527\pi$
$878$	36.9268	+	7.84904i	1.24622	+	0.264892i
$879$		0			0
$880$	1.01773	−	0.242396i	0.0343075	−	0.00817117i
$881$	−30.6218			−1.03167			−0.515837	−	0.856687i	$-0.672519\pi$
$881$	−30.6218			−1.03167			−0.515837	+	0.856687i	$0.672519\pi$
$882$		0			0
$883$	−21.8315	−	15.8615i	−0.734688	−	0.533782i	0.156355	−	0.987701i	$-0.450026\pi$
$883$	−21.8315	−	15.8615i	−0.734688	−	0.533782i	−0.891043	+	0.453919i	$0.850026\pi$
$884$	0.0379992	+	0.0169184i	0.00127805	+	0.000569026i
$885$		0			0
$886$	−10.0502	−	11.1619i	−0.337643	−	0.374990i
$887$	3.95536	+	37.6327i	0.132808	+	1.26358i	0.834462	+	0.551065i	$0.185778\pi$
$887$	3.95536	+	37.6327i	0.132808	+	1.26358i	−0.701654	+	0.712518i	$0.747555\pi$
$888$		0			0
$889$	25.9448	−	28.8146i	0.870162	−	0.966412i
$890$	1.33039			0.0445947
$891$		0			0
$892$	3.39508			0.113676
$893$	−30.1796	+	33.5178i	−1.00992	+	1.12163i
$894$		0			0
$895$	0.0190500	+	0.181248i	0.000636771	+	0.00605847i
$896$	16.5895	+	18.4245i	0.554217	+	0.615520i
$897$		0			0
$898$	−22.1301	−	9.85298i	−0.738493	−	0.328798i
$899$	−4.30443	−	3.12735i	−0.143561	−	0.104303i
$900$		0			0
$901$	−0.282480			−0.00941078
$902$	12.9788	+	21.2654i	0.432148	+	0.708062i
$903$		0			0
$904$	29.4759	+	6.26531i	0.980355	+	0.208381i
$905$	0.941911	−	0.419366i	0.0313102	−	0.0139402i
$906$		0			0
$907$	−26.7712	+	5.69039i	−0.888922	+	0.188946i	−0.629669	−	0.776863i	$-0.716810\pi$
$907$	−26.7712	+	5.69039i	−0.888922	+	0.188946i	−0.259253	+	0.965810i	$0.583476\pi$
$908$	−0.197567	+	0.608049i	−0.00655650	+	0.0201788i
$909$		0			0
$910$	−0.187841	−	0.136474i	−0.00622685	−	0.00452407i
$911$	−12.7296	+	14.1376i	−0.421750	+	0.468401i	−0.916151	−	0.400833i	$-0.868721\pi$
$911$	−12.7296	+	14.1376i	−0.421750	+	0.468401i	0.494401	+	0.869234i	$0.335387\pi$
$912$		0			0
$913$	−28.5282	+	52.3174i	−0.944146	+	1.73145i
$914$	17.4364	−	30.2008i	0.576746	−	0.998953i
$915$		0			0
$916$	−0.101195	+	0.962808i	−0.00334358	+	0.0318121i
$917$	−13.6739	+	9.93465i	−0.451551	+	0.328071i
$918$		0			0
$919$	−0.367135	+	1.12992i	−0.0121107	+	0.0372728i	−0.956929	−	0.290321i	$-0.906238\pi$
$919$	−0.367135	+	1.12992i	−0.0121107	+	0.0372728i	0.944819	+	0.327594i	$0.106238\pi$
$920$	−1.20779	−	0.537742i	−0.0398196	−	0.0177288i
$921$		0			0
$922$	−11.3086	−	2.40371i	−0.372428	−	0.0791621i
$923$	−0.855997	+	1.48263i	−0.0281755	+	0.0488014i
$924$		0			0
$925$	23.9366	+	41.4594i	0.787031	+	1.36318i
$926$	−13.6634	−	42.0517i	−0.449008	−	1.38191i
$927$		0			0
$928$	2.95712	−	2.14847i	0.0970722	−	0.0705271i
$929$	10.2650	−	2.18189i	0.336783	−	0.0715854i	−0.0364162	−	0.999337i	$-0.511594\pi$
$929$	10.2650	−	2.18189i	0.336783	−	0.0715854i	0.373199	+	0.927751i	$0.378261\pi$
$930$		0			0
$931$	1.73574	+	16.5145i	0.0568866	+	0.541240i
$932$	3.86025	−	1.71869i	0.126447	−	0.0562976i
$933$		0			0
$934$	−26.8479	−	46.5019i	−0.878489	−	1.52159i
$935$	0.0127966	−	0.0429166i	0.000418494	−	0.00140352i
$936$		0			0
$937$	2.89184	+	8.90017i	0.0944723	+	0.290756i	0.987116	−	0.160007i	$-0.0511518\pi$
$937$	2.89184	+	8.90017i	0.0944723	+	0.290756i	−0.892643	+	0.450763i	$0.851152\pi$
$938$	−0.270761	+	2.57612i	−0.00884067	+	0.0841133i
$939$		0			0
$940$	−0.0843772	−	0.0937104i	−0.00275208	−	0.00305650i
$941$	10.9981	+	12.2146i	0.358528	+	0.398186i	0.895243	−	0.445578i	$-0.147002\pi$
$941$	10.9981	+	12.2146i	0.358528	+	0.398186i	−0.536715	+	0.843763i	$0.680335\pi$
$942$		0			0
$943$	3.62466	−	34.4863i	0.118035	−	1.12303i
$944$	−7.15128	−	22.0094i	−0.232754	−	0.716345i
$945$		0			0
$946$	31.7609	−	24.2802i	1.03264	−	0.789418i
$947$	−1.37786	−	2.38652i	−0.0447744	−	0.0775515i	0.842770	−	0.538274i	$-0.180924\pi$
$947$	−1.37786	−	2.38652i	−0.0447744	−	0.0775515i	−0.887544	+	0.460723i	$0.847590\pi$
$948$		0			0
$949$	−11.6686	+	5.19519i	−0.378779	+	0.168643i
$950$	4.02343	+	38.2803i	0.130537	+	1.24198i
$951$		0			0
$952$	0.950561	−	0.202048i	0.0308079	−	0.00654841i
$953$	42.5222	−	30.8942i	1.37743	−	1.00076i	0.380313	−	0.924858i	$-0.375816\pi$
$953$	42.5222	−	30.8942i	1.37743	−	1.00076i	0.997115	−	0.0759025i	$-0.0241838\pi$
$954$		0			0
$955$	0.382200	+	1.17629i	0.0123677	+	0.0380639i
$956$	1.43501	+	2.48550i	0.0464114	+	0.0803869i
$957$		0			0
$958$	5.55056	−	9.61385i	0.179330	−	0.310609i
$959$	13.9751	+	2.97050i	0.451279	+	0.0959223i
$960$		0			0
$961$	−25.8407	−	11.5050i	−0.833570	−	0.371129i
$962$	4.87535	−	15.0048i	0.157188	−	0.483774i
$963$		0			0
$964$	−0.0262761	+	0.0190907i	−0.000846297	+	0.000614871i
$965$	−0.125797	+	1.19688i	−0.00404954	+	0.0385288i
$966$		0			0
$967$	19.5173	−	33.8050i	0.627636	−	1.08710i	−0.360389	−	0.932802i	$-0.617356\pi$
$967$	19.5173	−	33.8050i	0.627636	−	1.08710i	0.988025	−	0.154295i	$-0.0493105\pi$
$968$	13.4235	−	26.1121i	0.431448	−	0.839276i
$969$		0			0
$970$	0.750525	−	0.833543i	0.0240979	−	0.0267634i
$971$	4.37355	+	3.17757i	0.140354	+	0.101973i	0.655747	−	0.754981i	$-0.272354\pi$
$971$	4.37355	+	3.17757i	0.140354	+	0.101973i	−0.515393	+	0.856954i	$0.672354\pi$
$972$		0			0
$973$	−3.16203	+	9.73171i	−0.101370	+	0.311984i
$974$	−11.4774	+	2.43959i	−0.367759	+	0.0781697i
$975$		0			0
$976$	−28.1943	+	12.5529i	−0.902476	+	0.401808i
$977$	−28.4847	−	6.05462i	−0.911307	−	0.193704i	−0.271678	−	0.962388i	$-0.587579\pi$
$977$	−28.4847	−	6.05462i	−0.911307	−	0.193704i	−0.639629	+	0.768684i	$0.720912\pi$
$978$		0			0
$979$	26.7634	−	31.2219i	0.855362	−	0.997855i
$980$	−0.0464261			−0.00148303
$981$		0			0
$982$	−24.7159	−	17.9571i	−0.788715	−	0.573035i
$983$	12.9821	+	5.78001i	0.414065	+	0.184354i	0.603187	−	0.797600i	$-0.293897\pi$
$983$	12.9821	+	5.78001i	0.414065	+	0.184354i	−0.189122	+	0.981954i	$0.560564\pi$
$984$		0			0
$985$	0.976011	+	1.08397i	0.0310983	+	0.0345382i
$986$	−0.0934997	−	0.889590i	−0.00297764	−	0.0283303i
$987$		0			0
$988$	0.774442	−	0.860105i	0.0246383	−	0.0273636i
$989$	−55.6454			−1.76942
$990$		0			0
$991$	−23.9992			−0.762358			−0.381179	−	0.924501i	$-0.624482\pi$
$991$	−23.9992			−0.762358			−0.381179	+	0.924501i	$0.624482\pi$
$992$	−1.24754	+	1.38553i	−0.0396094	+	0.0439907i
$993$		0			0
$994$	−0.466610	−	4.43950i	−0.0148000	−	0.140812i
$995$	0.773569	+	0.859135i	0.0245238	+	0.0272364i
$996$		0			0
$997$	46.9500	+	20.9035i	1.48692	+	0.662021i	0.979823	−	0.199867i	$-0.0640509\pi$
$997$	46.9500	+	20.9035i	1.48692	+	0.662021i	0.507100	+	0.861887i	$0.330718\pi$
$998$	−17.4704	−	12.6930i	−0.553015	−	0.401789i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.280.7		72
3.2	odd	2		99.2.m.b.49.3	yes	72
9.2	odd	6		99.2.m.b.16.7	✓	72
9.4	even	3		891.2.f.e.82.7		36
9.5	odd	6		891.2.f.f.82.3		36
9.7	even	3	inner	297.2.n.b.181.3		72
11.9	even	5	inner	297.2.n.b.64.3		72
33.8	even	10		1089.2.e.o.364.5		36
33.14	odd	10		1089.2.e.p.364.14		36
33.20	odd	10		99.2.m.b.31.7	yes	72
99.14	odd	30		9801.2.a.cm.1.5		18
99.20	odd	30		99.2.m.b.97.3	yes	72
99.31	even	15		891.2.f.e.163.7		36
99.41	even	30		9801.2.a.co.1.14		18
99.47	odd	30		1089.2.e.p.727.14		36
99.58	even	15		9801.2.a.cp.1.14		18
99.74	even	30		1089.2.e.o.727.5		36
99.85	odd	30		9801.2.a.cn.1.5		18
99.86	odd	30		891.2.f.f.163.3		36
99.97	even	15	inner	297.2.n.b.262.7		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.7	✓	72	9.2	odd	6
99.2.m.b.31.7	yes	72	33.20	odd	10
99.2.m.b.49.3	yes	72	3.2	odd	2
99.2.m.b.97.3	yes	72	99.20	odd	30
297.2.n.b.64.3		72	11.9	even	5	inner
297.2.n.b.181.3		72	9.7	even	3	inner
297.2.n.b.262.7		72	99.97	even	15	inner
297.2.n.b.280.7		72	1.1	even	1	trivial
891.2.f.e.82.7		36	9.4	even	3
891.2.f.e.163.7		36	99.31	even	15
891.2.f.f.82.3		36	9.5	odd	6
891.2.f.f.163.3		36	99.86	odd	30
1089.2.e.o.364.5		36	33.8	even	10
1089.2.e.o.727.5		36	99.74	even	30
1089.2.e.p.364.14		36	33.14	odd	10
1089.2.e.p.727.14		36	99.47	odd	30
9801.2.a.cm.1.5		18	99.14	odd	30
9801.2.a.cn.1.5		18	99.85	odd	30
9801.2.a.co.1.14		18	99.41	even	30
9801.2.a.cp.1.14		18	99.58	even	15

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.992662 - 1.10246i) q^{2} +(-0.0209894 - 0.199701i) q^{4} +(0.0483964 + 0.0537496i) q^{5} +(1.78161 + 0.793226i) q^{7} +(2.15937 + 1.56887i) q^{8} +0.107298 q^{10} +(2.15852 - 2.51810i) q^{11} +(-1.08533 - 0.230693i) q^{13} +(2.64304 - 1.17676i) q^{14} +(4.26598 - 0.906761i) q^{16} +(0.0576906 - 0.177553i) q^{17} +(-4.20255 - 3.05333i) q^{19} +(0.00971804 - 0.0107930i) q^{20} +(-0.633432 - 4.87930i) q^{22} +(-3.42420 + 5.93089i) q^{23} +(0.522096 - 4.96741i) q^{25} +(-1.33169 + 0.967532i) q^{26} +(0.121013 - 0.372440i) q^{28} +(2.95048 + 1.31364i) q^{29} +(-1.61139 - 0.342511i) q^{31} +(0.565872 - 0.980120i) q^{32} +(-0.138479 - 0.239852i) q^{34} +(0.0435881 + 0.134150i) q^{35} +(-7.75416 + 5.63373i) q^{37} +(-7.53790 + 1.60223i) q^{38} +(0.0201793 + 0.191993i) q^{40} +(-4.62566 + 2.05948i) q^{41} +(4.06266 + 7.03673i) q^{43} +(-0.548173 - 0.378204i) q^{44} +(3.13951 + 9.66242i) q^{46} +(0.907572 - 8.63497i) q^{47} +(-2.13897 - 2.37557i) q^{49} +(-4.95812 - 5.50655i) q^{50} +(-0.0232893 + 0.221583i) q^{52} +(-0.467571 - 1.43904i) q^{53} +(0.239811 - 0.00584740i) q^{55} +(2.60269 + 4.50800i) q^{56} +(4.37707 - 1.94880i) q^{58} +(-0.554654 - 5.27718i) q^{59} +(-6.92183 + 1.47128i) q^{61} +(-1.97717 + 1.43649i) q^{62} +(2.17659 + 6.69887i) q^{64} +(-0.0401262 - 0.0695006i) q^{65} +(-0.447660 + 0.775370i) q^{67} +(-0.0366685 - 0.00779413i) q^{68} +(0.191164 + 0.0851116i) q^{70} +(0.476791 - 1.46741i) q^{71} +(9.31301 - 6.76630i) q^{73} +(-1.48629 + 14.1411i) q^{74} +(-0.521545 + 0.903343i) q^{76} +(5.84306 - 2.77409i) q^{77} +(-8.87869 + 9.86078i) q^{79} +(0.255196 + 0.185411i) q^{80} +(-2.32122 + 7.14398i) q^{82} +(-17.5744 + 3.73556i) q^{83} +(0.0123354 - 0.00549209i) q^{85} +(11.7906 + 2.50616i) q^{86} +(8.61161 - 2.05107i) q^{88} +12.3990 q^{89} +(-1.75064 - 1.27192i) q^{91} +(1.25628 + 0.559331i) q^{92} +(-8.61882 - 9.57217i) q^{94} +(-0.0392728 - 0.373656i) q^{95} +(6.99476 - 7.76847i) q^{97} -4.74225 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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