LMFDB - Embedded newform 552.2.n.b.91.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

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

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

chi := DirichletCharacter("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.21
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38507 - 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} -2.80468 q^{5} +(-1.38507 + 0.285614i) q^{6} +0.415199 q^{7} +(2.31819 - 1.62049i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.38507 - 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} -2.80468 q^{5} +(-1.38507 + 0.285614i) q^{6} +0.415199 q^{7} +(2.31819 - 1.62049i) q^{8} +1.00000 q^{9} +(-3.88469 + 0.801057i) q^{10} -5.54747i q^{11} +(-1.83685 + 0.791193i) q^{12} -3.19024i q^{13} +(0.575080 - 0.118587i) q^{14} +2.80468 q^{15} +(2.74803 - 2.90660i) q^{16} -2.01349i q^{17} +(1.38507 - 0.285614i) q^{18} +2.50622i q^{19} +(-5.15178 + 2.21904i) q^{20} -0.415199 q^{21} +(-1.58444 - 7.68365i) q^{22} +(2.87533 - 3.83829i) q^{23} +(-2.31819 + 1.62049i) q^{24} +2.86624 q^{25} +(-0.911179 - 4.41871i) q^{26} -1.00000 q^{27} +(0.762658 - 0.328502i) q^{28} -4.69915i q^{29} +(3.88469 - 0.801057i) q^{30} +8.16330i q^{31} +(2.97605 - 4.81073i) q^{32} +5.54747i q^{33} +(-0.575080 - 2.78882i) q^{34} -1.16450 q^{35} +(1.83685 - 0.791193i) q^{36} -3.59504 q^{37} +(0.715812 + 3.47129i) q^{38} +3.19024i q^{39} +(-6.50179 + 4.54496i) q^{40} +2.52410 q^{41} +(-0.575080 + 0.118587i) q^{42} +1.80649i q^{43} +(-4.38912 - 10.1899i) q^{44} -2.80468 q^{45} +(2.88627 - 6.13755i) q^{46} +3.58339i q^{47} +(-2.74803 + 2.90660i) q^{48} -6.82761 q^{49} +(3.96995 - 0.818639i) q^{50} +2.01349i q^{51} +(-2.52410 - 5.85999i) q^{52} +0.270501 q^{53} +(-1.38507 + 0.285614i) q^{54} +15.5589i q^{55} +(0.962511 - 0.672826i) q^{56} -2.50622i q^{57} +(-1.34214 - 6.50865i) q^{58} -0.657857 q^{59} +(5.15178 - 2.21904i) q^{60} +11.8024 q^{61} +(2.33155 + 11.3068i) q^{62} +0.415199 q^{63} +(2.74803 - 7.51321i) q^{64} +8.94761i q^{65} +(1.58444 + 7.68365i) q^{66} +5.41363i q^{67} +(-1.59306 - 3.69847i) q^{68} +(-2.87533 + 3.83829i) q^{69} +(-1.61292 + 0.332598i) q^{70} +6.09004i q^{71} +(2.31819 - 1.62049i) q^{72} -2.82330 q^{73} +(-4.97938 + 1.02679i) q^{74} -2.86624 q^{75} +(1.98290 + 4.60355i) q^{76} -2.30330i q^{77} +(0.911179 + 4.41871i) q^{78} +15.0378 q^{79} +(-7.70734 + 8.15210i) q^{80} +1.00000 q^{81} +(3.49606 - 0.720918i) q^{82} +11.1848i q^{83} +(-0.762658 + 0.328502i) q^{84} +5.64719i q^{85} +(0.515959 + 2.50212i) q^{86} +4.69915i q^{87} +(-8.98962 - 12.8601i) q^{88} -4.02672i q^{89} +(-3.88469 + 0.801057i) q^{90} -1.32459i q^{91} +(2.24472 - 9.32530i) q^{92} -8.16330i q^{93} +(1.02347 + 4.96325i) q^{94} -7.02915i q^{95} +(-2.97605 + 4.81073i) q^{96} -14.5135i q^{97} +(-9.45673 + 1.95006i) q^{98} -5.54747i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	1.38507	−	0.285614i	0.979394	−	0.201960i
$2$	1.38507	−	0.285614i	0.979394	−	0.201960i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.83685	−	0.791193i	0.918424	−	0.395596i
$5$	−2.80468			−1.25429			−0.627146	−	0.778902i	$-0.715777\pi$
$5$	−2.80468			−1.25429			−0.627146	+	0.778902i	$0.715777\pi$
$6$	−1.38507	+	0.285614i	−0.565453	+	0.116602i
$7$	0.415199			0.156930			0.0784652	−	0.996917i	$-0.474998\pi$
$7$	0.415199			0.156930			0.0784652	+	0.996917i	$0.474998\pi$
$8$	2.31819	−	1.62049i	0.819605	−	0.572930i
$9$	1.00000			0.333333
$10$	−3.88469	+	0.801057i	−1.22845	+	0.253317i
$11$		−	5.54747i		−	1.67263i	−0.548253	−	0.836313i	$-0.684707\pi$
$11$		−	5.54747i		−	1.67263i	0.548253	−	0.836313i	$-0.315293\pi$
$12$	−1.83685	+	0.791193i	−0.530253	+	0.228398i
$13$		−	3.19024i		−	0.884814i	−0.896814	−	0.442407i	$-0.854125\pi$
$13$		−	3.19024i		−	0.884814i	0.896814	−	0.442407i	$-0.145875\pi$
$14$	0.575080	−	0.118587i	0.153697	−	0.0316937i
$15$	2.80468			0.724166
$16$	2.74803	−	2.90660i	0.687007	−	0.726651i
$17$		−	2.01349i		−	0.488342i	−0.969732	−	0.244171i	$-0.921484\pi$
$17$		−	2.01349i		−	0.488342i	0.969732	−	0.244171i	$-0.0785158\pi$
$18$	1.38507	−	0.285614i	0.326465	−	0.0673199i
$19$			2.50622i			0.574966i	0.957786	+	0.287483i	$0.0928185\pi$
$19$			2.50622i			0.574966i	−0.957786	+	0.287483i	$0.907182\pi$
$20$	−5.15178	+	2.21904i	−1.15197	+	0.496193i
$21$	−0.415199			−0.0906038
$22$	−1.58444	−	7.68365i	−0.337803	−	1.63816i
$23$	2.87533	−	3.83829i	0.599548	−	0.800339i
$23$	2.87533	−	3.83829i	0.599548	−	0.800339i
$24$	−2.31819	+	1.62049i	−0.473199	+	0.330781i
$25$	2.86624			0.573248
$26$	−0.911179	−	4.41871i	−0.178697	−	0.866581i
$27$	−1.00000			−0.192450
$28$	0.762658	−	0.328502i	0.144129	−	0.0620811i
$29$		−	4.69915i		−	0.872609i	−0.899799	−	0.436305i	$-0.856287\pi$
$29$		−	4.69915i		−	0.872609i	0.899799	−	0.436305i	$-0.143713\pi$
$30$	3.88469	−	0.801057i	0.709243	−	0.146252i
$31$			8.16330i			1.46617i	0.680136	+	0.733086i	$0.261921\pi$
$31$			8.16330i			1.46617i	−0.680136	+	0.733086i	$0.738079\pi$
$32$	2.97605	−	4.81073i	0.526096	−	0.850425i
$33$			5.54747i			0.965691i
$34$	−0.575080	−	2.78882i	−0.0986255	−	0.478279i
$35$	−1.16450			−0.196837
$36$	1.83685	−	0.791193i	0.306141	−	0.131865i
$37$	−3.59504			−0.591020			−0.295510	−	0.955340i	$-0.595490\pi$
$37$	−3.59504			−0.591020			−0.295510	+	0.955340i	$0.595490\pi$
$38$	0.715812	+	3.47129i	0.116120	+	0.563118i
$39$			3.19024i			0.510848i
$40$	−6.50179	+	4.54496i	−1.02802	+	0.718621i
$41$	2.52410			0.394198			0.197099	−	0.980384i	$-0.436848\pi$
$41$	2.52410			0.394198			0.197099	+	0.980384i	$0.436848\pi$
$42$	−0.575080	+	0.118587i	−0.0887368	+	0.0182983i
$43$			1.80649i			0.275487i	0.990468	+	0.137743i	$0.0439849\pi$
$43$			1.80649i			0.275487i	−0.990468	+	0.137743i	$0.956015\pi$
$44$	−4.38912	−	10.1899i	−0.661685	−	1.53618i
$45$	−2.80468			−0.418097
$46$	2.88627	−	6.13755i	0.425557	−	0.904932i
$47$			3.58339i			0.522690i	0.965245	+	0.261345i	$0.0841661\pi$
$47$			3.58339i			0.522690i	−0.965245	+	0.261345i	$0.915834\pi$
$48$	−2.74803	+	2.90660i	−0.396644	+	0.419532i
$49$	−6.82761			−0.975373
$50$	3.96995	−	0.818639i	0.561436	−	0.115773i
$51$			2.01349i			0.281944i
$52$	−2.52410	−	5.85999i	−0.350029	−	0.812635i
$53$	0.270501			0.0371562			0.0185781	−	0.999827i	$-0.494086\pi$
$53$	0.270501			0.0371562			0.0185781	+	0.999827i	$0.494086\pi$
$54$	−1.38507	+	0.285614i	−0.188484	+	0.0388672i
$55$			15.5589i			2.09796i
$56$	0.962511	−	0.672826i	0.128621	−	0.0899101i
$57$		−	2.50622i		−	0.331957i
$58$	−1.34214	−	6.50865i	−0.176232	−	0.854628i
$59$	−0.657857			−0.0856456			−0.0428228	−	0.999083i	$-0.513635\pi$
$59$	−0.657857			−0.0856456			−0.0428228	+	0.999083i	$0.513635\pi$
$60$	5.15178	−	2.21904i	0.665092	−	0.286477i
$61$	11.8024			1.51114			0.755572	−	0.655065i	$-0.227359\pi$
$61$	11.8024			1.51114			0.755572	+	0.655065i	$0.227359\pi$
$62$	2.33155	+	11.3068i	0.296108	+	1.43596i
$63$	0.415199			0.0523102
$64$	2.74803	−	7.51321i	0.343503	−	0.939151i
$65$			8.94761i			1.10981i
$66$	1.58444	+	7.68365i	0.195031	+	0.945791i
$67$			5.41363i			0.661380i	0.943739	+	0.330690i	$0.107281\pi$
$67$			5.41363i			0.661380i	−0.943739	+	0.330690i	$0.892719\pi$
$68$	−1.59306	−	3.69847i	−0.193186	−	0.448505i
$69$	−2.87533	+	3.83829i	−0.346149	+	0.462076i
$70$	−1.61292	+	0.332598i	−0.192781	+	0.0397531i
$71$			6.09004i			0.722755i	0.932420	+	0.361377i	$0.117693\pi$
$71$			6.09004i			0.722755i	−0.932420	+	0.361377i	$0.882307\pi$
$72$	2.31819	−	1.62049i	0.273202	−	0.190977i
$73$	−2.82330			−0.330442			−0.165221	−	0.986257i	$-0.552834\pi$
$73$	−2.82330			−0.330442			−0.165221	+	0.986257i	$0.552834\pi$
$74$	−4.97938	+	1.02679i	−0.578841	+	0.119362i
$75$	−2.86624			−0.330965
$76$	1.98290	+	4.60355i	0.227455	+	0.528063i
$77$		−	2.30330i		−	0.262486i
$78$	0.911179	+	4.41871i	0.103171	+	0.500321i
$79$	15.0378			1.69188			0.845942	−	0.533276i	$-0.179039\pi$
$79$	15.0378			1.69188			0.845942	+	0.533276i	$0.179039\pi$
$80$	−7.70734	+	8.15210i	−0.861707	+	0.911432i
$81$	1.00000			0.111111
$82$	3.49606	−	0.720918i	0.386075	−	0.0796121i
$83$			11.1848i			1.22769i	0.789428	+	0.613844i	$0.210377\pi$
$83$			11.1848i			1.22769i	−0.789428	+	0.613844i	$0.789623\pi$
$84$	−0.762658	+	0.328502i	−0.0832128	+	0.0358426i
$85$			5.64719i			0.612523i
$86$	0.515959	+	2.50212i	0.0556373	+	0.269810i
$87$			4.69915i			0.503801i
$88$	−8.98962	−	12.8601i	−0.958296	−	1.37089i
$89$		−	4.02672i		−	0.426831i	−0.976962	−	0.213416i	$-0.931541\pi$
$89$		−	4.02672i		−	0.426831i	0.976962	−	0.213416i	$-0.0684588\pi$
$90$	−3.88469	+	0.801057i	−0.409482	+	0.0844389i
$91$		−	1.32459i		−	0.138854i
$92$	2.24472	−	9.32530i	0.234028	−	0.972230i
$93$		−	8.16330i		−	0.846494i
$94$	1.02347	+	4.96325i	0.105562	+	0.511920i
$95$		−	7.02915i		−	0.721175i
$96$	−2.97605	+	4.81073i	−0.303742	+	0.490993i
$97$		−	14.5135i		−	1.47362i	−0.676100	−	0.736810i	$-0.736331\pi$
$97$		−	14.5135i		−	1.47362i	0.676100	−	0.736810i	$-0.263669\pi$
$98$	−9.45673	+	1.95006i	−0.955274	+	0.196986i
$99$		−	5.54747i		−	0.557542i
$100$	5.26485	−	2.26775i	0.526485	−	0.226775i
$101$			7.00245i			0.696770i	0.937352	+	0.348385i	$0.113270\pi$
$101$			7.00245i			0.696770i	−0.937352	+	0.348385i	$0.886730\pi$
$102$	0.575080	+	2.78882i	0.0569415	+	0.276135i
$103$	18.4881			1.82169			0.910845	−	0.412750i	$-0.135432\pi$
$103$	18.4881			1.82169			0.910845	+	0.412750i	$0.135432\pi$
$104$	−5.16975	−	7.39559i	−0.506936	−	0.725198i
$105$	1.16450			0.113644
$106$	0.374663	−	0.0772590i	0.0363905	−	0.00750405i
$107$			2.34324i			0.226530i	0.993565	+	0.113265i	$0.0361308\pi$
$107$			2.34324i			0.226530i	−0.993565	+	0.113265i	$0.963869\pi$
$108$	−1.83685	+	0.791193i	−0.176751	+	0.0761326i
$109$	−9.34569			−0.895155			−0.447578	−	0.894245i	$-0.647713\pi$
$109$	−9.34569			−0.895155			−0.447578	+	0.894245i	$0.647713\pi$
$110$	4.44384	+	21.5502i	0.423704	+	2.05473i
$111$	3.59504			0.341226
$112$	1.14098	−	1.20682i	0.107812	−	0.114034i
$113$		−	18.5203i		−	1.74225i	−0.491064	−	0.871123i	$-0.663392\pi$
$113$		−	18.5203i		−	1.74225i	0.491064	−	0.871123i	$-0.336608\pi$
$114$	−0.715812	−	3.47129i	−0.0670419	−	0.325116i
$115$	−8.06438	+	10.7652i	−0.752008	+	1.00386i
$116$	−3.71793	−	8.63162i	−0.345201	−	0.801426i
$117$		−	3.19024i		−	0.294938i
$118$	−0.911179	+	0.187893i	−0.0838808	+	0.0172970i
$119$		−	0.835997i		−	0.0766357i
$120$	6.50179	−	4.54496i	0.593530	−	0.414896i
$121$	−19.7744			−1.79768
$122$	16.3472	−	3.37094i	1.48001	−	0.305190i
$123$	−2.52410			−0.227590
$124$	6.45874	+	14.9947i	0.580012	+	1.34657i
$125$	5.98452			0.535272
$126$	0.575080	−	0.118587i	0.0512322	−	0.0105646i
$127$			5.31443i			0.471580i	0.971804	+	0.235790i	$0.0757677\pi$
$127$			5.31443i			0.471580i	−0.971804	+	0.235790i	$0.924232\pi$
$128$	1.66034	−	11.1912i	0.146754	−	0.989173i
$129$		−	1.80649i		−	0.159052i
$130$	2.55557	+	12.3931i	0.224138	+	1.08695i
$131$	1.82236			0.159220			0.0796101	−	0.996826i	$-0.474632\pi$
$131$	1.82236			0.159220			0.0796101	+	0.996826i	$0.474632\pi$
$132$	4.38912	+	10.1899i	0.382024	+	0.886914i
$133$			1.04058i			0.0902297i
$134$	1.54621	+	7.49827i	0.133572	+	0.647751i
$135$	2.80468			0.241389
$136$	−3.26283	−	4.66765i	−0.279786	−	0.400247i
$137$			18.7457i			1.60155i	0.598962	+	0.800777i	$0.295580\pi$
$137$			18.7457i			1.60155i	−0.598962	+	0.800777i	$0.704420\pi$
$138$	−2.88627	+	6.13755i	−0.245695	+	0.522463i
$139$	−7.64330			−0.648296			−0.324148	−	0.946006i	$-0.605078\pi$
$139$	−7.64330			−0.648296			−0.324148	+	0.946006i	$0.605078\pi$
$140$	−2.13901	+	0.921345i	−0.180780	+	0.0778679i
$141$		−	3.58339i		−	0.301775i
$142$	1.73940	+	8.43515i	0.145967	+	0.707862i
$143$	−17.6978			−1.47996
$144$	2.74803	−	2.90660i	0.229002	−	0.242217i
$145$			13.1796i			1.09451i
$146$	−3.91047	+	0.806375i	−0.323633	+	0.0667360i
$147$	6.82761			0.563132
$148$	−6.60354	+	2.84437i	−0.542807	+	0.233805i
$149$	−10.0586			−0.824032			−0.412016	−	0.911177i	$-0.635175\pi$
$149$	−10.0586			−0.824032			−0.412016	+	0.911177i	$0.635175\pi$
$150$	−3.96995	+	0.818639i	−0.324145	+	0.0668416i
$151$			16.6249i			1.35292i	0.736480	+	0.676459i	$0.236486\pi$
$151$			16.6249i			1.35292i	−0.736480	+	0.676459i	$0.763514\pi$
$152$	4.06130	+	5.80990i	0.329415	+	0.471245i
$153$		−	2.01349i		−	0.162781i
$154$	−0.657857	−	3.19024i	−0.0530116	−	0.257077i
$155$		−	22.8954i		−	1.83901i
$156$	2.52410	+	5.85999i	0.202089	+	0.469175i
$157$	−6.29506			−0.502401			−0.251200	−	0.967935i	$-0.580825\pi$
$157$	−6.29506			−0.502401			−0.251200	+	0.967935i	$0.580825\pi$
$158$	20.8284	−	4.29501i	1.65702	−	0.341692i
$159$	−0.270501			−0.0214521
$160$	−8.34687	+	13.4926i	−0.659878	+	1.06668i
$161$	1.19383	−	1.59365i	0.0940873	−	0.125598i
$162$	1.38507	−	0.285614i	0.108822	−	0.0224400i
$163$	18.3381			1.43635			0.718175	−	0.695862i	$-0.244978\pi$
$163$	18.3381			1.43635			0.718175	+	0.695862i	$0.244978\pi$
$164$	4.63638	−	1.99705i	0.362041	−	0.155943i
$165$		−	15.5589i		−	1.21126i
$166$	3.19453	+	15.4917i	0.247944	+	1.20239i
$167$		−	19.7559i		−	1.52876i	−0.644766	−	0.764380i	$-0.723045\pi$
$167$		−	19.7559i		−	1.52876i	0.644766	−	0.764380i	$-0.276955\pi$
$168$	−0.962511	+	0.672826i	−0.0742593	+	0.0519096i
$169$	2.82236			0.217104
$170$	1.61292	+	7.82176i	0.123705	+	0.599902i
$171$			2.50622i			0.191655i
$172$	1.42928	+	3.31825i	0.108982	+	0.253014i
$173$		−	11.3869i		−	0.865731i	−0.901459	−	0.432865i	$-0.857503\pi$
$173$		−	11.3869i		−	0.865731i	0.901459	−	0.432865i	$-0.142497\pi$
$174$	1.34214	+	6.50865i	0.101748	+	0.493420i
$175$	1.19006			0.0899601
$176$	−16.1243	−	15.2446i	−1.21541	−	1.14911i
$177$	0.657857			0.0494475
$178$	−1.15009	−	5.57729i	−0.0862028	−	0.418036i
$179$	19.1156			1.42877			0.714385	−	0.699753i	$-0.246707\pi$
$179$	19.1156			1.42877			0.714385	+	0.699753i	$0.246707\pi$
$180$	−5.15178	+	2.21904i	−0.383991	+	0.165398i
$181$	5.60596			0.416688			0.208344	−	0.978056i	$-0.433193\pi$
$181$	5.60596			0.416688			0.208344	+	0.978056i	$0.433193\pi$
$182$	−0.378321	−	1.83465i	−0.0280430	−	0.135993i
$183$	−11.8024			−0.872460
$184$	0.445655	−	13.5573i	0.0328541	−	0.999460i
$185$	10.0829			0.741312
$186$	−2.33155	−	11.3068i	−0.170958	−	0.829051i
$187$	−11.1698			−0.816813
$188$	2.83515	+	6.58214i	0.206774	+	0.480052i
$189$	−0.415199			−0.0302013
$190$	−2.00763	−	9.73587i	−0.145648	−	0.706315i
$191$	−25.0291			−1.81104			−0.905522	−	0.424298i	$-0.860521\pi$
$191$	−25.0291			−1.81104			−0.905522	+	0.424298i	$0.860521\pi$
$192$	−2.74803	+	7.51321i	−0.198322	+	0.542219i
$193$	24.6407			1.77367			0.886837	−	0.462082i	$-0.152898\pi$
$193$	24.6407			1.77367			0.886837	+	0.462082i	$0.152898\pi$
$194$	−4.14525	−	20.1022i	−0.297612	−	1.44325i
$195$		−	8.94761i		−	0.640752i
$196$	−12.5413	+	5.40196i	−0.895806	+	0.385854i
$197$			2.39584i			0.170697i	0.996351	+	0.0853483i	$0.0272003\pi$
$197$			2.39584i			0.170697i	−0.996351	+	0.0853483i	$0.972800\pi$
$198$	−1.58444	−	7.68365i	−0.112601	−	0.546053i
$199$	−3.76352			−0.266789			−0.133395	−	0.991063i	$-0.542588\pi$
$199$	−3.76352			−0.266789			−0.133395	+	0.991063i	$0.542588\pi$
$200$	6.64449	−	4.64471i	0.469837	−	0.328431i
$201$		−	5.41363i		−	0.381848i
$202$	2.00000	+	9.69890i	0.140720	+	0.682412i
$203$		−	1.95108i		−	0.136939i
$204$	1.59306	+	3.69847i	0.111536	+	0.258945i
$205$	−7.07929			−0.494439
$206$	25.6074	−	5.28047i	1.78415	−	0.367908i
$207$	2.87533	−	3.83829i	0.199849	−	0.266780i
$208$	−9.27277	−	8.76687i	−0.642951	−	0.607873i
$209$	13.9032			0.961703
$210$	1.61292	−	0.332598i	0.111302	−	0.0229515i
$211$	−17.0238			−1.17197			−0.585983	−	0.810323i	$-0.699292\pi$
$211$	−17.0238			−1.17197			−0.585983	+	0.810323i	$0.699292\pi$
$212$	0.496869	−	0.214018i	0.0341251	−	0.0146988i
$213$		−	6.09004i		−	0.417283i
$214$	0.669263	+	3.24556i	0.0457499	+	0.221862i
$215$		−	5.06662i		−	0.345541i
$216$	−2.31819	+	1.62049i	−0.157733	+	0.110260i
$217$			3.38939i			0.230087i
$218$	−12.9445	+	2.66926i	−0.876709	+	0.180785i
$219$	2.82330			0.190781
$220$	12.3101	+	28.5793i	0.829946	+	1.92682i
$221$	−6.42351			−0.432092
$222$	4.97938	−	1.02679i	0.334194	−	0.0689139i
$223$		−	15.8920i		−	1.06421i	−0.846678	−	0.532105i	$-0.821401\pi$
$223$		−	15.8920i		−	1.06421i	0.846678	−	0.532105i	$-0.178599\pi$
$224$	1.23565	−	1.99741i	0.0825605	−	0.133458i
$225$	2.86624			0.191083
$226$	−5.28967	−	25.6520i	−0.351864	−	1.70635i
$227$		−	0.778468i		−	0.0516687i	−0.999666	−	0.0258344i	$-0.991776\pi$
$227$		−	0.778468i		−	0.0516687i	0.999666	−	0.0258344i	$-0.00822425\pi$
$228$	−1.98290	−	4.60355i	−0.131321	−	0.304877i
$229$	18.3034			1.20952			0.604761	−	0.796407i	$-0.293269\pi$
$229$	18.3034			1.20952			0.604761	+	0.796407i	$0.293269\pi$
$230$	−8.09506	+	17.2139i	−0.533773	+	1.13505i
$231$			2.30330i			0.151546i
$232$	−7.61492	−	10.8935i	−0.499944	−	0.715195i
$233$	10.1288			0.663558			0.331779	−	0.943357i	$-0.392351\pi$
$233$	10.1288			0.663558			0.331779	+	0.943357i	$0.392351\pi$
$234$	−0.911179	−	4.41871i	−0.0595656	−	0.288860i
$235$		−	10.0503i		−	0.655606i
$236$	−1.20838	+	0.520491i	−0.0786590	+	0.0338811i
$237$	−15.0378			−0.976809
$238$	−0.238773	−	1.15792i	−0.0154773	−	0.0750566i
$239$		−	22.8436i		−	1.47763i	−0.673910	−	0.738813i	$-0.735387\pi$
$239$		−	22.8436i		−	1.47763i	0.673910	−	0.738813i	$-0.264613\pi$
$240$	7.70734	−	8.15210i	0.497507	−	0.526216i
$241$			26.9055i			1.73314i	0.499059	+	0.866568i	$0.333679\pi$
$241$			26.9055i			1.73314i	−0.499059	+	0.866568i	$0.666321\pi$
$242$	−27.3890	+	5.64786i	−1.76063	+	0.363058i
$243$	−1.00000			−0.0641500
$244$	21.6793	−	9.33799i	1.38787	−	0.597803i
$245$	19.1493			1.22340
$246$	−3.49606	+	0.720918i	−0.222900	+	0.0459641i
$247$	7.99544			0.508738
$248$	13.2285	+	18.9241i	0.840013	+	1.20168i
$249$		−	11.1848i		−	0.708806i
$250$	8.28899	−	1.70926i	0.524242	−	0.108103i
$251$			25.7950i			1.62817i	0.580747	+	0.814084i	$0.302761\pi$
$251$			25.7950i			1.62817i	−0.580747	+	0.814084i	$0.697239\pi$
$252$	0.762658	−	0.328502i	0.0480429	−	0.0206937i
$253$	−21.2928	−	15.9508i	−1.33867	−	1.00282i
$254$	1.51788	+	7.36087i	0.0952402	+	0.461862i
$255$		−	5.64719i		−	0.353641i
$256$	−0.896688	−	15.9749i	−0.0560430	−	0.998428i
$257$	−24.9514			−1.55642			−0.778212	−	0.628002i	$-0.783873\pi$
$257$	−24.9514			−1.55642			−0.778212	+	0.628002i	$0.783873\pi$
$258$	−0.515959	−	2.50212i	−0.0321222	−	0.155775i
$259$	−1.49265			−0.0927491
$260$	7.07929	+	16.4354i	0.439039	+	1.01928i
$261$		−	4.69915i		−	0.290870i
$262$	2.52410	−	0.520491i	0.155939	−	0.0321561i
$263$	4.92026			0.303396			0.151698	−	0.988427i	$-0.451526\pi$
$263$	4.92026			0.303396			0.151698	+	0.988427i	$0.451526\pi$
$264$	8.98962	+	12.8601i	0.553273	+	0.791484i
$265$	−0.758669			−0.0466047
$266$	0.297204	+	1.44128i	0.0182228	+	0.0883704i
$267$			4.02672i			0.246431i
$268$	4.28322	+	9.94402i	0.261640	+	0.607428i
$269$			8.77633i			0.535102i	0.963544	+	0.267551i	$0.0862144\pi$
$269$			8.77633i			0.535102i	−0.963544	+	0.267551i	$0.913786\pi$
$270$	3.88469	−	0.801057i	0.236414	−	0.0487508i
$271$			7.39559i			0.449250i	0.974445	+	0.224625i	$0.0721158\pi$
$271$			7.39559i			0.449250i	−0.974445	+	0.224625i	$0.927884\pi$
$272$	−5.85241	−	5.53312i	−0.354854	−	0.335494i
$273$			1.32459i			0.0801675i
$274$	5.35405	+	25.9642i	0.323450	+	1.56855i
$275$		−	15.9004i		−	0.958829i
$276$	−2.24472	+	9.32530i	−0.135116	+	0.561317i
$277$			8.71879i			0.523861i	0.965087	+	0.261931i	$0.0843592\pi$
$277$			8.71879i			0.523861i	−0.965087	+	0.261931i	$0.915641\pi$
$278$	−10.5865	+	2.18304i	−0.634938	+	0.130930i
$279$			8.16330i			0.488724i
$280$	−2.69954	+	1.88706i	−0.161328	+	0.112773i
$281$		−	5.18858i		−	0.309525i	−0.987952	−	0.154762i	$-0.950539\pi$
$281$		−	5.18858i		−	0.309525i	0.987952	−	0.154762i	$-0.0494612\pi$
$282$	−1.02347	−	4.96325i	−0.0609465	−	0.295557i
$283$		−	26.9752i		−	1.60351i	−0.597653	−	0.801755i	$-0.703900\pi$
$283$		−	26.9752i		−	1.60351i	0.597653	−	0.801755i	$-0.296100\pi$
$284$	4.81840	+	11.1865i	0.285919	+	0.663796i
$285$			7.02915i			0.416371i
$286$	−24.5127	+	5.05474i	−1.44947	+	0.298893i
$287$	1.04800			0.0618616
$288$	2.97605	−	4.81073i	0.175365	−	0.283475i
$289$	12.9459			0.761522
$290$	3.76429	+	18.2547i	0.221046	+	1.07195i
$291$			14.5135i			0.850795i
$292$	−5.18597	+	2.23377i	−0.303486	+	0.130722i
$293$	−22.7008			−1.32619			−0.663096	−	0.748534i	$-0.730758\pi$
$293$	−22.7008			−1.32619			−0.663096	+	0.748534i	$0.730758\pi$
$294$	9.45673	−	1.95006i	0.551528	−	0.113730i
$295$	1.84508			0.107425
$296$	−8.33398	+	5.82572i	−0.484403	+	0.338613i
$297$			5.54747i			0.321897i
$298$	−13.9319	+	2.87288i	−0.807051	+	0.166421i
$299$	−12.2451	−	9.17300i	−0.708151	−	0.530488i
$300$	−5.26485	+	2.26775i	−0.303966	+	0.130929i
$301$			0.750052i			0.0432323i
$302$	4.74832	+	23.0267i	0.273235	+	1.32504i
$303$		−	7.00245i		−	0.402280i
$304$	7.28458	+	6.88716i	0.417800	+	0.395006i
$305$	−33.1020			−1.89542
$306$	−0.575080	−	2.78882i	−0.0328752	−	0.159426i
$307$	4.84075			0.276276			0.138138	−	0.990413i	$-0.455888\pi$
$307$	4.84075			0.276276			0.138138	+	0.990413i	$0.455888\pi$
$308$	−1.82236	−	4.23082i	−0.103838	−	0.241073i
$309$	−18.4881			−1.05175
$310$	−6.53927	−	31.7118i	−0.371405	−	1.80111i
$311$		−	9.16116i		−	0.519482i	−0.965678	−	0.259741i	$-0.916363\pi$
$311$		−	9.16116i		−	0.519482i	0.965678	−	0.259741i	$-0.0836372\pi$
$312$	5.16975	+	7.39559i	0.292680	+	0.418693i
$313$		−	17.8518i		−	1.00904i	−0.863399	−	0.504522i	$-0.831669\pi$
$313$		−	17.8518i		−	1.00904i	0.863399	−	0.504522i	$-0.168331\pi$
$314$	−8.71912	+	1.79796i	−0.492048	+	0.101465i
$315$	−1.16450			−0.0656122
$316$	27.6221	−	11.8978i	1.55387	−	0.669303i
$317$			31.8091i			1.78658i	0.449485	+	0.893288i	$0.351607\pi$
$317$			31.8091i			1.78658i	−0.449485	+	0.893288i	$0.648393\pi$
$318$	−0.374663	+	0.0772590i	−0.0210101	+	0.00433247i
$319$	−26.0684			−1.45955
$320$	−7.70734	+	21.0722i	−0.430854	+	1.17797i
$321$		−	2.34324i		−	0.130787i
$322$	1.19838	−	2.54830i	0.0667828	−	0.142011i
$323$	5.04624			0.280780
$324$	1.83685	−	0.791193i	0.102047	−	0.0439552i
$325$		−	9.14400i		−	0.507218i
$326$	25.3996	−	5.23762i	1.40675	−	0.290085i
$327$	9.34569			0.516818
$328$	5.85134	−	4.09027i	0.323086	−	0.225847i
$329$			1.48782i			0.0820260i
$330$	−4.44384	−	21.5502i	−0.244625	−	1.18630i
$331$	−3.34810			−0.184028			−0.0920140	−	0.995758i	$-0.529330\pi$
$331$	−3.34810			−0.184028			−0.0920140	+	0.995758i	$0.529330\pi$
$332$	8.84930	+	20.5447i	0.485669	+	1.12754i
$333$	−3.59504			−0.197007
$334$	−5.64258	−	27.3634i	−0.308748	−	1.49726i
$335$		−	15.1835i		−	0.829564i
$336$	−1.14098	+	1.20682i	−0.0622455	+	0.0658374i
$337$		−	14.8251i		−	0.807574i	−0.914853	−	0.403787i	$-0.867694\pi$
$337$		−	14.8251i		−	0.807574i	0.914853	−	0.403787i	$-0.132306\pi$
$338$	3.90917	−	0.806106i	0.212631	−	0.0438464i
$339$			18.5203i			1.00589i
$340$	4.46801	+	10.3730i	0.242312	+	0.562557i
$341$	45.2856			2.45235
$342$	0.715812	+	3.47129i	0.0387067	+	0.187706i
$343$	−5.74121			−0.309996
$344$	2.92739	+	4.18779i	0.157835	+	0.225790i
$345$	8.06438	−	10.7652i	0.434172	−	0.579578i
$346$	−3.25227	−	15.7717i	−0.174843	−	0.847891i
$347$	32.8500			1.76348			0.881740	−	0.471736i	$-0.156372\pi$
$347$	32.8500			1.76348			0.881740	+	0.471736i	$0.156372\pi$
$348$	3.71793	+	8.63162i	0.199302	+	0.462703i
$349$		−	16.1566i		−	0.864844i	−0.901671	−	0.432422i	$-0.857659\pi$
$349$		−	16.1566i		−	0.864844i	0.901671	−	0.432422i	$-0.142341\pi$
$350$	1.64832	−	0.339898i	0.0881063	−	0.0181683i
$351$			3.19024i			0.170283i
$352$	−26.6874	−	16.5095i	−1.42244	−	0.879961i
$353$	1.52645			0.0812448			0.0406224	−	0.999175i	$-0.487066\pi$
$353$	1.52645			0.0812448			0.0406224	+	0.999175i	$0.487066\pi$
$354$	0.911179	−	0.187893i	0.0484286	−	0.00998642i
$355$		−	17.0806i		−	0.906546i
$356$	−3.18591	−	7.39647i	−0.168853	−	0.392012i
$357$			0.835997i			0.0442457i
$358$	26.4765	−	5.45970i	1.39933	−	0.288554i
$359$	30.2471			1.59638			0.798190	−	0.602405i	$-0.205791\pi$
$359$	30.2471			1.59638			0.798190	+	0.602405i	$0.205791\pi$
$360$	−6.50179	+	4.54496i	−0.342674	+	0.239540i
$361$	12.7189			0.669414
$362$	7.76466	−	1.60114i	0.408101	−	0.0841542i
$363$	19.7744			1.03789
$364$	−1.04800	−	2.43306i	−0.0549302	−	0.127527i
$365$	7.91846			0.414471
$366$	−16.3472	+	3.37094i	−0.854481	+	0.176202i
$367$	−1.47265			−0.0768718			−0.0384359	−	0.999261i	$-0.512238\pi$
$367$	−1.47265			−0.0768718			−0.0384359	+	0.999261i	$0.512238\pi$
$368$	−3.25491	−	18.9052i	−0.169674	−	0.985500i
$369$	2.52410			0.131399
$370$	13.9656	−	2.87983i	0.726036	−	0.149715i
$371$	0.112312			0.00583093
$372$	−6.45874	−	14.9947i	−0.334870	−	0.777441i
$373$	−12.4114			−0.642639			−0.321320	−	0.946971i	$-0.604126\pi$
$373$	−12.4114			−0.642639			−0.321320	+	0.946971i	$0.604126\pi$
$374$	−15.4709	+	3.19024i	−0.799982	+	0.164963i
$375$	−5.98452			−0.309039
$376$	5.80684	+	8.30697i	0.299465	+	0.428399i
$377$	−14.9914			−0.772097
$378$	−0.575080	+	0.118587i	−0.0295789	+	0.00609945i
$379$			27.0869i			1.39136i	0.718352	+	0.695679i	$0.244897\pi$
$379$			27.0869i			1.39136i	−0.718352	+	0.695679i	$0.755103\pi$
$380$	−5.56141	−	12.9115i	−0.285294	−	0.662345i
$381$		−	5.31443i		−	0.272267i
$382$	−34.6672	+	7.14868i	−1.77373	+	0.365758i
$383$	−30.4292			−1.55486			−0.777430	−	0.628970i	$-0.783477\pi$
$383$	−30.4292			−1.55486			−0.777430	+	0.628970i	$0.783477\pi$
$384$	−1.66034	+	11.1912i	−0.0847286	+	0.571099i
$385$			6.46003i			0.329234i
$386$	34.1291	−	7.03773i	1.73713	−	0.358211i
$387$			1.80649i			0.0918290i
$388$	−11.4830	−	26.6590i	−0.582959	−	1.35341i
$389$	16.9108			0.857413			0.428706	−	0.903444i	$-0.358970\pi$
$389$	16.9108			0.857413			0.428706	+	0.903444i	$0.358970\pi$
$390$	−2.55557	−	12.3931i	−0.129406	−	0.627548i
$391$	−7.72835	−	5.78944i	−0.390839	−	0.292784i
$392$	−15.8277	+	11.0641i	−0.799420	+	0.558820i
$393$	−1.82236			−0.0919258
$394$	0.684287	+	3.31841i	0.0344739	+	0.167179i
$395$	−42.1762			−2.12212
$396$	−4.38912	−	10.1899i	−0.220562	−	0.512060i
$397$		−	24.9043i		−	1.24991i	−0.780661	−	0.624955i	$-0.785117\pi$
$397$		−	24.9043i		−	1.24991i	0.780661	−	0.624955i	$-0.214883\pi$
$398$	−5.21275	+	1.07492i	−0.261292	+	0.0538807i
$399$		−	1.04058i		−	0.0520941i
$400$	7.87651	−	8.33102i	0.393825	−	0.416551i
$401$		−	9.00074i		−	0.449476i	−0.974419	−	0.224738i	$-0.927847\pi$
$401$		−	9.00074i		−	0.449476i	0.974419	−	0.224738i	$-0.0721526\pi$
$402$	−1.54621	−	7.49827i	−0.0771179	−	0.373979i
$403$	26.0429			1.29729
$404$	5.54029	+	12.8624i	0.275640	+	0.639930i
$405$	−2.80468			−0.139366
$406$	−0.557257	−	2.70239i	−0.0276562	−	0.134117i
$407$			19.9434i			0.988555i
$408$	3.26283	+	4.66765i	0.161534	+	0.231083i
$409$	−3.97216			−0.196411			−0.0982053	−	0.995166i	$-0.531310\pi$
$409$	−3.97216			−0.196411			−0.0982053	+	0.995166i	$0.531310\pi$
$410$	−9.80532	+	2.02195i	−0.484250	+	0.0998568i
$411$		−	18.7457i		−	0.924658i
$412$	33.9599	−	14.6277i	1.67308	−	0.720654i
$413$	−0.273141			−0.0134404
$414$	2.88627	−	6.13755i	0.141852	−	0.301644i
$415$		−	31.3697i		−	1.53988i
$416$	−15.3474	−	9.49431i	−0.752468	−	0.465497i
$417$	7.64330			0.374294
$418$	19.2569	−	3.97095i	0.941886	−	0.194225i
$419$			19.3554i			0.945572i	0.881177	+	0.472786i	$0.156752\pi$
$419$			19.3554i			0.945572i	−0.881177	+	0.472786i	$0.843248\pi$
$420$	2.13901	−	0.921345i	0.104373	−	0.0449570i
$421$	14.5334			0.708316			0.354158	−	0.935186i	$-0.384768\pi$
$421$	14.5334			0.708316			0.354158	+	0.935186i	$0.384768\pi$
$422$	−23.5792	+	4.86224i	−1.14782	+	0.236690i
$423$			3.58339i			0.174230i
$424$	0.627073	−	0.438344i	0.0304534	−	0.0212879i
$425$		−	5.77113i		−	0.279941i
$426$	−1.73940	−	8.43515i	−0.0842744	−	0.408684i
$427$	4.90035			0.237145
$428$	1.85396	+	4.30418i	0.0896143	+	0.208050i
$429$	17.6978			0.854456
$430$	−1.44710	−	7.01764i	−0.0697854	−	0.338421i
$431$	−11.2407			−0.541443			−0.270722	−	0.962658i	$-0.587262\pi$
$431$	−11.2407			−0.541443			−0.270722	+	0.962658i	$0.587262\pi$
$432$	−2.74803	+	2.90660i	−0.132215	+	0.139844i
$433$		−	5.81482i		−	0.279442i	−0.990191	−	0.139721i	$-0.955379\pi$
$433$		−	5.81482i		−	0.279442i	0.990191	−	0.139721i	$-0.0446206\pi$
$434$	0.968059	+	4.69455i	0.0464683	+	0.225346i
$435$		−	13.1796i		−	0.631914i
$436$	−17.1666	+	7.39425i	−0.822132	+	0.354120i
$437$	9.61960	+	7.20621i	0.460168	+	0.344720i
$438$	3.91047	−	0.806375i	0.186850	−	0.0385301i
$439$			41.2559i			1.96904i	0.175278	+	0.984519i	$0.443918\pi$
$439$			41.2559i			1.96904i	−0.175278	+	0.984519i	$0.556082\pi$
$440$	25.2130	+	36.0685i	1.20198	+	1.71950i
$441$	−6.82761			−0.325124
$442$	−8.89702	+	1.83465i	−0.423188	+	0.0872652i
$443$	−1.67570			−0.0796148			−0.0398074	−	0.999207i	$-0.512674\pi$
$443$	−1.67570			−0.0796148			−0.0398074	+	0.999207i	$0.512674\pi$
$444$	6.60354	−	2.84437i	0.313390	−	0.134988i
$445$			11.2937i			0.535371i
$446$	−4.53900	−	22.0116i	−0.214928	−	1.04228i
$447$	10.0586			0.475755
$448$	1.14098	−	3.11948i	0.0539062	−	0.147381i
$449$	−17.2494			−0.814049			−0.407024	−	0.913417i	$-0.633434\pi$
$449$	−17.2494			−0.814049			−0.407024	+	0.913417i	$0.633434\pi$
$450$	3.96995	−	0.818639i	0.187145	−	0.0385910i
$451$		−	14.0024i		−	0.659345i
$452$	−14.6532	−	34.0191i	−0.689227	−	1.60012i
$453$		−	16.6249i		−	0.781108i
$454$	−0.222342	−	1.07823i	−0.0104350	−	0.0506040i
$455$			3.71504i			0.174164i
$456$	−4.06130	−	5.80990i	−0.190188	−	0.272073i
$457$			22.5158i			1.05325i	0.850099	+	0.526623i	$0.176542\pi$
$457$			22.5158i			1.05325i	−0.850099	+	0.526623i	$0.823458\pi$
$458$	25.3515	−	5.22771i	1.18460	−	0.244275i
$459$			2.01349i			0.0939815i
$460$	−6.29572	+	26.1545i	−0.293539	+	1.21946i
$461$			34.5037i			1.60700i	0.595308	+	0.803498i	$0.297030\pi$
$461$			34.5037i			1.60700i	−0.595308	+	0.803498i	$0.702970\pi$
$462$	0.657857	+	3.19024i	0.0306063	+	0.148423i
$463$		−	28.5673i		−	1.32763i	−0.747895	−	0.663817i	$-0.768936\pi$
$463$		−	28.5673i		−	1.32763i	0.747895	−	0.663817i	$-0.231064\pi$
$464$	−13.6586	−	12.9134i	−0.634082	−	0.599489i
$465$			22.8954i			1.06175i
$466$	14.0291	−	2.89292i	0.649884	−	0.134012i
$467$			4.59322i			0.212549i	0.994337	+	0.106274i	$0.0338922\pi$
$467$			4.59322i			0.212549i	−0.994337	+	0.106274i	$0.966108\pi$
$468$	−2.52410	−	5.85999i	−0.116676	−	0.270878i
$469$			2.24773i			0.103791i
$470$	−2.87050	−	13.9203i	−0.132406	−	0.642097i
$471$	6.29506			0.290061
$472$	−1.52504	+	1.06605i	−0.0701956	+	0.0490689i
$473$	10.0214			0.460786
$474$	−20.8284	+	4.29501i	−0.956681	+	0.197276i
$475$			7.18342i			0.329598i
$476$	−0.661435	−	1.53560i	−0.0303168	−	0.0703841i
$477$	0.270501			0.0123854
$478$	−6.52445	−	31.6400i	−0.298421	−	1.44718i
$479$	−6.78356			−0.309949			−0.154974	−	0.987918i	$-0.549530\pi$
$479$	−6.78356			−0.309949			−0.154974	+	0.987918i	$0.549530\pi$
$480$	8.34687	−	13.4926i	0.380981	−	0.615849i
$481$			11.4690i			0.522943i
$482$	7.68460	+	37.2661i	0.350024	+	1.69742i
$483$	−1.19383	+	1.59365i	−0.0543213	+	0.0725138i
$484$	−36.3226	+	15.6454i	−1.65103	+	0.711154i
$485$			40.7057i			1.84835i
$486$	−1.38507	+	0.285614i	−0.0628281	+	0.0129557i
$487$		−	2.73804i		−	0.124073i	−0.998074	−	0.0620363i	$-0.980241\pi$
$487$		−	2.73804i		−	0.124073i	0.998074	−	0.0620363i	$-0.0197595\pi$
$488$	27.3603	−	19.1257i	1.23854	−	0.865779i
$489$	−18.3381			−0.829277
$490$	26.5231	−	5.46931i	1.19819	−	0.247078i
$491$	26.6421			1.20234			0.601170	−	0.799121i	$-0.294701\pi$
$491$	26.6421			1.20234			0.601170	+	0.799121i	$0.294701\pi$
$492$	−4.63638	+	1.99705i	−0.209024	+	0.0900338i
$493$	−9.46166			−0.426132
$494$	11.0743	−	2.28361i	0.498255	−	0.102745i
$495$			15.5589i			0.699320i
$496$	23.7275	+	22.4330i	1.06539	+	1.00727i
$497$			2.52858i			0.113422i
$498$	−3.19453	−	15.4917i	−0.143150	−	0.694200i
$499$	13.3190			0.596240			0.298120	−	0.954528i	$-0.403640\pi$
$499$	13.3190			0.596240			0.298120	+	0.954528i	$0.403640\pi$
$500$	10.9927	−	4.73491i	0.491607	−	0.211752i
$501$			19.7559i			0.882630i
$502$	7.36744	+	35.7280i	0.328825	+	1.59462i
$503$	−26.7050			−1.19072			−0.595359	−	0.803460i	$-0.702990\pi$
$503$	−26.7050			−1.19072			−0.595359	+	0.803460i	$0.702990\pi$
$504$	0.962511	−	0.672826i	0.0428736	−	0.0299700i
$505$		−	19.6396i		−	0.873953i
$506$	−34.0478	−	16.0115i	−1.51361	−	0.711797i
$507$	−2.82236			−0.125345
$508$	4.20474	+	9.76181i	0.186555	+	0.433110i
$509$			28.4096i			1.25923i	0.776906	+	0.629617i	$0.216788\pi$
$509$			28.4096i			1.25923i	−0.776906	+	0.629617i	$0.783212\pi$
$510$	−1.61292	−	7.82176i	−0.0714212	−	0.346353i
$511$	−1.17223			−0.0518564
$512$	−5.80462	−	21.8702i	−0.256531	−	0.966536i
$513$		−	2.50622i		−	0.110652i
$514$	−34.5594	+	7.12647i	−1.52435	+	0.314335i
$515$	−51.8533			−2.28493
$516$	−1.42928	−	3.31825i	−0.0629206	−	0.146078i
$517$	19.8787			0.874265
$518$	−2.06743	+	0.426324i	−0.0908379	+	0.0187316i
$519$			11.3869i			0.499830i
$520$	14.4995	+	20.7423i	0.635846	+	0.909609i
$521$			24.7986i			1.08645i	0.839588	+	0.543224i	$0.182797\pi$
$521$			24.7986i			1.08645i	−0.839588	+	0.543224i	$0.817203\pi$
$522$	−1.34214	−	6.50865i	−0.0587440	−	0.284876i
$523$			26.1728i			1.14446i	0.820094	+	0.572229i	$0.193921\pi$
$523$			26.1728i			1.14446i	−0.820094	+	0.572229i	$0.806079\pi$
$524$	3.34740	−	1.44184i	0.146232	−	0.0629869i
$525$	−1.19006			−0.0519385
$526$	6.81492	−	1.40530i	0.297144	−	0.0612739i
$527$	16.4367			0.715993
$528$	16.1243	+	15.2446i	0.701720	+	0.663436i
$529$	−6.46496	−	22.0727i	−0.281085	−	0.959683i
$530$	−1.05081	+	0.216687i	−0.0456443	+	0.00941227i
$531$	−0.657857			−0.0285485
$532$	0.823299	+	1.91139i	0.0356945	+	0.0828691i
$533$		−	8.05248i		−	0.348792i
$534$	1.15009	+	5.57729i	0.0497692	+	0.241353i
$535$		−	6.57204i		−	0.284134i
$536$	8.77273	+	12.5498i	0.378924	+	0.542070i
$537$	−19.1156			−0.824900
$538$	2.50664	+	12.1558i	0.108069	+	0.524076i
$539$			37.8760i			1.63143i
$540$	5.15178	−	2.21904i	0.221697	−	0.0954925i
$541$			21.3299i			0.917046i	0.888683	+	0.458523i	$0.151621\pi$
$541$			21.3299i			0.917046i	−0.888683	+	0.458523i	$0.848379\pi$
$542$	2.11229	+	10.2434i	0.0907305	+	0.439993i
$543$	−5.60596			−0.240575
$544$	−9.68634	−	5.99223i	−0.415298	−	0.256915i
$545$	26.2117			1.12279
$546$	0.378321	+	1.83465i	0.0161906	+	0.0785156i
$547$	−6.09639			−0.260663			−0.130331	−	0.991470i	$-0.541604\pi$
$547$	−6.09639			−0.260663			−0.130331	+	0.991470i	$0.541604\pi$
$548$	14.8315	+	34.4331i	0.633569	+	1.47091i
$549$	11.8024			0.503715
$550$	−4.54138	−	22.0232i	−0.193645	−	0.939071i
$551$	11.7771			0.501721
$552$	−0.445655	+	13.5573i	−0.0189683	+	0.577039i
$553$	6.24367			0.265508
$554$	2.49021	+	12.0762i	0.105799	+	0.513067i
$555$	−10.0829			−0.427997
$556$	−14.0396	+	6.04733i	−0.595411	+	0.256464i
$557$	21.1916			0.897915			0.448958	−	0.893553i	$-0.351795\pi$
$557$	21.1916			0.897915			0.448958	+	0.893553i	$0.351795\pi$
$558$	2.33155	+	11.3068i	0.0987026	+	0.478653i
$559$	5.76313			0.243755
$560$	−3.20008	+	3.38474i	−0.135228	+	0.143031i
$561$	11.1698			0.471587
$562$	−1.48193	−	7.18656i	−0.0625116	−	0.303147i
$563$		−	14.2901i		−	0.602254i	−0.953584	−	0.301127i	$-0.902637\pi$
$563$		−	14.2901i		−	0.602254i	0.953584	−	0.301127i	$-0.0973628\pi$
$564$	−2.83515	−	6.58214i	−0.119381	−	0.277158i
$565$			51.9436i			2.18529i
$566$	−7.70451	−	37.3626i	−0.323845	−	1.57047i
$567$	0.415199			0.0174367
$568$	9.86885	+	14.1179i	0.414088	+	0.592373i
$569$			31.9346i			1.33877i	0.742917	+	0.669384i	$0.233442\pi$
$569$			31.9346i			1.33877i	−0.742917	+	0.669384i	$0.766558\pi$
$570$	2.00763	+	9.73587i	0.0840902	+	0.407791i
$571$			25.5699i			1.07007i	0.844831	+	0.535034i	$0.179701\pi$
$571$			25.5699i			1.07007i	−0.844831	+	0.535034i	$0.820299\pi$
$572$	−32.5081	+	14.0024i	−1.35923	+	0.585468i
$573$	25.0291			1.04561
$574$	1.45156	−	0.299324i	0.0605869	−	0.0124936i
$575$	8.24138	−	11.0015i	0.343689	−	0.458793i
$576$	2.74803	−	7.51321i	0.114501	−	0.313050i
$577$	25.3417			1.05499			0.527494	−	0.849558i	$-0.323132\pi$
$577$	25.3417			1.05499			0.527494	+	0.849558i	$0.323132\pi$
$578$	17.9310	−	3.69753i	0.745830	−	0.153797i
$579$	−24.6407			−1.02403
$580$	10.4276	+	24.2089i	0.432983	+	1.00522i
$581$			4.64390i			0.192662i
$582$	4.14525	+	20.1022i	0.171826	+	0.833263i
$583$		−	1.50060i		−	0.0621483i
$584$	−6.54495	+	4.57513i	−0.270832	+	0.189320i
$585$			8.94761i			0.369938i
$586$	−31.4422	+	6.48366i	−1.29886	+	0.267838i
$587$	11.6750			0.481878			0.240939	−	0.970540i	$-0.422545\pi$
$587$	11.6750			0.481878			0.240939	+	0.970540i	$0.422545\pi$
$588$	12.5413	−	5.40196i	0.517194	−	0.222773i
$589$	−20.4590			−0.842999
$590$	2.55557	−	0.526981i	0.105211	−	0.0216955i
$591$		−	2.39584i		−	0.0985518i
$592$	−9.87926	+	10.4493i	−0.406035	+	0.429465i
$593$	−39.6476			−1.62813			−0.814065	−	0.580774i	$-0.802750\pi$
$593$	−39.6476			−1.62813			−0.814065	+	0.580774i	$0.802750\pi$
$594$	1.58444	+	7.68365i	0.0650102	+	0.315264i
$595$			2.34471i			0.0961236i
$596$	−18.4761	+	7.95828i	−0.756811	+	0.325984i
$597$	3.76352			0.154031
$598$	−19.5803	−	9.20789i	−0.800696	−	0.376539i
$599$			20.5586i			0.840003i	0.907523	+	0.420002i	$0.137970\pi$
$599$			20.5586i			0.840003i	−0.907523	+	0.420002i	$0.862030\pi$
$600$	−6.64449	+	4.64471i	−0.271260	+	0.189620i
$601$	−35.6416			−1.45385			−0.726926	−	0.686716i	$-0.759052\pi$
$601$	−35.6416			−1.45385			−0.726926	+	0.686716i	$0.759052\pi$
$602$	0.214226	+	1.03888i	0.00873118	+	0.0423414i
$603$			5.41363i			0.220460i
$604$	13.1535	+	30.5375i	0.535210	+	1.24255i
$605$	55.4610			2.25481
$606$	−2.00000	−	9.69890i	−0.0812444	−	0.393991i
$607$		−	23.1724i		−	0.940539i	−0.882523	−	0.470269i	$-0.844157\pi$
$607$		−	23.1724i		−	0.940539i	0.882523	−	0.470269i	$-0.155843\pi$
$608$	12.0567	+	7.45863i	0.488966	+	0.302487i
$609$			1.95108i			0.0790618i
$610$	−45.8487	+	9.45441i	−1.85636	+	0.382798i
$611$	11.4319			0.462484
$612$	−1.59306	−	3.69847i	−0.0643955	−	0.149502i
$613$	−24.7805			−1.00087			−0.500437	−	0.865773i	$-0.666827\pi$
$613$	−24.7805			−1.00087			−0.500437	+	0.865773i	$0.666827\pi$
$614$	6.70479	−	1.38259i	0.270583	−	0.0557967i
$615$	7.07929			0.285464
$616$	−3.73248	−	5.33950i	−0.150386	−	0.215135i
$617$			17.9944i			0.724428i	0.932095	+	0.362214i	$0.117979\pi$
$617$			17.9944i			0.724428i	−0.932095	+	0.362214i	$0.882021\pi$
$618$	−25.6074	+	5.28047i	−1.03008	+	0.212412i
$619$		−	45.4728i		−	1.82771i	−0.406043	−	0.913854i	$-0.633092\pi$
$619$		−	45.4728i		−	1.82771i	0.406043	−	0.913854i	$-0.366908\pi$
$620$	−18.1147	−	42.0555i	−0.727504	−	1.68899i
$621$	−2.87533	+	3.83829i	−0.115383	+	0.154025i
$622$	−2.61656	−	12.6889i	−0.104914	−	0.508777i
$623$		−	1.67189i		−	0.0669828i
$624$	9.27277	+	8.76687i	0.371208	+	0.350956i
$625$	−31.1159			−1.24463
$626$	−5.09873	−	24.7260i	−0.203786	−	0.988251i
$627$	−13.9032			−0.555239
$628$	−11.5631	+	4.98061i	−0.461417	+	0.198748i
$629$			7.23855i			0.288620i
$630$	−1.61292	+	0.332598i	−0.0642602	+	0.0132510i
$631$	38.7133			1.54115			0.770576	−	0.637349i	$-0.219969\pi$
$631$	38.7133			1.54115			0.770576	+	0.637349i	$0.219969\pi$
$632$	34.8605	−	24.3686i	1.38668	−	0.969330i
$633$	17.0238			0.676635
$634$	9.08513	+	44.0579i	0.360817	+	1.74976i
$635$		−	14.9053i		−	0.591499i
$636$	−0.496869	+	0.214018i	−0.0197022	+	0.00848638i
$637$			21.7817i			0.863023i
$638$	−36.1066	+	7.44550i	−1.42947	+	0.294770i
$639$			6.09004i			0.240918i
$640$	−4.65671	+	31.3878i	−0.184073	+	1.24071i
$641$		−	16.6975i		−	0.659512i	−0.944066	−	0.329756i	$-0.893033\pi$
$641$		−	16.6975i		−	0.659512i	0.944066	−	0.329756i	$-0.106967\pi$
$642$	−0.669263	−	3.24556i	−0.0264137	−	0.128092i
$643$		−	4.54910i		−	0.179399i	−0.995969	−	0.0896994i	$-0.971409\pi$
$643$		−	4.54910i		−	0.179399i	0.995969	−	0.0896994i	$-0.0285906\pi$
$644$	0.932004	−	3.87186i	0.0367261	−	0.152572i
$645$			5.06662i			0.199498i
$646$	6.98940	−	1.44128i	0.274994	−	0.0567063i
$647$			24.8216i			0.975838i	0.872889	+	0.487919i	$0.162244\pi$
$647$			24.8216i			0.975838i	−0.872889	+	0.487919i	$0.837756\pi$
$648$	2.31819	−	1.62049i	0.0910672	−	0.0636588i
$649$			3.64944i			0.143253i
$650$	−2.61166	−	12.6651i	−0.102438	−	0.496766i
$651$		−	3.38939i		−	0.132841i
$652$	33.6843	−	14.5090i	1.31918	−	0.568215i
$653$		−	20.1907i		−	0.790122i	−0.918655	−	0.395061i	$-0.870723\pi$
$653$		−	20.1907i		−	0.790122i	0.918655	−	0.395061i	$-0.129277\pi$
$654$	12.9445	−	2.66926i	0.506168	−	0.104376i
$655$	−5.11113			−0.199708
$656$	6.93629	−	7.33655i	0.270817	−	0.286444i
$657$	−2.82330			−0.110147
$658$	0.424942	+	2.06073i	0.0165660	+	0.0803358i
$659$		−	33.2939i		−	1.29695i	−0.761237	−	0.648474i	$-0.775408\pi$
$659$		−	33.2939i		−	1.29695i	0.761237	−	0.648474i	$-0.224592\pi$
$660$	−12.3101	−	28.5793i	−0.479169	−	1.11245i
$661$	32.2531			1.25450			0.627251	−	0.778818i	$-0.284180\pi$
$661$	32.2531			1.25450			0.627251	+	0.778818i	$0.284180\pi$
$662$	−4.63735	+	0.956264i	−0.180236	+	0.0371663i
$663$	6.42351			0.249468
$664$	18.1248	+	25.9284i	0.703378	+	1.00622i
$665$		−	2.91849i		−	0.113174i
$666$	−4.97938	+	1.02679i	−0.192947	+	0.0397874i
$667$	−18.0367	−	13.5116i	−0.698383	−	0.523171i
$668$	−15.6308	−	36.2887i	−0.604772	−	1.40405i
$669$			15.8920i			0.614422i
$670$	−4.33663	−	21.0302i	−0.167539	−	0.812469i
$671$		−	65.4735i		−	2.52758i
$672$	−1.23565	+	1.99741i	−0.0476663	+	0.0770518i
$673$	−39.3450			−1.51664			−0.758319	−	0.651884i	$-0.773979\pi$
$673$	−39.3450			−1.51664			−0.758319	+	0.651884i	$0.773979\pi$
$674$	−4.23426	−	20.5338i	−0.163098	−	0.790933i
$675$	−2.86624			−0.110322
$676$	5.18424	−	2.23303i	0.199394	−	0.0858857i
$677$	−15.4597			−0.594165			−0.297083	−	0.954852i	$-0.596014\pi$
$677$	−15.4597			−0.594165			−0.297083	+	0.954852i	$0.596014\pi$
$678$	5.28967	+	25.6520i	0.203149	+	0.985159i
$679$		−	6.02598i		−	0.231256i
$680$	9.15121	+	13.0913i	0.350933	+	0.502027i
$681$			0.778468i			0.0298310i
$682$	62.7239	−	12.9342i	2.40182	−	0.495277i
$683$	10.8401			0.414783			0.207392	−	0.978258i	$-0.433503\pi$
$683$	10.8401			0.414783			0.207392	+	0.978258i	$0.433503\pi$
$684$	1.98290	+	4.60355i	0.0758182	+	0.176021i
$685$		−	52.5758i		−	2.00882i
$686$	−7.95199	+	1.63977i	−0.303608	+	0.0626068i
$687$	−18.3034			−0.698318
$688$	5.25074	+	4.96428i	0.200183	+	0.189261i
$689$		−	0.862963i		−	0.0328763i
$690$	8.09506	−	17.2139i	0.308174	−	0.655320i
$691$	−31.6585			−1.20435			−0.602173	−	0.798366i	$-0.705698\pi$
$691$	−31.6585			−1.20435			−0.602173	+	0.798366i	$0.705698\pi$
$692$	−9.00924	−	20.9160i	−0.342480	−	0.795108i
$693$		−	2.30330i		−	0.0874953i
$694$	45.4996	−	9.38243i	1.72714	−	0.356152i
$695$	21.4370			0.813153
$696$	7.61492	+	10.8935i	0.288643	+	0.412918i
$697$		−	5.08223i		−	0.192503i
$698$	−4.61456	−	22.3781i	−0.174664	−	0.847022i
$699$	−10.1288			−0.383105
$700$	2.18596	−	0.941567i	0.0826215	−	0.0355879i
$701$	−25.0600			−0.946504			−0.473252	−	0.880927i	$-0.656920\pi$
$701$	−25.0600			−0.946504			−0.473252	+	0.880927i	$0.656920\pi$
$702$	0.911179	+	4.41871i	0.0343902	+	0.166774i
$703$		−	9.00995i		−	0.339817i
$704$	−41.6793	−	15.2446i	−1.57085	−	0.574553i
$705$			10.0503i			0.378514i
$706$	2.11424	−	0.435976i	0.0795706	−	0.0164082i
$707$			2.90741i			0.109344i
$708$	1.20838	−	0.520491i	0.0454138	−	0.0195613i
$709$	−1.51261			−0.0568072			−0.0284036	−	0.999597i	$-0.509042\pi$
$709$	−1.51261			−0.0568072			−0.0284036	+	0.999597i	$0.509042\pi$
$710$	−4.87847	−	23.6579i	−0.183086	−	0.887865i
$711$	15.0378			0.563961
$712$	−6.52525	−	9.33470i	−0.244544	−	0.349833i
$713$	31.3331	+	23.4722i	1.17343	+	0.879040i
$714$	0.238773	+	1.15792i	0.00893585	+	0.0433339i
$715$	49.6366			1.85630
$716$	35.1125	−	15.1241i	1.31222	−	0.565216i
$717$			22.8436i			0.853108i
$718$	41.8944	−	8.63900i	1.56349	−	0.322405i
$719$			14.5869i			0.543999i	0.962297	+	0.272000i	$0.0876850\pi$
$719$			14.5869i			0.543999i	−0.962297	+	0.272000i	$0.912315\pi$
$720$	−7.70734	+	8.15210i	−0.287236	+	0.303811i
$721$	7.67625			0.285878
$722$	17.6165	−	3.63269i	0.655620	−	0.135195i
$723$		−	26.9055i		−	1.00063i
$724$	10.2973	−	4.43540i	0.382696	−	0.164840i
$725$		−	13.4689i		−	0.500222i
$726$	27.3890	−	5.64786i	1.01650	−	0.209612i
$727$	−21.7360			−0.806142			−0.403071	−	0.915169i	$-0.632057\pi$
$727$	−21.7360			−0.806142			−0.403071	+	0.915169i	$0.632057\pi$
$728$	−2.14648	−	3.07064i	−0.0795537	−	0.113806i
$729$	1.00000			0.0370370
$730$	10.9676	−	2.26162i	0.405930	−	0.0837065i
$731$	3.63734			0.134532
$732$	−21.6793	+	9.33799i	−0.801288	+	0.345142i
$733$	8.74545			0.323021			0.161510	−	0.986871i	$-0.448363\pi$
$733$	8.74545			0.323021			0.161510	+	0.986871i	$0.448363\pi$
$734$	−2.03973	+	0.420610i	−0.0752877	+	0.0155250i
$735$	−19.1493			−0.706332
$736$	−9.90787	−	25.2554i	−0.365209	−	0.930926i
$737$	30.0319			1.10624
$738$	3.49606	−	0.720918i	0.128692	−	0.0265374i
$739$	−7.34669			−0.270253			−0.135126	−	0.990828i	$-0.543144\pi$
$739$	−7.34669			−0.270253			−0.135126	+	0.990828i	$0.543144\pi$
$740$	18.5208	−	7.97754i	0.680839	−	0.293260i
$741$	−7.99544			−0.293720
$742$	0.155560	−	0.0320778i	0.00571078	−	0.00117761i
$743$	−28.2818			−1.03756			−0.518779	−	0.854908i	$-0.673613\pi$
$743$	−28.2818			−1.03756			−0.518779	+	0.854908i	$0.673613\pi$
$744$	−13.2285	−	18.9241i	−0.484982	−	0.693791i
$745$	28.2111			1.03358
$746$	−17.1907	+	3.54488i	−0.629397	+	0.129787i
$747$			11.1848i			0.409229i
$748$	−20.5171	+	8.83743i	−0.750181	+	0.323128i
$749$			0.972911i			0.0355494i
$750$	−8.28899	+	1.70926i	−0.302671	+	0.0624135i
$751$	−45.1818			−1.64871			−0.824353	−	0.566076i	$-0.808461\pi$
$751$	−45.1818			−1.64871			−0.824353	+	0.566076i	$0.808461\pi$
$752$	10.4155	+	9.84724i	0.379813	+	0.359092i
$753$		−	25.7950i		−	0.940024i
$754$	−20.7642	+	4.28176i	−0.756187	+	0.155933i
$755$		−	46.6277i		−	1.69695i
$756$	−0.762658	+	0.328502i	−0.0277376	+	0.0119475i
$757$	−11.8830			−0.431894			−0.215947	−	0.976405i	$-0.569284\pi$
$757$	−11.8830			−0.431894			−0.215947	+	0.976405i	$0.569284\pi$
$758$	7.73640	+	37.5173i	0.280999	+	1.36269i
$759$	21.2928	+	15.9508i	0.772880	+	0.578978i
$760$	−11.3907	−	16.2949i	−0.413183	−	0.591079i
$761$	29.0606			1.05345			0.526723	−	0.850037i	$-0.323421\pi$
$761$	29.0606			1.05345			0.526723	+	0.850037i	$0.323421\pi$
$762$	−1.51788	−	7.36087i	−0.0549869	−	0.266656i
$763$	−3.88032			−0.140477
$764$	−45.9747	+	19.8029i	−1.66331	+	0.716443i
$765$			5.64719i			0.204174i
$766$	−42.1466	+	8.69101i	−1.52282	+	0.314019i
$767$			2.09872i			0.0757804i
$768$	0.896688	+	15.9749i	0.0323564	+	0.576443i
$769$		−	0.831518i		−	0.0299853i	−0.999888	−	0.0149927i	$-0.995228\pi$
$769$		−	0.831518i		−	0.0299853i	0.999888	−	0.0149927i	$-0.00477249\pi$
$770$	1.84508	+	8.94761i	0.0664920	+	0.322450i
$771$	24.9514			0.898602
$772$	45.2612	−	19.4955i	1.62899	−	0.701659i
$773$	−35.9982			−1.29477			−0.647383	−	0.762165i	$-0.724136\pi$
$773$	−35.9982			−1.29477			−0.647383	+	0.762165i	$0.724136\pi$
$774$	0.515959	+	2.50212i	0.0185458	+	0.0899367i
$775$			23.3980i			0.840480i
$776$	−23.5189	−	33.6450i	−0.844280	−	1.20779i
$777$	1.49265			0.0535487
$778$	23.4227	−	4.82997i	0.839745	−	0.173163i
$779$			6.32594i			0.226650i
$780$	−7.07929	−	16.4354i	−0.253479	−	0.588482i
$781$	33.7843			1.20890
$782$	−12.3579	−	5.81146i	−0.441916	−	0.207817i
$783$			4.69915i			0.167934i
$784$	−18.7625	+	19.8452i	−0.670088	+	0.708756i
$785$	17.6556			0.630157
$786$	−2.52410	+	0.520491i	−0.0900315	+	0.0185653i
$787$			17.0308i			0.607081i	0.952818	+	0.303541i	$0.0981688\pi$
$787$			17.0308i			0.607081i	−0.952818	+	0.303541i	$0.901831\pi$
$788$	1.89557	+	4.40080i	0.0675270	+	0.156772i
$789$	−4.92026			−0.175166
$790$	−58.4171	+	12.0461i	−2.07839	+	0.428582i
$791$		−	7.68962i		−	0.273412i
$792$	−8.98962	−	12.8601i	−0.319432	−	0.456964i
$793$		−	37.6526i		−	1.33708i
$794$	−7.11302	−	34.4942i	−0.252432	−	1.22415i
$795$	0.758669			0.0269072
$796$	−6.91302	+	2.97767i	−0.245026	+	0.105541i
$797$	9.38264			0.332350			0.166175	−	0.986096i	$-0.446858\pi$
$797$	9.38264			0.332350			0.166175	+	0.986096i	$0.446858\pi$
$798$	−0.297204	−	1.44128i	−0.0105209	−	0.0510207i
$799$	7.21510			0.255252
$800$	8.53007	−	13.7887i	0.301583	−	0.487505i
$801$		−	4.02672i		−	0.142277i
$802$	−2.57074	−	12.4667i	−0.0907760	−	0.440214i
$803$			15.6622i			0.552706i
$804$	−4.28322	−	9.94402i	−0.151058	−	0.350698i
$805$	−3.34832	+	4.46969i	−0.118013	+	0.157536i
$806$	36.0713	−	7.43822i	1.27056	−	0.262000i
$807$		−	8.77633i		−	0.308941i
$808$	11.3474	+	16.2330i	0.399200	+	0.571076i
$809$	−4.57653			−0.160902			−0.0804511	−	0.996759i	$-0.525636\pi$
$809$	−4.57653			−0.160902			−0.0804511	+	0.996759i	$0.525636\pi$
$810$	−3.88469	+	0.801057i	−0.136494	+	0.0281463i
$811$	23.5951			0.828537			0.414269	−	0.910155i	$-0.364037\pi$
$811$	23.5951			0.828537			0.414269	+	0.910155i	$0.364037\pi$
$812$	−1.54368	−	3.58384i	−0.0541726	−	0.125768i
$813$		−	7.39559i		−	0.259375i
$814$	5.69611	+	27.6230i	0.199648	+	0.968185i
$815$	−51.4325			−1.80160
$816$	5.85241	+	5.53312i	0.204875	+	0.193698i
$817$	−4.52745			−0.158396
$818$	−5.50172	+	1.13451i	−0.192363	+	0.0396670i
$819$		−	1.32459i		−	0.0462847i
$820$	−13.0036	+	5.60108i	−0.454105	+	0.195598i
$821$			19.9688i			0.696917i	0.937324	+	0.348458i	$0.113295\pi$
$821$			19.9688i			0.696917i	−0.937324	+	0.348458i	$0.886705\pi$
$822$	−5.35405	−	25.9642i	−0.186744	−	0.905604i
$823$		−	8.28082i		−	0.288651i	−0.989530	−	0.144326i	$-0.953899\pi$
$823$		−	8.28082i		−	0.288651i	0.989530	−	0.144326i	$-0.0461012\pi$
$824$	42.8590	−	29.9598i	1.49306	−	1.04370i
$825$			15.9004i			0.553580i
$826$	−0.378321	+	0.0780131i	−0.0131635	+	0.00271442i
$827$			9.29195i			0.323113i	0.986863	+	0.161556i	$0.0516514\pi$
$827$			9.29195i			0.323113i	−0.986863	+	0.161556i	$0.948349\pi$
$828$	2.24472	−	9.32530i	0.0780093	−	0.324077i
$829$		−	42.2445i		−	1.46721i	−0.679576	−	0.733605i	$-0.737836\pi$
$829$		−	42.2445i		−	1.46721i	0.679576	−	0.733605i	$-0.262164\pi$
$830$	−8.95964	−	43.4493i	−0.310994	−	1.50815i
$831$		−	8.71879i		−	0.302452i
$832$	−23.9690	−	8.76687i	−0.830974	−	0.303937i
$833$			13.7473i			0.476316i
$834$	10.5865	−	2.18304i	0.366581	−	0.0755924i
$835$			55.4091i			1.91751i
$836$	25.5380	−	11.0001i	0.883251	−	0.380446i
$837$		−	8.16330i		−	0.282165i
$838$	5.52817	+	26.8086i	0.190968	+	0.926087i
$839$	2.44511			0.0844145			0.0422072	−	0.999109i	$-0.486561\pi$
$839$	2.44511			0.0844145			0.0422072	+	0.999109i	$0.486561\pi$
$840$	2.69954	−	1.88706i	0.0931429	−	0.0651098i
$841$	6.91803			0.238553
$842$	20.1298	−	4.15096i	0.693720	−	0.143051i
$843$			5.18858i			0.178704i
$844$	−31.2701	+	13.4691i	−1.07636	+	0.463626i
$845$	−7.91581			−0.272312
$846$	1.02347	+	4.96325i	0.0351875	+	0.170640i
$847$	−8.21032			−0.282110
$848$	0.743344	−	0.786239i	0.0255265	−	0.0269996i
$849$			26.9752i			0.925787i
$850$	−1.64832	−	7.99344i	−0.0565369	−	0.274173i
$851$	−10.3369	+	13.7988i	−0.354345	+	0.473017i
$852$	−4.81840	−	11.1865i	−0.165076	−	0.383243i
$853$			12.3852i			0.424060i	0.977263	+	0.212030i	$0.0680075\pi$
$853$			12.3852i			0.424060i	−0.977263	+	0.212030i	$0.931992\pi$
$854$	6.78734	−	1.39961i	0.232258	−	0.0478937i
$855$		−	7.02915i		−	0.240392i
$856$	3.79720	+	5.43208i	0.129786	+	0.185665i
$857$	−39.9980			−1.36631			−0.683153	−	0.730275i	$-0.739392\pi$
$857$	−39.9980			−1.36631			−0.683153	+	0.730275i	$0.739392\pi$
$858$	24.5127	−	5.05474i	0.836849	−	0.172566i
$859$	−9.74110			−0.332362			−0.166181	−	0.986095i	$-0.553144\pi$
$859$	−9.74110			−0.332362			−0.166181	+	0.986095i	$0.553144\pi$
$860$	−4.00868	−	9.30662i	−0.136695	−	0.317353i
$861$	−1.04800			−0.0357158
$862$	−15.5691	+	3.21049i	−0.530286	+	0.109350i
$863$		−	11.8577i		−	0.403641i	−0.979423	−	0.201820i	$-0.935314\pi$
$863$		−	11.8577i		−	0.403641i	0.979423	−	0.201820i	$-0.0646857\pi$
$864$	−2.97605	+	4.81073i	−0.101247	+	0.163664i
$865$			31.9367i			1.08588i
$866$	−1.66080	−	8.05394i	−0.0564361	−	0.273684i
$867$	−12.9459			−0.439665
$868$	2.68166	+	6.22580i	0.0910216	+	0.211317i
$869$		−	83.4217i		−	2.82989i
$870$	−3.76429	−	18.2547i	−0.127621	−	0.618892i
$871$	17.2708			0.585198
$872$	−21.6651	+	15.1446i	−0.733673	+	0.512861i
$873$		−	14.5135i		−	0.491206i
$874$	15.3820	+	7.23362i	0.520305	+	0.244681i
$875$	2.48477			0.0840004
$876$	5.18597	−	2.23377i	0.175218	−	0.0754722i
$877$		−	44.9851i		−	1.51904i	−0.650484	−	0.759520i	$-0.725434\pi$
$877$		−	44.9851i		−	1.51904i	0.650484	−	0.759520i	$-0.274566\pi$
$878$	11.7833	+	57.1424i	0.397667	+	1.92846i
$879$	22.7008			0.765678
$880$	45.2235	+	42.7563i	1.52448	+	1.44131i
$881$		−	52.2081i		−	1.75893i	−0.475959	−	0.879467i	$-0.657899\pi$
$881$		−	52.2081i		−	1.75893i	0.475959	−	0.879467i	$-0.342101\pi$
$882$	−9.45673	+	1.95006i	−0.318425	+	0.0656620i
$883$	−21.1374			−0.711329			−0.355664	−	0.934614i	$-0.615745\pi$
$883$	−21.1374			−0.711329			−0.355664	+	0.934614i	$0.615745\pi$
$884$	−11.7990	+	5.08223i	−0.396844	+	0.170934i
$885$	−1.84508			−0.0620216
$886$	−2.32096	+	0.478603i	−0.0779742	+	0.0160790i
$887$			38.9103i			1.30648i	0.757151	+	0.653240i	$0.226591\pi$
$887$			38.9103i			1.30648i	−0.757151	+	0.653240i	$0.773409\pi$
$888$	8.33398	−	5.82572i	0.279670	−	0.195498i
$889$			2.20655i			0.0740052i
$890$	3.22563	+	15.6425i	0.108123	+	0.524339i
$891$		−	5.54747i		−	0.185847i
$892$	−12.5737	−	29.1913i	−0.420998	−	0.977397i
$893$	−8.98075			−0.300529
$894$	13.9319	−	2.87288i	0.465951	−	0.0960834i
$895$	−53.6133			−1.79209
$896$	0.689370	−	4.64658i	0.0230302	−	0.155231i
$897$	12.2451	+	9.17300i	0.408851	+	0.306277i
$898$	−23.8916	+	4.92667i	−0.797274	+	0.164405i
$899$	38.3605			1.27939
$900$	5.26485	−	2.26775i	0.175495	−	0.0755916i
$901$		−	0.544650i		−	0.0181449i
$902$	−3.99927	−	19.3943i	−0.133161	−	0.645758i
$903$		−	0.750052i		−	0.0249602i
$904$	−30.0120	−	42.9337i	−0.998185	−	1.42795i
$905$	−15.7229			−0.522648
$906$	−4.74832	−	23.0267i	−0.157752	−	0.765012i
$907$			26.4527i			0.878349i	0.898402	+	0.439174i	$0.144729\pi$
$907$			26.4527i			0.878349i	−0.898402	+	0.439174i	$0.855271\pi$
$908$	−0.615918	−	1.42993i	−0.0204400	−	0.0474538i
$909$			7.00245i			0.232257i
$910$	1.06107	+	5.14560i	0.0351741	+	0.170575i
$911$	44.2857			1.46725			0.733625	−	0.679554i	$-0.237827\pi$
$911$	44.2857			1.46725			0.733625	+	0.679554i	$0.237827\pi$
$912$	−7.28458	−	6.88716i	−0.241217	−	0.228057i
$913$	62.0471			2.05346
$914$	6.43085	+	31.1861i	0.212713	+	1.03154i
$915$	33.1020			1.09432
$916$	33.6205	−	14.4815i	1.11085	−	0.478482i
$917$	0.756641			0.0249865
$918$	0.575080	+	2.78882i	0.0189805	+	0.0920449i
$919$	−7.94858			−0.262199			−0.131100	−	0.991369i	$-0.541851\pi$
$919$	−7.94858			−0.262199			−0.131100	+	0.991369i	$0.541851\pi$
$920$	−1.24992	+	38.0240i	−0.0412087	+	1.25361i
$921$	−4.84075			−0.159508
$922$	9.85474	+	47.7901i	0.324549	+	1.57388i
$923$	19.4287			0.639504
$924$	1.82236	+	4.23082i	0.0599512	+	0.139184i
$925$	−10.3042			−0.338801
$926$	−8.15922	−	39.5677i	−0.268129	−	1.30028i
$927$	18.4881			0.607230
$928$	−22.6063	−	13.9849i	−0.742089	−	0.459076i
$929$	−12.3596			−0.405504			−0.202752	−	0.979230i	$-0.564988\pi$
$929$	−12.3596			−0.405504			−0.202752	+	0.979230i	$0.564988\pi$
$930$	6.53927	+	31.7118i	0.214431	+	1.03987i
$931$		−	17.1115i		−	0.560806i
$932$	18.6050	−	8.01381i	0.609428	−	0.262501i
$933$			9.16116i			0.299923i
$934$	1.31189	+	6.36194i	0.0429263	+	0.208169i
$935$	31.3276			1.02452
$936$	−5.16975	−	7.39559i	−0.168979	−	0.241733i
$937$		−	37.8690i		−	1.23713i	−0.785735	−	0.618563i	$-0.787715\pi$
$937$		−	37.8690i		−	1.23713i	0.785735	−	0.618563i	$-0.212285\pi$
$938$	0.641985	+	3.11327i	0.0209615	+	0.101652i
$939$			17.8518i			0.582571i
$940$	−7.95169	−	18.4608i	−0.259356	−	0.602125i
$941$	−40.8202			−1.33070			−0.665350	−	0.746532i	$-0.731718\pi$
$941$	−40.8202			−1.33070			−0.665350	+	0.746532i	$0.731718\pi$
$942$	8.71912	−	1.79796i	0.284084	−	0.0585807i
$943$	7.25761	−	9.68822i	0.236340	−	0.315492i
$944$	−1.80781	+	1.91213i	−0.0588391	+	0.0622345i
$945$	1.16450			0.0378812
$946$	13.8804	−	2.86227i	0.451291	−	0.0930603i
$947$	−35.2377			−1.14507			−0.572535	−	0.819880i	$-0.694040\pi$
$947$	−35.2377			−1.14507			−0.572535	+	0.819880i	$0.694040\pi$
$948$	−27.6221	+	11.8978i	−0.897125	+	0.386422i
$949$			9.00701i			0.292380i
$950$	2.05169	+	9.94956i	0.0665656	+	0.322806i
$951$		−	31.8091i		−	1.03148i
$952$	−1.35472	−	1.93800i	−0.0439069	−	0.0628110i
$953$		−	37.0278i		−	1.19945i	−0.800207	−	0.599723i	$-0.795277\pi$
$953$		−	37.0278i		−	1.19945i	0.800207	−	0.599723i	$-0.204723\pi$
$954$	0.374663	−	0.0772590i	0.0121302	−	0.00250135i
$955$	70.1988			2.27158
$956$	−18.0737	−	41.9602i	−0.584544	−	1.35709i
$957$	26.0684			0.842671
$958$	−9.39572	+	1.93748i	−0.303562	+	0.0625972i
$959$			7.78320i			0.251333i
$960$	7.70734	−	21.0722i	0.248753	−	0.680101i
$961$	−35.6394			−1.14966
$962$	3.27572	+	15.8854i	0.105613	+	0.512167i
$963$			2.34324i			0.0755099i
$964$	21.2874	+	49.4213i	0.685622	+	1.59175i
$965$	−69.1092			−2.22470
$966$	−1.19838	+	2.54830i	−0.0385571	+	0.0819903i
$967$			8.73002i			0.280738i	0.990099	+	0.140369i	$0.0448290\pi$
$967$			8.73002i			0.280738i	−0.990099	+	0.140369i	$0.955171\pi$
$968$	−45.8409	+	32.0442i	−1.47338	+	1.02994i
$969$	−5.04624			−0.162108
$970$	11.6261	+	56.3803i	0.373292	+	1.81026i
$971$		−	41.7254i		−	1.33903i	−0.742798	−	0.669516i	$-0.766502\pi$
$971$		−	41.7254i		−	1.33903i	0.742798	−	0.669516i	$-0.233498\pi$
$972$	−1.83685	+	0.791193i	−0.0589170	+	0.0253775i
$973$	−3.17349			−0.101737
$974$	−0.782025	−	3.79239i	−0.0250577	−	0.121516i
$975$			9.14400i			0.292842i
$976$	32.4334	−	34.3049i	1.03817	−	1.09807i
$977$		−	30.5474i		−	0.977297i	−0.872481	−	0.488648i	$-0.837490\pi$
$977$		−	30.5474i		−	0.977297i	0.872481	−	0.488648i	$-0.162510\pi$
$978$	−25.3996	+	5.23762i	−0.812189	+	0.167481i
$979$	−22.3381			−0.713929
$980$	35.1743	−	15.1508i	1.12360	−	0.483974i
$981$	−9.34569			−0.298385
$982$	36.9012	−	7.60936i	1.17756	−	0.242824i
$983$	44.5757			1.42174			0.710872	−	0.703322i	$-0.248301\pi$
$983$	44.5757			1.42174			0.710872	+	0.703322i	$0.248301\pi$
$984$	−5.85134	+	4.09027i	−0.186534	+	0.130393i
$985$		−	6.71957i		−	0.214103i
$986$	−13.1051	+	2.70239i	−0.417351	+	0.0860615i
$987$		−	1.48782i		−	0.0473578i
$988$	14.6864	−	6.32594i	0.467237	−	0.201255i
$989$	6.93383	+	5.19425i	0.220483	+	0.165168i
$990$	4.44384	+	21.5502i	0.141235	+	0.684910i
$991$			19.0485i			0.605096i	0.953134	+	0.302548i	$0.0978372\pi$
$991$			19.0485i			0.605096i	−0.953134	+	0.302548i	$0.902163\pi$
$992$	39.2714	+	24.2944i	1.24687	+	0.771347i
$993$	3.34810			0.106249
$994$	0.722198	+	3.50226i	0.0229067	+	0.111085i
$995$	10.5555			0.334631
$996$	−8.84930	−	20.5447i	−0.280401	−	0.650984i
$997$		−	47.6147i		−	1.50797i	−0.656889	−	0.753987i	$-0.728128\pi$
$997$		−	47.6147i		−	1.50797i	0.656889	−	0.753987i	$-0.271872\pi$
$998$	18.4478	−	3.80410i	0.583954	−	0.120417i
$999$	3.59504			0.113742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.b.91.21	✓	24
4.3	odd	2		2208.2.n.b.367.5		24
8.3	odd	2	inner	552.2.n.b.91.24	yes	24
8.5	even	2		2208.2.n.b.367.19		24
23.22	odd	2	inner	552.2.n.b.91.22	yes	24
92.91	even	2		2208.2.n.b.367.20		24
184.45	odd	2		2208.2.n.b.367.6		24
184.91	even	2	inner	552.2.n.b.91.23	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.21	✓	24	1.1	even	1	trivial
552.2.n.b.91.22	yes	24	23.22	odd	2	inner
552.2.n.b.91.23	yes	24	184.91	even	2	inner
552.2.n.b.91.24	yes	24	8.3	odd	2	inner
2208.2.n.b.367.5		24	4.3	odd	2
2208.2.n.b.367.6		24	184.45	odd	2
2208.2.n.b.367.19		24	8.5	even	2
2208.2.n.b.367.20		24	92.91	even	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38507 - 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} -2.80468 q^{5} +(-1.38507 + 0.285614i) q^{6} +0.415199 q^{7} +(2.31819 - 1.62049i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.38507 - 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} -2.80468 q^{5} +(-1.38507 + 0.285614i) q^{6} +0.415199 q^{7} +(2.31819 - 1.62049i) q^{8} +1.00000 q^{9} +(-3.88469 + 0.801057i) q^{10} -5.54747i q^{11} +(-1.83685 + 0.791193i) q^{12} -3.19024i q^{13} +(0.575080 - 0.118587i) q^{14} +2.80468 q^{15} +(2.74803 - 2.90660i) q^{16} -2.01349i q^{17} +(1.38507 - 0.285614i) q^{18} +2.50622i q^{19} +(-5.15178 + 2.21904i) q^{20} -0.415199 q^{21} +(-1.58444 - 7.68365i) q^{22} +(2.87533 - 3.83829i) q^{23} +(-2.31819 + 1.62049i) q^{24} +2.86624 q^{25} +(-0.911179 - 4.41871i) q^{26} -1.00000 q^{27} +(0.762658 - 0.328502i) q^{28} -4.69915i q^{29} +(3.88469 - 0.801057i) q^{30} +8.16330i q^{31} +(2.97605 - 4.81073i) q^{32} +5.54747i q^{33} +(-0.575080 - 2.78882i) q^{34} -1.16450 q^{35} +(1.83685 - 0.791193i) q^{36} -3.59504 q^{37} +(0.715812 + 3.47129i) q^{38} +3.19024i q^{39} +(-6.50179 + 4.54496i) q^{40} +2.52410 q^{41} +(-0.575080 + 0.118587i) q^{42} +1.80649i q^{43} +(-4.38912 - 10.1899i) q^{44} -2.80468 q^{45} +(2.88627 - 6.13755i) q^{46} +3.58339i q^{47} +(-2.74803 + 2.90660i) q^{48} -6.82761 q^{49} +(3.96995 - 0.818639i) q^{50} +2.01349i q^{51} +(-2.52410 - 5.85999i) q^{52} +0.270501 q^{53} +(-1.38507 + 0.285614i) q^{54} +15.5589i q^{55} +(0.962511 - 0.672826i) q^{56} -2.50622i q^{57} +(-1.34214 - 6.50865i) q^{58} -0.657857 q^{59} +(5.15178 - 2.21904i) q^{60} +11.8024 q^{61} +(2.33155 + 11.3068i) q^{62} +0.415199 q^{63} +(2.74803 - 7.51321i) q^{64} +8.94761i q^{65} +(1.58444 + 7.68365i) q^{66} +5.41363i q^{67} +(-1.59306 - 3.69847i) q^{68} +(-2.87533 + 3.83829i) q^{69} +(-1.61292 + 0.332598i) q^{70} +6.09004i q^{71} +(2.31819 - 1.62049i) q^{72} -2.82330 q^{73} +(-4.97938 + 1.02679i) q^{74} -2.86624 q^{75} +(1.98290 + 4.60355i) q^{76} -2.30330i q^{77} +(0.911179 + 4.41871i) q^{78} +15.0378 q^{79} +(-7.70734 + 8.15210i) q^{80} +1.00000 q^{81} +(3.49606 - 0.720918i) q^{82} +11.1848i q^{83} +(-0.762658 + 0.328502i) q^{84} +5.64719i q^{85} +(0.515959 + 2.50212i) q^{86} +4.69915i q^{87} +(-8.98962 - 12.8601i) q^{88} -4.02672i q^{89} +(-3.88469 + 0.801057i) q^{90} -1.32459i q^{91} +(2.24472 - 9.32530i) q^{92} -8.16330i q^{93} +(1.02347 + 4.96325i) q^{94} -7.02915i q^{95} +(-2.97605 + 4.81073i) q^{96} -14.5135i q^{97} +(-9.45673 + 1.95006i) q^{98} -5.54747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Introduction

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