LMFDB - Embedded newform 552.2.n.b.91.24

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			91.24
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.22

$q$-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} +(-5.07881 + 4.49507i) 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} +(-8.31837 + 4.77542i) 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	$-0.284223\pi$
$5$	2.80468			1.25429			0.627146	+	0.778902i	$0.284223\pi$
$6$	−1.38507	−	0.285614i	−0.565453	−	0.116602i
$7$	−0.415199			−0.156930			−0.0784652	−	0.996917i	$-0.525002\pi$
$7$	−0.415199			−0.156930			−0.0784652	+	0.996917i	$0.525002\pi$
$8$	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	$0.145875\pi$
$13$			3.19024i			0.884814i	−0.896814	+	0.442407i	$0.854125\pi$
$14$	−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	$0.143713\pi$
$29$			4.69915i			0.872609i	−0.899799	+	0.436305i	$0.856287\pi$
$30$	−3.88469	−	0.801057i	−0.709243	−	0.146252i
$31$		−	8.16330i		−	1.46617i	−0.680136	−	0.733086i	$-0.738079\pi$
$31$		−	8.16330i		−	1.46617i	0.680136	−	0.733086i	$-0.261921\pi$
$32$	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	$-0.404510\pi$
$37$	3.59504			0.591020			0.295510	+	0.955340i	$0.404510\pi$
$38$	−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
$46$	−5.07881	+	4.49507i	−0.748830	+	0.662763i
$47$		−	3.58339i		−	0.522690i	−0.965245	−	0.261345i	$-0.915834\pi$
$47$		−	3.58339i		−	0.522690i	0.965245	−	0.261345i	$-0.0841661\pi$
$48$	−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	$-0.505914\pi$
$53$	−0.270501			−0.0371562			−0.0185781	+	0.999827i	$0.505914\pi$
$54$	−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	$-0.772641\pi$
$61$	−11.8024			−1.51114			−0.755572	+	0.655065i	$0.772641\pi$
$62$	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	$-0.882307\pi$
$71$		−	6.09004i		−	0.722755i	0.932420	−	0.361377i	$-0.117693\pi$
$72$	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	$-0.820961\pi$
$79$	−15.0378			−1.69188			−0.845942	+	0.533276i	$0.820961\pi$
$80$	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
$92$	−8.31837	+	4.77542i	−0.867251	+	0.497872i
$93$			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	$-0.886730\pi$
$101$		−	7.00245i		−	0.696770i	0.937352	−	0.348385i	$-0.113270\pi$
$102$	−0.575080	+	2.78882i	−0.0569415	+	0.276135i
$103$	−18.4881			−1.82169			−0.910845	−	0.412750i	$-0.864568\pi$
$103$	−18.4881			−1.82169			−0.910845	+	0.412750i	$0.864568\pi$
$104$	−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	$-0.352287\pi$
$109$	9.34569			0.895155			0.447578	+	0.894245i	$0.352287\pi$
$110$	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	$-0.924232\pi$
$127$		−	5.31443i		−	0.471580i	0.971804	−	0.235790i	$-0.0757677\pi$
$128$	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	$0.704420\pi$
$138$	5.07881	−	4.49507i	0.432337	−	0.382646i
$139$	−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	$-0.364825\pi$
$149$	10.0586			0.824032			0.412016	+	0.911177i	$0.364825\pi$
$150$	−3.96995	−	0.818639i	−0.324145	−	0.0668416i
$151$		−	16.6249i		−	1.35292i	−0.736480	−	0.676459i	$-0.763514\pi$
$151$		−	16.6249i		−	1.35292i	0.736480	−	0.676459i	$-0.236486\pi$
$152$	−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	$-0.419175\pi$
$157$	6.29506			0.502401			0.251200	+	0.967935i	$0.419175\pi$
$158$	−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	$0.276955\pi$
$167$			19.7559i			1.52876i	−0.644766	+	0.764380i	$0.723045\pi$
$168$	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	$0.142497\pi$
$173$			11.3869i			0.865731i	−0.901459	+	0.432865i	$0.857503\pi$
$174$	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	$-0.566807\pi$
$181$	−5.60596			−0.416688			−0.208344	+	0.978056i	$0.566807\pi$
$182$	0.378321	−	1.83465i	0.0280430	−	0.135993i
$183$	11.8024			0.872460
$184$	−12.8855	+	4.23845i	−0.949930	+	0.312463i
$185$	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	$-0.139479\pi$
$191$	25.0291			1.81104			0.905522	+	0.424298i	$0.139479\pi$
$192$	−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	$-0.972800\pi$
$197$		−	2.39584i		−	0.170697i	0.996351	−	0.0853483i	$-0.0272003\pi$
$198$	1.58444	−	7.68365i	0.112601	−	0.546053i
$199$	3.76352			0.266789			0.133395	−	0.991063i	$-0.457412\pi$
$199$	3.76352			0.266789			0.133395	+	0.991063i	$0.457412\pi$
$200$	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	$0.178599\pi$
$223$			15.8920i			1.06421i	−0.846678	+	0.532105i	$0.821401\pi$
$224$	−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	$-0.706731\pi$
$229$	−18.3034			−1.20952			−0.604761	+	0.796407i	$0.706731\pi$
$230$	−14.2444	+	12.6073i	−0.939251	+	0.831298i
$231$		−	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	$0.264613\pi$
$239$			22.8436i			1.47763i	−0.673910	+	0.738813i	$0.735387\pi$
$240$	−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	$-0.548474\pi$
$263$	−4.92026			−0.303396			−0.151698	+	0.988427i	$0.548474\pi$
$264$	−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	$-0.913786\pi$
$269$		−	8.77633i		−	0.535102i	0.963544	−	0.267551i	$-0.0862144\pi$
$270$	−3.88469	−	0.801057i	−0.236414	−	0.0487508i
$271$		−	7.39559i		−	0.449250i	−0.974445	−	0.224625i	$-0.927884\pi$
$271$		−	7.39559i		−	0.449250i	0.974445	−	0.224625i	$-0.0721158\pi$
$272$	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
$276$	8.31837	−	4.77542i	0.500707	−	0.287447i
$277$		−	8.71879i		−	0.523861i	−0.965087	−	0.261931i	$-0.915641\pi$
$277$		−	8.71879i		−	0.523861i	0.965087	−	0.261931i	$-0.0843592\pi$
$278$	−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	$-0.269242\pi$
$293$	22.7008			1.32619			0.663096	+	0.748534i	$0.269242\pi$
$294$	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	$0.0836372\pi$
$311$			9.16116i			0.519482i	−0.965678	+	0.259741i	$0.916363\pi$
$312$	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	$-0.648393\pi$
$317$		−	31.8091i		−	1.78658i	0.449485	−	0.893288i	$-0.351607\pi$
$318$	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
$322$	2.10872	−	1.86635i	0.117514	−	0.104008i
$323$	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	$0.142341\pi$
$349$			16.1566i			0.864844i	−0.901671	+	0.432422i	$0.857659\pi$
$350$	−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	$-0.794209\pi$
$359$	−30.2471			−1.59638			−0.798190	+	0.602405i	$0.794209\pi$
$360$	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	$-0.487762\pi$
$367$	1.47265			0.0768718			0.0384359	+	0.999261i	$0.487762\pi$
$368$	−19.0579	+	2.19029i	−0.993460	+	0.114177i
$369$	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	$-0.395874\pi$
$373$	12.4114			0.642639			0.321320	+	0.946971i	$0.395874\pi$
$374$	−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	$-0.216523\pi$
$383$	30.4292			1.55486			0.777430	+	0.628970i	$0.216523\pi$
$384$	−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	$-0.641030\pi$
$389$	−16.9108			−0.857413			−0.428706	+	0.903444i	$0.641030\pi$
$390$	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	$0.214883\pi$
$397$			24.9043i			1.24991i	−0.780661	+	0.624955i	$0.785117\pi$
$398$	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
$414$	−5.07881	+	4.49507i	−0.249610	+	0.220921i
$415$			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	$-0.615232\pi$
$421$	−14.5334			−0.708316			−0.354158	+	0.935186i	$0.615232\pi$
$422$	−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	$-0.412738\pi$
$431$	11.2407			0.541443			0.270722	+	0.962658i	$0.412738\pi$
$432$	−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	$-0.556082\pi$
$439$		−	41.2559i		−	1.96904i	0.175278	−	0.984519i	$-0.443918\pi$
$440$	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
$460$	−23.3304	+	13.3935i	−1.08779	+	0.624477i
$461$		−	34.5037i		−	1.60700i	−0.595308	−	0.803498i	$-0.702970\pi$
$461$		−	34.5037i		−	1.60700i	0.595308	−	0.803498i	$-0.297030\pi$
$462$	0.657857	−	3.19024i	0.0306063	−	0.148423i
$463$			28.5673i			1.32763i	0.747895	+	0.663817i	$0.231064\pi$
$463$			28.5673i			1.32763i	−0.747895	+	0.663817i	$0.768936\pi$
$464$	−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	$-0.450470\pi$
$479$	6.78356			0.309949			0.154974	+	0.987918i	$0.450470\pi$
$480$	−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	$0.0197595\pi$
$487$			2.73804i			0.124073i	−0.998074	+	0.0620363i	$0.980241\pi$
$488$	−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	$-0.297010\pi$
$503$	26.7050			1.19072			0.595359	+	0.803460i	$0.297010\pi$
$504$	−0.962511	−	0.672826i	−0.0428736	−	0.0299700i
$505$		−	19.6396i		−	0.873953i
$506$	24.9363	+	28.1745i	1.10855	+	1.25251i
$507$	−2.82236			−0.125345
$508$	4.20474	−	9.76181i	0.186555	−	0.433110i
$509$		−	28.4096i		−	1.25923i	−0.776906	−	0.629617i	$-0.783212\pi$
$509$		−	28.4096i		−	1.25923i	0.776906	−	0.629617i	$-0.216788\pi$
$510$	−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	$-0.848379\pi$
$541$		−	21.3299i		−	0.917046i	0.888683	−	0.458523i	$-0.151621\pi$
$542$	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
$552$	12.8855	−	4.23845i	0.548442	−	0.180401i
$553$	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	$-0.648205\pi$
$557$	−21.1916			−0.897915			−0.448958	+	0.893553i	$0.648205\pi$
$558$	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
$598$	−14.3404	−	16.2026i	−0.586421	−	0.662575i
$599$		−	20.5586i		−	0.840003i	−0.907523	−	0.420002i	$-0.862030\pi$
$599$		−	20.5586i		−	0.840003i	0.907523	−	0.420002i	$-0.137970\pi$
$600$	−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	$0.155843\pi$
$607$			23.1724i			0.940539i	−0.882523	+	0.470269i	$0.844157\pi$
$608$	−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	$-0.333173\pi$
$613$	24.7805			1.00087			0.500437	+	0.865773i	$0.333173\pi$
$614$	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	$-0.780031\pi$
$631$	−38.7133			−1.54115			−0.770576	+	0.637349i	$0.780031\pi$
$632$	−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	$-0.0285906\pi$
$644$	3.45378	−	1.98275i	0.136098	−	0.0781313i
$645$		−	5.06662i		−	0.199498i
$646$	6.98940	+	1.44128i	0.274994	+	0.0567063i
$647$		−	24.8216i		−	0.975838i	−0.872889	−	0.487919i	$-0.837756\pi$
$647$		−	24.8216i		−	0.975838i	0.872889	−	0.487919i	$-0.162244\pi$
$648$	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	$0.129277\pi$
$653$			20.1907i			0.790122i	−0.918655	+	0.395061i	$0.870723\pi$
$654$	−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	$-0.715820\pi$
$661$	−32.2531			−1.25450			−0.627251	+	0.778818i	$0.715820\pi$
$662$	−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	$-0.403986\pi$
$677$	15.4597			0.594165			0.297083	+	0.954852i	$0.403986\pi$
$678$	−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
$690$	14.2444	−	12.6073i	0.542277	−	0.479950i
$691$	−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	$-0.343080\pi$
$701$	25.0600			0.946504			0.473252	+	0.880927i	$0.343080\pi$
$702$	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	$-0.490958\pi$
$709$	1.51261			0.0568072			0.0284036	+	0.999597i	$0.490958\pi$
$710$	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	$-0.912315\pi$
$719$		−	14.5869i		−	0.543999i	0.962297	−	0.272000i	$-0.0876850\pi$
$720$	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	$-0.367943\pi$
$727$	21.7360			0.806142			0.403071	+	0.915169i	$0.367943\pi$
$728$	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	$-0.551637\pi$
$733$	−8.74545			−0.323021			−0.161510	+	0.986871i	$0.551637\pi$
$734$	2.03973	+	0.420610i	0.0752877	+	0.0155250i
$735$	19.1493			0.706332
$736$	−27.0221	−	2.40950i	−0.996048	−	0.0888152i
$737$	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	$-0.326387\pi$
$743$	28.2818			1.03756			0.518779	+	0.854908i	$0.326387\pi$
$744$	−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	$-0.191539\pi$
$751$	45.1818			1.64871			0.824353	+	0.566076i	$0.191539\pi$
$752$	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	$-0.430716\pi$
$757$	11.8830			0.431894			0.215947	+	0.976405i	$0.430716\pi$
$758$	−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	$-0.275864\pi$
$773$	35.9982			1.29477			0.647383	+	0.762165i	$0.275864\pi$
$774$	−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
$782$	9.05077	+	10.2261i	0.323655	+	0.365685i
$783$		−	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	$-0.553142\pi$
$797$	−9.38264			−0.332350			−0.166175	+	0.986096i	$0.553142\pi$
$798$	−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	$-0.886705\pi$
$821$		−	19.9688i		−	0.696917i	0.937324	−	0.348458i	$-0.113295\pi$
$822$	5.35405	−	25.9642i	0.186744	−	0.905604i
$823$			8.28082i			0.288651i	0.989530	+	0.144326i	$0.0461012\pi$
$823$			8.28082i			0.288651i	−0.989530	+	0.144326i	$0.953899\pi$
$824$	−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	$0.948349\pi$
$828$	−8.31837	+	4.77542i	−0.289084	+	0.165957i
$829$			42.2445i			1.46721i	0.679576	+	0.733605i	$0.262164\pi$
$829$			42.2445i			1.46721i	−0.679576	+	0.733605i	$0.737836\pi$
$830$	−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	$-0.513439\pi$
$839$	−2.44511			−0.0844145			−0.0422072	+	0.999109i	$0.513439\pi$
$840$	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	$-0.931992\pi$
$853$		−	12.3852i		−	0.424060i	0.977263	−	0.212030i	$-0.0680075\pi$
$854$	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	$0.0646857\pi$
$863$			11.8577i			0.403641i	−0.979423	+	0.201820i	$0.935314\pi$
$864$	−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
$874$	−11.2656	−	12.7286i	−0.381066	−	0.430552i
$875$	2.48477			0.0840004
$876$	5.18597	+	2.23377i	0.175218	+	0.0754722i
$877$			44.9851i			1.51904i	0.650484	+	0.759520i	$0.274566\pi$
$877$			44.9851i			1.51904i	−0.650484	+	0.759520i	$0.725434\pi$
$878$	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	$-0.773409\pi$
$887$		−	38.9103i		−	1.30648i	0.757151	−	0.653240i	$-0.226591\pi$
$888$	−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	$-0.762173\pi$
$911$	−44.2857			−1.46725			−0.733625	+	0.679554i	$0.762173\pi$
$912$	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	$-0.458149\pi$
$919$	7.94858			0.262199			0.131100	+	0.991369i	$0.458149\pi$
$920$	−36.1397	+	11.8875i	−1.19149	+	0.391920i
$921$	−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	$-0.268282\pi$
$941$	40.8202			1.33070			0.665350	+	0.746532i	$0.268282\pi$
$942$	−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
$966$	−2.10872	+	1.86635i	−0.0678468	+	0.0600488i
$967$		−	8.73002i		−	0.280738i	−0.990099	−	0.140369i	$-0.955171\pi$
$967$		−	8.73002i		−	0.280738i	0.990099	−	0.140369i	$-0.0448290\pi$
$968$	−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	$-0.751699\pi$
$983$	−44.5757			−1.42174			−0.710872	+	0.703322i	$0.751699\pi$
$984$	−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	$-0.902163\pi$
$991$		−	19.0485i		−	0.605096i	0.953134	−	0.302548i	$-0.0978372\pi$
$992$	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	$0.271872\pi$
$997$			47.6147i			1.50797i	−0.656889	+	0.753987i	$0.728128\pi$
$998$	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.91.24	yes	24
4.3	odd	2		2208.2.n.b.367.19		24
8.3	odd	2	inner	552.2.n.b.91.21	✓	24
8.5	even	2		2208.2.n.b.367.5		24
23.22	odd	2	inner	552.2.n.b.91.23	yes	24
92.91	even	2		2208.2.n.b.367.6		24
184.45	odd	2		2208.2.n.b.367.20		24
184.91	even	2	inner	552.2.n.b.91.22	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.21	✓	24	8.3	odd	2	inner
552.2.n.b.91.22	yes	24	184.91	even	2	inner
552.2.n.b.91.23	yes	24	23.22	odd	2	inner
552.2.n.b.91.24	yes	24	1.1	even	1	trivial
2208.2.n.b.367.5		24	8.5	even	2
2208.2.n.b.367.6		24	92.91	even	2
2208.2.n.b.367.19		24	4.3	odd	2
2208.2.n.b.367.20		24	184.45	odd	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} +(-5.07881 + 4.49507i) 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} +(-8.31837 + 4.77542i) 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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