LMFDB - Embedded newform 288.2.v.d.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			253.1
Character	$\chi$	$=$	288.253
Dual form			288.2.v.d.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34416 + 0.439595i) q^{2} +(1.61351 - 1.18177i) q^{4} +(-0.184062 - 0.444366i) q^{5} +(-0.134531 + 0.134531i) q^{7} +(-1.64931 + 2.29777i) q^{8} +O(q^{10})$	\(q+(-1.34416 + 0.439595i) q^{2} +(1.61351 - 1.18177i) q^{4} +(-0.184062 - 0.444366i) q^{5} +(-0.134531 + 0.134531i) q^{7} +(-1.64931 + 2.29777i) q^{8} +(0.442749 + 0.516384i) q^{10} +(4.83050 - 2.00086i) q^{11} +(-0.237510 + 0.573400i) q^{13} +(0.121692 - 0.239970i) q^{14} +(1.20685 - 3.81360i) q^{16} -5.70425i q^{17} +(-0.459376 + 1.10903i) q^{19} +(-0.822124 - 0.499471i) q^{20} +(-5.61338 + 4.81293i) q^{22} +(4.07921 + 4.07921i) q^{23} +(3.37195 - 3.37195i) q^{25} +(0.0671870 - 0.875148i) q^{26} +(-0.0580831 + 0.376053i) q^{28} +(2.33405 + 0.966793i) q^{29} +10.2033 q^{31} +(0.0542480 + 5.65659i) q^{32} +(2.50756 + 7.66741i) q^{34} +(0.0845432 + 0.0350189i) q^{35} +(-3.05654 - 7.37913i) q^{37} +(0.129949 - 1.69265i) q^{38} +(1.32463 + 0.309965i) q^{40} +(0.877147 + 0.877147i) q^{41} +(-2.15605 + 0.893063i) q^{43} +(5.42952 - 8.93695i) q^{44} +(-7.27630 - 3.68990i) q^{46} +4.94536i q^{47} +6.96380i q^{49} +(-3.05014 + 6.01472i) q^{50} +(0.294401 + 1.20587i) q^{52} +(-9.74330 + 4.03581i) q^{53} +(-1.77823 - 1.77823i) q^{55} +(-0.0872381 - 0.531007i) q^{56} +(-3.56232 - 0.273487i) q^{58} +(-4.73462 - 11.4304i) q^{59} +(-9.46851 - 3.92198i) q^{61} +(-13.7148 + 4.48530i) q^{62} +(-2.55953 - 7.57950i) q^{64} +0.298516 q^{65} +(4.79416 + 1.98581i) q^{67} +(-6.74111 - 9.20388i) q^{68} +(-0.129033 - 0.00990617i) q^{70} +(-4.32992 + 4.32992i) q^{71} +(-6.12055 - 6.12055i) q^{73} +(7.35229 + 8.57507i) q^{74} +(0.569410 + 2.33231i) q^{76} +(-0.380675 + 0.919031i) q^{77} +11.9773i q^{79} +(-1.91677 + 0.165658i) q^{80} +(-1.56461 - 0.793434i) q^{82} +(-1.59989 + 3.86247i) q^{83} +(-2.53477 + 1.04994i) q^{85} +(2.50548 - 2.14820i) q^{86} +(-3.36949 + 14.3994i) q^{88} +(8.43934 - 8.43934i) q^{89} +(-0.0451877 - 0.109093i) q^{91} +(11.4025 + 1.76118i) q^{92} +(-2.17395 - 6.64733i) q^{94} +0.577370 q^{95} -9.21817 q^{97} +(-3.06125 - 9.36044i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

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 $

$2$	−1.34416	+	0.439595i	−0.950462	+	0.310841i
$2$	−1.34416	+	0.439595i	−0.950462	+	0.310841i
$3$		0			0
$3$		0			0
$4$	1.61351	−	1.18177i	0.806756	−	0.590884i
$5$	−0.184062	−	0.444366i	−0.0823152	−	0.198726i	0.877363	−	0.479827i	$-0.159301\pi$
$5$	−0.184062	−	0.444366i	−0.0823152	−	0.198726i	−0.959678	+	0.281101i	$0.909301\pi$
$6$		0			0
$7$	−0.134531	+	0.134531i	−0.0508480	+	0.0508480i	−0.732074	−	0.681226i	$-0.761447\pi$
$7$	−0.134531	+	0.134531i	−0.0508480	+	0.0508480i	0.681226	+	0.732074i	$0.261447\pi$
$8$	−1.64931	+	2.29777i	−0.583120	+	0.812386i
$9$		0			0
$10$	0.442749	+	0.516384i	0.140010	+	0.163295i
$11$	4.83050	−	2.00086i	1.45645	−	0.603282i	0.492727	−	0.870184i	$-0.336000\pi$
$11$	4.83050	−	2.00086i	1.45645	−	0.603282i	0.963724	+	0.266902i	$0.0860001\pi$
$12$		0			0
$13$	−0.237510	+	0.573400i	−0.0658735	+	0.159033i	−0.953388	−	0.301747i	$-0.902430\pi$
$13$	−0.237510	+	0.573400i	−0.0658735	+	0.159033i	0.887515	+	0.460780i	$0.152430\pi$
$14$	0.121692	−	0.239970i	0.0325235	−	0.0641347i
$15$		0			0
$16$	1.20685	−	3.81360i	0.301712	−	0.953399i
$17$		−	5.70425i		−	1.38348i	−0.722145	−	0.691742i	$-0.756843\pi$
$17$		−	5.70425i		−	1.38348i	0.722145	−	0.691742i	$-0.243157\pi$
$18$		0			0
$19$	−0.459376	+	1.10903i	−0.105388	+	0.254430i	−0.967773	−	0.251823i	$-0.918970\pi$
$19$	−0.459376	+	1.10903i	−0.105388	+	0.254430i	0.862385	+	0.506253i	$0.168970\pi$
$20$	−0.822124	−	0.499471i	−0.183833	−	0.111685i
$21$		0			0
$22$	−5.61338	+	4.81293i	−1.19678	+	1.02612i
$23$	4.07921	+	4.07921i	0.850575	+	0.850575i	0.990204	−	0.139629i	$-0.0445910\pi$
$23$	4.07921	+	4.07921i	0.850575	+	0.850575i	−0.139629	+	0.990204i	$0.544591\pi$
$24$		0			0
$25$	3.37195	−	3.37195i	0.674390	−	0.674390i
$26$	0.0671870	−	0.875148i	0.0131765	−	0.171631i
$27$		0			0
$28$	−0.0580831	+	0.376053i	−0.0109767	+	0.0710673i
$29$	2.33405	+	0.966793i	0.433421	+	0.179529i	0.588717	−	0.808339i	$-0.299633\pi$
$29$	2.33405	+	0.966793i	0.433421	+	0.179529i	−0.155296	+	0.987868i	$0.549633\pi$
$30$		0			0
$31$	10.2033			1.83256			0.916280	−	0.400539i	$-0.131177\pi$
$31$	10.2033			1.83256			0.916280	+	0.400539i	$0.131177\pi$
$32$	0.0542480	+	5.65659i	0.00958978	+	0.999954i
$33$		0			0
$34$	2.50756	+	7.66741i	0.430043	+	1.31495i
$35$	0.0845432	+	0.0350189i	0.0142904	+	0.00591928i
$36$		0			0
$37$	−3.05654	−	7.37913i	−0.502491	−	1.21312i	−0.948123	−	0.317905i	$-0.897021\pi$
$37$	−3.05654	−	7.37913i	−0.502491	−	1.21312i	0.445631	−	0.895217i	$-0.352979\pi$
$38$	0.129949	−	1.69265i	0.0210804	−	0.274585i
$39$		0			0
$40$	1.32463	+	0.309965i	0.209442	+	0.0490098i
$41$	0.877147	+	0.877147i	0.136987	+	0.136987i	0.772275	−	0.635288i	$-0.219119\pi$
$41$	0.877147	+	0.877147i	0.136987	+	0.136987i	−0.635288	+	0.772275i	$0.719119\pi$
$42$		0			0
$43$	−2.15605	+	0.893063i	−0.328794	+	0.136191i	−0.540973	−	0.841040i	$-0.681944\pi$
$43$	−2.15605	+	0.893063i	−0.328794	+	0.136191i	0.212179	+	0.977231i	$0.431944\pi$
$44$	5.42952	−	8.93695i	0.818531	−	1.34730i
$45$		0			0
$46$	−7.27630	−	3.68990i	−1.07283	−	0.544046i
$47$			4.94536i			0.721355i	0.932691	+	0.360677i	$0.117454\pi$
$47$			4.94536i			0.721355i	−0.932691	+	0.360677i	$0.882546\pi$
$48$		0			0
$49$			6.96380i			0.994829i
$50$	−3.05014	+	6.01472i	−0.431355	+	0.850610i
$51$		0			0
$52$	0.294401	+	1.20587i	0.0408261	+	0.167224i
$53$	−9.74330	+	4.03581i	−1.33834	+	0.554361i	−0.933024	−	0.359814i	$-0.882840\pi$
$53$	−9.74330	+	4.03581i	−1.33834	+	0.554361i	−0.405321	+	0.914175i	$0.632840\pi$
$54$		0			0
$55$	−1.77823	−	1.77823i	−0.239776	−	0.239776i
$56$	−0.0872381	−	0.531007i	−0.0116577	−	0.0709587i
$57$		0			0
$58$	−3.56232	−	0.273487i	−0.467756	−	0.0359106i
$59$	−4.73462	−	11.4304i	−0.616395	−	1.48811i	−0.855861	−	0.517205i	$-0.826972\pi$
$59$	−4.73462	−	11.4304i	−0.616395	−	1.48811i	0.239466	−	0.970905i	$-0.423028\pi$
$60$		0			0
$61$	−9.46851	−	3.92198i	−1.21232	−	0.502159i	−0.317358	−	0.948306i	$-0.602796\pi$
$61$	−9.46851	−	3.92198i	−1.21232	−	0.502159i	−0.894960	+	0.446147i	$0.852796\pi$
$62$	−13.7148	+	4.48530i	−1.74178	+	0.569634i
$63$		0			0
$64$	−2.55953	−	7.57950i	−0.319941	−	0.947437i
$65$	0.298516			0.0370264
$66$		0			0
$67$	4.79416	+	1.98581i	0.585700	+	0.242605i	0.655799	−	0.754935i	$-0.272332\pi$
$67$	4.79416	+	1.98581i	0.585700	+	0.242605i	−0.0700997	+	0.997540i	$0.522332\pi$
$68$	−6.74111	−	9.20388i	−0.817479	−	1.11613i
$69$		0			0
$70$	−0.129033	−	0.00990617i	−0.0154224	−	0.00118401i
$71$	−4.32992	+	4.32992i	−0.513867	+	0.513867i	−0.915709	−	0.401842i	$-0.868370\pi$
$71$	−4.32992	+	4.32992i	−0.513867	+	0.513867i	0.401842	+	0.915709i	$0.368370\pi$
$72$		0			0
$73$	−6.12055	−	6.12055i	−0.716356	−	0.716356i	0.251501	−	0.967857i	$-0.419076\pi$
$73$	−6.12055	−	6.12055i	−0.716356	−	0.716356i	−0.967857	+	0.251501i	$0.919076\pi$
$74$	7.35229	+	8.57507i	0.854686	+	0.996831i
$75$		0			0
$76$	0.569410	+	2.33231i	0.0653158	+	0.267535i
$77$	−0.380675	+	0.919031i	−0.0433820	+	0.104733i
$78$		0			0
$79$			11.9773i			1.34756i	0.738934	+	0.673778i	$0.235330\pi$
$79$			11.9773i			1.34756i	−0.738934	+	0.673778i	$0.764670\pi$
$80$	−1.91677	+	0.165658i	−0.214301	+	0.0185212i
$81$		0			0
$82$	−1.56461	−	0.793434i	−0.172783	−	0.0876201i
$83$	−1.59989	+	3.86247i	−0.175610	+	0.423961i	−0.987037	−	0.160493i	$-0.948691\pi$
$83$	−1.59989	+	3.86247i	−0.175610	+	0.423961i	0.811426	+	0.584455i	$0.198691\pi$
$84$		0			0
$85$	−2.53477	+	1.04994i	−0.274935	+	0.113882i
$86$	2.50548	−	2.14820i	0.270172	−	0.231647i
$87$		0			0
$88$	−3.36949	+	14.3994i	−0.359189	+	1.53499i
$89$	8.43934	−	8.43934i	0.894569	−	0.894569i	−0.100381	−	0.994949i	$-0.532006\pi$
$89$	8.43934	−	8.43934i	0.894569	−	0.894569i	0.994949	+	0.100381i	$0.0320060\pi$
$90$		0			0
$91$	−0.0451877	−	0.109093i	−0.00473696	−	0.0114360i
$92$	11.4025	+	1.76118i	1.18880	+	0.183615i
$93$		0			0
$94$	−2.17395	−	6.64733i	−0.224226	−	0.685620i
$95$	0.577370			0.0592369
$96$		0			0
$97$	−9.21817			−0.935964			−0.467982	−	0.883738i	$-0.655019\pi$
$97$	−9.21817			−0.935964			−0.467982	+	0.883738i	$0.655019\pi$
$98$	−3.06125	−	9.36044i	−0.309233	−	0.945547i
$99$		0			0
$100$	1.45582	−	9.42555i	0.145582	−	0.942555i
$101$	−1.27818	−	3.08581i	−0.127184	−	0.307050i	0.847442	−	0.530888i	$-0.178141\pi$
$101$	−1.27818	−	3.08581i	−0.127184	−	0.307050i	−0.974626	+	0.223838i	$0.928141\pi$
$102$		0			0
$103$	−7.17872	+	7.17872i	−0.707340	+	0.707340i	−0.965975	−	0.258635i	$-0.916727\pi$
$103$	−7.17872	+	7.17872i	−0.707340	+	0.707340i	0.258635	+	0.965975i	$0.416727\pi$
$104$	−0.925816	−	1.49146i	−0.0907837	−	0.146250i
$105$		0			0
$106$	11.3224	−	9.70786i	1.09973	−	0.942910i
$107$	−1.52273	+	0.630735i	−0.147208	+	0.0609755i	−0.455071	−	0.890455i	$-0.650386\pi$
$107$	−1.52273	+	0.630735i	−0.147208	+	0.0609755i	0.307863	+	0.951431i	$0.400386\pi$
$108$		0			0
$109$	−5.64602	+	13.6307i	−0.540791	+	1.30558i	0.383375	+	0.923593i	$0.374762\pi$
$109$	−5.64602	+	13.6307i	−0.540791	+	1.30558i	−0.924166	+	0.381992i	$0.875238\pi$
$110$	3.17191	+	1.60851i	0.302430	+	0.153366i
$111$		0			0
$112$	0.350689	+	0.675406i	0.0331370	+	0.0638199i
$113$			4.48349i			0.421771i	0.977511	+	0.210886i	$0.0676348\pi$
$113$			4.48349i			0.421771i	−0.977511	+	0.210886i	$0.932365\pi$
$114$		0			0
$115$	1.06183	−	2.56349i	0.0990164	−	0.239047i
$116$	4.90854	−	1.19837i	0.455746	−	0.111266i
$117$		0			0
$118$	11.3888	+	13.2829i	1.04843	+	1.22279i
$119$	0.767400	+	0.767400i	0.0703474	+	0.0703474i
$120$		0			0
$121$	11.5521	−	11.5521i	1.05019	−	1.05019i
$122$	14.4512	+	1.10945i	1.30835	+	0.100445i
$123$		0			0
$124$	16.4631	−	12.0579i	1.47843	−	1.08283i
$125$	−4.34086	−	1.79804i	−0.388258	−	0.160822i
$126$		0			0
$127$	10.5535			0.936470			0.468235	−	0.883604i	$-0.344890\pi$
$127$	10.5535			0.936470			0.468235	+	0.883604i	$0.344890\pi$
$128$	6.77232	+	9.06288i	0.598594	+	0.801053i
$129$		0			0
$130$	−0.401252	+	0.131226i	−0.0351922	+	0.0115093i
$131$	−6.23238	−	2.58153i	−0.544525	−	0.225550i	0.0934264	−	0.995626i	$-0.470218\pi$
$131$	−6.23238	−	2.58153i	−0.544525	−	0.225550i	−0.637952	+	0.770076i	$0.720218\pi$
$132$		0			0
$133$	−0.0873991	−	0.211000i	−0.00757846	−	0.0182960i
$134$	−7.31705	−	0.561745i	−0.632097	−	0.0485274i
$135$		0			0
$136$	13.1071	+	9.40810i	1.12392	+	0.806738i
$137$	10.4945	+	10.4945i	0.896606	+	0.896606i	0.995134	−	0.0985279i	$-0.0314134\pi$
$137$	10.4945	+	10.4945i	0.896606	+	0.896606i	−0.0985279	+	0.995134i	$0.531413\pi$
$138$		0			0
$139$	9.16542	−	3.79644i	0.777401	−	0.322010i	0.0415348	−	0.999137i	$-0.486775\pi$
$139$	9.16542	−	3.79644i	0.777401	−	0.322010i	0.735866	+	0.677127i	$0.236775\pi$
$140$	0.177796	−	0.0434070i	0.0150265	−	0.00366856i
$141$		0			0
$142$	3.91668	−	7.72350i	0.328681	−	0.648142i
$143$			3.24504i			0.271364i
$144$		0			0
$145$		−	1.21512i		−	0.100910i
$146$	10.9175	+	5.53641i	0.903542	+	0.458197i
$147$		0			0
$148$	−13.6522	−	8.29420i	−1.12220	−	0.681779i
$149$	−9.74535	+	4.03666i	−0.798370	+	0.330696i	−0.744303	−	0.667842i	$-0.767218\pi$
$149$	−9.74535	+	4.03666i	−0.798370	+	0.330696i	−0.0540667	+	0.998537i	$0.517218\pi$
$150$		0			0
$151$	−8.98745	−	8.98745i	−0.731388	−	0.731388i	0.239507	−	0.970895i	$-0.423014\pi$
$151$	−8.98745	−	8.98745i	−0.731388	−	0.731388i	−0.970895	+	0.239507i	$0.923014\pi$
$152$	−1.79065	−	2.88469i	−0.145241	−	0.233979i
$153$		0			0
$154$	0.107686	−	1.40266i	0.00867755	−	0.113030i
$155$	−1.87804	−	4.53398i	−0.150847	−	0.364178i
$156$		0			0
$157$	20.8461	+	8.63473i	1.66370	+	0.689127i	0.998351	−	0.0574062i	$-0.0182830\pi$
$157$	20.8461	+	8.63473i	1.66370	+	0.689127i	0.665348	+	0.746533i	$0.268283\pi$
$158$	−5.26518	−	16.0994i	−0.418875	−	1.28080i
$159$		0			0
$160$	2.50361	−	1.06527i	0.197928	−	0.0842171i
$161$	−1.09756			−0.0865001
$162$		0			0
$163$	−7.04554	−	2.91836i	−0.551849	−	0.228584i	0.0892930	−	0.996005i	$-0.471539\pi$
$163$	−7.04554	−	2.91836i	−0.551849	−	0.228584i	−0.641142	+	0.767422i	$0.721539\pi$
$164$	2.45187	+	0.378703i	0.191459	+	0.0295717i
$165$		0			0
$166$	0.452577	−	5.89507i	0.0351268	−	0.457546i
$167$	0.832153	−	0.832153i	0.0643940	−	0.0643940i	−0.674176	−	0.738570i	$-0.735501\pi$
$167$	0.832153	−	0.832153i	0.0643940	−	0.0643940i	0.738570	+	0.674176i	$0.235501\pi$
$168$		0			0
$169$	8.92001	+	8.92001i	0.686155	+	0.686155i
$170$	2.94559	−	2.52555i	0.225916	−	0.193701i
$171$		0			0
$172$	−2.42341	+	3.98891i	−0.184783	+	0.304152i
$173$	−4.67762	+	11.2928i	−0.355633	+	0.858573i	0.640271	+	0.768149i	$0.278822\pi$
$173$	−4.67762	+	11.2928i	−0.355633	+	0.858573i	−0.995903	+	0.0904237i	$0.971178\pi$
$174$		0			0
$175$			0.907266i			0.0685828i
$176$	−1.80080	−	20.8363i	−0.135740	−	1.57060i
$177$		0			0
$178$	−7.63390	+	15.0537i	−0.572185	+	1.12832i
$179$	−4.58465	+	11.0683i	−0.342673	+	0.827285i	0.654771	+	0.755828i	$0.272765\pi$
$179$	−4.58465	+	11.0683i	−0.342673	+	0.827285i	−0.997444	+	0.0714579i	$0.977235\pi$
$180$		0			0
$181$	4.59848	−	1.90475i	0.341802	−	0.141579i	−0.205178	−	0.978725i	$-0.565777\pi$
$181$	4.59848	−	1.90475i	0.341802	−	0.141579i	0.546980	+	0.837146i	$0.315777\pi$
$182$	0.108696	+	0.126774i	0.00805709	+	0.00939708i
$183$		0			0
$184$	−16.1010	+	2.64521i	−1.18698	+	0.195007i
$185$	−2.71644	+	2.71644i	−0.199717	+	0.199717i
$186$		0			0
$187$	−11.4134	−	27.5544i	−0.834631	−	2.01498i
$188$	5.84427	+	7.97940i	0.426237	+	0.581957i
$189$		0			0
$190$	−0.776075	+	0.253809i	−0.0563024	+	0.0184132i
$191$	16.3142			1.18045			0.590227	−	0.807238i	$-0.299038\pi$
$191$	16.3142			1.18045			0.590227	+	0.807238i	$0.299038\pi$
$192$		0			0
$193$	3.22234			0.231949			0.115975	−	0.993252i	$-0.463001\pi$
$193$	3.22234			0.231949			0.115975	+	0.993252i	$0.463001\pi$
$194$	12.3907	−	4.05226i	0.889598	−	0.290936i
$195$		0			0
$196$	8.22960	+	11.2362i	0.587829	+	0.802585i
$197$	−8.79059	−	21.2224i	−0.626303	−	1.51203i	−0.844183	−	0.536055i	$-0.819914\pi$
$197$	−8.79059	−	21.2224i	−0.626303	−	1.51203i	0.217880	−	0.975976i	$-0.430086\pi$
$198$		0			0
$199$	−7.10324	+	7.10324i	−0.503535	+	0.503535i	−0.912535	−	0.409000i	$-0.865878\pi$
$199$	−7.10324	+	7.10324i	−0.503535	+	0.503535i	0.409000	+	0.912535i	$0.365878\pi$
$200$	2.18658	+	13.3094i	0.154614	+	0.941116i
$201$		0			0
$202$	3.07459	+	3.58593i	0.216327	+	0.252305i
$203$	−0.444066	+	0.183938i	−0.0311673	+	0.0129099i
$204$		0			0
$205$	0.228324	−	0.551224i	0.0159469	−	0.0384992i
$206$	6.49359	−	12.8051i	0.452430	−	0.892170i
$207$		0			0
$208$	1.90008	+	1.59777i	0.131747	+	0.110786i
$209$			6.27633i			0.434143i
$210$		0			0
$211$	−4.72147	+	11.3986i	−0.325040	+	0.784715i	0.673906	+	0.738817i	$0.264615\pi$
$211$	−4.72147	+	11.3986i	−0.325040	+	0.784715i	−0.998946	+	0.0458984i	$0.985385\pi$
$212$	−10.9515	+	18.0261i	−0.752155	+	1.23804i
$213$		0			0
$214$	1.76952	−	1.51719i	0.120962	−	0.103713i
$215$	0.793693	+	0.793693i	0.0541294	+	0.0541294i
$216$		0			0
$217$	−1.37266	+	1.37266i	−0.0931820	+	0.0931820i
$218$	1.59715	−	20.8038i	0.108173	−	1.40901i
$219$		0			0
$220$	−4.97064	−	0.767739i	−0.335121	−	0.0517609i
$221$	3.27082	+	1.35482i	0.220019	+	0.0911349i
$222$		0			0
$223$	−13.9899			−0.936832			−0.468416	−	0.883508i	$-0.655175\pi$
$223$	−13.9899			−0.936832			−0.468416	+	0.883508i	$0.655175\pi$
$224$	−0.768287	−	0.753691i	−0.0513333	−	0.0503581i
$225$		0			0
$226$	−1.97092	−	6.02651i	−0.131104	−	0.400878i
$227$	−2.11043	−	0.874170i	−0.140074	−	0.0580207i	0.311545	−	0.950231i	$-0.399154\pi$
$227$	−2.11043	−	0.874170i	−0.140074	−	0.0580207i	−0.451619	+	0.892211i	$0.649154\pi$
$228$		0			0
$229$	−3.24245	−	7.82798i	−0.214267	−	0.517287i	0.779803	−	0.626025i	$-0.215319\pi$
$229$	−3.24245	−	7.82798i	−0.214267	−	0.517287i	−0.994070	+	0.108738i	$0.965319\pi$
$230$	−0.300372	+	3.91251i	−0.0198059	+	0.257983i
$231$		0			0
$232$	−6.07105	+	3.76856i	−0.398584	+	0.247418i
$233$	−7.83849	−	7.83849i	−0.513516	−	0.513516i	0.402086	−	0.915602i	$-0.368285\pi$
$233$	−7.83849	−	7.83849i	−0.513516	−	0.513516i	−0.915602	+	0.402086i	$0.868285\pi$
$234$		0			0
$235$	2.19755	−	0.910254i	0.143352	−	0.0593784i
$236$	−21.1474	−	12.8478i	−1.37658	−	0.836324i
$237$		0			0
$238$	−1.36885	−	0.694160i	−0.0887294	−	0.0449957i
$239$		−	8.50653i		−	0.550242i	−0.961410	−	0.275121i	$-0.911282\pi$
$239$		−	8.50653i		−	0.550242i	0.961410	−	0.275121i	$-0.0887179\pi$
$240$		0			0
$241$			10.3310i			0.665475i	0.943019	+	0.332738i	$0.107972\pi$
$241$			10.3310i			0.665475i	−0.943019	+	0.332738i	$0.892028\pi$
$242$	−10.4496	+	20.6061i	−0.671726	+	1.32461i
$243$		0			0
$244$	−19.9124	+	4.86141i	−1.27476	+	0.311220i
$245$	3.09448	−	1.28177i	0.197699	−	0.0818895i
$246$		0			0
$247$	−0.526813	−	0.526813i	−0.0335203	−	0.0335203i
$248$	−16.8284	+	23.4448i	−1.06860	+	1.48875i
$249$		0			0
$250$	6.62520	+	0.508631i	0.419015	+	0.0321686i
$251$	0.371186	+	0.896122i	0.0234291	+	0.0565627i	0.935161	−	0.354223i	$-0.115255\pi$
$251$	0.371186	+	0.896122i	0.0234291	+	0.0565627i	−0.911732	+	0.410785i	$0.865255\pi$
$252$		0			0
$253$	27.8666	+	11.5427i	1.75196	+	0.725684i
$254$	−14.1855	+	4.63926i	−0.890079	+	0.291093i
$255$		0			0
$256$	−13.0870	−	9.20485i	−0.817940	−	0.575303i
$257$	11.9183			0.743442			0.371721	−	0.928345i	$-0.378768\pi$
$257$	11.9183			0.743442			0.371721	+	0.928345i	$0.378768\pi$
$258$		0			0
$259$	1.40392	+	0.581524i	0.0872355	+	0.0361341i
$260$	0.481660	−	0.352777i	0.0298713	−	0.0218783i
$261$		0			0
$262$	9.51212	+	0.730265i	0.587661	+	0.0451159i
$263$	−0.627327	+	0.627327i	−0.0386827	+	0.0386827i	−0.726184	−	0.687501i	$-0.758708\pi$
$263$	−0.627327	+	0.627327i	−0.0386827	+	0.0386827i	0.687501	+	0.726184i	$0.258708\pi$
$264$		0			0
$265$	3.58675	+	3.58675i	0.220332	+	0.220332i
$266$	0.210233	+	0.245197i	0.0128902	+	0.0150340i
$267$		0			0
$268$	10.0822	−	2.46146i	0.615868	−	0.150358i
$269$	1.22418	−	2.95542i	0.0746393	−	0.180195i	−0.882156	−	0.470957i	$-0.843909\pi$
$269$	1.22418	−	2.95542i	0.0746393	−	0.180195i	0.956795	+	0.290762i	$0.0939087\pi$
$270$		0			0
$271$		−	26.7281i		−	1.62362i	−0.583925	−	0.811808i	$-0.698484\pi$
$271$		−	26.7281i		−	1.62362i	0.583925	−	0.811808i	$-0.301516\pi$
$272$	−21.7537	−	6.88415i	−1.31901	−	0.417413i
$273$		0			0
$274$	−18.7196	−	9.49293i	−1.13089	−	0.573489i
$275$	9.54142	−	23.0350i	0.575369	−	1.38906i
$276$		0			0
$277$	−26.1483	+	10.8310i	−1.57110	+	0.650770i	−0.986972	−	0.160893i	$-0.948563\pi$
$277$	−26.1483	+	10.8310i	−1.57110	+	0.650770i	−0.584126	+	0.811663i	$0.698563\pi$
$278$	−10.6509	+	9.13208i	−0.638796	+	0.547706i
$279$		0			0
$280$	−0.219904	+	0.136504i	−0.0131418	+	0.00815767i
$281$	13.5386	−	13.5386i	0.807646	−	0.807646i	−0.176631	−	0.984277i	$-0.556520\pi$
$281$	13.5386	−	13.5386i	0.807646	−	0.807646i	0.984277	+	0.176631i	$0.0565201\pi$
$282$		0			0
$283$	−4.00203	−	9.66174i	−0.237896	−	0.574331i	0.759169	−	0.650893i	$-0.225606\pi$
$283$	−4.00203	−	9.66174i	−0.237896	−	0.574331i	−0.997065	+	0.0765624i	$0.975606\pi$
$284$	−1.86942	+	12.1033i	−0.110930	+	0.718202i
$285$		0			0
$286$	−1.42650	−	4.36184i	−0.0843508	−	0.257921i
$287$	−0.236007			−0.0139311
$288$		0			0
$289$	−15.5385			−0.914029
$290$	0.534161	+	1.63331i	0.0313670	+	0.0959114i
$291$		0			0
$292$	−17.1087	−	2.64251i	−1.00121	−	0.154641i
$293$	11.0520	+	26.6818i	0.645663	+	1.55877i	0.818930	+	0.573893i	$0.194567\pi$
$293$	11.0520	+	26.6818i	0.645663	+	1.55877i	−0.173268	+	0.984875i	$0.555433\pi$
$294$		0			0
$295$	−4.20781	+	4.20781i	−0.244988	+	0.244988i
$296$	21.9968	+	5.14727i	1.27854	+	0.299179i
$297$		0			0
$298$	11.3248	−	9.70990i	0.656027	−	0.562480i
$299$	−3.30788	+	1.37017i	−0.191300	+	0.0792389i
$300$		0			0
$301$	0.169911	−	0.410200i	0.00979348	−	0.0236436i
$302$	16.0314	+	8.12970i	0.922501	+	0.467811i
$303$		0			0
$304$	3.67501	+	3.09031i	0.210776	+	0.177241i
$305$			4.92937i			0.282255i
$306$		0			0
$307$	−9.87747	+	23.8463i	−0.563737	+	1.36098i	0.343020	+	0.939328i	$0.388550\pi$
$307$	−9.87747	+	23.8463i	−0.563737	+	1.36098i	−0.906757	+	0.421653i	$0.861450\pi$
$308$	0.471858	+	1.93274i	0.0268866	+	0.110128i
$309$		0			0
$310$	4.51749	+	5.26880i	0.256576	+	0.299248i
$311$	−18.0382	−	18.0382i	−1.02285	−	1.02285i	−0.999733	−	0.0231182i	$-0.992641\pi$
$311$	−18.0382	−	18.0382i	−1.02285	−	1.02285i	−0.0231182	−	0.999733i	$-0.507359\pi$
$312$		0			0
$313$	13.4949	−	13.4949i	0.762778	−	0.762778i	−0.214046	−	0.976824i	$-0.568664\pi$
$313$	13.4949	−	13.4949i	0.762778	−	0.762778i	0.976824	+	0.214046i	$0.0686643\pi$
$314$	−31.8162	−	2.44260i	−1.79549	−	0.137844i
$315$		0			0
$316$	14.1544	+	19.3256i	0.796250	+	1.08715i
$317$	9.96898	+	4.12929i	0.559914	+	0.231924i	0.644648	−	0.764480i	$-0.277004\pi$
$317$	9.96898	+	4.12929i	0.559914	+	0.231924i	−0.0847339	+	0.996404i	$0.527004\pi$
$318$		0			0
$319$	13.2090			0.739564
$320$	−2.89696	+	2.53247i	−0.161945	+	0.141569i
$321$		0			0
$322$	1.47530	−	0.482483i	0.0822151	−	0.0268877i
$323$	6.32620	+	2.62040i	0.351999	+	0.145803i
$324$		0			0
$325$	1.13261	+	2.73435i	0.0628257	+	0.151675i
$326$	10.7532	+	0.825546i	0.595565	+	0.0457228i
$327$		0			0
$328$	−3.46218	+	0.568795i	−0.191167	+	0.0314064i
$329$	−0.665305	−	0.665305i	−0.0366795	−	0.0366795i
$330$		0			0
$331$	11.3038	−	4.68220i	0.621314	−	0.257357i	−0.0497433	−	0.998762i	$-0.515840\pi$
$331$	11.3038	−	4.68220i	0.621314	−	0.257357i	0.671058	+	0.741405i	$0.265840\pi$
$332$	1.98311	+	8.12284i	0.108837	+	0.445799i
$333$		0			0
$334$	−0.752734	+	1.48435i	−0.0411878	+	0.0812203i
$335$		−	2.49587i		−	0.136364i
$336$		0			0
$337$		−	1.45068i		−	0.0790237i	−0.999219	−	0.0395118i	$-0.987420\pi$
$337$		−	1.45068i		−	0.0790237i	0.999219	−	0.0395118i	$-0.0125803\pi$
$338$	−15.9111	−	8.06870i	−0.865449	−	0.438879i
$339$		0			0
$340$	−2.84911	+	4.68960i	−0.154514	+	0.254329i
$341$	49.2869	−	20.4153i	2.66903	−	1.10555i
$342$		0			0
$343$	−1.87857	−	1.87857i	−0.101433	−	0.101433i
$344$	1.50394	−	6.42704i	0.0810869	−	0.346523i
$345$		0			0
$346$	1.32321	−	17.2355i	0.0711360	−	0.926586i
$347$	4.88124	+	11.7844i	0.262039	+	0.632618i	0.999064	−	0.0432472i	$-0.0137703\pi$
$347$	4.88124	+	11.7844i	0.262039	+	0.632618i	−0.737026	+	0.675865i	$0.763770\pi$
$348$		0			0
$349$	−7.72369	−	3.19926i	−0.413440	−	0.171252i	0.166261	−	0.986082i	$-0.446831\pi$
$349$	−7.72369	−	3.19926i	−0.413440	−	0.171252i	−0.579701	+	0.814829i	$0.696831\pi$
$350$	−0.398829	−	1.21951i	−0.0213183	−	0.0651854i
$351$		0			0
$352$	11.5801	+	27.2156i	0.617221	+	1.45060i
$353$	−17.4309			−0.927751			−0.463875	−	0.885900i	$-0.653541\pi$
$353$	−17.4309			−0.927751			−0.463875	+	0.885900i	$0.653541\pi$
$354$		0			0
$355$	2.72104	+	1.12709i	0.144418	+	0.0598199i
$356$	3.64364	−	23.5903i	0.193112	−	1.25029i
$357$		0			0
$358$	1.29691	−	16.8929i	0.0685437	−	0.892820i
$359$	−4.53639	+	4.53639i	−0.239422	+	0.239422i	−0.816611	−	0.577189i	$-0.804150\pi$
$359$	−4.53639	+	4.53639i	−0.239422	+	0.239422i	0.577189	+	0.816611i	$0.304150\pi$
$360$		0			0
$361$	12.4161	+	12.4161i	0.653479	+	0.653479i
$362$	−5.34375	+	4.58175i	−0.280861	+	0.240811i
$363$		0			0
$364$	−0.201833	−	0.122621i	−0.0105789	−	0.00642710i
$365$	−1.59320	+	3.84632i	−0.0833919	+	0.201326i
$366$		0			0
$367$			7.18068i			0.374828i	0.982281	+	0.187414i	$0.0600106\pi$
$367$			7.18068i			0.374828i	−0.982281	+	0.187414i	$0.939989\pi$
$368$	20.4795	−	10.6335i	1.06757	−	0.554309i
$369$		0			0
$370$	2.45719	−	4.84545i	0.127743	−	0.251903i
$371$	0.767836	−	1.85372i	0.0398640	−	0.0962403i
$372$		0			0
$373$	14.3497	−	5.94383i	0.742998	−	0.307760i	0.0211168	−	0.999777i	$-0.493278\pi$
$373$	14.3497	−	5.94383i	0.742998	−	0.307760i	0.721881	+	0.692017i	$0.243278\pi$
$374$	27.4542	+	32.0201i	1.41962	+	1.65572i
$375$		0			0
$376$	−11.3633	−	8.15645i	−0.586018	−	0.420637i
$377$	−1.10872	+	1.10872i	−0.0571020	+	0.0571020i
$378$		0			0
$379$	3.45126	+	8.33209i	0.177280	+	0.427991i	0.987394	−	0.158281i	$-0.0505951\pi$
$379$	3.45126	+	8.33209i	0.177280	+	0.427991i	−0.810115	+	0.586272i	$0.800595\pi$
$380$	0.931594	−	0.682318i	0.0477897	−	0.0350022i
$381$		0			0
$382$	−21.9288	+	7.17164i	−1.12198	+	0.366933i
$383$	4.45958			0.227874			0.113937	−	0.993488i	$-0.463654\pi$
$383$	4.45958			0.227874			0.113937	+	0.993488i	$0.463654\pi$
$384$		0			0
$385$	0.478454			0.0243843
$386$	−4.33133	+	1.41652i	−0.220459	+	0.0720992i
$387$		0			0
$388$	−14.8736	+	10.8937i	−0.755095	+	0.553046i
$389$	−2.19268	−	5.29359i	−0.111173	−	0.268396i	0.858495	−	0.512823i	$-0.171400\pi$
$389$	−2.19268	−	5.29359i	−0.111173	−	0.268396i	−0.969668	+	0.244427i	$0.921400\pi$
$390$		0			0
$391$	23.2689	−	23.2689i	1.17676	−	1.17676i
$392$	−16.0012	−	11.4855i	−0.808185	−	0.580105i
$393$		0			0
$394$	21.1452	+	24.6619i	1.06528	+	1.24245i
$395$	5.32232	−	2.20458i	0.267795	−	0.110924i
$396$		0			0
$397$	5.25839	−	12.6949i	0.263911	−	0.637137i	−0.735263	−	0.677782i	$-0.762941\pi$
$397$	5.25839	−	12.6949i	0.263911	−	0.637137i	0.999174	+	0.0406449i	$0.0129412\pi$
$398$	6.42531	−	12.6704i	0.322072	−	0.635110i
$399$		0			0
$400$	−8.78984	−	16.9287i	−0.439492	−	0.846435i
$401$			22.6945i			1.13331i	0.823955	+	0.566655i	$0.191763\pi$
$401$			22.6945i			1.13331i	−0.823955	+	0.566655i	$0.808237\pi$
$402$		0			0
$403$	−2.42338	+	5.85055i	−0.120717	+	0.291437i
$404$	−5.70908	−	3.46848i	−0.284037	−	0.172563i
$405$		0			0
$406$	0.516036	−	0.442451i	0.0256104	−	0.0219585i
$407$	−29.5292	−	29.5292i	−1.46371	−	1.46371i
$408$		0			0
$409$	−18.9178	+	18.9178i	−0.935424	+	0.935424i	−0.998038	−	0.0626139i	$-0.980056\pi$
$409$	−18.9178	+	18.9178i	−0.935424	+	0.935424i	0.0626139	+	0.998038i	$0.480056\pi$
$410$	−0.0645885	+	0.841302i	−0.00318980	+	0.0415489i
$411$		0			0
$412$	−3.09937	+	20.0665i	−0.152695	+	0.988608i
$413$	2.17470	+	0.900790i	0.107010	+	0.0443250i
$414$		0			0
$415$	2.01083			0.0987077
$416$	−3.25638	−	1.31239i	−0.159657	−	0.0643454i
$417$		0			0
$418$	−2.75904	−	8.43637i	−0.134949	−	0.412636i
$419$	20.8524	+	8.63734i	1.01871	+	0.421962i	0.828623	−	0.559807i	$-0.189125\pi$
$419$	20.8524	+	8.63734i	1.01871	+	0.421962i	0.190082	+	0.981768i	$0.439125\pi$
$420$		0			0
$421$	−14.3106	−	34.5489i	−0.697456	−	1.68381i	−0.729189	−	0.684312i	$-0.760103\pi$
$421$	−14.3106	−	34.5489i	−0.697456	−	1.68381i	0.0317327	−	0.999496i	$-0.489897\pi$
$422$	1.33561	−	17.3971i	0.0650166	−	0.846877i
$423$		0			0
$424$	6.79639	−	29.0442i	0.330062	−	1.41051i
$425$	−19.2345	−	19.2345i	−0.933008	−	0.933008i
$426$		0			0
$427$	1.80144	−	0.746181i	0.0871777	−	0.0361102i
$428$	−1.71156	+	2.81721i	−0.0827314	+	0.136175i
$429$		0			0
$430$	−1.41575	−	0.717944i	−0.0682736	−	0.0346224i
$431$			38.4560i			1.85236i	0.377080	+	0.926181i	$0.376928\pi$
$431$			38.4560i			1.85236i	−0.377080	+	0.926181i	$0.623072\pi$
$432$		0			0
$433$		−	8.55433i		−	0.411095i	−0.978647	−	0.205547i	$-0.934102\pi$
$433$		−	8.55433i		−	0.411095i	0.978647	−	0.205547i	$-0.0658975\pi$
$434$	1.24165	−	2.44848i	0.0596012	−	0.117531i
$435$		0			0
$436$	6.99841	+	28.6656i	0.335163	+	1.37283i
$437$	−6.39787	+	2.65009i	−0.306052	+	0.126771i
$438$		0			0
$439$	5.13653	+	5.13653i	0.245153	+	0.245153i	0.818978	−	0.573825i	$-0.194541\pi$
$439$	5.13653	+	5.13653i	0.245153	+	0.245153i	−0.573825	+	0.818978i	$0.694541\pi$
$440$	7.01881	−	1.15311i	0.334609	−	0.0549723i
$441$		0			0
$442$	−4.99207	−	0.383252i	−0.237448	−	0.0182294i
$443$	−2.45339	−	5.92301i	−0.116564	−	0.281411i	0.854820	−	0.518925i	$-0.173667\pi$
$443$	−2.45339	−	5.92301i	−0.116564	−	0.281411i	−0.971384	+	0.237514i	$0.923667\pi$
$444$		0			0
$445$	−5.30352	−	2.19679i	−0.251411	−	0.104138i
$446$	18.8046	−	6.14988i	0.890423	−	0.291205i
$447$		0			0
$448$	1.36402	+	0.675343i	0.0644437	+	0.0319070i
$449$	−23.7582			−1.12122			−0.560610	−	0.828080i	$-0.689433\pi$
$449$	−23.7582			−1.12122			−0.560610	+	0.828080i	$0.689433\pi$
$450$		0			0
$451$	5.99211	+	2.48201i	0.282157	+	0.116873i
$452$	5.29845	+	7.23417i	0.249218	+	0.340267i
$453$		0			0
$454$	3.22103	+	0.247286i	0.151171	+	0.0116057i
$455$	−0.0401598	+	0.0401598i	−0.00188272	+	0.00188272i
$456$		0			0
$457$	−1.16506	−	1.16506i	−0.0544992	−	0.0544992i	0.679332	−	0.733831i	$-0.262270\pi$
$457$	−1.16506	−	1.16506i	−0.0544992	−	0.0544992i	−0.733831	+	0.679332i	$0.762270\pi$
$458$	7.79950	+	9.09666i	0.364447	+	0.425059i
$459$		0			0
$460$	−1.31617	−	5.39107i	−0.0613669	−	0.251360i
$461$	−1.61683	+	3.90337i	−0.0753032	+	0.181798i	−0.957049	−	0.289928i	$-0.906369\pi$
$461$	−1.61683	+	3.90337i	−0.0753032	+	0.181798i	0.881745	+	0.471726i	$0.156369\pi$
$462$		0			0
$463$		−	3.11687i		−	0.144853i	−0.997374	−	0.0724267i	$-0.976926\pi$
$463$		−	3.11687i		−	0.144853i	0.997374	−	0.0724267i	$-0.0230743\pi$
$464$	6.50380	−	7.73434i	0.301931	−	0.359058i
$465$		0			0
$466$	13.9819	+	7.09039i	0.647699	+	0.328456i
$467$	−7.59921	+	18.3461i	−0.351649	+	0.848957i	0.644767	+	0.764379i	$0.276954\pi$
$467$	−7.59921	+	18.3461i	−0.351649	+	0.848957i	−0.996417	+	0.0845781i	$0.973046\pi$
$468$		0			0
$469$	−0.912117	+	0.377811i	−0.0421176	+	0.0174457i
$470$	−2.55370	+	2.18955i	−0.117794	+	0.100997i
$471$		0			0
$472$	34.0733	+	7.97321i	1.56835	+	0.366997i
$473$	−8.62788	+	8.62788i	−0.396711	+	0.396711i
$474$		0			0
$475$	2.19061	+	5.28860i	0.100512	+	0.242658i
$476$	2.14510	+	0.331320i	0.0983204	+	0.0151860i
$477$		0			0
$478$	3.73943	+	11.4341i	0.171037	+	0.522984i
$479$	−14.5634			−0.665418			−0.332709	−	0.943030i	$-0.607963\pi$
$479$	−14.5634			−0.665418			−0.332709	+	0.943030i	$0.607963\pi$
$480$		0			0
$481$	4.95716			0.226027
$482$	−4.54144	−	13.8864i	−0.206857	−	0.632509i
$483$		0			0
$484$	4.98756	−	32.2914i	0.226707	−	1.46779i
$485$	1.69672	+	4.09624i	0.0770440	+	0.186001i
$486$		0			0
$487$	12.0901	−	12.0901i	0.547856	−	0.547856i	−0.377964	−	0.925820i	$-0.623376\pi$
$487$	12.0901	−	12.0901i	0.547856	−	0.547856i	0.925820	+	0.377964i	$0.123376\pi$
$488$	24.6284	−	15.2879i	1.11487	−	0.692051i
$489$		0			0
$490$	−3.59600	+	3.08322i	−0.162451	+	0.139286i
$491$	−20.2368	+	8.38236i	−0.913274	+	0.378290i	−0.789309	−	0.613996i	$-0.789561\pi$
$491$	−20.2368	+	8.38236i	−0.913274	+	0.378290i	−0.123965	+	0.992287i	$0.539561\pi$
$492$		0			0
$493$	5.51483	−	13.3140i	0.248376	−	0.599632i
$494$	0.939704	+	0.476535i	0.0422793	+	0.0214403i
$495$		0			0
$496$	12.3138	−	38.9111i	0.552904	−	1.74716i
$497$		−	1.16502i		−	0.0522583i
$498$		0			0
$499$	−3.26197	+	7.87508i	−0.146026	+	0.352537i	−0.979921	−	0.199385i	$-0.936106\pi$
$499$	−3.26197	+	7.87508i	−0.146026	+	0.352537i	0.833896	+	0.551922i	$0.186106\pi$
$500$	−9.12890	+	2.22873i	−0.408257	+	0.0996716i
$501$		0			0
$502$	−0.892863	−	1.04136i	−0.0398504	−	0.0464780i
$503$	12.2760	+	12.2760i	0.547362	+	0.547362i	0.925677	−	0.378315i	$-0.123496\pi$
$503$	12.2760	+	12.2760i	0.547362	+	0.547362i	−0.378315	+	0.925677i	$0.623496\pi$
$504$		0			0
$505$	−1.13596	+	1.13596i	−0.0505497	+	0.0505497i
$506$	−42.5311	−	3.26521i	−1.89074	−	0.145156i
$507$		0			0
$508$	17.0282	−	12.4718i	0.755503	−	0.553345i
$509$	0.842977	+	0.349172i	0.0373643	+	0.0154768i	0.401287	−	0.915952i	$-0.368563\pi$
$509$	0.842977	+	0.349172i	0.0373643	+	0.0154768i	−0.363923	+	0.931429i	$0.618563\pi$
$510$		0			0
$511$	1.64681			0.0728506
$512$	21.6374	+	6.61976i	0.956249	+	0.292555i
$513$		0			0
$514$	−16.0200	+	5.23922i	−0.706613	+	0.231092i
$515$	4.51131	+	1.86865i	0.198792	+	0.0823424i
$516$		0			0
$517$	9.89496	+	23.8886i	0.435180	+	1.05062i
$518$	−2.14273	−	0.164502i	−0.0941460	−	0.00722779i
$519$		0			0
$520$	−0.492347	+	0.685923i	−0.0215908	+	0.0300797i
$521$	−4.87761	−	4.87761i	−0.213692	−	0.213692i	0.592142	−	0.805834i	$-0.298283\pi$
$521$	−4.87761	−	4.87761i	−0.213692	−	0.213692i	−0.805834	+	0.592142i	$0.798283\pi$
$522$		0			0
$523$	−20.5648	+	8.51821i	−0.899235	+	0.372475i	−0.783926	−	0.620854i	$-0.786786\pi$
$523$	−20.5648	+	8.51821i	−0.899235	+	0.372475i	−0.115309	+	0.993330i	$0.536786\pi$
$524$	−13.1068	+	3.19989i	−0.572573	+	0.139788i
$525$		0			0
$526$	0.567456	−	1.11900i	0.0247423	−	0.0487905i
$527$		−	58.2020i		−	2.53532i
$528$		0			0
$529$			10.2800i			0.446955i
$530$	−6.39787	−	3.24443i	−0.277906	−	0.140929i
$531$		0			0
$532$	−0.390373	−	0.237166i	−0.0169248	−	0.0102824i
$533$	−0.711288	+	0.294625i	−0.0308093	+	0.0127616i
$534$		0			0
$535$	0.560554	+	0.560554i	0.0242349	+	0.0242349i
$536$	−12.4700	+	7.74067i	−0.538622	+	0.334346i
$537$		0			0
$538$	−0.346295	+	4.51069i	−0.0149298	+	0.194470i
$539$	13.9336	+	33.6387i	0.600162	+	1.44892i
$540$		0			0
$541$	−8.72081	−	3.61228i	−0.374937	−	0.155304i	0.187254	−	0.982312i	$-0.440041\pi$
$541$	−8.72081	−	3.61228i	−0.374937	−	0.155304i	−0.562191	+	0.827008i	$0.690041\pi$
$542$	11.7495	+	35.9267i	0.504686	+	1.54319i
$543$		0			0
$544$	32.2666	−	0.309444i	1.38342	−	0.0132673i
$545$	7.09624			0.303969
$546$		0			0
$547$	3.50970	+	1.45377i	0.150064	+	0.0621586i	0.456451	−	0.889748i	$-0.349120\pi$
$547$	3.50970	+	1.45377i	0.150064	+	0.0621586i	−0.306387	+	0.951907i	$0.599120\pi$
$548$	29.3351	+	4.53094i	1.25313	+	0.193552i
$549$		0			0
$550$	−2.69908	+	35.1570i	−0.115089	+	1.49910i
$551$	−2.14441	+	2.14441i	−0.0913550	+	0.0913550i
$552$		0			0
$553$	−1.61133	−	1.61133i	−0.0685206	−	0.0685206i
$554$	30.3861	−	26.0532i	1.29098	−	1.10689i
$555$		0			0
$556$	10.3020	−	16.9570i	0.436902	−	0.719138i
$557$	11.0388	−	26.6499i	0.467727	−	1.12919i	−0.497425	−	0.867507i	$-0.665721\pi$
$557$	11.0388	−	26.6499i	0.467727	−	1.12919i	0.965153	−	0.261687i	$-0.0842788\pi$
$558$		0			0
$559$		−	1.44839i		−	0.0612603i
$560$	0.235579	−	0.280151i	0.00995502	−	0.0118386i
$561$		0			0
$562$	−12.2465	+	24.1495i	−0.516588	+	1.01869i
$563$	0.499373	−	1.20559i	0.0210461	−	0.0508097i	−0.913007	−	0.407944i	$-0.866246\pi$
$563$	0.499373	−	1.20559i	0.0210461	−	0.0508097i	0.934053	+	0.357134i	$0.116246\pi$
$564$		0			0
$565$	1.99231	−	0.825242i	0.0838171	−	0.0347182i
$566$	9.62660	+	11.2276i	0.404636	+	0.471932i
$567$		0			0
$568$	−2.80778	−	17.0906i	−0.117812	−	0.717105i
$569$	−24.7043	+	24.7043i	−1.03566	+	1.03566i	−0.0363184	+	0.999340i	$0.511563\pi$
$569$	−24.7043	+	24.7043i	−1.03566	+	1.03566i	−0.999340	+	0.0363184i	$0.988437\pi$
$570$		0			0
$571$	12.4201	+	29.9848i	0.519765	+	1.25482i	0.938047	+	0.346507i	$0.112632\pi$
$571$	12.4201	+	29.9848i	0.519765	+	1.25482i	−0.418282	+	0.908317i	$0.637368\pi$
$572$	3.83488	+	5.23591i	0.160344	+	0.218924i
$573$		0			0
$574$	0.317231	−	0.103748i	0.0132410	−	0.00433034i
$575$	27.5098			1.14724
$576$		0			0
$577$	−38.7977			−1.61517			−0.807585	−	0.589752i	$-0.799226\pi$
$577$	−38.7977			−1.61517			−0.807585	+	0.589752i	$0.799226\pi$
$578$	20.8862	−	6.83064i	0.868750	−	0.284117i
$579$		0			0
$580$	−1.43599	−	1.96061i	−0.0596263	−	0.0814100i
$581$	−0.304388	−	0.734858i	−0.0126281	−	0.0304870i
$582$		0			0
$583$	−38.9899	+	38.9899i	−1.61480	+	1.61480i
$584$	24.1583	−	3.96893i	0.999679	−	0.164236i
$585$		0			0
$586$	−26.5848	−	31.0061i	−1.09821	−	1.28085i
$587$	32.3256	−	13.3897i	1.33422	−	0.552652i	0.402363	−	0.915480i	$-0.368189\pi$
$587$	32.3256	−	13.3897i	1.33422	−	0.552652i	0.931856	+	0.362828i	$0.118189\pi$
$588$		0			0
$589$	−4.68714	+	11.3157i	−0.193130	+	0.466257i
$590$	3.80622	−	7.50568i	0.156700	−	0.309004i
$591$		0			0
$592$	−31.8298	+	2.75092i	−1.30820	+	0.113062i
$593$		−	25.8554i		−	1.06176i	−0.847448	−	0.530878i	$-0.821862\pi$
$593$		−	25.8554i		−	1.06176i	0.847448	−	0.530878i	$-0.178138\pi$
$594$		0			0
$595$	0.199757	−	0.482256i	0.00818923	−	0.0197706i
$596$	−10.9539	+	18.0299i	−0.448687	+	0.738535i
$597$		0			0
$598$	3.84399	−	3.29585i	0.157192	−	0.134777i
$599$	27.4466	+	27.4466i	1.12144	+	1.12144i	0.991525	+	0.129914i	$0.0414701\pi$
$599$	27.4466	+	27.4466i	1.12144	+	1.12144i	0.129914	+	0.991525i	$0.458530\pi$
$600$		0			0
$601$	−17.2120	+	17.2120i	−0.702091	+	0.702091i	−0.964859	−	0.262768i	$-0.915365\pi$
$601$	−17.2120	+	17.2120i	−0.702091	+	0.702091i	0.262768	+	0.964859i	$0.415365\pi$
$602$	−0.0480644	+	0.626065i	−0.00195896	+	0.0255165i
$603$		0			0
$604$	−25.1224	−	3.88028i	−1.02222	−	0.157886i
$605$	−7.25968	−	3.00706i	−0.295148	−	0.122254i
$606$		0			0
$607$	−35.6136			−1.44551			−0.722756	−	0.691103i	$-0.757125\pi$
$607$	−35.6136			−1.44551			−0.722756	+	0.691103i	$0.757125\pi$
$608$	−6.29827	−	2.53834i	−0.255428	−	0.102943i
$609$		0			0
$610$	−2.16693	−	6.62584i	−0.0877362	−	0.268273i
$611$	−2.83567	−	1.17457i	−0.114719	−	0.0475181i
$612$		0			0
$613$	7.20887	+	17.4038i	0.291164	+	0.702931i	0.999997	−	0.00244484i	$-0.000778219\pi$
$613$	7.20887	+	17.4038i	0.291164	+	0.702931i	−0.708833	+	0.705376i	$0.750778\pi$
$614$	2.79414	−	36.3953i	0.112762	−	1.46879i
$615$		0			0
$616$	−1.48387	−	2.39048i	−0.0597869	−	0.0963150i
$617$	−12.8299	−	12.8299i	−0.516511	−	0.516511i	0.400003	−	0.916514i	$-0.369009\pi$
$617$	−12.8299	−	12.8299i	−0.516511	−	0.516511i	−0.916514	+	0.400003i	$0.869009\pi$
$618$		0			0
$619$	12.1156	−	5.01844i	0.486966	−	0.201708i	−0.125671	−	0.992072i	$-0.540108\pi$
$619$	12.1156	−	5.01844i	0.486966	−	0.201708i	0.612638	+	0.790364i	$0.290108\pi$
$620$	−8.38835	−	5.09623i	−0.336884	−	0.204669i
$621$		0			0
$622$	32.1756	+	16.3166i	1.29012	+	0.654237i
$623$			2.27071i			0.0909741i
$624$		0			0
$625$		−	21.5834i		−	0.863337i
$626$	−12.2070	+	24.0716i	−0.487889	+	0.962093i
$627$		0			0
$628$	43.8397	−	10.7030i	1.74939	−	0.427096i
$629$	−42.0924	+	17.4352i	−1.67833	+	0.695189i
$630$		0			0
$631$	−9.99914	−	9.99914i	−0.398059	−	0.398059i	0.479489	−	0.877548i	$-0.340822\pi$
$631$	−9.99914	−	9.99914i	−0.398059	−	0.398059i	−0.877548	+	0.479489i	$0.840822\pi$
$632$	−27.5212	−	19.7544i	−1.09474	−	0.785788i
$633$		0			0
$634$	−15.2151	−	1.16809i	−0.604268	−	0.0463910i
$635$	−1.94250	−	4.68960i	−0.0770857	−	0.186101i
$636$		0			0
$637$	−3.99305	−	1.65397i	−0.158210	−	0.0655329i
$638$	−17.7550	+	5.80662i	−0.702927	+	0.229886i
$639$		0			0
$640$	2.78070	−	4.67752i	0.109917	−	0.184895i
$641$	−28.5513			−1.12771			−0.563854	−	0.825875i	$-0.690682\pi$
$641$	−28.5513			−1.12771			−0.563854	+	0.825875i	$0.690682\pi$
$642$		0			0
$643$	−5.76614	−	2.38841i	−0.227394	−	0.0941898i	0.266077	−	0.963952i	$-0.414272\pi$
$643$	−5.76614	−	2.38841i	−0.227394	−	0.0941898i	−0.493472	+	0.869762i	$0.664272\pi$
$644$	−1.77093	+	1.29707i	−0.0697845	+	0.0511115i
$645$		0			0
$646$	−9.65532	−	0.741259i	−0.379883	−	0.0291645i
$647$	0.783090	−	0.783090i	0.0307864	−	0.0307864i	−0.691546	−	0.722332i	$-0.743070\pi$
$647$	0.783090	−	0.783090i	0.0307864	−	0.0307864i	0.722332	+	0.691546i	$0.243070\pi$
$648$		0			0
$649$	−45.7412	−	45.7412i	−1.79550	−	1.79550i
$650$	−2.72441	−	3.17751i	−0.106860	−	0.124632i
$651$		0			0
$652$	−14.8169	+	3.61739i	−0.580274	+	0.141668i
$653$	3.54194	−	8.55101i	0.138607	−	0.334627i	−0.839300	−	0.543669i	$-0.817035\pi$
$653$	3.54194	−	8.55101i	0.138607	−	0.334627i	0.977907	+	0.209042i	$0.0670346\pi$
$654$		0			0
$655$			3.24462i			0.126778i
$656$	4.40367	−	2.28650i	0.171934	−	0.0892730i
$657$		0			0
$658$	1.18674	+	0.601809i	0.0462639	+	0.0234610i
$659$	−17.7016	+	42.7355i	−0.689557	+	1.66474i	0.0561160	+	0.998424i	$0.482128\pi$
$659$	−17.7016	+	42.7355i	−0.689557	+	1.66474i	−0.745673	+	0.666313i	$0.767872\pi$
$660$		0			0
$661$	−0.187232	+	0.0775542i	−0.00728249	+	0.00301651i	−0.386322	−	0.922364i	$-0.626255\pi$
$661$	−0.187232	+	0.0775542i	−0.00728249	+	0.00301651i	0.379039	+	0.925381i	$0.376255\pi$
$662$	−13.1358	+	11.2627i	−0.510539	+	0.437738i
$663$		0			0
$664$	−6.23636	−	10.0466i	−0.242018	−	0.389884i
$665$	−0.0776743	+	0.0776743i	−0.00301208	+	0.00301208i
$666$		0			0
$667$	5.57731	+	13.4648i	0.215954	+	0.521360i
$668$	0.359277	−	2.32610i	0.0139009	−	0.0899996i
$669$		0			0
$670$	1.09717	+	3.35484i	0.0423875	+	0.129609i
$671$	−53.5850			−2.06862
$672$		0			0
$673$	48.7073			1.87753			0.938765	−	0.344558i	$-0.111971\pi$
$673$	48.7073			1.87753			0.938765	+	0.344558i	$0.111971\pi$
$674$	0.637712	+	1.94994i	0.0245638	+	0.0751090i
$675$		0			0
$676$	24.9339	+	3.85116i	0.958998	+	0.148122i
$677$	−10.9016	−	26.3188i	−0.418982	−	1.01151i	−0.982643	−	0.185506i	$-0.940607\pi$
$677$	−10.9016	−	26.3188i	−0.418982	−	1.01151i	0.563661	−	0.826006i	$-0.309393\pi$
$678$		0			0
$679$	1.24013	−	1.24013i	0.0475919	−	0.0475919i
$680$	1.76812	−	7.55601i	0.0678042	−	0.289760i
$681$		0			0
$682$	−57.2748	+	49.1076i	−2.19316	+	1.88043i
$683$	−16.7740	+	6.94800i	−0.641838	+	0.265858i	−0.679773	−	0.733422i	$-0.737922\pi$
$683$	−16.7740	+	6.94800i	−0.641838	+	0.265858i	0.0379356	+	0.999280i	$0.487922\pi$
$684$		0			0
$685$	2.73176	−	6.59504i	0.104375	−	0.251984i
$686$	3.35090	+	1.69928i	0.127938	+	0.0648788i
$687$		0			0
$688$	0.803768	+	9.30008i	0.0306434	+	0.354562i
$689$		−	6.54536i		−	0.249358i
$690$		0			0
$691$	17.5044	−	42.2593i	0.665898	−	1.60762i	−0.122509	−	0.992467i	$-0.539094\pi$
$691$	17.5044	−	42.2593i	0.665898	−	1.60762i	0.788407	−	0.615154i	$-0.210906\pi$
$692$	5.79804	+	23.7489i	0.220408	+	0.902797i
$693$		0			0
$694$	−11.7415	−	13.6943i	−0.445701	−	0.519827i
$695$	−3.37402	−	3.37402i	−0.127984	−	0.127984i
$696$		0			0
$697$	5.00347	−	5.00347i	0.189520	−	0.189520i
$698$	11.7882	+	0.905007i	0.446191	+	0.0342550i
$699$		0			0
$700$	1.07218	+	1.46388i	0.0405245	+	0.0553296i
$701$	9.76630	+	4.04533i	0.368868	+	0.152790i	0.559414	−	0.828888i	$-0.311026\pi$
$701$	9.76630	+	4.04533i	0.368868	+	0.152790i	−0.190547	+	0.981678i	$0.561026\pi$
$702$		0			0
$703$	9.58780			0.361611
$704$	−27.5293	−	31.4915i	−1.03755	−	1.18688i
$705$		0			0
$706$	23.4298	−	7.66251i	0.881792	−	0.288383i
$707$	0.587094	+	0.243182i	0.0220799	+	0.00914581i
$708$		0			0
$709$	−2.23164	−	5.38765i	−0.0838109	−	0.202337i	0.876418	−	0.481551i	$-0.159926\pi$
$709$	−2.23164	−	5.38765i	−0.0838109	−	0.202337i	−0.960229	+	0.279213i	$0.909926\pi$
$710$	−4.15297	−	0.318833i	−0.155858	−	0.0119656i
$711$		0			0
$712$	5.47258	+	33.3108i	0.205093	+	1.24838i
$713$	41.6213	+	41.6213i	1.55873	+	1.55873i
$714$		0			0
$715$	1.44198	−	0.597289i	0.0539271	−	0.0223373i
$716$	5.68281	+	23.2769i	0.212376	+	0.869898i
$717$		0			0
$718$	4.10344	−	8.09179i	0.153139	−	0.301983i
$719$		−	12.8188i		−	0.478059i	−0.971012	−	0.239030i	$-0.923171\pi$
$719$		−	12.8188i		−	0.478059i	0.971012	−	0.239030i	$-0.0768293\pi$
$720$		0			0
$721$		−	1.93152i		−	0.0719337i
$722$	−22.1472	−	11.2311i	−0.824235	−	0.417979i
$723$		0			0
$724$	5.16872	−	8.50767i	0.192094	−	0.316185i
$725$	11.1303	−	4.61031i	0.413368	−	0.171223i
$726$		0			0
$727$	22.1336	+	22.1336i	0.820889	+	0.820889i	0.986235	−	0.165347i	$-0.0528743\pi$
$727$	22.1336	+	22.1336i	0.820889	+	0.820889i	−0.165347	+	0.986235i	$0.552874\pi$
$728$	0.325199	+	0.0760971i	0.0120527	+	0.00282035i
$729$		0			0
$730$	0.450685	−	5.87042i	0.0166806	−	0.217274i
$731$	5.09426	+	12.2986i	0.188418	+	0.454881i
$732$		0			0
$733$	−17.7464	−	7.35081i	−0.655479	−	0.271508i	0.0300555	−	0.999548i	$-0.490432\pi$
$733$	−17.7464	−	7.35081i	−0.655479	−	0.271508i	−0.685535	+	0.728040i	$0.740432\pi$
$734$	−3.15659	−	9.65195i	−0.116512	−	0.356260i
$735$		0			0
$736$	−22.8532	+	23.2957i	−0.842379	+	0.858692i
$737$	27.1315			0.999402
$738$		0			0
$739$	20.4272	+	8.46123i	0.751428	+	0.311251i	0.725324	−	0.688408i	$-0.241690\pi$
$739$	20.4272	+	8.46123i	0.751428	+	0.311251i	0.0261037	+	0.999659i	$0.491690\pi$
$740$	−1.17281	+	7.59321i	−0.0431132	+	0.279132i
$741$		0			0
$742$	−0.217206	+	2.82923i	−0.00797387	+	0.103864i
$743$	26.6427	−	26.6427i	0.977427	−	0.977427i	−0.0223237	−	0.999751i	$-0.507106\pi$
$743$	26.6427	−	26.6427i	0.977427	−	0.977427i	0.999751	+	0.0223237i	$0.00710644\pi$
$744$		0			0
$745$	3.58750	+	3.58750i	0.131436	+	0.131436i
$746$	−16.6753	+	14.2975i	−0.610527	+	0.523468i
$747$		0			0
$748$	−50.9786	−	30.9714i	−1.86396	−	1.13243i
$749$	0.120001	−	0.289708i	0.00438474	−	0.0105857i
$750$		0			0
$751$			23.4989i			0.857486i	0.903427	+	0.428743i	$0.141043\pi$
$751$			23.4989i			0.857486i	−0.903427	+	0.428743i	$0.858957\pi$
$752$	18.8596	+	5.96829i	0.687739	+	0.217641i
$753$		0			0
$754$	1.00291	−	1.97768i	0.0365237	−	0.0720229i
$755$	−2.33946	+	5.64796i	−0.0851418	+	0.205550i
$756$		0			0
$757$	39.9311	−	16.5400i	1.45132	−	0.601157i	0.488809	−	0.872391i	$-0.337432\pi$
$757$	39.9311	−	16.5400i	1.45132	−	0.601157i	0.962513	+	0.271234i	$0.0874317\pi$
$758$	−8.30178	−	9.68247i	−0.301534	−	0.351683i
$759$		0			0
$760$	−0.952264	+	1.32667i	−0.0345423	+	0.0481232i
$761$	−33.7925	+	33.7925i	−1.22498	+	1.22498i	−0.259134	+	0.965841i	$0.583437\pi$
$761$	−33.7925	+	33.7925i	−1.22498	+	1.22498i	−0.965841	+	0.259134i	$0.916563\pi$
$762$		0			0
$763$	−1.07419	−	2.59332i	−0.0388883	−	0.0938845i
$764$	26.3232	−	19.2796i	0.952338	−	0.697511i
$765$		0			0
$766$	−5.99437	+	1.96041i	−0.216585	+	0.0708324i
$767$	7.67871			0.277262
$768$		0			0
$769$	−22.1545			−0.798913			−0.399457	−	0.916752i	$-0.630801\pi$
$769$	−22.1545			−0.798913			−0.399457	+	0.916752i	$0.630801\pi$
$770$	−0.643117	+	0.210326i	−0.0231763	+	0.00757962i
$771$		0			0
$772$	5.19929	−	3.80806i	0.187126	−	0.137055i
$773$	−4.56113	−	11.0116i	−0.164053	−	0.396058i	0.820380	−	0.571818i	$-0.193762\pi$
$773$	−4.56113	−	11.0116i	−0.164053	−	0.396058i	−0.984433	+	0.175760i	$0.943762\pi$
$774$		0			0
$775$	34.4049	−	34.4049i	1.23586	−	1.23586i
$776$	15.2037	−	21.1813i	0.545780	−	0.760364i
$777$		0			0
$778$	5.27434	+	6.15152i	0.189094	+	0.220543i
$779$	−1.37573	+	0.569844i	−0.0492905	+	0.0204168i
$780$		0			0
$781$	−12.2521	+	29.5793i	−0.438416	+	1.05843i
$782$	−21.0481	+	41.5059i	−0.752679	+	1.48425i
$783$		0			0
$784$	26.5571	+	8.40424i	0.948469	+	0.300151i
$785$		−	10.8526i		−	0.387347i
$786$		0			0
$787$	14.4233	−	34.8210i	0.514137	−	1.24124i	−0.427320	−	0.904101i	$-0.640542\pi$
$787$	14.4233	−	34.8210i	0.514137	−	1.24124i	0.941456	−	0.337135i	$-0.109458\pi$
$788$	−39.2636	−	23.8541i	−1.39871	−	0.849767i
$789$		0			0
$790$	−6.18491	+	5.30296i	−0.220049	+	0.188671i
$791$	−0.603170	−	0.603170i	−0.0214462	−	0.0214462i
$792$		0			0
$793$	4.49773	−	4.49773i	0.159719	−	0.159719i
$794$	−1.48749	+	19.3755i	−0.0527892	+	0.687609i
$795$		0			0
$796$	−3.06678	+	19.8555i	−0.108699	+	0.703761i
$797$	−5.47061	−	2.26600i	−0.193779	−	0.0802659i	0.283684	−	0.958918i	$-0.408443\pi$
$797$	−5.47061	−	2.26600i	−0.193779	−	0.0802659i	−0.477463	+	0.878652i	$0.658443\pi$
$798$		0			0
$799$	28.2096			0.997983
$800$	19.2567	+	18.8908i	0.680827	+	0.667892i
$801$		0			0
$802$	−9.97639	−	30.5050i	−0.352279	−	1.07717i
$803$	−41.8117	−	17.3190i	−1.47550	−	0.611173i
$804$		0			0
$805$	0.202020	+	0.487719i	0.00712027	+	0.0171899i
$806$	0.685526	−	8.92936i	0.0241466	−	0.314523i
$807$		0			0
$808$	9.19862	+	2.15249i	0.323606	+	0.0757244i
$809$	20.7326	+	20.7326i	0.728920	+	0.728920i	0.970405	−	0.241485i	$-0.0776344\pi$
$809$	20.7326	+	20.7326i	0.728920	+	0.728920i	−0.241485	+	0.970405i	$0.577634\pi$
$810$		0			0
$811$	−37.2071	+	15.4117i	−1.30652	+	0.541177i	−0.923866	−	0.382716i	$-0.874989\pi$
$811$	−37.2071	+	15.4117i	−1.30652	+	0.541177i	−0.382651	+	0.923893i	$0.624989\pi$
$812$	−0.499134	+	0.821570i	−0.0175162	+	0.0288314i
$813$		0			0
$814$	52.6727	+	26.7110i	1.84618	+	0.936219i
$815$			3.66796i			0.128483i
$816$		0			0
$817$		−	2.80138i		−	0.0980077i
$818$	17.1123	−	33.7446i	0.598317	−	1.17985i
$819$		0			0
$820$	−0.283015	−	1.15923i	−0.00988331	−	0.0404822i
$821$	29.1884	−	12.0902i	1.01868	−	0.421952i	0.190067	−	0.981771i	$-0.439130\pi$
$821$	29.1884	−	12.0902i	1.01868	−	0.421952i	0.828615	+	0.559820i	$0.189130\pi$
$822$		0			0
$823$	−3.31937	−	3.31937i	−0.115706	−	0.115706i	0.646883	−	0.762589i	$-0.276072\pi$
$823$	−3.31937	−	3.31937i	−0.115706	−	0.115706i	−0.762589	+	0.646883i	$0.776072\pi$
$824$	−4.65511	−	28.3350i	−0.162169	−	0.987098i
$825$		0			0
$826$	−3.31912	−	0.254816i	−0.115487	−	0.00886617i
$827$	−2.47114	−	5.96586i	−0.0859300	−	0.207453i	0.875073	−	0.483991i	$-0.160813\pi$
$827$	−2.47114	−	5.96586i	−0.0859300	−	0.207453i	−0.961003	+	0.276537i	$0.910813\pi$
$828$		0			0
$829$	−0.339967	−	0.140819i	−0.0118075	−	0.00489085i	0.376772	−	0.926306i	$-0.377034\pi$
$829$	−0.339967	−	0.140819i	−0.0118075	−	0.00489085i	−0.388579	+	0.921415i	$0.627034\pi$
$830$	−2.70287	+	0.883950i	−0.0938179	+	0.0306823i
$831$		0			0
$832$	4.95400	+	0.332575i	0.171749	+	0.0115299i
$833$	39.7233			1.37633
$834$		0			0
$835$	−0.522948	−	0.216612i	−0.0180974	−	0.00749618i
$836$	7.41717	+	10.1269i	0.256528	+	0.350247i
$837$		0			0
$838$	−31.8258	−	2.44333i	−1.09940	−	0.0844036i
$839$	32.9364	−	32.9364i	1.13709	−	1.13709i	0.148122	−	0.988969i	$-0.452677\pi$
$839$	32.9364	−	32.9364i	1.13709	−	1.13709i	0.988969	−	0.148122i	$-0.0473227\pi$
$840$		0			0
$841$	−15.9930	−	15.9930i	−0.551483	−	0.551483i
$842$	34.4232	+	40.1482i	1.18630	+	1.38360i
$843$		0			0
$844$	5.85240	+	23.9715i	0.201448	+	0.825135i
$845$	2.32191	−	5.60559i	0.0798761	−	0.192838i
$846$		0			0
$847$			3.10824i			0.106801i
$848$	3.63228	+	42.0276i	0.124733	+	1.44323i
$849$		0			0
$850$	34.3095	+	17.3988i	1.17681	+	0.596772i
$851$	17.6328	−	42.5693i	0.604444	−	1.45926i
$852$		0			0
$853$	2.43815	−	1.00992i	0.0834808	−	0.0345789i	−0.340552	−	0.940226i	$-0.610614\pi$
$853$	2.43815	−	1.00992i	0.0834808	−	0.0345789i	0.424033	+	0.905647i	$0.360614\pi$
$854$	−2.09340	+	1.79489i	−0.0716346	+	0.0614198i
$855$		0			0
$856$	1.06217	−	4.53917i	0.0363043	−	0.155146i
$857$	31.8225	−	31.8225i	1.08704	−	1.08704i	0.0912053	−	0.995832i	$-0.470928\pi$
$857$	31.8225	−	31.8225i	1.08704	−	1.08704i	0.995832	−	0.0912053i	$-0.0290720\pi$
$858$		0			0
$859$	11.6288	+	28.0745i	0.396771	+	0.957890i	0.988427	+	0.151699i	$0.0484744\pi$
$859$	11.6288	+	28.0745i	0.396771	+	0.957890i	−0.591656	+	0.806191i	$0.701526\pi$
$860$	2.21860	+	0.342672i	0.0756535	+	0.0116850i
$861$		0			0
$862$	−16.9051	−	51.6909i	−0.575789	−	1.76060i
$863$	−18.9524			−0.645148			−0.322574	−	0.946544i	$-0.604548\pi$
$863$	−18.9524			−0.645148			−0.322574	+	0.946544i	$0.604548\pi$
$864$		0			0
$865$	5.87909			0.199895
$866$	3.76044	+	11.4984i	0.127785	+	0.390730i
$867$		0			0
$868$	−0.592637	+	3.83696i	−0.0201154	+	0.130235i
$869$	23.9650	+	57.8566i	0.812956	+	1.96265i
$870$		0			0
$871$	−2.27732	+	2.27732i	−0.0771642	+	0.0771642i
$872$	−22.0082	−	35.4546i	−0.745292	−	1.20064i
$873$		0			0
$874$	7.43478	−	6.37460i	0.251485	−	0.215624i
$875$	0.825874	−	0.342088i	0.0279196	−	0.0115647i
$876$		0			0
$877$	16.0645	−	38.7831i	0.542459	−	1.30961i	−0.380523	−	0.924771i	$-0.624256\pi$
$877$	16.0645	−	38.7831i	0.542459	−	1.30961i	0.922983	−	0.384842i	$-0.125744\pi$
$878$	−9.16230	−	4.64631i	−0.309213	−	0.156805i
$879$		0			0
$880$	−8.92748	+	4.63539i	−0.300945	+	0.156259i
$881$		−	21.4254i		−	0.721841i	−0.932597	−	0.360921i	$-0.882463\pi$
$881$		−	21.4254i		−	0.721841i	0.932597	−	0.360921i	$-0.117537\pi$
$882$		0			0
$883$	2.94264	−	7.10415i	0.0990276	−	0.239074i	−0.866600	−	0.499004i	$-0.833699\pi$
$883$	2.94264	−	7.10415i	0.0990276	−	0.239074i	0.965627	+	0.259930i	$0.0836995\pi$
$884$	6.87859	−	1.67934i	0.231352	−	0.0564822i
$885$		0			0
$886$	5.90147	+	6.88295i	0.198264	+	0.231237i
$887$	30.7269	+	30.7269i	1.03171	+	1.03171i	0.999480	+	0.0322295i	$0.0102607\pi$
$887$	30.7269	+	30.7269i	1.03171	+	1.03171i	0.0322295	+	0.999480i	$0.489739\pi$
$888$		0			0
$889$	−1.41977	+	1.41977i	−0.0476176	+	0.0476176i
$890$	8.09446	+	0.621429i	0.271327	+	0.0208303i
$891$		0			0
$892$	−22.5728	+	16.5328i	−0.755795	+	0.553559i
$893$	−5.48456	−	2.27178i	−0.183534	−	0.0760222i
$894$		0			0
$895$	5.76225			0.192611
$896$	−2.13033	−	0.308152i	−0.0711693	−	0.0102946i
$897$		0			0
$898$	31.9348	−	10.4440i	1.06568	−	0.348521i
$899$	23.8149	+	9.86444i	0.794271	+	0.328998i
$900$		0			0
$901$	23.0213	+	55.5782i	0.766949	+	1.85158i
$902$	−9.14541	−	0.702113i	−0.304509	−	0.0233778i
$903$		0			0
$904$	−10.3021	−	7.39469i	−0.342641	−	0.245944i
$905$	−1.69281	−	1.69281i	−0.0562710	−	0.0562710i
$906$		0			0
$907$	32.8338	−	13.6002i	1.09023	−	0.451588i	0.236142	−	0.971718i	$-0.424117\pi$
$907$	32.8338	−	13.6002i	1.09023	−	0.451588i	0.854087	+	0.520131i	$0.174117\pi$
$908$	−4.43828	+	1.08356i	−0.147289	+	0.0359592i
$909$		0			0
$910$	0.0363270	−	0.0716350i	0.00120423	−	0.00237468i
$911$			15.3896i			0.509879i	0.966957	+	0.254940i	$0.0820556\pi$
$911$			15.3896i			0.509879i	−0.966957	+	0.254940i	$0.917944\pi$
$912$		0			0
$913$			21.8588i			0.723421i
$914$	2.07818	+	1.05387i	0.0687399	+	0.0348588i
$915$		0			0
$916$	−14.4826	−	8.79871i	−0.478518	−	0.290718i
$917$	1.18575	−	0.491152i	0.0391568	−	0.0162193i
$918$		0			0
$919$	1.60663	+	1.60663i	0.0529979	+	0.0529979i	0.733109	−	0.680111i	$-0.238068\pi$
$919$	1.60663	+	1.60663i	0.0529979	+	0.0529979i	−0.680111	+	0.733109i	$0.738068\pi$
$920$	4.13903	+	6.66785i	0.136460	+	0.219833i
$921$		0			0
$922$	0.457369	−	5.95749i	0.0150626	−	0.196199i
$923$	−1.45438	−	3.51118i	−0.0478715	−	0.115572i
$924$		0			0
$925$	−35.1886	−	14.5756i	−1.15699	−	0.479242i
$926$	1.37016	+	4.18956i	0.0450263	+	0.137678i
$927$		0			0
$928$	−5.34214	+	13.2552i	−0.175364	+	0.435123i
$929$	−8.22205			−0.269757			−0.134878	−	0.990862i	$-0.543064\pi$
$929$	−8.22205			−0.269757			−0.134878	+	0.990862i	$0.543064\pi$
$930$		0			0
$931$	−7.72308	−	3.19901i	−0.253114	−	0.104843i
$932$	−21.9108	−	3.38422i	−0.717711	−	0.110854i
$933$		0			0
$934$	2.14967	−	28.0006i	0.0703393	−	0.916208i
$935$	−10.1435	+	10.1435i	−0.331726	+	0.331726i
$936$		0			0
$937$	10.3496	+	10.3496i	0.338105	+	0.338105i	0.855654	−	0.517549i	$-0.173155\pi$
$937$	10.3496	+	10.3496i	0.338105	+	0.338105i	−0.517549	+	0.855654i	$0.673155\pi$
$938$	1.05994	−	0.908799i	0.0346084	−	0.0296733i
$939$		0			0
$940$	2.47006	−	4.06570i	0.0805645	−	0.132608i
$941$	19.5970	−	47.3114i	0.638844	−	1.54231i	−0.189376	−	0.981905i	$-0.560647\pi$
$941$	19.5970	−	47.3114i	0.638844	−	1.54231i	0.828221	−	0.560402i	$-0.189353\pi$
$942$		0			0
$943$			7.15614i			0.233036i
$944$	−49.3049	+	4.26122i	−1.60474	+	0.138691i
$945$		0			0
$946$	7.80445	−	15.3900i	0.253745	−	0.500372i
$947$	9.51949	−	22.9821i	0.309342	−	0.746817i	−0.690385	−	0.723442i	$-0.742559\pi$
$947$	9.51949	−	22.9821i	0.309342	−	0.746817i	0.999727	−	0.0233749i	$-0.00744115\pi$
$948$		0			0
$949$	4.96322	−	2.05583i	0.161113	−	0.0667352i
$950$	−5.26936	−	6.14572i	−0.170961	−	0.199394i
$951$		0			0
$952$	−3.02900	+	0.497628i	−0.0981703	+	0.0161282i
$953$	26.5521	−	26.5521i	0.860106	−	0.860106i	−0.131244	−	0.991350i	$-0.541897\pi$
$953$	26.5521	−	26.5521i	0.860106	−	0.860106i	0.991350	+	0.131244i	$0.0418972\pi$
$954$		0			0
$955$	−3.00283	−	7.24947i	−0.0971692	−	0.234587i
$956$	−10.0528	−	13.7254i	−0.325129	−	0.443911i
$957$		0			0
$958$	19.5755	−	6.40199i	0.632454	−	0.206839i
$959$	−2.82368			−0.0911813
$960$		0			0
$961$	73.1065			2.35827
$962$	−6.66319	+	2.17914i	−0.214830	+	0.0702583i
$963$		0			0
$964$	12.2088	+	16.6691i	0.393219	+	0.536876i
$965$	−0.593112	−	1.43190i	−0.0190929	−	0.0460944i
$966$		0			0
$967$	−17.5385	+	17.5385i	−0.564001	+	0.564001i	−0.930442	−	0.366440i	$-0.880576\pi$
$967$	−17.5385	+	17.5385i	−0.564001	+	0.564001i	0.366440	+	0.930442i	$0.380576\pi$
$968$	7.49109	+	45.5973i	0.240773	+	1.46555i
$969$		0			0
$970$	−4.08134	−	4.76012i	−0.131044	−	0.152838i
$971$	26.0783	−	10.8020i	0.836894	−	0.346653i	0.0772656	−	0.997011i	$-0.475381\pi$
$971$	26.0783	−	10.8020i	0.836894	−	0.346653i	0.759628	+	0.650358i	$0.225381\pi$
$972$		0			0
$973$	−0.722295	+	1.74378i	−0.0231557	+	0.0559029i
$974$	−10.9363	+	21.5658i	−0.350420	+	0.691012i
$975$		0			0
$976$	−26.3839	+	31.3758i	−0.844528	+	1.00432i
$977$			18.6808i			0.597651i	0.954308	+	0.298825i	$0.0965948\pi$
$977$			18.6808i			0.597651i	−0.954308	+	0.298825i	$0.903405\pi$
$978$		0			0
$979$	23.8803	−	57.6522i	0.763218	−	1.84257i
$980$	3.47822	−	5.72511i	0.111108	−	0.182882i
$981$		0			0
$982$	23.5166	−	20.1632i	0.750444	−	0.643433i
$983$	2.93163	+	2.93163i	0.0935046	+	0.0935046i	0.752312	−	0.658807i	$-0.228939\pi$
$983$	2.93163	+	2.93163i	0.0935046	+	0.0935046i	−0.658807	+	0.752312i	$0.728939\pi$
$984$		0			0
$985$	−7.81247	+	7.81247i	−0.248926	+	0.248926i
$986$	−1.56004	+	20.3204i	−0.0496817	+	0.647132i
$987$		0			0
$988$	−1.47259	−	0.227448i	−0.0468494	−	0.00723610i
$989$	−12.4380	−	5.15197i	−0.395504	−	0.163823i
$990$		0			0
$991$	−56.5710			−1.79704			−0.898519	−	0.438935i	$-0.855356\pi$
$991$	−56.5710			−1.79704			−0.898519	+	0.438935i	$0.855356\pi$
$992$	0.553506	+	57.7157i	0.0175738	+	1.83248i
$993$		0			0
$994$	0.512137	+	1.56597i	0.0162440	+	0.0496695i
$995$	4.46387	+	1.84900i	0.141514	+	0.0586171i
$996$		0			0
$997$	3.90402	+	9.42514i	0.123642	+	0.298497i	0.973565	−	0.228408i	$-0.0733522\pi$
$997$	3.90402	+	9.42514i	0.123642	+	0.298497i	−0.849924	+	0.526906i	$0.823352\pi$
$998$	0.922746	−	12.0193i	0.0292090	−	0.380464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.253.1		32
3.2	odd	2		96.2.n.a.61.8	✓	32
4.3	odd	2		1152.2.v.c.721.4		32
12.11	even	2		384.2.n.a.337.6		32
24.5	odd	2		768.2.n.a.673.7		32
24.11	even	2		768.2.n.b.673.3		32
32.11	odd	8		1152.2.v.c.433.4		32
32.21	even	8	inner	288.2.v.d.181.1		32
96.5	odd	8		768.2.n.a.97.7		32
96.11	even	8		384.2.n.a.49.6		32
96.53	odd	8		96.2.n.a.85.8	yes	32
96.59	even	8		768.2.n.b.97.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.8	✓	32	3.2	odd	2
96.2.n.a.85.8	yes	32	96.53	odd	8
288.2.v.d.181.1		32	32.21	even	8	inner
288.2.v.d.253.1		32	1.1	even	1	trivial
384.2.n.a.49.6		32	96.11	even	8
384.2.n.a.337.6		32	12.11	even	2
768.2.n.a.97.7		32	96.5	odd	8
768.2.n.a.673.7		32	24.5	odd	2
768.2.n.b.97.3		32	96.59	even	8
768.2.n.b.673.3		32	24.11	even	2
1152.2.v.c.433.4		32	32.11	odd	8
1152.2.v.c.721.4		32	4.3	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34416 + 0.439595i) q^{2} +(1.61351 - 1.18177i) q^{4} +(-0.184062 - 0.444366i) q^{5} +(-0.134531 + 0.134531i) q^{7} +(-1.64931 + 2.29777i) q^{8} +O(q^{10})\)	\(q+(-1.34416 + 0.439595i) q^{2} +(1.61351 - 1.18177i) q^{4} +(-0.184062 - 0.444366i) q^{5} +(-0.134531 + 0.134531i) q^{7} +(-1.64931 + 2.29777i) q^{8} +(0.442749 + 0.516384i) q^{10} +(4.83050 - 2.00086i) q^{11} +(-0.237510 + 0.573400i) q^{13} +(0.121692 - 0.239970i) q^{14} +(1.20685 - 3.81360i) q^{16} -5.70425i q^{17} +(-0.459376 + 1.10903i) q^{19} +(-0.822124 - 0.499471i) q^{20} +(-5.61338 + 4.81293i) q^{22} +(4.07921 + 4.07921i) q^{23} +(3.37195 - 3.37195i) q^{25} +(0.0671870 - 0.875148i) q^{26} +(-0.0580831 + 0.376053i) q^{28} +(2.33405 + 0.966793i) q^{29} +10.2033 q^{31} +(0.0542480 + 5.65659i) q^{32} +(2.50756 + 7.66741i) q^{34} +(0.0845432 + 0.0350189i) q^{35} +(-3.05654 - 7.37913i) q^{37} +(0.129949 - 1.69265i) q^{38} +(1.32463 + 0.309965i) q^{40} +(0.877147 + 0.877147i) q^{41} +(-2.15605 + 0.893063i) q^{43} +(5.42952 - 8.93695i) q^{44} +(-7.27630 - 3.68990i) q^{46} +4.94536i q^{47} +6.96380i q^{49} +(-3.05014 + 6.01472i) q^{50} +(0.294401 + 1.20587i) q^{52} +(-9.74330 + 4.03581i) q^{53} +(-1.77823 - 1.77823i) q^{55} +(-0.0872381 - 0.531007i) q^{56} +(-3.56232 - 0.273487i) q^{58} +(-4.73462 - 11.4304i) q^{59} +(-9.46851 - 3.92198i) q^{61} +(-13.7148 + 4.48530i) q^{62} +(-2.55953 - 7.57950i) q^{64} +0.298516 q^{65} +(4.79416 + 1.98581i) q^{67} +(-6.74111 - 9.20388i) q^{68} +(-0.129033 - 0.00990617i) q^{70} +(-4.32992 + 4.32992i) q^{71} +(-6.12055 - 6.12055i) q^{73} +(7.35229 + 8.57507i) q^{74} +(0.569410 + 2.33231i) q^{76} +(-0.380675 + 0.919031i) q^{77} +11.9773i q^{79} +(-1.91677 + 0.165658i) q^{80} +(-1.56461 - 0.793434i) q^{82} +(-1.59989 + 3.86247i) q^{83} +(-2.53477 + 1.04994i) q^{85} +(2.50548 - 2.14820i) q^{86} +(-3.36949 + 14.3994i) q^{88} +(8.43934 - 8.43934i) q^{89} +(-0.0451877 - 0.109093i) q^{91} +(11.4025 + 1.76118i) q^{92} +(-2.17395 - 6.64733i) q^{94} +0.577370 q^{95} -9.21817 q^{97} +(-3.06125 - 9.36044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Introduction

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