LMFDB - Embedded newform 288.2.v.d.109.6

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			109.6
Character	$\chi$	$=$	288.109
Dual form			288.2.v.d.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.603367 - 1.27904i) q^{2} +(-1.27190 - 1.54346i) q^{4} +(-3.68816 + 1.52768i) q^{5} +(-1.63704 + 1.63704i) q^{7} +(-2.74158 + 0.695531i) q^{8} +O(q^{10})$	\(q+(0.603367 - 1.27904i) q^{2} +(-1.27190 - 1.54346i) q^{4} +(-3.68816 + 1.52768i) q^{5} +(-1.63704 + 1.63704i) q^{7} +(-2.74158 + 0.695531i) q^{8} +(-0.271341 + 5.63906i) q^{10} +(-1.20420 - 2.90719i) q^{11} +(-3.30127 - 1.36743i) q^{13} +(1.10611 + 3.08158i) q^{14} +(-0.764563 + 3.92625i) q^{16} -0.511560i q^{17} +(-0.254077 - 0.105242i) q^{19} +(7.04888 + 3.74948i) q^{20} +(-4.44500 - 0.213885i) q^{22} +(3.17185 + 3.17185i) q^{23} +(7.73315 - 7.73315i) q^{25} +(-3.74088 + 3.39740i) q^{26} +(4.60886 + 0.444569i) q^{28} +(2.75087 - 6.64118i) q^{29} -5.82083 q^{31} +(4.56053 + 3.34688i) q^{32} +(-0.654306 - 0.308659i) q^{34} +(3.53678 - 8.53855i) q^{35} +(-5.53467 + 2.29253i) q^{37} +(-0.287911 + 0.261476i) q^{38} +(9.04881 - 6.75349i) q^{40} +(-3.94823 - 3.94823i) q^{41} +(1.30801 + 3.15781i) q^{43} +(-2.95553 + 5.55628i) q^{44} +(5.97071 - 2.14313i) q^{46} +9.41403i q^{47} +1.64019i q^{49} +(-5.22509 - 14.5570i) q^{50} +(2.08829 + 6.83462i) q^{52} +(-2.50482 - 6.04717i) q^{53} +(8.88255 + 8.88255i) q^{55} +(3.34946 - 5.62669i) q^{56} +(-6.83457 - 7.52555i) q^{58} +(-13.3423 + 5.52657i) q^{59} +(3.35835 - 8.10777i) q^{61} +(-3.51210 + 7.44509i) q^{62} +(7.03247 - 3.81370i) q^{64} +14.2646 q^{65} +(-1.11643 + 2.69530i) q^{67} +(-0.789574 + 0.650651i) q^{68} +(-8.78718 - 9.67558i) q^{70} +(-1.26611 + 1.26611i) q^{71} +(-7.51616 - 7.51616i) q^{73} +(-0.407191 + 8.46231i) q^{74} +(0.160722 + 0.526017i) q^{76} +(6.73052 + 2.78787i) q^{77} -0.709730i q^{79} +(-3.17824 - 15.6486i) q^{80} +(-7.43218 + 2.66772i) q^{82} +(1.40823 + 0.583309i) q^{83} +(0.781502 + 1.88671i) q^{85} +(4.82818 + 0.232323i) q^{86} +(5.32345 + 7.13273i) q^{88} +(0.0856897 - 0.0856897i) q^{89} +(7.64285 - 3.16577i) q^{91} +(0.861374 - 8.92989i) q^{92} +(12.0409 + 5.68012i) q^{94} +1.09785 q^{95} -0.677647 q^{97} +(2.09787 + 0.989638i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	0.603367	−	1.27904i	0.426645	−	0.904419i
$2$	0.603367	−	1.27904i	0.426645	−	0.904419i
$3$		0			0
$3$		0			0
$4$	−1.27190	−	1.54346i	−0.635948	−	0.771732i
$5$	−3.68816	+	1.52768i	−1.64939	+	0.683201i	−0.997195	−	0.0748462i	$-0.976153\pi$
$5$	−3.68816	+	1.52768i	−1.64939	+	0.683201i	−0.652199	+	0.758048i	$0.726153\pi$
$6$		0			0
$7$	−1.63704	+	1.63704i	−0.618743	+	0.618743i	−0.945209	−	0.326466i	$-0.894142\pi$
$7$	−1.63704	+	1.63704i	−0.618743	+	0.618743i	0.326466	+	0.945209i	$0.394142\pi$
$8$	−2.74158	+	0.695531i	−0.969293	+	0.245908i
$9$		0			0
$10$	−0.271341	+	5.63906i	−0.0858057	+	1.78323i
$11$	−1.20420	−	2.90719i	−0.363080	−	0.876552i	−0.994846	−	0.101393i	$-0.967670\pi$
$11$	−1.20420	−	2.90719i	−0.363080	−	0.876552i	0.631767	−	0.775158i	$-0.282330\pi$
$12$		0			0
$13$	−3.30127	−	1.36743i	−0.915607	−	0.379257i	−0.125407	−	0.992105i	$-0.540024\pi$
$13$	−3.30127	−	1.36743i	−0.915607	−	0.379257i	−0.790200	+	0.612849i	$0.790024\pi$
$14$	1.10611	+	3.08158i	0.295619	+	0.823587i
$15$		0			0
$16$	−0.764563	+	3.92625i	−0.191141	+	0.981563i
$17$		−	0.511560i		−	0.124071i	−0.998074	−	0.0620357i	$-0.980241\pi$
$17$		−	0.511560i		−	0.124071i	0.998074	−	0.0620357i	$-0.0197593\pi$
$18$		0			0
$19$	−0.254077	−	0.105242i	−0.0582894	−	0.0241442i	0.353348	−	0.935492i	$-0.385043\pi$
$19$	−0.254077	−	0.105242i	−0.0582894	−	0.0241442i	−0.411638	+	0.911348i	$0.635043\pi$
$20$	7.04888	+	3.74948i	1.57618	+	0.838410i
$21$		0			0
$22$	−4.44500	−	0.213885i	−0.947676	−	0.0456004i
$23$	3.17185	+	3.17185i	0.661376	+	0.661376i	0.955704	−	0.294329i	$-0.0950960\pi$
$23$	3.17185	+	3.17185i	0.661376	+	0.661376i	−0.294329	+	0.955704i	$0.595096\pi$
$24$		0			0
$25$	7.73315	−	7.73315i	1.54663	−	1.54663i
$26$	−3.74088	+	3.39740i	−0.733646	+	0.666284i
$27$		0			0
$28$	4.60886	+	0.444569i	0.870993	+	0.0840157i
$29$	2.75087	−	6.64118i	0.510823	−	1.23324i	−0.432582	−	0.901595i	$-0.642397\pi$
$29$	2.75087	−	6.64118i	0.510823	−	1.23324i	0.943405	−	0.331642i	$-0.107603\pi$
$30$		0			0
$31$	−5.82083			−1.04545			−0.522726	−	0.852501i	$-0.675085\pi$
$31$	−5.82083			−1.04545			−0.522726	+	0.852501i	$0.675085\pi$
$32$	4.56053	+	3.34688i	0.806195	+	0.591650i
$33$		0			0
$34$	−0.654306	−	0.308659i	−0.112213	−	0.0529345i
$35$	3.53678	−	8.53855i	0.597825	−	1.44328i
$36$		0			0
$37$	−5.53467	+	2.29253i	−0.909894	+	0.376890i	−0.788016	−	0.615655i	$-0.788892\pi$
$37$	−5.53467	+	2.29253i	−0.909894	+	0.376890i	−0.121878	+	0.992545i	$0.538892\pi$
$38$	−0.287911	+	0.261476i	−0.0467054	+	0.0424170i
$39$		0			0
$40$	9.04881	−	6.75349i	1.43074	−	1.06782i
$41$	−3.94823	−	3.94823i	−0.616610	−	0.616610i	0.328050	−	0.944660i	$-0.393608\pi$
$41$	−3.94823	−	3.94823i	−0.616610	−	0.616610i	−0.944660	+	0.328050i	$0.893608\pi$
$42$		0			0
$43$	1.30801	+	3.15781i	0.199469	+	0.481561i	0.991686	−	0.128678i	$-0.0410733\pi$
$43$	1.30801	+	3.15781i	0.199469	+	0.481561i	−0.792217	+	0.610239i	$0.791073\pi$
$44$	−2.95553	+	5.55628i	−0.445563	+	0.837641i
$45$		0			0
$46$	5.97071	−	2.14313i	0.880333	−	0.315988i
$47$			9.41403i			1.37318i	0.727046	+	0.686589i	$0.240893\pi$
$47$			9.41403i			1.37318i	−0.727046	+	0.686589i	$0.759107\pi$
$48$		0			0
$49$			1.64019i			0.234313i
$50$	−5.22509	−	14.5570i	−0.738940	−	2.05866i
$51$		0			0
$52$	2.08829	+	6.83462i	0.289594	+	0.947791i
$53$	−2.50482	−	6.04717i	−0.344063	−	0.830642i	−0.997296	−	0.0734852i	$-0.976588\pi$
$53$	−2.50482	−	6.04717i	−0.344063	−	0.830642i	0.653233	−	0.757157i	$-0.273412\pi$
$54$		0			0
$55$	8.88255	+	8.88255i	1.19772	+	1.19772i
$56$	3.34946	−	5.62669i	0.447590	−	0.751898i
$57$		0			0
$58$	−6.83457	−	7.52555i	−0.897423	−	0.988153i
$59$	−13.3423	+	5.52657i	−1.73702	+	0.719498i	−0.738023	+	0.674775i	$0.764241\pi$
$59$	−13.3423	+	5.52657i	−1.73702	+	0.719498i	−0.998999	+	0.0447232i	$0.985759\pi$
$60$		0			0
$61$	3.35835	−	8.10777i	0.429992	−	1.03809i	−0.549297	−	0.835627i	$-0.685104\pi$
$61$	3.35835	−	8.10777i	0.429992	−	1.03809i	0.979289	−	0.202466i	$-0.0648955\pi$
$62$	−3.51210	+	7.44509i	−0.446037	+	0.945527i
$63$		0			0
$64$	7.03247	−	3.81370i	0.879059	−	0.476713i
$65$	14.2646			1.76931
$66$		0			0
$67$	−1.11643	+	2.69530i	−0.136394	+	0.329283i	−0.977288	−	0.211916i	$-0.932030\pi$
$67$	−1.11643	+	2.69530i	−0.136394	+	0.329283i	0.840894	+	0.541199i	$0.182030\pi$
$68$	−0.789574	+	0.650651i	−0.0957500	+	0.0789030i
$69$		0			0
$70$	−8.78718	−	9.67558i	−1.05027	−	1.15645i
$71$	−1.26611	+	1.26611i	−0.150259	+	0.150259i	−0.778234	−	0.627975i	$-0.783884\pi$
$71$	−1.26611	+	1.26611i	−0.150259	+	0.150259i	0.627975	+	0.778234i	$0.283884\pi$
$72$		0			0
$73$	−7.51616	−	7.51616i	−0.879700	−	0.879700i	0.113804	−	0.993503i	$-0.463697\pi$
$73$	−7.51616	−	7.51616i	−0.879700	−	0.879700i	−0.993503	+	0.113804i	$0.963697\pi$
$74$	−0.407191	+	8.46231i	−0.0473350	+	0.983723i
$75$		0			0
$76$	0.160722	+	0.526017i	0.0184361	+	0.0603383i
$77$	6.73052	+	2.78787i	0.767014	+	0.317707i
$78$		0			0
$79$		−	0.709730i		−	0.0798509i	−0.999203	−	0.0399254i	$-0.987288\pi$
$79$		−	0.709730i		−	0.0798509i	0.999203	−	0.0399254i	$-0.0127120\pi$
$80$	−3.17824	−	15.6486i	−0.355338	−	1.74957i
$81$		0			0
$82$	−7.43218	+	2.66772i	−0.820747	+	0.294600i
$83$	1.40823	+	0.583309i	0.154574	+	0.0640265i	0.458629	−	0.888628i	$-0.348341\pi$
$83$	1.40823	+	0.583309i	0.154574	+	0.0640265i	−0.304055	+	0.952654i	$0.598341\pi$
$84$		0			0
$85$	0.781502	+	1.88671i	0.0847658	+	0.204643i
$86$	4.82818	+	0.232323i	0.520636	+	0.0250520i
$87$		0			0
$88$	5.32345	+	7.13273i	0.567481	+	0.760352i
$89$	0.0856897	−	0.0856897i	0.00908309	−	0.00908309i	−0.702551	−	0.711634i	$-0.747956\pi$
$89$	0.0856897	−	0.0856897i	0.00908309	−	0.00908309i	0.711634	+	0.702551i	$0.247956\pi$
$90$		0			0
$91$	7.64285	−	3.16577i	0.801188	−	0.331863i
$92$	0.861374	−	8.92989i	0.0898044	−	0.931005i
$93$		0			0
$94$	12.0409	+	5.68012i	1.24193	+	0.585860i
$95$	1.09785			0.112638
$96$		0			0
$97$	−0.677647			−0.0688046			−0.0344023	−	0.999408i	$-0.510953\pi$
$97$	−0.677647			−0.0688046			−0.0344023	+	0.999408i	$0.510953\pi$
$98$	2.09787	+	0.989638i	0.211917	+	0.0999686i
$99$		0			0
$100$	−21.7716	−	2.10008i	−2.17716	−	0.210008i
$101$	−10.0095	+	4.14605i	−0.995978	+	0.412548i	−0.820321	−	0.571904i	$-0.806205\pi$
$101$	−10.0095	+	4.14605i	−0.995978	+	0.412548i	−0.175657	+	0.984451i	$0.556205\pi$
$102$		0			0
$103$	8.25191	−	8.25191i	0.813085	−	0.813085i	−0.172010	−	0.985095i	$-0.555026\pi$
$103$	8.25191	−	8.25191i	0.813085	−	0.813085i	0.985095	+	0.172010i	$0.0550263\pi$
$104$	10.0018	+	1.45278i	0.980754	+	0.142456i
$105$		0			0
$106$	−9.24590	−	0.444896i	−0.898041	−	0.0432121i
$107$	0.162056	+	0.391238i	0.0156665	+	0.0378224i	0.931519	−	0.363692i	$-0.118484\pi$
$107$	0.162056	+	0.391238i	0.0156665	+	0.0378224i	−0.915853	+	0.401514i	$0.868484\pi$
$108$		0			0
$109$	5.41943	+	2.24480i	0.519087	+	0.215013i	0.626816	−	0.779167i	$-0.284358\pi$
$109$	5.41943	+	2.24480i	0.519087	+	0.215013i	−0.107729	+	0.994180i	$0.534358\pi$
$110$	16.7206	−	6.00171i	1.59425	−	0.572241i
$111$		0			0
$112$	−5.17581	−	7.67906i	−0.489068	−	0.725603i
$113$		−	3.60406i		−	0.339041i	−0.985527	−	0.169521i	$-0.945778\pi$
$113$		−	3.60406i		−	0.339041i	0.985527	−	0.169521i	$-0.0542219\pi$
$114$		0			0
$115$	−16.5438	−	6.85269i	−1.54272	−	0.639016i
$116$	−13.7492	+	4.20103i	−1.27659	+	0.390055i
$117$		0			0
$118$	−0.981608	+	20.3999i	−0.0903643	+	1.87797i
$119$	0.837445	+	0.837445i	0.0767684	+	0.0767684i
$120$		0			0
$121$	0.776498	−	0.776498i	0.0705908	−	0.0705908i
$122$	−8.34385	−	9.18743i	−0.755417	−	0.831791i
$123$		0			0
$124$	7.40349	+	8.98425i	0.664853	+	0.806809i
$125$	−9.06884	+	21.8941i	−0.811142	+	1.95827i
$126$		0			0
$127$	−0.146652			−0.0130133			−0.00650663	−	0.999979i	$-0.502071\pi$
$127$	−0.146652			−0.0130133			−0.00650663	+	0.999979i	$0.502071\pi$
$128$	−0.634722	−	11.2959i	−0.0561021	−	0.998425i
$129$		0			0
$130$	8.60679	−	18.2450i	0.754866	−	1.60019i
$131$	−1.16280	+	2.80726i	−0.101595	+	0.245271i	−0.966501	−	0.256661i	$-0.917377\pi$
$131$	−1.16280	+	2.80726i	−0.101595	+	0.245271i	0.864907	+	0.501933i	$0.167377\pi$
$132$		0			0
$133$	0.588221	−	0.243649i	0.0510053	−	0.0211271i
$134$	2.77378	+	3.05421i	0.239618	+	0.263844i
$135$		0			0
$136$	0.355806	+	1.40248i	0.0305101	+	0.120262i
$137$	11.6890	+	11.6890i	0.998662	+	0.998662i	0.999999	−	0.00133685i	$-0.000425532\pi$
$137$	11.6890	+	11.6890i	0.998662	+	0.998662i	−0.00133685	+	0.999999i	$0.500426\pi$
$138$		0			0
$139$	7.96071	+	19.2188i	0.675218	+	1.63012i	0.772615	+	0.634875i	$0.218949\pi$
$139$	7.96071	+	19.2188i	0.675218	+	1.63012i	−0.0973963	+	0.995246i	$0.531051\pi$
$140$	−17.6774	+	5.40124i	−1.49401	+	0.456489i
$141$		0			0
$142$	0.855476	+	2.38333i	0.0717900	+	0.200005i
$143$			11.2441i			0.940277i
$144$		0			0
$145$			28.6962i			2.38309i
$146$	−14.1485	+	5.07847i	−1.17094	+	0.420297i
$147$		0			0
$148$	10.5780	+	5.62670i	0.869503	+	0.462512i
$149$	0.110593	+	0.266995i	0.00906011	+	0.0218730i	0.928345	−	0.371720i	$-0.121232\pi$
$149$	0.110593	+	0.266995i	0.00906011	+	0.0218730i	−0.919285	+	0.393593i	$0.871232\pi$
$150$		0			0
$151$	−4.70680	−	4.70680i	−0.383034	−	0.383034i	0.489160	−	0.872194i	$-0.337303\pi$
$151$	−4.70680	−	4.70680i	−0.383034	−	0.383034i	−0.872194	+	0.489160i	$0.837303\pi$
$152$	0.769772	+	0.111811i	0.0624367	+	0.00906906i
$153$		0			0
$154$	7.62678	−	6.92650i	0.614583	−	0.558153i
$155$	21.4681	−	8.89240i	1.72436	−	0.714255i
$156$		0			0
$157$	−7.43264	+	17.9440i	−0.593189	+	1.43208i	0.287218	+	0.957865i	$0.407270\pi$
$157$	−7.43264	+	17.9440i	−0.593189	+	1.43208i	−0.880407	+	0.474220i	$0.842730\pi$
$158$	−0.907774	−	0.428228i	−0.0722186	−	0.0340680i
$159$		0			0
$160$	−21.9329	−	5.37678i	−1.73395	−	0.425071i
$161$	−10.3849			−0.818444
$162$		0			0
$163$	5.94686	−	14.3570i	0.465794	−	1.12453i	−0.500188	−	0.865917i	$-0.666736\pi$
$163$	5.94686	−	14.3570i	0.465794	−	1.12453i	0.965982	−	0.258609i	$-0.0832641\pi$
$164$	−1.07222	+	11.1157i	−0.0837260	+	0.867989i
$165$		0			0
$166$	1.59576	−	1.44924i	0.123855	−	0.112483i
$167$	10.7086	−	10.7086i	0.828655	−	0.828655i	−0.158676	−	0.987331i	$-0.550723\pi$
$167$	10.7086	−	10.7086i	0.828655	−	0.828655i	0.987331	+	0.158676i	$0.0507225\pi$
$168$		0			0
$169$	−0.163883	−	0.163883i	−0.0126064	−	0.0126064i
$170$	2.88472	+	0.138807i	0.221248	+	0.0106460i
$171$		0			0
$172$	3.21032	−	6.03526i	0.244784	−	0.460185i
$173$	−2.46513	−	1.02109i	−0.187420	−	0.0776320i	0.287000	−	0.957931i	$-0.407342\pi$
$173$	−2.46513	−	1.02109i	−0.187420	−	0.0776320i	−0.474420	+	0.880299i	$0.657342\pi$
$174$		0			0
$175$			25.3190i			1.91393i
$176$	12.3351	−	2.50525i	0.929790	−	0.188840i
$177$		0			0
$178$	−0.0578983	−	0.161303i	−0.00433966	−	0.0120902i
$179$	−9.77295	−	4.04809i	−0.730465	−	0.302568i	−0.0137219	−	0.999906i	$-0.504368\pi$
$179$	−9.77295	−	4.04809i	−0.730465	−	0.302568i	−0.716743	+	0.697337i	$0.754368\pi$
$180$		0			0
$181$	−7.36413	−	17.7786i	−0.547371	−	1.32147i	−0.919427	−	0.393261i	$-0.871347\pi$
$181$	−7.36413	−	17.7786i	−0.547371	−	1.32147i	0.372056	−	0.928210i	$-0.378653\pi$
$182$	0.562292	−	11.6856i	0.0416799	−	0.866198i
$183$		0			0
$184$	−10.9020	−	6.48974i	−0.803704	−	0.478430i
$185$	16.9105	−	16.9105i	1.24328	−	1.24328i
$186$		0			0
$187$	−1.48720	+	0.616020i	−0.108755	+	0.0450478i
$188$	14.5302	−	11.9737i	1.05973	−	0.873269i
$189$		0			0
$190$	0.662410	−	1.40420i	0.0480563	−	0.101872i
$191$	−10.1764			−0.736335			−0.368168	−	0.929759i	$-0.620015\pi$
$191$	−10.1764			−0.736335			−0.368168	+	0.929759i	$0.620015\pi$
$192$		0			0
$193$	−7.17480			−0.516454			−0.258227	−	0.966084i	$-0.583138\pi$
$193$	−7.17480			−0.516454			−0.258227	+	0.966084i	$0.583138\pi$
$194$	−0.408870	+	0.866739i	−0.0293552	+	0.0622282i
$195$		0			0
$196$	2.53158	−	2.08615i	0.180827	−	0.149011i
$197$	−9.81153	+	4.06407i	−0.699042	+	0.289553i	−0.703762	−	0.710436i	$-0.748498\pi$
$197$	−9.81153	+	4.06407i	−0.699042	+	0.289553i	0.00471943	+	0.999989i	$0.498498\pi$
$198$		0			0
$199$	−7.92887	+	7.92887i	−0.562063	+	0.562063i	−0.929893	−	0.367830i	$-0.880101\pi$
$199$	−7.92887	+	7.92887i	−0.562063	+	0.562063i	0.367830	+	0.929893i	$0.380101\pi$
$200$	−15.8224	+	26.5797i	−1.11881	+	1.87947i
$201$		0			0
$202$	−0.736405	+	15.3041i	−0.0518133	+	1.07679i
$203$	6.36861	+	15.3752i	0.446989	+	1.07913i
$204$		0			0
$205$	20.5933	+	8.53004i	1.43830	+	0.595764i
$206$	−5.57560	−	15.5335i	−0.388471	−	1.08227i
$207$		0			0
$208$	7.89290	−	11.9161i	0.547274	−	0.826234i
$209$			0.865385i			0.0598599i
$210$		0			0
$211$	−23.9700	−	9.92869i	−1.65016	−	0.683519i	−0.652898	−	0.757446i	$-0.726447\pi$
$211$	−23.9700	−	9.92869i	−1.65016	−	0.683519i	−0.997264	+	0.0739270i	$0.976447\pi$
$212$	−6.14772	+	11.5575i	−0.422227	+	0.793770i
$213$		0			0
$214$	0.598189	+	0.0287837i	0.0408913	+	0.00196762i
$215$	−9.64827	−	9.64827i	−0.658007	−	0.658007i
$216$		0			0
$217$	9.52894	−	9.52894i	0.646867	−	0.646867i
$218$	6.14110	−	5.57724i	0.415928	−	0.377738i
$219$		0			0
$220$	2.41222	−	25.0076i	0.162632	−	1.68601i
$221$	−0.699522	+	1.68880i	−0.0470550	+	0.113601i
$222$		0			0
$223$	−0.573216			−0.0383854			−0.0191927	−	0.999816i	$-0.506110\pi$
$223$	−0.573216			−0.0383854			−0.0191927	+	0.999816i	$0.506110\pi$
$224$	−12.9447	+	1.98679i	−0.864907	+	0.132748i
$225$		0			0
$226$	−4.60974	−	2.17457i	−0.306635	−	0.144650i
$227$	1.44349	−	3.48488i	0.0958075	−	0.231300i	−0.868709	−	0.495323i	$-0.835050\pi$
$227$	1.44349	−	3.48488i	0.0958075	−	0.231300i	0.964516	+	0.264023i	$0.0850496\pi$
$228$		0			0
$229$	−7.10429	+	2.94269i	−0.469465	+	0.194459i	−0.604858	−	0.796333i	$-0.706770\pi$
$229$	−7.10429	+	2.94269i	−0.469465	+	0.194459i	0.135393	+	0.990792i	$0.456770\pi$
$230$	−18.7469	+	17.0256i	−1.23613	+	1.12263i
$231$		0			0
$232$	−2.92256	+	20.1206i	−0.191876	+	1.32098i
$233$	−1.38129	−	1.38129i	−0.0904912	−	0.0904912i	0.660412	−	0.750903i	$-0.270382\pi$
$233$	−1.38129	−	1.38129i	−0.0904912	−	0.0904912i	−0.750903	+	0.660412i	$0.770382\pi$
$234$		0			0
$235$	−14.3817	−	34.7204i	−0.938157	−	2.26491i
$236$	25.5001	+	13.5642i	1.65992	+	0.882953i
$237$		0			0
$238$	1.57641	−	0.565840i	0.102184	−	0.0366779i
$239$		−	4.58455i		−	0.296550i	−0.988946	−	0.148275i	$-0.952628\pi$
$239$		−	4.58455i		−	0.296550i	0.988946	−	0.148275i	$-0.0473721\pi$
$240$		0			0
$241$		−	15.9551i		−	1.02776i	−0.857862	−	0.513880i	$-0.828208\pi$
$241$		−	15.9551i		−	1.02776i	0.857862	−	0.513880i	$-0.171792\pi$
$242$	−0.524660	−	1.46169i	−0.0337264	−	0.0939608i
$243$		0			0
$244$	−16.7855	+	5.12874i	−1.07458	+	0.328334i
$245$	−2.50570	−	6.04929i	−0.160083	−	0.386475i
$246$		0			0
$247$	0.694866	+	0.694866i	0.0442133	+	0.0442133i
$248$	15.9583	−	4.04857i	1.01335	−	0.257085i
$249$		0			0
$250$	22.5316	+	24.8096i	1.42503	+	1.56910i
$251$	20.0790	−	8.31700i	1.26738	−	0.524964i	0.355211	−	0.934786i	$-0.384409\pi$
$251$	20.0790	−	8.31700i	1.26738	−	0.524964i	0.912166	+	0.409822i	$0.134409\pi$
$252$		0			0
$253$	5.40164	−	13.0407i	0.339598	−	0.819862i
$254$	−0.0884851	+	0.187574i	−0.00555205	+	0.0117694i
$255$		0			0
$256$	−14.8309	−	6.00374i	−0.926930	−	0.375233i
$257$	−0.677979			−0.0422912			−0.0211456	−	0.999776i	$-0.506731\pi$
$257$	−0.677979			−0.0422912			−0.0211456	+	0.999776i	$0.506731\pi$
$258$		0			0
$259$	5.30750	−	12.8134i	0.329792	−	0.796189i
$260$	−18.1431	−	22.0169i	−1.12519	−	1.36543i
$261$		0			0
$262$	2.88900	+	3.18108i	0.178483	+	0.196528i
$263$	−7.67357	+	7.67357i	−0.473173	+	0.473173i	−0.902940	−	0.429767i	$-0.858596\pi$
$263$	−7.67357	+	7.67357i	−0.473173	+	0.473173i	0.429767	+	0.902940i	$0.358596\pi$
$264$		0			0
$265$	18.4763	+	18.4763i	1.13499	+	1.13499i
$266$	0.0432760	−	0.899370i	0.00265342	−	0.0551439i
$267$		0			0
$268$	5.58008	−	1.70497i	0.340857	−	0.104148i
$269$	−22.0482	−	9.13266i	−1.34430	−	0.556828i	−0.409602	−	0.912264i	$-0.634332\pi$
$269$	−22.0482	−	9.13266i	−1.34430	−	0.556828i	−0.934701	+	0.355436i	$0.884332\pi$
$270$		0			0
$271$		−	0.778886i		−	0.0473140i	−0.999720	−	0.0236570i	$-0.992469\pi$
$271$		−	0.778886i		−	0.0473140i	0.999720	−	0.0236570i	$-0.00753096\pi$
$272$	2.00851	+	0.391120i	0.121784	+	0.0237151i
$273$		0			0
$274$	22.0036	−	7.89799i	1.32928	−	0.477135i
$275$	−31.7940	−	13.1695i	−1.91725	−	0.794151i
$276$		0			0
$277$	1.47054	+	3.55020i	0.0883564	+	0.213311i	0.961881	−	0.273469i	$-0.0881712\pi$
$277$	1.47054	+	3.55020i	0.0883564	+	0.213311i	−0.873524	+	0.486780i	$0.838171\pi$
$278$	29.3849	+	1.41395i	1.76239	+	0.0848030i
$279$		0			0
$280$	−3.75753	+	25.8690i	−0.224555	+	1.54597i
$281$	3.60771	−	3.60771i	0.215218	−	0.215218i	−0.591262	−	0.806480i	$-0.701370\pi$
$281$	3.60771	−	3.60771i	0.215218	−	0.215218i	0.806480	+	0.591262i	$0.201370\pi$
$282$		0			0
$283$	12.3134	−	5.10036i	0.731953	−	0.303185i	0.0145986	−	0.999893i	$-0.495353\pi$
$283$	12.3134	−	5.10036i	0.731953	−	0.303185i	0.717354	+	0.696709i	$0.245353\pi$
$284$	3.56455	+	0.343835i	0.211517	+	0.0204029i
$285$		0			0
$286$	14.3816	+	6.78431i	0.850405	+	0.401165i
$287$	12.9268			0.763047
$288$		0			0
$289$	16.7383			0.984606
$290$	36.7036	+	17.3143i	2.15531	+	1.01673i
$291$		0			0
$292$	−2.04115	+	21.1607i	−0.119449	+	1.23834i
$293$	21.1509	−	8.76099i	1.23565	−	0.511822i	0.333297	−	0.942822i	$-0.391839\pi$
$293$	21.1509	−	8.76099i	1.23565	−	0.511822i	0.902352	+	0.431000i	$0.141839\pi$
$294$		0			0
$295$	40.7657	−	40.7657i	2.37347	−	2.37347i
$296$	13.5792	−	10.1347i	0.789274	−	0.589067i
$297$		0			0
$298$	0.408225	+	0.0196430i	0.0236479	+	0.00113789i
$299$	−6.13384	−	14.8084i	−0.354729	−	0.856391i
$300$		0			0
$301$	−7.31072	−	3.02820i	−0.421383	−	0.174543i
$302$	−8.86013	+	3.18027i	−0.509843	+	0.183004i
$303$		0			0
$304$	0.607466	−	0.917107i	0.0348406	−	0.0525997i
$305$			35.0332i			2.00600i
$306$		0			0
$307$	29.7333	+	12.3159i	1.69697	+	0.702908i	0.999901	−	0.0140946i	$-0.00448661\pi$
$307$	29.7333	+	12.3159i	1.69697	+	0.702908i	0.697070	+	0.717003i	$0.254487\pi$
$308$	−4.25754	−	13.9342i	−0.242596	−	0.793974i
$309$		0			0
$310$	1.57943	−	32.8240i	0.0897057	−	1.86428i
$311$	5.08789	+	5.08789i	0.288508	+	0.288508i	0.836490	−	0.547982i	$-0.184604\pi$
$311$	5.08789	+	5.08789i	0.288508	+	0.288508i	−0.547982	+	0.836490i	$0.684604\pi$
$312$		0			0
$313$	−10.3695	+	10.3695i	−0.586117	+	0.586117i	−0.936578	−	0.350460i	$-0.886025\pi$
$313$	−10.3695	+	10.3695i	−0.586117	+	0.586117i	0.350460	+	0.936578i	$0.386025\pi$
$314$	18.4665	+	20.3335i	1.04212	+	1.14748i
$315$		0			0
$316$	−1.09544	+	0.902702i	−0.0616235	+	0.0507810i
$317$	6.18851	−	14.9404i	0.347582	−	0.839136i	−0.649323	−	0.760513i	$-0.724948\pi$
$317$	6.18851	−	14.9404i	0.347582	−	0.839136i	0.996904	−	0.0786232i	$-0.0250524\pi$
$318$		0			0
$319$	−22.6198			−1.26647
$320$	−20.1107	+	24.8089i	−1.12422	+	1.38686i
$321$		0			0
$322$	−6.26590	+	13.2827i	−0.349185	+	0.740216i
$323$	−0.0538378	+	0.129976i	−0.00299561	+	0.00723205i
$324$		0			0
$325$	−36.1037	+	14.9547i	−2.00268	+	0.829535i
$326$	−14.7750	−	16.2688i	−0.818314	−	0.901046i
$327$		0			0
$328$	13.5705	+	8.07825i	0.749305	+	0.446047i
$329$	−15.4112	−	15.4112i	−0.849645	−	0.849645i
$330$		0			0
$331$	12.0185	+	29.0153i	0.660599	+	1.59483i	0.796867	+	0.604155i	$0.206489\pi$
$331$	12.0185	+	29.0153i	0.660599	+	1.59483i	−0.136268	+	0.990672i	$0.543511\pi$
$332$	−0.890808	−	2.91547i	−0.0488895	−	0.160007i
$333$		0			0
$334$	−7.23551	−	20.1579i	−0.395910	−	1.10299i
$335$		−	11.6462i		−	0.636302i
$336$		0			0
$337$			2.12023i			0.115496i	0.998331	+	0.0577480i	$0.0183920\pi$
$337$			2.12023i			0.115496i	−0.998331	+	0.0577480i	$0.981608\pi$
$338$	−0.308494	+	0.110731i	−0.0167799	+	0.00602299i
$339$		0			0
$340$	1.91809	−	3.60592i	0.104023	−	0.195559i
$341$	7.00944	+	16.9223i	0.379582	+	0.916393i
$342$		0			0
$343$	−14.1444	−	14.1444i	−0.763723	−	0.763723i
$344$	−5.78235	−	7.74761i	−0.311764	−	0.417723i
$345$		0			0
$346$	−2.79340	+	2.53691i	−0.150174	+	0.136385i
$347$	−15.6587	+	6.48607i	−0.840606	+	0.348190i	−0.761092	−	0.648644i	$-0.775337\pi$
$347$	−15.6587	+	6.48607i	−0.840606	+	0.348190i	−0.0795133	+	0.996834i	$0.525337\pi$
$348$		0			0
$349$	−2.54342	+	6.14035i	−0.136146	+	0.328685i	−0.977218	−	0.212238i	$-0.931925\pi$
$349$	−2.54342	+	6.14035i	−0.136146	+	0.328685i	0.841072	+	0.540923i	$0.181925\pi$
$350$	32.3840	+	15.2766i	1.73100	+	0.816571i
$351$		0			0
$352$	4.23825	−	17.2886i	0.225899	−	0.921487i
$353$	−26.7822			−1.42547			−0.712737	−	0.701431i	$-0.752545\pi$
$353$	−26.7822			−1.42547			−0.712737	+	0.701431i	$0.752545\pi$
$354$		0			0
$355$	2.73539	−	6.60382i	0.145179	−	0.350494i
$356$	−0.241247	−	0.0232706i	−0.0127861	−	0.00123334i
$357$		0			0
$358$	−11.0744	+	10.0575i	−0.585298	+	0.531557i
$359$	21.9626	−	21.9626i	1.15914	−	1.15914i	0.174480	−	0.984661i	$-0.444176\pi$
$359$	21.9626	−	21.9626i	1.15914	−	1.15914i	0.984661	−	0.174480i	$-0.0558243\pi$
$360$		0			0
$361$	−13.3815	−	13.3815i	−0.704292	−	0.704292i
$362$	−27.1828	−	1.30799i	−1.42870	−	0.0687463i
$363$		0			0
$364$	−14.6072	−	7.76993i	−0.765623	−	0.407255i
$365$	39.2031	+	16.2385i	2.05198	+	0.849959i
$366$		0			0
$367$		−	20.1290i		−	1.05073i	−0.850878	−	0.525363i	$-0.823929\pi$
$367$		−	20.1290i		−	1.05073i	0.850878	−	0.525363i	$-0.176071\pi$
$368$	−14.8785	+	10.0284i	−0.775597	+	0.522766i
$369$		0			0
$370$	−11.4260	−	31.8324i	−0.594007	−	1.65489i
$371$	13.9999	+	5.79897i	0.726841	+	0.301067i
$372$		0			0
$373$	0.278651	+	0.672724i	0.0144280	+	0.0348323i	0.930929	−	0.365199i	$-0.118999\pi$
$373$	0.278651	+	0.672724i	0.0144280	+	0.0348323i	−0.916501	+	0.400032i	$0.868999\pi$
$374$	−0.109415	+	2.27388i	−0.00565771	+	0.117580i
$375$		0			0
$376$	−6.54776	−	25.8093i	−0.337675	−	1.33101i
$377$	−18.1627	+	18.1627i	−0.935427	+	0.935427i
$378$		0			0
$379$	−33.2934	+	13.7906i	−1.71017	+	0.708375i	−0.710177	+	0.704023i	$0.751385\pi$
$379$	−33.2934	+	13.7906i	−1.71017	+	0.708375i	−0.999991	+	0.00435195i	$0.998615\pi$
$380$	−1.39636	−	1.69450i	−0.0716316	−	0.0869260i
$381$		0			0
$382$	−6.14008	+	13.0160i	−0.314154	+	0.665955i
$383$	−30.6643			−1.56687			−0.783435	−	0.621473i	$-0.786534\pi$
$383$	−30.6643			−1.56687			−0.783435	+	0.621473i	$0.786534\pi$
$384$		0			0
$385$	−29.0822			−1.48217
$386$	−4.32904	+	9.17687i	−0.220342	+	0.467091i
$387$		0			0
$388$	0.861896	+	1.04592i	0.0437561	+	0.0530987i
$389$	9.95840	−	4.12490i	0.504911	−	0.209141i	−0.115664	−	0.993288i	$-0.536899\pi$
$389$	9.95840	−	4.12490i	0.504911	−	0.209141i	0.620575	+	0.784147i	$0.286899\pi$
$390$		0			0
$391$	1.62259	−	1.62259i	0.0820579	−	0.0820579i
$392$	−1.14081	−	4.49671i	−0.0576194	−	0.227118i
$393$		0			0
$394$	−0.721844	+	15.0015i	−0.0363660	+	0.755764i
$395$	1.08424	+	2.61760i	0.0545542	+	0.131706i
$396$		0			0
$397$	33.1225	+	13.7198i	1.66237	+	0.688577i	0.998255	−	0.0590504i	$-0.0188073\pi$
$397$	33.1225	+	13.7198i	1.66237	+	0.688577i	0.664118	+	0.747628i	$0.268807\pi$
$398$	5.35733	+	14.9254i	0.268539	+	0.748142i
$399$		0			0
$400$	24.4498	+	36.2748i	1.22249	+	1.81374i
$401$			1.21160i			0.0605046i	0.999542	+	0.0302523i	$0.00963107\pi$
$401$			1.21160i			0.0605046i	−0.999542	+	0.0302523i	$0.990369\pi$
$402$		0			0
$403$	19.2161	+	7.95958i	0.957224	+	0.396495i
$404$	19.1303	+	10.1759i	0.951766	+	0.506269i
$405$		0			0
$406$	23.5081	+	1.13117i	1.16669	+	0.0561389i
$407$	13.3297	+	13.3297i	0.660728	+	0.660728i
$408$		0			0
$409$	−20.0380	+	20.0380i	−0.990817	+	0.990817i	−0.999958	−	0.00914144i	$-0.997090\pi$
$409$	−20.0380	+	20.0380i	−0.990817	+	0.990817i	0.00914144	+	0.999958i	$0.497090\pi$
$410$	23.3356	−	21.1930i	1.15246	−	1.04665i
$411$		0			0
$412$	−23.2321	−	2.24096i	−1.14456	−	0.110404i
$413$	12.7947	−	30.8892i	0.629587	−	1.51996i
$414$		0			0
$415$	−6.08490			−0.298696
$416$	−10.4789	−	17.2851i	−0.513770	−	0.847474i
$417$		0			0
$418$	1.10686	+	0.522145i	0.0541385	+	0.0255390i
$419$	−1.34843	+	3.25539i	−0.0658749	+	0.159036i	−0.953389	−	0.301745i	$-0.902431\pi$
$419$	−1.34843	+	3.25539i	−0.0658749	+	0.159036i	0.887514	+	0.460781i	$0.152431\pi$
$420$		0			0
$421$	10.4207	−	4.31639i	0.507873	−	0.210368i	−0.114008	−	0.993480i	$-0.536369\pi$
$421$	10.4207	−	4.31639i	0.507873	−	0.210368i	0.621881	+	0.783112i	$0.286369\pi$
$422$	−27.1619	+	24.6680i	−1.32222	+	1.20082i
$423$		0			0
$424$	11.0731	+	14.8366i	0.537759	+	0.720528i
$425$	−3.95597	−	3.95597i	−0.191893	−	0.191893i
$426$		0			0
$427$	7.77500	+	18.7705i	0.376258	+	0.908368i
$428$	0.397743	−	0.747741i	0.0192256	−	0.0361434i
$429$		0			0
$430$	−18.1620	+	6.51909i	−0.875849	+	0.314378i
$431$		−	35.6433i		−	1.71688i	−0.512914	−	0.858440i	$-0.671434\pi$
$431$		−	35.6433i		−	1.71688i	0.512914	−	0.858440i	$-0.328566\pi$
$432$		0			0
$433$			9.75449i			0.468771i	0.972144	+	0.234385i	$0.0753078\pi$
$433$			9.75449i			0.468771i	−0.972144	+	0.234385i	$0.924692\pi$
$434$	−6.43846	−	17.9374i	−0.309056	−	0.861021i
$435$		0			0
$436$	−3.42818	−	11.2198i	−0.164180	−	0.537333i
$437$	−0.472082	−	1.13971i	−0.0225828	−	0.0545196i
$438$		0			0
$439$	−11.2645	−	11.2645i	−0.537625	−	0.537625i	0.385206	−	0.922831i	$-0.374130\pi$
$439$	−11.2645	−	11.2645i	−0.537625	−	0.537625i	−0.922831	+	0.385206i	$0.874130\pi$
$440$	−30.5303	−	18.1741i	−1.45547	−	0.866416i
$441$		0			0
$442$	1.73797	+	1.91368i	0.0826669	+	0.0910246i
$443$	−22.1985	+	9.19492i	−1.05468	+	0.436864i	−0.841561	−	0.540162i	$-0.818363\pi$
$443$	−22.1985	+	9.19492i	−1.05468	+	0.436864i	−0.213122	+	0.977026i	$0.568363\pi$
$444$		0			0
$445$	−0.185130	+	0.446944i	−0.00877601	+	0.0211872i
$446$	−0.345860	+	0.733168i	−0.0163769	+	0.0347165i
$447$		0			0
$448$	−5.26926	+	17.7556i	−0.248949	+	0.838875i
$449$	12.5831			0.593834			0.296917	−	0.954903i	$-0.404042\pi$
$449$	12.5831			0.593834			0.296917	+	0.954903i	$0.404042\pi$
$450$		0			0
$451$	−6.72381	+	16.2327i	−0.316612	+	0.764369i
$452$	−5.56273	+	4.58398i	−0.261649	+	0.215612i
$453$		0			0
$454$	−3.58636	−	3.94894i	−0.168316	−	0.185333i
$455$	−23.3517	+	23.3517i	−1.09475	+	1.09475i
$456$		0			0
$457$	−28.8488	−	28.8488i	−1.34949	−	1.34949i	−0.886216	−	0.463273i	$-0.846675\pi$
$457$	−28.8488	−	28.8488i	−1.34949	−	1.34949i	−0.463273	−	0.886216i	$-0.653325\pi$
$458$	−0.522670	+	10.8622i	−0.0244227	+	0.507558i
$459$		0			0
$460$	10.4652	+	34.2507i	0.487941	+	1.59695i
$461$	−11.8188	−	4.89549i	−0.550454	−	0.228006i	0.0900809	−	0.995934i	$-0.471287\pi$
$461$	−11.8188	−	4.89549i	−0.550454	−	0.228006i	−0.640535	+	0.767929i	$0.721287\pi$
$462$		0			0
$463$			18.0311i			0.837976i	0.907992	+	0.418988i	$0.137615\pi$
$463$			18.0311i			0.837976i	−0.907992	+	0.418988i	$0.862385\pi$
$464$	23.9717	+	15.8782i	1.11286	+	0.737127i
$465$		0			0
$466$	−2.60015	+	0.933301i	−0.120450	+	0.0432343i
$467$	22.2527	+	9.21739i	1.02973	+	0.426530i	0.832616	−	0.553850i	$-0.186842\pi$
$467$	22.2527	+	9.21739i	1.02973	+	0.426530i	0.197118	+	0.980380i	$0.436842\pi$
$468$		0			0
$469$	−2.58467	−	6.23995i	−0.119349	−	0.288134i
$470$	−53.0863	−	2.55442i	−2.44869	−	0.117826i
$471$		0			0
$472$	32.7351	−	24.4315i	1.50675	−	1.12455i
$473$	7.60526	−	7.60526i	0.349690	−	0.349690i
$474$		0			0
$475$	−2.77867	+	1.15096i	−0.127494	+	0.0528099i
$476$	0.227424	−	2.35771i	0.0104239	−	0.108065i
$477$		0			0
$478$	−5.86383	−	2.76617i	−0.268206	−	0.126522i
$479$	−11.2525			−0.514141			−0.257070	−	0.966393i	$-0.582757\pi$
$479$	−11.2525			−0.514141			−0.257070	+	0.966393i	$0.582757\pi$
$480$		0			0
$481$	21.4063			0.976043
$482$	−20.4073	−	9.62681i	−0.929526	−	0.438489i
$483$		0			0
$484$	−2.18612	−	0.210873i	−0.0993692	−	0.00958512i
$485$	2.49927	−	1.03523i	0.113486	−	0.0470074i
$486$		0			0
$487$	−23.1247	+	23.1247i	−1.04788	+	1.04788i	−0.0490867	+	0.998795i	$0.515631\pi$
$487$	−23.1247	+	23.1247i	−1.04788	+	1.04788i	−0.998795	+	0.0490867i	$0.984369\pi$
$488$	−3.56795	+	24.5639i	−0.161514	+	1.11195i
$489$		0			0
$490$	−9.24915	−	0.445052i	−0.417834	−	0.0201054i
$491$	9.92916	+	23.9711i	0.448097	+	1.08180i	0.973034	+	0.230661i	$0.0740888\pi$
$491$	9.92916	+	23.9711i	0.448097	+	1.08180i	−0.524937	+	0.851141i	$0.675911\pi$
$492$		0			0
$493$	−3.39736	−	1.40723i	−0.153010	−	0.0633786i
$494$	1.30802	−	0.469503i	0.0588507	−	0.0211240i
$495$		0			0
$496$	4.45040	−	22.8540i	0.199829	−	1.02618i
$497$		−	4.14534i		−	0.185944i
$498$		0			0
$499$	−0.662766	−	0.274527i	−0.0296695	−	0.0122895i	0.367799	−	0.929905i	$-0.380111\pi$
$499$	−0.662766	−	0.274527i	−0.0296695	−	0.0122895i	−0.397469	+	0.917616i	$0.630111\pi$
$500$	45.3274	−	13.8496i	2.02710	−	0.619373i
$501$		0			0
$502$	1.47723	−	30.7001i	0.0659321	−	1.37021i
$503$	5.46400	+	5.46400i	0.243628	+	0.243628i	0.818349	−	0.574721i	$-0.194890\pi$
$503$	5.46400	+	5.46400i	0.243628	+	0.243628i	−0.574721	+	0.818349i	$0.694890\pi$
$504$		0			0
$505$	30.5826	−	30.5826i	1.36091	−	1.36091i
$506$	−13.4204	−	14.7773i	−0.596611	−	0.656929i
$507$		0			0
$508$	0.186526	+	0.226352i	0.00827576	+	0.0100428i
$509$	3.15891	−	7.62628i	0.140016	−	0.338029i	−0.838280	−	0.545240i	$-0.816439\pi$
$509$	3.15891	−	7.62628i	0.140016	−	0.338029i	0.978296	+	0.207211i	$0.0664386\pi$
$510$		0			0
$511$	24.6085			1.08862
$512$	−16.6275	+	15.3469i	−0.734839	+	0.678242i
$513$		0			0
$514$	−0.409070	+	0.867163i	−0.0180433	+	0.0382489i
$515$	−17.8280	+	43.0407i	−0.785597	+	1.89660i
$516$		0			0
$517$	27.3684	−	11.3364i	1.20366	−	0.498573i
$518$	−13.1866	−	14.5197i	−0.579384	−	0.637961i
$519$		0			0
$520$	−39.1075	+	9.92148i	−1.71498	+	0.435086i
$521$	−17.3737	−	17.3737i	−0.761157	−	0.761157i	0.215375	−	0.976531i	$-0.430903\pi$
$521$	−17.3737	−	17.3737i	−0.761157	−	0.761157i	−0.976531	+	0.215375i	$0.930903\pi$
$522$		0			0
$523$	6.26194	+	15.1177i	0.273816	+	0.661049i	0.999640	−	0.0268308i	$-0.00854153\pi$
$523$	6.26194	+	15.1177i	0.273816	+	0.661049i	−0.725824	+	0.687880i	$0.758542\pi$
$524$	5.81187	−	1.77579i	0.253893	−	0.0775758i
$525$		0			0
$526$	5.18484	+	14.4448i	0.226070	+	0.629823i
$527$			2.97770i			0.129711i
$528$		0			0
$529$		−	2.87879i		−	0.125165i
$530$	34.7800	−	12.4840i	1.51075	−	0.542269i
$531$		0			0
$532$	−1.12422	−	0.598002i	−0.0487411	−	0.0259267i
$533$	7.63524	+	18.4331i	0.330719	+	0.798426i
$534$		0			0
$535$	−1.19538	−	1.19538i	−0.0516806	−	0.0516806i
$536$	1.18611	−	8.16588i	0.0512321	−	0.352712i
$537$		0			0
$538$	−24.9842	+	22.6902i	−1.07715	+	0.978244i
$539$	4.76835	−	1.97512i	0.205388	−	0.0850743i
$540$		0			0
$541$	10.7750	−	26.0132i	0.463255	−	1.11840i	−0.503799	−	0.863821i	$-0.668065\pi$
$541$	10.7750	−	26.0132i	0.463255	−	1.11840i	0.967053	−	0.254574i	$-0.0819354\pi$
$542$	−0.996228	−	0.469955i	−0.0427917	−	0.0201863i
$543$		0			0
$544$	1.71213	−	2.33298i	0.0734069	−	0.100026i
$545$	−23.4171			−1.00308
$546$		0			0
$547$	−13.7101	+	33.0991i	−0.586201	+	1.41521i	0.300908	+	0.953653i	$0.402710\pi$
$547$	−13.7101	+	33.0991i	−0.586201	+	1.41521i	−0.887109	+	0.461561i	$0.847290\pi$
$548$	3.17438	−	32.9089i	0.135603	−	1.40580i
$549$		0			0
$550$	−36.0278	+	32.7198i	−1.53623	+	1.39518i
$551$	−1.39787	+	1.39787i	−0.0595512	+	0.0595512i
$552$		0			0
$553$	1.16186	+	1.16186i	0.0494072	+	0.0494072i
$554$	5.42814	+	0.261192i	0.230619	+	0.0110970i
$555$		0			0
$556$	19.5384	−	36.7314i	0.828613	−	1.55776i
$557$	21.4363	+	8.87921i	0.908286	+	0.376224i	0.787400	−	0.616442i	$-0.211427\pi$
$557$	21.4363	+	8.87921i	0.908286	+	0.376224i	0.120886	+	0.992666i	$0.461427\pi$
$558$		0			0
$559$		−	12.2134i		−	0.516571i
$560$	30.8204	+	20.4146i	1.30240	+	0.862673i
$561$		0			0
$562$	−2.43764	−	6.79118i	−0.102825	−	0.286469i
$563$	41.3211	+	17.1158i	1.74148	+	0.721343i	0.998655	+	0.0518544i	$0.0165132\pi$
$563$	41.3211	+	17.1158i	1.74148	+	0.721343i	0.742822	+	0.669489i	$0.233487\pi$
$564$		0			0
$565$	5.50586	+	13.2923i	0.231633	+	0.559212i
$566$	0.905905	−	18.8267i	0.0380780	−	0.791344i
$567$		0			0
$568$	2.59051	−	4.35175i	0.108695	−	0.182595i
$569$	−29.0924	+	29.0924i	−1.21962	+	1.21962i	−0.251848	+	0.967767i	$0.581038\pi$
$569$	−29.0924	+	29.0924i	−1.21962	+	1.21962i	−0.967767	+	0.251848i	$0.918962\pi$
$570$		0			0
$571$	0.414172	−	0.171556i	0.0173326	−	0.00717938i	−0.374000	−	0.927429i	$-0.622014\pi$
$571$	0.414172	−	0.171556i	0.0173326	−	0.00717938i	0.391333	+	0.920249i	$0.372014\pi$
$572$	17.3548	−	14.3013i	0.725642	−	0.597967i
$573$		0			0
$574$	7.79963	−	16.5340i	0.325550	−	0.690114i
$575$	49.0567			2.04581
$576$		0			0
$577$	23.7041			0.986813			0.493406	−	0.869799i	$-0.335752\pi$
$577$	23.7041			0.986813			0.493406	+	0.869799i	$0.335752\pi$
$578$	10.0993	−	21.4090i	0.420078	−	0.890497i
$579$		0			0
$580$	44.2915	−	36.4986i	1.83911	−	1.51552i
$581$	−3.26024	+	1.35043i	−0.135257	+	0.0560255i
$582$		0			0
$583$	−14.5640	+	14.5640i	−0.603178	+	0.603178i
$584$	25.8338	+	15.3784i	1.06901	+	0.636362i
$585$		0			0
$586$	1.55609	−	32.3390i	0.0642816	−	1.33591i
$587$	6.09999	+	14.7267i	0.251773	+	0.607835i	0.998347	−	0.0574676i	$-0.0183026\pi$
$587$	6.09999	+	14.7267i	0.251773	+	0.607835i	−0.746574	+	0.665302i	$0.768303\pi$
$588$		0			0
$589$	1.47894	+	0.612598i	0.0609388	+	0.0252417i
$590$	−27.5444	−	76.7378i	−1.13398	−	3.15925i
$591$		0			0
$592$	−4.76946	−	23.4833i	−0.196024	−	0.965157i
$593$		−	6.36035i		−	0.261188i	−0.991436	−	0.130594i	$-0.958312\pi$
$593$		−	6.36035i		−	0.261188i	0.991436	−	0.130594i	$-0.0416885\pi$
$594$		0			0
$595$	−4.36798	−	1.80928i	−0.179070	−	0.0741731i
$596$	0.271434	−	0.510285i	0.0111184	−	0.0209021i
$597$		0			0
$598$	−22.6415	−	1.08947i	−0.925880	−	0.0445516i
$599$	4.61895	+	4.61895i	0.188725	+	0.188725i	0.795145	−	0.606420i	$-0.207395\pi$
$599$	4.61895	+	4.61895i	0.188725	+	0.188725i	−0.606420	+	0.795145i	$0.707395\pi$
$600$		0			0
$601$	−10.9077	+	10.9077i	−0.444936	+	0.444936i	−0.893667	−	0.448731i	$-0.851876\pi$
$601$	−10.9077	+	10.9077i	−0.444936	+	0.444936i	0.448731	+	0.893667i	$0.351876\pi$
$602$	−8.28425	+	7.52360i	−0.337641	+	0.306639i
$603$		0			0
$604$	−1.27822	+	13.2513i	−0.0520101	+	0.539190i
$605$	−1.67760	+	4.05009i	−0.0682043	+	0.164660i
$606$		0			0
$607$	−0.957019			−0.0388442			−0.0194221	−	0.999811i	$-0.506183\pi$
$607$	−0.957019			−0.0388442			−0.0194221	+	0.999811i	$0.506183\pi$
$608$	−0.806493	−	1.33033i	−0.0327076	−	0.0539519i
$609$		0			0
$610$	44.8089	+	21.1379i	1.81426	+	0.855849i
$611$	12.8730	−	31.0782i	0.520787	−	1.25729i
$612$		0			0
$613$	−2.24424	+	0.929594i	−0.0906440	+	0.0375460i	−0.427545	−	0.903994i	$-0.640621\pi$
$613$	−2.24424	+	0.929594i	−0.0906440	+	0.0375460i	0.336901	+	0.941540i	$0.390621\pi$
$614$	33.6927	−	30.5991i	1.35973	−	1.23488i
$615$		0			0
$616$	−20.3913	−	2.96187i	−0.821588	−	0.119337i
$617$	22.5163	+	22.5163i	0.906472	+	0.906472i	0.995986	−	0.0895138i	$-0.0285313\pi$
$617$	22.5163	+	22.5163i	0.906472	+	0.906472i	−0.0895138	+	0.995986i	$0.528531\pi$
$618$		0			0
$619$	−3.44381	−	8.31410i	−0.138419	−	0.334172i	0.839436	−	0.543459i	$-0.182886\pi$
$619$	−3.44381	−	8.31410i	−0.138419	−	0.334172i	−0.977854	+	0.209287i	$0.932886\pi$
$620$	−41.0303	−	21.8251i	−1.64782	−	0.876518i
$621$		0			0
$622$	9.57750	−	3.43776i	0.384023	−	0.137842i
$623$			0.280555i			0.0112402i
$624$		0			0
$625$		−	39.9216i		−	1.59687i
$626$	7.00639	+	19.5196i	0.280031	+	0.780160i
$627$		0			0
$628$	37.1494	−	11.3509i	1.48242	−	0.452948i
$629$	1.17277	+	2.83131i	0.0467613	+	0.112892i
$630$		0			0
$631$	28.2240	+	28.2240i	1.12358	+	1.12358i	0.991199	+	0.132379i	$0.0422617\pi$
$631$	28.2240	+	28.2240i	1.12358	+	1.12358i	0.132379	+	0.991199i	$0.457738\pi$
$632$	0.493640	+	1.94578i	0.0196359	+	0.0773989i
$633$		0			0
$634$	−15.3754	−	16.9299i	−0.610637	−	0.672373i
$635$	0.540876	−	0.224038i	0.0214640	−	0.00889068i
$636$		0			0
$637$	2.24285	−	5.41471i	0.0888649	−	0.214539i
$638$	−13.6480	+	28.9317i	−0.540331	+	1.14542i
$639$		0			0
$640$	19.5975	+	40.6914i	0.774660	+	1.60847i
$641$	30.2846			1.19617			0.598084	−	0.801433i	$-0.295929\pi$
$641$	30.2846			1.19617			0.598084	+	0.801433i	$0.295929\pi$
$642$		0			0
$643$	0.944867	−	2.28111i	0.0372619	−	0.0899582i	−0.904153	−	0.427209i	$-0.859497\pi$
$643$	0.944867	−	2.28111i	0.0372619	−	0.0899582i	0.941415	+	0.337251i	$0.109497\pi$
$644$	13.2085	+	16.0287i	0.520487	+	0.631619i
$645$		0			0
$646$	0.133761	+	0.147284i	0.00526274	+	0.00579481i
$647$	−8.32184	+	8.32184i	−0.327165	+	0.327165i	−0.851508	−	0.524342i	$-0.824311\pi$
$647$	−8.32184	+	8.32184i	−0.327165	+	0.327165i	0.524342	+	0.851508i	$0.324311\pi$
$648$		0			0
$649$	32.1336	+	32.1336i	1.26136	+	1.26136i
$650$	−2.65619	+	55.2014i	−0.104184	+	2.16518i
$651$		0			0
$652$	−29.7233	+	9.08182i	−1.16405	+	0.355672i
$653$	−19.1159	−	7.91806i	−0.748062	−	0.309858i	−0.0241116	−	0.999709i	$-0.507676\pi$
$653$	−19.1159	−	7.91806i	−0.748062	−	0.309858i	−0.723951	+	0.689852i	$0.757676\pi$
$654$		0			0
$655$		−	12.1300i		−	0.473959i
$656$	18.5204	−	12.4831i	0.723101	−	0.487382i
$657$		0			0
$658$	−29.0101	+	10.4129i	−1.13093	+	0.405938i
$659$	−29.0382	−	12.0280i	−1.13117	−	0.468546i	−0.262991	−	0.964798i	$-0.584709\pi$
$659$	−29.0382	−	12.0280i	−1.13117	−	0.468546i	−0.868178	+	0.496253i	$0.834709\pi$
$660$		0			0
$661$	−6.92538	−	16.7193i	−0.269366	−	0.650307i	0.730088	−	0.683353i	$-0.239479\pi$
$661$	−6.92538	−	16.7193i	−0.269366	−	0.650307i	−0.999454	+	0.0330463i	$0.989479\pi$
$662$	44.3634	+	2.13469i	1.72423	+	0.0829669i
$663$		0			0
$664$	−4.26649	−	0.619716i	−0.165572	−	0.0240496i
$665$	−1.79723	+	1.79723i	−0.0696937	+	0.0696937i
$666$		0			0
$667$	29.7901	−	12.3395i	1.15348	−	0.477787i
$668$	−30.1485	−	2.90811i	−1.16648	−	0.112518i
$669$		0			0
$670$	−14.8960	−	7.02696i	−0.575484	−	0.271475i
$671$	−27.6150			−1.06606
$672$		0			0
$673$	−19.3968			−0.747691			−0.373846	−	0.927491i	$-0.621961\pi$
$673$	−19.3968			−0.747691			−0.373846	+	0.927491i	$0.621961\pi$
$674$	2.71186	+	1.27928i	0.104457	+	0.0492758i
$675$		0			0
$676$	−0.0445054	+	0.461389i	−0.00171175	+	0.0177457i
$677$	1.10973	−	0.459664i	0.0426503	−	0.0176663i	−0.361256	−	0.932467i	$-0.617652\pi$
$677$	1.10973	−	0.459664i	0.0426503	−	0.0176663i	0.403907	+	0.914800i	$0.367652\pi$
$678$		0			0
$679$	1.10934	−	1.10934i	0.0425724	−	0.0425724i
$680$	−3.45482	−	4.62901i	−0.132486	−	0.177514i
$681$		0			0
$682$	25.8736	+	1.24499i	0.990750	+	0.0476731i
$683$	2.49553	+	6.02475i	0.0954889	+	0.230531i	0.964405	−	0.264428i	$-0.0851832\pi$
$683$	2.49553	+	6.02475i	0.0954889	+	0.230531i	−0.868916	+	0.494959i	$0.835183\pi$
$684$		0			0
$685$	−60.9682	−	25.2539i	−2.32948	−	0.964900i
$686$	−26.6255	+	9.55697i	−1.01656	+	0.364887i
$687$		0			0
$688$	−13.3984	+	2.72122i	−0.510809	+	0.103745i
$689$			23.3885i			0.891030i
$690$		0			0
$691$	−12.2382	−	5.06922i	−0.465563	−	0.192842i	0.137556	−	0.990494i	$-0.456075\pi$
$691$	−12.2382	−	5.06922i	−0.465563	−	0.192842i	−0.603118	+	0.797652i	$0.706075\pi$
$692$	1.55937	+	5.10356i	0.0592784	+	0.194008i
$693$		0			0
$694$	−1.15203	+	23.9417i	−0.0437304	+	0.908813i
$695$	−58.7207	−	58.7207i	−2.22740	−	2.22740i
$696$		0			0
$697$	−2.01976	+	2.01976i	−0.0765037	+	0.0765037i
$698$	6.31915	+	6.95802i	0.239183	+	0.263365i
$699$		0			0
$700$	39.0789	−	32.2031i	1.47704	−	1.21716i
$701$	−14.9505	+	36.0936i	−0.564671	+	1.36324i	0.341322	+	0.939946i	$0.389125\pi$
$701$	−14.9505	+	36.0936i	−0.564671	+	1.36324i	−0.905994	+	0.423291i	$0.860875\pi$
$702$		0			0
$703$	1.64751			0.0621369
$704$	−19.5557	−	15.8523i	−0.737032	−	0.597456i
$705$		0			0
$706$	−16.1595	+	34.2556i	−0.608172	+	1.28923i
$707$	9.59863	−	23.1731i	0.360994	−	0.871516i
$708$		0			0
$709$	31.0545	−	12.8632i	1.16627	−	0.483087i	0.286315	−	0.958136i	$-0.407570\pi$
$709$	31.0545	−	12.8632i	1.16627	−	0.483087i	0.879959	+	0.475049i	$0.157570\pi$
$710$	−6.79611	−	7.48321i	−0.255054	−	0.280840i
$711$		0			0
$712$	−0.175325	+	0.294525i	−0.00657058	+	0.0110378i
$713$	−18.4628	−	18.4628i	−0.691437	−	0.691437i
$714$		0			0
$715$	−17.1774	−	41.4699i	−0.642399	−	1.55089i
$716$	6.18209	+	20.2330i	0.231036	+	0.756141i
$717$		0			0
$718$	−14.8395	−	41.3426i	−0.553807	−	1.54289i
$719$		−	12.6636i		−	0.472274i	−0.971720	−	0.236137i	$-0.924119\pi$
$719$		−	12.6636i		−	0.472274i	0.971720	−	0.236137i	$-0.0758815\pi$
$720$		0			0
$721$			27.0174i			1.00618i
$722$	−25.1896	+	9.04157i	−0.937458	+	0.336492i
$723$		0			0
$724$	−18.0742	+	33.9787i	−0.671722	+	1.26281i
$725$	−30.0844	−	72.6302i	−1.11731	−	2.69742i
$726$		0			0
$727$	33.0425	+	33.0425i	1.22548	+	1.22548i	0.965657	+	0.259821i	$0.0836636\pi$
$727$	33.0425	+	33.0425i	1.22548	+	1.22548i	0.259821	+	0.965657i	$0.416336\pi$
$728$	−18.7516	+	13.9950i	−0.694979	+	0.518691i
$729$		0			0
$730$	44.4235	−	40.3446i	1.64419	−	1.49322i
$731$	1.61541	−	0.669124i	0.0597480	−	0.0247484i
$732$		0			0
$733$	1.87261	−	4.52088i	0.0691664	−	0.166982i	−0.885516	−	0.464609i	$-0.846195\pi$
$733$	1.87261	−	4.52088i	0.0691664	−	0.166982i	0.954682	+	0.297626i	$0.0961950\pi$
$734$	−25.7459	−	12.1452i	−0.950297	−	0.448288i
$735$		0			0
$736$	3.84950	+	25.0811i	0.141894	+	0.924501i
$737$	9.18015			0.338155
$738$		0			0
$739$	15.0628	−	36.3648i	0.554093	−	1.33770i	−0.360287	−	0.932842i	$-0.617321\pi$
$739$	15.0628	−	36.3648i	0.554093	−	1.33770i	0.914380	−	0.404857i	$-0.132679\pi$
$740$	−47.6090	−	4.59235i	−1.75014	−	0.168818i
$741$		0			0
$742$	15.8642	−	14.4076i	0.582394	−	0.528920i
$743$	20.9250	−	20.9250i	0.767664	−	0.767664i	−0.210031	−	0.977695i	$-0.567356\pi$
$743$	20.9250	−	20.9250i	0.767664	−	0.767664i	0.977695	+	0.210031i	$0.0673563\pi$
$744$		0			0
$745$	−0.815767	−	0.815767i	−0.0298874	−	0.0298874i
$746$	1.02857	+	0.0494929i	0.0376587	+	0.00181207i
$747$		0			0
$748$	2.84237	+	1.51193i	0.103927	+	0.0552817i
$749$	−0.905765	−	0.375180i	−0.0330959	−	0.0137088i
$750$		0			0
$751$		−	2.47050i		−	0.0901497i	−0.998984	−	0.0450749i	$-0.985647\pi$
$751$		−	2.47050i		−	0.0901497i	0.998984	−	0.0450749i	$-0.0143526\pi$
$752$	−36.9618	−	7.19763i	−1.34786	−	0.262470i
$753$		0			0
$754$	12.2721	+	34.1896i	0.446923	+	1.24511i
$755$	24.5499	+	10.1689i	0.893464	+	0.370085i
$756$		0			0
$757$	2.84324	+	6.86420i	0.103339	+	0.249483i	0.967089	−	0.254437i	$-0.0818903\pi$
$757$	2.84324	+	6.86420i	0.103339	+	0.249483i	−0.863750	+	0.503921i	$0.831890\pi$
$758$	−2.44943	+	50.9045i	−0.0889673	+	1.84893i
$759$		0			0
$760$	−3.00985	+	0.763593i	−0.109179	+	0.0276984i
$761$	29.8039	−	29.8039i	1.08039	−	1.08039i	0.0839198	−	0.996473i	$-0.473256\pi$
$761$	29.8039	−	29.8039i	1.08039	−	1.08039i	0.996473	−	0.0839198i	$-0.0267439\pi$
$762$		0			0
$763$	−12.5467	+	5.19700i	−0.454220	+	0.188144i
$764$	12.9433	+	15.7068i	0.468271	+	0.568253i
$765$		0			0
$766$	−18.5018	+	39.2209i	−0.668498	+	1.41711i
$767$	51.6038			1.86330
$768$		0			0
$769$	−50.3024			−1.81395			−0.906976	−	0.421182i	$-0.861615\pi$
$769$	−50.3024			−1.81395			−0.906976	+	0.421182i	$0.861615\pi$
$770$	−17.5473	+	37.1973i	−0.632359	+	1.34050i
$771$		0			0
$772$	9.12560	+	11.0741i	0.328438	+	0.398564i
$773$	0.373623	−	0.154760i	0.0134383	−	0.00556632i	−0.375954	−	0.926638i	$-0.622685\pi$
$773$	0.373623	−	0.154760i	0.0134383	−	0.00556632i	0.389392	+	0.921072i	$0.372685\pi$
$774$		0			0
$775$	−45.0134	+	45.0134i	−1.61693	+	1.61693i
$776$	1.85782	−	0.471325i	0.0666919	−	0.0169196i
$777$		0			0
$778$	0.732649	−	15.2260i	0.0262667	−	0.545880i
$779$	0.587635	+	1.41868i	0.0210542	+	0.0508294i
$780$		0			0
$781$	5.20546	+	2.15617i	0.186266	+	0.0771540i
$782$	−1.09634	−	3.05438i	−0.0392051	−	0.109224i
$783$		0			0
$784$	−6.43980	−	1.25403i	−0.229993	−	0.0447868i
$785$		−	77.5349i		−	2.76734i
$786$		0			0
$787$	−13.9620	−	5.78325i	−0.497692	−	0.206151i	0.119695	−	0.992811i	$-0.461808\pi$
$787$	−13.9620	−	5.78325i	−0.497692	−	0.206151i	−0.617386	+	0.786660i	$0.711808\pi$
$788$	18.7520	+	9.97467i	0.668012	+	0.355333i
$789$		0			0
$790$	4.00221	+	0.192579i	0.142392	+	0.00685166i
$791$	5.89999	+	5.89999i	0.209779	+	0.209779i
$792$		0			0
$793$	−22.1736	+	22.1736i	−0.787408	+	0.787408i
$794$	37.5333	−	34.0870i	1.33201	−	1.20970i
$795$		0			0
$796$	22.3226	+	2.15323i	0.791204	+	0.0763193i
$797$	1.14025	−	2.75280i	0.0403896	−	0.0975092i	−0.902397	−	0.430905i	$-0.858194\pi$
$797$	1.14025	−	2.75280i	0.0403896	−	0.0975092i	0.942787	+	0.333396i	$0.108194\pi$
$798$		0			0
$799$	4.81584			0.170372
$800$	61.1492	−	9.38530i	2.16195	−	0.331821i
$801$		0			0
$802$	1.54969	+	0.731042i	0.0547215	+	0.0258140i
$803$	−12.8000	+	30.9019i	−0.451701	+	1.09050i
$804$		0			0
$805$	38.3011	−	15.8648i	1.34994	−	0.559162i
$806$	21.7750	−	19.7757i	0.766992	−	0.696569i
$807$		0			0
$808$	24.5580	−	18.3286i	0.863946	−	0.644798i
$809$	15.2034	+	15.2034i	0.534524	+	0.534524i	0.921915	−	0.387392i	$-0.126624\pi$
$809$	15.2034	+	15.2034i	0.534524	+	0.534524i	−0.387392	+	0.921915i	$0.626624\pi$
$810$		0			0
$811$	−1.72375	−	4.16149i	−0.0605289	−	0.146130i	0.890721	−	0.454550i	$-0.150200\pi$
$811$	−1.72375	−	4.16149i	−0.0605289	−	0.146130i	−0.951250	+	0.308420i	$0.900200\pi$
$812$	15.6308	−	29.3853i	0.548535	−	1.03122i
$813$		0			0
$814$	25.0919	−	9.00652i	0.879471	−	0.315678i
$815$			62.0357i			2.17302i
$816$		0			0
$817$		−	0.939986i		−	0.0328859i
$818$	13.5392	+	37.7198i	0.473386	+	1.31884i
$819$		0			0
$820$	−13.0268	−	42.6344i	−0.454914	−	1.48886i
$821$	18.5191	+	44.7092i	0.646323	+	1.56036i	0.818007	+	0.575209i	$0.195079\pi$
$821$	18.5191	+	44.7092i	0.646323	+	1.56036i	−0.171684	+	0.985152i	$0.554921\pi$
$822$		0			0
$823$	−9.78250	−	9.78250i	−0.340996	−	0.340996i	0.515745	−	0.856742i	$-0.327515\pi$
$823$	−9.78250	−	9.78250i	−0.340996	−	0.340996i	−0.856742	+	0.515745i	$0.827515\pi$
$824$	−16.8838	+	28.3627i	−0.588174	+	0.988061i
$825$		0			0
$826$	−31.7886	−	35.0025i	−1.10607	−	1.21789i
$827$	−21.3770	+	8.85466i	−0.743352	+	0.307907i	−0.722026	−	0.691866i	$-0.756789\pi$
$827$	−21.3770	+	8.85466i	−0.743352	+	0.307907i	−0.0213264	+	0.999773i	$0.506789\pi$
$828$		0			0
$829$	−4.53604	+	10.9510i	−0.157543	+	0.380343i	−0.982867	−	0.184317i	$-0.940993\pi$
$829$	−4.53604	+	10.9510i	−0.157543	+	0.380343i	0.825324	+	0.564660i	$0.190993\pi$
$830$	−3.67143	+	7.78284i	−0.127437	+	0.270146i
$831$		0			0
$832$	−28.4310	+	2.97365i	−0.985669	+	0.103093i
$833$	0.839056			0.0290716
$834$		0			0
$835$	−23.1356	+	55.8543i	−0.800640	+	1.93292i
$836$	1.33569	−	1.10068i	0.0461958	−	0.0380678i
$837$		0			0
$838$	3.35018	+	3.68889i	0.115730	+	0.127430i
$839$	−2.23832	+	2.23832i	−0.0772752	+	0.0772752i	−0.744688	−	0.667413i	$-0.767402\pi$
$839$	−2.23832	+	2.23832i	−0.0772752	+	0.0772752i	0.667413	+	0.744688i	$0.267402\pi$
$840$		0			0
$841$	−16.0319	−	16.0319i	−0.552826	−	0.552826i
$842$	0.766660	−	15.9329i	0.0264208	−	0.549082i
$843$		0			0
$844$	15.1627	+	49.6251i	0.521923	+	1.70816i
$845$	0.854786	+	0.354064i	0.0294055	+	0.0121802i
$846$		0			0
$847$			2.54232i			0.0873551i
$848$	25.6578	−	5.21110i	0.881092	−	0.178950i
$849$		0			0
$850$	−7.44675	+	2.67295i	−0.255422	+	0.0916813i
$851$	−24.8267	−	10.2835i	−0.851047	−	0.352515i
$852$		0			0
$853$	8.29470	+	20.0252i	0.284005	+	0.685649i	0.999921	−	0.0125373i	$-0.00399085\pi$
$853$	8.29470	+	20.0252i	0.284005	+	0.685649i	−0.715916	+	0.698186i	$0.753991\pi$
$854$	28.6994	+	1.38096i	0.982074	+	0.0472556i
$855$		0			0
$856$	−0.716407	−	0.959893i	−0.0244863	−	0.0328085i
$857$	−20.9308	+	20.9308i	−0.714984	+	0.714984i	−0.967574	−	0.252590i	$-0.918718\pi$
$857$	−20.9308	+	20.9308i	−0.714984	+	0.714984i	0.252590	+	0.967574i	$0.418718\pi$
$858$		0			0
$859$	4.72981	−	1.95915i	0.161379	−	0.0668453i	−0.300532	−	0.953772i	$-0.597164\pi$
$859$	4.72981	−	1.95915i	0.161379	−	0.0668453i	0.461911	+	0.886927i	$0.347164\pi$
$860$	−2.62017	+	27.1634i	−0.0893470	+	0.926263i
$861$		0			0
$862$	−45.5893	−	21.5060i	−1.55278	−	0.732498i
$863$	−52.6045			−1.79068			−0.895340	−	0.445384i	$-0.853067\pi$
$863$	−52.6045			−1.79068			−0.895340	+	0.445384i	$0.853067\pi$
$864$		0			0
$865$	10.6517			0.362168
$866$	12.4764	+	5.88554i	0.423965	+	0.199999i
$867$		0			0
$868$	−26.8274	−	2.58776i	−0.910581	−	0.0878344i
$869$	−2.06332	+	0.854656i	−0.0699934	+	0.0289922i
$870$		0			0
$871$	7.37126	−	7.37126i	0.249766	−	0.249766i
$872$	−16.4191	−	2.38491i	−0.556021	−	0.0807632i
$873$		0			0
$874$	−1.74257	−	0.0838494i	−0.0589434	−	0.00283625i
$875$	−20.9955	−	50.6876i	−0.709778	−	1.71355i
$876$		0			0
$877$	−41.7255	−	17.2833i	−1.40897	−	0.583614i	−0.456906	−	0.889515i	$-0.651042\pi$
$877$	−41.7255	−	17.2833i	−1.40897	−	0.583614i	−0.952063	+	0.305901i	$0.901042\pi$
$878$	−21.2044	+	7.61112i	−0.715613	+	0.256863i
$879$		0			0
$880$	−41.6664	+	28.0838i	−1.40457	+	0.946706i
$881$		−	51.6942i		−	1.74162i	−0.491619	−	0.870811i	$-0.663595\pi$
$881$		−	51.6942i		−	1.74162i	0.491619	−	0.870811i	$-0.336405\pi$
$882$		0			0
$883$	28.5743	+	11.8358i	0.961601	+	0.398308i	0.807579	−	0.589760i	$-0.200777\pi$
$883$	28.5743	+	11.8358i	0.961601	+	0.398308i	0.154022	+	0.988067i	$0.450777\pi$
$884$	3.49632	−	1.06828i	0.117594	−	0.0359303i
$885$		0			0
$886$	−1.63317	+	33.9407i	−0.0548673	+	1.14026i
$887$	−10.8240	−	10.8240i	−0.363433	−	0.363433i	0.501642	−	0.865075i	$-0.332729\pi$
$887$	−10.8240	−	10.8240i	−0.363433	−	0.363433i	−0.865075	+	0.501642i	$0.832729\pi$
$888$		0			0
$889$	0.240075	−	0.240075i	0.00805187	−	0.00805187i
$890$	0.459958	+	0.506461i	0.0154178	+	0.0169766i
$891$		0			0
$892$	0.729071	+	0.884739i	0.0244111	+	0.0296232i
$893$	0.990755	−	2.39189i	0.0331543	−	0.0800417i
$894$		0			0
$895$	42.2284			1.41154
$896$	19.5309	+	17.4528i	0.652482	+	0.583056i
$897$		0			0
$898$	7.59224	−	16.0943i	0.253356	−	0.537075i
$899$	−16.0123	+	38.6572i	−0.534042	+	1.28929i
$900$		0			0
$901$	−3.09349	+	1.28136i	−0.103059	+	0.0426884i
$902$	16.7054	+	18.3943i	0.556229	+	0.612464i
$903$		0			0
$904$	2.50673	+	9.88079i	0.0833727	+	0.328630i
$905$	54.3201	+	54.3201i	1.80566	+	1.80566i
$906$		0			0
$907$	−12.4155	−	29.9736i	−0.412249	−	0.995257i	−0.984533	−	0.175201i	$-0.943942\pi$
$907$	−12.4155	−	29.9736i	−0.412249	−	0.995257i	0.572284	−	0.820056i	$-0.306058\pi$
$908$	−7.21475	+	2.20444i	−0.239430	+	0.0731568i
$909$		0			0
$910$	15.7782	+	43.9575i	0.523041	+	1.45718i
$911$			27.7454i			0.919247i	0.888114	+	0.459623i	$0.152016\pi$
$911$			27.7454i			0.919247i	−0.888114	+	0.459623i	$0.847984\pi$
$912$		0			0
$913$		−	4.79643i		−	0.158739i
$914$	−54.3052	+	19.4924i	−1.79626	+	0.644750i
$915$		0			0
$916$	13.5779	+	7.22242i	0.448625	+	0.238635i
$917$	−2.69204	−	6.49915i	−0.0888989	−	0.214621i
$918$		0			0
$919$	−22.9579	−	22.9579i	−0.757311	−	0.757311i	0.218521	−	0.975832i	$-0.429877\pi$
$919$	−22.9579	−	22.9579i	−0.757311	−	0.757311i	−0.975832	+	0.218521i	$0.929877\pi$
$920$	50.1225	+	7.28039i	1.65249	+	0.240027i
$921$		0			0
$922$	−13.3926	+	12.1629i	−0.441061	+	0.400564i
$923$	5.91107	−	2.44845i	0.194565	−	0.0805916i
$924$		0			0
$925$	−25.0719	+	60.5289i	−0.824359	+	1.99018i
$926$	23.0625	+	10.8794i	0.757881	+	0.357518i
$927$		0			0
$928$	34.7727	−	21.0805i	1.14147	−	0.692000i
$929$	14.7767			0.484807			0.242404	−	0.970175i	$-0.422064\pi$
$929$	14.7767			0.484807			0.242404	+	0.970175i	$0.422064\pi$
$930$		0			0
$931$	0.172618	−	0.416736i	0.00565731	−	0.0136580i
$932$	−0.375114	+	3.88882i	−0.0122873	+	0.127383i
$933$		0			0
$934$	25.2160	−	22.9007i	0.825093	−	0.749334i
$935$	4.54396	−	4.54396i	0.148603	−	0.148603i
$936$		0			0
$937$	25.7038	+	25.7038i	0.839707	+	0.839707i	0.988820	−	0.149113i	$-0.0476418\pi$
$937$	25.7038	+	25.7038i	0.839707	+	0.839707i	−0.149113	+	0.988820i	$0.547642\pi$
$938$	−9.54067	−	0.459080i	−0.311514	−	0.0149895i
$939$		0			0
$940$	−35.2978	+	66.3584i	−1.15129	+	2.16437i
$941$	4.00523	+	1.65902i	0.130567	+	0.0540826i	0.447010	−	0.894529i	$-0.352489\pi$
$941$	4.00523	+	1.65902i	0.130567	+	0.0540826i	−0.316443	+	0.948611i	$0.602489\pi$
$942$		0			0
$943$		−	25.0464i		−	0.815622i
$944$	−11.4977	−	56.6107i	−0.374217	−	1.84252i
$945$		0			0
$946$	−5.13868	−	14.3162i	−0.167073	−	0.465460i
$947$	15.2678	+	6.32413i	0.496136	+	0.205506i	0.616699	−	0.787199i	$-0.288470\pi$
$947$	15.2678	+	6.32413i	0.496136	+	0.205506i	−0.120562	+	0.992706i	$0.538470\pi$
$948$		0			0
$949$	14.5350	+	35.0907i	0.471827	+	1.13909i
$950$	−0.204430	+	4.24850i	−0.00663258	+	0.137839i
$951$		0			0
$952$	−2.87839	−	1.71345i	−0.0932890	−	0.0555332i
$953$	−19.6560	+	19.6560i	−0.636719	+	0.636719i	−0.949745	−	0.313026i	$-0.898657\pi$
$953$	−19.6560	+	19.6560i	−0.636719	+	0.636719i	0.313026	+	0.949745i	$0.398657\pi$
$954$		0			0
$955$	37.5320	−	15.5463i	1.21451	−	0.503065i
$956$	−7.07609	+	5.83107i	−0.228857	+	0.188590i
$957$		0			0
$958$	−6.78941	+	14.3924i	−0.219356	+	0.464999i
$959$	−38.2709			−1.23583
$960$		0			0
$961$	2.88209			0.0929707
$962$	12.9159	−	27.3795i	0.416424	−	0.882752i
$963$		0			0
$964$	−24.6262	+	20.2933i	−0.793156	+	0.653602i
$965$	26.4618	−	10.9608i	0.851836	−	0.352842i
$966$		0			0
$967$	13.4891	−	13.4891i	0.433781	−	0.433781i	−0.456131	−	0.889912i	$-0.650765\pi$
$967$	13.4891	−	13.4891i	0.433781	−	0.433781i	0.889912	+	0.456131i	$0.150765\pi$
$968$	−1.58875	+	2.66891i	−0.0510644	+	0.0857820i
$969$		0			0
$970$	0.183874	−	3.82129i	0.00590383	−	0.122694i
$971$	−16.3983	−	39.5889i	−0.526246	−	1.27047i	−0.933966	−	0.357362i	$-0.883676\pi$
$971$	−16.3983	−	39.5889i	−0.526246	−	1.27047i	0.407720	−	0.913107i	$-0.366324\pi$
$972$		0			0
$973$	−44.4940	−	18.4300i	−1.42641	−	0.590840i
$974$	15.6248	+	43.5302i	0.500650	+	1.39480i
$975$		0			0
$976$	29.2655	+	19.3846i	0.936764	+	0.620486i
$977$		−	15.7216i		−	0.502979i	−0.967860	−	0.251489i	$-0.919080\pi$
$977$		−	15.7216i		−	0.502979i	0.967860	−	0.251489i	$-0.0809203\pi$
$978$		0			0
$979$	−0.352304	−	0.145929i	−0.0112597	−	0.00466391i
$980$	−6.14987	+	11.5615i	−0.196451	+	0.369319i
$981$		0			0
$982$	36.6510	+	1.76358i	1.16958	+	0.0562781i
$983$	−10.9749	−	10.9749i	−0.350046	−	0.350046i	0.510080	−	0.860127i	$-0.329616\pi$
$983$	−10.9749	−	10.9749i	−0.350046	−	0.350046i	−0.860127	+	0.510080i	$0.829616\pi$
$984$		0			0
$985$	29.9778	−	29.9778i	0.955173	−	0.955173i
$986$	−3.84977	+	3.49629i	−0.122602	+	0.111345i
$987$		0			0
$988$	0.188704	−	1.95630i	0.00600347	−	0.0622382i
$989$	−5.86728	+	14.1649i	−0.186569	+	0.450417i
$990$		0			0
$991$	32.2476			1.02438			0.512190	−	0.858872i	$-0.328834\pi$
$991$	32.2476			1.02438			0.512190	+	0.858872i	$0.328834\pi$
$992$	−26.5461	−	19.4816i	−0.842838	−	0.618542i
$993$		0			0
$994$	−5.30206	−	2.50116i	−0.168171	−	0.0793321i
$995$	17.1301	−	41.3557i	0.543061	−	1.31107i
$996$		0			0
$997$	22.2570	−	9.21915i	0.704886	−	0.291973i	−0.00130036	−	0.999999i	$-0.500414\pi$
$997$	22.2570	−	9.21915i	0.704886	−	0.291973i	0.706187	+	0.708026i	$0.250414\pi$
$998$	−0.751023	+	0.682065i	−0.0237732	+	0.0215904i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.109.6		32
3.2	odd	2		96.2.n.a.13.3	✓	32
4.3	odd	2		1152.2.v.c.145.1		32
12.11	even	2		384.2.n.a.145.4		32
24.5	odd	2		768.2.n.a.289.1		32
24.11	even	2		768.2.n.b.289.5		32
32.5	even	8	inner	288.2.v.d.37.6		32
32.27	odd	8		1152.2.v.c.1009.1		32
96.5	odd	8		96.2.n.a.37.3	yes	32
96.11	even	8		768.2.n.b.481.5		32
96.53	odd	8		768.2.n.a.481.1		32
96.59	even	8		384.2.n.a.241.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.3	✓	32	3.2	odd	2
96.2.n.a.37.3	yes	32	96.5	odd	8
288.2.v.d.37.6		32	32.5	even	8	inner
288.2.v.d.109.6		32	1.1	even	1	trivial
384.2.n.a.145.4		32	12.11	even	2
384.2.n.a.241.4		32	96.59	even	8
768.2.n.a.289.1		32	24.5	odd	2
768.2.n.a.481.1		32	96.53	odd	8
768.2.n.b.289.5		32	24.11	even	2
768.2.n.b.481.5		32	96.11	even	8
1152.2.v.c.145.1		32	4.3	odd	2
1152.2.v.c.1009.1		32	32.27	odd	8

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)

\(f(q)\)	\(=\)	\(q+(0.603367 - 1.27904i) q^{2} +(-1.27190 - 1.54346i) q^{4} +(-3.68816 + 1.52768i) q^{5} +(-1.63704 + 1.63704i) q^{7} +(-2.74158 + 0.695531i) q^{8} +O(q^{10})\)	\(q+(0.603367 - 1.27904i) q^{2} +(-1.27190 - 1.54346i) q^{4} +(-3.68816 + 1.52768i) q^{5} +(-1.63704 + 1.63704i) q^{7} +(-2.74158 + 0.695531i) q^{8} +(-0.271341 + 5.63906i) q^{10} +(-1.20420 - 2.90719i) q^{11} +(-3.30127 - 1.36743i) q^{13} +(1.10611 + 3.08158i) q^{14} +(-0.764563 + 3.92625i) q^{16} -0.511560i q^{17} +(-0.254077 - 0.105242i) q^{19} +(7.04888 + 3.74948i) q^{20} +(-4.44500 - 0.213885i) q^{22} +(3.17185 + 3.17185i) q^{23} +(7.73315 - 7.73315i) q^{25} +(-3.74088 + 3.39740i) q^{26} +(4.60886 + 0.444569i) q^{28} +(2.75087 - 6.64118i) q^{29} -5.82083 q^{31} +(4.56053 + 3.34688i) q^{32} +(-0.654306 - 0.308659i) q^{34} +(3.53678 - 8.53855i) q^{35} +(-5.53467 + 2.29253i) q^{37} +(-0.287911 + 0.261476i) q^{38} +(9.04881 - 6.75349i) q^{40} +(-3.94823 - 3.94823i) q^{41} +(1.30801 + 3.15781i) q^{43} +(-2.95553 + 5.55628i) q^{44} +(5.97071 - 2.14313i) q^{46} +9.41403i q^{47} +1.64019i q^{49} +(-5.22509 - 14.5570i) q^{50} +(2.08829 + 6.83462i) q^{52} +(-2.50482 - 6.04717i) q^{53} +(8.88255 + 8.88255i) q^{55} +(3.34946 - 5.62669i) q^{56} +(-6.83457 - 7.52555i) q^{58} +(-13.3423 + 5.52657i) q^{59} +(3.35835 - 8.10777i) q^{61} +(-3.51210 + 7.44509i) q^{62} +(7.03247 - 3.81370i) q^{64} +14.2646 q^{65} +(-1.11643 + 2.69530i) q^{67} +(-0.789574 + 0.650651i) q^{68} +(-8.78718 - 9.67558i) q^{70} +(-1.26611 + 1.26611i) q^{71} +(-7.51616 - 7.51616i) q^{73} +(-0.407191 + 8.46231i) q^{74} +(0.160722 + 0.526017i) q^{76} +(6.73052 + 2.78787i) q^{77} -0.709730i q^{79} +(-3.17824 - 15.6486i) q^{80} +(-7.43218 + 2.66772i) q^{82} +(1.40823 + 0.583309i) q^{83} +(0.781502 + 1.88671i) q^{85} +(4.82818 + 0.232323i) q^{86} +(5.32345 + 7.13273i) q^{88} +(0.0856897 - 0.0856897i) q^{89} +(7.64285 - 3.16577i) q^{91} +(0.861374 - 8.92989i) q^{92} +(12.0409 + 5.68012i) q^{94} +1.09785 q^{95} -0.677647 q^{97} +(2.09787 + 0.989638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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