LMFDB - Embedded newform 1512.2.s.n.1297.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(865,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1512.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.s (of order $3$, degree $2$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} + 28x^{5} + 14x^{4} - 52x^{3} + 306x^{2} + 1052x + 1051 $ x^8 - 3x^7 + 4x^6 + 28x^5 + 14x^4 - 52x^3 + 306x^2 + 1052*x + 1051
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1297.4
Root			$-1.54823 + 0.711712i$ of defining polynomial
Character	$\chi$	$=$	1512.1297
Dual form			1512.2.s.n.865.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99232 - 3.45080i) q^{5} +(-0.657753 + 2.56269i) q^{7} +O(q^{10})$	$q+(1.99232 - 3.45080i) q^{5} +(-0.657753 + 2.56269i) q^{7} +(-0.444095 - 0.769196i) q^{11} -6.98465 q^{13} +(-0.342247 - 0.592789i) q^{17} +(1.73272 - 3.00116i) q^{19} +(2.94638 - 5.10328i) q^{23} +(-5.43870 - 9.42011i) q^{25} -5.87741 q^{29} +(-0.604133 - 1.04639i) q^{31} +(7.53287 + 7.37548i) q^{35} +(4.32689 - 7.49440i) q^{37} -6.30015 q^{41} +0.888190 q^{43} +(1.59417 - 2.76119i) q^{47} +(-6.13472 - 3.37123i) q^{49} +(-0.890475 - 1.54235i) q^{53} -3.53912 q^{55} +(5.11552 + 8.86034i) q^{59} +(0.882798 - 1.52905i) q^{61} +(-13.9157 + 24.1027i) q^{65} +(-5.83457 - 10.1058i) q^{67} -8.50385 q^{71} +(5.14240 + 8.90690i) q^{73} +(2.26331 - 0.632136i) q^{77} +(-2.64011 + 4.57281i) q^{79} +11.4120 q^{83} -2.72747 q^{85} +(5.77099 - 9.99565i) q^{89} +(4.59417 - 17.8995i) q^{91} +(-6.90428 - 11.9586i) q^{95} -10.6003 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} - 4 q^{7}+O(q^{10}) $ 8 * q - 2 * q^5 - 4 * q^7	$ 8 q - 2 q^{5} - 4 q^{7} - q^{11} - 20 q^{13} - 4 q^{17} + q^{19} + 12 q^{23} - 14 q^{25} + 12 q^{29} + 8 q^{31} + 9 q^{35} - 12 q^{41} + 2 q^{43} - 9 q^{47} + 6 q^{49} + 7 q^{53} - 36 q^{55} - 4 q^{59} - 25 q^{61} - 28 q^{65} - 30 q^{67} - 22 q^{71} + 4 q^{73} - 37 q^{77} + 7 q^{79} + 58 q^{83} + 14 q^{85} + 9 q^{89} + 15 q^{91} - 4 q^{95} - 8 q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 - 4 * q^7 - q^11 - 20 * q^13 - 4 * q^17 + q^19 + 12 * q^23 - 14 * q^25 + 12 * q^29 + 8 * q^31 + 9 * q^35 - 12 * q^41 + 2 * q^43 - 9 * q^47 + 6 * q^49 + 7 * q^53 - 36 * q^55 - 4 * q^59 - 25 * q^61 - 28 * q^65 - 30 * q^67 - 22 * q^71 + 4 * q^73 - 37 * q^77 + 7 * q^79 + 58 * q^83 + 14 * q^85 + 9 * q^89 + 15 * q^91 - 4 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.99232	−	3.45080i	0.890994	−	1.54325i	0.0523084	−	0.998631i	$-0.483342\pi$
$5$	1.99232	−	3.45080i	0.890994	−	1.54325i	0.838686	−	0.544616i	$-0.183325\pi$
$6$		0			0
$7$	−0.657753	+	2.56269i	−0.248607	+	0.968604i
$7$	−0.657753	+	2.56269i	−0.248607	+	0.968604i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.444095	−	0.769196i	−0.133900	−	0.231921i	0.791277	−	0.611458i	$-0.209417\pi$
$11$	−0.444095	−	0.769196i	−0.133900	−	0.231921i	−0.925177	+	0.379537i	$0.876083\pi$
$12$		0			0
$13$	−6.98465			−1.93719			−0.968596	−	0.248639i	$-0.920017\pi$
$13$	−6.98465			−1.93719			−0.968596	+	0.248639i	$0.920017\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.342247	−	0.592789i	−0.0830071	−	0.143773i	0.821533	−	0.570161i	$-0.193119\pi$
$17$	−0.342247	−	0.592789i	−0.0830071	−	0.143773i	−0.904540	+	0.426388i	$0.859786\pi$
$18$		0			0
$19$	1.73272	−	3.00116i	0.397514	−	0.688514i	−0.595905	−	0.803055i	$-0.703206\pi$
$19$	1.73272	−	3.00116i	0.397514	−	0.688514i	0.993419	+	0.114541i	$0.0365398\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.94638	−	5.10328i	0.614363	−	1.06411i	−0.376133	−	0.926566i	$-0.622747\pi$
$23$	2.94638	−	5.10328i	0.614363	−	1.06411i	0.990496	−	0.137542i	$-0.0439201\pi$
$24$		0			0
$25$	−5.43870	−	9.42011i	−1.08774	−	1.88402i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.87741			−1.09141			−0.545703	−	0.837978i	$-0.683737\pi$
$29$	−5.87741			−1.09141			−0.545703	+	0.837978i	$0.683737\pi$
$30$		0			0
$31$	−0.604133	−	1.04639i	−0.108505	−	0.187937i	0.806660	−	0.591016i	$-0.201273\pi$
$31$	−0.604133	−	1.04639i	−0.108505	−	0.187937i	−0.915165	+	0.403079i	$0.867940\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.53287	+	7.37548i	1.27329	+	1.24668i
$36$		0			0
$37$	4.32689	−	7.49440i	0.711337	−	1.23207i	−0.253019	−	0.967461i	$-0.581423\pi$
$37$	4.32689	−	7.49440i	0.711337	−	1.23207i	0.964355	−	0.264610i	$-0.0852433\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.30015			−0.983918			−0.491959	−	0.870618i	$-0.663719\pi$
$41$	−6.30015			−0.983918			−0.491959	+	0.870618i	$0.663719\pi$
$42$		0			0
$43$	0.888190			0.135448			0.0677239	−	0.997704i	$-0.478426\pi$
$43$	0.888190			0.135448			0.0677239	+	0.997704i	$0.478426\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.59417	−	2.76119i	0.232534	−	0.402760i	−0.726019	−	0.687674i	$-0.758632\pi$
$47$	1.59417	−	2.76119i	0.232534	−	0.402760i	0.958553	+	0.284914i	$0.0919650\pi$
$48$		0			0
$49$	−6.13472	−	3.37123i	−0.876389	−	0.481604i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.890475	−	1.54235i	−0.122316	−	0.211858i	0.798365	−	0.602174i	$-0.205699\pi$
$53$	−0.890475	−	1.54235i	−0.122316	−	0.211858i	−0.920681	+	0.390317i	$0.872366\pi$
$54$		0			0
$55$	−3.53912			−0.477215
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.11552	+	8.86034i	0.665984	+	1.15352i	0.979018	+	0.203776i	$0.0653214\pi$
$59$	5.11552	+	8.86034i	0.665984	+	1.15352i	−0.313034	+	0.949742i	$0.601345\pi$
$60$		0			0
$61$	0.882798	−	1.52905i	0.113031	−	0.195775i	−0.803960	−	0.594683i	$-0.797277\pi$
$61$	0.882798	−	1.52905i	0.113031	−	0.195775i	0.916991	+	0.398908i	$0.130611\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−13.9157	+	24.1027i	−1.72603	+	2.98957i
$66$		0			0
$67$	−5.83457	−	10.1058i	−0.712806	−	1.23462i	−0.963800	−	0.266628i	$-0.914091\pi$
$67$	−5.83457	−	10.1058i	−0.712806	−	1.23462i	0.250993	−	0.967989i	$-0.419243\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.50385			−1.00922			−0.504611	−	0.863347i	$-0.668364\pi$
$71$	−8.50385			−1.00922			−0.504611	+	0.863347i	$0.668364\pi$
$72$		0			0
$73$	5.14240	+	8.90690i	0.601872	+	1.04247i	0.992537	+	0.121941i	$0.0389117\pi$
$73$	5.14240	+	8.90690i	0.601872	+	1.04247i	−0.390665	+	0.920533i	$0.627755\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.26331	−	0.632136i	0.257928	−	0.0720386i
$78$		0			0
$79$	−2.64011	+	4.57281i	−0.297036	+	0.514482i	−0.975456	−	0.220192i	$-0.929332\pi$
$79$	−2.64011	+	4.57281i	−0.297036	+	0.514482i	0.678420	+	0.734674i	$0.262665\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	11.4120			1.25263			0.626313	−	0.779572i	$-0.284563\pi$
$83$	11.4120			1.25263			0.626313	+	0.779572i	$0.284563\pi$
$84$		0			0
$85$	−2.72747			−0.295835
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.77099	−	9.99565i	0.611724	−	1.05954i	−0.379226	−	0.925304i	$-0.623810\pi$
$89$	5.77099	−	9.99565i	0.611724	−	1.05954i	0.990950	−	0.134232i	$-0.0428568\pi$
$90$		0			0
$91$	4.59417	−	17.8995i	0.481600	−	1.87637i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.90428	−	11.9586i	−0.708365	−	1.22692i
$96$		0			0
$97$	−10.6003			−1.07630			−0.538149	−	0.842850i	$-0.680876\pi$
$97$	−10.6003			−1.07630			−0.538149	+	0.842850i	$0.680876\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.29248	+	12.6309i	0.725628	+	1.25683i	0.958715	+	0.284369i	$0.0917842\pi$
$101$	7.29248	+	12.6309i	0.725628	+	1.25683i	−0.233086	+	0.972456i	$0.574883\pi$
$102$		0			0
$103$	−7.88280	+	13.6534i	−0.776715	+	1.34531i	0.157110	+	0.987581i	$0.449782\pi$
$103$	−7.88280	+	13.6534i	−0.776715	+	1.34531i	−0.933825	+	0.357729i	$0.883551\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.869126	−	1.50537i	0.0840216	−	0.145530i	−0.820952	−	0.570997i	$-0.806557\pi$
$107$	0.869126	−	1.50537i	0.0840216	−	0.145530i	0.904974	+	0.425467i	$0.139890\pi$
$108$		0			0
$109$	−3.31551	−	5.74262i	−0.317568	−	0.550044i	0.662412	−	0.749140i	$-0.269533\pi$
$109$	−3.31551	−	5.74262i	−0.317568	−	0.550044i	−0.979980	+	0.199096i	$0.936199\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.17299			−0.204418			−0.102209	−	0.994763i	$-0.532591\pi$
$113$	−2.17299			−0.204418			−0.102209	+	0.994763i	$0.532591\pi$
$114$		0			0
$115$	−11.7403	−	20.3348i	−1.09479	−	1.89623i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.74425	−	0.487163i	0.159895	−	0.0446582i
$120$		0			0
$121$	5.10556	−	8.84309i	0.464142	−	0.803917i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−23.4194			−2.09469
$126$		0			0
$127$	−19.2387			−1.70716			−0.853581	−	0.520960i	$-0.825574\pi$
$127$	−19.2387			−1.70716			−0.853581	+	0.520960i	$0.825574\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.5198	−	18.2208i	0.919120	−	1.59196i	0.118364	−	0.992970i	$-0.462235\pi$
$131$	10.5198	−	18.2208i	0.919120	−	1.59196i	0.800755	−	0.598992i	$-0.204432\pi$
$132$		0			0
$133$	6.55134	+	6.41445i	0.568073	+	0.556203i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.66914	−	6.35514i	−0.313476	−	0.542956i	0.665637	−	0.746276i	$-0.268160\pi$
$137$	−3.66914	−	6.35514i	−0.313476	−	0.542956i	−0.979112	+	0.203320i	$0.934827\pi$
$138$		0			0
$139$	9.17756			0.778430			0.389215	−	0.921147i	$-0.372746\pi$
$139$	9.17756			0.778430			0.389215	+	0.921147i	$0.372746\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.10185	+	5.37256i	0.259390	+	0.449276i
$144$		0			0
$145$	−11.7097	+	20.2818i	−0.972437	+	1.68431i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.1002	−	19.2261i	0.909361	−	1.57506i	0.0944073	−	0.995534i	$-0.469904\pi$
$149$	11.1002	−	19.2261i	0.909361	−	1.57506i	0.814954	−	0.579526i	$-0.196762\pi$
$150$		0			0
$151$	0.326893	+	0.566196i	0.0266022	+	0.0460764i	0.879020	−	0.476785i	$-0.158198\pi$
$151$	0.326893	+	0.566196i	0.0266022	+	0.0460764i	−0.852418	+	0.522861i	$0.824865\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.81451			−0.386711
$156$		0			0
$157$	2.48236	+	4.29958i	0.198114	+	0.343144i	0.947917	−	0.318518i	$-0.103185\pi$
$157$	2.48236	+	4.29958i	0.198114	+	0.343144i	−0.749803	+	0.661661i	$0.769852\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	11.1401	+	10.9073i	0.877964	+	0.859619i
$162$		0			0
$163$	−6.93642	+	12.0142i	−0.543302	+	0.941027i	0.455409	+	0.890282i	$0.349493\pi$
$163$	−6.93642	+	12.0142i	−0.543302	+	0.941027i	−0.998712	+	0.0507449i	$0.983840\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	20.1084			1.55604			0.778019	−	0.628241i	$-0.216225\pi$
$167$	20.1084			1.55604			0.778019	+	0.628241i	$0.216225\pi$
$168$		0			0
$169$	35.7853			2.75271
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.730438	−	1.26516i	0.0555341	−	0.0961880i	−0.836922	−	0.547322i	$-0.815647\pi$
$173$	0.730438	−	1.26516i	0.0555341	−	0.0961880i	0.892456	+	0.451134i	$0.148981\pi$
$174$		0			0
$175$	27.7181	−	7.74159i	2.09529	−	0.585209i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.88508	+	8.46121i	0.365128	+	0.632421i	0.988797	−	0.149268i	$-0.0476918\pi$
$179$	4.88508	+	8.46121i	0.365128	+	0.632421i	−0.623669	+	0.781689i	$0.714358\pi$
$180$		0			0
$181$	1.83928			0.136712			0.0683562	−	0.997661i	$-0.478225\pi$
$181$	1.83928			0.136712			0.0683562	+	0.997661i	$0.478225\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−17.2411	−	29.8625i	−1.26759	−	2.19554i
$186$		0			0
$187$	−0.303981	+	0.526510i	−0.0222293	+	0.0385022i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.44410	−	2.50125i	0.104491	−	0.180984i	−0.809039	−	0.587755i	$-0.800012\pi$
$191$	1.44410	−	2.50125i	0.104491	−	0.180984i	0.913530	+	0.406771i	$0.133345\pi$
$192$		0			0
$193$	−0.849924	−	1.47211i	−0.0611789	−	0.105965i	0.833814	−	0.552046i	$-0.186153\pi$
$193$	−0.849924	−	1.47211i	−0.0611789	−	0.105965i	−0.894993	+	0.446081i	$0.852819\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.5465			−1.10765			−0.553823	−	0.832635i	$-0.686831\pi$
$197$	−15.5465			−1.10765			−0.553823	+	0.832635i	$0.686831\pi$
$198$		0			0
$199$	−5.59646	−	9.69335i	−0.396722	−	0.687143i	0.596597	−	0.802541i	$-0.296519\pi$
$199$	−5.59646	−	9.69335i	−0.396722	−	0.687143i	−0.993319	+	0.115398i	$0.963186\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.86588	−	15.0619i	0.271332	−	1.05714i
$204$		0			0
$205$	−12.5519	+	21.7406i	−0.876665	+	1.51843i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.07797			−0.212908
$210$		0			0
$211$	17.3155			1.19205			0.596024	−	0.802966i	$-0.296746\pi$
$211$	17.3155			1.19205			0.596024	+	0.802966i	$0.296746\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.76956	−	3.06497i	0.120683	−	0.209029i
$216$		0			0
$217$	3.07894	−	0.859937i	0.209012	−	0.0583764i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.39048	+	4.14042i	0.160801	+	0.278515i
$222$		0			0
$223$	0.595735			0.0398934			0.0199467	−	0.999801i	$-0.493650\pi$
$223$	0.595735			0.0398934			0.0199467	+	0.999801i	$0.493650\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.4310	+	19.7991i	0.758704	+	1.31411i	0.943512	+	0.331339i	$0.107500\pi$
$227$	11.4310	+	19.7991i	0.758704	+	1.31411i	−0.184808	+	0.982775i	$0.559166\pi$
$228$		0			0
$229$	11.4830	−	19.8891i	0.758816	−	1.31431i	−0.184639	−	0.982806i	$-0.559112\pi$
$229$	11.4830	−	19.8891i	0.758816	−	1.31431i	0.943455	−	0.331501i	$-0.107555\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.41735	+	9.38313i	−0.354903	+	0.614709i	−0.987101	−	0.160097i	$-0.948819\pi$
$233$	−5.41735	+	9.38313i	−0.354903	+	0.614709i	0.632199	+	0.774806i	$0.282153\pi$
$234$		0			0
$235$	−6.35221	−	11.0023i	−0.414372	−	0.717714i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.60003			0.297551			0.148776	−	0.988871i	$-0.452467\pi$
$239$	4.60003			0.297551			0.148776	+	0.988871i	$0.452467\pi$
$240$		0			0
$241$	−4.68834	−	8.12045i	−0.302003	−	0.523084i	0.674587	−	0.738196i	$-0.264322\pi$
$241$	−4.68834	−	8.12045i	−0.302003	−	0.523084i	−0.976589	+	0.215112i	$0.930988\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−23.8558	+	14.4532i	−1.52409	+	0.923378i
$246$		0			0
$247$	−12.1025	+	20.9621i	−0.770061	+	1.33378i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.88819			0.119182			0.0595908	−	0.998223i	$-0.481020\pi$
$251$	1.88819			0.119182			0.0595908	+	0.998223i	$0.481020\pi$
$252$		0			0
$253$	−5.23389			−0.329052
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.9747	+	19.0087i	−0.684582	+	1.18573i	0.288986	+	0.957333i	$0.406682\pi$
$257$	−10.9747	+	19.0087i	−0.684582	+	1.18573i	−0.973568	+	0.228398i	$0.926651\pi$
$258$		0			0
$259$	16.3598	+	16.0179i	1.01655	+	0.995306i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.92106	+	17.1838i	0.611759	+	1.05960i	0.990944	+	0.134277i	$0.0428711\pi$
$263$	9.92106	+	17.1838i	0.611759	+	1.05960i	−0.379185	+	0.925321i	$0.623796\pi$
$264$		0			0
$265$	−7.09646			−0.435932
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.51139	+	11.2781i	0.397006	+	0.687635i	0.993355	−	0.115090i	$-0.0367158\pi$
$269$	6.51139	+	11.2781i	0.397006	+	0.687635i	−0.596349	+	0.802725i	$0.703382\pi$
$270$		0			0
$271$	−14.4211	+	24.9780i	−0.876017	+	1.51731i	−0.0203422	+	0.999793i	$0.506476\pi$
$271$	−14.4211	+	24.9780i	−0.876017	+	1.51731i	−0.855675	+	0.517513i	$0.826858\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.83060	+	8.36685i	−0.291296	+	0.504540i
$276$		0			0
$277$	−11.2051	−	19.4078i	−0.673251	−	1.16610i	−0.976977	−	0.213345i	$-0.931564\pi$
$277$	−11.2051	−	19.4078i	−0.673251	−	1.16610i	0.303726	−	0.952759i	$-0.401769\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.0965			0.960234			0.480117	−	0.877204i	$-0.340594\pi$
$281$	16.0965			0.960234			0.480117	+	0.877204i	$0.340594\pi$
$282$		0			0
$283$	15.4279	+	26.7219i	0.917095	+	1.58845i	0.803805	+	0.594892i	$0.202805\pi$
$283$	15.4279	+	26.7219i	0.917095	+	1.58845i	0.113289	+	0.993562i	$0.463861\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.14394	−	16.1453i	0.244609	−	0.953028i
$288$		0			0
$289$	8.26573	−	14.3167i	0.486220	−	0.842157i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.154783			−0.00904250			−0.00452125	−	0.999990i	$-0.501439\pi$
$293$	−0.154783			−0.00904250			−0.00452125	+	0.999990i	$0.501439\pi$
$294$		0			0
$295$	40.7671			2.37355
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−20.5794	+	35.6446i	−1.19014	+	2.06138i
$300$		0			0
$301$	−0.584210	+	2.27615i	−0.0336733	+	0.131195i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.51764	−	6.09273i	−0.201419	−	0.348869i
$306$		0			0
$307$	14.6430			0.835720			0.417860	−	0.908511i	$-0.362780\pi$
$307$	14.6430			0.835720			0.417860	+	0.908511i	$0.362780\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.7702	−	22.1186i	−0.724130	−	1.25423i	−0.959331	−	0.282283i	$-0.908908\pi$
$311$	−12.7702	−	22.1186i	−0.724130	−	1.25423i	0.235202	−	0.971947i	$-0.424425\pi$
$312$		0			0
$313$	−9.48465	+	16.4279i	−0.536104	+	0.928559i	0.463005	+	0.886356i	$0.346771\pi$
$313$	−9.48465	+	16.4279i	−0.536104	+	0.928559i	−0.999109	+	0.0422036i	$0.986562\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.395867	−	0.685662i	0.0222341	−	0.0385106i	−0.854694	−	0.519132i	$-0.826255\pi$
$317$	0.395867	−	0.685662i	0.0222341	−	0.0385106i	0.876928	+	0.480621i	$0.159589\pi$
$318$		0			0
$319$	2.61013	+	4.52087i	0.146139	+	0.253120i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.37208			−0.131986
$324$		0			0
$325$	37.9874	+	65.7961i	2.10716	+	3.64971i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.02748	+	5.90154i	0.332306	+	0.325362i
$330$		0			0
$331$	−9.25253	+	16.0258i	−0.508565	+	0.880860i	0.491386	+	0.870942i	$0.336490\pi$
$331$	−9.25253	+	16.0258i	−0.508565	+	0.880860i	−0.999951	+	0.00991827i	$0.996843\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−46.4974			−2.54042
$336$		0			0
$337$	−2.41169			−0.131373			−0.0656865	−	0.997840i	$-0.520924\pi$
$337$	−2.41169			−0.131373			−0.0656865	+	0.997840i	$0.520924\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.536585	+	0.929392i	−0.0290577	+	0.0503294i
$342$		0			0
$343$	12.6745	−	13.5039i	0.684360	−	0.729144i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.60185	+	11.4347i	0.354406	+	0.613849i	0.987016	−	0.160621i	$-0.0513498\pi$
$347$	6.60185	+	11.4347i	0.354406	+	0.613849i	−0.632610	+	0.774470i	$0.718016\pi$
$348$		0			0
$349$	−24.0885			−1.28943			−0.644715	−	0.764423i	$-0.723024\pi$
$349$	−24.0885			−1.28943			−0.644715	+	0.764423i	$0.723024\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.0550	−	17.4159i	−0.535176	−	0.926952i	−0.999155	−	0.0411059i	$-0.986912\pi$
$353$	−10.0550	−	17.4159i	−0.535176	−	0.926952i	0.463979	−	0.885846i	$-0.346421\pi$
$354$		0			0
$355$	−16.9424	+	29.3451i	−0.899210	+	1.55748i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.67514	−	16.7578i	0.510634	−	0.884444i	−0.489290	−	0.872121i	$-0.662744\pi$
$359$	9.67514	−	16.7578i	0.510634	−	0.884444i	0.999924	−	0.0123231i	$-0.00392266\pi$
$360$		0			0
$361$	3.49535	+	6.05412i	0.183966	+	0.318638i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	40.9813			2.14506
$366$		0			0
$367$	12.3982	+	21.4742i	0.647178	+	1.12095i	0.983794	+	0.179303i	$0.0573844\pi$
$367$	12.3982	+	21.4742i	0.647178	+	1.12095i	−0.336616	+	0.941642i	$0.609282\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.53827	−	1.26752i	0.235615	−	0.0658066i
$372$		0			0
$373$	9.19291	−	15.9226i	0.475991	−	0.824440i	−0.523631	−	0.851945i	$-0.675423\pi$
$373$	9.19291	−	15.9226i	0.475991	−	0.824440i	0.999622	+	0.0275049i	$0.00875618\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	41.0516			2.11426
$378$		0			0
$379$	−8.23588			−0.423049			−0.211524	−	0.977373i	$-0.567843\pi$
$379$	−8.23588			−0.423049			−0.211524	+	0.977373i	$0.567843\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.47554	+	14.6801i	−0.433080	+	0.750117i	−0.997137	−	0.0756194i	$-0.975907\pi$
$383$	−8.47554	+	14.6801i	−0.433080	+	0.750117i	0.564057	+	0.825736i	$0.309240\pi$
$384$		0			0
$385$	2.32787	−	9.06967i	0.118639	−	0.462233i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.00371	−	10.3987i	−0.304400	−	0.527237i	0.672727	−	0.739890i	$-0.265123\pi$
$389$	−6.00371	−	10.3987i	−0.304400	−	0.527237i	−0.977128	+	0.212654i	$0.931789\pi$
$390$		0			0
$391$	−4.03356			−0.203986
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.5199	+	18.2210i	0.529315	+	0.916800i
$396$		0			0
$397$	−3.77939	+	6.54609i	−0.189682	+	0.328539i	−0.945144	−	0.326653i	$-0.894079\pi$
$397$	−3.77939	+	6.54609i	−0.189682	+	0.328539i	0.755462	+	0.655192i	$0.227412\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.32306	−	9.21982i	0.265821	−	0.460416i	−0.701957	−	0.712219i	$-0.747690\pi$
$401$	5.32306	−	9.21982i	0.265821	−	0.460416i	0.967778	+	0.251803i	$0.0810236\pi$
$402$		0			0
$403$	4.21965	+	7.30865i	0.210196	+	0.364070i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.68621			−0.380991
$408$		0			0
$409$	3.45177	+	5.97864i	0.170679	+	0.295625i	0.938657	−	0.344851i	$-0.112071\pi$
$409$	3.45177	+	5.97864i	0.170679	+	0.295625i	−0.767978	+	0.640476i	$0.778737\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−26.0710	+	7.28156i	−1.28287	+	0.358302i
$414$		0			0
$415$	22.7363	−	39.3805i	1.11608	−	1.93311i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	21.2205			1.03669			0.518345	−	0.855171i	$-0.326548\pi$
$419$	21.2205			1.03669			0.518345	+	0.855171i	$0.326548\pi$
$420$		0			0
$421$	19.8529			0.967572			0.483786	−	0.875186i	$-0.339261\pi$
$421$	19.8529			0.967572			0.483786	+	0.875186i	$0.339261\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.72276	+	6.44801i	−0.180580	+	0.312774i
$426$		0			0
$427$	3.33782	+	3.26807i	0.161528	+	0.158153i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.7923	−	23.8890i	−0.664354	−	1.15069i	−0.979460	−	0.201638i	$-0.935374\pi$
$431$	−13.7923	−	23.8890i	−0.664354	−	1.15069i	0.315107	−	0.949056i	$-0.397960\pi$
$432$		0			0
$433$	1.90046			0.0913301			0.0456650	−	0.998957i	$-0.485459\pi$
$433$	1.90046			0.0913301			0.0456650	+	0.998957i	$0.485459\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.2105	−	17.6851i	−0.488435	−	0.845995i
$438$		0			0
$439$	15.0604	−	26.0853i	0.718792	−	1.24498i	−0.242687	−	0.970105i	$-0.578029\pi$
$439$	15.0604	−	26.0853i	0.718792	−	1.24498i	0.961479	−	0.274879i	$-0.0886378\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.3154	−	29.9911i	0.822679	−	1.42492i	−0.0810014	−	0.996714i	$-0.525812\pi$
$443$	17.3154	−	29.9911i	0.822679	−	1.42492i	0.903680	−	0.428208i	$-0.140855\pi$
$444$		0			0
$445$	−22.9953	−	39.8291i	−1.09008	−	1.88808i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	23.2342			1.09649			0.548244	−	0.836318i	$-0.315296\pi$
$449$	23.2342			1.09649			0.548244	+	0.836318i	$0.315296\pi$
$450$		0			0
$451$	2.79787	+	4.84605i	0.131746	+	0.228192i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−52.6145	−	51.5151i	−2.46660	−	2.41506i
$456$		0			0
$457$	1.01367	−	1.75573i	0.0474176	−	0.0821297i	−0.841342	−	0.540502i	$-0.818234\pi$
$457$	1.01367	−	1.75573i	0.0474176	−	0.0821297i	0.888760	+	0.458373i	$0.151568\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	35.2371			1.64115			0.820577	−	0.571535i	$-0.193652\pi$
$461$	35.2371			1.64115			0.820577	+	0.571535i	$0.193652\pi$
$462$		0			0
$463$	6.28195			0.291947			0.145973	−	0.989289i	$-0.453369\pi$
$463$	6.28195			0.291947			0.145973	+	0.989289i	$0.453369\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.74579	−	13.4161i	0.358432	−	0.620823i	−0.629267	−	0.777189i	$-0.716645\pi$
$467$	7.74579	−	13.4161i	0.358432	−	0.620823i	0.987699	+	0.156366i	$0.0499780\pi$
$468$		0			0
$469$	29.7356	−	8.30507i	1.37306	−	0.383493i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.394441	−	0.683192i	−0.0181364	−	0.0314132i
$474$		0			0
$475$	−37.6950			−1.72957
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.2119	−	31.5439i	−0.832121	−	1.44128i	−0.896353	−	0.443341i	$-0.853793\pi$
$479$	−18.2119	−	31.5439i	−0.832121	−	1.44128i	0.0642320	−	0.997935i	$-0.479540\pi$
$480$		0			0
$481$	−30.2218	+	52.3457i	−1.37800	+	2.38676i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.1192	+	36.5796i	−0.958975	+	1.66099i
$486$		0			0
$487$	−12.6178	−	21.8547i	−0.571767	−	0.990330i	−0.996385	−	0.0849571i	$-0.972925\pi$
$487$	−12.6178	−	21.8547i	−0.571767	−	0.990330i	0.424617	−	0.905373i	$-0.360409\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	30.0305			1.35526			0.677628	−	0.735405i	$-0.263008\pi$
$491$	30.0305			1.35526			0.677628	+	0.735405i	$0.263008\pi$
$492$		0			0
$493$	2.01153	+	3.48406i	0.0905945	+	0.156914i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.59343	−	21.7927i	0.250900	−	0.977536i
$498$		0			0
$499$	4.96247	−	8.59526i	0.222151	−	0.384777i	−0.733310	−	0.679894i	$-0.762026\pi$
$499$	4.96247	−	8.59526i	0.222151	−	0.384777i	0.955461	+	0.295118i	$0.0953589\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−5.12095			−0.228332			−0.114166	−	0.993462i	$-0.536420\pi$
$503$	−5.12095			−0.228332			−0.114166	+	0.993462i	$0.536420\pi$
$504$		0			0
$505$	58.1159			2.58612
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.14851	−	3.72133i	0.0952311	−	0.164945i	−0.814474	−	0.580200i	$-0.802974\pi$
$509$	2.14851	−	3.72133i	0.0952311	−	0.164945i	0.909705	+	0.415255i	$0.136308\pi$
$510$		0			0
$511$	−26.2080	+	7.31982i	−1.15937	+	0.323810i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	31.4102	+	54.4040i	1.38410	+	2.39733i
$516$		0			0
$517$	−2.83186			−0.124545
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.52520	−	11.3020i	−0.285874	−	0.495148i	0.686947	−	0.726708i	$-0.258951\pi$
$521$	−6.52520	−	11.3020i	−0.285874	−	0.495148i	−0.972821	+	0.231559i	$0.925617\pi$
$522$		0			0
$523$	−3.16543	+	5.48269i	−0.138415	+	0.239741i	−0.926897	−	0.375317i	$-0.877534\pi$
$523$	−3.16543	+	5.48269i	−0.138415	+	0.239741i	0.788482	+	0.615058i	$0.210867\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.413525	+	0.716247i	−0.0180134	+	0.0312002i
$528$		0			0
$529$	−5.86231	−	10.1538i	−0.254883	−	0.441470i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	44.0043			1.90604
$534$		0			0
$535$	−3.46316	−	5.99837i	−0.149725	−	0.259332i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.131267	+	6.21595i	0.00565407	+	0.267740i
$540$		0			0
$541$	−10.2043	+	17.6744i	−0.438717	+	0.759880i	−0.997591	−	0.0693725i	$-0.977900\pi$
$541$	−10.2043	+	17.6744i	−0.438717	+	0.759880i	0.558874	+	0.829253i	$0.311234\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−26.4222			−1.13180
$546$		0			0
$547$	8.08732			0.345789			0.172894	−	0.984940i	$-0.444688\pi$
$547$	8.08732			0.345789			0.172894	+	0.984940i	$0.444688\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.1839	+	17.6391i	−0.433849	+	0.751449i
$552$		0			0
$553$	−9.98214	−	9.77357i	−0.424484	−	0.415614i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.99018	−	5.17914i	−0.126698	−	0.219447i	0.795698	−	0.605694i	$-0.207105\pi$
$557$	−2.99018	−	5.17914i	−0.126698	−	0.219447i	−0.922395	+	0.386247i	$0.873771\pi$
$558$		0			0
$559$	−6.20370			−0.262388
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.20059	+	12.4718i	0.303469	+	0.525623i	0.976919	−	0.213609i	$-0.0685219\pi$
$563$	7.20059	+	12.4718i	0.303469	+	0.525623i	−0.673451	+	0.739232i	$0.735189\pi$
$564$		0			0
$565$	−4.32930	+	7.49856i	−0.182135	+	0.315467i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.36830	−	7.56612i	0.183129	−	0.317188i	−0.759816	−	0.650139i	$-0.774711\pi$
$569$	4.36830	−	7.56612i	0.183129	−	0.317188i	0.942944	+	0.332950i	$0.108044\pi$
$570$		0			0
$571$	0.123197	+	0.213384i	0.00515564	+	0.00892983i	0.868592	−	0.495528i	$-0.165026\pi$
$571$	0.123197	+	0.213384i	0.00515564	+	0.00892983i	−0.863436	+	0.504458i	$0.831692\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−64.0979			−2.67307
$576$		0			0
$577$	−3.74257	−	6.48231i	−0.155805	−	0.269862i	0.777547	−	0.628825i	$-0.216464\pi$
$577$	−3.74257	−	6.48231i	−0.155805	−	0.269862i	−0.933352	+	0.358963i	$0.883130\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.50625	+	29.2453i	−0.311412	+	1.21330i
$582$		0			0
$583$	−0.790911	+	1.36990i	−0.0327562	+	0.0567354i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.2800			−0.465574			−0.232787	−	0.972528i	$-0.574784\pi$
$587$	−11.2800			−0.465574			−0.232787	+	0.972528i	$0.574784\pi$
$588$		0			0
$589$	−4.18718			−0.172530
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.51846	−	2.63005i	0.0623557	−	0.108003i	−0.833162	−	0.553029i	$-0.813472\pi$
$593$	1.51846	−	2.63005i	0.0623557	−	0.108003i	0.895518	+	0.445025i	$0.146805\pi$
$594$		0			0
$595$	1.79400	−	6.98964i	0.0735468	−	0.286547i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.22901	+	5.59281i	0.131934	+	0.228516i	0.924422	−	0.381371i	$-0.124548\pi$
$599$	3.22901	+	5.59281i	0.131934	+	0.228516i	−0.792488	+	0.609887i	$0.791215\pi$
$600$		0			0
$601$	35.0578			1.43004			0.715019	−	0.699105i	$-0.246418\pi$
$601$	35.0578			1.43004			0.715019	+	0.699105i	$0.246418\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−20.3438	−	35.2366i	−0.827095	−	1.43257i
$606$		0			0
$607$	7.04055	−	12.1946i	0.285767	−	0.494963i	−0.687028	−	0.726631i	$-0.741085\pi$
$607$	7.04055	−	12.1946i	0.285767	−	0.494963i	0.972795	+	0.231668i	$0.0744183\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.1347	+	19.2859i	−0.450463	+	0.780224i
$612$		0			0
$613$	0.160037	+	0.277193i	0.00646385	+	0.0111957i	0.869239	−	0.494392i	$-0.164609\pi$
$613$	0.160037	+	0.277193i	0.00646385	+	0.0111957i	−0.862775	+	0.505587i	$0.831276\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.2145			0.894321			0.447161	−	0.894454i	$-0.352435\pi$
$617$	22.2145			0.894321			0.447161	+	0.894454i	$0.352435\pi$
$618$		0			0
$619$	0.754894	+	1.30752i	0.0303418	+	0.0525535i	0.880798	−	0.473493i	$-0.157007\pi$
$619$	0.754894	+	1.30752i	0.0303418	+	0.0525535i	−0.850456	+	0.526047i	$0.823674\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	21.8198	+	21.3639i	0.874193	+	0.855927i
$624$		0			0
$625$	−19.4655	+	33.7152i	−0.778619	+	1.34861i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.92347			−0.236184
$630$		0			0
$631$	−2.55733			−0.101806			−0.0509029	−	0.998704i	$-0.516210\pi$
$631$	−2.55733			−0.101806			−0.0509029	+	0.998704i	$0.516210\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−38.3298	+	66.3891i	−1.52107	+	2.63457i
$636$		0			0
$637$	42.8489	+	23.5468i	1.69773	+	0.932960i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.3160	+	21.3319i	0.486452	+	0.842559i	0.999879	−	0.0155743i	$-0.00495766\pi$
$641$	12.3160	+	21.3319i	0.486452	+	0.842559i	−0.513427	+	0.858133i	$0.671624\pi$
$642$		0			0
$643$	−30.7486			−1.21261			−0.606303	−	0.795234i	$-0.707348\pi$
$643$	−30.7486			−1.21261			−0.606303	+	0.795234i	$0.707348\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.2787	+	24.7314i	0.561352	+	0.972291i	0.997379	+	0.0723568i	$0.0230520\pi$
$647$	14.2787	+	24.7314i	0.561352	+	0.972291i	−0.436027	+	0.899934i	$0.643615\pi$
$648$		0			0
$649$	4.54356	−	7.86967i	0.178350	−	0.308912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.8545	−	23.9967i	0.542169	−	0.939064i	−0.456610	−	0.889667i	$-0.650937\pi$
$653$	13.8545	−	23.9967i	0.542169	−	0.939064i	0.998779	−	0.0493974i	$-0.0157301\pi$
$654$		0			0
$655$	−41.9177	−	72.6036i	−1.63786	−	2.83686i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−34.7244			−1.35267			−0.676335	−	0.736594i	$-0.736433\pi$
$659$	−34.7244			−1.35267			−0.676335	+	0.736594i	$0.736433\pi$
$660$		0			0
$661$	−20.1254	−	34.8582i	−0.782786	−	1.35582i	−0.930313	−	0.366767i	$-0.880465\pi$
$661$	−20.1254	−	34.8582i	−0.782786	−	1.35582i	0.147527	−	0.989058i	$-0.452869\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	35.1874	−	9.82773i	1.36451	−	0.381103i
$666$		0			0
$667$	−17.3171	+	29.9940i	−0.670520	+	1.16137i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.56819			−0.0605391
$672$		0			0
$673$	−19.6202			−0.756304			−0.378152	−	0.925743i	$-0.623440\pi$
$673$	−19.6202			−0.756304			−0.378152	+	0.925743i	$0.623440\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.22290	−	10.7784i	0.239165	−	0.414247i	−0.721310	−	0.692613i	$-0.756460\pi$
$677$	6.22290	−	10.7784i	0.239165	−	0.414247i	0.960475	+	0.278366i	$0.0897928\pi$
$678$		0			0
$679$	6.97238	−	27.1653i	0.267575	−	1.04251i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.36602	−	5.83011i	−0.128797	−	0.223083i	0.794414	−	0.607377i	$-0.207778\pi$
$683$	−3.36602	−	5.83011i	−0.128797	−	0.223083i	−0.923211	+	0.384294i	$0.874445\pi$
$684$		0			0
$685$	−29.2405			−1.11722
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.21965	+	10.7728i	0.236950	+	0.410409i
$690$		0			0
$691$	−24.1891	+	41.8967i	−0.920196	+	1.59383i	−0.121086	+	0.992642i	$0.538638\pi$
$691$	−24.1891	+	41.8967i	−0.920196	+	1.59383i	−0.799110	+	0.601184i	$0.794696\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	18.2847	−	31.6700i	0.693577	−	1.20131i
$696$		0			0
$697$	2.15621	+	3.73466i	0.0816722	+	0.141460i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	20.6903			0.781461			0.390730	−	0.920505i	$-0.372222\pi$
$701$	20.6903			0.781461			0.390730	+	0.920505i	$0.372222\pi$
$702$		0			0
$703$	−14.9946	−	25.9714i	−0.565532	−	0.979531i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−37.1658	+	10.3803i	−1.39776	+	0.390391i
$708$		0			0
$709$	−13.4717	+	23.3337i	−0.505941	+	0.876315i	0.494036	+	0.869442i	$0.335521\pi$
$709$	−13.4717	+	23.3337i	−0.505941	+	0.876315i	−0.999976	+	0.00687356i	$0.997812\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.12002			−0.266647
$714$		0			0
$715$	24.7195			0.924458
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.48080	−	7.76097i	0.167106	−	0.289435i	−0.770295	−	0.637687i	$-0.779891\pi$
$719$	4.48080	−	7.76097i	0.167106	−	0.289435i	0.937401	+	0.348252i	$0.113225\pi$
$720$		0			0
$721$	−29.8045	−	29.1817i	−1.10998	−	1.08678i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	31.9655	+	55.3658i	1.18717	+	2.05623i
$726$		0			0
$727$	−1.86854			−0.0693004			−0.0346502	−	0.999400i	$-0.511032\pi$
$727$	−1.86854			−0.0693004			−0.0346502	+	0.999400i	$0.511032\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.303981	−	0.526510i	−0.0112431	−	0.0194737i
$732$		0			0
$733$	16.2585	−	28.1606i	0.600522	−	1.04014i	−0.392220	−	0.919872i	$-0.628293\pi$
$733$	16.2585	−	28.1606i	0.600522	−	1.04014i	0.992742	−	0.120263i	$-0.0383739\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.18221	+	8.97585i	−0.190889	+	0.330630i
$738$		0			0
$739$	−18.8522	−	32.6530i	−0.693490	−	1.20116i	−0.970687	−	0.240347i	$-0.922739\pi$
$739$	−18.8522	−	32.6530i	−0.693490	−	1.20116i	0.277197	−	0.960813i	$-0.410595\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.3073			−0.781689			−0.390844	−	0.920457i	$-0.627817\pi$
$743$	−21.3073			−0.781689			−0.390844	+	0.920457i	$0.627817\pi$
$744$		0			0
$745$	−44.2302	−	76.6090i	−1.62047	−	2.80674i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.28612	+	3.21746i	0.120072	+	0.117563i
$750$		0			0
$751$	2.24028	−	3.88028i	0.0817490	−	0.141593i	−0.822252	−	0.569123i	$-0.807283\pi$
$751$	2.24028	−	3.88028i	0.0817490	−	0.141593i	0.904001	+	0.427530i	$0.140616\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.60511			0.0948096
$756$		0			0
$757$	−42.1970			−1.53367			−0.766837	−	0.641841i	$-0.778171\pi$
$757$	−42.1970			−1.53367			−0.766837	+	0.641841i	$0.778171\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.9791	+	27.6766i	−0.579243	+	1.00328i	0.416324	+	0.909216i	$0.363318\pi$
$761$	−15.9791	+	27.6766i	−0.579243	+	1.00328i	−0.995566	+	0.0940611i	$0.970015\pi$
$762$		0			0
$763$	16.8973	−	4.71937i	0.611724	−	0.170853i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−35.7301	−	61.8863i	−1.29014	−	2.23459i
$768$		0			0
$769$	−2.12716			−0.0767075			−0.0383537	−	0.999264i	$-0.512211\pi$
$769$	−2.12716			−0.0767075			−0.0383537	+	0.999264i	$0.512211\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.11167	−	7.12162i	−0.147887	−	0.256147i	0.782560	−	0.622576i	$-0.213914\pi$
$773$	−4.11167	−	7.12162i	−0.147887	−	0.256147i	−0.930446	+	0.366429i	$0.880580\pi$
$774$		0			0
$775$	−6.57140	+	11.3820i	−0.236052	+	0.408853i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.9164	+	18.9078i	−0.391121	+	0.677442i
$780$		0			0
$781$	3.77652	+	6.54112i	0.135134	+	0.234060i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	19.7827			0.706074
$786$		0			0
$787$	5.86744	+	10.1627i	0.209152	+	0.362262i	0.951448	−	0.307811i	$-0.0995964\pi$
$787$	5.86744	+	10.1627i	0.209152	+	0.362262i	−0.742296	+	0.670072i	$0.766263\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.42929	−	5.56869i	0.0508197	−	0.198000i
$792$		0			0
$793$	−6.16603	+	10.6799i	−0.218962	+	0.379254i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21.3167			−0.755077			−0.377538	−	0.925994i	$-0.623229\pi$
$797$	−21.3167			−0.755077			−0.377538	+	0.925994i	$0.623229\pi$
$798$		0			0
$799$	−2.18240			−0.0772078
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.56743	−	7.91102i	0.161181	−	0.279174i
$804$		0			0
$805$	59.8338	−	16.7114i	2.10887	−	0.589000i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−17.9632	−	31.1131i	−0.631551	−	1.09388i	−0.987235	−	0.159272i	$-0.949085\pi$
$809$	−17.9632	−	31.1131i	−0.631551	−	1.09388i	0.355684	−	0.934606i	$-0.384248\pi$
$810$		0			0
$811$	−24.7179			−0.867962			−0.433981	−	0.900922i	$-0.642892\pi$
$811$	−24.7179			−0.867962			−0.433981	+	0.900922i	$0.642892\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	27.6392	+	47.8725i	0.968158	+	1.67690i
$816$		0			0
$817$	1.53899	−	2.66560i	0.0538423	−	0.0932577i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.4426	+	18.0870i	−0.364448	+	0.631242i	−0.988687	−	0.149991i	$-0.952075\pi$
$821$	−10.4426	+	18.0870i	−0.364448	+	0.631242i	0.624240	+	0.781233i	$0.285409\pi$
$822$		0			0
$823$	6.60341	+	11.4374i	0.230180	+	0.398684i	0.957861	−	0.287232i	$-0.0927350\pi$
$823$	6.60341	+	11.4374i	0.230180	+	0.398684i	−0.727681	+	0.685916i	$0.759402\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.29125			−0.149221			−0.0746107	−	0.997213i	$-0.523771\pi$
$827$	−4.29125			−0.149221			−0.0746107	+	0.997213i	$0.523771\pi$
$828$		0			0
$829$	−13.9754	−	24.2061i	−0.485387	−	0.840714i	0.514472	−	0.857507i	$-0.327988\pi$
$829$	−13.9754	−	24.2061i	−0.485387	−	0.840714i	−0.999859	+	0.0167927i	$0.994654\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.101162	+	4.79039i	0.00350507	+	0.165977i
$834$		0			0
$835$	40.0625	−	69.3903i	1.38642	−	2.40135i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	31.5189			1.08815			0.544077	−	0.839035i	$-0.316880\pi$
$839$	31.5189			1.08815			0.544077	+	0.839035i	$0.316880\pi$
$840$		0			0
$841$	5.54390			0.191169
$842$		0			0
$843$		0			0
$844$		0			0
$845$	71.2958	−	123.488i	2.45265	−	4.24812i
$846$		0			0
$847$	19.3039	+	18.9005i	0.663289	+	0.649429i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−25.4973	−	44.1627i	−0.874038	−	1.51388i
$852$		0			0
$853$	9.81650			0.336111			0.168055	−	0.985778i	$-0.446251\pi$
$853$	9.81650			0.336111			0.168055	+	0.985778i	$0.446251\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.3443	+	23.1130i	0.455832	+	0.789524i	0.998736	−	0.0502711i	$-0.0160085\pi$
$857$	13.3443	+	23.1130i	0.455832	+	0.789524i	−0.542904	+	0.839795i	$0.682675\pi$
$858$		0			0
$859$	17.0349	−	29.5053i	0.581223	−	1.00671i	−0.414111	−	0.910226i	$-0.635908\pi$
$859$	17.0349	−	29.5053i	0.581223	−	1.00671i	0.995335	−	0.0964822i	$-0.0307591\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.66218	+	8.07514i	−0.158703	+	0.274881i	−0.934401	−	0.356223i	$-0.884064\pi$
$863$	−4.66218	+	8.07514i	−0.158703	+	0.274881i	0.775698	+	0.631104i	$0.217398\pi$
$864$		0			0
$865$	−2.91054	−	5.04120i	−0.0989612	−	0.171406i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.68985			0.159092
$870$		0			0
$871$	40.7524	+	70.5852i	1.38084	+	2.39169i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	15.4042	−	60.0165i	0.520756	−	2.02893i
$876$		0			0
$877$	0.592608	−	1.02643i	0.0200109	−	0.0346600i	−0.855847	−	0.517230i	$-0.826963\pi$
$877$	0.592608	−	1.02643i	0.0200109	−	0.0346600i	0.875857	+	0.482570i	$0.160297\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−39.2538			−1.32249			−0.661247	−	0.750168i	$-0.729973\pi$
$881$	−39.2538			−1.32249			−0.661247	+	0.750168i	$0.729973\pi$
$882$		0			0
$883$	−23.4854			−0.790346			−0.395173	−	0.918607i	$-0.629315\pi$
$883$	−23.4854			−0.790346			−0.395173	+	0.918607i	$0.629315\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.86542	+	17.0874i	−0.331248	+	0.573739i	−0.982757	−	0.184902i	$-0.940803\pi$
$887$	−9.86542	+	17.0874i	−0.331248	+	0.573739i	0.651509	+	0.758641i	$0.274136\pi$
$888$		0			0
$889$	12.6543	−	49.3028i	0.424413	−	1.65356i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.52451	−	9.56873i	−0.184871	−	0.320205i
$894$		0			0
$895$	38.9307			1.30131
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.55073	+	6.15005i	0.118424	+	0.205116i
$900$		0			0
$901$	−0.609525	+	1.05573i	−0.0203062	+	0.0351714i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.66443	−	6.34699i	0.121810	−	0.210981i
$906$		0			0
$907$	0.707545	+	1.22550i	0.0234936	+	0.0406922i	0.877533	−	0.479516i	$-0.159188\pi$
$907$	0.707545	+	1.22550i	0.0234936	+	0.0406922i	−0.854040	+	0.520208i	$0.825854\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.4256			−0.709862			−0.354931	−	0.934893i	$-0.615496\pi$
$911$	−21.4256			−0.709862			−0.354931	+	0.934893i	$0.615496\pi$
$912$		0			0
$913$	−5.06800	−	8.77803i	−0.167726	−	0.290510i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	39.7749	+	38.9438i	1.31348	+	1.28604i
$918$		0			0
$919$	−7.48008	+	12.9559i	−0.246745	+	0.427375i	−0.962621	−	0.270853i	$-0.912694\pi$
$919$	−7.48008	+	12.9559i	−0.246745	+	0.427375i	0.715876	+	0.698228i	$0.246028\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	59.3964			1.95506
$924$		0			0
$925$	−94.1307			−3.09500
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.9699	−	20.7325i	0.392720	−	0.680210i	−0.600088	−	0.799934i	$-0.704868\pi$
$929$	11.9699	−	20.7325i	0.392720	−	0.680210i	0.992807	+	0.119724i	$0.0382010\pi$
$930$		0			0
$931$	−20.7474	+	12.5699i	−0.679968	+	0.411962i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.21126	+	2.09796i	0.0396123	+	0.0686105i
$936$		0			0
$937$	−3.81330			−0.124575			−0.0622876	−	0.998058i	$-0.519840\pi$
$937$	−3.81330			−0.124575			−0.0622876	+	0.998058i	$0.519840\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.5406	−	47.7016i	−0.897796	−	1.55503i	−0.830305	−	0.557309i	$-0.811834\pi$
$941$	−27.5406	−	47.7016i	−0.897796	−	1.55503i	−0.0674911	−	0.997720i	$-0.521499\pi$
$942$		0			0
$943$	−18.5626	+	32.1514i	−0.604483	+	1.04699i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.6905	−	35.8370i	0.672351	−	1.16455i	−0.304884	−	0.952389i	$-0.598618\pi$
$947$	20.6905	−	35.8370i	0.672351	−	1.16455i	0.977236	−	0.212157i	$-0.0680488\pi$
$948$		0			0
$949$	−35.9178	−	62.2115i	−1.16594	−	2.01947i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.2037			−0.881215			−0.440608	−	0.897700i	$-0.645237\pi$
$953$	−27.2037			−0.881215			−0.440608	+	0.897700i	$0.645237\pi$
$954$		0			0
$955$	−5.75421	−	9.96658i	−0.186202	−	0.322511i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.6996	−	5.22275i	0.603842	−	0.168651i
$960$		0			0
$961$	14.7700	−	25.5825i	0.476453	−	0.825241i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.77329			−0.218040
$966$		0			0
$967$	−25.0322			−0.804981			−0.402490	−	0.915424i	$-0.631855\pi$
$967$	−25.0322			−0.804981			−0.402490	+	0.915424i	$0.631855\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.28109	−	7.41506i	0.137387	−	0.237961i	−0.789120	−	0.614239i	$-0.789463\pi$
$971$	4.28109	−	7.41506i	0.137387	−	0.237961i	0.926507	+	0.376278i	$0.122796\pi$
$972$		0			0
$973$	−6.03657	+	23.5192i	−0.193523	+	0.753991i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.3744	+	19.7011i	0.363900	+	0.630294i	0.988599	−	0.150572i	$-0.0481115\pi$
$977$	11.3744	+	19.7011i	0.363900	+	0.630294i	−0.624699	+	0.780866i	$0.714778\pi$
$978$		0			0
$979$	−10.2515			−0.327639
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−15.4945	−	26.8372i	−0.494197	−	0.855975i	0.505780	−	0.862662i	$-0.331205\pi$
$983$	−15.4945	−	26.8372i	−0.494197	−	0.855975i	−0.999978	+	0.00668727i	$0.997871\pi$
$984$		0			0
$985$	−30.9737	+	53.6481i	−0.986906	+	1.70937i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.61695	−	4.53268i	0.0832141	−	0.144131i
$990$		0			0
$991$	6.37667	+	11.0447i	0.202561	+	0.350847i	0.949353	−	0.314211i	$-0.101740\pi$
$991$	6.37667	+	11.0447i	0.202561	+	0.350847i	−0.746792	+	0.665058i	$0.768407\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−44.5998			−1.41391
$996$		0			0
$997$	8.92720	+	15.4624i	0.282727	+	0.489698i	0.972055	−	0.234751i	$-0.0754276\pi$
$997$	8.92720	+	15.4624i	0.282727	+	0.489698i	−0.689328	+	0.724449i	$0.742094\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.s.n.1297.4	yes	8
3.2	odd	2		1512.2.s.o.1297.1	yes	8
7.4	even	3	inner	1512.2.s.n.865.4	✓	8
21.11	odd	6		1512.2.s.o.865.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.n.865.4	✓	8	7.4	even	3	inner
1512.2.s.n.1297.4	yes	8	1.1	even	1	trivial
1512.2.s.o.865.1	yes	8	21.11	odd	6
1512.2.s.o.1297.1	yes	8	3.2	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99232 - 3.45080i) q^{5} +(-0.657753 + 2.56269i) q^{7} +O(q^{10})\)	\(q+(1.99232 - 3.45080i) q^{5} +(-0.657753 + 2.56269i) q^{7} +(-0.444095 - 0.769196i) q^{11} -6.98465 q^{13} +(-0.342247 - 0.592789i) q^{17} +(1.73272 - 3.00116i) q^{19} +(2.94638 - 5.10328i) q^{23} +(-5.43870 - 9.42011i) q^{25} -5.87741 q^{29} +(-0.604133 - 1.04639i) q^{31} +(7.53287 + 7.37548i) q^{35} +(4.32689 - 7.49440i) q^{37} -6.30015 q^{41} +0.888190 q^{43} +(1.59417 - 2.76119i) q^{47} +(-6.13472 - 3.37123i) q^{49} +(-0.890475 - 1.54235i) q^{53} -3.53912 q^{55} +(5.11552 + 8.86034i) q^{59} +(0.882798 - 1.52905i) q^{61} +(-13.9157 + 24.1027i) q^{65} +(-5.83457 - 10.1058i) q^{67} -8.50385 q^{71} +(5.14240 + 8.90690i) q^{73} +(2.26331 - 0.632136i) q^{77} +(-2.64011 + 4.57281i) q^{79} +11.4120 q^{83} -2.72747 q^{85} +(5.77099 - 9.99565i) q^{89} +(4.59417 - 17.8995i) q^{91} +(-6.90428 - 11.9586i) q^{95} -10.6003 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} - 4 q^{7}+O(q^{10}) \) 8 * q - 2 * q^5 - 4 * q^7	\( 8 q - 2 q^{5} - 4 q^{7} - q^{11} - 20 q^{13} - 4 q^{17} + q^{19} + 12 q^{23} - 14 q^{25} + 12 q^{29} + 8 q^{31} + 9 q^{35} - 12 q^{41} + 2 q^{43} - 9 q^{47} + 6 q^{49} + 7 q^{53} - 36 q^{55} - 4 q^{59} - 25 q^{61} - 28 q^{65} - 30 q^{67} - 22 q^{71} + 4 q^{73} - 37 q^{77} + 7 q^{79} + 58 q^{83} + 14 q^{85} + 9 q^{89} + 15 q^{91} - 4 q^{95} - 8 q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 - 4 * q^7 - q^11 - 20 * q^13 - 4 * q^17 + q^19 + 12 * q^23 - 14 * q^25 + 12 * q^29 + 8 * q^31 + 9 * q^35 - 12 * q^41 + 2 * q^43 - 9 * q^47 + 6 * q^49 + 7 * q^53 - 36 * q^55 - 4 * q^59 - 25 * q^61 - 28 * q^65 - 30 * q^67 - 22 * q^71 + 4 * q^73 - 37 * q^77 + 7 * q^79 + 58 * q^83 + 14 * q^85 + 9 * q^89 + 15 * q^91 - 4 * q^95 - 8 * q^97

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