LMFDB - Embedded newform 1728.2.i.l.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(577,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1728.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.i (of order $3$, degree $2$, not 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:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1728.577
Dual form			1728.2.i.l.1153.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{7} +(-0.866025 - 1.50000i) q^{11} +(-1.50000 + 2.59808i) q^{13} -4.00000 q^{17} -6.92820 q^{19} +(-4.33013 + 7.50000i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{29} +(-2.59808 + 4.50000i) q^{31} +1.73205 q^{35} +8.00000 q^{37} +(2.50000 - 4.33013i) q^{41} +(-4.33013 - 7.50000i) q^{43} +(6.06218 + 10.5000i) q^{47} +(2.00000 - 3.46410i) q^{49} -8.00000 q^{53} -1.73205 q^{55} +(-0.866025 + 1.50000i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(1.50000 + 2.59808i) q^{65} +(-4.33013 + 7.50000i) q^{67} -3.46410 q^{71} -12.0000 q^{73} +(1.50000 - 2.59808i) q^{77} +(2.59808 + 4.50000i) q^{79} +(4.33013 + 7.50000i) q^{83} +(-2.00000 + 3.46410i) q^{85} +4.00000 q^{89} -5.19615 q^{91} +(-3.46410 + 6.00000i) q^{95} +(1.50000 + 2.59808i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5}+O(q^{10}) $ 4 * q + 2 * q^5	$ 4 q + 2 q^{5} - 6 q^{13} - 16 q^{17} + 8 q^{25} - 2 q^{29} + 32 q^{37} + 10 q^{41} + 8 q^{49} - 32 q^{53} - 14 q^{61} + 6 q^{65} - 48 q^{73} + 6 q^{77} - 8 q^{85} + 16 q^{89} + 6 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - 6 * q^13 - 16 * q^17 + 8 * q^25 - 2 * q^29 + 32 * q^37 + 10 * q^41 + 8 * q^49 - 32 * q^53 - 14 * q^61 + 6 * q^65 - 48 * q^73 + 6 * q^77 - 8 * q^85 + 16 * q^89 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	0.866025	+	1.50000i	0.327327	+	0.566947i	0.981981	−	0.188982i	$-0.0605189\pi$
$7$	0.866025	+	1.50000i	0.327327	+	0.566947i	−0.654654	+	0.755929i	$0.727186\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.866025	−	1.50000i	−0.261116	−	0.452267i	0.705422	−	0.708787i	$-0.250757\pi$
$11$	−0.866025	−	1.50000i	−0.261116	−	0.452267i	−0.966539	+	0.256520i	$0.917424\pi$
$12$		0			0
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	−0.995535	−	0.0943882i	$-0.969911\pi$
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	0.579510	+	0.814965i	$0.303244\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$	−6.92820			−1.58944			−0.794719	−	0.606977i	$-0.792382\pi$
$19$	−6.92820			−1.58944			−0.794719	+	0.606977i	$0.792382\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.33013	+	7.50000i	−0.902894	+	1.56386i	−0.0791743	+	0.996861i	$0.525228\pi$
$23$	−4.33013	+	7.50000i	−0.902894	+	1.56386i	−0.823720	+	0.566997i	$0.808105\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	−2.59808	+	4.50000i	−0.466628	+	0.808224i	−0.999273	−	0.0381148i	$-0.987865\pi$
$31$	−2.59808	+	4.50000i	−0.466628	+	0.808224i	0.532645	+	0.846339i	$0.321198\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.73205			0.292770
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$		0			0
$43$	−4.33013	−	7.50000i	−0.660338	−	1.14374i	−0.980527	−	0.196385i	$-0.937080\pi$
$43$	−4.33013	−	7.50000i	−0.660338	−	1.14374i	0.320189	−	0.947354i	$-0.396254\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.06218	+	10.5000i	0.884260	+	1.53158i	0.846560	+	0.532293i	$0.178670\pi$
$47$	6.06218	+	10.5000i	0.884260	+	1.53158i	0.0376995	+	0.999289i	$0.487997\pi$
$48$		0			0
$49$	2.00000	−	3.46410i	0.285714	−	0.494872i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.00000			−1.09888			−0.549442	−	0.835532i	$-0.685160\pi$
$53$	−8.00000			−1.09888			−0.549442	+	0.835532i	$0.685160\pi$
$54$		0			0
$55$	−1.73205			−0.233550
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.866025	+	1.50000i	−0.112747	+	0.195283i	−0.916877	−	0.399170i	$-0.869298\pi$
$59$	−0.866025	+	1.50000i	−0.112747	+	0.195283i	0.804130	+	0.594454i	$0.202632\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$	−4.33013	+	7.50000i	−0.529009	+	0.916271i	0.470418	+	0.882443i	$0.344103\pi$
$67$	−4.33013	+	7.50000i	−0.529009	+	0.916271i	−0.999428	+	0.0338274i	$0.989230\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.46410			−0.411113			−0.205557	−	0.978645i	$-0.565900\pi$
$71$	−3.46410			−0.411113			−0.205557	+	0.978645i	$0.565900\pi$
$72$		0			0
$73$	−12.0000			−1.40449			−0.702247	−	0.711934i	$-0.747820\pi$
$73$	−12.0000			−1.40449			−0.702247	+	0.711934i	$0.747820\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.50000	−	2.59808i	0.170941	−	0.296078i
$78$		0			0
$79$	2.59808	+	4.50000i	0.292306	+	0.506290i	0.974355	−	0.225018i	$-0.0722440\pi$
$79$	2.59808	+	4.50000i	0.292306	+	0.506290i	−0.682048	+	0.731307i	$0.738911\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.33013	+	7.50000i	0.475293	+	0.823232i	0.999600	−	0.0282978i	$-0.00900866\pi$
$83$	4.33013	+	7.50000i	0.475293	+	0.823232i	−0.524306	+	0.851530i	$0.675675\pi$
$84$		0			0
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.00000			0.423999			0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000			0.423999			0.212000	+	0.977270i	$0.432002\pi$
$90$		0			0
$91$	−5.19615			−0.544705
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.46410	+	6.00000i	−0.355409	+	0.615587i
$96$		0			0
$97$	1.50000	+	2.59808i	0.152302	+	0.263795i	0.932073	−	0.362270i	$-0.117998\pi$
$97$	1.50000	+	2.59808i	0.152302	+	0.263795i	−0.779771	+	0.626064i	$0.784665\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	0.983889	+	0.178782i	$0.0572157\pi$
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	−0.337115	+	0.941464i	$0.609451\pi$
$102$		0			0
$103$	−0.866025	+	1.50000i	−0.0853320	+	0.147799i	−0.905533	−	0.424277i	$-0.860528\pi$
$103$	−0.866025	+	1.50000i	−0.0853320	+	0.147799i	0.820201	+	0.572076i	$0.193862\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.92820			−0.669775			−0.334887	−	0.942258i	$-0.608698\pi$
$107$	−6.92820			−0.669775			−0.334887	+	0.942258i	$0.608698\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	−0.888585	−	0.458712i	$-0.848311\pi$
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	0.841549	+	0.540181i	$0.181644\pi$
$114$		0			0
$115$	4.33013	+	7.50000i	0.403786	+	0.699379i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.46410	−	6.00000i	−0.317554	−	0.550019i
$120$		0			0
$121$	4.00000	−	6.92820i	0.363636	−	0.629837i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−13.8564			−1.22956			−0.614779	−	0.788700i	$-0.710755\pi$
$127$	−13.8564			−1.22956			−0.614779	+	0.788700i	$0.710755\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.79423	+	13.5000i	−0.680985	+	1.17950i	0.293696	+	0.955899i	$0.405115\pi$
$131$	−7.79423	+	13.5000i	−0.680985	+	1.17950i	−0.974681	+	0.223602i	$0.928219\pi$
$132$		0			0
$133$	−6.00000	−	10.3923i	−0.520266	−	0.901127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.50000	+	11.2583i	0.555332	+	0.961864i	0.997878	+	0.0651178i	$0.0207423\pi$
$137$	6.50000	+	11.2583i	0.555332	+	0.961864i	−0.442545	+	0.896746i	$0.645924\pi$
$138$		0			0
$139$	0.866025	−	1.50000i	0.0734553	−	0.127228i	−0.826958	−	0.562263i	$-0.809931\pi$
$139$	0.866025	−	1.50000i	0.0734553	−	0.127228i	0.900414	+	0.435035i	$0.143264\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.19615			0.434524
$144$		0			0
$145$	−1.00000			−0.0830455
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.50000	−	9.52628i	0.450578	−	0.780423i	−0.547844	−	0.836580i	$-0.684551\pi$
$149$	5.50000	−	9.52628i	0.450578	−	0.780423i	0.998422	+	0.0561570i	$0.0178847\pi$
$150$		0			0
$151$	−11.2583	−	19.5000i	−0.916190	−	1.58689i	−0.805150	−	0.593072i	$-0.797915\pi$
$151$	−11.2583	−	19.5000i	−0.916190	−	1.58689i	−0.111040	−	0.993816i	$-0.535418\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.59808	+	4.50000i	0.208683	+	0.361449i
$156$		0			0
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−15.0000			−1.18217
$162$		0			0
$163$	6.92820			0.542659			0.271329	−	0.962487i	$-0.412537\pi$
$163$	6.92820			0.542659			0.271329	+	0.962487i	$0.412537\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.79423	−	13.5000i	0.603136	−	1.04466i	−0.389208	−	0.921150i	$-0.627251\pi$
$167$	7.79423	−	13.5000i	0.603136	−	1.04466i	0.992343	−	0.123511i	$-0.0394155\pi$
$168$		0			0
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.50000	+	11.2583i	0.494186	+	0.855955i	0.999978	−	0.00670064i	$-0.00213290\pi$
$173$	6.50000	+	11.2583i	0.494186	+	0.855955i	−0.505792	+	0.862656i	$0.668800\pi$
$174$		0			0
$175$	−3.46410	+	6.00000i	−0.261861	+	0.453557i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.92820			0.517838			0.258919	−	0.965899i	$-0.416634\pi$
$179$	6.92820			0.517838			0.258919	+	0.965899i	$0.416634\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$		0			0
$187$	3.46410	+	6.00000i	0.253320	+	0.438763i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.866025	−	1.50000i	−0.0626634	−	0.108536i	0.832992	−	0.553285i	$-0.186626\pi$
$191$	−0.866025	−	1.50000i	−0.0626634	−	0.108536i	−0.895655	+	0.444749i	$0.853293\pi$
$192$		0			0
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	−3.46410			−0.245564			−0.122782	−	0.992434i	$-0.539182\pi$
$199$	−3.46410			−0.245564			−0.122782	+	0.992434i	$0.539182\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.866025	−	1.50000i	0.0607831	−	0.105279i
$204$		0			0
$205$	−2.50000	−	4.33013i	−0.174608	−	0.302429i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.00000	+	10.3923i	0.415029	+	0.718851i
$210$		0			0
$211$	−4.33013	+	7.50000i	−0.298098	+	0.516321i	−0.975701	−	0.219107i	$-0.929686\pi$
$211$	−4.33013	+	7.50000i	−0.298098	+	0.516321i	0.677603	+	0.735428i	$0.263019\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.66025			−0.590624
$216$		0			0
$217$	−9.00000			−0.610960
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	0.866025	+	1.50000i	0.0579934	+	0.100447i	0.893565	−	0.448935i	$-0.148196\pi$
$223$	0.866025	+	1.50000i	0.0579934	+	0.100447i	−0.835571	+	0.549382i	$0.814863\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.06218	+	10.5000i	0.402361	+	0.696909i	0.994010	−	0.109286i	$-0.0348564\pi$
$227$	6.06218	+	10.5000i	0.402361	+	0.696909i	−0.591649	+	0.806195i	$0.701523\pi$
$228$		0			0
$229$	7.50000	−	12.9904i	0.495614	−	0.858429i	−0.504373	−	0.863486i	$-0.668276\pi$
$229$	7.50000	−	12.9904i	0.495614	−	0.858429i	0.999987	+	0.00505719i	$0.00160976\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$		0			0
$235$	12.1244			0.790906
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.52628	−	16.5000i	0.616204	−	1.06730i	−0.373968	−	0.927442i	$-0.622003\pi$
$239$	9.52628	−	16.5000i	0.616204	−	1.06730i	0.990172	−	0.139855i	$-0.0446636\pi$
$240$		0			0
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	0.973779	−	0.227498i	$-0.0730544\pi$
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	−0.683908	+	0.729568i	$0.739721\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.00000	−	3.46410i	−0.127775	−	0.221313i
$246$		0			0
$247$	10.3923	−	18.0000i	0.661247	−	1.14531i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−20.7846			−1.31191			−0.655956	−	0.754799i	$-0.727735\pi$
$251$	−20.7846			−1.31191			−0.655956	+	0.754799i	$0.727735\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.5000	−	26.8468i	0.966863	−	1.67466i	0.262341	−	0.964975i	$-0.415506\pi$
$257$	15.5000	−	26.8468i	0.966863	−	1.67466i	0.704523	−	0.709681i	$-0.251161\pi$
$258$		0			0
$259$	6.92820	+	12.0000i	0.430498	+	0.745644i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.52628	−	16.5000i	−0.587416	−	1.01743i	−0.994570	−	0.104074i	$-0.966812\pi$
$263$	−9.52628	−	16.5000i	−0.587416	−	1.01743i	0.407154	−	0.913360i	$-0.366521\pi$
$264$		0			0
$265$	−4.00000	+	6.92820i	−0.245718	+	0.425596i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−16.0000			−0.975537			−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−16.0000			−0.975537			−0.487769	+	0.872973i	$0.662189\pi$
$270$		0			0
$271$	13.8564			0.841717			0.420858	−	0.907126i	$-0.361729\pi$
$271$	13.8564			0.841717			0.420858	+	0.907126i	$0.361729\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.46410	−	6.00000i	0.208893	−	0.361814i
$276$		0			0
$277$	13.5000	+	23.3827i	0.811136	+	1.40493i	0.912069	+	0.410036i	$0.134484\pi$
$277$	13.5000	+	23.3827i	0.811136	+	1.40493i	−0.100933	+	0.994893i	$0.532183\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	−0.996887	−	0.0788417i	$-0.974878\pi$
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	0.430165	−	0.902750i	$-0.358455\pi$
$282$		0			0
$283$	14.7224	−	25.5000i	0.875158	−	1.51582i	0.0185631	−	0.999828i	$-0.494091\pi$
$283$	14.7224	−	25.5000i	0.875158	−	1.51582i	0.856595	−	0.515990i	$-0.172576\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.66025			0.511199
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.50000	+	6.06218i	−0.204472	+	0.354156i	−0.949964	−	0.312358i	$-0.898881\pi$
$293$	−3.50000	+	6.06218i	−0.204472	+	0.354156i	0.745492	+	0.666514i	$0.232214\pi$
$294$		0			0
$295$	0.866025	+	1.50000i	0.0504219	+	0.0873334i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.9904	−	22.5000i	−0.751253	−	1.30121i
$300$		0			0
$301$	7.50000	−	12.9904i	0.432293	−	0.748753i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.00000			−0.400819
$306$		0			0
$307$	6.92820			0.395413			0.197707	−	0.980261i	$-0.436651\pi$
$307$	6.92820			0.395413			0.197707	+	0.980261i	$0.436651\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.59808	−	4.50000i	0.147323	−	0.255172i	−0.782914	−	0.622130i	$-0.786268\pi$
$311$	2.59808	−	4.50000i	0.147323	−	0.255172i	0.930237	+	0.366958i	$0.119601\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.50000	−	14.7224i	−0.477408	−	0.826894i	0.522257	−	0.852788i	$-0.325090\pi$
$317$	−8.50000	−	14.7224i	−0.477408	−	0.826894i	−0.999665	+	0.0258939i	$0.991757\pi$
$318$		0			0
$319$	−0.866025	+	1.50000i	−0.0484881	+	0.0839839i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	27.7128			1.54198
$324$		0			0
$325$	−12.0000			−0.665640
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.5000	+	18.1865i	−0.578884	+	1.00266i
$330$		0			0
$331$	−6.06218	−	10.5000i	−0.333207	−	0.577132i	0.649931	−	0.759993i	$-0.274798\pi$
$331$	−6.06218	−	10.5000i	−0.333207	−	0.577132i	−0.983139	+	0.182861i	$0.941464\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.33013	+	7.50000i	0.236580	+	0.409769i
$336$		0			0
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	−0.994728	−	0.102552i	$-0.967299\pi$
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	0.586177	+	0.810183i	$0.300632\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.00000			0.487377
$342$		0			0
$343$	19.0526			1.02874
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.2583	−	19.5000i	0.604379	−	1.04681i	−0.387770	−	0.921756i	$-0.626755\pi$
$347$	11.2583	−	19.5000i	0.604379	−	1.04681i	0.992149	−	0.125059i	$-0.0399120\pi$
$348$		0			0
$349$	5.50000	+	9.52628i	0.294408	+	0.509930i	0.974847	−	0.222875i	$-0.0715441\pi$
$349$	5.50000	+	9.52628i	0.294408	+	0.509930i	−0.680439	+	0.732805i	$0.738211\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.5000	+	25.1147i	0.771757	+	1.33672i	0.936599	+	0.350403i	$0.113955\pi$
$353$	14.5000	+	25.1147i	0.771757	+	1.33672i	−0.164842	+	0.986320i	$0.552711\pi$
$354$		0			0
$355$	−1.73205	+	3.00000i	−0.0919277	+	0.159223i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	29.0000			1.52632
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.00000	+	10.3923i	−0.314054	+	0.543958i
$366$		0			0
$367$	16.4545	+	28.5000i	0.858917	+	1.48769i	0.872963	+	0.487787i	$0.162196\pi$
$367$	16.4545	+	28.5000i	0.858917	+	1.48769i	−0.0140459	+	0.999901i	$0.504471\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.92820	−	12.0000i	−0.359694	−	0.623009i
$372$		0			0
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	10.3923			0.533817			0.266908	−	0.963722i	$-0.413998\pi$
$379$	10.3923			0.533817			0.266908	+	0.963722i	$0.413998\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.9904	+	22.5000i	−0.663777	+	1.14970i	0.315838	+	0.948813i	$0.397714\pi$
$383$	−12.9904	+	22.5000i	−0.663777	+	1.14970i	−0.979615	+	0.200883i	$0.935619\pi$
$384$		0			0
$385$	−1.50000	−	2.59808i	−0.0764471	−	0.132410i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.5000	+	25.1147i	0.735179	+	1.27337i	0.954645	+	0.297747i	$0.0962353\pi$
$389$	14.5000	+	25.1147i	0.735179	+	1.27337i	−0.219465	+	0.975620i	$0.570431\pi$
$390$		0			0
$391$	17.3205	−	30.0000i	0.875936	−	1.51717i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.19615			0.261447
$396$		0			0
$397$	−8.00000			−0.401508			−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000			−0.401508			−0.200754	+	0.979642i	$0.564339\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.50000	−	11.2583i	0.324595	−	0.562214i	−0.656836	−	0.754034i	$-0.728105\pi$
$401$	6.50000	−	11.2583i	0.324595	−	0.562214i	0.981430	+	0.191820i	$0.0614388\pi$
$402$		0			0
$403$	−7.79423	−	13.5000i	−0.388258	−	0.672483i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.92820	−	12.0000i	−0.343418	−	0.594818i
$408$		0			0
$409$	4.50000	−	7.79423i	0.222511	−	0.385400i	−0.733059	−	0.680165i	$-0.761908\pi$
$409$	4.50000	−	7.79423i	0.222511	−	0.385400i	0.955570	+	0.294765i	$0.0952414\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.00000			−0.147620
$414$		0			0
$415$	8.66025			0.425115
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.2583	−	19.5000i	0.550005	−	0.952637i	−0.448268	−	0.893899i	$-0.647959\pi$
$419$	11.2583	−	19.5000i	0.550005	−	0.952637i	0.998273	−	0.0587381i	$-0.0187077\pi$
$420$		0			0
$421$	−7.50000	−	12.9904i	−0.365528	−	0.633112i	0.623333	−	0.781956i	$-0.285778\pi$
$421$	−7.50000	−	12.9904i	−0.365528	−	0.633112i	−0.988861	+	0.148844i	$0.952445\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.00000	−	13.8564i	−0.388057	−	0.672134i
$426$		0			0
$427$	6.06218	−	10.5000i	0.293369	−	0.508131i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	27.7128			1.33488			0.667440	−	0.744664i	$-0.267390\pi$
$431$	27.7128			1.33488			0.667440	+	0.744664i	$0.267390\pi$
$432$		0			0
$433$	4.00000			0.192228			0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000			0.192228			0.0961139	+	0.995370i	$0.469359\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	30.0000	−	51.9615i	1.43509	−	2.48566i
$438$		0			0
$439$	2.59808	+	4.50000i	0.123999	+	0.214773i	0.921341	−	0.388755i	$-0.127095\pi$
$439$	2.59808	+	4.50000i	0.123999	+	0.214773i	−0.797342	+	0.603528i	$0.793761\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−16.4545	−	28.5000i	−0.781776	−	1.35408i	−0.930906	−	0.365258i	$-0.880981\pi$
$443$	−16.4545	−	28.5000i	−0.781776	−	1.35408i	0.149130	−	0.988818i	$-0.452353\pi$
$444$		0			0
$445$	2.00000	−	3.46410i	0.0948091	−	0.164214i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.0000			−0.943858			−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000			−0.943858			−0.471929	+	0.881636i	$0.656442\pi$
$450$		0			0
$451$	−8.66025			−0.407795
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.59808	+	4.50000i	−0.121800	+	0.210963i
$456$		0			0
$457$	−10.5000	−	18.1865i	−0.491169	−	0.850730i	0.508779	−	0.860897i	$-0.330097\pi$
$457$	−10.5000	−	18.1865i	−0.491169	−	0.850730i	−0.999948	+	0.0101670i	$0.996764\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.500000	−	0.866025i	−0.0232873	−	0.0403348i	0.854147	−	0.520032i	$-0.174080\pi$
$461$	−0.500000	−	0.866025i	−0.0232873	−	0.0403348i	−0.877434	+	0.479697i	$0.840747\pi$
$462$		0			0
$463$	−16.4545	+	28.5000i	−0.764705	+	1.32451i	0.175698	+	0.984444i	$0.443782\pi$
$463$	−16.4545	+	28.5000i	−0.764705	+	1.32451i	−0.940403	+	0.340063i	$0.889552\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.92820			0.320599			0.160300	−	0.987068i	$-0.448754\pi$
$467$	6.92820			0.320599			0.160300	+	0.987068i	$0.448754\pi$
$468$		0			0
$469$	−15.0000			−0.692636
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.50000	+	12.9904i	−0.344850	+	0.597298i
$474$		0			0
$475$	−13.8564	−	24.0000i	−0.635776	−	1.10120i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.33013	+	7.50000i	0.197849	+	0.342684i	0.947831	−	0.318774i	$-0.103271\pi$
$479$	4.33013	+	7.50000i	0.197849	+	0.342684i	−0.749982	+	0.661458i	$0.769938\pi$
$480$		0			0
$481$	−12.0000	+	20.7846i	−0.547153	+	0.947697i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.00000			0.136223
$486$		0			0
$487$	27.7128			1.25579			0.627894	−	0.778299i	$-0.283917\pi$
$487$	27.7128			1.25579			0.627894	+	0.778299i	$0.283917\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.866025	+	1.50000i	−0.0390832	+	0.0676941i	−0.884905	−	0.465771i	$-0.845777\pi$
$491$	−0.866025	+	1.50000i	−0.0390832	+	0.0676941i	0.845822	+	0.533465i	$0.179110\pi$
$492$		0			0
$493$	2.00000	+	3.46410i	0.0900755	+	0.156015i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		0			0
$499$	0.866025	−	1.50000i	0.0387686	−	0.0671492i	−0.845990	−	0.533199i	$-0.820990\pi$
$499$	0.866025	−	1.50000i	0.0387686	−	0.0671492i	0.884759	+	0.466049i	$0.154323\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.2487			−1.08120			−0.540598	−	0.841281i	$-0.681802\pi$
$503$	−24.2487			−1.08120			−0.540598	+	0.841281i	$0.681802\pi$
$504$		0			0
$505$	13.0000			0.578492
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−18.5000	+	32.0429i	−0.819998	+	1.42028i	0.0856847	+	0.996322i	$0.472692\pi$
$509$	−18.5000	+	32.0429i	−0.819998	+	1.42028i	−0.905683	+	0.423956i	$0.860641\pi$
$510$		0			0
$511$	−10.3923	−	18.0000i	−0.459728	−	0.796273i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.866025	+	1.50000i	0.0381616	+	0.0660979i
$516$		0			0
$517$	10.5000	−	18.1865i	0.461789	−	0.799843i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.0000			1.13908			0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000			1.13908			0.569540	+	0.821963i	$0.307121\pi$
$522$		0			0
$523$	−10.3923			−0.454424			−0.227212	−	0.973845i	$-0.572961\pi$
$523$	−10.3923			−0.454424			−0.227212	+	0.973845i	$0.572961\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.3923	−	18.0000i	0.452696	−	0.784092i
$528$		0			0
$529$	−26.0000	−	45.0333i	−1.13043	−	1.95797i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.50000	+	12.9904i	0.324861	+	0.562676i
$534$		0			0
$535$	−3.46410	+	6.00000i	−0.149766	+	0.259403i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.92820			−0.298419
$540$		0			0
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.79423	+	13.5000i	0.333257	+	0.577218i	0.983148	−	0.182809i	$-0.0585189\pi$
$547$	7.79423	+	13.5000i	0.333257	+	0.577218i	−0.649891	+	0.760027i	$0.725186\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.46410	+	6.00000i	0.147576	+	0.255609i
$552$		0			0
$553$	−4.50000	+	7.79423i	−0.191359	+	0.331444i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.0000			0.677942			0.338971	−	0.940797i	$-0.389921\pi$
$557$	16.0000			0.677942			0.338971	+	0.940797i	$0.389921\pi$
$558$		0			0
$559$	25.9808			1.09887
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.2583	−	19.5000i	0.474482	−	0.821827i	−0.525091	−	0.851046i	$-0.675969\pi$
$563$	11.2583	−	19.5000i	0.474482	−	0.821827i	0.999573	+	0.0292191i	$0.00930205\pi$
$564$		0			0
$565$	0.500000	+	0.866025i	0.0210352	+	0.0364340i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.5000	+	26.8468i	0.649794	+	1.12548i	0.983172	+	0.182683i	$0.0584781\pi$
$569$	15.5000	+	26.8468i	0.649794	+	1.12548i	−0.333378	+	0.942793i	$0.608189\pi$
$570$		0			0
$571$	−4.33013	+	7.50000i	−0.181210	+	0.313865i	−0.942293	−	0.334790i	$-0.891335\pi$
$571$	−4.33013	+	7.50000i	−0.181210	+	0.313865i	0.761083	+	0.648655i	$0.224668\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−34.6410			−1.44463
$576$		0			0
$577$	−4.00000			−0.166522			−0.0832611	−	0.996528i	$-0.526534\pi$
$577$	−4.00000			−0.166522			−0.0832611	+	0.996528i	$0.526534\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.50000	+	12.9904i	−0.311152	+	0.538932i
$582$		0			0
$583$	6.92820	+	12.0000i	0.286937	+	0.496989i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.59808	−	4.50000i	−0.107234	−	0.185735i	0.807415	−	0.589984i	$-0.200866\pi$
$587$	−2.59808	−	4.50000i	−0.107234	−	0.185735i	−0.914649	+	0.404249i	$0.867533\pi$
$588$		0			0
$589$	18.0000	−	31.1769i	0.741677	−	1.28462i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.0000			0.821302			0.410651	−	0.911793i	$-0.365302\pi$
$593$	20.0000			0.821302			0.410651	+	0.911793i	$0.365302\pi$
$594$		0			0
$595$	−6.92820			−0.284029
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.866025	−	1.50000i	0.0353848	−	0.0612883i	−0.847791	−	0.530331i	$-0.822068\pi$
$599$	0.866025	−	1.50000i	0.0353848	−	0.0612883i	0.883175	+	0.469043i	$0.155401\pi$
$600$		0			0
$601$	5.50000	+	9.52628i	0.224350	+	0.388585i	0.956124	−	0.292962i	$-0.0946409\pi$
$601$	5.50000	+	9.52628i	0.224350	+	0.388585i	−0.731774	+	0.681547i	$0.761308\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.00000	−	6.92820i	−0.162623	−	0.281672i
$606$		0			0
$607$	6.06218	−	10.5000i	0.246056	−	0.426182i	−0.716372	−	0.697719i	$-0.754199\pi$
$607$	6.06218	−	10.5000i	0.246056	−	0.426182i	0.962428	+	0.271537i	$0.0875319\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−36.3731			−1.47150
$612$		0			0
$613$	−8.00000			−0.323117			−0.161558	−	0.986863i	$-0.551652\pi$
$613$	−8.00000			−0.323117			−0.161558	+	0.986863i	$0.551652\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.50000	−	4.33013i	0.100646	−	0.174324i	−0.811305	−	0.584623i	$-0.801242\pi$
$617$	2.50000	−	4.33013i	0.100646	−	0.174324i	0.911951	+	0.410299i	$0.134576\pi$
$618$		0			0
$619$	7.79423	+	13.5000i	0.313276	+	0.542611i	0.979070	−	0.203526i	$-0.0652400\pi$
$619$	7.79423	+	13.5000i	0.313276	+	0.542611i	−0.665793	+	0.746136i	$0.731907\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.46410	+	6.00000i	0.138786	+	0.240385i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−32.0000			−1.27592
$630$		0			0
$631$	−41.5692			−1.65484			−0.827422	−	0.561580i	$-0.810194\pi$
$631$	−41.5692			−1.65484			−0.827422	+	0.561580i	$0.810194\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.92820	+	12.0000i	−0.274937	+	0.476205i
$636$		0			0
$637$	6.00000	+	10.3923i	0.237729	+	0.411758i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	3.50000	+	6.06218i	0.138242	+	0.239442i	0.926831	−	0.375478i	$-0.122522\pi$
$641$	3.50000	+	6.06218i	0.138242	+	0.239442i	−0.788589	+	0.614920i	$0.789188\pi$
$642$		0			0
$643$	2.59808	−	4.50000i	0.102458	−	0.177463i	−0.810239	−	0.586100i	$-0.800663\pi$
$643$	2.59808	−	4.50000i	0.102458	−	0.177463i	0.912697	+	0.408637i	$0.133996\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.8564			0.544752			0.272376	−	0.962191i	$-0.412191\pi$
$647$	13.8564			0.544752			0.272376	+	0.962191i	$0.412191\pi$
$648$		0			0
$649$	3.00000			0.117760
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.500000	−	0.866025i	0.0195665	−	0.0338902i	−0.856076	−	0.516849i	$-0.827105\pi$
$653$	0.500000	−	0.866025i	0.0195665	−	0.0338902i	0.875643	+	0.482959i	$0.160438\pi$
$654$		0			0
$655$	7.79423	+	13.5000i	0.304546	+	0.527489i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.9186	+	34.5000i	0.775918	+	1.34393i	0.934277	+	0.356548i	$0.116046\pi$
$659$	19.9186	+	34.5000i	0.775918	+	1.34393i	−0.158359	+	0.987382i	$0.550620\pi$
$660$		0			0
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	−0.982632	−	0.185565i	$-0.940588\pi$
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	0.652020	+	0.758202i	$0.273922\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.0000			−0.465340
$666$		0			0
$667$	8.66025			0.335326
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.06218	+	10.5000i	−0.234028	+	0.405348i
$672$		0			0
$673$	−2.50000	−	4.33013i	−0.0963679	−	0.166914i	0.813811	−	0.581130i	$-0.197389\pi$
$673$	−2.50000	−	4.33013i	−0.0963679	−	0.166914i	−0.910179	+	0.414216i	$0.864056\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.50000	−	9.52628i	−0.211382	−	0.366125i	0.740765	−	0.671764i	$-0.234463\pi$
$677$	−5.50000	−	9.52628i	−0.211382	−	0.366125i	−0.952147	+	0.305639i	$0.901130\pi$
$678$		0			0
$679$	−2.59808	+	4.50000i	−0.0997050	+	0.172694i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	34.6410			1.32550			0.662751	−	0.748840i	$-0.269389\pi$
$683$	34.6410			1.32550			0.662751	+	0.748840i	$0.269389\pi$
$684$		0			0
$685$	13.0000			0.496704
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	9.52628	+	16.5000i	0.362397	+	0.627690i	0.988355	−	0.152167i	$-0.0486252\pi$
$691$	9.52628	+	16.5000i	0.362397	+	0.627690i	−0.625958	+	0.779857i	$0.715292\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.866025	−	1.50000i	−0.0328502	−	0.0568982i
$696$		0			0
$697$	−10.0000	+	17.3205i	−0.378777	+	0.656061i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$		0			0
$703$	−55.4256			−2.09042
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.2583	+	19.5000i	−0.423413	+	0.733373i
$708$		0			0
$709$	13.5000	+	23.3827i	0.507003	+	0.878155i	0.999967	+	0.00810550i	$0.00258009\pi$
$709$	13.5000	+	23.3827i	0.507003	+	0.878155i	−0.492964	+	0.870050i	$0.664087\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−22.5000	−	38.9711i	−0.842632	−	1.45948i
$714$		0			0
$715$	2.59808	−	4.50000i	0.0971625	−	0.168290i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	41.5692			1.55027			0.775135	−	0.631795i	$-0.217682\pi$
$719$	41.5692			1.55027			0.775135	+	0.631795i	$0.217682\pi$
$720$		0			0
$721$	−3.00000			−0.111726
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$		0			0
$727$	−11.2583	−	19.5000i	−0.417548	−	0.723215i	0.578144	−	0.815935i	$-0.303777\pi$
$727$	−11.2583	−	19.5000i	−0.417548	−	0.723215i	−0.995692	+	0.0927199i	$0.970444\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	17.3205	+	30.0000i	0.640622	+	1.10959i
$732$		0			0
$733$	10.5000	−	18.1865i	0.387826	−	0.671735i	−0.604331	−	0.796734i	$-0.706559\pi$
$733$	10.5000	−	18.1865i	0.387826	−	0.671735i	0.992157	+	0.124999i	$0.0398927\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.0000			0.552532
$738$		0			0
$739$	3.46410			0.127429			0.0637145	−	0.997968i	$-0.479705\pi$
$739$	3.46410			0.127429			0.0637145	+	0.997968i	$0.479705\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.866025	−	1.50000i	0.0317714	−	0.0550297i	−0.849703	−	0.527262i	$-0.823218\pi$
$743$	0.866025	−	1.50000i	0.0317714	−	0.0550297i	0.881474	+	0.472233i	$0.156552\pi$
$744$		0			0
$745$	−5.50000	−	9.52628i	−0.201504	−	0.349016i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.00000	−	10.3923i	−0.219235	−	0.379727i
$750$		0			0
$751$	12.9904	−	22.5000i	0.474026	−	0.821037i	−0.525532	−	0.850774i	$-0.676134\pi$
$751$	12.9904	−	22.5000i	0.474026	−	0.821037i	0.999558	+	0.0297372i	$0.00946703\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−22.5167			−0.819465
$756$		0			0
$757$	−6.00000			−0.218074			−0.109037	−	0.994038i	$-0.534777\pi$
$757$	−6.00000			−0.218074			−0.109037	+	0.994038i	$0.534777\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.5000	+	37.2391i	−0.779374	+	1.34992i	0.152928	+	0.988237i	$0.451130\pi$
$761$	−21.5000	+	37.2391i	−0.779374	+	1.34992i	−0.932303	+	0.361679i	$0.882204\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.59808	−	4.50000i	−0.0938111	−	0.162486i
$768$		0			0
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	−0.856869	−	0.515534i	$-0.827594\pi$
$769$	0.500000	−	0.866025i	0.0180305	−	0.0312297i	0.874900	+	0.484304i	$0.160927\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	40.0000			1.43870			0.719350	−	0.694648i	$-0.244440\pi$
$773$	40.0000			1.43870			0.719350	+	0.694648i	$0.244440\pi$
$774$		0			0
$775$	−20.7846			−0.746605
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−17.3205	+	30.0000i	−0.620572	+	1.07486i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.50000	+	14.7224i	0.303378	+	0.525466i
$786$		0			0
$787$	−12.9904	+	22.5000i	−0.463057	+	0.802038i	−0.999112	−	0.0421450i	$-0.986581\pi$
$787$	−12.9904	+	22.5000i	−0.463057	+	0.802038i	0.536054	+	0.844183i	$0.319914\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.73205			−0.0615846
$792$		0			0
$793$	21.0000			0.745732
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.5000	+	25.1147i	−0.513616	+	0.889610i	0.486259	+	0.873815i	$0.338361\pi$
$797$	−14.5000	+	25.1147i	−0.513616	+	0.889610i	−0.999875	+	0.0157948i	$0.994972\pi$
$798$		0			0
$799$	−24.2487	−	42.0000i	−0.857858	−	1.48585i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.3923	+	18.0000i	0.366736	+	0.635206i
$804$		0			0
$805$	−7.50000	+	12.9904i	−0.264340	+	0.457851i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	4.00000			0.140633			0.0703163	−	0.997525i	$-0.477599\pi$
$809$	4.00000			0.140633			0.0703163	+	0.997525i	$0.477599\pi$
$810$		0			0
$811$	−20.7846			−0.729846			−0.364923	−	0.931038i	$-0.618905\pi$
$811$	−20.7846			−0.729846			−0.364923	+	0.931038i	$0.618905\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.46410	−	6.00000i	0.121342	−	0.210171i
$816$		0			0
$817$	30.0000	+	51.9615i	1.04957	+	1.81790i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.50000	+	6.06218i	0.122151	+	0.211571i	0.920616	−	0.390470i	$-0.127687\pi$
$821$	3.50000	+	6.06218i	0.122151	+	0.211571i	−0.798465	+	0.602042i	$0.794354\pi$
$822$		0			0
$823$	−23.3827	+	40.5000i	−0.815069	+	1.41174i	0.0942090	+	0.995552i	$0.469968\pi$
$823$	−23.3827	+	40.5000i	−0.815069	+	1.41174i	−0.909278	+	0.416189i	$0.863366\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.92820			0.240917			0.120459	−	0.992718i	$-0.461563\pi$
$827$	6.92820			0.240917			0.120459	+	0.992718i	$0.461563\pi$
$828$		0			0
$829$	−24.0000			−0.833554			−0.416777	−	0.909009i	$-0.636840\pi$
$829$	−24.0000			−0.833554			−0.416777	+	0.909009i	$0.636840\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.00000	+	13.8564i	−0.277184	+	0.480096i
$834$		0			0
$835$	−7.79423	−	13.5000i	−0.269730	−	0.467187i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.9904	+	22.5000i	0.448478	+	0.776786i	0.998287	−	0.0585039i	$-0.0186330\pi$
$839$	12.9904	+	22.5000i	0.448478	+	0.776786i	−0.549809	+	0.835290i	$0.685300\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.00000			0.137604
$846$		0			0
$847$	13.8564			0.476112
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−34.6410	+	60.0000i	−1.18748	+	2.05677i
$852$		0			0
$853$	−11.5000	−	19.9186i	−0.393753	−	0.681999i	0.599189	−	0.800608i	$-0.295490\pi$
$853$	−11.5000	−	19.9186i	−0.393753	−	0.681999i	−0.992941	+	0.118609i	$0.962157\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.5000	−	37.2391i	−0.734426	−	1.27206i	−0.954975	−	0.296687i	$-0.904118\pi$
$857$	−21.5000	−	37.2391i	−0.734426	−	1.27206i	0.220549	−	0.975376i	$-0.429215\pi$
$858$		0			0
$859$	−18.1865	+	31.5000i	−0.620517	+	1.07477i	0.368873	+	0.929480i	$0.379744\pi$
$859$	−18.1865	+	31.5000i	−0.620517	+	1.07477i	−0.989390	+	0.145286i	$0.953590\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−55.4256			−1.88671			−0.943355	−	0.331785i	$-0.892349\pi$
$863$	−55.4256			−1.88671			−0.943355	+	0.331785i	$0.892349\pi$
$864$		0			0
$865$	13.0000			0.442013
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.50000	−	7.79423i	0.152652	−	0.264401i
$870$		0			0
$871$	−12.9904	−	22.5000i	−0.440162	−	0.762383i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	7.79423	+	13.5000i	0.263493	+	0.456383i
$876$		0			0
$877$	−21.5000	+	37.2391i	−0.726003	+	1.25747i	0.232556	+	0.972583i	$0.425291\pi$
$877$	−21.5000	+	37.2391i	−0.726003	+	1.25747i	−0.958560	+	0.284892i	$0.908042\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−52.0000			−1.75192			−0.875962	−	0.482380i	$-0.839773\pi$
$881$	−52.0000			−1.75192			−0.875962	+	0.482380i	$0.839773\pi$
$882$		0			0
$883$	20.7846			0.699458			0.349729	−	0.936851i	$-0.386274\pi$
$883$	20.7846			0.699458			0.349729	+	0.936851i	$0.386274\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.59808	−	4.50000i	0.0872349	−	0.151095i	−0.819106	−	0.573641i	$-0.805530\pi$
$887$	2.59808	−	4.50000i	0.0872349	−	0.151095i	0.906341	+	0.422546i	$0.138864\pi$
$888$		0			0
$889$	−12.0000	−	20.7846i	−0.402467	−	0.697093i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−42.0000	−	72.7461i	−1.40548	−	2.43436i
$894$		0			0
$895$	3.46410	−	6.00000i	0.115792	−	0.200558i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.19615			0.173301
$900$		0			0
$901$	32.0000			1.06607
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.4545	+	28.5000i	0.546362	+	0.946327i	0.998520	+	0.0543890i	$0.0173211\pi$
$907$	16.4545	+	28.5000i	0.546362	+	0.946327i	−0.452158	+	0.891938i	$0.649346\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.4545	−	28.5000i	−0.545161	−	0.944247i	−0.998597	−	0.0529580i	$-0.983135\pi$
$911$	−16.4545	−	28.5000i	−0.545161	−	0.944247i	0.453435	−	0.891289i	$-0.350198\pi$
$912$		0			0
$913$	7.50000	−	12.9904i	0.248214	−	0.429919i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.0000			−0.891619
$918$		0			0
$919$	−13.8564			−0.457081			−0.228540	−	0.973534i	$-0.573395\pi$
$919$	−13.8564			−0.457081			−0.228540	+	0.973534i	$0.573395\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.19615	−	9.00000i	0.171033	−	0.296239i
$924$		0			0
$925$	16.0000	+	27.7128i	0.526077	+	0.911192i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	−0.996133	−	0.0878612i	$-0.971997\pi$
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	0.421976	−	0.906607i	$-0.361337\pi$
$930$		0			0
$931$	−13.8564	+	24.0000i	−0.454125	+	0.786568i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.92820			0.226576
$936$		0			0
$937$	4.00000			0.130674			0.0653372	−	0.997863i	$-0.479188\pi$
$937$	4.00000			0.130674			0.0653372	+	0.997863i	$0.479188\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	−0.917418	−	0.397924i	$-0.869731\pi$
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	0.803322	+	0.595545i	$0.203064\pi$
$942$		0			0
$943$	21.6506	+	37.5000i	0.705042	+	1.22117i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.79423	−	13.5000i	−0.253278	−	0.438691i	0.711148	−	0.703042i	$-0.248176\pi$
$947$	−7.79423	−	13.5000i	−0.253278	−	0.438691i	−0.964426	+	0.264351i	$0.914842\pi$
$948$		0			0
$949$	18.0000	−	31.1769i	0.584305	−	1.01205i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$		0			0
$955$	−1.73205			−0.0560478
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−11.2583	+	19.5000i	−0.363550	+	0.629688i
$960$		0			0
$961$	2.00000	+	3.46410i	0.0645161	+	0.111745i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.50000	−	9.52628i	−0.177051	−	0.306662i
$966$		0			0
$967$	−16.4545	+	28.5000i	−0.529140	+	0.916498i	0.470282	+	0.882516i	$0.344152\pi$
$967$	−16.4545	+	28.5000i	−0.529140	+	0.916498i	−0.999422	+	0.0339820i	$0.989181\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−38.1051			−1.22285			−0.611426	−	0.791302i	$-0.709404\pi$
$971$	−38.1051			−1.22285			−0.611426	+	0.791302i	$0.709404\pi$
$972$		0			0
$973$	3.00000			0.0961756
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.5000	+	21.6506i	−0.399910	+	0.692665i	−0.993714	−	0.111945i	$-0.964292\pi$
$977$	−12.5000	+	21.6506i	−0.399910	+	0.692665i	0.593804	+	0.804610i	$0.297625\pi$
$978$		0			0
$979$	−3.46410	−	6.00000i	−0.110713	−	0.191761i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.33013	+	7.50000i	0.138110	+	0.239213i	0.926781	−	0.375602i	$-0.122564\pi$
$983$	4.33013	+	7.50000i	0.138110	+	0.239213i	−0.788671	+	0.614815i	$0.789231\pi$
$984$		0			0
$985$	−11.0000	+	19.0526i	−0.350489	+	0.607065i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	75.0000			2.38486
$990$		0			0
$991$	−55.4256			−1.76065			−0.880327	−	0.474368i	$-0.842677\pi$
$991$	−55.4256			−1.76065			−0.880327	+	0.474368i	$0.842677\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.73205	+	3.00000i	−0.0549097	+	0.0951064i
$996$		0			0
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	0.744548	−	0.667568i	$-0.232665\pi$
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	−0.950405	+	0.311014i	$0.899332\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.i.l.577.2		4
3.2	odd	2		576.2.i.k.193.2		4
4.3	odd	2	inner	1728.2.i.l.577.1		4
8.3	odd	2		864.2.i.d.577.1		4
8.5	even	2		864.2.i.d.577.2		4
9.2	odd	6		576.2.i.k.385.2		4
9.4	even	3		5184.2.a.bl.1.1		2
9.5	odd	6		5184.2.a.bx.1.1		2
9.7	even	3	inner	1728.2.i.l.1153.2		4
12.11	even	2		576.2.i.k.193.1		4
24.5	odd	2		288.2.i.d.193.1	yes	4
24.11	even	2		288.2.i.d.193.2	yes	4
36.7	odd	6	inner	1728.2.i.l.1153.1		4
36.11	even	6		576.2.i.k.385.1		4
36.23	even	6		5184.2.a.bx.1.2		2
36.31	odd	6		5184.2.a.bl.1.2		2
72.5	odd	6		2592.2.a.l.1.1		2
72.11	even	6		288.2.i.d.97.2	yes	4
72.13	even	6		2592.2.a.p.1.1		2
72.29	odd	6		288.2.i.d.97.1	✓	4
72.43	odd	6		864.2.i.d.289.1		4
72.59	even	6		2592.2.a.l.1.2		2
72.61	even	6		864.2.i.d.289.2		4
72.67	odd	6		2592.2.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.i.d.97.1	✓	4	72.29	odd	6
288.2.i.d.97.2	yes	4	72.11	even	6
288.2.i.d.193.1	yes	4	24.5	odd	2
288.2.i.d.193.2	yes	4	24.11	even	2
576.2.i.k.193.1		4	12.11	even	2
576.2.i.k.193.2		4	3.2	odd	2
576.2.i.k.385.1		4	36.11	even	6
576.2.i.k.385.2		4	9.2	odd	6
864.2.i.d.289.1		4	72.43	odd	6
864.2.i.d.289.2		4	72.61	even	6
864.2.i.d.577.1		4	8.3	odd	2
864.2.i.d.577.2		4	8.5	even	2
1728.2.i.l.577.1		4	4.3	odd	2	inner
1728.2.i.l.577.2		4	1.1	even	1	trivial
1728.2.i.l.1153.1		4	36.7	odd	6	inner
1728.2.i.l.1153.2		4	9.7	even	3	inner
2592.2.a.l.1.1		2	72.5	odd	6
2592.2.a.l.1.2		2	72.59	even	6
2592.2.a.p.1.1		2	72.13	even	6
2592.2.a.p.1.2		2	72.67	odd	6
5184.2.a.bl.1.1		2	9.4	even	3
5184.2.a.bl.1.2		2	36.31	odd	6
5184.2.a.bx.1.1		2	9.5	odd	6
5184.2.a.bx.1.2		2	36.23	even	6

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{7} +(-0.866025 - 1.50000i) q^{11} +(-1.50000 + 2.59808i) q^{13} -4.00000 q^{17} -6.92820 q^{19} +(-4.33013 + 7.50000i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{29} +(-2.59808 + 4.50000i) q^{31} +1.73205 q^{35} +8.00000 q^{37} +(2.50000 - 4.33013i) q^{41} +(-4.33013 - 7.50000i) q^{43} +(6.06218 + 10.5000i) q^{47} +(2.00000 - 3.46410i) q^{49} -8.00000 q^{53} -1.73205 q^{55} +(-0.866025 + 1.50000i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(1.50000 + 2.59808i) q^{65} +(-4.33013 + 7.50000i) q^{67} -3.46410 q^{71} -12.0000 q^{73} +(1.50000 - 2.59808i) q^{77} +(2.59808 + 4.50000i) q^{79} +(4.33013 + 7.50000i) q^{83} +(-2.00000 + 3.46410i) q^{85} +4.00000 q^{89} -5.19615 q^{91} +(-3.46410 + 6.00000i) q^{95} +(1.50000 + 2.59808i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5}+O(q^{10}) \) 4 * q + 2 * q^5	\( 4 q + 2 q^{5} - 6 q^{13} - 16 q^{17} + 8 q^{25} - 2 q^{29} + 32 q^{37} + 10 q^{41} + 8 q^{49} - 32 q^{53} - 14 q^{61} + 6 q^{65} - 48 q^{73} + 6 q^{77} - 8 q^{85} + 16 q^{89} + 6 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - 6 * q^13 - 16 * q^17 + 8 * q^25 - 2 * q^29 + 32 * q^37 + 10 * q^41 + 8 * q^49 - 32 * q^53 - 14 * q^61 + 6 * q^65 - 48 * q^73 + 6 * q^77 - 8 * q^85 + 16 * q^89 + 6 * q^97

Introduction

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