LMFDB - Embedded newform 1728.2.i.l.577.1

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			577.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1728.577
Dual form			1728.2.i.l.1153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(-0.866025 - 1.50000i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(-0.866025 - 1.50000i) q^{7} +(0.866025 + 1.50000i) q^{11} +(-1.50000 + 2.59808i) q^{13} -4.00000 q^{17} +6.92820 q^{19} +(4.33013 - 7.50000i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{29} +(2.59808 - 4.50000i) q^{31} -1.73205 q^{35} +8.00000 q^{37} +(2.50000 - 4.33013i) q^{41} +(4.33013 + 7.50000i) q^{43} +(-6.06218 - 10.5000i) q^{47} +(2.00000 - 3.46410i) q^{49} -8.00000 q^{53} +1.73205 q^{55} +(0.866025 - 1.50000i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(1.50000 + 2.59808i) q^{65} +(4.33013 - 7.50000i) q^{67} +3.46410 q^{71} -12.0000 q^{73} +(1.50000 - 2.59808i) q^{77} +(-2.59808 - 4.50000i) q^{79} +(-4.33013 - 7.50000i) q^{83} +(-2.00000 + 3.46410i) q^{85} +4.00000 q^{89} +5.19615 q^{91} +(3.46410 - 6.00000i) q^{95} +(1.50000 + 2.59808i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.654654	−	0.755929i	$-0.272814\pi$
$7$	−0.866025	−	1.50000i	−0.327327	−	0.566947i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.866025	+	1.50000i	0.261116	+	0.452267i	0.966539	−	0.256520i	$-0.0825760\pi$
$11$	0.866025	+	1.50000i	0.261116	+	0.452267i	−0.705422	+	0.708787i	$0.749243\pi$
$12$		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	$-0.207618\pi$
$19$	6.92820			1.58944			0.794719	+	0.606977i	$0.207618\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.33013	−	7.50000i	0.902894	−	1.56386i	0.0791743	−	0.996861i	$-0.474772\pi$
$23$	4.33013	−	7.50000i	0.902894	−	1.56386i	0.823720	−	0.566997i	$-0.191895\pi$
$24$		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	−0.532645	−	0.846339i	$-0.678802\pi$
$31$	2.59808	−	4.50000i	0.466628	−	0.808224i	0.999273	+	0.0381148i	$0.0121353\pi$
$32$		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	$0.0629204\pi$
$43$	4.33013	+	7.50000i	0.660338	+	1.14374i	−0.320189	+	0.947354i	$0.603746\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.06218	−	10.5000i	−0.884260	−	1.53158i	−0.846560	−	0.532293i	$-0.821330\pi$
$47$	−6.06218	−	10.5000i	−0.884260	−	1.53158i	−0.0376995	−	0.999289i	$-0.512003\pi$
$48$		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	−0.804130	−	0.594454i	$-0.797368\pi$
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	0.916877	+	0.399170i	$0.130702\pi$
$60$		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	$-0.655897\pi$
$67$	4.33013	−	7.50000i	0.529009	−	0.916271i	0.999428	−	0.0338274i	$-0.0107696\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.46410			0.411113			0.205557	−	0.978645i	$-0.434100\pi$
$71$	3.46410			0.411113			0.205557	+	0.978645i	$0.434100\pi$
$72$		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	0.682048	−	0.731307i	$-0.261089\pi$
$79$	−2.59808	−	4.50000i	−0.292306	−	0.506290i	−0.974355	+	0.225018i	$0.927756\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.33013	−	7.50000i	−0.475293	−	0.823232i	0.524306	−	0.851530i	$-0.324325\pi$
$83$	−4.33013	−	7.50000i	−0.475293	−	0.823232i	−0.999600	+	0.0282978i	$0.990991\pi$
$84$		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	−0.820201	−	0.572076i	$-0.806138\pi$
$103$	0.866025	−	1.50000i	0.0853320	−	0.147799i	0.905533	+	0.424277i	$0.139472\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.92820			0.669775			0.334887	−	0.942258i	$-0.391302\pi$
$107$	6.92820			0.669775			0.334887	+	0.942258i	$0.391302\pi$
$108$		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	$-0.289245\pi$
$127$	13.8564			1.22956			0.614779	+	0.788700i	$0.289245\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.79423	−	13.5000i	0.680985	−	1.17950i	−0.293696	−	0.955899i	$-0.594885\pi$
$131$	7.79423	−	13.5000i	0.680985	−	1.17950i	0.974681	−	0.223602i	$-0.0717814\pi$
$132$		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	−0.900414	−	0.435035i	$-0.856736\pi$
$139$	−0.866025	+	1.50000i	−0.0734553	+	0.127228i	0.826958	+	0.562263i	$0.190069\pi$
$140$		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	$0.202085\pi$
$151$	11.2583	+	19.5000i	0.916190	+	1.58689i	0.111040	+	0.993816i	$0.464582\pi$
$152$		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	$-0.587463\pi$
$163$	−6.92820			−0.542659			−0.271329	+	0.962487i	$0.587463\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.79423	+	13.5000i	−0.603136	+	1.04466i	0.389208	+	0.921150i	$0.372749\pi$
$167$	−7.79423	+	13.5000i	−0.603136	+	1.04466i	−0.992343	+	0.123511i	$0.960584\pi$
$168$		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	$-0.583366\pi$
$179$	−6.92820			−0.517838			−0.258919	+	0.965899i	$0.583366\pi$
$180$		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	0.895655	−	0.444749i	$-0.146707\pi$
$191$	0.866025	+	1.50000i	0.0626634	+	0.108536i	−0.832992	+	0.553285i	$0.813374\pi$
$192$		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	$-0.460818\pi$
$199$	3.46410			0.245564			0.122782	+	0.992434i	$0.460818\pi$
$200$		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	−0.677603	−	0.735428i	$-0.736981\pi$
$211$	4.33013	−	7.50000i	0.298098	−	0.516321i	0.975701	+	0.219107i	$0.0703144\pi$
$212$		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	0.835571	−	0.549382i	$-0.185137\pi$
$223$	−0.866025	−	1.50000i	−0.0579934	−	0.100447i	−0.893565	+	0.448935i	$0.851804\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.06218	−	10.5000i	−0.402361	−	0.696909i	0.591649	−	0.806195i	$-0.298477\pi$
$227$	−6.06218	−	10.5000i	−0.402361	−	0.696909i	−0.994010	+	0.109286i	$0.965144\pi$
$228$		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	$0.377997\pi$
$239$	−9.52628	+	16.5000i	−0.616204	+	1.06730i	−0.990172	+	0.139855i	$0.955336\pi$
$240$		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	$-0.272265\pi$
$251$	20.7846			1.31191			0.655956	+	0.754799i	$0.272265\pi$
$252$		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	$0.0331879\pi$
$263$	9.52628	+	16.5000i	0.587416	+	1.01743i	−0.407154	+	0.913360i	$0.633479\pi$
$264$		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	$-0.638271\pi$
$271$	−13.8564			−0.841717			−0.420858	+	0.907126i	$0.638271\pi$
$272$		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	$0.505909\pi$
$283$	−14.7224	+	25.5000i	−0.875158	+	1.51582i	−0.856595	+	0.515990i	$0.827424\pi$
$284$		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	$-0.563349\pi$
$307$	−6.92820			−0.395413			−0.197707	+	0.980261i	$0.563349\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.59808	+	4.50000i	−0.147323	+	0.255172i	−0.930237	−	0.366958i	$-0.880399\pi$
$311$	−2.59808	+	4.50000i	−0.147323	+	0.255172i	0.782914	+	0.622130i	$0.213732\pi$
$312$		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	0.983139	−	0.182861i	$-0.0585357\pi$
$331$	6.06218	+	10.5000i	0.333207	+	0.577132i	−0.649931	+	0.759993i	$0.725202\pi$
$332$		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	$0.373245\pi$
$347$	−11.2583	+	19.5000i	−0.604379	+	1.04681i	−0.992149	+	0.125059i	$0.960088\pi$
$348$		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	$-0.837804\pi$
$367$	−16.4545	−	28.5000i	−0.858917	−	1.48769i	0.0140459	−	0.999901i	$-0.495529\pi$
$368$		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	$-0.586002\pi$
$379$	−10.3923			−0.533817			−0.266908	+	0.963722i	$0.586002\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.9904	−	22.5000i	0.663777	−	1.14970i	−0.315838	−	0.948813i	$-0.602286\pi$
$383$	12.9904	−	22.5000i	0.663777	−	1.14970i	0.979615	−	0.200883i	$-0.0643811\pi$
$384$		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	$0.352041\pi$
$419$	−11.2583	+	19.5000i	−0.550005	+	0.952637i	−0.998273	+	0.0587381i	$0.981292\pi$
$420$		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	$-0.732610\pi$
$431$	−27.7128			−1.33488			−0.667440	+	0.744664i	$0.732610\pi$
$432$		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	0.797342	−	0.603528i	$-0.206239\pi$
$439$	−2.59808	−	4.50000i	−0.123999	−	0.214773i	−0.921341	+	0.388755i	$0.872905\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.4545	+	28.5000i	0.781776	+	1.35408i	0.930906	+	0.365258i	$0.119019\pi$
$443$	16.4545	+	28.5000i	0.781776	+	1.35408i	−0.149130	+	0.988818i	$0.547647\pi$
$444$		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	$-0.556218\pi$
$463$	16.4545	−	28.5000i	0.764705	−	1.32451i	0.940403	−	0.340063i	$-0.110448\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.92820			−0.320599			−0.160300	−	0.987068i	$-0.551246\pi$
$467$	−6.92820			−0.320599			−0.160300	+	0.987068i	$0.551246\pi$
$468$		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	0.749982	−	0.661458i	$-0.230062\pi$
$479$	−4.33013	−	7.50000i	−0.197849	−	0.342684i	−0.947831	+	0.318774i	$0.896729\pi$
$480$		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	$-0.716083\pi$
$487$	−27.7128			−1.25579			−0.627894	+	0.778299i	$0.716083\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.866025	−	1.50000i	0.0390832	−	0.0676941i	−0.845822	−	0.533465i	$-0.820890\pi$
$491$	0.866025	−	1.50000i	0.0390832	−	0.0676941i	0.884905	+	0.465771i	$0.154223\pi$
$492$		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	−0.884759	−	0.466049i	$-0.845677\pi$
$499$	−0.866025	+	1.50000i	−0.0387686	+	0.0671492i	0.845990	+	0.533199i	$0.179010\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24.2487			1.08120			0.540598	−	0.841281i	$-0.318198\pi$
$503$	24.2487			1.08120			0.540598	+	0.841281i	$0.318198\pi$
$504$		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	$-0.427039\pi$
$523$	10.3923			0.454424			0.227212	+	0.973845i	$0.427039\pi$
$524$		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	0.649891	−	0.760027i	$-0.274814\pi$
$547$	−7.79423	−	13.5000i	−0.333257	−	0.577218i	−0.983148	+	0.182809i	$0.941481\pi$
$548$		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	−0.999573	−	0.0292191i	$-0.990698\pi$
$563$	−11.2583	+	19.5000i	−0.474482	+	0.821827i	0.525091	+	0.851046i	$0.324031\pi$
$564$		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	−0.761083	−	0.648655i	$-0.775332\pi$
$571$	4.33013	−	7.50000i	0.181210	−	0.313865i	0.942293	+	0.334790i	$0.108665\pi$
$572$		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	0.914649	−	0.404249i	$-0.132467\pi$
$587$	2.59808	+	4.50000i	0.107234	+	0.185735i	−0.807415	+	0.589984i	$0.799134\pi$
$588$		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	−0.883175	−	0.469043i	$-0.844599\pi$
$599$	−0.866025	+	1.50000i	−0.0353848	+	0.0612883i	0.847791	+	0.530331i	$0.177932\pi$
$600$		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	−0.962428	−	0.271537i	$-0.912468\pi$
$607$	−6.06218	+	10.5000i	−0.246056	+	0.426182i	0.716372	+	0.697719i	$0.245801\pi$
$608$		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	0.665793	−	0.746136i	$-0.268093\pi$
$619$	−7.79423	−	13.5000i	−0.313276	−	0.542611i	−0.979070	+	0.203526i	$0.934760\pi$
$620$		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	$-0.189806\pi$
$631$	41.5692			1.65484			0.827422	+	0.561580i	$0.189806\pi$
$632$		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	−0.912697	−	0.408637i	$-0.866004\pi$
$643$	−2.59808	+	4.50000i	−0.102458	+	0.177463i	0.810239	+	0.586100i	$0.199337\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.8564			−0.544752			−0.272376	−	0.962191i	$-0.587809\pi$
$647$	−13.8564			−0.544752			−0.272376	+	0.962191i	$0.587809\pi$
$648$		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	$-0.883954\pi$
$659$	−19.9186	−	34.5000i	−0.775918	−	1.34393i	0.158359	−	0.987382i	$-0.449380\pi$
$660$		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	$-0.730611\pi$
$683$	−34.6410			−1.32550			−0.662751	+	0.748840i	$0.730611\pi$
$684$		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	0.625958	−	0.779857i	$-0.284708\pi$
$691$	−9.52628	−	16.5000i	−0.362397	−	0.627690i	−0.988355	+	0.152167i	$0.951375\pi$
$692$		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	$-0.782318\pi$
$719$	−41.5692			−1.55027			−0.775135	+	0.631795i	$0.782318\pi$
$720$		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	0.995692	−	0.0927199i	$-0.0295561\pi$
$727$	11.2583	+	19.5000i	0.417548	+	0.723215i	−0.578144	+	0.815935i	$0.696223\pi$
$728$		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	$-0.520295\pi$
$739$	−3.46410			−0.127429			−0.0637145	+	0.997968i	$0.520295\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.866025	+	1.50000i	−0.0317714	+	0.0550297i	−0.881474	−	0.472233i	$-0.843448\pi$
$743$	−0.866025	+	1.50000i	−0.0317714	+	0.0550297i	0.849703	+	0.527262i	$0.176782\pi$
$744$		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	−0.999558	−	0.0297372i	$-0.990533\pi$
$751$	−12.9904	+	22.5000i	−0.474026	+	0.821037i	0.525532	+	0.850774i	$0.323866\pi$
$752$		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	−0.536054	−	0.844183i	$-0.680086\pi$
$787$	12.9904	−	22.5000i	0.463057	−	0.802038i	0.999112	+	0.0421450i	$0.0134192\pi$
$788$		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	$-0.381095\pi$
$811$	20.7846			0.729846			0.364923	+	0.931038i	$0.381095\pi$
$812$		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	$-0.530032\pi$
$823$	23.3827	−	40.5000i	0.815069	−	1.41174i	0.909278	−	0.416189i	$-0.136634\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.92820			−0.240917			−0.120459	−	0.992718i	$-0.538437\pi$
$827$	−6.92820			−0.240917			−0.120459	+	0.992718i	$0.538437\pi$
$828$		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	0.549809	−	0.835290i	$-0.314700\pi$
$839$	−12.9904	−	22.5000i	−0.448478	−	0.776786i	−0.998287	+	0.0585039i	$0.981367\pi$
$840$		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	$-0.620256\pi$
$859$	18.1865	−	31.5000i	0.620517	−	1.07477i	0.989390	−	0.145286i	$-0.0464103\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	55.4256			1.88671			0.943355	−	0.331785i	$-0.107651\pi$
$863$	55.4256			1.88671			0.943355	+	0.331785i	$0.107651\pi$
$864$		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	$-0.613726\pi$
$883$	−20.7846			−0.699458			−0.349729	+	0.936851i	$0.613726\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.59808	+	4.50000i	−0.0872349	+	0.151095i	−0.906341	−	0.422546i	$-0.861136\pi$
$887$	−2.59808	+	4.50000i	−0.0872349	+	0.151095i	0.819106	+	0.573641i	$0.194470\pi$
$888$		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	$-0.982679\pi$
$907$	−16.4545	−	28.5000i	−0.546362	−	0.946327i	0.452158	−	0.891938i	$-0.350654\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	16.4545	+	28.5000i	0.545161	+	0.944247i	0.998597	+	0.0529580i	$0.0168649\pi$
$911$	16.4545	+	28.5000i	0.545161	+	0.944247i	−0.453435	+	0.891289i	$0.649802\pi$
$912$		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	$-0.426605\pi$
$919$	13.8564			0.457081			0.228540	+	0.973534i	$0.426605\pi$
$920$		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	0.964426	−	0.264351i	$-0.0851578\pi$
$947$	7.79423	+	13.5000i	0.253278	+	0.438691i	−0.711148	+	0.703042i	$0.751824\pi$
$948$		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	$-0.655848\pi$
$967$	16.4545	−	28.5000i	0.529140	−	0.916498i	0.999422	−	0.0339820i	$-0.0108189\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	38.1051			1.22285			0.611426	−	0.791302i	$-0.290596\pi$
$971$	38.1051			1.22285			0.611426	+	0.791302i	$0.290596\pi$
$972$		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	0.788671	−	0.614815i	$-0.210769\pi$
$983$	−4.33013	−	7.50000i	−0.138110	−	0.239213i	−0.926781	+	0.375602i	$0.877436\pi$
$984$		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	$-0.157323\pi$
$991$	55.4256			1.76065			0.880327	+	0.474368i	$0.157323\pi$
$992$		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.577.1		4
3.2	odd	2		576.2.i.k.193.1		4
4.3	odd	2	inner	1728.2.i.l.577.2		4
8.3	odd	2		864.2.i.d.577.2		4
8.5	even	2		864.2.i.d.577.1		4
9.2	odd	6		576.2.i.k.385.1		4
9.4	even	3		5184.2.a.bl.1.2		2
9.5	odd	6		5184.2.a.bx.1.2		2
9.7	even	3	inner	1728.2.i.l.1153.1		4
12.11	even	2		576.2.i.k.193.2		4
24.5	odd	2		288.2.i.d.193.2	yes	4
24.11	even	2		288.2.i.d.193.1	yes	4
36.7	odd	6	inner	1728.2.i.l.1153.2		4
36.11	even	6		576.2.i.k.385.2		4
36.23	even	6		5184.2.a.bx.1.1		2
36.31	odd	6		5184.2.a.bl.1.1		2
72.5	odd	6		2592.2.a.l.1.2		2
72.11	even	6		288.2.i.d.97.1	✓	4
72.13	even	6		2592.2.a.p.1.2		2
72.29	odd	6		288.2.i.d.97.2	yes	4
72.43	odd	6		864.2.i.d.289.2		4
72.59	even	6		2592.2.a.l.1.1		2
72.61	even	6		864.2.i.d.289.1		4
72.67	odd	6		2592.2.a.p.1.1		2

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