LMFDB - Embedded newform 2340.2.dj.c.901.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2340,2,Mod(361,2340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2340, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2340.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.dj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 780)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.3
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2340.901
Dual form			2340.2.dj.c.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{5} +(-2.18034 + 1.25882i) q^{7} +(-0.590770 - 0.341081i) q^{11} +(-3.08725 - 1.86250i) q^{13} +(2.39778 + 4.15307i) q^{17} +(5.65099 - 3.26260i) q^{19} +(-3.68715 + 6.38633i) q^{23} -1.00000 q^{25} +(2.31431 - 4.00851i) q^{29} +0.600398i q^{31} +(-1.25882 - 2.18034i) q^{35} +(-8.85666 - 5.11339i) q^{37} +(1.31431 + 0.758819i) q^{41} +(-3.47323 - 6.01581i) q^{43} +4.73910i q^{47} +(-0.330749 + 0.572874i) q^{49} -10.3631 q^{53} +(0.341081 - 0.590770i) q^{55} +(-8.19868 + 4.73351i) q^{59} +(-5.66158 - 9.80614i) q^{61} +(1.86250 - 3.08725i) q^{65} +(-3.81225 - 2.20100i) q^{67} +(-0.291069 + 0.168049i) q^{71} -4.50354i q^{73} +1.71744 q^{77} -9.19615 q^{79} -10.0392i q^{83} +(-4.15307 + 2.39778i) q^{85} +(-11.2869 - 6.51652i) q^{89} +(9.07579 + 0.174599i) q^{91} +(3.26260 + 5.65099i) q^{95} +(7.97021 - 4.60160i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{11} - 4 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 8 q^{29} - 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 16 q^{53} + 4 q^{55} - 24 q^{59} + 8 q^{61} + 24 q^{67} + 12 q^{71} + 8 q^{77} - 32 q^{79}+ \cdots + 48 q^{97}+O(q^{100}) $ 8 * q + 12 * q^11 - 4 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 8 * q^29 - 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 16 * q^53 + 4 * q^55 - 24 * q^59 + 8 * q^61 + 24 * q^67 + 12 * q^71 + 8 * q^77 - 32 * q^79 + 12 * q^89 + 8 * q^91 + 12 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−2.18034	+	1.25882i	−0.824091	+	0.475789i	−0.851825	−	0.523826i	$-0.824504\pi$
$7$	−2.18034	+	1.25882i	−0.824091	+	0.475789i	0.0277345	+	0.999615i	$0.491171\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.590770	−	0.341081i	−0.178124	−	0.102840i	0.408287	−	0.912854i	$-0.366126\pi$
$11$	−0.590770	−	0.341081i	−0.178124	−	0.102840i	−0.586411	+	0.810014i	$0.699460\pi$
$12$		0			0
$13$	−3.08725	−	1.86250i	−0.856248	−	0.516565i
$13$	−3.08725	−	1.86250i	−0.856248	−	0.516565i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.39778	+	4.15307i	0.581546	+	1.00727i	0.995296	+	0.0968774i	$0.0308855\pi$
$17$	2.39778	+	4.15307i	0.581546	+	1.00727i	−0.413750	+	0.910391i	$0.635781\pi$
$18$		0			0
$19$	5.65099	−	3.26260i	1.29643	−	0.748492i	0.316641	−	0.948545i	$-0.397445\pi$
$19$	5.65099	−	3.26260i	1.29643	−	0.748492i	0.979785	+	0.200053i	$0.0641116\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.68715	+	6.38633i	−0.768823	+	1.33164i	0.169378	+	0.985551i	$0.445824\pi$
$23$	−3.68715	+	6.38633i	−0.768823	+	1.33164i	−0.938201	+	0.346090i	$0.887509\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.31431	−	4.00851i	0.429757	−	0.744361i	−0.567094	−	0.823653i	$-0.691933\pi$
$29$	2.31431	−	4.00851i	0.429757	−	0.744361i	0.996851	+	0.0792916i	$0.0252658\pi$
$30$		0			0
$31$			0.600398i			0.107835i	0.998545	+	0.0539174i	$0.0171708\pi$
$31$			0.600398i			0.107835i	−0.998545	+	0.0539174i	$0.982829\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.25882	−	2.18034i	−0.212779	−	0.368544i
$36$		0			0
$37$	−8.85666	−	5.11339i	−1.45603	−	0.840636i	−0.457213	−	0.889357i	$-0.651152\pi$
$37$	−8.85666	−	5.11339i	−1.45603	−	0.840636i	−0.998812	+	0.0487209i	$0.984486\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.31431	+	0.758819i	0.205261	+	0.118508i	0.599107	−	0.800669i	$-0.295522\pi$
$41$	1.31431	+	0.758819i	0.205261	+	0.118508i	−0.393846	+	0.919176i	$0.628856\pi$
$42$		0			0
$43$	−3.47323	−	6.01581i	−0.529663	−	0.917403i	−0.999401	−	0.0345974i	$-0.988985\pi$
$43$	−3.47323	−	6.01581i	−0.529663	−	0.917403i	0.469738	−	0.882806i	$-0.344348\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			4.73910i			0.691269i	0.938369	+	0.345634i	$0.112336\pi$
$47$			4.73910i			0.691269i	−0.938369	+	0.345634i	$0.887664\pi$
$48$		0			0
$49$	−0.330749	+	0.572874i	−0.0472499	+	0.0818392i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.3631			−1.42348			−0.711739	−	0.702444i	$-0.752092\pi$
$53$	−10.3631			−1.42348			−0.711739	+	0.702444i	$0.752092\pi$
$54$		0			0
$55$	0.341081	−	0.590770i	0.0459914	−	0.0796594i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.19868	+	4.73351i	−1.06738	+	0.616251i	−0.927464	−	0.373913i	$-0.878016\pi$
$59$	−8.19868	+	4.73351i	−1.06738	+	0.616251i	−0.139914	+	0.990164i	$0.544682\pi$
$60$		0			0
$61$	−5.66158	−	9.80614i	−0.724891	−	1.25555i	−0.959019	−	0.283342i	$-0.908557\pi$
$61$	−5.66158	−	9.80614i	−0.724891	−	1.25555i	0.234128	−	0.972206i	$-0.424777\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.86250	−	3.08725i	0.231015	−	0.382926i
$66$		0			0
$67$	−3.81225	−	2.20100i	−0.465740	−	0.268895i	0.248715	−	0.968577i	$-0.419992\pi$
$67$	−3.81225	−	2.20100i	−0.465740	−	0.268895i	−0.714455	+	0.699682i	$0.753325\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.291069	+	0.168049i	−0.0345435	+	0.0199437i	−0.517172	−	0.855881i	$-0.673015\pi$
$71$	−0.291069	+	0.168049i	−0.0345435	+	0.0199437i	0.482629	+	0.875825i	$0.339682\pi$
$72$		0			0
$73$		−	4.50354i		−	0.527100i	−0.964646	−	0.263550i	$-0.915107\pi$
$73$		−	4.50354i		−	0.527100i	0.964646	−	0.263550i	$-0.0848933\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.71744			0.195720
$78$		0			0
$79$	−9.19615			−1.03465			−0.517324	−	0.855790i	$-0.673072\pi$
$79$	−9.19615			−1.03465			−0.517324	+	0.855790i	$0.673072\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	10.0392i		−	1.10194i	−0.834524	−	0.550972i	$-0.814257\pi$
$83$		−	10.0392i		−	1.10194i	0.834524	−	0.550972i	$-0.185743\pi$
$84$		0			0
$85$	−4.15307	+	2.39778i	−0.450464	+	0.260075i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.2869	−	6.51652i	−1.19641	−	0.690750i	−0.236660	−	0.971593i	$-0.576053\pi$
$89$	−11.2869	−	6.51652i	−1.19641	−	0.690750i	−0.959754	+	0.280843i	$0.909386\pi$
$90$		0			0
$91$	9.07579	+	0.174599i	0.951402	+	0.0183030i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.26260	+	5.65099i	0.334736	+	0.579779i
$96$		0			0
$97$	7.97021	−	4.60160i	0.809252	−	0.467222i	−0.0374442	−	0.999299i	$-0.511922\pi$
$97$	7.97021	−	4.60160i	0.809252	−	0.467222i	0.846696	+	0.532077i	$0.178588\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.33279	−	12.7008i	0.729640	−	1.26377i	−0.227396	−	0.973802i	$-0.573021\pi$
$101$	7.33279	−	12.7008i	0.729640	−	1.26377i	0.957036	−	0.289971i	$-0.0936456\pi$
$102$		0			0
$103$	4.97569			0.490269			0.245135	−	0.969489i	$-0.421168\pi$
$103$	4.97569			0.490269			0.245135	+	0.969489i	$0.421168\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.86394	−	4.96050i	0.276868	−	0.479549i	−0.693737	−	0.720229i	$-0.744037\pi$
$107$	2.86394	−	4.96050i	0.276868	−	0.479549i	0.970605	+	0.240679i	$0.0773702\pi$
$108$		0			0
$109$		−	5.45465i		−	0.522461i	−0.965276	−	0.261230i	$-0.915872\pi$
$109$		−	5.45465i		−	0.522461i	0.965276	−	0.261230i	$-0.0841282\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.36773	+	7.56512i	0.410881	+	0.711667i	0.994986	−	0.100011i	$-0.0318878\pi$
$113$	4.36773	+	7.56512i	0.410881	+	0.711667i	−0.584105	+	0.811678i	$0.698554\pi$
$114$		0			0
$115$	−6.38633	−	3.68715i	−0.595528	−	0.343828i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.4559	−	6.03674i	−0.958494	−	0.553387i
$120$		0			0
$121$	−5.26733	−	9.12328i	−0.478848	−	0.829389i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−11.0294	+	19.1035i	−0.978704	+	1.69516i	−0.311576	+	0.950221i	$0.600857\pi$
$127$	−11.0294	+	19.1035i	−0.978704	+	1.69516i	−0.667128	+	0.744943i	$0.732477\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.85666			0.686439			0.343220	−	0.939255i	$-0.388483\pi$
$131$	7.85666			0.686439			0.343220	+	0.939255i	$0.388483\pi$
$132$		0			0
$133$	−8.21405	+	14.2271i	−0.712248	+	1.23365i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.1725	−	7.60514i	1.12540	−	0.649751i	0.182627	−	0.983182i	$-0.441540\pi$
$137$	13.1725	−	7.60514i	1.12540	−	0.649751i	0.942774	+	0.333431i	$0.108206\pi$
$138$		0			0
$139$	6.77792	+	11.7397i	0.574895	+	0.995748i	0.996053	+	0.0887606i	$0.0282906\pi$
$139$	6.77792	+	11.7397i	0.574895	+	0.995748i	−0.421158	+	0.906987i	$0.638376\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.18859	+	2.15331i	0.0993948	+	0.180069i
$144$		0			0
$145$	4.00851	+	2.31431i	0.332888	+	0.192193i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.14760	+	4.12667i	−0.585554	+	0.338070i	−0.763338	−	0.646000i	$-0.776441\pi$
$149$	−7.14760	+	4.12667i	−0.585554	+	0.338070i	0.177783	+	0.984070i	$0.443107\pi$
$150$		0			0
$151$		−	3.83307i		−	0.311931i	−0.987763	−	0.155965i	$-0.950151\pi$
$151$		−	3.83307i		−	0.311931i	0.987763	−	0.155965i	$-0.0498489\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.600398			−0.0482252
$156$		0			0
$157$	−21.8654			−1.74505			−0.872524	−	0.488572i	$-0.837518\pi$
$157$	−21.8654			−1.74505			−0.872524	+	0.488572i	$0.837518\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	18.5658i		−	1.46319i
$162$		0			0
$163$	−6.94402	+	4.00913i	−0.543897	+	0.314019i	−0.746657	−	0.665209i	$-0.768342\pi$
$163$	−6.94402	+	4.00913i	−0.543897	+	0.314019i	0.202760	+	0.979229i	$0.435009\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.76368	−	4.48236i	−0.600771	−	0.346856i	0.168574	−	0.985689i	$-0.446084\pi$
$167$	−7.76368	−	4.48236i	−0.600771	−	0.346856i	−0.769345	+	0.638834i	$0.779417\pi$
$168$		0			0
$169$	6.06218	+	11.5000i	0.466321	+	0.884615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.97652	−	10.3516i	−0.454386	−	0.787020i	0.544267	−	0.838912i	$-0.316808\pi$
$173$	−5.97652	−	10.3516i	−0.454386	−	0.787020i	−0.998653	+	0.0518925i	$0.983475\pi$
$174$		0			0
$175$	2.18034	−	1.25882i	0.164818	−	0.0951578i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.60426	+	16.6351i	−0.717856	+	1.24336i	0.243991	+	0.969777i	$0.421543\pi$
$179$	−9.60426	+	16.6351i	−0.717856	+	1.24336i	−0.961848	+	0.273586i	$0.911790\pi$
$180$		0			0
$181$	−14.2526			−1.05939			−0.529694	−	0.848189i	$-0.677693\pi$
$181$	−14.2526			−1.05939			−0.529694	+	0.848189i	$0.677693\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.11339	−	8.85666i	0.375944	−	0.651154i
$186$		0			0
$187$		−	3.27135i		−	0.239225i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.84058	−	8.38414i	−0.350252	−	0.606655i	0.636041	−	0.771655i	$-0.280571\pi$
$191$	−4.84058	−	8.38414i	−0.350252	−	0.606655i	−0.986294	+	0.165000i	$0.947237\pi$
$192$		0			0
$193$	11.1428	+	6.43331i	0.802078	+	0.463080i	0.844197	−	0.536033i	$-0.180078\pi$
$193$	11.1428	+	6.43331i	0.802078	+	0.463080i	−0.0421193	+	0.999113i	$0.513411\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.6883	+	8.48030i	1.04650	+	0.604196i	0.921667	−	0.387982i	$-0.126828\pi$
$197$	14.6883	+	8.48030i	1.04650	+	0.604196i	0.124831	+	0.992178i	$0.460161\pi$
$198$		0			0
$199$	−1.30260	−	2.25617i	−0.0923391	−	0.159936i	0.816156	−	0.577832i	$-0.196101\pi$
$199$	−1.30260	−	2.25617i	−0.0923391	−	0.159936i	−0.908495	+	0.417896i	$0.862768\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			11.6532i			0.817895i
$204$		0			0
$205$	−0.758819	+	1.31431i	−0.0529982	+	0.0917956i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.45125			−0.307899
$210$		0			0
$211$	0.649913	−	1.12568i	0.0447418	−	0.0774951i	−0.842787	−	0.538247i	$-0.819087\pi$
$211$	0.649913	−	1.12568i	0.0447418	−	0.0774951i	0.887529	+	0.460752i	$0.152420\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.01581	−	3.47323i	0.410275	−	0.236872i
$216$		0			0
$217$	−0.755793	−	1.30907i	−0.0513066	−	0.0888656i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.332573	−	17.2874i	0.0223713	−	1.16288i
$222$		0			0
$223$	16.6814	+	9.63103i	1.11707	+	0.644941i	0.940652	−	0.339374i	$-0.110215\pi$
$223$	16.6814	+	9.63103i	1.11707	+	0.644941i	0.176420	+	0.984315i	$0.443548\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.2774	+	11.1298i	−1.27949	+	0.738713i	−0.976754	−	0.214363i	$-0.931233\pi$
$227$	−19.2774	+	11.1298i	−1.27949	+	0.738713i	−0.302734	+	0.953075i	$0.597899\pi$
$228$		0			0
$229$		−	10.5393i		−	0.696456i	−0.937410	−	0.348228i	$-0.886783\pi$
$229$		−	10.5393i		−	0.696456i	0.937410	−	0.348228i	$-0.113217\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−28.3517			−1.85738			−0.928689	−	0.370859i	$-0.879063\pi$
$233$	−28.3517			−1.85738			−0.928689	+	0.370859i	$0.879063\pi$
$234$		0			0
$235$	−4.73910			−0.309145
$236$		0			0
$237$		0			0
$238$		0			0
$239$			7.76660i			0.502379i	0.967938	+	0.251190i	$0.0808218\pi$
$239$			7.76660i			0.502379i	−0.967938	+	0.251190i	$0.919178\pi$
$240$		0			0
$241$	−0.256282	+	0.147964i	−0.0165086	+	0.00953122i	−0.508232	−	0.861220i	$-0.669701\pi$
$241$	−0.256282	+	0.147964i	−0.0165086	+	0.00953122i	0.491723	+	0.870752i	$0.336367\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.572874	−	0.330749i	−0.0365996	−	0.0211308i
$246$		0			0
$247$	−23.5226	−	0.452525i	−1.49671	−	0.0287935i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.07554	−	1.86288i	−0.0678872	−	0.117584i	0.830084	−	0.557639i	$-0.188292\pi$
$251$	−1.07554	−	1.86288i	−0.0678872	−	0.117584i	−0.897971	+	0.440054i	$0.854959\pi$
$252$		0			0
$253$	4.35651	−	2.51523i	0.273892	−	0.158131i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.89682	−	3.28538i	0.118320	−	0.204936i	−0.800782	−	0.598956i	$-0.795582\pi$
$257$	1.89682	−	3.28538i	0.118320	−	0.204936i	0.919102	+	0.394020i	$0.128916\pi$
$258$		0			0
$259$	25.7473			1.59986
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.59153	−	9.68481i	0.344788	−	0.597191i	−0.640527	−	0.767936i	$-0.721284\pi$
$263$	5.59153	−	9.68481i	0.344788	−	0.597191i	0.985315	+	0.170745i	$0.0546174\pi$
$264$		0			0
$265$		−	10.3631i		−	0.636599i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.8540	+	23.9957i	0.844690	+	1.46305i	0.885890	+	0.463896i	$0.153549\pi$
$269$	13.8540	+	23.9957i	0.844690	+	1.46305i	−0.0411996	+	0.999151i	$0.513118\pi$
$270$		0			0
$271$	27.0381	+	15.6104i	1.64245	+	0.948267i	0.979960	+	0.199194i	$0.0638322\pi$
$271$	27.0381	+	15.6104i	1.64245	+	0.948267i	0.662487	+	0.749074i	$0.269501\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.590770	+	0.341081i	0.0356248	+	0.0205680i
$276$		0			0
$277$	1.07520	+	1.86230i	0.0646023	+	0.111894i	0.896518	−	0.443008i	$-0.146089\pi$
$277$	1.07520	+	1.86230i	0.0646023	+	0.111894i	−0.831915	+	0.554903i	$0.812755\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			20.0311i			1.19496i	0.801885	+	0.597478i	$0.203830\pi$
$281$			20.0311i			1.19496i	−0.801885	+	0.597478i	$0.796170\pi$
$282$		0			0
$283$	8.45461	−	14.6438i	0.502574	−	0.870484i	−0.497421	−	0.867509i	$-0.665720\pi$
$283$	8.45461	−	14.6438i	0.502574	−	0.870484i	0.999996	−	0.00297501i	$-0.000946976\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.82086			−0.225538
$288$		0			0
$289$	−2.99867	+	5.19386i	−0.176393	+	0.305521i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	10.9754	−	6.33668i	0.641192	−	0.370193i	−0.143881	−	0.989595i	$-0.545958\pi$
$293$	10.9754	−	6.33668i	0.641192	−	0.370193i	0.785074	+	0.619402i	$0.212625\pi$
$294$		0			0
$295$	−4.73351	−	8.19868i	−0.275596	−	0.477346i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	23.2777	−	12.8488i	1.34618	−	0.743068i
$300$		0			0
$301$	15.1456	+	8.74434i	0.872980	+	0.504015i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.80614	−	5.66158i	0.561498	−	0.324181i
$306$		0			0
$307$			7.54738i			0.430752i	0.976531	+	0.215376i	$0.0690976\pi$
$307$			7.54738i			0.430752i	−0.976531	+	0.215376i	$0.930902\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−22.0924			−1.25274			−0.626372	−	0.779524i	$-0.715461\pi$
$311$	−22.0924			−1.25274			−0.626372	+	0.779524i	$0.715461\pi$
$312$		0			0
$313$	−10.9392			−0.618318			−0.309159	−	0.951010i	$-0.600048\pi$
$313$	−10.9392			−0.618318			−0.309159	+	0.951010i	$0.600048\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			20.9873i			1.17877i	0.807854	+	0.589383i	$0.200629\pi$
$317$			20.9873i			1.17877i	−0.807854	+	0.589383i	$0.799371\pi$
$318$		0			0
$319$	−2.73445	+	1.57874i	−0.153100	+	0.0883924i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	27.0996	+	15.6460i	1.50786	+	0.870566i
$324$		0			0
$325$	3.08725	+	1.86250i	0.171250	+	0.103313i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.96567	−	10.3328i	−0.328898	−	0.569668i
$330$		0			0
$331$	12.1031	−	6.98771i	0.665245	−	0.384079i	−0.129028	−	0.991641i	$-0.541186\pi$
$331$	12.1031	−	6.98771i	0.665245	−	0.384079i	0.794272	+	0.607562i	$0.207852\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.20100	−	3.81225i	0.120254	−	0.208285i
$336$		0			0
$337$	−21.2954			−1.16004			−0.580018	−	0.814603i	$-0.696955\pi$
$337$	−21.2954			−1.16004			−0.580018	+	0.814603i	$0.696955\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.204785	−	0.354697i	0.0110897	−	0.0192079i
$342$		0			0
$343$		−	19.2889i		−	1.04150i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.7167	+	20.2939i	0.628986	+	1.08944i	0.987756	+	0.156009i	$0.0498630\pi$
$347$	11.7167	+	20.2939i	0.628986	+	1.08944i	−0.358770	+	0.933426i	$0.616804\pi$
$348$		0			0
$349$	−13.2104	−	7.62701i	−0.707135	−	0.408264i	0.102865	−	0.994695i	$-0.467199\pi$
$349$	−13.2104	−	7.62701i	−0.707135	−	0.408264i	−0.809999	+	0.586431i	$0.800533\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−19.9325	−	11.5080i	−1.06090	−	0.612510i	−0.135217	−	0.990816i	$-0.543173\pi$
$353$	−19.9325	−	11.5080i	−1.06090	−	0.612510i	−0.925680	+	0.378306i	$0.876507\pi$
$354$		0			0
$355$	−0.168049	−	0.291069i	−0.00891910	−	0.0154483i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	2.03111i		−	0.107198i	−0.998563	−	0.0535990i	$-0.982931\pi$
$359$		−	2.03111i		−	0.107198i	0.998563	−	0.0535990i	$-0.0170693\pi$
$360$		0			0
$361$	11.7891	−	20.4194i	0.620480	−	1.07470i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.50354			0.235726
$366$		0			0
$367$	−13.0719	+	22.6412i	−0.682348	+	1.18186i	0.291915	+	0.956444i	$0.405708\pi$
$367$	−13.0719	+	22.6412i	−0.682348	+	1.18186i	−0.974262	+	0.225417i	$0.927626\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	22.5950	−	13.0452i	1.17308	−	0.677275i
$372$		0			0
$373$	−5.12680	−	8.87988i	−0.265456	−	0.459783i	0.702227	−	0.711953i	$-0.252189\pi$
$373$	−5.12680	−	8.87988i	−0.265456	−	0.459783i	−0.967683	+	0.252170i	$0.918856\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.6107	+	8.06484i	−0.752490	+	0.415360i
$378$		0			0
$379$	−13.0013	−	7.50632i	−0.667833	−	0.385574i	0.127422	−	0.991849i	$-0.459330\pi$
$379$	−13.0013	−	7.50632i	−0.667833	−	0.385574i	−0.795255	+	0.606275i	$0.792663\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.60256	+	3.81199i	−0.337375	+	0.194784i	−0.659111	−	0.752046i	$-0.729067\pi$
$383$	−6.60256	+	3.81199i	−0.337375	+	0.194784i	0.321736	+	0.946830i	$0.395734\pi$
$384$		0			0
$385$			1.71744i			0.0875288i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.91824			−0.249364			−0.124682	−	0.992197i	$-0.539791\pi$
$389$	−4.91824			−0.249364			−0.124682	+	0.992197i	$0.539791\pi$
$390$		0			0
$391$	−35.3638			−1.78843
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	9.19615i		−	0.462709i
$396$		0			0
$397$	16.9432	−	9.78215i	0.850353	−	0.490952i	−0.0104167	−	0.999946i	$-0.503316\pi$
$397$	16.9432	−	9.78215i	0.850353	−	0.490952i	0.860770	+	0.508994i	$0.169982\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.23851	+	3.60181i	0.311536	+	0.179866i	0.647614	−	0.761969i	$-0.275767\pi$
$401$	6.23851	+	3.60181i	0.311536	+	0.179866i	−0.336077	+	0.941834i	$0.609100\pi$
$402$		0			0
$403$	1.11824	−	1.85358i	0.0557036	−	0.0923333i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.48817	+	6.04168i	0.172902	+	0.299475i
$408$		0			0
$409$	24.6051	−	14.2057i	1.21664	−	0.702429i	0.252444	−	0.967611i	$-0.418766\pi$
$409$	24.6051	−	14.2057i	1.21664	−	0.702429i	0.964198	+	0.265182i	$0.0854322\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	11.9173	−	20.6413i	0.586410	−	1.01569i
$414$		0			0
$415$	10.0392			0.492805
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−17.7177	+	30.6879i	−0.865564	+	1.49920i	0.000921968		1.00000i	$0.499707\pi$
$419$	−17.7177	+	30.6879i	−0.865564	+	1.49920i	−0.866486	+	0.499201i	$0.833627\pi$
$420$		0			0
$421$		−	24.9625i		−	1.21660i	−0.793708	−	0.608299i	$-0.791852\pi$
$421$		−	24.9625i		−	1.21660i	0.793708	−	0.608299i	$-0.208148\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.39778	−	4.15307i	−0.116309	−	0.201454i
$426$		0			0
$427$	24.6883	+	14.2538i	1.19475	+	0.689790i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.463797	+	0.267773i	0.0223403	+	0.0128982i	0.511129	−	0.859504i	$-0.329228\pi$
$431$	0.463797	+	0.267773i	0.0223403	+	0.0128982i	−0.488788	+	0.872402i	$0.662561\pi$
$432$		0			0
$433$	6.34967	+	10.9980i	0.305146	+	0.528528i	0.977294	−	0.211889i	$-0.0679615\pi$
$433$	6.34967	+	10.9980i	0.305146	+	0.528528i	−0.672148	+	0.740417i	$0.734628\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			48.1188i			2.30183i
$438$		0			0
$439$	−6.71752	+	11.6351i	−0.320610	+	0.555312i	−0.980614	−	0.195949i	$-0.937221\pi$
$439$	−6.71752	+	11.6351i	−0.320610	+	0.555312i	0.660004	+	0.751262i	$0.270554\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.83564			0.0872138			0.0436069	−	0.999049i	$-0.486115\pi$
$443$	1.83564			0.0872138			0.0436069	+	0.999049i	$0.486115\pi$
$444$		0			0
$445$	6.51652	−	11.2869i	0.308913	−	0.535052i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7.49598	+	4.32780i	−0.353757	+	0.204242i	−0.666339	−	0.745649i	$-0.732140\pi$
$449$	−7.49598	+	4.32780i	−0.353757	+	0.204242i	0.312582	+	0.949891i	$0.398806\pi$
$450$		0			0
$451$	−0.517638	−	0.896575i	−0.0243746	−	0.0422181i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.174599	+	9.07579i	−0.00818533	+	0.425480i
$456$		0			0
$457$	32.3298	+	18.6656i	1.51232	+	0.873141i	0.999896	+	0.0144108i	$0.00458726\pi$
$457$	32.3298	+	18.6656i	1.51232	+	0.873141i	0.512428	+	0.858730i	$0.328746\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.0005	−	12.7020i	1.02466	−	0.591590i	0.109212	−	0.994018i	$-0.465167\pi$
$461$	22.0005	−	12.7020i	1.02466	−	0.591590i	0.915451	+	0.402429i	$0.131834\pi$
$462$		0			0
$463$			22.2244i			1.03285i	0.856331	+	0.516427i	$0.172738\pi$
$463$			22.2244i			1.03285i	−0.856331	+	0.516427i	$0.827262\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.97104			−0.137483			−0.0687417	−	0.997634i	$-0.521898\pi$
$467$	−2.97104			−0.137483			−0.0687417	+	0.997634i	$0.521898\pi$
$468$		0			0
$469$	11.0827			0.511750
$470$		0			0
$471$		0			0
$472$		0			0
$473$			4.73862i			0.217882i
$474$		0			0
$475$	−5.65099	+	3.26260i	−0.259285	+	0.149698i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.6262	−	9.02178i	−0.713979	−	0.412216i	0.0985537	−	0.995132i	$-0.468578\pi$
$479$	−15.6262	−	9.02178i	−0.713979	−	0.412216i	−0.812533	+	0.582916i	$0.801912\pi$
$480$		0			0
$481$	17.8190	+	32.2818i	0.812475	+	1.47192i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.60160	+	7.97021i	0.208948	+	0.361908i
$486$		0			0
$487$	31.9312	−	18.4355i	1.44694	−	0.835393i	0.448644	−	0.893710i	$-0.351907\pi$
$487$	31.9312	−	18.4355i	1.44694	−	0.835393i	0.998298	+	0.0583177i	$0.0185736\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.24668	−	10.8196i	0.281909	−	0.488280i	−0.689946	−	0.723861i	$-0.742366\pi$
$491$	6.24668	−	10.8196i	0.281909	−	0.488280i	0.971855	+	0.235580i	$0.0756991\pi$
$492$		0			0
$493$	22.1968			0.999695
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.423086	−	0.732806i	0.0189780	−	0.0328709i
$498$		0			0
$499$			25.2232i			1.12914i	0.825384	+	0.564572i	$0.190959\pi$
$499$			25.2232i			1.12914i	−0.825384	+	0.564572i	$0.809041\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.1455	+	36.6251i	0.942833	+	1.63303i	0.760033	+	0.649884i	$0.225183\pi$
$503$	21.1455	+	36.6251i	0.942833	+	1.63303i	0.182800	+	0.983150i	$0.441484\pi$
$504$		0			0
$505$	12.7008	+	7.33279i	0.565177	+	0.326305i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	32.0972	+	18.5313i	1.42268	+	0.821387i	0.996528	−	0.0832618i	$-0.0265338\pi$
$509$	32.0972	+	18.5313i	1.42268	+	0.821387i	0.426157	+	0.904649i	$0.359867\pi$
$510$		0			0
$511$	5.66914	+	9.81925i	0.250788	+	0.434378i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			4.97569i			0.219255i
$516$		0			0
$517$	1.61642	−	2.79972i	0.0710900	−	0.123131i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.6983			0.687754			0.343877	−	0.939015i	$-0.388260\pi$
$521$	15.6983			0.687754			0.343877	+	0.939015i	$0.388260\pi$
$522$		0			0
$523$	−11.8549	+	20.5333i	−0.518378	+	0.897858i	0.481394	+	0.876505i	$0.340131\pi$
$523$	−11.8549	+	20.5333i	−0.518378	+	0.897858i	−0.999772	+	0.0213532i	$0.993203\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.49350	+	1.43962i	−0.108618	+	0.0627109i
$528$		0			0
$529$	−15.6901	−	27.1761i	−0.682178	−	1.18157i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.64431	−	4.79057i	−0.114538	−	0.207503i
$534$		0			0
$535$	4.96050	+	2.86394i	0.214461	+	0.123819i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.390794	−	0.225625i	0.0168327	−	0.00971835i
$540$		0			0
$541$		−	33.9788i		−	1.46086i	−0.682987	−	0.730431i	$-0.739319\pi$
$541$		−	33.9788i		−	1.46086i	0.682987	−	0.730431i	$-0.260681\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.45465			0.233652
$546$		0			0
$547$	−11.5043			−0.491888			−0.245944	−	0.969284i	$-0.579098\pi$
$547$	−11.5043			−0.491888			−0.245944	+	0.969284i	$0.579098\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	30.2027i		−	1.28668i
$552$		0			0
$553$	20.0507	−	11.5763i	0.852644	−	0.492274i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.4808	−	6.62845i	−0.486458	−	0.280856i	0.236646	−	0.971596i	$-0.423952\pi$
$557$	−11.4808	−	6.62845i	−0.486458	−	0.280856i	−0.723104	+	0.690739i	$0.757285\pi$
$558$		0			0
$559$	−0.481740	+	25.0412i	−0.0203754	+	1.05913i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.1263	+	33.1277i	0.806077	+	1.39617i	0.915562	+	0.402177i	$0.131746\pi$
$563$	19.1263	+	33.1277i	0.806077	+	1.39617i	−0.109485	+	0.993988i	$0.534920\pi$
$564$		0			0
$565$	−7.56512	+	4.36773i	−0.318267	+	0.183752i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.68122	+	2.91196i	−0.0704803	+	0.122076i	−0.899112	−	0.437719i	$-0.855787\pi$
$569$	−1.68122	+	2.91196i	−0.0704803	+	0.122076i	0.828632	+	0.559794i	$0.189120\pi$
$570$		0			0
$571$	11.7625			0.492246			0.246123	−	0.969239i	$-0.420843\pi$
$571$	11.7625			0.492246			0.246123	+	0.969239i	$0.420843\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.68715	−	6.38633i	0.153765	−	0.266328i
$576$		0			0
$577$			9.86954i			0.410874i	0.978670	+	0.205437i	$0.0658616\pi$
$577$			9.86954i			0.410874i	−0.978670	+	0.205437i	$0.934138\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.6375	+	21.8888i	0.524293	+	0.908102i
$582$		0			0
$583$	6.12220	+	3.53465i	0.253556	+	0.146390i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−23.5364	−	13.5888i	−0.971453	−	0.560869i	−0.0717740	−	0.997421i	$-0.522866\pi$
$587$	−23.5364	−	13.5888i	−0.971453	−	0.560869i	−0.899679	+	0.436552i	$0.856199\pi$
$588$		0			0
$589$	1.95886	+	3.39285i	0.0807134	+	0.139800i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	44.1747i		−	1.81404i	−0.421090	−	0.907019i	$-0.638352\pi$
$593$		−	44.1747i		−	1.81404i	0.421090	−	0.907019i	$-0.361648\pi$
$594$		0			0
$595$	6.03674	−	10.4559i	0.247482	−	0.428651i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.1581			−0.660203			−0.330101	−	0.943945i	$-0.607083\pi$
$599$	−16.1581			−0.660203			−0.330101	+	0.943945i	$0.607083\pi$
$600$		0			0
$601$	7.11685	−	12.3267i	0.290302	−	0.502819i	−0.683579	−	0.729877i	$-0.739577\pi$
$601$	7.11685	−	12.3267i	0.290302	−	0.502819i	0.973881	+	0.227058i	$0.0729108\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.12328	−	5.26733i	0.370914	−	0.214147i
$606$		0			0
$607$	3.96336	+	6.86475i	0.160868	+	0.278631i	0.935180	−	0.354172i	$-0.115237\pi$
$607$	3.96336	+	6.86475i	0.160868	+	0.278631i	−0.774312	+	0.632804i	$0.781904\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.82658	−	14.6308i	0.357085	−	0.591897i
$612$		0			0
$613$	−16.9541	−	9.78846i	−0.684770	−	0.395352i	0.116880	−	0.993146i	$-0.462711\pi$
$613$	−16.9541	−	9.78846i	−0.684770	−	0.395352i	−0.801650	+	0.597794i	$0.796044\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.3970	+	15.2403i	−1.06270	+	0.613552i	−0.926179	−	0.377084i	$-0.876927\pi$
$617$	−26.3970	+	15.2403i	−1.06270	+	0.613552i	−0.136525	+	0.990637i	$0.543593\pi$
$618$		0			0
$619$			36.7094i			1.47548i	0.675087	+	0.737738i	$0.264106\pi$
$619$			36.7094i			1.47548i	−0.675087	+	0.737738i	$0.735894\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	32.8125			1.31460
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	49.0431i		−	1.95548i
$630$		0			0
$631$	−5.94414	+	3.43185i	−0.236633	+	0.136620i	−0.613628	−	0.789595i	$-0.710291\pi$
$631$	−5.94414	+	3.43185i	−0.236633	+	0.136620i	0.376996	+	0.926215i	$0.376957\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−19.1035	−	11.0294i	−0.758101	−	0.437690i
$636$		0			0
$637$	2.08808	−	1.15258i	0.0827329	−	0.0456670i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.31212	−	12.6650i	−0.288812	−	0.500236i	0.684715	−	0.728811i	$-0.259927\pi$
$641$	−7.31212	−	12.6650i	−0.288812	−	0.500236i	−0.973526	+	0.228575i	$0.926593\pi$
$642$		0			0
$643$	18.5342	−	10.7007i	0.730919	−	0.421996i	−0.0878394	−	0.996135i	$-0.527996\pi$
$643$	18.5342	−	10.7007i	0.730919	−	0.421996i	0.818758	+	0.574138i	$0.194663\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.37395	−	12.7721i	0.289900	−	0.502122i	−0.683886	−	0.729589i	$-0.739711\pi$
$647$	7.37395	−	12.7721i	0.289900	−	0.502122i	0.973786	+	0.227468i	$0.0730446\pi$
$648$		0			0
$649$	6.45805			0.253501
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.96066	+	12.0562i	−0.272392	+	0.471796i	−0.969474	−	0.245195i	$-0.921148\pi$
$653$	−6.96066	+	12.0562i	−0.272392	+	0.471796i	0.697082	+	0.716991i	$0.254481\pi$
$654$		0			0
$655$			7.85666i			0.306985i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.60229	+	2.77524i	0.0624162	+	0.108108i	0.895545	−	0.444971i	$-0.146786\pi$
$659$	1.60229	+	2.77524i	0.0624162	+	0.108108i	−0.833129	+	0.553079i	$0.813453\pi$
$660$		0			0
$661$	−26.8607	−	15.5080i	−1.04476	−	0.603192i	−0.123582	−	0.992334i	$-0.539438\pi$
$661$	−26.8607	−	15.5080i	−1.04476	−	0.603192i	−0.921178	+	0.389142i	$0.872771\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−14.2271	−	8.21405i	−0.551705	−	0.318527i
$666$		0			0
$667$	17.0664	+	29.5599i	0.660815	+	1.14456i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			7.72424i			0.298191i
$672$		0			0
$673$	9.74082	−	16.8716i	0.375481	−	0.650352i	−0.614918	−	0.788591i	$-0.710811\pi$
$673$	9.74082	−	16.8716i	0.375481	−	0.650352i	0.990399	+	0.138239i	$0.0441442\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−44.0602			−1.69337			−0.846685	−	0.532095i	$-0.821405\pi$
$677$	−44.0602			−1.69337			−0.846685	+	0.532095i	$0.821405\pi$
$678$		0			0
$679$	−11.5852	+	20.0661i	−0.444598	+	0.770066i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.1167	+	8.72765i	−0.578426	+	0.333954i	−0.760507	−	0.649329i	$-0.775050\pi$
$683$	−15.1167	+	8.72765i	−0.578426	+	0.333954i	0.182082	+	0.983283i	$0.441716\pi$
$684$		0			0
$685$	7.60514	+	13.1725i	0.290578	+	0.503295i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	31.9934	+	19.3013i	1.21885	+	0.735319i
$690$		0			0
$691$	26.4277	+	15.2580i	1.00536	+	0.580443i	0.909829	−	0.414984i	$-0.136213\pi$
$691$	26.4277	+	15.2580i	1.00536	+	0.580443i	0.0955281	+	0.995427i	$0.469546\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.7397	+	6.77792i	−0.445312	+	0.257101i
$696$		0			0
$697$			7.27792i			0.275671i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	26.9510			1.01792			0.508962	−	0.860789i	$-0.330029\pi$
$701$	26.9510			1.01792			0.508962	+	0.860789i	$0.330029\pi$
$702$		0			0
$703$	−66.7318			−2.51684
$704$		0			0
$705$		0			0
$706$		0			0
$707$			36.9226i			1.38862i
$708$		0			0
$709$	−0.508972	+	0.293855i	−0.0191148	+	0.0110360i	−0.509527	−	0.860455i	$-0.670180\pi$
$709$	−0.508972	+	0.293855i	−0.0191148	+	0.0110360i	0.490412	+	0.871491i	$0.336846\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.83434	−	2.21376i	−0.143597	−	0.0829058i
$714$		0			0
$715$	−2.15331	+	1.18859i	−0.0805293	+	0.0444507i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.67083	+	8.09011i	0.174192	+	0.301710i	0.939882	−	0.341501i	$-0.110935\pi$
$719$	4.67083	+	8.09011i	0.174192	+	0.301710i	−0.765689	+	0.643211i	$0.777602\pi$
$720$		0			0
$721$	−10.8487	+	6.26349i	−0.404026	+	0.233265i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.31431	+	4.00851i	−0.0859514	+	0.148872i
$726$		0			0
$727$	−6.51180			−0.241509			−0.120755	−	0.992682i	$-0.538531\pi$
$727$	−6.51180			−0.241509			−0.120755	+	0.992682i	$0.538531\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	16.6561	−	28.8492i	0.616047	−	1.06702i
$732$		0			0
$733$			20.7661i			0.767014i	0.923538	+	0.383507i	$0.125284\pi$
$733$			20.7661i			0.767014i	−0.923538	+	0.383507i	$0.874716\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.50144	+	2.60057i	0.0553063	+	0.0957934i
$738$		0			0
$739$	−37.4028	−	21.5945i	−1.37588	−	0.794367i	−0.384223	−	0.923240i	$-0.625531\pi$
$739$	−37.4028	−	21.5945i	−1.37588	−	0.794367i	−0.991661	+	0.128874i	$0.958864\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.44574	−	4.87615i	−0.309844	−	0.178889i	0.337013	−	0.941500i	$-0.390584\pi$
$743$	−8.44574	−	4.87615i	−0.309844	−	0.178889i	−0.646857	+	0.762612i	$0.723917\pi$
$744$		0			0
$745$	−4.12667	−	7.14760i	−0.151189	−	0.261868i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			14.4207i			0.526923i
$750$		0			0
$751$	20.1431	−	34.8888i	0.735031	−	1.27311i	−0.219679	−	0.975572i	$-0.570501\pi$
$751$	20.1431	−	34.8888i	0.735031	−	1.27311i	0.954710	−	0.297539i	$-0.0961658\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.83307			0.139500
$756$		0			0
$757$	−4.06486	+	7.04055i	−0.147740	+	0.255893i	−0.930392	−	0.366567i	$-0.880533\pi$
$757$	−4.06486	+	7.04055i	−0.147740	+	0.255893i	0.782652	+	0.622460i	$0.213867\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.1452	+	7.01203i	−0.440263	+	0.254186i	−0.703709	−	0.710488i	$-0.748474\pi$
$761$	−12.1452	+	7.01203i	−0.440263	+	0.254186i	0.263446	+	0.964674i	$0.415141\pi$
$762$		0			0
$763$	6.86642	+	11.8930i	0.248581	+	0.430555i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	34.1275	+	0.656541i	1.23227	+	0.0237063i
$768$		0			0
$769$	31.2076	+	18.0177i	1.12538	+	0.649736i	0.942768	−	0.333450i	$-0.108213\pi$
$769$	31.2076	+	18.0177i	1.12538	+	0.649736i	0.182607	+	0.983186i	$0.441546\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15.9183	+	9.19044i	−0.572542	+	0.330557i	−0.758164	−	0.652064i	$-0.773903\pi$
$773$	−15.9183	+	9.19044i	−0.572542	+	0.330557i	0.185622	+	0.982621i	$0.440570\pi$
$774$		0			0
$775$		−	0.600398i		−	0.0215669i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.90289			0.354808
$780$		0			0
$781$	0.229273			0.00820404
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	21.8654i		−	0.780409i
$786$		0			0
$787$	−2.22029	+	1.28189i	−0.0791449	+	0.0456943i	−0.539050	−	0.842274i	$-0.681217\pi$
$787$	−2.22029	+	1.28189i	−0.0791449	+	0.0456943i	0.459905	+	0.887968i	$0.347883\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−19.0462	−	10.9964i	−0.677206	−	0.390985i
$792$		0			0
$793$	−0.785265	+	40.8187i	−0.0278856	+	1.44951i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.6111	−	25.3072i	−0.517552	−	0.896427i	−0.999792	−	0.0203879i	$-0.993510\pi$
$797$	−14.6111	−	25.3072i	−0.517552	−	0.896427i	0.482240	−	0.876039i	$-0.339823\pi$
$798$		0			0
$799$	−19.6818	+	11.3633i	−0.696293	+	0.402005i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.53607	+	2.66056i	−0.0542069	+	0.0938891i
$804$		0			0
$805$	18.5658			0.654359
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.5166	−	18.2154i	0.369745	−	0.640418i	−0.619780	−	0.784776i	$-0.712778\pi$
$809$	10.5166	−	18.2154i	0.369745	−	0.640418i	0.989526	+	0.144358i	$0.0461116\pi$
$810$		0			0
$811$			39.9501i			1.40284i	0.712750	+	0.701419i	$0.247450\pi$
$811$			39.9501i			1.40284i	−0.712750	+	0.701419i	$0.752550\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.00913	−	6.94402i	−0.140434	−	0.243238i
$816$		0			0
$817$	−39.2544	−	22.6635i	−1.37334	−	0.792897i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−36.6162	−	21.1404i	−1.27791	−	0.737804i	−0.301450	−	0.953482i	$-0.597471\pi$
$821$	−36.6162	−	21.1404i	−1.27791	−	0.737804i	−0.976465	+	0.215678i	$0.930804\pi$
$822$		0			0
$823$	3.91824	+	6.78658i	0.136581	+	0.236565i	0.926200	−	0.377032i	$-0.123055\pi$
$823$	3.91824	+	6.78658i	0.136581	+	0.236565i	−0.789619	+	0.613597i	$0.789722\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	36.0916i		−	1.25503i	−0.778605	−	0.627515i	$-0.784072\pi$
$827$		−	36.0916i		−	1.25503i	0.778605	−	0.627515i	$-0.215928\pi$
$828$		0			0
$829$	−12.7220	+	22.0351i	−0.441852	+	0.765309i	−0.997827	−	0.0658893i	$-0.979012\pi$
$829$	−12.7220	+	22.0351i	−0.441852	+	0.765309i	0.555975	+	0.831199i	$0.312345\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.17225			−0.109912
$834$		0			0
$835$	4.48236	−	7.76368i	0.155119	−	0.268673i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	41.3763	−	23.8886i	1.42847	−	0.824727i	0.431469	−	0.902128i	$-0.357996\pi$
$839$	41.3763	−	23.8886i	1.42847	−	0.824727i	0.997000	+	0.0774010i	$0.0246622\pi$
$840$		0			0
$841$	3.78791	+	6.56085i	0.130618	+	0.226236i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11.5000	+	6.06218i	−0.395612	+	0.208545i
$846$		0			0
$847$	22.9691	+	13.2612i	0.789228	+	0.455661i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	65.3116	−	37.7077i	2.23885	−	1.29260i
$852$		0			0
$853$		−	3.49165i		−	0.119552i	−0.998212	−	0.0597759i	$-0.980961\pi$
$853$		−	3.49165i		−	0.119552i	0.998212	−	0.0597759i	$-0.0190386\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.0170			−0.820404			−0.410202	−	0.911995i	$-0.634542\pi$
$857$	−24.0170			−0.820404			−0.410202	+	0.911995i	$0.634542\pi$
$858$		0			0
$859$	1.09887			0.0374928			0.0187464	−	0.999824i	$-0.494032\pi$
$859$	1.09887			0.0374928			0.0187464	+	0.999824i	$0.494032\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	19.6082i		−	0.667472i	−0.942667	−	0.333736i	$-0.891691\pi$
$863$		−	19.6082i		−	0.667472i	0.942667	−	0.333736i	$-0.108309\pi$
$864$		0			0
$865$	10.3516	−	5.97652i	0.351966	−	0.203208i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.43281	+	3.13664i	0.184296	+	0.106403i
$870$		0			0
$871$	7.66998	+	13.8954i	0.259887	+	0.470826i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.25882	+	2.18034i	0.0425559	+	0.0737089i
$876$		0			0
$877$	30.7427	−	17.7493i	1.03811	−	0.599352i	0.118812	−	0.992917i	$-0.462091\pi$
$877$	30.7427	−	17.7493i	1.03811	−	0.599352i	0.919297	+	0.393564i	$0.128758\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.30663	−	10.9234i	0.212476	−	0.368019i	−0.740013	−	0.672592i	$-0.765181\pi$
$881$	6.30663	−	10.9234i	0.212476	−	0.368019i	0.952489	+	0.304574i	$0.0985141\pi$
$882$		0			0
$883$	−16.9815			−0.571474			−0.285737	−	0.958308i	$-0.592238\pi$
$883$	−16.9815			−0.571474			−0.285737	+	0.958308i	$0.592238\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.4683	+	23.3278i	−0.452222	+	0.783272i	−0.998524	−	0.0543167i	$-0.982702\pi$
$887$	−13.4683	+	23.3278i	−0.452222	+	0.783272i	0.546302	+	0.837589i	$0.316035\pi$
$888$		0			0
$889$		−	55.5362i		−	1.86263i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.4618	+	26.7806i	0.517409	+	0.896179i
$894$		0			0
$895$	−16.6351	−	9.60426i	−0.556049	−	0.321035i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.40670	+	1.38951i	0.0802680	+	0.0463427i
$900$		0			0
$901$	−24.8484	−	43.0386i	−0.827819	−	1.43382i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	14.2526i		−	0.473773i
$906$		0			0
$907$	11.5207	−	19.9544i	0.382538	−	0.662575i	−0.608887	−	0.793257i	$-0.708384\pi$
$907$	11.5207	−	19.9544i	0.382538	−	0.662575i	0.991424	+	0.130683i	$0.0417169\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.8698			0.757709			0.378854	−	0.925456i	$-0.376318\pi$
$911$	22.8698			0.757709			0.378854	+	0.925456i	$0.376318\pi$
$912$		0			0
$913$	−3.42418	+	5.93086i	−0.113324	+	0.196283i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.1302	+	9.89011i	−0.565688	+	0.326600i
$918$		0			0
$919$	−13.9537	−	24.1686i	−0.460291	−	0.797248i	0.538684	−	0.842508i	$-0.318922\pi$
$919$	−13.9537	−	24.1686i	−0.460291	−	0.797248i	−0.998975	+	0.0452601i	$0.985588\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.21159	+	0.0233085i	0.0398801	+	0.000767208i
$924$		0			0
$925$	8.85666	+	5.11339i	0.291205	+	0.168127i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−30.6659	+	17.7050i	−1.00612	+	0.580882i	−0.910052	−	0.414494i	$-0.863959\pi$
$929$	−30.6659	+	17.7050i	−1.00612	+	0.580882i	−0.0960642	+	0.995375i	$0.530625\pi$
$930$		0			0
$931$			4.31641i			0.141465i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.27135			0.106985
$936$		0			0
$937$	11.9030			0.388855			0.194428	−	0.980917i	$-0.437715\pi$
$937$	11.9030			0.388855			0.194428	+	0.980917i	$0.437715\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			5.02987i			0.163969i	0.996634	+	0.0819845i	$0.0261258\pi$
$941$			5.02987i			0.163969i	−0.996634	+	0.0819845i	$0.973874\pi$
$942$		0			0
$943$	−9.69213	+	5.59575i	−0.315619	+	0.182223i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.70716	−	4.44973i	−0.250449	−	0.144597i	0.369521	−	0.929222i	$-0.379522\pi$
$947$	−7.70716	−	4.44973i	−0.250449	−	0.144597i	−0.619970	+	0.784626i	$0.712855\pi$
$948$		0			0
$949$	−8.38785	+	13.9035i	−0.272281	+	0.451328i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.298508	−	0.517032i	−0.00966963	−	0.0167483i	0.861150	−	0.508351i	$-0.169745\pi$
$953$	−0.298508	−	0.517032i	−0.00966963	−	0.0167483i	−0.870820	+	0.491602i	$0.836411\pi$
$954$		0			0
$955$	8.38414	−	4.84058i	0.271304	−	0.156638i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.1470	+	33.1636i	−0.618289	+	1.07091i
$960$		0			0
$961$	30.6395			0.988372
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.43331	+	11.1428i	−0.207096	+	0.358700i
$966$		0			0
$967$		−	33.2641i		−	1.06970i	−0.844946	−	0.534851i	$-0.820368\pi$
$967$		−	33.2641i		−	1.06970i	0.844946	−	0.534851i	$-0.179632\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.1490	−	33.1671i	−0.614521	−	1.06438i	−0.990468	−	0.137740i	$-0.956016\pi$
$971$	−19.1490	−	33.1671i	−0.614521	−	1.06438i	0.375947	−	0.926641i	$-0.377317\pi$
$972$		0			0
$973$	−29.5563	−	17.0643i	−0.947532	−	0.547058i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.0098	+	6.35651i	0.352235	+	0.203363i	0.665669	−	0.746247i	$-0.268146\pi$
$977$	11.0098	+	6.35651i	0.352235	+	0.203363i	−0.313434	+	0.949610i	$0.601480\pi$
$978$		0			0
$979$	4.44533	+	7.69953i	0.142073	+	0.246078i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			48.3272i			1.54140i	0.637198	+	0.770700i	$0.280093\pi$
$983$			48.3272i			1.54140i	−0.637198	+	0.770700i	$0.719907\pi$
$984$		0			0
$985$	−8.48030	+	14.6883i	−0.270205	+	0.468008i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	51.2253			1.62887
$990$		0			0
$991$	−1.74548	+	3.02326i	−0.0554469	+	0.0960369i	−0.892417	−	0.451212i	$-0.850992\pi$
$991$	−1.74548	+	3.02326i	−0.0554469	+	0.0960369i	0.836970	+	0.547249i	$0.184325\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.25617	−	1.30260i	0.0715256	−	0.0412953i
$996$		0			0
$997$	−2.46671	−	4.27247i	−0.0781215	−	0.135310i	0.824318	−	0.566127i	$-0.191559\pi$
$997$	−2.46671	−	4.27247i	−0.0781215	−	0.135310i	−0.902439	+	0.430817i	$0.858226\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.dj.c.901.3		8
3.2	odd	2		780.2.cc.b.121.1	✓	8
13.10	even	6	inner	2340.2.dj.c.361.1		8
15.2	even	4		3900.2.bw.g.2149.3		8
15.8	even	4		3900.2.bw.l.2149.2		8
15.14	odd	2		3900.2.cd.l.901.4		8
39.23	odd	6		780.2.cc.b.361.3	yes	8
195.23	even	12		3900.2.bw.g.49.3		8
195.62	even	12		3900.2.bw.l.49.2		8
195.179	odd	6		3900.2.cd.l.2701.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.cc.b.121.1	✓	8	3.2	odd	2
780.2.cc.b.361.3	yes	8	39.23	odd	6
2340.2.dj.c.361.1		8	13.10	even	6	inner
2340.2.dj.c.901.3		8	1.1	even	1	trivial
3900.2.bw.g.49.3		8	195.23	even	12
3900.2.bw.g.2149.3		8	15.2	even	4
3900.2.bw.l.49.2		8	195.62	even	12
3900.2.bw.l.2149.2		8	15.8	even	4
3900.2.cd.l.901.4		8	15.14	odd	2
3900.2.cd.l.2701.4		8	195.179	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.dj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{5} +(-2.18034 + 1.25882i) q^{7} +(-0.590770 - 0.341081i) q^{11} +(-3.08725 - 1.86250i) q^{13} +(2.39778 + 4.15307i) q^{17} +(5.65099 - 3.26260i) q^{19} +(-3.68715 + 6.38633i) q^{23} -1.00000 q^{25} +(2.31431 - 4.00851i) q^{29} +0.600398i q^{31} +(-1.25882 - 2.18034i) q^{35} +(-8.85666 - 5.11339i) q^{37} +(1.31431 + 0.758819i) q^{41} +(-3.47323 - 6.01581i) q^{43} +4.73910i q^{47} +(-0.330749 + 0.572874i) q^{49} -10.3631 q^{53} +(0.341081 - 0.590770i) q^{55} +(-8.19868 + 4.73351i) q^{59} +(-5.66158 - 9.80614i) q^{61} +(1.86250 - 3.08725i) q^{65} +(-3.81225 - 2.20100i) q^{67} +(-0.291069 + 0.168049i) q^{71} -4.50354i q^{73} +1.71744 q^{77} -9.19615 q^{79} -10.0392i q^{83} +(-4.15307 + 2.39778i) q^{85} +(-11.2869 - 6.51652i) q^{89} +(9.07579 + 0.174599i) q^{91} +(3.26260 + 5.65099i) q^{95} +(7.97021 - 4.60160i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{11} - 4 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 8 q^{29} - 8 q^{35} - 24 q^{37} - 16 q^{43} - 4 q^{49} - 16 q^{53} + 4 q^{55} - 24 q^{59} + 8 q^{61} + 24 q^{67} + 12 q^{71} + 8 q^{77} - 32 q^{79}+ \cdots + 48 q^{97}+O(q^{100}) \) 8 * q + 12 * q^11 - 4 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 8 * q^29 - 8 * q^35 - 24 * q^37 - 16 * q^43 - 4 * q^49 - 16 * q^53 + 4 * q^55 - 24 * q^59 + 8 * q^61 + 24 * q^67 + 12 * q^71 + 8 * q^77 - 32 * q^79 + 12 * q^89 + 8 * q^91 + 12 * q^95 + 48 * q^97

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