LMFDB - Embedded newform 2520.2.bi.r.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,2,Mod(361,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2520.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2520.bi (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.1223013094$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 $ x^10 + 29x^8 + 247x^6 + 855x^4 + 1212x^2 + 588
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$2.19149i$ of defining polynomial
Character	$\chi$	$=$	2520.361
Dual form			2520.2.bi.r.1801.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(-0.780339 - 2.52806i) q^{7} +O(q^{10})$	$q+(-0.500000 - 0.866025i) q^{5} +(-0.780339 - 2.52806i) q^{7} +(-2.39788 + 4.15326i) q^{11} +5.94151 q^{13} +(3.41674 - 5.91796i) q^{17} +(-4.26995 - 7.39577i) q^{19} +(4.48961 + 7.77623i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.414934 q^{29} +(-2.80796 + 4.86353i) q^{31} +(-1.79919 + 1.93982i) q^{35} +(-2.79919 - 4.84834i) q^{37} +0.325591 q^{41} +3.90381 q^{43} +(-4.86864 - 8.43273i) q^{47} +(-5.78214 + 3.94548i) q^{49} +(-0.927128 + 1.60583i) q^{53} +4.79577 q^{55} +(4.58830 - 7.94717i) q^{59} +(-6.33063 - 10.9650i) q^{61} +(-2.97076 - 5.14550i) q^{65} +(1.34102 - 2.32271i) q^{67} +5.17660 q^{71} +(4.40454 - 7.62889i) q^{73} +(12.3708 + 2.82104i) q^{77} +(-1.81624 - 3.14582i) q^{79} -9.07619 q^{83} -6.83347 q^{85} +(-0.646788 - 1.12027i) q^{89} +(-4.63640 - 15.0205i) q^{91} +(-4.26995 + 7.39577i) q^{95} -10.0101 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{5} - q^{7}+O(q^{10}) $ 10 * q - 5 * q^5 - q^7	$ 10 q - 5 q^{5} - q^{7} - 2 q^{11} + 6 q^{13} + 2 q^{17} + q^{19} + 8 q^{23} - 5 q^{25} + 7 q^{31} - q^{35} - 11 q^{37} + 20 q^{41} + 6 q^{43} - 23 q^{49} - 14 q^{53} + 4 q^{55} + 4 q^{59} - 6 q^{61} - 3 q^{65} - 7 q^{67} - 32 q^{71} + 3 q^{73} + 8 q^{77} - 19 q^{79} + 28 q^{83} - 4 q^{85} - 18 q^{89} - 21 q^{91} + q^{95} + 48 q^{97}+O(q^{100}) $ 10 * q - 5 * q^5 - q^7 - 2 * q^11 + 6 * q^13 + 2 * q^17 + q^19 + 8 * q^23 - 5 * q^25 + 7 * q^31 - q^35 - 11 * q^37 + 20 * q^41 + 6 * q^43 - 23 * q^49 - 14 * q^53 + 4 * q^55 + 4 * q^59 - 6 * q^61 - 3 * q^65 - 7 * q^67 - 32 * q^71 + 3 * q^73 + 8 * q^77 - 19 * q^79 + 28 * q^83 - 4 * q^85 - 18 * q^89 - 21 * q^91 + q^95 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.780339	−	2.52806i	−0.294941	−	0.955516i
$7$	−0.780339	−	2.52806i	−0.294941	−	0.955516i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.39788	+	4.15326i	−0.722989	+	1.25225i	0.236807	+	0.971557i	$0.423899\pi$
$11$	−2.39788	+	4.15326i	−0.722989	+	1.25225i	−0.959796	+	0.280697i	$0.909434\pi$
$12$		0			0
$13$	5.94151			1.64788			0.823939	−	0.566678i	$-0.191772\pi$
$13$	5.94151			1.64788			0.823939	+	0.566678i	$0.191772\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.41674	−	5.91796i	0.828680	−	1.43532i	−0.0703939	−	0.997519i	$-0.522426\pi$
$17$	3.41674	−	5.91796i	0.828680	−	1.43532i	0.899074	−	0.437797i	$-0.144241\pi$
$18$		0			0
$19$	−4.26995	−	7.39577i	−0.979593	−	1.69671i	−0.663860	−	0.747857i	$-0.731083\pi$
$19$	−4.26995	−	7.39577i	−0.979593	−	1.69671i	−0.315733	−	0.948848i	$-0.602250\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.48961	+	7.77623i	0.936148	+	1.62146i	0.772574	+	0.634925i	$0.218969\pi$
$23$	4.48961	+	7.77623i	0.936148	+	1.62146i	0.163574	+	0.986531i	$0.447698\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.414934			0.0770514			0.0385257	−	0.999258i	$-0.487734\pi$
$29$	0.414934			0.0770514			0.0385257	+	0.999258i	$0.487734\pi$
$30$		0			0
$31$	−2.80796	+	4.86353i	−0.504325	+	0.873516i	0.495663	+	0.868515i	$0.334925\pi$
$31$	−2.80796	+	4.86353i	−0.504325	+	0.873516i	−0.999987	+	0.00500080i	$0.998408\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.79919	+	1.93982i	−0.304119	+	0.327890i
$36$		0			0
$37$	−2.79919	−	4.84834i	−0.460184	−	0.797063i	0.538786	−	0.842443i	$-0.318883\pi$
$37$	−2.79919	−	4.84834i	−0.460184	−	0.797063i	−0.998970	+	0.0453805i	$0.985550\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.325591			0.0508487			0.0254244	−	0.999677i	$-0.491906\pi$
$41$	0.325591			0.0508487			0.0254244	+	0.999677i	$0.491906\pi$
$42$		0			0
$43$	3.90381			0.595325			0.297663	−	0.954671i	$-0.403793\pi$
$43$	3.90381			0.595325			0.297663	+	0.954671i	$0.403793\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.86864	−	8.43273i	−0.710164	−	1.23004i	−0.964795	−	0.263002i	$-0.915287\pi$
$47$	−4.86864	−	8.43273i	−0.710164	−	1.23004i	0.254631	−	0.967038i	$-0.418046\pi$
$48$		0			0
$49$	−5.78214	+	3.94548i	−0.826020	+	0.563641i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.927128	+	1.60583i	−0.127351	+	0.220578i	−0.922649	−	0.385640i	$-0.873981\pi$
$53$	−0.927128	+	1.60583i	−0.127351	+	0.220578i	0.795299	+	0.606218i	$0.207314\pi$
$54$		0			0
$55$	4.79577			0.646661
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.58830	−	7.94717i	0.597346	−	1.03463i	−0.395865	−	0.918309i	$-0.629555\pi$
$59$	4.58830	−	7.94717i	0.597346	−	1.03463i	0.993211	−	0.116325i	$-0.0371113\pi$
$60$		0			0
$61$	−6.33063	−	10.9650i	−0.810554	−	1.40392i	−0.912477	−	0.409128i	$-0.865833\pi$
$61$	−6.33063	−	10.9650i	−0.810554	−	1.40392i	0.101923	−	0.994792i	$-0.467500\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.97076	−	5.14550i	−0.368477	−	0.638221i
$66$		0			0
$67$	1.34102	−	2.32271i	0.163831	−	0.283764i	−0.772408	−	0.635126i	$-0.780948\pi$
$67$	1.34102	−	2.32271i	0.163831	−	0.283764i	0.936240	+	0.351362i	$0.114281\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.17660			0.614349			0.307175	−	0.951653i	$-0.400616\pi$
$71$	5.17660			0.614349			0.307175	+	0.951653i	$0.400616\pi$
$72$		0			0
$73$	4.40454	−	7.62889i	0.515513	−	0.892894i	−0.484325	−	0.874888i	$-0.660935\pi$
$73$	4.40454	−	7.62889i	0.515513	−	0.892894i	0.999838	−	0.0180061i	$-0.00573183\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	12.3708	+	2.82104i	1.40979	+	0.321487i
$78$		0			0
$79$	−1.81624	−	3.14582i	−0.204343	−	0.353933i	0.745580	−	0.666416i	$-0.232173\pi$
$79$	−1.81624	−	3.14582i	−0.204343	−	0.353933i	−0.949923	+	0.312483i	$0.898839\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−9.07619			−0.996241			−0.498120	−	0.867108i	$-0.665976\pi$
$83$	−9.07619			−0.996241			−0.498120	+	0.867108i	$0.665976\pi$
$84$		0			0
$85$	−6.83347			−0.741194
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.646788	−	1.12027i	−0.0685594	−	0.118748i	0.829708	−	0.558198i	$-0.188507\pi$
$89$	−0.646788	−	1.12027i	−0.0685594	−	0.118748i	−0.898267	+	0.439449i	$0.855174\pi$
$90$		0			0
$91$	−4.63640	−	15.0205i	−0.486026	−	1.57457i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.26995	+	7.39577i	−0.438087	+	0.758790i
$96$		0			0
$97$	−10.0101			−1.01637			−0.508184	−	0.861248i	$-0.669683\pi$
$97$	−10.0101			−1.01637			−0.508184	+	0.861248i	$0.669683\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.570762	−	0.988589i	0.0567930	−	0.0983683i	−0.836231	−	0.548377i	$-0.815246\pi$
$101$	0.570762	−	0.988589i	0.0567930	−	0.0983683i	0.893024	+	0.450009i	$0.148579\pi$
$102$		0			0
$103$	−6.58799	−	11.4107i	−0.649134	−	1.12433i	−0.983330	−	0.181830i	$-0.941798\pi$
$103$	−6.58799	−	11.4107i	−0.649134	−	1.12433i	0.334196	−	0.942504i	$-0.391535\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.41674	+	7.65001i	0.426982	+	0.739554i	0.996603	−	0.0823529i	$-0.0262435\pi$
$107$	4.41674	+	7.65001i	0.426982	+	0.739554i	−0.569621	+	0.821907i	$0.692910\pi$
$108$		0			0
$109$	5.75775	−	9.97272i	0.551493	−	0.955214i	−0.446674	−	0.894697i	$-0.647392\pi$
$109$	5.75775	−	9.97272i	0.551493	−	0.955214i	0.998167	−	0.0605170i	$-0.0192749\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.12136			−0.105488			−0.0527442	−	0.998608i	$-0.516797\pi$
$113$	−1.12136			−0.105488			−0.0527442	+	0.998608i	$0.516797\pi$
$114$		0			0
$115$	4.48961	−	7.77623i	0.418658	−	0.725137i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−17.6272	−	4.01968i	−1.61588	−	0.368484i
$120$		0			0
$121$	−5.99969	−	10.3918i	−0.545426	−	0.944706i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−5.54674			−0.492194			−0.246097	−	0.969245i	$-0.579148\pi$
$127$	−5.54674			−0.492194			−0.246097	+	0.969245i	$0.579148\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.19042	+	3.79391i	0.191378	+	0.331476i	0.945707	−	0.325020i	$-0.105371\pi$
$131$	2.19042	+	3.79391i	0.191378	+	0.331476i	−0.754329	+	0.656496i	$0.772038\pi$
$132$		0			0
$133$	−15.3649	+	16.5659i	−1.33231	+	1.43644i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.75986	+	15.1725i	−0.748406	+	1.29628i	0.200181	+	0.979759i	$0.435847\pi$
$137$	−8.75986	+	15.1725i	−0.748406	+	1.29628i	−0.948587	+	0.316518i	$0.897486\pi$
$138$		0			0
$139$	0.727208			0.0616810			0.0308405	−	0.999524i	$-0.490182\pi$
$139$	0.727208			0.0616810			0.0308405	+	0.999524i	$0.490182\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−14.2471	+	24.6766i	−1.19140	+	2.06356i
$144$		0			0
$145$	−0.207467	−	0.359344i	−0.0172292	−	0.0298419i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.5776	−	18.3209i	−0.866551	−	1.50091i	−0.865499	−	0.500910i	$-0.832999\pi$
$149$	−10.5776	−	18.3209i	−0.866551	−	1.50091i	−0.00105144	−	0.999999i	$-0.500335\pi$
$150$		0			0
$151$	−4.02582	+	6.97292i	−0.327617	+	0.567449i	−0.982038	−	0.188681i	$-0.939579\pi$
$151$	−4.02582	+	6.97292i	−0.327617	+	0.567449i	0.654422	+	0.756130i	$0.272912\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.61592			0.451082
$156$		0			0
$157$	9.34948	−	16.1938i	0.746170	−	1.29240i	−0.203477	−	0.979080i	$-0.565224\pi$
$157$	9.34948	−	16.1938i	0.746170	−	1.29240i	0.949646	−	0.313324i	$-0.101443\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	16.1553	−	17.4181i	1.27322	−	1.37274i
$162$		0			0
$163$	−6.70642	−	11.6159i	−0.525288	−	0.909825i	−0.999566	−	0.0294501i	$-0.990624\pi$
$163$	−6.70642	−	11.6159i	−0.525288	−	0.909825i	0.474279	−	0.880375i	$-0.342709\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.97922			−0.540068			−0.270034	−	0.962851i	$-0.587035\pi$
$167$	−6.97922			−0.540068			−0.270034	+	0.962851i	$0.587035\pi$
$168$		0			0
$169$	22.3016			1.71550
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.48781	−	4.30901i	−0.189144	−	0.327608i	0.755821	−	0.654779i	$-0.227238\pi$
$173$	−2.48781	−	4.30901i	−0.189144	−	0.327608i	−0.944965	+	0.327171i	$0.893905\pi$
$174$		0			0
$175$	2.57953	+	0.588234i	0.194994	+	0.0444663i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.40797	+	2.43867i	−0.105236	+	0.182275i	−0.913835	−	0.406086i	$-0.866893\pi$
$179$	−1.40797	+	2.43867i	−0.105236	+	0.182275i	0.808598	+	0.588361i	$0.200227\pi$
$180$		0			0
$181$	11.5922			0.861638			0.430819	−	0.902438i	$-0.358225\pi$
$181$	11.5922			0.861638			0.430819	+	0.902438i	$0.358225\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.79919	+	4.84834i	−0.205801	+	0.356457i
$186$		0			0
$187$	16.3859	+	28.3812i	1.19825	+	2.07544i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.27279	−	10.8648i	−0.453883	−	0.786149i	0.544740	−	0.838605i	$-0.316628\pi$
$191$	−6.27279	−	10.8648i	−0.453883	−	0.786149i	−0.998623	+	0.0524561i	$0.983295\pi$
$192$		0			0
$193$	6.14867	−	10.6498i	0.442591	−	0.766590i	−0.555290	−	0.831657i	$-0.687393\pi$
$193$	6.14867	−	10.6498i	0.442591	−	0.766590i	0.997881	+	0.0650668i	$0.0207261\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.7518			0.908525			0.454262	−	0.890868i	$-0.349903\pi$
$197$	12.7518			0.908525			0.454262	+	0.890868i	$0.349903\pi$
$198$		0			0
$199$	−0.0635238	+	0.110027i	−0.00450309	+	0.00779957i	−0.868268	−	0.496095i	$-0.834767\pi$
$199$	−0.0635238	+	0.110027i	−0.00450309	+	0.00779957i	0.863765	+	0.503895i	$0.168100\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.323790	−	1.04898i	−0.0227256	−	0.0736238i
$204$		0			0
$205$	−0.162795	−	0.281970i	−0.0113701	−	0.0196936i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	40.9553			2.83294
$210$		0			0
$211$	16.5909			1.14217			0.571083	−	0.820892i	$-0.306523\pi$
$211$	16.5909			1.14217			0.571083	+	0.820892i	$0.306523\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.95190	−	3.38080i	−0.133119	−	0.230568i
$216$		0			0
$217$	14.4864	+	3.30348i	0.983404	+	0.224255i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	20.3006	−	35.1616i	1.36556	−	2.36523i
$222$		0			0
$223$	−3.00438			−0.201188			−0.100594	−	0.994928i	$-0.532074\pi$
$223$	−3.00438			−0.201188			−0.100594	+	0.994928i	$0.532074\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.270991	+	0.469370i	−0.0179863	+	0.0311532i	−0.874878	−	0.484343i	$-0.839059\pi$
$227$	−0.270991	+	0.469370i	−0.0179863	+	0.0311532i	0.856892	+	0.515496i	$0.172392\pi$
$228$		0			0
$229$	3.33094	+	5.76935i	0.220114	+	0.381249i	0.954843	−	0.297112i	$-0.0960236\pi$
$229$	3.33094	+	5.76935i	0.220114	+	0.381249i	−0.734728	+	0.678362i	$0.762690\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.1383	+	22.7562i	0.860717	+	1.49081i	0.871238	+	0.490861i	$0.163318\pi$
$233$	13.1383	+	22.7562i	0.860717	+	1.49081i	−0.0105206	+	0.999945i	$0.503349\pi$
$234$		0			0
$235$	−4.86864	+	8.43273i	−0.317595	+	0.550091i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−21.1831			−1.37022			−0.685109	−	0.728440i	$-0.740246\pi$
$239$	−21.1831			−1.37022			−0.685109	+	0.728440i	$0.740246\pi$
$240$		0			0
$241$	0.206732	−	0.358071i	0.0133168	−	0.0230654i	−0.859290	−	0.511488i	$-0.829094\pi$
$241$	0.206732	−	0.358071i	0.0133168	−	0.0230654i	0.872607	+	0.488423i	$0.162428\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.30796	+	3.03474i	0.403001	+	0.193882i
$246$		0			0
$247$	−25.3699	−	43.9420i	−1.61425	−	2.79596i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	21.7010			1.36976			0.684879	−	0.728657i	$-0.259855\pi$
$251$	21.7010			1.36976			0.684879	+	0.728657i	$0.259855\pi$
$252$		0			0
$253$	−43.0622			−2.70730
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.14755	−	10.6479i	−0.383473	−	0.664195i	0.608083	−	0.793874i	$-0.291939\pi$
$257$	−6.14755	−	10.6479i	−0.383473	−	0.664195i	−0.991556	+	0.129678i	$0.958606\pi$
$258$		0			0
$259$	−10.0726	+	10.8599i	−0.625879	+	0.674799i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.41915	−	4.19010i	0.149171	−	0.258373i	−0.781750	−	0.623592i	$-0.785673\pi$
$263$	2.41915	−	4.19010i	0.149171	−	0.258373i	0.930921	+	0.365219i	$0.119006\pi$
$264$		0			0
$265$	1.85426			0.113906
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.01754	+	5.22653i	−0.183983	+	0.318667i	−0.943233	−	0.332131i	$-0.892232\pi$
$269$	−3.01754	+	5.22653i	−0.183983	+	0.318667i	0.759251	+	0.650798i	$0.225566\pi$
$270$		0			0
$271$	14.0748	+	24.3782i	0.854980	+	1.48087i	0.876663	+	0.481105i	$0.159764\pi$
$271$	14.0748	+	24.3782i	0.854980	+	1.48087i	−0.0216828	+	0.999765i	$0.506902\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.39788	−	4.15326i	−0.144598	−	0.250451i
$276$		0			0
$277$	−2.51943	+	4.36378i	−0.151378	+	0.262194i	−0.931734	−	0.363141i	$-0.881704\pi$
$277$	−2.51943	+	4.36378i	−0.151378	+	0.262194i	0.780356	+	0.625335i	$0.215038\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.05865			0.421084			0.210542	−	0.977585i	$-0.432477\pi$
$281$	7.05865			0.421084			0.210542	+	0.977585i	$0.432477\pi$
$282$		0			0
$283$	11.4422	−	19.8186i	0.680171	−	1.17809i	−0.294758	−	0.955572i	$-0.595239\pi$
$283$	11.4422	−	19.8186i	0.680171	−	1.17809i	0.974928	−	0.222519i	$-0.0714278\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.254071	−	0.823112i	−0.0149974	−	0.0485868i
$288$		0			0
$289$	−14.8482	−	25.7178i	−0.873421	−	1.51281i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−18.8308			−1.10011			−0.550053	−	0.835130i	$-0.685392\pi$
$293$	−18.8308			−1.10011			−0.550053	+	0.835130i	$0.685392\pi$
$294$		0			0
$295$	−9.17660			−0.534282
$296$		0			0
$297$		0			0
$298$		0			0
$299$	26.6751	+	46.2026i	1.54266	+	2.67196i
$300$		0			0
$301$	−3.04630	−	9.86905i	−0.175586	−	0.568842i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.33063	+	10.9650i	−0.362491	+	0.627852i
$306$		0			0
$307$	−17.1788			−0.980449			−0.490224	−	0.871596i	$-0.663085\pi$
$307$	−17.1788			−0.980449			−0.490224	+	0.871596i	$0.663085\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.19415	+	5.53243i	−0.181124	+	0.313715i	−0.942263	−	0.334873i	$-0.891307\pi$
$311$	−3.19415	+	5.53243i	−0.181124	+	0.313715i	0.761140	+	0.648588i	$0.224640\pi$
$312$		0			0
$313$	0.754520	+	1.30687i	0.0426480	+	0.0738685i	0.886561	−	0.462611i	$-0.153087\pi$
$313$	0.754520	+	1.30687i	0.0426480	+	0.0738685i	−0.843913	+	0.536479i	$0.819754\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.4093	−	23.2255i	−0.753140	−	1.30448i	−0.946294	−	0.323308i	$-0.895205\pi$
$317$	−13.4093	−	23.2255i	−0.753140	−	1.30448i	0.193154	−	0.981168i	$-0.438128\pi$
$318$		0			0
$319$	−0.994965	+	1.72333i	−0.0557073	+	0.0964879i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−58.3571			−3.24708
$324$		0			0
$325$	−2.97076	+	5.14550i	−0.164788	+	0.285421i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−17.5192	+	18.8886i	−0.965866	+	1.04136i
$330$		0			0
$331$	−0.780259	−	1.35145i	−0.0428869	−	0.0742823i	0.843785	−	0.536681i	$-0.180322\pi$
$331$	−0.780259	−	1.35145i	−0.0428869	−	0.0742823i	−0.886672	+	0.462399i	$0.846989\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.68204			−0.146535
$336$		0			0
$337$	22.7841			1.24113			0.620564	−	0.784156i	$-0.286904\pi$
$337$	22.7841			1.24113			0.620564	+	0.784156i	$0.286904\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−13.4663	−	23.3244i	−0.729242	−	1.26308i
$342$		0			0
$343$	14.4864	+	11.5388i	0.782194	+	0.623035i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.74622	−	3.02453i	0.0937417	−	0.162365i	−0.815341	−	0.578981i	$-0.803451\pi$
$347$	1.74622	−	3.02453i	0.0937417	−	0.162365i	0.909083	+	0.416616i	$0.136784\pi$
$348$		0			0
$349$	0.192385			0.0102981			0.00514907	−	0.999987i	$-0.498361\pi$
$349$	0.192385			0.0102981			0.00514907	+	0.999987i	$0.498361\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.69716	+	11.5998i	−0.356454	+	0.617396i	−0.987366	−	0.158459i	$-0.949348\pi$
$353$	−6.69716	+	11.5998i	−0.356454	+	0.617396i	0.630912	+	0.775854i	$0.282681\pi$
$354$		0			0
$355$	−2.58830	−	4.48307i	−0.137373	−	0.237936i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.50465	+	16.4625i	0.501636	+	0.868859i	0.999998	+	0.00189015i	$0.000601655\pi$
$359$	9.50465	+	16.4625i	0.501636	+	0.868859i	−0.498362	+	0.866969i	$0.666065\pi$
$360$		0			0
$361$	−26.9649	+	46.7046i	−1.41921	+	2.45814i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.80908			−0.461089
$366$		0			0
$367$	0.773990	−	1.34059i	0.0404019	−	0.0699782i	−0.845117	−	0.534581i	$-0.820469\pi$
$367$	0.773990	−	1.34059i	0.0404019	−	0.0699782i	0.885519	+	0.464603i	$0.153803\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.78311	+	1.09074i	0.248327	+	0.0566282i
$372$		0			0
$373$	15.0952	+	26.1457i	0.781601	+	1.35377i	0.931009	+	0.364997i	$0.118930\pi$
$373$	15.0952	+	26.1457i	0.781601	+	1.35377i	−0.149408	+	0.988776i	$0.547737\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.46534			0.126971
$378$		0			0
$379$	−18.2959			−0.939796			−0.469898	−	0.882721i	$-0.655709\pi$
$379$	−18.2959			−0.939796			−0.469898	+	0.882721i	$0.655709\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.3590	+	21.4064i	0.631514	+	1.09382i	0.987242	+	0.159226i	$0.0508997\pi$
$383$	12.3590	+	21.4064i	0.631514	+	1.09382i	−0.355728	+	0.934590i	$0.615767\pi$
$384$		0			0
$385$	−3.74233	−	12.1240i	−0.190727	−	0.617895i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.2496	−	19.4848i	0.570375	−	0.987918i	−0.426152	−	0.904651i	$-0.640131\pi$
$389$	11.2496	−	19.4848i	0.570375	−	0.987918i	0.996527	−	0.0832670i	$-0.0265354\pi$
$390$		0			0
$391$	61.3592			3.10307
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.81624	+	3.14582i	−0.0913851	+	0.158284i
$396$		0			0
$397$	15.3594	+	26.6032i	0.770865	+	1.33518i	0.937090	+	0.349089i	$0.113509\pi$
$397$	15.3594	+	26.6032i	0.770865	+	1.33518i	−0.166225	+	0.986088i	$0.553158\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.3218	+	24.8062i	0.715199	+	1.23876i	0.962883	+	0.269920i	$0.0869972\pi$
$401$	14.3218	+	24.8062i	0.715199	+	1.23876i	−0.247684	+	0.968841i	$0.579669\pi$
$402$		0			0
$403$	−16.6835	+	28.8967i	−0.831066	+	1.43945i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	26.8485			1.33083
$408$		0			0
$409$	−5.07506	+	8.79027i	−0.250946	+	0.434651i	−0.963786	−	0.266675i	$-0.914075\pi$
$409$	−5.07506	+	8.79027i	−0.250946	+	0.434651i	0.712841	+	0.701326i	$0.247408\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−23.6713	−	5.39799i	−1.16479	−	0.265618i
$414$		0			0
$415$	4.53809	+	7.86021i	0.222766	+	0.385842i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.59691			0.126868			0.0634338	−	0.997986i	$-0.479795\pi$
$419$	2.59691			0.126868			0.0634338	+	0.997986i	$0.479795\pi$
$420$		0			0
$421$	−9.28805			−0.452672			−0.226336	−	0.974049i	$-0.572675\pi$
$421$	−9.28805			−0.452672			−0.226336	+	0.974049i	$0.572675\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.41674	+	5.91796i	0.165736	+	0.287063i
$426$		0			0
$427$	−22.7800	+	24.5606i	−1.10240	+	1.18857i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.8655	−	32.6760i	0.908718	−	1.57395i	0.0928719	−	0.995678i	$-0.470395\pi$
$431$	18.8655	−	32.6760i	0.908718	−	1.57395i	0.815847	−	0.578268i	$-0.196271\pi$
$432$		0			0
$433$	36.7159			1.76445			0.882226	−	0.470826i	$-0.156044\pi$
$433$	36.7159			1.76445			0.882226	+	0.470826i	$0.156044\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	38.3408	−	66.4082i	1.83409	−	3.17673i
$438$		0			0
$439$	8.66191	+	15.0029i	0.413410	+	0.716048i	0.995260	−	0.0972486i	$-0.0310042\pi$
$439$	8.66191	+	15.0029i	0.413410	+	0.716048i	−0.581850	+	0.813296i	$0.697671\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.30542	−	5.72516i	−0.157045	−	0.272011i	0.776756	−	0.629801i	$-0.216864\pi$
$443$	−3.30542	−	5.72516i	−0.157045	−	0.272011i	−0.933802	+	0.357790i	$0.883530\pi$
$444$		0			0
$445$	−0.646788	+	1.12027i	−0.0306607	+	0.0531059i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	19.2861			0.910168			0.455084	−	0.890449i	$-0.349609\pi$
$449$	19.2861			0.910168			0.455084	+	0.890449i	$0.349609\pi$
$450$		0			0
$451$	−0.780729	+	1.35226i	−0.0367631	+	0.0636755i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−10.6899	+	11.5255i	−0.501151	+	0.540323i
$456$		0			0
$457$	9.51700	+	16.4839i	0.445186	+	0.771086i	0.998065	−	0.0621761i	$-0.0198041\pi$
$457$	9.51700	+	16.4839i	0.445186	+	0.771086i	−0.552879	+	0.833262i	$0.686471\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.71780			−0.219730			−0.109865	−	0.993947i	$-0.535042\pi$
$461$	−4.71780			−0.219730			−0.109865	+	0.993947i	$0.535042\pi$
$462$		0			0
$463$	25.3128			1.17639			0.588193	−	0.808721i	$-0.299840\pi$
$463$	25.3128			1.17639			0.588193	+	0.808721i	$0.299840\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.18992	−	14.1854i	−0.378984	−	0.656420i	0.611931	−	0.790911i	$-0.290393\pi$
$467$	−8.18992	−	14.1854i	−0.378984	−	0.656420i	−0.990915	+	0.134492i	$0.957060\pi$
$468$		0			0
$469$	−6.91840	−	1.57767i	−0.319462	−	0.0728499i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.36088	+	16.2135i	−0.430414	+	0.745498i
$474$		0			0
$475$	8.53989			0.391837
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.07541	−	8.79086i	0.231901	−	0.401665i	−0.726466	−	0.687202i	$-0.758839\pi$
$479$	5.07541	−	8.79086i	0.231901	−	0.401665i	0.958368	+	0.285537i	$0.0921720\pi$
$480$		0			0
$481$	−16.6314	−	28.8065i	−0.758328	−	1.31346i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.00504	+	8.66898i	0.227267	+	0.393638i
$486$		0			0
$487$	−4.28938	+	7.42942i	−0.194370	+	0.336659i	−0.946694	−	0.322134i	$-0.895600\pi$
$487$	−4.28938	+	7.42942i	−0.194370	+	0.336659i	0.752324	+	0.658794i	$0.228933\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−31.2669			−1.41106			−0.705528	−	0.708682i	$-0.749290\pi$
$491$	−31.2669			−1.41106			−0.705528	+	0.708682i	$0.749290\pi$
$492$		0			0
$493$	1.41772	−	2.45557i	0.0638510	−	0.110593i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.03951	−	13.0867i	−0.181197	−	0.587020i
$498$		0			0
$499$	3.76279	+	6.51734i	0.168446	+	0.291756i	0.937874	−	0.346977i	$-0.112792\pi$
$499$	3.76279	+	6.51734i	0.168446	+	0.291756i	−0.769428	+	0.638734i	$0.779459\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−7.11292			−0.317149			−0.158575	−	0.987347i	$-0.550690\pi$
$503$	−7.11292			−0.317149			−0.158575	+	0.987347i	$0.550690\pi$
$504$		0			0
$505$	−1.14152			−0.0507972
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.57400	−	13.1185i	−0.335711	−	0.581469i	0.647910	−	0.761717i	$-0.275643\pi$
$509$	−7.57400	−	13.1185i	−0.335711	−	0.581469i	−0.983621	+	0.180248i	$0.942310\pi$
$510$		0			0
$511$	−22.7233	−	5.18181i	−1.00522	−	0.229230i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.58799	+	11.4107i	−0.290302	+	0.502817i
$516$		0			0
$517$	46.6977			2.05376
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.76801	−	11.7225i	0.296512	−	0.513574i	−0.678823	−	0.734302i	$-0.737510\pi$
$521$	6.76801	−	11.7225i	0.296512	−	0.513574i	0.975336	+	0.220728i	$0.0708432\pi$
$522$		0			0
$523$	11.3787	+	19.7085i	0.497557	+	0.861794i	0.999996	−	0.00281888i	$-0.000897277\pi$
$523$	11.3787	+	19.7085i	0.497557	+	0.861794i	−0.502439	+	0.864613i	$0.667564\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	19.1881	+	33.2348i	0.835847	+	1.44773i
$528$		0			0
$529$	−28.8132	+	49.9059i	−1.25275	+	2.16982i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.93450			0.0837926
$534$		0			0
$535$	4.41674	−	7.65001i	0.190952	−	0.330739i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.52171	−	33.4755i	−0.108618	−	1.44189i
$540$		0			0
$541$	−10.8916	−	18.8648i	−0.468267	−	0.811062i	0.531075	−	0.847325i	$-0.321788\pi$
$541$	−10.8916	−	18.8648i	−0.468267	−	0.811062i	−0.999342	+	0.0362623i	$0.988455\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.5155			−0.493270
$546$		0			0
$547$	−4.26935			−0.182544			−0.0912721	−	0.995826i	$-0.529093\pi$
$547$	−4.26935			−0.182544			−0.0912721	+	0.995826i	$0.529093\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.77175	−	3.06876i	−0.0754790	−	0.130733i
$552$		0			0
$553$	−6.53554	+	7.04637i	−0.277919	+	0.299642i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.3255	+	24.8125i	−0.606991	+	1.05134i	0.384743	+	0.923024i	$0.374290\pi$
$557$	−14.3255	+	24.8125i	−0.606991	+	1.05134i	−0.991733	+	0.128315i	$0.959043\pi$
$558$		0			0
$559$	23.1945			0.981024
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.0489	+	17.4053i	−0.423512	+	0.733544i	−0.996280	−	0.0861730i	$-0.972536\pi$
$563$	−10.0489	+	17.4053i	−0.423512	+	0.733544i	0.572768	+	0.819717i	$0.305870\pi$
$564$		0			0
$565$	0.560679	+	0.971124i	0.0235879	+	0.0408555i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.32186	+	9.21773i	0.223104	+	0.386427i	0.955749	−	0.294184i	$-0.0950478\pi$
$569$	5.32186	+	9.21773i	0.223104	+	0.386427i	−0.732645	+	0.680611i	$0.761714\pi$
$570$		0			0
$571$	−4.75837	+	8.24174i	−0.199132	+	0.344906i	−0.948247	−	0.317533i	$-0.897145\pi$
$571$	−4.75837	+	8.24174i	−0.199132	+	0.344906i	0.749115	+	0.662439i	$0.230479\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−8.97922			−0.374459
$576$		0			0
$577$	−8.84321	+	15.3169i	−0.368148	+	0.637650i	−0.989276	−	0.146058i	$-0.953341\pi$
$577$	−8.84321	+	15.3169i	−0.368148	+	0.637650i	0.621128	+	0.783709i	$0.286675\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.08251	+	22.9451i	0.293832	+	0.951924i
$582$		0			0
$583$	−4.44629	−	7.70120i	−0.184146	−	0.318951i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.4738			−0.679946			−0.339973	−	0.940435i	$-0.610418\pi$
$587$	−16.4738			−0.679946			−0.339973	+	0.940435i	$0.610418\pi$
$588$		0			0
$589$	47.9594			1.97613
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.41612	+	9.38099i	0.222413	+	0.385231i	0.955540	−	0.294861i	$-0.0952732\pi$
$593$	5.41612	+	9.38099i	0.222413	+	0.385231i	−0.733127	+	0.680092i	$0.761940\pi$
$594$		0			0
$595$	5.33243	+	17.2754i	0.218608	+	0.708222i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	11.3633	−	19.6818i	0.464292	−	0.804177i	−0.534878	−	0.844930i	$-0.679642\pi$
$599$	11.3633	−	19.6818i	0.464292	−	0.804177i	0.999169	+	0.0407528i	$0.0129756\pi$
$600$		0			0
$601$	−3.36346			−0.137198			−0.0685991	−	0.997644i	$-0.521853\pi$
$601$	−3.36346			−0.137198			−0.0685991	+	0.997644i	$0.521853\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.99969	+	10.3918i	−0.243922	+	0.422486i
$606$		0			0
$607$	−12.6564	−	21.9215i	−0.513707	−	0.889767i	−0.999874	−	0.0159007i	$-0.994938\pi$
$607$	−12.6564	−	21.9215i	−0.513707	−	0.889767i	0.486166	−	0.873866i	$-0.338395\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−28.9271	−	50.1032i	−1.17026	−	2.02696i
$612$		0			0
$613$	7.97790	−	13.8181i	0.322224	−	0.558109i	−0.658722	−	0.752386i	$-0.728903\pi$
$613$	7.97790	−	13.8181i	0.322224	−	0.558109i	0.980947	+	0.194277i	$0.0622361\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	37.2040			1.49778			0.748888	−	0.662697i	$-0.230588\pi$
$617$	37.2040			1.49778			0.748888	+	0.662697i	$0.230588\pi$
$618$		0			0
$619$	19.6698	−	34.0690i	0.790594	−	1.36935i	−0.135006	−	0.990845i	$-0.543105\pi$
$619$	19.6698	−	34.0690i	0.790594	−	1.36935i	0.925600	−	0.378504i	$-0.123561\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.32739	+	2.50931i	−0.0932450	+	0.100533i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−38.2564			−1.52538
$630$		0			0
$631$	0.331822			0.0132096			0.00660481	−	0.999978i	$-0.497898\pi$
$631$	0.331822			0.0132096			0.00660481	+	0.999978i	$0.497898\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.77337	+	4.80362i	0.110058	+	0.190626i
$636$		0			0
$637$	−34.3547	+	23.4421i	−1.36118	+	0.928812i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.8039	+	25.6411i	−0.584718	+	1.01276i	0.410192	+	0.911999i	$0.365462\pi$
$641$	−14.8039	+	25.6411i	−0.584718	+	1.01276i	−0.994911	+	0.100763i	$0.967872\pi$
$642$		0			0
$643$	−3.27639			−0.129208			−0.0646042	−	0.997911i	$-0.520578\pi$
$643$	−3.27639			−0.129208			−0.0646042	+	0.997911i	$0.520578\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.4487	+	18.0976i	−0.410779	+	0.711490i	−0.994975	−	0.100122i	$-0.968077\pi$
$647$	−10.4487	+	18.0976i	−0.410779	+	0.711490i	0.584196	+	0.811613i	$0.301410\pi$
$648$		0			0
$649$	22.0044	+	38.1128i	0.863749	+	1.49606i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.93656	−	10.2824i	−0.232315	−	0.402382i	0.726174	−	0.687511i	$-0.241297\pi$
$653$	−5.93656	−	10.2824i	−0.232315	−	0.402382i	−0.958489	+	0.285129i	$0.907963\pi$
$654$		0			0
$655$	2.19042	−	3.79391i	0.0855866	−	0.148240i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.5722			0.567653			0.283827	−	0.958876i	$-0.408396\pi$
$659$	14.5722			0.567653			0.283827	+	0.958876i	$0.408396\pi$
$660$		0			0
$661$	−8.37367	+	14.5036i	−0.325698	+	0.564126i	−0.981653	−	0.190674i	$-0.938933\pi$
$661$	−8.37367	+	14.5036i	−0.325698	+	0.564126i	0.655955	+	0.754800i	$0.272266\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	22.0289	+	5.02346i	0.854245	+	0.194801i
$666$		0			0
$667$	1.86289	+	3.22663i	0.0721315	+	0.124935i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	60.7204			2.34409
$672$		0			0
$673$	41.7595			1.60971			0.804855	−	0.593471i	$-0.202243\pi$
$673$	41.7595			1.60971			0.804855	+	0.593471i	$0.202243\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.5380	+	23.4485i	0.520308	+	0.901199i	0.999721	+	0.0236102i	$0.00751605\pi$
$677$	13.5380	+	23.4485i	0.520308	+	0.901199i	−0.479414	+	0.877589i	$0.659151\pi$
$678$		0			0
$679$	7.81125	+	25.3060i	0.299768	+	0.971156i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.5859	+	26.9955i	−0.596377	+	1.03295i	0.396974	+	0.917830i	$0.370060\pi$
$683$	−15.5859	+	26.9955i	−0.596377	+	1.03295i	−0.993351	+	0.115125i	$0.963273\pi$
$684$		0			0
$685$	17.5197			0.669394
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.50854	+	9.54107i	−0.209859	+	0.363486i
$690$		0			0
$691$	8.16704	+	14.1457i	0.310689	+	0.538129i	0.978512	−	0.206192i	$-0.0661070\pi$
$691$	8.16704	+	14.1457i	0.310689	+	0.538129i	−0.667823	+	0.744320i	$0.732774\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.363604	−	0.629780i	−0.0137923	−	0.0238889i
$696$		0			0
$697$	1.11246	−	1.92683i	0.0421373	−	0.0729840i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	49.6205			1.87414			0.937070	−	0.349143i	$-0.113527\pi$
$701$	49.6205			1.87414			0.937070	+	0.349143i	$0.113527\pi$
$702$		0			0
$703$	−23.9048	+	41.4043i	−0.901587	+	1.56159i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.94460	−	0.671484i	−0.110743	−	0.0252538i
$708$		0			0
$709$	−9.48953	−	16.4363i	−0.356387	−	0.617280i	0.630968	−	0.775809i	$-0.282658\pi$
$709$	−9.48953	−	16.4363i	−0.356387	−	0.617280i	−0.987354	+	0.158529i	$0.949325\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−50.4266			−1.88849
$714$		0			0
$715$	28.4941			1.06562
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.13828	−	15.8280i	−0.340800	−	0.590283i	0.643781	−	0.765210i	$-0.277365\pi$
$719$	−9.13828	−	15.8280i	−0.340800	−	0.590283i	−0.984582	+	0.174926i	$0.944031\pi$
$720$		0			0
$721$	−23.7061	+	25.5591i	−0.882862	+	0.951869i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.207467	+	0.359344i	−0.00770514	+	0.0133457i
$726$		0			0
$727$	−27.2878			−1.01205			−0.506024	−	0.862519i	$-0.668885\pi$
$727$	−27.2878			−1.01205			−0.506024	+	0.862519i	$0.668885\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	13.3383	−	23.1026i	0.493334	−	0.854480i
$732$		0			0
$733$	17.8175	+	30.8609i	0.658106	+	1.13987i	0.981105	+	0.193474i	$0.0619755\pi$
$733$	17.8175	+	30.8609i	0.658106	+	1.13987i	−0.322999	+	0.946399i	$0.604691\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.43121	+	11.1392i	0.236897	+	0.410317i
$738$		0			0
$739$	6.37114	−	11.0351i	0.234366	−	0.405934i	−0.724722	−	0.689041i	$-0.758032\pi$
$739$	6.37114	−	11.0351i	0.234366	−	0.405934i	0.959088	+	0.283107i	$0.0913652\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	12.5025			0.458674			0.229337	−	0.973347i	$-0.426344\pi$
$743$	12.5025			0.458674			0.229337	+	0.973347i	$0.426344\pi$
$744$		0			0
$745$	−10.5776	+	18.3209i	−0.387533	+	0.671227i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.8931	−	17.1354i	0.580721	−	0.626113i
$750$		0			0
$751$	4.50331	+	7.79997i	0.164328	+	0.284625i	0.936417	−	0.350890i	$-0.114121\pi$
$751$	4.50331	+	7.79997i	0.164328	+	0.284625i	−0.772088	+	0.635515i	$0.780788\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.05164			0.293029
$756$		0			0
$757$	46.1180			1.67619			0.838094	−	0.545526i	$-0.183670\pi$
$757$	46.1180			1.67619			0.838094	+	0.545526i	$0.183670\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.70540	−	4.68588i	−0.0980705	−	0.169863i	0.812815	−	0.582521i	$-0.197934\pi$
$761$	−2.70540	−	4.68588i	−0.0980705	−	0.169863i	−0.910886	+	0.412658i	$0.864600\pi$
$762$		0			0
$763$	−29.7046	−	6.77382i	−1.07538	−	0.245229i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.2614	−	47.2182i	0.984353	−	1.70495i
$768$		0			0
$769$	4.36121			0.157269			0.0786346	−	0.996904i	$-0.474944\pi$
$769$	4.36121			0.157269			0.0786346	+	0.996904i	$0.474944\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.38010	−	7.58655i	0.157541	−	0.272869i	−0.776440	−	0.630191i	$-0.782977\pi$
$773$	4.38010	−	7.58655i	0.157541	−	0.272869i	0.933981	+	0.357322i	$0.116310\pi$
$774$		0			0
$775$	−2.80796	−	4.86353i	−0.100865	−	0.174703i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.39026	−	2.40799i	−0.0498111	−	0.0862753i
$780$		0			0
$781$	−12.4129	+	21.4997i	−0.444168	+	0.769321i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−18.6990			−0.667394
$786$		0			0
$787$	0.0341019	−	0.0590662i	0.00121560	−	0.00210548i	−0.865417	−	0.501052i	$-0.832946\pi$
$787$	0.0341019	−	0.0590662i	0.00121560	−	0.00210548i	0.866633	+	0.498947i	$0.166280\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.875040	+	2.83486i	0.0311128	+	0.100796i
$792$		0			0
$793$	−37.6135	−	65.1485i	−1.33569	−	2.31349i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−38.0302			−1.34710			−0.673550	−	0.739142i	$-0.735231\pi$
$797$	−38.0302			−1.34710			−0.673550	+	0.739142i	$0.735231\pi$
$798$		0			0
$799$	−66.5394			−2.35400
$800$		0			0
$801$		0			0
$802$		0			0
$803$	21.1232	+	36.5864i	0.745420	+	1.29111i
$804$		0			0
$805$	−23.1622	−	5.28188i	−0.816359	−	0.186162i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−13.5293	+	23.4335i	−0.475666	+	0.823877i	−0.999611	−	0.0278745i	$-0.991126\pi$
$809$	−13.5293	+	23.4335i	−0.475666	+	0.823877i	0.523946	+	0.851752i	$0.324459\pi$
$810$		0			0
$811$	28.7345			1.00901			0.504503	−	0.863410i	$-0.331676\pi$
$811$	28.7345			1.00901			0.504503	+	0.863410i	$0.331676\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.70642	+	11.6159i	−0.234916	+	0.406886i
$816$		0			0
$817$	−16.6691	−	28.8716i	−0.583176	−	1.01009i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−26.4671	−	45.8424i	−0.923708	−	1.59991i	−0.793626	−	0.608406i	$-0.791809\pi$
$821$	−26.4671	−	45.8424i	−0.923708	−	1.59991i	−0.130083	−	0.991503i	$-0.541524\pi$
$822$		0			0
$823$	−24.1683	+	41.8608i	−0.842455	+	1.45917i	0.0453589	+	0.998971i	$0.485557\pi$
$823$	−24.1683	+	41.8608i	−0.842455	+	1.45917i	−0.887814	+	0.460203i	$0.847776\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.1524			0.978954			0.489477	−	0.872016i	$-0.337188\pi$
$827$	28.1524			0.978954			0.489477	+	0.872016i	$0.337188\pi$
$828$		0			0
$829$	2.27573	−	3.94168i	0.0790394	−	0.136900i	−0.823796	−	0.566886i	$-0.808148\pi$
$829$	2.27573	−	3.94168i	0.0790394	−	0.136900i	0.902836	+	0.429986i	$0.141481\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.59317	+	47.6992i	0.124496	+	1.65268i
$834$		0			0
$835$	3.48961	+	6.04418i	0.120763	+	0.209167i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−34.9914			−1.20804			−0.604019	−	0.796970i	$-0.706435\pi$
$839$	−34.9914			−1.20804			−0.604019	+	0.796970i	$0.706435\pi$
$840$		0			0
$841$	−28.8278			−0.994063
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11.1508	−	19.3137i	−0.383598	−	0.664412i
$846$		0			0
$847$	−21.5892	+	23.2767i	−0.741813	+	0.799796i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	25.1345	−	43.5343i	0.861601	−	1.49234i
$852$		0			0
$853$	−6.20800			−0.212558			−0.106279	−	0.994336i	$-0.533894\pi$
$853$	−6.20800			−0.212558			−0.106279	+	0.994336i	$0.533894\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.49652	+	12.9844i	−0.256076	+	0.443537i	−0.965187	−	0.261560i	$-0.915763\pi$
$857$	−7.49652	+	12.9844i	−0.256076	+	0.443537i	0.709111	+	0.705097i	$0.249097\pi$
$858$		0			0
$859$	−8.66191	−	15.0029i	−0.295540	−	0.511891i	0.679570	−	0.733611i	$-0.262166\pi$
$859$	−8.66191	−	15.0029i	−0.295540	−	0.511891i	−0.975110	+	0.221720i	$0.928833\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.09626	−	15.7552i	−0.309640	−	0.536313i	0.668643	−	0.743583i	$-0.266875\pi$
$863$	−9.09626	−	15.7552i	−0.309640	−	0.536313i	−0.978284	+	0.207271i	$0.933542\pi$
$864$		0			0
$865$	−2.48781	+	4.30901i	−0.0845880	+	0.146511i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	17.4206			0.590952
$870$		0			0
$871$	7.96768	−	13.8004i	0.269974	−	0.467609i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.780339	−	2.52806i	−0.0263803	−	0.0854639i
$876$		0			0
$877$	−19.1168	−	33.1113i	−0.645530	−	1.11809i	−0.984179	−	0.177177i	$-0.943303\pi$
$877$	−19.1168	−	33.1113i	−0.645530	−	1.11809i	0.338649	−	0.940913i	$-0.390030\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	32.0744			1.08061			0.540307	−	0.841468i	$-0.318308\pi$
$881$	32.0744			1.08061			0.540307	+	0.841468i	$0.318308\pi$
$882$		0			0
$883$	4.85786			0.163480			0.0817400	−	0.996654i	$-0.473952\pi$
$883$	4.85786			0.163480			0.0817400	+	0.996654i	$0.473952\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.2226	−	26.3663i	−0.511124	−	0.885293i	−0.999917	−	0.0128929i	$-0.995896\pi$
$887$	−15.2226	−	26.3663i	−0.511124	−	0.885293i	0.488793	−	0.872400i	$-0.337437\pi$
$888$		0			0
$889$	4.32834	+	14.0225i	0.145168	+	0.470299i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−41.5777	+	72.0146i	−1.39134	+	2.40988i
$894$		0			0
$895$	2.81593			0.0941263
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.16512	+	2.01805i	−0.0388589	+	0.0673056i
$900$		0			0
$901$	6.33550	+	10.9734i	0.211066	+	0.365577i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.79608	−	10.0391i	−0.192668	−	0.333711i
$906$		0			0
$907$	17.8008	−	30.8319i	0.591067	−	1.02376i	−0.403022	−	0.915190i	$-0.632040\pi$
$907$	17.8008	−	30.8319i	0.591067	−	1.02376i	0.994089	−	0.108567i	$-0.0346263\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.6011			0.748809			0.374405	−	0.927265i	$-0.377847\pi$
$911$	22.6011			0.748809			0.374405	+	0.927265i	$0.377847\pi$
$912$		0			0
$913$	21.7636	−	37.6957i	0.720271	−	1.24755i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.88196	−	8.49804i	0.260285	−	0.280630i
$918$		0			0
$919$	−4.17126	−	7.22483i	−0.137597	−	0.238325i	0.788990	−	0.614407i	$-0.210605\pi$
$919$	−4.17126	−	7.22483i	−0.137597	−	0.238325i	−0.926587	+	0.376082i	$0.877271\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	30.7568			1.01237
$924$		0			0
$925$	5.59838			0.184074
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.5787	−	28.7152i	−0.543930	−	0.942114i	−0.998673	−	0.0514914i	$-0.983603\pi$
$929$	−16.5787	−	28.7152i	−0.543930	−	0.942114i	0.454744	−	0.890622i	$-0.349731\pi$
$930$		0			0
$931$	53.8693	+	25.9163i	1.76550	+	0.849374i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	16.3859	−	28.3812i	0.535875	−	0.928163i
$936$		0			0
$937$	35.2176			1.15051			0.575254	−	0.817975i	$-0.304903\pi$
$937$	35.2176			1.15051			0.575254	+	0.817975i	$0.304903\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.76737	+	9.98937i	−0.188011	+	0.325644i	−0.944587	−	0.328261i	$-0.893537\pi$
$941$	−5.76737	+	9.98937i	−0.188011	+	0.325644i	0.756576	+	0.653906i	$0.226871\pi$
$942$		0			0
$943$	1.46178	+	2.53187i	0.0476020	+	0.0824490i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.31632	−	10.9402i	−0.205253	−	0.355508i	0.744960	−	0.667109i	$-0.232468\pi$
$947$	−6.31632	−	10.9402i	−0.205253	−	0.355508i	−0.950213	+	0.311600i	$0.899135\pi$
$948$		0			0
$949$	26.1696	−	45.3271i	0.849502	−	1.47138i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	12.3444			0.399876			0.199938	−	0.979809i	$-0.435926\pi$
$953$	12.3444			0.399876			0.199938	+	0.979809i	$0.435926\pi$
$954$		0			0
$955$	−6.27279	+	10.8648i	−0.202983	+	0.351577i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	45.1927	+	10.3057i	1.45935	+	0.332789i
$960$		0			0
$961$	−0.269283	−	0.466411i	−0.00868654	−	0.0150455i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.2973			−0.395865
$966$		0			0
$967$	22.5901			0.726448			0.363224	−	0.931702i	$-0.381676\pi$
$967$	22.5901			0.726448			0.363224	+	0.931702i	$0.381676\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.2916	+	19.5576i	0.362365	+	0.627634i	0.988350	−	0.152201i	$-0.0486361\pi$
$971$	11.2916	+	19.5576i	0.362365	+	0.627634i	−0.625985	+	0.779835i	$0.715303\pi$
$972$		0			0
$973$	−0.567469	−	1.83842i	−0.0181922	−	0.0589371i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.0625	+	29.5532i	−0.545879	+	0.945490i	0.452672	+	0.891677i	$0.350471\pi$
$977$	−17.0625	+	29.5532i	−0.545879	+	0.945490i	−0.998551	+	0.0538130i	$0.982863\pi$
$978$		0			0
$979$	6.20369			0.198271
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.49170	+	4.31574i	−0.0794727	+	0.137651i	−0.903023	−	0.429593i	$-0.858657\pi$
$983$	−2.49170	+	4.31574i	−0.0794727	+	0.137651i	0.823550	+	0.567244i	$0.191990\pi$
$984$		0			0
$985$	−6.37588	−	11.0433i	−0.203152	−	0.351870i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	17.5266	+	30.3569i	0.557312	+	0.965293i
$990$		0			0
$991$	27.5672	−	47.7478i	0.875701	−	1.51676i	0.0196864	−	0.999806i	$-0.493733\pi$
$991$	27.5672	−	47.7478i	0.875701	−	1.51676i	0.856014	−	0.516952i	$-0.172933\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.127048			0.00402768
$996$		0			0
$997$	−3.84386	+	6.65777i	−0.121736	+	0.210854i	−0.920452	−	0.390854i	$-0.872180\pi$
$997$	−3.84386	+	6.65777i	−0.121736	+	0.210854i	0.798716	+	0.601708i	$0.205513\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.2.bi.r.361.2	✓	10
3.2	odd	2		2520.2.bi.s.361.2	yes	10
7.2	even	3	inner	2520.2.bi.r.1801.2	yes	10
21.2	odd	6		2520.2.bi.s.1801.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2520.2.bi.r.361.2	✓	10	1.1	even	1	trivial
2520.2.bi.r.1801.2	yes	10	7.2	even	3	inner
2520.2.bi.s.361.2	yes	10	3.2	odd	2
2520.2.bi.s.1801.2	yes	10	21.2	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:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.bi (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(-0.780339 - 2.52806i) q^{7} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{5} +(-0.780339 - 2.52806i) q^{7} +(-2.39788 + 4.15326i) q^{11} +5.94151 q^{13} +(3.41674 - 5.91796i) q^{17} +(-4.26995 - 7.39577i) q^{19} +(4.48961 + 7.77623i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.414934 q^{29} +(-2.80796 + 4.86353i) q^{31} +(-1.79919 + 1.93982i) q^{35} +(-2.79919 - 4.84834i) q^{37} +0.325591 q^{41} +3.90381 q^{43} +(-4.86864 - 8.43273i) q^{47} +(-5.78214 + 3.94548i) q^{49} +(-0.927128 + 1.60583i) q^{53} +4.79577 q^{55} +(4.58830 - 7.94717i) q^{59} +(-6.33063 - 10.9650i) q^{61} +(-2.97076 - 5.14550i) q^{65} +(1.34102 - 2.32271i) q^{67} +5.17660 q^{71} +(4.40454 - 7.62889i) q^{73} +(12.3708 + 2.82104i) q^{77} +(-1.81624 - 3.14582i) q^{79} -9.07619 q^{83} -6.83347 q^{85} +(-0.646788 - 1.12027i) q^{89} +(-4.63640 - 15.0205i) q^{91} +(-4.26995 + 7.39577i) q^{95} -10.0101 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{5} - q^{7}+O(q^{10}) \) 10 * q - 5 * q^5 - q^7	\( 10 q - 5 q^{5} - q^{7} - 2 q^{11} + 6 q^{13} + 2 q^{17} + q^{19} + 8 q^{23} - 5 q^{25} + 7 q^{31} - q^{35} - 11 q^{37} + 20 q^{41} + 6 q^{43} - 23 q^{49} - 14 q^{53} + 4 q^{55} + 4 q^{59} - 6 q^{61} - 3 q^{65} - 7 q^{67} - 32 q^{71} + 3 q^{73} + 8 q^{77} - 19 q^{79} + 28 q^{83} - 4 q^{85} - 18 q^{89} - 21 q^{91} + q^{95} + 48 q^{97}+O(q^{100}) \) 10 * q - 5 * q^5 - q^7 - 2 * q^11 + 6 * q^13 + 2 * q^17 + q^19 + 8 * q^23 - 5 * q^25 + 7 * q^31 - q^35 - 11 * q^37 + 20 * q^41 + 6 * q^43 - 23 * q^49 - 14 * q^53 + 4 * q^55 + 4 * q^59 - 6 * q^61 - 3 * q^65 - 7 * q^67 - 32 * q^71 + 3 * q^73 + 8 * q^77 - 19 * q^79 + 28 * q^83 - 4 * q^85 - 18 * q^89 - 21 * q^91 + q^95 + 48 * q^97

Introduction

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