LMFDB - Embedded newform 1710.2.d.g.1369.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$8$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.1
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.g.1369.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-1.41421 - 1.73205i) q^{5} -1.03528i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.41421 - 1.73205i) q^{5} -1.03528i q^{7} +1.00000i q^{8} +(-1.73205 + 1.41421i) q^{10} -3.86370 q^{11} -1.03528i q^{13} -1.03528 q^{14} +1.00000 q^{16} +7.46410i q^{17} +1.00000 q^{19} +(1.41421 + 1.73205i) q^{20} +3.86370i q^{22} +1.46410i q^{23} +(-1.00000 + 4.89898i) q^{25} -1.03528 q^{26} +1.03528i q^{28} -9.52056 q^{29} +2.92820 q^{31} -1.00000i q^{32} +7.46410 q^{34} +(-1.79315 + 1.46410i) q^{35} -6.69213i q^{37} -1.00000i q^{38} +(1.73205 - 1.41421i) q^{40} +6.69213 q^{41} +1.79315i q^{43} +3.86370 q^{44} +1.46410 q^{46} +9.46410i q^{47} +5.92820 q^{49} +(4.89898 + 1.00000i) q^{50} +1.03528i q^{52} -6.00000i q^{53} +(5.46410 + 6.69213i) q^{55} +1.03528 q^{56} +9.52056i q^{58} +12.6264 q^{59} -2.00000 q^{61} -2.92820i q^{62} -1.00000 q^{64} +(-1.79315 + 1.46410i) q^{65} +3.58630i q^{67} -7.46410i q^{68} +(1.46410 + 1.79315i) q^{70} -15.4548 q^{71} +13.3843i q^{73} -6.69213 q^{74} -1.00000 q^{76} +4.00000i q^{77} +4.00000 q^{79} +(-1.41421 - 1.73205i) q^{80} -6.69213i q^{82} +4.39230i q^{83} +(12.9282 - 10.5558i) q^{85} +1.79315 q^{86} -3.86370i q^{88} -1.03528 q^{89} -1.07180 q^{91} -1.46410i q^{92} +9.46410 q^{94} +(-1.41421 - 1.73205i) q^{95} +17.2480i q^{97} -5.92820i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 8 q^{16} + 8 q^{19} - 8 q^{25} - 32 q^{31} + 32 q^{34} - 16 q^{46} - 8 q^{49} + 16 q^{55} - 16 q^{61} - 8 q^{64} - 16 q^{70} - 8 q^{76} + 32 q^{79} + 48 q^{85} - 64 q^{91} + 48 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 + 8 * q^16 + 8 * q^19 - 8 * q^25 - 32 * q^31 + 32 * q^34 - 16 * q^46 - 8 * q^49 + 16 * q^55 - 16 * q^61 - 8 * q^64 - 16 * q^70 - 8 * q^76 + 32 * q^79 + 48 * q^85 - 64 * q^91 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$5$	−1.41421	−	1.73205i	−0.632456	−	0.774597i
$6$		0			0
$7$		−	1.03528i		−	0.391298i	−0.980674	−	0.195649i	$-0.937319\pi$
$7$		−	1.03528i		−	0.391298i	0.980674	−	0.195649i	$-0.0626813\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.73205	+	1.41421i	−0.547723	+	0.447214i
$11$	−3.86370			−1.16495			−0.582475	−	0.812848i	$-0.697916\pi$
$11$	−3.86370			−1.16495			−0.582475	+	0.812848i	$0.697916\pi$
$12$		0			0
$13$		−	1.03528i		−	0.287134i	−0.989641	−	0.143567i	$-0.954143\pi$
$13$		−	1.03528i		−	0.287134i	0.989641	−	0.143567i	$-0.0458572\pi$
$14$	−1.03528			−0.276689
$15$		0			0
$16$	1.00000			0.250000
$17$			7.46410i			1.81031i	0.425081	+	0.905155i	$0.360246\pi$
$17$			7.46410i			1.81031i	−0.425081	+	0.905155i	$0.639754\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	1.41421	+	1.73205i	0.316228	+	0.387298i
$21$		0			0
$22$			3.86370i			0.823744i
$23$			1.46410i			0.305286i	0.988281	+	0.152643i	$0.0487785\pi$
$23$			1.46410i			0.305286i	−0.988281	+	0.152643i	$0.951221\pi$
$24$		0			0
$25$	−1.00000	+	4.89898i	−0.200000	+	0.979796i
$26$	−1.03528			−0.203034
$27$		0			0
$28$			1.03528i			0.195649i
$29$	−9.52056			−1.76792			−0.883962	−	0.467560i	$-0.845133\pi$
$29$	−9.52056			−1.76792			−0.883962	+	0.467560i	$0.845133\pi$
$30$		0			0
$31$	2.92820			0.525921			0.262960	−	0.964807i	$-0.415301\pi$
$31$	2.92820			0.525921			0.262960	+	0.964807i	$0.415301\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	7.46410			1.28008
$35$	−1.79315	+	1.46410i	−0.303098	+	0.247478i
$36$		0			0
$37$		−	6.69213i		−	1.10018i	−0.835106	−	0.550090i	$-0.814594\pi$
$37$		−	6.69213i		−	1.10018i	0.835106	−	0.550090i	$-0.185406\pi$
$38$		−	1.00000i		−	0.162221i
$39$		0			0
$40$	1.73205	−	1.41421i	0.273861	−	0.223607i
$41$	6.69213			1.04514			0.522568	−	0.852598i	$-0.324974\pi$
$41$	6.69213			1.04514			0.522568	+	0.852598i	$0.324974\pi$
$42$		0			0
$43$			1.79315i			0.273453i	0.990609	+	0.136726i	$0.0436581\pi$
$43$			1.79315i			0.273453i	−0.990609	+	0.136726i	$0.956342\pi$
$44$	3.86370			0.582475
$45$		0			0
$46$	1.46410			0.215870
$47$			9.46410i			1.38048i	0.723580	+	0.690241i	$0.242495\pi$
$47$			9.46410i			1.38048i	−0.723580	+	0.690241i	$0.757505\pi$
$48$		0			0
$49$	5.92820			0.846886
$50$	4.89898	+	1.00000i	0.692820	+	0.141421i
$51$		0			0
$52$			1.03528i			0.143567i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$	5.46410	+	6.69213i	0.736779	+	0.902367i
$56$	1.03528			0.138345
$57$		0			0
$58$			9.52056i			1.25011i
$59$	12.6264			1.64382			0.821908	−	0.569621i	$-0.192910\pi$
$59$	12.6264			1.64382			0.821908	+	0.569621i	$0.192910\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$		−	2.92820i		−	0.371882i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.79315	+	1.46410i	−0.222413	+	0.181599i
$66$		0			0
$67$			3.58630i			0.438137i	0.975710	+	0.219068i	$0.0703017\pi$
$67$			3.58630i			0.438137i	−0.975710	+	0.219068i	$0.929698\pi$
$68$		−	7.46410i		−	0.905155i
$69$		0			0
$70$	1.46410	+	1.79315i	0.174994	+	0.214323i
$71$	−15.4548			−1.83415			−0.917074	−	0.398716i	$-0.869456\pi$
$71$	−15.4548			−1.83415			−0.917074	+	0.398716i	$0.869456\pi$
$72$		0			0
$73$			13.3843i			1.56651i	0.621701	+	0.783255i	$0.286442\pi$
$73$			13.3843i			1.56651i	−0.621701	+	0.783255i	$0.713558\pi$
$74$	−6.69213			−0.777944
$75$		0			0
$76$	−1.00000			−0.114708
$77$			4.00000i			0.455842i
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	−1.41421	−	1.73205i	−0.158114	−	0.193649i
$81$		0			0
$82$		−	6.69213i		−	0.739022i
$83$			4.39230i			0.482118i	0.970510	+	0.241059i	$0.0774947\pi$
$83$			4.39230i			0.482118i	−0.970510	+	0.241059i	$0.922505\pi$
$84$		0			0
$85$	12.9282	−	10.5558i	1.40226	−	1.14494i
$86$	1.79315			0.193360
$87$		0			0
$88$		−	3.86370i		−	0.411872i
$89$	−1.03528			−0.109739			−0.0548695	−	0.998494i	$-0.517474\pi$
$89$	−1.03528			−0.109739			−0.0548695	+	0.998494i	$0.517474\pi$
$90$		0			0
$91$	−1.07180			−0.112355
$92$		−	1.46410i		−	0.152643i
$93$		0			0
$94$	9.46410			0.976148
$95$	−1.41421	−	1.73205i	−0.145095	−	0.177705i
$96$		0			0
$97$			17.2480i			1.75127i	0.482978	+	0.875633i	$0.339555\pi$
$97$			17.2480i			1.75127i	−0.482978	+	0.875633i	$0.660445\pi$
$98$		−	5.92820i		−	0.598839i
$99$		0			0
$100$	1.00000	−	4.89898i	0.100000	−	0.489898i
$101$	−0.757875			−0.0754114			−0.0377057	−	0.999289i	$-0.512005\pi$
$101$	−0.757875			−0.0754114			−0.0377057	+	0.999289i	$0.512005\pi$
$102$		0			0
$103$			4.89898i			0.482711i	0.970437	+	0.241355i	$0.0775919\pi$
$103$			4.89898i			0.482711i	−0.970437	+	0.241355i	$0.922408\pi$
$104$	1.03528			0.101517
$105$		0			0
$106$	−6.00000			−0.582772
$107$			10.9282i			1.05647i	0.849098	+	0.528235i	$0.177146\pi$
$107$			10.9282i			1.05647i	−0.849098	+	0.528235i	$0.822854\pi$
$108$		0			0
$109$	4.92820			0.472036			0.236018	−	0.971749i	$-0.424158\pi$
$109$	4.92820			0.472036			0.236018	+	0.971749i	$0.424158\pi$
$110$	6.69213	−	5.46410i	0.638070	−	0.520982i
$111$		0			0
$112$		−	1.03528i		−	0.0978244i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$	2.53590	−	2.07055i	0.236474	−	0.193080i
$116$	9.52056			0.883962
$117$		0			0
$118$		−	12.6264i		−	1.16235i
$119$	7.72741			0.708370
$120$		0			0
$121$	3.92820			0.357109
$122$			2.00000i			0.181071i
$123$		0			0
$124$	−2.92820			−0.262960
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$		0			0
$127$			8.48528i			0.752947i	0.926427	+	0.376473i	$0.122863\pi$
$127$			8.48528i			0.752947i	−0.926427	+	0.376473i	$0.877137\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	1.46410	+	1.79315i	0.128410	+	0.157270i
$131$	−11.5911			−1.01272			−0.506360	−	0.862322i	$-0.669009\pi$
$131$	−11.5911			−1.01272			−0.506360	+	0.862322i	$0.669009\pi$
$132$		0			0
$133$		−	1.03528i		−	0.0897698i
$134$	3.58630			0.309809
$135$		0			0
$136$	−7.46410			−0.640041
$137$			7.46410i			0.637701i	0.947805	+	0.318851i	$0.103297\pi$
$137$			7.46410i			0.637701i	−0.947805	+	0.318851i	$0.896703\pi$
$138$		0			0
$139$	6.92820			0.587643			0.293821	−	0.955860i	$-0.405073\pi$
$139$	6.92820			0.587643			0.293821	+	0.955860i	$0.405073\pi$
$140$	1.79315	−	1.46410i	0.151549	−	0.123739i
$141$		0			0
$142$			15.4548i			1.29694i
$143$			4.00000i			0.334497i
$144$		0			0
$145$	13.4641	+	16.4901i	1.11813	+	1.36943i
$146$	13.3843			1.10769
$147$		0			0
$148$			6.69213i			0.550090i
$149$	9.04008			0.740593			0.370296	−	0.928914i	$-0.379256\pi$
$149$	9.04008			0.740593			0.370296	+	0.928914i	$0.379256\pi$
$150$		0			0
$151$	−21.8564			−1.77865			−0.889325	−	0.457277i	$-0.848825\pi$
$151$	−21.8564			−1.77865			−0.889325	+	0.457277i	$0.848825\pi$
$152$			1.00000i			0.0811107i
$153$		0			0
$154$	4.00000			0.322329
$155$	−4.14110	−	5.07180i	−0.332622	−	0.407377i
$156$		0			0
$157$			14.1421i			1.12867i	0.825547	+	0.564333i	$0.190866\pi$
$157$			14.1421i			1.12867i	−0.825547	+	0.564333i	$0.809134\pi$
$158$		−	4.00000i		−	0.318223i
$159$		0			0
$160$	−1.73205	+	1.41421i	−0.136931	+	0.111803i
$161$	1.51575			0.119458
$162$		0			0
$163$		−	18.7637i		−	1.46969i	−0.678236	−	0.734844i	$-0.737255\pi$
$163$		−	18.7637i		−	1.46969i	0.678236	−	0.734844i	$-0.262745\pi$
$164$	−6.69213			−0.522568
$165$		0			0
$166$	4.39230			0.340909
$167$		−	2.92820i		−	0.226591i	−0.993561	−	0.113296i	$-0.963859\pi$
$167$		−	2.92820i		−	0.226591i	0.993561	−	0.113296i	$-0.0361407\pi$
$168$		0			0
$169$	11.9282			0.917554
$170$	−10.5558	−	12.9282i	−0.809595	−	0.991548i
$171$		0			0
$172$		−	1.79315i		−	0.136726i
$173$		−	18.7846i		−	1.42817i	−0.700060	−	0.714084i	$-0.746844\pi$
$173$		−	18.7846i		−	1.42817i	0.700060	−	0.714084i	$-0.253156\pi$
$174$		0			0
$175$	5.07180	+	1.03528i	0.383392	+	0.0782595i
$176$	−3.86370			−0.291238
$177$		0			0
$178$			1.03528i			0.0775972i
$179$	−22.4243			−1.67607			−0.838037	−	0.545613i	$-0.816297\pi$
$179$	−22.4243			−1.67607			−0.838037	+	0.545613i	$0.816297\pi$
$180$		0			0
$181$	−7.85641			−0.583962			−0.291981	−	0.956424i	$-0.594314\pi$
$181$	−7.85641			−0.583962			−0.291981	+	0.956424i	$0.594314\pi$
$182$			1.07180i			0.0794469i
$183$		0			0
$184$	−1.46410			−0.107935
$185$	−11.5911	+	9.46410i	−0.852195	+	0.695815i
$186$		0			0
$187$		−	28.8391i		−	2.10892i
$188$		−	9.46410i		−	0.690241i
$189$		0			0
$190$	−1.73205	+	1.41421i	−0.125656	+	0.102598i
$191$	−2.55103			−0.184586			−0.0922929	−	0.995732i	$-0.529420\pi$
$191$	−2.55103			−0.184586			−0.0922929	+	0.995732i	$0.529420\pi$
$192$		0			0
$193$			5.93426i			0.427157i	0.976926	+	0.213579i	$0.0685119\pi$
$193$			5.93426i			0.427157i	−0.976926	+	0.213579i	$0.931488\pi$
$194$	17.2480			1.23833
$195$		0			0
$196$	−5.92820			−0.423443
$197$			16.5359i			1.17813i	0.808084	+	0.589067i	$0.200505\pi$
$197$			16.5359i			1.17813i	−0.808084	+	0.589067i	$0.799495\pi$
$198$		0			0
$199$	−26.9282			−1.90889			−0.954445	−	0.298387i	$-0.903551\pi$
$199$	−26.9282			−1.90889			−0.954445	+	0.298387i	$0.903551\pi$
$200$	−4.89898	−	1.00000i	−0.346410	−	0.0707107i
$201$		0			0
$202$			0.757875i			0.0533239i
$203$			9.85641i			0.691784i
$204$		0			0
$205$	−9.46410	−	11.5911i	−0.661002	−	0.809558i
$206$	4.89898			0.341328
$207$		0			0
$208$		−	1.03528i		−	0.0717835i
$209$	−3.86370			−0.267258
$210$		0			0
$211$	9.85641			0.678543			0.339272	−	0.940688i	$-0.389819\pi$
$211$	9.85641			0.678543			0.339272	+	0.940688i	$0.389819\pi$
$212$			6.00000i			0.412082i
$213$		0			0
$214$	10.9282			0.747037
$215$	3.10583	−	2.53590i	0.211816	−	0.172947i
$216$		0			0
$217$		−	3.03150i		−	0.205792i
$218$		−	4.92820i		−	0.333780i
$219$		0			0
$220$	−5.46410	−	6.69213i	−0.368390	−	0.451183i
$221$	7.72741			0.519802
$222$		0			0
$223$			0.757875i			0.0507510i	0.999678	+	0.0253755i	$0.00807815\pi$
$223$			0.757875i			0.0507510i	−0.999678	+	0.0253755i	$0.991922\pi$
$224$	−1.03528			−0.0691723
$225$		0			0
$226$	−6.00000			−0.399114
$227$			25.8564i			1.71615i	0.513524	+	0.858075i	$0.328340\pi$
$227$			25.8564i			1.71615i	−0.513524	+	0.858075i	$0.671660\pi$
$228$		0			0
$229$	−23.8564			−1.57648			−0.788238	−	0.615371i	$-0.789006\pi$
$229$	−23.8564			−1.57648			−0.788238	+	0.615371i	$0.789006\pi$
$230$	−2.07055	−	2.53590i	−0.136528	−	0.167212i
$231$		0			0
$232$		−	9.52056i		−	0.625055i
$233$		−	19.4641i		−	1.27514i	−0.770394	−	0.637568i	$-0.779941\pi$
$233$		−	19.4641i		−	1.27514i	0.770394	−	0.637568i	$-0.220059\pi$
$234$		0			0
$235$	16.3923	−	13.3843i	1.06932	−	0.873093i
$236$	−12.6264			−0.821908
$237$		0			0
$238$		−	7.72741i		−	0.500893i
$239$	−18.0058			−1.16470			−0.582350	−	0.812938i	$-0.697867\pi$
$239$	−18.0058			−1.16470			−0.582350	+	0.812938i	$0.697867\pi$
$240$		0			0
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$		−	3.92820i		−	0.252514i
$243$		0			0
$244$	2.00000			0.128037
$245$	−8.38375	−	10.2679i	−0.535618	−	0.655995i
$246$		0			0
$247$		−	1.03528i		−	0.0658730i
$248$			2.92820i			0.185941i
$249$		0			0
$250$	−5.19615	−	9.89949i	−0.328634	−	0.626099i
$251$	25.5302			1.61145			0.805725	−	0.592290i	$-0.201776\pi$
$251$	25.5302			1.61145			0.805725	+	0.592290i	$0.201776\pi$
$252$		0			0
$253$		−	5.65685i		−	0.355643i
$254$	8.48528			0.532414
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	18.7846i		−	1.17175i	−0.810401	−	0.585876i	$-0.800751\pi$
$257$		−	18.7846i		−	1.17175i	0.810401	−	0.585876i	$-0.199249\pi$
$258$		0			0
$259$	−6.92820			−0.430498
$260$	1.79315	−	1.46410i	0.111207	−	0.0907997i
$261$		0			0
$262$			11.5911i			0.716101i
$263$			15.3205i			0.944703i	0.881410	+	0.472351i	$0.156595\pi$
$263$			15.3205i			0.944703i	−0.881410	+	0.472351i	$0.843405\pi$
$264$		0			0
$265$	−10.3923	+	8.48528i	−0.638394	+	0.521247i
$266$	−1.03528			−0.0634769
$267$		0			0
$268$		−	3.58630i		−	0.219068i
$269$	−12.1459			−0.740549			−0.370275	−	0.928922i	$-0.620736\pi$
$269$	−12.1459			−0.740549			−0.370275	+	0.928922i	$0.620736\pi$
$270$		0			0
$271$	−2.92820			−0.177876			−0.0889378	−	0.996037i	$-0.528347\pi$
$271$	−2.92820			−0.177876			−0.0889378	+	0.996037i	$0.528347\pi$
$272$			7.46410i			0.452578i
$273$		0			0
$274$	7.46410			0.450923
$275$	3.86370	−	18.9282i	0.232990	−	1.14141i
$276$		0			0
$277$			1.31268i			0.0788712i	0.999222	+	0.0394356i	$0.0125560\pi$
$277$			1.31268i			0.0788712i	−0.999222	+	0.0394356i	$0.987444\pi$
$278$		−	6.92820i		−	0.415526i
$279$		0			0
$280$	−1.46410	−	1.79315i	−0.0874968	−	0.107161i
$281$	22.7017			1.35427			0.677136	−	0.735858i	$-0.263221\pi$
$281$	22.7017			1.35427			0.677136	+	0.735858i	$0.263221\pi$
$282$		0			0
$283$			19.3185i			1.14837i	0.818727	+	0.574183i	$0.194680\pi$
$283$			19.3185i			1.14837i	−0.818727	+	0.574183i	$0.805320\pi$
$284$	15.4548			0.917074
$285$		0			0
$286$	4.00000			0.236525
$287$		−	6.92820i		−	0.408959i
$288$		0			0
$289$	−38.7128			−2.27722
$290$	16.4901	−	13.4641i	0.968331	−	0.790639i
$291$		0			0
$292$		−	13.3843i		−	0.783255i
$293$		−	7.85641i		−	0.458976i	−0.973311	−	0.229488i	$-0.926295\pi$
$293$		−	7.85641i		−	0.458976i	0.973311	−	0.229488i	$-0.0737052\pi$
$294$		0			0
$295$	−17.8564	−	21.8695i	−1.03964	−	1.27329i
$296$	6.69213			0.388972
$297$		0			0
$298$		−	9.04008i		−	0.523678i
$299$	1.51575			0.0876581
$300$		0			0
$301$	1.85641			0.107001
$302$			21.8564i			1.25769i
$303$		0			0
$304$	1.00000			0.0573539
$305$	2.82843	+	3.46410i	0.161955	+	0.198354i
$306$		0			0
$307$		−	11.8685i		−	0.677372i	−0.940900	−	0.338686i	$-0.890018\pi$
$307$		−	11.8685i		−	0.677372i	0.940900	−	0.338686i	$-0.109982\pi$
$308$		−	4.00000i		−	0.227921i
$309$		0			0
$310$	−5.07180	+	4.14110i	−0.288059	+	0.235199i
$311$	−6.69213			−0.379476			−0.189738	−	0.981835i	$-0.560764\pi$
$311$	−6.69213			−0.379476			−0.189738	+	0.981835i	$0.560764\pi$
$312$		0			0
$313$		−	19.5959i		−	1.10763i	−0.832641	−	0.553813i	$-0.813172\pi$
$313$		−	19.5959i		−	1.10763i	0.832641	−	0.553813i	$-0.186828\pi$
$314$	14.1421			0.798087
$315$		0			0
$316$	−4.00000			−0.225018
$317$			14.0000i			0.786318i	0.919470	+	0.393159i	$0.128618\pi$
$317$			14.0000i			0.786318i	−0.919470	+	0.393159i	$0.871382\pi$
$318$		0			0
$319$	36.7846			2.05954
$320$	1.41421	+	1.73205i	0.0790569	+	0.0968246i
$321$		0			0
$322$		−	1.51575i		−	0.0844694i
$323$			7.46410i			0.415314i
$324$		0			0
$325$	5.07180	+	1.03528i	0.281333	+	0.0574268i
$326$	−18.7637			−1.03923
$327$		0			0
$328$			6.69213i			0.369511i
$329$	9.79796			0.540179
$330$		0			0
$331$	−13.8564			−0.761617			−0.380808	−	0.924654i	$-0.624354\pi$
$331$	−13.8564			−0.761617			−0.380808	+	0.924654i	$0.624354\pi$
$332$		−	4.39230i		−	0.241059i
$333$		0			0
$334$	−2.92820			−0.160224
$335$	6.21166	−	5.07180i	0.339379	−	0.277102i
$336$		0			0
$337$		−	3.86370i		−	0.210469i	−0.994447	−	0.105235i	$-0.966441\pi$
$337$		−	3.86370i		−	0.210469i	0.994447	−	0.105235i	$-0.0335594\pi$
$338$		−	11.9282i		−	0.648809i
$339$		0			0
$340$	−12.9282	+	10.5558i	−0.701130	+	0.572470i
$341$	−11.3137			−0.612672
$342$		0			0
$343$		−	13.3843i		−	0.722682i
$344$	−1.79315			−0.0966802
$345$		0			0
$346$	−18.7846			−1.00987
$347$			25.4641i			1.36698i	0.729958	+	0.683492i	$0.239540\pi$
$347$			25.4641i			1.36698i	−0.729958	+	0.683492i	$0.760460\pi$
$348$		0			0
$349$	−31.8564			−1.70523			−0.852617	−	0.522536i	$-0.824986\pi$
$349$	−31.8564			−1.70523			−0.852617	+	0.522536i	$0.824986\pi$
$350$	1.03528	−	5.07180i	0.0553378	−	0.271099i
$351$		0			0
$352$			3.86370i			0.205936i
$353$			13.3205i			0.708979i	0.935060	+	0.354490i	$0.115345\pi$
$353$			13.3205i			0.708979i	−0.935060	+	0.354490i	$0.884655\pi$
$354$		0			0
$355$	21.8564	+	26.7685i	1.16002	+	1.42073i
$356$	1.03528			0.0548695
$357$		0			0
$358$			22.4243i			1.18516i
$359$	9.31749			0.491758			0.245879	−	0.969301i	$-0.420923\pi$
$359$	9.31749			0.491758			0.245879	+	0.969301i	$0.420923\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$			7.85641i			0.412924i
$363$		0			0
$364$	1.07180			0.0561774
$365$	23.1822	−	18.9282i	1.21341	−	0.990747i
$366$		0			0
$367$		−	20.0764i		−	1.04798i	−0.851725	−	0.523990i	$-0.824443\pi$
$367$		−	20.0764i		−	1.04798i	0.851725	−	0.523990i	$-0.175557\pi$
$368$			1.46410i			0.0763216i
$369$		0			0
$370$	9.46410	+	11.5911i	0.492015	+	0.602593i
$371$	−6.21166			−0.322493
$372$		0			0
$373$			0.480473i			0.0248780i	0.999923	+	0.0124390i	$0.00395955\pi$
$373$			0.480473i			0.0248780i	−0.999923	+	0.0124390i	$0.996040\pi$
$374$	−28.8391			−1.49123
$375$		0			0
$376$	−9.46410			−0.488074
$377$			9.85641i			0.507631i
$378$		0			0
$379$	−19.7128			−1.01258			−0.506290	−	0.862364i	$-0.668983\pi$
$379$	−19.7128			−1.01258			−0.506290	+	0.862364i	$0.668983\pi$
$380$	1.41421	+	1.73205i	0.0725476	+	0.0888523i
$381$		0			0
$382$			2.55103i			0.130522i
$383$			9.07180i			0.463547i	0.972770	+	0.231774i	$0.0744528\pi$
$383$			9.07180i			0.463547i	−0.972770	+	0.231774i	$0.925547\pi$
$384$		0			0
$385$	6.92820	−	5.65685i	0.353094	−	0.288300i
$386$	5.93426			0.302046
$387$		0			0
$388$		−	17.2480i		−	0.875633i
$389$	19.7990			1.00385			0.501924	−	0.864912i	$-0.332626\pi$
$389$	19.7990			1.00385			0.501924	+	0.864912i	$0.332626\pi$
$390$		0			0
$391$	−10.9282			−0.552663
$392$			5.92820i			0.299419i
$393$		0			0
$394$	16.5359			0.833067
$395$	−5.65685	−	6.92820i	−0.284627	−	0.348596i
$396$		0			0
$397$		−	1.31268i		−	0.0658814i	−0.999457	−	0.0329407i	$-0.989513\pi$
$397$		−	1.31268i		−	0.0658814i	0.999457	−	0.0329407i	$-0.0104872\pi$
$398$			26.9282i			1.34979i
$399$		0			0
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$	4.62158			0.230791			0.115395	−	0.993320i	$-0.463187\pi$
$401$	4.62158			0.230791			0.115395	+	0.993320i	$0.463187\pi$
$402$		0			0
$403$		−	3.03150i		−	0.151010i
$404$	0.757875			0.0377057
$405$		0			0
$406$	9.85641			0.489165
$407$			25.8564i			1.28165i
$408$		0			0
$409$	7.07180			0.349678			0.174839	−	0.984597i	$-0.444060\pi$
$409$	7.07180			0.349678			0.174839	+	0.984597i	$0.444060\pi$
$410$	−11.5911	+	9.46410i	−0.572444	+	0.467399i
$411$		0			0
$412$		−	4.89898i		−	0.241355i
$413$		−	13.0718i		−	0.643221i
$414$		0			0
$415$	7.60770	−	6.21166i	0.373447	−	0.304918i
$416$	−1.03528			−0.0507586
$417$		0			0
$418$			3.86370i			0.188980i
$419$	−24.4206			−1.19302			−0.596511	−	0.802605i	$-0.703447\pi$
$419$	−24.4206			−1.19302			−0.596511	+	0.802605i	$0.703447\pi$
$420$		0			0
$421$	−25.7128			−1.25317			−0.626583	−	0.779355i	$-0.715547\pi$
$421$	−25.7128			−1.25317			−0.626583	+	0.779355i	$0.715547\pi$
$422$		−	9.85641i		−	0.479802i
$423$		0			0
$424$	6.00000			0.291386
$425$	−36.5665	−	7.46410i	−1.77373	−	0.362062i
$426$		0			0
$427$			2.07055i			0.100201i
$428$		−	10.9282i		−	0.528235i
$429$		0			0
$430$	−2.53590	−	3.10583i	−0.122292	−	0.149776i
$431$	−36.0117			−1.73462			−0.867311	−	0.497767i	$-0.834153\pi$
$431$	−36.0117			−1.73462			−0.867311	+	0.497767i	$0.834153\pi$
$432$		0			0
$433$		−	13.6617i		−	0.656538i	−0.944584	−	0.328269i	$-0.893535\pi$
$433$		−	13.6617i		−	0.656538i	0.944584	−	0.328269i	$-0.106465\pi$
$434$	−3.03150			−0.145517
$435$		0			0
$436$	−4.92820			−0.236018
$437$			1.46410i			0.0700375i
$438$		0			0
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$	−6.69213	+	5.46410i	−0.319035	+	0.260491i
$441$		0			0
$442$		−	7.72741i		−	0.367555i
$443$			4.39230i			0.208685i	0.994541	+	0.104342i	$0.0332738\pi$
$443$			4.39230i			0.208685i	−0.994541	+	0.104342i	$0.966726\pi$
$444$		0			0
$445$	1.46410	+	1.79315i	0.0694051	+	0.0850035i
$446$	0.757875			0.0358864
$447$		0			0
$448$			1.03528i			0.0489122i
$449$	−3.66063			−0.172756			−0.0863779	−	0.996262i	$-0.527529\pi$
$449$	−3.66063			−0.172756			−0.0863779	+	0.996262i	$0.527529\pi$
$450$		0			0
$451$	−25.8564			−1.21753
$452$			6.00000i			0.282216i
$453$		0			0
$454$	25.8564			1.21350
$455$	1.51575	+	1.85641i	0.0710594	+	0.0870297i
$456$		0			0
$457$		−	33.9411i		−	1.58770i	−0.608114	−	0.793849i	$-0.708074\pi$
$457$		−	33.9411i		−	1.58770i	0.608114	−	0.793849i	$-0.291926\pi$
$458$			23.8564i			1.11474i
$459$		0			0
$460$	−2.53590	+	2.07055i	−0.118237	+	0.0965400i
$461$	17.7284			0.825696			0.412848	−	0.910800i	$-0.364534\pi$
$461$	17.7284			0.825696			0.412848	+	0.910800i	$0.364534\pi$
$462$		0			0
$463$			34.0155i			1.58083i	0.612570	+	0.790416i	$0.290136\pi$
$463$			34.0155i			1.58083i	−0.612570	+	0.790416i	$0.709864\pi$
$464$	−9.52056			−0.441981
$465$		0			0
$466$	−19.4641			−0.901657
$467$			9.46410i			0.437946i	0.975731	+	0.218973i	$0.0702707\pi$
$467$			9.46410i			0.437946i	−0.975731	+	0.218973i	$0.929729\pi$
$468$		0			0
$469$	3.71281			0.171442
$470$	−13.3843	−	16.3923i	−0.617370	−	0.756121i
$471$		0			0
$472$			12.6264i			0.581177i
$473$		−	6.92820i		−	0.318559i
$474$		0			0
$475$	−1.00000	+	4.89898i	−0.0458831	+	0.224781i
$476$	−7.72741			−0.354185
$477$		0			0
$478$			18.0058i			0.823568i
$479$	−31.3901			−1.43425			−0.717125	−	0.696944i	$-0.754542\pi$
$479$	−31.3901			−1.43425			−0.717125	+	0.696944i	$0.754542\pi$
$480$		0			0
$481$	−6.92820			−0.315899
$482$		−	10.0000i		−	0.455488i
$483$		0			0
$484$	−3.92820			−0.178555
$485$	29.8744	−	24.3923i	1.35652	−	1.10760i
$486$		0			0
$487$			26.0106i			1.17865i	0.807894	+	0.589327i	$0.200607\pi$
$487$			26.0106i			1.17865i	−0.807894	+	0.589327i	$0.799393\pi$
$488$		−	2.00000i		−	0.0905357i
$489$		0			0
$490$	−10.2679	+	8.38375i	−0.463859	+	0.378739i
$491$	−15.7322			−0.709985			−0.354992	−	0.934869i	$-0.615517\pi$
$491$	−15.7322			−0.709985			−0.354992	+	0.934869i	$0.615517\pi$
$492$		0			0
$493$		−	71.0624i		−	3.20049i
$494$	−1.03528			−0.0465793
$495$		0			0
$496$	2.92820			0.131480
$497$			16.0000i			0.717698i
$498$		0			0
$499$	1.85641			0.0831042			0.0415521	−	0.999136i	$-0.486770\pi$
$499$	1.85641			0.0831042			0.0415521	+	0.999136i	$0.486770\pi$
$500$	−9.89949	+	5.19615i	−0.442719	+	0.232379i
$501$		0			0
$502$		−	25.5302i		−	1.13947i
$503$		−	23.3205i		−	1.03981i	−0.854224	−	0.519905i	$-0.825967\pi$
$503$		−	23.3205i		−	1.03981i	0.854224	−	0.519905i	$-0.174033\pi$
$504$		0			0
$505$	1.07180	+	1.31268i	0.0476943	+	0.0584134i
$506$	−5.65685			−0.251478
$507$		0			0
$508$		−	8.48528i		−	0.376473i
$509$	22.3500			0.990647			0.495324	−	0.868709i	$-0.335050\pi$
$509$	22.3500			0.990647			0.495324	+	0.868709i	$0.335050\pi$
$510$		0			0
$511$	13.8564			0.612971
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−18.7846			−0.828554
$515$	8.48528	−	6.92820i	0.373906	−	0.305293i
$516$		0			0
$517$		−	36.5665i		−	1.60819i
$518$			6.92820i			0.304408i
$519$		0			0
$520$	−1.46410	−	1.79315i	−0.0642051	−	0.0786349i
$521$	4.62158			0.202475			0.101238	−	0.994862i	$-0.467720\pi$
$521$	4.62158			0.202475			0.101238	+	0.994862i	$0.467720\pi$
$522$		0			0
$523$		−	7.17260i		−	0.313636i	−0.987628	−	0.156818i	$-0.949876\pi$
$523$		−	7.17260i		−	0.313636i	0.987628	−	0.156818i	$-0.0501236\pi$
$524$	11.5911			0.506360
$525$		0			0
$526$	15.3205			0.668006
$527$			21.8564i			0.952080i
$528$		0			0
$529$	20.8564			0.906800
$530$	8.48528	+	10.3923i	0.368577	+	0.451413i
$531$		0			0
$532$			1.03528i			0.0448849i
$533$		−	6.92820i		−	0.300094i
$534$		0			0
$535$	18.9282	−	15.4548i	0.818338	−	0.668170i
$536$	−3.58630			−0.154905
$537$		0			0
$538$			12.1459i			0.523647i
$539$	−22.9048			−0.986580
$540$		0			0
$541$	26.0000			1.11783			0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000			1.11783			0.558914	+	0.829226i	$0.311218\pi$
$542$			2.92820i			0.125777i
$543$		0			0
$544$	7.46410			0.320021
$545$	−6.96953	−	8.53590i	−0.298542	−	0.365638i
$546$		0			0
$547$			38.6370i			1.65200i	0.563670	+	0.826000i	$0.309389\pi$
$547$			38.6370i			1.65200i	−0.563670	+	0.826000i	$0.690611\pi$
$548$		−	7.46410i		−	0.318851i
$549$		0			0
$550$	−18.9282	−	3.86370i	−0.807101	−	0.164749i
$551$	−9.52056			−0.405589
$552$		0			0
$553$		−	4.14110i		−	0.176098i
$554$	1.31268			0.0557703
$555$		0			0
$556$	−6.92820			−0.293821
$557$			24.5359i			1.03962i	0.854282	+	0.519810i	$0.173997\pi$
$557$			24.5359i			1.03962i	−0.854282	+	0.519810i	$0.826003\pi$
$558$		0			0
$559$	1.85641			0.0785176
$560$	−1.79315	+	1.46410i	−0.0757745	+	0.0618696i
$561$		0			0
$562$		−	22.7017i		−	0.957615i
$563$			1.85641i			0.0782382i	0.999235	+	0.0391191i	$0.0124552\pi$
$563$			1.85641i			0.0782382i	−0.999235	+	0.0391191i	$0.987545\pi$
$564$		0			0
$565$	−10.3923	+	8.48528i	−0.437208	+	0.356978i
$566$	19.3185			0.812018
$567$		0			0
$568$		−	15.4548i		−	0.648470i
$569$	−9.72363			−0.407636			−0.203818	−	0.979009i	$-0.565335\pi$
$569$	−9.72363			−0.407636			−0.203818	+	0.979009i	$0.565335\pi$
$570$		0			0
$571$	1.07180			0.0448533			0.0224266	−	0.999748i	$-0.492861\pi$
$571$	1.07180			0.0448533			0.0224266	+	0.999748i	$0.492861\pi$
$572$		−	4.00000i		−	0.167248i
$573$		0			0
$574$	−6.92820			−0.289178
$575$	−7.17260	−	1.46410i	−0.299118	−	0.0610573i
$576$		0			0
$577$			5.65685i			0.235498i	0.993043	+	0.117749i	$0.0375678\pi$
$577$			5.65685i			0.235498i	−0.993043	+	0.117749i	$0.962432\pi$
$578$			38.7128i			1.61024i
$579$		0			0
$580$	−13.4641	−	16.4901i	−0.559066	−	0.684714i
$581$	4.54725			0.188652
$582$		0			0
$583$			23.1822i			0.960109i
$584$	−13.3843			−0.553845
$585$		0			0
$586$	−7.85641			−0.324545
$587$			3.60770i			0.148906i	0.997225	+	0.0744528i	$0.0237210\pi$
$587$			3.60770i			0.148906i	−0.997225	+	0.0744528i	$0.976279\pi$
$588$		0			0
$589$	2.92820			0.120655
$590$	−21.8695	+	17.8564i	−0.900355	+	0.735137i
$591$		0			0
$592$		−	6.69213i		−	0.275045i
$593$			11.4641i			0.470774i	0.971902	+	0.235387i	$0.0756358\pi$
$593$			11.4641i			0.470774i	−0.971902	+	0.235387i	$0.924364\pi$
$594$		0			0
$595$	−10.9282	−	13.3843i	−0.448013	−	0.548701i
$596$	−9.04008			−0.370296
$597$		0			0
$598$		−	1.51575i		−	0.0619836i
$599$	30.3548			1.24026			0.620132	−	0.784497i	$-0.287079\pi$
$599$	30.3548			1.24026			0.620132	+	0.784497i	$0.287079\pi$
$600$		0			0
$601$	22.7846			0.929404			0.464702	−	0.885467i	$-0.346162\pi$
$601$	22.7846			0.929404			0.464702	+	0.885467i	$0.346162\pi$
$602$		−	1.85641i		−	0.0756615i
$603$		0			0
$604$	21.8564			0.889325
$605$	−5.55532	−	6.80385i	−0.225856	−	0.276616i
$606$		0			0
$607$			22.9791i			0.932695i	0.884602	+	0.466347i	$0.154430\pi$
$607$			22.9791i			0.932695i	−0.884602	+	0.466347i	$0.845570\pi$
$608$		−	1.00000i		−	0.0405554i
$609$		0			0
$610$	3.46410	−	2.82843i	0.140257	−	0.114520i
$611$	9.79796			0.396383
$612$		0			0
$613$			45.0518i			1.81962i	0.415021	+	0.909812i	$0.363774\pi$
$613$			45.0518i			1.81962i	−0.415021	+	0.909812i	$0.636226\pi$
$614$	−11.8685			−0.478974
$615$		0			0
$616$	−4.00000			−0.161165
$617$		−	20.2487i		−	0.815182i	−0.913165	−	0.407591i	$-0.866369\pi$
$617$		−	20.2487i		−	0.815182i	0.913165	−	0.407591i	$-0.133631\pi$
$618$		0			0
$619$	−34.6410			−1.39234			−0.696170	−	0.717877i	$-0.745114\pi$
$619$	−34.6410			−1.39234			−0.696170	+	0.717877i	$0.745114\pi$
$620$	4.14110	+	5.07180i	0.166311	+	0.203688i
$621$		0			0
$622$			6.69213i			0.268330i
$623$			1.07180i			0.0429406i
$624$		0			0
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	−19.5959			−0.783210
$627$		0			0
$628$		−	14.1421i		−	0.564333i
$629$	49.9507			1.99167
$630$		0			0
$631$	−5.85641			−0.233140			−0.116570	−	0.993182i	$-0.537190\pi$
$631$	−5.85641			−0.233140			−0.116570	+	0.993182i	$0.537190\pi$
$632$			4.00000i			0.159111i
$633$		0			0
$634$	14.0000			0.556011
$635$	14.6969	−	12.0000i	0.583230	−	0.476205i
$636$		0			0
$637$		−	6.13733i		−	0.243170i
$638$		−	36.7846i		−	1.45632i
$639$		0			0
$640$	1.73205	−	1.41421i	0.0684653	−	0.0559017i
$641$	2.55103			0.100759			0.0503797	−	0.998730i	$-0.483957\pi$
$641$	2.55103			0.100759			0.0503797	+	0.998730i	$0.483957\pi$
$642$		0			0
$643$			22.3500i			0.881399i	0.897655	+	0.440699i	$0.145269\pi$
$643$			22.3500i			0.881399i	−0.897655	+	0.440699i	$0.854731\pi$
$644$	−1.51575			−0.0597289
$645$		0			0
$646$	7.46410			0.293671
$647$			6.53590i			0.256953i	0.991713	+	0.128476i	$0.0410086\pi$
$647$			6.53590i			0.256953i	−0.991713	+	0.128476i	$0.958991\pi$
$648$		0			0
$649$	−48.7846			−1.91496
$650$	1.03528	−	5.07180i	0.0406069	−	0.198932i
$651$		0			0
$652$			18.7637i			0.734844i
$653$		−	24.2487i		−	0.948925i	−0.880276	−	0.474463i	$-0.842642\pi$
$653$		−	24.2487i		−	0.948925i	0.880276	−	0.474463i	$-0.157358\pi$
$654$		0			0
$655$	16.3923	+	20.0764i	0.640500	+	0.784450i
$656$	6.69213			0.261284
$657$		0			0
$658$		−	9.79796i		−	0.381964i
$659$	9.04008			0.352152			0.176076	−	0.984377i	$-0.443660\pi$
$659$	9.04008			0.352152			0.176076	+	0.984377i	$0.443660\pi$
$660$		0			0
$661$	30.7846			1.19738			0.598691	−	0.800980i	$-0.295688\pi$
$661$	30.7846			1.19738			0.598691	+	0.800980i	$0.295688\pi$
$662$			13.8564i			0.538545i
$663$		0			0
$664$	−4.39230			−0.170454
$665$	−1.79315	+	1.46410i	−0.0695354	+	0.0567754i
$666$		0			0
$667$		−	13.9391i		−	0.539723i
$668$			2.92820i			0.113296i
$669$		0			0
$670$	−5.07180	−	6.21166i	−0.195941	−	0.239977i
$671$	7.72741			0.298313
$672$		0			0
$673$			32.1480i			1.23921i	0.784912	+	0.619607i	$0.212708\pi$
$673$			32.1480i			1.23921i	−0.784912	+	0.619607i	$0.787292\pi$
$674$	−3.86370			−0.148824
$675$		0			0
$676$	−11.9282			−0.458777
$677$		−	32.6410i		−	1.25450i	−0.778820	−	0.627248i	$-0.784181\pi$
$677$		−	32.6410i		−	1.25450i	0.778820	−	0.627248i	$-0.215819\pi$
$678$		0			0
$679$	17.8564			0.685266
$680$	10.5558	+	12.9282i	0.404798	+	0.495774i
$681$		0			0
$682$			11.3137i			0.433224i
$683$		−	5.07180i		−	0.194067i	−0.995281	−	0.0970335i	$-0.969065\pi$
$683$		−	5.07180i		−	0.194067i	0.995281	−	0.0970335i	$-0.0309354\pi$
$684$		0			0
$685$	12.9282	−	10.5558i	0.493961	−	0.403318i
$686$	−13.3843			−0.511013
$687$		0			0
$688$			1.79315i			0.0683632i
$689$	−6.21166			−0.236645
$690$		0			0
$691$	25.0718			0.953776			0.476888	−	0.878964i	$-0.341765\pi$
$691$	25.0718			0.953776			0.476888	+	0.878964i	$0.341765\pi$
$692$			18.7846i			0.714084i
$693$		0			0
$694$	25.4641			0.966604
$695$	−9.79796	−	12.0000i	−0.371658	−	0.455186i
$696$		0			0
$697$			49.9507i			1.89202i
$698$			31.8564i			1.20578i
$699$		0			0
$700$	−5.07180	−	1.03528i	−0.191696	−	0.0391298i
$701$	41.4655			1.56613			0.783064	−	0.621941i	$-0.213655\pi$
$701$	41.4655			1.56613			0.783064	+	0.621941i	$0.213655\pi$
$702$		0			0
$703$		−	6.69213i		−	0.252398i
$704$	3.86370			0.145619
$705$		0			0
$706$	13.3205			0.501324
$707$			0.784610i			0.0295083i
$708$		0			0
$709$	−15.8564			−0.595500			−0.297750	−	0.954644i	$-0.596236\pi$
$709$	−15.8564			−0.595500			−0.297750	+	0.954644i	$0.596236\pi$
$710$	26.7685	−	21.8564i	1.00460	−	0.820256i
$711$		0			0
$712$		−	1.03528i		−	0.0387986i
$713$			4.28719i			0.160556i
$714$		0			0
$715$	6.92820	−	5.65685i	0.259100	−	0.211554i
$716$	22.4243			0.838037
$717$		0			0
$718$		−	9.31749i		−	0.347725i
$719$	26.8429			1.00107			0.500535	−	0.865716i	$-0.333137\pi$
$719$	26.8429			1.00107			0.500535	+	0.865716i	$0.333137\pi$
$720$		0			0
$721$	5.07180			0.188884
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	7.85641			0.291981
$725$	9.52056	−	46.6410i	0.353585	−	1.73220i
$726$		0			0
$727$		−	10.2784i		−	0.381206i	−0.981667	−	0.190603i	$-0.938956\pi$
$727$		−	10.2784i		−	0.381206i	0.981667	−	0.190603i	$-0.0610443\pi$
$728$		−	1.07180i		−	0.0397234i
$729$		0			0
$730$	−18.9282	−	23.1822i	−0.700564	−	0.858012i
$731$	−13.3843			−0.495035
$732$		0			0
$733$			12.0716i			0.445874i	0.974833	+	0.222937i	$0.0715644\pi$
$733$			12.0716i			0.445874i	−0.974833	+	0.222937i	$0.928436\pi$
$734$	−20.0764			−0.741033
$735$		0			0
$736$	1.46410			0.0539675
$737$		−	13.8564i		−	0.510407i
$738$		0			0
$739$	31.7128			1.16657			0.583287	−	0.812266i	$-0.301766\pi$
$739$	31.7128			1.16657			0.583287	+	0.812266i	$0.301766\pi$
$740$	11.5911	−	9.46410i	0.426098	−	0.347907i
$741$		0			0
$742$			6.21166i			0.228037i
$743$		−	34.6410i		−	1.27086i	−0.772160	−	0.635428i	$-0.780824\pi$
$743$		−	34.6410i		−	1.27086i	0.772160	−	0.635428i	$-0.219176\pi$
$744$		0			0
$745$	−12.7846	−	15.6579i	−0.468392	−	0.573661i
$746$	0.480473			0.0175914
$747$		0			0
$748$			28.8391i			1.05446i
$749$	11.3137			0.413394
$750$		0			0
$751$	−21.8564			−0.797552			−0.398776	−	0.917048i	$-0.630565\pi$
$751$	−21.8564			−0.797552			−0.398776	+	0.917048i	$0.630565\pi$
$752$			9.46410i			0.345120i
$753$		0			0
$754$	9.85641			0.358949
$755$	30.9096	+	37.8564i	1.12492	+	1.37774i
$756$		0			0
$757$			50.1538i			1.82287i	0.411443	+	0.911436i	$0.365025\pi$
$757$			50.1538i			1.82287i	−0.411443	+	0.911436i	$0.634975\pi$
$758$			19.7128i			0.716002i
$759$		0			0
$760$	1.73205	−	1.41421i	0.0628281	−	0.0512989i
$761$	−6.21166			−0.225172			−0.112586	−	0.993642i	$-0.535913\pi$
$761$	−6.21166			−0.225172			−0.112586	+	0.993642i	$0.535913\pi$
$762$		0			0
$763$		−	5.10205i		−	0.184707i
$764$	2.55103			0.0922929
$765$		0			0
$766$	9.07180			0.327777
$767$		−	13.0718i		−	0.471995i
$768$		0			0
$769$	−8.14359			−0.293665			−0.146833	−	0.989161i	$-0.546908\pi$
$769$	−8.14359			−0.293665			−0.146833	+	0.989161i	$0.546908\pi$
$770$	−5.65685	−	6.92820i	−0.203859	−	0.249675i
$771$		0			0
$772$		−	5.93426i		−	0.213579i
$773$		−	19.8564i		−	0.714185i	−0.934069	−	0.357093i	$-0.883768\pi$
$773$		−	19.8564i		−	0.714185i	0.934069	−	0.357093i	$-0.116232\pi$
$774$		0			0
$775$	−2.92820	+	14.3452i	−0.105184	+	0.515295i
$776$	−17.2480			−0.619166
$777$		0			0
$778$		−	19.7990i		−	0.709828i
$779$	6.69213			0.239770
$780$		0			0
$781$	59.7128			2.13669
$782$			10.9282i			0.390792i
$783$		0			0
$784$	5.92820			0.211722
$785$	24.4949	−	20.0000i	0.874260	−	0.713831i
$786$		0			0
$787$			26.7685i			0.954195i	0.878850	+	0.477097i	$0.158311\pi$
$787$			26.7685i			0.954195i	−0.878850	+	0.477097i	$0.841689\pi$
$788$		−	16.5359i		−	0.589067i
$789$		0			0
$790$	−6.92820	+	5.65685i	−0.246494	+	0.201262i
$791$	−6.21166			−0.220861
$792$		0			0
$793$			2.07055i			0.0735275i
$794$	−1.31268			−0.0465852
$795$		0			0
$796$	26.9282			0.954445
$797$		−	28.6410i		−	1.01452i	−0.861794	−	0.507258i	$-0.830659\pi$
$797$		−	28.6410i		−	1.01452i	0.861794	−	0.507258i	$-0.169341\pi$
$798$		0			0
$799$	−70.6410			−2.49910
$800$	4.89898	+	1.00000i	0.173205	+	0.0353553i
$801$		0			0
$802$		−	4.62158i		−	0.163194i
$803$		−	51.7128i		−	1.82491i
$804$		0			0
$805$	−2.14359	−	2.62536i	−0.0755517	−	0.0925316i
$806$	−3.03150			−0.106780
$807$		0			0
$808$		−	0.757875i		−	0.0266619i
$809$	33.5350			1.17903			0.589514	−	0.807758i	$-0.299319\pi$
$809$	33.5350			1.17903			0.589514	+	0.807758i	$0.299319\pi$
$810$		0			0
$811$	56.4974			1.98389			0.991946	−	0.126658i	$-0.0404251\pi$
$811$	56.4974			1.98389			0.991946	+	0.126658i	$0.0404251\pi$
$812$		−	9.85641i		−	0.345892i
$813$		0			0
$814$	25.8564			0.906267
$815$	−32.4997	+	26.5359i	−1.13842	+	0.929512i
$816$		0			0
$817$			1.79315i			0.0627344i
$818$		−	7.07180i		−	0.247260i
$819$		0			0
$820$	9.46410	+	11.5911i	0.330501	+	0.404779i
$821$	−37.3244			−1.30263			−0.651314	−	0.758808i	$-0.725782\pi$
$821$	−37.3244			−1.30263			−0.651314	+	0.758808i	$0.725782\pi$
$822$		0			0
$823$		−	55.6819i		−	1.94095i	−0.241202	−	0.970475i	$-0.577542\pi$
$823$		−	55.6819i		−	1.94095i	0.241202	−	0.970475i	$-0.422458\pi$
$824$	−4.89898			−0.170664
$825$		0			0
$826$	−13.0718			−0.454826
$827$		−	6.92820i		−	0.240917i	−0.992718	−	0.120459i	$-0.961563\pi$
$827$		−	6.92820i		−	0.240917i	0.992718	−	0.120459i	$-0.0384365\pi$
$828$		0			0
$829$	26.7846			0.930268			0.465134	−	0.885240i	$-0.346006\pi$
$829$	26.7846			0.930268			0.465134	+	0.885240i	$0.346006\pi$
$830$	−6.21166	−	7.60770i	−0.215610	−	0.264067i
$831$		0			0
$832$			1.03528i			0.0358917i
$833$			44.2487i			1.53313i
$834$		0			0
$835$	−5.07180	+	4.14110i	−0.175517	+	0.143309i
$836$	3.86370			0.133629
$837$		0			0
$838$			24.4206i			0.843595i
$839$	28.2843			0.976481			0.488241	−	0.872709i	$-0.337639\pi$
$839$	28.2843			0.976481			0.488241	+	0.872709i	$0.337639\pi$
$840$		0			0
$841$	61.6410			2.12555
$842$			25.7128i			0.886122i
$843$		0			0
$844$	−9.85641			−0.339272
$845$	−16.8690	−	20.6603i	−0.580312	−	0.710734i
$846$		0			0
$847$		−	4.06678i		−	0.139736i
$848$		−	6.00000i		−	0.206041i
$849$		0			0
$850$	−7.46410	+	36.5665i	−0.256017	+	1.25422i
$851$	9.79796			0.335870
$852$		0			0
$853$		−	14.6969i		−	0.503214i	−0.967830	−	0.251607i	$-0.919041\pi$
$853$		−	14.6969i		−	0.503214i	0.967830	−	0.251607i	$-0.0809590\pi$
$854$	2.07055			0.0708528
$855$		0			0
$856$	−10.9282			−0.373518
$857$		−	52.6410i		−	1.79818i	−0.437761	−	0.899091i	$-0.644228\pi$
$857$		−	52.6410i		−	1.79818i	0.437761	−	0.899091i	$-0.355772\pi$
$858$		0			0
$859$	−36.7846			−1.25507			−0.627537	−	0.778586i	$-0.715937\pi$
$859$	−36.7846			−1.25507			−0.627537	+	0.778586i	$0.715937\pi$
$860$	−3.10583	+	2.53590i	−0.105908	+	0.0864734i
$861$		0			0
$862$			36.0117i			1.22656i
$863$			20.7846i			0.707516i	0.935337	+	0.353758i	$0.115096\pi$
$863$			20.7846i			0.707516i	−0.935337	+	0.353758i	$0.884904\pi$
$864$		0			0
$865$	−32.5359	+	26.5654i	−1.10625	+	0.903252i
$866$	−13.6617			−0.464242
$867$		0			0
$868$			3.03150i			0.102896i
$869$	−15.4548			−0.524269
$870$		0			0
$871$	3.71281			0.125804
$872$			4.92820i			0.166890i
$873$		0			0
$874$	1.46410			0.0495240
$875$	−5.37945	−	10.2487i	−0.181859	−	0.346470i
$876$		0			0
$877$		−	43.8134i		−	1.47947i	−0.672896	−	0.739737i	$-0.734950\pi$
$877$		−	43.8134i		−	1.47947i	0.672896	−	0.739737i	$-0.265050\pi$
$878$			20.0000i			0.674967i
$879$		0			0
$880$	5.46410	+	6.69213i	0.184195	+	0.225592i
$881$	10.3528			0.348793			0.174397	−	0.984675i	$-0.444202\pi$
$881$	10.3528			0.348793			0.174397	+	0.984675i	$0.444202\pi$
$882$		0			0
$883$		−	24.0144i		−	0.808150i	−0.914726	−	0.404075i	$-0.867594\pi$
$883$		−	24.0144i		−	0.808150i	0.914726	−	0.404075i	$-0.132406\pi$
$884$	−7.72741			−0.259901
$885$		0			0
$886$	4.39230			0.147562
$887$			39.7128i			1.33343i	0.745315	+	0.666713i	$0.232299\pi$
$887$			39.7128i			1.33343i	−0.745315	+	0.666713i	$0.767701\pi$
$888$		0			0
$889$	8.78461			0.294626
$890$	1.79315	−	1.46410i	0.0601066	−	0.0490768i
$891$		0			0
$892$		−	0.757875i		−	0.0253755i
$893$			9.46410i			0.316704i
$894$		0			0
$895$	31.7128	+	38.8401i	1.06004	+	1.29828i
$896$	1.03528			0.0345861
$897$		0			0
$898$			3.66063i			0.122157i
$899$	−27.8781			−0.929788
$900$		0			0
$901$	44.7846			1.49199
$902$			25.8564i			0.860924i
$903$		0			0
$904$	6.00000			0.199557
$905$	11.1106	+	13.6077i	0.369330	+	0.452335i
$906$		0			0
$907$		−	2.62536i		−	0.0871735i	−0.999050	−	0.0435867i	$-0.986122\pi$
$907$		−	2.62536i		−	0.0871735i	0.999050	−	0.0435867i	$-0.0138785\pi$
$908$		−	25.8564i		−	0.858075i
$909$		0			0
$910$	1.85641	−	1.51575i	0.0615393	−	0.0502466i
$911$	45.2548			1.49936			0.749680	−	0.661801i	$-0.230208\pi$
$911$	45.2548			1.49936			0.749680	+	0.661801i	$0.230208\pi$
$912$		0			0
$913$		−	16.9706i		−	0.561644i
$914$	−33.9411			−1.12267
$915$		0			0
$916$	23.8564			0.788238
$917$			12.0000i			0.396275i
$918$		0			0
$919$	27.7128			0.914161			0.457081	−	0.889425i	$-0.348895\pi$
$919$	27.7128			0.914161			0.457081	+	0.889425i	$0.348895\pi$
$920$	2.07055	+	2.53590i	0.0682641	+	0.0836061i
$921$		0			0
$922$		−	17.7284i		−	0.583855i
$923$			16.0000i			0.526646i
$924$		0			0
$925$	32.7846	+	6.69213i	1.07795	+	0.220036i
$926$	34.0155			1.11782
$927$		0			0
$928$			9.52056i			0.312528i
$929$	−11.3137			−0.371191			−0.185595	−	0.982626i	$-0.559421\pi$
$929$	−11.3137			−0.371191			−0.185595	+	0.982626i	$0.559421\pi$
$930$		0			0
$931$	5.92820			0.194289
$932$			19.4641i			0.637568i
$933$		0			0
$934$	9.46410			0.309675
$935$	−49.9507	+	40.7846i	−1.63356	+	1.33380i
$936$		0			0
$937$			30.3548i			0.991649i	0.868423	+	0.495824i	$0.165134\pi$
$937$			30.3548i			0.991649i	−0.868423	+	0.495824i	$0.834866\pi$
$938$		−	3.71281i		−	0.121228i
$939$		0			0
$940$	−16.3923	+	13.3843i	−0.534658	+	0.436546i
$941$	20.8343			0.679178			0.339589	−	0.940574i	$-0.389712\pi$
$941$	20.8343			0.679178			0.339589	+	0.940574i	$0.389712\pi$
$942$		0			0
$943$			9.79796i			0.319065i
$944$	12.6264			0.410954
$945$		0			0
$946$	−6.92820			−0.225255
$947$			37.1769i			1.20809i	0.796951	+	0.604044i	$0.206445\pi$
$947$			37.1769i			1.20809i	−0.796951	+	0.604044i	$0.793555\pi$
$948$		0			0
$949$	13.8564			0.449798
$950$	4.89898	+	1.00000i	0.158944	+	0.0324443i
$951$		0			0
$952$			7.72741i			0.250447i
$953$		−	30.0000i		−	0.971795i	−0.874016	−	0.485898i	$-0.838493\pi$
$953$		−	30.0000i		−	0.971795i	0.874016	−	0.485898i	$-0.161507\pi$
$954$		0			0
$955$	3.60770	+	4.41851i	0.116742	+	0.142980i
$956$	18.0058			0.582350
$957$		0			0
$958$			31.3901i			1.01417i
$959$	7.72741			0.249531
$960$		0			0
$961$	−22.4256			−0.723407
$962$			6.92820i			0.223374i
$963$		0			0
$964$	−10.0000			−0.322078
$965$	10.2784	−	8.39230i	0.330874	−	0.270158i
$966$		0			0
$967$			2.55103i			0.0820355i	0.999158	+	0.0410177i	$0.0130600\pi$
$967$			2.55103i			0.0820355i	−0.999158	+	0.0410177i	$0.986940\pi$
$968$			3.92820i			0.126257i
$969$		0			0
$970$	−24.3923	−	29.8744i	−0.783190	−	0.959208i
$971$	24.9010			0.799112			0.399556	−	0.916709i	$-0.369164\pi$
$971$	24.9010			0.799112			0.399556	+	0.916709i	$0.369164\pi$
$972$		0			0
$973$		−	7.17260i		−	0.229943i
$974$	26.0106			0.833435
$975$		0			0
$976$	−2.00000			−0.0640184
$977$		−	49.7128i		−	1.59045i	−0.606312	−	0.795227i	$-0.707352\pi$
$977$		−	49.7128i		−	1.59045i	0.606312	−	0.795227i	$-0.292648\pi$
$978$		0			0
$979$	4.00000			0.127841
$980$	8.38375	+	10.2679i	0.267809	+	0.327998i
$981$		0			0
$982$			15.7322i			0.502035i
$983$		−	48.7846i		−	1.55599i	−0.628272	−	0.777994i	$-0.716238\pi$
$983$		−	48.7846i		−	1.55599i	0.628272	−	0.777994i	$-0.283762\pi$
$984$		0			0
$985$	28.6410	−	23.3853i	0.912579	−	0.745117i
$986$	−71.0624			−2.26309
$987$		0			0
$988$			1.03528i			0.0329365i
$989$	−2.62536			−0.0834814
$990$		0			0
$991$	20.7846			0.660245			0.330122	−	0.943938i	$-0.392910\pi$
$991$	20.7846			0.660245			0.330122	+	0.943938i	$0.392910\pi$
$992$		−	2.92820i		−	0.0929705i
$993$		0			0
$994$	16.0000			0.507489
$995$	38.0822	+	46.6410i	1.20729	+	1.47862i
$996$		0			0
$997$		−	1.31268i		−	0.0415729i	−0.999784	−	0.0207865i	$-0.993383\pi$
$997$		−	1.31268i		−	0.0415729i	0.999784	−	0.0207865i	$-0.00661701\pi$
$998$		−	1.85641i		−	0.0587635i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.g.1369.1	✓	8
3.2	odd	2	inner	1710.2.d.g.1369.8	yes	8
5.2	odd	4		8550.2.a.cv.1.3		4
5.3	odd	4		8550.2.a.cu.1.2		4
5.4	even	2	inner	1710.2.d.g.1369.6	yes	8
15.2	even	4		8550.2.a.cu.1.3		4
15.8	even	4		8550.2.a.cv.1.2		4
15.14	odd	2	inner	1710.2.d.g.1369.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.d.g.1369.1	✓	8	1.1	even	1	trivial
1710.2.d.g.1369.3	yes	8	15.14	odd	2	inner
1710.2.d.g.1369.6	yes	8	5.4	even	2	inner
1710.2.d.g.1369.8	yes	8	3.2	odd	2	inner
8550.2.a.cu.1.2		4	5.3	odd	4
8550.2.a.cu.1.3		4	15.2	even	4
8550.2.a.cv.1.2		4	15.8	even	4
8550.2.a.cv.1.3		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.41421 - 1.73205i) q^{5} -1.03528i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.41421 - 1.73205i) q^{5} -1.03528i q^{7} +1.00000i q^{8} +(-1.73205 + 1.41421i) q^{10} -3.86370 q^{11} -1.03528i q^{13} -1.03528 q^{14} +1.00000 q^{16} +7.46410i q^{17} +1.00000 q^{19} +(1.41421 + 1.73205i) q^{20} +3.86370i q^{22} +1.46410i q^{23} +(-1.00000 + 4.89898i) q^{25} -1.03528 q^{26} +1.03528i q^{28} -9.52056 q^{29} +2.92820 q^{31} -1.00000i q^{32} +7.46410 q^{34} +(-1.79315 + 1.46410i) q^{35} -6.69213i q^{37} -1.00000i q^{38} +(1.73205 - 1.41421i) q^{40} +6.69213 q^{41} +1.79315i q^{43} +3.86370 q^{44} +1.46410 q^{46} +9.46410i q^{47} +5.92820 q^{49} +(4.89898 + 1.00000i) q^{50} +1.03528i q^{52} -6.00000i q^{53} +(5.46410 + 6.69213i) q^{55} +1.03528 q^{56} +9.52056i q^{58} +12.6264 q^{59} -2.00000 q^{61} -2.92820i q^{62} -1.00000 q^{64} +(-1.79315 + 1.46410i) q^{65} +3.58630i q^{67} -7.46410i q^{68} +(1.46410 + 1.79315i) q^{70} -15.4548 q^{71} +13.3843i q^{73} -6.69213 q^{74} -1.00000 q^{76} +4.00000i q^{77} +4.00000 q^{79} +(-1.41421 - 1.73205i) q^{80} -6.69213i q^{82} +4.39230i q^{83} +(12.9282 - 10.5558i) q^{85} +1.79315 q^{86} -3.86370i q^{88} -1.03528 q^{89} -1.07180 q^{91} -1.46410i q^{92} +9.46410 q^{94} +(-1.41421 - 1.73205i) q^{95} +17.2480i q^{97} -5.92820i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 8 q^{16} + 8 q^{19} - 8 q^{25} - 32 q^{31} + 32 q^{34} - 16 q^{46} - 8 q^{49} + 16 q^{55} - 16 q^{61} - 8 q^{64} - 16 q^{70} - 8 q^{76} + 32 q^{79} + 48 q^{85} - 64 q^{91} + 48 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 + 8 * q^16 + 8 * q^19 - 8 * q^25 - 32 * q^31 + 32 * q^34 - 16 * q^46 - 8 * q^49 + 16 * q^55 - 16 * q^61 - 8 * q^64 - 16 * q^70 - 8 * q^76 + 32 * q^79 + 48 * q^85 - 64 * q^91 + 48 * q^94

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