LMFDB - Embedded newform 1512.2.q.c.793.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.2
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.c.1369.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71796 - 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +O(q^{10})$	$q+(-1.71796 - 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +(2.20469 - 3.81863i) q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.542270 - 0.939239i) q^{17} +(-3.74273 + 6.48261i) q^{19} +(-2.16279 - 3.74606i) q^{23} +(-3.40276 + 5.89375i) q^{25} +(-1.68485 - 2.91825i) q^{29} +9.37469 q^{31} +(-6.31828 + 6.53590i) q^{35} +(-2.50767 + 4.34341i) q^{37} +(1.20160 - 2.08122i) q^{41} +(3.31412 + 5.74023i) q^{43} -3.00831 q^{47} +(-5.94023 + 3.70320i) q^{49} +(0.530699 + 0.919198i) q^{53} -15.1502 q^{55} -12.4094 q^{59} -5.42668 q^{61} -10.2666 q^{65} +3.33998 q^{67} +12.9064 q^{71} +(-8.21382 - 14.2267i) q^{73} +(-11.3181 - 2.82823i) q^{77} -2.35031 q^{79} +(1.60602 + 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-5.67524 + 9.82981i) q^{89} +(-7.66974 - 1.91656i) q^{91} +25.7194 q^{95} +(-6.40321 - 11.0907i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 - 5 * q^7	$ 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.71796	−	2.97559i	−0.768294	−	1.33072i	−0.938487	−	0.345314i	$-0.887773\pi$
$5$	−1.71796	−	2.97559i	−0.768294	−	1.33072i	0.170193	−	0.985411i	$-0.445561\pi$
$6$		0			0
$7$	−0.727932	−	2.54364i	−0.275132	−	0.961406i
$7$	−0.727932	−	2.54364i	−0.275132	−	0.961406i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.20469	−	3.81863i	0.664739	−	1.15136i	−0.314618	−	0.949219i	$-0.601876\pi$
$11$	2.20469	−	3.81863i	0.664739	−	1.15136i	0.979356	−	0.202143i	$-0.0647904\pi$
$12$		0			0
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	−0.580997	−	0.813906i	$-0.697337\pi$
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	0.995362	+	0.0962048i	$0.0306704\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.542270	−	0.939239i	−0.131520	−	0.227799i	0.792743	−	0.609556i	$-0.208652\pi$
$17$	−0.542270	−	0.939239i	−0.131520	−	0.227799i	−0.924263	+	0.381757i	$0.875319\pi$
$18$		0			0
$19$	−3.74273	+	6.48261i	−0.858642	+	1.48721i	0.0145824	+	0.999894i	$0.495358\pi$
$19$	−3.74273	+	6.48261i	−0.858642	+	1.48721i	−0.873225	+	0.487318i	$0.837975\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.16279	−	3.74606i	−0.450972	−	0.781107i	0.547474	−	0.836823i	$-0.315589\pi$
$23$	−2.16279	−	3.74606i	−0.450972	−	0.781107i	−0.998447	+	0.0557153i	$0.982256\pi$
$24$		0			0
$25$	−3.40276	+	5.89375i	−0.680552	+	1.17875i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.68485	−	2.91825i	−0.312870	−	0.541906i	0.666113	−	0.745851i	$-0.267957\pi$
$29$	−1.68485	−	2.91825i	−0.312870	−	0.541906i	−0.978982	+	0.203945i	$0.934624\pi$
$30$		0			0
$31$	9.37469			1.68374			0.841872	−	0.539678i	$-0.181454\pi$
$31$	9.37469			1.68374			0.841872	+	0.539678i	$0.181454\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.31828	+	6.53590i	−1.06798	+	1.10477i
$36$		0			0
$37$	−2.50767	+	4.34341i	−0.412258	+	0.714052i	−0.995136	−	0.0985079i	$-0.968593\pi$
$37$	−2.50767	+	4.34341i	−0.412258	+	0.714052i	0.582878	+	0.812559i	$0.301926\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.20160	−	2.08122i	0.187658	−	0.325033i	−0.756811	−	0.653634i	$-0.773244\pi$
$41$	1.20160	−	2.08122i	0.187658	−	0.325033i	0.944469	+	0.328601i	$0.106577\pi$
$42$		0			0
$43$	3.31412	+	5.74023i	0.505399	+	0.875377i	0.999980	+	0.00624563i	$0.00198806\pi$
$43$	3.31412	+	5.74023i	0.505399	+	0.875377i	−0.494581	+	0.869131i	$0.664679\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00831			−0.438807			−0.219403	−	0.975634i	$-0.570411\pi$
$47$	−3.00831			−0.438807			−0.219403	+	0.975634i	$0.570411\pi$
$48$		0			0
$49$	−5.94023	+	3.70320i	−0.848604	+	0.529028i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.530699	+	0.919198i	0.0728971	+	0.126262i	0.900170	−	0.435539i	$-0.143442\pi$
$53$	0.530699	+	0.919198i	0.0728971	+	0.126262i	−0.827273	+	0.561801i	$0.810109\pi$
$54$		0			0
$55$	−15.1502			−2.04286
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−12.4094			−1.61557			−0.807783	−	0.589480i	$-0.799332\pi$
$59$	−12.4094			−1.61557			−0.807783	+	0.589480i	$0.799332\pi$
$60$		0			0
$61$	−5.42668			−0.694816			−0.347408	−	0.937714i	$-0.612938\pi$
$61$	−5.42668			−0.694816			−0.347408	+	0.937714i	$0.612938\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.2666			−1.27342
$66$		0			0
$67$	3.33998			0.408043			0.204022	−	0.978966i	$-0.434599\pi$
$67$	3.33998			0.408043			0.204022	+	0.978966i	$0.434599\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.9064			1.53171			0.765857	−	0.643011i	$-0.222315\pi$
$71$	12.9064			1.53171			0.765857	+	0.643011i	$0.222315\pi$
$72$		0			0
$73$	−8.21382	−	14.2267i	−0.961355	−	1.66511i	−0.719106	−	0.694901i	$-0.755448\pi$
$73$	−8.21382	−	14.2267i	−0.961355	−	1.66511i	−0.242249	−	0.970214i	$-0.577885\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.3181	−	2.82823i	−1.28982	−	0.322307i
$78$		0			0
$79$	−2.35031			−0.264431			−0.132216	−	0.991221i	$-0.542209\pi$
$79$	−2.35031			−0.264431			−0.132216	+	0.991221i	$0.542209\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.60602	+	2.78171i	0.176283	+	0.305332i	0.940605	−	0.339504i	$-0.110259\pi$
$83$	1.60602	+	2.78171i	0.176283	+	0.305332i	−0.764321	+	0.644836i	$0.776926\pi$
$84$		0			0
$85$	−1.86319	+	3.22715i	−0.202092	+	0.350033i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.67524	+	9.82981i	−0.601575	+	1.04196i	0.391008	+	0.920387i	$0.372126\pi$
$89$	−5.67524	+	9.82981i	−0.601575	+	1.04196i	−0.992583	+	0.121570i	$0.961207\pi$
$90$		0			0
$91$	−7.66974	−	1.91656i	−0.804008	−	0.200910i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	25.7194			2.63876
$96$		0			0
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	−0.983087	−	0.183140i	$-0.941374\pi$
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	0.332939	−	0.942948i	$-0.391960\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.388110	+	0.672227i	−0.0386184	+	0.0668891i	−0.884689	−	0.466182i	$-0.845629\pi$
$101$	−0.388110	+	0.672227i	−0.0386184	+	0.0668891i	0.846070	+	0.533072i	$0.178962\pi$
$102$		0			0
$103$	−1.14131	−	1.97681i	−0.112457	−	0.194781i	0.804304	−	0.594219i	$-0.202539\pi$
$103$	−1.14131	−	1.97681i	−0.112457	−	0.194781i	−0.916760	+	0.399438i	$0.869205\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.27468	−	3.93986i	0.219901	−	0.380880i	−0.734876	−	0.678201i	$-0.762760\pi$
$107$	2.27468	−	3.93986i	0.219901	−	0.380880i	0.954778	+	0.297321i	$0.0960931\pi$
$108$		0			0
$109$	2.36710	+	4.09994i	0.226727	+	0.392703i	0.956836	−	0.290627i	$-0.0938640\pi$
$109$	2.36710	+	4.09994i	0.226727	+	0.392703i	−0.730109	+	0.683331i	$0.760531\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.175367	+	0.303745i	−0.0164972	+	0.0285740i	−0.874156	−	0.485645i	$-0.838585\pi$
$113$	−0.175367	+	0.303745i	−0.0164972	+	0.0285740i	0.857659	+	0.514219i	$0.171918\pi$
$114$		0			0
$115$	−7.43116	+	12.8711i	−0.692959	+	1.20024i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.99435	+	2.06304i	−0.182822	+	0.189119i
$120$		0			0
$121$	−4.22130	−	7.31151i	−0.383755	−	0.664683i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.20360			0.554867
$126$		0			0
$127$	12.4175			1.10187			0.550935	−	0.834548i	$-0.314271\pi$
$127$	12.4175			1.10187			0.550935	+	0.834548i	$0.314271\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.87152	+	13.6339i	0.687738	+	1.19120i	0.972568	+	0.232619i	$0.0747296\pi$
$131$	7.87152	+	13.6339i	0.687738	+	1.19120i	−0.284830	+	0.958578i	$0.591937\pi$
$132$		0			0
$133$	19.2139	+	4.80128i	1.66606	+	0.416324i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.11510	+	3.66346i	−0.180705	+	0.312990i	−0.942121	−	0.335274i	$-0.891171\pi$
$137$	−2.11510	+	3.66346i	−0.180705	+	0.312990i	0.761416	+	0.648264i	$0.224505\pi$
$138$		0			0
$139$	9.80367	−	16.9805i	0.831537	−	1.44026i	−0.0652824	−	0.997867i	$-0.520795\pi$
$139$	9.80367	−	16.9805i	0.831537	−	1.44026i	0.896819	−	0.442397i	$-0.145872\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.58767	−	11.4102i	−0.550889	−	0.954167i
$144$		0			0
$145$	−5.78902	+	10.0269i	−0.480752	+	0.832686i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.86326	−	8.42341i	−0.398414	−	0.690073i	0.595117	−	0.803639i	$-0.297106\pi$
$149$	−4.86326	−	8.42341i	−0.398414	−	0.690073i	−0.993530	+	0.113567i	$0.963772\pi$
$150$		0			0
$151$	4.91074	−	8.50565i	0.399630	−	0.692180i	−0.594050	−	0.804428i	$-0.702472\pi$
$151$	4.91074	−	8.50565i	0.399630	−	0.692180i	0.993680	+	0.112248i	$0.0358051\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−16.1053	−	27.8952i	−1.29361	−	2.24060i
$156$		0			0
$157$	−12.0408			−0.960962			−0.480481	−	0.877005i	$-0.659538\pi$
$157$	−12.0408			−0.960962			−0.480481	+	0.877005i	$0.659538\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.95427	+	8.22824i	−0.626884	+	0.648476i
$162$		0			0
$163$	0.885601	−	1.53391i	0.0693656	−	0.120145i	−0.829257	−	0.558868i	$-0.811236\pi$
$163$	0.885601	−	1.53391i	0.0693656	−	0.120145i	0.898622	+	0.438723i	$0.144569\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.86350	−	13.6200i	0.608496	−	1.05395i	−0.382993	−	0.923751i	$-0.625107\pi$
$167$	7.86350	−	13.6200i	0.608496	−	1.05395i	0.991489	−	0.130194i	$-0.0415600\pi$
$168$		0			0
$169$	2.03584	+	3.52618i	0.156603	+	0.271245i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−18.8063			−1.42981			−0.714907	−	0.699220i	$-0.753531\pi$
$173$	−18.8063			−1.42981			−0.714907	+	0.699220i	$0.753531\pi$
$174$		0			0
$175$	17.4686	+	4.36515i	1.32050	+	0.329974i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.34201	−	5.78853i	−0.249794	−	0.432655i	0.713675	−	0.700477i	$-0.247029\pi$
$179$	−3.34201	−	5.78853i	−0.249794	−	0.432655i	−0.963468	+	0.267822i	$0.913696\pi$
$180$		0			0
$181$	4.73726			0.352117			0.176059	−	0.984380i	$-0.443665\pi$
$181$	4.73726			0.352117			0.176059	+	0.984380i	$0.443665\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	17.2323			1.26694
$186$		0			0
$187$	−4.78214			−0.349705
$188$		0			0
$189$		0			0
$190$		0			0
$191$	23.0693			1.66924			0.834618	−	0.550829i	$-0.185688\pi$
$191$	23.0693			1.66924			0.834618	+	0.550829i	$0.185688\pi$
$192$		0			0
$193$	18.3070			1.31777			0.658885	−	0.752244i	$-0.271028\pi$
$193$	18.3070			1.31777			0.658885	+	0.752244i	$0.271028\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.5866			−1.03925			−0.519625	−	0.854395i	$-0.673928\pi$
$197$	−14.5866			−1.03925			−0.519625	+	0.854395i	$0.673928\pi$
$198$		0			0
$199$	−0.912102	−	1.57981i	−0.0646572	−	0.111990i	0.831885	−	0.554949i	$-0.187262\pi$
$199$	−0.912102	−	1.57981i	−0.0646572	−	0.111990i	−0.896542	+	0.442959i	$0.853929\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.19653	+	6.40996i	−0.434911	+	0.449891i
$204$		0			0
$205$	−8.25716			−0.576705
$206$		0			0
$207$		0			0
$208$		0			0
$209$	16.5031	+	28.5843i	1.14155	+	1.97721i
$210$		0			0
$211$	−2.77359	+	4.80400i	−0.190942	+	0.330721i	−0.945563	−	0.325440i	$-0.894488\pi$
$211$	−2.77359	+	4.80400i	−0.190942	+	0.330721i	0.754621	+	0.656161i	$0.227821\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	11.3870	−	19.7229i	0.776590	−	1.34509i
$216$		0			0
$217$	−6.82413	−	23.8458i	−0.463252	−	1.61876i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.24064			−0.217989
$222$		0			0
$223$	6.01726	+	10.4222i	0.402946	+	0.697922i	0.994080	−	0.108651i	$-0.0346530\pi$
$223$	6.01726	+	10.4222i	0.402946	+	0.697922i	−0.591134	+	0.806573i	$0.701320\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.57834	+	11.3940i	−0.436620	+	0.756248i	−0.997426	−	0.0716991i	$-0.977158\pi$
$227$	−6.57834	+	11.3940i	−0.436620	+	0.756248i	0.560806	+	0.827947i	$0.310491\pi$
$228$		0			0
$229$	−6.24159	−	10.8108i	−0.412456	−	0.714395i	0.582702	−	0.812686i	$-0.301996\pi$
$229$	−6.24159	−	10.8108i	−0.412456	−	0.714395i	−0.995158	+	0.0982915i	$0.968662\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.01687	−	3.49332i	0.132130	−	0.228855i	−0.792368	−	0.610044i	$-0.791152\pi$
$233$	2.01687	−	3.49332i	0.132130	−	0.228855i	0.924497	+	0.381189i	$0.124485\pi$
$234$		0			0
$235$	5.16814	+	8.95149i	0.337133	+	0.583931i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.8679	+	24.0200i	−0.897043	+	1.55372i	−0.0657873	+	0.997834i	$0.520956\pi$
$239$	−13.8679	+	24.0200i	−0.897043	+	1.55372i	−0.831256	+	0.555890i	$0.812377\pi$
$240$		0			0
$241$	−11.9567	+	20.7096i	−0.770199	+	1.33402i	0.167254	+	0.985914i	$0.446510\pi$
$241$	−11.9567	+	20.7096i	−0.770199	+	1.33402i	−0.937453	+	0.348111i	$0.886823\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	21.2243	+	11.3138i	1.35597	+	0.722809i
$246$		0			0
$247$	11.1834	+	19.3702i	0.711582	+	1.23250i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	3.33510			0.210509			0.105255	−	0.994445i	$-0.466434\pi$
$251$	3.33510			0.210509			0.105255	+	0.994445i	$0.466434\pi$
$252$		0			0
$253$	−19.0731			−1.19912
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.9345	−	18.9392i	−0.682078	−	1.18139i	−0.974346	−	0.225057i	$-0.927743\pi$
$257$	−10.9345	−	18.9392i	−0.682078	−	1.18139i	0.292268	−	0.956336i	$-0.405590\pi$
$258$		0			0
$259$	12.8735	+	3.21690i	0.799919	+	0.199889i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.75522	−	4.77218i	0.169894	−	0.294265i	−0.768488	−	0.639864i	$-0.778991\pi$
$263$	2.75522	−	4.77218i	0.169894	−	0.294265i	0.938382	+	0.345599i	$0.112324\pi$
$264$		0			0
$265$	1.82344	−	3.15829i	0.112013	−	0.194012i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.37393	−	5.84382i	−0.205712	−	0.356304i	0.744647	−	0.667458i	$-0.232618\pi$
$269$	−3.37393	−	5.84382i	−0.205712	−	0.356304i	−0.950359	+	0.311154i	$0.899284\pi$
$270$		0			0
$271$	6.21944	−	10.7724i	0.377804	−	0.654376i	−0.612938	−	0.790131i	$-0.710013\pi$
$271$	6.21944	−	10.7724i	0.377804	−	0.654376i	0.990742	+	0.135755i	$0.0433459\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.0040	+	25.9878i	0.904778	+	1.56712i
$276$		0			0
$277$	4.85945	−	8.41681i	0.291976	−	0.505717i	−0.682301	−	0.731071i	$-0.739021\pi$
$277$	4.85945	−	8.41681i	0.291976	−	0.505717i	0.974277	+	0.225354i	$0.0723539\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.66772	+	16.7450i	0.576728	+	0.998922i	0.995852	+	0.0909928i	$0.0290040\pi$
$281$	9.66772	+	16.7450i	0.576728	+	0.998922i	−0.419124	+	0.907929i	$0.637663\pi$
$282$		0			0
$283$	8.30900			0.493919			0.246959	−	0.969026i	$-0.420569\pi$
$283$	8.30900			0.493919			0.246959	+	0.969026i	$0.420569\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.16857	−	1.54144i	−0.364119	−	0.0909882i
$288$		0			0
$289$	7.91189	−	13.7038i	0.465405	−	0.806105i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.97318	−	6.88175i	0.232116	−	0.402036i	−0.726315	−	0.687362i	$-0.758769\pi$
$293$	3.97318	−	6.88175i	0.232116	−	0.402036i	0.958430	+	0.285326i	$0.0921019\pi$
$294$		0			0
$295$	21.3188	+	36.9253i	1.24123	+	2.14987i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.9249			−0.747469
$300$		0			0
$301$	12.1886	−	12.6084i	0.702541	−	0.726739i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.32281	+	16.1476i	0.533823	+	0.924608i
$306$		0			0
$307$	−26.9180			−1.53629			−0.768145	−	0.640276i	$-0.778820\pi$
$307$	−26.9180			−1.53629			−0.768145	+	0.640276i	$0.778820\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.34917			−0.530143			−0.265071	−	0.964229i	$-0.585396\pi$
$311$	−9.34917			−0.530143			−0.265071	+	0.964229i	$0.585396\pi$
$312$		0			0
$313$	15.8380			0.895219			0.447610	−	0.894229i	$-0.352275\pi$
$313$	15.8380			0.895219			0.447610	+	0.894229i	$0.352275\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	28.4591			1.59843			0.799213	−	0.601049i	$-0.205250\pi$
$317$	28.4591			1.59843			0.799213	+	0.601049i	$0.205250\pi$
$318$		0			0
$319$	−14.8583			−0.831906
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.11829			0.451714
$324$		0			0
$325$	10.1675	+	17.6107i	0.563994	+	0.976865i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.18984	+	7.65205i	0.120730	+	0.421871i
$330$		0			0
$331$	−19.5904			−1.07679			−0.538393	−	0.842694i	$-0.680968\pi$
$331$	−19.5904			−1.07679			−0.538393	+	0.842694i	$0.680968\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.73794	−	9.93841i	−0.313497	−	0.542993i
$336$		0			0
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	−0.524023	−	0.851704i	$-0.675569\pi$
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	0.999609	+	0.0279654i	$0.00890283\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	20.6683	−	35.7985i	1.11925	−	1.93860i
$342$		0			0
$343$	13.7437	+	12.4141i	0.742090	+	0.670301i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.4502			1.04414			0.522070	−	0.852903i	$-0.325160\pi$
$347$	19.4502			1.04414			0.522070	+	0.852903i	$0.325160\pi$
$348$		0			0
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	0.989582	−	0.143971i	$-0.0459872\pi$
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	−0.619474	+	0.785018i	$0.712654\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.92295	−	10.2588i	0.315247	−	0.546023i	−0.664243	−	0.747517i	$-0.731246\pi$
$353$	5.92295	−	10.2588i	0.315247	−	0.546023i	0.979490	+	0.201493i	$0.0645794\pi$
$354$		0			0
$355$	−22.1727	−	38.4043i	−1.17681	−	2.03829i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.628489	−	1.08858i	0.0331704	−	0.0574528i	−0.848964	−	0.528451i	$-0.822773\pi$
$359$	0.628489	−	1.08858i	0.0331704	−	0.0574528i	0.882134	+	0.470998i	$0.156106\pi$
$360$		0			0
$361$	−18.5161	−	32.0709i	−0.974533	−	1.68794i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−28.2220	+	48.8819i	−1.47721	+	2.55860i
$366$		0			0
$367$	7.61928	−	13.1970i	0.397723	−	0.688877i	−0.595721	−	0.803191i	$-0.703134\pi$
$367$	7.61928	−	13.1970i	0.397723	−	0.688877i	0.993445	+	0.114314i	$0.0364671\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.95180	−	2.01902i	0.101332	−	0.104822i
$372$		0			0
$373$	−8.66756	−	15.0127i	−0.448789	−	0.777326i	0.549518	−	0.835482i	$-0.314811\pi$
$373$	−8.66756	−	15.0127i	−0.448789	−	0.777326i	−0.998308	+	0.0581556i	$0.981478\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.0688			−0.518569
$378$		0			0
$379$	15.6319			0.802955			0.401478	−	0.915869i	$-0.368497\pi$
$379$	15.6319			0.802955			0.401478	+	0.915869i	$0.368497\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.90615	−	15.4259i	−0.455083	−	0.788227i	0.543610	−	0.839338i	$-0.317057\pi$
$383$	−8.90615	−	15.4259i	−0.455083	−	0.788227i	−0.998693	+	0.0511113i	$0.983724\pi$
$384$		0			0
$385$	11.0284	+	38.5368i	0.562057	+	1.96402i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.7074	−	25.4740i	0.745695	−	1.29158i	−0.204175	−	0.978934i	$-0.565451\pi$
$389$	14.7074	−	25.4740i	0.745695	−	1.29158i	0.949869	−	0.312647i	$-0.101216\pi$
$390$		0			0
$391$	−2.34563	+	4.06275i	−0.118624	+	0.205462i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.03774	+	6.99357i	0.203161	+	0.351885i
$396$		0			0
$397$	−1.55930	+	2.70079i	−0.0782592	+	0.135549i	−0.902499	−	0.430692i	$-0.858270\pi$
$397$	−1.55930	+	2.70079i	−0.0782592	+	0.135549i	0.824240	+	0.566241i	$0.191603\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.8613	−	30.9367i	−0.891950	−	1.54490i	−0.837534	−	0.546385i	$-0.816004\pi$
$401$	−17.8613	−	30.9367i	−0.891950	−	1.54490i	−0.0544157	−	0.998518i	$-0.517330\pi$
$402$		0			0
$403$	14.0059	−	24.2590i	0.697684	−	1.20842i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11.0572	+	19.1517i	0.548087	+	0.949315i
$408$		0			0
$409$	9.81652			0.485396			0.242698	−	0.970102i	$-0.421968\pi$
$409$	9.81652			0.485396			0.242698	+	0.970102i	$0.421968\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.03320	+	31.5651i	0.444494	+	1.55321i
$414$		0			0
$415$	5.51814	−	9.55771i	0.270875	−	0.469169i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.09812	+	10.5623i	−0.297913	+	0.516000i	−0.975658	−	0.219297i	$-0.929624\pi$
$419$	−6.09812	+	10.5623i	−0.297913	+	0.516000i	0.677746	+	0.735297i	$0.262957\pi$
$420$		0			0
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	0.714562	−	0.699572i	$-0.246626\pi$
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	−0.963128	+	0.269043i	$0.913293\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.38085			0.358024
$426$		0			0
$427$	3.95026	+	13.8035i	0.191166	+	0.668000i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	5.70254	+	9.87710i	0.274682	+	0.475763i	0.970055	−	0.242886i	$-0.0780941\pi$
$431$	5.70254	+	9.87710i	0.274682	+	0.475763i	−0.695373	+	0.718649i	$0.744761\pi$
$432$		0			0
$433$	26.2391			1.26097			0.630486	−	0.776201i	$-0.282856\pi$
$433$	26.2391			1.26097			0.630486	+	0.776201i	$0.282856\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	32.3790			1.54890
$438$		0			0
$439$	22.9554			1.09560			0.547801	−	0.836609i	$-0.315465\pi$
$439$	22.9554			1.09560			0.547801	+	0.836609i	$0.315465\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−22.4025			−1.06438			−0.532188	−	0.846626i	$-0.678630\pi$
$443$	−22.4025			−1.06438			−0.532188	+	0.846626i	$0.678630\pi$
$444$		0			0
$445$	38.9993			1.84874
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−17.0576			−0.805000			−0.402500	−	0.915420i	$-0.631859\pi$
$449$	−17.0576			−0.805000			−0.402500	+	0.915420i	$0.631859\pi$
$450$		0			0
$451$	−5.29829	−	9.17690i	−0.249487	−	0.432123i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.47340	+	26.1146i	0.350358	+	1.22427i
$456$		0			0
$457$	9.54729			0.446604			0.223302	−	0.974749i	$-0.428316\pi$
$457$	9.54729			0.446604			0.223302	+	0.974749i	$0.428316\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.1213	−	17.5305i	−0.471394	−	0.816478i	0.528070	−	0.849201i	$-0.322916\pi$
$461$	−10.1213	−	17.5305i	−0.471394	−	0.816478i	−0.999464	+	0.0327222i	$0.989582\pi$
$462$		0			0
$463$	−7.81948	+	13.5437i	−0.363402	+	0.629431i	−0.988518	−	0.151101i	$-0.951718\pi$
$463$	−7.81948	+	13.5437i	−0.363402	+	0.629431i	0.625116	+	0.780532i	$0.285052\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.96638	−	5.13793i	0.137268	−	0.237755i	−0.789194	−	0.614144i	$-0.789501\pi$
$467$	2.96638	−	5.13793i	0.137268	−	0.237755i	0.926461	+	0.376390i	$0.122835\pi$
$468$		0			0
$469$	−2.43128	−	8.49571i	−0.112266	−	0.392295i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	29.2264			1.34383
$474$		0			0
$475$	−25.4712	−	44.1175i	−1.16870	−	2.02425i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.69708	+	15.0638i	−0.397380	+	0.688282i	−0.993402	−	0.114686i	$-0.963414\pi$
$479$	−8.69708	+	15.0638i	−0.397380	+	0.688282i	0.596022	+	0.802968i	$0.296747\pi$
$480$		0			0
$481$	7.49298	+	12.9782i	0.341650	+	0.591756i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−22.0009	+	38.1067i	−0.999009	+	1.73033i
$486$		0			0
$487$	−9.76967	−	16.9216i	−0.442706	−	0.766790i	0.555183	−	0.831728i	$-0.312648\pi$
$487$	−9.76967	−	16.9216i	−0.442706	−	0.766790i	−0.997889	+	0.0649386i	$0.979315\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.16702	−	10.6816i	0.278314	−	0.482054i	−0.692652	−	0.721272i	$-0.743558\pi$
$491$	6.16702	−	10.6816i	0.278314	−	0.482054i	0.970966	+	0.239218i	$0.0768911\pi$
$492$		0			0
$493$	−1.82729	+	3.16496i	−0.0822971	+	0.142543i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.39502	−	32.8294i	−0.421424	−	1.47260i
$498$		0			0
$499$	−9.27308	−	16.0614i	−0.415120	−	0.719009i	0.580321	−	0.814388i	$-0.302927\pi$
$499$	−9.27308	−	16.0614i	−0.415120	−	0.719009i	−0.995441	+	0.0953788i	$0.969594\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.3264			0.638782			0.319391	−	0.947623i	$-0.396522\pi$
$503$	14.3264			0.638782			0.319391	+	0.947623i	$0.396522\pi$
$504$		0			0
$505$	2.66703			0.118681
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.43056	−	14.6022i	−0.373678	−	0.647229i	0.616450	−	0.787394i	$-0.288570\pi$
$509$	−8.43056	−	14.6022i	−0.373678	−	0.647229i	−0.990128	+	0.140165i	$0.955237\pi$
$510$		0			0
$511$	−30.2087	+	31.2491i	−1.33635	+	1.38238i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.92145	+	6.79215i	−0.172800	+	0.299298i
$516$		0			0
$517$	−6.63238	+	11.4876i	−0.291692	+	0.505225i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.8132	−	18.7291i	−0.473737	−	0.820536i	0.525811	−	0.850601i	$-0.323762\pi$
$521$	−10.8132	−	18.7291i	−0.473737	−	0.820536i	−0.999548	+	0.0300652i	$0.990428\pi$
$522$		0			0
$523$	8.27472	−	14.3322i	0.361828	−	0.626705i	−0.626433	−	0.779475i	$-0.715486\pi$
$523$	8.27472	−	14.3322i	0.361828	−	0.626705i	0.988262	+	0.152770i	$0.0488193\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.08361	−	8.80507i	−0.221446	−	0.383555i
$528$		0			0
$529$	2.14470	−	3.71472i	0.0932476	−	0.161510i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.59040	−	6.21876i	−0.155517	−	0.269364i
$534$		0			0
$535$	−15.6312			−0.675796
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.04479	+	30.8480i	0.0450025	+	1.32872i
$540$		0			0
$541$	−11.9542	+	20.7053i	−0.513952	+	0.890191i	0.485917	+	0.874005i	$0.338486\pi$
$541$	−11.9542	+	20.7053i	−0.513952	+	0.890191i	−0.999869	+	0.0161861i	$0.994848\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.13317	−	14.0871i	0.348387	−	0.603423i
$546$		0			0
$547$	−14.8193	−	25.6678i	−0.633627	−	1.09747i	−0.986804	−	0.161918i	$-0.948232\pi$
$547$	−14.8193	−	25.6678i	−0.633627	−	1.09747i	0.353177	−	0.935556i	$-0.385101\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	25.2238			1.07457
$552$		0			0
$553$	1.71087	+	5.97836i	0.0727536	+	0.254226i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.8366	+	18.7695i	0.459160	+	0.795288i	0.998917	−	0.0465330i	$-0.0148173\pi$
$557$	10.8366	+	18.7695i	0.459160	+	0.795288i	−0.539757	+	0.841821i	$0.681484\pi$
$558$		0			0
$559$	19.8054			0.837679
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.1556			−0.596589			−0.298294	−	0.954474i	$-0.596418\pi$
$563$	−14.1556			−0.596589			−0.298294	+	0.954474i	$0.596418\pi$
$564$		0			0
$565$	1.20510			0.0506988
$566$		0			0
$567$		0			0
$568$		0			0
$569$	34.0356			1.42684			0.713422	−	0.700734i	$-0.247144\pi$
$569$	34.0356			1.42684			0.713422	+	0.700734i	$0.247144\pi$
$570$		0			0
$571$	−5.34970			−0.223878			−0.111939	−	0.993715i	$-0.535706\pi$
$571$	−5.34970			−0.223878			−0.111939	+	0.993715i	$0.535706\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	29.4378			1.22764
$576$		0			0
$577$	11.1865	+	19.3756i	0.465699	+	0.806615i	0.999233	−	0.0391640i	$-0.0124695\pi$
$577$	11.1865	+	19.3756i	0.465699	+	0.806615i	−0.533533	+	0.845779i	$0.679136\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.90659	−	6.11003i	0.245047	−	0.253487i
$582$		0			0
$583$	4.68011			0.193830
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.49899	+	4.32839i	0.103145	+	0.178652i	0.912979	−	0.408007i	$-0.133776\pi$
$587$	2.49899	+	4.32839i	0.103145	+	0.178652i	−0.809834	+	0.586659i	$0.800443\pi$
$588$		0			0
$589$	−35.0870	+	60.7724i	−1.44573	+	2.50408i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.1698	+	21.0788i	−0.499755	+	0.865601i	−1.00000		0.000282582i	$-0.999910\pi$
$593$	−12.1698	+	21.0788i	−0.499755	+	0.865601i	0.500245	+	0.865884i	$0.333243\pi$
$594$		0			0
$595$	9.56498	+	2.39015i	0.392126	+	0.0979868i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−46.2145			−1.88827			−0.944137	−	0.329552i	$-0.893102\pi$
$599$	−46.2145			−1.88827			−0.944137	+	0.329552i	$0.893102\pi$
$600$		0			0
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	−0.975644	−	0.219359i	$-0.929603\pi$
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	0.297852	−	0.954612i	$-0.403730\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.5040	+	25.1217i	−0.589673	+	1.02134i
$606$		0			0
$607$	−21.9318	−	37.9869i	−0.890182	−	1.54184i	−0.839656	−	0.543118i	$-0.817244\pi$
$607$	−21.9318	−	37.9869i	−0.890182	−	1.54184i	−0.0505262	−	0.998723i	$-0.516090\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.49445	+	7.78462i	−0.181826	+	0.314932i
$612$		0			0
$613$	1.81569	+	3.14487i	0.0733351	+	0.127020i	0.900361	−	0.435144i	$-0.143302\pi$
$613$	1.81569	+	3.14487i	0.0733351	+	0.127020i	−0.827026	+	0.562164i	$0.809969\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.4542	+	18.1073i	−0.420872	+	0.728971i	−0.996025	−	0.0890744i	$-0.971609\pi$
$617$	−10.4542	+	18.1073i	−0.420872	+	0.728971i	0.575153	+	0.818046i	$0.304942\pi$
$618$		0			0
$619$	−11.9745	+	20.7405i	−0.481296	+	0.833629i	−0.999770	−	0.0214645i	$-0.993167\pi$
$619$	−11.9745	+	20.7405i	−0.481296	+	0.833629i	0.518474	+	0.855094i	$0.326500\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	29.1347	+	7.28035i	1.16726	+	0.291681i
$624$		0			0
$625$	6.35626	+	11.0094i	0.254251	+	0.440375i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.43933			0.216880
$630$		0			0
$631$	−6.06918			−0.241610			−0.120805	−	0.992676i	$-0.538548\pi$
$631$	−6.06918			−0.241610			−0.120805	+	0.992676i	$0.538548\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−21.3327	−	36.9492i	−0.846561	−	1.46629i
$636$		0			0
$637$	0.708008	+	20.9042i	0.0280523	+	0.828255i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.69407	+	15.0586i	−0.343395	+	0.594778i	−0.985061	−	0.172207i	$-0.944910\pi$
$641$	−8.69407	+	15.0586i	−0.343395	+	0.594778i	0.641666	+	0.766984i	$0.278244\pi$
$642$		0			0
$643$	9.66411	−	16.7387i	0.381115	−	0.660111i	−0.610107	−	0.792319i	$-0.708873\pi$
$643$	9.66411	−	16.7387i	0.381115	−	0.660111i	0.991222	+	0.132208i	$0.0422068\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.7041	−	22.0042i	−0.499451	−	0.865075i	0.500549	−	0.865708i	$-0.333132\pi$
$647$	−12.7041	−	22.0042i	−0.499451	−	0.865075i	−1.00000		0.000633482i	$0.999798\pi$
$648$		0			0
$649$	−27.3588	+	47.3869i	−1.07393	+	1.86010i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.9064	−	22.3545i	−0.505065	−	0.874799i	−0.999983	−	0.00585902i	$-0.998135\pi$
$653$	−12.9064	−	22.3545i	−0.505065	−	0.874799i	0.494917	−	0.868940i	$-0.335198\pi$
$654$		0			0
$655$	27.0459	−	46.8449i	1.05677	−	1.83038i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.62598	−	14.9406i	−0.336020	−	0.582004i	0.647660	−	0.761930i	$-0.275748\pi$
$659$	−8.62598	−	14.9406i	−0.336020	−	0.582004i	−0.983680	+	0.179925i	$0.942414\pi$
$660$		0			0
$661$	12.9635			0.504222			0.252111	−	0.967698i	$-0.418875\pi$
$661$	12.9635			0.504222			0.252111	+	0.967698i	$0.418875\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−18.7220	−	65.4210i	−0.726008	−	2.53692i
$666$		0			0
$667$	−7.28797	+	12.6231i	−0.282191	+	0.488769i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.9641	+	20.7225i	−0.461871	+	0.799984i
$672$		0			0
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	−0.918289	−	0.395910i	$-0.870429\pi$
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	0.116277	−	0.993217i	$-0.462904\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.1998			0.853209			0.426605	−	0.904438i	$-0.359710\pi$
$677$	22.1998			0.853209			0.426605	+	0.904438i	$0.359710\pi$
$678$		0			0
$679$	−23.5496	+	24.3607i	−0.903752	+	0.934879i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.60315	+	7.97289i	0.176135	+	0.305074i	0.940553	−	0.339646i	$-0.110307\pi$
$683$	4.60315	+	7.97289i	0.176135	+	0.305074i	−0.764419	+	0.644720i	$0.776974\pi$
$684$		0			0
$685$	14.5346			0.555338
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.17149			0.120824
$690$		0			0
$691$	−40.0585			−1.52390			−0.761949	−	0.647636i	$-0.775758\pi$
$691$	−40.0585			−1.52390			−0.761949	+	0.647636i	$0.775758\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−67.3692			−2.55546
$696$		0			0
$697$	−2.60636			−0.0987228
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.3868			−1.29877			−0.649385	−	0.760459i	$-0.724974\pi$
$701$	−34.3868			−1.29877			−0.649385	+	0.760459i	$0.724974\pi$
$702$		0			0
$703$	−18.7711	−	32.5124i	−0.707964	−	1.22623i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.99242	+	0.497878i	0.0749328	+	0.0187246i
$708$		0			0
$709$	21.1840			0.795582			0.397791	−	0.917476i	$-0.369777\pi$
$709$	21.1840			0.795582			0.397791	+	0.917476i	$0.369777\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−20.2755	−	35.1181i	−0.759322	−	1.31518i
$714$		0			0
$715$	−22.6347	+	39.2044i	−0.846489	+	1.46616i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.5994	−	37.4113i	0.805523	−	1.39521i	−0.110414	−	0.993886i	$-0.535218\pi$
$719$	21.5994	−	37.4113i	0.805523	−	1.39521i	0.915937	−	0.401321i	$-0.131449\pi$
$720$		0			0
$721$	−4.19750	+	4.34207i	−0.156323	+	0.161707i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	22.9326			0.851696
$726$		0			0
$727$	20.5571	+	35.6059i	0.762420	+	1.32055i	0.941600	+	0.336734i	$0.109322\pi$
$727$	20.5571	+	35.6059i	0.762420	+	1.32055i	−0.179180	+	0.983816i	$0.557344\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.59430	−	6.22551i	0.132940	−	0.230259i
$732$		0			0
$733$	−26.0425	−	45.1070i	−0.961903	−	1.66607i	−0.717715	−	0.696337i	$-0.754812\pi$
$733$	−26.0425	−	45.1070i	−0.961903	−	1.66607i	−0.244189	−	0.969728i	$-0.578522\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.36361	−	12.7541i	0.271242	−	0.469805i
$738$		0			0
$739$	7.18624	+	12.4469i	0.264350	+	0.457868i	0.967393	−	0.253279i	$-0.0815092\pi$
$739$	7.18624	+	12.4469i	0.264350	+	0.457868i	−0.703043	+	0.711147i	$0.748176\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	21.3167	−	36.9216i	0.782034	−	1.35452i	−0.148721	−	0.988879i	$-0.547516\pi$
$743$	21.3167	−	36.9216i	0.782034	−	1.35452i	0.930755	−	0.365643i	$-0.119151\pi$
$744$		0			0
$745$	−16.7097	+	28.9421i	−0.612198	+	1.06036i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−11.6774	−	2.91802i	−0.426683	−	0.106622i
$750$		0			0
$751$	18.9846	+	32.8823i	0.692758	+	1.19989i	0.970931	+	0.239360i	$0.0769378\pi$
$751$	18.9846	+	32.8823i	0.692758	+	1.19989i	−0.278173	+	0.960531i	$0.589729\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.7458			−1.22813
$756$		0			0
$757$	27.6692			1.00565			0.502827	−	0.864387i	$-0.332293\pi$
$757$	27.6692			1.00565			0.502827	+	0.864387i	$0.332293\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.97210	+	10.3440i	0.216488	+	0.374969i	0.953732	−	0.300658i	$-0.0972063\pi$
$761$	5.97210	+	10.3440i	0.216488	+	0.374969i	−0.737244	+	0.675627i	$0.763873\pi$
$762$		0			0
$763$	8.70570	−	9.00554i	0.315167	−	0.326023i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.5398	+	32.1119i	−0.669434	+	1.15949i
$768$		0			0
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	0.360487	+	0.932764i	$0.382610\pi$
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	−0.988041	+	0.154191i	$0.950723\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.5014	+	23.3851i	0.485611	+	0.841103i	0.999863	−	0.0165363i	$-0.00526391\pi$
$773$	13.5014	+	23.3851i	0.485611	+	0.841103i	−0.514253	+	0.857639i	$0.671931\pi$
$774$		0			0
$775$	−31.8998	+	55.2521i	−1.14587	+	1.98471i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.99450	+	15.5789i	0.322261	+	0.558173i
$780$		0			0
$781$	28.4547	−	49.2850i	1.01819	−	1.76356i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	20.6856	+	35.8286i	0.738302	+	1.27878i
$786$		0			0
$787$	21.2840			0.758693			0.379347	−	0.925255i	$-0.376149\pi$
$787$	21.2840			0.758693			0.379347	+	0.925255i	$0.376149\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.900275	+	0.224966i	0.0320101	+	0.00799887i
$792$		0			0
$793$	−8.10754	+	14.0427i	−0.287907	+	0.498670i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.3062	−	17.8508i	0.365064	−	0.632309i	−0.623723	−	0.781646i	$-0.714381\pi$
$797$	10.3062	−	17.8508i	0.365064	−	0.632309i	0.988786	+	0.149337i	$0.0477138\pi$
$798$		0			0
$799$	1.63131	+	2.82552i	0.0577117	+	0.0999597i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−72.4356			−2.55620
$804$		0			0
$805$	38.1490	+	9.53289i	1.34457	+	0.335990i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−2.54223	−	4.40328i	−0.0893802	−	0.154811i	0.817869	−	0.575404i	$-0.195155\pi$
$809$	−2.54223	−	4.40328i	−0.0893802	−	0.154811i	−0.907249	+	0.420593i	$0.861822\pi$
$810$		0			0
$811$	−7.58775			−0.266442			−0.133221	−	0.991086i	$-0.542532\pi$
$811$	−7.58775			−0.266442			−0.133221	+	0.991086i	$0.542532\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.08570			−0.213173
$816$		0			0
$817$	−49.6155			−1.73583
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−20.2696			−0.707413			−0.353706	−	0.935357i	$-0.615079\pi$
$821$	−20.2696			−0.707413			−0.353706	+	0.935357i	$0.615079\pi$
$822$		0			0
$823$	21.7911			0.759588			0.379794	−	0.925071i	$-0.375995\pi$
$823$	21.7911			0.759588			0.379794	+	0.925071i	$0.375995\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−26.3796			−0.917307			−0.458654	−	0.888615i	$-0.651668\pi$
$827$	−26.3796			−0.917307			−0.458654	+	0.888615i	$0.651668\pi$
$828$		0			0
$829$	9.33400	+	16.1670i	0.324183	+	0.561502i	0.981347	−	0.192246i	$-0.0615773\pi$
$829$	9.33400	+	16.1670i	0.324183	+	0.561502i	−0.657164	+	0.753748i	$0.728244\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.69940	+	3.57116i	0.232120	+	0.123733i
$834$		0			0
$835$	−54.0366			−1.87001
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.5265	−	21.6966i	−0.432464	−	0.749050i	0.564621	−	0.825351i	$-0.309023\pi$
$839$	−12.5265	−	21.6966i	−0.432464	−	0.749050i	−0.997085	+	0.0763004i	$0.975689\pi$
$840$		0			0
$841$	8.82253	−	15.2811i	0.304225	−	0.526934i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.99499	−	12.1157i	0.240635	−	0.416792i
$846$		0			0
$847$	−15.5250	+	16.0598i	−0.533447	+	0.551820i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	21.6942			0.743668
$852$		0			0
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	−0.981095	−	0.193526i	$-0.938008\pi$
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	0.322949	−	0.946416i	$-0.395326\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.00299	+	10.3975i	−0.205058	+	0.355172i	−0.950151	−	0.311789i	$-0.899072\pi$
$857$	−6.00299	+	10.3975i	−0.205058	+	0.355172i	0.745093	+	0.666961i	$0.232405\pi$
$858$		0			0
$859$	6.30154	+	10.9146i	0.215006	+	0.372401i	0.953274	−	0.302106i	$-0.0976896\pi$
$859$	6.30154	+	10.9146i	0.215006	+	0.372401i	−0.738269	+	0.674507i	$0.764356\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.210643	−	0.364845i	0.00717038	−	0.0124195i	−0.862418	−	0.506197i	$-0.831051\pi$
$863$	0.210643	−	0.364845i	0.00717038	−	0.0124195i	0.869588	+	0.493777i	$0.164384\pi$
$864$		0			0
$865$	32.3084	+	55.9597i	1.09852	+	1.90269i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.18171	+	8.97499i	−0.175778	+	0.304456i
$870$		0			0
$871$	4.98997	−	8.64289i	0.169079	−	0.292853i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.51580	−	15.7797i	−0.152662	−	0.533453i
$876$		0			0
$877$	−0.893424	−	1.54746i	−0.0301688	−	0.0522539i	0.850547	−	0.525899i	$-0.176271\pi$
$877$	−0.893424	−	1.54746i	−0.0301688	−	0.0522539i	−0.880716	+	0.473645i	$0.842938\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	49.8891			1.68081			0.840403	−	0.541962i	$-0.182318\pi$
$881$	49.8891			1.68081			0.840403	+	0.541962i	$0.182318\pi$
$882$		0			0
$883$	34.7935			1.17090			0.585448	−	0.810710i	$-0.300919\pi$
$883$	34.7935			1.17090			0.585448	+	0.810710i	$0.300919\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.9040	+	20.6184i	0.399698	+	0.692297i	0.993688	−	0.112175i	$-0.0357817\pi$
$887$	11.9040	+	20.6184i	0.399698	+	0.692297i	−0.593991	+	0.804472i	$0.702448\pi$
$888$		0			0
$889$	−9.03906	−	31.5855i	−0.303160	−	1.05935i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11.2593	−	19.5017i	0.376778	−	0.652598i
$894$		0			0
$895$	−11.4829	+	19.8889i	−0.383830	+	0.664813i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−15.7950	−	27.3577i	−0.526792	−	0.912431i
$900$		0			0
$901$	0.575564	−	0.996907i	0.0191748	−	0.0332118i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.13841	−	14.0961i	−0.270530	−	0.468571i
$906$		0			0
$907$	−17.1406	+	29.6885i	−0.569146	+	0.985789i	0.427505	+	0.904013i	$0.359393\pi$
$907$	−17.1406	+	29.6885i	−0.569146	+	0.985789i	−0.996651	+	0.0817761i	$0.973941\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.9839	−	25.9529i	−0.496438	−	0.859857i	0.503553	−	0.863964i	$-0.332026\pi$
$911$	−14.9839	−	25.9529i	−0.496438	−	0.859857i	−0.999992	+	0.00410771i	$0.998692\pi$
$912$		0			0
$913$	14.1631			0.468730
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.9498	−	29.9469i	0.956006	−	0.988933i
$918$		0			0
$919$	−0.391037	+	0.677296i	−0.0128991	+	0.0223419i	−0.872403	−	0.488787i	$-0.837439\pi$
$919$	−0.391037	+	0.677296i	−0.0128991	+	0.0223419i	0.859504	+	0.511129i	$0.170773\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	19.2824	−	33.3981i	0.634688	−	1.09931i
$924$		0			0
$925$	−17.0660	−	29.5591i	−0.561126	−	0.971898i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.5324			0.443983			0.221992	−	0.975049i	$-0.428744\pi$
$929$	13.5324			0.443983			0.221992	+	0.975049i	$0.428744\pi$
$930$		0			0
$931$	−1.77367	−	52.3683i	−0.0581297	−	1.71630i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	8.21552	+	14.2297i	0.268676	+	0.465361i
$936$		0			0
$937$	−2.27674			−0.0743777			−0.0371889	−	0.999308i	$-0.511840\pi$
$937$	−2.27674			−0.0743777			−0.0371889	+	0.999308i	$0.511840\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	8.15440			0.265826			0.132913	−	0.991128i	$-0.457567\pi$
$941$	8.15440			0.265826			0.132913	+	0.991128i	$0.457567\pi$
$942$		0			0
$943$	−10.3952			−0.338514
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.87106			−0.255775			−0.127888	−	0.991789i	$-0.540820\pi$
$947$	−7.87106			−0.255775			−0.127888	+	0.991789i	$0.540820\pi$
$948$		0			0
$949$	−49.0862			−1.59341
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−43.1097			−1.39646			−0.698230	−	0.715873i	$-0.746029\pi$
$953$	−43.1097			−1.39646			−0.698230	+	0.715873i	$0.746029\pi$
$954$		0			0
$955$	−39.6321	−	68.6448i	−1.28246	−	2.22129i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	10.8582	+	2.71330i	0.350629	+	0.0876172i
$960$		0			0
$961$	56.8847			1.83499
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−31.4507	−	54.4742i	−1.01243	−	1.75359i
$966$		0			0
$967$	13.9537	−	24.1684i	0.448719	−	0.777205i	−0.549584	−	0.835439i	$-0.685214\pi$
$967$	13.9537	−	24.1684i	0.448719	−	0.777205i	0.998303	+	0.0582340i	$0.0185470\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−21.0705	+	36.4952i	−0.676185	+	1.17119i	0.299936	+	0.953959i	$0.403035\pi$
$971$	−21.0705	+	36.4952i	−0.676185	+	1.17119i	−0.976121	+	0.217228i	$0.930299\pi$
$972$		0			0
$973$	−50.3286	−	12.5764i	−1.61346	−	0.403181i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.8549			0.443259			0.221629	−	0.975131i	$-0.428863\pi$
$977$	13.8549			0.443259			0.221629	+	0.975131i	$0.428863\pi$
$978$		0			0
$979$	25.0243	+	43.3433i	0.799780	+	1.38526i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.97938	−	6.89249i	0.126923	−	0.219836i	−0.795560	−	0.605874i	$-0.792823\pi$
$983$	3.97938	−	6.89249i	0.126923	−	0.219836i	0.922483	+	0.386038i	$0.126157\pi$
$984$		0			0
$985$	25.0591	+	43.4036i	0.798449	+	1.38296i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.3355	−	24.8298i	0.455842	−	0.789542i
$990$		0			0
$991$	4.36428	+	7.55916i	0.138636	+	0.240125i	0.926981	−	0.375109i	$-0.122395\pi$
$991$	4.36428	+	7.55916i	0.138636	+	0.240125i	−0.788345	+	0.615234i	$0.789062\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.13391	+	5.42809i	−0.0993515	+	0.172082i
$996$		0			0
$997$	1.15190	−	1.99514i	0.0364810	−	0.0631869i	−0.847208	−	0.531261i	$-0.821719\pi$
$997$	1.15190	−	1.99514i	0.0364810	−	0.0631869i	0.883689	+	0.468074i	$0.155052\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.c.793.2		22
3.2	odd	2		504.2.q.d.121.2	yes	22
4.3	odd	2		3024.2.q.k.2305.2		22
7.4	even	3		1512.2.t.d.361.10		22
9.2	odd	6		504.2.t.d.457.5	yes	22
9.7	even	3		1512.2.t.d.289.10		22
12.11	even	2		1008.2.q.k.625.10		22
21.11	odd	6		504.2.t.d.193.5	yes	22
28.11	odd	6		3024.2.t.l.1873.10		22
36.7	odd	6		3024.2.t.l.289.10		22
36.11	even	6		1008.2.t.k.961.7		22
63.11	odd	6		504.2.q.d.25.2	✓	22
63.25	even	3	inner	1512.2.q.c.1369.2		22
84.11	even	6		1008.2.t.k.193.7		22
252.11	even	6		1008.2.q.k.529.10		22
252.151	odd	6		3024.2.q.k.2881.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.2	✓	22	63.11	odd	6
504.2.q.d.121.2	yes	22	3.2	odd	2
504.2.t.d.193.5	yes	22	21.11	odd	6
504.2.t.d.457.5	yes	22	9.2	odd	6
1008.2.q.k.529.10		22	252.11	even	6
1008.2.q.k.625.10		22	12.11	even	2
1008.2.t.k.193.7		22	84.11	even	6
1008.2.t.k.961.7		22	36.11	even	6
1512.2.q.c.793.2		22	1.1	even	1	trivial
1512.2.q.c.1369.2		22	63.25	even	3	inner
1512.2.t.d.289.10		22	9.7	even	3
1512.2.t.d.361.10		22	7.4	even	3
3024.2.q.k.2305.2		22	4.3	odd	2
3024.2.q.k.2881.2		22	252.151	odd	6
3024.2.t.l.289.10		22	36.7	odd	6
3024.2.t.l.1873.10		22	28.11	odd	6

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71796 - 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +O(q^{10})\)	\(q+(-1.71796 - 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +(2.20469 - 3.81863i) q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.542270 - 0.939239i) q^{17} +(-3.74273 + 6.48261i) q^{19} +(-2.16279 - 3.74606i) q^{23} +(-3.40276 + 5.89375i) q^{25} +(-1.68485 - 2.91825i) q^{29} +9.37469 q^{31} +(-6.31828 + 6.53590i) q^{35} +(-2.50767 + 4.34341i) q^{37} +(1.20160 - 2.08122i) q^{41} +(3.31412 + 5.74023i) q^{43} -3.00831 q^{47} +(-5.94023 + 3.70320i) q^{49} +(0.530699 + 0.919198i) q^{53} -15.1502 q^{55} -12.4094 q^{59} -5.42668 q^{61} -10.2666 q^{65} +3.33998 q^{67} +12.9064 q^{71} +(-8.21382 - 14.2267i) q^{73} +(-11.3181 - 2.82823i) q^{77} -2.35031 q^{79} +(1.60602 + 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-5.67524 + 9.82981i) q^{89} +(-7.66974 - 1.91656i) q^{91} +25.7194 q^{95} +(-6.40321 - 11.0907i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 - 5 * q^7	\( 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

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