LMFDB - Embedded newform 2100.2.s.c.1457.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1457,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 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("2100.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.2
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.c.1793.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69214 + 0.369667i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.72669 - 1.25106i) q^{9} +O(q^{10})$	$q+(-1.69214 + 0.369667i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.72669 - 1.25106i) q^{9} +4.03821i q^{11} +(3.70112 - 3.70112i) q^{13} +(5.26756 - 5.26756i) q^{17} +2.18379i q^{19} +(-1.45792 - 0.935131i) q^{21} +(-3.73460 - 3.73460i) q^{23} +(-4.15147 + 3.12494i) q^{27} -7.12019 q^{29} -3.41796 q^{31} +(-1.49279 - 6.83322i) q^{33} +(4.40822 + 4.40822i) q^{37} +(-4.89464 + 7.63100i) q^{39} -0.501135i q^{41} +(8.62698 - 8.62698i) q^{43} +(-5.51062 + 5.51062i) q^{47} +1.00000i q^{49} +(-6.96622 + 10.8607i) q^{51} +(-5.79236 - 5.79236i) q^{53} +(-0.807276 - 3.69528i) q^{57} +13.0602 q^{59} +12.3462 q^{61} +(2.81270 + 1.04343i) q^{63} +(5.56252 + 5.56252i) q^{67} +(7.70003 + 4.93891i) q^{69} -11.2044i q^{71} +(0.731795 - 0.731795i) q^{73} +(-2.85544 + 2.85544i) q^{77} +3.73515i q^{79} +(5.86970 - 6.82251i) q^{81} +(-1.07942 - 1.07942i) q^{83} +(12.0484 - 2.63210i) q^{87} +8.06582 q^{89} +5.23417 q^{91} +(5.78367 - 1.26351i) q^{93} +(1.14555 + 1.14555i) q^{97} +(5.05204 + 11.0109i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{21} + 48 q^{31} - 32 q^{51} + 16 q^{61} + 64 q^{81} + 32 q^{91}+O(q^{100}) $ 32 * q - 8 * q^21 + 48 * q^31 - 32 * q^51 + 16 * q^61 + 64 * q^81 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−1.69214	+	0.369667i	−0.976959	+	0.213428i
$3$	−1.69214	+	0.369667i	−0.976959	+	0.213428i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$	2.72669	−	1.25106i	0.908897	−	0.417020i
$10$		0			0
$11$			4.03821i			1.21756i	0.793337	+	0.608782i	$0.208342\pi$
$11$			4.03821i			1.21756i	−0.793337	+	0.608782i	$0.791658\pi$
$12$		0			0
$13$	3.70112	−	3.70112i	1.02651	−	1.02651i	0.0268663	−	0.999639i	$-0.491447\pi$
$13$	3.70112	−	3.70112i	1.02651	−	1.02651i	0.999639	−	0.0268663i	$-0.00855285\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.26756	−	5.26756i	1.27757	−	1.27757i	0.335549	−	0.942023i	$-0.391078\pi$
$17$	5.26756	−	5.26756i	1.27757	−	1.27757i	0.942023	−	0.335549i	$-0.108922\pi$
$18$		0			0
$19$			2.18379i			0.500995i	0.968117	+	0.250498i	$0.0805943\pi$
$19$			2.18379i			0.500995i	−0.968117	+	0.250498i	$0.919406\pi$
$20$		0			0
$21$	−1.45792	−	0.935131i	−0.318144	−	0.204062i
$22$		0			0
$23$	−3.73460	−	3.73460i	−0.778717	−	0.778717i	0.200895	−	0.979613i	$-0.435615\pi$
$23$	−3.73460	−	3.73460i	−0.778717	−	0.778717i	−0.979613	+	0.200895i	$0.935615\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.15147	+	3.12494i	−0.798952	+	0.601395i
$28$		0			0
$29$	−7.12019			−1.32219			−0.661093	−	0.750304i	$-0.729907\pi$
$29$	−7.12019			−1.32219			−0.661093	+	0.750304i	$0.729907\pi$
$30$		0			0
$31$	−3.41796			−0.613884			−0.306942	−	0.951728i	$-0.599306\pi$
$31$	−3.41796			−0.613884			−0.306942	+	0.951728i	$0.599306\pi$
$32$		0			0
$33$	−1.49279	−	6.83322i	−0.259862	−	1.18951i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.40822	+	4.40822i	0.724708	+	0.724708i	0.969560	−	0.244853i	$-0.0787396\pi$
$37$	4.40822	+	4.40822i	0.724708	+	0.724708i	−0.244853	+	0.969560i	$0.578740\pi$
$38$		0			0
$39$	−4.89464	+	7.63100i	−0.783769	+	1.22194i
$40$		0			0
$41$		−	0.501135i		−	0.0782642i	−0.999234	−	0.0391321i	$-0.987541\pi$
$41$		−	0.501135i		−	0.0782642i	0.999234	−	0.0391321i	$-0.0124593\pi$
$42$		0			0
$43$	8.62698	−	8.62698i	1.31560	−	1.31560i	0.398383	−	0.917219i	$-0.369571\pi$
$43$	8.62698	−	8.62698i	1.31560	−	1.31560i	0.917219	−	0.398383i	$-0.130429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.51062	+	5.51062i	−0.803807	+	0.803807i	−0.983688	−	0.179882i	$-0.942429\pi$
$47$	−5.51062	+	5.51062i	−0.803807	+	0.803807i	0.179882	+	0.983688i	$0.442429\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−6.96622	+	10.8607i	−0.975466	+	1.52080i
$52$		0			0
$53$	−5.79236	−	5.79236i	−0.795642	−	0.795642i	0.186763	−	0.982405i	$-0.440200\pi$
$53$	−5.79236	−	5.79236i	−0.795642	−	0.795642i	−0.982405	+	0.186763i	$0.940200\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.807276	−	3.69528i	−0.106926	−	0.489452i
$58$		0			0
$59$	13.0602			1.70030			0.850150	−	0.526541i	$-0.176511\pi$
$59$	13.0602			1.70030			0.850150	+	0.526541i	$0.176511\pi$
$60$		0			0
$61$	12.3462			1.58076			0.790382	−	0.612614i	$-0.209882\pi$
$61$	12.3462			1.58076			0.790382	+	0.612614i	$0.209882\pi$
$62$		0			0
$63$	2.81270	+	1.04343i	0.354366	+	0.131460i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.56252	+	5.56252i	0.679570	+	0.679570i	0.959903	−	0.280333i	$-0.0904448\pi$
$67$	5.56252	+	5.56252i	0.679570	+	0.679570i	−0.280333	+	0.959903i	$0.590445\pi$
$68$		0			0
$69$	7.70003	+	4.93891i	0.926974	+	0.594575i
$70$		0			0
$71$		−	11.2044i		−	1.32972i	−0.746966	−	0.664862i	$-0.768490\pi$
$71$		−	11.2044i		−	1.32972i	0.746966	−	0.664862i	$-0.231510\pi$
$72$		0			0
$73$	0.731795	−	0.731795i	0.0856501	−	0.0856501i	−0.662984	−	0.748634i	$-0.730710\pi$
$73$	0.731795	−	0.731795i	0.0856501	−	0.0856501i	0.748634	+	0.662984i	$0.230710\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.85544	+	2.85544i	−0.325408	+	0.325408i
$78$		0			0
$79$			3.73515i			0.420238i	0.977676	+	0.210119i	$0.0673851\pi$
$79$			3.73515i			0.420238i	−0.977676	+	0.210119i	$0.932615\pi$
$80$		0			0
$81$	5.86970	−	6.82251i	0.652189	−	0.758057i
$82$		0			0
$83$	−1.07942	−	1.07942i	−0.118482	−	0.118482i	0.645380	−	0.763862i	$-0.276699\pi$
$83$	−1.07942	−	1.07942i	−0.118482	−	0.118482i	−0.763862	+	0.645380i	$0.776699\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	12.0484	−	2.63210i	1.29172	−	0.282191i
$88$		0			0
$89$	8.06582			0.854975			0.427488	−	0.904021i	$-0.359399\pi$
$89$	8.06582			0.854975			0.427488	+	0.904021i	$0.359399\pi$
$90$		0			0
$91$	5.23417			0.548690
$92$		0			0
$93$	5.78367	−	1.26351i	0.599739	−	0.131020i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.14555	+	1.14555i	0.116313	+	0.116313i	0.762868	−	0.646554i	$-0.223791\pi$
$97$	1.14555	+	1.14555i	0.116313	+	0.116313i	−0.646554	+	0.762868i	$0.723791\pi$
$98$		0			0
$99$	5.05204	+	11.0109i	0.507749	+	1.10664i
$100$		0			0
$101$			1.93078i			0.192120i	0.995376	+	0.0960598i	$0.0306240\pi$
$101$			1.93078i			0.192120i	−0.995376	+	0.0960598i	$0.969376\pi$
$102$		0			0
$103$	−3.19442	+	3.19442i	−0.314755	+	0.314755i	−0.846749	−	0.531993i	$-0.821443\pi$
$103$	−3.19442	+	3.19442i	−0.314755	+	0.314755i	0.531993	+	0.846749i	$0.321443\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.4714	−	12.4714i	1.20565	−	1.20565i	0.233231	−	0.972421i	$-0.425070\pi$
$107$	12.4714	−	12.4714i	1.20565	−	1.20565i	0.972421	−	0.233231i	$-0.0749299\pi$
$108$		0			0
$109$			1.36758i			0.130990i	0.997853	+	0.0654951i	$0.0208627\pi$
$109$			1.36758i			0.130990i	−0.997853	+	0.0654951i	$0.979137\pi$
$110$		0			0
$111$	−9.08892	−	5.82977i	−0.862682	−	0.553337i
$112$		0			0
$113$	−9.20243	−	9.20243i	−0.865691	−	0.865691i	0.126301	−	0.991992i	$-0.459690\pi$
$113$	−9.20243	−	9.20243i	−0.865691	−	0.865691i	−0.991992	+	0.126301i	$0.959690\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.46149	−	14.7221i	0.504915	−	1.36106i
$118$		0			0
$119$	7.44946			0.682891
$120$		0			0
$121$	−5.30710			−0.482464
$122$		0			0
$123$	0.185253	+	0.847992i	0.0167037	+	0.0764609i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.728797	+	0.728797i	0.0646703	+	0.0646703i	0.738702	−	0.674032i	$-0.235439\pi$
$127$	0.728797	+	0.728797i	0.0646703	+	0.0646703i	−0.674032	+	0.738702i	$0.735439\pi$
$128$		0			0
$129$	−11.4090	+	17.7872i	−1.00450	+	1.56608i
$130$		0			0
$131$			6.42407i			0.561273i	0.959814	+	0.280637i	$0.0905456\pi$
$131$			6.42407i			0.561273i	−0.959814	+	0.280637i	$0.909454\pi$
$132$		0			0
$133$	−1.54417	+	1.54417i	−0.133897	+	0.133897i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.82288	+	2.82288i	−0.241175	+	0.241175i	−0.817336	−	0.576161i	$-0.804550\pi$
$137$	−2.82288	+	2.82288i	−0.241175	+	0.241175i	0.576161	+	0.817336i	$0.304550\pi$
$138$		0			0
$139$		−	9.96312i		−	0.845061i	−0.906349	−	0.422530i	$-0.861142\pi$
$139$		−	9.96312i		−	0.845061i	0.906349	−	0.422530i	$-0.138858\pi$
$140$		0			0
$141$	7.28766	−	11.3619i	0.613731	−	0.956840i
$142$		0			0
$143$	14.9459	+	14.9459i	1.24984	+	1.24984i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.369667	−	1.69214i	−0.0304897	−	0.139566i
$148$		0			0
$149$	−4.15343			−0.340262			−0.170131	−	0.985421i	$-0.554419\pi$
$149$	−4.15343			−0.340262			−0.170131	+	0.985421i	$0.554419\pi$
$150$		0			0
$151$	11.0670			0.900619			0.450309	−	0.892873i	$-0.351314\pi$
$151$	11.0670			0.900619			0.450309	+	0.892873i	$0.351314\pi$
$152$		0			0
$153$	7.77299	−	20.9531i	0.628409	−	1.69395i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	13.8476	+	13.8476i	1.10516	+	1.10516i	0.993778	+	0.111379i	$0.0355269\pi$
$157$	13.8476	+	13.8476i	1.10516	+	1.10516i	0.111379	+	0.993778i	$0.464473\pi$
$158$		0			0
$159$	11.9428	+	7.66025i	0.947122	+	0.607498i
$160$		0			0
$161$		−	5.28152i		−	0.416242i
$162$		0			0
$163$	17.3889	−	17.3889i	1.36200	−	1.36200i	0.490636	−	0.871365i	$-0.336764\pi$
$163$	17.3889	−	17.3889i	1.36200	−	1.36200i	0.871365	−	0.490636i	$-0.163236\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.879154	−	0.879154i	0.0680310	−	0.0680310i	−0.672273	−	0.740304i	$-0.734682\pi$
$167$	0.879154	−	0.879154i	0.0680310	−	0.0680310i	0.740304	+	0.672273i	$0.234682\pi$
$168$		0			0
$169$		−	14.3965i		−	1.10743i
$170$		0			0
$171$	2.73205	+	5.95452i	0.208925	+	0.455353i
$172$		0			0
$173$	15.8678	+	15.8678i	1.20641	+	1.20641i	0.972182	+	0.234226i	$0.0752555\pi$
$173$	15.8678	+	15.8678i	1.20641	+	1.20641i	0.234226	+	0.972182i	$0.424745\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−22.0998	+	4.82795i	−1.66112	+	0.362891i
$178$		0			0
$179$	16.9266			1.26515			0.632576	−	0.774498i	$-0.281998\pi$
$179$	16.9266			1.26515			0.632576	+	0.774498i	$0.281998\pi$
$180$		0			0
$181$	14.7292			1.09481			0.547407	−	0.836867i	$-0.315615\pi$
$181$	14.7292			1.09481			0.547407	+	0.836867i	$0.315615\pi$
$182$		0			0
$183$	−20.8915	+	4.56397i	−1.54434	+	0.337379i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	21.2715	+	21.2715i	1.55553	+	1.55553i
$188$		0			0
$189$	−5.14520	−	0.725869i	−0.374258	−	0.0527992i
$190$		0			0
$191$			10.3345i			0.747780i	0.927473	+	0.373890i	$0.121976\pi$
$191$			10.3345i			0.747780i	−0.927473	+	0.373890i	$0.878024\pi$
$192$		0			0
$193$	1.01859	−	1.01859i	0.0733200	−	0.0733200i	−0.669496	−	0.742816i	$-0.733490\pi$
$193$	1.01859	−	1.01859i	0.0733200	−	0.0733200i	0.742816	+	0.669496i	$0.233490\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.76865	+	7.76865i	−0.553493	+	0.553493i	−0.927447	−	0.373954i	$-0.878002\pi$
$197$	−7.76865	+	7.76865i	−0.553493	+	0.553493i	0.373954	+	0.927447i	$0.378002\pi$
$198$		0			0
$199$			3.12642i			0.221626i	0.993841	+	0.110813i	$0.0353455\pi$
$199$			3.12642i			0.221626i	−0.993841	+	0.110813i	$0.964655\pi$
$200$		0			0
$201$	−11.4689	−	7.35630i	−0.808951	−	0.518873i
$202$		0			0
$203$	−5.03474	−	5.03474i	−0.353369	−	0.353369i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−14.8553	−	5.51089i	−1.03251	−	0.383033i
$208$		0			0
$209$	−8.81859			−0.609994
$210$		0			0
$211$	−17.2620			−1.18837			−0.594183	−	0.804330i	$-0.702524\pi$
$211$	−17.2620			−1.18837			−0.594183	+	0.804330i	$0.702524\pi$
$212$		0			0
$213$	4.14192	+	18.9595i	0.283800	+	1.29909i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.41686	−	2.41686i	−0.164067	−	0.164067i
$218$		0			0
$219$	−0.967781	+	1.50882i	−0.0653966	+	0.101957i
$220$		0			0
$221$		−	38.9918i		−	2.62287i
$222$		0			0
$223$	−10.2046	+	10.2046i	−0.683349	+	0.683349i	−0.960753	−	0.277404i	$-0.910526\pi$
$223$	−10.2046	+	10.2046i	−0.683349	+	0.683349i	0.277404	+	0.960753i	$0.410526\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.84739	−	7.84739i	0.520849	−	0.520849i	−0.396979	−	0.917828i	$-0.629941\pi$
$227$	7.84739	−	7.84739i	0.520849	−	0.520849i	0.917828	+	0.396979i	$0.129941\pi$
$228$		0			0
$229$			16.0085i			1.05787i	0.848662	+	0.528935i	$0.177409\pi$
$229$			16.0085i			1.05787i	−0.848662	+	0.528935i	$0.822591\pi$
$230$		0			0
$231$	3.77625	−	5.88738i	0.248459	−	0.387361i
$232$		0			0
$233$	−4.99044	−	4.99044i	−0.326935	−	0.326935i	0.524485	−	0.851420i	$-0.324258\pi$
$233$	−4.99044	−	4.99044i	−0.326935	−	0.326935i	−0.851420	+	0.524485i	$0.824258\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.38077	−	6.32041i	−0.0896903	−	0.410555i
$238$		0			0
$239$	0.710589			0.0459642			0.0229821	−	0.999736i	$-0.492684\pi$
$239$	0.710589			0.0459642			0.0229821	+	0.999736i	$0.492684\pi$
$240$		0			0
$241$	22.6008			1.45585			0.727923	−	0.685658i	$-0.240486\pi$
$241$	22.6008			1.45585			0.727923	+	0.685658i	$0.240486\pi$
$242$		0			0
$243$	−7.41030	+	13.7145i	−0.475371	+	0.879785i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.08246	+	8.08246i	0.514275	+	0.514275i
$248$		0			0
$249$	2.22556	+	1.42750i	0.141039	+	0.0904644i
$250$		0			0
$251$			2.31088i			0.145862i	0.997337	+	0.0729308i	$0.0232352\pi$
$251$			2.31088i			0.145862i	−0.997337	+	0.0729308i	$0.976765\pi$
$252$		0			0
$253$	15.0811	−	15.0811i	0.948139	−	0.948139i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.3424	−	10.3424i	0.645138	−	0.645138i	−0.306676	−	0.951814i	$-0.599217\pi$
$257$	10.3424	−	10.3424i	0.645138	−	0.645138i	0.951814	+	0.306676i	$0.0992168\pi$
$258$		0			0
$259$			6.23417i			0.387373i
$260$		0			0
$261$	−19.4146	+	8.90779i	−1.20173	+	0.551378i
$262$		0			0
$263$	−4.31716	−	4.31716i	−0.266208	−	0.266208i	0.561362	−	0.827570i	$-0.310277\pi$
$263$	−4.31716	−	4.31716i	−0.266208	−	0.266208i	−0.827570	+	0.561362i	$0.810277\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−13.6485	+	2.98167i	−0.835276	+	0.182475i
$268$		0			0
$269$	2.58085			0.157357			0.0786786	−	0.996900i	$-0.474930\pi$
$269$	2.58085			0.157357			0.0786786	+	0.996900i	$0.474930\pi$
$270$		0			0
$271$	0.667337			0.0405378			0.0202689	−	0.999795i	$-0.493548\pi$
$271$	0.667337			0.0405378			0.0202689	+	0.999795i	$0.493548\pi$
$272$		0			0
$273$	−8.85696	+	1.93490i	−0.536048	+	0.117106i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−12.9874	−	12.9874i	−0.780339	−	0.780339i	0.199549	−	0.979888i	$-0.436052\pi$
$277$	−12.9874	−	12.9874i	−0.780339	−	0.780339i	−0.979888	+	0.199549i	$0.936052\pi$
$278$		0			0
$279$	−9.31972	+	4.27607i	−0.557957	+	0.256002i
$280$		0			0
$281$			20.9016i			1.24689i	0.781869	+	0.623443i	$0.214267\pi$
$281$			20.9016i			1.24689i	−0.781869	+	0.623443i	$0.785733\pi$
$282$		0			0
$283$	−13.4774	+	13.4774i	−0.801147	+	0.801147i	−0.983275	−	0.182127i	$-0.941702\pi$
$283$	−13.4774	+	13.4774i	−0.801147	+	0.801147i	0.182127	+	0.983275i	$0.441702\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.354356	−	0.354356i	0.0209170	−	0.0209170i
$288$		0			0
$289$		−	38.4945i		−	2.26438i
$290$		0			0
$291$	−2.36192	−	1.51497i	−0.138458	−	0.0888090i
$292$		0			0
$293$	−20.0132	−	20.0132i	−1.16918	−	1.16918i	−0.982402	−	0.186780i	$-0.940195\pi$
$293$	−20.0132	−	20.0132i	−1.16918	−	1.16918i	−0.186780	−	0.982402i	$-0.559805\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.6192	−	16.7645i	−0.732238	−	0.972775i
$298$		0			0
$299$	−27.6444			−1.59871
$300$		0			0
$301$	12.2004			0.703219
$302$		0			0
$303$	−0.713746	−	3.26715i	−0.0410036	−	0.187693i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−2.81548	−	2.81548i	−0.160688	−	0.160688i	0.622184	−	0.782871i	$-0.286246\pi$
$307$	−2.81548	−	2.81548i	−0.160688	−	0.160688i	−0.782871	+	0.622184i	$0.786246\pi$
$308$		0			0
$309$	4.22454	−	6.58628i	0.240325	−	0.374680i
$310$		0			0
$311$			26.0658i			1.47805i	0.673675	+	0.739027i	$0.264715\pi$
$311$			26.0658i			1.47805i	−0.673675	+	0.739027i	$0.735285\pi$
$312$		0			0
$313$	−10.9696	+	10.9696i	−0.620038	+	0.620038i	−0.945541	−	0.325503i	$-0.894466\pi$
$313$	−10.9696	+	10.9696i	−0.620038	+	0.620038i	0.325503	+	0.945541i	$0.394466\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.36184	+	2.36184i	−0.132654	+	0.132654i	−0.770316	−	0.637662i	$-0.779902\pi$
$317$	−2.36184	+	2.36184i	−0.132654	+	0.132654i	0.637662	+	0.770316i	$0.279902\pi$
$318$		0			0
$319$		−	28.7528i		−	1.60985i
$320$		0			0
$321$	−16.4931	+	25.7136i	−0.920553	+	1.43519i
$322$		0			0
$323$	11.5032	+	11.5032i	0.640058	+	0.640058i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.505549	−	2.31414i	−0.0279569	−	0.127972i
$328$		0			0
$329$	−7.79319			−0.429653
$330$		0			0
$331$	−30.5396			−1.67861			−0.839303	−	0.543664i	$-0.817037\pi$
$331$	−30.5396			−1.67861			−0.839303	+	0.543664i	$0.817037\pi$
$332$		0			0
$333$	17.5348	+	6.50492i	0.960902	+	0.356467i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	4.43131	+	4.43131i	0.241389	+	0.241389i	0.817424	−	0.576036i	$-0.195401\pi$
$337$	4.43131	+	4.43131i	0.241389	+	0.241389i	−0.576036	+	0.817424i	$0.695401\pi$
$338$		0			0
$339$	18.9737	+	12.1700i	1.03051	+	0.660982i
$340$		0			0
$341$		−	13.8024i		−	0.747443i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.86429	+	4.86429i	−0.261129	+	0.261129i	−0.825513	−	0.564384i	$-0.809114\pi$
$347$	−4.86429	+	4.86429i	−0.261129	+	0.261129i	0.564384	+	0.825513i	$0.309114\pi$
$348$		0			0
$349$		−	24.0155i		−	1.28552i	−0.766068	−	0.642759i	$-0.777790\pi$
$349$		−	24.0155i		−	1.28552i	0.766068	−	0.642759i	$-0.222210\pi$
$350$		0			0
$351$	−3.79932	+	26.9309i	−0.202793	+	1.43746i
$352$		0			0
$353$	−9.05518	−	9.05518i	−0.481959	−	0.481959i	0.423798	−	0.905757i	$-0.360697\pi$
$353$	−9.05518	−	9.05518i	−0.481959	−	0.481959i	−0.905757	+	0.423798i	$0.860697\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−12.6055	+	2.75382i	−0.667156	+	0.145748i
$358$		0			0
$359$	−16.6520			−0.878860			−0.439430	−	0.898277i	$-0.644820\pi$
$359$	−16.6520			−0.878860			−0.439430	+	0.898277i	$0.644820\pi$
$360$		0			0
$361$	14.2311			0.749004
$362$		0			0
$363$	8.98038	−	1.96186i	0.471347	−	0.102971i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.82498	+	4.82498i	0.251862	+	0.251862i	0.821734	−	0.569872i	$-0.193007\pi$
$367$	4.82498	+	4.82498i	0.251862	+	0.251862i	−0.569872	+	0.821734i	$0.693007\pi$
$368$		0			0
$369$	−0.626950	−	1.36644i	−0.0326377	−	0.0711341i
$370$		0			0
$371$		−	8.19164i		−	0.425289i
$372$		0			0
$373$	13.8256	−	13.8256i	0.715864	−	0.715864i	−0.251891	−	0.967756i	$-0.581052\pi$
$373$	13.8256	−	13.8256i	0.715864	−	0.715864i	0.967756	+	0.251891i	$0.0810525\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−26.3527	+	26.3527i	−1.35723	+	1.35723i
$378$		0			0
$379$		−	1.35853i		−	0.0697828i	−0.999391	−	0.0348914i	$-0.988891\pi$
$379$		−	1.35853i		−	0.0697828i	0.999391	−	0.0348914i	$-0.0111085\pi$
$380$		0			0
$381$	−1.50264	−	0.963815i	−0.0769826	−	0.0493778i
$382$		0			0
$383$	15.5094	+	15.5094i	0.792491	+	0.792491i	0.981899	−	0.189407i	$-0.0606567\pi$
$383$	15.5094	+	15.5094i	0.792491	+	0.792491i	−0.189407	+	0.981899i	$0.560657\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	12.7302	−	34.3160i	0.647115	−	1.74438i
$388$		0			0
$389$	−11.2676			−0.571291			−0.285646	−	0.958335i	$-0.592208\pi$
$389$	−11.2676			−0.571291			−0.285646	+	0.958335i	$0.592208\pi$
$390$		0			0
$391$	−39.3445			−1.98973
$392$		0			0
$393$	−2.37477	−	10.8704i	−0.119791	−	0.548341i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.97144	−	7.97144i	−0.400075	−	0.400075i	0.478184	−	0.878260i	$-0.341295\pi$
$397$	−7.97144	−	7.97144i	−0.400075	−	0.400075i	−0.878260	+	0.478184i	$0.841295\pi$
$398$		0			0
$399$	2.04213	−	3.18379i	0.102234	−	0.159389i
$400$		0			0
$401$			38.3735i			1.91628i	0.286302	+	0.958140i	$0.407574\pi$
$401$			38.3735i			1.91628i	−0.286302	+	0.958140i	$0.592426\pi$
$402$		0			0
$403$	−12.6503	+	12.6503i	−0.630155	+	0.630155i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.8013	+	17.8013i	−0.882379	+	0.882379i
$408$		0			0
$409$		−	20.7754i		−	1.02727i	−0.858007	−	0.513637i	$-0.828298\pi$
$409$		−	20.7754i		−	1.02727i	0.858007	−	0.513637i	$-0.171702\pi$
$410$		0			0
$411$	3.73319	−	5.82024i	0.184145	−	0.287091i
$412$		0			0
$413$	9.23499	+	9.23499i	0.454424	+	0.454424i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.68304	+	16.8590i	0.180359	+	0.825589i
$418$		0			0
$419$	−32.4419			−1.58489			−0.792445	−	0.609944i	$-0.791192\pi$
$419$	−32.4419			−1.58489			−0.792445	+	0.609944i	$0.791192\pi$
$420$		0			0
$421$	32.6205			1.58983			0.794914	−	0.606723i	$-0.207516\pi$
$421$	32.6205			1.58983			0.794914	+	0.606723i	$0.207516\pi$
$422$		0			0
$423$	−8.13165	+	21.9199i	−0.395374	+	1.06578i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	8.73006	+	8.73006i	0.422477	+	0.422477i
$428$		0			0
$429$	−30.8156	−	19.7655i	−1.48779	−	0.954289i
$430$		0			0
$431$			8.42014i			0.405584i	0.979222	+	0.202792i	$0.0650015\pi$
$431$			8.42014i			0.405584i	−0.979222	+	0.202792i	$0.934998\pi$
$432$		0			0
$433$	−1.03089	+	1.03089i	−0.0495412	+	0.0495412i	−0.731443	−	0.681902i	$-0.761153\pi$
$433$	−1.03089	+	1.03089i	−0.0495412	+	0.0495412i	0.681902	+	0.731443i	$0.261153\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.15557	−	8.15557i	0.390134	−	0.390134i
$438$		0			0
$439$		−	33.3968i		−	1.59394i	−0.604017	−	0.796971i	$-0.706434\pi$
$439$		−	33.3968i		−	1.59394i	0.604017	−	0.796971i	$-0.293566\pi$
$440$		0			0
$441$	1.25106	+	2.72669i	0.0595743	+	0.129842i
$442$		0			0
$443$	−23.0348	−	23.0348i	−1.09442	−	1.09442i	−0.995051	−	0.0993662i	$-0.968318\pi$
$443$	−23.0348	−	23.0348i	−1.09442	−	1.09442i	−0.0993662	−	0.995051i	$-0.531682\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.02820	−	1.53539i	0.332422	−	0.0726214i
$448$		0			0
$449$	−4.12450			−0.194647			−0.0973237	−	0.995253i	$-0.531028\pi$
$449$	−4.12450			−0.194647			−0.0973237	+	0.995253i	$0.531028\pi$
$450$		0			0
$451$	2.02369			0.0952917
$452$		0			0
$453$	−18.7269	+	4.09110i	−0.879867	+	0.192217i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−18.0345	−	18.0345i	−0.843619	−	0.843619i	0.145709	−	0.989328i	$-0.453454\pi$
$457$	−18.0345	−	18.0345i	−0.843619	−	0.843619i	−0.989328	+	0.145709i	$0.953454\pi$
$458$		0			0
$459$	−5.40733	+	38.3290i	−0.252393	+	1.78904i
$460$		0			0
$461$		−	11.2611i		−	0.524481i	−0.965003	−	0.262241i	$-0.915539\pi$
$461$		−	11.2611i		−	0.524481i	0.965003	−	0.262241i	$-0.0844614\pi$
$462$		0			0
$463$	−5.56932	+	5.56932i	−0.258828	+	0.258828i	−0.824577	−	0.565749i	$-0.808587\pi$
$463$	−5.56932	+	5.56932i	−0.258828	+	0.258828i	0.565749	+	0.824577i	$0.308587\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.8229	−	10.8229i	0.500822	−	0.500822i	−0.410871	−	0.911693i	$-0.634775\pi$
$467$	10.8229	−	10.8229i	0.500822	−	0.500822i	0.911693	+	0.410871i	$0.134775\pi$
$468$		0			0
$469$			7.86659i			0.363246i
$470$		0			0
$471$	−28.5511	−	18.3131i	−1.31556	−	0.843822i
$472$		0			0
$473$	34.8375	+	34.8375i	1.60183	+	1.60183i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−23.0406	−	8.54739i	−1.05496	−	0.391358i
$478$		0			0
$479$	7.06355			0.322742			0.161371	−	0.986894i	$-0.448408\pi$
$479$	7.06355			0.322742			0.161371	+	0.986894i	$0.448408\pi$
$480$		0			0
$481$	32.6307			1.48783
$482$		0			0
$483$	1.95241	+	8.93708i	0.0888375	+	0.406651i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	10.2597	+	10.2597i	0.464913	+	0.464913i	0.900262	−	0.435349i	$-0.143375\pi$
$487$	10.2597	+	10.2597i	0.464913	+	0.464913i	−0.435349	+	0.900262i	$0.643375\pi$
$488$		0			0
$489$	−22.9963	+	35.8525i	−1.03993	+	1.62131i
$490$		0			0
$491$		−	8.60260i		−	0.388230i	−0.980979	−	0.194115i	$-0.937817\pi$
$491$		−	8.60260i		−	0.388230i	0.980979	−	0.194115i	$-0.0621835\pi$
$492$		0			0
$493$	−37.5061	+	37.5061i	−1.68919	+	1.68919i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.92274	−	7.92274i	0.355384	−	0.355384i
$498$		0			0
$499$		−	17.7241i		−	0.793441i	−0.917939	−	0.396721i	$-0.870148\pi$
$499$		−	17.7241i		−	0.793441i	0.917939	−	0.396721i	$-0.129852\pi$
$500$		0			0
$501$	−1.16266	+	1.81265i	−0.0519438	+	0.0809832i
$502$		0			0
$503$	16.5869	+	16.5869i	0.739573	+	0.739573i	0.972495	−	0.232922i	$-0.0748287\pi$
$503$	16.5869	+	16.5869i	0.739573	+	0.739573i	−0.232922	+	0.972495i	$0.574829\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.32193	+	24.3610i	0.236355	+	1.08191i
$508$		0			0
$509$	36.8614			1.63385			0.816926	−	0.576742i	$-0.195676\pi$
$509$	36.8614			1.63385			0.816926	+	0.576742i	$0.195676\pi$
$510$		0			0
$511$	1.03491			0.0457819
$512$		0			0
$513$	−6.82421	−	9.06594i	−0.301296	−	0.400271i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−22.2530	−	22.2530i	−0.978687	−	0.978687i
$518$		0			0
$519$	−32.7164	−	20.9848i	−1.43609	−	0.921130i
$520$		0			0
$521$		−	20.7823i		−	0.910491i	−0.890366	−	0.455245i	$-0.849552\pi$
$521$		−	20.7823i		−	0.910491i	0.890366	−	0.455245i	$-0.150448\pi$
$522$		0			0
$523$	−8.13422	+	8.13422i	−0.355684	+	0.355684i	−0.862219	−	0.506535i	$-0.830926\pi$
$523$	−8.13422	+	8.13422i	−0.355684	+	0.355684i	0.506535	+	0.862219i	$0.330926\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−18.0043	+	18.0043i	−0.784281	+	0.784281i
$528$		0			0
$529$			4.89442i			0.212801i
$530$		0			0
$531$	35.6113	−	16.3392i	1.54540	−	0.709059i
$532$		0			0
$533$	−1.85476	−	1.85476i	−0.0803386	−	0.0803386i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−28.6422	+	6.25721i	−1.23600	+	0.270018i
$538$		0			0
$539$	−4.03821			−0.173938
$540$		0			0
$541$	−23.6052			−1.01486			−0.507432	−	0.861692i	$-0.669405\pi$
$541$	−23.6052			−1.01486			−0.507432	+	0.861692i	$0.669405\pi$
$542$		0			0
$543$	−24.9239	+	5.44491i	−1.06959	+	0.233663i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.421111	+	0.421111i	0.0180054	+	0.0180054i	0.716052	−	0.698047i	$-0.245947\pi$
$547$	0.421111	+	0.421111i	0.0180054	+	0.0180054i	−0.698047	+	0.716052i	$0.745947\pi$
$548$		0			0
$549$	33.6642	−	15.4458i	1.43675	−	0.659210i
$550$		0			0
$551$		−	15.5490i		−	0.662409i
$552$		0			0
$553$	−2.64115	+	2.64115i	−0.112313	+	0.112313i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.7063	+	11.7063i	−0.496010	+	0.496010i	−0.910193	−	0.414184i	$-0.864067\pi$
$557$	−11.7063	+	11.7063i	−0.496010	+	0.496010i	0.414184	+	0.910193i	$0.364067\pi$
$558$		0			0
$559$		−	63.8589i		−	2.70095i
$560$		0			0
$561$	−43.8578	−	28.1310i	−1.85168	−	1.18769i
$562$		0			0
$563$	15.0035	+	15.0035i	0.632323	+	0.632323i	0.948650	−	0.316327i	$-0.102450\pi$
$563$	15.0035	+	15.0035i	0.632323	+	0.632323i	−0.316327	+	0.948650i	$0.602450\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	8.97475	−	0.673741i	0.376904	−	0.0282944i
$568$		0			0
$569$	9.77215			0.409670			0.204835	−	0.978797i	$-0.434334\pi$
$569$	9.77215			0.409670			0.204835	+	0.978797i	$0.434334\pi$
$570$		0			0
$571$	−0.0880438			−0.00368452			−0.00184226	−	0.999998i	$-0.500586\pi$
$571$	−0.0880438			−0.00368452			−0.00184226	+	0.999998i	$0.500586\pi$
$572$		0			0
$573$	−3.82034	−	17.4875i	−0.159597	−	0.730551i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−5.88795	−	5.88795i	−0.245118	−	0.245118i	0.573845	−	0.818964i	$-0.305451\pi$
$577$	−5.88795	−	5.88795i	−0.245118	−	0.245118i	−0.818964	+	0.573845i	$0.805451\pi$
$578$		0			0
$579$	−1.34707	+	2.10015i	−0.0559821	+	0.0872792i
$580$		0			0
$581$		−	1.52653i		−	0.0633311i
$582$		0			0
$583$	23.3907	−	23.3907i	0.968746	−	0.968746i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.1279	−	21.1279i	0.872042	−	0.872042i	−0.120653	−	0.992695i	$-0.538499\pi$
$587$	21.1279	−	21.1279i	0.872042	−	0.872042i	0.992695	+	0.120653i	$0.0384989\pi$
$588$		0			0
$589$		−	7.46410i		−	0.307553i
$590$		0			0
$591$	10.2738	−	16.0175i	0.422610	−	0.658871i
$592$		0			0
$593$	−26.0929	−	26.0929i	−1.07151	−	1.07151i	−0.997238	−	0.0742681i	$-0.976338\pi$
$593$	−26.0929	−	26.0929i	−1.07151	−	1.07151i	−0.0742681	−	0.997238i	$-0.523662\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.15574	−	5.29035i	−0.0473011	−	0.216519i
$598$		0			0
$599$	1.53040			0.0625306			0.0312653	−	0.999511i	$-0.490046\pi$
$599$	1.53040			0.0625306			0.0312653	+	0.999511i	$0.490046\pi$
$600$		0			0
$601$	−20.0845			−0.819265			−0.409632	−	0.912251i	$-0.634343\pi$
$601$	−20.0845			−0.819265			−0.409632	+	0.912251i	$0.634343\pi$
$602$		0			0
$603$	22.1263	+	8.20823i	0.901054	+	0.334265i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−12.1386	−	12.1386i	−0.492692	−	0.492692i	0.416462	−	0.909153i	$-0.363270\pi$
$607$	−12.1386	−	12.1386i	−0.492692	−	0.492692i	−0.909153	+	0.416462i	$0.863270\pi$
$608$		0			0
$609$	10.3807	+	6.65831i	0.420646	+	0.269808i
$610$		0			0
$611$			40.7909i			1.65022i
$612$		0			0
$613$	−32.2937	+	32.2937i	−1.30433	+	1.30433i	−0.378885	+	0.925444i	$0.623692\pi$
$613$	−32.2937	+	32.2937i	−1.30433	+	1.30433i	−0.925444	+	0.378885i	$0.876308\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.62124	−	4.62124i	0.186044	−	0.186044i	−0.607939	−	0.793983i	$-0.708004\pi$
$617$	4.62124	−	4.62124i	0.186044	−	0.186044i	0.793983	+	0.607939i	$0.208004\pi$
$618$		0			0
$619$			20.8998i			0.840034i	0.907516	+	0.420017i	$0.137976\pi$
$619$			20.8998i			0.840034i	−0.907516	+	0.420017i	$0.862024\pi$
$620$		0			0
$621$	27.1745	+	3.83369i	1.09047	+	0.153841i
$622$		0			0
$623$	5.70340	+	5.70340i	0.228502	+	0.228502i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	14.9223	−	3.25995i	0.595940	−	0.130190i
$628$		0			0
$629$	46.4412			1.85173
$630$		0			0
$631$	−15.4621			−0.615538			−0.307769	−	0.951461i	$-0.599582\pi$
$631$	−15.4621			−0.615538			−0.307769	+	0.951461i	$0.599582\pi$
$632$		0			0
$633$	29.2098	−	6.38120i	1.16098	−	0.253630i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.70112	+	3.70112i	0.146644	+	0.146644i
$638$		0			0
$639$	−14.0174	−	30.5511i	−0.554521	−	1.20858i
$640$		0			0
$641$			22.2245i			0.877815i	0.898532	+	0.438907i	$0.144634\pi$
$641$			22.2245i			0.877815i	−0.898532	+	0.438907i	$0.855366\pi$
$642$		0			0
$643$	19.6685	−	19.6685i	0.775649	−	0.775649i	−0.203439	−	0.979088i	$-0.565212\pi$
$643$	19.6685	−	19.6685i	0.775649	−	0.775649i	0.979088	+	0.203439i	$0.0652117\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.31036	−	5.31036i	0.208772	−	0.208772i	−0.594974	−	0.803745i	$-0.702838\pi$
$647$	5.31036	−	5.31036i	0.208772	−	0.208772i	0.803745	+	0.594974i	$0.202838\pi$
$648$		0			0
$649$			52.7400i			2.07022i
$650$		0			0
$651$	4.98311	+	3.19624i	0.195304	+	0.125271i
$652$		0			0
$653$	21.5932	+	21.5932i	0.845006	+	0.845006i	0.989505	−	0.144499i	$-0.0461570\pi$
$653$	21.5932	+	21.5932i	0.845006	+	0.845006i	−0.144499	+	0.989505i	$0.546157\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.07986	−	2.91090i	0.0421294	−	0.113565i
$658$		0			0
$659$	17.2414			0.671629			0.335815	−	0.941928i	$-0.390988\pi$
$659$	17.2414			0.671629			0.335815	+	0.941928i	$0.390988\pi$
$660$		0			0
$661$	20.0262			0.778930			0.389465	−	0.921041i	$-0.372660\pi$
$661$	20.0262			0.778930			0.389465	+	0.921041i	$0.372660\pi$
$662$		0			0
$663$	14.4140	+	65.9796i	0.559793	+	2.56244i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	26.5910	+	26.5910i	1.02961	+	1.02961i
$668$		0			0
$669$	13.4953	−	21.0399i	0.521759	−	0.813450i
$670$		0			0
$671$			49.8563i			1.92468i
$672$		0			0
$673$	−3.75909	+	3.75909i	−0.144902	+	0.144902i	−0.775836	−	0.630934i	$-0.782672\pi$
$673$	−3.75909	+	3.75909i	−0.144902	+	0.144902i	0.630934	+	0.775836i	$0.282672\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.7768	+	16.7768i	−0.644785	+	0.644785i	−0.951728	−	0.306943i	$-0.900694\pi$
$677$	−16.7768	+	16.7768i	−0.644785	+	0.644785i	0.306943	+	0.951728i	$0.400694\pi$
$678$		0			0
$679$			1.62006i			0.0621722i
$680$		0			0
$681$	−10.3780	+	16.1798i	−0.397685	+	0.620012i
$682$		0			0
$683$	−12.7708	−	12.7708i	−0.488662	−	0.488662i	0.419222	−	0.907884i	$-0.362303\pi$
$683$	−12.7708	−	12.7708i	−0.488662	−	0.488662i	−0.907884	+	0.419222i	$0.862303\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.91781	−	27.0886i	−0.225779	−	1.03350i
$688$		0			0
$689$	−42.8764			−1.63346
$690$		0			0
$691$	44.8477			1.70609			0.853044	−	0.521839i	$-0.174754\pi$
$691$	44.8477			1.70609			0.853044	+	0.521839i	$0.174754\pi$
$692$		0			0
$693$	−4.21358	+	11.3582i	−0.160061	+	0.431464i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.63976	−	2.63976i	−0.0999881	−	0.0999881i
$698$		0			0
$699$	10.2893	+	6.59974i	0.389179	+	0.249625i
$700$		0			0
$701$		−	16.5197i		−	0.623940i	−0.950092	−	0.311970i	$-0.899011\pi$
$701$		−	16.5197i		−	0.623940i	0.950092	−	0.311970i	$-0.100989\pi$
$702$		0			0
$703$	−9.62663	+	9.62663i	−0.363075	+	0.363075i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.36527	+	1.36527i	−0.0513461	+	0.0513461i
$708$		0			0
$709$			46.1113i			1.73175i	0.500263	+	0.865874i	$0.333237\pi$
$709$			46.1113i			1.73175i	−0.500263	+	0.865874i	$0.666763\pi$
$710$		0			0
$711$	4.67290	+	10.1846i	0.175248	+	0.381953i
$712$		0			0
$713$	12.7647	+	12.7647i	0.478042	+	0.478042i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.20242	+	0.262682i	−0.0449051	+	0.00981003i
$718$		0			0
$719$	−32.2823			−1.20393			−0.601964	−	0.798523i	$-0.705615\pi$
$719$	−32.2823			−1.20393			−0.601964	+	0.798523i	$0.705615\pi$
$720$		0			0
$721$	−4.51759			−0.168244
$722$		0			0
$723$	−38.2438	+	8.35479i	−1.42230	+	0.310718i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−3.89414	−	3.89414i	−0.144426	−	0.144426i	0.631197	−	0.775623i	$-0.282564\pi$
$727$	−3.89414	−	3.89414i	−0.144426	−	0.144426i	−0.775623	+	0.631197i	$0.782564\pi$
$728$		0			0
$729$	7.46949	−	25.9462i	0.276648	−	0.960971i
$730$		0			0
$731$		−	90.8863i		−	3.36155i
$732$		0			0
$733$	20.4310	−	20.4310i	0.754638	−	0.754638i	−0.220703	−	0.975341i	$-0.570835\pi$
$733$	20.4310	−	20.4310i	0.754638	−	0.754638i	0.975341	+	0.220703i	$0.0708352\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−22.4626	+	22.4626i	−0.827421	+	0.827421i
$738$		0			0
$739$			16.2705i			0.598519i	0.954172	+	0.299260i	$0.0967397\pi$
$739$			16.2705i			0.598519i	−0.954172	+	0.299260i	$0.903260\pi$
$740$		0			0
$741$	−16.6645	−	10.6888i	−0.612185	−	0.392665i
$742$		0			0
$743$	−8.98855	−	8.98855i	−0.329758	−	0.329758i	0.522736	−	0.852494i	$-0.324911\pi$
$743$	−8.98855	−	8.98855i	−0.329758	−	0.329758i	−0.852494	+	0.522736i	$0.824911\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.29366	−	1.59283i	−0.157097	−	0.0582784i
$748$		0			0
$749$	17.6372			0.644448
$750$		0			0
$751$	−38.9439			−1.42108			−0.710541	−	0.703656i	$-0.751550\pi$
$751$	−38.9439			−1.42108			−0.710541	+	0.703656i	$0.751550\pi$
$752$		0			0
$753$	−0.854258	−	3.91034i	−0.0311309	−	0.142501i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	27.1204	+	27.1204i	0.985706	+	0.985706i	0.999899	−	0.0141931i	$-0.00451796\pi$
$757$	27.1204	+	27.1204i	0.985706	+	0.985706i	−0.0141931	+	0.999899i	$0.504518\pi$
$758$		0			0
$759$	−19.9443	+	31.0943i	−0.723934	+	1.12865i
$760$		0			0
$761$		−	38.1968i		−	1.38463i	−0.721594	−	0.692317i	$-0.756590\pi$
$761$		−	38.1968i		−	1.38463i	0.721594	−	0.692317i	$-0.243410\pi$
$762$		0			0
$763$	−0.967023	+	0.967023i	−0.0350086	+	0.0350086i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	48.3375	−	48.3375i	1.74537	−	1.74537i
$768$		0			0
$769$		−	33.8103i		−	1.21923i	−0.792698	−	0.609615i	$-0.791324\pi$
$769$		−	33.8103i		−	1.21923i	0.792698	−	0.609615i	$-0.208676\pi$
$770$		0			0
$771$	−13.6775	+	21.3240i	−0.492583	+	0.767964i
$772$		0			0
$773$	31.9284	+	31.9284i	1.14839	+	1.14839i	0.986870	+	0.161515i	$0.0516380\pi$
$773$	31.9284	+	31.9284i	1.14839	+	1.14839i	0.161515	+	0.986870i	$0.448362\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.30457	−	10.5491i	−0.0826760	−	0.378447i
$778$		0			0
$779$	1.09437			0.0392100
$780$		0			0
$781$	45.2459			1.61902
$782$		0			0
$783$	29.5593	−	22.2502i	1.05636	−	0.795157i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−15.9530	−	15.9530i	−0.568661	−	0.568661i	0.363092	−	0.931753i	$-0.381721\pi$
$787$	−15.9530	−	15.9530i	−0.568661	−	0.568661i	−0.931753	+	0.363092i	$0.881721\pi$
$788$		0			0
$789$	8.90116	+	5.70934i	0.316890	+	0.203258i
$790$		0			0
$791$		−	13.0142i		−	0.462732i
$792$		0			0
$793$	45.6946	−	45.6946i	1.62266	−	1.62266i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.55804	+	1.55804i	−0.0551887	+	0.0551887i	−0.734163	−	0.678974i	$-0.762425\pi$
$797$	−1.55804	+	1.55804i	−0.0551887	+	0.0551887i	0.678974	+	0.734163i	$0.262425\pi$
$798$		0			0
$799$			58.0551i			2.05384i
$800$		0			0
$801$	21.9930	−	10.0908i	0.777085	−	0.356542i
$802$		0			0
$803$	2.95514	+	2.95514i	0.104285	+	0.104285i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.36717	+	0.954057i	−0.153732	+	0.0335844i
$808$		0			0
$809$	−40.5723			−1.42644			−0.713222	−	0.700938i	$-0.752765\pi$
$809$	−40.5723			−1.42644			−0.713222	+	0.700938i	$0.752765\pi$
$810$		0			0
$811$	−33.3205			−1.17004			−0.585021	−	0.811018i	$-0.698914\pi$
$811$	−33.3205			−1.17004			−0.585021	+	0.811018i	$0.698914\pi$
$812$		0			0
$813$	−1.12923	+	0.246693i	−0.0396038	+	0.00865189i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	18.8395	+	18.8395i	0.659111	+	0.659111i
$818$		0			0
$819$	14.2720	−	6.54826i	0.498703	−	0.228815i
$820$		0			0
$821$		−	5.00023i		−	0.174509i	−0.996186	−	0.0872546i	$-0.972191\pi$
$821$		−	5.00023i		−	0.174509i	0.996186	−	0.0872546i	$-0.0278094\pi$
$822$		0			0
$823$	−13.3054	+	13.3054i	−0.463797	+	0.463797i	−0.899898	−	0.436101i	$-0.856359\pi$
$823$	−13.3054	+	13.3054i	−0.463797	+	0.463797i	0.436101	+	0.899898i	$0.356359\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.0487	−	28.0487i	0.975349	−	0.975349i	−0.0243539	−	0.999703i	$-0.507753\pi$
$827$	28.0487	−	28.0487i	0.975349	−	0.975349i	0.999703	+	0.0243539i	$0.00775285\pi$
$828$		0			0
$829$			38.4634i			1.33589i	0.744210	+	0.667945i	$0.232826\pi$
$829$			38.4634i			1.33589i	−0.744210	+	0.667945i	$0.767174\pi$
$830$		0			0
$831$	26.7776	+	17.1756i	0.928905	+	0.595813i
$832$		0			0
$833$	5.26756	+	5.26756i	0.182510	+	0.182510i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	14.1896	−	10.6809i	0.490463	−	0.369187i
$838$		0			0
$839$	16.2844			0.562201			0.281101	−	0.959678i	$-0.409301\pi$
$839$	16.2844			0.562201			0.281101	+	0.959678i	$0.409301\pi$
$840$		0			0
$841$	21.6971			0.748177
$842$		0			0
$843$	−7.72665	−	35.3685i	−0.266120	−	1.21816i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−3.75269	−	3.75269i	−0.128944	−	0.128944i
$848$		0			0
$849$	17.8235	−	27.7878i	0.611701	−	0.953675i
$850$		0			0
$851$		−	32.9259i		−	1.12868i
$852$		0			0
$853$	−32.2526	+	32.2526i	−1.10431	+	1.10431i	−0.110423	+	0.993885i	$0.535221\pi$
$853$	−32.2526	+	32.2526i	−1.10431	+	1.10431i	−0.993885	+	0.110423i	$0.964779\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−36.3551	+	36.3551i	−1.24187	+	1.24187i	−0.282642	+	0.959225i	$0.591211\pi$
$857$	−36.3551	+	36.3551i	−1.24187	+	1.24187i	−0.959225	+	0.282642i	$0.908789\pi$
$858$		0			0
$859$		−	2.01075i		−	0.0686060i	−0.999411	−	0.0343030i	$-0.989079\pi$
$859$		−	2.01075i		−	0.0686060i	0.999411	−	0.0343030i	$-0.0109211\pi$
$860$		0			0
$861$	−0.468627	+	0.730615i	−0.0159708	+	0.0248993i
$862$		0			0
$863$	−25.6710	−	25.6710i	−0.873852	−	0.873852i	0.119037	−	0.992890i	$-0.462019\pi$
$863$	−25.6710	−	25.6710i	−0.873852	−	0.873852i	−0.992890	+	0.119037i	$0.962019\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	14.2302	+	65.1381i	0.483281	+	2.21221i
$868$		0			0
$869$	−15.0833			−0.511667
$870$		0			0
$871$	41.1751			1.39516
$872$		0			0
$873$	4.55673	+	1.69042i	0.154222	+	0.0572119i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.8267	−	15.8267i	−0.534428	−	0.534428i	0.387459	−	0.921887i	$-0.373353\pi$
$877$	−15.8267	−	15.8267i	−0.534428	−	0.534428i	−0.921887	+	0.387459i	$0.873353\pi$
$878$		0			0
$879$	41.2634	+	26.4669i	1.39178	+	0.892707i
$880$		0			0
$881$			10.5440i			0.355236i	0.984100	+	0.177618i	$0.0568391\pi$
$881$			10.5440i			0.355236i	−0.984100	+	0.177618i	$0.943161\pi$
$882$		0			0
$883$	13.7596	−	13.7596i	0.463048	−	0.463048i	−0.436605	−	0.899653i	$-0.643819\pi$
$883$	13.7596	−	13.7596i	0.463048	−	0.463048i	0.899653	+	0.436605i	$0.143819\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.01621	−	2.01621i	0.0676978	−	0.0676978i	−0.672447	−	0.740145i	$-0.734757\pi$
$887$	2.01621	−	2.01621i	0.0676978	−	0.0676978i	0.740145	+	0.672447i	$0.234757\pi$
$888$		0			0
$889$			1.03067i			0.0345677i
$890$		0			0
$891$	27.5507	+	23.7030i	0.922983	+	0.794082i
$892$		0			0
$893$	−12.0340	−	12.0340i	−0.402703	−	0.402703i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	46.7782	−	10.2192i	1.56188	−	0.341210i
$898$		0			0
$899$	24.3365			0.811669
$900$		0			0
$901$	−61.0233			−2.03298
$902$		0			0
$903$	−20.6448	+	4.51009i	−0.687016	+	0.150086i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.39044	+	6.39044i	0.212191	+	0.212191i	0.805198	−	0.593007i	$-0.202059\pi$
$907$	6.39044	+	6.39044i	0.212191	+	0.212191i	−0.593007	+	0.805198i	$0.702059\pi$
$908$		0			0
$909$	2.41552	+	5.26464i	0.0801177	+	0.174617i
$910$		0			0
$911$			43.0010i			1.42469i	0.701831	+	0.712344i	$0.252366\pi$
$911$			43.0010i			1.42469i	−0.701831	+	0.712344i	$0.747634\pi$
$912$		0			0
$913$	4.35892	−	4.35892i	0.144259	−	0.144259i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.54250	+	4.54250i	−0.150007	+	0.150007i
$918$		0			0
$919$		−	52.2248i		−	1.72274i	−0.507980	−	0.861369i	$-0.669608\pi$
$919$		−	52.2248i		−	1.72274i	0.507980	−	0.861369i	$-0.330392\pi$
$920$		0			0
$921$	5.80498	+	3.72340i	0.191281	+	0.122690i
$922$		0			0
$923$	−41.4690	−	41.4690i	−1.36497	−	1.36497i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.71378	+	12.7066i	−0.154821	+	0.417339i
$928$		0			0
$929$	57.2248			1.87749			0.938743	−	0.344619i	$-0.111992\pi$
$929$	57.2248			1.87749			0.938743	+	0.344619i	$0.111992\pi$
$930$		0			0
$931$	−2.18379			−0.0715708
$932$		0			0
$933$	−9.63567	−	44.1070i	−0.315458	−	1.44400i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−4.78270	−	4.78270i	−0.156244	−	0.156244i	0.624656	−	0.780900i	$-0.285239\pi$
$937$	−4.78270	−	4.78270i	−0.156244	−	0.156244i	−0.780900	+	0.624656i	$0.785239\pi$
$938$		0			0
$939$	14.5070	−	22.6172i	0.473418	−	0.738085i
$940$		0			0
$941$			4.54340i			0.148110i	0.997254	+	0.0740552i	$0.0235941\pi$
$941$			4.54340i			0.148110i	−0.997254	+	0.0740552i	$0.976406\pi$
$942$		0			0
$943$	−1.87154	+	1.87154i	−0.0609457	+	0.0609457i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.9836	+	32.9836i	−1.07182	+	1.07182i	−0.0746109	+	0.997213i	$0.523771\pi$
$947$	−32.9836	+	32.9836i	−1.07182	+	1.07182i	−0.997213	+	0.0746109i	$0.976229\pi$
$948$		0			0
$949$		−	5.41692i		−	0.175841i
$950$		0			0
$951$	3.12348	−	4.86967i	0.101286	−	0.157910i
$952$		0			0
$953$	−36.1748	−	36.1748i	−1.17182	−	1.17182i	−0.981776	−	0.190042i	$-0.939138\pi$
$953$	−36.1748	−	36.1748i	−1.17182	−	1.17182i	−0.190042	−	0.981776i	$-0.560862\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	10.6290	+	48.6538i	0.343586	+	1.57276i
$958$		0			0
$959$	−3.99215			−0.128913
$960$		0			0
$961$	−19.3176			−0.623147
$962$		0			0
$963$	18.4031	−	49.6080i	0.593033	−	1.59860i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−32.4059	−	32.4059i	−1.04210	−	1.04210i	−0.999074	−	0.0430291i	$-0.986299\pi$
$967$	−32.4059	−	32.4059i	−1.04210	−	1.04210i	−0.0430291	−	0.999074i	$-0.513701\pi$
$968$		0			0
$969$	−23.7175	−	15.2128i	−0.761916	−	0.488704i
$970$		0			0
$971$			21.3519i			0.685216i	0.939479	+	0.342608i	$0.111310\pi$
$971$			21.3519i			0.685216i	−0.939479	+	0.342608i	$0.888690\pi$
$972$		0			0
$973$	7.04499	−	7.04499i	0.225852	−	0.225852i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.42366	−	7.42366i	0.237504	−	0.237504i	−0.578312	−	0.815816i	$-0.696288\pi$
$977$	7.42366	−	7.42366i	0.237504	−	0.237504i	0.815816	+	0.578312i	$0.196288\pi$
$978$		0			0
$979$			32.5714i			1.04099i
$980$		0			0
$981$	1.71092	+	3.72896i	0.0546255	+	0.119057i
$982$		0			0
$983$	−22.5911	−	22.5911i	−0.720545	−	0.720545i	0.248171	−	0.968716i	$-0.420170\pi$
$983$	−22.5911	−	22.5911i	−0.720545	−	0.720545i	−0.968716	+	0.248171i	$0.920170\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	13.1872	−	2.88089i	0.419753	−	0.0916997i
$988$		0			0
$989$	−64.4366			−2.04896
$990$		0			0
$991$	−38.9966			−1.23877			−0.619384	−	0.785088i	$-0.712617\pi$
$991$	−38.9966			−1.23877			−0.619384	+	0.785088i	$0.712617\pi$
$992$		0			0
$993$	51.6773	−	11.2895i	1.63993	−	0.358261i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	19.0775	+	19.0775i	0.604192	+	0.604192i	0.941422	−	0.337230i	$-0.109490\pi$
$997$	19.0775	+	19.0775i	0.604192	+	0.604192i	−0.337230	+	0.941422i	$0.609490\pi$
$998$		0			0
$999$	−32.0761	−	4.52519i	−1.01484	−	0.143171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.c.1457.2	✓	32
3.2	odd	2	inner	2100.2.s.c.1457.7	yes	32
5.2	odd	4	inner	2100.2.s.c.1793.10	yes	32
5.3	odd	4	inner	2100.2.s.c.1793.7	yes	32
5.4	even	2	inner	2100.2.s.c.1457.15	yes	32
15.2	even	4	inner	2100.2.s.c.1793.15	yes	32
15.8	even	4	inner	2100.2.s.c.1793.2	yes	32
15.14	odd	2	inner	2100.2.s.c.1457.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.s.c.1457.2	✓	32	1.1	even	1	trivial
2100.2.s.c.1457.7	yes	32	3.2	odd	2	inner
2100.2.s.c.1457.10	yes	32	15.14	odd	2	inner
2100.2.s.c.1457.15	yes	32	5.4	even	2	inner
2100.2.s.c.1793.2	yes	32	15.8	even	4	inner
2100.2.s.c.1793.7	yes	32	5.3	odd	4	inner
2100.2.s.c.1793.10	yes	32	5.2	odd	4	inner
2100.2.s.c.1793.15	yes	32	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69214 + 0.369667i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.72669 - 1.25106i) q^{9} +O(q^{10})\)	\(q+(-1.69214 + 0.369667i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.72669 - 1.25106i) q^{9} +4.03821i q^{11} +(3.70112 - 3.70112i) q^{13} +(5.26756 - 5.26756i) q^{17} +2.18379i q^{19} +(-1.45792 - 0.935131i) q^{21} +(-3.73460 - 3.73460i) q^{23} +(-4.15147 + 3.12494i) q^{27} -7.12019 q^{29} -3.41796 q^{31} +(-1.49279 - 6.83322i) q^{33} +(4.40822 + 4.40822i) q^{37} +(-4.89464 + 7.63100i) q^{39} -0.501135i q^{41} +(8.62698 - 8.62698i) q^{43} +(-5.51062 + 5.51062i) q^{47} +1.00000i q^{49} +(-6.96622 + 10.8607i) q^{51} +(-5.79236 - 5.79236i) q^{53} +(-0.807276 - 3.69528i) q^{57} +13.0602 q^{59} +12.3462 q^{61} +(2.81270 + 1.04343i) q^{63} +(5.56252 + 5.56252i) q^{67} +(7.70003 + 4.93891i) q^{69} -11.2044i q^{71} +(0.731795 - 0.731795i) q^{73} +(-2.85544 + 2.85544i) q^{77} +3.73515i q^{79} +(5.86970 - 6.82251i) q^{81} +(-1.07942 - 1.07942i) q^{83} +(12.0484 - 2.63210i) q^{87} +8.06582 q^{89} +5.23417 q^{91} +(5.78367 - 1.26351i) q^{93} +(1.14555 + 1.14555i) q^{97} +(5.05204 + 11.0109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{21} + 48 q^{31} - 32 q^{51} + 16 q^{61} + 64 q^{81} + 32 q^{91}+O(q^{100}) \) 32 * q - 8 * q^21 + 48 * q^31 - 32 * q^51 + 16 * q^61 + 64 * q^81 + 32 * q^91

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