LMFDB - Embedded newform 2100.2.s.c.1793.2

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			1793.2
Character	$\chi$	$=$	2100.1793
Dual form			2100.2.s.c.1457.2

$q$-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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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	$-0.791658\pi$
$11$		−	4.03821i		−	1.21756i	0.793337	−	0.608782i	$-0.208342\pi$
$12$		0			0
$13$	3.70112	+	3.70112i	1.02651	+	1.02651i	0.999639	+	0.0268663i	$0.00855285\pi$
$13$	3.70112	+	3.70112i	1.02651	+	1.02651i	0.0268663	+	0.999639i	$0.491447\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.26756	+	5.26756i	1.27757	+	1.27757i	0.942023	+	0.335549i	$0.108922\pi$
$17$	5.26756	+	5.26756i	1.27757	+	1.27757i	0.335549	+	0.942023i	$0.391078\pi$
$18$		0			0
$19$		−	2.18379i		−	0.500995i	−0.968117	−	0.250498i	$-0.919406\pi$
$19$		−	2.18379i		−	0.500995i	0.968117	−	0.250498i	$-0.0805943\pi$
$20$		0			0
$21$	−1.45792	+	0.935131i	−0.318144	+	0.204062i
$22$		0			0
$23$	−3.73460	+	3.73460i	−0.778717	+	0.778717i	−0.979613	−	0.200895i	$-0.935615\pi$
$23$	−3.73460	+	3.73460i	−0.778717	+	0.778717i	0.200895	+	0.979613i	$0.435615\pi$
$24$		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	−0.244853	−	0.969560i	$-0.578740\pi$
$37$	4.40822	−	4.40822i	0.724708	−	0.724708i	0.969560	+	0.244853i	$0.0787396\pi$
$38$		0			0
$39$	−4.89464	−	7.63100i	−0.783769	−	1.22194i
$40$		0			0
$41$			0.501135i			0.0782642i	0.999234	+	0.0391321i	$0.0124593\pi$
$41$			0.501135i			0.0782642i	−0.999234	+	0.0391321i	$0.987541\pi$
$42$		0			0
$43$	8.62698	+	8.62698i	1.31560	+	1.31560i	0.917219	+	0.398383i	$0.130429\pi$
$43$	8.62698	+	8.62698i	1.31560	+	1.31560i	0.398383	+	0.917219i	$0.369571\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.51062	−	5.51062i	−0.803807	−	0.803807i	0.179882	−	0.983688i	$-0.442429\pi$
$47$	−5.51062	−	5.51062i	−0.803807	−	0.803807i	−0.983688	+	0.179882i	$0.942429\pi$
$48$		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	−0.982405	−	0.186763i	$-0.940200\pi$
$53$	−5.79236	+	5.79236i	−0.795642	+	0.795642i	0.186763	+	0.982405i	$0.440200\pi$
$54$		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	−0.280333	−	0.959903i	$-0.590445\pi$
$67$	5.56252	−	5.56252i	0.679570	−	0.679570i	0.959903	+	0.280333i	$0.0904448\pi$
$68$		0			0
$69$	7.70003	−	4.93891i	0.926974	−	0.594575i
$70$		0			0
$71$			11.2044i			1.32972i	0.746966	+	0.664862i	$0.231510\pi$
$71$			11.2044i			1.32972i	−0.746966	+	0.664862i	$0.768490\pi$
$72$		0			0
$73$	0.731795	+	0.731795i	0.0856501	+	0.0856501i	0.748634	−	0.662984i	$-0.230710\pi$
$73$	0.731795	+	0.731795i	0.0856501	+	0.0856501i	−0.662984	+	0.748634i	$0.730710\pi$
$74$		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	$-0.932615\pi$
$79$		−	3.73515i		−	0.420238i	0.977676	−	0.210119i	$-0.0673851\pi$
$80$		0			0
$81$	5.86970	+	6.82251i	0.652189	+	0.758057i
$82$		0			0
$83$	−1.07942	+	1.07942i	−0.118482	+	0.118482i	−0.763862	−	0.645380i	$-0.776699\pi$
$83$	−1.07942	+	1.07942i	−0.118482	+	0.118482i	0.645380	+	0.763862i	$0.276699\pi$
$84$		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	−0.646554	−	0.762868i	$-0.723791\pi$
$97$	1.14555	−	1.14555i	0.116313	−	0.116313i	0.762868	+	0.646554i	$0.223791\pi$
$98$		0			0
$99$	5.05204	−	11.0109i	0.507749	−	1.10664i
$100$		0			0
$101$		−	1.93078i		−	0.192120i	−0.995376	−	0.0960598i	$-0.969376\pi$
$101$		−	1.93078i		−	0.192120i	0.995376	−	0.0960598i	$-0.0306240\pi$
$102$		0			0
$103$	−3.19442	−	3.19442i	−0.314755	−	0.314755i	0.531993	−	0.846749i	$-0.321443\pi$
$103$	−3.19442	−	3.19442i	−0.314755	−	0.314755i	−0.846749	+	0.531993i	$0.821443\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.4714	+	12.4714i	1.20565	+	1.20565i	0.972421	+	0.233231i	$0.0749299\pi$
$107$	12.4714	+	12.4714i	1.20565	+	1.20565i	0.233231	+	0.972421i	$0.425070\pi$
$108$		0			0
$109$		−	1.36758i		−	0.130990i	−0.997853	−	0.0654951i	$-0.979137\pi$
$109$		−	1.36758i		−	0.130990i	0.997853	−	0.0654951i	$-0.0208627\pi$
$110$		0			0
$111$	−9.08892	+	5.82977i	−0.862682	+	0.553337i
$112$		0			0
$113$	−9.20243	+	9.20243i	−0.865691	+	0.865691i	−0.991992	−	0.126301i	$-0.959690\pi$
$113$	−9.20243	+	9.20243i	−0.865691	+	0.865691i	0.126301	+	0.991992i	$0.459690\pi$
$114$		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	−0.674032	−	0.738702i	$-0.735439\pi$
$127$	0.728797	−	0.728797i	0.0646703	−	0.0646703i	0.738702	+	0.674032i	$0.235439\pi$
$128$		0			0
$129$	−11.4090	−	17.7872i	−1.00450	−	1.56608i
$130$		0			0
$131$		−	6.42407i		−	0.561273i	−0.959814	−	0.280637i	$-0.909454\pi$
$131$		−	6.42407i		−	0.561273i	0.959814	−	0.280637i	$-0.0905456\pi$
$132$		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	0.576161	−	0.817336i	$-0.304550\pi$
$137$	−2.82288	−	2.82288i	−0.241175	−	0.241175i	−0.817336	+	0.576161i	$0.804550\pi$
$138$		0			0
$139$			9.96312i			0.845061i	0.906349	+	0.422530i	$0.138858\pi$
$139$			9.96312i			0.845061i	−0.906349	+	0.422530i	$0.861142\pi$
$140$		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	0.111379	−	0.993778i	$-0.464473\pi$
$157$	13.8476	−	13.8476i	1.10516	−	1.10516i	0.993778	−	0.111379i	$-0.0355269\pi$
$158$		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	0.871365	+	0.490636i	$0.163236\pi$
$163$	17.3889	+	17.3889i	1.36200	+	1.36200i	0.490636	+	0.871365i	$0.336764\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.879154	+	0.879154i	0.0680310	+	0.0680310i	0.740304	−	0.672273i	$-0.234682\pi$
$167$	0.879154	+	0.879154i	0.0680310	+	0.0680310i	−0.672273	+	0.740304i	$0.734682\pi$
$168$		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	0.234226	−	0.972182i	$-0.424745\pi$
$173$	15.8678	−	15.8678i	1.20641	−	1.20641i	0.972182	−	0.234226i	$-0.0752555\pi$
$174$		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	$-0.878024\pi$
$191$		−	10.3345i		−	0.747780i	0.927473	−	0.373890i	$-0.121976\pi$
$192$		0			0
$193$	1.01859	+	1.01859i	0.0733200	+	0.0733200i	0.742816	−	0.669496i	$-0.233490\pi$
$193$	1.01859	+	1.01859i	0.0733200	+	0.0733200i	−0.669496	+	0.742816i	$0.733490\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.76865	−	7.76865i	−0.553493	−	0.553493i	0.373954	−	0.927447i	$-0.378002\pi$
$197$	−7.76865	−	7.76865i	−0.553493	−	0.553493i	−0.927447	+	0.373954i	$0.878002\pi$
$198$		0			0
$199$		−	3.12642i		−	0.221626i	−0.993841	−	0.110813i	$-0.964655\pi$
$199$		−	3.12642i		−	0.221626i	0.993841	−	0.110813i	$-0.0353455\pi$
$200$		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	0.277404	−	0.960753i	$-0.410526\pi$
$223$	−10.2046	−	10.2046i	−0.683349	−	0.683349i	−0.960753	+	0.277404i	$0.910526\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.84739	+	7.84739i	0.520849	+	0.520849i	0.917828	−	0.396979i	$-0.129941\pi$
$227$	7.84739	+	7.84739i	0.520849	+	0.520849i	−0.396979	+	0.917828i	$0.629941\pi$
$228$		0			0
$229$		−	16.0085i		−	1.05787i	−0.848662	−	0.528935i	$-0.822591\pi$
$229$		−	16.0085i		−	1.05787i	0.848662	−	0.528935i	$-0.177409\pi$
$230$		0			0
$231$	3.77625	+	5.88738i	0.248459	+	0.387361i
$232$		0			0
$233$	−4.99044	+	4.99044i	−0.326935	+	0.326935i	−0.851420	−	0.524485i	$-0.824258\pi$
$233$	−4.99044	+	4.99044i	−0.326935	+	0.326935i	0.524485	+	0.851420i	$0.324258\pi$
$234$		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	$-0.976765\pi$
$251$		−	2.31088i		−	0.145862i	0.997337	−	0.0729308i	$-0.0232352\pi$
$252$		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	0.951814	−	0.306676i	$-0.0992168\pi$
$257$	10.3424	+	10.3424i	0.645138	+	0.645138i	−0.306676	+	0.951814i	$0.599217\pi$
$258$		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	−0.827570	−	0.561362i	$-0.810277\pi$
$263$	−4.31716	+	4.31716i	−0.266208	+	0.266208i	0.561362	+	0.827570i	$0.310277\pi$
$264$		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	−0.979888	−	0.199549i	$-0.936052\pi$
$277$	−12.9874	+	12.9874i	−0.780339	+	0.780339i	0.199549	+	0.979888i	$0.436052\pi$
$278$		0			0
$279$	−9.31972	−	4.27607i	−0.557957	−	0.256002i
$280$		0			0
$281$		−	20.9016i		−	1.24689i	−0.781869	−	0.623443i	$-0.785733\pi$
$281$		−	20.9016i		−	1.24689i	0.781869	−	0.623443i	$-0.214267\pi$
$282$		0			0
$283$	−13.4774	−	13.4774i	−0.801147	−	0.801147i	0.182127	−	0.983275i	$-0.441702\pi$
$283$	−13.4774	−	13.4774i	−0.801147	−	0.801147i	−0.983275	+	0.182127i	$0.941702\pi$
$284$		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	−0.186780	+	0.982402i	$0.559805\pi$
$293$	−20.0132	+	20.0132i	−1.16918	+	1.16918i	−0.982402	+	0.186780i	$0.940195\pi$
$294$		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	−0.782871	−	0.622184i	$-0.786246\pi$
$307$	−2.81548	+	2.81548i	−0.160688	+	0.160688i	0.622184	+	0.782871i	$0.286246\pi$
$308$		0			0
$309$	4.22454	+	6.58628i	0.240325	+	0.374680i
$310$		0			0
$311$		−	26.0658i		−	1.47805i	−0.673675	−	0.739027i	$-0.735285\pi$
$311$		−	26.0658i		−	1.47805i	0.673675	−	0.739027i	$-0.264715\pi$
$312$		0			0
$313$	−10.9696	−	10.9696i	−0.620038	−	0.620038i	0.325503	−	0.945541i	$-0.394466\pi$
$313$	−10.9696	−	10.9696i	−0.620038	−	0.620038i	−0.945541	+	0.325503i	$0.894466\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.36184	−	2.36184i	−0.132654	−	0.132654i	0.637662	−	0.770316i	$-0.279902\pi$
$317$	−2.36184	−	2.36184i	−0.132654	−	0.132654i	−0.770316	+	0.637662i	$0.779902\pi$
$318$		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	−0.576036	−	0.817424i	$-0.695401\pi$
$337$	4.43131	−	4.43131i	0.241389	−	0.241389i	0.817424	+	0.576036i	$0.195401\pi$
$338$		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	0.564384	−	0.825513i	$-0.309114\pi$
$347$	−4.86429	−	4.86429i	−0.261129	−	0.261129i	−0.825513	+	0.564384i	$0.809114\pi$
$348$		0			0
$349$			24.0155i			1.28552i	0.766068	+	0.642759i	$0.222210\pi$
$349$			24.0155i			1.28552i	−0.766068	+	0.642759i	$0.777790\pi$
$350$		0			0
$351$	−3.79932	−	26.9309i	−0.202793	−	1.43746i
$352$		0			0
$353$	−9.05518	+	9.05518i	−0.481959	+	0.481959i	−0.905757	−	0.423798i	$-0.860697\pi$
$353$	−9.05518	+	9.05518i	−0.481959	+	0.481959i	0.423798	+	0.905757i	$0.360697\pi$
$354$		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	−0.569872	−	0.821734i	$-0.693007\pi$
$367$	4.82498	−	4.82498i	0.251862	−	0.251862i	0.821734	+	0.569872i	$0.193007\pi$
$368$		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	0.967756	−	0.251891i	$-0.0810525\pi$
$373$	13.8256	+	13.8256i	0.715864	+	0.715864i	−0.251891	+	0.967756i	$0.581052\pi$
$374$		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	$0.0111085\pi$
$379$			1.35853i			0.0697828i	−0.999391	+	0.0348914i	$0.988891\pi$
$380$		0			0
$381$	−1.50264	+	0.963815i	−0.0769826	+	0.0493778i
$382$		0			0
$383$	15.5094	−	15.5094i	0.792491	−	0.792491i	−0.189407	−	0.981899i	$-0.560657\pi$
$383$	15.5094	−	15.5094i	0.792491	−	0.792491i	0.981899	+	0.189407i	$0.0606567\pi$
$384$		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	−0.878260	−	0.478184i	$-0.841295\pi$
$397$	−7.97144	+	7.97144i	−0.400075	+	0.400075i	0.478184	+	0.878260i	$0.341295\pi$
$398$		0			0
$399$	2.04213	+	3.18379i	0.102234	+	0.159389i
$400$		0			0
$401$		−	38.3735i		−	1.91628i	−0.286302	−	0.958140i	$-0.592426\pi$
$401$		−	38.3735i		−	1.91628i	0.286302	−	0.958140i	$-0.407574\pi$
$402$		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	$0.171702\pi$
$409$			20.7754i			1.02727i	−0.858007	+	0.513637i	$0.828298\pi$
$410$		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	$-0.934998\pi$
$431$		−	8.42014i		−	0.405584i	0.979222	−	0.202792i	$-0.0650015\pi$
$432$		0			0
$433$	−1.03089	−	1.03089i	−0.0495412	−	0.0495412i	0.681902	−	0.731443i	$-0.261153\pi$
$433$	−1.03089	−	1.03089i	−0.0495412	−	0.0495412i	−0.731443	+	0.681902i	$0.761153\pi$
$434$		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	$0.293566\pi$
$439$			33.3968i			1.59394i	−0.604017	+	0.796971i	$0.706434\pi$
$440$		0			0
$441$	1.25106	−	2.72669i	0.0595743	−	0.129842i
$442$		0			0
$443$	−23.0348	+	23.0348i	−1.09442	+	1.09442i	−0.0993662	+	0.995051i	$0.531682\pi$
$443$	−23.0348	+	23.0348i	−1.09442	+	1.09442i	−0.995051	+	0.0993662i	$0.968318\pi$
$444$		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	−0.989328	−	0.145709i	$-0.953454\pi$
$457$	−18.0345	+	18.0345i	−0.843619	+	0.843619i	0.145709	+	0.989328i	$0.453454\pi$
$458$		0			0
$459$	−5.40733	−	38.3290i	−0.252393	−	1.78904i
$460$		0			0
$461$			11.2611i			0.524481i	0.965003	+	0.262241i	$0.0844614\pi$
$461$			11.2611i			0.524481i	−0.965003	+	0.262241i	$0.915539\pi$
$462$		0			0
$463$	−5.56932	−	5.56932i	−0.258828	−	0.258828i	0.565749	−	0.824577i	$-0.308587\pi$
$463$	−5.56932	−	5.56932i	−0.258828	−	0.258828i	−0.824577	+	0.565749i	$0.808587\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.8229	+	10.8229i	0.500822	+	0.500822i	0.911693	−	0.410871i	$-0.134775\pi$
$467$	10.8229	+	10.8229i	0.500822	+	0.500822i	−0.410871	+	0.911693i	$0.634775\pi$
$468$		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	−0.435349	−	0.900262i	$-0.643375\pi$
$487$	10.2597	−	10.2597i	0.464913	−	0.464913i	0.900262	+	0.435349i	$0.143375\pi$
$488$		0			0
$489$	−22.9963	−	35.8525i	−1.03993	−	1.62131i
$490$		0			0
$491$			8.60260i			0.388230i	0.980979	+	0.194115i	$0.0621835\pi$
$491$			8.60260i			0.388230i	−0.980979	+	0.194115i	$0.937817\pi$
$492$		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	$0.129852\pi$
$499$			17.7241i			0.793441i	−0.917939	+	0.396721i	$0.870148\pi$
$500$		0			0
$501$	−1.16266	−	1.81265i	−0.0519438	−	0.0809832i
$502$		0			0
$503$	16.5869	−	16.5869i	0.739573	−	0.739573i	−0.232922	−	0.972495i	$-0.574829\pi$
$503$	16.5869	−	16.5869i	0.739573	−	0.739573i	0.972495	+	0.232922i	$0.0748287\pi$
$504$		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	$0.150448\pi$
$521$			20.7823i			0.910491i	−0.890366	+	0.455245i	$0.849552\pi$
$522$		0			0
$523$	−8.13422	−	8.13422i	−0.355684	−	0.355684i	0.506535	−	0.862219i	$-0.330926\pi$
$523$	−8.13422	−	8.13422i	−0.355684	−	0.355684i	−0.862219	+	0.506535i	$0.830926\pi$
$524$		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	−0.698047	−	0.716052i	$-0.745947\pi$
$547$	0.421111	−	0.421111i	0.0180054	−	0.0180054i	0.716052	+	0.698047i	$0.245947\pi$
$548$		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	0.414184	−	0.910193i	$-0.364067\pi$
$557$	−11.7063	−	11.7063i	−0.496010	−	0.496010i	−0.910193	+	0.414184i	$0.864067\pi$
$558$		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	−0.316327	−	0.948650i	$-0.602450\pi$
$563$	15.0035	−	15.0035i	0.632323	−	0.632323i	0.948650	+	0.316327i	$0.102450\pi$
$564$		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	−0.818964	−	0.573845i	$-0.805451\pi$
$577$	−5.88795	+	5.88795i	−0.245118	+	0.245118i	0.573845	+	0.818964i	$0.305451\pi$
$578$		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	0.992695	−	0.120653i	$-0.0384989\pi$
$587$	21.1279	+	21.1279i	0.872042	+	0.872042i	−0.120653	+	0.992695i	$0.538499\pi$
$588$		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	−0.0742681	+	0.997238i	$0.523662\pi$
$593$	−26.0929	+	26.0929i	−1.07151	+	1.07151i	−0.997238	+	0.0742681i	$0.976338\pi$
$594$		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	−0.909153	−	0.416462i	$-0.863270\pi$
$607$	−12.1386	+	12.1386i	−0.492692	+	0.492692i	0.416462	+	0.909153i	$0.363270\pi$
$608$		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	−0.925444	−	0.378885i	$-0.876308\pi$
$613$	−32.2937	−	32.2937i	−1.30433	−	1.30433i	−0.378885	−	0.925444i	$-0.623692\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.62124	+	4.62124i	0.186044	+	0.186044i	0.793983	−	0.607939i	$-0.208004\pi$
$617$	4.62124	+	4.62124i	0.186044	+	0.186044i	−0.607939	+	0.793983i	$0.708004\pi$
$618$		0			0
$619$		−	20.8998i		−	0.840034i	−0.907516	−	0.420017i	$-0.862024\pi$
$619$		−	20.8998i		−	0.840034i	0.907516	−	0.420017i	$-0.137976\pi$
$620$		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	$-0.855366\pi$
$641$		−	22.2245i		−	0.877815i	0.898532	−	0.438907i	$-0.144634\pi$
$642$		0			0
$643$	19.6685	+	19.6685i	0.775649	+	0.775649i	0.979088	−	0.203439i	$-0.0652117\pi$
$643$	19.6685	+	19.6685i	0.775649	+	0.775649i	−0.203439	+	0.979088i	$0.565212\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.31036	+	5.31036i	0.208772	+	0.208772i	0.803745	−	0.594974i	$-0.202838\pi$
$647$	5.31036	+	5.31036i	0.208772	+	0.208772i	−0.594974	+	0.803745i	$0.702838\pi$
$648$		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	−0.144499	−	0.989505i	$-0.546157\pi$
$653$	21.5932	−	21.5932i	0.845006	−	0.845006i	0.989505	+	0.144499i	$0.0461570\pi$
$654$		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	0.630934	−	0.775836i	$-0.282672\pi$
$673$	−3.75909	−	3.75909i	−0.144902	−	0.144902i	−0.775836	+	0.630934i	$0.782672\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.7768	−	16.7768i	−0.644785	−	0.644785i	0.306943	−	0.951728i	$-0.400694\pi$
$677$	−16.7768	−	16.7768i	−0.644785	−	0.644785i	−0.951728	+	0.306943i	$0.900694\pi$
$678$		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	−0.907884	−	0.419222i	$-0.862303\pi$
$683$	−12.7708	+	12.7708i	−0.488662	+	0.488662i	0.419222	+	0.907884i	$0.362303\pi$
$684$		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	$0.100989\pi$
$701$			16.5197i			0.623940i	−0.950092	+	0.311970i	$0.899011\pi$
$702$		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	$-0.666763\pi$
$709$		−	46.1113i		−	1.73175i	0.500263	−	0.865874i	$-0.333237\pi$
$710$		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	−0.775623	−	0.631197i	$-0.782564\pi$
$727$	−3.89414	+	3.89414i	−0.144426	+	0.144426i	0.631197	+	0.775623i	$0.282564\pi$
$728$		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	0.975341	−	0.220703i	$-0.0708352\pi$
$733$	20.4310	+	20.4310i	0.754638	+	0.754638i	−0.220703	+	0.975341i	$0.570835\pi$
$734$		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	$-0.903260\pi$
$739$		−	16.2705i		−	0.598519i	0.954172	−	0.299260i	$-0.0967397\pi$
$740$		0			0
$741$	−16.6645	+	10.6888i	−0.612185	+	0.392665i
$742$		0			0
$743$	−8.98855	+	8.98855i	−0.329758	+	0.329758i	−0.852494	−	0.522736i	$-0.824911\pi$
$743$	−8.98855	+	8.98855i	−0.329758	+	0.329758i	0.522736	+	0.852494i	$0.324911\pi$
$744$		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	−0.0141931	−	0.999899i	$-0.504518\pi$
$757$	27.1204	−	27.1204i	0.985706	−	0.985706i	0.999899	+	0.0141931i	$0.00451796\pi$
$758$		0			0
$759$	−19.9443	−	31.0943i	−0.723934	−	1.12865i
$760$		0			0
$761$			38.1968i			1.38463i	0.721594	+	0.692317i	$0.243410\pi$
$761$			38.1968i			1.38463i	−0.721594	+	0.692317i	$0.756590\pi$
$762$		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	$0.208676\pi$
$769$			33.8103i			1.21923i	−0.792698	+	0.609615i	$0.791324\pi$
$770$		0			0
$771$	−13.6775	−	21.3240i	−0.492583	−	0.767964i
$772$		0			0
$773$	31.9284	−	31.9284i	1.14839	−	1.14839i	0.161515	−	0.986870i	$-0.448362\pi$
$773$	31.9284	−	31.9284i	1.14839	−	1.14839i	0.986870	−	0.161515i	$-0.0516380\pi$
$774$		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	−0.931753	−	0.363092i	$-0.881721\pi$
$787$	−15.9530	+	15.9530i	−0.568661	+	0.568661i	0.363092	+	0.931753i	$0.381721\pi$
$788$		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	0.678974	−	0.734163i	$-0.262425\pi$
$797$	−1.55804	−	1.55804i	−0.0551887	−	0.0551887i	−0.734163	+	0.678974i	$0.762425\pi$
$798$		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	$0.0278094\pi$
$821$			5.00023i			0.174509i	−0.996186	+	0.0872546i	$0.972191\pi$
$822$		0			0
$823$	−13.3054	−	13.3054i	−0.463797	−	0.463797i	0.436101	−	0.899898i	$-0.356359\pi$
$823$	−13.3054	−	13.3054i	−0.463797	−	0.463797i	−0.899898	+	0.436101i	$0.856359\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.0487	+	28.0487i	0.975349	+	0.975349i	0.999703	−	0.0243539i	$-0.00775285\pi$
$827$	28.0487	+	28.0487i	0.975349	+	0.975349i	−0.0243539	+	0.999703i	$0.507753\pi$
$828$		0			0
$829$		−	38.4634i		−	1.33589i	−0.744210	−	0.667945i	$-0.767174\pi$
$829$		−	38.4634i		−	1.33589i	0.744210	−	0.667945i	$-0.232826\pi$
$830$		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	−0.993885	−	0.110423i	$-0.964779\pi$
$853$	−32.2526	−	32.2526i	−1.10431	−	1.10431i	−0.110423	−	0.993885i	$-0.535221\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−36.3551	−	36.3551i	−1.24187	−	1.24187i	−0.959225	−	0.282642i	$-0.908789\pi$
$857$	−36.3551	−	36.3551i	−1.24187	−	1.24187i	−0.282642	−	0.959225i	$-0.591211\pi$
$858$		0			0
$859$			2.01075i			0.0686060i	0.999411	+	0.0343030i	$0.0109211\pi$
$859$			2.01075i			0.0686060i	−0.999411	+	0.0343030i	$0.989079\pi$
$860$		0			0
$861$	−0.468627	−	0.730615i	−0.0159708	−	0.0248993i
$862$		0			0
$863$	−25.6710	+	25.6710i	−0.873852	+	0.873852i	−0.992890	−	0.119037i	$-0.962019\pi$
$863$	−25.6710	+	25.6710i	−0.873852	+	0.873852i	0.119037	+	0.992890i	$0.462019\pi$
$864$		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	−0.921887	−	0.387459i	$-0.873353\pi$
$877$	−15.8267	+	15.8267i	−0.534428	+	0.534428i	0.387459	+	0.921887i	$0.373353\pi$
$878$		0			0
$879$	41.2634	−	26.4669i	1.39178	−	0.892707i
$880$		0			0
$881$		−	10.5440i		−	0.355236i	−0.984100	−	0.177618i	$-0.943161\pi$
$881$		−	10.5440i		−	0.355236i	0.984100	−	0.177618i	$-0.0568391\pi$
$882$		0			0
$883$	13.7596	+	13.7596i	0.463048	+	0.463048i	0.899653	−	0.436605i	$-0.143819\pi$
$883$	13.7596	+	13.7596i	0.463048	+	0.463048i	−0.436605	+	0.899653i	$0.643819\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.01621	+	2.01621i	0.0676978	+	0.0676978i	0.740145	−	0.672447i	$-0.234757\pi$
$887$	2.01621	+	2.01621i	0.0676978	+	0.0676978i	−0.672447	+	0.740145i	$0.734757\pi$
$888$		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	−0.593007	−	0.805198i	$-0.702059\pi$
$907$	6.39044	−	6.39044i	0.212191	−	0.212191i	0.805198	+	0.593007i	$0.202059\pi$
$908$		0			0
$909$	2.41552	−	5.26464i	0.0801177	−	0.174617i
$910$		0			0
$911$		−	43.0010i		−	1.42469i	−0.701831	−	0.712344i	$-0.747634\pi$
$911$		−	43.0010i		−	1.42469i	0.701831	−	0.712344i	$-0.252366\pi$
$912$		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	$0.330392\pi$
$919$			52.2248i			1.72274i	−0.507980	+	0.861369i	$0.669608\pi$
$920$		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	−0.780900	−	0.624656i	$-0.785239\pi$
$937$	−4.78270	+	4.78270i	−0.156244	+	0.156244i	0.624656	+	0.780900i	$0.285239\pi$
$938$		0			0
$939$	14.5070	+	22.6172i	0.473418	+	0.738085i
$940$		0			0
$941$		−	4.54340i		−	0.148110i	−0.997254	−	0.0740552i	$-0.976406\pi$
$941$		−	4.54340i		−	0.148110i	0.997254	−	0.0740552i	$-0.0235941\pi$
$942$		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	−0.997213	−	0.0746109i	$-0.976229\pi$
$947$	−32.9836	−	32.9836i	−1.07182	−	1.07182i	−0.0746109	−	0.997213i	$-0.523771\pi$
$948$		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	−0.190042	+	0.981776i	$0.560862\pi$
$953$	−36.1748	+	36.1748i	−1.17182	+	1.17182i	−0.981776	+	0.190042i	$0.939138\pi$
$954$		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	−0.0430291	+	0.999074i	$0.513701\pi$
$967$	−32.4059	+	32.4059i	−1.04210	+	1.04210i	−0.999074	+	0.0430291i	$0.986299\pi$
$968$		0			0
$969$	−23.7175	+	15.2128i	−0.761916	+	0.488704i
$970$		0			0
$971$		−	21.3519i		−	0.685216i	−0.939479	−	0.342608i	$-0.888690\pi$
$971$		−	21.3519i		−	0.685216i	0.939479	−	0.342608i	$-0.111310\pi$
$972$		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	0.815816	−	0.578312i	$-0.196288\pi$
$977$	7.42366	+	7.42366i	0.237504	+	0.237504i	−0.578312	+	0.815816i	$0.696288\pi$
$978$		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	−0.968716	−	0.248171i	$-0.920170\pi$
$983$	−22.5911	+	22.5911i	−0.720545	+	0.720545i	0.248171	+	0.968716i	$0.420170\pi$
$984$		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	−0.337230	−	0.941422i	$-0.609490\pi$
$997$	19.0775	−	19.0775i	0.604192	−	0.604192i	0.941422	+	0.337230i	$0.109490\pi$
$998$		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.1793.2	yes	32
3.2	odd	2	inner	2100.2.s.c.1793.7	yes	32
5.2	odd	4	inner	2100.2.s.c.1457.7	yes	32
5.3	odd	4	inner	2100.2.s.c.1457.10	yes	32
5.4	even	2	inner	2100.2.s.c.1793.15	yes	32
15.2	even	4	inner	2100.2.s.c.1457.2	✓	32
15.8	even	4	inner	2100.2.s.c.1457.15	yes	32
15.14	odd	2	inner	2100.2.s.c.1793.10	yes	32

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