LMFDB - Embedded newform 1500.2.i.a.557.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(557,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1500.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.i (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:	$11.9775603032$
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			557.16
Character	$\chi$	$=$	1500.557
Dual form			1500.2.i.a.1193.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72157 - 0.190209i) q^{3} +(-0.111556 - 0.111556i) q^{7} +(2.92764 - 0.654920i) q^{9} +O(q^{10})$	\(q+(1.72157 - 0.190209i) q^{3} +(-0.111556 - 0.111556i) q^{7} +(2.92764 - 0.654920i) q^{9} -1.01268i q^{11} +(2.98178 - 2.98178i) q^{13} +(-1.27381 + 1.27381i) q^{17} -4.73740i q^{19} +(-0.213271 - 0.170833i) q^{21} +(-0.327375 - 0.327375i) q^{23} +(4.91558 - 1.68436i) q^{27} +6.26999 q^{29} -3.35442 q^{31} +(-0.192621 - 1.74340i) q^{33} +(-1.73128 - 1.73128i) q^{37} +(4.56619 - 5.70051i) q^{39} +5.46847i q^{41} +(3.13594 - 3.13594i) q^{43} +(-6.07024 + 6.07024i) q^{47} -6.97511i q^{49} +(-1.95067 + 2.43525i) q^{51} +(4.90038 + 4.90038i) q^{53} +(-0.901098 - 8.15579i) q^{57} +14.3166 q^{59} +2.26526 q^{61} +(-0.399657 - 0.253536i) q^{63} +(5.84691 + 5.84691i) q^{67} +(-0.625870 - 0.501330i) q^{69} -13.4796i q^{71} +(-6.11772 + 6.11772i) q^{73} +(-0.112971 + 0.112971i) q^{77} -6.81117i q^{79} +(8.14216 - 3.83474i) q^{81} +(-3.18778 - 3.18778i) q^{83} +(10.7943 - 1.19261i) q^{87} +13.7359 q^{89} -0.665271 q^{91} +(-5.77488 + 0.638042i) q^{93} +(-7.71608 - 7.71608i) q^{97} +(-0.663223 - 2.96476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 12 q^{21} - 32 q^{31} + 100 q^{51} + 48 q^{61} + 52 q^{81} + 232 q^{91}+O(q^{100}) $ 32 * q - 12 * q^21 - 32 * q^31 + 100 * q^51 + 48 * q^61 + 52 * q^81 + 232 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	1.72157	−	0.190209i	0.993952	−	0.109817i
$3$	1.72157	−	0.190209i	0.993952	−	0.109817i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.111556	−	0.111556i	−0.0421643	−	0.0421643i	0.685710	−	0.727875i	$-0.259492\pi$
$7$	−0.111556	−	0.111556i	−0.0421643	−	0.0421643i	−0.727875	+	0.685710i	$0.759492\pi$
$8$		0			0
$9$	2.92764	−	0.654920i	0.975880	−	0.218307i
$10$		0			0
$11$		−	1.01268i		−	0.305334i	−0.988278	−	0.152667i	$-0.951214\pi$
$11$		−	1.01268i		−	0.305334i	0.988278	−	0.152667i	$-0.0487862\pi$
$12$		0			0
$13$	2.98178	−	2.98178i	0.826996	−	0.826996i	−0.160104	−	0.987100i	$-0.551183\pi$
$13$	2.98178	−	2.98178i	0.826996	−	0.826996i	0.987100	+	0.160104i	$0.0511830\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.27381	+	1.27381i	−0.308944	+	0.308944i	−0.844500	−	0.535556i	$-0.820102\pi$
$17$	−1.27381	+	1.27381i	−0.308944	+	0.308944i	0.535556	+	0.844500i	$0.320102\pi$
$18$		0			0
$19$		−	4.73740i		−	1.08683i	−0.839463	−	0.543417i	$-0.817130\pi$
$19$		−	4.73740i		−	1.08683i	0.839463	−	0.543417i	$-0.182870\pi$
$20$		0			0
$21$	−0.213271	−	0.170833i	−0.0465396	−	0.0372789i
$22$		0			0
$23$	−0.327375	−	0.327375i	−0.0682623	−	0.0682623i	0.672151	−	0.740414i	$-0.265370\pi$
$23$	−0.327375	−	0.327375i	−0.0682623	−	0.0682623i	−0.740414	+	0.672151i	$0.765370\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.91558	−	1.68436i	0.946004	−	0.324155i
$28$		0			0
$29$	6.26999			1.16431			0.582154	−	0.813079i	$-0.302210\pi$
$29$	6.26999			1.16431			0.582154	+	0.813079i	$0.302210\pi$
$30$		0			0
$31$	−3.35442			−0.602471			−0.301235	−	0.953550i	$-0.597399\pi$
$31$	−3.35442			−0.602471			−0.301235	+	0.953550i	$0.597399\pi$
$32$		0			0
$33$	−0.192621	−	1.74340i	−0.0335310	−	0.303487i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.73128	−	1.73128i	−0.284621	−	0.284621i	0.550328	−	0.834949i	$-0.314503\pi$
$37$	−1.73128	−	1.73128i	−0.284621	−	0.284621i	−0.834949	+	0.550328i	$0.814503\pi$
$38$		0			0
$39$	4.56619	−	5.70051i	0.731175	−	0.912813i
$40$		0			0
$41$			5.46847i			0.854032i	0.904244	+	0.427016i	$0.140435\pi$
$41$			5.46847i			0.854032i	−0.904244	+	0.427016i	$0.859565\pi$
$42$		0			0
$43$	3.13594	−	3.13594i	0.478227	−	0.478227i	−0.426337	−	0.904564i	$-0.640196\pi$
$43$	3.13594	−	3.13594i	0.478227	−	0.478227i	0.904564	+	0.426337i	$0.140196\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.07024	+	6.07024i	−0.885435	+	0.885435i	−0.994081	−	0.108646i	$-0.965349\pi$
$47$	−6.07024	+	6.07024i	−0.885435	+	0.885435i	0.108646	+	0.994081i	$0.465349\pi$
$48$		0			0
$49$		−	6.97511i		−	0.996444i
$50$		0			0
$51$	−1.95067	+	2.43525i	−0.273148	+	0.341003i
$52$		0			0
$53$	4.90038	+	4.90038i	0.673119	+	0.673119i	0.958434	−	0.285315i	$-0.0920983\pi$
$53$	4.90038	+	4.90038i	0.673119	+	0.673119i	−0.285315	+	0.958434i	$0.592098\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.901098	−	8.15579i	−0.119353	−	1.08026i
$58$		0			0
$59$	14.3166			1.86387			0.931934	−	0.362627i	$-0.118120\pi$
$59$	14.3166			1.86387			0.931934	+	0.362627i	$0.118120\pi$
$60$		0			0
$61$	2.26526			0.290037			0.145019	−	0.989429i	$-0.453676\pi$
$61$	2.26526			0.290037			0.145019	+	0.989429i	$0.453676\pi$
$62$		0			0
$63$	−0.399657	−	0.253536i	−0.0503520	−	0.0319426i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.84691	+	5.84691i	0.714314	+	0.714314i	0.967435	−	0.253121i	$-0.0814571\pi$
$67$	5.84691	+	5.84691i	0.714314	+	0.714314i	−0.253121	+	0.967435i	$0.581457\pi$
$68$		0			0
$69$	−0.625870	−	0.501330i	−0.0753459	−	0.0603531i
$70$		0			0
$71$		−	13.4796i		−	1.59974i	−0.600176	−	0.799868i	$-0.704903\pi$
$71$		−	13.4796i		−	1.59974i	0.600176	−	0.799868i	$-0.295097\pi$
$72$		0			0
$73$	−6.11772	+	6.11772i	−0.716025	+	0.716025i	−0.967789	−	0.251764i	$-0.918989\pi$
$73$	−6.11772	+	6.11772i	−0.716025	+	0.716025i	0.251764	+	0.967789i	$0.418989\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.112971	+	0.112971i	−0.0128742	+	0.0128742i
$78$		0			0
$79$		−	6.81117i		−	0.766316i	−0.923683	−	0.383158i	$-0.874836\pi$
$79$		−	6.81117i		−	0.766316i	0.923683	−	0.383158i	$-0.125164\pi$
$80$		0			0
$81$	8.14216	−	3.83474i	0.904685	−	0.426082i
$82$		0			0
$83$	−3.18778	−	3.18778i	−0.349904	−	0.349904i	0.510170	−	0.860074i	$-0.329583\pi$
$83$	−3.18778	−	3.18778i	−0.349904	−	0.349904i	−0.860074	+	0.510170i	$0.829583\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	10.7943	−	1.19261i	1.15727	−	0.127861i
$88$		0			0
$89$	13.7359			1.45600			0.728002	−	0.685575i	$-0.240449\pi$
$89$	13.7359			1.45600			0.728002	+	0.685575i	$0.240449\pi$
$90$		0			0
$91$	−0.665271			−0.0697394
$92$		0			0
$93$	−5.77488	+	0.638042i	−0.598827	+	0.0661618i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.71608	−	7.71608i	−0.783450	−	0.783450i	0.196962	−	0.980411i	$-0.436893\pi$
$97$	−7.71608	−	7.71608i	−0.783450	−	0.783450i	−0.980411	+	0.196962i	$0.936893\pi$
$98$		0			0
$99$	−0.663223	−	2.96476i	−0.0666564	−	0.297969i
$100$		0			0
$101$			14.7314i			1.46582i	0.680323	+	0.732912i	$0.261839\pi$
$101$			14.7314i			1.46582i	−0.680323	+	0.732912i	$0.738161\pi$
$102$		0			0
$103$	−13.5549	+	13.5549i	−1.33560	+	1.33560i	−0.435331	+	0.900270i	$0.643369\pi$
$103$	−13.5549	+	13.5549i	−1.33560	+	1.33560i	−0.900270	+	0.435331i	$0.856631\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.8294	+	12.8294i	−1.24026	+	1.24026i	−0.280368	+	0.959893i	$0.590456\pi$
$107$	−12.8294	+	12.8294i	−1.24026	+	1.24026i	−0.959893	+	0.280368i	$0.909544\pi$
$108$		0			0
$109$		−	7.32624i		−	0.701726i	−0.936427	−	0.350863i	$-0.885888\pi$
$109$		−	7.32624i		−	0.701726i	0.936427	−	0.350863i	$-0.114112\pi$
$110$		0			0
$111$	−3.30984	−	2.65123i	−0.314156	−	0.251643i
$112$		0			0
$113$	−9.08982	−	9.08982i	−0.855098	−	0.855098i	0.135658	−	0.990756i	$-0.456685\pi$
$113$	−9.08982	−	9.08982i	−0.855098	−	0.855098i	−0.990756	+	0.135658i	$0.956685\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.77675	−	10.6824i	0.626510	−	0.987587i
$118$		0			0
$119$	0.284203			0.0260528
$120$		0			0
$121$	9.97448			0.906771
$122$		0			0
$123$	1.04016	+	9.41439i	0.0937876	+	0.848867i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.44135	+	8.44135i	0.749048	+	0.749048i	0.974301	−	0.225252i	$-0.0723206\pi$
$127$	8.44135	+	8.44135i	0.749048	+	0.749048i	−0.225252	+	0.974301i	$0.572321\pi$
$128$		0			0
$129$	4.80227	−	5.99525i	0.422817	−	0.527852i
$130$		0			0
$131$		−	5.59898i		−	0.489185i	−0.969626	−	0.244592i	$-0.921346\pi$
$131$		−	5.59898i		−	0.489185i	0.969626	−	0.244592i	$-0.0786542\pi$
$132$		0			0
$133$	−0.528486	+	0.528486i	−0.0458256	+	0.0458256i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.37098	+	9.37098i	−0.800617	+	0.800617i	−0.983192	−	0.182575i	$-0.941557\pi$
$137$	−9.37098	+	9.37098i	−0.800617	+	0.800617i	0.182575	+	0.983192i	$0.441557\pi$
$138$		0			0
$139$			7.01703i			0.595176i	0.954694	+	0.297588i	$0.0961822\pi$
$139$			7.01703i			0.595176i	−0.954694	+	0.297588i	$0.903818\pi$
$140$		0			0
$141$	−9.29575	+	11.6050i	−0.782843	+	0.977316i
$142$		0			0
$143$	−3.01958	−	3.01958i	−0.252510	−	0.252510i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.32673	−	12.0082i	−0.109427	−	0.990418i
$148$		0			0
$149$	−13.9750			−1.14488			−0.572438	−	0.819948i	$-0.694002\pi$
$149$	−13.9750			−1.14488			−0.572438	+	0.819948i	$0.694002\pi$
$150$		0			0
$151$	−12.8568			−1.04627			−0.523134	−	0.852250i	$-0.675237\pi$
$151$	−12.8568			−1.04627			−0.523134	+	0.852250i	$0.675237\pi$
$152$		0			0
$153$	−2.89502	+	4.56350i	−0.234048	+	0.368937i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.34487	−	5.34487i	−0.426567	−	0.426567i	0.460890	−	0.887457i	$-0.347530\pi$
$157$	−5.34487	−	5.34487i	−0.426567	−	0.426567i	−0.887457	+	0.460890i	$0.847530\pi$
$158$		0			0
$159$	9.36846	+	7.50427i	0.742967	+	0.595127i
$160$		0			0
$161$			0.0730414i			0.00575646i
$162$		0			0
$163$	11.2821	−	11.2821i	0.883681	−	0.883681i	−0.110225	−	0.993907i	$-0.535157\pi$
$163$	11.2821	−	11.2821i	0.883681	−	0.883681i	0.993907	+	0.110225i	$0.0351572\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.235499	−	0.235499i	0.0182234	−	0.0182234i	−0.697936	−	0.716160i	$-0.745898\pi$
$167$	0.235499	−	0.235499i	0.0182234	−	0.0182234i	0.716160	+	0.697936i	$0.245898\pi$
$168$		0			0
$169$		−	4.78198i		−	0.367844i
$170$		0			0
$171$	−3.10261	−	13.8694i	−0.237263	−	1.06062i
$172$		0			0
$173$	13.8099	+	13.8099i	1.04995	+	1.04995i	0.998685	+	0.0512637i	$0.0163249\pi$
$173$	13.8099	+	13.8099i	1.04995	+	1.04995i	0.0512637	+	0.998685i	$0.483675\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	24.6472	−	2.72316i	1.85260	−	0.204685i
$178$		0			0
$179$	−8.29535			−0.620023			−0.310012	−	0.950733i	$-0.600333\pi$
$179$	−8.29535			−0.620023			−0.310012	+	0.950733i	$0.600333\pi$
$180$		0			0
$181$	−1.45245			−0.107960			−0.0539798	−	0.998542i	$-0.517191\pi$
$181$	−1.45245			−0.107960			−0.0539798	+	0.998542i	$0.517191\pi$
$182$		0			0
$183$	3.89982	−	0.430874i	0.288283	−	0.0318511i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.28996	+	1.28996i	0.0943313	+	0.0943313i
$188$		0			0
$189$	−0.736264	−	0.360463i	−0.0535553	−	0.0262198i
$190$		0			0
$191$			0.756375i			0.0547294i	0.999626	+	0.0273647i	$0.00871154\pi$
$191$			0.756375i			0.0547294i	−0.999626	+	0.0273647i	$0.991288\pi$
$192$		0			0
$193$	5.72724	−	5.72724i	0.412256	−	0.412256i	−0.470268	−	0.882524i	$-0.655843\pi$
$193$	5.72724	−	5.72724i	0.412256	−	0.412256i	0.882524	+	0.470268i	$0.155843\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.1795	+	14.1795i	−1.01025	+	1.01025i	−0.0102995	+	0.999947i	$0.503278\pi$
$197$	−14.1795	+	14.1795i	−1.01025	+	1.01025i	−0.999947	+	0.0102995i	$0.996722\pi$
$198$		0			0
$199$			8.28331i			0.587188i	0.955930	+	0.293594i	$0.0948514\pi$
$199$			8.28331i			0.587188i	−0.955930	+	0.293594i	$0.905149\pi$
$200$		0			0
$201$	11.1780	+	8.95376i	0.788437	+	0.631549i
$202$		0			0
$203$	−0.699456	−	0.699456i	−0.0490922	−	0.0490922i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.17284	−	0.744031i	−0.0815180	−	0.0517137i
$208$		0			0
$209$	−4.79746			−0.331847
$210$		0			0
$211$	−6.66629			−0.458926			−0.229463	−	0.973317i	$-0.573697\pi$
$211$	−6.66629			−0.458926			−0.229463	+	0.973317i	$0.573697\pi$
$212$		0			0
$213$	−2.56395	−	23.2062i	−0.175679	−	1.59006i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.374206	+	0.374206i	0.0254028	+	0.0254028i
$218$		0			0
$219$	−9.36846	+	11.6958i	−0.633062	+	0.790326i
$220$		0			0
$221$			7.59644i			0.510992i
$222$		0			0
$223$	−5.04773	+	5.04773i	−0.338021	+	0.338021i	−0.855622	−	0.517601i	$-0.826825\pi$
$223$	−5.04773	+	5.04773i	−0.338021	+	0.338021i	0.517601	+	0.855622i	$0.326825\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.772665	−	0.772665i	0.0512836	−	0.0512836i	−0.681000	−	0.732283i	$-0.738455\pi$
$227$	0.772665	−	0.772665i	0.0512836	−	0.0512836i	0.732283	+	0.681000i	$0.238455\pi$
$228$		0			0
$229$			23.3034i			1.53993i	0.638086	+	0.769965i	$0.279727\pi$
$229$			23.3034i			1.53993i	−0.638086	+	0.769965i	$0.720273\pi$
$230$		0			0
$231$	−0.172999	+	0.215975i	−0.0113825	+	0.0142101i
$232$		0			0
$233$	8.85432	+	8.85432i	0.580066	+	0.580066i	0.934921	−	0.354856i	$-0.115470\pi$
$233$	8.85432	+	8.85432i	0.580066	+	0.580066i	−0.354856	+	0.934921i	$0.615470\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.29555	−	11.7259i	−0.0841549	−	0.761682i
$238$		0			0
$239$	−15.1633			−0.980833			−0.490416	−	0.871488i	$-0.663155\pi$
$239$	−15.1633			−0.980833			−0.490416	+	0.871488i	$0.663155\pi$
$240$		0			0
$241$	22.8748			1.47350			0.736748	−	0.676168i	$-0.236360\pi$
$241$	22.8748			1.47350			0.736748	+	0.676168i	$0.236360\pi$
$242$		0			0
$243$	13.2879	−	8.15051i	0.852422	−	0.522855i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−14.1259	−	14.1259i	−0.898807	−	0.898807i
$248$		0			0
$249$	−6.09434	−	4.88165i	−0.386213	−	0.309362i
$250$		0			0
$251$		−	16.6541i		−	1.05120i	−0.850732	−	0.525599i	$-0.823841\pi$
$251$		−	16.6541i		−	1.05120i	0.850732	−	0.525599i	$-0.176159\pi$
$252$		0			0
$253$	−0.331525	+	0.331525i	−0.0208428	+	0.0208428i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.9350	+	13.9350i	−0.869239	+	0.869239i	−0.992388	−	0.123149i	$-0.960701\pi$
$257$	−13.9350	+	13.9350i	−0.869239	+	0.869239i	0.123149	+	0.992388i	$0.460701\pi$
$258$		0			0
$259$			0.386271i			0.0240017i
$260$		0			0
$261$	18.3563	−	4.10634i	1.13623	−	0.254176i
$262$		0			0
$263$	−9.65365	−	9.65365i	−0.595270	−	0.595270i	0.343780	−	0.939050i	$-0.388292\pi$
$263$	−9.65365	−	9.65365i	−0.595270	−	0.595270i	−0.939050	+	0.343780i	$0.888292\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	23.6474	−	2.61270i	1.44720	−	0.159895i
$268$		0			0
$269$	−17.8779			−1.09004			−0.545019	−	0.838424i	$-0.683478\pi$
$269$	−17.8779			−1.09004			−0.545019	+	0.838424i	$0.683478\pi$
$270$		0			0
$271$	−0.292812			−0.0177871			−0.00889354	−	0.999960i	$-0.502831\pi$
$271$	−0.292812			−0.0177871			−0.00889354	+	0.999960i	$0.502831\pi$
$272$		0			0
$273$	−1.14531	+	0.126541i	−0.0693176	+	0.00765860i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	20.3176	+	20.3176i	1.22077	+	1.22077i	0.967360	+	0.253407i	$0.0815512\pi$
$277$	20.3176	+	20.3176i	1.22077	+	1.22077i	0.253407	+	0.967360i	$0.418449\pi$
$278$		0			0
$279$	−9.82052	+	2.19687i	−0.587939	+	0.131523i
$280$		0			0
$281$			4.00557i			0.238952i	0.992837	+	0.119476i	$0.0381215\pi$
$281$			4.00557i			0.238952i	−0.992837	+	0.119476i	$0.961878\pi$
$282$		0			0
$283$	18.3664	−	18.3664i	1.09177	−	1.09177i	0.0964266	−	0.995340i	$-0.469259\pi$
$283$	18.3664	−	18.3664i	1.09177	−	1.09177i	0.995340	−	0.0964266i	$-0.0307413\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.610042	−	0.610042i	0.0360096	−	0.0360096i
$288$		0			0
$289$			13.7548i			0.809107i
$290$		0			0
$291$	−14.7515	−	11.8161i	−0.864747	−	0.692675i
$292$		0			0
$293$	−5.71430	−	5.71430i	−0.333833	−	0.333833i	0.520207	−	0.854040i	$-0.325855\pi$
$293$	−5.71430	−	5.71430i	−0.333833	−	0.333833i	−0.854040	+	0.520207i	$0.825855\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.70571	−	4.97790i	−0.0989755	−	0.288847i
$298$		0			0
$299$	−1.95232			−0.112905
$300$		0			0
$301$	−0.699668			−0.0403282
$302$		0			0
$303$	2.80204	+	25.3611i	0.160973	+	1.45696i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−17.5326	−	17.5326i	−1.00064	−	1.00064i	−1.00000		0.000639219i	$-0.999797\pi$
$307$	−17.5326	−	17.5326i	−1.00064	−	1.00064i	−0.000639219	−	1.00000i	$-0.500203\pi$
$308$		0			0
$309$	−20.7575	+	25.9140i	−1.18085	+	1.47420i
$310$		0			0
$311$			1.32645i			0.0752158i	0.999293	+	0.0376079i	$0.0119738\pi$
$311$			1.32645i			0.0752158i	−0.999293	+	0.0376079i	$0.988026\pi$
$312$		0			0
$313$	16.7435	−	16.7435i	0.946398	−	0.946398i	−0.0522368	−	0.998635i	$-0.516635\pi$
$313$	16.7435	−	16.7435i	0.946398	−	0.946398i	0.998635	+	0.0522368i	$0.0166351\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.09524	+	5.09524i	−0.286177	+	0.286177i	−0.835567	−	0.549389i	$-0.814860\pi$
$317$	−5.09524	+	5.09524i	−0.286177	+	0.286177i	0.549389	+	0.835567i	$0.314860\pi$
$318$		0			0
$319$		−	6.34948i		−	0.355503i
$320$		0			0
$321$	−19.6464	+	24.5270i	−1.09656	+	1.36896i
$322$		0			0
$323$	6.03455	+	6.03455i	0.335771	+	0.335771i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.39352	−	12.6127i	−0.0770618	−	0.697482i
$328$		0			0
$329$	1.35435			0.0746675
$330$		0			0
$331$	−22.0928			−1.21433			−0.607166	−	0.794575i	$-0.707694\pi$
$331$	−22.0928			−1.21433			−0.607166	+	0.794575i	$0.707694\pi$
$332$		0			0
$333$	−6.20242	−	3.93472i	−0.339891	−	0.215621i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	13.4942	+	13.4942i	0.735074	+	0.735074i	0.971620	−	0.236546i	$-0.0760155\pi$
$337$	13.4942	+	13.4942i	0.735074	+	0.735074i	−0.236546	+	0.971620i	$0.576016\pi$
$338$		0			0
$339$	−17.3778	−	13.9198i	−0.943831	−	0.756021i
$340$		0			0
$341$			3.39694i			0.183955i
$342$		0			0
$343$	−1.55901	+	1.55901i	−0.0841787	+	0.0841787i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.8697	+	20.8697i	−1.12035	+	1.12035i	−0.128657	+	0.991689i	$0.541067\pi$
$347$	−20.8697	+	20.8697i	−1.12035	+	1.12035i	−0.991689	+	0.128657i	$0.958933\pi$
$348$		0			0
$349$			29.6420i			1.58670i	0.608765	+	0.793351i	$0.291665\pi$
$349$			29.6420i			1.58670i	−0.608765	+	0.793351i	$0.708335\pi$
$350$		0			0
$351$	9.63478	−	19.6795i	0.514267	−	1.05042i
$352$		0			0
$353$	20.7804	+	20.7804i	1.10603	+	1.10603i	0.993667	+	0.112361i	$0.0358412\pi$
$353$	20.7804	+	20.7804i	1.10603	+	1.10603i	0.112361	+	0.993667i	$0.464159\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.489277	−	0.0540581i	0.0258953	−	0.00286106i
$358$		0			0
$359$	−18.6237			−0.982919			−0.491460	−	0.870900i	$-0.663537\pi$
$359$	−18.6237			−0.982919			−0.491460	+	0.870900i	$0.663537\pi$
$360$		0			0
$361$	−3.44294			−0.181207
$362$		0			0
$363$	17.1718	−	1.89724i	0.901287	−	0.0995793i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.84287	+	6.84287i	0.357195	+	0.357195i	0.862778	−	0.505583i	$-0.168723\pi$
$367$	6.84287	+	6.84287i	0.357195	+	0.357195i	−0.505583	+	0.862778i	$0.668723\pi$
$368$		0			0
$369$	3.58141	+	16.0097i	0.186441	+	0.833433i
$370$		0			0
$371$		−	1.09334i		−	0.0567631i
$372$		0			0
$373$	−16.0133	+	16.0133i	−0.829135	+	0.829135i	−0.987397	−	0.158262i	$-0.949411\pi$
$373$	−16.0133	+	16.0133i	−0.829135	+	0.829135i	0.158262	+	0.987397i	$0.449411\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	18.6957	−	18.6957i	0.962878	−	0.962878i
$378$		0			0
$379$			14.1990i			0.729354i	0.931134	+	0.364677i	$0.118821\pi$
$379$			14.1990i			0.729354i	−0.931134	+	0.364677i	$0.881179\pi$
$380$		0			0
$381$	16.1380	+	12.9268i	0.826777	+	0.662259i
$382$		0			0
$383$	−27.1293	−	27.1293i	−1.38624	−	1.38624i	−0.833063	−	0.553178i	$-0.813415\pi$
$383$	−27.1293	−	27.1293i	−1.38624	−	1.38624i	−0.553178	−	0.833063i	$-0.686585\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.12712	−	11.2347i	0.362292	−	0.571092i
$388$		0			0
$389$	−17.2242			−0.873300			−0.436650	−	0.899631i	$-0.643835\pi$
$389$	−17.2242			−0.873300			−0.436650	+	0.899631i	$0.643835\pi$
$390$		0			0
$391$	0.834027			0.0421785
$392$		0			0
$393$	−1.06498	−	9.63906i	−0.0537211	−	0.486226i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.79625	−	5.79625i	−0.290906	−	0.290906i	0.546532	−	0.837438i	$-0.315948\pi$
$397$	−5.79625	−	5.79625i	−0.290906	−	0.290906i	−0.837438	+	0.546532i	$0.815948\pi$
$398$		0			0
$399$	−0.809306	+	1.01035i	−0.0405160	+	0.0505809i
$400$		0			0
$401$			7.77803i			0.388416i	0.980960	+	0.194208i	$0.0622137\pi$
$401$			7.77803i			0.388416i	−0.980960	+	0.194208i	$0.937786\pi$
$402$		0			0
$403$	−10.0021	+	10.0021i	−0.498241	+	0.498241i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.75323	+	1.75323i	−0.0869045	+	0.0869045i
$408$		0			0
$409$		−	19.2912i		−	0.953889i	−0.878933	−	0.476945i	$-0.841744\pi$
$409$		−	19.2912i		−	0.953889i	0.878933	−	0.476945i	$-0.158256\pi$
$410$		0			0
$411$	−14.3504	+	17.9153i	−0.707853	+	0.883697i
$412$		0			0
$413$	−1.59711	−	1.59711i	−0.0785887	−	0.0785887i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.33470	+	12.0803i	0.0653608	+	0.591577i
$418$		0			0
$419$	2.19138			0.107056			0.0535279	−	0.998566i	$-0.482953\pi$
$419$	2.19138			0.107056			0.0535279	+	0.998566i	$0.482953\pi$
$420$		0			0
$421$	20.5045			0.999330			0.499665	−	0.866219i	$-0.333456\pi$
$421$	20.5045			0.999330			0.499665	+	0.866219i	$0.333456\pi$
$422$		0			0
$423$	−13.7960	+	21.7470i	−0.670782	+	1.05737i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.252704	−	0.252704i	−0.0122292	−	0.0122292i
$428$		0			0
$429$	−5.77279	−	4.62408i	−0.278713	−	0.223253i
$430$		0			0
$431$			5.55384i			0.267519i	0.991014	+	0.133759i	$0.0427049\pi$
$431$			5.55384i			0.267519i	−0.991014	+	0.133759i	$0.957295\pi$
$432$		0			0
$433$	−17.1045	+	17.1045i	−0.821989	+	0.821989i	−0.986393	−	0.164404i	$-0.947430\pi$
$433$	−17.1045	+	17.1045i	−0.821989	+	0.821989i	0.164404	+	0.986393i	$0.447430\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.55090	+	1.55090i	−0.0741898	+	0.0741898i
$438$		0			0
$439$			31.0964i			1.48415i	0.670316	+	0.742076i	$0.266159\pi$
$439$			31.0964i			1.48415i	−0.670316	+	0.742076i	$0.733841\pi$
$440$		0			0
$441$	−4.56814	−	20.4206i	−0.217530	−	0.972410i
$442$		0			0
$443$	−11.0690	−	11.0690i	−0.525904	−	0.525904i	0.393445	−	0.919348i	$-0.371283\pi$
$443$	−11.0690	−	11.0690i	−0.525904	−	0.525904i	−0.919348	+	0.393445i	$0.871283\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−24.0590	+	2.65817i	−1.13795	+	0.125727i
$448$		0			0
$449$	18.7897			0.886740			0.443370	−	0.896339i	$-0.353783\pi$
$449$	18.7897			0.886740			0.443370	+	0.896339i	$0.353783\pi$
$450$		0			0
$451$	5.53780			0.260765
$452$		0			0
$453$	−22.1339	+	2.44548i	−1.03994	+	0.114899i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.53453	−	9.53453i	−0.446006	−	0.446006i	0.448018	−	0.894025i	$-0.352130\pi$
$457$	−9.53453	−	9.53453i	−0.446006	−	0.446006i	−0.894025	+	0.448018i	$0.852130\pi$
$458$		0			0
$459$	−4.11597	+	8.40707i	−0.192117	+	0.392409i
$460$		0			0
$461$		−	14.6739i		−	0.683431i	−0.939803	−	0.341716i	$-0.888992\pi$
$461$		−	14.6739i		−	0.683431i	0.939803	−	0.341716i	$-0.111008\pi$
$462$		0			0
$463$	−12.6442	+	12.6442i	−0.587626	+	0.587626i	−0.936988	−	0.349362i	$-0.886398\pi$
$463$	−12.6442	+	12.6442i	−0.587626	+	0.587626i	0.349362	+	0.936988i	$0.386398\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.94101	−	4.94101i	0.228643	−	0.228643i	−0.583483	−	0.812125i	$-0.698310\pi$
$467$	4.94101	−	4.94101i	0.228643	−	0.228643i	0.812125	+	0.583483i	$0.198310\pi$
$468$		0			0
$469$		−	1.30452i		−	0.0602371i
$470$		0			0
$471$	−10.2182	−	8.18495i	−0.470832	−	0.377143i
$472$		0			0
$473$	−3.17570	−	3.17570i	−0.146019	−	0.146019i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	17.5559	+	11.1372i	0.803829	+	0.509937i
$478$		0			0
$479$	−20.4964			−0.936502			−0.468251	−	0.883595i	$-0.655116\pi$
$479$	−20.4964			−0.936502			−0.468251	+	0.883595i	$0.655116\pi$
$480$		0			0
$481$	−10.3246			−0.470761
$482$		0			0
$483$	0.0138932	+	0.125746i	0.000632160	+	0.00572165i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.549665	+	0.549665i	0.0249077	+	0.0249077i	0.719451	−	0.694543i	$-0.244394\pi$
$487$	0.549665	+	0.549665i	0.0249077	+	0.0249077i	−0.694543	+	0.719451i	$0.744394\pi$
$488$		0			0
$489$	17.2770	−	21.5689i	0.781293	−	0.975380i
$490$		0			0
$491$		−	25.7709i		−	1.16302i	−0.813538	−	0.581512i	$-0.802461\pi$
$491$		−	25.7709i		−	1.16302i	0.813538	−	0.581512i	$-0.197539\pi$
$492$		0			0
$493$	−7.98678	+	7.98678i	−0.359706	+	0.359706i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.50374	+	1.50374i	−0.0674517	+	0.0674517i
$498$		0			0
$499$		−	10.0170i		−	0.448424i	−0.974540	−	0.224212i	$-0.928019\pi$
$499$		−	10.0170i		−	0.448424i	0.974540	−	0.224212i	$-0.0719808\pi$
$500$		0			0
$501$	0.360634	−	0.450223i	0.0161120	−	0.0201145i
$502$		0			0
$503$	16.5378	+	16.5378i	0.737385	+	0.737385i	0.972071	−	0.234686i	$-0.0754063\pi$
$503$	16.5378	+	16.5378i	0.737385	+	0.737385i	−0.234686	+	0.972071i	$0.575406\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.909577	−	8.23253i	−0.0403957	−	0.365619i
$508$		0			0
$509$	−35.9439			−1.59318			−0.796592	−	0.604518i	$-0.793366\pi$
$509$	−35.9439			−1.59318			−0.796592	+	0.604518i	$0.793366\pi$
$510$		0			0
$511$	1.36494			0.0603814
$512$		0			0
$513$	−7.97947	−	23.2871i	−0.352302	−	1.02815i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.14720	+	6.14720i	0.270353	+	0.270353i
$518$		0			0
$519$	26.4016	+	21.1480i	1.15890	+	0.928296i
$520$		0			0
$521$			41.3270i			1.81057i	0.424807	+	0.905284i	$0.360342\pi$
$521$			41.3270i			1.81057i	−0.424807	+	0.905284i	$0.639658\pi$
$522$		0			0
$523$	−4.87037	+	4.87037i	−0.212966	+	0.212966i	−0.805526	−	0.592560i	$-0.798117\pi$
$523$	−4.87037	+	4.87037i	−0.212966	+	0.212966i	0.592560	+	0.805526i	$0.298117\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.27289	−	4.27289i	0.186130	−	0.186130i
$528$		0			0
$529$		−	22.7857i		−	0.990681i
$530$		0			0
$531$	41.9140	−	9.37625i	1.81891	−	0.406895i
$532$		0			0
$533$	16.3058	+	16.3058i	0.706281	+	0.706281i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−14.2811	+	1.57785i	−0.616273	+	0.0680894i
$538$		0			0
$539$	−7.06354			−0.304248
$540$		0			0
$541$	26.3745			1.13393			0.566964	−	0.823743i	$-0.308118\pi$
$541$	26.3745			1.13393			0.566964	+	0.823743i	$0.308118\pi$
$542$		0			0
$543$	−2.50050	+	0.276269i	−0.107307	+	0.0118559i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.17137	−	4.17137i	−0.178355	−	0.178355i	0.612283	−	0.790638i	$-0.290251\pi$
$547$	−4.17137	−	4.17137i	−0.178355	−	0.178355i	−0.790638	+	0.612283i	$0.790251\pi$
$548$		0			0
$549$	6.63187	−	1.48356i	0.283041	−	0.0633170i
$550$		0			0
$551$		−	29.7034i		−	1.26541i
$552$		0			0
$553$	−0.759828	+	0.759828i	−0.0323112	+	0.0323112i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.76492	−	5.76492i	0.244267	−	0.244267i	−0.574346	−	0.818613i	$-0.694743\pi$
$557$	5.76492	−	5.76492i	0.244267	−	0.244267i	0.818613	+	0.574346i	$0.194743\pi$
$558$		0			0
$559$		−	18.7014i		−	0.790983i
$560$		0			0
$561$	2.46613	+	1.97540i	0.104120	+	0.0834015i
$562$		0			0
$563$	−17.4526	−	17.4526i	−0.735541	−	0.735541i	0.236171	−	0.971712i	$-0.424108\pi$
$563$	−17.4526	−	17.4526i	−0.735541	−	0.735541i	−0.971712	+	0.236171i	$0.924108\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.33610	−	0.480520i	−0.0561108	−	0.0201799i
$568$		0			0
$569$	29.4348			1.23397			0.616986	−	0.786974i	$-0.288354\pi$
$569$	29.4348			1.23397			0.616986	+	0.786974i	$0.288354\pi$
$570$		0			0
$571$	3.35011			0.140198			0.0700989	−	0.997540i	$-0.477669\pi$
$571$	3.35011			0.140198			0.0700989	+	0.997540i	$0.477669\pi$
$572$		0			0
$573$	0.143870	+	1.30216i	0.00601024	+	0.0543983i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	24.5318	+	24.5318i	1.02127	+	1.02127i	0.999769	+	0.0215023i	$0.00684493\pi$
$577$	24.5318	+	24.5318i	1.02127	+	1.02127i	0.0215023	+	0.999769i	$0.493155\pi$
$578$		0			0
$579$	8.77049	−	10.9492i	0.364489	−	0.455035i
$580$		0			0
$581$			0.711233i			0.0295069i
$582$		0			0
$583$	4.96251	−	4.96251i	0.205526	−	0.205526i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.58383	−	9.58383i	0.395567	−	0.395567i	−0.481099	−	0.876666i	$-0.659762\pi$
$587$	9.58383	−	9.58383i	0.395567	−	0.395567i	0.876666	+	0.481099i	$0.159762\pi$
$588$		0			0
$589$			15.8912i			0.654786i
$590$		0			0
$591$	−21.7140	+	27.1081i	−0.893194	+	1.11508i
$592$		0			0
$593$	26.9983	+	26.9983i	1.10869	+	1.10869i	0.993323	+	0.115365i	$0.0368037\pi$
$593$	26.9983	+	26.9983i	1.10869	+	1.10869i	0.115365	+	0.993323i	$0.463196\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.57556	+	14.2603i	0.0644835	+	0.583636i
$598$		0			0
$599$	40.0022			1.63445			0.817223	−	0.576322i	$-0.195513\pi$
$599$	40.0022			1.63445			0.817223	+	0.576322i	$0.195513\pi$
$600$		0			0
$601$	−35.8170			−1.46101			−0.730504	−	0.682909i	$-0.760715\pi$
$601$	−35.8170			−1.46101			−0.730504	+	0.682909i	$0.760715\pi$
$602$		0			0
$603$	20.9469	+	13.2884i	0.853024	+	0.541145i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.6563	−	11.6563i	−0.473114	−	0.473114i	0.429807	−	0.902921i	$-0.358582\pi$
$607$	−11.6563	−	11.6563i	−0.473114	−	0.473114i	−0.902921	+	0.429807i	$0.858582\pi$
$608$		0			0
$609$	−1.33721	−	1.07112i	−0.0541865	−	0.0434041i
$610$		0			0
$611$			36.2002i			1.46450i
$612$		0			0
$613$	26.9028	−	26.9028i	1.08659	−	1.08659i	0.0907173	−	0.995877i	$-0.471084\pi$
$613$	26.9028	−	26.9028i	1.08659	−	1.08659i	0.995877	−	0.0907173i	$-0.0289160\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.86030	−	1.86030i	0.0748927	−	0.0748927i	−0.668668	−	0.743561i	$-0.733135\pi$
$617$	1.86030	−	1.86030i	0.0748927	−	0.0748927i	0.743561	+	0.668668i	$0.233135\pi$
$618$		0			0
$619$		−	15.5836i		−	0.626359i	−0.949694	−	0.313180i	$-0.898606\pi$
$619$		−	15.5836i		−	0.626359i	0.949694	−	0.313180i	$-0.101394\pi$
$620$		0			0
$621$	−2.16065	−	1.05782i	−0.0867040	−	0.0424489i
$622$		0			0
$623$	−1.53233	−	1.53233i	−0.0613914	−	0.0613914i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.25919	+	0.912522i	−0.329840	+	0.0364426i
$628$		0			0
$629$	4.41065			0.175864
$630$		0			0
$631$	−41.6912			−1.65970			−0.829851	−	0.557986i	$-0.811574\pi$
$631$	−41.6912			−1.65970			−0.829851	+	0.557986i	$0.811574\pi$
$632$		0			0
$633$	−11.4765	+	1.26799i	−0.456150	+	0.0503981i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−20.7982	−	20.7982i	−0.824055	−	0.824055i
$638$		0			0
$639$	−8.82806	−	39.4635i	−0.349233	−	1.56115i
$640$		0			0
$641$		−	11.3178i		−	0.447026i	−0.974701	−	0.223513i	$-0.928247\pi$
$641$		−	11.3178i		−	0.447026i	0.974701	−	0.223513i	$-0.0717526\pi$
$642$		0			0
$643$	17.7923	−	17.7923i	0.701660	−	0.701660i	−0.263107	−	0.964767i	$-0.584747\pi$
$643$	17.7923	−	17.7923i	0.701660	−	0.701660i	0.964767	+	0.263107i	$0.0847472\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.8246	−	11.8246i	0.464874	−	0.464874i	−0.435375	−	0.900249i	$-0.643384\pi$
$647$	11.8246	−	11.8246i	0.464874	−	0.464874i	0.900249	+	0.435375i	$0.143384\pi$
$648$		0			0
$649$		−	14.4982i		−	0.569103i
$650$		0			0
$651$	0.715401	+	0.573046i	0.0280388	+	0.0224594i
$652$		0			0
$653$	−28.1676	−	28.1676i	−1.10228	−	1.10228i	−0.994135	−	0.108148i	$-0.965508\pi$
$653$	−28.1676	−	28.1676i	−1.10228	−	1.10228i	−0.108148	−	0.994135i	$-0.534492\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−13.9039	+	21.9171i	−0.542442	+	0.855067i
$658$		0			0
$659$	22.7953			0.887977			0.443989	−	0.896032i	$-0.353563\pi$
$659$	22.7953			0.887977			0.443989	+	0.896032i	$0.353563\pi$
$660$		0			0
$661$	2.25051			0.0875346			0.0437673	−	0.999042i	$-0.486064\pi$
$661$	2.25051			0.0875346			0.0437673	+	0.999042i	$0.486064\pi$
$662$		0			0
$663$	1.44491	+	13.0778i	0.0561158	+	0.507901i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.05264	−	2.05264i	−0.0794784	−	0.0794784i
$668$		0			0
$669$	−7.72992	+	9.65017i	−0.298856	+	0.373097i
$670$		0			0
$671$		−	2.29398i		−	0.0885582i
$672$		0			0
$673$	−0.293887	+	0.293887i	−0.0113285	+	0.0113285i	−0.712748	−	0.701420i	$-0.752550\pi$
$673$	−0.293887	+	0.293887i	−0.0113285	+	0.0113285i	0.701420	+	0.712748i	$0.252550\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.36621	−	8.36621i	0.321540	−	0.321540i	−0.527818	−	0.849358i	$-0.676990\pi$
$677$	8.36621	−	8.36621i	0.321540	−	0.321540i	0.849358	+	0.527818i	$0.176990\pi$
$678$		0			0
$679$			1.72155i			0.0660672i
$680$		0			0
$681$	1.18323	−	1.47717i	0.0453416	−	0.0566052i
$682$		0			0
$683$	−2.10728	−	2.10728i	−0.0806327	−	0.0806327i	0.665640	−	0.746273i	$-0.268159\pi$
$683$	−2.10728	−	2.10728i	−0.0806327	−	0.0806327i	−0.746273	+	0.665640i	$0.768159\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.43252	+	40.1185i	0.169111	+	1.53062i
$688$		0			0
$689$	29.2237			1.11333
$690$		0			0
$691$	29.1968			1.11070			0.555350	−	0.831617i	$-0.312584\pi$
$691$	29.1968			1.11070			0.555350	+	0.831617i	$0.312584\pi$
$692$		0			0
$693$	−0.256751	+	0.404724i	−0.00975315	+	0.0153742i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−6.96580	−	6.96580i	−0.263848	−	0.263848i
$698$		0			0
$699$	16.9275	+	13.5592i	0.640259	+	0.512856i
$700$		0			0
$701$		−	5.88318i		−	0.222205i	−0.993809	−	0.111102i	$-0.964562\pi$
$701$		−	5.88318i		−	0.222205i	0.993809	−	0.111102i	$-0.0354381\pi$
$702$		0			0
$703$	−8.20178	+	8.20178i	−0.309336	+	0.309336i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.64337	−	1.64337i	0.0618055	−	0.0618055i
$708$		0			0
$709$		−	30.4817i		−	1.14476i	−0.819987	−	0.572382i	$-0.806019\pi$
$709$		−	30.4817i		−	1.14476i	0.819987	−	0.572382i	$-0.193981\pi$
$710$		0			0
$711$	−4.46077	−	19.9407i	−0.167292	−	0.747833i
$712$		0			0
$713$	1.09815	+	1.09815i	0.0411261	+	0.0411261i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−26.1048	+	2.88420i	−0.974900	+	0.107713i
$718$		0			0
$719$	38.1170			1.42152			0.710762	−	0.703433i	$-0.248351\pi$
$719$	38.1170			1.42152			0.710762	+	0.703433i	$0.248351\pi$
$720$		0			0
$721$	3.02426			0.112629
$722$		0			0
$723$	39.3807	−	4.35100i	1.46458	−	0.161816i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−9.08333	−	9.08333i	−0.336882	−	0.336882i	0.518310	−	0.855193i	$-0.326561\pi$
$727$	−9.08333	−	9.08333i	−0.336882	−	0.336882i	−0.855193	+	0.518310i	$0.826561\pi$
$728$		0			0
$729$	21.3259	−	16.5592i	0.789847	−	0.613304i
$730$		0			0
$731$			7.98919i			0.295491i
$732$		0			0
$733$	11.6105	−	11.6105i	0.428845	−	0.428845i	−0.459390	−	0.888235i	$-0.651932\pi$
$733$	11.6105	−	11.6105i	0.428845	−	0.428845i	0.888235	+	0.459390i	$0.151932\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.92104	−	5.92104i	0.218104	−	0.218104i
$738$		0			0
$739$			4.77501i			0.175652i	0.996136	+	0.0878258i	$0.0279919\pi$
$739$			4.77501i			0.175652i	−0.996136	+	0.0878258i	$0.972008\pi$
$740$		0			0
$741$	−27.0056	−	21.6319i	−0.992075	−	0.794666i
$742$		0			0
$743$	−34.9192	−	34.9192i	−1.28106	−	1.28106i	−0.940064	−	0.340999i	$-0.889235\pi$
$743$	−34.9192	−	34.9192i	−1.28106	−	1.28106i	−0.340999	−	0.940064i	$-0.610765\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−11.4204	−	7.24493i	−0.417851	−	0.265078i
$748$		0			0
$749$	2.86239			0.104589
$750$		0			0
$751$	26.5575			0.969097			0.484548	−	0.874764i	$-0.338984\pi$
$751$	26.5575			0.969097			0.484548	+	0.874764i	$0.338984\pi$
$752$		0			0
$753$	−3.16777	−	28.6713i	−0.115440	−	1.04484i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	30.0325	+	30.0325i	1.09155	+	1.09155i	0.995363	+	0.0961876i	$0.0306649\pi$
$757$	30.0325	+	30.0325i	1.09155	+	1.09155i	0.0961876	+	0.995363i	$0.469335\pi$
$758$		0			0
$759$	−0.507686	+	0.633805i	−0.0184278	+	0.0230057i
$760$		0			0
$761$		−	10.7650i		−	0.390230i	−0.980780	−	0.195115i	$-0.937492\pi$
$761$		−	10.7650i		−	0.390230i	0.980780	−	0.195115i	$-0.0625080\pi$
$762$		0			0
$763$	−0.817287	+	0.817287i	−0.0295878	+	0.0295878i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	42.6890	−	42.6890i	1.54141	−	1.54141i
$768$		0			0
$769$		−	53.3247i		−	1.92294i	−0.274913	−	0.961469i	$-0.588649\pi$
$769$		−	53.3247i		−	1.92294i	0.274913	−	0.961469i	$-0.411351\pi$
$770$		0			0
$771$	−21.3395	+	26.6407i	−0.768524	+	0.959440i
$772$		0			0
$773$	35.5162	+	35.5162i	1.27743	+	1.27743i	0.942101	+	0.335330i	$0.108848\pi$
$773$	35.5162	+	35.5162i	1.27743	+	1.27743i	0.335330	+	0.942101i	$0.391152\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.0734723	+	0.664994i	0.00263581	+	0.0238565i
$778$		0			0
$779$	25.9063			0.928191
$780$		0			0
$781$	−13.6505			−0.488454
$782$		0			0
$783$	30.8206	−	10.5609i	1.10144	−	0.377416i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	28.0977	+	28.0977i	1.00157	+	1.00157i	0.999999	+	0.00157487i	$0.000501296\pi$
$787$	28.0977	+	28.0977i	1.00157	+	1.00157i	0.00157487	+	0.999999i	$0.499499\pi$
$788$		0			0
$789$	−18.4557	−	14.7833i	−0.657040	−	0.526298i
$790$		0			0
$791$			2.02805i			0.0721092i
$792$		0			0
$793$	6.75450	−	6.75450i	0.239859	−	0.239859i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	25.3304	−	25.3304i	0.897248	−	0.897248i	−0.0979442	−	0.995192i	$-0.531227\pi$
$797$	25.3304	−	25.3304i	0.897248	−	0.897248i	0.995192	+	0.0979442i	$0.0312267\pi$
$798$		0			0
$799$		−	15.4647i		−	0.547100i
$800$		0			0
$801$	40.2138	−	8.99592i	1.42089	−	0.317855i
$802$		0			0
$803$	6.19528	+	6.19528i	0.218627	+	0.218627i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−30.7782	+	3.40055i	−1.08344	+	0.119705i
$808$		0			0
$809$	29.2296			1.02766			0.513829	−	0.857893i	$-0.328227\pi$
$809$	29.2296			1.02766			0.513829	+	0.857893i	$0.328227\pi$
$810$		0			0
$811$	3.97765			0.139674			0.0698371	−	0.997558i	$-0.477752\pi$
$811$	3.97765			0.139674			0.0698371	+	0.997558i	$0.477752\pi$
$812$		0			0
$813$	−0.504098	+	0.0556957i	−0.0176795	+	0.00195333i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−14.8562	−	14.8562i	−0.519753	−	0.519753i
$818$		0			0
$819$	−1.94768	+	0.435699i	−0.0680573	+	0.0152246i
$820$		0			0
$821$			5.75434i			0.200828i	0.994946	+	0.100414i	$0.0320167\pi$
$821$			5.75434i			0.200828i	−0.994946	+	0.100414i	$0.967983\pi$
$822$		0			0
$823$	16.3410	−	16.3410i	0.569612	−	0.569612i	−0.362408	−	0.932020i	$-0.618045\pi$
$823$	16.3410	−	16.3410i	0.569612	−	0.569612i	0.932020	+	0.362408i	$0.118045\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.9312	+	18.9312i	−0.658302	+	0.658302i	−0.954978	−	0.296676i	$-0.904122\pi$
$827$	−18.9312	+	18.9312i	−0.658302	+	0.658302i	0.296676	+	0.954978i	$0.404122\pi$
$828$		0			0
$829$			23.0338i			0.799997i	0.916516	+	0.399999i	$0.130989\pi$
$829$			23.0338i			0.799997i	−0.916516	+	0.399999i	$0.869011\pi$
$830$		0			0
$831$	38.8429	+	31.1137i	1.34744	+	1.07932i
$832$		0			0
$833$	8.88497	+	8.88497i	0.307846	+	0.307846i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−16.4889	+	5.65004i	−0.569940	+	0.195294i
$838$		0			0
$839$	16.4801			0.568957			0.284479	−	0.958682i	$-0.408180\pi$
$839$	16.4801			0.568957			0.284479	+	0.958682i	$0.408180\pi$
$840$		0			0
$841$	10.3128			0.355613
$842$		0			0
$843$	0.761897	+	6.89589i	0.0262411	+	0.237507i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.11272	−	1.11272i	−0.0382334	−	0.0382334i
$848$		0			0
$849$	28.1256	−	35.1125i	0.965268	−	1.20506i
$850$		0			0
$851$			1.13356i			0.0388578i
$852$		0			0
$853$	1.51307	−	1.51307i	0.0518066	−	0.0518066i	−0.680729	−	0.732535i	$-0.738337\pi$
$853$	1.51307	−	1.51307i	0.0518066	−	0.0518066i	0.732535	+	0.680729i	$0.238337\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.46476	+	2.46476i	−0.0841947	+	0.0841947i	−0.747950	−	0.663755i	$-0.768962\pi$
$857$	−2.46476	+	2.46476i	−0.0841947	+	0.0841947i	0.663755	+	0.747950i	$0.268962\pi$
$858$		0			0
$859$		−	18.9804i		−	0.647601i	−0.946125	−	0.323801i	$-0.895039\pi$
$859$		−	18.9804i		−	0.647601i	0.946125	−	0.323801i	$-0.104961\pi$
$860$		0			0
$861$	0.934198	−	1.16627i	0.0318374	−	0.0397463i
$862$		0			0
$863$	18.1114	+	18.1114i	0.616518	+	0.616518i	0.944637	−	0.328118i	$-0.106415\pi$
$863$	18.1114	+	18.1114i	0.616518	+	0.616518i	−0.328118	+	0.944637i	$0.606415\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2.61630	+	23.6799i	0.0888540	+	0.804213i
$868$		0			0
$869$	−6.89752			−0.233982
$870$		0			0
$871$	34.8683			1.18147
$872$		0			0
$873$	−27.6433	−	17.5365i	−0.935585	−	0.593521i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−22.6363	−	22.6363i	−0.764375	−	0.764375i	0.212735	−	0.977110i	$-0.431763\pi$
$877$	−22.6363	−	22.6363i	−0.764375	−	0.764375i	−0.977110	+	0.212735i	$0.931763\pi$
$878$		0			0
$879$	−10.9245	−	8.75069i	−0.368475	−	0.295153i
$880$		0			0
$881$		−	19.3924i		−	0.653345i	−0.945138	−	0.326673i	$-0.894073\pi$
$881$		−	19.3924i		−	0.653345i	0.945138	−	0.326673i	$-0.105927\pi$
$882$		0			0
$883$	7.25483	−	7.25483i	0.244144	−	0.244144i	−0.574418	−	0.818562i	$-0.694772\pi$
$883$	7.25483	−	7.25483i	0.244144	−	0.244144i	0.818562	+	0.574418i	$0.194772\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	21.8434	−	21.8434i	0.733431	−	0.733431i	−0.237867	−	0.971298i	$-0.576448\pi$
$887$	21.8434	−	21.8434i	0.733431	−	0.733431i	0.971298	+	0.237867i	$0.0764482\pi$
$888$		0			0
$889$		−	1.88337i		−	0.0631662i
$890$		0			0
$891$	−3.88336	−	8.24539i	−0.130097	−	0.276231i
$892$		0			0
$893$	28.7571	+	28.7571i	0.962320	+	0.962320i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−3.36106	+	0.371349i	−0.112222	+	0.0123990i
$898$		0			0
$899$	−21.0322			−0.701462
$900$		0			0
$901$	−12.4843			−0.415912
$902$		0			0
$903$	−1.20453	+	0.133083i	−0.0400843	+	0.00442874i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	12.4881	+	12.4881i	0.414662	+	0.414662i	0.883359	−	0.468697i	$-0.155276\pi$
$907$	12.4881	+	12.4881i	0.414662	+	0.414662i	−0.468697	+	0.883359i	$0.655276\pi$
$908$		0			0
$909$	9.64785	+	43.1281i	0.319999	+	1.43047i
$910$		0			0
$911$		−	5.91275i		−	0.195898i	−0.995191	−	0.0979490i	$-0.968772\pi$
$911$		−	5.91275i		−	0.195898i	0.995191	−	0.0979490i	$-0.0312282\pi$
$912$		0			0
$913$	−3.22819	+	3.22819i	−0.106838	+	0.106838i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.624601	+	0.624601i	−0.0206261	+	0.0206261i
$918$		0			0
$919$		−	30.6407i		−	1.01074i	−0.862902	−	0.505372i	$-0.831355\pi$
$919$		−	30.6407i		−	1.01074i	0.862902	−	0.505372i	$-0.168645\pi$
$920$		0			0
$921$	−33.5186	−	26.8488i	−1.10447	−	0.884699i
$922$		0			0
$923$	−40.1932	−	40.1932i	−1.32298	−	1.32298i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−30.8065	+	48.5612i	−1.01182	+	1.59496i
$928$		0			0
$929$	40.1327			1.31671			0.658356	−	0.752707i	$-0.271252\pi$
$929$	40.1327			1.31671			0.658356	+	0.752707i	$0.271252\pi$
$930$		0			0
$931$	−33.0439			−1.08297
$932$		0			0
$933$	0.252302	+	2.28358i	0.00826001	+	0.0747609i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−35.6008	−	35.6008i	−1.16303	−	1.16303i	−0.983809	−	0.179218i	$-0.942643\pi$
$937$	−35.6008	−	35.6008i	−1.16303	−	1.16303i	−0.179218	−	0.983809i	$-0.557357\pi$
$938$		0			0
$939$	25.6404	−	32.0099i	0.836743	−	1.04460i
$940$		0			0
$941$			4.16398i			0.135742i	0.997694	+	0.0678709i	$0.0216206\pi$
$941$			4.16398i			0.135742i	−0.997694	+	0.0678709i	$0.978379\pi$
$942$		0			0
$943$	1.79024	−	1.79024i	0.0582982	−	0.0582982i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.58663	−	4.58663i	0.149046	−	0.149046i	−0.628646	−	0.777692i	$-0.716391\pi$
$947$	4.58663	−	4.58663i	0.149046	−	0.149046i	0.777692	+	0.628646i	$0.216391\pi$
$948$		0			0
$949$			36.4833i			1.18430i
$950$		0			0
$951$	−7.80268	+	9.74100i	−0.253019	+	0.315874i
$952$		0			0
$953$	3.72806	+	3.72806i	0.120764	+	0.120764i	0.764906	−	0.644142i	$-0.222786\pi$
$953$	3.72806	+	3.72806i	0.120764	+	0.120764i	−0.644142	+	0.764906i	$0.722786\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.20773	−	10.9311i	−0.0390404	−	0.353353i
$958$		0			0
$959$	2.09078			0.0675149
$960$		0			0
$961$	−19.7479			−0.637029
$962$		0			0
$963$	−29.1575	+	45.9619i	−0.939589	+	1.48110i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	36.3290	+	36.3290i	1.16826	+	1.16826i	0.982617	+	0.185646i	$0.0594379\pi$
$967$	36.3290	+	36.3290i	1.16826	+	1.16826i	0.185646	+	0.982617i	$0.440562\pi$
$968$		0			0
$969$	11.5368	+	9.24110i	0.370614	+	0.296867i
$970$		0			0
$971$		−	5.57600i		−	0.178942i	−0.995989	−	0.0894712i	$-0.971482\pi$
$971$		−	5.57600i		−	0.178942i	0.995989	−	0.0894712i	$-0.0285177\pi$
$972$		0			0
$973$	0.782793	−	0.782793i	0.0250952	−	0.0250952i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	37.4734	−	37.4734i	1.19888	−	1.19888i	0.224376	−	0.974503i	$-0.427965\pi$
$977$	37.4734	−	37.4734i	1.19888	−	1.19888i	0.974503	−	0.224376i	$-0.0720345\pi$
$978$		0			0
$979$		−	13.9101i		−	0.444568i
$980$		0			0
$981$	−4.79810	−	21.4486i	−0.153191	−	0.684801i
$982$		0			0
$983$	−3.11736	−	3.11736i	−0.0994284	−	0.0994284i	0.655643	−	0.755071i	$-0.272398\pi$
$983$	−3.11736	−	3.11736i	−0.0994284	−	0.0994284i	−0.755071	+	0.655643i	$0.772398\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.33161	−	0.257609i	0.0742159	−	0.00819979i
$988$		0			0
$989$	−2.05326			−0.0652897
$990$		0			0
$991$	19.5731			0.621759			0.310880	−	0.950449i	$-0.399376\pi$
$991$	19.5731			0.621759			0.310880	+	0.950449i	$0.399376\pi$
$992$		0			0
$993$	−38.0345	+	4.20226i	−1.20699	+	0.133355i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	24.5349	+	24.5349i	0.777029	+	0.777029i	0.979324	−	0.202296i	$-0.0648402\pi$
$997$	24.5349	+	24.5349i	0.777029	+	0.777029i	−0.202296	+	0.979324i	$0.564840\pi$
$998$		0			0
$999$	−11.4264	−	5.59416i	−0.361514	−	0.176991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.i.a.557.16	yes	32
3.2	odd	2	inner	1500.2.i.a.557.9	yes	32
5.2	odd	4	inner	1500.2.i.a.1193.8	yes	32
5.3	odd	4	inner	1500.2.i.a.1193.9	yes	32
5.4	even	2	inner	1500.2.i.a.557.1	✓	32
15.2	even	4	inner	1500.2.i.a.1193.1	yes	32
15.8	even	4	inner	1500.2.i.a.1193.16	yes	32
15.14	odd	2	inner	1500.2.i.a.557.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1500.2.i.a.557.1	✓	32	5.4	even	2	inner
1500.2.i.a.557.8	yes	32	15.14	odd	2	inner
1500.2.i.a.557.9	yes	32	3.2	odd	2	inner
1500.2.i.a.557.16	yes	32	1.1	even	1	trivial
1500.2.i.a.1193.1	yes	32	15.2	even	4	inner
1500.2.i.a.1193.8	yes	32	5.2	odd	4	inner
1500.2.i.a.1193.9	yes	32	5.3	odd	4	inner
1500.2.i.a.1193.16	yes	32	15.8	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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72157 - 0.190209i) q^{3} +(-0.111556 - 0.111556i) q^{7} +(2.92764 - 0.654920i) q^{9} +O(q^{10})\)	\(q+(1.72157 - 0.190209i) q^{3} +(-0.111556 - 0.111556i) q^{7} +(2.92764 - 0.654920i) q^{9} -1.01268i q^{11} +(2.98178 - 2.98178i) q^{13} +(-1.27381 + 1.27381i) q^{17} -4.73740i q^{19} +(-0.213271 - 0.170833i) q^{21} +(-0.327375 - 0.327375i) q^{23} +(4.91558 - 1.68436i) q^{27} +6.26999 q^{29} -3.35442 q^{31} +(-0.192621 - 1.74340i) q^{33} +(-1.73128 - 1.73128i) q^{37} +(4.56619 - 5.70051i) q^{39} +5.46847i q^{41} +(3.13594 - 3.13594i) q^{43} +(-6.07024 + 6.07024i) q^{47} -6.97511i q^{49} +(-1.95067 + 2.43525i) q^{51} +(4.90038 + 4.90038i) q^{53} +(-0.901098 - 8.15579i) q^{57} +14.3166 q^{59} +2.26526 q^{61} +(-0.399657 - 0.253536i) q^{63} +(5.84691 + 5.84691i) q^{67} +(-0.625870 - 0.501330i) q^{69} -13.4796i q^{71} +(-6.11772 + 6.11772i) q^{73} +(-0.112971 + 0.112971i) q^{77} -6.81117i q^{79} +(8.14216 - 3.83474i) q^{81} +(-3.18778 - 3.18778i) q^{83} +(10.7943 - 1.19261i) q^{87} +13.7359 q^{89} -0.665271 q^{91} +(-5.77488 + 0.638042i) q^{93} +(-7.71608 - 7.71608i) q^{97} +(-0.663223 - 2.96476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 12 q^{21} - 32 q^{31} + 100 q^{51} + 48 q^{61} + 52 q^{81} + 232 q^{91}+O(q^{100}) \) 32 * q - 12 * q^21 - 32 * q^31 + 100 * q^51 + 48 * q^61 + 52 * q^81 + 232 * q^91

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