LMFDB - Embedded newform 980.2.m.b.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(97,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("980.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.m (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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.7
Character	$\chi$	$=$	980.97
Dual form			980.2.m.b.293.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395749 + 0.395749i) q^{3} +(-0.677040 + 2.13111i) q^{5} -2.68677i q^{9} -4.99721 q^{11} +(-0.796463 - 0.796463i) q^{13} +(-1.11132 + 0.575445i) q^{15} +(-3.90618 + 3.90618i) q^{17} +2.20585 q^{19} +(-5.18498 + 5.18498i) q^{23} +(-4.08323 - 2.88569i) q^{25} +(2.25053 - 2.25053i) q^{27} +2.10975i q^{29} +4.03440i q^{31} +(-1.97764 - 1.97764i) q^{33} +(-6.75885 - 6.75885i) q^{37} -0.630399i q^{39} -9.32264i q^{41} +(3.09875 - 3.09875i) q^{43} +(5.72579 + 1.81905i) q^{45} +(-2.13508 + 2.13508i) q^{47} -3.09173 q^{51} +(-2.55035 + 2.55035i) q^{53} +(3.38331 - 10.6496i) q^{55} +(0.872963 + 0.872963i) q^{57} -9.47353 q^{59} +1.73263i q^{61} +(2.23659 - 1.15811i) q^{65} +(-7.46291 - 7.46291i) q^{67} -4.10390 q^{69} -2.88392 q^{71} +(7.64924 + 7.64924i) q^{73} +(-0.473927 - 2.75794i) q^{75} +3.83408i q^{79} -6.27901 q^{81} +(11.9932 + 11.9932i) q^{83} +(-5.67984 - 10.9691i) q^{85} +(-0.834929 + 0.834929i) q^{87} -3.63809 q^{89} +(-1.59661 + 1.59661i) q^{93} +(-1.49345 + 4.70091i) q^{95} +(-8.67691 + 8.67691i) q^{97} +13.4263i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{11} - 48 q^{23} + 32 q^{25} - 32 q^{37} + 16 q^{43} + 48 q^{51} - 24 q^{53} + 64 q^{65} - 32 q^{67} + 8 q^{81} - 64 q^{85} - 96 q^{93} + 64 q^{95}+O(q^{100}) $ 24 * q + 16 * q^11 - 48 * q^23 + 32 * q^25 - 32 * q^37 + 16 * q^43 + 48 * q^51 - 24 * q^53 + 64 * q^65 - 32 * q^67 + 8 * q^81 - 64 * q^85 - 96 * q^93 + 64 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.395749	+	0.395749i	0.228486	+	0.228486i	0.812060	−	0.583574i	$-0.198346\pi$
$3$	0.395749	+	0.395749i	0.228486	+	0.228486i	−0.583574	+	0.812060i	$0.698346\pi$
$4$		0			0
$5$	−0.677040	+	2.13111i	−0.302781	+	0.953060i
$5$	−0.677040	+	2.13111i	−0.302781	+	0.953060i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		−	2.68677i		−	0.895589i
$10$		0			0
$11$	−4.99721			−1.50671			−0.753357	−	0.657612i	$-0.771567\pi$
$11$	−4.99721			−1.50671			−0.753357	+	0.657612i	$0.771567\pi$
$12$		0			0
$13$	−0.796463	−	0.796463i	−0.220899	−	0.220899i	0.587978	−	0.808877i	$-0.299924\pi$
$13$	−0.796463	−	0.796463i	−0.220899	−	0.220899i	−0.808877	+	0.587978i	$0.799924\pi$
$14$		0			0
$15$	−1.11132	+	0.575445i	−0.286942	+	0.148579i
$16$		0			0
$17$	−3.90618	+	3.90618i	−0.947387	+	0.947387i	−0.998683	−	0.0512963i	$-0.983665\pi$
$17$	−3.90618	+	3.90618i	−0.947387	+	0.947387i	0.0512963	+	0.998683i	$0.483665\pi$
$18$		0			0
$19$	2.20585			0.506057			0.253029	−	0.967459i	$-0.418573\pi$
$19$	2.20585			0.506057			0.253029	+	0.967459i	$0.418573\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.18498	+	5.18498i	−1.08114	+	1.08114i	−0.0847395	+	0.996403i	$0.527006\pi$
$23$	−5.18498	+	5.18498i	−1.08114	+	1.08114i	−0.996403	+	0.0847395i	$0.972994\pi$
$24$		0			0
$25$	−4.08323	−	2.88569i	−0.816647	−	0.577138i
$26$		0			0
$27$	2.25053	−	2.25053i	0.433115	−	0.433115i
$28$		0			0
$29$			2.10975i			0.391770i	0.980627	+	0.195885i	$0.0627579\pi$
$29$			2.10975i			0.391770i	−0.980627	+	0.195885i	$0.937242\pi$
$30$		0			0
$31$			4.03440i			0.724600i	0.932061	+	0.362300i	$0.118008\pi$
$31$			4.03440i			0.724600i	−0.932061	+	0.362300i	$0.881992\pi$
$32$		0			0
$33$	−1.97764	−	1.97764i	−0.344263	−	0.344263i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.75885	−	6.75885i	−1.11115	−	1.11115i	−0.992995	−	0.118152i	$-0.962303\pi$
$37$	−6.75885	−	6.75885i	−1.11115	−	1.11115i	−0.118152	−	0.992995i	$-0.537697\pi$
$38$		0			0
$39$		−	0.630399i		−	0.100945i
$40$		0			0
$41$		−	9.32264i		−	1.45595i	−0.685603	−	0.727976i	$-0.740461\pi$
$41$		−	9.32264i		−	1.45595i	0.685603	−	0.727976i	$-0.259539\pi$
$42$		0			0
$43$	3.09875	−	3.09875i	0.472555	−	0.472555i	−0.430185	−	0.902741i	$-0.641552\pi$
$43$	3.09875	−	3.09875i	0.472555	−	0.472555i	0.902741	+	0.430185i	$0.141552\pi$
$44$		0			0
$45$	5.72579	+	1.81905i	0.853550	+	0.271168i
$46$		0			0
$47$	−2.13508	+	2.13508i	−0.311434	+	0.311434i	−0.845465	−	0.534031i	$-0.820677\pi$
$47$	−2.13508	+	2.13508i	−0.311434	+	0.311434i	0.534031	+	0.845465i	$0.320677\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.09173			−0.432929
$52$		0			0
$53$	−2.55035	+	2.55035i	−0.350317	+	0.350317i	−0.860228	−	0.509910i	$-0.829679\pi$
$53$	−2.55035	+	2.55035i	−0.350317	+	0.350317i	0.509910	+	0.860228i	$0.329679\pi$
$54$		0			0
$55$	3.38331	−	10.6496i	0.456205	−	1.43599i
$56$		0			0
$57$	0.872963	+	0.872963i	0.115627	+	0.115627i
$58$		0			0
$59$	−9.47353			−1.23335			−0.616674	−	0.787218i	$-0.711520\pi$
$59$	−9.47353			−1.23335			−0.616674	+	0.787218i	$0.711520\pi$
$60$		0			0
$61$			1.73263i			0.221840i	0.993829	+	0.110920i	$0.0353797\pi$
$61$			1.73263i			0.221840i	−0.993829	+	0.110920i	$0.964620\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.23659	−	1.15811i	0.277414	−	0.143646i
$66$		0			0
$67$	−7.46291	−	7.46291i	−0.911739	−	0.911739i	0.0846700	−	0.996409i	$-0.473016\pi$
$67$	−7.46291	−	7.46291i	−0.911739	−	0.911739i	−0.996409	+	0.0846700i	$0.973016\pi$
$68$		0			0
$69$	−4.10390			−0.494051
$70$		0			0
$71$	−2.88392			−0.342258			−0.171129	−	0.985249i	$-0.554741\pi$
$71$	−2.88392			−0.342258			−0.171129	+	0.985249i	$0.554741\pi$
$72$		0			0
$73$	7.64924	+	7.64924i	0.895276	+	0.895276i	0.995014	−	0.0997378i	$-0.0318004\pi$
$73$	7.64924	+	7.64924i	0.895276	+	0.895276i	−0.0997378	+	0.995014i	$0.531800\pi$
$74$		0			0
$75$	−0.473927	−	2.75794i	−0.0547244	−	0.318460i
$76$		0			0
$77$		0			0
$78$		0			0
$79$			3.83408i			0.431368i	0.976463	+	0.215684i	$0.0691981\pi$
$79$			3.83408i			0.431368i	−0.976463	+	0.215684i	$0.930802\pi$
$80$		0			0
$81$	−6.27901			−0.697668
$82$		0			0
$83$	11.9932	+	11.9932i	1.31642	+	1.31642i	0.916588	+	0.399834i	$0.130932\pi$
$83$	11.9932	+	11.9932i	1.31642	+	1.31642i	0.399834	+	0.916588i	$0.369068\pi$
$84$		0			0
$85$	−5.67984	−	10.9691i	−0.616066	−	1.18977i
$86$		0			0
$87$	−0.834929	+	0.834929i	−0.0895138	+	0.0895138i
$88$		0			0
$89$	−3.63809			−0.385637			−0.192819	−	0.981234i	$-0.561763\pi$
$89$	−3.63809			−0.385637			−0.192819	+	0.981234i	$0.561763\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.59661	+	1.59661i	−0.165561	+	0.165561i
$94$		0			0
$95$	−1.49345	+	4.70091i	−0.153225	+	0.482303i
$96$		0			0
$97$	−8.67691	+	8.67691i	−0.881007	+	0.881007i	−0.993637	−	0.112630i	$-0.964072\pi$
$97$	−8.67691	+	8.67691i	−0.881007	+	0.881007i	0.112630	+	0.993637i	$0.464072\pi$
$98$		0			0
$99$			13.4263i			1.34940i
$100$		0			0
$101$		−	1.96701i		−	0.195724i	−0.995200	−	0.0978622i	$-0.968800\pi$
$101$		−	1.96701i		−	0.195724i	0.995200	−	0.0978622i	$-0.0312004\pi$
$102$		0			0
$103$	12.7499	+	12.7499i	1.25629	+	1.25629i	0.952852	+	0.303435i	$0.0981334\pi$
$103$	12.7499	+	12.7499i	1.25629	+	1.25629i	0.303435	+	0.952852i	$0.401867\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.36258	+	1.36258i	0.131725	+	0.131725i	0.769895	−	0.638170i	$-0.220308\pi$
$107$	1.36258	+	1.36258i	0.131725	+	0.131725i	−0.638170	+	0.769895i	$0.720308\pi$
$108$		0			0
$109$		−	1.00319i		−	0.0960880i	−0.998845	−	0.0480440i	$-0.984701\pi$
$109$		−	1.00319i		−	0.0960880i	0.998845	−	0.0480440i	$-0.0152988\pi$
$110$		0			0
$111$		−	5.34961i		−	0.507763i
$112$		0			0
$113$	5.97014	−	5.97014i	0.561624	−	0.561624i	−0.368145	−	0.929768i	$-0.620007\pi$
$113$	5.97014	−	5.97014i	0.561624	−	0.561624i	0.929768	+	0.368145i	$0.120007\pi$
$114$		0			0
$115$	−7.53931	−	14.5602i	−0.703044	−	1.35774i
$116$		0			0
$117$	−2.13991	+	2.13991i	−0.197835	+	0.197835i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	13.9721			1.27019
$122$		0			0
$123$	3.68942	−	3.68942i	0.332664	−	0.332664i
$124$		0			0
$125$	8.91422	−	6.74808i	0.797312	−	0.603567i
$126$		0			0
$127$	10.0097	+	10.0097i	0.888220	+	0.888220i	0.994352	−	0.106132i	$-0.0338465\pi$
$127$	10.0097	+	10.0097i	0.888220	+	0.888220i	−0.106132	+	0.994352i	$0.533847\pi$
$128$		0			0
$129$	2.45266			0.215944
$130$		0			0
$131$		−	4.19185i		−	0.366244i	−0.983090	−	0.183122i	$-0.941380\pi$
$131$		−	4.19185i		−	0.366244i	0.983090	−	0.183122i	$-0.0586203\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	3.27242	+	6.31982i	0.281645	+	0.543923i
$136$		0			0
$137$	9.57846	+	9.57846i	0.818343	+	0.818343i	0.985868	−	0.167525i	$-0.0535775\pi$
$137$	9.57846	+	9.57846i	0.818343	+	0.818343i	−0.167525	+	0.985868i	$0.553578\pi$
$138$		0			0
$139$	−17.9770			−1.52479			−0.762393	−	0.647114i	$-0.775976\pi$
$139$	−17.9770			−1.52479			−0.762393	+	0.647114i	$0.775976\pi$
$140$		0			0
$141$	−1.68991			−0.142316
$142$		0			0
$143$	3.98009	+	3.98009i	0.332832	+	0.332832i
$144$		0			0
$145$	−4.49610	−	1.42838i	−0.373380	−	0.118621i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	21.0256i		−	1.72249i	−0.508192	−	0.861244i	$-0.669686\pi$
$149$		−	21.0256i		−	1.72249i	0.508192	−	0.861244i	$-0.330314\pi$
$150$		0			0
$151$	18.3554			1.49374			0.746869	−	0.664971i	$-0.231556\pi$
$151$	18.3554			1.49374			0.746869	+	0.664971i	$0.231556\pi$
$152$		0			0
$153$	10.4950	+	10.4950i	0.848469	+	0.848469i
$154$		0			0
$155$	−8.59775	−	2.73145i	−0.690588	−	0.219396i
$156$		0			0
$157$	1.56986	−	1.56986i	0.125288	−	0.125288i	−0.641682	−	0.766970i	$-0.721763\pi$
$157$	1.56986	−	1.56986i	0.125288	−	0.125288i	0.766970	+	0.641682i	$0.221763\pi$
$158$		0			0
$159$	−2.01860			−0.160085
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.9078	+	10.9078i	−0.854367	+	0.854367i	−0.990668	−	0.136300i	$-0.956479\pi$
$163$	−10.9078	+	10.9078i	−0.854367	+	0.854367i	0.136300	+	0.990668i	$0.456479\pi$
$164$		0			0
$165$	5.55350	−	2.87562i	0.432339	−	0.223867i
$166$		0			0
$167$	−13.8034	+	13.8034i	−1.06814	+	1.06814i	−0.0706395	+	0.997502i	$0.522504\pi$
$167$	−13.8034	+	13.8034i	−1.06814	+	1.06814i	−0.997502	+	0.0706395i	$0.977496\pi$
$168$		0			0
$169$		−	11.7313i		−	0.902407i
$170$		0			0
$171$		−	5.92661i		−	0.453219i
$172$		0			0
$173$	−16.1755	−	16.1755i	−1.22980	−	1.22980i	−0.964039	−	0.265759i	$-0.914377\pi$
$173$	−16.1755	−	16.1755i	−1.22980	−	1.22980i	−0.265759	−	0.964039i	$-0.585623\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.74914	−	3.74914i	−0.281802	−	0.281802i
$178$		0			0
$179$			14.1759i			1.05955i	0.848137	+	0.529777i	$0.177724\pi$
$179$			14.1759i			1.05955i	−0.848137	+	0.529777i	$0.822276\pi$
$180$		0			0
$181$			6.24223i			0.463981i	0.972718	+	0.231991i	$0.0745239\pi$
$181$			6.24223i			0.463981i	−0.972718	+	0.231991i	$0.925476\pi$
$182$		0			0
$183$	−0.685685	+	0.685685i	−0.0506873	+	0.0506873i
$184$		0			0
$185$	18.9798	−	9.82782i	1.39543	−	0.722556i
$186$		0			0
$187$	19.5200	−	19.5200i	1.42744	−	1.42744i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.5432			0.907593			0.453797	−	0.891105i	$-0.350069\pi$
$191$	12.5432			0.907593			0.453797	+	0.891105i	$0.350069\pi$
$192$		0			0
$193$	14.7971	−	14.7971i	1.06512	−	1.06512i	0.0673890	−	0.997727i	$-0.478533\pi$
$193$	14.7971	−	14.7971i	1.06512	−	1.06512i	0.997727	−	0.0673890i	$-0.0214669\pi$
$194$		0			0
$195$	1.34345	+	0.426805i	0.0962062	+	0.0305641i
$196$		0			0
$197$	1.81646	+	1.81646i	0.129417	+	0.129417i	0.768848	−	0.639431i	$-0.220830\pi$
$197$	1.81646	+	1.81646i	0.129417	+	0.129417i	−0.639431	+	0.768848i	$0.720830\pi$
$198$		0			0
$199$	−20.1267			−1.42675			−0.713373	−	0.700784i	$-0.752834\pi$
$199$	−20.1267			−1.42675			−0.713373	+	0.700784i	$0.752834\pi$
$200$		0			0
$201$		−	5.90687i		−	0.416639i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	19.8675	+	6.31180i	1.38761	+	0.440835i
$206$		0			0
$207$	13.9308	+	13.9308i	0.968259	+	0.968259i
$208$		0			0
$209$	−11.0231			−0.762484
$210$		0			0
$211$	−16.2260			−1.11705			−0.558523	−	0.829489i	$-0.688632\pi$
$211$	−16.2260			−1.11705			−0.558523	+	0.829489i	$0.688632\pi$
$212$		0			0
$213$	−1.14131	−	1.14131i	−0.0782010	−	0.0782010i
$214$		0			0
$215$	4.50580	+	8.70175i	0.307293	+	0.593455i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			6.05436i			0.409115i
$220$		0			0
$221$	6.22225			0.418554
$222$		0			0
$223$	7.64230	+	7.64230i	0.511766	+	0.511766i	0.915067	−	0.403301i	$-0.132137\pi$
$223$	7.64230	+	7.64230i	0.511766	+	0.511766i	−0.403301	+	0.915067i	$0.632137\pi$
$224$		0			0
$225$	−7.75317	+	10.9707i	−0.516878	+	0.731380i
$226$		0			0
$227$	−0.222004	+	0.222004i	−0.0147349	+	0.0147349i	−0.714436	−	0.699701i	$-0.753317\pi$
$227$	−0.222004	+	0.222004i	−0.0147349	+	0.0147349i	0.699701	+	0.714436i	$0.253317\pi$
$228$		0			0
$229$	16.9987			1.12330			0.561652	−	0.827374i	$-0.310166\pi$
$229$	16.9987			1.12330			0.561652	+	0.827374i	$0.310166\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.12070	+	4.12070i	−0.269956	+	0.269956i	−0.829082	−	0.559126i	$-0.811137\pi$
$233$	−4.12070	+	4.12070i	−0.269956	+	0.269956i	0.559126	+	0.829082i	$0.311137\pi$
$234$		0			0
$235$	−3.10456	−	5.99563i	−0.202519	−	0.391112i
$236$		0			0
$237$	−1.51733	+	1.51733i	−0.0985614	+	0.0985614i
$238$		0			0
$239$			23.7873i			1.53867i	0.638844	+	0.769337i	$0.279413\pi$
$239$			23.7873i			1.53867i	−0.638844	+	0.769337i	$0.720587\pi$
$240$		0			0
$241$		−	27.8142i		−	1.79167i	−0.444386	−	0.895835i	$-0.646578\pi$
$241$		−	27.8142i		−	1.79167i	0.444386	−	0.895835i	$-0.353422\pi$
$242$		0			0
$243$	−9.23650	−	9.23650i	−0.592522	−	0.592522i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.75688	−	1.75688i	−0.111788	−	0.111788i
$248$		0			0
$249$			9.49256i			0.601567i
$250$		0			0
$251$			10.1517i			0.640772i	0.947287	+	0.320386i	$0.103813\pi$
$251$			10.1517i			0.640772i	−0.947287	+	0.320386i	$0.896187\pi$
$252$		0			0
$253$	25.9104	−	25.9104i	1.62897	−	1.62897i
$254$		0			0
$255$	2.09322	−	6.58881i	0.131083	−	0.412607i
$256$		0			0
$257$	−15.5762	+	15.5762i	−0.971615	+	0.971615i	−0.999608	−	0.0279932i	$-0.991088\pi$
$257$	−15.5762	+	15.5762i	−0.971615	+	0.971615i	0.0279932	+	0.999608i	$0.491088\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.66839			0.350865
$262$		0			0
$263$	10.1848	−	10.1848i	0.628024	−	0.628024i	−0.319546	−	0.947571i	$-0.603531\pi$
$263$	10.1848	−	10.1848i	0.628024	−	0.628024i	0.947571	+	0.319546i	$0.103531\pi$
$264$		0			0
$265$	−3.70838	−	7.16176i	−0.227804	−	0.439943i
$266$		0			0
$267$	−1.43977	−	1.43977i	−0.0881126	−	0.0881126i
$268$		0			0
$269$	12.2530			0.747078			0.373539	−	0.927615i	$-0.378144\pi$
$269$	12.2530			0.747078			0.373539	+	0.927615i	$0.378144\pi$
$270$		0			0
$271$			21.0736i			1.28013i	0.768320	+	0.640066i	$0.221093\pi$
$271$			21.0736i			1.28013i	−0.768320	+	0.640066i	$0.778907\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	20.4048	+	14.4204i	1.23045	+	0.869582i
$276$		0			0
$277$	12.0501	+	12.0501i	0.724018	+	0.724018i	0.969421	−	0.245404i	$-0.0789205\pi$
$277$	12.0501	+	12.0501i	0.724018	+	0.724018i	−0.245404	+	0.969421i	$0.578920\pi$
$278$		0			0
$279$	10.8395			0.648944
$280$		0			0
$281$	5.27669			0.314781			0.157390	−	0.987536i	$-0.449692\pi$
$281$	5.27669			0.314781			0.157390	+	0.987536i	$0.449692\pi$
$282$		0			0
$283$	8.22426	+	8.22426i	0.488882	+	0.488882i	0.907953	−	0.419072i	$-0.137644\pi$
$283$	8.22426	+	8.22426i	0.488882	+	0.488882i	−0.419072	+	0.907953i	$0.637644\pi$
$284$		0			0
$285$	−2.45141	+	1.26935i	−0.145209	+	0.0751896i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		−	13.5164i		−	0.795085i
$290$		0			0
$291$	−6.86775			−0.402595
$292$		0			0
$293$	11.9914	+	11.9914i	0.700547	+	0.700547i	0.964528	−	0.263981i	$-0.0850357\pi$
$293$	11.9914	+	11.9914i	0.700547	+	0.700547i	−0.263981	+	0.964528i	$0.585036\pi$
$294$		0			0
$295$	6.41396	−	20.1891i	0.373435	−	1.17546i
$296$		0			0
$297$	−11.2464	+	11.2464i	−0.652580	+	0.652580i
$298$		0			0
$299$	8.25929			0.477647
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.778440	−	0.778440i	0.0447202	−	0.0447202i
$304$		0			0
$305$	−3.69241	−	1.17306i	−0.211427	−	0.0671690i
$306$		0			0
$307$	−11.2784	+	11.2784i	−0.643691	+	0.643691i	−0.951461	−	0.307770i	$-0.900417\pi$
$307$	−11.2784	+	11.2784i	−0.643691	+	0.643691i	0.307770	+	0.951461i	$0.400417\pi$
$308$		0			0
$309$			10.0915i			0.574087i
$310$		0			0
$311$		−	17.6641i		−	1.00164i	−0.865551	−	0.500821i	$-0.833032\pi$
$311$		−	17.6641i		−	1.00164i	0.865551	−	0.500821i	$-0.166968\pi$
$312$		0			0
$313$	3.71255	+	3.71255i	0.209846	+	0.209846i	0.804202	−	0.594356i	$-0.202593\pi$
$313$	3.71255	+	3.71255i	0.209846	+	0.209846i	−0.594356	+	0.804202i	$0.702593\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.66271	+	5.66271i	0.318050	+	0.318050i	0.848018	−	0.529968i	$-0.177796\pi$
$317$	5.66271	+	5.66271i	0.318050	+	0.318050i	−0.529968	+	0.848018i	$0.677796\pi$
$318$		0			0
$319$		−	10.5428i		−	0.590286i
$320$		0			0
$321$			1.07848i			0.0601947i
$322$		0			0
$323$	−8.61645	+	8.61645i	−0.479432	+	0.479432i
$324$		0			0
$325$	0.953801	+	5.55049i	0.0529074	+	0.307886i
$326$		0			0
$327$	0.397010	−	0.397010i	0.0219547	−	0.0219547i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.20974			0.121458			0.0607292	−	0.998154i	$-0.480657\pi$
$331$	2.20974			0.121458			0.0607292	+	0.998154i	$0.480657\pi$
$332$		0			0
$333$	−18.1594	+	18.1594i	−0.995131	+	0.995131i
$334$		0			0
$335$	20.9569	−	10.8516i	1.14500	−	0.592884i
$336$		0			0
$337$	−13.9395	−	13.9395i	−0.759331	−	0.759331i	0.216870	−	0.976201i	$-0.430415\pi$
$337$	−13.9395	−	13.9395i	−0.759331	−	0.759331i	−0.976201	+	0.216870i	$0.930415\pi$
$338$		0			0
$339$	4.72535			0.256646
$340$		0			0
$341$		−	20.1608i		−	1.09177i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.77850	−	8.74584i	0.149590	−	0.470860i
$346$		0			0
$347$	−12.5707	−	12.5707i	−0.674833	−	0.674833i	0.283993	−	0.958826i	$-0.408341\pi$
$347$	−12.5707	−	12.5707i	−0.674833	−	0.674833i	−0.958826	+	0.283993i	$0.908341\pi$
$348$		0			0
$349$	−34.5979			−1.85198			−0.925992	−	0.377544i	$-0.876769\pi$
$349$	−34.5979			−1.85198			−0.925992	+	0.377544i	$0.876769\pi$
$350$		0			0
$351$	−3.58493			−0.191349
$352$		0			0
$353$	9.05779	+	9.05779i	0.482098	+	0.482098i	0.905801	−	0.423703i	$-0.139270\pi$
$353$	9.05779	+	9.05779i	0.482098	+	0.482098i	−0.423703	+	0.905801i	$0.639270\pi$
$354$		0			0
$355$	1.95253	−	6.14594i	0.103629	−	0.326192i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	5.80249i		−	0.306244i	−0.988207	−	0.153122i	$-0.951067\pi$
$359$		−	5.80249i		−	0.306244i	0.988207	−	0.153122i	$-0.0489327\pi$
$360$		0			0
$361$	−14.1342			−0.743906
$362$		0			0
$363$	5.52943	+	5.52943i	0.290220	+	0.290220i
$364$		0			0
$365$	−21.4802	+	11.1225i	−1.12432	+	0.582179i
$366$		0			0
$367$	−0.810316	+	0.810316i	−0.0422982	+	0.0422982i	−0.727940	−	0.685641i	$-0.759522\pi$
$367$	−0.810316	+	0.810316i	−0.0422982	+	0.0422982i	0.685641	+	0.727940i	$0.259522\pi$
$368$		0			0
$369$	−25.0477			−1.30393
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.87296	+	1.87296i	−0.0969784	+	0.0969784i	−0.753931	−	0.656953i	$-0.771845\pi$
$373$	−1.87296	+	1.87296i	−0.0969784	+	0.0969784i	0.656953	+	0.753931i	$0.271845\pi$
$374$		0			0
$375$	6.19834	+	0.857247i	0.320081	+	0.0442681i
$376$		0			0
$377$	1.68034	−	1.68034i	0.0865417	−	0.0865417i
$378$		0			0
$379$		−	23.1300i		−	1.18811i	−0.804426	−	0.594053i	$-0.797527\pi$
$379$		−	23.1300i		−	1.18811i	0.804426	−	0.594053i	$-0.202473\pi$
$380$		0			0
$381$			7.92268i			0.405891i
$382$		0			0
$383$	6.24026	+	6.24026i	0.318862	+	0.318862i	0.848330	−	0.529468i	$-0.177608\pi$
$383$	6.24026	+	6.24026i	0.318862	+	0.318862i	−0.529468	+	0.848330i	$0.677608\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.32562	−	8.32562i	−0.423215	−	0.423215i
$388$		0			0
$389$		−	10.5299i		−	0.533887i	−0.963712	−	0.266943i	$-0.913986\pi$
$389$		−	10.5299i		−	0.533887i	0.963712	−	0.266943i	$-0.0860137\pi$
$390$		0			0
$391$		−	40.5069i		−	2.04852i
$392$		0			0
$393$	1.65892	−	1.65892i	0.0836814	−	0.0836814i
$394$		0			0
$395$	−8.17084	−	2.59583i	−0.411119	−	0.130610i
$396$		0			0
$397$	3.28192	−	3.28192i	0.164715	−	0.164715i	−0.619937	−	0.784652i	$-0.712842\pi$
$397$	3.28192	−	3.28192i	0.164715	−	0.164715i	0.784652	+	0.619937i	$0.212842\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−33.9036			−1.69306			−0.846532	−	0.532338i	$-0.821314\pi$
$401$	−33.9036			−1.69306			−0.846532	+	0.532338i	$0.821314\pi$
$402$		0			0
$403$	3.21325	−	3.21325i	0.160064	−	0.160064i
$404$		0			0
$405$	4.25114	−	13.3812i	0.211241	−	0.664919i
$406$		0			0
$407$	33.7754	+	33.7754i	1.67418	+	1.67418i
$408$		0			0
$409$	−19.5864			−0.968485			−0.484243	−	0.874934i	$-0.660905\pi$
$409$	−19.5864			−0.968485			−0.484243	+	0.874934i	$0.660905\pi$
$410$		0			0
$411$			7.58132i			0.373959i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−33.6786	+	17.4389i	−1.65322	+	0.856041i
$416$		0			0
$417$	−7.11436	−	7.11436i	−0.348392	−	0.348392i
$418$		0			0
$419$	16.1121			0.787126			0.393563	−	0.919298i	$-0.371242\pi$
$419$	16.1121			0.787126			0.393563	+	0.919298i	$0.371242\pi$
$420$		0			0
$421$	8.54870			0.416638			0.208319	−	0.978061i	$-0.433201\pi$
$421$	8.54870			0.416638			0.208319	+	0.978061i	$0.433201\pi$
$422$		0			0
$423$	5.73647	+	5.73647i	0.278917	+	0.278917i
$424$		0			0
$425$	27.2218	−	4.67783i	1.32045	−	0.226908i
$426$		0			0
$427$		0			0
$428$		0			0
$429$			3.15023i			0.152095i
$430$		0			0
$431$	8.88314			0.427886			0.213943	−	0.976846i	$-0.431369\pi$
$431$	8.88314			0.427886			0.213943	+	0.976846i	$0.431369\pi$
$432$		0			0
$433$	2.78047	+	2.78047i	0.133621	+	0.133621i	0.770754	−	0.637133i	$-0.219880\pi$
$433$	2.78047	+	2.78047i	0.133621	+	0.133621i	−0.637133	+	0.770754i	$0.719880\pi$
$434$		0			0
$435$	−1.21404	−	2.34460i	−0.0582089	−	0.112415i
$436$		0			0
$437$	−11.4373	+	11.4373i	−0.547120	+	0.547120i
$438$		0			0
$439$	−17.2101			−0.821393			−0.410696	−	0.911772i	$-0.634714\pi$
$439$	−17.2101			−0.821393			−0.410696	+	0.911772i	$0.634714\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.75852	+	8.75852i	−0.416130	+	0.416130i	−0.883867	−	0.467738i	$-0.845069\pi$
$443$	−8.75852	+	8.75852i	−0.416130	+	0.416130i	0.467738	+	0.883867i	$0.345069\pi$
$444$		0			0
$445$	2.46314	−	7.75317i	0.116764	−	0.367535i
$446$		0			0
$447$	8.32087	−	8.32087i	0.393564	−	0.393564i
$448$		0			0
$449$			17.7855i			0.839347i	0.907675	+	0.419674i	$0.137855\pi$
$449$			17.7855i			0.839347i	−0.907675	+	0.419674i	$0.862145\pi$
$450$		0			0
$451$			46.5871i			2.19370i
$452$		0			0
$453$	7.26411	+	7.26411i	0.341298	+	0.341298i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.09360	+	2.09360i	0.0979346	+	0.0979346i	0.754377	−	0.656442i	$-0.227939\pi$
$457$	2.09360	+	2.09360i	0.0979346	+	0.0979346i	−0.656442	+	0.754377i	$0.727939\pi$
$458$		0			0
$459$			17.5819i			0.820655i
$460$		0			0
$461$		−	19.7304i		−	0.918938i	−0.888194	−	0.459469i	$-0.848040\pi$
$461$		−	19.7304i		−	0.918938i	0.888194	−	0.459469i	$-0.151960\pi$
$462$		0			0
$463$	15.7963	−	15.7963i	0.734115	−	0.734115i	−0.237317	−	0.971432i	$-0.576268\pi$
$463$	15.7963	−	15.7963i	0.734115	−	0.734115i	0.971432	+	0.237317i	$0.0762680\pi$
$464$		0			0
$465$	−2.32158	−	4.48352i	−0.107661	−	0.207918i
$466$		0			0
$467$	2.02017	−	2.02017i	0.0934822	−	0.0934822i	−0.658819	−	0.752301i	$-0.728944\pi$
$467$	2.02017	−	2.02017i	0.0934822	−	0.0934822i	0.752301	+	0.658819i	$0.228944\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.24254			0.0572531
$472$		0			0
$473$	−15.4851	+	15.4851i	−0.712006	+	0.712006i
$474$		0			0
$475$	−9.00701	−	6.36540i	−0.413270	−	0.292065i
$476$		0			0
$477$	6.85219	+	6.85219i	0.313740	+	0.313740i
$478$		0			0
$479$	−0.109514			−0.00500380			−0.00250190	−	0.999997i	$-0.500796\pi$
$479$	−0.109514			−0.00500380			−0.00250190	+	0.999997i	$0.500796\pi$
$480$		0			0
$481$			10.7663i			0.490903i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−12.6168	−	24.3660i	−0.572900	−	1.10640i
$486$		0			0
$487$	−22.3471	−	22.3471i	−1.01264	−	1.01264i	−0.999919	−	0.0127248i	$-0.995949\pi$
$487$	−22.3471	−	22.3471i	−1.01264	−	1.01264i	−0.0127248	−	0.999919i	$-0.504051\pi$
$488$		0			0
$489$	−8.63352			−0.390421
$490$		0			0
$491$	−36.7012			−1.65630			−0.828152	−	0.560504i	$-0.810607\pi$
$491$	−36.7012			−1.65630			−0.828152	+	0.560504i	$0.810607\pi$
$492$		0			0
$493$	−8.24104	−	8.24104i	−0.371158	−	0.371158i
$494$		0			0
$495$	−28.6129	−	9.09016i	−1.28606	−	0.408572i
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	20.6792i		−	0.925727i	−0.886430	−	0.462863i	$-0.846822\pi$
$499$		−	20.6792i		−	0.925727i	0.886430	−	0.462863i	$-0.153178\pi$
$500$		0			0
$501$	−10.9254			−0.488110
$502$		0			0
$503$	−19.8290	−	19.8290i	−0.884133	−	0.884133i	0.109819	−	0.993952i	$-0.464973\pi$
$503$	−19.8290	−	19.8290i	−0.884133	−	0.884133i	−0.993952	+	0.109819i	$0.964973\pi$
$504$		0			0
$505$	4.19190	+	1.33174i	0.186537	+	0.0592617i
$506$		0			0
$507$	4.64264	−	4.64264i	0.206187	−	0.206187i
$508$		0			0
$509$	−1.60862			−0.0713008			−0.0356504	−	0.999364i	$-0.511350\pi$
$509$	−1.60862			−0.0713008			−0.0356504	+	0.999364i	$0.511350\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.96434	−	4.96434i	0.219181	−	0.219181i
$514$		0			0
$515$	−35.8036	+	18.5392i	−1.57770	+	0.816937i
$516$		0			0
$517$	10.6695	−	10.6695i	0.469242	−	0.469242i
$518$		0			0
$519$		−	12.8028i		−	0.561983i
$520$		0			0
$521$			14.1016i			0.617801i	0.951094	+	0.308901i	$0.0999610\pi$
$521$			14.1016i			0.617801i	−0.951094	+	0.308901i	$0.900039\pi$
$522$		0			0
$523$	6.28279	+	6.28279i	0.274727	+	0.274727i	0.831000	−	0.556273i	$-0.187769\pi$
$523$	6.28279	+	6.28279i	0.274727	+	0.274727i	−0.556273	+	0.831000i	$0.687769\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.7591	−	15.7591i	−0.686477	−	0.686477i
$528$		0			0
$529$		−	30.7680i		−	1.33774i
$530$		0			0
$531$			25.4532i			1.10457i
$532$		0			0
$533$	−7.42514	+	7.42514i	−0.321618	+	0.321618i
$534$		0			0
$535$	−3.82632	+	1.98128i	−0.165426	+	0.0856582i
$536$		0			0
$537$	−5.61008	+	5.61008i	−0.242093	+	0.242093i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−11.2895			−0.485372			−0.242686	−	0.970105i	$-0.578028\pi$
$541$	−11.2895			−0.485372			−0.242686	+	0.970105i	$0.578028\pi$
$542$		0			0
$543$	−2.47036	+	2.47036i	−0.106013	+	0.106013i
$544$		0			0
$545$	2.13790	+	0.679198i	0.0915776	+	0.0290937i
$546$		0			0
$547$	−17.2149	−	17.2149i	−0.736057	−	0.736057i	0.235756	−	0.971812i	$-0.424243\pi$
$547$	−17.2149	−	17.2149i	−0.736057	−	0.736057i	−0.971812	+	0.235756i	$0.924243\pi$
$548$		0			0
$549$	4.65516			0.198677
$550$		0			0
$551$			4.65379i			0.198258i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	11.4006	+	3.62190i	0.483928	+	0.153741i
$556$		0			0
$557$	−16.2578	−	16.2578i	−0.688865	−	0.688865i	0.273116	−	0.961981i	$-0.411946\pi$
$557$	−16.2578	−	16.2578i	−0.688865	−	0.688865i	−0.961981	+	0.273116i	$0.911946\pi$
$558$		0			0
$559$	−4.93609			−0.208774
$560$		0			0
$561$	15.4500			0.652300
$562$		0			0
$563$	21.7262	+	21.7262i	0.915649	+	0.915649i	0.996709	−	0.0810603i	$-0.0258306\pi$
$563$	21.7262	+	21.7262i	0.915649	+	0.915649i	−0.0810603	+	0.996709i	$0.525831\pi$
$564$		0			0
$565$	8.68099	+	16.7650i	0.365212	+	0.705310i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			18.0076i			0.754919i	0.926026	+	0.377460i	$0.123202\pi$
$569$			18.0076i			0.754919i	−0.926026	+	0.377460i	$0.876798\pi$
$570$		0			0
$571$	−36.9558			−1.54655			−0.773276	−	0.634069i	$-0.781384\pi$
$571$	−36.9558			−1.54655			−0.773276	+	0.634069i	$0.781384\pi$
$572$		0			0
$573$	4.96395	+	4.96395i	0.207372	+	0.207372i
$574$		0			0
$575$	36.1337	−	6.20925i	1.50688	−	0.258944i
$576$		0			0
$577$	−14.7610	+	14.7610i	−0.614507	+	0.614507i	−0.944117	−	0.329610i	$-0.893083\pi$
$577$	−14.7610	+	14.7610i	−0.614507	+	0.614507i	0.329610	+	0.944117i	$0.393083\pi$
$578$		0			0
$579$	11.7118			0.486727
$580$		0			0
$581$		0			0
$582$		0			0
$583$	12.7446	−	12.7446i	0.527828	−	0.527828i
$584$		0			0
$585$	−3.11157	−	6.00918i	−0.128648	−	0.248449i
$586$		0			0
$587$	−2.20587	+	2.20587i	−0.0910459	+	0.0910459i	−0.751163	−	0.660117i	$-0.770507\pi$
$587$	−2.20587	+	2.20587i	−0.0910459	+	0.0910459i	0.660117	+	0.751163i	$0.270507\pi$
$588$		0			0
$589$			8.89930i			0.366689i
$590$		0			0
$591$			1.43772i			0.0591400i
$592$		0			0
$593$	−8.98961	−	8.98961i	−0.369159	−	0.369159i	0.498012	−	0.867170i	$-0.334064\pi$
$593$	−8.98961	−	8.98961i	−0.369159	−	0.369159i	−0.867170	+	0.498012i	$0.834064\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.96513	−	7.96513i	−0.325991	−	0.325991i
$598$		0			0
$599$			23.3467i			0.953920i	0.878925	+	0.476960i	$0.158261\pi$
$599$			23.3467i			0.953920i	−0.878925	+	0.476960i	$0.841739\pi$
$600$		0			0
$601$			6.61530i			0.269844i	0.990856	+	0.134922i	$0.0430784\pi$
$601$			6.61530i			0.269844i	−0.990856	+	0.134922i	$0.956922\pi$
$602$		0			0
$603$	−20.0511	+	20.0511i	−0.816543	+	0.816543i
$604$		0			0
$605$	−9.45965	+	29.7760i	−0.384589	+	1.21057i
$606$		0			0
$607$	1.35864	−	1.35864i	0.0551455	−	0.0551455i	−0.678996	−	0.734142i	$-0.737585\pi$
$607$	1.35864	−	1.35864i	0.0551455	−	0.0551455i	0.734142	+	0.678996i	$0.237585\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.40103			0.137591
$612$		0			0
$613$	4.19764	−	4.19764i	0.169541	−	0.169541i	−0.617237	−	0.786778i	$-0.711748\pi$
$613$	4.19764	−	4.19764i	0.169541	−	0.169541i	0.786778	+	0.617237i	$0.211748\pi$
$614$		0			0
$615$	5.36467	+	10.3604i	0.216324	+	0.417773i
$616$		0			0
$617$	−6.88647	−	6.88647i	−0.277239	−	0.277239i	0.554767	−	0.832006i	$-0.312807\pi$
$617$	−6.88647	−	6.88647i	−0.277239	−	0.277239i	−0.832006	+	0.554767i	$0.812807\pi$
$618$		0			0
$619$	−10.3270			−0.415075			−0.207538	−	0.978227i	$-0.566545\pi$
$619$	−10.3270			−0.415075			−0.207538	+	0.978227i	$0.566545\pi$
$620$		0			0
$621$			23.3379i			0.936518i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	8.34560	+	23.5659i	0.333824	+	0.942635i
$626$		0			0
$627$	−4.36238	−	4.36238i	−0.174217	−	0.174217i
$628$		0			0
$629$	52.8025			2.10537
$630$		0			0
$631$	31.1964			1.24191			0.620955	−	0.783846i	$-0.286745\pi$
$631$	31.1964			1.24191			0.620955	+	0.783846i	$0.286745\pi$
$632$		0			0
$633$	−6.42143	−	6.42143i	−0.255229	−	0.255229i
$634$		0			0
$635$	−28.1088	+	14.5548i	−1.11546	+	0.577591i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			7.74841i			0.306522i
$640$		0			0
$641$	−4.03049			−0.159195			−0.0795974	−	0.996827i	$-0.525363\pi$
$641$	−4.03049			−0.159195			−0.0795974	+	0.996827i	$0.525363\pi$
$642$		0			0
$643$	−26.0807	−	26.0807i	−1.02852	−	1.02852i	−0.999581	−	0.0289406i	$-0.990787\pi$
$643$	−26.0807	−	26.0807i	−1.02852	−	1.02852i	−0.0289406	−	0.999581i	$-0.509213\pi$
$644$		0			0
$645$	−1.66055	+	5.22687i	−0.0653839	+	0.205808i
$646$		0			0
$647$	30.1907	−	30.1907i	1.18692	−	1.18692i	0.209003	−	0.977915i	$-0.432978\pi$
$647$	30.1907	−	30.1907i	1.18692	−	1.18692i	0.977915	−	0.209003i	$-0.0670219\pi$
$648$		0			0
$649$	47.3412			1.85830
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.5195	+	20.5195i	−0.802990	+	0.802990i	−0.983562	−	0.180572i	$-0.942205\pi$
$653$	−20.5195	+	20.5195i	−0.802990	+	0.802990i	0.180572	+	0.983562i	$0.442205\pi$
$654$		0			0
$655$	8.93328	+	2.83805i	0.349052	+	0.110892i
$656$		0			0
$657$	20.5517	−	20.5517i	0.801799	−	0.801799i
$658$		0			0
$659$		−	23.9938i		−	0.934665i	−0.884082	−	0.467332i	$-0.845215\pi$
$659$		−	23.9938i		−	0.934665i	0.884082	−	0.467332i	$-0.154785\pi$
$660$		0			0
$661$		−	41.5368i		−	1.61559i	−0.589461	−	0.807797i	$-0.700660\pi$
$661$		−	41.5368i		−	1.61559i	0.589461	−	0.807797i	$-0.299340\pi$
$662$		0			0
$663$	2.46245	+	2.46245i	0.0956336	+	0.0956336i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.9390	−	10.9390i	−0.423559	−	0.423559i
$668$		0			0
$669$			6.04886i			0.233862i
$670$		0			0
$671$		−	8.65829i		−	0.334250i
$672$		0			0
$673$	−9.10772	+	9.10772i	−0.351077	+	0.351077i	−0.860510	−	0.509433i	$-0.829855\pi$
$673$	−9.10772	+	9.10772i	−0.351077	+	0.351077i	0.509433	+	0.860510i	$0.329855\pi$
$674$		0			0
$675$	−15.6838	+	2.69511i	−0.603669	+	0.103735i
$676$		0			0
$677$	−18.9702	+	18.9702i	−0.729084	+	0.729084i	−0.970437	−	0.241353i	$-0.922409\pi$
$677$	−18.9702	+	18.9702i	−0.729084	+	0.729084i	0.241353	+	0.970437i	$0.422409\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.175715			−0.00673342
$682$		0			0
$683$	18.5664	−	18.5664i	0.710423	−	0.710423i	−0.256201	−	0.966624i	$-0.582471\pi$
$683$	18.5664	−	18.5664i	0.710423	−	0.710423i	0.966624	+	0.256201i	$0.0824709\pi$
$684$		0			0
$685$	−26.8977	+	13.9277i	−1.02771	+	0.532151i
$686$		0			0
$687$	6.72720	+	6.72720i	0.256659	+	0.256659i
$688$		0			0
$689$	4.06252			0.154770
$690$		0			0
$691$		−	16.5327i		−	0.628935i	−0.949268	−	0.314467i	$-0.898174\pi$
$691$		−	16.5327i		−	0.628935i	0.949268	−	0.314467i	$-0.101826\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.1711	−	38.3109i	0.461677	−	1.45321i
$696$		0			0
$697$	36.4159	+	36.4159i	1.37935	+	1.37935i
$698$		0			0
$699$	−3.26152			−0.123362
$700$		0			0
$701$	−0.636652			−0.0240460			−0.0120230	−	0.999928i	$-0.503827\pi$
$701$	−0.636652			−0.0240460			−0.0120230	+	0.999928i	$0.503827\pi$
$702$		0			0
$703$	−14.9090	−	14.9090i	−0.562304	−	0.562304i
$704$		0			0
$705$	1.14414	−	3.60139i	0.0430908	−	0.135636i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			30.2388i			1.13564i	0.823152	+	0.567821i	$0.192213\pi$
$709$			30.2388i			1.13564i	−0.823152	+	0.567821i	$0.807787\pi$
$710$		0			0
$711$	10.3013			0.386328
$712$		0			0
$713$	−20.9183	−	20.9183i	−0.783396	−	0.783396i
$714$		0			0
$715$	−11.1767	+	5.78732i	−0.417984	+	0.216434i
$716$		0			0
$717$	−9.41380	+	9.41380i	−0.351565	+	0.351565i
$718$		0			0
$719$	−23.3926			−0.872397			−0.436198	−	0.899850i	$-0.643675\pi$
$719$	−23.3926			−0.872397			−0.436198	+	0.899850i	$0.643675\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	11.0074	−	11.0074i	0.409371	−	0.409371i
$724$		0			0
$725$	6.08807	−	8.61459i	0.226105	−	0.319938i
$726$		0			0
$727$	16.5463	−	16.5463i	0.613669	−	0.613669i	−0.330231	−	0.943900i	$-0.607127\pi$
$727$	16.5463	−	16.5463i	0.613669	−	0.613669i	0.943900	+	0.330231i	$0.107127\pi$
$728$		0			0
$729$			11.5264i			0.426902i
$730$		0			0
$731$			24.2086i			0.895386i
$732$		0			0
$733$	−6.08742	−	6.08742i	−0.224844	−	0.224844i	0.585691	−	0.810535i	$-0.300823\pi$
$733$	−6.08742	−	6.08742i	−0.224844	−	0.224844i	−0.810535	+	0.585691i	$0.800823\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	37.2937	+	37.2937i	1.37373	+	1.37373i
$738$		0			0
$739$		−	31.5684i		−	1.16126i	−0.814167	−	0.580631i	$-0.802806\pi$
$739$		−	31.5684i		−	1.16126i	0.814167	−	0.580631i	$-0.197194\pi$
$740$		0			0
$741$		−	1.39057i		−	0.0510837i
$742$		0			0
$743$	0.283311	−	0.283311i	0.0103937	−	0.0103937i	−0.701891	−	0.712285i	$-0.747661\pi$
$743$	0.283311	−	0.283311i	0.0103937	−	0.0103937i	0.712285	+	0.701891i	$0.247661\pi$
$744$		0			0
$745$	44.8079	+	14.2352i	1.64163	+	0.521537i
$746$		0			0
$747$	32.2228	−	32.2228i	1.17897	−	1.17897i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−6.29073			−0.229552			−0.114776	−	0.993391i	$-0.536615\pi$
$751$	−6.29073			−0.229552			−0.114776	+	0.993391i	$0.536615\pi$
$752$		0			0
$753$	−4.01754	+	4.01754i	−0.146407	+	0.146407i
$754$		0			0
$755$	−12.4273	+	39.1172i	−0.452276	+	1.42362i
$756$		0			0
$757$	−28.1189	−	28.1189i	−1.02200	−	1.02200i	−0.999753	−	0.0222456i	$-0.992918\pi$
$757$	−28.1189	−	28.1189i	−1.02200	−	1.02200i	−0.0222456	−	0.999753i	$-0.507082\pi$
$758$		0			0
$759$	20.5080			0.744394
$760$		0			0
$761$		−	35.5923i		−	1.29022i	−0.764089	−	0.645111i	$-0.776811\pi$
$761$		−	35.5923i		−	1.29022i	0.764089	−	0.645111i	$-0.223189\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−29.4715	+	15.2604i	−1.06554	+	0.551741i
$766$		0			0
$767$	7.54532	+	7.54532i	0.272446	+	0.272446i
$768$		0			0
$769$	36.0689			1.30068			0.650338	−	0.759645i	$-0.274627\pi$
$769$	36.0689			1.30068			0.650338	+	0.759645i	$0.274627\pi$
$770$		0			0
$771$	−12.3285			−0.444000
$772$		0			0
$773$	−33.1356	−	33.1356i	−1.19181	−	1.19181i	−0.976560	−	0.215247i	$-0.930944\pi$
$773$	−33.1356	−	33.1356i	−1.19181	−	1.19181i	−0.215247	−	0.976560i	$-0.569056\pi$
$774$		0			0
$775$	11.6420	−	16.4734i	0.418194	−	0.591743i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	20.5644i		−	0.736795i
$780$		0			0
$781$	14.4115			0.515685
$782$		0			0
$783$	4.74805	+	4.74805i	0.169681	+	0.169681i
$784$		0			0
$785$	2.28268	+	4.40839i	0.0814722	+	0.157342i
$786$		0			0
$787$	13.0055	−	13.0055i	0.463594	−	0.463594i	−0.436237	−	0.899832i	$-0.643689\pi$
$787$	13.0055	−	13.0055i	0.463594	−	0.463594i	0.899832	+	0.436237i	$0.143689\pi$
$788$		0			0
$789$	8.06128			0.286989
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.37997	−	1.37997i	0.0490043	−	0.0490043i
$794$		0			0
$795$	1.36667	−	4.30184i	0.0484708	−	0.152571i
$796$		0			0
$797$	−17.7624	+	17.7624i	−0.629176	+	0.629176i	−0.947861	−	0.318685i	$-0.896759\pi$
$797$	−17.7624	+	17.7624i	−0.629176	+	0.629176i	0.318685	+	0.947861i	$0.396759\pi$
$798$		0			0
$799$		−	16.6800i		−	0.590097i
$800$		0			0
$801$			9.77471i			0.345372i
$802$		0			0
$803$	−38.2248	−	38.2248i	−1.34893	−	1.34893i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.84910	+	4.84910i	0.170697	+	0.170697i
$808$		0			0
$809$			12.5720i			0.442009i	0.975273	+	0.221004i	$0.0709335\pi$
$809$			12.5720i			0.442009i	−0.975273	+	0.221004i	$0.929067\pi$
$810$		0			0
$811$			42.0169i			1.47541i	0.675122	+	0.737706i	$0.264091\pi$
$811$			42.0169i			1.47541i	−0.675122	+	0.737706i	$0.735909\pi$
$812$		0			0
$813$	−8.33986	+	8.33986i	−0.292492	+	0.292492i
$814$		0			0
$815$	−15.8607	−	30.6308i	−0.555577	−	1.07295i
$816$		0			0
$817$	6.83539	−	6.83539i	0.239140	−	0.239140i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.6654			0.651429			0.325714	−	0.945468i	$-0.394395\pi$
$821$	18.6654			0.651429			0.325714	+	0.945468i	$0.394395\pi$
$822$		0			0
$823$	−18.9202	+	18.9202i	−0.659517	+	0.659517i	−0.955266	−	0.295748i	$-0.904431\pi$
$823$	−18.9202	+	18.9202i	−0.659517	+	0.659517i	0.295748	+	0.955266i	$0.404431\pi$
$824$		0			0
$825$	2.36831	+	13.7820i	0.0824540	+	0.479828i
$826$		0			0
$827$	−20.9144	−	20.9144i	−0.727266	−	0.727266i	0.242809	−	0.970074i	$-0.421931\pi$
$827$	−20.9144	−	20.9144i	−0.727266	−	0.727266i	−0.970074	+	0.242809i	$0.921931\pi$
$828$		0			0
$829$	43.9505			1.52646			0.763232	−	0.646125i	$-0.223611\pi$
$829$	43.9505			1.52646			0.763232	+	0.646125i	$0.223611\pi$
$830$		0			0
$831$			9.53759i			0.330855i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−20.0711	−	38.7621i	−0.694590	−	1.34142i
$836$		0			0
$837$	9.07955	+	9.07955i	0.313835	+	0.313835i
$838$		0			0
$839$	−20.4994			−0.707719			−0.353860	−	0.935299i	$-0.615131\pi$
$839$	−20.4994			−0.707719			−0.353860	+	0.935299i	$0.615131\pi$
$840$		0			0
$841$	24.5490			0.846516
$842$		0			0
$843$	2.08824	+	2.08824i	0.0719229	+	0.0719229i
$844$		0			0
$845$	25.0006	+	7.94255i	0.860048	+	0.273232i
$846$		0			0
$847$		0			0
$848$		0			0
$849$			6.50948i			0.223405i
$850$		0			0
$851$	70.0890			2.40262
$852$		0			0
$853$	−5.82507	−	5.82507i	−0.199446	−	0.199446i	0.600316	−	0.799763i	$-0.295041\pi$
$853$	−5.82507	−	5.82507i	−0.199446	−	0.199446i	−0.799763	+	0.600316i	$0.795041\pi$
$854$		0			0
$855$	12.6302	+	4.01255i	0.431945	+	0.137226i
$856$		0			0
$857$	1.58415	−	1.58415i	0.0541134	−	0.0541134i	−0.679532	−	0.733646i	$-0.737817\pi$
$857$	1.58415	−	1.58415i	0.0541134	−	0.0541134i	0.733646	+	0.679532i	$0.237817\pi$
$858$		0			0
$859$	−36.4128			−1.24239			−0.621195	−	0.783656i	$-0.713352\pi$
$859$	−36.4128			−1.24239			−0.621195	+	0.783656i	$0.713352\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32.5461	−	32.5461i	1.10788	−	1.10788i	0.114452	−	0.993429i	$-0.463489\pi$
$863$	32.5461	−	32.5461i	1.10788	−	1.10788i	0.993429	−	0.114452i	$-0.0365111\pi$
$864$		0			0
$865$	45.4231	−	23.5202i	1.54443	−	0.799712i
$866$		0			0
$867$	5.34912	−	5.34912i	0.181666	−	0.181666i
$868$		0			0
$869$		−	19.1597i		−	0.649948i
$870$		0			0
$871$			11.8879i			0.402805i
$872$		0			0
$873$	23.3128	+	23.3128i	0.789020	+	0.789020i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	28.0988	+	28.0988i	0.948830	+	0.948830i	0.998753	−	0.0499226i	$-0.0158975\pi$
$877$	28.0988	+	28.0988i	0.948830	+	0.948830i	−0.0499226	+	0.998753i	$0.515897\pi$
$878$		0			0
$879$			9.49118i			0.320130i
$880$		0			0
$881$			18.7851i			0.632886i	0.948611	+	0.316443i	$0.102489\pi$
$881$			18.7851i			0.632886i	−0.948611	+	0.316443i	$0.897511\pi$
$882$		0			0
$883$	−9.79247	+	9.79247i	−0.329543	+	0.329543i	−0.852413	−	0.522870i	$-0.824861\pi$
$883$	−9.79247	+	9.79247i	−0.329543	+	0.329543i	0.522870	+	0.852413i	$0.324861\pi$
$884$		0			0
$885$	10.5281	−	5.45150i	0.353899	−	0.183250i
$886$		0			0
$887$	−36.4721	+	36.4721i	−1.22461	+	1.22461i	−0.258640	+	0.965974i	$0.583274\pi$
$887$	−36.4721	+	36.4721i	−1.22461	+	1.22461i	−0.965974	+	0.258640i	$0.916726\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	31.3775			1.05119
$892$		0			0
$893$	−4.70968	+	4.70968i	−0.157604	+	0.157604i
$894$		0			0
$895$	−30.2103	−	9.59763i	−1.00982	−	0.320813i
$896$		0			0
$897$	3.26860	+	3.26860i	0.109135	+	0.109135i
$898$		0			0
$899$	−8.51157			−0.283877
$900$		0			0
$901$		−	19.9242i		−	0.663773i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−13.3029	−	4.22624i	−0.442202	−	0.140485i
$906$		0			0
$907$	3.96956	+	3.96956i	0.131807	+	0.131807i	0.769932	−	0.638125i	$-0.220290\pi$
$907$	3.96956	+	3.96956i	0.131807	+	0.131807i	−0.638125	+	0.769932i	$0.720290\pi$
$908$		0			0
$909$	−5.28488			−0.175289
$910$		0			0
$911$	35.5372			1.17740			0.588701	−	0.808351i	$-0.299640\pi$
$911$	35.5372			1.17740			0.588701	+	0.808351i	$0.299640\pi$
$912$		0			0
$913$	−59.9323	−	59.9323i	−1.98347	−	1.98347i
$914$		0			0
$915$	−0.997032	−	1.92550i	−0.0329608	−	0.0636552i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			38.6636i			1.27540i	0.770287	+	0.637698i	$0.220113\pi$
$919$			38.6636i			1.27540i	−0.770287	+	0.637698i	$0.779887\pi$
$920$		0			0
$921$	−8.92680			−0.294148
$922$		0			0
$923$	2.29693	+	2.29693i	0.0756045	+	0.0756045i
$924$		0			0
$925$	8.09403	+	47.1019i	0.266130	+	1.54870i
$926$		0			0
$927$	34.2560	−	34.2560i	1.12512	−	1.12512i
$928$		0			0
$929$	19.3909			0.636195			0.318097	−	0.948058i	$-0.396956\pi$
$929$	19.3909			0.636195			0.318097	+	0.948058i	$0.396956\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6.99056	−	6.99056i	0.228861	−	0.228861i
$934$		0			0
$935$	28.3834	+	54.8150i	0.928235	+	1.79264i
$936$		0			0
$937$	−16.5370	+	16.5370i	−0.540241	+	0.540241i	−0.923600	−	0.383359i	$-0.874767\pi$
$937$	−16.5370	+	16.5370i	−0.540241	+	0.540241i	0.383359	+	0.923600i	$0.374767\pi$
$938$		0			0
$939$			2.93848i			0.0958936i
$940$		0			0
$941$		−	35.8082i		−	1.16731i	−0.812001	−	0.583656i	$-0.801622\pi$
$941$		−	35.8082i		−	1.16731i	0.812001	−	0.583656i	$-0.198378\pi$
$942$		0			0
$943$	48.3377	+	48.3377i	1.57409	+	1.57409i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	34.6835	+	34.6835i	1.12706	+	1.12706i	0.990652	+	0.136411i	$0.0435568\pi$
$947$	34.6835	+	34.6835i	1.12706	+	1.12706i	0.136411	+	0.990652i	$0.456443\pi$
$948$		0			0
$949$		−	12.1847i		−	0.395531i
$950$		0			0
$951$			4.48202i			0.145340i
$952$		0			0
$953$	−29.7557	+	29.7557i	−0.963883	+	0.963883i	−0.999370	−	0.0354872i	$-0.988702\pi$
$953$	−29.7557	+	29.7557i	−0.963883	+	0.963883i	0.0354872	+	0.999370i	$0.488702\pi$
$954$		0			0
$955$	−8.49224	+	26.7309i	−0.274802	+	0.864991i
$956$		0			0
$957$	4.17231	−	4.17231i	0.134872	−	0.134872i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14.7236			0.474954
$962$		0			0
$963$	3.66093	−	3.66093i	0.117972	−	0.117972i
$964$		0			0
$965$	21.5159	+	41.5523i	0.692622	+	1.33762i
$966$		0			0
$967$	14.7694	+	14.7694i	0.474950	+	0.474950i	0.903512	−	0.428562i	$-0.140980\pi$
$967$	14.7694	+	14.7694i	0.474950	+	0.474950i	−0.428562	+	0.903512i	$0.640980\pi$
$968$		0			0
$969$	−6.81990			−0.219087
$970$		0			0
$971$		−	16.0071i		−	0.513693i	−0.966452	−	0.256846i	$-0.917317\pi$
$971$		−	16.0071i		−	0.513693i	0.966452	−	0.256846i	$-0.0826835\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.81913	+	2.57407i	−0.0582589	+	0.0824361i
$976$		0			0
$977$	−10.6616	−	10.6616i	−0.341093	−	0.341093i	0.515685	−	0.856778i	$-0.327538\pi$
$977$	−10.6616	−	10.6616i	−0.341093	−	0.341093i	−0.856778	+	0.515685i	$0.827538\pi$
$978$		0			0
$979$	18.1803			0.581045
$980$		0			0
$981$	−2.69533			−0.0860553
$982$		0			0
$983$	−2.56581	−	2.56581i	−0.0818367	−	0.0818367i	0.665004	−	0.746840i	$-0.268430\pi$
$983$	−2.56581	−	2.56581i	−0.0818367	−	0.0818367i	−0.746840	+	0.665004i	$0.768430\pi$
$984$		0			0
$985$	−5.10088	+	2.64125i	−0.162528	+	0.0841573i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			32.1339i			1.02180i
$990$		0			0
$991$	25.0005			0.794167			0.397084	−	0.917782i	$-0.370022\pi$
$991$	25.0005			0.794167			0.397084	+	0.917782i	$0.370022\pi$
$992$		0			0
$993$	0.874502	+	0.874502i	0.0277515	+	0.0277515i
$994$		0			0
$995$	13.6266	−	42.8922i	0.431992	−	1.35978i
$996$		0			0
$997$	−19.5035	+	19.5035i	−0.617681	+	0.617681i	−0.944936	−	0.327255i	$-0.893876\pi$
$997$	−19.5035	+	19.5035i	−0.617681	+	0.617681i	0.327255	+	0.944936i	$0.393876\pi$
$998$		0			0
$999$	−30.4220			−0.962509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.m.b.97.7	yes	24
5.3	odd	4	inner	980.2.m.b.293.6	yes	24
7.2	even	3		980.2.v.c.717.6		48
7.3	odd	6		980.2.v.c.117.6		48
7.4	even	3		980.2.v.c.117.7		48
7.5	odd	6		980.2.v.c.717.7		48
7.6	odd	2	inner	980.2.m.b.97.6	✓	24
35.3	even	12		980.2.v.c.313.6		48
35.13	even	4	inner	980.2.m.b.293.7	yes	24
35.18	odd	12		980.2.v.c.313.7		48
35.23	odd	12		980.2.v.c.913.6		48
35.33	even	12		980.2.v.c.913.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.m.b.97.6	✓	24	7.6	odd	2	inner
980.2.m.b.97.7	yes	24	1.1	even	1	trivial
980.2.m.b.293.6	yes	24	5.3	odd	4	inner
980.2.m.b.293.7	yes	24	35.13	even	4	inner
980.2.v.c.117.6		48	7.3	odd	6
980.2.v.c.117.7		48	7.4	even	3
980.2.v.c.313.6		48	35.3	even	12
980.2.v.c.313.7		48	35.18	odd	12
980.2.v.c.717.6		48	7.2	even	3
980.2.v.c.717.7		48	7.5	odd	6
980.2.v.c.913.6		48	35.23	odd	12
980.2.v.c.913.7		48	35.33	even	12

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395749 + 0.395749i) q^{3} +(-0.677040 + 2.13111i) q^{5} -2.68677i q^{9} -4.99721 q^{11} +(-0.796463 - 0.796463i) q^{13} +(-1.11132 + 0.575445i) q^{15} +(-3.90618 + 3.90618i) q^{17} +2.20585 q^{19} +(-5.18498 + 5.18498i) q^{23} +(-4.08323 - 2.88569i) q^{25} +(2.25053 - 2.25053i) q^{27} +2.10975i q^{29} +4.03440i q^{31} +(-1.97764 - 1.97764i) q^{33} +(-6.75885 - 6.75885i) q^{37} -0.630399i q^{39} -9.32264i q^{41} +(3.09875 - 3.09875i) q^{43} +(5.72579 + 1.81905i) q^{45} +(-2.13508 + 2.13508i) q^{47} -3.09173 q^{51} +(-2.55035 + 2.55035i) q^{53} +(3.38331 - 10.6496i) q^{55} +(0.872963 + 0.872963i) q^{57} -9.47353 q^{59} +1.73263i q^{61} +(2.23659 - 1.15811i) q^{65} +(-7.46291 - 7.46291i) q^{67} -4.10390 q^{69} -2.88392 q^{71} +(7.64924 + 7.64924i) q^{73} +(-0.473927 - 2.75794i) q^{75} +3.83408i q^{79} -6.27901 q^{81} +(11.9932 + 11.9932i) q^{83} +(-5.67984 - 10.9691i) q^{85} +(-0.834929 + 0.834929i) q^{87} -3.63809 q^{89} +(-1.59661 + 1.59661i) q^{93} +(-1.49345 + 4.70091i) q^{95} +(-8.67691 + 8.67691i) q^{97} +13.4263i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{11} - 48 q^{23} + 32 q^{25} - 32 q^{37} + 16 q^{43} + 48 q^{51} - 24 q^{53} + 64 q^{65} - 32 q^{67} + 8 q^{81} - 64 q^{85} - 96 q^{93} + 64 q^{95}+O(q^{100}) \) 24 * q + 16 * q^11 - 48 * q^23 + 32 * q^25 - 32 * q^37 + 16 * q^43 + 48 * q^51 - 24 * q^53 + 64 * q^65 - 32 * q^67 + 8 * q^81 - 64 * q^85 - 96 * q^93 + 64 * q^95

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