LMFDB - Embedded newform 280.2.l.a.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(29,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.l (of order $2$, degree $1$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36669 + 0.363546i) q^{2} +0.460762 q^{3} +(1.73567 - 0.993708i) q^{4} +(-2.19557 - 0.423658i) q^{5} +(-0.629718 + 0.167508i) q^{6} +1.00000i q^{7} +(-2.01086 + 1.98908i) q^{8} -2.78770 q^{9} +O(q^{10})$	\(q+(-1.36669 + 0.363546i) q^{2} +0.460762 q^{3} +(1.73567 - 0.993708i) q^{4} +(-2.19557 - 0.423658i) q^{5} +(-0.629718 + 0.167508i) q^{6} +1.00000i q^{7} +(-2.01086 + 1.98908i) q^{8} -2.78770 q^{9} +(3.15467 - 0.219182i) q^{10} +4.70105i q^{11} +(0.799730 - 0.457863i) q^{12} +0.906993 q^{13} +(-0.363546 - 1.36669i) q^{14} +(-1.01163 - 0.195206i) q^{15} +(2.02509 - 3.44949i) q^{16} +7.25402i q^{17} +(3.80991 - 1.01346i) q^{18} +2.15170i q^{19} +(-4.23177 + 1.44642i) q^{20} +0.460762i q^{21} +(-1.70905 - 6.42487i) q^{22} -5.89989i q^{23} +(-0.926527 + 0.916494i) q^{24} +(4.64103 + 1.86034i) q^{25} +(-1.23958 + 0.329734i) q^{26} -2.66675 q^{27} +(0.993708 + 1.73567i) q^{28} +6.91659i q^{29} +(1.45355 - 0.100991i) q^{30} -8.02835 q^{31} +(-1.51362 + 5.45059i) q^{32} +2.16607i q^{33} +(-2.63717 - 9.91398i) q^{34} +(0.423658 - 2.19557i) q^{35} +(-4.83852 + 2.77016i) q^{36} -6.21426 q^{37} +(-0.782242 - 2.94070i) q^{38} +0.417908 q^{39} +(5.25766 - 3.51525i) q^{40} -6.21775 q^{41} +(-0.167508 - 0.629718i) q^{42} +9.32915 q^{43} +(4.67147 + 8.15947i) q^{44} +(6.12058 + 1.18103i) q^{45} +(2.14488 + 8.06330i) q^{46} -3.80960i q^{47} +(0.933085 - 1.58940i) q^{48} -1.00000 q^{49} +(-7.01915 - 0.855274i) q^{50} +3.34238i q^{51} +(1.57424 - 0.901285i) q^{52} +4.96064 q^{53} +(3.64462 - 0.969487i) q^{54} +(1.99164 - 10.3215i) q^{55} +(-1.98908 - 2.01086i) q^{56} +0.991422i q^{57} +(-2.51450 - 9.45282i) q^{58} -11.7227i q^{59} +(-1.94984 + 0.666456i) q^{60} +6.20163i q^{61} +(10.9722 - 2.91867i) q^{62} -2.78770i q^{63} +(0.0870983 - 7.99953i) q^{64} +(-1.99136 - 0.384255i) q^{65} +(-0.787465 - 2.96034i) q^{66} +5.42728 q^{67} +(7.20838 + 12.5906i) q^{68} -2.71844i q^{69} +(0.219182 + 3.15467i) q^{70} +1.74762 q^{71} +(5.60566 - 5.54496i) q^{72} -5.82777i q^{73} +(8.49296 - 2.25917i) q^{74} +(2.13841 + 0.857174i) q^{75} +(2.13816 + 3.73464i) q^{76} -4.70105 q^{77} +(-0.571149 + 0.151929i) q^{78} +8.05583 q^{79} +(-5.90763 + 6.71565i) q^{80} +7.13436 q^{81} +(8.49771 - 2.26044i) q^{82} -10.5144 q^{83} +(0.457863 + 0.799730i) q^{84} +(3.07322 - 15.9267i) q^{85} +(-12.7500 + 3.39157i) q^{86} +3.18690i q^{87} +(-9.35078 - 9.45315i) q^{88} +11.5168 q^{89} +(-8.79428 + 0.611012i) q^{90} +0.906993i q^{91} +(-5.86276 - 10.2402i) q^{92} -3.69916 q^{93} +(1.38496 + 5.20653i) q^{94} +(0.911585 - 4.72420i) q^{95} +(-0.697417 + 2.51143i) q^{96} +11.6450i q^{97} +(1.36669 - 0.363546i) q^{98} -13.1051i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−1.36669	+	0.363546i	−0.966394	+	0.257066i
$2$	−1.36669	+	0.363546i	−0.966394	+	0.257066i
$3$	0.460762			0.266021			0.133011	−	0.991115i	$-0.457536\pi$
$3$	0.460762			0.266021			0.133011	+	0.991115i	$0.457536\pi$
$4$	1.73567	−	0.993708i	0.867834	−	0.496854i
$5$	−2.19557	−	0.423658i	−0.981887	−	0.189466i
$5$	−2.19557	−	0.423658i	−0.981887	−	0.189466i
$6$	−0.629718	+	0.167508i	−0.257081	+	0.0683850i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.01086	+	1.98908i	−0.710946	+	0.703247i
$9$	−2.78770			−0.929233
$10$	3.15467	−	0.219182i	0.997595	−	0.0693113i
$11$			4.70105i			1.41742i	0.705500	+	0.708710i	$0.250723\pi$
$11$			4.70105i			1.41742i	−0.705500	+	0.708710i	$0.749277\pi$
$12$	0.799730	−	0.457863i	0.230862	−	0.132174i
$13$	0.906993			0.251554			0.125777	−	0.992059i	$-0.459858\pi$
$13$	0.906993			0.251554			0.125777	+	0.992059i	$0.459858\pi$
$14$	−0.363546	−	1.36669i	−0.0971618	−	0.365263i
$15$	−1.01163	−	0.195206i	−0.261203	−	0.0504018i
$16$	2.02509	−	3.44949i	0.506273	−	0.862373i
$17$			7.25402i			1.75936i	0.475567	+	0.879679i	$0.342243\pi$
$17$			7.25402i			1.75936i	−0.475567	+	0.879679i	$0.657757\pi$
$18$	3.80991	−	1.01346i	0.898005	−	0.238874i
$19$			2.15170i			0.493634i	0.969062	+	0.246817i	$0.0793846\pi$
$19$			2.15170i			0.493634i	−0.969062	+	0.246817i	$0.920615\pi$
$20$	−4.23177	+	1.44642i	−0.946252	+	0.323430i
$21$			0.460762i			0.100547i
$22$	−1.70905	−	6.42487i	−0.364370	−	1.36979i
$23$		−	5.89989i		−	1.23021i	−0.788445	−	0.615106i	$-0.789113\pi$
$23$		−	5.89989i		−	1.23021i	0.788445	−	0.615106i	$-0.210887\pi$
$24$	−0.926527	+	0.916494i	−0.189127	+	0.187079i
$25$	4.64103	+	1.86034i	0.928206	+	0.372068i
$26$	−1.23958	+	0.329734i	−0.243101	+	0.0646661i
$27$	−2.66675			−0.513217
$28$	0.993708	+	1.73567i	0.187793	+	0.328011i
$29$			6.91659i			1.28438i	0.766546	+	0.642189i	$0.221974\pi$
$29$			6.91659i			1.28438i	−0.766546	+	0.642189i	$0.778026\pi$
$30$	1.45355	−	0.100991i	0.265381	−	0.0184383i
$31$	−8.02835			−1.44193			−0.720967	−	0.692970i	$-0.756302\pi$
$31$	−8.02835			−1.44193			−0.720967	+	0.692970i	$0.756302\pi$
$32$	−1.51362	+	5.45059i	−0.267572	+	0.963538i
$33$			2.16607i			0.377064i
$34$	−2.63717	−	9.91398i	−0.452271	−	1.70023i
$35$	0.423658	−	2.19557i	0.0716113	−	0.371119i
$36$	−4.83852	+	2.77016i	−0.806420	+	0.461693i
$37$	−6.21426			−1.02162			−0.510809	−	0.859694i	$-0.670654\pi$
$37$	−6.21426			−1.02162			−0.510809	+	0.859694i	$0.670654\pi$
$38$	−0.782242	−	2.94070i	−0.126896	−	0.477045i
$39$	0.417908			0.0669188
$40$	5.25766	−	3.51525i	0.831310	−	0.555810i
$41$	−6.21775			−0.971049			−0.485524	−	0.874223i	$-0.661371\pi$
$41$	−6.21775			−0.971049			−0.485524	+	0.874223i	$0.661371\pi$
$42$	−0.167508	−	0.629718i	−0.0258471	−	0.0971676i
$43$	9.32915			1.42268			0.711341	−	0.702847i	$-0.248088\pi$
$43$	9.32915			1.42268			0.711341	+	0.702847i	$0.248088\pi$
$44$	4.67147	+	8.15947i	0.704251	+	1.23009i
$45$	6.12058	+	1.18103i	0.912402	+	0.176058i
$46$	2.14488	+	8.06330i	0.316245	+	1.18887i
$47$		−	3.80960i		−	0.555687i	−0.960626	−	0.277844i	$-0.910380\pi$
$47$		−	3.80960i		−	0.555687i	0.960626	−	0.277844i	$-0.0896197\pi$
$48$	0.933085	−	1.58940i	0.134679	−	0.229410i
$49$	−1.00000			−0.142857
$50$	−7.01915	−	0.855274i	−0.992658	−	0.120954i
$51$			3.34238i			0.468027i
$52$	1.57424	−	0.901285i	0.218308	−	0.124986i
$53$	4.96064			0.681396			0.340698	−	0.940173i	$-0.389337\pi$
$53$	4.96064			0.681396			0.340698	+	0.940173i	$0.389337\pi$
$54$	3.64462	−	0.969487i	0.495969	−	0.131930i
$55$	1.99164	−	10.3215i	0.268552	−	1.39175i
$56$	−1.98908	−	2.01086i	−0.265802	−	0.268712i
$57$			0.991422i			0.131317i
$58$	−2.51450	−	9.45282i	−0.330170	−	1.24122i
$59$		−	11.7227i		−	1.52616i	−0.646303	−	0.763081i	$-0.723686\pi$
$59$		−	11.7227i		−	1.52616i	0.646303	−	0.763081i	$-0.276314\pi$
$60$	−1.94984	+	0.666456i	−0.251723	+	0.0860391i
$61$			6.20163i			0.794038i	0.917810	+	0.397019i	$0.129955\pi$
$61$			6.20163i			0.794038i	−0.917810	+	0.397019i	$0.870045\pi$
$62$	10.9722	−	2.91867i	1.39348	−	0.370672i
$63$		−	2.78770i		−	0.351217i
$64$	0.0870983	−	7.99953i	0.0108873	−	0.999941i
$65$	−1.99136	−	0.384255i	−0.246998	−	0.0476609i
$66$	−0.787465	−	2.96034i	−0.0969302	−	0.364392i
$67$	5.42728			0.663047			0.331524	−	0.943447i	$-0.392437\pi$
$67$	5.42728			0.663047			0.331524	+	0.943447i	$0.392437\pi$
$68$	7.20838	+	12.5906i	0.874144	+	1.52683i
$69$		−	2.71844i		−	0.327262i
$70$	0.219182	+	3.15467i	0.0261972	+	0.377055i
$71$	1.74762			0.207405			0.103702	−	0.994608i	$-0.466931\pi$
$71$	1.74762			0.207405			0.103702	+	0.994608i	$0.466931\pi$
$72$	5.60566	−	5.54496i	0.660634	−	0.653480i
$73$		−	5.82777i		−	0.682089i	−0.940047	−	0.341045i	$-0.889219\pi$
$73$		−	5.82777i		−	0.682089i	0.940047	−	0.341045i	$-0.110781\pi$
$74$	8.49296	−	2.25917i	0.987286	−	0.262623i
$75$	2.13841	+	0.857174i	0.246922	+	0.0989779i
$76$	2.13816	+	3.73464i	0.245264	+	0.428392i
$77$	−4.70105			−0.535735
$78$	−0.571149	+	0.151929i	−0.0646699	+	0.0172025i
$79$	8.05583			0.906352			0.453176	−	0.891421i	$-0.350291\pi$
$79$	8.05583			0.906352			0.453176	+	0.891421i	$0.350291\pi$
$80$	−5.90763	+	6.71565i	−0.660493	+	0.750832i
$81$	7.13436			0.792706
$82$	8.49771	−	2.26044i	0.938416	−	0.249623i
$83$	−10.5144			−1.15410			−0.577052	−	0.816707i	$-0.695797\pi$
$83$	−10.5144			−1.15410			−0.577052	+	0.816707i	$0.695797\pi$
$84$	0.457863	+	0.799730i	0.0499569	+	0.0872577i
$85$	3.07322	−	15.9267i	0.333338	−	1.72749i
$86$	−12.7500	+	3.39157i	−1.37487	+	0.365723i
$87$			3.18690i			0.341672i
$88$	−9.35078	−	9.45315i	−0.996797	−	1.00771i
$89$	11.5168			1.22078			0.610391	−	0.792100i	$-0.291012\pi$
$89$	11.5168			1.22078			0.610391	+	0.792100i	$0.291012\pi$
$90$	−8.79428	+	0.611012i	−0.926998	+	0.0644064i
$91$			0.906993i			0.0950787i
$92$	−5.86276	−	10.2402i	−0.611235	−	1.06762i
$93$	−3.69916			−0.383585
$94$	1.38496	+	5.20653i	0.142848	+	0.537013i
$95$	0.911585	−	4.72420i	0.0935266	−	0.484693i
$96$	−0.697417	+	2.51143i	−0.0711798	+	0.256321i
$97$			11.6450i			1.18237i	0.806536	+	0.591184i	$0.201339\pi$
$97$			11.6450i			1.18237i	−0.806536	+	0.591184i	$0.798661\pi$
$98$	1.36669	−	0.363546i	0.138056	−	0.0367237i
$99$		−	13.1051i		−	1.31711i
$100$	9.90392	−	1.38289i	0.990392	−	0.138289i
$101$		−	10.4414i		−	1.03896i	−0.854482	−	0.519481i	$-0.826125\pi$
$101$		−	10.4414i		−	1.03896i	0.854482	−	0.519481i	$-0.173875\pi$
$102$	−1.21511	−	4.56799i	−0.120314	−	0.452298i
$103$			0.974021i			0.0959731i	0.998848	+	0.0479866i	$0.0152805\pi$
$103$			0.974021i			0.0959731i	−0.998848	+	0.0479866i	$0.984720\pi$
$104$	−1.82383	+	1.80408i	−0.178842	+	0.176905i
$105$	0.195206	−	1.01163i	0.0190501	−	0.0987254i
$106$	−6.77964	+	1.80342i	−0.658497	+	0.175164i
$107$	−3.56456			−0.344599			−0.172300	−	0.985045i	$-0.555120\pi$
$107$	−3.56456			−0.344599			−0.172300	+	0.985045i	$0.555120\pi$
$108$	−4.62860	+	2.64997i	−0.445387	+	0.254994i
$109$			10.9852i			1.05219i	0.850426	+	0.526095i	$0.176344\pi$
$109$			10.9852i			1.05219i	−0.850426	+	0.526095i	$0.823656\pi$
$110$	1.03038	+	14.8303i	0.0982433	+	1.41401i
$111$	−2.86330			−0.271772
$112$	3.44949	+	2.02509i	0.325947	+	0.191353i
$113$			13.6270i			1.28192i	0.767574	+	0.640961i	$0.221464\pi$
$113$			13.6270i			1.28192i	−0.767574	+	0.640961i	$0.778536\pi$
$114$	−0.360427	−	1.35496i	−0.0337571	−	0.126904i
$115$	−2.49953	+	12.9536i	−0.233083	+	1.20793i
$116$	6.87307	+	12.0049i	0.638148	+	1.11463i
$117$	−2.52842			−0.233753
$118$	4.26173	+	16.0212i	0.392324	+	1.47487i
$119$	−7.25402			−0.664975
$120$	2.42253	−	1.61969i	0.221146	−	0.147857i
$121$	−11.0999			−1.00908
$122$	−2.25458	−	8.47569i	−0.204120	−	0.767353i
$123$	−2.86490			−0.258319
$124$	−13.9345	+	7.97783i	−1.25136	+	0.716430i
$125$	−9.40154	−	6.05071i	−0.840899	−	0.541192i
$126$	1.01346	+	3.80991i	0.0902859	+	0.339414i
$127$			9.10398i			0.807847i	0.914793	+	0.403924i	$0.132354\pi$
$127$			9.10398i			0.807847i	−0.914793	+	0.403924i	$0.867646\pi$
$128$	2.78916	+	10.9645i	0.246529	+	0.969135i
$129$	4.29852			0.378463
$130$	2.86126	−	0.198796i	0.250950	−	0.0174356i
$131$		−	3.54709i		−	0.309911i	−0.987921	−	0.154955i	$-0.950477\pi$
$131$		−	3.54709i		−	0.309911i	0.987921	−	0.154955i	$-0.0495234\pi$
$132$	2.15244	+	3.75957i	0.187346	+	0.327229i
$133$	−2.15170			−0.186576
$134$	−7.41739	+	1.97306i	−0.640765	+	0.170447i
$135$	5.85503	+	1.12979i	0.503921	+	0.0972369i
$136$	−14.4289	−	14.5868i	−1.23726	−	1.25081i
$137$			8.61460i			0.735995i	0.929827	+	0.367998i	$0.119957\pi$
$137$			8.61460i			0.735995i	−0.929827	+	0.367998i	$0.880043\pi$
$138$	0.988280	+	3.71526i	0.0841280	+	0.316264i
$139$			2.63222i			0.223262i	0.993750	+	0.111631i	$0.0356075\pi$
$139$			2.63222i			0.223262i	−0.993750	+	0.111631i	$0.964393\pi$
$140$	−1.44642	−	4.23177i	−0.122245	−	0.357650i
$141$		−	1.75532i		−	0.147824i
$142$	−2.38845	+	0.635341i	−0.200435	+	0.0533166i
$143$			4.26382i			0.356559i
$144$	−5.64534	+	9.61615i	−0.470445	+	0.801346i
$145$	2.93027	−	15.1858i	0.243346	−	1.26112i
$146$	2.11866	+	7.96475i	0.175342	+	0.659167i
$147$	−0.460762			−0.0380030
$148$	−10.7859	+	6.17516i	−0.886596	+	0.507595i
$149$			1.34906i			0.110519i	0.998472	+	0.0552597i	$0.0175987\pi$
$149$			1.34906i			0.110519i	−0.998472	+	0.0552597i	$0.982401\pi$
$150$	−3.23416	−	0.394078i	−0.264068	−	0.0321763i
$151$	1.05365			0.0857447			0.0428723	−	0.999081i	$-0.486349\pi$
$151$	1.05365			0.0857447			0.0428723	+	0.999081i	$0.486349\pi$
$152$	−4.27991	−	4.32676i	−0.347146	−	0.350947i
$153$		−	20.2220i		−	1.63485i
$154$	6.42487	−	1.70905i	0.517731	−	0.137719i
$155$	17.6268	+	3.40127i	1.41582	+	0.273197i
$156$	0.725349	−	0.415278i	0.0580744	−	0.0332489i
$157$	6.90765			0.551291			0.275645	−	0.961259i	$-0.411108\pi$
$157$	6.90765			0.551291			0.275645	+	0.961259i	$0.411108\pi$
$158$	−11.0098	+	2.92867i	−0.875893	+	0.232992i
$159$	2.28567			0.181266
$160$	5.63243	−	11.3259i	0.445283	−	0.895390i
$161$	5.89989			0.464976
$162$	−9.75043	+	2.59367i	−0.766066	+	0.203778i
$163$	3.81159			0.298547			0.149273	−	0.988796i	$-0.452307\pi$
$163$	3.81159			0.298547			0.149273	+	0.988796i	$0.452307\pi$
$164$	−10.7919	+	6.17862i	−0.842709	+	0.482469i
$165$	0.917671	−	4.75575i	0.0714406	−	0.370234i
$166$	14.3699	−	3.82246i	1.11532	−	0.296681i
$167$			5.96816i			0.461830i	0.972974	+	0.230915i	$0.0741719\pi$
$167$			5.96816i			0.461830i	−0.972974	+	0.230915i	$0.925828\pi$
$168$	−0.916494	−	0.926527i	−0.0707091	−	0.0714831i
$169$	−12.1774			−0.936720
$170$	1.58995	+	22.8841i	0.121944	+	1.75513i
$171$		−	5.99829i		−	0.458701i
$172$	16.1923	−	9.27044i	1.23465	−	0.706865i
$173$	−9.53599			−0.725008			−0.362504	−	0.931982i	$-0.618078\pi$
$173$	−9.53599			−0.725008			−0.362504	+	0.931982i	$0.618078\pi$
$174$	−1.15859	−	4.35550i	−0.0878322	−	0.330190i
$175$	−1.86034	+	4.64103i	−0.140628	+	0.350829i
$176$	16.2163	+	9.52006i	1.22235	+	0.717601i
$177$		−	5.40136i		−	0.405991i
$178$	−15.7399	+	4.18690i	−1.17976	+	0.313821i
$179$		−	16.7514i		−	1.25206i	−0.779800	−	0.626028i	$-0.784679\pi$
$179$		−	16.7514i		−	1.25206i	0.779800	−	0.626028i	$-0.215321\pi$
$180$	11.7969	−	4.03219i	0.879289	−	0.300541i
$181$		−	4.40466i		−	0.327396i	−0.986511	−	0.163698i	$-0.947658\pi$
$181$		−	4.40466i		−	0.327396i	0.986511	−	0.163698i	$-0.0523422\pi$
$182$	−0.329734	−	1.23958i	−0.0244415	−	0.0918834i
$183$			2.85748i			0.211231i
$184$	11.7354	+	11.8638i	0.865143	+	0.874613i
$185$	13.6438	+	2.63272i	1.00311	+	0.193562i
$186$	5.05559	−	1.34481i	0.370694	−	0.0986066i
$187$	−34.1015			−2.49375
$188$	−3.78563	−	6.61220i	−0.276095	−	0.482244i
$189$		−	2.66675i		−	0.193978i
$190$	0.471613	+	6.78791i	0.0342144	+	0.492447i
$191$	23.6219			1.70922			0.854609	−	0.519272i	$-0.173797\pi$
$191$	23.6219			1.70922			0.854609	+	0.519272i	$0.173797\pi$
$192$	0.0401316	−	3.68588i	0.00289625	−	0.266005i
$193$		−	16.9843i		−	1.22255i	−0.791417	−	0.611277i	$-0.790656\pi$
$193$		−	16.9843i		−	1.22255i	0.791417	−	0.611277i	$-0.209344\pi$
$194$	−4.23349	−	15.9151i	−0.303947	−	1.14263i
$195$	−0.917545	−	0.177050i	−0.0657067	−	0.0126788i
$196$	−1.73567	+	0.993708i	−0.123976	+	0.0709791i
$197$	7.12840			0.507877			0.253939	−	0.967220i	$-0.418274\pi$
$197$	7.12840			0.507877			0.253939	+	0.967220i	$0.418274\pi$
$198$	4.76431	+	17.9106i	0.338585	+	1.27285i
$199$	−7.59968			−0.538727			−0.269363	−	0.963039i	$-0.586813\pi$
$199$	−7.59968			−0.538727			−0.269363	+	0.963039i	$0.586813\pi$
$200$	−13.0328	+	5.49051i	−0.921559	+	0.388238i
$201$	2.50068			0.176385
$202$	3.79594	+	14.2702i	0.267081	+	1.00405i
$203$	−6.91659			−0.485449
$204$	3.32135	+	5.80126i	0.232541	+	0.406170i
$205$	13.6515	+	2.63420i	0.953460	+	0.183980i
$206$	−0.354101	−	1.33118i	−0.0246714	−	0.0927479i
$207$			16.4471i			1.14315i
$208$	1.83674	−	3.12867i	0.127355	−	0.216934i
$209$	−10.1153			−0.699687
$210$	0.100991	+	1.45355i	0.00696902	+	0.100305i
$211$			12.5535i			0.864220i	0.901821	+	0.432110i	$0.142231\pi$
$211$			12.5535i			0.864220i	−0.901821	+	0.432110i	$0.857769\pi$
$212$	8.61002	−	4.92942i	0.591338	−	0.338554i
$213$	0.805238			0.0551740
$214$	4.87164	−	1.29588i	0.333019	−	0.0885847i
$215$	−20.4828	−	3.95237i	−1.39691	−	0.269549i
$216$	5.36246	−	5.30439i	0.364869	−	0.360918i
$217$		−	8.02835i		−	0.545000i
$218$	−3.99362	−	15.0133i	−0.270482	−	1.01683i
$219$		−	2.68522i		−	0.181450i
$220$	−6.79970	−	19.8938i	−0.458436	−	1.34124i
$221$			6.57934i			0.442575i
$222$	3.91323	−	1.04094i	0.262639	−	0.0698633i
$223$			7.22407i			0.483760i	0.970306	+	0.241880i	$0.0777640\pi$
$223$			7.22407i			0.483760i	−0.970306	+	0.241880i	$0.922236\pi$
$224$	−5.45059	−	1.51362i	−0.364183	−	0.101133i
$225$	−12.9378	−	5.18606i	−0.862519	−	0.345738i
$226$	−4.95405	−	18.6239i	−0.329538	−	1.23884i
$227$	6.31624			0.419224			0.209612	−	0.977785i	$-0.432780\pi$
$227$	6.31624			0.419224			0.209612	+	0.977785i	$0.432780\pi$
$228$	0.985183	+	1.72078i	0.0652454	+	0.113961i
$229$			20.4708i			1.35275i	0.736559	+	0.676373i	$0.236449\pi$
$229$			20.4708i			1.35275i	−0.736559	+	0.676373i	$0.763551\pi$
$230$	−1.29315	−	18.6122i	−0.0852676	−	1.22725i
$231$	−2.16607			−0.142517
$232$	−13.7577	−	13.9083i	−0.903235	−	0.913123i
$233$			12.6153i			0.826458i	0.910627	+	0.413229i	$0.135599\pi$
$233$			12.6153i			0.826458i	−0.910627	+	0.413229i	$0.864401\pi$
$234$	3.45556	−	0.919198i	0.225897	−	0.0600898i
$235$	−1.61397	+	8.36423i	−0.105284	+	0.545622i
$236$	−11.6489	−	20.3467i	−0.758279	−	1.32446i
$237$	3.71182			0.241109
$238$	9.91398	−	2.63717i	0.642628	−	0.170942i
$239$	24.7537			1.60119			0.800593	−	0.599209i	$-0.204518\pi$
$239$	24.7537			1.60119			0.800593	+	0.599209i	$0.204518\pi$
$240$	−2.72201	+	3.09432i	−0.175705	+	0.199737i
$241$	9.84368			0.634087			0.317043	−	0.948411i	$-0.397310\pi$
$241$	9.84368			0.634087			0.317043	+	0.948411i	$0.397310\pi$
$242$	15.1701	−	4.03532i	0.975170	−	0.259400i
$243$	11.2875			0.724093
$244$	6.16261	+	10.7640i	0.394521	+	0.689093i
$245$	2.19557	+	0.423658i	0.140270	+	0.0270665i
$246$	3.91542	−	1.04152i	0.249638	−	0.0664051i
$247$			1.95158i			0.124176i
$248$	16.1439	−	15.9690i	1.02514	−	1.01404i
$249$	−4.84463			−0.307016
$250$	15.0487	+	4.85153i	0.951762	+	0.306838i
$251$			5.68663i			0.358937i	0.983764	+	0.179469i	$0.0574378\pi$
$251$			5.68663i			0.358937i	−0.983764	+	0.179469i	$0.942562\pi$
$252$	−2.77016	−	4.83852i	−0.174503	−	0.304798i
$253$	27.7357			1.74373
$254$	−3.30971	−	12.4423i	−0.207670	−	0.780699i
$255$	1.41603	−	7.33842i	0.0886749	−	0.459549i
$256$	−7.79802	−	13.9711i	−0.487376	−	0.873192i
$257$		−	9.85759i		−	0.614899i	−0.951564	−	0.307450i	$-0.900524\pi$
$257$		−	9.85759i		−	0.614899i	0.951564	−	0.307450i	$-0.0994756\pi$
$258$	−5.87473	+	1.56271i	−0.365745	+	0.0972900i
$259$		−	6.21426i		−	0.386136i
$260$	−3.83818	+	1.31189i	−0.238034	+	0.0813602i
$261$		−	19.2814i		−	1.19349i
$262$	1.28953	+	4.84776i	0.0796675	+	0.299496i
$263$			4.80107i			0.296047i	0.988984	+	0.148023i	$0.0472911\pi$
$263$			4.80107i			0.296047i	−0.988984	+	0.148023i	$0.952709\pi$
$264$	−4.30849	−	4.35565i	−0.265169	−	0.268072i
$265$	−10.8914	−	2.10161i	−0.669054	−	0.129101i
$266$	2.94070	−	0.782242i	0.180306	−	0.0479623i
$267$	5.30652			0.324754
$268$	9.41995	−	5.39312i	0.575415	−	0.329438i
$269$			24.3324i			1.48358i	0.670635	+	0.741788i	$0.266022\pi$
$269$			24.3324i			1.48358i	−0.670635	+	0.741788i	$0.733978\pi$
$270$	−8.41273	+	0.584503i	−0.511982	+	0.0355717i
$271$	−21.7578			−1.32169			−0.660846	−	0.750521i	$-0.729802\pi$
$271$	−21.7578			−1.32169			−0.660846	+	0.750521i	$0.729802\pi$
$272$	25.0227	+	14.6901i	1.51722	+	0.890715i
$273$			0.417908i			0.0252929i
$274$	−3.13181	−	11.7735i	−0.189199	−	0.711261i
$275$	−8.74555	+	21.8177i	−0.527377	+	1.31566i
$276$	−2.70134	−	4.71832i	−0.162601	−	0.284009i
$277$	−11.0672			−0.664966			−0.332483	−	0.943109i	$-0.607886\pi$
$277$	−11.0672			−0.664966			−0.332483	+	0.943109i	$0.607886\pi$
$278$	−0.956934	−	3.59742i	−0.0573931	−	0.215759i
$279$	22.3806			1.33989
$280$	3.51525	+	5.25766i	0.210076	+	0.314205i
$281$	7.46541			0.445349			0.222675	−	0.974893i	$-0.428521\pi$
$281$	7.46541			0.445349			0.222675	+	0.974893i	$0.428521\pi$
$282$	0.638139	+	2.39897i	0.0380006	+	0.142857i
$283$	12.9066			0.767215			0.383608	−	0.923496i	$-0.374682\pi$
$283$	12.9066			0.767215			0.383608	+	0.923496i	$0.374682\pi$
$284$	3.03329	−	1.73663i	0.179993	−	0.103050i
$285$	0.420024	−	2.17673i	0.0248801	−	0.128939i
$286$	−1.55009	−	5.82731i	−0.0916590	−	0.344576i
$287$		−	6.21775i		−	0.367022i
$288$	4.21950	−	15.1946i	0.248637	−	0.895351i
$289$	−35.6208			−2.09534
$290$	1.51599	+	21.8196i	0.0890220	+	1.28129i
$291$			5.36557i			0.314535i
$292$	−5.79110	−	10.1151i	−0.338899	−	0.591941i
$293$	−16.5980			−0.969668			−0.484834	−	0.874606i	$-0.661120\pi$
$293$	−16.5980			−0.969668			−0.484834	+	0.874606i	$0.661120\pi$
$294$	0.629718	−	0.167508i	0.0367259	−	0.00976928i
$295$	−4.96640	+	25.7379i	−0.289155	+	1.49852i
$296$	12.4960	−	12.3607i	0.726315	−	0.718450i
$297$		−	12.5365i		−	0.727444i
$298$	−0.490446	−	1.84374i	−0.0284107	−	0.106805i
$299$		−	5.35115i		−	0.309465i
$300$	4.56335	−	0.637185i	0.263465	−	0.0367879i
$301$			9.32915i			0.537723i
$302$	−1.44001	+	0.383050i	−0.0828631	+	0.0220420i
$303$		−	4.81102i		−	0.276386i
$304$	7.42227	+	4.35739i	0.425697	+	0.249913i
$305$	2.62737	−	13.6161i	0.150443	−	0.779655i
$306$	7.35164	+	27.6372i	0.420265	+	1.57991i
$307$	22.4910			1.28363			0.641815	−	0.766860i	$-0.278182\pi$
$307$	22.4910			1.28363			0.641815	+	0.766860i	$0.278182\pi$
$308$	−8.15947	+	4.67147i	−0.464929	+	0.266182i
$309$			0.448792i			0.0255309i
$310$	−25.3268	+	1.75967i	−1.43847	+	0.0999424i
$311$	−13.5423			−0.767911			−0.383955	−	0.923352i	$-0.625438\pi$
$311$	−13.5423			−0.767911			−0.383955	+	0.923352i	$0.625438\pi$
$312$	−0.840353	+	0.831253i	−0.0475756	+	0.0470605i
$313$		−	8.36225i		−	0.472662i	−0.971673	−	0.236331i	$-0.924055\pi$
$313$		−	8.36225i		−	0.472662i	0.971673	−	0.236331i	$-0.0759450\pi$
$314$	−9.44060	+	2.51125i	−0.532764	+	0.141718i
$315$	−1.18103	+	6.12058i	−0.0665435	+	0.344856i
$316$	13.9823	−	8.00514i	0.786563	−	0.450324i
$317$	−9.55188			−0.536487			−0.268244	−	0.963351i	$-0.586443\pi$
$317$	−9.55188			−0.536487			−0.268244	+	0.963351i	$0.586443\pi$
$318$	−3.12380	+	0.830947i	−0.175174	+	0.0465972i
$319$	−32.5153			−1.82050
$320$	−3.58029	+	17.5266i	−0.200144	+	0.979766i
$321$	−1.64242			−0.0916707
$322$	−8.06330	+	2.14488i	−0.449350	+	0.119530i
$323$	−15.6085			−0.868479
$324$	12.3829	−	7.08946i	0.687938	−	0.393859i
$325$	4.20938	+	1.68731i	0.233494	+	0.0935953i
$326$	−5.20925	+	1.38569i	−0.288514	+	0.0767462i
$327$			5.06156i			0.279905i
$328$	12.5030	−	12.3676i	0.690363	−	0.682887i
$329$	3.80960			0.210030
$330$	0.474762	+	6.83323i	0.0261348	+	0.376157i
$331$			4.02356i			0.221155i	0.993868	+	0.110577i	$0.0352700\pi$
$331$			4.02356i			0.221155i	−0.993868	+	0.110577i	$0.964730\pi$
$332$	−18.2495	+	10.4482i	−1.00157	+	0.573421i
$333$	17.3235			0.949322
$334$	−2.16970	−	8.15661i	−0.118721	−	0.446310i
$335$	−11.9159	−	2.29931i	−0.651038	−	0.125625i
$336$	1.58940	+	0.933085i	0.0867087	+	0.0509040i
$337$			2.35080i			0.128056i	0.997948	+	0.0640282i	$0.0203947\pi$
$337$			2.35080i			0.128056i	−0.997948	+	0.0640282i	$0.979605\pi$
$338$	16.6426	−	4.42703i	0.905241	−	0.240799i
$339$			6.27881i			0.341018i
$340$	−10.4924	−	30.6973i	−0.569029	−	1.66480i
$341$		−	37.7417i		−	2.04383i
$342$	2.18065	+	8.19779i	0.117916	+	0.443286i
$343$		−	1.00000i		−	0.0539949i
$344$	−18.7596	+	18.5564i	−1.01145	+	1.00050i
$345$	−1.15169	+	5.96853i	−0.0620049	+	0.321335i
$346$	13.0327	−	3.46677i	0.700643	−	0.186375i
$347$	18.8580			1.01235			0.506175	−	0.862431i	$-0.331059\pi$
$347$	18.8580			1.01235			0.506175	+	0.862431i	$0.331059\pi$
$348$	3.16685	+	5.53141i	0.169761	+	0.296515i
$349$			36.6217i			1.96032i	0.198215	+	0.980159i	$0.436486\pi$
$349$			36.6217i			1.96032i	−0.198215	+	0.980159i	$0.563514\pi$
$350$	0.855274	−	7.01915i	0.0457163	−	0.375190i
$351$	−2.41872			−0.129102
$352$	−25.6235	−	7.11559i	−1.36574	−	0.379262i
$353$		−	4.26233i		−	0.226861i	−0.993546	−	0.113430i	$-0.963816\pi$
$353$		−	4.26233i		−	0.226861i	0.993546	−	0.113430i	$-0.0361839\pi$
$354$	1.96364	+	7.38197i	0.104367	+	0.392348i
$355$	−3.83702	−	0.740394i	−0.203648	−	0.0392960i
$356$	19.9894	−	11.4444i	1.05944	−	0.606550i
$357$	−3.34238			−0.176897
$358$	6.08990	+	22.8939i	0.321861	+	1.20998i
$359$	10.2985			0.543532			0.271766	−	0.962363i	$-0.412392\pi$
$359$	10.2985			0.543532			0.271766	+	0.962363i	$0.412392\pi$
$360$	−14.6568	+	9.79945i	−0.772480	+	0.516477i
$361$	14.3702			0.756326
$362$	1.60130	+	6.01979i	0.0841623	+	0.316393i
$363$	−5.11441			−0.268437
$364$	0.901285	+	1.57424i	0.0472402	+	0.0825125i
$365$	−2.46898	+	12.7953i	−0.129232	+	0.669735i
$366$	−1.03882	−	3.90528i	−0.0543002	−	0.204132i
$367$			21.6339i			1.12928i	0.825337	+	0.564640i	$0.190985\pi$
$367$			21.6339i			1.12928i	−0.825337	+	0.564640i	$0.809015\pi$
$368$	−20.3516	−	11.9478i	−1.06090	−	0.622822i
$369$	17.3332			0.902330
$370$	−19.6040	+	1.36205i	−1.01916	+	0.0708098i
$371$			4.96064i			0.257543i
$372$	−6.42051	+	3.67588i	−0.332888	+	0.190586i
$373$	−1.59921			−0.0828039			−0.0414020	−	0.999143i	$-0.513182\pi$
$373$	−1.59921			−0.0828039			−0.0414020	+	0.999143i	$0.513182\pi$
$374$	46.6061	−	12.3975i	2.40995	−	0.641058i
$375$	−4.33187	−	2.78794i	−0.223697	−	0.143968i
$376$	7.57761	+	7.66056i	0.390785	+	0.395063i
$377$			6.27330i			0.323091i
$378$	0.969487	+	3.64462i	0.0498650	+	0.187459i
$379$			9.67642i			0.497044i	0.968626	+	0.248522i	$0.0799449\pi$
$379$			9.67642i			0.497044i	−0.968626	+	0.248522i	$0.920055\pi$
$380$	−3.11226	−	9.10549i	−0.159656	−	0.467102i
$381$			4.19477i			0.214904i
$382$	−32.2837	+	8.58764i	−1.65178	+	0.439382i
$383$		−	0.198092i		−	0.0101220i	−0.999987	−	0.00506102i	$-0.998389\pi$
$383$		−	0.198092i		−	0.0101220i	0.999987	−	0.00506102i	$-0.00161098\pi$
$384$	1.28514	+	5.05203i	0.0655820	+	0.257810i
$385$	10.3215	+	1.99164i	0.526031	+	0.101503i
$386$	6.17456	+	23.2122i	0.314277	+	1.18147i
$387$	−26.0068			−1.32200
$388$	11.5717	+	20.2118i	0.587464	+	1.02610i
$389$		−	27.9997i		−	1.41964i	−0.704382	−	0.709821i	$-0.748776\pi$
$389$		−	27.9997i		−	1.41964i	0.704382	−	0.709821i	$-0.251224\pi$
$390$	1.31836	−	0.0915977i	0.0667579	−	0.00463823i
$391$	42.7979			2.16438
$392$	2.01086	−	1.98908i	0.101564	−	0.100464i
$393$		−	1.63437i		−	0.0824428i
$394$	−9.74229	+	2.59150i	−0.490810	+	0.130558i
$395$	−17.6871	−	3.41292i	−0.889935	−	0.171722i
$396$	−13.0227	−	22.7461i	−0.654413	−	1.14304i
$397$	9.16728			0.460093			0.230046	−	0.973180i	$-0.426112\pi$
$397$	9.16728			0.460093			0.230046	+	0.973180i	$0.426112\pi$
$398$	10.3864	−	2.76283i	0.520622	−	0.138488i
$399$	−0.991422			−0.0496332
$400$	15.8157	−	12.2418i	0.790786	−	0.612092i
$401$	−25.8889			−1.29283			−0.646416	−	0.762986i	$-0.723733\pi$
$401$	−25.8889			−1.29283			−0.646416	+	0.762986i	$0.723733\pi$
$402$	−3.41765	+	0.909113i	−0.170457	+	0.0453425i
$403$	−7.28165			−0.362725
$404$	−10.3757	−	18.1229i	−0.516212	−	0.901646i
$405$	−15.6640	−	3.02253i	−0.778348	−	0.150191i
$406$	9.45282	−	2.51450i	0.469135	−	0.124792i
$407$		−	29.2136i		−	1.44806i
$408$	−6.64827	−	6.72105i	−0.329138	−	0.332741i
$409$	−2.34443			−0.115924			−0.0579622	−	0.998319i	$-0.518460\pi$
$409$	−2.34443			−0.115924			−0.0579622	+	0.998319i	$0.518460\pi$
$410$	−19.6150	+	1.36282i	−0.968713	+	0.0673047i
$411$			3.96928i			0.195790i
$412$	0.967892	+	1.69058i	0.0476846	+	0.0832888i
$413$	11.7227			0.576835
$414$	−5.97928	−	22.4781i	−0.293866	−	1.10474i
$415$	23.0850	+	4.45450i	1.13320	+	0.218663i
$416$	−1.37284	+	4.94365i	−0.0673089	+	0.242382i
$417$			1.21283i			0.0593924i
$418$	13.8244	−	3.67736i	0.676173	−	0.179866i
$419$		−	20.5898i		−	1.00588i	−0.864323	−	0.502938i	$-0.832253\pi$
$419$		−	20.5898i		−	1.00588i	0.864323	−	0.502938i	$-0.167747\pi$
$420$	−0.666456	−	1.94984i	−0.0325197	−	0.0951424i
$421$		−	2.24931i		−	0.109625i	−0.998497	−	0.0548123i	$-0.982544\pi$
$421$		−	2.24931i		−	0.109625i	0.998497	−	0.0548123i	$-0.0174560\pi$
$422$	−4.56378	−	17.1567i	−0.222161	−	0.835177i
$423$			10.6200i			0.516363i
$424$	−9.97513	+	9.86711i	−0.484435	+	0.479189i
$425$	−13.4949	+	33.6661i	−0.654601	+	1.63305i
$426$	−1.10051	+	0.292741i	−0.0533198	+	0.0141834i
$427$	−6.20163			−0.300118
$428$	−6.18690	+	3.54213i	−0.299055	+	0.171215i
$429$			1.96461i			0.0948521i
$430$	29.4304	−	2.04478i	1.41926	−	0.0986080i
$431$	−2.18110			−0.105060			−0.0525299	−	0.998619i	$-0.516728\pi$
$431$	−2.18110			−0.105060			−0.0525299	+	0.998619i	$0.516728\pi$
$432$	−5.40041	+	9.19894i	−0.259828	+	0.442584i
$433$			7.03200i			0.337936i	0.985622	+	0.168968i	$0.0540435\pi$
$433$			7.03200i			0.337936i	−0.985622	+	0.168968i	$0.945956\pi$
$434$	2.91867	+	10.9722i	0.140101	+	0.526684i
$435$	1.35016	−	6.99706i	0.0647351	−	0.335483i
$436$	10.9161	+	19.0667i	0.522785	+	0.913127i
$437$	12.6948			0.607274
$438$	0.976200	+	3.66985i	0.0466447	+	0.175352i
$439$	5.52633			0.263757			0.131879	−	0.991266i	$-0.457899\pi$
$439$	5.52633			0.263757			0.131879	+	0.991266i	$0.457899\pi$
$440$	16.5254	+	24.7166i	0.787816	+	1.17832i
$441$	2.78770			0.132748
$442$	−2.39189	−	8.99191i	−0.113771	−	0.427701i
$443$	16.0527			0.762685			0.381342	−	0.924434i	$-0.375462\pi$
$443$	16.0527			0.762685			0.381342	+	0.924434i	$0.375462\pi$
$444$	−4.96974	+	2.84528i	−0.235853	+	0.135031i
$445$	−25.2860	−	4.87920i	−1.19867	−	0.231296i
$446$	−2.62628	−	9.87305i	−0.124358	−	0.467502i
$447$			0.621596i			0.0294005i
$448$	7.99953	+	0.0870983i	0.377942	+	0.00411501i
$449$	35.7937			1.68921			0.844606	−	0.535389i	$-0.179835\pi$
$449$	35.7937			1.68921			0.844606	+	0.535389i	$0.179835\pi$
$450$	19.5673	+	2.38425i	0.922410	+	0.112394i
$451$		−	29.2300i		−	1.37638i
$452$	13.5413	+	23.6520i	0.636927	+	1.11250i
$453$	0.485481			0.0228099
$454$	−8.63233	+	2.29625i	−0.405135	+	0.107768i
$455$	0.384255	−	1.99136i	0.0180141	−	0.0933565i
$456$	−1.97202	−	1.99361i	−0.0923483	−	0.0933593i
$457$		−	10.5179i		−	0.492007i	−0.969269	−	0.246004i	$-0.920882\pi$
$457$		−	10.5179i		−	0.492007i	0.969269	−	0.246004i	$-0.0791175\pi$
$458$	−7.44206	−	27.9771i	−0.347745	−	1.30729i
$459$		−	19.3447i		−	0.902932i
$460$	8.53372	+	24.9670i	0.397887	+	1.16409i
$461$			3.48563i			0.162342i	0.996700	+	0.0811711i	$0.0258660\pi$
$461$			3.48563i			0.162342i	−0.996700	+	0.0811711i	$0.974134\pi$
$462$	2.96034	−	0.787465i	0.137727	−	0.0366362i
$463$		−	17.0646i		−	0.793060i	−0.918022	−	0.396530i	$-0.870214\pi$
$463$		−	17.0646i		−	0.793060i	0.918022	−	0.396530i	$-0.129786\pi$
$464$	23.8587	+	14.0067i	1.10761	+	0.650246i
$465$	8.12175	+	1.56718i	0.376637	+	0.0726761i
$466$	−4.58626	−	17.2412i	−0.212454	−	0.798684i
$467$	20.2827			0.938572			0.469286	−	0.883046i	$-0.344511\pi$
$467$	20.2827			0.938572			0.469286	+	0.883046i	$0.344511\pi$
$468$	−4.38850	+	2.51251i	−0.202859	+	0.116141i
$469$			5.42728i			0.250608i
$470$	−0.834994	−	12.0180i	−0.0385154	−	0.554351i
$471$	3.18278			0.146655
$472$	23.3174	+	23.5726i	1.07327	+	1.08502i
$473$			43.8568i			2.01654i
$474$	−5.07290	+	1.34942i	−0.233006	+	0.0619808i
$475$	−4.00289	+	9.98610i	−0.183665	+	0.458194i
$476$	−12.5906	+	7.20838i	−0.577088	+	0.330395i
$477$	−13.8288			−0.633175
$478$	−33.8306	+	8.99912i	−1.54738	+	0.411610i
$479$	−29.4100			−1.34378			−0.671889	−	0.740652i	$-0.734517\pi$
$479$	−29.4100			−1.34378			−0.671889	+	0.740652i	$0.734517\pi$
$480$	2.59521	−	5.21854i	0.118455	−	0.238193i
$481$	−5.63629			−0.256993
$482$	−13.4532	+	3.57863i	−0.612778	+	0.163002i
$483$	2.71844			0.123694
$484$	−19.2657	+	11.0301i	−0.875716	+	0.501366i
$485$	4.93349	−	25.5673i	0.224018	−	1.16095i
$486$	−15.4265	+	4.10352i	−0.699759	+	0.186140i
$487$		−	8.24187i		−	0.373475i	−0.982410	−	0.186737i	$-0.940209\pi$
$487$		−	8.24187i		−	0.373475i	0.982410	−	0.186737i	$-0.0597914\pi$
$488$	−12.3356	−	12.4706i	−0.558405	−	0.564518i
$489$	1.75624			0.0794198
$490$	−3.15467	+	0.219182i	−0.142514	+	0.00990162i
$491$		−	13.7812i		−	0.621937i	−0.950420	−	0.310969i	$-0.899347\pi$
$491$		−	13.7812i		−	0.621937i	0.950420	−	0.310969i	$-0.100653\pi$
$492$	−4.97252	+	2.84687i	−0.224179	+	0.128347i
$493$	−50.1731			−2.25968
$494$	−0.709488	−	2.66719i	−0.0319214	−	0.120003i
$495$	−5.55209	+	28.7732i	−0.249548	+	1.29326i
$496$	−16.2581	+	27.6937i	−0.730012	+	1.24349i
$497$			1.74762i			0.0783916i
$498$	6.62110	−	1.76125i	0.296699	−	0.0789234i
$499$		−	9.19790i		−	0.411755i	−0.978578	−	0.205877i	$-0.933995\pi$
$499$		−	9.19790i		−	0.411755i	0.978578	−	0.205877i	$-0.0660048\pi$
$500$	−22.3306	−	1.15964i	−0.998654	−	0.0518607i
$501$			2.74990i			0.122857i
$502$	−2.06735	−	7.77185i	−0.0922705	−	0.346875i
$503$		−	37.3905i		−	1.66716i	−0.552400	−	0.833579i	$-0.686288\pi$
$503$		−	37.3905i		−	1.66716i	0.552400	−	0.833579i	$-0.313712\pi$
$504$	5.54496	+	5.60566i	0.246992	+	0.249696i
$505$	−4.42359	+	22.9249i	−0.196847	+	1.02014i
$506$	−37.9060	+	10.0832i	−1.68513	+	0.448253i
$507$	−5.61087			−0.249187
$508$	9.04669	+	15.8015i	0.401382	+	0.701077i
$509$			34.5582i			1.53177i	0.642980	+	0.765883i	$0.277698\pi$
$509$			34.5582i			1.53177i	−0.642980	+	0.765883i	$0.722302\pi$
$510$	0.732588	+	10.5441i	0.0324396	+	0.466901i
$511$	5.82777			0.257806
$512$	15.7366	+	16.2592i	0.695465	+	0.718560i
$513$		−	5.73805i		−	0.253341i
$514$	3.58369	+	13.4722i	0.158070	+	0.594235i
$515$	0.412652	−	2.13853i	0.0181836	−	0.0942348i
$516$	7.46080	−	4.27147i	0.328443	−	0.188041i
$517$	17.9091			0.787642
$518$	2.25917	+	8.49296i	0.0992623	+	0.373159i
$519$	−4.39382			−0.192867
$520$	4.76866	−	3.18830i	0.209120	−	0.139816i
$521$	39.5046			1.73073			0.865363	−	0.501146i	$-0.167088\pi$
$521$	39.5046			1.73073			0.865363	+	0.501146i	$0.167088\pi$
$522$	7.00966	+	26.3516i	0.306805	+	1.15338i
$523$	−10.0402			−0.439026			−0.219513	−	0.975610i	$-0.570447\pi$
$523$	−10.0402			−0.439026			−0.219513	+	0.975610i	$0.570447\pi$
$524$	−3.52477	−	6.15658i	−0.153980	−	0.268951i
$525$	−0.857174	+	2.13841i	−0.0374101	+	0.0933279i
$526$	−1.74541	−	6.56156i	−0.0761035	−	0.286098i
$527$		−	58.2378i		−	2.53688i
$528$	7.47183	+	4.38648i	0.325170	+	0.190897i
$529$	−11.8087			−0.513420
$530$	15.6492	−	1.08728i	0.679757	−	0.0472284i
$531$			32.6793i			1.41816i
$532$	−3.73464	+	2.13816i	−0.161917	+	0.0927010i
$533$	−5.63945			−0.244272
$534$	−7.25236	+	1.92917i	−0.313840	+	0.0834831i
$535$	7.82624	+	1.51016i	0.338358	+	0.0652897i
$536$	−10.9135	+	10.7953i	−0.471390	+	0.466286i
$537$		−	7.71840i		−	0.333074i
$538$	−8.84596	−	33.2548i	−0.381377	−	1.43372i
$539$		−	4.70105i		−	0.202489i
$540$	11.2851	−	3.85725i	0.485632	−	0.165990i
$541$			2.72177i			0.117018i	0.998287	+	0.0585090i	$0.0186346\pi$
$541$			2.72177i			0.117018i	−0.998287	+	0.0585090i	$0.981365\pi$
$542$	29.7361	−	7.90996i	1.27728	−	0.339762i
$543$		−	2.02950i		−	0.0870942i
$544$	−39.5387	−	10.9798i	−1.69521	−	0.470755i
$545$	4.65396	−	24.1187i	0.199354	−	1.03313i
$546$	−0.151929	−	0.571149i	−0.00650195	−	0.0244429i
$547$	−16.6603			−0.712342			−0.356171	−	0.934421i	$-0.615918\pi$
$547$	−16.6603			−0.712342			−0.356171	+	0.934421i	$0.615918\pi$
$548$	8.56040	+	14.9521i	0.365682	+	0.638722i
$549$		−	17.2883i		−	0.737846i
$550$	4.02069	−	32.9974i	0.171443	−	1.40701i
$551$	−14.8824			−0.634013
$552$	5.40721	+	5.46641i	0.230146	+	0.232666i
$553$			8.05583i			0.342569i
$554$	15.1255	−	4.02345i	0.642619	−	0.170940i
$555$	6.28656	+	1.21306i	0.266850	+	0.0514915i
$556$	2.61566	+	4.56866i	0.110929	+	0.193754i
$557$	18.4977			0.783774			0.391887	−	0.920013i	$-0.371822\pi$
$557$	18.4977			0.783774			0.391887	+	0.920013i	$0.371822\pi$
$558$	−30.5873	+	8.13638i	−1.29486	+	0.344441i
$559$	8.46147			0.357882
$560$	−6.71565	−	5.90763i	−0.283788	−	0.249643i
$561$	−15.7127			−0.663391
$562$	−10.2029	+	2.71402i	−0.430383	+	0.114484i
$563$	38.2569			1.61234			0.806169	−	0.591685i	$-0.201537\pi$
$563$	38.2569			1.61234			0.806169	+	0.591685i	$0.201537\pi$
$564$	−1.74427	−	3.04665i	−0.0734472	−	0.128287i
$565$	5.77319	−	29.9190i	0.242880	−	1.25870i
$566$	−17.6392	+	4.69213i	−0.741432	+	0.197225i
$567$			7.13436i			0.299615i
$568$	−3.51422	+	3.47617i	−0.147453	+	0.145857i
$569$	−29.2380			−1.22572			−0.612859	−	0.790192i	$-0.709981\pi$
$569$	−29.2380			−1.22572			−0.612859	+	0.790192i	$0.709981\pi$
$570$	0.217302	+	3.12761i	0.00910176	+	0.131001i
$571$		−	23.5861i		−	0.987046i	−0.869733	−	0.493523i	$-0.835709\pi$
$571$		−	23.5861i		−	0.987046i	0.869733	−	0.493523i	$-0.164291\pi$
$572$	4.23699	+	7.40058i	0.177157	+	0.309434i
$573$	10.8841			0.454688
$574$	2.26044	+	8.49771i	0.0943488	+	0.354688i
$575$	10.9758	−	27.3815i	0.457722	−	1.14189i
$576$	−0.242804	+	22.3003i	−0.0101168	+	0.929178i
$577$			19.5025i			0.811898i	0.913896	+	0.405949i	$0.133059\pi$
$577$			19.5025i			0.811898i	−0.913896	+	0.405949i	$0.866941\pi$
$578$	48.6825	−	12.9498i	2.02493	−	0.538641i
$579$		−	7.82570i		−	0.325225i
$580$	−10.0043	−	29.2694i	−0.415406	−	1.21535i
$581$		−	10.5144i		−	0.436210i
$582$	−1.95063	−	7.33305i	−0.0808562	−	0.303965i
$583$			23.3202i			0.965824i
$584$	11.5919	+	11.7188i	0.479677	+	0.484928i
$585$	5.55132	+	1.07119i	0.229519	+	0.0442881i
$586$	22.6843	−	6.03415i	0.937081	−	0.249269i
$587$	26.1827			1.08067			0.540337	−	0.841449i	$-0.318297\pi$
$587$	26.1827			1.08067			0.540337	+	0.841449i	$0.318297\pi$
$588$	−0.799730	+	0.457863i	−0.0329803	+	0.0188819i
$589$		−	17.2746i		−	0.711787i
$590$	−2.56940	−	36.9812i	−0.105780	−	1.52249i
$591$	3.28450			0.135106
$592$	−12.5844	+	21.4361i	−0.517218	+	0.881017i
$593$			12.4309i			0.510474i	0.966878	+	0.255237i	$0.0821536\pi$
$593$			12.4309i			0.510474i	−0.966878	+	0.255237i	$0.917846\pi$
$594$	4.55761	+	17.1335i	0.187001	+	0.702997i
$595$	15.9267	+	3.07322i	0.652931	+	0.125990i
$596$	1.34057	+	2.34152i	0.0549119	+	0.0959125i
$597$	−3.50164			−0.143313
$598$	1.94539	+	7.31335i	0.0795529	+	0.299065i
$599$	−2.39815			−0.0979859			−0.0489929	−	0.998799i	$-0.515601\pi$
$599$	−2.39815			−0.0979859			−0.0489929	+	0.998799i	$0.515601\pi$
$600$	−6.00503	+	2.52982i	−0.245154	+	0.103279i
$601$	−9.37275			−0.382322			−0.191161	−	0.981559i	$-0.561225\pi$
$601$	−9.37275			−0.382322			−0.191161	+	0.981559i	$0.561225\pi$
$602$	−3.39157	−	12.7500i	−0.138230	−	0.519652i
$603$	−15.1296			−0.616125
$604$	1.82878	−	1.04702i	0.0744122	−	0.0426026i
$605$	24.3706	+	4.70256i	0.990804	+	0.191186i
$606$	1.74903	+	6.57515i	0.0710493	+	0.267097i
$607$		−	34.0497i		−	1.38203i	−0.722839	−	0.691017i	$-0.757163\pi$
$607$		−	34.0497i		−	1.38203i	0.722839	−	0.691017i	$-0.242837\pi$
$608$	−11.7280	−	3.25685i	−0.475635	−	0.132083i
$609$	−3.18690			−0.129140
$610$	1.35928	+	19.5641i	0.0550358	+	0.792128i
$611$		−	3.45528i		−	0.139786i
$612$	−20.0948	−	35.0987i	−0.812283	−	1.41878i
$613$	−2.83753			−0.114607			−0.0573035	−	0.998357i	$-0.518250\pi$
$613$	−2.83753			−0.114607			−0.0573035	+	0.998357i	$0.518250\pi$
$614$	−30.7382	+	8.17651i	−1.24049	+	0.329977i
$615$	6.29008	+	1.21374i	0.253641	+	0.0489427i
$616$	9.45315	−	9.35078i	0.380878	−	0.376754i
$617$		−	32.4594i		−	1.30677i	−0.757027	−	0.653384i	$-0.773349\pi$
$617$		−	32.4594i		−	1.30677i	0.757027	−	0.653384i	$-0.226651\pi$
$618$	−0.163157	−	0.613358i	−0.00656312	−	0.0246729i
$619$			10.5243i			0.423006i	0.977377	+	0.211503i	$0.0678359\pi$
$619$			10.5243i			0.423006i	−0.977377	+	0.211503i	$0.932164\pi$
$620$	33.9741	−	11.6124i	1.36443	−	0.466364i
$621$			15.7335i			0.631365i
$622$	18.5080	−	4.92323i	0.742104	−	0.197404i
$623$			11.5168i			0.461412i
$624$	0.846301	−	1.44157i	0.0338792	−	0.0577090i
$625$	18.0783	+	17.2678i	0.723131	+	0.690711i
$626$	3.04006	+	11.4286i	0.121505	+	0.456778i
$627$	−4.66073			−0.186131
$628$	11.9894	−	6.86419i	0.478429	−	0.273911i
$629$		−	45.0784i		−	1.79739i
$630$	−0.611012	−	8.79428i	−0.0243433	−	0.350372i
$631$	−8.92822			−0.355427			−0.177713	−	0.984082i	$-0.556870\pi$
$631$	−8.92822			−0.355427			−0.177713	+	0.984082i	$0.556870\pi$
$632$	−16.1991	+	16.0237i	−0.644367	+	0.637389i
$633$			5.78419i			0.229901i
$634$	13.0544	−	3.47255i	0.518458	−	0.137913i
$635$	3.85697	−	19.9884i	0.153059	−	0.793215i
$636$	3.96717	−	2.27129i	0.157309	−	0.0900625i
$637$	−0.906993			−0.0359364
$638$	44.4382	−	11.8208i	1.75932	−	0.467990i
$639$	−4.87184			−0.192727
$640$	−1.47858	−	25.2550i	−0.0584461	−	0.998291i
$641$	3.21151			0.126847			0.0634235	−	0.997987i	$-0.479798\pi$
$641$	3.21151			0.126847			0.0634235	+	0.997987i	$0.479798\pi$
$642$	2.24467	−	0.597094i	0.0885900	−	0.0235654i
$643$	−19.3330			−0.762418			−0.381209	−	0.924489i	$-0.624492\pi$
$643$	−19.3330			−0.762418			−0.381209	+	0.924489i	$0.624492\pi$
$644$	10.2402	−	5.86276i	0.403522	−	0.231025i
$645$	−9.43768	−	1.82110i	−0.371608	−	0.0717058i
$646$	21.3319	−	5.67440i	0.839293	−	0.223256i
$647$		−	44.1500i		−	1.73571i	−0.496814	−	0.867857i	$-0.665497\pi$
$647$		−	44.1500i		−	1.73571i	0.496814	−	0.867857i	$-0.334503\pi$
$648$	−14.3462	+	14.1908i	−0.563571	+	0.557468i
$649$	55.1089			2.16321
$650$	−6.36632	−	0.775727i	−0.249708	−	0.0304265i
$651$		−	3.69916i		−	0.144981i
$652$	6.61566	−	3.78761i	0.259089	−	0.148334i
$653$	−15.5908			−0.610114			−0.305057	−	0.952334i	$-0.598676\pi$
$653$	−15.5908			−0.610114			−0.305057	+	0.952334i	$0.598676\pi$
$654$	−1.84011	−	6.91757i	−0.0719540	−	0.270498i
$655$	−1.50275	+	7.78788i	−0.0587174	+	0.304298i
$656$	−12.5915	+	21.4481i	−0.491615	+	0.837407i
$657$			16.2461i			0.633820i
$658$	−5.20653	+	1.38496i	−0.202972	+	0.0539915i
$659$			46.2070i			1.79997i	0.435923	+	0.899984i	$0.356422\pi$
$659$			46.2070i			1.79997i	−0.435923	+	0.899984i	$0.643578\pi$
$660$	−3.13305	−	9.16629i	−0.121954	−	0.356798i
$661$			20.3644i			0.792082i	0.918233	+	0.396041i	$0.129616\pi$
$661$			20.3644i			0.792082i	−0.918233	+	0.396041i	$0.870384\pi$
$662$	−1.46275	−	5.49894i	−0.0568513	−	0.213723i
$663$			3.03151i			0.117734i
$664$	21.1429	−	20.9140i	0.820505	−	0.811620i
$665$	4.72420	+	0.911585i	0.183197	+	0.0353497i
$666$	−23.6758	+	6.29789i	−0.917419	+	0.244038i
$667$	40.8071			1.58006
$668$	5.93060	+	10.3587i	0.229462	+	0.400792i
$669$			3.32858i			0.128690i
$670$	17.1213	−	1.18956i	0.661453	−	0.0459567i
$671$	−29.1542			−1.12549
$672$	−2.51143	−	0.697417i	−0.0968804	−	0.0269034i
$673$		−	7.07374i		−	0.272673i	−0.990663	−	0.136336i	$-0.956467\pi$
$673$		−	7.07374i		−	0.272673i	0.990663	−	0.136336i	$-0.0435328\pi$
$674$	−0.854624	−	3.21281i	−0.0329189	−	0.123753i
$675$	−12.3765	−	4.96106i	−0.476371	−	0.190951i
$676$	−21.1359	+	12.1007i	−0.812918	+	0.465413i
$677$	−6.92717			−0.266233			−0.133116	−	0.991100i	$-0.542498\pi$
$677$	−6.92717			−0.266233			−0.133116	+	0.991100i	$0.542498\pi$
$678$	−2.28264	−	8.58117i	−0.0876641	−	0.329558i
$679$	−11.6450			−0.446893
$680$	25.4997	+	38.1392i	0.977869	+	1.46257i
$681$	2.91029			0.111522
$682$	13.7208	+	51.5811i	0.525398	+	1.97514i
$683$	−34.8750			−1.33445			−0.667227	−	0.744855i	$-0.732519\pi$
$683$	−34.8750			−1.33445			−0.667227	+	0.744855i	$0.732519\pi$
$684$	−5.96055	−	10.4110i	−0.227907	−	0.398076i
$685$	3.64965	−	18.9139i	0.139446	−	0.722664i
$686$	0.363546	+	1.36669i	0.0138803	+	0.0521804i
$687$			9.43215i			0.359859i
$688$	18.8924	−	32.1808i	0.720265	−	1.22688i
$689$	4.49926			0.171408
$690$	−0.595833	−	8.57580i	−0.0226830	−	0.326475i
$691$		−	16.0227i		−	0.609534i	−0.952427	−	0.304767i	$-0.901421\pi$
$691$		−	16.0227i		−	0.609534i	0.952427	−	0.304767i	$-0.0985785\pi$
$692$	−16.5513	+	9.47599i	−0.629187	+	0.360223i
$693$	13.1051			0.497822
$694$	−25.7730	+	6.85575i	−0.978329	+	0.260241i
$695$	1.11516	−	5.77922i	0.0423005	−	0.219218i
$696$	−6.33901	−	6.40841i	−0.240280	−	0.242910i
$697$		−	45.1037i		−	1.70842i
$698$	−13.3137	−	50.0505i	−0.503931	−	1.89444i
$699$			5.81267i			0.219855i
$700$	1.38289	+	9.90392i	0.0522684	+	0.374333i
$701$			18.2912i			0.690848i	0.938447	+	0.345424i	$0.112265\pi$
$701$			18.2912i			0.690848i	−0.938447	+	0.345424i	$0.887735\pi$
$702$	3.30564	−	0.879318i	0.124763	−	0.0331877i
$703$		−	13.3712i		−	0.504306i
$704$	37.6062	+	0.409454i	1.41734	+	0.0154319i
$705$	−0.743655	+	3.85392i	−0.0280077	+	0.145147i
$706$	1.54955	+	5.82527i	0.0583181	+	0.219237i
$707$	10.4414			0.392690
$708$	−5.36738	−	9.37498i	−0.201718	−	0.352333i
$709$		−	14.3639i		−	0.539446i	−0.962938	−	0.269723i	$-0.913068\pi$
$709$		−	14.3639i		−	0.539446i	0.962938	−	0.269723i	$-0.0869321\pi$
$710$	5.51318	−	0.383047i	0.206906	−	0.0143755i
$711$	−22.4572			−0.842212
$712$	−23.1587	+	22.9079i	−0.867910	+	0.858512i
$713$			47.3663i			1.77388i
$714$	4.56799	−	1.21511i	0.170953	−	0.0454743i
$715$	1.80640	−	9.36150i	0.0675556	−	0.350100i
$716$	−16.6460	−	29.0748i	−0.622089	−	1.08658i
$717$	11.4056			0.425949
$718$	−14.0748	+	3.74396i	−0.525266	+	0.139723i
$719$	45.5549			1.69891			0.849456	−	0.527659i	$-0.176930\pi$
$719$	45.5549			1.69891			0.849456	+	0.527659i	$0.176930\pi$
$720$	16.4687	−	18.7212i	0.613752	−	0.697698i
$721$	−0.974021			−0.0362744
$722$	−19.6396	+	5.22423i	−0.730909	+	0.194426i
$723$	4.53559			0.168681
$724$	−4.37694	−	7.64503i	−0.162668	−	0.284125i
$725$	−12.8672	+	32.1001i	−0.477876	+	1.19217i
$726$	6.98980	−	1.85932i	0.259416	−	0.0690060i
$727$			36.7749i			1.36390i	0.731397	+	0.681952i	$0.238869\pi$
$727$			36.7749i			1.36390i	−0.731397	+	0.681952i	$0.761131\pi$
$728$	−1.80408	−	1.82383i	−0.0668638	−	0.0675958i
$729$	−16.2022			−0.600082
$730$	−1.27734	−	18.3847i	−0.0472765	−	0.680449i
$731$			67.6738i			2.50301i
$732$	2.83950	+	4.95963i	0.104951	+	0.183313i
$733$	10.0181			0.370028			0.185014	−	0.982736i	$-0.440767\pi$
$733$	10.0181			0.370028			0.185014	+	0.982736i	$0.440767\pi$
$734$	−7.86492	−	29.5668i	−0.290299	−	1.09133i
$735$	1.01163	+	0.195206i	0.0373147	+	0.00720026i
$736$	32.1579	+	8.93016i	1.18536	+	0.329170i
$737$			25.5139i			0.939817i
$738$	−23.6891	+	6.30142i	−0.872006	+	0.231958i
$739$			6.41780i			0.236082i	0.993009	+	0.118041i	$0.0376615\pi$
$739$			6.41780i			0.236082i	−0.993009	+	0.118041i	$0.962339\pi$
$740$	26.2973	−	8.98845i	0.966709	−	0.330422i
$741$			0.899212i			0.0330334i
$742$	−1.80342	−	6.77964i	−0.0662056	−	0.248888i
$743$			19.0455i			0.698712i	0.936990	+	0.349356i	$0.113600\pi$
$743$			19.0455i			0.698712i	−0.936990	+	0.349356i	$0.886400\pi$
$744$	7.43848	−	7.35793i	0.272708	−	0.269755i
$745$	0.571540	−	2.96195i	0.0209396	−	0.108518i
$746$	2.18562	−	0.581386i	0.0800212	−	0.0212861i
$747$	29.3109			1.07243
$748$	−59.1890	+	33.8870i	−2.16416	+	1.23903i
$749$		−	3.56456i		−	0.130246i
$750$	6.93386	+	2.23540i	0.253189	+	0.0816253i
$751$	27.9139			1.01859			0.509296	−	0.860591i	$-0.329906\pi$
$751$	27.9139			1.01859			0.509296	+	0.860591i	$0.329906\pi$
$752$	−13.1412	−	7.71478i	−0.479210	−	0.281329i
$753$			2.62019i			0.0954849i
$754$	−2.28063	−	8.57363i	−0.0830557	−	0.312233i
$755$	−2.31335	−	0.446386i	−0.0841916	−	0.0162457i
$756$	−2.64997	−	4.62860i	−0.0963785	−	0.168340i
$757$	−39.2145			−1.42528			−0.712638	−	0.701532i	$-0.752500\pi$
$757$	−39.2145			−1.42528			−0.712638	+	0.701532i	$0.752500\pi$
$758$	−3.51782	−	13.2246i	−0.127773	−	0.480341i
$759$	12.7796			0.463868
$760$	7.56376	+	11.3129i	0.274366	+	0.410362i
$761$	−19.8361			−0.719057			−0.359529	−	0.933134i	$-0.617063\pi$
$761$	−19.8361			−0.719057			−0.359529	+	0.933134i	$0.617063\pi$
$762$	−1.52499	−	5.73294i	−0.0552446	−	0.207682i
$763$	−10.9852			−0.397691
$764$	40.9997	−	23.4732i	1.48332	−	0.849231i
$765$	−8.56722	+	44.3988i	−0.309749	+	1.60524i
$766$	0.0720156	+	0.270730i	0.00260203	+	0.00978187i
$767$		−	10.6324i		−	0.383913i
$768$	−3.59303	−	6.43734i	−0.129652	−	0.232288i
$769$	11.4291			0.412144			0.206072	−	0.978537i	$-0.433932\pi$
$769$	11.4291			0.412144			0.206072	+	0.978537i	$0.433932\pi$
$770$	−14.8303	+	1.03038i	−0.534446	+	0.0371325i
$771$		−	4.54200i		−	0.163576i
$772$	−16.8774	−	29.4791i	−0.607431	−	1.06097i
$773$	−49.5840			−1.78341			−0.891707	−	0.452614i	$-0.850492\pi$
$773$	−49.5840			−1.78341			−0.891707	+	0.452614i	$0.850492\pi$
$774$	35.5432	−	9.45469i	1.27757	−	0.339842i
$775$	−37.2598	−	14.9354i	−1.33841	−	0.536497i
$776$	−23.1628	−	23.4164i	−0.831497	−	0.840600i
$777$		−	2.86330i		−	0.102720i
$778$	10.1792	+	38.2669i	0.364941	+	1.37193i
$779$		−	13.3787i		−	0.479342i
$780$	−1.76849	+	0.604471i	−0.0633221	+	0.0216435i
$781$			8.21566i			0.293980i
$782$	−58.4914	+	15.5590i	−2.09165	+	0.556389i
$783$		−	18.4448i		−	0.659164i
$784$	−2.02509	+	3.44949i	−0.0723247	+	0.123196i
$785$	−15.1662	−	2.92648i	−0.541305	−	0.104451i
$786$	0.594167	+	2.23367i	0.0211932	+	0.0796722i
$787$	−21.3743			−0.761911			−0.380955	−	0.924593i	$-0.624405\pi$
$787$	−21.3743			−0.761911			−0.380955	+	0.924593i	$0.624405\pi$
$788$	12.3725	−	7.08354i	0.440753	−	0.252341i
$789$			2.21215i			0.0787547i
$790$	25.4135	−	1.76569i	0.904172	−	0.0628205i
$791$	−13.6270			−0.484521
$792$	26.0672	+	26.3525i	0.926256	+	0.936396i
$793$			5.62483i			0.199744i
$794$	−12.5288	+	3.33273i	−0.444631	+	0.118274i
$795$	−5.01835	−	0.968343i	−0.177982	−	0.0343436i
$796$	−13.1905	+	7.55185i	−0.467526	+	0.267668i
$797$	20.4572			0.724630			0.362315	−	0.932056i	$-0.381986\pi$
$797$	20.4572			0.724630			0.362315	+	0.932056i	$0.381986\pi$
$798$	1.35496	−	0.360427i	0.0479652	−	0.0127590i
$799$	27.6349			0.977653
$800$	−17.1647	+	22.4805i	−0.606863	+	0.794806i
$801$	−32.1055			−1.13439
$802$	35.3821	−	9.41182i	1.24938	−	0.332343i
$803$	27.3967			0.966808
$804$	4.34036	−	2.48495i	0.153073	−	0.0876373i
$805$	−12.9536	−	2.49953i	−0.456554	−	0.0880970i
$806$	9.95174	−	2.64722i	0.350535	−	0.0932442i
$807$			11.2115i			0.394662i
$808$	20.7689	+	20.9962i	0.730646	+	0.738645i
$809$	−34.2917			−1.20563			−0.602816	−	0.797881i	$-0.705955\pi$
$809$	−34.2917			−1.20563			−0.602816	+	0.797881i	$0.705955\pi$
$810$	22.5066	−	1.56372i	0.790800	−	0.0549435i
$811$		−	36.9434i		−	1.29726i	−0.761104	−	0.648630i	$-0.775342\pi$
$811$		−	36.9434i		−	1.29726i	0.761104	−	0.648630i	$-0.224658\pi$
$812$	−12.0049	+	6.87307i	−0.421290	+	0.241197i
$813$	−10.0252			−0.351598
$814$	10.6205	+	39.9258i	0.372248	+	1.39940i
$815$	−8.36860	−	1.61481i	−0.293139	−	0.0565644i
$816$	11.5295	+	6.76862i	0.403614	+	0.236949i
$817$			20.0735i			0.702284i
$818$	3.20410	−	0.852307i	0.112029	−	0.0298002i
$819$		−	2.52842i		−	0.0883502i
$820$	26.3121	−	8.99348i	0.918857	−	0.314066i
$821$			25.4645i			0.888718i	0.895849	+	0.444359i	$0.146568\pi$
$821$			25.4645i			0.888718i	−0.895849	+	0.444359i	$0.853432\pi$
$822$	−1.44302	−	5.42477i	−0.0503310	−	0.189211i
$823$		−	24.8734i		−	0.867032i	−0.901146	−	0.433516i	$-0.857273\pi$
$823$		−	24.8734i		−	0.867032i	0.901146	−	0.433516i	$-0.142727\pi$
$824$	−1.93741	−	1.95862i	−0.0674928	−	0.0682317i
$825$	−4.02962	+	10.0528i	−0.140293	+	0.349993i
$826$	−16.0212	+	4.26173i	−0.557450	+	0.148285i
$827$	4.26715			0.148383			0.0741917	−	0.997244i	$-0.476362\pi$
$827$	4.26715			0.148383			0.0741917	+	0.997244i	$0.476362\pi$
$828$	16.3436	+	28.5467i	0.567980	+	0.992067i
$829$		−	30.6203i		−	1.06349i	−0.846906	−	0.531743i	$-0.821537\pi$
$829$		−	30.6203i		−	1.06349i	0.846906	−	0.531743i	$-0.178463\pi$
$830$	−33.1695	+	2.30456i	−1.15133	+	0.0799925i
$831$	−5.09937			−0.176895
$832$	0.0789975	−	7.25551i	0.00273875	−	0.251540i
$833$		−	7.25402i		−	0.251337i
$834$	−0.440919	−	1.65756i	−0.0152678	−	0.0573965i
$835$	2.52846	−	13.1035i	0.0875009	−	0.453465i
$836$	−17.5567	+	10.0516i	−0.607212	+	0.347642i
$837$	21.4096			0.740024
$838$	7.48532	+	28.1398i	0.258576	+	0.972072i
$839$	−18.2282			−0.629308			−0.314654	−	0.949206i	$-0.601888\pi$
$839$	−18.2282			−0.629308			−0.314654	+	0.949206i	$0.601888\pi$
$840$	1.61969	+	2.42253i	0.0558847	+	0.0835853i
$841$	−18.8392			−0.649628
$842$	0.817727	+	3.07410i	0.0281807	+	0.105940i
$843$	3.43978			0.118472
$844$	12.4745	+	21.7888i	0.429391	+	0.750000i
$845$	26.7362	+	5.15904i	0.919754	+	0.177476i
$846$	−3.86086	−	14.5142i	−0.132739	−	0.499010i
$847$		−	11.0999i		−	0.381397i
$848$	10.0457	−	17.1117i	0.344972	−	0.587618i
$849$	5.94685			0.204095
$850$	6.20418	−	50.9171i	0.212801	−	1.74644i
$851$			36.6635i			1.25681i
$852$	1.39763	−	0.800171i	0.0478819	−	0.0274134i
$853$	55.5473			1.90190			0.950951	−	0.309340i	$-0.100108\pi$
$853$	55.5473			1.90190			0.950951	+	0.309340i	$0.100108\pi$
$854$	8.47569	−	2.25458i	0.290032	−	0.0771501i
$855$	−2.54122	+	13.1696i	−0.0869080	+	0.450392i
$856$	7.16783	−	7.09021i	0.244991	−	0.242338i
$857$		−	18.4129i		−	0.628974i	−0.949262	−	0.314487i	$-0.898168\pi$
$857$		−	18.4129i		−	0.628974i	0.949262	−	0.314487i	$-0.101832\pi$
$858$	−0.714225	−	2.68500i	−0.0243832	−	0.0916645i
$859$			54.3135i			1.85315i	0.376108	+	0.926576i	$0.377262\pi$
$859$			54.3135i			1.85315i	−0.376108	+	0.926576i	$0.622738\pi$
$860$	−39.4788	+	13.4939i	−1.34622	+	0.460137i
$861$		−	2.86490i		−	0.0976356i
$862$	2.98088	−	0.792930i	0.101529	−	0.0270073i
$863$			54.3942i			1.85160i	0.378012	+	0.925801i	$0.376608\pi$
$863$			54.3942i			1.85160i	−0.378012	+	0.925801i	$0.623392\pi$
$864$	4.03644	−	14.5354i	0.137322	−	0.494504i
$865$	20.9369	+	4.04000i	0.711876	+	0.137364i
$866$	−2.55646	−	9.61054i	−0.0868719	−	0.326580i
$867$	−16.4127			−0.557406
$868$	−7.97783	−	13.9345i	−0.270785	−	0.472969i
$869$			37.8709i			1.28468i
$870$	0.698511	+	10.0536i	0.0236817	+	0.340850i
$871$	4.92250			0.166792
$872$	−21.8505	−	22.0897i	−0.739950	−	0.748050i
$873$		−	32.4627i		−	1.09870i
$874$	−17.3498	+	4.61514i	−0.586866	+	0.156109i
$875$	6.05071	−	9.40154i	0.204551	−	0.317830i
$876$	−2.66832	−	4.66065i	−0.0901542	−	0.157469i
$877$	42.2117			1.42539			0.712694	−	0.701475i	$-0.247475\pi$
$877$	42.2117			1.42539			0.712694	+	0.701475i	$0.247475\pi$
$878$	−7.55277	+	2.00908i	−0.254894	+	0.0678030i
$879$	−7.64775			−0.257952
$880$	−31.5706	−	27.7721i	−1.06425	−	0.936196i
$881$	−11.6420			−0.392230			−0.196115	−	0.980581i	$-0.562833\pi$
$881$	−11.6420			−0.392230			−0.196115	+	0.980581i	$0.562833\pi$
$882$	−3.80991	+	1.01346i	−0.128286	+	0.0341249i
$883$	−47.4507			−1.59684			−0.798421	−	0.602099i	$-0.794331\pi$
$883$	−47.4507			−1.59684			−0.798421	+	0.602099i	$0.794331\pi$
$884$	6.53794	+	11.4196i	0.219895	+	0.384081i
$885$	−2.28833	+	11.8591i	−0.0769214	+	0.398638i
$886$	−21.9390	+	5.83588i	−0.737054	+	0.196060i
$887$			48.2129i			1.61883i	0.587236	+	0.809416i	$0.300216\pi$
$887$			48.2129i			1.61883i	−0.587236	+	0.809416i	$0.699784\pi$
$888$	5.75768	−	5.69534i	0.193215	−	0.191123i
$889$	−9.10398			−0.305338
$890$	36.3319	−	2.52428i	1.21785	−	0.0846141i
$891$			33.5390i			1.12360i
$892$	7.17861	+	12.5386i	0.240358	+	0.419823i
$893$	8.19711			0.274306
$894$	−0.225979	−	0.849527i	−0.00755786	−	0.0284124i
$895$	−7.09685	+	36.7788i	−0.237222	+	1.22938i
$896$	−10.9645	+	2.78916i	−0.366299	+	0.0931793i
$897$		−	2.46561i		−	0.0823243i
$898$	−48.9189	+	13.0127i	−1.63244	+	0.434239i
$899$		−	55.5288i		−	1.85199i
$900$	−27.6091	+	3.85509i	−0.920305	+	0.128503i
$901$			35.9846i			1.19882i
$902$	10.6264	+	39.9482i	0.353821	+	1.33013i
$903$			4.29852i			0.143046i
$904$	−27.1053	−	27.4020i	−0.901507	−	0.911376i
$905$	−1.86607	+	9.67073i	−0.0620302	+	0.321466i
$906$	−0.663501	+	0.176495i	−0.0220433	+	0.00586364i
$907$	−20.0205			−0.664770			−0.332385	−	0.943144i	$-0.607853\pi$
$907$	−20.0205			−0.664770			−0.332385	+	0.943144i	$0.607853\pi$
$908$	10.9629	−	6.27650i	0.363817	−	0.208293i
$909$			29.1076i			0.965437i
$910$	0.198796	+	2.86126i	0.00659003	+	0.0948500i
$911$	−27.8697			−0.923365			−0.461682	−	0.887045i	$-0.652754\pi$
$911$	−27.8697			−0.923365			−0.461682	+	0.887045i	$0.652754\pi$
$912$	3.41990	+	2.00772i	0.113244	+	0.0664822i
$913$		−	49.4287i		−	1.63585i
$914$	3.82375	+	14.3747i	0.126478	+	0.475473i
$915$	1.21059	−	6.27378i	0.0400210	−	0.207405i
$916$	20.3420	+	35.5305i	0.672117	+	1.17396i
$917$	3.54709			0.117135
$918$	7.03268	+	26.4381i	0.232113	+	0.872588i
$919$	−30.5251			−1.00693			−0.503465	−	0.864016i	$-0.667942\pi$
$919$	−30.5251			−1.00693			−0.503465	+	0.864016i	$0.667942\pi$
$920$	−20.7396	−	31.0196i	−0.683763	−	1.02269i
$921$	10.3630			0.341472
$922$	−1.26719	−	4.76377i	−0.0417326	−	0.156886i
$923$	1.58508			0.0521736
$924$	−3.75957	+	2.15244i	−0.123681	+	0.0708100i
$925$	−28.8406	−	11.5606i	−0.948272	−	0.380111i
$926$	6.20378	+	23.3220i	0.203869	+	0.766409i
$927$		−	2.71528i		−	0.0891814i
$928$	−37.6995	−	10.4691i	−1.23755	−	0.343664i
$929$	9.09643			0.298444			0.149222	−	0.988804i	$-0.452323\pi$
$929$	9.09643			0.298444			0.149222	+	0.988804i	$0.452323\pi$
$930$	−11.6696	+	0.810788i	−0.382662	+	0.0265868i
$931$		−	2.15170i		−	0.0705191i
$932$	12.5360	+	21.8960i	0.410629	+	0.717229i
$933$	−6.23976			−0.204281
$934$	−27.7201	+	7.37370i	−0.907030	+	0.241275i
$935$	74.8722	+	14.4474i	2.44858	+	0.472480i
$936$	5.08430	−	5.02924i	0.166185	−	0.164386i
$937$		−	23.6954i		−	0.774095i	−0.922060	−	0.387047i	$-0.873495\pi$
$937$		−	23.6954i		−	0.774095i	0.922060	−	0.387047i	$-0.126505\pi$
$938$	−1.97306	−	7.41739i	−0.0644228	−	0.242186i
$939$		−	3.85301i		−	0.125738i
$940$	5.51029	+	16.1213i	0.179726	+	0.525820i
$941$			21.8195i			0.711294i	0.934620	+	0.355647i	$0.115739\pi$
$941$			21.8195i			0.711294i	−0.934620	+	0.355647i	$0.884261\pi$
$942$	−4.34987	+	1.15709i	−0.141726	+	0.0377000i
$943$			36.6840i			1.19460i
$944$	−40.4373	−	23.7395i	−1.31612	−	0.772654i
$945$	−1.12979	+	5.85503i	−0.0367521	+	0.190464i
$946$	−15.9440	−	59.9385i	−0.518383	−	1.94877i
$947$	−48.8564			−1.58762			−0.793809	−	0.608167i	$-0.791905\pi$
$947$	−48.8564			−1.58762			−0.793809	+	0.608167i	$0.791905\pi$
$948$	6.44249	−	3.68846i	0.209242	−	0.119796i
$949$		−	5.28575i		−	0.171583i
$950$	1.84029	−	15.1031i	0.0597070	−	0.490010i
$951$	−4.40115			−0.142717
$952$	14.5868	−	14.4289i	0.472761	−	0.467642i
$953$		−	9.57502i		−	0.310165i	−0.987901	−	0.155083i	$-0.950436\pi$
$953$		−	9.57502i		−	0.310165i	0.987901	−	0.155083i	$-0.0495644\pi$
$954$	18.8996	−	5.02739i	0.611897	−	0.162768i
$955$	−51.8634	−	10.0076i	−1.67826	−	0.323838i
$956$	42.9643	−	24.5980i	1.38956	−	0.795555i
$957$	−14.9818			−0.484293
$958$	40.1943	−	10.6919i	1.29862	−	0.345439i
$959$	−8.61460			−0.278180
$960$	−1.64966	+	8.07559i	−0.0532427	+	0.260639i
$961$	33.4544			1.07917
$962$	7.70305	−	2.04905i	0.248356	−	0.0660641i
$963$	9.93693			0.320213
$964$	17.0854	−	9.78174i	0.550282	−	0.315048i
$965$	−7.19552	+	37.2901i	−0.231632	+	1.20041i
$966$	−3.71526	+	0.988280i	−0.119537	+	0.0317974i
$967$		−	47.6790i		−	1.53325i	−0.642094	−	0.766626i	$-0.721934\pi$
$967$		−	47.6790i		−	1.53325i	0.642094	−	0.766626i	$-0.278066\pi$
$968$	22.3203	−	22.0786i	0.717402	−	0.709634i
$969$	−7.19179			−0.231034
$970$	2.55237	+	36.7361i	0.0819516	+	1.17953i
$971$		−	10.4524i		−	0.335435i	−0.985835	−	0.167717i	$-0.946360\pi$
$971$		−	10.4524i		−	0.335435i	0.985835	−	0.167717i	$-0.0536396\pi$
$972$	19.5914	−	11.2165i	0.628393	−	0.359768i
$973$	−2.63222			−0.0843851
$974$	2.99630	+	11.2641i	0.0960077	+	0.360924i
$975$	1.93952	+	0.777450i	0.0621144	+	0.0248983i
$976$	21.3925	+	12.5589i	0.684757	+	0.402000i
$977$			51.6435i			1.65222i	0.563507	+	0.826111i	$0.309452\pi$
$977$			51.6435i			1.65222i	−0.563507	+	0.826111i	$0.690548\pi$
$978$	−2.40023	+	0.638473i	−0.0767508	+	0.0204161i
$979$			54.1413i			1.73036i
$980$	4.23177	−	1.44642i	0.135179	−	0.0462042i
$981$		−	30.6234i		−	0.977730i
$982$	5.01010	+	18.8346i	0.159879	+	0.601036i
$983$			32.3755i			1.03262i	0.856403	+	0.516308i	$0.172694\pi$
$983$			32.3755i			1.03262i	−0.856403	+	0.516308i	$0.827306\pi$
$984$	5.76091	−	5.69853i	0.183651	−	0.181662i
$985$	−15.6509	−	3.02000i	−0.498678	−	0.0962253i
$986$	68.5709	−	18.2402i	2.18374	−	0.580887i
$987$	1.75532			0.0558724
$988$	1.93930	+	3.38729i	0.0616972	+	0.107764i
$989$		−	55.0409i		−	1.75020i
$990$	−2.87240	−	41.3424i	−0.0912909	−	1.31395i
$991$	19.5212			0.620110			0.310055	−	0.950719i	$-0.399653\pi$
$991$	19.5212			0.620110			0.310055	+	0.950719i	$0.399653\pi$
$992$	12.1518	−	43.7593i	0.385821	−	1.38936i
$993$			1.85390i			0.0588318i
$994$	−0.635341	−	2.38845i	−0.0201518	−	0.0757571i
$995$	16.6856	+	3.21966i	0.528969	+	0.102070i
$996$	−8.40868	+	4.81415i	−0.266439	+	0.152542i
$997$	9.19720			0.291278			0.145639	−	0.989338i	$-0.453476\pi$
$997$	9.19720			0.291278			0.145639	+	0.989338i	$0.453476\pi$
$998$	3.34386	+	12.5707i	0.105848	+	0.397917i
$999$	16.5719			0.524312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.l.a.29.6	yes	36
4.3	odd	2		1120.2.l.a.1009.14		36
5.4	even	2	inner	280.2.l.a.29.31	yes	36
8.3	odd	2		1120.2.l.a.1009.23		36
8.5	even	2	inner	280.2.l.a.29.32	yes	36
20.19	odd	2		1120.2.l.a.1009.24		36
40.19	odd	2		1120.2.l.a.1009.13		36
40.29	even	2	inner	280.2.l.a.29.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.5	✓	36	40.29	even	2	inner
280.2.l.a.29.6	yes	36	1.1	even	1	trivial
280.2.l.a.29.31	yes	36	5.4	even	2	inner
280.2.l.a.29.32	yes	36	8.5	even	2	inner
1120.2.l.a.1009.13		36	40.19	odd	2
1120.2.l.a.1009.14		36	4.3	odd	2
1120.2.l.a.1009.23		36	8.3	odd	2
1120.2.l.a.1009.24		36	20.19	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36669 + 0.363546i) q^{2} +0.460762 q^{3} +(1.73567 - 0.993708i) q^{4} +(-2.19557 - 0.423658i) q^{5} +(-0.629718 + 0.167508i) q^{6} +1.00000i q^{7} +(-2.01086 + 1.98908i) q^{8} -2.78770 q^{9} +O(q^{10})\)	\(q+(-1.36669 + 0.363546i) q^{2} +0.460762 q^{3} +(1.73567 - 0.993708i) q^{4} +(-2.19557 - 0.423658i) q^{5} +(-0.629718 + 0.167508i) q^{6} +1.00000i q^{7} +(-2.01086 + 1.98908i) q^{8} -2.78770 q^{9} +(3.15467 - 0.219182i) q^{10} +4.70105i q^{11} +(0.799730 - 0.457863i) q^{12} +0.906993 q^{13} +(-0.363546 - 1.36669i) q^{14} +(-1.01163 - 0.195206i) q^{15} +(2.02509 - 3.44949i) q^{16} +7.25402i q^{17} +(3.80991 - 1.01346i) q^{18} +2.15170i q^{19} +(-4.23177 + 1.44642i) q^{20} +0.460762i q^{21} +(-1.70905 - 6.42487i) q^{22} -5.89989i q^{23} +(-0.926527 + 0.916494i) q^{24} +(4.64103 + 1.86034i) q^{25} +(-1.23958 + 0.329734i) q^{26} -2.66675 q^{27} +(0.993708 + 1.73567i) q^{28} +6.91659i q^{29} +(1.45355 - 0.100991i) q^{30} -8.02835 q^{31} +(-1.51362 + 5.45059i) q^{32} +2.16607i q^{33} +(-2.63717 - 9.91398i) q^{34} +(0.423658 - 2.19557i) q^{35} +(-4.83852 + 2.77016i) q^{36} -6.21426 q^{37} +(-0.782242 - 2.94070i) q^{38} +0.417908 q^{39} +(5.25766 - 3.51525i) q^{40} -6.21775 q^{41} +(-0.167508 - 0.629718i) q^{42} +9.32915 q^{43} +(4.67147 + 8.15947i) q^{44} +(6.12058 + 1.18103i) q^{45} +(2.14488 + 8.06330i) q^{46} -3.80960i q^{47} +(0.933085 - 1.58940i) q^{48} -1.00000 q^{49} +(-7.01915 - 0.855274i) q^{50} +3.34238i q^{51} +(1.57424 - 0.901285i) q^{52} +4.96064 q^{53} +(3.64462 - 0.969487i) q^{54} +(1.99164 - 10.3215i) q^{55} +(-1.98908 - 2.01086i) q^{56} +0.991422i q^{57} +(-2.51450 - 9.45282i) q^{58} -11.7227i q^{59} +(-1.94984 + 0.666456i) q^{60} +6.20163i q^{61} +(10.9722 - 2.91867i) q^{62} -2.78770i q^{63} +(0.0870983 - 7.99953i) q^{64} +(-1.99136 - 0.384255i) q^{65} +(-0.787465 - 2.96034i) q^{66} +5.42728 q^{67} +(7.20838 + 12.5906i) q^{68} -2.71844i q^{69} +(0.219182 + 3.15467i) q^{70} +1.74762 q^{71} +(5.60566 - 5.54496i) q^{72} -5.82777i q^{73} +(8.49296 - 2.25917i) q^{74} +(2.13841 + 0.857174i) q^{75} +(2.13816 + 3.73464i) q^{76} -4.70105 q^{77} +(-0.571149 + 0.151929i) q^{78} +8.05583 q^{79} +(-5.90763 + 6.71565i) q^{80} +7.13436 q^{81} +(8.49771 - 2.26044i) q^{82} -10.5144 q^{83} +(0.457863 + 0.799730i) q^{84} +(3.07322 - 15.9267i) q^{85} +(-12.7500 + 3.39157i) q^{86} +3.18690i q^{87} +(-9.35078 - 9.45315i) q^{88} +11.5168 q^{89} +(-8.79428 + 0.611012i) q^{90} +0.906993i q^{91} +(-5.86276 - 10.2402i) q^{92} -3.69916 q^{93} +(1.38496 + 5.20653i) q^{94} +(0.911585 - 4.72420i) q^{95} +(-0.697417 + 2.51143i) q^{96} +11.6450i q^{97} +(1.36669 - 0.363546i) q^{98} -13.1051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Introduction

L-functions

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