LMFDB - Embedded newform 169.2.h.a.12.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, degree $12$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.13
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63772 - 1.13043i) q^{2} +(1.71106 + 0.898032i) q^{3} +(0.695024 - 1.83263i) q^{4} +(-2.41202 - 2.72261i) q^{5} +(3.81739 - 0.463516i) q^{6} +(0.903389 + 3.66519i) q^{7} +(0.0190509 + 0.0772924i) q^{8} +(0.417062 + 0.604219i) q^{9} +O(q^{10})$	\(q+(1.63772 - 1.13043i) q^{2} +(1.71106 + 0.898032i) q^{3} +(0.695024 - 1.83263i) q^{4} +(-2.41202 - 2.72261i) q^{5} +(3.81739 - 0.463516i) q^{6} +(0.903389 + 3.66519i) q^{7} +(0.0190509 + 0.0772924i) q^{8} +(0.417062 + 0.604219i) q^{9} +(-7.02794 - 1.73223i) q^{10} +(-3.80102 - 2.62366i) q^{11} +(2.83499 - 2.51158i) q^{12} +(-2.55888 + 2.54010i) q^{13} +(5.62276 + 4.98133i) q^{14} +(-1.68212 - 6.82461i) q^{15} +(3.05273 + 2.70448i) q^{16} +(2.84446 - 0.701095i) q^{17} +(1.36606 + 0.518078i) q^{18} -1.26518i q^{19} +(-6.66594 + 2.52806i) q^{20} +(-1.74571 + 7.08263i) q^{21} -9.19086 q^{22} +4.29299 q^{23} +(-0.0368140 + 0.149360i) q^{24} +(-0.992070 + 8.17043i) q^{25} +(-1.31931 + 7.05261i) q^{26} +(-0.527767 - 4.34655i) q^{27} +(7.34482 + 0.891822i) q^{28} +(-2.02128 - 2.92833i) q^{29} +(-10.4696 - 9.27526i) q^{30} +(-3.31023 + 0.401935i) q^{31} +(7.89870 + 0.959076i) q^{32} +(-4.14764 - 7.90266i) q^{33} +(3.86587 - 4.36367i) q^{34} +(7.79989 - 11.3001i) q^{35} +(1.39718 - 0.344373i) q^{36} +(1.65918 - 0.201461i) q^{37} +(-1.43021 - 2.07201i) q^{38} +(-6.65949 + 2.04830i) q^{39} +(0.164486 - 0.238299i) q^{40} +(-5.13358 + 9.78122i) q^{41} +(5.14747 + 13.5728i) q^{42} +(0.701553 - 5.77781i) q^{43} +(-7.44999 + 5.14236i) q^{44} +(0.639089 - 2.59289i) q^{45} +(7.03071 - 4.85295i) q^{46} +(3.14343 - 1.19215i) q^{47} +(2.79469 + 7.36898i) q^{48} +(-6.41934 + 3.36913i) q^{49} +(7.61140 + 14.5023i) q^{50} +(5.49663 + 1.35480i) q^{51} +(2.87657 + 6.45492i) q^{52} +(-0.861654 + 0.212379i) q^{53} +(-5.77782 - 6.52181i) q^{54} +(2.02495 + 16.6770i) q^{55} +(-0.266081 + 0.139650i) q^{56} +(1.13618 - 2.16480i) q^{57} +(-6.62057 - 2.51085i) q^{58} +(-8.59852 - 9.70573i) q^{59} +(-13.6761 - 1.66058i) q^{60} +(12.3810 + 3.05165i) q^{61} +(-4.96686 + 4.40026i) q^{62} +(-1.83781 + 2.07446i) q^{63} +(6.79750 - 3.56760i) q^{64} +(13.0878 + 0.840067i) q^{65} +(-15.7261 - 8.25369i) q^{66} +(11.2990 - 4.28513i) q^{67} +(0.692119 - 5.70011i) q^{68} +(7.34556 + 3.85525i) q^{69} -27.3236i q^{70} +(-0.912946 + 1.73947i) q^{71} +(-0.0387561 + 0.0437466i) q^{72} +(-5.47692 - 3.78045i) q^{73} +(2.48953 - 2.20553i) q^{74} +(-9.03480 + 13.0892i) q^{75} +(-2.31861 - 0.879333i) q^{76} +(6.18240 - 16.3017i) q^{77} +(-8.59090 + 10.8826i) q^{78} +(2.89225 + 7.62624i) q^{79} -14.8347i q^{80} +(3.78134 - 9.97057i) q^{81} +(2.64968 + 21.8220i) q^{82} +(3.41513 + 6.50698i) q^{83} +(11.7665 + 8.12184i) q^{84} +(-8.76969 - 6.05328i) q^{85} +(-5.38249 - 10.2555i) q^{86} +(-0.828792 - 6.82572i) q^{87} +(0.130376 - 0.343773i) q^{88} -4.91886i q^{89} +(-1.88444 - 4.96886i) q^{90} +(-11.6216 - 7.08411i) q^{91} +(2.98374 - 7.86746i) q^{92} +(-6.02495 - 2.28496i) q^{93} +(3.80041 - 5.50584i) q^{94} +(-3.44460 + 3.05165i) q^{95} +(12.6538 + 8.73432i) q^{96} +(1.72450 - 1.94656i) q^{97} +(-6.70448 + 12.7743i) q^{98} -3.39088i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	1.63772	−	1.13043i	1.15804	−	0.799338i	0.175334	−	0.984509i	$-0.443899\pi$
$2$	1.63772	−	1.13043i	1.15804	−	0.799338i	0.982706	+	0.185171i	$0.0592840\pi$
$3$	1.71106	+	0.898032i	0.987880	+	0.518479i	0.879637	−	0.475645i	$-0.157785\pi$
$3$	1.71106	+	0.898032i	0.987880	+	0.518479i	0.108242	+	0.994125i	$0.465478\pi$
$4$	0.695024	−	1.83263i	0.347512	−	0.916314i
$5$	−2.41202	−	2.72261i	−1.07869	−	1.21759i	−0.974819	−	0.222997i	$-0.928416\pi$
$5$	−2.41202	−	2.72261i	−1.07869	−	1.21759i	−0.103869	−	0.994591i	$-0.533122\pi$
$6$	3.81739	−	0.463516i	1.55844	−	0.189229i
$7$	0.903389	+	3.66519i	0.341449	+	1.38531i	0.851132	+	0.524951i	$0.175916\pi$
$7$	0.903389	+	3.66519i	0.341449	+	1.38531i	−0.509683	+	0.860362i	$0.670237\pi$
$8$	0.0190509	+	0.0772924i	0.00673550	+	0.0273270i
$9$	0.417062	+	0.604219i	0.139021	+	0.201406i
$10$	−7.02794	−	1.73223i	−2.22243	−	0.547779i
$11$	−3.80102	−	2.62366i	−1.14605	−	0.791062i	−0.165284	−	0.986246i	$-0.552854\pi$
$11$	−3.80102	−	2.62366i	−1.14605	−	0.791062i	−0.980767	+	0.195184i	$0.937470\pi$
$12$	2.83499	−	2.51158i	0.818390	−	0.725030i
$13$	−2.55888	+	2.54010i	−0.709707	+	0.704497i
$13$	−2.55888	+	2.54010i	−0.709707	+	0.704497i
$14$	5.62276	+	4.98133i	1.50274	+	1.33132i
$15$	−1.68212	−	6.82461i	−0.434320	−	1.76211i
$16$	3.05273	+	2.70448i	0.763183	+	0.676121i
$17$	2.84446	−	0.701095i	0.689882	−	0.170041i	0.121237	−	0.992624i	$-0.461314\pi$
$17$	2.84446	−	0.701095i	0.689882	−	0.170041i	0.568645	+	0.822583i	$0.307468\pi$
$18$	1.36606	+	0.518078i	0.321983	+	0.122112i
$19$		−	1.26518i		−	0.290253i	−0.989413	−	0.145126i	$-0.953641\pi$
$19$		−	1.26518i		−	0.290253i	0.989413	−	0.145126i	$-0.0463589\pi$
$20$	−6.66594	+	2.52806i	−1.49055	+	0.565291i
$21$	−1.74571	+	7.08263i	−0.380946	+	1.54556i
$22$	−9.19086			−1.95950
$23$	4.29299			0.895151			0.447576	−	0.894246i	$-0.352288\pi$
$23$	4.29299			0.895151			0.447576	+	0.894246i	$0.352288\pi$
$24$	−0.0368140	+	0.149360i	−0.00751462	+	0.0304880i
$25$	−0.992070	+	8.17043i	−0.198414	+	1.63409i
$26$	−1.31931	+	7.05261i	−0.258738	+	1.38313i
$27$	−0.527767	−	4.34655i	−0.101569	−	0.836494i
$28$	7.34482	+	0.891822i	1.38804	+	0.168539i
$29$	−2.02128	−	2.92833i	−0.375342	−	0.543777i	0.589104	−	0.808058i	$-0.299481\pi$
$29$	−2.02128	−	2.92833i	−0.375342	−	0.543777i	−0.964446	+	0.264280i	$0.914866\pi$
$30$	−10.4696	−	9.27526i	−1.91148	−	1.69342i
$31$	−3.31023	+	0.401935i	−0.594536	+	0.0721897i	−0.412273	−	0.911060i	$-0.635265\pi$
$31$	−3.31023	+	0.401935i	−0.594536	+	0.0721897i	−0.182262	+	0.983250i	$0.558342\pi$
$32$	7.89870	+	0.959076i	1.39631	+	0.169542i
$33$	−4.14764	−	7.90266i	−0.722011	−	1.37568i
$34$	3.86587	−	4.36367i	0.662991	−	0.748362i
$35$	7.79989	−	11.3001i	1.31842	−	1.91007i
$36$	1.39718	−	0.344373i	0.232863	−	0.0573955i
$37$	1.65918	−	0.201461i	0.272768	−	0.0331200i	0.0169901	−	0.999856i	$-0.494592\pi$
$37$	1.65918	−	0.201461i	0.272768	−	0.0331200i	0.255778	+	0.966736i	$0.417669\pi$
$38$	−1.43021	−	2.07201i	−0.232010	−	0.336125i
$39$	−6.65949	+	2.04830i	−1.06637	+	0.327990i
$40$	0.164486	−	0.238299i	0.0260075	−	0.0376784i
$41$	−5.13358	+	9.78122i	−0.801731	+	1.52757i	0.0470912	+	0.998891i	$0.485005\pi$
$41$	−5.13358	+	9.78122i	−0.801731	+	1.52757i	−0.848822	+	0.528679i	$0.822687\pi$
$42$	5.14747	+	13.5728i	0.794271	+	2.09432i
$43$	0.701553	−	5.77781i	0.106986	−	0.881108i	−0.836104	−	0.548570i	$-0.815172\pi$
$43$	0.701553	−	5.77781i	0.106986	−	0.881108i	0.943090	−	0.332537i	$-0.107905\pi$
$44$	−7.44999	+	5.14236i	−1.12313	+	0.775239i
$45$	0.639089	−	2.59289i	0.0952697	−	0.386525i
$46$	7.03071	−	4.85295i	1.03662	−	0.715528i
$47$	3.14343	−	1.19215i	0.458516	−	0.173892i	−0.114522	−	0.993421i	$-0.536534\pi$
$47$	3.14343	−	1.19215i	0.458516	−	0.173892i	0.573039	+	0.819528i	$0.305764\pi$
$48$	2.79469	+	7.36898i	0.403378	+	1.06362i
$49$	−6.41934	+	3.36913i	−0.917049	+	0.481304i
$50$	7.61140	+	14.5023i	1.07642	+	2.05094i
$51$	5.49663	+	1.35480i	0.769683	+	0.189710i
$52$	2.87657	+	6.45492i	0.398909	+	0.895136i
$53$	−0.861654	+	0.212379i	−0.118357	+	0.0291725i	−0.298049	−	0.954550i	$-0.596336\pi$
$53$	−0.861654	+	0.212379i	−0.118357	+	0.0291725i	0.179692	+	0.983723i	$0.442490\pi$
$54$	−5.77782	−	6.52181i	−0.786262	−	0.887506i
$55$	2.02495	+	16.6770i	0.273045	+	2.24873i
$56$	−0.266081	+	0.139650i	−0.0355566	+	0.0186616i
$57$	1.13618	−	2.16480i	0.150490	−	0.286735i
$58$	−6.62057	−	2.51085i	−0.869323	−	0.329691i
$59$	−8.59852	−	9.70573i	−1.11943	−	1.26358i	−0.961103	−	0.276192i	$-0.910928\pi$
$59$	−8.59852	−	9.70573i	−1.11943	−	1.26358i	−0.158330	−	0.987386i	$-0.550611\pi$
$60$	−13.6761	−	1.66058i	−1.76558	−	0.214380i
$61$	12.3810	+	3.05165i	1.58523	+	0.390724i	0.930837	−	0.365434i	$-0.119079\pi$
$61$	12.3810	+	3.05165i	1.58523	+	0.390724i	0.654390	+	0.756157i	$0.272925\pi$
$62$	−4.96686	+	4.40026i	−0.630792	+	0.558833i
$63$	−1.83781	+	2.07446i	−0.231542	+	0.261357i
$64$	6.79750	−	3.56760i	0.849688	−	0.445950i
$65$	13.0878	+	0.840067i	1.62334	+	0.104198i
$66$	−15.7261	−	8.25369i	−1.93575	−	1.01596i
$67$	11.2990	−	4.28513i	1.38039	−	0.523512i	0.450969	−	0.892540i	$-0.351078\pi$
$67$	11.2990	−	4.28513i	1.38039	−	0.523512i	0.929418	+	0.369028i	$0.120309\pi$
$68$	0.692119	−	5.70011i	0.0839317	−	0.691240i
$69$	7.34556	+	3.85525i	0.884302	+	0.464117i
$70$		−	27.3236i		−	3.26580i
$71$	−0.912946	+	1.73947i	−0.108347	+	0.206437i	−0.933593	−	0.358336i	$-0.883344\pi$
$71$	−0.912946	+	1.73947i	−0.108347	+	0.206437i	0.825246	+	0.564774i	$0.191036\pi$
$72$	−0.0387561	+	0.0437466i	−0.00456746	+	0.00515559i
$73$	−5.47692	−	3.78045i	−0.641026	−	0.442468i	0.202701	−	0.979241i	$-0.435028\pi$
$73$	−5.47692	−	3.78045i	−0.641026	−	0.442468i	−0.843727	+	0.536773i	$0.819643\pi$
$74$	2.48953	−	2.20553i	0.289402	−	0.256388i
$75$	−9.03480	+	13.0892i	−1.04325	+	1.51141i
$76$	−2.31861	−	0.879333i	−0.265963	−	0.100866i
$77$	6.18240	−	16.3017i	0.704550	−	1.85775i
$78$	−8.59090	+	10.8826i	−0.972727	+	1.23222i
$79$	2.89225	+	7.62624i	0.325404	+	0.858019i	0.993488	+	0.113934i	$0.0363452\pi$
$79$	2.89225	+	7.62624i	0.325404	+	0.858019i	−0.668085	+	0.744085i	$0.732886\pi$
$80$		−	14.8347i		−	1.65857i
$81$	3.78134	−	9.97057i	0.420149	−	1.10784i
$82$	2.64968	+	21.8220i	0.292608	+	2.40984i
$83$	3.41513	+	6.50698i	0.374859	+	0.714234i	0.997676	−	0.0681335i	$-0.0217044\pi$
$83$	3.41513	+	6.50698i	0.374859	+	0.714234i	−0.622817	+	0.782367i	$0.714012\pi$
$84$	11.7665	+	8.12184i	1.28383	+	0.886166i
$85$	−8.76969	−	6.05328i	−0.951207	−	0.656571i
$86$	−5.38249	−	10.2555i	−0.580409	−	1.10588i
$87$	−0.828792	−	6.82572i	−0.0888558	−	0.731794i
$88$	0.130376	−	0.343773i	0.0138981	−	0.0366463i
$89$		−	4.91886i		−	0.521398i	−0.965420	−	0.260699i	$-0.916047\pi$
$89$		−	4.91886i		−	0.521398i	0.965420	−	0.260699i	$-0.0839530\pi$
$90$	−1.88444	−	4.96886i	−0.198637	−	0.523764i
$91$	−11.6216	−	7.08411i	−1.21828	−	0.742617i
$92$	2.98374	−	7.86746i	0.311076	−	0.820240i
$93$	−6.02495	−	2.28496i	−0.624758	−	0.236940i
$94$	3.80041	−	5.50584i	0.391982	−	0.567884i
$95$	−3.44460	+	3.05165i	−0.353408	+	0.313092i
$96$	12.6538	+	8.73432i	1.29148	+	0.891443i
$97$	1.72450	−	1.94656i	0.175097	−	0.197643i	−0.654410	−	0.756140i	$-0.727083\pi$
$97$	1.72450	−	1.94656i	0.175097	−	0.197643i	0.829507	+	0.558496i	$0.188622\pi$
$98$	−6.70448	+	12.7743i	−0.677255	+	1.29040i
$99$		−	3.39088i		−	0.340796i
$100$	14.2839	+	7.49674i	1.42839	+	0.749674i
$101$	−1.17230	+	9.65478i	−0.116649	+	0.960687i	0.810434	+	0.585830i	$0.199231\pi$
$101$	−1.17230	+	9.65478i	−0.116649	+	0.960687i	−0.927083	+	0.374857i	$0.877692\pi$
$102$	10.5334	−	3.99481i	1.04297	−	0.395545i
$103$	−10.5012	−	5.51148i	−1.03472	−	0.543062i	−0.140214	−	0.990121i	$-0.544779\pi$
$103$	−10.5012	−	5.51148i	−1.03472	−	0.543062i	−0.894504	+	0.447059i	$0.852471\pi$
$104$	−0.245079	−	0.149391i	−0.0240320	−	0.0146490i
$105$	23.4939	−	12.3306i	2.29277	−	1.20334i
$106$	−1.17107	+	1.32186i	−0.113744	+	0.128390i
$107$	−9.20575	+	8.15558i	−0.889953	+	0.788430i	−0.978199	−	0.207669i	$-0.933412\pi$
$107$	−9.20575	+	8.15558i	−0.889953	+	0.788430i	0.0882460	+	0.996099i	$0.471874\pi$
$108$	−8.33243	−	2.05376i	−0.801788	−	0.197623i
$109$	−4.14191	−	0.502919i	−0.396723	−	0.0481709i	−0.0802558	−	0.996774i	$-0.525574\pi$
$109$	−4.14191	−	0.502919i	−0.396723	−	0.0481709i	−0.316467	+	0.948603i	$0.602497\pi$
$110$	22.1686	+	25.0231i	2.11369	+	2.38586i
$111$	3.01987	+	1.14529i	0.286634	+	0.108706i
$112$	−7.15465	+	13.6321i	−0.676051	+	1.28811i
$113$	8.18046	−	4.29343i	0.769553	−	0.403892i	−0.0337753	−	0.999429i	$-0.510753\pi$
$113$	8.18046	−	4.29343i	0.769553	−	0.403892i	0.803328	+	0.595537i	$0.203061\pi$
$114$	−0.586432	−	4.82970i	−0.0549244	−	0.452343i
$115$	−10.3548	−	11.6881i	−0.965589	−	1.08992i
$116$	−6.77138	+	1.66900i	−0.628707	+	0.154962i
$117$	−2.60199	−	0.486747i	−0.240554	−	0.0449998i
$118$	−25.0536	−	6.17516i	−2.30637	−	0.568470i
$119$	5.13930	+	9.79212i	0.471119	+	0.897642i
$120$	0.495445	−	0.260030i	0.0452277	−	0.0237373i
$121$	3.66354	+	9.65995i	0.333049	+	0.878178i
$122$	23.7263	−	8.99820i	2.14808	−	0.814658i
$123$	−17.5677	+	12.1261i	−1.58403	+	1.09337i
$124$	−1.56410	+	6.34578i	−0.140460	+	0.569868i
$125$	9.67030	−	6.67493i	0.864938	−	0.597024i
$126$	−0.664773	+	5.47490i	−0.0592227	+	0.487743i
$127$	3.47833	+	9.17159i	0.308652	+	0.813847i	0.996150	+	0.0876617i	$0.0279395\pi$
$127$	3.47833	+	9.17159i	0.308652	+	0.813847i	−0.687499	+	0.726186i	$0.741291\pi$
$128$	−0.295897	+	0.563785i	−0.0261539	+	0.0498321i
$129$	6.38906	−	9.25615i	0.562525	−	0.814958i
$130$	22.3837	−	13.4191i	1.96318	−	1.17693i
$131$	−3.41682	−	4.95012i	−0.298529	−	0.432494i	0.644801	−	0.764351i	$-0.276940\pi$
$131$	−3.41682	−	4.95012i	−0.298529	−	0.432494i	−0.943330	+	0.331856i	$0.892325\pi$
$132$	−17.3654	+	2.10854i	−1.51146	+	0.183525i
$133$	4.63714	−	1.14295i	0.402091	−	0.0991066i
$134$	13.6604	−	19.7906i	1.18008	−	1.70964i
$135$	−10.5610	+	11.9209i	−0.908944	+	1.02599i
$136$	0.108379	+	0.206498i	0.00929340	+	0.0177071i
$137$	6.68322	+	0.811490i	0.570986	+	0.0693303i	0.400937	−	0.916105i	$-0.368684\pi$
$137$	6.68322	+	0.811490i	0.570986	+	0.0693303i	0.170049	+	0.985436i	$0.445608\pi$
$138$	16.3880	−	1.98987i	1.39504	−	0.169389i
$139$	−2.68151	−	2.37561i	−0.227443	−	0.201497i	0.541703	−	0.840570i	$-0.317780\pi$
$139$	−2.68151	−	2.37561i	−0.227443	−	0.201497i	−0.769146	+	0.639073i	$0.779318\pi$
$140$	−15.2878	−	22.1482i	−1.29205	−	1.87186i
$141$	6.44918	+	0.783072i	0.543119	+	0.0659465i
$142$	0.471213	+	3.88079i	0.0395433	+	0.325668i
$143$	16.3907	−	2.94134i	1.37066	−	0.245967i
$144$	−0.360921	+	2.97246i	−0.0300768	+	0.247705i
$145$	−3.09733	+	12.5663i	−0.257219	+	1.04358i
$146$	−13.2432			−1.09601
$147$	−14.0095			−1.15548
$148$	0.783968	−	3.18068i	0.0644418	−	0.261450i
$149$	2.44485	−	0.927209i	0.200290	−	0.0759599i	−0.252420	−	0.967618i	$-0.581227\pi$
$149$	2.44485	−	0.927209i	0.200290	−	0.0759599i	0.452710	+	0.891658i	$0.350457\pi$
$150$			31.6496i			2.58418i
$151$	0.929723	+	0.352597i	0.0756598	+	0.0286940i	0.392144	−	0.919904i	$-0.371733\pi$
$151$	0.929723	+	0.352597i	0.0756598	+	0.0286940i	−0.316485	+	0.948598i	$0.602503\pi$
$152$	0.0977891	−	0.0241028i	0.00793174	−	0.00195500i
$153$	1.60993	+	1.42627i	0.130155	+	0.115307i
$154$	−8.30293	−	33.6863i	−0.669069	−	2.71452i
$155$	9.07866	+	8.04299i	0.729216	+	0.646029i
$156$	−0.874742	+	13.6280i	−0.0700354	+	1.09111i
$157$	−15.2411	+	13.5025i	−1.21637	+	1.07761i	−0.221640	+	0.975129i	$0.571141\pi$
$157$	−15.2411	+	13.5025i	−1.21637	+	1.07761i	−0.994735	+	0.102485i	$0.967321\pi$
$158$	13.3577	+	9.22012i	1.06268	+	0.733513i
$159$	−1.66506	−	0.410401i	−0.132048	−	0.0325469i
$160$	−16.4406	−	23.8184i	−1.29975	−	1.88301i
$161$	3.87824	+	15.7347i	0.305648	+	1.24006i
$162$	−5.07831	−	20.6035i	−0.398990	−	1.61876i
$163$	7.39981	−	0.898500i	0.579598	−	0.0703759i	0.174513	−	0.984655i	$-0.444165\pi$
$163$	7.39981	−	0.898500i	0.579598	−	0.0703759i	0.405085	+	0.914279i	$0.367242\pi$
$164$	14.3574	+	16.2061i	1.12112	+	1.26549i
$165$	−11.5117	+	30.3538i	−0.896182	+	2.36304i
$166$	12.9487	+	6.79601i	1.00502	+	0.527473i
$167$	−14.7958	+	10.2128i	−1.14494	+	0.790292i	−0.980582	−	0.196110i	$-0.937169\pi$
$167$	−14.7958	+	10.2128i	−1.14494	+	0.790292i	−0.164353	+	0.986402i	$0.552554\pi$
$168$	−0.580691			−0.0448013
$169$	0.0957826	−	12.9996i	0.00736789	−	0.999973i
$170$	−21.2051			−1.62636
$171$	0.764447	−	0.527660i	0.0584588	−	0.0403512i
$172$	−10.1010	−	5.30140i	−0.770193	−	0.404228i
$173$	−9.12493	+	24.0605i	−0.693755	+	1.82928i	−0.152748	+	0.988265i	$0.548812\pi$
$173$	−9.12493	+	24.0605i	−0.693755	+	1.82928i	−0.541008	+	0.841018i	$0.681957\pi$
$174$	−9.07335	−	10.2417i	−0.687849	−	0.776421i
$175$	−30.8424	+	3.74495i	−2.33147	+	0.283092i
$176$	−4.50786	−	18.2891i	−0.339793	−	1.37859i
$177$	−5.99651	−	24.3288i	−0.450726	−	1.82867i
$178$	−5.56045	−	8.05570i	−0.416773	−	0.603800i
$179$	−9.86848	−	2.43236i	−0.737605	−	0.181803i	−0.147423	−	0.989074i	$-0.547098\pi$
$179$	−9.86848	−	2.43236i	−0.737605	−	0.181803i	−0.590182	+	0.807270i	$0.700944\pi$
$180$	−4.30761	−	2.97333i	−0.321071	−	0.221619i
$181$	−3.89561	+	3.45121i	−0.289558	+	0.256526i	−0.795379	−	0.606112i	$-0.792728\pi$
$181$	−3.89561	+	3.45121i	−0.289558	+	0.256526i	0.505821	+	0.862639i	$0.331190\pi$
$182$	−27.0411	+	1.53572i	−2.00442	+	0.113835i
$183$	18.4442	+	16.3401i	1.36343	+	1.20790i
$184$	0.0817853	+	0.331816i	0.00602929	+	0.0244618i
$185$	−4.55048	−	4.03137i	−0.334558	−	0.296392i
$186$	−12.4502	+	3.06869i	−0.912890	+	0.225007i
$187$	−12.6513	−	4.79799i	−0.925152	−	0.350864i
$188$		−	6.58931i		−	0.480575i
$189$	15.4542	−	5.86100i	1.12413	−	0.426325i
$190$	−2.19159	+	8.89162i	−0.158995	+	0.645066i
$191$	20.7770			1.50337			0.751684	−	0.659524i	$-0.229242\pi$
$191$	20.7770			1.50337			0.751684	+	0.659524i	$0.229242\pi$
$192$	14.8347			1.07061
$193$	−0.378098	+	1.53400i	−0.0272161	+	0.110420i	−0.982979	−	0.183718i	$-0.941187\pi$
$193$	−0.378098	+	1.53400i	−0.0272161	+	0.110420i	0.955763	+	0.294138i	$0.0950327\pi$
$194$	0.623787	−	5.13735i	0.0447853	−	0.368840i
$195$	21.6395	+	13.1907i	1.54964	+	0.944602i
$196$	1.71277	+	14.1059i	0.122340	+	1.00756i
$197$	9.98608	+	1.21253i	0.711479	+	0.0863892i	0.468271	−	0.883585i	$-0.344877\pi$
$197$	9.98608	+	1.21253i	0.711479	+	0.0863892i	0.243208	+	0.969974i	$0.421800\pi$
$198$	−3.83316	−	5.55329i	−0.272411	−	0.394655i
$199$	−11.4902	−	10.1794i	−0.814515	−	0.721598i	0.149120	−	0.988819i	$-0.452356\pi$
$199$	−11.4902	−	10.1794i	−0.814515	−	0.721598i	−0.963635	+	0.267221i	$0.913894\pi$
$200$	−0.650412	+	0.0789743i	−0.0459911	+	0.00558433i
$201$	23.1814	+	2.81473i	1.63509	+	0.198535i
$202$	8.99420	+	17.1370i	0.632829	+	1.20576i
$203$	8.90690	−	10.0538i	0.625141	−	0.705639i
$204$	6.30314	−	9.13167i	0.441308	−	0.639345i
$205$	39.0127	−	9.61577i	2.72477	−	0.671595i
$206$	−23.4284	+	2.84472i	−1.63234	+	0.198201i
$207$	1.79045	+	2.59391i	0.124445	+	0.180289i
$208$	−14.6812	+	0.833780i	−1.01796	+	0.0578123i
$209$	−3.31940	+	4.80899i	−0.229608	+	0.332645i
$210$	24.5375	−	46.7523i	1.69325	−	3.22622i
$211$	−0.829178	−	2.18636i	−0.0570830	−	0.150515i	0.903441	−	0.428712i	$-0.141033\pi$
$211$	−0.829178	−	2.18636i	−0.0570830	−	0.150515i	−0.960524	+	0.278197i	$0.910263\pi$
$212$	−0.209659	+	1.72670i	−0.0143995	+	0.118590i
$213$	−3.12420	+	2.15648i	−0.214067	+	0.147760i
$214$	−5.85706	+	23.7630i	−0.400380	+	1.62441i
$215$	−17.4229	+	12.0261i	−1.18823	+	0.820176i
$216$	0.325901	−	0.123598i	0.0221748	−	0.00840978i
$217$	−4.46360	−	11.7695i	−0.303009	−	0.798969i
$218$	−7.35179	+	3.85852i	−0.497926	+	0.261332i
$219$	−5.97637	−	11.3870i	−0.403846	−	0.769464i
$220$	31.9701	+	7.87993i	2.15543	+	0.531265i
$221$	−5.49778	+	9.01923i	−0.369821	+	0.606699i
$222$	6.24037	−	1.53811i	0.418826	−	0.103231i
$223$	2.93099	+	3.30840i	0.196274	+	0.221547i	0.838405	−	0.545047i	$-0.183488\pi$
$223$	2.93099	+	3.30840i	0.196274	+	0.221547i	−0.642132	+	0.766594i	$0.721950\pi$
$224$	3.62040	+	29.8167i	0.241898	+	1.99221i
$225$	−5.35048	+	2.80815i	−0.356699	+	0.187210i
$226$	8.54382	−	16.2789i	0.568327	−	1.08286i
$227$	3.95870	+	1.50134i	0.262748	+	0.0996471i	0.482461	−	0.875917i	$-0.339743\pi$
$227$	3.95870	+	1.50134i	0.262748	+	0.0996471i	−0.219713	+	0.975564i	$0.570512\pi$
$228$	−3.17761	−	3.58678i	−0.210442	−	0.237540i
$229$	−1.84669	−	0.224229i	−0.122033	−	0.0148174i	0.0592925	−	0.998241i	$-0.481116\pi$
$229$	−1.84669	−	0.224229i	−0.122033	−	0.0148174i	−0.181325	+	0.983423i	$0.558039\pi$
$230$	−30.1709	−	7.43646i	−1.98941	−	0.490345i
$231$	25.2179	−	22.3411i	1.65921	−	1.46994i
$232$	0.187831	−	0.212017i	0.0123317	−	0.0139196i
$233$	2.07031	−	1.08658i	0.135630	−	0.0711843i	−0.395543	−	0.918447i	$-0.629444\pi$
$233$	2.07031	−	1.08658i	0.135630	−	0.0711843i	0.531173	+	0.847263i	$0.321751\pi$
$234$	−4.81156	+	2.14423i	−0.314541	+	0.140172i
$235$	−10.8278	−	5.68285i	−0.706325	−	0.370708i
$236$	−23.7632	+	9.01218i	−1.54685	+	0.586643i
$237$	−1.89980	+	15.6463i	−0.123405	+	1.01633i
$238$	19.4861	+	10.2271i	1.26309	+	0.662923i
$239$		−	2.01629i		−	0.130423i	−0.997871	−	0.0652116i	$-0.979228\pi$
$239$		−	2.01629i		−	0.130423i	0.997871	−	0.0652116i	$-0.0207722\pi$
$240$	13.3220	−	25.3830i	0.859932	−	1.63846i
$241$	−8.21949	+	9.27788i	−0.529464	+	0.597641i	−0.951008	−	0.309167i	$-0.899950\pi$
$241$	−8.21949	+	9.27788i	−0.529464	+	0.597641i	0.421544	+	0.906808i	$0.361488\pi$
$242$	16.9198	+	11.6789i	1.08764	+	0.750747i
$243$	5.59197	−	4.95405i	0.358725	−	0.317803i
$244$	14.1977	−	20.5688i	0.908911	−	1.31679i
$245$	24.6564	+	9.35094i	1.57524	+	0.597410i
$246$	−15.0631	+	39.7183i	−0.960391	+	2.53234i
$247$	3.21369	+	3.23746i	0.204482	+	0.205994i
$248$	−0.0941294	−	0.248199i	−0.00597722	−	0.0157606i
$249$			14.2007i			0.899933i
$250$	8.29165	−	21.8633i	0.524410	−	1.38276i
$251$	−1.25372	−	10.3253i	−0.0791340	−	0.651727i	−0.977268	−	0.212006i	$-0.932000\pi$
$251$	−1.25372	−	10.3253i	−0.0791340	−	0.651727i	0.898134	−	0.439721i	$-0.144923\pi$
$252$	2.52439	+	4.80982i	0.159022	+	0.302990i
$253$	−16.3178	−	11.2633i	−1.02589	−	0.708120i
$254$	16.0644	+	11.0885i	1.00797	+	0.695751i
$255$	−9.56941	−	18.2330i	−0.599260	−	1.14179i
$256$	2.00341	+	16.4995i	0.125213	+	1.03122i
$257$	−8.73470	+	23.0315i	−0.544855	+	1.43667i	0.326115	+	0.945330i	$0.394260\pi$
$257$	−8.73470	+	23.0315i	−0.544855	+	1.43667i	−0.870970	+	0.491336i	$0.836509\pi$
$258$		−	22.3814i		−	1.39340i
$259$	2.23728	+	5.89922i	0.139018	+	0.366560i
$260$	10.6359	−	23.4012i	0.659608	−	1.45128i
$261$	0.926353	−	2.44259i	0.0573398	−	0.151193i
$262$	−11.1916	−	4.24441i	−0.691418	−	0.262220i
$263$	12.0287	−	17.4266i	0.741722	−	1.07457i	−0.252538	−	0.967587i	$-0.581265\pi$
$263$	12.0287	−	17.4266i	0.741722	−	1.07457i	0.994261	−	0.106984i	$-0.0341192\pi$
$264$	0.531800	−	0.471134i	0.0327300	−	0.0289963i
$265$	2.65655	+	1.83369i	0.163191	+	0.112642i
$266$	6.30229	−	7.11381i	0.386418	−	0.436176i
$267$	4.41729	−	8.41645i	0.270334	−	0.515078i
$268$		−	23.6851i		−	1.44680i
$269$	−13.1469	−	6.90001i	−0.801579	−	0.420701i	0.0136022	−	0.999907i	$-0.495670\pi$
$269$	−13.1469	−	6.90001i	−0.801579	−	0.420701i	−0.815181	+	0.579207i	$0.803362\pi$
$270$	−3.82012	+	31.4615i	−0.232485	+	1.91469i
$271$	2.00101	−	0.758883i	0.121553	−	0.0460989i	−0.293079	−	0.956088i	$-0.594680\pi$
$271$	2.00101	−	0.758883i	0.121553	−	0.0460989i	0.414631	+	0.909989i	$0.363911\pi$
$272$	10.5795	+	5.55253i	0.641474	+	0.336672i
$273$	−13.5235	−	22.5579i	−0.818481	−	1.36527i
$274$	11.8626	−	6.22595i	0.716643	−	0.376123i
$275$	25.2073	−	28.4531i	1.52006	−	1.71579i
$276$	12.1706	−	10.7822i	0.732583	−	0.649012i
$277$	12.0082	+	2.95975i	0.721500	+	0.177834i	0.582934	−	0.812519i	$-0.301905\pi$
$277$	12.0082	+	2.95975i	0.721500	+	0.177834i	0.138566	+	0.990353i	$0.455751\pi$
$278$	−7.07703	−	0.859307i	−0.424452	−	0.0515378i
$279$	−1.62343	−	1.83247i	−0.0971922	−	0.109707i
$280$	1.02201	+	0.387596i	0.0610766	+	0.0231633i
$281$	12.1305	−	23.1127i	0.723642	−	1.37879i	−0.193850	−	0.981031i	$-0.562097\pi$
$281$	12.1305	−	23.1127i	0.723642	−	1.37879i	0.917492	−	0.397754i	$-0.130210\pi$
$282$	11.4471	−	6.00792i	0.681667	−	0.357766i
$283$	0.330770	+	2.72413i	0.0196622	+	0.161933i	0.999233	−	0.0391687i	$-0.0124710\pi$
$283$	0.330770	+	2.72413i	0.0196622	+	0.161933i	−0.979570	+	0.201102i	$0.935548\pi$
$284$	2.55329	+	2.88207i	0.151510	+	0.171019i
$285$	−8.63438	+	2.12818i	−0.511457	+	0.126063i
$286$	23.5184	−	23.3457i	1.39067	−	1.38046i
$287$	−40.4877	−	9.97932i	−2.38991	−	0.589061i
$288$	2.71476	+	5.17254i	0.159969	+	0.304795i
$289$	−7.45336	+	3.91182i	−0.438433	+	0.230107i
$290$	9.13288	+	24.0814i	0.536301	+	1.41411i
$291$	4.69880	−	1.78202i	0.275448	−	0.104464i
$292$	−10.7348	+	7.40967i	−0.628204	+	0.433618i
$293$	0.282549	−	1.14635i	0.0165067	−	0.0669703i	−0.962111	−	0.272658i	$-0.912097\pi$
$293$	0.282549	−	1.14635i	0.0165067	−	0.0669703i	0.978618	+	0.205688i	$0.0659433\pi$
$294$	−22.9435	+	15.8368i	−1.33809	+	0.923619i
$295$	−5.68508	+	46.8208i	−0.330998	+	2.72601i
$296$	0.0471802	+	0.124404i	0.00274230	+	0.00723084i
$297$	−9.39780	+	17.9060i	−0.545316	+	1.03901i
$298$	2.95582	−	4.28225i	0.171226	−	0.248064i
$299$	−10.9853	+	10.9046i	−0.635295	+	0.630631i
$300$	17.7082	+	25.6547i	1.02238	+	1.48118i
$301$	21.8106	−	2.64828i	1.25714	−	0.152644i
$302$	1.92121	−	0.473536i	0.110553	−	0.0272489i
$303$	−10.6762	+	15.4671i	−0.613331	+	0.888563i
$304$	3.42167	−	3.86226i	0.196246	−	0.221516i
$305$	−21.5548	−	41.0693i	−1.23423	−	2.35162i
$306$	4.24892	+	0.515912i	0.242894	+	0.0294927i
$307$	27.5721	−	3.34786i	1.57362	−	0.191072i	0.713313	−	0.700846i	$-0.247194\pi$
$307$	27.5721	−	3.34786i	1.57362	−	0.191072i	0.860309	+	0.509773i	$0.170271\pi$
$308$	−25.5780	−	22.6601i	−1.45744	−	1.29118i
$309$	−13.0187	−	18.8609i	−0.740611	−	1.07296i
$310$	23.9604	+	2.90931i	1.36086	+	0.165238i
$311$	−1.46279	−	12.0472i	−0.0829474	−	0.683133i	−0.973570	−	0.228390i	$-0.926654\pi$
$311$	−1.46279	−	12.0472i	−0.0829474	−	0.683133i	0.890622	−	0.454744i	$-0.150269\pi$
$312$	−0.285187	−	0.475706i	−0.0161455	−	0.0269316i
$313$	3.42709	−	28.2246i	0.193710	−	1.59535i	−0.494065	−	0.869425i	$-0.664490\pi$
$313$	3.42709	−	28.2246i	0.193710	−	1.59535i	0.687776	−	0.725923i	$-0.258587\pi$
$314$	−9.69700	+	39.3423i	−0.547234	+	2.22021i
$315$	10.0808			0.567987
$316$	15.9863			0.899297
$317$	2.40019	−	9.73795i	0.134808	−	0.546938i	−0.864230	−	0.503096i	$-0.832194\pi$
$317$	2.40019	−	9.73795i	0.134808	−	0.546938i	0.999038	−	0.0438416i	$-0.0139597\pi$
$318$	−3.19083	+	1.21012i	−0.178933	+	0.0678604i
$319$			16.4338i			0.920115i
$320$	−26.1089	−	9.90180i	−1.45953	−	0.553527i
$321$	−23.0755	+	5.68761i	−1.28795	+	0.317451i
$322$	24.1385	+	21.3848i	1.34518	+	1.19173i
$323$	−0.887014	−	3.59876i	−0.0493548	−	0.200240i
$324$	−15.6442	−	13.8596i	−0.869123	−	0.769976i
$325$	−18.2151	−	23.4271i	−1.01039	−	1.29950i
$326$	11.1031	−	9.83648i	0.614944	−	0.544793i
$327$	−6.63541	−	4.58009i	−0.366939	−	0.253280i
$328$	−0.853813	−	0.210446i	−0.0471440	−	0.0116199i
$329$	7.20919	+	10.4443i	0.397455	+	0.575813i
$330$	15.4601	+	62.7241i	0.851050	+	3.45285i
$331$	1.91389	+	7.76494i	0.105197	+	0.426800i	0.999799	−	0.0200640i	$-0.00638700\pi$
$331$	1.91389	+	7.76494i	0.105197	+	0.426800i	−0.894602	+	0.446864i	$0.852541\pi$
$332$	14.2985	−	1.73615i	0.784731	−	0.0952835i
$333$	0.813708	+	0.918486i	0.0445909	+	0.0503327i
$334$	−12.6864	+	33.4514i	−0.694171	+	1.83038i
$335$	−38.9201	−	20.4268i	−2.12643	−	1.11604i
$336$	−24.4840	+	16.9001i	−1.33571	+	0.921977i
$337$	−29.8467			−1.62585			−0.812927	−	0.582366i	$-0.802127\pi$
$337$	−29.8467			−1.62585			−0.812927	+	0.582366i	$0.802127\pi$
$338$	−14.5384	−	21.3980i	−0.790784	−	1.16390i
$339$	17.8529			0.969635
$340$	−17.1886	+	11.8644i	−0.932181	+	0.643438i
$341$	13.6368	+	7.15715i	0.738474	+	0.387581i
$342$	0.655463	−	1.72831i	0.0354434	−	0.0934566i
$343$	−0.625201	−	0.705706i	−0.0337577	−	0.0381045i
$344$	0.459946	−	0.0558476i	0.0247986	−	0.00301110i
$345$	−7.22131	−	29.2980i	−0.388782	−	1.57735i
$346$	12.2547	+	49.7193i	0.658818	+	2.67293i
$347$	−19.7318	−	28.5865i	−1.05926	−	1.53460i	−0.827205	−	0.561900i	$-0.810070\pi$
$347$	−19.7318	−	28.5865i	−1.05926	−	1.53460i	−0.232055	−	0.972703i	$-0.574545\pi$
$348$	−13.0850	−	3.22517i	−0.701432	−	0.172887i
$349$	19.4163	+	13.4021i	1.03933	+	0.717397i	0.960156	−	0.279464i	$-0.0901568\pi$
$349$	19.4163	+	13.4021i	1.03933	+	0.717397i	0.0791726	+	0.996861i	$0.474772\pi$
$350$	−46.2778	+	40.9985i	−2.47365	+	2.19146i
$351$	12.3912	+	9.78174i	0.661392	+	0.522111i
$352$	−27.5068	−	24.3689i	−1.46612	−	1.29887i
$353$	−1.60792	−	6.52357i	−0.0855808	−	0.347215i	0.912505	−	0.409066i	$-0.134146\pi$
$353$	−1.60792	−	6.52357i	−0.0855808	−	0.347215i	−0.998085	+	0.0618517i	$0.980299\pi$
$354$	−37.3227	−	33.0650i	−1.98368	−	1.75739i
$355$	6.93795	−	1.71005i	0.368228	−	0.0907600i
$356$	−9.01444	−	3.41873i	−0.477764	−	0.181192i
$357$			21.3701i			1.13103i
$358$	−18.9114	+	7.17215i	−0.999499	+	0.379060i
$359$	−2.70328	+	10.9676i	−0.142674	+	0.578849i	0.855465	+	0.517861i	$0.173271\pi$
$359$	−2.70328	+	10.9676i	−0.142674	+	0.578849i	−0.998138	+	0.0609886i	$0.980575\pi$
$360$	0.212586			0.0112042
$361$	17.3993			0.915753
$362$	−2.47854	+	10.0558i	−0.130269	+	0.528523i
$363$	−2.40643	+	19.8187i	−0.126305	+	1.04021i
$364$	−21.0599	+	16.3745i	−1.10384	+	0.858257i
$365$	2.91777	+	24.0300i	0.152723	+	1.25779i
$366$	48.6777	+	5.91055i	2.54443	+	0.308949i
$367$	15.2831	+	22.1415i	0.797774	+	1.15578i	0.984846	+	0.173429i	$0.0554847\pi$
$367$	15.2831	+	22.1415i	0.797774	+	1.15578i	−0.187073	+	0.982346i	$0.559900\pi$
$368$	13.1054	+	11.6103i	0.683164	+	0.605230i
$369$	−8.05102	+	0.977571i	−0.419119	+	0.0508903i
$370$	−12.0096	−	1.45823i	−0.624349	−	0.0758097i
$371$	−1.55682	−	2.96627i	−0.0808260	−	0.154001i
$372$	−8.37498	+	9.45340i	−0.434222	+	0.490136i
$373$	8.71629	−	12.6277i	0.451312	−	0.653839i	−0.529609	−	0.848242i	$-0.677662\pi$
$373$	8.71629	−	12.6277i	0.451312	−	0.653839i	0.980922	+	0.194403i	$0.0622769\pi$
$374$	−26.1430	+	6.44367i	−1.35182	+	0.333194i
$375$	22.5408	−	2.73694i	1.16400	−	0.141335i
$376$	0.152029	+	0.220252i	0.00784029	+	0.0113586i
$377$	12.6105	+	2.35900i	0.649473	+	0.121495i
$378$	18.6841	−	27.0686i	0.961006	−	1.39226i
$379$	−7.29865	+	13.9064i	−0.374906	+	0.714325i	−0.997680	−	0.0680776i	$-0.978313\pi$
$379$	−7.29865	+	13.9064i	−0.374906	+	0.714325i	0.622774	+	0.782402i	$0.286006\pi$
$380$	3.19846	+	8.43364i	0.164077	+	0.432637i
$381$	−2.28477	+	18.8168i	−0.117052	+	0.964013i
$382$	34.0268	−	23.4870i	1.74096	−	1.20170i
$383$	7.36668	−	29.8878i	0.376420	−	1.52719i	−0.411496	−	0.911412i	$-0.634994\pi$
$383$	7.36668	−	29.8878i	0.376420	−	1.52719i	0.787916	−	0.615783i	$-0.211160\pi$
$384$	−1.01260	+	0.698944i	−0.0516738	+	0.0356678i
$385$	−59.2951	+	22.4877i	−3.02196	+	1.14608i
$386$	1.11487	+	2.93968i	0.0567455	+	0.149626i
$387$	3.78365	−	1.98581i	0.192334	−	0.100945i
$388$	−2.36875	−	4.51328i	−0.120255	−	0.229127i
$389$	5.50879	+	1.35779i	0.279307	+	0.0688429i	0.376481	−	0.926425i	$-0.377134\pi$
$389$	5.50879	+	1.35779i	0.279307	+	0.0688429i	−0.0971740	+	0.995267i	$0.530980\pi$
$390$	50.3506	−	2.85952i	2.54960	−	0.144797i
$391$	12.2112	−	3.00980i	0.617549	−	0.152212i
$392$	−0.382702	−	0.431982i	−0.0193294	−	0.0218184i
$393$	−1.40101	−	11.5384i	−0.0706717	−	0.582034i
$394$	17.7251	−	9.30283i	0.892975	−	0.468670i
$395$	13.7871	−	26.2691i	0.693704	−	1.32174i
$396$	−6.21422	−	2.35674i	−0.312276	−	0.118431i
$397$	−24.6716	−	27.8484i	−1.23823	−	1.39767i	−0.887250	−	0.461290i	$-0.847387\pi$
$397$	−24.6716	−	27.8484i	−1.23823	−	1.39767i	−0.350980	−	0.936383i	$-0.614152\pi$
$398$	−30.3247	−	3.68209i	−1.52004	−	0.184567i
$399$	8.96082	+	2.20864i	0.448602	+	0.110571i
$400$	−25.1253	+	22.2591i	−1.25627	+	1.11295i
$401$	1.93206	−	2.18085i	0.0964826	−	0.108906i	−0.698286	−	0.715819i	$-0.746054\pi$
$401$	1.93206	−	2.18085i	0.0964826	−	0.108906i	0.794769	+	0.606912i	$0.207592\pi$
$402$	41.1464	−	21.5953i	2.05219	−	1.07707i
$403$	7.44955	−	9.43683i	0.371089	−	0.470082i
$404$	16.8789	+	8.85871i	0.839754	+	0.440737i
$405$	−36.2666	+	13.7541i	−1.80210	+	0.683447i
$406$	3.22180	−	26.5339i	0.159895	−	1.31686i
$407$	−6.83514	−	3.58736i	−0.338805	−	0.177819i
$408$			0.450658i			0.0223109i
$409$	10.6827	−	20.3542i	0.528226	−	1.00645i	−0.464445	−	0.885602i	$-0.653746\pi$
$409$	10.6827	−	20.3542i	0.528226	−	1.00645i	0.992671	−	0.120848i	$-0.0385614\pi$
$410$	53.0218	−	59.8492i	2.61856	−	2.95574i
$411$	10.7066	+	7.39025i	0.528119	+	0.364534i
$412$	−17.3991	+	15.4143i	−0.857193	+	0.759406i
$413$	27.8056	−	40.2833i	1.36822	−	1.98221i
$414$	5.86448	+	2.22411i	0.288224	+	0.109309i
$415$	9.47860	−	24.9930i	0.465286	−	1.22686i
$416$	−22.6480	+	17.6093i	−1.11041	+	0.863368i
$417$	−2.45484	−	6.47289i	−0.120214	−	0.316979i
$418$			11.6281i			0.568750i
$419$	3.32692	−	8.77237i	0.162531	−	0.428558i	−0.828866	−	0.559447i	$-0.811014\pi$
$419$	3.32692	−	8.77237i	0.162531	−	0.428558i	0.991397	+	0.130888i	$0.0417829\pi$
$420$	−6.26849	−	51.6257i	−0.305871	−	2.51908i
$421$	6.30466	+	12.0125i	0.307270	+	0.585454i	0.989304	−	0.145866i	$-0.0465968\pi$
$421$	6.30466	+	12.0125i	0.307270	+	0.585454i	−0.682034	+	0.731320i	$0.738904\pi$
$422$	−3.82950	−	2.64331i	−0.186417	−	0.128674i
$423$	2.03132	+	1.40212i	0.0987663	+	0.0681735i
$424$	−0.0328305	−	0.0625534i	−0.00159439	−	0.00303786i
$425$	2.90635	+	23.9360i	0.140979	+	1.16106i
$426$	−2.67880	+	7.06342i	−0.129788	+	0.342224i
$427$			48.1357i			2.32945i
$428$	8.54793	+	22.5390i	0.413180	+	1.08947i
$429$	30.6869	+	9.68659i	1.48158	+	0.467673i
$430$	−14.9390	+	39.3908i	−0.720421	+	1.89959i
$431$	−14.8509	−	5.63221i	−0.715344	−	0.271294i	−0.0300371	−	0.999549i	$-0.509563\pi$
$431$	−14.8509	−	5.63221i	−0.715344	−	0.271294i	−0.685307	+	0.728255i	$0.740332\pi$
$432$	10.1440	−	14.6962i	0.488056	−	0.707071i
$433$	17.4400	−	15.4505i	0.838113	−	0.742503i	−0.130401	−	0.991461i	$-0.541627\pi$
$433$	17.4400	−	15.4505i	0.838113	−	0.742503i	0.968514	+	0.248958i	$0.0800881\pi$
$434$	−20.6148	−	14.2294i	−0.989542	−	0.683032i
$435$	−16.5847	+	18.7202i	−0.795175	+	0.897567i
$436$	−3.80039	+	7.24104i	−0.182006	+	0.346783i
$437$		−	5.43142i		−	0.259820i
$438$	−22.6599	−	11.8928i	−1.08273	−	0.568261i
$439$	2.00618	−	16.5224i	0.0957500	−	0.788572i	−0.863174	−	0.504907i	$-0.831527\pi$
$439$	2.00618	−	16.5224i	0.0957500	−	0.788572i	0.958924	−	0.283665i	$-0.0915502\pi$
$440$	−1.25043	+	0.474225i	−0.0596118	+	0.0226078i
$441$	−4.71296	−	2.47355i	−0.224427	−	0.117788i
$442$	1.19183	+	20.9858i	0.0566896	+	0.998193i
$443$	−5.38514	+	2.82634i	−0.255856	+	0.134283i	−0.587775	−	0.809024i	$-0.699996\pi$
$443$	−5.38514	+	2.82634i	−0.255856	+	0.134283i	0.331919	+	0.943308i	$0.392304\pi$
$444$	4.19777	−	4.73830i	0.199217	−	0.224870i
$445$	−13.3921	+	11.8644i	−0.634848	+	0.562426i
$446$	8.54006	+	2.10494i	0.404384	+	0.0996716i
$447$	5.01594	+	0.609045i	0.237246	+	0.0288069i
$448$	19.2167	+	21.6912i	0.907906	+	1.02481i
$449$	19.9713	+	7.57412i	0.942505	+	0.357445i	0.777525	−	0.628852i	$-0.216475\pi$
$449$	19.9713	+	7.57412i	0.942505	+	0.357445i	0.164980	+	0.986297i	$0.447244\pi$
$450$	−5.58815	+	10.6473i	−0.263428	+	0.501920i
$451$	45.1754	−	23.7099i	2.12723	−	1.11645i
$452$	−2.18265	−	17.9758i	−0.102663	−	0.845510i
$453$	1.27417	+	1.43824i	0.0598655	+	0.0675742i
$454$	8.18038	−	2.01628i	0.383924	−	0.0946288i
$455$	8.74435	+	48.7282i	0.409941	+	2.28441i
$456$	0.188968	+	0.0465764i	0.00884923	+	0.00218114i
$457$	−3.78621	−	7.21402i	−0.177111	−	0.337457i	0.780676	−	0.624936i	$-0.214875\pi$
$457$	−3.78621	−	7.21402i	−0.177111	−	0.337457i	−0.957787	+	0.287479i	$0.907183\pi$
$458$	−3.27783	+	1.72034i	−0.153163	+	0.0803860i
$459$	−4.54856	−	11.9936i	−0.212308	−	0.559811i
$460$	−28.6169	+	10.8529i	−1.33427	+	0.506021i
$461$	−1.02681	+	0.708758i	−0.0478235	+	0.0330102i	−0.591737	−	0.806131i	$-0.701557\pi$
$461$	−1.02681	+	0.708758i	−0.0478235	+	0.0330102i	0.543913	+	0.839142i	$0.316942\pi$
$462$	16.0446	−	65.0955i	0.746462	−	3.02852i
$463$	8.69066	−	5.99873i	0.403889	−	0.278785i	−0.348753	−	0.937215i	$-0.613395\pi$
$463$	8.69066	−	5.99873i	0.403889	−	0.278785i	0.752642	+	0.658430i	$0.228779\pi$
$464$	1.74920	−	14.4059i	0.0812044	−	0.668778i
$465$	8.31125	+	21.9150i	0.385425	+	1.01628i
$466$	2.16227	−	4.11986i	0.100165	−	0.190849i
$467$	11.0810	−	16.0537i	0.512769	−	0.742875i	−0.478011	−	0.878354i	$-0.658642\pi$
$467$	11.0810	−	16.0537i	0.512769	−	0.742875i	0.990780	+	0.135479i	$0.0432574\pi$
$468$	−2.70047	+	4.43018i	−0.124829	+	0.204785i
$469$	25.9132	+	37.5417i	1.19656	+	1.73352i
$470$	−24.1569	+	2.93318i	−1.11427	+	0.135297i
$471$	−38.2041	+	9.41646i	−1.76035	+	0.433888i
$472$	0.586370	−	0.849503i	0.0269899	−	0.0391016i
$473$	−17.8256	+	20.1209i	−0.819622	+	0.925162i
$474$	14.5757	+	27.7718i	0.669486	+	1.27560i
$475$	10.3371	+	1.25515i	0.474298	+	0.0575902i
$476$	21.5173	−	2.61267i	0.986242	−	0.119751i
$477$	−0.487687	−	0.432053i	−0.0223296	−	0.0197823i
$478$	−2.27929	−	3.30212i	−0.104252	−	0.151035i
$479$	−34.6383	−	4.20586i	−1.58267	−	0.192170i	−0.718554	−	0.695471i	$-0.755196\pi$
$479$	−34.6383	−	4.20586i	−1.58267	−	0.192170i	−0.864112	+	0.503300i	$0.832119\pi$
$480$	−6.74121	−	55.5188i	−0.307693	−	2.53408i
$481$	−3.73392	+	4.73000i	−0.170252	+	0.215669i
$482$	−2.97315	+	24.4861i	−0.135423	+	1.11531i
$483$	−7.49433	+	30.4057i	−0.341004	+	1.38351i
$484$	20.2494			0.920425
$485$	−9.45926			−0.429523
$486$	3.55783	−	14.4347i	0.161386	−	0.654770i
$487$	−28.1167	+	10.6633i	−1.27409	+	0.483198i	−0.896611	−	0.442820i	$-0.853978\pi$
$487$	−28.1167	+	10.6633i	−1.27409	+	0.483198i	−0.377479	+	0.926018i	$0.623209\pi$
$488$			1.01510i			0.0459512i
$489$	13.4684	+	5.10788i	0.609061	+	0.230986i
$490$	50.9508	−	12.5583i	2.30172	−	0.567324i
$491$	−1.48662	−	1.31703i	−0.0670901	−	0.0594367i	0.628911	−	0.777477i	$-0.283501\pi$
$491$	−1.48662	−	1.31703i	−0.0670901	−	0.0594367i	−0.696001	+	0.718040i	$0.745039\pi$
$492$	10.0127	+	40.6230i	0.451406	+	1.83143i
$493$	−7.80248	−	6.91240i	−0.351406	−	0.311319i
$494$	8.92285	+	1.66917i	0.401458	+	0.0750996i
$495$	−9.23203	+	8.17886i	−0.414949	+	0.367613i
$496$	−11.1923	−	7.72547i	−0.502548	−	0.346884i
$497$	−7.20025	−	1.77470i	−0.322975	−	0.0796063i
$498$	16.0530	+	23.2567i	0.719351	+	1.04216i
$499$	−6.75942	−	27.4241i	−0.302593	−	1.22767i	−0.903583	−	0.428413i	$-0.859073\pi$
$499$	−6.75942	−	27.4241i	−0.302593	−	1.22767i	0.600990	−	0.799257i	$-0.294773\pi$
$500$	−5.51157	−	22.3613i	−0.246485	−	1.00003i
$501$	−34.4880	+	4.18760i	−1.54081	+	0.187088i
$502$	−13.7253	−	15.4927i	−0.612590	−	0.691471i
$503$	12.2389	−	32.2714i	0.545707	−	1.43891i	−0.324340	−	0.945941i	$-0.605142\pi$
$503$	12.2389	−	32.2714i	0.545707	−	1.43891i	0.870046	−	0.492970i	$-0.164089\pi$
$504$	−0.195352	−	0.102529i	−0.00870166	−	0.00456698i
$505$	29.1138	−	20.0958i	1.29555	−	0.894252i
$506$	−39.4563			−1.75405
$507$	11.8380	−	22.1571i	0.525744	−	0.984033i
$508$	19.2256			0.853000
$509$	−0.754264	+	0.520631i	−0.0334322	+	0.0230765i	−0.584664	−	0.811276i	$-0.698774\pi$
$509$	−0.754264	+	0.520631i	−0.0334322	+	0.0230765i	0.551231	+	0.834352i	$0.314158\pi$
$510$	−36.2832	−	19.0429i	−1.60665	−	0.843233i
$511$	8.90828	−	23.4892i	0.394079	−	1.03910i
$512$	21.0882	+	23.8037i	0.931976	+	1.05198i
$513$	−5.49918	+	0.667722i	−0.242795	+	0.0294806i
$514$	11.7306	+	47.5931i	0.517416	+	2.09924i
$515$	10.3236	+	41.8846i	0.454913	+	1.84565i
$516$	−12.5225	−	18.1420i	−0.551274	−	0.798658i
$517$	−15.0760	−	3.71591i	−0.663043	−	0.163425i
$518$	10.3327	+	7.13215i	0.453993	+	0.313369i
$519$	−37.2203	+	32.9744i	−1.63379	+	1.44741i
$520$	0.184403	+	1.02759i	0.00808660	+	0.0450628i
$521$	16.5717	+	14.6812i	0.726018	+	0.643196i	0.942928	−	0.332996i	$-0.108059\pi$
$521$	16.5717	+	14.6812i	0.726018	+	0.643196i	−0.216910	+	0.976192i	$0.569598\pi$
$522$	−1.24409	−	5.04745i	−0.0544521	−	0.220921i
$523$	17.0527	+	15.1073i	0.745661	+	0.660598i	0.947839	−	0.318751i	$-0.103263\pi$
$523$	17.0527	+	15.1073i	0.745661	+	0.660598i	−0.202178	+	0.979349i	$0.564802\pi$
$524$	−11.4465	+	2.82131i	−0.500043	+	0.123250i
$525$	−56.1363	−	21.2897i	−2.44999	−	0.929158i
$526$		−	42.1375i		−	1.83728i
$527$	−9.13402	+	3.46408i	−0.397884	+	0.150898i
$528$	8.71100	−	35.3419i	0.379098	−	1.53806i
$529$	−4.57020			−0.198704
$530$	6.42354			0.279021
$531$	2.27826	−	9.24328i	0.0988682	−	0.401124i
$532$	1.12832	−	9.29254i	0.0489188	−	0.402883i
$533$	−11.7090	−	38.0688i	−0.507175	−	1.64894i
$534$	−2.27997	−	18.7772i	−0.0986638	−	0.812570i
$535$	44.4089	+	5.39222i	1.91996	+	0.233126i
$536$	0.546463	+	0.791688i	0.0236036	+	0.0341957i
$537$	−14.7012	−	13.0241i	−0.634404	−	0.562033i
$538$	−29.3308	+	3.56141i	−1.26454	+	0.153543i
$539$	33.2395	+	4.03601i	1.43173	+	0.173843i
$540$	14.5064	+	27.6396i	0.624256	+	1.18942i
$541$	−4.64006	+	5.23754i	−0.199492	+	0.225180i	−0.839740	−	0.542988i	$-0.817293\pi$
$541$	−4.64006	+	5.23754i	−0.199492	+	0.225180i	0.640249	+	0.768168i	$0.278831\pi$
$542$	2.41922	−	3.50485i	0.103914	−	0.150546i
$543$	−9.76491	+	2.40683i	−0.419052	+	0.103287i
$544$	23.1399	−	2.80969i	0.992115	−	0.120465i
$545$	8.62112	+	12.4899i	0.369288	+	0.535007i
$546$	−47.6479	−	21.6560i	−2.03914	−	0.926793i
$547$	−0.526092	+	0.762177i	−0.0224941	+	0.0325883i	−0.834070	−	0.551659i	$-0.813995\pi$
$547$	−0.526092	+	0.762177i	−0.0224941	+	0.0325883i	0.811576	+	0.584248i	$0.198610\pi$
$548$	6.13216	−	11.6839i	0.261953	−	0.499110i
$549$	3.31979	+	8.75358i	0.141685	+	0.373593i
$550$	9.11798	−	75.0933i	0.388792	−	3.20199i
$551$	−3.70487	+	2.55729i	−0.157833	+	0.108944i
$552$	−0.158042	+	0.641202i	−0.00672672	+	0.0272914i
$553$	−25.3388	+	17.4901i	−1.07752	+	0.743756i
$554$	23.0118	−	8.72721i	0.977676	−	0.370784i
$555$	−4.16583	−	10.9844i	−0.176830	−	0.466261i
$556$	−6.21733	+	3.26311i	−0.263674	+	0.138387i
$557$	−4.87768	−	9.29365i	−0.206674	−	0.393785i	0.759951	−	0.649981i	$-0.225223\pi$
$557$	−4.87768	−	9.29365i	−0.206674	−	0.393785i	−0.966625	+	0.256196i	$0.917531\pi$
$558$	−4.73021	−	1.16589i	−0.200246	−	0.0493561i
$559$	12.8810	+	16.5668i	0.544809	+	0.700699i
$560$	54.3719	−	13.4015i	2.29763	−	0.566316i
$561$	−17.3383	−	19.5709i	−0.732023	−	0.826284i
$562$	−6.26108	−	51.5647i	−0.264108	−	2.17512i
$563$	−33.2748	+	17.4639i	−1.40236	+	0.736018i	−0.984973	−	0.172709i	$-0.944748\pi$
$563$	−33.2748	+	17.4639i	−1.40236	+	0.736018i	−0.417392	+	0.908727i	$0.637056\pi$
$564$	5.91741	−	11.2747i	0.249168	−	0.474750i
$565$	−31.4208	−	11.9163i	−1.32188	−	0.501324i
$566$	3.62116	+	4.08744i	0.152209	+	0.171808i
$567$	39.9601	+	4.85203i	1.67817	+	0.203766i
$568$	−0.151840	−	0.0374253i	−0.00637108	−	0.00157033i
$569$	−24.7657	+	21.9405i	−1.03823	+	0.919794i	−0.996847	−	0.0793489i	$-0.974716\pi$
$569$	−24.7657	+	21.9405i	−1.03823	+	0.919794i	−0.0413863	+	0.999143i	$0.513177\pi$
$570$	−11.7349	+	13.2460i	−0.491521	+	0.554812i
$571$	17.1470	−	8.99946i	0.717581	−	0.376616i	−0.0660715	−	0.997815i	$-0.521047\pi$
$571$	17.1470	−	8.99946i	0.717581	−	0.376616i	0.783653	+	0.621199i	$0.213354\pi$
$572$	6.00156	−	32.0824i	0.250938	−	1.34143i
$573$	35.5506	+	18.6584i	1.48515	+	0.779465i
$574$	−77.5883	+	29.4254i	−3.23847	+	1.22819i
$575$	−4.25895	+	35.0756i	−0.177610	+	1.46275i
$576$	4.99059	+	2.61927i	0.207941	+	0.109136i
$577$			43.1555i			1.79659i	0.439394	+	0.898294i	$0.355193\pi$
$577$			43.1555i			1.79659i	−0.439394	+	0.898294i	$0.644807\pi$
$578$	−7.78443	+	14.8320i	−0.323790	+	0.616929i
$579$	−2.02453	+	2.28522i	−0.0841367	+	0.0949707i
$580$	20.8767	+	14.4102i	0.866859	+	0.598350i
$581$	−20.7642	+	18.3954i	−0.861442	+	0.763171i
$582$	5.68084	−	8.23012i	0.235478	−	0.341149i
$583$	3.83237	+	1.45343i	0.158721	+	0.0601948i
$584$	0.187860	−	0.495346i	0.00777369	−	0.0204975i
$585$	4.95083	+	8.25824i	0.204692	+	0.341436i
$586$	−0.833134	−	2.19679i	−0.0344165	−	0.0907488i
$587$			38.4606i			1.58744i	0.608285	+	0.793719i	$0.291858\pi$
$587$			38.4606i			1.58744i	−0.608285	+	0.793719i	$0.708142\pi$
$588$	−9.73691	+	25.6741i	−0.401544	+	1.05878i
$589$	0.508522	+	4.18805i	0.0209533	+	0.172566i
$590$	43.6173	+	83.1058i	1.79570	+	3.42141i
$591$	15.9979	+	11.0425i	0.658065	+	0.454229i
$592$	5.60988	+	3.87222i	0.230565	+	0.159147i
$593$	21.0399	+	40.0881i	0.864004	+	1.64622i	0.758377	+	0.651816i	$0.225993\pi$
$593$	21.0399	+	40.0881i	0.864004	+	1.64622i	0.105627	+	0.994406i	$0.466315\pi$
$594$	4.85063	+	39.9486i	0.199024	+	1.63911i
$595$	14.2640	−	37.6111i	0.584767	−	1.54190i
$596$		−	5.12493i		−	0.209925i
$597$	−10.5189	−	27.7361i	−0.430510	−	1.13516i
$598$	−5.66380	+	30.2768i	−0.231610	+	1.23811i
$599$	13.6373	−	35.9587i	0.557207	−	1.46923i	−0.299838	−	0.953990i	$-0.596932\pi$
$599$	13.6373	−	35.9587i	0.557207	−	1.46923i	0.857044	−	0.515243i	$-0.172298\pi$
$600$	−1.18381	−	0.448962i	−0.0483290	−	0.0183288i
$601$	0.967183	−	1.40121i	0.0394522	−	0.0571564i	−0.802761	−	0.596300i	$-0.796637\pi$
$601$	0.967183	−	1.40121i	0.0394522	−	0.0571564i	0.842214	+	0.539144i	$0.181252\pi$
$602$	32.7258	−	28.9925i	1.33380	−	1.18165i
$603$	7.30153	+	5.03988i	0.297341	+	0.205240i
$604$	1.29236	−	1.45877i	0.0525854	−	0.0593566i
$605$	17.4637	−	33.2744i	0.710002	−	1.35280i
$606$			37.3995i			1.51925i
$607$	−8.14219	−	4.27335i	−0.330481	−	0.173450i	0.291319	−	0.956626i	$-0.405906\pi$
$607$	−8.14219	−	4.27335i	−0.330481	−	0.173450i	−0.621800	+	0.783176i	$0.713598\pi$
$608$	1.21341	−	9.99330i	0.0492101	−	0.405282i
$609$	24.2689	−	9.20396i	0.983424	−	0.372963i
$610$	−81.7269	−	42.8936i	−3.30902	−	1.73671i
$611$	−5.01551	+	11.0352i	−0.202906	+	0.446436i
$612$	3.73277	−	1.95911i	0.150888	−	0.0791923i
$613$	13.7762	−	15.5501i	0.556416	−	0.628064i	−0.401242	−	0.915972i	$-0.631421\pi$
$613$	13.7762	−	15.5501i	0.556416	−	0.628064i	0.957658	+	0.287908i	$0.0929598\pi$
$614$	41.3707	−	36.6513i	1.66959	−	1.47912i
$615$	75.3883	+	18.5816i	3.03995	+	0.749280i
$616$	1.37777	+	0.167292i	0.0555121	+	0.00674039i
$617$	25.8779	+	29.2101i	1.04180	+	1.17595i	0.984099	+	0.177620i	$0.0568398\pi$
$617$	25.8779	+	29.2101i	1.04180	+	1.17595i	0.0577051	+	0.998334i	$0.481622\pi$
$618$	−42.6420	−	16.1720i	−1.71531	−	0.650533i
$619$	1.23329	−	2.34983i	0.0495700	−	0.0944477i	−0.859411	−	0.511286i	$-0.829169\pi$
$619$	1.23329	−	2.34983i	0.0495700	−	0.0944477i	0.908981	+	0.416838i	$0.136862\pi$
$620$	21.0497	−	11.0477i	0.845377	−	0.443688i
$621$	−2.26570	−	18.6597i	−0.0909194	−	0.748789i
$622$	−16.0142	−	18.0763i	−0.642110	−	0.724793i
$623$	18.0286	−	4.44364i	0.722299	−	0.178031i
$624$	−25.8692	−	11.7576i	−1.03560	−	0.470680i
$625$	−1.54180	−	0.380020i	−0.0616720	−	0.0152008i
$626$	−26.2934	−	50.0980i	−1.05090	−	2.00232i
$627$	−9.99832	+	5.24752i	−0.399294	+	0.209566i
$628$	14.1520	+	37.3159i	0.564728	+	1.48907i
$629$	4.57822	−	1.73629i	0.182546	−	0.0692304i
$630$	16.5095	−	11.3957i	0.657752	−	0.454014i
$631$	5.00465	−	20.3047i	0.199232	−	0.808316i	−0.783212	−	0.621755i	$-0.786420\pi$
$631$	5.00465	−	20.3047i	0.199232	−	0.808316i	0.982443	−	0.186560i	$-0.0597340\pi$
$632$	−0.534351	+	0.368836i	−0.0212553	+	0.0146715i
$633$	0.544653	−	4.48562i	0.0216480	−	0.178288i
$634$	−7.07728	−	18.6613i	−0.281075	−	0.741133i
$635$	16.5809	−	31.5922i	0.657991	−	1.25370i
$636$	−1.90937	+	2.76620i	−0.0757116	+	0.109687i
$637$	7.86843	−	24.9270i	0.311759	−	0.987643i
$638$	18.5773	+	26.9139i	0.735483	+	1.06553i
$639$	−1.43178	+	0.173849i	−0.0566402	+	0.00687737i
$640$	2.24868	−	0.554249i	0.0888868	−	0.0219086i
$641$	−16.5939	+	24.0404i	−0.655418	+	0.949537i	0.344524	+	0.938778i	$0.388040\pi$
$641$	−16.5939	+	24.0404i	−0.655418	+	0.949537i	−0.999942	+	0.0107595i	$0.996575\pi$
$642$	−31.3617	+	35.4001i	−1.23775	+	1.39713i
$643$	14.3305	+	27.3044i	0.565138	+	1.07678i	0.985540	+	0.169443i	$0.0541969\pi$
$643$	14.3305	+	27.3044i	0.565138	+	1.07678i	−0.420402	+	0.907338i	$0.638111\pi$
$644$	31.5313	+	3.82859i	1.24251	+	0.150867i
$645$	−40.6114	+	4.93112i	−1.59907	+	0.194163i
$646$	−5.52084	−	4.89103i	−0.217214	−	0.192435i
$647$	−6.41594	−	9.29509i	−0.252237	−	0.365428i	0.676327	−	0.736602i	$-0.263571\pi$
$647$	−6.41594	−	9.29509i	−0.252237	−	0.365428i	−0.928563	+	0.371174i	$0.878955\pi$
$648$	0.842687	+	0.102321i	0.0331039	+	0.00401954i
$649$	7.21869	+	59.4512i	0.283358	+	2.33366i
$650$	−56.3140	−	17.7760i	−2.20882	−	0.697233i
$651$	2.93196	−	24.1468i	0.114912	−	0.946389i
$652$	3.49643	−	14.1856i	0.136931	−	0.555550i
$653$	13.2532			0.518638			0.259319	−	0.965792i	$-0.416502\pi$
$653$	13.2532			0.518638			0.259319	+	0.965792i	$0.416502\pi$
$654$	−16.0444			−0.627386
$655$	−5.23580	+	21.2425i	−0.204580	+	0.830012i
$656$	−42.1246	+	15.9757i	−1.64469	+	0.623748i
$657$		−	4.88594i		−	0.190619i
$658$	23.6132	+	8.95531i	0.920539	+	0.349114i
$659$	−6.83636	+	1.68501i	−0.266307	+	0.0656388i	−0.370208	−	0.928949i	$-0.620714\pi$
$659$	−6.83636	+	1.68501i	−0.266307	+	0.0656388i	0.103901	+	0.994588i	$0.466867\pi$
$660$	47.6263	+	42.1932i	1.85385	+	1.64237i
$661$	−5.01035	−	20.3278i	−0.194880	−	0.790659i	−0.984256	−	0.176749i	$-0.943442\pi$
$661$	−5.01035	−	20.3278i	−0.194880	−	0.790659i	0.789376	−	0.613910i	$-0.210404\pi$
$662$	11.9122	+	10.5533i	0.462979	+	0.410164i
$663$	−17.5066	+	10.4952i	−0.679899	+	0.407601i
$664$	−0.437879	+	0.387927i	−0.0169930	+	0.0150545i
$665$	−14.2967	−	9.86829i	−0.554402	−	0.382676i
$666$	2.37091	+	0.584377i	0.0918710	+	0.0226442i
$667$	−8.67734	−	12.5713i	−0.335988	−	0.486763i
$668$	8.43285	+	34.2134i	0.326277	+	1.32376i
$669$	2.04404	+	8.29299i	0.0790271	+	0.320626i
$670$	−86.8312	+	10.5432i	−3.35458	+	0.407320i
$671$	−39.0541	−	44.0829i	−1.50766	−	1.70180i
$672$	−20.5816	+	54.2693i	−0.793954	+	2.09348i
$673$	12.2974	+	6.45416i	0.474029	+	0.248790i	0.684780	−	0.728750i	$-0.259898\pi$
$673$	12.2974	+	6.45416i	0.474029	+	0.248790i	−0.210750	+	0.977540i	$0.567591\pi$
$674$	−48.8805	+	33.7397i	−1.88280	+	1.29961i
$675$	36.0368			1.38706
$676$	−23.7570	−	9.21061i	−0.913729	−	0.354254i
$677$	−6.91227			−0.265660			−0.132830	−	0.991139i	$-0.542406\pi$
$677$	−6.91227			−0.265660			−0.132830	+	0.991139i	$0.542406\pi$
$678$	29.2379	−	20.1815i	1.12288	−	0.775066i
$679$	8.69242	+	4.56213i	0.333584	+	0.175079i
$680$	0.300803	−	0.793151i	0.0115353	−	0.0304160i
$681$	5.42531	+	6.12391i	0.207898	+	0.234669i
$682$	30.4239	−	3.69413i	1.16499	−	0.141456i
$683$	−2.19588	−	8.90902i	−0.0840229	−	0.340894i	0.913852	−	0.406046i	$-0.133093\pi$
$683$	−2.19588	−	8.90902i	−0.0840229	−	0.340894i	−0.997875	+	0.0651522i	$0.979247\pi$
$684$	−0.435695	−	1.76768i	−0.0166592	−	0.0675891i
$685$	−13.9107	−	20.1531i	−0.531500	−	0.770011i
$686$	−1.82166	−	0.448998i	−0.0695511	−	0.0171428i
$687$	−2.95843	−	2.04205i	−0.112871	−	0.0779092i
$688$	17.7676	−	15.7408i	0.677385	−	0.600111i
$689$	1.66541	−	2.73214i	0.0634471	−	0.104086i
$690$	−44.9459	−	39.8186i	−1.71106	−	1.51587i
$691$	−6.93468	−	28.1351i	−0.263808	−	1.07031i	−0.942050	−	0.335471i	$-0.891104\pi$
$691$	−6.93468	−	28.1351i	−0.263808	−	1.07031i	0.678243	−	0.734838i	$-0.262742\pi$
$692$	37.7518	+	33.4452i	1.43511	+	1.27140i
$693$	12.4282	−	3.06328i	0.472109	−	0.116364i
$694$	−64.6303	−	24.5110i	−2.45333	−	0.930426i
$695$			13.0307i			0.494284i
$696$	0.511787	−	0.194095i	0.0193992	−	0.00735716i
$697$	−7.74467	+	31.4214i	−0.293350	+	1.19017i
$698$	46.9485			1.77703
$699$	4.51820			0.170894
$700$	−14.5731	+	59.1256i	−0.550813	+	2.23474i
$701$	−2.65231	+	21.8438i	−0.100176	+	0.825027i	0.852853	+	0.522151i	$0.174870\pi$
$701$	−2.65231	+	21.8438i	−0.100176	+	0.825027i	−0.953030	+	0.302877i	$0.902053\pi$
$702$	31.3508	+	2.01232i	1.18326	+	0.0759502i
$703$	−0.254885	−	2.09917i	−0.00961317	−	0.0791716i
$704$	−35.1976	−	4.27376i	−1.32656	−	0.161073i
$705$	−13.4235	−	19.4474i	−0.505560	−	0.732430i
$706$	−10.0078	−	8.86612i	−0.376648	−	0.333681i
$707$	−36.4457	+	4.42531i	−1.37068	+	0.166431i
$708$	−48.7534	−	5.91973i	−1.83226	−	0.222477i
$709$	−2.60743	−	4.96805i	−0.0979242	−	0.186579i	0.831566	−	0.555426i	$-0.187445\pi$
$709$	−2.60743	−	4.96805i	−0.0979242	−	0.186579i	−0.929490	+	0.368847i	$0.879753\pi$
$710$	9.42929	−	10.6435i	0.353875	−	0.399442i
$711$	−3.40167	+	4.92817i	−0.127573	+	0.184821i
$712$	0.380191	−	0.0937085i	0.0142482	−	0.00351188i
$713$	−14.2108	+	1.72551i	−0.532199	+	0.0646207i
$714$	24.1575	+	34.9982i	0.904073	+	1.30978i
$715$	−47.5429	−	37.5309i	−1.77800	−	1.40358i
$716$	−11.3165	+	16.3947i	−0.422916	+	0.612699i
$717$	1.81070	−	3.44999i	0.0676217	−	0.128842i
$718$	7.97098	+	21.0177i	0.297474	+	0.784375i
$719$	0.733788	−	6.04329i	0.0273657	−	0.225377i	−0.972609	−	0.232446i	$-0.925327\pi$
$719$	0.733788	−	6.04329i	0.0273657	−	0.225377i	0.999975	+	0.00706924i	$0.00225023\pi$
$720$	8.96338	−	6.18698i	0.334046	−	0.230575i
$721$	10.7139	−	43.4681i	0.399007	−	1.61884i
$722$	28.4951	−	19.6688i	1.06048	−	0.731996i
$723$	−22.3959	+	8.49363i	−0.832911	+	0.315881i
$724$	3.61724	+	9.53788i	0.134434	+	0.354473i
$725$	25.9310	−	13.6096i	0.963052	−	0.505449i
$726$	18.4627	+	35.1777i	0.685215	+	1.30557i
$727$	3.88142	+	0.956683i	0.143954	+	0.0354814i	0.310634	−	0.950530i	$-0.399459\pi$
$727$	3.88142	+	0.956683i	0.143954	+	0.0354814i	−0.166680	+	0.986011i	$0.553305\pi$
$728$	0.326146	−	1.03322i	0.0120878	−	0.0382938i
$729$	−17.0439	+	4.20094i	−0.631255	+	0.155590i
$730$	31.9429	+	36.0560i	1.18226	+	1.33449i
$731$	−2.05526	−	16.9266i	−0.0760165	−	0.626052i
$732$	42.7645	−	22.4445i	1.58062	−	0.829574i
$733$	−1.79061	+	3.41173i	−0.0661379	+	0.126015i	−0.916280	−	0.400538i	$-0.868823\pi$
$733$	−1.79061	+	3.41173i	−0.0661379	+	0.126015i	0.850142	+	0.526553i	$0.176516\pi$
$734$	50.0589	+	18.9848i	1.84771	+	0.700744i
$735$	33.7911	+	38.1423i	1.24640	+	1.40690i
$736$	33.9091	+	4.11731i	1.24990	+	0.151766i
$737$	−54.1903	−	13.3567i	−1.99612	−	0.492001i
$738$	−12.0802	+	10.7021i	−0.444679	+	0.393951i
$739$	−9.02719	+	10.1896i	−0.332070	+	0.374830i	−0.890703	−	0.454585i	$-0.849788\pi$
$739$	−9.02719	+	10.1896i	−0.332070	+	0.374830i	0.558633	+	0.829415i	$0.311326\pi$
$740$	−10.5507	+	5.53743i	−0.387851	+	0.203560i
$741$	2.59147	+	8.42548i	0.0952000	+	0.309518i
$742$	−5.90280	−	3.09803i	−0.216699	−	0.113732i
$743$	2.82747	−	1.07232i	0.103730	−	0.0393396i	−0.302194	−	0.953246i	$-0.597719\pi$
$743$	2.82747	−	1.07232i	0.103730	−	0.0393396i	0.405924	+	0.913907i	$0.366950\pi$
$744$	0.0618297	−	0.509214i	0.00226679	−	0.0186687i
$745$	−8.42145	−	4.41992i	−0.308538	−	0.161933i
$746$		−	30.5338i		−	1.11792i
$747$	−2.50732	+	4.77730i	−0.0917380	+	0.174792i
$748$	−17.5859	+	19.8504i	−0.643003	+	0.725801i
$749$	−38.2082	−	26.3732i	−1.39610	−	0.963655i
$750$	33.8214	−	29.9632i	1.23498	−	1.09410i
$751$	−25.5551	+	37.0229i	−0.932518	+	1.35099i	0.00386028	+	0.999993i	$0.498771\pi$
$751$	−25.5551	+	37.0229i	−0.932518	+	1.35099i	−0.936378	+	0.350993i	$0.885844\pi$
$752$	12.8202	+	4.86206i	0.467504	+	0.177301i
$753$	7.12727	−	18.7931i	0.259732	−	0.684857i
$754$	23.3191	−	10.3919i	0.849231	−	0.378452i
$755$	−1.28253	−	3.38174i	−0.0466759	−	0.123074i
$756$		−	32.3953i		−	1.17821i
$757$	−14.6780	+	38.7026i	−0.533480	+	1.40667i	0.349357	+	0.936990i	$0.386400\pi$
$757$	−14.6780	+	38.7026i	−0.533480	+	1.40667i	−0.882837	+	0.469680i	$0.844369\pi$
$758$	3.76717	+	31.0254i	0.136830	+	1.12689i
$759$	−17.8058	−	33.9261i	−0.646309	−	1.23144i
$760$	−0.301492	−	0.208105i	−0.0109363	−	0.00754875i
$761$	40.8034	+	28.1646i	1.47912	+	1.02097i	0.988771	+	0.149442i	$0.0477477\pi$
$761$	40.8034	+	28.1646i	1.47912	+	1.02097i	0.490353	+	0.871524i	$0.336868\pi$
$762$	17.5293	+	33.3993i	0.635020	+	1.20993i
$763$	−1.89846	−	15.6352i	−0.0687289	−	0.566034i
$764$	14.4405	−	38.0764i	0.522439	−	1.37756i
$765$		−	7.82341i		−	0.282856i
$766$	−21.7216	−	57.2753i	−0.784835	−	2.06944i
$767$	46.6561	+	2.99473i	1.68466	+	0.108133i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63772 - 1.13043i) q^{2} +(1.71106 + 0.898032i) q^{3} +(0.695024 - 1.83263i) q^{4} +(-2.41202 - 2.72261i) q^{5} +(3.81739 - 0.463516i) q^{6} +(0.903389 + 3.66519i) q^{7} +(0.0190509 + 0.0772924i) q^{8} +(0.417062 + 0.604219i) q^{9} +O(q^{10})\)	\(q+(1.63772 - 1.13043i) q^{2} +(1.71106 + 0.898032i) q^{3} +(0.695024 - 1.83263i) q^{4} +(-2.41202 - 2.72261i) q^{5} +(3.81739 - 0.463516i) q^{6} +(0.903389 + 3.66519i) q^{7} +(0.0190509 + 0.0772924i) q^{8} +(0.417062 + 0.604219i) q^{9} +(-7.02794 - 1.73223i) q^{10} +(-3.80102 - 2.62366i) q^{11} +(2.83499 - 2.51158i) q^{12} +(-2.55888 + 2.54010i) q^{13} +(5.62276 + 4.98133i) q^{14} +(-1.68212 - 6.82461i) q^{15} +(3.05273 + 2.70448i) q^{16} +(2.84446 - 0.701095i) q^{17} +(1.36606 + 0.518078i) q^{18} -1.26518i q^{19} +(-6.66594 + 2.52806i) q^{20} +(-1.74571 + 7.08263i) q^{21} -9.19086 q^{22} +4.29299 q^{23} +(-0.0368140 + 0.149360i) q^{24} +(-0.992070 + 8.17043i) q^{25} +(-1.31931 + 7.05261i) q^{26} +(-0.527767 - 4.34655i) q^{27} +(7.34482 + 0.891822i) q^{28} +(-2.02128 - 2.92833i) q^{29} +(-10.4696 - 9.27526i) q^{30} +(-3.31023 + 0.401935i) q^{31} +(7.89870 + 0.959076i) q^{32} +(-4.14764 - 7.90266i) q^{33} +(3.86587 - 4.36367i) q^{34} +(7.79989 - 11.3001i) q^{35} +(1.39718 - 0.344373i) q^{36} +(1.65918 - 0.201461i) q^{37} +(-1.43021 - 2.07201i) q^{38} +(-6.65949 + 2.04830i) q^{39} +(0.164486 - 0.238299i) q^{40} +(-5.13358 + 9.78122i) q^{41} +(5.14747 + 13.5728i) q^{42} +(0.701553 - 5.77781i) q^{43} +(-7.44999 + 5.14236i) q^{44} +(0.639089 - 2.59289i) q^{45} +(7.03071 - 4.85295i) q^{46} +(3.14343 - 1.19215i) q^{47} +(2.79469 + 7.36898i) q^{48} +(-6.41934 + 3.36913i) q^{49} +(7.61140 + 14.5023i) q^{50} +(5.49663 + 1.35480i) q^{51} +(2.87657 + 6.45492i) q^{52} +(-0.861654 + 0.212379i) q^{53} +(-5.77782 - 6.52181i) q^{54} +(2.02495 + 16.6770i) q^{55} +(-0.266081 + 0.139650i) q^{56} +(1.13618 - 2.16480i) q^{57} +(-6.62057 - 2.51085i) q^{58} +(-8.59852 - 9.70573i) q^{59} +(-13.6761 - 1.66058i) q^{60} +(12.3810 + 3.05165i) q^{61} +(-4.96686 + 4.40026i) q^{62} +(-1.83781 + 2.07446i) q^{63} +(6.79750 - 3.56760i) q^{64} +(13.0878 + 0.840067i) q^{65} +(-15.7261 - 8.25369i) q^{66} +(11.2990 - 4.28513i) q^{67} +(0.692119 - 5.70011i) q^{68} +(7.34556 + 3.85525i) q^{69} -27.3236i q^{70} +(-0.912946 + 1.73947i) q^{71} +(-0.0387561 + 0.0437466i) q^{72} +(-5.47692 - 3.78045i) q^{73} +(2.48953 - 2.20553i) q^{74} +(-9.03480 + 13.0892i) q^{75} +(-2.31861 - 0.879333i) q^{76} +(6.18240 - 16.3017i) q^{77} +(-8.59090 + 10.8826i) q^{78} +(2.89225 + 7.62624i) q^{79} -14.8347i q^{80} +(3.78134 - 9.97057i) q^{81} +(2.64968 + 21.8220i) q^{82} +(3.41513 + 6.50698i) q^{83} +(11.7665 + 8.12184i) q^{84} +(-8.76969 - 6.05328i) q^{85} +(-5.38249 - 10.2555i) q^{86} +(-0.828792 - 6.82572i) q^{87} +(0.130376 - 0.343773i) q^{88} -4.91886i q^{89} +(-1.88444 - 4.96886i) q^{90} +(-11.6216 - 7.08411i) q^{91} +(2.98374 - 7.86746i) q^{92} +(-6.02495 - 2.28496i) q^{93} +(3.80041 - 5.50584i) q^{94} +(-3.44460 + 3.05165i) q^{95} +(12.6538 + 8.73432i) q^{96} +(1.72450 - 1.94656i) q^{97} +(-6.70448 + 12.7743i) q^{98} -3.39088i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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