LMFDB - Embedded newform 585.2.bs.a.334.2

Newspace parameters

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.2
Root			$-1.02826 + 0.593667i$ of defining polynomial
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.a.289.2

$q$-expansion

$f(q)$	$=$	$q+(-1.02826 - 0.593667i) q^{2} +(-0.295120 - 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +O(q^{10})$	\(q+(-1.02826 - 0.593667i) q^{2} +(-0.295120 - 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +(0.465813 + 2.61378i) q^{10} +(1.94045 - 3.36096i) q^{11} +(-2.96232 - 2.05540i) q^{13} +2.40976 q^{14} +(1.23557 - 2.14007i) q^{16} +(-4.71996 + 2.72507i) q^{17} +(2.94045 + 5.09301i) q^{19} +(-0.449133 + 1.24105i) q^{20} +(-3.99058 + 2.30396i) q^{22} +(-0.298874 - 0.172555i) q^{23} +(-0.850210 + 4.92718i) q^{25} +(1.82581 + 3.87212i) q^{26} +(1.03743 + 0.598962i) q^{28} +(-1.50000 + 2.59808i) q^{29} +1.18048 q^{31} +(2.78591 - 1.60845i) q^{32} +6.47114 q^{34} +(4.26737 + 1.54436i) q^{35} +(4.71996 + 2.72507i) q^{37} -6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(0.0902394 - 0.156299i) q^{41} +(-1.15990 + 0.669668i) q^{43} -2.29066 q^{44} +(0.204880 + 0.354863i) q^{46} +12.2807i q^{47} +(-1.44045 + 2.49493i) q^{49} +(3.79934 - 4.56169i) q^{50} +(-0.176407 + 2.12081i) q^{52} -2.42636i q^{53} +(-8.54334 + 1.52255i) q^{55} +(-3.12093 - 5.40561i) q^{56} +(3.08478 - 1.78100i) q^{58} +(3.53069 + 6.11533i) q^{59} +(-3.38090 - 5.85589i) q^{61} +(-1.21384 - 0.700811i) q^{62} -8.76180 q^{64} +(0.751722 + 8.02714i) q^{65} +(-3.81417 - 2.20211i) q^{67} +(2.78591 + 1.60845i) q^{68} +(-3.47114 - 4.12140i) q^{70} +(-0.940450 - 1.62891i) q^{71} +8.86014i q^{73} +(-3.23557 - 5.60417i) q^{74} +(1.73557 - 3.00609i) q^{76} +7.87651i q^{77} -11.1805 q^{79} +(-5.43992 + 0.969475i) q^{80} +(-0.185579 + 0.107144i) q^{82} -7.83540i q^{83} +(11.4595 + 4.14720i) q^{85} +1.59024 q^{86} +(10.3365 + 5.96781i) q^{88} +(-6.12093 + 10.6018i) q^{89} +(7.29249 + 0.606582i) q^{91} +0.203698i q^{92} +(7.29066 - 12.6278i) q^{94} +(4.47497 - 12.3653i) q^{95} +(5.02801 - 2.90292i) q^{97} +(2.96232 - 1.71029i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5	$ 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 7 * q^10 + 44 * q^14 - 16 * q^16 + 12 * q^19 + q^20 - 2 * q^25 - 24 * q^26 - 18 * q^29 - 16 * q^31 + 16 * q^34 - 10 * q^35 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 10 * q^46 + 6 * q^49 + 31 * q^50 - 26 * q^55 + 16 * q^56 + 4 * q^59 + 6 * q^61 - 12 * q^64 - 23 * q^65 + 20 * q^70 + 12 * q^71 - 8 * q^74 - 10 * q^76 - 104 * q^79 - 33 * q^80 + 21 * q^85 + 4 * q^86 - 20 * q^89 - 44 * q^91 + 56 * q^94 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.02826	−	0.593667i	−0.727090	−	0.419786i	0.0902665	−	0.995918i	$-0.471228\pi$
$2$	−1.02826	−	0.593667i	−0.727090	−	0.419786i	−0.817357	+	0.576132i	$0.804561\pi$
$3$		0			0
$3$		0			0
$4$	−0.295120	−	0.511162i	−0.147560	−	0.255581i
$5$	−1.44045	−	1.71029i	−0.644189	−	0.764867i
$5$	−1.44045	−	1.71029i	−0.644189	−	0.764867i
$6$		0			0
$7$	−1.75765	+	1.01478i	−0.664328	+	0.383550i	−0.793924	−	0.608017i	$-0.791965\pi$
$7$	−1.75765	+	1.01478i	−0.664328	+	0.383550i	0.129596	+	0.991567i	$0.458632\pi$
$8$			3.07548i			1.08735i
$9$		0			0
$10$	0.465813	+	2.61378i	0.147303	+	0.826548i
$11$	1.94045	−	3.36096i	0.585068	−	1.01337i	−0.409799	−	0.912176i	$-0.634401\pi$
$11$	1.94045	−	3.36096i	0.585068	−	1.01337i	0.994867	−	0.101191i	$-0.0322653\pi$
$12$		0			0
$13$	−2.96232	−	2.05540i	−0.821599	−	0.570066i
$13$	−2.96232	−	2.05540i	−0.821599	−	0.570066i
$14$	2.40976			0.644036
$15$		0			0
$16$	1.23557	−	2.14007i	0.308892	−	0.535017i
$17$	−4.71996	+	2.72507i	−1.14476	+	0.660927i	−0.947605	−	0.319445i	$-0.896503\pi$
$17$	−4.71996	+	2.72507i	−1.14476	+	0.660927i	−0.197155	+	0.980372i	$0.563170\pi$
$18$		0			0
$19$	2.94045	+	5.09301i	0.674585	+	1.16842i	0.976590	+	0.215110i	$0.0690109\pi$
$19$	2.94045	+	5.09301i	0.674585	+	1.16842i	−0.302005	+	0.953306i	$0.597656\pi$
$20$	−0.449133	+	1.24105i	−0.100429	+	0.277506i
$21$		0			0
$22$	−3.99058	+	2.30396i	−0.850794	+	0.491206i
$23$	−0.298874	−	0.172555i	−0.0623195	−	0.0359802i	0.468516	−	0.883455i	$-0.344789\pi$
$23$	−0.298874	−	0.172555i	−0.0623195	−	0.0359802i	−0.530836	+	0.847475i	$0.678122\pi$
$24$		0			0
$25$	−0.850210	+	4.92718i	−0.170042	+	0.985437i
$26$	1.82581	+	3.87212i	0.358071	+	0.759385i
$27$		0			0
$28$	1.03743	+	0.598962i	0.196056	+	0.113193i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	1.18048			0.212020			0.106010	−	0.994365i	$-0.466192\pi$
$31$	1.18048			0.212020			0.106010	+	0.994365i	$0.466192\pi$
$32$	2.78591	−	1.60845i	0.492484	−	0.284336i
$33$		0			0
$34$	6.47114			1.10979
$35$	4.26737	+	1.54436i	0.721318	+	0.261044i
$36$		0			0
$37$	4.71996	+	2.72507i	0.775957	+	0.447999i	0.834996	−	0.550257i	$-0.185470\pi$
$37$	4.71996	+	2.72507i	0.775957	+	0.447999i	−0.0590384	+	0.998256i	$0.518803\pi$
$38$		−	6.98259i		−	1.13273i
$39$		0			0
$40$	5.25997	−	4.43007i	0.831674	−	0.700456i
$41$	0.0902394	−	0.156299i	0.0140930	−	0.0244098i	−0.858893	−	0.512155i	$-0.828847\pi$
$41$	0.0902394	−	0.156299i	0.0140930	−	0.0244098i	0.872986	+	0.487745i	$0.162181\pi$
$42$		0			0
$43$	−1.15990	+	0.669668i	−0.176883	+	0.102123i	−0.585827	−	0.810436i	$-0.699230\pi$
$43$	−1.15990	+	0.669668i	−0.176883	+	0.102123i	0.408944	+	0.912559i	$0.365897\pi$
$44$	−2.29066			−0.345330
$45$		0			0
$46$	0.204880	+	0.354863i	0.0302079	+	0.0523217i
$47$			12.2807i			1.79133i	0.444731	+	0.895664i	$0.353299\pi$
$47$			12.2807i			1.79133i	−0.444731	+	0.895664i	$0.646701\pi$
$48$		0			0
$49$	−1.44045	+	2.49493i	−0.205779	+	0.356419i
$50$	3.79934	−	4.56169i	0.537308	−	0.645120i
$51$		0			0
$52$	−0.176407	+	2.12081i	−0.0244633	+	0.294104i
$53$		−	2.42636i		−	0.333286i	−0.986017	−	0.166643i	$-0.946707\pi$
$53$		−	2.42636i		−	0.333286i	0.986017	−	0.166643i	$-0.0532928\pi$
$54$		0			0
$55$	−8.54334	+	1.52255i	−1.15198	+	0.205301i
$56$	−3.12093	−	5.40561i	−0.417052	−	0.722355i
$57$		0			0
$58$	3.08478	−	1.78100i	0.405052	−	0.233857i
$59$	3.53069	+	6.11533i	0.459657	+	0.796149i	0.998943	−	0.0459741i	$-0.0146392\pi$
$59$	3.53069	+	6.11533i	0.459657	+	0.796149i	−0.539286	+	0.842123i	$0.681306\pi$
$60$		0			0
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	0.564240	−	0.825611i	$-0.309169\pi$
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	−0.997120	+	0.0758409i	$0.975836\pi$
$62$	−1.21384	−	0.700811i	−0.154158	−	0.0890031i
$63$		0			0
$64$	−8.76180			−1.09522
$65$	0.751722	+	8.02714i	0.0932396	+	0.995644i
$66$		0			0
$67$	−3.81417	−	2.20211i	−0.465975	−	0.269031i	0.248578	−	0.968612i	$-0.420037\pi$
$67$	−3.81417	−	2.20211i	−0.465975	−	0.269031i	−0.714553	+	0.699581i	$0.753370\pi$
$68$	2.78591	+	1.60845i	0.337841	+	0.195053i
$69$		0			0
$70$	−3.47114	−	4.12140i	−0.414880	−	0.492601i
$71$	−0.940450	−	1.62891i	−0.111611	−	0.193316i	0.804809	−	0.593534i	$-0.202268\pi$
$71$	−0.940450	−	1.62891i	−0.111611	−	0.193316i	−0.916420	+	0.400218i	$0.868934\pi$
$72$		0			0
$73$			8.86014i			1.03700i	0.855077	+	0.518501i	$0.173510\pi$
$73$			8.86014i			1.03700i	−0.855077	+	0.518501i	$0.826490\pi$
$74$	−3.23557	−	5.60417i	−0.376127	−	0.651472i
$75$		0			0
$76$	1.73557	−	3.00609i	0.199083	−	0.344823i
$77$			7.87651i			0.897611i
$78$		0			0
$79$	−11.1805			−1.25790			−0.628951	−	0.777445i	$-0.716515\pi$
$79$	−11.1805			−1.25790			−0.628951	+	0.777445i	$0.716515\pi$
$80$	−5.43992	+	0.969475i	−0.608202	+	0.108391i
$81$		0			0
$82$	−0.185579	+	0.107144i	−0.0204938	+	0.0118321i
$83$		−	7.83540i		−	0.860047i	−0.902818	−	0.430024i	$-0.858505\pi$
$83$		−	7.83540i		−	0.860047i	0.902818	−	0.430024i	$-0.141495\pi$
$84$		0			0
$85$	11.4595	+	4.14720i	1.24296	+	0.449827i
$86$	1.59024			0.171480
$87$		0			0
$88$	10.3365	+	5.96781i	1.10188	+	0.636171i
$89$	−6.12093	+	10.6018i	−0.648817	+	1.12378i	0.334589	+	0.942364i	$0.391403\pi$
$89$	−6.12093	+	10.6018i	−0.648817	+	1.12378i	−0.983406	+	0.181420i	$0.941931\pi$
$90$		0			0
$91$	7.29249	+	0.606582i	0.764460	+	0.0635870i
$92$			0.203698i			0.0212369i
$93$		0			0
$94$	7.29066	−	12.6278i	0.751974	−	1.30246i
$95$	4.47497	−	12.3653i	0.459122	−	1.26865i
$96$		0			0
$97$	5.02801	−	2.90292i	0.510517	−	0.294747i	−0.222529	−	0.974926i	$-0.571431\pi$
$97$	5.02801	−	2.90292i	0.510517	−	0.294747i	0.733046	+	0.680179i	$0.238098\pi$
$98$	2.96232	−	1.71029i	0.299239	−	0.172766i
$99$		0			0
$100$	2.76950	−	1.01951i	0.276950	−	0.101951i
$101$	−2.97114	+	5.14616i	−0.295639	+	0.512062i	−0.975133	−	0.221619i	$-0.928866\pi$
$101$	−2.97114	+	5.14616i	−0.295639	+	0.512062i	0.679494	+	0.733681i	$0.262199\pi$
$102$		0			0
$103$		−	6.43378i		−	0.633939i	−0.948436	−	0.316970i	$-0.897335\pi$
$103$		−	6.43378i		−	0.633939i	0.948436	−	0.316970i	$-0.102665\pi$
$104$	6.32135	−	9.11054i	0.619859	−	0.893362i
$105$		0			0
$106$	−1.44045	+	2.49493i	−0.139909	+	0.242329i
$107$	−15.3106	−	8.83959i	−1.48013	−	0.854555i	−0.480387	−	0.877057i	$-0.659504\pi$
$107$	−15.3106	−	8.83959i	−1.48013	−	0.854555i	−0.999747	+	0.0225015i	$0.992837\pi$
$108$		0			0
$109$	−5.76180			−0.551880			−0.275940	−	0.961175i	$-0.588989\pi$
$109$	−5.76180			−0.551880			−0.275940	+	0.961175i	$0.588989\pi$
$110$	9.68867	+	3.50632i	0.923779	+	0.334314i
$111$		0			0
$112$			5.01532i			0.473903i
$113$	4.12222	−	2.37996i	0.387785	−	0.223888i	−0.293415	−	0.955985i	$-0.594792\pi$
$113$	4.12222	−	2.37996i	0.387785	−	0.223888i	0.681200	+	0.732097i	$0.261458\pi$
$114$		0			0
$115$	0.135393	+	0.759719i	0.0126255	+	0.0708442i
$116$	1.77072			0.164407
$117$		0			0
$118$		−	8.38421i		−	0.771829i
$119$	5.53069	−	9.57943i	0.506997	−	0.878145i
$120$		0			0
$121$	−2.03069	−	3.51726i	−0.184608	−	0.319751i
$122$			8.02851i			0.726867i
$123$		0			0
$124$	−0.348383	−	0.603416i	−0.0312857	−	0.0541884i
$125$	9.65162	−	5.64325i	0.863267	−	0.504748i
$126$		0			0
$127$	−14.4679	−	8.35307i	−1.28382	−	0.741215i	−0.306277	−	0.951942i	$-0.599083\pi$
$127$	−14.4679	−	8.35307i	−1.28382	−	0.741215i	−0.977545	+	0.210728i	$0.932417\pi$
$128$	3.43760	+	1.98470i	0.303844	+	0.175424i
$129$		0			0
$130$	3.99248	−	8.70026i	0.350163	−	0.763063i
$131$	−10.0000			−0.873704			−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000			−0.873704			−0.436852	+	0.899533i	$0.643907\pi$
$132$		0			0
$133$	−10.3365	−	5.96781i	−0.896292	−	0.517475i
$134$	2.61464	+	4.52869i	0.225871	+	0.391219i
$135$		0			0
$136$	−8.38090	−	14.5161i	−0.718656	−	1.24475i
$137$	1.71288	−	0.988931i	0.146341	−	0.0844901i	−0.425042	−	0.905174i	$-0.639741\pi$
$137$	1.71288	−	0.988931i	0.146341	−	0.0844901i	0.571383	+	0.820684i	$0.306407\pi$
$138$		0			0
$139$	4.35021	+	7.53478i	0.368980	+	0.639092i	0.989406	−	0.145173i	$-0.0463737\pi$
$139$	4.35021	+	7.53478i	0.368980	+	0.639092i	−0.620426	+	0.784265i	$0.713040\pi$
$140$	−0.469969	−	2.63709i	−0.0397196	−	0.222875i
$141$		0			0
$142$			2.23325i			0.187411i
$143$	−12.6563	+	5.96781i	−1.05838	+	0.499053i
$144$		0			0
$145$	6.60415	−	1.17696i	0.548445	−	0.0977410i
$146$	5.25997	−	9.11054i	0.435318	−	0.753993i
$147$		0			0
$148$		−	3.21689i		−	0.264427i
$149$	−11.1516	−	19.3152i	−0.913576	−	1.58236i	−0.808973	−	0.587846i	$-0.799976\pi$
$149$	−11.1516	−	19.3152i	−0.913576	−	1.58236i	−0.104603	−	0.994514i	$-0.533357\pi$
$150$		0			0
$151$	−19.1626			−1.55943			−0.779717	−	0.626132i	$-0.784637\pi$
$151$	−19.1626			−1.55943			−0.779717	+	0.626132i	$0.784637\pi$
$152$	−15.6634	+	9.04329i	−1.27047	+	0.733507i
$153$		0			0
$154$	4.67602	−	8.09910i	0.376804	−	0.652644i
$155$	−1.70042	−	2.01897i	−0.136581	−	0.162167i
$156$		0			0
$157$			6.20265i			0.495025i	0.968885	+	0.247513i	$0.0796132\pi$
$157$			6.20265i			0.495025i	−0.968885	+	0.247513i	$0.920387\pi$
$158$	11.4964	+	6.63748i	0.914608	+	0.528049i
$159$		0			0
$160$	−6.76387	−	2.44784i	−0.534731	−	0.193519i
$161$	0.700420			0.0552008
$162$		0			0
$163$	10.3365	−	5.96781i	0.809621	−	0.467435i	−0.0372032	−	0.999308i	$-0.511845\pi$
$163$	10.3365	−	5.96781i	0.809621	−	0.467435i	0.846824	+	0.531873i	$0.178512\pi$
$164$	−0.106526			−0.00831826
$165$		0			0
$166$	−4.65162	+	8.05684i	−0.361036	+	0.625332i
$167$	1.75765	+	1.01478i	0.136011	+	0.0785259i	0.566461	−	0.824088i	$-0.308312\pi$
$167$	1.75765	+	1.01478i	0.136011	+	0.0785259i	−0.430451	+	0.902614i	$0.641645\pi$
$168$		0			0
$169$	4.55063	+	12.1775i	0.350048	+	0.936732i
$170$	−9.32135	−	11.0675i	−0.714915	−	0.848842i
$171$		0			0
$172$	0.684619	+	0.395265i	0.0522017	+	0.0301387i
$173$	−1.15990	+	0.669668i	−0.0881855	+	0.0509139i	−0.543444	−	0.839445i	$-0.682880\pi$
$173$	−1.15990	+	0.669668i	−0.0881855	+	0.0509139i	0.455259	+	0.890359i	$0.349547\pi$
$174$		0			0
$175$	−3.50563	−	9.52303i	−0.265001	−	0.719873i
$176$	−4.79512	−	8.30539i	−0.361446	−	0.626042i
$177$		0			0
$178$	12.5878	−	7.26758i	0.943497	−	0.544728i
$179$	−10.1120	+	17.5145i	−0.755807	+	1.30910i	0.189165	+	0.981945i	$0.439422\pi$
$179$	−10.1120	+	17.5145i	−0.755807	+	1.30910i	−0.944972	+	0.327151i	$0.893911\pi$
$180$		0			0
$181$	19.8232			1.47345			0.736723	−	0.676195i	$-0.236372\pi$
$181$	19.8232			1.47345			0.736723	+	0.676195i	$0.236372\pi$
$182$	−7.13847	−	4.95303i	−0.529139	−	0.367143i
$183$		0			0
$184$	0.530689	−	0.919180i	0.0391229	−	0.0677629i
$185$	−2.13820	−	11.9979i	−0.157203	−	0.882100i
$186$		0			0
$187$			21.1515i			1.54675i
$188$	6.27745	−	3.62429i	0.457830	−	0.264328i
$189$		0			0
$190$	−11.9423	+	10.0581i	−0.866384	+	0.729689i
$191$	0.768891	+	1.33176i	0.0556350	+	0.0963626i	0.892502	−	0.451044i	$-0.148948\pi$
$191$	0.768891	+	1.33176i	0.0556350	+	0.0963626i	−0.836867	+	0.547407i	$0.815615\pi$
$192$		0			0
$193$	−18.3625	−	10.6016i	−1.32176	−	0.763118i	−0.337750	−	0.941236i	$-0.609666\pi$
$193$	−18.3625	−	10.6016i	−1.32176	−	0.763118i	−0.984009	+	0.178117i	$0.942999\pi$
$194$	−6.89347			−0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	8.01675	+	4.62847i	0.571170	+	0.329765i	0.757616	−	0.652700i	$-0.226364\pi$
$197$	8.01675	+	4.62847i	0.571170	+	0.329765i	−0.186447	+	0.982465i	$0.559697\pi$
$198$		0			0
$199$	−8.70225	−	15.0727i	−0.616886	−	1.06848i	−0.990050	−	0.140713i	$-0.955061\pi$
$199$	−8.70225	−	15.0727i	−0.616886	−	1.06848i	0.373164	−	0.927765i	$-0.378273\pi$
$200$	−15.1534	−	2.61480i	−1.07151	−	0.184894i
$201$		0			0
$202$	6.11021	−	3.52773i	0.429913	−	0.248210i
$203$		−	6.08867i		−	0.427341i
$204$		0			0
$205$	−0.397303	+	0.0708053i	−0.0277488	+	0.00494526i
$206$	−3.81952	+	6.61560i	−0.266119	+	0.460931i
$207$		0			0
$208$	−8.05885	+	3.79997i	−0.558781	+	0.263480i
$209$	22.8232			1.57871
$210$		0			0
$211$	3.64087	−	6.30617i	0.250648	−	0.434135i	−0.713057	−	0.701107i	$-0.752690\pi$
$211$	3.64087	−	6.30617i	0.250648	−	0.434135i	0.963704	+	0.266972i	$0.0860231\pi$
$212$	−1.24026	+	0.716067i	−0.0851817	+	0.0491797i
$213$		0			0
$214$	10.4955	+	18.1788i	0.717460	+	1.24268i
$215$	2.81611	+	1.01915i	0.192057	+	0.0695052i
$216$		0			0
$217$	−2.07487	+	1.19792i	−0.140851	+	0.0813204i
$218$	5.92463	+	3.42059i	0.401267	+	0.231671i
$219$		0			0
$220$	3.29958	+	3.91770i	0.222458	+	0.264131i
$221$	19.5831	+	1.62891i	1.31731	+	0.109572i
$222$		0			0
$223$	16.8589	+	9.73351i	1.12896	+	0.651804i	0.943672	−	0.330881i	$-0.107346\pi$
$223$	16.8589	+	9.73351i	1.12896	+	0.651804i	0.185285	+	0.982685i	$0.440679\pi$
$224$	−3.26443	+	5.65416i	−0.218114	+	0.377784i
$225$		0			0
$226$	−5.65162			−0.375940
$227$	4.16698	−	2.40581i	0.276572	−	0.159679i	−0.355298	−	0.934753i	$-0.615621\pi$
$227$	4.16698	−	2.40581i	0.276572	−	0.159679i	0.631871	+	0.775074i	$0.282287\pi$
$228$		0			0
$229$	−1.52360			−0.100682			−0.0503410	−	0.998732i	$-0.516031\pi$
$229$	−1.52360			−0.100682			−0.0503410	+	0.998732i	$0.516031\pi$
$230$	0.311800	−	0.861568i	0.0205595	−	0.0568101i
$231$		0			0
$232$	−7.99033	−	4.61322i	−0.524591	−	0.302873i
$233$			13.9652i			0.914889i	0.889238	+	0.457445i	$0.151235\pi$
$233$			13.9652i			0.914889i	−0.889238	+	0.457445i	$0.848765\pi$
$234$		0			0
$235$	21.0037	−	17.6898i	1.37013	−	1.15395i
$236$	2.08395	−	3.60951i	0.135654	−	0.234959i
$237$		0			0
$238$	−11.3740	+	6.56677i	−0.737266	+	0.425661i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	8.73294	+	15.1259i	0.562538	+	0.974344i	0.997274	+	0.0737864i	$0.0235083\pi$
$241$	8.73294	+	15.1259i	0.562538	+	0.974344i	−0.434736	+	0.900558i	$0.643158\pi$
$242$			4.82221i			0.309983i
$243$		0			0
$244$	−1.99554	+	3.45638i	−0.127751	+	0.221272i
$245$	6.34196	−	1.13023i	0.405173	−	0.0722078i
$246$		0			0
$247$	1.75765	−	21.1309i	0.111836	−	1.34453i
$248$			3.63054i			0.230539i
$249$		0			0
$250$	−13.2746	+	0.0728904i	−0.839559	+	0.00460999i
$251$	4.64979	+	8.05367i	0.293492	+	0.508343i	0.974633	−	0.223809i	$-0.0718492\pi$
$251$	4.64979	+	8.05367i	0.293492	+	0.508343i	−0.681141	+	0.732152i	$0.738516\pi$
$252$		0			0
$253$	−1.15990	+	0.669668i	−0.0729223	+	0.0421017i
$254$	9.91788	+	17.1783i	0.622303	+	1.07786i
$255$		0			0
$256$	6.40530	+	11.0943i	0.400331	+	0.693394i
$257$	−9.43076	−	5.44485i	−0.588274	−	0.339640i	0.176141	−	0.984365i	$-0.443639\pi$
$257$	−9.43076	−	5.44485i	−0.588274	−	0.339640i	−0.764415	+	0.644725i	$0.776972\pi$
$258$		0			0
$259$	−11.0614			−0.687321
$260$	3.88132	−	2.75322i	0.240709	−	0.170747i
$261$		0			0
$262$	10.2826	+	5.93667i	0.635262	+	0.366769i
$263$	−11.6399	−	6.72031i	−0.717749	−	0.414392i	0.0961749	−	0.995364i	$-0.469339\pi$
$263$	−11.6399	−	6.72031i	−0.717749	−	0.414392i	−0.813923	+	0.580972i	$0.802673\pi$
$264$		0			0
$265$	−4.14979	+	3.49505i	−0.254920	+	0.214699i
$266$	7.08578	+	12.2729i	0.434457	+	0.752502i
$267$		0			0
$268$			2.59955i			0.158793i
$269$	−1.83027	−	3.17012i	−0.111593	−	0.193286i	0.804819	−	0.593520i	$-0.202262\pi$
$269$	−1.83027	−	3.17012i	−0.111593	−	0.193286i	−0.916413	+	0.400234i	$0.868929\pi$
$270$		0			0
$271$	−11.0018	+	19.0557i	−0.668313	+	1.15755i	0.310062	+	0.950716i	$0.399650\pi$
$271$	−11.0018	+	19.0557i	−0.668313	+	1.15755i	−0.978376	+	0.206837i	$0.933683\pi$
$272$			13.4681i			0.816621i
$273$		0			0
$274$	−2.34838			−0.141871
$275$	14.9103	+	12.4185i	0.899123	+	0.748862i
$276$		0			0
$277$	−8.56973	+	4.94774i	−0.514905	+	0.297281i	−0.734848	−	0.678232i	$-0.762746\pi$
$277$	−8.56973	+	4.94774i	−0.514905	+	0.297281i	0.219943	+	0.975513i	$0.429413\pi$
$278$		−	10.3303i		−	0.619570i
$279$		0			0
$280$	−4.74964	+	13.1242i	−0.283845	+	0.784321i
$281$	−4.06138			−0.242281			−0.121141	−	0.992635i	$-0.538655\pi$
$281$	−4.06138			−0.242281			−0.121141	+	0.992635i	$0.538655\pi$
$282$		0			0
$283$	5.27294	+	3.04434i	0.313444	+	0.180967i	0.648467	−	0.761243i	$-0.275411\pi$
$283$	5.27294	+	3.04434i	0.313444	+	0.180967i	−0.335023	+	0.942210i	$0.608744\pi$
$284$	−0.555090	+	0.961445i	−0.0329386	+	0.0570513i
$285$		0			0
$286$	16.5569	+	1.37719i	0.979031	+	0.0814348i
$287$			0.366292i			0.0216215i
$288$		0			0
$289$	6.35204	−	11.0021i	0.373649	−	0.647180i
$290$	−7.48951	−	2.71044i	−0.439799	−	0.159163i
$291$		0			0
$292$	4.52897	−	2.61480i	0.265038	−	0.153020i
$293$	8.48019	−	4.89604i	0.495418	−	0.286030i	−0.231401	−	0.972858i	$-0.574331\pi$
$293$	8.48019	−	4.89604i	0.495418	−	0.286030i	0.726819	+	0.686829i	$0.240998\pi$
$294$		0			0
$295$	5.37324	−	14.8473i	0.312842	−	0.864446i
$296$	−8.38090	+	14.5161i	−0.487130	+	0.843734i
$297$		0			0
$298$			26.4814i			1.53402i
$299$	0.530689	+	1.12547i	0.0306905	+	0.0650876i
$300$		0			0
$301$	1.35913	−	2.35408i	0.0783390	−	0.135687i
$302$	19.7042	+	11.3762i	1.13385	+	0.654628i
$303$		0			0
$304$	14.5325			0.833497
$305$	−5.14528	+	14.2174i	−0.294618	+	0.814088i
$306$		0			0
$307$			22.1046i			1.26158i	0.775955	+	0.630788i	$0.217268\pi$
$307$			22.1046i			1.26158i	−0.775955	+	0.630788i	$0.782732\pi$
$308$	4.02617	−	2.32451i	0.229412	−	0.132451i
$309$		0			0
$310$	0.549883	+	3.08551i	0.0312313	+	0.175245i
$311$	−7.63904			−0.433170			−0.216585	−	0.976264i	$-0.569492\pi$
$311$	−7.63904			−0.433170			−0.216585	+	0.976264i	$0.569492\pi$
$312$		0			0
$313$			26.1425i			1.47766i	0.673891	+	0.738831i	$0.264622\pi$
$313$			26.1425i			1.47766i	−0.673891	+	0.738831i	$0.735378\pi$
$314$	3.68231	−	6.37794i	0.207805	−	0.359928i
$315$		0			0
$316$	3.29958	+	5.71504i	0.185616	+	0.321496i
$317$			11.8428i			0.665159i	0.943075	+	0.332580i	$0.107919\pi$
$317$			11.8428i			0.665159i	−0.943075	+	0.332580i	$0.892081\pi$
$318$		0			0
$319$	5.82135	+	10.0829i	0.325933	+	0.564532i
$320$	12.6209	+	14.9852i	0.705531	+	0.837701i
$321$		0			0
$322$	−0.720215	−	0.415816i	−0.0401360	−	0.0231725i
$323$	−27.7576	−	16.0259i	−1.54448	−	0.891704i
$324$		0			0
$325$	12.6459	−	12.8484i	0.701471	−	0.712698i
$326$	−14.1716			−0.784890
$327$		0			0
$328$	0.480695	+	0.277529i	0.0265419	+	0.0153240i
$329$	−12.4622	−	21.5852i	−0.687064	−	1.19003i
$330$		0			0
$331$	6.35021	+	10.9989i	0.349039	+	0.604553i	0.986079	−	0.166277i	$-0.0531747\pi$
$331$	6.35021	+	10.9989i	0.349039	+	0.604553i	−0.637040	+	0.770831i	$0.719841\pi$
$332$	−4.00516	+	2.31238i	−0.219812	+	0.126908i
$333$		0			0
$334$	−1.20488	−	2.08691i	−0.0659281	−	0.114191i
$335$	1.72786	+	9.69538i	0.0944031	+	0.529715i
$336$		0			0
$337$			15.2939i			0.833113i	0.909110	+	0.416556i	$0.136763\pi$
$337$			15.2939i			0.833113i	−0.909110	+	0.416556i	$0.863237\pi$
$338$	2.55015	−	15.2232i	0.138710	−	0.828034i
$339$		0			0
$340$	−1.26205	−	7.08161i	−0.0684441	−	0.384054i
$341$	2.29066	−	3.96754i	0.124046	−	0.214854i
$342$		0			0
$343$		−	20.0538i		−	1.08281i
$344$	−2.05955	−	3.56725i	−0.111044	−	0.192333i
$345$		0			0
$346$	1.59024			0.0854918
$347$	10.5998	−	6.11981i	0.569029	−	0.328529i	−0.187733	−	0.982220i	$-0.560114\pi$
$347$	10.5998	−	6.11981i	0.569029	−	0.328529i	0.756761	+	0.653691i	$0.226781\pi$
$348$		0			0
$349$	9.35021	−	16.1950i	0.500505	−	0.866901i	−0.499495	−	0.866317i	$-0.666481\pi$
$349$	9.35021	−	16.1950i	0.500505	−	0.866901i	1.00000		0.000583538i	$-0.000185746\pi$
$350$	−2.04880	+	11.8733i	−0.109513	+	0.634656i
$351$		0			0
$352$		−	12.4844i		−	0.665422i
$353$	1.13348	+	0.654413i	0.0603288	+	0.0348309i	0.529861	−	0.848084i	$-0.322244\pi$
$353$	1.13348	+	0.654413i	0.0603288	+	0.0348309i	−0.469532	+	0.882915i	$0.655577\pi$
$354$		0			0
$355$	−1.43124	+	3.95480i	−0.0759623	+	0.209899i
$356$	7.22563			0.382957
$357$		0			0
$358$	20.7956	−	12.0063i	1.09908	−	0.634554i
$359$	−29.4082			−1.55210			−0.776051	−	0.630670i	$-0.782780\pi$
$359$	−29.4082			−1.55210			−0.776051	+	0.630670i	$0.782780\pi$
$360$		0			0
$361$	−7.79249	+	13.4970i	−0.410131	+	0.710368i
$362$	−20.3834	−	11.7684i	−1.07133	−	0.618531i
$363$		0			0
$364$	−1.84210	−	3.90666i	−0.0965520	−	0.204765i
$365$	15.1534	−	12.7626i	0.793168	−	0.668024i
$366$		0			0
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.999912	−	0.0132473i	$-0.995783\pi$
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.511429	−	0.859326i	$-0.670884\pi$
$368$	−0.738559	+	0.426407i	−0.0385001	+	0.0222280i
$369$		0			0
$370$	−4.92410	+	13.6063i	−0.255992	+	0.707358i
$371$	2.46222	+	4.26469i	0.127832	+	0.221412i
$372$		0			0
$373$	−29.8589	+	17.2391i	−1.54604	+	0.892604i	−0.547598	+	0.836742i	$0.684458\pi$
$373$	−29.8589	+	17.2391i	−1.54604	+	0.892604i	−0.998438	+	0.0558628i	$0.982209\pi$
$374$	12.5569	−	21.7492i	0.649303	−	1.12463i
$375$		0			0
$376$	−37.7691			−1.94779
$377$	9.78357	−	4.61322i	0.503879	−	0.237593i
$378$		0			0
$379$	−8.70225	+	15.0727i	−0.447004	+	0.774234i	−0.998189	−	0.0601487i	$-0.980843\pi$
$379$	−8.70225	+	15.0727i	−0.447004	+	0.774234i	0.551185	+	0.834383i	$0.314176\pi$
$380$	−7.64130	+	1.36179i	−0.391991	+	0.0698585i
$381$		0			0
$382$		−	1.82586i		−	0.0934191i
$383$	−1.51271	+	0.873366i	−0.0772961	+	0.0446269i	−0.538150	−	0.842849i	$-0.680877\pi$
$383$	−1.51271	+	0.873366i	−0.0772961	+	0.0446269i	0.460854	+	0.887476i	$0.347543\pi$
$384$		0			0
$385$	13.4711	−	11.3457i	0.686553	−	0.578231i
$386$	12.5876	+	21.8024i	0.640692	+	1.10971i
$387$		0			0
$388$	−2.96773	−	1.71342i	−0.150664	−	0.0869857i
$389$	22.0435			1.11765			0.558826	−	0.829285i	$-0.311252\pi$
$389$	22.0435			1.11765			0.558826	+	0.829285i	$0.311252\pi$
$390$		0			0
$391$	1.88090			0.0951212
$392$	−7.67311	−	4.43007i	−0.387550	−	0.223752i
$393$		0			0
$394$	−5.49554	−	9.51855i	−0.276861	−	0.479538i
$395$	16.1049	+	19.1219i	0.810326	+	0.962127i
$396$		0			0
$397$	19.5132	−	11.2660i	0.979339	−	0.565422i	0.0772687	−	0.997010i	$-0.475380\pi$
$397$	19.5132	−	11.2660i	0.979339	−	0.565422i	0.902071	+	0.431588i	$0.142047\pi$
$398$			20.6649i			1.03584i
$399$		0			0
$400$	9.49402	+	7.90739i	0.474701	+	0.395369i
$401$	−1.85204	+	3.20782i	−0.0924863	+	0.160191i	−0.908557	−	0.417761i	$-0.862815\pi$
$401$	−1.85204	+	3.20782i	−0.0924863	+	0.160191i	0.816070	+	0.577953i	$0.196148\pi$
$402$		0			0
$403$	−3.49695	−	2.42636i	−0.174196	−	0.120866i
$404$	3.50737			0.174498
$405$		0			0
$406$	−3.61464	+	6.26074i	−0.179392	+	0.310715i
$407$	18.3177	−	10.5757i	0.907975	−	0.524220i
$408$		0			0
$409$	−6.74186	−	11.6772i	−0.333363	−	0.577402i	0.649806	−	0.760100i	$-0.274850\pi$
$409$	−6.74186	−	11.6772i	−0.333363	−	0.577402i	−0.983169	+	0.182698i	$0.941517\pi$
$410$	0.450566	+	0.163059i	0.0222519	+	0.00805292i
$411$		0			0
$412$	−3.28871	+	1.89874i	−0.162023	+	0.0935440i
$413$	−12.4114	−	7.16573i	−0.610726	−	0.352603i
$414$		0			0
$415$	−13.4008	+	11.2865i	−0.657821	+	0.554033i
$416$	−11.5587	−	0.961445i	−0.566714	−	0.0471387i
$417$		0			0
$418$	−23.4682	−	13.5494i	−1.14787	−	0.662721i
$419$	−8.41159	+	14.5693i	−0.410933	+	0.711757i	−0.994992	−	0.0999544i	$-0.968130\pi$
$419$	−8.41159	+	14.5693i	−0.410933	+	0.711757i	0.584059	+	0.811711i	$0.301464\pi$
$420$		0			0
$421$	17.1013			0.833464			0.416732	−	0.909029i	$-0.363175\pi$
$421$	17.1013			0.833464			0.416732	+	0.909029i	$0.363175\pi$
$422$	−7.48753	+	4.32293i	−0.364487	+	0.210437i
$423$		0			0
$424$	7.46222			0.362397
$425$	−9.41397	−	25.5730i	−0.456645	−	1.24047i
$426$		0			0
$427$	11.8849	+	6.86173i	0.575149	+	0.332062i
$428$			10.4349i			0.504392i
$429$		0			0
$430$	−2.29066	−	2.71978i	−0.110465	−	0.131159i
$431$	4.83027	−	8.36627i	0.232666	−	0.402989i	−0.725926	−	0.687773i	$-0.758588\pi$
$431$	4.83027	−	8.36627i	0.232666	−	0.402989i	0.958592	+	0.284784i	$0.0919218\pi$
$432$		0			0
$433$	21.4538	−	12.3863i	1.03100	−	0.595249i	0.113730	−	0.993512i	$-0.463720\pi$
$433$	21.4538	−	12.3863i	1.03100	−	0.595249i	0.917272	+	0.398262i	$0.130387\pi$
$434$	2.84467			0.136549
$435$		0			0
$436$	1.70042	+	2.94521i	0.0814354	+	0.141050i
$437$		−	2.02956i		−	0.0970869i
$438$		0			0
$439$	3.53069	−	6.11533i	0.168511	−	0.291869i	−0.769386	−	0.638784i	$-0.779438\pi$
$439$	3.53069	−	6.11533i	0.168511	−	0.291869i	0.937896	+	0.346915i	$0.112771\pi$
$440$	−4.68257	−	26.2749i	−0.223233	−	1.25261i
$441$		0			0
$442$	−19.1696	−	13.3008i	−0.911803	−	0.632655i
$443$			38.2438i			1.81702i	0.417865	+	0.908509i	$0.362778\pi$
$443$			38.2438i			1.81702i	−0.417865	+	0.908509i	$0.637222\pi$
$444$		0			0
$445$	26.9490	−	4.80271i	1.27751	−	0.227670i
$446$	−11.5569	−	20.0172i	−0.547236	−	0.947840i
$447$		0			0
$448$	15.4002	−	8.89128i	0.727589	−	0.420074i
$449$	6.24003	+	10.8080i	0.294485	+	0.510063i	0.974865	−	0.222796i	$-0.0715185\pi$
$449$	6.24003	+	10.8080i	0.294485	+	0.510063i	−0.680380	+	0.732860i	$0.738185\pi$
$450$		0			0
$451$	−0.350210	−	0.606582i	−0.0164908	−	0.0285628i
$452$	−2.43309	−	1.40475i	−0.114443	−	0.0660738i
$453$		0			0
$454$	−5.71300			−0.268124
$455$	−9.46703	−	13.3460i	−0.443821	−	0.625672i
$456$		0			0
$457$	7.12930	+	4.11610i	0.333495	+	0.192543i	0.657392	−	0.753549i	$-0.271660\pi$
$457$	7.12930	+	4.11610i	0.333495	+	0.192543i	−0.323897	+	0.946092i	$0.604993\pi$
$458$	1.56665	+	0.904508i	0.0732050	+	0.0422649i
$459$		0			0
$460$	0.348383	−	0.293416i	0.0162434	−	0.0136806i
$461$	−2.27072	−	3.93300i	−0.105758	−	0.183178i	0.808290	−	0.588785i	$-0.200394\pi$
$461$	−2.27072	−	3.93300i	−0.105758	−	0.183178i	−0.914048	+	0.405607i	$0.867060\pi$
$462$		0			0
$463$		−	1.98845i		−	0.0924113i	−0.998932	−	0.0462056i	$-0.985287\pi$
$463$		−	1.98845i		−	0.0924113i	0.998932	−	0.0462056i	$-0.0147130\pi$
$464$	3.70671	+	6.42021i	0.172080	+	0.298051i
$465$		0			0
$466$	8.29066	−	14.3598i	0.384057	−	0.665207i
$467$		−	32.8043i		−	1.51800i	−0.651091	−	0.759000i	$-0.725688\pi$
$467$		−	32.8043i		−	1.51800i	0.651091	−	0.759000i	$-0.274312\pi$
$468$		0			0
$469$	8.93862			0.412747
$470$	−32.0991	+	5.72053i	−1.48062	+	0.263868i
$471$		0			0
$472$	−18.8076	+	10.8586i	−0.865689	+	0.499806i
$473$			5.19783i			0.238997i
$474$		0			0
$475$	−27.5942	+	10.1580i	−1.26611	+	0.466081i
$476$	−6.52886			−0.299250
$477$		0			0
$478$	−4.11304	−	2.37467i	−0.188126	−	0.108615i
$479$	15.4027	−	26.6782i	0.703766	−	1.21896i	−0.263369	−	0.964695i	$-0.584834\pi$
$479$	15.4027	−	26.6782i	0.703766	−	1.21896i	0.967135	−	0.254263i	$-0.0818329\pi$
$480$		0			0
$481$	−8.38090	−	17.7740i	−0.382136	−	0.810423i
$482$		−	20.7378i		−	0.944582i
$483$		0			0
$484$	−1.19859	+	2.07602i	−0.0544815	+	0.0943647i
$485$	−12.2074	−	4.41786i	−0.554312	−	0.200605i
$486$		0			0
$487$	19.3341	−	11.1626i	0.876113	−	0.505824i	0.00673807	−	0.999977i	$-0.497855\pi$
$487$	19.3341	−	11.1626i	0.876113	−	0.505824i	0.869375	+	0.494153i	$0.164522\pi$
$488$	18.0097	−	10.3979i	0.815259	−	0.470690i
$489$		0			0
$490$	−7.19217	−	2.60284i	−0.324909	−	0.117584i
$491$	5.34129	−	9.25139i	0.241049	−	0.417509i	−0.719964	−	0.694011i	$-0.755842\pi$
$491$	5.34129	−	9.25139i	0.241049	−	0.417509i	0.961013	+	0.276502i	$0.0891752\pi$
$492$		0			0
$493$		−	16.3504i		−	0.736386i
$494$	−14.3520	+	20.6846i	−0.645729	+	0.930646i
$495$		0			0
$496$	1.45856	−	2.52631i	0.0654914	−	0.113434i
$497$	3.30596	+	1.90870i	0.148292	+	0.0856167i
$498$		0			0
$499$	−18.8195			−0.842477			−0.421239	−	0.906950i	$-0.638405\pi$
$499$	−18.8195			−0.842477			−0.421239	+	0.906950i	$0.638405\pi$
$500$	−5.73300	−	3.26811i	−0.256388	−	0.146154i
$501$		0			0
$502$		−	11.0417i		−	0.492815i
$503$	4.92013	−	2.84064i	0.219378	−	0.126658i	−0.386284	−	0.922380i	$-0.626242\pi$
$503$	4.92013	−	2.84064i	0.219378	−	0.126658i	0.605662	+	0.795722i	$0.292908\pi$
$504$		0			0
$505$	13.0812	−	2.33127i	0.582107	−	0.103740i
$506$	1.59024			0.0706948
$507$		0			0
$508$			9.86062i			0.437494i
$509$	−13.9622	+	24.1833i	−0.618864	+	1.07190i	0.370829	+	0.928701i	$0.379074\pi$
$509$	−13.9622	+	24.1833i	−0.618864	+	1.07190i	−0.989693	+	0.143203i	$0.954260\pi$
$510$		0			0
$511$	−8.99108	−	15.5730i	−0.397742	−	0.688909i
$512$		−	23.1492i		−	1.02306i
$513$		0			0
$514$	6.46485	+	11.1975i	0.285152	+	0.493898i
$515$	−11.0037	+	9.26754i	−0.484879	+	0.408376i
$516$		0			0
$517$	41.2750	+	23.8301i	1.81527	+	1.04805i
$518$	11.3740	+	6.56677i	0.499744	+	0.288527i
$519$		0			0
$520$	−24.6873	+	2.31190i	−1.08261	+	0.101384i
$521$	−6.29958			−0.275990			−0.137995	−	0.990433i	$-0.544066\pi$
$521$	−6.29958			−0.275990			−0.137995	+	0.990433i	$0.544066\pi$
$522$		0			0
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	0.000305526	−	1.00000i	$-0.499903\pi$
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	−0.865873	+	0.500265i	$0.833236\pi$
$524$	2.95120	+	5.11162i	0.128924	+	0.223302i
$525$		0			0
$526$	7.97925	+	13.8205i	0.347912	+	0.602601i
$527$	−5.57182	+	3.21689i	−0.242712	+	0.140130i
$528$		0			0
$529$	−11.4404	−	19.8154i	−0.497411	−	0.861541i
$530$	6.34196	−	1.13023i	0.275477	−	0.0490941i
$531$		0			0
$532$			7.04487i			0.305434i
$533$	−0.588576	+	0.277529i	−0.0254940	+	0.0120211i
$534$		0			0
$535$	6.93588	+	38.9186i	0.299864	+	1.68260i
$536$	6.77255	−	11.7304i	0.292529	−	0.506676i
$537$		0			0
$538$			4.34628i			0.187381i
$539$	5.59024	+	9.68258i	0.240789	+	0.417058i
$540$		0			0
$541$	−9.48006			−0.407580			−0.203790	−	0.979015i	$-0.565326\pi$
$541$	−9.48006			−0.407580			−0.203790	+	0.979015i	$0.565326\pi$
$542$	22.6255	−	13.0628i	0.971848	−	0.561097i
$543$		0			0
$544$	−8.76626	+	15.1836i	−0.375850	+	0.650992i
$545$	8.29958	+	9.85437i	0.355515	+	0.422115i
$546$		0			0
$547$		−	33.3911i		−	1.42770i	−0.700299	−	0.713850i	$-0.746950\pi$
$547$		−	33.3911i		−	1.42770i	0.700299	−	0.713850i	$-0.253050\pi$
$548$	−1.01101	−	0.583706i	−0.0431882	−	0.0249347i
$549$		0			0
$550$	−7.95921	−	21.6212i	−0.339382	−	0.921929i
$551$	−17.6427			−0.751604
$552$		0			0
$553$	19.6513	−	11.3457i	0.835660	−	0.482469i
$554$	11.7492			0.499177
$555$		0			0
$556$	2.56767	−	4.44733i	0.108893	−	0.188609i
$557$	32.7053	+	18.8824i	1.38577	+	0.800073i	0.992835	−	0.119495i	$-0.0381274\pi$
$557$	32.7053	+	18.8824i	1.38577	+	0.800073i	0.392932	+	0.919567i	$0.371461\pi$
$558$		0			0
$559$	4.81243	+	0.400293i	0.203544	+	0.0169306i
$560$	8.57766	−	7.22431i	0.362472	−	0.305283i
$561$		0			0
$562$	4.17616	+	2.41110i	0.176161	+	0.101706i
$563$	−22.4307	+	12.9504i	−0.945343	+	0.545794i	−0.891631	−	0.452762i	$-0.850439\pi$
$563$	−22.4307	+	12.9504i	−0.945343	+	0.545794i	−0.0537120	+	0.998556i	$0.517105\pi$
$564$		0			0
$565$	−10.0083	−	3.62198i	−0.421051	−	0.152378i
$566$	−3.61464	−	6.26074i	−0.151935	−	0.263159i
$567$		0			0
$568$	5.00967	−	2.89233i	0.210201	−	0.121360i
$569$	10.7725	−	18.6586i	0.451609	−	0.782209i	−0.546878	−	0.837213i	$-0.684184\pi$
$569$	10.7725	−	18.6586i	0.451609	−	0.782209i	0.998486	+	0.0550035i	$0.0175170\pi$
$570$		0			0
$571$	−2.22036			−0.0929192			−0.0464596	−	0.998920i	$-0.514794\pi$
$571$	−2.22036			−0.0929192			−0.0464596	+	0.998920i	$0.514794\pi$
$572$	6.78566	+	4.70823i	0.283723	+	0.196861i
$573$		0			0
$574$	0.217455	−	0.376644i	0.00907641	−	0.0157208i
$575$	1.10432	−	1.32590i	0.0460532	−	0.0552938i
$576$		0			0
$577$		−	6.20265i		−	0.258220i	−0.991630	−	0.129110i	$-0.958788\pi$
$577$		−	6.20265i		−	0.258220i	0.991630	−	0.129110i	$-0.0412120\pi$
$578$	−13.0631	+	7.54199i	−0.543353	+	0.313705i
$579$		0			0
$580$	−2.55063	−	3.02845i	−0.105909	−	0.125749i
$581$	7.95120	+	13.7719i	0.329871	+	0.571354i
$582$		0			0
$583$	−8.15489	−	4.70823i	−0.337741	−	0.194995i
$584$	−27.2492			−1.12758
$585$		0			0
$586$	−11.6265			−0.480285
$587$	−1.58391	−	0.914469i	−0.0653748	−	0.0377442i	0.466956	−	0.884280i	$-0.345351\pi$
$587$	−1.58391	−	0.914469i	−0.0653748	−	0.0377442i	−0.532331	+	0.846536i	$0.678684\pi$
$588$		0			0
$589$	3.47114	+	6.01219i	0.143026	+	0.247728i
$590$	−14.3395	+	12.0770i	−0.590346	+	0.497204i
$591$		0			0
$592$	11.6637	−	6.73403i	0.479374	−	0.276767i
$593$		−	0.0728761i		−	0.00299266i	−0.999999	−	0.00149633i	$-0.999524\pi$
$593$		−	0.0728761i		−	0.00299266i	0.999999	−	0.00149633i	$-0.000476297\pi$
$594$		0			0
$595$	−24.3503	+	4.33959i	−0.998266	+	0.177906i
$596$	−6.58212	+	11.4006i	−0.269614	+	0.466986i
$597$		0			0
$598$	0.122467	−	1.47233i	0.00500804	−	0.0602080i
$599$	−14.5813			−0.595777			−0.297888	−	0.954601i	$-0.596282\pi$
$599$	−14.5813			−0.595777			−0.297888	+	0.954601i	$0.596282\pi$
$600$		0			0
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.0857795	−	0.996314i	$-0.472662\pi$
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.819944	−	0.572444i	$-0.194005\pi$
$602$	−2.79508	+	1.61374i	−0.113919	+	0.0657712i
$603$		0			0
$604$	5.65527	+	9.79522i	0.230110	+	0.398562i
$605$	−3.09044	+	8.53951i	−0.125644	+	0.347180i
$606$		0			0
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.298024	−	0.954558i	$-0.403672\pi$
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.975684	+	0.219183i	$0.0703392\pi$
$608$	16.3836	+	9.45910i	0.664445	+	0.383617i
$609$		0			0
$610$	13.7311	−	11.5647i	0.555956	−	0.468239i
$611$	25.2419	−	36.3794i	1.02118	−	1.47175i
$612$		0			0
$613$	2.90838	+	1.67915i	0.117468	+	0.0678203i	0.557583	−	0.830121i	$-0.311729\pi$
$613$	2.90838	+	1.67915i	0.117468	+	0.0678203i	−0.440115	+	0.897942i	$0.645062\pi$
$614$	13.1228	−	22.7293i	0.529591	−	0.917279i
$615$		0			0
$616$	−24.2240			−0.976013
$617$	18.3441	−	10.5910i	0.738507	−	0.426377i	−0.0830194	−	0.996548i	$-0.526456\pi$
$617$	18.3441	−	10.5910i	0.738507	−	0.426377i	0.821526	+	0.570171i	$0.193123\pi$
$618$		0			0
$619$	−25.4082			−1.02124			−0.510620	−	0.859807i	$-0.670584\pi$
$619$	−25.4082			−1.02124			−0.510620	+	0.859807i	$0.670584\pi$
$620$	−0.530192	+	1.46503i	−0.0212930	+	0.0588369i
$621$		0			0
$622$	7.85493	+	4.53504i	0.314954	+	0.181839i
$623$		−	24.8455i		−	0.995416i
$624$		0			0
$625$	−23.5543	−	8.37828i	−0.942171	−	0.335131i
$626$	15.5199	−	26.8813i	0.620302	−	1.07439i
$627$		0			0
$628$	3.17056	−	1.83052i	0.126519	−	0.0730459i
$629$	−29.7041			−1.18438
$630$		0			0
$631$	−21.7725	−	37.7112i	−0.866751	−	1.50126i	−0.865298	−	0.501258i	$-0.832871\pi$
$631$	−21.7725	−	37.7112i	−0.866751	−	1.50126i	−0.00145375	−	0.999999i	$-0.500463\pi$
$632$		−	34.3853i		−	1.36777i
$633$		0			0
$634$	7.03069	−	12.1775i	0.279224	−	0.483631i
$635$	6.55413	+	36.7766i	0.260093	+	1.45943i
$636$		0			0
$637$	9.39516	−	4.43007i	0.372250	−	0.175526i
$638$		−	13.8238i		−	0.547288i
$639$		0			0
$640$	−1.55727	−	8.73816i	−0.0615565	−	0.345406i
$641$	24.1427	+	41.8164i	0.953579	+	1.65165i	0.737586	+	0.675253i	$0.235965\pi$
$641$	24.1427	+	41.8164i	0.953579	+	1.65165i	0.215993	+	0.976395i	$0.430701\pi$
$642$		0			0
$643$	−36.6710	+	21.1720i	−1.44616	+	0.834943i	−0.998250	−	0.0591344i	$-0.981166\pi$
$643$	−36.6710	+	21.1720i	−1.44616	+	0.834943i	−0.447913	+	0.894077i	$0.647833\pi$
$644$	−0.206708	−	0.358028i	−0.00814543	−	0.0141083i
$645$		0			0
$646$	19.0281	+	32.9576i	0.748649	+	1.29670i
$647$	29.7958	+	17.2026i	1.17139	+	0.676305i	0.954008	−	0.299781i	$-0.0969136\pi$
$647$	29.7958	+	17.2026i	1.17139	+	0.676305i	0.217386	+	0.976086i	$0.430247\pi$
$648$		0			0
$649$	27.4045			1.07572
$650$	−20.6310	+	5.70398i	−0.809213	+	0.223729i
$651$		0			0
$652$	−6.10104	−	3.52244i	−0.238935	−	0.137949i
$653$	−12.4114	−	7.16573i	−0.485696	−	0.280417i	0.237091	−	0.971487i	$-0.423806\pi$
$653$	−12.4114	−	7.16573i	−0.485696	−	0.280417i	−0.722787	+	0.691071i	$0.757139\pi$
$654$		0			0
$655$	14.4045	+	17.1029i	0.562830	+	0.668267i
$656$	−0.222994	−	0.386237i	−0.00870646	−	0.0150800i
$657$		0			0
$658$			29.5936i			1.15368i
$659$	−11.4116	−	19.7655i	−0.444532	−	0.769953i	0.553487	−	0.832858i	$-0.313297\pi$
$659$	−11.4116	−	19.7655i	−0.444532	−	0.769953i	−0.998020	+	0.0629051i	$0.979963\pi$
$660$		0			0
$661$	−7.20934	+	12.4869i	−0.280411	+	0.485686i	−0.971486	−	0.237097i	$-0.923804\pi$
$661$	−7.20934	+	12.4869i	−0.280411	+	0.485686i	0.691075	+	0.722783i	$0.257137\pi$
$662$		−	15.0796i		−	0.586087i
$663$		0			0
$664$	24.0976			0.935168
$665$	4.68257	+	26.2749i	0.181582	+	1.01890i
$666$		0			0
$667$	0.896622	−	0.517665i	0.0347173	−	0.0200441i
$668$		−	1.19792i		−	0.0463491i
$669$		0			0
$670$	3.97913	−	10.9952i	0.153727	−	0.424780i
$671$	−26.2419			−1.01306
$672$		0			0
$673$	29.5956	+	17.0871i	1.14083	+	0.658657i	0.946636	−	0.322306i	$-0.104458\pi$
$673$	29.5956	+	17.0871i	1.14083	+	0.658657i	0.194193	+	0.980963i	$0.437791\pi$
$674$	9.07949	−	15.7261i	0.349729	−	0.605748i
$675$		0			0
$676$	4.88170	−	5.91993i	0.187758	−	0.227690i
$677$			5.84695i			0.224716i	0.993668	+	0.112358i	$0.0358404\pi$
$677$			5.84695i			0.224716i	−0.993668	+	0.112358i	$0.964160\pi$
$678$		0			0
$679$	−5.89165	+	10.2046i	−0.226101	+	0.391618i
$680$	−12.7546	+	35.2436i	−0.489117	+	1.35153i
$681$		0			0
$682$	−4.71079	+	2.71978i	−0.180386	+	0.104146i
$683$	9.82834	−	5.67439i	0.376071	−	0.217125i	−0.300036	−	0.953928i	$-0.596999\pi$
$683$	9.82834	−	5.67439i	0.376071	−	0.217125i	0.676107	+	0.736803i	$0.263666\pi$
$684$		0			0
$685$	−4.15868	−	1.50502i	−0.158895	−	0.0575039i
$686$	−11.9053	+	20.6206i	−0.454546	+	0.787298i
$687$		0			0
$688$			3.30969i			0.126181i
$689$	−4.98715	+	7.18765i	−0.189995	+	0.273828i
$690$		0			0
$691$	9.41159	−	16.3013i	0.358034	−	0.620133i	−0.629599	−	0.776921i	$-0.716781\pi$
$691$	9.41159	−	16.3013i	0.358034	−	0.620133i	0.987632	+	0.156788i	$0.0501140\pi$
$692$	0.684619	+	0.395265i	0.0260253	+	0.0150257i
$693$		0			0
$694$	−14.5325			−0.551647
$695$	6.62044	−	18.2936i	0.251128	−	0.693916i
$696$		0			0
$697$			0.983636i			0.0372579i
$698$	−19.2289	+	11.1018i	−0.727825	+	0.420210i
$699$		0			0
$700$	−3.83323	+	4.60238i	−0.144883	+	0.173954i
$701$	−19.1626			−0.723763			−0.361881	−	0.932224i	$-0.617865\pi$
$701$	−19.1626			−0.723763			−0.361881	+	0.932224i	$0.617865\pi$
$702$		0			0
$703$			32.0518i			1.20885i
$704$	−17.0018	+	29.4480i	−0.640780	+	1.10986i
$705$		0			0
$706$	−0.777006	−	1.34581i	−0.0292430	−	0.0506504i
$707$		−	12.0602i		−	0.453570i
$708$		0			0
$709$	11.7419	+	20.3375i	0.440975	+	0.763791i	0.997762	−	0.0668645i	$-0.0212995\pi$
$709$	11.7419	+	20.3375i	0.440975	+	0.763791i	−0.556787	+	0.830655i	$0.687966\pi$
$710$	3.81952	−	3.21689i	0.143344	−	0.120728i
$711$		0			0
$712$	−32.6055	−	18.8248i	−1.22194	−	0.705488i
$713$	−0.352814	−	0.203698i	−0.0132130	−	0.00762853i
$714$		0			0
$715$	28.4375	+	13.0497i	1.06350	+	0.488033i
$716$	11.9370			0.446107
$717$		0			0
$718$	30.2393	+	17.4586i	1.12852	+	0.651551i
$719$	7.05429	+	12.2184i	0.263080	+	0.455669i	0.967059	−	0.254553i	$-0.0819282\pi$
$719$	7.05429	+	12.2184i	0.263080	+	0.455669i	−0.703978	+	0.710221i	$0.748595\pi$
$720$		0			0
$721$	6.52886	+	11.3083i	0.243148	+	0.421144i
$722$	16.0254	−	9.25228i	0.596404	−	0.344334i
$723$		0			0
$724$	−5.85021	−	10.1329i	−0.217421	−	0.376585i
$725$	−11.5259	−	9.59969i	−0.428061	−	0.356523i
$726$		0			0
$727$		−	25.3762i		−	0.941153i	−0.882359	−	0.470576i	$-0.844046\pi$
$727$		−	25.3762i		−	0.941153i	0.882359	−	0.470576i	$-0.155954\pi$
$728$	−1.86553	+	22.4279i	−0.0691411	+	0.831233i
$729$		0			0
$730$	−23.1584	+	4.12717i	−0.857131	+	0.152754i
$731$	3.64979	−	6.32162i	0.134992	−	0.233814i
$732$		0			0
$733$		−	10.6692i		−	0.394074i	−0.980396	−	0.197037i	$-0.936868\pi$
$733$		−	10.6692i		−	0.394074i	0.980396	−	0.197037i	$-0.0631320\pi$
$734$	19.8476	+	34.3770i	0.732587	+	1.26888i
$735$		0			0
$736$	−1.11018			−0.0409218
$737$	−14.8024	+	8.54617i	−0.545254	+	0.314802i
$738$		0			0
$739$	−0.707513	+	1.22545i	−0.0260263	+	0.0450788i	−0.878745	−	0.477291i	$-0.841619\pi$
$739$	−0.707513	+	1.22545i	−0.0260263	+	0.0450788i	0.852719	+	0.522370i	$0.174952\pi$
$740$	−5.50183	+	4.63377i	−0.202251	+	0.170341i
$741$		0			0
$742$		−	5.84695i		−	0.214648i
$743$	−25.8748	−	14.9389i	−0.949256	−	0.548053i	−0.0564064	−	0.998408i	$-0.517964\pi$
$743$	−25.8748	−	14.9389i	−0.949256	−	0.548053i	−0.892850	+	0.450355i	$0.851298\pi$
$744$		0			0
$745$	−16.9713	+	46.8951i	−0.621779	+	1.71810i
$746$	40.9370			1.49881
$747$		0			0
$748$	10.8118	−	6.24221i	0.395320	−	0.228238i
$749$	35.8809			1.31106
$750$		0			0
$751$	9.99291	−	17.3082i	0.364646	−	0.631586i	−0.624073	−	0.781366i	$-0.714523\pi$
$751$	9.99291	−	17.3082i	0.364646	−	0.631586i	0.988719	+	0.149780i	$0.0478565\pi$
$752$	26.2816	+	15.1737i	0.958391	+	0.553328i
$753$		0			0
$754$	−12.7988	−	1.06459i	−0.466104	−	0.0387701i
$755$	27.6028	+	32.7737i	1.00457	+	1.19276i
$756$		0			0
$757$	−14.8024	−	8.54617i	−0.538003	−	0.310616i	0.206266	−	0.978496i	$-0.433869\pi$
$757$	−14.8024	−	8.54617i	−0.538003	−	0.310616i	−0.744269	+	0.667880i	$0.767202\pi$
$758$	17.8964	−	10.3325i	0.650025	−	0.375292i
$759$		0			0
$760$	38.0291	+	13.7627i	1.37946	+	0.499225i
$761$	−21.1120	−	36.5671i	−0.765310	−	1.32556i	−0.940083	−	0.340947i	$-0.889252\pi$
$761$	−21.1120	−	36.5671i	−0.765310	−	1.32556i	0.174773	−	0.984609i	$-0.444081\pi$
$762$		0			0
$763$	10.1272	−	5.84695i	0.366630	−	0.211674i
$764$	0.453830	−	0.786056i	0.0164190	−	0.0284385i
$765$		0			0
$766$	2.07395			0.0749350
$767$	2.11046	−	25.3725i	0.0762044	−	0.916149i
$768$		0			0
$769$	−11.8827	+	20.5815i	−0.428502	+	0.742187i	−0.996740	−	0.0806767i	$-0.974292\pi$
$769$	−11.8827	+	20.5815i	−0.428502	+	0.742187i	0.568238	+	0.822864i	$0.307625\pi$
$770$	−20.5874	+	3.66898i	−0.741919	+	0.132221i
$771$		0			0
$772$			12.5149i			0.450422i
$773$	0.246026	−	0.142043i	0.00884894	−	0.00510894i	−0.495569	−	0.868569i	$-0.665040\pi$
$773$	0.246026	−	0.142043i	0.00884894	−	0.00510894i	0.504418	+	0.863460i	$0.331707\pi$
$774$		0			0
$775$	−1.00366	+	5.81644i	−0.0360524	+	0.208933i
$776$	8.92787	+	15.4635i	0.320492	+	0.555108i
$777$		0			0
$778$	−22.6665	−	13.0865i	−0.812634	−	0.469174i
$779$	1.06138			0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$	−1.93405	−	1.11663i	−0.0691617	−	0.0399305i
$783$		0			0
$784$	3.55955	+	6.16532i	0.127127	+	0.220190i
$785$	10.6084	−	8.93460i	0.378628	−	0.318890i
$786$		0

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02826 - 0.593667i) q^{2} +(-0.295120 - 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +O(q^{10})\)	\(q+(-1.02826 - 0.593667i) q^{2} +(-0.295120 - 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(-1.75765 + 1.01478i) q^{7} +3.07548i q^{8} +(0.465813 + 2.61378i) q^{10} +(1.94045 - 3.36096i) q^{11} +(-2.96232 - 2.05540i) q^{13} +2.40976 q^{14} +(1.23557 - 2.14007i) q^{16} +(-4.71996 + 2.72507i) q^{17} +(2.94045 + 5.09301i) q^{19} +(-0.449133 + 1.24105i) q^{20} +(-3.99058 + 2.30396i) q^{22} +(-0.298874 - 0.172555i) q^{23} +(-0.850210 + 4.92718i) q^{25} +(1.82581 + 3.87212i) q^{26} +(1.03743 + 0.598962i) q^{28} +(-1.50000 + 2.59808i) q^{29} +1.18048 q^{31} +(2.78591 - 1.60845i) q^{32} +6.47114 q^{34} +(4.26737 + 1.54436i) q^{35} +(4.71996 + 2.72507i) q^{37} -6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(0.0902394 - 0.156299i) q^{41} +(-1.15990 + 0.669668i) q^{43} -2.29066 q^{44} +(0.204880 + 0.354863i) q^{46} +12.2807i q^{47} +(-1.44045 + 2.49493i) q^{49} +(3.79934 - 4.56169i) q^{50} +(-0.176407 + 2.12081i) q^{52} -2.42636i q^{53} +(-8.54334 + 1.52255i) q^{55} +(-3.12093 - 5.40561i) q^{56} +(3.08478 - 1.78100i) q^{58} +(3.53069 + 6.11533i) q^{59} +(-3.38090 - 5.85589i) q^{61} +(-1.21384 - 0.700811i) q^{62} -8.76180 q^{64} +(0.751722 + 8.02714i) q^{65} +(-3.81417 - 2.20211i) q^{67} +(2.78591 + 1.60845i) q^{68} +(-3.47114 - 4.12140i) q^{70} +(-0.940450 - 1.62891i) q^{71} +8.86014i q^{73} +(-3.23557 - 5.60417i) q^{74} +(1.73557 - 3.00609i) q^{76} +7.87651i q^{77} -11.1805 q^{79} +(-5.43992 + 0.969475i) q^{80} +(-0.185579 + 0.107144i) q^{82} -7.83540i q^{83} +(11.4595 + 4.14720i) q^{85} +1.59024 q^{86} +(10.3365 + 5.96781i) q^{88} +(-6.12093 + 10.6018i) q^{89} +(7.29249 + 0.606582i) q^{91} +0.203698i q^{92} +(7.29066 - 12.6278i) q^{94} +(4.47497 - 12.3653i) q^{95} +(5.02801 - 2.90292i) q^{97} +(2.96232 - 1.71029i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5	\( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 7 * q^10 + 44 * q^14 - 16 * q^16 + 12 * q^19 + q^20 - 2 * q^25 - 24 * q^26 - 18 * q^29 - 16 * q^31 + 16 * q^34 - 10 * q^35 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 10 * q^46 + 6 * q^49 + 31 * q^50 - 26 * q^55 + 16 * q^56 + 4 * q^59 + 6 * q^61 - 12 * q^64 - 23 * q^65 + 20 * q^70 + 12 * q^71 - 8 * q^74 - 10 * q^76 - 104 * q^79 - 33 * q^80 + 21 * q^85 + 4 * q^86 - 20 * q^89 - 44 * q^91 + 56 * q^94 - 20 * q^95

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