LMFDB - Embedded newform 546.2.e.g.545.1

Newspace parameters

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.e (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.303595776.1
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			545.1
Root			$-1.26217 - 1.18614i$ of defining polynomial
Character	$\chi$	$=$	546.545
Dual form			546.2.e.g.545.2

$q$-expansion

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.26217 - 1.18614i) q^{3} +1.00000 q^{4} +3.37228i q^{5} +(-1.26217 - 1.18614i) q^{6} +(-2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.26217 - 1.18614i) q^{3} +1.00000 q^{4} +3.37228i q^{5} +(-1.26217 - 1.18614i) q^{6} +(-2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} +3.37228i q^{10} -5.74456 q^{11} +(-1.26217 - 1.18614i) q^{12} +(-3.46410 + 1.00000i) q^{13} +(-2.52434 - 0.792287i) q^{14} +(4.00000 - 4.25639i) q^{15} +1.00000 q^{16} +0.792287 q^{17} +(0.186141 + 2.99422i) q^{18} -2.37686 q^{19} +3.37228i q^{20} +(2.24638 + 3.99422i) q^{21} -5.74456 q^{22} +0.147477i q^{23} +(-1.26217 - 1.18614i) q^{24} -6.37228 q^{25} +(-3.46410 + 1.00000i) q^{26} +(3.31662 - 4.00000i) q^{27} +(-2.52434 - 0.792287i) q^{28} +2.37686i q^{29} +(4.00000 - 4.25639i) q^{30} +4.10891 q^{31} +1.00000 q^{32} +(7.25061 + 6.81386i) q^{33} +0.792287 q^{34} +(2.67181 - 8.51278i) q^{35} +(0.186141 + 2.99422i) q^{36} +8.36530i q^{37} -2.37686 q^{38} +(5.55842 + 2.84674i) q^{39} +3.37228i q^{40} -8.37228i q^{41} +(2.24638 + 3.99422i) q^{42} -2.62772 q^{43} -5.74456 q^{44} +(-10.0974 + 0.627719i) q^{45} +0.147477i q^{46} +10.3723i q^{47} +(-1.26217 - 1.18614i) q^{48} +(5.74456 + 4.00000i) q^{49} -6.37228 q^{50} +(-1.00000 - 0.939764i) q^{51} +(-3.46410 + 1.00000i) q^{52} +10.0974i q^{53} +(3.31662 - 4.00000i) q^{54} -19.3723i q^{55} +(-2.52434 - 0.792287i) q^{56} +(3.00000 + 2.81929i) q^{57} +2.37686i q^{58} +2.74456i q^{59} +(4.00000 - 4.25639i) q^{60} -7.74456i q^{61} +4.10891 q^{62} +(1.90240 - 7.70590i) q^{63} +1.00000 q^{64} +(-3.37228 - 11.6819i) q^{65} +(7.25061 + 6.81386i) q^{66} -5.98844i q^{67} +0.792287 q^{68} +(0.174928 - 0.186141i) q^{69} +(2.67181 - 8.51278i) q^{70} -2.00000 q^{71} +(0.186141 + 2.99422i) q^{72} +10.2448 q^{73} +8.36530i q^{74} +(8.04290 + 7.55842i) q^{75} -2.37686 q^{76} +(14.5012 + 4.55134i) q^{77} +(5.55842 + 2.84674i) q^{78} -3.62772 q^{79} +3.37228i q^{80} +(-8.93070 + 1.11469i) q^{81} -8.37228i q^{82} +6.74456i q^{83} +(2.24638 + 3.99422i) q^{84} +2.67181i q^{85} -2.62772 q^{86} +(2.81929 - 3.00000i) q^{87} -5.74456 q^{88} -10.0000i q^{89} +(-10.0974 + 0.627719i) q^{90} +(9.53685 + 0.220225i) q^{91} +0.147477i q^{92} +(-5.18614 - 4.87375i) q^{93} +10.3723i q^{94} -8.01544i q^{95} +(-1.26217 - 1.18614i) q^{96} +9.15759 q^{97} +(5.74456 + 4.00000i) q^{98} +(-1.06930 - 17.2005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9} + 32 q^{15} + 8 q^{16} - 10 q^{18} + 14 q^{21} - 28 q^{25} + 32 q^{30} + 8 q^{32} - 10 q^{36} + 10 q^{39} + 14 q^{42} - 44 q^{43} - 28 q^{50} - 8 q^{51} + 24 q^{57} + 32 q^{60} - 4 q^{63} + 8 q^{64} - 4 q^{65} - 16 q^{71} - 10 q^{72} + 10 q^{78} - 52 q^{79} - 14 q^{81} + 14 q^{84} - 44 q^{86} + 24 q^{91} - 30 q^{93} - 66 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9 + 32 * q^15 + 8 * q^16 - 10 * q^18 + 14 * q^21 - 28 * q^25 + 32 * q^30 + 8 * q^32 - 10 * q^36 + 10 * q^39 + 14 * q^42 - 44 * q^43 - 28 * q^50 - 8 * q^51 + 24 * q^57 + 32 * q^60 - 4 * q^63 + 8 * q^64 - 4 * q^65 - 16 * q^71 - 10 * q^72 + 10 * q^78 - 52 * q^79 - 14 * q^81 + 14 * q^84 - 44 * q^86 + 24 * q^91 - 30 * q^93 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.26217	−	1.18614i	−0.728714	−	0.684819i
$3$	−1.26217	−	1.18614i	−0.728714	−	0.684819i
$4$	1.00000			0.500000
$5$			3.37228i			1.50813i	0.656800	+	0.754065i	$0.271910\pi$
$5$			3.37228i			1.50813i	−0.656800	+	0.754065i	$0.728090\pi$
$6$	−1.26217	−	1.18614i	−0.515278	−	0.484240i
$7$	−2.52434	−	0.792287i	−0.954110	−	0.299456i
$7$	−2.52434	−	0.792287i	−0.954110	−	0.299456i
$8$	1.00000			0.353553
$9$	0.186141	+	2.99422i	0.0620469	+	0.998073i
$10$			3.37228i			1.06641i
$11$	−5.74456			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$11$	−5.74456			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$12$	−1.26217	−	1.18614i	−0.364357	−	0.342409i
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$13$	−3.46410	+	1.00000i	−0.960769	+	0.277350i
$14$	−2.52434	−	0.792287i	−0.674658	−	0.211748i
$15$	4.00000	−	4.25639i	1.03280	−	1.09899i
$16$	1.00000			0.250000
$17$	0.792287			0.192158			0.0960789	−	0.995374i	$-0.469370\pi$
$17$	0.792287			0.192158			0.0960789	+	0.995374i	$0.469370\pi$
$18$	0.186141	+	2.99422i	0.0438738	+	0.705744i
$19$	−2.37686			−0.545289			−0.272645	−	0.962115i	$-0.587898\pi$
$19$	−2.37686			−0.545289			−0.272645	+	0.962115i	$0.587898\pi$
$20$			3.37228i			0.754065i
$21$	2.24638	+	3.99422i	0.490200	+	0.871610i
$22$	−5.74456			−1.22474
$23$			0.147477i			0.0307510i	0.999882	+	0.0153755i	$0.00489437\pi$
$23$			0.147477i			0.0307510i	−0.999882	+	0.0153755i	$0.995106\pi$
$24$	−1.26217	−	1.18614i	−0.257639	−	0.242120i
$25$	−6.37228			−1.27446
$26$	−3.46410	+	1.00000i	−0.679366	+	0.196116i
$27$	3.31662	−	4.00000i	0.638285	−	0.769800i
$28$	−2.52434	−	0.792287i	−0.477055	−	0.149728i
$29$			2.37686i			0.441372i	0.975345	+	0.220686i	$0.0708296\pi$
$29$			2.37686i			0.441372i	−0.975345	+	0.220686i	$0.929170\pi$
$30$	4.00000	−	4.25639i	0.730297	−	0.777107i
$31$	4.10891			0.737982			0.368991	−	0.929433i	$-0.379703\pi$
$31$	4.10891			0.737982			0.368991	+	0.929433i	$0.379703\pi$
$32$	1.00000			0.176777
$33$	7.25061	+	6.81386i	1.26217	+	1.18614i
$34$	0.792287			0.135876
$35$	2.67181	−	8.51278i	0.451619	−	1.43892i
$36$	0.186141	+	2.99422i	0.0310234	+	0.499037i
$37$			8.36530i			1.37525i	0.726067	+	0.687623i	$0.241346\pi$
$37$			8.36530i			1.37525i	−0.726067	+	0.687623i	$0.758654\pi$
$38$	−2.37686			−0.385578
$39$	5.55842	+	2.84674i	0.890060	+	0.455844i
$40$			3.37228i			0.533204i
$41$		−	8.37228i		−	1.30753i	−0.756697	−	0.653765i	$-0.773188\pi$
$41$		−	8.37228i		−	1.30753i	0.756697	−	0.653765i	$-0.226812\pi$
$42$	2.24638	+	3.99422i	0.346623	+	0.616321i
$43$	−2.62772			−0.400723			−0.200362	−	0.979722i	$-0.564212\pi$
$43$	−2.62772			−0.400723			−0.200362	+	0.979722i	$0.564212\pi$
$44$	−5.74456			−0.866025
$45$	−10.0974	+	0.627719i	−1.50522	+	0.0935748i
$46$			0.147477i			0.0217443i
$47$			10.3723i			1.51295i	0.654021	+	0.756476i	$0.273081\pi$
$47$			10.3723i			1.51295i	−0.654021	+	0.756476i	$0.726919\pi$
$48$	−1.26217	−	1.18614i	−0.182178	−	0.171205i
$49$	5.74456	+	4.00000i	0.820652	+	0.571429i
$50$	−6.37228			−0.901177
$51$	−1.00000	−	0.939764i	−0.140028	−	0.131593i
$52$	−3.46410	+	1.00000i	−0.480384	+	0.138675i
$53$			10.0974i			1.38698i	0.720467	+	0.693489i	$0.243927\pi$
$53$			10.0974i			1.38698i	−0.720467	+	0.693489i	$0.756073\pi$
$54$	3.31662	−	4.00000i	0.451335	−	0.544331i
$55$		−	19.3723i		−	2.61216i
$56$	−2.52434	−	0.792287i	−0.337329	−	0.105874i
$57$	3.00000	+	2.81929i	0.397360	+	0.373424i
$58$			2.37686i			0.312097i
$59$			2.74456i			0.357312i	0.983912	+	0.178656i	$0.0571749\pi$
$59$			2.74456i			0.357312i	−0.983912	+	0.178656i	$0.942825\pi$
$60$	4.00000	−	4.25639i	0.516398	−	0.549497i
$61$		−	7.74456i		−	0.991590i	−0.868440	−	0.495795i	$-0.834877\pi$
$61$		−	7.74456i		−	0.991590i	0.868440	−	0.495795i	$-0.165123\pi$
$62$	4.10891			0.521832
$63$	1.90240	−	7.70590i	0.239680	−	0.970852i
$64$	1.00000			0.125000
$65$	−3.37228	−	11.6819i	−0.418280	−	1.44896i
$66$	7.25061	+	6.81386i	0.892488	+	0.838728i
$67$		−	5.98844i		−	0.731604i	−0.930693	−	0.365802i	$-0.880795\pi$
$67$		−	5.98844i		−	0.731604i	0.930693	−	0.365802i	$-0.119205\pi$
$68$	0.792287			0.0960789
$69$	0.174928	−	0.186141i	0.0210589	−	0.0224087i
$70$	2.67181	−	8.51278i	0.319343	−	1.01747i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	0.186141	+	2.99422i	0.0219369	+	0.352872i
$73$	10.2448			1.19907			0.599533	−	0.800350i	$-0.295353\pi$
$73$	10.2448			1.19907			0.599533	+	0.800350i	$0.295353\pi$
$74$			8.36530i			0.972446i
$75$	8.04290	+	7.55842i	0.928714	+	0.872771i
$76$	−2.37686			−0.272645
$77$	14.5012	+	4.55134i	1.65257	+	0.518674i
$78$	5.55842	+	2.84674i	0.629367	+	0.322330i
$79$	−3.62772			−0.408150			−0.204075	−	0.978955i	$-0.565419\pi$
$79$	−3.62772			−0.408150			−0.204075	+	0.978955i	$0.565419\pi$
$80$			3.37228i			0.377033i
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$		−	8.37228i		−	0.924564i
$83$			6.74456i			0.740312i	0.928970	+	0.370156i	$0.120696\pi$
$83$			6.74456i			0.740312i	−0.928970	+	0.370156i	$0.879304\pi$
$84$	2.24638	+	3.99422i	0.245100	+	0.435805i
$85$			2.67181i			0.289799i
$86$	−2.62772			−0.283354
$87$	2.81929	−	3.00000i	0.302260	−	0.321634i
$88$	−5.74456			−0.612372
$89$		−	10.0000i		−	1.06000i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$		−	10.0000i		−	1.06000i	0.847998	−	0.529999i	$-0.177808\pi$
$90$	−10.0974	+	0.627719i	−1.06435	+	0.0661674i
$91$	9.53685	+	0.220225i	0.999733	+	0.0230858i
$92$			0.147477i			0.0153755i
$93$	−5.18614	−	4.87375i	−0.537778	−	0.505384i
$94$			10.3723i			1.06982i
$95$		−	8.01544i		−	0.822367i
$96$	−1.26217	−	1.18614i	−0.128820	−	0.121060i
$97$	9.15759			0.929812			0.464906	−	0.885360i	$-0.346088\pi$
$97$	9.15759			0.929812			0.464906	+	0.885360i	$0.346088\pi$
$98$	5.74456	+	4.00000i	0.580288	+	0.404061i
$99$	−1.06930	−	17.2005i	−0.107468	−	1.72871i
$100$	−6.37228			−0.637228
$101$	−17.6704			−1.75827			−0.879133	−	0.476576i	$-0.841878\pi$
$101$	−17.6704			−1.75827			−0.879133	+	0.476576i	$0.841878\pi$
$102$	−1.00000	−	0.939764i	−0.0990148	−	0.0930505i
$103$			7.37228i			0.726412i	0.931709	+	0.363206i	$0.118318\pi$
$103$			7.37228i			0.726412i	−0.931709	+	0.363206i	$0.881682\pi$
$104$	−3.46410	+	1.00000i	−0.339683	+	0.0980581i
$105$	−13.4696	+	7.57541i	−1.31450	+	0.739285i
$106$			10.0974i			0.980741i
$107$		−	17.0256i		−	1.64592i	−0.568098	−	0.822961i	$-0.692320\pi$
$107$		−	17.0256i		−	1.64592i	0.568098	−	0.822961i	$-0.307680\pi$
$108$	3.31662	−	4.00000i	0.319142	−	0.384900i
$109$		−	19.6974i		−	1.88667i	−0.331848	−	0.943333i	$-0.607672\pi$
$109$		−	19.6974i		−	1.88667i	0.331848	−	0.943333i	$-0.392328\pi$
$110$		−	19.3723i		−	1.84707i
$111$	9.92242	−	10.5584i	0.941795	−	1.00216i
$112$	−2.52434	−	0.792287i	−0.238528	−	0.0748641i
$113$			5.69349i			0.535598i	0.963475	+	0.267799i	$0.0862963\pi$
$113$			5.69349i			0.535598i	−0.963475	+	0.267799i	$0.913704\pi$
$114$	3.00000	+	2.81929i	0.280976	+	0.264051i
$115$	−0.497333			−0.0463766
$116$			2.37686i			0.220686i
$117$	−3.63903	−	10.1861i	−0.336428	−	0.941709i
$118$			2.74456i			0.252657i
$119$	−2.00000	−	0.627719i	−0.183340	−	0.0575429i
$120$	4.00000	−	4.25639i	0.365148	−	0.388553i
$121$	22.0000			2.00000
$122$		−	7.74456i		−	0.701160i
$123$	−9.93070	+	10.5672i	−0.895421	+	0.952815i
$124$	4.10891			0.368991
$125$		−	4.62772i		−	0.413916i
$126$	1.90240	−	7.70590i	0.169479	−	0.686496i
$127$	−10.3723			−0.920391			−0.460196	−	0.887818i	$-0.652221\pi$
$127$	−10.3723			−0.920391			−0.460196	+	0.887818i	$0.652221\pi$
$128$	1.00000			0.0883883
$129$	3.31662	+	3.11684i	0.292013	+	0.274423i
$130$	−3.37228	−	11.6819i	−0.295769	−	1.02457i
$131$	−3.96143			−0.346112			−0.173056	−	0.984912i	$-0.555364\pi$
$131$	−3.96143			−0.346112			−0.173056	+	0.984912i	$0.555364\pi$
$132$	7.25061	+	6.81386i	0.631084	+	0.593070i
$133$	6.00000	+	1.88316i	0.520266	+	0.163290i
$134$		−	5.98844i		−	0.517322i
$135$	13.4891	+	11.1846i	1.16096	+	0.962616i
$136$	0.792287			0.0679380
$137$	−18.1168			−1.54783			−0.773913	−	0.633292i	$-0.781703\pi$
$137$	−18.1168			−1.54783			−0.773913	+	0.633292i	$0.781703\pi$
$138$	0.174928	−	0.186141i	0.0148909	−	0.0158453i
$139$			5.25544i			0.445760i	0.974846	+	0.222880i	$0.0715459\pi$
$139$			5.25544i			0.445760i	−0.974846	+	0.222880i	$0.928454\pi$
$140$	2.67181	−	8.51278i	0.225810	−	0.719461i
$141$	12.3030	−	13.0916i	1.03610	−	1.10251i
$142$	−2.00000			−0.167836
$143$	19.8997	−	5.74456i	1.66410	−	0.480384i
$144$	0.186141	+	2.99422i	0.0155117	+	0.249518i
$145$	−8.01544			−0.665646
$146$	10.2448			0.847868
$147$	−2.50605	−	11.8625i	−0.206695	−	0.978405i
$148$			8.36530i			0.687623i
$149$	−7.62772			−0.624887			−0.312444	−	0.949936i	$-0.601148\pi$
$149$	−7.62772			−0.624887			−0.312444	+	0.949936i	$0.601148\pi$
$150$	8.04290	+	7.55842i	0.656700	+	0.617143i
$151$			17.8178i			1.45000i	0.688751	+	0.724998i	$0.258159\pi$
$151$			17.8178i			1.45000i	−0.688751	+	0.724998i	$0.741841\pi$
$152$	−2.37686			−0.192789
$153$	0.147477	+	2.37228i	0.0119228	+	0.191788i
$154$	14.5012	+	4.55134i	1.16854	+	0.366758i
$155$			13.8564i			1.11297i
$156$	5.55842	+	2.84674i	0.445030	+	0.227922i
$157$			8.25544i			0.658856i	0.944181	+	0.329428i	$0.106856\pi$
$157$			8.25544i			0.658856i	−0.944181	+	0.329428i	$0.893144\pi$
$158$	−3.62772			−0.288606
$159$	11.9769	−	12.7446i	0.949828	−	1.01071i
$160$			3.37228i			0.266602i
$161$	0.116844	−	0.372281i	0.00920859	−	0.0293399i
$162$	−8.93070	+	1.11469i	−0.701662	+	0.0875785i
$163$			8.21782i			0.643670i	0.946796	+	0.321835i	$0.104300\pi$
$163$			8.21782i			0.643670i	−0.946796	+	0.321835i	$0.895700\pi$
$164$		−	8.37228i		−	0.653765i
$165$	−22.9783	+	24.4511i	−1.78885	+	1.90351i
$166$			6.74456i			0.523480i
$167$			12.6277i			0.977162i	0.872518	+	0.488581i	$0.162485\pi$
$167$			12.6277i			0.977162i	−0.872518	+	0.488581i	$0.837515\pi$
$168$	2.24638	+	3.99422i	0.173312	+	0.308161i
$169$	11.0000	−	6.92820i	0.846154	−	0.532939i
$170$			2.67181i			0.204919i
$171$	−0.442430	−	7.11684i	−0.0338335	−	0.544239i
$172$	−2.62772			−0.200362
$173$	−10.6873			−0.812537			−0.406269	−	0.913754i	$-0.633170\pi$
$173$	−10.6873			−0.812537			−0.406269	+	0.913754i	$0.633170\pi$
$174$	2.81929	−	3.00000i	0.213730	−	0.227429i
$175$	16.0858	+	5.04868i	1.21597	+	0.381644i
$176$	−5.74456			−0.433013
$177$	3.25544	−	3.46410i	0.244694	−	0.260378i
$178$		−	10.0000i		−	0.749532i
$179$			20.1947i			1.50942i	0.656057	+	0.754711i	$0.272223\pi$
$179$			20.1947i			1.50942i	−0.656057	+	0.754711i	$0.727777\pi$
$180$	−10.0974	+	0.627719i	−0.752612	+	0.0467874i
$181$			20.3723i			1.51426i	0.653264	+	0.757130i	$0.273399\pi$
$181$			20.3723i			1.51426i	−0.653264	+	0.757130i	$0.726601\pi$
$182$	9.53685	+	0.220225i	0.706918	+	0.0163242i
$183$	−9.18614	+	9.77495i	−0.679059	+	0.722585i
$184$			0.147477i			0.0108721i
$185$	−28.2101			−2.07405
$186$	−5.18614	−	4.87375i	−0.380266	−	0.357360i
$187$	−4.55134			−0.332827
$188$			10.3723i			0.756476i
$189$	−11.5414	+	7.46963i	−0.839515	+	0.543336i
$190$		−	8.01544i		−	0.581501i
$191$			2.96677i			0.214668i	0.994223	+	0.107334i	$0.0342314\pi$
$191$			2.96677i			0.214668i	−0.994223	+	0.107334i	$0.965769\pi$
$192$	−1.26217	−	1.18614i	−0.0910892	−	0.0856023i
$193$			20.7846i			1.49611i	0.663637	+	0.748054i	$0.269012\pi$
$193$			20.7846i			1.49611i	−0.663637	+	0.748054i	$0.730988\pi$
$194$	9.15759			0.657476
$195$	−9.60002	+	18.7446i	−0.687472	+	1.34233i
$196$	5.74456	+	4.00000i	0.410326	+	0.285714i
$197$	21.1168			1.50451			0.752256	−	0.658870i	$-0.228965\pi$
$197$	21.1168			1.50451			0.752256	+	0.658870i	$0.228965\pi$
$198$	−1.06930	−	17.2005i	−0.0759916	−	1.22239i
$199$		−	12.1168i		−	0.858940i	−0.903081	−	0.429470i	$-0.858700\pi$
$199$		−	12.1168i		−	0.858940i	0.903081	−	0.429470i	$-0.141300\pi$
$200$	−6.37228			−0.450588
$201$	−7.10313	+	7.55842i	−0.501016	+	0.533130i
$202$	−17.6704			−1.24328
$203$	1.88316	−	6.00000i	0.132172	−	0.421117i
$204$	−1.00000	−	0.939764i	−0.0700140	−	0.0657966i
$205$	28.2337			1.97193
$206$			7.37228i			0.513651i
$207$	−0.441578	+	0.0274514i	−0.0306918	+	0.00190801i
$208$	−3.46410	+	1.00000i	−0.240192	+	0.0693375i
$209$	13.6540			0.944469
$210$	−13.4696	+	7.57541i	−0.929493	+	0.522753i
$211$	17.3723			1.19596			0.597979	−	0.801512i	$-0.295971\pi$
$211$	17.3723			1.19596			0.597979	+	0.801512i	$0.295971\pi$
$212$			10.0974i			0.693489i
$213$	2.52434	+	2.37228i	0.172965	+	0.162546i
$214$		−	17.0256i		−	1.16384i
$215$		−	8.86141i		−	0.604343i
$216$	3.31662	−	4.00000i	0.225668	−	0.272166i
$217$	−10.3723	−	3.25544i	−0.704116	−	0.220993i
$218$		−	19.6974i		−	1.33407i
$219$	−12.9307	−	12.1518i	−0.873776	−	0.821143i
$220$		−	19.3723i		−	1.30608i
$221$	−2.74456	+	0.792287i	−0.184619	+	0.0532950i
$222$	9.92242	−	10.5584i	0.665949	−	0.708635i
$223$	0.644810			0.0431797			0.0215898	−	0.999767i	$-0.493127\pi$
$223$	0.644810			0.0431797			0.0215898	+	0.999767i	$0.493127\pi$
$224$	−2.52434	−	0.792287i	−0.168664	−	0.0529369i
$225$	−1.18614	−	19.0800i	−0.0790760	−	1.27200i
$226$			5.69349i			0.378725i
$227$			11.4891i			0.762560i	0.924460	+	0.381280i	$0.124517\pi$
$227$			11.4891i			0.762560i	−0.924460	+	0.381280i	$0.875483\pi$
$228$	3.00000	+	2.81929i	0.198680	+	0.186712i
$229$	−5.04868			−0.333626			−0.166813	−	0.985989i	$-0.553348\pi$
$229$	−5.04868			−0.333626			−0.166813	+	0.985989i	$0.553348\pi$
$230$	−0.497333			−0.0327932
$231$	−12.9045	−	22.9450i	−0.849051	−	1.50967i
$232$			2.37686i			0.156049i
$233$		−	10.7422i		−	0.703742i	−0.936048	−	0.351871i	$-0.885546\pi$
$233$		−	10.7422i		−	0.703742i	0.936048	−	0.351871i	$-0.114454\pi$
$234$	−3.63903	−	10.1861i	−0.237891	−	0.665889i
$235$	−34.9783			−2.28173
$236$			2.74456i			0.178656i
$237$	4.57879	+	4.30298i	0.297425	+	0.279509i
$238$	−2.00000	−	0.627719i	−0.129641	−	0.0406890i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$	4.00000	−	4.25639i	0.258199	−	0.274749i
$241$	−16.4356			−1.05871			−0.529357	−	0.848399i	$-0.677567\pi$
$241$	−16.4356			−1.05871			−0.529357	+	0.848399i	$0.677567\pi$
$242$	22.0000			1.41421
$243$	12.5942	+	9.18614i	0.807921	+	0.589291i
$244$		−	7.74456i		−	0.495795i
$245$	−13.4891	+	19.3723i	−0.861789	+	1.23765i
$246$	−9.93070	+	10.5672i	−0.633159	+	0.673742i
$247$	8.23369	−	2.37686i	0.523897	−	0.151236i
$248$	4.10891			0.260916
$249$	8.00000	−	8.51278i	0.506979	−	0.539475i
$250$		−	4.62772i		−	0.292683i
$251$	−6.78073			−0.427996			−0.213998	−	0.976834i	$-0.568649\pi$
$251$	−6.78073			−0.427996			−0.213998	+	0.976834i	$0.568649\pi$
$252$	1.90240	−	7.70590i	0.119840	−	0.485426i
$253$		−	0.847190i		−	0.0532624i
$254$	−10.3723			−0.650815
$255$	3.16915	−	3.37228i	0.198460	−	0.211180i
$256$	1.00000			0.0625000
$257$	−18.9051			−1.17927			−0.589633	−	0.807671i	$-0.700728\pi$
$257$	−18.9051			−1.17927			−0.589633	+	0.807671i	$0.700728\pi$
$258$	3.31662	+	3.11684i	0.206484	+	0.194046i
$259$	6.62772	−	21.1168i	0.411826	−	1.31214i
$260$	−3.37228	−	11.6819i	−0.209140	−	0.724482i
$261$	−7.11684	+	0.442430i	−0.440522	+	0.0273858i
$262$	−3.96143			−0.244738
$263$		−	7.22316i		−	0.445399i	−0.974887	−	0.222699i	$-0.928513\pi$
$263$		−	7.22316i		−	0.445399i	0.974887	−	0.222699i	$-0.0714869\pi$
$264$	7.25061	+	6.81386i	0.446244	+	0.419364i
$265$	−34.0511			−2.09174
$266$	6.00000	+	1.88316i	0.367884	+	0.115464i
$267$	−11.8614	+	12.6217i	−0.725906	+	0.772435i
$268$		−	5.98844i		−	0.365802i
$269$	14.5012			0.884155			0.442077	−	0.896977i	$-0.354242\pi$
$269$	14.5012			0.884155			0.442077	+	0.896977i	$0.354242\pi$
$270$	13.4891	+	11.1846i	0.820922	+	0.680673i
$271$	11.3321			0.688374			0.344187	−	0.938901i	$-0.388155\pi$
$271$	11.3321			0.688374			0.344187	+	0.938901i	$0.388155\pi$
$272$	0.792287			0.0480395
$273$	−11.7759	−	11.5900i	−0.712710	−	0.701459i
$274$	−18.1168			−1.09448
$275$	36.6060			2.20742
$276$	0.174928	−	0.186141i	0.0105294	−	0.0112044i
$277$	17.4891			1.05082			0.525410	−	0.850849i	$-0.323912\pi$
$277$	17.4891			1.05082			0.525410	+	0.850849i	$0.323912\pi$
$278$			5.25544i			0.315200i
$279$	0.764836	+	12.3030i	0.0457895	+	0.736560i
$280$	2.67181	−	8.51278i	0.159671	−	0.508736i
$281$	−14.0000			−0.835170			−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000			−0.835170			−0.417585	+	0.908638i	$0.637123\pi$
$282$	12.3030	−	13.0916i	0.732632	−	0.779592i
$283$			0.372281i			0.0221298i	0.999939	+	0.0110649i	$0.00352214\pi$
$283$			0.372281i			0.0221298i	−0.999939	+	0.0110649i	$0.996478\pi$
$284$	−2.00000			−0.118678
$285$	−9.50744	+	10.1168i	−0.563172	+	0.599270i
$286$	19.8997	−	5.74456i	1.17670	−	0.339683i
$287$	−6.63325	+	21.1345i	−0.391548	+	1.24753i
$288$	0.186141	+	2.99422i	0.0109684	+	0.176436i
$289$	−16.3723			−0.963075
$290$	−8.01544			−0.470683
$291$	−11.5584	−	10.8622i	−0.677567	−	0.636753i
$292$	10.2448			0.599533
$293$		−	11.4891i		−	0.671202i	−0.942004	−	0.335601i	$-0.891061\pi$
$293$		−	11.4891i		−	0.671202i	0.942004	−	0.335601i	$-0.108939\pi$
$294$	−2.50605	−	11.8625i	−0.146156	−	0.691837i
$295$	−9.25544			−0.538872
$296$			8.36530i			0.486223i
$297$	−19.0526	+	22.9783i	−1.10554	+	1.33333i
$298$	−7.62772			−0.441862
$299$	−0.147477	−	0.510875i	−0.00852880	−	0.0295446i
$300$	8.04290	+	7.55842i	0.464357	+	0.436386i
$301$	6.63325	+	2.08191i	0.382334	+	0.119999i
$302$			17.8178i			1.02530i
$303$	22.3030	+	20.9595i	1.28127	+	1.20409i
$304$	−2.37686			−0.136322
$305$	26.1168			1.49545
$306$	0.147477	+	2.37228i	0.00843069	+	0.135614i
$307$	−31.8766			−1.81930			−0.909648	−	0.415381i	$-0.863648\pi$
$307$	−31.8766			−1.81930			−0.909648	+	0.415381i	$0.863648\pi$
$308$	14.5012	+	4.55134i	0.826284	+	0.259337i
$309$	8.74456	−	9.30506i	0.497461	−	0.529347i
$310$			13.8564i			0.786991i
$311$	10.3923			0.589294			0.294647	−	0.955606i	$-0.404798\pi$
$311$	10.3923			0.589294			0.294647	+	0.955606i	$0.404798\pi$
$312$	5.55842	+	2.84674i	0.314684	+	0.161165i
$313$		−	2.74456i		−	0.155132i	−0.996987	−	0.0775659i	$-0.975285\pi$
$313$		−	2.74456i		−	0.155132i	0.996987	−	0.0775659i	$-0.0247148\pi$
$314$			8.25544i			0.465881i
$315$	25.9865	+	6.41543i	1.46417	+	0.361468i
$316$	−3.62772			−0.204075
$317$	−3.86141			−0.216878			−0.108439	−	0.994103i	$-0.534585\pi$
$317$	−3.86141			−0.216878			−0.108439	+	0.994103i	$0.534585\pi$
$318$	11.9769	−	12.7446i	0.671630	−	0.714680i
$319$		−	13.6540i		−	0.764479i
$320$			3.37228i			0.188516i
$321$	−20.1947	+	21.4891i	−1.12716	+	1.19941i
$322$	0.116844	−	0.372281i	0.00651146	−	0.0207464i
$323$	−1.88316			−0.104782
$324$	−8.93070	+	1.11469i	−0.496150	+	0.0619273i
$325$	22.0742	−	6.37228i	1.22446	−	0.353471i
$326$			8.21782i			0.455143i
$327$	−23.3639	+	24.8614i	−1.29202	+	1.37484i
$328$		−	8.37228i		−	0.462282i
$329$	8.21782	−	26.1831i	0.453063	−	1.44352i
$330$	−22.9783	+	24.4511i	−1.26491	+	1.34599i
$331$		−	17.0805i		−	0.938827i	−0.882979	−	0.469413i	$-0.844465\pi$
$331$		−	17.0805i		−	0.938827i	0.882979	−	0.469413i	$-0.155535\pi$
$332$			6.74456i			0.370156i
$333$	−25.0475	+	1.55712i	−1.37260	+	0.0853298i
$334$			12.6277i			0.690958i
$335$	20.1947			1.10335
$336$	2.24638	+	3.99422i	0.122550	+	0.217903i
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	11.0000	−	6.92820i	0.598321	−	0.376845i
$339$	6.75327	−	7.18614i	0.366788	−	0.390298i
$340$			2.67181i			0.144899i
$341$	−23.6039			−1.27822
$342$	−0.442430	−	7.11684i	−0.0239239	−	0.384835i
$343$	−11.3321	−	14.6487i	−0.611874	−	0.790955i
$344$	−2.62772			−0.141677
$345$	0.627719	+	0.589907i	0.0337952	+	0.0317595i
$346$	−10.6873			−0.574551
$347$			19.2000i			1.03071i	0.856976	+	0.515356i	$0.172340\pi$
$347$			19.2000i			1.03071i	−0.856976	+	0.515356i	$0.827660\pi$
$348$	2.81929	−	3.00000i	0.151130	−	0.160817i
$349$	16.4356			0.879780			0.439890	−	0.898052i	$-0.355017\pi$
$349$	16.4356			0.879780			0.439890	+	0.898052i	$0.355017\pi$
$350$	16.0858	+	5.04868i	0.859822	+	0.269863i
$351$	−7.48913	+	17.1730i	−0.399740	+	0.916629i
$352$	−5.74456			−0.306186
$353$		−	11.1168i		−	0.591690i	−0.955236	−	0.295845i	$-0.904399\pi$
$353$		−	11.1168i		−	0.591690i	0.955236	−	0.295845i	$-0.0956012\pi$
$354$	3.25544	−	3.46410i	0.173025	−	0.184115i
$355$		−	6.74456i		−	0.357964i
$356$		−	10.0000i		−	0.529999i
$357$	1.77978	+	3.16457i	0.0941957	+	0.167487i
$358$			20.1947i			1.06732i
$359$	6.23369			0.329001			0.164501	−	0.986377i	$-0.447399\pi$
$359$	6.23369			0.329001			0.164501	+	0.986377i	$0.447399\pi$
$360$	−10.0974	+	0.627719i	−0.532177	+	0.0330837i
$361$	−13.3505			−0.702660
$362$			20.3723i			1.07074i
$363$	−27.7677	−	26.0951i	−1.45743	−	1.36964i
$364$	9.53685	+	0.220225i	0.499867	+	0.0115429i
$365$			34.5484i			1.80835i
$366$	−9.18614	+	9.77495i	−0.480167	+	0.510945i
$367$			4.74456i			0.247664i	0.992303	+	0.123832i	$0.0395184\pi$
$367$			4.74456i			0.247664i	−0.992303	+	0.123832i	$0.960482\pi$
$368$			0.147477i			0.00768776i
$369$	25.0684	−	1.55842i	1.30501	−	0.0811282i
$370$	−28.2101			−1.46658
$371$	8.00000	−	25.4891i	0.415339	−	1.32333i
$372$	−5.18614	−	4.87375i	−0.268889	−	0.252692i
$373$	−12.2337			−0.633436			−0.316718	−	0.948520i	$-0.602581\pi$
$373$	−12.2337			−0.633436			−0.316718	+	0.948520i	$0.602581\pi$
$374$	−4.55134			−0.235344
$375$	−5.48913	+	5.84096i	−0.283457	+	0.301626i
$376$			10.3723i			0.534910i
$377$	−2.37686	−	8.23369i	−0.122415	−	0.424057i
$378$	−11.5414	+	7.46963i	−0.593627	+	0.384196i
$379$		−	18.3152i		−	0.940787i	−0.882457	−	0.470394i	$-0.844112\pi$
$379$		−	18.3152i		−	0.940787i	0.882457	−	0.470394i	$-0.155888\pi$
$380$		−	8.01544i		−	0.411184i
$381$	13.0916	+	12.3030i	0.670701	+	0.630301i
$382$			2.96677i			0.151793i
$383$			3.51087i			0.179397i	0.995969	+	0.0896987i	$0.0285904\pi$
$383$			3.51087i			0.179397i	−0.995969	+	0.0896987i	$0.971410\pi$
$384$	−1.26217	−	1.18614i	−0.0644098	−	0.0605300i
$385$	−15.3484	+	48.9022i	−0.782227	+	2.49229i
$386$			20.7846i			1.05791i
$387$	−0.489125	−	7.86797i	−0.0248636	−	0.399951i
$388$	9.15759			0.464906
$389$		−	25.2434i		−	1.27989i	−0.768421	−	0.639945i	$-0.778957\pi$
$389$		−	25.2434i		−	1.27989i	0.768421	−	0.639945i	$-0.221043\pi$
$390$	−9.60002	+	18.7446i	−0.486116	+	0.949168i
$391$			0.116844i			0.00590905i
$392$	5.74456	+	4.00000i	0.290144	+	0.202031i
$393$	5.00000	+	4.69882i	0.252217	+	0.237024i
$394$	21.1168			1.06385
$395$		−	12.2337i		−	0.615544i
$396$	−1.06930	−	17.2005i	−0.0537342	−	0.864357i
$397$	6.63325			0.332913			0.166457	−	0.986049i	$-0.446767\pi$
$397$	6.63325			0.332913			0.166457	+	0.986049i	$0.446767\pi$
$398$		−	12.1168i		−	0.607363i
$399$	−5.33933	−	9.49370i	−0.267301	−	0.475280i
$400$	−6.37228			−0.318614
$401$	28.9783			1.44710			0.723552	−	0.690269i	$-0.242508\pi$
$401$	28.9783			1.44710			0.723552	+	0.690269i	$0.242508\pi$
$402$	−7.10313	+	7.55842i	−0.354272	+	0.376980i
$403$	−14.2337	+	4.10891i	−0.709030	+	0.204679i
$404$	−17.6704			−0.879133
$405$	−3.75906	−	30.1168i	−0.186789	−	1.49652i
$406$	1.88316	−	6.00000i	0.0934595	−	0.297775i
$407$		−	48.0550i		−	2.38200i
$408$	−1.00000	−	0.939764i	−0.0495074	−	0.0465252i
$409$	29.7947			1.47325			0.736627	−	0.676299i	$-0.236417\pi$
$409$	29.7947			1.47325			0.736627	+	0.676299i	$0.236417\pi$
$410$	28.2337			1.39436
$411$	22.8665	+	21.4891i	1.12792	+	1.05998i
$412$			7.37228i			0.363206i
$413$	2.17448	−	6.92820i	0.106999	−	0.340915i
$414$	−0.441578	+	0.0274514i	−0.0217024	+	0.00134916i
$415$	−22.7446			−1.11649
$416$	−3.46410	+	1.00000i	−0.169842	+	0.0490290i
$417$	6.23369	−	6.63325i	0.305265	−	0.324832i
$418$	13.6540			0.667840
$419$	4.90120			0.239439			0.119720	−	0.992808i	$-0.461800\pi$
$419$	4.90120			0.239439			0.119720	+	0.992808i	$0.461800\pi$
$420$	−13.4696	+	7.57541i	−0.657251	+	0.369642i
$421$			23.0140i			1.12163i	0.827940	+	0.560817i	$0.189513\pi$
$421$			23.0140i			1.12163i	−0.827940	+	0.560817i	$0.810487\pi$
$422$	17.3723			0.845669
$423$	−31.0569	+	1.93070i	−1.51004	+	0.0938740i
$424$			10.0974i			0.490371i
$425$	−5.04868			−0.244897
$426$	2.52434	+	2.37228i	0.122305	+	0.114937i
$427$	−6.13592	+	19.5499i	−0.296938	+	0.946086i
$428$		−	17.0256i		−	0.822961i
$429$	−31.9307	−	16.3533i	−1.54163	−	0.789544i
$430$		−	8.86141i		−	0.427335i
$431$	−28.2337			−1.35997			−0.679984	−	0.733227i	$-0.738013\pi$
$431$	−28.2337			−1.35997			−0.679984	+	0.733227i	$0.738013\pi$
$432$	3.31662	−	4.00000i	0.159571	−	0.192450i
$433$			30.4674i			1.46417i	0.681214	+	0.732084i	$0.261452\pi$
$433$			30.4674i			1.46417i	−0.681214	+	0.732084i	$0.738548\pi$
$434$	−10.3723	−	3.25544i	−0.497885	−	0.156266i
$435$	10.1168	+	9.50744i	0.485066	+	0.455847i
$436$		−	19.6974i		−	0.943333i
$437$		−	0.350532i		−	0.0167682i
$438$	−12.9307	−	12.1518i	−0.617853	−	0.580636i
$439$			5.60597i			0.267558i	0.991011	+	0.133779i	$0.0427113\pi$
$439$			5.60597i			0.267558i	−0.991011	+	0.133779i	$0.957289\pi$
$440$		−	19.3723i		−	0.923537i
$441$	−10.9076	+	17.9450i	−0.519409	+	0.854526i
$442$	−2.74456	+	0.792287i	−0.130546	+	0.0376852i
$443$			16.7306i			0.794895i	0.917625	+	0.397447i	$0.130104\pi$
$443$			16.7306i			0.794895i	−0.917625	+	0.397447i	$0.869896\pi$
$444$	9.92242	−	10.5584i	0.470897	−	0.501081i
$445$	33.7228			1.59861
$446$	0.644810			0.0305326
$447$	9.62747	+	9.04755i	0.455364	+	0.427934i
$448$	−2.52434	−	0.792287i	−0.119264	−	0.0374320i
$449$	14.1168			0.666215			0.333108	−	0.942889i	$-0.391903\pi$
$449$	14.1168			0.666215			0.333108	+	0.942889i	$0.391903\pi$
$450$	−1.18614	−	19.0800i	−0.0559152	−	0.899440i
$451$			48.0951i			2.26471i
$452$			5.69349i			0.267799i
$453$	21.1345	−	22.4891i	0.992984	−	1.05663i
$454$			11.4891i			0.539211i
$455$	−0.742660	+	32.1609i	−0.0348164	+	1.50773i
$456$	3.00000	+	2.81929i	0.140488	+	0.132025i
$457$		−	23.6588i		−	1.10671i	−0.832945	−	0.553356i	$-0.813347\pi$
$457$		−	23.6588i		−	1.10671i	0.832945	−	0.553356i	$-0.186653\pi$
$458$	−5.04868			−0.235909
$459$	2.62772	−	3.16915i	0.122651	−	0.147923i
$460$	−0.497333			−0.0231883
$461$			21.6060i			1.00629i	0.864202	+	0.503145i	$0.167824\pi$
$461$			21.6060i			1.00629i	−0.864202	+	0.503145i	$0.832176\pi$
$462$	−12.9045	−	22.9450i	−0.600369	−	1.06750i
$463$		−	31.6742i		−	1.47203i	−0.676967	−	0.736014i	$-0.736706\pi$
$463$		−	31.6742i		−	1.47203i	0.676967	−	0.736014i	$-0.263294\pi$
$464$			2.37686i			0.110343i
$465$	16.4356	−	17.4891i	0.762185	−	0.811039i
$466$		−	10.7422i		−	0.497621i
$467$	−21.5769			−0.998460			−0.499230	−	0.866470i	$-0.666384\pi$
$467$	−21.5769			−0.998460			−0.499230	+	0.866470i	$0.666384\pi$
$468$	−3.63903	−	10.1861i	−0.168214	−	0.470855i
$469$	−4.74456	+	15.1168i	−0.219084	+	0.698031i
$470$	−34.9783			−1.61343
$471$	9.79211	−	10.4198i	0.451197	−	0.480117i
$472$			2.74456i			0.126329i
$473$	15.0951			0.694073
$474$	4.57879	+	4.30298i	0.210311	+	0.197643i
$475$	15.1460			0.694947
$476$	−2.00000	−	0.627719i	−0.0916698	−	0.0287714i
$477$	−30.2337	+	1.87953i	−1.38431	+	0.0860577i
$478$	18.0000			0.823301
$479$		−	28.6277i		−	1.30803i	−0.756480	−	0.654017i	$-0.773082\pi$
$479$		−	28.6277i		−	1.30803i	0.756480	−	0.654017i	$-0.226918\pi$
$480$	4.00000	−	4.25639i	0.182574	−	0.194277i
$481$	−8.36530	−	28.9783i	−0.381425	−	1.32129i
$482$	−16.4356			−0.748623
$483$	−0.589055	+	0.331289i	−0.0268029	+	0.0150741i
$484$	22.0000			1.00000
$485$			30.8820i			1.40228i
$486$	12.5942	+	9.18614i	0.571286	+	0.416692i
$487$			37.5152i			1.69998i	0.526802	+	0.849988i	$0.323391\pi$
$487$			37.5152i			1.69998i	−0.526802	+	0.849988i	$0.676609\pi$
$488$		−	7.74456i		−	0.350580i
$489$	9.74749	−	10.3723i	0.440797	−	0.469051i
$490$	−13.4891	+	19.3723i	−0.609377	+	0.875150i
$491$			11.6819i			0.527198i	0.964632	+	0.263599i	$0.0849095\pi$
$491$			11.6819i			0.527198i	−0.964632	+	0.263599i	$0.915090\pi$
$492$	−9.93070	+	10.5672i	−0.447711	+	0.476408i
$493$			1.88316i			0.0848131i
$494$	8.23369	−	2.37686i	0.370451	−	0.106940i
$495$	58.0049	−	3.60597i	2.60712	−	0.162076i
$496$	4.10891			0.184496
$497$	5.04868	+	1.58457i	0.226464	+	0.0710779i
$498$	8.00000	−	8.51278i	0.358489	−	0.381467i
$499$		−	10.4472i		−	0.467681i	−0.972275	−	0.233841i	$-0.924871\pi$
$499$		−	10.4472i		−	0.467681i	0.972275	−	0.233841i	$-0.0751294\pi$
$500$		−	4.62772i		−	0.206958i
$501$	14.9783	−	15.9383i	0.669179	−	0.712071i
$502$	−6.78073			−0.302639
$503$	27.4179			1.22250			0.611251	−	0.791437i	$-0.290667\pi$
$503$	27.4179			1.22250			0.611251	+	0.791437i	$0.290667\pi$
$504$	1.90240	−	7.70590i	0.0847396	−	0.343248i
$505$		−	59.5894i		−	2.65170i
$506$		−	0.847190i		−	0.0376622i
$507$	−22.1017	−	4.30298i	−0.981570	−	0.191102i
$508$	−10.3723			−0.460196
$509$		−	22.1168i		−	0.980312i	−0.871635	−	0.490156i	$-0.836940\pi$
$509$		−	22.1168i		−	0.980312i	0.871635	−	0.490156i	$-0.163060\pi$
$510$	3.16915	−	3.37228i	0.140332	−	0.149327i
$511$	−25.8614	−	8.11684i	−1.14404	−	0.359068i
$512$	1.00000			0.0441942
$513$	−7.88316	+	9.50744i	−0.348050	+	0.419764i
$514$	−18.9051			−0.833867
$515$	−24.8614			−1.09552
$516$	3.31662	+	3.11684i	0.146006	+	0.137211i
$517$		−	59.5842i		−	2.62051i
$518$	6.62772	−	21.1168i	0.291205	−	0.927821i
$519$	13.4891	+	12.6766i	0.592107	+	0.556441i
$520$	−3.37228	−	11.6819i	−0.147884	−	0.512286i
$521$	−20.3971			−0.893612			−0.446806	−	0.894631i	$-0.647439\pi$
$521$	−20.3971			−0.893612			−0.446806	+	0.894631i	$0.647439\pi$
$522$	−7.11684	+	0.442430i	−0.311496	+	0.0193647i
$523$			37.3505i			1.63322i	0.577186	+	0.816612i	$0.304151\pi$
$523$			37.3505i			1.63322i	−0.577186	+	0.816612i	$0.695849\pi$
$524$	−3.96143			−0.173056
$525$	−14.3145	−	25.4523i	−0.624738	−	1.11083i
$526$		−	7.22316i		−	0.314945i
$527$	3.25544			0.141809
$528$	7.25061	+	6.81386i	0.315542	+	0.296535i
$529$	22.9783			0.999054
$530$	−34.0511			−1.47909
$531$	−8.21782	+	0.510875i	−0.356623	+	0.0221701i
$532$	6.00000	+	1.88316i	0.260133	+	0.0816452i
$533$	8.37228	+	29.0024i	0.362644	+	1.25623i
$534$	−11.8614	+	12.6217i	−0.513293	+	0.546194i
$535$	57.4150			2.48227
$536$		−	5.98844i		−	0.258661i
$537$	23.9538	−	25.4891i	1.03368	−	1.09994i
$538$	14.5012			0.625192
$539$	−33.0000	−	22.9783i	−1.42141	−	0.989743i
$540$	13.4891	+	11.1846i	0.580480	+	0.481308i
$541$			24.4511i			1.05123i	0.850721	+	0.525617i	$0.176166\pi$
$541$			24.4511i			1.05123i	−0.850721	+	0.525617i	$0.823834\pi$
$542$	11.3321			0.486754
$543$	24.1644	−	25.7133i	1.03699	−	1.10346i
$544$	0.792287			0.0339690
$545$	66.4251			2.84534
$546$	−11.7759	−	11.5900i	−0.503962	−	0.496006i
$547$	−5.48913			−0.234698			−0.117349	−	0.993091i	$-0.537440\pi$
$547$	−5.48913			−0.234698			−0.117349	+	0.993091i	$0.537440\pi$
$548$	−18.1168			−0.773913
$549$	23.1889	−	1.44158i	0.989679	−	0.0615251i
$550$	36.6060			1.56088
$551$		−	5.64947i		−	0.240675i
$552$	0.174928	−	0.186141i	0.00744544	−	0.00792267i
$553$	9.15759	+	2.87419i	0.389420	+	0.122223i
$554$	17.4891			0.743042
$555$	35.6060	+	33.4612i	1.51139	+	1.42035i
$556$			5.25544i			0.222880i
$557$	30.3723			1.28691			0.643457	−	0.765482i	$-0.277499\pi$
$557$	30.3723			1.28691			0.643457	+	0.765482i	$0.277499\pi$
$558$	0.764836	+	12.3030i	0.0323781	+	0.520827i
$559$	9.10268	−	2.62772i	0.385003	−	0.111141i
$560$	2.67181	−	8.51278i	0.112905	−	0.359730i
$561$	5.74456	+	5.39853i	0.242536	+	0.227926i
$562$	−14.0000			−0.590554
$563$	−9.25016			−0.389848			−0.194924	−	0.980818i	$-0.562446\pi$
$563$	−9.25016			−0.389848			−0.194924	+	0.980818i	$0.562446\pi$
$564$	12.3030	−	13.0916i	0.518049	−	0.551255i
$565$	−19.2000			−0.807752
$566$			0.372281i			0.0156482i
$567$	23.4273	+	4.26182i	0.983853	+	0.178980i
$568$	−2.00000			−0.0839181
$569$			10.1523i			0.425605i	0.977095	+	0.212802i	$0.0682590\pi$
$569$			10.1523i			0.425605i	−0.977095	+	0.212802i	$0.931741\pi$
$570$	−9.50744	+	10.1168i	−0.398223	+	0.423748i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$	19.8997	−	5.74456i	0.832050	−	0.240192i
$573$	3.51900	−	3.74456i	0.147009	−	0.156431i
$574$	−6.63325	+	21.1345i	−0.276866	+	0.882136i
$575$		−	0.939764i		−	0.0391909i
$576$	0.186141	+	2.99422i	0.00775586	+	0.124759i
$577$	6.92820			0.288425			0.144212	−	0.989547i	$-0.453935\pi$
$577$	6.92820			0.288425			0.144212	+	0.989547i	$0.453935\pi$
$578$	−16.3723			−0.680997
$579$	24.6535	−	26.2337i	1.02456	−	1.09023i
$580$	−8.01544			−0.332823
$581$	5.34363	−	17.0256i	0.221691	−	0.706339i
$582$	−11.5584	−	10.8622i	−0.479112	−	0.450252i
$583$		−	58.0049i		−	2.40232i
$584$	10.2448			0.423934
$585$	34.3505	−	12.2718i	1.42022	−	0.507378i
$586$		−	11.4891i		−	0.474611i
$587$			16.7446i			0.691122i	0.938396	+	0.345561i	$0.112311\pi$
$587$			16.7446i			0.691122i	−0.938396	+	0.345561i	$0.887689\pi$
$588$	−2.50605	−	11.8625i	−0.103348	−	0.489203i
$589$	−9.76631			−0.402414
$590$	−9.25544			−0.381040
$591$	−26.6530	−	25.0475i	−1.09636	−	1.03032i
$592$			8.36530i			0.343812i
$593$		−	19.2554i		−	0.790726i	−0.918525	−	0.395363i	$-0.870619\pi$
$593$		−	19.2554i		−	0.790726i	0.918525	−	0.395363i	$-0.129381\pi$
$594$	−19.0526	+	22.9783i	−0.781736	+	0.942809i
$595$	2.11684	−	6.74456i	0.0867821	−	0.276500i
$596$	−7.62772			−0.312444
$597$	−14.3723	+	15.2935i	−0.588218	+	0.625921i
$598$	−0.147477	−	0.510875i	−0.00603078	−	0.0208912i
$599$		−	11.8294i		−	0.483336i	−0.970359	−	0.241668i	$-0.922305\pi$
$599$		−	11.8294i		−	0.483336i	0.970359	−	0.241668i	$-0.0776945\pi$
$600$	8.04290	+	7.55842i	0.328350	+	0.308571i
$601$			26.0000i			1.06056i	0.847822	+	0.530281i	$0.177914\pi$
$601$			26.0000i			1.06056i	−0.847822	+	0.530281i	$0.822086\pi$
$602$	6.63325	+	2.08191i	0.270351	+	0.0848522i
$603$	17.9307	−	1.11469i	0.730195	−	0.0453938i
$604$			17.8178i			0.724998i
$605$			74.1902i			3.01626i
$606$	22.3030	+	20.9595i	0.905997	+	0.851423i
$607$		−	18.1168i		−	0.735340i	−0.929956	−	0.367670i	$-0.880156\pi$
$607$		−	18.1168i		−	0.735340i	0.929956	−	0.367670i	$-0.119844\pi$
$608$	−2.37686			−0.0963944
$609$	−9.49370	+	5.33933i	−0.384704	+	0.216360i
$610$	26.1168			1.05744
$611$	−10.3723	−	35.9306i	−0.419618	−	1.45360i
$612$	0.147477	+	2.37228i	0.00596140	+	0.0958938i
$613$			16.8781i			0.681699i	0.940118	+	0.340850i	$0.110715\pi$
$613$			16.8781i			0.681699i	−0.940118	+	0.340850i	$0.889285\pi$
$614$	−31.8766			−1.28644
$615$	−35.6357	−	33.4891i	−1.43697	−	1.35041i
$616$	14.5012	+	4.55134i	0.584271	+	0.183379i
$617$	−17.6060			−0.708790			−0.354395	−	0.935096i	$-0.615313\pi$
$617$	−17.6060			−0.708790			−0.354395	+	0.935096i	$0.615313\pi$
$618$	8.74456	−	9.30506i	0.351758	−	0.374305i
$619$	13.0641			0.525091			0.262546	−	0.964920i	$-0.415438\pi$
$619$	13.0641			0.525091			0.262546	+	0.964920i	$0.415438\pi$
$620$			13.8564i			0.556487i
$621$	0.589907	+	0.489125i	0.0236722	+	0.0196279i
$622$	10.3923			0.416693
$623$	−7.92287	+	25.2434i	−0.317423	+	1.01135i
$624$	5.55842	+	2.84674i	0.222515	+	0.113961i
$625$	−16.2554			−0.650217
$626$		−	2.74456i		−	0.109695i
$627$	−17.2337	−	16.1956i	−0.688247	−	0.646790i
$628$			8.25544i			0.329428i
$629$			6.62772i			0.264264i
$630$	25.9865	+	6.41543i	1.03533	+	0.255597i
$631$		−	12.1793i		−	0.484849i	−0.970170	−	0.242424i	$-0.922057\pi$
$631$		−	12.1793i		−	0.484849i	0.970170	−	0.242424i	$-0.0779426\pi$
$632$	−3.62772			−0.144303
$633$	−21.9268	−	20.6060i	−0.871510	−	0.819014i
$634$	−3.86141			−0.153356
$635$		−	34.9783i		−	1.38807i
$636$	11.9769	−	12.7446i	0.474914	−	0.505355i
$637$	−23.8997	−	8.11184i	−0.946943	−	0.321403i
$638$		−	13.6540i		−	0.540568i
$639$	−0.372281	−	5.98844i	−0.0147272	−	0.236899i
$640$			3.37228i			0.133301i
$641$		−	8.86263i		−	0.350053i	−0.984564	−	0.175026i	$-0.943999\pi$
$641$		−	8.86263i		−	0.350053i	0.984564	−	0.175026i	$-0.0560011\pi$
$642$	−20.1947	+	21.4891i	−0.797021	+	0.848108i
$643$	18.4077			0.725931			0.362965	−	0.931803i	$-0.381764\pi$
$643$	18.4077			0.725931			0.362965	+	0.931803i	$0.381764\pi$
$644$	0.116844	−	0.372281i	0.00460430	−	0.0146699i
$645$	−10.5109	+	11.1846i	−0.413865	+	0.440393i
$646$	−1.88316			−0.0740918
$647$	26.1282			1.02721			0.513604	−	0.858028i	$-0.328310\pi$
$647$	26.1282			1.02721			0.513604	+	0.858028i	$0.328310\pi$
$648$	−8.93070	+	1.11469i	−0.350831	+	0.0437892i
$649$		−	15.7663i		−	0.618882i
$650$	22.0742	−	6.37228i	0.865823	−	0.249941i
$651$	9.23016	+	16.4119i	0.361759	+	0.643233i
$652$			8.21782i			0.321835i
$653$		−	14.6487i		−	0.573248i	−0.958043	−	0.286624i	$-0.907467\pi$
$653$		−	14.6487i		−	0.573248i	0.958043	−	0.286624i	$-0.0925330\pi$
$654$	−23.3639	+	24.8614i	−0.913599	+	0.972158i
$655$		−	13.3591i		−	0.521982i
$656$		−	8.37228i		−	0.326883i
$657$	1.90698	+	30.6753i	0.0743983	+	1.19676i
$658$	8.21782	−	26.1831i	0.320364	−	1.02073i
$659$		−	37.9200i		−	1.47715i	−0.674170	−	0.738576i	$-0.735499\pi$
$659$		−	37.9200i		−	1.47715i	0.674170	−	0.738576i	$-0.264501\pi$
$660$	−22.9783	+	24.4511i	−0.894427	+	0.951757i
$661$	−42.2689			−1.64407			−0.822035	−	0.569436i	$-0.807162\pi$
$661$	−42.2689			−1.64407			−0.822035	+	0.569436i	$0.807162\pi$
$662$		−	17.0805i		−	0.663851i
$663$	4.40387	+	2.25544i	0.171032	+	0.0875939i
$664$			6.74456i			0.261740i
$665$	−6.35053	+	20.2337i	−0.246263	+	0.784629i
$666$	−25.0475	+	1.55712i	−0.970573	+	0.0603373i
$667$	−0.350532			−0.0135726
$668$			12.6277i			0.488581i
$669$	−0.813859	−	0.764836i	−0.0314656	−	0.0295703i
$670$	20.1947			0.780189
$671$			44.4891i			1.71748i
$672$	2.24638	+	3.99422i	0.0866559	+	0.154080i
$673$	−45.2337			−1.74363			−0.871815	−	0.489835i	$-0.837057\pi$
$673$	−45.2337			−1.74363			−0.871815	+	0.489835i	$0.837057\pi$
$674$	5.00000			0.192593
$675$	−21.1345	+	25.4891i	−0.813466	+	0.981077i
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	20.5446			0.789592			0.394796	−	0.918769i	$-0.370815\pi$
$677$	20.5446			0.789592			0.394796	+	0.918769i	$0.370815\pi$
$678$	6.75327	−	7.18614i	0.259358	−	0.275982i
$679$	−23.1168	−	7.25544i	−0.887143	−	0.278438i
$680$			2.67181i			0.102459i
$681$	13.6277	−	14.5012i	0.522215	−	0.555688i
$682$	−23.6039			−0.903840
$683$	−19.0000			−0.727015			−0.363507	−	0.931591i	$-0.618421\pi$
$683$	−19.0000			−0.727015			−0.363507	+	0.931591i	$0.618421\pi$
$684$	−0.442430	−	7.11684i	−0.0169168	−	0.272119i
$685$		−	61.0951i		−	2.33432i
$686$	−11.3321	−	14.6487i	−0.432660	−	0.559290i
$687$	6.37228	+	5.98844i	0.243118	+	0.228473i
$688$	−2.62772			−0.100181
$689$	−10.0974	−	34.9783i	−0.384678	−	1.33257i
$690$	0.627719	+	0.589907i	0.0238968	+	0.0224574i
$691$	−31.1769			−1.18603			−0.593013	−	0.805193i	$-0.702062\pi$
$691$	−31.1769			−1.18603			−0.593013	+	0.805193i	$0.702062\pi$
$692$	−10.6873			−0.406269
$693$	−10.9285	+	44.2670i	−0.415138	+	1.68156i
$694$			19.2000i			0.728823i
$695$	−17.7228			−0.672265
$696$	2.81929	−	3.00000i	0.106865	−	0.113715i
$697$		−	6.63325i		−	0.251252i
$698$	16.4356			0.622098
$699$	−12.7417	+	13.5584i	−0.481936	+	0.512827i
$700$	16.0858	+	5.04868i	0.607986	+	0.190822i
$701$		−	13.2665i		−	0.501069i	−0.968108	−	0.250534i	$-0.919394\pi$
$701$		−	13.2665i		−	0.501069i	0.968108	−	0.250534i	$-0.0806063\pi$
$702$	−7.48913	+	17.1730i	−0.282659	+	0.648154i
$703$		−	19.8832i		−	0.749907i
$704$	−5.74456			−0.216506
$705$	44.1485	+	41.4891i	1.66273	+	1.56257i
$706$		−	11.1168i		−	0.418388i
$707$	44.6060	+	14.0000i	1.67758	+	0.526524i
$708$	3.25544	−	3.46410i	0.122347	−	0.130189i
$709$			33.7013i			1.26568i	0.774284	+	0.632839i	$0.218110\pi$
$709$			33.7013i			1.26568i	−0.774284	+	0.632839i	$0.781890\pi$
$710$		−	6.74456i		−	0.253119i
$711$	−0.675266	−	10.8622i	−0.0253245	−	0.407364i
$712$		−	10.0000i		−	0.374766i
$713$			0.605969i			0.0226937i
$714$	1.77978	+	3.16457i	0.0666064	+	0.118431i
$715$	19.3723	+	67.1076i	0.724482	+	2.50968i
$716$			20.1947i			0.754711i
$717$	−22.7190	−	21.3505i	−0.848458	−	0.797350i
$718$	6.23369			0.232639
$719$	16.4356			0.612946			0.306473	−	0.951879i	$-0.400851\pi$
$719$	16.4356			0.612946			0.306473	+	0.951879i	$0.400851\pi$
$720$	−10.0974	+	0.627719i	−0.376306	+	0.0233937i
$721$	5.84096	−	18.6101i	0.217529	−	0.693077i
$722$	−13.3505			−0.496855
$723$	20.7446	+	19.4950i	0.771499	+	0.725026i
$724$			20.3723i			0.757130i
$725$		−	15.1460i		−	0.562509i
$726$	−27.7677	−	26.0951i	−1.03056	−	0.968480i
$727$		−	1.13859i		−	0.0422281i	−0.999777	−	0.0211140i	$-0.993279\pi$
$727$		−	1.13859i		−	0.0422281i	0.999777	−	0.0211140i	$-0.00672131\pi$
$728$	9.53685	+	0.220225i	0.353459	+	0.00816208i
$729$	−5.00000	−	26.5330i	−0.185185	−	0.982704i
$730$			34.5484i			1.27870i
$731$	−2.08191			−0.0770021
$732$	−9.18614	+	9.77495i	−0.339530	+	0.361292i
$733$	−18.6101			−0.687381			−0.343690	−	0.939083i	$-0.611677\pi$
$733$	−18.6101			−0.687381			−0.343690	+	0.939083i	$0.611677\pi$
$734$			4.74456i			0.175125i
$735$	40.0038	−	8.45109i	1.47556	−	0.311723i
$736$			0.147477i			0.00543607i
$737$			34.4010i			1.26718i
$738$	25.0684	−	1.55842i	0.922782	−	0.0573663i
$739$			44.8482i			1.64977i	0.565303	+	0.824883i	$0.308759\pi$
$739$			44.8482i			1.64977i	−0.565303	+	0.824883i	$0.691241\pi$
$740$	−28.2101			−1.03703
$741$	−13.2116	−	6.76631i	−0.485340	−	0.248567i
$742$	8.00000	−	25.4891i	0.293689	−	0.935735i
$743$	0.978251			0.0358885			0.0179443	−	0.999839i	$-0.494288\pi$
$743$	0.978251			0.0358885			0.0179443	+	0.999839i	$0.494288\pi$
$744$	−5.18614	−	4.87375i	−0.190133	−	0.178680i
$745$		−	25.7228i		−	0.942411i
$746$	−12.2337			−0.447907
$747$	−20.1947	+	1.25544i	−0.738886	+	0.0459341i
$748$	−4.55134			−0.166414
$749$	−13.4891	+	42.9783i	−0.492882	+	1.57039i
$750$	−5.48913	+	5.84096i	−0.200435	+	0.213282i
$751$	18.6060			0.678941			0.339471	−	0.940617i	$-0.389752\pi$
$751$	18.6060			0.678941			0.339471	+	0.940617i	$0.389752\pi$
$752$			10.3723i			0.378238i
$753$	8.55842	+	8.04290i	0.311886	+	0.293099i
$754$	−2.37686	−	8.23369i	−0.0865602	−	0.299853i
$755$	−60.0868			−2.18678
$756$	−11.5414	+	7.46963i	−0.419758	+	0.271668i
$757$	50.4674			1.83427			0.917134	−	0.398579i	$-0.130497\pi$
$757$	50.4674			1.83427			0.917134	+	0.398579i	$0.130497\pi$
$758$		−	18.3152i		−	0.665237i
$759$	−1.00489	+	1.06930i	−0.0364751	+	0.0388130i
$760$		−	8.01544i		−	0.290751i
$761$			2.13859i			0.0775239i	0.999248	+	0.0387620i	$0.0123414\pi$
$761$			2.13859i			0.0775239i	−0.999248	+	0.0387620i	$0.987659\pi$
$762$	13.0916	+	12.3030i	0.474258	+	0.445690i
$763$	−15.6060	+	49.7228i	−0.564974	+	1.80009i
$764$			2.96677i			0.107334i
$765$	−8.00000	+	0.497333i	−0.289241	+	0.0179811i
$766$			3.51087i			0.126853i
$767$	−2.74456	−	9.50744i	−0.0991004	−	0.343294i
$768$	−1.26217	−	1.18614i	−0.0455446	−	0.0428012i
$769$	34.1986			1.23323			0.616616	−	0.787264i	$-0.288503\pi$
$769$	34.1986			1.23323			0.616616	+	0.787264i	$0.288503\pi$
$770$	−15.3484	+	48.9022i	−0.553118	+	1.76231i
$771$	23.8614	+	22.4241i	0.859348	+	0.807584i
$772$			20.7846i			0.748054i
$773$			18.8614i			0.678398i	0.940715	+	0.339199i	$0.110156\pi$
$773$			18.8614i			0.678398i	−0.940715	+	0.339199i	$0.889844\pi$
$774$	−0.489125	−	7.86797i	−0.0175812	−	0.282808i
$775$	−26.1831			−0.940526
$776$	9.15759			0.328738
$777$	−33.4128	+	18.7916i	−1.19868	+	0.674146i
$778$		−	25.2434i		−	0.905019i
$779$			19.8997i			0.712982i
$780$	−9.60002	+	18.7446i	−0.343736

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.26217 - 1.18614i) q^{3} +1.00000 q^{4} +3.37228i q^{5} +(-1.26217 - 1.18614i) q^{6} +(-2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.26217 - 1.18614i) q^{3} +1.00000 q^{4} +3.37228i q^{5} +(-1.26217 - 1.18614i) q^{6} +(-2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} +3.37228i q^{10} -5.74456 q^{11} +(-1.26217 - 1.18614i) q^{12} +(-3.46410 + 1.00000i) q^{13} +(-2.52434 - 0.792287i) q^{14} +(4.00000 - 4.25639i) q^{15} +1.00000 q^{16} +0.792287 q^{17} +(0.186141 + 2.99422i) q^{18} -2.37686 q^{19} +3.37228i q^{20} +(2.24638 + 3.99422i) q^{21} -5.74456 q^{22} +0.147477i q^{23} +(-1.26217 - 1.18614i) q^{24} -6.37228 q^{25} +(-3.46410 + 1.00000i) q^{26} +(3.31662 - 4.00000i) q^{27} +(-2.52434 - 0.792287i) q^{28} +2.37686i q^{29} +(4.00000 - 4.25639i) q^{30} +4.10891 q^{31} +1.00000 q^{32} +(7.25061 + 6.81386i) q^{33} +0.792287 q^{34} +(2.67181 - 8.51278i) q^{35} +(0.186141 + 2.99422i) q^{36} +8.36530i q^{37} -2.37686 q^{38} +(5.55842 + 2.84674i) q^{39} +3.37228i q^{40} -8.37228i q^{41} +(2.24638 + 3.99422i) q^{42} -2.62772 q^{43} -5.74456 q^{44} +(-10.0974 + 0.627719i) q^{45} +0.147477i q^{46} +10.3723i q^{47} +(-1.26217 - 1.18614i) q^{48} +(5.74456 + 4.00000i) q^{49} -6.37228 q^{50} +(-1.00000 - 0.939764i) q^{51} +(-3.46410 + 1.00000i) q^{52} +10.0974i q^{53} +(3.31662 - 4.00000i) q^{54} -19.3723i q^{55} +(-2.52434 - 0.792287i) q^{56} +(3.00000 + 2.81929i) q^{57} +2.37686i q^{58} +2.74456i q^{59} +(4.00000 - 4.25639i) q^{60} -7.74456i q^{61} +4.10891 q^{62} +(1.90240 - 7.70590i) q^{63} +1.00000 q^{64} +(-3.37228 - 11.6819i) q^{65} +(7.25061 + 6.81386i) q^{66} -5.98844i q^{67} +0.792287 q^{68} +(0.174928 - 0.186141i) q^{69} +(2.67181 - 8.51278i) q^{70} -2.00000 q^{71} +(0.186141 + 2.99422i) q^{72} +10.2448 q^{73} +8.36530i q^{74} +(8.04290 + 7.55842i) q^{75} -2.37686 q^{76} +(14.5012 + 4.55134i) q^{77} +(5.55842 + 2.84674i) q^{78} -3.62772 q^{79} +3.37228i q^{80} +(-8.93070 + 1.11469i) q^{81} -8.37228i q^{82} +6.74456i q^{83} +(2.24638 + 3.99422i) q^{84} +2.67181i q^{85} -2.62772 q^{86} +(2.81929 - 3.00000i) q^{87} -5.74456 q^{88} -10.0000i q^{89} +(-10.0974 + 0.627719i) q^{90} +(9.53685 + 0.220225i) q^{91} +0.147477i q^{92} +(-5.18614 - 4.87375i) q^{93} +10.3723i q^{94} -8.01544i q^{95} +(-1.26217 - 1.18614i) q^{96} +9.15759 q^{97} +(5.74456 + 4.00000i) q^{98} +(-1.06930 - 17.2005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9} + 32 q^{15} + 8 q^{16} - 10 q^{18} + 14 q^{21} - 28 q^{25} + 32 q^{30} + 8 q^{32} - 10 q^{36} + 10 q^{39} + 14 q^{42} - 44 q^{43} - 28 q^{50} - 8 q^{51} + 24 q^{57} + 32 q^{60} - 4 q^{63} + 8 q^{64} - 4 q^{65} - 16 q^{71} - 10 q^{72} + 10 q^{78} - 52 q^{79} - 14 q^{81} + 14 q^{84} - 44 q^{86} + 24 q^{91} - 30 q^{93} - 66 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9 + 32 * q^15 + 8 * q^16 - 10 * q^18 + 14 * q^21 - 28 * q^25 + 32 * q^30 + 8 * q^32 - 10 * q^36 + 10 * q^39 + 14 * q^42 - 44 * q^43 - 28 * q^50 - 8 * q^51 + 24 * q^57 + 32 * q^60 - 4 * q^63 + 8 * q^64 - 4 * q^65 - 16 * q^71 - 10 * q^72 + 10 * q^78 - 52 * q^79 - 14 * q^81 + 14 * q^84 - 44 * q^86 + 24 * q^91 - 30 * q^93 - 66 * q^99

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