LMFDB - Embedded newform 441.2.y.a.25.6

Newspace parameters

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.y (of order $21$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			25.6
Character	$\chi$	$=$	441.25
Dual form			441.2.y.a.247.6

$q$-expansion

$f(q)$	$=$	$q+(-0.524692 + 2.29882i) q^{2} +(1.63349 + 0.575929i) q^{3} +(-3.20735 - 1.54458i) q^{4} +(-1.57024 - 4.00089i) q^{5} +(-2.18104 + 3.45293i) q^{6} +(2.51000 + 0.836609i) q^{7} +(2.29328 - 2.87568i) q^{8} +(2.33661 + 1.88155i) q^{9} +O(q^{10})$	\(q+(-0.524692 + 2.29882i) q^{2} +(1.63349 + 0.575929i) q^{3} +(-3.20735 - 1.54458i) q^{4} +(-1.57024 - 4.00089i) q^{5} +(-2.18104 + 3.45293i) q^{6} +(2.51000 + 0.836609i) q^{7} +(2.29328 - 2.87568i) q^{8} +(2.33661 + 1.88155i) q^{9} +(10.0212 - 1.51046i) q^{10} +(5.43233 - 1.67565i) q^{11} +(-4.34962 - 4.37027i) q^{12} +(-1.22443 + 0.377686i) q^{13} +(-3.24019 + 5.33108i) q^{14} +(-0.260740 - 7.43978i) q^{15} +(0.968309 + 1.21422i) q^{16} +(0.175783 - 2.34566i) q^{17} +(-5.55136 + 4.38422i) q^{18} +(1.68254 + 2.91425i) q^{19} +(-1.14340 + 15.2576i) q^{20} +(3.61824 + 2.81218i) q^{21} +(1.00173 + 13.3672i) q^{22} +(3.48335 - 2.37491i) q^{23} +(5.40225 - 3.37664i) q^{24} +(-9.87625 + 9.16382i) q^{25} +(-0.225787 - 3.01292i) q^{26} +(2.73320 + 4.41923i) q^{27} +(-6.75823 - 6.56019i) q^{28} +(-0.163743 + 2.18500i) q^{29} +(17.2396 + 3.30420i) q^{30} -3.87928 q^{31} +(3.32843 - 1.60289i) q^{32} +(9.83873 + 0.391468i) q^{33} +(5.30003 + 1.63484i) q^{34} +(-0.594101 - 11.3559i) q^{35} +(-4.58812 - 9.64389i) q^{36} +(2.71058 + 1.84804i) q^{37} +(-7.58217 + 2.33879i) q^{38} +(-2.21762 - 0.0882357i) q^{39} +(-15.1063 - 4.65967i) q^{40} +(-10.6831 - 1.61022i) q^{41} +(-8.36316 + 6.84217i) q^{42} +(3.19155 - 0.481048i) q^{43} +(-20.0116 - 3.01626i) q^{44} +(3.85887 - 12.3030i) q^{45} +(3.63181 + 9.25370i) q^{46} +(1.01578 - 4.45042i) q^{47} +(0.882422 + 2.54110i) q^{48} +(5.60017 + 4.19977i) q^{49} +(-15.8840 - 27.5119i) q^{50} +(1.63808 - 3.73039i) q^{51} +(4.51054 + 0.679855i) q^{52} +(-0.636820 + 0.434177i) q^{53} +(-11.5931 + 3.96441i) q^{54} +(-15.2341 - 19.1030i) q^{55} +(8.16195 - 5.29937i) q^{56} +(1.07002 + 5.72944i) q^{57} +(-4.93702 - 1.52287i) q^{58} +(2.57889 + 3.23383i) q^{59} +(-10.6551 + 24.2647i) q^{60} +(5.18995 - 2.49935i) q^{61} +(2.03542 - 8.91777i) q^{62} +(4.29076 + 6.67753i) q^{63} +(2.62953 + 11.5207i) q^{64} +(3.43372 + 4.30575i) q^{65} +(-6.06222 + 22.4121i) q^{66} +0.982056 q^{67} +(-4.18686 + 7.25185i) q^{68} +(7.05781 - 1.87324i) q^{69} +(26.4169 + 4.59261i) q^{70} +(3.61418 + 1.74050i) q^{71} +(10.7693 - 2.40442i) q^{72} +(-9.47692 - 2.92324i) q^{73} +(-5.67054 + 5.26149i) q^{74} +(-21.4105 + 9.28104i) q^{75} +(-0.895218 - 11.9459i) q^{76} +(15.0370 + 0.338856i) q^{77} +(1.36640 - 5.05162i) q^{78} +2.50673 q^{79} +(3.33750 - 5.78071i) q^{80} +(1.91950 + 8.79292i) q^{81} +(9.30692 - 23.7137i) q^{82} +(-14.8875 - 4.59219i) q^{83} +(-7.26134 - 14.6083i) q^{84} +(-9.66076 + 2.97995i) q^{85} +(-0.568732 + 7.58920i) q^{86} +(-1.52588 + 3.47489i) q^{87} +(7.63921 - 19.4644i) q^{88} +(-1.32080 + 1.22552i) q^{89} +(26.2577 + 15.3262i) q^{90} +(-3.38929 - 0.0763771i) q^{91} +(-14.8406 + 2.23685i) q^{92} +(-6.33678 - 2.23419i) q^{93} +(9.69777 + 4.67020i) q^{94} +(9.01762 - 11.3077i) q^{95} +(6.36012 - 0.701368i) q^{96} +(-3.17809 + 5.50461i) q^{97} +(-12.5929 + 10.6702i) q^{98} +(15.8461 + 6.30588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 5 q^{2} - 13 q^{3} - 109 q^{4} - 12 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 3 q^{9}+O(q^{10}) $ 648 * q - 5 * q^2 - 13 * q^3 - 109 * q^4 - 12 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 3 * q^9	\( 648 q - 5 q^{2} - 13 q^{3} - 109 q^{4} - 12 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 3 q^{9} - 22 q^{10} - 8 q^{11} - 64 q^{12} - 4 q^{13} - 26 q^{14} - 4 q^{15} - 97 q^{16} - 37 q^{17} - q^{18} - 14 q^{19} - 11 q^{20} - 33 q^{21} - q^{22} + 31 q^{23} - 20 q^{24} + 38 q^{25} - 44 q^{26} - 49 q^{27} - 22 q^{28} + 73 q^{29} - 12 q^{30} - 20 q^{31} - q^{32} - 43 q^{33} - 7 q^{34} - 32 q^{35} + 20 q^{36} - 39 q^{37} - 40 q^{38} + q^{39} - q^{40} - 17 q^{41} + 82 q^{42} - q^{43} - 31 q^{44} - 177 q^{45} + 56 q^{46} + 5 q^{47} - 23 q^{48} - q^{49} - 21 q^{50} - 18 q^{51} - 48 q^{52} + 50 q^{53} - 15 q^{54} + 20 q^{55} + 127 q^{56} + 33 q^{57} - 82 q^{58} + 53 q^{59} + 43 q^{60} + 42 q^{61} - 30 q^{62} + 57 q^{63} - 88 q^{64} - 11 q^{65} - 90 q^{66} - 26 q^{67} + 145 q^{68} + 64 q^{69} - 46 q^{70} - 19 q^{71} - 46 q^{72} - 40 q^{73} + 18 q^{74} - 114 q^{75} + 43 q^{76} + 7 q^{77} - 129 q^{78} - 26 q^{79} + 163 q^{80} + 85 q^{81} - 28 q^{82} - 221 q^{83} - 113 q^{84} - 10 q^{85} - 18 q^{86} + 37 q^{87} - 4 q^{88} - 104 q^{89} - 60 q^{90} - 49 q^{91} + 119 q^{92} - 149 q^{93} - 13 q^{94} + 37 q^{95} + 186 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) 648 * q - 5 * q^2 - 13 * q^3 - 109 * q^4 - 12 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 3 * q^9 - 22 * q^10 - 8 * q^11 - 64 * q^12 - 4 * q^13 - 26 * q^14 - 4 * q^15 - 97 * q^16 - 37 * q^17 - q^18 - 14 * q^19 - 11 * q^20 - 33 * q^21 - q^22 + 31 * q^23 - 20 * q^24 + 38 * q^25 - 44 * q^26 - 49 * q^27 - 22 * q^28 + 73 * q^29 - 12 * q^30 - 20 * q^31 - q^32 - 43 * q^33 - 7 * q^34 - 32 * q^35 + 20 * q^36 - 39 * q^37 - 40 * q^38 + q^39 - q^40 - 17 * q^41 + 82 * q^42 - q^43 - 31 * q^44 - 177 * q^45 + 56 * q^46 + 5 * q^47 - 23 * q^48 - q^49 - 21 * q^50 - 18 * q^51 - 48 * q^52 + 50 * q^53 - 15 * q^54 + 20 * q^55 + 127 * q^56 + 33 * q^57 - 82 * q^58 + 53 * q^59 + 43 * q^60 + 42 * q^61 - 30 * q^62 + 57 * q^63 - 88 * q^64 - 11 * q^65 - 90 * q^66 - 26 * q^67 + 145 * q^68 + 64 * q^69 - 46 * q^70 - 19 * q^71 - 46 * q^72 - 40 * q^73 + 18 * q^74 - 114 * q^75 + 43 * q^76 + 7 * q^77 - 129 * q^78 - 26 * q^79 + 163 * q^80 + 85 * q^81 - 28 * q^82 - 221 * q^83 - 113 * q^84 - 10 * q^85 - 18 * q^86 + 37 * q^87 - 4 * q^88 - 104 * q^89 - 60 * q^90 - 49 * q^91 + 119 * q^92 - 149 * q^93 - 13 * q^94 + 37 * q^95 + 186 * q^96 - 11 * q^97 - 33 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.524692	+	2.29882i	−0.371013	+	1.62551i	0.352927	+	0.935651i	$0.385186\pi$
$2$	−0.524692	+	2.29882i	−0.371013	+	1.62551i	−0.723940	+	0.689863i	$0.757671\pi$
$3$	1.63349	+	0.575929i	0.943099	+	0.332513i
$3$	1.63349	+	0.575929i	0.943099	+	0.332513i
$4$	−3.20735	−	1.54458i	−1.60368	−	0.772290i
$5$	−1.57024	−	4.00089i	−0.702230	−	1.78925i	−0.608347	−	0.793671i	$-0.708167\pi$
$5$	−1.57024	−	4.00089i	−0.702230	−	1.78925i	−0.0938831	−	0.995583i	$-0.529928\pi$
$6$	−2.18104	+	3.45293i	−0.890406	+	1.40965i
$7$	2.51000	+	0.836609i	0.948690	+	0.316209i
$7$	2.51000	+	0.836609i	0.948690	+	0.316209i
$8$	2.29328	−	2.87568i	0.810797	−	1.01671i
$9$	2.33661	+	1.88155i	0.778870	+	0.627185i
$10$	10.0212	−	1.51046i	3.16899	−	0.477649i
$11$	5.43233	−	1.67565i	1.63791	−	0.505228i	0.667076	−	0.744989i	$-0.267545\pi$
$11$	5.43233	−	1.67565i	1.63791	−	0.505228i	0.970832	+	0.239762i	$0.0770693\pi$
$12$	−4.34962	−	4.37027i	−1.25563	−	1.26159i
$13$	−1.22443	+	0.377686i	−0.339596	+	0.104751i	−0.459862	−	0.887990i	$-0.652101\pi$
$13$	−1.22443	+	0.377686i	−0.339596	+	0.104751i	0.120267	+	0.992742i	$0.461625\pi$
$14$	−3.24019	+	5.33108i	−0.865978	+	1.42479i
$15$	−0.260740	−	7.43978i	−0.0673227	−	1.92094i
$16$	0.968309	+	1.21422i	0.242077	+	0.303555i
$17$	0.175783	−	2.34566i	0.0426336	−	0.568906i	−0.934456	−	0.356078i	$-0.884114\pi$
$17$	0.175783	−	2.34566i	0.0426336	−	0.568906i	0.977090	−	0.212828i	$-0.0682674\pi$
$18$	−5.55136	+	4.38422i	−1.30847	+	1.03337i
$19$	1.68254	+	2.91425i	0.386002	+	0.668575i	0.991908	−	0.126961i	$-0.0405224\pi$
$19$	1.68254	+	2.91425i	0.386002	+	0.668575i	−0.605906	+	0.795537i	$0.707189\pi$
$20$	−1.14340	+	15.2576i	−0.255672	+	3.41171i
$21$	3.61824	+	2.81218i	0.789565	+	0.613667i
$22$	1.00173	+	13.3672i	0.213570	+	2.84989i
$23$	3.48335	−	2.37491i	0.726328	−	0.495202i	−0.142823	−	0.989748i	$-0.545618\pi$
$23$	3.48335	−	2.37491i	0.726328	−	0.495202i	0.869151	+	0.494546i	$0.164666\pi$
$24$	5.40225	−	3.37664i	1.10273	−	0.689255i
$25$	−9.87625	+	9.16382i	−1.97525	+	1.83276i
$26$	−0.225787	−	3.01292i	−0.0442804	−	0.590881i
$27$	2.73320	+	4.41923i	0.526005	+	0.850482i
$28$	−6.75823	−	6.56019i	−1.27719	−	1.23976i
$29$	−0.163743	+	2.18500i	−0.0304064	+	0.405745i	0.961146	+	0.276040i	$0.0890221\pi$
$29$	−0.163743	+	2.18500i	−0.0304064	+	0.405745i	−0.991553	+	0.129705i	$0.958597\pi$
$30$	17.2396	+	3.30420i	3.14750	+	0.603261i
$31$	−3.87928			−0.696739			−0.348369	−	0.937357i	$-0.613265\pi$
$31$	−3.87928			−0.696739			−0.348369	+	0.937357i	$0.613265\pi$
$32$	3.32843	−	1.60289i	0.588388	−	0.283353i
$33$	9.83873	+	0.391468i	1.71270	+	0.0681459i
$34$	5.30003	+	1.63484i	0.908948	+	0.280373i
$35$	−0.594101	−	11.3559i	−0.100421	−	1.91950i
$36$	−4.58812	−	9.64389i	−0.764687	−	1.60731i
$37$	2.71058	+	1.84804i	0.445616	+	0.303816i	0.765259	−	0.643722i	$-0.222611\pi$
$37$	2.71058	+	1.84804i	0.445616	+	0.303816i	−0.319643	+	0.947538i	$0.603563\pi$
$38$	−7.58217	+	2.33879i	−1.22999	+	0.379402i
$39$	−2.21762	−	0.0882357i	−0.355103	−	0.0141290i
$40$	−15.1063	−	4.65967i	−2.38851	−	0.736759i
$41$	−10.6831	−	1.61022i	−1.66842	−	0.251473i	−0.754184	−	0.656663i	$-0.771967\pi$
$41$	−10.6831	−	1.61022i	−1.66842	−	0.251473i	−0.914233	+	0.405189i	$0.867206\pi$
$42$	−8.36316	+	6.84217i	−1.29046	+	1.05577i
$43$	3.19155	−	0.481048i	0.486706	−	0.0733591i	0.0988947	−	0.995098i	$-0.468469\pi$
$43$	3.19155	−	0.481048i	0.486706	−	0.0733591i	0.387811	+	0.921739i	$0.373231\pi$
$44$	−20.0116	−	3.01626i	−3.01686	−	0.454718i
$45$	3.85887	−	12.3030i	0.575247	−	1.83403i
$46$	3.63181	+	9.25370i	0.535481	+	1.36438i
$47$	1.01578	−	4.45042i	0.148167	−	0.649161i	−0.845227	−	0.534407i	$-0.820535\pi$
$47$	1.01578	−	4.45042i	0.148167	−	0.649161i	0.993394	−	0.114754i	$-0.0366080\pi$
$48$	0.882422	+	2.54110i	0.127367	+	0.366776i
$49$	5.60017	+	4.19977i	0.800024	+	0.599968i
$50$	−15.8840	−	27.5119i	−2.24634	−	3.89078i
$51$	1.63808	−	3.73039i	0.229376	−	0.522359i
$52$	4.51054	+	0.679855i	0.625500	+	0.0942789i
$53$	−0.636820	+	0.434177i	−0.0874740	+	0.0596388i	−0.606267	−	0.795261i	$-0.707334\pi$
$53$	−0.636820	+	0.434177i	−0.0874740	+	0.0596388i	0.518793	+	0.854900i	$0.326381\pi$
$54$	−11.5931	+	3.96441i	−1.57762	+	0.539488i
$55$	−15.2341	−	19.1030i	−2.05417	−	2.57585i
$56$	8.16195	−	5.29937i	1.09069	−	0.708159i
$57$	1.07002	+	5.72944i	0.141728	+	0.758883i
$58$	−4.93702	−	1.52287i	−0.648263	−	0.199963i
$59$	2.57889	+	3.23383i	0.335743	+	0.421009i	0.920831	−	0.389961i	$-0.127511\pi$
$59$	2.57889	+	3.23383i	0.335743	+	0.421009i	−0.585088	+	0.810970i	$0.698940\pi$
$60$	−10.6551	+	24.2647i	−1.37556	+	3.13256i
$61$	5.18995	−	2.49935i	0.664504	−	0.320008i	−0.0710513	−	0.997473i	$-0.522635\pi$
$61$	5.18995	−	2.49935i	0.664504	−	0.320008i	0.735556	+	0.677464i	$0.236921\pi$
$62$	2.03542	−	8.91777i	0.258499	−	1.13256i
$63$	4.29076	+	6.67753i	0.540585	+	0.841289i
$64$	2.62953	+	11.5207i	0.328691	+	1.44009i
$65$	3.43372	+	4.30575i	0.425901	+	0.534063i
$66$	−6.06222	+	22.4121i	−0.746207	+	2.75874i
$67$	0.982056			0.119977			0.0599886	−	0.998199i	$-0.480894\pi$
$67$	0.982056			0.119977			0.0599886	+	0.998199i	$0.480894\pi$
$68$	−4.18686	+	7.25185i	−0.507731	+	0.879416i
$69$	7.05781	−	1.87324i	0.849660	−	0.225511i
$70$	26.4169	+	4.59261i	3.15743	+	0.548922i
$71$	3.61418	+	1.74050i	0.428925	+	0.206559i	0.635875	−	0.771792i	$-0.280640\pi$
$71$	3.61418	+	1.74050i	0.428925	+	0.206559i	−0.206950	+	0.978351i	$0.566354\pi$
$72$	10.7693	−	2.40442i	1.26917	−	0.283364i
$73$	−9.47692	−	2.92324i	−1.10919	−	0.342140i	−0.314562	−	0.949237i	$-0.601858\pi$
$73$	−9.47692	−	2.92324i	−1.10919	−	0.342140i	−0.794627	+	0.607097i	$0.792334\pi$
$74$	−5.67054	+	5.26149i	−0.659186	+	0.611636i
$75$	−21.4105	+	9.28104i	−2.47227	+	1.07168i
$76$	−0.895218	−	11.9459i	−0.102689	−	1.37028i
$77$	15.0370	+	0.338856i	1.71362	+	0.0386163i
$78$	1.36640	−	5.05162i	0.154715	−	0.571983i
$79$	2.50673			0.282029			0.141014	−	0.990008i	$-0.454964\pi$
$79$	2.50673			0.282029			0.141014	+	0.990008i	$0.454964\pi$
$80$	3.33750	−	5.78071i	0.373143	−	0.646303i
$81$	1.91950	+	8.79292i	0.213278	+	0.976992i
$82$	9.30692	−	23.7137i	1.02778	−	2.61874i
$83$	−14.8875	−	4.59219i	−1.63412	−	0.504058i	−0.664212	−	0.747545i	$-0.731233\pi$
$83$	−14.8875	−	4.59219i	−1.63412	−	0.504058i	−0.969904	+	0.243486i	$0.921709\pi$
$84$	−7.26134	−	14.6083i	−0.792277	−	1.59390i
$85$	−9.66076	+	2.97995i	−1.04786	+	0.323221i
$86$	−0.568732	+	7.58920i	−0.0613280	+	0.818365i
$87$	−1.52588	+	3.47489i	−0.163592	+	0.372547i
$88$	7.63921	−	19.4644i	0.814342	−	2.07491i
$89$	−1.32080	+	1.22552i	−0.140005	+	0.129905i	−0.747067	−	0.664749i	$-0.768538\pi$
$89$	−1.32080	+	1.22552i	−0.140005	+	0.129905i	0.607062	+	0.794654i	$0.292348\pi$
$90$	26.2577	+	15.3262i	2.76781	+	1.61552i
$91$	−3.38929	−	0.0763771i	−0.355294	−	0.00800650i
$92$	−14.8406	+	2.23685i	−1.54723	+	0.233208i
$93$	−6.33678	−	2.23419i	−0.657093	−	0.231675i
$94$	9.69777	+	4.67020i	1.00025	+	0.481694i
$95$	9.01762	−	11.3077i	0.925188	−	1.16015i
$96$	6.36012	−	0.701368i	0.649127	−	0.0715831i
$97$	−3.17809	+	5.50461i	−0.322686	+	0.558909i	−0.981041	−	0.193799i	$-0.937919\pi$
$97$	−3.17809	+	5.50461i	−0.322686	+	0.558909i	0.658355	+	0.752707i	$0.271252\pi$
$98$	−12.5929	+	10.6702i	−1.27208	+	1.07785i
$99$	15.8461	+	6.30588i	1.59259	+	0.633764i
$100$	45.8309	−	14.1370i	4.58309	−	1.41370i
$101$	−6.92123	−	1.04321i	−0.688688	−	0.103803i	−0.204630	−	0.978839i	$-0.565599\pi$
$101$	−6.92123	−	1.04321i	−0.688688	−	0.103803i	−0.484057	+	0.875036i	$0.660837\pi$
$102$	7.71602	+	5.72295i	0.764000	+	0.566656i
$103$	−1.76628	−	4.50041i	−0.174037	−	0.443439i	0.817065	−	0.576546i	$-0.195600\pi$
$103$	−1.76628	−	4.50041i	−0.174037	−	0.443439i	−0.991102	+	0.133107i	$0.957505\pi$
$104$	−1.72185	+	4.38721i	−0.168842	+	0.430201i
$105$	5.56974	−	18.8920i	0.543551	−	1.84367i
$106$	−0.663962	−	1.69175i	−0.0644896	−	0.164317i
$107$	−1.87764	+	1.74220i	−0.181519	+	0.168425i	−0.765699	−	0.643199i	$-0.777607\pi$
$107$	−1.87764	+	1.74220i	−0.181519	+	0.168425i	0.584180	+	0.811624i	$0.301416\pi$
$108$	−1.94048	−	18.3957i	−0.186723	−	1.77012i
$109$	−2.04940	−	1.90157i	−0.196297	−	0.182137i	0.575900	−	0.817520i	$-0.304652\pi$
$109$	−2.04940	−	1.90157i	−0.196297	−	0.182137i	−0.772197	+	0.635383i	$0.780842\pi$
$110$	51.9076	−	24.9974i	4.94920	−	2.38341i
$111$	3.36337	+	4.57986i	0.319237	+	0.434702i
$112$	1.41462	+	3.85779i	0.133669	+	0.364527i
$113$	−10.5648	+	9.80271i	−0.993854	+	0.922162i	−0.996966	−	0.0778336i	$-0.975200\pi$
$113$	−10.5648	+	9.80271i	−0.993854	+	0.922162i	0.00311256	+	0.999995i	$0.499009\pi$
$114$	−13.7324	−	0.546392i	−1.28616	−	0.0511743i
$115$	−14.9714	−	10.2073i	−1.39609	−	0.951840i
$116$	3.90009	−	6.75516i	0.362114	−	0.627201i
$117$	−3.57165	−	1.42132i	−0.330199	−	0.131401i
$118$	−8.78713	+	4.23166i	−0.808921	+	0.389556i
$119$	2.40362	−	5.74054i	0.220339	−	0.526235i
$120$	−21.9924	−	16.3117i	−2.00762	−	1.48905i
$121$	17.6137	−	12.0088i	1.60125	−	1.09171i
$122$	3.02244	+	13.2422i	0.273638	+	1.19889i
$123$	−16.5234	−	8.78298i	−1.48986	−	0.791934i
$124$	12.4422	+	5.99185i	1.11734	+	0.538084i
$125$	32.8097	+	15.8003i	2.93459	+	1.41322i
$126$	−17.6018	+	6.36006i	−1.56809	+	0.566599i
$127$	−3.53623	+	1.70296i	−0.313790	+	0.151113i	−0.584149	−	0.811646i	$-0.698572\pi$
$127$	−3.53623	+	1.70296i	−0.313790	+	0.151113i	0.270359	+	0.962759i	$0.412857\pi$
$128$	−20.4752			−1.80977
$129$	5.49042	+	1.05231i	0.483405	+	0.0926511i
$130$	−11.6998	+	5.63434i	−1.02614	+	0.494164i
$131$	−0.799524	+	0.120509i	−0.0698547	+	0.0105289i	−0.183877	−	0.982949i	$-0.558865\pi$
$131$	−0.799524	+	0.120509i	−0.0698547	+	0.0105289i	0.114022	+	0.993478i	$0.463627\pi$
$132$	−30.9516	−	16.4523i	−2.69399	−	1.43199i
$133$	1.78509	+	8.72239i	0.154787	+	0.756327i
$134$	−0.515276	+	2.25757i	−0.0445131	+	0.195025i
$135$	13.3891	−	17.8745i	1.15235	−	1.53839i
$136$	−6.34226	−	5.88475i	−0.543844	−	0.504613i
$137$	−5.53414	+	14.1008i	−0.472813	+	1.20471i	0.473308	+	0.880897i	$0.343060\pi$
$137$	−5.53414	+	14.1008i	−0.472813	+	1.20471i	−0.946122	+	0.323812i	$0.895036\pi$
$138$	0.603067	+	17.2075i	0.0513364	+	1.46480i
$139$	5.51557	+	0.831338i	0.467824	+	0.0705132i	0.378724	−	0.925510i	$-0.376363\pi$
$139$	5.51557	+	0.831338i	0.467824	+	0.0705132i	0.0891000	+	0.996023i	$0.471601\pi$
$140$	−15.6346	+	37.3400i	−1.32137	+	3.15581i
$141$	4.22240	−	6.68473i	0.355590	−	0.562956i
$142$	−5.89743	+	7.39514i	−0.494901	+	0.620587i
$143$	−6.01863	+	4.10343i	−0.503303	+	0.343146i
$144$	−0.0220618	+	4.65909i	−0.00183848	+	0.388257i
$145$	8.99908	−	2.77585i	0.747333	−	0.230522i
$146$	11.6925	−	20.2520i	0.967676	−	1.67606i
$147$	6.72908	+	10.0856i	0.555005	+	0.831847i
$148$	−5.83933	−	10.1140i	−0.479990	−	0.831367i
$149$	−8.81302	−	8.17729i	−0.721991	−	0.669910i	0.230985	−	0.972957i	$-0.425805\pi$
$149$	−8.81302	−	8.17729i	−0.721991	−	0.669910i	−0.952975	+	0.303048i	$0.901996\pi$
$150$	−10.1015	−	54.0887i	−0.824788	−	4.41632i
$151$	−0.693283	−	9.25122i	−0.0564186	−	0.752854i	−0.951637	−	0.307225i	$-0.900599\pi$
$151$	−0.693283	−	9.25122i	−0.0564186	−	0.752854i	0.895218	−	0.445628i	$-0.147020\pi$
$152$	12.2390	+	1.84473i	0.992714	+	0.149628i
$153$	4.82423	−	5.15015i	0.390016	−	0.416365i
$154$	−8.66875	+	34.3896i	−0.698548	+	2.77119i
$155$	6.09138	+	15.5206i	0.489271	+	1.24664i
$156$	6.97640	+	3.70829i	0.558559	+	0.296901i
$157$	−6.79189	−	8.51676i	−0.542052	−	0.679712i	0.433075	−	0.901358i	$-0.357428\pi$
$157$	−6.79189	−	8.51676i	−0.542052	−	0.679712i	−0.975127	+	0.221646i	$0.928857\pi$
$158$	−1.31526	+	5.76252i	−0.104636	+	0.458442i
$159$	−1.29030	+	0.342462i	−0.102327	+	0.0271590i
$160$	−11.6394	−	10.7998i	−0.920175	−	0.853797i
$161$	10.7301	−	3.04681i	0.845647	−	0.240122i
$162$	−21.2205	−	0.200972i	−1.66724	−	0.0157898i
$163$	−5.02679	+	12.8081i	−0.393729	+	1.00320i	0.587304	+	0.809366i	$0.300189\pi$
$163$	−5.02679	+	12.8081i	−0.393729	+	1.00320i	−0.981033	+	0.193839i	$0.937906\pi$
$164$	31.7773	+	21.6654i	2.48139	+	1.69178i
$165$	−13.8829	−	39.9784i	−1.08078	−	3.11232i
$166$	18.3680	−	31.8143i	1.42563	−	2.46927i
$167$	7.50023	+	5.11357i	0.580385	+	0.395700i	0.817625	−	0.575751i	$-0.195290\pi$
$167$	7.50023	+	5.11357i	0.580385	+	0.395700i	−0.237240	+	0.971451i	$0.576243\pi$
$168$	16.3846	−	3.95580i	1.26410	−	0.305196i
$169$	−9.38452	+	6.39826i	−0.721886	+	0.492174i
$170$	−1.78146	−	23.7719i	−0.136632	−	1.82322i
$171$	−1.55187	+	9.97527i	−0.118675	+	0.762828i
$172$	−10.9794	−	3.38670i	−0.837173	−	0.258234i
$173$	−13.1565	−	6.33586i	−1.00027	−	0.481706i	−0.139242	−	0.990258i	$-0.544467\pi$
$173$	−13.1565	−	6.33586i	−1.00027	−	0.481706i	−0.861031	+	0.508552i	$0.830181\pi$
$174$	−7.18753	−	5.33097i	−0.544885	−	0.404140i
$175$	−32.4559	+	14.7386i	−2.45344	+	1.11413i
$176$	7.29478	+	4.97350i	0.549865	+	0.374891i
$177$	2.35015	+	6.76771i	0.176648	+	0.508692i
$178$	−2.12425	−	3.67931i	−0.159219	−	0.275776i
$179$	0.0412249	−	0.550109i	0.00308130	−	0.0411171i	−0.995451	−	0.0952727i	$-0.969628\pi$
$179$	0.0412249	−	0.550109i	0.00308130	−	0.0411171i	0.998533	+	0.0541557i	$0.0172467\pi$
$180$	−31.3797	+	33.4998i	−2.33891	+	2.49693i
$181$	3.36359	+	14.7369i	0.250014	+	1.09538i	0.931554	+	0.363602i	$0.118453\pi$
$181$	3.36359	+	14.7369i	0.250014	+	1.09538i	−0.681540	+	0.731780i	$0.738690\pi$
$182$	1.95391	−	7.75130i	0.144833	−	0.574565i
$183$	9.91720	−	1.09363i	0.733100	−	0.0808433i
$184$	1.15882	−	15.4633i	0.0854291	−	1.13997i
$185$	3.13757	−	13.7466i	0.230679	−	1.01067i
$186$	8.46086	−	13.3949i	0.620380	−	0.982160i
$187$	−2.97560	−	13.0369i	−0.217597	−	0.953356i
$188$	−10.1320	+	12.7051i	−0.738952	+	0.926616i
$189$	3.16315	+	13.3789i	0.230086	+	0.973170i
$190$	21.2630	+	26.6630i	1.54258	+	1.93434i
$191$	6.28713	−	7.88382i	0.454921	−	0.570453i	−0.500486	−	0.865745i	$-0.666845\pi$
$191$	6.28713	−	7.88382i	0.454921	−	0.570453i	0.955407	+	0.295292i	$0.0954168\pi$
$192$	−2.33979	+	20.3334i	−0.168860	+	1.46744i
$193$	14.1648	−	17.7621i	1.01961	−	1.27854i	0.0597011	−	0.998216i	$-0.480985\pi$
$193$	14.1648	−	17.7621i	1.01961	−	1.27854i	0.959904	−	0.280328i	$-0.0904433\pi$
$194$	−10.9866	−	10.1941i	−0.788793	−	0.731893i
$195$	3.12916	+	9.01101i	0.224084	+	0.645292i
$196$	−11.4748	−	22.1201i	−0.819631	−	1.58000i
$197$	−23.8590			−1.69988			−0.849942	−	0.526877i	$-0.823363\pi$
$197$	−23.8590			−1.69988			−0.849942	+	0.526877i	$0.823363\pi$
$198$	−22.8104	+	33.1187i	−1.62106	+	2.35364i
$199$	3.17046	+	8.07819i	0.224748	+	0.572648i	0.998119	−	0.0613056i	$-0.0195264\pi$
$199$	3.17046	+	8.07819i	0.224748	+	0.572648i	−0.773371	+	0.633953i	$0.781431\pi$
$200$	3.70323	+	49.4162i	0.261858	+	3.49425i
$201$	1.60418	+	0.565595i	0.113150	+	0.0398940i
$202$	6.02966	−	15.3633i	0.424245	−	1.08096i
$203$	−2.23899	+	5.34736i	−0.157146	+	0.375311i
$204$	−11.0158	+	9.43453i	−0.771258	+	0.660549i
$205$	10.3326	+	45.2703i	0.721664	+	3.16181i
$206$	11.2724	−	1.69904i	0.785386	−	0.118378i
$207$	12.6077	+	1.00488i	0.876299	+	0.0698438i
$208$	−1.64422	−	1.12101i	−0.114006	−	0.0777281i
$209$	14.0234	+	13.0118i	0.970018	+	0.900046i
$210$	40.5069	+	22.7163i	2.79524	+	1.56757i
$211$	−8.17141	+	7.58196i	−0.562543	+	0.521963i	−0.909382	−	0.415961i	$-0.863445\pi$
$211$	−8.17141	+	7.58196i	−0.562543	+	0.521963i	0.346840	+	0.937924i	$0.387255\pi$
$212$	2.71313	−	0.408938i	0.186338	−	0.0280860i
$213$	4.90134	+	4.92461i	0.335835	+	0.337429i
$214$	−3.01982	−	5.23049i	−0.206431	−	0.357549i
$215$	−6.93610	−	12.0137i	−0.473038	−	0.819326i
$216$	18.9763	+	2.27472i	1.29117	+	0.154775i
$217$	−9.73697	−	3.24544i	−0.660989	−	0.220315i
$218$	5.44667	−	3.71348i	0.368895	−	0.251509i
$219$	−13.7969	−	10.2331i	−0.932309	−	0.691491i
$220$	19.3551	+	84.8004i	1.30492	+	5.71724i
$221$	0.670691	+	2.93849i	0.0451155	+	0.197664i
$222$	−12.2930	+	5.32879i	−0.825055	+	0.357645i
$223$	6.18619	−	4.21767i	0.414258	−	0.282436i	−0.338203	−	0.941073i	$-0.609819\pi$
$223$	6.18619	−	4.21767i	0.414258	−	0.282436i	0.752461	+	0.658637i	$0.228867\pi$
$224$	9.69533	−	1.23865i	0.647797	−	0.0827605i
$225$	−40.3192	+	2.82958i	−2.68795	+	0.188639i
$226$	−16.9914	−	29.4300i	−1.13025	−	1.95766i
$227$	5.74021	+	9.94234i	0.380991	+	0.659896i	0.991204	−	0.132341i	$-0.0422494\pi$
$227$	5.74021	+	9.94234i	0.380991	+	0.659896i	−0.610213	+	0.792237i	$0.708916\pi$
$228$	5.41763	−	20.0291i	0.358791	−	1.32646i
$229$	18.8639	−	2.84327i	1.24656	−	0.187889i	0.507573	−	0.861609i	$-0.330543\pi$
$229$	18.8639	−	2.84327i	1.24656	−	0.187889i	0.738987	+	0.673720i	$0.235305\pi$
$230$	31.3203	−	29.0610i	2.06520	−	1.91622i
$231$	24.3677	+	9.21376i	1.60328	+	0.606221i
$232$	5.90786	+	5.48169i	0.387870	+	0.359891i
$233$	−11.7590	−	8.01716i	−0.770359	−	0.525222i	0.113183	−	0.993574i	$-0.463895\pi$
$233$	−11.7590	−	8.01716i	−0.770359	−	0.525222i	−0.883542	+	0.468352i	$0.844848\pi$
$234$	5.14139	−	7.46484i	0.336103	−	0.487992i
$235$	−19.4007	+	2.92418i	−1.26556	+	0.190753i
$236$	−3.27651	−	14.3553i	−0.213283	−	0.934453i
$237$	4.09473	+	1.44370i	0.265981	+	0.0937782i
$238$	11.9353	+	8.53751i	0.773653	+	0.553404i
$239$	0.641249	−	1.63388i	0.0414789	−	0.105687i	−0.908633	−	0.417595i	$-0.862873\pi$
$239$	0.641249	−	1.63388i	0.0414789	−	0.105687i	0.950112	+	0.311909i	$0.100968\pi$
$240$	8.78106	−	7.52060i	0.566815	−	0.485453i
$241$	0.411294	+	5.48834i	0.0264938	+	0.353535i	0.994658	+	0.103221i	$0.0329149\pi$
$241$	0.411294	+	5.48834i	0.0264938	+	0.353535i	−0.968165	+	0.250314i	$0.919466\pi$
$242$	18.3644	+	46.7918i	1.18051	+	3.00789i
$243$	−1.92860	+	15.4687i	−0.123720	+	0.992317i
$244$	−20.5064			−1.31279
$245$	8.00926	−	29.0003i	0.511693	−	1.85276i
$246$	28.8602	−	33.3760i	1.84006	−	2.12798i
$247$	−3.16083	−	2.93282i	−0.201119	−	0.186611i
$248$	−8.89627	+	11.1556i	−0.564914	+	0.708379i
$249$	−21.6739	−	16.0755i	−1.37353	−	1.01874i
$250$	−53.5371	+	67.1335i	−3.38599	+	4.24589i
$251$	16.6637	+	20.8956i	1.05180	+	1.31892i	0.945870	+	0.324545i	$0.105211\pi$
$251$	16.6637	+	20.8956i	1.05180	+	1.31892i	0.105932	+	0.994373i	$0.466217\pi$
$252$	−3.44801	−	28.0446i	−0.217204	−	1.76664i
$253$	14.9432	−	18.7381i	0.939469	−	1.17806i
$254$	−2.05937	−	9.02270i	−0.129217	−	0.566135i
$255$	−17.4970	−	0.696181i	−1.09571	−	0.0435965i
$256$	5.48412	−	24.0275i	0.342757	−	1.50172i
$257$	−0.101862	+	1.35925i	−0.00635397	+	0.0847878i	−0.999479	−	0.0322686i	$-0.989727\pi$
$257$	−0.101862	+	1.35925i	−0.00635397	+	0.0847878i	0.993125	+	0.117056i	$0.0373458\pi$
$258$	−5.29986	+	12.0694i	−0.329955	+	0.751406i
$259$	5.25745	+	6.90627i	0.326682	+	0.429135i
$260$	−4.36258	−	19.1137i	−0.270556	−	1.18538i
$261$	−4.49381	+	4.79741i	−0.278160	+	0.296952i
$262$	0.142475	−	1.90119i	0.00880213	−	0.117456i
$263$	2.59130	+	4.48826i	0.159786	+	0.276758i	0.934792	−	0.355197i	$-0.115586\pi$
$263$	2.59130	+	4.48826i	0.159786	+	0.276758i	−0.775005	+	0.631955i	$0.782253\pi$
$264$	23.6887	−	27.3953i	1.45794	−	1.68607i
$265$	2.73705	+	1.86609i	0.168136	+	0.114633i
$266$	−20.9879	−	0.472958i	−1.28685	−	0.0289989i
$267$	−2.86334	+	1.24120i	−0.175233	+	0.0759602i
$268$	−3.14980	−	1.51686i	−0.192405	−	0.0926572i
$269$	−16.0157	−	4.94019i	−0.976494	−	0.301208i	−0.234872	−	0.972026i	$-0.575467\pi$
$269$	−16.0157	−	4.94019i	−0.976494	−	0.301208i	−0.741622	+	0.670818i	$0.765943\pi$
$270$	34.0651	+	40.1578i	2.07314	+	2.44393i
$271$	−0.314129	−	4.19177i	−0.0190820	−	0.254632i	−0.998584	−	0.0531973i	$-0.983059\pi$
$271$	−0.314129	−	4.19177i	−0.0190820	−	0.254632i	0.979502	−	0.201434i	$-0.0645603\pi$
$272$	3.01836	−	2.05789i	0.183015	−	0.124778i
$273$	−5.49240	−	2.07675i	−0.332415	−	0.125691i
$274$	−29.5114	−	20.1206i	−1.78285	−	1.21553i
$275$	−38.2957	+	66.3300i	−2.30932	+	3.99985i
$276$	−25.5302	−	4.89322i	−1.53674	−	0.294537i
$277$	−19.7160	−	13.4421i	−1.18462	−	0.807660i	−0.199562	−	0.979885i	$-0.563952\pi$
$277$	−19.7160	−	13.4421i	−1.18462	−	0.807660i	−0.985058	+	0.172225i	$0.944904\pi$
$278$	−4.80507	+	12.2431i	−0.288189	+	0.734294i
$279$	−9.06436	−	7.29907i	−0.542669	−	0.436984i
$280$	−34.0184	−	24.3338i	−2.03299	−	1.45422i
$281$	−6.82065	−	6.32864i	−0.406886	−	0.377535i	0.450011	−	0.893023i	$-0.351420\pi$
$281$	−6.82065	−	6.32864i	−0.406886	−	0.377535i	−0.856897	+	0.515488i	$0.827611\pi$
$282$	13.1516	+	13.2140i	0.783164	+	0.786881i
$283$	−4.30189	+	18.8478i	−0.255721	+	1.12038i	0.670055	+	0.742311i	$0.266271\pi$
$283$	−4.30189	+	18.8478i	−0.255721	+	1.12038i	−0.925776	+	0.378074i	$0.876587\pi$
$284$	−8.90362	−	11.1648i	−0.528332	−	0.662508i
$285$	21.2427	−	13.2776i	1.25831	−	0.786498i
$286$	−6.27514	−	15.9888i	−0.371057	−	0.945438i
$287$	−25.4674	−	12.9792i	−1.50329	−	0.766138i
$288$	10.7932	+	2.51730i	0.635993	+	0.148333i
$289$	11.3389	+	1.70906i	0.666994	+	0.100533i
$290$	1.65945	+	22.1438i	0.0974460	+	1.30033i
$291$	−8.36166	+	7.16140i	−0.490169	+	0.419809i
$292$	25.8806	+	24.0137i	1.51455	+	1.40530i
$293$	−11.8906	−	20.5951i	−0.694655	−	1.20318i	−0.970297	−	0.241917i	$-0.922224\pi$
$293$	−11.8906	−	20.5951i	−0.694655	−	1.20318i	0.275642	−	0.961260i	$-0.411109\pi$
$294$	−26.7157	+	10.1771i	−1.55809	+	0.593542i
$295$	8.88874	−	15.3958i	0.517523	−	0.896376i
$296$	11.5305	−	3.55668i	0.670196	−	0.206728i
$297$	22.2527	+	19.4268i	1.29123	+	1.12726i
$298$	23.4223	−	15.9690i	1.35682	−	0.925061i
$299$	−3.36814	+	4.22352i	−0.194785	+	0.244252i
$300$	83.0064	+	3.30270i	4.79238	+	0.190681i
$301$	8.41322	+	1.46265i	0.484930	+	0.0843056i
$302$	21.6307	+	3.26030i	1.24471	+	0.187609i
$303$	−10.7050	−	5.69021i	−0.614985	−	0.326894i
$304$	−1.90932	+	4.86487i	−0.109507	+	0.279020i
$305$	−18.1491	−	16.8399i	−1.03921	−	0.964248i
$306$	9.30806	+	13.7923i	0.532107	+	0.788453i
$307$	−3.13605	+	13.7399i	−0.178984	+	0.784178i	0.803117	+	0.595821i	$0.203173\pi$
$307$	−3.13605	+	13.7399i	−0.178984	+	0.784178i	−0.982101	+	0.188357i	$0.939684\pi$
$308$	−47.7055	−	24.3127i	−2.71827	−	1.38534i
$309$	−0.293293	−	8.36865i	−0.0166849	−	0.476076i
$310$	−38.8752	+	5.85949i	−2.20796	+	0.332797i
$311$	4.06084	−	1.95560i	0.230269	−	0.110892i	−0.315192	−	0.949028i	$-0.602069\pi$
$311$	4.06084	−	1.95560i	0.230269	−	0.110892i	0.545461	+	0.838136i	$0.316355\pi$
$312$	−5.33936	+	6.17482i	−0.302282	+	0.349580i
$313$	−10.8848			−0.615247			−0.307624	−	0.951508i	$-0.599534\pi$
$313$	−10.8848			−0.615247			−0.307624	+	0.951508i	$0.599534\pi$
$314$	23.1422	−	11.1447i	1.30599	−	0.628931i
$315$	19.9786	−	27.6522i	1.12567	−	1.55802i
$316$	−8.03995	−	3.87184i	−0.452283	−	0.217808i
$317$	17.7819	+	8.56333i	0.998733	+	0.480965i	0.860508	−	0.509436i	$-0.170146\pi$
$317$	17.7819	+	8.56333i	0.998733	+	0.480965i	0.138225	+	0.990401i	$0.455860\pi$
$318$	−0.110252	−	3.14585i	−0.00618261	−	0.176411i
$319$	2.77179	+	12.1440i	0.155191	+	0.679935i
$320$	41.9641	−	28.6107i	2.34587	−	1.59939i
$321$	−4.07050	+	1.76448i	−0.227193	+	0.0984838i
$322$	1.37410	+	26.2652i	0.0765756	+	1.46370i
$323$	7.13161	−	3.43440i	0.396813	−	0.191095i
$324$	7.42484	−	31.1668i	0.412491	−	1.73149i
$325$	8.63172	−	14.9506i	0.478802	−	0.829309i
$326$	−26.8060	−	18.2760i	−1.48464	−	1.01221i
$327$	−2.25252	−	4.28651i	−0.124565	−	0.237045i
$328$	−29.1298	+	27.0285i	−1.60842	+	1.49240i
$329$	6.27287	−	10.3207i	0.345835	−	0.569001i
$330$	99.1876	−	10.9380i	5.46010	−	0.602117i
$331$	−3.46841	+	1.67030i	−0.190641	+	0.0918078i	−0.526769	−	0.850008i	$-0.676597\pi$
$331$	−3.46841	+	1.67030i	−0.190641	+	0.0918078i	0.336128	+	0.941816i	$0.390882\pi$
$332$	40.6565	+	37.7237i	2.23131	+	2.07036i
$333$	2.85638	+	9.41825i	0.156528	+	0.516117i
$334$	−15.6905	+	14.5587i	−0.858546	+	0.796614i
$335$	−1.54206	−	3.92910i	−0.0842517	−	0.214670i
$336$	0.0889688	+	7.11640i	0.00485365	+	0.388231i
$337$	−8.34239	+	21.2561i	−0.454439	+	1.15789i	0.501716	+	0.865032i	$0.332702\pi$
$337$	−8.34239	+	21.2561i	−0.454439	+	1.15789i	−0.956155	+	0.292860i	$0.905393\pi$
$338$	−9.78449	−	24.9305i	−0.532206	−	1.35604i
$339$	−22.9032	+	9.92810i	−1.24393	+	0.539220i
$340$	35.5882	+	5.36406i	1.93004	+	0.290907i
$341$	−21.0735	+	6.50031i	−1.14119	+	0.352012i
$342$	−22.1171	−	8.80142i	−1.19596	−	0.475926i
$343$	10.5428	+	15.2266i	0.569260	+	0.822158i
$344$	5.93576	−	10.2810i	0.320035	−	0.554317i
$345$	−18.5770	−	25.2961i	−1.00015	−	1.36190i
$346$	21.4682	−	26.9202i	1.15413	−	1.44724i
$347$	18.4611	+	8.89039i	0.991043	+	0.477261i	0.857890	−	0.513834i	$-0.171775\pi$
$347$	18.4611	+	8.89039i	0.991043	+	0.477261i	0.133154	+	0.991095i	$0.457490\pi$
$348$	10.2613	−	8.78834i	0.550062	−	0.471104i
$349$	8.90845	−	1.34273i	0.476859	−	0.0718749i	0.0937845	−	0.995593i	$-0.470104\pi$
$349$	8.90845	−	1.34273i	0.476859	−	0.0718749i	0.383074	+	0.923718i	$0.374865\pi$
$350$	−16.8521	−	82.3436i	−0.900784	−	4.40145i
$351$	−5.01569	−	4.37874i	−0.267718	−	0.233720i
$352$	15.3952	−	14.2847i	0.820568	−	0.761376i
$353$	8.94786	−	22.7988i	0.476247	−	1.21346i	−0.467856	−	0.883805i	$-0.654973\pi$
$353$	8.94786	−	22.7988i	0.476247	−	1.21346i	0.944103	−	0.329652i	$-0.106931\pi$
$354$	−16.7909	+	1.85163i	−0.892425	+	0.0984130i
$355$	1.28843	−	17.1930i	0.0683830	−	0.912507i
$356$	6.12919	−	1.89061i	0.324847	−	0.100202i
$357$	7.23244	−	7.99283i	0.382781	−	0.423026i
$358$	1.24297	+	0.383406i	0.0656931	+	0.0202637i
$359$	6.35761	−	16.1989i	0.335542	−	0.854946i	−0.659147	−	0.752014i	$-0.729082\pi$
$359$	6.35761	−	16.1989i	0.335542	−	0.854946i	0.994688	−	0.102932i	$-0.0328224\pi$
$360$	−26.5301	−	39.3111i	−1.39826	−	2.07188i
$361$	3.83809	−	6.64777i	0.202005	−	0.349883i
$362$	−35.6423			−1.87332
$363$	35.6882	−	9.47212i	1.87314	−	0.497157i
$364$	10.7527	+	5.47999i	0.563593	+	0.287230i
$365$	3.18541	+	42.5063i	0.166732	+	2.22488i
$366$	−2.68941	+	23.3717i	−0.140578	+	1.22166i
$367$	15.1709	−	14.0765i	0.791913	−	0.734787i	−0.176457	−	0.984308i	$-0.556464\pi$
$367$	15.1709	−	14.0765i	0.791913	−	0.734787i	0.968369	+	0.249521i	$0.0802731\pi$
$368$	6.25662	+	1.92991i	0.326149	+	0.100604i
$369$	−21.9325	−	23.8633i	−1.14176	−	1.24227i
$370$	29.9547	+	14.4254i	1.55727	+	0.749943i
$371$	−1.96165	+	0.557012i	−0.101844	+	0.0289186i
$372$	16.8734	+	16.9535i	0.874845	+	0.878997i
$373$	12.1103	−	20.9756i	0.627047	−	1.08608i	−0.361094	−	0.932529i	$-0.617597\pi$
$373$	12.1103	−	20.9756i	0.627047	−	1.08608i	0.988141	−	0.153548i	$-0.0490700\pi$
$374$	31.5309			1.63043
$375$	44.4946	+	44.7058i	2.29769	+	2.30860i
$376$	−10.4685	−	13.1271i	−0.539874	−	0.676980i
$377$	−0.624754	−	2.73722i	−0.0321764	−	0.140974i
$378$	−32.4154	+	0.251747i	−1.66727	+	0.0129484i
$379$	0.824185	−	3.61099i	0.0423356	−	0.185484i	−0.949339	−	0.314254i	$-0.898246\pi$
$379$	0.824185	−	3.61099i	0.0423356	−	0.185484i	0.991675	+	0.128770i	$0.0411028\pi$
$380$	−46.3884	+	22.3395i	−2.37967	+	1.14599i
$381$	−6.75720	+	0.745157i	−0.346182	+	0.0381755i
$382$	14.8247	+	18.5896i	0.758498	+	0.951126i
$383$	0.393739	+	0.121452i	0.0201191	+	0.00620592i	0.304798	−	0.952417i	$-0.401411\pi$
$383$	0.393739	+	0.121452i	0.0201191	+	0.00620592i	−0.284679	+	0.958623i	$0.591887\pi$
$384$	−33.4462	−	11.7923i	−1.70679	−	0.601772i
$385$	−22.2559	−	60.6935i	−1.13426	−	3.09323i
$386$	33.3998	+	41.8820i	1.70001	+	2.13174i
$387$	8.36252	+	4.88104i	0.425091	+	0.248117i
$388$	18.6956	−	12.7464i	0.949123	−	0.647101i
$389$	7.98882	+	1.20412i	0.405049	+	0.0610513i	0.348407	−	0.937343i	$-0.386723\pi$
$389$	7.98882	+	1.20412i	0.405049	+	0.0610513i	0.0566418	+	0.998395i	$0.481961\pi$
$390$	−22.3566	+	2.46539i	−1.13207	+	0.124840i
$391$	−4.95841	−	8.58822i	−0.250758	−	0.434325i
$392$	24.9200	−	6.47305i	1.25865	−	0.326938i
$393$	−1.37542	−	0.263619i	−0.0693809	−	0.0132978i
$394$	12.5186	−	54.8476i	0.630679	−	2.76318i
$395$	−3.93615	−	10.0291i	−0.198049	−	0.504621i
$396$	−41.0840	−	44.7007i	−2.06455	−	2.24629i
$397$	−28.9169	−	4.35851i	−1.45130	−	0.218748i	−0.624401	−	0.781104i	$-0.714657\pi$
$397$	−28.9169	−	4.35851i	−1.45130	−	0.218748i	−0.826895	+	0.562357i	$0.809895\pi$
$398$	−20.2338	+	3.04976i	−1.01423	+	0.152871i
$399$	−2.10755	+	15.2761i	−0.105509	+	0.764760i
$400$	−20.6902	−	3.11854i	−1.03451	−	0.155927i
$401$	11.0715	+	3.41510i	0.552883	+	0.170542i	0.558593	−	0.829442i	$-0.311341\pi$
$401$	11.0715	+	3.41510i	0.552883	+	0.170542i	−0.00570998	+	0.999984i	$0.501818\pi$
$402$	−2.14190	+	3.39097i	−0.106828	+	0.169126i
$403$	4.74990	−	1.46515i	0.236609	−	0.0729843i
$404$	20.5875	+	14.0363i	1.02427	+	0.698333i
$405$	32.1655	−	21.4867i	1.59832	−	1.06768i
$406$	−11.1179	−	7.95275i	−0.551770	−	0.394689i
$407$	17.8214	+	5.49718i	0.883375	+	0.272485i
$408$	−6.97084	−	13.2654i	−0.345108	−	0.656735i
$409$	24.4393	−	11.7694i	1.20845	−	0.581958i	0.282375	−	0.959304i	$-0.408878\pi$
$409$	24.4393	−	11.7694i	1.20845	−	0.581958i	0.926072	+	0.377346i	$0.123163\pi$
$410$	−109.490			−5.40732
$411$	−17.1610	+	19.8462i	−0.846491	+	0.978943i
$412$	−1.28616	+	17.1626i	−0.0633644	+	0.845539i
$413$	3.76756	+	10.2744i	0.185390	+	0.505572i
$414$	−8.92521	+	28.4557i	−0.438650	+	1.39852i
$415$	5.00403	+	66.7741i	0.245638	+	3.27781i
$416$	−3.47004	+	3.21972i	−0.170132	+	0.157860i
$417$	8.53086	+	4.53456i	0.417758	+	0.222058i
$418$	−37.2698	+	25.4101i	−1.82293	+	1.24285i
$419$	−0.271554	−	3.62364i	−0.0132663	−	0.177027i	−0.999901	−	0.0140781i	$-0.995519\pi$
$419$	−0.271554	−	3.62364i	−0.0132663	−	0.177027i	0.986635	−	0.162948i	$-0.0521004\pi$
$420$	−47.0443	+	51.9903i	−2.29552	+	2.53687i
$421$	−2.10404	+	28.0765i	−0.102545	+	1.36836i	0.674201	+	0.738548i	$0.264488\pi$
$421$	−2.10404	+	28.0765i	−0.102545	+	1.36836i	−0.776745	+	0.629815i	$0.783131\pi$
$422$	−13.1421	−	22.7628i	−0.639748	−	1.10808i
$423$	10.7472	−	8.48767i	0.522547	−	0.412684i
$424$	−0.211853	+	2.82698i	−0.0102885	+	0.137290i
$425$	19.7591	+	24.7772i	0.958460	+	1.20187i
$426$	−13.8925	+	8.68343i	−0.673094	+	0.420713i
$427$	15.1177	−	1.93139i	0.731598	−	0.0934667i
$428$	8.71322	−	2.68767i	0.421170	−	0.129914i
$429$	−12.1947	+	3.23663i	−0.588765	+	0.156266i
$430$	31.2566	−	9.64139i	1.50733	−	0.464949i
$431$	−5.35975	+	0.807852i	−0.258170	+	0.0389129i	−0.276852	−	0.960913i	$-0.589291\pi$
$431$	−5.35975	+	0.807852i	−0.258170	+	0.0389129i	0.0186818	+	0.999825i	$0.494053\pi$
$432$	−2.71934	+	7.59789i	−0.130834	+	0.365554i
$433$	−11.3252	+	14.2013i	−0.544254	+	0.682473i	−0.975560	−	0.219733i	$-0.929481\pi$
$433$	−11.3252	+	14.2013i	−0.544254	+	0.682473i	0.431306	+	0.902206i	$0.358053\pi$
$434$	12.5696	−	20.6807i	0.603360	−	0.992707i
$435$	16.2986	+	0.648498i	0.781460	+	0.0310931i
$436$	3.63603	+	9.26446i	0.174134	+	0.443687i
$437$	12.7820	+	6.15547i	0.611444	+	0.294456i
$438$	30.7633	−	26.3474i	1.46993	−	1.25893i
$439$	−0.165967	+	0.727149i	−0.00792118	+	0.0347049i	−0.978734	−	0.205133i	$-0.934237\pi$
$439$	−0.165967	+	0.727149i	−0.00792118	+	0.0347049i	0.970813	+	0.239838i	$0.0770944\pi$
$440$	−89.8703			−4.28440
$441$	5.18332	+	20.3503i	0.246825	+	0.969060i
$442$	−7.10697			−0.338044
$443$	−7.19337	+	31.5162i	−0.341767	+	1.49738i	0.453574	+	0.891219i	$0.350149\pi$
$443$	−7.19337	+	31.5162i	−0.341767	+	1.49738i	−0.795341	+	0.606162i	$0.792708\pi$
$444$	−3.71356	−	19.8842i	−0.176238	−	0.943664i
$445$	6.97716	+	3.36002i	0.330749	+	0.159280i
$446$	6.44984	+	16.4339i	0.305409	+	0.778169i
$447$	−9.68649	−	18.4332i	−0.458155	−	0.871862i
$448$	−3.03823	+	31.1168i	−0.143543	+	1.47013i
$449$	22.9440	−	28.7708i	1.08279	−	1.35778i	0.153623	−	0.988130i	$-0.450906\pi$
$449$	22.9440	−	28.7708i	1.08279	−	1.35778i	0.929171	−	0.369651i	$-0.120523\pi$
$450$	14.6504	−	94.1714i	0.690628	−	4.43928i
$451$	−60.7322	+	9.15390i	−2.85977	+	0.431040i
$452$	49.0261	−	15.1226i	2.30600	−	0.711305i
$453$	4.19557	−	15.5111i	0.197125	−	0.728775i
$454$	−25.8675	+	7.97908i	−1.21402	+	0.374477i
$455$	5.01640	+	13.6801i	0.235173	+	0.641334i
$456$	18.9299	+	10.0622i	0.886474	+	0.471204i
$457$	−14.8561	−	18.6290i	−0.694939	−	0.871427i	0.301695	−	0.953405i	$-0.402448\pi$
$457$	−14.8561	−	18.6290i	−0.694939	−	0.871427i	−0.996634	+	0.0819780i	$0.973876\pi$
$458$	−3.36153	+	44.8566i	−0.157074	+	2.09601i
$459$	10.8465	−	5.63434i	0.506270	−	0.262988i
$460$	32.2526	+	55.8631i	1.50378	+	2.60463i
$461$	−2.79857	+	37.3443i	−0.130342	+	1.73930i	0.422812	+	0.906218i	$0.361043\pi$
$461$	−2.79857	+	37.3443i	−0.130342	+	1.73930i	−0.553154	+	0.833079i	$0.686576\pi$
$462$	−33.9663	+	51.1826i	−1.58026	+	2.38123i
$463$	−0.155199	−	2.07099i	−0.00721272	−	0.0962470i	0.992436	−	0.122767i	$-0.0391766\pi$
$463$	−0.155199	−	2.07099i	−0.00721272	−	0.0962470i	−0.999648	+	0.0265195i	$0.991558\pi$
$464$	−2.81163	+	1.91694i	−0.130527	+	0.0889915i
$465$	1.01148	+	28.8610i	0.0469063	+	1.33840i
$466$	24.5999	−	22.8254i	1.13957	−	1.05736i
$467$	2.28150	+	30.4445i	0.105575	+	1.40880i	0.758644	+	0.651506i	$0.225862\pi$
$467$	2.28150	+	30.4445i	0.105575	+	1.40880i	−0.653069	+	0.757299i	$0.726519\pi$
$468$	9.26020	+	10.0754i	0.428053	+	0.465735i
$469$	2.46496	+	0.821597i	0.113821	+	0.0379378i
$470$	3.45720	−	46.1331i	0.159469	−	2.12796i
$471$	−6.18947	−	17.8237i	−0.285196	−	0.821275i
$472$	15.2136			0.700262
$473$	16.5314	−	7.96113i	0.760117	−	0.366053i
$474$	−5.46727	+	8.65556i	−0.251120	+	0.397563i
$475$	−43.3229	−	13.3633i	−1.98779	−	0.613152i
$476$	−16.5760	+	14.6994i	−0.759758	+	0.673744i
$477$	−2.30493	−	0.183710i	−0.105535	−	0.00841150i
$478$	3.41953	+	2.33140i	0.156406	+	0.106636i
$479$	16.1069	−	4.96831i	0.735941	−	0.227008i	0.0959459	−	0.995387i	$-0.469412\pi$
$479$	16.1069	−	4.96831i	0.735941	−	0.227008i	0.639995	+	0.768379i	$0.278936\pi$
$480$	−12.7930	−	24.3448i	−0.583917	−	1.11119i
$481$	−4.01689	−	1.23905i	−0.183154	−	0.0564956i
$482$	−12.8325	−	1.93419i	−0.584506	−	0.0881001i
$483$	19.2822	+	1.20281i	0.877373	+	0.0547299i
$484$	−75.0421	+	11.3108i	−3.41100	+	0.514126i
$485$	27.0137	+	4.07166i	1.22663	+	0.184885i
$486$	−34.5479	−	12.5498i	−1.56712	−	0.569271i
$487$	5.25186	+	13.3815i	0.237985	+	0.606375i	0.999108	−	0.0422326i	$-0.0134470\pi$
$487$	5.25186	+	13.3815i	0.237985	+	0.606375i	−0.761123	+	0.648607i	$0.775352\pi$
$488$	4.71467	−	20.6563i	0.213423	−	0.935068i
$489$	−15.5878	+	18.0268i	−0.704904	+	0.815201i
$490$	62.4642	+	33.6281i	2.82185	+	1.51916i
$491$	−3.91473	−	6.78051i	−0.176669	−	0.306000i	0.764068	−	0.645135i	$-0.223199\pi$
$491$	−3.91473	−	6.78051i	−0.176669	−	0.306000i	−0.940738	+	0.339135i	$0.889866\pi$
$492$	39.4303	+	53.6918i	1.77766	+	2.42061i
$493$	5.09649	+	0.768173i	0.229534	+	0.0345968i
$494$	8.40050	−	5.72736i	0.377956	−	0.257686i
$495$	0.347091	−	73.3001i	0.0156006	−	3.29460i
$496$	−3.75634	−	4.71030i	−0.168665	−	0.211499i
$497$	7.61547	+	7.39230i	0.341601	+	0.331590i
$498$	48.3268	−	41.3898i	2.16557	−	1.85472i
$499$	−16.9599	−	5.23144i	−0.759231	−	0.234192i	−0.109117	−	0.994029i	$-0.534802\pi$
$499$	−16.9599	−	5.23144i	−0.759231	−	0.234192i	−0.650113	+	0.759837i	$0.725279\pi$
$500$	−80.8274	−	101.354i	−3.61471	−	4.53271i
$501$	9.30653	+	12.6726i	0.415785	+	0.566170i
$502$	−56.7786	+	27.3431i	−2.53415	+	1.22038i
$503$	7.54029	−	33.0362i	0.336205	−	1.47301i	−0.470682	−	0.882303i	$-0.655992\pi$
$503$	7.54029	−	33.0362i	0.336205	−	1.47301i	0.806886	−	0.590707i	$-0.201151\pi$
$504$	29.0424	+	2.97457i	1.29365	+	0.132498i
$505$	6.69419	+	29.3292i	0.297888	+	1.30513i
$506$	35.2351	+	44.1835i	1.56639	+	1.96419i
$507$	−19.0145	+	5.04670i	−0.844464	+	0.224132i
$508$	13.9723			0.619921
$509$	−11.1779	+	19.3608i	−0.495454	+	0.858151i	−0.999986	−	0.00524186i	$-0.998331\pi$
$509$	−11.1779	+	19.3608i	−0.495454	+	0.858151i	0.504533	+	0.863393i	$0.331665\pi$
$510$	10.7809	−	39.8573i	0.477388	−	1.76491i
$511$	−21.3414	−	15.2658i	−0.944089	−	0.675320i
$512$	15.4624	+	7.44632i	0.683350	+	0.329084i
$513$	−8.28002	+	15.4008i	−0.365572	+	0.679961i
$514$	−3.07123	−	0.947350i	−0.135466	−	0.0417858i
$515$	−15.2322	+	14.1334i	−0.671210	+	0.622792i
$516$	−15.9843	−	11.8555i	−0.703671	−	0.521911i
$517$	−1.93931	−	25.8783i	−0.0852906	−	1.13812i
$518$	−18.6348	+	8.46230i	−0.818768	+	0.371812i
$519$	−17.8421	−	17.9268i	−0.783183	−	0.786901i
$520$	20.2565			0.888305
$521$	7.14257	−	12.3713i	0.312922	−	0.541996i	−0.666072	−	0.745888i	$-0.732026\pi$
$521$	7.14257	−	12.3713i	0.312922	−	0.541996i	0.978994	+	0.203891i	$0.0653590\pi$
$522$	−8.67054	−	12.8476i	−0.379499	−	0.562325i
$523$	9.87267	−	25.1551i	0.431702	−	1.09996i	−0.535181	−	0.844737i	$-0.679757\pi$
$523$	9.87267	−	25.1551i	0.431702	−	1.09996i	0.966883	−	0.255221i	$-0.0821481\pi$
$524$	2.75049	+	0.848414i	0.120156	+	0.0370631i
$525$	−61.5050	+	5.38313i	−2.68430	+	0.234939i
$526$	−11.6773	+	3.60198i	−0.509156	+	0.157054i
$527$	−0.681911	+	9.09947i	−0.0297045	+	0.396379i
$528$	9.05160	+	12.3255i	0.393921	+	0.536397i
$529$	−1.90931	+	4.86484i	−0.0830135	+	0.211515i
$530$	−5.72592	+	5.31288i	−0.248718	+	0.230777i
$531$	−0.0587570	+	12.4085i	−0.00254984	+	0.538485i
$532$	7.74702	−	30.7330i	0.335876	−	1.33244i
$533$	13.6888	−	2.06326i	0.592929	−	0.0893697i
$534$	−1.35093	−	7.23355i	−0.0584605	−	0.313027i
$535$	9.91869	+	4.77659i	0.428822	+	0.206510i
$536$	2.25213	−	2.82408i	0.0972771	−	0.121982i
$537$	0.384164	−	0.874857i	0.0165779	−	0.0377529i
$538$	19.7599	−	34.2252i	0.851910	−	1.47555i
$539$	37.4593	+	13.4306i	1.61349	+	0.578497i
$540$	−70.5521	+	36.6492i	−3.03608	+	1.57713i
$541$	7.06959	−	2.18068i	0.303945	−	0.0937547i	−0.139031	−	0.990288i	$-0.544399\pi$
$541$	7.06959	−	2.18068i	0.303945	−	0.0937547i	0.442976	+	0.896533i	$0.353923\pi$
$542$	9.80095	+	1.47726i	0.420987	+	0.0634536i
$543$	−2.99298	+	26.0098i	−0.128441	+	1.11619i
$544$	−3.17475	−	8.08912i	−0.136116	−	0.346818i
$545$	−4.38993	+	11.1854i	−0.188044	+	0.479128i
$546$	7.65590	−	11.5364i	0.327642	−	0.493713i
$547$	15.6292	+	39.8225i	0.668256	+	1.70269i	0.710610	+	0.703586i	$0.248419\pi$
$547$	15.6292	+	39.8225i	0.668256	+	1.70269i	−0.0423544	+	0.999103i	$0.513486\pi$
$548$	39.5297	−	36.6782i	1.68862	−	1.56681i
$549$	16.8295	+	3.92517i	0.718267	+	0.167522i
$550$	−132.388	−	122.838i	−5.64503	−	5.23782i
$551$	−6.64315	+	3.19917i	−0.283008	+	0.136289i
$552$	10.7987	−	24.5919i	0.459623	−	1.04670i
$553$	6.29188	+	2.09715i	0.267558	+	0.0891799i
$554$	41.2459	−	38.2706i	1.75237	−	1.62596i
$555$	13.0423	−	20.6480i	0.553613	−	0.876457i
$556$	−16.4063	−	11.1856i	−0.695782	−	0.474376i
$557$	1.34725	−	2.33350i	0.0570847	−	0.0988737i	−0.836071	−	0.548622i	$-0.815153\pi$
$557$	1.34725	−	2.33350i	0.0570847	−	0.0988737i	0.893156	+	0.449748i	$0.148486\pi$
$558$	21.5353	−	17.0076i	0.911661	−	0.719990i
$559$	−3.72614	+	1.79441i	−0.157599	+	0.0758956i
$560$	13.2133	−	11.7174i	0.558364	−	0.495150i
$561$	2.64773	−	23.0095i	0.111787	−	0.971463i
$562$	18.1272	−	12.3589i	0.764648	−	0.521328i
$563$	7.39536	+	32.4012i	0.311677	+	1.36555i	0.851759	+	0.523935i	$0.175536\pi$
$563$	7.39536	+	32.4012i	0.311677	+	1.36555i	−0.540081	+	0.841613i	$0.681606\pi$
$564$	−23.8678	+	14.9184i	−1.00502	+	0.628180i
$565$	55.8088	+	26.8761i	2.34790	+	1.13069i
$566$	−41.0706	−	19.7786i	−1.72633	−	0.831355i
$567$	−2.53829	+	23.6761i	−0.106598	+	0.994302i
$568$	13.2935	−	6.40179i	0.557781	−	0.268613i
$569$	43.8836			1.83969			0.919847	−	0.392277i	$-0.128312\pi$
$569$	43.8836			1.83969			0.919847	+	0.392277i	$0.128312\pi$
$570$	19.3771	+	55.7999i	0.811615	+	2.33720i
$571$	2.94223	−	1.41690i	0.123128	−	0.0592955i	−0.371305	−	0.928511i	$-0.621090\pi$
$571$	2.94223	−	1.41690i	0.123128	−	0.0592955i	0.494434	+	0.869215i	$0.335375\pi$
$572$	25.6419	−	3.86490i	1.07214	−	0.161600i
$573$	14.8105	−	9.25723i	0.618718	−	0.386726i
$574$	43.1994	−	51.7349i	1.80311	−	2.15937i
$575$	−12.6392	+	55.3760i	−0.527091	+	2.30934i
$576$	−15.5327	+	31.8670i	−0.647194	+	1.32779i
$577$	24.8154	+	23.0253i	1.03308	+	0.958557i	0.999165	−	0.0408678i	$-0.0130122\pi$
$577$	24.8154	+	23.0253i	1.03308	+	0.958557i	0.0339142	+	0.999425i	$0.489203\pi$
$578$	−9.87826	+	25.1694i	−0.410881	+	1.04691i
$579$	33.3679	−	20.8564i	1.38672	−	0.866762i
$580$	−33.1507	−	4.99667i	−1.37651	−	0.207475i
$581$	−33.5257	−	23.9814i	−1.39088	−	0.994916i
$582$	−12.0755	−	22.9795i	−0.500546	−	0.952531i
$583$	−2.73189	+	3.42568i	−0.113143	+	0.141877i
$584$	−30.1395	+	20.5488i	−1.24718	+	0.850315i
$585$	−0.0782333	+	16.5216i	−0.00323455	+	0.683085i
$586$	53.5833	−	16.5283i	2.21351	−	0.682777i
$587$	11.3098	−	19.5891i	0.466805	−	0.808529i	−0.532476	−	0.846445i	$-0.678739\pi$
$587$	11.3098	−	19.5891i	0.466805	−	0.808529i	0.999281	+	0.0379157i	$0.0120718\pi$
$588$	−6.00449	−	42.7417i	−0.247621	−	1.76264i
$589$	−6.52705	−	11.3052i	−0.268943	−	0.465822i
$590$	30.7283	+	28.5117i	1.26506	+	1.17381i
$591$	−38.9736	−	13.7411i	−1.60316	−	0.565233i
$592$	0.380747	+	5.08071i	0.0156486	+	0.208816i
$593$	30.2171	+	4.55450i	1.24087	+	0.187031i	0.736488	−	0.676450i	$-0.236483\pi$
$593$	30.2171	+	4.55450i	1.24087	+	0.187031i	0.504381	+	0.863481i	$0.331721\pi$
$594$	−56.3347	+	40.9620i	−2.31144	+	1.68069i
$595$	−26.7415	−	0.602617i	−1.09630	−	0.0247049i
$596$	15.6360	+	39.8398i	0.640475	+	1.63190i
$597$	0.526458	+	15.0216i	0.0215465	+	0.614795i
$598$	−7.94189	−	9.95881i	−0.324768	−	0.407246i
$599$	−4.77165	+	20.9060i	−0.194964	+	0.854195i	0.778915	+	0.627129i	$0.215770\pi$
$599$	−4.77165	+	20.9060i	−0.194964	+	0.854195i	−0.973879	+	0.227065i	$0.927087\pi$
$600$	−22.4110	+	82.8539i	−0.914926	+	3.38250i
$601$	17.4913	+	16.2295i	0.713483	+	0.662016i	0.950938	−	0.309383i	$-0.100123\pi$
$601$	17.4913	+	16.2295i	0.713483	+	0.662016i	−0.237454	+	0.971399i	$0.576313\pi$
$602$	−7.77671	+	18.5731i	−0.316955	+	0.756982i
$603$	2.29468	+	1.84779i	0.0934467	+	0.0752479i
$604$	−12.0656	+	30.7427i	−0.490944	+	1.25090i
$605$	−75.7038	−	51.6140i	−3.07780	−	2.09841i
$606$	18.6976	−	21.6232i	0.759538	−	0.878384i
$607$	−9.09201	+	15.7478i	−0.369033	+	0.639185i	−0.989415	−	0.145116i	$-0.953645\pi$
$607$	−9.09201	+	15.7478i	−0.369033	+	0.639185i	0.620381	+	0.784300i	$0.286978\pi$
$608$	10.2714	+	7.00295i	0.416562	+	0.284007i
$609$	−6.73708	+	7.44539i	−0.273000	+	0.301702i
$610$	48.2345	−	32.8857i	1.95296	−	1.33150i
$611$	0.437114	+	5.83288i	0.0176837	+	0.235973i
$612$	−23.4278	+	9.06695i	−0.947013	+	0.366510i
$613$	28.7978	+	8.88295i	1.16313	+	0.358779i	0.815447	−	0.578832i	$-0.196491\pi$
$613$	28.7978	+	8.88295i	1.16313	+	0.358779i	0.347686	+	0.937611i	$0.386967\pi$
$614$	−29.9402	−	14.4184i	−1.20829	−	0.581881i
$615$	−9.19415	+	79.8997i	−0.370744	+	3.22187i
$616$	35.4585	−	42.4645i	1.42866	−	1.71094i
$617$	13.5547	+	9.24146i	0.545693	+	0.372047i	0.804565	−	0.593865i	$-0.202398\pi$
$617$	13.5547	+	9.24146i	0.545693	+	0.372047i	−0.258872	+	0.965912i	$0.583351\pi$
$618$	19.3919	+	3.71673i	0.780058	+	0.149509i
$619$	−16.0987	−	27.8838i	−0.647063	−	1.12075i	−0.983821	−	0.179154i	$-0.942664\pi$
$619$	−16.0987	−	27.8838i	−0.647063	−	1.12075i	0.336758	−	0.941591i	$-0.390669\pi$
$620$	4.43557	−	59.1886i	0.178137	−	2.37707i
$621$	20.0160	+	8.90263i	0.803213	+	0.357250i
$622$	2.36489	+	10.3613i	0.0948234	+	0.415448i
$623$	−4.34049	+	1.97107i	−0.173898	+	0.0789692i
$624$	−2.04020	−	2.77812i	−0.0816735	−	0.111214i
$625$	6.66235	−	88.9028i	0.266494	−	3.55611i
$626$	5.71118	−	25.0223i	0.228265	−	1.00009i
$627$	15.4133	+	29.3312i	0.615546	+	1.17138i
$628$	8.62917	+	37.8069i	0.344342	+	1.50866i
$629$	4.81135	−	6.03324i	0.191841	−	0.240561i
$630$	53.0849	+	60.4361i	2.11495	+	2.40783i
$631$	−30.9839	−	38.8526i	−1.23345	−	1.54670i	−0.731587	−	0.681748i	$-0.761220\pi$
$631$	−30.9839	−	38.8526i	−1.23345	−	1.54670i	−0.501862	−	0.864948i	$-0.667351\pi$
$632$	5.74863	−	7.20855i	0.228668	−	0.286741i
$633$	−17.7146	+	7.67894i	−0.704093	+	0.305210i
$634$	−29.0156	+	36.3844i	−1.15236	+	1.44501i
$635$	12.3661	+	11.4740i	0.490733	+	0.455334i
$636$	4.66740	+	0.894571i	0.185074	+	0.0354720i
$637$	−8.44321	−	3.02722i	−0.334532	−	0.119943i
$638$	−29.3713			−1.16282
$639$	5.17010	+	10.8672i	0.204526	+	0.429898i
$640$	32.1509	+	81.9191i	1.27088	+	3.23814i
$641$	−0.758216	−	10.1177i	−0.0299477	−	0.399625i	−0.991954	−	0.126598i	$-0.959594\pi$
$641$	−0.758216	−	10.1177i	−0.0299477	−	0.399625i	0.962006	−	0.273027i	$-0.0880248\pi$
$642$	−1.92048	−	10.2832i	−0.0757951	−	0.405845i
$643$	5.14414	−	13.1071i	0.202865	−	0.516892i	−0.792845	−	0.609424i	$-0.791401\pi$
$643$	5.14414	−	13.1071i	0.202865	−	0.516892i	0.995710	+	0.0925320i	$0.0294960\pi$
$644$	−39.1211	−	6.80125i	−1.54159	−	0.268007i
$645$	−4.41106	−	23.6190i	−0.173685	−	0.929996i
$646$	4.15319	+	18.1963i	0.163405	+	0.715924i
$647$	−31.3436	+	4.72428i	−1.23224	+	0.185731i	−0.732696	−	0.680556i	$-0.761738\pi$
$647$	−31.3436	+	4.72428i	−1.23224	+	0.185731i	−0.499547	+	0.866287i	$0.666500\pi$
$648$	29.6876	+	14.6448i	1.16624	+	0.575300i
$649$	19.4282	+	13.2459i	0.762622	+	0.519947i
$650$	29.8398	+	27.6872i	1.17041	+	1.08598i
$651$	−14.0362	−	10.9092i	−0.550120	−	0.427566i
$652$	35.9058	−	33.3157i	1.40618	−	1.30474i
$653$	−34.3164	+	5.17237i	−1.34291	+	0.202411i	−0.780866	−	0.624699i	$-0.785222\pi$
$653$	−34.3164	+	5.17237i	−1.34291	+	0.202411i	−0.562041	+	0.827110i	$0.689984\pi$
$654$	11.0358	−	2.92905i	0.431534	−	0.114535i
$655$	1.73758	+	3.00958i	0.0678930	+	0.117594i
$656$	−8.38936	−	14.5308i	−0.327550	−	0.567333i
$657$	−16.6436	−	24.6618i	−0.649330	−	0.962149i
$658$	20.4342	+	19.8354i	0.796610	+	0.773266i
$659$	−20.8679	+	14.2275i	−0.812898	+	0.554224i	−0.896896	−	0.442242i	$-0.854183\pi$
$659$	−20.8679	+	14.2275i	−0.812898	+	0.554224i	0.0839981	+	0.996466i	$0.473231\pi$
$660$	−17.2225	+	149.668i	−0.670385	+	5.82582i
$661$	3.31610	+	14.5288i	0.128981	+	0.565105i	0.997576	+	0.0695816i	$0.0221664\pi$
$661$	3.31610	+	14.5288i	0.128981	+	0.565105i	−0.868595	+	0.495523i	$0.834976\pi$
$662$	−2.01987	−	8.84964i	−0.0785046	−	0.343951i
$663$	−0.596791	+	5.18627i	−0.0231774	+	0.201418i
$664$	−47.3469	+	32.2806i	−1.83742	+	1.25273i
$665$	32.0944	−	20.8382i	1.24457	−	0.808069i
$666$	−23.1496	+	1.62463i	−0.897029	+	0.0629531i
$667$	4.61880	+	8.00000i	0.178841	+	0.309761i
$668$	−16.1576	−	27.9857i	−0.625155	−	1.08280i
$669$	12.5342	−	3.32674i	0.484599	−	0.128619i
$670$	9.84142	−	1.48335i	0.380207	−	0.0573070i
$671$	24.0055	−	22.2738i	0.926720	−	0.859871i
$672$	16.5506	+	3.56050i	0.638455	+	0.137349i
$673$	−0.415171	−	0.385222i	−0.0160037	−	0.0148492i	0.672130	−	0.740433i	$-0.265379\pi$
$673$	−0.415171	−	0.385222i	−0.0160037	−	0.0148492i	−0.688134	+	0.725584i	$0.741570\pi$
$674$	−44.4868	−	30.3306i	−1.71357	−	1.16829i
$675$	−67.4908	−	18.5989i	−2.59772	−	0.715872i
$676$	39.9821	−	6.02633i	1.53777	−	0.231782i
$677$	−8.25651	−	36.1741i	−0.317323	−	1.39028i	−0.842227	−	0.539123i	$-0.818756\pi$
$677$	−8.25651	−	36.1741i	−0.317323	−	1.39028i	0.524904	−	0.851161i	$-0.324101\pi$
$678$	−10.8058	−	57.8597i	−0.414995	−	2.22209i
$679$	−12.5822	+	11.1577i	−0.482861	+	0.428195i
$680$	−13.5854	+	34.6151i	−0.520978	+	1.32743i
$681$	3.65052	+	19.5467i	0.139888	+	0.749032i
$682$	−3.88599	−	51.8549i	−0.148802	−	1.98563i
$683$	−18.8443	−	48.0145i	−0.721057	−	1.83722i	−0.511126	−	0.859506i	$-0.670772\pi$
$683$	−18.8443	−	48.0145i	−0.721057	−	1.83722i	−0.209930	−	0.977716i	$-0.567324\pi$
$684$	20.3850	−	29.5972i	0.779440	−	1.13168i
$685$	65.1055			2.48755
$686$	−40.5349	+	16.2469i	−1.54763	+	0.620309i
$687$	32.4516	+	6.21979i	1.23810	+	0.237300i
$688$	3.67450	+	3.40944i	0.140089	+	0.129984i
$689$	0.615759	−	0.772137i	0.0234585	−	0.0294161i
$690$	67.8986	−	29.4327i	2.58485	−	1.12048i
$691$	32.3892	−	40.6147i	1.23214	−	1.54506i	0.495820	−	0.868425i	$-0.334868\pi$
$691$	32.3892	−	40.6147i	1.23214	−	1.54506i	0.736322	−	0.676631i	$-0.236561\pi$
$692$	32.4114	+	40.6427i	1.23210	+	1.54500i
$693$	34.4980	+	29.0847i	1.31047	+	1.10484i
$694$	−30.1238	+	37.7741i	−1.14348	+	1.43388i
$695$	−5.33464	−	23.3726i	−0.202355	−	0.886573i
$696$	6.49339	+	12.3568i	0.246131	+	0.468384i
$697$	−5.65492	+	24.7758i	−0.214196	+	0.938452i
$698$	−1.58748	+	21.1835i	−0.0600871	+	0.801807i
$699$	−14.5910	−	19.8684i	−0.551881	−	0.751490i
$700$	126.862	+	2.85883i	4.79495	+	0.108053i
$701$	−6.14896	−	26.9404i	−0.232243	−	1.01752i	−0.947774	−	0.318943i	$-0.896672\pi$
$701$	−6.14896	−	26.9404i	−0.232243	−	1.01752i	0.715531	−	0.698581i	$-0.246185\pi$
$702$	12.6977	−	9.23271i	0.479242	−	0.348466i
$703$	−0.824989	+	11.0087i	−0.0311150	+	0.415201i
$704$	33.5891	+	58.1781i	1.26594	+	2.19267i
$705$	−33.3751	−	6.39678i	−1.25698	−	0.240917i
$706$	47.7155	+	32.5319i	1.79580	+	1.22435i
$707$	−16.4995	−	8.40881i	−0.620527	−	0.316246i
$708$	2.91549	−	25.3364i	0.109571	−	0.952201i
$709$	−23.9549	−	11.5361i	−0.899644	−	0.433246i	−0.0738839	−	0.997267i	$-0.523539\pi$
$709$	−23.9549	−	11.5361i	−0.899644	−	0.433246i	−0.825761	+	0.564021i	$0.809254\pi$
$710$	38.8475	+	11.9829i	1.45792	+	0.449709i
$711$	5.85725	+	4.71654i	0.219664	+	0.176884i
$712$	0.495252	+	6.60867i	0.0185603	+	0.247671i
$713$	−13.5129	+	9.21292i	−0.506061	+	0.345027i
$714$	14.5793	+	20.8199i	0.545617	+	0.779164i
$715$	25.8681	+	17.6365i	0.967410	+	0.659569i
$716$	−0.981909	+	1.70072i	−0.0366957	+	0.0635588i
$717$	1.98847	−	2.29961i	0.0742609	−	0.0858806i
$718$	33.9027	+	23.1145i	1.26524	+	0.862624i
$719$	−3.03793	+	7.74052i	−0.113296	+	0.288673i	−0.976263	−	0.216586i	$-0.930508\pi$
$719$	−3.03793	+	7.74052i	−0.113296	+	0.288673i	0.862968	+	0.505259i	$0.168603\pi$
$720$	18.6752	−	7.22760i	0.695982	−	0.269357i
$721$	−0.668275	−	12.7737i	−0.0248879	−	0.475718i
$722$	13.2682	+	12.3111i	0.493793	+	0.458173i
$723$	−2.48905	+	9.20205i	−0.0925687	+	0.342228i
$724$	11.9740	−	52.4616i	0.445011	−	1.94972i
$725$	−18.4058	−	23.0801i	−0.683574	−	0.857175i
$726$	3.04944	+	87.0108i	0.113175	+	3.22927i
$727$	1.41232	+	3.59853i	0.0523801	+	0.133462i	0.954669	−	0.297670i	$-0.0962095\pi$
$727$	1.41232	+	3.59853i	0.0523801	+	0.133462i	−0.902289	+	0.431132i	$0.858114\pi$
$728$	−7.99223	+	9.57136i	−0.296212	+	0.354738i
$729$	−12.0592	+	24.1573i	−0.446638	+	0.894715i
$730$	−99.3859	−	14.9800i	−3.67844	−	0.554435i
$731$	−0.567356	−	7.57084i	−0.0209844	−	0.280018i
$732$	−33.4971	−	11.8102i	−1.23809	−	0.436519i
$733$	−18.2574	−	16.9404i	−0.674354	−	0.625709i	0.266774	−	0.963759i	$-0.414042\pi$
$733$	−18.2574	−	16.9404i	−0.674354	−	0.625709i	−0.941128	+	0.338050i	$0.890233\pi$
$734$	24.3994	+	42.2610i	0.900597	+	1.55988i
$735$	29.7852	−	42.7591i	1.09864	−	1.57719i
$736$	7.78737	−	13.4881i	0.287046	−	0.497179i
$737$	5.33485	−	1.64558i	0.196512	−	0.0606158i
$738$	66.3652	−	37.8981i	2.44294	−	1.39505i
$739$	37.2871	−	25.4219i	1.37163	−	0.935160i	0.371651	−	0.928372i	$-0.378792\pi$
$739$	37.2871	−	25.4219i	1.37163	−	0.935160i	0.999977	−	0.00678784i	$-0.00216065\pi$
$740$	−31.2960	+	39.2439i	−1.15046	+	1.44264i
$741$	−3.47410	−	6.61116i	−0.127624	−	0.242867i
$742$	−0.251211	−	4.80175i	−0.00922224	−	0.176278i
$743$	−53.4056	−	8.04959i	−1.95926	−	0.295311i	−0.999914	−	0.0130782i	$-0.995837\pi$
$743$	−53.4056	−	8.04959i	−1.95926	−	0.295311i	−0.959346	−	0.282233i	$-0.908925\pi$
$744$	−20.9568	+	13.0989i	−0.768314	+	0.480231i
$745$	−18.8779	+	48.1002i	−0.691634	+	1.76226i
$746$	41.8651	+	38.8452i	1.53279	+	1.42222i
$747$	−26.1459	−	38.7418i	−0.956627	−	1.41749i
$748$	−10.5928	+	46.4101i	−0.387311	+	1.69692i
$749$	−6.17042	+	2.80206i	−0.225462	+	0.102385i
$750$	−126.117	+	78.8285i	−4.60513	+	2.87841i
$751$	31.6275	−	4.76707i	1.15410	−	0.173953i	0.456019	−	0.889970i	$-0.349275\pi$
$751$	31.6275	−	4.76707i	1.15410	−	0.173953i	0.698083	+	0.716017i	$0.254037\pi$
$752$	6.38739	−	3.07600i	0.232924	−	0.112170i
$753$	15.1857	+	43.7300i	0.553396	+	1.59361i
$754$	6.62020			0.241093
$755$	−35.9245	+	17.3003i	−1.30743	+	0.629624i
$756$	10.5194	−	47.7965i	0.382587	−	1.73834i
$757$	−7.74607	−	3.73031i	−0.281536	−	0.135580i	0.287787	−	0.957694i	$-0.407080\pi$
$757$	−7.74607	−	3.73031i	−0.281536	−	0.135580i	−0.569323	+	0.822114i	$0.692795\pi$
$758$	7.86859	+	3.78931i	0.285800	+	0.137634i
$759$	35.2014	−	22.0025i	1.27773	−	0.798639i
$760$	−11.8375	−	51.8636i	−0.429392	−	1.88129i
$761$	14.0344	−	9.56852i	0.508748	−	0.346859i	−0.281585	−	0.959536i	$-0.590860\pi$
$761$	14.0344	−	9.56852i	0.508748	−	0.346859i	0.790333	+	0.612678i	$0.209908\pi$
$762$	1.83246	−	15.9246i	0.0663831	−	0.576887i
$763$	−3.55313	−	6.48748i	−0.128632	−	0.234862i
$764$	−32.3422	+	15.5752i	−1.17010	+	0.563491i
$765$	−28.1804	−	11.2143i	−1.01886	−	0.405453i
$766$	−0.485789	+	0.841411i	−0.0175523	+	0.0304014i
$767$	−4.37905	−	2.98558i	−0.158118	−	0.107803i
$768$	22.7964	−	36.0903i	0.822595	−	1.30230i
$769$	8.19128	−	7.60040i	0.295385	−	0.274077i	−0.518532	−	0.855058i	$-0.673521\pi$
$769$	8.19128	−	7.60040i	0.295385	−	0.274077i	0.813917	+	0.580981i	$0.197331\pi$
$770$	151.201	−	19.3170i	5.44891	−	0.696136i
$771$	−0.949223	+	2.16167i	−0.0341854	+	0.0778505i

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.524692 + 2.29882i) q^{2} +(1.63349 + 0.575929i) q^{3} +(-3.20735 - 1.54458i) q^{4} +(-1.57024 - 4.00089i) q^{5} +(-2.18104 + 3.45293i) q^{6} +(2.51000 + 0.836609i) q^{7} +(2.29328 - 2.87568i) q^{8} +(2.33661 + 1.88155i) q^{9} +O(q^{10})\)	\(q+(-0.524692 + 2.29882i) q^{2} +(1.63349 + 0.575929i) q^{3} +(-3.20735 - 1.54458i) q^{4} +(-1.57024 - 4.00089i) q^{5} +(-2.18104 + 3.45293i) q^{6} +(2.51000 + 0.836609i) q^{7} +(2.29328 - 2.87568i) q^{8} +(2.33661 + 1.88155i) q^{9} +(10.0212 - 1.51046i) q^{10} +(5.43233 - 1.67565i) q^{11} +(-4.34962 - 4.37027i) q^{12} +(-1.22443 + 0.377686i) q^{13} +(-3.24019 + 5.33108i) q^{14} +(-0.260740 - 7.43978i) q^{15} +(0.968309 + 1.21422i) q^{16} +(0.175783 - 2.34566i) q^{17} +(-5.55136 + 4.38422i) q^{18} +(1.68254 + 2.91425i) q^{19} +(-1.14340 + 15.2576i) q^{20} +(3.61824 + 2.81218i) q^{21} +(1.00173 + 13.3672i) q^{22} +(3.48335 - 2.37491i) q^{23} +(5.40225 - 3.37664i) q^{24} +(-9.87625 + 9.16382i) q^{25} +(-0.225787 - 3.01292i) q^{26} +(2.73320 + 4.41923i) q^{27} +(-6.75823 - 6.56019i) q^{28} +(-0.163743 + 2.18500i) q^{29} +(17.2396 + 3.30420i) q^{30} -3.87928 q^{31} +(3.32843 - 1.60289i) q^{32} +(9.83873 + 0.391468i) q^{33} +(5.30003 + 1.63484i) q^{34} +(-0.594101 - 11.3559i) q^{35} +(-4.58812 - 9.64389i) q^{36} +(2.71058 + 1.84804i) q^{37} +(-7.58217 + 2.33879i) q^{38} +(-2.21762 - 0.0882357i) q^{39} +(-15.1063 - 4.65967i) q^{40} +(-10.6831 - 1.61022i) q^{41} +(-8.36316 + 6.84217i) q^{42} +(3.19155 - 0.481048i) q^{43} +(-20.0116 - 3.01626i) q^{44} +(3.85887 - 12.3030i) q^{45} +(3.63181 + 9.25370i) q^{46} +(1.01578 - 4.45042i) q^{47} +(0.882422 + 2.54110i) q^{48} +(5.60017 + 4.19977i) q^{49} +(-15.8840 - 27.5119i) q^{50} +(1.63808 - 3.73039i) q^{51} +(4.51054 + 0.679855i) q^{52} +(-0.636820 + 0.434177i) q^{53} +(-11.5931 + 3.96441i) q^{54} +(-15.2341 - 19.1030i) q^{55} +(8.16195 - 5.29937i) q^{56} +(1.07002 + 5.72944i) q^{57} +(-4.93702 - 1.52287i) q^{58} +(2.57889 + 3.23383i) q^{59} +(-10.6551 + 24.2647i) q^{60} +(5.18995 - 2.49935i) q^{61} +(2.03542 - 8.91777i) q^{62} +(4.29076 + 6.67753i) q^{63} +(2.62953 + 11.5207i) q^{64} +(3.43372 + 4.30575i) q^{65} +(-6.06222 + 22.4121i) q^{66} +0.982056 q^{67} +(-4.18686 + 7.25185i) q^{68} +(7.05781 - 1.87324i) q^{69} +(26.4169 + 4.59261i) q^{70} +(3.61418 + 1.74050i) q^{71} +(10.7693 - 2.40442i) q^{72} +(-9.47692 - 2.92324i) q^{73} +(-5.67054 + 5.26149i) q^{74} +(-21.4105 + 9.28104i) q^{75} +(-0.895218 - 11.9459i) q^{76} +(15.0370 + 0.338856i) q^{77} +(1.36640 - 5.05162i) q^{78} +2.50673 q^{79} +(3.33750 - 5.78071i) q^{80} +(1.91950 + 8.79292i) q^{81} +(9.30692 - 23.7137i) q^{82} +(-14.8875 - 4.59219i) q^{83} +(-7.26134 - 14.6083i) q^{84} +(-9.66076 + 2.97995i) q^{85} +(-0.568732 + 7.58920i) q^{86} +(-1.52588 + 3.47489i) q^{87} +(7.63921 - 19.4644i) q^{88} +(-1.32080 + 1.22552i) q^{89} +(26.2577 + 15.3262i) q^{90} +(-3.38929 - 0.0763771i) q^{91} +(-14.8406 + 2.23685i) q^{92} +(-6.33678 - 2.23419i) q^{93} +(9.69777 + 4.67020i) q^{94} +(9.01762 - 11.3077i) q^{95} +(6.36012 - 0.701368i) q^{96} +(-3.17809 + 5.50461i) q^{97} +(-12.5929 + 10.6702i) q^{98} +(15.8461 + 6.30588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 5 q^{2} - 13 q^{3} - 109 q^{4} - 12 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 3 q^{9}+O(q^{10}) \) 648 * q - 5 * q^2 - 13 * q^3 - 109 * q^4 - 12 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 3 * q^9	\( 648 q - 5 q^{2} - 13 q^{3} - 109 q^{4} - 12 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 3 q^{9} - 22 q^{10} - 8 q^{11} - 64 q^{12} - 4 q^{13} - 26 q^{14} - 4 q^{15} - 97 q^{16} - 37 q^{17} - q^{18} - 14 q^{19} - 11 q^{20} - 33 q^{21} - q^{22} + 31 q^{23} - 20 q^{24} + 38 q^{25} - 44 q^{26} - 49 q^{27} - 22 q^{28} + 73 q^{29} - 12 q^{30} - 20 q^{31} - q^{32} - 43 q^{33} - 7 q^{34} - 32 q^{35} + 20 q^{36} - 39 q^{37} - 40 q^{38} + q^{39} - q^{40} - 17 q^{41} + 82 q^{42} - q^{43} - 31 q^{44} - 177 q^{45} + 56 q^{46} + 5 q^{47} - 23 q^{48} - q^{49} - 21 q^{50} - 18 q^{51} - 48 q^{52} + 50 q^{53} - 15 q^{54} + 20 q^{55} + 127 q^{56} + 33 q^{57} - 82 q^{58} + 53 q^{59} + 43 q^{60} + 42 q^{61} - 30 q^{62} + 57 q^{63} - 88 q^{64} - 11 q^{65} - 90 q^{66} - 26 q^{67} + 145 q^{68} + 64 q^{69} - 46 q^{70} - 19 q^{71} - 46 q^{72} - 40 q^{73} + 18 q^{74} - 114 q^{75} + 43 q^{76} + 7 q^{77} - 129 q^{78} - 26 q^{79} + 163 q^{80} + 85 q^{81} - 28 q^{82} - 221 q^{83} - 113 q^{84} - 10 q^{85} - 18 q^{86} + 37 q^{87} - 4 q^{88} - 104 q^{89} - 60 q^{90} - 49 q^{91} + 119 q^{92} - 149 q^{93} - 13 q^{94} + 37 q^{95} + 186 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) 648 * q - 5 * q^2 - 13 * q^3 - 109 * q^4 - 12 * q^5 + 2 * q^6 - 7 * q^7 - 16 * q^8 - 3 * q^9 - 22 * q^10 - 8 * q^11 - 64 * q^12 - 4 * q^13 - 26 * q^14 - 4 * q^15 - 97 * q^16 - 37 * q^17 - q^18 - 14 * q^19 - 11 * q^20 - 33 * q^21 - q^22 + 31 * q^23 - 20 * q^24 + 38 * q^25 - 44 * q^26 - 49 * q^27 - 22 * q^28 + 73 * q^29 - 12 * q^30 - 20 * q^31 - q^32 - 43 * q^33 - 7 * q^34 - 32 * q^35 + 20 * q^36 - 39 * q^37 - 40 * q^38 + q^39 - q^40 - 17 * q^41 + 82 * q^42 - q^43 - 31 * q^44 - 177 * q^45 + 56 * q^46 + 5 * q^47 - 23 * q^48 - q^49 - 21 * q^50 - 18 * q^51 - 48 * q^52 + 50 * q^53 - 15 * q^54 + 20 * q^55 + 127 * q^56 + 33 * q^57 - 82 * q^58 + 53 * q^59 + 43 * q^60 + 42 * q^61 - 30 * q^62 + 57 * q^63 - 88 * q^64 - 11 * q^65 - 90 * q^66 - 26 * q^67 + 145 * q^68 + 64 * q^69 - 46 * q^70 - 19 * q^71 - 46 * q^72 - 40 * q^73 + 18 * q^74 - 114 * q^75 + 43 * q^76 + 7 * q^77 - 129 * q^78 - 26 * q^79 + 163 * q^80 + 85 * q^81 - 28 * q^82 - 221 * q^83 - 113 * q^84 - 10 * q^85 - 18 * q^86 + 37 * q^87 - 4 * q^88 - 104 * q^89 - 60 * q^90 - 49 * q^91 + 119 * q^92 - 149 * q^93 - 13 * q^94 + 37 * q^95 + 186 * q^96 - 11 * q^97 - 33 * q^98 + 62 * q^99

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