LMFDB - Embedded newform 441.2.y.a.151.52

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			151.52
Character	$\chi$	$=$	441.151
Dual form			441.2.y.a.184.52

$q$-expansion

$f(q)$	$=$	$q+(2.32120 - 1.11783i) q^{2} +(-0.647872 + 1.60632i) q^{3} +(2.89143 - 3.62573i) q^{4} +(-0.476675 - 0.442290i) q^{5} +(0.291752 + 4.45279i) q^{6} +(2.64170 - 0.146332i) q^{7} +(1.51204 - 6.62468i) q^{8} +(-2.16052 - 2.08138i) q^{9} +O(q^{10})$	\(q+(2.32120 - 1.11783i) q^{2} +(-0.647872 + 1.60632i) q^{3} +(2.89143 - 3.62573i) q^{4} +(-0.476675 - 0.442290i) q^{5} +(0.291752 + 4.45279i) q^{6} +(2.64170 - 0.146332i) q^{7} +(1.51204 - 6.62468i) q^{8} +(-2.16052 - 2.08138i) q^{9} +(-1.60086 - 0.493800i) q^{10} +(3.93542 + 2.68312i) q^{11} +(3.95081 + 6.99357i) q^{12} +(-3.23220 - 2.20368i) q^{13} +(5.96833 - 3.29263i) q^{14} +(1.01928 - 0.479145i) q^{15} +(-1.83164 - 8.02494i) q^{16} +(-3.53970 + 0.533524i) q^{17} +(-7.34162 - 2.41619i) q^{18} +(2.69554 + 4.66882i) q^{19} +(-2.98190 + 0.449448i) q^{20} +(-1.47643 + 4.33822i) q^{21} +(12.1341 + 1.82893i) q^{22} +(-0.665542 - 1.69577i) q^{23} +(9.66174 + 6.72076i) q^{24} +(-0.342052 - 4.56436i) q^{25} +(-9.96590 - 1.50212i) q^{26} +(4.74310 - 2.12202i) q^{27} +(7.10773 - 10.0012i) q^{28} +(-4.13932 + 0.623901i) q^{29} +(1.83035 - 2.25157i) q^{30} +2.97936 q^{31} +(-4.74882 - 5.95483i) q^{32} +(-6.85960 + 4.58322i) q^{33} +(-7.61995 + 5.19519i) q^{34} +(-1.32395 - 1.09864i) q^{35} +(-13.7935 + 1.81533i) q^{36} +(-2.55648 + 6.51381i) q^{37} +(11.4758 + 7.82408i) q^{38} +(5.63386 - 3.76425i) q^{39} +(-3.65078 + 2.48906i) q^{40} +(-5.17779 + 1.59714i) q^{41} +(1.42231 + 11.7203i) q^{42} +(-12.0827 - 3.72703i) q^{43} +(21.1073 - 6.51072i) q^{44} +(0.109295 + 1.94772i) q^{45} +(-3.44044 - 3.19226i) q^{46} +(-6.40143 + 3.08277i) q^{47} +(14.0773 + 2.25694i) q^{48} +(6.95717 - 0.773129i) q^{49} +(-5.89614 - 10.2124i) q^{50} +(1.43626 - 6.03155i) q^{51} +(-17.3356 + 5.34733i) q^{52} +(3.33328 + 8.49307i) q^{53} +(8.63761 - 10.2276i) q^{54} +(-0.689197 - 3.01957i) q^{55} +(3.02496 - 17.7217i) q^{56} +(-9.24598 + 1.30511i) q^{57} +(-8.91074 + 6.07524i) q^{58} +(0.866460 + 3.79621i) q^{59} +(1.20993 - 5.08106i) q^{60} +(-4.93850 - 6.19269i) q^{61} +(6.91568 - 3.33042i) q^{62} +(-6.01203 - 5.18223i) q^{63} +(-2.84710 - 1.37109i) q^{64} +(0.566045 + 2.48001i) q^{65} +(-10.7992 + 18.3064i) q^{66} -1.43413 q^{67} +(-8.30037 + 14.3767i) q^{68} +(3.15514 + 0.0295711i) q^{69} +(-4.30125 - 1.07022i) q^{70} +(-5.33059 + 6.68435i) q^{71} +(-17.0553 + 11.1656i) q^{72} +(4.76734 - 3.25032i) q^{73} +(1.34723 + 17.9775i) q^{74} +(7.55343 + 2.40768i) q^{75} +(24.7219 + 3.72622i) q^{76} +(10.7888 + 6.51213i) q^{77} +(8.86951 - 15.0352i) q^{78} +4.33387 q^{79} +(-2.67625 + 4.63540i) q^{80} +(0.335725 + 8.99374i) q^{81} +(-10.2333 + 9.49515i) q^{82} +(-1.81914 + 1.24027i) q^{83} +(11.4602 + 17.8968i) q^{84} +(1.92326 + 1.31126i) q^{85} +(-32.2125 + 4.85526i) q^{86} +(1.67956 - 7.05327i) q^{87} +(23.7253 - 22.0139i) q^{88} +(-0.498638 - 6.65386i) q^{89} +(2.43091 + 4.39886i) q^{90} +(-8.86098 - 5.34848i) q^{91} +(-8.07279 - 2.49012i) q^{92} +(-1.93025 + 4.78581i) q^{93} +(-11.4130 + 14.3114i) q^{94} +(0.780072 - 3.41772i) q^{95} +(12.6420 - 3.77015i) q^{96} +(8.43105 - 14.6030i) q^{97} +(15.2847 - 9.57151i) q^{98} +(-2.91797 - 13.9880i) 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.32120	−	1.11783i	1.64133	−	0.790424i	0.641606	−	0.767034i	$-0.278268\pi$
$2$	2.32120	−	1.11783i	1.64133	−	0.790424i	0.999726	−	0.0233902i	$-0.00744601\pi$
$3$	−0.647872	+	1.60632i	−0.374049	+	0.927409i
$3$	−0.647872	+	1.60632i	−0.374049	+	0.927409i
$4$	2.89143	−	3.62573i	1.44571	−	1.81287i
$5$	−0.476675	−	0.442290i	−0.213176	−	0.197798i	0.566356	−	0.824160i	$-0.308353\pi$
$5$	−0.476675	−	0.442290i	−0.213176	−	0.197798i	−0.779532	+	0.626362i	$0.784543\pi$
$6$	0.291752	+	4.45279i	0.119107	+	1.81784i
$7$	2.64170	−	0.146332i	0.998469	−	0.0553082i
$7$	2.64170	−	0.146332i	0.998469	−	0.0553082i
$8$	1.51204	−	6.62468i	0.534587	−	2.34218i
$9$	−2.16052	−	2.08138i	−0.720175	−	0.693793i
$10$	−1.60086	−	0.493800i	−0.506236	−	0.156153i
$11$	3.93542	+	2.68312i	1.18657	+	0.808992i	0.985348	−	0.170554i	$-0.0545556\pi$
$11$	3.93542	+	2.68312i	1.18657	+	0.808992i	0.201224	+	0.979545i	$0.435508\pi$
$12$	3.95081	+	6.99357i	1.14050	+	2.01887i
$13$	−3.23220	−	2.20368i	−0.896451	−	0.611190i	0.0249986	−	0.999687i	$-0.492042\pi$
$13$	−3.23220	−	2.20368i	−0.896451	−	0.611190i	−0.921450	+	0.388497i	$0.872994\pi$
$14$	5.96833	−	3.29263i	1.59510	−	0.879993i
$15$	1.01928	−	0.479145i	0.263178	−	0.123715i
$16$	−1.83164	−	8.02494i	−0.457910	−	2.00624i
$17$	−3.53970	+	0.533524i	−0.858504	+	0.129399i	−0.563519	−	0.826103i	$-0.690553\pi$
$17$	−3.53970	+	0.533524i	−0.858504	+	0.129399i	−0.294985	+	0.955502i	$0.595315\pi$
$18$	−7.34162	−	2.41619i	−1.73044	−	0.569502i
$19$	2.69554	+	4.66882i	0.618400	+	1.07110i	0.989778	+	0.142618i	$0.0455522\pi$
$19$	2.69554	+	4.66882i	0.618400	+	1.07110i	−0.371378	+	0.928482i	$0.621115\pi$
$20$	−2.98190	+	0.449448i	−0.666772	+	0.100500i
$21$	−1.47643	+	4.33822i	−0.322183	+	0.946677i
$22$	12.1341	+	1.82893i	2.58701	+	0.389929i
$23$	−0.665542	−	1.69577i	−0.138775	−	0.353593i	0.844543	−	0.535488i	$-0.179872\pi$
$23$	−0.665542	−	1.69577i	−0.138775	−	0.353593i	−0.983318	+	0.181895i	$0.941777\pi$
$24$	9.66174	+	6.72076i	1.97219	+	1.37187i
$25$	−0.342052	−	4.56436i	−0.0684103	−	0.912872i
$26$	−9.96590	−	1.50212i	−1.95447	−	0.294590i
$27$	4.74310	−	2.12202i	0.912810	−	0.408384i
$28$	7.10773	−	10.0012i	1.34323	−	1.89005i
$29$	−4.13932	+	0.623901i	−0.768652	+	0.115856i	−0.521650	−	0.853160i	$-0.674683\pi$
$29$	−4.13932	+	0.623901i	−0.768652	+	0.115856i	−0.247001	+	0.969015i	$0.579445\pi$
$30$	1.83035	−	2.25157i	0.334175	−	0.411079i
$31$	2.97936			0.535109			0.267555	−	0.963543i	$-0.413784\pi$
$31$	2.97936			0.535109			0.267555	+	0.963543i	$0.413784\pi$
$32$	−4.74882	−	5.95483i	−0.839481	−	1.05268i
$33$	−6.85960	+	4.58322i	−1.19410	+	0.797836i
$34$	−7.61995	+	5.19519i	−1.30681	+	0.890968i
$35$	−1.32395	−	1.09864i	−0.223789	−	0.185705i
$36$	−13.7935	+	1.81533i	−2.29892	+	0.302555i
$37$	−2.55648	+	6.51381i	−0.420283	+	1.07086i	0.551330	+	0.834287i	$0.314121\pi$
$37$	−2.55648	+	6.51381i	−0.420283	+	1.07086i	−0.971613	+	0.236576i	$0.923975\pi$
$38$	11.4758	+	7.82408i	1.86162	+	1.26923i
$39$	5.63386	−	3.76425i	0.902140	−	0.602762i
$40$	−3.65078	+	2.48906i	−0.577239	+	0.393555i
$41$	−5.17779	+	1.59714i	−0.808635	+	0.249431i	−0.671388	−	0.741106i	$-0.734302\pi$
$41$	−5.17779	+	1.59714i	−0.808635	+	0.249431i	−0.137247	+	0.990537i	$0.543825\pi$
$42$	1.42231	+	11.7203i	0.219467	+	1.80847i
$43$	−12.0827	−	3.72703i	−1.84260	−	0.568366i	−0.999533	−	0.0305553i	$-0.990272\pi$
$43$	−12.0827	−	3.72703i	−1.84260	−	0.568366i	−0.843065	−	0.537811i	$-0.819251\pi$
$44$	21.1073	−	6.51072i	3.18204	−	0.981529i
$45$	0.109295	+	1.94772i	0.0162928	+	0.290349i
$46$	−3.44044	−	3.19226i	−0.507265	−	0.470673i
$47$	−6.40143	+	3.08277i	−0.933745	+	0.449668i	−0.837959	−	0.545734i	$-0.816251\pi$
$47$	−6.40143	+	3.08277i	−0.933745	+	0.449668i	−0.0957866	+	0.995402i	$0.530537\pi$
$48$	14.0773	+	2.25694i	2.03188	+	0.325761i
$49$	6.95717	−	0.773129i	0.993882	−	0.110447i
$50$	−5.89614	−	10.2124i	−0.833841	−	1.44425i
$51$	1.43626	−	6.03155i	0.201117	−	0.844585i
$52$	−17.3356	+	5.34733i	−2.40402	+	0.741541i
$53$	3.33328	+	8.49307i	0.457862	+	1.16661i	0.954382	+	0.298587i	$0.0965155\pi$
$53$	3.33328	+	8.49307i	0.457862	+	1.16661i	−0.496521	+	0.868025i	$0.665389\pi$
$54$	8.63761	−	10.2276i	1.17543	−	1.39180i
$55$	−0.689197	−	3.01957i	−0.0929314	−	0.407159i
$56$	3.02496	−	17.7217i	0.404227	−	2.36816i
$57$	−9.24598	+	1.30511i	−1.22466	+	0.172866i
$58$	−8.91074	+	6.07524i	−1.17004	+	0.797718i
$59$	0.866460	+	3.79621i	0.112803	+	0.494224i	0.999492	+	0.0318579i	$0.0101424\pi$
$59$	0.866460	+	3.79621i	0.112803	+	0.494224i	−0.886689	+	0.462366i	$0.847000\pi$
$60$	1.20993	−	5.08106i	0.156201	−	0.655962i
$61$	−4.93850	−	6.19269i	−0.632311	−	0.792892i	0.357707	−	0.933834i	$-0.383559\pi$
$61$	−4.93850	−	6.19269i	−0.632311	−	0.792892i	−0.990018	+	0.140941i	$0.954987\pi$
$62$	6.91568	−	3.33042i	0.878292	−	0.422963i
$63$	−6.01203	−	5.18223i	−0.757445	−	0.652899i
$64$	−2.84710	−	1.37109i	−0.355888	−	0.171387i
$65$	0.566045	+	2.48001i	0.0702093	+	0.307607i
$66$	−10.7992	+	18.3064i	−1.32929	+	2.25336i
$67$	−1.43413			−0.175207			−0.0876033	−	0.996155i	$-0.527921\pi$
$67$	−1.43413			−0.175207			−0.0876033	+	0.996155i	$0.527921\pi$
$68$	−8.30037	+	14.3767i	−1.00657	+	1.74343i
$69$	3.15514	+	0.0295711i	0.379834	+	0.00355995i
$70$	−4.30125	−	1.07022i	−0.514098	−	0.127915i
$71$	−5.33059	+	6.68435i	−0.632625	+	0.793287i	−0.990059	−	0.140651i	$-0.955080\pi$
$71$	−5.33059	+	6.68435i	−0.632625	+	0.793287i	0.357434	+	0.933938i	$0.383652\pi$
$72$	−17.0553	+	11.1656i	−2.00998	+	1.31588i
$73$	4.76734	−	3.25032i	0.557975	−	0.380421i	−0.251248	−	0.967923i	$-0.580841\pi$
$73$	4.76734	−	3.25032i	0.557975	−	0.380421i	0.809223	+	0.587502i	$0.199888\pi$
$74$	1.34723	+	17.9775i	0.156612	+	2.08985i
$75$	7.55343	+	2.40768i	0.872195	+	0.278015i
$76$	24.7219	+	3.72622i	2.83579	+	0.427427i
$77$	10.7888	+	6.51213i	1.22950	+	0.742126i
$78$	8.86951	−	15.0352i	1.00427	−	1.70241i
$79$	4.33387			0.487599			0.243799	−	0.969826i	$-0.421606\pi$
$79$	4.33387			0.487599			0.243799	+	0.969826i	$0.421606\pi$
$80$	−2.67625	+	4.63540i	−0.299214	+	0.518254i
$81$	0.335725	+	8.99374i	0.0373028	+	0.999304i
$82$	−10.2333	+	9.49515i	−1.13008	+	1.04856i
$83$	−1.81914	+	1.24027i	−0.199676	+	0.136137i	−0.659031	−	0.752116i	$-0.729033\pi$
$83$	−1.81914	+	1.24027i	−0.199676	+	0.136137i	0.459354	+	0.888253i	$0.348081\pi$
$84$	11.4602	+	17.8968i	1.25042	+	1.95270i
$85$	1.92326	+	1.31126i	0.208607	+	0.142226i
$86$	−32.2125	+	4.85526i	−3.47357	+	0.523556i
$87$	1.67956	−	7.05327i	0.180068	−	0.756190i
$88$	23.7253	−	22.0139i	2.52913	−	2.34669i
$89$	−0.498638	−	6.65386i	−0.0528555	−	0.705307i	−0.959193	−	0.282753i	$-0.908752\pi$
$89$	−0.498638	−	6.65386i	−0.0528555	−	0.705307i	0.906337	−	0.422555i	$-0.138867\pi$
$90$	2.43091	+	4.39886i	0.256241	+	0.463681i
$91$	−8.86098	−	5.34848i	−0.928883	−	0.560673i
$92$	−8.07279	−	2.49012i	−0.841646	−	0.259613i
$93$	−1.93025	+	4.78581i	−0.200157	+	0.496265i
$94$	−11.4130	+	14.3114i	−1.17716	+	1.47611i
$95$	0.780072	−	3.41772i	0.0800337	−	0.350651i
$96$	12.6420	−	3.77015i	1.29027	−	0.384790i
$97$	8.43105	−	14.6030i	0.856043	−	1.48271i	−0.0196309	−	0.999807i	$-0.506249\pi$
$97$	8.43105	−	14.6030i	0.856043	−	1.48271i	0.875674	−	0.482903i	$-0.160418\pi$
$98$	15.2847	−	9.57151i	1.54399	−	0.966869i
$99$	−2.91797	−	13.9880i	−0.293267	−	1.40585i
$100$	−17.5382	−	11.9573i	−1.75382	−	1.19573i
$101$	8.92588	−	2.75327i	0.888159	−	0.273961i	0.183087	−	0.983097i	$-0.441391\pi$
$101$	8.92588	−	2.75327i	0.888159	−	0.273961i	0.705072	+	0.709136i	$0.250915\pi$
$102$	−3.40839	−	15.6059i	−0.337481	−	1.54521i
$103$	−7.69993	−	7.14449i	−0.758697	−	0.703968i	0.202667	−	0.979248i	$-0.435039\pi$
$103$	−7.69993	−	7.14449i	−0.758697	−	0.703968i	−0.961364	+	0.275280i	$0.911229\pi$
$104$	−19.4859	+	18.0802i	−1.91075	+	1.77291i
$105$	2.62253	−	1.41491i	0.255932	−	0.138081i
$106$	17.2310	+	15.9880i	1.67362	+	1.55289i
$107$	0.214273	+	2.85928i	0.0207146	+	0.276417i	0.997937	+	0.0641997i	$0.0204495\pi$
$107$	0.214273	+	2.85928i	0.0207146	+	0.276417i	−0.977222	+	0.212217i	$0.931931\pi$
$108$	6.02044	−	23.3329i	0.579317	−	2.24521i
$109$	0.888813	−	11.8604i	0.0851329	−	1.13602i	−0.777056	−	0.629432i	$-0.783288\pi$
$109$	0.888813	−	11.8604i	0.0851329	−	1.13602i	0.862189	−	0.506588i	$-0.169093\pi$
$110$	−4.97512	−	6.23861i	−0.474360	−	0.594828i
$111$	−8.80698	−	8.32664i	−0.835922	−	0.790330i
$112$	−6.01295	−	20.9315i	−0.568170	−	1.97784i
$113$	−0.924664	−	12.3388i	−0.0869851	−	1.16074i	−0.854411	−	0.519598i	$-0.826082\pi$
$113$	−0.924664	−	12.3388i	−0.0869851	−	1.16074i	0.767426	−	0.641138i	$-0.221537\pi$
$114$	−20.0028	+	13.3648i	−1.87344	+	1.25173i
$115$	−0.432776	+	1.10269i	−0.0403565	+	0.102827i
$116$	−9.70642	+	16.8120i	−0.901219	+	1.56096i
$117$	2.39656	+	11.4885i	0.221562	+	1.06212i
$118$	6.25473	+	7.84319i	0.575795	+	0.722024i
$119$	−9.27276	+	1.92738i	−0.850033	+	0.176683i
$120$	−1.63299	−	7.47691i	−0.149071	−	0.682545i
$121$	4.26961	+	10.8788i	0.388146	+	0.988981i
$122$	−18.3856	−	8.85403i	−1.66455	−	0.801607i
$123$	0.789034	−	9.35193i	0.0711448	−	0.843235i
$124$	8.61461	−	10.8024i	0.773615	−	0.970082i
$125$	−3.88288	+	4.86898i	−0.347295	+	0.435494i
$126$	−19.7479	−	5.30854i	−1.75929	−	0.472923i
$127$	10.0685	+	12.6255i	0.893433	+	1.12033i	0.992130	+	0.125212i	$0.0399610\pi$
$127$	10.0685	+	12.6255i	0.893433	+	1.12033i	−0.0986975	+	0.995117i	$0.531468\pi$
$128$	7.09170			0.626824
$129$	13.8149	−	16.9941i	1.21633	−	1.49625i
$130$	4.08612	+	5.12384i	0.358377	+	0.449390i
$131$	14.0535	+	4.33492i	1.22786	+	0.378744i	0.839803	−	0.542892i	$-0.182671\pi$
$131$	14.0535	+	4.33492i	1.22786	+	0.378744i	0.388056	+	0.921636i	$0.373147\pi$
$132$	−3.21649	+	38.1231i	−0.279960	+	3.31819i
$133$	7.80402	+	11.9392i	0.676694	+	1.03526i
$134$	−3.32889	+	1.60311i	−0.287572	+	0.138488i
$135$	−3.19947	−	1.08631i	−0.275366	−	0.0934946i
$136$	−1.81774	+	24.2561i	−0.155870	+	2.07994i
$137$	3.05135	−	2.83124i	0.260694	−	0.241889i	−0.538986	−	0.842314i	$-0.681193\pi$
$137$	3.05135	−	2.83124i	0.260694	−	0.241889i	0.799681	+	0.600425i	$0.205002\pi$
$138$	7.35675	−	3.45826i	0.626248	−	0.294387i
$139$	16.9042	−	5.21426i	1.43380	−	0.442267i	0.522012	−	0.852938i	$-0.325182\pi$
$139$	16.9042	−	5.21426i	1.43380	−	0.442267i	0.911784	+	0.410671i	$0.134705\pi$
$140$	−7.81151	+	1.62365i	−0.660193	+	0.137224i
$141$	−0.804600	−	12.2800i	−0.0677595	−	1.03416i
$142$	−4.90139	+	21.4744i	−0.411315	+	1.80209i
$143$	−6.80732	−	17.3448i	−0.569257	−	1.45044i
$144$	−12.7456	+	21.1504i	−1.06214	+	1.76253i
$145$	2.24905	+	1.53338i	0.186774	+	0.127340i
$146$	7.43263	−	12.8737i	0.615129	−	1.06543i
$147$	−3.26547	+	11.6763i	−0.269331	+	0.963048i
$148$	16.2255	+	28.1033i	1.33372	+	2.31008i
$149$	−0.717825	+	9.57871i	−0.0588065	+	0.784719i	0.887368	+	0.461062i	$0.152531\pi$
$149$	−0.717825	+	9.57871i	−0.0588065	+	0.784719i	−0.946175	+	0.323657i	$0.895088\pi$
$150$	20.2244	−	2.85475i	1.65131	−	0.233089i
$151$	14.2746	+	2.15156i	1.16165	+	0.175091i	0.701448	−	0.712721i	$-0.252537\pi$
$151$	14.2746	+	2.15156i	1.16165	+	0.175091i	0.460206	+	0.887812i	$0.347775\pi$
$152$	35.0052	−	10.7977i	2.83930	−	0.875807i
$153$	8.75807	+	6.21477i	0.708048	+	0.502434i
$154$	32.3224	+	3.05587i	2.60461	+	0.246249i
$155$	−1.42019	−	1.31774i	−0.114072	−	0.105844i
$156$	2.64174	−	31.3109i	0.211509	−	2.50688i
$157$	−0.302570	−	1.32565i	−0.0241477	−	0.105798i	0.961418	−	0.275092i	$-0.0887084\pi$
$157$	−0.302570	−	1.32565i	−0.0241477	−	0.105798i	−0.985566	+	0.169294i	$0.945851\pi$
$158$	10.0598	−	4.84453i	0.800312	−	0.385410i
$159$	−15.8021	−	0.148103i	−1.25319	−	0.0117454i
$160$	−0.370118	+	4.93888i	−0.0292604	+	0.390452i
$161$	−2.00631	−	4.38234i	−0.158119	−	0.345376i
$162$	10.8327	+	20.5009i	0.851100	+	1.61071i
$163$	10.3825	−	9.63358i	0.813223	−	0.754560i	−0.159334	−	0.987225i	$-0.550935\pi$
$163$	10.3825	−	9.63358i	0.813223	−	0.754560i	0.972557	+	0.232664i	$0.0747443\pi$
$164$	−9.18041	+	23.3913i	−0.716869	+	1.82655i
$165$	5.29691	+	0.849225i	0.412364	+	0.0661120i
$166$	−2.83617	+	4.91239i	−0.220129	+	0.381275i
$167$	2.00723	−	5.11435i	0.155324	−	0.395760i	−0.831936	−	0.554871i	$-0.812768\pi$
$167$	2.00723	−	5.11435i	0.155324	−	0.395760i	0.987261	+	0.159111i	$0.0508628\pi$
$168$	26.5069	+	16.3404i	2.04505	+	1.26069i
$169$	0.841495	+	2.14409i	0.0647304	+	0.164930i
$170$	5.93002	+	0.893807i	0.454812	+	0.0685518i
$171$	3.89379	−	15.6975i	0.297766	−	1.20042i
$172$	−48.4495	+	33.0323i	−3.69424	+	2.51869i
$173$	−12.3148	+	15.4422i	−0.936274	+	1.17405i	0.0482563	+	0.998835i	$0.484634\pi$
$173$	−12.3148	+	15.4422i	−0.936274	+	1.17405i	−0.984530	+	0.175215i	$0.943938\pi$
$174$	−3.98576	−	18.2495i	−0.302159	−	1.38349i
$175$	−1.57151	−	12.0076i	−0.118795	−	0.907691i
$176$	14.3236	−	36.4960i	1.07968	−	2.75099i
$177$	−6.65928	−	1.06765i	−0.500542	−	0.0802492i
$178$	−8.59531	−	14.8875i	−0.644245	−	1.11587i
$179$	−18.2198	+	2.74619i	−1.36181	+	0.205260i	−0.788982	−	0.614417i	$-0.789391\pi$
$179$	−18.2198	+	2.74619i	−1.36181	+	0.205260i	−0.572827	+	0.819676i	$0.694153\pi$
$180$	7.37793	+	5.23541i	0.549918	+	0.390224i
$181$	15.5157	+	7.47195i	1.15327	+	0.555385i	0.910014	−	0.414577i	$-0.136070\pi$
$181$	15.5157	+	7.47195i	1.15327	+	0.555385i	0.243255	+	0.969962i	$0.421785\pi$
$182$	−26.5467	−	2.50982i	−1.96778	−	0.186040i
$183$	13.1470	−	3.92074i	0.971851	−	0.289830i
$184$	−12.2403	+	1.84492i	−0.902365	+	0.136010i
$185$	4.09960	−	1.97426i	0.301409	−	0.145151i
$186$	0.869236	+	13.2665i	0.0637355	+	0.972745i
$187$	−15.3617	−	7.39781i	−1.12336	−	0.540981i
$188$	−7.33198	+	32.1235i	−0.534739	+	2.34285i
$189$	12.2193	−	6.29982i	0.888826	−	0.458244i
$190$	−2.00973	−	8.80518i	−0.145801	−	0.638795i
$191$	−1.45931	+	6.39365i	−0.105592	+	0.462629i	0.894293	+	0.447481i	$0.147679\pi$
$191$	−1.45931	+	6.39365i	−0.105592	+	0.462629i	−0.999885	+	0.0151473i	$0.995178\pi$
$192$	4.04697	−	3.68507i	0.292065	−	0.265947i
$193$	−0.629363	+	2.75742i	−0.0453025	+	0.198483i	−0.992515	−	0.122123i	$-0.961030\pi$
$193$	−0.629363	+	2.75742i	−0.0453025	+	0.198483i	0.947212	+	0.320607i	$0.103887\pi$
$194$	3.24645	−	43.3209i	0.233082	−	3.11026i
$195$	−4.35041	−	0.697477i	−0.311539	−	0.0499474i
$196$	17.3130	−	27.4603i	1.23664	−	1.96145i
$197$	22.5704			1.60808			0.804039	−	0.594577i	$-0.202680\pi$
$197$	22.5704			1.60808			0.804039	+	0.594577i	$0.202680\pi$
$198$	−22.4094	−	29.2072i	−1.59257	−	2.07566i
$199$	0.178378	+	0.165510i	0.0126449	+	0.0117327i	0.686470	−	0.727158i	$-0.259159\pi$
$199$	0.178378	+	0.165510i	0.0126449	+	0.0117327i	−0.673825	+	0.738891i	$0.735350\pi$
$200$	−30.7546	−	4.63551i	−2.17468	−	0.327780i
$201$	0.929132	−	2.30367i	0.0655359	−	0.162488i
$202$	17.6410	−	16.3685i	1.24122	−	1.15168i
$203$	−10.8435	+	2.25387i	−0.761067	+	0.158191i
$204$	−17.7159	−	22.6473i	−1.24036	−	1.58563i
$205$	3.17452	+	1.52877i	0.221718	+	0.106774i
$206$	−25.8594	−	7.97656i	−1.80171	−	0.555753i
$207$	−2.09163	+	5.04900i	−0.145378	+	0.350930i
$208$	−11.7641	+	29.9746i	−0.815697	+	2.07836i
$209$	−1.91892	+	25.6062i	−0.132734	+	1.77122i
$210$	4.50577	−	6.21582i	0.310928	−	0.428932i
$211$	−1.42836	−	19.0601i	−0.0983321	−	1.31215i	−0.800153	−	0.599797i	$-0.795248\pi$
$211$	−1.42836	−	19.0601i	−0.0983321	−	1.31215i	0.701820	−	0.712354i	$-0.252371\pi$
$212$	40.4315	+	12.4715i	2.77685	+	0.856545i
$213$	−7.28366	−	12.8932i	−0.499068	−	0.883431i
$214$	3.69356	+	6.39743i	0.252486	+	0.437319i
$215$	4.11111	+	7.12065i	0.280375	+	0.485624i
$216$	−6.88597	−	34.6301i	−0.468531	−	2.35628i
$217$	7.87059	−	0.435975i	0.534290	−	0.0295959i
$218$	−11.1948	−	28.5238i	−0.758206	−	1.93188i
$219$	2.13242	+	9.76366i	0.144096	+	0.659767i
$220$	−12.9409	−	6.23202i	−0.872477	−	0.420163i
$221$	12.6167	+	6.07590i	0.848694	+	0.408709i
$222$	−29.7505	−	9.48306i	−1.99672	−	0.636461i
$223$	2.91589	+	7.42957i	0.195263	+	0.497521i	0.994651	−	0.103294i	$-0.0329382\pi$
$223$	2.91589	+	7.42957i	0.195263	+	0.497521i	−0.799388	+	0.600815i	$0.794843\pi$
$224$	−13.4164	−	15.0360i	−0.896418	−	1.00463i
$225$	−8.76116	+	10.5734i	−0.584077	+	0.704890i
$226$	−15.9390	−	27.6071i	−1.06024	−	1.83640i
$227$	−11.1261	−	19.2709i	−0.738462	−	1.27905i	−0.953188	−	0.302379i	$-0.902219\pi$
$227$	−11.1261	−	19.2709i	−0.738462	−	1.27905i	0.214726	−	0.976674i	$-0.431114\pi$
$228$	−22.0021	+	37.2971i	−1.45712	+	2.47006i
$229$	2.24633	+	0.692900i	0.148442	+	0.0457881i	0.368085	−	0.929792i	$-0.380013\pi$
$229$	2.24633	+	0.692900i	0.148442	+	0.0457881i	−0.219644	+	0.975580i	$0.570490\pi$
$230$	0.228067	+	3.04334i	0.0150383	+	0.200672i
$231$	−17.4503	+	13.1113i	−1.14815	+	0.862658i
$232$	−2.12566	+	28.3650i	−0.139557	+	1.86225i
$233$	1.67994	−	4.28043i	0.110057	−	0.280420i	−0.865225	−	0.501383i	$-0.832825\pi$
$233$	1.67994	−	4.28043i	0.110057	−	0.280420i	0.975282	+	0.220963i	$0.0709200\pi$
$234$	18.4051	+	23.9882i	1.20318	+	1.56816i
$235$	4.41488	+	1.36181i	0.287995	+	0.0888347i
$236$	16.2693	+	7.83491i	1.05904	+	0.510009i
$237$	−2.80779	+	6.96158i	−0.182386	+	0.452203i
$238$	−19.3694	+	14.8392i	−1.25553	+	0.961882i
$239$	−14.2590	+	13.2304i	−0.922339	+	0.855805i	−0.989879	−	0.141911i	$-0.954675\pi$
$239$	−14.2590	+	13.2304i	−0.922339	+	0.855805i	0.0675407	+	0.997717i	$0.478485\pi$
$240$	−5.71207	−	7.30206i	−0.368713	−	0.471346i
$241$	−28.4157	−	4.28297i	−1.83041	−	0.275890i	−0.858773	−	0.512356i	$-0.828773\pi$
$241$	−28.4157	−	4.28297i	−1.83041	−	0.275890i	−0.971640	+	0.236466i	$0.924011\pi$
$242$	22.0712	+	20.4791i	1.41879	+	1.31645i
$243$	−14.6643	−	5.28751i	−0.940717	−	0.339194i
$244$	−36.7324			−2.35155
$245$	−3.65826	−	2.70856i	−0.233718	−	0.173043i
$246$	−8.62235	−	22.5896i	−0.549741	−	1.44026i
$247$	1.57603	−	21.0307i	0.100280	−	1.33815i
$248$	4.50491	−	19.7373i	0.286062	−	1.25332i
$249$	−0.813697	−	3.72565i	−0.0515659	−	0.236104i
$250$	−3.57024	+	15.6422i	−0.225802	+	0.989302i
$251$	−1.18540	−	5.19358i	−0.0748218	−	0.327816i	0.923640	−	0.383261i	$-0.125199\pi$
$251$	−1.18540	−	5.19358i	−0.0748218	−	0.327816i	−0.998462	+	0.0554457i	$0.982342\pi$
$252$	−36.1727	+	6.81399i	−2.27867	+	0.429241i
$253$	1.93078	−	8.45930i	0.121387	−	0.531832i
$254$	37.4840	+	18.0513i	2.35196	+	1.13264i
$255$	−3.35232	+	2.23984i	−0.209931	+	0.140264i
$256$	22.1554	−	10.6695i	1.38471	−	0.666844i
$257$	−7.55656	+	1.13897i	−0.471365	+	0.0710468i	−0.380429	−	0.924810i	$-0.624224\pi$
$257$	−7.55656	+	1.13897i	−0.471365	+	0.0710468i	−0.0909355	+	0.995857i	$0.528986\pi$
$258$	13.0705	−	54.8892i	0.813734	−	3.41725i
$259$	−5.80028	+	17.5816i	−0.360412	+	1.09247i
$260$	10.6285	+	5.11843i	0.659153	+	0.317431i
$261$	10.2417	+	7.26753i	0.633943	+	0.449849i
$262$	37.4666	−	5.64718i	2.31469	−	0.348884i
$263$	−9.83115	−	17.0281i	−0.606215	−	1.04999i	−0.991858	−	0.127347i	$-0.959354\pi$
$263$	−9.83115	−	17.0281i	−0.606215	−	1.04999i	0.385643	−	0.922648i	$-0.373979\pi$
$264$	19.9904	+	52.3726i	1.23032	+	3.22331i
$265$	2.16750	−	5.52271i	0.133149	−	0.339257i
$266$	31.4606	+	18.9896i	1.92897	+	1.16433i
$267$	11.0113	+	3.50988i	0.673879	+	0.214801i
$268$	−4.14668	+	5.19977i	−0.253299	+	0.317626i
$269$	−17.3694	+	11.8422i	−1.05903	+	0.722033i	−0.961945	−	0.273243i	$-0.911904\pi$
$269$	−17.3694	+	11.8422i	−1.05903	+	0.722033i	−0.0970833	+	0.995276i	$0.530951\pi$
$270$	−8.64090	+	1.05492i	−0.525868	+	0.0642004i
$271$	2.02737	+	0.305577i	0.123154	+	0.0185625i	0.210330	−	0.977630i	$-0.432546\pi$
$271$	2.02737	+	0.305577i	0.123154	+	0.0185625i	−0.0871760	+	0.996193i	$0.527784\pi$
$272$	10.7650	+	27.4287i	0.652722	+	1.66311i
$273$	14.3322	−	10.7684i	0.867421	−	0.651735i
$274$	3.91794	−	9.98274i	0.236691	−	0.603079i
$275$	10.9006	−	18.8804i	0.657332	−	1.13853i
$276$	9.23007	−	11.3542i	0.555585	−	0.683442i
$277$	−3.11278	+	7.93124i	−0.187029	+	0.476542i	−0.993377	−	0.114899i	$-0.963346\pi$
$277$	−3.11278	+	7.93124i	−0.187029	+	0.476542i	0.806348	+	0.591441i	$0.201441\pi$
$278$	33.4093	−	30.9993i	2.00376	−	1.85921i
$279$	−6.43698	−	6.20118i	−0.385372	−	0.371255i
$280$	−9.28004	+	7.10958i	−0.554588	+	0.424878i
$281$	0.197859	−	2.64024i	0.0118033	−	0.157504i	−0.988188	−	0.153248i	$-0.951027\pi$
$281$	0.197859	−	2.64024i	0.0118033	−	0.157504i	0.999991	−	0.00425509i	$-0.00135444\pi$
$282$	−15.5946	−	27.6048i	−0.928642	−	1.64384i
$283$	−4.09547	+	1.97227i	−0.243450	+	0.117239i	−0.551631	−	0.834088i	$-0.685994\pi$
$283$	−4.09547	+	1.97227i	−0.243450	+	0.117239i	0.308180	+	0.951328i	$0.400280\pi$
$284$	8.82267	+	38.6546i	0.523529	+	2.29373i
$285$	4.98456	+	3.46729i	0.295260	+	0.205385i
$286$	−35.1896	−	32.6512i	−2.08081	−	1.93071i
$287$	−13.4445	+	4.97683i	−0.793602	+	0.293773i
$288$	−2.13432	+	22.7497i	−0.125766	+	1.34054i
$289$	−3.99990	+	1.23381i	−0.235288	+	0.0725768i
$290$	6.93455	+	1.04521i	0.407211	+	0.0613771i
$291$	17.9948	+	23.0038i	1.05488	+	1.34851i
$292$	1.99963	−	26.6832i	0.117019	−	1.56151i
$293$	−0.732578	−	1.26886i	−0.0427977	−	0.0741278i	0.843833	−	0.536606i	$-0.180294\pi$
$293$	−0.732578	−	1.26886i	−0.0427977	−	0.0741278i	−0.886631	+	0.462478i	$0.846960\pi$
$294$	5.47235	+	30.7533i	0.319154	+	1.79357i
$295$	1.26600	−	2.19278i	0.0737096	−	0.127669i
$296$	39.2864	+	26.7850i	2.28347	+	1.55685i
$297$	24.3597	+	4.37527i	1.41349	+	0.253879i
$298$	9.04115	+	23.0365i	0.523740	+	1.33447i
$299$	−1.58577	+	6.94772i	−0.0917075	+	0.401797i
$300$	30.5698	−	20.4251i	1.76495	−	1.17924i
$301$	−32.4643	−	8.07761i	−1.87121	−	0.465586i
$302$	35.5393	−	10.9624i	2.04506	−	0.630817i
$303$	−1.36020	+	16.1216i	−0.0781414	+	0.926161i
$304$	32.5297	−	30.1832i	1.86571	−	1.73112i
$305$	−0.384901	+	5.13615i	−0.0220394	+	0.294095i
$306$	27.2762	+	4.63566i	1.55928	+	0.265003i
$307$	11.0840	−	5.33776i	0.632596	−	0.304642i	−0.0899697	−	0.995945i	$-0.528677\pi$
$307$	11.0840	−	5.33776i	0.632596	−	0.304642i	0.722566	+	0.691302i	$0.242963\pi$
$308$	54.8063	−	20.2881i	3.12288	−	1.15602i
$309$	16.4649	−	7.73983i	0.936656	−	0.440304i
$310$	−4.76954	−	1.47121i	−0.270892	−	0.0835590i
$311$	7.96698	+	9.99028i	0.451766	+	0.566497i	0.954602	−	0.297885i	$-0.0962813\pi$
$311$	7.96698	+	9.99028i	0.451766	+	0.566497i	−0.502836	+	0.864382i	$0.667710\pi$
$312$	−16.4183	−	43.0142i	−0.929503	−	2.43520i
$313$	−29.0460			−1.64178			−0.820888	−	0.571090i	$-0.806521\pi$
$313$	−29.0460			−1.64178			−0.820888	+	0.571090i	$0.806521\pi$
$314$	−2.18417	−	2.73886i	−0.123260	−	0.154563i
$315$	0.573738	+	5.12930i	0.0323265	+	0.289003i
$316$	12.5311	−	15.7135i	0.704928	−	0.883951i
$317$	5.43854	−	6.81971i	0.305459	−	0.383033i	−0.605282	−	0.796011i	$-0.706940\pi$
$317$	5.43854	−	6.81971i	0.305459	−	0.383033i	0.910741	+	0.412978i	$0.135511\pi$
$318$	−36.8454	+	17.3203i	−2.06618	+	0.971273i
$319$	−17.9639	−	8.65097i	−1.00579	−	0.484362i
$320$	0.750723	+	1.91281i	0.0419667	+	0.106929i
$321$	−4.73174	−	1.50826i	−0.264100	−	0.0841827i
$322$	−9.55573	−	7.92955i	−0.532520	−	0.441896i
$323$	−12.0323	−	15.0881i	−0.669498	−	0.839523i
$324$	33.5796	+	24.7875i	1.86553	+	1.37708i
$325$	−8.95280	+	15.5067i	−0.496612	+	0.860157i
$326$	13.3312	−	33.9673i	0.738346	−	1.88128i
$327$	18.4757	+	9.11173i	1.02171	+	0.503880i
$328$	2.75149	+	36.7161i	0.151926	+	2.02731i
$329$	−16.4596	+	9.08049i	−0.907446	+	0.500623i
$330$	13.2444	−	3.94982i	0.729083	−	0.217430i
$331$	6.03054	+	7.56206i	0.331468	+	0.415648i	0.919438	−	0.393235i	$-0.128644\pi$
$331$	6.03054	+	7.56206i	0.331468	+	0.415648i	−0.587970	+	0.808883i	$0.700073\pi$
$332$	−0.763024	+	10.1819i	−0.0418764	+	0.558802i
$333$	19.0810	−	8.75223i	1.04563	−	0.479619i
$334$	−1.05778	−	14.1151i	−0.0578793	−	0.772346i
$335$	0.683613	+	0.634300i	0.0373498	+	0.0346555i
$336$	37.5183	+	3.90220i	2.04679	+	0.212882i
$337$	−7.07363	+	6.56337i	−0.385325	+	0.357529i	−0.848923	−	0.528516i	$-0.822749\pi$
$337$	−7.07363	+	6.56337i	−0.385325	+	0.357529i	0.463598	+	0.886046i	$0.346558\pi$
$338$	4.35000	+	4.03621i	0.236609	+	0.219541i
$339$	20.4191	+	6.50865i	1.10901	+	0.353501i
$340$	10.3152	−	3.18183i	0.559422	−	0.172559i
$341$	11.7250	+	7.99399i	0.634946	+	0.432899i
$342$	−8.50890	−	40.7896i	−0.460109	−	2.20565i
$343$	18.2656	−	3.06043i	0.986252	−	0.165248i
$344$	−42.9599	+	74.4088i	−2.31624	+	4.01185i
$345$	−1.49090	−	1.40958i	−0.0802672	−	0.0758893i
$346$	−11.3232	+	49.6102i	−0.608739	+	2.66706i
$347$	18.9085	−	23.7105i	1.01506	−	1.27285i	0.0534089	−	0.998573i	$-0.482991\pi$
$347$	18.9085	−	23.7105i	1.01506	−	1.27285i	0.961652	−	0.274273i	$-0.0884372\pi$
$348$	−20.7170	−	26.4837i	−1.11055	−	1.41967i
$349$	6.95277	+	2.14464i	0.372173	+	0.114800i	0.475199	−	0.879879i	$-0.342376\pi$
$349$	6.95277	+	2.14464i	0.372173	+	0.114800i	−0.103026	+	0.994679i	$0.532852\pi$
$350$	−17.0703	−	26.1154i	−0.912443	−	1.39593i
$351$	−20.0069	−	3.59346i	−1.06789	−	0.191805i
$352$	−2.71105	−	36.1764i	−0.144499	−	1.92821i
$353$	5.15665	−	4.78467i	0.274461	−	0.254662i	−0.530918	−	0.847423i	$-0.678153\pi$
$353$	5.15665	−	4.78467i	0.274461	−	0.254662i	0.805378	+	0.592761i	$0.201962\pi$
$354$	−16.6509	+	4.96572i	−0.884987	+	0.263925i
$355$	5.49738	−	0.828597i	0.291771	−	0.0439774i
$356$	−25.5669	−	17.4312i	−1.35504	−	0.923852i
$357$	2.91157	−	16.1437i	0.154097	−	0.854416i
$358$	−39.2219	+	26.7410i	−2.07294	+	1.41331i
$359$	−3.51217	+	3.25882i	−0.185365	+	0.171994i	−0.767397	−	0.641172i	$-0.778448\pi$
$359$	−3.51217	+	3.25882i	−0.185365	+	0.171994i	0.582032	+	0.813166i	$0.302258\pi$
$360$	13.0683	+	2.22098i	0.688758	+	0.117056i
$361$	−5.03191	+	8.71552i	−0.264837	+	0.458711i
$362$	44.3672			2.33189
$363$	−20.2410	−	0.189706i	−1.06238	−	0.00995698i
$364$	−45.0130	+	16.6628i	−2.35932	+	0.873368i
$365$	−3.71006	−	0.559201i	−0.194193	−	0.0292699i
$366$	26.1339	−	23.7969i	1.36604	−	1.24388i
$367$	2.04480	+	27.2860i	0.106738	+	1.42432i	0.751398	+	0.659849i	$0.229380\pi$
$367$	2.04480	+	27.2860i	0.106738	+	1.42432i	−0.644661	+	0.764469i	$0.723001\pi$
$368$	−12.3894	+	8.44698i	−0.645844	+	0.440329i
$369$	14.5110	+	7.32629i	0.755412	+	0.381392i
$370$	7.30909	−	9.16530i	0.379981	−	0.476481i
$371$	10.0483	+	21.9484i	0.521684	+	1.13950i
$372$	11.7709	+	20.8364i	0.610293	+	1.08032i
$373$	−1.24136	+	2.15009i	−0.0642751	+	0.111328i	−0.896372	−	0.443302i	$-0.853807\pi$
$373$	−1.24136	+	2.15009i	−0.0642751	+	0.111328i	0.832097	+	0.554630i	$0.187140\pi$
$374$	−43.9270			−2.27141
$375$	−5.30552	−	9.39162i	−0.273976	−	0.484981i
$376$	10.7431	+	47.0687i	0.554034	+	2.42738i
$377$	14.7540	+	7.10514i	0.759868	+	0.365933i
$378$	21.3214	−	28.2822i	1.09665	−	1.45468i
$379$	−24.3562	+	11.7293i	−1.25109	+	0.602494i	−0.937804	−	0.347164i	$-0.887145\pi$
$379$	−24.3562	+	11.7293i	−1.25109	+	0.602494i	−0.313288	+	0.949658i	$0.601430\pi$
$380$	−10.1362	−	12.7104i	−0.519977	−	0.652031i
$381$	−26.8036	+	7.99350i	−1.37319	+	0.409519i
$382$	3.75967	+	16.4722i	0.192361	+	0.842790i
$383$	24.2761	−	16.5511i	1.24045	−	0.845723i	0.248045	−	0.968749i	$-0.420212\pi$
$383$	24.2761	−	16.5511i	1.24045	−	0.845723i	0.992404	+	0.123025i	$0.0392596\pi$
$384$	−4.59452	+	11.3915i	−0.234463	+	0.581322i
$385$	−2.26251	−	7.87595i	−0.115308	−	0.401396i
$386$	1.62145	+	7.10403i	0.0825295	+	0.361585i
$387$	18.3477	+	33.2011i	0.932664	+	1.68770i
$388$	−28.5688	−	72.7922i	−1.45036	−	3.69547i
$389$	7.08953	−	2.18683i	0.359453	−	0.110877i	−0.109768	−	0.993957i	$-0.535011\pi$
$389$	7.08953	−	2.18683i	0.359453	−	0.110877i	0.469221	+	0.883081i	$0.344535\pi$
$390$	−10.8778	+	3.24403i	−0.550819	+	0.164268i
$391$	3.26055	+	5.64745i	0.164893	+	0.285604i
$392$	5.39779	−	47.2580i	0.272630	−	2.38689i
$393$	−16.0681	+	19.7659i	−0.810530	+	0.997058i
$394$	52.3904	−	25.2299i	2.63939	−	1.27106i
$395$	−2.06585	−	1.91683i	−0.103944	−	0.0964460i
$396$	−59.1540	−	29.8656i	−2.97260	−	1.50080i
$397$	19.9840	−	6.16424i	1.00297	−	0.309374i	0.250580	−	0.968096i	$-0.419379\pi$
$397$	19.9840	−	6.16424i	1.00297	−	0.309374i	0.752387	+	0.658721i	$0.228902\pi$
$398$	0.599061	+	0.184786i	0.0300282	+	0.00926248i
$399$	−24.2341	+	4.80068i	−1.21322	+	0.240335i
$400$	−36.0022	+	11.1052i	−1.80011	+	0.555261i
$401$	−30.6063	+	20.8670i	−1.52841	+	1.04205i	−0.550048	+	0.835133i	$0.685391\pi$
$401$	−30.6063	+	20.8670i	−1.52841	+	1.04205i	−0.978359	+	0.206917i	$0.933657\pi$
$402$	−0.418410	−	6.38587i	−0.0208684	−	0.318498i
$403$	−9.62990	−	6.56555i	−0.479699	−	0.327053i
$404$	15.8259	−	40.3238i	0.787368	−	2.00618i
$405$	3.81781	−	4.43558i	0.189708	−	0.220406i
$406$	−22.6505	+	17.3529i	−1.12413	+	0.861210i
$407$	−27.5382	+	18.7752i	−1.36502	+	0.930652i
$408$	−37.7854	−	18.6347i	−1.87065	−	0.922556i
$409$	−7.19653	−	9.02417i	−0.355846	−	0.446216i	0.571399	−	0.820672i	$-0.306401\pi$
$409$	−7.19653	−	9.02417i	−0.355846	−	0.446216i	−0.927245	+	0.374456i	$0.877829\pi$
$410$	9.07758			0.448310
$411$	2.57099	+	6.73572i	0.126818	+	0.332249i
$412$	−48.1678	+	7.26013i	−2.37306	+	0.357681i
$413$	2.84443	+	9.90166i	0.139965	+	0.487229i
$414$	0.788845	+	14.0578i	0.0387696	+	0.690903i
$415$	1.41569	+	0.213382i	0.0694937	+	0.0104745i
$416$	2.22661	+	29.7121i	0.109169	+	1.45676i
$417$	−2.57600	+	30.5317i	−0.126147	+	1.49514i
$418$	24.1692	+	61.5820i	1.18215	+	3.01208i
$419$	30.6643	+	4.62190i	1.49805	+	0.225795i	0.846328	−	0.532662i	$-0.178808\pi$
$419$	30.6643	+	4.62190i	1.49805	+	0.225795i	0.651723	+	0.758457i	$0.274047\pi$
$420$	2.45275	−	13.5997i	0.119682	−	0.663597i
$421$	21.6693	−	3.26612i	1.05610	−	0.159181i	0.402037	−	0.915623i	$-0.368302\pi$
$421$	21.6693	−	3.26612i	1.05610	−	0.159181i	0.654061	+	0.756442i	$0.273064\pi$
$422$	−24.6214	−	42.6455i	−1.19855	−	2.07595i
$423$	20.2469	+	6.66342i	0.984436	+	0.323986i
$424$	61.3039	−	9.24008i	2.97718	−	0.448738i
$425$	3.64596	+	15.9740i	0.176855	+	0.774852i
$426$	−31.3192	−	21.7858i	−1.51742	−	1.05553i
$427$	−13.9522	−	15.6366i	−0.675196	−	0.756707i
$428$	10.9865	+	7.49050i	0.531055	+	0.362067i
$429$	32.2715	+	0.302461i	1.55808	+	0.0146029i
$430$	17.5023	+	11.9329i	0.844038	+	0.575455i
$431$	17.2643	+	5.32533i	0.831593	+	0.256512i	0.681185	−	0.732112i	$-0.261465\pi$
$431$	17.2643	+	5.32533i	0.831593	+	0.256512i	0.150408	+	0.988624i	$0.451941\pi$
$432$	−25.7168	−	34.1763i	−1.23730	−	1.64431i
$433$	2.18934	−	9.59211i	0.105213	−	0.460968i	−0.894685	−	0.446697i	$-0.852600\pi$
$433$	2.18934	−	9.59211i	0.105213	−	0.460968i	0.999898	−	0.0142706i	$-0.00454263\pi$
$434$	17.7818	−	9.80995i	0.853555	−	0.470893i
$435$	−3.92019	+	2.61926i	−0.187959	+	0.125584i
$436$	−40.4327	−	37.5160i	−1.93637	−	1.79669i
$437$	6.12326	−	7.67832i	0.292915	−	0.367304i
$438$	15.8639	+	20.2797i	0.758005	+	0.969001i
$439$	−15.1148	+	7.27890i	−0.721390	+	0.347403i	−0.758291	−	0.651916i	$-0.773965\pi$
$439$	−15.1148	+	7.27890i	−0.721390	+	0.347403i	0.0369016	+	0.999319i	$0.488251\pi$
$440$	−21.0458			−1.00332
$441$	−16.6403	−	12.8102i	−0.792396	−	0.610007i
$442$	36.0777			1.71604
$443$	−12.4325	+	5.98717i	−0.590685	+	0.284459i	−0.705252	−	0.708957i	$-0.749166\pi$
$443$	−12.4325	+	5.98717i	−0.590685	+	0.284459i	0.114567	+	0.993415i	$0.463452\pi$
$444$	−55.6549	+	7.85591i	−2.64127	+	0.372825i
$445$	−2.70524	+	3.39227i	−0.128241	+	0.160809i
$446$	15.0733	+	13.9860i	0.713744	+	0.662257i
$447$	−14.9214	−	7.35884i	−0.705759	−	0.348061i
$448$	−7.72184	−	3.20540i	−0.364822	−	0.151441i
$449$	−3.12342	+	13.6846i	−0.147403	+	0.645815i	0.846198	+	0.532869i	$0.178886\pi$
$449$	−3.12342	+	13.6846i	−0.147403	+	0.645815i	−0.993601	+	0.112946i	$0.963971\pi$
$450$	−8.51716	+	34.3363i	−0.401503	+	1.61863i
$451$	−24.6621	−	7.60724i	−1.16129	−	0.358211i
$452$	−47.4108	−	32.3241i	−2.23001	−	1.52040i
$453$	−12.7042	+	21.5357i	−0.596897	+	1.01184i
$454$	−47.3673	−	32.2945i	−2.22306	−	1.51565i
$455$	1.85823	+	6.46861i	0.0871150	+	0.303253i
$456$	−5.33438	+	63.2250i	−0.249805	+	2.96078i
$457$	2.63602	+	11.5492i	0.123308	+	0.540248i	0.998413	+	0.0563147i	$0.0179350\pi$
$457$	2.63602	+	11.5492i	0.123308	+	0.540248i	−0.875105	+	0.483933i	$0.839208\pi$
$458$	5.98871	−	0.902653i	0.279834	−	0.0421782i
$459$	−15.6570	+	10.0419i	−0.730807	+	0.468715i
$460$	2.74674	+	4.75749i	0.128067	+	0.221819i
$461$	33.5059	−	5.05020i	1.56052	−	0.235211i	0.688706	−	0.725041i	$-0.258179\pi$
$461$	33.5059	−	5.05020i	1.56052	−	0.235211i	0.871818	+	0.489830i	$0.162941\pi$
$462$	−25.8495	+	49.9403i	−1.20263	+	2.32343i
$463$	−14.9329	−	2.25078i	−0.693993	−	0.104603i	−0.207432	−	0.978249i	$-0.566511\pi$
$463$	−14.9329	−	2.25078i	−0.693993	−	0.104603i	−0.486561	+	0.873647i	$0.661749\pi$
$464$	12.5885	+	32.0750i	0.584407	+	1.48904i
$465$	3.03681	−	1.42755i	0.140829	−	0.0662009i
$466$	−0.885307	−	11.8136i	−0.0410111	−	0.547255i
$467$	−7.50996	−	1.13194i	−0.347519	−	0.0523801i	−0.0270366	−	0.999634i	$-0.508607\pi$
$467$	−7.50996	−	1.13194i	−0.347519	−	0.0523801i	−0.320483	+	0.947254i	$0.603845\pi$
$468$	48.5838	+	24.5290i	2.24579	+	1.13385i
$469$	−3.78854	+	0.209858i	−0.174939	+	0.00969036i
$470$	11.7701	−	1.77405i	0.542913	−	0.0818309i
$471$	2.32544	+	0.372825i	0.107151	+	0.0171789i
$472$	26.4588			1.21786
$473$	−37.5505	−	47.0868i	−1.72657	−	2.16505i
$474$	1.26442	+	19.2978i	0.0580766	+	0.886378i
$475$	20.3882	−	13.9004i	0.935473	−	0.637795i
$476$	−19.8233	+	39.1935i	−0.908601	+	1.79643i
$477$	10.4757	−	25.2873i	0.479647	−	1.15783i
$478$	−18.3086	+	46.6495i	−0.837416	+	2.13370i
$479$	−22.4088	−	15.2781i	−1.02388	−	0.698073i	−0.0697848	−	0.997562i	$-0.522231\pi$
$479$	−22.4088	−	15.2781i	−1.02388	−	0.698073i	−0.954100	+	0.299490i	$0.903184\pi$
$480$	−7.69362	−	3.79429i	−0.351164	−	0.173185i
$481$	22.6174	−	15.4203i	1.03126	−	0.703104i
$482$	−70.7459	+	21.8222i	−3.22239	+	0.993975i
$483$	8.33926	−	0.383579i	0.379450	−	0.0174534i
$484$	51.7889	+	15.9747i	2.35404	+	0.726125i
$485$	−10.4776	+	3.23192i	−0.475765	+	0.146754i
$486$	−39.9493	+	4.11886i	−1.81214	+	0.186835i
$487$	−21.1320	−	19.6077i	−0.957584	−	0.888508i	0.0362551	−	0.999343i	$-0.488457\pi$
$487$	−21.1320	−	19.6077i	−0.957584	−	0.888508i	−0.993839	+	0.110835i	$0.964648\pi$
$488$	−48.4918	+	23.3524i	−2.19512	+	1.05711i
$489$	8.74806	+	22.9190i	0.395601	+	1.03643i
$490$	−11.5192	−	2.19778i	−0.520386	−	0.0992856i
$491$	−11.7900	−	20.4210i	−0.532077	−	0.921585i	−0.999299	−	0.0374446i	$-0.988078\pi$
$491$	−11.7900	−	20.4210i	−0.532077	−	0.921585i	0.467221	−	0.884140i	$-0.345255\pi$
$492$	−31.6262	−	29.9012i	−1.42582	−	1.34805i
$493$	14.3191	−	4.41685i	0.644899	−	0.198925i
$494$	−19.8504	−	50.5780i	−0.893112	−	2.27561i
$495$	−4.79584	+	7.95834i	−0.215557	+	0.357701i
$496$	−5.45712	−	23.9092i	−0.245032	−	1.07356i
$497$	−13.1037	+	18.4381i	−0.587782	+	0.827062i
$498$	−6.05339	−	7.73839i	−0.271259	−	0.346766i
$499$	26.4030	−	18.0012i	1.18196	−	0.805846i	0.197302	−	0.980343i	$-0.436782\pi$
$499$	26.4030	−	18.0012i	1.18196	−	0.805846i	0.984658	+	0.174497i	$0.0558298\pi$
$500$	6.42655	+	28.1566i	0.287404	+	1.25920i
$501$	6.91484	+	6.53770i	0.308932	+	0.292083i
$502$	−8.55708	−	10.7302i	−0.381921	−	0.478914i
$503$	25.1960	−	12.1338i	1.12344	−	0.541018i	0.222484	−	0.974936i	$-0.428584\pi$
$503$	25.1960	−	12.1338i	1.12344	−	0.541018i	0.900952	+	0.433918i	$0.142869\pi$
$504$	−43.4210	+	31.9920i	−1.93413	+	1.42504i
$505$	−5.47249	−	2.63541i	−0.243523	−	0.117274i
$506$	−4.97433	−	21.7940i	−0.221136	−	0.968860i
$507$	−3.98928	−	0.0373890i	−0.177170	−	0.00166051i
$508$	74.8888			3.32265
$509$	−10.7370	+	18.5971i	−0.475911	+	0.824302i	−0.999619	−	0.0275956i	$-0.991215\pi$
$509$	−10.7370	+	18.5971i	−0.475911	+	0.824302i	0.523708	+	0.851898i	$0.324548\pi$
$510$	−5.27763	+	8.94643i	−0.233697	+	0.396155i
$511$	12.1183	−	9.28398i	0.536081	−	0.410699i
$512$	30.6572	−	38.4429i	1.35487	−	1.69895i
$513$	22.6926	+	16.4247i	1.00190	+	0.725167i
$514$	−16.2671	+	11.0907i	−0.717510	+	0.489190i
$515$	0.510429	+	6.81120i	0.0224922	+	0.300137i
$516$	−21.6714	−	99.2261i	−0.954029	−	4.36819i
$517$	−33.4638	−	5.04385i	−1.47173	−	0.221828i
$518$	6.18966	+	47.2941i	0.271958	+	2.07798i
$519$	−16.8267	−	29.7860i	−0.738612	−	1.30746i
$520$	17.2851			0.758003
$521$	7.69446	−	13.3272i	0.337100	−	0.583875i	−0.646786	−	0.762672i	$-0.723887\pi$
$521$	7.69446	−	13.3272i	0.337100	−	0.583875i	0.983886	+	0.178797i	$0.0572205\pi$
$522$	31.8968	+	5.42093i	1.39608	+	0.237268i
$523$	−28.0248	+	26.0032i	−1.22544	+	1.13704i	−0.239329	+	0.970938i	$0.576928\pi$
$523$	−28.0248	+	26.0032i	−1.22544	+	1.13704i	−0.986109	+	0.166102i	$0.946882\pi$
$524$	56.3519	−	38.4201i	2.46174	−	1.67839i
$525$	20.3062	+	5.25506i	0.886236	+	0.229350i
$526$	−41.8545	−	28.5359i	−1.82494	−	1.24422i
$527$	−10.5461	+	1.58956i	−0.459393	+	0.0692424i
$528$	49.3444	+	46.6531i	2.14744	+	2.03031i
$529$	14.4275	−	13.3868i	0.627282	−	0.582033i
$530$	−1.14224	−	15.2422i	−0.0496159	−	0.662078i
$531$	6.02934	−	10.0052i	0.261651	−	0.434190i
$532$	65.8530	+	6.22597i	2.85509	+	0.269930i
$533$	20.2552	+	6.24791i	0.877352	+	0.270627i
$534$	29.4828	−	4.16161i	1.27584	−	0.180090i
$535$	1.16249	−	1.45772i	0.0502589	−	0.0630227i
$536$	−2.16846	+	9.50064i	−0.0936632	+	0.410365i
$537$	7.39282	−	31.0459i	0.319024	−	1.33973i
$538$	−27.0801	+	46.9041i	−1.16751	+	2.02218i
$539$	29.4538	+	15.6244i	1.26866	+	0.672989i
$540$	−13.1897	+	8.45943i	−0.567594	+	0.364036i
$541$	−5.55963	−	3.79049i	−0.239027	−	0.162966i	0.437882	−	0.899032i	$-0.355729\pi$
$541$	−5.55963	−	3.79049i	−0.239027	−	0.162966i	−0.676909	+	0.736066i	$0.736681\pi$
$542$	5.04750	−	1.55695i	0.216809	−	0.0668767i
$543$	−22.0545	+	20.0822i	−0.946449	+	0.861811i
$544$	19.9865	+	18.5447i	0.856912	+	0.795098i
$545$	−5.66940	+	5.26044i	−0.242851	+	0.225332i
$546$	21.2305	−	41.0165i	0.908580	−	1.75534i
$547$	16.5958	+	15.3986i	0.709585	+	0.658399i	0.949992	−	0.312273i	$-0.101090\pi$
$547$	16.5958	+	15.3986i	0.709585	+	0.658399i	−0.240407	+	0.970672i	$0.577281\pi$
$548$	−1.44257	−	19.2497i	−0.0616233	−	0.822306i
$549$	−2.21957	+	23.6583i	−0.0947291	+	1.00971i
$550$	4.19738	−	56.0102i	0.178977	−	2.38828i
$551$	−14.0706	−	17.6440i	−0.599427	−	0.751658i
$552$	4.96659	−	20.8571i	0.211392	−	0.887736i
$553$	11.4488	−	0.634183i	0.486852	−	0.0269682i
$554$	1.64039	+	21.8895i	0.0696936	+	0.929996i
$555$	0.515281	+	7.86434i	0.0218725	+	0.333823i
$556$	29.9717	−	76.3668i	1.27109	−	3.23867i
$557$	−8.63112	+	14.9495i	−0.365712	+	0.633432i	−0.988890	−	0.148648i	$-0.952508\pi$
$557$	−8.63112	+	14.9495i	−0.365712	+	0.633432i	0.623178	+	0.782080i	$0.285841\pi$
$558$	−21.8734	−	7.19871i	−0.925973	−	0.304746i
$559$	30.8406	+	38.6729i	1.30442	+	1.63569i
$560$	−6.39155	+	12.6370i	−0.270092	+	0.534010i
$561$	21.8357	−	19.8830i	0.921902	−	0.839460i
$562$	−2.49207	−	6.34969i	−0.105122	−	0.267845i
$563$	12.6053	+	6.07037i	0.531248	+	0.255836i	0.680223	−	0.733005i	$-0.261883\pi$
$563$	12.6053	+	6.07037i	0.531248	+	0.255836i	−0.148975	+	0.988841i	$0.547597\pi$
$564$	−46.8504	−	32.5894i	−1.97276	−	1.37226i
$565$	−5.01655	+	6.29056i	−0.211048	+	0.264646i
$566$	−7.30171	+	9.15606i	−0.306914	+	0.384858i
$567$	2.20295	+	23.7096i	0.0925153	+	0.995711i
$568$	36.2216	+	45.4205i	1.51983	+	1.90580i
$569$	−11.0471			−0.463117			−0.231559	−	0.972821i	$-0.574383\pi$
$569$	−11.0471			−0.463117			−0.231559	+	0.972821i	$0.574383\pi$
$570$	15.4460	+	2.47637i	0.646961	+	0.103724i
$571$	22.6027	+	28.3428i	0.945892	+	1.18611i	0.982402	+	0.186777i	$0.0598043\pi$
$571$	22.6027	+	28.3428i	0.945892	+	1.18611i	−0.0365105	+	0.999333i	$0.511624\pi$
$572$	−82.5704	−	25.4696i	−3.45244	−	1.06494i
$573$	−9.32480	−	6.48639i	−0.389549	−	0.270973i
$574$	−25.6440	+	26.5808i	−1.07036	+	1.10946i
$575$	−7.51247	+	3.61782i	−0.313292	+	0.150873i
$576$	3.29747	+	8.88818i	0.137395	+	0.370341i
$577$	2.58502	−	34.4947i	0.107616	−	1.43603i	−0.638194	−	0.769875i	$-0.720318\pi$
$577$	2.58502	−	34.4947i	0.107616	−	1.43603i	0.745810	−	0.666158i	$-0.232063\pi$
$578$	−7.90537	+	7.33511i	−0.328820	+	0.305100i
$579$	−4.02155	−	2.79741i	−0.167130	−	0.116256i
$580$	12.0626	−	3.72082i	0.500872	−	0.154499i
$581$	−4.62413	+	3.54261i	−0.191841	+	0.146972i
$582$	67.4839	+	33.2812i	2.79730	+	1.37955i
$583$	−9.67007	+	42.3674i	−0.400493	+	1.75468i
$584$	−14.3239	−	36.4967i	−0.592727	−	1.51025i
$585$	3.93888	−	6.53627i	0.162853	−	0.270241i
$586$	−3.11883	−	2.12638i	−0.128838	−	0.0878400i
$587$	2.27623	−	3.94254i	0.0939499	−	0.162726i	−0.815220	−	0.579152i	$-0.803384\pi$
$587$	2.27623	−	3.94254i	0.0939499	−	0.162726i	0.909170	+	0.416425i	$0.136717\pi$
$588$	32.8934	+	45.6010i	1.35650	+	1.88055i
$589$	8.03100	+	13.9101i	0.330912	+	0.573156i
$590$	0.487487	−	6.50506i	0.0200695	−	0.267809i
$591$	−14.6228	+	36.2553i	−0.601500	+	1.49135i
$592$	56.9555	+	8.58466i	2.34086	+	0.352827i
$593$	12.3480	−	3.80885i	0.507071	−	0.156411i	−0.0306555	−	0.999530i	$-0.509759\pi$
$593$	12.3480	−	3.80885i	0.507071	−	0.156411i	0.537727	+	0.843119i	$0.319283\pi$
$594$	61.4345	−	17.0741i	2.52069	−	0.700561i
$595$	5.27255	+	3.18251i	0.216154	+	0.130470i
$596$	32.6543	+	30.2988i	1.33757	+	1.24109i
$597$	−0.381428	+	0.179302i	−0.0156108	+	0.00733834i
$598$	4.08547	+	17.8996i	0.167067	+	0.731970i
$599$	4.48047	−	2.15768i	0.183067	−	0.0881604i	−0.340105	−	0.940387i	$-0.610463\pi$
$599$	4.48047	−	2.15768i	0.183067	−	0.0881604i	0.523172	+	0.852227i	$0.324748\pi$
$600$	27.3712	−	46.3985i	1.11742	−	1.89421i
$601$	−2.79314	+	37.2718i	−0.113934	+	1.52035i	0.588440	+	0.808541i	$0.299742\pi$
$601$	−2.79314	+	37.2718i	−0.113934	+	1.52035i	−0.702374	+	0.711808i	$0.747877\pi$
$602$	−84.3854	+	17.5399i	−3.43929	+	0.714871i
$603$	3.09847	+	2.98496i	0.126179	+	0.121557i
$604$	49.0751	−	45.5350i	1.99684	−	1.85279i
$605$	2.77636	−	7.07405i	0.112875	−	0.287601i
$606$	14.8639	+	38.9418i	0.603804	+	1.58190i
$607$	−8.82147	+	15.2792i	−0.358053	+	0.620165i	−0.987635	−	0.156768i	$-0.949892\pi$
$607$	−8.82147	+	15.2792i	−0.358053	+	0.620165i	0.629583	+	0.776933i	$0.283226\pi$
$608$	15.0014	−	38.2229i	0.608386	−	1.55014i
$609$	3.40478	−	18.8784i	0.137969	−	0.764992i
$610$	4.84790	+	12.3523i	0.196286	+	0.500128i
$611$	27.4841	+	4.14257i	1.11189	+	0.167590i
$612$	47.8564	−	13.7849i	1.93448	−	0.557222i
$613$	−2.33985	+	1.59528i	−0.0945057	+	0.0644329i	−0.609651	−	0.792670i	$-0.708690\pi$
$613$	−2.33985	+	1.59528i	−0.0945057	+	0.0644329i	0.515145	+	0.857103i	$0.327738\pi$
$614$	19.7614	−	24.7800i	0.797504	−	1.00004i
$615$	−4.51237	+	4.10885i	−0.181956	+	0.165685i
$616$	59.4539	−	61.6259i	2.39547	−	2.48298i
$617$	−3.70535	+	9.44108i	−0.149172	+	0.380084i	−0.985854	−	0.167605i	$-0.946397\pi$
$617$	−3.70535	+	9.44108i	−0.149172	+	0.380084i	0.836682	+	0.547688i	$0.184492\pi$
$618$	29.5665	−	36.3706i	1.18934	−	1.46304i
$619$	14.0749	+	24.3784i	0.565716	+	0.979849i	0.996983	+	0.0776244i	$0.0247335\pi$
$619$	14.0749	+	24.3784i	0.565716	+	0.979849i	−0.431267	+	0.902225i	$0.641933\pi$
$620$	−8.88415	+	1.33907i	−0.356796	+	0.0537783i
$621$	−6.75520	−	6.63093i	−0.271077	−	0.266090i
$622$	29.6603	+	14.2837i	1.18927	+	0.572723i
$623$	−2.29092	−	17.5045i	−0.0917838	−	0.701304i
$624$	−40.5271	−	38.3167i	−1.62238	−	1.53389i
$625$	−18.6258	+	2.80739i	−0.745033	+	0.112296i
$626$	−67.4214	+	32.4684i	−2.69470	+	1.29770i
$627$	−39.8885	−	19.6719i	−1.59299	−	0.785622i
$628$	−5.68130	−	2.73597i	−0.226709	−	0.109177i
$629$	5.57391	−	24.4209i	0.222246	−	0.973724i
$630$	7.06543	+	11.2648i	0.281494	+	0.448799i
$631$	6.60324	+	28.9307i	0.262871	+	1.15171i	0.918121	+	0.396300i	$0.129706\pi$
$631$	6.60324	+	28.9307i	0.262871	+	1.15171i	−0.655250	+	0.755412i	$0.727437\pi$
$632$	6.55299	−	28.7105i	0.260664	−	1.14204i
$633$	31.5420	+	10.0541i	1.25368	+	0.399615i
$634$	5.00064	−	21.9092i	0.198601	−	0.870127i
$635$	0.784725	−	10.4714i	0.0311409	−	0.415546i
$636$	−46.2276	+	56.8660i	−1.83305	+	2.25489i
$637$	−24.1907	−	12.8325i	−0.958471	−	0.508440i
$638$	−51.3681			−2.03368
$639$	25.4295	−	3.34672i	1.00598	−	0.132394i
$640$	−3.38044	−	3.13659i	−0.133624	−	0.123985i
$641$	14.6614	+	2.20985i	0.579091	+	0.0872839i	0.432055	−	0.901847i	$-0.357789\pi$
$641$	14.6614	+	2.20985i	0.579091	+	0.0872839i	0.147036	+	0.989131i	$0.453027\pi$
$642$	−12.6693	+	1.78832i	−0.500016	+	0.0705792i
$643$	−24.9023	+	23.1059i	−0.982049	+	0.911209i	−0.996059	−	0.0886931i	$-0.971731\pi$
$643$	−24.9023	+	23.1059i	−0.982049	+	0.911209i	0.0140095	+	0.999902i	$0.495540\pi$
$644$	−21.6903	−	5.39686i	−0.854717	−	0.212666i
$645$	−14.1015	+	1.99048i	−0.555246	+	0.0783752i
$646$	−44.7953	−	21.5723i	−1.76245	−	0.848750i
$647$	5.89441	+	1.81818i	0.231733	+	0.0714802i	0.408447	−	0.912782i	$-0.366071\pi$
$647$	5.89441	+	1.81818i	0.231733	+	0.0714802i	−0.176714	+	0.984262i	$0.556547\pi$
$648$	60.0882	+	11.3748i	2.36049	+	0.446845i
$649$	−6.77581	+	17.2645i	−0.265974	+	0.677690i
$650$	−3.44736	+	46.0018i	−0.135216	+	1.80434i
$651$	−4.39882	+	12.9251i	−0.172403	+	0.506576i
$652$	−4.90848	−	65.4991i	−0.192231	−	2.56514i
$653$	−11.3163	−	3.49061i	−0.442840	−	0.136598i	0.0653132	−	0.997865i	$-0.479195\pi$
$653$	−11.3163	−	3.49061i	−0.442840	−	0.136598i	−0.508153	+	0.861267i	$0.669672\pi$
$654$	53.0711	+	0.497403i	2.07525	+	0.0194500i
$655$	−4.78165	−	8.28206i	−0.186835	−	0.323607i
$656$	22.3008	+	38.6261i	0.870699	+	1.50810i
$657$	−17.0651	−	2.90025i	−0.665773	−	0.113150i
$658$	−28.0555	+	39.4766i	−1.09372	+	1.53896i
$659$	−18.0437	−	45.9747i	−0.702884	−	1.79092i	−0.605760	−	0.795648i	$-0.707131\pi$
$659$	−18.0437	−	45.9747i	−0.702884	−	1.79092i	−0.0971244	−	0.995272i	$-0.530964\pi$
$660$	18.3947	−	16.7497i	0.716012	−	0.651981i
$661$	−9.24296	−	4.45118i	−0.359510	−	0.173131i	0.245406	−	0.969420i	$-0.421079\pi$
$661$	−9.24296	−	4.45118i	−0.359510	−	0.173131i	−0.604915	+	0.796290i	$0.706793\pi$
$662$	22.4511	+	10.8119i	0.872589	+	0.420217i
$663$	−17.9339	+	16.3301i	−0.696494	+	0.634209i
$664$	5.46576	+	13.9265i	0.212113	+	0.540454i
$665$	1.56060	−	9.14274i	0.0605174	−	0.354540i
$666$	34.5073	−	41.6450i	1.33713	−	1.61371i
$667$	3.81288	+	6.60411i	0.147635	+	0.255712i
$668$	−12.7395	−	22.0654i	−0.492906	−	0.853738i
$669$	−13.8234	−	0.129558i	−0.534443	−	0.00500900i
$670$	2.29584	+	0.708172i	0.0886960	+	0.0273591i
$671$	−2.81933	−	37.6214i	−0.108839	−	1.45236i
$672$	32.8447	−	11.8095i	1.26701	−	0.455563i
$673$	1.12036	−	14.9502i	0.0431868	−	0.576287i	−0.933073	−	0.359686i	$-0.882884\pi$
$673$	1.12036	−	14.9502i	0.0431868	−	0.576287i	0.976260	−	0.216601i	$-0.0694972\pi$
$674$	−9.08255	+	23.1420i	−0.349847	+	0.891395i
$675$	−11.3081	−	20.9234i	−0.435248	−	0.805342i
$676$	10.2070	+	3.14845i	0.392578	+	0.121094i
$677$	−19.8827	−	9.57499i	−0.764153	−	0.367997i	0.0108608	−	0.999941i	$-0.496543\pi$
$677$	−19.8827	−	9.57499i	−0.764153	−	0.367997i	−0.775014	+	0.631944i	$0.782257\pi$
$678$	54.6723	−	7.71721i	2.09968	−	0.296378i
$679$	20.1354	−	39.8105i	0.772727	−	1.52779i
$680$	11.5947	−	10.7583i	0.444636	−	0.412562i
$681$	38.1635	−	5.38692i	1.46243	−	0.206427i
$682$	36.1520	+	5.44904i	1.38433	+	0.208654i
$683$	−12.8637	−	11.9357i	−0.492214	−	0.456708i	0.394588	−	0.918858i	$-0.370887\pi$
$683$	−12.8637	−	11.9357i	−0.492214	−	0.456708i	−0.886801	+	0.462151i	$0.847078\pi$
$684$	−45.6565	−	59.5061i	−1.74572	−	2.27527i
$685$	−2.70673			−0.103419
$686$	38.9771	−	27.5217i	1.48815	−	1.05078i
$687$	−2.56835	+	3.15941i	−0.0979888	+	0.120539i
$688$	−7.77797	+	103.790i	−0.296532	+	3.95695i
$689$	7.94214	−	34.7968i	0.302571	−	1.32565i
$690$	−5.03633	−	1.60535i	−0.191730	−	0.0611145i
$691$	3.87250	−	16.9665i	0.147317	−	0.645437i	−0.846307	−	0.532695i	$-0.821179\pi$
$691$	3.87250	−	16.9665i	0.147317	−	0.645437i	0.993624	−	0.112742i	$-0.0359635\pi$
$692$	20.3822	+	89.3001i	0.774814	+	3.39468i
$693$	−9.75529	−	36.5252i	−0.370573	−	1.38748i
$694$	17.3860	−	76.1731i	0.659964	−	2.89149i
$695$	−10.3640	−	4.99105i	−0.393130	−	0.189321i
$696$	−44.1861	−	21.7914i	−1.67487	−	0.826000i
$697$	17.4757	−	8.41586i	0.661940	−	0.318774i
$698$	18.5361	−	2.79386i	0.701601	−	0.105749i
$699$	5.78735	+	5.47170i	0.218898	+	0.206959i
$700$	−48.0804	−	29.0213i	−1.81727	−	1.09690i
$701$	33.9658	+	16.3571i	1.28287	+	0.617798i	0.946126	−	0.323798i	$-0.104960\pi$
$701$	33.9658	+	16.3571i	1.28287	+	0.617798i	0.336744	+	0.941596i	$0.390674\pi$
$702$	−50.4568	+	14.0232i	−1.90437	+	0.529271i
$703$	−37.3029	+	5.62251i	−1.40691	+	0.212057i
$704$	−7.52573	−	13.0350i	−0.283637	−	0.491273i
$705$	−5.04778	+	6.20943i	−0.190110	+	0.233861i
$706$	6.62115	−	16.8704i	0.249190	−	0.634926i
$707$	23.1766	−	8.57946i	0.871647	−	0.322664i
$708$	−23.1258	+	21.0578i	−0.869121	+	0.791399i
$709$	−17.6040	+	22.0747i	−0.661132	+	0.829033i	−0.993466	−	0.114129i	$-0.963592\pi$
$709$	−17.6040	+	22.0747i	−0.661132	+	0.829033i	0.332334	+	0.943162i	$0.392164\pi$
$710$	11.8343	−	8.06847i	0.444132	−	0.302804i
$711$	−9.36343	−	9.02043i	−0.351156	−	0.338292i
$712$	−44.8336	−	6.75758i	−1.68021	−	0.253251i
$713$	−1.98289	−	5.05232i	−0.0742598	−	0.189211i
$714$	−11.2876	−	40.7274i	−0.422427	−	1.52418i
$715$	−4.42654	+	11.2786i	−0.165543	+	0.421797i
$716$	−42.7242	+	74.0004i	−1.59668	+	2.76552i
$717$	−12.0143	−	31.4761i	−0.448681	−	1.17550i
$718$	−4.50963	+	11.4904i	−0.168298	+	0.428816i
$719$	−7.41770	+	6.88262i	−0.276634	+	0.256679i	−0.806272	−	0.591545i	$-0.798518\pi$
$719$	−7.41770	+	6.88262i	−0.276634	+	0.256679i	0.529638	+	0.848224i	$0.322328\pi$
$720$	15.4301	−	4.44461i	0.575047	−	0.165641i
$721$	−21.3864	−	17.7469i	−0.796471	−	0.660928i
$722$	−1.93758	+	25.8552i	−0.0721093	+	0.962232i
$723$	25.2895	−	42.8698i	0.940528	−	1.59434i
$724$	71.9537	−	34.6511i	2.67414	−	1.28780i
$725$	4.26357	+	18.6799i	0.158345	+	0.693755i
$726$	−47.1953	+	22.1856i	−1.75158	+	0.823385i
$727$	−29.8012	−	27.6514i	−1.10526	−	1.02554i	−0.999515	−	0.0311426i	$-0.990085\pi$
$727$	−29.8012	−	27.6514i	−1.10526	−	1.02554i	−0.105749	−	0.994393i	$-0.533724\pi$
$728$	−48.8301	+	50.6140i	−1.80977	+	1.87588i
$729$	17.9940	−	20.1300i	0.666446	−	0.745554i
$730$	−9.23685	+	2.84919i	−0.341871	+	0.105453i
$731$	44.7577	+	6.74614i	1.65542	+	0.249515i
$732$	23.7979	−	59.0039i	0.879594	−	2.18085i
$733$	−0.365408	+	4.87603i	−0.0134966	+	0.180100i	0.986381	+	0.164475i	$0.0525930\pi$
$733$	−0.365408	+	4.87603i	−0.0134966	+	0.180100i	−0.999878	+	0.0156253i	$0.995026\pi$
$734$	35.2475	+	61.0504i	1.30101	+	2.25341i
$735$	6.72089	−	4.12153i	0.247904	−	0.152025i
$736$	−6.93751	+	12.0161i	−0.255720	+	0.442920i
$737$	−5.64389	−	3.84794i	−0.207895	−	0.141741i
$738$	41.8724	+	0.784956i	1.54134	+	0.0288946i
$739$	5.62893	+	14.3423i	0.207063	+	0.527589i	0.996246	−	0.0865698i	$-0.0275906\pi$
$739$	5.62893	+	14.3423i	0.207063	+	0.527589i	−0.789182	+	0.614159i	$0.789495\pi$
$740$	4.69554	−	20.5725i	0.172611	−	0.756260i
$741$	32.7609	+	16.1568i	1.20350	+	0.593534i
$742$	47.8587	+	39.7142i	1.75695	+	1.45795i
$743$	−20.1510	+	6.21575i	−0.739267	+	0.228034i	−0.641444	−	0.767170i	$-0.721664\pi$
$743$	−20.1510	+	6.21575i	−0.739267	+	0.228034i	−0.0978235	+	0.995204i	$0.531188\pi$
$744$	28.7858	+	20.0236i	1.05534	+	0.734100i
$745$	4.57874	−	4.24845i	0.167752	−	0.155651i
$746$	−0.477996	+	6.37841i	−0.0175007	+	0.233530i
$747$	6.51176	+	1.10669i	0.238253	+	0.0404916i
$748$	−71.2397	+	34.3072i	−2.60478	+	1.25440i
$749$	0.984450	+	7.52201i	0.0359710	+	0.274848i
$750$	−22.8134	−	15.8691i	−0.833026	−	0.579458i
$751$	19.9950	+	6.16765i	0.729630	+	0.225061i	0.637244	−	0.770662i	$-0.280074\pi$
$751$	19.9950	+	6.16765i	0.729630	+	0.225061i	0.0923859	+	0.995723i	$0.470551\pi$
$752$	36.4642	+	45.7246i	1.32971	+	1.66740i
$753$	9.11053	+	1.46064i	0.332006	+	0.0532288i
$754$	42.1892			1.53644
$755$	−5.85275	−	7.33912i	−0.213004	−	0.267098i
$756$	12.4899	−	62.5195i	0.454252	−	2.27381i
$757$	−4.29547	+	5.38635i	−0.156122	+	0.195770i	−0.853740	−	0.520699i	$-0.825671\pi$
$757$	−4.29547	+	5.38635i	−0.156122	+	0.195770i	0.697619	+	0.716469i	$0.254243\pi$
$758$	−43.4240	+	54.4520i	−1.57723	+	1.97779i
$759$	12.3374	+	8.58199i	0.447821	+	0.311507i
$760$	−21.4618	−	10.3355i	−0.778501	−	0.374906i
$761$	13.3536	+	34.0243i	0.484067	+	1.23338i	0.939327	+	0.343023i	$0.111451\pi$
$761$	13.3536	+	34.0243i	0.484067	+	1.23338i	−0.455260	+	0.890358i	$0.650454\pi$
$762$	−53.2811	+	48.5163i	−1.93017	+	1.75756i
$763$	0.612429	−	31.4617i	0.0221714	−	1.13899i
$764$	18.9622	+	23.7778i	0.686028	+	0.860252i
$765$	−1.42603	−	6.83603i	−0.0515581	−	0.247157i
$766$	37.8481	−	65.5549i	1.36751	−	2.36859i
$767$	5.56505	−	14.1795i	0.200942	−	0.511992i
$768$	2.78473	+	42.5012i	0.100485	+	1.53363i
$769$	−2.71222	−	36.1921i	−0.0978052	−	1.30512i	−0.802945	−	0.596052i	$-0.796735\pi$
$769$	−2.71222	−	36.1921i	−0.0978052	−	1.30512i	0.705140	−	0.709068i	$-0.250884\pi$
$770$	−14.0557	−	15.7525i	−0.506532	−	0.567682i
$771$	3.06614	−	12.8761i	0.110424	−	0.463723i

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)

\(f(q)\)	\(=\)	\(q+(2.32120 - 1.11783i) q^{2} +(-0.647872 + 1.60632i) q^{3} +(2.89143 - 3.62573i) q^{4} +(-0.476675 - 0.442290i) q^{5} +(0.291752 + 4.45279i) q^{6} +(2.64170 - 0.146332i) q^{7} +(1.51204 - 6.62468i) q^{8} +(-2.16052 - 2.08138i) q^{9} +O(q^{10})\)	\(q+(2.32120 - 1.11783i) q^{2} +(-0.647872 + 1.60632i) q^{3} +(2.89143 - 3.62573i) q^{4} +(-0.476675 - 0.442290i) q^{5} +(0.291752 + 4.45279i) q^{6} +(2.64170 - 0.146332i) q^{7} +(1.51204 - 6.62468i) q^{8} +(-2.16052 - 2.08138i) q^{9} +(-1.60086 - 0.493800i) q^{10} +(3.93542 + 2.68312i) q^{11} +(3.95081 + 6.99357i) q^{12} +(-3.23220 - 2.20368i) q^{13} +(5.96833 - 3.29263i) q^{14} +(1.01928 - 0.479145i) q^{15} +(-1.83164 - 8.02494i) q^{16} +(-3.53970 + 0.533524i) q^{17} +(-7.34162 - 2.41619i) q^{18} +(2.69554 + 4.66882i) q^{19} +(-2.98190 + 0.449448i) q^{20} +(-1.47643 + 4.33822i) q^{21} +(12.1341 + 1.82893i) q^{22} +(-0.665542 - 1.69577i) q^{23} +(9.66174 + 6.72076i) q^{24} +(-0.342052 - 4.56436i) q^{25} +(-9.96590 - 1.50212i) q^{26} +(4.74310 - 2.12202i) q^{27} +(7.10773 - 10.0012i) q^{28} +(-4.13932 + 0.623901i) q^{29} +(1.83035 - 2.25157i) q^{30} +2.97936 q^{31} +(-4.74882 - 5.95483i) q^{32} +(-6.85960 + 4.58322i) q^{33} +(-7.61995 + 5.19519i) q^{34} +(-1.32395 - 1.09864i) q^{35} +(-13.7935 + 1.81533i) q^{36} +(-2.55648 + 6.51381i) q^{37} +(11.4758 + 7.82408i) q^{38} +(5.63386 - 3.76425i) q^{39} +(-3.65078 + 2.48906i) q^{40} +(-5.17779 + 1.59714i) q^{41} +(1.42231 + 11.7203i) q^{42} +(-12.0827 - 3.72703i) q^{43} +(21.1073 - 6.51072i) q^{44} +(0.109295 + 1.94772i) q^{45} +(-3.44044 - 3.19226i) q^{46} +(-6.40143 + 3.08277i) q^{47} +(14.0773 + 2.25694i) q^{48} +(6.95717 - 0.773129i) q^{49} +(-5.89614 - 10.2124i) q^{50} +(1.43626 - 6.03155i) q^{51} +(-17.3356 + 5.34733i) q^{52} +(3.33328 + 8.49307i) q^{53} +(8.63761 - 10.2276i) q^{54} +(-0.689197 - 3.01957i) q^{55} +(3.02496 - 17.7217i) q^{56} +(-9.24598 + 1.30511i) q^{57} +(-8.91074 + 6.07524i) q^{58} +(0.866460 + 3.79621i) q^{59} +(1.20993 - 5.08106i) q^{60} +(-4.93850 - 6.19269i) q^{61} +(6.91568 - 3.33042i) q^{62} +(-6.01203 - 5.18223i) q^{63} +(-2.84710 - 1.37109i) q^{64} +(0.566045 + 2.48001i) q^{65} +(-10.7992 + 18.3064i) q^{66} -1.43413 q^{67} +(-8.30037 + 14.3767i) q^{68} +(3.15514 + 0.0295711i) q^{69} +(-4.30125 - 1.07022i) q^{70} +(-5.33059 + 6.68435i) q^{71} +(-17.0553 + 11.1656i) q^{72} +(4.76734 - 3.25032i) q^{73} +(1.34723 + 17.9775i) q^{74} +(7.55343 + 2.40768i) q^{75} +(24.7219 + 3.72622i) q^{76} +(10.7888 + 6.51213i) q^{77} +(8.86951 - 15.0352i) q^{78} +4.33387 q^{79} +(-2.67625 + 4.63540i) q^{80} +(0.335725 + 8.99374i) q^{81} +(-10.2333 + 9.49515i) q^{82} +(-1.81914 + 1.24027i) q^{83} +(11.4602 + 17.8968i) q^{84} +(1.92326 + 1.31126i) q^{85} +(-32.2125 + 4.85526i) q^{86} +(1.67956 - 7.05327i) q^{87} +(23.7253 - 22.0139i) q^{88} +(-0.498638 - 6.65386i) q^{89} +(2.43091 + 4.39886i) q^{90} +(-8.86098 - 5.34848i) q^{91} +(-8.07279 - 2.49012i) q^{92} +(-1.93025 + 4.78581i) q^{93} +(-11.4130 + 14.3114i) q^{94} +(0.780072 - 3.41772i) q^{95} +(12.6420 - 3.77015i) q^{96} +(8.43105 - 14.6030i) q^{97} +(15.2847 - 9.57151i) q^{98} +(-2.91797 - 13.9880i) 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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