LMFDB - Embedded newform 441.2.y.a.151.49

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			151.49
Character	$\chi$	$=$	441.151
Dual form			441.2.y.a.184.49

$q$-expansion

$f(q)$	$=$	$q+(2.08709 - 1.00509i) q^{2} +(1.51033 - 0.847884i) q^{3} +(2.09877 - 2.63177i) q^{4} +(-1.46653 - 1.36074i) q^{5} +(2.29999 - 3.28763i) q^{6} +(-2.55799 + 0.675802i) q^{7} +(0.704215 - 3.08537i) q^{8} +(1.56218 - 2.56117i) q^{9} +O(q^{10})$	\(q+(2.08709 - 1.00509i) q^{2} +(1.51033 - 0.847884i) q^{3} +(2.09877 - 2.63177i) q^{4} +(-1.46653 - 1.36074i) q^{5} +(2.29999 - 3.28763i) q^{6} +(-2.55799 + 0.675802i) q^{7} +(0.704215 - 3.08537i) q^{8} +(1.56218 - 2.56117i) q^{9} +(-4.42846 - 1.36600i) q^{10} +(2.74156 + 1.86917i) q^{11} +(0.938391 - 5.75435i) q^{12} +(3.06522 + 2.08983i) q^{13} +(-4.65951 + 3.98147i) q^{14} +(-3.36870 - 0.811720i) q^{15} +(-0.133230 - 0.583719i) q^{16} +(-5.17133 + 0.779453i) q^{17} +(0.686217 - 6.91553i) q^{18} +(0.930856 + 1.61229i) q^{19} +(-6.65909 + 1.00370i) q^{20} +(-3.29040 + 3.18956i) q^{21} +(7.60058 + 1.14560i) q^{22} +(-0.869454 - 2.21533i) q^{23} +(-1.55244 - 5.25701i) q^{24} +(-0.0745547 - 0.994864i) q^{25} +(8.49788 + 1.28085i) q^{26} +(0.187838 - 5.19276i) q^{27} +(-3.59006 + 8.15039i) q^{28} +(4.97460 - 0.749800i) q^{29} +(-7.84665 + 1.69172i) q^{30} -1.71754 q^{31} +(3.08158 + 3.86418i) q^{32} +(5.72550 + 0.498527i) q^{33} +(-10.0096 + 6.82445i) q^{34} +(4.67097 + 2.48968i) q^{35} +(-3.46175 - 9.48661i) q^{36} +(-3.33948 + 8.50886i) q^{37} +(3.56328 + 2.42940i) q^{38} +(6.40143 + 0.557381i) q^{39} +(-5.23116 + 3.56654i) q^{40} +(0.0854054 - 0.0263441i) q^{41} +(-3.66157 + 9.96405i) q^{42} +(4.12102 + 1.27117i) q^{43} +(10.6731 - 3.29222i) q^{44} +(-5.77609 + 1.63031i) q^{45} +(-4.04124 - 3.74972i) q^{46} +(-8.72599 + 4.20221i) q^{47} +(-0.696147 - 0.768644i) q^{48} +(6.08658 - 3.45739i) q^{49} +(-1.15553 - 2.00144i) q^{50} +(-7.14952 + 5.56192i) q^{51} +(11.9332 - 3.68089i) q^{52} +(0.956134 + 2.43619i) q^{53} +(-4.82716 - 11.0266i) q^{54} +(-1.47714 - 6.47176i) q^{55} +(0.283727 + 8.36824i) q^{56} +(2.77293 + 1.64583i) q^{57} +(9.62883 - 6.56483i) q^{58} +(-2.95513 - 12.9473i) q^{59} +(-9.20639 + 7.16204i) q^{60} +(4.18227 + 5.24440i) q^{61} +(-3.58466 + 1.72628i) q^{62} +(-2.26520 + 7.60716i) q^{63} +(11.3943 + 5.48719i) q^{64} +(-1.65152 - 7.23580i) q^{65} +(12.4507 - 4.71418i) q^{66} -7.10843 q^{67} +(-8.80208 + 15.2457i) q^{68} +(-3.19151 - 2.60868i) q^{69} +(12.2511 + 0.501442i) q^{70} +(6.33459 - 7.94333i) q^{71} +(-6.80203 - 6.62353i) q^{72} +(-6.80720 + 4.64107i) q^{73} +(1.58237 + 21.1153i) q^{74} +(-0.956131 - 1.43936i) q^{75} +(6.19683 + 0.934023i) q^{76} +(-8.27607 - 2.92855i) q^{77} +(13.9206 - 5.27072i) q^{78} -10.2518 q^{79} +(-0.598906 + 1.03734i) q^{80} +(-4.11916 - 8.00203i) q^{81} +(0.151771 - 0.140823i) q^{82} +(-1.31391 + 0.895808i) q^{83} +(1.48842 + 15.3537i) q^{84} +(8.64457 + 5.89377i) q^{85} +(9.87860 - 1.48896i) q^{86} +(6.87754 - 5.35033i) q^{87} +(7.69772 - 7.14244i) q^{88} +(-1.11803 - 14.9191i) q^{89} +(-10.4166 + 9.20809i) q^{90} +(-9.25312 - 3.27428i) q^{91} +(-7.65503 - 2.36126i) q^{92} +(-2.59404 + 1.45627i) q^{93} +(-13.9883 + 17.5408i) q^{94} +(0.828783 - 3.63114i) q^{95} +(7.93058 + 3.22336i) q^{96} +(-0.0150907 + 0.0261379i) q^{97} +(9.22827 - 13.3335i) q^{98} +(9.07008 - 4.10162i) 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 $

$2$	2.08709	−	1.00509i	1.47580	−	0.710707i	0.488943	−	0.872316i	$-0.337383\pi$
$2$	2.08709	−	1.00509i	1.47580	−	0.710707i	0.986855	+	0.161609i	$0.0516685\pi$
$3$	1.51033	−	0.847884i	0.871989	−	0.489526i
$3$	1.51033	−	0.847884i	0.871989	−	0.489526i
$4$	2.09877	−	2.63177i	1.04938	−	1.31589i
$5$	−1.46653	−	1.36074i	−0.655854	−	0.608543i	0.280393	−	0.959885i	$-0.409535\pi$
$5$	−1.46653	−	1.36074i	−0.655854	−	0.608543i	−0.936247	+	0.351342i	$0.885726\pi$
$6$	2.29999	−	3.28763i	0.938969	−	1.34217i
$7$	−2.55799	+	0.675802i	−0.966828	+	0.255429i
$7$	−2.55799	+	0.675802i	−0.966828	+	0.255429i
$8$	0.704215	−	3.08537i	0.248978	−	1.09084i
$9$	1.56218	−	2.56117i	0.520728	−	0.853723i
$10$	−4.42846	−	1.36600i	−1.40040	−	0.431967i
$11$	2.74156	+	1.86917i	0.826613	+	0.563575i	0.901082	−	0.433648i	$-0.142774\pi$
$11$	2.74156	+	1.86917i	0.826613	+	0.563575i	−0.0744695	+	0.997223i	$0.523726\pi$
$12$	0.938391	−	5.75435i	0.270890	−	1.66114i
$13$	3.06522	+	2.08983i	0.850140	+	0.579616i	0.908124	−	0.418702i	$-0.137515\pi$
$13$	3.06522	+	2.08983i	0.850140	+	0.579616i	−0.0579835	+	0.998318i	$0.518467\pi$
$14$	−4.65951	+	3.98147i	−1.24531	+	1.06409i
$15$	−3.36870	−	0.811720i	−0.869795	−	0.209585i
$16$	−0.133230	−	0.583719i	−0.0333075	−	0.145930i
$17$	−5.17133	+	0.779453i	−1.25423	+	0.189045i	−0.742351	−	0.670011i	$-0.766289\pi$
$17$	−5.17133	+	0.779453i	−1.25423	+	0.189045i	−0.511881	+	0.859056i	$0.671051\pi$
$18$	0.686217	−	6.91553i	0.161743	−	1.63001i
$19$	0.930856	+	1.61229i	0.213553	+	0.369885i	0.952824	−	0.303523i	$-0.0981630\pi$
$19$	0.930856	+	1.61229i	0.213553	+	0.369885i	−0.739271	+	0.673408i	$0.764830\pi$
$20$	−6.65909	+	1.00370i	−1.48902	+	0.224433i
$21$	−3.29040	+	3.18956i	−0.718023	+	0.696019i
$22$	7.60058	+	1.14560i	1.62045	+	0.244243i
$23$	−0.869454	−	2.21533i	−0.181294	−	0.461929i	0.811119	−	0.584881i	$-0.198859\pi$
$23$	−0.869454	−	2.21533i	−0.181294	−	0.461929i	−0.992413	+	0.122953i	$0.960764\pi$
$24$	−1.55244	−	5.25701i	−0.316890	−	1.07308i
$25$	−0.0745547	−	0.994864i	−0.0149109	−	0.198973i
$26$	8.49788	+	1.28085i	1.66657	+	0.251195i
$27$	0.187838	−	5.19276i	0.0361494	−	0.999346i
$28$	−3.59006	+	8.15039i	−0.678458	+	1.54028i
$29$	4.97460	−	0.749800i	0.923760	−	0.139234i	0.330096	−	0.943947i	$-0.392919\pi$
$29$	4.97460	−	0.749800i	0.923760	−	0.139234i	0.593664	+	0.804713i	$0.297681\pi$
$30$	−7.84665	+	1.69172i	−1.43259	+	0.308864i
$31$	−1.71754			−0.308479			−0.154239	−	0.988034i	$-0.549293\pi$
$31$	−1.71754			−0.308479			−0.154239	+	0.988034i	$0.549293\pi$
$32$	3.08158	+	3.86418i	0.544752	+	0.683097i
$33$	5.72550	+	0.498527i	0.996682	+	0.0867823i
$34$	−10.0096	+	6.82445i	−1.71664	+	1.17038i
$35$	4.67097	+	2.48968i	0.789538	+	0.420832i
$36$	−3.46175	−	9.48661i	−0.576958	−	1.58110i
$37$	−3.33948	+	8.50886i	−0.549008	+	1.39885i	0.339770	+	0.940509i	$0.389651\pi$
$37$	−3.33948	+	8.50886i	−0.549008	+	1.39885i	−0.888777	+	0.458340i	$0.848444\pi$
$38$	3.56328	+	2.42940i	0.578041	+	0.394101i
$39$	6.40143	+	0.557381i	1.02505	+	0.0892524i
$40$	−5.23116	+	3.56654i	−0.827118	+	0.563920i
$41$	0.0854054	−	0.0263441i	0.0133381	−	0.00411425i	−0.288079	−	0.957607i	$-0.593017\pi$
$41$	0.0854054	−	0.0263441i	0.0133381	−	0.00411425i	0.301417	+	0.953492i	$0.402540\pi$
$42$	−3.66157	+	9.96405i	−0.564992	+	1.53749i
$43$	4.12102	+	1.27117i	0.628450	+	0.193851i	0.592588	−	0.805506i	$-0.298106\pi$
$43$	4.12102	+	1.27117i	0.628450	+	0.193851i	0.0358620	+	0.999357i	$0.488582\pi$
$44$	10.6731	−	3.29222i	1.60903	−	0.496322i
$45$	−5.77609	+	1.63031i	−0.861049	+	0.243032i
$46$	−4.04124	−	3.74972i	−0.595848	−	0.552867i
$47$	−8.72599	+	4.20221i	−1.27282	+	0.612956i	−0.943534	−	0.331276i	$-0.892521\pi$
$47$	−8.72599	+	4.20221i	−1.27282	+	0.612956i	−0.329282	+	0.944232i	$0.606807\pi$
$48$	−0.696147	−	0.768644i	−0.100480	−	0.110944i
$49$	6.08658	−	3.45739i	0.869512	−	0.493912i
$50$	−1.15553	−	2.00144i	−0.163417	−	0.283046i
$51$	−7.14952	+	5.56192i	−1.00113	+	0.778824i
$52$	11.9332	−	3.68089i	1.65483	−	0.510448i
$53$	0.956134	+	2.43619i	0.131335	+	0.334636i	0.981381	−	0.192073i	$-0.0615209\pi$
$53$	0.956134	+	2.43619i	0.131335	+	0.334636i	−0.850046	+	0.526709i	$0.823426\pi$
$54$	−4.82716	−	11.0266i	−0.656893	−	1.50052i
$55$	−1.47714	−	6.47176i	−0.199177	−	0.872653i
$56$	0.283727	+	8.36824i	0.0379146	+	1.11825i
$57$	2.77293	+	1.64583i	0.367284	+	0.217995i
$58$	9.62883	−	6.56483i	1.26433	−	0.862004i
$59$	−2.95513	−	12.9473i	−0.384726	−	1.68559i	−0.682443	−	0.730939i	$-0.739083\pi$
$59$	−2.95513	−	12.9473i	−0.384726	−	1.68559i	0.297718	−	0.954654i	$-0.403775\pi$
$60$	−9.20639	+	7.16204i	−1.18854	+	0.924616i
$61$	4.18227	+	5.24440i	0.535485	+	0.671477i	0.973816	−	0.227337i	$-0.0730017\pi$
$61$	4.18227	+	5.24440i	0.535485	+	0.671477i	−0.438331	+	0.898814i	$0.644430\pi$
$62$	−3.58466	+	1.72628i	−0.455252	+	0.219238i
$63$	−2.26520	+	7.60716i	−0.285389	+	0.958412i
$64$	11.3943	+	5.48719i	1.42428	+	0.685899i
$65$	−1.65152	−	7.23580i	−0.204846	−	0.897491i
$66$	12.4507	−	4.71418i	1.53258	−	0.580275i
$67$	−7.10843			−0.868434			−0.434217	−	0.900808i	$-0.642975\pi$
$67$	−7.10843			−0.868434			−0.434217	+	0.900808i	$0.642975\pi$
$68$	−8.80208	+	15.2457i	−1.06741	+	1.84881i
$69$	−3.19151	−	2.60868i	−0.384212	−	0.314049i
$70$	12.2511	+	0.501442i	1.46429	+	0.0599338i
$71$	6.33459	−	7.94333i	0.751778	−	0.942700i	−0.247882	−	0.968790i	$-0.579734\pi$
$71$	6.33459	−	7.94333i	0.751778	−	0.942700i	0.999660	+	0.0260905i	$0.00830582\pi$
$72$	−6.80203	−	6.62353i	−0.801627	−	0.780590i
$73$	−6.80720	+	4.64107i	−0.796722	+	0.543196i	−0.891883	−	0.452266i	$-0.850616\pi$
$73$	−6.80720	+	4.64107i	−0.796722	+	0.543196i	0.0951611	+	0.995462i	$0.469663\pi$
$74$	1.58237	+	21.1153i	0.183947	+	2.45460i
$75$	−0.956131	−	1.43936i	−0.110405	−	0.166203i
$76$	6.19683	+	0.934023i	0.710826	+	0.107140i
$77$	−8.27607	−	2.92855i	−0.943146	−	0.333739i
$78$	13.9206	−	5.27072i	1.57620	−	0.596791i
$79$	−10.2518			−1.15342			−0.576710	−	0.816949i	$-0.695664\pi$
$79$	−10.2518			−1.15342			−0.576710	+	0.816949i	$0.695664\pi$
$80$	−0.598906	+	1.03734i	−0.0669597	+	0.115978i
$81$	−4.11916	−	8.00203i	−0.457684	−	0.889115i
$82$	0.151771	−	0.140823i	0.0167603	−	0.0155513i
$83$	−1.31391	+	0.895808i	−0.144220	+	0.0983278i	−0.633281	−	0.773922i	$-0.718292\pi$
$83$	−1.31391	+	0.895808i	−0.144220	+	0.0983278i	0.489060	+	0.872250i	$0.337340\pi$
$84$	1.48842	+	15.3537i	0.162399	+	1.67523i
$85$	8.64457	+	5.89377i	0.937635	+	0.639269i
$86$	9.87860	−	1.48896i	1.06524	−	0.160559i
$87$	6.87754	−	5.35033i	0.737349	−	0.573616i
$88$	7.69772	−	7.14244i	0.820580	−	0.761387i
$89$	−1.11803	−	14.9191i	−0.118511	−	1.58142i	−0.666868	−	0.745176i	$-0.732365\pi$
$89$	−1.11803	−	14.9191i	−0.118511	−	1.58142i	0.548357	−	0.836244i	$-0.315254\pi$
$90$	−10.4166	+	9.20809i	−1.09801	+	0.970618i
$91$	−9.25312	−	3.27428i	−0.969990	−	0.343238i
$92$	−7.65503	−	2.36126i	−0.798092	−	0.246179i
$93$	−2.59404	+	1.45627i	−0.268990	+	0.151008i
$94$	−13.9883	+	17.5408i	−1.44279	+	1.80920i
$95$	0.828783	−	3.63114i	0.0850314	−	0.372547i
$96$	7.93058	+	3.22336i	0.809411	+	0.328983i
$97$	−0.0150907	+	0.0261379i	−0.00153223	+	0.00265390i	−0.866791	−	0.498672i	$-0.833821\pi$
$97$	−0.0150907	+	0.0261379i	−0.00153223	+	0.00265390i	0.865258	+	0.501326i	$0.167154\pi$
$98$	9.22827	−	13.3335i	0.932196	−	1.34688i
$99$	9.07008	−	4.10162i	0.911577	−	0.412229i
$100$	−2.77473	−	1.89178i	−0.277473	−	0.189178i
$101$	−13.6846	+	4.22113i	−1.36166	+	0.420018i	−0.887658	−	0.460504i	$-0.847669\pi$
$101$	−13.6846	+	4.22113i	−1.36166	+	0.420018i	−0.474006	+	0.880522i	$0.657193\pi$
$102$	−9.33148	+	18.7942i	−0.923954	+	1.86090i
$103$	−9.35143	−	8.67685i	−0.921423	−	0.854956i	0.0683418	−	0.997662i	$-0.478229\pi$
$103$	−9.35143	−	8.67685i	−0.921423	−	0.854956i	−0.989765	+	0.142706i	$0.954420\pi$
$104$	8.60649	−	7.98566i	0.843936	−	0.783058i
$105$	9.16565	−	0.200208i	0.894476	−	0.0195383i
$106$	4.44413	+	4.12355i	0.431652	+	0.400515i
$107$	0.842287	+	11.2395i	0.0814270	+	1.08657i	0.876930	+	0.480618i	$0.159588\pi$
$107$	0.842287	+	11.2395i	0.0814270	+	1.08657i	−0.795503	+	0.605949i	$0.792793\pi$
$108$	−13.2719	−	11.3927i	−1.27709	−	1.09627i
$109$	−0.833354	+	11.1203i	−0.0798209	+	1.06514i	0.803171	+	0.595748i	$0.203144\pi$
$109$	−0.833354	+	11.1203i	−0.0798209	+	1.06514i	−0.882992	+	0.469388i	$0.844475\pi$
$110$	−9.58764	−	12.0225i	−0.914145	−	1.14630i
$111$	2.17082	+	15.6827i	0.206045	+	1.48853i
$112$	0.735279	+	1.40311i	0.0694773	+	0.132581i
$113$	−0.500270	−	6.67564i	−0.0470615	−	0.627992i	−0.970010	−	0.243067i	$-0.921847\pi$
$113$	−0.500270	−	6.67564i	−0.0470615	−	0.627992i	0.922948	−	0.384925i	$-0.125773\pi$
$114$	7.44158	+	0.647948i	0.696968	+	0.0606859i
$115$	−1.73942	+	4.43196i	−0.162202	+	0.413283i
$116$	8.46723	−	14.6657i	0.786163	−	1.36167i
$117$	10.1409	−	4.58585i	0.937523	−	0.423962i
$118$	−19.1808	−	24.0520i	−1.76574	−	2.21417i
$119$	12.7014	−	5.48863i	1.16434	−	0.503142i
$120$	−4.87675	+	9.82206i	−0.445184	+	0.896628i
$121$	0.00363791	+	0.00926925i	0.000330719	+	0.000842659i
$122$	13.9999	+	6.74199i	1.26749	+	0.610391i
$123$	0.106653	−	0.112202i	0.00961662	−	0.0101169i
$124$	−3.60471	+	4.52017i	−0.323713	+	0.405923i
$125$	−7.48114	+	9.38106i	−0.669134	+	0.839067i
$126$	2.91820	+	18.1536i	0.259974	+	1.61725i
$127$	5.08618	+	6.37787i	0.451326	+	0.565944i	0.954489	−	0.298247i	$-0.0964019\pi$
$127$	5.08618	+	6.37787i	0.451326	+	0.565944i	−0.503163	+	0.864191i	$0.667831\pi$
$128$	19.4111			1.71571
$129$	7.30190	−	1.57427i	0.642897	−	0.138607i
$130$	−10.7195	−	13.4419i	−0.940164	−	1.17893i
$131$	14.6137	+	4.50772i	1.27680	+	0.393842i	0.857725	−	0.514108i	$-0.171877\pi$
$131$	14.6137	+	4.50772i	1.27680	+	0.393842i	0.419078	+	0.907950i	$0.362353\pi$
$132$	13.3285	−	14.0219i	1.16010	−	1.22045i
$133$	−3.47071	−	3.49514i	−0.300949	−	0.303067i
$134$	−14.8360	+	7.14462i	−1.28163	+	0.617201i
$135$	−7.34148	+	7.35975i	−0.631854	+	0.633427i
$136$	−1.23683	+	16.5044i	−0.106057	+	1.41524i
$137$	9.22028	−	8.55517i	0.787742	−	0.730918i	−0.179780	−	0.983707i	$-0.557538\pi$
$137$	9.22028	−	8.55517i	0.787742	−	0.730918i	0.967521	+	0.252789i	$0.0813480\pi$
$138$	−9.28293	−	2.23681i	−0.790216	−	0.190410i
$139$	2.43661	−	0.751595i	0.206671	−	0.0637495i	−0.189691	−	0.981844i	$-0.560749\pi$
$139$	2.43661	−	0.751595i	0.206671	−	0.0637495i	0.396362	+	0.918094i	$0.370273\pi$
$140$	16.3555	−	7.06767i	1.38230	−	0.597327i
$141$	−9.61612	+	13.7454i	−0.809823	+	1.15757i
$142$	5.23712	−	22.9453i	0.439489	−	1.92553i
$143$	4.49726	+	11.4588i	0.376080	+	0.958236i
$144$	−1.70313	−	0.570652i	−0.141928	−	0.0475543i
$145$	−8.31570	−	5.66955i	−0.690582	−	0.470831i
$146$	−9.54255	+	16.5282i	−0.789747	+	1.36788i
$147$	6.26127	−	10.3825i	0.516421	−	0.856335i
$148$	15.3846	+	26.6469i	1.26461	+	2.19036i
$149$	1.78351	−	23.7993i	0.146111	−	1.94972i	−0.136866	−	0.990590i	$-0.543703\pi$
$149$	1.78351	−	23.7993i	0.146111	−	1.94972i	0.282977	−	0.959127i	$-0.408678\pi$
$150$	−3.44222	−	2.04307i	−0.281056	−	0.166816i
$151$	−20.3523	−	3.06761i	−1.65624	−	0.249639i	−0.746675	−	0.665190i	$-0.768351\pi$
$151$	−20.3523	−	3.06761i	−1.65624	−	0.249639i	−0.909570	+	0.415551i	$0.863589\pi$
$152$	5.63004	−	1.73664i	0.456656	−	0.140860i
$153$	−6.08226	+	14.4623i	−0.491722	+	1.16921i
$154$	−20.2164	+	2.20605i	−1.62908	+	0.177769i
$155$	2.51883	+	2.33713i	0.202317	+	0.187723i
$156$	14.9020	−	15.6773i	1.19312	−	1.25519i
$157$	2.90098	+	12.7100i	0.231523	+	1.01437i	0.948377	+	0.317146i	$0.102725\pi$
$157$	2.90098	+	12.7100i	0.231523	+	1.01437i	−0.716853	+	0.697224i	$0.754418\pi$
$158$	−21.3965	+	10.3040i	−1.70221	+	0.819743i
$159$	3.50968	+	2.86876i	0.278336	+	0.227507i
$160$	0.738920	−	9.86020i	0.0584167	−	0.779517i
$161$	3.72118	+	5.07921i	0.293270	+	0.400298i
$162$	−16.6398	−	12.5609i	−1.30735	−	0.986874i
$163$	−8.47226	+	7.86111i	−0.663599	+	0.615730i	−0.938309	−	0.345797i	$-0.887608\pi$
$163$	−8.47226	+	7.86111i	−0.663599	+	0.615730i	0.274711	+	0.961527i	$0.411418\pi$
$164$	0.109915	−	0.280058i	0.00858288	−	0.0218688i
$165$	−7.71827	−	8.52205i	−0.600867	−	0.663441i
$166$	−1.84188	+	3.19023i	−0.142958	+	0.247610i
$167$	−2.03430	+	5.18331i	−0.157419	+	0.401097i	−0.987723	−	0.156213i	$-0.950071\pi$
$167$	−2.03430	+	5.18331i	−0.157419	+	0.401097i	0.830305	+	0.557310i	$0.188166\pi$
$168$	7.52382	+	12.3982i	0.580475	+	0.956544i
$169$	0.278758	+	0.710265i	0.0214430	+	0.0546358i
$170$	23.9658	+	3.61226i	1.83809	+	0.277048i
$171$	5.58352	+	0.134616i	0.426982	+	0.0102943i
$172$	11.9945	−	8.17771i	0.914572	−	0.623545i
$173$	13.2069	−	16.5609i	1.00410	−	1.25910i	0.0384504	−	0.999261i	$-0.487758\pi$
$173$	13.2069	−	16.5609i	1.00410	−	1.25910i	0.965651	−	0.259843i	$-0.0836707\pi$
$174$	8.97649	−	18.0792i	0.680506	−	1.37058i
$175$	0.863041	+	2.49446i	0.0652398	+	0.188564i
$176$	0.725809	−	1.84933i	0.0547099	−	0.139399i
$177$	−15.4410	−	17.0490i	−1.16062	−	1.28148i
$178$	−17.3285	−	30.0138i	−1.29882	−	2.24963i
$179$	13.2303	−	1.99414i	0.988878	−	0.149049i	0.365367	−	0.930864i	$-0.380944\pi$
$179$	13.2303	−	1.99414i	0.988878	−	0.149049i	0.623511	+	0.781814i	$0.285706\pi$
$180$	−7.83209	+	18.6230i	−0.583769	+	1.38808i
$181$	14.0078	+	6.74580i	1.04119	+	0.501411i	0.874717	−	0.484635i	$-0.161047\pi$
$181$	14.0078	+	6.74580i	1.04119	+	0.501411i	0.166474	+	0.986046i	$0.446762\pi$
$182$	−22.6031	+	2.46649i	−1.67545	+	0.182829i
$183$	10.7633	+	4.37469i	0.795642	+	0.323386i
$184$	−7.44740	+	1.12252i	−0.549030	+	0.0827529i
$185$	16.4759	−	7.93435i	1.21133	−	0.583345i
$186$	−3.95032	+	5.64663i	−0.289652	+	0.414031i
$187$	−15.6345	−	7.52916i	−1.14330	−	0.550587i
$188$	−7.25456	+	31.7843i	−0.529093	+	2.31811i
$189$	3.02879	+	13.4099i	0.220312	+	0.975429i
$190$	−1.91987	−	8.41152i	−0.139282	−	0.610236i
$191$	3.12506	−	13.6918i	0.226122	−	0.990703i	−0.726648	−	0.687010i	$-0.758923\pi$
$191$	3.12506	−	13.6918i	0.226122	−	0.990703i	0.952770	−	0.303694i	$-0.0982199\pi$
$192$	21.8616	−	1.37356i	1.57773	−	0.0991283i
$193$	5.87884	−	25.7569i	0.423168	−	1.85402i	−0.0903016	−	0.995914i	$-0.528783\pi$
$193$	5.87884	−	25.7569i	0.423168	−	1.85402i	0.513470	−	0.858108i	$-0.328360\pi$
$194$	−0.00522477	+	0.0697197i	−0.000375117	+	0.00500558i
$195$	−8.62947	−	9.52813i	−0.617969	−	0.682324i
$196$	3.67527	−	23.2748i	0.262520	−	1.66248i
$197$	0.662920			0.0472311			0.0236155	−	0.999721i	$-0.492482\pi$
$197$	0.662920			0.0472311			0.0236155	+	0.999721i	$0.492482\pi$
$198$	14.8076	−	17.6767i	1.05233	−	1.25623i
$199$	12.1281	+	11.2532i	0.859737	+	0.797719i	0.980819	−	0.194923i	$-0.0624458\pi$
$199$	12.1281	+	11.2532i	0.859737	+	0.797719i	−0.121081	+	0.992643i	$0.538636\pi$
$200$	−3.12202	−	0.470569i	−0.220760	−	0.0332743i
$201$	−10.7361	+	6.02713i	−0.757264	+	0.425121i
$202$	−24.3183	+	22.5641i	−1.71103	+	1.58760i
$203$	−12.2182	+	5.27982i	−0.857552	+	0.370571i
$204$	−0.367485	+	30.4891i	−0.0257291	+	2.13466i
$205$	−0.161097	−	0.0775804i	−0.0112515	−	0.00541845i
$206$	−28.2383	−	8.71037i	−1.96746	−	0.606880i
$207$	−7.03208	−	1.23394i	−0.488764	−	0.0857648i
$208$	0.811496	−	2.06766i	0.0562671	−	0.143366i
$209$	−0.461637	+	6.16012i	−0.0319321	+	0.426105i
$210$	18.9283	−	9.63017i	1.30618	−	0.664545i
$211$	1.06827	+	14.2551i	0.0735427	+	0.981359i	0.904901	+	0.425622i	$0.139945\pi$
$211$	1.06827	+	14.2551i	0.0735427	+	0.981359i	−0.831358	+	0.555737i	$0.812436\pi$
$212$	8.41820	+	2.59667i	0.578164	+	0.178340i
$213$	2.83229	−	17.3680i	0.194066	−	1.19004i
$214$	13.0547	+	22.6114i	0.892400	+	1.54568i
$215$	−4.31389	−	7.47187i	−0.294205	−	0.509577i
$216$	−15.8893	−	4.23637i	−1.08113	−	0.288248i
$217$	4.39343	−	1.16072i	0.298246	−	0.0787945i
$218$	9.43767	+	24.0468i	0.639199	+	1.62865i
$219$	−6.34601	+	12.7813i	−0.428824	+	0.863677i
$220$	−20.1324	−	9.69524i	−1.35733	−	0.653653i
$221$	−17.4802	−	8.41803i	−1.17585	−	0.566258i
$222$	20.2932	+	30.5493i	1.36199	+	2.05034i
$223$	−2.57369	−	6.55766i	−0.172347	−	0.439134i	0.818435	−	0.574599i	$-0.194842\pi$
$223$	−2.57369	−	6.55766i	−0.172347	−	0.439134i	−0.990782	+	0.135466i	$0.956747\pi$
$224$	−10.4941	−	7.80198i	−0.701164	−	0.521292i
$225$	−2.66448	−	1.36321i	−0.177632	−	0.0908809i
$226$	−7.75374	−	13.4299i	−0.515771	−	0.893341i
$227$	−3.22262	−	5.58175i	−0.213893	−	0.370474i	0.739037	−	0.673665i	$-0.235281\pi$
$227$	−3.22262	−	5.58175i	−0.213893	−	0.370474i	−0.952930	+	0.303192i	$0.901948\pi$
$228$	10.1512	−	3.84352i	0.672280	−	0.254543i
$229$	−1.45351	−	0.448347i	−0.0960503	−	0.0296276i	0.246358	−	0.969179i	$-0.420766\pi$
$229$	−1.45351	−	0.448347i	−0.0960503	−	0.0296276i	−0.342408	+	0.939551i	$0.611242\pi$
$230$	0.824201	+	10.9982i	0.0543462	+	0.725199i
$231$	−14.9827	+	2.59408i	−0.985786	+	0.170678i
$232$	1.18978	−	15.8765i	0.0781128	−	1.04234i
$233$	−7.58340	+	19.3222i	−0.496805	+	1.26584i	0.434194	+	0.900819i	$0.357033\pi$
$233$	−7.58340	+	19.3222i	−0.496805	+	1.26584i	−0.931000	+	0.365020i	$0.881062\pi$
$234$	16.5557	−	19.7636i	1.08228	−	1.29199i
$235$	18.5151	+	5.71115i	1.20779	+	0.372554i
$236$	−40.2764	−	19.3961i	−2.62177	−	1.26258i
$237$	−15.4836	+	8.69236i	−1.00577	+	0.564629i
$238$	20.9925	−	24.2214i	1.36074	−	1.57004i
$239$	−4.06667	+	3.77332i	−0.263051	+	0.244076i	−0.800660	−	0.599118i	$-0.795518\pi$
$239$	−4.06667	+	3.77332i	−0.263051	+	0.244076i	0.537610	+	0.843194i	$0.319327\pi$
$240$	−0.0250042	+	2.07452i	−0.00161401	+	0.133910i
$241$	2.17142	+	0.327289i	0.139873	+	0.0210825i	0.218606	−	0.975813i	$-0.429849\pi$
$241$	2.17142	+	0.327289i	0.139873	+	0.0210825i	−0.0787323	+	0.996896i	$0.525087\pi$
$242$	0.0169091	+	0.0156894i	0.00108696	+	0.00100855i
$243$	−13.0061	−	8.59313i	−0.834341	−	0.551249i
$244$	22.5797			1.44552
$245$	−13.6308	−	3.21191i	−0.870840	−	0.205201i
$246$	0.109822	−	0.341373i	0.00700202	−	0.0217651i
$247$	−0.516137	+	6.88737i	−0.0328410	+	0.438233i
$248$	−1.20952	+	5.29923i	−0.0768043	+	0.336502i
$249$	−1.22489	+	2.46701i	−0.0776245	+	0.156340i
$250$	−6.18503	+	27.0984i	−0.391175	+	1.71385i
$251$	−0.870105	−	3.81218i	−0.0549205	−	0.240622i	0.940016	−	0.341131i	$-0.110810\pi$
$251$	−0.870105	−	3.81218i	−0.0549205	−	0.240622i	−0.994936	+	0.100509i	$0.967953\pi$
$252$	15.2662	+	21.9272i	0.961679	+	1.38128i
$253$	1.75716	−	7.69863i	0.110472	−	0.484009i
$254$	17.0257	+	8.19913i	1.06829	+	0.514459i
$255$	18.0534	+	1.57193i	1.13055	+	0.0984381i
$256$	17.7242	−	8.53552i	1.10776	−	0.533470i
$257$	24.0583	−	3.62620i	1.50071	−	0.226196i	0.653288	−	0.757109i	$-0.273389\pi$
$257$	24.0583	−	3.62620i	1.50071	−	0.226196i	0.847426	+	0.530913i	$0.178151\pi$
$258$	13.6575	−	10.6247i	0.850277	−	0.661467i
$259$	2.79204	−	24.0224i	0.173489	−	1.49268i
$260$	−22.5091	−	10.8398i	−1.39596	−	0.672258i
$261$	5.85088	−	13.9121i	0.362160	−	0.861138i
$262$	35.0308	−	5.28004i	2.16421	−	0.326202i
$263$	1.19607	+	2.07166i	0.0737529	+	0.127744i	0.900543	−	0.434766i	$-0.143169\pi$
$263$	1.19607	+	2.07166i	0.0737529	+	0.127744i	−0.826790	+	0.562510i	$0.809836\pi$
$264$	5.57012	−	17.3142i	0.342817	−	1.06562i
$265$	1.91283	−	4.87381i	0.117504	−	0.299396i
$266$	−10.7566	−	3.80631i	−0.659531	−	0.233380i
$267$	−14.3383	−	21.5848i	−0.877487	−	1.32097i
$268$	−14.9190	+	18.7078i	−0.911321	+	1.14276i
$269$	2.12249	−	1.44709i	0.129410	−	0.0882305i	−0.496885	−	0.867817i	$-0.665523\pi$
$269$	2.12249	−	1.44709i	0.129410	−	0.0882305i	0.626295	+	0.779586i	$0.284570\pi$
$270$	−7.92514	+	22.7393i	−0.482309	+	1.38387i
$271$	−10.7566	−	1.62130i	−0.653420	−	0.0984872i	−0.186038	−	0.982543i	$-0.559565\pi$
$271$	−10.7566	−	1.62130i	−0.653420	−	0.0984872i	−0.467382	+	0.884055i	$0.654803\pi$
$272$	1.14396	+	2.91476i	0.0693626	+	0.176733i
$273$	−16.7515	+	2.90033i	−1.01384	+	0.175536i
$274$	10.6449	−	27.1227i	0.643079	−	1.63854i
$275$	1.65517	−	2.86684i	0.0998105	−	0.172877i
$276$	−13.5637	+	2.92430i	−0.816438	+	0.176022i
$277$	−8.17992	+	20.8421i	−0.491484	+	1.25228i	0.443079	+	0.896483i	$0.353886\pi$
$277$	−8.17992	+	20.8421i	−0.491484	+	1.25228i	−0.934563	+	0.355798i	$0.884209\pi$
$278$	4.33001	−	4.01766i	0.259697	−	0.240963i
$279$	−2.68311	+	4.39890i	−0.160634	+	0.263355i
$280$	10.9709	−	12.6584i	0.655639	−	0.756483i
$281$	0.508012	−	6.77895i	0.0303054	−	0.404398i	−0.961336	−	0.275377i	$-0.911197\pi$
$281$	0.508012	−	6.77895i	0.0303054	−	0.404398i	0.991642	−	0.129021i	$-0.0411835\pi$
$282$	−6.25440	+	38.3529i	−0.372444	+	2.28388i
$283$	3.02063	−	1.45466i	0.179558	−	0.0864705i	−0.341945	−	0.939720i	$-0.611086\pi$
$283$	3.02063	−	1.45466i	0.179558	−	0.0864705i	0.521503	+	0.853249i	$0.325371\pi$
$284$	−7.61019	−	33.3424i	−0.451582	−	1.97851i
$285$	−1.82705	−	6.18692i	−0.108225	−	0.366482i
$286$	20.9034	+	19.3955i	1.23604	+	1.14688i
$287$	−0.200662	+	0.125105i	−0.0118447	+	0.00738471i
$288$	14.7108	−	1.85588i	0.866843	−	0.109359i
$289$	9.89037	−	3.05077i	0.581786	−	0.179457i
$290$	−23.0541	−	3.47484i	−1.35378	−	0.204050i
$291$	−0.000630034		0.0522720i	−3.69332e−5		0.00306424i
$292$	−2.07249	+	27.6555i	−0.121284	+	1.61842i
$293$	7.49552	+	12.9826i	0.437893	+	0.758453i	0.997527	−	0.0702870i	$-0.0223915\pi$
$293$	7.49552	+	12.9826i	0.437893	+	0.758453i	−0.559634	+	0.828740i	$0.689058\pi$
$294$	2.63250	−	27.9624i	0.153530	−	1.63080i
$295$	−13.2841	+	23.0088i	−0.773433	+	1.33962i
$296$	23.9013	+	16.2956i	1.38923	+	0.947163i
$297$	10.2211	−	13.8852i	0.593088	−	0.805700i
$298$	−20.1981	−	51.4640i	−1.17005	−	2.98123i
$299$	1.96461	−	8.60750i	0.113616	−	0.497785i
$300$	−5.79476	−	0.504557i	−0.334561	−	0.0291306i
$301$	−11.4006	−	0.466630i	−0.657118	−	0.0268961i
$302$	−45.5603	+	14.0535i	−2.62170	+	0.808688i
$303$	−17.0891	+	17.9782i	−0.981746	+	1.03282i
$304$	0.817106	−	0.758164i	0.0468643	−	0.0434837i
$305$	1.00285	−	13.3821i	0.0574230	−	0.766257i
$306$	1.84167	+	36.2974i	0.105281	+	2.07498i
$307$	20.5909	−	9.91607i	1.17519	−	0.565940i	0.258681	−	0.965963i	$-0.416712\pi$
$307$	20.5909	−	9.91607i	1.17519	−	0.565940i	0.916505	+	0.400023i	$0.130998\pi$
$308$	−25.0768	+	15.6344i	−1.42888	+	0.890852i
$309$	−21.4807	−	5.17597i	−1.22199	−	0.294451i
$310$	7.60605	+	2.34616i	0.431994	+	0.133253i
$311$	−13.0278	−	16.3364i	−0.738740	−	0.926350i	0.260495	−	0.965475i	$-0.416114\pi$
$311$	−13.0278	−	16.3364i	−0.738740	−	0.926350i	−0.999234	+	0.0391251i	$0.987543\pi$
$312$	6.22771	−	19.3583i	0.352575	−	1.09595i
$313$	33.5075			1.89396			0.946979	−	0.321295i	$-0.104118\pi$
$313$	33.5075			1.89396			0.946979	+	0.321295i	$0.104118\pi$
$314$	18.8293	+	23.6112i	1.06260	+	1.33246i
$315$	13.6734	−	8.07379i	0.770408	−	0.454907i
$316$	−21.5162	+	26.9805i	−1.21038	+	1.51777i
$317$	3.72810	−	4.67489i	0.209391	−	0.262568i	−0.666035	−	0.745921i	$-0.732010\pi$
$317$	3.72810	−	4.67489i	0.209391	−	0.262568i	0.875426	+	0.483353i	$0.160581\pi$
$318$	10.2084	+	2.45981i	0.572458	+	0.137939i
$319$	15.0397	+	7.24273i	0.842061	+	0.405515i
$320$	−9.24342	−	23.5519i	−0.516723	−	1.31659i
$321$	10.8020	+	16.2612i	0.602907	+	0.907614i
$322$	12.8715	+	6.86066i	0.717301	+	0.382330i
$323$	−6.07047	−	7.61213i	−0.337770	−	0.423550i
$324$	−29.7047	−	5.95372i	−1.65026	−	0.330762i
$325$	1.85057	−	3.20529i	0.102651	−	0.177797i
$326$	−9.78126	+	24.9223i	−0.541734	+	1.38032i
$327$	8.17012	+	17.5020i	0.451809	+	0.967860i
$328$	−0.0211374	−	0.282059i	−0.00116712	−	0.0155741i
$329$	19.4811	−	16.6462i	1.07403	−	0.917737i
$330$	−24.6742	−	10.0287i	−1.35827	−	0.552064i
$331$	−10.7149	−	13.4360i	−0.588943	−	0.738511i	0.394666	−	0.918825i	$-0.370860\pi$
$331$	−10.7149	−	13.4360i	−0.588943	−	0.738511i	−0.983609	+	0.180313i	$0.942289\pi$
$332$	−0.400028	+	5.33801i	−0.0219544	+	0.292961i
$333$	16.5757	+	21.8454i	0.908345	+	1.19712i
$334$	0.963926	+	12.8627i	0.0527437	+	0.703816i
$335$	10.4248	+	9.67276i	0.569565	+	0.528480i
$336$	2.30019	+	1.49572i	0.125485	+	0.0815983i
$337$	18.3136	−	16.9925i	0.997603	−	0.925640i	0.000371408	−	1.00000i	$-0.499882\pi$
$337$	18.3136	−	16.9925i	0.997603	−	0.925640i	0.997231	+	0.0743597i	$0.0236913\pi$
$338$	1.29568	+	1.20221i	0.0704755	+	0.0653917i
$339$	−6.41574	−	9.65824i	−0.348455	−	0.524564i
$340$	33.6540	−	10.3809i	1.82514	−	0.562982i
$341$	−4.70874	−	3.21036i	−0.254992	−	0.173851i
$342$	11.7886	−	5.33099i	0.637455	−	0.288267i
$343$	−13.2329	+	12.9573i	−0.714508	+	0.699627i
$344$	6.82411	−	11.8197i	0.367931	−	0.637276i
$345$	1.13070	+	8.16855i	0.0608749	+	0.439780i
$346$	10.9188	−	47.8383i	0.586997	−	2.57180i
$347$	−11.1743	+	14.0121i	−0.599867	+	0.752210i	−0.985357	−	0.170502i	$-0.945461\pi$
$347$	−11.1743	+	14.0121i	−0.599867	+	0.752210i	0.385490	+	0.922712i	$0.374032\pi$
$348$	0.353505	−	29.3292i	0.0189499	−	1.57221i
$349$	23.1543	+	7.14216i	1.23942	+	0.382311i	0.844077	−	0.536222i	$-0.180149\pi$
$349$	23.1543	+	7.14216i	1.23942	+	0.382311i	0.395344	+	0.918533i	$0.370625\pi$
$350$	4.30841	+	4.33874i	0.230294	+	0.231915i
$351$	11.4278	−	15.5244i	0.609969	−	0.828632i
$352$	1.22555	+	16.3539i	0.0653223	+	0.871665i
$353$	−5.18807	+	4.81383i	−0.276133	+	0.256214i	−0.806066	−	0.591825i	$-0.798408\pi$
$353$	−5.18807	+	4.81383i	−0.276133	+	0.256214i	0.529933	+	0.848040i	$0.322217\pi$
$354$	−49.3627	−	20.0633i	−2.62360	−	1.06635i
$355$	−20.0987	+	3.02940i	−1.06673	+	0.160784i
$356$	−41.6101	−	28.3693i	−2.20533	−	1.50357i
$357$	14.5296	−	19.0590i	0.768989	−	1.00871i
$358$	25.6085	−	17.4596i	1.35345	−	0.922769i
$359$	−18.4310	+	17.1015i	−0.972753	+	0.902583i	−0.995268	−	0.0971634i	$-0.969023\pi$
$359$	−18.4310	+	17.1015i	−0.972753	+	0.902583i	0.0225152	+	0.999747i	$0.492833\pi$
$360$	0.962481	+	18.9695i	0.0507272	+	0.999778i
$361$	7.76701	−	13.4529i	0.408790	−	0.708045i
$362$	36.0157			1.89294
$363$	0.0133537	+	0.0109151i	0.000700887	+	0.000572893i
$364$	−28.0373	+	17.4801i	−1.46955	+	0.916208i
$365$	16.2983	+	2.45657i	0.853091	+	0.128583i
$366$	26.8609	−	1.68766i	1.40404	−	0.0882157i
$367$	0.285969	+	3.81600i	0.0149275	+	0.199193i	0.999681	+	0.0252402i	$0.00803507\pi$
$367$	0.285969	+	3.81600i	0.0149275	+	0.199193i	−0.984754	+	0.173953i	$0.944346\pi$
$368$	−1.17729	+	0.802665i	−0.0613707	+	0.0418418i
$369$	0.0659474	−	0.259892i	0.00343308	−	0.0135294i
$370$	26.4119	−	33.1195i	1.37309	−	1.72180i
$371$	−4.09216	−	5.58558i	−0.212454	−	0.289989i
$372$	−1.61172	+	9.88331i	−0.0835639	+	0.512426i
$373$	16.6661	−	28.8666i	0.862939	−	1.49465i	−0.00613959	−	0.999981i	$-0.501954\pi$
$373$	16.6661	−	28.8666i	0.862939	−	1.49465i	0.869079	−	0.494674i	$-0.164712\pi$
$374$	−40.1981			−2.07859
$375$	−3.34493	+	20.5116i	−0.172732	+	1.05922i
$376$	6.82041	+	29.8822i	0.351736	+	1.54105i
$377$	16.8152	+	8.09778i	0.866028	+	0.417057i
$378$	19.7996	+	24.9436i	1.01838	+	1.28296i
$379$	0.599933	−	0.288913i	0.0308165	−	0.0148404i	−0.418412	−	0.908257i	$-0.637413\pi$
$379$	0.599933	−	0.288913i	0.0308165	−	0.0148404i	0.449229	+	0.893417i	$0.351699\pi$
$380$	−7.81690	−	9.80208i	−0.400999	−	0.502836i
$381$	13.0895	+	5.32018i	0.670595	+	0.272561i
$382$	−7.23920	−	31.7170i	−0.370390	−	1.62278i
$383$	−12.0064	+	8.18584i	−0.613500	+	0.418277i	−0.829809	−	0.558048i	$-0.811551\pi$
$383$	−12.0064	+	8.18584i	−0.613500	+	0.418277i	0.216309	+	0.976325i	$0.430598\pi$
$384$	29.3171	−	16.4584i	1.49608	−	0.839887i
$385$	8.15213	+	15.5564i	0.415471	+	0.792829i
$386$	−13.6183	−	59.6658i	−0.693155	−	3.03691i
$387$	9.69347	−	8.56884i	0.492747	−	0.435578i
$388$	0.0371170	+	0.0945727i	0.00188433	+	0.00480120i
$389$	1.19097	−	0.367364i	0.0603844	−	0.0186261i	−0.264416	−	0.964409i	$-0.585179\pi$
$389$	1.19097	−	0.367364i	0.0603844	−	0.0186261i	0.324800	+	0.945783i	$0.394703\pi$
$390$	−27.5871	−	11.2127i	−1.39693	−	0.567777i
$391$	6.22298	+	10.7785i	0.314710	+	0.545093i
$392$	−6.38105	−	21.2141i	−0.322292	−	1.07147i
$393$	25.8935	−	5.58257i	1.30615	−	0.281603i
$394$	1.38357	−	0.666295i	0.0697035	−	0.0335674i
$395$	15.0346	+	13.9501i	0.756475	+	0.701906i
$396$	8.24146	−	32.4787i	0.414149	−	1.63212i
$397$	20.2020	−	6.23150i	1.01391	−	0.312750i	0.257101	−	0.966385i	$-0.417233\pi$
$397$	20.2020	−	6.23150i	1.01391	−	0.312750i	0.756811	+	0.653634i	$0.226757\pi$
$398$	36.6229	+	11.2967i	1.83574	+	0.566251i
$399$	−8.20538	−	2.33605i	−0.410783	−	0.116949i
$400$	−0.570788	+	0.176065i	−0.0285394	+	0.00880323i
$401$	−31.2045	+	21.2749i	−1.55828	+	1.06242i	−0.591665	+	0.806184i	$0.701529\pi$
$401$	−31.2045	+	21.2749i	−1.55828	+	1.06242i	−0.966615	+	0.256233i	$0.917518\pi$
$402$	−16.3494	+	23.3699i	−0.815432	+	1.16559i
$403$	−5.26463	−	3.58937i	−0.262250	−	0.178799i
$404$	−17.6117	+	44.8738i	−0.876213	+	2.23255i
$405$	−4.84783	+	17.3404i	−0.240891	+	0.861650i
$406$	−20.1939	+	23.2999i	−1.00221	+	1.15636i
$407$	−25.0599	+	17.0855i	−1.24217	+	0.846899i
$408$	12.1258	+	25.9757i	0.600315	+	1.28599i
$409$	4.96548	+	6.22651i	0.245527	+	0.307881i	0.889290	−	0.457344i	$-0.151199\pi$
$409$	4.96548	+	6.22651i	0.245527	+	0.307881i	−0.643763	+	0.765225i	$0.722628\pi$
$410$	−0.414201			−0.0204559
$411$	6.67186	−	20.7389i	0.329099	−	1.02297i
$412$	−42.4620	+	6.40012i	−2.09195	+	0.315311i
$413$	16.3090	+	31.1219i	0.802513	+	1.53141i
$414$	−15.9168	+	4.49254i	−0.782270	+	0.220796i
$415$	3.14586	+	0.474162i	0.154424	+	0.0232757i
$416$	1.37024	+	18.2846i	0.0671815	+	0.896475i
$417$	3.04282	−	3.20112i	0.149007	−	0.156760i
$418$	5.22800	+	13.3207i	0.255710	+	0.651539i
$419$	20.4730	+	3.08581i	1.00017	+	0.150751i	0.628663	−	0.777678i	$-0.283603\pi$
$419$	20.4730	+	3.08581i	1.00017	+	0.150751i	0.371508	+	0.928430i	$0.378841\pi$
$420$	18.7097	−	24.5421i	0.912939	−	1.19753i
$421$	−9.92897	+	1.49655i	−0.483908	+	0.0729375i	−0.386466	−	0.922304i	$-0.626304\pi$
$421$	−9.92897	+	1.49655i	−0.483908	+	0.0729375i	−0.0974426	+	0.995241i	$0.531066\pi$
$422$	16.5572	+	28.6779i	0.805992	+	1.39602i
$423$	−2.86903	+	28.9134i	−0.139497	+	1.40582i
$424$	8.18987	−	1.23442i	0.397735	−	0.0599489i
$425$	1.16100	+	5.08666i	0.0563166	+	0.246739i
$426$	−11.5452	−	39.0954i	−0.559367	−	1.89418i
$427$	−14.2424	−	10.5887i	−0.689237	−	0.512424i
$428$	31.3477	+	21.3725i	1.51525	+	1.03308i
$429$	16.5081	+	13.4934i	0.797019	+	0.651470i
$430$	−16.5134	−	11.2586i	−0.796346	−	0.542940i
$431$	−35.1742	−	10.8498i	−1.69428	−	0.522617i	−0.710765	−	0.703430i	$-0.751651\pi$
$431$	−35.1742	−	10.8498i	−1.69428	−	0.522617i	−0.983518	+	0.180813i	$0.942127\pi$
$432$	−3.05614	+	0.582187i	−0.147038	+	0.0280105i
$433$	−7.00190	+	30.6773i	−0.336490	+	1.47426i	0.469819	+	0.882763i	$0.344319\pi$
$433$	−7.00190	+	30.6773i	−0.336490	+	1.47426i	−0.806309	+	0.591495i	$0.798538\pi$
$434$	8.00288	−	6.83832i	0.384150	−	0.328250i
$435$	−17.3666	−	1.51213i	−0.832663	−	0.0725011i
$436$	27.5172	+	25.5322i	1.31783	+	1.22277i
$437$	2.76242	−	3.46397i	0.132145	−	0.165704i
$438$	−0.398400	+	33.0540i	−0.0190363	+	1.57938i
$439$	−23.6354	+	11.3822i	−1.12805	+	0.543242i	−0.902372	−	0.430959i	$-0.858175\pi$
$439$	−23.6354	+	11.3822i	−1.12805	+	0.543242i	−0.225682	+	0.974201i	$0.572461\pi$
$440$	−21.0080			−1.00152
$441$	0.653418	−	20.9898i	0.0311151	−	0.999516i
$442$	−44.9437			−2.13775
$443$	−14.4029	+	6.93609i	−0.684304	+	0.329544i	−0.743532	−	0.668701i	$-0.766851\pi$
$443$	−14.4029	+	6.93609i	−0.684304	+	0.329544i	0.0592271	+	0.998245i	$0.481136\pi$
$444$	45.8293	+	27.2012i	2.17496	+	1.29091i
$445$	−18.6614	+	23.4007i	−0.884637	+	1.10930i
$446$	−11.9626	−	11.0997i	−0.566445	−	0.525584i
$447$	−17.4854	−	37.4570i	−0.827030	−	1.77166i
$448$	−32.8547	−	6.33588i	−1.55224	−	0.299342i
$449$	0.190671	−	0.835382i	0.00899830	−	0.0394241i	−0.970229	−	0.242188i	$-0.922135\pi$
$449$	0.190671	−	0.835382i	0.00899830	−	0.0394241i	0.979228	+	0.202763i	$0.0649922\pi$
$450$	−6.93117	−	0.167107i	−0.326739	−	0.00787750i
$451$	0.283386	+	0.0874129i	0.0133441	+	0.00411611i
$452$	−18.6187	−	12.6940i	−0.875751	−	0.597077i
$453$	−33.3396	+	12.6233i	−1.56643	+	0.593093i
$454$	−12.3361	−	8.41059i	−0.578961	−	0.394729i
$455$	9.11455	+	17.3930i	0.427297	+	0.815395i
$456$	7.03074	−	7.39651i	0.329244	−	0.346373i
$457$	6.53024	+	28.6109i	0.305472	+	1.33836i	0.861737	+	0.507355i	$0.169377\pi$
$457$	6.53024	+	28.6109i	0.305472	+	1.33836i	−0.556265	+	0.831005i	$0.687766\pi$
$458$	−3.48423	+	0.525163i	−0.162807	+	0.0245393i
$459$	3.07614	+	26.9999i	0.143582	+	1.26025i
$460$	8.01329	+	13.8794i	0.373621	+	0.647131i
$461$	20.3429	−	3.06620i	0.947463	−	0.142807i	0.342907	−	0.939370i	$-0.388589\pi$
$461$	20.3429	−	3.06620i	0.947463	−	0.142807i	0.604556	+	0.796562i	$0.293350\pi$
$462$	−28.6629	+	20.4730i	−1.33352	+	0.952491i
$463$	5.46932	+	0.824367i	0.254181	+	0.0383116i	0.274897	−	0.961474i	$-0.411356\pi$
$463$	5.46932	+	0.824367i	0.254181	+	0.0383116i	−0.0207157	+	0.999785i	$0.506594\pi$
$464$	−1.10044	−	2.80387i	−0.0510866	−	0.130166i
$465$	5.78587	+	1.39416i	0.268313	+	0.0646526i
$466$	3.59330	+	47.9492i	0.166456	+	2.22121i
$467$	−4.94593	−	0.745480i	−0.228871	−	0.0344967i	0.0336056	−	0.999435i	$-0.489301\pi$
$467$	−4.94593	−	0.745480i	−0.228871	−	0.0344967i	−0.262476	+	0.964938i	$0.584539\pi$
$468$	9.21442	−	36.3131i	0.425937	−	1.67857i
$469$	18.1833	−	4.80390i	0.839626	−	0.221823i
$470$	44.3830	−	6.68965i	2.04723	−	0.308571i
$471$	15.1581	+	16.7366i	0.698446	+	0.771182i
$472$	−42.0282			−1.93450
$473$	8.92203	+	11.1879i	0.410235	+	0.514419i
$474$	−23.5791	+	33.7042i	−1.08303	+	1.54809i
$475$	1.53461	−	1.04628i	0.0704127	−	0.0480066i
$476$	12.2126	−	44.9466i	0.559761	−	2.06013i
$477$	7.73315	+	1.35696i	0.354077	+	0.0621308i
$478$	−4.69499	+	11.9626i	−0.214744	+	0.547158i
$479$	13.5728	+	9.25378i	0.620157	+	0.422816i	0.832224	−	0.554439i	$-0.187067\pi$
$479$	13.5728	+	9.25378i	0.620157	+	0.422816i	−0.212067	+	0.977255i	$0.568020\pi$
$480$	−7.24430	−	15.5187i	−0.330655	−	0.708327i
$481$	−28.0184	+	19.1026i	−1.27753	+	0.871004i
$482$	4.86091	−	1.49939i	0.221408	−	0.0682954i
$483$	9.92678	+	4.51615i	0.451684	+	0.205492i
$484$	0.0320297	+	0.00987985i	0.00145590	+	0.000449084i
$485$	0.0576980	−	0.0177975i	0.00261993	−	0.000808142i
$486$	−35.7818	−	4.86236i	−1.62309	−	0.220561i
$487$	29.6493	+	27.5106i	1.34354	+	1.24662i	0.944016	+	0.329900i	$0.107015\pi$
$487$	29.6493	+	27.5106i	1.34354	+	1.24662i	0.399524	+	0.916723i	$0.369175\pi$
$488$	19.1261	−	9.21066i	0.865800	−	0.416947i
$489$	−6.13059	+	19.0564i	−0.277235	+	0.861758i
$490$	−31.6770	+	6.99664i	−1.43102	+	0.316076i
$491$	6.06164	+	10.4991i	0.273558	+	0.473817i	0.969770	−	0.244019i	$-0.0784661\pi$
$491$	6.06164	+	10.4991i	0.273558	+	0.473817i	−0.696212	+	0.717836i	$0.745133\pi$
$492$	−0.0714495	−	0.516174i	−0.00322119	−	0.0232709i
$493$	−25.1409	+	7.75493i	−1.13229	+	0.349264i
$494$	5.84521	+	14.8933i	0.262988	+	0.670083i
$495$	−18.8828	−	6.32689i	−0.848720	−	0.284373i
$496$	0.228827	+	1.00256i	0.0102747	+	0.0450162i
$497$	−10.8357	+	24.5999i	−0.486047	+	1.10345i
$498$	−0.0768982	+	6.38000i	−0.00344589	+	0.285895i
$499$	−11.4192	+	7.78551i	−0.511196	+	0.348527i	−0.791286	−	0.611446i	$-0.790588\pi$
$499$	−11.4192	+	7.78551i	−0.511196	+	0.348527i	0.280090	+	0.959974i	$0.409636\pi$
$500$	8.98762	+	39.3773i	0.401939	+	1.76101i
$501$	1.32239	+	9.55335i	0.0590799	+	0.426812i
$502$	−5.64757	−	7.08183i	−0.252064	−	0.316078i
$503$	−12.5484	+	6.04301i	−0.559507	+	0.269444i	−0.692192	−	0.721714i	$-0.743355\pi$
$503$	−12.5484	+	6.04301i	−0.559507	+	0.269444i	0.132684	+	0.991158i	$0.457640\pi$
$504$	21.8757	+	12.3461i	0.974421	+	0.549937i
$505$	25.8127	+	12.4308i	1.14865	+	0.553161i
$506$	−4.07046	−	17.8339i	−0.180954	−	0.792812i
$507$	1.02324	+	0.836378i	0.0454437	+	0.0371449i
$508$	27.4598			1.21833
$509$	−1.88279	+	3.26108i	−0.0834531	+	0.144545i	−0.904731	−	0.425983i	$-0.859928\pi$
$509$	−1.88279	+	3.26108i	−0.0834531	+	0.144545i	0.821278	+	0.570528i	$0.193262\pi$
$510$	39.2590	−	14.8645i	1.73842	−	0.658212i
$511$	14.2763	−	16.4721i	0.631545	−	0.728683i
$512$	4.20783	−	5.27645i	0.185961	−	0.233188i
$513$	8.54708	−	4.53086i	0.377363	−	0.200042i
$514$	46.5672	−	31.7490i	2.05399	−	1.40039i
$515$	1.90720	+	25.4498i	0.0840412	+	1.12145i
$516$	11.1819	−	22.5210i	0.492255	−	0.991431i
$517$	−31.7775	−	4.78969i	−1.39757	−	0.210650i
$518$	−18.3174	−	52.9432i	−0.804822	−	2.32619i
$519$	5.90500	−	36.2103i	0.259201	−	1.58946i
$520$	−23.4881			−1.03002
$521$	16.6368	−	28.8157i	0.728870	−	1.26244i	−0.228492	−	0.973546i	$-0.573379\pi$
$521$	16.6368	−	28.8157i	0.728870	−	1.26244i	0.957361	−	0.288893i	$-0.0932874\pi$
$522$	−1.77161	−	34.9165i	−0.0775413	−	1.52825i
$523$	28.1933	−	26.1596i	1.23281	−	1.14388i	0.248274	−	0.968690i	$-0.420137\pi$
$523$	28.1933	−	26.1596i	1.23281	−	1.14388i	0.984535	−	0.175189i	$-0.0560537\pi$
$524$	42.5340	−	28.9992i	1.85811	−	1.26684i
$525$	3.41849	+	3.03570i	0.149195	+	0.132489i
$526$	4.57851	+	3.12158i	0.199633	+	0.136107i
$527$	8.88195	−	1.33874i	0.386904	−	0.0583164i
$528$	−0.471809	−	3.40850i	−0.0205329	−	0.148336i
$529$	12.7084	−	11.7917i	0.552541	−	0.512683i
$530$	−0.906369	−	12.0947i	−0.0393702	−	0.525358i
$531$	−37.7766	−	12.6575i	−1.63937	−	0.549287i
$532$	−16.4826	+	1.79862i	−0.714613	+	0.0779801i
$533$	0.316841	+	0.0977326i	0.0137239	+	0.00423327i
$534$	−51.6199	−	30.6382i	−2.23381	−	1.32584i
$535$	14.0589	−	17.6293i	0.607819	−	0.762181i
$536$	−5.00587	+	21.9321i	−0.216221	+	0.947324i
$537$	18.2913	−	14.2296i	0.789327	−	0.614051i
$538$	2.97537	−	5.15350i	0.128278	−	0.222183i
$539$	23.1492	+	1.89819i	0.997106	+	0.0817609i
$540$	3.96112	+	34.7675i	0.170459	+	1.49616i
$541$	−24.9409	−	17.0044i	−1.07229	−	0.731076i	−0.107530	−	0.994202i	$-0.534294\pi$
$541$	−24.9409	−	17.0044i	−1.07229	−	0.731076i	−0.964761	+	0.263126i	$0.915246\pi$
$542$	−24.0797	+	7.42759i	−1.03431	+	0.319043i
$543$	26.8760	−	1.68862i	1.15336	−	0.0724655i
$544$	−18.9478	−	17.5810i	−0.812381	−	0.753780i
$545$	16.3541	−	15.1744i	0.700532	−	0.649999i
$546$	−32.0467	+	22.8900i	−1.37147	+	0.979601i
$547$	10.6642	+	9.89493i	0.455968	+	0.423077i	0.874425	−	0.485160i	$-0.161239\pi$
$547$	10.6642	+	9.89493i	0.455968	+	0.423077i	−0.418457	+	0.908236i	$0.637429\pi$
$548$	−3.16403	−	42.2210i	−0.135161	−	1.80359i
$549$	19.9653	−	2.51878i	0.852097	−	0.107499i
$550$	0.573060	−	7.64695i	0.0244353	−	0.326067i
$551$	5.83953	+	7.32254i	0.248772	+	0.311951i
$552$	−10.2963	+	8.00990i	−0.438238	+	0.340924i
$553$	26.2240	−	6.92821i	1.11516	−	0.294617i
$554$	3.87595	+	51.7210i	0.164673	+	2.19741i
$555$	18.1565	−	25.9531i	0.770702	−	1.10165i
$556$	3.13586	−	7.99003i	0.132990	−	0.338853i
$557$	2.54846	−	4.41406i	0.107982	−	0.187030i	−0.806971	−	0.590591i	$-0.798895\pi$
$557$	2.54846	−	4.41406i	0.107982	−	0.187030i	0.914952	+	0.403562i	$0.132228\pi$
$558$	−1.17860	+	11.8777i	−0.0498943	+	0.502822i
$559$	9.97533	+	12.5087i	0.421912	+	0.529060i
$560$	0.830959	−	3.05823i	0.0351144	−	0.129234i
$561$	−29.9970	+	1.88471i	−1.26648	+	0.0795725i
$562$	−5.75319	−	14.6589i	−0.242684	−	0.618348i
$563$	−9.61115	−	4.62848i	−0.405062	−	0.195067i	0.220248	−	0.975444i	$-0.429313\pi$
$563$	−9.61115	−	4.62848i	−0.405062	−	0.195067i	−0.625310	+	0.780376i	$0.715027\pi$
$564$	15.9926	+	54.1558i	0.673412	+	2.28037i
$565$	−8.35018	+	10.4708i	−0.351295	+	0.440510i
$566$	4.84227	−	6.07202i	0.203536	−	0.255226i
$567$	15.9445	+	17.6853i	0.669608	+	0.742715i
$568$	−20.0472	−	25.1384i	−0.841161	−	1.05478i
$569$	−12.4841			−0.523362			−0.261681	−	0.965154i	$-0.584277\pi$
$569$	−12.4841			−0.523362			−0.261681	+	0.965154i	$0.584277\pi$
$570$	−10.0316	−	11.0763i	−0.420179	−	0.463936i
$571$	−12.1794	−	15.2725i	−0.509692	−	0.639133i	0.458693	−	0.888595i	$-0.348318\pi$
$571$	−12.1794	−	15.2725i	−0.509692	−	0.639133i	−0.968385	+	0.249462i	$0.919746\pi$
$572$	39.5957	+	12.2137i	1.65558	+	0.510679i
$573$	−6.88919	−	23.3288i	−0.287800	−	0.974574i
$574$	−0.293059	+	0.462789i	−0.0122321	+	0.0193165i
$575$	−2.13913	+	1.03015i	−0.0892079	+	0.0429603i
$576$	31.8536	−	20.6106i	1.32723	−	0.858777i
$577$	−2.13216	+	28.4517i	−0.0887631	+	1.18446i	0.757914	+	0.652354i	$0.226219\pi$
$577$	−2.13216	+	28.4517i	−0.0887631	+	1.18446i	−0.846677	+	0.532107i	$0.821400\pi$
$578$	17.5758	−	16.3080i	0.731057	−	0.678322i
$579$	−12.9599	−	43.8860i	−0.538594	−	1.82384i
$580$	−32.3737	+	9.98597i	−1.34425	+	0.414645i
$581$	2.75557	−	3.17941i	0.114320	−	0.131904i
$582$	0.0512231	+	0.109730i	0.00212327	+	0.00454844i
$583$	−1.93234	+	8.46614i	−0.0800294	+	0.350632i
$584$	9.52568	+	24.2710i	0.394175	+	1.00434i
$585$	−21.1121	−	7.07382i	−0.872877	−	0.292467i
$586$	28.6926	+	19.5623i	1.18528	+	0.808110i
$587$	−1.22363	+	2.11938i	−0.0505044	+	0.0874762i	−0.890172	−	0.455624i	$-0.849416\pi$
$587$	−1.22363	+	2.11938i	−0.0505044	+	0.0874762i	0.839668	+	0.543100i	$0.182750\pi$
$588$	−14.1834	−	38.2687i	−0.584915	−	1.57818i
$589$	−1.59878	−	2.76917i	−0.0658766	−	0.114102i
$590$	−4.59929	+	61.3733i	−0.189350	+	2.52670i
$591$	1.00123	−	0.562079i	0.0411850	−	0.0231209i
$592$	5.41170	+	0.815683i	0.222420	+	0.0335244i
$593$	30.1917	−	9.31290i	1.23982	−	0.382435i	0.395599	−	0.918424i	$-0.370537\pi$
$593$	30.1917	−	9.31290i	1.23982	−	0.382435i	0.844225	+	0.535989i	$0.180061\pi$
$594$	7.37651	−	39.2528i	0.302662	−	1.61056i
$595$	−26.0957	−	9.23415i	−1.06982	−	0.378563i
$596$	−58.8912	−	54.6431i	−2.41228	−	2.23827i
$597$	27.8588	+	6.71284i	1.14019	+	0.274738i
$598$	−4.55101	−	19.9393i	−0.186105	−	0.815377i
$599$	18.8465	−	9.07599i	0.770047	−	0.370835i	−0.00724609	−	0.999974i	$-0.502307\pi$
$599$	18.8465	−	9.07599i	0.770047	−	0.370835i	0.777293	+	0.629139i	$0.216592\pi$
$600$	−5.11427	+	1.93640i	−0.208789	+	0.0790532i
$601$	1.88661	−	25.1750i	0.0769563	−	1.02691i	−0.816378	−	0.577518i	$-0.804021\pi$
$601$	1.88661	−	25.1750i	0.0769563	−	1.02691i	0.893334	−	0.449393i	$-0.148360\pi$
$602$	−24.2631	+	10.4847i	−0.988889	+	0.427325i
$603$	−11.1047	+	18.2059i	−0.452218	+	0.741401i
$604$	−50.7880	+	47.1243i	−2.06653	+	1.91746i
$605$	0.00727796	−	0.0185439i	0.000295891	−	0.000753918i
$606$	−17.5969	+	54.6983i	−0.714825	+	2.22197i
$607$	−0.573980	+	0.994162i	−0.0232971	+	0.0403518i	−0.877439	−	0.479688i	$-0.840750\pi$
$607$	−0.573980	+	0.994162i	−0.0232971	+	0.0403518i	0.854142	+	0.520040i	$0.174083\pi$
$608$	−3.36167	+	8.56540i	−0.136334	+	0.347373i
$609$	−13.9769	+	18.3339i	−0.566371	+	0.742928i
$610$	−11.3572	−	28.9376i	−0.459839	−	1.17165i
$611$	−35.5290	−	5.35514i	−1.43735	−	0.216646i
$612$	25.2962	+	46.3601i	1.02254	+	1.87400i
$613$	38.0021	−	25.9094i	1.53489	−	1.04647i	0.558749	−	0.829337i	$-0.311282\pi$
$613$	38.0021	−	25.9094i	1.53489	−	1.04647i	0.976142	−	0.217134i	$-0.0696708\pi$
$614$	33.0086	−	41.3915i	1.33212	−	1.67043i
$615$	−0.309089	+	0.0194200i	−0.0124637	+	0.000783092i
$616$	−14.8638	+	23.4724i	−0.598879	+	0.945730i
$617$	−7.13357	+	18.1760i	−0.287187	+	0.731740i	0.712365	+	0.701809i	$0.247624\pi$
$617$	−7.13357	+	18.1760i	−0.287187	+	0.731740i	−0.999552	+	0.0299311i	$0.990471\pi$
$618$	−50.0345	+	10.7873i	−2.01268	+	0.433929i
$619$	7.65077	+	13.2515i	0.307510	+	0.532624i	0.977817	−	0.209461i	$-0.0671708\pi$
$619$	7.65077	+	13.2515i	0.307510	+	0.532624i	−0.670307	+	0.742084i	$0.733837\pi$
$620$	11.4372	−	1.72388i	0.459330	−	0.0692328i
$621$	−11.6670	+	4.09874i	−0.468180	+	0.164477i
$622$	−43.6098	−	21.0014i	−1.74859	−	0.842078i
$623$	12.9423	+	37.4073i	0.518521	+	1.49869i
$624$	−0.527509	−	3.81090i	−0.0211173	−	0.152558i
$625$	18.8040	−	2.83425i	0.752161	−	0.113370i
$626$	69.9333	−	33.6781i	2.79510	−	1.34605i
$627$	4.52585	+	9.69523i	0.180745	+	0.387190i
$628$	39.5384	+	19.0407i	1.57775	+	0.759806i
$629$	10.6373	−	46.6051i	0.424137	−	1.85827i
$630$	20.4227	−	30.5938i	0.813662	−	1.21888i
$631$	−2.22630	−	9.75404i	−0.0886275	−	0.388302i	0.911087	−	0.412215i	$-0.135245\pi$
$631$	−2.22630	−	9.75404i	−0.0886275	−	0.388302i	−0.999714	+	0.0239128i	$0.992388\pi$
$632$	−7.21949	+	31.6307i	−0.287176	+	1.25820i
$633$	13.7001	+	20.6241i	0.544529	+	0.819732i
$634$	3.08220	−	13.5040i	0.122410	−	0.536313i
$635$	1.21959	−	16.2744i	0.0483981	−	0.645828i
$636$	14.9159	−	3.21583i	0.591455	−	0.127516i
$637$	25.8821	+	2.12229i	1.02549	+	0.0840880i
$638$	38.6688			1.53091
$639$	−10.4484	−	28.6329i	−0.413332	−	1.13270i
$640$	−28.4670	−	26.4135i	−1.12526	−	1.04409i
$641$	−24.9721	−	3.76394i	−0.986340	−	0.148667i	−0.363987	−	0.931404i	$-0.618585\pi$
$641$	−24.9721	−	3.76394i	−0.986340	−	0.148667i	−0.622352	+	0.782737i	$0.713823\pi$
$642$	38.8887	+	23.0818i	1.53482	+	0.910964i
$643$	−11.9403	+	11.0790i	−0.470879	+	0.436912i	−0.879576	−	0.475758i	$-0.842174\pi$
$643$	−11.9403	+	11.0790i	−0.470879	+	0.436912i	0.408697	+	0.912670i	$0.365983\pi$
$644$	21.1772	+	0.866792i	0.834499	+	0.0341564i
$645$	−12.8507	−	7.62730i	−0.505995	−	0.300325i
$646$	−20.3205	−	9.78584i	−0.799500	−	0.385019i
$647$	−14.2196	−	4.38617i	−0.559031	−	0.172438i	0.00234758	−	0.999997i	$-0.499253\pi$
$647$	−14.2196	−	4.38617i	−0.559031	−	0.172438i	−0.561379	+	0.827559i	$0.689729\pi$
$648$	−27.5900	+	7.07398i	−1.08384	+	0.277892i
$649$	16.0989	−	41.0194i	0.631939	−	1.61015i
$650$	0.640713	−	8.54973i	0.0251308	−	0.335348i
$651$	5.65138	−	5.47819i	0.221495	−	0.214707i
$652$	2.90734	+	38.7957i	0.113860	+	1.51936i
$653$	−6.60262	−	2.03664i	−0.258380	−	0.0796998i	0.162859	−	0.986649i	$-0.447929\pi$
$653$	−6.60262	−	2.03664i	−0.258380	−	0.0796998i	−0.421239	+	0.906950i	$0.638405\pi$
$654$	34.6429	+	28.3165i	1.35464	+	1.10726i
$655$	−15.2976	−	26.4962i	−0.597727	−	1.03529i
$656$	−0.0267561	−	0.0463429i	−0.00104465	−	0.00180939i
$657$	1.25246	+	24.6846i	0.0488630	+	0.963037i
$658$	23.9278	−	54.3225i	0.932804	−	2.11771i
$659$	0.412373	+	1.05071i	0.0160638	+	0.0409298i	0.938681	−	0.344788i	$-0.112049\pi$
$659$	0.412373	+	1.05071i	0.0160638	+	0.0409298i	−0.922617	+	0.385718i	$0.873954\pi$
$660$	−38.6270	+	2.42693i	−1.50355	+	0.0944680i
$661$	9.71117	+	4.67665i	0.377721	+	0.181901i	0.613104	−	0.790002i	$-0.289920\pi$
$661$	9.71117	+	4.67665i	0.377721	+	0.181901i	−0.235384	+	0.971902i	$0.575635\pi$
$662$	−35.8674	−	17.2728i	−1.39403	−	0.671327i
$663$	−33.5384	+	2.10721i	−1.30252	+	0.0818374i
$664$	1.83862	+	4.68474i	0.0713525	+	0.181803i
$665$	0.333915	+	9.84849i	0.0129487	+	0.381908i
$666$	56.5517	+	28.9332i	2.19133	+	1.12114i
$667$	−5.98624	−	10.3685i	−0.231788	−	0.401469i
$668$	9.37177	+	16.2324i	0.362605	+	0.628050i
$669$	−9.44726	−	7.72203i	−0.365252	−	0.298551i
$670$	31.4794	+	9.71012i	1.21616	+	0.375135i
$671$	1.66330	+	22.1952i	0.0642111	+	0.856837i
$672$	−22.4647	−	2.88580i	−0.866593	−	0.111322i
$673$	2.27968	−	30.4202i	0.0878751	−	1.17261i	−0.762698	−	0.646755i	$-0.776126\pi$
$673$	2.27968	−	30.4202i	0.0878751	−	1.17261i	0.850573	−	0.525857i	$-0.176255\pi$
$674$	21.1431	−	53.8717i	0.814401	−	2.07506i
$675$	−5.18009	+	0.200272i	−0.199382	+	0.00770846i
$676$	2.45431	+	0.757053i	0.0943964	+	0.0291174i
$677$	−16.5239	−	7.95750i	−0.635066	−	0.305831i	0.0885114	−	0.996075i	$-0.471789\pi$
$677$	−16.5239	−	7.95750i	−0.635066	−	0.305831i	−0.723577	+	0.690244i	$0.757503\pi$
$678$	−23.0977	−	13.7092i	−0.887060	−	0.526500i
$679$	0.0209378	−	0.0770587i	0.000803518	−	0.00295724i
$680$	24.2721	−	22.5212i	0.930792	−	0.863649i
$681$	−9.59989	−	5.69786i	−0.367869	−	0.218342i
$682$	−13.0543	−	1.96762i	−0.499874	−	0.0753439i
$683$	−27.7301	−	25.7297i	−1.06106	−	0.984521i	−0.0611541	−	0.998128i	$-0.519478\pi$
$683$	−27.7301	−	25.7297i	−1.06106	−	0.984521i	−0.999907	+	0.0136071i	$0.995669\pi$
$684$	12.0728	−	14.4120i	0.461615	−	0.551057i
$685$	−25.1633			−0.961439
$686$	−14.5950	+	40.3433i	−0.557240	+	1.54031i
$687$	−2.57542	+	0.555253i	−0.0982583	+	0.0211842i
$688$	0.192960	−	2.57488i	0.00735654	−	0.0981663i
$689$	−2.16047	+	9.46563i	−0.0823073	+	0.360612i
$690$	10.5700	+	15.9121i	0.402393	+	0.605762i
$691$	−3.22197	+	14.1164i	−0.122569	+	0.537011i	0.875939	+	0.482421i	$0.160242\pi$
$691$	−3.22197	+	14.1164i	−0.122569	+	0.537011i	−0.998509	+	0.0545904i	$0.982615\pi$
$692$	−15.8664	−	69.5151i	−0.603149	−	2.64257i
$693$	−20.4292	+	16.6215i	−0.776043	+	0.631398i
$694$	−9.23833	+	40.4758i	−0.350682	+	1.53644i
$695$	−4.59610	−	2.21337i	−0.174340	−	0.0839577i
$696$	−11.6645	−	24.9875i	−0.442141	−	0.947150i
$697$	−0.421125	+	0.202803i	−0.0159513	+	0.00768172i
$698$	55.5037	−	8.36584i	2.10085	−	0.316652i
$699$	4.92956	+	35.6127i	0.186453	+	1.34700i
$700$	8.37618	+	2.96397i	0.316590	+	0.112028i
$701$	28.3092	+	13.6330i	1.06923	+	0.514912i	0.883857	−	0.467757i	$-0.154938\pi$
$701$	28.3092	+	13.6330i	1.06923	+	0.514912i	0.185368	+	0.982669i	$0.440652\pi$
$702$	8.24736	−	43.8868i	0.311277	−	1.65640i
$703$	−16.8273	+	2.53631i	−0.634655	+	0.0956589i
$704$	20.9817	+	36.3413i	0.790776	+	1.36966i
$705$	32.8063	−	7.07295i	1.23556	−	0.266383i
$706$	−5.98965	+	15.2614i	−0.225424	+	0.574370i
$707$	32.1522	−	20.0456i	1.20921	−	0.753894i
$708$	−77.2763	+	4.85526i	−2.90422	+	0.182472i
$709$	−11.0619	+	13.8712i	−0.415437	+	0.520942i	−0.944886	−	0.327400i	$-0.893828\pi$
$709$	−11.0619	+	13.8712i	−0.415437	+	0.520942i	0.529448	+	0.848342i	$0.322399\pi$
$710$	−38.9031	+	26.5237i	−1.46001	+	0.995416i
$711$	−16.0152	+	26.2566i	−0.600618	+	0.984701i
$712$	−46.8182	−	7.05671i	−1.75459	−	0.264462i
$713$	1.49332	+	3.80491i	0.0559252	+	0.142495i
$714$	11.1687	−	54.3814i	0.417976	−	2.03517i
$715$	8.99716	−	22.9244i	0.336475	−	0.857323i
$716$	22.5192	−	39.0044i	0.841581	−	1.45766i
$717$	−2.94267	+	9.14701i	−0.109896	+	0.341601i
$718$	−21.2787	+	54.2173i	−0.794115	+	2.02337i
$719$	2.84818	−	2.64273i	0.106219	−	0.0985570i	−0.625276	−	0.780404i	$-0.715013\pi$
$719$	2.84818	−	2.64273i	0.106219	−	0.0985570i	0.731495	+	0.681847i	$0.238823\pi$
$720$	1.72119	+	3.15441i	0.0641449	+	0.117558i
$721$	29.7847	+	15.8756i	1.10924	+	0.591237i
$722$	2.68913	−	35.8839i	0.100079	−	1.33546i
$723$	3.55706	−	1.34680i	0.132289	−	0.0500880i
$724$	47.1525	−	22.7075i	1.75241	−	0.843916i
$725$	−1.11683	−	4.89315i	−0.0414780	−	0.181727i
$726$	0.0388411	+	0.00935912i	0.00144153	+	0.000347349i
$727$	−22.5343	−	20.9088i	−0.835752	−	0.775464i	0.140961	−	0.990015i	$-0.454981\pi$
$727$	−22.5343	−	20.9088i	−0.835752	−	0.775464i	−0.976713	+	0.214551i	$0.931171\pi$
$728$	−16.6186	+	26.2435i	−0.615925	+	0.972648i
$729$	−26.9294	−	1.95079i	−0.997386	−	0.0722515i
$730$	36.4851	−	11.2542i	1.35037	−	0.416535i
$731$	−22.3020	−	3.36148i	−0.824869	−	0.124329i
$732$	34.1028	−	19.1450i	1.26047	−	0.707618i
$733$	2.40366	−	32.0746i	0.0887812	−	1.18470i	−0.757816	−	0.652468i	$-0.773734\pi$
$733$	2.40366	−	32.0746i	0.0887812	−	1.18470i	0.846597	−	0.532234i	$-0.178647\pi$
$734$	4.43227	+	7.67691i	0.163598	+	0.283360i
$735$	−23.3103	+	6.70630i	−0.859814	+	0.247366i
$736$	5.88115	−	10.1865i	0.216782	−	0.375478i
$737$	−19.4882	−	13.2868i	−0.717858	−	0.489427i
$738$	−0.123577	−	0.608701i	−0.00454892	−	0.0224066i
$739$	3.57398	+	9.10635i	0.131471	+	0.334982i	0.981417	−	0.191887i	$-0.0614608\pi$
$739$	3.57398	+	9.10635i	0.131471	+	0.334982i	−0.849946	+	0.526870i	$0.823366\pi$
$740$	13.6976	−	60.0131i	0.503533	−	2.20612i
$741$	5.06016	+	10.8398i	0.185889	+	0.398210i
$742$	−14.1547	−	7.54463i	−0.519637	−	0.276972i
$743$	−6.23213	+	1.92236i	−0.228635	+	0.0705245i	−0.406956	−	0.913448i	$-0.633410\pi$
$743$	−6.23213	+	1.92236i	−0.228635	+	0.0705245i	0.178321	+	0.983972i	$0.442933\pi$
$744$	2.66637	+	9.02911i	0.0977539	+	0.331023i
$745$	−35.0004	+	32.4756i	−1.28231	+	1.18981i
$746$	5.77022	−	76.9982i	0.211263	−	2.81910i
$747$	0.241747	+	4.76456i	0.00884504	+	0.174326i
$748$	−52.6281	+	25.3444i	−1.92428	+	0.926682i
$749$	−9.75027	−	28.1814i	−0.356267	−	1.02972i
$750$	13.6349	+	46.1716i	0.497875	+	1.68595i
$751$	−2.25335	−	0.695067i	−0.0822260	−	0.0253634i	0.253369	−	0.967370i	$-0.418461\pi$
$751$	−2.25335	−	0.695067i	−0.0822260	−	0.0253634i	−0.335595	+	0.942006i	$0.608937\pi$
$752$	3.61548	+	4.53366i	0.131843	+	0.165326i
$753$	−4.54643	−	5.01989i	−0.165681	−	0.182935i
$754$	43.2339			1.57449
$755$	25.6731	+	32.1930i	0.934338	+	1.17162i
$756$	41.6486	+	20.1733i	1.51475	+	0.733695i
$757$	−8.40387	+	10.5381i	−0.305444	+	0.383014i	−0.910736	−	0.412989i	$-0.864485\pi$
$757$	−8.40387	+	10.5381i	−0.305444	+	0.383014i	0.605292	+	0.796003i	$0.293056\pi$
$758$	0.961733	−	1.20597i	0.0349317	−	0.0438030i
$759$	−3.87366	−	13.1173i	−0.140605	−	0.476129i
$760$	−10.6198	−	5.11420i	−0.385219	−	0.185512i
$761$	17.7552	+	45.2396i	0.643627	+	1.63994i	0.762471	+	0.647022i	$0.223986\pi$
$761$	17.7552	+	45.2396i	0.643627	+	1.63994i	−0.118844	+	0.992913i	$0.537919\pi$
$762$	32.6663	−	2.05242i	1.18337	−	0.0743513i
$763$	−5.38345	−	29.0089i	−0.194894	−	1.05019i
$764$	−29.4749	−	36.9604i	−1.06636	−	1.33718i
$765$	28.5993	−	12.9330i	1.03401	−	0.467595i
$766$	−16.8310	+	29.1522i	−0.608129	+	1.05331i
$767$	17.9995	−	45.8621i	0.649926	−	1.65598i
$768$	19.5322	−	27.9195i	0.704808	−	1.00746i
$769$	−0.651071	−	8.68793i	−0.0234782	−	0.313295i	−0.996562	−	0.0828452i	$-0.973599\pi$
$769$	−0.651071	−	8.68793i	−0.0234782	−	0.313295i	0.973084	−	0.230450i	$-0.0740197\pi$
$770$	32.6499	+	24.2741i	1.17662	+	0.874777i
$771$	33.2613	−	25.8754i	1.19788

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)

\(f(q)\)	\(=\)	\(q+(2.08709 - 1.00509i) q^{2} +(1.51033 - 0.847884i) q^{3} +(2.09877 - 2.63177i) q^{4} +(-1.46653 - 1.36074i) q^{5} +(2.29999 - 3.28763i) q^{6} +(-2.55799 + 0.675802i) q^{7} +(0.704215 - 3.08537i) q^{8} +(1.56218 - 2.56117i) q^{9} +O(q^{10})\)	\(q+(2.08709 - 1.00509i) q^{2} +(1.51033 - 0.847884i) q^{3} +(2.09877 - 2.63177i) q^{4} +(-1.46653 - 1.36074i) q^{5} +(2.29999 - 3.28763i) q^{6} +(-2.55799 + 0.675802i) q^{7} +(0.704215 - 3.08537i) q^{8} +(1.56218 - 2.56117i) q^{9} +(-4.42846 - 1.36600i) q^{10} +(2.74156 + 1.86917i) q^{11} +(0.938391 - 5.75435i) q^{12} +(3.06522 + 2.08983i) q^{13} +(-4.65951 + 3.98147i) q^{14} +(-3.36870 - 0.811720i) q^{15} +(-0.133230 - 0.583719i) q^{16} +(-5.17133 + 0.779453i) q^{17} +(0.686217 - 6.91553i) q^{18} +(0.930856 + 1.61229i) q^{19} +(-6.65909 + 1.00370i) q^{20} +(-3.29040 + 3.18956i) q^{21} +(7.60058 + 1.14560i) q^{22} +(-0.869454 - 2.21533i) q^{23} +(-1.55244 - 5.25701i) q^{24} +(-0.0745547 - 0.994864i) q^{25} +(8.49788 + 1.28085i) q^{26} +(0.187838 - 5.19276i) q^{27} +(-3.59006 + 8.15039i) q^{28} +(4.97460 - 0.749800i) q^{29} +(-7.84665 + 1.69172i) q^{30} -1.71754 q^{31} +(3.08158 + 3.86418i) q^{32} +(5.72550 + 0.498527i) q^{33} +(-10.0096 + 6.82445i) q^{34} +(4.67097 + 2.48968i) q^{35} +(-3.46175 - 9.48661i) q^{36} +(-3.33948 + 8.50886i) q^{37} +(3.56328 + 2.42940i) q^{38} +(6.40143 + 0.557381i) q^{39} +(-5.23116 + 3.56654i) q^{40} +(0.0854054 - 0.0263441i) q^{41} +(-3.66157 + 9.96405i) q^{42} +(4.12102 + 1.27117i) q^{43} +(10.6731 - 3.29222i) q^{44} +(-5.77609 + 1.63031i) q^{45} +(-4.04124 - 3.74972i) q^{46} +(-8.72599 + 4.20221i) q^{47} +(-0.696147 - 0.768644i) q^{48} +(6.08658 - 3.45739i) q^{49} +(-1.15553 - 2.00144i) q^{50} +(-7.14952 + 5.56192i) q^{51} +(11.9332 - 3.68089i) q^{52} +(0.956134 + 2.43619i) q^{53} +(-4.82716 - 11.0266i) q^{54} +(-1.47714 - 6.47176i) q^{55} +(0.283727 + 8.36824i) q^{56} +(2.77293 + 1.64583i) q^{57} +(9.62883 - 6.56483i) q^{58} +(-2.95513 - 12.9473i) q^{59} +(-9.20639 + 7.16204i) q^{60} +(4.18227 + 5.24440i) q^{61} +(-3.58466 + 1.72628i) q^{62} +(-2.26520 + 7.60716i) q^{63} +(11.3943 + 5.48719i) q^{64} +(-1.65152 - 7.23580i) q^{65} +(12.4507 - 4.71418i) q^{66} -7.10843 q^{67} +(-8.80208 + 15.2457i) q^{68} +(-3.19151 - 2.60868i) q^{69} +(12.2511 + 0.501442i) q^{70} +(6.33459 - 7.94333i) q^{71} +(-6.80203 - 6.62353i) q^{72} +(-6.80720 + 4.64107i) q^{73} +(1.58237 + 21.1153i) q^{74} +(-0.956131 - 1.43936i) q^{75} +(6.19683 + 0.934023i) q^{76} +(-8.27607 - 2.92855i) q^{77} +(13.9206 - 5.27072i) q^{78} -10.2518 q^{79} +(-0.598906 + 1.03734i) q^{80} +(-4.11916 - 8.00203i) q^{81} +(0.151771 - 0.140823i) q^{82} +(-1.31391 + 0.895808i) q^{83} +(1.48842 + 15.3537i) q^{84} +(8.64457 + 5.89377i) q^{85} +(9.87860 - 1.48896i) q^{86} +(6.87754 - 5.35033i) q^{87} +(7.69772 - 7.14244i) q^{88} +(-1.11803 - 14.9191i) q^{89} +(-10.4166 + 9.20809i) q^{90} +(-9.25312 - 3.27428i) q^{91} +(-7.65503 - 2.36126i) q^{92} +(-2.59404 + 1.45627i) q^{93} +(-13.9883 + 17.5408i) q^{94} +(0.828783 - 3.63114i) q^{95} +(7.93058 + 3.22336i) q^{96} +(-0.0150907 + 0.0261379i) q^{97} +(9.22827 - 13.3335i) q^{98} +(9.07008 - 4.10162i) 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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