LMFDB - Embedded newform 441.2.bn.a.5.6

Newspace parameters

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bn (of order $42$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	441.5
Dual form			441.2.bn.a.353.6

$q$-expansion

$f(q)$	$=$	$q+(-1.86842 + 1.49001i) q^{2} +(-1.41768 + 0.995078i) q^{3} +(0.825803 - 3.61808i) q^{4} +(-1.88505 - 1.28520i) q^{5} +(1.16614 - 3.97158i) q^{6} +(-0.922050 + 2.47988i) q^{7} +(1.77425 + 3.68427i) q^{8} +(1.01964 - 2.82141i) q^{9} +O(q^{10})$	\(q+(-1.86842 + 1.49001i) q^{2} +(-1.41768 + 0.995078i) q^{3} +(0.825803 - 3.61808i) q^{4} +(-1.88505 - 1.28520i) q^{5} +(1.16614 - 3.97158i) q^{6} +(-0.922050 + 2.47988i) q^{7} +(1.77425 + 3.68427i) q^{8} +(1.01964 - 2.82141i) q^{9} +(5.43702 - 0.407448i) q^{10} +(-0.775241 - 5.14339i) q^{11} +(2.42955 + 5.95102i) q^{12} +(0.0919355 + 0.609952i) q^{13} +(-1.97228 - 6.00733i) q^{14} +(3.95127 - 0.0537608i) q^{15} +(-2.11745 - 1.01971i) q^{16} +(-1.39998 + 1.29899i) q^{17} +(2.29882 + 6.79084i) q^{18} +(4.54187 + 2.62225i) q^{19} +(-6.20664 + 5.75892i) q^{20} +(-1.16051 - 4.43320i) q^{21} +(9.11220 + 8.45488i) q^{22} +(-0.184426 - 0.597895i) q^{23} +(-6.18146 - 3.45760i) q^{24} +(0.0749465 + 0.190961i) q^{25} +(-1.08061 - 1.00266i) q^{26} +(1.36200 + 5.01448i) q^{27} +(8.21098 + 5.38394i) q^{28} +(5.12493 + 5.52337i) q^{29} +(-7.30252 + 5.98789i) q^{30} -4.69739i q^{31} +(-2.49776 + 0.570098i) q^{32} +(6.21712 + 6.52026i) q^{33} +(0.680231 - 4.51303i) q^{34} +(4.92526 - 3.48967i) q^{35} +(-9.36605 - 6.01906i) q^{36} +(-5.42578 - 1.67363i) q^{37} +(-12.3933 + 1.86799i) q^{38} +(-0.737285 - 0.773235i) q^{39} +(1.39049 - 9.22529i) q^{40} +(-0.543928 + 7.25822i) q^{41} +(8.77383 + 6.55389i) q^{42} +(0.446996 + 5.96474i) q^{43} +(-19.2494 - 1.44254i) q^{44} +(-5.54814 + 4.00804i) q^{45} +(1.23546 + 0.842319i) q^{46} +(1.56059 + 1.95692i) q^{47} +(4.01655 - 0.661403i) q^{48} +(-5.29965 - 4.57315i) q^{49} +(-0.424565 - 0.245123i) q^{50} +(0.692125 - 3.23464i) q^{51} +(2.28278 + 0.171070i) q^{52} +(-1.70161 - 5.51649i) q^{53} +(-10.0164 - 7.33974i) q^{54} +(-5.14893 + 10.6919i) q^{55} +(-10.7725 + 1.00285i) q^{56} +(-9.04827 + 0.802002i) q^{57} +(-17.8054 - 2.68373i) q^{58} +(11.3514 + 5.46656i) q^{59} +(3.06846 - 14.3404i) q^{60} +(0.101088 - 0.0230726i) q^{61} +(6.99918 + 8.77669i) q^{62} +(6.05660 + 5.13006i) q^{63} +(6.74805 - 8.46179i) q^{64} +(0.610609 - 1.26794i) q^{65} +(-21.3315 - 2.91898i) q^{66} +12.1517 q^{67} +(3.54374 + 6.13793i) q^{68} +(0.856409 + 0.664105i) q^{69} +(-4.00278 + 13.8589i) q^{70} +(-2.65016 - 0.604882i) q^{71} +(12.2039 - 1.24926i) q^{72} +(-1.02444 + 6.79671i) q^{73} +(12.6314 - 4.95744i) q^{74} +(-0.296271 - 0.196144i) q^{75} +(13.2382 - 14.2674i) q^{76} +(13.4698 + 2.81996i) q^{77} +(2.52969 + 0.346160i) q^{78} +13.3560 q^{79} +(2.68095 + 4.64354i) q^{80} +(-6.92067 - 5.75363i) q^{81} +(-9.79856 - 14.3718i) q^{82} +(14.9414 + 2.25206i) q^{83} +(-16.9980 + 0.537853i) q^{84} +(4.30848 - 0.649399i) q^{85} +(-9.72272 - 10.4786i) q^{86} +(-12.7617 - 2.73066i) q^{87} +(17.5742 - 11.9819i) q^{88} +(2.61883 + 6.67267i) q^{89} +(4.39422 - 15.7555i) q^{90} +(-1.59738 - 0.334417i) q^{91} +(-2.31553 + 0.173525i) q^{92} +(4.67427 + 6.65940i) q^{93} +(-5.83166 - 1.33104i) q^{94} +(-5.19151 - 10.7803i) q^{95} +(2.97374 - 3.29369i) q^{96} +(10.2826 - 5.93664i) q^{97} +(16.7160 + 0.648019i) q^{98} +(-15.3021 - 3.05713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9}+O(q^{10}) $ 648 * q - 21 * q^2 - 11 * q^3 + 99 * q^4 - 18 * q^5 - 34 * q^6 - 5 * q^7 - 23 * q^9	\( 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9} - 22 q^{10} - 18 q^{11} - 72 q^{12} - 4 q^{13} + 66 q^{14} - 10 q^{15} - 105 q^{16} - 9 q^{17} - 27 q^{18} - 36 q^{19} - 27 q^{20} - 11 q^{21} - 9 q^{22} - 27 q^{23} - 8 q^{24} + 38 q^{25} + 6 q^{26} - 29 q^{27} - 26 q^{28} + 3 q^{29} - 16 q^{30} - 21 q^{32} - 11 q^{33} - 13 q^{34} + 28 q^{36} - 13 q^{37} - 90 q^{38} - 15 q^{39} - 31 q^{40} - 27 q^{41} - 4 q^{42} - 9 q^{43} + 51 q^{44} - 11 q^{45} - 108 q^{46} + 75 q^{47} - 15 q^{48} - 13 q^{49} - 45 q^{50} - 38 q^{51} + 64 q^{52} - 12 q^{53} - 41 q^{54} + 14 q^{55} + 3 q^{56} - 7 q^{57} - 90 q^{58} + 15 q^{59} - 69 q^{60} - 56 q^{61} + 66 q^{62} + 13 q^{63} + 64 q^{64} - 21 q^{65} - 204 q^{66} - 26 q^{67} + 3 q^{68} + 58 q^{69} - 22 q^{70} - 63 q^{71} - 18 q^{72} - 22 q^{73} - 12 q^{74} + 118 q^{75} - 63 q^{76} - 69 q^{77} - 147 q^{78} - 2 q^{79} - 45 q^{80} + 29 q^{81} - 28 q^{82} - 51 q^{83} - 31 q^{84} - 10 q^{85} - 72 q^{86} - 67 q^{87} + 4 q^{88} + 132 q^{89} + 58 q^{90} - 13 q^{91} - 15 q^{92} + 217 q^{93} - 7 q^{94} - 21 q^{95} - 44 q^{96} + 3 q^{97} + 21 q^{98} - 148 q^{99}+O(q^{100}) \) 648 * q - 21 * q^2 - 11 * q^3 + 99 * q^4 - 18 * q^5 - 34 * q^6 - 5 * q^7 - 23 * q^9 - 22 * q^10 - 18 * q^11 - 72 * q^12 - 4 * q^13 + 66 * q^14 - 10 * q^15 - 105 * q^16 - 9 * q^17 - 27 * q^18 - 36 * q^19 - 27 * q^20 - 11 * q^21 - 9 * q^22 - 27 * q^23 - 8 * q^24 + 38 * q^25 + 6 * q^26 - 29 * q^27 - 26 * q^28 + 3 * q^29 - 16 * q^30 - 21 * q^32 - 11 * q^33 - 13 * q^34 + 28 * q^36 - 13 * q^37 - 90 * q^38 - 15 * q^39 - 31 * q^40 - 27 * q^41 - 4 * q^42 - 9 * q^43 + 51 * q^44 - 11 * q^45 - 108 * q^46 + 75 * q^47 - 15 * q^48 - 13 * q^49 - 45 * q^50 - 38 * q^51 + 64 * q^52 - 12 * q^53 - 41 * q^54 + 14 * q^55 + 3 * q^56 - 7 * q^57 - 90 * q^58 + 15 * q^59 - 69 * q^60 - 56 * q^61 + 66 * q^62 + 13 * q^63 + 64 * q^64 - 21 * q^65 - 204 * q^66 - 26 * q^67 + 3 * q^68 + 58 * q^69 - 22 * q^70 - 63 * q^71 - 18 * q^72 - 22 * q^73 - 12 * q^74 + 118 * q^75 - 63 * q^76 - 69 * q^77 - 147 * q^78 - 2 * q^79 - 45 * q^80 + 29 * q^81 - 28 * q^82 - 51 * q^83 - 31 * q^84 - 10 * q^85 - 72 * q^86 - 67 * q^87 + 4 * q^88 + 132 * q^89 + 58 * q^90 - 13 * q^91 - 15 * q^92 + 217 * q^93 - 7 * q^94 - 21 * q^95 - 44 * q^96 + 3 * q^97 + 21 * q^98 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.86842	+	1.49001i	−1.32117	+	1.05360i	−0.327086	+	0.944995i	$0.606067\pi$
$2$	−1.86842	+	1.49001i	−1.32117	+	1.05360i	−0.994085	+	0.108604i	$0.965362\pi$
$3$	−1.41768	+	0.995078i	−0.818499	+	0.574509i
$3$	−1.41768	+	0.995078i	−0.818499	+	0.574509i
$4$	0.825803	−	3.61808i	0.412901	−	1.80904i
$5$	−1.88505	−	1.28520i	−0.843018	−	0.574760i	0.0629931	−	0.998014i	$-0.479935\pi$
$5$	−1.88505	−	1.28520i	−0.843018	−	0.574760i	−0.906011	+	0.423254i	$0.860888\pi$
$6$	1.16614	−	3.97158i	0.476075	−	1.62139i
$7$	−0.922050	+	2.47988i	−0.348502	+	0.937308i
$7$	−0.922050	+	2.47988i	−0.348502	+	0.937308i
$8$	1.77425	+	3.68427i	0.627293	+	1.30259i
$9$	1.01964	−	2.82141i	0.339880	−	0.940469i
$10$	5.43702	−	0.407448i	1.71934	−	0.128846i
$11$	−0.775241	−	5.14339i	−0.233744	−	1.55079i	−0.730507	−	0.682905i	$-0.760716\pi$
$11$	−0.775241	−	5.14339i	−0.233744	−	1.55079i	0.496763	−	0.867886i	$-0.334522\pi$
$12$	2.42955	+	5.95102i	0.701349	+	1.71791i
$13$	0.0919355	+	0.609952i	0.0254983	+	0.169170i	0.997956	−	0.0639108i	$-0.0203573\pi$
$13$	0.0919355	+	0.609952i	0.0254983	+	0.169170i	−0.972457	+	0.233081i	$0.925119\pi$
$14$	−1.97228	−	6.00733i	−0.527115	−	1.60553i
$15$	3.95127	−	0.0537608i	1.02021	−	0.0138810i
$16$	−2.11745	−	1.01971i	−0.529362	−	0.254927i
$17$	−1.39998	+	1.29899i	−0.339544	+	0.315051i	−0.831452	−	0.555596i	$-0.812490\pi$
$17$	−1.39998	+	1.29899i	−0.339544	+	0.315051i	0.491908	+	0.870647i	$0.336300\pi$
$18$	2.29882	+	6.79084i	0.541838	+	1.60062i
$19$	4.54187	+	2.62225i	1.04198	+	0.601586i	0.920393	−	0.390996i	$-0.127869\pi$
$19$	4.54187	+	2.62225i	1.04198	+	0.601586i	0.121584	+	0.992581i	$0.461203\pi$
$20$	−6.20664	+	5.75892i	−1.38785	+	1.28773i
$21$	−1.16051	−	4.43320i	−0.253243	−	0.967403i
$22$	9.11220	+	8.45488i	1.94273	+	1.80259i
$23$	−0.184426	−	0.597895i	−0.0384555	−	0.124670i	0.934310	−	0.356462i	$-0.116017\pi$
$23$	−0.184426	−	0.597895i	−0.0384555	−	0.124670i	−0.972765	+	0.231793i	$0.925541\pi$
$24$	−6.18146	−	3.45760i	−1.26179	−	0.705780i
$25$	0.0749465	+	0.190961i	0.0149893	+	0.0381921i
$26$	−1.08061	−	1.00266i	−0.211925	−	0.196638i
$27$	1.36200	+	5.01448i	0.262117	+	0.965036i
$28$	8.21098	+	5.38394i	1.55173	+	1.01747i
$29$	5.12493	+	5.52337i	0.951676	+	1.02566i	0.999640	+	0.0268142i	$0.00853625\pi$
$29$	5.12493	+	5.52337i	0.951676	+	1.02566i	−0.0479640	+	0.998849i	$0.515273\pi$
$30$	−7.30252	+	5.98789i	−1.33325	+	1.09323i
$31$		−	4.69739i		−	0.843677i	−0.906671	−	0.421838i	$-0.861385\pi$
$31$		−	4.69739i		−	0.843677i	0.906671	−	0.421838i	$-0.138615\pi$
$32$	−2.49776	+	0.570098i	−0.441547	+	0.100780i
$33$	6.21712	+	6.52026i	1.08226	+	1.13503i
$34$	0.680231	−	4.51303i	0.116659	−	0.773979i
$35$	4.92526	−	3.48967i	0.832521	−	0.589862i
$36$	−9.36605	−	6.01906i	−1.56101	−	1.00318i
$37$	−5.42578	−	1.67363i	−0.891993	−	0.275143i	−0.185315	−	0.982679i	$-0.559331\pi$
$37$	−5.42578	−	1.67363i	−0.891993	−	0.275143i	−0.706678	+	0.707536i	$0.749807\pi$
$38$	−12.3933	+	1.86799i	−2.01046	+	0.303028i
$39$	−0.737285	−	0.773235i	−0.118060	−	0.123817i
$40$	1.39049	−	9.22529i	0.219856	−	1.45865i
$41$	−0.543928	+	7.25822i	−0.0849473	+	1.13354i	0.778005	+	0.628258i	$0.216232\pi$
$41$	−0.543928	+	7.25822i	−0.0849473	+	1.13354i	−0.862952	+	0.505285i	$0.831387\pi$
$42$	8.77383	+	6.55389i	1.35383	+	1.01129i
$43$	0.446996	+	5.96474i	0.0681662	+	0.909615i	0.921532	+	0.388302i	$0.126938\pi$
$43$	0.446996	+	5.96474i	0.0681662	+	0.909615i	−0.853366	+	0.521312i	$0.825443\pi$
$44$	−19.2494	−	1.44254i	−2.90195	−	0.217471i
$45$	−5.54814	+	4.00804i	−0.827068	+	0.597483i
$46$	1.23546	+	0.842319i	0.182158	+	0.124193i
$47$	1.56059	+	1.95692i	0.227635	+	0.285446i	0.882512	−	0.470290i	$-0.155851\pi$
$47$	1.56059	+	1.95692i	0.227635	+	0.285446i	−0.654877	+	0.755736i	$0.727279\pi$
$48$	4.01655	−	0.661403i	0.579740	−	0.0954654i
$49$	−5.29965	−	4.57315i	−0.757092	−	0.653308i
$50$	−0.424565	−	0.245123i	−0.0600426	−	0.0346656i
$51$	0.692125	−	3.23464i	0.0969169	−	0.452940i
$52$	2.28278	+	0.171070i	0.316564	+	0.0237232i
$53$	−1.70161	−	5.51649i	−0.233735	−	0.757749i	−0.994121	−	0.108278i	$-0.965466\pi$
$53$	−1.70161	−	5.51649i	−0.233735	−	0.757749i	0.760386	−	0.649471i	$-0.225010\pi$
$54$	−10.0164	−	7.33974i	−1.36306	−	0.998812i
$55$	−5.14893	+	10.6919i	−0.694282	+	1.44169i
$56$	−10.7725	+	1.00285i	−1.43954	+	0.134012i
$57$	−9.04827	+	0.802002i	−1.19847	+	0.106228i
$58$	−17.8054	−	2.68373i	−2.33796	−	0.352391i
$59$	11.3514	+	5.46656i	1.47783	+	0.711685i	0.987171	−	0.159667i	$-0.0510420\pi$
$59$	11.3514	+	5.46656i	1.47783	+	0.711685i	0.490658	+	0.871352i	$0.336756\pi$
$60$	3.06846	−	14.3404i	0.396136	−	1.85134i
$61$	0.101088	−	0.0230726i	0.0129429	−	0.00295414i	−0.216045	−	0.976384i	$-0.569316\pi$
$61$	0.101088	−	0.0230726i	0.0129429	−	0.00295414i	0.228988	+	0.973429i	$0.426459\pi$
$62$	6.99918	+	8.77669i	0.888896	+	1.11464i
$63$	6.05660	+	5.13006i	0.763060	+	0.646327i
$64$	6.74805	−	8.46179i	0.843506	−	1.05772i
$65$	0.610609	−	1.26794i	0.0757368	−	0.157269i
$66$	−21.3315	−	2.91898i	−2.62572	−	0.359301i
$67$	12.1517			1.48456			0.742281	−	0.670088i	$-0.233744\pi$
$67$	12.1517			1.48456			0.742281	+	0.670088i	$0.233744\pi$
$68$	3.54374	+	6.13793i	0.429741	+	0.744333i
$69$	0.856409	+	0.664105i	0.103100	+	0.0799489i
$70$	−4.00278	+	13.8589i	−0.478424	+	1.65645i
$71$	−2.65016	−	0.604882i	−0.314516	−	0.0717862i	0.0623490	−	0.998054i	$-0.480141\pi$
$71$	−2.65016	−	0.604882i	−0.314516	−	0.0717862i	−0.376865	+	0.926268i	$0.622998\pi$
$72$	12.2039	−	1.24926i	1.43825	−	0.147227i
$73$	−1.02444	+	6.79671i	−0.119902	+	0.795495i	0.845358	+	0.534201i	$0.179387\pi$
$73$	−1.02444	+	6.79671i	−0.119902	+	0.795495i	−0.965259	+	0.261294i	$0.915851\pi$
$74$	12.6314	−	4.95744i	1.46837	−	0.576291i
$75$	−0.296271	−	0.196144i	−0.0342104	−	0.0226487i
$76$	13.2382	−	14.2674i	1.51853	−	1.63658i
$77$	13.4698	+	2.81996i	1.53503	+	0.321364i
$78$	2.52969	+	0.346160i	0.286431	+	0.0391949i
$79$	13.3560			1.50266			0.751332	−	0.659925i	$-0.229412\pi$
$79$	13.3560			1.50266			0.751332	+	0.659925i	$0.229412\pi$
$80$	2.68095	+	4.64354i	0.299739	+	0.519164i
$81$	−6.92067	−	5.75363i	−0.768964	−	0.639292i
$82$	−9.79856	−	14.3718i	−1.08207	−	1.58710i
$83$	14.9414	+	2.25206i	1.64003	+	0.247195i	0.903307	−	0.428995i	$-0.141132\pi$
$83$	14.9414	+	2.25206i	1.64003	+	0.247195i	0.736727	+	0.676190i	$0.236370\pi$
$84$	−16.9980	+	0.537853i	−1.85463	+	0.0586845i
$85$	4.30848	−	0.649399i	0.467320	−	0.0704372i
$86$	−9.72272	−	10.4786i	−1.04843	−	1.12994i
$87$	−12.7617	−	2.73066i	−1.36820	−	0.292758i
$88$	17.5742	−	11.9819i	1.87341	−	1.27727i
$89$	2.61883	+	6.67267i	0.277596	+	0.707302i	0.999877	+	0.0157024i	$0.00499843\pi$
$89$	2.61883	+	6.67267i	0.277596	+	0.707302i	−0.722281	+	0.691600i	$0.756906\pi$
$90$	4.39422	−	15.7555i	0.463191	−	1.66078i
$91$	−1.59738	−	0.334417i	−0.167451	−	0.0350565i
$92$	−2.31553	+	0.173525i	−0.241411	+	0.0180912i
$93$	4.67427	+	6.65940i	0.484699	+	0.690548i
$94$	−5.83166	−	1.33104i	−0.601490	−	0.137286i
$95$	−5.19151	−	10.7803i	−0.532638	−	1.10603i
$96$	2.97374	−	3.29369i	0.303506	−	0.336161i
$97$	10.2826	−	5.93664i	1.04404	−	0.602775i	0.123063	−	0.992399i	$-0.460728\pi$
$97$	10.2826	−	5.93664i	1.04404	−	0.602775i	0.920974	+	0.389624i	$0.127395\pi$
$98$	16.7160	+	0.648019i	1.68857	+	0.0654598i
$99$	−15.3021	−	3.05713i	−1.53792	−	0.307253i
$100$	0.752801	−	0.113467i	0.0752801	−	0.0113467i
$101$	0.0644688	−	0.860277i	0.00641489	−	0.0856008i	−0.993077	−	0.117462i	$-0.962524\pi$
$101$	0.0644688	−	0.860277i	0.00641489	−	0.0856008i	0.999492	+	0.0318609i	$0.0101433\pi$
$102$	3.52647	+	7.07493i	0.349173	+	0.700522i
$103$	9.87441	−	14.4831i	0.972954	−	1.42706i	0.0698909	−	0.997555i	$-0.477735\pi$
$103$	9.87441	−	14.4831i	0.972954	−	1.42706i	0.903063	−	0.429507i	$-0.141313\pi$
$104$	−2.08411	+	1.42092i	−0.204364	+	0.139333i
$105$	−3.50995	+	9.84826i	−0.342536	+	0.961092i
$106$	11.3990	+	7.77169i	1.10717	+	0.754853i
$107$	6.91589	−	2.71429i	0.668584	−	0.262400i	−0.00667807	−	0.999978i	$-0.502126\pi$
$107$	6.91589	−	2.71429i	0.668584	−	0.262400i	0.675262	+	0.737578i	$0.264030\pi$
$108$	19.2675	−	0.786847i	1.85402	−	0.0757144i
$109$	−5.55422	+	14.1519i	−0.531998	+	1.35551i	0.372103	+	0.928191i	$0.378637\pi$
$109$	−5.55422	+	14.1519i	−0.531998	+	1.35551i	−0.904101	+	0.427318i	$0.859458\pi$
$110$	−6.31067	−	27.6489i	−0.601699	−	2.63621i
$111$	9.35742	−	3.02640i	0.888167	−	0.287253i
$112$	4.48115	−	4.31080i	0.423429	−	0.407332i
$113$	0.743634	−	0.291855i	0.0699552	−	0.0274554i	−0.330105	−	0.943944i	$-0.607084\pi$
$113$	0.743634	−	0.291855i	0.0699552	−	0.0274554i	0.400061	+	0.916489i	$0.368989\pi$
$114$	15.7110	−	14.9805i	1.47147	−	1.40305i
$115$	−0.420764	+	1.36408i	−0.0392364	+	0.127201i
$116$	24.2161	−	13.9812i	2.24841	−	1.29812i
$117$	1.81466	+	0.362544i	0.167766	+	0.0335172i
$118$	−29.3544	+	6.69996i	−2.70230	+	0.616781i
$119$	−1.93049	−	4.66951i	−0.176968	−	0.428053i
$120$	7.20862	+	14.4622i	0.658054	+	1.32021i
$121$	−15.3422	+	4.73243i	−1.39474	+	0.430221i
$122$	−0.154495	+	0.193731i	−0.0139874	+	0.0175396i
$123$	−6.45138	−	10.8311i	−0.581701	−	0.976607i
$124$	−16.9955	−	3.87912i	−1.52624	−	0.348355i
$125$	−2.43424	+	10.6651i	−0.217725	+	0.953915i
$126$	−18.9601	−	0.560684i	−1.68910	−	0.0499497i
$127$	−2.48820	−	10.9015i	−0.220792	−	0.967355i	−0.956883	−	0.290472i	$-0.906188\pi$
$127$	−2.48820	−	10.9015i	−0.220792	−	0.967355i	0.736091	−	0.676882i	$-0.236669\pi$
$128$			20.7408i			1.83325i
$129$	−6.56908	−	8.01131i	−0.578375	−	0.705356i
$130$	0.748379	+	3.27886i	0.0656372	+	0.287575i
$131$	1.04910	+	13.9993i	0.0916605	+	1.22312i	0.833489	+	0.552535i	$0.186340\pi$
$131$	1.04910	+	13.9993i	0.0916605	+	1.22312i	−0.741829	+	0.670589i	$0.766041\pi$
$132$	28.7249	−	17.1096i	2.50018	−	1.48920i
$133$	−10.6907	+	8.84547i	−0.927002	+	0.766999i
$134$	−22.7044	+	18.1061i	−1.96136	+	1.56413i
$135$	3.87719	−	11.2030i	0.333695	−	0.964197i
$136$	−7.26974	−	2.85316i	−0.623375	−	0.244657i
$137$	−5.85400	−	8.58624i	−0.500141	−	0.733572i	0.490293	−	0.871557i	$-0.336890\pi$
$137$	−5.85400	−	8.58624i	−0.500141	−	0.733572i	−0.990434	+	0.137986i	$0.955937\pi$
$138$	−2.58966	+	0.0352348i	−0.220446	+	0.00299938i
$139$	−3.34061	−	0.250344i	−0.283347	−	0.0212339i	−0.0677012	−	0.997706i	$-0.521566\pi$
$139$	−3.34061	−	0.250344i	−0.283347	−	0.0212339i	−0.215645	+	0.976472i	$0.569186\pi$
$140$	−8.55861	−	20.7017i	−0.723335	−	1.74962i
$141$	−4.15970	−	1.22138i	−0.350310	−	0.102858i
$142$	5.85289	−	2.81860i	0.491163	−	0.236532i
$143$	3.06595	−	0.945721i	0.256388	−	0.0790851i
$144$	−5.03604	+	4.93444i	−0.419670	+	0.411204i
$145$	−2.56209	−	16.9984i	−0.212770	−	1.41164i
$146$	−8.21311	−	14.2255i	−0.679722	−	1.17731i
$147$	12.0639	+	1.20971i	0.995010	+	0.0997754i
$148$	−10.5360	+	18.2488i	−0.866050	+	1.50004i
$149$	17.9607	+	7.04905i	1.47140	+	0.577480i	0.959535	−	0.281588i	$-0.0908612\pi$
$149$	17.9607	+	7.04905i	1.47140	+	0.577480i	0.511861	+	0.859069i	$0.328956\pi$
$150$	0.845814	−	0.0749696i	0.0690604	−	0.00612124i
$151$	6.79459	+	6.30446i	0.552936	+	0.513049i	0.906412	−	0.422394i	$-0.138810\pi$
$151$	6.79459	+	6.30446i	0.552936	+	0.513049i	−0.353477	+	0.935443i	$0.615001\pi$
$152$	−1.60266	+	21.3860i	−0.129993	+	1.73464i
$153$	2.23750	+	5.27440i	0.180891	+	0.426410i
$154$	−29.3690	+	14.8014i	−2.36662	+	1.19273i
$155$	−6.03710	+	8.85480i	−0.484911	+	0.711234i
$156$	−3.40648	+	2.02902i	−0.272736	+	0.162451i
$157$	7.60393	−	15.7897i	0.606860	−	1.26016i	−0.340578	−	0.940216i	$-0.610623\pi$
$157$	7.60393	−	15.7897i	0.606860	−	1.26016i	0.947438	−	0.319941i	$-0.103663\pi$
$158$	−24.9545	+	19.9006i	−1.98528	+	1.58320i
$159$	7.90169	+	6.12739i	0.626645	+	0.485934i
$160$	5.44109	+	2.13547i	0.430156	+	0.168824i
$161$	1.65276	+	0.0939337i	0.130256	+	0.00740301i
$162$	21.5037	+	0.438292i	1.68949	+	0.0344355i
$163$	5.34850	−	3.64655i	0.418927	−	0.285620i	−0.335454	−	0.942057i	$-0.608890\pi$
$163$	5.34850	−	3.64655i	0.418927	−	0.285620i	0.754381	+	0.656437i	$0.227937\pi$
$164$	25.8116	+	7.96183i	2.01555	+	0.621715i
$165$	−3.33970	−	20.2812i	−0.259995	−	1.57889i
$166$	−31.2724	+	18.0551i	−2.42721	+	1.40135i
$167$	−11.4226	−	3.52340i	−0.883907	−	0.272649i	−0.180618	−	0.983553i	$-0.557810\pi$
$167$	−11.4226	−	3.52340i	−0.883907	−	0.272649i	−0.703289	+	0.710904i	$0.748286\pi$
$168$	14.2741	−	12.1412i	1.10127	−	0.936716i
$169$	12.0589	−	3.71966i	0.927604	−	0.286128i
$170$	−7.08243	+	7.63304i	−0.543197	+	0.585428i
$171$	12.0295	−	10.1407i	0.919919	−	0.775480i
$172$	21.9500	+	3.30843i	1.67367	+	0.252266i
$173$	2.44579	−	10.7157i	0.185950	−	0.814700i	−0.792773	−	0.609516i	$-0.791364\pi$
$173$	2.44579	−	10.7157i	0.185950	−	0.814700i	0.978723	−	0.205184i	$-0.0657792\pi$
$174$	27.9129	−	13.9131i	2.11607	−	1.05475i
$175$	−0.542664	+	0.00978337i	−0.0410216	+	0.000739553i
$176$	−3.60323	+	11.6814i	−0.271603	+	0.880517i
$177$	−21.5323	+	3.54572i	−1.61847	+	0.266513i
$178$	−14.8354	−	8.56525i	−1.11196	−	0.641992i
$179$	−3.28564	−	3.54108i	−0.245581	−	0.264673i	0.598217	−	0.801334i	$-0.295876\pi$
$179$	−3.28564	−	3.54108i	−0.245581	−	0.264673i	−0.843798	+	0.536661i	$0.819685\pi$
$180$	9.91972	+	23.3835i	0.739372	+	1.74290i
$181$	9.98850	+	7.96556i	0.742439	+	0.592075i	0.919946	−	0.392044i	$-0.128232\pi$
$181$	9.98850	+	7.96556i	0.742439	+	0.592075i	−0.177507	+	0.984119i	$0.556803\pi$
$182$	3.48286	−	1.75529i	0.258167	−	0.130110i
$183$	−0.120351	+	0.133300i	−0.00889660	+	0.00985379i
$184$	1.87559	−	1.74029i	0.138270	−	0.128296i
$185$	8.07689	+	10.1281i	0.593825	+	0.744633i
$186$	−18.6561	−	5.47782i	−1.36793	−	0.401653i
$187$	7.76652	+	6.19360i	0.567944	+	0.452921i
$188$	8.36901	−	4.03030i	0.610373	−	0.293940i
$189$	−13.6911	−	1.24600i	−0.995884	−	0.0906333i
$190$	25.7627	+	12.4067i	1.86902	+	0.900073i
$191$	−3.12238	−	6.48369i	−0.225928	−	0.469143i	0.756933	−	0.653492i	$-0.226697\pi$
$191$	−3.12238	−	6.48369i	−0.225928	−	0.469143i	−0.982861	+	0.184349i	$0.940982\pi$
$192$	−1.14644	+	18.7110i	−0.0827374	+	1.35035i
$193$	−23.6457	+	11.3872i	−1.70206	+	0.819667i	−0.708579	+	0.705632i	$0.750663\pi$
$193$	−23.6457	+	11.3872i	−1.70206	+	0.819667i	−0.993477	+	0.114035i	$0.963622\pi$
$194$	−10.3665	+	26.4133i	−0.744268	+	1.89636i
$195$	0.396054	+	2.40514i	0.0283620	+	0.172236i
$196$	−20.9225	+	15.3980i	−1.49446	+	1.09986i
$197$		−	14.2362i		−	1.01429i	−0.861861	−	0.507144i	$-0.830701\pi$
$197$		−	14.2362i		−	1.01429i	0.861861	−	0.507144i	$-0.169299\pi$
$198$	33.1458	−	17.0883i	2.35557	−	1.21441i
$199$	−5.46115	+	8.01003i	−0.387131	+	0.567816i	−0.969495	−	0.245112i	$-0.921175\pi$
$199$	−5.46115	+	8.01003i	−0.387131	+	0.567816i	0.582364	+	0.812928i	$0.302128\pi$
$200$	−0.570577	+	0.614936i	−0.0403459	+	0.0434825i
$201$	−17.2272	+	12.0919i	−1.21511	+	0.852894i
$202$	1.16137	+	1.70342i	0.0817137	+	0.119852i
$203$	−18.4228	+	7.61642i	−1.29302	+	0.534568i
$204$	−11.1316	−	5.17533i	−0.779368	−	0.362346i
$205$	10.3536	−	12.9830i	0.723128	−	0.906773i
$206$	3.13049	+	41.7735i	0.218111	+	2.91050i
$207$	−1.87495	−	0.0892956i	−0.130318	−	0.00620647i
$208$	0.427305	−	1.38529i	0.0296283	−	0.0960525i
$209$	9.96621	−	25.3935i	0.689377	−	1.75651i
$210$	−8.11599	−	23.6305i	−0.560056	−	1.63066i
$211$	−5.45339	−	13.8950i	−0.375427	−	0.956573i	−0.986317	−	0.164858i	$-0.947284\pi$
$211$	−5.45339	−	13.8950i	−0.375427	−	0.956573i	0.610890	−	0.791715i	$-0.290812\pi$
$212$	−21.3643	+	1.60103i	−1.46731	+	0.109959i
$213$	4.35898	−	1.77959i	0.298673	−	0.121935i
$214$	−8.87744	+	15.3762i	−0.606850	+	1.05109i
$215$	6.82329	−	11.8183i	0.465345	−	0.806001i
$216$	−16.0582	+	13.9149i	−1.09262	+	0.946790i
$217$	11.6490	+	4.33123i	0.790785	+	0.294023i
$218$	−10.7090	−	34.7176i	−0.725302	−	2.35137i
$219$	−5.31093	−	10.6550i	−0.358880	−	0.719996i
$220$	34.4320	+	27.4586i	2.32141	+	1.85126i
$221$	−0.921028	−	0.734495i	−0.0619551	−	0.0494075i
$222$	−12.9742	+	19.5973i	−0.870771	+	1.31528i
$223$	3.30654	+	10.7196i	0.221423	+	0.717834i	0.996317	+	0.0857440i	$0.0273267\pi$
$223$	3.30654	+	10.7196i	0.221423	+	0.717834i	−0.774895	+	0.632090i	$0.782197\pi$
$224$	0.889287	−	6.71983i	0.0594180	−	0.448987i
$225$	0.615196	−	0.0167438i	0.0410131	−	0.00111625i
$226$	−0.954552	+	1.65333i	−0.0634958	+	0.109978i
$227$	−8.22366	+	14.2438i	−0.545824	+	0.945394i	0.452731	+	0.891647i	$0.350450\pi$
$227$	−8.22366	+	14.2438i	−0.545824	+	0.945394i	−0.998555	+	0.0537472i	$0.982883\pi$
$228$	−4.57038	+	33.3996i	−0.302681	+	2.21194i
$229$	−17.4878	+	1.31053i	−1.15563	+	0.0866024i	−0.638721	−	0.769439i	$-0.720536\pi$
$229$	−17.4878	+	1.31053i	−1.15563	+	0.0866024i	−0.516908	+	0.856041i	$0.672917\pi$
$230$	−1.24634	−	3.17562i	−0.0821812	−	0.209394i
$231$	−21.9020	+	9.40573i	−1.44105	+	0.618852i
$232$	−11.2567	+	28.6815i	−0.739036	+	1.88303i
$233$	−6.03806	+	19.5749i	−0.395567	+	1.28240i	0.510726	+	0.859744i	$0.329377\pi$
$233$	−6.03806	+	19.5749i	−0.395567	+	1.28240i	−0.906292	+	0.422652i	$0.861099\pi$
$234$	−3.93075	+	2.02649i	−0.256961	+	0.132476i
$235$	−0.426747	−	5.69455i	−0.0278379	−	0.371471i
$236$	29.1525	−	36.5560i	1.89766	−	2.37959i
$237$	−18.9345	+	13.2902i	−1.22993	+	0.863293i
$238$	10.5646	+	5.84814i	0.684801	+	0.379078i
$239$	−15.1521	−	22.2241i	−0.980110	−	1.43756i	−0.897520	−	0.440974i	$-0.854633\pi$
$239$	−15.1521	−	22.2241i	−0.980110	−	1.43756i	−0.0825907	−	0.996584i	$-0.526319\pi$
$240$	−8.42142	−	3.91531i	−0.543600	−	0.252732i
$241$	−11.6197	+	12.5231i	−0.748492	+	0.806682i	−0.986358	−	0.164616i	$-0.947362\pi$
$241$	−11.6197	+	12.5231i	−0.748492	+	0.806682i	0.237866	+	0.971298i	$0.423552\pi$
$242$	21.6142	−	31.7022i	1.38941	−	2.03789i
$243$	15.5366	+	1.27020i	0.996675	+	0.0814836i
$244$		−	0.384796i		−	0.0246341i
$245$	4.11265	+	15.4317i	0.262747	+	0.985897i
$246$	28.1923	+	10.6244i	1.79748	+	0.677385i
$247$	−1.18189	+	3.01140i	−0.0752018	+	0.191611i
$248$	17.3065	−	8.33436i	1.09896	−	0.529232i
$249$	−23.4231	+	11.6752i	−1.48438	+	0.739885i
$250$	−11.3430	−	23.5539i	−0.717391	−	1.48968i
$251$	5.01961	+	2.41732i	0.316835	+	0.152580i	0.585542	−	0.810642i	$-0.300882\pi$
$251$	5.01961	+	2.41732i	0.316835	+	0.152580i	−0.268706	+	0.963222i	$0.586596\pi$
$252$	23.5625	−	17.6768i	1.48430	−	1.11354i
$253$	−2.93223	+	1.41209i	−0.184348	+	0.0887772i
$254$	20.8924	+	16.6612i	1.31091	+	1.04541i
$255$	−5.46185	+	5.20792i	−0.342034	+	0.326132i
$256$	−17.4080	−	21.8290i	−1.08800	−	1.36431i
$257$	5.46780	−	5.07338i	0.341072	−	0.316469i	−0.490975	−	0.871174i	$-0.663359\pi$
$257$	5.46780	−	5.07338i	0.341072	−	0.316469i	0.832047	+	0.554705i	$0.187169\pi$
$258$	24.2107	+	5.18045i	1.50729	+	0.322520i
$259$	9.15325	−	11.9121i	0.568756	−	0.740184i
$260$	−4.08328	−	3.25630i	−0.253234	−	0.201947i
$261$	20.8092	−	8.82769i	1.28806	−	0.546420i
$262$	−22.8193	−	24.5934i	−1.40978	−	1.51938i
$263$	6.19928	+	3.57916i	0.382264	+	0.220700i	0.678803	−	0.734321i	$-0.262499\pi$
$263$	6.19928	+	3.57916i	0.382264	+	0.220700i	−0.296539	+	0.955021i	$0.595832\pi$
$264$	−12.9917	+	34.4742i	−0.799583	+	2.12174i
$265$	−3.88219	+	12.5858i	−0.238481	+	0.773137i
$266$	6.79485	−	32.4563i	0.416619	−	1.99002i
$267$	−10.3525	−	6.85378i	−0.633563	−	0.419445i
$268$	10.0349	−	43.9657i	0.612978	−	2.68563i
$269$	13.0298	+	1.96393i	0.794440	+	0.119743i	0.533708	−	0.845669i	$-0.320798\pi$
$269$	13.0298	+	1.96393i	0.794440	+	0.119743i	0.260732	+	0.965411i	$0.416036\pi$
$270$	9.44835	+	26.7089i	0.575008	+	1.62545i
$271$	−4.58657	+	4.94315i	−0.278614	+	0.300275i	−0.856819	−	0.515617i	$-0.827563\pi$
$271$	−4.58657	+	4.94315i	−0.278614	+	0.300275i	0.578205	+	0.815892i	$0.303753\pi$
$272$	4.28896	−	1.32297i	0.260057	−	0.0802168i
$273$	2.59735	−	1.11542i	0.157199	−	0.0675083i
$274$	23.7313	+	7.32014i	1.43366	+	0.442226i
$275$	0.924083	−	0.533520i	0.0557243	−	0.0321725i
$276$	3.11001	−	2.55013i	0.187201	−	0.153500i
$277$	18.5880	+	5.73363i	1.11684	+	0.344500i	0.797609	−	0.603175i	$-0.206098\pi$
$277$	18.5880	+	5.73363i	1.11684	+	0.344500i	0.319234	+	0.947676i	$0.396574\pi$
$278$	6.61466	−	4.50980i	0.396721	−	0.270480i
$279$	−13.2533	−	4.78964i	−0.793452	−	0.286748i
$280$	21.5956	+	11.9544i	1.29058	+	0.714414i
$281$	18.2269	+	7.15355i	1.08733	+	0.426745i	0.840222	−	0.542243i	$-0.182425\pi$
$281$	18.2269	+	7.15355i	1.08733	+	0.426745i	0.247107	+	0.968988i	$0.420520\pi$
$282$	9.59192	−	3.91597i	0.571191	−	0.233193i
$283$	−8.44124	+	6.73166i	−0.501779	+	0.400156i	−0.841405	−	0.540405i	$-0.818271\pi$
$283$	−8.44124	+	6.73166i	−0.501779	+	0.400156i	0.339626	+	0.940561i	$0.389700\pi$
$284$	−4.37702	+	9.08897i	−0.259728	+	0.539331i
$285$	18.0871	+	10.1170i	1.07139	+	0.599282i
$286$	−4.31934	+	6.33531i	−0.255408	+	0.374615i
$287$	−17.4980	−	8.04132i	−1.03288	−	0.474664i
$288$	−0.938338	+	7.62850i	−0.0552921	+	0.449514i
$289$	−0.997848	+	13.3154i	−0.0586970	+	0.783257i
$290$	30.1149	+	27.9425i	1.76841	+	1.64084i
$291$	−8.66998	+	18.6482i	−0.508243	+	1.09318i
$292$	23.7451	+	9.31925i	1.38957	+	0.545368i
$293$	8.56348	−	14.8324i	0.500284	−	0.866518i	−0.499716	−	0.866189i	$-0.666562\pi$
$293$	8.56348	−	14.8324i	0.500284	−	0.866518i	1.00000		0.000328097i	$-0.000104437\pi$
$294$	−24.3428	+	15.7151i	−1.41970	+	0.916521i
$295$	−14.3723	−	24.8936i	−0.836789	−	1.44936i
$296$	−3.46059	−	22.9595i	−0.201143	−	1.33449i
$297$	24.7355	−	10.8927i	1.43530	−	0.632060i
$298$	−44.0612	+	13.5911i	−2.55240	+	0.787310i
$299$	0.347732	−	0.167459i	0.0201099	−	0.00968440i
$300$	−0.954324	+	0.909955i	−0.0550979	+	0.0525363i
$301$	−15.2040	−	4.39129i	−0.876345	−	0.253110i
$302$	−22.0889	−	1.65533i	−1.27107	−	0.0952536i
$303$	0.764647	+	1.28375i	0.0439278	+	0.0737495i
$304$	−6.94324	−	10.1839i	−0.398222	−	0.584084i
$305$	−0.220208	−	0.0864251i	−0.0126091	−	0.00494869i
$306$	−12.0395	−	6.52087i	−0.688253	−	0.372773i
$307$	−4.73908	+	3.77929i	−0.270474	+	0.215696i	−0.749328	−	0.662199i	$-0.769624\pi$
$307$	−4.73908	+	3.77929i	−0.270474	+	0.215696i	0.478855	+	0.877894i	$0.341052\pi$
$308$	21.3262	−	46.4061i	1.21518	−	2.64424i
$309$	0.413053	+	30.3582i	0.0234977	+	1.72702i
$310$	−1.91394	−	25.5398i	−0.108705	−	1.45056i
$311$	−1.99969	−	8.76121i	−0.113392	−	0.496803i	−0.999448	−	0.0332244i	$-0.989422\pi$
$311$	−1.99969	−	8.76121i	−0.113392	−	0.496803i	0.886056	−	0.463578i	$-0.153435\pi$
$312$	1.54068	−	4.08827i	0.0872237	−	0.231453i
$313$		−	17.2783i		−	0.976625i	−0.872669	−	0.488312i	$-0.837613\pi$
$313$		−	17.2783i		−	0.976625i	0.872669	−	0.488312i	$-0.162387\pi$
$314$	9.31958	+	40.8317i	0.525934	+	2.30427i
$315$	−4.82380	−	17.4544i	−0.271790	−	0.983442i
$316$	11.0294	−	48.3229i	0.620452	−	2.71838i
$317$	4.28935	+	0.979015i	0.240914	+	0.0549870i	0.341273	−	0.939964i	$-0.389142\pi$
$317$	4.28935	+	0.979015i	0.240914	+	0.0549870i	−0.100359	+	0.994951i	$0.531999\pi$
$318$	−23.8935	+	0.325095i	−1.33988	+	0.0182304i
$319$	24.4358	−	30.6415i	1.36814	−	1.71559i
$320$	−23.5955	+	7.27824i	−1.31903	+	0.406866i
$321$	−7.10360	+	10.7298i	−0.396484	+	0.598881i
$322$	−3.22801	+	2.28713i	−0.179890	+	0.127457i
$323$	−9.76478	+	2.22875i	−0.543327	+	0.124011i
$324$	−26.5322	+	20.2882i	−1.47401	+	1.12712i
$325$	−0.109587	+	0.0632699i	−0.00607877	+	0.00350958i
$326$	−4.55983	+	14.7826i	−0.252546	+	0.818733i
$327$	−6.20816	−	25.5898i	−0.343312	−	1.41512i
$328$	−27.7063	+	10.8739i	−1.52983	+	0.600413i
$329$	−6.29187	+	2.06570i	−0.346882	+	0.113886i
$330$	36.4593	+	32.9176i	2.00702	+	1.81206i
$331$	−3.85303	−	16.8812i	−0.211782	−	0.927876i	−0.963356	−	0.268227i	$-0.913562\pi$
$331$	−3.85303	−	16.8812i	−0.211782	−	0.927876i	0.751574	−	0.659649i	$-0.229295\pi$
$332$	20.4868	−	52.1995i	1.12436	−	2.86482i
$333$	−10.2543	+	13.6018i	−0.561934	+	0.745376i
$334$	26.5921	−	10.4366i	1.45505	−	0.571067i
$335$	−22.9064	−	15.6174i	−1.25151	−	0.853267i
$336$	−2.06326	+	10.5704i	−0.112560	+	0.576664i
$337$	16.8928	−	11.5173i	0.920212	−	0.627390i	−0.00778822	−	0.999970i	$-0.502479\pi$
$337$	16.8928	−	11.5173i	0.920212	−	0.627390i	0.928000	+	0.372580i	$0.121527\pi$
$338$	−16.9886	+	24.9177i	−0.924060	+	1.35535i
$339$	−0.763818	+	1.15373i	−0.0414849	+	0.0626621i
$340$	1.20838	−	16.1247i	0.0655335	−	0.874484i
$341$	−24.1605	+	3.64161i	−1.30837	+	0.197204i
$342$	−7.36633	+	36.8712i	−0.398326	+	1.99377i
$343$	16.2274	−	8.92583i	0.876199	−	0.481949i
$344$	−21.1827	+	12.2298i	−1.14209	+	0.659387i
$345$	−0.760860	−	2.35253i	−0.0409634	−	0.126656i
$346$	11.3968	+	23.6657i	0.612695	+	1.27227i
$347$	33.6924	+	7.69006i	1.80870	+	0.412824i	0.987475	−	0.157778i	$-0.0504331\pi$
$347$	33.6924	+	7.69006i	1.80870	+	0.412824i	0.821226	+	0.570602i	$0.193290\pi$
$348$	−20.4184	+	43.9178i	−1.09454	+	2.35424i
$349$	−25.0083	+	1.87411i	−1.33866	+	0.100319i	−0.724726	−	0.689037i	$-0.758034\pi$
$349$	−25.0083	+	1.87411i	−1.33866	+	0.100319i	−0.613936	+	0.789356i	$0.710415\pi$
$350$	0.999346	−	0.826857i	0.0534173	−	0.0441973i
$351$	−2.93337	+	1.29176i	−0.156572	+	0.0689492i
$352$	4.86861	+	12.4050i	0.259498	+	0.661190i
$353$	−27.1358	+	18.5009i	−1.44429	+	0.984703i	−0.448432	+	0.893817i	$0.648017\pi$
$353$	−27.1358	+	18.5009i	−1.44429	+	0.984703i	−0.995861	+	0.0908857i	$0.971030\pi$
$354$	34.9482	−	38.7084i	1.85748	−	2.05733i
$355$	4.21828	+	4.54622i	0.223883	+	0.241288i
$356$	26.3049	−	3.96482i	1.39416	−	0.210135i
$357$	7.38335	+	4.69889i	0.390768	+	0.248691i
$358$	11.4152	+	1.72057i	0.603313	+	0.0909348i
$359$	6.56260	+	9.62556i	0.346361	+	0.508018i	0.959405	−	0.282030i	$-0.0910079\pi$
$359$	6.56260	+	9.62556i	0.346361	+	0.508018i	−0.613045	+	0.790048i	$0.710056\pi$
$360$	−24.6105	−	13.3296i	−1.29709	−	0.702532i
$361$	4.25240	+	7.36537i	0.223810	+	0.387651i
$362$	−30.5315			−1.60470
$363$	17.0412	−	21.9757i	0.894429	−	1.15343i
$364$	−2.52907	+	5.50328i	−0.132559	+	0.288450i
$365$	10.6663	−	11.4955i	0.558298	−	0.601702i
$366$	0.0262476	−	0.428384i	0.00137198	−	0.0223920i
$367$	1.98206	−	0.777900i	0.103463	−	0.0406060i	−0.313045	−	0.949738i	$-0.601349\pi$
$367$	1.98206	−	0.777900i	0.103463	−	0.0406060i	0.416508	+	0.909132i	$0.363254\pi$
$368$	−0.219166	+	1.45407i	−0.0114248	+	0.0757987i
$369$	19.9238	+	8.93541i	1.03719	+	0.465159i
$370$	−30.1820	−	6.88884i	−1.56909	−	0.358134i
$371$	15.2492	+	0.866682i	0.791701	+	0.0449959i
$372$	27.9543	−	11.4125i	1.44936	−	0.591712i
$373$	2.34351	+	4.05908i	0.121342	+	0.210171i	0.920297	−	0.391220i	$-0.127947\pi$
$373$	2.34351	+	4.05908i	0.121342	+	0.210171i	−0.798955	+	0.601391i	$0.794613\pi$
$374$	−23.7396			−1.22755
$375$	−7.16163	−	17.5420i	−0.369825	−	0.905863i
$376$	−4.44093	+	9.22170i	−0.229024	+	0.475573i
$377$	−2.89783	+	3.63376i	−0.149246	+	0.187148i
$378$	27.4373	−	18.0719i	1.41122	−	0.929520i
$379$	5.42380	+	6.80123i	0.278602	+	0.349356i	0.901369	−	0.433051i	$-0.142563\pi$
$379$	5.42380	+	6.80123i	0.278602	+	0.349356i	−0.622767	+	0.782407i	$0.713992\pi$
$380$	−43.2911	+	9.88090i	−2.22079	+	0.506880i
$381$	14.3754	+	12.9789i	0.736472	+	0.664931i
$382$	15.4947	+	7.46185i	0.792778	+	0.381782i
$383$	−6.07330	−	0.915403i	−0.310331	−	0.0467749i	−0.00796978	−	0.999968i	$-0.502537\pi$
$383$	−6.07330	−	0.915403i	−0.310331	−	0.0467749i	−0.302362	+	0.953193i	$0.597775\pi$
$384$	−20.6388	−	29.4039i	−1.05322	−	1.50051i
$385$	−21.7670	−	22.6272i	−1.10935	−	1.15319i
$386$	27.2130	−	56.5084i	1.38511	−	2.87620i
$387$	17.2847	+	4.82073i	0.878633	+	0.245051i
$388$	−12.9879	−	42.1056i	−0.659359	−	2.13759i
$389$	19.3479	+	1.44992i	0.980976	+	0.0735140i	0.555553	−	0.831481i	$-0.312506\pi$
$389$	19.3479	+	1.44992i	0.980976	+	0.0735140i	0.425423	+	0.904995i	$0.360125\pi$
$390$	−4.32369	−	3.90369i	−0.218939	−	0.197671i
$391$	1.03485	+	0.597471i	0.0523346	+	0.0302154i
$392$	7.44584	−	27.6393i	0.376072	−	1.39599i
$393$	−15.4177	−	18.8026i	−0.777720	−	0.948466i
$394$	21.2121	+	26.5992i	1.06865	+	1.34005i
$395$	−25.1766	−	17.1651i	−1.26677	−	0.863671i
$396$	−23.6974	+	52.8395i	−1.19084	+	2.65528i
$397$	3.83629	+	0.287490i	0.192538	+	0.0144287i	0.170650	−	0.985332i	$-0.445413\pi$
$397$	3.83629	+	0.287490i	0.192538	+	0.0144287i	0.0218879	+	0.999760i	$0.493032\pi$
$398$	−1.73135	−	23.1033i	−0.0867848	−	1.15806i
$399$	6.35409	−	23.1781i	0.318102	−	1.16036i
$400$	0.0360289	−	0.480772i	0.00180145	−	0.0240386i
$401$	4.22550	−	28.0344i	0.211012	−	1.39997i	−0.592926	−	0.805257i	$-0.702027\pi$
$401$	4.22550	−	28.0344i	0.211012	−	1.39997i	0.803938	−	0.594714i	$-0.202735\pi$
$402$	14.1706	−	48.2614i	0.706763	−	2.40706i
$403$	2.86519	−	0.431857i	0.142725	−	0.0215123i
$404$	−3.05931	−	0.943672i	−0.152206	−	0.0469494i
$405$	5.65120	+	19.7403i	0.280811	+	0.980905i
$406$	23.0728	−	41.6808i	1.14509	−	2.06858i
$407$	−4.40185	+	29.2044i	−0.218192	+	1.44761i
$408$	13.1453	−	3.18908i	0.650789	−	0.157883i
$409$	17.9278	−	4.09191i	0.886473	−	0.202332i	0.245042	−	0.969512i	$-0.421198\pi$
$409$	17.9278	−	4.09191i	0.886473	−	0.202332i	0.641431	+	0.767181i	$0.278341\pi$
$410$			39.6847i			1.95989i
$411$	16.8431	+	6.34736i	0.830808	+	0.313092i
$412$	−44.2467	−	47.6865i	−2.17988	−	2.34935i
$413$	−24.0230	+	23.1098i	−1.18209	+	1.13716i
$414$	3.63624	−	2.62686i	0.178712	−	0.129103i
$415$	−25.2709	−	23.4480i	−1.24050	−	1.15102i
$416$	−0.577366	−	1.47110i	−0.0283077	−	0.0721269i
$417$	4.98503	−	2.96926i	0.244118	−	0.145405i
$418$	19.2156	+	62.2954i	0.939866	+	3.04697i
$419$	14.1920	+	13.1682i	0.693324	+	0.643311i	0.945972	−	0.324248i	$-0.105111\pi$
$419$	14.1920	+	13.1682i	0.693324	+	0.643311i	−0.252648	+	0.967558i	$0.581302\pi$
$420$	32.7332	+	20.8320i	1.59722	+	1.01650i
$421$	−18.8589	+	17.4985i	−0.919125	+	0.852824i	−0.989476	−	0.144699i	$-0.953779\pi$
$421$	−18.8589	+	17.4985i	−0.919125	+	0.852824i	0.0703504	+	0.997522i	$0.477588\pi$
$422$	30.8930	+	17.8361i	1.50385	+	0.868246i
$423$	7.11249	−	2.40771i	0.345821	−	0.117067i
$424$	17.3052	−	16.0569i	0.840414	−	0.779790i
$425$	−0.352979	−	0.169986i	−0.0171220	−	0.00824551i
$426$	−5.49280	+	9.81996i	−0.266127	+	0.475778i
$427$	−0.0359905	+	0.271960i	−0.00174170	+	0.0131610i
$428$	−4.10934	−	27.2637i	−0.198632	−	1.31784i
$429$	−3.40547	+	4.39159i	−0.164418	+	0.212028i
$430$	4.86065	+	32.2483i	0.234401	+	1.55515i
$431$	19.6353	−	1.47146i	0.945797	−	0.0708777i	0.407106	−	0.913381i	$-0.366538\pi$
$431$	19.6353	−	1.47146i	0.945797	−	0.0708777i	0.538691	+	0.842503i	$0.318919\pi$
$432$	2.22935	−	12.0067i	0.107259	−	0.577674i
$433$	−2.53480	−	5.26356i	−0.121814	−	0.252950i	0.831140	−	0.556063i	$-0.187689\pi$
$433$	−2.53480	−	5.26356i	−0.121814	−	0.252950i	−0.952955	+	0.303112i	$0.901974\pi$
$434$	−28.2188	+	9.26459i	−1.35454	+	0.444715i
$435$	20.5469	+	21.5488i	0.985150	+	1.03319i
$436$	46.6161	+	31.7823i	2.23251	+	1.52210i
$437$	0.730190	−	3.19917i	0.0349297	−	0.153037i
$438$	25.7991	+	11.9946i	1.23273	+	0.573123i
$439$	−1.75007	+	1.39564i	−0.0835263	+	0.0666100i	−0.664363	−	0.747410i	$-0.731297\pi$
$439$	−1.75007	+	1.39564i	−0.0835263	+	0.0666100i	0.580836	+	0.814020i	$0.302726\pi$
$440$	−48.5273			−2.31345
$441$	−18.3065	+	10.2895i	−0.871736	+	0.489976i
$442$	2.81527			0.133909
$443$	15.3251	−	12.2213i	0.728116	−	0.580653i	−0.187712	−	0.982224i	$-0.560107\pi$
$443$	15.3251	−	12.2213i	0.728116	−	0.580653i	0.915828	+	0.401571i	$0.131536\pi$
$444$	−3.22237	−	36.3551i	−0.152927	−	1.72534i
$445$	3.63912	−	15.9440i	0.172511	−	0.755819i
$446$	−22.1503	−	15.1018i	−1.04885	−	0.715091i
$447$	−32.4769	+	7.87898i	−1.53610	+	0.372663i
$448$	14.7622	+	24.5366i	0.697449	+	1.15924i
$449$	−4.07501	−	8.46185i	−0.192312	−	0.399339i	0.782409	−	0.622764i	$-0.213990\pi$
$449$	−4.07501	−	8.46185i	−0.192312	−	0.399339i	−0.974721	+	0.223425i	$0.928276\pi$
$450$	−1.12449	+	0.947934i	−0.0530092	+	0.0446861i
$451$	37.7535	−	2.82924i	1.77774	−	0.133224i
$452$	−0.441859	−	2.93154i	−0.0207833	−	0.137888i
$453$	−15.9060	−	2.17656i	−0.747329	−	0.102264i
$454$	−5.85822	−	38.8667i	−0.274940	−	1.82411i
$455$	2.58134	+	2.68335i	0.121015	+	0.125797i
$456$	−19.0087	−	31.9133i	−0.890164	−	1.49448i
$457$	14.7219	+	7.08970i	0.688662	+	0.331642i	0.745278	−	0.666754i	$-0.232317\pi$
$457$	14.7219	+	7.08970i	0.688662	+	0.331642i	−0.0566159	+	0.998396i	$0.518031\pi$
$458$	30.7219	−	28.5057i	1.43554	−	1.33198i
$459$	−8.42051	−	5.25093i	−0.393036	−	0.245092i
$460$	4.58789	+	2.64882i	0.213912	+	0.123502i
$461$	−17.8625	+	16.5740i	−0.831941	+	0.771928i	−0.976030	−	0.217636i	$-0.930165\pi$
$461$	−17.8625	+	16.5740i	−0.831941	+	0.771928i	0.144089	+	0.989565i	$0.453975\pi$
$462$	26.9074	−	50.2081i	1.25185	−	2.33589i
$463$	−11.5118	−	10.6814i	−0.535001	−	0.496408i	0.365769	−	0.930706i	$-0.380806\pi$
$463$	−11.5118	−	10.6814i	−0.535001	−	0.496408i	−0.900769	+	0.434298i	$0.856997\pi$
$464$	−5.21955	−	16.9214i	−0.242312	−	0.785555i
$465$	−0.252536	−	18.5607i	−0.0117111	−	0.860730i
$466$	−17.8853	−	45.5709i	−0.828519	−	2.11103i
$467$	24.4592	+	22.6948i	1.13184	+	1.05019i	0.998249	+	0.0591522i	$0.0188397\pi$
$467$	24.4592	+	22.6948i	1.13184	+	1.05019i	0.133586	+	0.991037i	$0.457351\pi$
$468$	2.81027	−	6.26621i	0.129905	−	0.289656i
$469$	−11.2044	+	30.1347i	−0.517373	+	1.39149i
$470$	9.28229	+	10.0039i	0.428160	+	0.461447i
$471$	4.93206	+	29.9513i	0.227257	+	1.38008i
$472$			51.5208i			2.37144i
$473$	30.3325	−	6.92319i	1.39469	−	0.318329i
$474$	15.5749	−	53.0444i	0.715380	−	2.43641i
$475$	−0.160349	+	1.06385i	−0.00735732	+	0.0488126i
$476$	−18.4889	+	3.12857i	−0.847435	+	0.143398i
$477$	−17.2993	−	0.823889i	−0.792081	−	0.0377233i
$478$	61.4247	+	18.9470i	2.80950	+	0.866617i
$479$	−38.0150	+	5.72984i	−1.73695	+	0.261803i	−0.939738	−	0.341895i	$-0.888931\pi$
$479$	−38.0150	+	5.72984i	−1.73695	+	0.261803i	−0.797213	+	0.603698i	$0.793693\pi$
$480$	−9.83869	+	2.38689i	−0.449073	+	0.108946i
$481$	0.522014	−	3.46333i	0.0238018	−	0.157914i
$482$	3.05093	−	40.7119i	0.138966	−	1.85437i
$483$	−2.43656	+	1.51146i	−0.110867	+	0.0687737i
$484$	4.45271	+	59.4172i	0.202396	+	2.70078i
$485$	−27.0129	−	2.02434i	−1.22659	−	0.0919204i
$486$	−30.9215	+	20.7765i	−1.40263	+	0.942441i
$487$	15.4696	+	10.5470i	0.700995	+	0.477930i	0.860620	−	0.509248i	$-0.170076\pi$
$487$	15.4696	+	10.5470i	0.700995	+	0.477930i	−0.159625	+	0.987178i	$0.551029\pi$
$488$	0.264361	+	0.331498i	0.0119670	+	0.0150062i
$489$	−3.95387	+	10.4918i	−0.178800	+	0.474456i
$490$	−30.6776	−	22.7050i	−1.38587	−	1.02571i
$491$	−12.8248	−	7.40437i	−0.578773	−	0.334155i	0.181873	−	0.983322i	$-0.441784\pi$
$491$	−12.8248	−	7.40437i	−0.578773	−	0.334155i	−0.760646	+	0.649167i	$0.775117\pi$
$492$	−44.5153	+	14.3972i	−2.00690	+	0.649078i
$493$	−14.3496	−	1.07535i	−0.646272	−	0.0484314i
$494$	−2.27877	−	7.38759i	−0.102527	−	0.332383i
$495$	24.9161	+	25.4291i	1.11989	+	1.14295i
$496$	−4.78997	+	9.94648i	−0.215076	+	0.446610i
$497$	3.94362	−	6.01436i	0.176895	−	0.269781i
$498$	26.3680	−	56.7149i	1.18158	−	2.54146i
$499$	−3.39045	−	0.511029i	−0.151778	−	0.0228768i	0.0727139	−	0.997353i	$-0.476834\pi$
$499$	−3.39045	−	0.511029i	−0.151778	−	0.0228768i	−0.224491	+	0.974476i	$0.572072\pi$
$500$	36.5769	+	17.6145i	1.63577	+	0.787745i
$501$	19.6997	−	6.37131i	0.880116	−	0.284649i
$502$	−12.9806	+	2.96273i	−0.579351	+	0.132233i
$503$	7.17705	+	8.99973i	0.320009	+	0.401278i	0.915653	−	0.401970i	$-0.131675\pi$
$503$	7.17705	+	8.99973i	0.320009	+	0.401278i	−0.595644	+	0.803249i	$0.703103\pi$
$504$	−8.15462	+	31.4162i	−0.363235	+	1.39939i
$505$	−1.22716	+	1.53881i	−0.0546078	+	0.0684760i
$506$	3.37460	−	7.00743i	0.150019	−	0.311518i
$507$	−13.3943	+	17.2728i	−0.594860	+	0.767112i
$508$	−41.4974			−1.84115
$509$	−5.94460	−	10.2963i	−0.263490	−	0.456377i	0.703677	−	0.710520i	$-0.251540\pi$
$509$	−5.94460	−	10.2963i	−0.263490	−	0.456377i	−0.967167	+	0.254142i	$0.918207\pi$
$510$	2.44515	−	17.8688i	0.108273	−	0.791243i
$511$	−15.9105	−	8.80740i	−0.703838	−	0.389617i
$512$	24.6092	+	5.61690i	1.08759	+	0.248234i
$513$	−6.96319	+	26.3466i	−0.307432	+	1.16323i
$514$	−2.65673	+	17.6263i	−0.117184	+	0.777462i
$515$	−37.2274	+	14.6107i	−1.64044	+	0.643824i
$516$	−34.4103	+	17.1517i	−1.51483	+	0.755061i
$517$	8.85535	−	9.54380i	0.389458	−	0.419736i
$518$	0.647135	+	35.8953i	0.0284335	+	1.57715i
$519$	7.19562	+	17.6252i	0.315853	+	0.773661i
$520$	5.75483			0.252366
$521$	−12.6917	−	21.9826i	−0.556032	−	0.963075i	−0.997822	−	0.0659572i	$-0.978990\pi$
$521$	−12.6917	−	21.9826i	−0.556032	−	0.963075i	0.441791	−	0.897118i	$-0.354343\pi$
$522$	−25.7270	+	47.4999i	−1.12604	+	2.07901i
$523$	−14.7381	−	21.6169i	−0.644454	−	0.945240i	−0.999944	−	0.0105602i	$-0.996639\pi$
$523$	−14.7381	−	21.6169i	−0.644454	−	0.945240i	0.355490	−	0.934680i	$-0.384314\pi$
$524$	51.5169	+	7.76492i	2.25053	+	0.339212i
$525$	0.759590	−	0.553863i	0.0331512	−	0.0241726i
$526$	−16.9158	+	2.54965i	−0.737565	+	0.111170i
$527$	6.10186	+	6.57624i	0.265801	+	0.286465i
$528$	−6.51566	−	20.1460i	−0.283557	−	0.876740i
$529$	18.6800	−	12.7358i	0.812175	−	0.553732i
$530$	−11.4994	−	29.3000i	−0.499502	−	1.27271i
$531$	26.9977	−	26.4531i	1.17160	−	1.14797i
$532$	23.1752	+	45.9844i	1.00477	+	1.99368i
$533$	−4.47717	+	0.335518i	−0.193928	+	0.0145329i
$534$	29.5550	−	2.61964i	1.27897	−	0.113363i
$535$	−16.5252	−	3.77176i	−0.714445	−	0.163067i
$536$	21.5601	+	44.7701i	0.931256	+	1.93377i
$537$	8.18165	+	1.75065i	0.353064	+	0.0755462i
$538$	−27.2714	+	15.7451i	−1.17575	+	0.678821i
$539$	−19.4130	+	30.8035i	−0.836178	+	1.32680i
$540$	−37.3314	−	23.2794i	−1.60649	−	1.00179i
$541$	−29.6823	+	4.47388i	−1.27614	+	0.192347i	−0.751931	−	0.659242i	$-0.770877\pi$
$541$	−29.6823	+	4.47388i	−1.27614	+	0.192347i	−0.524209	+	0.851589i	$0.675639\pi$
$542$	1.20427	−	16.0699i	0.0517280	−	0.690262i
$543$	−22.0869	−	1.35329i	−0.947838	−	0.0580752i
$544$	2.75626	−	4.04269i	0.118174	−	0.173329i
$545$	28.6581	−	19.5387i	1.22758	−	0.836947i
$546$	−3.19094	+	5.95415i	−0.136559	+	0.254814i
$547$	21.3645	+	14.5660i	0.913478	+	0.622799i	0.926164	−	0.377121i	$-0.123086\pi$
$547$	21.3645	+	14.5660i	0.913478	+	0.622799i	−0.0126860	+	0.999920i	$0.504038\pi$
$548$	−35.8999	+	14.0897i	−1.53357	+	0.601881i
$549$	0.0379757	−	0.308735i	0.00162076	−	0.0131765i
$550$	−0.931622	+	2.37373i	−0.0397245	+	0.101216i
$551$	8.79314	+	38.5253i	0.374601	+	1.64123i
$552$	−0.927260	+	4.33354i	−0.0394668	+	0.184448i
$553$	−12.3149	+	33.1212i	−0.523682	+	1.40846i
$554$	−43.2733	+	16.9835i	−1.83851	+	0.721560i
$555$	−21.5287	−	6.32128i	−0.913842	−	0.268323i
$556$	−3.66445	+	11.8798i	−0.155407	+	0.503817i
$557$	−18.4058	+	10.6266i	−0.779879	+	0.450263i	−0.836387	−	0.548139i	$-0.815337\pi$
$557$	−18.4058	+	10.6266i	−0.779879	+	0.450263i	0.0565085	+	0.998402i	$0.482003\pi$
$558$	31.8992	−	10.7985i	1.35040	−	0.457136i
$559$	−3.59711	+	0.821018i	−0.152142	+	0.0347253i
$560$	−13.9874	+	2.36687i	−0.591076	+	0.100018i
$561$	−17.1736	−	1.05224i	−0.725068	−	0.0444258i
$562$	−44.7144	+	13.7926i	−1.88616	+	0.581805i
$563$	−16.5225	+	20.7186i	−0.696342	+	0.873185i	−0.996744	−	0.0806272i	$-0.974308\pi$
$563$	−16.5225	+	20.7186i	−0.696342	+	0.873185i	0.300402	+	0.953813i	$0.402879\pi$
$564$	−7.85412	+	14.0415i	−0.330718	+	0.591254i
$565$	−1.77688	−	0.405561i	−0.0747538	−	0.0170621i
$566$	5.74149	−	25.1551i	0.241333	−	1.05735i
$567$	20.6495	−	11.8573i	0.867199	−	0.497961i
$568$	−2.47350	−	10.8371i	−0.103786	−	0.454716i
$569$			8.01207i			0.335884i	0.985797	+	0.167942i	$0.0537121\pi$
$569$			8.01207i			0.335884i	−0.985797	+	0.167942i	$0.946288\pi$
$570$	−48.8688	+	8.04720i	−2.04689	+	0.337060i
$571$	1.14536	+	5.01813i	0.0479316	+	0.210002i	0.993223	−	0.116225i	$-0.0370795\pi$
$571$	1.14536	+	5.01813i	0.0479316	+	0.210002i	−0.945291	+	0.326228i	$0.894222\pi$
$572$	−0.889820	−	11.8738i	−0.0372053	−	0.496470i
$573$	10.8783	+	6.08479i	0.454448	+	0.254196i
$574$	44.6753	−	11.0477i	1.86471	−	0.461123i
$575$	0.100352	−	0.0800282i	0.00418498	−	0.00333741i
$576$	−16.9936	−	27.6670i	−0.708065	−	1.15279i
$577$	−12.0713	−	4.73762i	−0.502533	−	0.197230i	0.100513	−	0.994936i	$-0.467952\pi$
$577$	−12.0713	−	4.73762i	−0.502533	−	0.197230i	−0.603047	+	0.797706i	$0.706047\pi$
$578$	−17.9757	−	26.3655i	−0.747689	−	1.09666i
$579$	22.1909	−	39.6727i	0.922224	−	1.64874i
$580$	−63.6172	−	4.76745i	−2.64156	−	0.197958i
$581$	−19.3616	+	34.9765i	−0.803254	+	1.45107i
$582$	−11.5870	−	47.7610i	−0.480295	−	1.97976i
$583$	−27.0543	+	13.0287i	−1.12048	+	0.539593i
$584$	−26.8586	+	8.28477i	−1.11142	+	0.342826i
$585$	−2.95478	−	3.01562i	−0.122165	−	0.124681i
$586$	6.10029	+	40.4728i	0.252001	+	1.67192i
$587$	10.5278	+	18.2346i	0.434527	+	0.752624i	0.997257	−	0.0740175i	$-0.0235821\pi$
$587$	10.5278	+	18.2346i	0.434527	+	0.752624i	−0.562730	+	0.826641i	$0.690249\pi$
$588$	14.3392	−	42.6490i	0.591338	−	1.75881i
$589$	12.3177	−	21.3350i	0.507544	−	0.879091i
$590$	63.9453	+	25.0967i	2.63258	+	1.03321i
$591$	14.1661	+	20.1824i	0.582717	+	0.830193i
$592$	9.78218	+	9.07654i	0.402045	+	0.373044i
$593$	−0.231356	+	3.08723i	−0.00950063	+	0.126777i	−0.999937	−	0.0111904i	$-0.996438\pi$
$593$	−0.231356	+	3.08723i	−0.00950063	+	0.126777i	0.990437	+	0.137968i	$0.0440570\pi$
$594$	−29.9860	+	57.2084i	−1.23034	+	2.34729i
$595$	−2.36220	+	11.2833i	−0.0968408	+	0.462571i
$596$	40.3360	−	59.1620i	1.65223	−	2.42337i
$597$	−0.228443	−	16.7899i	−0.00934956	−	0.687167i
$598$	−0.400192	+	0.831008i	−0.0163651	+	0.0339825i
$599$	22.7681	−	18.1570i	0.930279	−	0.741873i	−0.0360047	−	0.999352i	$-0.511463\pi$
$599$	22.7681	−	18.1570i	0.930279	−	0.741873i	0.966284	+	0.257479i	$0.0828917\pi$
$600$	0.196987	−	1.43955i	0.00804196	−	0.0587694i
$601$	2.02988	+	0.796669i	0.0828005	+	0.0324968i	0.406380	−	0.913704i	$-0.366791\pi$
$601$	2.02988	+	0.796669i	0.0828005	+	0.0324968i	−0.323579	+	0.946201i	$0.604886\pi$
$602$	34.9505	−	14.4494i	1.42448	−	0.588914i
$603$	12.3903	−	34.2848i	0.504573	−	1.39619i
$604$	28.4210	−	19.3771i	1.15643	−	0.788444i
$605$	35.0028	+	10.7969i	1.42307	+	0.438958i
$606$	−3.34148	−	1.25925i	−0.135738	−	0.0511534i
$607$	18.3324	−	10.5842i	0.744088	−	0.429600i	−0.0794657	−	0.996838i	$-0.525321\pi$
$607$	18.3324	−	10.5842i	0.744088	−	0.429600i	0.823554	+	0.567238i	$0.191988\pi$
$608$	−12.8395	−	3.96045i	−0.520709	−	0.160617i
$609$	18.5387	−	29.1297i	0.751224	−	1.18040i
$610$	0.540214	−	0.166634i	0.0218726	−	0.00674682i
$611$	−1.05015	+	1.13179i	−0.0424846	+	0.0457875i
$612$	20.9309	−	3.73985i	0.846083	−	0.151174i
$613$	−37.7894	−	5.69583i	−1.52630	−	0.230052i	−0.668373	−	0.743826i	$-0.733009\pi$
$613$	−37.7894	−	5.69583i	−1.52630	−	0.230052i	−0.857926	+	0.513774i	$0.828247\pi$
$614$	3.22339	−	14.1226i	0.130085	−	0.569941i
$615$	−1.75900	+	28.7084i	−0.0709297	+	1.15764i
$616$	13.5094	+	54.6298i	0.544308	+	2.20110i
$617$	−1.54879	+	5.02104i	−0.0623518	+	0.202140i	−0.981389	−	0.192032i	$-0.938492\pi$
$617$	−1.54879	+	5.02104i	−0.0623518	+	0.202140i	0.919037	+	0.394172i	$0.128968\pi$
$618$	−46.0059	−	56.1064i	−1.85063	−	2.25693i
$619$	30.1560	+	17.4106i	1.21207	+	0.699791i	0.963211	−	0.268748i	$-0.0866099\pi$
$619$	30.1560	+	17.4106i	1.21207	+	0.699791i	0.248863	+	0.968539i	$0.419943\pi$
$620$	27.0519	+	29.1550i	1.08643	+	1.17089i
$621$	2.74694	−	1.73913i	0.110231	−	0.0697889i
$622$	16.7906	+	13.3900i	0.673241	+	0.536892i
$623$	−18.9621	+	0.341857i	−0.759702	+	0.0136962i
$624$	0.772688	+	2.38910i	0.0309323	+	0.0956405i
$625$	19.0473	−	17.6734i	0.761894	−	0.706934i
$626$	25.7448	+	32.2830i	1.02897	+	1.29029i
$627$	11.1396	+	45.9170i	0.444873	+	1.83375i
$628$	−50.8491	−	40.5508i	−2.02910	−	1.61815i
$629$	9.76999	−	4.70498i	0.389555	−	0.187600i
$630$	35.0201	+	25.4245i	1.39523	+	1.01294i
$631$	−4.39900	−	2.11845i	−0.175122	−	0.0843341i	0.344269	−	0.938871i	$-0.388127\pi$
$631$	−4.39900	−	2.11845i	−0.175122	−	0.0843341i	−0.519391	+	0.854537i	$0.673841\pi$
$632$	23.6969	+	49.2070i	0.942610	+	1.95735i
$633$	21.5578	+	14.2722i	0.856846	+	0.567267i
$634$	−9.47303	+	4.56197i	−0.376222	+	0.181179i
$635$	−9.32030	+	23.7477i	−0.369865	+	0.942400i
$636$	28.6946	−	23.5289i	1.13782	−	0.932982i
$637$	2.30218	−	3.65297i	0.0912157	−	0.144736i
$638$			93.6607i			3.70806i
$639$	−4.40882	+	6.86042i	−0.174410	+	0.271394i
$640$	26.6562	−	39.0974i	1.05368	−	1.54546i
$641$	5.38282	−	5.80130i	0.212609	−	0.229138i	−0.617739	−	0.786383i	$-0.711951\pi$
$641$	5.38282	−	5.80130i	0.212609	−	0.229138i	0.830348	+	0.557245i	$0.188142\pi$
$642$	−2.71512	−	30.6323i	−0.107157	−	1.20896i
$643$	18.0279	+	26.4421i	0.710952	+	1.04278i	0.996433	+	0.0843908i	$0.0268944\pi$
$643$	18.0279	+	26.4421i	0.710952	+	1.04278i	−0.285481	+	0.958384i	$0.592153\pi$
$644$	1.70471	−	5.90224i	0.0671751	−	0.232581i
$645$	2.08687	+	23.5443i	0.0821704	+	0.927055i
$646$	14.9238	−	18.7139i	0.587170	−	0.736288i
$647$	−1.21356	−	16.1938i	−0.0477099	−	0.636644i	−0.968887	−	0.247502i	$-0.920390\pi$
$647$	−1.21356	−	16.1938i	−0.0477099	−	0.636644i	0.921178	−	0.389142i	$-0.127229\pi$
$648$	8.91893	−	35.7060i	0.350369	−	1.40267i
$649$	19.3165	−	62.6227i	0.758241	−	2.45816i
$650$	0.110481	−	0.281500i	0.00433341	−	0.0110413i
$651$	−20.8245	+	5.45135i	−0.816175	+	0.213655i
$652$	−8.77668	−	22.3626i	−0.343721	−	0.875788i
$653$	10.2848	−	0.770737i	0.402474	−	0.0301613i	0.128044	−	0.991768i	$-0.459130\pi$
$653$	10.2848	−	0.770737i	0.402474	−	0.0301613i	0.274430	+	0.961607i	$0.411511\pi$
$654$	49.7286	+	38.5622i	1.94454	+	1.50790i
$655$	16.0143	−	27.7376i	0.625731	−	1.08380i
$656$	8.55301	−	14.8142i	0.333939	−	0.578399i
$657$	18.1317	+	9.82055i	0.707386	+	0.383136i
$658$	8.67791	−	13.2346i	0.338300	−	0.515937i
$659$	−7.76847	−	25.1847i	−0.302616	−	0.981058i	−0.971369	−	0.237574i	$-0.923648\pi$
$659$	−7.76847	−	25.1847i	−0.302616	−	0.981058i	0.668753	−	0.743485i	$-0.266828\pi$
$660$	−76.1371	−	4.66501i	−2.96363	−	0.181585i
$661$	4.79058	+	3.82036i	0.186332	+	0.148595i	0.712213	−	0.701963i	$-0.247693\pi$
$661$	4.79058	+	3.82036i	0.186332	+	0.148595i	−0.525881	+	0.850558i	$0.676264\pi$
$662$	32.3523	+	25.8001i	1.25741	+	1.00275i
$663$	2.03660	+	0.124785i	0.0790952	+	0.00484626i
$664$	18.2127	+	59.0440i	0.706788	+	2.29135i
$665$	31.5207	−	2.93438i	1.22232	−	0.113790i
$666$	−1.10754	−	40.6930i	−0.0429163	−	1.57682i
$667$	2.35722	−	4.08282i	0.0912719	−	0.158088i
$668$	−22.1807	+	38.4182i	−0.858199	+	1.48644i
$669$	−15.3544	−	11.9066i	−0.593636	−	0.460337i
$670$	66.0689	−	4.95118i	2.55246	−	0.191281i
$671$	−0.197039	−	0.502046i	−0.00760659	−	0.0193813i
$672$	5.42603	+	10.4115i	0.209314	+	0.401631i
$673$	0.364579	−	0.928931i	0.0140535	−	0.0358077i	−0.923675	−	0.383177i	$-0.874830\pi$
$673$	0.364579	−	0.928931i	0.0140535	−	0.0358077i	0.937728	+	0.347370i	$0.112925\pi$
$674$	−14.4019	+	46.6898i	−0.554740	+	1.79842i
$675$	−0.855490	+	0.635905i	−0.0329278	+	0.0244760i
$676$	−3.49980	−	46.7016i	−0.134608	−	1.79621i
$677$	−1.18452	+	1.48535i	−0.0455249	+	0.0570865i	−0.804073	−	0.594531i	$-0.797338\pi$
$677$	−1.18452	+	1.48535i	−0.0455249	+	0.0570865i	0.758548	+	0.651617i	$0.225909\pi$
$678$	−0.291945	−	3.29375i	−0.0112121	−	0.126496i
$679$	5.24114	+	30.9735i	0.201137	+	1.18865i
$680$	10.0369	+	14.7214i	0.384897	+	0.564541i
$681$	−2.51517	−	28.3764i	−0.0963814	−	1.08738i
$682$	39.7159	−	42.8036i	1.52080	−	1.63903i
$683$	−1.31320	+	1.92611i	−0.0502481	+	0.0737004i	−0.850541	−	0.525909i	$-0.823725\pi$
$683$	−1.31320	+	1.92611i	−0.0502481	+	0.0737004i	0.800293	+	0.599610i	$0.204678\pi$
$684$	−26.7559	−	51.8979i	−1.02304	−	1.98437i
$685$			23.7090i			0.905875i
$686$	−17.0200	+	40.8563i	−0.649827	+	1.55990i
$687$	23.4881	−	19.2597i	0.896126	−	0.734802i
$688$	5.13581	−	13.0858i	0.195801	−	0.498892i
$689$	3.20836	−	1.54506i	0.122229	−	0.0588623i
$690$	4.92690	+	3.26181i	0.187564	+	0.124175i
$691$	0.0948732	+	0.197006i	0.00360915	+	0.00749447i	0.902766	−	0.430133i	$-0.141533\pi$
$691$	0.0948732	+	0.197006i	0.00360915	+	0.00749447i	−0.899157	+	0.437627i	$0.855819\pi$
$692$	−36.7505	−	17.6981i	−1.39705	−	0.672782i
$693$	21.6906	−	35.1285i	0.823958	−	1.33442i
$694$	−74.4097	+	35.8338i	−2.82455	+	1.36023i
$695$	5.97545	+	4.76527i	0.226662	+	0.180757i
$696$	−12.5820	−	51.8625i	−0.476919	−	1.96584i
$697$	−8.66685	−	10.8679i	−0.328280	−	0.411651i
$698$	43.9334	−	40.7643i	1.66290	−	1.54295i
$699$	−10.9185	−	33.7593i	−0.412977	−	1.27690i
$700$	−0.412737	+	1.97148i	−0.0156000	+	0.0745150i
$701$	31.4744	+	25.1000i	1.18877	+	0.948015i	0.999425	−	0.0338947i	$-0.0107911\pi$
$701$	31.4744	+	25.1000i	1.18877	+	0.948015i	0.189348	+	0.981910i	$0.439363\pi$
$702$	3.55603	−	6.78432i	0.134214	−	0.256058i
$703$	−20.2545	−	21.8292i	−0.763914	−	0.823303i
$704$	−48.7536	−	28.1479i	−1.83747	−	1.06087i
$705$	6.27151	+	7.64840i	0.236199	+	0.288056i
$706$	23.1345	−	75.0001i	0.870677	−	2.82267i
$707$	2.07394	+	0.953094i	0.0779987	+	0.0358448i
$708$	−4.95278	+	80.8338i	−0.186137	+	3.03792i
$709$	6.07496	−	26.6161i	0.228150	−	0.999590i	−0.722997	−	0.690851i	$-0.757236\pi$
$709$	6.07496	−	26.6161i	0.228150	−	0.999590i	0.951147	−	0.308739i	$-0.0999068\pi$
$710$	−14.6554	−	2.20895i	−0.550008	−	0.0829004i
$711$	13.6183	−	37.6826i	0.510725	−	1.41321i
$712$	−19.9375	+	21.4875i	−0.747189	+	0.805278i
$713$	−2.80855	+	0.866322i	−0.105181	+	0.0324440i
$714$	−20.7966	+	2.22180i	−0.778292	+	0.0831489i
$715$	−6.99490	−	2.15764i	−0.261594	−	0.0806912i
$716$	−15.5252	+	8.96348i	−0.580204	+	0.334981i
$717$	43.5956	+	16.4291i	1.62811	+	0.613557i
$718$	−26.6039	−	8.20621i	−0.992848	−	0.306253i
$719$	19.2131	−	13.0992i	0.716526	−	0.488519i	−0.149346	−	0.988785i	$-0.547717\pi$
$719$	19.2131	−	13.0992i	0.716526	−	0.488519i	0.865872	+	0.500266i	$0.166764\pi$
$720$	15.8349	−	2.82932i	0.590133	−	0.105442i
$721$	26.8117	+	37.8415i	0.998520	+	1.40929i
$722$	−18.9197	−	7.42545i	−0.704120	−	0.276347i
$723$	4.01161	−	29.3162i	0.149193	−	1.09028i
$724$	37.0685	−	29.5612i	1.37764	−	1.09863i
$725$	−0.670649	+	1.39262i	−0.0249073	+	0.0517205i
$726$	0.904135	+	66.4514i	0.0335556	+	2.46624i
$727$	−23.2845	+	34.1522i	−0.863576	+	1.26663i	0.0988537	+	0.995102i	$0.468482\pi$
$727$	−23.2845	+	34.1522i	−0.863576	+	1.26663i	−0.962430	+	0.271531i	$0.912470\pi$
$728$	−1.60207	−	6.47852i	−0.0593767	−	0.240110i
$729$	−23.2899	+	13.6594i	−0.862590	+	0.505904i
$730$	−2.80059	+	37.3713i	−0.103654	+	1.38317i
$731$	−8.37391	−	7.76985i	−0.309720	−	0.287378i
$732$	0.382902	+	0.545518i	0.0141525	+	0.0201629i
$733$	−28.9659	−	11.3683i	−1.06988	−	0.419897i	−0.235950	−	0.971765i	$-0.575820\pi$
$733$	−28.9659	−	11.3683i	−1.06988	−	0.419897i	−0.833932	+	0.551868i	$0.813915\pi$
$734$	−2.54423	+	4.40673i	−0.0939092	+	0.162655i
$735$	−21.1862	−	17.7849i	−0.781464	−	0.656004i
$736$	0.801512	+	1.38826i	0.0295441	+	0.0511719i
$737$	−9.42048	−	62.5008i	−0.347008	−	2.30225i
$738$	−50.5398	+	12.9916i	−1.86040	+	0.478228i
$739$	−7.05135	+	2.17505i	−0.259388	+	0.0800107i	−0.421722	−	0.906725i	$-0.638574\pi$
$739$	−7.05135	+	2.17505i	−0.259388	+	0.0800107i	0.162334	+	0.986736i	$0.448098\pi$
$740$	43.3142	−	20.8590i	1.59226	−	0.766792i
$741$	−1.32104	−	5.44528i	−0.0485296	−	0.200037i
$742$	−29.7833	+	21.1022i	−1.09338	+	0.774688i
$743$	−11.6020	−	0.869446i	−0.425634	−	0.0318969i	−0.139809	−	0.990179i	$-0.544649\pi$
$743$	−11.6020	−	0.869446i	−0.425634	−	0.0318969i	−0.285826	+	0.958282i	$0.592268\pi$
$744$	−16.2417	+	29.0368i	−0.595450	+	1.06454i
$745$	−24.7972	−	36.3709i	−0.908501	−	1.33253i
$746$	−10.4267	−	4.09219i	−0.381750	−	0.149826i
$747$	21.5888	−	39.8595i	0.789894	−	1.45838i
$748$	28.8225	−	22.9852i	1.05386	−	0.840422i
$749$	0.354318	+	19.6533i	0.0129465	+	0.718116i
$750$	39.5187	+	22.1048i	1.44302	+	0.807152i
$751$	2.77419	+	37.0189i	0.101231	+	1.35084i	0.784253	+	0.620441i	$0.213047\pi$
$751$	2.77419	+	37.0189i	0.101231	+	1.35084i	−0.683021	+	0.730398i	$0.739334\pi$
$752$	−1.30898	−	5.73501i	−0.0477335	−	0.209134i
$753$	−9.52163	+	1.56792i	−0.346988	+	0.0571382i
$754$		−	11.1072i		−	0.404500i
$755$	−4.70561	−	20.6166i	−0.171255	−	0.750315i
$756$	−15.8143	+	48.5067i	−0.575161	+	1.76417i
$757$	−8.45735	+	37.0541i	−0.307388	+	1.34675i	0.551323	+	0.834292i	$0.314123\pi$
$757$	−8.45735	+	37.0541i	−0.307388	+	1.34675i	−0.858711	+	0.512461i	$0.828734\pi$
$758$	−20.2679	−	4.62601i	−0.736162	−	0.168024i
$759$	2.75183	−	4.91969i	0.0998851	−	0.178573i
$760$	30.5065	−	38.2539i	1.10659	−	1.38761i
$761$	6.74462	−	2.08044i	0.244492	−	0.0754158i	−0.170087	−	0.985429i	$-0.554405\pi$
$761$	6.74462	−	2.08044i	0.244492	−	0.0754158i	0.414579	+	0.910013i	$0.363929\pi$
$762$	−46.1980	−	2.83060i	−1.67358	−	0.102542i
$763$	−29.9739	−	26.8226i	−1.08513	−	0.971044i
$764$	−26.0370	+	5.94277i	−0.941985	+	0.215002i
$765$	2.56088	−	12.8181i	0.0925886	−	0.463440i
$766$	12.7114	−	7.33895i	0.459283	−	0.265167i
$767$	−2.29074	+	7.42640i	−0.0827138	+	0.268152i
$768$	46.4005	+	13.6242i	1.67434	+	0.491620i
$769$	20.8070	−	8.16614i	0.750319	−	0.294478i	0.0408023	−	0.999167i	$-0.487009\pi$
$769$	20.8070	−	8.16614i	0.750319	−	0.294478i	0.709517	+	0.704689i	$0.248913\pi$
$770$	74.3847	+	9.84390i	2.68064	+	0.354750i
$771$	−2.70319

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.bn (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86842 + 1.49001i) q^{2} +(-1.41768 + 0.995078i) q^{3} +(0.825803 - 3.61808i) q^{4} +(-1.88505 - 1.28520i) q^{5} +(1.16614 - 3.97158i) q^{6} +(-0.922050 + 2.47988i) q^{7} +(1.77425 + 3.68427i) q^{8} +(1.01964 - 2.82141i) q^{9} +O(q^{10})\)	\(q+(-1.86842 + 1.49001i) q^{2} +(-1.41768 + 0.995078i) q^{3} +(0.825803 - 3.61808i) q^{4} +(-1.88505 - 1.28520i) q^{5} +(1.16614 - 3.97158i) q^{6} +(-0.922050 + 2.47988i) q^{7} +(1.77425 + 3.68427i) q^{8} +(1.01964 - 2.82141i) q^{9} +(5.43702 - 0.407448i) q^{10} +(-0.775241 - 5.14339i) q^{11} +(2.42955 + 5.95102i) q^{12} +(0.0919355 + 0.609952i) q^{13} +(-1.97228 - 6.00733i) q^{14} +(3.95127 - 0.0537608i) q^{15} +(-2.11745 - 1.01971i) q^{16} +(-1.39998 + 1.29899i) q^{17} +(2.29882 + 6.79084i) q^{18} +(4.54187 + 2.62225i) q^{19} +(-6.20664 + 5.75892i) q^{20} +(-1.16051 - 4.43320i) q^{21} +(9.11220 + 8.45488i) q^{22} +(-0.184426 - 0.597895i) q^{23} +(-6.18146 - 3.45760i) q^{24} +(0.0749465 + 0.190961i) q^{25} +(-1.08061 - 1.00266i) q^{26} +(1.36200 + 5.01448i) q^{27} +(8.21098 + 5.38394i) q^{28} +(5.12493 + 5.52337i) q^{29} +(-7.30252 + 5.98789i) q^{30} -4.69739i q^{31} +(-2.49776 + 0.570098i) q^{32} +(6.21712 + 6.52026i) q^{33} +(0.680231 - 4.51303i) q^{34} +(4.92526 - 3.48967i) q^{35} +(-9.36605 - 6.01906i) q^{36} +(-5.42578 - 1.67363i) q^{37} +(-12.3933 + 1.86799i) q^{38} +(-0.737285 - 0.773235i) q^{39} +(1.39049 - 9.22529i) q^{40} +(-0.543928 + 7.25822i) q^{41} +(8.77383 + 6.55389i) q^{42} +(0.446996 + 5.96474i) q^{43} +(-19.2494 - 1.44254i) q^{44} +(-5.54814 + 4.00804i) q^{45} +(1.23546 + 0.842319i) q^{46} +(1.56059 + 1.95692i) q^{47} +(4.01655 - 0.661403i) q^{48} +(-5.29965 - 4.57315i) q^{49} +(-0.424565 - 0.245123i) q^{50} +(0.692125 - 3.23464i) q^{51} +(2.28278 + 0.171070i) q^{52} +(-1.70161 - 5.51649i) q^{53} +(-10.0164 - 7.33974i) q^{54} +(-5.14893 + 10.6919i) q^{55} +(-10.7725 + 1.00285i) q^{56} +(-9.04827 + 0.802002i) q^{57} +(-17.8054 - 2.68373i) q^{58} +(11.3514 + 5.46656i) q^{59} +(3.06846 - 14.3404i) q^{60} +(0.101088 - 0.0230726i) q^{61} +(6.99918 + 8.77669i) q^{62} +(6.05660 + 5.13006i) q^{63} +(6.74805 - 8.46179i) q^{64} +(0.610609 - 1.26794i) q^{65} +(-21.3315 - 2.91898i) q^{66} +12.1517 q^{67} +(3.54374 + 6.13793i) q^{68} +(0.856409 + 0.664105i) q^{69} +(-4.00278 + 13.8589i) q^{70} +(-2.65016 - 0.604882i) q^{71} +(12.2039 - 1.24926i) q^{72} +(-1.02444 + 6.79671i) q^{73} +(12.6314 - 4.95744i) q^{74} +(-0.296271 - 0.196144i) q^{75} +(13.2382 - 14.2674i) q^{76} +(13.4698 + 2.81996i) q^{77} +(2.52969 + 0.346160i) q^{78} +13.3560 q^{79} +(2.68095 + 4.64354i) q^{80} +(-6.92067 - 5.75363i) q^{81} +(-9.79856 - 14.3718i) q^{82} +(14.9414 + 2.25206i) q^{83} +(-16.9980 + 0.537853i) q^{84} +(4.30848 - 0.649399i) q^{85} +(-9.72272 - 10.4786i) q^{86} +(-12.7617 - 2.73066i) q^{87} +(17.5742 - 11.9819i) q^{88} +(2.61883 + 6.67267i) q^{89} +(4.39422 - 15.7555i) q^{90} +(-1.59738 - 0.334417i) q^{91} +(-2.31553 + 0.173525i) q^{92} +(4.67427 + 6.65940i) q^{93} +(-5.83166 - 1.33104i) q^{94} +(-5.19151 - 10.7803i) q^{95} +(2.97374 - 3.29369i) q^{96} +(10.2826 - 5.93664i) q^{97} +(16.7160 + 0.648019i) q^{98} +(-15.3021 - 3.05713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9}+O(q^{10}) \) 648 * q - 21 * q^2 - 11 * q^3 + 99 * q^4 - 18 * q^5 - 34 * q^6 - 5 * q^7 - 23 * q^9	\( 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9} - 22 q^{10} - 18 q^{11} - 72 q^{12} - 4 q^{13} + 66 q^{14} - 10 q^{15} - 105 q^{16} - 9 q^{17} - 27 q^{18} - 36 q^{19} - 27 q^{20} - 11 q^{21} - 9 q^{22} - 27 q^{23} - 8 q^{24} + 38 q^{25} + 6 q^{26} - 29 q^{27} - 26 q^{28} + 3 q^{29} - 16 q^{30} - 21 q^{32} - 11 q^{33} - 13 q^{34} + 28 q^{36} - 13 q^{37} - 90 q^{38} - 15 q^{39} - 31 q^{40} - 27 q^{41} - 4 q^{42} - 9 q^{43} + 51 q^{44} - 11 q^{45} - 108 q^{46} + 75 q^{47} - 15 q^{48} - 13 q^{49} - 45 q^{50} - 38 q^{51} + 64 q^{52} - 12 q^{53} - 41 q^{54} + 14 q^{55} + 3 q^{56} - 7 q^{57} - 90 q^{58} + 15 q^{59} - 69 q^{60} - 56 q^{61} + 66 q^{62} + 13 q^{63} + 64 q^{64} - 21 q^{65} - 204 q^{66} - 26 q^{67} + 3 q^{68} + 58 q^{69} - 22 q^{70} - 63 q^{71} - 18 q^{72} - 22 q^{73} - 12 q^{74} + 118 q^{75} - 63 q^{76} - 69 q^{77} - 147 q^{78} - 2 q^{79} - 45 q^{80} + 29 q^{81} - 28 q^{82} - 51 q^{83} - 31 q^{84} - 10 q^{85} - 72 q^{86} - 67 q^{87} + 4 q^{88} + 132 q^{89} + 58 q^{90} - 13 q^{91} - 15 q^{92} + 217 q^{93} - 7 q^{94} - 21 q^{95} - 44 q^{96} + 3 q^{97} + 21 q^{98} - 148 q^{99}+O(q^{100}) \) 648 * q - 21 * q^2 - 11 * q^3 + 99 * q^4 - 18 * q^5 - 34 * q^6 - 5 * q^7 - 23 * q^9 - 22 * q^10 - 18 * q^11 - 72 * q^12 - 4 * q^13 + 66 * q^14 - 10 * q^15 - 105 * q^16 - 9 * q^17 - 27 * q^18 - 36 * q^19 - 27 * q^20 - 11 * q^21 - 9 * q^22 - 27 * q^23 - 8 * q^24 + 38 * q^25 + 6 * q^26 - 29 * q^27 - 26 * q^28 + 3 * q^29 - 16 * q^30 - 21 * q^32 - 11 * q^33 - 13 * q^34 + 28 * q^36 - 13 * q^37 - 90 * q^38 - 15 * q^39 - 31 * q^40 - 27 * q^41 - 4 * q^42 - 9 * q^43 + 51 * q^44 - 11 * q^45 - 108 * q^46 + 75 * q^47 - 15 * q^48 - 13 * q^49 - 45 * q^50 - 38 * q^51 + 64 * q^52 - 12 * q^53 - 41 * q^54 + 14 * q^55 + 3 * q^56 - 7 * q^57 - 90 * q^58 + 15 * q^59 - 69 * q^60 - 56 * q^61 + 66 * q^62 + 13 * q^63 + 64 * q^64 - 21 * q^65 - 204 * q^66 - 26 * q^67 + 3 * q^68 + 58 * q^69 - 22 * q^70 - 63 * q^71 - 18 * q^72 - 22 * q^73 - 12 * q^74 + 118 * q^75 - 63 * q^76 - 69 * q^77 - 147 * q^78 - 2 * q^79 - 45 * q^80 + 29 * q^81 - 28 * q^82 - 51 * q^83 - 31 * q^84 - 10 * q^85 - 72 * q^86 - 67 * q^87 + 4 * q^88 + 132 * q^89 + 58 * q^90 - 13 * q^91 - 15 * q^92 + 217 * q^93 - 7 * q^94 - 21 * q^95 - 44 * q^96 + 3 * q^97 + 21 * q^98 - 148 * q^99

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