LMFDB - Embedded newform 483.2.y.a.25.14

Newspace parameters

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.y (of order $33$, degree $20$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.14
Character	$\chi$	$=$	483.25
Dual form			483.2.y.a.58.14

$q$-expansion

$f(q)$	$=$	$q+(0.0924412 - 1.94058i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-1.76636 - 0.168667i) q^{4} +(0.940033 + 3.87487i) q^{5} +(-0.807060 + 1.76721i) q^{6} +(-1.58926 - 2.11524i) q^{7} +(0.0623778 - 0.433847i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(0.0924412 - 1.94058i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-1.76636 - 0.168667i) q^{4} +(0.940033 + 3.87487i) q^{5} +(-0.807060 + 1.76721i) q^{6} +(-1.58926 - 2.11524i) q^{7} +(0.0623778 - 0.433847i) q^{8} +(0.723734 + 0.690079i) q^{9} +(7.60638 - 1.46601i) q^{10} +(-0.161604 - 3.39248i) q^{11} +(1.57714 + 0.813073i) q^{12} +(-2.43028 - 2.80470i) q^{13} +(-4.25171 + 2.88855i) q^{14} +(0.567447 - 3.94668i) q^{15} +(-4.32080 - 0.832766i) q^{16} +(-1.66660 - 2.34041i) q^{17} +(1.40606 - 1.34067i) q^{18} +(2.81544 - 3.95373i) q^{19} +(-1.00687 - 7.00295i) q^{20} +(0.689263 + 2.55439i) q^{21} -6.59831 q^{22} +(0.0390912 - 4.79567i) q^{23} +(-0.219154 + 0.379586i) q^{24} +(-9.68676 + 4.99387i) q^{25} +(-5.66739 + 4.45689i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(2.45043 + 4.00433i) q^{28} +(3.14457 - 6.88565i) q^{29} +(-7.60638 - 1.46601i) q^{30} +(5.49009 + 4.31745i) q^{31} +(-1.80880 + 7.45596i) q^{32} +(-1.11083 + 3.20953i) q^{33} +(-4.69582 + 3.01782i) q^{34} +(6.70232 - 8.14657i) q^{35} +(-1.16198 - 1.34100i) q^{36} +(-4.04011 - 3.85224i) q^{37} +(-7.41226 - 5.82907i) q^{38} +(1.21380 + 3.50703i) q^{39} +(1.73974 - 0.166125i) q^{40} +(8.04593 + 2.36250i) q^{41} +(5.02071 - 1.10144i) q^{42} +(0.792764 + 5.51379i) q^{43} +(-0.286748 + 6.01959i) q^{44} +(-1.99363 + 3.45307i) q^{45} +(-9.30277 - 0.519177i) q^{46} +(1.81624 + 3.14583i) q^{47} +(3.70178 + 2.37899i) q^{48} +(-1.94850 + 6.72334i) q^{49} +(8.79554 + 19.2596i) q^{50} +(0.677375 + 2.79218i) q^{51} +(3.81969 + 5.36400i) q^{52} +(1.16363 + 3.36210i) q^{53} +(-1.80361 + 0.722058i) q^{54} +(12.9935 - 3.81523i) q^{55} +(-1.01683 + 0.557552i) q^{56} +(-4.08322 + 2.62412i) q^{57} +(-13.0715 - 6.73881i) q^{58} +(7.25656 - 1.39859i) q^{59} +(-1.66799 + 6.87553i) q^{60} +(-10.0672 + 4.03031i) q^{61} +(8.88587 - 10.2548i) q^{62} +(0.309482 - 2.62759i) q^{63} +(5.85752 + 1.71992i) q^{64} +(8.58328 - 12.0535i) q^{65} +(6.12566 + 2.45235i) q^{66} +(-6.11412 + 3.15205i) q^{67} +(2.54906 + 4.41511i) q^{68} +(-1.81866 + 4.43762i) q^{69} +(-15.1895 - 13.7595i) q^{70} +(-1.06578 - 0.684937i) q^{71} +(0.344534 - 0.270944i) q^{72} +(-10.8644 - 1.03742i) q^{73} +(-7.84904 + 7.48405i) q^{74} +(10.8489 - 1.03595i) q^{75} +(-5.63993 + 6.50883i) q^{76} +(-6.91909 + 5.73337i) q^{77} +(6.91788 - 2.03127i) q^{78} +(1.62220 - 4.68704i) q^{79} +(-0.834835 - 17.5253i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(5.32839 - 15.3954i) q^{82} +(4.29313 - 1.26058i) q^{83} +(-0.786644 - 4.62822i) q^{84} +(7.50214 - 8.65793i) q^{85} +(10.7732 - 1.02872i) q^{86} +(-5.47846 + 5.22370i) q^{87} +(-1.48190 - 0.141504i) q^{88} +(3.11101 - 2.44652i) q^{89} +(6.51666 + 4.18800i) q^{90} +(-2.07026 + 9.59803i) q^{91} +(-0.877919 + 8.46427i) q^{92} +(-3.49219 - 6.04865i) q^{93} +(6.27262 - 3.23376i) q^{94} +(17.9668 + 7.19282i) q^{95} +(4.45033 - 6.24961i) q^{96} +(10.1814 + 2.98952i) q^{97} +(12.8671 + 4.40273i) q^{98} +(2.22412 - 2.56677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21} - 176 q^{22} - 18 q^{23} - 6 q^{24} + 8 q^{25} - 14 q^{26} + 32 q^{27} + 46 q^{28} + 34 q^{29} - 8 q^{30} + 52 q^{31} - 8 q^{32} - 5 q^{33} - 24 q^{34} - 12 q^{35} - 14 q^{36} - 30 q^{37} - 157 q^{38} + 88 q^{40} - 28 q^{41} - 45 q^{42} + 64 q^{43} - 71 q^{44} - 2 q^{45} + 4 q^{46} + 36 q^{47} + 60 q^{48} + 28 q^{49} + 210 q^{50} - 26 q^{51} - 198 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{55} + 44 q^{57} + 31 q^{58} + 10 q^{59} - 2 q^{60} - 34 q^{61} - 8 q^{62} + 2 q^{63} + 84 q^{64} + 38 q^{65} - 12 q^{67} - 22 q^{68} + 8 q^{69} - 336 q^{70} - 144 q^{71} + 6 q^{72} - 16 q^{73} - 68 q^{74} - 30 q^{75} + 8 q^{76} + 98 q^{77} + 16 q^{78} + 26 q^{79} + 225 q^{80} + 16 q^{81} - 122 q^{82} + 44 q^{84} - 240 q^{85} - 26 q^{86} - 16 q^{87} + 43 q^{88} + 68 q^{89} - 16 q^{90} + 40 q^{91} - 222 q^{92} - 8 q^{93} + 137 q^{94} - 49 q^{95} + 30 q^{96} - 8 q^{97} + 137 q^{98} - 10 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	0.0924412	−	1.94058i	0.0653658	−	1.37220i	−0.693268	−	0.720679i	$-0.743830\pi$
$2$	0.0924412	−	1.94058i	0.0653658	−	1.37220i	0.758634	−	0.651517i	$-0.225867\pi$
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−1.76636	−	0.168667i	−0.883178	−	0.0843333i
$5$	0.940033	+	3.87487i	0.420395	+	1.73289i	0.650298	+	0.759680i	$0.274644\pi$
$5$	0.940033	+	3.87487i	0.420395	+	1.73289i	−0.229902	+	0.973214i	$0.573841\pi$
$6$	−0.807060	+	1.76721i	−0.329481	+	0.721462i
$7$	−1.58926	−	2.11524i	−0.600684	−	0.799486i
$7$	−1.58926	−	2.11524i	−0.600684	−	0.799486i
$8$	0.0623778	−	0.433847i	0.0220539	−	0.153388i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	7.60638	−	1.46601i	2.40535	−	0.463593i
$11$	−0.161604	−	3.39248i	−0.0487254	−	1.02287i	−0.882366	−	0.470564i	$-0.844051\pi$
$11$	−0.161604	−	3.39248i	−0.0487254	−	1.02287i	0.833641	−	0.552307i	$-0.186253\pi$
$12$	1.57714	+	0.813073i	0.455282	+	0.234714i
$13$	−2.43028	−	2.80470i	−0.674039	−	0.777883i	0.310963	−	0.950422i	$-0.399348\pi$
$13$	−2.43028	−	2.80470i	−0.674039	−	0.777883i	−0.985003	+	0.172539i	$0.944803\pi$
$14$	−4.25171	+	2.88855i	−1.13632	+	0.771998i
$15$	0.567447	−	3.94668i	0.146514	−	1.01903i
$16$	−4.32080	−	0.832766i	−1.08020	−	0.208191i
$17$	−1.66660	−	2.34041i	−0.404210	−	0.567634i	0.561427	−	0.827526i	$-0.310252\pi$
$17$	−1.66660	−	2.34041i	−0.404210	−	0.567634i	−0.965638	+	0.259892i	$0.916313\pi$
$18$	1.40606	−	1.34067i	0.331410	−	0.315999i
$19$	2.81544	−	3.95373i	0.645906	−	0.907048i	−0.353693	−	0.935362i	$-0.615074\pi$
$19$	2.81544	−	3.95373i	0.645906	−	0.907048i	0.999599	+	0.0283135i	$0.00901367\pi$
$20$	−1.00687	−	7.00295i	−0.225143	−	1.56591i
$21$	0.689263	+	2.55439i	0.150410	+	0.557414i
$22$	−6.59831			−1.40677
$23$	0.0390912	−	4.79567i	0.00815108	−	0.999967i
$23$	0.0390912	−	4.79567i	0.00815108	−	0.999967i
$24$	−0.219154	+	0.379586i	−0.0447347	+	0.0774827i
$25$	−9.68676	+	4.99387i	−1.93735	+	0.998774i
$26$	−5.66739	+	4.45689i	−1.11147	+	0.874067i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	2.45043	+	4.00433i	0.463088	+	0.756747i
$29$	3.14457	−	6.88565i	0.583932	−	1.27863i	−0.355108	−	0.934825i	$-0.615556\pi$
$29$	3.14457	−	6.88565i	0.583932	−	1.27863i	0.939040	−	0.343808i	$-0.111717\pi$
$30$	−7.60638	−	1.46601i	−1.38873	−	0.267656i
$31$	5.49009	+	4.31745i	0.986049	+	0.775438i	0.974475	−	0.224495i	$-0.0720733\pi$
$31$	5.49009	+	4.31745i	0.986049	+	0.775438i	0.0115741	+	0.999933i	$0.496316\pi$
$32$	−1.80880	+	7.45596i	−0.319753	+	1.31804i
$33$	−1.11083	+	3.20953i	−0.193371	+	0.558708i
$34$	−4.69582	+	3.01782i	−0.805327	+	0.517552i
$35$	6.70232	−	8.14657i	1.13290	−	1.37702i
$36$	−1.16198	−	1.34100i	−0.193663	−	0.223499i
$37$	−4.04011	−	3.85224i	−0.664190	−	0.633304i	0.281045	−	0.959695i	$-0.409319\pi$
$37$	−4.04011	−	3.85224i	−0.664190	−	0.633304i	−0.945235	+	0.326391i	$0.894168\pi$
$38$	−7.41226	−	5.82907i	−1.20243	−	0.945600i
$39$	1.21380	+	3.50703i	0.194363	+	0.561575i
$40$	1.73974	−	0.166125i	0.275077	−	0.0262666i
$41$	8.04593	+	2.36250i	1.25656	+	0.368960i	0.841214	−	0.540702i	$-0.181841\pi$
$41$	8.04593	+	2.36250i	1.25656	+	0.368960i	0.415349	+	0.909662i	$0.363660\pi$
$42$	5.02071	−	1.10144i	0.774713	−	0.169956i
$43$	0.792764	+	5.51379i	0.120895	+	0.840846i	0.956545	+	0.291583i	$0.0941821\pi$
$43$	0.792764	+	5.51379i	0.120895	+	0.840846i	−0.835650	+	0.549262i	$0.814909\pi$
$44$	−0.286748	+	6.01959i	−0.0432289	+	0.907487i
$45$	−1.99363	+	3.45307i	−0.297193	+	0.514753i
$46$	−9.30277	−	0.519177i	−1.37162	−	0.0765485i
$47$	1.81624	+	3.14583i	0.264926	+	0.458866i	0.967544	−	0.252701i	$-0.0813190\pi$
$47$	1.81624	+	3.14583i	0.264926	+	0.458866i	−0.702618	+	0.711567i	$0.747986\pi$
$48$	3.70178	+	2.37899i	0.534306	+	0.343378i
$49$	−1.94850	+	6.72334i	−0.278357	+	0.960478i
$50$	8.79554	+	19.2596i	1.24388	+	2.72371i
$51$	0.677375	+	2.79218i	0.0948515	+	0.390983i
$52$	3.81969	+	5.36400i	0.529695	+	0.743853i
$53$	1.16363	+	3.36210i	0.159837	+	0.461819i	0.996274	−	0.0862440i	$-0.0274865\pi$
$53$	1.16363	+	3.36210i	0.159837	+	0.461819i	−0.836437	+	0.548063i	$0.815365\pi$
$54$	−1.80361	+	0.722058i	−0.245441	+	0.0982597i
$55$	12.9935	−	3.81523i	1.75204	−	0.514446i
$56$	−1.01683	+	0.557552i	−0.135879	+	0.0745061i
$57$	−4.08322	+	2.62412i	−0.540835	+	0.347574i
$58$	−13.0715	−	6.73881i	−1.71637	−	0.884849i
$59$	7.25656	−	1.39859i	0.944724	−	0.182081i	0.306447	−	0.951888i	$-0.400860\pi$
$59$	7.25656	−	1.39859i	0.944724	−	0.182081i	0.638277	+	0.769807i	$0.279648\pi$
$60$	−1.66799	+	6.87553i	−0.215336	+	0.887627i
$61$	−10.0672	+	4.03031i	−1.28898	+	0.516029i	−0.911999	−	0.410193i	$-0.865461\pi$
$61$	−10.0672	+	4.03031i	−1.28898	+	0.516029i	−0.376979	+	0.926222i	$0.623037\pi$
$62$	8.88587	−	10.2548i	1.12851	−	1.30237i
$63$	0.309482	−	2.62759i	0.0389910	−	0.331045i
$64$	5.85752	+	1.71992i	0.732191	+	0.214991i
$65$	8.58328	−	12.0535i	1.06462	−	1.49506i
$66$	6.12566	+	2.45235i	0.754017	+	0.301863i
$67$	−6.11412	+	3.15205i	−0.746959	+	0.385084i	−0.789291	−	0.614020i	$-0.789552\pi$
$67$	−6.11412	+	3.15205i	−0.746959	+	0.385084i	0.0423321	+	0.999104i	$0.486521\pi$
$68$	2.54906	+	4.41511i	0.309119	+	0.535410i
$69$	−1.81866	+	4.43762i	−0.218941	+	0.534227i
$70$	−15.1895	−	13.7595i	−1.81549	−	1.64457i
$71$	−1.06578	−	0.684937i	−0.126485	−	0.0812870i	0.475868	−	0.879516i	$-0.342134\pi$
$71$	−1.06578	−	0.684937i	−0.126485	−	0.0812870i	−0.602353	+	0.798229i	$0.705770\pi$
$72$	0.344534	−	0.270944i	0.0406037	−	0.0319311i
$73$	−10.8644	−	1.03742i	−1.27158	−	0.121421i	−0.562648	−	0.826696i	$-0.690217\pi$
$73$	−10.8644	−	1.03742i	−1.27158	−	0.121421i	−0.708934	+	0.705275i	$0.750823\pi$
$74$	−7.84904	+	7.48405i	−0.912433	+	0.870003i
$75$	10.8489	−	1.03595i	1.25272	−	0.119621i
$76$	−5.63993	+	6.50883i	−0.646944	+	0.746614i
$77$	−6.91909	+	5.73337i	−0.788503	+	0.653378i
$78$	6.91788	−	2.03127i	0.783296	−	0.229996i
$79$	1.62220	−	4.68704i	0.182512	−	0.527333i	−0.816217	−	0.577746i	$-0.803933\pi$
$79$	1.62220	−	4.68704i	0.182512	−	0.527333i	0.998728	+	0.0504129i	$0.0160537\pi$
$80$	−0.834835	−	17.5253i	−0.0933374	−	1.95939i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	5.32839	−	15.3954i	0.588422	−	1.70013i
$83$	4.29313	−	1.26058i	0.471232	−	0.138366i	−0.0374898	−	0.999297i	$-0.511936\pi$
$83$	4.29313	−	1.26058i	0.471232	−	0.138366i	0.508722	+	0.860931i	$0.330118\pi$
$84$	−0.786644	−	4.62822i	−0.0858299	−	0.504980i
$85$	7.50214	−	8.65793i	0.813721	−	0.939084i
$86$	10.7732	−	1.02872i	1.16171	−	0.110930i
$87$	−5.47846	+	5.22370i	−0.587352	+	0.560039i
$88$	−1.48190	−	0.141504i	−0.157971	−	0.0150844i
$89$	3.11101	−	2.44652i	0.329766	−	0.259331i	−0.439524	−	0.898231i	$-0.644853\pi$
$89$	3.11101	−	2.44652i	0.329766	−	0.259331i	0.769290	+	0.638900i	$0.220610\pi$
$90$	6.51666	+	4.18800i	0.686916	+	0.441454i
$91$	−2.07026	+	9.59803i	−0.217022	+	1.00615i
$92$	−0.877919	+	8.46427i	−0.0915293	+	0.882461i
$93$	−3.49219	−	6.04865i	−0.362123	−	0.627215i
$94$	6.27262	−	3.23376i	0.646971	−	0.333537i
$95$	17.9668	+	7.19282i	1.84335	+	0.737967i
$96$	4.45033	−	6.24961i	0.454210	−	0.637849i
$97$	10.1814	+	2.98952i	1.03376	+	0.303540i	0.754239	−	0.656600i	$-0.228006\pi$
$97$	10.1814	+	2.98952i	1.03376	+	0.303540i	0.279522	+	0.960139i	$0.409824\pi$
$98$	12.8671	+	4.40273i	1.29977	+	0.444743i
$99$	2.22412	−	2.56677i	0.223533	−	0.257970i
$100$	17.9526	−	7.18712i	1.79526	−	0.718712i
$101$	0.214122	−	0.882621i	0.0213059	−	0.0878241i	−0.960166	−	0.279430i	$-0.909854\pi$
$101$	0.214122	−	0.882621i	0.0213059	−	0.0878241i	0.981472	+	0.191606i	$0.0613696\pi$
$102$	5.48106	−	1.05639i	0.542706	−	0.104598i
$103$	−13.5010	−	6.96024i	−1.33029	−	0.685813i	−0.361194	−	0.932491i	$-0.617631\pi$
$103$	−13.5010	−	6.96024i	−1.33029	−	0.685813i	−0.969098	+	0.246677i	$0.920661\pi$
$104$	−1.36841	+	0.879421i	−0.134183	+	0.0862343i
$105$	−9.25000	+	5.07201i	−0.902707	+	0.494978i
$106$	6.63198	−	1.94732i	0.644155	−	0.189141i
$107$	5.51288	−	2.20702i	0.532950	−	0.213361i	−0.0895480	−	0.995983i	$-0.528542\pi$
$107$	5.51288	−	2.20702i	0.532950	−	0.213361i	0.622498	+	0.782622i	$0.286118\pi$
$108$	0.580346	+	1.67680i	0.0558439	+	0.161350i
$109$	9.25195	+	12.9925i	0.886176	+	1.24446i	0.968791	+	0.247879i	$0.0797334\pi$
$109$	9.25195	+	12.9925i	0.886176	+	1.24446i	−0.0826151	+	0.996582i	$0.526327\pi$
$110$	−6.20263	−	25.5676i	−0.591398	−	2.43777i
$111$	2.31898	+	5.07785i	0.220108	+	0.481968i
$112$	5.10538	+	10.4630i	0.482413	+	0.988662i
$113$	−15.4901	−	9.95487i	−1.45718	−	0.936475i	−0.998862	−	0.0476886i	$-0.984814\pi$
$113$	−15.4901	−	9.95487i	−1.45718	−	0.936475i	−0.458321	−	0.888786i	$-0.651549\pi$
$114$	4.71486	+	8.16638i	0.441587	+	0.764852i
$115$	18.6193	−	4.35661i	1.73626	−	0.406256i
$116$	−6.71581	+	11.6321i	−0.623548	+	1.08002i
$117$	0.176583	−	3.70694i	0.0163251	−	0.342707i
$118$	−2.04326	−	14.2112i	−0.188098	−	1.30825i
$119$	−2.30188	+	7.24480i	−0.211013	+	0.664129i
$120$	−1.67686	−	0.492370i	−0.153076	−	0.0449470i
$121$	−0.532614	+	0.0508584i	−0.0484194	+	0.00462349i
$122$	6.89052	+	19.9088i	0.623838	+	1.80246i
$123$	−6.59153	−	5.18364i	−0.594338	−	0.467393i
$124$	−8.96925	−	8.55216i	−0.805462	−	0.768007i
$125$	−15.4009	−	17.7736i	−1.37750	−	1.58972i
$126$	−5.07043	−	0.843471i	−0.451710	−	0.0751424i
$127$	6.95635	−	4.47057i	0.617276	−	0.396699i	−0.194303	−	0.980942i	$-0.562245\pi$
$127$	6.95635	−	4.47057i	0.617276	−	0.396699i	0.811579	+	0.584242i	$0.198608\pi$
$128$	−1.13956	+	3.29253i	−0.100724	+	0.291022i
$129$	1.31329	−	5.41347i	0.115629	−	0.476629i
$130$	−22.5974	−	17.7708i	−1.98192	−	1.55860i
$131$	−8.19382	−	1.57923i	−0.715897	−	0.137978i	−0.181720	−	0.983350i	$-0.558166\pi$
$131$	−8.19382	−	1.57923i	−0.715897	−	0.137978i	−0.534177	+	0.845372i	$0.679379\pi$
$132$	2.50346	−	5.48182i	0.217898	−	0.477131i
$133$	−12.8376	+	0.328176i	−1.11316	+	0.0284565i
$134$	5.55160	+	12.1563i	0.479585	+	1.05015i
$135$	3.13420	−	2.46476i	0.269749	−	0.212133i
$136$	−1.11934	+	0.577061i	−0.0959827	+	0.0494825i
$137$	−1.28960	+	2.23365i	−0.110178	+	0.190833i	−0.915842	−	0.401539i	$-0.868475\pi$
$137$	−1.28960	+	2.23365i	−0.110178	+	0.190833i	0.805664	+	0.592373i	$0.201809\pi$
$138$	8.44343	+	3.93948i	0.718753	+	0.335350i
$139$	−5.11214			−0.433606			−0.216803	−	0.976215i	$-0.569563\pi$
$139$	−5.11214			−0.433606			−0.216803	+	0.976215i	$0.569563\pi$
$140$	−13.2127	+	13.2593i	−1.11668	+	1.12061i
$141$	−0.516957	−	3.59551i	−0.0435356	−	0.302797i
$142$	−1.42770	+	2.00492i	−0.119810	+	0.168249i
$143$	−9.12213	+	8.69794i	−0.762831	+	0.727358i
$144$	−2.55244	−	3.58439i	−0.212703	−	0.298699i
$145$	29.6370	+	5.71206i	2.46122	+	0.474361i
$146$	−3.01752	+	20.9873i	−0.249732	+	1.73692i
$147$	4.30774	−	5.51755i	0.355296	−	0.455080i
$148$	6.48653	+	7.48586i	0.533190	+	0.615334i
$149$	1.17307	+	0.604762i	0.0961020	+	0.0495440i	0.505607	−	0.862764i	$-0.331268\pi$
$149$	1.17307	+	0.604762i	0.0961020	+	0.0495440i	−0.409505	+	0.912308i	$0.634299\pi$
$150$	−1.00745	−	21.1489i	−0.0822577	−	1.72680i
$151$	13.8443	−	2.66826i	1.12663	−	0.217140i	0.408304	−	0.912846i	$-0.366120\pi$
$151$	13.8443	−	2.66826i	1.12663	−	0.217140i	0.718327	+	0.695706i	$0.244908\pi$
$152$	−1.53969	−	1.46810i	−0.124886	−	0.119078i
$153$	0.408895	−	2.84393i	0.0330572	−	0.229918i
$154$	10.4864	+	13.9570i	0.845022	+	1.12469i
$155$	−11.5687	+	25.3319i	−0.929220	+	2.03471i
$156$	−1.55248	−	6.39940i	−0.124298	−	0.512362i
$157$	14.8901	+	1.42183i	1.18836	+	0.113475i	0.670446	−	0.741958i	$-0.266103\pi$
$157$	14.8901	+	1.42183i	1.18836	+	0.113475i	0.517914	+	0.855433i	$0.326709\pi$
$158$	−8.94561	−	3.58128i	−0.711674	−	0.284911i
$159$	0.169286	−	3.55374i	0.0134252	−	0.281830i
$160$	−30.5912			−2.41845
$161$	−10.2061	+	7.53889i	−0.804356	+	0.594148i
$162$	1.94278			0.152639
$163$	−0.289952	+	6.08684i	−0.0227108	+	0.476758i	0.958650	+	0.284586i	$0.0918562\pi$
$163$	−0.289952	+	6.08684i	−0.0227108	+	0.476758i	−0.981361	+	0.192172i	$0.938447\pi$
$164$	−13.8135	−	5.53009i	−1.07865	−	0.431828i
$165$	−13.4807	−	1.28725i	−1.04947	−	0.100213i
$166$	−2.04939	−	8.44769i	−0.159063	−	0.655668i
$167$	1.60797	−	3.52096i	0.124428	−	0.272460i	−0.837159	−	0.546960i	$-0.815785\pi$
$167$	1.60797	−	3.52096i	0.124428	−	0.272460i	0.961587	+	0.274500i	$0.0885123\pi$
$168$	1.15121	−	0.139698i	0.0888178	−	0.0107779i
$169$	−0.109952	+	0.764732i	−0.00845784	+	0.0588256i
$170$	−16.1079	−	15.3588i	−1.23542	−	1.17797i
$171$	4.76602	−	0.918574i	0.364466	−	0.0702451i
$172$	−0.470311	−	9.87304i	−0.0358609	−	0.752812i
$173$	13.8639	+	7.14734i	1.05405	+	0.543402i	0.896012	−	0.444030i	$-0.146452\pi$
$173$	13.8639	+	7.14734i	1.05405	+	0.543402i	0.158041	+	0.987433i	$0.449482\pi$
$174$	9.63056	+	11.1143i	0.730091	+	0.842570i
$175$	25.9580	+	12.5533i	1.96224	+	0.948938i
$176$	−2.12688	+	14.7928i	−0.160320	+	1.11505i
$177$	−7.25656	−	1.39859i	−0.545436	−	0.105124i
$178$	−4.46009	−	6.26331i	−0.334298	−	0.469455i
$179$	18.3653	−	17.5113i	1.37269	−	1.30886i	0.467409	−	0.884041i	$-0.345187\pi$
$179$	18.3653	−	17.5113i	1.37269	−	1.30886i	0.905280	−	0.424816i	$-0.139661\pi$
$180$	4.10388	−	5.76309i	0.305885	−	0.429556i
$181$	3.52978	+	24.5501i	0.262366	+	1.82480i	0.514948	+	0.857221i	$0.327811\pi$
$181$	3.52978	+	24.5501i	0.262366	+	1.82480i	−0.252582	+	0.967575i	$0.581280\pi$
$182$	18.4344	+	4.90475i	1.36645	+	0.363564i
$183$	10.8440			0.801613
$184$	−2.07815	−	0.316103i	−0.153203	−	0.0233034i
$185$	11.1291	−	19.2761i	0.818226	−	1.41721i
$186$	−12.0607	+	6.21772i	−0.884333	+	0.455905i
$187$	−7.67048	+	6.03213i	−0.560921	+	0.441113i
$188$	−2.67754	−	5.86299i	−0.195280	−	0.427602i
$189$	−1.26389	+	2.32435i	−0.0919344	+	0.169071i
$190$	15.6191	−	34.2010i	1.13313	−	2.48120i
$191$	−3.95014	−	0.761328i	−0.285822	−	0.0550877i	0.0443249	−	0.999017i	$-0.485886\pi$
$191$	−3.95014	−	0.761328i	−0.285822	−	0.0550877i	−0.330147	+	0.943929i	$0.607098\pi$
$192$	−4.79871	−	3.77374i	−0.346317	−	0.272347i
$193$	1.15624	−	4.76607i	0.0832276	−	0.343069i	−0.914939	−	0.403592i	$-0.867762\pi$
$193$	1.15624	−	4.76607i	0.0832276	−	0.343069i	0.998167	+	0.0605227i	$0.0192768\pi$
$194$	6.74258	−	19.4814i	0.484089	−	1.39868i
$195$	−12.4483	+	8.00003i	−0.891440	+	0.572894i
$196$	4.57574	−	11.5472i	0.326839	−	0.824798i
$197$	17.6086	+	20.3214i	1.25456	+	1.44784i	0.844298	+	0.535874i	$0.180018\pi$
$197$	17.6086	+	20.3214i	1.25456	+	1.44784i	0.410264	+	0.911967i	$0.365437\pi$
$198$	−4.77542	−	4.55336i	−0.339375	−	0.323593i
$199$	−3.66118	−	2.87918i	−0.259534	−	0.204100i	0.479910	−	0.877318i	$-0.340669\pi$
$199$	−3.66118	−	2.87918i	−0.259534	−	0.204100i	−0.739444	+	0.673218i	$0.764912\pi$
$200$	1.56234	+	4.51408i	0.110474	+	0.319194i
$201$	6.84765	−	0.653871i	0.482996	−	0.0461205i
$202$	−1.69300	−	0.497110i	−0.119119	−	0.0349766i
$203$	−19.5624	+	4.29157i	−1.37301	+	0.301209i
$204$	−0.725539	−	5.04623i	−0.0507979	−	0.353307i
$205$	−1.59093	+	33.3977i	−0.111115	+	2.33260i
$206$	−14.7549	+	25.5563i	−1.02803	+	1.78059i
$207$	3.33768	−	3.44382i	0.231985	−	0.239362i
$208$	8.16511	+	14.1424i	0.566149	+	0.980598i
$209$	−13.8679	−	8.91238i	−0.959265	−	0.616482i
$210$	8.98756	+	18.4192i	0.620201	+	1.27105i
$211$	−4.48777	−	9.82684i	−0.308951	−	0.676508i	0.689927	−	0.723879i	$-0.257643\pi$
$211$	−4.48777	−	9.82684i	−0.308951	−	0.676508i	−0.998877	+	0.0473715i	$0.984916\pi$
$212$	−1.48832	−	6.13493i	−0.102218	−	0.421348i
$213$	0.734873	+	1.03198i	0.0503527	+	0.0707104i
$214$	−3.77328	−	10.9022i	−0.257936	−	0.745258i
$215$	−20.6200	+	8.25500i	−1.40627	+	0.562986i
$216$	−0.420554	+	0.123486i	−0.0286151	+	0.00840214i
$217$	0.407274	−	18.4744i	0.0276475	−	1.25413i
$218$	26.0683	−	16.7531i	1.76557	−	1.13466i
$219$	9.70059	+	5.00100i	0.655505	+	0.337936i
$220$	−23.5946	+	4.54750i	−1.59075	+	0.306592i
$221$	−2.51384	+	10.3622i	−0.169099	+	0.697036i
$222$	10.0683	−	4.03075i	0.675743	−	0.270527i
$223$	9.00754	−	10.3953i	0.603189	−	0.696117i	−0.369235	−	0.929336i	$-0.620380\pi$
$223$	9.00754	−	10.3953i	0.603189	−	0.696117i	0.972424	+	0.233219i	$0.0749257\pi$
$224$	18.6458	−	8.02343i	1.24583	−	0.536088i
$225$	−10.4568	−	3.07039i	−0.697120	−	0.204693i
$226$	−20.7501	+	29.1395i	−1.38028	+	1.93833i
$227$	9.06406	+	3.62870i	0.601603	+	0.240845i	0.652414	−	0.757863i	$-0.273756\pi$
$227$	9.06406	+	3.62870i	0.601603	+	0.240845i	−0.0508112	+	0.998708i	$0.516181\pi$
$228$	7.65502	−	3.94644i	0.506966	−	0.261359i
$229$	−7.52223	−	13.0289i	−0.497083	−	0.860973i	0.502911	−	0.864338i	$-0.332262\pi$
$229$	−7.52223	−	13.0289i	−0.497083	−	0.860973i	−0.999994	+	0.00336494i	$0.998929\pi$
$230$	−6.73316	−	36.5350i	−0.443971	−	2.40905i
$231$	8.55433	−	2.75111i	0.562834	−	0.181010i
$232$	−2.79117	−	1.79378i	−0.183249	−	0.117767i
$233$	15.9820	−	12.5684i	1.04702	−	0.823382i	0.0623883	−	0.998052i	$-0.480128\pi$
$233$	15.9820	−	12.5684i	1.04702	−	0.823382i	0.984627	+	0.174670i	$0.0558859\pi$
$234$	−7.17729	−	0.685348i	−0.469194	−	0.0448026i
$235$	−10.4823	+	9.99488i	−0.683792	+	0.651994i
$236$	−13.0536	+	1.24646i	−0.849715	+	0.0811379i
$237$	−3.24799	+	3.74838i	−0.210980	+	0.243484i
$238$	13.8463	+	5.13669i	0.897523	+	0.332962i
$239$	−2.42779	+	0.712865i	−0.157041	+	0.0461114i	−0.359308	−	0.933219i	$-0.616987\pi$
$239$	−2.42779	+	0.712865i	−0.157041	+	0.0461114i	0.202267	+	0.979330i	$0.435169\pi$
$240$	−5.73848	+	16.5802i	−0.370417	+	1.07025i
$241$	−0.578919	−	12.1530i	−0.0372914	−	0.782844i	−0.937626	−	0.347645i	$-0.886981\pi$
$241$	−0.578919	−	12.1530i	−0.0372914	−	0.782844i	0.900335	−	0.435198i	$-0.143322\pi$
$242$	0.0494594	+	1.03828i	0.00317937	+	0.0667432i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	18.4621	−	5.42096i	1.18192	−	0.347042i
$245$	−27.8837	−	1.23001i	−1.78143	−	0.0785822i
$246$	−10.6686	+	12.3122i	−0.680204	+	0.784997i
$247$	−17.9313	+	1.71223i	−1.14094	+	0.108947i
$248$	2.21558	−	2.11255i	0.140689	−	0.134147i
$249$	−4.45412	−	0.425316i	−0.282268	−	0.0269533i
$250$	−35.9148	+	28.2437i	−2.27145	+	1.78629i
$251$	15.1028	+	9.70600i	0.953283	+	0.612638i	0.922131	−	0.386877i	$-0.126446\pi$
$251$	15.1028	+	9.70600i	0.953283	+	0.612638i	0.0311514	+	0.999515i	$0.490083\pi$
$252$	−0.989841	+	4.58906i	−0.0623541	+	0.289084i
$253$	−16.2755	+	0.642382i	−1.02323	+	0.0403862i
$254$	−8.03245	−	13.9126i	−0.504001	−	0.872955i
$255$	−10.1826	+	5.24948i	−0.637657	+	0.328735i
$256$	17.6191	+	7.05362i	1.10119	+	0.440851i
$257$	2.65991	−	3.73533i	0.165921	−	0.233003i	−0.723241	−	0.690595i	$-0.757349\pi$
$257$	2.65991	−	3.73533i	0.165921	−	0.233003i	0.889162	+	0.457592i	$0.151288\pi$
$258$	−10.3839	−	3.04898i	−0.646471	−	0.189821i
$259$	−1.72762	+	14.6680i	−0.107349	+	0.911427i
$260$	−17.1942	+	19.8431i	−1.06634	+	1.23062i
$261$	7.02748	−	2.81338i	0.434990	−	0.174144i
$262$	−3.82207	+	15.7548i	−0.236128	+	0.973333i
$263$	−16.6471	+	3.20848i	−1.02651	+	0.197843i	−0.674594	−	0.738189i	$-0.735681\pi$
$263$	−16.6471	+	3.20848i	−1.02651	+	0.197843i	−0.351914	+	0.936032i	$0.614469\pi$
$264$	1.32316	+	0.682134i	0.0814346	+	0.0419824i
$265$	−11.9338	+	7.66940i	−0.733089	+	0.471128i
$266$	−0.549867	+	24.9426i	−0.0337145	+	1.52933i
$267$	−3.79744	+	1.11503i	−0.232400	+	0.0682387i
$268$	11.3314	−	4.53639i	0.692173	−	0.277104i
$269$	1.33105	+	3.84582i	0.0811557	+	0.234484i	0.978278	−	0.207299i	$-0.0664673\pi$
$269$	1.33105	+	3.84582i	0.0811557	+	0.234484i	−0.897122	+	0.441783i	$0.854346\pi$
$270$	−4.49333	−	6.31001i	−0.273456	−	0.384015i
$271$	−2.50489	−	10.3253i	−0.152161	−	0.627217i	−0.995900	−	0.0904625i	$-0.971165\pi$
$271$	−2.50489	−	10.3253i	−0.152161	−	0.627217i	0.843739	−	0.536754i	$-0.180350\pi$
$272$	5.25203	+	11.5004i	0.318451	+	0.697311i
$273$	5.48919	−	8.14107i	0.332221	−	0.492720i
$274$	4.21535	+	2.70904i	0.254659	+	0.163659i
$275$	18.5070	+	32.0551i	1.11602	+	1.93300i
$276$	3.96088	−	7.53167i	0.238417	−	0.453353i
$277$	0.662874	−	1.14813i	0.0398282	−	0.0689845i	−0.845424	−	0.534096i	$-0.820652\pi$
$277$	0.662874	−	1.14813i	0.0398282	−	0.0689845i	0.885252	+	0.465111i	$0.153986\pi$
$278$	−0.472572	+	9.92051i	−0.0283430	+	0.594993i
$279$	0.993980	+	6.91328i	0.0595080	+	0.413888i
$280$	−3.11629	−	3.41595i	−0.186234	−	0.204142i
$281$	−6.98789	−	2.05183i	−0.416862	−	0.122402i	0.0665737	−	0.997782i	$-0.478793\pi$
$281$	−6.98789	−	2.05183i	−0.416862	−	0.122402i	−0.483436	+	0.875380i	$0.660611\pi$
$282$	−7.02517	+	0.670822i	−0.418342	+	0.0399469i
$283$	3.10565	+	8.97318i	0.184612	+	0.533400i	0.998891	−	0.0470723i	$-0.0149891\pi$
$283$	3.10565	+	8.97318i	0.184612	+	0.533400i	−0.814280	+	0.580472i	$0.802868\pi$
$284$	1.76703	+	1.38960i	0.104854	+	0.0824578i
$285$	−14.0065	−	13.3552i	−0.829673	−	0.791091i
$286$	16.0358	+	18.5063i	0.948215	+	1.09430i
$287$	−7.78983	−	20.7737i	−0.459819	−	1.22623i
$288$	−6.45429	+	4.14792i	−0.380323	+	0.244419i
$289$	2.86018	−	8.26393i	0.168246	−	0.486114i
$290$	13.8244	−	56.9849i	0.811796	−	3.34627i
$291$	−8.34097	−	6.55941i	−0.488956	−	0.384519i
$292$	19.0154	+	3.66492i	1.11279	+	0.214473i
$293$	−3.52932	+	7.72813i	−0.206185	+	0.451482i	−0.984269	−	0.176678i	$-0.943465\pi$
$293$	−3.52932	+	7.72813i	−0.206185	+	0.451482i	0.778084	+	0.628161i	$0.216192\pi$
$294$	−10.3090	−	8.86955i	−0.601235	−	0.517283i
$295$	12.2407	+	26.8035i	0.712684	+	1.56056i
$296$	−1.92330	+	1.51250i	−0.111789	+	0.0879121i
$297$	−3.01878	+	1.55629i	−0.175167	+	0.0903049i
$298$	1.28203	−	2.22054i	0.0742659	−	0.128632i
$299$	−13.5454	+	11.5452i	−0.783351	+	0.667676i
$300$	−19.3378			−1.11647
$301$	10.4031	−	10.4397i	0.599625	−	0.601737i
$302$	−3.89820	−	27.1126i	−0.224316	−	1.56015i
$303$	−0.526821	+	0.739816i	−0.0302651	+	0.0425013i
$304$	−15.4575	+	14.7387i	−0.886547	+	0.845321i
$305$	−25.0805	−	35.2206i	−1.43610	−	2.01672i
$306$	−5.48106	−	1.05639i	−0.313331	−	0.0603897i
$307$	3.58381	−	24.9260i	0.204539	−	1.42260i	−0.586061	−	0.810267i	$-0.699322\pi$
$307$	3.58381	−	24.9260i	0.204539	−	1.42260i	0.790600	−	0.612333i	$-0.209769\pi$
$308$	13.1886	−	8.96015i	0.751490	−	0.510552i
$309$	9.94702	+	11.4795i	0.565866	+	0.653045i
$310$	48.0892	+	24.7917i	2.73128	+	1.40807i
$311$	0.978801	+	20.5476i	0.0555027	+	1.16515i	0.839136	+	0.543922i	$0.183061\pi$
$311$	0.978801	+	20.5476i	0.0555027	+	1.16515i	−0.783633	+	0.621224i	$0.786636\pi$
$312$	1.59723	−	0.307841i	0.0904254	−	0.0174281i
$313$	−12.2095	−	11.6417i	−0.690120	−	0.658029i	0.261536	−	0.965194i	$-0.415771\pi$
$313$	−12.2095	−	11.6417i	−0.690120	−	0.658029i	−0.951656	+	0.307165i	$0.900620\pi$
$314$	4.13564	−	28.7640i	0.233387	−	1.62325i
$315$	10.4725	−	1.27082i	0.590057	−	0.0716025i
$316$	−3.65593	+	8.00537i	−0.205662	+	0.450337i
$317$	0.154116	+	0.635276i	0.00865603	+	0.0356807i	0.975976	−	0.217879i	$-0.0699138\pi$
$317$	0.154116	+	0.635276i	0.00865603	+	0.0356807i	−0.967320	+	0.253560i	$0.918399\pi$
$318$	−6.88066	−	0.657024i	−0.385849	−	0.0368441i
$319$	−23.8676	−	9.55515i	−1.33633	−	0.534986i
$320$	−1.15821	+	24.3139i	−0.0647462	+	1.35919i
$321$	−5.93824			−0.331440
$322$	13.6863	+	20.5027i	0.762710	+	1.14257i
$323$	−13.9456			−0.775953
$324$	0.0844289	−	1.77238i	0.00469050	−	0.0984656i
$325$	37.5478	+	15.0319i	2.08278	+	0.833819i
$326$	11.7852	+	1.12535i	0.652721	+	0.0623273i
$327$	−3.76037	−	15.5005i	−0.207949	−	0.857178i
$328$	1.52685	−	3.34334i	0.0843062	−	0.184605i
$329$	3.76770	−	8.84133i	0.207720	−	0.487439i
$330$	−3.74419	+	26.0414i	−0.206111	+	1.43353i
$331$	−18.8699	−	17.9924i	−1.03718	−	0.988950i	−0.0372345	−	0.999307i	$-0.511855\pi$
$331$	−18.8699	−	17.9924i	−1.03718	−	0.988950i	−0.999946	+	0.0103566i	$0.996703\pi$
$332$	−7.79582	+	1.50252i	−0.427851	+	0.0824615i
$333$	−0.265617	−	5.57599i	−0.0145557	−	0.305562i
$334$	−6.68405	−	3.44587i	−0.365735	−	0.188550i
$335$	−17.9612	−	20.7284i	−0.981327	−	1.13251i
$336$	−0.850958	−	11.6110i	−0.0464235	−	0.633432i
$337$	3.06172	−	21.2947i	0.166783	−	1.16000i	−0.718698	−	0.695322i	$-0.755262\pi$
$337$	3.06172	−	21.2947i	0.166783	−	1.16000i	0.885481	−	0.464676i	$-0.153829\pi$
$338$	1.47386	+	0.284063i	0.0801674	+	0.0154510i
$339$	10.6806	+	14.9989i	0.580093	+	0.814626i
$340$	−14.7118	+	14.0276i	−0.797857	+	0.760755i
$341$	13.7597	−	19.3227i	0.745127	−	1.04638i
$342$	−1.34199	−	9.33374i	−0.0725665	−	0.504711i
$343$	17.3182	−	6.56361i	0.935093	−	0.354401i
$344$	2.44159			0.131642
$345$	−18.9048	−	2.87557i	−1.01780	−	0.154815i
$346$	15.1516	−	26.2433i	0.814553	−	1.41085i
$347$	−9.33136	+	4.81065i	−0.500934	+	0.258249i	−0.690124	−	0.723691i	$-0.742444\pi$
$347$	−9.33136	+	4.81065i	−0.500934	+	0.258249i	0.189190	+	0.981940i	$0.439414\pi$
$348$	10.5580	−	8.30288i	0.565967	−	0.445081i
$349$	11.2308	+	24.5920i	0.601170	+	1.31638i	0.928452	+	0.371452i	$0.121140\pi$
$349$	11.2308	+	24.5920i	0.601170	+	1.31638i	−0.327282	+	0.944927i	$0.606133\pi$
$350$	26.7602	−	49.2132i	1.43039	−	2.63055i
$351$	−1.54167	+	3.37578i	−0.0822880	+	0.180186i
$352$	25.5865	+	4.93140i	1.36377	+	0.262844i
$353$	15.0206	+	11.8124i	0.799468	+	0.628709i	0.931995	−	0.362471i	$-0.118067\pi$
$353$	15.0206	+	11.8124i	0.799468	+	0.628709i	−0.132527	+	0.991179i	$0.542309\pi$
$354$	−3.38487	+	13.9526i	−0.179904	+	0.741574i
$355$	1.65217	−	4.77363i	0.0876880	−	0.253358i
$356$	−5.90779	+	3.79671i	−0.313112	+	0.201225i
$357$	4.82961	−	5.87032i	0.255610	−	0.310690i
$358$	−32.2844	−	37.2581i	−1.70628	−	1.96915i
$359$	2.37793	+	2.26735i	0.125502	+	0.119666i	0.750231	−	0.661175i	$-0.229942\pi$
$359$	2.37793	+	2.26735i	0.125502	+	0.119666i	−0.624729	+	0.780842i	$0.714791\pi$
$360$	1.37375	+	1.08033i	0.0724028	+	0.0569382i
$361$	−1.49100	−	4.30796i	−0.0784737	−	0.226735i
$362$	47.9678	−	4.58037i	2.52113	−	0.240739i
$363$	0.513364	+	0.150737i	0.0269446	+	0.00791165i
$364$	5.27568	−	16.6044i	0.276521	−	0.870305i
$365$	−6.19301	−	43.0733i	−0.324157	−	2.25456i
$366$	1.00243	−	21.0437i	0.0523980	−	1.09997i
$367$	−7.14585	+	12.3770i	−0.373010	+	0.646072i	−0.990027	−	0.140877i	$-0.955008\pi$
$367$	−7.14585	+	12.3770i	−0.373010	+	0.646072i	0.617017	+	0.786950i	$0.288341\pi$
$368$	−4.16258	+	20.6886i	−0.216989	+	1.07847i
$369$	4.19280	+	7.26215i	0.218269	+	0.378052i
$370$	−36.3780	−	23.3787i	−1.89120	−	1.21540i
$371$	5.26233	−	7.80461i	0.273207	−	0.405195i
$372$	5.14824	+	11.2731i	0.266924	+	0.584482i
$373$	1.79756	+	7.40964i	0.0930741	+	0.383657i	0.999228	−	0.0392920i	$-0.0125102\pi$
$373$	1.79756	+	7.40964i	0.0930741	+	0.383657i	−0.906154	+	0.422949i	$0.860995\pi$
$374$	10.9968	+	15.4428i	0.568629	+	0.798528i
$375$	7.69195	+	22.2244i	0.397211	+	1.14766i
$376$	1.47810	−	0.591742i	0.0762272	−	0.0305168i
$377$	−26.9544	+	7.91451i	−1.38822	+	0.407618i
$378$	4.39374	+	2.66754i	0.225990	+	0.137204i
$379$	−13.8587	+	8.90647i	−0.711876	+	0.457495i	−0.845802	−	0.533497i	$-0.820878\pi$
$379$	−13.8587	+	8.90647i	−0.711876	+	0.457495i	0.133927	+	0.990991i	$0.457241\pi$
$380$	−30.5226	−	15.7355i	−1.56577	−	0.807213i
$381$	−8.11960	+	1.56492i	−0.415979	+	0.0801735i
$382$	−1.84257	+	7.59519i	−0.0942742	+	0.388604i
$383$	14.1918	−	5.68152i	0.725165	−	0.290312i	0.0204381	−	0.999791i	$-0.493494\pi$
$383$	14.1918	−	5.68152i	0.725165	−	0.290312i	0.704727	+	0.709479i	$0.251070\pi$
$384$	2.28164	−	2.63315i	0.116434	−	0.134372i
$385$	−28.7202	−	21.4210i	−1.46372	−	1.09171i
$386$	−9.14204	−	2.68435i	−0.465318	−	0.136630i
$387$	−3.23120	+	4.53759i	−0.164251	+	0.230659i
$388$	−17.4797	−	6.99781i	−0.887397	−	0.355260i
$389$	24.4554	−	12.6076i	1.23994	−	0.639232i	0.291614	−	0.956536i	$-0.405808\pi$
$389$	24.4554	−	12.6076i	1.23994	−	0.639232i	0.948324	+	0.317304i	$0.102778\pi$
$390$	14.3739	+	24.8964i	0.727853	+	1.26068i
$391$	−11.2890	+	7.90099i	−0.570910	+	0.399570i
$392$	2.79536	+	1.26474i	0.141187	+	0.0638789i
$393$	7.01994	+	4.51144i	0.354109	+	0.227572i
$394$	41.0631	−	32.2924i	2.06873	−	1.62687i
$395$	19.6866	+	1.87984i	0.990539	+	0.0945850i
$396$	−4.36152	+	4.15870i	−0.219175	+	0.208983i
$397$	0.563666	−	0.0538236i	0.0282896	−	0.00270133i	−0.0809017	−	0.996722i	$-0.525780\pi$
$397$	0.563666	−	0.0538236i	0.0282896	−	0.00270133i	0.109191	+	0.994021i	$0.465174\pi$
$398$	−5.92572	+	6.83865i	−0.297030	+	0.342790i
$399$	12.0400	+	4.46657i	0.602752	+	0.223608i
$400$	46.0133	−	13.5107i	2.30066	−	0.675535i
$401$	−6.27209	+	18.1220i	−0.313213	+	0.904970i	0.673022	+	0.739622i	$0.264996\pi$
$401$	−6.27209	+	18.1220i	−0.313213	+	0.904970i	−0.986235	+	0.165348i	$0.947125\pi$
$402$	−0.635884	−	13.3488i	−0.0317150	−	0.665780i
$403$	−1.23332	−	25.8907i	−0.0614363	−	1.28971i
$404$	−0.527084	+	1.52291i	−0.0262234	+	0.0757675i
$405$	−3.82575	+	1.12334i	−0.190103	+	0.0558193i
$406$	6.51976	+	38.3590i	0.323570	+	1.90373i
$407$	−12.4157	+	14.3285i	−0.615426	+	0.710239i
$408$	1.25363	−	0.119707i	0.0620640	−	0.00592640i
$409$	−28.2689	+	26.9543i	−1.39781	+	1.33280i	−0.519691	+	0.854354i	$0.673953\pi$
$409$	−28.2689	+	26.9543i	−1.39781	+	1.33280i	−0.878115	+	0.478450i	$0.841199\pi$
$410$	64.6638	+	6.17465i	3.19352	+	0.304944i
$411$	2.02738	−	1.59435i	0.100003	−	0.0786435i
$412$	22.6736	+	14.5714i	1.11705	+	0.717883i
$413$	−14.4909	−	13.1267i	−0.713052	−	0.645921i
$414$	−6.37445	−	6.79539i	−0.313287	−	0.333975i
$415$	8.92025	+	15.4503i	0.437878	+	0.758427i
$416$	25.3076	−	13.0470i	1.24081	−	0.639680i
$417$	4.74595	+	1.89999i	0.232410	+	0.0930429i
$418$	−18.5771	+	26.0880i	−0.908638	+	1.27600i
$419$	25.0372	+	7.35159i	1.22315	+	0.359149i	0.828660	−	0.559753i	$-0.189104\pi$
$419$	25.0372	+	7.35159i	1.22315	+	0.359149i	0.394488	+	0.918901i	$0.370922\pi$
$420$	17.1943	−	7.39882i	0.838995	−	0.361025i
$421$	−12.7706	+	14.7381i	−0.622403	+	0.718291i	−0.976161	−	0.217046i	$-0.930358\pi$
$421$	−12.7706	+	14.7381i	−0.622403	+	0.718291i	0.353759	+	0.935337i	$0.384903\pi$
$422$	−19.4846	+	7.80046i	−0.948496	+	0.379721i
$423$	−0.856391	+	3.53009i	−0.0416392	+	0.171639i
$424$	1.53122	−	0.295119i	0.0743626	−	0.0143322i
$425$	27.8317	+	14.3482i	1.35004	+	0.695992i
$426$	2.07058	−	1.33068i	0.100320	−	0.0644717i
$427$	24.5246	+	14.8894i	1.18683	+	0.720550i
$428$	−10.1100	+	2.96855i	−0.488683	+	0.143490i
$429$	11.7014	−	4.68453i	0.564949	−	0.226171i
$430$	14.1133	+	40.7778i	0.680606	+	1.96648i
$431$	2.86531	+	4.02376i	0.138017	+	0.193818i	0.877799	−	0.479028i	$-0.159011\pi$
$431$	2.86531	+	4.02376i	0.138017	+	0.193818i	−0.739782	+	0.672846i	$0.765072\pi$
$432$	1.03741	+	4.27628i	0.0499126	+	0.205743i
$433$	1.33652	+	2.92657i	0.0642290	+	0.140642i	0.939024	−	0.343851i	$-0.111731\pi$
$433$	1.33652	+	2.92657i	0.0642290	+	0.140642i	−0.874795	+	0.484493i	$0.839004\pi$
$434$	−35.8134	−	2.49814i	−1.71910	−	0.119915i
$435$	−25.3911	−	16.3178i	−1.21741	−	0.782381i
$436$	−14.1508	−	24.5100i	−0.677702	−	1.17381i
$437$	−18.8507	−	13.6565i	−0.901753	−	0.653278i
$438$	10.6016	−	18.3625i	0.506563	−	0.877392i
$439$	−0.634343	+	13.3165i	−0.0302755	+	0.635562i	0.931832	+	0.362891i	$0.118210\pi$
$439$	−0.634343	+	13.3165i	−0.0302755	+	0.635562i	−0.962107	+	0.272671i	$0.912093\pi$
$440$	−0.844723	−	5.87518i	−0.0402706	−	0.280088i
$441$	−6.04983	+	3.52130i	−0.288087	+	0.167681i
$442$	19.8762	+	5.83619i	0.945417	+	0.277599i
$443$	4.24136	−	0.405001i	0.201513	−	0.0192422i	0.00618868	−	0.999981i	$-0.498030\pi$
$443$	4.24136	−	0.405001i	0.201513	−	0.0192422i	0.195324	+	0.980739i	$0.437424\pi$
$444$	−3.23968	−	9.36043i	−0.153748	−	0.444226i
$445$	12.4044	+	9.75493i	0.588025	+	0.462428i
$446$	−19.3401	−	18.4408i	−0.915782	−	0.873196i
$447$	−0.864277	−	0.997429i	−0.0408789	−	0.0471768i
$448$	−5.67108	−	15.1235i	−0.267933	−	0.714518i
$449$	26.7750	−	17.2072i	1.26359	−	0.812059i	0.274817	−	0.961496i	$-0.411383\pi$
$449$	26.7750	−	17.2072i	1.26359	−	0.812059i	0.988771	+	0.149437i	$0.0477462\pi$
$450$	−6.92498	+	20.0084i	−0.326447	+	0.943206i
$451$	6.71447	−	27.6774i	0.316172	−	1.30328i
$452$	25.6819	+	20.1965i	1.20798	+	0.949964i
$453$	−13.8443	−	2.66826i	−0.650461	−	0.125366i
$454$	7.87967	−	17.2541i	0.369811	−	0.809774i
$455$	−39.1372	+	1.00049i	−1.83478	+	0.0469039i
$456$	0.883767	+	1.93518i	0.0413862	+	0.0906231i
$457$	26.3547	−	20.7256i	1.23282	−	0.969503i	0.232828	−	0.972518i	$-0.425202\pi$
$457$	26.3547	−	20.7256i	1.23282	−	0.969503i	0.999995	+	0.00301528i	$0.000959793\pi$
$458$	−25.9789	+	13.3931i	−1.21392	+	0.625817i
$459$	−1.43658	+	2.48824i	−0.0670540	+	0.116141i
$460$	−33.6232	+	4.55487i	−1.56769	+	0.212372i
$461$	−27.1719			−1.26552			−0.632762	−	0.774347i	$-0.718079\pi$
$461$	−27.1719			−1.26552			−0.632762	+	0.774347i	$0.718079\pi$
$462$	−4.54797	−	16.8547i	−0.211591	−	0.784150i
$463$	−5.01108	−	34.8528i	−0.232885	−	1.61975i	−0.685521	−	0.728052i	$-0.740426\pi$
$463$	−5.01108	−	34.8528i	−0.232885	−	1.61975i	0.452637	−	0.891695i	$-0.350483\pi$
$464$	−19.3212	+	27.1328i	−0.896964	+	1.25961i
$465$	20.1549	−	19.2177i	0.934663	−	0.891199i
$466$	−22.9125	−	32.1762i	−1.06140	−	1.49053i
$467$	3.59120	+	0.692147i	0.166181	+	0.0320288i	0.271663	−	0.962392i	$-0.412426\pi$
$467$	3.59120	+	0.692147i	0.166181	+	0.0320288i	−0.105482	+	0.994421i	$0.533639\pi$
$468$	−0.937146	+	6.51800i	−0.0433196	+	0.301294i
$469$	16.3843	+	7.92342i	0.756556	+	0.365869i
$470$	18.4269	+	21.2657i	0.849967	+	0.980915i
$471$	−13.2951	−	6.85408i	−0.612604	−	0.315819i
$472$	−0.154125	−	3.23548i	−0.00709417	−	0.148925i
$473$	18.5773	−	3.58048i	0.854186	−	0.164631i
$474$	6.97379	+	6.64949i	0.320317	+	0.305421i
$475$	−7.52805	+	52.3588i	−0.345411	+	2.40238i
$476$	5.28789	−	12.4086i	0.242370	−	0.568749i
$477$	−1.47795	+	3.23626i	−0.0676707	+	0.148178i
$478$	1.15894	+	4.77722i	0.0530088	+	0.218505i
$479$	6.39137	+	0.610301i	0.292029	+	0.0278854i	0.240042	−	0.970762i	$-0.422839\pi$
$479$	6.39137	+	0.610301i	0.292029	+	0.0278854i	0.0519866	+	0.998648i	$0.483445\pi$
$480$	28.3999	+	11.3696i	1.29627	+	0.518949i
$481$	−0.985744	+	20.6933i	−0.0449461	+	0.943534i
$482$	−23.6374			−1.07665
$483$	12.2770	−	3.20563i	0.558621	−	0.145861i
$484$	0.949364			0.0431529
$485$	−2.01317	+	42.2617i	−0.0914135	+	1.91901i
$486$	−1.80361	−	0.722058i	−0.0818136	−	0.0327532i
$487$	12.6260	+	1.20564i	0.572140	+	0.0546328i	0.377117	−	0.926166i	$-0.376916\pi$
$487$	12.6260	+	1.20564i	0.572140	+	0.0546328i	0.195024	+	0.980799i	$0.437522\pi$
$488$	1.12057	+	4.61904i	0.0507257	+	0.209094i
$489$	2.53143	−	5.54306i	0.114475	−	0.250666i
$490$	−4.96453	+	53.9968i	−0.224274	+	2.43933i
$491$	5.63005	−	39.1579i	0.254081	−	1.76717i	−0.319081	−	0.947727i	$-0.603374\pi$
$491$	5.63005	−	39.1579i	0.254081	−	1.76717i	0.573162	−	0.819442i	$-0.305717\pi$
$492$	10.7687	+	10.2679i	0.485490	+	0.462914i
$493$	−21.3560	+	4.11604i	−0.961827	+	0.185377i
$494$	1.66513	+	34.9554i	0.0749179	+	1.57272i
$495$	12.0366	+	6.20532i	0.541007	+	0.278909i
$496$	−20.1261	−	23.2268i	−0.903691	−	1.04291i
$497$	0.245000	+	3.34293i	0.0109897	+	0.149951i
$498$	−1.23710	+	8.60424i	−0.0554359	+	0.385565i
$499$	−0.469926	−	0.0905709i	−0.0210368	−	0.00405451i	0.178722	−	0.983900i	$-0.442804\pi$
$499$	−0.469926	−	0.0905709i	−0.0210368	−	0.00405451i	−0.199759	+	0.979845i	$0.564016\pi$
$500$	24.2057	+	33.9922i	1.08251	+	1.52018i
$501$	−2.80139	+	2.67112i	−0.125157	+	0.119337i
$502$	20.2314	−	28.4110i	0.902971	−	1.26805i
$503$	1.98898	+	13.8337i	0.0886843	+	0.616813i	0.984891	+	0.173176i	$0.0554029\pi$
$503$	1.98898	+	13.8337i	0.0886843	+	0.616813i	−0.896207	+	0.443637i	$0.853688\pi$
$504$	−1.12067	−	0.298171i	−0.0499185	−	0.0132816i
$505$	3.62132			0.161147
$506$	−0.257936	+	31.6433i	−0.0114667	+	1.40672i
$507$	0.386298	−	0.669088i	0.0171561	−	0.0297152i
$508$	−13.0414	+	6.72332i	−0.578620	+	0.298299i
$509$	−23.2593	+	18.2913i	−1.03095	+	0.810749i	−0.982158	−	0.188060i	$-0.939780\pi$
$509$	−23.2593	+	18.2913i	−1.03095	+	0.810749i	−0.0487940	+	0.998809i	$0.515538\pi$
$510$	9.24574	+	20.2453i	0.409408	+	0.896479i
$511$	15.0720	+	24.6296i	0.666745	+	1.08955i
$512$	12.4221	−	27.2006i	0.548984	−	1.20211i
$513$	−4.76602	−	0.918574i	−0.210425	−	0.0405560i
$514$	−7.00281	−	5.50707i	−0.308881	−	0.242906i
$515$	14.2786	−	58.8574i	0.629192	−	2.59357i
$516$	−3.23282	+	9.34061i	−0.142317	+	0.411197i
$517$	10.3786	−	6.66995i	0.456452	−	0.293344i
$518$	28.3048	+	4.70852i	1.24364	+	0.206880i
$519$	−10.2144	−	11.7881i	−0.448363	−	0.517438i
$520$	−4.69398	−	4.47570i	−0.205845	−	0.196273i
$521$	−21.1867	−	16.6614i	−0.928206	−	0.729949i	0.0348102	−	0.999394i	$-0.488917\pi$
$521$	−21.1867	−	16.6614i	−0.928206	−	0.729949i	−0.963016	+	0.269445i	$0.913160\pi$
$522$	−4.80995	−	13.8974i	−0.210526	−	0.608275i
$523$	−31.7092	+	3.02787i	−1.38655	+	0.132399i	−0.761489	−	0.648178i	$-0.775531\pi$
$523$	−31.7092	+	3.02787i	−1.38655	+	0.132399i	−0.625059	+	0.780577i	$0.714925\pi$
$524$	14.2068	+	4.17151i	0.620629	+	0.182233i
$525$	−19.4330	−	21.3017i	−0.848127	−	0.929681i
$526$	4.68742	+	32.6017i	0.204381	+	1.42150i
$527$	0.954840	−	20.0446i	0.0415935	−	0.873155i
$528$	7.47246	−	12.9427i	0.325197	−	0.563258i
$529$	−22.9969	−	0.374937i	−0.999867	−	0.0163016i
$530$	13.7799	+	23.8675i	0.598561	+	1.03674i
$531$	6.21696	+	3.99539i	0.269793	+	0.173385i
$532$	22.7311	+	1.58559i	0.985517	+	0.0687441i
$533$	−12.9278	−	28.3079i	−0.559965	−	1.22615i
$534$	1.81276	+	7.47231i	0.0784459	+	0.323358i
$535$	13.7342	+	19.2870i	0.593781	+	0.833849i
$536$	0.986122	+	2.84921i	0.0425940	+	0.123067i
$537$	−23.5581	+	9.43123i	−1.01661	+	0.406988i
$538$	7.58616	−	2.22750i	0.327063	−	0.0960343i
$539$	23.1237	+	5.52372i	0.996008	+	0.237923i
$540$	−5.95184	+	3.82501i	−0.256126	+	0.164602i
$541$	2.77012	+	1.42809i	0.119097	+	0.0613986i	0.516745	−	0.856139i	$-0.327143\pi$
$541$	2.77012	+	1.42809i	0.119097	+	0.0613986i	−0.397649	+	0.917538i	$0.630174\pi$
$542$	−20.2686	+	3.90645i	−0.870610	+	0.167796i
$543$	5.84743	−	24.1034i	0.250937	−	1.03438i
$544$	20.4646	−	8.19279i	0.877412	−	0.351263i
$545$	−41.6472	+	48.0635i	−1.78397	+	2.05881i
$546$	−15.2910	−	11.4048i	−0.654393	−	0.488079i
$547$	43.8152	+	12.8653i	1.87340	+	0.550081i	0.997742	+	0.0671567i	$0.0213928\pi$
$547$	43.8152	+	12.8653i	1.87340	+	0.550081i	0.875662	+	0.482924i	$0.160425\pi$
$548$	2.65463	−	3.72790i	0.113400	−	0.159248i
$549$	−10.0672	−	4.03031i	−0.429659	−	0.172010i
$550$	63.9163	−	32.9511i	2.72540	−	1.40504i
$551$	−18.3707	−	31.8189i	−0.782617	−	1.35553i
$552$	1.81180	+	1.06583i	0.0771155	+	0.0453648i
$553$	−12.4923	+	4.01758i	−0.531227	+	0.170845i
$554$	−2.16676	−	1.39249i	−0.0920569	−	0.0591614i
$555$	−17.4961	+	13.7591i	−0.742667	+	0.584040i
$556$	9.02986	+	0.862247i	0.382951	+	0.0365674i
$557$	−7.96638	+	7.59593i	−0.337547	+	0.321850i	−0.839826	−	0.542855i	$-0.817343\pi$
$557$	−7.96638	+	7.59593i	−0.337547	+	0.321850i	0.502280	+	0.864705i	$0.332495\pi$
$558$	13.5077	−	1.28982i	0.571825	−	0.0546026i
$559$	13.5379	−	15.6235i	0.572591	−	0.660805i
$560$	−35.7436	+	29.6182i	−1.51044	+	1.25160i
$561$	9.36295	−	2.74921i	0.395304	−	0.116072i
$562$	−4.62770	+	13.3709i	−0.195208	+	0.564016i
$563$	−0.365464	−	7.67204i	−0.0154025	−	0.323338i	−0.993399	−	0.114714i	$-0.963405\pi$
$563$	−0.365464	−	7.67204i	−0.0154025	−	0.323338i	0.977996	−	0.208623i	$-0.0668983\pi$
$564$	0.306687	+	6.43815i	0.0129139	+	0.271095i
$565$	24.0126	−	69.3799i	1.01022	−	2.91883i
$566$	17.7002	−	5.19726i	0.743997	−	0.218457i
$567$	2.03723	−	1.68811i	0.0855555	−	0.0708939i
$568$	−0.363639	+	0.419662i	−0.0152580	+	0.0176086i
$569$	4.26851	−	0.407593i	0.178945	−	0.0170872i	−0.00519869	−	0.999986i	$-0.501655\pi$
$569$	4.26851	−	0.407593i	0.178945	−	0.0170872i	0.184144	+	0.982899i	$0.441049\pi$
$570$	−27.2115	+	25.9461i	−1.13976	+	1.08676i
$571$	−2.92643	−	0.279440i	−0.122467	−	0.0116942i	0.0336424	−	0.999434i	$-0.489289\pi$
$571$	−2.92643	−	0.279440i	−0.122467	−	0.0116942i	−0.156110	+	0.987740i	$0.549895\pi$
$572$	17.5800	−	13.8251i	0.735056	−	0.578055i
$573$	3.38423	+	2.17491i	0.141378	+	0.0908583i
$574$	−41.0331	+	13.1964i	−1.71269	+	0.550808i
$575$	23.5703	+	46.6497i	0.982949	+	1.94543i
$576$	3.05241	+	5.28692i	0.127184	+	0.220288i
$577$	−15.0781	+	7.77330i	−0.627709	+	0.323607i	−0.742563	−	0.669776i	$-0.766390\pi$
$577$	−15.0781	+	7.77330i	−0.627709	+	0.323607i	0.114854	+	0.993382i	$0.463360\pi$
$578$	−15.7724	−	6.31432i	−0.656046	−	0.262641i
$579$	−2.84478	+	3.99493i	−0.118225	+	0.166024i
$580$	−51.3860	−	15.0883i	−2.13369	−	0.626508i
$581$	−9.48933	−	7.07763i	−0.393684	−	0.293629i
$582$	−13.5001	+	15.5799i	−0.559597	+	0.645809i
$583$	11.2178	−	4.49093i	0.464594	−	0.185995i
$584$	−1.12778	+	4.64878i	−0.0466679	+	0.192368i
$585$	14.5299	−	2.80041i	0.600737	−	0.115783i
$586$	14.6708	+	7.56332i	0.606045	+	0.312438i
$587$	21.6261	−	13.8982i	0.892603	−	0.573641i	−0.0119848	−	0.999928i	$-0.503815\pi$
$587$	21.6261	−	13.8982i	0.892603	−	0.573641i	0.904588	+	0.426287i	$0.140179\pi$
$588$	−8.53963	+	9.01940i	−0.352168	+	0.371954i
$589$	32.5271	−	9.55081i	1.34025	−	0.393534i
$590$	53.1458	−	21.2764i	2.18798	−	0.875935i
$591$	−8.79456	−	25.4102i	−0.361760	−	1.04524i
$592$	14.2485	+	20.0092i	0.585610	+	0.822374i
$593$	3.49435	+	14.4039i	0.143496	+	0.591497i	0.997464	+	0.0711724i	$0.0226740\pi$
$593$	3.49435	+	14.4039i	0.143496	+	0.591497i	−0.853968	+	0.520325i	$0.825811\pi$
$594$	2.74104	+	6.00204i	0.112466	+	0.246267i
$595$	−30.2365	−	2.10913i	−1.23957	−	0.0864657i
$596$	−1.97006	−	1.26608i	−0.0806970	−	0.0518608i
$597$	2.32884	+	4.03366i	0.0953129	+	0.165087i
$598$	21.1522	+	27.3532i	0.864979	+	1.11855i
$599$	−7.54118	+	13.0617i	−0.308124	+	0.533687i	−0.977952	−	0.208830i	$-0.933035\pi$
$599$	−7.54118	+	13.0617i	−0.308124	+	0.533687i	0.669828	+	0.742517i	$0.266368\pi$
$600$	0.227289	−	4.77139i	0.00927904	−	0.194791i
$601$	0.530322	+	3.68847i	0.0216323	+	0.150456i	0.997775	−	0.0666753i	$-0.0212392\pi$
$601$	0.530322	+	3.68847i	0.0216323	+	0.150456i	−0.976142	+	0.217131i	$0.930330\pi$
$602$	−19.2975	−	21.1531i	−0.786506	−	0.862136i
$603$	−6.60016	−	1.93798i	−0.268779	−	0.0789207i
$604$	−24.9040	+	2.37804i	−1.01333	+	0.0967611i
$605$	−0.697744	−	2.01600i	−0.0283673	−	0.0819620i
$606$	1.38697	+	1.09073i	0.0563419	+	0.0443077i
$607$	24.3766	+	23.2431i	0.989416	+	0.943407i	0.998400	−	0.0565531i	$-0.0180110\pi$
$607$	24.3766	+	23.2431i	0.989416	+	0.943407i	−0.00898325	+	0.999960i	$0.502859\pi$
$608$	24.3863	+	28.1433i	0.988995	+	1.14136i
$609$	19.7561	+	3.28644i	0.800557	+	0.133173i
$610$	−70.6668	+	45.4148i	−2.86121	+	1.83879i
$611$	4.40910	−	12.7393i	0.178373	−	0.515375i
$612$	−1.20193	+	4.95442i	−0.0485851	+	0.200270i
$613$	−5.00972	−	3.93969i	−0.202341	−	0.159122i	0.511847	−	0.859076i	$-0.328961\pi$
$613$	−5.00972	−	3.93969i	−0.202341	−	0.159122i	−0.714188	+	0.699954i	$0.753204\pi$
$614$	−48.0395	−	9.25885i	−1.93872	−	0.373657i
$615$	13.8896	−	30.4141i	0.560085	−	1.22641i
$616$	2.05581	+	3.35946i	0.0828309	+	0.135357i
$617$	5.78666	+	12.6710i	0.232962	+	0.510116i	0.989622	−	0.143692i	$-0.0458975\pi$
$617$	5.78666	+	12.6710i	0.232962	+	0.510116i	−0.756660	+	0.653808i	$0.773170\pi$
$618$	23.1963	−	18.2418i	0.933094	−	0.733793i
$619$	6.07621	−	3.13250i	0.244223	−	0.125906i	−0.331770	−	0.943360i	$-0.607646\pi$
$619$	6.07621	−	3.13250i	0.244223	−	0.125906i	0.575993	+	0.817454i	$0.304615\pi$
$620$	24.7071	−	42.7939i	0.992261	−	1.71865i
$621$	−4.37854	+	1.95664i	−0.175705	+	0.0785171i
$622$	39.9646			1.60244
$623$	−10.1192	−	2.69237i	−0.405417	−	0.107867i
$624$	−2.32403	−	16.1640i	−0.0930358	−	0.647078i
$625$	22.7850	−	31.9971i	0.911402	−	1.27988i
$626$	−23.7203	+	22.6173i	−0.948055	+	0.903968i
$627$	9.56215	+	13.4282i	0.381876	+	0.536269i
$628$	−26.0614	−	5.02293i	−1.03996	−	0.200437i
$629$	−2.28258	+	15.8757i	−0.0910124	+	0.633005i
$630$	−1.49804	−	20.4401i	−0.0596832	−	0.814355i
$631$	−25.2683	−	29.1612i	−1.00592	−	1.16089i	−0.986943	−	0.161070i	$-0.948506\pi$
$631$	−25.2683	−	29.1612i	−1.00592	−	1.16089i	−0.0189738	−	0.999820i	$-0.506040\pi$
$632$	−1.93227	−	0.996153i	−0.0768615	−	0.0396249i
$633$	0.514032	+	10.7909i	0.0204309	+	0.428898i
$634$	1.24705	−	0.240349i	0.0495267	−	0.00954548i
$635$	23.8621	+	22.7524i	0.946938	+	0.902903i
$636$	−0.898416	+	6.24862i	−0.0356245	+	0.247774i
$637$	23.5923	−	10.8747i	0.934762	−	0.430871i
$638$	−20.7489	+	45.4337i	−0.821456	+	1.79874i
$639$	−0.298682	−	1.23119i	−0.0118157	−	0.0487050i
$640$	−13.8293	−	1.32054i	−0.546653	−	0.0521990i
$641$	−2.49457	−	0.998676i	−0.0985297	−	0.0394453i	0.321874	−	0.946783i	$-0.395687\pi$
$641$	−2.49457	−	0.998676i	−0.0985297	−	0.0394453i	−0.420404	+	0.907337i	$0.638112\pi$
$642$	−0.548938	+	11.5236i	−0.0216649	+	0.454801i
$643$	23.7405			0.936235			0.468117	−	0.883666i	$-0.344932\pi$
$643$	23.7405			0.936235			0.468117	+	0.883666i	$0.344932\pi$
$644$	19.2992	−	11.5949i	0.760496	−	0.456904i
$645$	22.2110			0.874558
$646$	−1.28915	+	27.0625i	−0.0507208	+	1.06476i
$647$	−10.9627	−	4.38882i	−0.430990	−	0.172542i	0.146016	−	0.989282i	$-0.453355\pi$
$647$	−10.9627	−	4.38882i	−0.430990	−	0.172542i	−0.577006	+	0.816740i	$0.695779\pi$
$648$	0.436324	+	0.0416639i	0.0171404	+	0.00163671i
$649$	−5.91737	−	24.3917i	−0.232277	−	0.957459i
$650$	32.6415	−	71.4750i	1.28031	−	2.80348i
$651$	−7.24435	+	16.9997i	−0.283929	+	0.666271i
$652$	1.53880	−	10.7026i	0.0602642	−	0.419147i
$653$	11.3827	+	10.8534i	0.445440	+	0.424726i	0.879310	−	0.476249i	$-0.158004\pi$
$653$	11.3827	+	10.8534i	0.445440	+	0.424726i	−0.433870	+	0.900975i	$0.642852\pi$
$654$	−30.4275	+	5.86442i	−1.18981	+	0.229317i
$655$	−1.58315	−	33.2345i	−0.0618589	−	1.29858i
$656$	−32.7974	−	16.9082i	−1.28052	−	0.660156i
$657$	−7.14703	−	8.24811i	−0.278832	−	0.321790i
$658$	−16.8090	−	8.12882i	−0.655284	−	0.316894i
$659$	4.88905	−	34.0041i	0.190450	−	1.32461i	−0.640369	−	0.768068i	$-0.721218\pi$
$659$	4.88905	−	34.0041i	0.190450	−	1.32461i	0.830819	−	0.556543i	$-0.187872\pi$
$660$	23.5946	+	4.54750i	0.918420	+	0.177011i
$661$	10.8934	+	15.2976i	0.423704	+	0.595008i	0.970156	−	0.242482i	$-0.0779615\pi$
$661$	10.8934	+	15.2976i	0.423704	+	0.595008i	−0.546452	+	0.837490i	$0.684022\pi$
$662$	−36.6600	+	34.9552i	−1.42483	+	1.35857i
$663$	6.18500	−	8.68562i	0.240206	−	0.337321i
$664$	−0.279102	−	1.94120i	−0.0108312	−	0.0753330i
$665$	−13.3394	−	49.4354i	−0.517279	−	1.91702i
$666$	−10.8452			−0.420243
$667$	−32.8984	−	15.3495i	−1.27383	−	0.594335i
$668$	−3.43411	+	5.94806i	−0.132870	+	0.230137i
$669$	−12.2258	+	6.30285i	−0.472678	+	0.243682i
$670$	−41.8854	+	32.9390i	−1.61817	+	1.27255i
$671$	15.2997	+	33.5016i	0.590637	+	1.29331i
$672$	−20.2922	+	0.518745i	−0.782788	+	0.0200110i
$673$	−8.88002	+	19.4445i	−0.342300	+	0.749531i	−0.999993	−	0.00375431i	$-0.998805\pi$
$673$	−8.88002	+	19.4445i	−0.342300	+	0.749531i	0.657693	+	0.753286i	$0.271532\pi$
$674$	−41.0411	−	7.91002i	−1.58084	−	0.304683i
$675$	8.56661	+	6.73685i	0.329729	+	0.259302i
$676$	0.323199	−	1.33224i	0.0124307	−	0.0512402i
$677$	−2.25099	+	6.50381i	−0.0865126	+	0.249962i	−0.979956	−	0.199214i	$-0.936161\pi$
$677$	−2.25099	+	6.50381i	−0.0865126	+	0.249962i	0.893443	+	0.449176i	$0.148282\pi$
$678$	30.0938	−	19.3401i	1.15575	−	0.742752i
$679$	−9.85730	−	26.2872i	−0.378288	−	1.00881i
$680$	−3.28825	−	3.79484i	−0.126099	−	0.145526i
$681$	−7.06613	−	6.73754i	−0.270775	−	0.258183i
$682$	−36.2253	−	28.4879i	−1.38714	−	1.09086i
$683$	13.7379	+	39.6930i	0.525665	+	1.51881i	0.825266	+	0.564744i	$0.191025\pi$
$683$	13.7379	+	39.6930i	0.525665	+	1.51881i	−0.299601	+	0.954065i	$0.596854\pi$
$684$	−8.57342	+	0.818662i	−0.327813	+	0.0313023i
$685$	−9.86734	−	2.89731i	−0.377012	−	0.110701i
$686$	−11.1363	−	34.2140i	−0.425185	−	1.30630i
$687$	2.14105	+	14.8913i	0.0816862	+	0.568140i
$688$	1.16633	−	24.4842i	0.0444657	−	0.933451i
$689$	6.60170	−	11.4345i	0.251505	−	0.435619i
$690$	−7.32785	+	36.4204i	−0.278966	+	1.38650i
$691$	−14.6978	−	25.4573i	−0.559130	−	0.968442i	−0.997569	−	0.0696812i	$-0.977802\pi$
$691$	−14.6978	−	25.4573i	−0.559130	−	0.968442i	0.438439	−	0.898761i	$-0.355532\pi$
$692$	−23.2831	−	14.9631i	−0.885090	−	0.568813i
$693$	−8.96405	−	0.625282i	−0.340516	−	0.0237525i
$694$	8.47284	+	18.5529i	0.321625	+	0.704260i
$695$	−4.80558	−	19.8089i	−0.182286	−	0.751393i
$696$	1.92455	+	2.70266i	0.0729500	+	0.102444i
$697$	−7.88013	−	22.7682i	−0.298481	−	0.862405i
$698$	48.7609	−	19.5209i	1.84563	−	0.738877i
$699$	−19.5084	+	5.72817i	−0.737874	+	0.216659i
$700$	−43.7338	−	26.5518i	−1.65298	−	1.00356i
$701$	−7.83550	+	5.03557i	−0.295943	+	0.190191i	−0.680183	−	0.733042i	$-0.738100\pi$
$701$	−7.83550	+	5.03557i	−0.295943	+	0.190191i	0.384240	+	0.923233i	$0.374463\pi$
$702$	6.40845	+	3.30378i	0.241871	+	0.124693i
$703$	−26.6054	+	5.12777i	−1.00344	+	0.193397i
$704$	4.88821	−	20.1495i	0.184231	−	0.759412i
$705$	13.4462	−	5.38304i	0.506412	−	0.202737i
$706$	24.3113	−	28.0568i	0.914969	−	1.05593i
$707$	−2.20725	+	0.949797i	−0.0830123	+	0.0357208i
$708$	12.5818	+	3.69434i	0.472852	+	0.138842i
$709$	0.624644	−	0.877189i	0.0234590	−	0.0329435i	−0.802680	−	0.596410i	$-0.796593\pi$
$709$	0.624644	−	0.877189i	0.0234590	−	0.0329435i	0.826139	+	0.563467i	$0.190533\pi$
$710$	−9.11087	−	3.64744i	−0.341925	−	0.136886i
$711$	4.40847	−	2.27272i	0.165330	−	0.0852337i
$712$	−0.867359	−	1.50231i	−0.0325057	−	0.0563015i
$713$	20.9197	−	26.1599i	0.783449	−	0.979696i
$714$	−10.9454	−	9.91490i	−0.409620	−	0.371056i
$715$	−42.2784	−	27.1707i	−1.58112	−	1.01613i
$716$	−35.3933	+	27.8336i	−1.32271	+	1.04019i
$717$	2.51883	+	0.240519i	0.0940675	+	0.00898236i
$718$	4.61980	−	4.40497i	0.172409	−	0.164392i
$719$	19.6536	−	1.87669i	0.732957	−	0.0699889i	0.278098	−	0.960553i	$-0.410296\pi$
$719$	19.6536	−	1.87669i	0.732957	−	0.0699889i	0.454859	+	0.890564i	$0.349690\pi$
$720$	11.4897	−	13.2598i	0.428195	−	0.494163i
$721$	6.73400	+	39.6195i	0.250787	+	1.47551i
$722$	−8.49776	+	2.49517i	−0.316254	+	0.0928606i
$723$	−3.97937	+	11.4976i	−0.147994	+	0.427601i
$724$	−2.09406	−	43.9596i	−0.0778250	−	1.63375i
$725$	3.92535	+	82.4032i	0.145784	+	3.06038i
$726$	0.339973	−	0.982288i	0.0126176	−	0.0364561i
$727$	−10.4257	+	3.06127i	−0.386669	+	0.113536i	−0.469289	−	0.883045i	$-0.655490\pi$
$727$	−10.4257	+	3.06127i	−0.386669	+	0.113536i	0.0826195	+	0.996581i	$0.473671\pi$
$728$	4.03494	+	1.49688i	0.149545	+	0.0554780i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−84.1597	+	8.03627i	−3.11489	+	0.297436i
$731$	11.5833	−	11.0447i	0.428425	−	0.408503i
$732$	−19.1544	−	1.82902i	−0.707967	−	0.0676027i
$733$	−25.2349	+	19.8450i	−0.932073	+	0.732990i	−0.963834	−	0.266505i	$-0.914131\pi$
$733$	−25.2349	+	19.8450i	−0.932073	+	0.732990i	0.0317604	+	0.999496i	$0.489889\pi$
$734$	23.3579	+	15.0112i	0.862156	+	0.554074i
$735$	25.4292	+	11.5052i	0.937970	+	0.424377i
$736$	35.6856	+	8.96586i	1.31539	+	0.330486i
$737$	11.6813	+	20.2326i	0.430287	+	0.745279i
$738$	14.4804	−	7.46514i	0.533029	−	0.274796i
$739$	2.41337	+	0.966167i	0.0887772	+	0.0355410i	0.415626	−	0.909536i	$-0.363563\pi$
$739$	2.41337	+	0.966167i	0.0887772	+	0.0355410i	−0.326849	+	0.945077i	$0.605987\pi$
$740$	−22.9091	+	32.1714i	−0.842157	+	1.18264i
$741$	17.2832	+	5.07482i	0.634916	+	0.186428i
$742$	−14.6590	−	10.9334i	−0.538149	−	0.401379i
$743$	3.78472	−	4.36780i	0.138848	−	0.160239i	−0.682067	−	0.731290i	$-0.738919\pi$
$743$	3.78472	−	4.36780i	0.138848	−	0.160239i	0.820915	+	0.571051i	$0.193464\pi$
$744$	−2.84202	+	1.13777i	−0.104194	+	0.0417128i
$745$	−1.24064	+	5.11400i	−0.0454537	+	0.187363i
$746$	14.5452	−	2.80335i	0.532536	−	0.102638i
$747$	3.97698	+	2.05028i	0.145510	+	0.0750157i
$748$	14.5662	−	9.36114i	0.532594	−	0.342277i
$749$	−13.4298	−	8.15353i	−0.490714	−	0.297924i
$750$	43.8393	−	12.8724i	1.60078	−	0.470033i
$751$	1.45678	−	0.583205i	0.0531585	−	0.0212815i	−0.344931	−	0.938628i	$-0.612098\pi$
$751$	1.45678	−	0.583205i	0.0531585	−	0.0212815i	0.398089	+	0.917347i	$0.369673\pi$
$752$	−5.22789	−	15.1050i	−0.190641	−	0.550822i
$753$	−10.4136	−	14.6239i	−0.379494	−	0.532925i
$754$	12.8670	+	53.0387i	0.468590	+	1.93156i
$755$	23.3532	+	51.1365i	0.849911	+	1.86105i
$756$	2.62452	−	3.89245i	0.0954528	−	0.141567i
$757$	−23.8276	−	15.3130i	−0.866027	−	0.556562i	0.0305079	−	0.999535i	$-0.490288\pi$
$757$	−23.8276	−	15.3130i	−0.866027	−	0.556562i	−0.896535	+	0.442973i	$0.853924\pi$
$758$	16.0026	+	27.7173i	0.581240	+	1.00674i
$759$	15.3484	+	5.45264i	0.557113	+	0.197918i
$760$	4.24131	−	7.34617i	0.153849	−	0.266473i
$761$	0.910772	−	19.1195i	0.0330155	−	0.693080i	−0.920320	−	0.391167i	$-0.872072\pi$
$761$	0.910772	−	19.1195i	0.0330155	−	0.693080i	0.953335	−	0.301913i	$-0.0976254\pi$
$762$	2.28627	+	15.9014i	0.0828229	+	0.576046i
$763$	12.7786	−	40.2187i	0.462617	−	1.45601i
$764$	6.84895	+	2.01103i	0.247786	+	0.0727566i
$765$	11.4042	−	1.08897i	0.412320	−	0.0393718i
$766$	−9.71354	−	28.0654i	−0.350964	−	1.01404i
$767$	−21.5581	−	16.9535i	−0.778418	−	0.612155i
$768$	−13.7354	−	13.0967i	−0.495635	−	0.472587i
$769$	12.1968	+	14.0759i	0.439828	+	0.507589i	0.931775	−	0.363036i	$-0.118260\pi$
$769$	12.1968	+	14.0759i	0.439828	+	0.507589i	−0.491947	+	0.870625i	$0.663714\pi$
$770$	−44.2240	+	53.7536i	−1.59372	+	1.93715i
$771$	−3.85766	+	2.47917i

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0924412 - 1.94058i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-1.76636 - 0.168667i) q^{4} +(0.940033 + 3.87487i) q^{5} +(-0.807060 + 1.76721i) q^{6} +(-1.58926 - 2.11524i) q^{7} +(0.0623778 - 0.433847i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(0.0924412 - 1.94058i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-1.76636 - 0.168667i) q^{4} +(0.940033 + 3.87487i) q^{5} +(-0.807060 + 1.76721i) q^{6} +(-1.58926 - 2.11524i) q^{7} +(0.0623778 - 0.433847i) q^{8} +(0.723734 + 0.690079i) q^{9} +(7.60638 - 1.46601i) q^{10} +(-0.161604 - 3.39248i) q^{11} +(1.57714 + 0.813073i) q^{12} +(-2.43028 - 2.80470i) q^{13} +(-4.25171 + 2.88855i) q^{14} +(0.567447 - 3.94668i) q^{15} +(-4.32080 - 0.832766i) q^{16} +(-1.66660 - 2.34041i) q^{17} +(1.40606 - 1.34067i) q^{18} +(2.81544 - 3.95373i) q^{19} +(-1.00687 - 7.00295i) q^{20} +(0.689263 + 2.55439i) q^{21} -6.59831 q^{22} +(0.0390912 - 4.79567i) q^{23} +(-0.219154 + 0.379586i) q^{24} +(-9.68676 + 4.99387i) q^{25} +(-5.66739 + 4.45689i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(2.45043 + 4.00433i) q^{28} +(3.14457 - 6.88565i) q^{29} +(-7.60638 - 1.46601i) q^{30} +(5.49009 + 4.31745i) q^{31} +(-1.80880 + 7.45596i) q^{32} +(-1.11083 + 3.20953i) q^{33} +(-4.69582 + 3.01782i) q^{34} +(6.70232 - 8.14657i) q^{35} +(-1.16198 - 1.34100i) q^{36} +(-4.04011 - 3.85224i) q^{37} +(-7.41226 - 5.82907i) q^{38} +(1.21380 + 3.50703i) q^{39} +(1.73974 - 0.166125i) q^{40} +(8.04593 + 2.36250i) q^{41} +(5.02071 - 1.10144i) q^{42} +(0.792764 + 5.51379i) q^{43} +(-0.286748 + 6.01959i) q^{44} +(-1.99363 + 3.45307i) q^{45} +(-9.30277 - 0.519177i) q^{46} +(1.81624 + 3.14583i) q^{47} +(3.70178 + 2.37899i) q^{48} +(-1.94850 + 6.72334i) q^{49} +(8.79554 + 19.2596i) q^{50} +(0.677375 + 2.79218i) q^{51} +(3.81969 + 5.36400i) q^{52} +(1.16363 + 3.36210i) q^{53} +(-1.80361 + 0.722058i) q^{54} +(12.9935 - 3.81523i) q^{55} +(-1.01683 + 0.557552i) q^{56} +(-4.08322 + 2.62412i) q^{57} +(-13.0715 - 6.73881i) q^{58} +(7.25656 - 1.39859i) q^{59} +(-1.66799 + 6.87553i) q^{60} +(-10.0672 + 4.03031i) q^{61} +(8.88587 - 10.2548i) q^{62} +(0.309482 - 2.62759i) q^{63} +(5.85752 + 1.71992i) q^{64} +(8.58328 - 12.0535i) q^{65} +(6.12566 + 2.45235i) q^{66} +(-6.11412 + 3.15205i) q^{67} +(2.54906 + 4.41511i) q^{68} +(-1.81866 + 4.43762i) q^{69} +(-15.1895 - 13.7595i) q^{70} +(-1.06578 - 0.684937i) q^{71} +(0.344534 - 0.270944i) q^{72} +(-10.8644 - 1.03742i) q^{73} +(-7.84904 + 7.48405i) q^{74} +(10.8489 - 1.03595i) q^{75} +(-5.63993 + 6.50883i) q^{76} +(-6.91909 + 5.73337i) q^{77} +(6.91788 - 2.03127i) q^{78} +(1.62220 - 4.68704i) q^{79} +(-0.834835 - 17.5253i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(5.32839 - 15.3954i) q^{82} +(4.29313 - 1.26058i) q^{83} +(-0.786644 - 4.62822i) q^{84} +(7.50214 - 8.65793i) q^{85} +(10.7732 - 1.02872i) q^{86} +(-5.47846 + 5.22370i) q^{87} +(-1.48190 - 0.141504i) q^{88} +(3.11101 - 2.44652i) q^{89} +(6.51666 + 4.18800i) q^{90} +(-2.07026 + 9.59803i) q^{91} +(-0.877919 + 8.46427i) q^{92} +(-3.49219 - 6.04865i) q^{93} +(6.27262 - 3.23376i) q^{94} +(17.9668 + 7.19282i) q^{95} +(4.45033 - 6.24961i) q^{96} +(10.1814 + 2.98952i) q^{97} +(12.8671 + 4.40273i) q^{98} +(2.22412 - 2.56677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9	\( 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21} - 176 q^{22} - 18 q^{23} - 6 q^{24} + 8 q^{25} - 14 q^{26} + 32 q^{27} + 46 q^{28} + 34 q^{29} - 8 q^{30} + 52 q^{31} - 8 q^{32} - 5 q^{33} - 24 q^{34} - 12 q^{35} - 14 q^{36} - 30 q^{37} - 157 q^{38} + 88 q^{40} - 28 q^{41} - 45 q^{42} + 64 q^{43} - 71 q^{44} - 2 q^{45} + 4 q^{46} + 36 q^{47} + 60 q^{48} + 28 q^{49} + 210 q^{50} - 26 q^{51} - 198 q^{52} - 10 q^{53} - 2 q^{54} - 4 q^{55} + 44 q^{57} + 31 q^{58} + 10 q^{59} - 2 q^{60} - 34 q^{61} - 8 q^{62} + 2 q^{63} + 84 q^{64} + 38 q^{65} - 12 q^{67} - 22 q^{68} + 8 q^{69} - 336 q^{70} - 144 q^{71} + 6 q^{72} - 16 q^{73} - 68 q^{74} - 30 q^{75} + 8 q^{76} + 98 q^{77} + 16 q^{78} + 26 q^{79} + 225 q^{80} + 16 q^{81} - 122 q^{82} + 44 q^{84} - 240 q^{85} - 26 q^{86} - 16 q^{87} + 43 q^{88} + 68 q^{89} - 16 q^{90} + 40 q^{91} - 222 q^{92} - 8 q^{93} + 137 q^{94} - 49 q^{95} + 30 q^{96} - 8 q^{97} + 137 q^{98} - 10 q^{99}+O(q^{100}) \) 320 * q + 2 * q^2 - 16 * q^3 + 18 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^7 - 12 * q^8 + 16 * q^9 + 8 * q^10 - 6 * q^11 - 18 * q^12 - 10 * q^14 + 18 * q^15 + 8 * q^16 + 4 * q^17 + 2 * q^18 + 18 * q^20 + 4 * q^21 - 176 * q^22 - 18 * q^23 - 6 * q^24 + 8 * q^25 - 14 * q^26 + 32 * q^27 + 46 * q^28 + 34 * q^29 - 8 * q^30 + 52 * q^31 - 8 * q^32 - 5 * q^33 - 24 * q^34 - 12 * q^35 - 14 * q^36 - 30 * q^37 - 157 * q^38 + 88 * q^40 - 28 * q^41 - 45 * q^42 + 64 * q^43 - 71 * q^44 - 2 * q^45 + 4 * q^46 + 36 * q^47 + 60 * q^48 + 28 * q^49 + 210 * q^50 - 26 * q^51 - 198 * q^52 - 10 * q^53 - 2 * q^54 - 4 * q^55 + 44 * q^57 + 31 * q^58 + 10 * q^59 - 2 * q^60 - 34 * q^61 - 8 * q^62 + 2 * q^63 + 84 * q^64 + 38 * q^65 - 12 * q^67 - 22 * q^68 + 8 * q^69 - 336 * q^70 - 144 * q^71 + 6 * q^72 - 16 * q^73 - 68 * q^74 - 30 * q^75 + 8 * q^76 + 98 * q^77 + 16 * q^78 + 26 * q^79 + 225 * q^80 + 16 * q^81 - 122 * q^82 + 44 * q^84 - 240 * q^85 - 26 * q^86 - 16 * q^87 + 43 * q^88 + 68 * q^89 - 16 * q^90 + 40 * q^91 - 222 * q^92 - 8 * q^93 + 137 * q^94 - 49 * q^95 + 30 * q^96 - 8 * q^97 + 137 * q^98 - 10 * q^99

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