LMFDB - Embedded newform 576.2.bl.a.11.4

Newspace parameters

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bl (of order $48$, degree $16$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$1504$
Relative dimension:	$94$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	576.11
Dual form			576.2.bl.a.419.4

$q$-expansion

$f(q)$	$=$	$q+(-1.40127 - 0.190903i) q^{2} +(-0.555798 - 1.64045i) q^{3} +(1.92711 + 0.535013i) q^{4} +(-0.879249 - 0.433598i) q^{5} +(0.465655 + 2.40482i) q^{6} +(-3.05138 - 3.97664i) q^{7} +(-2.59827 - 1.11759i) q^{8} +(-2.38218 + 1.82352i) q^{9} +O(q^{10})$	\(q+(-1.40127 - 0.190903i) q^{2} +(-0.555798 - 1.64045i) q^{3} +(1.92711 + 0.535013i) q^{4} +(-0.879249 - 0.433598i) q^{5} +(0.465655 + 2.40482i) q^{6} +(-3.05138 - 3.97664i) q^{7} +(-2.59827 - 1.11759i) q^{8} +(-2.38218 + 1.82352i) q^{9} +(1.14929 + 0.775439i) q^{10} +(2.06133 + 1.80774i) q^{11} +(-0.193420 - 3.45870i) q^{12} +(-5.93848 - 0.389228i) q^{13} +(3.51666 + 6.15486i) q^{14} +(-0.222612 + 1.68336i) q^{15} +(3.42752 + 2.06206i) q^{16} +(4.41144 + 4.41144i) q^{17} +(3.68619 - 2.10048i) q^{18} +(1.16778 - 1.74771i) q^{19} +(-1.46243 - 1.30600i) q^{20} +(-4.82754 + 7.21586i) q^{21} +(-2.54337 - 2.92664i) q^{22} +(-0.346500 + 0.451567i) q^{23} +(-0.389243 + 4.88349i) q^{24} +(-2.45874 - 3.20429i) q^{25} +(8.24710 + 1.67909i) q^{26} +(4.31541 + 2.89434i) q^{27} +(-3.75280 - 9.29596i) q^{28} +(-1.12262 + 3.30713i) q^{29} +(0.633298 - 2.31634i) q^{30} +(0.0585556 + 0.101421i) q^{31} +(-4.40923 - 3.54383i) q^{32} +(1.81983 - 4.38625i) q^{33} +(-5.33946 - 7.02378i) q^{34} +(0.958664 + 4.81953i) q^{35} +(-5.56633 + 2.23963i) q^{36} +(2.22576 - 1.48721i) q^{37} +(-1.97002 + 2.22607i) q^{38} +(2.66208 + 9.95813i) q^{39} +(1.79994 + 2.10924i) q^{40} +(-5.78272 - 4.43724i) q^{41} +(8.14221 - 9.18977i) q^{42} +(6.20046 + 5.43765i) q^{43} +(3.00525 + 4.58655i) q^{44} +(2.88520 - 0.570423i) q^{45} +(0.571745 - 0.566620i) q^{46} +(0.187150 + 0.698454i) q^{47} +(1.47771 - 6.76878i) q^{48} +(-4.69099 + 17.5070i) q^{49} +(2.83364 + 4.95945i) q^{50} +(4.78490 - 9.68864i) q^{51} +(-11.2359 - 3.92725i) q^{52} +(2.93681 + 0.584167i) q^{53} +(-5.49452 - 4.87958i) q^{54} +(-1.02859 - 2.48324i) q^{55} +(3.48406 + 13.7426i) q^{56} +(-3.51608 - 0.944317i) q^{57} +(2.20443 - 4.41986i) q^{58} +(-2.82777 + 5.73414i) q^{59} +(-1.32962 + 3.12492i) q^{60} +(-4.78134 + 14.0854i) q^{61} +(-0.0626906 - 0.153297i) q^{62} +(14.5204 + 3.90880i) q^{63} +(5.50199 + 5.80759i) q^{64} +(5.05263 + 2.91714i) q^{65} +(-3.38742 + 5.79891i) q^{66} +(3.61240 - 3.16799i) q^{67} +(6.14116 + 10.8615i) q^{68} +(0.933359 + 0.317437i) q^{69} +(-0.423283 - 6.93647i) q^{70} +(-3.60738 - 1.49422i) q^{71} +(8.22748 - 2.07570i) q^{72} +(-3.24012 + 1.34210i) q^{73} +(-3.40281 + 1.65907i) q^{74} +(-3.88992 + 5.81438i) q^{75} +(3.18549 - 2.74325i) q^{76} +(0.898814 - 13.7133i) q^{77} +(-1.82926 - 14.4622i) q^{78} +(-1.75457 - 6.54816i) q^{79} +(-2.11954 - 3.29923i) q^{80} +(2.34954 - 8.68790i) q^{81} +(7.25607 + 7.32171i) q^{82} +(-15.1674 + 7.47972i) q^{83} +(-13.1638 + 11.3230i) q^{84} +(-1.96597 - 5.79155i) q^{85} +(-7.65044 - 8.80330i) q^{86} +(6.04914 + 0.00350914i) q^{87} +(-3.33558 - 7.00070i) q^{88} +(4.73059 + 1.95948i) q^{89} +(-4.15184 + 0.248523i) q^{90} +(16.5727 + 24.8029i) q^{91} +(-0.909338 + 0.684839i) q^{92} +(0.133832 - 0.152428i) q^{93} +(-0.128911 - 1.01445i) q^{94} +(-1.78457 + 1.03032i) q^{95} +(-3.36285 + 9.20279i) q^{96} +(-7.12705 - 4.11480i) q^{97} +(9.91548 - 23.6365i) q^{98} +(-8.20690 - 0.547472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1504 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 1504 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 1504 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} - 16 q^{12} - 8 q^{13} - 24 q^{14} - 16 q^{15} - 8 q^{16} - 16 q^{18} - 32 q^{19} - 24 q^{20} - 16 q^{21} - 8 q^{22} - 24 q^{23} - 96 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} + 64 q^{30} - 16 q^{31} - 24 q^{32} - 8 q^{34} + 64 q^{36} - 32 q^{37} - 24 q^{38} - 16 q^{39} - 8 q^{40} - 24 q^{41} - 96 q^{42} - 8 q^{43} - 16 q^{45} - 32 q^{46} - 24 q^{47} - 16 q^{48} - 8 q^{49} - 24 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{54} - 32 q^{55} - 24 q^{56} - 16 q^{57} + 64 q^{58} - 24 q^{59} - 16 q^{60} - 8 q^{61} - 32 q^{64} - 48 q^{65} - 8 q^{67} - 24 q^{68} - 16 q^{69} - 8 q^{70} - 16 q^{72} - 32 q^{73} - 24 q^{74} - 16 q^{75} - 56 q^{76} - 24 q^{77} - 40 q^{78} - 8 q^{79} - 16 q^{81} - 32 q^{82} - 24 q^{83} - 128 q^{84} - 8 q^{85} - 24 q^{86} - 16 q^{87} - 8 q^{88} - 160 q^{90} - 32 q^{91} - 480 q^{92} + 8 q^{93} - 8 q^{94} - 48 q^{95} - 152 q^{96} - 16 q^{99}+O(q^{100}) $ 1504 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 - 16 * q^12 - 8 * q^13 - 24 * q^14 - 16 * q^15 - 8 * q^16 - 16 * q^18 - 32 * q^19 - 24 * q^20 - 16 * q^21 - 8 * q^22 - 24 * q^23 - 96 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 + 64 * q^30 - 16 * q^31 - 24 * q^32 - 8 * q^34 + 64 * q^36 - 32 * q^37 - 24 * q^38 - 16 * q^39 - 8 * q^40 - 24 * q^41 - 96 * q^42 - 8 * q^43 - 16 * q^45 - 32 * q^46 - 24 * q^47 - 16 * q^48 - 8 * q^49 - 24 * q^50 - 16 * q^51 - 8 * q^52 - 16 * q^54 - 32 * q^55 - 24 * q^56 - 16 * q^57 + 64 * q^58 - 24 * q^59 - 16 * q^60 - 8 * q^61 - 32 * q^64 - 48 * q^65 - 8 * q^67 - 24 * q^68 - 16 * q^69 - 8 * q^70 - 16 * q^72 - 32 * q^73 - 24 * q^74 - 16 * q^75 - 56 * q^76 - 24 * q^77 - 40 * q^78 - 8 * q^79 - 16 * q^81 - 32 * q^82 - 24 * q^83 - 128 * q^84 - 8 * q^85 - 24 * q^86 - 16 * q^87 - 8 * q^88 - 160 * q^90 - 32 * q^91 - 480 * q^92 + 8 * q^93 - 8 * q^94 - 48 * q^95 - 152 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	−1.40127	−	0.190903i	−0.990847	−	0.134989i
$2$	−1.40127	−	0.190903i	−0.990847	−	0.134989i
$3$	−0.555798	−	1.64045i	−0.320890	−	0.947116i
$3$	−0.555798	−	1.64045i	−0.320890	−	0.947116i
$4$	1.92711	+	0.535013i	0.963556	+	0.267507i
$5$	−0.879249	−	0.433598i	−0.393212	−	0.193911i	0.234925	−	0.972014i	$-0.424516\pi$
$5$	−0.879249	−	0.433598i	−0.393212	−	0.193911i	−0.628137	+	0.778103i	$0.716182\pi$
$6$	0.465655	+	2.40482i	0.190103	+	0.981764i
$7$	−3.05138	−	3.97664i	−1.15331	−	1.50303i	−0.830893	−	0.556432i	$-0.812170\pi$
$7$	−3.05138	−	3.97664i	−1.15331	−	1.50303i	−0.322421	−	0.946596i	$-0.604497\pi$
$8$	−2.59827	−	1.11759i	−0.918626	−	0.395128i
$9$	−2.38218	+	1.82352i	−0.794059	+	0.607841i
$10$	1.14929	+	0.775439i	0.363437	+	0.245215i
$11$	2.06133	+	1.80774i	0.621514	+	0.545053i	0.911145	−	0.412085i	$-0.135199\pi$
$11$	2.06133	+	1.80774i	0.621514	+	0.545053i	−0.289631	+	0.957138i	$0.593533\pi$
$12$	−0.193420	−	3.45870i	−0.0558356	−	0.998440i
$13$	−5.93848	−	0.389228i	−1.64704	−	0.107953i	−0.786585	−	0.617483i	$-0.788153\pi$
$13$	−5.93848	−	0.389228i	−1.64704	−	0.107953i	−0.860453	+	0.509530i	$0.829819\pi$
$14$	3.51666	+	6.15486i	0.939866	+	1.64496i
$15$	−0.222612	+	1.68336i	−0.0574782	+	0.434642i
$16$	3.42752	+	2.06206i	0.856880	+	0.515515i
$17$	4.41144	+	4.41144i	1.06993	+	1.06993i	0.997363	+	0.0725684i	$0.0231196\pi$
$17$	4.41144	+	4.41144i	1.06993	+	1.06993i	0.0725684	+	0.997363i	$0.476880\pi$
$18$	3.68619	−	2.10048i	0.868843	−	0.495088i
$19$	1.16778	−	1.74771i	0.267907	−	0.400951i	−0.672986	−	0.739655i	$-0.734989\pi$
$19$	1.16778	−	1.74771i	0.267907	−	0.400951i	0.940893	+	0.338704i	$0.109989\pi$
$20$	−1.46243	−	1.30600i	−0.327009	−	0.292031i
$21$	−4.82754	+	7.21586i	−1.05346	+	1.57463i
$22$	−2.54337	−	2.92664i	−0.542249	−	0.623962i
$23$	−0.346500	+	0.451567i	−0.0722502	+	0.0941583i	−0.828080	−	0.560609i	$-0.810567\pi$
$23$	−0.346500	+	0.451567i	−0.0722502	+	0.0941583i	0.755830	+	0.654768i	$0.227234\pi$
$24$	−0.389243	+	4.88349i	−0.0794538	+	0.996839i
$25$	−2.45874	−	3.20429i	−0.491747	−	0.640857i
$26$	8.24710	+	1.67909i	1.61739	+	0.329296i
$27$	4.31541	+	2.89434i	0.830501	+	0.557016i
$28$	−3.75280	−	9.29596i	−0.709213	−	1.75677i
$29$	−1.12262	+	3.30713i	−0.208465	+	0.614118i	0.791531	+	0.611130i	$0.209285\pi$
$29$	−1.12262	+	3.30713i	−0.208465	+	0.614118i	−0.999996	+	0.00298845i	$0.999049\pi$
$30$	0.633298	−	2.31634i	0.115624	−	0.422905i
$31$	0.0585556	+	0.101421i	0.0105169	+	0.0182158i	0.871236	−	0.490864i	$-0.163319\pi$
$31$	0.0585556	+	0.101421i	0.0105169	+	0.0182158i	−0.860719	+	0.509080i	$0.829986\pi$
$32$	−4.40923	−	3.54383i	−0.779449	−	0.626466i
$33$	1.81983	−	4.38625i	0.316791	−	0.763548i
$34$	−5.33946	−	7.02378i	−0.915710	−	1.20457i
$35$	0.958664	+	4.81953i	0.162044	+	0.814649i
$36$	−5.56633	+	2.23963i	−0.927722	+	0.373272i
$37$	2.22576	−	1.48721i	0.365913	−	0.244495i	−0.358997	−	0.933339i	$-0.616881\pi$
$37$	2.22576	−	1.48721i	0.365913	−	0.244495i	0.724910	+	0.688843i	$0.241881\pi$
$38$	−1.97002	+	2.22607i	−0.319579	+	0.361117i
$39$	2.66208	+	9.95813i	0.426274	+	1.59458i
$40$	1.79994	+	2.10924i	0.284596	+	0.333501i
$41$	−5.78272	−	4.43724i	−0.903109	−	0.692980i	0.0489802	−	0.998800i	$-0.484403\pi$
$41$	−5.78272	−	4.43724i	−0.903109	−	0.692980i	−0.952089	+	0.305820i	$0.901070\pi$
$42$	8.14221	−	9.18977i	1.25637	−	1.41801i
$43$	6.20046	+	5.43765i	0.945561	+	0.829234i	0.985449	−	0.169970i	$-0.0543670\pi$
$43$	6.20046	+	5.43765i	0.945561	+	0.829234i	−0.0398887	+	0.999204i	$0.512700\pi$
$44$	3.00525	+	4.58655i	0.453058	+	0.691449i
$45$	2.88520	−	0.570423i	0.430101	−	0.0850337i
$46$	0.571745	−	0.566620i	0.0842992	−	0.0835435i
$47$	0.187150	+	0.698454i	0.0272986	+	0.101880i	0.978231	−	0.207519i	$-0.0665389\pi$
$47$	0.187150	+	0.698454i	0.0272986	+	0.101880i	−0.950932	+	0.309399i	$0.899872\pi$
$48$	1.47771	−	6.76878i	0.213289	−	0.976989i
$49$	−4.69099	+	17.5070i	−0.670141	+	2.50100i
$50$	2.83364	+	4.95945i	0.400738	+	0.701372i
$51$	4.78490	−	9.68864i	0.670020	−	1.35668i
$52$	−11.2359	−	3.92725i	−1.55813	−	0.544612i
$53$	2.93681	+	0.584167i	0.403402	+	0.0802416i	0.392621	−	0.919700i	$-0.371568\pi$
$53$	2.93681	+	0.584167i	0.403402	+	0.0802416i	0.0107805	+	0.999942i	$0.496568\pi$
$54$	−5.49452	−	4.87958i	−0.747709	−	0.664027i
$55$	−1.02859	−	2.48324i	−0.138695	−	0.334840i
$56$	3.48406	+	13.7426i	0.465577	+	1.83643i
$57$	−3.51608	−	0.944317i	−0.465716	−	0.125078i
$58$	2.20443	−	4.41986i	0.289456	−	0.580357i
$59$	−2.82777	+	5.73414i	−0.368144	+	0.746522i	−0.999582	−	0.0289042i	$-0.990798\pi$
$59$	−2.82777	+	5.73414i	−0.368144	+	0.746522i	0.631438	+	0.775426i	$0.282465\pi$
$60$	−1.32962	+	3.12492i	−0.171653	+	0.403426i
$61$	−4.78134	+	14.0854i	−0.612188	+	1.80345i	−0.0170088	+	0.999855i	$0.505414\pi$
$61$	−4.78134	+	14.0854i	−0.612188	+	1.80345i	−0.595179	+	0.803593i	$0.702919\pi$
$62$	−0.0626906	−	0.153297i	−0.00796171	−	0.0194687i
$63$	14.5204	+	3.90880i	1.82940	+	0.492462i
$64$	5.50199	+	5.80759i	0.687748	+	0.725949i
$65$	5.05263	+	2.91714i	0.626702	+	0.361827i
$66$	−3.38742	+	5.79891i	−0.416962	+	0.713796i
$67$	3.61240	−	3.16799i	0.441324	−	0.387031i	−0.409646	−	0.912244i	$-0.634348\pi$
$67$	3.61240	−	3.16799i	0.441324	−	0.387031i	0.850971	+	0.525213i	$0.176014\pi$
$68$	6.14116	+	10.8615i	0.744725	+	1.31715i
$69$	0.933359	+	0.317437i	0.112363	+	0.0382149i
$70$	−0.423283	−	6.93647i	−0.0505920	−	0.829067i
$71$	−3.60738	−	1.49422i	−0.428117	−	0.177332i	0.158212	−	0.987405i	$-0.449427\pi$
$71$	−3.60738	−	1.49422i	−0.428117	−	0.177332i	−0.586328	+	0.810073i	$0.699427\pi$
$72$	8.22748	−	2.07570i	0.969618	−	0.244624i
$73$	−3.24012	+	1.34210i	−0.379227	+	0.157081i	−0.564151	−	0.825672i	$-0.690796\pi$
$73$	−3.24012	+	1.34210i	−0.379227	+	0.157081i	0.184923	+	0.982753i	$0.440796\pi$
$74$	−3.40281	+	1.65907i	−0.395568	+	0.192863i
$75$	−3.88992	+	5.81438i	−0.449170	+	0.671386i
$76$	3.18549	−	2.74325i	0.365400	−	0.314672i
$77$	0.898814	−	13.7133i	0.102429	−	1.56277i
$78$	−1.82926	−	14.4622i	−0.207123	−	1.63752i
$79$	−1.75457	−	6.54816i	−0.197405	−	0.736726i	−0.991631	−	0.129103i	$-0.958790\pi$
$79$	−1.75457	−	6.54816i	−0.197405	−	0.736726i	0.794226	−	0.607622i	$-0.207877\pi$
$80$	−2.11954	−	3.29923i	−0.236972	−	0.368865i
$81$	2.34954	−	8.68790i	0.261060	−	0.965323i
$82$	7.25607	+	7.32171i	0.801299	+	0.808547i
$83$	−15.1674	+	7.47972i	−1.66484	+	0.821006i	−0.667778	+	0.744361i	$0.732754\pi$
$83$	−15.1674	+	7.47972i	−1.66484	+	0.821006i	−0.997058	+	0.0766454i	$0.975579\pi$
$84$	−13.1638	+	11.3230i	−1.43629	+	1.23544i
$85$	−1.96597	−	5.79155i	−0.213239	−	0.628182i
$86$	−7.65044	−	8.80330i	−0.824969	−	0.949285i
$87$	6.04914	+	0.00350914i	0.648536	+	0.000376219i
$88$	−3.33558	−	7.00070i	−0.355574	−	0.746278i
$89$	4.73059	+	1.95948i	0.501442	+	0.207704i	0.619043	−	0.785357i	$-0.287521\pi$
$89$	4.73059	+	1.95948i	0.501442	+	0.207704i	−0.117602	+	0.993061i	$0.537521\pi$
$90$	−4.15184	+	0.248523i	−0.437642	+	0.0261966i
$91$	16.5727	+	24.8029i	1.73730	+	2.60005i
$92$	−0.909338	+	0.684839i	−0.0948051	+	0.0713994i
$93$	0.133832	−	0.152428i	0.0138777	−	0.0158060i
$94$	−0.128911	−	1.01445i	−0.0132961	−	0.104632i
$95$	−1.78457	+	1.03032i	−0.183093	+	0.105709i
$96$	−3.36285	+	9.20279i	−0.343219	+	0.939255i
$97$	−7.12705	−	4.11480i	−0.723642	−	0.417795i	0.0924494	−	0.995717i	$-0.470530\pi$
$97$	−7.12705	−	4.11480i	−0.723642	−	0.417795i	−0.816092	+	0.577922i	$0.803864\pi$
$98$	9.91548	−	23.6365i	1.00161	−	2.38765i
$99$	−8.20690	−	0.547472i	−0.824824	−	0.0550230i
$100$	−3.02392	−	7.49047i	−0.302392	−	0.749047i
$101$	−9.68656	+	0.634890i	−0.963848	+	0.0631740i	−0.539194	−	0.842182i	$-0.681271\pi$
$101$	−9.68656	+	0.634890i	−0.963848	+	0.0631740i	−0.424654	+	0.905356i	$0.639604\pi$
$102$	−8.55452	+	12.6629i	−0.847024	+	1.25382i
$103$	0.00307183	+	0.0233329i	0.000302677	+	0.00229906i	0.991596	−	0.129377i	$-0.0412976\pi$
$103$	0.00307183	+	0.0233329i	0.000302677	+	0.00229906i	−0.991293	+	0.131676i	$0.957964\pi$
$104$	14.9948	+	7.64810i	1.47036	+	0.749958i
$105$	7.37339	−	4.25133i	0.719569	−	0.414887i
$106$	−4.00374	−	1.37922i	−0.388878	−	0.133962i
$107$	−11.3462	−	2.25689i	−1.09688	−	0.218182i	−0.386699	−	0.922206i	$-0.626385\pi$
$107$	−11.3462	−	2.25689i	−1.09688	−	0.218182i	−0.710177	+	0.704024i	$0.751385\pi$
$108$	6.76777	+	7.88653i	0.651229	+	0.758881i
$109$	−6.43133	−	4.29728i	−0.616010	−	0.411604i	0.208041	−	0.978120i	$-0.433291\pi$
$109$	−6.43133	−	4.29728i	−0.616010	−	0.411604i	−0.824051	+	0.566516i	$0.808291\pi$
$110$	0.967275	+	3.67605i	0.0922261	+	0.350497i
$111$	−3.67677	−	2.82467i	−0.348983	−	0.268106i
$112$	−2.25860	−	19.9222i	−0.213418	−	1.88247i
$113$	−3.12134	−	0.836360i	−0.293631	−	0.0786781i	0.108997	−	0.994042i	$-0.465236\pi$
$113$	−3.12134	−	0.836360i	−0.293631	−	0.0786781i	−0.402627	+	0.915364i	$0.631903\pi$
$114$	4.74670	+	1.99447i	0.444569	+	0.186800i
$115$	0.500458	−	0.246799i	0.0466680	−	0.0230141i
$116$	−3.93277	+	5.77259i	−0.365148	+	0.535971i
$117$	14.8563	−	9.90173i	1.37346	−	0.915415i
$118$	5.05713	−	7.49525i	0.465546	−	0.689994i
$119$	4.08172	−	31.0037i	0.374170	−	2.84211i
$120$	2.45971	−	4.12503i	0.224540	−	0.376562i
$121$	−0.454624	−	3.45321i	−0.0413294	−	0.313928i
$122$	9.38889	−	18.8246i	0.850030	−	1.70430i
$123$	−4.06506	+	11.9525i	−0.366534	+	1.07772i
$124$	0.0585815	+	0.226778i	0.00526077	+	0.0203653i
$125$	1.72875	+	8.69103i	0.154624	+	0.777349i
$126$	−19.6008	−	8.24927i	−1.74618	−	0.734903i
$127$		−	14.7610i		−	1.30982i	−0.755706	−	0.654912i	$-0.772706\pi$
$127$		−	14.7610i		−	1.30982i	0.755706	−	0.654912i	$-0.227294\pi$
$128$	−6.60108	−	9.18835i	−0.583458	−	0.812143i
$129$	5.47402	−	13.1938i	0.481960	−	1.16165i
$130$	−6.52321	−	5.05226i	−0.572123	−	0.443113i
$131$	9.85375	+	11.2360i	0.860926	+	0.981698i	0.999963	−	0.00858899i	$-0.00273400\pi$
$131$	9.85375	+	11.2360i	0.860926	+	0.981698i	−0.139037	+	0.990287i	$0.544401\pi$
$132$	5.85371	−	7.47917i	0.509500	−	0.650978i
$133$	−10.5133	+	0.689080i	−0.911622	+	0.0597508i
$134$	−5.66672	+	3.74958i	−0.489530	+	0.323915i
$135$	−2.53934	−	4.41600i	−0.218552	−	0.380069i
$136$	−6.53192	−	16.3923i	−0.560108	−	1.40563i
$137$	−13.3408	−	1.75635i	−1.13978	−	0.150055i	−0.463082	−	0.886315i	$-0.653256\pi$
$137$	−13.3408	−	1.75635i	−1.13978	−	0.150055i	−0.676698	+	0.736261i	$0.736590\pi$
$138$	−1.24729	−	0.622996i	−0.106176	−	0.0530329i
$139$	−3.62497	−	10.6788i	−0.307466	−	0.905765i	−0.985342	−	0.170589i	$-0.945433\pi$
$139$	−3.62497	−	10.6788i	−0.307466	−	0.905765i	0.677877	−	0.735176i	$-0.262900\pi$
$140$	−0.731060	+	9.80067i	−0.0617858	+	0.828308i
$141$	1.04176	−	0.695210i	0.0877323	−	0.0585473i
$142$	4.76965	+	2.78247i	0.400260	+	0.233500i
$143$	−11.5375	−	11.5375i	−0.964817	−	0.964817i
$144$	−11.9252	+	1.33796i	−0.993765	+	0.111497i
$145$	2.42102	−	2.42102i	0.201055	−	0.201055i
$146$	4.79649	−	1.26210i	0.396961	−	0.104452i
$147$	31.3267	−	2.03501i	2.58378	−	0.167845i
$148$	5.08497	−	1.67520i	0.417982	−	0.137701i
$149$	6.13668	−	2.08312i	0.502736	−	0.170656i	−0.0585390	−	0.998285i	$-0.518644\pi$
$149$	6.13668	−	2.08312i	0.502736	−	0.170656i	0.561275	+	0.827629i	$0.310311\pi$
$150$	6.56081	−	7.40491i	0.535688	−	0.604608i
$151$	−0.271652	+	2.06340i	−0.0221067	+	0.167917i	−0.998937	−	0.0460986i	$-0.985321\pi$
$151$	−0.271652	+	2.06340i	−0.0221067	+	0.167917i	0.976830	+	0.214016i	$0.0686545\pi$
$152$	−4.98742	+	3.23591i	−0.404533	+	0.262467i
$153$	−18.5532	−	2.46448i	−1.49994	−	0.199241i
$154$	−3.87738	+	19.0444i	−0.312449	+	1.53464i
$155$	−0.00750893	−	0.114564i	−0.000603132	−	0.00920202i
$156$	−0.197602	+	20.6147i	−0.0158209	+	1.65050i
$157$	−4.79002	+	4.20074i	−0.382285	+	0.335255i	−0.828824	−	0.559509i	$-0.810990\pi$
$157$	−4.79002	+	4.20074i	−0.382285	+	0.335255i	0.446539	+	0.894764i	$0.352656\pi$
$158$	1.20857	+	9.51069i	0.0961484	+	0.756630i
$159$	−0.673972	−	5.14238i	−0.0534495	−	0.407817i
$160$	2.34021	+	5.02774i	0.185010	+	0.397478i
$161$	2.85302			0.224850
$162$	−4.95088	+	11.7256i	−0.388978	+	0.921247i
$163$	8.20918	−	1.63291i	0.642992	−	0.127899i	0.137185	−	0.990545i	$-0.456195\pi$
$163$	8.20918	−	1.63291i	0.642992	−	0.127899i	0.505808	+	0.862646i	$0.331195\pi$
$164$	−8.76997	−	11.6449i	−0.684820	−	0.909313i
$165$	−3.50195	+	3.06754i	−0.272626	+	0.238807i
$166$	22.6815	−	7.58561i	1.76042	−	0.588757i
$167$	3.98383	−	0.524481i	0.308278	−	0.0405856i	0.0251998	−	0.999682i	$-0.491978\pi$
$167$	3.98383	−	0.524481i	0.308278	−	0.0405856i	0.283078	+	0.959097i	$0.408644\pi$
$168$	20.6076	−	13.3535i	1.58991	−	1.03025i
$169$	22.2252	+	2.92601i	1.70963	+	0.225078i
$170$	1.64922	+	8.49083i	0.126490	+	0.651217i
$171$	0.405121	+	6.29281i	0.0309804	+	0.481224i
$172$	9.03975	+	13.7963i	0.689275	+	1.05196i
$173$	4.12292	+	8.36045i	0.313460	+	0.635633i	0.995403	−	0.0957715i	$-0.0305318\pi$
$173$	4.12292	+	8.36045i	0.313460	+	0.635633i	−0.681944	+	0.731405i	$0.738865\pi$
$174$	−8.47580	−	1.15972i	−0.642549	−	0.0879179i
$175$	−5.23975	+	19.5550i	−0.396088	+	1.47822i
$176$	3.33758	+	10.4466i	0.251580	+	0.787445i
$177$	10.9783	+	1.45180i	0.825177	+	0.109124i
$178$	−6.25476	−	3.64884i	−0.468814	−	0.273492i
$179$	−0.988830	+	1.47989i	−0.0739086	+	0.110612i	−0.866583	−	0.499034i	$-0.833688\pi$
$179$	−0.988830	+	1.47989i	−0.0739086	+	0.110612i	0.792674	+	0.609646i	$0.208688\pi$
$180$	5.86529	+	0.444352i	0.437173	+	0.0331201i
$181$	−3.16347	+	15.9038i	−0.235139	+	1.18212i	0.665110	+	0.746745i	$0.268385\pi$
$181$	−3.16347	+	15.9038i	−0.235139	+	1.18212i	−0.900249	+	0.435376i	$0.856615\pi$
$182$	−18.4879	−	37.9193i	−1.37042	−	2.81076i
$183$	25.7639	+	0.0149458i	1.90452	+	0.00110482i
$184$	1.40497	−	0.786048i	0.103575	−	0.0579482i
$185$	−2.60185	+	0.342540i	−0.191292	+	0.0251840i
$186$	−0.216633	+	0.188043i	−0.0158843	+	0.0137880i
$187$	1.11871	+	17.0682i	0.0818079	+	1.24815i
$188$	−0.0130229	+	1.44613i	−0.000949792	+	0.105470i
$189$	−1.65822	−	25.9926i	−0.120618	−	1.89068i
$190$	2.69735	−	1.10308i	0.195687	−	0.0800257i
$191$	6.39384	−	11.0745i	0.462642	−	0.801320i	−0.536450	−	0.843932i	$-0.680235\pi$
$191$	6.39384	−	11.0745i	0.462642	−	0.801320i	0.999092	+	0.0426128i	$0.0135682\pi$
$192$	6.46910	−	12.2536i	0.466867	−	0.884328i
$193$	−12.4690	−	21.5970i	−0.897540	−	1.55459i	−0.830629	−	0.556826i	$-0.812019\pi$
$193$	−12.4690	−	21.5970i	−0.897540	−	1.55459i	−0.0669112	−	0.997759i	$-0.521314\pi$
$194$	9.20139	+	7.12653i	0.660621	+	0.511655i
$195$	1.97719	−	9.90995i	0.141589	−	0.709666i
$196$	−18.4065	+	31.2282i	−1.31475	+	2.23059i
$197$	−15.3914	+	10.2842i	−1.09659	+	0.732718i	−0.965954	−	0.258713i	$-0.916702\pi$
$197$	−15.3914	+	10.2842i	−1.09659	+	0.732718i	−0.130635	+	0.991430i	$0.541702\pi$
$198$	11.3956	+	2.33388i	0.809847	+	0.165862i
$199$	2.28526	−	5.51711i	0.161998	−	0.391098i	−0.821948	−	0.569562i	$-0.807113\pi$
$199$	2.28526	−	5.51711i	0.161998	−	0.391098i	0.983946	+	0.178464i	$0.0571129\pi$
$200$	2.80737	+	11.0734i	0.198511	+	0.783011i
$201$	−7.20470	−	4.16521i	−0.508180	−	0.293791i
$202$	13.6947	+	0.959541i	0.963554	+	0.0675131i
$203$	16.5768	−	5.62706i	1.16346	−	0.394942i
$204$	14.4046	−	16.1111i	1.00852	−	1.12800i
$205$	3.16048	+	6.40881i	0.220737	+	0.447611i
$206$	0.000149856	−	0.0332821i	1.04409e−5	−	0.00231887i
$207$	0.00198113	−	1.70756i	0.000137698	−	0.118684i
$208$	−19.5516	−	13.5796i	−1.35566	−	0.941576i
$209$	5.56657	−	1.49156i	0.385048	−	0.103173i
$210$	−11.1437	+	4.54965i	−0.768988	+	0.313956i
$211$	−9.70985	−	0.636417i	−0.668454	−	0.0438128i	−0.272601	−	0.962127i	$-0.587884\pi$
$211$	−9.70985	−	0.636417i	−0.668454	−	0.0438128i	−0.395852	+	0.918314i	$0.629551\pi$
$212$	5.34702	+	2.69699i	0.367235	+	0.185230i
$213$	−0.446233	+	6.74822i	−0.0305754	+	0.462380i
$214$	15.4682	+	5.32854i	1.05738	+	0.364251i
$215$	−3.09399	−	7.46955i	−0.211008	−	0.509419i
$216$	−7.97791	−	12.3431i	−0.542828	−	0.839844i
$217$	0.224640	−	0.542330i	0.0152496	−	0.0368157i
$218$	8.19166	+	7.24940i	0.554809	+	0.490991i
$219$	4.00251	+	4.56933i	0.270464	+	0.308767i
$220$	−0.653644	−	5.33579i	−0.0440687	−	0.359739i
$221$	−24.4802	−	27.9143i	−1.64672	−	1.87772i
$222$	4.61290	+	4.66004i	0.309598	+	0.312761i
$223$	1.86168	−	3.22452i	0.124667	−	0.215930i	−0.796936	−	0.604064i	$-0.793547\pi$
$223$	1.86168	−	3.22452i	0.124667	−	0.215930i	0.921603	+	0.388134i	$0.126880\pi$
$224$	−0.638289	+	28.3475i	−0.0426475	+	1.89405i
$225$	11.7002	+	3.14962i	0.780015	+	0.209975i
$226$	4.21417	+	1.76784i	0.280323	+	0.117595i
$227$	−10.2488	−	3.47901i	−0.680239	−	0.230910i	−0.0401302	−	0.999194i	$-0.512777\pi$
$227$	−10.2488	−	3.47901i	−0.680239	−	0.230910i	−0.640108	+	0.768285i	$0.721111\pi$
$228$	−6.27066	−	3.70095i	−0.415284	−	0.245102i
$229$	−16.7873	−	8.27860i	−1.10934	−	0.547065i	−0.207107	−	0.978318i	$-0.566405\pi$
$229$	−16.7873	−	8.27860i	−1.10934	−	0.547065i	−0.902231	+	0.431253i	$0.858072\pi$
$230$	−0.748391	+	0.250292i	−0.0493475	+	0.0165038i
$231$	−22.9955	+	6.14734i	−1.51299	+	0.404465i
$232$	6.61287	−	7.33817i	0.434156	−	0.481775i
$233$	−25.0019	+	10.3561i	−1.63793	+	0.678453i	−0.996087	−	0.0883812i	$-0.971831\pi$
$233$	−25.0019	+	10.3561i	−1.63793	+	0.678453i	−0.641845	+	0.766835i	$0.721831\pi$
$234$	−22.7079	+	11.0389i	−1.48446	+	0.721635i
$235$	0.138296	−	0.695263i	0.00902146	−	0.0453539i
$236$	−8.51727	+	9.53744i	−0.554427	+	0.620835i
$237$	−9.76676	+	6.51775i	−0.634420	+	0.423373i
$238$	−11.6383	+	42.6653i	−0.754398	+	2.76558i
$239$	15.5586	+	4.16890i	1.00640	+	0.269664i	0.724124	−	0.689670i	$-0.242244\pi$
$239$	15.5586	+	4.16890i	1.00640	+	0.269664i	0.282275	+	0.959334i	$0.408911\pi$
$240$	−4.23420	+	5.31071i	−0.273316	+	0.342805i
$241$	−2.50949	+	0.672415i	−0.161650	+	0.0433141i	−0.338736	−	0.940881i	$-0.610000\pi$
$241$	−2.50949	+	0.672415i	−0.161650	+	0.0433141i	0.177086	+	0.984195i	$0.443333\pi$
$242$	−0.0221783	+	4.92567i	−0.00142567	+	0.316634i
$243$	−15.5580	+	0.974412i	−0.998044	+	0.0625085i
$244$	−16.7501	+	24.5860i	−1.07231	+	1.57396i
$245$	11.7155	−	13.3590i	0.748479	−	0.853476i
$246$	7.97801	−	15.9726i	0.508659	−	1.01838i
$247$	−7.61509	+	9.92418i	−0.484536	+	0.631460i
$248$	−0.0387958	−	0.328961i	−0.00246353	−	0.0208890i
$249$	20.7001	+	20.7242i	1.31182	+	1.31334i
$250$	−0.763305	−	12.5085i	−0.0482756	−	0.791107i
$251$	−13.7572	−	20.5891i	−0.868347	−	1.29957i	−0.952940	−	0.303158i	$-0.901959\pi$
$251$	−13.7572	−	20.5891i	−0.868347	−	1.29957i	0.0845928	−	0.996416i	$-0.473041\pi$
$252$	25.8912	+	15.3013i	1.63099	+	0.963892i
$253$	−1.53057	+	0.304448i	−0.0962258	+	0.0191405i
$254$	−2.81791	+	20.6841i	−0.176812	+	1.29783i
$255$	−8.40809	+	6.44401i	−0.526535	+	0.403539i
$256$	7.49580	+	14.1355i	0.468488	+	0.883470i
$257$	20.4339	−	11.7975i	1.27463	−	0.735909i	0.298775	−	0.954323i	$-0.403422\pi$
$257$	20.4339	−	11.7975i	1.27463	−	0.735909i	0.975856	+	0.218415i	$0.0700885\pi$
$258$	−10.1893	+	17.4431i	−0.634359	+	1.08596i
$259$	−12.7057	−	4.31302i	−0.789496	−	0.267998i
$260$	8.17628	+	8.32488i	0.507071	+	0.516287i
$261$	−3.35634	−	9.92528i	−0.207752	−	0.614360i
$262$	−11.6628	−	17.6258i	−0.720528	−	1.08893i
$263$	−10.4556	+	8.02289i	−0.644722	+	0.494712i	−0.878603	−	0.477553i	$-0.841524\pi$
$263$	−10.4556	+	8.02289i	−0.644722	+	0.494712i	0.233881	+	0.972265i	$0.424857\pi$
$264$	−9.63043	+	9.36284i	−0.592712	+	0.576243i
$265$	−2.32889	−	1.78702i	−0.143063	−	0.109776i
$266$	14.8636	+	1.04144i	0.911343	+	0.0638548i
$267$	0.585175	−	8.84939i	0.0358122	−	0.541574i
$268$	8.65641	−	4.17238i	0.528774	−	0.254869i
$269$	20.5328	+	13.7196i	1.25191	+	0.836497i	0.991639	−	0.129040i	$-0.0411895\pi$
$269$	20.5328	+	13.7196i	1.25191	+	0.836497i	0.260267	+	0.965537i	$0.416189\pi$
$270$	2.71527	+	6.67277i	0.165246	+	0.406092i
$271$	−21.4675	+	21.4675i	−1.30406	+	1.30406i	−0.378429	+	0.925630i	$0.623536\pi$
$271$	−21.4675	+	21.4675i	−1.30406	+	1.30406i	−0.925630	+	0.378429i	$0.876464\pi$
$272$	6.02365	+	24.2170i	0.365237	+	1.46837i
$273$	31.4769	−	40.9722i	1.90507	−	2.47975i
$274$	18.3587	+	5.00791i	1.10909	+	0.302539i
$275$	0.724244	−	11.0498i	0.0436736	−	0.666330i
$276$	1.62885	+	1.11110i	0.0980455	+	0.0668801i
$277$	7.57571	−	8.63844i	0.455180	−	0.519033i	−0.478040	−	0.878338i	$-0.658653\pi$
$277$	7.57571	−	8.63844i	0.455180	−	0.519033i	0.933220	+	0.359305i	$0.116986\pi$
$278$	3.04094	+	15.6559i	0.182383	+	0.938979i
$279$	−0.324434	−	0.134826i	−0.0194233	−	0.00807183i
$280$	2.89539	−	13.5938i	0.173033	−	0.812386i
$281$	15.8903	−	12.1931i	0.947937	−	0.727377i	−0.0142129	−	0.999899i	$-0.504524\pi$
$281$	15.8903	−	12.1931i	0.947937	−	0.727377i	0.962150	+	0.272522i	$0.0878576\pi$
$282$	−1.59251	+	0.775301i	−0.0948325	+	0.0461685i
$283$	1.50599	−	3.05384i	0.0895216	−	0.181532i	−0.847507	−	0.530784i	$-0.821898\pi$
$283$	1.50599	−	3.05384i	0.0895216	−	0.181532i	0.937029	+	0.349252i	$0.113564\pi$
$284$	−6.15239	−	4.80953i	−0.365077	−	0.285393i
$285$	2.68206	+	2.35485i	0.158871	+	0.139489i
$286$	13.9646	+	18.3697i	0.825747	+	1.08623i
$287$			36.5355i			2.15662i
$288$	16.9658	+	0.401707i	0.999720	+	0.0236708i
$289$			21.9216i			1.28951i
$290$	−3.85469	+	2.93033i	−0.226355	+	0.172075i
$291$	−2.78895	+	13.9786i	−0.163491	+	0.819440i
$292$	−6.96212	+	0.852872i	−0.407427	+	0.0499106i
$293$	−9.52520	+	19.3152i	−0.556468	+	1.12841i	0.418943	+	0.908013i	$0.362401\pi$
$293$	−9.52520	+	19.3152i	−0.556468	+	1.12841i	−0.975411	+	0.220393i	$0.929266\pi$
$294$	−44.2856	−	3.12877i	−2.58279	−	0.182473i
$295$	4.97262	−	3.81563i	0.289517	−	0.222154i
$296$	−7.44521	+	1.37667i	−0.432744	+	0.0800174i
$297$	3.66328	+	13.7673i	0.212565	+	0.798861i
$298$	−8.99682	+	1.74750i	−0.521172	+	0.101230i
$299$	2.23344	−	2.54676i	0.129163	−	0.147283i
$300$	−10.6071	+	9.12379i	−0.612400	+	0.526763i
$301$	2.70362	−	41.2493i	0.155834	−	2.37757i
$302$	0.774568	−	2.83952i	0.0445714	−	0.163396i
$303$	6.42528	+	15.5375i	0.369122	+	0.892605i
$304$	7.60646	−	3.58226i	0.436261	−	0.205457i
$305$	10.3114	−	10.3114i	0.590428	−	0.590428i
$306$	25.5276	+	6.99526i	1.45931	+	0.399892i
$307$	6.74380	+	4.50606i	0.384889	+	0.257175i	0.732929	−	0.680305i	$-0.238153\pi$
$307$	6.74380	+	4.50606i	0.384889	+	0.257175i	−0.348040	+	0.937480i	$0.613153\pi$
$308$	9.06889	−	25.9461i	0.516748	−	1.47842i
$309$	0.0365692	−	0.0180076i	0.00208035	−	0.00102441i
$310$	−0.0113486	+	0.161969i	−0.000644558	+	0.00919921i
$311$	−19.0863	−	14.6454i	−1.08228	−	0.830465i	−0.0959760	−	0.995384i	$-0.530597\pi$
$311$	−19.0863	−	14.6454i	−1.08228	−	0.830465i	−0.986307	+	0.164919i	$0.947264\pi$
$312$	4.21230	−	28.8490i	0.238475	−	1.63325i
$313$	−23.7369	+	18.2140i	−1.34169	+	1.02951i	−0.345860	+	0.938286i	$0.612413\pi$
$313$	−23.7369	+	18.2140i	−1.34169	+	1.02951i	−0.995830	+	0.0912288i	$0.970921\pi$
$314$	7.51404	−	4.97193i	0.424042	−	0.280582i
$315$	−11.0722	−	9.73283i	−0.623849	−	0.548383i
$316$	0.122093	−	13.5578i	0.00686824	−	0.762683i
$317$	17.6046	+	5.97594i	0.988770	+	0.335642i	0.768537	−	0.639805i	$-0.220985\pi$
$317$	17.6046	+	5.97594i	0.988770	+	0.335642i	0.220233	+	0.975447i	$0.429318\pi$
$318$	−0.0372792	+	7.33452i	−0.00209052	+	0.411299i
$319$	−8.29250	+	4.78768i	−0.464291	+	0.268059i
$320$	−2.31946	−	7.49197i	−0.129662	−	0.418814i
$321$	2.60385	+	19.8673i	0.145333	+	1.10888i
$322$	−3.99785	−	0.544651i	−0.222792	−	0.0303522i
$323$	12.8615	−	2.55831i	0.715633	−	0.142348i
$324$	9.17597	−	15.4855i	0.509776	−	0.860307i
$325$	13.3539	+	19.9856i	0.740744	+	1.10860i
$326$	−11.8150	+	0.720985i	−0.654372	+	0.0399317i
$327$	−3.47496	+	12.9387i	−0.192166	+	0.715513i
$328$	10.0660	+	17.9918i	0.555804	+	0.993433i
$329$	2.20643	−	2.87548i	0.121644	−	0.158530i
$330$	5.49278	−	3.62991i	0.302367	−	0.199820i
$331$	6.02524	−	6.87047i	0.331177	−	0.377635i	−0.562155	−	0.827032i	$-0.690028\pi$
$331$	6.02524	−	6.87047i	0.331177	−	0.377635i	0.893332	+	0.449397i	$0.148361\pi$
$332$	−33.2310	+	6.29951i	−1.82379	+	0.345731i
$333$	−2.59021	+	7.60152i	−0.141942	+	0.416561i
$334$	−5.68254	−	0.0255862i	−0.310935	−	0.00140001i
$335$	−4.54983	+	1.21912i	−0.248584	+	0.0666078i
$336$	−31.4260	+	14.7778i	−1.71443	+	0.806196i
$337$	27.3579	+	7.33052i	1.49028	+	0.399319i	0.909831	−	0.414979i	$-0.136211\pi$
$337$	27.3579	+	7.33052i	1.49028	+	0.399319i	0.580447	+	0.814298i	$0.302878\pi$
$338$	−30.5850	−	8.34299i	−1.66360	−	0.453799i
$339$	0.362823	+	5.58526i	0.0197059	+	0.303350i
$340$	−0.690080	−	12.2128i	−0.0374248	−	0.662331i
$341$	−0.0626407	+	0.314916i	−0.00339218	+	0.0170537i
$342$	0.633634	−	8.89527i	0.0342630	−	0.481001i
$343$	51.5168	−	21.3390i	2.78164	−	1.15220i
$344$	−10.0334	−	21.0580i	−0.540963	−	1.13537i
$345$	−0.683015	−	0.683808i	−0.0367723	−	0.0368150i
$346$	−4.18128	−	12.5023i	−0.224787	−	0.672129i
$347$	−4.85978	−	2.39658i	−0.260886	−	0.128655i	0.307142	−	0.951664i	$-0.400627\pi$
$347$	−4.85978	−	2.39658i	−0.260886	−	0.128655i	−0.568029	+	0.823009i	$0.692294\pi$
$348$	11.6555	+	3.24313i	0.624800	+	0.173850i
$349$	15.5118	+	5.26555i	0.830328	+	0.281858i	0.704062	−	0.710138i	$-0.251368\pi$
$349$	15.5118	+	5.26555i	0.830328	+	0.281858i	0.126265	+	0.991997i	$0.459701\pi$
$350$	11.0754	−	26.4015i	0.592005	−	1.41122i
$351$	−24.5004	−	18.8677i	−1.30774	−	1.00708i
$352$	−2.68256	−	15.2757i	−0.142981	−	0.814199i
$353$	−12.2866	+	21.2809i	−0.653947	+	1.13267i	0.328209	+	0.944605i	$0.393555\pi$
$353$	−12.2866	+	21.2809i	−0.653947	+	1.13267i	−0.982157	+	0.188065i	$0.939778\pi$
$354$	−15.1064	−	4.13014i	−0.802894	−	0.219515i
$355$	2.52389	+	2.87794i	0.133954	+	0.152745i
$356$	8.06804	+	6.30706i	0.427605	+	0.334273i
$357$	−53.1288	+	10.5359i	−2.81187	+	0.557621i
$358$	1.66813	−	1.88495i	0.0881635	−	0.0996228i
$359$	7.90113	−	19.0750i	0.417006	−	1.00674i	−0.566205	−	0.824265i	$-0.691589\pi$
$359$	7.90113	−	19.0750i	0.417006	−	1.00674i	0.983210	−	0.182476i	$-0.0584112\pi$
$360$	−8.13403	−	1.74236i	−0.428701	−	0.0918304i
$361$	5.58022	+	13.4718i	0.293696	+	0.709044i
$362$	7.46896	−	21.6816i	0.392560	−	1.13956i
$363$	−5.41215	+	2.66508i	−0.284064	+	0.139880i
$364$	18.6677	+	56.6645i	0.978452	+	2.97003i
$365$	3.43080	+	0.224867i	0.179577	+	0.0117701i
$366$	−36.0993	−	4.93935i	−1.88694	−	0.258184i
$367$	3.17884	−	0.851769i	0.165934	−	0.0444620i	−0.174895	−	0.984587i	$-0.555959\pi$
$367$	3.17884	−	0.851769i	0.165934	−	0.0444620i	0.340830	+	0.940125i	$0.389292\pi$
$368$	−2.11880	+	0.833253i	−0.110450	+	0.0434363i
$369$	21.8669	+	0.0253702i	1.13834	+	0.00132072i
$370$	3.71128	+	0.0167104i	0.192940	+	0.000868732i
$371$	−6.63830	−	13.4611i	−0.344643	−	0.698868i
$372$	0.339460	−	0.222143i	0.0176002	−	0.0115176i
$373$	−17.3981	+	5.90585i	−0.900838	+	0.305793i	−0.733166	−	0.680050i	$-0.761958\pi$
$373$	−17.3981	+	5.90585i	−0.900838	+	0.305793i	−0.167672	+	0.985843i	$0.553625\pi$
$374$	1.69076	−	24.1307i	0.0874269	−	1.24777i
$375$	13.2964	−	7.66640i	0.686623	−	0.395891i
$376$	0.294319	−	2.02393i	0.0151783	−	0.104376i
$377$	7.95387	−	19.2023i	0.409645	−	0.988971i
$378$	−2.63845	+	36.7392i	−0.135707	+	1.88966i
$379$	19.7359	−	13.1871i	1.01377	−	0.677376i	0.0664867	−	0.997787i	$-0.478821\pi$
$379$	19.7359	−	13.1871i	1.01377	−	0.677376i	0.947279	+	0.320411i	$0.103821\pi$
$380$	−3.99030	+	1.03078i	−0.204698	+	0.0528777i
$381$	−24.2147	+	8.20411i	−1.24056	+	0.420309i
$382$	−11.0736	+	14.2977i	−0.566577	+	0.731534i
$383$	−4.28416	−	7.42039i	−0.218910	−	0.379164i	0.735565	−	0.677455i	$-0.236917\pi$
$383$	−4.28416	−	7.42039i	−0.218910	−	0.379164i	−0.954475	+	0.298290i	$0.903584\pi$
$384$	−11.4042	+	15.9356i	−0.581968	+	0.813212i
$385$	−6.73632	+	11.6676i	−0.343315	+	0.594638i
$386$	13.3495	+	32.6436i	0.679473	+	1.66151i
$387$	−24.6863	−	1.64679i	−1.25487	−	0.0837110i
$388$	−11.5331	−	11.7428i	−0.585507	−	0.596148i
$389$	0.0182123	+	0.277866i	0.000923400	+	0.0140884i	0.998296	−	0.0583573i	$-0.0185863\pi$
$389$	0.0182123	+	0.277866i	0.000923400	+	0.0140884i	−0.997372	+	0.0724457i	$0.976920\pi$
$390$	−4.66241	+	13.5091i	−0.236091	+	0.684058i
$391$	−3.52063	+	0.463499i	−0.178046	+	0.0234402i
$392$	31.7541	−	40.2453i	1.60382	−	2.03269i
$393$	12.9555	−	22.4096i	0.653520	−	1.13041i
$394$	23.5307	−	11.4727i	1.18546	−	0.577984i
$395$	−1.29656	+	6.51824i	−0.0652370	+	0.327968i
$396$	−15.5227	−	5.44584i	−0.780045	−	0.273664i
$397$	8.87150	−	13.2771i	0.445248	−	0.666361i	−0.539172	−	0.842196i	$-0.681263\pi$
$397$	8.87150	−	13.2771i	0.445248	−	0.666361i	0.984420	+	0.175835i	$0.0562626\pi$
$398$	−4.25550	+	7.29469i	−0.213309	+	0.365650i
$399$	6.97369	+	16.8636i	0.349121	+	0.844238i
$400$	−1.81993	−	16.0528i	−0.0909966	−	0.802641i
$401$	−2.28813	+	8.53941i	−0.114264	+	0.426438i	−0.999231	−	0.0392158i	$-0.987514\pi$
$401$	−2.28813	+	8.53941i	−0.114264	+	0.426438i	0.884967	+	0.465654i	$0.154181\pi$
$402$	9.30057	+	7.21198i	0.463870	+	0.359701i
$403$	−0.308255	−	0.625080i	−0.0153553	−	0.0311374i
$404$	−19.0068	−	3.95893i	−0.945621	−	0.196964i
$405$	−5.83288	+	6.62008i	−0.289838	+	0.328954i
$406$	−24.3028	+	4.72047i	−1.20613	+	0.234273i
$407$	7.27651	+	0.957971i	0.360683	+	0.0474848i
$408$	−23.2604	+	19.8261i	−1.15156	+	0.981539i
$409$	34.0611	−	4.48423i	1.68421	−	0.221731i	0.773215	−	0.634144i	$-0.218647\pi$
$409$	34.0611	−	4.48423i	1.68421	−	0.221731i	0.910997	+	0.412413i	$0.135314\pi$
$410$	−3.20522	−	9.58382i	−0.158294	−	0.473311i
$411$	4.53357	+	22.8611i	0.223625	+	1.12766i
$412$	−0.00656364	+	0.0466086i	−0.000323367	+	0.00229624i
$413$	31.4312	−	6.25206i	1.54663	−	0.307644i
$414$	−0.328755	+	2.39238i	−0.0161574	+	0.117579i
$415$	16.5791			0.813836
$416$	24.8047	+	22.7611i	1.21615	+	1.11596i
$417$	−15.5033	+	11.8819i	−0.759202	+	0.581857i
$418$	−8.08501	+	1.02740i	−0.395451	+	0.0502517i
$419$	10.7762	−	9.45044i	0.526450	−	0.461684i	−0.354390	−	0.935098i	$-0.615312\pi$
$419$	10.7762	−	9.45044i	0.526450	−	0.461684i	0.880840	+	0.473413i	$0.156978\pi$
$420$	16.4839	−	4.24792i	0.804330	−	0.207277i
$421$	1.02985	+	15.7124i	0.0501917	+	0.765777i	0.946572	+	0.322492i	$0.104520\pi$
$421$	1.02985	+	15.7124i	0.0501917	+	0.765777i	−0.896381	+	0.443285i	$0.853813\pi$
$422$	13.4846	+	2.74543i	0.656421	+	0.133646i
$423$	−1.71947	−	1.32257i	−0.0836035	−	0.0643055i
$424$	−6.97775	−	4.79997i	−0.338870	−	0.233107i
$425$	3.28895	−	24.9821i	0.159538	−	1.21181i
$426$	1.91355	−	9.37089i	0.0927118	−	0.454021i
$427$	70.6022	−	23.9662i	3.41668	−	1.15981i
$428$	−20.6579	−	10.4196i	−0.998536	−	0.503652i
$429$	−12.5143	+	25.3393i	−0.604194	+	1.22339i
$430$	2.90955	+	11.0575i	0.140311	+	0.533241i
$431$	−11.5379	+	11.5379i	−0.555759	+	0.555759i	−0.928097	−	0.372338i	$-0.878556\pi$
$431$	−11.5379	+	11.5379i	−0.555759	+	0.555759i	0.372338	+	0.928097i	$0.378556\pi$
$432$	8.82286	+	18.8191i	0.424490	+	0.905433i
$433$	−1.08368	−	1.08368i	−0.0520783	−	0.0520783i	0.680588	−	0.732666i	$-0.261724\pi$
$433$	−1.08368	−	1.08368i	−0.0520783	−	0.0520783i	−0.732666	+	0.680588i	$0.761724\pi$
$434$	−0.418314	+	0.717066i	−0.0200797	+	0.0344202i
$435$	−5.31718	−	2.62598i	−0.254939	−	0.125906i
$436$	−10.0948	−	11.7222i	−0.483453	−	0.561391i
$437$	0.384571	+	1.13291i	0.0183965	+	0.0541945i
$438$	−4.73629	−	7.16695i	−0.226309	−	0.342450i
$439$	−12.1739	−	1.60272i	−0.581028	−	0.0764938i	−0.165717	−	0.986173i	$-0.552994\pi$
$439$	−12.1739	−	1.60272i	−0.581028	−	0.0764938i	−0.415311	+	0.909680i	$0.636327\pi$
$440$	−0.102687	+	7.60166i	−0.00489541	+	0.362395i
$441$	−20.7496	−	50.2589i	−0.988078	−	2.39328i
$442$	28.9744	+	43.7888i	1.37817	+	2.08282i
$443$	−21.8286	+	1.43072i	−1.03711	+	0.0679758i	−0.574433	−	0.818551i	$-0.694778\pi$
$443$	−21.8286	+	1.43072i	−1.03711	+	0.0679758i	−0.462677	+	0.886527i	$0.653111\pi$
$444$	−5.57431	−	7.41058i	−0.264545	−	0.351691i
$445$	−3.30974	−	3.77404i	−0.156897	−	0.178907i
$446$	−3.22428	+	4.16302i	−0.152674	+	0.197125i
$447$	−6.82802	−	8.90915i	−0.322954	−	0.421388i
$448$	6.30604	−	39.6006i	0.297932	−	1.87095i
$449$		−	2.80452i		−	0.132353i	−0.997808	−	0.0661767i	$-0.978920\pi$
$449$		−	2.80452i		−	0.132353i	0.997808	−	0.0661767i	$-0.0210801\pi$
$450$	−15.7939	−	6.64708i	−0.744532	−	0.313346i
$451$	−3.89873	−	19.6002i	−0.183584	−	0.922940i
$452$	−5.56770	−	3.28172i	−0.261883	−	0.154359i
$453$	3.53590	−	0.701202i	0.166131	−	0.0329454i
$454$	13.6972	+	6.83156i	0.642842	+	0.320621i
$455$	−3.81711	−	28.9938i	−0.178949	−	1.35925i
$456$	8.08035	+	6.38312i	0.378397	+	0.298917i
$457$	−4.00723	+	30.4380i	−0.187451	+	1.42383i	0.596305	+	0.802758i	$0.296635\pi$
$457$	−4.00723	+	30.4380i	−0.187451	+	1.42383i	−0.783755	+	0.621070i	$0.786698\pi$
$458$	21.9432	+	14.8053i	1.02534	+	0.691806i
$459$	6.26897	+	31.8054i	0.292610	+	1.48455i
$460$	1.09648	−	0.207857i	0.0511236	−	0.00969137i
$461$	10.2876	−	5.07328i	0.479141	−	0.236286i	−0.186647	−	0.982427i	$-0.559762\pi$
$461$	10.2876	−	5.07328i	0.479141	−	0.236286i	0.665788	+	0.746141i	$0.268095\pi$
$462$	33.3965	−	4.22416i	1.55374	−	0.196526i
$463$	−28.9496	−	7.75702i	−1.34540	−	0.360499i	−0.486966	−	0.873421i	$-0.661897\pi$
$463$	−28.9496	−	7.75702i	−1.34540	−	0.360499i	−0.858436	+	0.512921i	$0.828563\pi$
$464$	−10.6673	+	9.02034i	−0.495217	+	0.418759i
$465$	−0.183764	+	0.0759926i	−0.00852184	+	0.00352407i
$466$	37.0115	−	9.73880i	1.71452	−	0.451141i
$467$	15.7795	+	10.5435i	0.730186	+	0.487895i	0.864240	−	0.503079i	$-0.167800\pi$
$467$	15.7795	+	10.5435i	0.730186	+	0.487895i	−0.134054	+	0.990974i	$0.542800\pi$
$468$	33.9273	−	11.1334i	1.56829	−	0.514643i
$469$	−23.6207	−	4.69846i	−1.09070	−	0.216955i
$470$	−0.326518	+	0.947849i	−0.0150612	+	0.0437210i
$471$	9.55340	+	5.52305i	0.440197	+	0.254489i
$472$	13.7557	−	11.7386i	0.633158	−	0.540311i
$473$	2.95133	+	22.4176i	0.135702	+	1.03076i
$474$	14.9301	−	7.26862i	0.685763	−	0.333859i
$475$	−8.47141	+	0.555245i	−0.388695	+	0.0254764i
$476$	24.4533	−	57.5638i	1.12082	−	2.63843i
$477$	−8.06124	+	3.96374i	−0.369099	+	0.181487i
$478$	−21.0059	−	8.81193i	−0.960786	−	0.403048i
$479$	−35.3259	−	20.3954i	−1.61408	−	0.931890i	−0.988411	−	0.151803i	$-0.951492\pi$
$479$	−35.3259	−	20.3954i	−1.61408	−	0.931890i	−0.625670	−	0.780087i	$-0.715175\pi$
$480$	6.94709	−	6.63342i	0.317090	−	0.302773i
$481$	−13.7965	+	7.96542i	−0.629067	+	0.363192i
$482$	3.64483	−	0.463166i	0.166018	−	0.0210966i
$483$	−1.58570	−	4.68025i	−0.0721521	−	0.212959i
$484$	0.971403	−	6.89795i	0.0441547	−	0.313543i
$485$	4.48228	+	6.70821i	0.203530	+	0.304604i
$486$	21.9869	+	1.60465i	0.997347	+	0.0727885i
$487$	−4.56554	−	1.89111i	−0.206885	−	0.0856944i	0.276835	−	0.960917i	$-0.410714\pi$
$487$	−4.56554	−	1.89111i	−0.206885	−	0.0856944i	−0.483719	+	0.875223i	$0.660714\pi$
$488$	28.1649	−	31.2540i	1.27496	−	1.41480i
$489$	−7.24135	−	12.5592i	−0.327465	−	0.567947i
$490$	−18.9669	+	16.4831i	−0.856838	+	0.744628i
$491$	9.44235	+	27.8163i	0.426127	+	1.25533i	0.922086	+	0.386985i	$0.126483\pi$
$491$	9.44235	+	27.8163i	0.426127	+	1.25533i	−0.495959	+	0.868346i	$0.665183\pi$
$492$	−14.2286	+	20.8589i	−0.641473	+	0.940393i
$493$	−19.5416	+	9.63683i	−0.880108	+	0.434021i
$494$	12.5653	−	12.4527i	0.565342	−	0.560273i
$495$	6.97853	+	4.03986i	0.313661	+	0.181578i
$496$	−0.00843635	+	0.468369i	−0.000378803	+	0.0210304i
$497$	5.06549	+	18.9047i	0.227218	+	0.847991i
$498$	−25.0502	−	32.9919i	−1.12252	−	1.47840i
$499$	0.529169	−	8.07356i	0.0236889	−	0.361422i	−0.969515	−	0.245033i	$-0.921201\pi$
$499$	0.529169	−	8.07356i	0.0236889	−	0.361422i	0.993204	−	0.116389i	$-0.0371320\pi$
$500$	−1.31832	+	17.6735i	−0.0589569	+	0.790383i
$501$	−3.07459	−	6.24378i	−0.137363	−	0.278952i
$502$	15.3470	+	31.4772i	0.684972	+	1.40490i
$503$	−10.1887	+	4.22028i	−0.454290	+	0.188173i	−0.598082	−	0.801435i	$-0.704070\pi$
$503$	−10.1887	+	4.22028i	−0.454290	+	0.188173i	0.143792	+	0.989608i	$0.454070\pi$
$504$	−33.3595	−	26.3840i	−1.48595	−	1.17524i
$505$	8.79218	+	3.64184i	0.391247	+	0.162060i
$506$	2.20285	−	0.134424i	0.0979288	−	0.00597590i
$507$	−7.55276	−	38.0857i	−0.335430	−	1.69145i
$508$	7.89731	−	28.4460i	0.350386	−	1.26209i
$509$	−23.7782	+	20.8529i	−1.05395	+	0.924289i	−0.997251	−	0.0741018i	$-0.976391\pi$
$509$	−23.7782	+	20.8529i	−1.05395	+	0.924289i	−0.0566995	+	0.998391i	$0.518058\pi$
$510$	13.0122	−	7.42466i	0.576189	−	0.328769i
$511$	15.2239	+	8.78952i	0.673466	+	0.388825i
$512$	−7.80513	−	21.2386i	−0.344941	−	0.938624i
$513$	10.0979	−	4.16212i	0.445833	−	0.183762i
$514$	−30.8856	+	12.6306i	−1.36230	+	0.557112i
$515$	0.00741618	−	0.0218474i	0.000326796	−	0.000962710i
$516$	17.6079	−	22.4973i	0.775145	−	0.990386i
$517$	−0.876843	+	1.77806i	−0.0385635	+	0.0781990i
$518$	16.9808	+	8.46926i	0.746093	+	0.372118i
$519$	11.4234	−	11.4102i	0.501432	−	0.500851i
$520$	−9.86793	−	13.2263i	−0.432737	−	0.580011i
$521$	−8.56604	−	20.6802i	−0.375285	−	0.906018i	−0.992836	−	0.119487i	$-0.961875\pi$
$521$	−8.56604	−	20.6802i	−0.375285	−	0.906018i	0.617551	−	0.786531i	$-0.288125\pi$
$522$	2.80837	+	14.5487i	0.122919	+	0.636781i
$523$	−10.2043	−	2.02976i	−0.446203	−	0.0887553i	−0.0331256	−	0.999451i	$-0.510546\pi$
$523$	−10.2043	−	2.02976i	−0.446203	−	0.0887553i	−0.413077	+	0.910696i	$0.635546\pi$
$524$	12.9778	+	26.9250i	0.566940	+	1.17622i
$525$	34.9913	−	2.27307i	1.52715	−	0.0992048i
$526$	16.1827	−	9.24621i	0.705601	−	0.403154i
$527$	−0.189100	+	0.705729i	−0.00823730	+	0.0307420i
$528$	15.2822	−	11.2814i	0.665073	−	0.490959i
$529$	5.86899	+	21.9034i	0.255173	+	0.952320i
$530$	2.92226	+	2.94869i	0.126935	+	0.128083i
$531$	−3.72009	−	18.8162i	−0.161438	−	0.816555i
$532$	−20.6290	−	4.29684i	−0.894382	−	0.186292i
$533$	32.6135	+	28.6012i	1.41265	+	1.23886i
$534$	−2.50936	+	12.2887i	−0.108591	+	0.531783i
$535$	8.99753	+	6.90405i	0.388997	+	0.298488i
$536$	−12.9265	+	4.19410i	−0.558339	+	0.181157i
$537$	2.97728	+	0.799611i	0.128479	+	0.0345057i
$538$	−26.1529	−	23.1446i	−1.12753	−	0.997834i
$539$	−41.3177	+	27.6076i	−1.77968	+	1.18914i
$540$	−2.53098	−	9.86871i	−0.108916	−	0.424682i
$541$	−7.30961	−	36.7479i	−0.314265	−	1.57992i	−0.738430	−	0.674330i	$-0.764432\pi$
$541$	−7.30961	−	36.7479i	−0.314265	−	1.57992i	0.424165	−	0.905585i	$-0.360568\pi$
$542$	34.1800	−	25.9836i	1.46816	−	1.11609i
$543$	27.8477	−	3.64979i	1.19506	−	0.156627i
$544$	−3.81765	−	35.0844i	−0.163681	−	1.50423i
$545$	3.79145	+	6.56699i	0.162408	+	0.281299i
$546$	−51.9293	+	51.4041i	−2.22237	+	2.19989i
$547$	−0.694261	+	2.04523i	−0.0296844	+	0.0874476i	−0.960762	−	0.277373i	$-0.910536\pi$
$547$	−0.694261	+	2.04523i	−0.0296844	+	0.0874476i	0.931078	+	0.364820i	$0.118870\pi$
$548$	−24.7695	−	10.5222i	−1.05810	−	0.449485i
$549$	−14.2950	−	42.2728i	−0.610095	−	1.80416i
$550$	−3.12431	+	15.3455i	−0.133221	+	0.654336i
$551$	4.46891	+	5.82400i	0.190382	+	0.248111i
$552$	−2.07035	−	1.86790i	−0.0881201	−	0.0795030i
$553$	−20.6858	+	26.9582i	−0.879649	+	1.14638i
$554$	−12.2647	+	10.6586i	−0.521078	+	0.452838i
$555$	2.00802	+	4.07783i	0.0852359	+	0.173094i
$556$	−1.27241	−	22.5187i	−0.0539623	−	0.955004i
$557$	−4.58203	+	6.85749i	−0.194147	+	0.290561i	−0.915752	−	0.401743i	$-0.868404\pi$
$557$	−4.58203	+	6.85749i	−0.194147	+	0.290561i	0.721606	+	0.692304i	$0.243404\pi$
$558$	0.428881	+	0.250863i	0.0181560	+	0.0106199i
$559$	−34.7048	−	34.7048i	−1.46786	−	1.46786i
$560$	−6.65232	+	18.4959i	−0.281112	+	0.781593i
$561$	27.3778	−	11.3216i	1.15589	−	0.478000i
$562$	−24.5943	+	14.0523i	−1.03745	+	0.592759i
$563$	−25.9754	−	1.70252i	−1.09473	−	0.0717527i	−0.492682	−	0.870209i	$-0.663983\pi$
$563$	−25.9754	−	1.70252i	−1.09473	−	0.0717527i	−0.602052	+	0.798457i	$0.705650\pi$
$564$	2.37954	−	0.782390i	0.100197	−	0.0329446i
$565$	2.38179	+	2.08877i	0.100203	+	0.0878754i
$566$	−2.69328	+	3.99175i	−0.113207	+	0.167786i
$567$	−41.7180	+	17.1669i	−1.75199	+	0.720940i
$568$	7.70300	+	7.91396i	0.323211	+	0.332062i
$569$	−11.8642	−	15.4617i	−0.497373	−	0.648189i	0.475449	−	0.879743i	$-0.342286\pi$
$569$	−11.8642	−	15.4617i	−0.497373	−	0.648189i	−0.972822	+	0.231554i	$0.925619\pi$
$570$	−3.30873	−	3.81180i	−0.138588	−	0.159659i
$571$	−17.5264	−	8.64308i	−0.733459	−	0.361702i	0.0368946	−	0.999319i	$-0.488253\pi$
$571$	−17.5264	−	8.64308i	−0.733459	−	0.361702i	−0.770353	+	0.637617i	$0.779920\pi$
$572$	−16.0614	−	28.4069i	−0.671560	−	1.18775i
$573$	−21.7208	−	4.33364i	−0.907400	−	0.181040i
$574$	6.97474	−	51.1961i	0.291120	−	2.13688i
$575$	2.29890			0.0958708
$576$	−23.6970	−	3.80173i	−0.987374	−	0.158405i
$577$	2.40590			0.100159			0.0500795	−	0.998745i	$-0.484053\pi$
$577$	2.40590			0.100159			0.0500795	+	0.998745i	$0.484053\pi$
$578$	4.18491	−	30.7181i	0.174069	−	1.27771i
$579$	−28.4986	+	32.4584i	−1.18436	+	1.34893i
$580$	5.96086	−	3.37030i	0.247511	−	0.139944i
$581$	76.0256	+	37.4917i	3.15407	+	1.55542i
$582$	6.57662	−	19.0554i	0.272610	−	0.789870i
$583$	4.99771	+	6.51314i	0.206984	+	0.269747i
$584$	9.91862	+	0.133986i	0.410435	+	0.00554437i
$585$	−17.3557	+	2.26444i	−0.717571	+	0.0936232i
$586$	17.0347	−	25.2474i	0.703697	−	1.04296i
$587$	18.3745	+	16.1140i	0.758398	+	0.665097i	0.948539	−	0.316659i	$-0.102561\pi$
$587$	18.3745	+	16.1140i	0.758398	+	0.665097i	−0.190141	+	0.981757i	$0.560895\pi$
$588$	61.4588	+	12.8385i	2.53452	+	0.529451i
$589$	0.245635	+	0.0160997i	0.0101212	+	0.000663378i
$590$	−7.69640	+	4.39743i	−0.316856	+	0.181039i
$591$	25.4252	+	19.5329i	1.04585	+	0.803476i
$592$	10.6956	−	0.507774i	0.439585	−	0.0208694i
$593$	6.06305	+	6.06305i	0.248980	+	0.248980i	0.820552	−	0.571572i	$-0.193666\pi$
$593$	6.06305	+	6.06305i	0.248980	+	0.248980i	−0.571572	+	0.820552i	$0.693666\pi$
$594$	−2.50501	−	19.9911i	−0.102782	−	0.820243i
$595$	−17.0320	+	25.4902i	−0.698243	+	1.04499i
$596$	12.9406	−	0.731204i	0.530066	−	0.0299513i
$597$	−10.3207	−	0.682468i	−0.422398	−	0.0279316i
$598$	−3.61584	+	3.14232i	−0.147863	+	0.128499i
$599$	18.6099	−	24.2529i	0.760379	−	0.990945i	−0.239420	−	0.970916i	$-0.576957\pi$
$599$	18.6099	−	24.2529i	0.760379	−	0.990945i	0.999799	−	0.0200292i	$-0.00637593\pi$
$600$	16.6051	−	10.7600i	0.677902	−	0.439274i
$601$	9.15406	+	11.9298i	0.373402	+	0.486627i	0.941822	−	0.336111i	$-0.109112\pi$
$601$	9.15406	+	11.9298i	0.373402	+	0.486627i	−0.568420	+	0.822738i	$0.692445\pi$
$602$	−11.6631	+	57.2853i	−0.475354	+	2.33477i
$603$	−2.82848	+	14.1340i	−0.115184	+	0.575580i
$604$	−1.62745	+	3.83107i	−0.0662201	+	0.155884i
$605$	−1.09758	+	3.23336i	−0.0446228	+	0.131455i
$606$	−6.03739	−	22.9988i	−0.245252	−	0.934262i
$607$	−15.8299	−	27.4181i	−0.642514	−	1.11287i	−0.984870	−	0.173297i	$-0.944558\pi$
$607$	−15.8299	−	27.4181i	−0.642514	−	1.11287i	0.342355	−	0.939571i	$-0.388775\pi$
$608$	−11.3426	+	3.56762i	−0.460002	+	0.144686i
$609$	−18.4443	−	24.0659i	−0.747400	−	0.975201i
$610$	−16.4175	+	12.4805i	−0.664725	+	0.505323i
$611$	−0.839529	−	4.22060i	−0.0339637	−	0.170747i
$612$	−34.4356	−	14.6755i	−1.39198	−	0.593223i
$613$	−5.40029	+	3.60836i	−0.218116	+	0.145740i	−0.659828	−	0.751416i	$-0.729371\pi$
$613$	−5.40029	+	3.60836i	−0.218116	+	0.145740i	0.441713	+	0.897157i	$0.354371\pi$
$614$	−8.58966	−	7.60162i	−0.346650	−	0.306776i
$615$	8.75677	−	8.74662i	0.353107	−	0.352698i
$616$	−17.6612	+	34.6262i	−0.711588	+	1.39513i
$617$	−13.0970	−	10.0497i	−0.527266	−	0.404585i	0.310535	−	0.950562i	$-0.399492\pi$
$617$	−13.0970	−	10.0497i	−0.527266	−	0.404585i	−0.837800	+	0.545977i	$0.816159\pi$
$618$	−0.0546810	+	0.0182523i	−0.00219959	+	0.000734214i
$619$	−21.2482	−	18.6342i	−0.854038	−	0.748971i	0.115657	−	0.993289i	$-0.463103\pi$
$619$	−21.2482	−	18.6342i	−0.854038	−	0.748971i	−0.969695	+	0.244318i	$0.921436\pi$
$620$	0.0468228	−	0.224795i	0.00188045	−	0.00902800i
$621$	−2.80228	+	0.945810i	−0.112452	+	0.0379541i
$622$	23.9492	+	24.1658i	0.960274	+	0.968960i
$623$	−6.64272	−	24.7910i	−0.266135	−	0.993229i
$624$	−11.4099	+	39.6211i	−0.456763	+	1.58611i
$625$	−2.97833	+	11.1153i	−0.119133	+	0.444612i
$626$	36.7389	−	20.9912i	1.46838	−	0.838979i
$627$	−5.54072	−	8.30269i	−0.221275	−	0.331578i
$628$	−11.4784	+	5.53256i	−0.458036	+	0.220773i
$629$	16.3796	+	3.25810i	0.653095	+	0.129909i
$630$	13.6571	+	15.7520i	0.544113	+	0.627576i
$631$	−3.85790	−	9.31380i	−0.153581	−	0.370776i	0.828298	−	0.560288i	$-0.189310\pi$
$631$	−3.85790	−	9.31380i	−0.153581	−	0.370776i	−0.981878	+	0.189512i	$0.939310\pi$
$632$	−2.75930	+	18.9748i	−0.109759	+	0.754776i
$633$	4.35270	+	16.2823i	0.173004	+	0.647162i
$634$	−23.5279	−	11.7347i	−0.934412	−	0.466043i
$635$	−6.40032	+	12.9786i	−0.253989	+	0.515038i
$636$	1.45242	−	10.2705i	0.0575922	−	0.407253i
$637$	34.6716	−	102.139i	1.37374	−	4.04690i
$638$	12.5340	−	5.12576i	0.496226	−	0.202931i
$639$	11.3182	−	3.01862i	0.447739	−	0.119415i
$640$	1.81994	+	10.9411i	0.0719396	+	0.432483i
$641$	−19.0609	−	11.0048i	−0.752862	−	0.434665i	0.0738650	−	0.997268i	$-0.476467\pi$
$641$	−19.0609	−	11.0048i	−0.752862	−	0.434665i	−0.826727	+	0.562603i	$0.809800\pi$
$642$	0.144026	−	28.3365i	0.00568425	−	1.11835i
$643$	16.4232	−	14.4027i	0.647666	−	0.567988i	−0.271217	−	0.962518i	$-0.587426\pi$
$643$	16.4232	−	14.4027i	0.647666	−	0.567988i	0.918883	+	0.394530i	$0.129093\pi$
$644$	5.49810	+	1.52641i	0.216655	+	0.0601488i
$645$	−10.5338	+	9.22711i	−0.414769	+	0.363317i
$646$	−18.5108	+	1.12958i	−0.728298	+	0.0444428i
$647$	11.4696	+	4.75086i	0.450916	+	0.186776i	0.596572	−	0.802560i	$-0.296529\pi$
$647$	11.4696	+	4.75086i	0.450916	+	0.186776i	−0.145655	+	0.989335i	$0.546529\pi$
$648$	−15.8142	+	19.9477i	−0.621242	+	0.783619i
$649$	−16.1948	+	6.70810i	−0.635701	+	0.263316i
$650$	−14.8972	−	30.5545i	−0.584315	−	1.19845i
$651$	−1.01452	−	0.0670863i	−0.0397622	−	0.00262932i
$652$	16.6936	+	1.24523i	0.653773	+	0.0487668i
$653$	0.858260	−	13.0945i	0.0335863	−	0.512428i	−0.947612	−	0.319425i	$-0.896510\pi$
$653$	0.858260	−	13.0945i	0.0335863	−	0.512428i	0.981198	−	0.193004i	$-0.0618229\pi$
$654$	7.33940	−	17.4672i	0.286993	−	0.683023i
$655$	−3.79198	−	14.1519i	−0.148165	−	0.552959i
$656$	−10.6705	−	27.1331i	−0.416615	−	1.05937i
$657$	5.27119	−	9.10555i	0.205649	−	0.355241i
$658$	−3.64074	+	3.60810i	−0.141931	+	0.140659i
$659$	−14.6824	+	7.24055i	−0.571944	+	0.282052i	−0.705175	−	0.709033i	$-0.749132\pi$
$659$	−14.6824	+	7.24055i	−0.571944	+	0.282052i	0.133231	+	0.991085i	$0.457465\pi$
$660$	−8.38982	+	4.03789i	−0.326573	+	0.157175i
$661$	15.0872	+	44.4453i	0.586822	+	1.72872i	0.680136	+	0.733086i	$0.261921\pi$
$661$	15.0872	+	44.4453i	0.586822	+	1.72872i	−0.0933139	+	0.995637i	$0.529746\pi$
$662$	−9.75458	+	8.47714i	−0.379122	+	0.329473i
$663$	−32.1861	+	55.6733i	−1.25000	+	2.16217i
$664$	47.7682	−	2.48342i	1.85376	−	0.0963752i
$665$	9.54262	+	3.95268i	0.370047	+	0.153278i
$666$	5.08073	−	10.1573i	0.196874	−	0.393587i
$667$	−1.10440	−	1.65286i	−0.0427627	−	0.0639989i
$668$	7.95789	+	1.12067i	0.307900	+	0.0433599i
$669$	−6.32439	−	1.26181i	−0.244515	−	0.0487846i
$670$	6.60827	−	0.839743i	0.255300	−	0.0324421i
$671$	−35.3186	+	20.3912i	−1.36346	+	0.787193i
$672$	46.8575	−	14.7084i	1.80757	−	0.567388i
$673$	4.08707	+	2.35967i	0.157545	+	0.0909585i	0.576700	−	0.816956i	$-0.304340\pi$
$673$	4.08707	+	2.35967i	0.157545	+	0.0909585i	−0.419155	+	0.907915i	$0.637674\pi$
$674$	−36.9363	−	15.4947i	−1.42273	−	0.596835i
$675$	−1.33616	−	20.9442i	−0.0514287	−	0.806144i
$676$	41.2651	+	17.5295i	1.58712	+	0.674213i
$677$	22.2905	−	1.46100i	0.856694	−	0.0561507i	0.369276	−	0.929320i	$-0.379606\pi$
$677$	22.2905	−	1.46100i	0.856694	−	0.0561507i	0.487418	+	0.873169i	$0.337939\pi$
$678$	0.557830	−	7.89572i	0.0214233	−	0.303233i
$679$	5.38426	+	40.8975i	0.206629	+	1.56950i
$680$	−1.36447	+	17.2451i	−0.0523250	+	0.661321i
$681$	−0.0108749	+	18.7464i	−0.000416726	+	0.718362i
$682$	0.147895	−	0.429324i	0.00566319	−	0.0164397i
$683$	−9.76370	−	1.94212i	−0.373598	−	0.0743132i	0.00472035	−	0.999989i	$-0.498497\pi$
$683$	−9.76370	−	1.94212i	−0.373598	−	0.0743132i	−0.378318	+	0.925676i	$0.623497\pi$
$684$	−2.58603	+	12.3437i	−0.0988792	+	0.471973i
$685$	10.9683	+	7.32880i	0.419078	+	0.280019i
$686$	−76.2626	+	20.0669i	−2.91172	+	0.766158i
$687$	−4.25029	+	32.1401i	−0.162159	+	1.22622i
$688$	10.0394	+	31.4234i	0.382749	+	1.19801i
$689$	−17.2128	−	4.61215i	−0.655755	−	0.175709i
$690$	0.826547	+	1.08859i	0.0314661	+	0.0414419i
$691$	3.34491	−	1.64953i	0.127246	−	0.0627509i	−0.377551	−	0.925989i	$-0.623234\pi$
$691$	3.34491	−	1.64953i	0.127246	−	0.0627509i	0.504798	+	0.863238i	$0.331567\pi$
$692$	3.47237	+	18.3173i	0.132000	+	0.696321i
$693$	22.8653	+	34.3064i	0.868580	+	1.30319i
$694$	6.35234	+	4.28600i	0.241132	+	0.162694i
$695$	−1.44306	+	10.9611i	−0.0547383	+	0.415779i
$696$	−15.7134	−	6.76957i	−0.595613	−	0.256600i
$697$	−5.93552	−	45.0848i	−0.224824	−	1.70771i
$698$	−20.7310	−	10.3397i	−0.784680	−	0.391363i
$699$	30.8848	+	35.2586i	1.16817	+	1.33360i
$700$	−20.5598	+	34.8813i	−0.777086	+	1.31839i
$701$	−1.38367	−	6.95619i	−0.0522606	−	0.262732i	0.945818	−	0.324698i	$-0.105263\pi$
$701$	−1.38367	−	6.95619i	−0.0522606	−	0.262732i	−0.998078	+	0.0619667i	$0.980263\pi$
$702$	30.7298	+	31.1159i	1.15982	+	1.17439i
$703$		−	5.62671i		−	0.212215i
$704$	0.842803	+	21.9175i	0.0317643	+	0.826047i
$705$	−1.21741	+	0.159557i	−0.0458503	+	0.00600926i
$706$	21.2794	−	27.4748i	0.800860	−	1.03403i
$707$	32.0821	+	36.5826i	1.20657	+	1.37583i
$708$	20.3796	+	8.67129i	0.765913	+	0.325887i
$709$	40.6290	−	2.66297i	1.52585	−	0.100010i	0.720772	−	0.693172i	$-0.243788\pi$
$709$	40.6290	−	2.66297i	1.52585	−	0.100010i	0.805083	+	0.593163i	$0.202121\pi$
$710$	−2.98724	−	4.51459i	−0.112109	−	0.169430i
$711$	16.1204	+	12.3994i	0.604563	+	0.465013i
$712$	−10.1015	−	10.3781i	−0.378568	−	0.388936i
$713$	−0.0660881	−	0.00870066i	−0.00247502	−	0.000325842i
$714$	76.4590	−	4.62123i	2.86141	−	0.172945i
$715$	5.14172	+	15.1470i	0.192289	+	0.566466i
$716$	−2.69735	+	2.32287i	−0.100805	+	0.0868099i
$717$	−1.80852	−	27.8402i	−0.0675405	−	1.03971i
$718$	−14.7131	+	25.2209i	−0.549088	+	0.941235i
$719$	19.5575	+	19.5575i	0.729371	+	0.729371i	0.970495	−	0.241123i	$-0.0775158\pi$
$719$	19.5575	+	19.5575i	0.729371	+	0.729371i	−0.241123	+	0.970495i	$0.577516\pi$
$720$	11.0653	+	3.99433i	0.412381	+	0.148860i
$721$	0.0834131	−	0.0834131i	0.00310647	−	0.00310647i
$722$	−5.24757	−	19.9430i	−0.195295	−	0.742200i
$723$	2.49783	+	3.74297i	0.0928954	+	0.139203i
$724$	−14.6051	+	28.9559i	−0.542795	+	1.07614i
$725$	13.3572	−	4.53416i	0.496074	−	0.168394i
$726$	8.09266	−	2.70129i	0.300347	−	0.100254i
$727$	−2.25127	+	17.1001i	−0.0834948	+	0.634206i	0.897619	+	0.440773i	$0.145296\pi$
$727$	−2.25127	+	17.1001i	−0.0834948	+	0.634206i	−0.981113	+	0.193433i	$0.938038\pi$
$728$	−15.3410	−	82.9660i	−0.568575	−	3.07492i
$729$	10.2456	+	24.9806i	0.379465	+	0.925206i
$730$	−4.76455	−	0.970050i	−0.176344	−	0.0359032i
$731$	3.36506	+	51.3408i	0.124461	+	1.89891i
$732$	49.6419	+	13.8128i	1.83482	+	0.510537i
$733$	4.44213	−	3.89564i	0.164074	−	0.143889i	−0.573372	−	0.819295i	$-0.694365\pi$
$733$	4.44213	−	3.89564i	0.164074	−	0.143889i	0.737446	+	0.675406i	$0.236032\pi$
$734$	−4.61702	+	0.586706i	−0.170417	+	0.0216557i
$735$	−28.4263	−	11.7939i	−1.04852	−	0.435024i
$736$	3.12807	−	0.763127i	0.115302	−	0.0281292i
$737$	13.1732			0.485242
$738$	−30.6365	−	4.21000i	−1.12775	−	0.154972i
$739$	−1.54877	+	0.308070i	−0.0569725	+	0.0113325i	−0.223494	−	0.974705i	$-0.571746\pi$
$739$	−1.54877	+	0.308070i	−0.0569725	+	0.0113325i	0.166522	+	0.986038i	$0.446746\pi$
$740$	−5.19732	−	0.731911i	−0.191057	−	0.0269056i
$741$	20.5126	+	6.97636i	0.753549	+	0.256283i
$742$	6.73227	+	20.1300i	0.247150	+	0.738994i
$743$	49.9848	−	6.58062i	1.83376	−	0.241419i	0.867220	−	0.497925i	$-0.165905\pi$
$743$	49.9848	−	6.58062i	1.83376	−	0.241419i	0.966543	+	0.256506i	$0.0825712\pi$
$744$	−0.518083	+	0.246478i	−0.0189938	+	0.00903634i
$745$	−6.29891	−	0.829267i	−0.230774	−	0.0303820i
$746$	25.5068	−	4.95434i	0.933871	−	0.181391i
$747$	22.4919	−	45.4761i	0.822937	−	1.66388i
$748$	−6.97582	+	33.4908i	−0.255061	+	1.22454i
$749$	25.6467	+	52.0063i	0.937109	+	1.90027i
$750$	−20.0954	+	8.20436i	−0.733779	+	0.299581i
$751$	−5.43372	+	20.2789i	−0.198279	+	0.739988i	0.793114	+	0.609073i	$0.208458\pi$
$751$	−5.43372	+	20.2789i	−0.198279	+	0.739988i	−0.991394	+	0.130915i	$0.958208\pi$
$752$	−0.798793	+	2.77988i	−0.0291290	+	0.101372i
$753$	−26.1293	+	34.0115i	−0.952204	+	1.23945i
$754$	−14.8113	+	25.3892i	−0.539396	+	0.924622i
$755$	1.13354	−	1.69646i	0.0412536	−	0.0617404i
$756$	10.7108	−	50.9778i	0.389548	−	1.85404i
$757$	5.75236	−	28.9191i	0.209073	−	1.05108i	−0.723562	−	0.690259i	$-0.757496\pi$
$757$	5.75236	−	28.9191i	0.209073	−	1.05108i	0.932635	−	0.360821i	$-0.117504\pi$
$758$	−30.1728	+	14.7110i	−1.09592	+	0.534329i
$759$	1.35012	+	2.34161i	0.0490062	+	0.0849950i
$760$	5.78827	−	0.682635i	0.209963	−	0.0247618i
$761$	3.69162	−	0.486011i	0.133821	−	0.0176179i	−0.0633180	−	0.997993i	$-0.520168\pi$
$761$	3.69162	−	0.486011i	0.133821	−	0.0176179i	0.197139	+	0.980376i	$0.436835\pi$
$762$	35.4975	−	6.87351i	1.28594	−	0.249001i
$763$	2.53573	+	38.6877i	0.0917994	+	1.40059i
$764$	18.2466	−	17.9209i	0.660140	−	0.648356i
$765$	15.2443	+	10.2115i	0.551158	+	0.369198i
$766$	4.58669	+	11.2158i	0.165724	+	0.405244i
$767$	19.0245	−	32.9514i	0.686936	−	1.18981i
$768$	19.0225	−	20.1530i	0.686416	−	0.727209i
$769$	−4.58327	−	7.93845i	−0.165277	−	0.286268i	0.771477	−	0.636258i	$-0.219518\pi$
$769$	−4.58327	−	7.93845i	−0.165277	−	0.286268i	−0.936754	+	0.349990i	$0.886185\pi$
$770$	11.6668	−	15.0635i	0.420442	−	0.542852i

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40127 - 0.190903i) q^{2} +(-0.555798 - 1.64045i) q^{3} +(1.92711 + 0.535013i) q^{4} +(-0.879249 - 0.433598i) q^{5} +(0.465655 + 2.40482i) q^{6} +(-3.05138 - 3.97664i) q^{7} +(-2.59827 - 1.11759i) q^{8} +(-2.38218 + 1.82352i) q^{9} +O(q^{10})\)	\(q+(-1.40127 - 0.190903i) q^{2} +(-0.555798 - 1.64045i) q^{3} +(1.92711 + 0.535013i) q^{4} +(-0.879249 - 0.433598i) q^{5} +(0.465655 + 2.40482i) q^{6} +(-3.05138 - 3.97664i) q^{7} +(-2.59827 - 1.11759i) q^{8} +(-2.38218 + 1.82352i) q^{9} +(1.14929 + 0.775439i) q^{10} +(2.06133 + 1.80774i) q^{11} +(-0.193420 - 3.45870i) q^{12} +(-5.93848 - 0.389228i) q^{13} +(3.51666 + 6.15486i) q^{14} +(-0.222612 + 1.68336i) q^{15} +(3.42752 + 2.06206i) q^{16} +(4.41144 + 4.41144i) q^{17} +(3.68619 - 2.10048i) q^{18} +(1.16778 - 1.74771i) q^{19} +(-1.46243 - 1.30600i) q^{20} +(-4.82754 + 7.21586i) q^{21} +(-2.54337 - 2.92664i) q^{22} +(-0.346500 + 0.451567i) q^{23} +(-0.389243 + 4.88349i) q^{24} +(-2.45874 - 3.20429i) q^{25} +(8.24710 + 1.67909i) q^{26} +(4.31541 + 2.89434i) q^{27} +(-3.75280 - 9.29596i) q^{28} +(-1.12262 + 3.30713i) q^{29} +(0.633298 - 2.31634i) q^{30} +(0.0585556 + 0.101421i) q^{31} +(-4.40923 - 3.54383i) q^{32} +(1.81983 - 4.38625i) q^{33} +(-5.33946 - 7.02378i) q^{34} +(0.958664 + 4.81953i) q^{35} +(-5.56633 + 2.23963i) q^{36} +(2.22576 - 1.48721i) q^{37} +(-1.97002 + 2.22607i) q^{38} +(2.66208 + 9.95813i) q^{39} +(1.79994 + 2.10924i) q^{40} +(-5.78272 - 4.43724i) q^{41} +(8.14221 - 9.18977i) q^{42} +(6.20046 + 5.43765i) q^{43} +(3.00525 + 4.58655i) q^{44} +(2.88520 - 0.570423i) q^{45} +(0.571745 - 0.566620i) q^{46} +(0.187150 + 0.698454i) q^{47} +(1.47771 - 6.76878i) q^{48} +(-4.69099 + 17.5070i) q^{49} +(2.83364 + 4.95945i) q^{50} +(4.78490 - 9.68864i) q^{51} +(-11.2359 - 3.92725i) q^{52} +(2.93681 + 0.584167i) q^{53} +(-5.49452 - 4.87958i) q^{54} +(-1.02859 - 2.48324i) q^{55} +(3.48406 + 13.7426i) q^{56} +(-3.51608 - 0.944317i) q^{57} +(2.20443 - 4.41986i) q^{58} +(-2.82777 + 5.73414i) q^{59} +(-1.32962 + 3.12492i) q^{60} +(-4.78134 + 14.0854i) q^{61} +(-0.0626906 - 0.153297i) q^{62} +(14.5204 + 3.90880i) q^{63} +(5.50199 + 5.80759i) q^{64} +(5.05263 + 2.91714i) q^{65} +(-3.38742 + 5.79891i) q^{66} +(3.61240 - 3.16799i) q^{67} +(6.14116 + 10.8615i) q^{68} +(0.933359 + 0.317437i) q^{69} +(-0.423283 - 6.93647i) q^{70} +(-3.60738 - 1.49422i) q^{71} +(8.22748 - 2.07570i) q^{72} +(-3.24012 + 1.34210i) q^{73} +(-3.40281 + 1.65907i) q^{74} +(-3.88992 + 5.81438i) q^{75} +(3.18549 - 2.74325i) q^{76} +(0.898814 - 13.7133i) q^{77} +(-1.82926 - 14.4622i) q^{78} +(-1.75457 - 6.54816i) q^{79} +(-2.11954 - 3.29923i) q^{80} +(2.34954 - 8.68790i) q^{81} +(7.25607 + 7.32171i) q^{82} +(-15.1674 + 7.47972i) q^{83} +(-13.1638 + 11.3230i) q^{84} +(-1.96597 - 5.79155i) q^{85} +(-7.65044 - 8.80330i) q^{86} +(6.04914 + 0.00350914i) q^{87} +(-3.33558 - 7.00070i) q^{88} +(4.73059 + 1.95948i) q^{89} +(-4.15184 + 0.248523i) q^{90} +(16.5727 + 24.8029i) q^{91} +(-0.909338 + 0.684839i) q^{92} +(0.133832 - 0.152428i) q^{93} +(-0.128911 - 1.01445i) q^{94} +(-1.78457 + 1.03032i) q^{95} +(-3.36285 + 9.20279i) q^{96} +(-7.12705 - 4.11480i) q^{97} +(9.91548 - 23.6365i) q^{98} +(-8.20690 - 0.547472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1504 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 1504 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 1504 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} - 16 q^{12} - 8 q^{13} - 24 q^{14} - 16 q^{15} - 8 q^{16} - 16 q^{18} - 32 q^{19} - 24 q^{20} - 16 q^{21} - 8 q^{22} - 24 q^{23} - 96 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} + 64 q^{30} - 16 q^{31} - 24 q^{32} - 8 q^{34} + 64 q^{36} - 32 q^{37} - 24 q^{38} - 16 q^{39} - 8 q^{40} - 24 q^{41} - 96 q^{42} - 8 q^{43} - 16 q^{45} - 32 q^{46} - 24 q^{47} - 16 q^{48} - 8 q^{49} - 24 q^{50} - 16 q^{51} - 8 q^{52} - 16 q^{54} - 32 q^{55} - 24 q^{56} - 16 q^{57} + 64 q^{58} - 24 q^{59} - 16 q^{60} - 8 q^{61} - 32 q^{64} - 48 q^{65} - 8 q^{67} - 24 q^{68} - 16 q^{69} - 8 q^{70} - 16 q^{72} - 32 q^{73} - 24 q^{74} - 16 q^{75} - 56 q^{76} - 24 q^{77} - 40 q^{78} - 8 q^{79} - 16 q^{81} - 32 q^{82} - 24 q^{83} - 128 q^{84} - 8 q^{85} - 24 q^{86} - 16 q^{87} - 8 q^{88} - 160 q^{90} - 32 q^{91} - 480 q^{92} + 8 q^{93} - 8 q^{94} - 48 q^{95} - 152 q^{96} - 16 q^{99}+O(q^{100}) \) 1504 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 - 16 * q^12 - 8 * q^13 - 24 * q^14 - 16 * q^15 - 8 * q^16 - 16 * q^18 - 32 * q^19 - 24 * q^20 - 16 * q^21 - 8 * q^22 - 24 * q^23 - 96 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 + 64 * q^30 - 16 * q^31 - 24 * q^32 - 8 * q^34 + 64 * q^36 - 32 * q^37 - 24 * q^38 - 16 * q^39 - 8 * q^40 - 24 * q^41 - 96 * q^42 - 8 * q^43 - 16 * q^45 - 32 * q^46 - 24 * q^47 - 16 * q^48 - 8 * q^49 - 24 * q^50 - 16 * q^51 - 8 * q^52 - 16 * q^54 - 32 * q^55 - 24 * q^56 - 16 * q^57 + 64 * q^58 - 24 * q^59 - 16 * q^60 - 8 * q^61 - 32 * q^64 - 48 * q^65 - 8 * q^67 - 24 * q^68 - 16 * q^69 - 8 * q^70 - 16 * q^72 - 32 * q^73 - 24 * q^74 - 16 * q^75 - 56 * q^76 - 24 * q^77 - 40 * q^78 - 8 * q^79 - 16 * q^81 - 32 * q^82 - 24 * q^83 - 128 * q^84 - 8 * q^85 - 24 * q^86 - 16 * q^87 - 8 * q^88 - 160 * q^90 - 32 * q^91 - 480 * q^92 + 8 * q^93 - 8 * q^94 - 48 * q^95 - 152 * q^96 - 16 * q^99

Introduction

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