LMFDB - Embedded newform 576.2.bl.a.11.9

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			11.9
Character	$\chi$	$=$	576.11
Dual form			576.2.bl.a.419.9

$q$-expansion

$f(q)$	$=$	$q+(-1.35939 + 0.389931i) q^{2} +(1.72496 + 0.156592i) q^{3} +(1.69591 - 1.06014i) q^{4} +(1.33127 + 0.656508i) q^{5} +(-2.40596 + 0.459744i) q^{6} +(-1.06088 - 1.38257i) q^{7} +(-1.89203 + 2.10244i) q^{8} +(2.95096 + 0.540229i) q^{9} +O(q^{10})$	\(q+(-1.35939 + 0.389931i) q^{2} +(1.72496 + 0.156592i) q^{3} +(1.69591 - 1.06014i) q^{4} +(1.33127 + 0.656508i) q^{5} +(-2.40596 + 0.459744i) q^{6} +(-1.06088 - 1.38257i) q^{7} +(-1.89203 + 2.10244i) q^{8} +(2.95096 + 0.540229i) q^{9} +(-2.06571 - 0.373352i) q^{10} +(-4.22175 - 3.70237i) q^{11} +(3.09138 - 1.56313i) q^{12} +(5.42788 + 0.355762i) q^{13} +(1.98127 + 1.46579i) q^{14} +(2.19358 + 1.34091i) q^{15} +(1.75221 - 3.59580i) q^{16} +(5.24770 + 5.24770i) q^{17} +(-4.22217 + 0.416286i) q^{18} +(1.08713 - 1.62700i) q^{19} +(2.95370 - 0.297952i) q^{20} +(-1.61348 - 2.55100i) q^{21} +(7.18269 + 3.38680i) q^{22} +(1.32665 - 1.72892i) q^{23} +(-3.59289 + 3.33034i) q^{24} +(-1.70254 - 2.21879i) q^{25} +(-7.51736 + 1.63288i) q^{26} +(5.00568 + 1.39397i) q^{27} +(-3.26488 - 1.22003i) q^{28} +(-0.774434 + 2.28141i) q^{29} +(-3.50480 - 0.967489i) q^{30} +(1.28939 + 2.23328i) q^{31} +(-0.979827 + 5.57135i) q^{32} +(-6.70257 - 7.04753i) q^{33} +(-9.17994 - 5.08746i) q^{34} +(-0.504650 - 2.53705i) q^{35} +(5.57727 - 2.21225i) q^{36} +(3.04121 - 2.03207i) q^{37} +(-0.843418 + 2.63564i) q^{38} +(9.30716 + 1.46364i) q^{39} +(-3.89906 + 1.55677i) q^{40} +(-4.61951 - 3.54467i) q^{41} +(3.18807 + 2.83867i) q^{42} +(-2.60452 - 2.28410i) q^{43} +(-11.0847 - 1.80324i) q^{44} +(3.57385 + 2.65652i) q^{45} +(-1.12928 + 2.86759i) q^{46} +(1.37640 + 5.13681i) q^{47} +(3.58555 - 5.92822i) q^{48} +(1.02571 - 3.82799i) q^{49} +(3.17960 + 2.35234i) q^{50} +(8.23032 + 9.87381i) q^{51} +(9.58234 - 5.15097i) q^{52} +(-0.894480 - 0.177923i) q^{53} +(-7.34825 + 0.0569183i) q^{54} +(-3.18963 - 7.70046i) q^{55} +(4.91398 + 0.385421i) q^{56} +(2.13003 - 2.63627i) q^{57} +(0.163170 - 3.40331i) q^{58} +(-3.98177 + 8.07423i) q^{59} +(5.14166 - 0.0514298i) q^{60} +(-4.03610 + 11.8900i) q^{61} +(-2.62361 - 2.53314i) q^{62} +(-2.38372 - 4.65303i) q^{63} +(-0.840471 - 7.95573i) q^{64} +(6.99240 + 4.03706i) q^{65} +(11.8595 + 6.96683i) q^{66} +(6.22230 - 5.45681i) q^{67} +(14.4629 + 3.33632i) q^{68} +(2.55915 - 2.77457i) q^{69} +(1.67529 + 3.25207i) q^{70} +(2.70303 + 1.11963i) q^{71} +(-6.71909 + 5.18207i) q^{72} +(-3.45201 + 1.42987i) q^{73} +(-3.34183 + 3.94824i) q^{74} +(-2.58936 - 4.09392i) q^{75} +(0.118819 - 3.91175i) q^{76} +(-0.640009 + 9.76465i) q^{77} +(-13.2228 + 1.63949i) q^{78} +(1.94771 + 7.26895i) q^{79} +(4.69333 - 3.63663i) q^{80} +(8.41631 + 3.18838i) q^{81} +(7.66191 + 3.01732i) q^{82} +(-2.39800 + 1.18257i) q^{83} +(-5.44073 - 2.61575i) q^{84} +(3.54093 + 10.4313i) q^{85} +(4.43121 + 2.08941i) q^{86} +(-1.69312 + 3.81406i) q^{87} +(15.7717 - 1.87096i) q^{88} +(-3.03816 - 1.25845i) q^{89} +(-5.89413 - 2.21770i) q^{90} +(-5.26648 - 7.88185i) q^{91} +(0.416974 - 4.33852i) q^{92} +(1.87442 + 4.05422i) q^{93} +(-3.87408 - 6.44625i) q^{94} +(2.51540 - 1.45227i) q^{95} +(-2.56259 + 9.45691i) q^{96} +(-13.7525 - 7.94002i) q^{97} +(0.0983112 + 5.60370i) q^{98} +(-10.4581 - 13.2063i) 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 $

$2$	−1.35939	+	0.389931i	−0.961237	+	0.275723i
$2$	−1.35939	+	0.389931i	−0.961237	+	0.275723i
$3$	1.72496	+	0.156592i	0.995905	+	0.0904083i
$3$	1.72496	+	0.156592i	0.995905	+	0.0904083i
$4$	1.69591	−	1.06014i	0.847954	−	0.530070i
$5$	1.33127	+	0.656508i	0.595361	+	0.293599i	0.714896	−	0.699231i	$-0.246474\pi$
$5$	1.33127	+	0.656508i	0.595361	+	0.293599i	−0.119536	+	0.992830i	$0.538141\pi$
$6$	−2.40596	+	0.459744i	−0.982228	+	0.187690i
$7$	−1.06088	−	1.38257i	−0.400976	−	0.522562i	0.548606	−	0.836081i	$-0.315159\pi$
$7$	−1.06088	−	1.38257i	−0.400976	−	0.522562i	−0.949582	+	0.313519i	$0.898492\pi$
$8$	−1.89203	+	2.10244i	−0.668932	+	0.743323i
$9$	2.95096	+	0.540229i	0.983653	+	0.180076i
$10$	−2.06571	−	0.373352i	−0.653235	−	0.118064i
$11$	−4.22175	−	3.70237i	−1.27290	−	1.11631i	−0.987453	−	0.157914i	$-0.949523\pi$
$11$	−4.22175	−	3.70237i	−1.27290	−	1.11631i	−0.285451	−	0.958393i	$-0.592144\pi$
$12$	3.09138	−	1.56313i	0.892404	−	0.451237i
$13$	5.42788	+	0.355762i	1.50542	+	0.0986707i	0.795649	−	0.605758i	$-0.207130\pi$
$13$	5.42788	+	0.355762i	1.50542	+	0.0986707i	0.709775	+	0.704429i	$0.248797\pi$
$14$	1.98127	+	1.46579i	0.529516	+	0.391748i
$15$	2.19358	+	1.34091i	0.566379	+	0.346223i
$16$	1.75221	−	3.59580i	0.438052	−	0.898950i
$17$	5.24770	+	5.24770i	1.27276	+	1.27276i	0.944637	+	0.328118i	$0.106415\pi$
$17$	5.24770	+	5.24770i	1.27276	+	1.27276i	0.328118	+	0.944637i	$0.393585\pi$
$18$	−4.22217	+	0.416286i	−0.995175	+	0.0981195i
$19$	1.08713	−	1.62700i	0.249404	−	0.373260i	−0.685552	−	0.728024i	$-0.740439\pi$
$19$	1.08713	−	1.62700i	0.249404	−	0.373260i	0.934956	+	0.354764i	$0.115439\pi$
$20$	2.95370	−	0.297952i	0.660467	−	0.0666241i
$21$	−1.61348	−	2.55100i	−0.352090	−	0.556674i
$22$	7.18269	+	3.38680i	1.53135	+	0.722067i
$23$	1.32665	−	1.72892i	0.276625	−	0.360505i	−0.634292	−	0.773093i	$-0.718708\pi$
$23$	1.32665	−	1.72892i	0.276625	−	0.360505i	0.910918	+	0.412588i	$0.135375\pi$
$24$	−3.59289	+	3.33034i	−0.733396	+	0.679802i
$25$	−1.70254	−	2.21879i	−0.340508	−	0.443758i
$26$	−7.51736	+	1.63288i	−1.47427	+	0.320234i
$27$	5.00568	+	1.39397i	0.963344	+	0.268269i
$28$	−3.26488	−	1.22003i	−0.617004	−	0.230563i
$29$	−0.774434	+	2.28141i	−0.143809	+	0.423647i	−0.994839	−	0.101470i	$-0.967645\pi$
$29$	−0.774434	+	2.28141i	−0.143809	+	0.423647i	0.851030	+	0.525117i	$0.175979\pi$
$30$	−3.50480	−	0.967489i	−0.639886	−	0.176639i
$31$	1.28939	+	2.23328i	0.231580	+	0.401109i	0.958273	−	0.285853i	$-0.0922770\pi$
$31$	1.28939	+	2.23328i	0.231580	+	0.401109i	−0.726693	+	0.686962i	$0.758944\pi$
$32$	−0.979827	+	5.57135i	−0.173210	+	0.984885i
$33$	−6.70257	−	7.04753i	−1.16677	−	1.22682i
$34$	−9.17994	−	5.08746i	−1.57435	−	0.872492i
$35$	−0.504650	−	2.53705i	−0.0853015	−	0.428840i
$36$	5.57727	−	2.21225i	0.929545	−	0.368708i
$37$	3.04121	−	2.03207i	0.499971	−	0.334070i	−0.279880	−	0.960035i	$-0.590295\pi$
$37$	3.04121	−	2.03207i	0.499971	−	0.334070i	0.779851	+	0.625965i	$0.215295\pi$
$38$	−0.843418	+	2.63564i	−0.136820	+	0.427558i
$39$	9.30716	+	1.46364i	1.49034	+	0.234369i
$40$	−3.89906	+	1.55677i	−0.616495	+	0.246147i
$41$	−4.61951	−	3.54467i	−0.721446	−	0.553585i	0.181473	−	0.983396i	$-0.441914\pi$
$41$	−4.61951	−	3.54467i	−0.721446	−	0.553585i	−0.902919	+	0.429811i	$0.858580\pi$
$42$	3.18807	+	2.83867i	0.491930	+	0.438017i
$43$	−2.60452	−	2.28410i	−0.397185	−	0.348322i	0.437336	−	0.899298i	$-0.355922\pi$
$43$	−2.60452	−	2.28410i	−0.397185	−	0.348322i	−0.834521	+	0.550976i	$0.814255\pi$
$44$	−11.0847	−	1.80324i	−1.67109	−	0.271849i
$45$	3.57385	+	2.65652i	0.532758	+	0.396010i
$46$	−1.12928	+	2.86759i	−0.166503	+	0.422803i
$47$	1.37640	+	5.13681i	0.200769	+	0.749280i	0.990698	+	0.136082i	$0.0434509\pi$
$47$	1.37640	+	5.13681i	0.200769	+	0.749280i	−0.789929	+	0.613199i	$0.789882\pi$
$48$	3.58555	−	5.92822i	0.517530	−	0.855665i
$49$	1.02571	−	3.82799i	0.146529	−	0.546856i
$50$	3.17960	+	2.35234i	0.449663	+	0.332671i
$51$	8.23032	+	9.87381i	1.15248	+	1.38261i
$52$	9.58234	−	5.15097i	1.32883	−	0.714312i
$53$	−0.894480	−	0.177923i	−0.122866	−	0.0244396i	0.133274	−	0.991079i	$-0.457451\pi$
$53$	−0.894480	−	0.177923i	−0.122866	−	0.0244396i	−0.256140	+	0.966640i	$0.582451\pi$
$54$	−7.34825	+	0.0569183i	−0.999970	+	0.00774561i
$55$	−3.18963	−	7.70046i	−0.430090	−	1.03833i
$56$	4.91398	+	0.385421i	0.656659	+	0.0515040i
$57$	2.13003	−	2.63627i	0.282129	−	0.349183i
$58$	0.163170	−	3.40331i	0.0214252	−	0.446877i
$59$	−3.98177	+	8.07423i	−0.518382	+	1.05117i	0.467540	+	0.883972i	$0.345140\pi$
$59$	−3.98177	+	8.07423i	−0.518382	+	1.05117i	−0.985922	+	0.167203i	$0.946526\pi$
$60$	5.14166	−	0.0514298i	0.663785	−	0.00663956i
$61$	−4.03610	+	11.8900i	−0.516770	+	1.52236i	0.304896	+	0.952386i	$0.401378\pi$
$61$	−4.03610	+	11.8900i	−0.516770	+	1.52236i	−0.821666	+	0.569969i	$0.806955\pi$
$62$	−2.62361	−	2.53314i	−0.333199	−	0.321709i
$63$	−2.38372	−	4.65303i	−0.300320	−	0.586226i
$64$	−0.840471	−	7.95573i	−0.105059	−	0.994466i
$65$	6.99240	+	4.03706i	0.867300	+	0.500736i
$66$	11.8595	+	6.96683i	1.45980	+	0.857557i
$67$	6.22230	−	5.45681i	0.760176	−	0.666656i	−0.188797	−	0.982016i	$-0.560459\pi$
$67$	6.22230	−	5.45681i	0.760176	−	0.666656i	0.948972	+	0.315360i	$0.102125\pi$
$68$	14.4629	+	3.33632i	1.75389	+	0.404588i
$69$	2.55915	−	2.77457i	0.308085	−	0.334019i
$70$	1.67529	+	3.25207i	0.200236	+	0.388697i
$71$	2.70303	+	1.11963i	0.320791	+	0.132876i	0.537267	−	0.843412i	$-0.319457\pi$
$71$	2.70303	+	1.11963i	0.320791	+	0.132876i	−0.216477	+	0.976288i	$0.569457\pi$
$72$	−6.71909	+	5.18207i	−0.791852	+	0.610713i
$73$	−3.45201	+	1.42987i	−0.404027	+	0.167354i	−0.575437	−	0.817846i	$-0.695168\pi$
$73$	−3.45201	+	1.42987i	−0.404027	+	0.167354i	0.171410	+	0.985200i	$0.445168\pi$
$74$	−3.34183	+	3.94824i	−0.388480	+	0.458974i
$75$	−2.58936	−	4.09392i	−0.298994	−	0.472726i
$76$	0.118819	−	3.91175i	0.0136295	−	0.448709i
$77$	−0.640009	+	9.76465i	−0.0729358	+	1.11278i
$78$	−13.2228	+	1.63949i	−1.49719	+	0.185635i
$79$	1.94771	+	7.26895i	0.219134	+	0.817820i	0.984670	+	0.174427i	$0.0558073\pi$
$79$	1.94771	+	7.26895i	0.219134	+	0.817820i	−0.765536	+	0.643393i	$0.777526\pi$
$80$	4.69333	−	3.63663i	0.524730	−	0.406588i
$81$	8.41631	+	3.18838i	0.935145	+	0.354265i
$82$	7.66191	+	3.01732i	0.846117	+	0.333207i
$83$	−2.39800	+	1.18257i	−0.263215	+	0.129803i	−0.569109	−	0.822262i	$-0.692712\pi$
$83$	−2.39800	+	1.18257i	−0.263215	+	0.129803i	0.305893	+	0.952066i	$0.401045\pi$
$84$	−5.44073	−	2.61575i	−0.593632	−	0.285401i
$85$	3.54093	+	10.4313i	0.384068	+	1.13143i
$86$	4.43121	+	2.08941i	0.477829	+	0.225307i
$87$	−1.69312	+	3.81406i	−0.181521	+	0.408911i
$88$	15.7717	−	1.87096i	1.68126	−	0.199445i
$89$	−3.03816	−	1.25845i	−0.322045	−	0.133395i	0.215804	−	0.976437i	$-0.430763\pi$
$89$	−3.03816	−	1.25845i	−0.322045	−	0.133395i	−0.537849	+	0.843041i	$0.680763\pi$
$90$	−5.89413	−	2.21770i	−0.621296	−	0.233766i
$91$	−5.26648	−	7.88185i	−0.552077	−	0.826242i
$92$	0.416974	−	4.33852i	0.0434725	−	0.452322i
$93$	1.87442	+	4.05422i	0.194368	+	0.420403i
$94$	−3.87408	−	6.44625i	−0.399580	−	0.664880i
$95$	2.51540	−	1.45227i	0.258074	−	0.148999i
$96$	−2.56259	+	9.45691i	−0.261543	+	0.965192i
$97$	−13.7525	−	7.94002i	−1.39636	−	0.806187i	−0.402348	−	0.915487i	$-0.631806\pi$
$97$	−13.7525	−	7.94002i	−1.39636	−	0.806187i	−0.994009	+	0.109299i	$0.965139\pi$
$98$	0.0983112	+	5.60370i	0.00993093	+	0.566059i
$99$	−10.4581	−	13.2063i	−1.05108	−	1.32728i
$100$	−5.23958	−	1.95794i	−0.523958	−	0.195794i
$101$	16.9274	−	1.10948i	1.68434	−	0.110398i	0.807090	−	0.590429i	$-0.201041\pi$
$101$	16.9274	−	1.10948i	1.68434	−	0.110398i	0.877251	+	0.480032i	$0.159375\pi$
$102$	−15.0384	−	10.2132i	−1.48902	−	1.01125i
$103$	−1.32503	−	10.0646i	−0.130559	−	0.991696i	−0.923824	−	0.382819i	$-0.874953\pi$
$103$	−1.32503	−	10.0646i	−0.130559	−	0.991696i	0.793264	−	0.608877i	$-0.208380\pi$
$104$	−11.0177	+	10.7387i	−1.08037	+	1.05301i
$105$	−0.473219	−	4.45533i	−0.0461815	−	0.434795i
$106$	1.28533	−	0.106918i	0.124842	−	0.0103848i
$107$	−8.72847	−	1.73620i	−0.843813	−	0.167845i	−0.245789	−	0.969323i	$-0.579047\pi$
$107$	−8.72847	−	1.73620i	−0.843813	−	0.167845i	−0.598024	+	0.801478i	$0.704047\pi$
$108$	9.96698	−	2.94268i	0.959073	−	0.283160i
$109$	−2.32843	−	1.55581i	−0.223023	−	0.149019i	0.439040	−	0.898468i	$-0.355319\pi$
$109$	−2.32843	−	1.55581i	−0.223023	−	0.149019i	−0.662063	+	0.749448i	$0.730319\pi$
$110$	7.33862	+	9.22422i	0.699710	+	0.879495i
$111$	5.56416	−	3.02900i	0.528126	−	0.287500i
$112$	−6.83033	+	1.39218i	−0.645406	+	0.131548i
$113$	−5.63874	−	1.51089i	−0.530448	−	0.142133i	−0.0163526	−	0.999866i	$-0.505205\pi$
$113$	−5.63874	−	1.51089i	−0.530448	−	0.142133i	−0.514095	+	0.857733i	$0.671872\pi$
$114$	−1.86758	+	4.41430i	−0.174915	+	0.413437i
$115$	2.90117	−	1.43070i	0.270536	−	0.133414i
$116$	1.10524	+	4.69007i	0.102619	+	0.435462i
$117$	15.8253	+	3.98214i	1.46305	+	0.368149i
$118$	2.26440	−	12.5287i	0.208455	−	1.15336i
$119$	1.68812	−	12.8225i	0.154749	−	1.17544i
$120$	−6.96949	+	2.07480i	−0.636224	+	0.189403i
$121$	2.67979	+	20.3551i	0.243618	+	1.85046i
$122$	0.850388	−	17.7370i	0.0769905	−	1.60583i
$123$	−7.41339	−	6.83779i	−0.668443	−	0.616543i
$124$	4.55427	+	2.42051i	0.408985	+	0.217368i
$125$	−2.25778	−	11.3506i	−0.201942	−	1.01523i
$126$	5.05477	+	5.39581i	0.450315	+	0.480697i
$127$			15.4522i			1.37116i	0.727996	+	0.685582i	$0.240452\pi$
$127$			15.4522i			1.37116i	−0.727996	+	0.685582i	$0.759548\pi$
$128$	4.24472	+	10.4872i	0.375183	+	0.926951i
$129$	−4.13501	−	4.34782i	−0.364067	−	0.382804i
$130$	−11.0796	−	2.76141i	−0.971746	−	0.242192i
$131$	−8.90475	−	10.1539i	−0.778012	−	0.887152i	0.218039	−	0.975940i	$-0.430034\pi$
$131$	−8.90475	−	10.1539i	−0.778012	−	0.887152i	−0.996051	+	0.0887877i	$0.971701\pi$
$132$	−18.8383	−	4.84629i	−1.63966	−	0.421815i
$133$	−3.40276	+	0.223029i	−0.295057	+	0.0193390i
$134$	−6.33079	+	9.84423i	−0.546897	+	0.850412i
$135$	5.74875	+	5.14201i	0.494773	+	0.442554i
$136$	−20.9618	+	1.10416i	−1.79746	+	0.0946813i
$137$	−20.3268	−	2.67608i	−1.73664	−	0.228633i	−0.805321	−	0.592839i	$-0.798007\pi$
$137$	−20.3268	−	2.67608i	−1.73664	−	0.228633i	−0.931318	+	0.364206i	$0.881340\pi$
$138$	−2.39700	+	4.76963i	−0.204046	+	0.406018i
$139$	0.102545	+	0.302087i	0.00869772	+	0.0256226i	0.951192	−	0.308599i	$-0.0998600\pi$
$139$	0.102545	+	0.302087i	0.00869772	+	0.0256226i	−0.942495	+	0.334221i	$0.891527\pi$
$140$	−3.54547	−	3.76760i	−0.299647	−	0.318420i
$141$	1.56986	+	9.07631i	0.132206	+	0.764363i
$142$	−4.11106	−	0.468026i	−0.344993	−	0.0392759i
$143$	−21.5980	−	21.5980i	−1.80611	−	1.80611i
$144$	7.11324	−	9.66446i	0.592770	−	0.805372i
$145$	−2.52874	+	2.52874i	−0.210001	+	0.210001i
$146$	4.13509	−	3.28980i	0.342223	−	0.272266i
$147$	2.36873	−	6.44250i	0.195370	−	0.531369i
$148$	3.00333	−	6.67030i	0.246872	−	0.548296i
$149$	−3.86182	+	1.31091i	−0.316373	+	0.107394i	−0.475109	−	0.879927i	$-0.657591\pi$
$149$	−3.86182	+	1.31091i	−0.316373	+	0.107394i	0.158736	+	0.987321i	$0.449258\pi$
$150$	5.11631	+	4.55559i	0.417745	+	0.371962i
$151$	−3.17480	+	24.1150i	−0.258361	+	1.96245i	0.0128139	+	0.999918i	$0.495921\pi$
$151$	−3.17480	+	24.1150i	−0.258361	+	1.96245i	−0.271175	+	0.962530i	$0.587412\pi$
$152$	1.36379	+	5.36395i	0.110618	+	0.435074i
$153$	12.6508	+	18.3207i	1.02276	+	1.48114i
$154$	−2.93751	−	13.5236i	−0.236712	−	1.08976i
$155$	0.250349	+	3.81958i	0.0201085	+	0.306796i
$156$	17.3357	−	7.38470i	1.38797	−	0.591249i
$157$	−9.96381	+	8.73803i	−0.795199	+	0.697371i	−0.957202	−	0.289419i	$-0.906538\pi$
$157$	−9.96381	+	8.73803i	−0.795199	+	0.697371i	0.162003	+	0.986790i	$0.448204\pi$
$158$	−5.48209	−	9.12189i	−0.436132	−	0.725699i
$159$	−1.51508	−	0.446978i	−0.120154	−	0.0354477i
$160$	−4.96205	+	6.77369i	−0.392284	+	0.535507i
$161$	−3.79777			−0.299307
$162$	−12.6843	−	1.05249i	−0.996575	−	0.0826917i
$163$	−9.78189	+	1.94574i	−0.766177	+	0.152402i	−0.562681	−	0.826674i	$-0.690230\pi$
$163$	−9.78189	+	1.94574i	−0.766177	+	0.152402i	−0.203496	+	0.979076i	$0.565230\pi$
$164$	−11.5921	−	1.11411i	−0.905192	−	0.0869977i
$165$	−4.29615	−	13.7824i	−0.334455	−	1.07296i
$166$	2.79872	−	2.54263i	0.217222	−	0.197346i
$167$	−21.9872	+	2.89466i	−1.70142	+	0.223996i	−0.917743	−	0.397176i	$-0.869990\pi$
$167$	−21.9872	+	2.89466i	−1.70142	+	0.223996i	−0.783675	+	0.621171i	$0.786657\pi$
$168$	8.41606	+	1.43432i	0.649313	+	0.110661i
$169$	16.4465	+	2.16523i	1.26512	+	0.166556i
$170$	−8.88100	−	12.7995i	−0.681141	−	0.981675i
$171$	4.08702	−	4.21392i	0.312542	−	0.322246i
$172$	−6.83848	−	1.11247i	−0.521430	−	0.0848250i
$173$	−9.55555	−	19.3767i	−0.726495	−	1.47319i	−0.874922	−	0.484263i	$-0.839088\pi$
$173$	−9.55555	−	19.3767i	−0.726495	−	1.47319i	0.148427	−	0.988923i	$-0.452579\pi$
$174$	0.814391	−	5.84502i	0.0617388	−	0.443110i
$175$	−1.26144	+	4.70776i	−0.0953559	+	0.355873i
$176$	−20.7104	+	8.69323i	−1.56110	+	0.655277i
$177$	−8.13274	+	13.3042i	−0.611294	+	1.00000i
$178$	4.62077	+	0.526054i	0.346341	+	0.0394294i
$179$	1.01874	−	1.52465i	0.0761441	−	0.113958i	−0.791443	−	0.611243i	$-0.790670\pi$
$179$	1.01874	−	1.52465i	0.0761441	−	0.113958i	0.867587	+	0.497285i	$0.165670\pi$
$180$	8.87720	+	0.716428i	0.661667	+	0.0533994i
$181$	−1.70149	+	8.55397i	−0.126471	+	0.635812i	0.864598	+	0.502464i	$0.167573\pi$
$181$	−1.70149	+	8.55397i	−0.126471	+	0.635812i	−0.991069	+	0.133348i	$0.957427\pi$
$182$	10.2326	+	8.66098i	0.758491	+	0.641994i
$183$	−8.82398	+	19.8777i	−0.652287	+	1.46940i
$184$	1.12489	+	6.06036i	0.0829282	+	0.446775i
$185$	5.38273	−	0.708649i	0.395746	−	0.0521009i
$186$	−4.12894	−	4.78039i	−0.302749	−	0.350515i
$187$	−2.72552	−	41.5834i	−0.199310	−	3.04088i
$188$	7.77999	+	7.25237i	0.567414	+	0.528934i
$189$	−3.38319	−	8.39954i	−0.246091	−	0.610977i
$190$	−2.85314	+	2.95503i	−0.206988	+	0.214381i
$191$	6.65431	−	11.5256i	0.481489	−	0.833963i	−0.518286	−	0.855208i	$-0.673430\pi$
$191$	6.65431	−	11.5256i	0.481489	−	0.833963i	0.999774	+	0.0212447i	$0.00676290\pi$
$192$	−0.203974	−	13.8549i	−0.0147206	−	0.999892i
$193$	6.94214	+	12.0241i	0.499706	+	0.865516i	1.00000		0.000339280i	$-0.000107996\pi$
$193$	6.94214	+	12.0241i	0.499706	+	0.865516i	−0.500294	+	0.865856i	$0.666775\pi$
$194$	21.7912	+	5.43109i	1.56451	+	0.389930i
$195$	11.4294	+	8.05871i	0.818478	+	0.577097i
$196$	−2.31870	−	7.57931i	−0.165621	−	0.541379i
$197$	19.3947	−	12.9592i	1.38182	−	0.923301i	0.381819	−	0.924237i	$-0.375298\pi$
$197$	19.3947	−	12.9592i	1.38182	−	0.923301i	1.00000		0.000935986i	$0.000297934\pi$
$198$	19.3662	+	13.8746i	1.37629	+	0.986024i
$199$	0.955781	−	2.30746i	0.0677535	−	0.163572i	−0.886376	−	0.462967i	$-0.846785\pi$
$199$	0.955781	−	2.30746i	0.0677535	−	0.163572i	0.954129	+	0.299395i	$0.0967849\pi$
$200$	7.88611	+	0.618535i	0.557632	+	0.0437370i
$201$	11.5877	−	8.43841i	0.817334	−	0.595200i
$202$	−22.5784	+	8.10875i	−1.58861	+	0.570529i
$203$	3.97579	−	1.34960i	0.279046	−	0.0947233i
$204$	24.4255	+	8.01979i	1.71013	+	0.561497i
$205$	−3.82269	−	7.75165i	−0.266988	−	0.541399i
$206$	5.72575	+	13.1651i	0.398932	+	0.917257i
$207$	4.84890	−	4.38528i	0.337022	−	0.304798i
$208$	10.7900	−	18.8942i	0.748153	−	1.31008i
$209$	−10.6133	+	2.84384i	−0.734141	+	0.196712i
$210$	2.38056	+	5.87202i	0.164274	+	0.405208i
$211$	11.2900	+	0.739989i	0.777239	+	0.0509429i	0.448859	−	0.893603i	$-0.351831\pi$
$211$	11.2900	+	0.739989i	0.777239	+	0.0509429i	0.328380	+	0.944546i	$0.393497\pi$
$212$	−1.70558	+	0.646533i	−0.117140	+	0.0444041i
$213$	4.48729	+	2.35459i	0.307464	+	0.161334i
$214$	12.5424	−	1.04332i	0.857383	−	0.0713198i
$215$	−1.96778	−	4.75063i	−0.134201	−	0.323990i
$216$	−12.4016	+	7.88670i	−0.843823	+	0.536622i
$217$	1.71978	−	4.15192i	0.116746	−	0.281850i
$218$	3.77191	+	1.20703i	0.255466	+	0.0817503i
$219$	−6.17848	+	1.92591i	−0.417503	+	0.130141i
$220$	−13.5729	−	9.67781i	−0.915084	−	0.652478i
$221$	26.6170	+	30.3508i	1.79045	+	2.04162i
$222$	−6.38278	+	6.28725i	−0.428384	+	0.421973i
$223$	2.45075	−	4.24483i	0.164115	−	0.284255i	−0.772226	−	0.635348i	$-0.780857\pi$
$223$	2.45075	−	4.24483i	0.164115	−	0.284255i	0.936341	+	0.351093i	$0.114190\pi$
$224$	8.74226	−	4.55587i	0.584117	−	0.304402i
$225$	−3.82547	−	7.46732i	−0.255031	−	0.497821i
$226$	8.25441	−	0.144815i	0.549075	−	0.00963296i
$227$	20.4625	+	6.94608i	1.35814	+	0.461028i	0.903096	−	0.429439i	$-0.141289\pi$
$227$	20.4625	+	6.94608i	1.35814	+	0.461028i	0.455048	+	0.890467i	$0.349622\pi$
$228$	0.817506	−	6.72900i	0.0541407	−	0.445639i
$229$	−11.9961	−	5.91581i	−0.792723	−	0.390928i	0.000391686	−	1.00000i	$-0.499875\pi$
$229$	−11.9961	−	5.91581i	−0.792723	−	0.390928i	−0.793115	+	0.609072i	$0.791542\pi$
$230$	−3.38597	+	3.07614i	−0.223264	+	0.202835i
$231$	−2.63305	+	16.7434i	−0.173242	+	1.10163i
$232$	−3.33127	−	5.94468i	−0.218708	−	0.390288i
$233$	0.809861	−	0.335456i	0.0530558	−	0.0219764i	−0.355998	−	0.934487i	$-0.615859\pi$
$233$	0.809861	−	0.335456i	0.0530558	−	0.0219764i	0.409054	+	0.912510i	$0.365859\pi$
$234$	−23.0655	+	0.757463i	−1.50784	+	0.0495169i
$235$	−1.54000	+	7.74208i	−0.100458	+	0.505038i
$236$	1.80710	+	17.9144i	0.117632	+	1.16613i
$237$	2.22146	+	12.8436i	0.144299	+	0.834283i
$238$	2.70508	+	18.0891i	0.175344	+	1.17254i
$239$	−14.7832	−	3.96115i	−0.956247	−	0.256226i	−0.253236	−	0.967405i	$-0.581495\pi$
$239$	−14.7832	−	3.96115i	−0.956247	−	0.256226i	−0.703011	+	0.711179i	$0.748162\pi$
$240$	8.66526	−	5.53810i	0.559340	−	0.357483i
$241$	−25.0770	+	6.71937i	−1.61535	+	0.432833i	−0.949632	−	0.313367i	$-0.898543\pi$
$241$	−25.0770	+	6.71937i	−1.61535	+	0.432833i	−0.665722	+	0.746200i	$0.731876\pi$
$242$	−11.5800	−	26.6256i	−0.744388	−	1.71156i
$243$	14.0185	+	6.81775i	0.899287	+	0.437359i
$244$	5.76018	+	24.4431i	0.368758	+	1.56481i
$245$	3.87860	−	4.42269i	0.247794	−	0.282555i
$246$	12.7440	+	6.40455i	0.812527	+	0.408339i
$247$	6.47963	−	8.44442i	0.412289	−	0.537305i
$248$	−7.13488	−	1.51458i	−0.453065	−	0.0961757i
$249$	−4.32164	+	1.66437i	−0.273873	+	0.105475i
$250$	7.49519	+	14.5496i	0.474037	+	0.920199i
$251$	−11.0017	−	16.4651i	−0.694418	−	1.03927i	−0.996302	−	0.0859256i	$-0.972615\pi$
$251$	−11.0017	−	16.4651i	−0.694418	−	1.03927i	0.301883	−	0.953345i	$-0.402385\pi$
$252$	−8.97543	−	5.36403i	−0.565399	−	0.337902i
$253$	−12.0019	+	2.38732i	−0.754552	+	0.150090i
$254$	−6.02530	−	21.0057i	−0.378061	−	1.31801i
$255$	4.47451	+	18.5480i	0.280205	+	1.16152i
$256$	−9.85955	−	12.6012i	−0.616222	−	0.787573i
$257$	7.03586	−	4.06216i	0.438885	−	0.253390i	−0.264239	−	0.964457i	$-0.585121\pi$
$257$	7.03586	−	4.06216i	0.438885	−	0.253390i	0.703125	+	0.711067i	$0.251788\pi$
$258$	7.31646	+	4.29804i	0.455503	+	0.267584i
$259$	−6.03584	−	2.04889i	−0.375049	−	0.127312i
$260$	16.1383	−	0.566435i	1.00086	−	0.0351288i
$261$	−3.51780	+	6.31397i	−0.217747	+	0.390825i
$262$	16.0644	+	10.3310i	0.992462	+	0.638248i
$263$	−15.3807	+	11.8020i	−0.948413	+	0.727743i	−0.962252	−	0.272162i	$-0.912261\pi$
$263$	−15.3807	+	11.8020i	−0.948413	+	0.727743i	0.0138389	+	0.999904i	$0.495595\pi$
$264$	27.4984	−	0.757619i	1.69241	−	0.0466282i
$265$	−1.07398	−	0.824097i	−0.0659743	−	0.0506239i
$266$	4.53873	−	1.63003i	0.278287	−	0.0999433i
$267$	−5.04364	−	2.64652i	−0.308666	−	0.161965i
$268$	4.76747	−	15.8508i	0.291219	−	0.968240i
$269$	24.8804	+	16.6245i	1.51698	+	1.01362i	0.986097	+	0.166173i	$0.0531409\pi$
$269$	24.8804	+	16.6245i	1.51698	+	1.01362i	0.530886	+	0.847443i	$0.321859\pi$
$270$	−9.81985	−	4.74841i	−0.597617	−	0.288979i
$271$	−1.78469	+	1.78469i	−0.108412	+	0.108412i	−0.759232	−	0.650820i	$-0.774425\pi$
$271$	−1.78469	+	1.78469i	−0.108412	+	0.108412i	0.650820	+	0.759232i	$0.274425\pi$
$272$	28.0647	−	9.67463i	1.70168	−	0.586611i
$273$	−7.85023	−	14.4205i	−0.475117	−	0.872771i
$274$	28.6757	−	4.28822i	1.73236	−	0.259061i
$275$	−1.02711	+	15.6706i	−0.0619368	+	0.944973i
$276$	1.39864	−	7.41847i	0.0841882	−	0.446540i
$277$	5.31428	−	6.05977i	0.319304	−	0.364096i	−0.569815	−	0.821773i	$-0.692985\pi$
$277$	5.31428	−	6.05977i	0.319304	−	0.364096i	0.889119	+	0.457677i	$0.151318\pi$
$278$	−0.257191	−	0.370670i	−0.0154253	−	0.0222313i
$279$	2.59844	+	7.28688i	0.155564	+	0.436254i
$280$	6.28879	+	3.73917i	0.375827	+	0.223458i
$281$	−11.6984	+	8.97647i	−0.697866	+	0.535491i	−0.895653	−	0.444754i	$-0.853291\pi$
$281$	−11.6984	+	8.97647i	−0.697866	+	0.535491i	0.197787	+	0.980245i	$0.436625\pi$
$282$	−5.67319	−	11.7262i	−0.337833	−	0.698282i
$283$	−2.05726	+	4.17172i	−0.122292	+	0.247983i	−0.949406	−	0.314050i	$-0.898314\pi$
$283$	−2.05726	+	4.17172i	−0.122292	+	0.247983i	0.827115	+	0.562033i	$0.189981\pi$
$284$	5.77105	−	0.966798i	0.342449	−	0.0573689i
$285$	4.56637	−	2.11121i	0.270488	−	0.125057i
$286$	37.7819	+	20.9385i	2.23409	+	1.23812i
$287$			10.1473i			0.598975i
$288$	−5.90123	+	15.9115i	−0.347733	+	0.937593i
$289$			38.0768i			2.23981i
$290$	2.45152	−	4.42359i	0.143958	−	0.259762i
$291$	−22.4792	−	15.8497i	−1.31775	−	0.929128i
$292$	−4.33843	+	6.08454i	−0.253887	+	0.356071i
$293$	5.02943	−	10.1987i	0.293823	−	0.595813i	−0.699039	−	0.715083i	$-0.746389\pi$
$293$	5.02943	−	10.1987i	0.293823	−	0.595813i	0.992862	+	0.119270i	$0.0380554\pi$
$294$	−0.707911	+	9.68154i	−0.0412862	+	0.564639i
$295$	−10.6016	+	8.13489i	−0.617249	+	0.473631i
$296$	−1.48175	+	10.2387i	−0.0861249	+	0.595110i
$297$	−15.9717	−	24.4179i	−0.926774	−	1.41687i
$298$	4.73857	−	3.28789i	0.274498	−	0.190462i
$299$	7.81597	−	8.91241i	0.452009	−	0.515418i
$300$	−8.73145	−	4.19783i	−0.504111	−	0.242362i
$301$	−0.394840	+	6.02409i	−0.0227582	+	0.347223i
$302$	−5.08737	−	34.0197i	−0.292745	−	1.95761i
$303$	29.3728	+	0.736887i	1.68742	+	0.0423330i
$304$	−3.94550	−	6.75994i	−0.226290	−	0.387709i
$305$	−13.1790	+	13.1790i	−0.754627	+	0.754627i
$306$	−24.3412	−	19.9721i	−1.39150	−	1.14173i
$307$	21.9659	+	14.6771i	1.25366	+	0.837669i	0.991845	−	0.127449i	$-0.0406791\pi$
$307$	21.9659	+	14.6771i	1.25366	+	0.837669i	0.261815	+	0.965118i	$0.415679\pi$
$308$	9.26650	+	17.2384i	0.528008	+	0.982251i
$309$	−0.709587	−	17.5685i	−0.0403670	−	0.999439i
$310$	−1.82970	−	5.09470i	−0.103920	−	0.289360i
$311$	−6.16932	−	4.73389i	−0.349830	−	0.268434i	0.418866	−	0.908048i	$-0.362428\pi$
$311$	−6.16932	−	4.73389i	−0.349830	−	0.268434i	−0.768696	+	0.639614i	$0.779094\pi$
$312$	−20.6866	+	16.7985i	−1.17115	+	0.951025i
$313$	15.2016	−	11.6646i	0.859247	−	0.659324i	−0.0821514	−	0.996620i	$-0.526179\pi$
$313$	15.2016	−	11.6646i	0.859247	−	0.659324i	0.941399	+	0.337296i	$0.109512\pi$
$314$	10.1375	−	15.7636i	0.572094	−	0.889593i
$315$	−0.118616	−	7.75935i	−0.00668324	−	0.437190i
$316$	11.0092	+	10.2626i	0.619318	+	0.577317i
$317$	11.2885	+	3.83194i	0.634028	+	0.215223i	0.619905	−	0.784677i	$-0.287171\pi$
$317$	11.2885	+	3.83194i	0.634028	+	0.215223i	0.0141228	+	0.999900i	$0.495504\pi$
$318$	2.23388	+	0.0168436i	0.125270	+	0.000944545i
$319$	11.7161	−	6.76429i	0.655975	−	0.378727i
$320$	4.10411	−	11.1430i	0.229427	−	0.622911i
$321$	−14.7844	−	4.36168i	−0.825183	−	0.243445i
$322$	5.16267	−	1.48087i	0.287705	−	0.0825256i
$323$	14.2430	−	2.83310i	0.792499	−	0.157638i
$324$	17.6534	−	3.51526i	0.980745	−	0.195292i
$325$	−8.45181	−	12.6490i	−0.468822	−	0.701642i
$326$	12.5388	−	6.45929i	0.694457	−	0.357747i
$327$	−3.77282	−	3.04832i	−0.208637	−	0.168572i
$328$	16.1927	−	3.00560i	0.894091	−	0.165957i
$329$	5.64179	−	7.35253i	0.311042	−	0.405358i
$330$	11.2144	+	17.0606i	0.617330	+	0.939153i
$331$	10.5097	−	11.9840i	0.577666	−	0.658702i	−0.387030	−	0.922067i	$-0.626499\pi$
$331$	10.5097	−	11.9840i	0.577666	−	0.658702i	0.964696	+	0.263365i	$0.0848325\pi$
$332$	−2.81311	+	4.54774i	−0.154389	+	0.249590i
$333$	10.0723	−	4.35360i	0.551956	−	0.238576i
$334$	28.7605	−	12.5085i	1.57370	−	0.684433i
$335$	11.8660	−	3.17948i	0.648308	−	0.173714i
$336$	−12.0000	+	1.33187i	−0.654656	+	0.0726595i
$337$	−3.58563	−	0.960767i	−0.195322	−	0.0523363i	0.159832	−	0.987144i	$-0.448905\pi$
$337$	−3.58563	−	0.960767i	−0.195322	−	0.0523363i	−0.355154	+	0.934808i	$0.615571\pi$
$338$	−23.2016	+	3.46962i	−1.26200	+	0.188722i
$339$	−9.48999	−	3.48921i	−0.515425	−	0.189508i
$340$	17.0637	+	13.9366i	0.925408	+	0.755816i
$341$	2.82498	−	14.2021i	0.152981	−	0.769088i
$342$	−3.91274	+	7.32203i	−0.211577	+	0.395930i
$343$	−17.6509	+	7.31123i	−0.953058	+	0.394770i
$344$	9.72999	−	1.15425i	0.524606	−	0.0622330i
$345$	5.22844	−	2.01360i	0.281490	−	0.108408i
$346$	20.5454	+	22.6146i	1.10453	+	1.21577i
$347$	−14.3389	−	7.07117i	−0.769753	−	0.379600i	0.0146169	−	0.999893i	$-0.495347\pi$
$347$	−14.3389	−	7.07117i	−0.769753	−	0.379600i	−0.784370	+	0.620293i	$0.787014\pi$
$348$	1.17207	+	8.26324i	0.0628297	+	0.442956i
$349$	−13.2267	−	4.48985i	−0.708008	−	0.240336i	−0.0558716	−	0.998438i	$-0.517794\pi$
$349$	−13.2267	−	4.48985i	−0.708008	−	0.240336i	−0.652136	+	0.758102i	$0.726127\pi$
$350$	−0.120906	−	6.89158i	−0.00646268	−	0.368370i
$351$	26.6743	+	9.34712i	1.42377	+	0.498912i
$352$	24.7638	−	19.8931i	1.31991	−	1.06031i
$353$	0.477365	−	0.826820i	0.0254076	−	0.0440072i	−0.853042	−	0.521842i	$-0.825245\pi$
$353$	0.477365	−	0.826820i	0.0254076	−	0.0440072i	0.878450	+	0.477835i	$0.158578\pi$
$354$	5.86789	−	21.2568i	0.311875	−	1.12979i
$355$	2.86341	+	3.26509i	0.151974	+	0.173293i
$356$	−6.48658	+	1.08667i	−0.343788	+	0.0575932i
$357$	4.91983	−	21.8540i	0.260385	−	1.15663i
$358$	−0.790359	+	2.46984i	−0.0417718	+	0.130535i
$359$	−6.17516	+	14.9082i	−0.325912	+	0.786822i	0.672975	+	0.739665i	$0.265016\pi$
$359$	−6.17516	+	14.9082i	−0.325912	+	0.786822i	−0.998887	+	0.0471570i	$0.984984\pi$
$360$	−12.3470	+	2.48759i	−0.650743	+	0.131107i
$361$	5.80570	+	14.0162i	0.305563	+	0.737694i
$362$	−1.02246	−	12.2917i	−0.0537394	−	0.646037i
$363$	1.43510	+	35.5312i	0.0753230	+	1.86491i
$364$	−17.2873	−	7.78368i	−0.906102	−	0.407976i
$365$	−5.53427	−	0.362735i	−0.289677	−	0.0189864i
$366$	4.24435	−	30.4624i	0.221856	−	1.59229i
$367$	−27.8708	+	7.46795i	−1.45484	+	0.389824i	−0.897705	−	0.440597i	$-0.854767\pi$
$367$	−27.8708	+	7.46795i	−1.45484	+	0.389824i	−0.557137	+	0.830421i	$0.688100\pi$
$368$	−3.89229	−	7.79979i	−0.202900	−	0.406592i
$369$	−11.7170	−	12.9558i	−0.609965	−	0.674451i
$370$	−7.04093	+	3.06223i	−0.366040	+	0.159198i
$371$	0.702948	+	1.42544i	0.0364952	+	0.0740050i
$372$	7.47689	+	4.88844i	0.387659	+	0.253454i
$373$	−0.141980	+	0.0481958i	−0.00735145	+	0.00249548i	−0.325113	−	0.945675i	$-0.605402\pi$
$373$	−0.141980	+	0.0481958i	−0.00735145	+	0.00249548i	0.317761	+	0.948171i	$0.397069\pi$
$374$	19.9197	+	55.4655i	1.03002	+	2.86805i
$375$	−2.11716	−	19.9329i	−0.109330	−	1.02933i
$376$	−13.4040	−	6.82518i	−0.691259	−	0.351982i
$377$	−5.01517	+	12.1077i	−0.258295	+	0.623578i
$378$	7.87433	+	10.0991i	0.405012	+	0.519441i
$379$	16.2749	−	10.8746i	0.835986	−	0.558588i	−0.0622705	−	0.998059i	$-0.519834\pi$
$379$	16.2749	−	10.8746i	0.835986	−	0.558588i	0.898257	+	0.439471i	$0.144834\pi$
$380$	2.72628	−	5.12958i	0.139855	−	0.263142i
$381$	−2.41969	+	26.6544i	−0.123965	+	1.36555i
$382$	−4.55164	+	18.2626i	−0.232882	+	0.934394i
$383$	11.6118	+	20.1123i	0.593336	+	1.02769i	0.993779	+	0.111367i	$0.0355230\pi$
$383$	11.6118	+	20.1123i	0.593336	+	1.02769i	−0.400443	+	0.916322i	$0.631144\pi$
$384$	5.67974	+	18.7547i	0.289843	+	0.957074i
$385$	−7.26259	+	12.5792i	−0.370136	+	0.641094i
$386$	−14.1257	−	13.6386i	−0.718979	−	0.694186i
$387$	−6.45188	−	8.14732i	−0.327968	−	0.414151i
$388$	−31.7406	+	1.11405i	−1.61138	+	0.0565575i
$389$	−0.317472	−	4.84369i	−0.0160965	−	0.245585i	−0.998323	−	0.0578864i	$-0.981564\pi$
$389$	−0.317472	−	4.84369i	−0.0160965	−	0.245585i	0.982227	−	0.187699i	$-0.0601028\pi$
$390$	−18.6794	−	6.49829i	−0.945870	−	0.329054i
$391$	16.0347	−	2.11101i	0.810911	−	0.106758i
$392$	6.10744	+	9.39914i	0.308472	+	0.474728i
$393$	−13.7703	−	18.9095i	−0.694620	−	0.953858i
$394$	−21.3119	+	25.1792i	−1.07368	+	1.26851i
$395$	−2.17920	+	10.9556i	−0.109648	+	0.551236i
$396$	−31.7364	−	11.3096i	−1.59481	−	0.568327i
$397$	16.7532	−	25.0729i	0.840819	−	1.25837i	−0.123157	−	0.992387i	$-0.539302\pi$
$397$	16.7532	−	25.0729i	0.840819	−	1.25837i	0.963976	−	0.265988i	$-0.0856981\pi$
$398$	−0.399534	+	3.50944i	−0.0200268	+	0.175912i
$399$	−5.90454	−	0.148130i	−0.295597	−	0.00741575i
$400$	−10.9615	+	2.23421i	−0.548076	+	0.111710i
$401$	5.96302	−	22.2543i	0.297779	−	1.11133i	−0.641206	−	0.767368i	$-0.721566\pi$
$401$	5.96302	−	22.2543i	0.297779	−	1.11133i	0.938985	−	0.343957i	$-0.111768\pi$
$402$	−12.4619	+	15.9895i	−0.621541	+	0.797486i
$403$	6.20411	+	12.5807i	0.309049	+	0.626689i
$404$	27.5311	−	19.8270i	1.36972	−	0.986431i
$405$	9.11115	+	9.76996i	0.452737	+	0.485473i
$406$	−4.87842	+	3.38492i	−0.242112	+	0.167991i
$407$	−20.3627	−	2.68080i	−1.00934	−	0.132882i
$408$	−36.3310	−	1.37780i	−1.79865	−	0.0682114i
$409$	−39.8579	+	5.24739i	−1.97085	+	0.259467i	−0.971059	+	0.238840i	$0.923233\pi$
$409$	−39.8579	+	5.24739i	−1.97085	+	0.259467i	−0.999787	+	0.0206270i	$0.993434\pi$
$410$	8.21916	+	9.04697i	0.405915	+	0.446798i
$411$	−34.6439	−	7.79914i	−1.70886	−	0.384703i
$412$	−12.9170	−	15.6639i	−0.636377	−	0.771707i
$413$	15.3874	−	3.06074i	0.757163	−	0.150609i
$414$	−4.88161	+	7.85206i	−0.239918	+	0.385908i
$415$	−3.96875			−0.194818
$416$	−7.30046	+	29.8920i	−0.357934	+	1.46558i
$417$	0.129581	+	0.537144i	0.00634560	+	0.0263041i
$418$	13.3188	−	8.00437i	0.651445	−	0.391507i
$419$	−22.8361	+	20.0268i	−1.11562	+	0.978371i	−0.999889	−	0.0149096i	$-0.995254\pi$
$419$	−22.8361	+	20.0268i	−1.11562	+	0.978371i	−0.115730	+	0.993281i	$0.536921\pi$
$420$	−5.52581	−	7.05414i	−0.269632	−	0.344207i
$421$	0.324158	+	4.94570i	0.0157985	+	0.241039i	0.998453	+	0.0555950i	$0.0177056\pi$
$421$	0.324158	+	4.94570i	0.0157985	+	0.241039i	−0.982655	+	0.185444i	$0.940628\pi$
$422$	−15.6362	+	3.39640i	−0.761157	+	0.165334i
$423$	1.28666	+	15.9021i	0.0625595	+	0.773185i
$424$	2.06645	−	1.54395i	0.100356	−	0.0749809i
$425$	2.70914	−	20.5780i	0.131413	−	0.998178i
$426$	−7.01812	−	1.45108i	−0.340029	−	0.0703053i
$427$	20.7206	−	7.03368i	1.00274	−	0.340384i
$428$	−16.6433	+	6.30896i	−0.804484	+	0.304955i
$429$	−33.8735	−	40.6377i	−1.63543	−	1.96200i
$430$	4.52740	+	5.69069i	0.218331	+	0.274429i
$431$	11.3926	−	11.3926i	0.548760	−	0.548760i	−0.377322	−	0.926082i	$-0.623155\pi$
$431$	11.3926	−	11.3926i	0.548760	−	0.548760i	0.926082	+	0.377322i	$0.123155\pi$
$432$	13.7834	−	15.5569i	0.663155	−	0.748482i
$433$	8.11968	+	8.11968i	0.390207	+	0.390207i	0.874761	−	0.484554i	$-0.161018\pi$
$433$	8.11968	+	8.11968i	0.390207	+	0.390207i	−0.484554	+	0.874761i	$0.661018\pi$
$434$	−0.718899	+	6.31469i	−0.0345083	+	0.303115i
$435$	−4.75795	+	3.96599i	−0.228126	+	0.190155i
$436$	−5.59818	−	0.170044i	−0.268104	−	0.00814362i
$437$	−1.37072	−	4.03802i	−0.0655705	−	0.193165i
$438$	7.64802	−	5.02725i	0.365436	−	0.240211i
$439$	35.9815	+	4.73706i	1.71730	+	0.226087i	0.923907	−	0.382617i	$-0.124977\pi$
$439$	35.9815	+	4.73706i	1.71730	+	0.226087i	0.793397	+	0.608705i	$0.208311\pi$
$440$	22.2246	+	7.86347i	1.05952	+	0.374876i
$441$	5.09481	−	10.7421i	0.242610	−	0.511529i
$442$	−48.0177	−	30.8800i	−2.28397	−	1.46881i
$443$	28.4998	−	1.86798i	1.35407	−	0.0887502i	0.628987	−	0.777416i	$-0.283470\pi$
$443$	28.4998	−	1.86798i	1.35407	−	0.0887502i	0.725079	+	0.688665i	$0.241803\pi$
$444$	6.22513	−	11.0357i	0.295431	−	0.523731i
$445$	−3.21842	−	3.66991i	−0.152568	−	0.173970i
$446$	−1.67635	+	6.72602i	−0.0793775	+	0.318486i
$447$	−6.86676	+	1.65654i	−0.324786	+	0.0783515i
$448$	−10.1077	+	9.60211i	−0.477545	+	0.453657i
$449$		−	32.7529i		−	1.54570i	−0.634587	−	0.772852i	$-0.718830\pi$
$449$		−	32.7529i		−	1.54570i	0.634587	−	0.772852i	$-0.281170\pi$
$450$	8.11206	+	8.65937i	0.382406	+	0.408207i
$451$	6.37869	+	32.0679i	0.300361	+	1.51002i
$452$	−11.1645	+	3.41551i	−0.525136	+	0.160652i
$453$	−9.25259	+	41.1001i	−0.434725	+	1.93105i
$454$	−30.5251	−	1.46351i	−1.43261	−	0.0686858i
$455$	−1.83660	−	13.9503i	−0.0861010	−	0.654002i
$456$	1.51253	+	9.46614i	0.0708308	+	0.443293i
$457$	2.22058	−	16.8670i	0.103874	−	0.789003i	−0.857640	−	0.514250i	$-0.828070\pi$
$457$	2.22058	−	16.8670i	0.103874	−	0.789003i	0.961515	−	0.274753i	$-0.0885962\pi$
$458$	18.6142	+	3.36428i	0.869783	+	0.157202i
$459$	18.9532	+	33.5835i	0.884660	+	1.56754i
$460$	3.40338	−	5.50199i	0.158683	−	0.256531i
$461$	−27.6606	+	13.6407i	−1.28828	+	0.635310i	−0.951898	−	0.306415i	$-0.900871\pi$
$461$	−27.6606	+	13.6407i	−1.28828	+	0.635310i	−0.336384	+	0.941725i	$0.609204\pi$
$462$	−2.94941	−	23.7876i	−0.137219	−	1.10670i
$463$	4.29993	+	1.15216i	0.199835	+	0.0535456i	0.357348	−	0.933971i	$-0.383681\pi$
$463$	4.29993	+	1.15216i	0.199835	+	0.0535456i	−0.157513	+	0.987517i	$0.550348\pi$
$464$	6.84652	+	6.78221i	0.317842	+	0.314856i
$465$	−0.166275	+	6.62782i	−0.00771080	+	0.307358i
$466$	−0.970117	+	0.771807i	−0.0449398	+	0.0357533i
$467$	5.12027	+	3.42126i	0.236938	+	0.158317i	0.668371	−	0.743828i	$-0.266992\pi$
$467$	5.12027	+	3.42126i	0.236938	+	0.158317i	−0.431433	+	0.902145i	$0.641992\pi$
$468$	31.0598	−	10.0237i	1.43574	−	0.463343i
$469$	−14.1456	−	2.81373i	−0.653182	−	0.129926i
$470$	−0.925415	−	11.1250i	−0.0426862	−	0.513160i
$471$	−18.5555	+	13.5125i	−0.854991	+	0.622622i
$472$	−9.44193	−	23.6481i	−0.434600	−	1.08849i
$473$	2.53902	+	19.2858i	0.116744	+	0.886761i
$474$	−8.02796	−	16.5933i	−0.368736	−	0.762157i
$475$	−5.46086	+	0.357923i	−0.250561	+	0.0164227i
$476$	−10.7308	−	23.5355i	−0.491844	−	1.07875i
$477$	−2.54345	−	1.00827i	−0.116457	−	0.0461654i
$478$	21.6408	−	0.379666i	0.989827	−	0.0173655i
$479$	17.4895	+	10.0975i	0.799114	+	0.461369i	0.843161	−	0.537661i	$-0.180692\pi$
$479$	17.4895	+	10.0975i	0.799114	+	0.461369i	−0.0440473	+	0.999029i	$0.514025\pi$
$480$	−9.62003	+	10.9073i	−0.439092	+	0.497848i
$481$	17.2302	−	9.94788i	0.785631	−	0.453584i
$482$	31.4695	−	18.9126i	1.43340	−	0.861445i
$483$	−6.55100	−	0.594700i	−0.298081	−	0.0270598i
$484$	26.1239	+	31.6793i	1.18745	+	1.43997i
$485$	−13.0956	−	19.5989i	−0.594640	−	0.889942i
$486$	−21.7151	−	3.80177i	−0.985018	−	0.172452i
$487$	9.69239	+	4.01472i	0.439204	+	0.181924i	0.591318	−	0.806439i	$-0.298608\pi$
$487$	9.69239	+	4.01472i	0.439204	+	0.181924i	−0.152114	+	0.988363i	$0.548608\pi$
$488$	−17.3615	−	30.9818i	−0.785918	−	1.40248i
$489$	−17.1780	+	1.82455i	−0.776818	+	0.0825092i
$490$	−3.54800	+	7.52457i	−0.160282	+	0.339925i
$491$	2.16706	+	6.38395i	0.0977980	+	0.288103i	0.984808	−	0.173647i	$-0.0555550\pi$
$491$	2.16706	+	6.38395i	0.0977980	+	0.288103i	−0.887010	+	0.461750i	$0.847222\pi$
$492$	−19.8214	−	3.73703i	−0.893620	−	0.168478i
$493$	−16.0362	+	7.90816i	−0.722232	+	0.356165i
$494$	−5.51563	+	14.0059i	−0.248160	+	0.630155i
$495$	−5.25247	−	24.4469i	−0.236081	−	1.09880i
$496$	10.2897	−	0.723202i	0.462021	−	0.0324727i
$497$	−1.31963	−	4.92493i	−0.0591935	−	0.220913i
$498$	5.22582	−	3.94767i	0.234175	−	0.176899i
$499$	0.664548	−	10.1390i	0.0297492	−	0.453886i	−0.956835	−	0.290632i	$-0.906134\pi$
$499$	0.664548	−	10.1390i	0.0297492	−	0.453886i	0.986584	−	0.163254i	$-0.0521989\pi$
$500$	−15.8623	−	16.8561i	−0.709382	−	0.753827i
$501$	−38.3802	+	1.55016i	−1.71470	+	0.0692562i
$502$	21.3759	+	18.0927i	0.954051	+	0.807518i
$503$	−2.77257	+	1.14844i	−0.123623	+	0.0512062i	−0.443637	−	0.896206i	$-0.646312\pi$
$503$	−2.77257	+	1.14844i	−0.123623	+	0.0512062i	0.320015	+	0.947413i	$0.396312\pi$
$504$	14.2927	+	3.79204i	0.636650	+	0.168911i
$505$	23.2633	+	9.63597i	1.03520	+	0.428795i
$506$	15.3844	−	7.92522i	0.683920	−	0.352319i
$507$	28.0305	+	6.31032i	1.24488	+	0.280251i
$508$	16.3815	+	26.2056i	0.726813	+	1.16268i
$509$	9.93615	−	8.71377i	0.440412	−	0.386231i	−0.410225	−	0.911984i	$-0.634550\pi$
$509$	9.93615	−	8.71377i	0.440412	−	0.386231i	0.850637	+	0.525753i	$0.176217\pi$
$510$	−13.3150	−	23.4692i	−0.589600	−	1.03924i
$511$	5.63907	+	3.25572i	0.249458	+	0.144025i
$512$	18.3166	+	13.2854i	0.809487	+	0.587138i
$513$	7.70981	−	6.62883i	0.340396	−	0.292670i
$514$	−7.98056	+	8.26558i	−0.352007	+	0.364579i
$515$	4.84353	−	14.2686i	0.213432	−	0.628749i
$516$	−11.6219	−	2.98981i	−0.511625	−	0.131619i
$517$	13.2075	−	26.7823i	0.580867	−	1.17788i
$518$	9.00402	+	0.431692i	0.395614	+	0.0189675i
$519$	−13.4487	−	34.9204i	−0.590332	−	1.53284i
$520$	−21.7175	+	7.06284i	−0.952374	+	0.309726i
$521$	10.4186	+	25.1527i	0.456447	+	1.10196i	0.969826	+	0.243798i	$0.0783935\pi$
$521$	10.4186	+	25.1527i	0.456447	+	1.10196i	−0.513379	+	0.858162i	$0.671607\pi$
$522$	2.32007	−	9.95488i	0.101547	−	0.435713i
$523$	−17.2443	−	3.43011i	−0.754043	−	0.149988i	−0.196921	−	0.980419i	$-0.563094\pi$
$523$	−17.2443	−	3.43011i	−0.754043	−	0.149988i	−0.557122	+	0.830431i	$0.688094\pi$
$524$	−25.8662	−	7.77983i	−1.12997	−	0.339864i
$525$	−2.91313	+	7.92315i	−0.127139	+	0.345795i
$526$	16.3064	−	22.0410i	0.710994	−	0.961032i
$527$	−4.95328	+	18.4859i	−0.215768	+	0.805259i
$528$	−37.0858	+	11.7524i	−1.61395	+	0.511457i
$529$	4.72366	+	17.6290i	0.205377	+	0.766476i
$530$	1.78131	+	0.701493i	0.0773751	+	0.0304709i
$531$	−16.1120	+	21.6756i	−0.699199	+	0.940643i
$532$	−5.53433	+	3.98564i	−0.239944	+	0.172799i
$533$	−23.8131	−	20.8835i	−1.03146	−	0.904565i
$534$	7.88826	+	1.63100i	0.341358	+	0.0705801i
$535$	−10.4801	−	8.04166i	−0.453094	−	0.347671i
$536$	−0.300165	+	23.4064i	−0.0129651	+	1.01100i
$537$	1.99603	−	2.47043i	0.0861350	−	0.106607i
$538$	−40.3047	−	12.8977i	−1.73766	−	0.556058i
$539$	−18.5029	+	12.3632i	−0.796977	+	0.532523i
$540$	15.2006	+	2.62590i	0.654130	+	0.113001i
$541$	4.90712	+	24.6698i	0.210974	+	1.06064i	0.930534	+	0.366206i	$0.119344\pi$
$541$	4.90712	+	24.6698i	0.210974	+	1.06064i	−0.719560	+	0.694430i	$0.755656\pi$
$542$	1.73019	−	3.12201i	0.0743182	−	0.134102i
$543$	−4.27448	+	14.4888i	−0.183436	+	0.621774i
$544$	−34.3786	+	24.0950i	−1.47397	+	1.03306i
$545$	−2.07836	−	3.59983i	−0.0890272	−	0.154200i
$546$	16.2946	+	16.5422i	0.697343	+	0.707939i
$547$	2.23311	−	6.57854i	0.0954811	−	0.281278i	−0.888687	−	0.458514i	$-0.848382\pi$
$547$	2.23311	−	6.57854i	0.0954811	−	0.281278i	0.984168	+	0.177235i	$0.0567154\pi$
$548$	−37.3095	+	17.0109i	−1.59378	+	0.726670i
$549$	−18.3337	+	32.9064i	−0.782462	+	1.40441i
$550$	−4.71421	−	21.7030i	−0.201015	−	0.925421i
$551$	2.86995	+	3.74019i	0.122264	+	0.159337i
$552$	0.991389	+	10.6300i	0.0421963	+	0.452443i
$553$	7.98354	−	10.4043i	0.339495	−	0.442438i
$554$	−4.86131	+	10.3098i	−0.206537	+	0.438022i
$555$	9.39594	−	0.379499i	0.398836	−	0.0161088i
$556$	0.494160	+	0.403599i	0.0209571	+	0.0171164i
$557$	14.7722	−	22.1081i	0.625917	−	0.936750i	−0.374040	−	0.927413i	$-0.622028\pi$
$557$	14.7722	−	22.1081i	0.625917	−	0.936750i	0.999956	−	0.00933768i	$-0.00297232\pi$
$558$	−6.37368	−	8.89253i	−0.269820	−	0.376451i
$559$	−13.3244	−	13.3244i	−0.563562	−	0.563562i
$560$	−10.0070	−	2.63081i	−0.422872	−	0.111172i
$561$	1.81022	−	72.1564i	0.0764274	−	3.04645i
$562$	12.4025	−	16.7641i	0.523167	−	0.707152i
$563$	29.2595	+	1.91777i	1.23314	+	0.0808244i	0.667995	−	0.744166i	$-0.267153\pi$
$563$	29.2595	+	1.91777i	1.23314	+	0.0808244i	0.565147	+	0.824990i	$0.308819\pi$
$564$	12.2845	+	13.7283i	0.517270	+	0.578066i
$565$	−6.51475	−	5.71328i	−0.274077	−	0.240359i
$566$	1.16995	−	6.47320i	0.0491767	−	0.272089i
$567$	−4.52056	−	15.0186i	−0.189845	−	0.630724i
$568$	−7.46816	+	3.56457i	−0.313357	+	0.149566i
$569$	7.47275	+	9.73867i	0.313274	+	0.408266i	0.923278	−	0.384132i	$-0.125499\pi$
$569$	7.47275	+	9.73867i	0.313274	+	0.408266i	−0.610005	+	0.792398i	$0.708832\pi$
$570$	−5.38427	+	4.65053i	−0.225522	+	0.194789i
$571$	24.4524	+	12.0586i	1.02330	+	0.504636i	0.874906	−	0.484292i	$-0.160923\pi$
$571$	24.4524	+	12.0586i	1.02330	+	0.504636i	0.148395	+	0.988928i	$0.452589\pi$
$572$	−59.5250	−	13.7313i	−2.48887	−	0.574134i
$573$	13.2832	−	18.8392i	0.554914	−	0.787017i
$574$	−3.95674	−	13.7942i	−0.165151	−	0.575757i
$575$	−6.09478			−0.254170
$576$	1.81772	−	23.9311i	0.0757383	−	0.997128i
$577$	−8.01152			−0.333524			−0.166762	−	0.985997i	$-0.553331\pi$
$577$	−8.01152			−0.333524			−0.166762	+	0.985997i	$0.553331\pi$
$578$	−14.8473	−	51.7614i	−0.617567	−	2.15299i
$579$	10.0920	+	21.8282i	0.419410	+	0.907150i
$580$	−1.60769	+	6.96933i	−0.0667558	+	0.289386i
$581$	4.17898	+	2.06085i	0.173373	+	0.0854983i
$582$	36.7384	+	12.7807i	1.52285	+	0.529778i
$583$	3.11753	+	4.06284i	0.129115	+	0.168266i
$584$	3.52509	−	9.96298i	0.145869	−	0.412271i
$585$	18.4533	+	15.6907i	0.762952	+	0.648730i
$586$	−2.86020	+	15.8252i	−0.118154	+	0.653732i
$587$	4.75971	+	4.17415i	0.196454	+	0.172286i	0.751921	−	0.659253i	$-0.229127\pi$
$587$	4.75971	+	4.17415i	0.196454	+	0.172286i	−0.555467	+	0.831538i	$0.687461\pi$
$588$	−2.81280	−	13.4371i	−0.115998	−	0.554136i
$589$	5.03528	+	0.330030i	0.207475	+	0.0135986i
$590$	11.2397	−	15.1924i	0.462731	−	0.625462i
$591$	35.4844	−	19.3169i	1.45963	−	0.794592i
$592$	−1.97809	−	14.4962i	−0.0812991	−	0.595789i
$593$	21.1413	+	21.1413i	0.868169	+	0.868169i	0.992270	−	0.124101i	$-0.0396045\pi$
$593$	21.1413	+	21.1413i	0.868169	+	0.868169i	−0.124101	+	0.992270i	$0.539605\pi$
$594$	31.2332	+	26.9657i	1.28151	+	1.10641i
$595$	10.6654	−	15.9619i	0.437240	−	0.654376i
$596$	−5.15954	+	6.31726i	−0.211343	+	0.258765i
$597$	2.01001	−	3.83060i	0.0822643	−	0.156776i
$598$	−7.14977	+	15.1632i	−0.292376	+	0.620068i
$599$	−5.65225	+	7.36616i	−0.230945	+	0.300973i	−0.894423	−	0.447223i	$-0.852413\pi$
$599$	−5.65225	+	7.36616i	−0.230945	+	0.300973i	0.663478	+	0.748196i	$0.269080\pi$
$600$	13.5064	+	2.30185i	0.551395	+	0.0939725i
$601$	1.41569	+	1.84497i	0.0577474	+	0.0752579i	0.821334	−	0.570447i	$-0.193230\pi$
$601$	1.41569	+	1.84497i	0.0577474	+	0.0752579i	−0.763587	+	0.645705i	$0.776563\pi$
$602$	−1.81224	−	8.34308i	−0.0738612	−	0.340038i
$603$	21.3097	−	12.7414i	0.867798	−	0.518868i
$604$	20.1811	+	44.2625i	0.821156	+	1.80101i
$605$	−9.79574	+	28.8573i	−0.398253	+	1.17322i
$606$	−40.2166	+	10.4516i	−1.63369	+	0.424569i
$607$	−14.6115	−	25.3079i	−0.593064	−	1.02722i	−0.993817	−	0.111031i	$-0.964585\pi$
$607$	−14.6115	−	25.3079i	−0.593064	−	1.02722i	0.400753	−	0.916186i	$-0.368749\pi$
$608$	7.99940	+	7.65095i	0.324419	+	0.310287i
$609$	7.06941	−	1.70543i	0.286467	−	0.0691073i
$610$	12.7766	−	23.0544i	0.517308	−	0.933443i
$611$	5.64347	+	28.3717i	0.228310	+	1.14779i
$612$	40.8771	+	17.6586i	1.65236	+	0.713808i
$613$	26.9612	−	18.0149i	1.08895	−	0.727615i	0.124593	−	0.992208i	$-0.460238\pi$
$613$	26.9612	−	18.0149i	1.08895	−	0.727615i	0.964360	+	0.264593i	$0.0852375\pi$
$614$	−35.5834	−	11.3868i	−1.43603	−	0.459536i
$615$	−5.38014	−	13.9699i	−0.216948	−	0.563320i
$616$	−19.3186	−	19.8205i	−0.778370	−	0.798593i
$617$	15.9495	+	12.2385i	0.642103	+	0.492703i	0.877739	−	0.479138i	$-0.159051\pi$
$617$	15.9495	+	12.2385i	0.642103	+	0.492703i	−0.235636	+	0.971841i	$0.575717\pi$
$618$	7.81512	+	23.6059i	0.314370	+	0.949567i
$619$	−19.5150	−	17.1142i	−0.784373	−	0.687877i	0.170346	−	0.985384i	$-0.445511\pi$
$619$	−19.5150	−	17.1142i	−0.784373	−	0.687877i	−0.954719	+	0.297508i	$0.903845\pi$
$620$	4.47386	+	6.21226i	0.179675	+	0.249490i
$621$	9.05084	−	6.80513i	0.363198	−	0.273080i
$622$	10.2324	+	4.02961i	0.410283	+	0.161573i
$623$	1.48324	+	5.53554i	0.0594249	+	0.221777i
$624$	21.5710	−	30.9021i	0.863531	−	1.23707i
$625$	0.826849	−	3.08584i	0.0330740	−	0.123434i
$626$	−16.1166	+	21.7844i	−0.644150	+	0.870680i
$627$	−18.7529	+	3.24354i	−0.748918	+	0.129534i
$628$	−7.63417	+	25.3819i	−0.304637	+	1.01285i
$629$	26.6230	+	5.29565i	1.06153	+	0.211151i
$630$	3.18686	+	10.5018i	0.126967	+	0.418400i
$631$	5.32817	+	12.8633i	0.212111	+	0.512081i	0.993747	−	0.111653i	$-0.0356146\pi$
$631$	5.32817	+	12.8633i	0.212111	+	0.512081i	−0.781636	+	0.623735i	$0.785615\pi$
$632$	−18.9676	−	9.65811i	−0.754491	−	0.384179i
$633$	19.3590	+	3.04438i	0.769450	+	0.121003i
$634$	−16.8398	−	0.807372i	−0.668793	−	0.0320649i
$635$	−10.1445	+	20.5710i	−0.402573	+	0.816337i
$636$	−3.04329	+	0.848162i	−0.120674	+	0.0336318i
$637$	6.92927	−	20.4130i	0.274548	−	0.808791i
$638$	−13.2892	+	13.7638i	−0.526124	+	0.544914i
$639$	7.37167	+	4.76424i	0.291619	+	0.188470i
$640$	−1.23412	+	16.7480i	−0.0487827	+	0.662024i
$641$	35.0737	+	20.2498i	1.38533	+	0.799820i	0.992784	−	0.119912i	$-0.0382613\pi$
$641$	35.0737	+	20.2498i	1.38533	+	0.799820i	0.392545	+	0.919733i	$0.371595\pi$
$642$	21.7985	+	0.164363i	0.860320	+	0.00648688i
$643$	19.1216	−	16.7692i	0.754082	−	0.661312i	−0.193401	−	0.981120i	$-0.561952\pi$
$643$	19.1216	−	16.7692i	0.754082	−	0.661312i	0.947482	+	0.319808i	$0.103618\pi$
$644$	−6.44067	+	4.02617i	−0.253798	+	0.158653i
$645$	−2.65042	−	8.50278i	−0.104360	−	0.334797i
$646$	−18.2571	+	9.40507i	−0.718315	+	0.370037i
$647$	−16.9878	−	7.03658i	−0.667859	−	0.276636i	0.0228822	−	0.999738i	$-0.492716\pi$
$647$	−16.9878	−	7.03658i	−0.667859	−	0.276636i	−0.690741	+	0.723102i	$0.742716\pi$
$648$	−22.6272	+	11.6622i	−0.888882	+	0.458136i
$649$	46.7038	−	19.3453i	1.83328	−	0.759371i
$650$	16.4216	+	13.8994i	0.644108	+	0.545180i
$651$	3.61670	−	6.89258i	0.141750	−	0.270141i
$652$	−14.5264	+	13.6700i	−0.568899	+	0.535357i
$653$	0.922037	−	14.0676i	0.0360821	−	0.550506i	−0.941103	−	0.338119i	$-0.890209\pi$
$653$	0.922037	−	14.0676i	0.0360821	−	0.550506i	0.977186	−	0.212388i	$-0.0681239\pi$
$654$	6.31738	+	2.67273i	0.247029	+	0.104512i
$655$	−5.18847	−	19.3636i	−0.202730	−	0.756599i
$656$	−20.8403	+	10.3998i	−0.813676	+	0.406045i
$657$	−10.9592	+	2.35461i	−0.427559	+	0.0918621i
$658$	−4.80245	+	12.1949i	−0.187219	+	0.475407i
$659$	16.5466	−	8.15988i	0.644564	−	0.317864i	−0.0904650	−	0.995900i	$-0.528835\pi$
$659$	16.5466	−	8.15988i	0.644564	−	0.317864i	0.735029	+	0.678036i	$0.237169\pi$
$660$	−21.8972	−	18.8192i	−0.852347	−	0.732537i
$661$	6.86084	+	20.2114i	0.266856	+	0.786131i	0.994924	+	0.100627i	$0.0320849\pi$
$661$	6.86084	+	20.2114i	0.266856	+	0.786131i	−0.728069	+	0.685504i	$0.759582\pi$
$662$	−9.61390	+	20.3891i	−0.373655	+	0.792444i
$663$	41.1605	+	56.5219i	1.59854	+	2.19513i
$664$	2.05082	−	7.27909i	0.0795873	−	0.282484i
$665$	−4.67640	−	1.93703i	−0.181343	−	0.0751148i
$666$	−11.9946	+	9.84575i	−0.464780	+	0.381515i
$667$	2.91698	+	4.36556i	0.112946	+	0.169035i
$668$	−34.2194	+	28.2186i	−1.32399	+	1.09181i
$669$	4.89215	−	6.93838i	0.189142	−	0.268253i
$670$	−14.8908	+	8.94909i	−0.575281	+	0.345733i
$671$	61.0605	−	35.2533i	2.35721	−	1.36094i
$672$	15.7934	−	6.48972i	0.609246	−	0.250346i
$673$	−2.54263	−	1.46799i	−0.0980111	−	0.0565867i	0.450193	−	0.892931i	$-0.351355\pi$
$673$	−2.54263	−	1.46799i	−0.0980111	−	0.0565867i	−0.548204	+	0.836344i	$0.684688\pi$
$674$	5.24892	−	0.0920869i	0.202181	−	0.00354706i
$675$	−5.42944	−	13.4798i	−0.208979	−	0.518840i
$676$	30.1873	−	13.7636i	1.16105	−	0.529370i
$677$	9.24034	−	0.605644i	0.355135	−	0.0232768i	0.113208	−	0.993571i	$-0.463887\pi$
$677$	9.24034	−	0.605644i	0.355135	−	0.0232768i	0.241927	+	0.970295i	$0.422221\pi$
$678$	14.2612	+	1.04277i	0.547698	+	0.0400475i
$679$	3.61219	+	27.4373i	0.138623	+	1.05295i
$680$	−28.6306	−	12.2916i	−1.09793	−	0.471362i
$681$	34.2093	+	15.1860i	1.31090	+	0.581927i
$682$	1.69759	+	20.4078i	0.0650040	+	0.781457i
$683$	−19.7177	−	3.92209i	−0.754476	−	0.150075i	−0.197155	−	0.980372i	$-0.563170\pi$
$683$	−19.7177	−	3.92209i	−0.754476	−	0.150075i	−0.557320	+	0.830298i	$0.688170\pi$
$684$	2.46387	−	11.4792i	0.0942085	−	0.438919i
$685$	−25.3036	−	16.9073i	−0.966800	−	0.645995i
$686$	21.1436	−	16.8215i	0.807268	−	0.642247i
$687$	−19.7664	−	12.0830i	−0.754134	−	0.460996i
$688$	−12.7768	+	5.36310i	−0.487111	+	0.204466i
$689$	−4.79183	−	1.28397i	−0.182554	−	0.0489153i
$690$	−6.32235	+	4.77600i	−0.240688	+	0.181819i
$691$	25.8482	−	12.7469i	0.983312	−	0.484916i	0.121746	−	0.992561i	$-0.461151\pi$
$691$	25.8482	−	12.7469i	0.983312	−	0.484916i	0.861566	+	0.507646i	$0.169484\pi$
$692$	−36.7474	−	22.7310i	−1.39693	−	0.864101i
$693$	−7.16378	+	28.4693i	−0.272130	+	1.08146i
$694$	22.2495	+	4.02133i	0.844580	+	0.152647i
$695$	−0.0618081	+	0.469479i	−0.00234451	+	0.0178084i
$696$	−4.81540	−	10.7760i	−0.182527	−	0.408462i
$697$	−5.64042	−	42.8432i	−0.213646	−	1.62280i
$698$	19.7310	+	0.945991i	0.746830	+	0.0358063i
$699$	1.44951	−	0.451829i	0.0548254	−	0.0170897i
$700$	2.85160	+	9.32123i	0.107780	+	0.352309i
$701$	8.24172	+	41.4339i	0.311286	+	1.56494i	0.746982	+	0.664844i	$0.231502\pi$
$701$	8.24172	+	41.4339i	0.311286	+	1.56494i	−0.435696	+	0.900094i	$0.643498\pi$
$702$	−39.9057	−	2.30528i	−1.50614	−	0.0870073i
$703$		−	7.15717i		−	0.269938i
$704$	−25.9068	+	36.6988i	−0.976400	+	1.38314i
$705$	−3.86878	+	13.1136i	−0.145707	+	0.493887i
$706$	−0.326525	+	1.31011i	−0.0122889	+	0.0493068i
$707$	−19.4920	−	22.2263i	−0.733070	−	0.835906i
$708$	0.311925	+	31.1845i	0.0117229	+	1.17199i
$709$	2.46396	−	0.161497i	0.0925361	−	0.00606513i	−0.0190648	−	0.999818i	$-0.506069\pi$
$709$	2.46396	−	0.161497i	0.0925361	−	0.00606513i	0.111601	+	0.993753i	$0.464402\pi$
$710$	−5.16566	−	3.32201i	−0.193864	−	0.124673i
$711$	1.82071	+	22.5026i	0.0682821	+	0.843912i
$712$	8.39409	−	4.00652i	0.314582	−	0.150151i
$713$	5.57173	+	0.733532i	0.208663	+	0.0274710i
$714$	1.83354	+	31.6266i	0.0686185	+	1.18359i
$715$	−14.5734	−	42.9319i	−0.545015	−	1.60556i
$716$	0.111344	−	3.66567i	0.00416112	−	0.136993i
$717$	−24.8801	−	9.14775i	−0.929166	−	0.341629i
$718$	2.58133	−	22.6739i	0.0963343	−	0.846184i
$719$	−21.1172	−	21.1172i	−0.787538	−	0.787538i	0.193552	−	0.981090i	$-0.437999\pi$
$719$	−21.1172	−	21.1172i	−0.787538	−	0.787538i	−0.981090	+	0.193552i	$0.937999\pi$
$720$	15.8144	−	8.19608i	0.589369	−	0.305450i
$721$	−12.5093	+	12.5093i	−0.465872	+	0.465872i
$722$	−13.3576	−	16.7897i	−0.497118	−	0.624849i
$723$	−44.3090	+	7.66377i	−1.64787	+	0.285019i
$724$	6.18284	+	16.3106i	0.229783	+	0.606178i
$725$	6.38047	−	2.16588i	0.236965	−	0.0804387i
$726$	−15.8056	−	47.7414i	−0.586600	−	1.77185i
$727$	−0.0519977	+	0.394962i	−0.00192849	+	0.0146483i	−0.992382	−	0.123198i	$-0.960685\pi$
$727$	−0.0519977	+	0.394962i	−0.00192849	+	0.0146483i	0.990454	+	0.137847i	$0.0440182\pi$
$728$	26.5354	+	3.84023i	0.983468	+	0.142328i
$729$	23.1137	+	13.9555i	0.856063	+	0.516871i
$730$	7.66469	−	1.66488i	0.283683	−	0.0616200i
$731$	−1.68145	−	25.6540i	−0.0621908	−	0.948848i
$732$	6.10847	+	43.0654i	0.225776	+	1.59174i
$733$	20.0277	−	17.5639i	0.739742	−	0.648736i	−0.204170	−	0.978936i	$-0.565449\pi$
$733$	20.0277	−	17.5639i	0.739742	−	0.648736i	0.943911	+	0.330200i	$0.107116\pi$
$734$	34.9754	−	21.0196i	1.29096	−	0.775846i
$735$	7.38297	−	7.02160i	0.272325	−	0.258995i
$736$	8.33254	+	9.08526i	0.307142	+	0.334887i
$737$	−46.4721			−1.71182
$738$	20.9799	+	13.0432i	0.772282	+	0.480126i
$739$	−33.4320	+	6.65005i	−1.22982	+	0.244626i	−0.766895	−	0.641773i	$-0.778199\pi$
$739$	−33.4320	+	6.65005i	−1.22982	+	0.244626i	−0.462923	+	0.886399i	$0.653199\pi$
$740$	8.37734	−	6.90825i	0.307957	−	0.253952i
$741$	12.4994	−	13.5516i	0.459177	−	0.497831i
$742$	−1.51141	−	1.66363i	−0.0554855	−	0.0610738i
$743$	34.4077	−	4.52986i	1.26230	−	0.166184i	0.530486	−	0.847693i	$-0.322009\pi$
$743$	34.4077	−	4.52986i	1.26230	−	0.166184i	0.731810	+	0.681509i	$0.238676\pi$
$744$	−12.0702	−	3.72985i	−0.442515	−	0.136743i
$745$	−6.00174	−	0.790144i	−0.219887	−	0.0289486i
$746$	0.174214	−	0.120880i	0.00637843	−	0.00442571i
$747$	−7.71527	+	2.19423i	−0.282287	+	0.0802826i
$748$	−48.7065	−	67.6322i	−1.78089	−	2.47288i
$749$	6.85947	+	13.9096i	0.250640	+	0.508247i
$750$	10.6505	+	26.2712i	0.388902	+	0.959288i
$751$	1.83130	−	6.83452i	0.0668253	−	0.249395i	−0.924430	−	0.381351i	$-0.875459\pi$
$751$	1.83130	−	6.83452i	0.0668253	−	0.249395i	0.991256	+	0.131956i	$0.0421256\pi$
$752$	20.8827	+	4.05148i	0.761513	+	0.147742i
$753$	−16.3991	−	30.1244i	−0.597616	−	1.09780i
$754$	2.09643	−	18.4147i	0.0763476	−	0.670624i
$755$	−20.0582	+	30.0192i	−0.729992	+	1.09251i
$756$	−14.6423	−	10.6582i	−0.532534	−	0.387635i
$757$	−8.77051	+	44.0923i	−0.318770	+	1.60256i	0.406201	+	0.913784i	$0.366853\pi$
$757$	−8.77051	+	44.0923i	−0.318770	+	1.60256i	−0.724971	+	0.688780i	$0.758147\pi$
$758$	−17.8837	+	21.1289i	−0.649566	+	0.767436i
$759$	−21.0766	+	2.23863i	−0.765031	+	0.0812573i
$760$	−1.70590	+	8.03619i	−0.0618797	+	0.291503i
$761$	−30.1453	+	3.96871i	−1.09277	+	0.143866i	−0.655300	−	0.755369i	$-0.727458\pi$
$761$	−30.1453	+	3.96871i	−1.09277	+	0.143866i	−0.437468	+	0.899234i	$0.644125\pi$
$762$	−7.10407	−	37.1774i	−0.257353	−	1.34680i
$763$	0.319180	+	4.86975i	0.0115551	+	0.176297i
$764$	−0.933657	−	26.6008i	−0.0337785	−	0.962385i
$765$	4.81388	+	32.6951i	0.174046	+	1.18209i
$766$	−23.6274	−	22.8127i	−0.853694	−	0.824256i
$767$	−24.4851	+	42.4094i	−0.884104	+	1.53131i
$768$	−15.0341	−	23.2804i	−0.542495	−	0.840059i
$769$	−19.0233	−	32.9493i	−0.685997	−	1.18818i	−0.973122	−	0.230288i	$-0.926033\pi$
$769$	−19.0233	−	32.9493i	−0.685997	−	1.18818i	0.287126	−	0.957893i	$-0.407300\pi$
$770$	4.96772	−	19.9320i	0.179024	−	0.718299i
$771$	12.7727	−

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)

\(f(q)\)	\(=\)	\(q+(-1.35939 + 0.389931i) q^{2} +(1.72496 + 0.156592i) q^{3} +(1.69591 - 1.06014i) q^{4} +(1.33127 + 0.656508i) q^{5} +(-2.40596 + 0.459744i) q^{6} +(-1.06088 - 1.38257i) q^{7} +(-1.89203 + 2.10244i) q^{8} +(2.95096 + 0.540229i) q^{9} +O(q^{10})\)	\(q+(-1.35939 + 0.389931i) q^{2} +(1.72496 + 0.156592i) q^{3} +(1.69591 - 1.06014i) q^{4} +(1.33127 + 0.656508i) q^{5} +(-2.40596 + 0.459744i) q^{6} +(-1.06088 - 1.38257i) q^{7} +(-1.89203 + 2.10244i) q^{8} +(2.95096 + 0.540229i) q^{9} +(-2.06571 - 0.373352i) q^{10} +(-4.22175 - 3.70237i) q^{11} +(3.09138 - 1.56313i) q^{12} +(5.42788 + 0.355762i) q^{13} +(1.98127 + 1.46579i) q^{14} +(2.19358 + 1.34091i) q^{15} +(1.75221 - 3.59580i) q^{16} +(5.24770 + 5.24770i) q^{17} +(-4.22217 + 0.416286i) q^{18} +(1.08713 - 1.62700i) q^{19} +(2.95370 - 0.297952i) q^{20} +(-1.61348 - 2.55100i) q^{21} +(7.18269 + 3.38680i) q^{22} +(1.32665 - 1.72892i) q^{23} +(-3.59289 + 3.33034i) q^{24} +(-1.70254 - 2.21879i) q^{25} +(-7.51736 + 1.63288i) q^{26} +(5.00568 + 1.39397i) q^{27} +(-3.26488 - 1.22003i) q^{28} +(-0.774434 + 2.28141i) q^{29} +(-3.50480 - 0.967489i) q^{30} +(1.28939 + 2.23328i) q^{31} +(-0.979827 + 5.57135i) q^{32} +(-6.70257 - 7.04753i) q^{33} +(-9.17994 - 5.08746i) q^{34} +(-0.504650 - 2.53705i) q^{35} +(5.57727 - 2.21225i) q^{36} +(3.04121 - 2.03207i) q^{37} +(-0.843418 + 2.63564i) q^{38} +(9.30716 + 1.46364i) q^{39} +(-3.89906 + 1.55677i) q^{40} +(-4.61951 - 3.54467i) q^{41} +(3.18807 + 2.83867i) q^{42} +(-2.60452 - 2.28410i) q^{43} +(-11.0847 - 1.80324i) q^{44} +(3.57385 + 2.65652i) q^{45} +(-1.12928 + 2.86759i) q^{46} +(1.37640 + 5.13681i) q^{47} +(3.58555 - 5.92822i) q^{48} +(1.02571 - 3.82799i) q^{49} +(3.17960 + 2.35234i) q^{50} +(8.23032 + 9.87381i) q^{51} +(9.58234 - 5.15097i) q^{52} +(-0.894480 - 0.177923i) q^{53} +(-7.34825 + 0.0569183i) q^{54} +(-3.18963 - 7.70046i) q^{55} +(4.91398 + 0.385421i) q^{56} +(2.13003 - 2.63627i) q^{57} +(0.163170 - 3.40331i) q^{58} +(-3.98177 + 8.07423i) q^{59} +(5.14166 - 0.0514298i) q^{60} +(-4.03610 + 11.8900i) q^{61} +(-2.62361 - 2.53314i) q^{62} +(-2.38372 - 4.65303i) q^{63} +(-0.840471 - 7.95573i) q^{64} +(6.99240 + 4.03706i) q^{65} +(11.8595 + 6.96683i) q^{66} +(6.22230 - 5.45681i) q^{67} +(14.4629 + 3.33632i) q^{68} +(2.55915 - 2.77457i) q^{69} +(1.67529 + 3.25207i) q^{70} +(2.70303 + 1.11963i) q^{71} +(-6.71909 + 5.18207i) q^{72} +(-3.45201 + 1.42987i) q^{73} +(-3.34183 + 3.94824i) q^{74} +(-2.58936 - 4.09392i) q^{75} +(0.118819 - 3.91175i) q^{76} +(-0.640009 + 9.76465i) q^{77} +(-13.2228 + 1.63949i) q^{78} +(1.94771 + 7.26895i) q^{79} +(4.69333 - 3.63663i) q^{80} +(8.41631 + 3.18838i) q^{81} +(7.66191 + 3.01732i) q^{82} +(-2.39800 + 1.18257i) q^{83} +(-5.44073 - 2.61575i) q^{84} +(3.54093 + 10.4313i) q^{85} +(4.43121 + 2.08941i) q^{86} +(-1.69312 + 3.81406i) q^{87} +(15.7717 - 1.87096i) q^{88} +(-3.03816 - 1.25845i) q^{89} +(-5.89413 - 2.21770i) q^{90} +(-5.26648 - 7.88185i) q^{91} +(0.416974 - 4.33852i) q^{92} +(1.87442 + 4.05422i) q^{93} +(-3.87408 - 6.44625i) q^{94} +(2.51540 - 1.45227i) q^{95} +(-2.56259 + 9.45691i) q^{96} +(-13.7525 - 7.94002i) q^{97} +(0.0983112 + 5.60370i) q^{98} +(-10.4581 - 13.2063i) 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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