LMFDB - Embedded newform 224.2.bd.a.37.15

Newspace parameters

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	224.37
Dual form			224.2.bd.a.109.15

$q$-expansion

$f(q)$	$=$	$q+(0.0713999 + 1.41241i) q^{2} +(0.118403 - 0.154306i) q^{3} +(-1.98980 + 0.201692i) q^{4} +(2.39583 - 1.83839i) q^{5} +(0.226398 + 0.156217i) q^{6} +(1.47323 - 2.19764i) q^{7} +(-0.426943 - 2.79602i) q^{8} +(0.766666 + 2.86124i) q^{9} +O(q^{10})$	\(q+(0.0713999 + 1.41241i) q^{2} +(0.118403 - 0.154306i) q^{3} +(-1.98980 + 0.201692i) q^{4} +(2.39583 - 1.83839i) q^{5} +(0.226398 + 0.156217i) q^{6} +(1.47323 - 2.19764i) q^{7} +(-0.426943 - 2.79602i) q^{8} +(0.766666 + 2.86124i) q^{9} +(2.76762 + 3.25263i) q^{10} +(5.43183 - 0.715114i) q^{11} +(-0.204477 + 0.330920i) q^{12} +(-5.50652 + 2.28087i) q^{13} +(3.20915 + 1.92389i) q^{14} -0.587363i q^{15} +(3.91864 - 0.802655i) q^{16} +(-3.70249 + 2.13763i) q^{17} +(-3.98650 + 1.28714i) q^{18} +(0.183696 - 1.39531i) q^{19} +(-4.39645 + 4.14125i) q^{20} +(-0.164674 - 0.487536i) q^{21} +(1.39787 + 7.62091i) q^{22} +(-0.326660 - 1.21911i) q^{23} +(-0.481995 - 0.265178i) q^{24} +(1.06625 - 3.97929i) q^{25} +(-3.61470 - 7.61461i) q^{26} +(1.07136 + 0.443773i) q^{27} +(-2.48819 + 4.67000i) q^{28} +(0.497218 + 1.20039i) q^{29} +(0.829598 - 0.0419377i) q^{30} +(-0.251275 - 0.435222i) q^{31} +(1.41347 + 5.47742i) q^{32} +(0.532801 - 0.922838i) q^{33} +(-3.28357 - 5.07681i) q^{34} +(-0.510497 - 7.97352i) q^{35} +(-2.10260 - 5.53867i) q^{36} +(5.39866 - 4.14254i) q^{37} +(1.98386 + 0.159829i) q^{38} +(-0.300037 + 1.11975i) q^{39} +(-6.16304 - 5.91390i) q^{40} +(-3.02206 + 3.02206i) q^{41} +(0.676843 - 0.267397i) q^{42} +(-3.49881 + 8.44689i) q^{43} +(-10.6640 + 2.51849i) q^{44} +(7.09686 + 5.44561i) q^{45} +(1.69856 - 0.548423i) q^{46} +(-7.99998 - 4.61879i) q^{47} +(0.340126 - 0.699708i) q^{48} +(-2.65920 - 6.47523i) q^{49} +(5.69652 + 1.22186i) q^{50} +(-0.108537 + 0.824421i) q^{51} +(10.4969 - 5.64911i) q^{52} +(-7.09730 + 0.934377i) q^{53} +(-0.550295 + 1.54489i) q^{54} +(11.6991 - 11.6991i) q^{55} +(-6.77361 - 3.18091i) q^{56} +(-0.193554 - 0.193554i) q^{57} +(-1.65994 + 0.787983i) q^{58} +(0.00968333 + 0.0735522i) q^{59} +(0.118466 + 1.16874i) q^{60} +(9.08657 + 1.19627i) q^{61} +(0.596771 - 0.385979i) q^{62} +(7.41743 + 2.53040i) q^{63} +(-7.63544 + 2.38748i) q^{64} +(-8.99956 + 15.5877i) q^{65} +(1.34147 + 0.686643i) q^{66} +(0.469449 - 0.611798i) q^{67} +(6.93609 - 5.00024i) q^{68} +(-0.226794 - 0.0939414i) q^{69} +(11.2254 - 1.29034i) q^{70} +(-7.84105 - 7.84105i) q^{71} +(7.67275 - 3.36520i) q^{72} +(-6.92569 - 1.85573i) q^{73} +(6.23643 + 7.32935i) q^{74} +(-0.487783 - 0.635691i) q^{75} +(-0.0840962 + 2.81344i) q^{76} +(6.43076 - 12.9907i) q^{77} +(-1.60297 - 0.343825i) q^{78} +(-0.877666 - 0.506720i) q^{79} +(7.91281 - 9.12700i) q^{80} +(-7.50061 + 4.33048i) q^{81} +(-4.48416 - 4.05261i) q^{82} +(-6.18602 + 2.56233i) q^{83} +(0.426001 + 0.936888i) q^{84} +(-4.94075 + 11.9280i) q^{85} +(-12.1803 - 4.33865i) q^{86} +(0.244100 + 0.0654064i) q^{87} +(-4.31856 - 14.8822i) q^{88} +(-13.9937 + 3.74960i) q^{89} +(-7.18472 + 10.4125i) q^{90} +(-3.09982 + 15.4616i) q^{91} +(0.895875 + 2.35991i) q^{92} +(-0.0969094 - 0.0127584i) q^{93} +(5.95243 - 11.6290i) q^{94} +(-2.12501 - 3.68062i) q^{95} +(1.01256 + 0.430438i) q^{96} +0.451869 q^{97} +(8.95582 - 4.21821i) q^{98} +(6.21051 + 14.9935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	0.0713999	+	1.41241i	0.0504874	+	0.998725i
$2$	0.0713999	+	1.41241i	0.0504874	+	0.998725i
$3$	0.118403	−	0.154306i	0.0683603	−	0.0890888i	−0.757922	−	0.652346i	$-0.773785\pi$
$3$	0.118403	−	0.154306i	0.0683603	−	0.0890888i	0.826282	+	0.563257i	$0.190452\pi$
$4$	−1.98980	+	0.201692i	−0.994902	+	0.100846i
$5$	2.39583	−	1.83839i	1.07145	−	0.822151i	0.0867170	−	0.996233i	$-0.472362\pi$
$5$	2.39583	−	1.83839i	1.07145	−	0.822151i	0.984731	+	0.174082i	$0.0556958\pi$
$6$	0.226398	+	0.156217i	0.0924265	+	0.0637752i
$7$	1.47323	−	2.19764i	0.556828	−	0.830628i
$7$	1.47323	−	2.19764i	0.556828	−	0.830628i
$8$	−0.426943	−	2.79602i	−0.150947	−	0.988542i
$9$	0.766666	+	2.86124i	0.255555	+	0.953746i
$10$	2.76762	+	3.25263i	0.875197	+	1.02857i
$11$	5.43183	−	0.715114i	1.63776	−	0.215615i	0.745295	−	0.666735i	$-0.232309\pi$
$11$	5.43183	−	0.715114i	1.63776	−	0.215615i	0.892464	+	0.451120i	$0.148975\pi$
$12$	−0.204477	+	0.330920i	−0.0590275	+	0.0955285i
$13$	−5.50652	+	2.28087i	−1.52723	+	0.632601i	−0.979025	−	0.203741i	$-0.934690\pi$
$13$	−5.50652	+	2.28087i	−1.52723	+	0.632601i	−0.548209	+	0.836342i	$0.684690\pi$
$14$	3.20915	+	1.92389i	0.857681	+	0.514181i
$15$		−	0.587363i		−	0.151657i
$16$	3.91864	−	0.802655i	0.979660	−	0.200664i
$17$	−3.70249	+	2.13763i	−0.897986	+	0.518453i	−0.876546	−	0.481318i	$-0.840158\pi$
$17$	−3.70249	+	2.13763i	−0.897986	+	0.518453i	−0.0214399	+	0.999770i	$0.506825\pi$
$18$	−3.98650	+	1.28714i	−0.939627	+	0.303382i
$19$	0.183696	−	1.39531i	0.0421427	−	0.320105i	−0.957369	−	0.288867i	$-0.906722\pi$
$19$	0.183696	−	1.39531i	0.0421427	−	0.320105i	0.999512	−	0.0312385i	$-0.00994513\pi$
$20$	−4.39645	+	4.14125i	−0.983075	+	0.926011i
$21$	−0.164674	−	0.487536i	−0.0359348	−	0.106389i
$22$	1.39787	+	7.62091i	0.298026	+	1.62478i
$23$	−0.326660	−	1.21911i	−0.0681133	−	0.254202i	0.923470	−	0.383670i	$-0.125340\pi$
$23$	−0.326660	−	1.21911i	−0.0681133	−	0.254202i	−0.991584	+	0.129467i	$0.958673\pi$
$24$	−0.481995	−	0.265178i	−0.0983868	−	0.0541293i
$25$	1.06625	−	3.97929i	0.213250	−	0.795859i
$26$	−3.61470	−	7.61461i	−0.708900	−	1.49335i
$27$	1.07136	+	0.443773i	0.206184	+	0.0854042i
$28$	−2.48819	+	4.67000i	−0.470224	+	0.882547i
$29$	0.497218	+	1.20039i	0.0923310	+	0.222907i	0.963298	−	0.268435i	$-0.0865065\pi$
$29$	0.497218	+	1.20039i	0.0923310	+	0.222907i	−0.870967	+	0.491342i	$0.836507\pi$
$30$	0.829598	−	0.0419377i	0.151463	−	0.00765674i
$31$	−0.251275	−	0.435222i	−0.0451304	−	0.0781682i	0.842578	−	0.538575i	$-0.181037\pi$
$31$	−0.251275	−	0.435222i	−0.0451304	−	0.0781682i	−0.887708	+	0.460406i	$0.847704\pi$
$32$	1.41347	+	5.47742i	0.249868	+	0.968280i
$33$	0.532801	−	0.922838i	0.0927487	−	0.160646i
$34$	−3.28357	−	5.07681i	−0.563128	−	0.870666i
$35$	−0.510497	−	7.97352i	−0.0862897	−	1.34777i
$36$	−2.10260	−	5.53867i	−0.350434	−	0.923112i
$37$	5.39866	−	4.14254i	0.887535	−	0.681029i	−0.0608517	−	0.998147i	$-0.519382\pi$
$37$	5.39866	−	4.14254i	0.887535	−	0.681029i	0.948386	+	0.317118i	$0.102715\pi$
$38$	1.98386	+	0.159829i	0.321825	+	0.0259276i
$39$	−0.300037	+	1.11975i	−0.0480444	+	0.179304i
$40$	−6.16304	−	5.91390i	−0.974463	−	0.935070i
$41$	−3.02206	+	3.02206i	−0.471966	+	0.471966i	−0.902550	−	0.430584i	$-0.858308\pi$
$41$	−3.02206	+	3.02206i	−0.471966	+	0.471966i	0.430584	+	0.902550i	$0.358308\pi$
$42$	0.676843	−	0.267397i	0.104439	−	0.0412603i
$43$	−3.49881	+	8.44689i	−0.533564	+	1.28814i	0.395584	+	0.918430i	$0.370542\pi$
$43$	−3.49881	+	8.44689i	−0.533564	+	1.28814i	−0.929148	+	0.369708i	$0.879458\pi$
$44$	−10.6640	+	2.51849i	−1.60767	+	0.379677i
$45$	7.09686	+	5.44561i	1.05794	+	0.811784i
$46$	1.69856	−	0.548423i	0.250439	−	0.0808605i
$47$	−7.99998	−	4.61879i	−1.16692	−	0.673720i	−0.213965	−	0.976841i	$-0.568638\pi$
$47$	−7.99998	−	4.61879i	−1.16692	−	0.673720i	−0.952952	+	0.303121i	$0.901971\pi$
$48$	0.340126	−	0.699708i	0.0490929	−	0.100994i
$49$	−2.65920	−	6.47523i	−0.379886	−	0.925033i
$50$	5.69652	+	1.22186i	0.805610	+	0.172797i
$51$	−0.108537	+	0.824421i	−0.0151982	+	0.115442i
$52$	10.4969	−	5.64911i	1.45565	−	0.783391i
$53$	−7.09730	+	0.934377i	−0.974889	+	0.128347i	−0.601106	−	0.799169i	$-0.705273\pi$
$53$	−7.09730	+	0.934377i	−0.974889	+	0.128347i	−0.373783	+	0.927516i	$0.621940\pi$
$54$	−0.550295	+	1.54489i	−0.0748856	+	0.210233i
$55$	11.6991	−	11.6991i	1.57751	−	1.57751i
$56$	−6.77361	−	3.18091i	−0.905162	−	0.425066i
$57$	−0.193554	−	0.193554i	−0.0256369	−	0.0256369i
$58$	−1.65994	+	0.787983i	−0.217961	+	0.103467i
$59$	0.00968333	+	0.0735522i	0.00126066	+	0.00957568i	0.992064	−	0.125737i	$-0.0401295\pi$
$59$	0.00968333	+	0.0735522i	0.00126066	+	0.00957568i	−0.990803	+	0.135313i	$0.956796\pi$
$60$	0.118466	+	1.16874i	0.0152939	+	0.150883i
$61$	9.08657	+	1.19627i	1.16342	+	0.153167i	0.687406	−	0.726273i	$-0.258749\pi$
$61$	9.08657	+	1.19627i	1.16342	+	0.153167i	0.476010	+	0.879440i	$0.342083\pi$
$62$	0.596771	−	0.385979i	0.0757900	−	0.0490194i
$63$	7.41743	+	2.53040i	0.934508	+	0.318800i
$64$	−7.63544	+	2.38748i	−0.954430	+	0.298435i
$65$	−8.99956	+	15.5877i	−1.11626	+	1.93342i
$66$	1.34147	+	0.686643i	0.165123	+	0.0845199i
$67$	0.469449	−	0.611798i	0.0573523	−	0.0747430i	−0.763796	−	0.645457i	$-0.776667\pi$
$67$	0.469449	−	0.611798i	0.0573523	−	0.0747430i	0.821149	+	0.570714i	$0.193334\pi$
$68$	6.93609	−	5.00024i	0.841124	−	0.606368i
$69$	−0.226794	−	0.0939414i	−0.0273028	−	0.0113092i
$70$	11.2254	−	1.29034i	1.34170	−	0.154225i
$71$	−7.84105	−	7.84105i	−0.930561	−	0.930561i	0.0671798	−	0.997741i	$-0.478600\pi$
$71$	−7.84105	−	7.84105i	−0.930561	−	0.930561i	−0.997741	+	0.0671798i	$0.978600\pi$
$72$	7.67275	−	3.36520i	0.904242	−	0.396592i
$73$	−6.92569	−	1.85573i	−0.810591	−	0.217197i	−0.170362	−	0.985382i	$-0.554494\pi$
$73$	−6.92569	−	1.85573i	−0.810591	−	0.217197i	−0.640229	+	0.768184i	$0.721160\pi$
$74$	6.23643	+	7.32935i	0.724970	+	0.852019i
$75$	−0.487783	−	0.635691i	−0.0563243	−	0.0734033i
$76$	−0.0840962	+	2.81344i	−0.00964650	+	0.322723i
$77$	6.43076	−	12.9907i	0.732854	−	1.48043i
$78$	−1.60297	−	0.343825i	−0.181501	−	0.0389305i
$79$	−0.877666	−	0.506720i	−0.0987451	−	0.0570105i	0.449814	−	0.893122i	$-0.351490\pi$
$79$	−0.877666	−	0.506720i	−0.0987451	−	0.0570105i	−0.548559	+	0.836112i	$0.684824\pi$
$80$	7.91281	−	9.12700i	0.884679	−	1.02043i
$81$	−7.50061	+	4.33048i	−0.833402	+	0.481165i
$82$	−4.48416	−	4.05261i	−0.495193	−	0.447536i
$83$	−6.18602	+	2.56233i	−0.679004	+	0.281253i	−0.695411	−	0.718613i	$-0.744777\pi$
$83$	−6.18602	+	2.56233i	−0.679004	+	0.281253i	0.0164063	+	0.999865i	$0.494777\pi$
$84$	0.426001	+	0.936888i	0.0464805	+	0.102223i
$85$	−4.94075	+	11.9280i	−0.535899	+	1.29378i
$86$	−12.1803	−	4.33865i	−1.31343	−	0.467849i
$87$	0.244100	+	0.0654064i	0.0261703	+	0.00701231i
$88$	−4.31856	−	14.8822i	−0.460360	−	1.58645i
$89$	−13.9937	+	3.74960i	−1.48333	+	0.397456i	−0.907478	−	0.420100i	$-0.861995\pi$
$89$	−13.9937	+	3.74960i	−1.48333	+	0.397456i	−0.575849	+	0.817556i	$0.695328\pi$
$90$	−7.18472	+	10.4125i	−0.757336	+	1.09757i
$91$	−3.09982	+	15.4616i	−0.324950	+	1.62081i
$92$	0.895875	+	2.35991i	0.0934014	+	0.246038i
$93$	−0.0969094	−	0.0127584i	−0.0100490	−	0.00132298i
$94$	5.95243	−	11.6290i	0.613946	−	1.19944i
$95$	−2.12501	−	3.68062i	−0.218021	−	0.377624i
$96$	1.01256	+	0.430438i	0.103344	+	0.0439314i
$97$	0.451869			0.0458804			0.0229402	−	0.999737i	$-0.492697\pi$
$97$	0.451869			0.0458804			0.0229402	+	0.999737i	$0.492697\pi$
$98$	8.95582	−	4.21821i	0.904674	−	0.426104i
$99$	6.21051	+	14.9935i	0.624180	+	1.50690i
$100$	−1.31903	+	8.13307i	−0.131903	+	0.813307i
$101$	0.453155	+	3.44206i	0.0450906	+	0.342497i	0.999089	+	0.0426844i	$0.0135910\pi$
$101$	0.453155	+	3.44206i	0.0450906	+	0.342497i	−0.953998	+	0.299813i	$0.903076\pi$
$102$	−1.17217	−	0.0944353i	−0.116062	−	0.00935049i
$103$	8.80466	−	2.35920i	0.867549	−	0.232459i	0.202522	−	0.979278i	$-0.435086\pi$
$103$	8.80466	−	2.35920i	0.867549	−	0.232459i	0.665028	+	0.746819i	$0.268420\pi$
$104$	8.72834	+	14.4225i	0.855884	+	1.41424i
$105$	−1.29081	−	0.865320i	−0.125970	−	0.0844466i
$106$	−1.82647	−	9.95758i	−0.177402	−	0.967166i
$107$	7.67351	+	10.0003i	0.741826	+	0.966766i	1.00000		0.000667722i	$0.000212542\pi$
$107$	7.67351	+	10.0003i	0.741826	+	0.966766i	−0.258174	+	0.966098i	$0.583121\pi$
$108$	−2.22131	−	0.666937i	−0.213746	−	0.0641760i
$109$	11.0120	+	8.44984i	1.05476	+	0.809348i	0.982166	−	0.188014i	$-0.0602049\pi$
$109$	11.0120	+	8.44984i	1.05476	+	0.809348i	0.0725963	+	0.997361i	$0.476872\pi$
$110$	17.3592	+	15.6886i	1.65514	+	1.49585i
$111$		−	1.32354i		−	0.125625i
$112$	4.00911	−	9.79424i	0.378825	−	0.925468i
$113$			0.0684958i			0.00644354i	0.999995	+	0.00322177i	$0.00102552\pi$
$113$			0.0684958i			0.00644354i	−0.999995	+	0.00322177i	$0.998974\pi$
$114$	0.259559	−	0.287198i	0.0243099	−	0.0268986i
$115$	−3.02382	−	2.32026i	−0.281973	−	0.216365i
$116$	−1.23147	−	2.28826i	−0.114340	−	0.212459i
$117$	−10.7478	−	14.0068i	−0.993633	−	1.29493i
$118$	−0.103194	+	0.0189284i	−0.00949982	+	0.00174250i
$119$	−0.756872	+	11.2859i	−0.0693823	+	1.03458i
$120$	−1.64228	+	0.250771i	−0.149919	+	0.0228921i
$121$	18.3682	−	4.92175i	1.66984	−	0.447432i
$122$	−1.04084	+	12.9194i	−0.0942335	+	1.16967i
$123$	0.108501	+	0.824145i	0.00978318	+	0.0743107i
$124$	0.587770	+	0.815326i	0.0527833	+	0.0732184i
$125$	1.01736	+	2.45613i	0.0909957	+	0.219683i
$126$	−3.04436	+	10.6571i	−0.271213	+	0.949412i
$127$	−6.18288			−0.548642			−0.274321	−	0.961638i	$-0.588453\pi$
$127$	−6.18288			−0.548642			−0.274321	+	0.961638i	$0.588453\pi$
$128$	−3.91728	−	10.6139i	−0.346242	−	0.938145i
$129$	0.889137	+	1.54003i	0.0782841	+	0.135592i
$130$	−22.6588	−	11.5981i	−1.98731	−	1.01722i
$131$	8.65291	+	1.13918i	0.756009	+	0.0995304i	0.498671	−	0.866791i	$-0.333822\pi$
$131$	8.65291	+	1.13918i	0.756009	+	0.0995304i	0.257337	+	0.966322i	$0.417155\pi$
$132$	−0.874040	+	1.94373i	−0.0760755	+	0.169180i
$133$	−2.79575	−	2.45930i	−0.242422	−	0.213248i
$134$	0.897628	+	0.619372i	0.0775432	+	0.0535056i
$135$	3.38263	−	0.906374i	0.291131	−	0.0780082i
$136$	7.55762	+	9.43959i	0.648061	+	0.809438i
$137$	11.1426	+	2.98566i	0.951980	+	0.255082i	0.701202	−	0.712962i	$-0.252647\pi$
$137$	11.1426	+	2.98566i	0.951980	+	0.255082i	0.250778	+	0.968045i	$0.419314\pi$
$138$	0.116491	−	0.327034i	0.00991634	−	0.0278390i
$139$	6.81777	−	16.4595i	0.578275	−	1.39608i	−0.316084	−	0.948731i	$-0.602368\pi$
$139$	6.81777	−	16.4595i	0.578275	−	1.39608i	0.894359	−	0.447349i	$-0.147632\pi$
$140$	2.62398	+	15.7628i	0.221767	+	1.33220i
$141$	−1.65993	+	0.687567i	−0.139792	+	0.0579036i
$142$	10.5149	−	11.6346i	0.882393	−	0.976356i
$143$	−28.2794	+	16.3271i	−2.36484	+	1.36534i
$144$	5.30087	+	10.5968i	0.441739	+	0.883066i
$145$	3.39803	+	1.96185i	0.282191	+	0.162923i
$146$	2.12656	−	9.91441i	0.175996	−	0.820523i
$147$	−1.31403	−	0.356358i	−0.108379	−	0.0293919i
$148$	−9.90676	+	9.33171i	−0.814331	+	0.767062i
$149$	7.52295	+	9.80409i	0.616304	+	0.803183i	0.992355	−	0.123416i	$-0.0393850\pi$
$149$	7.52295	+	9.80409i	0.616304	+	0.803183i	−0.376051	+	0.926599i	$0.622718\pi$
$150$	0.863029	−	0.734338i	0.0704660	−	0.0599584i
$151$	−6.48936	−	1.73882i	−0.528097	−	0.141503i	−0.0150875	−	0.999886i	$-0.504803\pi$
$151$	−6.48936	−	1.73882i	−0.528097	−	0.141503i	−0.513009	+	0.858383i	$0.671469\pi$
$152$	−3.97973	+	0.0821008i	−0.322799	+	0.00665925i
$153$	−8.95485	−	8.95485i	−0.723957	−	0.723957i
$154$	18.8074	+	8.15534i	1.51554	+	0.657176i
$155$	−1.40212	−	0.580777i	−0.112621	−	0.0466491i
$156$	0.371170	−	2.28861i	0.0297174	−	0.183235i
$157$	0.632229	−	0.823937i	0.0504574	−	0.0657573i	−0.767443	−	0.641117i	$-0.778471\pi$
$157$	0.632229	−	0.823937i	0.0504574	−	0.0657573i	0.817900	+	0.575360i	$0.195138\pi$
$158$	0.653032	−	1.27580i	0.0519524	−	0.101497i
$159$	−0.696164	+	1.20579i	−0.0552094	+	0.0956255i
$160$	13.4560	+	10.5245i	1.06379	+	0.832032i
$161$	−3.16041	−	1.07815i	−0.249075	−	0.0849701i
$162$	−6.65196	−	10.2847i	−0.522627	−	0.808046i
$163$	2.67408	+	0.352050i	0.209450	+	0.0275747i	0.234521	−	0.972111i	$-0.424648\pi$
$163$	2.67408	+	0.352050i	0.209450	+	0.0275747i	−0.0250708	+	0.999686i	$0.507981\pi$
$164$	5.40378	−	6.62283i	0.421964	−	0.517156i
$165$	−0.420032	−	3.19046i	−0.0326994	−	0.248377i
$166$	−4.06075	−	8.55425i	−0.315175	−	0.663939i
$167$	4.37579	+	4.37579i	0.338609	+	0.338609i	0.855843	−	0.517235i	$-0.173039\pi$
$167$	4.37579	+	4.37579i	0.338609	+	0.338609i	−0.517235	+	0.855843i	$0.673039\pi$
$168$	−1.29285	+	0.668582i	−0.0997458	+	0.0515822i
$169$	15.9270	−	15.9270i	1.22515	−	1.22515i
$170$	−17.2000	−	6.12670i	−1.31918	−	0.469897i
$171$	4.13313	−	0.544137i	0.316069	−	0.0416112i
$172$	5.25829	−	17.5133i	0.400941	−	1.33538i
$173$	0.198608	−	1.50858i	0.0150999	−	0.114695i	−0.982235	−	0.187655i	$-0.939911\pi$
$173$	0.198608	−	1.50858i	0.0150999	−	0.114695i	0.997335	+	0.0729600i	$0.0232446\pi$
$174$	−0.0749520	+	0.349439i	−0.00568209	+	0.0264909i
$175$	−7.17421	−	8.20563i	−0.542319	−	0.620287i
$176$	20.7114	−	7.16216i	1.56118	−	0.539868i
$177$	0.0124961	+	0.00721463i	0.000939265	+	0.000542285i
$178$	−6.29511	−	19.4971i	−0.471839	−	1.46137i
$179$	−17.8811	−	13.7206i	−1.33650	−	1.02553i	−0.996368	−	0.0851496i	$-0.972863\pi$
$179$	−17.8811	−	13.7206i	−1.33650	−	1.02553i	−0.340127	−	0.940379i	$-0.610470\pi$
$180$	−15.2197	−	9.40432i	−1.13441	−	0.700957i
$181$	6.77001	−	16.3442i	0.503211	−	1.21486i	−0.444515	−	0.895772i	$-0.646624\pi$
$181$	6.77001	−	16.3442i	0.503211	−	1.21486i	0.947726	−	0.319087i	$-0.103376\pi$
$182$	−22.0594	−	3.27427i	−1.63515	−	0.242705i
$183$	1.26047	−	1.26047i	0.0931769	−	0.0931769i
$184$	−3.26919	+	1.43384i	−0.241008	+	0.105704i
$185$	5.31870	−	19.8496i	0.391038	−	1.45937i
$186$	0.0111007	−	0.137787i	0.000813944	−	0.0101030i
$187$	−18.5827	+	14.2590i	−1.35890	+	1.04272i
$188$	16.8500	+	7.57696i	1.22891	+	0.552607i
$189$	2.55361	−	1.70069i	0.185748	−	0.123707i
$190$	5.04682	−	3.26418i	0.366135	−	0.236808i
$191$	10.0442	−	17.3971i	0.726772	−	1.25881i	−0.231468	−	0.972843i	$-0.574353\pi$
$191$	10.0442	−	17.3971i	0.726772	−	1.25881i	0.958240	−	0.285964i	$-0.0923139\pi$
$192$	−0.535658	+	1.46088i	−0.0386578	+	0.105430i
$193$	8.76441	+	15.1804i	0.630876	+	1.09271i	0.987373	+	0.158413i	$0.0506376\pi$
$193$	8.76441	+	15.1804i	0.630876	+	1.09271i	−0.356497	+	0.934296i	$0.616029\pi$
$194$	0.0322634	+	0.638225i	0.00231638	+	0.0458219i
$195$	1.33970	+	3.23433i	0.0959380	+	0.231615i
$196$	6.59729	+	12.3481i	0.471235	+	0.882008i
$197$	−8.32147	−	3.44687i	−0.592880	−	0.245579i	0.0660089	−	0.997819i	$-0.478973\pi$
$197$	−8.32147	−	3.44687i	−0.592880	−	0.245579i	−0.658889	+	0.752240i	$0.728973\pi$
$198$	−20.7335	+	9.84232i	−1.47347	+	0.699463i
$199$	−2.15738	+	8.05144i	−0.152932	+	0.570751i	0.846341	+	0.532641i	$0.178800\pi$
$199$	−2.15738	+	8.05144i	−0.152932	+	0.570751i	−0.999274	+	0.0381102i	$0.987866\pi$
$200$	−11.5814	−	1.28232i	−0.818929	−	0.0906735i
$201$	−0.0388199	−	0.144878i	−0.00273815	−	0.0102189i
$202$	−4.82924	+	0.885804i	−0.339784	+	0.0623249i
$203$	3.37053	+	0.675744i	0.236565	+	0.0474279i
$204$	0.0496885	−	1.66233i	0.00347889	−	0.116386i
$205$	−1.68463	+	12.7960i	−0.117660	+	0.893715i
$206$	3.96081	+	12.2673i	0.275963	+	0.854707i
$207$	3.23773	−	1.86930i	0.225038	−	0.129926i
$208$	−19.7473	+	13.3578i	−1.36923	+	0.926194i
$209$		−	7.71043i		−	0.533342i
$210$	1.13002	−	1.88494i	0.0779790	−	0.130073i
$211$	−0.534006	+	0.221193i	−0.0367625	+	0.0152275i	−0.400989	−	0.916083i	$-0.631333\pi$
$211$	−0.534006	+	0.221193i	−0.0367625	+	0.0152275i	0.364226	+	0.931310i	$0.381333\pi$
$212$	13.9338	−	3.29070i	0.956976	−	0.226006i
$213$	−2.13833	+	0.281517i	−0.146516	+	0.0192892i
$214$	−13.5766	+	11.5522i	−0.928080	+	0.789689i
$215$	7.14607	+	26.6695i	0.487358	+	1.81884i
$216$	0.783387	−	3.18502i	0.0533027	−	0.216713i
$217$	−1.32664	−	0.0889691i	−0.0900585	−	0.00603961i
$218$	−11.1484	+	16.1568i	−0.755064	+	1.09428i
$219$	−1.10638	+	0.848953i	−0.0747620	+	0.0573669i
$220$	−20.9193	+	25.6385i	−1.41038	+	1.72855i
$221$	15.5122	−	20.2158i	1.04346	−	1.35986i
$222$	1.86938	−	0.0945006i	0.125465	−	0.00634246i
$223$	−5.07246			−0.339677			−0.169839	−	0.985472i	$-0.554325\pi$
$223$	−5.07246			−0.339677			−0.169839	+	0.985472i	$0.554325\pi$
$224$	14.1197	+	4.96320i	0.943414	+	0.331617i
$225$	12.2032			0.813544
$226$	−0.0967441	+	0.00489059i	−0.00643532	+	0.000325317i
$227$	6.69399	−	8.72378i	0.444296	−	0.579018i	−0.516496	−	0.856290i	$-0.672764\pi$
$227$	6.69399	−	8.72378i	0.444296	−	0.579018i	0.960791	+	0.277272i	$0.0894304\pi$
$228$	0.424174	+	0.346097i	0.0280916	+	0.0229208i
$229$	12.5005	−	9.59199i	0.826058	−	0.633856i	−0.106728	−	0.994288i	$-0.534037\pi$
$229$	12.5005	−	9.59199i	0.826058	−	0.633856i	0.932786	+	0.360432i	$0.117371\pi$
$230$	3.06126	−	4.43654i	0.201853	−	0.292537i
$231$	−1.24312	−	2.53045i	−0.0817916	−	0.166492i
$232$	3.14403	−	1.90273i	0.206416	−	0.124920i
$233$	−3.50730	−	13.0894i	−0.229771	−	0.857516i	−0.980437	−	0.196834i	$-0.936934\pi$
$233$	−3.50730	−	13.0894i	−0.229771	−	0.857516i	0.750666	−	0.660682i	$-0.229733\pi$
$234$	19.0159	−	16.1804i	1.24311	−	1.05774i
$235$	−27.6577	+	3.64121i	−1.80419	+	0.237526i
$236$	−0.0341028	−	0.144401i	−0.00221990	−	0.00939973i
$237$	−0.182109	+	0.0754319i	−0.0118292	+	0.00489983i
$238$	−15.9944	−	0.263198i	−1.03676	−	0.0170606i
$239$			5.02121i			0.324795i	0.986725	+	0.162397i	$0.0519227\pi$
$239$			5.02121i			0.324795i	−0.986725	+	0.162397i	$0.948077\pi$
$240$	−0.471450	−	2.30167i	−0.0304320	−	0.148572i
$241$	−20.7477	+	11.9787i	−1.33648	+	0.771615i	−0.986283	−	0.165062i	$-0.947218\pi$
$241$	−20.7477	+	11.9787i	−1.33648	+	0.771615i	−0.350194	+	0.936677i	$0.613884\pi$
$242$	8.26302	+	25.5920i	0.531167	+	1.64512i
$243$	−0.673966	+	5.11928i	−0.0432349	+	0.328402i
$244$	−18.3218	−	0.547655i	−1.17293	−	0.0350600i
$245$	−18.2750	−	10.6249i	−1.16755	−	0.678802i
$246$	−1.15628	+	0.212091i	−0.0737220	+	0.0135225i
$247$	2.17100	+	8.10227i	0.138137	+	0.515535i
$248$	−1.10961	+	0.888386i	−0.0704602	+	0.0564126i
$249$	−0.337062	+	1.25793i	−0.0213604	+	0.0797182i
$250$	−3.39642	+	1.61230i	−0.214809	+	0.101971i
$251$	15.8433	+	6.56249i	1.00002	+	0.414221i	0.821803	−	0.569771i	$-0.192968\pi$
$251$	15.8433	+	6.56249i	1.00002	+	0.414221i	0.178214	+	0.983992i	$0.442968\pi$
$252$	−15.2696	−	3.53897i	−0.961894	−	0.222934i
$253$	−2.64617	−	6.38841i	−0.166363	−	0.401636i
$254$	−0.441457	−	8.73276i	−0.0276995	−	0.547942i
$255$	1.25557	+	2.17471i	0.0786267	+	0.136185i
$256$	14.7115	−	6.29063i	0.919468	−	0.393164i
$257$	1.21717	−	2.10820i	0.0759249	−	0.131506i	−0.825563	−	0.564310i	$-0.809142\pi$
$257$	1.21717	−	2.10820i	0.0759249	−	0.131506i	0.901488	+	0.432804i	$0.142476\pi$
$258$	−2.11167	+	1.36578i	−0.131467	+	0.0850300i
$259$	−1.15033	−	17.9672i	−0.0714782	−	1.11643i
$260$	14.7634	−	32.8316i	0.915590	−	2.03613i
$261$	−3.05340	+	2.34296i	−0.189001	+	0.145025i
$262$	−0.991169	+	12.3028i	−0.0612346	+	0.760069i
$263$	7.18443	−	26.8126i	0.443011	−	1.65334i	−0.278125	−	0.960545i	$-0.589713\pi$
$263$	7.18443	−	26.8126i	0.443011	−	1.65334i	0.721136	−	0.692794i	$-0.243620\pi$
$264$	−2.80775	−	1.09572i	−0.172805	−	0.0674370i
$265$	−15.2862	+	15.2862i	−0.939023	+	0.939023i
$266$	3.27392	−	4.12434i	0.200737	−	0.252879i
$267$	−1.07831	+	2.60328i	−0.0659917	+	0.159318i
$268$	−0.810717	+	1.31204i	−0.0495224	+	0.0801457i
$269$	−7.77004	−	5.96216i	−0.473747	−	0.363519i	0.344120	−	0.938926i	$-0.388177\pi$
$269$	−7.77004	−	5.96216i	−0.473747	−	0.363519i	−0.817868	+	0.575406i	$0.804844\pi$
$270$	1.52169	+	4.71295i	0.0926072	+	0.286821i
$271$	23.9839	+	13.8471i	1.45692	+	0.841152i	0.998858	−	0.0477701i	$-0.0152115\pi$
$271$	23.9839	+	13.8471i	1.45692	+	0.841152i	0.458059	+	0.888922i	$0.348545\pi$
$272$	−12.7930	+	11.3484i	−0.775687	+	0.688101i
$273$	2.01879	+	2.30903i	0.122183	+	0.139749i
$274$	−3.42139	+	15.9512i	−0.206694	+	0.963644i
$275$	2.94603	−	22.3773i	0.177652	−	1.34940i
$276$	0.470224	+	0.141182i	0.0283041	+	0.00849817i
$277$	1.11886	−	0.147300i	0.0672256	−	0.00885042i	−0.0968384	−	0.995300i	$-0.530873\pi$
$277$	1.11886	−	0.147300i	0.0672256	−	0.00885042i	0.164064	+	0.986450i	$0.447540\pi$
$278$	23.7344	+	8.45427i	1.42350	+	0.507054i
$279$	1.05263	−	1.05263i	0.0630192	−	0.0630192i
$280$	−22.0762	+	4.83160i	−1.31930	+	0.288743i
$281$	6.68419	+	6.68419i	0.398746	+	0.398746i	0.877790	−	0.479045i	$-0.159017\pi$
$281$	6.68419	+	6.68419i	0.398746	+	0.398746i	−0.479045	+	0.877790i	$0.659017\pi$
$282$	−1.08965	−	2.29542i	−0.0648875	−	0.136690i
$283$	−2.81117	−	21.3530i	−0.167107	−	1.26930i	−0.845250	−	0.534372i	$-0.820548\pi$
$283$	−2.81117	−	21.3530i	−0.167107	−	1.26930i	0.678143	−	0.734930i	$-0.262785\pi$
$284$	17.1836	+	14.0207i	1.01966	+	0.831974i
$285$	−0.819552	−	0.107896i	−0.0485460	−	0.00639121i
$286$	−25.0797	−	38.7763i	−1.48300	−	2.29289i
$287$	2.18920	+	11.0936i	0.129225	+	0.654832i
$288$	−14.5885	+	8.24362i	−0.859637	+	0.485760i
$289$	0.638965	−	1.10672i	0.0375862	−	0.0651012i
$290$	−2.52832	+	4.93949i	−0.148468	+	0.290057i
$291$	0.0535029	−	0.0697263i	0.00313639	−	0.00408743i
$292$	14.1551	+	2.29569i	0.828362	+	0.134345i
$293$	−11.8675	−	4.91570i	−0.693309	−	0.287178i	0.00806883	−	0.999967i	$-0.497432\pi$
$293$	−11.8675	−	4.91570i	−0.693309	−	0.287178i	−0.701378	+	0.712789i	$0.747432\pi$
$294$	0.409503	−	1.88139i	0.0238827	−	0.109725i
$295$	0.158417	+	0.158417i	0.00922339	+	0.00922339i
$296$	−13.8875	−	13.3261i	−0.807197	−	0.774565i
$297$	6.13682	+	1.64435i	0.356094	+	0.0954151i
$298$	−13.3103	+	11.3255i	−0.771043	+	0.656068i
$299$	4.57940	+	5.96799i	0.264834	+	0.345138i
$300$	1.09881	+	1.16652i	0.0634396	+	0.0673490i
$301$	13.4086	+	20.1333i	0.772860	+	1.16046i
$302$	1.99259	−	9.28979i	0.114660	−	0.534567i
$303$	0.584787	+	0.337627i	0.0335951	+	0.0193961i
$304$	−0.400112	−	5.61515i	−0.0229480	−	0.322051i
$305$	23.9691	−	13.8386i	1.37247	−	0.792394i
$306$	12.0085	−	13.2873i	0.686483	−	0.759584i
$307$	18.8697	−	7.81608i	1.07695	−	0.446087i	0.227512	−	0.973775i	$-0.426941\pi$
$307$	18.8697	−	7.81608i	1.07695	−	0.446087i	0.849438	+	0.527688i	$0.176941\pi$
$308$	−10.1758	+	27.1460i	−0.579822	+	1.54679i
$309$	0.678463	−	1.63795i	0.0385964	−	0.0931799i
$310$	0.720184	−	2.02183i	0.0409037	−	0.114832i
$311$	2.85627	+	0.765335i	0.161964	+	0.0433981i	0.338890	−	0.940826i	$-0.389949\pi$
$311$	2.85627	+	0.765335i	0.161964	+	0.0433981i	−0.176926	+	0.984224i	$0.556615\pi$
$312$	3.25895	+	0.360838i	0.184502	+	0.0204284i
$313$	26.9261	−	7.21483i	1.52195	−	0.407806i	0.601569	−	0.798821i	$-0.294542\pi$
$313$	26.9261	−	7.21483i	1.52195	−	0.407806i	0.920384	+	0.391015i	$0.127876\pi$
$314$	1.20888	+	0.834137i	0.0682209	+	0.0470731i
$315$	22.4228	−	7.57368i	1.26338	−	0.426729i
$316$	1.84858	+	0.831256i	0.103991	+	0.0467618i
$317$	−32.5474	−	4.28495i	−1.82805	−	0.240667i	−0.863457	−	0.504422i	$-0.831705\pi$
$317$	−32.5474	−	4.28495i	−1.82805	−	0.240667i	−0.964590	+	0.263756i	$0.915039\pi$
$318$	−1.75278	−	0.897176i	−0.0982910	−	0.0503111i
$319$	3.55922	+	6.16475i	0.199278	+	0.345160i
$320$	−13.9041	+	19.7569i	−0.777263	+	1.10444i
$321$	2.45168			0.136839
$322$	1.29714	−	4.54077i	0.0722866	−	0.253047i
$323$	2.30252	+	5.55878i	0.128116	+	0.309299i
$324$	14.0513	−	10.1296i	0.780629	−	0.562757i
$325$	3.20495	+	24.3440i	0.177779	+	1.35036i
$326$	−0.306309	+	3.80204i	−0.0169649	+	0.210575i
$327$	2.60773	−	0.698739i	0.144208	−	0.0386403i
$328$	9.73998	+	7.15948i	0.537800	+	0.395316i
$329$	−21.9362	+	10.7765i	−1.20938	+	0.594128i
$330$	4.47624	−	0.821055i	0.246409	−	0.0451976i
$331$	3.65442	+	4.76253i	0.200865	+	0.261772i	0.882915	−	0.469534i	$-0.155578\pi$
$331$	3.65442	+	4.76253i	0.200865	+	0.261772i	−0.682050	+	0.731306i	$0.738911\pi$
$332$	11.7922	−	6.34621i	0.647180	−	0.348294i
$333$	15.9918	+	12.2709i	0.876343	+	0.672441i
$334$	−5.86797	+	6.49284i	−0.321081	+	0.355272i
$335$		−	2.32879i		−	0.127236i
$336$	−1.03662	−	1.77830i	−0.0565523	−	0.0970143i
$337$			8.26077i			0.449993i	0.974360	+	0.224996i	$0.0722370\pi$
$337$			8.26077i			0.449993i	−0.974360	+	0.224996i	$0.927763\pi$
$338$	23.6326	+	21.3582i	1.28544	+	1.16173i
$339$	0.0105693	+	0.00811014i	0.000574048	+	0.000440482i
$340$	7.42533	−	24.7309i	0.402695	−	1.34122i
$341$	−1.67612	−	2.18436i	−0.0907670	−	0.118290i
$342$	1.06365	+	5.79883i	0.0575156	+	0.313565i
$343$	−18.1478	−	3.69554i	−0.979890	−	0.199540i
$344$	25.1114	+	6.17641i	1.35392	+	0.333010i
$345$	−0.716062	+	0.191868i	−0.0385515	+	0.0103298i
$346$	2.14491	+	0.172804i	0.115311	+	0.00929000i
$347$	3.23389	+	24.5639i	0.173605	+	1.31866i	0.827240	+	0.561848i	$0.189910\pi$
$347$	3.23389	+	24.5639i	0.173605	+	1.31866i	−0.653636	+	0.756809i	$0.726757\pi$
$348$	−0.498903	−	0.0809130i	−0.0267440	−	0.00433739i
$349$	7.17014	+	17.3102i	0.383809	+	0.926596i	0.991222	+	0.132210i	$0.0422073\pi$
$349$	7.17014	+	17.3102i	0.383809	+	0.926596i	−0.607413	+	0.794386i	$0.707793\pi$
$350$	11.0775	−	10.7188i	0.592116	−	0.572944i
$351$	−6.91168			−0.368918
$352$	11.5947	+	28.7416i	0.618000	+	1.53193i
$353$	−1.24335	−	2.15355i	−0.0661769	−	0.114622i	0.831039	−	0.556215i	$-0.187747\pi$
$353$	−1.24335	−	2.15355i	−0.0661769	−	0.114622i	−0.897215	+	0.441593i	$0.854413\pi$
$354$	−0.00929780	+	0.0181648i	−0.000494172	+	0.000965446i
$355$	−33.2007	−	4.37095i	−1.76211	−	0.231986i
$356$	27.0884	−	10.2834i	1.43568	−	0.545018i
$357$	1.65188	+	1.45309i	0.0874266	+	0.0769054i
$358$	18.1025	−	26.2351i	0.956745	−	1.38657i
$359$	−16.1733	+	4.33362i	−0.853594	+	0.228720i	−0.658980	−	0.752160i	$-0.729012\pi$
$359$	−16.1733	+	4.33362i	−0.853594	+	0.228720i	−0.194614	+	0.980880i	$0.562345\pi$
$360$	12.1961	−	22.1679i	0.642789	−	1.16835i
$361$	16.4395	+	4.40494i	0.865234	+	0.231839i
$362$	23.5682	+	8.39505i	1.23871	+	0.441234i
$363$	1.41540	−	3.41709i	0.0742894	−	0.179350i
$364$	3.04957	−	31.3907i	0.159841	−	1.64532i
$365$	−20.0043	+	8.28607i	−1.04707	+	0.433712i
$366$	1.87030	+	1.69031i	0.0977623	+	0.0883538i
$367$	−6.07154	+	3.50540i	−0.316932	+	0.182981i	−0.650024	−	0.759914i	$-0.725241\pi$
$367$	−6.07154	+	3.50540i	−0.316932	+	0.182981i	0.333092	+	0.942894i	$0.391908\pi$
$368$	−2.25859	−	4.51507i	−0.117737	−	0.235364i
$369$	−10.9637	−	6.32991i	−0.570749	−	0.329522i
$370$	28.4156	+	6.09492i	1.47726	+	0.316860i
$371$	−8.40252	+	16.9738i	−0.436237	+	0.881237i
$372$	0.195404	+	0.00584081i	0.0101312	+	0.000302832i
$373$	10.9932	+	14.3266i	0.569207	+	0.741805i	0.985917	−	0.167234i	$-0.0534836\pi$
$373$	10.9932	+	14.3266i	0.569207	+	0.741805i	−0.416710	+	0.909039i	$0.636817\pi$
$374$	−21.4663	−	25.2282i	−1.11000	−	1.30452i
$375$	0.499456	+	0.133829i	0.0257918	+	0.00691089i
$376$	−9.49869	+	24.3401i	−0.489857	+	1.25524i
$377$	−5.47588	−	5.47588i	−0.282022	−	0.282022i
$378$	2.58440	+	3.48532i	0.132927	+	0.179266i
$379$	−3.29244	−	1.36377i	−0.169121	−	0.0700523i	0.296516	−	0.955028i	$-0.404175\pi$
$379$	−3.29244	−	1.36377i	−0.169121	−	0.0700523i	−0.465638	+	0.884975i	$0.654175\pi$
$380$	4.97070	+	6.89512i	0.254992	+	0.353712i
$381$	−0.732074	+	0.954058i	−0.0375053	+	0.0488779i
$382$	25.2889	+	12.9444i	1.29389	+	0.662292i
$383$	−10.0023	+	17.3246i	−0.511096	+	0.885244i	0.488821	+	0.872384i	$0.337427\pi$
$383$	−10.0023	+	17.3246i	−0.511096	+	0.885244i	−0.999917	+	0.0128604i	$0.995906\pi$
$384$	−2.10161	−	0.652262i	−0.107247	−	0.0332856i
$385$	−8.47491	−	42.9458i	−0.431922	−	2.18872i
$386$	−20.8152	+	13.4628i	−1.05946	+	0.685239i
$387$	−26.8510	−	3.53500i	−1.36491	−	0.179694i
$388$	−0.899131	+	0.0911384i	−0.0456465	+	0.00462685i
$389$	−0.604023	−	4.58801i	−0.0306252	−	0.232621i	0.969286	−	0.245936i	$-0.0790952\pi$
$389$	−0.604023	−	4.58801i	−0.0306252	−	0.232621i	−0.999911	+	0.0133142i	$0.995762\pi$
$390$	−4.47254	+	2.12314i	−0.226476	+	0.107509i
$391$	3.81547	+	3.81547i	0.192957	+	0.192957i
$392$	−16.9695	+	10.1997i	−0.857091	+	0.515164i
$393$	1.20032	−	1.20032i	0.0605480	−	0.0605480i
$394$	4.27424	−	11.9994i	0.215333	−	0.604523i
$395$	−3.03429	+	0.399471i	−0.152671	+	0.0200996i
$396$	−15.3818	−	28.5815i	−0.772963	−	1.43628i
$397$	3.56041	−	27.0440i	0.178692	−	1.35730i	−0.633425	−	0.773804i	$-0.718352\pi$
$397$	3.56041	−	27.0440i	0.178692	−	1.35730i	0.812117	−	0.583495i	$-0.198315\pi$
$398$	−11.5260	−	2.47223i	−0.577745	−	0.123922i
$399$	−0.710512	+	0.140212i	−0.0355701	+	0.00701940i
$400$	0.984246	−	16.4493i	0.0492123	−	0.822463i
$401$	1.09372	+	0.631459i	0.0546177	+	0.0315336i	0.527060	−	0.849828i	$-0.323294\pi$
$401$	1.09372	+	0.631459i	0.0546177	+	0.0315336i	−0.472442	+	0.881362i	$0.656628\pi$
$402$	0.201855	−	0.0651739i	0.0100676	−	0.00325058i
$403$	2.37634	+	1.82343i	0.118374	+	0.0908315i
$404$	−1.59593	−	6.75762i	−0.0794003	−	0.336204i
$405$	−10.0091	+	24.1641i	−0.497357	+	1.20072i
$406$	−0.713772	+	4.80882i	−0.0354239	+	0.238658i
$407$	26.3622	−	26.3622i	1.30673	−	1.30673i
$408$	2.35144	−	0.0485095i	0.116413	−	0.00240158i
$409$	−2.26792	+	8.46400i	−0.112142	+	0.418518i	−0.999057	−	0.0434134i	$-0.986177\pi$
$409$	−2.26792	+	8.46400i	−0.112142	+	0.418518i	0.886916	+	0.461931i	$0.152843\pi$
$410$	−18.1936	−	1.46575i	−0.898515	−	0.0723884i
$411$	1.78003	−	1.36587i	0.0878026	−	0.0673733i
$412$	−17.0437	+	6.47018i	−0.839684	+	0.318763i
$413$	0.175907	+	0.0870787i	0.00865580	+	0.00428486i
$414$	2.87140	+	4.43953i	0.141121	+	0.218191i
$415$	−10.1101	+	17.5112i	−0.496286	+	0.859592i
$416$	−20.2766	−	26.9376i	−0.994142	−	1.32072i
$417$	−1.73257	−	3.00089i	−0.0848441	−	0.146954i
$418$	10.8903	−	0.550524i	0.532662	−	0.0269270i
$419$	0.789499	+	1.90602i	0.0385696	+	0.0931152i	0.941990	−	0.335640i	$-0.108952\pi$
$419$	0.789499	+	1.90602i	0.0385696	+	0.0931152i	−0.903421	+	0.428755i	$0.858952\pi$
$420$	2.74299	+	1.46147i	0.133844	+	0.0713125i
$421$	8.35055	+	3.45891i	0.406981	+	0.168577i	0.576776	−	0.816902i	$-0.304311\pi$
$421$	8.35055	+	3.45891i	0.406981	+	0.168577i	−0.169795	+	0.985479i	$0.554311\pi$
$422$	−0.350543	−	0.738442i	−0.0170641	−	0.0359468i
$423$	7.08214	−	26.4309i	0.344346	−	1.28512i
$424$	5.64268	+	19.4453i	0.274033	+	0.944345i
$425$	4.55850	+	17.0126i	0.221120	+	0.825230i
$426$	−0.550293	−	3.00010i	−0.0266618	−	0.145355i
$427$	16.0156	−	18.2066i	0.775047	−	0.881079i
$428$	−17.2858	−	18.3510i	−0.835538	−	0.887028i
$429$	−0.829000	+	6.29688i	−0.0400245	+	0.304016i
$430$	−37.1580	+	11.9974i	−1.79192	+	0.578565i
$431$	2.36261	−	1.36406i	0.113803	−	0.0657043i	−0.442018	−	0.897006i	$-0.645737\pi$
$431$	2.36261	−	1.36406i	0.113803	−	0.0657043i	0.555821	+	0.831302i	$0.312404\pi$
$432$	4.55449	+	0.879053i	0.219128	+	0.0422935i
$433$			23.1713i			1.11354i	0.830666	+	0.556771i	$0.187960\pi$
$433$			23.1713i			1.11354i	−0.830666	+	0.556771i	$0.812040\pi$
$434$	0.0309385	−	1.88012i	0.00148509	−	0.0902486i
$435$	0.705065	−	0.292047i	0.0338053	−	0.0140026i
$436$	−23.6161	−	14.5925i	−1.13101	−	0.698853i
$437$	−1.76104	+	0.231845i	−0.0842420	+	0.0110907i
$438$	−1.27806	−	1.50204i	−0.0610683	−	0.0717704i
$439$	−4.54888	−	16.9766i	−0.217106	−	0.810251i	−0.985415	−	0.170171i	$-0.945568\pi$
$439$	−4.54888	−	16.9766i	−0.217106	−	0.810251i	0.768308	−	0.640080i	$-0.221099\pi$
$440$	−37.7057	−	27.7160i	−1.79755	−	1.32131i
$441$	16.4885	−	12.5729i	0.785165	−	0.598712i
$442$	29.6606	+	20.4661i	1.41081	+	0.973474i
$443$	5.38327	−	4.13073i	0.255767	−	0.196257i	−0.472917	−	0.881107i	$-0.656799\pi$
$443$	5.38327	−	4.13073i	0.255767	−	0.196257i	0.728684	+	0.684850i	$0.240132\pi$
$444$	0.266947	+	2.63358i	0.0126687	+	0.124984i
$445$	−26.6333	+	34.7092i	−1.26254	+	1.64537i
$446$	−0.362173	−	7.16440i	−0.0171494	−	0.339244i
$447$	2.40358			0.113685
$448$	−6.00192	+	20.2972i	−0.283564	+	0.958953i
$449$	18.3637			0.866635			0.433318	−	0.901241i	$-0.357343\pi$
$449$	18.3637			0.866635			0.433318	+	0.901241i	$0.357343\pi$
$450$	0.871304	+	17.2359i	0.0410737	+	0.812506i
$451$	−14.2542	+	18.5764i	−0.671204	+	0.874730i
$452$	−0.0138150	−	0.136293i	−0.000649805	−	0.00641069i
$453$	−1.03667	+	0.795468i	−0.0487072	+	0.0373743i
$454$	12.7995	+	8.83178i	0.600710	+	0.414496i
$455$	20.9977	+	42.7420i	0.984386	+	2.00377i
$456$	−0.458545	+	0.623819i	−0.0214733	+	0.0292130i
$457$	−6.02250	−	22.4763i	−0.281720	−	1.05140i	−0.951203	−	0.308567i	$-0.900151\pi$
$457$	−6.02250	−	22.4763i	−0.281720	−	1.05140i	0.669482	−	0.742828i	$-0.266516\pi$
$458$	14.4404	+	16.9710i	0.674753	+	0.793002i
$459$	−4.91534	+	0.647117i	−0.229428	+	0.0302048i
$460$	6.48479	+	4.00698i	0.302355	+	0.186826i
$461$	−25.1245	+	10.4069i	−1.17016	+	0.484698i	−0.881247	−	0.472657i	$-0.843295\pi$
$461$	−25.1245	+	10.4069i	−1.17016	+	0.484698i	−0.288917	+	0.957354i	$0.593295\pi$
$462$	3.48528	−	1.93648i	0.162150	−	0.0900930i
$463$		−	11.5497i		−	0.536761i	−0.963313	−	0.268381i	$-0.913512\pi$
$463$		−	11.5497i		−	0.536761i	0.963313	−	0.268381i	$-0.0864885\pi$
$464$	2.91192	+	4.30480i	0.135182	+	0.199845i
$465$	−0.255633	+	0.147590i	−0.0118547	+	0.00684432i
$466$	18.2372	−	5.88833i	0.844822	−	0.272772i
$467$	1.34169	−	10.1912i	0.0620861	−	0.471590i	−0.931954	−	0.362576i	$-0.881897\pi$
$467$	1.34169	−	10.1912i	0.0620861	−	0.471590i	0.994040	−	0.109014i	$-0.0347694\pi$
$468$	24.2110	+	25.7030i	1.11916	+	1.18812i
$469$	−0.652903	−	1.93299i	−0.0301483	−	0.0892574i
$470$	−7.11764	−	38.8041i	−0.328312	−	1.78990i
$471$	−0.0522806	−	0.195114i	−0.00240896	−	0.00899037i
$472$	0.201519	−	0.0584774i	0.00927566	−	0.00269164i
$473$	−12.9645	+	48.3841i	−0.596108	+	2.22470i
$474$	−0.119543	−	0.251826i	−0.00549081	−	0.0115668i
$475$	−5.35647	−	2.21872i	−0.245772	−	0.101802i
$476$	−0.770258	−	22.6095i	−0.0353047	−	1.03630i
$477$	−8.11473	−	19.5907i	−0.371548	−	0.896997i
$478$	−7.09200	+	0.358514i	−0.324381	+	0.0163980i
$479$	−8.77291	−	15.1951i	−0.400844	−	0.694283i	0.592984	−	0.805215i	$-0.297950\pi$
$479$	−8.77291	−	15.1951i	−0.400844	−	0.694283i	−0.993828	+	0.110932i	$0.964617\pi$
$480$	3.21723	−	0.830219i	0.146846	−	0.0378941i
$481$	−20.2792	+	35.1246i	−0.924653	+	1.60155i
$482$	−18.4002	−	28.4490i	−0.838106	−	1.29582i
$483$	−0.540569	+	0.360015i	−0.0245967	+	0.0163812i
$484$	−35.5565	+	13.4980i	−1.61620	+	0.613547i
$485$	1.08260	−	0.830710i	0.0491584	−	0.0377206i
$486$	−7.27865	−	0.586400i	−0.330166	−	0.0265997i
$487$	−3.33054	+	12.4297i	−0.150921	+	0.563245i	0.848499	+	0.529197i	$0.177507\pi$
$487$	−3.33054	+	12.4297i	−0.150921	+	0.563245i	−0.999420	+	0.0340483i	$0.989160\pi$
$488$	−0.534660	−	25.9170i	−0.0242029	−	1.17321i
$489$	0.370944	−	0.370944i	0.0167747	−	0.0167747i
$490$	13.7019	−	26.5704i	0.618990	−	1.20033i
$491$	15.2024	−	36.7019i	0.686076	−	1.65633i	−0.0664663	−	0.997789i	$-0.521172\pi$
$491$	15.2024	−	36.7019i	0.686076	−	1.65633i	0.752542	−	0.658544i	$-0.228828\pi$
$492$	−0.382119	−	1.61800i	−0.0172272	−	0.0729452i
$493$	−4.40694	−	3.38156i	−0.198479	−	0.152298i
$494$	−11.2887	+	3.64484i	−0.507903	+	0.163989i
$495$	42.4432	+	24.5046i	1.90768	+	1.10140i
$496$	−1.33399	−	1.50379i	−0.0598980	−	0.0675222i
$497$	−28.7834	+	5.68011i	−1.29111	+	0.254788i
$498$	−1.80078	−	0.386253i	−0.0806950	−	0.0173084i
$499$	3.23014	−	24.5353i	0.144601	−	1.09835i	−0.753150	−	0.657849i	$-0.771467\pi$
$499$	3.23014	−	24.5353i	0.144601	−	1.09835i	0.897751	−	0.440504i	$-0.145200\pi$
$500$	−2.51973	−	4.68203i	−0.112686	−	0.209387i
$501$	1.19332	−	0.157104i	0.0533136	−	0.00701887i
$502$	−8.13772	+	22.8457i	−0.363204	+	1.01965i
$503$	−13.6066	+	13.6066i	−0.606689	+	0.606689i	−0.942079	−	0.335390i	$-0.891132\pi$
$503$	−13.6066	+	13.6066i	−0.606689	+	0.606689i	0.335390	+	0.942079i	$0.391132\pi$
$504$	3.90822	−	21.8196i	0.174086	−	0.971922i
$505$	7.41351	+	7.41351i	0.329897	+	0.329897i
$506$	8.83412	−	4.19361i	0.392725	−	0.186428i
$507$	−0.571825	−	4.34344i	−0.0253956	−	0.192899i
$508$	12.3027	−	1.24704i	0.545845	−	0.0553283i
$509$	−24.1716	−	3.18225i	−1.07139	−	0.141051i	−0.425861	−	0.904789i	$-0.640029\pi$
$509$	−24.1716	−	3.18225i	−1.07139	−	0.141051i	−0.645527	+	0.763738i	$0.723362\pi$
$510$	−2.98193	+	1.92865i	−0.132042	+	0.0854021i
$511$	−14.2813	+	12.4862i	−0.631769	+	0.552358i
$512$	9.93535	+	20.3295i	0.439085	+	0.898446i
$513$	0.816005	−	1.41336i	0.0360275	−	0.0624014i
$514$	3.06455	+	1.56862i	0.135171	+	0.0691887i
$515$	16.7574	−	21.8386i	0.738418	−	0.962324i
$516$	−2.07982	−	2.88503i	−0.0915589	−	0.127006i
$517$	−46.7575	−	19.3676i	−2.05639	−	0.851786i
$518$	25.2949	−	2.90760i	1.11139	−	0.127752i
$519$	−0.209268	−	0.209268i	−0.00918583	−	0.00918583i
$520$	47.4258	+	18.5079i	2.07976	+	0.811624i
$521$	19.7383	+	5.28886i	0.864750	+	0.231709i	0.663816	−	0.747896i	$-0.268936\pi$
$521$	19.7383	+	5.28886i	0.864750	+	0.231709i	0.200934	+	0.979605i	$0.435602\pi$
$522$	−3.52723	−	4.14537i	−0.154383	−	0.181438i
$523$	−21.5776	−	28.1205i	−0.943525	−	1.22963i	−0.973175	−	0.230065i	$-0.926106\pi$
$523$	−21.5776	−	28.1205i	−0.943525	−	1.22963i	0.0296506	−	0.999560i	$-0.490561\pi$
$524$	−17.4474	−	0.521518i	−0.762192	−	0.0227826i
$525$	−2.11563	+	0.135451i	−0.0923338	+	0.00591158i
$526$	38.3834	+	8.23294i	1.67360	+	0.358973i
$527$	1.86069	+	1.07427i	0.0810530	+	0.0467960i
$528$	1.34713	−	4.04393i	0.0586265	−	0.175989i
$529$	18.5391	−	10.7035i	0.806046	−	0.465371i
$530$	−22.6818	−	20.4989i	−0.985234	−	0.890417i
$531$	−0.203026	+	0.0840963i	−0.00881059	+	0.00364947i
$532$	6.05901	+	4.32964i	0.262692	+	0.187714i
$533$	9.74808	−	23.5340i	0.422236	−	1.01937i
$534$	−3.75389	−	1.33715i	−0.162447	−	0.0578640i
$535$	36.7688	+	9.85218i	1.58966	+	0.425947i
$536$	−1.91103	−	1.05138i	−0.0825438	−	0.0454129i
$537$	−4.23437	+	1.13459i	−0.182726	+	0.0489614i
$538$	7.86623	−	11.4002i	0.339137	−	0.491496i
$539$	−19.0749	−	33.2707i	−0.821613	−	1.43307i
$540$	−6.54797	+	2.48576i	−0.281780	+	0.106970i
$541$	9.81306	+	1.29191i	0.421896	+	0.0555437i	0.338486	−	0.940972i	$-0.390085\pi$
$541$	9.81306	+	1.29191i	0.421896	+	0.0555437i	0.0834107	+	0.996515i	$0.473419\pi$
$542$	−17.8453	+	34.8638i	−0.766523	+	1.49753i
$543$	−1.72043	−	2.97987i	−0.0738307	−	0.127878i
$544$	−16.9421	−	17.2586i	−0.726385	−	0.739957i
$545$	41.9171			1.79553
$546$	−3.11715	+	3.01622i	−0.133402	+	0.129082i
$547$	−2.30920	−	5.57491i	−0.0987344	−	0.238366i	0.866793	−	0.498669i	$-0.166178\pi$
$547$	−2.30920	−	5.57491i	−0.0987344	−	0.238366i	−0.965527	+	0.260303i	$0.916178\pi$
$548$	−22.7739	−	3.69350i	−0.972851	−	0.157779i
$549$	3.54356	+	26.9160i	0.151235	+	1.14875i
$550$	31.8163	+	2.56327i	1.35665	+	0.109298i
$551$	1.76625	−	0.473265i	0.0752447	−	0.0201618i
$552$	−0.165833	+	0.674229i	−0.00705834	+	0.0286971i
$553$	−2.40659	+	1.18227i	−0.102339	+	0.0502754i
$554$	0.287935	+	1.56977i	0.0122332	+	0.0666930i
$555$	−2.43317	−	3.17098i	−0.103283	−	0.134600i
$556$	−10.2463	+	34.1264i	−0.434538	+	1.44728i
$557$	−26.1993	−	20.1034i	−1.11010	−	0.851810i	−0.120085	−	0.992764i	$-0.538317\pi$
$557$	−26.1993	−	20.1034i	−1.11010	−	0.851810i	−0.990016	+	0.140953i	$0.954983\pi$
$558$	1.56190	+	1.41159i	0.0661205	+	0.0597572i
$559$		−	54.4933i		−	2.30482i
$560$	−8.40044	−	30.8356i	−0.354983	−	1.30304i
$561$			4.55574i			0.192343i
$562$	−8.96357	+	9.91807i	−0.378105	+	0.418369i
$563$	33.6425	+	25.8148i	1.41786	+	1.08797i	0.982196	+	0.187858i	$0.0601543\pi$
$563$	33.6425	+	25.8148i	1.41786	+	1.08797i	0.435668	+	0.900108i	$0.356512\pi$
$564$	3.16427	−	1.70292i	0.133240	−	0.0717059i
$565$	0.125922	+	0.164104i	0.00529757	+	0.00690392i
$566$	29.9584	−	5.49512i	1.25925	−	0.230977i
$567$	−1.53329	+	22.8634i	−0.0643922	+	0.960172i
$568$	−18.5760	+	25.2714i	−0.779433	+	1.06036i
$569$	−0.667826	+	0.178943i	−0.0279967	+	0.00750170i	−0.272790	−	0.962074i	$-0.587946\pi$
$569$	−0.667826	+	0.178943i	−0.0279967	+	0.00750170i	0.244794	+	0.969575i	$0.421280\pi$
$570$	0.0938775	−	1.16525i	0.00393210	−	0.0488068i
$571$	−0.400155	−	3.03948i	−0.0167460	−	0.127198i	0.981030	−	0.193856i	$-0.0620996\pi$
$571$	−0.400155	−	3.03948i	−0.0167460	−	0.127198i	−0.997776	+	0.0666583i	$0.978766\pi$
$572$	52.9774	−	38.1915i	2.21510	−	1.59687i
$573$	−1.49521	−	3.60975i	−0.0624633	−	0.150800i
$574$	−15.5123	+	3.88413i	−0.647473	+	0.162120i
$575$	−5.19951			−0.216834
$576$	−12.6850	−	20.0164i	−0.528541	−	0.834016i
$577$	−23.0936	−	39.9993i	−0.961399	−	1.66519i	−0.718993	−	0.695017i	$-0.755397\pi$
$577$	−23.0936	−	39.9993i	−0.961399	−	1.66519i	−0.242406	−	0.970175i	$-0.577936\pi$
$578$	1.60876	+	0.823461i	0.0669158	+	0.0342515i
$579$	3.38017	+	0.445008i	0.140475	+	0.0184939i
$580$	−7.15710	−	3.21835i	−0.297183	−	0.133635i
$581$	−3.48234	+	17.3695i	−0.144472	+	0.720609i
$582$	0.102302	+	0.0705895i	0.00424056	+	0.00292603i
$583$	−37.8832	+	10.1508i	−1.56896	+	0.420402i
$584$	−2.23179	+	20.1566i	−0.0923519	+	0.834088i
$585$	−51.4997	−	13.7993i	−2.12925	−	0.570531i
$586$	6.09564	−	17.1128i	0.251809	−	0.706924i
$587$	−0.997077	+	2.40716i	−0.0411538	+	0.0993540i	−0.943120	−	0.332453i	$-0.892124\pi$
$587$	−0.997077	+	2.40716i	−0.0411538	+	0.0993540i	0.901966	+	0.431807i	$0.142124\pi$
$588$	2.68653	+	0.444054i	0.110791	+	0.0183125i
$589$	−0.653426	+	0.270658i	−0.0269239	+	0.0111523i
$590$	−0.212439	+	0.235061i	−0.00874596	+	0.00967729i
$591$	−1.51716	+	0.875935i	−0.0624078	+	0.0360312i
$592$	17.8304	−	20.5664i	0.732824	−	0.845273i
$593$	19.2249	+	11.0995i	0.789473	+	0.455802i	0.839777	−	0.542932i	$-0.182686\pi$
$593$	19.2249	+	11.0995i	0.789473	+	0.455802i	−0.0503042	+	0.998734i	$0.516019\pi$
$594$	−1.88434	+	8.78511i	−0.0773152	+	0.360457i
$595$	18.9346	+	28.4306i	0.776243	+	1.16554i
$596$	−16.9466	−	17.9909i	−0.694160	−	0.736936i
$597$	0.986948	+	1.28622i	0.0403931	+	0.0526413i
$598$	−8.10228	+	6.89411i	−0.331327	+	0.281921i
$599$	−19.3702	−	5.19023i	−0.791446	−	0.212067i	−0.159621	−	0.987178i	$-0.551027\pi$
$599$	−19.3702	−	5.19023i	−0.791446	−	0.212067i	−0.631825	+	0.775111i	$0.717694\pi$
$600$	−1.56915	+	1.63525i	−0.0640602	+	0.0667590i
$601$	17.5555	+	17.5555i	0.716102	+	0.716102i	0.967805	−	0.251703i	$-0.0809905\pi$
$601$	17.5555	+	17.5555i	0.716102	+	0.716102i	−0.251703	+	0.967805i	$0.580991\pi$
$602$	−27.4791	+	20.3760i	−1.11996	+	0.830463i
$603$	2.11041	+	0.874160i	0.0859425	+	0.0355985i
$604$	13.2633	+	2.15106i	0.539675	+	0.0875253i
$605$	34.9591	−	45.5596i	1.42129	−	1.85226i
$606$	−0.435114	+	0.850065i	−0.0176753	+	0.0345315i
$607$	15.1703	−	26.2757i	0.615742	−	1.06650i	−0.374512	−	0.927222i	$-0.622190\pi$
$607$	15.1703	−	26.2757i	0.615742	−	1.06650i	0.990254	−	0.139274i	$-0.0444768\pi$
$608$	7.90232	−	0.966044i	0.320482	−	0.0391782i
$609$	0.503355	−	0.440084i	0.0203970	−	0.0178331i
$610$	21.2571	+	32.8661i	0.860676	+	1.33071i
$611$	54.5869	+	7.18651i	2.20835	+	0.290735i
$612$	19.6245	+	16.0123i	0.793274	+	0.647258i
$613$	−0.908361	−	6.89968i	−0.0366883	−	0.278676i	−0.999949	−	0.0101071i	$-0.996783\pi$
$613$	−0.908361	−	6.89968i	−0.0366883	−	0.278676i	0.963261	−	0.268569i	$-0.0865506\pi$
$614$	12.3868	+	26.0937i	0.499891	+	1.05305i
$615$	1.77505	+	1.77505i	0.0715768	+	0.0715768i
$616$	−39.0678	−	12.4342i	−1.57409	−	0.500990i
$617$	3.00134	−	3.00134i	0.120829	−	0.120829i	−0.644106	−	0.764936i	$-0.722771\pi$
$617$	3.00134	−	3.00134i	0.120829	−	0.120829i	0.764936	+	0.644106i	$0.222771\pi$
$618$	2.36190	+	0.841318i	0.0950097	+	0.0338428i
$619$	0.367838	−	0.0484268i	0.0147847	−	0.00194644i	−0.123130	−	0.992391i	$-0.539293\pi$
$619$	0.367838	−	0.0484268i	0.0147847	−	0.00194644i	0.137915	+	0.990444i	$0.455960\pi$
$620$	2.90708	+	0.872836i	0.116751	+	0.0350539i
$621$	0.191038	−	1.45108i	0.00766608	−	0.0582297i
$622$	−0.877029	+	4.08887i	−0.0351657	+	0.163949i
$623$	−12.3756	+	36.2770i	−0.495819	+	1.45341i
$624$	−0.276962	+	4.62874i	−0.0110874	+	0.185298i
$625$	24.7914	+	14.3133i	0.991657	+	0.572534i
$626$	12.1128	+	37.5156i	0.484126	+	1.49942i
$627$	−1.18977	−	0.912942i	−0.0475148	−	0.0364594i
$628$	−1.09183	+	1.76699i	−0.0435688	+	0.0705105i
$629$	−11.1333	+	26.8781i	−0.443912	+	1.07170i
$630$	12.2981	+	31.1294i	0.489969	+	1.24022i
$631$	−34.5848	+	34.5848i	−1.37680	+	1.37680i	−0.526830	+	0.849971i	$0.676619\pi$
$631$	−34.5848	+	34.5848i	−1.37680	+	1.37680i	−0.849971	+	0.526830i	$0.823381\pi$
$632$	−1.04209	+	2.67031i	−0.0414520	+	0.106219i
$633$	−0.0290967	+	0.108591i	−0.00115649	+	0.00431609i
$634$	3.72822	−	46.2763i	0.148067	−	1.83787i
$635$	−14.8131	+	11.3665i	−0.587841	+	0.451067i
$636$	1.14203	−	2.53970i	0.0452845	−	0.100706i
$637$	29.4121	+	29.5907i	1.16535	+	1.17243i
$638$	−8.45302	+	5.46724i	−0.334658	+	0.216450i
$639$	16.4236	−	28.4466i	0.649709	−	1.12533i
$640$	−28.8976	−	18.2277i	−1.14228	−	0.720511i
$641$	3.23073	+	5.59579i	0.127606	+	0.221021i	0.922749	−	0.385402i	$-0.125937\pi$
$641$	3.23073	+	5.59579i	0.127606	+	0.221021i	−0.795142	+	0.606423i	$0.792604\pi$
$642$	0.175050	+	3.46278i	0.00690866	+	0.136665i
$643$	2.82466	+	6.81934i	0.111394	+	0.268929i	0.969739	−	0.244144i	$-0.0785070\pi$
$643$	2.82466	+	6.81934i	0.111394	+	0.268929i	−0.858345	+	0.513073i	$0.828507\pi$
$644$	6.50605	+	1.50788i	0.256374	+	0.0594187i
$645$	4.96139	+	2.05508i	0.195355	+	0.0809185i
$646$	−7.68688	+	3.64900i	−0.302436	+	0.143568i
$647$	−0.271500	+	1.01325i	−0.0106738	+	0.0398351i	−0.971057	−	0.238846i	$-0.923231\pi$
$647$	−0.271500	+	1.01325i	−0.0106738	+	0.0398351i	0.960384	+	0.278682i	$0.0898974\pi$
$648$	15.3104	+	19.1230i	0.601451	+	0.751222i
$649$	0.105196	+	0.392598i	0.00412932	+	0.0154108i
$650$	−34.1549	+	6.26487i	−1.33967	+	0.245728i
$651$	−0.170808	+	0.194176i	−0.00669449	+	0.00761034i
$652$	−5.39191	−	0.161169i	−0.211163	−	0.00631187i
$653$	1.71660	−	13.0389i	0.0671757	−	0.510250i	−0.924470	−	0.381256i	$-0.875492\pi$
$653$	1.71660	−	13.0389i	0.0671757	−	0.510250i	0.991645	−	0.128994i	$-0.0411749\pi$
$654$	1.17310	+	3.63329i	0.0458717	+	0.142073i
$655$	22.8252	−	13.1781i	0.891853	−	0.514912i
$656$	−9.41669	+	14.2680i	−0.367660	+	0.557073i
$657$		−	21.2388i		−	0.828603i
$658$	−16.7871	−	30.2135i	−0.654429	−	1.17784i
$659$	−9.08982	+	3.76512i	−0.354089	+	0.146668i	−0.552636	−	0.833423i	$-0.686378\pi$
$659$	−9.08982	+	3.76512i	−0.354089	+	0.146668i	0.198547	+	0.980091i	$0.436378\pi$
$660$	1.47927	+	6.26367i	0.0575805	+	0.243813i
$661$	26.6893	−	3.51371i	1.03809	−	0.136668i	0.407837	−	0.913055i	$-0.366283\pi$
$661$	26.6893	−	3.51371i	1.03809	−	0.136668i	0.630256	+	0.776387i	$0.282950\pi$
$662$	−6.46572	+	5.50158i	−0.251297	+	0.213825i
$663$	−1.28274	−	4.78725i	−0.0498175	−	0.185921i
$664$	9.80542	+	16.2023i	0.380524	+	0.628770i
$665$	−11.2193	−	0.752401i	−0.435065	−	0.0291769i
$666$	−16.1897	+	23.4631i	−0.627340	+	0.909175i
$667$	1.30099	−	0.998284i	0.0503745	−	0.0386537i
$668$	−9.58952	−	7.82440i	−0.371030	−	0.302735i
$669$	−0.600597	+	0.782713i	−0.0232204	+	0.0302614i
$670$	3.28921	−	0.166276i	0.127073	−	0.00642379i
$671$	50.2122			1.93842
$672$	2.43768	−	1.59110i	0.0940354	−	0.0613782i
$673$	−28.1530			−1.08522			−0.542609	−	0.839985i	$-0.682563\pi$
$673$	−28.1530			−1.08522			−0.542609	+	0.839985i	$0.682563\pi$
$674$	−11.6676	+	0.589818i	−0.449419	+	0.0227189i
$675$	2.90824	−	3.79010i	0.111938	−	0.145881i
$676$	−28.4792	+	34.9039i	−1.09535	+	1.34246i
$677$	20.6879	−	15.8744i	0.795102	−	0.610103i	−0.129264	−	0.991610i	$-0.541261\pi$
$677$	20.6879	−	15.8744i	0.795102	−	0.610103i	0.924366	+	0.381507i	$0.124595\pi$
$678$	−0.0107002	+	0.0155073i	−0.000410938	+	0.000595554i
$679$	0.665706	−	0.993044i	0.0255475	−	0.0381095i
$680$	35.4604	+	8.72183i	1.35984	+	0.334467i
$681$	−0.553543	−	2.06585i	−0.0212118	−	0.0791636i
$682$	2.96554	−	2.52333i	0.113556	−	0.0966233i
$683$	3.51722	−	0.463050i	0.134583	−	0.0177181i	−0.0629339	−	0.998018i	$-0.520046\pi$
$683$	3.51722	−	0.463050i	0.134583	−	0.0177181i	0.197516	+	0.980300i	$0.436712\pi$
$684$	−8.11438	+	1.91635i	−0.310261	+	0.0732734i
$685$	32.1847	−	13.3313i	1.22971	−	0.509364i
$686$	3.92386	−	25.8960i	0.149814	−	0.988714i
$687$		−	3.06463i		−	0.116923i
$688$	−6.93067	+	35.9087i	−0.264229	+	1.36900i
$689$	36.9502	−	21.3332i	1.40769	−	0.812731i
$690$	−0.322123	−	0.997673i	−0.0122630	−	0.0379808i
$691$	−0.159432	+	1.21101i	−0.00606507	+	0.0460688i	−0.994210	−	0.107457i	$-0.965729\pi$
$691$	−0.159432	+	1.21101i	−0.00606507	+	0.0460688i	0.988145	+	0.153525i	$0.0490627\pi$
$692$	−0.0909233	+	3.04184i	−0.00345639	+	0.115633i
$693$	42.0997	+	8.44040i	1.59924	+	0.320624i
$694$	−34.4634	+	6.32144i	−1.30821	+	0.239959i
$695$	−13.9248	−	51.9680i	−0.528197	−	1.97126i
$696$	0.0786606	−	0.710433i	0.00298162	−	0.0269289i
$697$	4.72909	−	17.6492i	0.179127	−	0.668511i
$698$	−23.9372	+	11.3631i	−0.906037	+	0.430101i
$699$	−2.43506	−	1.00863i	−0.0921023	−	0.0381500i
$700$	15.9303	+	14.8806i	0.602108	+	0.562434i
$701$	9.67092	+	23.3477i	0.365266	+	0.881830i	0.994512	+	0.104623i	$0.0333637\pi$
$701$	9.67092	+	23.3477i	0.365266	+	0.881830i	−0.629246	+	0.777206i	$0.716636\pi$
$702$	−0.493493	−	9.76212i	−0.0186257	−	0.368447i
$703$	−4.78840	−	8.29375i	−0.180598	−	0.312805i
$704$	−39.7671	+	18.4286i	−1.49878	+	0.694555i
$705$	−2.71291	+	4.69890i	−0.102174	+	0.176971i
$706$	2.95292	−	1.90988i	0.111134	−	0.0718794i
$707$	8.23199	+	4.07506i	0.309596	+	0.153259i
$708$	−0.0263199	−	0.0118353i	−0.000989164	−	0.000444799i
$709$	−1.27025	+	0.974694i	−0.0477051	+	0.0366054i	−0.632339	−	0.774692i	$-0.717905\pi$
$709$	−1.27025	+	0.974694i	−0.0477051	+	0.0366054i	0.584634	+	0.811297i	$0.301238\pi$
$710$	3.80305	−	47.2051i	0.142726	−	1.77157i
$711$	0.776971	−	2.89969i	0.0291387	−	0.108747i
$712$	16.4584	+	37.5257i	0.616806	+	1.40634i
$713$	−0.448503	+	0.448503i	−0.0167966	+	0.0167966i
$714$	−1.93441	+	2.43688i	−0.0723934	+	0.0911979i
$715$	−37.7371	+	91.1054i	−1.41129	+	3.40715i
$716$	38.3472	+	23.6949i	1.43310	+	0.885521i
$717$	0.774804	+	0.594528i	0.0289356	+	0.0222031i
$718$	−7.27563	−	22.5339i	−0.271524	−	0.840958i
$719$	−6.32208	−	3.65005i	−0.235774	−	0.136124i	0.377459	−	0.926026i	$-0.376798\pi$
$719$	−6.32208	−	3.65005i	−0.235774	−	0.136124i	−0.613233	+	0.789902i	$0.710131\pi$
$720$	32.1810	+	15.6431i	1.19931	+	0.582983i
$721$	7.78661	−	22.8251i	0.289988	−	0.850050i
$722$	−5.04780	+	23.5338i	−0.187860	+	0.875836i
$723$	−0.608211	+	4.61982i	−0.0226196	+	0.171813i
$724$	−10.1745	+	33.8873i	−0.378132	+	1.25941i
$725$	5.30686	−	0.698662i	0.197092	−	0.0259476i
$726$	4.92739	+	1.75515i	0.182872	+	0.0651397i
$727$	−15.9338	+	15.9338i	−0.590952	+	0.590952i	−0.937888	−	0.346937i	$-0.887222\pi$
$727$	−15.9338	+	15.9338i	−0.590952	+	0.590952i	0.346937	+	0.937888i	$0.387222\pi$
$728$	44.5543	+	2.06595i	1.65129	+	0.0765692i
$729$	−17.6625	−	17.6625i	−0.654168	−	0.654168i
$730$	−13.1316	−	27.6627i	−0.486023	−	1.02384i
$731$	−5.10202	−	38.7537i	−0.188705	−	1.43336i
$732$	−2.25387	+	2.76232i	−0.0833054	+	0.102098i
$733$	8.04946	+	1.05973i	0.297314	+	0.0391421i	0.277707	−	0.960666i	$-0.410425\pi$
$733$	8.04946	+	1.05973i	0.297314	+	0.0391421i	0.0196063	+	0.999808i	$0.493759\pi$
$734$	−5.38457	−	8.32521i	−0.198748	−	0.307289i
$735$	−3.80331	+	1.56192i	−0.140287	+	0.0576122i
$736$	6.21586	−	3.51243i	0.229120	−	0.129470i
$737$	2.11246	−	3.65889i	0.0778135	−	0.134777i
$738$	8.15763	−	15.9372i	0.300286	−	0.586658i
$739$	−24.1438	+	31.4648i	−0.888143	+	1.15745i	0.0985941	+	0.995128i	$0.468565\pi$
$739$	−24.1438	+	31.4648i	−0.888143	+	1.15745i	−0.986738	+	0.162323i	$0.948101\pi$
$740$	−6.57965	+	40.5696i	−0.241873	+	1.49137i
$741$	1.50728	+	0.624338i	0.0553715	+	0.0229356i
$742$	−24.5739	−	10.6559i	−0.902138	−	0.391189i
$743$	−33.9729	−	33.9729i	−1.24634	−	1.24634i	−0.957323	−	0.289020i	$-0.906671\pi$
$743$	−33.9729	−	33.9729i	−1.24634	−	1.24634i	−0.289020	−	0.957323i	$-0.593329\pi$
$744$	0.00570221	+	0.276408i	0.000209053	+	0.0101336i
$745$	36.0474	+	9.65887i	1.32067	+	0.353874i
$746$	−19.4502	+	16.5498i	−0.712121	+	0.605933i
$747$	−12.0741	−	15.7352i	−0.441767	−	0.575722i
$748$	34.0999	−	32.1205i	1.24682	−	1.17444i
$749$	33.2818	−	2.13084i	1.21609	−	0.0778591i
$750$	−0.153360	+	0.714992i	−0.00559992	+	0.0261078i
$751$	9.05161	+	5.22595i	0.330298	+	0.190698i	0.655973	−	0.754784i	$-0.272258\pi$
$751$	9.05161	+	5.22595i	0.330298	+	0.190698i	−0.325675	+	0.945482i	$0.605592\pi$
$752$	−35.0564	−	11.6782i	−1.27837	−	0.425859i
$753$	2.88853	−	1.66769i	0.105264	−	0.0607741i
$754$	7.34321	−	8.12516i	0.267424	−	0.295901i
$755$	−18.7440	+	7.76403i	−0.682165	+	0.282562i
$756$	−4.73818	+	3.89908i	−0.172326	+	0.141808i
$757$	2.64470	−	6.38487i	0.0961232	−	0.232062i	−0.868503	−	0.495684i	$-0.834917\pi$
$757$	2.64470	−	6.38487i	0.0961232	−	0.232062i	0.964626	+	0.263622i	$0.0849173\pi$
$758$	1.69113	−	4.74765i	0.0614245	−	0.172442i
$759$	−1.29909	−	0.348090i	−0.0471539	−	0.0126349i
$760$	−9.38383	+	7.51298i	−0.340387	+	0.272524i
$761$	−43.3060	+	11.6038i	−1.56984	+	0.420637i	−0.935762	−	0.352632i	$-0.885287\pi$
$761$	−43.3060	+	11.6038i	−1.56984	+	0.420637i	−0.634078	+	0.773269i	$0.718620\pi$
$762$	−1.39979	−	0.965870i	−0.0507091	−	0.0349898i
$763$	34.7929	−	11.7519i	1.25959	−	0.425448i
$764$	−16.4771	+	36.6426i	−0.596122	+	1.32568i
$765$	−37.9168	−	4.99184i	−1.37088	−	0.180480i
$766$	−25.1836	−	12.8904i	−0.909919	−	0.465751i
$767$	−0.221085	−	0.382930i	−0.00798291	−	0.0138268i
$768$	0.771207	−	3.01491i	0.0278285	−	0.108791i
$769$	−24.3333			−0.877480			−0.438740	−	0.898614i	$-0.644575\pi$
$769$	−24.3333			−0.877480			−0.438740	+	0.898614i	$0.644575\pi$
$770$	60.0519	−	15.0364i	2.16412	−	0.541873i

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0713999 + 1.41241i) q^{2} +(0.118403 - 0.154306i) q^{3} +(-1.98980 + 0.201692i) q^{4} +(2.39583 - 1.83839i) q^{5} +(0.226398 + 0.156217i) q^{6} +(1.47323 - 2.19764i) q^{7} +(-0.426943 - 2.79602i) q^{8} +(0.766666 + 2.86124i) q^{9} +O(q^{10})\)	\(q+(0.0713999 + 1.41241i) q^{2} +(0.118403 - 0.154306i) q^{3} +(-1.98980 + 0.201692i) q^{4} +(2.39583 - 1.83839i) q^{5} +(0.226398 + 0.156217i) q^{6} +(1.47323 - 2.19764i) q^{7} +(-0.426943 - 2.79602i) q^{8} +(0.766666 + 2.86124i) q^{9} +(2.76762 + 3.25263i) q^{10} +(5.43183 - 0.715114i) q^{11} +(-0.204477 + 0.330920i) q^{12} +(-5.50652 + 2.28087i) q^{13} +(3.20915 + 1.92389i) q^{14} -0.587363i q^{15} +(3.91864 - 0.802655i) q^{16} +(-3.70249 + 2.13763i) q^{17} +(-3.98650 + 1.28714i) q^{18} +(0.183696 - 1.39531i) q^{19} +(-4.39645 + 4.14125i) q^{20} +(-0.164674 - 0.487536i) q^{21} +(1.39787 + 7.62091i) q^{22} +(-0.326660 - 1.21911i) q^{23} +(-0.481995 - 0.265178i) q^{24} +(1.06625 - 3.97929i) q^{25} +(-3.61470 - 7.61461i) q^{26} +(1.07136 + 0.443773i) q^{27} +(-2.48819 + 4.67000i) q^{28} +(0.497218 + 1.20039i) q^{29} +(0.829598 - 0.0419377i) q^{30} +(-0.251275 - 0.435222i) q^{31} +(1.41347 + 5.47742i) q^{32} +(0.532801 - 0.922838i) q^{33} +(-3.28357 - 5.07681i) q^{34} +(-0.510497 - 7.97352i) q^{35} +(-2.10260 - 5.53867i) q^{36} +(5.39866 - 4.14254i) q^{37} +(1.98386 + 0.159829i) q^{38} +(-0.300037 + 1.11975i) q^{39} +(-6.16304 - 5.91390i) q^{40} +(-3.02206 + 3.02206i) q^{41} +(0.676843 - 0.267397i) q^{42} +(-3.49881 + 8.44689i) q^{43} +(-10.6640 + 2.51849i) q^{44} +(7.09686 + 5.44561i) q^{45} +(1.69856 - 0.548423i) q^{46} +(-7.99998 - 4.61879i) q^{47} +(0.340126 - 0.699708i) q^{48} +(-2.65920 - 6.47523i) q^{49} +(5.69652 + 1.22186i) q^{50} +(-0.108537 + 0.824421i) q^{51} +(10.4969 - 5.64911i) q^{52} +(-7.09730 + 0.934377i) q^{53} +(-0.550295 + 1.54489i) q^{54} +(11.6991 - 11.6991i) q^{55} +(-6.77361 - 3.18091i) q^{56} +(-0.193554 - 0.193554i) q^{57} +(-1.65994 + 0.787983i) q^{58} +(0.00968333 + 0.0735522i) q^{59} +(0.118466 + 1.16874i) q^{60} +(9.08657 + 1.19627i) q^{61} +(0.596771 - 0.385979i) q^{62} +(7.41743 + 2.53040i) q^{63} +(-7.63544 + 2.38748i) q^{64} +(-8.99956 + 15.5877i) q^{65} +(1.34147 + 0.686643i) q^{66} +(0.469449 - 0.611798i) q^{67} +(6.93609 - 5.00024i) q^{68} +(-0.226794 - 0.0939414i) q^{69} +(11.2254 - 1.29034i) q^{70} +(-7.84105 - 7.84105i) q^{71} +(7.67275 - 3.36520i) q^{72} +(-6.92569 - 1.85573i) q^{73} +(6.23643 + 7.32935i) q^{74} +(-0.487783 - 0.635691i) q^{75} +(-0.0840962 + 2.81344i) q^{76} +(6.43076 - 12.9907i) q^{77} +(-1.60297 - 0.343825i) q^{78} +(-0.877666 - 0.506720i) q^{79} +(7.91281 - 9.12700i) q^{80} +(-7.50061 + 4.33048i) q^{81} +(-4.48416 - 4.05261i) q^{82} +(-6.18602 + 2.56233i) q^{83} +(0.426001 + 0.936888i) q^{84} +(-4.94075 + 11.9280i) q^{85} +(-12.1803 - 4.33865i) q^{86} +(0.244100 + 0.0654064i) q^{87} +(-4.31856 - 14.8822i) q^{88} +(-13.9937 + 3.74960i) q^{89} +(-7.18472 + 10.4125i) q^{90} +(-3.09982 + 15.4616i) q^{91} +(0.895875 + 2.35991i) q^{92} +(-0.0969094 - 0.0127584i) q^{93} +(5.95243 - 11.6290i) q^{94} +(-2.12501 - 3.68062i) q^{95} +(1.01256 + 0.430438i) q^{96} +0.451869 q^{97} +(8.95582 - 4.21821i) q^{98} +(6.21051 + 14.9935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

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