LMFDB - Embedded newform 225.2.q.a.196.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			196.10
Character	$\chi$	$=$	225.196
Dual form			225.2.q.a.31.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.727367 - 0.807823i) q^{2} +(-0.917090 - 1.46933i) q^{3} +(0.0855417 - 0.813875i) q^{4} +(0.934297 - 2.03152i) q^{5} +(-0.519901 + 1.80959i) q^{6} +(1.73969 - 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(-1.31789 + 2.69503i) q^{9} +O(q^{10})$	\(q+(-0.727367 - 0.807823i) q^{2} +(-0.917090 - 1.46933i) q^{3} +(0.0855417 - 0.813875i) q^{4} +(0.934297 - 2.03152i) q^{5} +(-0.519901 + 1.80959i) q^{6} +(1.73969 - 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(-1.31789 + 2.69503i) q^{9} +(-2.32069 + 0.722917i) q^{10} +(2.35402 + 2.61440i) q^{11} +(-1.27430 + 0.620708i) q^{12} +(1.45133 - 1.61187i) q^{13} +(-3.69956 + 0.786365i) q^{14} +(-3.84182 + 0.490296i) q^{15} +(1.65656 + 0.352114i) q^{16} +(-1.54674 + 1.12377i) q^{17} +(3.13570 - 0.895651i) q^{18} +(-0.970198 + 0.704890i) q^{19} +(-1.57349 - 0.934181i) q^{20} +(-6.02291 + 0.207218i) q^{21} +(0.399739 - 3.80326i) q^{22} +(-1.96627 + 0.417944i) q^{23} +(4.91898 + 1.99035i) q^{24} +(-3.25418 - 3.79609i) q^{25} -2.35776 q^{26} +(5.16852 - 0.535160i) q^{27} +(-2.30358 - 1.67365i) q^{28} +(-3.26898 + 1.45544i) q^{29} +(3.19049 + 2.74689i) q^{30} +(5.79773 + 2.58132i) q^{31} +(2.14316 + 3.71207i) q^{32} +(1.68259 - 5.85649i) q^{33} +(2.03286 + 0.432098i) q^{34} +(-4.49607 - 6.34948i) q^{35} +(2.08068 + 1.30314i) q^{36} +(2.46324 + 7.58107i) q^{37} +(1.27512 + 0.271034i) q^{38} +(-3.69938 - 0.654265i) q^{39} +(1.34261 + 6.71767i) q^{40} +(1.73464 - 1.92652i) q^{41} +(4.54826 + 4.71472i) q^{42} +(5.34941 - 9.26545i) q^{43} +(2.32917 - 1.69224i) q^{44} +(4.24371 + 5.19528i) q^{45} +(1.76783 + 1.28440i) q^{46} +(11.9942 - 5.34016i) q^{47} +(-1.00185 - 2.75697i) q^{48} +(-2.55306 - 4.42203i) q^{49} +(-0.699589 + 5.38996i) q^{50} +(3.06970 + 1.24208i) q^{51} +(-1.18771 - 1.31909i) q^{52} +(-11.2674 - 8.18624i) q^{53} +(-4.19173 - 3.78599i) q^{54} +(7.51058 - 2.33962i) q^{55} +(1.11423 + 10.6012i) q^{56} +(1.92548 + 0.779098i) q^{57} +(3.55349 + 1.58212i) q^{58} +(-3.64544 + 4.04867i) q^{59} +(0.0704032 + 3.16871i) q^{60} +(0.353232 + 0.392304i) q^{61} +(-2.13183 - 6.56111i) q^{62} +(5.82802 + 8.65963i) q^{63} +(2.48651 - 7.65270i) q^{64} +(-1.91857 - 4.45438i) q^{65} +(-5.95487 + 2.90059i) q^{66} +(-9.83507 - 4.37885i) q^{67} +(0.782301 + 1.35499i) q^{68} +(2.41735 + 2.50582i) q^{69} +(-1.85897 + 8.25044i) q^{70} +(6.38098 + 4.63605i) q^{71} +(-1.58667 - 9.05296i) q^{72} +(-2.75054 + 8.46529i) q^{73} +(4.33248 - 7.50408i) q^{74} +(-2.59336 + 8.26284i) q^{75} +(0.490700 + 0.849917i) q^{76} +(11.9731 - 2.54496i) q^{77} +(2.16228 + 3.46434i) q^{78} +(6.17366 - 2.74869i) q^{79} +(2.26305 - 3.03637i) q^{80} +(-5.52633 - 7.10350i) q^{81} -2.81801 q^{82} +(0.372037 + 3.53969i) q^{83} +(-0.346560 + 4.91962i) q^{84} +(0.837858 + 4.19218i) q^{85} +(-11.3758 + 2.41801i) q^{86} +(5.13649 + 3.46846i) q^{87} +(-10.5425 - 2.24087i) q^{88} +(2.71707 - 8.36227i) q^{89} +(1.11013 - 7.20704i) q^{90} +(-2.33207 - 7.17736i) q^{91} +(0.171956 + 1.63605i) q^{92} +(-1.52423 - 10.8861i) q^{93} +(-13.0381 - 5.80493i) q^{94} +(0.525548 + 2.62956i) q^{95} +(3.48880 - 6.55333i) q^{96} +(-15.6914 + 6.98627i) q^{97} +(-1.71520 + 5.27886i) q^{98} +(-10.1482 + 2.89865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.727367	−	0.807823i	−0.514326	−	0.571217i	0.428907	−	0.903349i	$-0.358899\pi$
$2$	−0.727367	−	0.807823i	−0.514326	−	0.571217i	−0.943233	+	0.332131i	$0.892232\pi$
$3$	−0.917090	−	1.46933i	−0.529482	−	0.848321i
$3$	−0.917090	−	1.46933i	−0.529482	−	0.848321i
$4$	0.0855417	−	0.813875i	0.0427709	−	0.406938i
$5$	0.934297	−	2.03152i	0.417830	−	0.908525i
$5$	0.934297	−	2.03152i	0.417830	−	0.908525i
$6$	−0.519901	+	1.80959i	−0.212249	+	0.738763i
$7$	1.73969	−	3.01324i	0.657542	−	1.13890i	−0.323708	−	0.946157i	$-0.604930\pi$
$7$	1.73969	−	3.01324i	0.657542	−	1.13890i	0.981250	−	0.192739i	$-0.0617370\pi$
$8$	−2.47854	+	1.80077i	−0.876298	+	0.636668i
$9$	−1.31789	+	2.69503i	−0.439297	+	0.898342i
$10$	−2.32069	+	0.722917i	−0.733866	+	0.228607i
$11$	2.35402	+	2.61440i	0.709764	+	0.788272i	0.984898	−	0.173133i	$-0.0553891\pi$
$11$	2.35402	+	2.61440i	0.709764	+	0.788272i	−0.275135	+	0.961406i	$0.588722\pi$
$12$	−1.27430	+	0.620708i	−0.367860	+	0.179183i
$13$	1.45133	−	1.61187i	0.402527	−	0.447052i	−0.507468	−	0.861671i	$-0.669418\pi$
$13$	1.45133	−	1.61187i	0.402527	−	0.447052i	0.909995	+	0.414619i	$0.136085\pi$
$14$	−3.69956	+	0.786365i	−0.988748	+	0.210165i
$15$	−3.84182	+	0.490296i	−0.991955	+	0.126594i
$16$	1.65656	+	0.352114i	0.414141	+	0.0880284i
$17$	−1.54674	+	1.12377i	−0.375140	+	0.272555i	−0.759339	−	0.650695i	$-0.774478\pi$
$17$	−1.54674	+	1.12377i	−0.375140	+	0.272555i	0.384199	+	0.923250i	$0.374478\pi$
$18$	3.13570	−	0.895651i	0.739090	−	0.211107i
$19$	−0.970198	+	0.704890i	−0.222579	+	0.161713i	−0.693487	−	0.720469i	$-0.743926\pi$
$19$	−0.970198	+	0.704890i	−0.222579	+	0.161713i	0.470908	+	0.882182i	$0.343926\pi$
$20$	−1.57349	−	0.934181i	−0.351842	−	0.208889i
$21$	−6.02291	+	0.207218i	−1.31431	+	0.0452188i
$22$	0.399739	−	3.80326i	0.0852247	−	0.810859i
$23$	−1.96627	+	0.417944i	−0.409996	+	0.0871474i	−0.408293	−	0.912851i	$-0.633876\pi$
$23$	−1.96627	+	0.417944i	−0.409996	+	0.0871474i	−0.00170377	+	0.999999i	$0.500542\pi$
$24$	4.91898	+	1.99035i	1.00408	+	0.406278i
$25$	−3.25418	−	3.79609i	−0.650836	−	0.759219i
$26$	−2.35776			−0.462394
$27$	5.16852	−	0.535160i	0.994682	−	0.102991i
$28$	−2.30358	−	1.67365i	−0.435336	−	0.316290i
$29$	−3.26898	+	1.45544i	−0.607035	+	0.270269i	−0.687149	−	0.726516i	$-0.741138\pi$
$29$	−3.26898	+	1.45544i	−0.607035	+	0.270269i	0.0801144	+	0.996786i	$0.474471\pi$
$30$	3.19049	+	2.74689i	0.582501	+	0.501511i
$31$	5.79773	+	2.58132i	1.04130	+	0.463618i	0.854866	−	0.518849i	$-0.173639\pi$
$31$	5.79773	+	2.58132i	1.04130	+	0.463618i	0.186437	+	0.982467i	$0.440306\pi$
$32$	2.14316	+	3.71207i	0.378862	+	0.656207i
$33$	1.68259	−	5.85649i	0.292901	−	1.01948i
$34$	2.03286	+	0.432098i	0.348633	+	0.0741042i
$35$	−4.49607	−	6.34948i	−0.759975	−	1.07326i
$36$	2.08068	+	1.30314i	0.346780	+	0.217189i
$37$	2.46324	+	7.58107i	0.404954	+	1.24632i	0.920934	+	0.389719i	$0.127428\pi$
$37$	2.46324	+	7.58107i	0.404954	+	1.24632i	−0.515980	+	0.856601i	$0.672572\pi$
$38$	1.27512	+	0.271034i	0.206851	+	0.0439676i
$39$	−3.69938	−	0.654265i	−0.592375	−	0.104766i
$40$	1.34261	+	6.71767i	0.212285	+	1.06216i
$41$	1.73464	−	1.92652i	0.270906	−	0.300871i	−0.592306	−	0.805713i	$-0.701782\pi$
$41$	1.73464	−	1.92652i	0.270906	−	0.300871i	0.863212	+	0.504842i	$0.168449\pi$
$42$	4.54826	+	4.71472i	0.701812	+	0.727497i
$43$	5.34941	−	9.26545i	0.815778	−	1.41297i	−0.0929908	−	0.995667i	$-0.529643\pi$
$43$	5.34941	−	9.26545i	0.815778	−	1.41297i	0.908768	−	0.417301i	$-0.137024\pi$
$44$	2.32917	−	1.69224i	0.351135	−	0.255114i
$45$	4.24371	+	5.19528i	0.632615	+	0.774467i
$46$	1.76783	+	1.28440i	0.260652	+	0.189375i
$47$	11.9942	−	5.34016i	1.74953	−	0.778942i	0.757518	−	0.652814i	$-0.226412\pi$
$47$	11.9942	−	5.34016i	1.74953	−	0.778942i	0.992014	−	0.126128i	$-0.0402549\pi$
$48$	−1.00185	−	2.75697i	−0.144604	−	0.397934i
$49$	−2.55306	−	4.42203i	−0.364723	−	0.631718i
$50$	−0.699589	+	5.38996i	−0.0989369	+	0.762255i
$51$	3.06970	+	1.24208i	0.429845	+	0.173926i
$52$	−1.18771	−	1.31909i	−0.164706	−	0.182924i
$53$	−11.2674	−	8.18624i	−1.54770	−	1.12447i	−0.945269	−	0.326293i	$-0.894200\pi$
$53$	−11.2674	−	8.18624i	−1.54770	−	1.12447i	−0.602427	−	0.798174i	$-0.705800\pi$
$54$	−4.19173	−	3.78599i	−0.570422	−	0.515208i
$55$	7.51058	−	2.33962i	1.01273	−	0.315474i
$56$	1.11423	+	10.6012i	0.148896	+	1.41665i
$57$	1.92548	+	0.779098i	0.255036	+	0.103194i
$58$	3.55349	+	1.58212i	0.466597	+	0.207742i
$59$	−3.64544	+	4.04867i	−0.474596	+	0.527092i	−0.932142	−	0.362094i	$-0.882062\pi$
$59$	−3.64544	+	4.04867i	−0.474596	+	0.527092i	0.457545	+	0.889186i	$0.348729\pi$
$60$	0.0704032	+	3.16871i	0.00908902	+	0.409078i
$61$	0.353232	+	0.392304i	0.0452268	+	0.0502294i	0.765334	−	0.643634i	$-0.222574\pi$
$61$	0.353232	+	0.392304i	0.0452268	+	0.0502294i	−0.720107	+	0.693863i	$0.755907\pi$
$62$	−2.13183	−	6.56111i	−0.270743	−	0.833262i
$63$	5.82802	+	8.65963i	0.734262	+	1.09101i
$64$	2.48651	−	7.65270i	0.310814	−	0.956588i
$65$	−1.91857	−	4.45438i	−0.237970	−	0.552498i
$66$	−5.95487	+	2.90059i	−0.732993	+	0.357037i
$67$	−9.83507	−	4.37885i	−1.20154	−	0.534962i	−0.294360	−	0.955695i	$-0.595106\pi$
$67$	−9.83507	−	4.37885i	−1.20154	−	0.534962i	−0.907185	+	0.420732i	$0.861773\pi$
$68$	0.782301	+	1.35499i	0.0948680	+	0.164316i
$69$	2.41735	+	2.50582i	0.291015	+	0.301665i
$70$	−1.85897	+	8.25044i	−0.222189	+	0.986116i
$71$	6.38098	+	4.63605i	0.757283	+	0.550198i	0.898076	−	0.439841i	$-0.144965\pi$
$71$	6.38098	+	4.63605i	0.757283	+	0.550198i	−0.140793	+	0.990039i	$0.544965\pi$
$72$	−1.58667	−	9.05296i	−0.186990	−	1.06690i
$73$	−2.75054	+	8.46529i	−0.321926	+	0.990787i	0.650883	+	0.759178i	$0.274399\pi$
$73$	−2.75054	+	8.46529i	−0.321926	+	0.990787i	−0.972809	+	0.231609i	$0.925601\pi$
$74$	4.33248	−	7.50408i	0.503641	−	0.872332i
$75$	−2.59336	+	8.26284i	−0.299455	+	0.954110i
$76$	0.490700	+	0.849917i	0.0562871	+	0.0974922i
$77$	11.9731	−	2.54496i	1.36446	−	0.290025i
$78$	2.16228	+	3.46434i	0.244830	+	0.392259i
$79$	6.17366	−	2.74869i	0.694591	−	0.309252i	−0.0289032	−	0.999582i	$-0.509201\pi$
$79$	6.17366	−	2.74869i	0.694591	−	0.309252i	0.723494	+	0.690330i	$0.242535\pi$
$80$	2.26305	−	3.03637i	0.253017	−	0.339477i
$81$	−5.52633	−	7.10350i	−0.614037	−	0.789278i
$82$	−2.81801			−0.311197
$83$	0.372037	+	3.53969i	0.0408363	+	0.388532i	0.995782	+	0.0917511i	$0.0292464\pi$
$83$	0.372037	+	3.53969i	0.0408363	+	0.388532i	−0.954946	+	0.296781i	$0.904087\pi$
$84$	−0.346560	+	4.91962i	−0.0378128	+	0.536775i
$85$	0.837858	+	4.19218i	0.0908784	+	0.454706i
$86$	−11.3758	+	2.41801i	−1.22669	+	0.260741i
$87$	5.13649	+	3.46846i	0.550689	+	0.371857i
$88$	−10.5425	−	2.24087i	−1.12383	−	0.238878i
$89$	2.71707	−	8.36227i	0.288008	−	0.886399i	−0.697472	−	0.716612i	$-0.745692\pi$
$89$	2.71707	−	8.36227i	0.288008	−	0.886399i	0.985481	−	0.169787i	$-0.0543080\pi$
$90$	1.11013	−	7.20704i	0.117018	−	0.759689i
$91$	−2.33207	−	7.17736i	−0.244467	−	0.752392i
$92$	0.171956	+	1.63605i	0.0179277	+	0.170570i
$93$	−1.52423	−	10.8861i	−0.158055	−	1.12884i
$94$	−13.0381	−	5.80493i	−1.34478	−	0.598733i
$95$	0.525548	+	2.62956i	0.0539201	+	0.269787i
$96$	3.48880	−	6.55333i	0.356074	−	0.668846i
$97$	−15.6914	+	6.98627i	−1.59322	+	0.709348i	−0.995712	−	0.0925124i	$-0.970510\pi$
$97$	−15.6914	+	6.98627i	−1.59322	+	0.709348i	−0.597511	+	0.801861i	$0.703844\pi$
$98$	−1.71520	+	5.27886i	−0.173262	+	0.533245i
$99$	−10.1482	+	2.89865i	−1.01994	+	0.291325i
$100$	−3.36791	+	2.32377i	−0.336791	+	0.232377i
$101$	4.67773	−	8.10206i	0.465451	−	0.806185i	−0.533770	−	0.845629i	$-0.679225\pi$
$101$	4.67773	−	8.10206i	0.465451	−	0.806185i	0.999222	+	0.0394441i	$0.0125587\pi$
$102$	−1.22942	−	3.38323i	−0.121731	−	0.334989i
$103$	−0.837734	+	7.97051i	−0.0825444	+	0.785358i	0.872444	+	0.488714i	$0.162534\pi$
$103$	−0.837734	+	7.97051i	−0.0825444	+	0.785358i	−0.954988	+	0.296643i	$0.904133\pi$
$104$	−0.694592	+	6.60860i	−0.0681104	+	0.648027i
$105$	−5.20621	+	12.4293i	−0.508075	+	1.21297i
$106$	1.58250	+	15.0565i	0.153706	+	1.46241i
$107$	5.04642			0.487855			0.243928	−	0.969793i	$-0.421564\pi$
$107$	5.04642			0.487855			0.243928	+	0.969793i	$0.421564\pi$
$108$	0.00657114	−	4.25231i	0.000632308	−	0.409179i
$109$	−1.49707	−	4.60752i	−0.143394	−	0.441320i	0.853407	−	0.521245i	$-0.174532\pi$
$109$	−1.49707	−	4.60752i	−0.143394	−	0.441320i	−0.996801	+	0.0799245i	$0.974532\pi$
$110$	−7.35295	−	4.36546i	−0.701076	−	0.416230i
$111$	8.88012	−	10.5718i	0.842864	−	1.00344i
$112$	3.94291	−	4.37905i	0.372570	−	0.413781i
$113$	1.47427	−	1.63734i	0.138688	−	0.154028i	−0.669800	−	0.742542i	$-0.733620\pi$
$113$	1.47427	−	1.63734i	0.138688	−	0.154028i	0.808487	+	0.588514i	$0.200287\pi$
$114$	−0.771157	−	2.12214i	−0.0722254	−	0.198756i
$115$	−0.988019	+	4.38501i	−0.0921333	+	0.408905i
$116$	0.904916	+	2.78505i	0.0840193	+	0.258585i
$117$	2.43133	+	6.03565i	0.224777	+	0.557996i
$118$	5.92219			0.545182
$119$	0.695340	+	6.61572i	0.0637418	+	0.606462i
$120$	8.63922	−	8.13345i	0.788650	−	0.742479i
$121$	−0.143885	+	1.36898i	−0.0130805	+	0.124453i
$122$	0.0599828	−	0.570699i	0.00543059	−	0.0516686i
$123$	−4.42152	−	0.781982i	−0.398675	−	0.0705090i
$124$	2.59682	−	4.49782i	0.233201	−	0.403916i
$125$	−10.7522	+	3.06426i	−0.961708	+	0.274076i
$126$	2.75634	−	11.0067i	0.245554	−	0.980559i
$127$	−5.91345	+	18.1997i	−0.524734	+	1.61497i	0.240106	+	0.970747i	$0.422818\pi$
$127$	−5.91345	+	18.1997i	−0.524734	+	1.61497i	−0.764841	+	0.644219i	$0.777182\pi$
$128$	−0.159129	+	0.0708488i	−0.0140652	+	0.00626221i
$129$	−18.5199	+	0.637180i	−1.63059	+	0.0561005i
$130$	−2.20285	+	4.78984i	−0.193202	+	0.420097i
$131$	−7.04977	−	3.13876i	−0.615941	−	0.274235i	0.0749569	−	0.997187i	$-0.476118\pi$
$131$	−7.04977	−	3.13876i	−0.615941	−	0.274235i	−0.690898	+	0.722952i	$0.742785\pi$
$132$	−4.62252	−	1.87039i	−0.402339	−	0.162797i
$133$	0.436154	+	4.14972i	0.0378193	+	0.359827i
$134$	3.61637	+	11.1300i	0.312407	+	0.961488i
$135$	3.74174	−	11.0000i	0.322038	−	0.946727i
$136$	1.81001	−	5.57065i	0.155207	−	0.477679i
$137$	−6.13544	−	1.30413i	−0.524186	−	0.111419i	−0.0617840	−	0.998090i	$-0.519679\pi$
$137$	−6.13544	−	1.30413i	−0.524186	−	0.111419i	−0.462402	+	0.886670i	$0.653012\pi$
$138$	0.265959	−	3.77544i	0.0226399	−	0.321387i
$139$	19.9459	−	4.23963i	1.69179	−	0.359601i	0.741496	−	0.670958i	$-0.234117\pi$
$139$	19.9459	−	4.23963i	1.69179	−	0.359601i	0.950293	+	0.311357i	$0.100783\pi$
$140$	−5.55229	+	3.11609i	−0.469254	+	0.263358i
$141$	−18.8462	−	12.7261i	−1.58714	−	1.07173i
$142$	−0.896205	−	8.52682i	−0.0752078	−	0.715555i
$143$	7.63054			0.638098
$144$	−3.13213	+	4.00044i	−0.261011	+	0.333370i
$145$	−0.0974297	+	8.00083i	−0.00809110	+	0.664433i
$146$	8.83911	−	3.93543i	0.731530	−	0.325698i
$147$	−4.15605	+	7.80669i	−0.342785	+	0.643885i
$148$	6.38075	−	1.35627i	0.524495	−	0.111485i
$149$	−3.52387	−	6.10353i	−0.288687	−	0.500021i	0.684810	−	0.728722i	$-0.259885\pi$
$149$	−3.52387	−	6.10353i	−0.288687	−	0.500021i	−0.973497	+	0.228701i	$0.926552\pi$
$150$	8.56124	−	3.91514i	0.699022	−	0.319670i
$151$	0.0155849	−	0.0269939i	0.00126828	−	0.00219673i	−0.865391	−	0.501098i	$-0.832930\pi$
$151$	0.0155849	−	0.0269939i	0.00126828	−	0.00219673i	0.866659	+	0.498901i	$0.166263\pi$
$152$	1.13533	−	3.49420i	0.0920878	−	0.283417i
$153$	−0.990164	−	5.64952i	−0.0800500	−	0.456737i
$154$	−10.7647	−	7.82102i	−0.867445	−	0.630236i
$155$	10.6608	−	9.36651i	0.856297	−	0.752337i
$156$	−0.848942	+	2.95487i	−0.0679697	+	0.236579i
$157$	−0.694083	−	1.20219i	−0.0553938	−	0.0959450i	0.836999	−	0.547205i	$-0.184308\pi$
$157$	−0.694083	−	1.20219i	−0.0553938	−	0.0959450i	−0.892393	+	0.451260i	$0.850975\pi$
$158$	−6.71098	−	2.98792i	−0.533897	−	0.237706i
$159$	−1.69511	+	24.0631i	−0.134431	+	1.90833i
$160$	9.54351	−	0.885714i	0.754481	−	0.0700219i
$161$	−2.16135	+	6.65194i	−0.170338	+	0.524246i
$162$	−1.71870	+	9.63115i	−0.135034	+	0.756695i
$163$	0.385069	+	1.18512i	0.0301609	+	0.0928258i	0.965004	−	0.262236i	$-0.0844598\pi$
$163$	0.385069	+	1.18512i	0.0301609	+	0.0928258i	−0.934843	+	0.355062i	$0.884460\pi$
$164$	−1.41956	−	1.57658i	−0.110849	−	0.123110i
$165$	−10.3256	−	8.88991i	−0.803844	−	0.692079i
$166$	2.58884	−	2.87520i	0.200933	−	0.223159i
$167$	0.203316	+	0.0905220i	0.0157330	+	0.00700480i	0.414588	−	0.910009i	$-0.363926\pi$
$167$	0.203316	+	0.0905220i	0.0157330	+	0.00700480i	−0.398855	+	0.917014i	$0.630592\pi$
$168$	14.5549	−	11.3595i	1.12293	−	0.876401i
$169$	0.867117	+	8.25007i	0.0667013	+	0.634621i
$170$	2.77711	−	3.72610i	0.212995	−	0.285779i
$171$	−0.621082	−	3.54368i	−0.0474953	−	0.270992i
$172$	−7.08332	−	5.14634i	−0.540098	−	0.392404i
$173$	12.7920	+	14.2070i	0.972561	+	1.08014i	0.996760	+	0.0804313i	$0.0256298\pi$
$173$	12.7920	+	14.2070i	0.972561	+	1.08014i	−0.0241991	+	0.999707i	$0.507704\pi$
$174$	−0.934214	−	6.67222i	−0.0708226	−	0.505819i
$175$	−17.0998	+	3.20157i	−1.29262	+	0.242016i
$176$	2.97902	+	5.15981i	0.224552	+	0.388935i
$177$	9.29206	+	1.64338i	0.698434	+	0.123524i
$178$	−8.73154	+	3.88753i	−0.654457	+	0.291383i
$179$	15.4208	+	11.2038i	1.15260	+	0.837415i	0.988825	−	0.149082i	$-0.0476320\pi$
$179$	15.4208	+	11.2038i	1.15260	+	0.837415i	0.163778	+	0.986497i	$0.447632\pi$
$180$	4.59132	−	3.00944i	0.342217	−	0.224310i
$181$	9.13951	−	6.64024i	0.679335	−	0.493565i	−0.193802	−	0.981041i	$-0.562082\pi$
$181$	9.13951	−	6.64024i	0.679335	−	0.493565i	0.873137	+	0.487475i	$0.162082\pi$
$182$	−4.10177	+	7.10448i	−0.304044	+	0.526619i
$183$	0.252480	−	0.878795i	0.0186639	−	0.0649624i
$184$	4.12088	−	4.57670i	0.303795	−	0.337398i
$185$	17.7025	+	2.07884i	1.30152	+	0.152840i
$186$	−7.68538	+	9.14951i	−0.563520	+	0.670874i
$187$	−6.57906	−	1.39842i	−0.481109	−	0.102263i
$188$	−3.32022	−	10.2186i	−0.242152	−	0.745266i
$189$	7.37907	−	16.5050i	0.536749	−	1.20056i
$190$	1.74195	−	2.33720i	0.126374	−	0.169559i
$191$	2.20315	+	0.468294i	0.159414	+	0.0338845i	0.286927	−	0.957952i	$-0.407366\pi$
$191$	2.20315	+	0.468294i	0.159414	+	0.0338845i	−0.127513	+	0.991837i	$0.540699\pi$
$192$	−13.5247	+	3.36470i	−0.976064	+	0.242826i
$193$	7.89562	+	13.6756i	0.568339	+	0.984393i	0.996730	+	0.0807992i	$0.0257472\pi$
$193$	7.89562	+	13.6756i	0.568339	+	0.984393i	−0.428391	+	0.903593i	$0.640919\pi$
$194$	17.0571	+	7.59431i	1.22463	+	0.545240i
$195$	−4.78547	+	6.90410i	−0.342695	+	0.494413i
$196$	−3.81737	+	1.69960i	−0.272669	+	0.121400i
$197$	17.3982	+	12.6405i	1.23957	+	0.900601i	0.997570	−	0.0696750i	$-0.0221962\pi$
$197$	17.3982	+	12.6405i	1.23957	+	0.900601i	0.242001	+	0.970276i	$0.422196\pi$
$198$	9.72308	+	6.08959i	0.690989	+	0.432769i
$199$	−17.1687			−1.21706			−0.608530	−	0.793531i	$-0.708240\pi$
$199$	−17.1687			−1.21706			−0.608530	+	0.793531i	$0.708240\pi$
$200$	14.9015	+	3.54877i	1.05370	+	0.250936i
$201$	2.58564	+	18.4668i	0.182377	+	1.30255i
$202$	−9.94746	+	2.11440i	−0.699901	+	0.148769i
$203$	−1.30143	+	12.3822i	−0.0913422	+	0.869063i
$204$	1.27349	−	2.39211i	0.0891619	−	0.167481i
$205$	−2.29309	−	5.32391i	−0.160157	−	0.371838i
$206$	7.04810	−	5.12075i	0.491065	−	0.356779i
$207$	1.46496	−	5.84996i	0.101822	−	0.406600i
$208$	2.97179	−	2.15913i	0.206056	−	0.149709i
$209$	−4.12673	−	0.877164i	−0.285452	−	0.0606747i
$210$	13.8275	−	4.83495i	0.954188	−	0.333643i
$211$	13.3645	−	2.84072i	0.920053	−	0.195563i	0.276544	−	0.961001i	$-0.410811\pi$
$211$	13.3645	−	2.84072i	0.920053	−	0.195563i	0.643510	+	0.765438i	$0.277478\pi$
$212$	−7.62641	+	8.46999i	−0.523784	+	0.581721i
$213$	0.959980	−	13.6275i	0.0657768	−	0.933740i
$214$	−3.67060	−	4.07661i	−0.250917	−	0.278672i
$215$	−13.8250	−	19.5241i	−0.942860	−	1.33154i
$216$	−11.8467	+	10.6337i	−0.806067	+	0.723533i
$217$	17.8644	−	12.9792i	1.21271	−	0.881088i
$218$	−2.63314	+	4.56073i	−0.178339	+	0.308892i
$219$	14.9608	−	3.72197i	1.01096	−	0.251508i
$220$	−1.26169	−	6.31281i	−0.0850631	−	0.425609i
$221$	−0.433462	+	4.12412i	−0.0291578	+	0.277418i
$222$	−14.9993	+	0.516051i	−1.00669	+	0.0346351i
$223$	14.6520	+	16.2727i	0.981169	+	1.08970i	0.995959	+	0.0898080i	$0.0286253\pi$
$223$	14.6520	+	16.2727i	0.981169	+	1.08970i	−0.0147900	+	0.999891i	$0.504708\pi$
$224$	14.9138			0.996469
$225$	14.5192	−	3.76726i	0.967948	−	0.251151i
$226$	−2.39502			−0.159314
$227$	−17.3202	−	19.2360i	−1.14958	−	1.27674i	−0.955248	−	0.295806i	$-0.904412\pi$
$227$	−17.3202	−	19.2360i	−1.14958	−	1.27674i	−0.194334	−	0.980935i	$-0.562255\pi$
$228$	0.798797	−	1.50045i	0.0529016	−	0.0993700i
$229$	−2.40196	+	22.8532i	−0.158726	+	1.51018i	0.567872	+	0.823117i	$0.307767\pi$
$229$	−2.40196	+	22.8532i	−0.158726	+	1.51018i	−0.726598	+	0.687063i	$0.758900\pi$
$230$	4.26097	−	2.39137i	0.280960	−	0.157682i
$231$	−14.7198	−	15.2585i	−0.968491	−	1.00394i
$232$	5.48140	−	9.49406i	0.359872	−	0.623316i
$233$	−7.19284	+	5.22590i	−0.471219	+	0.342360i	−0.797916	−	0.602769i	$-0.794064\pi$
$233$	−7.19284	+	5.22590i	−0.471219	+	0.342360i	0.326697	+	0.945129i	$0.394064\pi$
$234$	3.10727	−	6.35422i	0.203128	−	0.415388i
$235$	0.357478	−	29.3558i	0.0233193	−	1.91496i
$236$	2.98328	+	3.31327i	0.194195	+	0.215675i
$237$	−9.70055	−	6.55038i	−0.630119	−	0.425493i
$238$	4.83857	−	5.37377i	0.313638	−	0.348330i
$239$	5.06749	−	1.07713i	0.327788	−	0.0696736i	−0.0410781	−	0.999156i	$-0.513079\pi$
$239$	5.06749	−	1.07713i	0.327788	−	0.0696736i	0.368867	+	0.929482i	$0.379746\pi$
$240$	−6.53687	−	0.540552i	−0.421953	−	0.0348925i
$241$	6.41203	+	1.36292i	0.413035	+	0.0877933i	0.409742	−	0.912201i	$-0.365619\pi$
$241$	6.41203	+	1.36292i	0.413035	+	0.0877933i	0.00329255	+	0.999995i	$0.498952\pi$
$242$	1.21055	−	0.879516i	0.0778171	−	0.0565374i
$243$	−5.36928	+	14.6346i	−0.344439	+	0.938809i
$244$	0.349503	−	0.253929i	0.0223746	−	0.0162561i
$245$	−11.3688	+	1.05511i	−0.726324	+	0.0674087i
$246$	2.58437	+	4.14060i	0.164773	+	0.263995i
$247$	−0.271890	+	2.58686i	−0.0173000	+	0.164598i
$248$	−19.0183	+	4.04246i	−1.20766	+	0.256697i
$249$	4.85980	−	3.79287i	0.307978	−	0.240363i
$250$	10.2962	+	6.45705i	0.651189	+	0.408380i
$251$	−7.14839			−0.451202			−0.225601	−	0.974220i	$-0.572435\pi$
$251$	−7.14839			−0.451202			−0.225601	+	0.974220i	$0.572435\pi$
$252$	7.54640	−	4.00252i	0.475378	−	0.252135i
$253$	−5.72132	−	4.15678i	−0.359696	−	0.261335i
$254$	19.0034	−	8.46087i	1.19238	−	0.530882i
$255$	5.39133	−	5.07571i	0.337618	−	0.317853i
$256$	−14.5288	−	6.46862i	−0.908048	−	0.404289i
$257$	2.06283	+	3.57292i	0.128676	+	0.222873i	0.923164	−	0.384407i	$-0.125594\pi$
$257$	2.06283	+	3.57292i	0.128676	+	0.222873i	−0.794488	+	0.607280i	$0.792261\pi$
$258$	13.9855	+	14.4974i	0.870701	+	0.902567i
$259$	27.1288	+	5.76641i	1.68570	+	0.358307i
$260$	−3.78943	+	1.18044i	−0.235010	+	0.0732080i
$261$	0.385700	−	10.7281i	0.0238742	−	0.664053i
$262$	2.59221	+	7.97800i	0.160147	+	0.492883i
$263$	−17.2609	−	3.66892i	−1.06435	−	0.226235i	−0.357730	−	0.933825i	$-0.616449\pi$
$263$	−17.2609	−	3.66892i	−1.06435	−	0.226235i	−0.706623	+	0.707590i	$0.749782\pi$
$264$	6.37581	+	17.5455i	0.392404	+	1.07985i
$265$	−27.1576	+	15.2416i	−1.66828	+	0.936284i
$266$	3.03500	−	3.37071i	0.186088	−	0.206671i
$267$	−14.7788	+	3.67668i	−0.904446	+	0.225009i
$268$	−4.40515	+	7.62994i	−0.269087	+	0.466073i
$269$	−21.6298	+	15.7150i	−1.31879	+	0.958158i	−0.318845	+	0.947807i	$0.603295\pi$
$269$	−21.6298	+	15.7150i	−1.31879	+	0.958158i	−0.999946	+	0.0103508i	$0.996705\pi$
$270$	−11.6077	+	4.97835i	−0.706419	+	0.302973i
$271$	17.6749	+	12.8416i	1.07367	+	0.780069i	0.976569	−	0.215205i	$-0.0690419\pi$
$271$	17.6749	+	12.8416i	1.07367	+	0.780069i	0.0971044	+	0.995274i	$0.469042\pi$
$272$	−2.95798	+	1.31698i	−0.179354	+	0.0798534i
$273$	−8.40724	+	10.0089i	−0.508829	+	0.605765i
$274$	3.40921	+	5.90493i	0.205958	+	0.356730i
$275$	2.26412	−	17.4438i	0.136532	−	1.05190i
$276$	2.24621	−	1.75307i	0.135206	−	0.105522i
$277$	−9.51723	−	10.5700i	−0.571835	−	0.635087i	0.385968	−	0.922512i	$-0.373867\pi$
$277$	−9.51723	−	10.5700i	−0.571835	−	0.635087i	−0.957803	+	0.287425i	$0.907201\pi$
$278$	−17.9329	−	13.0290i	−1.07554	−	0.781427i
$279$	−14.5975	+	12.2231i	−0.873929	+	0.731781i
$280$	22.5777	+	7.64110i	1.34927	+	0.456643i
$281$	0.750893	+	7.14427i	0.0447945	+	0.426192i	0.993821	+	0.110995i	$0.0354038\pi$
$281$	0.750893	+	7.14427i	0.0447945	+	0.426192i	−0.949026	+	0.315197i	$0.897930\pi$
$282$	3.42772	+	24.4810i	0.204117	+	1.45782i
$283$	12.3369	+	5.49275i	0.733353	+	0.326510i	0.739212	−	0.673473i	$-0.235198\pi$
$283$	12.3369	+	5.49275i	0.733353	+	0.326510i	−0.00585864	+	0.999983i	$0.501865\pi$
$284$	4.31901	−	4.79675i	0.256286	−	0.284635i
$285$	3.38172	−	3.18375i	0.200316	−	0.188589i
$286$	−5.55021	−	6.16413i	−0.328191	−	0.364493i
$287$	−2.78730	−	8.57843i	−0.164529	−	0.506369i
$288$	−12.8286	+	0.883782i	−0.755931	+	0.0520774i
$289$	−4.12374	+	12.6916i	−0.242573	+	0.746564i
$290$	6.53413	−	5.74084i	0.383697	−	0.337114i
$291$	24.6556	+	16.6489i	1.44534	+	0.975977i
$292$	6.65441	+	2.96273i	0.389420	+	0.173381i
$293$	−0.157560	−	0.272902i	−0.00920475	−	0.0159431i	0.861386	−	0.507950i	$-0.169597\pi$
$293$	−0.157560	−	0.272902i	−0.00920475	−	0.0159431i	−0.870591	+	0.492007i	$0.836263\pi$
$294$	9.32941	−	2.32098i	0.544102	−	0.135362i
$295$	4.81905	+	11.1885i	0.280576	+	0.651418i
$296$	−19.7570	−	14.3543i	−1.14835	−	0.834327i
$297$	13.5659	+	12.2528i	0.787175	+	0.710981i
$298$	−2.36742	+	7.28617i	−0.137141	+	0.422077i
$299$	−2.18005	+	3.77595i	−0.126075	+	0.218369i
$300$	6.50308	+	2.81749i	0.375455	+	0.162668i
$301$	−18.6127	−	32.2381i	−1.07282	−	1.85817i
$302$	−0.0331423	+	0.00704461i	−0.00190712	+	0.000405372i
$303$	−16.1945	+	0.557174i	−0.930352	+	0.0320088i
$304$	−1.85540	+	0.826076i	−0.106414	+	0.0473787i
$305$	1.12700	−	0.351071i	0.0645318	−	0.0201023i
$306$	−3.84360	+	4.90916i	−0.219724	+	0.280638i
$307$	−8.35636			−0.476923			−0.238461	−	0.971152i	$-0.576643\pi$
$307$	−8.35636			−0.476923			−0.238461	+	0.971152i	$0.576643\pi$
$308$	−1.04708	−	9.96230i	−0.0596629	−	0.567655i
$309$	12.4796	−	6.07876i	0.709941	−	0.345809i
$310$	−15.3208	−	1.79915i	−0.870164	−	0.102185i
$311$	−19.9820	+	4.24731i	−1.13308	+	0.240843i	−0.736025	−	0.676954i	$-0.763299\pi$
$311$	−19.9820	+	4.24731i	−1.13308	+	0.240843i	−0.397050	+	0.917797i	$0.629966\pi$
$312$	10.3473	−	5.04010i	0.585798	−	0.285339i
$313$	−15.4110	−	3.27572i	−0.871083	−	0.185154i	−0.249378	−	0.968406i	$-0.580226\pi$
$313$	−15.4110	−	3.27572i	−0.871083	−	0.185154i	−0.621705	+	0.783252i	$0.713560\pi$
$314$	−0.466301	+	1.43513i	−0.0263149	+	0.0809889i
$315$	23.0373	−	3.74910i	1.29801	−	0.211238i
$316$	−1.70899	−	5.25972i	−0.0961380	−	0.295882i
$317$	−1.33731	−	12.7236i	−0.0751108	−	0.714631i	−0.965671	−	0.259767i	$-0.916354\pi$
$317$	−1.33731	−	12.7236i	−0.0751108	−	0.714631i	0.890561	−	0.454865i	$-0.150312\pi$
$318$	20.6717	−	16.1334i	1.15921	−	0.904714i
$319$	−11.5004	−	5.12029i	−0.643897	−	0.286681i
$320$	−13.2235	−	12.2013i	−0.739217	−	0.682074i
$321$	−4.62802	−	7.41488i	−0.258311	−	0.413858i
$322$	6.94568	−	3.09242i	0.387068	−	0.172334i
$323$	0.708509	−	2.18057i	0.0394225	−	0.121330i
$324$	−6.25409	+	3.89010i	−0.347450	+	0.216116i
$325$	−10.8417	−	0.264088i	−0.601389	−	0.0146489i
$326$	0.677282	−	1.17309i	0.0375112	−	0.0649712i
$327$	−5.39704	+	6.42521i	−0.298457	+	0.355315i
$328$	−0.830181	+	7.89865i	−0.0458391	+	0.436130i
$329$	4.77505	−	45.4315i	0.263257	−	2.50472i
$330$	0.328997	+	14.8075i	0.0181107	+	0.815124i
$331$	−2.62711	−	24.9953i	−0.144399	−	1.37386i	−0.791364	−	0.611345i	$-0.790629\pi$
$331$	−2.62711	−	24.9953i	−0.144399	−	1.37386i	0.646965	−	0.762519i	$-0.276038\pi$
$332$	2.91269			0.159855
$333$	−23.6775	−	3.35253i	−1.29752	−	0.183717i
$334$	−0.0747594	−	0.230086i	−0.00409065	−	0.0125897i
$335$	−18.0846	+	15.8890i	−0.988068	+	0.868110i
$336$	−10.0503	−	1.77748i	−0.548289	−	0.0969693i
$337$	12.6373	−	14.0351i	0.688396	−	0.764541i	−0.293088	−	0.956085i	$-0.594683\pi$
$337$	12.6373	−	14.0351i	0.688396	−	0.764541i	0.981484	+	0.191545i	$0.0613497\pi$
$338$	6.03388	−	6.70131i	0.328200	−	0.364503i
$339$	−3.75784	−	0.664605i	−0.204098	−	0.0360964i
$340$	3.48359	−	0.323305i	0.188924	−	0.0175337i
$341$	6.89937	+	21.2341i	0.373622	+	1.14989i
$342$	−2.41091	+	3.07928i	−0.130367	+	0.166508i
$343$	6.58955			0.355802
$344$	3.42618	+	32.5979i	0.184727	+	1.75756i
$345$	7.34916	−	2.56972i	0.395665	−	0.138349i
$346$	2.17223	−	20.6674i	0.116780	−	1.11109i
$347$	2.94999	−	28.0672i	0.158364	−	1.50673i	−0.570061	−	0.821603i	$-0.693080\pi$
$347$	2.94999	−	28.0672i	0.158364	−	1.50673i	0.728424	−	0.685126i	$-0.240253\pi$
$348$	3.26227	−	3.88376i	0.174876	−	0.208192i
$349$	10.1548	−	17.5887i	0.543575	−	0.941500i	−0.455120	−	0.890430i	$-0.650404\pi$
$349$	10.1548	−	17.5887i	0.543575	−	0.941500i	0.998695	−	0.0510695i	$-0.0162630\pi$
$350$	15.0241	+	11.4849i	0.803074	+	0.613893i
$351$	6.63864	−	9.10767i	0.354344	−	0.486132i
$352$	−4.65980	+	14.3414i	−0.248368	+	0.764398i
$353$	8.23808	−	3.66783i	0.438469	−	0.195219i	−0.175616	−	0.984459i	$-0.556192\pi$
$353$	8.23808	−	3.66783i	0.438469	−	0.195219i	0.614085	+	0.789240i	$0.289525\pi$
$354$	−5.43118	−	8.70168i	−0.288664	−	0.462489i
$355$	15.3800	−	8.63166i	0.816285	−	0.458121i
$356$	−6.57342	−	2.92668i	−0.348391	−	0.155113i
$357$	9.08302	−	7.08890i	0.480725	−	0.375185i
$358$	−2.16584	−	20.6066i	−0.114468	−	1.08909i
$359$	2.84427	+	8.75376i	0.150115	+	0.462006i	0.997633	−	0.0687601i	$-0.0219043\pi$
$359$	2.84427	+	8.75376i	0.150115	+	0.462006i	−0.847518	+	0.530766i	$0.821904\pi$
$360$	−19.8737	−	5.23480i	−1.04744	−	0.275898i
$361$	−5.42691	+	16.7023i	−0.285627	+	0.879069i
$362$	−12.0119	−	2.55321i	−0.631333	−	0.134194i
$363$	2.14344	−	1.04406i	0.112502	−	0.0547990i
$364$	−6.04097	+	1.28405i	−0.316633	+	0.0673024i
$365$	14.6276	+	13.4969i	0.765645	+	0.706459i
$366$	−0.893557	+	0.435247i	−0.0467070	+	0.0227507i
$367$	1.99047	+	18.9381i	0.103902	+	0.988558i	0.914947	+	0.403575i	$0.132232\pi$
$367$	1.99047	+	18.9381i	0.103902	+	0.988558i	−0.811045	+	0.584984i	$0.801101\pi$
$368$	−3.40442			−0.177468
$369$	2.90594	+	7.21385i	0.151277	+	0.375538i
$370$	−11.1969	−	15.8126i	−0.582099	−	0.822057i
$371$	−44.2689	+	19.7098i	−2.29833	+	1.02328i
$372$	−8.99032	+	0.309312i	−0.466126	+	0.0160371i
$373$	−4.19359	+	0.891374i	−0.217136	+	0.0461536i	−0.315195	−	0.949027i	$-0.602070\pi$
$373$	−4.19359	+	0.891374i	−0.217136	+	0.0461536i	0.0980592	+	0.995181i	$0.468737\pi$
$374$	3.65572	+	6.33189i	0.189033	+	0.327414i
$375$	14.3632	+	12.9884i	0.741712	+	0.670719i
$376$	−20.1117	+	34.8346i	−1.03718	+	1.79646i
$377$	−2.39840	+	7.38151i	−0.123524	+	0.380167i
$378$	−18.7004	+	6.04420i	−0.961845	+	0.310880i
$379$	−7.81297	−	5.67645i	−0.401325	−	0.291580i	0.368755	−	0.929526i	$-0.379784\pi$
$379$	−7.81297	−	5.67645i	−0.401325	−	0.291580i	−0.770081	+	0.637947i	$0.779784\pi$
$380$	2.18509	−	0.202794i	0.112093	−	0.0104031i
$381$	32.1647	−	8.00196i	1.64785	−	0.409953i
$382$	−1.22420	−	2.12038i	−0.0626355	−	0.108488i
$383$	8.53168	+	3.79855i	0.435948	+	0.194097i	0.612963	−	0.790111i	$-0.289977\pi$
$383$	8.53168	+	3.79855i	0.435948	+	0.194097i	−0.177015	+	0.984208i	$0.556644\pi$
$384$	0.250036	+	0.168839i	0.0127596	+	0.00861604i
$385$	6.01627	−	26.7014i	0.306618	−	1.36083i
$386$	5.30447	−	16.3255i	0.269990	−	0.830944i
$387$	17.9207	+	26.6277i	0.910960	+	1.35356i
$388$	4.34368	+	13.3685i	0.220517	+	0.678682i
$389$	−17.3886	−	19.3120i	−0.881638	−	0.979158i	0.118267	−	0.992982i	$-0.462266\pi$
$389$	−17.3886	−	19.3120i	−0.881638	−	0.979158i	−0.999904	+	0.0138240i	$0.995600\pi$
$390$	9.05809	−	1.15600i	0.458674	−	0.0585363i
$391$	2.57164	−	2.85610i	0.130054	−	0.144439i
$392$	14.2909	+	6.36272i	0.721800	+	0.321366i
$393$	1.85339	+	13.2370i	0.0934910	+	0.667718i
$394$	−2.44357	−	23.2490i	−0.123105	−	1.17127i
$395$	0.184002	−	15.1100i	0.00925812	−	0.760268i
$396$	1.49104	+	8.50735i	0.0749276	+	0.427510i
$397$	10.9374	+	7.94651i	0.548934	+	0.398824i	0.827392	−	0.561624i	$-0.189823\pi$
$397$	10.9374	+	7.94651i	0.548934	+	0.398824i	−0.278458	+	0.960448i	$0.589823\pi$
$398$	12.4880	+	13.8693i	0.625966	+	0.695205i
$399$	5.69734	−	4.44653i	0.285224	−	0.222605i
$400$	−4.05410	−	7.43431i	−0.202705	−	0.371716i
$401$	3.70665	+	6.42010i	0.185101	+	0.320604i	0.943611	−	0.331057i	$-0.107405\pi$
$401$	3.70665	+	6.42010i	0.185101	+	0.320604i	−0.758509	+	0.651662i	$0.774072\pi$
$402$	13.0372	−	15.5209i	0.650237	−	0.774112i
$403$	12.5752	−	5.59883i	0.626415	−	0.278898i
$404$	−6.19393	−	4.50015i	−0.308159	−	0.223891i
$405$	−19.5942	+	4.59009i	−0.973642	+	0.228083i
$406$	10.9493	−	7.95511i	0.543403	−	0.394806i
$407$	−14.0215	+	24.2859i	−0.695018	+	1.20381i
$408$	−9.84510	+	2.44927i	−0.487405	+	0.121257i
$409$	7.17339	−	7.96686i	0.354701	−	0.393936i	−0.539216	−	0.842167i	$-0.681279\pi$
$409$	7.17339	−	7.96686i	0.354701	−	0.393936i	0.893917	+	0.448232i	$0.147946\pi$
$410$	−2.63286	+	5.72485i	−0.130027	+	0.282730i
$411$	3.71055	+	10.2110i	0.183028	+	0.503673i
$412$	6.41534	+	1.36362i	0.316061	+	0.0671809i
$413$	5.85766	+	18.0280i	0.288237	+	0.887101i
$414$	−5.79130	+	3.07164i	−0.284627	+	0.150963i
$415$	7.53857	+	2.55132i	0.370054	+	0.125240i
$416$	9.09382	+	1.93295i	0.445861	+	0.0947707i
$417$	−24.5216	−	25.4191i	−1.20083	−	1.24478i
$418$	2.29306	+	3.97169i	0.112157	+	0.194262i
$419$	−10.9245	−	4.86390i	−0.533697	−	0.237617i	0.122149	−	0.992512i	$-0.461021\pi$
$419$	−10.9245	−	4.86390i	−0.533697	−	0.237617i	−0.655846	+	0.754895i	$0.727688\pi$
$420$	9.67054	+	5.30043i	0.471874	+	0.258635i
$421$	−8.07815	+	3.59663i	−0.393705	+	0.175289i	−0.594034	−	0.804440i	$-0.702466\pi$
$421$	−8.07815	+	3.59663i	−0.393705	+	0.175289i	0.200329	+	0.979729i	$0.435799\pi$
$422$	−12.0157	−	8.72994i	−0.584917	−	0.424967i
$423$	−1.41517	+	39.3624i	−0.0688078	+	1.91386i
$424$	42.6683			2.07215
$425$	9.29933	+	2.21462i	0.451084	+	0.107425i
$426$	−11.7069	+	9.13669i	−0.567199	+	0.442674i
$427$	1.79662	−	0.381884i	0.0869446	−	0.0184806i
$428$	0.431679	−	4.10715i	0.0208660	−	0.198527i
$429$	−6.99790	−	11.2118i	−0.337862	−	0.541312i
$430$	−5.71617	+	25.3694i	−0.275658	+	1.22342i
$431$	−2.85794	+	2.07642i	−0.137662	+	0.100017i	−0.654485	−	0.756075i	$-0.727115\pi$
$431$	−2.85794	+	2.07642i	−0.137662	+	0.100017i	0.516823	+	0.856092i	$0.327115\pi$
$432$	8.75042	+	0.933380i	0.421005	+	0.0449073i
$433$	−2.00164	+	1.45427i	−0.0961924	+	0.0698879i	−0.634842	−	0.772642i	$-0.718935\pi$
$433$	−2.00164	+	1.45427i	−0.0961924	+	0.0698879i	0.538649	+	0.842530i	$0.318935\pi$
$434$	−23.4789	−	4.99059i	−1.12702	−	0.239556i
$435$	11.8453	−	7.19433i	0.567937	−	0.344942i
$436$	−3.87801	+	0.824296i	−0.185723	+	0.0394766i
$437$	1.61307	−	1.79149i	0.0771635	−	0.0856988i
$438$	−13.8887	−	9.37848i	−0.663629	−	0.448121i
$439$	−5.56157	−	6.17675i	−0.265439	−	0.294800i	0.595660	−	0.803236i	$-0.296890\pi$
$439$	−5.56157	−	6.17675i	−0.265439	−	0.294800i	−0.861100	+	0.508436i	$0.830224\pi$
$440$	−14.4022	+	19.3237i	−0.686598	+	0.921219i
$441$	15.2821	−	1.05281i	0.727720	−	0.0501338i
$442$	3.64685	−	2.64959i	0.173463	−	0.126028i
$443$	11.6123	−	20.1132i	0.551719	−	0.955606i	−0.446432	−	0.894818i	$-0.647305\pi$
$443$	11.6123	−	20.1132i	0.551719	−	0.955606i	0.998151	−	0.0607879i	$-0.0193613\pi$
$444$	−7.84455	−	8.13164i	−0.372286	−	0.385911i
$445$	−14.4496	−	13.3326i	−0.684977	−	0.632027i
$446$	2.48807	−	23.6724i	0.117814	−	1.12092i
$447$	−5.73642	+	10.7752i	−0.271323	+	0.509651i
$448$	−18.7336	−	20.8058i	−0.885081	−	0.982982i
$449$	18.8212			0.888227			0.444114	−	0.895970i	$-0.353519\pi$
$449$	18.8212			0.888227			0.444114	+	0.895970i	$0.353519\pi$
$450$	−13.6041	−	8.98878i	−0.641303	−	0.423735i
$451$	9.12008			0.429448
$452$	−1.20648	−	1.33993i	−0.0567481	−	0.0630251i
$453$	−0.0539559	+	0.00185636i	−0.00253507	+	8.72192e-5i
$454$	−2.94117	+	27.9833i	−0.138036	+	1.31332i
$455$	−16.7598	−	1.96814i	−0.785713	−	0.0922678i
$456$	−6.17536	+	1.53631i	−0.289188	+	0.0719444i
$457$	−1.31514	+	2.27788i	−0.0615194	+	0.106555i	−0.895145	−	0.445776i	$-0.852928\pi$
$457$	−1.31514	+	2.27788i	−0.0615194	+	0.106555i	0.833625	+	0.552330i	$0.186261\pi$
$458$	20.2084	−	14.6823i	0.944278	−	0.686058i
$459$	−7.39297	+	6.63601i	−0.345074	+	0.309742i
$460$	3.48434	+	1.17923i	0.162458	+	0.0549817i
$461$	−13.0570	−	14.5013i	−0.608126	−	0.675392i	0.357923	−	0.933751i	$-0.383485\pi$
$461$	−13.0570	−	14.5013i	−0.608126	−	0.675392i	−0.966049	+	0.258359i	$0.916818\pi$
$462$	−1.61949	+	22.9895i	−0.0753453	+	1.06957i
$463$	1.02652	−	1.14007i	0.0477065	−	0.0529834i	−0.718819	−	0.695197i	$-0.755317\pi$
$463$	1.02652	−	1.14007i	0.0477065	−	0.0529834i	0.766526	+	0.642214i	$0.221984\pi$
$464$	−5.92776	+	1.25998i	−0.275189	+	0.0584933i
$465$	−23.5395	−	7.07436i	−1.09162	−	0.328066i
$466$	9.45344	+	2.00939i	0.437922	+	0.0930833i
$467$	−5.25538	+	3.81826i	−0.243190	+	0.176688i	−0.702703	−	0.711483i	$-0.748024\pi$
$467$	−5.25538	+	3.81826i	−0.243190	+	0.176688i	0.459513	+	0.888171i	$0.348024\pi$
$468$	5.12024	−	1.46250i	0.236683	−	0.0676041i
$469$	−30.3045	+	22.0175i	−1.39933	+	1.01667i
$470$	−23.9743	+	21.0637i	−1.10585	+	0.971594i
$471$	−1.12988	+	2.12235i	−0.0520621	+	0.0977929i
$472$	1.74467	−	16.5994i	0.0803049	−	0.764050i
$473$	36.8163	−	7.82554i	1.69281	−	0.359819i
$474$	1.76432	+	12.6009i	0.0810378	+	0.578777i
$475$	5.83302	+	1.38912i	0.267637	+	0.0637373i
$476$	5.44385			0.249519
$477$	36.9113	−	19.5774i	1.69005	−	0.896385i
$478$	−4.55605	−	3.31017i	−0.208389	−	0.151403i
$479$	5.00312	−	2.22753i	0.228598	−	0.101779i	−0.289241	−	0.957256i	$-0.593403\pi$
$479$	5.00312	−	2.22753i	0.228598	−	0.101779i	0.517840	+	0.855478i	$0.326736\pi$
$480$	−10.0537	−	13.2103i	−0.458885	−	0.602966i
$481$	15.7947	+	7.03224i	0.720175	+	0.320643i
$482$	−3.56290	−	6.17113i	−0.162286	−	0.281087i
$483$	11.7561	−	2.92469i	0.534920	−	0.133078i
$484$	1.10187	+	0.234209i	0.0500850	+	0.0106459i
$485$	−0.467672	+	38.4047i	−0.0212359	+	1.74387i
$486$	15.7276	−	6.30729i	0.713418	−	0.286104i
$487$	−10.8960	−	33.5344i	−0.493744	−	1.51959i	−0.818905	−	0.573929i	$-0.805419\pi$
$487$	−10.8960	−	33.5344i	−0.493744	−	1.51959i	0.325162	−	0.945658i	$-0.394581\pi$
$488$	−1.58195	−	0.336254i	−0.0716116	−	0.0152215i
$489$	1.38820	−	1.65266i	0.0627764	−	0.0747358i
$490$	9.12161	+	8.41650i	0.412072	+	0.380219i
$491$	1.91440	−	2.12616i	0.0863958	−	0.0959523i	−0.698397	−	0.715711i	$-0.746103\pi$
$491$	1.91440	−	2.12616i	0.0863958	−	0.0959523i	0.784792	+	0.619759i	$0.212769\pi$
$492$	−1.01466	+	3.53168i	−0.0457444	+	0.159220i
$493$	3.42068	−	5.92480i	0.154060	−	0.266839i
$494$	2.28749	−	1.66196i	0.102919	−	0.0747751i
$495$	−3.59279	+	23.3246i	−0.161484	+	1.04836i
$496$	8.69540	+	6.31758i	0.390435	+	0.283668i
$497$	25.0705	−	11.1621i	1.12456	−	0.500688i
$498$	−6.59883	−	1.16706i	−0.295701	−	0.0522971i
$499$	18.3438	+	31.7725i	0.821183	+	1.42233i	0.904802	+	0.425833i	$0.140019\pi$
$499$	18.3438	+	31.7725i	0.821183	+	1.42233i	−0.0836188	+	0.996498i	$0.526648\pi$
$500$	1.57416	+	9.01309i	0.0703987	+	0.403078i
$501$	−0.0534517	−	0.381756i	−0.00238805	−	0.0170556i
$502$	5.19950	+	5.77463i	0.232065	+	0.257734i
$503$	14.2611	+	10.3613i	0.635873	+	0.461989i	0.858430	−	0.512931i	$-0.171440\pi$
$503$	14.2611	+	10.3613i	0.635873	+	0.461989i	−0.222557	+	0.974920i	$0.571440\pi$
$504$	−30.0390	−	10.9684i	−1.33804	−	0.488570i
$505$	−12.0891	−	17.0726i	−0.537960	−	0.759723i
$506$	0.803556	+	7.64533i	0.0357224	+	0.339876i
$507$	11.3269	−	8.84014i	0.503045	−	0.392604i
$508$	14.3065	+	6.36965i	0.634747	+	0.282608i
$509$	−10.0917	+	11.2080i	−0.447306	+	0.496784i	−0.924057	−	0.382255i	$-0.875148\pi$
$509$	−10.0917	+	11.2080i	−0.447306	+	0.496784i	0.476751	+	0.879038i	$0.341814\pi$
$510$	−8.02175	−	0.663341i	−0.355209	−	0.0293733i
$511$	20.7228	+	23.0150i	0.916724	+	1.01812i
$512$	5.44990	+	16.7731i	0.240854	+	0.741272i
$513$	−4.63726	+	4.16245i	−0.204740	+	0.183777i
$514$	1.38585	−	4.26522i	0.0611274	−	0.188131i
$515$	15.4096	+	9.14870i	0.679028	+	0.403140i
$516$	−1.06564	+	15.1274i	−0.0469123	+	0.665948i
$517$	42.1959	+	18.7868i	1.85577	+	0.826243i
$518$	−15.0744	−	26.1096i	−0.662330	−	1.14719i
$519$	9.14339	−	31.8249i	0.401350	−	1.39696i
$520$	12.7766	+	7.58548i	0.560290	+	0.332645i
$521$	29.3467	+	21.3216i	1.28570	+	0.934118i	0.999709	−	0.0241133i	$-0.00767623\pi$
$521$	29.3467	+	21.3216i	1.28570	+	0.934118i	0.285994	+	0.958231i	$0.407676\pi$
$522$	−8.94696	+	7.49170i	−0.391598	+	0.327903i
$523$	−2.83321	+	8.71972i	−0.123888	+	0.381287i	−0.993697	−	0.112102i	$-0.964242\pi$
$523$	−2.83321	+	8.71972i	−0.123888	+	0.381287i	0.869809	+	0.493388i	$0.164242\pi$
$524$	−3.15761	+	5.46914i	−0.137941	+	0.238920i
$525$	20.3862	+	22.1892i	0.889728	+	0.968416i
$526$	9.59118	+	16.6124i	0.418195	+	0.724336i
$527$	−11.8684	+	2.52271i	−0.516996	+	0.109891i
$528$	4.84946	−	9.10919i	0.211046	−	0.396427i
$529$	−17.3200	+	7.71136i	−0.753043	+	0.335276i
$530$	32.0661	+	10.8523i	1.39286	+	0.471395i
$531$	−6.10699	−	15.1603i	−0.265021	−	0.657900i
$532$	3.41467			0.148045
$533$	−0.587747	−	5.59204i	−0.0254581	−	0.242218i
$534$	13.7197	+	9.26434i	0.593709	+	0.400907i
$535$	4.71485	−	10.2519i	0.203841	−	0.443229i
$536$	32.2620	−	6.85749i	1.39350	−	0.296198i
$537$	2.31996	−	32.9332i	0.100114	−	1.42117i
$538$	28.4277	+	6.04249i	1.22561	+	0.260510i
$539$	5.55101	−	17.0843i	0.239099	−	0.735871i
$540$	−8.63253	−	3.98627i	−0.371485	−	0.171542i
$541$	−4.66886	−	14.3693i	−0.200730	−	0.617784i	−0.999862	−	0.0166277i	$-0.994707\pi$
$541$	−4.66886	−	14.3693i	−0.200730	−	0.617784i	0.799132	−	0.601156i	$-0.205293\pi$
$542$	−2.48243	−	23.6187i	−0.106629	−	1.01451i
$543$	−18.1385	−	7.33930i	−0.778398	−	0.314960i
$544$	−7.48645	−	3.33318i	−0.320979	−	0.142909i
$545$	−10.7590	−	1.26345i	−0.460865	−	0.0541202i
$546$	14.2006	−	0.488571i	0.607728	−	0.0209089i
$547$	−35.3098	+	15.7209i	−1.50974	+	0.672178i	−0.983951	−	0.178439i	$-0.942895\pi$
$547$	−35.3098	+	15.7209i	−1.50974	+	0.672178i	−0.525785	+	0.850617i	$0.676229\pi$
$548$	−1.58623	+	4.88193i	−0.0677606	+	0.208546i
$549$	−1.52279	+	0.434956i	−0.0649912	+	0.0185635i
$550$	−15.7384	+	10.8591i	−0.671086	+	0.463032i
$551$	2.14563	−	3.71634i	0.0914069	−	0.158321i
$552$	−10.5039	−	1.85770i	−0.447076	−	0.0790691i
$553$	2.45782	−	23.3846i	0.104517	−	0.994413i
$554$	−1.61613	+	15.3765i	−0.0686629	+	0.653284i
$555$	−13.1803	−	27.9174i	−0.559472	−	1.18503i
$556$	−1.74432	−	16.5961i	−0.0739758	−	0.703833i
$557$	−16.9105			−0.716522			−0.358261	−	0.933621i	$-0.616630\pi$
$557$	−16.9105			−0.716522			−0.358261	+	0.933621i	$0.616630\pi$
$558$	20.4919	+	2.90148i	0.867490	+	0.122829i
$559$	−7.17092	−	22.0698i	−0.303297	−	0.933453i
$560$	−5.21229	−	12.1015i	−0.220259	−	0.511380i
$561$	3.97884	+	10.9493i	0.167987	+	0.462281i
$562$	5.22514	−	5.80310i	0.220409	−	0.244789i
$563$	−15.1527	+	16.8287i	−0.638609	+	0.709247i	−0.972379	−	0.233408i	$-0.925012\pi$
$563$	−15.1527	+	16.8287i	−0.638609	+	0.709247i	0.333770	+	0.942654i	$0.391679\pi$
$564$	−11.9696	+	14.2499i	−0.504010	+	0.600028i
$565$	−1.94889	−	4.52478i	−0.0819906	−	0.190359i
$566$	−4.53630	−	13.9613i	−0.190675	−	0.586837i
$567$	−31.0186	+	4.29423i	−1.30266	+	0.180341i
$568$	−24.1640			−1.01390
$569$	1.87892	+	17.8767i	0.0787683	+	0.749431i	0.960613	+	0.277890i	$0.0896352\pi$
$569$	1.87892	+	17.8767i	0.0787683	+	0.749431i	−0.881844	+	0.471540i	$0.843698\pi$
$570$	−5.03166	−	0.416082i	−0.210753	−	0.0174278i
$571$	1.55774	−	14.8209i	0.0651893	−	0.620235i	−0.912340	−	0.409434i	$-0.865726\pi$
$571$	1.55774	−	14.8209i	0.0651893	−	0.620235i	0.977529	−	0.210801i	$-0.0676071\pi$
$572$	0.652730	−	6.21031i	0.0272920	−	0.259666i
$573$	−1.33241	−	3.66663i	−0.0556620	−	0.153176i
$574$	−4.90247	+	8.49132i	−0.204625	+	0.354421i
$575$	7.98516	+	6.10409i	0.333004	+	0.254558i
$576$	17.3473	+	16.7866i	0.722803	+	0.699444i
$577$	−7.48625	+	23.0403i	−0.311657	+	0.959181i	0.665452	+	0.746441i	$0.268239\pi$
$577$	−7.48625	+	23.0403i	−0.311657	+	0.959181i	−0.977109	+	0.212740i	$0.931761\pi$
$578$	13.2520	−	5.90018i	0.551212	−	0.245415i
$579$	12.8531	−	24.1431i	0.534155	−	1.00335i
$580$	6.50335	+	0.763701i	0.270037	+	0.0317109i
$581$	11.3132	+	5.03694i	0.469349	+	0.208968i
$582$	−4.48432	−	32.0273i	−0.185881	−	1.32757i
$583$	−5.12153	−	48.7281i	−0.212112	−	2.01811i
$584$	−8.42669	−	25.9347i	−0.348699	−	1.07319i
$585$	14.5331	+	0.699783i	0.600872	+	0.0289324i
$586$	−0.105852	+	0.325780i	−0.00437272	+	0.0134579i
$587$	9.91962	+	2.10848i	0.409426	+	0.0870263i	0.408021	−	0.912973i	$-0.366219\pi$
$587$	9.91962	+	2.10848i	0.409426	+	0.0870263i	0.00140582	+	0.999999i	$0.499553\pi$
$588$	5.99816	+	4.05031i	0.247360	+	0.167032i
$589$	−7.44449	+	1.58238i	−0.306745	+	0.0652006i
$590$	5.53308	−	12.0311i	0.227793	−	0.495311i
$591$	2.61746	−	37.1563i	0.107668	−	1.52841i
$592$	1.41112	+	13.4259i	0.0579965	+	0.551800i
$593$	28.7337			1.17995			0.589975	−	0.807422i	$-0.299138\pi$
$593$	28.7337			1.17995			0.589975	+	0.807422i	$0.299138\pi$
$594$	0.0307071	−	19.8712i	0.00125993	−	0.815324i
$595$	14.0897	+	4.76845i	0.577619	+	0.195487i
$596$	−5.26895	+	2.34589i	−0.215825	+	0.0960913i
$597$	15.7453	+	25.2266i	0.644412	+	1.03246i
$598$	4.63600	−	0.985411i	0.189580	−	0.0402965i
$599$	−0.738992	−	1.27997i	−0.0301944	−	0.0522982i	0.850533	−	0.525921i	$-0.176279\pi$
$599$	−0.738992	−	1.27997i	−0.0301944	−	0.0522982i	−0.880728	+	0.473623i	$0.842946\pi$
$600$	−8.45170	−	25.1498i	−0.345039	−	1.02674i
$601$	−9.97465	+	17.2766i	−0.406874	+	0.704727i	−0.994538	−	0.104378i	$-0.966715\pi$
$601$	−9.97465	+	17.2766i	−0.406874	+	0.704727i	0.587663	+	0.809106i	$0.300048\pi$
$602$	−12.5044	+	38.4847i	−0.509642	+	1.56852i
$603$	24.7627	−	20.7349i	1.00841	−	0.844391i
$604$	−0.0206365	−	0.0149933i	−0.000839688	−	0.000610069i
$605$	2.64668	+	1.57134i	0.107603	+	0.0638840i
$606$	12.2295	+	12.6771i	0.496789	+	0.514970i
$607$	−11.5351	−	19.9793i	−0.468194	−	0.810935i	0.531146	−	0.847281i	$-0.321762\pi$
$607$	−11.5351	−	19.9793i	−0.468194	−	0.810935i	−0.999339	+	0.0363452i	$0.988428\pi$
$608$	−4.69589	−	2.09075i	−0.190444	−	0.0847910i
$609$	19.3872	−	9.44340i	0.785608	−	0.382666i
$610$	−1.10335	−	0.655059i	−0.0446732	−	0.0265225i
$611$	8.79993	−	27.0834i	0.356007	−	1.09568i
$612$	−4.68271	+	0.322599i	−0.189287	+	0.0130403i
$613$	−7.36834	−	22.6774i	−0.297605	−	0.915932i	−0.982334	−	0.187135i	$-0.940080\pi$
$613$	−7.36834	−	22.6774i	−0.297605	−	0.915932i	0.684730	−	0.728797i	$-0.259920\pi$
$614$	6.07815	+	6.75047i	0.245294	+	0.272427i
$615$	−5.71963	+	8.25183i	−0.230638	+	0.332746i
$616$	−25.0929	+	27.8685i	−1.01102	+	1.12286i
$617$	0.814192	+	0.362502i	0.0327782	+	0.0145938i	0.423060	−	0.906102i	$-0.360956\pi$
$617$	0.814192	+	0.362502i	0.0327782	+	0.0145938i	−0.390282	+	0.920695i	$0.627623\pi$
$618$	−13.9878	−	5.65984i	−0.562673	−	0.227672i
$619$	0.0314900	+	0.299608i	0.00126569	+	0.0120422i	0.995137	−	0.0985054i	$-0.0314062\pi$
$619$	0.0314900	+	0.299608i	0.00126569	+	0.0120422i	−0.993871	+	0.110548i	$0.964740\pi$
$620$	−6.71123	−	9.47780i	−0.269529	−	0.380638i
$621$	−9.93906	+	3.21242i	−0.398841	+	0.128910i
$622$	17.9653	+	13.0526i	0.720344	+	0.523361i
$623$	−20.4706	−	22.7349i	−0.820138	−	0.910856i
$624$	−5.89788	−	2.38643i	−0.236104	−	0.0955338i
$625$	−3.82065	+	24.7063i	−0.152826	+	0.988253i
$626$	8.56328	+	14.8320i	0.342258	+	0.592808i
$627$	2.49574	+	6.86799i	0.0996702	+	0.274281i
$628$	−1.03780	+	0.462060i	−0.0414129	+	0.0184382i
$629$	−12.3294	−	8.95784i	−0.491606	−	0.357173i
$630$	−19.7852	−	15.8831i	−0.788262	−	0.632799i
$631$	−11.5670	+	8.40394i	−0.460476	+	0.334556i	−0.793718	−	0.608286i	$-0.791857\pi$
$631$	−11.5670	+	8.40394i	−0.460476	+	0.334556i	0.333242	+	0.942841i	$0.391857\pi$
$632$	−10.3519	+	17.9301i	−0.411778	+	0.713221i
$633$	−16.4305	−	17.0318i	−0.653052	−	0.676953i
$634$	−9.30574	+	10.3351i	−0.369578	+	0.410458i
$635$	31.4483	+	29.0173i	1.24799	+	1.15152i
$636$	19.4394	+	3.43801i	0.770821	+	0.136326i
$637$	−10.8331	−	2.30264i	−0.429222	−	0.0912339i
$638$	4.22870	+	13.0146i	0.167416	+	0.515253i
$639$	−20.9037	+	11.0871i	−0.826939	+	0.438599i
$640$	−0.00474273	+	0.389468i	−0.000187473	+	0.0153951i
$641$	−1.18274	−	0.251398i	−0.0467152	−	0.00992963i	0.184495	−	0.982833i	$-0.440935\pi$
$641$	−1.18274	−	0.251398i	−0.0467152	−	0.00992963i	−0.231210	+	0.972904i	$0.574268\pi$
$642$	−2.62364	+	9.13196i	−0.103547	+	0.360410i
$643$	−12.3127	−	21.3262i	−0.485566	−	0.841025i	0.514297	−	0.857612i	$-0.328053\pi$
$643$	−12.3127	−	21.3262i	−0.485566	−	0.841025i	−0.999862	+	0.0165876i	$0.994720\pi$
$644$	5.22896	+	2.32808i	0.206050	+	0.0917394i
$645$	−16.0087	+	38.2190i	−0.630341	+	1.50487i
$646$	−2.27686	+	1.01372i	−0.0895818	+	0.0398844i
$647$	5.45922	+	3.96635i	0.214624	+	0.155933i	0.689903	−	0.723901i	$-0.257653\pi$
$647$	5.45922	+	3.96635i	0.214624	+	0.155933i	−0.475279	+	0.879835i	$0.657653\pi$
$648$	26.4890	+	7.65470i	1.04059	+	0.300705i
$649$	−19.1663			−0.752344
$650$	7.67256	+	8.95027i	0.300943	+	0.351058i
$651$	−35.4541	−	14.3456i	−1.38956	−	0.562250i
$652$	0.997480	−	0.212021i	0.0390643	−	0.00830338i
$653$	0.182163	−	1.73317i	0.00712860	−	0.0678241i	−0.990379	−	0.138380i	$-0.955811\pi$
$653$	0.182163	−	1.73317i	0.00712860	−	0.0678241i	0.997508	+	0.0705556i	$0.0224772\pi$
$654$	9.11606	−	0.313639i	0.356466	−	0.0122642i
$655$	−12.9630	+	11.3892i	−0.506508	+	0.445015i
$656$	3.55190	−	2.58061i	0.138678	−	0.100756i
$657$	−19.1893	−	18.5691i	−0.748645	−	0.724450i
$658$	−40.1739	+	29.1880i	−1.56614	+	1.13787i
$659$	−32.0109	−	6.80414i	−1.24697	−	0.265051i	−0.463284	−	0.886210i	$-0.653329\pi$
$659$	−32.0109	−	6.80414i	−1.24697	−	0.265051i	−0.783685	+	0.621158i	$0.786662\pi$
$660$	−8.11855	+	7.64326i	−0.316014	+	0.297513i
$661$	−43.1830	+	9.17882i	−1.67962	+	0.357015i	−0.946406	−	0.322980i	$-0.895315\pi$
$661$	−43.1830	+	9.17882i	−1.67962	+	0.357015i	−0.733217	+	0.679995i	$0.761982\pi$
$662$	−18.2809	+	20.3030i	−0.710507	+	0.789098i
$663$	6.45724	−	3.14529i	0.250778	−	0.122153i
$664$	−7.29628	−	8.10334i	−0.283150	−	0.314470i
$665$	8.83776	+	2.99102i	0.342714	+	0.115987i
$666$	14.5140	+	21.5657i	0.562405	+	0.835655i
$667$	5.81942	−	4.22805i	0.225329	−	0.163711i
$668$	0.0910656	−	0.157730i	0.00352343	−	0.00610276i
$669$	10.4728	−	36.4522i	0.404902	−	1.40932i
$670$	25.9897	+	3.05202i	1.00407	+	0.117910i
$671$	−0.194126	+	1.84698i	−0.00749415	+	0.0713020i
$672$	−13.6773	−	21.9133i	−0.527613	−	0.845326i
$673$	4.23131	+	4.69934i	0.163105	+	0.181146i	0.819157	−	0.573569i	$-0.194442\pi$
$673$	4.23131	+	4.69934i	0.163105	+	0.181146i	−0.656052	+	0.754715i	$0.727775\pi$
$674$	−20.5298			−0.790779
$675$	−18.8508	−	17.8787i	−0.725568	−	0.688151i
$676$	6.78870			0.261104
$677$	33.5415	+	37.2516i	1.28911	+	1.43170i	0.844116	+	0.536161i	$0.180126\pi$
$677$	33.5415	+	37.2516i	1.28911	+	1.43170i	0.444989	+	0.895536i	$0.353207\pi$
$678$	2.19645	+	3.51908i	0.0843541	+	0.135150i
$679$	−6.24697	+	59.4359i	−0.239737	+	2.28094i
$680$	−9.62582	−	8.88173i	−0.369133	−	0.340599i
$681$	−12.3800	+	43.0904i	−0.474402	+	1.65123i
$682$	12.1350	−	21.0185i	0.464674	−	0.804838i
$683$	15.2867	−	11.1065i	0.584931	−	0.424977i	−0.255568	−	0.966791i	$-0.582262\pi$
$683$	15.2867	−	11.1065i	0.584931	−	0.424977i	0.840498	+	0.541814i	$0.182262\pi$
$684$	−2.93724	+	0.202351i	−0.112308	+	0.00773709i
$685$	−8.38169	+	11.2459i	−0.320248	+	0.429682i
$686$	−4.79302	−	5.32319i	−0.182999	−	0.203240i
$687$	35.7818	−	17.4291i	1.36516	−	0.664963i
$688$	12.1241	−	13.4652i	0.462228	−	0.513357i
$689$	−29.5479	+	6.28060i	−1.12569	+	0.239272i
$690$	−7.42142	−	4.06769i	−0.282529	−	0.154854i
$691$	−27.3183	−	5.80669i	−1.03924	−	0.220897i	−0.343470	−	0.939163i	$-0.611603\pi$
$691$	−27.3183	−	5.80669i	−1.03924	−	0.220897i	−0.695768	+	0.718266i	$0.744936\pi$
$692$	12.6570	−	9.19584i	0.481146	−	0.349573i
$693$	−8.92049	+	35.6217i	−0.338861	+	1.35316i
$694$	−24.8191	+	18.0321i	−0.942120	+	0.684490i
$695$	10.0225	−	44.4816i	0.380174	−	1.68728i
$696$	−18.9769	+	0.652901i	−0.719318	+	0.0247482i
$697$	−0.518077	+	4.92917i	−0.0196236	+	0.186706i
$698$	−21.5948	+	4.59012i	−0.817376	+	0.173739i
$699$	14.2751	+	5.77606i	0.539933	+	0.218471i
$700$	1.14293	+	14.1910i	0.0431988	+	0.536368i
$701$	−14.8415			−0.560556			−0.280278	−	0.959919i	$-0.590427\pi$
$701$	−14.8415			−0.560556			−0.280278	+	0.959919i	$0.590427\pi$
$702$	−12.1861	+	1.26178i	−0.459935	+	0.0476227i
$703$	−7.73365	−	5.61882i	−0.291680	−	0.211918i
$704$	25.8606	−	11.5139i	0.974657	−	0.433945i
$705$	−43.4613	+	26.3966i	−1.63685	+	0.994155i
$706$	−8.95506	−	3.98705i	−0.337028	−	0.150055i
$707$	−16.2756	−	28.1902i	−0.612107	−	1.06020i
$708$	2.13236	−	7.42200i	0.0801391	−	0.278936i
$709$	−1.56454	−	0.332554i	−0.0587577	−	0.0124893i	0.178439	−	0.983951i	$-0.442895\pi$
$709$	−1.56454	−	0.332554i	−0.0587577	−	0.0124893i	−0.237197	+	0.971462i	$0.576229\pi$
$710$	−18.1598	−	6.14592i	−0.681524	−	0.230652i
$711$	−0.728416	+	20.2607i	−0.0273177	+	0.759834i
$712$	8.32414	+	25.6191i	0.311960	+	0.960115i
$713$	−12.4788	−	2.65244i	−0.467334	−	0.0993348i
$714$	−12.3333	−	2.18124i	−0.461561	−	0.0816309i
$715$	7.12919	−	15.5016i	0.266617	−	0.579728i
$716$	10.4377	−	11.5922i	0.390073	−	0.433220i
$717$	−6.23000	−	6.45801i	−0.232664	−	0.241179i
$718$	5.00266	−	8.66487i	0.186698	−	0.323370i
$719$	−19.6770	+	14.2962i	−0.733830	+	0.533159i	−0.890773	−	0.454449i	$-0.849836\pi$
$719$	−19.6770	+	14.2962i	−0.733830	+	0.533159i	0.156943	+	0.987608i	$0.449836\pi$
$720$	5.20065	+	10.1006i	0.193817	+	0.376427i
$721$	22.5596	+	16.3905i	0.840164	+	0.610415i
$722$	17.4399	−	7.76473i	0.649045	−	0.288973i
$723$	−3.87782	−	10.6713i	−0.144218	−	0.396871i
$724$	−4.62252	−	8.00644i	−0.171795	−	0.297557i
$725$	16.1629	+	7.67309i	0.600273	+	0.284971i
$726$	−2.40249	−	0.972108i	−0.0891646	−	0.0360783i
$727$	−8.01143	−	8.89759i	−0.297127	−	0.329993i	0.576033	−	0.817426i	$-0.304600\pi$
$727$	−8.01143	−	8.89759i	−0.297127	−	0.329993i	−0.873160	+	0.487433i	$0.837933\pi$
$728$	18.7049	+	13.5899i	0.693250	+	0.503675i
$729$	26.4272	−	5.53197i	0.978786	−	0.204888i
$730$	0.263443	−	21.6337i	0.00975048	−	0.800700i
$731$	2.13811	+	20.3428i	0.0790810	+	0.752406i
$732$	−0.693632	−	0.280661i	−0.0256374	−	0.0103735i
$733$	−9.53117	−	4.24355i	−0.352042	−	0.156739i	0.223094	−	0.974797i	$-0.428384\pi$
$733$	−9.53117	−	4.24355i	−0.352042	−	0.156739i	−0.575136	+	0.818058i	$0.695051\pi$
$734$	13.8508	−	15.3829i	0.511242	−	0.567792i
$735$	11.9765	+	15.7369i	0.441760	+	0.580464i
$736$	−5.76548	−	6.40322i	−0.212519	−	0.236026i
$737$	−11.7039	−	36.0208i	−0.431117	−	1.32684i
$738$	3.71383	−	7.59460i	0.136708	−	0.279561i
$739$	9.63830	−	29.6636i	0.354551	−	1.09119i	−0.601719	−	0.798708i	$-0.705517\pi$
$739$	9.63830	−	29.6636i	0.354551	−	1.09119i	0.956270	−	0.292487i	$-0.0944827\pi$
$740$	3.20622	−	14.2298i	0.117863	−	0.523098i
$741$	4.05031	−	1.97289i	0.148792	−	0.0724758i
$742$	48.1217	+	21.4252i	1.76660	+	0.786543i
$743$	17.4838	+	30.2828i	0.641418	+	1.11097i	0.985116	+	0.171889i	$0.0549870\pi$
$743$	17.4838	+	30.2828i	0.641418	+	1.11097i	−0.343698	+	0.939080i	$0.611680\pi$
$744$	23.3812	+	24.2369i	0.857197	+	0.888569i
$745$	−15.6918	+	1.45633i	−0.574903	+	0.0533556i
$746$	3.77035	+	2.73932i	0.138042	+	0.100294i
$747$	−10.0299	−	3.66228i	−0.366974	−	0.133996i
$748$	−1.70093	+	5.23491i	−0.0621920	+	0.191407i
$749$	8.77921	−	15.2060i	0.320785	−	0.555617i
$750$	0.0450274	−	21.0503i	0.00164417	−	0.768647i
$751$	−13.7941	−	23.8921i	−0.503354	−	0.871835i	−0.999992	−	0.00387741i	$-0.998766\pi$
$751$	−13.7941	−	23.8921i	−0.503354	−	0.871835i	0.496638	−	0.867958i	$-0.334568\pi$
$752$	21.7495	−	4.62300i	0.793122	−	0.168583i
$753$	6.55571	+	10.5034i	0.238904	+	0.382764i
$754$	7.70747	−	3.43159i	0.280689	−	0.124971i
$755$	−0.0402778	−	0.0568815i	−0.00146586	−	0.00207013i
$756$	−12.8018	−	7.41751i	−0.465596	−	0.269772i
$757$	31.2879			1.13718			0.568589	−	0.822622i	$-0.307489\pi$
$757$	31.2879			1.13718			0.568589	+	0.822622i	$0.307489\pi$
$758$	1.09733	+	10.4404i	0.0398567	+	0.379211i
$759$	−0.860738	+	12.2187i	−0.0312428	+	0.443510i
$760$	−6.03781	−	5.57108i	−0.219015	−	0.202084i
$761$	18.3181	−	3.89364i	0.664032	−	0.141144i	0.136448	−	0.990647i	$-0.456431\pi$
$761$	18.3181	−	3.89364i	0.664032	−	0.141144i	0.527584	+	0.849503i	$0.323098\pi$
$762$	−29.8597	−	20.1630i	−1.08170	−	0.730429i
$763$	−16.4880	−	3.50463i	−0.596905	−	0.126876i
$764$	0.569594	−	1.75303i	0.0206072	−	0.0634224i
$765$	−12.4023	−	3.26679i	−0.448404	−	0.118111i
$766$	−3.13711	−	9.65503i	−0.113348	−	0.348850i

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.727367 - 0.807823i) q^{2} +(-0.917090 - 1.46933i) q^{3} +(0.0855417 - 0.813875i) q^{4} +(0.934297 - 2.03152i) q^{5} +(-0.519901 + 1.80959i) q^{6} +(1.73969 - 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(-1.31789 + 2.69503i) q^{9} +O(q^{10})\)	\(q+(-0.727367 - 0.807823i) q^{2} +(-0.917090 - 1.46933i) q^{3} +(0.0855417 - 0.813875i) q^{4} +(0.934297 - 2.03152i) q^{5} +(-0.519901 + 1.80959i) q^{6} +(1.73969 - 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(-1.31789 + 2.69503i) q^{9} +(-2.32069 + 0.722917i) q^{10} +(2.35402 + 2.61440i) q^{11} +(-1.27430 + 0.620708i) q^{12} +(1.45133 - 1.61187i) q^{13} +(-3.69956 + 0.786365i) q^{14} +(-3.84182 + 0.490296i) q^{15} +(1.65656 + 0.352114i) q^{16} +(-1.54674 + 1.12377i) q^{17} +(3.13570 - 0.895651i) q^{18} +(-0.970198 + 0.704890i) q^{19} +(-1.57349 - 0.934181i) q^{20} +(-6.02291 + 0.207218i) q^{21} +(0.399739 - 3.80326i) q^{22} +(-1.96627 + 0.417944i) q^{23} +(4.91898 + 1.99035i) q^{24} +(-3.25418 - 3.79609i) q^{25} -2.35776 q^{26} +(5.16852 - 0.535160i) q^{27} +(-2.30358 - 1.67365i) q^{28} +(-3.26898 + 1.45544i) q^{29} +(3.19049 + 2.74689i) q^{30} +(5.79773 + 2.58132i) q^{31} +(2.14316 + 3.71207i) q^{32} +(1.68259 - 5.85649i) q^{33} +(2.03286 + 0.432098i) q^{34} +(-4.49607 - 6.34948i) q^{35} +(2.08068 + 1.30314i) q^{36} +(2.46324 + 7.58107i) q^{37} +(1.27512 + 0.271034i) q^{38} +(-3.69938 - 0.654265i) q^{39} +(1.34261 + 6.71767i) q^{40} +(1.73464 - 1.92652i) q^{41} +(4.54826 + 4.71472i) q^{42} +(5.34941 - 9.26545i) q^{43} +(2.32917 - 1.69224i) q^{44} +(4.24371 + 5.19528i) q^{45} +(1.76783 + 1.28440i) q^{46} +(11.9942 - 5.34016i) q^{47} +(-1.00185 - 2.75697i) q^{48} +(-2.55306 - 4.42203i) q^{49} +(-0.699589 + 5.38996i) q^{50} +(3.06970 + 1.24208i) q^{51} +(-1.18771 - 1.31909i) q^{52} +(-11.2674 - 8.18624i) q^{53} +(-4.19173 - 3.78599i) q^{54} +(7.51058 - 2.33962i) q^{55} +(1.11423 + 10.6012i) q^{56} +(1.92548 + 0.779098i) q^{57} +(3.55349 + 1.58212i) q^{58} +(-3.64544 + 4.04867i) q^{59} +(0.0704032 + 3.16871i) q^{60} +(0.353232 + 0.392304i) q^{61} +(-2.13183 - 6.56111i) q^{62} +(5.82802 + 8.65963i) q^{63} +(2.48651 - 7.65270i) q^{64} +(-1.91857 - 4.45438i) q^{65} +(-5.95487 + 2.90059i) q^{66} +(-9.83507 - 4.37885i) q^{67} +(0.782301 + 1.35499i) q^{68} +(2.41735 + 2.50582i) q^{69} +(-1.85897 + 8.25044i) q^{70} +(6.38098 + 4.63605i) q^{71} +(-1.58667 - 9.05296i) q^{72} +(-2.75054 + 8.46529i) q^{73} +(4.33248 - 7.50408i) q^{74} +(-2.59336 + 8.26284i) q^{75} +(0.490700 + 0.849917i) q^{76} +(11.9731 - 2.54496i) q^{77} +(2.16228 + 3.46434i) q^{78} +(6.17366 - 2.74869i) q^{79} +(2.26305 - 3.03637i) q^{80} +(-5.52633 - 7.10350i) q^{81} -2.81801 q^{82} +(0.372037 + 3.53969i) q^{83} +(-0.346560 + 4.91962i) q^{84} +(0.837858 + 4.19218i) q^{85} +(-11.3758 + 2.41801i) q^{86} +(5.13649 + 3.46846i) q^{87} +(-10.5425 - 2.24087i) q^{88} +(2.71707 - 8.36227i) q^{89} +(1.11013 - 7.20704i) q^{90} +(-2.33207 - 7.17736i) q^{91} +(0.171956 + 1.63605i) q^{92} +(-1.52423 - 10.8861i) q^{93} +(-13.0381 - 5.80493i) q^{94} +(0.525548 + 2.62956i) q^{95} +(3.48880 - 6.55333i) q^{96} +(-15.6914 + 6.98627i) q^{97} +(-1.71520 + 5.27886i) q^{98} +(-10.1482 + 2.89865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

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