LMFDB - Embedded newform 507.2.q.b.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.27058 + 0.183300i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(3.14784 + 0.511574i) q^{4} +(2.05738 + 1.82268i) q^{5} +(-1.82111 - 1.36847i) q^{6} +(0.613173 - 0.638380i) q^{7} +(2.63011 + 0.648264i) q^{8} +(0.428693 + 0.903450i) q^{9} +(4.33734 + 4.51565i) q^{10} +(-2.07407 + 4.37102i) q^{11} +(-2.38711 - 2.11479i) q^{12} +(2.41492 - 2.67734i) q^{13} +(1.50927 - 1.33710i) q^{14} +(-0.764715 - 2.64010i) q^{15} +(-0.196976 - 0.0657601i) q^{16} +(-0.313274 + 0.326153i) q^{17} +(0.807779 + 2.12994i) q^{18} +(2.37867 - 4.11997i) q^{19} +(5.54386 + 6.78999i) q^{20} +(-0.859440 + 0.211833i) q^{21} +(-5.51056 + 9.54458i) q^{22} +(-0.832328 - 1.44163i) q^{23} +(-1.87647 - 1.95361i) q^{24} +(0.307964 + 2.53631i) q^{25} +(5.97403 - 5.63647i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.25675 - 1.69584i) q^{28} +(-4.00678 - 0.323460i) q^{29} +(-1.25242 - 6.13474i) q^{30} +(-0.237716 + 1.95777i) q^{31} +(-5.41932 - 2.30896i) q^{32} +(4.08915 - 2.58582i) q^{33} +(-0.771098 + 0.683134i) q^{34} +(2.42509 - 0.195773i) q^{35} +(0.887275 + 3.06323i) q^{36} +(6.81284 - 2.90268i) q^{37} +(6.15615 - 8.91872i) q^{38} +(-3.47201 + 0.972172i) q^{39} +(4.22955 + 6.12756i) q^{40} +(-4.88393 - 3.08841i) q^{41} +(-1.99026 + 0.323448i) q^{42} +(-5.14583 - 2.19243i) q^{43} +(-8.76496 + 12.6982i) q^{44} +(-0.764715 + 2.64010i) q^{45} +(-1.62562 - 3.42592i) q^{46} +(-1.89526 + 4.99740i) q^{47} +(0.131335 + 0.160857i) q^{48} +(0.250313 + 6.21145i) q^{49} +(0.234351 + 5.81535i) q^{50} +(0.439094 - 0.108227i) q^{51} +(8.97144 - 7.19244i) q^{52} +(3.38092 + 0.833322i) q^{53} +(0.455652 - 2.23193i) q^{54} +(-12.2341 + 5.21246i) q^{55} +(2.02655 - 1.28151i) q^{56} +(-4.21241 + 2.21084i) q^{57} +(-9.03842 - 1.46889i) q^{58} +(-8.53430 + 2.84917i) q^{59} +(-1.05659 - 8.70184i) q^{60} +(1.48056 - 5.11150i) q^{61} +(-0.898614 + 4.40170i) q^{62} +(0.839607 + 0.280302i) q^{63} +(-11.5140 - 6.04303i) q^{64} +(9.84832 - 1.10668i) q^{65} +(9.75872 - 5.12177i) q^{66} +(-4.59669 + 0.747036i) q^{67} +(-1.15299 + 0.866415i) q^{68} +(-0.0670290 + 1.66331i) q^{69} +5.54224 q^{70} +(0.602647 - 14.9545i) q^{71} +(0.541835 + 2.65408i) q^{72} +(2.97453 + 4.30935i) q^{73} +(16.0012 - 5.34198i) q^{74} +(1.09528 - 2.30826i) q^{75} +(9.59534 - 11.7522i) q^{76} +(1.51861 + 4.00424i) q^{77} +(-8.06169 + 1.57097i) q^{78} +(1.75279 - 4.62173i) q^{79} +(-0.285393 - 0.494316i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-10.5233 - 7.90772i) q^{82} +(-10.1110 - 5.30667i) q^{83} +(-2.81375 + 0.227149i) q^{84} +(-1.23899 + 0.100022i) q^{85} +(-11.2822 - 5.92133i) q^{86} +(3.21361 + 2.41487i) q^{87} +(-8.28862 + 10.1517i) q^{88} +(7.09801 + 12.2941i) q^{89} +(-2.22028 + 5.85440i) q^{90} +(-0.228401 - 3.18331i) q^{91} +(-1.88253 - 4.96384i) q^{92} +(1.24728 - 1.52764i) q^{93} +(-5.21937 + 10.9996i) q^{94} +(12.4032 - 4.14079i) q^{95} +(3.34630 + 4.84795i) q^{96} +(0.170500 + 0.835166i) q^{97} +(-0.570205 + 14.1495i) q^{98} -4.83814 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	2.27058	+	0.183300i	1.60554	+	0.129613i	0.850469	−	0.526026i	$-0.176318\pi$
$2$	2.27058	+	0.183300i	1.60554	+	0.129613i	0.755075	+	0.655638i	$0.227600\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	3.14784	+	0.511574i	1.57392	+	0.255787i
$5$	2.05738	+	1.82268i	0.920086	+	0.815125i	0.983134	−	0.182885i	$-0.0585437\pi$
$5$	2.05738	+	1.82268i	0.920086	+	0.815125i	−0.0630481	+	0.998010i	$0.520082\pi$
$6$	−1.82111	−	1.36847i	−0.743463	−	0.558676i
$7$	0.613173	−	0.638380i	0.231757	−	0.241285i	−0.595162	−	0.803606i	$-0.702912\pi$
$7$	0.613173	−	0.638380i	0.231757	−	0.241285i	0.826919	+	0.562321i	$0.190091\pi$
$8$	2.63011	+	0.648264i	0.929885	+	0.229196i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	4.33734	+	4.51565i	1.37159	+	1.42797i
$11$	−2.07407	+	4.37102i	−0.625357	+	1.31791i	0.305383	+	0.952230i	$0.401216\pi$
$11$	−2.07407	+	4.37102i	−0.625357	+	1.31791i	−0.930740	+	0.365682i	$0.880836\pi$
$12$	−2.38711	−	2.11479i	−0.689098	−	0.610488i
$13$	2.41492	−	2.67734i	0.669778	−	0.742561i
$13$	2.41492	−	2.67734i	0.669778	−	0.742561i
$14$	1.50927	−	1.33710i	0.403370	−	0.357355i
$15$	−0.764715	−	2.64010i	−0.197449	−	0.681672i
$16$	−0.196976	−	0.0657601i	−0.0492439	−	0.0164400i
$17$	−0.313274	+	0.326153i	−0.0759801	+	0.0791037i	−0.758107	−	0.652130i	$-0.773876\pi$
$17$	−0.313274	+	0.326153i	−0.0759801	+	0.0791037i	0.682127	+	0.731234i	$0.261055\pi$
$18$	0.807779	+	2.12994i	0.190395	+	0.502031i
$19$	2.37867	−	4.11997i	0.545704	−	0.945187i	−0.452859	−	0.891582i	$-0.649596\pi$
$19$	2.37867	−	4.11997i	0.545704	−	0.945187i	0.998562	−	0.0536042i	$-0.0170709\pi$
$20$	5.54386	+	6.78999i	1.23964	+	1.51829i
$21$	−0.859440	+	0.211833i	−0.187545	+	0.0462257i
$22$	−5.51056	+	9.54458i	−1.17486	+	2.03491i
$23$	−0.832328	−	1.44163i	−0.173552	−	0.300602i	0.766107	−	0.642713i	$-0.222191\pi$
$23$	−0.832328	−	1.44163i	−0.173552	−	0.300602i	−0.939659	+	0.342112i	$0.888858\pi$
$24$	−1.87647	−	1.95361i	−0.383033	−	0.398779i
$25$	0.307964	+	2.53631i	0.0615928	+	0.507262i
$26$	5.97403	−	5.63647i	1.17160	−	1.10540i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	2.25675	−	1.69584i	0.426486	−	0.320483i
$29$	−4.00678	−	0.323460i	−0.744040	−	0.0600651i	−0.297368	−	0.954763i	$-0.596109\pi$
$29$	−4.00678	−	0.323460i	−0.744040	−	0.0600651i	−0.446672	+	0.894698i	$0.647391\pi$
$30$	−1.25242	−	6.13474i	−0.228659	−	1.12005i
$31$	−0.237716	+	1.95777i	−0.0426951	+	0.351626i	0.955669	+	0.294444i	$0.0951345\pi$
$31$	−0.237716	+	1.95777i	−0.0426951	+	0.351626i	−0.998364	+	0.0571816i	$0.981789\pi$
$32$	−5.41932	−	2.30896i	−0.958010	−	0.408170i
$33$	4.08915	−	2.58582i	0.711829	−	0.450133i
$34$	−0.771098	+	0.683134i	−0.132242	+	0.117156i
$35$	2.42509	−	0.195773i	0.409914	−	0.0330917i
$36$	0.887275	+	3.06323i	0.147879	+	0.510538i
$37$	6.81284	−	2.90268i	1.12002	−	0.477198i	0.249033	−	0.968495i	$-0.419887\pi$
$37$	6.81284	−	2.90268i	1.12002	−	0.477198i	0.870992	+	0.491297i	$0.163477\pi$
$38$	6.15615	−	8.91872i	0.998660	−	1.44681i
$39$	−3.47201	+	0.972172i	−0.555967	+	0.155672i
$40$	4.22955	+	6.12756i	0.668751	+	0.968853i
$41$	−4.88393	−	3.08841i	−0.762742	−	0.482329i	0.0955917	−	0.995421i	$-0.469526\pi$
$41$	−4.88393	−	3.08841i	−0.762742	−	0.482329i	−0.858334	+	0.513092i	$0.828500\pi$
$42$	−1.99026	+	0.323448i	−0.307103	+	0.0499092i
$43$	−5.14583	−	2.19243i	−0.784732	−	0.334343i	−0.0378359	−	0.999284i	$-0.512046\pi$
$43$	−5.14583	−	2.19243i	−0.784732	−	0.334343i	−0.746896	+	0.664941i	$0.768457\pi$
$44$	−8.76496	+	12.6982i	−1.32137	+	1.91433i
$45$	−0.764715	+	2.64010i	−0.113997	+	0.393563i
$46$	−1.62562	−	3.42592i	−0.239684	−	0.505124i
$47$	−1.89526	+	4.99740i	−0.276452	+	0.728945i	0.722828	+	0.691028i	$0.242842\pi$
$47$	−1.89526	+	4.99740i	−0.276452	+	0.728945i	−0.999281	+	0.0379176i	$0.987928\pi$
$48$	0.131335	+	0.160857i	0.0189566	+	0.0232176i
$49$	0.250313	+	6.21145i	0.0357590	+	0.887350i
$50$	0.234351	+	5.81535i	0.0331422	+	0.822415i
$51$	0.439094	−	0.108227i	0.0614854	−	0.0151548i
$52$	8.97144	−	7.19244i	1.24412	−	0.997412i
$53$	3.38092	+	0.833322i	0.464405	+	0.114466i	0.464574	−	0.885534i	$-0.346208\pi$
$53$	3.38092	+	0.833322i	0.464405	+	0.114466i	−0.000168798		1.00000i	$0.500054\pi$
$54$	0.455652	−	2.23193i	0.0620064	−	0.303728i
$55$	−12.2341	+	5.21246i	−1.64965	+	0.702848i
$56$	2.02655	−	1.28151i	0.270809	−	0.171249i
$57$	−4.21241	+	2.21084i	−0.557947	+	0.292833i
$58$	−9.03842	−	1.46889i	−1.18680	−	0.192874i
$59$	−8.53430	+	2.84917i	−1.11107	+	0.370930i	−0.812209	−	0.583366i	$-0.801735\pi$
$59$	−8.53430	+	2.84917i	−1.11107	+	0.370930i	−0.298862	+	0.954296i	$0.596607\pi$
$60$	−1.05659	−	8.70184i	−0.136406	−	1.12340i
$61$	1.48056	−	5.11150i	0.189567	−	0.654460i	−0.808276	−	0.588804i	$-0.799599\pi$
$61$	1.48056	−	5.11150i	0.189567	−	0.654460i	0.997842	−	0.0656557i	$-0.0209139\pi$
$62$	−0.898614	+	4.40170i	−0.114124	+	0.559017i
$63$	0.839607	+	0.280302i	0.105781	+	0.0353147i
$64$	−11.5140	−	6.04303i	−1.43925	−	0.755379i
$65$	9.84832	−	1.10668i	1.22153	−	0.137267i
$66$	9.75872	−	5.12177i	1.20122	−	0.630447i
$67$	−4.59669	+	0.747036i	−0.561576	+	0.0912649i	−0.434572	−	0.900637i	$-0.643100\pi$
$67$	−4.59669	+	0.747036i	−0.561576	+	0.0912649i	−0.127004	+	0.991902i	$0.540536\pi$
$68$	−1.15299	+	0.866415i	−0.139820	+	0.105068i
$69$	−0.0670290	+	1.66331i	−0.00806934	+	0.200239i
$70$	5.54224			0.662425
$71$	0.602647	−	14.9545i	0.0715210	−	1.77478i	−0.423501	−	0.905896i	$-0.639199\pi$
$71$	0.602647	−	14.9545i	0.0715210	−	1.77478i	0.495022	−	0.868880i	$-0.335160\pi$
$72$	0.541835	+	2.65408i	0.0638558	+	0.312787i
$73$	2.97453	+	4.30935i	0.348142	+	0.504371i	0.957464	−	0.288552i	$-0.0931737\pi$
$73$	2.97453	+	4.30935i	0.348142	+	0.504371i	−0.609322	+	0.792923i	$0.708558\pi$
$74$	16.0012	−	5.34198i	1.86010	−	0.620992i
$75$	1.09528	−	2.30826i	0.126472	−	0.266535i
$76$	9.59534	−	11.7522i	1.10066	−	1.34807i
$77$	1.51861	+	4.00424i	0.173061	+	0.456325i
$78$	−8.06169	+	1.57097i	−0.912807	+	0.177878i
$79$	1.75279	−	4.62173i	0.197204	−	0.519985i	−0.799540	−	0.600613i	$-0.794923\pi$
$79$	1.75279	−	4.62173i	0.197204	−	0.519985i	0.996744	+	0.0806278i	$0.0256925\pi$
$80$	−0.285393	−	0.494316i	−0.0319080	−	0.0552662i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−10.5233	−	7.90772i	−1.16210	−	0.873261i
$83$	−10.1110	−	5.30667i	−1.10983	−	0.582483i	−0.192773	−	0.981243i	$-0.561748\pi$
$83$	−10.1110	−	5.30667i	−1.10983	−	0.582483i	−0.917055	+	0.398761i	$0.869440\pi$
$84$	−2.81375	+	0.227149i	−0.307005	+	0.0247840i
$85$	−1.23899	+	0.100022i	−0.134388	+	0.0108489i
$86$	−11.2822	−	5.92133i	−1.21659	−	0.638514i
$87$	3.21361	+	2.41487i	0.344535	+	0.258901i
$88$	−8.28862	+	10.1517i	−0.883570	+	1.08218i
$89$	7.09801	+	12.2941i	0.752387	+	1.30317i	0.946663	+	0.322226i	$0.104431\pi$
$89$	7.09801	+	12.2941i	0.752387	+	1.30317i	−0.194275	+	0.980947i	$0.562236\pi$
$90$	−2.22028	+	5.85440i	−0.234038	+	0.617108i
$91$	−0.228401	−	3.18331i	−0.0239429	−	0.333702i
$92$	−1.88253	−	4.96384i	−0.196268	−	0.517516i
$93$	1.24728	−	1.52764i	0.129336	−	0.158408i
$94$	−5.21937	+	10.9996i	−0.538337	+	1.13452i
$95$	12.4032	−	4.14079i	1.27254	−	0.424836i
$96$	3.34630	+	4.84795i	0.341530	+	0.494792i
$97$	0.170500	+	0.835166i	0.0173117	+	0.0847982i	0.987529	−	0.157439i	$-0.0503238\pi$
$97$	0.170500	+	0.835166i	0.0173117	+	0.0847982i	−0.970217	+	0.242237i	$0.922119\pi$
$98$	−0.570205	+	14.1495i	−0.0575994	+	1.42931i
$99$	−4.83814			−0.486251
$100$	−0.328089	+	8.14145i	−0.0328089	+	0.814145i
$101$	−13.7143	+	10.3057i	−1.36463	+	1.02545i	−0.369259	+	0.929326i	$0.620389\pi$
$101$	−13.7143	+	10.3057i	−1.36463	+	1.02545i	−0.995369	+	0.0961253i	$0.969355\pi$
$102$	1.01684	−	0.165252i	0.100682	−	0.0163624i
$103$	−1.67689	+	0.880102i	−0.165229	+	0.0867191i	−0.545311	−	0.838234i	$-0.683588\pi$
$103$	−1.67689	+	0.880102i	−0.165229	+	0.0867191i	0.380081	+	0.924953i	$0.375896\pi$
$104$	8.08713	−	5.47620i	0.793009	−	0.536986i
$105$	−2.15429	−	1.13066i	−0.210237	−	0.110341i
$106$	7.52390	+	2.51185i	0.730786	+	0.243972i
$107$	−0.161571	+	0.791428i	−0.0156197	+	0.0765102i	−0.986853	−	0.161618i	$-0.948329\pi$
$107$	−0.161571	+	0.791428i	−0.0156197	+	0.0765102i	0.971234	+	0.238128i	$0.0765339\pi$
$108$	0.887275	−	3.06323i	0.0853780	−	0.294759i
$109$	−0.608721	−	5.01327i	−0.0583049	−	0.480184i	−0.992390	−	0.123134i	$-0.960706\pi$
$109$	−0.608721	−	5.01327i	−0.0583049	−	0.480184i	0.934085	−	0.357050i	$-0.116217\pi$
$110$	−28.7340	+	9.59281i	−2.73968	+	0.914638i
$111$	−7.30953	−	1.18791i	−0.693790	−	0.112752i
$112$	−0.162760	+	0.0854230i	−0.0153794	+	0.00807172i
$113$	10.1019	−	6.38809i	0.950311	−	0.600941i	0.0331475	−	0.999450i	$-0.489447\pi$
$113$	10.1019	−	6.38809i	0.950311	−	0.600941i	0.917164	+	0.398510i	$0.130473\pi$
$114$	−9.96987	+	4.24777i	−0.933764	+	0.397840i
$115$	0.915221	−	4.48305i	0.0853448	−	0.418046i
$116$	−12.4472	−	3.06796i	−1.15570	−	0.284853i
$117$	3.45410	+	1.03400i	0.319332	+	0.0955936i
$118$	−19.9001	+	4.90493i	−1.83195	+	0.451536i
$119$	0.0161185	+	0.399976i	0.00147758	+	0.0366657i
$120$	−0.299802	−	7.43951i	−0.0273680	−	0.679131i
$121$	−7.84712	−	9.61098i	−0.713374	−	0.873725i
$122$	4.29868	−	11.3347i	0.389184	−	1.02619i
$123$	2.47720	+	5.22059i	0.223362	+	0.470725i
$124$	−1.74984	+	6.04114i	−0.157140	+	0.542510i
$125$	3.81771	−	5.53091i	0.341466	−	0.494700i
$126$	1.85502	+	0.790349i	0.165258	+	0.0704099i
$127$	−5.41650	+	0.880267i	−0.480637	+	0.0781111i	−0.395903	−	0.918293i	$-0.629568\pi$
$127$	−5.41650	+	0.880267i	−0.480637	+	0.0781111i	−0.0847341	+	0.996404i	$0.527004\pi$
$128$	−15.0783	−	9.53496i	−1.33275	−	0.842780i
$129$	3.17742	+	4.60329i	0.279757	+	0.405297i
$130$	22.5643	−	0.707618i	1.97902	−	0.0620622i
$131$	−8.11040	+	11.7499i	−0.708609	+	1.02660i	0.288989	+	0.957332i	$0.406681\pi$
$131$	−8.11040	+	11.7499i	−0.708609	+	1.02660i	−0.997598	+	0.0692651i	$0.977935\pi$
$132$	14.1948	−	6.04785i	1.23550	−	0.526398i
$133$	−1.17158	−	4.04475i	−0.101588	−	0.350724i
$134$	−10.5741	+	0.853630i	−0.913463	+	0.0737424i
$135$	2.05738	−	1.82268i	0.177071	−	0.156871i
$136$	−1.03538	+	0.654734i	−0.0887830	+	0.0561430i
$137$	17.9063	+	7.62916i	1.52984	+	0.651804i	0.982694	−	0.185234i	$-0.0593044\pi$
$137$	17.9063	+	7.62916i	1.52984	+	0.651804i	0.547145	+	0.837038i	$0.315715\pi$
$138$	−0.457079	+	3.76439i	−0.0389092	+	0.320446i
$139$	3.91724	+	19.1879i	0.332256	+	1.62750i	0.711840	+	0.702341i	$0.247862\pi$
$139$	3.91724	+	19.1879i	0.332256	+	1.62750i	−0.379584	+	0.925157i	$0.623933\pi$
$140$	7.73394	+	0.624348i	0.653637	+	0.0527671i
$141$	4.27279	−	3.21080i	0.359834	−	0.270398i
$142$	4.10953	−	33.8450i	0.344864	−	2.84021i
$143$	6.69399	+	16.1087i	0.559780	+	1.34707i
$144$	−0.0250310	−	0.206149i	−0.00208591	−	0.0171790i
$145$	−7.65388	−	7.96853i	−0.635620	−	0.661750i
$146$	5.96400	+	10.3300i	0.493585	+	0.854914i
$147$	3.10825	−	5.38364i	0.256364	−	0.444035i
$148$	22.9307	−	5.65191i	1.88489	−	0.464584i
$149$	6.61455	+	8.10136i	0.541885	+	0.663689i	0.970866	−	0.239625i	$-0.0770244\pi$
$149$	6.61455	+	8.10136i	0.541885	+	0.663689i	−0.428980	+	0.903314i	$0.641127\pi$
$150$	2.91003	−	5.04033i	0.237603	−	0.411541i
$151$	−7.28984	−	19.2217i	−0.593239	−	1.56424i	−0.809008	−	0.587797i	$-0.799995\pi$
$151$	−7.28984	−	19.2217i	−0.593239	−	1.56424i	0.215770	−	0.976444i	$-0.430774\pi$
$152$	8.92699	−	9.29398i	0.724075	−	0.753842i
$153$	−0.428961	−	0.143208i	−0.0346795	−	0.0115777i
$154$	2.71414	+	9.37031i	0.218712	+	0.755081i
$155$	−4.05745	+	3.59459i	−0.325902	+	0.288724i
$156$	−11.4267	+	1.28405i	−0.914867	+	0.102806i
$157$	5.73011	+	5.07644i	0.457313	+	0.405144i	0.860080	−	0.510158i	$-0.170413\pi$
$157$	5.73011	+	5.07644i	0.457313	+	0.405144i	−0.402768	+	0.915302i	$0.631952\pi$
$158$	4.82702	−	10.1727i	0.384017	−	0.809299i
$159$	−2.41214	−	2.51130i	−0.191295	−	0.199159i
$160$	−6.94110	−	14.6281i	−0.548742	−	1.15645i
$161$	−1.43067	−	0.352629i	−0.112753	−	0.0277911i
$162$	−1.57800	+	1.64288i	−0.123980	+	0.129077i
$163$	15.3127	+	11.5067i	1.19938	+	0.901275i	0.996952	−	0.0780217i	$-0.0248603\pi$
$163$	15.3127	+	11.5067i	1.19938	+	0.901275i	0.202428	+	0.979297i	$0.435117\pi$
$164$	−13.7939	−	12.2203i	−1.07712	−	0.954247i
$165$	13.1260	+	2.13319i	1.02186	+	0.166068i
$166$	−21.9852	−	13.9026i	−1.70638	−	1.07905i
$167$	17.0659	+	1.37770i	1.32060	+	0.106610i	0.720577	−	0.693375i	$-0.243877\pi$
$167$	17.0659	+	1.37770i	1.32060	+	0.106610i	0.600020	+	0.799985i	$0.295159\pi$
$168$	−2.39775			−0.184990
$169$	−1.33633	−	12.9311i	−0.102795	−	0.994703i
$170$	−2.83157			−0.217171
$171$	4.74191	+	0.382806i	0.362623	+	0.0292739i
$172$	−15.0767	−	9.53391i	−1.14959	−	0.726954i
$173$	18.3302	+	2.97895i	1.39362	+	0.226485i	0.810422	−	0.585846i	$-0.199238\pi$
$173$	18.3302	+	2.97895i	1.39362	+	0.226485i	0.583196	+	0.812331i	$0.301802\pi$
$174$	6.85411	+	6.07222i	0.519609	+	0.460333i
$175$	1.80797	+	1.35860i	0.136669	+	0.102700i
$176$	0.695981	−	0.724593i	0.0524615	−	0.0546182i
$177$	8.73589	+	2.15320i	0.656630	+	0.161845i
$178$	13.8631	+	29.2159i	1.03908	+	2.18982i
$179$	17.2516	+	17.9608i	1.28945	+	1.34245i	0.908516	+	0.417851i	$0.137217\pi$
$179$	17.2516	+	17.9608i	1.28945	+	1.34245i	0.380930	+	0.924604i	$0.375604\pi$
$180$	−3.75781	+	7.91942i	−0.280091	+	0.590279i
$181$	9.13320	+	8.09131i	0.678865	+	0.601422i	0.930453	−	0.366412i	$-0.119414\pi$
$181$	9.13320	+	8.09131i	0.678865	+	0.601422i	−0.251587	+	0.967835i	$0.580953\pi$
$182$	0.0648996	−	7.26983i	0.00481068	−	0.538876i
$183$	−3.98328	+	3.52887i	−0.294452	+	0.260862i
$184$	−1.25456	−	4.33123i	−0.0924871	−	0.319302i
$185$	19.3072	+	6.44570i	1.41950	+	0.473897i
$186$	3.11206	−	3.24000i	0.228187	−	0.237568i
$187$	−0.775867	−	2.04579i	−0.0567370	−	0.149603i
$188$	−8.52253	+	14.7614i	−0.621569	+	1.07659i
$189$	−0.559816	−	0.685650i	−0.0407206	−	0.0498737i
$190$	28.9215	−	7.12850i	2.09818	−	0.517156i
$191$	2.22750	−	3.85814i	0.161176	−	0.279165i	−0.774115	−	0.633046i	$-0.781805\pi$
$191$	2.22750	−	3.85814i	0.161176	−	0.279165i	0.935291	+	0.353880i	$0.115138\pi$
$192$	6.50175	+	11.2614i	0.469224	+	0.812719i
$193$	−4.46196	−	4.64540i	−0.321179	−	0.334383i	0.540966	−	0.841045i	$-0.318059\pi$
$193$	−4.46196	−	4.64540i	−0.321179	−	0.334383i	−0.862145	+	0.506662i	$0.830879\pi$
$194$	0.234049	+	1.92756i	0.0168037	+	0.138391i
$195$	−8.91519	−	4.32823i	−0.638430	−	0.309951i
$196$	−2.38967	+	19.6807i	−0.170691	+	1.40577i
$197$	8.55124	−	6.42584i	0.609251	−	0.457822i	−0.250794	−	0.968040i	$-0.580692\pi$
$197$	8.55124	−	6.42584i	0.609251	−	0.457822i	0.860045	+	0.510218i	$0.170435\pi$
$198$	−10.9854	−	0.886832i	−0.780698	−	0.0630244i
$199$	−2.94165	−	14.4092i	−0.208528	−	1.02144i	−0.940419	−	0.340017i	$-0.889567\pi$
$199$	−2.94165	−	14.4092i	−0.208528	−	1.02144i	0.731891	−	0.681422i	$-0.238638\pi$
$200$	−0.834220	+	6.87042i	−0.0589883	+	0.485812i
$201$	4.28435	+	1.82539i	0.302194	+	0.128753i
$202$	−33.0286	+	20.8860i	−2.32388	+	1.46953i
$203$	−2.66334	+	2.35951i	−0.186929	+	0.165605i
$204$	1.43756	−	0.116052i	0.100650	−	0.00812528i
$205$	−4.41891	−	15.2558i	−0.308630	−	1.06551i
$206$	−3.96885	+	1.69097i	−0.276523	+	0.117815i
$207$	0.945633	−	1.36999i	0.0657260	−	0.0952206i
$208$	−0.651743	+	0.368566i	−0.0451902	+	0.0255554i
$209$	13.0749	+	18.9423i	0.904413	+	1.31027i
$210$	−4.68425	−	2.96214i	−0.323244	−	0.204407i
$211$	4.98142	−	0.809559i	0.342935	−	0.0557324i	0.0134952	−	0.999909i	$-0.495704\pi$
$211$	4.98142	−	0.809559i	0.342935	−	0.0557324i	0.329440	+	0.944177i	$0.393140\pi$
$212$	10.2163	+	4.35276i	0.701658	+	0.298948i
$213$	−8.50204	+	12.3173i	−0.582550	+	0.843969i
$214$	−0.511929	+	1.76739i	−0.0349948	+	0.120816i
$215$	−6.59081	−	13.8898i	−0.449490	−	0.947279i
$216$	0.960563	−	2.53280i	0.0653580	−	0.172335i
$217$	1.10404	+	1.35220i	0.0749471	+	0.0917935i
$218$	−0.463217	−	11.4946i	−0.0313730	−	0.778513i
$219$	−0.210842	−	5.23200i	−0.0142474	−	0.353546i
$220$	−41.1776	+	10.1494i	−2.77619	+	0.684270i
$221$	0.116691	+	1.62638i	0.00784951	+	0.109402i
$222$	−16.3791	−	4.03710i	−1.09930	−	0.270952i
$223$	−0.586687	+	2.87378i	−0.0392874	+	0.192443i	−0.994698	−	0.102837i	$-0.967208\pi$
$223$	−0.586687	+	2.87378i	−0.0392874	+	0.192443i	0.955411	+	0.295280i	$0.0954130\pi$
$224$	−4.79697	+	2.04380i	−0.320511	+	0.136557i
$225$	−2.15941	+	1.36553i	−0.143961	+	0.0910352i
$226$	24.1082	−	12.6530i	1.60366	−	0.841664i
$227$	0.761708	+	0.123790i	0.0505563	+	0.00821620i	0.185637	−	0.982618i	$-0.440565\pi$
$227$	0.761708	+	0.123790i	0.0505563	+	0.00821620i	−0.135081	+	0.990835i	$0.543129\pi$
$228$	−14.3910	+	4.80443i	−0.953068	+	0.318181i
$229$	−0.709443	−	5.84279i	−0.0468813	−	0.386102i	−0.997197	−	0.0748156i	$-0.976163\pi$
$229$	−0.709443	−	5.84279i	−0.0468813	−	0.386102i	0.950316	−	0.311287i	$-0.100760\pi$
$230$	2.89983	−	10.0114i	0.191209	−	0.660130i
$231$	0.856616	−	4.19598i	0.0563612	−	0.276075i
$232$	−10.3286	−	3.44819i	−0.678104	−	0.226385i
$233$	−21.8220	−	11.4530i	−1.42960	−	0.750314i	−0.440531	−	0.897738i	$-0.645210\pi$
$233$	−21.8220	−	11.4530i	−1.42960	−	0.750314i	−0.989073	+	0.147423i	$0.952902\pi$
$234$	7.65329	+	2.98093i	0.500311	+	0.194869i
$235$	−13.0079	+	6.82707i	−0.848542	+	0.445349i
$236$	−28.3222	+	4.60281i	−1.84362	+	0.299617i
$237$	−3.95160	+	2.96943i	−0.256684	+	0.192885i
$238$	−0.0367174	+	0.911133i	−0.00238004	+	0.0590600i
$239$	−4.71239			−0.304819			−0.152410	−	0.988317i	$-0.548703\pi$
$239$	−4.71239			−0.304819			−0.152410	+	0.988317i	$0.548703\pi$
$240$	−0.0229833	+	0.570324i	−0.00148356	+	0.0368142i
$241$	−5.03681	−	24.6719i	−0.324449	−	1.58926i	−0.735421	−	0.677610i	$-0.763016\pi$
$241$	−5.03681	−	24.6719i	−0.324449	−	1.58926i	0.410972	−	0.911648i	$-0.365189\pi$
$242$	−16.0558	−	23.2609i	−1.03211	−	1.49527i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	7.27549	−	15.3328i	0.465765	−	0.981580i
$245$	−10.8065	+	13.2355i	−0.690400	+	0.845586i
$246$	4.66775	+	12.3078i	0.297605	+	0.784720i
$247$	−5.28629	−	16.3179i	−0.336359	−	1.03828i
$248$	−1.89437	+	4.99505i	−0.120293	+	0.317186i
$249$	5.70949	+	9.88914i	0.361825	+	0.626698i
$250$	9.68224	−	11.8586i	0.612359	−	0.750003i
$251$	18.7875	+	14.1179i	1.18586	+	0.891114i	0.995881	−	0.0906748i	$-0.0289024\pi$
$251$	18.7875	+	14.1179i	1.18586	+	0.891114i	0.189977	+	0.981789i	$0.439159\pi$
$252$	2.49956	+	1.31187i	0.157457	+	0.0826399i
$253$	8.02772	−	0.648065i	0.504699	−	0.0407435i
$254$	−12.4600	+	1.00587i	−0.781807	+	0.0631140i
$255$	1.10064	+	0.577662i	0.0689249	+	0.0361746i
$256$	−11.6977	−	8.79027i	−0.731108	−	0.549392i
$257$	6.56929	−	8.04592i	0.409781	−	0.501890i	−0.527939	−	0.849282i	$-0.677035\pi$
$257$	6.56929	−	8.04592i	0.409781	−	0.501890i	0.937720	+	0.347392i	$0.112933\pi$
$258$	6.37082	+	11.0346i	0.396630	+	0.686983i
$259$	2.32443	−	6.12903i	0.144433	−	0.380839i
$260$	31.5671	+	1.55448i	1.95771	+	0.0964046i
$261$	−1.42544	−	3.75859i	−0.0882328	−	0.232651i
$262$	−20.5691	+	25.1926i	−1.27076	+	1.55640i
$263$	−9.52483	+	20.0732i	−0.587326	+	1.23776i	0.364522	+	0.931195i	$0.381232\pi$
$263$	−9.52483	+	20.0732i	−0.587326	+	1.23776i	−0.951848	+	0.306569i	$0.900819\pi$
$264$	12.4312	−	4.15015i	0.765088	−	0.255424i
$265$	5.43694	+	7.87677i	0.333989	+	0.483866i
$266$	−1.91875	−	9.39868i	−0.117646	−	0.576270i
$267$	0.571616	−	14.1845i	0.0349823	−	0.868077i
$268$	−14.8518			−0.907220
$269$	0.901087	−	22.3602i	0.0549402	−	1.36333i	−0.703087	−	0.711104i	$-0.748195\pi$
$269$	0.901087	−	22.3602i	0.0549402	−	1.36333i	0.758027	−	0.652223i	$-0.226164\pi$
$270$	5.00554	−	3.76142i	0.304627	−	0.228912i
$271$	4.96234	−	0.806459i	0.301441	−	0.0489889i	−0.00780979	−	0.999970i	$-0.502486\pi$
$271$	4.96234	−	0.806459i	0.301441	−	0.0489889i	0.309250	+	0.950981i	$0.399922\pi$
$272$	0.0831552	−	0.0436432i	0.00504203	−	0.00264626i
$273$	−1.50833	+	2.81257i	−0.0912882	+	0.170225i
$274$	39.2593	+	20.6049i	2.37174	+	1.24479i
$275$	−11.7250	−	3.91438i	−0.707044	−	0.236046i
$276$	−1.06190	+	5.20154i	−0.0639189	+	0.313096i
$277$	−3.36199	+	11.6069i	−0.202002	+	0.697393i	0.793988	+	0.607933i	$0.208001\pi$
$277$	−3.36199	+	11.6069i	−0.202002	+	0.697393i	−0.995990	+	0.0894597i	$0.971486\pi$
$278$	5.37727	+	44.2858i	0.322507	+	2.65609i
$279$	−1.87065	+	0.624516i	−0.111993	+	0.0373888i
$280$	6.50516	+	1.05719i	0.388758	+	0.0631793i
$281$	−13.3085	+	6.98485i	−0.793920	+	0.416681i	−0.812366	−	0.583149i	$-0.801821\pi$
$281$	−13.3085	+	6.98485i	−0.793920	+	0.416681i	0.0184456	+	0.999830i	$0.494128\pi$
$282$	10.2903	−	6.50717i	0.612777	−	0.387496i
$283$	−24.4702	+	10.4258i	−1.45460	+	0.619748i	−0.967334	−	0.253505i	$-0.918416\pi$
$283$	−24.4702	+	10.4258i	−1.45460	+	0.619748i	−0.487267	+	0.873253i	$0.662006\pi$
$284$	9.54739	−	46.7662i	0.566533	−	2.77506i
$285$	−12.6962	−	3.12932i	−0.752056	−	0.185365i
$286$	12.2465	+	37.8031i	0.724153	+	2.23534i
$287$	−4.96627	+	1.22408i	−0.293150	+	0.0722550i
$288$	−0.237195	−	5.88592i	−0.0139768	−	0.346831i
$289$	0.676286	+	16.7819i	0.0397815	+	0.987168i
$290$	−15.9181	−	19.4962i	−0.934744	−	1.14485i
$291$	0.302262	−	0.797000i	0.0177189	−	0.0467210i
$292$	7.15879	+	15.0868i	0.418937	+	0.882890i
$293$	−2.87641	+	9.93053i	−0.168042	+	0.580148i	0.831649	+	0.555301i	$0.187397\pi$
$293$	−2.87641	+	9.93053i	−0.168042	+	0.580148i	−0.999691	+	0.0248466i	$0.992090\pi$
$294$	8.04435	−	11.6542i	0.469156	−	0.679690i
$295$	−22.7514	−	9.69346i	−1.32464	−	0.564375i
$296$	19.8002	−	3.21785i	1.15087	−	0.187034i
$297$	4.08915	+	2.58582i	0.237276	+	0.150044i
$298$	13.5339	+	19.6072i	0.783998	+	1.13582i
$299$	−5.86976	−	1.25300i	−0.339457	−	0.0724631i
$300$	4.62862	−	6.70572i	0.267234	−	0.387155i
$301$	−4.55489	+	1.94066i	−0.262539	+	0.111858i
$302$	−13.0288	−	44.9807i	−0.749725	−	2.58835i
$303$	17.0993	−	1.38039i	0.982326	−	0.0793016i
$304$	−0.739469	+	0.655113i	−0.0424115	+	0.0375733i
$305$	12.3627	−	7.81768i	0.707884	−	0.447639i
$306$	−0.947742	−	0.403795i	−0.0541788	−	0.0230834i
$307$	−1.53884	+	12.6735i	−0.0878264	+	0.723315i	0.880573	+	0.473911i	$0.157158\pi$
$307$	−1.53884	+	12.6735i	−0.0878264	+	0.723315i	−0.968399	+	0.249405i	$0.919765\pi$
$308$	2.73187	+	13.3816i	0.155663	+	0.762486i
$309$	1.88768	+	0.152389i	0.107386	+	0.00866912i
$310$	−9.87166	+	7.41807i	−0.560672	+	0.421318i
$311$	2.69912	−	22.2292i	0.153053	−	1.26050i	−0.690450	−	0.723380i	$-0.742587\pi$
$311$	2.69912	−	22.2292i	0.153053	−	1.26050i	0.843503	−	0.537124i	$-0.180489\pi$
$312$	−9.76201	+	0.306137i	−0.552665	+	0.0173316i
$313$	4.12214	+	33.9489i	0.232997	+	1.91890i	0.371298	+	0.928514i	$0.378913\pi$
$313$	4.12214	+	33.9489i	0.232997	+	1.91890i	−0.138301	+	0.990390i	$0.544164\pi$
$314$	12.0802	+	12.5768i	0.681724	+	0.709750i
$315$	1.21649	+	2.10702i	0.0685413	+	0.118717i
$316$	7.88187	−	13.6518i	0.443390	−	0.767973i
$317$	−20.2755	+	4.99745i	−1.13878	+	0.280685i	−0.763237	−	0.646119i	$-0.776391\pi$
$317$	−20.2755	+	4.99745i	−1.13878	+	0.280685i	−0.375546	+	0.926804i	$0.622545\pi$
$318$	−5.01663	−	6.14426i	−0.281319	−	0.344553i
$319$	9.72420	−	16.8428i	0.544451	−	0.943016i
$320$	−12.6742	−	33.4191i	−0.708509	−	1.86819i
$321$	0.559549	−	0.582553i	0.0312310	−	0.0325149i
$322$	−3.18382	−	1.06292i	−0.177427	−	0.0592340i
$323$	0.598566	+	2.06649i	0.0333051	+	0.114983i
$324$	−2.38711	+	2.11479i	−0.132617	+	0.117488i
$325$	7.53428	+	5.30046i	0.417927	+	0.294017i
$326$	32.6595	+	28.9338i	1.80884	+	1.60249i
$327$	−2.16494	+	4.56250i	−0.119721	+	0.252307i
$328$	−10.8432	−	11.2889i	−0.598714	−	0.623328i
$329$	2.02812	+	4.27416i	0.111814	+	0.235642i
$330$	29.4127	+	7.24958i	1.61912	+	0.399076i
$331$	22.1429	−	23.0532i	1.21709	−	1.26712i	0.263964	−	0.964533i	$-0.414970\pi$
$331$	22.1429	−	23.0532i	1.21709	−	1.26712i	0.953122	−	0.302588i	$-0.0978505\pi$
$332$	−29.1131	−	21.8771i	−1.59779	−	1.20066i
$333$	5.54304	+	4.91071i	0.303757	+	0.269105i
$334$	38.4969	+	6.25636i	2.10646	+	0.342333i
$335$	−10.8187	−	6.84135i	−0.591090	−	0.373783i
$336$	0.183219	+	0.0147910i	0.00999541	+	0.000806913i
$337$	12.7122			0.692480			0.346240	−	0.938146i	$-0.387458\pi$
$337$	12.7122			0.692480			0.346240	+	0.938146i	$0.387458\pi$
$338$	−0.663964	−	29.6061i	−0.0361149	−	1.61036i
$339$	−11.9523			−0.649159
$340$	−3.95132	−	0.318984i	−0.214291	−	0.0172993i
$341$	−8.06440	−	5.09962i	−0.436712	−	0.276160i
$342$	10.6967	+	1.73839i	0.578412	+	0.0940012i
$343$	8.75662	+	7.75769i	0.472813	+	0.418876i
$344$	−12.1128	−	9.10220i	−0.653080	−	0.490758i
$345$	−3.16957	+	3.29987i	−0.170644	+	0.177659i
$346$	41.0742	+	10.1239i	2.20816	+	0.544263i
$347$	−12.6610	−	26.6825i	−0.679677	−	1.43239i	−0.890554	−	0.454877i	$-0.849683\pi$
$347$	−12.6610	−	26.6825i	−0.679677	−	1.43239i	0.210877	−	0.977513i	$-0.432368\pi$
$348$	8.88055	+	9.24563i	0.476047	+	0.495618i
$349$	−8.67261	+	18.2771i	−0.464234	+	0.978353i	0.527441	+	0.849591i	$0.323151\pi$
$349$	−8.67261	+	18.2771i	−0.464234	+	0.978353i	−0.991676	+	0.128761i	$0.958900\pi$
$350$	3.85610	+	3.41621i	0.206117	+	0.182604i
$351$	−2.36674	−	2.72003i	−0.126327	−	0.145184i
$352$	21.3326	−	18.8990i	1.13703	−	1.00732i
$353$	−5.88461	−	20.3160i	−0.313206	−	1.08131i	−0.950508	−	0.310699i	$-0.899437\pi$
$353$	−5.88461	−	20.3160i	−0.313206	−	1.08131i	0.637302	−	0.770614i	$-0.280050\pi$
$354$	19.4409	+	6.49032i	1.03327	+	0.344957i
$355$	28.4971	−	29.6686i	1.51247	−	1.57465i
$356$	16.0541	+	42.3311i	0.850863	+	2.24354i
$357$	0.200150	−	0.346671i	0.0105931	−	0.0183478i
$358$	35.8790	+	43.9437i	1.89626	+	2.32250i
$359$	−12.3850	+	3.05264i	−0.653657	+	0.161112i	−0.552179	−	0.833726i	$-0.686203\pi$
$359$	−12.3850	+	3.05264i	−0.653657	+	0.161112i	−0.101478	+	0.994838i	$0.532357\pi$
$360$	−3.72277	+	6.44803i	−0.196207	+	0.339841i
$361$	−1.81612	−	3.14560i	−0.0955850	−	0.165558i
$362$	19.2545	+	20.0461i	1.01200	+	1.05360i
$363$	1.49557	+	12.3171i	0.0784970	+	0.646481i
$364$	0.909530	−	10.1374i	0.0476723	−	0.531344i
$365$	−1.73482	+	14.2875i	−0.0908047	+	0.747844i
$366$	−9.69120	+	7.28246i	−0.506567	+	0.380660i
$367$	5.35315	+	0.432151i	0.279432	+	0.0225581i	0.219388	−	0.975638i	$-0.429594\pi$
$367$	5.35315	+	0.432151i	0.279432	+	0.0225581i	0.0600439	+	0.998196i	$0.480876\pi$
$368$	0.0691463	+	0.338701i	0.00360450	+	0.0176560i
$369$	0.696521	−	5.73637i	0.0362595	−	0.298623i
$370$	42.6571	+	18.1745i	2.21764	+	0.944847i
$371$	2.60506	−	1.64734i	0.135248	−	0.0855257i
$372$	4.70773	−	4.17068i	0.244084	−	0.216240i
$373$	−34.4919	+	2.78447i	−1.78592	+	0.144174i	−0.928714	−	0.370798i	$-0.879084\pi$
$373$	−34.4919	+	2.78447i	−1.78592	+	0.144174i	−0.857207	+	0.514972i	$0.827802\pi$
$374$	−1.38667	−	4.78736i	−0.0717032	−	0.247548i
$375$	−6.18277	+	2.63423i	−0.319277	+	0.136031i
$376$	−8.22439	+	11.9151i	−0.424140	+	0.614473i
$377$	−10.5421	+	9.94638i	−0.542943	+	0.512265i
$378$	−1.14543	−	1.65944i	−0.0589145	−	0.0853523i
$379$	−18.4758	−	11.6834i	−0.949038	−	0.600135i	−0.0322374	−	0.999480i	$-0.510263\pi$
$379$	−18.4758	−	11.6834i	−0.949038	−	0.600135i	−0.916801	+	0.399345i	$0.869238\pi$
$380$	41.1616	−	6.68941i	2.11154	−	0.343159i
$381$	5.04845	+	2.15094i	0.258640	+	0.110196i
$382$	5.76492	−	8.35193i	0.294959	−	0.427322i
$383$	2.96914	−	10.2506i	0.151716	−	0.523784i	−0.848268	−	0.529568i	$-0.822354\pi$
$383$	2.96914	−	10.2506i	0.151716	−	0.523784i	0.999983	+	0.00578443i	$0.00184125\pi$
$384$	7.64795	+	16.1177i	0.390283	+	0.822504i
$385$	−4.17408	+	11.0061i	−0.212731	+	0.560925i
$386$	−9.27975	−	11.3656i	−0.472327	−	0.578495i
$387$	−0.225224	−	5.58888i	−0.0114488	−	0.284099i
$388$	0.109459	+	2.71619i	0.00555693	+	0.137894i
$389$	−3.23593	+	0.797586i	−0.164068	+	0.0404392i	−0.320494	−	0.947250i	$-0.603849\pi$
$389$	−3.23593	+	0.797586i	−0.164068	+	0.0404392i	0.156426	+	0.987690i	$0.450003\pi$
$390$	−19.4493	−	11.4618i	−0.984854	−	0.580389i
$391$	0.730940	+	0.180161i	0.0369652	+	0.00911111i
$392$	−3.36831	+	16.4991i	−0.170125	+	0.833329i
$393$	13.1348	−	5.59620i	0.662562	−	0.282291i
$394$	20.5942	−	13.0230i	1.03752	−	0.656087i
$395$	12.0301	−	6.31386i	0.605298	−	0.317685i
$396$	−15.2297	−	2.47507i	−0.765321	−	0.124377i
$397$	14.9916	−	5.00492i	0.752405	−	0.251190i	0.0855060	−	0.996338i	$-0.472749\pi$
$397$	14.9916	−	5.00492i	0.752405	−	0.251190i	0.666899	+	0.745148i	$0.267621\pi$
$398$	−4.03806	−	33.2564i	−0.202410	−	1.66699i
$399$	−1.17158	+	4.04475i	−0.0586521	+	0.202491i
$400$	0.106127	−	0.519843i	0.00530634	−	0.0259921i
$401$	−6.32180	−	2.11053i	−0.315696	−	0.105395i	0.154405	−	0.988008i	$-0.450654\pi$
$401$	−6.32180	−	2.11053i	−0.315696	−	0.105395i	−0.470100	+	0.882613i	$0.655782\pi$
$402$	9.39336	+	4.93002i	0.468498	+	0.245887i
$403$	4.66755	+	5.36430i	0.232507	+	0.267215i
$404$	−48.4427	+	25.4247i	−2.41011	+	1.26493i
$405$	−2.71303	+	0.440910i	−0.134812	+	0.0219090i
$406$	−6.47982	+	4.86927i	−0.321588	+	0.241658i
$407$	−1.44267	+	35.7994i	−0.0715104	+	1.77451i
$408$	1.22503			0.0606478
$409$	−1.07338	+	26.6356i	−0.0530751	+	1.31704i	0.724946	+	0.688806i	$0.241865\pi$
$409$	−1.07338	+	26.6356i	−0.0530751	+	1.31704i	−0.778021	+	0.628238i	$0.783776\pi$
$410$	−7.23709	−	35.4496i	−0.357415	−	1.75073i
$411$	−11.0567	−	16.0184i	−0.545387	−	0.790130i
$412$	−5.72884	+	1.91257i	−0.282240	+	0.0942254i
$413$	−3.41415	+	7.19516i	−0.167999	+	0.354051i
$414$	2.39825	−	2.93733i	0.117868	−	0.144362i
$415$	−11.1298	−	29.3469i	−0.546341	−	1.44058i
$416$	−19.2691	+	8.93344i	−0.944745	+	0.437998i
$417$	6.94448	−	18.3111i	0.340072	−	0.896697i
$418$	26.2156	+	45.4067i	1.28225	+	2.22092i
$419$	3.91678	−	4.79718i	0.191347	−	0.234358i	−0.670017	−	0.742346i	$-0.733713\pi$
$419$	3.91678	−	4.79718i	0.191347	−	0.234358i	0.861364	+	0.507988i	$0.169611\pi$
$420$	−6.20296	−	4.66122i	−0.302673	−	0.227444i
$421$	3.46158	+	1.81678i	0.168707	+	0.0885443i	0.546963	−	0.837157i	$-0.315784\pi$
$421$	3.46158	+	1.81678i	0.168707	+	0.0885443i	−0.378256	+	0.925701i	$0.623476\pi$
$422$	11.4591	−	0.925075i	0.557821	−	0.0450320i
$423$	−5.32738	+	0.430071i	−0.259026	+	0.0209108i
$424$	8.35198	+	4.38346i	0.405608	+	0.212880i
$425$	−0.923702	−	0.694117i	−0.0448061	−	0.0336696i
$426$	−21.5623	+	26.4091i	−1.04470	+	1.27952i
$427$	−2.35524	−	4.07939i	−0.113978	−	0.197416i
$428$	−0.913474	+	2.40863i	−0.0441544	+	0.116426i
$429$	2.95183	−	17.1926i	0.142516	−	0.830066i
$430$	−12.4190	−	32.7461i	−0.598896	−	1.57916i
$431$	−0.455928	+	0.558410i	−0.0219613	+	0.0268977i	−0.785469	−	0.618901i	$-0.787578\pi$
$431$	−0.455928	+	0.558410i	−0.0219613	+	0.0268977i	0.763508	+	0.645799i	$0.223476\pi$
$432$	−0.0890234	+	0.187613i	−0.00428314	+	0.00902653i
$433$	−11.2717	+	3.76303i	−0.541681	+	0.180840i	−0.574325	−	0.818627i	$-0.694736\pi$
$433$	−11.2717	+	3.76303i	−0.541681	+	0.180840i	0.0326438	+	0.999467i	$0.489607\pi$
$434$	2.25895	+	3.27266i	0.108433	+	0.157093i
$435$	2.21007	+	10.8257i	0.105965	+	0.519051i
$436$	0.648501	−	16.0924i	0.0310576	−	0.770685i
$437$	−7.91933			−0.378833
$438$	0.480293	−	11.9183i	0.0229493	−	0.569480i
$439$	−6.81684	+	5.12252i	−0.325350	+	0.244485i	−0.750848	−	0.660475i	$-0.770355\pi$
$439$	−6.81684	+	5.12252i	−0.325350	+	0.244485i	0.425499	+	0.904959i	$0.360099\pi$
$440$	−35.5561	+	5.77843i	−1.69507	+	0.275476i
$441$	−5.50443	+	2.88895i	−0.262116	+	0.137569i
$442$	−0.0331577	+	3.71421i	−0.00157715	+	0.176667i
$443$	9.44111	+	4.95508i	0.448561	+	0.235423i	0.673849	−	0.738869i	$-0.264640\pi$
$443$	9.44111	+	4.95508i	0.448561	+	0.235423i	−0.225288	+	0.974292i	$0.572332\pi$
$444$	−22.4015	−	7.47874i	−1.06313	−	0.354925i
$445$	−7.80491	+	38.2310i	−0.369988	+	1.81232i
$446$	−1.85889	+	6.41762i	−0.0880208	+	0.303883i
$447$	−1.26066	−	10.3824i	−0.0596270	−	0.491073i
$448$	−10.9178	+	3.64491i	−0.515819	+	0.172206i
$449$	−23.4410	−	3.80953i	−1.10625	−	0.179783i	−0.420267	−	0.907401i	$-0.638063\pi$
$449$	−23.4410	−	3.80953i	−1.10625	−	0.179783i	−0.685983	+	0.727618i	$0.740628\pi$
$450$	−5.15342	+	2.70472i	−0.242934	+	0.127502i
$451$	23.6291	−	14.9422i	1.11265	−	0.703599i
$452$	35.0673	−	14.9408i	1.64943	−	0.702756i
$453$	−4.11205	+	20.1422i	−0.193201	+	0.946362i
$454$	1.70683	+	0.420696i	0.0801055	+	0.0197442i
$455$	5.33223	−	6.96556i	0.249979	−	0.326551i
$456$	−12.5123	+	3.08401i	−0.585943	+	0.144422i
$457$	0.345842	+	8.58197i	0.0161778	+	0.401448i	0.986909	+	0.161279i	$0.0515618\pi$
$457$	0.345842	+	8.58197i	0.0161778	+	0.401448i	−0.970731	+	0.240169i	$0.922797\pi$
$458$	−0.539863	−	13.3966i	−0.0252261	−	0.625980i
$459$	0.286014	+	0.350303i	0.0133500	+	0.0163508i
$460$	5.17438	−	13.6437i	0.241257	−	0.636142i
$461$	4.75720	+	10.0256i	0.221565	+	0.466938i	0.983545	−	0.180662i	$-0.0578240\pi$
$461$	4.75720	+	10.0256i	0.221565	+	0.466938i	−0.761980	+	0.647600i	$0.775773\pi$
$462$	2.71414	−	9.37031i	0.126273	−	0.435946i
$463$	−18.7622	+	27.1818i	−0.871955	+	1.26325i	0.0916163	+	0.995794i	$0.470797\pi$
$463$	−18.7622	+	27.1818i	−0.871955	+	1.26325i	−0.963572	+	0.267451i	$0.913819\pi$
$464$	0.767966	+	0.327200i	0.0356519	+	0.0151899i
$465$	5.35050	−	0.869541i	0.248123	−	0.0403240i
$466$	−47.4492	−	30.0051i	−2.19804	−	1.38996i
$467$	−14.8100	−	21.4560i	−0.685327	−	0.992867i	−0.999060	−	0.0433561i	$-0.986195\pi$
$467$	−14.8100	−	21.4560i	−0.685327	−	0.992867i	0.313733	−	0.949511i	$-0.398420\pi$
$468$	10.3440	+	5.02191i	0.478152	+	0.232138i
$469$	−2.34167	+	3.39250i	−0.108128	+	0.156651i
$470$	−30.7869	+	13.1171i	−1.42009	+	0.605045i
$471$	−2.12985	−	7.35311i	−0.0981385	−	0.338813i
$472$	−24.2932	+	1.96115i	−1.11818	+	0.0902692i
$473$	20.2560	−	17.9453i	0.931372	−	0.825124i
$474$	−9.51672	+	6.01801i	−0.437118	+	0.276416i
$475$	11.1821	+	4.76424i	0.513069	+	0.218598i
$476$	−0.153879	+	1.26731i	−0.00705303	+	0.0580869i
$477$	0.696510	+	3.41173i	0.0318910	+	0.156212i
$478$	−10.6999	−	0.863783i	−0.489401	−	0.0395085i
$479$	−24.4215	+	18.3515i	−1.11585	+	0.838504i	−0.988178	−	0.153313i	$-0.951006\pi$
$479$	−24.4215	+	18.3515i	−1.11585	+	0.838504i	−0.127668	+	0.991817i	$0.540749\pi$
$480$	−1.95165	+	16.0733i	−0.0890802	+	0.733641i
$481$	8.68099	−	25.2501i	0.395819	−	1.15130i
$482$	−6.91412	−	56.9429i	−0.314929	−	2.59368i
$483$	1.02072	+	1.06268i	0.0464444	+	0.0483538i
$484$	−19.7848	−	34.2682i	−0.899308	−	1.55765i
$485$	−1.17145	+	2.02902i	−0.0531929	+	0.0921329i
$486$	2.21177	−	0.545154i	0.100328	−	0.0247287i
$487$	5.56550	+	6.81650i	0.252197	+	0.308885i	0.885151	−	0.465304i	$-0.154055\pi$
$487$	5.56550	+	6.81650i	0.252197	+	0.308885i	−0.632954	+	0.774190i	$0.718158\pi$
$488$	7.20765	−	12.4840i	0.326275	−	0.565124i
$489$	−6.79216	−	17.9095i	−0.307152	−	0.809893i
$490$	−26.9630	+	28.0715i	−1.21807	+	1.26814i
$491$	14.3685	+	4.79692i	0.648442	+	0.216482i	0.621816	−	0.783164i	$-0.286395\pi$
$491$	14.3685	+	4.79692i	0.648442	+	0.216482i	0.0266267	+	0.999645i	$0.491523\pi$
$492$	5.12712	+	17.7009i	0.231148	+	0.798017i
$493$	1.36072	−	1.20549i	0.0612836	−	0.0542925i
$494$	−9.01187	−	38.0201i	−0.405463	−	1.71061i
$495$	−9.95387	−	8.81836i	−0.447393	−	0.396356i
$496$	0.175567	−	0.370000i	0.00788321	−	0.0166135i
$497$	−9.17715	−	9.55442i	−0.411651	−	0.428574i
$498$	11.1512	+	23.5006i	0.499697	+	1.05309i
$499$	0.488404	+	0.120381i	0.0218640	+	0.00538899i	0.250232	−	0.968186i	$-0.419493\pi$
$499$	0.488404	+	0.120381i	0.0218640	+	0.00538899i	−0.228369	+	0.973575i	$0.573339\pi$
$500$	14.8470	−	15.4574i	0.663979	−	0.691275i
$501$	−13.6876	−	10.2855i	−0.611516	−	0.459524i
$502$	40.0708	+	35.4996i	1.78845	+	1.58442i
$503$	−0.695811	−	0.113080i	−0.0310247	−	0.00504200i	0.144879	−	0.989449i	$-0.453721\pi$
$503$	−0.695811	−	0.113080i	−0.0310247	−	0.00504200i	−0.175904	+	0.984407i	$0.556285\pi$
$504$	2.02655	+	1.28151i	0.0902698	+	0.0570831i
$505$	−46.9994	−	3.79419i	−2.09145	−	0.168839i
$506$	18.3464			0.815597
$507$	−5.78180	+	11.6435i	−0.256779	+	0.517105i
$508$	−17.5006			−0.776464
$509$	26.9354	+	2.17445i	1.19389	+	0.0963807i	0.661385	−	0.750047i	$-0.269969\pi$
$509$	26.9354	+	2.17445i	1.19389	+	0.0963807i	0.532504	+	0.846427i	$0.321251\pi$
$510$	2.39321	+	1.51338i	0.105973	+	0.0670135i
$511$	4.57490	+	0.743494i	0.202382	+	0.0328902i
$512$	1.75774	+	1.55723i	0.0776821	+	0.0688203i
$513$	−3.80322	−	2.85793i	−0.167916	−	0.126181i
$514$	16.3909	−	17.0648i	0.722973	−	0.752694i
$515$	−5.05414	−	1.24573i	−0.222712	−	0.0548936i
$516$	7.64710	+	16.1159i	0.336645	+	0.709464i
$517$	−17.9128	−	18.6492i	−0.787804	−	0.820191i
$518$	6.40127	−	13.4904i	0.281256	−	0.592734i
$519$	−13.9003	−	12.3146i	−0.610158	−	0.540552i
$520$	26.6196	+	3.47361i	1.16735	+	0.152328i
$521$	4.52681	−	4.01041i	0.198323	−	0.175699i	−0.558116	−	0.829763i	$-0.688476\pi$
$521$	4.52681	−	4.01041i	0.198323	−	0.175699i	0.756439	+	0.654064i	$0.226937\pi$
$522$	−2.54764	−	8.79547i	−0.111507	−	0.384967i
$523$	−14.0471	−	4.68962i	−0.614238	−	0.205063i	−0.00750911	−	0.999972i	$-0.502390\pi$
$523$	−14.0471	−	4.68962i	−0.614238	−	0.205063i	−0.606728	+	0.794909i	$0.707518\pi$
$524$	−31.5412	+	32.8379i	−1.37789	+	1.43453i
$525$	−0.801950	−	2.11457i	−0.0350000	−	0.0922873i
$526$	−25.3063	+	43.8318i	−1.10341	+	1.91116i
$527$	−0.564062	−	0.690850i	−0.0245709	−	0.0300939i
$528$	−0.975506	+	0.240441i	−0.0424535	+	0.0104638i
$529$	10.1145	−	17.5188i	0.439759	−	0.761685i
$530$	10.9012	+	18.8815i	0.473518	+	0.820158i
$531$	−6.23268	−	6.48890i	−0.270475	−	0.281594i
$532$	−1.61875	−	13.3316i	−0.0701816	−	0.577997i
$533$	−20.0630	+	5.61770i	−0.869027	+	0.243329i
$534$	3.89792	−	32.1023i	0.168680	−	1.38920i
$535$	−1.77493	+	1.33377i	−0.0767368	+	0.0576640i
$536$	−12.5741	−	1.01509i	−0.543118	−	0.0438450i
$537$	−4.98144	−	24.4007i	−0.214965	−	1.05297i
$538$	6.14463	−	50.6056i	0.264914	−	2.18176i
$539$	−27.6695	−	11.7889i	−1.19181	−	0.507783i
$540$	7.40873	−	4.68499i	0.318821	−	0.201610i
$541$	19.5067	−	17.2814i	0.838659	−	0.742987i	−0.129964	−	0.991519i	$-0.541486\pi$
$541$	19.5067	−	17.2814i	0.838659	−	0.742987i	0.968624	+	0.248531i	$0.0799479\pi$
$542$	11.4152	−	0.921532i	0.490326	−	0.0395832i
$543$	−3.39476	−	11.7201i	−0.145683	−	0.502957i
$544$	2.45081	−	1.04419i	0.105077	−	0.0447693i
$545$	7.88519	−	11.4237i	0.337765	−	0.489336i
$546$	−3.94033	+	6.10970i	−0.168631	+	0.261471i
$547$	10.4039	+	15.0726i	0.444837	+	0.644458i	0.979697	−	0.200483i	$-0.0642511\pi$
$547$	10.4039	+	15.0726i	0.444837	+	0.644458i	−0.534860	+	0.844941i	$0.679636\pi$
$548$	52.4633	+	33.1758i	2.24112	+	1.41720i
$549$	5.25269	−	0.853645i	0.224179	−	0.0364327i
$550$	−25.9051	−	11.0371i	−1.10460	−	0.470624i
$551$	−10.8634	+	15.7384i	−0.462798	+	0.670478i
$552$	−1.25456	+	4.33123i	−0.0533974	+	0.184349i
$553$	−1.87566	−	3.95286i	−0.0797611	−	0.168093i
$554$	−9.76122	+	25.7382i	−0.414715	+	1.09351i
$555$	−12.8733	−	15.7669i	−0.546440	−	0.669267i
$556$	2.51482	+	62.4045i	0.106652	+	2.64654i
$557$	−0.815942	−	20.2474i	−0.0345726	−	0.857909i	−0.919714	−	0.392588i	$-0.871580\pi$
$557$	−0.815942	−	20.2474i	−0.0345726	−	0.857909i	0.885142	−	0.465321i	$-0.154061\pi$
$558$	−4.36195	+	1.07512i	−0.184656	+	0.0455136i
$559$	−18.2967	+	8.48260i	−0.773866	+	0.358776i
$560$	−0.490557	−	0.120911i	−0.0207298	−	0.00510944i
$561$	−0.437651	+	2.14376i	−0.0184777	+	0.0905095i
$562$	−31.4984	+	13.4202i	−1.32868	+	0.566098i
$563$	4.42519	−	2.79832i	0.186499	−	0.117935i	−0.437953	−	0.898998i	$-0.644296\pi$
$563$	4.42519	−	2.79832i	0.186499	−	0.117935i	0.624453	+	0.781063i	$0.285322\pi$
$564$	15.0926	−	7.92123i	0.635515	−	0.333544i
$565$	32.4269	+	5.26989i	1.36421	+	0.221706i
$566$	−57.4726	+	19.1872i	−2.41575	+	0.806497i
$567$	0.106694	+	0.878707i	0.00448074	+	0.0369022i
$568$	11.2795	−	38.9414i	0.473278	−	1.63395i
$569$	6.30234	−	30.8709i	0.264208	−	1.29417i	−0.603605	−	0.797283i	$-0.706270\pi$
$569$	6.30234	−	30.8709i	0.264208	−	1.29417i	0.867813	−	0.496891i	$-0.165525\pi$
$570$	−28.2541	−	9.43259i	−1.18343	−	0.395088i
$571$	34.9983	+	18.3685i	1.46463	+	0.768698i	0.993550	−	0.113392i	$-0.0361716\pi$
$571$	34.9983	+	18.3685i	1.46463	+	0.768698i	0.471081	+	0.882090i	$0.343864\pi$
$572$	12.8309	+	54.1320i	0.536485	+	2.26337i
$573$	−3.94471	+	2.07034i	−0.164792	+	0.0864898i
$574$	−11.5007	+	1.86905i	−0.480030	+	0.0780125i
$575$	3.40011	−	2.55501i	0.141794	−	0.106551i
$576$	0.523598	−	12.9930i	0.0218166	−	0.541373i
$577$	−35.4527			−1.47591			−0.737957	−	0.674848i	$-0.764209\pi$
$577$	−35.4527			−1.47591			−0.737957	+	0.674848i	$0.764209\pi$
$578$	−1.54056	+	38.2286i	−0.0640788	+	1.59010i
$579$	1.28840	+	6.31101i	0.0535441	+	0.262277i
$580$	−20.0167	−	28.9992i	−0.831148	−	1.20413i
$581$	−9.58747	+	3.20077i	−0.397755	+	0.132790i
$582$	0.832402	−	1.75425i	0.0345042	−	0.0727160i
$583$	−10.6547	+	13.0497i	−0.441274	+	0.540463i
$584$	5.02974	+	13.2623i	0.208132	+	0.548800i
$585$	5.22174	+	8.42304i	0.215892	+	0.348250i
$586$	−8.35140	+	22.0208i	−0.344993	+	0.909672i
$587$	8.15917	+	14.1321i	0.336765	+	0.583294i	0.983822	−	0.179148i	$-0.0573339\pi$
$587$	8.15917	+	14.1321i	0.336765	+	0.583294i	−0.647057	+	0.762441i	$0.724001\pi$
$588$	12.5384	−	15.3567i	0.517075	−	0.633302i
$589$	7.50051	+	5.63626i	0.309053	+	0.232238i
$590$	−49.8820	−	26.1801i	−2.05361	−	1.07782i
$591$	−10.6618	+	0.860711i	−0.438569	+	0.0354049i
$592$	−1.53284	+	0.123744i	−0.0629995	+	0.00508585i
$593$	11.0463	+	5.79757i	0.453619	+	0.238077i	0.676028	−	0.736876i	$-0.263700\pi$
$593$	11.0463	+	5.79757i	0.453619	+	0.238077i	−0.222409	+	0.974953i	$0.571392\pi$
$594$	8.81076	+	6.62086i	0.361510	+	0.271657i
$595$	−0.695865	+	0.852280i	−0.0285277	+	0.0349401i
$596$	16.6771	+	28.8856i	0.683122	+	1.18320i
$597$	−5.21495	+	13.7507i	−0.213434	+	0.562779i
$598$	−13.0981	−	3.92098i	−0.535621	−	0.160341i
$599$	−6.87028	−	18.1154i	−0.280712	−	0.740177i	−0.999012	−	0.0444433i	$-0.985849\pi$
$599$	−6.87028	−	18.1154i	−0.280712	−	0.740177i	0.718300	−	0.695734i	$-0.244921\pi$
$600$	4.37708	−	5.36095i	0.178694	−	0.218860i
$601$	−6.38546	+	13.4571i	−0.260468	+	0.548925i	−0.990986	−	0.133969i	$-0.957228\pi$
$601$	−6.38546	+	13.4571i	−0.260468	+	0.548925i	0.730517	+	0.682894i	$0.239279\pi$
$602$	−10.6980	+	3.57151i	−0.436017	+	0.145564i
$603$	−2.64548	−	3.83264i	−0.107732	−	0.156077i
$604$	−13.1139	−	64.2362i	−0.533598	−	2.61374i
$605$	1.37322	−	34.0761i	0.0558294	−	1.38539i
$606$	39.0783			1.58745
$607$	0.681913	−	16.9215i	0.0276780	−	0.686823i	−0.924483	−	0.381224i	$-0.875503\pi$
$607$	0.681913	−	16.9215i	0.0276780	−	0.686823i	0.952161	−	0.305598i	$-0.0988564\pi$
$608$	−22.4036	+	16.8352i	−0.908586	+	0.682758i
$609$	3.51210	−	0.570772i	0.142318	−	0.0231289i
$610$	29.5034	−	15.4846i	1.19456	−	0.626953i
$611$	8.80284	+	17.1426i	0.356125	+	0.693514i
$612$	−1.27704	−	0.670243i	−0.0516213	−	0.0270930i
$613$	−34.5739	−	11.5425i	−1.39643	−	0.466196i	−0.483868	−	0.875141i	$-0.660768\pi$
$613$	−34.5739	−	11.5425i	−1.39643	−	0.466196i	−0.912559	+	0.408945i	$0.865897\pi$
$614$	−5.81713	+	28.4942i	−0.234760	+	1.14993i
$615$	−4.41891	+	15.2558i	−0.178188	+	0.615175i
$616$	1.39830	+	11.5160i	0.0563392	+	0.463995i
$617$	−16.7519	+	5.59259i	−0.674405	+	0.225149i	−0.633185	−	0.774001i	$-0.718253\pi$
$617$	−16.7519	+	5.59259i	−0.674405	+	0.225149i	−0.0412199	+	0.999150i	$0.513124\pi$
$618$	4.25820	+	0.692025i	0.171290	+	0.0278373i
$619$	−38.5760	+	20.2462i	−1.55050	+	0.813765i	−0.999781	−	0.0209255i	$-0.993339\pi$
$619$	−38.5760	+	20.2462i	−1.55050	+	0.813765i	−0.550719	+	0.834691i	$0.685646\pi$
$620$	−14.6111	+	9.23950i	−0.586796	+	0.371067i
$621$	−1.53145	+	0.652490i	−0.0614550	+	0.0261835i
$622$	10.2032	−	49.9786i	0.409111	−	2.00396i
$623$	12.2006	+	3.00718i	0.488808	+	0.120480i
$624$	0.747832	+	0.0368259i	0.0299372	+	0.00147422i
$625$	30.3390	−	7.47789i	1.21356	−	0.299116i
$626$	3.13682	+	77.8393i	0.125372	+	3.11108i
$627$	−0.926787	−	22.9980i	−0.0370123	−	0.918451i
$628$	15.4405	+	18.9112i	0.616144	+	0.754639i
$629$	−1.18757	+	3.13136i	−0.0473515	+	0.124856i
$630$	2.37592	+	5.00714i	0.0946588	+	0.199489i
$631$	1.86749	−	6.44731i	0.0743434	−	0.256663i	−0.914735	−	0.404055i	$-0.867601\pi$
$631$	1.86749	−	6.44731i	0.0743434	−	0.256663i	0.989078	+	0.147391i	$0.0470877\pi$
$632$	7.60614	−	11.0194i	0.302556	−	0.438328i
$633$	−4.64293	−	1.97817i	−0.184540	−	0.0786251i
$634$	−46.9531	+	7.63063i	−1.86475	+	0.303051i
$635$	−12.7482	−	8.06148i	−0.505897	−	0.319910i
$636$	−6.30831	−	9.13917i	−0.250141	−	0.362391i
$637$	17.2347	+	14.3300i	0.682862	+	0.567774i
$638$	25.1669	−	36.4605i	0.996366	−	1.44349i
$639$	13.7690	−	5.86643i	0.544694	−	0.232073i
$640$	−13.6427	−	47.0999i	−0.539273	−	1.86179i
$641$	−18.6437	+	1.50507i	−0.736380	+	0.0594468i	−0.442966	−	0.896539i	$-0.646074\pi$
$641$	−18.6437	+	1.50507i	−0.736380	+	0.0594468i	−0.293415	+	0.955985i	$0.594792\pi$
$642$	1.37728	−	1.22017i	0.0543571	−	0.0481562i
$643$	30.0172	−	18.9817i	1.18376	−	0.748565i	0.210349	−	0.977626i	$-0.432540\pi$
$643$	30.0172	−	18.9817i	1.18376	−	0.748565i	0.973412	+	0.229061i	$0.0735655\pi$
$644$	−4.32313	−	1.84192i	−0.170355	−	0.0725816i
$645$	−1.85316	+	15.2621i	−0.0729680	+	0.600945i
$646$	0.980305	+	4.80185i	0.0385696	+	0.188926i
$647$	28.0052	+	2.26082i	1.10100	+	0.0888819i	0.617581	−	0.786507i	$-0.288113\pi$
$647$	28.0052	+	2.26082i	1.10100	+	0.0888819i	0.483419	+	0.875389i	$0.339395\pi$
$648$	−2.16555	+	1.62731i	−0.0850709	+	0.0639266i
$649$	5.24701	−	43.2130i	0.205963	−	1.69626i
$650$	16.1356	+	13.4162i	0.632891	+	0.526225i
$651$	−0.210417	−	1.73294i	−0.00824690	−	0.0679193i
$652$	42.3153	+	44.0549i	1.65719	+	1.72532i
$653$	17.9523	+	31.0944i	0.702529	+	1.21682i	0.967576	+	0.252580i	$0.0812792\pi$
$653$	17.9523	+	31.0944i	0.702529	+	1.21682i	−0.265047	+	0.964236i	$0.585387\pi$
$654$	−5.75197	+	9.96271i	−0.224920	+	0.389573i
$655$	−38.1025	+	9.39142i	−1.48879	+	0.366953i
$656$	0.758921	+	0.929510i	0.0296309	+	0.0362913i
$657$	−2.61812	+	4.53472i	−0.102143	+	0.176916i
$658$	3.82155	+	10.0766i	0.148979	+	0.392827i
$659$	25.2645	−	26.3031i	0.984165	−	1.02462i	−0.0155287	−	0.999879i	$-0.504943\pi$
$659$	25.2645	−	26.3031i	0.984165	−	1.02462i	0.999694	−	0.0247450i	$-0.00787739\pi$
$660$	40.2274	+	13.4299i	1.56585	+	0.522757i
$661$	1.18858	+	4.10345i	0.0462304	+	0.159606i	0.980312	−	0.197453i	$-0.0632669\pi$
$661$	1.18858	+	4.10345i	0.0462304	+	0.159606i	−0.934082	+	0.357058i	$0.883780\pi$
$662$	54.5030	−	48.2854i	2.11832	−	1.87667i
$663$	0.770616	−	1.43696i	0.0299282	−	0.0558071i
$664$	−23.1530	−	20.5117i	−0.898510	−	0.796010i
$665$	4.96189	−	10.4570i	0.192414	−	0.405504i
$666$	11.6858	+	12.1662i	0.452816	+	0.471431i
$667$	2.86864	+	6.04553i	0.111074	+	0.234084i
$668$	53.0159	+	13.0672i	2.05125	+	0.505587i
$669$	2.03180	−	2.11533i	0.0785539	−	0.0817833i
$670$	−23.3108	−	17.5169i	−0.900574	−	0.676738i
$671$	19.2716	+	17.0732i	0.743974	+	0.659103i
$672$	5.14669	+	0.836419i	0.198538	+	0.0322656i
$673$	10.7036	+	6.76852i	0.412592	+	0.260907i	0.724597	−	0.689173i	$-0.242026\pi$
$673$	10.7036	+	6.76852i	0.412592	+	0.260907i	−0.312005	+	0.950081i	$0.601000\pi$
$674$	28.8642	+	2.33016i	1.11181	+	0.0897544i
$675$	2.55494			0.0983396
$676$	2.40868	−	41.3888i	0.0926416	−	1.59188i
$677$	19.2408			0.739486			0.369743	−	0.929134i	$-0.379446\pi$
$677$	19.2408			0.739486			0.369743	+	0.929134i	$0.379446\pi$
$678$	−27.1386	−	2.19086i	−1.04225	−	0.0841394i
$679$	0.637699	+	0.403257i	0.0244727	+	0.0154756i
$680$	−3.32353	−	0.540126i	−0.127452	−	0.0207129i
$681$	−0.577627	−	0.511733i	−0.0221347	−	0.0196096i
$682$	−17.3761	−	13.0573i	−0.665366	−	0.499990i
$683$	−2.29072	+	2.38489i	−0.0876520	+	0.0912554i	−0.763584	−	0.645709i	$-0.776562\pi$
$683$	−2.29072	+	2.38489i	−0.0876520	+	0.0912554i	0.675932	+	0.736964i	$0.263741\pi$
$684$	14.7309	+	3.63085i	0.563252	+	0.138829i
$685$	22.9345	+	48.3334i	0.876282	+	1.84673i
$686$	18.4606	+	19.2196i	0.704830	+	0.733806i
$687$	−2.52316	+	5.31744i	−0.0962644	+	0.202873i
$688$	0.869429	+	0.770246i	0.0331467	+	0.0293654i
$689$	10.3957	−	7.03947i	0.396046	−	0.268183i
$690$	−7.80164	+	6.91165i	−0.297003	+	0.263122i
$691$	−9.39390	−	32.4315i	−0.357361	−	1.23375i	−0.914927	−	0.403620i	$-0.867752\pi$
$691$	−9.39390	−	32.4315i	−0.357361	−	1.23375i	0.557566	−	0.830133i	$-0.311736\pi$
$692$	56.1766	+	18.7545i	2.13551	+	0.712939i
$693$	−2.96661	+	3.08857i	−0.112692	+	0.117325i
$694$	−23.8569	−	62.9055i	−0.905596	−	2.38786i
$695$	−26.9141	+	46.6166i	−1.02091	+	1.76827i
$696$	6.88668	+	8.43465i	0.261039	+	0.319714i
$697$	2.53730	−	0.625389i	0.0961072	−	0.0236883i
$698$	−23.0421	+	39.9100i	−0.872155	+	1.51062i
$699$	12.3224	+	21.3431i	0.466078	+	0.807270i
$700$	4.99617	+	5.20156i	0.188837	+	0.196600i
$701$	−0.342508	−	2.82080i	−0.0129363	−	0.106540i	0.984810	−	0.173633i	$-0.0555507\pi$
$701$	−0.342508	−	2.82080i	−0.0129363	−	0.106540i	−0.997747	+	0.0670929i	$0.978628\pi$
$702$	−4.87528	−	6.60987i	−0.184006	−	0.249474i
$703$	4.24652	−	34.9732i	0.160161	−	1.31904i
$704$	50.2951	−	37.7943i	1.89557	−	1.42443i
$705$	14.6430	+	1.18210i	0.551487	+	0.0445206i
$706$	−9.63755	−	47.2078i	−0.362714	−	1.77669i
$707$	−1.83033	+	15.0741i	−0.0688366	+	0.566920i
$708$	26.3977	+	11.2470i	0.992086	+	0.422688i
$709$	−1.03929	+	0.657207i	−0.0390313	+	0.0246819i	−0.553839	−	0.832624i	$-0.686838\pi$
$709$	−1.03929	+	0.657207i	−0.0390313	+	0.0246819i	0.514808	+	0.857306i	$0.327863\pi$
$710$	70.1433	−	62.1416i	2.63243	−	2.33213i
$711$	4.92691	−	0.397741i	0.184774	−	0.0149165i
$712$	10.6987	+	36.9363i	0.400952	+	1.38425i
$713$	3.02025	−	1.28681i	0.113109	−	0.0481913i
$714$	0.518003	−	0.750456i	0.0193858	−	0.0280851i
$715$	−15.5888	+	45.3425i	−0.582988	+	1.69571i
$716$	45.1170	+	65.3633i	1.68610	+	2.44274i
$717$	3.98287	+	2.51861i	0.148743	+	0.0940593i
$718$	−28.6808	+	4.66108i	−1.07036	+	0.173950i
$719$	31.2537	+	13.3160i	1.16557	+	0.496601i	0.886073	−	0.463546i	$-0.153423\pi$
$719$	31.2537	+	13.3160i	1.16557	+	0.496601i	0.279493	+	0.960148i	$0.409833\pi$
$720$	0.324244	−	0.469748i	0.0120839	−	0.0175065i
$721$	−0.466386	+	1.61015i	−0.0173691	+	0.0599652i
$722$	−3.54705	−	7.47525i	−0.132007	−	0.278200i
$723$	−8.92924	+	23.5445i	−0.332082	+	0.875628i
$724$	24.6106	+	30.1425i	0.914644	+	1.12024i
$725$	−0.413546	−	10.2620i	−0.0153587	−	0.381123i
$726$	1.13808	+	28.2412i	0.0422381	+	1.04813i
$727$	0.883470	−	0.217756i	0.0327661	−	0.00807611i	−0.222899	−	0.974842i	$-0.571552\pi$
$727$	0.883470	−	0.217756i	0.0327661	−	0.00807611i	0.255665	+	0.966766i	$0.417706\pi$
$728$	1.46291	−	8.52052i	0.0542190	−	0.315792i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−6.55797	+	32.1230i	−0.242721	+	1.18893i
$731$	2.32712	−	0.991495i	0.0860718	−	0.0366718i
$732$	−14.3440	+	9.07060i	−0.530170	+	0.335259i
$733$	12.9652	−	6.80467i	0.478881	−	0.251336i	−0.207969	−	0.978135i	$-0.566685\pi$
$733$	12.9652	−	6.80467i	0.478881	−	0.251336i	0.686850	+	0.726799i	$0.258993\pi$
$734$	12.0756	+	1.96247i	0.445717	+	0.0724360i
$735$	16.2075	−	5.41084i	0.597821	−	0.199582i
$736$	1.18198	+	9.73449i	0.0435684	+	0.358818i
$737$	6.26858	−	21.6416i	0.230906	−	0.797180i
$738$	2.63299	−	12.8972i	0.0969216	−	0.474753i
$739$	−1.73909	−	0.580595i	−0.0639736	−	0.0213575i	0.284501	−	0.958676i	$-0.408172\pi$
$739$	−1.73909	−	0.580595i	−0.0639736	−	0.0213575i	−0.348475	+	0.937318i	$0.613300\pi$
$740$	57.4786	+	30.1671i	2.11296	+	1.10897i
$741$	−4.25345	+	16.6171i	−0.156254	+	0.610444i
$742$	6.21697	−	3.26292i	0.228232	−	0.119785i
$743$	−11.4969	+	1.86843i	−0.421780	+	0.0685459i	−0.367597	−	0.929985i	$-0.619819\pi$
$743$	−11.4969	+	1.86843i	−0.421780	+	0.0685459i	−0.0541827	+	0.998531i	$0.517255\pi$
$744$	4.27079	−	3.20929i	0.156575	−	0.117658i
$745$	−1.15753	+	28.7237i	−0.0424085	+	1.05236i
$746$	−78.8270			−2.88606
$747$	0.459796	−	11.4097i	0.0168231	−	0.417460i
$748$	−1.39573	−	6.83674i	−0.0510330	−	0.249976i
$749$	0.406161	+	0.588425i	0.0148408	+	0.0215006i
$750$	−14.5214	+	4.84794i	−0.530245	+	0.177022i
$751$	14.0153	−	29.5366i	0.511424	−	1.07780i	−0.469413	−	0.882978i	$-0.655535\pi$
$751$	14.0153	−	29.5366i	0.511424	−	1.07780i	0.980838	−	0.194826i	$-0.0624141\pi$
$752$	0.701950	−	0.859732i	0.0255975	−	0.0313512i
$753$	−8.33348	−	21.9736i	−0.303689	−	0.800762i
$754$	−25.7598	+	20.6517i	−0.938115	+	0.752091i
$755$	20.0370	−	52.8333i	0.729222	−	1.92280i
$756$	−1.41145	−	2.44471i	−0.0513340	−	0.0889131i
$757$	32.7147	−	40.0682i	1.18903	−	1.45630i	0.330304	−	0.943874i	$-0.392849\pi$
$757$	32.7147	−	40.0682i	1.18903	−	1.45630i	0.858730	−	0.512428i	$-0.171254\pi$
$758$	−39.8092	−	29.9147i	−1.44594	−	1.08655i
$759$	−7.13132	−	3.74281i	−0.258850	−	0.135855i
$760$	35.3061	−	2.85020i	1.28069	−	0.103388i
$761$	−47.1852	+	3.80919i	−1.71046	+	0.138083i	−0.896562	−	0.442919i	$-0.853943\pi$
$761$	−47.1852	+	3.80919i	−1.71046	+	0.138083i	−0.813902	+	0.581002i	$0.802661\pi$
$762$	11.0686	+	5.80927i	0.400975	+	0.210448i
$763$	−3.57362	−	2.68540i	−0.129374	−	0.0972181i
$764$	8.98554	−	11.0053i	0.325086	−	0.398158i
$765$	−0.621512	−	1.07649i	−0.0224708	−	0.0389206i
$766$	8.62061	−	22.7307i	0.311475	−	0.821293i
$767$	−12.9815	+	29.7298i	−0.468733	+	1.07348i
$768$	5.18870	+	13.6815i	0.187231	+	0.493688i
$769$	−2.25498	+	2.76185i	−0.0813166	+	0.0995947i	−0.813661	−

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.27058 + 0.183300i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(3.14784 + 0.511574i) q^{4} +(2.05738 + 1.82268i) q^{5} +(-1.82111 - 1.36847i) q^{6} +(0.613173 - 0.638380i) q^{7} +(2.63011 + 0.648264i) q^{8} +(0.428693 + 0.903450i) q^{9} +(4.33734 + 4.51565i) q^{10} +(-2.07407 + 4.37102i) q^{11} +(-2.38711 - 2.11479i) q^{12} +(2.41492 - 2.67734i) q^{13} +(1.50927 - 1.33710i) q^{14} +(-0.764715 - 2.64010i) q^{15} +(-0.196976 - 0.0657601i) q^{16} +(-0.313274 + 0.326153i) q^{17} +(0.807779 + 2.12994i) q^{18} +(2.37867 - 4.11997i) q^{19} +(5.54386 + 6.78999i) q^{20} +(-0.859440 + 0.211833i) q^{21} +(-5.51056 + 9.54458i) q^{22} +(-0.832328 - 1.44163i) q^{23} +(-1.87647 - 1.95361i) q^{24} +(0.307964 + 2.53631i) q^{25} +(5.97403 - 5.63647i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.25675 - 1.69584i) q^{28} +(-4.00678 - 0.323460i) q^{29} +(-1.25242 - 6.13474i) q^{30} +(-0.237716 + 1.95777i) q^{31} +(-5.41932 - 2.30896i) q^{32} +(4.08915 - 2.58582i) q^{33} +(-0.771098 + 0.683134i) q^{34} +(2.42509 - 0.195773i) q^{35} +(0.887275 + 3.06323i) q^{36} +(6.81284 - 2.90268i) q^{37} +(6.15615 - 8.91872i) q^{38} +(-3.47201 + 0.972172i) q^{39} +(4.22955 + 6.12756i) q^{40} +(-4.88393 - 3.08841i) q^{41} +(-1.99026 + 0.323448i) q^{42} +(-5.14583 - 2.19243i) q^{43} +(-8.76496 + 12.6982i) q^{44} +(-0.764715 + 2.64010i) q^{45} +(-1.62562 - 3.42592i) q^{46} +(-1.89526 + 4.99740i) q^{47} +(0.131335 + 0.160857i) q^{48} +(0.250313 + 6.21145i) q^{49} +(0.234351 + 5.81535i) q^{50} +(0.439094 - 0.108227i) q^{51} +(8.97144 - 7.19244i) q^{52} +(3.38092 + 0.833322i) q^{53} +(0.455652 - 2.23193i) q^{54} +(-12.2341 + 5.21246i) q^{55} +(2.02655 - 1.28151i) q^{56} +(-4.21241 + 2.21084i) q^{57} +(-9.03842 - 1.46889i) q^{58} +(-8.53430 + 2.84917i) q^{59} +(-1.05659 - 8.70184i) q^{60} +(1.48056 - 5.11150i) q^{61} +(-0.898614 + 4.40170i) q^{62} +(0.839607 + 0.280302i) q^{63} +(-11.5140 - 6.04303i) q^{64} +(9.84832 - 1.10668i) q^{65} +(9.75872 - 5.12177i) q^{66} +(-4.59669 + 0.747036i) q^{67} +(-1.15299 + 0.866415i) q^{68} +(-0.0670290 + 1.66331i) q^{69} +5.54224 q^{70} +(0.602647 - 14.9545i) q^{71} +(0.541835 + 2.65408i) q^{72} +(2.97453 + 4.30935i) q^{73} +(16.0012 - 5.34198i) q^{74} +(1.09528 - 2.30826i) q^{75} +(9.59534 - 11.7522i) q^{76} +(1.51861 + 4.00424i) q^{77} +(-8.06169 + 1.57097i) q^{78} +(1.75279 - 4.62173i) q^{79} +(-0.285393 - 0.494316i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-10.5233 - 7.90772i) q^{82} +(-10.1110 - 5.30667i) q^{83} +(-2.81375 + 0.227149i) q^{84} +(-1.23899 + 0.100022i) q^{85} +(-11.2822 - 5.92133i) q^{86} +(3.21361 + 2.41487i) q^{87} +(-8.28862 + 10.1517i) q^{88} +(7.09801 + 12.2941i) q^{89} +(-2.22028 + 5.85440i) q^{90} +(-0.228401 - 3.18331i) q^{91} +(-1.88253 - 4.96384i) q^{92} +(1.24728 - 1.52764i) q^{93} +(-5.21937 + 10.9996i) q^{94} +(12.4032 - 4.14079i) q^{95} +(3.34630 + 4.84795i) q^{96} +(0.170500 + 0.835166i) q^{97} +(-0.570205 + 14.1495i) q^{98} -4.83814 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

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