LMFDB - Embedded newform 504.2.cj.e.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 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("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30853 + 0.536416i) q^{2} +(1.42451 - 1.40384i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 + 2.60110i) q^{8} +O(q^{10})$	\(q+(-1.30853 + 0.536416i) q^{2} +(1.42451 - 1.40384i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 + 2.60110i) q^{8} +(-5.01398 - 0.678758i) q^{10} +(-0.815768 + 0.470984i) q^{11} +6.15117i q^{13} +(-2.61517 - 2.67598i) q^{14} +(0.0584850 - 3.99957i) q^{16} +(-1.89187 - 3.27682i) q^{17} +(-2.09110 - 1.20730i) q^{19} +(6.92506 - 1.80141i) q^{20} +(0.814815 - 1.05389i) q^{22} +(1.49371 - 2.58719i) q^{23} +(3.90019 + 6.75532i) q^{25} +(-3.29959 - 8.04900i) q^{26} +(4.85747 + 2.09879i) q^{28} +2.68125i q^{29} +(-5.35686 - 9.27835i) q^{31} +(2.06891 + 5.26494i) q^{32} +(4.23332 + 3.27300i) q^{34} +(-1.30906 + 9.37491i) q^{35} +(1.47851 + 0.853618i) q^{37} +(3.38389 + 0.458087i) q^{38} +(-8.09536 + 6.07191i) q^{40} +4.56000 q^{41} +3.50672i q^{43} +(-0.500889 + 1.81613i) q^{44} +(-0.566763 + 4.18667i) q^{46} +(-3.42292 + 5.92866i) q^{47} +(-5.02673 + 4.87155i) q^{49} +(-8.72718 - 6.74743i) q^{50} +(8.63523 + 8.76243i) q^{52} +(6.57466 - 3.79588i) q^{53} -3.37013 q^{55} +(-7.48199 - 0.140711i) q^{56} +(-1.43827 - 3.50851i) q^{58} +(0.100623 - 0.0580947i) q^{59} +(7.06184 + 4.07716i) q^{61} +(11.9867 + 9.26752i) q^{62} +(-5.53143 - 5.77955i) q^{64} +(-11.0037 + 19.0590i) q^{65} +(3.44314 - 1.98790i) q^{67} +(-7.29513 - 2.01200i) q^{68} +(-3.31590 - 12.9696i) q^{70} +3.92572 q^{71} +(-3.11438 - 5.39427i) q^{73} +(-2.39257 - 0.323890i) q^{74} +(-4.67365 + 1.21575i) q^{76} +(-1.96525 - 1.53261i) q^{77} +(2.73628 - 4.73937i) q^{79} +(7.33597 - 12.2878i) q^{80} +(-5.96690 + 2.44606i) q^{82} +1.19560i q^{83} -13.5373i q^{85} +(-1.88106 - 4.58866i) q^{86} +(-0.318771 - 2.64515i) q^{88} +(-0.910509 + 1.57705i) q^{89} +(-15.0840 + 6.10992i) q^{91} +(-1.50417 - 5.78242i) q^{92} +(1.29876 - 9.59396i) q^{94} +(-4.31942 - 7.48146i) q^{95} +12.0241 q^{97} +(3.96446 - 9.07100i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.30853	+	0.536416i	−0.925272	+	0.379304i
$2$	−1.30853	+	0.536416i	−0.925272	+	0.379304i
$3$		0			0
$3$		0			0
$4$	1.42451	−	1.40384i	0.712257	−	0.701918i
$5$	3.09843	+	1.78888i	1.38566	+	0.800012i	0.992823	−	0.119596i	$-0.0381600\pi$
$5$	3.09843	+	1.78888i	1.38566	+	0.800012i	0.392838	+	0.919608i	$0.371493\pi$
$6$		0			0
$7$	0.993295	+	2.45222i	0.375430	+	0.926851i
$7$	0.993295	+	2.45222i	0.375430	+	0.926851i
$8$	−1.11098	+	2.60110i	−0.392792	+	0.919627i
$9$		0			0
$10$	−5.01398	−	0.678758i	−1.58556	−	0.214642i
$11$	−0.815768	+	0.470984i	−0.245963	+	0.142007i	−0.617914	−	0.786245i	$-0.712022\pi$
$11$	−0.815768	+	0.470984i	−0.245963	+	0.142007i	0.371951	+	0.928252i	$0.378689\pi$
$12$		0			0
$13$			6.15117i			1.70603i	0.521889	+	0.853013i	$0.325228\pi$
$13$			6.15117i			1.70603i	−0.521889	+	0.853013i	$0.674772\pi$
$14$	−2.61517	−	2.67598i	−0.698933	−	0.715187i
$15$		0			0
$16$	0.0584850	−	3.99957i	0.0146212	−	0.999893i
$17$	−1.89187	−	3.27682i	−0.458847	−	0.794746i	0.540053	−	0.841631i	$-0.318404\pi$
$17$	−1.89187	−	3.27682i	−0.458847	−	0.794746i	−0.998900	+	0.0468845i	$0.985071\pi$
$18$		0			0
$19$	−2.09110	−	1.20730i	−0.479731	−	0.276973i	0.240573	−	0.970631i	$-0.422665\pi$
$19$	−2.09110	−	1.20730i	−0.479731	−	0.276973i	−0.720305	+	0.693658i	$0.755998\pi$
$20$	6.92506	−	1.80141i	1.54849	−	0.402806i
$21$		0			0
$22$	0.814815	−	1.05389i	0.173719	−	0.224690i
$23$	1.49371	−	2.58719i	0.311461	−	0.539466i	−0.667218	−	0.744863i	$-0.732515\pi$
$23$	1.49371	−	2.58719i	0.311461	−	0.539466i	0.978679	+	0.205396i	$0.0658483\pi$
$24$		0			0
$25$	3.90019	+	6.75532i	0.780037	+	1.35106i
$26$	−3.29959	−	8.04900i	−0.647102	−	1.57854i
$27$		0			0
$28$	4.85747	+	2.09879i	0.917976	+	0.396635i
$29$			2.68125i			0.497897i	0.968517	+	0.248948i	$0.0800849\pi$
$29$			2.68125i			0.497897i	−0.968517	+	0.248948i	$0.919915\pi$
$30$		0			0
$31$	−5.35686	−	9.27835i	−0.962120	−	1.66644i	−0.717160	−	0.696908i	$-0.754559\pi$
$31$	−5.35686	−	9.27835i	−0.962120	−	1.66644i	−0.244960	−	0.969533i	$-0.578775\pi$
$32$	2.06891	+	5.26494i	0.365735	+	0.930719i
$33$		0			0
$34$	4.23332	+	3.27300i	0.726009	+	0.561314i
$35$	−1.30906	+	9.37491i	−0.221272	+	1.58465i
$36$		0			0
$37$	1.47851	+	0.853618i	0.243065	+	0.140334i	0.616585	−	0.787288i	$-0.288516\pi$
$37$	1.47851	+	0.853618i	0.243065	+	0.140334i	−0.373519	+	0.927622i	$0.621849\pi$
$38$	3.38389	+	0.458087i	0.548939	+	0.0743116i
$39$		0			0
$40$	−8.09536	+	6.07191i	−1.27999	+	0.960054i
$41$	4.56000			0.712152			0.356076	−	0.934457i	$-0.384114\pi$
$41$	4.56000			0.712152			0.356076	+	0.934457i	$0.384114\pi$
$42$		0			0
$43$			3.50672i			0.534770i	0.963590	+	0.267385i	$0.0861596\pi$
$43$			3.50672i			0.534770i	−0.963590	+	0.267385i	$0.913840\pi$
$44$	−0.500889	+	1.81613i	−0.0755118	+	0.273792i
$45$		0			0
$46$	−0.566763	+	4.18667i	−0.0835647	+	0.617291i
$47$	−3.42292	+	5.92866i	−0.499284	+	0.864785i	−1.00000		0.000827022i	$-0.999737\pi$
$47$	−3.42292	+	5.92866i	−0.499284	+	0.864785i	0.500716	+	0.865612i	$0.333070\pi$
$48$		0			0
$49$	−5.02673	+	4.87155i	−0.718104	+	0.695936i
$50$	−8.72718	−	6.74743i	−1.23421	−	0.954231i
$51$		0			0
$52$	8.63523	+	8.76243i	1.19749	+	1.21513i
$53$	6.57466	−	3.79588i	0.903099	−	0.521404i	0.0248947	−	0.999690i	$-0.492075\pi$
$53$	6.57466	−	3.79588i	0.903099	−	0.521404i	0.878204	+	0.478286i	$0.158742\pi$
$54$		0			0
$55$	−3.37013			−0.454429
$56$	−7.48199	−	0.140711i	−0.999823	−	0.0188033i
$57$		0			0
$58$	−1.43827	−	3.50851i	−0.188854	−	0.460690i
$59$	0.100623	−	0.0580947i	0.0131000	−	0.00756328i	−0.493436	−	0.869782i	$-0.664259\pi$
$59$	0.100623	−	0.0580947i	0.0131000	−	0.00756328i	0.506536	+	0.862219i	$0.330926\pi$
$60$		0			0
$61$	7.06184	+	4.07716i	0.904176	+	0.522027i	0.878553	−	0.477645i	$-0.158510\pi$
$61$	7.06184	+	4.07716i	0.904176	+	0.522027i	0.0256236	+	0.999672i	$0.491843\pi$
$62$	11.9867	+	9.26752i	1.52231	+	1.17698i
$63$		0			0
$64$	−5.53143	−	5.77955i	−0.691429	−	0.722444i
$65$	−11.0037	+	19.0590i	−1.36484	+	2.36397i
$66$		0			0
$67$	3.44314	−	1.98790i	0.420647	−	0.242861i	−0.274707	−	0.961528i	$-0.588581\pi$
$67$	3.44314	−	1.98790i	0.420647	−	0.242861i	0.695354	+	0.718667i	$0.255248\pi$
$68$	−7.29513	−	2.01200i	−0.884664	−	0.243991i
$69$		0			0
$70$	−3.31590	−	12.9696i	−0.396326	−	1.55016i
$71$	3.92572			0.465897			0.232949	−	0.972489i	$-0.425163\pi$
$71$	3.92572			0.465897			0.232949	+	0.972489i	$0.425163\pi$
$72$		0			0
$73$	−3.11438	−	5.39427i	−0.364511	−	0.631351i	0.624187	−	0.781275i	$-0.285430\pi$
$73$	−3.11438	−	5.39427i	−0.364511	−	0.631351i	−0.988698	+	0.149924i	$0.952097\pi$
$74$	−2.39257	−	0.323890i	−0.278131	−	0.0376514i
$75$		0			0
$76$	−4.67365	+	1.21575i	−0.536105	+	0.139456i
$77$	−1.96525	−	1.53261i	−0.223961	−	0.174657i
$78$		0			0
$79$	2.73628	−	4.73937i	0.307855	−	0.533221i	−0.670038	−	0.742327i	$-0.733722\pi$
$79$	2.73628	−	4.73937i	0.307855	−	0.533221i	0.977893	+	0.209106i	$0.0670555\pi$
$80$	7.33597	−	12.2878i	0.820186	−	1.37382i
$81$		0			0
$82$	−5.96690	+	2.44606i	−0.658934	+	0.270122i
$83$			1.19560i			0.131234i	0.997845	+	0.0656172i	$0.0209016\pi$
$83$			1.19560i			0.131234i	−0.997845	+	0.0656172i	$0.979098\pi$
$84$		0			0
$85$		−	13.5373i		−	1.46833i
$86$	−1.88106	−	4.58866i	−0.202840	−	0.494808i
$87$		0			0
$88$	−0.318771	−	2.64515i	−0.0339811	−	0.281974i
$89$	−0.910509	+	1.57705i	−0.0965138	+	0.167167i	−0.910239	−	0.414082i	$-0.864103\pi$
$89$	−0.910509	+	1.57705i	−0.0965138	+	0.167167i	0.813726	+	0.581249i	$0.197436\pi$
$90$		0			0
$91$	−15.0840	+	6.10992i	−1.58123	+	0.640494i
$92$	−1.50417	−	5.78242i	−0.156821	−	0.602859i
$93$		0			0
$94$	1.29876	−	9.59396i	0.133957	−	0.989541i
$95$	−4.31942	−	7.48146i	−0.443163	−	0.767581i
$96$		0			0
$97$	12.0241			1.22086			0.610431	−	0.792069i	$-0.290996\pi$
$97$	12.0241			1.22086			0.610431	+	0.792069i	$0.290996\pi$
$98$	3.96446	−	9.07100i	0.400471	−	0.916309i
$99$		0			0
$100$	15.0392	+	4.14783i	1.50392	+	0.414783i
$101$	1.54240	−	0.890504i	0.153474	−	0.0886085i	−0.421296	−	0.906923i	$-0.638425\pi$
$101$	1.54240	−	0.890504i	0.153474	−	0.0886085i	0.574770	+	0.818315i	$0.305091\pi$
$102$		0			0
$103$	6.21150	−	10.7586i	0.612037	−	1.06008i	−0.378859	−	0.925454i	$-0.623684\pi$
$103$	6.21150	−	10.7586i	0.612037	−	1.06008i	0.990897	−	0.134625i	$-0.0429831\pi$
$104$	−15.9998	−	6.83384i	−1.56891	−	0.670113i
$105$		0			0
$106$	−6.56698	+	8.49379i	−0.637842	+	0.824990i
$107$	8.41266	+	4.85705i	0.813283	+	0.469549i	0.848095	−	0.529845i	$-0.177750\pi$
$107$	8.41266	+	4.85705i	0.813283	+	0.469549i	−0.0348118	+	0.999394i	$0.511083\pi$
$108$		0			0
$109$	12.3647	−	7.13874i	1.18432	−	0.683767i	0.227309	−	0.973823i	$-0.427007\pi$
$109$	12.3647	−	7.13874i	1.18432	−	0.683767i	0.957010	+	0.290055i	$0.0936738\pi$
$110$	4.40993	−	1.80779i	0.420470	−	0.172366i
$111$		0			0
$112$	9.86591	−	3.82934i	0.932241	−	0.361838i
$113$	13.8775			1.30549			0.652743	−	0.757580i	$-0.273618\pi$
$113$	13.8775			1.30549			0.652743	+	0.757580i	$0.273618\pi$
$114$		0			0
$115$	9.25634	−	5.34415i	0.863159	−	0.498345i
$116$	3.76404	+	3.81949i	0.349483	+	0.354630i
$117$		0			0
$118$	−0.100505	+	0.129995i	−0.00925228	+	0.0119670i
$119$	6.15629	−	7.89414i	0.564346	−	0.723654i
$120$		0			0
$121$	−5.05635	+	8.75785i	−0.459668	+	0.796168i
$122$	−11.4277	−	1.54700i	−1.03462	−	0.140059i
$123$		0			0
$124$	−20.6562	−	5.69699i	−1.85498	−	0.511605i
$125$			10.0191i			0.896131i
$126$		0			0
$127$	7.77389			0.689822			0.344911	−	0.938635i	$-0.387909\pi$
$127$	7.77389			0.689822			0.344911	+	0.938635i	$0.387909\pi$
$128$	10.3383	+	4.59558i	0.913786	+	0.406196i
$129$		0			0
$130$	4.17516	−	30.8418i	0.366185	−	2.70501i
$131$	−6.10134	−	3.52261i	−0.533076	−	0.307772i	0.209192	−	0.977875i	$-0.432917\pi$
$131$	−6.10134	−	3.52261i	−0.533076	−	0.307772i	−0.742268	+	0.670103i	$0.766250\pi$
$132$		0			0
$133$	0.883475	−	6.32703i	0.0766070	−	0.548623i
$134$	−3.43912	+	4.44819i	−0.297095	+	0.384265i
$135$		0			0
$136$	10.6252	−	1.28046i	0.911102	−	0.109798i
$137$	−9.05379	−	15.6816i	−0.773518	−	1.33977i	−0.935624	−	0.352999i	$-0.885162\pi$
$137$	−9.05379	−	15.6816i	−0.773518	−	1.33977i	0.162106	−	0.986773i	$-0.448171\pi$
$138$		0			0
$139$			8.32721i			0.706305i	0.935566	+	0.353152i	$0.114890\pi$
$139$			8.32721i			0.706305i	−0.935566	+	0.353152i	$0.885110\pi$
$140$	11.2961	+	15.1924i	0.954691	+	1.28399i
$141$		0			0
$142$	−5.13693	+	2.10582i	−0.431082	+	0.176716i
$143$	−2.89710	−	5.01792i	−0.242268	−	0.419620i
$144$		0			0
$145$	−4.79644	+	8.30768i	−0.398323	+	0.689916i
$146$	6.96884	+	5.38797i	0.576746	+	0.445911i
$147$		0			0
$148$	3.30450	−	0.859595i	0.271628	−	0.0706582i
$149$	−17.9316	−	10.3528i	−1.46901	−	0.848134i	−0.469614	−	0.882872i	$-0.655607\pi$
$149$	−17.9316	−	10.3528i	−1.46901	−	0.848134i	−0.999396	+	0.0347378i	$0.988940\pi$
$150$		0			0
$151$	−1.97783	−	3.42570i	−0.160954	−	0.278780i	0.774257	−	0.632871i	$-0.218124\pi$
$151$	−1.97783	−	3.42570i	−0.160954	−	0.278780i	−0.935211	+	0.354091i	$0.884790\pi$
$152$	5.46348	−	4.09787i	0.443147	−	0.332381i
$153$		0			0
$154$	3.39371	+	0.951280i	0.273473	+	0.0766564i
$155$		−	38.3311i		−	3.07883i
$156$		0			0
$157$	−10.2803	+	5.93532i	−0.820456	+	0.473690i	−0.850574	−	0.525856i	$-0.823745\pi$
$157$	−10.2803	+	5.93532i	−0.820456	+	0.473690i	0.0301179	+	0.999546i	$0.490412\pi$
$158$	−1.03823	+	7.66940i	−0.0825972	+	0.610145i
$159$		0			0
$160$	−3.00799	+	20.0141i	−0.237802	+	1.58225i
$161$	7.82805	+	1.09307i	0.616937	+	0.0861459i
$162$		0			0
$163$	−14.7683	−	8.52649i	−1.15674	−	0.667846i	−0.206222	−	0.978505i	$-0.566117\pi$
$163$	−14.7683	−	8.52649i	−1.15674	−	0.667846i	−0.950522	+	0.310659i	$0.899450\pi$
$164$	6.49578	−	6.40149i	0.507235	−	0.499872i
$165$		0			0
$166$	−0.641341	−	1.56449i	−0.0497777	−	0.121428i
$167$	−10.4339			−0.807396			−0.403698	−	0.914892i	$-0.632275\pi$
$167$	−10.4339			−0.807396			−0.403698	+	0.914892i	$0.632275\pi$
$168$		0			0
$169$	−24.8369			−1.91053
$170$	7.26166	+	17.7141i	0.556944	+	1.35861i
$171$		0			0
$172$	4.92287	+	4.99538i	0.375365	+	0.380894i
$173$	12.6216	+	7.28708i	0.959602	+	0.554027i	0.896051	−	0.443952i	$-0.146424\pi$
$173$	12.6216	+	7.28708i	0.959602	+	0.554027i	0.0635517	+	0.997979i	$0.479757\pi$
$174$		0			0
$175$	−12.6915	+	16.2741i	−0.959385	+	1.23021i
$176$	1.83602	+	3.29027i	0.138395	+	0.248013i
$177$		0			0
$178$	0.345476	−	2.55203i	0.0258945	−	0.191283i
$179$	3.27323	−	1.88980i	0.244653	−	0.141251i	−0.372660	−	0.927968i	$-0.621554\pi$
$179$	3.27323	−	1.88980i	0.244653	−	0.141251i	0.617313	+	0.786717i	$0.288221\pi$
$180$		0			0
$181$		−	1.12363i		−	0.0835189i	−0.999128	−	0.0417595i	$-0.986704\pi$
$181$		−	1.12363i		−	0.0835189i	0.999128	−	0.0417595i	$-0.0132963\pi$
$182$	16.4604	−	16.0863i	1.22013	−	1.19240i
$183$		0			0
$184$	5.07004	+	6.75962i	0.373769	+	0.498326i
$185$	3.05404	+	5.28975i	0.224537	+	0.388910i
$186$		0			0
$187$	3.08666	+	1.78208i	0.225719	+	0.130319i
$188$	3.44688	+	13.2507i	0.251390	+	0.966406i
$189$		0			0
$190$	9.66528	+	7.47272i	0.701193	+	0.542128i
$191$	7.01502	−	12.1504i	0.507589	−	0.879169i	−0.492373	−	0.870384i	$-0.663870\pi$
$191$	7.01502	−	12.1504i	0.507589	−	0.879169i	0.999961	−	0.00878494i	$-0.00279637\pi$
$192$		0			0
$193$	−0.390098	−	0.675669i	−0.0280798	−	0.0486357i	0.851644	−	0.524121i	$-0.175606\pi$
$193$	−0.390098	−	0.675669i	−0.0280798	−	0.0486357i	−0.879724	+	0.475485i	$0.842273\pi$
$194$	−15.7339	+	6.44993i	−1.12963	+	0.463078i
$195$		0			0
$196$	−0.321791	+	13.9963i	−0.0229851	+	0.999736i
$197$			2.37637i			0.169309i	0.996410	+	0.0846545i	$0.0269787\pi$
$197$			2.37637i			0.169309i	−0.996410	+	0.0846545i	$0.973021\pi$
$198$		0			0
$199$	6.79196	+	11.7640i	0.481469	+	0.833929i	0.999774	−	0.0212671i	$-0.00677004\pi$
$199$	6.79196	+	11.7640i	0.481469	+	0.833929i	−0.518305	+	0.855196i	$0.673437\pi$
$200$	−21.9043	+	2.63972i	−1.54887	+	0.186657i
$201$		0			0
$202$	−1.54060	+	1.99262i	−0.108396	+	0.140200i
$203$	−6.57502	+	2.66328i	−0.461476	+	0.186925i
$204$		0			0
$205$	14.1288	+	8.15729i	0.986801	+	0.569730i
$206$	−2.35684	+	17.4100i	−0.164209	+	1.21301i
$207$		0			0
$208$	24.6020	+	0.359751i	1.70584	+	0.0249442i
$209$	2.27447			0.157328
$210$		0			0
$211$		−	14.1932i		−	0.977103i	−0.872535	−	0.488551i	$-0.837526\pi$
$211$		−	14.1932i		−	0.977103i	0.872535	−	0.488551i	$-0.162474\pi$
$212$	4.03690	−	14.6370i	0.277256	−	1.00528i
$213$		0			0
$214$	−13.6136	−	1.84292i	−0.930610	−	0.125980i
$215$	−6.27311	+	10.8653i	−0.427823	+	0.741010i
$216$		0			0
$217$	17.4316	−	22.3523i	1.18333	−	1.51737i
$218$	−12.3502	+	15.9739i	−0.836462	+	1.08189i
$219$		0			0
$220$	−4.80081	+	4.73112i	−0.323670	+	0.318972i
$221$	20.1563	−	11.6372i	1.35586	−	0.782805i
$222$		0			0
$223$	−0.198178			−0.0132710			−0.00663548	−	0.999978i	$-0.502112\pi$
$223$	−0.198178			−0.0132710			−0.00663548	+	0.999978i	$0.502112\pi$
$224$	−10.8557	+	10.3030i	−0.725330	+	0.688401i
$225$		0			0
$226$	−18.1592	+	7.44412i	−1.20793	+	0.495175i
$227$	−22.3054	+	12.8780i	−1.48046	+	0.854744i	−0.999755	−	0.0221381i	$-0.992953\pi$
$227$	−22.3054	+	12.8780i	−1.48046	+	0.854744i	−0.480705	+	0.876882i	$0.659619\pi$
$228$		0			0
$229$	−13.9965	−	8.08087i	−0.924913	−	0.533999i	−0.0397138	−	0.999211i	$-0.512645\pi$
$229$	−13.9965	−	8.08087i	−0.924913	−	0.533999i	−0.885199	+	0.465212i	$0.845978\pi$
$230$	−9.24554	+	11.9583i	−0.609633	+	0.788504i
$231$		0			0
$232$	−6.97421	−	2.97883i	−0.457879	−	0.195570i
$233$	12.5619	−	21.7579i	0.822959	−	1.42541i	−0.0805094	−	0.996754i	$-0.525655\pi$
$233$	12.5619	−	21.7579i	0.822959	−	1.42541i	0.903469	−	0.428654i	$-0.141012\pi$
$234$		0			0
$235$	−21.2113	+	12.2464i	−1.38368	+	0.798865i
$236$	0.0617834	−	0.224015i	0.00402176	−	0.0145821i
$237$		0			0
$238$	−3.82116	+	13.6321i	−0.247689	+	0.883636i
$239$	−16.0389			−1.03747			−0.518736	−	0.854935i	$-0.673597\pi$
$239$	−16.0389			−1.03747			−0.518736	+	0.854935i	$0.673597\pi$
$240$		0			0
$241$	6.58453	+	11.4047i	0.424147	+	0.734643i	0.996340	−	0.0854750i	$-0.0272408\pi$
$241$	6.58453	+	11.4047i	0.424147	+	0.734643i	−0.572194	+	0.820119i	$0.693907\pi$
$242$	1.91854	−	14.1722i	0.123328	−	0.911026i
$243$		0			0
$244$	15.7834	−	4.10570i	1.01043	−	0.262841i
$245$	−24.2896	+	6.10194i	−1.55181	+	0.389839i
$246$		0			0
$247$	7.42629	−	12.8627i	0.472523	−	0.818435i
$248$	30.0853	−	3.62563i	1.91042	−	0.230228i
$249$		0			0
$250$	−5.37439	−	13.1103i	−0.339906	−	0.829166i
$251$		−	8.64704i		−	0.545796i	−0.962043	−	0.272898i	$-0.912018\pi$
$251$		−	8.64704i		−	0.545796i	0.962043	−	0.272898i	$-0.0879822\pi$
$252$		0			0
$253$			2.81406i			0.176918i
$254$	−10.1724	+	4.17004i	−0.638273	+	0.261652i
$255$		0			0
$256$	−15.9932	−	0.467830i	−0.999572	−	0.0292394i
$257$	−7.23254	+	12.5271i	−0.451154	+	0.781421i	−0.998458	−	0.0555126i	$-0.982321\pi$
$257$	−7.23254	+	12.5271i	−0.451154	+	0.781421i	0.547304	+	0.836934i	$0.315654\pi$
$258$		0			0
$259$	−0.624659	+	4.47352i	−0.0388144	+	0.277971i
$260$	11.0807	+	42.5972i	0.687199	+	2.64177i
$261$		0			0
$262$	9.87338	+	1.33659i	0.609980	+	0.0825748i
$263$	9.94833	+	17.2310i	0.613440	+	1.06251i	0.990656	+	0.136384i	$0.0435481\pi$
$263$	9.94833	+	17.2310i	0.613440	+	1.06251i	−0.377216	+	0.926125i	$0.623119\pi$
$264$		0			0
$265$	27.1615			1.66852
$266$	2.23787	+	8.75304i	0.137213	+	0.536683i
$267$		0			0
$268$	2.11412	−	7.66540i	0.129141	−	0.468239i
$269$	−14.6930	+	8.48299i	−0.895847	+	0.517217i	−0.875850	−	0.482583i	$-0.839699\pi$
$269$	−14.6930	+	8.48299i	−0.895847	+	0.517217i	−0.0199962	+	0.999800i	$0.506365\pi$
$270$		0			0
$271$	−0.538186	+	0.932165i	−0.0326925	+	0.0566250i	−0.881909	−	0.471420i	$-0.843742\pi$
$271$	−0.538186	+	0.932165i	−0.0326925	+	0.0566250i	0.849216	+	0.528045i	$0.177075\pi$
$272$	−13.2165	+	7.37504i	−0.801370	+	0.447178i
$273$		0			0
$274$	20.2591	+	15.6633i	1.22390	+	0.946256i
$275$	−6.36329	−	3.67385i	−0.383721	−	0.221541i
$276$		0			0
$277$	4.23611	−	2.44572i	0.254523	−	0.146949i	−0.367311	−	0.930098i	$-0.619721\pi$
$277$	4.23611	−	2.44572i	0.254523	−	0.146949i	0.621834	+	0.783149i	$0.286388\pi$
$278$	−4.46685	−	10.8964i	−0.267904	−	0.653524i
$279$		0			0
$280$	−22.9307	−	13.8204i	−1.37037	−	0.825925i
$281$	0.754188			0.0449911			0.0224956	−	0.999747i	$-0.492839\pi$
$281$	0.754188			0.0449911			0.0224956	+	0.999747i	$0.492839\pi$
$282$		0			0
$283$	16.8270	−	9.71510i	1.00026	−	0.577503i	0.0919376	−	0.995765i	$-0.470694\pi$
$283$	16.8270	−	9.71510i	1.00026	−	0.577503i	0.908326	+	0.418262i	$0.137361\pi$
$284$	5.59224	−	5.51107i	0.331839	−	0.327022i
$285$		0			0
$286$	6.48265	+	5.01206i	0.383327	+	0.296370i
$287$	4.52942	+	11.1821i	0.267363	+	0.660058i
$288$		0			0
$289$	1.34162	−	2.32376i	0.0789189	−	0.136691i
$290$	1.81992	−	13.4438i	0.106870	−	0.789445i
$291$		0			0
$292$	−12.0092	−	3.31213i	−0.702782	−	0.193828i
$293$		−	21.9433i		−	1.28194i	−0.767564	−	0.640972i	$-0.778532\pi$
$293$		−	21.9433i		−	1.28194i	0.767564	−	0.640972i	$-0.221468\pi$
$294$		0			0
$295$	0.415698			0.0242029
$296$	−3.86294	+	2.89739i	−0.224529	+	0.168408i
$297$		0			0
$298$	29.0174	+	3.92818i	1.68094	+	0.227553i
$299$	15.9142	+	9.18809i	0.920344	+	0.531361i
$300$		0			0
$301$	−8.59925	+	3.48321i	−0.495652	+	0.200769i
$302$	4.42566	+	3.42170i	0.254668	+	0.196897i
$303$		0			0
$304$	−4.95097	+	8.29290i	−0.283958	+	0.475630i
$305$	14.5871	+	25.2656i	0.835255	+	1.44670i
$306$		0			0
$307$			2.18555i			0.124736i	0.998053	+	0.0623679i	$0.0198652\pi$
$307$			2.18555i			0.124736i	−0.998053	+	0.0623679i	$0.980135\pi$
$308$	−4.95107	+	0.575663i	−0.282113	+	0.0328014i
$309$		0			0
$310$	20.5614	+	50.1575i	1.16781	+	2.84876i
$311$	13.6343	+	23.6152i	0.773129	+	1.33910i	0.935840	+	0.352424i	$0.114643\pi$
$311$	13.6343	+	23.6152i	0.773129	+	1.33910i	−0.162712	+	0.986674i	$0.552024\pi$
$312$		0			0
$313$	0.683268	−	1.18346i	0.0386206	−	0.0668929i	−0.846069	−	0.533073i	$-0.821037\pi$
$313$	0.683268	−	1.18346i	0.0386206	−	0.0668929i	0.884690	+	0.466181i	$0.154370\pi$
$314$	10.2683	−	13.2811i	0.579472	−	0.749494i
$315$		0			0
$316$	−2.75543	−	10.5926i	−0.155005	−	0.595879i
$317$	−7.09368	−	4.09554i	−0.398421	−	0.230028i	0.287382	−	0.957816i	$-0.407215\pi$
$317$	−7.09368	−	4.09554i	−0.398421	−	0.230028i	−0.685802	+	0.727788i	$0.740549\pi$
$318$		0			0
$319$	−1.26283	−	2.18728i	−0.0707048	−	0.122464i
$320$	−6.79984	−	27.8026i	−0.380123	−	1.55421i
$321$		0			0
$322$	−10.8296	+	2.76878i	−0.603510	+	0.154298i
$323$			9.13622i			0.508353i
$324$		0			0
$325$	−41.5531	+	23.9907i	−2.30495	+	1.33076i
$326$	23.8986	+	3.23522i	1.32362	+	0.179183i
$327$		0			0
$328$	−5.06608	+	11.8610i	−0.279727	+	0.654914i
$329$	−17.9383	−	2.50482i	−0.988972	−	0.138095i
$330$		0			0
$331$	13.3643	+	7.71590i	0.734570	+	0.424104i	0.820092	−	0.572232i	$-0.193922\pi$
$331$	13.3643	+	7.71590i	0.734570	+	0.424104i	−0.0855218	+	0.996336i	$0.527256\pi$
$332$	1.67843	+	1.70315i	0.0921159	+	0.0934727i
$333$		0			0
$334$	13.6530	−	5.59689i	0.747061	−	0.306248i
$335$	14.2245			0.777165
$336$		0			0
$337$	−0.543923			−0.0296294			−0.0148147	−	0.999890i	$-0.504716\pi$
$337$	−0.543923			−0.0296294			−0.0148147	+	0.999890i	$0.504716\pi$
$338$	32.4998	−	13.3229i	1.76776	−	0.724670i
$339$		0			0
$340$	−19.0042	−	19.2842i	−1.03065	−	1.04583i
$341$	8.73990	+	5.04599i	0.473292	+	0.273255i
$342$		0			0
$343$	−16.9391	−	7.48774i	−0.914626	−	0.404300i
$344$	−9.12134	−	3.89591i	−0.491790	−	0.210053i
$345$		0			0
$346$	−20.4247	−	2.76495i	−1.09804	−	0.148645i
$347$	−9.92740	+	5.73159i	−0.532931	+	0.307688i	−0.742209	−	0.670168i	$-0.766222\pi$
$347$	−9.92740	+	5.73159i	−0.532931	+	0.307688i	0.209278	+	0.977856i	$0.432889\pi$
$348$		0			0
$349$		−	1.23092i		−	0.0658899i	−0.999457	−	0.0329449i	$-0.989511\pi$
$349$		−	1.23092i		−	0.0658899i	0.999457	−	0.0329449i	$-0.0104886\pi$
$350$	7.87749	−	28.1031i	0.421070	−	1.50218i
$351$		0			0
$352$	−4.16745	−	3.32055i	−0.222126	−	0.176986i
$353$	−17.1091	−	29.6339i	−0.910628	−	1.57725i	−0.813179	−	0.582013i	$-0.802265\pi$
$353$	−17.1091	−	29.6339i	−0.910628	−	1.57725i	−0.0974483	−	0.995241i	$-0.531068\pi$
$354$		0			0
$355$	12.1636	+	7.02264i	0.645575	+	0.372723i
$356$	0.916884	+	3.52473i	0.0485948	+	0.186811i
$357$		0			0
$358$	−3.26941	+	4.22869i	−0.172794	+	0.223493i
$359$	16.9536	−	29.3645i	0.894777	−	1.54980i	0.0606972	−	0.998156i	$-0.480668\pi$
$359$	16.9536	−	29.3645i	0.894777	−	1.54980i	0.834080	−	0.551643i	$-0.185999\pi$
$360$		0			0
$361$	−6.58487	−	11.4053i	−0.346572	−	0.600280i
$362$	0.602735	+	1.47031i	0.0316790	+	0.0772777i
$363$		0			0
$364$	−12.9100	+	29.8791i	−0.676670	+	1.56609i
$365$		−	22.2850i		−	1.16645i
$366$		0			0
$367$	9.62235	+	16.6664i	0.502282	+	0.869979i	0.999997	+	0.00263748i	$0.000839536\pi$
$367$	9.62235	+	16.6664i	0.502282	+	0.869979i	−0.497714	+	0.867341i	$0.665827\pi$
$368$	−10.2603	−	6.12553i	−0.534855	−	0.319315i
$369$		0			0
$370$	−6.83382	−	5.28358i	−0.355273	−	0.274680i
$371$	15.8389	+	12.3521i	0.822315	+	0.641287i
$372$		0			0
$373$	12.8464	+	7.41686i	0.665160	+	0.384030i	0.794240	−	0.607604i	$-0.207869\pi$
$373$	12.8464	+	7.41686i	0.665160	+	0.384030i	−0.129080	+	0.991634i	$0.541202\pi$
$374$	−4.99493	−	0.676180i	−0.258282	−	0.0349644i
$375$		0			0
$376$	−11.6182	−	15.4900i	−0.599165	−	0.798835i
$377$	−16.4928			−0.849425
$378$		0			0
$379$		−	11.7500i		−	0.603555i	−0.953378	−	0.301778i	$-0.902420\pi$
$379$		−	11.7500i		−	0.603555i	0.953378	−	0.301778i	$-0.0975800\pi$
$380$	−16.6558	−	4.59368i	−0.854426	−	0.235651i
$381$		0			0
$382$	−2.66172	+	19.6621i	−0.136186	+	1.00600i
$383$	9.53274	−	16.5112i	0.487100	−	0.843682i	−0.512790	−	0.858514i	$-0.671388\pi$
$383$	9.53274	−	16.5112i	0.487100	−	0.843682i	0.999890	+	0.0148320i	$0.00472133\pi$
$384$		0			0
$385$	−3.34754	−	8.26430i	−0.170606	−	0.421188i
$386$	0.872895	+	0.674880i	0.0444292	+	0.0343505i
$387$		0			0
$388$	17.1285	−	16.8799i	0.869569	−	0.856946i
$389$	1.73492	−	1.00165i	0.0879638	−	0.0507859i	−0.455373	−	0.890301i	$-0.650494\pi$
$389$	1.73492	−	1.00165i	0.0879638	−	0.0507859i	0.543337	+	0.839515i	$0.317161\pi$
$390$		0			0
$391$	−11.3037			−0.571652
$392$	−7.08677	−	18.4872i	−0.357936	−	0.933746i
$393$		0			0
$394$	−1.27472	−	3.10955i	−0.0642196	−	0.156657i
$395$	16.9563	−	9.78974i	0.853165	−	0.492575i
$396$		0			0
$397$	−7.34718	−	4.24190i	−0.368744	−	0.212895i	0.304165	−	0.952619i	$-0.401622\pi$
$397$	−7.34718	−	4.24190i	−0.368744	−	0.212895i	−0.672910	+	0.739725i	$0.734956\pi$
$398$	−15.1979	−	11.7503i	−0.761802	−	0.588988i
$399$		0			0
$400$	27.2465	−	15.2040i	1.36232	−	0.760199i
$401$	−7.04632	+	12.2046i	−0.351876	+	0.609468i	−0.986578	−	0.163289i	$-0.947790\pi$
$401$	−7.04632	+	12.2046i	−0.351876	+	0.609468i	0.634702	+	0.772757i	$0.281123\pi$
$402$		0			0
$403$	57.0727	−	32.9509i	2.84299	−	1.64140i
$404$	0.947047	−	3.43381i	0.0471173	−	0.170838i
$405$		0			0
$406$	7.17500	−	7.01193i	0.356089	−	0.347996i
$407$	−1.60816			−0.0797135
$408$		0			0
$409$	−15.1789	−	26.2906i	−0.750547	−	1.29998i	−0.947558	−	0.319584i	$-0.896457\pi$
$409$	−15.1789	−	26.2906i	−0.750547	−	1.29998i	0.197011	−	0.980401i	$-0.436876\pi$
$410$	−22.8637	−	3.09514i	−1.12916	−	0.152858i
$411$		0			0
$412$	−6.25499	−	24.0458i	−0.308161	−	1.18465i
$413$	0.242409	+	0.189044i	0.0119282	+	0.00930225i
$414$		0			0
$415$	−2.13879	+	3.70449i	−0.104989	+	0.181846i
$416$	−32.3855	+	12.7262i	−1.58783	+	0.623953i
$417$		0			0
$418$	−2.97622	+	1.22006i	−0.145572	+	0.0596752i
$419$			30.8896i			1.50905i	0.656269	+	0.754527i	$0.272134\pi$
$419$			30.8896i			1.50905i	−0.656269	+	0.754527i	$0.727866\pi$
$420$		0			0
$421$		−	20.0940i		−	0.979321i	−0.871913	−	0.489661i	$-0.837121\pi$
$421$		−	20.0940i		−	0.979321i	0.871913	−	0.489661i	$-0.162879\pi$
$422$	7.61348	+	18.5723i	0.370619	+	0.904086i
$423$		0			0
$424$	2.56913	+	21.3185i	0.124768	+	1.03532i
$425$	14.7573	−	25.5604i	0.715835	−	1.23986i
$426$		0			0
$427$	−2.98358	+	21.3670i	−0.144385	+	1.03402i
$428$	18.8025	−	4.89106i	0.908852	−	0.236418i
$429$		0			0
$430$	2.38022	−	17.5827i	0.114784	−	0.847911i
$431$	4.00873	+	6.94333i	0.193094	+	0.334448i	0.946274	−	0.323366i	$-0.104814\pi$
$431$	4.00873	+	6.94333i	0.193094	+	0.334448i	−0.753180	+	0.657814i	$0.771481\pi$
$432$		0			0
$433$	−26.9812			−1.29663			−0.648316	−	0.761371i	$-0.724527\pi$
$433$	−26.9812			−1.29663			−0.648316	+	0.761371i	$0.724527\pi$
$434$	−10.8196	+	38.5993i	−0.519360	+	1.85283i
$435$		0			0
$436$	7.59201	−	27.5272i	0.363592	−	1.31831i
$437$	−6.24701	+	3.60672i	−0.298835	+	0.172533i
$438$		0			0
$439$	−18.2576	+	31.6231i	−0.871388	+	1.50929i	−0.0108272	+	0.999941i	$0.503446\pi$
$439$	−18.2576	+	31.6231i	−0.871388	+	1.50929i	−0.860561	+	0.509347i	$0.829887\pi$
$440$	3.74416	−	8.76605i	0.178496	−	0.417905i
$441$		0			0
$442$	−20.1328	+	26.0399i	−0.957617	+	1.23859i
$443$	−0.190464	−	0.109964i	−0.00904921	−	0.00522457i	0.495469	−	0.868626i	$-0.334996\pi$
$443$	−0.190464	−	0.109964i	−0.00904921	−	0.00522457i	−0.504518	+	0.863401i	$0.668330\pi$
$444$		0			0
$445$	−5.64230	+	3.25758i	−0.267471	+	0.154424i
$446$	0.259322	−	0.106306i	0.0122793	−	0.00503373i
$447$		0			0
$448$	8.67837	−	19.3051i	0.410014	−	0.912079i
$449$	−20.6799			−0.975946			−0.487973	−	0.872859i	$-0.662264\pi$
$449$	−20.6799			−0.975946			−0.487973	+	0.872859i	$0.662264\pi$
$450$		0			0
$451$	−3.71990	+	2.14768i	−0.175163	+	0.101130i
$452$	19.7687	−	19.4817i	0.929841	−	0.916344i
$453$		0			0
$454$	22.2793	−	28.8163i	1.04562	−	1.35242i
$455$	−57.6666	−	8.05227i	−2.70345	−	0.377496i
$456$		0			0
$457$	4.29209	−	7.43412i	0.200776	−	0.347753i	−0.748003	−	0.663695i	$-0.768987\pi$
$457$	4.29209	−	7.43412i	0.200776	−	0.347753i	0.948779	+	0.315942i	$0.102320\pi$
$458$	22.6495	+	3.06614i	1.05834	+	0.143271i
$459$		0			0
$460$	5.68348	−	20.6072i	0.264994	−	0.960817i
$461$		−	13.8203i		−	0.643676i	−0.946795	−	0.321838i	$-0.895699\pi$
$461$		−	13.8203i		−	0.643676i	0.946795	−	0.321838i	$-0.104301\pi$
$462$		0			0
$463$	28.8694			1.34168			0.670838	−	0.741604i	$-0.265935\pi$
$463$	28.8694			1.34168			0.670838	+	0.741604i	$0.265935\pi$
$464$	10.7239	+	0.156813i	0.497843	+	0.00727987i
$465$		0			0
$466$	−4.76640	+	35.2094i	−0.220799	+	1.63104i
$467$	10.7682	+	6.21705i	0.498295	+	0.287691i	0.728009	−	0.685567i	$-0.240446\pi$
$467$	10.7682	+	6.21705i	0.498295	+	0.287691i	−0.229714	+	0.973258i	$0.573779\pi$
$468$		0			0
$469$	8.29482	+	6.46876i	0.383019	+	0.298700i
$470$	21.1866	−	27.4029i	0.977264	−	1.26400i
$471$		0			0
$472$	0.0393197	+	0.326272i	0.00180983	+	0.0150179i
$473$	−1.65161	−	2.86067i	−0.0759411	−	0.131534i
$474$		0			0
$475$		−	18.8347i		−	0.864197i
$476$	−2.31236	−	19.8877i	−0.105987	−	0.911553i
$477$		0			0
$478$	20.9874	−	8.60354i	0.959944	−	0.393517i
$479$	19.1410	+	33.1532i	0.874575	+	1.51481i	0.857215	+	0.514958i	$0.172193\pi$
$479$	19.1410	+	33.1532i	0.874575	+	1.51481i	0.0173596	+	0.999849i	$0.494474\pi$
$480$		0			0
$481$	−5.25075	+	9.09456i	−0.239413	+	0.414676i
$482$	−14.7338	−	11.3914i	−0.671104	−	0.518865i
$483$		0			0
$484$	5.09175	+	19.5740i	0.231443	+	0.889726i
$485$	37.2559	+	21.5097i	1.69170	+	0.976704i
$486$		0			0
$487$	0.902290	+	1.56281i	0.0408867	+	0.0708178i	0.885745	−	0.464173i	$-0.153648\pi$
$487$	0.902290	+	1.56281i	0.0408867	+	0.0708178i	−0.844858	+	0.534991i	$0.820315\pi$
$488$	−18.4507	+	13.8389i	−0.835223	+	0.626458i
$489$		0			0
$490$	28.5105	−	21.0139i	1.28798	−	0.949313i
$491$		−	4.10278i		−	0.185156i	−0.995705	−	0.0925780i	$-0.970489\pi$
$491$		−	4.10278i		−	0.185156i	0.995705	−	0.0925780i	$-0.0295108\pi$
$492$		0			0
$493$	8.78600	−	5.07260i	0.395701	−	0.228458i
$494$	−2.81777	+	20.8149i	−0.126778	+	0.936505i
$495$		0			0
$496$	−37.4227	+	20.8825i	−1.68033	+	0.937652i
$497$	3.89940	+	9.62671i	0.174912	+	0.431817i
$498$		0			0
$499$	−38.4522	−	22.2004i	−1.72135	−	0.993825i	−0.916158	−	0.400817i	$-0.868726\pi$
$499$	−38.4522	−	22.2004i	−1.72135	−	0.993825i	−0.805197	−	0.593008i	$-0.797940\pi$
$500$	14.0651	+	14.2723i	0.629011	+	0.638276i
$501$		0			0
$502$	4.63841	+	11.3149i	0.207022	+	0.505010i
$503$	−8.88976			−0.396375			−0.198187	−	0.980164i	$-0.563505\pi$
$503$	−8.88976			−0.396375			−0.198187	+	0.980164i	$0.563505\pi$
$504$		0			0
$505$	6.37202			0.283551
$506$	−1.50951	−	3.68229i	−0.0671058	−	0.163698i
$507$		0			0
$508$	11.0740	−	10.9133i	0.491330	−	0.484198i
$509$	9.56641	+	5.52317i	0.424024	+	0.244810i	0.696797	−	0.717268i	$-0.254608\pi$
$509$	9.56641	+	5.52317i	0.424024	+	0.244810i	−0.272774	+	0.962078i	$0.587941\pi$
$510$		0			0
$511$	10.1344	−	12.9952i	0.448320	−	0.574875i
$512$	21.1785	−	7.96682i	0.935967	−	0.352087i
$513$		0			0
$514$	2.74426	−	20.2718i	0.121044	−	0.894152i
$515$	38.4918	−	22.2233i	1.69615	−	0.979274i
$516$		0			0
$517$		−	6.44855i		−	0.283607i
$518$	−1.58228	−	6.18882i	−0.0695215	−	0.271921i
$519$		0			0
$520$	−37.3493	−	49.7959i	−1.63788	−	2.18370i
$521$	−16.9975	−	29.4406i	−0.744675	−	1.28982i	−0.950346	−	0.311194i	$-0.899271\pi$
$521$	−16.9975	−	29.4406i	−0.744675	−	1.28982i	0.205671	−	0.978621i	$-0.434062\pi$
$522$		0			0
$523$	15.7706	+	9.10516i	0.689601	+	0.398141i	0.803462	−	0.595356i	$-0.202989\pi$
$523$	15.7706	+	9.10516i	0.689601	+	0.398141i	−0.113862	+	0.993497i	$0.536322\pi$
$524$	−13.6366	+	3.54727i	−0.595718	+	0.154963i
$525$		0			0
$526$	−22.2607	−	17.2109i	−0.970613	−	0.750430i
$527$	−20.2690	+	35.1070i	−0.882932	+	1.52928i
$528$		0			0
$529$	7.03763	+	12.1895i	0.305984	+	0.529980i
$530$	−35.5417	+	14.5699i	−1.54383	+	0.632875i
$531$		0			0
$532$	−7.62360	−	10.2532i	−0.330525	−	0.444533i
$533$			28.0493i			1.21495i
$534$		0			0
$535$	17.3774	+	30.0985i	0.751289	+	1.30127i
$536$	1.34545	+	11.1645i	0.0581146	+	0.482232i
$537$		0			0
$538$	14.6758	−	18.9818i	0.632720	−	0.818365i
$539$	1.80622	−	6.34156i	0.0777995	−	0.273150i
$540$		0			0
$541$	−26.0940	−	15.0654i	−1.12187	−	0.647712i	−0.179992	−	0.983668i	$-0.557607\pi$
$541$	−26.0940	−	15.0654i	−1.12187	−	0.647712i	−0.941877	+	0.335957i	$0.890940\pi$
$542$	0.204205	−	1.50846i	0.00877135	−	0.0647939i
$543$		0			0
$544$	13.3382	−	16.7401i	0.571869	−	0.717724i
$545$	51.0814			2.18809
$546$		0			0
$547$			36.0927i			1.54321i	0.636101	+	0.771606i	$0.280546\pi$
$547$			36.0927i			1.54321i	−0.636101	+	0.771606i	$0.719454\pi$
$548$	−34.9117	−	9.62867i	−1.49135	−	0.411316i
$549$		0			0
$550$	10.2973	+	1.39398i	0.439078	+	0.0594393i
$551$	3.23707	−	5.60677i	0.137904	−	0.238857i
$552$		0			0
$553$	14.3399	+	2.00235i	0.609794	+	0.0851485i
$554$	−4.23116	+	5.47262i	−0.179765	+	0.232509i
$555$		0			0
$556$	11.6900	+	11.8622i	0.495768	+	0.503071i
$557$	−36.7321	+	21.2073i	−1.55639	+	0.898583i	−0.558793	+	0.829307i	$0.688735\pi$
$557$	−36.7321	+	21.2073i	−1.55639	+	0.898583i	−0.997598	+	0.0692757i	$0.977931\pi$
$558$		0			0
$559$	−21.5704			−0.912333
$560$	37.4191	+	5.78399i	1.58124	+	0.244418i
$561$		0			0
$562$	−0.986880	+	0.404559i	−0.0416290	+	0.0170653i
$563$	−10.2656	+	5.92685i	−0.432644	+	0.249787i	−0.700472	−	0.713680i	$-0.747027\pi$
$563$	−10.2656	+	5.92685i	−0.432644	+	0.249787i	0.267828	+	0.963467i	$0.413694\pi$
$564$		0			0
$565$	42.9985	+	24.8252i	1.80896	+	1.04440i
$566$	−16.8074	+	21.7388i	−0.706468	+	0.913751i
$567$		0			0
$568$	−4.36141	+	10.2112i	−0.183001	+	0.428452i
$569$	2.71207	−	4.69744i	0.113696	−	0.196927i	−0.803562	−	0.595221i	$-0.797064\pi$
$569$	2.71207	−	4.69744i	0.113696	−	0.196927i	0.917258	+	0.398294i	$0.130398\pi$
$570$		0			0
$571$	−16.9613	+	9.79262i	−0.709809	+	0.409809i	−0.810990	−	0.585059i	$-0.801071\pi$
$571$	−16.9613	+	9.79262i	−0.709809	+	0.409809i	0.101181	+	0.994868i	$0.467738\pi$
$572$	−11.1713	−	3.08105i	−0.467096	−	0.128825i
$573$		0			0
$574$	−11.9252	−	12.2025i	−0.497747	−	0.509322i
$575$	23.3031			0.971804
$576$		0			0
$577$	−3.11174	−	5.38970i	−0.129544	−	0.224376i	0.793956	−	0.607975i	$-0.208018\pi$
$577$	−3.11174	−	5.38970i	−0.129544	−	0.224376i	−0.923500	+	0.383599i	$0.874685\pi$
$578$	−0.509054	+	3.76038i	−0.0211738	+	0.156411i
$579$		0			0
$580$	4.83003	+	18.5678i	0.200556	+	0.770988i
$581$	−2.93188	+	1.18759i	−0.121635	+	0.0492694i
$582$		0			0
$583$	−3.57560	+	6.19312i	−0.148086	+	0.256493i
$584$	17.4910	−	2.10788i	0.723785	−	0.0872246i
$585$		0			0
$586$	11.7708	+	28.7136i	0.486246	+	1.18615i
$587$		−	0.894279i		−	0.0369108i	−0.999830	−	0.0184554i	$-0.994125\pi$
$587$		−	0.894279i		−	0.0369108i	0.999830	−	0.0184554i	$-0.00587487\pi$
$588$		0			0
$589$			25.8693i			1.06593i
$590$	−0.543954	+	0.222987i	−0.0223942	+	0.00918023i
$591$		0			0
$592$	3.50058	−	5.86348i	0.143873	−	0.240988i
$593$	−11.3498	+	19.6584i	−0.466080	+	0.807275i	−0.999250	−	0.0387338i	$-0.987668\pi$
$593$	−11.3498	+	19.6584i	−0.466080	+	0.807275i	0.533169	+	0.846009i	$0.321001\pi$
$594$		0			0
$595$	33.1965	−	13.4466i	1.36092	−	0.551256i
$596$	−40.0774	+	10.4253i	−1.64163	+	0.427036i
$597$		0			0
$598$	−25.7529	−	3.48625i	−1.05312	−	0.142564i
$599$	−19.5178	−	33.8058i	−0.797476	−	1.38127i	−0.921255	−	0.388959i	$-0.872835\pi$
$599$	−19.5178	−	33.8058i	−0.797476	−	1.38127i	0.123780	−	0.992310i	$-0.460498\pi$
$600$		0			0
$601$	−0.397117			−0.0161987			−0.00809936	−	0.999967i	$-0.502578\pi$
$601$	−0.397117			−0.0161987			−0.00809936	+	0.999967i	$0.502578\pi$
$602$	9.38394	−	9.17067i	0.382461	−	0.373769i
$603$		0			0
$604$	−7.62658	−	2.10341i	−0.310321	−	0.0855867i
$605$	−31.3335	+	18.0904i	−1.27389	+	0.735480i
$606$		0			0
$607$	−10.9157	+	18.9066i	−0.443056	+	0.767395i	−0.997915	−	0.0645493i	$-0.979439\pi$
$607$	−10.9157	+	18.9066i	−0.443056	+	0.767395i	0.554859	+	0.831945i	$0.312772\pi$
$608$	2.03006	−	13.5073i	0.0823298	−	0.547794i
$609$		0			0
$610$	−32.6406	−	25.2361i	−1.32158	−	1.02178i
$611$	−36.4682	−	21.0549i	−1.47535	−	0.851791i
$612$		0			0
$613$	−21.6460	+	12.4973i	−0.874275	+	0.504763i	−0.868767	−	0.495222i	$-0.835087\pi$
$613$	−21.6460	+	12.4973i	−0.874275	+	0.504763i	−0.00550856	+	0.999985i	$0.501753\pi$
$614$	−1.17236	−	2.85986i	−0.0473127	−	0.115415i
$615$		0			0
$616$	6.16984	−	3.40911i	0.248590	−	0.137357i
$617$	17.0538			0.686560			0.343280	−	0.939233i	$-0.388462\pi$
$617$	17.0538			0.686560			0.343280	+	0.939233i	$0.388462\pi$
$618$		0			0
$619$	−4.32061	+	2.49451i	−0.173660	+	0.100263i	−0.584311	−	0.811530i	$-0.698635\pi$
$619$	−4.32061	+	2.49451i	−0.173660	+	0.100263i	0.410650	+	0.911793i	$0.365302\pi$
$620$	−53.8106	−	54.6032i	−2.16109	−	2.19292i
$621$		0			0
$622$	−30.5085	−	23.5877i	−1.22328	−	0.945780i
$623$	−4.77167	−	0.666291i	−0.191173	−	0.0266944i
$624$		0			0
$625$	1.57804	−	2.73324i	0.0631215	−	0.109330i
$626$	−0.259254	+	1.91511i	−0.0103619	+	0.0765430i
$627$		0			0
$628$	−6.31219	+	22.8868i	−0.251884	+	0.913282i
$629$		−	6.45975i		−	0.257567i
$630$		0			0
$631$	15.7236			0.625947			0.312973	−	0.949762i	$-0.398675\pi$
$631$	15.7236			0.625947			0.312973	+	0.949762i	$0.398675\pi$
$632$	9.28761	+	12.3827i	0.369441	+	0.492557i
$633$		0			0
$634$	11.4792	+	1.55398i	0.455898	+	0.0617163i
$635$	24.0869	+	13.9066i	0.955859	+	0.551865i
$636$		0			0
$637$	−29.9657	−	30.9203i	−1.18728	−	1.22511i
$638$	2.82574	+	2.18473i	0.111872	+	0.0864942i
$639$		0			0
$640$	23.8116	+	32.7331i	0.941236	+	1.29389i
$641$	12.3353	+	21.3654i	0.487216	+	0.843884i	0.999892	−	0.0146989i	$-0.00467896\pi$
$641$	12.3353	+	21.3654i	0.487216	+	0.843884i	−0.512676	+	0.858582i	$0.671346\pi$
$642$		0			0
$643$			47.6908i			1.88074i	0.340150	+	0.940371i	$0.389522\pi$
$643$			47.6908i			1.88074i	−0.340150	+	0.940371i	$0.610478\pi$
$644$	12.6857	−	9.43221i	0.499885	−	0.371681i
$645$		0			0
$646$	−4.90082	−	11.9550i	−0.192820	−	0.470365i
$647$	−9.64727	−	16.7096i	−0.379273	−	0.656921i	0.611683	−	0.791103i	$-0.290493\pi$
$647$	−9.64727	−	16.7096i	−0.379273	−	0.656921i	−0.990957	+	0.134182i	$0.957159\pi$
$648$		0			0
$649$	−0.0547233	+	0.0947835i	−0.00214808	+	0.00372058i
$650$	41.5046	−	53.6824i	1.62794	−	2.10560i
$651$		0			0
$652$	−33.0075	+	8.58619i	−1.29267	+	0.336261i
$653$	35.9797	+	20.7729i	1.40799	+	0.812905i	0.995195	−	0.0979172i	$-0.0312180\pi$
$653$	35.9797	+	20.7729i	1.40799	+	0.812905i	0.412799	+	0.910822i	$0.364551\pi$
$654$		0			0
$655$	−12.6030	−	21.8291i	−0.492442	−	0.852934i
$656$	0.266691	−	18.2380i	0.0104126	−	0.712076i
$657$		0			0
$658$	24.8165	−	6.34478i	0.967449	−	0.247345i
$659$		−	21.7026i		−	0.845414i	−0.906266	−	0.422707i	$-0.861080\pi$
$659$		−	21.7026i		−	0.845414i	0.906266	−	0.422707i	$-0.138920\pi$
$660$		0			0
$661$	12.7886	−	7.38348i	0.497417	−	0.287184i	−0.230229	−	0.973136i	$-0.573948\pi$
$661$	12.7886	−	7.38348i	0.497417	−	0.287184i	0.727646	+	0.685952i	$0.240614\pi$
$662$	−21.6266	−	2.92766i	−0.840541	−	0.113787i
$663$		0			0
$664$	−3.10988	−	1.32829i	−0.120687	−	0.0515478i
$665$	14.0557	−	18.0235i	0.545056	−	0.698919i
$666$		0			0
$667$	6.93691	+	4.00503i	0.268598	+	0.155075i
$668$	−14.8632	+	14.6474i	−0.575074	+	0.566726i
$669$		0			0
$670$	−18.6132	+	7.63023i	−0.719089	+	0.294782i
$671$	−7.68110			−0.296526
$672$		0			0
$673$	3.09088			0.119145			0.0595724	−	0.998224i	$-0.481026\pi$
$673$	3.09088			0.119145			0.0595724	+	0.998224i	$0.481026\pi$
$674$	0.711741	−	0.291769i	0.0274152	−	0.0112385i
$675$		0			0
$676$	−35.3805	+	34.8669i	−1.36079	+	1.34103i
$677$	33.6034	+	19.4009i	1.29148	+	0.745638i	0.978917	−	0.204258i	$-0.0654782\pi$
$677$	33.6034	+	19.4009i	1.29148	+	0.745638i	0.312566	+	0.949896i	$0.398812\pi$
$678$		0			0
$679$	11.9435	+	29.4857i	0.458349	+	1.13156i
$680$	35.2120	+	15.0398i	1.35032	+	0.576749i
$681$		0			0
$682$	−14.1432	−	1.91461i	−0.541571	−	0.0733142i
$683$	−22.5229	+	13.0036i	−0.861817	+	0.497570i	−0.864620	−	0.502426i	$-0.832441\pi$
$683$	−22.5229	+	13.0036i	−0.861817	+	0.497570i	0.00280354	+	0.999996i	$0.499108\pi$
$684$		0			0
$685$		−	64.7846i		−	2.47529i
$686$	26.1819	+	0.711533i	0.999631	+	0.0271664i
$687$		0			0
$688$	14.0254	+	0.205091i	0.534713	+	0.00781901i
$689$	23.3491	+	40.4418i	0.889530	+	1.54071i
$690$		0			0
$691$	−8.60842	−	4.97007i	−0.327480	−	0.189070i	0.327242	−	0.944941i	$-0.393881\pi$
$691$	−8.60842	−	4.97007i	−0.327480	−	0.189070i	−0.654722	+	0.755870i	$0.727214\pi$
$692$	28.2095	−	7.33810i	1.07237	−	0.278953i
$693$		0			0
$694$	9.91581	−	12.8252i	0.376399	−	0.486837i
$695$	−14.8964	+	25.8013i	−0.565052	+	0.978698i
$696$		0			0
$697$	−8.62694	−	14.9423i	−0.326769	−	0.565980i
$698$	0.660288	+	1.61071i	0.0249923	+	0.0609661i
$699$		0			0
$700$	4.76703	+	40.9995i	0.180177	+	1.54963i
$701$		−	32.3250i		−	1.22090i	−0.792056	−	0.610449i	$-0.790989\pi$
$701$		−	32.3250i		−	1.22090i	0.792056	−	0.610449i	$-0.209011\pi$
$702$		0			0
$703$	−2.06114	−	3.57000i	−0.0777374	−	0.134645i
$704$	7.23444	+	2.10956i	0.272658	+	0.0795069i
$705$		0			0
$706$	38.2840	+	29.5993i	1.44084	+	1.11398i
$707$	3.71576	+	2.89776i	0.139746	+	0.108981i
$708$		0			0
$709$	38.2056	+	22.0580i	1.43484	+	0.828406i	0.997485	−	0.0708817i	$-0.0225813\pi$
$709$	38.2056	+	22.0580i	1.43484	+	0.828406i	0.437357	+	0.899288i	$0.355915\pi$
$710$	−19.6835	−	2.66461i	−0.738708	−	0.100001i
$711$		0			0
$712$	−3.09050	−	4.12040i	−0.115821	−	0.154418i
$713$	−32.0065			−1.19865
$714$		0			0
$715$		−	20.7303i		−	0.775268i
$716$	2.00980	−	7.28714i	0.0751096	−	0.272333i
$717$		0			0
$718$	−6.43274	+	47.5186i	−0.240068	+	1.77338i
$719$	−3.22929	+	5.59330i	−0.120432	+	0.208595i	−0.919938	−	0.392063i	$-0.871761\pi$
$719$	−3.22929	+	5.59330i	−0.120432	+	0.208595i	0.799506	+	0.600658i	$0.205095\pi$
$720$		0			0
$721$	32.5523	+	4.54544i	1.21231	+	0.169281i
$722$	14.7345	+	11.3920i	0.548362	+	0.423966i
$723$		0			0
$724$	−1.57740	−	1.60063i	−0.0586235	−	0.0594870i
$725$	−18.1127	+	10.4574i	−0.672690	+	0.388378i
$726$		0			0
$727$	−25.6040			−0.949600			−0.474800	−	0.880094i	$-0.657480\pi$
$727$	−25.6040			−0.949600			−0.474800	+	0.880094i	$0.657480\pi$
$728$	0.865539	−	46.0230i	0.0320790	−	1.70573i
$729$		0			0
$730$	11.9541	+	29.1607i	0.442439	+	1.07929i
$731$	11.4909	−	6.63428i	0.425007	−	0.245378i
$732$		0			0
$733$	8.94596	+	5.16495i	0.330426	+	0.190772i	0.656030	−	0.754734i	$-0.272234\pi$
$733$	8.94596	+	5.16495i	0.330426	+	0.190772i	−0.325604	+	0.945506i	$0.605568\pi$
$734$	−21.5313	−	16.6469i	−0.794734	−	0.614449i
$735$		0			0
$736$	16.7118	+	2.51167i	0.616004	+	0.0925813i
$737$	−1.87254	+	3.24333i	−0.0689757	+	0.119470i
$738$		0			0
$739$	−40.1335	+	23.1711i	−1.47633	+	0.852362i	−0.999643	−	0.0267085i	$-0.991497\pi$
$739$	−40.1335	+	23.1711i	−1.47633	+	0.852362i	−0.476691	+	0.879071i	$0.658164\pi$
$740$	11.7765	+	3.24796i	0.432912	+	0.119397i
$741$		0			0
$742$	−27.3516	−	7.66682i	−1.00411	−	0.281458i
$743$	38.1002			1.39776			0.698880	−	0.715239i	$-0.253682\pi$
$743$	38.1002			1.39776			0.698880	+	0.715239i	$0.253682\pi$
$744$		0			0
$745$	−37.0398	−	64.1548i	−1.35703	−	2.35045i
$746$	−20.7884	−	2.81419i	−0.761119	−	0.103035i
$747$		0			0
$748$	6.89875	−	1.79456i	0.252243	−	0.0656157i
$749$	−3.55429	+	25.4542i	−0.129871	+	0.930075i
$750$		0			0
$751$	3.76000	−	6.51250i	0.137204	−	0.237645i	−0.789233	−	0.614094i	$-0.789522\pi$
$751$	3.76000	−	6.51250i	0.137204	−	0.237645i	0.926437	+	0.376449i	$0.122855\pi$
$752$	23.5119	+	14.0369i	0.857392	+	0.511874i
$753$		0			0
$754$	21.5814	−	8.84703i	0.785949	−	0.322190i
$755$		−	14.1524i		−	0.515059i
$756$		0			0
$757$			41.2006i			1.49746i	0.662873	+	0.748731i	$0.269337\pi$
$757$			41.2006i			1.49746i	−0.662873	+	0.748731i	$0.730663\pi$
$758$	6.30287	+	15.3752i	0.228931	+	0.558453i
$759$		0			0
$760$	24.2588	−	2.92347i	0.879960	−	0.106045i
$761$	14.3106	−	24.7867i	0.518759	−	0.898517i	−0.481003	−	0.876719i	$-0.659727\pi$
$761$	14.3106	−	24.7867i	0.518759	−	0.898517i	0.999762	−	0.0217985i	$-0.00693921\pi$
$762$		0			0
$763$	29.7875	+	23.2299i	1.07838	+	0.840980i
$764$	−7.06413	−	27.1563i	−0.255571	−	0.982481i
$765$		0			0
$766$	−3.61703	+	26.7189i	−0.130688	+	0.965395i
$767$	0.357350	+	0.618949i	0.0129032	+	0.0223489i
$768$		0			0
$769$	−14.6303			−0.527581			−0.263791	−	0.964580i	$-0.584973\pi$
$769$	−14.6303			−0.527581			−0.263791	+	0.964580i	$0.584973\pi$
$770$	8.81347	+	9.01843i	0.317615	+	0.325002i
$771$		0			0
$772$	−1.50423	−	0.414867i	−0.0541384	−	0.0149314i
$773$	36.7815	−	21.2358i	1.32294	−	0.763798i	0.338741	−	0.940880i	$-0.389999\pi$
$773$	36.7815	−	21.2358i	1.32294	−	0.763798i	0.984196	+	0.177082i	$0.0566656\pi$
$774$		0			0
$775$	41.7855	−	72.3746i	1.50098	−	2.59977i
$776$	−13.3586	+	31.2759i	−0.479545	+	1.12274i
$777$		0			0
$778$	−1.73289	+	2.24134i	−0.0621271	+	0.0803558i
$779$	−9.53541	−	5.50527i	−0.341642	−	0.197247i
$780$		0			0
$781$	−3.20247	+	1.84895i	−0.114594	+	0.0661606i
$782$	14.7912	−	6.06348i	0.528934	−	0.216830i
$783$		0			0
$784$	19.1901	+	20.3897i	0.685362	+	0.728203i
$785$	−42.4703			−1.51583
$786$		0			0
$787$	−6.55295	+	3.78335i	−0.233588	+	0.134862i	−0.612226	−	0.790683i	$-0.709726\pi$
$787$	−6.55295	+	3.78335i	−0.233588	+	0.134862i	0.378638	+	0.925545i	$0.376392\pi$
$788$	3.33603	+	3.38517i	0.118841	+	0.120592i
$789$		0			0
$790$	−16.9365	+	21.9058i	−0.602575	+	0.779375i
$791$	13.7844	+	34.0306i	0.490119	+	1.20999i
$792$		0			0
$793$	−25.0793	+	43.4386i	−0.890591	+	1.54255i
$794$	11.8894	+	1.60951i	0.421941	+	0.0571194i
$795$		0			0
$796$	26.1900	+	7.22321i	0.928280	+	0.256020i
$797$		−	11.4622i		−	0.406013i	−0.979177	−	0.203007i	$-0.934929\pi$
$797$		−	11.4622i		−	0.406013i	0.979177	−	0.203007i	$-0.0650713\pi$
$798$		0			0
$799$	25.9029			0.916379
$800$	−27.4972	+	34.5104i	−0.972175	+	1.22013i
$801$		0			0
$802$	2.67360	−	19.7499i	0.0944081	−	0.697392i
$803$	5.08122	+	2.93365i	0.179312	+	0.103526i
$804$		0			0
$805$	22.2993	+	17.3902i	0.785947	+	0.612925i
$806$	−57.0061	+	73.7321i	−2.00795	+	2.59710i
$807$		0			0
$808$	0.602711	+	5.00126i	0.0212033	+	0.175944i
$809$	8.54103	+	14.7935i	0.300287	+	0.520112i	0.976201	−	0.216869i	$-0.0695844\pi$
$809$	8.54103	+	14.7935i	0.300287	+	0.520112i	−0.675914	+	0.736980i	$0.736251\pi$
$810$		0			0
$811$		−	16.6693i		−	0.585338i	−0.956214	−	0.292669i	$-0.905457\pi$
$811$		−	16.6693i		−	0.585338i	0.956214	−	0.292669i	$-0.0945434\pi$
$812$	−5.62740	+	13.0241i	−0.197483	+	0.457057i
$813$		0			0
$814$	2.10433	−	0.862644i	0.0737567	−	0.0302356i
$815$	−30.5058	−	52.8375i	−1.06857	−	1.85082i
$816$		0			0
$817$	4.23366	−	7.33291i	0.148117	−	0.256546i
$818$	33.9647	+	26.2599i	1.18755	+	0.918155i
$819$		0			0
$820$	31.5782	−	8.21440i	1.10276	−	0.286859i
$821$	−37.2593	−	21.5117i	−1.30036	−	0.750762i	−0.319893	−	0.947454i	$-0.603647\pi$
$821$	−37.2593	−	21.5117i	−1.30036	−	0.750762i	−0.980465	+	0.196691i	$0.936980\pi$
$822$		0			0
$823$	−17.3255	−	30.0086i	−0.603928	−	1.04603i	−0.992220	−	0.124497i	$-0.960268\pi$
$823$	−17.3255	−	30.0086i	−0.603928	−	1.04603i	0.388292	−	0.921536i	$-0.373065\pi$
$824$	21.0834	+	28.1094i	0.734475	+	0.979237i
$825$		0			0
$826$	−0.418606	−	0.117338i	−0.0145652	−	0.00408272i
$827$			36.5937i			1.27249i	0.771489	+	0.636243i	$0.219513\pi$
$827$			36.5937i			1.27249i	−0.771489	+	0.636243i	$0.780487\pi$
$828$		0			0
$829$	−6.54607	+	3.77938i	−0.227354	+	0.131263i	−0.609351	−	0.792901i	$-0.708570\pi$
$829$	−6.54607	+	3.77938i	−0.227354	+	0.131263i	0.381997	+	0.924164i	$0.375237\pi$
$830$	0.811526	−	5.99473i	0.0281685	−	0.208080i
$831$		0			0
$832$	35.5510	−	34.0248i	1.23251	−	1.17960i
$833$	25.4731	+	7.25534i	0.882592	+	0.251383i
$834$		0			0
$835$	−32.3286	−	18.6649i	−1.11878	−	0.645926i
$836$	3.24002	−	3.19298i	0.112058	−	0.110432i
$837$		0			0
$838$	−16.5697	−	40.4200i	−0.572390	−	1.39629i
$839$	33.3899			1.15275			0.576374	−	0.817186i	$-0.304467\pi$
$839$	33.3899			1.15275			0.576374	+	0.817186i	$0.304467\pi$
$840$		0			0
$841$	21.8109			0.752099
$842$	10.7787	+	26.2936i	0.371460	+	0.906139i
$843$		0			0
$844$	−19.9250	−	20.2185i	−0.685846	−	0.695949i
$845$	−76.9553	−	44.4302i	−2.64734	−	1.52844i
$846$		0			0
$847$	−26.4986	−	3.70013i	−0.910503	−	0.127138i
$848$	−14.7974	−	26.5178i	−0.508144	−	0.910626i
$849$		0			0
$850$	−5.59940	+	41.3627i	−0.192058	+	1.41873i
$851$	4.41694	−	2.55012i	0.151411	−	0.0874171i
$852$		0			0
$853$		−	18.6855i		−	0.639779i	−0.947455	−	0.319889i	$-0.896354\pi$
$853$		−	18.6855i		−	0.639779i	0.947455	−	0.319889i	$-0.103646\pi$
$854$	−7.55750	−	29.5598i	−0.258612	−	1.01152i
$855$		0			0
$856$	−21.9800	+	16.4861i	−0.751261	+	0.563482i
$857$	−15.4441	−	26.7499i	−0.527559	−	0.913759i	−0.999484	−	0.0321205i	$-0.989774\pi$
$857$	−15.4441	−	26.7499i	−0.527559	−	0.913759i	0.471925	−	0.881639i	$-0.343559\pi$
$858$		0			0
$859$	−35.3861	−	20.4302i	−1.20736	−	0.697069i	−0.245178	−	0.969478i	$-0.578846\pi$
$859$	−35.3861	−	20.4302i	−1.20736	−	0.697069i	−0.962182	+	0.272409i	$0.912180\pi$
$860$	6.31703	+	24.2843i	0.215409	+	0.828087i
$861$		0			0
$862$	−8.97007	−	6.93522i	−0.305522	−	0.236215i
$863$	1.87676	−	3.25064i	0.0638857	−	0.110653i	−0.832313	−	0.554305i	$-0.812984\pi$
$863$	1.87676	−	3.25064i	0.0638857	−	0.110653i	0.896199	+	0.443652i	$0.146317\pi$
$864$		0			0
$865$	26.0714	+	45.1571i	0.886455	+	1.53539i
$866$	35.3058	−	14.4731i	1.19974	−	0.491818i
$867$		0			0
$868$	−6.54746	−	56.3123i	−0.222235	−	1.91136i
$869$			5.15496i			0.174870i
$870$		0			0
$871$	12.2279	+	21.1793i	0.414327	+	0.717635i
$872$	4.83164	+	40.0927i	0.163620	+	1.35771i
$873$		0			0
$874$	6.23972	−	8.07051i	0.211062	−	0.272989i
$875$	−24.5689	+	9.95188i	−0.830580	+	0.336435i
$876$		0			0
$877$	−26.0217	−	15.0236i	−0.878689	−	0.507311i	−0.00846311	−	0.999964i	$-0.502694\pi$
$877$	−26.0217	−	15.0236i	−0.878689	−	0.507311i	−0.870226	+	0.492653i	$0.836027\pi$
$878$	6.92752	−	51.1736i	0.233793	−	1.72702i
$879$		0			0
$880$	−0.197102	+	13.4791i	−0.00664432	+	0.454380i
$881$	−42.4160			−1.42903			−0.714516	−	0.699619i	$-0.753353\pi$
$881$	−42.4160			−1.42903			−0.714516	+	0.699619i	$0.753353\pi$
$882$		0			0
$883$		−	20.3124i		−	0.683568i	−0.939779	−	0.341784i	$-0.888969\pi$
$883$		−	20.3124i		−	0.683568i	0.939779	−	0.341784i	$-0.111031\pi$
$884$	12.3761	−	44.8736i	0.416255	−	1.50926i
$885$		0			0
$886$	0.308215	+	0.0417240i	0.0103547	+	0.00140175i
$887$	8.69219	−	15.0553i	0.291855	−	0.505508i	−0.682393	−	0.730985i	$-0.739061\pi$
$887$	8.69219	−	15.0553i	0.291855	−	0.505508i	0.974248	+	0.225477i	$0.0723941\pi$
$888$		0			0
$889$	7.72177	+	19.0633i	0.258980	+	0.639362i
$890$	5.63571	−	7.28928i	0.188909	−	0.244337i
$891$		0			0
$892$	−0.282307	+	0.278209i	−0.00945234	+	0.00931513i
$893$	14.3153	−	8.26496i	0.479044	−	0.276576i
$894$		0			0
$895$	13.5225			0.452008
$896$	−1.00037	+	29.9165i	−0.0334200	+	0.999441i
$897$		0			0
$898$	27.0604	−	11.0931i	0.903016	−	0.370180i
$899$	24.8776	−	14.3631i	0.829715	−	0.479036i
$900$		0			0
$901$	−24.8769	−	14.3627i	−0.828769	−	0.478490i
$902$	3.71555	−	4.80573i	0.123714	−	0.160013i
$903$		0			0
$904$	−15.4177	+	36.0967i	−0.512784	+	1.20056i
$905$	2.01004	−	3.48150i	0.0668161	−	0.115729i
$906$		0			0
$907$	−18.8970	+	10.9102i	−0.627464	+	0.362266i	−0.779769	−	0.626067i	$-0.784664\pi$
$907$	−18.8970	+	10.9102i	−0.627464	+	0.362266i	0.152306	+	0.988333i	$0.451330\pi$
$908$	−13.6957	+	49.6580i	−0.454508	+	1.64796i
$909$		0			0
$910$	79.7780	−	20.3967i	2.64462	−	0.676143i
$911$	−11.9139			−0.394727			−0.197363	−	0.980330i	$-0.563238\pi$
$911$	−11.9139			−0.394727			−0.197363	+	0.980330i	$0.563238\pi$
$912$		0			0
$913$	−0.563109	−	0.975334i	−0.0186362	−	0.0322789i
$914$	−1.62856	+	12.0301i	−0.0538679	+	0.397921i
$915$		0			0
$916$	−31.2824	+	8.13745i	−1.03360	+	0.268869i
$917$	2.57777	−	18.4608i	0.0851254	−	0.609629i
$918$		0			0
$919$	18.8832	−	32.7067i	0.622900	−	1.07890i	−0.366042	−	0.930598i	$-0.619288\pi$
$919$	18.8832	−	32.7067i	0.622900	−	1.07890i	0.988943	−	0.148297i	$-0.0473791\pi$
$920$	3.61703	+	30.0139i	0.119250	+	0.989530i
$921$		0			0
$922$	7.41344	+	18.0843i	0.244149	+	0.595575i
$923$			24.1477i			0.794833i
$924$		0			0
$925$			13.3171i			0.437863i
$926$	−37.7766	+	15.4860i	−1.24141	+	0.508902i
$927$		0			0
$928$	−14.1167	+	5.54727i	−0.463402	+	0.182098i
$929$	−17.2547	+	29.8860i	−0.566108	+	0.980528i	0.430837	+	0.902430i	$0.358218\pi$
$929$	−17.2547	+	29.8860i	−0.566108	+	0.980528i	−0.996946	+	0.0780988i	$0.975115\pi$
$930$		0			0
$931$	16.3928	−	4.11814i	0.537253	−	0.134967i
$932$	−12.6499	−	48.6294i	−0.414361	−	1.59291i
$933$		0			0
$934$	−17.4255	−	2.35895i	−0.570181	−	0.0771871i
$935$	6.37587	+	11.0433i	0.208513	+	0.361156i
$936$		0			0
$937$	2.63475			0.0860735			0.0430367	−	0.999073i	$-0.486297\pi$
$937$	2.63475			0.0860735			0.0430367	+	0.999073i	$0.486297\pi$
$938$	−14.3240	−	4.01511i	−0.467695	−	0.131098i
$939$		0			0
$940$	−13.0240	+	47.2224i	−0.424795	+	1.54022i
$941$	17.7673	−	10.2579i	0.579197	−	0.334399i	−0.181617	−	0.983369i	$-0.558133\pi$
$941$	17.7673	−	10.2579i	0.579197	−	0.334399i	0.760814	+	0.648970i	$0.224800\pi$
$942$		0			0
$943$	6.81133	−	11.7976i	0.221808	−	0.384182i
$944$	−0.226469	−	0.405846i	−0.00737094	−	0.0132092i
$945$		0			0
$946$	3.69570	+	2.85733i	0.120157	+	0.0928999i
$947$	−27.2353	−	15.7243i	−0.885029	−	0.510972i	−0.0127161	−	0.999919i	$-0.504048\pi$
$947$	−27.2353	−	15.7243i	−0.885029	−	0.510972i	−0.872313	+	0.488947i	$0.837381\pi$
$948$		0			0
$949$	33.1810	−	19.1571i	1.07710	−	0.621865i
$950$	10.1033	+	24.6459i	0.327793	+	0.799617i
$951$		0			0
$952$	13.6939	+	24.7834i	0.443822	+	0.803234i
$953$	−7.69660			−0.249317			−0.124659	−	0.992200i	$-0.539784\pi$
$953$	−7.69660			−0.249317			−0.124659	+	0.992200i	$0.539784\pi$
$954$		0			0
$955$	43.4711	−	25.0980i	1.40669	−	0.812154i
$956$	−22.8477	+	22.5160i	−0.738947	+	0.728220i
$957$		0			0
$958$	−42.8305	−	33.1145i	−1.38379	−	1.06988i
$959$	29.4617	−	37.7784i	0.951367	−	1.21993i
$960$		0			0
$961$	−41.8919	+	72.5589i	−1.35135	+	2.34061i
$962$	1.99230	−	14.7171i	0.0642344	−	0.474499i
$963$		0			0
$964$	25.3901	+	7.00261i	0.817761	+	0.225539i
$965$		−	2.79135i		−	0.0898568i
$966$		0			0
$967$	−58.4850			−1.88075			−0.940375	−	0.340140i	$-0.889526\pi$
$967$	−58.4850			−1.88075			−0.940375	+	0.340140i	$0.889526\pi$
$968$	−17.1625	−	22.8819i	−0.551625	−	0.735452i
$969$		0			0
$970$	−60.2887	−	8.16146i	−1.93575	−	0.262049i
$971$	−40.3828	−	23.3150i	−1.29595	−	0.748215i	−0.316245	−	0.948678i	$-0.602422\pi$
$971$	−40.3828	−	23.3150i	−1.29595	−	0.748215i	−0.979701	+	0.200463i	$0.935755\pi$
$972$		0			0
$973$	−20.4201	+	8.27137i	−0.654639	+	0.265168i
$974$	−2.01899	−	1.56099i	−0.0646927	−	0.0500173i
$975$		0			0
$976$	16.7199	−	28.0059i	0.535191	−	0.896447i
$977$	−0.754805	−	1.30736i	−0.0241484	−	0.0418262i	0.853699	−	0.520767i	$-0.174354\pi$
$977$	−0.754805	−	1.30736i	−0.0241484	−	0.0418262i	−0.877847	+	0.478941i	$0.841021\pi$
$978$		0			0
$979$		−	1.71534i		−	0.0548225i
$980$	−26.0348	+	42.7909i	−0.831650	+	1.36691i
$981$		0			0
$982$	2.20080	+	5.36863i	0.0702304	+	0.171320i
$983$	11.0830	+	19.1964i	0.353494	+	0.612270i	0.986859	−	0.161584i	$-0.0516601\pi$
$983$	11.0830	+	19.1964i	0.353494	+	0.612270i	−0.633365	+	0.773853i	$0.718327\pi$
$984$		0			0
$985$	−4.25103	+	7.36301i	−0.135449	+	0.234605i
$986$	−8.77574	+	11.3506i	−0.279476	+	0.361477i
$987$		0			0
$988$	−7.47829	−	28.7484i	−0.237916	−	0.914609i
$989$	9.07256	+	5.23805i	0.288491	+	0.166560i
$990$		0			0
$991$	28.9420	+	50.1291i	0.919374	+	1.59240i	0.800368	+	0.599510i	$0.204638\pi$
$991$	28.9420	+	50.1291i	0.919374	+	1.59240i	0.119007	+	0.992893i	$0.462029\pi$
$992$	37.7672	−	47.3996i	1.19911	−	1.50494i
$993$		0			0
$994$	−10.2664	−	10.5052i	−0.325631	−	0.333204i
$995$			48.6000i			1.54072i
$996$		0			0
$997$	−44.1522	+	25.4913i	−1.39831	+	0.807317i	−0.994216	−	0.107399i	$-0.965748\pi$
$997$	−44.1522	+	25.4913i	−1.39831	+	0.807317i	−0.404098	+	0.914716i	$0.632414\pi$
$998$	62.2245	+	8.42353i	1.96968	+	0.266642i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.2		32
3.2	odd	2		168.2.bc.a.37.15	yes	32
4.3	odd	2		2016.2.cr.e.1297.16		32
7.4	even	3	inner	504.2.cj.e.109.10		32
8.3	odd	2		2016.2.cr.e.1297.1		32
8.5	even	2	inner	504.2.cj.e.37.10		32
12.11	even	2		672.2.bk.a.625.1		32
21.2	odd	6		1176.2.c.e.589.5		16
21.5	even	6		1176.2.c.f.589.5		16
21.11	odd	6		168.2.bc.a.109.7	yes	32
24.5	odd	2		168.2.bc.a.37.7	✓	32
24.11	even	2		672.2.bk.a.625.16		32
28.11	odd	6		2016.2.cr.e.1873.1		32
56.11	odd	6		2016.2.cr.e.1873.16		32
56.53	even	6	inner	504.2.cj.e.109.2		32
84.11	even	6		672.2.bk.a.529.16		32
84.23	even	6		4704.2.c.e.2353.8		16
84.47	odd	6		4704.2.c.f.2353.9		16
168.5	even	6		1176.2.c.f.589.6		16
168.11	even	6		672.2.bk.a.529.1		32
168.53	odd	6		168.2.bc.a.109.15	yes	32
168.107	even	6		4704.2.c.e.2353.9		16
168.131	odd	6		4704.2.c.f.2353.8		16
168.149	odd	6		1176.2.c.e.589.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.7	✓	32	24.5	odd	2
168.2.bc.a.37.15	yes	32	3.2	odd	2
168.2.bc.a.109.7	yes	32	21.11	odd	6
168.2.bc.a.109.15	yes	32	168.53	odd	6
504.2.cj.e.37.2		32	1.1	even	1	trivial
504.2.cj.e.37.10		32	8.5	even	2	inner
504.2.cj.e.109.2		32	56.53	even	6	inner
504.2.cj.e.109.10		32	7.4	even	3	inner
672.2.bk.a.529.1		32	168.11	even	6
672.2.bk.a.529.16		32	84.11	even	6
672.2.bk.a.625.1		32	12.11	even	2
672.2.bk.a.625.16		32	24.11	even	2
1176.2.c.e.589.5		16	21.2	odd	6
1176.2.c.e.589.6		16	168.149	odd	6
1176.2.c.f.589.5		16	21.5	even	6
1176.2.c.f.589.6		16	168.5	even	6
2016.2.cr.e.1297.1		32	8.3	odd	2
2016.2.cr.e.1297.16		32	4.3	odd	2
2016.2.cr.e.1873.1		32	28.11	odd	6
2016.2.cr.e.1873.16		32	56.11	odd	6
4704.2.c.e.2353.8		16	84.23	even	6
4704.2.c.e.2353.9		16	168.107	even	6
4704.2.c.f.2353.8		16	168.131	odd	6
4704.2.c.f.2353.9		16	84.47	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30853 + 0.536416i) q^{2} +(1.42451 - 1.40384i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 + 2.60110i) q^{8} +O(q^{10})\)	\(q+(-1.30853 + 0.536416i) q^{2} +(1.42451 - 1.40384i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 + 2.60110i) q^{8} +(-5.01398 - 0.678758i) q^{10} +(-0.815768 + 0.470984i) q^{11} +6.15117i q^{13} +(-2.61517 - 2.67598i) q^{14} +(0.0584850 - 3.99957i) q^{16} +(-1.89187 - 3.27682i) q^{17} +(-2.09110 - 1.20730i) q^{19} +(6.92506 - 1.80141i) q^{20} +(0.814815 - 1.05389i) q^{22} +(1.49371 - 2.58719i) q^{23} +(3.90019 + 6.75532i) q^{25} +(-3.29959 - 8.04900i) q^{26} +(4.85747 + 2.09879i) q^{28} +2.68125i q^{29} +(-5.35686 - 9.27835i) q^{31} +(2.06891 + 5.26494i) q^{32} +(4.23332 + 3.27300i) q^{34} +(-1.30906 + 9.37491i) q^{35} +(1.47851 + 0.853618i) q^{37} +(3.38389 + 0.458087i) q^{38} +(-8.09536 + 6.07191i) q^{40} +4.56000 q^{41} +3.50672i q^{43} +(-0.500889 + 1.81613i) q^{44} +(-0.566763 + 4.18667i) q^{46} +(-3.42292 + 5.92866i) q^{47} +(-5.02673 + 4.87155i) q^{49} +(-8.72718 - 6.74743i) q^{50} +(8.63523 + 8.76243i) q^{52} +(6.57466 - 3.79588i) q^{53} -3.37013 q^{55} +(-7.48199 - 0.140711i) q^{56} +(-1.43827 - 3.50851i) q^{58} +(0.100623 - 0.0580947i) q^{59} +(7.06184 + 4.07716i) q^{61} +(11.9867 + 9.26752i) q^{62} +(-5.53143 - 5.77955i) q^{64} +(-11.0037 + 19.0590i) q^{65} +(3.44314 - 1.98790i) q^{67} +(-7.29513 - 2.01200i) q^{68} +(-3.31590 - 12.9696i) q^{70} +3.92572 q^{71} +(-3.11438 - 5.39427i) q^{73} +(-2.39257 - 0.323890i) q^{74} +(-4.67365 + 1.21575i) q^{76} +(-1.96525 - 1.53261i) q^{77} +(2.73628 - 4.73937i) q^{79} +(7.33597 - 12.2878i) q^{80} +(-5.96690 + 2.44606i) q^{82} +1.19560i q^{83} -13.5373i q^{85} +(-1.88106 - 4.58866i) q^{86} +(-0.318771 - 2.64515i) q^{88} +(-0.910509 + 1.57705i) q^{89} +(-15.0840 + 6.10992i) q^{91} +(-1.50417 - 5.78242i) q^{92} +(1.29876 - 9.59396i) q^{94} +(-4.31942 - 7.48146i) q^{95} +12.0241 q^{97} +(3.96446 - 9.07100i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

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