LMFDB - Embedded newform 504.2.cj.e.37.10

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			37.10
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.189716 + 1.40143i) q^{2} +(-1.92802 + 0.531748i) q^{4} +(-3.09843 - 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 - 2.60110i) q^{8} +O(q^{10})$	\(q+(0.189716 + 1.40143i) q^{2} +(-1.92802 + 0.531748i) q^{4} +(-3.09843 - 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 - 2.60110i) q^{8} +(1.91917 - 4.68162i) q^{10} +(0.815768 - 0.470984i) q^{11} -6.15117i q^{13} +(-3.24817 + 1.85726i) q^{14} +(3.43449 - 2.05044i) q^{16} +(-1.89187 - 3.27682i) q^{17} +(2.09110 + 1.20730i) q^{19} +(6.92506 + 1.80141i) q^{20} +(0.814815 + 1.05389i) q^{22} +(1.49371 - 2.58719i) q^{23} +(3.90019 + 6.75532i) q^{25} +(8.62043 - 1.16697i) q^{26} +(-3.21905 - 4.19973i) q^{28} -2.68125i q^{29} +(-5.35686 - 9.27835i) q^{31} +(3.52512 + 4.42420i) q^{32} +(4.23332 - 3.27300i) q^{34} +(1.30906 - 9.37491i) q^{35} +(-1.47851 - 0.853618i) q^{37} +(-1.29523 + 3.15958i) q^{38} +(-1.21075 + 10.0467i) q^{40} +4.56000 q^{41} -3.50672i q^{43} +(-1.32237 + 1.34185i) q^{44} +(3.90915 + 1.60251i) q^{46} +(-3.42292 + 5.92866i) q^{47} +(-5.02673 + 4.87155i) q^{49} +(-8.72718 + 6.74743i) q^{50} +(3.27087 + 11.8595i) q^{52} +(-6.57466 + 3.79588i) q^{53} -3.37013 q^{55} +(5.27492 - 5.30803i) q^{56} +(3.75759 - 0.508677i) q^{58} +(-0.100623 + 0.0580947i) q^{59} +(-7.06184 - 4.07716i) q^{61} +(11.9867 - 9.26752i) q^{62} +(-5.53143 + 5.77955i) q^{64} +(-11.0037 + 19.0590i) q^{65} +(-3.44314 + 1.98790i) q^{67} +(5.39001 + 5.31177i) q^{68} +(13.3866 + 0.0559922i) q^{70} +3.92572 q^{71} +(-3.11438 - 5.39427i) q^{73} +(0.915789 - 2.23397i) q^{74} +(-4.67365 - 1.21575i) q^{76} +(1.96525 + 1.53261i) q^{77} +(2.73628 - 4.73937i) q^{79} +(-14.3095 + 0.209245i) q^{80} +(0.865104 + 6.39052i) q^{82} -1.19560i q^{83} +13.5373i q^{85} +(4.91443 - 0.665282i) q^{86} +(-2.13138 - 1.59864i) q^{88} +(-0.910509 + 1.57705i) q^{89} +(15.0840 - 6.10992i) q^{91} +(-1.50417 + 5.78242i) q^{92} +(-8.95799 - 3.67222i) q^{94} +(-4.31942 - 7.48146i) q^{95} +12.0241 q^{97} +(-7.78079 - 6.12040i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.189716	+	1.40143i	0.134149	+	0.990961i
$2$	0.189716	+	1.40143i	0.134149	+	0.990961i
$3$		0			0
$3$		0			0
$4$	−1.92802	+	0.531748i	−0.964008	+	0.265874i
$5$	−3.09843	−	1.78888i	−1.38566	−	0.800012i	−0.392838	−	0.919608i	$-0.628507\pi$
$5$	−3.09843	−	1.78888i	−1.38566	−	0.800012i	−0.992823	+	0.119596i	$0.961840\pi$
$6$		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
$10$	1.91917	−	4.68162i	0.606895	−	1.48046i
$11$	0.815768	−	0.470984i	0.245963	−	0.142007i	−0.371951	−	0.928252i	$-0.621311\pi$
$11$	0.815768	−	0.470984i	0.245963	−	0.142007i	0.617914	+	0.786245i	$0.287978\pi$
$12$		0			0
$13$		−	6.15117i		−	1.70603i	−0.521889	−	0.853013i	$-0.674772\pi$
$13$		−	6.15117i		−	1.70603i	0.521889	−	0.853013i	$-0.325228\pi$
$14$	−3.24817	+	1.85726i	−0.868109	+	0.496373i
$15$		0			0
$16$	3.43449	−	2.05044i	0.858622	−	0.512609i
$17$	−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	0.720305	−	0.693658i	$-0.244002\pi$
$19$	2.09110	+	1.20730i	0.479731	+	0.276973i	−0.240573	+	0.970631i	$0.577335\pi$
$20$	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
$26$	8.62043	−	1.16697i	1.69061	−	0.228863i
$27$		0			0
$28$	−3.21905	−	4.19973i	−0.608343	−	0.793674i
$29$		−	2.68125i		−	0.497897i	−0.968517	−	0.248948i	$-0.919915\pi$
$29$		−	2.68125i		−	0.497897i	0.968517	−	0.248948i	$-0.0800849\pi$
$30$		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	$-0.578775\pi$
$32$	3.52512	+	4.42420i	0.623159	+	0.782095i
$33$		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	0.373519	−	0.927622i	$-0.378151\pi$
$37$	−1.47851	−	0.853618i	−0.243065	−	0.140334i	−0.616585	+	0.787288i	$0.711484\pi$
$38$	−1.29523	+	3.15958i	−0.210114	+	0.512551i
$39$		0			0
$40$	−1.21075	+	10.0467i	−0.191436	+	1.58853i
$41$	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	$-0.913840\pi$
$43$		−	3.50672i		−	0.534770i	0.963590	−	0.267385i	$-0.0861596\pi$
$44$	−1.32237	+	1.34185i	−0.199355	+	0.202291i
$45$		0			0
$46$	3.90915	+	1.60251i	0.576372	+	0.236277i
$47$	−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
$52$	3.27087	+	11.8595i	0.453588	+	1.64462i
$53$	−6.57466	+	3.79588i	−0.903099	+	0.521404i	−0.878204	−	0.478286i	$-0.841258\pi$
$53$	−6.57466	+	3.79588i	−0.903099	+	0.521404i	−0.0248947	+	0.999690i	$0.507925\pi$
$54$		0			0
$55$	−3.37013			−0.454429
$56$	5.27492	−	5.30803i	0.704891	−	0.709315i
$57$		0			0
$58$	3.75759	−	0.508677i	0.493396	−	0.0667926i
$59$	−0.100623	+	0.0580947i	−0.0131000	+	0.00756328i	−0.506536	−	0.862219i	$-0.669074\pi$
$59$	−0.100623	+	0.0580947i	−0.0131000	+	0.00756328i	0.493436	+	0.869782i	$0.335741\pi$
$60$		0			0
$61$	−7.06184	−	4.07716i	−0.904176	−	0.522027i	−0.0256236	−	0.999672i	$-0.508157\pi$
$61$	−7.06184	−	4.07716i	−0.904176	−	0.522027i	−0.878553	+	0.477645i	$0.841490\pi$
$62$	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	−0.695354	−	0.718667i	$-0.744752\pi$
$67$	−3.44314	+	1.98790i	−0.420647	+	0.242861i	0.274707	+	0.961528i	$0.411419\pi$
$68$	5.39001	+	5.31177i	0.653634	+	0.644146i
$69$		0			0
$70$	13.3866	+	0.0559922i	1.60001	+	0.00669235i
$71$	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	$0.952097\pi$
$74$	0.915789	−	2.23397i	0.106458	−	0.259694i
$75$		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	$0.0670555\pi$
$80$	−14.3095	+	0.209245i	−1.59985	+	0.0233943i
$81$		0			0
$82$	0.865104	+	6.39052i	0.0955348	+	0.705715i
$83$		−	1.19560i		−	0.131234i	−0.997845	−	0.0656172i	$-0.979098\pi$
$83$		−	1.19560i		−	0.131234i	0.997845	−	0.0656172i	$-0.0209016\pi$
$84$		0			0
$85$			13.5373i			1.46833i
$86$	4.91443	−	0.665282i	0.529937	−	0.0717392i
$87$		0			0
$88$	−2.13138	−	1.59864i	−0.227206	−	0.170415i
$89$	−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
$94$	−8.95799	−	3.67222i	−0.923947	−	0.378760i
$95$	−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	$0.290996\pi$
$98$	−7.78079	−	6.12040i	−0.785978	−	0.618254i
$99$		0			0
$100$	−11.1117	−	10.9504i	−1.11117	−	1.09504i
$101$	−1.54240	+	0.890504i	−0.153474	+	0.0886085i	−0.574770	−	0.818315i	$-0.694909\pi$
$101$	−1.54240	+	0.890504i	−0.153474	+	0.0886085i	0.421296	+	0.906923i	$0.361575\pi$
$102$		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	0.0348118	−	0.999394i	$-0.488917\pi$
$107$	−8.41266	−	4.85705i	−0.813283	−	0.469549i	−0.848095	+	0.529845i	$0.822250\pi$
$108$		0			0
$109$	−12.3647	+	7.13874i	−1.18432	+	0.683767i	−0.957010	−	0.290055i	$-0.906326\pi$
$109$	−12.3647	+	7.13874i	−1.18432	+	0.683767i	−0.227309	+	0.973823i	$0.572993\pi$
$110$	−0.639368	−	4.72301i	−0.0609614	−	0.450321i
$111$		0			0
$112$	8.43957	+	6.38542i	0.797465	+	0.603366i
$113$	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
$116$	1.42575	+	5.16950i	0.132378	+	0.479976i
$117$		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
$122$	4.37411	−	10.6702i	0.396013	−	0.966033i
$123$		0			0
$124$	15.2619	+	15.0403i	1.37055	+	1.35066i
$125$		−	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	$0.387909\pi$
$128$	−9.14905	−	6.65545i	−0.808669	−	0.588264i
$129$		0			0
$130$	−28.7974	−	11.8051i	−2.52570	−	1.03538i
$131$	6.10134	+	3.52261i	0.533076	+	0.307772i	0.742268	−	0.670103i	$-0.233750\pi$
$131$	6.10134	+	3.52261i	0.533076	+	0.307772i	−0.209192	+	0.977875i	$0.567083\pi$
$132$		0			0
$133$	−0.883475	+	6.32703i	−0.0766070	+	0.548623i
$134$	−3.43912	−	4.44819i	−0.297095	−	0.384265i
$135$		0			0
$136$	−6.42150	+	8.56145i	−0.550639	+	0.734138i
$137$	−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	$-0.885110\pi$
$139$		−	8.32721i		−	0.706305i	0.935566	−	0.353152i	$-0.114890\pi$
$140$	2.46119	+	18.7711i	0.208009	+	1.58644i
$141$		0			0
$142$	0.744772	+	5.50162i	0.0624998	+	0.461686i
$143$	−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	0.999396	−	0.0347378i	$-0.0110596\pi$
$149$	17.9316	+	10.3528i	1.46901	+	0.848134i	0.469614	+	0.882872i	$0.344393\pi$
$150$		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	$0.884790\pi$
$152$	0.817123	−	6.78045i	0.0662775	−	0.549967i
$153$		0			0
$154$	−1.77501	+	3.04493i	−0.143034	+	0.245367i
$155$			38.3311i			3.07883i
$156$		0			0
$157$	10.2803	−	5.93532i	0.820456	−	0.473690i	−0.0301179	−	0.999546i	$-0.509588\pi$
$157$	10.2803	−	5.93532i	0.820456	−	0.473690i	0.850574	+	0.525856i	$0.176255\pi$
$158$	7.16101	+	2.93557i	0.569699	+	0.233541i
$159$		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	0.950522	−	0.310659i	$-0.100550\pi$
$163$	14.7683	+	8.52649i	1.15674	+	0.667846i	0.206222	+	0.978505i	$0.433883\pi$
$164$	−8.79175	+	2.42477i	−0.686520	+	0.189343i
$165$		0			0
$166$	1.67555	−	0.226825i	0.130048	−	0.0176050i
$167$	−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
$170$	−18.9717	+	2.56825i	−1.45506	+	0.196976i
$171$		0			0
$172$	1.86469	+	6.76102i	0.142181	+	0.515523i
$173$	−12.6216	−	7.28708i	−0.959602	−	0.554027i	−0.0635517	−	0.997979i	$-0.520243\pi$
$173$	−12.6216	−	7.28708i	−0.959602	−	0.554027i	−0.896051	+	0.443952i	$0.853576\pi$
$174$		0			0
$175$	−12.6915	+	16.2741i	−0.959385	+	1.23021i
$176$	1.83602	−	3.29027i	0.138395	−	0.248013i
$177$		0			0
$178$	−2.38286	−	0.976824i	−0.178603	−	0.0732161i
$179$	−3.27323	+	1.88980i	−0.244653	+	0.141251i	−0.617313	−	0.786717i	$-0.711779\pi$
$179$	−3.27323	+	1.88980i	−0.244653	+	0.141251i	0.372660	+	0.927968i	$0.378446\pi$
$180$		0			0
$181$			1.12363i			0.0835189i	0.999128	+	0.0417595i	$0.0132963\pi$
$181$			1.12363i			0.0835189i	−0.999128	+	0.0417595i	$0.986704\pi$
$182$	11.4243	+	19.9800i	0.846826	+	1.48102i
$183$		0			0
$184$	−8.38903	−	1.01098i	−0.618447	−	0.0745302i
$185$	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	$0.842273\pi$
$194$	2.28117	+	16.8509i	0.163778	+	1.20983i
$195$		0			0
$196$	7.10118	−	12.0654i	0.507227	−	0.861812i
$197$		−	2.37637i		−	0.169309i	−0.996410	−	0.0846545i	$-0.973021\pi$
$197$		−	2.37637i		−	0.169309i	0.996410	−	0.0846545i	$-0.0269787\pi$
$198$		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	$0.673437\pi$
$200$	13.2382	−	17.6498i	0.936083	−	1.24803i
$201$		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
$206$	16.2559	+	6.66390i	1.13260	+	0.464296i
$207$		0			0
$208$	−12.6126	−	21.1261i	−0.874525	−	1.46483i
$209$	2.27447			0.157328
$210$		0			0
$211$			14.1932i			0.977103i	0.872535	+	0.488551i	$0.162474\pi$
$211$			14.1932i			0.977103i	−0.872535	+	0.488551i	$0.837526\pi$
$212$	10.6576	−	10.8146i	0.731967	−	0.742748i
$213$		0			0
$214$	5.21081	−	12.7112i	0.356203	−	0.868921i
$215$	−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
$220$	6.49767	−	1.79206i	0.438073	−	0.120821i
$221$	−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	$0.502112\pi$
$224$	−7.34760	+	13.0389i	−0.490932	+	0.871198i
$225$		0			0
$226$	2.63278	+	19.4483i	0.175130	+	1.29368i
$227$	22.3054	−	12.8780i	1.48046	−	0.854744i	0.480705	−	0.876882i	$-0.340381\pi$
$227$	22.3054	−	12.8780i	1.48046	−	0.854744i	0.999755	+	0.0221381i	$0.00704735\pi$
$228$		0			0
$229$	13.9965	+	8.08087i	0.924913	+	0.533999i	0.885199	−	0.465212i	$-0.154022\pi$
$229$	13.9965	+	8.08087i	0.924913	+	0.533999i	0.0397138	+	0.999211i	$0.487355\pi$
$230$	−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
$236$	0.163111	−	0.165513i	0.0106176	−	0.0107740i
$237$		0			0
$238$	12.2310	+	7.12997i	0.792820	+	0.462167i
$239$	−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	$0.693907\pi$
$242$	−13.2328	−	5.42462i	−0.850636	−	0.348708i
$243$		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
$248$	−18.1825	+	24.2418i	−1.15459	+	1.53936i
$249$		0			0
$250$	14.0410	−	1.90078i	0.888031	−	0.120216i
$251$			8.64704i			0.545796i	0.962043	+	0.272898i	$0.0879822\pi$
$251$			8.64704i			0.545796i	−0.962043	+	0.272898i	$0.912018\pi$
$252$		0			0
$253$		−	2.81406i		−	0.176918i
$254$	1.47483	+	10.8946i	0.0925392	+	0.683586i
$255$		0			0
$256$	7.59143	−	14.0844i	0.474464	−	0.880275i
$257$	−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
$262$	−3.77917	+	9.21890i	−0.233478	+	0.569545i
$263$	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
$266$	−9.03451	−	0.0377886i	−0.553941	−	0.00231697i
$267$		0			0
$268$	5.58137	−	5.66358i	0.340937	−	0.345958i
$269$	14.6930	−	8.48299i	0.895847	−	0.517217i	0.0199962	−	0.999800i	$-0.493635\pi$
$269$	14.6930	−	8.48299i	0.895847	−	0.517217i	0.875850	+	0.482583i	$0.160301\pi$
$270$		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	−0.621834	−	0.783149i	$-0.713612\pi$
$277$	−4.23611	+	2.44572i	−0.254523	+	0.146949i	0.367311	+	0.930098i	$0.380279\pi$
$278$	11.6700	−	1.57980i	0.699920	−	0.0947504i
$279$		0			0
$280$	−25.8394	+	7.01036i	−1.54420	+	0.418949i
$281$	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	−0.908326	−	0.418262i	$-0.862639\pi$
$283$	−16.8270	+	9.71510i	−1.00026	+	0.577503i	−0.0919376	+	0.995765i	$0.529306\pi$
$284$	−7.56885	+	2.08749i	−0.449128	+	0.123870i
$285$		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
$290$	−12.5526	−	5.14578i	−0.737114	−	0.302171i
$291$		0			0
$292$	8.87297	+	8.74417i	0.519251	+	0.511714i
$293$			21.9433i			1.28194i	0.767564	+	0.640972i	$0.221468\pi$
$293$			21.9433i			1.28194i	−0.767564	+	0.640972i	$0.778532\pi$
$294$		0			0
$295$	0.415698			0.0242029
$296$	−0.577746	+	4.79410i	−0.0335808	+	0.278652i
$297$		0			0
$298$	−11.1068	+	27.0939i	−0.643401	+	1.56951i
$299$	−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
$304$	9.65735	−	0.141218i	0.553887	−	0.00809938i
$305$	14.5871	+	25.2656i	0.835255	+	1.44670i
$306$		0			0
$307$		−	2.18555i		−	0.124736i	−0.998053	−	0.0623679i	$-0.980135\pi$
$307$		−	2.18555i		−	0.124736i	0.998053	−	0.0623679i	$-0.0198652\pi$
$308$	−4.60400	−	1.90988i	−0.262337	−	0.108826i
$309$		0			0
$310$	−53.7184	+	7.27203i	−3.05100	+	0.413023i
$311$	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	0.685802	−	0.727788i	$-0.259451\pi$
$317$	7.09368	+	4.09554i	0.398421	+	0.230028i	−0.287382	+	0.957816i	$0.592785\pi$
$318$		0			0
$319$	−1.26283	−	2.18728i	−0.0707048	−	0.122464i
$320$	27.4777	−	8.01248i	1.53605	−	0.447911i
$321$		0			0
$322$	−0.0467535	+	11.1778i	−0.00260547	+	0.622917i
$323$		−	9.13622i		−	0.508353i
$324$		0			0
$325$	41.5531	−	23.9907i	2.30495	−	1.33076i
$326$	−9.14750	+	22.3144i	−0.506633	+	1.23588i
$327$		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	0.0855218	−	0.996336i	$-0.472744\pi$
$331$	−13.3643	−	7.71590i	−0.734570	−	0.424104i	−0.820092	+	0.572232i	$0.806078\pi$
$332$	0.635759	+	2.30514i	0.0348918	+	0.126511i
$333$		0			0
$334$	−1.97947	−	14.6223i	−0.108312	−	0.800098i
$335$	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	$0.504716\pi$
$338$	−4.71195	−	34.8071i	−0.256296	−	1.89326i
$339$		0			0
$340$	−7.19845	−	26.1002i	−0.390391	−	1.41548i
$341$	−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
$346$	7.81782	−	19.0708i	0.420289	−	1.02525i
$347$	9.92740	−	5.73159i	0.532931	−	0.307688i	−0.209278	−	0.977856i	$-0.567111\pi$
$347$	9.92740	−	5.73159i	0.532931	−	0.307688i	0.742209	+	0.670168i	$0.233778\pi$
$348$		0			0
$349$			1.23092i			0.0658899i	0.999457	+	0.0329449i	$0.0104886\pi$
$349$			1.23092i			0.0658899i	−0.999457	+	0.0329449i	$0.989511\pi$
$350$	−25.2148	−	14.6988i	−1.34779	−	0.785681i
$351$		0			0
$352$	4.95940	+	1.94884i	0.264337	+	0.103874i
$353$	−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
$362$	−1.57469	+	0.213171i	−0.0827640	+	0.0112040i
$363$		0			0
$364$	−25.8332	+	19.8009i	−1.35403	+	1.03785i
$365$			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	$0.665827\pi$
$368$	−0.174720	−	11.9484i	−0.00910790	−	0.622855i
$369$		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	0.129080	−	0.991634i	$-0.458798\pi$
$373$	−12.8464	−	7.41686i	−0.665160	−	0.384030i	−0.794240	+	0.607604i	$0.792131\pi$
$374$	1.91188	−	4.66383i	0.0988609	−	0.241161i
$375$		0			0
$376$	19.2238	+	2.31670i	0.991394	+	0.119475i
$377$	−16.4928			−0.849425
$378$		0			0
$379$			11.7500i			0.603555i	0.953378	+	0.301778i	$0.0975800\pi$
$379$			11.7500i			0.603555i	−0.953378	+	0.301778i	$0.902420\pi$
$380$	12.3062	+	12.1275i	0.631293	+	0.622129i
$381$		0			0
$382$	18.3588	+	7.52594i	0.939315	+	0.385061i
$383$	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
$388$	−23.1827	+	6.39379i	−1.17692	+	0.324595i
$389$	−1.73492	+	1.00165i	−0.0879638	+	0.0507859i	−0.543337	−	0.839515i	$-0.682839\pi$
$389$	−1.73492	+	1.00165i	−0.0879638	+	0.0507859i	0.455373	+	0.890301i	$0.349506\pi$
$390$		0			0
$391$	−11.3037			−0.571652
$392$	18.2560	+	7.66281i	0.922067	+	0.387031i
$393$		0			0
$394$	3.33031	−	0.450835i	0.167779	−	0.0227127i
$395$	−16.9563	+	9.78974i	−0.853165	+	0.492575i
$396$		0			0
$397$	7.34718	+	4.24190i	0.368744	+	0.212895i	0.672910	−	0.739725i	$-0.265044\pi$
$397$	7.34718	+	4.24190i	0.368744	+	0.212895i	−0.304165	+	0.952619i	$0.598378\pi$
$398$	−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
$404$	2.50024	−	2.53707i	0.124392	−	0.126224i
$405$		0			0
$406$	4.97978	+	8.70916i	0.247143	+	0.432229i
$407$	−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	$-0.436876\pi$
$410$	8.75141	−	21.3482i	0.432201	−	1.05431i
$411$		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
$416$	27.2140	−	21.6836i	1.33428	−	1.06313i
$417$		0			0
$418$	0.431503	+	3.18751i	0.0211055	+	0.155906i
$419$		−	30.8896i		−	1.50905i	−0.656269	−	0.754527i	$-0.727866\pi$
$419$		−	30.8896i		−	1.50905i	0.656269	−	0.754527i	$-0.272134\pi$
$420$		0			0
$421$			20.0940i			0.979321i	0.871913	+	0.489661i	$0.162879\pi$
$421$			20.0940i			0.979321i	−0.871913	+	0.489661i	$0.837121\pi$
$422$	−19.8908	+	2.69268i	−0.968271	+	0.131078i
$423$		0			0
$424$	17.1778	+	12.8842i	0.834228	+	0.625711i
$425$	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
$430$	−16.4171	−	6.73000i	−0.791705	−	0.324549i
$431$	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	$0.724527\pi$
$434$	34.6323	+	20.1886i	1.66240	+	0.969082i
$435$		0			0
$436$	20.0432	−	20.3385i	0.959897	−	0.974036i
$437$	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	0.504518	−	0.863401i	$-0.331670\pi$
$443$	0.190464	+	0.109964i	0.00904921	+	0.00522457i	−0.495469	+	0.868626i	$0.665004\pi$
$444$		0			0
$445$	5.64230	−	3.25758i	0.267471	−	0.154424i
$446$	−0.0375975	−	0.277732i	−0.00178029	−	0.0131510i
$447$		0			0
$448$	−19.6671	−	7.82347i	−0.929181	−	0.369624i
$449$	−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
$452$	−26.7560	+	7.37933i	−1.25850	+	0.347094i
$453$		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	$0.102320\pi$
$458$	−8.66942	+	21.1482i	−0.405095	+	0.988188i
$459$		0			0
$460$	15.0046	−	15.2256i	0.699595	−	0.709900i
$461$			13.8203i			0.643676i	0.946795	+	0.321838i	$0.104301\pi$
$461$			13.8203i			0.643676i	−0.946795	+	0.321838i	$0.895699\pi$
$462$		0			0
$463$	28.8694			1.34168			0.670838	−	0.741604i	$-0.265935\pi$
$463$	28.8694			1.34168			0.670838	+	0.741604i	$0.265935\pi$
$464$	−5.49774	−	9.20874i	−0.255226	−	0.427505i
$465$		0			0
$466$	32.8754	+	13.4769i	1.52292	+	0.624303i
$467$	−10.7682	−	6.21705i	−0.498295	−	0.287691i	0.229714	−	0.973258i	$-0.426221\pi$
$467$	−10.7682	−	6.21705i	−0.498295	−	0.287691i	−0.728009	+	0.685567i	$0.759554\pi$
$468$		0			0
$469$	−8.29482	−	6.46876i	−0.383019	−	0.298700i
$470$	21.1866	+	27.4029i	0.977264	+	1.26400i
$471$		0			0
$472$	0.262900	+	0.197188i	0.0121010	+	0.00907632i
$473$	−1.65161	−	2.86067i	−0.0759411	−	0.131534i
$474$		0			0
$475$			18.8347i			0.864197i
$476$	−7.67173	+	18.4936i	−0.351633	+	0.847653i
$477$		0			0
$478$	−3.04284	−	22.4774i	−0.139176	−	1.02809i
$479$	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	$0.820315\pi$
$488$	−2.75950	+	22.8982i	−0.124917	+	1.03655i
$489$		0			0
$490$	13.1596	+	32.8825i	0.594489	+	1.48548i
$491$			4.10278i			0.185156i	0.995705	+	0.0925780i	$0.0295108\pi$
$491$			4.10278i			0.185156i	−0.995705	+	0.0925780i	$0.970489\pi$
$492$		0			0
$493$	−8.78600	+	5.07260i	−0.395701	+	0.228458i
$494$	19.4351	+	7.96717i	0.874426	+	0.358460i
$495$		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	$0.131274\pi$
$499$	38.4522	+	22.2004i	1.72135	+	0.993825i	0.805197	+	0.593008i	$0.202060\pi$
$500$	5.32761	+	19.3169i	0.238258	+	0.863878i
$501$		0			0
$502$	−12.1182	+	1.64048i	−0.540863	+	0.0732183i
$503$	−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
$506$	3.94371	−	0.533872i	0.175319	−	0.0237335i
$507$		0			0
$508$	−14.9882	+	4.13375i	−0.664993	+	0.183405i
$509$	−9.56641	−	5.52317i	−0.424024	−	0.244810i	0.272774	−	0.962078i	$-0.412059\pi$
$509$	−9.56641	−	5.52317i	−0.424024	−	0.244810i	−0.696797	+	0.717268i	$0.745392\pi$
$510$		0			0
$511$	10.1344	−	12.9952i	0.448320	−	0.574875i
$512$	21.1785	+	7.96682i	0.935967	+	0.352087i
$513$		0			0
$514$	−18.9280	−	7.75931i	−0.834880	−	0.342249i
$515$	−38.4918	+	22.2233i	−1.69615	+	0.979274i
$516$		0			0
$517$			6.44855i			0.283607i
$518$	6.38783	+	0.0267184i	0.280665	+	0.00117394i
$519$		0			0
$520$	61.7992	+	7.44753i	2.71007	+	0.326596i
$521$	−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	0.113862	−	0.993497i	$-0.463678\pi$
$523$	−15.7706	−	9.10516i	−0.689601	−	0.398141i	−0.803462	+	0.595356i	$0.797011\pi$
$524$	−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
$530$	5.15297	+	38.0650i	0.223831	+	1.65344i
$531$		0			0
$532$	−1.66103	−	12.6684i	−0.0720149	−	0.549245i
$533$		−	28.0493i		−	1.21495i
$534$		0			0
$535$	17.3774	+	30.0985i	0.751289	+	1.30127i
$536$	8.99599	+	6.74743i	0.388568	+	0.291445i
$537$		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	0.941877	−	0.335957i	$-0.109060\pi$
$541$	26.0940	+	15.0654i	1.12187	+	0.647712i	0.179992	+	0.983668i	$0.442393\pi$
$542$	−1.40847	−	0.577383i	−0.0604988	−	0.0248007i
$543$		0			0
$544$	7.82822	−	19.9212i	0.335632	−	0.854115i
$545$	51.0814			2.18809
$546$		0			0
$547$		−	36.0927i		−	1.54321i	−0.636101	−	0.771606i	$-0.719454\pi$
$547$		−	36.0927i		−	1.54321i	0.636101	−	0.771606i	$-0.280546\pi$
$548$	25.7945	+	25.4201i	1.10189	+	1.08589i
$549$		0			0
$550$	−3.94142	+	9.61470i	−0.168063	+	0.409972i
$551$	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
$556$	4.42797	+	16.0550i	0.187788	+	0.680883i
$557$	36.7321	−	21.2073i	1.55639	−	0.898583i	0.558793	−	0.829307i	$-0.311265\pi$
$557$	36.7321	−	21.2073i	1.55639	−	0.898583i	0.997598	−	0.0692757i	$-0.0220688\pi$
$558$		0			0
$559$	−21.5704			−0.912333
$560$	−14.7267	−	34.8822i	−0.622316	−	1.47404i
$561$		0			0
$562$	0.143082	+	1.05694i	0.00603553	+	0.0445844i
$563$	10.2656	−	5.92685i	0.432644	−	0.249787i	−0.267828	−	0.963467i	$-0.586306\pi$
$563$	10.2656	−	5.92685i	0.432644	−	0.249787i	0.700472	+	0.713680i	$0.252973\pi$
$564$		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	−0.101181	−	0.994868i	$-0.532262\pi$
$571$	16.9613	−	9.79262i	0.709809	−	0.409809i	0.810990	+	0.585059i	$0.198929\pi$
$572$	8.25392	+	8.13411i	0.345114	+	0.340104i
$573$		0			0
$574$	−14.8116	+	8.46910i	−0.618226	+	0.353493i
$575$	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	$0.874685\pi$
$578$	3.51111	+	1.43933i	0.146043	+	0.0598684i
$579$		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
$584$	−10.5710	+	14.0938i	−0.437431	+	0.583204i
$585$		0			0
$586$	−30.7521	+	4.16300i	−1.27036	+	0.171972i
$587$			0.894279i			0.0369108i	0.999830	+	0.0184554i	$0.00587487\pi$
$587$			0.894279i			0.0369108i	−0.999830	+	0.0184554i	$0.994125\pi$
$588$		0			0
$589$		−	25.8693i		−	1.06593i
$590$	0.0788645	+	0.582572i	0.00324680	+	0.0239841i
$591$		0			0
$592$	−6.82821	+	0.0998477i	−0.280638	+	0.00410371i
$593$	−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
$598$	9.85728	−	24.0458i	0.403094	−	0.983307i
$599$	−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	$0.502578\pi$
$602$	6.51290	+	11.3904i	0.265446	+	0.464239i
$603$		0			0
$604$	5.63490	+	5.55310i	0.229281	+	0.225953i
$605$	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	0.00550856	−	0.999985i	$-0.498247\pi$
$613$	21.6460	−	12.4973i	0.874275	−	0.504763i	0.868767	+	0.495222i	$0.164913\pi$
$614$	3.06289	−	0.414633i	0.123608	−	0.0167332i
$615$		0			0
$616$	1.80312	−	6.81452i	0.0726496	−	0.274565i
$617$	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	−0.410650	−	0.911793i	$-0.634698\pi$
$619$	4.32061	−	2.49451i	0.173660	−	0.100263i	0.584311	+	0.811530i	$0.301365\pi$
$620$	−20.3825	−	73.9030i	−0.818580	−	2.96802i
$621$		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
$626$	1.78816	+	0.733033i	0.0714692	+	0.0292979i
$627$		0			0
$628$	−16.6644	+	16.9099i	−0.664984	+	0.674779i
$629$			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	$0.398675\pi$
$632$	−15.3675	−	1.85197i	−0.611287	−	0.0736673i
$633$		0			0
$634$	−4.39383	+	10.7183i	−0.174501	+	0.425677i
$635$	−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
$640$	16.4419	+	36.9880i	0.649923	+	1.46208i
$641$	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	$-0.610478\pi$
$643$		−	47.6908i		−	1.88074i	0.340150	−	0.940371i	$-0.389522\pi$
$644$	−15.6738	+	2.05509i	−0.617636	+	0.0809820i
$645$		0			0
$646$	12.8038	−	1.73329i	0.503758	−	0.0681953i
$647$	−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	−0.412799	−	0.910822i	$-0.635449\pi$
$653$	−35.9797	−	20.7729i	−1.40799	−	0.812905i	−0.995195	+	0.0979172i	$0.968782\pi$
$654$		0			0
$655$	−12.6030	−	21.8291i	−0.492442	−	0.852934i
$656$	15.6613	−	9.34998i	0.611469	−	0.365055i
$657$		0			0
$658$	0.107138	−	25.6145i	0.00417667	−	0.998558i
$659$			21.7026i			0.845414i	0.906266	+	0.422707i	$0.138920\pi$
$659$			21.7026i			0.845414i	−0.906266	+	0.422707i	$0.861080\pi$
$660$		0			0
$661$	−12.7886	+	7.38348i	−0.497417	+	0.287184i	−0.727646	−	0.685952i	$-0.759386\pi$
$661$	−12.7886	+	7.38348i	−0.497417	+	0.287184i	0.230229	+	0.973136i	$0.426052\pi$
$662$	8.27787	−	20.1930i	0.321729	−	0.784823i
$663$		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
$668$	20.1166	−	5.54818i	0.778336	−	0.214665i
$669$		0			0
$670$	2.69861	+	19.9346i	0.104256	+	0.770140i
$671$	−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	$0.481026\pi$
$674$	−0.103191	−	0.762271i	−0.00397477	−	0.0293616i
$675$		0			0
$676$	47.8859	−	13.2069i	1.84176	−	0.507959i
$677$	−33.6034	−	19.4009i	−1.29148	−	0.745638i	−0.312566	−	0.949896i	$-0.601188\pi$
$677$	−33.6034	−	19.4009i	−1.29148	−	0.745638i	−0.978917	+	0.204258i	$0.934522\pi$
$678$		0			0
$679$	11.9435	+	29.4857i	0.458349	+	1.13156i
$680$	35.2120	−	15.0398i	1.35032	−	0.576749i
$681$		0			0
$682$	5.41350	−	13.2057i	0.207294	−	0.505671i
$683$	22.5229	−	13.0036i	0.861817	−	0.497570i	−0.00280354	−	0.999996i	$-0.500892\pi$
$683$	22.5229	−	13.0036i	0.861817	−	0.497570i	0.864620	+	0.502426i	$0.167559\pi$
$684$		0			0
$685$			64.7846i			2.47529i
$686$	7.27993	−	25.1595i	0.277949	−	0.960596i
$687$		0			0
$688$	−7.19031	−	12.0438i	−0.274128	−	0.459166i
$689$	23.3491	+	40.4418i	0.889530	+	1.54071i
$690$		0			0
$691$	8.60842	+	4.97007i	0.327480	+	0.189070i	0.654722	−	0.755870i	$-0.272786\pi$
$691$	8.60842	+	4.97007i	0.327480	+	0.189070i	−0.327242	+	0.944941i	$0.606119\pi$
$692$	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
$698$	−1.72506	+	0.233526i	−0.0652943	+	0.00883910i
$699$		0			0
$700$	15.8156	−	38.1254i	0.597774	−	1.44101i
$701$			32.3250i			1.22090i	0.792056	+	0.610449i	$0.209011\pi$
$701$			32.3250i			1.22090i	−0.792056	+	0.610449i	$0.790989\pi$
$702$		0			0
$703$	−2.06114	−	3.57000i	−0.0777374	−	0.134645i
$704$	−1.79029	+	7.31999i	−0.0674741	+	0.275882i
$705$		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	−0.437357	−	0.899288i	$-0.644085\pi$
$709$	−38.2056	−	22.0580i	−1.43484	−	0.828406i	−0.997485	+	0.0708817i	$0.977419\pi$
$710$	7.53412	−	18.3787i	0.282750	−	0.689741i
$711$		0			0
$712$	5.11362	+	0.616251i	0.191641	+	0.0230950i
$713$	−32.0065			−1.19865
$714$		0			0
$715$			20.7303i			0.775268i
$716$	5.30595	−	5.38411i	0.198293	−	0.201213i
$717$		0			0
$718$	44.3687	+	18.1884i	1.65583	+	0.678785i
$719$	−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
$724$	−0.597489	−	2.16638i	−0.0222055	−	0.0805129i
$725$	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	$0.657480\pi$
$728$	−32.6506	−	32.4469i	−1.21011	−	1.20256i
$729$		0			0
$730$	−31.2309	+	4.22783i	−1.15591	+	0.156479i
$731$	−11.4909	+	6.63428i	−0.425007	+	0.245378i
$732$		0			0
$733$	−8.94596	−	5.16495i	−0.330426	−	0.190772i	0.325604	−	0.945506i	$-0.394432\pi$
$733$	−8.94596	−	5.16495i	−0.330426	−	0.190772i	−0.656030	+	0.754734i	$0.727766\pi$
$734$	−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	0.476691	−	0.879071i	$-0.341836\pi$
$739$	40.1335	−	23.1711i	1.47633	−	0.852362i	0.999643	+	0.0267085i	$0.00850260\pi$
$740$	−8.70105	−	8.57475i	−0.319857	−	0.315214i
$741$		0			0
$742$	14.3057	−	24.5405i	0.525177	−	0.900910i
$743$	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
$746$	7.95705	−	19.4104i	0.291328	−	0.710665i
$747$		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	$0.122855\pi$
$752$	0.400378	+	27.3804i	0.0146003	+	0.998460i
$753$		0			0
$754$	−3.12896	−	23.1136i	−0.113950	−	0.841747i
$755$			14.1524i			0.515059i
$756$		0			0
$757$		−	41.2006i		−	1.49746i	−0.662873	−	0.748731i	$-0.730663\pi$
$757$		−	41.2006i		−	1.49746i	0.662873	−	0.748731i	$-0.269337\pi$
$758$	−16.4668	+	2.22916i	−0.598100	+	0.0809666i
$759$		0			0
$760$	−14.6612	+	19.5470i	−0.531818	+	0.709045i
$761$	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
$766$	24.9478	+	10.2270i	0.901400	+	0.369518i
$767$	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	$0.584973\pi$
$770$	10.9468	−	6.25921i	0.394494	−	0.225566i
$771$		0			0
$772$	1.11140	+	1.09527i	0.0400001	+	0.0394195i
$773$	−36.7815	+	21.2358i	−1.32294	+	0.763798i	−0.984196	−	0.177082i	$-0.943334\pi$
$773$	−36.7815	+	21.2358i	−1.32294	+	0.763798i	−0.338741	+	0.940880i	$0.610001\pi$
$774$		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
$782$	−2.14449	−	15.8413i	−0.0766868	−	0.566485i
$783$		0			0
$784$	−7.27545	+	27.0383i	−0.259837	+	0.965652i
$785$	−42.4703			−1.51583
$786$		0			0
$787$	6.55295	−	3.78335i	0.233588	−	0.134862i	−0.378638	−	0.925545i	$-0.623608\pi$
$787$	6.55295	−	3.78335i	0.233588	−	0.134862i	0.612226	+	0.790683i	$0.290274\pi$
$788$	1.26363	+	4.58167i	0.0450149	+	0.163215i
$789$		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
$794$	−4.55085	+	11.1013i	−0.161503	+	0.393971i
$795$		0			0
$796$	−19.3505	−	19.0696i	−0.685860	−	0.675904i
$797$			11.4622i			0.406013i	0.979177	+	0.203007i	$0.0650713\pi$
$797$			11.4622i			0.406013i	−0.979177	+	0.203007i	$0.934929\pi$
$798$		0			0
$799$	25.9029			0.916379
$800$	−16.1382	+	41.0685i	−0.570573	+	1.45199i
$801$		0			0
$802$	−18.4407	−	7.55952i	−0.651163	−	0.266936i
$803$	−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
$808$	4.02987	+	3.02260i	0.141770	+	0.106335i
$809$	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	$0.0945434\pi$
$811$			16.6693i			0.585338i	−0.956214	+	0.292669i	$0.905457\pi$
$812$	−11.2605	+	8.63109i	−0.395168	+	0.302892i
$813$		0			0
$814$	−0.305094	−	2.25372i	−0.0106935	−	0.0789930i
$815$	−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	0.980465	−	0.196691i	$-0.0630197\pi$
$821$	37.2593	+	21.5117i	1.30036	+	0.750762i	0.319893	+	0.947454i	$0.396353\pi$
$822$		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	$-0.373065\pi$
$824$	−34.8851	−	4.20407i	−1.21528	−	0.146456i
$825$		0			0
$826$	0.218943	−	0.375584i	0.00761801	−	0.0130682i
$827$		−	36.5937i		−	1.27249i	−0.771489	−	0.636243i	$-0.780487\pi$
$827$		−	36.5937i		−	1.27249i	0.771489	−	0.636243i	$-0.219513\pi$
$828$		0			0
$829$	6.54607	−	3.77938i	0.227354	−	0.131263i	−0.381997	−	0.924164i	$-0.624763\pi$
$829$	6.54607	−	3.77938i	0.227354	−	0.131263i	0.609351	+	0.792901i	$0.291430\pi$
$830$	−5.59735	−	2.29456i	−0.194287	−	0.0796455i
$831$		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
$836$	−4.38521	+	1.20944i	−0.151666	+	0.0418295i
$837$		0			0
$838$	43.2896	−	5.86025i	1.49541	−	0.202439i
$839$	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
$842$	−28.1603	+	3.81215i	−0.970469	+	0.131375i
$843$		0			0
$844$	−7.54722	−	27.3648i	−0.259786	−	0.941935i
$845$	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
$850$	38.6209	+	15.8321i	1.32469	+	0.543038i
$851$	−4.41694	+	2.55012i	−0.151411	+	0.0874171i
$852$		0			0
$853$			18.6855i			0.639779i	0.947455	+	0.319889i	$0.103646\pi$
$853$			18.6855i			0.639779i	−0.947455	+	0.319889i	$0.896354\pi$
$854$	30.5104	+	0.127616i	1.04404	+	0.00436692i
$855$		0			0
$856$	−3.28735	+	27.2783i	−0.112359	+	0.932352i
$857$	−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	0.962182	−	0.272409i	$-0.0878203\pi$
$859$	35.3861	+	20.4302i	1.20736	+	0.697069i	0.245178	+	0.969478i	$0.421154\pi$
$860$	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
$866$	−5.11876	−	37.8123i	−0.173943	−	1.28491i
$867$		0			0
$868$	−21.7226	+	52.3648i	−0.737312	+	1.77738i
$869$		−	5.15496i		−	0.174870i
$870$		0			0
$871$	12.2279	+	21.1793i	0.414327	+	0.717635i
$872$	32.3055	+	24.2307i	1.09400	+	0.820554i
$873$		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	0.870226	−	0.492653i	$-0.163973\pi$
$877$	26.0217	+	15.0236i	0.878689	+	0.507311i	0.00846311	+	0.999964i	$0.497306\pi$
$878$	−47.7814	−	19.5874i	−1.61254	−	0.661042i
$879$		0			0
$880$	−11.5747	+	6.91024i	−0.390183	+	0.232944i
$881$	−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	$0.111031\pi$
$883$			20.3124i			0.683568i	−0.939779	+	0.341784i	$0.888969\pi$
$884$	32.6736	−	33.1548i	1.09893	−	1.11512i
$885$		0			0
$886$	−0.117973	+	0.287784i	−0.00396339	+	0.00966829i
$887$	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
$892$	0.382090	−	0.105381i	0.0127933	−	0.00352840i
$893$	−14.3153	+	8.26496i	−0.479044	+	0.276576i
$894$		0			0
$895$	13.5225			0.452008
$896$	7.23289	−	29.0463i	0.241634	−	0.970367i
$897$		0			0
$898$	−3.92331	−	28.9815i	−0.130923	−	0.967125i
$899$	−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	−0.152306	−	0.988333i	$-0.548670\pi$
$907$	18.8970	−	10.9102i	0.627464	−	0.362266i	0.779769	+	0.626067i	$0.215336\pi$
$908$	−36.1573	+	36.6899i	−1.19992	+	1.21760i
$909$		0			0
$910$	0.344418	−	82.3434i	0.0114173	−	2.72966i
$911$	−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
$914$	11.2327	+	4.60470i	0.371544	+	0.152310i
$915$		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	$-0.0473791\pi$
$920$	24.1843	+	18.1394i	0.797333	+	0.598039i
$921$		0			0
$922$	−19.3682	+	2.62193i	−0.637858	+	0.0863488i
$923$		−	24.1477i		−	0.794833i
$924$		0			0
$925$		−	13.3171i		−	0.437863i
$926$	5.47699	+	40.4585i	0.179985	+	1.32955i
$927$		0			0
$928$	11.8624	−	9.45175i	0.389402	−	0.310269i
$929$	−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
$934$	6.66986	−	16.2704i	0.218244	−	0.532385i
$935$	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	$0.486297\pi$
$938$	7.49186	−	12.8518i	0.244618	−	0.419627i
$939$		0			0
$940$	−34.3838	+	34.8903i	−1.12148	+	1.13800i
$941$	−17.7673	+	10.2579i	−0.579197	+	0.334399i	−0.760814	−	0.648970i	$-0.775200\pi$
$941$	−17.7673	+	10.2579i	−0.579197	+	0.334399i	0.181617	+	0.983369i	$0.441867\pi$
$942$		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	0.872313	−	0.488947i	$-0.162619\pi$
$947$	27.2353	+	15.7243i	0.885029	+	0.510972i	0.0127161	+	0.999919i	$0.495952\pi$
$948$		0			0
$949$	−33.1810	+	19.1571i	−1.07710	+	0.621865i
$950$	−26.3956	+	3.57325i	−0.856386	+	0.115932i
$951$		0			0
$952$	−27.3730	−	7.24286i	−0.887163	−	0.234743i
$953$	−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
$956$	30.9233	−	8.52866i	1.00013	−	0.275837i
$957$		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
$962$	−13.7415	−	5.63317i	−0.443045	−	0.181621i
$963$		0			0
$964$	−18.7595	−	18.4872i	−0.604203	−	0.595433i
$965$			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	$0.889526\pi$
$968$	28.3976	+	3.42224i	0.912732	+	0.109995i
$969$		0			0
$970$	23.0763	−	56.2922i	0.740935	−	1.80743i
$971$	40.3828	+	23.3150i	1.29595	+	0.748215i	0.979701	−	0.200463i	$-0.0642447\pi$
$971$	40.3828	+	23.3150i	1.29595	+	0.748215i	0.316245	+	0.948678i	$0.397578\pi$
$972$		0			0
$973$	20.4201	−	8.27137i	0.654639	−	0.265168i
$974$	−2.01899	+	1.56099i	−0.0646927	+	0.0500173i
$975$		0			0
$976$	−32.6138	+	0.476905i	−1.04394	+	0.0152654i
$977$	−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
$980$	−43.5860	+	24.6806i	−1.39230	+	0.788392i
$981$		0			0
$982$	−5.74977	+	0.778364i	−0.183482	+	0.0248386i
$983$	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	$0.462029\pi$
$992$	22.1657	−	56.4071i	0.703761	−	1.79093i
$993$		0			0
$994$	−12.7514	+	7.29108i	−0.404449	+	0.231259i
$995$		−	48.6000i		−	1.54072i
$996$		0			0
$997$	44.1522	−	25.4913i	1.39831	−	0.807317i	0.404098	−	0.914716i	$-0.367586\pi$
$997$	44.1522	−	25.4913i	1.39831	−	0.807317i	0.994216	+	0.107399i	$0.0342523\pi$
$998$	−23.8173	+	58.0998i	−0.753923	+	1.83912i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.189716 + 1.40143i) q^{2} +(-1.92802 + 0.531748i) q^{4} +(-3.09843 - 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 - 2.60110i) q^{8} +O(q^{10})\)	\(q+(0.189716 + 1.40143i) q^{2} +(-1.92802 + 0.531748i) q^{4} +(-3.09843 - 1.78888i) q^{5} +(0.993295 + 2.45222i) q^{7} +(-1.11098 - 2.60110i) q^{8} +(1.91917 - 4.68162i) q^{10} +(0.815768 - 0.470984i) q^{11} -6.15117i q^{13} +(-3.24817 + 1.85726i) q^{14} +(3.43449 - 2.05044i) q^{16} +(-1.89187 - 3.27682i) q^{17} +(2.09110 + 1.20730i) q^{19} +(6.92506 + 1.80141i) q^{20} +(0.814815 + 1.05389i) q^{22} +(1.49371 - 2.58719i) q^{23} +(3.90019 + 6.75532i) q^{25} +(8.62043 - 1.16697i) q^{26} +(-3.21905 - 4.19973i) q^{28} -2.68125i q^{29} +(-5.35686 - 9.27835i) q^{31} +(3.52512 + 4.42420i) q^{32} +(4.23332 - 3.27300i) q^{34} +(1.30906 - 9.37491i) q^{35} +(-1.47851 - 0.853618i) q^{37} +(-1.29523 + 3.15958i) q^{38} +(-1.21075 + 10.0467i) q^{40} +4.56000 q^{41} -3.50672i q^{43} +(-1.32237 + 1.34185i) q^{44} +(3.90915 + 1.60251i) q^{46} +(-3.42292 + 5.92866i) q^{47} +(-5.02673 + 4.87155i) q^{49} +(-8.72718 + 6.74743i) q^{50} +(3.27087 + 11.8595i) q^{52} +(-6.57466 + 3.79588i) q^{53} -3.37013 q^{55} +(5.27492 - 5.30803i) q^{56} +(3.75759 - 0.508677i) q^{58} +(-0.100623 + 0.0580947i) q^{59} +(-7.06184 - 4.07716i) q^{61} +(11.9867 - 9.26752i) q^{62} +(-5.53143 + 5.77955i) q^{64} +(-11.0037 + 19.0590i) q^{65} +(-3.44314 + 1.98790i) q^{67} +(5.39001 + 5.31177i) q^{68} +(13.3866 + 0.0559922i) q^{70} +3.92572 q^{71} +(-3.11438 - 5.39427i) q^{73} +(0.915789 - 2.23397i) q^{74} +(-4.67365 - 1.21575i) q^{76} +(1.96525 + 1.53261i) q^{77} +(2.73628 - 4.73937i) q^{79} +(-14.3095 + 0.209245i) q^{80} +(0.865104 + 6.39052i) q^{82} -1.19560i q^{83} +13.5373i q^{85} +(4.91443 - 0.665282i) q^{86} +(-2.13138 - 1.59864i) q^{88} +(-0.910509 + 1.57705i) q^{89} +(15.0840 - 6.10992i) q^{91} +(-1.50417 + 5.78242i) q^{92} +(-8.95799 - 3.67222i) q^{94} +(-4.31942 - 7.48146i) q^{95} +12.0241 q^{97} +(-7.78079 - 6.12040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 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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