LMFDB - Embedded newform 504.2.cj.e.37.9

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			37.9
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.267238 - 1.38873i) q^{2} +(-1.85717 + 0.742246i) q^{4} +(-1.56250 - 0.902108i) q^{5} +(2.63683 - 0.217074i) q^{7} +(1.52709 + 2.38076i) q^{8} +O(q^{10})$	\(q+(-0.267238 - 1.38873i) q^{2} +(-1.85717 + 0.742246i) q^{4} +(-1.56250 - 0.902108i) q^{5} +(2.63683 - 0.217074i) q^{7} +(1.52709 + 2.38076i) q^{8} +(-0.835229 + 2.41097i) q^{10} +(4.48004 - 2.58655i) q^{11} -0.840031i q^{13} +(-1.00612 - 3.60385i) q^{14} +(2.89814 - 2.75695i) q^{16} +(-2.45590 - 4.25375i) q^{17} +(-4.87773 - 2.81616i) q^{19} +(3.57140 + 0.515608i) q^{20} +(-4.78927 - 5.53036i) q^{22} +(-3.05110 + 5.28467i) q^{23} +(-0.872403 - 1.51105i) q^{25} +(-1.16658 + 0.224488i) q^{26} +(-4.73591 + 2.36032i) q^{28} +0.439783i q^{29} +(-3.66760 - 6.35247i) q^{31} +(-4.60317 - 3.28799i) q^{32} +(-5.25102 + 4.54736i) q^{34} +(-4.31586 - 2.03953i) q^{35} +(4.56250 + 2.63416i) q^{37} +(-2.60738 + 7.52645i) q^{38} +(-0.238373 - 5.09752i) q^{40} +6.23785 q^{41} -7.34846i q^{43} +(-6.40032 + 8.12895i) q^{44} +(8.15437 + 2.82491i) q^{46} +(2.83696 - 4.91375i) q^{47} +(6.90576 - 1.14477i) q^{49} +(-1.86530 + 1.61535i) q^{50} +(0.623510 + 1.56008i) q^{52} +(1.15952 - 0.669452i) q^{53} -9.33339 q^{55} +(4.54348 + 5.94616i) q^{56} +(0.610741 - 0.117527i) q^{58} +(7.31087 - 4.22093i) q^{59} +(4.77538 + 2.75707i) q^{61} +(-7.84178 + 6.79095i) q^{62} +(-3.33600 + 7.27125i) q^{64} +(-0.757798 + 1.31255i) q^{65} +(0.647433 - 0.373796i) q^{67} +(7.71836 + 6.07704i) q^{68} +(-1.67900 + 6.53863i) q^{70} -9.08033 q^{71} +(3.70739 + 6.42139i) q^{73} +(2.43888 - 7.04006i) q^{74} +(11.1490 + 1.60960i) q^{76} +(11.2516 - 7.79280i) q^{77} +(-8.68074 + 15.0355i) q^{79} +(-7.01540 + 1.69329i) q^{80} +(-1.66699 - 8.66271i) q^{82} -1.45486i q^{83} +8.86196i q^{85} +(-10.2051 + 1.96379i) q^{86} +(12.9994 + 6.71598i) q^{88} +(3.10088 - 5.37088i) q^{89} +(-0.182349 - 2.21502i) q^{91} +(1.74389 - 12.0792i) q^{92} +(-7.58204 - 2.62664i) q^{94} +(5.08095 + 8.80047i) q^{95} -5.81776 q^{97} +(-3.43527 - 9.28434i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.267238	−	1.38873i	−0.188966	−	0.981984i
$2$	−0.267238	−	1.38873i	−0.188966	−	0.981984i
$3$		0			0
$3$		0			0
$4$	−1.85717	+	0.742246i	−0.928584	+	0.371123i
$5$	−1.56250	−	0.902108i	−0.698770	−	0.403435i	0.108119	−	0.994138i	$-0.465517\pi$
$5$	−1.56250	−	0.902108i	−0.698770	−	0.403435i	−0.806889	+	0.590703i	$0.798850\pi$
$6$		0			0
$7$	2.63683	−	0.217074i	0.996629	−	0.0820461i
$7$	2.63683	−	0.217074i	0.996629	−	0.0820461i
$8$	1.52709	+	2.38076i	0.539908	+	0.841724i
$9$		0			0
$10$	−0.835229	+	2.41097i	−0.264123	+	0.762416i
$11$	4.48004	−	2.58655i	1.35078	−	0.779874i	0.362423	−	0.932014i	$-0.381950\pi$
$11$	4.48004	−	2.58655i	1.35078	−	0.779874i	0.988359	+	0.152139i	$0.0486162\pi$
$12$		0			0
$13$		−	0.840031i		−	0.232983i	−0.993192	−	0.116491i	$-0.962835\pi$
$13$		−	0.840031i		−	0.232983i	0.993192	−	0.116491i	$-0.0371647\pi$
$14$	−1.00612	−	3.60385i	−0.268897	−	0.963169i
$15$		0			0
$16$	2.89814	−	2.75695i	0.724535	−	0.689238i
$17$	−2.45590	−	4.25375i	−0.595644	−	1.03169i	−0.993456	−	0.114219i	$-0.963563\pi$
$17$	−2.45590	−	4.25375i	−0.595644	−	1.03169i	0.397811	−	0.917467i	$-0.369770\pi$
$18$		0			0
$19$	−4.87773	−	2.81616i	−1.11903	−	0.646071i	−0.177875	−	0.984053i	$-0.556922\pi$
$19$	−4.87773	−	2.81616i	−1.11903	−	0.646071i	−0.941152	+	0.337982i	$0.890256\pi$
$20$	3.57140	+	0.515608i	0.798590	+	0.115293i
$21$		0			0
$22$	−4.78927	−	5.53036i	−1.02108	−	1.17908i
$23$	−3.05110	+	5.28467i	−0.636199	+	1.10193i	0.350061	+	0.936727i	$0.386161\pi$
$23$	−3.05110	+	5.28467i	−0.636199	+	1.10193i	−0.986260	+	0.165202i	$0.947172\pi$
$24$		0			0
$25$	−0.872403	−	1.51105i	−0.174481	−	0.302209i
$26$	−1.16658	+	0.224488i	−0.228785	+	0.0440258i
$27$		0			0
$28$	−4.73591	+	2.36032i	−0.895004	+	0.446059i
$29$			0.439783i			0.0816656i	0.999166	+	0.0408328i	$0.0130011\pi$
$29$			0.439783i			0.0816656i	−0.999166	+	0.0408328i	$0.986999\pi$
$30$		0			0
$31$	−3.66760	−	6.35247i	−0.658721	−	1.14094i	−0.980947	−	0.194275i	$-0.937765\pi$
$31$	−3.66760	−	6.35247i	−0.658721	−	1.14094i	0.322226	−	0.946663i	$-0.395569\pi$
$32$	−4.60317	−	3.28799i	−0.813733	−	0.581239i
$33$		0			0
$34$	−5.25102	+	4.54736i	−0.900542	+	0.779867i
$35$	−4.31586	−	2.03953i	−0.729514	−	0.344743i
$36$		0			0
$37$	4.56250	+	2.63416i	0.750071	+	0.433054i	0.825720	−	0.564081i	$-0.190769\pi$
$37$	4.56250	+	2.63416i	0.750071	+	0.433054i	−0.0756485	+	0.997135i	$0.524103\pi$
$38$	−2.60738	+	7.52645i	−0.422973	+	1.22095i
$39$		0			0
$40$	−0.238373	−	5.09752i	−0.0376901	−	0.805989i
$41$	6.23785			0.974188			0.487094	−	0.873350i	$-0.338057\pi$
$41$	6.23785			0.974188			0.487094	+	0.873350i	$0.338057\pi$
$42$		0			0
$43$		−	7.34846i		−	1.12063i	−0.828280	−	0.560315i	$-0.810680\pi$
$43$		−	7.34846i		−	1.12063i	0.828280	−	0.560315i	$-0.189320\pi$
$44$	−6.40032	+	8.12895i	−0.964885	+	1.22549i
$45$		0			0
$46$	8.15437	+	2.82491i	1.20230	+	0.416510i
$47$	2.83696	−	4.91375i	0.413812	−	0.716744i	−0.581491	−	0.813553i	$-0.697530\pi$
$47$	2.83696	−	4.91375i	0.413812	−	0.716744i	0.995303	+	0.0968090i	$0.0308636\pi$
$48$		0			0
$49$	6.90576	−	1.14477i	0.986537	−	0.163539i
$50$	−1.86530	+	1.61535i	−0.263794	+	0.228444i
$51$		0			0
$52$	0.623510	+	1.56008i	0.0864653	+	0.216344i
$53$	1.15952	−	0.669452i	0.159273	−	0.0919562i	−0.418245	−	0.908334i	$-0.637355\pi$
$53$	1.15952	−	0.669452i	0.159273	−	0.0919562i	0.577518	+	0.816378i	$0.304021\pi$
$54$		0			0
$55$	−9.33339			−1.25851
$56$	4.54348	+	5.94616i	0.607148	+	0.794589i
$57$		0			0
$58$	0.610741	−	0.117527i	0.0801943	−	0.0154320i
$59$	7.31087	−	4.22093i	0.951794	−	0.549519i	0.0581564	−	0.998307i	$-0.481478\pi$
$59$	7.31087	−	4.22093i	0.951794	−	0.549519i	0.893638	+	0.448789i	$0.148144\pi$
$60$		0			0
$61$	4.77538	+	2.75707i	0.611425	+	0.353007i	0.773523	−	0.633768i	$-0.218493\pi$
$61$	4.77538	+	2.75707i	0.611425	+	0.353007i	−0.162098	+	0.986775i	$0.551826\pi$
$62$	−7.84178	+	6.79095i	−0.995906	+	0.862452i
$63$		0			0
$64$	−3.33600	+	7.27125i	−0.417000	+	0.908907i
$65$	−0.757798	+	1.31255i	−0.0939933	+	0.162801i
$66$		0			0
$67$	0.647433	−	0.373796i	0.0790965	−	0.0456664i	−0.459930	−	0.887955i	$-0.652126\pi$
$67$	0.647433	−	0.373796i	0.0790965	−	0.0456664i	0.539027	+	0.842289i	$0.318792\pi$
$68$	7.71836	+	6.07704i	0.935988	+	0.736950i
$69$		0			0
$70$	−1.67900	+	6.53863i	−0.200679	+	0.781516i
$71$	−9.08033			−1.07764			−0.538818	−	0.842422i	$-0.681129\pi$
$71$	−9.08033			−1.07764			−0.538818	+	0.842422i	$0.681129\pi$
$72$		0			0
$73$	3.70739	+	6.42139i	0.433917	+	0.751567i	0.997207	−	0.0746931i	$-0.0237977\pi$
$73$	3.70739	+	6.42139i	0.433917	+	0.751567i	−0.563289	+	0.826260i	$0.690464\pi$
$74$	2.43888	−	7.04006i	0.283514	−	0.818390i
$75$		0			0
$76$	11.1490	+	1.60960i	1.27888	+	0.184634i
$77$	11.2516	−	7.79280i	1.28224	−	0.888072i
$78$		0			0
$79$	−8.68074	+	15.0355i	−0.976659	+	1.69162i	−0.302311	+	0.953209i	$0.597758\pi$
$79$	−8.68074	+	15.0355i	−0.976659	+	1.69162i	−0.674348	+	0.738414i	$0.735575\pi$
$80$	−7.01540	+	1.69329i	−0.784346	+	0.189316i
$81$		0			0
$82$	−1.66699	−	8.66271i	−0.184088	−	0.956637i
$83$		−	1.45486i		−	0.159691i	−0.996807	−	0.0798456i	$-0.974557\pi$
$83$		−	1.45486i		−	0.159691i	0.996807	−	0.0798456i	$-0.0254427\pi$
$84$		0			0
$85$			8.86196i			0.961215i
$86$	−10.2051	+	1.96379i	−1.10044	+	0.211761i
$87$		0			0
$88$	12.9994	+	6.71598i	1.38574	+	0.715926i
$89$	3.10088	−	5.37088i	0.328693	−	0.569312i	−0.653560	−	0.756875i	$-0.726725\pi$
$89$	3.10088	−	5.37088i	0.328693	−	0.569312i	0.982253	+	0.187562i	$0.0600587\pi$
$90$		0			0
$91$	−0.182349	−	2.21502i	−0.0191153	−	0.232197i
$92$	1.74389	−	12.0792i	0.181813	−	1.25934i
$93$		0			0
$94$	−7.58204	−	2.62664i	−0.782028	−	0.270917i
$95$	5.08095	+	8.80047i	0.521295	+	0.902909i
$96$		0			0
$97$	−5.81776			−0.590704			−0.295352	−	0.955388i	$-0.595437\pi$
$97$	−5.81776			−0.590704			−0.295352	+	0.955388i	$0.595437\pi$
$98$	−3.43527	−	9.28434i	−0.347015	−	0.937860i
$99$		0			0
$100$	2.74177	+	2.15873i	0.274177	+	0.215873i
$101$	−3.53959	+	2.04358i	−0.352203	+	0.203344i	−0.665655	−	0.746260i	$-0.731848\pi$
$101$	−3.53959	+	2.04358i	−0.352203	+	0.203344i	0.313452	+	0.949604i	$0.398514\pi$
$102$		0			0
$103$	−3.94745	+	6.83719i	−0.388954	+	0.673688i	−0.992309	−	0.123784i	$-0.960497\pi$
$103$	−3.94745	+	6.83719i	−0.388954	+	0.673688i	0.603355	+	0.797473i	$0.293830\pi$
$104$	1.99991	−	1.28280i	0.196107	−	0.125789i
$105$		0			0
$106$	−1.23956	−	1.43137i	−0.120397	−	0.139027i
$107$	1.99756	+	1.15329i	0.193111	+	0.111493i	0.593438	−	0.804880i	$-0.297770\pi$
$107$	1.99756	+	1.15329i	0.193111	+	0.111493i	−0.400327	+	0.916372i	$0.631103\pi$
$108$		0			0
$109$	5.53206	−	3.19394i	0.529875	−	0.305924i	−0.211091	−	0.977467i	$-0.567701\pi$
$109$	5.53206	−	3.19394i	0.529875	−	0.305924i	0.740966	+	0.671543i	$0.234368\pi$
$110$	2.49424	+	12.9616i	0.237816	+	1.23584i
$111$		0			0
$112$	7.04345	−	7.89872i	0.665543	−	0.746359i
$113$	5.69927			0.536142			0.268071	−	0.963399i	$-0.413614\pi$
$113$	5.69927			0.536142			0.268071	+	0.963399i	$0.413614\pi$
$114$		0			0
$115$	9.53467	−	5.50485i	0.889113	−	0.513330i
$116$	−0.326427	−	0.816750i	−0.0303080	−	0.0758333i
$117$		0			0
$118$	−7.81550	−	9.02486i	−0.719475	−	0.830806i
$119$	−7.39918	−	10.6833i	−0.678282	−	0.979338i
$120$		0			0
$121$	7.88049	−	13.6494i	0.716408	−	1.24086i
$122$	2.55267	−	7.36854i	0.231108	−	0.667116i
$123$		0			0
$124$	11.5265	+	9.07534i	1.03511	+	0.814990i
$125$			12.1691i			1.08844i
$126$		0			0
$127$	13.8948			1.23297			0.616483	−	0.787368i	$-0.288557\pi$
$127$	13.8948			1.23297			0.616483	+	0.787368i	$0.288557\pi$
$128$	10.9893	+	2.68966i	0.971330	+	0.237734i
$129$		0			0
$130$	2.02529	+	0.701618i	0.177630	+	0.0615360i
$131$	−16.3363	−	9.43177i	−1.42731	−	0.824058i	−0.430402	−	0.902637i	$-0.641628\pi$
$131$	−16.3363	−	9.43177i	−1.42731	−	0.824058i	−0.996908	+	0.0785794i	$0.974962\pi$
$132$		0			0
$133$	−13.4731	−	6.36690i	−1.16826	−	0.552081i
$134$	−0.692122	−	0.799220i	−0.0597902	−	0.0690421i
$135$		0			0
$136$	6.37676	−	12.3428i	0.546802	−	1.05838i
$137$	7.87121	+	13.6333i	0.672483	+	1.16477i	0.977198	+	0.212331i	$0.0681054\pi$
$137$	7.87121	+	13.6333i	0.672483	+	1.16477i	−0.304715	+	0.952444i	$0.598561\pi$
$138$		0			0
$139$			11.4530i			0.971428i	0.874118	+	0.485714i	$0.161440\pi$
$139$			11.4530i			0.971428i	−0.874118	+	0.485714i	$0.838560\pi$
$140$	9.52911	+	0.584314i	0.805357	+	0.0493835i
$141$		0			0
$142$	2.42661	+	12.6102i	0.203637	+	1.05822i
$143$	−2.17278	−	3.76337i	−0.181697	−	0.314709i
$144$		0			0
$145$	0.396731	−	0.687159i	0.0329467	−	0.0570654i
$146$	7.92685	−	6.86462i	0.656030	−	0.568120i
$147$		0			0
$148$	−10.4285	−	1.50558i	−0.857220	−	0.123758i
$149$	13.4705	+	7.77722i	1.10355	+	0.637135i	0.937151	−	0.348924i	$-0.113453\pi$
$149$	13.4705	+	7.77722i	1.10355	+	0.637135i	0.166399	+	0.986059i	$0.446786\pi$
$150$		0			0
$151$	−1.39837	−	2.42205i	−0.113798	−	0.197103i	0.803501	−	0.595304i	$-0.202968\pi$
$151$	−1.39837	−	2.42205i	−0.113798	−	0.197103i	−0.917298	+	0.398200i	$0.869635\pi$
$152$	−0.744142	−	15.9132i	−0.0603579	−	1.29073i
$153$		0			0
$154$	−13.8290	−	13.5430i	−1.11437	−	1.09133i
$155$			13.2343i			1.06300i
$156$		0			0
$157$	4.45662	−	2.57303i	0.355677	−	0.205350i	−0.311506	−	0.950244i	$-0.600833\pi$
$157$	4.45662	−	2.57303i	0.355677	−	0.205350i	0.667183	+	0.744894i	$0.267500\pi$
$158$	23.2001	+	8.03718i	1.84570	+	0.639404i
$159$		0			0
$160$	4.22631	+	9.29002i	0.334120	+	0.734440i
$161$	−6.89808	+	14.5971i	−0.543645	+	1.15041i
$162$		0			0
$163$	14.9838	+	8.65091i	1.17362	+	0.677591i	0.954531	−	0.298113i	$-0.0963571\pi$
$163$	14.9838	+	8.65091i	1.17362	+	0.677591i	0.219092	+	0.975704i	$0.429690\pi$
$164$	−11.5847	+	4.63002i	−0.904615	+	0.361544i
$165$		0			0
$166$	−2.02041	+	0.388793i	−0.156814	+	0.0301762i
$167$	15.1060			1.16893			0.584467	−	0.811417i	$-0.301304\pi$
$167$	15.1060			1.16893			0.584467	+	0.811417i	$0.301304\pi$
$168$		0			0
$169$	12.2943			0.945719
$170$	12.3069	−	2.36826i	0.943897	−	0.181637i
$171$		0			0
$172$	5.45437	+	13.6473i	0.415892	+	1.04060i
$173$	−11.0288	−	6.36747i	−0.838503	−	0.484110i	0.0182524	−	0.999833i	$-0.494190\pi$
$173$	−11.0288	−	6.36747i	−0.838503	−	0.484110i	−0.856755	+	0.515724i	$0.827523\pi$
$174$		0			0
$175$	−2.62839	−	3.79500i	−0.198688	−	0.286875i
$176$	5.85279	−	19.8474i	0.441170	−	1.49606i
$177$		0			0
$178$	−8.28740	−	2.87099i	−0.621167	−	0.215190i
$179$	−18.2138	+	10.5157i	−1.36136	+	0.785983i	−0.989805	−	0.142427i	$-0.954509\pi$
$179$	−18.2138	+	10.5157i	−1.36136	+	0.785983i	−0.371557	+	0.928410i	$0.621176\pi$
$180$		0			0
$181$			20.7554i			1.54274i	0.636387	+	0.771370i	$0.280428\pi$
$181$			20.7554i			1.54274i	−0.636387	+	0.771370i	$0.719572\pi$
$182$	−3.02734	+	0.845172i	−0.224402	+	0.0626483i
$183$		0			0
$184$	−17.2408	+	0.806224i	−1.27101	+	0.0594356i
$185$	−4.75260	−	8.23174i	−0.349418	−	0.605210i
$186$		0			0
$187$	−22.0051	−	12.7046i	−1.60917	−	0.929055i
$188$	−1.62149	+	11.2314i	−0.118259	+	0.819132i
$189$		0			0
$190$	10.8637	−	9.40792i	0.788135	−	0.682522i
$191$	1.44226	−	2.49806i	0.104358	−	0.180753i	−0.809118	−	0.587647i	$-0.800055\pi$
$191$	1.44226	−	2.49806i	0.104358	−	0.180753i	0.913476	+	0.406893i	$0.133388\pi$
$192$		0			0
$193$	−0.101224	−	0.175325i	−0.00728624	−	0.0126201i	0.862359	−	0.506297i	$-0.168986\pi$
$193$	−0.101224	−	0.175325i	−0.00728624	−	0.0126201i	−0.869646	+	0.493677i	$0.835653\pi$
$194$	1.55473	+	8.07933i	0.111623	+	0.580062i
$195$		0			0
$196$	−11.9754	+	7.25181i	−0.855389	+	0.517986i
$197$			12.1825i			0.867964i	0.900922	+	0.433982i	$0.142892\pi$
$197$			12.1825i			0.867964i	−0.900922	+	0.433982i	$0.857108\pi$
$198$		0			0
$199$	−0.639202	−	1.10713i	−0.0453118	−	0.0784824i	0.842480	−	0.538728i	$-0.181095\pi$
$199$	−0.639202	−	1.10713i	−0.0453118	−	0.0784824i	−0.887792	+	0.460245i	$0.847761\pi$
$200$	2.26520	−	4.38448i	0.160174	−	0.310030i
$201$		0			0
$202$	3.78391	+	4.36943i	0.266235	+	0.307432i
$203$	0.0954652	+	1.15963i	0.00670035	+	0.0813903i
$204$		0			0
$205$	−9.74661	−	5.62721i	−0.680733	−	0.393021i
$206$	10.5500	+	3.65481i	0.735050	+	0.254642i
$207$		0			0
$208$	−2.31592	−	2.43453i	−0.160580	−	0.168804i
$209$	−29.1365			−2.01542
$210$		0			0
$211$		−	10.5627i		−	0.727166i	−0.931562	−	0.363583i	$-0.881553\pi$
$211$		−	10.5627i		−	0.727166i	0.931562	−	0.363583i	$-0.118447\pi$
$212$	−1.65653	+	2.10394i	−0.113771	+	0.144499i
$213$		0			0
$214$	1.06779	−	3.08228i	0.0729926	−	0.210700i
$215$	−6.62911	+	11.4819i	−0.452101	+	0.783062i
$216$		0			0
$217$	−11.0498	−	15.9543i	−0.750109	−	1.08305i
$218$	−5.91391	−	6.82902i	−0.400540	−	0.462519i
$219$		0			0
$220$	17.3337	−	6.92767i	1.16864	−	0.467064i
$221$	−3.57328	+	2.06304i	−0.240365	+	0.138775i
$222$		0			0
$223$	8.79939			0.589251			0.294625	−	0.955613i	$-0.404805\pi$
$223$	8.79939			0.589251			0.294625	+	0.955613i	$0.404805\pi$
$224$	−12.8515	−	7.67064i	−0.858678	−	0.512516i
$225$		0			0
$226$	−1.52306	−	7.91478i	−0.101313	−	0.526483i
$227$	15.8399	−	9.14518i	1.05133	−	0.606987i	0.128311	−	0.991734i	$-0.459045\pi$
$227$	15.8399	−	9.14518i	1.05133	−	0.606987i	0.923022	+	0.384747i	$0.125711\pi$
$228$		0			0
$229$	−17.6127	−	10.1687i	−1.16388	−	0.671965i	−0.211647	−	0.977346i	$-0.567883\pi$
$229$	−17.6127	−	10.1687i	−1.16388	−	0.671965i	−0.952230	+	0.305381i	$0.901216\pi$
$230$	−10.1928	−	11.7700i	−0.672093	−	0.776093i
$231$		0			0
$232$	−1.04702	+	0.671587i	−0.0687399	+	0.0440919i
$233$	7.01442	−	12.1493i	0.459530	−	0.795930i	−0.539406	−	0.842046i	$-0.681351\pi$
$233$	7.01442	−	12.1493i	0.459530	−	0.795930i	0.998936	+	0.0461162i	$0.0146845\pi$
$234$		0			0
$235$	−8.86546	+	5.11848i	−0.578319	+	0.333893i
$236$	−10.4445	+	13.2654i	−0.679882	+	0.863507i
$237$		0			0
$238$	−12.8589	+	13.1305i	−0.833521	+	0.851123i
$239$	−15.0486			−0.973410			−0.486705	−	0.873566i	$-0.661801\pi$
$239$	−15.0486			−0.973410			−0.486705	+	0.873566i	$0.661801\pi$
$240$		0			0
$241$	7.02860	+	12.1739i	0.452752	+	0.784189i	0.998556	−	0.0537236i	$-0.0171090\pi$
$241$	7.02860	+	12.1739i	0.452752	+	0.784189i	−0.545804	+	0.837913i	$0.683776\pi$
$242$	−21.0614	−	7.29627i	−1.35388	−	0.469022i
$243$		0			0
$244$	−10.9151	−	1.57583i	−0.698768	−	0.100882i
$245$	−11.8229	−	4.44103i	−0.755339	−	0.283727i
$246$		0			0
$247$	−2.36566	+	4.09744i	−0.150523	+	0.260714i
$248$	9.52293	−	18.4325i	0.604707	−	1.17046i
$249$		0			0
$250$	16.8996	−	3.25205i	1.06883	−	0.205677i
$251$			3.97744i			0.251054i	0.992090	+	0.125527i	$0.0400622\pi$
$251$			3.97744i			0.251054i	−0.992090	+	0.125527i	$0.959938\pi$
$252$		0			0
$253$			31.5673i			1.98462i
$254$	−3.71323	−	19.2962i	−0.232989	−	1.21075i
$255$		0			0
$256$	0.798445	−	15.9801i	0.0499028	−	0.998754i
$257$	3.33373	−	5.77418i	0.207952	−	0.360184i	−0.743117	−	0.669161i	$-0.766653\pi$
$257$	3.33373	−	5.77418i	0.207952	−	0.360184i	0.951069	+	0.308978i	$0.0999868\pi$
$258$		0			0
$259$	12.6024	+	5.95544i	0.783073	+	0.370053i
$260$	0.433127	−	3.00009i	0.0268614	−	0.186058i
$261$		0			0
$262$	−8.73254	+	25.2073i	−0.539498	+	1.55731i
$263$	0.798115	+	1.38238i	0.0492139	+	0.0852409i	0.889583	−	0.456774i	$-0.150995\pi$
$263$	0.798115	+	1.38238i	0.0492139	+	0.0852409i	−0.840369	+	0.542015i	$0.817662\pi$
$264$		0			0
$265$	−2.41567			−0.148393
$266$	−5.24142	+	20.4120i	−0.321372	+	1.25154i
$267$		0			0
$268$	−0.924943	+	1.17476i	−0.0564999	+	0.0717596i
$269$	−11.2827	+	6.51409i	−0.687920	+	0.397171i	−0.802833	−	0.596205i	$-0.796675\pi$
$269$	−11.2827	+	6.51409i	−0.687920	+	0.397171i	0.114912	+	0.993376i	$0.463341\pi$
$270$		0			0
$271$	4.00694	−	6.94023i	0.243405	−	0.421589i	−0.718277	−	0.695757i	$-0.755069\pi$
$271$	4.00694	−	6.94023i	0.243405	−	0.421589i	0.961682	+	0.274168i	$0.0884024\pi$
$272$	−18.8449	−	5.55716i	−1.14264	−	0.336953i
$273$		0			0
$274$	16.8296	−	14.5744i	1.01671	−	0.880470i
$275$	−7.81680	−	4.51303i	−0.471371	−	0.272146i
$276$		0			0
$277$	8.51021	−	4.91337i	0.511329	−	0.295216i	−0.222051	−	0.975035i	$-0.571275\pi$
$277$	8.51021	−	4.91337i	0.511329	−	0.295216i	0.733380	+	0.679819i	$0.237942\pi$
$278$	15.9051	−	3.06067i	0.953926	−	0.183567i
$279$		0			0
$280$	−1.73509	−	13.3896i	−0.103691	−	0.800179i
$281$	22.1632			1.32215			0.661073	−	0.750322i	$-0.270101\pi$
$281$	22.1632			1.32215			0.661073	+	0.750322i	$0.270101\pi$
$282$		0			0
$283$	−14.1158	+	8.14978i	−0.839099	+	0.484454i	−0.856958	−	0.515386i	$-0.827648\pi$
$283$	−14.1158	+	8.14978i	−0.839099	+	0.484454i	0.0178588	+	0.999841i	$0.494315\pi$
$284$	16.8637	−	6.73984i	1.00068	−	0.399936i
$285$		0			0
$286$	−4.64567	+	4.02314i	−0.274704	+	0.237893i
$287$	16.4481	−	1.35407i	0.970904	−	0.0799284i
$288$		0			0
$289$	−3.56293	+	6.17118i	−0.209584	+	0.363010i
$290$	−1.06030	−	0.367319i	−0.0622631	−	0.0215697i
$291$		0			0
$292$	−11.6515	−	9.17380i	−0.681852	−	0.536856i
$293$			6.07163i			0.354708i	0.984147	+	0.177354i	$0.0567538\pi$
$293$			6.07163i			0.354708i	−0.984147	+	0.177354i	$0.943246\pi$
$294$		0			0
$295$	−15.2309			−0.886780
$296$	0.696052	+	14.8848i	0.0404572	+	0.865162i
$297$		0			0
$298$	7.20065	−	20.7854i	0.417123	−	1.20406i
$299$	4.43928	+	2.56302i	0.256730	+	0.148223i
$300$		0			0
$301$	−1.59516	−	19.3767i	−0.0919434	−	1.11685i
$302$	−2.98988	+	2.58923i	−0.172048	+	0.148993i
$303$		0			0
$304$	−21.9003	+	5.28603i	−1.25607	+	0.303175i
$305$	−4.97435	−	8.61582i	−0.284830	−	0.493340i
$306$		0			0
$307$			19.9815i			1.14040i	0.821505	+	0.570202i	$0.193135\pi$
$307$			19.9815i			1.14040i	−0.821505	+	0.570202i	$0.806865\pi$
$308$	−15.1120	+	22.8240i	−0.861085	+	1.30052i
$309$		0			0
$310$	18.3789	−	3.53671i	1.04385	−	0.200872i
$311$	5.40981	+	9.37006i	0.306762	+	0.531327i	0.977652	−	0.210229i	$-0.0674211\pi$
$311$	5.40981	+	9.37006i	0.306762	+	0.531327i	−0.670890	+	0.741557i	$0.734088\pi$
$312$		0			0
$313$	−5.81191	+	10.0665i	−0.328509	+	0.568994i	−0.982216	−	0.187754i	$-0.939879\pi$
$313$	−5.81191	+	10.0665i	−0.328509	+	0.568994i	0.653708	+	0.756747i	$0.273213\pi$
$314$	−4.76424	−	5.50145i	−0.268861	−	0.310465i
$315$		0			0
$316$	4.96155	−	34.3666i	0.279109	−	1.93327i
$317$	6.22813	+	3.59581i	0.349807	+	0.201961i	0.664600	−	0.747199i	$-0.268602\pi$
$317$	6.22813	+	3.59581i	0.349807	+	0.201961i	−0.314794	+	0.949160i	$0.601935\pi$
$318$		0			0
$319$	1.13752	+	1.97024i	0.0636889	+	0.110312i
$320$	11.7719	−	8.35188i	0.658071	−	0.466884i
$321$		0			0
$322$	22.1149	+	5.67870i	1.23242	+	0.316462i
$323$			27.6648i			1.53931i
$324$		0			0
$325$	−1.26933	+	0.732846i	−0.0704096	+	0.0406510i
$326$	8.00957	−	23.1204i	0.443609	−	1.28052i
$327$		0			0
$328$	9.52575	+	14.8508i	0.525971	+	0.819998i
$329$	6.41393	−	13.5726i	0.353611	−	0.748279i
$330$		0			0
$331$	−27.0677	−	15.6275i	−1.48777	−	0.858967i	−0.487872	−	0.872915i	$-0.662227\pi$
$331$	−27.0677	−	15.6275i	−1.48777	−	0.858967i	−0.999903	+	0.0139478i	$0.995560\pi$
$332$	1.07986	+	2.70191i	0.0592651	+	0.148287i
$333$		0			0
$334$	−4.03689	−	20.9782i	−0.220889	−	1.14787i
$335$	−1.34882			−0.0736937
$336$		0			0
$337$	−30.6794			−1.67121			−0.835607	−	0.549327i	$-0.814884\pi$
$337$	−30.6794			−1.67121			−0.835607	+	0.549327i	$0.814884\pi$
$338$	−3.28552	−	17.0736i	−0.178709	−	0.928681i
$339$		0			0
$340$	−6.57776	−	16.4581i	−0.356729	−	0.892568i
$341$	−32.8620	−	18.9729i	−1.77958	−	1.02744i
$342$		0			0
$343$	17.9608	−	4.51763i	0.969793	−	0.243929i
$344$	17.4949	−	11.2218i	0.943262	−	0.605037i
$345$		0			0
$346$	−5.89541	+	17.0177i	−0.316939	+	0.914876i
$347$	−0.985835	+	0.569172i	−0.0529224	+	0.0305548i	−0.526228	−	0.850344i	$-0.676394\pi$
$347$	−0.985835	+	0.569172i	−0.0529224	+	0.0305548i	0.473305	+	0.880898i	$0.343061\pi$
$348$		0			0
$349$		−	33.8150i		−	1.81007i	−0.425333	−	0.905037i	$-0.639843\pi$
$349$		−	33.8150i		−	1.81007i	0.425333	−	0.905037i	$-0.360157\pi$
$350$	−4.56784	+	4.66430i	−0.244161	+	0.249318i
$351$		0			0
$352$	−29.1269	−	2.82397i	−1.55247	−	0.150518i
$353$	13.6786	+	23.6920i	0.728036	+	1.26100i	0.957712	+	0.287728i	$0.0929000\pi$
$353$	13.6786	+	23.6920i	0.728036	+	1.26100i	−0.229676	+	0.973267i	$0.573767\pi$
$354$		0			0
$355$	14.1880	+	8.19144i	0.753020	+	0.434756i
$356$	−1.77234	+	12.2762i	−0.0939336	+	0.650639i
$357$		0			0
$358$	19.4710	+	22.4839i	1.02907	+	1.18831i
$359$	13.3868	−	23.1866i	0.706529	−	1.22374i	−0.259609	−	0.965714i	$-0.583594\pi$
$359$	13.3868	−	23.1866i	0.706529	−	1.22374i	0.966137	−	0.258029i	$-0.0830731\pi$
$360$		0			0
$361$	6.36148	+	11.0184i	0.334815	+	0.579916i
$362$	28.8238	−	5.54665i	1.51494	−	0.291525i
$363$		0			0
$364$	1.98274	+	3.97832i	0.103924	+	0.208520i
$365$		−	13.3779i		−	0.700229i
$366$		0			0
$367$	−14.2792	−	24.7323i	−0.745367	−	1.29101i	−0.950023	−	0.312179i	$-0.898941\pi$
$367$	−14.2792	−	24.7323i	−0.745367	−	1.29101i	0.204656	−	0.978834i	$-0.434392\pi$
$368$	5.72704	+	23.7274i	0.298542	+	1.23688i
$369$		0			0
$370$	−10.1616	+	8.79993i	−0.528278	+	0.457487i
$371$	2.91215	−	2.01693i	0.151191	−	0.104714i
$372$		0			0
$373$	31.8838	+	18.4081i	1.65088	+	0.953135i	0.976712	+	0.214555i	$0.0688302\pi$
$373$	31.8838	+	18.4081i	1.65088	+	0.953135i	0.674166	+	0.738580i	$0.264503\pi$
$374$	−11.7628	+	33.9544i	−0.608239	+	1.75574i
$375$		0			0
$376$	16.0307	−	0.749638i	0.826722	−	0.0386596i
$377$	0.369431			0.0190267
$378$		0			0
$379$			7.23648i			0.371713i	0.982577	+	0.185856i	$0.0595059\pi$
$379$			7.23648i			0.371713i	−0.982577	+	0.185856i	$0.940494\pi$
$380$	−15.9683	−	12.5726i	−0.819156	−	0.644962i
$381$		0			0
$382$	−3.85457	−	1.33533i	−0.197217	−	0.0683216i
$383$	−8.27468	+	14.3322i	−0.422816	+	0.732339i	−0.996214	−	0.0869381i	$-0.972292\pi$
$383$	−8.27468	+	14.3322i	−0.422816	+	0.732339i	0.573397	+	0.819277i	$0.305625\pi$
$384$		0			0
$385$	−24.6106	+	2.02603i	−1.25427	+	0.103256i
$386$	−0.216428	+	0.187426i	−0.0110159	+	0.00953974i
$387$		0			0
$388$	10.8046	−	4.31821i	0.548519	−	0.219224i
$389$	−1.90616	+	1.10052i	−0.0966460	+	0.0557986i	−0.547544	−	0.836777i	$-0.684437\pi$
$389$	−1.90616	+	1.10052i	−0.0966460	+	0.0557986i	0.450898	+	0.892575i	$0.351104\pi$
$390$		0			0
$391$	29.9729			1.51579
$392$	13.2711	+	14.6928i	0.670294	+	0.742096i
$393$		0			0
$394$	16.9182	−	3.25562i	0.852326	−	0.164016i
$395$	27.1272	−	15.6619i	1.36492	−	0.788037i
$396$		0			0
$397$	6.06629	+	3.50238i	0.304458	+	0.175779i	0.644444	−	0.764651i	$-0.277089\pi$
$397$	6.06629	+	3.50238i	0.304458	+	0.175779i	−0.339986	+	0.940431i	$0.610422\pi$
$398$	−1.36669	+	1.18355i	−0.0685060	+	0.0593260i
$399$		0			0
$400$	−6.69423	−	1.97405i	−0.334712	−	0.0987027i
$401$	−5.46495	+	9.46556i	−0.272906	+	0.472688i	−0.969605	−	0.244676i	$-0.921318\pi$
$401$	−5.46495	+	9.46556i	−0.272906	+	0.472688i	0.696698	+	0.717364i	$0.254652\pi$
$402$		0			0
$403$	−5.33627	+	3.08090i	−0.265819	+	0.153471i
$404$	5.05677	−	6.42253i	0.251584	−	0.319533i
$405$		0			0
$406$	1.58491	−	0.442474i	0.0786578	−	0.0219596i
$407$	27.2536			1.35091
$408$		0			0
$409$	17.1135	+	29.6415i	0.846209	+	1.46568i	0.884567	+	0.466412i	$0.154454\pi$
$409$	17.1135	+	29.6415i	0.846209	+	1.46568i	−0.0383589	+	0.999264i	$0.512213\pi$
$410$	−5.21003	+	15.0393i	−0.257305	+	0.742736i
$411$		0			0
$412$	2.25620	−	15.6278i	0.111155	−	0.769926i
$413$	18.3613	−	12.7169i	0.903499	−	0.625757i
$414$		0			0
$415$	−1.31244	+	2.27321i	−0.0644250	+	0.111587i
$416$	−2.76201	+	3.86680i	−0.135419	+	0.189586i
$417$		0			0
$418$	7.78640	+	40.4629i	0.380845	+	1.97911i
$419$			6.15497i			0.300690i	0.988634	+	0.150345i	$0.0480384\pi$
$419$			6.15497i			0.300690i	−0.988634	+	0.150345i	$0.951962\pi$
$420$		0			0
$421$		−	32.2922i		−	1.57382i	−0.617065	−	0.786912i	$-0.711678\pi$
$421$		−	32.2922i		−	1.57382i	0.617065	−	0.786912i	$-0.288322\pi$
$422$	−14.6688	+	2.82276i	−0.714065	+	0.137410i
$423$		0			0
$424$	3.36450	+	1.73823i	0.163394	+	0.0844160i
$425$	−4.28508	+	7.42197i	−0.207857	+	0.360019i
$426$		0			0
$427$	13.1904	+	6.23332i	0.638327	+	0.301651i
$428$	−4.56582	−	0.659174i	−0.220697	−	0.0318624i
$429$		0			0
$430$	17.7169	+	6.13765i	0.854386	+	0.295984i
$431$	−6.91841	−	11.9830i	−0.333248	−	0.577202i	0.649899	−	0.760021i	$-0.274811\pi$
$431$	−6.91841	−	11.9830i	−0.333248	−	0.577202i	−0.983147	+	0.182818i	$0.941478\pi$
$432$		0			0
$433$	−16.6754			−0.801367			−0.400684	−	0.916216i	$-0.631227\pi$
$433$	−16.6754			−0.801367			−0.400684	+	0.916216i	$0.631227\pi$
$434$	−19.2033	+	19.6088i	−0.921788	+	0.941254i
$435$		0			0
$436$	−7.90327	+	10.0378i	−0.378498	+	0.480724i
$437$	29.7649	−	17.1848i	1.42385	−	0.822059i
$438$		0			0
$439$	16.7225	−	28.9642i	0.798120	−	1.38239i	−0.122718	−	0.992442i	$-0.539161\pi$
$439$	16.7225	−	28.9642i	0.798120	−	1.38239i	0.920839	−	0.389944i	$-0.127506\pi$
$440$	−14.2529	−	22.2205i	−0.679481	−	1.05932i
$441$		0			0
$442$	3.81993	+	4.41102i	0.181695	+	0.209811i
$443$	2.69056	+	1.55339i	0.127832	+	0.0738039i	0.562552	−	0.826762i	$-0.309819\pi$
$443$	2.69056	+	1.55339i	0.127832	+	0.0738039i	−0.434720	+	0.900566i	$0.643153\pi$
$444$		0			0
$445$	−9.69023	+	5.59465i	−0.459361	+	0.265212i
$446$	−2.35153	−	12.2200i	−0.111348	−	0.578635i
$447$		0			0
$448$	−7.21806	+	19.8972i	−0.341021	+	0.940056i
$449$	−20.1372			−0.950333			−0.475167	−	0.879896i	$-0.657612\pi$
$449$	−20.1372			−0.950333			−0.475167	+	0.879896i	$0.657612\pi$
$450$		0			0
$451$	27.9458	−	16.1345i	1.31592	−	0.759744i
$452$	−10.5845	+	4.23026i	−0.497853	+	0.198975i
$453$		0			0
$454$	−16.9333	−	19.5535i	−0.794718	−	0.917691i
$455$	−1.71327	+	3.62546i	−0.0803192	+	0.169964i
$456$		0			0
$457$	14.3781	−	24.9036i	0.672578	−	1.16494i	−0.304593	−	0.952483i	$-0.598520\pi$
$457$	14.3781	−	24.9036i	0.672578	−	1.16494i	0.977171	−	0.212457i	$-0.0681464\pi$
$458$	−9.41481	+	27.1768i	−0.439925	+	1.26989i
$459$		0			0
$460$	−13.6215	+	17.3005i	−0.635107	+	0.806640i
$461$		−	17.0846i		−	0.795707i	−0.917449	−	0.397854i	$-0.869755\pi$
$461$		−	17.0846i		−	0.795707i	0.917449	−	0.397854i	$-0.130245\pi$
$462$		0			0
$463$	5.05747			0.235041			0.117520	−	0.993070i	$-0.462505\pi$
$463$	5.05747			0.235041			0.117520	+	0.993070i	$0.462505\pi$
$464$	1.21246	+	1.27455i	0.0562870	+	0.0591696i
$465$		0			0
$466$	−18.7467	−	6.49440i	−0.868425	−	0.300847i
$467$	−6.23154	−	3.59778i	−0.288361	−	0.166485i	0.348841	−	0.937182i	$-0.386575\pi$
$467$	−6.23154	−	3.59778i	−0.288361	−	0.166485i	−0.637203	+	0.770696i	$0.719909\pi$
$468$		0			0
$469$	1.62603	−	1.12618i	0.0750831	−	0.0520020i
$470$	9.47740	+	10.9439i	0.437160	+	0.504806i
$471$		0			0
$472$	21.2134	+	10.9597i	0.976424	+	0.504459i
$473$	−19.0072	−	32.9214i	−0.873951	−	1.51373i
$474$		0			0
$475$			9.82730i			0.450907i
$476$	21.6712	+	14.3487i	0.993296	+	0.657671i
$477$		0			0
$478$	4.02155	+	20.8984i	0.183941	+	0.955873i
$479$	−4.70408	−	8.14770i	−0.214935	−	0.372278i	0.738318	−	0.674453i	$-0.235621\pi$
$479$	−4.70408	−	8.14770i	−0.214935	−	0.372278i	−0.953252	+	0.302175i	$0.902287\pi$
$480$		0			0
$481$	2.21278	−	3.83264i	0.100894	−	0.174754i
$482$	15.0280	−	13.0142i	0.684506	−	0.592780i
$483$		0			0
$484$	−4.50417	+	31.1985i	−0.204735	+	1.41811i
$485$	9.09024	+	5.24825i	0.412766	+	0.238311i
$486$		0			0
$487$	12.4852	+	21.6251i	0.565760	+	0.979926i	0.996979	+	0.0776780i	$0.0247506\pi$
$487$	12.4852	+	21.6251i	0.565760	+	0.979926i	−0.431218	+	0.902248i	$0.641916\pi$
$488$	0.728529	+	15.5793i	0.0329789	+	0.705242i
$489$		0			0
$490$	−3.00788	+	17.6057i	−0.135882	+	0.795346i
$491$			6.10161i			0.275362i	0.990477	+	0.137681i	$0.0439649\pi$
$491$			6.10161i			0.275362i	−0.990477	+	0.137681i	$0.956035\pi$
$492$		0			0
$493$	1.87073	−	1.08006i	0.0842533	−	0.0486436i
$494$	6.32245	+	2.19028i	0.284461	+	0.0985453i
$495$		0			0
$496$	−28.1427	−	8.29897i	−1.26364	−	0.372635i
$497$	−23.9433	+	1.97110i	−1.07400	+	0.0884159i
$498$		0			0
$499$	4.76604	+	2.75167i	0.213357	+	0.123182i	0.602871	−	0.797839i	$-0.294024\pi$
$499$	4.76604	+	2.75167i	0.213357	+	0.123182i	−0.389513	+	0.921021i	$0.627357\pi$
$500$	−9.03246	−	22.6000i	−0.403944	−	1.01070i
$501$		0			0
$502$	5.52361	−	1.06293i	0.246531	−	0.0474407i
$503$	−21.9913			−0.980544			−0.490272	−	0.871570i	$-0.663103\pi$
$503$	−21.9913			−0.980544			−0.490272	+	0.871570i	$0.663103\pi$
$504$		0			0
$505$	7.37413			0.328145
$506$	43.8386	−	8.43600i	1.94887	−	0.375026i
$507$		0			0
$508$	−25.8050	+	10.3134i	−1.14491	+	0.457583i
$509$	13.6465	+	7.87883i	0.604872	+	0.349223i	0.770956	−	0.636888i	$-0.219779\pi$
$509$	13.6465	+	7.87883i	0.604872	+	0.349223i	−0.166084	+	0.986112i	$0.553112\pi$
$510$		0			0
$511$	11.1697	+	16.1273i	0.494117	+	0.713431i
$512$	−22.4054	+	3.16166i	−0.990190	+	0.139727i
$513$		0			0
$514$	−8.90971	−	3.08658i	−0.392990	−	0.136143i
$515$	12.3358	−	7.12206i	0.543579	−	0.313835i
$516$		0			0
$517$		−	29.3517i		−	1.29089i
$518$	4.90270	−	19.0929i	0.215412	−	0.838892i
$519$		0			0
$520$	−4.28208	+	0.200241i	−0.187781	+	0.00878114i
$521$	9.06309	+	15.6977i	0.397061	+	0.687730i	0.993362	−	0.115031i	$-0.0366968\pi$
$521$	9.06309	+	15.6977i	0.397061	+	0.687730i	−0.596301	+	0.802761i	$0.703363\pi$
$522$		0			0
$523$	12.4676	+	7.19819i	0.545171	+	0.314755i	0.747172	−	0.664631i	$-0.231411\pi$
$523$	12.4676	+	7.19819i	0.545171	+	0.314755i	−0.202001	+	0.979385i	$0.564744\pi$
$524$	37.3400	+	5.39082i	1.63120	+	0.235499i
$525$		0			0
$526$	1.70647	−	1.47779i	0.0744054	−	0.0644349i
$527$	−18.0146	+	31.2021i	−0.784727	+	1.35919i
$528$		0			0
$529$	−7.11846	−	12.3295i	−0.309498	−	0.536067i
$530$	0.645559	+	3.35472i	0.0280413	+	0.145720i
$531$		0			0
$532$	29.7475	+	1.82408i	1.28972	+	0.0790840i
$533$		−	5.23998i		−	0.226969i
$534$		0			0
$535$	−2.08078	−	3.60402i	−0.0899601	−	0.155816i
$536$	1.87860	+	0.970561i	0.0811433	+	0.0419218i
$537$		0			0
$538$	12.0615	+	13.9279i	0.520009	+	0.600475i
$539$	27.9770	−	22.9907i	1.20506	−	0.990281i
$540$		0			0
$541$	−12.9396	−	7.47069i	−0.556318	−	0.321190i	0.195348	−	0.980734i	$-0.437416\pi$
$541$	−12.9396	−	7.47069i	−0.556318	−	0.321190i	−0.751666	+	0.659544i	$0.770750\pi$
$542$	−10.7089	−	3.70989i	−0.459989	−	0.159353i
$543$		0			0
$544$	−2.68133	+	27.6557i	−0.114961	+	1.18573i
$545$	−11.5251			−0.493681
$546$		0			0
$547$			8.03696i			0.343636i	0.985129	+	0.171818i	$0.0549640\pi$
$547$			8.03696i			0.343636i	−0.985129	+	0.171818i	$0.945036\pi$
$548$	−24.7374	−	19.4770i	−1.05673	−	0.832016i
$549$		0			0
$550$	−4.17845	+	12.0615i	−0.178170	+	0.514305i
$551$	1.23850	−	2.14514i	0.0527617	−	0.0913860i
$552$		0			0
$553$	−19.6258	+	41.5304i	−0.834575	+	1.76605i
$554$	−9.09763	−	10.5054i	−0.386521	−	0.446331i
$555$		0			0
$556$	−8.50092	−	21.2701i	−0.360519	−	0.902052i
$557$	−6.94427	+	4.00928i	−0.294238	+	0.169878i	−0.639852	−	0.768498i	$-0.721004\pi$
$557$	−6.94427	+	4.00928i	−0.294238	+	0.169878i	0.345613	+	0.938377i	$0.387671\pi$
$558$		0			0
$559$	−6.17294			−0.261087
$560$	−18.1309	+	5.98778i	−0.766169	+	0.253030i
$561$		0			0
$562$	−5.92286	−	30.7788i	−0.249841	−	1.29833i
$563$	−4.64261	+	2.68041i	−0.195663	+	0.112966i	−0.594631	−	0.803999i	$-0.702702\pi$
$563$	−4.64261	+	2.68041i	−0.195663	+	0.112966i	0.398968	+	0.916965i	$0.369368\pi$
$564$		0			0
$565$	−8.90509	−	5.14136i	−0.374640	−	0.216299i
$566$	15.0902	+	17.4252i	0.634287	+	0.732436i
$567$		0			0
$568$	−13.8665	−	21.6180i	−0.581824	−	0.907073i
$569$	−2.74603	+	4.75626i	−0.115119	+	0.199393i	−0.917827	−	0.396979i	$-0.870058\pi$
$569$	−2.74603	+	4.75626i	−0.115119	+	0.199393i	0.802708	+	0.596372i	$0.203392\pi$
$570$		0			0
$571$	8.90172	−	5.13941i	0.372525	−	0.215078i	−0.302036	−	0.953297i	$-0.597666\pi$
$571$	8.90172	−	5.13941i	0.372525	−	0.215078i	0.674561	+	0.738219i	$0.264333\pi$
$572$	6.82857	+	5.37647i	0.285517	+	0.224801i
$573$		0			0
$574$	−6.27602	−	22.4803i	−0.261956	−	0.938308i
$575$	10.6472			0.444018
$576$		0			0
$577$	−2.86786	−	4.96728i	−0.119391	−	0.206791i	0.800136	−	0.599819i	$-0.204761\pi$
$577$	−2.86786	−	4.96728i	−0.119391	−	0.206791i	−0.919526	+	0.393028i	$0.871427\pi$
$578$	9.52228	+	3.29879i	0.396075	+	0.137212i
$579$		0			0
$580$	−0.226755	+	1.57064i	−0.00941551	+	0.0652173i
$581$	−0.315811	−	3.83621i	−0.0131020	−	0.159153i
$582$		0			0
$583$	3.46314	−	5.99834i	0.143429	−	0.248426i
$584$	−9.62624	+	18.6324i	−0.398337	+	0.771015i
$585$		0			0
$586$	8.43188	−	1.62257i	0.348318	−	0.0670278i
$587$			22.9642i			0.947836i	0.880569	+	0.473918i	$0.157161\pi$
$587$			22.9642i			0.947836i	−0.880569	+	0.473918i	$0.842839\pi$
$588$		0			0
$589$			41.3142i			1.70232i
$590$	4.07029	+	21.1517i	0.167571	+	0.870803i
$591$		0			0
$592$	20.4850	−	4.94442i	0.841930	−	0.203215i
$593$	−16.9476	+	29.3541i	−0.695954	+	1.20543i	0.273904	+	0.961757i	$0.411685\pi$
$593$	−16.9476	+	29.3541i	−0.695954	+	1.20543i	−0.969858	+	0.243671i	$0.921648\pi$
$594$		0			0
$595$	1.92370	+	23.3675i	0.0788639	+	0.957974i
$596$	−30.7897	−	4.44514i	−1.26119	−	0.182080i
$597$		0			0
$598$	2.37301	−	6.84992i	0.0970396	−	0.280114i
$599$	−1.70841	−	2.95905i	−0.0698038	−	0.120904i	0.829011	−	0.559232i	$-0.188904\pi$
$599$	−1.70841	−	2.95905i	−0.0698038	−	0.120904i	−0.898815	+	0.438329i	$0.855571\pi$
$600$		0			0
$601$	−11.9964			−0.489345			−0.244672	−	0.969606i	$-0.578680\pi$
$601$	−11.9964			−0.489345			−0.244672	+	0.969606i	$0.578680\pi$
$602$	−26.4827	+	7.39344i	−1.07936	+	0.301334i
$603$		0			0
$604$	4.39476	+	3.46021i	0.178820	+	0.140794i
$605$	−24.6265	+	14.2181i	−1.00121	+	0.578048i
$606$		0			0
$607$	−15.0378	+	26.0463i	−0.610366	+	1.05719i	0.380813	+	0.924652i	$0.375644\pi$
$607$	−15.0378	+	26.0463i	−0.610366	+	1.05719i	−0.991179	+	0.132533i	$0.957689\pi$
$608$	13.1935	+	29.0011i	0.535067	+	1.17615i
$609$		0			0
$610$	−10.6358	+	9.21052i	−0.430629	+	0.372923i
$611$	−4.12770	−	2.38313i	−0.166989	−	0.0964111i
$612$		0			0
$613$	11.3479	−	6.55170i	0.458336	−	0.264621i	−0.253008	−	0.967464i	$-0.581420\pi$
$613$	11.3479	−	6.55170i	0.458336	−	0.264621i	0.711344	+	0.702844i	$0.248087\pi$
$614$	27.7490	−	5.33982i	1.11986	−	0.215498i
$615$		0			0
$616$	35.7350	+	14.8871i	1.43980	+	0.599818i
$617$	22.8490			0.919867			0.459933	−	0.887953i	$-0.347873\pi$
$617$	22.8490			0.919867			0.459933	+	0.887953i	$0.347873\pi$
$618$		0			0
$619$	41.0813	−	23.7183i	1.65120	−	0.953319i	0.674615	−	0.738170i	$-0.264310\pi$
$619$	41.0813	−	23.7183i	1.65120	−	0.953319i	0.976581	−	0.215149i	$-0.0690236\pi$
$620$	−9.82310	−	24.5783i	−0.394505	−	0.987088i
$621$		0			0
$622$	11.5668	−	10.0168i	0.463787	−	0.401638i
$623$	7.01062	−	14.8352i	0.280875	−	0.594361i
$624$		0			0
$625$	6.61581	−	11.4589i	0.264632	−	0.458357i
$626$	15.5329	+	5.38104i	0.620819	+	0.215070i
$627$		0			0
$628$	−6.36687	+	8.08646i	−0.254066	+	0.322685i
$629$		−	25.8770i		−	1.03178i
$630$		0			0
$631$	−18.2432			−0.726250			−0.363125	−	0.931740i	$-0.618290\pi$
$631$	−18.2432			−0.726250			−0.363125	+	0.931740i	$0.618290\pi$
$632$	−49.0521	+	2.29380i	−1.95119	+	0.0912425i
$633$		0			0
$634$	3.32923	−	9.61016i	0.132221	−	0.381668i
$635$	−21.7106	−	12.5346i	−0.861560	−	0.497422i
$636$		0			0
$637$	−0.961645	−	5.80105i	−0.0381018	−	0.229846i
$638$	2.43216	−	2.10624i	0.0962900	−	0.0833868i
$639$		0			0
$640$	−14.7445	−	14.1162i	−0.582826	−	0.557990i
$641$	−8.14275	−	14.1037i	−0.321619	−	0.557061i	0.659203	−	0.751965i	$-0.270894\pi$
$641$	−8.14275	−	14.1037i	−0.321619	−	0.557061i	−0.980822	+	0.194904i	$0.937561\pi$
$642$		0			0
$643$		−	26.7550i		−	1.05511i	−0.849519	−	0.527557i	$-0.823108\pi$
$643$		−	26.7550i		−	1.05511i	0.849519	−	0.527557i	$-0.176892\pi$
$644$	1.97626	−	32.2293i	0.0778756	−	1.27001i
$645$		0			0
$646$	38.4191	−	7.39311i	1.51158	−	0.290878i
$647$	−0.780952	−	1.35265i	−0.0307024	−	0.0531781i	0.850266	−	0.526353i	$-0.176441\pi$
$647$	−0.780952	−	1.35265i	−0.0307024	−	0.0531781i	−0.880968	+	0.473175i	$0.843108\pi$
$648$		0			0
$649$	21.8353	−	37.8199i	0.857111	−	1.48456i
$650$	1.35694	+	1.56691i	0.0532236	+	0.0614594i
$651$		0			0
$652$	−34.2486	−	4.94451i	−1.34128	−	0.193642i
$653$	8.45468	+	4.88131i	0.330857	+	0.191020i	0.656222	−	0.754568i	$-0.272154\pi$
$653$	8.45468	+	4.88131i	0.330857	+	0.191020i	−0.325364	+	0.945589i	$0.605487\pi$
$654$		0			0
$655$	17.0169	+	29.4742i	0.664907	+	1.15165i
$656$	18.0782	−	17.1974i	0.705834	−	0.671447i
$657$		0			0
$658$	−20.5627	−	5.28013i	−0.801619	−	0.205841i
$659$		−	48.0046i		−	1.87000i	−0.354654	−	0.934998i	$-0.615401\pi$
$659$		−	48.0046i		−	1.87000i	0.354654	−	0.934998i	$-0.384599\pi$
$660$		0			0
$661$	−38.0896	+	21.9910i	−1.48151	+	0.855353i	−0.999780	−	0.0209650i	$-0.993326\pi$
$661$	−38.0896	+	21.9910i	−1.48151	+	0.855353i	−0.481734	+	0.876318i	$0.659993\pi$
$662$	−14.4690	+	41.7661i	−0.562353	+	1.62329i
$663$		0			0
$664$	3.46366	−	2.22169i	0.134416	−	0.0862185i
$665$	15.3080	+	22.1024i	0.593617	+	0.857095i
$666$		0			0
$667$	−2.32410	−	1.34182i	−0.0899897	−	0.0519556i
$668$	−28.0543	+	11.2123i	−1.08545	+	0.433818i
$669$		0			0
$670$	0.360455	+	1.87315i	0.0139256	+	0.0723660i
$671$	28.5252			1.10120
$672$		0			0
$673$	13.7056			0.528314			0.264157	−	0.964480i	$-0.414906\pi$
$673$	13.7056			0.528314			0.264157	+	0.964480i	$0.414906\pi$
$674$	8.19872	+	42.6056i	0.315803	+	1.64111i
$675$		0			0
$676$	−22.8327	+	9.12543i	−0.878179	+	0.350978i
$677$	35.0505	+	20.2364i	1.34710	+	0.777749i	0.987838	−	0.155488i	$-0.0496949\pi$
$677$	35.0505	+	20.2364i	1.34710	+	0.777749i	0.359263	+	0.933237i	$0.383028\pi$
$678$		0			0
$679$	−15.3405	+	1.26288i	−0.588713	+	0.0484650i
$680$	−21.0982	+	13.5330i	−0.809078	+	0.518967i
$681$		0			0
$682$	−17.5663	+	50.7069i	−0.672649	+	1.94167i
$683$	−1.44887	+	0.836508i	−0.0554396	+	0.0320081i	−0.527464	−	0.849578i	$-0.676857\pi$
$683$	−1.44887	+	0.836508i	−0.0554396	+	0.0320081i	0.472024	+	0.881586i	$0.343524\pi$
$684$		0			0
$685$		−	28.4027i		−	1.08521i
$686$	−11.0736	−	23.7355i	−0.422792	−	0.906227i
$687$		0			0
$688$	−20.2594	−	21.2969i	−0.772381	−	0.811936i
$689$	−0.562360	−	0.974036i	−0.0214242	−	0.0371078i
$690$		0			0
$691$	−38.3701	−	22.1530i	−1.45967	−	0.842739i	−0.460672	−	0.887570i	$-0.652392\pi$
$691$	−38.3701	−	22.1530i	−1.45967	−	0.842739i	−0.998995	+	0.0448312i	$0.985725\pi$
$692$	25.2085	+	3.63939i	0.958284	+	0.138349i
$693$		0			0
$694$	1.05388	+	1.21696i	0.0400048	+	0.0461951i
$695$	10.3318	−	17.8952i	0.391908	−	0.678804i
$696$		0			0
$697$	−15.3196	−	26.5342i	−0.580269	−	1.00506i
$698$	−46.9600	+	9.03666i	−1.77746	+	0.342043i
$699$		0			0
$700$	7.69818	+	5.09704i	0.290964	+	0.192650i
$701$			22.0525i			0.832911i	0.909156	+	0.416455i	$0.136728\pi$
$701$			22.0525i			0.832911i	−0.909156	+	0.416455i	$0.863272\pi$
$702$		0			0
$703$	−14.8364	−	25.6975i	−0.559567	−	0.969198i
$704$	3.86208	+	41.2042i	0.145557	+	1.55294i
$705$		0			0
$706$	29.2464	−	25.3273i	1.10070	−	0.953205i
$707$	−8.88970	+	6.15694i	−0.334332	+	0.231556i
$708$		0			0
$709$	1.49907	+	0.865489i	0.0562988	+	0.0325041i	0.527885	−	0.849316i	$-0.322985\pi$
$709$	1.49907	+	0.865489i	0.0562988	+	0.0325041i	−0.471586	+	0.881820i	$0.656318\pi$
$710$	7.58416	−	21.8924i	0.284628	−	0.821607i
$711$		0			0
$712$	17.5221	−	0.819377i	0.656668	−	0.0307075i
$713$	44.7609			1.67631
$714$		0			0
$715$			7.84034i			0.293212i
$716$	26.0208	−	33.0486i	0.972443	−	1.23508i
$717$		0			0
$718$	−35.7775	−	12.3944i	−1.33521	−	0.462554i
$719$	16.9639	−	29.3824i	0.632648	−	1.09578i	−0.354361	−	0.935109i	$-0.615301\pi$
$719$	16.9639	−	29.3824i	0.632648	−	1.09578i	0.987008	−	0.160669i	$-0.0513652\pi$
$720$		0			0
$721$	−8.92459	+	18.8854i	−0.332369	+	0.703329i
$722$	13.6016	−	11.7789i	0.506199	−	0.438367i
$723$		0			0
$724$	−15.4056	−	38.5463i	−0.572546	−	1.43256i
$725$	0.664532	−	0.383668i	0.0246801	−	0.0142491i
$726$		0			0
$727$	15.1266			0.561016			0.280508	−	0.959852i	$-0.409497\pi$
$727$	15.1266			0.561016			0.280508	+	0.959852i	$0.409497\pi$
$728$	4.99496	−	3.81666i	0.185125	−	0.141455i
$729$		0			0
$730$	−18.5783	+	3.57508i	−0.687614	+	0.132320i
$731$	−31.2585	+	18.0471i	−1.15614	+	0.667497i
$732$		0			0
$733$	16.6021	+	9.58520i	0.613211	+	0.354038i	0.774221	−	0.632915i	$-0.218142\pi$
$733$	16.6021	+	9.58520i	0.613211	+	0.354038i	−0.161010	+	0.986953i	$0.551475\pi$
$734$	−30.5306	+	26.4394i	−1.12690	+	0.975896i
$735$		0			0
$736$	31.4206	−	14.2942i	1.15818	−	0.526892i
$737$	1.93368	−	3.34924i	0.0712281	−	0.123371i
$738$		0			0
$739$	−30.4240	+	17.5653i	−1.11917	+	0.646151i	−0.941188	−	0.337883i	$-0.890289\pi$
$739$	−30.4240	+	17.5653i	−1.11917	+	0.646151i	−0.177979	+	0.984034i	$0.556956\pi$
$740$	14.9363	+	11.7601i	0.549071	+	0.432311i
$741$		0			0
$742$	−3.57922	−	3.50520i	−0.131397	−	0.128680i
$743$	−4.72474			−0.173334			−0.0866670	−	0.996237i	$-0.527622\pi$
$743$	−4.72474			−0.173334			−0.0866670	+	0.996237i	$0.527622\pi$
$744$		0			0
$745$	−14.0318	−	24.3038i	−0.514085	−	0.890421i
$746$	17.0434	−	49.1974i	0.624003	−	1.80125i
$747$		0			0
$748$	50.2971	+	7.26146i	1.83904	+	0.265505i
$749$	5.51757	+	2.60741i	0.201608	+	0.0952729i
$750$		0			0
$751$	5.11917	−	8.86667i	0.186801	−	0.323549i	−0.757381	−	0.652973i	$-0.773521\pi$
$751$	5.11917	−	8.86667i	0.186801	−	0.323549i	0.944182	+	0.329424i	$0.106855\pi$
$752$	−5.32507	−	22.0621i	−0.194185	−	0.804522i
$753$		0			0
$754$	−0.0987261	−	0.513042i	−0.00359539	−	0.0186839i
$755$			5.04592i			0.183640i
$756$		0			0
$757$		−	25.9298i		−	0.942433i	−0.882018	−	0.471216i	$-0.843815\pi$
$757$		−	25.9298i		−	0.942433i	0.882018	−	0.471216i	$-0.156185\pi$
$758$	10.0495	−	1.93386i	0.365016	−	0.0702411i
$759$		0			0
$760$	−13.1927	+	25.5356i	−0.478550	+	0.926274i
$761$	20.0624	−	34.7490i	0.727260	−	1.25965i	−0.230777	−	0.973007i	$-0.574127\pi$
$761$	20.0624	−	34.7490i	0.727260	−	1.25965i	0.958037	−	0.286644i	$-0.0925398\pi$
$762$		0			0
$763$	13.8938	−	9.62273i	0.502989	−	0.348366i
$764$	−0.824335	+	5.70983i	−0.0298234	+	0.206574i
$765$		0			0
$766$	22.1149	+	7.66123i	0.799043	+	0.276811i
$767$	−3.54571	−	6.14136i	−0.128028	−	0.221752i
$768$		0			0
$769$	8.81137			0.317746			0.158873	−	0.987299i	$-0.449214\pi$
$769$	8.81137			0.317746			0.158873	+	0.987299i	$0.449214\pi$
$770$	9.39051	+	33.6361i	0.338411	+	1.21216i
$771$		0			0
$772$	0.318123	+	0.250474i	0.0114495	+	0.00901476i
$773$	26.8893	−	15.5246i	0.967142	−	0.558380i	0.0687785	−	0.997632i	$-0.478090\pi$
$773$	26.8893	−	15.5246i	0.967142	−	0.558380i	0.898364	+	0.439252i	$0.144756\pi$
$774$		0			0
$775$	−6.39926	+	11.0838i	−0.229868	+	0.398143i
$776$	−8.88425	−	13.8507i	−0.318926	−	0.497210i
$777$		0			0
$778$	2.03773	+	2.35304i	0.0730561	+	0.0843607i
$779$	−30.4265	−	17.5668i	−1.09014	−	0.629394i
$780$		0			0
$781$	−40.6802	+	23.4867i	−1.45565	+	0.840422i
$782$	−8.00990	−	41.6244i	−0.286433	−	1.48848i
$783$		0			0
$784$	16.8578	−	22.3565i	0.602064	−	0.798448i
$785$	−9.28460			−0.331382
$786$		0			0
$787$	−20.7082	+	11.9559i	−0.738166	+	0.426180i	−0.821402	−	0.570350i	$-0.806808\pi$
$787$	−20.7082	+	11.9559i	−0.738166	+	0.426180i	0.0832361	+	0.996530i	$0.473474\pi$
$788$	−9.04238	−	22.6249i	−0.322122	−	0.805977i
$789$		0			0
$790$	−28.9997	−	33.4871i	−1.03176	−	1.19142i
$791$	15.0280	−	1.23716i	0.534335	−	0.0439884i
$792$		0			0
$793$	2.31602	−	4.01147i	0.0822444	−	0.142451i
$794$	3.24272	−	9.36044i	0.115080	−	0.332189i
$795$		0			0
$796$	2.00887	+	1.58168i	0.0712024	+	0.0560612i
$797$		−	28.2309i		−	0.999991i	−0.866028	−	0.499995i	$-0.833335\pi$
$797$		−	28.2309i		−	0.999991i	0.866028	−	0.499995i	$-0.166665\pi$
$798$		0			0
$799$	−27.8692			−0.985940
$800$	−0.952483	+	9.82405i	−0.0336753	+	0.347333i
$801$		0			0
$802$	14.6056	+	5.05980i	0.515742	+	0.178668i
$803$	33.2185	+	19.1787i	1.17226	+	0.676802i
$804$		0			0
$805$	23.9464	−	16.5851i	0.843999	−	0.584547i
$806$	5.70461	+	6.58733i	0.200936	+	0.232029i
$807$		0			0
$808$	−10.2706	−	5.30617i	−0.361317	−	0.186670i
$809$	7.85432	+	13.6041i	0.276143	+	0.478294i	0.970423	−	0.241411i	$-0.0776102\pi$
$809$	7.85432	+	13.6041i	0.276143	+	0.478294i	−0.694280	+	0.719705i	$0.744277\pi$
$810$		0			0
$811$			29.0665i			1.02066i	0.859978	+	0.510331i	$0.170477\pi$
$811$			29.0665i			1.02066i	−0.859978	+	0.510331i	$0.829523\pi$
$812$	−1.03803	−	2.08277i	−0.0364276	−	0.0730910i
$813$		0			0
$814$	−7.28320	−	37.8480i	−0.255276	−	1.32657i
$815$	−15.6081	−	27.0340i	−0.546728	−	0.946961i
$816$		0			0
$817$	−20.6944	+	35.8438i	−0.724006	+	1.25402i
$818$	36.5907	−	31.6875i	1.27937	−	1.10793i
$819$		0			0
$820$	22.2779	+	3.21628i	0.777977	+	0.112317i
$821$	−44.7290	−	25.8243i	−1.56105	−	0.901274i	−0.997151	−	0.0754320i	$-0.975966\pi$
$821$	−44.7290	−	25.8243i	−1.56105	−	0.901274i	−0.563901	−	0.825842i	$-0.690700\pi$
$822$		0			0
$823$	−13.7031	−	23.7344i	−0.477659	−	0.827329i	0.522013	−	0.852937i	$-0.325181\pi$
$823$	−13.7031	−	23.7344i	−0.477659	−	0.827329i	−0.999672	+	0.0256081i	$0.991848\pi$
$824$	−22.3058	+	1.04308i	−0.777059	+	0.0363373i
$825$		0			0
$826$	−22.5672	−	22.1005i	−0.785214	−	0.768975i
$827$		−	8.50078i		−	0.295601i	−0.989017	−	0.147801i	$-0.952781\pi$
$827$		−	8.50078i		−	0.295601i	0.989017	−	0.147801i	$-0.0472194\pi$
$828$		0			0
$829$	−19.8897	+	11.4833i	−0.690798	+	0.398833i	−0.803911	−	0.594750i	$-0.797251\pi$
$829$	−19.8897	+	11.4833i	−0.690798	+	0.398833i	0.113113	+	0.993582i	$0.463918\pi$
$830$	3.50761	+	1.21514i	0.121751	+	0.0421781i
$831$		0			0
$832$	6.10808	+	2.80234i	0.211760	+	0.0971537i
$833$	−21.8295	−	26.5639i	−0.756346	−	0.920385i
$834$		0			0
$835$	−23.6030	−	13.6272i	−0.816816	−	0.471589i
$836$	54.1114	−	21.6265i	1.87148	−	0.747967i
$837$		0			0
$838$	8.54762	−	1.64484i	0.295272	−	0.0568202i
$839$	−4.60615			−0.159022			−0.0795110	−	0.996834i	$-0.525336\pi$
$839$	−4.60615			−0.159022			−0.0795110	+	0.996834i	$0.525336\pi$
$840$		0			0
$841$	28.8066			0.993331
$842$	−44.8453	+	8.62971i	−1.54547	+	0.297399i
$843$		0			0
$844$	7.84012	+	19.6167i	0.269868	+	0.675234i
$845$	−19.2099	−	11.0908i	−0.660840	−	0.381536i
$846$		0			0
$847$	17.8166	−	37.7018i	0.612186	−	1.29545i
$848$	1.51482	−	5.13692i	0.0520191	−	0.176402i
$849$		0			0
$850$	11.4523	+	3.96740i	0.392810	+	0.136081i
$851$	−27.8413	+	16.0742i	−0.954389	+	0.551017i
$852$		0			0
$853$			41.5763i			1.42354i	0.702410	+	0.711772i	$0.252107\pi$
$853$			41.5763i			1.42354i	−0.702410	+	0.711772i	$0.747893\pi$
$854$	5.13145	−	19.9837i	0.175595	−	0.683828i
$855$		0			0
$856$	0.304746	+	6.51687i	0.0104160	+	0.222742i
$857$	−2.41304	−	4.17950i	−0.0824277	−	0.142769i	0.821864	−	0.569683i	$-0.192934\pi$
$857$	−2.41304	−	4.17950i	−0.0824277	−	0.142769i	−0.904292	+	0.426914i	$0.859601\pi$
$858$		0			0
$859$	26.4996	+	15.2996i	0.904155	+	0.522014i	0.878546	−	0.477658i	$-0.158514\pi$
$859$	26.4996	+	15.2996i	0.904155	+	0.522014i	0.0256092	+	0.999672i	$0.491847\pi$
$860$	3.78893	−	26.2443i	0.129201	−	0.894924i
$861$		0			0
$862$	−14.7924	+	12.8102i	−0.503831	+	0.436316i
$863$	−26.9000	+	46.5922i	−0.915688	+	1.58602i	−0.109797	+	0.993954i	$0.535020\pi$
$863$	−26.9000	+	46.5922i	−0.915688	+	1.58602i	−0.805891	+	0.592064i	$0.798313\pi$
$864$		0			0
$865$	11.4883	+	19.8983i	0.390613	+	0.676562i
$866$	4.45630	+	23.1577i	0.151431	+	0.786930i
$867$		0			0
$868$	32.3633	+	21.4281i	1.09848	+	0.727316i
$869$			89.8127i			3.04669i
$870$		0			0
$871$	−0.314000	−	0.543864i	−0.0106395	−	0.0184281i
$872$	16.0519	+	8.29306i	0.543587	+	0.280838i
$873$		0			0
$874$	−31.8194	−	36.7431i	−1.07631	−	1.24285i
$875$	2.64159	+	32.0878i	0.0893020	+	1.08477i
$876$		0			0
$877$	30.3224	+	17.5067i	1.02392	+	0.591158i	0.915236	−	0.402918i	$-0.132004\pi$
$877$	30.3224	+	17.5067i	1.02392	+	0.591158i	0.108680	+	0.994077i	$0.465338\pi$
$878$	−44.6925	−	15.4827i	−1.50830	−	0.522517i
$879$		0			0
$880$	−27.0495	+	25.7317i	−0.911838	+	0.867415i
$881$	−0.947112			−0.0319090			−0.0159545	−	0.999873i	$-0.505079\pi$
$881$	−0.947112			−0.0319090			−0.0159545	+	0.999873i	$0.505079\pi$
$882$		0			0
$883$		−	10.0621i		−	0.338617i	−0.985563	−	0.169308i	$-0.945847\pi$
$883$		−	10.0621i		−	0.338617i	0.985563	−	0.169308i	$-0.0541534\pi$
$884$	5.10490	−	6.48366i	0.171696	−	0.218069i
$885$		0			0
$886$	1.43823	−	4.15159i	0.0483183	−	0.139475i
$887$	−16.5339	+	28.6375i	−0.555153	+	0.961553i	0.442739	+	0.896651i	$0.354007\pi$
$887$	−16.5339	+	28.6375i	−0.555153	+	0.961553i	−0.997892	+	0.0649023i	$0.979326\pi$
$888$		0			0
$889$	36.6383	−	3.01620i	1.22881	−	0.101160i
$890$	10.3591	+	11.9620i	0.347237	+	0.400969i
$891$		0			0
$892$	−16.3419	+	6.53131i	−0.547169	+	0.218685i
$893$	−27.6758	+	15.9786i	−0.926135	+	0.534704i
$894$		0			0
$895$	37.9453			1.26837
$896$	29.5609	+	4.70667i	0.987561	+	0.157239i
$897$		0			0
$898$	5.38143	+	27.9652i	0.179581	+	0.933212i
$899$	2.79371	−	1.61295i	0.0931754	−	0.0537948i
$900$		0			0
$901$	−5.69536	−	3.28822i	−0.189740	−	0.109546i
$902$	−29.8747	−	34.4975i	−0.994720	−	1.14864i
$903$		0			0
$904$	8.70330	+	13.5686i	0.289467	+	0.451284i
$905$	18.7236	−	32.4303i	0.622395	−	1.07802i
$906$		0			0
$907$	5.29226	−	3.05549i	0.175727	−	0.101456i	−0.409557	−	0.912285i	$-0.634317\pi$
$907$	5.29226	−	3.05549i	0.175727	−	0.101456i	0.585283	+	0.810829i	$0.300983\pi$
$908$	−22.6294	+	28.7413i	−0.750983	+	0.953812i
$909$		0			0
$910$	5.49265	+	1.41041i	0.182080	+	0.0467547i
$911$	−31.5874			−1.04654			−0.523269	−	0.852168i	$-0.675288\pi$
$911$	−31.5874			−1.04654			−0.523269	+	0.852168i	$0.675288\pi$
$912$		0			0
$913$	−3.76306	−	6.51781i	−0.124539	−	0.215708i
$914$	−38.4268	−	13.3121i	−1.27105	−	0.440327i
$915$		0			0
$916$	40.2573	+	5.81200i	1.33014	+	0.192034i
$917$	−45.1235	−	21.3238i	−1.49011	−	0.704174i
$918$		0			0
$919$	−22.1407	+	38.3488i	−0.730353	+	1.26501i	0.226379	+	0.974039i	$0.427311\pi$
$919$	−22.1407	+	38.3488i	−0.730353	+	1.26501i	−0.956732	+	0.290970i	$0.906022\pi$
$920$	27.6660	+	14.2933i	0.912121	+	0.471237i
$921$		0			0
$922$	−23.7259	+	4.56565i	−0.781372	+	0.150362i
$923$			7.62776i			0.251071i
$924$		0			0
$925$		−	9.19221i		−	0.302238i
$926$	−1.35155	−	7.02349i	−0.0444147	−	0.230806i
$927$		0			0
$928$	1.44600	−	2.02439i	0.0474673	−	0.0664540i
$929$	−28.5577	+	49.4634i	−0.936948	+	1.62284i	−0.165824	+	0.986155i	$0.553029\pi$
$929$	−28.5577	+	49.4634i	−0.936948	+	1.62284i	−0.771123	+	0.636686i	$0.780305\pi$
$930$		0			0
$931$	−36.9083	−	13.8638i	−1.20962	−	0.454368i
$932$	−4.00916	+	27.7698i	−0.131324	+	0.909630i
$933$		0			0
$934$	−3.33105	+	9.61541i	−0.108995	+	0.314626i
$935$	22.9219	+	39.7019i	0.749627	+	1.29839i
$936$		0			0
$937$	20.8245			0.680307			0.340153	−	0.940370i	$-0.389521\pi$
$937$	20.8245			0.680307			0.340153	+	0.940370i	$0.389521\pi$
$938$	−1.99850	−	1.95717i	−0.0652533	−	0.0639038i
$939$		0			0
$940$	12.6655	−	16.0862i	0.413102	−	0.524675i
$941$	−20.9815	+	12.1137i	−0.683977	+	0.394894i	−0.801352	−	0.598193i	$-0.795885\pi$
$941$	−20.9815	+	12.1137i	−0.683977	+	0.394894i	0.117375	+	0.993088i	$0.462552\pi$
$942$		0			0
$943$	−19.0323	+	32.9649i	−0.619777	+	1.07349i
$944$	9.55103	−	32.3886i	0.310860	−	1.05416i
$945$		0			0
$946$	−40.6396	+	35.1938i	−1.32131	+	1.14425i
$947$	33.8488	+	19.5426i	1.09994	+	0.635050i	0.936205	−	0.351455i	$-0.114313\pi$
$947$	33.8488	+	19.5426i	1.09994	+	0.635050i	0.163733	+	0.986505i	$0.447646\pi$
$948$		0			0
$949$	5.39416	−	3.11432i	0.175102	−	0.101095i
$950$	13.6475	−	2.62623i	0.442784	−	0.0852062i
$951$		0			0
$952$	14.1351	−	33.9300i	0.458123	−	1.09968i
$953$	13.0442			0.422542			0.211271	−	0.977428i	$-0.432240\pi$
$953$	13.0442			0.422542			0.211271	+	0.977428i	$0.432240\pi$
$954$		0			0
$955$	−4.50704	+	2.60214i	−0.145844	+	0.0842033i
$956$	27.9477	−	11.1697i	0.903893	−	0.361255i
$957$		0			0
$958$	−10.0579	+	8.71010i	−0.324956	+	0.281410i
$959$	23.7145	+	34.2402i	0.765781	+	1.10567i
$960$		0			0
$961$	−11.4026	+	19.7499i	−0.367826	+	0.637094i
$962$	−5.91387	−	2.04873i	−0.190671	−	0.0660538i
$963$		0			0
$964$	−22.0893	−	17.3920i	−0.711449	−	0.560159i
$965$			0.365259i			0.0117581i
$966$		0			0
$967$	5.01478			0.161264			0.0806322	−	0.996744i	$-0.474306\pi$
$967$	5.01478			0.161264			0.0806322	+	0.996744i	$0.474306\pi$
$968$	44.5301	−	2.08234i	1.43125	−	0.0669291i
$969$		0			0
$970$	4.85917	−	14.0265i	0.156018	−	0.450362i
$971$	−6.95295	−	4.01429i	−0.223131	−	0.128825i	0.384268	−	0.923221i	$-0.374454\pi$
$971$	−6.95295	−	4.01429i	−0.223131	−	0.128825i	−0.607399	+	0.794397i	$0.707787\pi$
$972$		0			0
$973$	2.48614	+	30.1995i	0.0797019	+	0.968153i
$974$	26.6950	−	23.1177i	0.855361	−	0.740740i
$975$		0			0
$976$	21.4408	−	5.17512i	0.686305	−	0.165652i
$977$	10.1933	+	17.6553i	0.326112	+	0.564843i	0.981737	−	0.190244i	$-0.0609280\pi$
$977$	10.1933	+	17.6553i	0.326112	+	0.564843i	−0.655625	+	0.755087i	$0.727595\pi$
$978$		0			0
$979$		−	32.0823i		−	1.02536i
$980$	25.2535	−	0.527783i	0.806693	−	0.0168594i
$981$		0			0
$982$	8.47352	−	1.63059i	0.270401	−	0.0520341i
$983$	−31.2771	−	54.1735i	−0.997584	−	1.72787i	−0.558953	−	0.829199i	$-0.688797\pi$
$983$	−31.2771	−	54.1735i	−0.997584	−	1.72787i	−0.438631	−	0.898667i	$-0.644536\pi$
$984$		0			0
$985$	10.9899	−	19.0350i	0.350167	−	0.606507i
$986$	−1.99985	−	2.30931i	−0.0636883	−	0.0735433i
$987$		0			0
$988$	1.35211	−	9.36554i	0.0430165	−	0.297957i
$989$	38.8342	+	22.4209i	1.23485	+	0.712944i
$990$		0			0
$991$	−6.90294	−	11.9562i	−0.219279	−	0.379803i	0.735309	−	0.677732i	$-0.237037\pi$
$991$	−6.90294	−	11.9562i	−0.219279	−	0.379803i	−0.954588	+	0.297930i	$0.903704\pi$
$992$	−4.00426	+	41.3005i	−0.127135	+	1.31129i
$993$		0			0
$994$	9.13590	+	32.7241i	0.289773	+	1.03795i
$995$			2.30652i			0.0731214i
$996$		0			0
$997$	−11.1778	+	6.45348i	−0.354003	+	0.204384i	−0.666447	−	0.745552i	$-0.732186\pi$
$997$	−11.1778	+	6.45348i	−0.354003	+	0.204384i	0.312444	+	0.949936i	$0.398852\pi$
$998$	2.54768	−	7.35411i	0.0806453	−	0.232790i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.9		32
3.2	odd	2		168.2.bc.a.37.8	yes	32
4.3	odd	2		2016.2.cr.e.1297.5		32
7.4	even	3	inner	504.2.cj.e.109.15		32
8.3	odd	2		2016.2.cr.e.1297.12		32
8.5	even	2	inner	504.2.cj.e.37.15		32
12.11	even	2		672.2.bk.a.625.6		32
21.2	odd	6		1176.2.c.e.589.13		16
21.5	even	6		1176.2.c.f.589.13		16
21.11	odd	6		168.2.bc.a.109.2	yes	32
24.5	odd	2		168.2.bc.a.37.2	✓	32
24.11	even	2		672.2.bk.a.625.11		32
28.11	odd	6		2016.2.cr.e.1873.12		32
56.11	odd	6		2016.2.cr.e.1873.5		32
56.53	even	6	inner	504.2.cj.e.109.9		32
84.11	even	6		672.2.bk.a.529.11		32
84.23	even	6		4704.2.c.e.2353.3		16
84.47	odd	6		4704.2.c.f.2353.14		16
168.5	even	6		1176.2.c.f.589.14		16
168.11	even	6		672.2.bk.a.529.6		32
168.53	odd	6		168.2.bc.a.109.8	yes	32
168.107	even	6		4704.2.c.e.2353.14		16
168.131	odd	6		4704.2.c.f.2353.3		16
168.149	odd	6		1176.2.c.e.589.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.2	✓	32	24.5	odd	2
168.2.bc.a.37.8	yes	32	3.2	odd	2
168.2.bc.a.109.2	yes	32	21.11	odd	6
168.2.bc.a.109.8	yes	32	168.53	odd	6
504.2.cj.e.37.9		32	1.1	even	1	trivial
504.2.cj.e.37.15		32	8.5	even	2	inner
504.2.cj.e.109.9		32	56.53	even	6	inner
504.2.cj.e.109.15		32	7.4	even	3	inner
672.2.bk.a.529.6		32	168.11	even	6
672.2.bk.a.529.11		32	84.11	even	6
672.2.bk.a.625.6		32	12.11	even	2
672.2.bk.a.625.11		32	24.11	even	2
1176.2.c.e.589.13		16	21.2	odd	6
1176.2.c.e.589.14		16	168.149	odd	6
1176.2.c.f.589.13		16	21.5	even	6
1176.2.c.f.589.14		16	168.5	even	6
2016.2.cr.e.1297.5		32	4.3	odd	2
2016.2.cr.e.1297.12		32	8.3	odd	2
2016.2.cr.e.1873.5		32	56.11	odd	6
2016.2.cr.e.1873.12		32	28.11	odd	6
4704.2.c.e.2353.3		16	84.23	even	6
4704.2.c.e.2353.14		16	168.107	even	6
4704.2.c.f.2353.3		16	168.131	odd	6
4704.2.c.f.2353.14		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)

\(f(q)\)	\(=\)	\(q+(-0.267238 - 1.38873i) q^{2} +(-1.85717 + 0.742246i) q^{4} +(-1.56250 - 0.902108i) q^{5} +(2.63683 - 0.217074i) q^{7} +(1.52709 + 2.38076i) q^{8} +O(q^{10})\)	\(q+(-0.267238 - 1.38873i) q^{2} +(-1.85717 + 0.742246i) q^{4} +(-1.56250 - 0.902108i) q^{5} +(2.63683 - 0.217074i) q^{7} +(1.52709 + 2.38076i) q^{8} +(-0.835229 + 2.41097i) q^{10} +(4.48004 - 2.58655i) q^{11} -0.840031i q^{13} +(-1.00612 - 3.60385i) q^{14} +(2.89814 - 2.75695i) q^{16} +(-2.45590 - 4.25375i) q^{17} +(-4.87773 - 2.81616i) q^{19} +(3.57140 + 0.515608i) q^{20} +(-4.78927 - 5.53036i) q^{22} +(-3.05110 + 5.28467i) q^{23} +(-0.872403 - 1.51105i) q^{25} +(-1.16658 + 0.224488i) q^{26} +(-4.73591 + 2.36032i) q^{28} +0.439783i q^{29} +(-3.66760 - 6.35247i) q^{31} +(-4.60317 - 3.28799i) q^{32} +(-5.25102 + 4.54736i) q^{34} +(-4.31586 - 2.03953i) q^{35} +(4.56250 + 2.63416i) q^{37} +(-2.60738 + 7.52645i) q^{38} +(-0.238373 - 5.09752i) q^{40} +6.23785 q^{41} -7.34846i q^{43} +(-6.40032 + 8.12895i) q^{44} +(8.15437 + 2.82491i) q^{46} +(2.83696 - 4.91375i) q^{47} +(6.90576 - 1.14477i) q^{49} +(-1.86530 + 1.61535i) q^{50} +(0.623510 + 1.56008i) q^{52} +(1.15952 - 0.669452i) q^{53} -9.33339 q^{55} +(4.54348 + 5.94616i) q^{56} +(0.610741 - 0.117527i) q^{58} +(7.31087 - 4.22093i) q^{59} +(4.77538 + 2.75707i) q^{61} +(-7.84178 + 6.79095i) q^{62} +(-3.33600 + 7.27125i) q^{64} +(-0.757798 + 1.31255i) q^{65} +(0.647433 - 0.373796i) q^{67} +(7.71836 + 6.07704i) q^{68} +(-1.67900 + 6.53863i) q^{70} -9.08033 q^{71} +(3.70739 + 6.42139i) q^{73} +(2.43888 - 7.04006i) q^{74} +(11.1490 + 1.60960i) q^{76} +(11.2516 - 7.79280i) q^{77} +(-8.68074 + 15.0355i) q^{79} +(-7.01540 + 1.69329i) q^{80} +(-1.66699 - 8.66271i) q^{82} -1.45486i q^{83} +8.86196i q^{85} +(-10.2051 + 1.96379i) q^{86} +(12.9994 + 6.71598i) q^{88} +(3.10088 - 5.37088i) q^{89} +(-0.182349 - 2.21502i) q^{91} +(1.74389 - 12.0792i) q^{92} +(-7.58204 - 2.62664i) q^{94} +(5.08095 + 8.80047i) q^{95} -5.81776 q^{97} +(-3.43527 - 9.28434i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 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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