LMFDB - Embedded newform 513.2.bo.a.224.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(71,513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(513, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("513.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.bo (of order $18$, degree $6$, not 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:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			224.5
Character	$\chi$	$=$	513.224
Dual form			513.2.bo.a.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28121 + 1.07506i) q^{2} +(0.138440 - 0.785130i) q^{4} +(0.199661 - 0.548565i) q^{5} +(-1.25763 - 2.17828i) q^{7} +(-1.00580 - 1.74210i) q^{8} +(0.333933 + 0.917472i) q^{10} -0.404547i q^{11} +(2.33106 + 6.40453i) q^{13} +(3.95307 + 1.43880i) q^{14} +(4.65983 + 1.69604i) q^{16} +(-1.57381 + 4.32400i) q^{17} +(-3.47008 + 2.63790i) q^{19} +(-0.403054 - 0.232703i) q^{20} +(0.434912 + 0.518308i) q^{22} +(6.06451 + 1.06934i) q^{23} +(3.56916 + 2.99488i) q^{25} +(-9.87182 - 5.69950i) q^{26} +(-1.88434 + 0.685845i) q^{28} +(-0.264049 + 1.49750i) q^{29} -2.99963i q^{31} +(-4.01296 + 1.46060i) q^{32} +(-2.63218 - 7.23187i) q^{34} +(-1.44603 + 0.254974i) q^{35} +7.01209i q^{37} +(1.60999 - 7.11024i) q^{38} +(-1.15648 + 0.203918i) q^{40} +(-3.94971 + 3.31420i) q^{41} +(-0.105574 - 0.598738i) q^{43} +(-0.317622 - 0.0560053i) q^{44} +(-8.91949 + 5.14967i) q^{46} +(4.36769 + 0.770141i) q^{47} +(0.336719 - 0.583215i) q^{49} -7.79251 q^{50} +(5.35110 - 0.943543i) q^{52} +(2.63029 + 2.20707i) q^{53} +(-0.221920 - 0.0807723i) q^{55} +(-2.52986 + 4.38185i) q^{56} +(-1.27160 - 2.20247i) q^{58} +(1.31593 + 7.46301i) q^{59} +(-10.7552 + 3.91458i) q^{61} +(3.22478 + 3.84315i) q^{62} +(-1.38769 + 2.40355i) q^{64} +3.97872 q^{65} +(1.54091 - 1.83638i) q^{67} +(3.17702 + 1.83425i) q^{68} +(1.57855 - 1.88124i) q^{70} +(-5.10921 + 4.28714i) q^{71} +(-2.34660 - 13.3082i) q^{73} +(-7.53841 - 8.98393i) q^{74} +(1.59070 + 3.08966i) q^{76} +(-0.881218 + 0.508771i) q^{77} +(-0.472257 + 1.29752i) q^{79} +(1.86078 - 2.21759i) q^{80} +(1.49743 - 8.49234i) q^{82} +(11.3968 - 6.57996i) q^{83} +(2.05776 + 1.72667i) q^{85} +(0.778940 + 0.653608i) q^{86} +(-0.704762 + 0.406895i) q^{88} +(1.53648 - 8.71380i) q^{89} +(11.0193 - 13.1323i) q^{91} +(1.67914 - 4.61339i) q^{92} +(-6.42386 + 3.70882i) q^{94} +(0.754220 + 2.43025i) q^{95} +(-2.35590 - 2.80765i) q^{97} +(0.195584 + 1.10921i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 9 q^{2} - 3 q^{4} + 9 q^{5} + 3 q^{7} - 12 q^{10} - 6 q^{13} + 9 q^{14} - 9 q^{16} - 27 q^{17} - 15 q^{19} + 18 q^{20} + 30 q^{22} + 45 q^{23} - 3 q^{25} + 72 q^{26} - 36 q^{28} + 9 q^{29} + 9 q^{32}+ \cdots + 27 q^{98}+O(q^{100}) $ 108 * q + 9 * q^2 - 3 * q^4 + 9 * q^5 + 3 * q^7 - 12 * q^10 - 6 * q^13 + 9 * q^14 - 9 * q^16 - 27 * q^17 - 15 * q^19 + 18 * q^20 + 30 * q^22 + 45 * q^23 - 3 * q^25 + 72 * q^26 - 36 * q^28 + 9 * q^29 + 9 * q^32 + 33 * q^34 - 45 * q^35 + 9 * q^38 + 15 * q^40 + 9 * q^41 + 9 * q^43 + 63 * q^44 - 18 * q^46 + 9 * q^47 - 15 * q^49 - 126 * q^50 - 39 * q^52 + 3 * q^55 - 63 * q^56 - 6 * q^58 - 36 * q^59 - 24 * q^61 - 18 * q^62 + 18 * q^65 - 63 * q^67 - 54 * q^68 + 39 * q^70 - 45 * q^73 + 117 * q^74 - 3 * q^76 + 18 * q^77 + 3 * q^79 - 126 * q^80 - 3 * q^82 - 27 * q^83 - 3 * q^85 + 171 * q^86 - 9 * q^88 - 54 * q^89 - 9 * q^91 + 27 * q^92 - 99 * q^95 - 57 * q^97 + 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−1.28121	+	1.07506i	−0.905949	+	0.760182i	−0.971344	−	0.237678i	$-0.923614\pi$
$2$	−1.28121	+	1.07506i	−0.905949	+	0.760182i	0.0653946	+	0.997859i	$0.479169\pi$
$3$		0			0
$3$		0			0
$4$	0.138440	−	0.785130i	0.0692198	−	0.392565i
$5$	0.199661	−	0.548565i	0.0892912	−	0.245326i	−0.887007	−	0.461757i	$-0.847219\pi$
$5$	0.199661	−	0.548565i	0.0892912	−	0.245326i	0.976298	+	0.216431i	$0.0694416\pi$
$6$		0			0
$7$	−1.25763	−	2.17828i	−0.475341	−	0.823314i	0.524261	−	0.851558i	$-0.324342\pi$
$7$	−1.25763	−	2.17828i	−0.475341	−	0.823314i	−0.999601	+	0.0282440i	$0.991008\pi$
$8$	−1.00580	−	1.74210i	−0.355605	−	0.615927i
$9$		0			0
$10$	0.333933	+	0.917472i	0.105599	+	0.290130i
$11$		−	0.404547i		−	0.121975i	−0.998139	−	0.0609877i	$-0.980575\pi$
$11$		−	0.404547i		−	0.121975i	0.998139	−	0.0609877i	$-0.0194250\pi$
$12$		0			0
$13$	2.33106	+	6.40453i	0.646519	+	1.77630i	0.630203	+	0.776430i	$0.282972\pi$
$13$	2.33106	+	6.40453i	0.646519	+	1.77630i	0.0163159	+	0.999867i	$0.494806\pi$
$14$	3.95307	+	1.43880i	1.05650	+	0.384536i
$15$		0			0
$16$	4.65983	+	1.69604i	1.16496	+	0.424010i
$17$	−1.57381	+	4.32400i	−0.381704	+	1.04872i	0.588935	+	0.808181i	$0.299548\pi$
$17$	−1.57381	+	4.32400i	−0.381704	+	1.04872i	−0.970639	+	0.240542i	$0.922675\pi$
$18$		0			0
$19$	−3.47008	+	2.63790i	−0.796091	+	0.605176i
$19$	−3.47008	+	2.63790i	−0.796091	+	0.605176i
$20$	−0.403054	−	0.232703i	−0.0901255	−	0.0520340i
$21$		0			0
$22$	0.434912	+	0.518308i	0.0927235	+	0.110504i
$23$	6.06451	+	1.06934i	1.26454	+	0.222972i	0.765403	−	0.643552i	$-0.222540\pi$
$23$	6.06451	+	1.06934i	1.26454	+	0.222972i	0.499136	+	0.866524i	$0.333651\pi$
$24$		0			0
$25$	3.56916	+	2.99488i	0.713833	+	0.598977i
$26$	−9.87182	−	5.69950i	−1.93602	−	1.11776i
$27$		0			0
$28$	−1.88434	+	0.685845i	−0.356107	+	0.129612i
$29$	−0.264049	+	1.49750i	−0.0490327	+	0.278078i	−0.999460	−	0.0328698i	$-0.989535\pi$
$29$	−0.264049	+	1.49750i	−0.0490327	+	0.278078i	0.950427	+	0.310948i	$0.100646\pi$
$30$		0			0
$31$		−	2.99963i		−	0.538750i	−0.963035	−	0.269375i	$-0.913183\pi$
$31$		−	2.99963i		−	0.538750i	0.963035	−	0.269375i	$-0.0868171\pi$
$32$	−4.01296	+	1.46060i	−0.709398	+	0.258200i
$33$		0			0
$34$	−2.63218	−	7.23187i	−0.451416	−	1.24025i
$35$	−1.44603	+	0.254974i	−0.244424	+	0.0430985i
$36$		0			0
$37$			7.01209i			1.15278i	0.817175	+	0.576390i	$0.195539\pi$
$37$			7.01209i			1.15278i	−0.817175	+	0.576390i	$0.804461\pi$
$38$	1.60999	−	7.11024i	0.261174	−	1.15343i
$39$		0			0
$40$	−1.15648	+	0.203918i	−0.182855	+	0.0322423i
$41$	−3.94971	+	3.31420i	−0.616841	+	0.517591i	−0.896809	−	0.442418i	$-0.854121\pi$
$41$	−3.94971	+	3.31420i	−0.616841	+	0.517591i	0.279968	+	0.960009i	$0.409676\pi$
$42$		0			0
$43$	−0.105574	−	0.598738i	−0.0160998	−	0.0913066i	0.975699	−	0.219115i	$-0.0703169\pi$
$43$	−0.105574	−	0.598738i	−0.0160998	−	0.0913066i	−0.991799	+	0.127808i	$0.959206\pi$
$44$	−0.317622	−	0.0560053i	−0.0478833	−	0.00844312i
$45$		0			0
$46$	−8.91949	+	5.14967i	−1.31511	+	0.759278i
$47$	4.36769	+	0.770141i	0.637093	+	0.112337i	0.482860	−	0.875698i	$-0.339598\pi$
$47$	4.36769	+	0.770141i	0.637093	+	0.112337i	0.154233	+	0.988034i	$0.450709\pi$
$48$		0			0
$49$	0.336719	−	0.583215i	0.0481028	−	0.0833164i
$50$	−7.79251			−1.10203
$51$		0			0
$52$	5.35110	−	0.943543i	0.742064	−	0.130846i
$53$	2.63029	+	2.20707i	0.361297	+	0.303165i	0.805308	−	0.592857i	$-0.202000\pi$
$53$	2.63029	+	2.20707i	0.361297	+	0.303165i	−0.444010	+	0.896022i	$0.646445\pi$
$54$		0			0
$55$	−0.221920	−	0.0807723i	−0.0299237	−	0.0108913i
$56$	−2.52986	+	4.38185i	−0.338067	+	0.585550i
$57$		0			0
$58$	−1.27160	−	2.20247i	−0.166969	−	0.289198i
$59$	1.31593	+	7.46301i	0.171320	+	0.971602i	0.942307	+	0.334751i	$0.108652\pi$
$59$	1.31593	+	7.46301i	0.171320	+	0.971602i	−0.770987	+	0.636851i	$0.780237\pi$
$60$		0			0
$61$	−10.7552	+	3.91458i	−1.37706	+	0.501211i	−0.921287	−	0.388883i	$-0.872861\pi$
$61$	−10.7552	+	3.91458i	−1.37706	+	0.501211i	−0.455778	+	0.890094i	$0.650639\pi$
$62$	3.22478	+	3.84315i	0.409548	+	0.488080i
$63$		0			0
$64$	−1.38769	+	2.40355i	−0.173461	+	0.300443i
$65$	3.97872			0.493500
$66$		0			0
$67$	1.54091	−	1.83638i	0.188252	−	0.224349i	−0.663661	−	0.748033i	$-0.730998\pi$
$67$	1.54091	−	1.83638i	0.188252	−	0.224349i	0.851913	+	0.523684i	$0.175443\pi$
$68$	3.17702	+	1.83425i	0.385271	+	0.222436i
$69$		0			0
$70$	1.57855	−	1.88124i	0.188673	−	0.224852i
$71$	−5.10921	+	4.28714i	−0.606352	+	0.508790i	−0.893480	−	0.449102i	$-0.851744\pi$
$71$	−5.10921	+	4.28714i	−0.606352	+	0.508790i	0.287128	+	0.957892i	$0.407299\pi$
$72$		0			0
$73$	−2.34660	−	13.3082i	−0.274649	−	1.55761i	−0.740075	−	0.672524i	$-0.765210\pi$
$73$	−2.34660	−	13.3082i	−0.274649	−	1.55761i	0.465426	−	0.885087i	$-0.345901\pi$
$74$	−7.53841	−	8.98393i	−0.876323	−	1.04436i
$75$		0			0
$76$	1.59070	+	3.08966i	0.182466	+	0.354408i
$77$	−0.881218	+	0.508771i	−0.100424	+	0.0579799i
$78$		0			0
$79$	−0.472257	+	1.29752i	−0.0531331	+	0.145982i	−0.963420	−	0.267996i	$-0.913639\pi$
$79$	−0.472257	+	1.29752i	−0.0531331	+	0.145982i	0.910287	+	0.413978i	$0.135861\pi$
$80$	1.86078	−	2.21759i	0.208041	−	0.247934i
$81$		0			0
$82$	1.49743	−	8.49234i	0.165363	−	0.937822i
$83$	11.3968	−	6.57996i	1.25096	−	0.722245i	0.279664	−	0.960098i	$-0.409777\pi$
$83$	11.3968	−	6.57996i	1.25096	−	0.722245i	0.971301	+	0.237853i	$0.0764437\pi$
$84$		0			0
$85$	2.05776	+	1.72667i	0.223196	+	0.187284i
$86$	0.778940	+	0.653608i	0.0839953	+	0.0704804i
$87$		0			0
$88$	−0.704762	+	0.406895i	−0.0751279	+	0.0433751i
$89$	1.53648	−	8.71380i	0.162866	−	0.923661i	−0.788371	−	0.615201i	$-0.789075\pi$
$89$	1.53648	−	8.71380i	0.162866	−	0.923661i	0.951237	−	0.308461i	$-0.0998138\pi$
$90$		0			0
$91$	11.0193	−	13.1323i	1.15513	−	1.37663i
$92$	1.67914	−	4.61339i	0.175062	−	0.480979i
$93$		0			0
$94$	−6.42386	+	3.70882i	−0.662570	+	0.382535i
$95$	0.754220	+	2.43025i	0.0773813	+	0.249339i
$96$		0			0
$97$	−2.35590	−	2.80765i	−0.239206	−	0.285074i	0.633064	−	0.774099i	$-0.281797\pi$
$97$	−2.35590	−	2.80765i	−0.239206	−	0.285074i	−0.872270	+	0.489025i	$0.837353\pi$
$98$	0.195584	+	1.10921i	0.0197570	+	0.112047i
$99$		0			0
$100$	2.84549	−	2.38765i	0.284549	−	0.238765i
$101$	−5.71285	+	6.80830i	−0.568449	+	0.677452i	−0.971312	−	0.237809i	$-0.923571\pi$
$101$	−5.71285	+	6.80830i	−0.568449	+	0.677452i	0.402863	+	0.915260i	$0.368015\pi$
$102$		0			0
$103$	−0.240253	−	0.138710i	−0.0236728	−	0.0136675i	0.488117	−	0.872778i	$-0.337684\pi$
$103$	−0.240253	−	0.138710i	−0.0236728	−	0.0136675i	−0.511790	+	0.859111i	$0.671017\pi$
$104$	8.81277	−	10.5026i	0.864163	−	1.02987i
$105$		0			0
$106$	−5.74267			−0.557777
$107$	−2.99056	+	5.17980i	−0.289108	+	0.500750i	−0.973597	−	0.228273i	$-0.926692\pi$
$107$	−2.99056	+	5.17980i	−0.289108	+	0.500750i	0.684489	+	0.729023i	$0.260025\pi$
$108$		0			0
$109$	5.96323	+	7.10670i	0.571174	+	0.680698i	0.971871	−	0.235512i	$-0.0756767\pi$
$109$	5.96323	+	7.10670i	0.571174	+	0.680698i	−0.400698	+	0.916210i	$0.631232\pi$
$110$	0.371160	−	0.135091i	0.0353888	−	0.0128805i
$111$		0			0
$112$	−2.16590	−	12.2834i	−0.204658	−	1.16068i
$113$	10.0435	+	17.3958i	0.944812	+	1.63646i	0.756128	+	0.654424i	$0.227089\pi$
$113$	10.0435	+	17.3958i	0.944812	+	1.63646i	0.188684	+	0.982038i	$0.439578\pi$
$114$		0			0
$115$	1.79745	−	3.11327i	0.167613	−	0.290314i
$116$	1.13917	+	0.414626i	0.105770	+	0.0384970i
$117$		0			0
$118$	−9.70916	−	8.14695i	−0.893801	−	0.749988i
$119$	11.3982	−	2.00980i	1.04487	−	0.184238i
$120$		0			0
$121$	10.8363			0.985122
$122$	9.57125	−	16.5779i	0.866540	−	1.50089i
$123$		0			0
$124$	−2.35510	−	0.415268i	−0.211494	−	0.0372922i
$125$	4.88331	−	2.81938i	0.436777	−	0.252173i
$126$		0			0
$127$	14.8487	+	2.61823i	1.31761	+	0.232331i	0.787877	−	0.615833i	$-0.211180\pi$
$127$	14.8487	+	2.61823i	1.31761	+	0.232331i	0.529735	+	0.848163i	$0.322291\pi$
$128$	−2.28917	−	12.9825i	−0.202336	−	1.14751i
$129$		0			0
$130$	−5.09756	+	4.27736i	−0.447086	+	0.375149i
$131$	−8.30606	+	1.46458i	−0.725704	+	0.127961i	−0.524283	−	0.851544i	$-0.675667\pi$
$131$	−8.30606	+	1.46458i	−0.725704	+	0.127961i	−0.201420	+	0.979505i	$0.564556\pi$
$132$		0			0
$133$	10.1102	+	4.24131i	0.876665	+	0.367768i
$134$			4.00935i			0.346355i
$135$		0			0
$136$	9.11579	−	1.60736i	0.781672	−	0.137830i
$137$	−5.33163	−	14.6485i	−0.455512	−	1.25151i	−0.928793	−	0.370598i	$-0.879153\pi$
$137$	−5.33163	−	14.6485i	−0.455512	−	1.25151i	0.473281	−	0.880911i	$-0.343069\pi$
$138$		0			0
$139$	5.28626	−	1.92404i	0.448375	−	0.163195i	−0.107957	−	0.994156i	$-0.534431\pi$
$139$	5.28626	−	1.92404i	0.448375	−	0.163195i	0.556331	+	0.830961i	$0.312209\pi$
$140$			1.17062i			0.0989355i
$141$		0			0
$142$	1.93703	−	10.9854i	0.162552	−	0.921876i
$143$	2.59093	−	0.943022i	0.216665	−	0.0788595i
$144$		0			0
$145$	0.768753	+	0.443840i	0.0638415	+	0.0368589i
$146$	17.3136	+	14.5279i	1.43289	+	1.20233i
$147$		0			0
$148$	5.50540	+	0.970751i	0.452541	+	0.0797952i
$149$	−13.0336	−	15.5328i	−1.06775	−	1.27250i	−0.960503	−	0.278268i	$-0.910240\pi$
$149$	−13.0336	−	15.5328i	−1.06775	−	1.27250i	−0.107251	−	0.994232i	$-0.534205\pi$
$150$		0			0
$151$	−0.772652	−	0.446091i	−0.0628775	−	0.0363023i	0.468232	−	0.883606i	$-0.344891\pi$
$151$	−0.772652	−	0.446091i	−0.0628775	−	0.0363023i	−0.531109	+	0.847303i	$0.678225\pi$
$152$	8.08572	+	3.39203i	0.655839	+	0.275130i
$153$		0			0
$154$	0.582062	−	1.59920i	0.0469039	−	0.128867i
$155$	−1.64549	−	0.598911i	−0.132169	−	0.0481057i
$156$		0			0
$157$	−6.33046	−	2.30410i	−0.505226	−	0.183887i	0.0768172	−	0.997045i	$-0.475524\pi$
$157$	−6.33046	−	2.30410i	−0.505226	−	0.183887i	−0.582043	+	0.813158i	$0.697746\pi$
$158$	−0.789848	−	2.17009i	−0.0628369	−	0.172643i
$159$		0			0
$160$			2.49299i			0.197089i
$161$	−5.29761	−	14.5551i	−0.417510	−	1.14710i
$162$		0			0
$163$	7.41814	+	12.8486i	0.581034	+	1.00638i	0.995357	+	0.0962505i	$0.0306850\pi$
$163$	7.41814	+	12.8486i	0.581034	+	1.00638i	−0.414323	+	0.910130i	$0.635982\pi$
$164$	2.05528	+	3.55985i	0.160491	+	0.277978i
$165$		0			0
$166$	−7.52784	+	20.6826i	−0.584273	+	1.60528i
$167$	−0.834702	+	4.73383i	−0.0645912	+	0.366315i	0.935330	+	0.353776i	$0.115102\pi$
$167$	−0.834702	+	4.73383i	−0.0645912	+	0.366315i	−0.999921	+	0.0125388i	$0.996009\pi$
$168$		0			0
$169$	−25.6256	+	21.5024i	−1.97120	+	1.65403i
$170$	−4.49269			−0.344574
$171$		0			0
$172$	−0.484702			−0.0369582
$173$	6.00586	−	5.03951i	0.456617	−	0.383147i	−0.385268	−	0.922805i	$-0.625891\pi$
$173$	6.00586	−	5.03951i	0.456617	−	0.383147i	0.841884	+	0.539658i	$0.181446\pi$
$174$		0			0
$175$	2.03501	−	11.5411i	0.153832	−	0.872426i
$176$	0.686127	−	1.88512i	0.0517188	−	0.142096i
$177$		0			0
$178$	7.39931	+	12.8160i	0.554602	+	0.960599i
$179$	0.189879	+	0.328881i	0.0141923	+	0.0245817i	0.873034	−	0.487659i	$-0.162149\pi$
$179$	0.189879	+	0.328881i	0.0141923	+	0.0245817i	−0.858842	+	0.512240i	$0.828816\pi$
$180$		0			0
$181$	−4.35197	−	11.9569i	−0.323479	−	0.888752i	−0.989720	−	0.143015i	$-0.954320\pi$
$181$	−4.35197	−	11.9569i	−0.323479	−	0.888752i	0.666241	−	0.745736i	$-0.267902\pi$
$182$			28.6715i			2.12527i
$183$		0			0
$184$	−4.23681	−	11.6406i	−0.312342	−	0.858153i
$185$	3.84658	+	1.40004i	0.282807	+	0.102933i
$186$		0			0
$187$	1.74926	+	0.636678i	0.127918	+	0.0465585i
$188$	1.20932	−	3.32259i	0.0881989	−	0.242325i
$189$		0			0
$190$	−3.57898	−	2.30282i	−0.259646	−	0.167064i
$191$	−16.9778	−	9.80211i	−1.22847	−	0.709256i	−0.261758	−	0.965134i	$-0.584302\pi$
$191$	−16.9778	−	9.80211i	−1.22847	−	0.709256i	−0.966709	+	0.255878i	$0.917636\pi$
$192$		0			0
$193$	0.0560858	+	0.0668404i	0.00403714	+	0.00481128i	0.768059	−	0.640379i	$-0.221223\pi$
$193$	0.0560858	+	0.0668404i	0.00403714	+	0.00481128i	−0.764022	+	0.645190i	$0.776778\pi$
$194$	6.03679	+	1.06445i	0.433416	+	0.0764230i
$195$		0			0
$196$	−0.411284	−	0.345108i	−0.0293774	−	0.0246506i
$197$	−12.6355	−	7.29511i	−0.900242	−	0.519755i	−0.0229632	−	0.999736i	$-0.507310\pi$
$197$	−12.6355	−	7.29511i	−0.900242	−	0.519755i	−0.877279	+	0.479981i	$0.840643\pi$
$198$		0			0
$199$	8.66420	−	3.15351i	0.614189	−	0.223547i	−0.0161461	−	0.999870i	$-0.505140\pi$
$199$	8.66420	−	3.15351i	0.614189	−	0.223547i	0.630335	+	0.776323i	$0.282917\pi$
$200$	1.62752	−	9.23012i	0.115083	−	0.652668i
$201$		0			0
$202$		−	14.8645i		−	1.04586i
$203$	3.59405	−	1.30813i	0.252253	−	0.0918125i
$204$		0			0
$205$	1.02945	+	2.82839i	0.0718998	+	0.197543i
$206$	0.456935	−	0.0805699i	0.0318362	−	0.00561357i
$207$		0			0
$208$			33.7976i			2.34344i
$209$	1.06716	+	1.40381i	0.0738167	+	0.0971036i
$210$		0			0
$211$	−6.98414	+	1.23149i	−0.480808	+	0.0847794i	−0.408799	−	0.912625i	$-0.634052\pi$
$211$	−6.98414	+	1.23149i	−0.480808	+	0.0847794i	−0.0720091	+	0.997404i	$0.522941\pi$
$212$	2.09697	−	1.75957i	0.144021	−	0.120848i
$213$		0			0
$214$	−1.73707	−	9.85142i	−0.118744	−	0.673429i
$215$	−0.349525	−	0.0616307i	−0.0238374	−	0.00420318i
$216$		0			0
$217$	−6.53405	+	3.77244i	−0.443560	+	0.256090i
$218$	−15.2802	−	2.69432i	−1.03491	−	0.182482i
$219$		0			0
$220$	−0.0941393	+	0.163054i	−0.00634687	+	0.0109931i
$221$	−31.3618			−2.10962
$222$		0			0
$223$	13.6087	−	2.39958i	0.911306	−	0.160688i	0.301710	−	0.953400i	$-0.402443\pi$
$223$	13.6087	−	2.39958i	0.911306	−	0.160688i	0.609596	+	0.792712i	$0.291332\pi$
$224$	8.22843	+	6.90448i	0.549785	+	0.461325i
$225$		0			0
$226$	−31.5693	−	11.4903i	−2.09996	−	0.764323i
$227$	−4.85622	+	8.41122i	−0.322319	+	0.558272i	−0.980966	−	0.194179i	$-0.937796\pi$
$227$	−4.85622	+	8.41122i	−0.322319	+	0.558272i	0.658647	+	0.752452i	$0.271129\pi$
$228$		0			0
$229$	1.12422	+	1.94720i	0.0742903	+	0.128675i	0.900777	−	0.434281i	$-0.142998\pi$
$229$	1.12422	+	1.94720i	0.0742903	+	0.128675i	−0.826487	+	0.562956i	$0.809664\pi$
$230$	1.04405	+	5.92111i	0.0688427	+	0.390426i
$231$		0			0
$232$	2.87437	−	1.04619i	0.188712	−	0.0686855i
$233$	18.5722	+	22.1335i	1.21671	+	1.45002i	0.855715	+	0.517447i	$0.173118\pi$
$233$	18.5722	+	22.1335i	1.21671	+	1.45002i	0.360992	+	0.932569i	$0.382438\pi$
$234$		0			0
$235$	1.29453	−	2.24219i	0.0844459	−	0.146265i
$236$	6.04161			0.393275
$237$		0			0
$238$	−12.4427	+	14.8287i	−0.806543	+	0.961200i
$239$	8.75151	+	5.05269i	0.566088	+	0.326831i	0.755585	−	0.655050i	$-0.227353\pi$
$239$	8.75151	+	5.05269i	0.566088	+	0.326831i	−0.189497	+	0.981881i	$0.560686\pi$
$240$		0			0
$241$	−4.27935	+	5.09993i	−0.275657	+	0.328516i	−0.886056	−	0.463579i	$-0.846565\pi$
$241$	−4.27935	+	5.09993i	−0.275657	+	0.328516i	0.610398	+	0.792095i	$0.291009\pi$
$242$	−13.8836	+	11.6497i	−0.892471	+	0.748872i
$243$		0			0
$244$	1.58451	+	8.98618i	0.101438	+	0.575281i
$245$	−0.252701	−	0.301158i	−0.0161445	−	0.0192403i
$246$		0			0
$247$	−24.9835	−	16.0751i	−1.58966	−	1.02284i
$248$	−5.22567	+	3.01704i	−0.331830	+	0.191582i
$249$		0			0
$250$	−3.22553	+	8.86206i	−0.204000	+	0.560486i
$251$	−12.9843	+	15.4741i	−0.819561	+	0.976714i	−0.999976	−	0.00687624i	$-0.997811\pi$
$251$	−12.9843	+	15.4741i	−0.819561	+	0.976714i	0.180416	+	0.983590i	$0.442256\pi$
$252$		0			0
$253$	0.432597	−	2.45338i	0.0271971	−	0.154243i
$254$	−21.8390	+	12.6088i	−1.37030	+	0.791145i
$255$		0			0
$256$	12.6378	+	10.6044i	0.789861	+	0.662772i
$257$	12.8250	+	10.7615i	0.800004	+	0.671283i	0.948200	−	0.317675i	$-0.102902\pi$
$257$	12.8250	+	10.7615i	0.800004	+	0.671283i	−0.148196	+	0.988958i	$0.547346\pi$
$258$		0			0
$259$	15.2743	−	8.81863i	0.949100	−	0.547963i
$260$	0.550813	−	3.12381i	0.0341600	−	0.193731i
$261$		0			0
$262$	9.06726	−	10.8059i	0.560177	−	0.667593i
$263$	−0.131317	+	0.360791i	−0.00809736	+	0.0222473i	−0.943675	−	0.330873i	$-0.892657\pi$
$263$	−0.131317	+	0.360791i	−0.00809736	+	0.0222473i	0.935578	+	0.353120i	$0.114879\pi$
$264$		0			0
$265$	1.73589	−	1.00222i	0.106635	−	0.0615656i
$266$	−17.5129	+	5.43506i	−1.07378	+	0.333245i
$267$		0			0
$268$	−1.22847	−	1.46404i	−0.0750410	−	0.0894304i
$269$	−5.48235	−	31.0919i	−0.334265	−	1.89571i	−0.434375	−	0.900732i	$-0.643031\pi$
$269$	−5.48235	−	31.0919i	−0.334265	−	1.89571i	0.100110	−	0.994976i	$-0.468080\pi$
$270$		0			0
$271$	−7.01972	+	5.89025i	−0.426418	+	0.357807i	−0.830598	−	0.556872i	$-0.812001\pi$
$271$	−7.01972	+	5.89025i	−0.426418	+	0.357807i	0.404180	+	0.914679i	$0.367557\pi$
$272$	−14.6673	+	17.4799i	−0.889338	+	1.05987i
$273$		0			0
$274$	22.5790	+	13.0360i	1.36405	+	0.787532i
$275$	1.21157	−	1.44389i	0.0730604	−	0.0870700i
$276$		0			0
$277$	12.7744			0.767542			0.383771	−	0.923428i	$-0.374625\pi$
$277$	12.7744			0.767542			0.383771	+	0.923428i	$0.374625\pi$
$278$	−4.70433	+	8.14814i	−0.282147	+	0.488693i
$279$		0			0
$280$	1.89861	+	2.26268i	0.113464	+	0.135221i
$281$	2.26386	−	0.823978i	0.135051	−	0.0491544i	−0.273611	−	0.961841i	$-0.588218\pi$
$281$	2.26386	−	0.823978i	0.135051	−	0.0491544i	0.408661	+	0.912686i	$0.365996\pi$
$282$		0			0
$283$	−4.81731	−	27.3203i	−0.286359	−	1.62402i	−0.700390	−	0.713761i	$-0.746990\pi$
$283$	−4.81731	−	27.3203i	−0.286359	−	1.62402i	0.414030	−	0.910263i	$-0.364121\pi$
$284$	2.65864	+	4.60491i	0.157761	+	0.273251i
$285$		0			0
$286$	−2.30571	+	3.99361i	−0.136340	+	0.236147i
$287$	12.1865	+	4.43554i	0.719349	+	0.261822i
$288$		0			0
$289$	−3.19732	−	2.68287i	−0.188078	−	0.157816i
$290$	−1.46209	+	0.257805i	−0.0858566	+	0.0151388i
$291$		0			0
$292$	−10.7736			−0.630475
$293$	−15.6142	+	27.0446i	−0.912193	+	1.57996i	−0.101233	+	0.994863i	$0.532279\pi$
$293$	−15.6142	+	27.0446i	−0.912193	+	1.57996i	−0.810960	+	0.585101i	$0.801055\pi$
$294$		0			0
$295$	4.35669	+	0.768201i	0.253656	+	0.0447264i
$296$	12.2158	−	7.05278i	0.710028	−	0.409935i
$297$		0			0
$298$	33.3975	+	5.88888i	1.93466	+	0.341133i
$299$	7.28813	+	41.3330i	0.421483	+	2.39035i
$300$		0			0
$301$	−1.17145	+	0.982961i	−0.0675211	+	0.0566569i
$302$	1.46950	−	0.259112i	0.0845602	−	0.0149102i
$303$		0			0
$304$	−20.6440	+	6.40679i	−1.18401	+	0.367454i
$305$			6.68152i			0.382583i
$306$		0			0
$307$	−11.1605	+	1.96789i	−0.636961	+	0.112313i	−0.482798	−	0.875732i	$-0.660379\pi$
$307$	−11.1605	+	1.96789i	−0.636961	+	0.112313i	−0.154164	+	0.988045i	$0.549268\pi$
$308$	0.277456	+	0.762305i	0.0158095	+	0.0434363i
$309$		0			0
$310$	2.75208	−	1.00168i	0.156308	−	0.0568913i
$311$		−	24.3216i		−	1.37915i	−0.724214	−	0.689576i	$-0.757797\pi$
$311$		−	24.3216i		−	1.37915i	0.724214	−	0.689576i	$-0.242203\pi$
$312$		0			0
$313$	−2.25649	+	12.7972i	−0.127545	+	0.723341i	0.852219	+	0.523185i	$0.175256\pi$
$313$	−2.25649	+	12.7972i	−0.127545	+	0.723341i	−0.979764	+	0.200157i	$0.935855\pi$
$314$	10.5877	−	3.85360i	0.597497	−	0.217471i
$315$		0			0
$316$	0.953339	+	0.550411i	0.0536295	+	0.0309630i
$317$	−2.68688	−	2.25456i	−0.150910	−	0.126629i	0.564207	−	0.825634i	$-0.309182\pi$
$317$	−2.68688	−	2.25456i	−0.150910	−	0.126629i	−0.715117	+	0.699005i	$0.753627\pi$
$318$		0			0
$319$	0.605807	+	0.106820i	0.0339187	+	0.00598078i
$320$	1.04143	+	1.24113i	0.0582179	+	0.0693814i
$321$		0			0
$322$	22.4349	+	12.9528i	1.25025	+	0.721831i
$323$	−5.94505	−	19.1562i	−0.330791	−	1.06588i
$324$		0			0
$325$	−10.8609	+	29.8401i	−0.602454	+	1.65523i
$326$	−23.3172	−	8.48676i	−1.29142	−	0.470038i
$327$		0			0
$328$	9.74631	+	3.54737i	0.538150	+	0.195871i
$329$	−3.81536	−	10.4826i	−0.210348	−	0.577926i
$330$		0			0
$331$		−	14.5165i		−	0.797901i	−0.916973	−	0.398950i	$-0.869375\pi$
$331$		−	14.5165i		−	0.797901i	0.916973	−	0.398950i	$-0.130625\pi$
$332$	−3.58835	−	9.85892i	−0.196937	−	0.541079i
$333$		0			0
$334$	−4.01972	−	6.96236i	−0.219949	−	0.380964i
$335$	−0.699714	−	1.21194i	−0.0382295	−	0.0662154i
$336$		0			0
$337$	−3.62311	+	9.95441i	−0.197363	+	0.542251i	−0.998411	−	0.0563492i	$-0.982054\pi$
$337$	−3.62311	+	9.95441i	−0.197363	+	0.542251i	0.801048	+	0.598600i	$0.204276\pi$
$338$	9.71528	−	55.0981i	0.528441	−	2.99694i
$339$		0			0
$340$	1.64054	−	1.37657i	0.0889705	−	0.0746551i
$341$	−1.21349			−0.0657143
$342$		0			0
$343$	−19.3007			−1.04214
$344$	−0.936876	+	0.786133i	−0.0505130	+	0.0423854i
$345$		0			0
$346$	−2.27696	+	12.9133i	−0.122410	+	0.694224i
$347$	12.5772	−	34.5556i	0.675179	−	1.85504i	0.186826	−	0.982393i	$-0.440180\pi$
$347$	12.5772	−	34.5556i	0.675179	−	1.85504i	0.488353	−	0.872646i	$-0.337598\pi$
$348$		0			0
$349$	−10.4080	−	18.0272i	−0.557129	−	0.964976i	−0.997734	−	0.0672748i	$-0.978570\pi$
$349$	−10.4080	−	18.0272i	−0.557129	−	0.964976i	0.440606	−	0.897701i	$-0.354764\pi$
$350$	9.80012	+	16.9743i	0.523838	+	0.907315i
$351$		0			0
$352$	0.590881	+	1.62343i	0.0314940	+	0.0865292i
$353$		−	0.532095i		−	0.0283205i	−0.999900	−	0.0141603i	$-0.995492\pi$
$353$		−	0.532095i		−	0.0283205i	0.999900	−	0.0141603i	$-0.00450751\pi$
$354$		0			0
$355$	1.33166	+	3.65871i	0.0706772	+	0.194184i
$356$	−6.62876	−	2.41267i	−0.351324	−	0.127871i
$357$		0			0
$358$	−0.596841	−	0.217232i	−0.0315440	−	0.0114811i
$359$	9.26844	−	25.4648i	0.489170	−	1.34398i	−0.412264	−	0.911064i	$-0.635262\pi$
$359$	9.26844	−	25.4648i	0.489170	−	1.34398i	0.901433	−	0.432918i	$-0.142516\pi$
$360$		0			0
$361$	5.08294	−	18.3075i	0.267523	−	0.963551i
$362$	18.4302	+	10.6407i	0.968669	+	0.559261i
$363$		0			0
$364$	−8.78502	−	10.4696i	−0.460460	−	0.548755i
$365$	−7.76895	−	1.36988i	−0.406646	−	0.0717026i
$366$		0			0
$367$	−17.6986	−	14.8509i	−0.923857	−	0.775208i	0.0508471	−	0.998706i	$-0.483808\pi$
$367$	−17.6986	−	14.8509i	−0.923857	−	0.775208i	−0.974704	+	0.223498i	$0.928252\pi$
$368$	26.4460	+	15.2686i	1.37859	+	0.795930i
$369$		0			0
$370$	−6.43340	+	2.34156i	−0.334456	+	0.121732i
$371$	1.49970	−	8.50519i	0.0778603	−	0.441568i
$372$		0			0
$373$			25.0670i			1.29792i	0.760823	+	0.648959i	$0.224795\pi$
$373$			25.0670i			1.29792i	−0.760823	+	0.648959i	$0.775205\pi$
$374$	−2.92563	+	1.06484i	−0.151281	+	0.0550616i
$375$		0			0
$376$	−3.05137	−	8.38358i	−0.157363	−	0.432350i
$377$	−10.2063	+	1.79964i	−0.525650	+	0.0926862i
$378$		0			0
$379$			19.7225i			1.01308i	0.862217	+	0.506538i	$0.169075\pi$
$379$			19.7225i			1.01308i	−0.862217	+	0.506538i	$0.830925\pi$
$380$	2.01248	−	0.255718i	0.103238	−	0.0131180i
$381$		0			0
$382$	32.2898	−	5.69357i	1.65209	−	0.291308i
$383$	16.3804	−	13.7448i	0.836999	−	0.702325i	−0.119888	−	0.992787i	$-0.538253\pi$
$383$	16.3804	−	13.7448i	0.836999	−	0.702325i	0.956887	+	0.290462i	$0.0938090\pi$
$384$		0			0
$385$	0.103149	+	0.584987i	0.00525696	+	0.0298137i
$386$	−0.143715	−	0.0253408i	−0.00731489	−	0.00128981i
$387$		0			0
$388$	−2.53052	+	1.46100i	−0.128468	+	0.0741710i
$389$	25.6112	+	4.51595i	1.29854	+	0.228968i	0.779835	−	0.625985i	$-0.215303\pi$
$389$	25.6112	+	4.51595i	1.29854	+	0.228968i	0.518706	+	0.854953i	$0.326414\pi$
$390$		0			0
$391$	−14.1682	+	24.5400i	−0.716515	+	1.24104i
$392$	−1.35469			−0.0684224
$393$		0			0
$394$	24.0313	−	4.23738i	1.21068	−	0.213476i
$395$	0.617480	+	0.518127i	0.0310688	+	0.0260698i
$396$		0			0
$397$	2.93642	+	1.06877i	0.147375	+	0.0536400i	0.414654	−	0.909979i	$-0.363903\pi$
$397$	2.93642	+	1.06877i	0.147375	+	0.0536400i	−0.267280	+	0.963619i	$0.586125\pi$
$398$	−7.71042	+	13.3548i	−0.386488	+	0.669417i
$399$		0			0
$400$	11.5523	+	20.0091i	0.577613	+	1.00045i
$401$	1.57136	+	8.91162i	0.0784700	+	0.445025i	0.998576	+	0.0533550i	$0.0169915\pi$
$401$	1.57136	+	8.91162i	0.0784700	+	0.445025i	−0.920106	+	0.391670i	$0.871897\pi$
$402$		0			0
$403$	19.2112	−	6.99232i	0.956980	−	0.348312i
$404$	4.55452	+	5.42787i	0.226596	+	0.270046i
$405$		0			0
$406$	−3.19840	+	5.53980i	−0.158734	+	0.274935i
$407$	2.83672			0.140611
$408$		0			0
$409$	24.5093	−	29.2091i	1.21191	−	1.44430i	0.350366	−	0.936613i	$-0.386057\pi$
$409$	24.5093	−	29.2091i	1.21191	−	1.44430i	0.861543	−	0.507684i	$-0.169498\pi$
$410$	−4.35962	−	2.51703i	−0.215306	−	0.124307i
$411$		0			0
$412$	−0.142166	+	0.169427i	−0.00700401	+	0.00834705i
$413$	14.6016	−	12.2522i	0.718498	−	0.602891i
$414$		0			0
$415$	−1.33403	−	7.56566i	−0.0654850	−	0.371384i
$416$	−18.7089	−	22.2964i	−0.917279	−	1.09317i
$417$		0			0
$418$	−2.87643	−	0.651315i	−0.140691	−	0.0318569i
$419$	10.2452	−	5.91508i	0.500512	−	0.288971i	−0.228413	−	0.973564i	$-0.573354\pi$
$419$	10.2452	−	5.91508i	0.500512	−	0.288971i	0.728925	+	0.684594i	$0.240020\pi$
$420$		0			0
$421$	−1.20018	+	3.29748i	−0.0584934	+	0.160709i	−0.965497	−	0.260413i	$-0.916141\pi$
$421$	−1.20018	+	3.29748i	−0.0584934	+	0.160709i	0.907004	+	0.421122i	$0.138364\pi$
$422$	7.62419	−	9.08616i	0.371140	−	0.442307i
$423$		0			0
$424$	1.19940	−	6.80211i	0.0582478	−	0.330340i
$425$	−18.5670	+	10.7197i	−0.900634	+	0.519981i
$426$		0			0
$427$	22.0532	+	18.5048i	1.06723	+	0.895511i
$428$	3.65280	+	3.06507i	0.176565	+	0.148156i
$429$		0			0
$430$	0.514071	−	0.296799i	0.0247907	−	0.0143129i
$431$	−0.452949	+	2.56880i	−0.0218178	+	0.123735i	−0.993771	−	0.111438i	$-0.964454\pi$
$431$	−0.452949	+	2.56880i	−0.0218178	+	0.123735i	0.971954	+	0.235173i	$0.0755655\pi$
$432$		0			0
$433$	3.13200	−	3.73257i	0.150514	−	0.179376i	−0.685519	−	0.728055i	$-0.740425\pi$
$433$	3.13200	−	3.73257i	0.150514	−	0.179376i	0.836033	+	0.548679i	$0.184869\pi$
$434$	4.31587	−	11.8578i	0.207169	−	0.569191i
$435$		0			0
$436$	6.40523	−	3.69806i	0.306755	−	0.177105i
$437$	−23.8652	+	12.2869i	−1.14163	+	0.587763i
$438$		0			0
$439$	−10.5687	−	12.5953i	−0.504418	−	0.601142i	0.452405	−	0.891813i	$-0.350566\pi$
$439$	−10.5687	−	12.5953i	−0.504418	−	0.601142i	−0.956823	+	0.290670i	$0.906122\pi$
$440$	0.0824944	+	0.467849i	0.00393276	+	0.0223038i
$441$		0			0
$442$	40.1809	−	33.7158i	1.91121	−	1.60370i
$443$	10.5311	−	12.5505i	0.500349	−	0.596293i	−0.455469	−	0.890252i	$-0.650528\pi$
$443$	10.5311	−	12.5505i	0.500349	−	0.596293i	0.955818	+	0.293959i	$0.0949729\pi$
$444$		0			0
$445$	−4.47331	−	2.58267i	−0.212055	−	0.122430i
$446$	−14.8559	+	17.7045i	−0.703445	+	0.838334i
$447$		0			0
$448$	6.98081			0.329812
$449$	−12.6656	+	21.9375i	−0.597728	+	1.03529i	0.395428	+	0.918497i	$0.370596\pi$
$449$	−12.6656	+	21.9375i	−0.597728	+	1.03529i	−0.993156	+	0.116798i	$0.962737\pi$
$450$		0			0
$451$	1.34075	+	1.59784i	0.0631334	+	0.0752394i
$452$	15.0484	−	5.47717i	0.707817	−	0.257625i
$453$		0			0
$454$	−2.82074	−	15.9972i	−0.132384	−	0.750787i
$455$	−5.00377	−	8.66679i	−0.234580	−	0.406305i
$456$		0			0
$457$	10.8524	−	18.7969i	0.507654	−	0.879282i	−0.492307	−	0.870422i	$-0.663846\pi$
$457$	10.8524	−	18.7969i	0.507654	−	0.879282i	0.999961	−	0.00886020i	$-0.00282033\pi$
$458$	−3.53371	−	1.28616i	−0.165119	−	0.0600985i
$459$		0			0
$460$	−2.19549	−	1.84223i	−0.102365	−	0.0858945i
$461$	22.9177	−	4.04101i	1.06738	−	0.188208i	0.387753	−	0.921763i	$-0.373251\pi$
$461$	22.9177	−	4.04101i	1.06738	−	0.188208i	0.679630	+	0.733555i	$0.262140\pi$
$462$		0			0
$463$	25.0104			1.16233			0.581165	−	0.813785i	$-0.302597\pi$
$463$	25.0104			1.16233			0.581165	+	0.813785i	$0.302597\pi$
$464$	−3.77024	+	6.53024i	−0.175029	+	0.303159i
$465$		0			0
$466$	−47.5897	−	8.39135i	−2.20455	−	0.388722i
$467$	−13.6784	+	7.89724i	−0.632961	+	0.365440i	−0.781898	−	0.623406i	$-0.785748\pi$
$467$	−13.6784	+	7.89724i	−0.632961	+	0.365440i	0.148937	+	0.988847i	$0.452415\pi$
$468$		0			0
$469$	−5.93805	−	1.04704i	−0.274194	−	0.0483477i
$470$	0.751930	+	4.26441i	0.0346840	+	0.196703i
$471$		0			0
$472$	11.6778	−	9.79881i	0.537513	−	0.451027i
$473$	−0.242217	+	0.0427094i	−0.0111372	+	0.00196378i
$474$		0			0
$475$	−20.2855	−	0.977385i	−0.930763	−	0.0448455i
$476$		−	9.22728i		−	0.422931i
$477$		0			0
$478$	−16.6444	+	2.93486i	−0.761298	+	0.134237i
$479$	−8.78811	−	24.1451i	−0.401539	−	1.10322i	−0.961525	−	0.274717i	$-0.911416\pi$
$479$	−8.78811	−	24.1451i	−0.401539	−	1.10322i	0.559986	−	0.828502i	$-0.310806\pi$
$480$		0			0
$481$	−44.9091	+	16.3456i	−2.04768	+	0.745295i
$482$		−	11.1346i		−	0.507168i
$483$		0			0
$484$	1.50018	−	8.50794i	0.0681900	−	0.386724i
$485$	−2.01056	+	0.731785i	−0.0912949	+	0.0332286i
$486$		0			0
$487$	−17.2791	−	9.97610i	−0.782991	−	0.452060i	0.0544981	−	0.998514i	$-0.482644\pi$
$487$	−17.2791	−	9.97610i	−0.782991	−	0.452060i	−0.837489	+	0.546454i	$0.815977\pi$
$488$	17.6372	+	14.7994i	0.798400	+	0.669938i
$489$		0			0
$490$	0.647525	+	0.114176i	0.0292522	+	0.00515795i
$491$	27.0303	+	32.2134i	1.21986	+	1.45377i	0.851716	+	0.524003i	$0.175562\pi$
$491$	27.0303	+	32.2134i	1.21986	+	1.45377i	0.368143	+	0.929769i	$0.379994\pi$
$492$		0			0
$493$	−6.05961	−	3.49851i	−0.272911	−	0.157565i
$494$	49.2907	−	6.26318i	2.21769	−	0.281794i
$495$		0			0
$496$	5.08750	−	13.9778i	0.228435	−	0.627621i
$497$	15.7641	+	5.73767i	0.707117	+	0.257370i
$498$		0			0
$499$	−5.31693	−	1.93520i	−0.238018	−	0.0866316i	0.220257	−	0.975442i	$-0.429310\pi$
$499$	−5.31693	−	1.93520i	−0.238018	−	0.0866316i	−0.458275	+	0.888810i	$0.651533\pi$
$500$	−1.53754	−	4.22435i	−0.0687608	−	0.188919i
$501$		0			0
$502$		−	33.7843i		−	1.50787i
$503$	1.26270	+	3.46923i	0.0563009	+	0.154685i	0.964655	−	0.263517i	$-0.0848825\pi$
$503$	1.26270	+	3.46923i	0.0563009	+	0.154685i	−0.908354	+	0.418202i	$0.862660\pi$
$504$		0			0
$505$	2.59416	+	4.49322i	0.115439	+	0.199946i
$506$	2.08328	+	3.60835i	0.0926132	+	0.160411i
$507$		0			0
$508$	4.11131	−	11.2957i	0.182410	−	0.501167i
$509$	−0.901032	+	5.11001i	−0.0399376	+	0.226497i	−0.998243	−	0.0592476i	$-0.981130\pi$
$509$	−0.901032	+	5.11001i	−0.0399376	+	0.226497i	0.958306	+	0.285745i	$0.0922410\pi$
$510$		0			0
$511$	−26.0380	+	21.8484i	−1.15185	+	0.966518i
$512$	−1.22629			−0.0541947
$513$		0			0
$514$	−28.0008			−1.23506
$515$	−0.124061	+	0.104099i	−0.00546676	+	0.00458716i
$516$		0			0
$517$	0.311558	−	1.76693i	0.0137023	−	0.0777097i
$518$	−10.0890	+	27.7193i	−0.443285	+	1.21792i
$519$		0			0
$520$	−4.00181	−	6.93134i	−0.175491	−	0.303960i
$521$	−18.4067	−	31.8814i	−0.806413	−	1.39675i	−0.915333	−	0.402698i	$-0.868072\pi$
$521$	−18.4067	−	31.8814i	−0.806413	−	1.39675i	0.108919	−	0.994051i	$-0.465261\pi$
$522$		0			0
$523$	−2.82677	−	7.76649i	−0.123606	−	0.339605i	0.862421	−	0.506192i	$-0.168947\pi$
$523$	−2.82677	−	7.76649i	−0.123606	−	0.339605i	−0.986027	+	0.166587i	$0.946725\pi$
$524$			6.72409i			0.293743i
$525$		0			0
$526$	−0.219627	−	0.603421i	−0.00957621	−	0.0263104i
$527$	12.9704	+	4.72084i	0.565000	+	0.205643i
$528$		0			0
$529$	14.0219	+	5.10356i	0.609648	+	0.221894i
$530$	−1.14659	+	3.15023i	−0.0498046	+	0.136837i
$531$		0			0
$532$	4.72963	−	7.35065i	0.205056	−	0.318691i
$533$	−30.4329	−	17.5704i	−1.31819	−	0.761060i
$534$		0			0
$535$	2.24436	+	2.67472i	0.0970320	+	0.115638i
$536$	−4.74901	−	0.837379i	−0.205126	−	0.0361693i
$537$		0			0
$538$	40.4497	+	33.9413i	1.74391	+	1.46331i
$539$	−0.235938	−	0.136219i	−0.0101626	−	0.00586735i
$540$		0			0
$541$	−10.7032	+	3.89566i	−0.460168	+	0.167487i	−0.561693	−	0.827346i	$-0.689850\pi$
$541$	−10.7032	+	3.89566i	−0.460168	+	0.167487i	0.101526	+	0.994833i	$0.467628\pi$
$542$	2.66135	−	15.0932i	0.114315	−	0.648310i
$543$		0			0
$544$		−	19.6507i		−	0.842518i
$545$	5.08911	−	1.85228i	0.217993	−	0.0793431i
$546$		0			0
$547$	0.617530	+	1.69665i	0.0264037	+	0.0725435i	0.952194	−	0.305493i	$-0.0988214\pi$
$547$	0.617530	+	1.69665i	0.0264037	+	0.0725435i	−0.925790	+	0.378037i	$0.876599\pi$
$548$	−12.2391	+	2.15809i	−0.522829	+	0.0921889i
$549$		0			0
$550$			3.15244i			0.134420i
$551$	−3.03398	−	5.89297i	−0.129252	−	0.251049i
$552$		0			0
$553$	3.42028	−	0.603088i	0.145445	−	0.0256459i
$554$	−16.3667	+	13.7333i	−0.695354	+	0.583471i
$555$		0			0
$556$	−0.778795	−	4.41677i	−0.0330283	−	0.187313i
$557$	2.75569	+	0.485903i	0.116763	+	0.0205884i	0.231724	−	0.972782i	$-0.425563\pi$
$557$	2.75569	+	0.485903i	0.116763	+	0.0205884i	−0.114962	+	0.993370i	$0.536674\pi$
$558$		0			0
$559$	3.58853	−	2.07184i	0.151779	−	0.0876296i
$560$	−7.17070	−	1.26439i	−0.303018	−	0.0534302i
$561$		0			0
$562$	−2.01465	+	3.48947i	−0.0849828	+	0.147195i
$563$	36.2091			1.52603			0.763017	−	0.646379i	$-0.223717\pi$
$563$	36.2091			1.52603			0.763017	+	0.646379i	$0.223717\pi$
$564$		0			0
$565$	11.5480	−	2.03623i	0.485829	−	0.0856648i
$566$	35.5429	+	29.8241i	1.49398	+	1.25360i
$567$		0			0
$568$	12.6075	+	4.58876i	0.528999	+	0.192540i
$569$	−7.47528	+	12.9476i	−0.313380	+	0.542790i	−0.979092	−	0.203419i	$-0.934795\pi$
$569$	−7.47528	+	12.9476i	−0.313380	+	0.542790i	0.665712	+	0.746209i	$0.268128\pi$
$570$		0			0
$571$	−7.37174	−	12.7682i	−0.308498	−	0.534334i	0.669536	−	0.742779i	$-0.266493\pi$
$571$	−7.37174	−	12.7682i	−0.308498	−	0.534334i	−0.978034	+	0.208446i	$0.933160\pi$
$572$	−0.381707	−	2.16477i	−0.0159600	−	0.0905136i
$573$		0			0
$574$	−20.3820	+	7.41842i	−0.850726	+	0.309639i
$575$	18.4427	+	21.9792i	0.769114	+	0.916594i
$576$		0			0
$577$	−18.2291	+	31.5737i	−0.758886	+	1.31443i	0.184533	+	0.982826i	$0.440923\pi$
$577$	−18.2291	+	31.5737i	−0.758886	+	1.31443i	−0.943419	+	0.331603i	$0.892411\pi$
$578$	6.98067			0.290358
$579$		0			0
$580$	0.454898	−	0.542126i	0.0188886	−	0.0225106i
$581$	−28.6661	−	16.5504i	−1.18927	−	0.686625i
$582$		0			0
$583$	0.892863	−	1.06407i	0.0369786	−	0.0440694i
$584$	−20.8241	+	17.4735i	−0.861707	+	0.723058i
$585$		0			0
$586$	−9.06955	−	51.4360i	−0.374660	−	2.12480i
$587$	1.91259	+	2.27934i	0.0789410	+	0.0940782i	0.804069	−	0.594535i	$-0.202664\pi$
$587$	1.91259	+	2.27934i	0.0789410	+	0.0940782i	−0.725128	+	0.688614i	$0.758220\pi$
$588$		0			0
$589$	7.91274	+	10.4090i	0.326039	+	0.428894i
$590$	−6.40767	+	3.69947i	−0.263800	+	0.152305i
$591$		0			0
$592$	−11.8928	+	32.6751i	−0.488790	+	1.34294i
$593$	−1.72884	+	2.06035i	−0.0709948	+	0.0846083i	−0.800373	−	0.599503i	$-0.795365\pi$
$593$	−1.72884	+	2.06035i	−0.0709948	+	0.0846083i	0.729378	+	0.684111i	$0.239810\pi$
$594$		0			0
$595$	1.17326	−	6.65391i	0.0480991	−	0.272784i
$596$	−13.9997	+	8.08272i	−0.573449	+	0.331081i
$597$		0			0
$598$	−53.7731	−	45.1210i	−2.19894	−	1.84513i
$599$	−18.1064	−	15.1931i	−0.739809	−	0.620773i	0.192978	−	0.981203i	$-0.438186\pi$
$599$	−18.1064	−	15.1931i	−0.739809	−	0.620773i	−0.932786	+	0.360430i	$0.882630\pi$
$600$		0			0
$601$	−13.4725	+	7.77837i	−0.549556	+	0.317286i	−0.748943	−	0.662634i	$-0.769438\pi$
$601$	−13.4725	+	7.77837i	−0.549556	+	0.317286i	0.199387	+	0.979921i	$0.436105\pi$
$602$	0.444124	−	2.51875i	0.0181011	−	0.102657i
$603$		0			0
$604$	−0.457205	+	0.544875i	−0.0186034	+	0.0221707i
$605$	2.16360	−	5.94444i	0.0879627	−	0.241676i
$606$		0			0
$607$	−4.10356	+	2.36919i	−0.166558	+	0.0961626i	−0.580962	−	0.813931i	$-0.697324\pi$
$607$	−4.10356	+	2.36919i	−0.166558	+	0.0961626i	0.414404	+	0.910093i	$0.363990\pi$
$608$	10.0724	−	15.6542i	0.408489	−	0.634862i
$609$		0			0
$610$	−7.18304	−	8.56041i	−0.290833	−	0.346601i
$611$	5.24894	+	29.7682i	0.212350	+	1.20429i
$612$		0			0
$613$	29.7951	−	25.0010i	1.20341	−	1.00978i	0.203885	−	0.978995i	$-0.434643\pi$
$613$	29.7951	−	25.0010i	1.20341	−	1.00978i	0.999526	−	0.0307869i	$-0.00980132\pi$
$614$	12.1833	−	14.5194i	0.491676	−	0.585957i
$615$		0			0
$616$	1.77266	+	1.02345i	0.0714227	+	0.0412359i
$617$	−4.98288	+	5.93837i	−0.200603	+	0.239070i	−0.856962	−	0.515379i	$-0.827651\pi$
$617$	−4.98288	+	5.93837i	−0.200603	+	0.239070i	0.656359	+	0.754449i	$0.272096\pi$
$618$		0			0
$619$	26.3144			1.05767			0.528833	−	0.848726i	$-0.322630\pi$
$619$	26.3144			1.05767			0.528833	+	0.848726i	$0.322630\pi$
$620$	−0.698024	+	1.20901i	−0.0280333	+	0.0485551i
$621$		0			0
$622$	26.1472	+	31.1610i	1.04841	+	1.24944i
$623$	−20.9135	+	7.61188i	−0.837880	+	0.304963i
$624$		0			0
$625$	3.47371	+	19.7004i	0.138949	+	0.788016i
$626$	−10.8667	−	18.8217i	−0.434322	−	0.752268i
$627$		0			0
$628$	−2.68540	+	4.65126i	−0.107159	+	0.185605i
$629$	−30.3202	−	11.0357i	−1.20895	−	0.440021i
$630$		0			0
$631$	−4.47423	−	3.75433i	−0.178116	−	0.149457i	0.549371	−	0.835579i	$-0.314867\pi$
$631$	−4.47423	−	3.75433i	−0.178116	−	0.149457i	−0.727487	+	0.686121i	$0.759312\pi$
$632$	2.73540	−	0.482326i	0.108809	−	0.0191859i
$633$		0			0
$634$	5.86624			0.232978
$635$	4.40099	−	7.62273i	0.174648	−	0.302499i
$636$		0			0
$637$	4.52013	+	0.797021i	0.179094	+	0.0315791i
$638$	−0.891002	+	0.514420i	−0.0352751	+	0.0203661i
$639$		0			0
$640$	−7.57882	−	1.33635i	−0.299579	−	0.0528239i
$641$	−0.555772	−	3.15194i	−0.0219517	−	0.124494i	0.971863	−	0.235548i	$-0.0756885\pi$
$641$	−0.555772	−	3.15194i	−0.0219517	−	0.124494i	−0.993814	+	0.111054i	$0.964577\pi$
$642$		0			0
$643$	−30.3291	+	25.4492i	−1.19606	+	1.00362i	−0.196331	+	0.980538i	$0.562903\pi$
$643$	−30.3291	+	25.4492i	−1.19606	+	1.00362i	−0.999734	+	0.0230796i	$0.992653\pi$
$644$	−12.1610	+	2.14432i	−0.479211	+	0.0844979i
$645$		0			0
$646$	28.2109	+	18.1517i	1.10994	+	0.714170i
$647$		−	27.5631i		−	1.08362i	−0.840502	−	0.541808i	$-0.817740\pi$
$647$		−	27.5631i		−	1.08362i	0.840502	−	0.541808i	$-0.182260\pi$
$648$		0			0
$649$	3.01914	−	0.532355i	0.118512	−	0.0208968i
$650$	−18.1648	−	49.9074i	−0.712482	−	1.95753i
$651$		0			0
$652$	11.1148	−	4.04545i	0.435289	−	0.158432i
$653$			13.3174i			0.521149i	0.965454	+	0.260574i	$0.0839119\pi$
$653$			13.3174i			0.521149i	−0.965454	+	0.260574i	$0.916088\pi$
$654$		0			0
$655$	−0.854980	+	4.84883i	−0.0334068	+	0.189460i
$656$	−24.0260	+	8.74475i	−0.938057	+	0.341425i
$657$		0			0
$658$	16.1577	+	9.32866i	0.629893	+	0.363669i
$659$	8.52225	+	7.15102i	0.331980	+	0.278564i	0.793506	−	0.608562i	$-0.208254\pi$
$659$	8.52225	+	7.15102i	0.331980	+	0.278564i	−0.461526	+	0.887127i	$0.652698\pi$
$660$		0			0
$661$	2.27762	+	0.401606i	0.0885892	+	0.0156207i	0.217767	−	0.976001i	$-0.430123\pi$
$661$	2.27762	+	0.401606i	0.0885892	+	0.0156207i	−0.129178	+	0.991621i	$0.541234\pi$
$662$	15.6061	+	18.5987i	0.606550	+	0.722858i
$663$		0			0
$664$	−22.9260	−	13.2363i	−0.889700	−	0.513668i
$665$	4.34525	−	4.69927i	0.168501	−	0.182230i
$666$		0			0
$667$	−3.20266	+	8.79923i	−0.124007	+	0.340707i
$668$	3.60112	+	1.31070i	0.139331	+	0.0507125i
$669$		0			0
$670$	2.19939	+	0.800511i	0.0849697	+	0.0309264i
$671$	1.58363	+	4.35099i	0.0611354	+	0.167968i
$672$		0			0
$673$		−	16.1918i		−	0.624147i	−0.950058	−	0.312073i	$-0.898977\pi$
$673$		−	16.1918i		−	0.624147i	0.950058	−	0.312073i	$-0.101023\pi$
$674$	−6.05963	−	16.6487i	−0.233408	−	0.641284i
$675$		0			0
$676$	13.3346	+	23.0962i	0.512869	+	0.888316i
$677$	21.0773	+	36.5070i	0.810068	+	1.40308i	0.912816	+	0.408371i	$0.133903\pi$
$677$	21.0773	+	36.5070i	0.810068	+	1.40308i	−0.102748	+	0.994707i	$0.532764\pi$
$678$		0			0
$679$	−3.15301	+	8.66282i	−0.121001	+	0.332449i
$680$	0.938329	−	5.32153i	0.0359833	−	0.204071i
$681$		0			0
$682$	1.55473	−	1.30458i	0.0595338	−	0.0499548i
$683$	−13.0918			−0.500945			−0.250472	−	0.968124i	$-0.580586\pi$
$683$	−13.0918			−0.500945			−0.250472	+	0.968124i	$0.580586\pi$
$684$		0			0
$685$	−9.10020			−0.347701
$686$	24.7282	−	20.7494i	0.944128	−	0.792217i
$687$		0			0
$688$	0.523528	−	2.96907i	0.0199593	−	0.113195i
$689$	−8.00391	+	21.9906i	−0.304925	+	0.837773i
$690$		0			0
$691$	13.9770	+	24.2089i	0.531710	+	0.920949i	0.999315	+	0.0370110i	$0.0117836\pi$
$691$	13.9770	+	24.2089i	0.531710	+	0.920949i	−0.467605	+	0.883938i	$0.654883\pi$
$692$	−3.12522	−	5.41305i	−0.118803	−	0.205773i
$693$		0			0
$694$	21.0353	+	57.7940i	0.798489	+	2.19383i
$695$		−	3.28401i		−	0.124570i
$696$		0			0
$697$	−8.11451	−	22.2944i	−0.307359	−	0.844462i
$698$	32.7152	+	11.9073i	1.23829	+	0.450700i
$699$		0			0
$700$	−8.77955	−	3.19550i	−0.331836	−	0.120778i
$701$	−5.74896	+	15.7951i	−0.217135	+	0.596574i	−0.999661	−	0.0260446i	$-0.991709\pi$
$701$	−5.74896	+	15.7951i	−0.217135	+	0.596574i	0.782526	+	0.622618i	$0.213931\pi$
$702$		0			0
$703$	−18.4972	−	24.3325i	−0.697635	−	0.917718i
$704$	0.972347	+	0.561385i	0.0366467	+	0.0211580i
$705$		0			0
$706$	0.572034	+	0.681723i	0.0215288	+	0.0256570i
$707$	22.0151	+	3.88185i	0.827962	+	0.145992i
$708$		0			0
$709$	25.8623	+	21.7010i	0.971278	+	0.814999i	0.982751	−	0.184935i	$-0.0592075\pi$
$709$	25.8623	+	21.7010i	0.971278	+	0.814999i	−0.0114728	+	0.999934i	$0.503652\pi$
$710$	−5.63946	−	3.25595i	−0.211645	−	0.122193i
$711$		0			0
$712$	−16.7257	+	6.08767i	−0.626824	+	0.228145i
$713$	3.20762	−	18.1913i	0.120126	−	0.681270i
$714$		0			0
$715$		−	1.60958i		−	0.0601948i
$716$	0.284501	−	0.103550i	0.0106323	−	0.00386984i
$717$		0			0
$718$	15.5014	+	42.5898i	0.578508	+	1.58944i
$719$	−21.8362	+	3.85031i	−0.814352	+	0.143592i	−0.565287	−	0.824895i	$-0.691234\pi$
$719$	−21.8362	+	3.85031i	−0.814352	+	0.143592i	−0.249065	+	0.968487i	$0.580123\pi$
$720$		0			0
$721$			0.697785i			0.0259869i
$722$	13.1693	+	28.9201i	0.490112	+	1.07630i
$723$		0			0
$724$	−9.99023	+	1.76155i	−0.371284	+	0.0654674i
$725$	−5.42726	+	4.55401i	−0.201563	+	0.169132i
$726$		0			0
$727$	−1.60278	−	9.08980i	−0.0594437	−	0.337122i	0.940553	−	0.339647i	$-0.110307\pi$
$727$	−1.60278	−	9.08980i	−0.0594437	−	0.337122i	−0.999997	+	0.00252468i	$0.999196\pi$
$728$	−33.9610	−	5.98823i	−1.25868	−	0.221939i
$729$		0			0
$730$	11.4263	−	6.59699i	0.422907	−	0.244166i
$731$	2.75509	+	0.485797i	0.101901	+	0.0179678i
$732$		0			0
$733$	−3.07982	+	5.33441i	−0.113756	+	0.197031i	−0.917282	−	0.398239i	$-0.869621\pi$
$733$	−3.07982	+	5.33441i	−0.113756	+	0.197031i	0.803526	+	0.595270i	$0.202955\pi$
$734$	38.6411			1.42627
$735$		0			0
$736$	−25.8985	+	4.56661i	−0.954633	+	0.168328i
$737$	−0.742901	−	0.623368i	−0.0273651	−	0.0229621i
$738$		0			0
$739$	41.0076	+	14.9256i	1.50849	+	0.549045i	0.958243	−	0.285956i	$-0.0923112\pi$
$739$	41.0076	+	14.9256i	1.50849	+	0.549045i	0.550247	+	0.835002i	$0.314533\pi$
$740$	1.63173	−	2.82625i	0.0599838	−	0.103895i
$741$		0			0
$742$	7.22217	+	12.5092i	0.265134	+	0.459226i
$743$	−5.37307	−	30.4722i	−0.197119	−	1.11792i	−0.909369	−	0.415991i	$-0.863435\pi$
$743$	−5.37307	−	30.4722i	−0.197119	−	1.11792i	0.712250	−	0.701926i	$-0.247676\pi$
$744$		0			0
$745$	−11.1231	+	4.04847i	−0.407518	+	0.148324i
$746$	−26.9485	−	32.1160i	−0.986654	−	1.17585i
$747$		0			0
$748$	0.742042	−	1.28525i	0.0271317	−	0.0469935i
$749$	15.0441			0.549699
$750$		0			0
$751$	28.3565	−	33.7940i	1.03474	−	1.23316i	0.0627816	−	0.998027i	$-0.480003\pi$
$751$	28.3565	−	33.7940i	1.03474	−	1.23316i	0.971963	−	0.235133i	$-0.0755527\pi$
$752$	19.0465	+	10.9965i	0.694555	+	0.401001i
$753$		0			0
$754$	11.1416	−	13.2781i	0.405754	−	0.483558i
$755$	−0.398978	+	0.334782i	−0.0145203	+	0.0121840i
$756$		0			0
$757$	2.66165	+	15.0949i	0.0967392	+	0.548635i	0.994201	+	0.107542i	$0.0342980\pi$
$757$	2.66165	+	15.0949i	0.0967392	+	0.548635i	−0.897461	+	0.441093i	$0.854591\pi$
$758$	−21.2029	−	25.2686i	−0.770123	−	0.917797i
$759$		0			0
$760$	3.47515	−	3.75829i	0.126057	−	0.136327i
$761$	23.7318	−	13.7015i	0.860276	−	0.496680i	−0.00382896	−	0.999993i	$-0.501219\pi$
$761$	23.7318	−	13.7015i	0.860276	−	0.496680i	0.864105	+	0.503312i	$0.167885\pi$
$762$		0			0
$763$	7.98085	−	21.9272i	0.288926	−	0.793819i
$764$	−10.0463	+	11.9727i	−0.363463	+	0.433159i
$765$		0			0
$766$	−6.21020	+	35.2198i	−0.224384	+	1.27254i
$767$	−44.7296	+	25.8246i	−1.61509	+	0.932473i
$768$		0			0
$769$	11.6063	+	9.73884i	0.418534	+	0.351191i	0.827605	−	0.561311i	$-0.189703\pi$
$769$	11.6063	+	9.73884i	0.418534	+	0.351191i	−0.409071	+	0.912502i	$0.634147\pi$
$770$	−0.761051	−	0.638597i	−0.0274264	−	0.0230135i
$771$		0			0
$772$	0.0602429	−	0.0347813i	0.00216819	−	0.00125181i
$773$	2.17005	−	12.3070i	0.0780513	−	0.442651i	−0.920590	−	0.390531i	$-0.872291\pi$
$773$	2.17005	−	12.3070i	0.0780513	−	0.442651i	0.998641	−	0.0521193i	$-0.0165976\pi$
$774$		0			0
$775$	8.98355	−	10.7062i	0.322699	−	0.384577i
$776$	−2.52165	+	6.92817i	−0.0905219	+	0.248707i
$777$		0			0
$778$	−37.6682	+	21.7477i	−1.35047	+	0.779694i
$779$	4.96328	−	21.9195i	0.177828	−	0.785347i
$780$		0			0
$781$	1.73435	+	2.06692i	0.0620598	+	0.0739600i
$782$	−8.22961	−	46.6724i	−0.294290	−	1.66900i
$783$		0			0
$784$	2.55821	−	2.14659i	0.0913647	−	0.0766641i
$785$	−2.52790	+	3.01263i	−0.0902245	+	0.107525i
$786$		0			0
$787$	5.00564	+	2.89001i	0.178432	+	0.103018i	0.586556	−	0.809909i	$-0.300484\pi$
$787$	5.00564	+	2.89001i	0.178432	+	0.103018i	−0.408124	+	0.912927i	$0.633817\pi$
$788$	−7.47686	+	8.91058i	−0.266352	+	0.317426i
$789$		0			0
$790$	−1.34814			−0.0479645
$791$	25.2620	−	43.7551i	0.898215	−	1.55575i
$792$		0			0
$793$	−50.1421	−	59.7570i	−1.78060	−	2.12203i
$794$	−4.91115	+	1.78751i	−0.174290	+	0.0634364i
$795$		0			0
$796$	−1.27645	−	7.23910i	−0.0452425	−	0.256583i
$797$	15.0976	+	26.1497i	0.534783	+	0.926271i	0.999174	+	0.0406406i	$0.0129399\pi$
$797$	15.0976	+	26.1497i	0.534783	+	0.926271i	−0.464391	+	0.885630i	$0.653727\pi$
$798$		0			0
$799$	−10.2040	+	17.6738i	−0.360991	+	0.625255i
$800$	−18.6972	−	6.80524i	−0.661047	−	0.240602i
$801$		0			0
$802$	−11.5938	−	9.72832i	−0.409390	−	0.343519i
$803$	−5.38380	+	0.949310i	−0.189990	+	0.0335004i
$804$		0			0
$805$	−9.04212			−0.318693
$806$	−17.0964	+	29.6118i	−0.602195	+	1.04303i
$807$		0			0
$808$	17.6068	+	3.10455i	0.619404	+	0.109218i
$809$	−11.2366	+	6.48747i	−0.395059	+	0.228087i	−0.684350	−	0.729154i	$-0.739914\pi$
$809$	−11.2366	+	6.48747i	−0.395059	+	0.228087i	0.289291	+	0.957241i	$0.406581\pi$
$810$		0			0
$811$	55.4307	+	9.77392i	1.94643	+	0.343209i	0.999780	+	0.0209574i	$0.00667145\pi$
$811$	55.4307	+	9.77392i	1.94643	+	0.343209i	0.946654	+	0.322251i	$0.104440\pi$
$812$	−0.529491	−	3.00289i	−0.0185815	−	0.105381i
$813$		0			0
$814$	−3.63442	+	3.04964i	−0.127386	+	0.106890i
$815$	8.52941	−	1.50396i	0.298772	−	0.0526816i
$816$		0			0
$817$	1.94576	+	1.79918i	0.0680735	+	0.0629452i
$818$			63.7719i			2.22973i
$819$		0			0
$820$	2.36317	−	0.416690i	0.0825254	−	0.0145515i
$821$	4.62750	+	12.7139i	0.161501	+	0.443720i	0.993877	−	0.110491i	$-0.0352424\pi$
$821$	4.62750	+	12.7139i	0.161501	+	0.443720i	−0.832376	+	0.554211i	$0.813020\pi$
$822$		0			0
$823$	−4.57724	+	1.66598i	−0.159552	+	0.0580724i	−0.420562	−	0.907264i	$-0.638167\pi$
$823$	−4.57724	+	1.66598i	−0.159552	+	0.0580724i	0.261009	+	0.965336i	$0.415945\pi$
$824$			0.558060i			0.0194409i
$825$		0			0
$826$	−5.53582	+	31.3952i	−0.192616	+	1.09238i
$827$	22.6833	−	8.25604i	0.788775	−	0.287091i	0.0839482	−	0.996470i	$-0.473247\pi$
$827$	22.6833	−	8.25604i	0.788775	−	0.287091i	0.704827	+	0.709380i	$0.251025\pi$
$828$		0			0
$829$	45.1860	+	26.0882i	1.56938	+	0.906080i	0.996242	+	0.0866187i	$0.0276062\pi$
$829$	45.1860	+	26.0882i	1.56938	+	0.906080i	0.573135	+	0.819461i	$0.305727\pi$
$830$	9.84271	+	8.25901i	0.341645	+	0.286675i
$831$		0			0
$832$	−18.6284	−	3.28468i	−0.645822	−	0.113876i
$833$	1.99189	+	2.37384i	0.0690148	+	0.0822487i
$834$		0			0
$835$	2.43015	+	1.40305i	0.0840990	+	0.0485546i
$836$	1.24991	−	0.643513i	0.0432290	−	0.0222563i
$837$		0			0
$838$	−6.76718	+	18.5927i	−0.233768	+	0.642273i
$839$	9.47505	+	3.44864i	0.327115	+	0.119060i	0.500357	−	0.865819i	$-0.333202\pi$
$839$	9.47505	+	3.44864i	0.327115	+	0.119060i	−0.173242	+	0.984879i	$0.555424\pi$
$840$		0			0
$841$	25.0783	+	9.12776i	0.864769	+	0.314750i
$842$	−2.00730	−	5.51502i	−0.0691762	−	0.190060i
$843$		0			0
$844$			5.65394i			0.194617i
$845$	6.67904	+	18.3505i	0.229766	+	0.631276i
$846$		0			0
$847$	−13.6281	−	23.6046i	−0.468268	−	0.811065i
$848$	8.51340	+	14.7456i	0.292352	+	0.506368i
$849$		0			0
$850$	12.2639	−	33.6948i	0.420648	−	1.15572i
$851$	−7.49829	+	42.5249i	−0.257038	+	1.45773i
$852$		0			0
$853$	3.07507	−	2.58029i	0.105288	−	0.0883475i	−0.588624	−	0.808407i	$-0.700330\pi$
$853$	3.07507	−	2.58029i	0.105288	−	0.0883475i	0.693912	+	0.720060i	$0.255886\pi$
$854$	−48.1485			−1.64761
$855$		0			0
$856$	12.0317			0.411234
$857$	14.4590	−	12.1326i	0.493911	−	0.414441i	−0.361514	−	0.932367i	$-0.617740\pi$
$857$	14.4590	−	12.1326i	0.493911	−	0.414441i	0.855426	+	0.517926i	$0.173296\pi$
$858$		0			0
$859$	−5.24029	+	29.7192i	−0.178796	+	1.01400i	0.754874	+	0.655870i	$0.227698\pi$
$859$	−5.24029	+	29.7192i	−0.178796	+	1.01400i	−0.933670	+	0.358135i	$0.883413\pi$
$860$	−0.0967763	+	0.265891i	−0.00330004	+	0.00906680i
$861$		0			0
$862$	−2.18129	−	3.77811i	−0.0742952	−	0.128683i
$863$	−2.77666	−	4.80931i	−0.0945184	−	0.163711i	0.814889	−	0.579617i	$-0.196798\pi$
$863$	−2.77666	−	4.80931i	−0.0945184	−	0.163711i	−0.909408	+	0.415906i	$0.863464\pi$
$864$		0			0
$865$	−1.56536	−	4.30080i	−0.0532239	−	0.146231i
$866$			8.14928i			0.276924i
$867$		0			0
$868$	2.05728	+	5.65234i	0.0698287	+	0.191853i
$869$	0.524906	+	0.191050i	0.0178062	+	0.00648093i
$870$		0			0
$871$	15.3531	+	5.58807i	0.520219	+	0.189344i
$872$	6.38276	−	17.5365i	0.216148	−	0.593861i
$873$		0			0
$874$	17.3670	−	41.3985i	0.587449	−	1.40033i
$875$	−12.2828	−	7.09149i	−0.415235	−	0.239736i
$876$		0			0
$877$	−22.9693	−	27.3737i	−0.775617	−	0.924344i	0.223110	−	0.974793i	$-0.428379\pi$
$877$	−22.9693	−	27.3737i	−0.775617	−	0.924344i	−0.998727	+	0.0504489i	$0.983935\pi$
$878$	27.0815	+	4.77519i	0.913955	+	0.161155i
$879$		0			0
$880$	−0.897117	−	0.752771i	−0.0302418	−	0.0253759i
$881$	12.2972	+	7.09981i	0.414305	+	0.239199i	0.692638	−	0.721286i	$-0.256449\pi$
$881$	12.2972	+	7.09981i	0.414305	+	0.239199i	−0.278333	+	0.960485i	$0.589782\pi$
$882$		0			0
$883$	3.10982	−	1.13188i	0.104654	−	0.0380909i	−0.289163	−	0.957280i	$-0.593377\pi$
$883$	3.10982	−	1.13188i	0.104654	−	0.0380909i	0.393816	+	0.919189i	$0.371155\pi$
$884$	−4.34172	+	24.6231i	−0.146028	+	0.828164i
$885$		0			0
$886$			27.4014i			0.920567i
$887$	−38.9812	+	14.1880i	−1.30886	+	0.476386i	−0.899872	−	0.436154i	$-0.856340\pi$
$887$	−38.9812	+	14.1880i	−1.30886	+	0.476386i	−0.408988	+	0.912540i	$0.634118\pi$
$888$		0			0
$889$	−12.9710	−	35.6375i	−0.435033	−	1.19524i
$890$	8.50775	−	1.50015i	0.285180	−	0.0502850i
$891$		0			0
$892$		−	11.0168i		−	0.368870i
$893$	−17.1878	+	8.84909i	−0.575168	+	0.296123i
$894$		0			0
$895$	0.218324	−	0.0384964i	0.00729777	−	0.00128679i
$896$	−25.4007	+	21.3137i	−0.848578	+	0.712042i
$897$		0			0
$898$	−7.35685	−	41.7228i	−0.245501	−	1.39231i
$899$	4.49194	+	0.792050i	0.149815	+	0.0264163i
$900$		0			0
$901$	−13.6829	+	7.89984i	−0.455844	+	0.263182i
$902$	−3.43555	−	0.605780i	−0.114391	−	0.0201703i
$903$		0			0
$904$	20.2036	−	34.9936i	0.671960	−	1.16387i
$905$	−7.42807			−0.246917
$906$		0			0
$907$	18.6843	−	3.29455i	0.620403	−	0.109394i	0.145393	−	0.989374i	$-0.453555\pi$
$907$	18.6843	−	3.29455i	0.620403	−	0.109394i	0.475010	+	0.879980i	$0.342444\pi$
$908$	5.93161	+	4.97721i	0.196847	+	0.165175i
$909$		0			0
$910$	15.7282	+	5.72459i	0.521384	+	0.189768i
$911$	8.73004	−	15.1209i	0.289239	−	0.500977i	−0.684389	−	0.729117i	$-0.739931\pi$
$911$	8.73004	−	15.1209i	0.289239	−	0.500977i	0.973628	+	0.228140i	$0.0732644\pi$
$912$		0			0
$913$	−2.66190	−	4.61055i	−0.0880961	−	0.152587i
$914$	6.30363	+	35.7497i	0.208506	+	1.18249i
$915$		0			0
$916$	1.68444	−	0.613086i	0.0556555	−	0.0202569i
$917$	13.6362	+	16.2510i	0.450309	+	0.536657i
$918$		0			0
$919$	−20.9664	+	36.3149i	−0.691619	+	1.19792i	0.279689	+	0.960091i	$0.409769\pi$
$919$	−20.9664	+	36.3149i	−0.691619	+	1.19792i	−0.971307	+	0.237828i	$0.923565\pi$
$920$	−7.23152			−0.238416
$921$		0			0
$922$	−25.0180	+	29.8152i	−0.823923	+	0.981913i
$923$	−39.3670	−	22.7285i	−1.29578	−	0.748119i
$924$		0			0
$925$	−21.0004	+	25.0273i	−0.690489	+	0.822892i
$926$	−32.0434	+	26.8876i	−1.05301	+	0.883583i
$927$		0			0
$928$	−1.12762	−	6.39507i	−0.0370160	−	0.209928i
$929$	−9.16238	−	10.9193i	−0.300608	−	0.358251i	0.594503	−	0.804093i	$-0.297349\pi$
$929$	−9.16238	−	10.9193i	−0.300608	−	0.358251i	−0.895112	+	0.445842i	$0.852904\pi$
$930$		0			0
$931$	0.370021	+	2.91204i	0.0121269	+	0.0954381i
$932$	19.9488	−	11.5175i	0.653446	−	0.377267i
$933$		0			0
$934$	9.03487	−	24.8231i	0.295630	−	0.812236i
$935$	0.698518	−	0.832462i	0.0228440	−	0.0272244i
$936$		0			0
$937$	−5.18260	+	29.3920i	−0.169308	+	0.960194i	0.775203	+	0.631713i	$0.217648\pi$
$937$	−5.18260	+	29.3920i	−0.169308	+	0.960194i	−0.944511	+	0.328481i	$0.893463\pi$
$938$	8.73349	−	5.04228i	0.285159	−	0.164636i
$939$		0			0
$940$	−1.58120	−	1.32678i	−0.0515730	−	0.0432749i
$941$	−34.8696	−	29.2590i	−1.13672	−	0.953817i	−0.137389	−	0.990517i	$-0.543871\pi$
$941$	−34.8696	−	29.2590i	−1.13672	−	0.953817i	−0.999326	+	0.0366997i	$0.988315\pi$
$942$		0			0
$943$	−27.4971	+	15.8754i	−0.895427	+	0.516975i
$944$	−6.52555	+	37.0083i	−0.212389	+	1.20452i
$945$		0			0
$946$	0.264415	−	0.315118i	0.00859688	−	0.0102454i
$947$	19.6062	−	53.8677i	0.637118	−	1.75047i	−0.0234784	−	0.999724i	$-0.507474\pi$
$947$	19.6062	−	53.8677i	0.637118	−	1.75047i	0.660596	−	0.750742i	$-0.270304\pi$
$948$		0			0
$949$	79.7629	−	46.0511i	2.58921	−	1.49488i
$950$	27.0407	−	20.5559i	0.877315	−	0.666921i
$951$		0			0
$952$	−14.9656	−	17.8353i	−0.485038	−	0.578046i
$953$	3.12608	+	17.7289i	0.101264	+	0.574294i	0.992647	+	0.121044i	$0.0386243\pi$
$953$	3.12608	+	17.7289i	0.101264	+	0.574294i	−0.891384	+	0.453250i	$0.850265\pi$
$954$		0			0
$955$	−8.76689	+	7.35629i	−0.283690	+	0.238044i
$956$	5.17857	−	6.17158i	0.167487	−	0.199603i
$957$		0			0
$958$	37.2168	+	21.4871i	1.20242	+	0.694218i
$959$	−25.2035	+	30.0363i	−0.813862	+	0.969923i
$960$		0			0
$961$	22.0022			0.709748
$962$	39.9654	−	69.2221i	1.28854	−	2.23181i
$963$		0			0
$964$	3.41168	+	4.06588i	0.109883	+	0.130953i
$965$	0.0478645	−	0.0174212i	0.00154081	−	0.000560809i
$966$		0			0
$967$	−1.26590	−	7.17925i	−0.0407085	−	0.230869i	0.957665	−	0.287886i	$-0.0929523\pi$
$967$	−1.26590	−	7.17925i	−0.0407085	−	0.230869i	−0.998373	+	0.0570165i	$0.981841\pi$
$968$	−10.8992	−	18.8780i	−0.350315	−	0.606763i
$969$		0			0
$970$	1.78923	−	3.09904i	0.0574488	−	0.0995042i
$971$	−5.85755	−	2.13197i	−0.187978	−	0.0684183i	0.246316	−	0.969190i	$-0.420780\pi$
$971$	−5.85755	−	2.13197i	−0.187978	−	0.0684183i	−0.434294	+	0.900771i	$0.643002\pi$
$972$		0			0
$973$	−10.8393	−	9.09524i	−0.347491	−	0.291580i
$974$	32.8630	−	5.79463i	1.05300	−	0.185672i
$975$		0			0
$976$	−56.7568			−1.81674
$977$	−7.86310	+	13.6193i	−0.251563	+	0.435719i	−0.963956	−	0.266061i	$-0.914278\pi$
$977$	−7.86310	+	13.6193i	−0.251563	+	0.435719i	0.712394	+	0.701780i	$0.247611\pi$
$978$		0			0
$979$	−3.52514	−	0.621577i	−0.112664	−	0.0198657i
$980$	−0.271432	+	0.156711i	−0.00867057	+	0.00500596i
$981$		0			0
$982$	−69.2627	−	12.2129i	−2.21026	−	0.389729i
$983$	−1.40366	−	7.96055i	−0.0447698	−	0.253902i	0.954206	−	0.299150i	$-0.0967032\pi$
$983$	−1.40366	−	7.96055i	−0.0447698	−	0.253902i	−0.998976	+	0.0452483i	$0.985592\pi$
$984$		0			0
$985$	−6.52466	+	5.47484i	−0.207893	+	0.174443i
$986$	11.5247	−	2.03212i	0.367022	−	0.0647158i
$987$		0			0
$988$	−16.0798	+	17.3899i	−0.511566	+	0.553245i
$989$		−	3.74395i		−	0.119051i
$990$		0			0
$991$	−46.4300	+	8.18687i	−1.47490	+	0.260064i	−0.852538	−	0.522666i	$-0.824938\pi$
$991$	−46.4300	+	8.18687i	−1.47490	+	0.260064i	−0.622361	+	0.782730i	$0.713827\pi$
$992$	4.38126	+	12.0374i	0.139105	+	0.382188i
$993$		0			0
$994$	−26.3654	+	9.59623i	−0.836260	+	0.304374i
$995$		−	5.38251i		−	0.170637i
$996$		0			0
$997$	−0.765922	+	4.34376i	−0.0242570	+	0.137568i	−0.994531	−	0.104440i	$-0.966695\pi$
$997$	−0.765922	+	4.34376i	−0.0242570	+	0.137568i	0.970274	+	0.242008i	$0.0778061\pi$
$998$	8.89254	−	3.23662i	0.281488	−	0.102453i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.bo.a.224.5		108
3.2	odd	2		171.2.x.a.110.14	yes	108
9.4	even	3		171.2.bd.a.167.5	yes	108
9.5	odd	6		513.2.cd.a.395.14		108
19.14	odd	18		513.2.cd.a.413.14		108
57.14	even	18		171.2.bd.a.128.5	yes	108
171.14	even	18	inner	513.2.bo.a.71.5		108
171.166	odd	18		171.2.x.a.14.14	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.14	✓	108	171.166	odd	18
171.2.x.a.110.14	yes	108	3.2	odd	2
171.2.bd.a.128.5	yes	108	57.14	even	18
171.2.bd.a.167.5	yes	108	9.4	even	3
513.2.bo.a.71.5		108	171.14	even	18	inner
513.2.bo.a.224.5		108	1.1	even	1	trivial
513.2.cd.a.395.14		108	9.5	odd	6
513.2.cd.a.413.14		108	19.14	odd	18

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.bo (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28121 + 1.07506i) q^{2} +(0.138440 - 0.785130i) q^{4} +(0.199661 - 0.548565i) q^{5} +(-1.25763 - 2.17828i) q^{7} +(-1.00580 - 1.74210i) q^{8} +(0.333933 + 0.917472i) q^{10} -0.404547i q^{11} +(2.33106 + 6.40453i) q^{13} +(3.95307 + 1.43880i) q^{14} +(4.65983 + 1.69604i) q^{16} +(-1.57381 + 4.32400i) q^{17} +(-3.47008 + 2.63790i) q^{19} +(-0.403054 - 0.232703i) q^{20} +(0.434912 + 0.518308i) q^{22} +(6.06451 + 1.06934i) q^{23} +(3.56916 + 2.99488i) q^{25} +(-9.87182 - 5.69950i) q^{26} +(-1.88434 + 0.685845i) q^{28} +(-0.264049 + 1.49750i) q^{29} -2.99963i q^{31} +(-4.01296 + 1.46060i) q^{32} +(-2.63218 - 7.23187i) q^{34} +(-1.44603 + 0.254974i) q^{35} +7.01209i q^{37} +(1.60999 - 7.11024i) q^{38} +(-1.15648 + 0.203918i) q^{40} +(-3.94971 + 3.31420i) q^{41} +(-0.105574 - 0.598738i) q^{43} +(-0.317622 - 0.0560053i) q^{44} +(-8.91949 + 5.14967i) q^{46} +(4.36769 + 0.770141i) q^{47} +(0.336719 - 0.583215i) q^{49} -7.79251 q^{50} +(5.35110 - 0.943543i) q^{52} +(2.63029 + 2.20707i) q^{53} +(-0.221920 - 0.0807723i) q^{55} +(-2.52986 + 4.38185i) q^{56} +(-1.27160 - 2.20247i) q^{58} +(1.31593 + 7.46301i) q^{59} +(-10.7552 + 3.91458i) q^{61} +(3.22478 + 3.84315i) q^{62} +(-1.38769 + 2.40355i) q^{64} +3.97872 q^{65} +(1.54091 - 1.83638i) q^{67} +(3.17702 + 1.83425i) q^{68} +(1.57855 - 1.88124i) q^{70} +(-5.10921 + 4.28714i) q^{71} +(-2.34660 - 13.3082i) q^{73} +(-7.53841 - 8.98393i) q^{74} +(1.59070 + 3.08966i) q^{76} +(-0.881218 + 0.508771i) q^{77} +(-0.472257 + 1.29752i) q^{79} +(1.86078 - 2.21759i) q^{80} +(1.49743 - 8.49234i) q^{82} +(11.3968 - 6.57996i) q^{83} +(2.05776 + 1.72667i) q^{85} +(0.778940 + 0.653608i) q^{86} +(-0.704762 + 0.406895i) q^{88} +(1.53648 - 8.71380i) q^{89} +(11.0193 - 13.1323i) q^{91} +(1.67914 - 4.61339i) q^{92} +(-6.42386 + 3.70882i) q^{94} +(0.754220 + 2.43025i) q^{95} +(-2.35590 - 2.80765i) q^{97} +(0.195584 + 1.10921i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 9 q^{2} - 3 q^{4} + 9 q^{5} + 3 q^{7} - 12 q^{10} - 6 q^{13} + 9 q^{14} - 9 q^{16} - 27 q^{17} - 15 q^{19} + 18 q^{20} + 30 q^{22} + 45 q^{23} - 3 q^{25} + 72 q^{26} - 36 q^{28} + 9 q^{29} + 9 q^{32}+ \cdots + 27 q^{98}+O(q^{100}) \) 108 * q + 9 * q^2 - 3 * q^4 + 9 * q^5 + 3 * q^7 - 12 * q^10 - 6 * q^13 + 9 * q^14 - 9 * q^16 - 27 * q^17 - 15 * q^19 + 18 * q^20 + 30 * q^22 + 45 * q^23 - 3 * q^25 + 72 * q^26 - 36 * q^28 + 9 * q^29 + 9 * q^32 + 33 * q^34 - 45 * q^35 + 9 * q^38 + 15 * q^40 + 9 * q^41 + 9 * q^43 + 63 * q^44 - 18 * q^46 + 9 * q^47 - 15 * q^49 - 126 * q^50 - 39 * q^52 + 3 * q^55 - 63 * q^56 - 6 * q^58 - 36 * q^59 - 24 * q^61 - 18 * q^62 + 18 * q^65 - 63 * q^67 - 54 * q^68 + 39 * q^70 - 45 * q^73 + 117 * q^74 - 3 * q^76 + 18 * q^77 + 3 * q^79 - 126 * q^80 - 3 * q^82 - 27 * q^83 - 3 * q^85 + 171 * q^86 - 9 * q^88 - 54 * q^89 - 9 * q^91 + 27 * q^92 - 99 * q^95 - 57 * q^97 + 27 * q^98

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