LMFDB - Embedded newform 819.2.fn.e.73.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.8
Character	$\chi$	$=$	819.73
Dual form			819.2.fn.e.460.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.639966 - 2.38839i) q^{2} +(-3.56278 - 2.05697i) q^{4} +(1.58199 + 0.423894i) q^{5} +(-2.54693 + 0.716327i) q^{7} +(-3.69606 + 3.69606i) q^{8} +O(q^{10})$	\(q+(0.639966 - 2.38839i) q^{2} +(-3.56278 - 2.05697i) q^{4} +(1.58199 + 0.423894i) q^{5} +(-2.54693 + 0.716327i) q^{7} +(-3.69606 + 3.69606i) q^{8} +(2.02484 - 3.50713i) q^{10} +(-1.48887 - 5.55653i) q^{11} +(-3.57432 - 0.473526i) q^{13} +(0.0809133 + 6.54149i) q^{14} +(2.34832 + 4.06741i) q^{16} +(-0.991968 + 1.71814i) q^{17} +(-0.918664 - 0.246155i) q^{19} +(-4.76435 - 4.76435i) q^{20} -14.2240 q^{22} +(3.06647 - 1.77043i) q^{23} +(-2.00711 - 1.15881i) q^{25} +(-3.41841 + 8.23382i) q^{26} +(10.5476 + 2.68686i) q^{28} -2.83949 q^{29} +(1.16048 + 4.33096i) q^{31} +(1.11958 - 0.299990i) q^{32} +(3.46875 + 3.46875i) q^{34} +(-4.33288 + 0.0535944i) q^{35} +(-3.73806 - 1.00161i) q^{37} +(-1.17583 + 2.03659i) q^{38} +(-7.41388 + 4.28040i) q^{40} +(-4.02565 + 4.02565i) q^{41} -5.30948i q^{43} +(-6.12512 + 22.8593i) q^{44} +(-2.26603 - 8.45694i) q^{46} +(-0.120170 + 0.448482i) q^{47} +(5.97375 - 3.64888i) q^{49} +(-4.05216 + 4.05216i) q^{50} +(11.7605 + 9.03935i) q^{52} +(6.31835 - 10.9437i) q^{53} -9.42152i q^{55} +(6.76604 - 12.0612i) q^{56} +(-1.81718 + 6.78181i) q^{58} +(11.5955 - 3.10701i) q^{59} +(-4.38137 + 2.52958i) q^{61} +11.0867 q^{62} +6.52733i q^{64} +(-5.45382 - 2.26425i) q^{65} +(5.87066 - 1.57304i) q^{67} +(7.06833 - 4.08090i) q^{68} +(-2.64489 + 10.3829i) q^{70} +(4.84596 + 4.84596i) q^{71} +(-4.24311 + 1.13694i) q^{73} +(-4.78447 + 8.28694i) q^{74} +(2.76666 + 2.76666i) q^{76} +(7.77235 + 13.0856i) q^{77} +(-3.08258 - 5.33918i) q^{79} +(1.99088 + 7.43006i) q^{80} +(7.03853 + 12.1911i) q^{82} +(11.5176 - 11.5176i) q^{83} +(-2.29759 + 2.29759i) q^{85} +(-12.6811 - 3.39789i) q^{86} +(26.0402 + 15.0343i) q^{88} +(0.941005 - 3.51188i) q^{89} +(9.44276 - 1.35434i) q^{91} -14.5669 q^{92} +(0.994243 + 0.574027i) q^{94} +(-1.34898 - 0.778832i) q^{95} +(7.09855 - 7.09855i) q^{97} +(-4.89192 - 16.6028i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.639966	−	2.38839i	0.452524	−	1.68884i	−0.242741	−	0.970091i	$-0.578047\pi$
$2$	0.639966	−	2.38839i	0.452524	−	1.68884i	0.695266	−	0.718753i	$-0.255287\pi$
$3$		0			0
$3$		0			0
$4$	−3.56278	−	2.05697i	−1.78139	−	1.02849i
$5$	1.58199	+	0.423894i	0.707488	+	0.189571i	0.594582	−	0.804035i	$-0.297317\pi$
$5$	1.58199	+	0.423894i	0.707488	+	0.189571i	0.112906	+	0.993606i	$0.463984\pi$
$6$		0			0
$7$	−2.54693	+	0.716327i	−0.962651	+	0.270746i
$7$	−2.54693	+	0.716327i	−0.962651	+	0.270746i
$8$	−3.69606	+	3.69606i	−1.30676	+	1.30676i
$9$		0			0
$10$	2.02484	−	3.50713i	0.640311	−	1.10905i
$11$	−1.48887	−	5.55653i	−0.448911	−	1.67536i	−0.705399	−	0.708811i	$-0.749232\pi$
$11$	−1.48887	−	5.55653i	−0.448911	−	1.67536i	0.256488	−	0.966547i	$-0.417435\pi$
$12$		0			0
$13$	−3.57432	−	0.473526i	−0.991338	−	0.131333i
$13$	−3.57432	−	0.473526i	−0.991338	−	0.131333i
$14$	0.0809133	+	6.54149i	0.0216250	+	1.74829i
$15$		0			0
$16$	2.34832	+	4.06741i	0.587081	+	1.01685i
$17$	−0.991968	+	1.71814i	−0.240588	+	0.416710i	−0.960882	−	0.276959i	$-0.910673\pi$
$17$	−0.991968	+	1.71814i	−0.240588	+	0.416710i	0.720294	+	0.693669i	$0.244007\pi$
$18$		0			0
$19$	−0.918664	−	0.246155i	−0.210756	−	0.0564719i	0.151896	−	0.988396i	$-0.451462\pi$
$19$	−0.918664	−	0.246155i	−0.210756	−	0.0564719i	−0.362652	+	0.931925i	$0.618129\pi$
$20$	−4.76435	−	4.76435i	−1.06534	−	1.06534i
$21$		0			0
$22$	−14.2240			−3.03256
$23$	3.06647	−	1.77043i	0.639404	−	0.369160i	−0.144981	−	0.989434i	$-0.546312\pi$
$23$	3.06647	−	1.77043i	0.639404	−	0.369160i	0.784385	+	0.620274i	$0.212979\pi$
$24$		0			0
$25$	−2.00711	−	1.15881i	−0.401423	−	0.231761i
$26$	−3.41841	+	8.23382i	−0.670405	+	1.61478i
$27$		0			0
$28$	10.5476	+	2.68686i	1.99331	+	0.507768i
$29$	−2.83949			−0.527281			−0.263640	−	0.964621i	$-0.584923\pi$
$29$	−2.83949			−0.527281			−0.263640	+	0.964621i	$0.584923\pi$
$30$		0			0
$31$	1.16048	+	4.33096i	0.208428	+	0.777863i	0.988377	+	0.152021i	$0.0485780\pi$
$31$	1.16048	+	4.33096i	0.208428	+	0.777863i	−0.779950	+	0.625842i	$0.784755\pi$
$32$	1.11958	−	0.299990i	0.197915	−	0.0530312i
$33$		0			0
$34$	3.46875	+	3.46875i	0.594886	+	0.594886i
$35$	−4.33288	+	0.0535944i	−0.732390	+	0.00905911i
$36$		0			0
$37$	−3.73806	−	1.00161i	−0.614534	−	0.164664i	−0.0618923	−	0.998083i	$-0.519714\pi$
$37$	−3.73806	−	1.00161i	−0.614534	−	0.164664i	−0.552642	+	0.833419i	$0.686380\pi$
$38$	−1.17583	+	2.03659i	−0.190745	+	0.330379i
$39$		0			0
$40$	−7.41388	+	4.28040i	−1.17224	+	0.676791i
$41$	−4.02565	+	4.02565i	−0.628701	+	0.628701i	−0.947741	−	0.319040i	$-0.896640\pi$
$41$	−4.02565	+	4.02565i	−0.628701	+	0.628701i	0.319040	+	0.947741i	$0.396640\pi$
$42$		0			0
$43$		−	5.30948i		−	0.809688i	−0.914386	−	0.404844i	$-0.867326\pi$
$43$		−	5.30948i		−	0.809688i	0.914386	−	0.404844i	$-0.132674\pi$
$44$	−6.12512	+	22.8593i	−0.923397	+	3.44616i
$45$		0			0
$46$	−2.26603	−	8.45694i	−0.334108	−	1.24691i
$47$	−0.120170	+	0.448482i	−0.0175287	+	0.0654178i	−0.974136	−	0.225962i	$-0.927448\pi$
$47$	−0.120170	+	0.448482i	−0.0175287	+	0.0654178i	0.956608	+	0.291380i	$0.0941142\pi$
$48$		0			0
$49$	5.97375	−	3.64888i	0.853393	−	0.521268i
$50$	−4.05216	+	4.05216i	−0.573062	+	0.573062i
$51$		0			0
$52$	11.7605	+	9.03935i	1.63089	+	1.25353i
$53$	6.31835	−	10.9437i	0.867891	−	1.50323i	0.00374432	−	0.999993i	$-0.498808\pi$
$53$	6.31835	−	10.9437i	0.867891	−	1.50323i	0.864147	−	0.503239i	$-0.167859\pi$
$54$		0			0
$55$		−	9.42152i		−	1.27040i
$56$	6.76604	−	12.0612i	0.904150	−	1.61175i
$57$		0			0
$58$	−1.81718	+	6.78181i	−0.238607	+	0.890495i
$59$	11.5955	−	3.10701i	1.50961	−	0.404499i	0.593304	−	0.804979i	$-0.297823\pi$
$59$	11.5955	−	3.10701i	1.50961	−	0.404499i	0.916305	+	0.400480i	$0.131157\pi$
$60$		0			0
$61$	−4.38137	+	2.52958i	−0.560977	+	0.323880i	−0.753537	−	0.657405i	$-0.771654\pi$
$61$	−4.38137	+	2.52958i	−0.560977	+	0.323880i	0.192561	+	0.981285i	$0.438321\pi$
$62$	11.0867			1.40801
$63$		0			0
$64$			6.52733i			0.815916i
$65$	−5.45382	−	2.26425i	−0.676464	−	0.280845i
$66$		0			0
$67$	5.87066	−	1.57304i	0.717215	−	0.192177i	0.118286	−	0.992980i	$-0.462260\pi$
$67$	5.87066	−	1.57304i	0.717215	−	0.192177i	0.598929	+	0.800802i	$0.295593\pi$
$68$	7.06833	−	4.08090i	0.857160	−	0.494882i
$69$		0			0
$70$	−2.64489	+	10.3829i	−0.316125	+	1.24099i
$71$	4.84596	+	4.84596i	0.575110	+	0.575110i	0.933552	−	0.358442i	$-0.116692\pi$
$71$	4.84596	+	4.84596i	0.575110	+	0.575110i	−0.358442	+	0.933552i	$0.616692\pi$
$72$		0			0
$73$	−4.24311	+	1.13694i	−0.496619	+	0.133069i	−0.498430	−	0.866930i	$-0.666090\pi$
$73$	−4.24311	+	1.13694i	−0.496619	+	0.133069i	0.00181149	+	0.999998i	$0.499423\pi$
$74$	−4.78447	+	8.28694i	−0.556183	+	0.963338i
$75$		0			0
$76$	2.76666	+	2.76666i	0.317358	+	0.317358i
$77$	7.77235	+	13.0856i	0.885741	+	1.49124i
$78$		0			0
$79$	−3.08258	−	5.33918i	−0.346817	−	0.600704i	0.638865	−	0.769319i	$-0.279404\pi$
$79$	−3.08258	−	5.33918i	−0.346817	−	0.600704i	−0.985682	+	0.168614i	$0.946071\pi$
$80$	1.99088	+	7.43006i	0.222587	+	0.830706i
$81$		0			0
$82$	7.03853	+	12.1911i	0.777276	+	1.34628i
$83$	11.5176	−	11.5176i	1.26422	−	1.26422i	0.315194	−	0.949027i	$-0.397930\pi$
$83$	11.5176	−	11.5176i	1.26422	−	1.26422i	0.949027	−	0.315194i	$-0.102070\pi$
$84$		0			0
$85$	−2.29759	+	2.29759i	−0.249209	+	0.249209i
$86$	−12.6811	−	3.39789i	−1.36744	−	0.366403i
$87$		0			0
$88$	26.0402	+	15.0343i	2.77590	+	1.60267i
$89$	0.941005	−	3.51188i	0.0997463	−	0.372258i	−0.897950	−	0.440098i	$-0.854944\pi$
$89$	0.941005	−	3.51188i	0.0997463	−	0.372258i	0.997696	+	0.0678393i	$0.0216105\pi$
$90$		0			0
$91$	9.44276	−	1.35434i	0.989870	−	0.141974i
$92$	−14.5669			−1.51870
$93$		0			0
$94$	0.994243	+	0.574027i	0.102548	+	0.0592063i
$95$	−1.34898	−	0.778832i	−0.138402	−	0.0799065i
$96$		0			0
$97$	7.09855	−	7.09855i	0.720749	−	0.720749i	−0.248009	−	0.968758i	$-0.579776\pi$
$97$	7.09855	−	7.09855i	0.720749	−	0.720749i	0.968758	+	0.248009i	$0.0797763\pi$
$98$	−4.89192	−	16.6028i	−0.494159	−	1.67713i
$99$		0			0
$100$	4.76727	+	8.25715i	0.476727	+	0.825715i
$101$	2.12979	−	3.68890i	0.211922	−	0.367059i	−0.740394	−	0.672173i	$-0.765361\pi$
$101$	2.12979	−	3.68890i	0.211922	−	0.367059i	0.952316	+	0.305114i	$0.0986944\pi$
$102$		0			0
$103$	−2.08562	−	3.61240i	−0.205502	−	0.355940i	0.744790	−	0.667298i	$-0.232549\pi$
$103$	−2.08562	−	3.61240i	−0.205502	−	0.355940i	−0.950293	+	0.311358i	$0.899216\pi$
$104$	14.9611	−	11.4607i	1.46706	−	1.12382i
$105$		0			0
$106$	−22.0942	−	22.0942i	−2.14598	−	2.14598i
$107$	−1.91482	−	3.31657i	−0.185113	−	0.320625i	0.758502	−	0.651671i	$-0.225932\pi$
$107$	−1.91482	−	3.31657i	−0.185113	−	0.320625i	−0.943615	+	0.331046i	$0.892598\pi$
$108$		0			0
$109$	1.38124	−	0.370102i	0.132299	−	0.0354494i	−0.192062	−	0.981383i	$-0.561517\pi$
$109$	1.38124	−	0.370102i	0.132299	−	0.0354494i	0.324361	+	0.945933i	$0.394851\pi$
$110$	−22.5022	−	6.02945i	−2.14550	−	0.574886i
$111$		0			0
$112$	−8.89462	−	8.67727i	−0.840463	−	0.819925i
$113$	−15.2149			−1.43129			−0.715647	−	0.698462i	$-0.753868\pi$
$113$	−15.2149			−1.43129			−0.715647	+	0.698462i	$0.753868\pi$
$114$		0			0
$115$	5.60161	−	1.50095i	0.522353	−	0.139964i
$116$	10.1165	+	5.84076i	0.939292	+	0.542301i
$117$		0			0
$118$		−	29.6830i		−	2.73254i
$119$	1.29573	−	5.08656i	0.118779	−	0.466284i
$120$		0			0
$121$	−19.1321	+	11.0459i	−1.73928	+	1.00417i
$122$	3.23769	+	12.0832i	0.293127	+	1.09397i
$123$		0			0
$124$	4.77414	−	17.8173i	0.428730	−	1.60004i
$125$	−8.47452	−	8.47452i	−0.757984	−	0.757984i
$126$		0			0
$127$			6.12999i			0.543949i	0.962304	+	0.271974i	$0.0876766\pi$
$127$			6.12999i			0.543949i	−0.962304	+	0.271974i	$0.912323\pi$
$128$	17.8289	+	4.77725i	1.57587	+	0.422253i
$129$		0			0
$130$	−8.89816	+	11.5768i	−0.780420	+	1.01535i
$131$	−1.30691	+	0.754542i	−0.114185	+	0.0659247i	−0.556005	−	0.831179i	$-0.687666\pi$
$131$	−1.30691	+	0.754542i	−0.114185	+	0.0659247i	0.441820	+	0.897104i	$0.354333\pi$
$132$		0			0
$133$	2.51611	−	0.0311223i	0.218174	−	0.00269865i
$134$		−	15.0281i		−	1.29823i
$135$		0			0
$136$	−2.68397	−	10.0167i	−0.230149	−	0.858927i
$137$	−1.76458	−	6.58552i	−0.150759	−	0.562639i	−0.999431	−	0.0337203i	$-0.989264\pi$
$137$	−1.76458	−	6.58552i	−0.150759	−	0.562639i	0.848673	−	0.528918i	$-0.177402\pi$
$138$		0			0
$139$			6.26924i			0.531750i	0.964007	+	0.265875i	$0.0856609\pi$
$139$			6.26924i			0.531750i	−0.964007	+	0.265875i	$0.914339\pi$
$140$	15.5473	+	8.72166i	1.31399	+	0.737115i
$141$		0			0
$142$	14.6753	−	8.47278i	1.23152	−	0.711020i
$143$	2.69053	+	20.5659i	0.224994	+	1.71980i
$144$		0			0
$145$	−4.49206	−	1.20364i	−0.373045	−	0.0999571i
$146$			10.8618i			0.898929i
$147$		0			0
$148$	11.2576	+	11.2576i	0.925370	+	0.925370i
$149$	0.700828	−	2.61553i	0.0574141	−	0.214272i	−0.931259	−	0.364358i	$-0.881288\pi$
$149$	0.700828	−	2.61553i	0.0574141	−	0.214272i	0.988673	+	0.150086i	$0.0479551\pi$
$150$		0			0
$151$	−0.0731992	−	0.273183i	−0.00595686	−	0.0222313i	0.962883	−	0.269918i	$-0.0869965\pi$
$151$	−0.0731992	−	0.273183i	−0.00595686	−	0.0222313i	−0.968840	+	0.247686i	$0.920330\pi$
$152$	4.30525	−	2.48563i	0.349202	−	0.201612i
$153$		0			0
$154$	36.2275	−	10.1890i	2.91930	−	0.821054i
$155$			7.34346i			0.589841i
$156$		0			0
$157$	−0.885412	−	0.511193i	−0.0706636	−	0.0407976i	0.464252	−	0.885703i	$-0.346323\pi$
$157$	−0.885412	−	0.511193i	−0.0706636	−	0.0407976i	−0.534916	+	0.844906i	$0.679657\pi$
$158$	−14.7248	+	3.94549i	−1.17144	+	0.313886i
$159$		0			0
$160$	1.89832			0.150076
$161$	−6.54190	+	6.70576i	−0.515574	+	0.528488i
$162$		0			0
$163$	16.3776	+	4.38836i	1.28279	+	0.343723i	0.834918	−	0.550374i	$-0.185515\pi$
$163$	16.3776	+	4.38836i	1.28279	+	0.343723i	0.447874	+	0.894097i	$0.352181\pi$
$164$	22.6232	−	6.06186i	1.76657	−	0.473352i
$165$		0			0
$166$	−20.1376	−	34.8794i	−1.56298	−	2.70716i
$167$	−0.350041	−	0.350041i	−0.0270870	−	0.0270870i	0.693434	−	0.720521i	$-0.256097\pi$
$167$	−0.350041	−	0.350041i	−0.0270870	−	0.0270870i	−0.720521	+	0.693434i	$0.756097\pi$
$168$		0			0
$169$	12.5515	+	3.38507i	0.965504	+	0.260390i
$170$	4.01716	+	6.95792i	0.308102	+	0.533648i
$171$		0			0
$172$	−10.9214	+	18.9165i	−0.832753	+	1.44237i
$173$	−1.98781	−	3.44298i	−0.151130	−	0.261765i	0.780513	−	0.625139i	$-0.214958\pi$
$173$	−1.98781	−	3.44298i	−0.151130	−	0.261765i	−0.931643	+	0.363374i	$0.881625\pi$
$174$		0			0
$175$	5.94207	+	1.51366i	0.449178	+	0.114422i
$176$	19.1044	−	19.1044i	1.44005	−	1.44005i
$177$		0			0
$178$	−7.78551	−	4.49497i	−0.583549	−	0.336912i
$179$	5.57272	+	3.21741i	0.416524	+	0.240481i	0.693589	−	0.720371i	$-0.256028\pi$
$179$	5.57272	+	3.21741i	0.416524	+	0.240481i	−0.277065	+	0.960851i	$0.589362\pi$
$180$		0			0
$181$	−10.7701			−0.800535			−0.400268	−	0.916398i	$-0.631083\pi$
$181$	−10.7701			−0.800535			−0.400268	+	0.916398i	$0.631083\pi$
$182$	2.80836	−	23.4197i	0.208169	−	1.73598i
$183$		0			0
$184$	−4.79026	+	17.8775i	−0.353142	+	1.31795i
$185$	−5.48901	−	3.16908i	−0.403560	−	0.232996i
$186$		0			0
$187$	11.0238	+	2.95382i	0.806141	+	0.216005i
$188$	1.35066	−	1.35066i	0.0985067	−	0.0985067i
$189$		0			0
$190$	−2.72345	+	2.72345i	−0.197580	+	0.197580i
$191$	1.02334	+	1.77247i	0.0740461	+	0.128252i	0.900671	−	0.434502i	$-0.143075\pi$
$191$	1.02334	+	1.77247i	0.0740461	+	0.128252i	−0.826625	+	0.562753i	$0.809742\pi$
$192$		0			0
$193$	−0.744802	−	2.77964i	−0.0536120	−	0.200083i	0.933925	−	0.357469i	$-0.116360\pi$
$193$	−0.744802	−	2.77964i	−0.0536120	−	0.200083i	−0.987537	+	0.157386i	$0.949693\pi$
$194$	−12.4112	−	21.4969i	−0.891076	−	1.54339i
$195$		0			0
$196$	−28.7888	+	0.712301i	−2.05634	+	0.0508786i
$197$	4.42190	+	4.42190i	0.315047	+	0.315047i	0.846861	−	0.531814i	$-0.178489\pi$
$197$	4.42190	+	4.42190i	0.315047	+	0.315047i	−0.531814	+	0.846861i	$0.678489\pi$
$198$		0			0
$199$	10.4063	−	18.0243i	0.737687	−	1.27771i	−0.215848	−	0.976427i	$-0.569252\pi$
$199$	10.4063	−	18.0243i	0.737687	−	1.27771i	0.953535	−	0.301284i	$-0.0974151\pi$
$200$	11.7014	−	3.13539i	0.827417	−	0.221706i
$201$		0			0
$202$	−7.44753	−	7.44753i	−0.524006	−	0.524006i
$203$	7.23200	−	2.03401i	0.507587	−	0.142759i
$204$		0			0
$205$	−8.07500	+	4.66210i	−0.563982	+	0.325615i
$206$	−9.96252	+	2.66945i	−0.694122	+	0.185989i
$207$		0			0
$208$	−6.46763	−	15.6502i	−0.448450	−	1.08515i
$209$			5.47108i			0.378443i
$210$		0			0
$211$	−15.4637			−1.06456			−0.532281	−	0.846568i	$-0.678665\pi$
$211$	−15.4637			−1.06456			−0.532281	+	0.846568i	$0.678665\pi$
$212$	−45.0217	+	25.9933i	−3.09211	+	1.78523i
$213$		0			0
$214$	−9.14666	+	2.45084i	−0.625253	+	0.167536i
$215$	2.25065	−	8.39955i	0.153493	−	0.572845i
$216$		0			0
$217$	−6.05804	−	10.1994i	−0.411247	−	0.692379i
$218$		−	3.53579i		−	0.239474i
$219$		0			0
$220$	−19.3798	+	33.5668i	−1.30659	+	2.26307i
$221$	4.35920	−	5.67146i	0.293231	−	0.381503i
$222$		0			0
$223$	−16.7037	+	16.7037i	−1.11856	+	1.11856i	−0.126611	+	0.991953i	$0.540410\pi$
$223$	−16.7037	+	16.7037i	−1.11856	+	1.11856i	−0.991953	+	0.126611i	$0.959590\pi$
$224$	−2.63660	+	1.56604i	−0.176165	+	0.104635i
$225$		0			0
$226$	−9.73700	+	36.3390i	−0.647696	+	2.41723i
$227$	−5.55282	−	20.7234i	−0.368553	−	1.37546i	−0.862539	−	0.505990i	$-0.831127\pi$
$227$	−5.55282	−	20.7234i	−0.368553	−	1.37546i	0.493986	−	0.869470i	$-0.335539\pi$
$228$		0			0
$229$	−0.261946	+	0.977595i	−0.0173099	+	0.0646013i	−0.974041	−	0.226374i	$-0.927313\pi$
$229$	−0.261946	+	0.977595i	−0.0173099	+	0.0646013i	0.956731	+	0.290975i	$0.0939796\pi$
$230$		−	14.3394i		−	0.945509i
$231$		0			0
$232$	10.4949	−	10.4949i	0.689027	−	0.689027i
$233$	1.88448	−	1.08800i	0.123456	−	0.0712775i	−0.437000	−	0.899461i	$-0.643959\pi$
$233$	1.88448	−	1.08800i	0.123456	−	0.0712775i	0.560456	+	0.828184i	$0.310626\pi$
$234$		0			0
$235$	−0.380217	+	0.658556i	−0.0248026	+	0.0429594i
$236$	−47.7034	−	12.7821i	−3.10522	−	0.832042i
$237$		0			0
$238$	−11.3194	−	6.34992i	−0.733731	−	0.411604i
$239$	8.20062	+	8.20062i	0.530454	+	0.530454i	0.920708	−	0.390253i	$-0.127613\pi$
$239$	8.20062	+	8.20062i	0.530454	+	0.530454i	−0.390253	+	0.920708i	$0.627613\pi$
$240$		0			0
$241$	−6.21307	+	1.66479i	−0.400219	+	0.107238i	−0.453314	−	0.891351i	$-0.649758\pi$
$241$	−6.21307	+	1.66479i	−0.400219	+	0.107238i	0.0530945	+	0.998589i	$0.483092\pi$
$242$	14.1380	+	52.7638i	0.908826	+	3.39178i
$243$		0			0
$244$	20.8131			1.33242
$245$	10.9972	−	3.24026i	0.702583	−	0.207012i
$246$		0			0
$247$	3.16704	+	1.31485i	0.201514	+	0.0836619i
$248$	−20.2967	−	11.7183i	−1.28884	−	0.744112i
$249$		0			0
$250$	−25.6638	+	14.8170i	−1.62312	+	0.937111i
$251$	−1.99071			−0.125652			−0.0628261	−	0.998024i	$-0.520011\pi$
$251$	−1.99071			−0.125652			−0.0628261	+	0.998024i	$0.520011\pi$
$252$		0			0
$253$	−14.4030	−	14.4030i	−0.905511	−	0.905511i
$254$	14.6408	+	3.92299i	0.918645	+	0.246150i
$255$		0			0
$256$	16.2925	−	28.2194i	1.01828	−	1.76371i
$257$	−1.05283	−	1.82355i	−0.0656735	−	0.113750i	0.831319	−	0.555796i	$-0.187586\pi$
$257$	−1.05283	−	1.82355i	−0.0656735	−	0.113750i	−0.896993	+	0.442046i	$0.854253\pi$
$258$		0			0
$259$	10.2381	−	0.126637i	0.636164	−	0.00786887i
$260$	14.7733	+	19.2854i	0.916200	+	1.19603i
$261$		0			0
$262$	0.965763	+	3.60428i	0.0596650	+	0.222673i
$263$	−10.1364	+	17.5568i	−0.625040	+	1.08260i	0.363493	+	0.931597i	$0.381584\pi$
$263$	−10.1364	+	17.5568i	−0.625040	+	1.08260i	−0.988533	+	0.151004i	$0.951749\pi$
$264$		0			0
$265$	14.6345	−	14.6345i	0.898992	−	0.898992i
$266$	1.53589	−	6.02935i	0.0941715	−	0.369683i
$267$		0			0
$268$	−24.1515	−	6.47139i	−1.47529	−	0.395303i
$269$	−1.14303	−	0.659927i	−0.0696916	−	0.0402365i	0.464749	−	0.885442i	$-0.346144\pi$
$269$	−1.14303	−	0.659927i	−0.0696916	−	0.0402365i	−0.534441	+	0.845206i	$0.679478\pi$
$270$		0			0
$271$	−7.12464	+	26.5895i	−0.432791	+	1.61520i	0.313508	+	0.949586i	$0.398496\pi$
$271$	−7.12464	+	26.5895i	−0.432791	+	1.61520i	−0.746298	+	0.665611i	$0.768171\pi$
$272$	−9.31784			−0.564977
$273$		0			0
$274$	−16.8580			−1.01843
$275$	−3.45062	+	12.8779i	−0.208081	+	0.776567i
$276$		0			0
$277$	−14.5623	−	8.40757i	−0.874966	−	0.505162i	−0.00597071	−	0.999982i	$-0.501901\pi$
$277$	−14.5623	−	8.40757i	−0.874966	−	0.505162i	−0.868995	+	0.494820i	$0.835234\pi$
$278$	14.9734	+	4.01210i	0.898043	+	0.240630i
$279$		0			0
$280$	15.8165	−	16.2127i	0.945216	−	0.968892i
$281$	14.9251	−	14.9251i	0.890356	−	0.890356i	−0.104200	−	0.994556i	$-0.533228\pi$
$281$	14.9251	−	14.9251i	0.890356	−	0.890356i	0.994556	+	0.104200i	$0.0332282\pi$
$282$		0			0
$283$	15.5423	−	26.9201i	0.923895	−	1.60023i	0.130567	−	0.991440i	$-0.458320\pi$
$283$	15.5423	−	26.9201i	0.923895	−	1.60023i	0.793328	−	0.608794i	$-0.208346\pi$
$284$	−7.29709	−	27.2331i	−0.433003	−	1.61599i
$285$		0			0
$286$	50.8411	+	6.73543i	3.00629	+	0.398274i
$287$	7.36939	−	13.1368i	0.435001	−	0.775438i
$288$		0			0
$289$	6.53200	+	11.3138i	0.384235	+	0.665515i
$290$	−5.74953	+	9.95847i	−0.337624	+	0.584782i
$291$		0			0
$292$	17.4559	+	4.67730i	1.02153	+	0.273718i
$293$	10.7578	+	10.7578i	0.628478	+	0.628478i	0.947685	−	0.319207i	$-0.103417\pi$
$293$	10.7578	+	10.7578i	0.628478	+	0.628478i	−0.319207	+	0.947685i	$0.603417\pi$
$294$		0			0
$295$	19.6611			1.14471
$296$	17.5181	−	10.1141i	1.01822	−	0.587870i
$297$		0			0
$298$	−5.79838	−	3.34769i	−0.335891	−	0.193927i
$299$	−11.7989	+	4.87603i	−0.682348	+	0.281988i
$300$		0			0
$301$	3.80332	+	13.5229i	0.219220	+	0.779447i
$302$	−0.699311			−0.0402408
$303$		0			0
$304$	−1.15610	−	4.31464i	−0.0663072	−	0.247462i
$305$	−8.00356	+	2.14455i	−0.458283	+	0.122796i
$306$		0			0
$307$	−18.9532	−	18.9532i	−1.08172	−	1.08172i	−0.996349	−	0.0853681i	$-0.972793\pi$
$307$	−18.9532	−	18.9532i	−1.08172	−	1.08172i	−0.0853681	−	0.996349i	$-0.527207\pi$
$308$	−0.774422	−	62.6087i	−0.0441268	−	3.56746i
$309$		0			0
$310$	17.5390	+	4.69957i	0.996149	+	0.266917i
$311$	5.62362	−	9.74040i	0.318886	−	0.552328i	−0.661370	−	0.750060i	$-0.730024\pi$
$311$	5.62362	−	9.74040i	0.318886	−	0.552328i	0.980256	+	0.197733i	$0.0633578\pi$
$312$		0			0
$313$	25.3774	−	14.6516i	1.43441	−	0.828159i	0.436960	−	0.899481i	$-0.356055\pi$
$313$	25.3774	−	14.6516i	1.43441	−	0.828159i	0.997453	+	0.0713218i	$0.0227217\pi$
$314$	−1.78756	+	1.78756i	−0.100878	+	0.100878i
$315$		0			0
$316$			25.3631i			1.42679i
$317$	−3.93824	+	14.6977i	−0.221194	+	0.825507i	0.762700	+	0.646752i	$0.223873\pi$
$317$	−3.93824	+	14.6977i	−0.221194	+	0.825507i	−0.983894	+	0.178754i	$0.942793\pi$
$318$		0			0
$319$	4.22763	+	15.7777i	0.236702	+	0.883384i
$320$	−2.76689	+	10.3262i	−0.154674	+	0.577251i
$321$		0			0
$322$	11.8294	+	19.9160i	0.659224	+	1.10988i
$323$	1.33421	−	1.33421i	0.0742377	−	0.0742377i
$324$		0			0
$325$	6.62534	+	5.09237i	0.367508	+	0.282474i
$326$	20.9622	−	36.3076i	1.16099	−	2.01089i
$327$		0			0
$328$		−	29.7581i		−	1.64312i
$329$	−0.0151936	−	1.22834i	−0.000837650	−	0.0677203i
$330$		0			0
$331$	6.65652	−	24.8425i	0.365876	−	1.36547i	−0.500354	−	0.865821i	$-0.666797\pi$
$331$	6.65652	−	24.8425i	0.365876	−	1.36547i	0.866230	−	0.499646i	$-0.166536\pi$
$332$	−64.7261	+	17.3433i	−3.55231	+	0.951837i
$333$		0			0
$334$	−1.06005	+	0.612019i	−0.0580032	+	0.0334882i
$335$	9.95413			0.543852
$336$		0			0
$337$			3.72672i			0.203008i	0.994835	+	0.101504i	$0.0323654\pi$
$337$			3.72672i			0.203008i	−0.994835	+	0.101504i	$0.967635\pi$
$338$	16.1174	−	27.8116i	0.876672	−	1.51275i
$339$		0			0
$340$	12.9119	−	3.45973i	0.700246	−	0.187630i
$341$	22.3373	−	12.8965i	1.20963	−	0.698382i
$342$		0			0
$343$	−12.6010	+	13.5726i	−0.680388	+	0.732852i
$344$	19.6242	+	19.6242i	1.05806	+	1.05806i
$345$		0			0
$346$	−9.49530	+	2.54426i	−0.510470	+	0.136780i
$347$	−6.77145	+	11.7285i	−0.363511	+	0.629619i	−0.988536	−	0.150986i	$-0.951755\pi$
$347$	−6.77145	+	11.7285i	−0.363511	+	0.629619i	0.625025	+	0.780604i	$0.285089\pi$
$348$		0			0
$349$	21.5796	+	21.5796i	1.15513	+	1.15513i	0.985509	+	0.169620i	$0.0542541\pi$
$349$	21.5796	+	21.5796i	1.15513	+	1.15513i	0.169620	+	0.985509i	$0.445746\pi$
$350$	7.41792	−	13.2233i	0.396505	−	0.706814i
$351$		0			0
$352$	−3.33380	−	5.77432i	−0.177692	−	0.307772i
$353$	0.717375	+	2.67728i	0.0381820	+	0.142497i	0.982386	−	0.186865i	$-0.0598328\pi$
$353$	0.717375	+	2.67728i	0.0381820	+	0.142497i	−0.944204	+	0.329363i	$0.893166\pi$
$354$		0			0
$355$	5.61210	+	9.72045i	0.297860	+	0.515908i
$356$	−10.5764	+	10.5764i	−0.560550	+	0.560550i
$357$		0			0
$358$	11.2508	−	11.2508i	0.594621	−	0.594621i
$359$	8.80969	+	2.36055i	0.464958	+	0.124585i	0.483690	−	0.875239i	$-0.339296\pi$
$359$	8.80969	+	2.36055i	0.464958	+	0.124585i	−0.0187320	+	0.999825i	$0.505963\pi$
$360$		0			0
$361$	−15.6711	−	9.04773i	−0.824796	−	0.476196i
$362$	−6.89250	+	25.7232i	−0.362262	+	1.35198i
$363$		0			0
$364$	−36.4283	−	14.5983i	−1.90936	−	0.765157i
$365$	−7.19451			−0.376578
$366$		0			0
$367$	10.4995	+	6.06190i	0.548071	+	0.316429i	0.748343	−	0.663311i	$-0.230850\pi$
$367$	10.4995	+	6.06190i	0.548071	+	0.316429i	−0.200273	+	0.979740i	$0.564183\pi$
$368$	14.4021	+	8.31508i	0.750763	+	0.433453i
$369$		0			0
$370$	−11.0818	+	11.0818i	−0.576114	+	0.576114i
$371$	−8.25315	+	32.3989i	−0.428482	+	1.68207i
$372$		0			0
$373$	−13.8527	−	23.9936i	−0.717266	−	1.24234i	−0.962079	−	0.272771i	$-0.912060\pi$
$373$	−13.8527	−	23.9936i	−0.717266	−	1.24234i	0.244813	−	0.969570i	$-0.421273\pi$
$374$	14.1097	−	24.4388i	0.729597	−	1.26370i
$375$		0			0
$376$	−1.21346	−	2.10177i	−0.0625794	−	0.108391i
$377$	10.1493	+	1.34457i	0.522714	+	0.0692491i
$378$		0			0
$379$	1.97532	+	1.97532i	0.101466	+	0.101466i	0.756017	−	0.654552i	$-0.227143\pi$
$379$	1.97532	+	1.97532i	0.101466	+	0.101466i	−0.654552	+	0.756017i	$0.727143\pi$
$380$	3.20407	+	5.54961i	0.164365	+	0.284689i
$381$		0			0
$382$	4.88825	−	1.30980i	0.250105	−	0.0670153i
$383$	17.5608	+	4.70541i	0.897317	+	0.240435i	0.677864	−	0.735188i	$-0.262906\pi$
$383$	17.5608	+	4.70541i	0.897317	+	0.240435i	0.219453	+	0.975623i	$0.429573\pi$
$384$		0			0
$385$	6.74889	+	23.9960i	0.343955	+	1.22295i
$386$	−7.11550			−0.362169
$387$		0			0
$388$	−39.8921	+	10.6891i	−2.02521	+	0.542654i
$389$	−4.76738	−	2.75245i	−0.241716	−	0.139555i	0.374249	−	0.927328i	$-0.377900\pi$
$389$	−4.76738	−	2.75245i	−0.241716	−	0.139555i	−0.615965	+	0.787773i	$0.711234\pi$
$390$		0			0
$391$			7.02483i			0.355261i
$392$	−8.59288	+	35.5658i	−0.434006	+	1.79635i
$393$		0			0
$394$	13.3911	−	7.73133i	0.674632	−	0.389499i
$395$	−2.61337	−	9.75322i	−0.131493	−	0.490738i
$396$		0			0
$397$	−6.45307	+	24.0832i	−0.323870	+	1.20870i	0.591572	+	0.806252i	$0.298507\pi$
$397$	−6.45307	+	24.0832i	−0.323870	+	1.20870i	−0.915443	+	0.402449i	$0.868159\pi$
$398$	−36.3893	−	36.3893i	−1.82403	−	1.82403i
$399$		0			0
$400$		−	10.8850i		−	0.544251i
$401$	−7.90338	−	2.11770i	−0.394676	−	0.105753i	0.0560222	−	0.998430i	$-0.482158\pi$
$401$	−7.90338	−	2.11770i	−0.394676	−	0.105753i	−0.450698	+	0.892676i	$0.648825\pi$
$402$		0			0
$403$	−2.09709	−	16.0298i	−0.104464	−	0.798499i
$404$	−15.1759	+	8.76183i	−0.755031	+	0.435917i
$405$		0			0
$406$	−0.229753	−	18.5745i	−0.0114024	−	0.921837i
$407$			22.2620i			1.10348i
$408$		0			0
$409$	1.16168	+	4.33547i	0.0574416	+	0.214375i	0.988681	−	0.150033i	$-0.0479380\pi$
$409$	1.16168	+	4.33547i	0.0574416	+	0.214375i	−0.931239	+	0.364408i	$0.881271\pi$
$410$	5.96718	+	22.2698i	0.294698	+	1.09983i
$411$		0			0
$412$			17.1602i			0.845424i
$413$	−27.3074	+	16.2195i	−1.34371	+	0.798112i
$414$		0			0
$415$	23.1030	−	13.3385i	1.13408	−	0.654762i
$416$	−4.14378	+	0.542110i	−0.203165	+	0.0265791i
$417$		0			0
$418$	13.0671	+	3.50131i	0.639131	+	0.171255i
$419$			35.1474i			1.71706i	0.512760	+	0.858532i	$0.328623\pi$
$419$			35.1474i			1.71706i	−0.512760	+	0.858532i	$0.671377\pi$
$420$		0			0
$421$	24.7123	+	24.7123i	1.20440	+	1.20440i	0.972814	+	0.231589i	$0.0743926\pi$
$421$	24.7123	+	24.7123i	1.20440	+	1.20440i	0.231589	+	0.972814i	$0.425607\pi$
$422$	−9.89621	+	36.9332i	−0.481740	+	1.79788i
$423$		0			0
$424$	17.0956	+	63.8016i	0.830235	+	3.09848i
$425$	3.98198	−	2.29900i	0.193155	−	0.111518i
$426$		0			0
$427$	9.34705	−	9.58117i	0.452335	−	0.463665i
$428$			15.7549i			0.761543i
$429$		0			0
$430$	−18.6210	−	10.7509i	−0.897986	−	0.518452i
$431$	34.5526	−	9.25833i	1.66434	−	0.445958i	0.700763	−	0.713395i	$-0.252843\pi$
$431$	34.5526	−	9.25833i	1.66434	−	0.445958i	0.963575	+	0.267437i	$0.0861766\pi$
$432$		0			0
$433$	3.82925			0.184022			0.0920110	−	0.995758i	$-0.470670\pi$
$433$	3.82925			0.184022			0.0920110	+	0.995758i	$0.470670\pi$
$434$	−28.2370	+	7.94168i	−1.35542	+	0.381213i
$435$		0			0
$436$	−5.68235	−	1.52258i	−0.272135	−	0.0729184i
$437$	−3.25286	+	0.871601i	−0.155605	+	0.0416943i
$438$		0			0
$439$	−2.14941	−	3.72288i	−0.102586	−	0.177684i	0.810164	−	0.586204i	$-0.199378\pi$
$439$	−2.14941	−	3.72288i	−0.102586	−	0.177684i	−0.912749	+	0.408520i	$0.866045\pi$
$440$	34.8225	+	34.8225i	1.66010	+	1.66010i
$441$		0			0
$442$	−10.7559	−	14.0410i	−0.511606	−	0.667861i
$443$	−7.37495	−	12.7738i	−0.350395	−	0.606901i	0.635924	−	0.771752i	$-0.280619\pi$
$443$	−7.37495	−	12.7738i	−0.350395	−	0.606901i	−0.986319	+	0.164851i	$0.947286\pi$
$444$		0			0
$445$	2.97732	−	5.15688i	0.141139	−	0.244459i
$446$	29.2051	+	50.5847i	1.38290	+	2.39526i
$447$		0			0
$448$	−4.67570	−	16.6247i	−0.220906	−	0.785442i
$449$	13.9834	−	13.9834i	0.659915	−	0.659915i	−0.295445	−	0.955360i	$-0.595468\pi$
$449$	13.9834	−	13.9834i	0.659915	−	0.659915i	0.955360	+	0.295445i	$0.0954678\pi$
$450$		0			0
$451$	28.3624	+	16.3750i	1.33553	+	0.771069i
$452$	54.2072	+	31.2966i	2.54969	+	1.47207i
$453$		0			0
$454$	−53.0491			−2.48972
$455$	15.5125	+	1.86017i	0.727236	+	0.0872060i
$456$		0			0
$457$	−7.91853	+	29.5523i	−0.370413	+	1.38240i	0.489519	+	0.871992i	$0.337172\pi$
$457$	−7.91853	+	29.5523i	−0.370413	+	1.38240i	−0.859932	+	0.510408i	$0.829494\pi$
$458$	2.16724	+	1.25126i	0.101268	+	0.0584673i
$459$		0			0
$460$	−23.0447	−	6.17481i	−1.07447	−	0.287902i
$461$	−4.39870	+	4.39870i	−0.204868	+	0.204868i	−0.802082	−	0.597214i	$-0.796274\pi$
$461$	−4.39870	+	4.39870i	−0.204868	+	0.204868i	0.597214	+	0.802082i	$0.296274\pi$
$462$		0			0
$463$	6.67812	−	6.67812i	0.310358	−	0.310358i	−0.534690	−	0.845048i	$-0.679572\pi$
$463$	6.67812	−	6.67812i	0.310358	−	0.310358i	0.845048	+	0.534690i	$0.179572\pi$
$464$	−6.66805	−	11.5494i	−0.309556	−	0.536167i
$465$		0			0
$466$	−1.39257	−	5.19714i	−0.0645096	−	0.240753i
$467$	−19.0523	−	32.9996i	−0.881636	−	1.52704i	−0.849521	−	0.527554i	$-0.823109\pi$
$467$	−19.0523	−	32.9996i	−0.881636	−	1.52704i	−0.0321149	−	0.999484i	$-0.510224\pi$
$468$		0			0
$469$	−13.8254	+	8.21173i	−0.638396	+	0.379183i
$470$	1.32956	+	1.32956i	0.0613280	+	0.0613280i
$471$		0			0
$472$	−31.3741	+	54.3415i	−1.44411	+	2.50127i
$473$	−29.5023	+	7.90512i	−1.35652	+	0.363478i
$474$		0			0
$475$	1.55862	+	1.55862i	0.0715142	+	0.0715142i
$476$	−15.0793	+	15.4570i	−0.691159	+	0.708471i
$477$		0			0
$478$	24.8344	−	14.3381i	1.13590	−	0.655811i
$479$	−11.2140	+	3.00477i	−0.512379	+	0.137291i	−0.505739	−	0.862686i	$-0.668780\pi$
$479$	−11.2140	+	3.00477i	−0.512379	+	0.137291i	−0.00663970	+	0.999978i	$0.502113\pi$
$480$		0			0
$481$	12.8868	+	5.35015i	0.587585	+	0.243946i
$482$			15.9046i			0.724436i
$483$		0			0
$484$	90.8845			4.13111
$485$	14.2389	−	8.22082i	0.646554	−	0.373288i
$486$		0			0
$487$	−32.1240	+	8.60759i	−1.45568	+	0.390047i	−0.897994	−	0.440008i	$-0.854976\pi$
$487$	−32.1240	+	8.60759i	−1.45568	+	0.390047i	−0.557681	+	0.830055i	$0.688309\pi$
$488$	6.84431	−	25.5433i	0.309827	−	1.15629i
$489$		0			0
$490$	−0.701175	−	28.3391i	−0.0316758	−	1.28023i
$491$			2.41523i			0.108998i	0.998514	+	0.0544989i	$0.0173561\pi$
$491$			2.41523i			0.108998i	−0.998514	+	0.0544989i	$0.982644\pi$
$492$		0			0
$493$	2.81669	−	4.87864i	0.126857	−	0.219723i
$494$	5.16717	−	6.72266i	0.232482	−	0.302467i
$495$		0			0
$496$	−14.8906	+	14.8906i	−0.668609	+	0.668609i
$497$	−15.8136	−	8.87106i	−0.709339	−	0.397921i
$498$		0			0
$499$	−0.127329	+	0.475197i	−0.00570002	+	0.0212727i	−0.968717	−	0.248167i	$-0.920172\pi$
$499$	−0.127329	+	0.475197i	−0.00570002	+	0.0212727i	0.963017	+	0.269440i	$0.0868385\pi$
$500$	12.7610	+	47.6247i	0.570689	+	2.12984i
$501$		0			0
$502$	−1.27398	+	4.75457i	−0.0568607	+	0.212207i
$503$		−	15.5328i		−	0.692575i	−0.938128	−	0.346288i	$-0.887442\pi$
$503$		−	15.5328i		−	0.692575i	0.938128	−	0.346288i	$-0.112558\pi$
$504$		0			0
$505$	4.93301	−	4.93301i	0.219516	−	0.219516i
$506$	−43.6174	+	25.1825i	−1.93903	+	1.11950i
$507$		0			0
$508$	12.6092	−	21.8398i	0.559444	−	0.968985i
$509$	33.6436	+	9.01478i	1.49123	+	0.399573i	0.910151	−	0.414276i	$-0.135965\pi$
$509$	33.6436	+	9.01478i	1.49123	+	0.399573i	0.581076	+	0.813849i	$0.302632\pi$
$510$		0			0
$511$	9.99251	−	5.93517i	0.442043	−	0.262556i
$512$	−30.8689	−	30.8689i	−1.36422	−	1.36422i
$513$		0			0
$514$	−5.02911	+	1.34755i	−0.221825	+	0.0594377i
$515$	−1.76816	−	6.59886i	−0.0779145	−	0.290781i
$516$		0			0
$517$	2.67092			0.117467
$518$	6.24957	−	24.5335i	0.274590	−	1.07794i
$519$		0			0
$520$	28.5265	−	11.7889i	1.25097	−	0.516976i
$521$	−4.95243	−	2.85928i	−0.216970	−	0.125268i	0.387577	−	0.921837i	$-0.373312\pi$
$521$	−4.95243	−	2.85928i	−0.216970	−	0.125268i	−0.604546	+	0.796570i	$0.706646\pi$
$522$		0			0
$523$	−23.2231	+	13.4079i	−1.01548	+	0.586286i	−0.912791	−	0.408428i	$-0.866077\pi$
$523$	−23.2231	+	13.4079i	−1.01548	+	0.586286i	−0.102686	+	0.994714i	$0.532744\pi$
$524$	6.20829			0.271210
$525$		0			0
$526$	35.4455	+	35.4455i	1.54550	+	1.54550i
$527$	−8.59234	−	2.30231i	−0.374288	−	0.100290i
$528$		0			0
$529$	−5.23116	+	9.06064i	−0.227442	+	0.393941i
$530$	−25.5873	−	44.3185i	−1.11144	−	1.92507i
$531$		0			0
$532$	−9.02835	−	5.06468i	−0.391429	−	0.219582i
$533$	16.2952	−	12.4827i	0.705825	−	0.540687i
$534$		0			0
$535$	−1.62336	−	6.05846i	−0.0701840	−	0.261930i
$536$	−15.8843	+	27.5123i	−0.686096	+	1.18835i
$537$		0			0
$538$	−2.30766	+	2.30766i	−0.0994903	+	0.0994903i
$539$	−29.1692	−	27.7607i	−1.25641	−	1.19574i
$540$		0			0
$541$	−19.2806	−	5.16622i	−0.828938	−	0.222113i	−0.180688	−	0.983541i	$-0.557832\pi$
$541$	−19.2806	−	5.16622i	−0.828938	−	0.222113i	−0.648250	+	0.761427i	$0.724499\pi$
$542$	58.9465	+	34.0328i	2.53197	+	1.46183i
$543$		0			0
$544$	−0.595160	+	2.22117i	−0.0255173	+	0.0952317i
$545$	2.34200			0.100320
$546$		0			0
$547$	−11.1973			−0.478763			−0.239382	−	0.970926i	$-0.576945\pi$
$547$	−11.1973			−0.478763			−0.239382	+	0.970926i	$0.576945\pi$
$548$	−7.25940	+	27.0924i	−0.310106	+	1.15733i
$549$		0			0
$550$	28.5491	+	16.4828i	1.21734	+	0.702831i
$551$	2.60854	+	0.698957i	0.111128	+	0.0297765i
$552$		0			0
$553$	11.6757	+	11.3904i	0.496502	+	0.484369i
$554$	−29.3999	+	29.3999i	−1.24908	+	1.24908i
$555$		0			0
$556$	12.8957	−	22.3359i	0.546898	−	0.947255i
$557$	−8.01858	−	29.9257i	−0.339758	−	1.26799i	−0.898618	−	0.438732i	$-0.855428\pi$
$557$	−8.01858	−	29.9257i	−0.339758	−	1.26799i	0.558860	−	0.829262i	$-0.311239\pi$
$558$		0			0
$559$	−2.51418	+	18.9778i	−0.106338	+	0.802675i
$560$	−10.3930	−	17.4978i	−0.439184	−	0.739415i
$561$		0			0
$562$	−26.0953	−	45.1984i	−1.10077	−	1.90658i
$563$	17.8356	−	30.8922i	0.751682	−	1.30195i	−0.195325	−	0.980739i	$-0.562576\pi$
$563$	17.8356	−	30.8922i	0.751682	−	1.30195i	0.947007	−	0.321213i	$-0.104090\pi$
$564$		0			0
$565$	−24.0698	−	6.44949i	−1.01262	−	0.271332i
$566$	−54.3490	−	54.3490i	−2.28446	−	2.28446i
$567$		0			0
$568$	−35.8220			−1.50306
$569$	−13.6314	+	7.87011i	−0.571459	+	0.329932i	−0.757732	−	0.652566i	$-0.773693\pi$
$569$	−13.6314	+	7.87011i	−0.571459	+	0.329932i	0.186273	+	0.982498i	$0.440359\pi$
$570$		0			0
$571$	−4.87728	−	2.81590i	−0.204108	−	0.117842i	0.394462	−	0.918912i	$-0.370931\pi$
$571$	−4.87728	−	2.81590i	−0.204108	−	0.117842i	−0.598570	+	0.801070i	$0.704264\pi$
$572$	32.7176	−	78.8060i	1.36799	−	3.29504i
$573$		0			0
$574$	−26.6595	−	26.0080i	−1.11275	−	1.08555i
$575$	−8.20634			−0.342228
$576$		0			0
$577$	−9.91860	−	37.0167i	−0.412917	−	1.54103i	−0.788972	−	0.614429i	$-0.789386\pi$
$577$	−9.91860	−	37.0167i	−0.412917	−	1.54103i	0.376055	−	0.926597i	$-0.377280\pi$
$578$	31.2019	−	8.36052i	1.29783	−	0.347752i
$579$		0			0
$580$	13.5283	+	13.5283i	0.561734	+	0.561734i
$581$	−21.0842	+	37.5850i	−0.874721	+	1.55929i
$582$		0			0
$583$	−70.2162	−	18.8144i	−2.90806	−	0.779212i
$584$	11.4806	−	19.8850i	0.475071	−	0.822847i
$585$		0			0
$586$	32.5784	−	18.8092i	1.34580	−	0.776999i
$587$	−18.6594	+	18.6594i	−0.770156	+	0.770156i	−0.978134	−	0.207977i	$-0.933312\pi$
$587$	−18.6594	+	18.6594i	−0.770156	+	0.770156i	0.207977	+	0.978134i	$0.433312\pi$
$588$		0			0
$589$		−	4.26435i		−	0.175710i
$590$	12.5824	−	46.9582i	0.518010	−	1.93324i
$591$		0			0
$592$	−4.70421	−	17.5564i	−0.193342	−	0.721562i
$593$	−11.8139	+	44.0900i	−0.485138	+	1.81056i	0.0943021	+	0.995544i	$0.469938\pi$
$593$	−11.8139	+	44.0900i	−0.485138	+	1.81056i	−0.579440	+	0.815015i	$0.696729\pi$
$594$		0			0
$595$	4.20599	−	7.49765i	0.172429	−	0.307374i
$596$	−7.87696	+	7.87696i	−0.322653	+	0.322653i
$597$		0			0
$598$	4.09494	+	31.3008i	0.167454	+	1.27999i
$599$	2.34380	−	4.05958i	0.0957650	−	0.165870i	−0.814163	−	0.580637i	$-0.802804\pi$
$599$	2.34380	−	4.05958i	0.0957650	−	0.165870i	0.909928	+	0.414767i	$0.136137\pi$
$600$		0			0
$601$			34.8781i			1.42271i	0.702835	+	0.711353i	$0.251917\pi$
$601$			34.8781i			1.42271i	−0.702835	+	0.711353i	$0.748083\pi$
$602$	34.7319	−	0.429607i	1.41557	−	0.0175095i
$603$		0			0
$604$	−0.301137	+	1.12386i	−0.0122531	+	0.0457292i
$605$	−34.9491	+	9.36458i	−1.42088	+	0.380724i
$606$		0			0
$607$	25.8405	−	14.9190i	1.04884	−	0.605545i	0.126512	−	0.991965i	$-0.459622\pi$
$607$	25.8405	−	14.9190i	1.04884	−	0.605545i	0.922323	+	0.386420i	$0.126288\pi$
$608$	−1.10236			−0.0447066
$609$		0			0
$610$			20.4880i			0.829536i
$611$	0.641896	−	1.54612i	0.0259683	−	0.0625491i
$612$		0			0
$613$	41.1194	−	11.0179i	1.66080	−	0.445009i	0.698190	−	0.715912i	$-0.253989\pi$
$613$	41.1194	−	11.0179i	1.66080	−	0.445009i	0.962607	+	0.270903i	$0.0873223\pi$
$614$	−57.3970	+	33.1382i	−2.31636	+	1.33735i
$615$		0			0
$616$	−77.0923	−	19.6382i	−3.10614	−	0.791244i
$617$	−13.3408	−	13.3408i	−0.537079	−	0.537079i	0.385591	−	0.922670i	$-0.373998\pi$
$617$	−13.3408	−	13.3408i	−0.537079	−	0.537079i	−0.922670	+	0.385591i	$0.873998\pi$
$618$		0			0
$619$	2.78249	−	0.745565i	0.111838	−	0.0299668i	−0.202466	−	0.979289i	$-0.564896\pi$
$619$	2.78249	−	0.745565i	0.111838	−	0.0299668i	0.314304	+	0.949322i	$0.398229\pi$
$620$	15.1053	−	26.1631i	0.606643	−	1.05074i
$621$		0			0
$622$	−19.6649	−	19.6649i	−0.788491	−	0.788491i
$623$	0.118975	+	9.61859i	0.00476662	+	0.385361i
$624$		0			0
$625$	−4.02029	−	6.96335i	−0.160812	−	0.278534i
$626$	−18.7531	−	69.9875i	−0.749524	−	2.79726i
$627$		0			0
$628$	2.10302	+	3.64254i	0.0839196	+	0.145353i
$629$	5.42895	−	5.42895i	0.216466	−	0.216466i
$630$		0			0
$631$	−25.3632	+	25.3632i	−1.00969	+	1.00969i	−0.00973923	+	0.999953i	$0.503100\pi$
$631$	−25.3632	+	25.3632i	−1.00969	+	1.00969i	−0.999953	+	0.00973923i	$0.996900\pi$
$632$	31.1273	+	8.34054i	1.23818	+	0.331769i
$633$		0			0
$634$	32.5835	+	18.8121i	1.29406	+	0.747124i
$635$	−2.59846	+	9.69760i	−0.103117	+	0.384838i
$636$		0			0
$637$	−23.0799	+	10.2135i	−0.914461	+	0.404675i
$638$	40.3889			1.59901
$639$		0			0
$640$	26.1802	+	15.1151i	1.03486	+	0.597478i
$641$	−2.83626	−	1.63751i	−0.112025	−	0.0646779i	0.442940	−	0.896551i	$-0.353935\pi$
$641$	−2.83626	−	1.63751i	−0.112025	−	0.0646779i	−0.554966	+	0.831873i	$0.687269\pi$
$642$		0			0
$643$	−30.3555	+	30.3555i	−1.19710	+	1.19710i	−0.222072	+	0.975030i	$0.571282\pi$
$643$	−30.3555	+	30.3555i	−1.19710	+	1.19710i	−0.975030	+	0.222072i	$0.928718\pi$
$644$	37.1009	−	10.4347i	1.46198	−	0.411183i
$645$		0			0
$646$	−2.33277	−	4.04047i	−0.0917815	−	0.158970i
$647$	16.6342	−	28.8112i	0.653956	−	1.13269i	−0.328198	−	0.944609i	$-0.606441\pi$
$647$	16.6342	−	28.8112i	0.653956	−	1.13269i	0.982154	−	0.188077i	$-0.0602254\pi$
$648$		0			0
$649$	−34.5284	−	59.8050i	−1.35536	−	2.34755i
$650$	16.4025	−	12.5649i	0.643361	−	0.492837i
$651$		0			0
$652$	−49.3230	−	49.3230i	−1.93164	−	1.93164i
$653$	−15.4772	−	26.8072i	−0.605668	−	1.04905i	−0.991946	−	0.126665i	$-0.959573\pi$
$653$	−15.4772	−	26.8072i	−0.605668	−	1.04905i	0.386278	−	0.922382i	$-0.373761\pi$
$654$		0			0
$655$	−2.38736	+	0.639691i	−0.0932819	+	0.0249948i
$656$	−25.8275	−	6.92047i	−1.00840	−	0.270199i
$657$		0			0
$658$	−2.94346	−	0.749805i	−0.114748	−	0.0292304i
$659$	43.2836			1.68609			0.843045	−	0.537843i	$-0.180761\pi$
$659$	43.2836			1.68609			0.843045	+	0.537843i	$0.180761\pi$
$660$		0			0
$661$	40.0343	−	10.7272i	1.55715	−	0.417238i	0.625393	−	0.780310i	$-0.284939\pi$
$661$	40.0343	−	10.7272i	1.55715	−	0.417238i	0.931761	+	0.363072i	$0.118272\pi$
$662$	−55.0735	−	31.7967i	−2.14049	−	1.23581i
$663$		0			0
$664$			85.1395i			3.30406i
$665$	3.99365	+	1.01733i	0.154867	+	0.0394502i
$666$		0			0
$667$	−8.70723	+	5.02712i	−0.337145	+	0.194651i
$668$	0.527095	+	1.96714i	0.0203939	+	0.0761111i
$669$		0			0
$670$	6.37031	−	23.7743i	0.246106	−	0.918482i
$671$	20.5790	+	20.5790i	0.794443	+	0.794443i
$672$		0			0
$673$			12.5591i			0.484116i	0.970262	+	0.242058i	$0.0778224\pi$
$673$			12.5591i			0.484116i	−0.970262	+	0.242058i	$0.922178\pi$
$674$	8.90085	+	2.38498i	0.342848	+	0.0918659i
$675$		0			0
$676$	−37.7554	−	37.8784i	−1.45213	−	1.45686i
$677$	−7.26874	+	4.19661i	−0.279361	+	0.161289i	−0.633134	−	0.774042i	$-0.718232\pi$
$677$	−7.26874	+	4.19661i	−0.279361	+	0.161289i	0.353773	+	0.935331i	$0.384898\pi$
$678$		0			0
$679$	−12.9947	+	23.1644i	−0.498689	+	0.888969i
$680$		−	16.9841i		−	0.651310i
$681$		0			0
$682$	−16.5066	−	61.6034i	−0.632070	−	2.35892i
$683$	−2.72266	−	10.1611i	−0.104180	−	0.388804i	0.894071	−	0.447925i	$-0.147837\pi$
$683$	−2.72266	−	10.1611i	−0.104180	−	0.388804i	−0.998251	+	0.0591213i	$0.981170\pi$
$684$		0			0
$685$		−	11.1662i		−	0.426640i
$686$	24.3524	+	38.7820i	0.929780	+	1.48070i
$687$		0			0
$688$	21.5959	−	12.4684i	0.823334	−	0.475352i
$689$	−27.7659	+	36.1244i	−1.05780	+	1.37623i
$690$		0			0
$691$	33.9813	+	9.10526i	1.29271	+	0.346380i	0.838689	−	0.544611i	$-0.183323\pi$
$691$	33.9813	+	9.10526i	1.29271	+	0.346380i	0.454021	+	0.890991i	$0.349989\pi$
$692$			16.3555i			0.621741i
$693$		0			0
$694$	23.6787	+	23.6787i	0.898830	+	0.898830i
$695$	−2.65749	+	9.91789i	−0.100804	+	0.376207i
$696$		0			0
$697$	−2.92331	−	10.9099i	−0.110728	−	0.413244i
$698$	65.3506	−	37.7302i	2.47356	−	1.42811i
$699$		0			0
$700$	−18.0567	−	17.6155i	−0.682481	−	0.665803i
$701$		−	0.321018i		−	0.0121247i	−0.999982	−	0.00606234i	$-0.998070\pi$
$701$		−	0.321018i		−	0.0121247i	0.999982	−	0.00606234i	$-0.00192972\pi$
$702$		0			0
$703$	3.18748	+	1.84029i	0.120218	+	0.0694078i
$704$	36.2693	−	9.71834i	1.36695	−	0.366274i
$705$		0			0
$706$	6.85348			0.257934
$707$	−2.78197	+	10.9210i	−0.104627	+	0.410727i
$708$		0			0
$709$	−24.2000	−	6.48436i	−0.908849	−	0.243525i	−0.226036	−	0.974119i	$-0.572577\pi$
$709$	−24.2000	−	6.48436i	−0.908849	−	0.243525i	−0.682813	+	0.730593i	$0.739243\pi$
$710$	26.8077	−	7.18311i	1.00608	−	0.269577i
$711$		0			0
$712$	9.50210	+	16.4581i	0.356106	+	0.616794i
$713$	11.2262	+	11.2262i	0.420425	+	0.420425i
$714$		0			0
$715$	−4.46134	+	33.6755i	−0.166844	+	1.25939i
$716$	−13.2362	−	22.9258i	−0.494662	−	0.856779i
$717$		0			0
$718$	11.2758	−	19.5303i	0.420809	−	0.728863i
$719$	−15.5251	−	26.8903i	−0.578990	−	1.00284i	−0.995596	−	0.0937521i	$-0.970114\pi$
$719$	−15.5251	−	26.8903i	−0.578990	−	1.00284i	0.416606	−	0.909087i	$-0.363219\pi$
$720$		0			0
$721$	7.89959	+	7.70655i	0.294196	+	0.287007i
$722$	−31.6385	+	31.6385i	−1.17746	+	1.17746i
$723$		0			0
$724$	38.3715	+	22.1538i	1.42607	+	0.823339i
$725$	5.69918	+	3.29043i	0.211662	+	0.122203i
$726$		0			0
$727$	40.0423			1.48509			0.742543	−	0.669798i	$-0.233619\pi$
$727$	40.0423			1.48509			0.742543	+	0.669798i	$0.233619\pi$
$728$	−29.8953	+	39.9068i	−1.10799	+	1.47904i
$729$		0			0
$730$	−4.60424	+	17.1833i	−0.170411	+	0.635982i
$731$	9.12242	+	5.26683i	0.337405	+	0.194801i
$732$		0			0
$733$	−13.2722	−	3.55628i	−0.490221	−	0.131354i	0.00523707	−	0.999986i	$-0.498333\pi$
$733$	−13.2722	−	3.55628i	−0.490221	−	0.131354i	−0.495458	+	0.868632i	$0.665000\pi$
$734$	21.1975	−	21.1975i	0.782414	−	0.782414i
$735$		0			0
$736$	2.90204	−	2.90204i	0.106971	−	0.106971i
$737$	−17.4813	−	30.2785i	−0.643931	−	1.11532i
$738$		0			0
$739$	−8.67355	−	32.3701i	−0.319062	−	1.19075i	−0.920148	−	0.391570i	$-0.871932\pi$
$739$	−8.67355	−	32.3701i	−0.319062	−	1.19075i	0.601087	−	0.799184i	$-0.294735\pi$
$740$	13.0374	+	22.5815i	0.479265	+	0.830112i
$741$		0			0
$742$	72.0993	+	40.4459i	2.64685	+	1.48482i
$743$	−16.7361	−	16.7361i	−0.613988	−	0.613988i	0.329994	−	0.943983i	$-0.392953\pi$
$743$	−16.7361	−	16.7361i	−0.613988	−	0.613988i	−0.943983	+	0.329994i	$0.892953\pi$
$744$		0			0
$745$	2.21741	−	3.84066i	0.0812396	−	0.140711i
$746$	−66.1712	+	17.7305i	−2.42270	+	0.649161i
$747$		0			0
$748$	−33.1995	−	33.1995i	−1.21389	−	1.21389i
$749$	7.25267	+	7.07544i	0.265007	+	0.258531i
$750$		0			0
$751$	9.94812	−	5.74355i	0.363012	−	0.209585i	−0.307389	−	0.951584i	$-0.599455\pi$
$751$	9.94812	−	5.74355i	0.363012	−	0.209585i	0.670401	+	0.741999i	$0.266122\pi$
$752$	−2.10636	+	0.564398i	−0.0768111	+	0.0205815i
$753$		0			0
$754$	9.70655	−	23.3799i	0.353492	−	0.851445i
$755$		−	0.463202i		−	0.0168576i
$756$		0			0
$757$	−17.1190			−0.622200			−0.311100	−	0.950377i	$-0.600697\pi$
$757$	−17.1190			−0.622200			−0.311100	+	0.950377i	$0.600697\pi$
$758$	5.98198	−	3.45370i	0.217275	−	0.125444i
$759$		0			0
$760$	7.86451	−	2.10729i	0.285276	−	0.0764394i
$761$	−8.84550	+	33.0119i	−0.320649	+	1.19668i	0.597965	+	0.801522i	$0.295976\pi$
$761$	−8.84550	+	33.0119i	−0.320649	+	1.19668i	−0.918614	+	0.395156i	$0.870690\pi$
$762$		0			0
$763$	−3.25282	+	1.93205i	−0.117760	+	0.0699448i
$764$		−	8.41991i		−	0.304622i
$765$		0			0
$766$	22.4767	−	38.9307i	0.812115	−	1.40663i
$767$	−42.9174	+	5.61467i	−1.54966	+	0.202734i
$768$		0			0
$769$	−5.13005	+	5.13005i	−0.184994	+	0.184994i	−0.793528	−	0.608534i	$-0.791758\pi$
$769$	−5.13005	+	5.13005i	−0.184994	+	0.184994i	0.608534	+	0.793528i	$0.291758\pi$
$770$	61.6307	−	0.762326i	2.22102	−	0.0274723i
$771$		0			0
$772$	−3.06407	+	11.4353i	−0.110278	+	0.411565i
$773$	5.60986	+	20.9363i	0.201773	+	0.753026i	0.990409	+	0.138166i	$0.0441208\pi$
$773$	5.60986	+	20.9363i	0.201773	+	0.753026i	−0.788636	+	0.614860i	$0.789213\pi$
$774$		0			0
$775$	2.68954	−	10.0375i	0.0966110	−	0.360557i
$776$			52.4734i			1.88368i
$777$		0			0
$778$	−9.62487	+	9.62487i	−0.345068	+	0.345068i
$779$	4.68916	−	2.70729i	0.168007	−	0.0969987i
$780$		0			0
$781$	19.7118	−	34.1418i	0.705342	−	1.22169i
$782$	16.7780	+	4.49566i	0.599981	+	0.160764i
$783$		0			0
$784$	28.8698	+	15.7290i	1.03106	+	0.561750i
$785$	−1.18402	−	1.18402i	−0.0422596	−	0.0422596i
$786$		0			0
$787$	−12.9263	+	3.46358i	−0.460771	+	0.123463i	−0.481735	−	0.876317i	$-0.659993\pi$
$787$	−12.9263	+	3.46358i	−0.460771	+	0.123463i	0.0209637	+	0.999780i	$0.493327\pi$
$788$	−6.65853	−	24.8500i	−0.237200	−	0.885243i
$789$		0			0
$790$	−24.9669			−0.888283
$791$	38.7513	−	10.8988i	1.37784	−	0.387518i
$792$		0			0
$793$	16.8582	−	6.96685i	0.598654	−	0.247400i
$794$	53.3902	+	30.8249i	1.89475	+	1.09393i
$795$		0			0
$796$	−74.1511	+	42.8111i	−2.62821	+	1.51740i
$797$	−53.9645			−1.91152			−0.955760	−	0.294149i	$-0.904964\pi$
$797$	−53.9645			−1.91152			−0.955760	+	0.294149i	$0.904964\pi$
$798$		0			0
$799$	−0.651349	−	0.651349i	−0.0230431	−	0.0230431i
$800$	−2.59475	−	0.695260i	−0.0917381	−	0.0245812i
$801$		0			0
$802$	−10.1158	+	17.5211i	−0.357201	+	0.618690i
$803$	12.6349	+	21.8843i	0.445875	+	0.772279i
$804$		0			0
$805$	−13.1918	+	7.83540i	−0.464949	+	0.276161i
$806$	−39.6273	−	5.24983i	−1.39581	−	0.184917i
$807$		0			0
$808$	5.76258	+	21.5062i	0.202727	+	0.756587i
$809$	12.7091	−	22.0129i	0.446829	−	0.773931i	−0.551348	−	0.834275i	$-0.685886\pi$
$809$	12.7091	−	22.0129i	0.446829	−	0.773931i	0.998178	+	0.0603439i	$0.0192197\pi$
$810$		0			0
$811$	15.9565	−	15.9565i	0.560310	−	0.560310i	−0.369085	−	0.929395i	$-0.620329\pi$
$811$	15.9565	−	15.9565i	0.560310	−	0.560310i	0.929395	+	0.369085i	$0.120329\pi$
$812$	−29.9499	−	7.62931i	−1.05104	−	0.267736i
$813$		0			0
$814$	53.1701	+	14.2469i	1.86361	+	0.499353i
$815$	24.0490	+	13.8847i	0.842401	+	0.486360i
$816$		0			0
$817$	−1.30696	+	4.87763i	−0.0457246	+	0.170647i
$818$	11.0982			0.388040
$819$		0			0
$820$	38.3593			1.33956
$821$	−10.1652	+	37.9371i	−0.354768	+	1.32401i	0.526008	+	0.850480i	$0.323688\pi$
$821$	−10.1652	+	37.9371i	−0.354768	+	1.32401i	−0.880776	+	0.473533i	$0.842979\pi$
$822$		0			0
$823$	−26.2415	−	15.1505i	−0.914722	−	0.528115i	−0.0327745	−	0.999463i	$-0.510434\pi$
$823$	−26.2415	−	15.1505i	−0.914722	−	0.528115i	−0.881947	+	0.471348i	$0.843768\pi$
$824$	21.0602	+	5.64307i	0.733667	+	0.196586i
$825$		0			0
$826$	21.2627	+	75.6006i	0.739825	+	2.63048i
$827$	7.62275	−	7.62275i	0.265069	−	0.265069i	−0.562041	−	0.827110i	$-0.689984\pi$
$827$	7.62275	−	7.62275i	0.265069	−	0.265069i	0.827110	+	0.562041i	$0.189984\pi$
$828$		0			0
$829$	−17.3492	+	30.0497i	−0.602563	+	1.04367i	0.389868	+	0.920871i	$0.372521\pi$
$829$	−17.3492	+	30.0497i	−0.602563	+	1.04367i	−0.992431	+	0.122800i	$0.960813\pi$
$830$	−17.0724	−	63.7151i	−0.592592	−	2.21158i
$831$		0			0
$832$	3.09086	−	23.3308i	0.107156	−	0.808849i
$833$	0.343505	+	13.8833i	0.0119017	+	0.481028i
$834$		0			0
$835$	−0.405382	−	0.702142i	−0.0140288	−	0.0242986i
$836$	11.2539	−	19.4923i	0.389223	−	0.674154i
$837$		0			0
$838$	83.9456	+	22.4932i	2.89985	+	0.777013i
$839$	5.64491	+	5.64491i	0.194884	+	0.194884i	0.797803	−	0.602919i	$-0.205996\pi$
$839$	5.64491	+	5.64491i	0.194884	+	0.194884i	−0.602919	+	0.797803i	$0.705996\pi$
$840$		0			0
$841$	−20.9373			−0.721975
$842$	74.8375	−	43.2074i	2.57907	−	1.48903i
$843$		0			0
$844$	55.0936	+	31.8083i	1.89640	+	1.09489i
$845$	18.4215	+	10.6757i	0.633720	+	0.367254i
$846$		0			0
$847$	40.8157	−	41.8380i	1.40244	−	1.43757i
$848$	59.3501			2.03809
$849$		0			0
$850$	−2.94256	−	10.9818i	−0.100929	−	0.376672i
$851$	−13.2360	+	3.54656i	−0.453723	+	0.121575i
$852$		0			0
$853$	5.56139	+	5.56139i	0.190418	+	0.190418i	0.795877	−	0.605458i	$-0.207010\pi$
$853$	5.56139	+	5.56139i	0.190418	+	0.190418i	−0.605458	+	0.795877i	$0.707010\pi$
$854$	−16.9017	−	28.4560i	−0.578366	−	0.973744i
$855$		0			0
$856$	19.3355	+	5.18094i	0.660875	+	0.177081i
$857$	15.3579	−	26.6007i	0.524617	−	0.908663i	−0.474972	−	0.880001i	$-0.657542\pi$
$857$	15.3579	−	26.6007i	0.524617	−	0.908663i	0.999589	−	0.0286624i	$-0.00912477\pi$
$858$		0			0
$859$	−8.40141	+	4.85056i	−0.286652	+	0.165499i	−0.636431	−	0.771333i	$-0.719590\pi$
$859$	−8.40141	+	4.85056i	−0.286652	+	0.165499i	0.349779	+	0.936832i	$0.386257\pi$
$860$	−25.2962	+	25.2962i	−0.862594	+	0.862594i
$861$		0			0
$862$		−	88.4499i		−	3.01261i
$863$	1.10156	−	4.11106i	0.0374974	−	0.139942i	−0.944639	−	0.328110i	$-0.893588\pi$
$863$	1.10156	−	4.11106i	0.0374974	−	0.139942i	0.982137	+	0.188168i	$0.0602549\pi$
$864$		0			0
$865$	−1.68524	−	6.28939i	−0.0572998	−	0.213846i
$866$	2.45059	−	9.14573i	0.0832745	−	0.310784i
$867$		0			0
$868$	0.603612	+	48.7994i	0.0204879	+	1.65636i
$869$	−25.0778	+	25.0778i	−0.850705	+	0.850705i
$870$		0			0
$871$	−21.7285	+	2.84263i	−0.736242	+	0.0963189i
$872$	−3.73723	+	6.47307i	−0.126559	+	0.219206i
$873$		0			0
$874$			8.32688i			0.281661i
$875$	27.6546	+	15.5135i	0.934895	+	0.524453i
$876$		0			0
$877$	−4.61225	+	17.2131i	−0.155745	+	0.581246i	0.843296	+	0.537449i	$0.180612\pi$
$877$	−4.61225	+	17.2131i	−0.155745	+	0.581246i	−0.999040	+	0.0437969i	$0.986055\pi$
$878$	−10.2672	+	2.75110i	−0.346502	+	0.0928450i
$879$		0			0
$880$	38.3212	−	22.1248i	1.29181	−	0.745826i
$881$	−38.7999			−1.30720			−0.653600	−	0.756840i	$-0.726742\pi$
$881$	−38.7999			−1.30720			−0.653600	+	0.756840i	$0.726742\pi$
$882$		0			0
$883$			42.2858i			1.42303i	0.702671	+	0.711514i	$0.251990\pi$
$883$			42.2858i			1.42303i	−0.702671	+	0.711514i	$0.748010\pi$
$884$	−27.1969	+	11.2394i	−0.914730	+	0.378022i
$885$		0			0
$886$	−35.2285	+	9.43944i	−1.18352	+	0.317124i
$887$	−21.4815	+	12.4023i	−0.721278	+	0.416430i	−0.815223	−	0.579147i	$-0.803386\pi$
$887$	−21.4815	+	12.4023i	−0.721278	+	0.416430i	0.0939448	+	0.995577i	$0.470052\pi$
$888$		0			0
$889$	−4.39108	−	15.6127i	−0.147272	−	0.523633i
$890$	−10.4112	−	10.4112i	−0.348985	−	0.348985i
$891$		0			0
$892$	93.8707	−	25.1526i	3.14302	−	0.842171i
$893$	0.220793	−	0.382424i	0.00738854	−	0.0127973i
$894$		0			0
$895$	7.45216	+	7.45216i	0.249098	+	0.249098i
$896$	−48.8312	+	0.604005i	−1.63134	+	0.0201784i
$897$		0			0
$898$	−24.4488	−	42.3465i	−0.815866	−	1.41312i
$899$	−3.29517	−	12.2977i	−0.109900	−	0.410152i
$900$		0			0
$901$	12.5352	+	21.7116i	0.417608	+	0.723318i
$902$	57.2608	−	57.2608i	1.90658	−	1.90658i
$903$		0			0
$904$	56.2351	−	56.2351i	1.87035	−	1.87035i
$905$	−17.0382	−	4.56538i	−0.566370	−	0.151758i
$906$		0			0
$907$	−31.7341	−	18.3217i	−1.05371	−	0.608361i	−0.130026	−	0.991511i	$-0.541506\pi$
$907$	−31.7341	−	18.3217i	−1.05371	−	0.608361i	−0.923686	+	0.383150i	$0.874839\pi$
$908$	−22.8440	+	85.2549i	−0.758104	+	2.82928i
$909$		0			0
$910$	14.3703	−	35.8593i	0.476369	−	1.18873i
$911$	22.0142			0.729363			0.364682	−	0.931132i	$-0.381178\pi$
$911$	22.0142			0.729363			0.364682	+	0.931132i	$0.381178\pi$
$912$		0			0
$913$	−81.1462	−	46.8498i	−2.68555	−	1.55050i
$914$	65.5148	+	37.8250i	2.16704	+	1.25114i
$915$		0			0
$916$	2.94414	−	2.94414i	0.0972772	−	0.0972772i
$917$	2.78810	−	2.85794i	0.0920713	−	0.0943776i
$918$		0			0
$919$	−16.8832	−	29.2425i	−0.556924	−	0.964621i	−0.997751	−	0.0670286i	$-0.978648\pi$
$919$	−16.8832	−	29.2425i	−0.556924	−	0.964621i	0.440827	−	0.897592i	$-0.354685\pi$
$920$	−15.1563	+	26.2515i	−0.499688	+	0.865486i
$921$		0			0
$922$	7.69077	+	13.3208i	0.253282	+	0.438697i
$923$	−15.0263	−	19.6157i	−0.494598	−	0.645659i
$924$		0			0
$925$	6.34205	+	6.34205i	0.208525	+	0.208525i
$926$	−11.6762	−	20.2237i	−0.383702	−	0.664592i
$927$		0			0
$928$	−3.17903	+	0.851818i	−0.104357	+	0.0279623i
$929$	−22.4304	−	6.01022i	−0.735919	−	0.197189i	−0.128655	−	0.991689i	$-0.541066\pi$
$929$	−22.4304	−	6.01022i	−0.735919	−	0.197189i	−0.607264	+	0.794500i	$0.707733\pi$
$930$		0			0
$931$	−6.38606	+	1.88162i	−0.209295	+	0.0616676i
$932$	−8.95197			−0.293231
$933$		0			0
$934$	−91.0086	+	24.3857i	−2.97789	+	0.797924i
$935$	16.1875	+	9.34584i	0.529387	+	0.305642i
$936$		0			0
$937$		−	7.15492i		−	0.233741i	−0.993147	−	0.116870i	$-0.962714\pi$
$937$		−	7.15492i		−	0.233741i	0.993147	−	0.116870i	$-0.0372862\pi$
$938$	10.7650	+	38.2755i	0.351490	+	1.24974i
$939$		0			0
$940$	2.70926	−	1.56419i	0.0883663	−	0.0510183i
$941$	1.24527	+	4.64742i	0.0405947	+	0.151502i	0.983248	−	0.182271i	$-0.0583449\pi$
$941$	1.24527	+	4.64742i	0.0405947	+	0.151502i	−0.942654	+	0.333773i	$0.891678\pi$
$942$		0			0
$943$	−5.21742	+	19.4717i	−0.169903	+	0.634085i
$944$	39.8676	+	39.8676i	1.29758	+	1.29758i
$945$		0			0
$946$			75.5219i			2.45543i
$947$	18.1875	+	4.87333i	0.591015	+	0.158362i	0.541917	−	0.840432i	$-0.317699\pi$
$947$	18.1875	+	4.87333i	0.591015	+	0.158362i	0.0490979	+	0.998794i	$0.484365\pi$
$948$		0			0
$949$	15.7046	−	2.05456i	0.509794	−	0.0666938i
$950$	4.72004	−	2.72512i	0.153138	−	0.0884145i
$951$		0			0
$952$	14.0111	+	23.5893i	0.454104	+	0.764535i
$953$		−	4.93813i		−	0.159962i	−0.996796	−	0.0799809i	$-0.974514\pi$
$953$		−	4.93813i		−	0.159962i	0.996796	−	0.0799809i	$-0.0254859\pi$
$954$		0			0
$955$	0.867572	+	3.23782i	0.0280740	+	0.104774i
$956$	−12.3486	−	46.0855i	−0.399381	−	1.49051i
$957$		0			0
$958$			28.7062i			0.927456i
$959$	9.21166	+	15.5089i	0.297460	+	0.500807i
$960$		0			0
$961$	9.43630	−	5.44805i	0.304397	−	0.175744i
$962$	21.0253	−	27.3546i	0.677883	−	0.881949i
$963$		0			0
$964$	25.5602	+	6.84884i	0.823239	+	0.220586i
$965$		−	4.71308i		−	0.151720i
$966$		0			0
$967$	−10.3931	−	10.3931i	−0.334219	−	0.334219i	0.519967	−	0.854186i	$-0.325944\pi$
$967$	−10.3931	−	10.3931i	−0.334219	−	0.334219i	−0.854186	+	0.519967i	$0.825944\pi$
$968$	29.8870	−	111.540i	0.960603	−	3.58502i
$969$		0			0
$970$	−10.5221	−	39.2690i	−0.337844	−	1.26085i
$971$	5.09889	−	2.94384i	0.163631	−	0.0944724i	−0.415948	−	0.909388i	$-0.636550\pi$
$971$	5.09889	−	2.94384i	0.163631	−	0.0944724i	0.579579	+	0.814916i	$0.303217\pi$
$972$		0			0
$973$	−4.49083	−	15.9674i	−0.143969	−	0.511890i
$974$			82.2330i			2.63491i
$975$		0			0
$976$	−20.5777	−	11.8806i	−0.658677	−	0.380287i
$977$	11.9143	−	3.19243i	0.381172	−	0.102135i	−0.0631450	−	0.998004i	$-0.520113\pi$
$977$	11.9143	−	3.19243i	0.381172	−	0.102135i	0.444317	+	0.895870i	$0.353446\pi$
$978$		0			0
$979$	−20.9149			−0.668443
$980$	−45.8456	−	11.0765i	−1.46448	−	0.353827i
$981$		0			0
$982$	5.76850	+	1.54567i	0.184080	+	0.0493242i
$983$	4.80462	−	1.28739i	0.153243	−	0.0410615i	−0.181382	−	0.983413i	$-0.558057\pi$
$983$	4.80462	−	1.28739i	0.153243	−	0.0410615i	0.334625	+	0.942351i	$0.391390\pi$
$984$		0			0
$985$	5.12099	+	8.86982i	0.163168	+	0.282616i
$986$	−9.84950	−	9.84950i	−0.313672	−	0.313672i
$987$		0			0
$988$	−8.57886	−	11.1990i	−0.272930	−	0.356289i
$989$	−9.40005	−	16.2814i	−0.298904	−	0.517717i
$990$		0			0
$991$	7.59737	−	13.1590i	0.241338	−	0.418010i	−0.719757	−	0.694226i	$-0.755747\pi$
$991$	7.59737	−	13.1590i	0.241338	−	0.418010i	0.961096	+	0.276215i	$0.0890803\pi$
$992$	2.59848	+	4.50071i	0.0825019	+	0.142898i
$993$		0			0
$994$	−31.3077	+	32.0919i	−0.993020	+	1.01789i
$995$	24.1032	−	24.1032i	0.764122	−	0.764122i
$996$		0			0
$997$	51.7874	+	29.8995i	1.64012	+	0.946926i	0.980788	+	0.195079i	$0.0624963\pi$
$997$	51.7874	+	29.8995i	1.64012	+	0.946926i	0.659337	+	0.751847i	$0.270837\pi$
$998$	1.05347	+	0.608220i	0.0333470	+	0.0192529i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.73.8		32
3.2	odd	2		91.2.bb.a.73.1	yes	32
7.5	odd	6	inner	819.2.fn.e.775.1		32
13.5	odd	4	inner	819.2.fn.e.577.1		32
21.2	odd	6		637.2.bc.b.411.8		32
21.5	even	6		91.2.bb.a.47.8	yes	32
21.11	odd	6		637.2.i.a.489.2		32
21.17	even	6		637.2.i.a.489.1		32
21.20	even	2		637.2.bc.b.619.1		32
39.5	even	4		91.2.bb.a.31.8	yes	32
91.5	even	12	inner	819.2.fn.e.460.8		32
273.5	odd	12		91.2.bb.a.5.1	✓	32
273.44	even	12		637.2.bc.b.460.1		32
273.83	odd	4		637.2.bc.b.31.8		32
273.122	odd	12		637.2.i.a.538.1		32
273.200	even	12		637.2.i.a.538.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.1	✓	32	273.5	odd	12
91.2.bb.a.31.8	yes	32	39.5	even	4
91.2.bb.a.47.8	yes	32	21.5	even	6
91.2.bb.a.73.1	yes	32	3.2	odd	2
637.2.i.a.489.1		32	21.17	even	6
637.2.i.a.489.2		32	21.11	odd	6
637.2.i.a.538.1		32	273.122	odd	12
637.2.i.a.538.2		32	273.200	even	12
637.2.bc.b.31.8		32	273.83	odd	4
637.2.bc.b.411.8		32	21.2	odd	6
637.2.bc.b.460.1		32	273.44	even	12
637.2.bc.b.619.1		32	21.20	even	2
819.2.fn.e.73.8		32	1.1	even	1	trivial
819.2.fn.e.460.8		32	91.5	even	12	inner
819.2.fn.e.577.1		32	13.5	odd	4	inner
819.2.fn.e.775.1		32	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.639966 - 2.38839i) q^{2} +(-3.56278 - 2.05697i) q^{4} +(1.58199 + 0.423894i) q^{5} +(-2.54693 + 0.716327i) q^{7} +(-3.69606 + 3.69606i) q^{8} +O(q^{10})\)	\(q+(0.639966 - 2.38839i) q^{2} +(-3.56278 - 2.05697i) q^{4} +(1.58199 + 0.423894i) q^{5} +(-2.54693 + 0.716327i) q^{7} +(-3.69606 + 3.69606i) q^{8} +(2.02484 - 3.50713i) q^{10} +(-1.48887 - 5.55653i) q^{11} +(-3.57432 - 0.473526i) q^{13} +(0.0809133 + 6.54149i) q^{14} +(2.34832 + 4.06741i) q^{16} +(-0.991968 + 1.71814i) q^{17} +(-0.918664 - 0.246155i) q^{19} +(-4.76435 - 4.76435i) q^{20} -14.2240 q^{22} +(3.06647 - 1.77043i) q^{23} +(-2.00711 - 1.15881i) q^{25} +(-3.41841 + 8.23382i) q^{26} +(10.5476 + 2.68686i) q^{28} -2.83949 q^{29} +(1.16048 + 4.33096i) q^{31} +(1.11958 - 0.299990i) q^{32} +(3.46875 + 3.46875i) q^{34} +(-4.33288 + 0.0535944i) q^{35} +(-3.73806 - 1.00161i) q^{37} +(-1.17583 + 2.03659i) q^{38} +(-7.41388 + 4.28040i) q^{40} +(-4.02565 + 4.02565i) q^{41} -5.30948i q^{43} +(-6.12512 + 22.8593i) q^{44} +(-2.26603 - 8.45694i) q^{46} +(-0.120170 + 0.448482i) q^{47} +(5.97375 - 3.64888i) q^{49} +(-4.05216 + 4.05216i) q^{50} +(11.7605 + 9.03935i) q^{52} +(6.31835 - 10.9437i) q^{53} -9.42152i q^{55} +(6.76604 - 12.0612i) q^{56} +(-1.81718 + 6.78181i) q^{58} +(11.5955 - 3.10701i) q^{59} +(-4.38137 + 2.52958i) q^{61} +11.0867 q^{62} +6.52733i q^{64} +(-5.45382 - 2.26425i) q^{65} +(5.87066 - 1.57304i) q^{67} +(7.06833 - 4.08090i) q^{68} +(-2.64489 + 10.3829i) q^{70} +(4.84596 + 4.84596i) q^{71} +(-4.24311 + 1.13694i) q^{73} +(-4.78447 + 8.28694i) q^{74} +(2.76666 + 2.76666i) q^{76} +(7.77235 + 13.0856i) q^{77} +(-3.08258 - 5.33918i) q^{79} +(1.99088 + 7.43006i) q^{80} +(7.03853 + 12.1911i) q^{82} +(11.5176 - 11.5176i) q^{83} +(-2.29759 + 2.29759i) q^{85} +(-12.6811 - 3.39789i) q^{86} +(26.0402 + 15.0343i) q^{88} +(0.941005 - 3.51188i) q^{89} +(9.44276 - 1.35434i) q^{91} -14.5669 q^{92} +(0.994243 + 0.574027i) q^{94} +(-1.34898 - 0.778832i) q^{95} +(7.09855 - 7.09855i) q^{97} +(-4.89192 - 16.6028i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

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