LMFDB - Embedded newform 810.2.m.h.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(53,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("810.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.m (of order $12$, degree $4$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	810.53
Dual form			810.2.m.h.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.792893 + 2.09077i) q^{5} +(-1.98004 - 0.530550i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.792893 + 2.09077i) q^{5} +(-1.98004 - 0.530550i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.22474 - 0.224745i) q^{10} +(-0.949490 + 0.548188i) q^{11} +(-5.77111 + 1.54636i) q^{13} +(-1.02494 + 1.77526i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.17121 - 4.17121i) q^{17} +4.44949i q^{19} +(0.358719 - 2.20711i) q^{20} +(0.283763 + 1.05902i) q^{22} +(-1.64310 - 6.13215i) q^{23} +(-3.74264 + 3.31552i) q^{25} +5.97469i q^{26} +(1.44949 + 1.44949i) q^{28} +(-1.57313 - 2.72474i) q^{29} +(0.724745 - 1.25529i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-5.10867 + 2.94949i) q^{34} +(-0.460702 - 4.56048i) q^{35} +(4.29788 + 1.15161i) q^{38} +(-2.03906 - 0.917738i) q^{40} +(-4.22474 - 2.43916i) q^{41} +(-2.64444 + 9.86919i) q^{43} +1.09638 q^{44} -6.34847 q^{46} +(-2.67838 + 9.99585i) q^{47} +(-2.42310 - 1.39898i) q^{49} +(2.23388 + 4.47323i) q^{50} +(5.77111 + 1.54636i) q^{52} +(5.65685 - 5.65685i) q^{53} +(-1.89898 - 1.55051i) q^{55} +(1.77526 - 1.02494i) q^{56} +(-3.03906 + 0.814313i) q^{58} +(1.41421 - 2.44949i) q^{59} +(4.22474 + 7.31747i) q^{61} +(-1.02494 - 1.02494i) q^{62} -1.00000i q^{64} +(-7.80896 - 10.8400i) q^{65} +(0.732051 + 2.73205i) q^{67} +(1.52677 + 5.69798i) q^{68} +(-4.52432 - 0.735335i) q^{70} +13.9993i q^{71} +(-4.44949 - 4.44949i) q^{73} +(2.22474 - 3.85337i) q^{76} +(2.17087 - 0.581683i) q^{77} +(4.71940 - 2.72474i) q^{79} +(-1.41421 + 1.73205i) q^{80} +(-3.44949 + 3.44949i) q^{82} +(13.9571 + 3.73980i) q^{83} +(5.41372 - 12.0284i) q^{85} +(8.84847 + 5.10867i) q^{86} +(0.283763 - 1.05902i) q^{88} +17.4634 q^{89} +12.2474 q^{91} +(-1.64310 + 6.13215i) q^{92} +(8.96204 + 5.17423i) q^{94} +(-9.30286 + 3.52797i) q^{95} +(-11.5422 - 3.09273i) q^{97} +(-1.97846 + 1.97846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q + 12 * q^5 + 4 * q^7	$ 8 q + 12 q^{5} + 4 q^{7} + 8 q^{10} + 12 q^{11} - 12 q^{13} + 4 q^{16} - 8 q^{22} - 36 q^{23} + 4 q^{25} - 8 q^{28} - 4 q^{31} + 12 q^{38} + 4 q^{40} - 24 q^{41} + 24 q^{43} + 8 q^{46} - 36 q^{47} + 24 q^{50} + 12 q^{52} + 24 q^{55} + 24 q^{56} - 4 q^{58} + 24 q^{61} - 24 q^{65} - 8 q^{67} + 24 q^{68} + 8 q^{70} - 16 q^{73} + 8 q^{76} + 60 q^{77} - 8 q^{82} + 12 q^{83} + 28 q^{85} + 12 q^{86} - 8 q^{88} - 36 q^{92} - 24 q^{95} - 24 q^{97}+O(q^{100}) $ 8 * q + 12 * q^5 + 4 * q^7 + 8 * q^10 + 12 * q^11 - 12 * q^13 + 4 * q^16 - 8 * q^22 - 36 * q^23 + 4 * q^25 - 8 * q^28 - 4 * q^31 + 12 * q^38 + 4 * q^40 - 24 * q^41 + 24 * q^43 + 8 * q^46 - 36 * q^47 + 24 * q^50 + 12 * q^52 + 24 * q^55 + 24 * q^56 - 4 * q^58 + 24 * q^61 - 24 * q^65 - 8 * q^67 + 24 * q^68 + 8 * q^70 - 16 * q^73 + 8 * q^76 + 60 * q^77 - 8 * q^82 + 12 * q^83 + 28 * q^85 + 12 * q^86 - 8 * q^88 - 36 * q^92 - 24 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.792893	+	2.09077i	0.354593	+	0.935021i
$5$	0.792893	+	2.09077i	0.354593	+	0.935021i
$6$		0			0
$7$	−1.98004	−	0.530550i	−0.748385	−	0.200529i	−0.135583	−	0.990766i	$-0.543291\pi$
$7$	−1.98004	−	0.530550i	−0.748385	−	0.200529i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	2.22474	−	0.224745i	0.703526	−	0.0710706i
$11$	−0.949490	+	0.548188i	−0.286282	+	0.165285i	−0.636264	−	0.771471i	$-0.719521\pi$
$11$	−0.949490	+	0.548188i	−0.286282	+	0.165285i	0.349982	+	0.936756i	$0.386188\pi$
$12$		0			0
$13$	−5.77111	+	1.54636i	−1.60062	+	0.428884i	−0.945229	−	0.326408i	$-0.894162\pi$
$13$	−5.77111	+	1.54636i	−1.60062	+	0.428884i	−0.655389	+	0.755292i	$0.727495\pi$
$14$	−1.02494	+	1.77526i	−0.273928	+	0.474457i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−4.17121	−	4.17121i	−1.01167	−	1.01167i	−0.999931	−	0.0117355i	$-0.996264\pi$
$17$	−4.17121	−	4.17121i	−1.01167	−	1.01167i	−0.0117355	−	0.999931i	$-0.503736\pi$
$18$		0			0
$19$			4.44949i			1.02078i	0.859942	+	0.510391i	$0.170499\pi$
$19$			4.44949i			1.02078i	−0.859942	+	0.510391i	$0.829501\pi$
$20$	0.358719	−	2.20711i	0.0802121	−	0.493524i
$21$		0			0
$22$	0.283763	+	1.05902i	0.0604985	+	0.225783i
$23$	−1.64310	−	6.13215i	−0.342611	−	1.27864i	−0.895378	−	0.445306i	$-0.853095\pi$
$23$	−1.64310	−	6.13215i	−0.342611	−	1.27864i	0.552767	−	0.833336i	$-0.313572\pi$
$24$		0			0
$25$	−3.74264	+	3.31552i	−0.748528	+	0.663103i
$26$			5.97469i			1.17173i
$27$		0			0
$28$	1.44949	+	1.44949i	0.273928	+	0.273928i
$29$	−1.57313	−	2.72474i	−0.292123	−	0.505972i	0.682188	−	0.731177i	$-0.261028\pi$
$29$	−1.57313	−	2.72474i	−0.292123	−	0.505972i	−0.974312	+	0.225204i	$0.927695\pi$
$30$		0			0
$31$	0.724745	−	1.25529i	0.130168	−	0.225458i	−0.793573	−	0.608475i	$-0.791782\pi$
$31$	0.724745	−	1.25529i	0.130168	−	0.225458i	0.923741	+	0.383017i	$0.125115\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	−5.10867	+	2.94949i	−0.876129	+	0.505833i
$35$	−0.460702	−	4.56048i	−0.0778728	−	0.770861i
$36$		0			0
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	4.29788	+	1.15161i	0.697208	+	0.186816i
$39$		0			0
$40$	−2.03906	−	0.917738i	−0.322403	−	0.145107i
$41$	−4.22474	−	2.43916i	−0.659794	−	0.380932i	0.132404	−	0.991196i	$-0.457730\pi$
$41$	−4.22474	−	2.43916i	−0.659794	−	0.380932i	−0.792199	+	0.610263i	$0.791064\pi$
$42$		0			0
$43$	−2.64444	+	9.86919i	−0.403273	+	1.50504i	0.403945	+	0.914783i	$0.367639\pi$
$43$	−2.64444	+	9.86919i	−0.403273	+	1.50504i	−0.807218	+	0.590253i	$0.799028\pi$
$44$	1.09638			0.165285
$45$		0			0
$46$	−6.34847			−0.936031
$47$	−2.67838	+	9.99585i	−0.390682	+	1.45805i	0.438330	+	0.898814i	$0.355570\pi$
$47$	−2.67838	+	9.99585i	−0.390682	+	1.45805i	−0.829012	+	0.559231i	$0.811097\pi$
$48$		0			0
$49$	−2.42310	−	1.39898i	−0.346158	−	0.199854i
$50$	2.23388	+	4.47323i	0.315918	+	0.632611i
$51$		0			0
$52$	5.77111	+	1.54636i	0.800309	+	0.214442i
$53$	5.65685	−	5.65685i	0.777029	−	0.777029i	−0.202296	−	0.979324i	$-0.564840\pi$
$53$	5.65685	−	5.65685i	0.777029	−	0.777029i	0.979324	+	0.202296i	$0.0648402\pi$
$54$		0			0
$55$	−1.89898	−	1.55051i	−0.256058	−	0.209071i
$56$	1.77526	−	1.02494i	0.237228	−	0.136964i
$57$		0			0
$58$	−3.03906	+	0.814313i	−0.399048	+	0.106925i
$59$	1.41421	−	2.44949i	0.184115	−	0.318896i	−0.759163	−	0.650901i	$-0.774391\pi$
$59$	1.41421	−	2.44949i	0.184115	−	0.318896i	0.943278	+	0.332004i	$0.107725\pi$
$60$		0			0
$61$	4.22474	+	7.31747i	0.540923	+	0.936906i	0.998851	+	0.0479172i	$0.0152584\pi$
$61$	4.22474	+	7.31747i	0.540923	+	0.936906i	−0.457928	+	0.888989i	$0.651408\pi$
$62$	−1.02494	−	1.02494i	−0.130168	−	0.130168i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−7.80896	−	10.8400i	−0.968583	−	1.34453i
$66$		0			0
$67$	0.732051	+	2.73205i	0.0894342	+	0.333773i	0.996117	−	0.0880402i	$-0.0280604\pi$
$67$	0.732051	+	2.73205i	0.0894342	+	0.333773i	−0.906683	+	0.421813i	$0.861394\pi$
$68$	1.52677	+	5.69798i	0.185148	+	0.690981i
$69$		0			0
$70$	−4.52432	−	0.735335i	−0.540760	−	0.0878893i
$71$			13.9993i			1.66141i	0.556714	+	0.830704i	$0.312062\pi$
$71$			13.9993i			1.66141i	−0.556714	+	0.830704i	$0.687938\pi$
$72$		0			0
$73$	−4.44949	−	4.44949i	−0.520773	−	0.520773i	0.397032	−	0.917805i	$-0.370040\pi$
$73$	−4.44949	−	4.44949i	−0.520773	−	0.520773i	−0.917805	+	0.397032i	$0.870040\pi$
$74$		0			0
$75$		0			0
$76$	2.22474	−	3.85337i	0.255196	−	0.442012i
$77$	2.17087	−	0.581683i	0.247393	−	0.0662889i
$78$		0			0
$79$	4.71940	−	2.72474i	0.530974	−	0.306558i	−0.210439	−	0.977607i	$-0.567489\pi$
$79$	4.71940	−	2.72474i	0.530974	−	0.306558i	0.741413	+	0.671049i	$0.234156\pi$
$80$	−1.41421	+	1.73205i	−0.158114	+	0.193649i
$81$		0			0
$82$	−3.44949	+	3.44949i	−0.380932	+	0.380932i
$83$	13.9571	+	3.73980i	1.53199	+	0.410497i	0.923669	−	0.383191i	$-0.125175\pi$
$83$	13.9571	+	3.73980i	1.53199	+	0.410497i	0.608325	+	0.793688i	$0.291842\pi$
$84$		0			0
$85$	5.41372	−	12.0284i	0.587200	−	1.30466i
$86$	8.84847	+	5.10867i	0.954155	+	0.550882i
$87$		0			0
$88$	0.283763	−	1.05902i	0.0302492	−	0.112892i
$89$	17.4634			1.85111			0.925557	−	0.378609i	$-0.123597\pi$
$89$	17.4634			1.85111			0.925557	+	0.378609i	$0.123597\pi$
$90$		0			0
$91$	12.2474			1.28388
$92$	−1.64310	+	6.13215i	−0.171306	+	0.639321i
$93$		0			0
$94$	8.96204	+	5.17423i	0.924364	+	0.533682i
$95$	−9.30286	+	3.52797i	−0.954453	+	0.361962i
$96$		0			0
$97$	−11.5422	−	3.09273i	−1.17193	−	0.314019i	−0.380212	−	0.924899i	$-0.624149\pi$
$97$	−11.5422	−	3.09273i	−1.17193	−	0.314019i	−0.791723	+	0.610880i	$0.790816\pi$
$98$	−1.97846	+	1.97846i	−0.199854	+	0.199854i
$99$		0			0
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$	−7.07321	+	4.08372i	−0.703811	+	0.406346i	−0.808765	−	0.588132i	$-0.799864\pi$
$101$	−7.07321	+	4.08372i	−0.703811	+	0.406346i	0.104954	+	0.994477i	$0.466530\pi$
$102$		0			0
$103$	−2.11804	+	0.567526i	−0.208696	+	0.0559200i	−0.361653	−	0.932313i	$-0.617787\pi$
$103$	−2.11804	+	0.567526i	−0.208696	+	0.0559200i	0.152956	+	0.988233i	$0.451121\pi$
$104$	2.98735	−	5.17423i	0.292933	−	0.507375i
$105$		0			0
$106$	−4.00000	−	6.92820i	−0.388514	−	0.672927i
$107$	−3.60697	−	3.60697i	−0.348699	−	0.348699i	0.510926	−	0.859625i	$-0.329303\pi$
$107$	−3.60697	−	3.60697i	−0.348699	−	0.348699i	−0.859625	+	0.510926i	$0.829303\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$	−1.98917	+	1.43297i	−0.189660	+	0.136628i
$111$		0			0
$112$	−0.530550	−	1.98004i	−0.0501323	−	0.187096i
$113$	−2.09670	−	7.82498i	−0.197241	−	0.736113i	−0.991675	−	0.128763i	$-0.958899\pi$
$113$	−2.09670	−	7.82498i	−0.197241	−	0.736113i	0.794435	−	0.607350i	$-0.207767\pi$
$114$		0			0
$115$	11.5181	−	8.29750i	1.07407	−	0.773745i
$116$			3.14626i			0.292123i
$117$		0			0
$118$	−2.00000	−	2.00000i	−0.184115	−	0.184115i
$119$	6.04612	+	10.4722i	0.554247	+	0.959984i
$120$		0			0
$121$	−4.89898	+	8.48528i	−0.445362	+	0.771389i
$122$	8.16158	−	2.18689i	0.738915	−	0.197992i
$123$		0			0
$124$	−1.25529	+	0.724745i	−0.112729	+	0.0650840i
$125$	−9.89949	−	5.19615i	−0.885438	−	0.464758i
$126$		0			0
$127$	−4.55051	+	4.55051i	−0.403792	+	0.403792i	−0.879567	−	0.475775i	$-0.842168\pi$
$127$	−4.55051	+	4.55051i	−0.403792	+	0.403792i	0.475775	+	0.879567i	$0.342168\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	−12.4917	+	4.73729i	−1.09560	+	0.415488i
$131$	−8.05051	−	4.64796i	−0.703376	−	0.406095i	0.105227	−	0.994448i	$-0.466443\pi$
$131$	−8.05051	−	4.64796i	−0.703376	−	0.406095i	−0.808604	+	0.588354i	$0.799776\pi$
$132$		0			0
$133$	2.36068	−	8.81017i	0.204697	−	0.763938i
$134$	2.82843			0.244339
$135$		0			0
$136$	5.89898			0.505833
$137$	5.64173	−	21.0552i	0.482005	−	1.79887i	−0.111178	−	0.993801i	$-0.535462\pi$
$137$	5.64173	−	21.0552i	0.482005	−	1.79887i	0.593183	−	0.805068i	$-0.297871\pi$
$138$		0			0
$139$	7.14250	+	4.12372i	0.605819	+	0.349770i	0.771327	−	0.636439i	$-0.219593\pi$
$139$	7.14250	+	4.12372i	0.605819	+	0.349770i	−0.165508	+	0.986208i	$0.552926\pi$
$140$	−1.88126	+	4.17984i	−0.158995	+	0.353261i
$141$		0			0
$142$	13.5223	+	3.62328i	1.13476	+	0.304059i
$143$	4.63191	−	4.63191i	0.387340	−	0.387340i
$144$		0			0
$145$	4.44949	−	5.44949i	0.369510	−	0.452555i
$146$	−5.44949	+	3.14626i	−0.451003	+	0.260387i
$147$		0			0
$148$		0			0
$149$	2.20881	−	3.82577i	0.180952	−	0.313419i	−0.761253	−	0.648455i	$-0.775415\pi$
$149$	2.20881	−	3.82577i	0.180952	−	0.313419i	0.942205	+	0.335036i	$0.108749\pi$
$150$		0			0
$151$	−12.0732	−	20.9114i	−0.982504	−	1.70175i	−0.652541	−	0.757753i	$-0.726297\pi$
$151$	−12.0732	−	20.9114i	−0.982504	−	1.70175i	−0.329963	−	0.943994i	$-0.607036\pi$
$152$	−3.14626	−	3.14626i	−0.255196	−	0.255196i
$153$		0			0
$154$		−	2.24745i		−	0.181105i
$155$	3.19918	+	0.519960i	0.256964	+	0.0417642i
$156$		0			0
$157$	2.93651	+	10.9592i	0.234359	+	0.874641i	0.978437	+	0.206547i	$0.0662227\pi$
$157$	2.93651	+	10.9592i	0.234359	+	0.874641i	−0.744077	+	0.668093i	$0.767111\pi$
$158$	−1.41043	−	5.26380i	−0.112208	−	0.418766i
$159$		0			0
$160$	1.30701	+	1.81431i	0.103328	+	0.143434i
$161$			13.0137i			1.02562i
$162$		0			0
$163$	−4.12372	−	4.12372i	−0.322995	−	0.322995i	0.526920	−	0.849915i	$-0.323347\pi$
$163$	−4.12372	−	4.12372i	−0.322995	−	0.322995i	−0.849915	+	0.526920i	$0.823347\pi$
$164$	2.43916	+	4.22474i	0.190466	+	0.329897i
$165$		0			0
$166$	7.22474	−	12.5136i	0.560749	−	0.971246i
$167$	−7.53225	+	2.01826i	−0.582863	+	0.156178i	−0.538189	−	0.842824i	$-0.680891\pi$
$167$	−7.53225	+	2.01826i	−0.582863	+	0.156178i	−0.0446737	+	0.999002i	$0.514225\pi$
$168$		0			0
$169$	19.6561	−	11.3485i	1.51201	−	0.872959i
$170$	−10.2173	−	8.34242i	−0.783634	−	0.639834i
$171$		0			0
$172$	7.22474	−	7.22474i	0.550882	−	0.550882i
$173$	−7.29323	−	1.95422i	−0.554494	−	0.148576i	−0.0293186	−	0.999570i	$-0.509334\pi$
$173$	−7.29323	−	1.95422i	−0.554494	−	0.148576i	−0.525176	+	0.850994i	$0.676000\pi$
$174$		0			0
$175$	9.16962	−	4.57919i	0.693158	−	0.346155i
$176$	−0.949490	−	0.548188i	−0.0715705	−	0.0413212i
$177$		0			0
$178$	4.51985	−	16.8683i	0.338777	−	1.26433i
$179$	7.84961			0.586707			0.293354	−	0.956004i	$-0.405229\pi$
$179$	7.84961			0.586707			0.293354	+	0.956004i	$0.405229\pi$
$180$		0			0
$181$	−4.24745			−0.315710			−0.157855	−	0.987462i	$-0.550458\pi$
$181$	−4.24745			−0.315710			−0.157855	+	0.987462i	$0.550458\pi$
$182$	3.16987	−	11.8301i	0.234967	−	0.876907i
$183$		0			0
$184$	5.49794	+	3.17423i	0.405313	+	0.234008i
$185$		0			0
$186$		0			0
$187$	6.24713	+	1.67391i	0.456835	+	0.122409i
$188$	7.31747	−	7.31747i	0.533682	−	0.533682i
$189$		0			0
$190$	1.00000	+	9.89898i	0.0725476	+	0.718147i
$191$	−13.8990	+	8.02458i	−1.00569	+	0.580638i	−0.909928	−	0.414766i	$-0.863864\pi$
$191$	−13.8990	+	8.02458i	−1.00569	+	0.580638i	−0.0957666	+	0.995404i	$0.530530\pi$
$192$		0			0
$193$	9.28618	−	2.48823i	0.668434	−	0.179106i	0.0913848	−	0.995816i	$-0.470871\pi$
$193$	9.28618	−	2.48823i	0.668434	−	0.179106i	0.577049	+	0.816709i	$0.304204\pi$
$194$	−5.97469	+	10.3485i	−0.428958	+	0.742977i
$195$		0			0
$196$	1.39898	+	2.42310i	0.0999271	+	0.173079i
$197$	−6.75323	−	6.75323i	−0.481148	−	0.481148i	0.424350	−	0.905498i	$-0.360503\pi$
$197$	−6.75323	−	6.75323i	−0.481148	−	0.481148i	−0.905498	+	0.424350i	$0.860503\pi$
$198$		0			0
$199$		−	12.5505i		−	0.889682i	−0.895610	−	0.444841i	$-0.853260\pi$
$199$		−	12.5505i		−	0.889682i	0.895610	−	0.444841i	$-0.146740\pi$
$200$	0.302023	−	4.99087i	0.0213563	−	0.352908i
$201$		0			0
$202$	2.11389	+	7.88915i	0.148733	+	0.555078i
$203$	1.66925	+	6.22973i	0.117158	+	0.437241i
$204$		0			0
$205$	1.74995	−	10.7670i	0.122222	−	0.751997i
$206$			2.19275i			0.152776i
$207$		0			0
$208$	−4.22474	−	4.22474i	−0.292933	−	0.292933i
$209$	−2.43916	−	4.22474i	−0.168720	−	0.292232i
$210$		0			0
$211$	−4.12372	+	7.14250i	−0.283889	+	0.491710i	−0.972339	−	0.233574i	$-0.924958\pi$
$211$	−4.12372	+	7.14250i	−0.283889	+	0.491710i	0.688450	+	0.725284i	$0.258291\pi$
$212$	−7.72741	+	2.07055i	−0.530720	+	0.142206i
$213$		0			0
$214$	−4.41761	+	2.55051i	−0.301982	+	0.174349i
$215$	−22.7310	+	2.29629i	−1.55024	+	0.156606i
$216$		0			0
$217$	−2.10102	+	2.10102i	−0.142627	+	0.142627i
$218$	3.86370	+	1.03528i	0.261683	+	0.0701178i
$219$		0			0
$220$	0.869309	+	2.29227i	0.0586088	+	0.154545i
$221$	30.5227	+	17.6223i	2.05318	+	1.18540i
$222$		0			0
$223$	−4.68438	+	17.4823i	−0.313689	+	1.17070i	0.611515	+	0.791233i	$0.290561\pi$
$223$	−4.68438	+	17.4823i	−0.313689	+	1.17070i	−0.925204	+	0.379471i	$0.876106\pi$
$224$	−2.04989			−0.136964
$225$		0			0
$226$	−8.10102			−0.538872
$227$	1.95422	−	7.29323i	0.129706	−	0.484069i	−0.870258	−	0.492597i	$-0.836048\pi$
$227$	1.95422	−	7.29323i	0.129706	−	0.484069i	0.999964	+	0.00852773i	$0.00271449\pi$
$228$		0			0
$229$	4.02834	+	2.32577i	0.266200	+	0.153691i	0.627160	−	0.778891i	$-0.284217\pi$
$229$	4.02834	+	2.32577i	0.266200	+	0.153691i	−0.360959	+	0.932582i	$0.617551\pi$
$230$	−5.03366	−	13.2732i	−0.331910	−	0.875208i
$231$		0			0
$232$	3.03906	+	0.814313i	0.199524	+	0.0534623i
$233$	3.46410	−	3.46410i	0.226941	−	0.226941i	−0.584473	−	0.811413i	$-0.698699\pi$
$233$	3.46410	−	3.46410i	0.226941	−	0.226941i	0.811413	+	0.584473i	$0.198699\pi$
$234$		0			0
$235$	−23.0227	+	2.32577i	−1.50184	+	0.151716i
$236$	−2.44949	+	1.41421i	−0.159448	+	0.0920575i
$237$		0			0
$238$	11.6802	−	3.12970i	0.757116	−	0.202869i
$239$	−3.07483	+	5.32577i	−0.198894	+	0.344495i	−0.948170	−	0.317763i	$-0.897068\pi$
$239$	−3.07483	+	5.32577i	−0.198894	+	0.344495i	0.749276	+	0.662258i	$0.230402\pi$
$240$		0			0
$241$	9.84847	+	17.0580i	0.634396	+	1.09881i	0.986643	+	0.162899i	$0.0520843\pi$
$241$	9.84847	+	17.0580i	0.634396	+	1.09881i	−0.352247	+	0.935907i	$0.614582\pi$
$242$	6.92820	+	6.92820i	0.445362	+	0.445362i
$243$		0			0
$244$		−	8.44949i		−	0.540923i
$245$	1.00368	−	6.17539i	0.0641229	−	0.394531i
$246$		0			0
$247$	−6.88053	−	25.6785i	−0.437798	−	1.63388i
$248$	0.375156	+	1.40010i	0.0238224	+	0.0889064i
$249$		0			0
$250$	−7.58128	+	8.21731i	−0.479482	+	0.519709i
$251$		−	1.73205i		−	0.109326i	−0.998505	−	0.0546630i	$-0.982592\pi$
$251$		−	1.73205i		−	0.109326i	0.998505	−	0.0546630i	$-0.0174085\pi$
$252$		0			0
$253$	4.92168	+	4.92168i	0.309424	+	0.309424i
$254$	3.21770	+	5.57321i	0.201896	+	0.349695i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.57097	+	0.956838i	−0.222751	+	0.0596859i	−0.368468	−	0.929640i	$-0.620118\pi$
$257$	−3.57097	+	0.956838i	−0.222751	+	0.0596859i	0.145717	+	0.989326i	$0.453451\pi$
$258$		0			0
$259$		0			0
$260$	1.34278	+	13.2922i	0.0832758	+	0.824345i
$261$		0			0
$262$	−6.57321	+	6.57321i	−0.406095	+	0.406095i
$263$	1.25866	+	0.337257i	0.0776123	+	0.0207962i	0.297416	−	0.954748i	$-0.403875\pi$
$263$	1.25866	+	0.337257i	0.0776123	+	0.0207962i	−0.219804	+	0.975544i	$0.570542\pi$
$264$		0			0
$265$	16.3125	+	7.34190i	1.00207	+	0.451009i
$266$	−7.89898	−	4.56048i	−0.484318	−	0.279621i
$267$		0			0
$268$	0.732051	−	2.73205i	0.0447171	−	0.166887i
$269$	−24.5665			−1.49785			−0.748924	−	0.662655i	$-0.769429\pi$
$269$	−24.5665			−1.49785			−0.748924	+	0.662655i	$0.769429\pi$
$270$		0			0
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$	1.52677	−	5.69798i	0.0925739	−	0.345491i
$273$		0			0
$274$	−18.8776	−	10.8990i	−1.14044	−	0.658431i
$275$	1.73607	−	5.19972i	0.104689	−	0.313555i
$276$		0			0
$277$	−13.0462	−	3.49573i	−0.783873	−	0.210038i	−0.155381	−	0.987855i	$-0.549661\pi$
$277$	−13.0462	−	3.49573i	−0.783873	−	0.210038i	−0.628491	+	0.777817i	$0.716327\pi$
$278$	5.83183	−	5.83183i	0.349770	−	0.349770i
$279$		0			0
$280$	3.55051	+	2.89898i	0.212184	+	0.173247i
$281$	7.65153	−	4.41761i	0.456452	−	0.263533i	−0.254099	−	0.967178i	$-0.581779\pi$
$281$	7.65153	−	4.41761i	0.456452	−	0.263533i	0.710551	+	0.703645i	$0.248446\pi$
$282$		0			0
$283$	−1.22803	+	0.329049i	−0.0729987	+	0.0195600i	−0.295134	−	0.955456i	$-0.595364\pi$
$283$	−1.22803	+	0.329049i	−0.0729987	+	0.0195600i	0.222135	+	0.975016i	$0.428697\pi$
$284$	6.99964	−	12.1237i	0.415352	−	0.719411i
$285$		0			0
$286$	−3.27526	−	5.67291i	−0.193670	−	0.335446i
$287$	7.07107	+	7.07107i	0.417392	+	0.417392i
$288$		0			0
$289$			17.7980i			1.04694i
$290$	−4.11219	−	5.70831i	−0.241476	−	0.335203i
$291$		0			0
$292$	1.62863	+	6.07812i	0.0953081	+	0.355695i
$293$	1.55291	+	5.79555i	0.0907222	+	0.338580i	0.996336	−	0.0855230i	$-0.0272561\pi$
$293$	1.55291	+	5.79555i	0.0907222	+	0.338580i	−0.905614	+	0.424103i	$0.860589\pi$
$294$		0			0
$295$	6.24264	+	1.01461i	0.363461	+	0.0590730i
$296$		0			0
$297$		0			0
$298$	−3.12372	−	3.12372i	−0.180952	−	0.180952i
$299$	18.9651	+	32.8485i	1.09678	+	1.89968i
$300$		0			0
$301$	10.4722	−	18.1384i	0.603607	−	1.04548i
$302$	−23.3237	+	6.24956i	−1.34213	+	0.359622i
$303$		0			0
$304$	−3.85337	+	2.22474i	−0.221006	+	0.127598i
$305$	−11.9494	+	14.6349i	−0.684220	+	0.837995i
$306$		0			0
$307$	21.6742	−	21.6742i	1.23701	−	1.23701i	0.275798	−	0.961216i	$-0.411058\pi$
$307$	21.6742	−	21.6742i	1.23701	−	1.23701i	0.961216	−	0.275798i	$-0.0889422\pi$
$308$	−2.17087	−	0.581683i	−0.123697	−	0.0331444i
$309$		0			0
$310$	1.33025	−	2.95559i	0.0755532	−	0.167866i
$311$	27.9217	+	16.1206i	1.58329	+	0.914115i	0.994374	+	0.105923i	$0.0337797\pi$
$311$	27.9217	+	16.1206i	1.58329	+	0.914115i	0.588919	+	0.808192i	$0.299554\pi$
$312$		0			0
$313$	1.18865	−	4.43610i	0.0671864	−	0.250743i	−0.924162	−	0.382001i	$-0.875235\pi$
$313$	1.18865	−	4.43610i	0.0671864	−	0.250743i	0.991348	+	0.131258i	$0.0419017\pi$
$314$	11.3458			0.640281
$315$		0			0
$316$	−5.44949			−0.306558
$317$	−0.569930	+	2.12701i	−0.0320105	+	0.119465i	−0.980082	−	0.198591i	$-0.936363\pi$
$317$	−0.569930	+	2.12701i	−0.0320105	+	0.119465i	0.948072	+	0.318056i	$0.103030\pi$
$318$		0			0
$319$	2.98735	+	1.72474i	0.167259	+	0.0965672i
$320$	2.09077	−	0.792893i	0.116878	−	0.0443241i
$321$		0			0
$322$	12.5702	+	3.36818i	0.700511	+	0.187701i
$323$	18.5597	−	18.5597i	1.03269	−	1.03269i
$324$		0			0
$325$	16.4722	−	24.9217i	0.913713	−	1.38241i
$326$	−5.05051	+	2.91591i	−0.279722	+	0.161498i
$327$		0			0
$328$	4.71209	−	1.26260i	0.260182	−	0.0697155i
$329$	10.6066	−	18.3712i	0.584761	−	1.01284i
$330$		0			0
$331$	10.5505	+	18.2740i	0.579908	+	1.00443i	0.995489	+	0.0948747i	$0.0302450\pi$
$331$	10.5505	+	18.2740i	0.579908	+	1.00443i	−0.415581	+	0.909556i	$0.636422\pi$
$332$	−10.2173	−	10.2173i	−0.560749	−	0.560749i
$333$		0			0
$334$			7.79796i			0.426685i
$335$	−5.13165	+	3.69677i	−0.280372	+	0.201976i
$336$		0			0
$337$	−2.59915	−	9.70017i	−0.141585	−	0.528402i	−0.999884	−	0.0152518i	$-0.995145\pi$
$337$	−2.59915	−	9.70017i	−0.141585	−	0.528402i	0.858299	−	0.513150i	$-0.171522\pi$
$338$	−5.87440	−	21.9236i	−0.319525	−	1.19248i
$339$		0			0
$340$	−10.7026	+	7.71001i	−0.580430	+	0.418134i
$341$			1.58919i			0.0860593i
$342$		0			0
$343$	14.2020	+	14.2020i	0.766838	+	0.766838i
$344$	−5.10867	−	8.84847i	−0.275441	−	0.477077i
$345$		0			0
$346$	−3.77526	+	6.53893i	−0.202959	+	0.351535i
$347$	−13.7620	+	3.68751i	−0.738782	+	0.197956i	−0.608537	−	0.793526i	$-0.708243\pi$
$347$	−13.7620	+	3.68751i	−0.738782	+	0.197956i	−0.130245	+	0.991482i	$0.541576\pi$
$348$		0			0
$349$	−17.3598	+	10.0227i	−0.929251	+	0.536503i	−0.886574	−	0.462586i	$-0.846922\pi$
$349$	−17.3598	+	10.0227i	−0.929251	+	0.536503i	−0.0426761	+	0.999089i	$0.513588\pi$
$350$	−2.04989	−	10.0424i	−0.109571	−	0.536787i
$351$		0			0
$352$	−0.775255	+	0.775255i	−0.0413212	+	0.0413212i
$353$	−1.83427	−	0.491492i	−0.0976285	−	0.0261595i	0.209674	−	0.977771i	$-0.432760\pi$
$353$	−1.83427	−	0.491492i	−0.0976285	−	0.0261595i	−0.307303	+	0.951612i	$0.599426\pi$
$354$		0			0
$355$	−29.2693	+	11.0999i	−1.55345	+	0.589123i
$356$	−15.1237	−	8.73169i	−0.801556	−	0.462778i
$357$		0			0
$358$	2.03163	−	7.58214i	0.107375	−	0.400728i
$359$	24.0416			1.26887			0.634434	−	0.772977i	$-0.281233\pi$
$359$	24.0416			1.26887			0.634434	+	0.772977i	$0.281233\pi$
$360$		0			0
$361$	−0.797959			−0.0419978
$362$	−1.09932	+	4.10272i	−0.0577790	+	0.215634i
$363$		0			0
$364$	−10.6066	−	6.12372i	−0.555937	−	0.320970i
$365$	5.77489	−	12.8308i	0.302272	−	0.671596i
$366$		0			0
$367$	−27.6585	−	7.41108i	−1.44376	−	0.386855i	−0.549914	−	0.835222i	$-0.685339\pi$
$367$	−27.6585	−	7.41108i	−1.44376	−	0.386855i	−0.893850	+	0.448366i	$0.852006\pi$
$368$	4.48905	−	4.48905i	0.234008	−	0.234008i
$369$		0			0
$370$		0			0
$371$	−14.2020	+	8.19955i	−0.737333	+	0.425700i
$372$		0			0
$373$	−26.4615	+	7.09034i	−1.37013	+	0.367124i	−0.867524	−	0.497395i	$-0.834290\pi$
$373$	−26.4615	+	7.09034i	−1.37013	+	0.367124i	−0.502601	+	0.864519i	$0.667623\pi$
$374$	3.23375	−	5.60102i	0.167213	−	0.289622i
$375$		0			0
$376$	−5.17423	−	8.96204i	−0.266841	−	0.462182i
$377$	13.2922	+	13.2922i	0.684581	+	0.684581i
$378$		0			0
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$	9.82050	+	1.59612i	0.503781	+	0.0818792i
$381$		0			0
$382$	4.15383	+	15.5023i	0.212528	+	0.793167i
$383$	5.21428	+	19.4600i	0.266437	+	0.994357i	0.961365	+	0.275278i	$0.0887697\pi$
$383$	5.21428	+	19.4600i	0.266437	+	0.994357i	−0.694928	+	0.719080i	$0.744564\pi$
$384$		0			0
$385$	2.93743	+	4.07758i	0.149705	+	0.207813i
$386$		−	9.61377i		−	0.489328i
$387$		0			0
$388$	8.44949	+	8.44949i	0.428958	+	0.428958i
$389$	−4.71940	−	8.17423i	−0.239283	−	0.414450i	0.721226	−	0.692700i	$-0.243579\pi$
$389$	−4.71940	−	8.17423i	−0.239283	−	0.414450i	−0.960509	+	0.278250i	$0.910246\pi$
$390$		0			0
$391$	−18.7247	+	32.4322i	−0.946951	+	1.64017i
$392$	2.70262	−	0.724165i	0.136503	−	0.0365759i
$393$		0			0
$394$	−8.27098	+	4.77526i	−0.416686	+	0.240574i
$395$	9.43879	+	7.70674i	0.474917	+	0.387768i
$396$		0			0
$397$	−19.5732	+	19.5732i	−0.982351	+	0.982351i	−0.999847	−	0.0174955i	$-0.994431\pi$
$397$	−19.5732	+	19.5732i	−0.982351	+	0.982351i	0.0174955	+	0.999847i	$0.494431\pi$
$398$	−12.1229	−	3.24831i	−0.607664	−	0.162823i
$399$		0			0
$400$	−4.74264	−	1.58346i	−0.237132	−	0.0791732i
$401$	−8.69694	−	5.02118i	−0.434304	−	0.250746i	0.266874	−	0.963731i	$-0.414009\pi$
$401$	−8.69694	−	5.02118i	−0.434304	−	0.250746i	−0.701179	+	0.712986i	$0.747342\pi$
$402$		0			0
$403$	−2.24144	+	8.36516i	−0.111654	+	0.416698i
$404$	8.16744			0.406346
$405$		0			0
$406$	6.44949			0.320083
$407$		0			0
$408$		0			0
$409$	−26.6718	−	15.3990i	−1.31884	−	0.761431i	−0.335295	−	0.942113i	$-0.608836\pi$
$409$	−26.6718	−	15.3990i	−1.31884	−	0.761431i	−0.983541	+	0.180683i	$0.942169\pi$
$410$	−9.94717	−	4.47701i	−0.491256	−	0.221104i
$411$		0			0
$412$	2.11804	+	0.567526i	0.104348	+	0.0279600i
$413$	−4.09978	+	4.09978i	−0.201737	+	0.201737i
$414$		0			0
$415$	3.24745	+	32.1464i	0.159411	+	1.57801i
$416$	−5.17423	+	2.98735i	−0.253688	+	0.146467i
$417$		0			0
$418$	−4.71209	+	1.26260i	−0.230476	+	0.0617558i
$419$	−17.0580	+	29.5454i	−0.833340	+	1.44339i	0.0620344	+	0.998074i	$0.480241\pi$
$419$	−17.0580	+	29.5454i	−0.833340	+	1.44339i	−0.895375	+	0.445314i	$0.853092\pi$
$420$		0			0
$421$	6.77526	+	11.7351i	0.330206	+	0.571933i	0.982552	−	0.185988i	$-0.0595485\pi$
$421$	6.77526	+	11.7351i	0.330206	+	0.571933i	−0.652346	+	0.757921i	$0.726215\pi$
$422$	5.83183	+	5.83183i	0.283889	+	0.283889i
$423$		0			0
$424$			8.00000i			0.388514i
$425$	29.4410	+	1.78163i	1.42810	+	0.0864217i
$426$		0			0
$427$	−4.48288	−	16.7303i	−0.216942	−	0.809637i
$428$	1.32024	+	4.92721i	0.0638163	+	0.238166i
$429$		0			0
$430$	−3.66516	+	22.5507i	−0.176750	+	1.08749i
$431$			22.6274i			1.08992i	0.838461	+	0.544962i	$0.183456\pi$
$431$			22.6274i			1.08992i	−0.838461	+	0.544962i	$0.816544\pi$
$432$		0			0
$433$	14.2474	+	14.2474i	0.684689	+	0.684689i	0.961053	−	0.276364i	$-0.0891296\pi$
$433$	14.2474	+	14.2474i	0.684689	+	0.684689i	−0.276364	+	0.961053i	$0.589130\pi$
$434$	1.48565	+	2.57321i	0.0713133	+	0.123518i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	27.2849	−	7.31098i	1.30522	−	0.349731i
$438$		0			0
$439$	−3.11416	+	1.79796i	−0.148631	+	0.0858119i	−0.572471	−	0.819925i	$-0.694015\pi$
$439$	−3.11416	+	1.79796i	−0.148631	+	0.0858119i	0.423840	+	0.905737i	$0.360682\pi$
$440$	2.43916	−	0.246405i	0.116282	−	0.0117469i
$441$		0			0
$442$	24.9217	−	24.9217i	1.18540	−	1.18540i
$443$	6.03457	+	1.61696i	0.286711	+	0.0768240i	0.399308	−	0.916817i	$-0.369250\pi$
$443$	6.03457	+	1.61696i	0.286711	+	0.0768240i	−0.112597	+	0.993641i	$0.535917\pi$
$444$		0			0
$445$	13.8466	+	36.5119i	0.656391	+	1.73083i
$446$	15.6742	+	9.04952i	0.742197	+	0.428507i
$447$		0			0
$448$	−0.530550	+	1.98004i	−0.0250661	+	0.0935481i
$449$	−15.5563			−0.734150			−0.367075	−	0.930191i	$-0.619641\pi$
$449$	−15.5563			−0.734150			−0.367075	+	0.930191i	$0.619641\pi$
$450$		0			0
$451$	5.34847			0.251850
$452$	−2.09670	+	7.82498i	−0.0986204	+	0.368056i
$453$		0			0
$454$	−6.53893	−	3.77526i	−0.306887	−	0.177182i
$455$	9.71092	+	25.6066i	0.455255	+	1.20046i
$456$		0			0
$457$	−20.0764	−	5.37945i	−0.939134	−	0.251640i	−0.243389	−	0.969929i	$-0.578259\pi$
$457$	−20.0764	−	5.37945i	−0.939134	−	0.251640i	−0.695745	+	0.718289i	$0.744926\pi$
$458$	3.28913	−	3.28913i	0.153691	−	0.153691i
$459$		0			0
$460$	−14.1237	+	1.42679i	−0.658522	+	0.0665242i
$461$	−2.44949	+	1.41421i	−0.114084	+	0.0658665i	−0.555956	−	0.831212i	$-0.687648\pi$
$461$	−2.44949	+	1.41421i	−0.114084	+	0.0658665i	0.441872	+	0.897078i	$0.354314\pi$
$462$		0			0
$463$	15.5023	−	4.15383i	0.720453	−	0.193045i	0.120079	−	0.992764i	$-0.461685\pi$
$463$	15.5023	−	4.15383i	0.720453	−	0.193045i	0.600374	+	0.799720i	$0.295019\pi$
$464$	1.57313	−	2.72474i	0.0730308	−	0.126493i
$465$		0			0
$466$	−2.44949	−	4.24264i	−0.113470	−	0.196537i
$467$	6.61037	+	6.61037i	0.305891	+	0.305891i	0.843313	−	0.537422i	$-0.180602\pi$
$467$	6.61037	+	6.61037i	0.305891	+	0.305891i	−0.537422	+	0.843313i	$0.680602\pi$
$468$		0			0
$469$		−	5.79796i		−	0.267725i
$470$	−3.71220	+	22.8402i	−0.171231	+	1.05354i
$471$		0			0
$472$	0.732051	+	2.73205i	0.0336954	+	0.125753i
$473$	−2.89930	−	10.8203i	−0.133310	−	0.497520i
$474$		0			0
$475$	−14.7524	−	16.6528i	−0.676884	−	0.764085i
$476$		−	12.0922i		−	0.554247i
$477$		0			0
$478$	4.34847	+	4.34847i	0.198894	+	0.198894i
$479$	−9.19239	−	15.9217i	−0.420011	−	0.727480i	0.575929	−	0.817500i	$-0.304640\pi$
$479$	−9.19239	−	15.9217i	−0.420011	−	0.727480i	−0.995940	+	0.0900194i	$0.971307\pi$
$480$		0			0
$481$		0			0
$482$	19.0258	−	5.09794i	0.866601	−	0.232205i
$483$		0			0
$484$	8.48528	−	4.89898i	0.385695	−	0.222681i
$485$	−2.68556	−	26.5843i	−0.121945	−	1.20713i
$486$		0			0
$487$	−14.6969	+	14.6969i	−0.665982	+	0.665982i	−0.956783	−	0.290802i	$-0.906078\pi$
$487$	−14.6969	+	14.6969i	−0.665982	+	0.665982i	0.290802	+	0.956783i	$0.406078\pi$
$488$	−8.16158	−	2.18689i	−0.369457	−	0.0989958i
$489$		0			0
$490$	−5.70520	−	2.56779i	−0.257735	−	0.116001i
$491$	−21.7980	−	12.5851i	−0.983728	−	0.567956i	−0.0803345	−	0.996768i	$-0.525599\pi$
$491$	−21.7980	−	12.5851i	−0.983728	−	0.567956i	−0.903394	+	0.428812i	$0.858932\pi$
$492$		0			0
$493$	−4.80362	+	17.9273i	−0.216344	+	0.807407i
$494$	−26.5843			−1.19609
$495$		0			0
$496$	1.44949			0.0650840
$497$	7.42731	−	27.7191i	0.333161	−	1.24337i
$498$		0			0
$499$	5.02118	+	2.89898i	0.224779	+	0.129776i	0.608161	−	0.793814i	$-0.291907\pi$
$499$	5.02118	+	2.89898i	0.224779	+	0.129776i	−0.383382	+	0.923590i	$0.625241\pi$
$500$	5.97514	+	9.44975i	0.267216	+	0.422606i
$501$		0			0
$502$	−1.67303	−	0.448288i	−0.0746711	−	0.0200081i
$503$	−26.1951	+	26.1951i	−1.16798	+	1.16798i	−0.185297	+	0.982682i	$0.559325\pi$
$503$	−26.1951	+	26.1951i	−1.16798	+	1.16798i	−0.982682	+	0.185297i	$0.940675\pi$
$504$		0			0
$505$	−14.1464	−	11.5505i	−0.629508	−	0.513991i
$506$	6.02781	−	3.48016i	0.267969	−	0.154712i
$507$		0			0
$508$	6.21611	−	1.66560i	0.275795	−	0.0738992i
$509$	9.42274	−	16.3207i	0.417656	−	0.723401i	−0.578048	−	0.816003i	$-0.696185\pi$
$509$	9.42274	−	16.3207i	0.417656	−	0.723401i	0.995703	+	0.0926024i	$0.0295185\pi$
$510$		0			0
$511$	6.44949	+	11.1708i	0.285309	+	0.494169i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			3.69694i			0.163065i
$515$	−2.86594	−	3.97834i	−0.126289	−	0.175307i
$516$		0			0
$517$	−2.93651	−	10.9592i	−0.129148	−	0.481986i
$518$		0			0
$519$		0			0
$520$	13.1868	+	2.14324i	0.578279	+	0.0939872i
$521$			4.59259i			0.201205i	0.994927	+	0.100602i	$0.0320770\pi$
$521$			4.59259i			0.201205i	−0.994927	+	0.100602i	$0.967923\pi$
$522$		0			0
$523$	4.77526	+	4.77526i	0.208807	+	0.208807i	0.803760	−	0.594953i	$-0.202829\pi$
$523$	4.77526	+	4.77526i	0.208807	+	0.208807i	−0.594953	+	0.803760i	$0.702829\pi$
$524$	4.64796	+	8.05051i	0.203047	+	0.351688i
$525$		0			0
$526$	0.651531	−	1.12848i	0.0284081	−	0.0492043i
$527$	−8.25916	+	2.21303i	−0.359775	+	0.0964013i
$528$		0			0
$529$	−14.9849	+	8.65153i	−0.651517	+	0.376154i
$530$	11.3137	−	13.8564i	0.491436	−	0.601884i
$531$		0			0
$532$	−6.44949	+	6.44949i	−0.279621	+	0.279621i
$533$	28.1533	+	7.54365i	1.21945	+	0.326752i
$534$		0			0
$535$	4.68140	−	10.4013i	0.202395	−	0.449686i
$536$	−2.44949	−	1.41421i	−0.105802	−	0.0610847i
$537$		0			0
$538$	−6.35829	+	23.7295i	−0.274125	+	1.02305i
$539$	3.06762			0.132132
$540$		0			0
$541$	−9.59592			−0.412561			−0.206280	−	0.978493i	$-0.566136\pi$
$541$	−9.59592			−0.412561			−0.206280	+	0.978493i	$0.566136\pi$
$542$	−1.55291	+	5.79555i	−0.0667034	+	0.248940i
$543$		0			0
$544$	−5.10867	−	2.94949i	−0.219032	−	0.126458i
$545$	−8.36308	+	3.17157i	−0.358235	+	0.135855i
$546$		0			0
$547$	18.4034	+	4.93117i	0.786871	+	0.210841i	0.629812	−	0.776748i	$-0.283132\pi$
$547$	18.4034	+	4.93117i	0.786871	+	0.210841i	0.157059	+	0.987589i	$0.449799\pi$
$548$	−15.4135	+	15.4135i	−0.658431	+	0.658431i
$549$		0			0
$550$	−4.57321	−	3.02270i	−0.195003	−	0.128889i
$551$	12.1237	−	6.99964i	0.516488	−	0.298194i
$552$		0			0
$553$	−10.7902	+	2.89123i	−0.458846	+	0.122947i
$554$	−6.75323	+	11.6969i	−0.286917	+	0.496955i
$555$		0			0
$556$	−4.12372	−	7.14250i	−0.174885	−	0.302909i
$557$	−12.1244	−	12.1244i	−0.513725	−	0.513725i	0.401940	−	0.915666i	$-0.368336\pi$
$557$	−12.1244	−	12.1244i	−0.513725	−	0.513725i	−0.915666	+	0.401940i	$0.868336\pi$
$558$		0			0
$559$		−	61.0454i		−	2.58195i
$560$	3.71914	−	2.67922i	0.157162	−	0.113218i
$561$		0			0
$562$	−2.28672	−	8.53417i	−0.0964597	−	0.359992i
$563$	5.00775	+	18.6892i	0.211052	+	0.787655i	0.987519	+	0.157498i	$0.0503428\pi$
$563$	5.00775	+	18.6892i	0.211052	+	0.787655i	−0.776468	+	0.630157i	$0.782990\pi$
$564$		0			0
$565$	14.6978	−	10.5881i	0.618341	−	0.445444i
$566$			1.27135i			0.0534388i
$567$		0			0
$568$	−9.89898	−	9.89898i	−0.415352	−	0.415352i
$569$	−11.0280	−	19.1010i	−0.462317	−	0.800756i	0.536759	−	0.843736i	$-0.319648\pi$
$569$	−11.0280	−	19.1010i	−0.462317	−	0.800756i	−0.999076	+	0.0429792i	$0.986315\pi$
$570$		0			0
$571$	0.775255	−	1.34278i	0.0324434	−	0.0561936i	−0.849348	−	0.527834i	$-0.823004\pi$
$571$	0.775255	−	1.34278i	0.0324434	−	0.0561936i	0.881791	+	0.471640i	$0.156338\pi$
$572$	−6.32731	+	1.69540i	−0.264558	+	0.0708881i
$573$		0			0
$574$	8.66025	−	5.00000i	0.361472	−	0.208696i
$575$	26.4808	+	17.5027i	1.10433	+	0.729913i
$576$		0			0
$577$	4.00000	−	4.00000i	0.166522	−	0.166522i	−0.618927	−	0.785449i	$-0.712432\pi$
$577$	4.00000	−	4.00000i	0.166522	−	0.166522i	0.785449	+	0.618927i	$0.212432\pi$
$578$	17.1915	+	4.60645i	0.715072	+	0.191603i
$579$		0			0
$580$	−6.57812	+	2.49465i	−0.273141	+	0.103585i
$581$	−25.6515	−	14.8099i	−1.06420	−	0.614419i
$582$		0			0
$583$	−2.27010	+	8.47215i	−0.0940181	+	0.350880i
$584$	6.29253			0.260387
$585$		0			0
$586$	6.00000			0.247858
$587$	−8.81160	+	32.8853i	−0.363694	+	1.35732i	0.505489	+	0.862833i	$0.331312\pi$
$587$	−8.81160	+	32.8853i	−0.363694	+	1.35732i	−0.869183	+	0.494490i	$0.835355\pi$
$588$		0			0
$589$	5.58542	+	3.22474i	0.230143	+	0.132873i
$590$	2.59575	−	5.76733i	0.106866	−	0.237437i
$591$		0			0
$592$		0			0
$593$	−23.9702	+	23.9702i	−0.984338	+	0.984338i	−0.999879	−	0.0155412i	$-0.995053\pi$
$593$	−23.9702	+	23.9702i	−0.984338	+	0.984338i	0.0155412	+	0.999879i	$0.495053\pi$
$594$		0			0
$595$	−17.1010	+	20.9444i	−0.701073	+	0.858636i
$596$	−3.82577	+	2.20881i	−0.156709	+	0.0904762i
$597$		0			0
$598$	36.6377	−	9.81704i	1.49823	−	0.401449i
$599$	9.29593	−	16.1010i	0.379821	−	0.657870i	−0.611215	−	0.791465i	$-0.709319\pi$
$599$	9.29593	−	16.1010i	0.379821	−	0.657870i	0.991036	+	0.133595i	$0.0426521\pi$
$600$		0			0
$601$	9.19694	+	15.9296i	0.375151	+	0.649780i	0.990350	−	0.138592i	$-0.0442575\pi$
$601$	9.19694	+	15.9296i	0.375151	+	0.649780i	−0.615199	+	0.788372i	$0.710924\pi$
$602$	−14.8099	−	14.8099i	−0.603607	−	0.603607i
$603$		0			0
$604$			24.1464i			0.982504i
$605$	−21.6251	−	3.51472i	−0.879187	−	0.142894i
$606$		0			0
$607$	−6.09488	−	22.7464i	−0.247384	−	0.923248i	−0.972170	−	0.234275i	$-0.924728\pi$
$607$	−6.09488	−	22.7464i	−0.247384	−	0.923248i	0.724787	−	0.688973i	$-0.241938\pi$
$608$	1.15161	+	4.29788i	0.0467041	+	0.174302i
$609$		0			0
$610$	11.0435	+	15.3300i	0.447140	+	0.620694i
$611$		−	61.8289i		−	2.50133i
$612$		0			0
$613$	−10.4722	−	10.4722i	−0.422968	−	0.422968i	0.463256	−	0.886224i	$-0.346681\pi$
$613$	−10.4722	−	10.4722i	−0.422968	−	0.422968i	−0.886224	+	0.463256i	$0.846681\pi$
$614$	−15.3260	−	26.5454i	−0.618507	−	1.07129i
$615$		0			0
$616$	−1.12372	+	1.94635i	−0.0452761	+	0.0784206i
$617$	−5.02479	+	1.34639i	−0.202290	+	0.0542035i	−0.358541	−	0.933514i	$-0.616726\pi$
$617$	−5.02479	+	1.34639i	−0.202290	+	0.0542035i	0.156251	+	0.987717i	$0.450059\pi$
$618$		0			0
$619$	−7.53177	+	4.34847i	−0.302727	+	0.174780i	−0.643667	−	0.765305i	$-0.722588\pi$
$619$	−7.53177	+	4.34847i	−0.302727	+	0.174780i	0.340940	+	0.940085i	$0.389255\pi$
$620$	−2.51059	−	2.04989i	−0.100828	−	0.0823255i
$621$		0			0
$622$	22.7980	−	22.7980i	0.914115	−	0.914115i
$623$	−34.5782	−	9.26519i	−1.38535	−	0.371202i
$624$		0			0
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	−3.97730	−	2.29629i	−0.158965	−	0.0917783i
$627$		0			0
$628$	2.93651	−	10.9592i	0.117180	−	0.437320i
$629$		0			0
$630$		0			0
$631$	4.49490			0.178939			0.0894695	−	0.995990i	$-0.471483\pi$
$631$	4.49490			0.178939			0.0894695	+	0.995990i	$0.471483\pi$
$632$	−1.41043	+	5.26380i	−0.0561040	+	0.209383i
$633$		0			0
$634$	1.90702	+	1.10102i	0.0757376	+	0.0437271i
$635$	−13.1221	−	5.90600i	−0.520736	−	0.234373i
$636$		0			0
$637$	16.1473	+	4.32666i	0.639780	+	0.171429i
$638$	2.43916	−	2.43916i	0.0965672	−	0.0965672i
$639$		0			0
$640$	−0.224745	−	2.22474i	−0.00888382	−	0.0879408i
$641$	24.1237	−	13.9278i	0.952830	−	0.550117i	0.0588710	−	0.998266i	$-0.481250\pi$
$641$	24.1237	−	13.9278i	0.952830	−	0.550117i	0.893959	+	0.448149i	$0.147917\pi$
$642$		0			0
$643$	44.8339	−	12.0132i	1.76807	−	0.473754i	0.779747	−	0.626095i	$-0.215348\pi$
$643$	44.8339	−	12.0132i	1.76807	−	0.473754i	0.988328	+	0.152341i	$0.0486811\pi$
$644$	6.50683	−	11.2702i	0.256405	−	0.444106i
$645$		0			0
$646$	−13.1237	−	22.7310i	−0.516346	−	0.894338i
$647$	−6.00680	−	6.00680i	−0.236152	−	0.236152i	0.579103	−	0.815254i	$-0.303403\pi$
$647$	−6.00680	−	6.00680i	−0.236152	−	0.236152i	−0.815254	+	0.579103i	$0.803403\pi$
$648$		0			0
$649$			3.10102i			0.121726i
$650$	−19.8092	−	22.3611i	−0.776980	−	0.877075i
$651$		0			0
$652$	1.50939	+	5.63311i	0.0591122	+	0.220610i
$653$	−3.86789	−	14.4352i	−0.151362	−	0.564892i	−0.999389	−	0.0349390i	$-0.988876\pi$
$653$	−3.86789	−	14.4352i	−0.151362	−	0.564892i	0.848027	−	0.529953i	$-0.177790\pi$
$654$		0			0
$655$	3.33463	−	20.5171i	0.130295	−	0.801670i
$656$		−	4.87832i		−	0.190466i
$657$		0			0
$658$	−15.0000	−	15.0000i	−0.584761	−	0.584761i
$659$	−16.0492	−	27.7980i	−0.625186	−	1.08285i	−0.988505	−	0.151190i	$-0.951690\pi$
$659$	−16.0492	−	27.7980i	−0.625186	−	1.08285i	0.363318	−	0.931665i	$-0.381644\pi$
$660$		0			0
$661$	10.0227	−	17.3598i	0.389838	−	0.675219i	−0.602589	−	0.798051i	$-0.705864\pi$
$661$	10.0227	−	17.3598i	0.389838	−	0.675219i	0.992427	+	0.122832i	$0.0391977\pi$
$662$	20.3820	−	5.46135i	0.792170	−	0.212261i
$663$		0			0
$664$	−12.5136	+	7.22474i	−0.485623	+	0.280374i
$665$	20.2918	−	2.04989i	0.786882	−	0.0794912i
$666$		0			0
$667$	−14.1237	+	14.1237i	−0.546873	+	0.546873i
$668$	7.53225	+	2.01826i	0.291432	+	0.0780888i
$669$		0			0
$670$	2.24264	+	5.91359i	0.0866408	+	0.228462i
$671$	−8.02270	−	4.63191i	−0.309713	−	0.178813i
$672$		0			0
$673$	12.7369	−	47.5349i	0.490973	−	1.83234i	−0.0605353	−	0.998166i	$-0.519281\pi$
$673$	12.7369	−	47.5349i	0.490973	−	1.83234i	0.551508	−	0.834170i	$-0.314053\pi$
$674$	−10.0424			−0.386817
$675$		0			0
$676$	−22.6969			−0.872959
$677$	−12.3187	+	45.9741i	−0.473447	+	1.76693i	0.153793	+	0.988103i	$0.450851\pi$
$677$	−12.3187	+	45.9741i	−0.473447	+	1.76693i	−0.627240	+	0.778826i	$0.715815\pi$
$678$		0			0
$679$	21.2132	+	12.2474i	0.814088	+	0.470014i
$680$	4.67726	+	12.3334i	0.179365	+	0.472965i
$681$		0			0
$682$	1.53504	+	0.411312i	0.0587796	+	0.0157499i
$683$	6.92820	−	6.92820i	0.265100	−	0.265100i	−0.562022	−	0.827122i	$-0.689976\pi$
$683$	6.92820	−	6.92820i	0.265100	−	0.265100i	0.827122	+	0.562022i	$0.189976\pi$
$684$		0			0
$685$	48.4949	−	4.89898i	1.85289	−	0.187180i
$686$	17.3939	−	10.0424i	0.664101	−	0.383419i
$687$		0			0
$688$	−9.86919	+	2.64444i	−0.376259	+	0.100818i
$689$	−23.8988	+	41.3939i	−0.910470	+	1.57698i
$690$		0			0
$691$	−11.4495	−	19.8311i	−0.435559	−	0.754411i	0.561782	−	0.827285i	$-0.310116\pi$
$691$	−11.4495	−	19.8311i	−0.435559	−	0.754411i	−0.997341	+	0.0728748i	$0.976783\pi$
$692$	5.33902	+	5.33902i	0.202959	+	0.202959i
$693$		0			0
$694$			14.2474i			0.540826i
$695$	−2.95852	+	18.2030i	−0.112223	+	0.690479i
$696$		0			0
$697$	7.44806	+	27.7965i	0.282115	+	1.05287i
$698$	5.18813	+	19.3624i	0.196374	+	0.732877i
$699$		0			0
$700$	−10.2307	−	0.619114i	−0.386685	−	0.0234003i
$701$		−	13.8243i		−	0.522137i	−0.965320	−	0.261068i	$-0.915925\pi$
$701$		−	13.8243i		−	0.522137i	0.965320	−	0.261068i	$-0.0840748\pi$
$702$		0			0
$703$		0			0
$704$	0.548188	+	0.949490i	0.0206606	+	0.0357852i
$705$		0			0
$706$	−0.949490	+	1.64456i	−0.0357345	+	0.0618940i
$707$	16.1719	−	4.33324i	0.608206	−	0.162968i
$708$		0			0
$709$	6.92820	−	4.00000i	0.260194	−	0.150223i	−0.364229	−	0.931309i	$-0.618667\pi$
$709$	6.92820	−	4.00000i	0.260194	−	0.150223i	0.624423	+	0.781086i	$0.285334\pi$
$710$	3.14626	+	31.1448i	0.118077	+	1.16884i
$711$		0			0
$712$	−12.3485	+	12.3485i	−0.462778	+	0.462778i
$713$	−8.88849	−	2.38166i	−0.332877	−	0.0891940i
$714$		0			0
$715$	13.3569	+	6.01165i	0.499519	+	0.224823i
$716$	−6.79796	−	3.92480i	−0.254052	−	0.146677i
$717$		0			0
$718$	6.22243	−	23.2224i	0.232219	−	0.866653i
$719$	−29.7627			−1.10996			−0.554981	−	0.831863i	$-0.687274\pi$
$719$	−29.7627			−1.10996			−0.554981	+	0.831863i	$0.687274\pi$
$720$		0			0
$721$	4.49490			0.167399
$722$	−0.206527	+	0.770769i	−0.00768614	+	0.0286851i
$723$		0			0
$724$	3.67840	+	2.12372i	0.136707	+	0.0789276i
$725$	14.9216	+	4.98200i	0.554174	+	0.185027i
$726$		0			0
$727$	33.4607	+	8.96575i	1.24099	+	0.332521i	0.818848	−	0.574010i	$-0.194613\pi$
$727$	33.4607	+	8.96575i	1.24099	+	0.332521i	0.422139	+	0.906531i	$0.361280\pi$
$728$	−8.66025	+	8.66025i	−0.320970	+	0.320970i
$729$		0			0
$730$	−10.8990	−	8.89898i	−0.403389	−	0.329366i
$731$	52.1969	−	30.1359i	1.93057	−	1.11462i
$732$		0			0
$733$	−32.2326	+	8.63671i	−1.19054	+	0.319004i	−0.799099	−	0.601200i	$-0.794690\pi$
$733$	−32.2326	+	8.63671i	−1.19054	+	0.319004i	−0.391440	+	0.920204i	$0.628023\pi$
$734$	−14.3171	+	24.7980i	−0.528454	+	0.915309i
$735$		0			0
$736$	−3.17423	−	5.49794i	−0.117004	−	0.202657i
$737$	−2.19275	−	2.19275i	−0.0807711	−	0.0807711i
$738$		0			0
$739$		−	9.84337i		−	0.362094i	−0.983474	−	0.181047i	$-0.942051\pi$
$739$		−	9.84337i		−	0.362094i	0.983474	−	0.181047i	$-0.0579486\pi$
$740$		0			0
$741$		0			0
$742$	4.24440	+	15.8403i	0.155817	+	0.581516i
$743$	−7.23254	−	26.9922i	−0.265336	−	0.990248i	−0.962044	−	0.272893i	$-0.912019\pi$
$743$	−7.23254	−	26.9922i	−0.265336	−	0.990248i	0.696708	−	0.717355i	$-0.254647\pi$
$744$		0			0
$745$	9.75014	+	1.58468i	0.357218	+	0.0580583i
$746$			27.3950i			1.00300i
$747$		0			0
$748$	−4.57321	−	4.57321i	−0.167213	−	0.167213i
$749$	5.22826	+	9.05561i	0.191036	+	0.330885i
$750$		0			0
$751$	−12.5227	+	21.6900i	−0.456960	+	0.791478i	−0.998799	−	0.0490047i	$-0.984395\pi$
$751$	−12.5227	+	21.6900i	−0.456960	+	0.791478i	0.541839	+	0.840483i	$0.317728\pi$
$752$	−9.99585	+	2.67838i	−0.364511	+	0.0976705i
$753$		0			0
$754$	16.2795	−	9.39898i	0.592865	−	0.342291i
$755$	34.1482	−	41.8228i	1.24278	−	1.52209i
$756$		0			0
$757$	2.02270	−	2.02270i	0.0735164	−	0.0735164i	−0.669393	−	0.742909i	$-0.733446\pi$
$757$	2.02270	−	2.02270i	0.0735164	−	0.0735164i	0.742909	+	0.669393i	$0.233446\pi$
$758$	−3.86370	−	1.03528i	−0.140336	−	0.0376029i
$759$		0			0
$760$	4.08346	−	9.07277i	0.148123	−	0.329104i
$761$	−3.92168	−	2.26418i	−0.142161	−	0.0820766i	0.427233	−	0.904142i	$-0.359489\pi$
$761$	−3.92168	−	2.26418i	−0.142161	−	0.0820766i	−0.569393	+	0.822065i	$0.692822\pi$
$762$		0			0
$763$	2.12220	−	7.92016i	0.0768288	−	0.286729i
$764$	16.0492			0.580638
$765$		0			0
$766$	20.1464			0.727920
$767$	−4.37378	+	16.3232i	−0.157928	+	0.589395i
$768$		0			0
$769$	27.4504	+	15.8485i	0.989885	+	0.571510i	0.905240	−	0.424901i	$-0.139691\pi$
$769$	27.4504	+	15.8485i	0.989885	+	0.571510i	0.0846451	+	0.996411i	$0.473024\pi$
$770$	4.69890	−	1.78199i	0.169337	−	0.0642183i
$771$		0			0
$772$	−9.28618	−	2.48823i	−0.334217	−	0.0895532i
$773$	1.12848	−	1.12848i	0.0405888	−	0.0405888i	−0.686521	−	0.727110i	$-0.740863\pi$
$773$	1.12848	−	1.12848i	0.0405888	−	0.0405888i	0.727110	+	0.686521i	$0.240863\pi$
$774$		0			0
$775$	1.44949	+	7.10102i	0.0520672	+	0.255076i
$776$	10.3485	−	5.97469i	0.371488	−	0.214479i
$777$		0			0
$778$	−9.11717	+	2.44294i	−0.326867	+	0.0875836i
$779$	10.8530	−	18.7980i	0.388849	−	0.673507i
$780$		0			0
$781$	−7.67423	−	13.2922i	−0.274606	−	0.475631i
$782$	26.4808	+	26.4808i	0.946951	+	0.946951i
$783$		0			0
$784$		−	2.79796i		−	0.0999271i
$785$	−20.5849	+	14.8291i	−0.734705	+	0.529272i
$786$		0			0
$787$	4.60212	+	17.1753i	0.164048	+	0.612234i	0.998160	+	0.0606393i	$0.0193139\pi$
$787$	4.60212	+	17.1753i	0.164048	+	0.612234i	−0.834112	+	0.551595i	$0.814019\pi$
$788$	2.47185	+	9.22508i	0.0880562	+	0.328630i
$789$		0			0
$790$	9.88708	−	7.12252i	0.351767	−	0.253408i
$791$			16.6062i			0.590448i
$792$		0			0
$793$	−35.6969	−	35.6969i	−1.26764	−	1.26764i
$794$	13.8404	+	23.9722i	0.491176	+	0.850741i
$795$		0			0
$796$	−6.27526	+	10.8691i	−0.222421	+	0.385244i
$797$	25.5482	−	6.84563i	0.904965	−	0.242485i	0.223818	−	0.974631i	$-0.428148\pi$
$797$	25.5482	−	6.84563i	0.904965	−	0.242485i	0.681147	+	0.732146i	$0.261481\pi$
$798$		0			0
$799$	52.8669	−	30.5227i	1.87030	−	1.07982i
$800$	−2.75699	+	4.17121i	−0.0974745	+	0.147474i
$801$		0			0
$802$	−7.10102	+	7.10102i	−0.250746	+	0.250746i
$803$	6.66390	+	1.78559i	0.235164	+	0.0630120i
$804$		0			0
$805$	−27.2086	+	10.3184i	−0.958976	+	0.363677i
$806$	7.50000	+	4.33013i	0.264176	+	0.152522i
$807$		0			0
$808$	2.11389	−	7.88915i	0.0743664	−	0.277539i
$809$	−15.6992			−0.551955			−0.275977	−	0.961164i	$-0.589002\pi$
$809$	−15.6992			−0.551955			−0.275977	+	0.961164i	$0.589002\pi$
$810$		0			0
$811$	30.8990			1.08501			0.542505	−	0.840053i	$-0.317476\pi$
$811$	30.8990			1.08501			0.542505	+	0.840053i	$0.317476\pi$
$812$	1.66925	−	6.22973i	0.0585792	−	0.218621i
$813$		0			0
$814$		0			0
$815$	5.35209	−	11.8914i	0.187475	−	0.416539i
$816$		0			0
$817$	−43.9128	−	11.7664i	−1.53632	−	0.411655i
$818$	−21.7774	+	21.7774i	−0.761431	+	0.761431i
$819$		0			0
$820$	−6.89898	+	8.44949i	−0.240923	+	0.295069i
$821$	−4.40408	+	2.54270i	−0.153704	+	0.0887408i	−0.574879	−	0.818238i	$-0.694951\pi$
$821$	−4.40408	+	2.54270i	−0.153704	+	0.0887408i	0.421176	+	0.906979i	$0.361618\pi$
$822$		0			0
$823$	5.46410	−	1.46410i	0.190467	−	0.0510354i	−0.162325	−	0.986737i	$-0.551899\pi$
$823$	5.46410	−	1.46410i	0.190467	−	0.0510354i	0.352791	+	0.935702i	$0.385233\pi$
$824$	1.09638	−	1.89898i	0.0381941	−	0.0661541i
$825$		0			0
$826$	2.89898	+	5.02118i	0.100868	+	0.174709i
$827$	−17.7491	−	17.7491i	−0.617197	−	0.617197i	0.327615	−	0.944811i	$-0.393755\pi$
$827$	−17.7491	−	17.7491i	−0.617197	−	0.617197i	−0.944811	+	0.327615i	$0.893755\pi$
$828$		0			0
$829$			25.7980i			0.896000i	0.894034	+	0.448000i	$0.147864\pi$
$829$			25.7980i			0.896000i	−0.894034	+	0.448000i	$0.852136\pi$
$830$	31.8916	+	5.18331i	1.10697	+	0.179915i
$831$		0			0
$832$	1.54636	+	5.77111i	0.0536105	+	0.200077i
$833$	4.27183	+	15.9427i	0.148010	+	0.552382i
$834$		0			0
$835$	−10.1920	−	14.1479i	−0.352708	−	0.489610i
$836$			4.87832i			0.168720i
$837$		0			0
$838$	24.1237	+	24.1237i	0.833340	+	0.833340i
$839$	−4.27475	−	7.40408i	−0.147581	−	0.255617i	0.782752	−	0.622334i	$-0.213815\pi$
$839$	−4.27475	−	7.40408i	−0.147581	−	0.255617i	−0.930333	+	0.366716i	$0.880482\pi$
$840$		0			0
$841$	9.55051	−	16.5420i	0.329328	−	0.570413i
$842$	13.0888	−	3.50713i	0.451069	−	0.120864i
$843$		0			0
$844$	7.14250	−	4.12372i	0.245855	−	0.141944i
$845$	39.3123	+	32.0983i	1.35238	+	1.10422i
$846$		0			0
$847$	14.2020	−	14.2020i	0.487988	−	0.487988i
$848$	7.72741	+	2.07055i	0.265360	+	0.0711031i
$849$		0			0
$850$	9.34082	−	27.9767i	0.320388	−	0.959594i
$851$		0			0
$852$		0			0
$853$	6.01262	−	22.4394i	0.205868	−	0.768311i	−0.783315	−	0.621625i	$-0.786473\pi$
$853$	6.01262	−	22.4394i	0.205868	−	0.768311i	0.989183	−	0.146686i	$-0.0468606\pi$
$854$	−17.3205			−0.592696
$855$		0			0
$856$	5.10102			0.174349
$857$	−8.87564	+	33.1244i	−0.303186	+	1.13151i	0.631309	+	0.775531i	$0.282518\pi$
$857$	−8.87564	+	33.1244i	−0.303186	+	1.13151i	−0.934495	+	0.355975i	$0.884149\pi$
$858$		0			0
$859$	−2.51059	−	1.44949i	−0.0856602	−	0.0494560i	0.456558	−	0.889694i	$-0.349082\pi$
$859$	−2.51059	−	1.44949i	−0.0856602	−	0.0494560i	−0.542218	+	0.840238i	$0.682415\pi$
$860$	20.8337	+	9.37683i	0.710424	+	0.319747i
$861$		0			0
$862$	21.8564	+	5.85641i	0.744432	+	0.199470i
$863$	−7.95315	+	7.95315i	−0.270728	+	0.270728i	−0.829393	−	0.558665i	$-0.811314\pi$
$863$	−7.95315	+	7.95315i	−0.270728	+	0.270728i	0.558665	+	0.829393i	$0.311314\pi$
$864$		0			0
$865$	−1.69694	−	16.7980i	−0.0576976	−	0.571148i
$866$	17.4495	−	10.0745i	0.592958	−	0.342344i
$867$		0			0
$868$	2.87005	−	0.769027i	0.0974158	−	0.0261025i
$869$	−2.98735	+	5.17423i	−0.101339	+	0.175524i
$870$		0			0
$871$	−8.44949	−	14.6349i	−0.286300	−	0.495886i
$872$	−2.82843	−	2.82843i	−0.0957826	−	0.0957826i
$873$		0			0
$874$		−	28.2474i		−	0.955484i
$875$	16.8446	+	15.5408i	0.569451	+	0.525374i
$876$		0			0
$877$	−9.12197	−	34.0437i	−0.308027	−	1.14957i	−0.930308	−	0.366779i	$-0.880461\pi$
$877$	−9.12197	−	34.0437i	−0.308027	−	1.14957i	0.622281	−	0.782794i	$-0.286206\pi$
$878$	0.930692	+	3.47339i	0.0314093	+	0.117221i
$879$		0			0
$880$	0.393292	−	2.41982i	0.0132579	−	0.0815721i
$881$		−	40.2337i		−	1.35551i	−0.735290	−	0.677753i	$-0.762954\pi$
$881$		−	40.2337i		−	1.35551i	0.735290	−	0.677753i	$-0.237046\pi$
$882$		0			0
$883$	33.1464	+	33.1464i	1.11547	+	1.11547i	0.992398	+	0.123068i	$0.0392733\pi$
$883$	33.1464	+	33.1464i	1.11547	+	1.11547i	0.123068	+	0.992398i	$0.460727\pi$
$884$	−17.6223	−	30.5227i	−0.592702	−	1.02659i
$885$		0			0
$886$	3.12372	−	5.41045i	0.104944	−	0.181768i
$887$	14.2499	−	3.81824i	0.478464	−	0.128204i	−0.0115234	−	0.999934i	$-0.503668\pi$
$887$	14.2499	−	3.81824i	0.478464	−	0.128204i	0.489987	+	0.871730i	$0.337001\pi$
$888$		0			0
$889$	11.4245	−	6.59592i	0.383164	−	0.221220i
$890$	38.8515	−	3.92480i	1.30231	−	0.131560i
$891$		0			0
$892$	12.7980	−	12.7980i	0.428507	−	0.428507i
$893$	−44.4764	−	11.9174i	−1.48835	−	0.398802i
$894$		0			0
$895$	6.22390	+	16.4117i	0.208042	+	0.548583i
$896$	1.77526	+	1.02494i	0.0593071	+	0.0342410i
$897$		0			0
$898$	−4.02628	+	15.0263i	−0.134359	+	0.501433i
$899$	−4.56048			−0.152100
$900$		0			0
$901$	−47.1918			−1.57219
$902$	1.38429	−	5.16622i	0.0460917	−	0.172016i
$903$		0			0
$904$	7.01569	+	4.05051i	0.233338	+	0.134718i
$905$	−3.36777	−	8.88044i	−0.111949	−	0.295196i
$906$		0			0
$907$	2.22502	+	0.596192i	0.0738805	+	0.0197962i	0.295570	−	0.955321i	$-0.404490\pi$
$907$	2.22502	+	0.596192i	0.0738805	+	0.0197962i	−0.221689	+	0.975117i	$0.571157\pi$
$908$	−5.33902	+	5.33902i	−0.177182	+	0.177182i
$909$		0			0
$910$	27.2474	−	2.75255i	0.903244	−	0.0912462i
$911$	−37.5959	+	21.7060i	−1.24561	+	0.719152i	−0.970230	−	0.242184i	$-0.922136\pi$
$911$	−37.5959	+	21.7060i	−1.24561	+	0.719152i	−0.275378	+	0.961336i	$0.588803\pi$
$912$		0			0
$913$	−15.3023	+	4.10023i	−0.506431	+	0.135698i
$914$	−10.3923	+	18.0000i	−0.343747	+	0.595387i
$915$		0			0
$916$	−2.32577	−	4.02834i	−0.0768455	−	0.133100i
$917$	13.4744	+	13.4744i	0.444962	+	0.444962i
$918$		0			0
$919$			5.65153i			0.186427i	0.995646	+	0.0932134i	$0.0297139\pi$
$919$			5.65153i			0.186427i	−0.995646	+	0.0932134i	$0.970286\pi$
$920$	−2.27732	+	14.0117i	−0.0750810	+	0.461954i
$921$		0			0
$922$	0.732051	+	2.73205i	0.0241088	+	0.0899753i
$923$	−21.6480	−	80.7913i	−0.712552	−	2.65928i
$924$		0			0
$925$		0			0
$926$		−	16.0492i		−	0.527408i
$927$		0			0
$928$	−2.22474	−	2.22474i	−0.0730308	−	0.0730308i
$929$	19.9025	+	34.4722i	0.652981	+	1.13100i	0.982396	+	0.186811i	$0.0598151\pi$
$929$	19.9025	+	34.4722i	0.652981	+	1.13100i	−0.329415	+	0.944185i	$0.606852\pi$
$930$		0			0
$931$	6.22474	−	10.7816i	0.204008	−	0.353352i
$932$	−4.73205	+	1.26795i	−0.155003	+	0.0415331i
$933$		0			0
$934$	8.09601	−	4.67423i	0.264910	−	0.152946i
$935$	1.45354	+	14.3885i	0.0475358	+	0.470556i
$936$		0			0
$937$	19.4949	−	19.4949i	0.636871	−	0.636871i	−0.312912	−	0.949782i	$-0.601304\pi$
$937$	19.4949	−	19.4949i	0.636871	−	0.636871i	0.949782	+	0.312912i	$0.101304\pi$
$938$	−5.60040	−	1.50062i	−0.182859	−	0.0489971i
$939$		0			0
$940$	21.1011	+	9.49718i	0.688243	+	0.309764i
$941$	−28.8712	−	16.6688i	−0.941173	−	0.543387i	−0.0508454	−	0.998707i	$-0.516192\pi$
$941$	−28.8712	−	16.6688i	−0.941173	−	0.543387i	−0.890328	+	0.455320i	$0.849525\pi$
$942$		0			0
$943$	−8.01558	+	29.9146i	−0.261023	+	0.974152i
$944$	2.82843			0.0920575
$945$		0			0
$946$	−11.2020			−0.364210
$947$	12.2547	−	45.7351i	0.398224	−	1.48619i	−0.417995	−	0.908449i	$-0.637267\pi$
$947$	12.2547	−	45.7351i	0.398224	−	1.48619i	0.816219	−	0.577742i	$-0.196066\pi$
$948$		0			0
$949$	32.5590	+	18.7980i	1.05691	+	0.610208i
$950$	−19.9036	+	9.93960i	−0.645758	+	0.322483i
$951$		0			0
$952$	−11.6802	−	3.12970i	−0.378558	−	0.101434i
$953$	−3.67840	+	3.67840i	−0.119155	+	0.119155i	−0.764170	−	0.645015i	$-0.776851\pi$
$953$	−3.67840	+	3.67840i	−0.119155	+	0.119155i	0.645015	+	0.764170i	$0.276851\pi$
$954$		0			0
$955$	−27.7980	−	22.6969i	−0.899521	−	0.734456i
$956$	5.32577	−	3.07483i	0.172248	−	0.0994472i
$957$		0			0
$958$	−17.7583	+	4.75833i	−0.573746	+	0.153735i
$959$	−22.3417	+	38.6969i	−0.721451	+	1.24959i
$960$		0			0
$961$	14.4495	+	25.0273i	0.466113	+	0.807331i
$962$		0			0
$963$		0			0
$964$		−	19.6969i		−	0.634396i
$965$	12.5653	+	17.4424i	0.404490	+	0.561490i
$966$		0			0
$967$	4.15383	+	15.5023i	0.133578	+	0.498520i	1.00000		0.000792900i	$-0.000252388\pi$
$967$	4.15383	+	15.5023i	0.133578	+	0.498520i	−0.866422	+	0.499313i	$0.833586\pi$
$968$	−2.53590	−	9.46410i	−0.0815069	−	0.304188i
$969$		0			0
$970$	−26.3736	−	4.28648i	−0.846804	−	0.137630i
$971$		−	37.8659i		−	1.21518i	−0.794253	−	0.607588i	$-0.792137\pi$
$971$		−	37.8659i		−	1.21518i	0.794253	−	0.607588i	$-0.207863\pi$
$972$		0			0
$973$	−11.9546	−	11.9546i	−0.383247	−	0.383247i
$974$	10.3923	+	18.0000i	0.332991	+	0.576757i
$975$		0			0
$976$	−4.22474	+	7.31747i	−0.135231	+	0.234227i
$977$	−19.2209	+	5.15023i	−0.614932	+	0.164771i	−0.552823	−	0.833299i	$-0.686449\pi$
$977$	−19.2209	+	5.15023i	−0.614932	+	0.164771i	−0.0621093	+	0.998069i	$0.519783\pi$
$978$		0			0
$979$	−16.5813	+	9.57321i	−0.529940	+	0.305961i
$980$	−3.95691	+	4.84621i	−0.126399	+	0.154806i
$981$		0			0
$982$	−17.7980	+	17.7980i	−0.567956	+	0.567956i
$983$	−16.6598	−	4.46397i	−0.531364	−	0.142378i	−0.0168458	−	0.999858i	$-0.505362\pi$
$983$	−16.6598	−	4.46397i	−0.531364	−	0.142378i	−0.514518	+	0.857480i	$0.672029\pi$
$984$		0			0
$985$	8.76486	−	19.4740i	0.279272	−	0.620495i
$986$	16.0732	+	9.27987i	0.511875	+	0.295531i
$987$		0			0
$988$	−6.88053	+	25.6785i	−0.218899	+	0.816942i
$989$	64.8644			2.06257
$990$		0			0
$991$	−41.7423			−1.32599			−0.662995	−	0.748624i	$-0.730715\pi$
$991$	−41.7423			−1.32599			−0.662995	+	0.748624i	$0.730715\pi$
$992$	0.375156	−	1.40010i	0.0119112	−	0.0444532i
$993$		0			0
$994$	−24.8523	−	14.3485i	−0.788266	−	0.455106i
$995$	26.2402	−	9.95121i	0.831871	−	0.315475i
$996$		0			0
$997$	20.3834	+	5.46172i	0.645549	+	0.172974i	0.566715	−	0.823914i	$-0.308214\pi$
$997$	20.3834	+	5.46172i	0.645549	+	0.172974i	0.0788332	+	0.996888i	$0.474881\pi$
$998$	4.09978	−	4.09978i	0.129776	−	0.129776i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.m.h.53.2		8
3.2	odd	2		810.2.m.a.53.1		8
5.2	odd	4	inner	810.2.m.h.377.2		8
9.2	odd	6	inner	810.2.m.h.593.2		8
9.4	even	3		270.2.f.a.53.3	yes	8
9.5	odd	6		270.2.f.a.53.2	✓	8
9.7	even	3		810.2.m.a.593.1		8
15.2	even	4		810.2.m.a.377.1		8
36.23	even	6		2160.2.w.f.593.2		8
36.31	odd	6		2160.2.w.f.593.3		8
45.2	even	12	inner	810.2.m.h.107.2		8
45.4	even	6		1350.2.f.f.593.1		8
45.7	odd	12		810.2.m.a.107.1		8
45.13	odd	12		1350.2.f.f.107.3		8
45.14	odd	6		1350.2.f.f.593.3		8
45.22	odd	12		270.2.f.a.107.1	yes	8
45.23	even	12		1350.2.f.f.107.1		8
45.32	even	12		270.2.f.a.107.4	yes	8
180.67	even	12		2160.2.w.f.1457.1		8
180.167	odd	12		2160.2.w.f.1457.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.f.a.53.2	✓	8	9.5	odd	6
270.2.f.a.53.3	yes	8	9.4	even	3
270.2.f.a.107.1	yes	8	45.22	odd	12
270.2.f.a.107.4	yes	8	45.32	even	12
810.2.m.a.53.1		8	3.2	odd	2
810.2.m.a.107.1		8	45.7	odd	12
810.2.m.a.377.1		8	15.2	even	4
810.2.m.a.593.1		8	9.7	even	3
810.2.m.h.53.2		8	1.1	even	1	trivial
810.2.m.h.107.2		8	45.2	even	12	inner
810.2.m.h.377.2		8	5.2	odd	4	inner
810.2.m.h.593.2		8	9.2	odd	6	inner
1350.2.f.f.107.1		8	45.23	even	12
1350.2.f.f.107.3		8	45.13	odd	12
1350.2.f.f.593.1		8	45.4	even	6
1350.2.f.f.593.3		8	45.14	odd	6
2160.2.w.f.593.2		8	36.23	even	6
2160.2.w.f.593.3		8	36.31	odd	6
2160.2.w.f.1457.1		8	180.67	even	12
2160.2.w.f.1457.4		8	180.167	odd	12

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.792893 + 2.09077i) q^{5} +(-1.98004 - 0.530550i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.792893 + 2.09077i) q^{5} +(-1.98004 - 0.530550i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.22474 - 0.224745i) q^{10} +(-0.949490 + 0.548188i) q^{11} +(-5.77111 + 1.54636i) q^{13} +(-1.02494 + 1.77526i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.17121 - 4.17121i) q^{17} +4.44949i q^{19} +(0.358719 - 2.20711i) q^{20} +(0.283763 + 1.05902i) q^{22} +(-1.64310 - 6.13215i) q^{23} +(-3.74264 + 3.31552i) q^{25} +5.97469i q^{26} +(1.44949 + 1.44949i) q^{28} +(-1.57313 - 2.72474i) q^{29} +(0.724745 - 1.25529i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-5.10867 + 2.94949i) q^{34} +(-0.460702 - 4.56048i) q^{35} +(4.29788 + 1.15161i) q^{38} +(-2.03906 - 0.917738i) q^{40} +(-4.22474 - 2.43916i) q^{41} +(-2.64444 + 9.86919i) q^{43} +1.09638 q^{44} -6.34847 q^{46} +(-2.67838 + 9.99585i) q^{47} +(-2.42310 - 1.39898i) q^{49} +(2.23388 + 4.47323i) q^{50} +(5.77111 + 1.54636i) q^{52} +(5.65685 - 5.65685i) q^{53} +(-1.89898 - 1.55051i) q^{55} +(1.77526 - 1.02494i) q^{56} +(-3.03906 + 0.814313i) q^{58} +(1.41421 - 2.44949i) q^{59} +(4.22474 + 7.31747i) q^{61} +(-1.02494 - 1.02494i) q^{62} -1.00000i q^{64} +(-7.80896 - 10.8400i) q^{65} +(0.732051 + 2.73205i) q^{67} +(1.52677 + 5.69798i) q^{68} +(-4.52432 - 0.735335i) q^{70} +13.9993i q^{71} +(-4.44949 - 4.44949i) q^{73} +(2.22474 - 3.85337i) q^{76} +(2.17087 - 0.581683i) q^{77} +(4.71940 - 2.72474i) q^{79} +(-1.41421 + 1.73205i) q^{80} +(-3.44949 + 3.44949i) q^{82} +(13.9571 + 3.73980i) q^{83} +(5.41372 - 12.0284i) q^{85} +(8.84847 + 5.10867i) q^{86} +(0.283763 - 1.05902i) q^{88} +17.4634 q^{89} +12.2474 q^{91} +(-1.64310 + 6.13215i) q^{92} +(8.96204 + 5.17423i) q^{94} +(-9.30286 + 3.52797i) q^{95} +(-11.5422 - 3.09273i) q^{97} +(-1.97846 + 1.97846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q + 12 * q^5 + 4 * q^7	\( 8 q + 12 q^{5} + 4 q^{7} + 8 q^{10} + 12 q^{11} - 12 q^{13} + 4 q^{16} - 8 q^{22} - 36 q^{23} + 4 q^{25} - 8 q^{28} - 4 q^{31} + 12 q^{38} + 4 q^{40} - 24 q^{41} + 24 q^{43} + 8 q^{46} - 36 q^{47} + 24 q^{50} + 12 q^{52} + 24 q^{55} + 24 q^{56} - 4 q^{58} + 24 q^{61} - 24 q^{65} - 8 q^{67} + 24 q^{68} + 8 q^{70} - 16 q^{73} + 8 q^{76} + 60 q^{77} - 8 q^{82} + 12 q^{83} + 28 q^{85} + 12 q^{86} - 8 q^{88} - 36 q^{92} - 24 q^{95} - 24 q^{97}+O(q^{100}) \) 8 * q + 12 * q^5 + 4 * q^7 + 8 * q^10 + 12 * q^11 - 12 * q^13 + 4 * q^16 - 8 * q^22 - 36 * q^23 + 4 * q^25 - 8 * q^28 - 4 * q^31 + 12 * q^38 + 4 * q^40 - 24 * q^41 + 24 * q^43 + 8 * q^46 - 36 * q^47 + 24 * q^50 + 12 * q^52 + 24 * q^55 + 24 * q^56 - 4 * q^58 + 24 * q^61 - 24 * q^65 - 8 * q^67 + 24 * q^68 + 8 * q^70 - 16 * q^73 + 8 * q^76 + 60 * q^77 - 8 * q^82 + 12 * q^83 + 28 * q^85 + 12 * q^86 - 8 * q^88 - 36 * q^92 - 24 * q^95 - 24 * q^97

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