LMFDB - Embedded newform 819.2.fm.f.370.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (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 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			370.8
Character	$\chi$	$=$	819.370
Dual form			819.2.fm.f.622.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.706652 + 2.63726i) q^{2} +(-4.72373 + 2.72725i) q^{4} +(-2.18431 - 2.18431i) q^{5} +(-1.85732 + 1.88424i) q^{7} +(-6.66928 - 6.66928i) q^{8} +O(q^{10})$	\(q+(0.706652 + 2.63726i) q^{2} +(-4.72373 + 2.72725i) q^{4} +(-2.18431 - 2.18431i) q^{5} +(-1.85732 + 1.88424i) q^{7} +(-6.66928 - 6.66928i) q^{8} +(4.21705 - 7.30414i) q^{10} +(0.456585 - 0.122342i) q^{11} +(2.45314 + 2.64236i) q^{13} +(-6.28171 - 3.56673i) q^{14} +(7.42128 - 12.8540i) q^{16} +(-1.14138 - 1.97693i) q^{17} +(1.51851 - 5.66717i) q^{19} +(16.2753 + 4.36094i) q^{20} +(0.645294 + 1.11768i) q^{22} +(-0.481898 - 0.278224i) q^{23} +4.54242i q^{25} +(-5.23509 + 8.33681i) q^{26} +(3.63468 - 13.9660i) q^{28} +(3.64605 - 6.31515i) q^{29} +(-2.74924 - 2.74924i) q^{31} +(20.9229 + 5.60626i) q^{32} +(4.40713 - 4.40713i) q^{34} +(8.17273 - 0.0588104i) q^{35} +(-6.41041 + 1.71767i) q^{37} +16.0189 q^{38} +29.1356i q^{40} +(-1.49535 + 0.400678i) q^{41} +(5.08624 - 2.93654i) q^{43} +(-1.82313 + 1.82313i) q^{44} +(0.393215 - 1.46750i) q^{46} +(-6.55220 + 6.55220i) q^{47} +(-0.100738 - 6.99928i) q^{49} +(-11.9795 + 3.20991i) q^{50} +(-18.7944 - 5.79150i) q^{52} -4.17698 q^{53} +(-1.26456 - 0.730092i) q^{55} +(24.9535 - 0.179564i) q^{56} +(19.2312 + 5.15298i) q^{58} +(-14.2781 - 3.82579i) q^{59} +(-0.553719 + 0.319690i) q^{61} +(5.30771 - 9.19322i) q^{62} +29.4556i q^{64} +(0.413319 - 11.1302i) q^{65} +(-2.17304 - 8.10989i) q^{67} +(10.7832 + 6.22567i) q^{68} +(5.93037 + 21.5120i) q^{70} +(2.13591 + 0.572316i) q^{71} +(2.43968 - 2.43968i) q^{73} +(-9.05986 - 15.6921i) q^{74} +(8.28273 + 30.9116i) q^{76} +(-0.617503 + 1.08755i) q^{77} -11.8014 q^{79} +(-44.2876 + 11.8668i) q^{80} +(-2.11339 - 3.66049i) q^{82} +(-1.80810 - 1.80810i) q^{83} +(-1.82510 + 6.81137i) q^{85} +(11.3386 + 11.3386i) q^{86} +(-3.86103 - 2.22917i) q^{88} +(-0.363443 - 1.35639i) q^{89} +(-9.53512 - 0.285396i) q^{91} +3.03514 q^{92} +(-21.9100 - 12.6497i) q^{94} +(-15.6957 + 9.06194i) q^{95} +(3.25005 - 12.1294i) q^{97} +(18.3877 - 5.21172i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.706652	+	2.63726i	0.499678	+	1.86482i	0.502069	+	0.864828i	$0.332572\pi$
$2$	0.706652	+	2.63726i	0.499678	+	1.86482i	−0.00239085	+	0.999997i	$0.500761\pi$
$3$		0			0
$3$		0			0
$4$	−4.72373	+	2.72725i	−2.36187	+	1.36362i
$5$	−2.18431	−	2.18431i	−0.976853	−	0.976853i	0.0228851	−	0.999738i	$-0.492715\pi$
$5$	−2.18431	−	2.18431i	−0.976853	−	0.976853i	−0.999738	+	0.0228851i	$0.992715\pi$
$6$		0			0
$7$	−1.85732	+	1.88424i	−0.702000	+	0.712177i
$7$	−1.85732	+	1.88424i	−0.702000	+	0.712177i
$8$	−6.66928	−	6.66928i	−2.35795	−	2.35795i
$9$		0			0
$10$	4.21705	−	7.30414i	1.33355	−	2.30977i
$11$	0.456585	−	0.122342i	0.137666	−	0.0368874i	−0.189328	−	0.981914i	$-0.560631\pi$
$11$	0.456585	−	0.122342i	0.137666	−	0.0368874i	0.326994	+	0.945026i	$0.393964\pi$
$12$		0			0
$13$	2.45314	+	2.64236i	0.680379	+	0.732860i
$13$	2.45314	+	2.64236i	0.680379	+	0.732860i
$14$	−6.28171	−	3.56673i	−1.67886	−	0.953248i
$15$		0			0
$16$	7.42128	−	12.8540i	1.85532	−	3.21351i
$17$	−1.14138	−	1.97693i	−0.276826	−	0.479477i	0.693768	−	0.720198i	$-0.255949\pi$
$17$	−1.14138	−	1.97693i	−0.276826	−	0.479477i	−0.970594	+	0.240722i	$0.922616\pi$
$18$		0			0
$19$	1.51851	−	5.66717i	0.348371	−	1.30014i	−0.540254	−	0.841502i	$-0.681672\pi$
$19$	1.51851	−	5.66717i	0.348371	−	1.30014i	0.888625	−	0.458635i	$-0.151661\pi$
$20$	16.2753	+	4.36094i	3.63926	+	0.975136i
$21$		0			0
$22$	0.645294	+	1.11768i	0.137577	+	0.238291i
$23$	−0.481898	−	0.278224i	−0.100483	−	0.0580137i	0.448917	−	0.893574i	$-0.351810\pi$
$23$	−0.481898	−	0.278224i	−0.100483	−	0.0580137i	−0.549399	+	0.835560i	$0.685143\pi$
$24$		0			0
$25$			4.54242i			0.908484i
$26$	−5.23509	+	8.33681i	−1.02668	+	1.63498i
$27$		0			0
$28$	3.63468	−	13.9660i	0.686890	−	2.63933i
$29$	3.64605	−	6.31515i	0.677055	−	1.17269i	−0.298809	−	0.954313i	$-0.596589\pi$
$29$	3.64605	−	6.31515i	0.677055	−	1.17269i	0.975864	−	0.218381i	$-0.0700774\pi$
$30$		0			0
$31$	−2.74924	−	2.74924i	−0.493778	−	0.493778i	0.415716	−	0.909494i	$-0.363531\pi$
$31$	−2.74924	−	2.74924i	−0.493778	−	0.493778i	−0.909494	+	0.415716i	$0.863531\pi$
$32$	20.9229	+	5.60626i	3.69867	+	0.991057i
$33$		0			0
$34$	4.40713	−	4.40713i	0.755816	−	0.755816i
$35$	8.17273	−	0.0588104i	1.38144	−	0.00994078i
$36$		0			0
$37$	−6.41041	+	1.71767i	−1.05387	+	0.282382i	−0.743848	−	0.668348i	$-0.767002\pi$
$37$	−6.41041	+	1.71767i	−1.05387	+	0.282382i	−0.310017	+	0.950731i	$0.600335\pi$
$38$	16.0189			2.59860
$39$		0			0
$40$			29.1356i			4.60674i
$41$	−1.49535	+	0.400678i	−0.233535	+	0.0625755i	−0.373688	−	0.927554i	$-0.621907\pi$
$41$	−1.49535	+	0.400678i	−0.233535	+	0.0625755i	0.140154	+	0.990130i	$0.455240\pi$
$42$		0			0
$43$	5.08624	−	2.93654i	0.775644	−	0.447818i	−0.0592406	−	0.998244i	$-0.518868\pi$
$43$	5.08624	−	2.93654i	0.775644	−	0.447818i	0.834884	+	0.550426i	$0.185535\pi$
$44$	−1.82313	+	1.82313i	−0.274848	+	0.274848i
$45$		0			0
$46$	0.393215	−	1.46750i	0.0579763	−	0.216371i
$47$	−6.55220	+	6.55220i	−0.955736	+	0.955736i	−0.999061	−	0.0433248i	$-0.986205\pi$
$47$	−6.55220	+	6.55220i	−0.955736	+	0.955736i	0.0433248	+	0.999061i	$0.486205\pi$
$48$		0			0
$49$	−0.100738	−	6.99928i	−0.0143911	−	0.999896i
$50$	−11.9795	+	3.20991i	−1.69416	+	0.453949i
$51$		0			0
$52$	−18.7944	−	5.79150i	−2.60631	−	0.803136i
$53$	−4.17698			−0.573753			−0.286876	−	0.957968i	$-0.592617\pi$
$53$	−4.17698			−0.573753			−0.286876	+	0.957968i	$0.592617\pi$
$54$		0			0
$55$	−1.26456	−	0.730092i	−0.170513	−	0.0984456i
$56$	24.9535	−	0.179564i	3.33456	−	0.0239953i
$57$		0			0
$58$	19.2312	+	5.15298i	2.52518	+	0.676619i
$59$	−14.2781	−	3.82579i	−1.85884	−	0.498076i	−0.858942	−	0.512072i	$-0.828878\pi$
$59$	−14.2781	−	3.82579i	−1.85884	−	0.498076i	−0.999902	+	0.0139966i	$0.995545\pi$
$60$		0			0
$61$	−0.553719	+	0.319690i	−0.0708965	+	0.0409321i	−0.535029	−	0.844834i	$-0.679699\pi$
$61$	−0.553719	+	0.319690i	−0.0708965	+	0.0409321i	0.464133	+	0.885766i	$0.346366\pi$
$62$	5.30771	−	9.19322i	0.674079	−	1.16754i
$63$		0			0
$64$			29.4556i			3.68195i
$65$	0.413319	−	11.1302i	0.0512659	−	1.38053i
$66$		0			0
$67$	−2.17304	−	8.10989i	−0.265479	−	0.990780i	−0.961957	−	0.273202i	$-0.911917\pi$
$67$	−2.17304	−	8.10989i	−0.265479	−	0.990780i	0.696478	−	0.717578i	$-0.254749\pi$
$68$	10.7832	+	6.22567i	1.30765	+	0.754973i
$69$		0			0
$70$	5.93037	+	21.5120i	0.708815	+	2.57118i
$71$	2.13591	+	0.572316i	0.253486	+	0.0679214i	0.383324	−	0.923614i	$-0.374779\pi$
$71$	2.13591	+	0.572316i	0.253486	+	0.0679214i	−0.129838	+	0.991535i	$0.541446\pi$
$72$		0			0
$73$	2.43968	−	2.43968i	0.285543	−	0.285543i	−0.549772	−	0.835315i	$-0.685285\pi$
$73$	2.43968	−	2.43968i	0.285543	−	0.285543i	0.835315	+	0.549772i	$0.185285\pi$
$74$	−9.05986	−	15.6921i	−1.05319	−	1.82417i
$75$		0			0
$76$	8.28273	+	30.9116i	0.950094	+	3.54580i
$77$	−0.617503	+	1.08755i	−0.0703710	+	0.123937i
$78$		0			0
$79$	−11.8014			−1.32776			−0.663878	−	0.747841i	$-0.731091\pi$
$79$	−11.8014			−1.32776			−0.663878	+	0.747841i	$0.731091\pi$
$80$	−44.2876	+	11.8668i	−4.95150	+	1.32675i
$81$		0			0
$82$	−2.11339	−	3.66049i	−0.233384	−	0.404234i
$83$	−1.80810	−	1.80810i	−0.198465	−	0.198465i	0.600877	−	0.799342i	$-0.294818\pi$
$83$	−1.80810	−	1.80810i	−0.198465	−	0.198465i	−0.799342	+	0.600877i	$0.794818\pi$
$84$		0			0
$85$	−1.82510	+	6.81137i	−0.197960	+	0.738796i
$86$	11.3386	+	11.3386i	1.22267	+	1.22267i
$87$		0			0
$88$	−3.86103	−	2.22917i	−0.411587	−	0.237630i
$89$	−0.363443	−	1.35639i	−0.0385248	−	0.143777i	0.943985	−	0.329990i	$-0.107045\pi$
$89$	−0.363443	−	1.35639i	−0.0385248	−	0.143777i	−0.982509	+	0.186213i	$0.940379\pi$
$90$		0			0
$91$	−9.53512	−	0.285396i	−0.999552	−	0.0299177i
$92$	3.03514			0.316436
$93$		0			0
$94$	−21.9100	−	12.6497i	−2.25984	−	1.30472i
$95$	−15.6957	+	9.06194i	−1.61035	+	0.929736i
$96$		0			0
$97$	3.25005	−	12.1294i	0.329993	−	1.23155i	−0.579204	−	0.815183i	$-0.696636\pi$
$97$	3.25005	−	12.1294i	0.329993	−	1.23155i	0.909197	−	0.416367i	$-0.136697\pi$
$98$	18.3877	−	5.21172i	1.85744	−	0.526463i
$99$		0			0
$100$	−12.3883	−	21.4572i	−1.23883	−	2.14572i
$101$	3.23413	−	5.60168i	0.321808	−	0.557388i	−0.659053	−	0.752096i	$-0.729043\pi$
$101$	3.23413	−	5.60168i	0.321808	−	0.557388i	0.980861	+	0.194708i	$0.0623761\pi$
$102$		0			0
$103$	−8.52900			−0.840388			−0.420194	−	0.907434i	$-0.638038\pi$
$103$	−8.52900			−0.840388			−0.420194	+	0.907434i	$0.638038\pi$
$104$	1.26197	−	33.9834i	0.123747	−	3.33235i
$105$		0			0
$106$	−2.95167	−	11.0158i	−0.286692	−	1.06995i
$107$	−2.34420	+	4.06027i	−0.226622	+	0.392521i	−0.956805	−	0.290731i	$-0.906102\pi$
$107$	−2.34420	+	4.06027i	−0.226622	+	0.392521i	0.730183	+	0.683252i	$0.239435\pi$
$108$		0			0
$109$	3.66100	−	3.66100i	0.350661	−	0.350661i	−0.509695	−	0.860355i	$-0.670242\pi$
$109$	3.66100	−	3.66100i	0.350661	−	0.350661i	0.860355	+	0.509695i	$0.170242\pi$
$110$	1.03184	−	3.85088i	0.0983822	−	0.367167i
$111$		0			0
$112$	10.4364	+	37.8575i	0.986150	+	3.57720i
$113$	4.41169	+	7.64128i	0.415017	+	0.718831i	0.995430	−	0.0954914i	$-0.0304422\pi$
$113$	4.41169	+	7.64128i	0.415017	+	0.718831i	−0.580413	+	0.814322i	$0.697109\pi$
$114$		0			0
$115$	0.444887	+	1.66034i	0.0414859	+	0.154828i
$116$			39.7748i			3.69300i
$117$		0			0
$118$		−	40.3584i		−	3.71530i
$119$	5.84493	+	1.52115i	0.535804	+	0.139444i
$120$		0			0
$121$	−9.33278	+	5.38828i	−0.848434	+	0.489844i
$122$	−1.23439	−	1.23439i	−0.111757	−	0.111757i
$123$		0			0
$124$	20.4845	+	5.48882i	1.83957	+	0.492910i
$125$	−0.999502	+	0.999502i	−0.0893982	+	0.0893982i
$126$		0			0
$127$	8.32452	+	4.80617i	0.738682	+	0.426478i	0.821590	−	0.570079i	$-0.193087\pi$
$127$	8.32452	+	4.80617i	0.738682	+	0.426478i	−0.0829079	+	0.996557i	$0.526421\pi$
$128$	−35.8364	+	9.60232i	−3.16752	+	0.848734i
$129$		0			0
$130$	29.6452	−	6.77512i	2.60006	−	0.594218i
$131$		−	15.6056i		−	1.36346i	−0.731602	−	0.681732i	$-0.761227\pi$
$131$		−	15.6056i		−	1.36346i	0.731602	−	0.681732i	$-0.238773\pi$
$132$		0			0
$133$	7.85795	+	13.3870i	0.681371	+	1.16080i
$134$	19.8523	−	11.4617i	1.71498	−	0.990143i
$135$		0			0
$136$	−5.57252	+	20.7969i	−0.477840	+	1.78332i
$137$	−5.03398	+	18.7871i	−0.430082	+	1.60509i	0.322488	+	0.946574i	$0.395481\pi$
$137$	−5.03398	+	18.7871i	−0.430082	+	1.60509i	−0.752569	+	0.658513i	$0.771186\pi$
$138$		0			0
$139$	−4.85118	+	2.80083i	−0.411472	+	0.237564i	−0.691422	−	0.722451i	$-0.743015\pi$
$139$	−4.85118	+	2.80083i	−0.411472	+	0.237564i	0.279950	+	0.960015i	$0.409682\pi$
$140$	−38.4454	+	22.5669i	−3.24923	+	1.90725i
$141$		0			0
$142$			6.03739i			0.506646i
$143$	1.44334	+	0.906344i	0.120698	+	0.0757923i
$144$		0			0
$145$	−21.7583	+	5.83013i	−1.80693	+	0.484166i
$146$	8.15808	+	4.71007i	0.675168	+	0.389808i
$147$		0			0
$148$	25.5966	−	25.5966i	2.10403	−	2.10403i
$149$	19.1586	+	5.13354i	1.56954	+	0.420556i	0.935667	−	0.352885i	$-0.114799\pi$
$149$	19.1586	+	5.13354i	1.56954	+	0.420556i	0.633869	+	0.773440i	$0.281466\pi$
$150$		0			0
$151$	0.637052	+	0.637052i	0.0518426	+	0.0518426i	0.732553	−	0.680710i	$-0.238329\pi$
$151$	0.637052	+	0.637052i	0.0518426	+	0.0518426i	−0.680710	+	0.732553i	$0.738329\pi$
$152$	−47.9233	+	27.6686i	−3.88710	+	2.24422i
$153$		0			0
$154$	−3.30450	−	0.860001i	−0.266284	−	0.0693008i
$155$			12.0104i			0.964697i
$156$		0			0
$157$			0.106383i			0.00849030i	0.999991	+	0.00424515i	$0.00135128\pi$
$157$			0.106383i			0.00849030i	−0.999991	+	0.00424515i	$0.998649\pi$
$158$	−8.33945	−	31.1232i	−0.663451	−	2.47603i
$159$		0			0
$160$	−33.4562	−	57.9478i	−2.64494	−	4.58118i
$161$	1.41928	−	0.391262i	0.111855	−	0.0308358i
$162$		0			0
$163$	3.70956	−	13.8443i	0.290555	−	1.08437i	−0.654128	−	0.756383i	$-0.726964\pi$
$163$	3.70956	−	13.8443i	0.290555	−	1.08437i	0.944684	−	0.327983i	$-0.106369\pi$
$164$	5.97090	−	5.97090i	0.466249	−	0.466249i
$165$		0			0
$166$	3.49074	−	6.04613i	0.270934	−	0.469271i
$167$	3.66050	+	13.6612i	0.283258	+	1.05713i	0.950103	+	0.311936i	$0.100977\pi$
$167$	3.66050	+	13.6612i	0.283258	+	1.05713i	−0.666845	+	0.745196i	$0.732356\pi$
$168$		0			0
$169$	−0.964180	+	12.9642i	−0.0741677	+	0.997246i
$170$	−19.2531			−1.47664
$171$		0			0
$172$	−16.0173	+	27.7429i	−1.22131	+	2.11537i
$173$	0.208401	+	0.360961i	0.0158444	+	0.0274434i	0.873839	−	0.486216i	$-0.161623\pi$
$173$	0.208401	+	0.360961i	0.0158444	+	0.0274434i	−0.857994	+	0.513659i	$0.828290\pi$
$174$		0			0
$175$	−8.55902	−	8.43671i	−0.647001	−	0.637756i
$176$	1.81586	−	6.77690i	0.136876	−	0.510828i
$177$		0			0
$178$	3.32032	−	1.91699i	0.248868	−	0.143684i
$179$	−8.99794	−	5.19496i	−0.672537	−	0.388290i	0.124500	−	0.992220i	$-0.460267\pi$
$179$	−8.99794	−	5.19496i	−0.672537	−	0.388290i	−0.797037	+	0.603930i	$0.793601\pi$
$180$		0			0
$181$	21.4482			1.59423			0.797117	−	0.603825i	$-0.206357\pi$
$181$	21.4482			1.59423			0.797117	+	0.603825i	$0.206357\pi$
$182$	−5.98535	−	25.3483i	−0.443663	−	1.87894i
$183$		0			0
$184$	1.35836	+	5.06947i	0.100140	+	0.373726i
$185$	17.7542	+	10.2504i	1.30532	+	0.753626i
$186$		0			0
$187$	−0.763000	−	0.763000i	−0.0557961	−	0.0557961i
$188$	13.0814	−	48.8203i	0.954057	−	3.56059i
$189$		0			0
$190$	−34.9901	−	34.9901i	−2.53845	−	2.53845i
$191$	−0.111216	−	0.192631i	−0.00804729	−	0.0139383i	0.861974	−	0.506953i	$-0.169228\pi$
$191$	−0.111216	−	0.192631i	−0.00804729	−	0.0139383i	−0.870021	+	0.493015i	$0.835895\pi$
$192$		0			0
$193$	−1.98209	+	0.531099i	−0.142674	+	0.0382293i	−0.329449	−	0.944173i	$-0.606863\pi$
$193$	−1.98209	+	0.531099i	−0.142674	+	0.0382293i	0.186775	+	0.982403i	$0.440196\pi$
$194$	34.2849			2.46152
$195$		0			0
$196$	19.5646	+	32.7880i	1.39747	+	2.34200i
$197$	−3.40878	−	12.7217i	−0.242865	−	0.906386i	−0.974444	−	0.224629i	$-0.927883\pi$
$197$	−3.40878	−	12.7217i	−0.242865	−	0.906386i	0.731579	−	0.681757i	$-0.238784\pi$
$198$		0			0
$199$	1.49318	+	2.58626i	0.105849	+	0.183335i	0.914085	−	0.405523i	$-0.132911\pi$
$199$	1.49318	+	2.58626i	0.105849	+	0.183335i	−0.808236	+	0.588859i	$0.799577\pi$
$200$	30.2947	−	30.2947i	2.14216	−	2.14216i
$201$		0			0
$202$	17.0585	+	4.57081i	1.20023	+	0.321601i
$203$	5.12739	+	18.5993i	0.359872	+	1.30541i
$204$		0			0
$205$	4.14152	+	2.39111i	0.289256	+	0.167002i
$206$	−6.02704	−	22.4932i	−0.419923	−	1.56718i
$207$		0			0
$208$	52.1705	−	11.9231i	3.61737	−	0.826715i
$209$		−	2.77332i		−	0.191835i
$210$		0			0
$211$	3.61160	−	6.25548i	0.248633	−	0.430645i	−0.714514	−	0.699621i	$-0.753352\pi$
$211$	3.61160	−	6.25548i	0.248633	−	0.430645i	0.963147	+	0.268976i	$0.0866853\pi$
$212$	19.7310	−	11.3917i	1.35513	−	0.782384i
$213$		0			0
$214$	−12.3645	−	3.31306i	−0.845222	−	0.226476i
$215$	−17.5242	−	4.69560i	−1.19514	−	0.320237i
$216$		0			0
$217$	10.2864	−	0.0740206i	0.698290	−	0.00502485i
$218$	12.2421	+	7.06797i	0.829138	+	0.478703i
$219$		0			0
$220$	7.96457			0.536971
$221$	2.42380	−	7.86565i	0.163043	−	0.529101i
$222$		0			0
$223$	−18.5687	+	4.97547i	−1.24345	+	0.333182i	−0.819804	−	0.572644i	$-0.805918\pi$
$223$	−18.5687	+	4.97547i	−1.24345	+	0.333182i	−0.423649	+	0.905827i	$0.639251\pi$
$224$	−49.4240	+	29.0111i	−3.30228	+	1.93839i
$225$		0			0
$226$	−17.0345	+	17.0345i	−1.13312	+	1.13312i
$227$	−3.99587	+	14.9128i	−0.265215	+	0.989797i	0.696903	+	0.717165i	$0.254561\pi$
$227$	−3.99587	+	14.9128i	−0.265215	+	0.989797i	−0.962118	+	0.272632i	$0.912106\pi$
$228$		0			0
$229$	8.38486	−	8.38486i	0.554087	−	0.554087i	−0.373531	−	0.927618i	$-0.621853\pi$
$229$	8.38486	−	8.38486i	0.554087	−	0.554087i	0.927618	+	0.373531i	$0.121853\pi$
$230$	−4.06437	+	2.34657i	−0.267997	+	0.154728i
$231$		0			0
$232$	−66.4341	+	17.8010i	−4.36161	+	1.16869i
$233$		−	19.9540i		−	1.30723i	−0.756828	−	0.653614i	$-0.773252\pi$
$233$		−	19.9540i		−	1.30723i	0.756828	−	0.653614i	$-0.226748\pi$
$234$		0			0
$235$	28.6241			1.86723
$236$	77.8796	−	20.8678i	5.06953	−	1.35838i
$237$		0			0
$238$	0.118658	+	16.4895i	0.00769143	+	1.06886i
$239$	5.27726	−	5.27726i	0.341357	−	0.341357i	−0.515520	−	0.856877i	$-0.672401\pi$
$239$	5.27726	−	5.27726i	0.341357	−	0.341357i	0.856877	+	0.515520i	$0.172401\pi$
$240$		0			0
$241$	−8.35123	−	2.23771i	−0.537950	−	0.144143i	−0.0203932	−	0.999792i	$-0.506492\pi$
$241$	−8.35123	−	2.23771i	−0.537950	−	0.144143i	−0.517557	+	0.855649i	$0.673158\pi$
$242$	−20.8053	−	20.8053i	−1.33742	−	1.33742i
$243$		0			0
$244$	1.74375	−	3.02026i	0.111632	−	0.193352i
$245$	−15.0685	+	15.5086i	−0.962694	+	0.990810i
$246$		0			0
$247$	18.6998	−	9.88990i	1.18984	−	0.629280i
$248$			36.6709i			2.32861i
$249$		0			0
$250$	−3.34225	−	1.92965i	−0.211382	−	0.122042i
$251$	8.48610	+	14.6984i	0.535638	+	0.927752i	0.999132	+	0.0416520i	$0.0132621\pi$
$251$	8.48610	+	14.6984i	0.535638	+	0.927752i	−0.463494	+	0.886100i	$0.653405\pi$
$252$		0			0
$253$	−0.254066	−	0.0680768i	−0.0159730	−	0.00427995i
$254$	−6.79257	+	25.3502i	−0.426204	+	1.59061i
$255$		0			0
$256$	−21.1921	−	36.7057i	−1.32450	−	2.29411i
$257$	3.36830	−	5.83406i	0.210109	−	0.363919i	−0.741640	−	0.670798i	$-0.765952\pi$
$257$	3.36830	−	5.83406i	0.210109	−	0.363919i	0.951748	+	0.306880i	$0.0992849\pi$
$258$		0			0
$259$	8.66968	−	15.2690i	0.538708	−	0.948771i
$260$	28.4023	+	53.7032i	1.76144	+	3.33053i
$261$		0			0
$262$	41.1559	−	11.0277i	2.54262	−	0.681294i
$263$	2.64276	−	4.57739i	0.162960	−	0.282254i	−0.772969	−	0.634443i	$-0.781229\pi$
$263$	2.64276	−	4.57739i	0.162960	−	0.282254i	0.935929	+	0.352189i	$0.114563\pi$
$264$		0			0
$265$	9.12383	+	9.12383i	0.560472	+	0.560472i
$266$	−29.7521	+	30.1834i	−1.82422	+	1.85066i
$267$		0			0
$268$	32.3825	+	32.3825i	1.97808	+	1.97808i
$269$	2.83734	−	1.63814i	0.172995	−	0.0998789i	−0.411002	−	0.911634i	$-0.634821\pi$
$269$	2.83734	−	1.63814i	0.172995	−	0.0998789i	0.583997	+	0.811755i	$0.301488\pi$
$270$		0			0
$271$	−3.01677	−	11.2587i	−0.183256	−	0.683919i	−0.994997	−	0.0999024i	$-0.968147\pi$
$271$	−3.01677	−	11.2587i	−0.183256	−	0.683919i	0.811742	−	0.584017i	$-0.198520\pi$
$272$	−33.8821			−2.05440
$273$		0			0
$274$	−53.1036			−3.20811
$275$	0.555727	+	2.07400i	0.0335116	+	0.125067i
$276$		0			0
$277$	3.66204	−	2.11428i	0.220031	−	0.127035i	−0.385934	−	0.922526i	$-0.626121\pi$
$277$	3.66204	−	2.11428i	0.220031	−	0.127035i	0.605964	+	0.795492i	$0.292787\pi$
$278$	−10.8146	−	10.8146i	−0.648618	−	0.648618i
$279$		0			0
$280$	−54.8985	−	54.1140i	−3.28081	−	3.23393i
$281$	−18.2360	−	18.2360i	−1.08787	−	1.08787i	−0.995748	−	0.0921208i	$-0.970635\pi$
$281$	−18.2360	−	18.2360i	−1.08787	−	1.08787i	−0.0921208	−	0.995748i	$-0.529365\pi$
$282$		0			0
$283$	−1.92179	+	3.32864i	−0.114239	+	0.197867i	−0.917475	−	0.397793i	$-0.869776\pi$
$283$	−1.92179	+	3.32864i	−0.114239	+	0.197867i	0.803236	+	0.595660i	$0.203110\pi$
$284$	−11.6503	+	3.12170i	−0.691320	+	0.185239i
$285$		0			0
$286$	−1.37032	+	4.44693i	−0.0810290	+	0.262953i
$287$	2.02237	−	3.56179i	0.119377	−	0.210246i
$288$		0			0
$289$	5.89449	−	10.2096i	0.346735	−	0.600562i
$290$	−30.7512	−	53.2626i	−1.80577	−	3.12768i
$291$		0			0
$292$	−4.87079	+	18.1780i	−0.285041	+	1.06379i
$293$	−28.6306	−	7.67154i	−1.67262	−	0.448176i	−0.706802	−	0.707412i	$-0.749863\pi$
$293$	−28.6306	−	7.67154i	−1.67262	−	0.448176i	−0.965814	+	0.259236i	$0.916529\pi$
$294$		0			0
$295$	22.8310	+	39.5444i	1.32927	+	2.30236i
$296$	54.2085	+	31.2973i	3.15080	+	1.81912i
$297$		0			0
$298$			54.1539i			3.13705i
$299$	−0.446995	−	1.95587i	−0.0258504	−	0.113111i
$300$		0			0
$301$	−3.91361	+	15.0378i	−0.225577	+	0.866764i
$302$	−1.22990	+	2.13025i	−0.0707727	+	0.122582i
$303$		0			0
$304$	−61.5766	−	61.5766i	−3.53166	−	3.53166i
$305$	1.90780	+	0.511192i	0.109240	+	0.0292708i
$306$		0			0
$307$	−20.2018	+	20.2018i	−1.15298	+	1.15298i	−0.167023	+	0.985953i	$0.553416\pi$
$307$	−20.2018	+	20.2018i	−1.15298	+	1.15298i	−0.985953	+	0.167023i	$0.946584\pi$
$308$	−0.0490861	−	6.82136i	−0.00279694	−	0.388683i
$309$		0			0
$310$	−31.6745	+	8.48716i	−1.79899	+	0.482038i
$311$	−24.6309			−1.39669			−0.698345	−	0.715762i	$-0.746080\pi$
$311$	−24.6309			−1.39669			−0.698345	+	0.715762i	$0.746080\pi$
$312$		0			0
$313$			8.19304i			0.463098i	0.972823	+	0.231549i	$0.0743794\pi$
$313$			8.19304i			0.463098i	−0.972823	+	0.231549i	$0.925621\pi$
$314$	−0.280560	+	0.0751759i	−0.0158329	+	0.00424242i
$315$		0			0
$316$	55.7465	−	32.1852i	3.13598	−	1.81056i
$317$	−6.24432	+	6.24432i	−0.350716	+	0.350716i	−0.860376	−	0.509660i	$-0.829771\pi$
$317$	−6.24432	+	6.24432i	−0.350716	+	0.350716i	0.509660	+	0.860376i	$0.329771\pi$
$318$		0			0
$319$	0.892129	−	3.32947i	0.0499496	−	0.186414i
$320$	64.3402	−	64.3402i	3.59672	−	3.59672i
$321$		0			0
$322$	2.03480	+	3.46652i	0.113395	+	0.193182i
$323$	−12.9368	+	3.46641i	−0.719823	+	0.192876i
$324$		0			0
$325$	−12.0027	+	11.1432i	−0.665791	+	0.618113i
$326$	39.1323			2.16734
$327$		0			0
$328$	12.6452	+	7.30069i	0.698213	+	0.403113i
$329$	−0.176412	−	24.5154i	−0.00972589	−	1.35158i
$330$		0			0
$331$	−28.6185	−	7.66830i	−1.57301	−	0.421488i	−0.636260	−	0.771475i	$-0.719519\pi$
$331$	−28.6185	−	7.66830i	−1.57301	−	0.421488i	−0.936755	+	0.349987i	$0.886186\pi$
$332$	13.4721	+	3.60985i	0.739379	+	0.198116i
$333$		0			0
$334$	−33.4413	+	19.3074i	−1.82983	+	1.05645i
$335$	−12.9679	+	22.4611i	−0.708513	+	1.22718i
$336$		0			0
$337$		−	24.6356i		−	1.34198i	−0.741464	−	0.670992i	$-0.765868\pi$
$337$		−	24.6356i		−	1.34198i	0.741464	−	0.670992i	$-0.234132\pi$
$338$	−34.8713	+	6.61838i	−1.89675	+	0.359992i
$339$		0			0
$340$	−9.95501	−	37.1526i	−0.539886	−	2.01488i
$341$	−1.59161	−	0.918916i	−0.0861905	−	0.0497621i
$342$		0			0
$343$	13.3754	+	12.8101i	0.722205	+	0.691679i
$344$	−53.5062	−	14.3369i	−2.88486	−	0.772996i
$345$		0			0
$346$	−0.804681	+	0.804681i	−0.0432599	+	0.0432599i
$347$	6.69623	+	11.5982i	0.359472	+	0.622624i	0.987873	−	0.155266i	$-0.0496234\pi$
$347$	6.69623	+	11.5982i	0.359472	+	0.622624i	−0.628401	+	0.777890i	$0.716290\pi$
$348$		0			0
$349$	2.72247	+	10.1604i	0.145730	+	0.543874i	0.999722	+	0.0235863i	$0.00750846\pi$
$349$	2.72247	+	10.1604i	0.145730	+	0.543874i	−0.853991	+	0.520287i	$0.825825\pi$
$350$	16.2016	−	28.5342i	0.866010	−	1.52522i
$351$		0			0
$352$	10.2390			0.545738
$353$	−14.9904	+	4.01667i	−0.797859	+	0.213786i	−0.634644	−	0.772805i	$-0.718853\pi$
$353$	−14.9904	+	4.01667i	−0.797859	+	0.213786i	−0.163215	+	0.986590i	$0.552187\pi$
$354$		0			0
$355$	−3.41538	−	5.91561i	−0.181270	−	0.313968i
$356$	5.41601	+	5.41601i	0.287048	+	0.287048i
$357$		0			0
$358$	7.34206	−	27.4009i	0.388040	−	1.44818i
$359$	7.20920	+	7.20920i	0.380487	+	0.380487i	0.871278	−	0.490791i	$-0.163292\pi$
$359$	7.20920	+	7.20920i	0.380487	+	0.380487i	−0.490791	+	0.871278i	$0.663292\pi$
$360$		0			0
$361$	−13.3564	−	7.71133i	−0.702969	−	0.405859i
$362$	15.1564	+	56.5645i	0.796604	+	2.97297i
$363$		0			0
$364$	45.8197	−	24.6565i	2.40161	−	1.29235i
$365$	−10.6580			−0.557868
$366$		0			0
$367$	−13.1818	−	7.61053i	−0.688085	−	0.397266i	0.114809	−	0.993388i	$-0.463374\pi$
$367$	−13.1818	−	7.61053i	−0.688085	−	0.397266i	−0.802894	+	0.596121i	$0.796708\pi$
$368$	−7.15260	+	4.12955i	−0.372855	+	0.215268i
$369$		0			0
$370$	−14.4870	+	54.0660i	−0.753141	+	2.81076i
$371$	7.75799	−	7.87045i	0.402775	−	0.408613i
$372$		0			0
$373$	16.3260	+	28.2774i	0.845326	+	1.46415i	0.885338	+	0.464948i	$0.153927\pi$
$373$	16.3260	+	28.2774i	0.845326	+	1.46415i	−0.0400122	+	0.999199i	$0.512740\pi$
$374$	1.47305	−	2.55141i	0.0761698	−	0.131930i
$375$		0			0
$376$	87.3969			4.50715
$377$	25.6312	−	5.85776i	1.32007	−	0.301690i
$378$		0			0
$379$	6.47610	+	24.1691i	0.332655	+	1.24149i	0.906389	+	0.422444i	$0.138828\pi$
$379$	6.47610	+	24.1691i	0.332655	+	1.24149i	−0.573734	+	0.819042i	$0.694506\pi$
$380$	49.4284	−	85.6124i	2.53562	−	4.39183i
$381$		0			0
$382$	0.429428	−	0.429428i	0.0219714	−	0.0219714i
$383$	−4.70967	+	17.5767i	−0.240653	+	0.898129i	0.734866	+	0.678213i	$0.237245\pi$
$383$	−4.70967	+	17.5767i	−0.240653	+	0.898129i	−0.975519	+	0.219917i	$0.929421\pi$
$384$		0			0
$385$	3.72435	−	1.02672i	0.189811	−	0.0523264i
$386$	−2.80129	−	4.85198i	−0.142582	−	0.246959i
$387$		0			0
$388$	17.7274	+	66.1596i	0.899973	+	3.35874i
$389$			6.12739i			0.310671i	0.987862	+	0.155336i	$0.0496459\pi$
$389$			6.12739i			0.310671i	−0.987862	+	0.155336i	$0.950354\pi$
$390$		0			0
$391$			1.27024i			0.0642388i
$392$	−46.0083	+	47.3520i	−2.32377	+	2.39164i
$393$		0			0
$394$	31.1417	−	17.9797i	1.56890	−	0.905803i
$395$	25.7778	+	25.7778i	1.29702	+	1.29702i
$396$		0			0
$397$	−12.7566	−	3.41813i	−0.640237	−	0.171551i	−0.0759261	−	0.997113i	$-0.524191\pi$
$397$	−12.7566	−	3.41813i	−0.640237	−	0.171551i	−0.564311	+	0.825563i	$0.690858\pi$
$398$	−5.76549	+	5.76549i	−0.288998	+	0.288998i
$399$		0			0
$400$	58.3884	+	33.7105i	2.91942	+	1.68553i
$401$	4.95448	−	1.32755i	0.247415	−	0.0662946i	−0.132980	−	0.991119i	$-0.542455\pi$
$401$	4.95448	−	1.32755i	0.247415	−	0.0662946i	0.380395	+	0.924824i	$0.375788\pi$
$402$		0			0
$403$	0.520216	−	14.0088i	0.0259138	−	0.697827i
$404$			35.2811i			1.75530i
$405$		0			0
$406$	−45.4279	+	26.6655i	−2.25455	+	1.32339i
$407$	−2.71676	+	1.56852i	−0.134665	+	0.0777488i
$408$		0			0
$409$	4.13326	−	15.4255i	0.204377	−	0.762744i	−0.785262	−	0.619164i	$-0.787472\pi$
$409$	4.13326	−	15.4255i	0.204377	−	0.762744i	0.989639	−	0.143580i	$-0.0458616\pi$
$410$	−3.37936	+	12.6119i	−0.166895	+	0.622859i
$411$		0			0
$412$	40.2887	−	23.2607i	1.98488	−	1.14597i
$413$	33.7276	−	19.7976i	1.65963	−	0.974176i
$414$		0			0
$415$			7.89891i			0.387742i
$416$	36.5130	+	69.0388i	1.79020	+	3.38491i
$417$		0			0
$418$	7.31398	−	1.95977i	0.357738	−	0.0958557i
$419$	12.6468	+	7.30162i	0.617836	+	0.356708i	0.776026	−	0.630701i	$-0.217233\pi$
$419$	12.6468	+	7.30162i	0.617836	+	0.356708i	−0.158190	+	0.987409i	$0.550566\pi$
$420$		0			0
$421$	2.04328	−	2.04328i	0.0995835	−	0.0995835i	−0.655560	−	0.755143i	$-0.727567\pi$
$421$	2.04328	−	2.04328i	0.0995835	−	0.0995835i	0.755143	+	0.655560i	$0.227567\pi$
$422$	19.0495	+	5.10429i	0.927314	+	0.248473i
$423$		0			0
$424$	27.8575	+	27.8575i	1.35288	+	1.35288i
$425$	8.98005	−	5.18464i	0.435597	−	0.251492i
$426$		0			0
$427$	0.426059	−	1.63711i	0.0206185	−	0.0792251i
$428$		−	25.5729i		−	1.23611i
$429$		0			0
$430$		−	49.5341i		−	2.38875i
$431$	−2.83206	−	10.5694i	−0.136416	−	0.509110i	−0.999988	−	0.00488525i	$-0.998445\pi$
$431$	−2.83206	−	10.5694i	−0.136416	−	0.509110i	0.863572	−	0.504225i	$-0.168222\pi$
$432$		0			0
$433$	17.9201	+	31.0385i	0.861184	+	1.49161i	0.870787	+	0.491660i	$0.163610\pi$
$433$	17.9201	+	31.0385i	0.861184	+	1.49161i	−0.00960365	+	0.999954i	$0.503057\pi$
$434$	7.46415	+	27.0757i	0.358291	+	1.29968i
$435$		0			0
$436$	−7.30914	+	27.2781i	−0.350044	+	1.30638i
$437$	−2.30851	+	2.30851i	−0.110431	+	0.110431i
$438$		0			0
$439$	−0.772225	+	1.33753i	−0.0368563	+	0.0638369i	−0.883865	−	0.467742i	$-0.845068\pi$
$439$	−0.772225	+	1.33753i	−0.0368563	+	0.0638369i	0.847009	+	0.531579i	$0.178401\pi$
$440$	3.56449	+	13.3029i	0.169931	+	0.634190i
$441$		0			0
$442$	22.4565	+	0.833923i	1.06815	+	0.0396657i
$443$	16.1657			0.768055			0.384027	−	0.923322i	$-0.374537\pi$
$443$	16.1657			0.768055			0.384027	+	0.923322i	$0.374537\pi$
$444$		0			0
$445$	−2.16890	+	3.75664i	−0.102816	+	0.178082i
$446$	−26.2432	−	45.4546i	−1.24265	−	2.15234i
$447$		0			0
$448$	−55.5015	−	54.7084i	−2.62220	−	2.58473i
$449$	3.96795	−	14.8086i	0.187259	−	0.698861i	−0.806876	−	0.590720i	$-0.798844\pi$
$449$	3.96795	−	14.8086i	0.187259	−	0.698861i	0.994136	−	0.108140i	$-0.0344896\pi$
$450$		0			0
$451$	−0.633736	+	0.365888i	−0.0298415	+	0.0172290i
$452$	−41.6793	−	24.0636i	−1.96043	−	1.13186i
$453$		0			0
$454$	−42.1526			−1.97832
$455$	20.2043	+	21.4511i	0.947191	+	1.00564i
$456$		0			0
$457$	−7.14198	−	26.6542i	−0.334088	−	1.24683i	−0.904855	−	0.425720i	$-0.860021\pi$
$457$	−7.14198	−	26.6542i	−0.334088	−	1.24683i	0.570767	−	0.821112i	$-0.306646\pi$
$458$	28.0382	+	16.1879i	1.31014	+	0.756410i
$459$		0			0
$460$	−6.62969	−	6.62969i	−0.309111	−	0.309111i
$461$	−0.630674	+	2.35371i	−0.0293734	+	0.109623i	−0.979056	−	0.203590i	$-0.934739\pi$
$461$	−0.630674	+	2.35371i	−0.0293734	+	0.109623i	0.949683	+	0.313214i	$0.101406\pi$
$462$		0			0
$463$	−15.9059	−	15.9059i	−0.739208	−	0.739208i	0.233216	−	0.972425i	$-0.425075\pi$
$463$	−15.9059	−	15.9059i	−0.739208	−	0.739208i	−0.972425	+	0.233216i	$0.925075\pi$
$464$	−54.1167	−	93.7330i	−2.51231	−	4.35144i
$465$		0			0
$466$	52.6238	−	14.1005i	2.43775	−	0.653193i
$467$	−6.66294			−0.308324			−0.154162	−	0.988046i	$-0.549268\pi$
$467$	−6.66294			−0.308324			−0.154162	+	0.988046i	$0.549268\pi$
$468$		0			0
$469$	19.3170	+	10.9681i	0.891977	+	0.506460i
$470$	20.2272	+	75.4891i	0.933013	+	3.48205i
$471$		0			0
$472$	69.7091	+	120.740i	3.20862	+	5.55750i
$473$	1.96304	−	1.96304i	0.0902607	−	0.0902607i
$474$		0			0
$475$	25.7426	+	6.89772i	1.18115	+	0.316489i
$476$	−31.7585	+	8.75507i	−1.45565	+	0.401288i
$477$		0			0
$478$	17.6467	+	10.1883i	0.807140	+	0.466003i
$479$	−5.91010	−	22.0568i	−0.270039	−	1.00780i	−0.959093	−	0.283090i	$-0.908640\pi$
$479$	−5.91010	−	22.0568i	−0.270039	−	1.00780i	0.689054	−	0.724710i	$-0.258026\pi$
$480$		0			0
$481$	−20.2644	−	12.7250i	−0.923975	−	0.580209i
$482$		−	23.6057i		−	1.07521i
$483$		0			0
$484$	29.3904	−	50.9056i	1.33593	−	2.31389i
$485$	−33.5934	+	19.3952i	−1.52540	+	0.880689i
$486$		0			0
$487$	12.0330	+	3.22424i	0.545269	+	0.146104i	0.520930	−	0.853600i	$-0.325585\pi$
$487$	12.0330	+	3.22424i	0.545269	+	0.146104i	0.0243387	+	0.999704i	$0.492252\pi$
$488$	5.82501	+	1.56081i	0.263686	+	0.0706544i
$489$		0			0
$490$	−51.5485	−	28.7805i	−2.32872	−	1.30017i
$491$	16.7889	+	9.69310i	0.757674	+	0.437443i	0.828460	−	0.560048i	$-0.189217\pi$
$491$	16.7889	+	9.69310i	0.757674	+	0.437443i	−0.0707859	+	0.997492i	$0.522551\pi$
$492$		0			0
$493$	−16.6462			−0.749706
$494$	39.2965	+	42.3276i	1.76803	+	1.90441i
$495$		0			0
$496$	−55.7417	+	14.9359i	−2.50288	+	0.670644i
$497$	−5.04545	+	2.96160i	−0.226319	+	0.132846i
$498$		0			0
$499$	−24.6585	+	24.6585i	−1.10386	+	1.10386i	−0.109925	+	0.993940i	$0.535061\pi$
$499$	−24.6585	+	24.6585i	−1.10386	+	1.10386i	−0.993940	+	0.109925i	$0.964939\pi$
$500$	1.99549	−	7.44727i	0.0892410	−	0.333052i
$501$		0			0
$502$	−32.7667	+	32.7667i	−1.46245	+	1.46245i
$503$	27.3019	−	15.7627i	1.21733	−	0.702826i	0.252984	−	0.967470i	$-0.418588\pi$
$503$	27.3019	−	15.7627i	1.21733	−	0.702826i	0.964346	+	0.264644i	$0.0852546\pi$
$504$		0			0
$505$	−19.3001	+	5.17146i	−0.858845	+	0.230127i
$506$		−	0.718145i		−	0.0319254i
$507$		0			0
$508$	−52.4305			−2.32623
$509$	−3.80510	+	1.01957i	−0.168658	+	0.0451918i	−0.342160	−	0.939642i	$-0.611158\pi$
$509$	−3.80510	+	1.01957i	−0.168658	+	0.0451918i	0.173502	+	0.984834i	$0.444492\pi$
$510$		0			0
$511$	0.0656861	+	9.12822i	0.00290578	+	0.403809i
$512$	29.3590	−	29.3590i	1.29750	−	1.29750i
$513$		0			0
$514$	17.7662	+	4.76043i	0.783632	+	0.209973i
$515$	18.6300	+	18.6300i	0.820935	+	0.820935i
$516$		0			0
$517$	−2.19003	+	3.79325i	−0.0963175	+	0.166827i
$518$	46.3948	+	12.0743i	2.03847	+	0.530515i
$519$		0			0
$520$	−76.9868	+	71.4737i	−3.37609	+	3.13433i
$521$		−	7.46834i		−	0.327194i	−0.986527	−	0.163597i	$-0.947690\pi$
$521$		−	7.46834i		−	0.327194i	0.986527	−	0.163597i	$-0.0523097\pi$
$522$		0			0
$523$	−10.8561	−	6.26775i	−0.474703	−	0.274070i	0.243504	−	0.969900i	$-0.421703\pi$
$523$	−10.8561	−	6.26775i	−0.474703	−	0.274070i	−0.718206	+	0.695830i	$0.755037\pi$
$524$	42.5603	+	73.7166i	1.85925	+	3.22032i
$525$		0			0
$526$	13.9393	+	3.73502i	0.607782	+	0.162855i
$527$	−2.29713	+	8.57300i	−0.100064	+	0.373446i
$528$		0			0
$529$	−11.3452	−	19.6504i	−0.493269	−	0.854367i
$530$	−17.6145	+	30.5093i	−0.765127	+	1.32524i
$531$		0			0
$532$	−73.6285	−	41.8059i	−3.19220	−	1.81252i
$533$	−4.72705	−	2.96834i	−0.204751	−	0.128573i
$534$		0			0
$535$	13.9893	−	3.74843i	0.604812	−	0.162059i
$536$	−39.5945	+	68.5797i	−1.71022	+	2.96219i
$537$		0			0
$538$	6.32520	+	6.32520i	0.272699	+	0.272699i
$539$	−0.902299	−	3.18344i	−0.0388648	−	0.137121i
$540$		0			0
$541$	−2.43106	−	2.43106i	−0.104519	−	0.104519i	0.652913	−	0.757433i	$-0.273547\pi$
$541$	−2.43106	−	2.43106i	−0.104519	−	0.104519i	−0.757433	+	0.652913i	$0.773547\pi$
$542$	27.5604	−	15.9120i	1.18382	−	0.683479i
$543$		0			0
$544$	−12.7978	−	47.7620i	−0.548701	−	2.04778i
$545$	−15.9935			−0.685088
$546$		0			0
$547$	28.6604			1.22543			0.612716	−	0.790303i	$-0.290077\pi$
$547$	28.6604			1.22543			0.612716	+	0.790303i	$0.290077\pi$
$548$	−27.4578	−	102.474i	−1.17294	−	4.37747i
$549$		0			0
$550$	−5.07698	+	2.93119i	−0.216483	+	0.124987i
$551$	−30.2524	−	30.2524i	−1.28880	−	1.28880i
$552$		0			0
$553$	21.9189	−	22.2366i	0.932085	−	0.945597i
$554$	8.16369	+	8.16369i	0.346842	+	0.346842i
$555$		0			0
$556$	15.2771	−	26.4608i	0.647895	−	1.12219i
$557$	40.3737	−	10.8181i	1.71069	−	0.458378i	0.735097	−	0.677962i	$-0.237137\pi$
$557$	40.3737	−	10.8181i	1.71069	−	0.458378i	0.975594	+	0.219584i	$0.0704701\pi$
$558$		0			0
$559$	20.2367	+	6.23594i	0.855920	+	0.263752i
$560$	59.8961	−	105.489i	2.53107	−	4.45772i
$561$		0			0
$562$	35.2066	−	60.9796i	1.48510	−	2.57227i
$563$	12.8281	+	22.2190i	0.540641	+	0.936418i	0.998867	+	0.0475822i	$0.0151516\pi$
$563$	12.8281	+	22.2190i	0.540641	+	0.936418i	−0.458226	+	0.888836i	$0.651515\pi$
$564$		0			0
$565$	7.05441	−	26.3274i	0.296781	−	1.10760i
$566$	−10.1365	−	2.71608i	−0.426070	−	0.114165i
$567$		0			0
$568$	−10.4281	−	18.0620i	−0.437552	−	0.757863i
$569$	−20.8100	−	12.0147i	−0.872401	−	0.503681i	−0.00425579	−	0.999991i	$-0.501355\pi$
$569$	−20.8100	−	12.0147i	−0.872401	−	0.503681i	−0.868145	+	0.496310i	$0.834688\pi$
$570$		0			0
$571$		−	9.57728i		−	0.400797i	−0.979714	−	0.200398i	$-0.935776\pi$
$571$		−	9.57728i		−	0.400797i	0.979714	−	0.200398i	$-0.0642236\pi$
$572$	−9.28978	−	0.344976i	−0.388425	−	0.0144242i
$573$		0			0
$574$	10.8225	+	2.81657i	0.451722	+	0.117561i
$575$	1.26381	−	2.18898i	0.0527045	−	0.0912868i
$576$		0			0
$577$	31.4027	+	31.4027i	1.30731	+	1.30731i	0.923347	+	0.383966i	$0.125442\pi$
$577$	31.4027	+	31.4027i	1.30731	+	1.30731i	0.383966	+	0.923347i	$0.374558\pi$
$578$	31.0906	+	8.33071i	1.29320	+	0.346512i
$579$		0			0
$580$	86.8804	−	86.8804i	3.60751	−	3.60751i
$581$	6.76512	−	0.0486814i	0.280664	−	0.00201964i
$582$		0			0
$583$	−1.90715	+	0.511019i	−0.0789861	+	0.0211643i
$584$	−32.5419			−1.34659
$585$		0			0
$586$		−	80.9274i		−	3.34308i
$587$	6.09066	−	1.63199i	0.251388	−	0.0673593i	−0.130924	−	0.991392i	$-0.541794\pi$
$587$	6.09066	−	1.63199i	0.251388	−	0.0673593i	0.382312	+	0.924033i	$0.375128\pi$
$588$		0			0
$589$	−19.7552	+	11.4056i	−0.813997	+	0.469961i
$590$	−88.1553	+	88.1553i	−3.62930	+	3.62930i
$591$		0			0
$592$	−25.4945	+	95.1470i	−1.04782	+	3.91052i
$593$	27.7021	−	27.7021i	1.13759	−	1.13759i	0.148708	−	0.988881i	$-0.452489\pi$
$593$	27.7021	−	27.7021i	1.13759	−	1.13759i	0.988881	−	0.148708i	$-0.0475115\pi$
$594$		0			0
$595$	−9.44447	−	16.0898i	−0.387186	−	0.659618i
$596$	−104.501	+	28.0009i	−4.28052	+	1.14696i
$597$		0			0
$598$	4.84227	−	2.56096i	0.198015	−	0.104726i
$599$	−3.79502			−0.155060			−0.0775301	−	0.996990i	$-0.524703\pi$
$599$	−3.79502			−0.155060			−0.0775301	+	0.996990i	$0.524703\pi$
$600$		0			0
$601$	−28.0748	−	16.2090i	−1.14520	−	0.661180i	−0.197485	−	0.980306i	$-0.563277\pi$
$601$	−28.0748	−	16.2090i	−1.14520	−	0.661180i	−0.947712	+	0.319126i	$0.896611\pi$
$602$	−42.4241	+	0.305281i	−1.72908	+	0.0124423i
$603$		0			0
$604$	−4.74667	−	1.27187i	−0.193139	−	0.0517515i
$605$	32.1553	+	8.61600i	1.30730	+	0.350290i
$606$		0			0
$607$	−7.81574	+	4.51242i	−0.317231	+	0.183154i	−0.650158	−	0.759799i	$-0.725297\pi$
$607$	−7.81574	+	4.51242i	−0.317231	+	0.183154i	0.332927	+	0.942953i	$0.391964\pi$
$608$	63.5433	−	110.060i	2.57702	−	4.46353i
$609$		0			0
$610$			5.39259i			0.218340i
$611$	−33.3868	−	1.23982i	−1.35068	−	0.0501576i
$612$		0			0
$613$	−6.48271	−	24.1938i	−0.261834	−	0.977179i	−0.964160	−	0.265323i	$-0.914521\pi$
$613$	−6.48271	−	24.1938i	−0.261834	−	0.977179i	0.702325	−	0.711856i	$-0.252145\pi$
$614$	−67.5530	−	39.0017i	−2.72622	−	1.57398i
$615$		0			0
$616$	11.3715	−	3.13484i	0.458169	−	0.126306i
$617$	−22.1083	−	5.92389i	−0.890045	−	0.238487i	−0.215309	−	0.976546i	$-0.569076\pi$
$617$	−22.1083	−	5.92389i	−0.890045	−	0.238487i	−0.674736	+	0.738059i	$0.735743\pi$
$618$		0			0
$619$	−27.9275	+	27.9275i	−1.12250	+	1.12250i	−0.131135	+	0.991365i	$0.541862\pi$
$619$	−27.9275	+	27.9275i	−1.12250	+	1.12250i	−0.991365	+	0.131135i	$0.958138\pi$
$620$	−32.7553	−	56.7339i	−1.31549	−	2.27849i
$621$		0			0
$622$	−17.4055	−	64.9581i	−0.697895	−	2.60458i
$623$	3.23079	+	1.83443i	0.129439	+	0.0734948i
$624$		0			0
$625$	27.0785			1.08314
$626$	−21.6072	+	5.78963i	−0.863597	+	0.231400i
$627$		0			0
$628$	−0.290133	−	0.502526i	−0.0115776	−	0.0200530i
$629$	10.7124	+	10.7124i	0.427133	+	0.427133i
$630$		0			0
$631$	−12.1764	+	45.4430i	−0.484736	+	1.80906i	0.0965126	+	0.995332i	$0.469231\pi$
$631$	−12.1764	+	45.4430i	−0.484736	+	1.80906i	−0.581248	+	0.813726i	$0.697435\pi$
$632$	78.7066	+	78.7066i	3.13078	+	3.13078i
$633$		0			0
$634$	−20.8805	−	12.0553i	−0.829269	−	0.478779i
$635$	−7.68518	−	28.6815i	−0.304977	−	1.13819i
$636$		0			0
$637$	18.2475	−	17.4364i	0.722993	−	0.690856i
$638$	9.41110			0.372589
$639$		0			0
$640$	99.2522	+	57.3033i	3.92329	+	2.26511i
$641$	2.21029	−	1.27611i	0.0873011	−	0.0504033i	−0.455714	−	0.890126i	$-0.650616\pi$
$641$	2.21029	−	1.27611i	0.0873011	−	0.0504033i	0.543015	+	0.839723i	$0.317283\pi$
$642$		0			0
$643$	7.09734	−	26.4876i	0.279892	−	1.04457i	−0.672600	−	0.740006i	$-0.734823\pi$
$643$	7.09734	−	26.4876i	0.279892	−	1.04457i	0.952492	−	0.304564i	$-0.0985107\pi$
$644$	−5.63723	+	5.71894i	−0.222138	+	0.225358i
$645$		0			0
$646$	−18.2836	−	31.6682i	−0.719360	−	1.24597i
$647$	−2.97944	+	5.16054i	−0.117134	+	0.202882i	−0.918631	−	0.395117i	$-0.870704\pi$
$647$	−2.97944	+	5.16054i	−0.117134	+	0.202882i	0.801497	+	0.597999i	$0.204037\pi$
$648$		0			0
$649$	−6.98721			−0.274272
$650$	−37.8693	−	23.7799i	−1.48535	−	0.932726i
$651$		0			0
$652$	20.2338	+	75.5135i	0.792416	+	2.95734i
$653$	9.88229	−	17.1166i	0.386724	−	0.669825i	−0.605283	−	0.796010i	$-0.706940\pi$
$653$	9.88229	−	17.1166i	0.386724	−	0.669825i	0.992007	+	0.126185i	$0.0402733\pi$
$654$		0			0
$655$	−34.0874	+	34.0874i	−1.33190	+	1.33190i
$656$	−5.94709	+	22.1949i	−0.232195	+	0.866563i
$657$		0			0
$658$	64.5289	−	17.7891i	2.51560	−	0.693492i
$659$	−0.623376	−	1.07972i	−0.0242833	−	0.0420599i	0.853628	−	0.520882i	$-0.174397\pi$
$659$	−0.623376	−	1.07972i	−0.0242833	−	0.0420599i	−0.877912	+	0.478823i	$0.841064\pi$
$660$		0			0
$661$	6.22445	+	23.2300i	0.242103	+	0.903541i	0.974817	+	0.223004i	$0.0715864\pi$
$661$	6.22445	+	23.2300i	0.242103	+	0.903541i	−0.732714	+	0.680536i	$0.761747\pi$
$662$		−	80.8932i		−	3.14400i
$663$		0			0
$664$			24.1175i			0.935940i
$665$	12.0771	−	46.4055i	0.468330	−	1.79953i
$666$		0			0
$667$	−3.51405	+	2.02884i	−0.136065	+	0.0785569i
$668$	−54.5486	−	54.5486i	−2.11055	−	2.11055i
$669$		0			0
$670$	−68.3995	−	18.3276i	−2.64250	−	0.708057i
$671$	−0.213709	+	0.213709i	−0.00825013	+	0.00825013i
$672$		0			0
$673$	−43.6649	−	25.2100i	−1.68316	−	0.971772i	−0.959540	−	0.281573i	$-0.909144\pi$
$673$	−43.6649	−	25.2100i	−1.68316	−	0.971772i	−0.723619	−	0.690199i	$-0.757523\pi$
$674$	64.9704	−	17.4088i	2.50257	−	0.670561i
$675$		0			0
$676$	−30.8021	−	63.8690i	−1.18469	−	2.45650i
$677$			30.3365i			1.16593i	0.812498	+	0.582964i	$0.198107\pi$
$677$			30.3365i			1.16593i	−0.812498	+	0.582964i	$0.801893\pi$
$678$		0			0
$679$	16.8183	+	28.6520i	0.645426	+	1.09956i
$680$	57.5991	−	33.2548i	2.20882	−	1.27526i
$681$		0			0
$682$	1.29871	−	4.84684i	0.0497301	−	0.185595i
$683$	6.38263	−	23.8203i	0.244224	−	0.911458i	−0.729547	−	0.683930i	$-0.760269\pi$
$683$	6.38263	−	23.8203i	0.244224	−	0.911458i	0.973772	−	0.227528i	$-0.0730642\pi$
$684$		0			0
$685$	52.0325	−	30.0410i	1.98806	−	1.14781i
$686$	−24.3317	+	44.3268i	−0.928989	+	1.69240i
$687$		0			0
$688$		−	87.1715i		−	3.32338i
$689$	−10.2467	−	11.0371i	−0.390370	−	0.420481i
$690$		0			0
$691$	−40.1209	+	10.7504i	−1.52627	+	0.408963i	−0.921800	−	0.387666i	$-0.873282\pi$
$691$	−40.1209	+	10.7504i	−1.52627	+	0.408963i	−0.604470	+	0.796628i	$0.706615\pi$
$692$	−1.96886	−	1.13672i	−0.0748449	−	0.0432117i
$693$		0			0
$694$	−25.8556	+	25.8556i	−0.981464	+	0.981464i
$695$	16.7144	+	4.47860i	0.634012	+	0.169883i
$696$		0			0
$697$	2.49888	+	2.49888i	0.0946519	+	0.0946519i
$698$	−24.8718	+	14.3597i	−0.941411	+	0.543524i
$699$		0			0
$700$	63.4395	+	16.5102i	2.39779	+	0.624028i
$701$		−	1.87133i		−	0.0706790i	−0.999375	−	0.0353395i	$-0.988749\pi$
$701$		−	1.87133i		−	0.0706790i	0.999375	−	0.0353395i	$-0.0112513\pi$
$702$		0			0
$703$			38.9372i			1.46854i
$704$	3.60365	+	13.4490i	0.135818	+	0.506878i
$705$		0			0
$706$	−21.1860	−	36.6952i	−0.797346	−	1.38104i
$707$	4.54811	+	16.4980i	0.171049	+	0.620471i
$708$		0			0
$709$	−1.15519	+	4.31123i	−0.0433841	+	0.161912i	−0.984219	−	0.176953i	$-0.943376\pi$
$709$	−1.15519	+	4.31123i	−0.0433841	+	0.161912i	0.940835	+	0.338864i	$0.110043\pi$
$710$	13.1875	−	13.1875i	0.494919	−	0.494919i
$711$		0			0
$712$	−6.62222	+	11.4700i	−0.248178	+	0.429858i
$713$	0.559949	+	2.08976i	0.0209702	+	0.0782620i
$714$		0			0
$715$	−1.17297	−	5.13244i	−0.0438665	−	0.191942i
$716$	56.6718			2.11793
$717$		0			0
$718$	−13.9181	+	24.1069i	−0.519421	+	0.899663i
$719$	9.74009	+	16.8703i	0.363244	+	0.629157i	0.988493	−	0.151269i	$-0.0483358\pi$
$719$	9.74009	+	16.8703i	0.363244	+	0.629157i	−0.625249	+	0.780426i	$0.715002\pi$
$720$		0			0
$721$	15.8411	−	16.0707i	0.589952	−	0.598504i
$722$	10.8984	−	40.6736i	0.405598	−	1.51371i
$723$		0			0
$724$	−101.316	+	58.4946i	−3.76537	+	2.17394i
$725$	28.6860	+	16.5619i	1.06537	+	0.615093i
$726$		0			0
$727$	36.9369			1.36991			0.684957	−	0.728583i	$-0.259821\pi$
$727$	36.9369			1.36991			0.684957	+	0.728583i	$0.259821\pi$
$728$	61.6891	+	65.4958i	2.28635	+	2.42744i
$729$		0			0
$730$	−7.53153	−	28.1080i	−0.278754	−	1.04033i
$731$	−11.6107	−	6.70343i	−0.429437	−	0.247935i
$732$		0			0
$733$	−7.39416	−	7.39416i	−0.273109	−	0.273109i	0.557241	−	0.830351i	$-0.311860\pi$
$733$	−7.39416	−	7.39416i	−0.273109	−	0.273109i	−0.830351	+	0.557241i	$0.811860\pi$
$734$	10.7560	−	40.1419i	0.397011	−	1.48166i
$735$		0			0
$736$	−8.52289	−	8.52289i	−0.314158	−	0.314158i
$737$	−1.98435	−	3.43700i	−0.0730946	−	0.126604i
$738$		0			0
$739$	−40.7446	+	10.9175i	−1.49882	+	0.401606i	−0.912703	−	0.408623i	$-0.866009\pi$
$739$	−40.7446	+	10.9175i	−1.49882	+	0.401606i	−0.586112	+	0.810230i	$0.699342\pi$
$740$	−111.822			−4.11065
$741$		0			0
$742$	26.2386	+	14.8982i	0.963250	+	0.546929i
$743$	0.209458	+	0.781707i	0.00768426	+	0.0286780i	0.969662	−	0.244452i	$-0.0786079\pi$
$743$	0.209458	+	0.781707i	0.00768426	+	0.0286780i	−0.961977	+	0.273130i	$0.911941\pi$
$744$		0			0
$745$	−30.6351	−	53.0616i	−1.12238	−	1.94403i
$746$	−63.0380	+	63.0380i	−2.30799	+	2.30799i
$747$		0			0
$748$	5.68510	+	1.52332i	0.207868	+	0.0556980i
$749$	−3.29661	−	11.9583i	−0.120456	−	0.436945i
$750$		0			0
$751$	41.4868	+	23.9524i	1.51387	+	0.874035i	0.999868	+	0.0162488i	$0.00517239\pi$
$751$	41.4868	+	23.9524i	1.51387	+	0.874035i	0.514006	+	0.857787i	$0.328161\pi$
$752$	35.5965	+	132.848i	1.29807	+	4.84446i
$753$		0			0
$754$	33.5608	+	63.4568i	1.22221	+	2.31096i
$755$		−	2.78304i		−	0.101285i
$756$		0			0
$757$	1.02223	−	1.77055i	0.0371534	−	0.0643516i	−0.846851	−	0.531831i	$-0.821504\pi$
$757$	1.02223	−	1.77055i	0.0371534	−	0.0643516i	0.884004	+	0.467479i	$0.154838\pi$
$758$	−59.1640	+	34.1583i	−2.14893	+	1.24069i
$759$		0			0
$760$	165.116	+	44.2427i	5.98939	+	1.60485i
$761$	13.8918	+	3.72230i	0.503578	+	0.134933i	0.501660	−	0.865065i	$-0.332723\pi$
$761$	13.8918	+	3.72230i	0.503578	+	0.134933i	0.00191784	+	0.999998i	$0.499390\pi$
$762$		0			0
$763$	0.0985690	+	13.6979i	0.00356844	+	0.495896i
$764$	1.05071	+	0.606626i	0.0380132	+	0.0219470i
$765$		0			0
$766$	−49.6825			−1.79510
$767$	−24.9170	−	47.1130i	−0.899700	−	1.70115i
$768$		0			0
$769$	9.09993	−	2.43832i	0.328152	−	0.0879280i	−0.0909818	−	0.995853i	$-0.529001\pi$
$769$	9.09993	−	2.43832i	0.328152	−	0.0879280i	0.419134	+	0.907925i	$0.362334\pi$
$770$	5.33954	+	9.09656i	0.192424	+	0.327817i
$771$		0			0
$772$	7.91442	−	7.91442i	0.284846	−	0.284846i
$773$	−6.89949	+	25.7493i	−0.248157	+	0.926136i	0.723613	+	0.690206i	$0.242480\pi$
$773$	−6.89949	+	25.7493i	−0.248157	+	0.926136i	−0.971770	+	0.235930i	$0.924186\pi$
$774$		0			0
$775$	12.4882	−	12.4882i	0.448589	−	0.448589i
$776$	−102.570	+	59.2186i	−3.68204	+	2.12583i
$777$		0			0
$778$	−16.1595	+	4.32993i	−0.579347	+	0.155236i
$779$			9.08284i			0.325427i
$780$		0			0
$781$	1.04525			0.0374018
$782$	−3.34995	+	0.897617i	−0.119794	+	0.0320987i
$783$		0			0
$784$	−90.7165	−	50.6487i	−3.23988	−	1.80888i
$785$	0.232374	−	0.232374i	0.00829378	−	0.00829378i
$786$		0			0
$787$	42.0566	+	11.2690i	1.49916	+	0.401698i	0.912817	−	0.408368i	$-0.133902\pi$
$787$	42.0566	+	11.2690i	1.49916	+	0.401698i	0.586339	+	0.810066i	$0.300569\pi$
$788$	50.7975	+	50.7975i	1.80959	+	1.80959i
$789$		0			0
$790$	−49.7669	+	86.1987i	−1.77063	+	3.06681i
$791$	−22.5919	−	5.87958i	−0.803277	−	0.209054i
$792$		0			0
$793$	−2.20309	−	0.678883i	−0.0782340	−	0.0241078i
$794$		−	36.0580i		−	1.27965i
$795$		0			0
$796$	−14.1068	−	8.14455i	−0.500001	−	0.288676i
$797$	8.97549	+	15.5460i	0.317928	+	0.550667i	0.980056	−	0.198724i	$-0.0636796\pi$
$797$	8.97549	+	15.5460i	0.317928	+	0.550667i	−0.662128	+	0.749391i	$0.730346\pi$
$798$		0			0
$799$	20.4318	+	5.47469i	0.722826	+	0.193681i
$800$	−25.4660	+	95.0404i	−0.900359	+	3.36019i
$801$		0			0
$802$	7.00218	+	12.1281i	0.247256	+	0.428259i
$803$	0.815449	−	1.41240i	0.0287766	−	0.0498425i
$804$		0			0
$805$	−3.95478	−	2.24551i	−0.139388	−	0.0791437i
$806$	37.3124	−	8.52738i	1.31427	−	0.300364i
$807$		0			0
$808$	−58.9285	+	15.7899i	−2.07310	+	0.555485i
$809$	11.6827	−	20.2350i	0.410741	−	0.711424i	−0.584230	−	0.811588i	$-0.698603\pi$
$809$	11.6827	−	20.2350i	0.410741	−	0.711424i	0.994971	+	0.100164i	$0.0319367\pi$
$810$		0			0
$811$	−6.31578	−	6.31578i	−0.221777	−	0.221777i	0.587469	−	0.809246i	$-0.300124\pi$
$811$	−6.31578	−	6.31578i	−0.221777	−	0.221777i	−0.809246	+	0.587469i	$0.800124\pi$
$812$	−74.9453	−	73.8744i	−2.63007	−	2.59248i
$813$		0			0
$814$	−6.05640	−	6.05640i	−0.212277	−	0.212277i
$815$	−38.3430	+	22.1373i	−1.34310	+	0.775437i
$816$		0			0
$817$	−8.91834	−	33.2837i	−0.312013	−	1.16445i
$818$	43.6020			1.52451
$819$		0			0
$820$	−26.0846			−0.910913
$821$	−0.0319770	−	0.119340i	−0.00111600	−	0.00416498i	0.965366	−	0.260901i	$-0.0840196\pi$
$821$	−0.0319770	−	0.119340i	−0.00111600	−	0.00416498i	−0.966482	+	0.256736i	$0.917353\pi$
$822$		0			0
$823$	−26.0725	+	15.0529i	−0.908829	+	0.524712i	−0.880054	−	0.474874i	$-0.842494\pi$
$823$	−26.0725	+	15.0529i	−0.908829	+	0.524712i	−0.0287745	+	0.999586i	$0.509160\pi$
$824$	56.8824	+	56.8824i	1.98159	+	1.98159i
$825$		0			0
$826$	76.0451	+	74.9585i	2.64595	+	2.60814i
$827$	−21.5722	−	21.5722i	−0.750140	−	0.750140i	0.224365	−	0.974505i	$-0.427969\pi$
$827$	−21.5722	−	21.5722i	−0.750140	−	0.750140i	−0.974505	+	0.224365i	$0.927969\pi$
$828$		0			0
$829$	9.38977	−	16.2636i	0.326120	−	0.564857i	−0.655618	−	0.755093i	$-0.727592\pi$
$829$	9.38977	−	16.2636i	0.326120	−	0.564857i	0.981738	+	0.190236i	$0.0609252\pi$
$830$	−20.8315	+	5.58178i	−0.723071	+	0.193746i
$831$		0			0
$832$	−77.8324	+	72.2588i	−2.69835	+	2.50512i
$833$	−13.7221	+	8.18800i	−0.475443	+	0.283697i
$834$		0			0
$835$	21.8445	−	37.8359i	0.755961	−	1.30936i
$836$	7.56354	+	13.1004i	0.261591	+	0.453088i
$837$		0			0
$838$	−10.3194	+	38.5126i	−0.356478	+	1.33039i
$839$	−27.4030	−	7.34262i	−0.946058	−	0.253495i	−0.247369	−	0.968921i	$-0.579566\pi$
$839$	−27.4030	−	7.34262i	−0.946058	−	0.253495i	−0.698689	+	0.715426i	$0.746233\pi$
$840$		0			0
$841$	−12.0874	−	20.9360i	−0.416807	−	0.721931i
$842$	6.83256	+	3.94478i	0.235466	+	0.135946i
$843$		0			0
$844$			39.3990i			1.35617i
$845$	30.4239	−	26.2117i	1.04661	−	0.901712i
$846$		0			0
$847$	7.18111	−	27.5930i	0.246746	−	0.948106i
$848$	−30.9986	+	53.6911i	−1.06450	+	1.84376i
$849$		0			0
$850$	20.0190	+	20.0190i	0.686646	+	0.686646i
$851$	3.56706	+	0.955791i	0.122277	+	0.0327641i
$852$		0			0
$853$	16.3889	−	16.3889i	0.561144	−	0.561144i	−0.368488	−	0.929632i	$-0.620124\pi$
$853$	16.3889	−	16.3889i	0.561144	−	0.561144i	0.929632	+	0.368488i	$0.120124\pi$
$854$	4.61855	−	0.0332348i	0.158044	−	0.00113727i
$855$		0			0
$856$	42.7132	−	11.4450i	1.45991	−	0.391181i
$857$	14.4403			0.493271			0.246636	−	0.969108i	$-0.420675\pi$
$857$	14.4403			0.493271			0.246636	+	0.969108i	$0.420675\pi$
$858$		0			0
$859$		−	39.7298i		−	1.35556i	−0.735264	−	0.677781i	$-0.762942\pi$
$859$		−	39.7298i		−	1.35556i	0.735264	−	0.677781i	$-0.237058\pi$
$860$	95.5859	−	25.6122i	3.25945	−	0.873367i
$861$		0			0
$862$	25.8730	−	14.9378i	0.881237	−	0.508782i
$863$	14.6873	−	14.6873i	0.499961	−	0.499961i	−0.411464	−	0.911426i	$-0.634983\pi$
$863$	14.6873	−	14.6873i	0.499961	−	0.499961i	0.911426	+	0.411464i	$0.134983\pi$
$864$		0			0
$865$	0.333238	−	1.24366i	0.0113304	−	0.0422858i
$866$	−69.1933	+	69.1933i	−2.35128	+	2.35128i
$867$		0			0
$868$	−48.3886	+	28.4034i	−1.64242	+	0.964073i
$869$	−5.38833	+	1.44380i	−0.182786	+	0.0489775i
$870$		0			0
$871$	16.0985	−	25.6367i	0.545477	−	0.868665i
$872$	−48.8326			−1.65368
$873$		0			0
$874$	−7.71945	−	4.45683i	−0.261114	−	0.150754i
$875$	−0.0269106	−	3.73970i	−0.000909745	−	0.126425i
$876$		0			0
$877$	16.7227	+	4.48084i	0.564687	+	0.151307i	0.529859	−	0.848086i	$-0.322245\pi$
$877$	16.7227	+	4.48084i	0.564687	+	0.151307i	0.0348281	+	0.999393i	$0.488912\pi$
$878$	−4.07311	−	1.09139i	−0.137461	−	0.0368326i
$879$		0			0
$880$	−18.7692	+	10.8364i	−0.632711	+	0.365296i
$881$	13.3851	−	23.1836i	0.450955	−	0.781076i	−0.547491	−	0.836812i	$-0.684417\pi$
$881$	13.3851	−	23.1836i	0.450955	−	0.781076i	0.998446	+	0.0557352i	$0.0177503\pi$
$882$		0			0
$883$		−	41.2346i		−	1.38766i	−0.720141	−	0.693828i	$-0.755923\pi$
$883$		−	41.2346i		−	1.38766i	0.720141	−	0.693828i	$-0.244077\pi$
$884$	10.0022	+	43.7655i	0.336410	+	1.47199i
$885$		0			0
$886$	11.4235	+	42.6331i	0.383780	+	1.43229i
$887$	−23.6672	−	13.6643i	−0.794668	−	0.458802i	0.0469355	−	0.998898i	$-0.485054\pi$
$887$	−23.6672	−	13.6643i	−0.794668	−	0.458802i	−0.841603	+	0.540096i	$0.818388\pi$
$888$		0			0
$889$	−24.5173	+	6.75884i	−0.822283	+	0.226684i
$890$	−11.4399	−	3.06531i	−0.383466	−	0.102749i
$891$		0			0
$892$	74.1443	−	74.1443i	2.48253	−	2.48253i
$893$	27.1828	+	47.0820i	0.909638	+	1.57554i
$894$		0			0
$895$	8.30688	+	31.0017i	0.277668	+	1.03627i
$896$	48.4664	−	85.3590i	1.61915	−	2.85164i
$897$		0			0
$898$	41.8581			1.39682
$899$	−27.3857	+	7.33799i	−0.913365	+	0.244736i
$900$		0			0
$901$	4.76754	+	8.25762i	0.158830	+	0.275101i
$902$	−1.41277	−	1.41277i	−0.0470402	−	0.0470402i
$903$		0			0
$904$	21.5390	−	80.3847i	0.716377	−	2.67355i
$905$	−46.8496	−	46.8496i	−1.55733	−	1.55733i
$906$		0			0
$907$	24.9677	+	14.4151i	0.829038	+	0.478645i	0.853523	−	0.521055i	$-0.174461\pi$
$907$	24.9677	+	14.4151i	0.829038	+	0.478645i	−0.0244850	+	0.999700i	$0.507795\pi$
$908$	−21.7955	−	81.3418i	−0.723308	−	2.69942i
$909$		0			0
$910$	−42.2946	+	68.4423i	−1.40205	+	2.26884i
$911$	55.1222			1.82628			0.913140	−	0.407646i	$-0.133650\pi$
$911$	55.1222			1.82628			0.913140	+	0.407646i	$0.133650\pi$
$912$		0			0
$913$	−1.04676	−	0.604347i	−0.0346427	−	0.0200010i
$914$	65.2472	−	37.6705i	2.15819	−	1.24603i
$915$		0			0
$916$	−16.7402	+	62.4755i	−0.553113	+	2.06425i
$917$	29.4047	+	28.9845i	0.971028	+	0.957153i
$918$		0			0
$919$	12.4821	+	21.6196i	0.411745	+	0.713164i	0.995081	−	0.0990678i	$-0.0315861\pi$
$919$	12.4821	+	21.6196i	0.411745	+	0.713164i	−0.583336	+	0.812231i	$0.698253\pi$
$920$	8.10621	−	14.0404i	0.267254	−	0.462897i
$921$		0			0
$922$	−6.65300			−0.219105
$923$	3.72743	+	7.04783i	0.122690	+	0.231982i
$924$		0			0
$925$	−7.80235	−	29.1188i	−0.256540	−	0.957420i
$926$	30.7080	−	53.1878i	1.00913	−	1.74786i
$927$		0			0
$928$	111.690	−	111.690i	3.66641	−	3.66641i
$929$	6.01016	−	22.4302i	0.197187	−	0.735911i	−0.794503	−	0.607260i	$-0.792269\pi$
$929$	6.01016	−	22.4302i	0.197187	−	0.735911i	0.991690	−	0.128651i	$-0.0410647\pi$
$930$		0			0
$931$	−39.8190	−	10.0576i	−1.30502	−	0.329624i
$932$	54.4194	+	94.2572i	1.78257	+	3.08750i
$933$		0			0
$934$	−4.70838	−	17.5719i	−0.154063	−	0.574971i
$935$			3.33326i			0.109009i
$936$		0			0
$937$			10.3813i			0.339143i	0.985518	+	0.169572i	$0.0542384\pi$
$937$			10.3813i			0.339143i	−0.985518	+	0.169572i	$0.945762\pi$
$938$	−15.2754	+	58.6946i	−0.498758	+	1.91645i
$939$		0			0
$940$	−135.212	+	78.0649i	−4.41014	+	2.54620i
$941$	21.0506	+	21.0506i	0.686232	+	0.686232i	0.961397	−	0.275165i	$-0.0887326\pi$
$941$	21.0506	+	21.0506i	0.686232	+	0.686232i	−0.275165	+	0.961397i	$0.588733\pi$
$942$		0			0
$943$	0.832085	+	0.222957i	0.0270964	+	0.00726046i
$944$	−155.138	+	155.138i	−5.04932	+	5.04932i
$945$		0			0
$946$	6.56423	+	3.78986i	0.213422	+	0.123219i
$947$	−12.9426	+	3.46795i	−0.420577	+	0.112693i	−0.462900	−	0.886411i	$-0.653191\pi$
$947$	−12.9426	+	3.46795i	−0.420577	+	0.112693i	0.0423224	+	0.999104i	$0.486524\pi$
$948$		0			0
$949$	12.4314	+	0.461641i	0.403541	+	0.0149855i
$950$			72.7643i			2.36079i
$951$		0			0
$952$	−28.8365	−	49.1265i	−0.934597	−	1.59220i
$953$	13.8070	−	7.97146i	0.447252	−	0.258221i	−0.259417	−	0.965765i	$-0.583530\pi$
$953$	13.8070	−	7.97146i	0.447252	−	0.258221i	0.706669	+	0.707544i	$0.250197\pi$
$954$		0			0
$955$	−0.177837	+	0.663696i	−0.00575466	+	0.0214767i
$956$	−10.5360	+	39.3208i	−0.340757	+	1.27172i
$957$		0			0
$958$	53.9931	−	31.1729i	1.74444	−	1.00715i
$959$	−26.0497	−	44.3788i	−0.841188	−	1.43307i
$960$		0			0
$961$		−	15.8834i		−	0.512366i
$962$	19.2392	−	62.4345i	0.620297	−	2.01297i
$963$		0			0
$964$	45.5518	−	12.2056i	1.46712	−	0.393115i
$965$	5.48958	+	3.16941i	0.176716	+	0.102027i
$966$		0			0
$967$	8.01251	−	8.01251i	0.257665	−	0.257665i	−0.566439	−	0.824104i	$-0.691679\pi$
$967$	8.01251	−	8.01251i	0.257665	−	0.257665i	0.824104	+	0.566439i	$0.191679\pi$
$968$	98.1789	+	26.3070i	3.15559	+	0.845538i
$969$		0			0
$970$	−74.8889	−	74.8889i	−2.40454	−	2.40454i
$971$	38.0478	−	21.9669i	1.22101	−	0.704951i	0.255878	−	0.966709i	$-0.417636\pi$
$971$	38.0478	−	21.9669i	1.22101	−	0.704951i	0.965134	+	0.261758i	$0.0843022\pi$
$972$		0			0
$973$	3.73275	−	14.3428i	0.119666	−	0.459810i
$974$			34.0126i			1.08984i
$975$		0			0
$976$			9.49003i			0.303768i
$977$	9.68314	+	36.1380i	0.309791	+	1.15616i	0.928742	+	0.370727i	$0.120891\pi$
$977$	9.68314	+	36.1380i	0.309791	+	1.15616i	−0.618951	+	0.785430i	$0.712442\pi$
$978$		0			0
$979$	−0.331885	−	0.574842i	−0.0106071	−	0.0183720i
$980$	28.8839	−	114.354i	0.922662	−	3.65291i
$981$		0			0
$982$	−13.6993	+	51.1264i	−0.437162	+	1.63151i
$983$	24.9501	−	24.9501i	0.795786	−	0.795786i	−0.186642	−	0.982428i	$-0.559761\pi$
$983$	24.9501	−	24.9501i	0.795786	−	0.795786i	0.982428	+	0.186642i	$0.0597606\pi$
$984$		0			0
$985$	−20.3424	+	35.2340i	−0.648162	+	1.12265i
$986$	−11.7630	−	43.9003i	−0.374612	−	1.39807i
$987$		0			0
$988$	−61.3609	+	97.7164i	−1.95215	+	3.10877i
$989$	−3.26806			−0.103918
$990$		0			0
$991$	−4.26766	+	7.39180i	−0.135567	+	0.234808i	−0.925814	−	0.377980i	$-0.876619\pi$
$991$	−4.26766	+	7.39180i	−0.135567	+	0.234808i	0.790247	+	0.612788i	$0.209952\pi$
$992$	−42.1090	−	72.9350i	−1.33696	−	2.31569i
$993$		0			0
$994$	−11.3759	−	11.2133i	−0.360822	−	0.355666i
$995$	2.38763	−	8.91077i	0.0756931	−	0.282490i
$996$		0			0
$997$	30.8124	−	17.7895i	0.975837	−	0.563400i	0.0748264	−	0.997197i	$-0.476160\pi$
$997$	30.8124	−	17.7895i	0.975837	−	0.563400i	0.901011	+	0.433797i	$0.142826\pi$
$998$	−82.4557	−	47.6058i	−2.61009	−	1.50694i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.370.8		32
3.2	odd	2		273.2.by.c.97.1	yes	32
7.6	odd	2		819.2.fm.e.370.8		32
13.11	odd	12		819.2.fm.e.622.8		32
21.20	even	2		273.2.by.d.97.1	yes	32
39.11	even	12		273.2.by.d.76.1	yes	32
91.76	even	12	inner	819.2.fm.f.622.8		32
273.167	odd	12		273.2.by.c.76.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.1	✓	32	273.167	odd	12
273.2.by.c.97.1	yes	32	3.2	odd	2
273.2.by.d.76.1	yes	32	39.11	even	12
273.2.by.d.97.1	yes	32	21.20	even	2
819.2.fm.e.370.8		32	7.6	odd	2
819.2.fm.e.622.8		32	13.11	odd	12
819.2.fm.f.370.8		32	1.1	even	1	trivial
819.2.fm.f.622.8		32	91.76	even	12	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.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.706652 + 2.63726i) q^{2} +(-4.72373 + 2.72725i) q^{4} +(-2.18431 - 2.18431i) q^{5} +(-1.85732 + 1.88424i) q^{7} +(-6.66928 - 6.66928i) q^{8} +O(q^{10})\)	\(q+(0.706652 + 2.63726i) q^{2} +(-4.72373 + 2.72725i) q^{4} +(-2.18431 - 2.18431i) q^{5} +(-1.85732 + 1.88424i) q^{7} +(-6.66928 - 6.66928i) q^{8} +(4.21705 - 7.30414i) q^{10} +(0.456585 - 0.122342i) q^{11} +(2.45314 + 2.64236i) q^{13} +(-6.28171 - 3.56673i) q^{14} +(7.42128 - 12.8540i) q^{16} +(-1.14138 - 1.97693i) q^{17} +(1.51851 - 5.66717i) q^{19} +(16.2753 + 4.36094i) q^{20} +(0.645294 + 1.11768i) q^{22} +(-0.481898 - 0.278224i) q^{23} +4.54242i q^{25} +(-5.23509 + 8.33681i) q^{26} +(3.63468 - 13.9660i) q^{28} +(3.64605 - 6.31515i) q^{29} +(-2.74924 - 2.74924i) q^{31} +(20.9229 + 5.60626i) q^{32} +(4.40713 - 4.40713i) q^{34} +(8.17273 - 0.0588104i) q^{35} +(-6.41041 + 1.71767i) q^{37} +16.0189 q^{38} +29.1356i q^{40} +(-1.49535 + 0.400678i) q^{41} +(5.08624 - 2.93654i) q^{43} +(-1.82313 + 1.82313i) q^{44} +(0.393215 - 1.46750i) q^{46} +(-6.55220 + 6.55220i) q^{47} +(-0.100738 - 6.99928i) q^{49} +(-11.9795 + 3.20991i) q^{50} +(-18.7944 - 5.79150i) q^{52} -4.17698 q^{53} +(-1.26456 - 0.730092i) q^{55} +(24.9535 - 0.179564i) q^{56} +(19.2312 + 5.15298i) q^{58} +(-14.2781 - 3.82579i) q^{59} +(-0.553719 + 0.319690i) q^{61} +(5.30771 - 9.19322i) q^{62} +29.4556i q^{64} +(0.413319 - 11.1302i) q^{65} +(-2.17304 - 8.10989i) q^{67} +(10.7832 + 6.22567i) q^{68} +(5.93037 + 21.5120i) q^{70} +(2.13591 + 0.572316i) q^{71} +(2.43968 - 2.43968i) q^{73} +(-9.05986 - 15.6921i) q^{74} +(8.28273 + 30.9116i) q^{76} +(-0.617503 + 1.08755i) q^{77} -11.8014 q^{79} +(-44.2876 + 11.8668i) q^{80} +(-2.11339 - 3.66049i) q^{82} +(-1.80810 - 1.80810i) q^{83} +(-1.82510 + 6.81137i) q^{85} +(11.3386 + 11.3386i) q^{86} +(-3.86103 - 2.22917i) q^{88} +(-0.363443 - 1.35639i) q^{89} +(-9.53512 - 0.285396i) q^{91} +3.03514 q^{92} +(-21.9100 - 12.6497i) q^{94} +(-15.6957 + 9.06194i) q^{95} +(3.25005 - 12.1294i) q^{97} +(18.3877 - 5.21172i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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