LMFDB - Embedded newform 819.2.fm.e.622.8

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			622.8
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.e.370.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.706652 - 2.63726i) q^{2} +(-4.72373 - 2.72725i) q^{4} +(2.18431 - 2.18431i) q^{5} +(0.666364 - 2.56046i) q^{7} +(-6.66928 + 6.66928i) q^{8} +O(q^{10})$	\(q+(0.706652 - 2.63726i) q^{2} +(-4.72373 - 2.72725i) q^{4} +(2.18431 - 2.18431i) q^{5} +(0.666364 - 2.56046i) q^{7} +(-6.66928 + 6.66928i) q^{8} +(-4.21705 - 7.30414i) q^{10} +(0.456585 + 0.122342i) q^{11} +(-2.45314 + 2.64236i) q^{13} +(-6.28171 - 3.56673i) q^{14} +(7.42128 + 12.8540i) q^{16} +(1.14138 - 1.97693i) q^{17} +(-1.51851 - 5.66717i) q^{19} +(-16.2753 + 4.36094i) q^{20} +(0.645294 - 1.11768i) q^{22} +(-0.481898 + 0.278224i) q^{23} -4.54242i q^{25} +(5.23509 + 8.33681i) q^{26} +(-10.1307 + 10.2776i) q^{28} +(3.64605 + 6.31515i) q^{29} +(2.74924 - 2.74924i) q^{31} +(20.9229 - 5.60626i) q^{32} +(-4.40713 - 4.40713i) q^{34} +(-4.13729 - 7.04838i) q^{35} +(-6.41041 - 1.71767i) q^{37} -16.0189 q^{38} +29.1356i q^{40} +(1.49535 + 0.400678i) q^{41} +(5.08624 + 2.93654i) q^{43} +(-1.82313 - 1.82313i) q^{44} +(0.393215 + 1.46750i) q^{46} +(6.55220 + 6.55220i) q^{47} +(-6.11192 - 3.41240i) q^{49} +(-11.9795 - 3.20991i) q^{50} +(18.7944 - 5.79150i) q^{52} -4.17698 q^{53} +(1.26456 - 0.730092i) q^{55} +(12.6323 + 21.5206i) q^{56} +(19.2312 - 5.15298i) q^{58} +(14.2781 - 3.82579i) q^{59} +(0.553719 + 0.319690i) q^{61} +(-5.30771 - 9.19322i) q^{62} -29.4556i q^{64} +(0.413319 + 11.1302i) q^{65} +(-2.17304 + 8.10989i) q^{67} +(-10.7832 + 6.22567i) q^{68} +(-21.5120 + 5.93037i) q^{70} +(2.13591 - 0.572316i) q^{71} +(-2.43968 - 2.43968i) q^{73} +(-9.05986 + 15.6921i) q^{74} +(-8.28273 + 30.9116i) q^{76} +(0.617503 - 1.08755i) q^{77} -11.8014 q^{79} +(44.2876 + 11.8668i) q^{80} +(2.11339 - 3.66049i) q^{82} +(1.80810 - 1.80810i) q^{83} +(-1.82510 - 6.81137i) q^{85} +(11.3386 - 11.3386i) q^{86} +(-3.86103 + 2.22917i) q^{88} +(0.363443 - 1.35639i) q^{89} +(5.13099 + 8.04195i) q^{91} +3.03514 q^{92} +(21.9100 - 12.6497i) q^{94} +(-15.6957 - 9.06194i) q^{95} +(-3.25005 - 12.1294i) q^{97} +(-13.3184 + 13.7073i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 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} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+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 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * 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 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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	−0.00239085	−	0.999997i	$-0.500761\pi$
$2$	0.706652	−	2.63726i	0.499678	−	1.86482i	0.502069	−	0.864828i	$-0.332572\pi$
$3$		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	$-0.507285\pi$
$5$	2.18431	−	2.18431i	0.976853	−	0.976853i	0.999738	+	0.0228851i	$0.00728519\pi$
$6$		0			0
$7$	0.666364	−	2.56046i	0.251862	−	0.967763i
$7$	0.666364	−	2.56046i	0.251862	−	0.967763i
$8$	−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	0.326994	−	0.945026i	$-0.393964\pi$
$11$	0.456585	+	0.122342i	0.137666	+	0.0368874i	−0.189328	+	0.981914i	$0.560631\pi$
$12$		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	$-0.744051\pi$
$17$	1.14138	−	1.97693i	0.276826	−	0.479477i	0.970594	+	0.240722i	$0.0773841\pi$
$18$		0			0
$19$	−1.51851	−	5.66717i	−0.348371	−	1.30014i	−0.888625	−	0.458635i	$-0.848339\pi$
$19$	−1.51851	−	5.66717i	−0.348371	−	1.30014i	0.540254	−	0.841502i	$-0.318328\pi$
$20$	−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	−0.549399	−	0.835560i	$-0.685143\pi$
$23$	−0.481898	+	0.278224i	−0.100483	+	0.0580137i	0.448917	+	0.893574i	$0.351810\pi$
$24$		0			0
$25$		−	4.54242i		−	0.908484i
$26$	5.23509	+	8.33681i	1.02668	+	1.63498i
$27$		0			0
$28$	−10.1307	+	10.2776i	−1.91453	+	1.94228i
$29$	3.64605	+	6.31515i	0.677055	+	1.17269i	0.975864	+	0.218381i	$0.0700774\pi$
$29$	3.64605	+	6.31515i	0.677055	+	1.17269i	−0.298809	+	0.954313i	$0.596589\pi$
$30$		0			0
$31$	2.74924	−	2.74924i	0.493778	−	0.493778i	−0.415716	−	0.909494i	$-0.636469\pi$
$31$	2.74924	−	2.74924i	0.493778	−	0.493778i	0.909494	+	0.415716i	$0.136469\pi$
$32$	20.9229	−	5.60626i	3.69867	−	0.991057i
$33$		0			0
$34$	−4.40713	−	4.40713i	−0.755816	−	0.755816i
$35$	−4.13729	−	7.04838i	−0.699330	−	1.19139i
$36$		0			0
$37$	−6.41041	−	1.71767i	−1.05387	−	0.282382i	−0.310017	−	0.950731i	$-0.600335\pi$
$37$	−6.41041	−	1.71767i	−1.05387	−	0.282382i	−0.743848	+	0.668348i	$0.767002\pi$
$38$	−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	$-0.378093\pi$
$41$	1.49535	+	0.400678i	0.233535	+	0.0625755i	−0.140154	+	0.990130i	$0.544760\pi$
$42$		0			0
$43$	5.08624	+	2.93654i	0.775644	+	0.447818i	0.834884	−	0.550426i	$-0.185535\pi$
$43$	5.08624	+	2.93654i	0.775644	+	0.447818i	−0.0592406	+	0.998244i	$0.518868\pi$
$44$	−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	$-0.0137950\pi$
$47$	6.55220	+	6.55220i	0.955736	+	0.955736i	−0.0433248	+	0.999061i	$0.513795\pi$
$48$		0			0
$49$	−6.11192	−	3.41240i	−0.873131	−	0.487485i
$50$	−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
$56$	12.6323	+	21.5206i	1.68806	+	2.87581i
$57$		0			0
$58$	19.2312	−	5.15298i	2.52518	−	0.676619i
$59$	14.2781	−	3.82579i	1.85884	−	0.498076i	0.858942	−	0.512072i	$-0.171122\pi$
$59$	14.2781	−	3.82579i	1.85884	−	0.498076i	0.999902	+	0.0139966i	$0.00445541\pi$
$60$		0			0
$61$	0.553719	+	0.319690i	0.0708965	+	0.0409321i	0.535029	−	0.844834i	$-0.320301\pi$
$61$	0.553719	+	0.319690i	0.0708965	+	0.0409321i	−0.464133	+	0.885766i	$0.653634\pi$
$62$	−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	0.696478	+	0.717578i	$0.254749\pi$
$67$	−2.17304	+	8.10989i	−0.265479	+	0.990780i	−0.961957	+	0.273202i	$0.911917\pi$
$68$	−10.7832	+	6.22567i	−1.30765	+	0.754973i
$69$		0			0
$70$	−21.5120	+	5.93037i	−2.57118	+	0.708815i
$71$	2.13591	−	0.572316i	0.253486	−	0.0679214i	−0.129838	−	0.991535i	$-0.541446\pi$
$71$	2.13591	−	0.572316i	0.253486	−	0.0679214i	0.383324	+	0.923614i	$0.374779\pi$
$72$		0			0
$73$	−2.43968	−	2.43968i	−0.285543	−	0.285543i	0.549772	−	0.835315i	$-0.314715\pi$
$73$	−2.43968	−	2.43968i	−0.285543	−	0.285543i	−0.835315	+	0.549772i	$0.814715\pi$
$74$	−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	$-0.705182\pi$
$83$	1.80810	−	1.80810i	0.198465	−	0.198465i	0.799342	+	0.600877i	$0.205182\pi$
$84$		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	$-0.892955\pi$
$89$	0.363443	−	1.35639i	0.0385248	−	0.143777i	0.982509	+	0.186213i	$0.0596214\pi$
$90$		0			0
$91$	5.13099	+	8.04195i	0.537873	+	0.843026i
$92$	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	−0.909197	−	0.416367i	$-0.863303\pi$
$97$	−3.25005	−	12.1294i	−0.329993	−	1.23155i	0.579204	−	0.815183i	$-0.303364\pi$
$98$	−13.3184	+	13.7073i	−1.34536	+	1.38465i
$99$		0			0
$100$	−12.3883	+	21.4572i	−1.23883	+	2.14572i
$101$	−3.23413	−	5.60168i	−0.321808	−	0.557388i	0.659053	−	0.752096i	$-0.270957\pi$
$101$	−3.23413	−	5.60168i	−0.321808	−	0.557388i	−0.980861	+	0.194708i	$0.937624\pi$
$102$		0			0
$103$	8.52900			0.840388			0.420194	−	0.907434i	$-0.361962\pi$
$103$	8.52900			0.840388			0.420194	+	0.907434i	$0.361962\pi$
$104$	−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	0.730183	−	0.683252i	$-0.239435\pi$
$107$	−2.34420	−	4.06027i	−0.226622	−	0.392521i	−0.956805	+	0.290731i	$0.906102\pi$
$108$		0			0
$109$	3.66100	+	3.66100i	0.350661	+	0.350661i	0.860355	−	0.509695i	$-0.170242\pi$
$109$	3.66100	+	3.66100i	0.350661	+	0.350661i	−0.509695	+	0.860355i	$0.670242\pi$
$110$	−1.03184	−	3.85088i	−0.0983822	−	0.367167i
$111$		0			0
$112$	37.8575	−	10.4364i	3.57720	−	0.986150i
$113$	4.41169	−	7.64128i	0.415017	−	0.718831i	−0.580413	−	0.814322i	$-0.697109\pi$
$113$	4.41169	−	7.64128i	0.415017	−	0.718831i	0.995430	+	0.0954914i	$0.0304422\pi$
$114$		0			0
$115$	−0.444887	+	1.66034i	−0.0414859	+	0.154828i
$116$		−	39.7748i		−	3.69300i
$117$		0			0
$118$		−	40.3584i		−	3.71530i
$119$	−4.30128	−	4.23982i	−0.394298	−	0.388664i
$120$		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	−0.0829079	−	0.996557i	$-0.526421\pi$
$127$	8.32452	−	4.80617i	0.738682	−	0.426478i	0.821590	+	0.570079i	$0.193087\pi$
$128$	−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
$133$	−15.5224	+	0.111698i	−1.34597	+	0.00968549i
$134$	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	−0.752569	−	0.658513i	$-0.771186\pi$
$137$	−5.03398	−	18.7871i	−0.430082	−	1.60509i	0.322488	−	0.946574i	$-0.395481\pi$
$138$		0			0
$139$	4.85118	+	2.80083i	0.411472	+	0.237564i	0.691422	−	0.722451i	$-0.256985\pi$
$139$	4.85118	+	2.80083i	0.411472	+	0.237564i	−0.279950	+	0.960015i	$0.590318\pi$
$140$	0.320781	+	44.5781i	0.0271110	+	3.76754i
$141$		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	0.633869	−	0.773440i	$-0.281466\pi$
$149$	19.1586	−	5.13354i	1.56954	−	0.420556i	0.935667	+	0.352885i	$0.114799\pi$
$150$		0			0
$151$	0.637052	−	0.637052i	0.0518426	−	0.0518426i	−0.680710	−	0.732553i	$-0.738329\pi$
$151$	0.637052	−	0.637052i	0.0518426	−	0.0518426i	0.732553	+	0.680710i	$0.238329\pi$
$152$	47.9233	+	27.6686i	3.88710	+	2.24422i
$153$		0			0
$154$	−2.43178	−	2.39703i	−0.195958	−	0.193158i
$155$		−	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
$161$	0.391262	+	1.41928i	0.0308358	+	0.111855i
$162$		0			0
$163$	3.70956	+	13.8443i	0.290555	+	1.08437i	0.944684	+	0.327983i	$0.106369\pi$
$163$	3.70956	+	13.8443i	0.290555	+	1.08437i	−0.654128	+	0.756383i	$0.726964\pi$
$164$	−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	0.666845	+	0.745196i	$0.267644\pi$
$167$	−3.66050	+	13.6612i	−0.283258	+	1.05713i	−0.950103	+	0.311936i	$0.899023\pi$
$168$		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	$-0.838377\pi$
$173$	−0.208401	+	0.360961i	−0.0158444	+	0.0274434i	0.857994	+	0.513659i	$0.171710\pi$
$174$		0			0
$175$	−11.6307	−	3.02690i	−0.879197	−	0.228812i
$176$	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	−0.797037	−	0.603930i	$-0.793601\pi$
$179$	−8.99794	+	5.19496i	−0.672537	+	0.388290i	0.124500	+	0.992220i	$0.460267\pi$
$180$		0			0
$181$	−21.4482			−1.59423			−0.797117	−	0.603825i	$-0.793643\pi$
$181$	−21.4482			−1.59423			−0.797117	+	0.603825i	$0.793643\pi$
$182$	24.8345	−	7.84888i	1.84086	−	0.581798i
$183$		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	−0.870021	−	0.493015i	$-0.835895\pi$
$191$	−0.111216	+	0.192631i	−0.00804729	+	0.0139383i	0.861974	+	0.506953i	$0.169228\pi$
$192$		0			0
$193$	−1.98209	−	0.531099i	−0.142674	−	0.0382293i	0.186775	−	0.982403i	$-0.440196\pi$
$193$	−1.98209	−	0.531099i	−0.142674	−	0.0382293i	−0.329449	+	0.944173i	$0.606863\pi$
$194$	−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	0.731579	+	0.681757i	$0.238784\pi$
$197$	−3.40878	+	12.7217i	−0.242865	+	0.906386i	−0.974444	+	0.224629i	$0.927883\pi$
$198$		0			0
$199$	−1.49318	+	2.58626i	−0.105849	+	0.183335i	−0.914085	−	0.405523i	$-0.867089\pi$
$199$	−1.49318	+	2.58626i	−0.105849	+	0.183335i	0.808236	+	0.588859i	$0.200423\pi$
$200$	30.2947	+	30.2947i	2.14216	+	2.14216i
$201$		0			0
$202$	−17.0585	+	4.57081i	−1.20023	+	0.321601i
$203$	18.5993	−	5.12739i	1.30541	−	0.359872i
$204$		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	0.963147	−	0.268976i	$-0.0866853\pi$
$211$	3.61160	+	6.25548i	0.248633	+	0.430645i	−0.714514	+	0.699621i	$0.753352\pi$
$212$	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
$217$	−5.20733	−	8.87132i	−0.353496	−	0.602224i
$218$	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	$-0.194082\pi$
$223$	18.5687	+	4.97547i	1.24345	+	0.333182i	0.423649	+	0.905827i	$0.360749\pi$
$224$	−0.412385	−	57.3080i	−0.0275536	−	3.82905i
$225$		0			0
$226$	−17.0345	−	17.0345i	−1.13312	−	1.13312i
$227$	3.99587	+	14.9128i	0.265215	+	0.989797i	0.962118	+	0.272632i	$0.0878941\pi$
$227$	3.99587	+	14.9128i	0.265215	+	0.989797i	−0.696903	+	0.717165i	$0.745439\pi$
$228$		0			0
$229$	−8.38486	−	8.38486i	−0.554087	−	0.554087i	0.373531	−	0.927618i	$-0.378147\pi$
$229$	−8.38486	−	8.38486i	−0.554087	−	0.554087i	−0.927618	+	0.373531i	$0.878147\pi$
$230$	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	$0.226748\pi$
$233$			19.9540i			1.30723i	−0.756828	+	0.653614i	$0.773252\pi$
$234$		0			0
$235$	28.6241			1.86723
$236$	−77.8796	−	20.8678i	−5.06953	−	1.35838i
$237$		0			0
$238$	−14.2210	+	8.34753i	−0.921812	+	0.541090i
$239$	5.27726	+	5.27726i	0.341357	+	0.341357i	0.856877	−	0.515520i	$-0.172401\pi$
$239$	5.27726	+	5.27726i	0.341357	+	0.341357i	−0.515520	+	0.856877i	$0.672401\pi$
$240$		0			0
$241$	8.35123	−	2.23771i	0.537950	−	0.144143i	0.0203932	−	0.999792i	$-0.493508\pi$
$241$	8.35123	−	2.23771i	0.537950	−	0.144143i	0.517557	+	0.855649i	$0.326842\pi$
$242$	−20.8053	+	20.8053i	−1.33742	+	1.33742i
$243$		0			0
$244$	−1.74375	−	3.02026i	−0.111632	−	0.193352i
$245$	−20.8041	+	5.89659i	−1.32912	+	0.376720i
$246$		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	0.463494	+	0.886100i	$0.346595\pi$
$251$	−8.48610	+	14.6984i	−0.535638	+	0.927752i	−0.999132	+	0.0416520i	$0.986738\pi$
$252$		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	$-0.234048\pi$
$257$	−3.36830	−	5.83406i	−0.210109	−	0.363919i	−0.951748	+	0.306880i	$0.900715\pi$
$258$		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	0.935929	−	0.352189i	$-0.114563\pi$
$263$	2.64276	+	4.57739i	0.162960	+	0.282254i	−0.772969	+	0.634443i	$0.781229\pi$
$264$		0			0
$265$	−9.12383	+	9.12383i	−0.560472	+	0.560472i
$266$	−10.6744	+	41.0156i	−0.654488	+	2.51483i
$267$		0			0
$268$	32.3825	−	32.3825i	1.97808	−	1.97808i
$269$	−2.83734	−	1.63814i	−0.172995	−	0.0998789i	0.411002	−	0.911634i	$-0.365179\pi$
$269$	−2.83734	−	1.63814i	−0.172995	−	0.0998789i	−0.583997	+	0.811755i	$0.698512\pi$
$270$		0			0
$271$	3.01677	−	11.2587i	0.183256	−	0.683919i	−0.811742	−	0.584017i	$-0.801480\pi$
$271$	3.01677	−	11.2587i	0.183256	−	0.683919i	0.994997	−	0.0999024i	$-0.0318531\pi$
$272$	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	0.605964	−	0.795492i	$-0.292787\pi$
$277$	3.66204	+	2.11428i	0.220031	+	0.127035i	−0.385934	+	0.922526i	$0.626121\pi$
$278$	10.8146	−	10.8146i	0.648618	−	0.648618i
$279$		0			0
$280$	74.6005	+	19.4149i	4.45823	+	1.16026i
$281$	−18.2360	+	18.2360i	−1.08787	+	1.08787i	−0.0921208	+	0.995748i	$0.529365\pi$
$281$	−18.2360	+	18.2360i	−1.08787	+	1.08787i	−0.995748	+	0.0921208i	$0.970635\pi$
$282$		0			0
$283$	1.92179	+	3.32864i	0.114239	+	0.197867i	0.917475	−	0.397793i	$-0.130224\pi$
$283$	1.92179	+	3.32864i	0.114239	+	0.197867i	−0.803236	+	0.595660i	$0.796890\pi$
$284$	−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	$-0.250137\pi$
$293$	28.6306	−	7.67154i	1.67262	−	0.448176i	0.965814	+	0.259236i	$0.0834707\pi$
$294$		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
$301$	10.9082	−	11.0663i	0.628737	−	0.637851i
$302$	−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	0.985953	+	0.167023i	$0.0534155\pi$
$307$	20.2018	+	20.2018i	1.15298	+	1.15298i	0.167023	+	0.985953i	$0.446584\pi$
$308$	−5.88293	+	3.45319i	−0.335211	+	0.196764i
$309$		0			0
$310$	−31.6745	−	8.48716i	−1.79899	−	0.482038i
$311$	24.6309			1.39669			0.698345	−	0.715762i	$-0.253920\pi$
$311$	24.6309			1.39669			0.698345	+	0.715762i	$0.253920\pi$
$312$		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	0.509660	−	0.860376i	$-0.329771\pi$
$317$	−6.24432	−	6.24432i	−0.350716	−	0.350716i	−0.860376	+	0.509660i	$0.829771\pi$
$318$		0			0
$319$	0.892129	+	3.32947i	0.0499496	+	0.186414i
$320$	−64.3402	−	64.3402i	−3.59672	−	3.59672i
$321$		0			0
$322$	4.01949	−	0.0289240i	0.223998	−	0.00161187i
$323$	−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
$329$	21.1428	−	12.4105i	1.16564	−	0.684213i
$330$		0			0
$331$	−28.6185	+	7.66830i	−1.57301	+	0.421488i	−0.936755	−	0.349987i	$-0.886186\pi$
$331$	−28.6185	+	7.66830i	−1.57301	+	0.421488i	−0.636260	+	0.771475i	$0.719519\pi$
$332$	−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	$0.234132\pi$
$337$			24.6356i			1.34198i	−0.741464	+	0.670992i	$0.765868\pi$
$338$	−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
$343$	−12.8101	+	13.3754i	−0.691679	+	0.722205i
$344$	−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	−0.628401	−	0.777890i	$-0.716290\pi$
$347$	6.69623	−	11.5982i	0.359472	−	0.622624i	0.987873	+	0.155266i	$0.0496234\pi$
$348$		0			0
$349$	−2.72247	+	10.1604i	−0.145730	+	0.543874i	0.853991	+	0.520287i	$0.174175\pi$
$349$	−2.72247	+	10.1604i	−0.145730	+	0.543874i	−0.999722	+	0.0235863i	$0.992492\pi$
$350$	−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	$-0.281147\pi$
$353$	14.9904	+	4.01667i	0.797859	+	0.213786i	0.163215	+	0.986590i	$0.447813\pi$
$354$		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	−0.490791	−	0.871278i	$-0.663292\pi$
$359$	7.20920	−	7.20920i	0.380487	−	0.380487i	0.871278	+	0.490791i	$0.163292\pi$
$360$		0			0
$361$	−13.3564	+	7.71133i	−0.702969	+	0.405859i
$362$	−15.1564	+	56.5645i	−0.796604	+	2.97297i
$363$		0			0
$364$	−2.30500	−	51.9815i	−0.120815	−	2.72457i
$365$	−10.6580			−0.557868
$366$		0			0
$367$	13.1818	−	7.61053i	0.688085	−	0.397266i	−0.114809	−	0.993388i	$-0.536626\pi$
$367$	13.1818	−	7.61053i	0.688085	−	0.397266i	0.802894	+	0.596121i	$0.203292\pi$
$368$	−7.15260	−	4.12955i	−0.372855	−	0.215268i
$369$		0			0
$370$	14.4870	+	54.0660i	0.753141	+	2.81076i
$371$	−2.78339	+	10.6950i	−0.144506	+	0.555257i
$372$		0			0
$373$	16.3260	−	28.2774i	0.845326	−	1.46415i	−0.0400122	−	0.999199i	$-0.512740\pi$
$373$	16.3260	−	28.2774i	0.845326	−	1.46415i	0.885338	−	0.464948i	$-0.153927\pi$
$374$	−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	−0.573734	−	0.819042i	$-0.694506\pi$
$379$	6.47610	−	24.1691i	0.332655	−	1.24149i	0.906389	−	0.422444i	$-0.138828\pi$
$380$	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	0.975519	+	0.219917i	$0.0705785\pi$
$383$	4.70967	+	17.5767i	0.240653	+	0.898129i	−0.734866	+	0.678213i	$0.762755\pi$
$384$		0			0
$385$	−1.02672	−	3.72435i	−0.0523264	−	0.189811i
$386$	−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	$-0.950354\pi$
$389$		−	6.12739i		−	0.310671i	0.987862	−	0.155336i	$-0.0496459\pi$
$390$		0			0
$391$			1.27024i			0.0642388i
$392$	63.5204	−	18.0039i	3.20826	−	0.909334i
$393$		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	$-0.475809\pi$
$397$	12.7566	−	3.41813i	0.640237	−	0.171551i	0.564311	+	0.825563i	$0.309142\pi$
$398$	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	0.380395	−	0.924824i	$-0.375788\pi$
$401$	4.95448	+	1.32755i	0.247415	+	0.0662946i	−0.132980	+	0.991119i	$0.542455\pi$
$402$		0			0
$403$	0.520216	+	14.0088i	0.0259138	+	0.697827i
$404$			35.2811i			1.75530i
$405$		0			0
$406$	−0.379042	−	52.6744i	−0.0188115	−	2.61419i
$407$	−2.71676	−	1.56852i	−0.134665	−	0.0777488i
$408$		0			0
$409$	−4.13326	−	15.4255i	−0.204377	−	0.762744i	−0.989639	−	0.143580i	$-0.954138\pi$
$409$	−4.13326	−	15.4255i	−0.204377	−	0.762744i	0.785262	−	0.619164i	$-0.212528\pi$
$410$	−3.37936	−	12.6119i	−0.166895	−	0.622859i
$411$		0			0
$412$	−40.2887	−	23.2607i	−1.98488	−	1.14597i
$413$	−0.281417	−	39.1078i	−0.0138476	−	1.92437i
$414$		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	$-0.782767\pi$
$419$	−12.6468	+	7.30162i	−0.617836	+	0.356708i	0.158190	+	0.987409i	$0.449434\pi$
$420$		0			0
$421$	2.04328	+	2.04328i	0.0995835	+	0.0995835i	0.755143	−	0.655560i	$-0.227567\pi$
$421$	2.04328	+	2.04328i	0.0995835	+	0.0995835i	−0.655560	+	0.755143i	$0.727567\pi$
$422$	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
$427$	1.18753	−	1.20475i	0.0574687	−	0.0583018i
$428$			25.5729i			1.23611i
$429$		0			0
$430$		−	49.5341i		−	2.38875i
$431$	−2.83206	+	10.5694i	−0.136416	+	0.509110i	0.863572	+	0.504225i	$0.168222\pi$
$431$	−2.83206	+	10.5694i	−0.136416	+	0.509110i	−0.999988	+	0.00488525i	$0.998445\pi$
$432$		0			0
$433$	−17.9201	+	31.0385i	−0.861184	+	1.49161i	0.00960365	+	0.999954i	$0.496943\pi$
$433$	−17.9201	+	31.0385i	−0.861184	+	1.49161i	−0.870787	+	0.491660i	$0.836390\pi$
$434$	−27.0757	+	7.46415i	−1.29968	+	0.358291i
$435$		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	$-0.154932\pi$
$439$	0.772225	+	1.33753i	0.0368563	+	0.0638369i	−0.847009	+	0.531579i	$0.821599\pi$
$440$	−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
$448$	−75.4199	−	19.6281i	−3.56326	−	0.927343i
$449$	3.96795	+	14.8086i	0.187259	+	0.698861i	0.994136	+	0.108140i	$0.0344896\pi$
$449$	3.96795	+	14.8086i	0.187259	+	0.698861i	−0.806876	+	0.590720i	$0.798844\pi$
$450$		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
$455$	28.7738	+	6.35845i	1.34894	+	0.298089i
$456$		0			0
$457$	−7.14198	+	26.6542i	−0.334088	+	1.24683i	0.570767	+	0.821112i	$0.306646\pi$
$457$	−7.14198	+	26.6542i	−0.334088	+	1.24683i	−0.904855	+	0.425720i	$0.860021\pi$
$458$	−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	$-0.0652611\pi$
$461$	0.630674	+	2.35371i	0.0293734	+	0.109623i	−0.949683	+	0.313214i	$0.898594\pi$
$462$		0			0
$463$	−15.9059	+	15.9059i	−0.739208	+	0.739208i	−0.972425	−	0.233216i	$-0.925075\pi$
$463$	−15.9059	+	15.9059i	−0.739208	+	0.739208i	0.233216	+	0.972425i	$0.425075\pi$
$464$	−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	$-0.450732\pi$
$467$	6.66294			0.308324			0.154162	+	0.988046i	$0.450732\pi$
$468$		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
$476$	8.75507	+	31.7585i	0.401288	+	1.45565i
$477$		0			0
$478$	17.6467	−	10.1883i	0.807140	−	0.466003i
$479$	5.91010	−	22.0568i	0.270039	−	1.00780i	−0.689054	−	0.724710i	$-0.741974\pi$
$479$	5.91010	−	22.0568i	0.270039	−	1.00780i	0.959093	−	0.283090i	$-0.0913596\pi$
$480$		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	0.0243387	−	0.999704i	$-0.492252\pi$
$487$	12.0330	−	3.22424i	0.545269	−	0.146104i	0.520930	+	0.853600i	$0.325585\pi$
$488$	−5.82501	+	1.56081i	−0.263686	+	0.0706544i
$489$		0			0
$490$	0.849633	+	59.0325i	0.0383825	+	2.66682i
$491$	16.7889	−	9.69310i	0.757674	−	0.437443i	−0.0707859	−	0.997492i	$-0.522551\pi$
$491$	16.7889	−	9.69310i	0.757674	−	0.437443i	0.828460	+	0.560048i	$0.189217\pi$
$492$		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
$497$	−0.0420983	−	5.85029i	−0.00188837	−	0.262421i
$498$		0			0
$499$	−24.6585	−	24.6585i	−1.10386	−	1.10386i	−0.993940	−	0.109925i	$-0.964939\pi$
$499$	−24.6585	−	24.6585i	−1.10386	−	1.10386i	−0.109925	−	0.993940i	$-0.535061\pi$
$500$	−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	$-0.581412\pi$
$503$	−27.3019	−	15.7627i	−1.21733	−	0.702826i	−0.964346	+	0.264644i	$0.914745\pi$
$504$		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	$-0.388842\pi$
$509$	3.80510	+	1.01957i	0.168658	+	0.0451918i	−0.173502	+	0.984834i	$0.555508\pi$
$510$		0			0
$511$	−7.87243	+	4.62100i	−0.348256	+	0.204421i
$512$	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
$518$	34.1419	+	33.6541i	1.50011	+	1.47868i
$519$		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	$-0.578297\pi$
$523$	10.8561	−	6.26775i	0.474703	−	0.274070i	0.718206	+	0.695830i	$0.244963\pi$
$524$	−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
$539$	−2.37314	−	2.30579i	−0.102218	−	0.0993175i
$540$		0			0
$541$	−2.43106	+	2.43106i	−0.104519	+	0.104519i	−0.757433	−	0.652913i	$-0.773547\pi$
$541$	−2.43106	+	2.43106i	−0.104519	+	0.104519i	0.652913	+	0.757433i	$0.273547\pi$
$542$	−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
$553$	−7.86399	+	30.2169i	−0.334411	+	1.28495i
$554$	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	0.975594	−	0.219584i	$-0.0704701\pi$
$557$	40.3737	+	10.8181i	1.71069	+	0.458378i	0.735097	+	0.677962i	$0.237137\pi$
$558$		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	0.458226	+	0.888836i	$0.348485\pi$
$563$	−12.8281	+	22.2190i	−0.540641	+	0.936418i	−0.998867	+	0.0475822i	$0.984848\pi$
$564$		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	−0.868145	−	0.496310i	$-0.834688\pi$
$569$	−20.8100	+	12.0147i	−0.872401	+	0.503681i	−0.00425579	+	0.999991i	$0.501355\pi$
$570$		0			0
$571$			9.57728i			0.400797i	0.979714	+	0.200398i	$0.0642236\pi$
$571$			9.57728i			0.400797i	−0.979714	+	0.200398i	$0.935776\pi$
$572$	9.28978	−	0.344976i	0.388425	−	0.0144242i
$573$		0			0
$574$	−7.96426	−	7.85046i	−0.332422	−	0.327672i
$575$	1.26381	+	2.18898i	0.0527045	+	0.0912868i
$576$		0			0
$577$	−31.4027	+	31.4027i	−1.30731	+	1.30731i	−0.383966	+	0.923347i	$0.625442\pi$
$577$	−31.4027	+	31.4027i	−1.30731	+	1.30731i	−0.923347	+	0.383966i	$0.874558\pi$
$578$	31.0906	−	8.33071i	1.29320	−	0.346512i
$579$		0			0
$580$	−86.8804	−	86.8804i	−3.60751	−	3.60751i
$581$	−3.42472	−	5.83443i	−0.142081	−	0.242053i
$582$		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	$-0.458206\pi$
$587$	−6.09066	−	1.63199i	−0.251388	−	0.0673593i	−0.382312	+	0.924033i	$0.624872\pi$
$588$		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	−0.988881	−	0.148708i	$-0.952489\pi$
$593$	−27.7021	−	27.7021i	−1.13759	−	1.13759i	−0.148708	−	0.988881i	$-0.547511\pi$
$594$		0			0
$595$	−18.6564	+	0.134250i	−0.764839	+	0.00550373i
$596$	−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	$-0.436723\pi$
$601$	28.0748	−	16.2090i	1.14520	−	0.661180i	0.947712	+	0.319126i	$0.103389\pi$
$602$	−21.4764	−	36.5877i	−0.875314	−	1.49120i
$603$		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	$-0.274703\pi$
$607$	7.81574	+	4.51242i	0.317231	+	0.183154i	−0.332927	+	0.942953i	$0.608036\pi$
$608$	−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	0.702325	+	0.711856i	$0.252145\pi$
$613$	−6.48271	+	24.1938i	−0.261834	+	0.977179i	−0.964160	+	0.265323i	$0.914521\pi$
$614$	67.5530	−	39.0017i	2.72622	−	1.57398i
$615$		0			0
$616$	3.13484	+	11.3715i	0.126306	+	0.458169i
$617$	−22.1083	+	5.92389i	−0.890045	+	0.238487i	−0.674736	−	0.738059i	$-0.735743\pi$
$617$	−22.1083	+	5.92389i	−0.890045	+	0.238487i	−0.215309	+	0.976546i	$0.569076\pi$
$618$		0			0
$619$	27.9275	+	27.9275i	1.12250	+	1.12250i	0.991365	+	0.131135i	$0.0418620\pi$
$619$	27.9275	+	27.9275i	1.12250	+	1.12250i	0.131135	+	0.991365i	$0.458138\pi$
$620$	−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	−0.581248	−	0.813726i	$-0.697435\pi$
$631$	−12.1764	−	45.4430i	−0.484736	−	1.80906i	0.0965126	−	0.995332i	$-0.469231\pi$
$632$	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
$637$	24.0102	−	7.77882i	0.951319	−	0.308208i
$638$	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	0.543015	−	0.839723i	$-0.317283\pi$
$641$	2.21029	+	1.27611i	0.0873011	+	0.0504033i	−0.455714	+	0.890126i	$0.650616\pi$
$642$		0			0
$643$	−7.09734	−	26.4876i	−0.279892	−	1.04457i	−0.952492	−	0.304564i	$-0.901489\pi$
$643$	−7.09734	−	26.4876i	−0.279892	−	1.04457i	0.672600	−	0.740006i	$-0.265177\pi$
$644$	2.02251	−	7.77136i	0.0796980	−	0.306235i
$645$		0			0
$646$	−18.2836	+	31.6682i	−0.719360	+	1.24597i
$647$	2.97944	+	5.16054i	0.117134	+	0.202882i	0.918631	−	0.395117i	$-0.129296\pi$
$647$	2.97944	+	5.16054i	0.117134	+	0.202882i	−0.801497	+	0.597999i	$0.795963\pi$
$648$		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	0.992007	−	0.126185i	$-0.0402733\pi$
$653$	9.88229	+	17.1166i	0.386724	+	0.669825i	−0.605283	+	0.796010i	$0.706940\pi$
$654$		0			0
$655$	−34.0874	−	34.0874i	−1.33190	−	1.33190i
$656$	5.94709	+	22.1949i	0.232195	+	0.866563i
$657$		0			0
$658$	−17.7891	−	64.5289i	−0.693492	−	2.51560i
$659$	−0.623376	+	1.07972i	−0.0242833	+	0.0420599i	−0.877912	−	0.478823i	$-0.841064\pi$
$659$	−0.623376	+	1.07972i	−0.0242833	+	0.0420599i	0.853628	+	0.520882i	$0.174397\pi$
$660$		0			0
$661$	−6.22445	+	23.2300i	−0.242103	+	0.903541i	0.732714	+	0.680536i	$0.238253\pi$
$661$	−6.22445	+	23.2300i	−0.242103	+	0.903541i	−0.974817	+	0.223004i	$0.928414\pi$
$662$			80.8932i			3.14400i
$663$		0			0
$664$			24.1175i			0.935940i
$665$	−33.6618	+	34.1498i	−1.30535	+	1.32427i
$666$		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	−0.723619	+	0.690199i	$0.757523\pi$
$673$	−43.6649	+	25.2100i	−1.68316	+	0.971772i	−0.959540	+	0.281573i	$0.909144\pi$
$674$	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
$679$	−33.2225	+	0.239067i	−1.27496	+	0.00917454i
$680$	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	0.973772	+	0.227528i	$0.0730642\pi$
$683$	6.38263	+	23.8203i	0.244224	+	0.911458i	−0.729547	+	0.683930i	$0.760269\pi$
$684$		0			0
$685$	−52.0325	−	30.0410i	−1.98806	−	1.14781i
$686$	26.2222	+	43.2353i	1.00117	+	1.65073i
$687$		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	$-0.126718\pi$
$691$	40.1209	+	10.7504i	1.52627	+	0.408963i	0.604470	+	0.796628i	$0.293385\pi$
$692$	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
$700$	46.6851	+	46.0181i	1.76453	+	1.73932i
$701$			1.87133i			0.0706790i	0.999375	+	0.0353395i	$0.0112513\pi$
$701$			1.87133i			0.0706790i	−0.999375	+	0.0353395i	$0.988749\pi$
$702$		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
$707$	−16.4980	+	4.54811i	−0.620471	+	0.171049i
$708$		0			0
$709$	−1.15519	−	4.31123i	−0.0433841	−	0.161912i	0.940835	−	0.338864i	$-0.110043\pi$
$709$	−1.15519	−	4.31123i	−0.0433841	−	0.161912i	−0.984219	+	0.176953i	$0.943376\pi$
$710$	−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	$-0.951664\pi$
$719$	−9.74009	+	16.8703i	−0.363244	+	0.629157i	0.625249	+	0.780426i	$0.284998\pi$
$720$		0			0
$721$	5.68342	−	21.8382i	0.211662	−	0.813296i
$722$	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	$-0.740179\pi$
$727$	−36.9369			−1.36991			−0.684957	+	0.728583i	$0.740179\pi$
$728$	−87.8541	−	19.4141i	−3.25609	−	0.719533i
$729$		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	$-0.688140\pi$
$733$	7.39416	−	7.39416i	0.273109	−	0.273109i	0.830351	+	0.557241i	$0.188140\pi$
$734$	−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	−0.586112	−	0.810230i	$-0.699342\pi$
$739$	−40.7446	−	10.9175i	−1.49882	−	0.401606i	−0.912703	+	0.408623i	$0.866009\pi$
$740$	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	−0.961977	−	0.273130i	$-0.911941\pi$
$743$	0.209458	−	0.781707i	0.00768426	−	0.0286780i	0.969662	+	0.244452i	$0.0786079\pi$
$744$		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
$749$	−11.9583	+	3.29661i	−0.436945	+	0.120456i
$750$		0			0
$751$	41.4868	−	23.9524i	1.51387	−	0.874035i	0.514006	−	0.857787i	$-0.328161\pi$
$751$	41.4868	−	23.9524i	1.51387	−	0.874035i	0.999868	−	0.0162488i	$-0.00517239\pi$
$752$	−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	0.884004	−	0.467479i	$-0.154838\pi$
$757$	1.02223	+	1.77055i	0.0371534	+	0.0643516i	−0.846851	+	0.531831i	$0.821504\pi$
$758$	−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	$-0.667277\pi$
$761$	−13.8918	+	3.72230i	−0.503578	+	0.134933i	−0.00191784	+	0.999998i	$0.500610\pi$
$762$		0			0
$763$	11.8134	−	6.93430i	0.427674	−	0.251038i
$764$	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	$-0.470999\pi$
$769$	−9.09993	−	2.43832i	−0.328152	−	0.0879280i	−0.419134	+	0.907925i	$0.637666\pi$
$770$	−10.5476	+	0.0759000i	−0.380110	+	0.00273525i
$771$		0			0
$772$	7.91442	+	7.91442i	0.284846	+	0.284846i
$773$	6.89949	+	25.7493i	0.248157	+	0.926136i	0.971770	+	0.235930i	$0.0758136\pi$
$773$	6.89949	+	25.7493i	0.248157	+	0.926136i	−0.723613	+	0.690206i	$0.757520\pi$
$774$		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
$784$	−1.49521	−	103.887i	−0.0534003	−	3.71026i
$785$	0.232374	+	0.232374i	0.00829378	+	0.00829378i
$786$		0			0
$787$	−42.0566	+	11.2690i	−1.49916	+	0.401698i	−0.912817	−	0.408368i	$-0.866098\pi$
$787$	−42.0566	+	11.2690i	−1.49916	+	0.401698i	−0.586339	+	0.810066i	$0.699431\pi$
$788$	50.7975	−	50.7975i	1.80959	−	1.80959i
$789$		0			0
$790$	49.7669	+	86.1987i	1.77063	+	3.06681i
$791$	−16.6254	−	16.3878i	−0.591131	−	0.582684i
$792$		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	$-0.936320\pi$
$797$	−8.97549	+	15.5460i	−0.317928	+	0.550667i	0.662128	+	0.749391i	$0.269654\pi$
$798$		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	0.994971	−	0.100164i	$-0.0319367\pi$
$809$	11.6827	+	20.2350i	0.410741	+	0.711424i	−0.584230	+	0.811588i	$0.698603\pi$
$810$		0			0
$811$	6.31578	−	6.31578i	0.221777	−	0.221777i	−0.587469	−	0.809246i	$-0.699876\pi$
$811$	6.31578	−	6.31578i	0.221777	−	0.221777i	0.809246	+	0.587469i	$0.199876\pi$
$812$	−101.842	−	26.5045i	−3.57395	−	0.930124i
$813$		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	−0.966482	−	0.256736i	$-0.917353\pi$
$821$	−0.0319770	+	0.119340i	−0.00111600	+	0.00416498i	0.965366	+	0.260901i	$0.0840196\pi$
$822$		0			0
$823$	−26.0725	−	15.0529i	−0.908829	−	0.524712i	−0.0287745	−	0.999586i	$-0.509160\pi$
$823$	−26.0725	−	15.0529i	−0.908829	−	0.524712i	−0.880054	+	0.474874i	$0.842494\pi$
$824$	−56.8824	+	56.8824i	−1.98159	+	1.98159i
$825$		0			0
$826$	−103.336	−	26.8934i	−3.59553	−	0.935741i
$827$	−21.5722	+	21.5722i	−0.750140	+	0.750140i	−0.974505	−	0.224365i	$-0.927969\pi$
$827$	−21.5722	+	21.5722i	−0.750140	+	0.750140i	0.224365	+	0.974505i	$0.427969\pi$
$828$		0			0
$829$	−9.38977	−	16.2636i	−0.326120	−	0.564857i	0.655618	−	0.755093i	$-0.272408\pi$
$829$	−9.38977	−	16.2636i	−0.326120	−	0.564857i	−0.981738	+	0.190236i	$0.939075\pi$
$830$	−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	$-0.420434\pi$
$839$	27.4030	−	7.34262i	0.946058	−	0.253495i	0.698689	+	0.715426i	$0.253767\pi$
$840$		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
$847$	−20.0155	+	20.3057i	−0.687741	+	0.697711i
$848$	−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	$-0.379876\pi$
$853$	−16.3889	−	16.3889i	−0.561144	−	0.561144i	−0.929632	+	0.368488i	$0.879876\pi$
$854$	−2.33806	−	3.98317i	−0.0800067	−	0.136301i
$855$		0			0
$856$	42.7132	+	11.4450i	1.45991	+	0.391181i
$857$	−14.4403			−0.493271			−0.246636	−	0.969108i	$-0.579325\pi$
$857$	−14.4403			−0.493271			−0.246636	+	0.969108i	$0.579325\pi$
$858$		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	0.911426	−	0.411464i	$-0.134983\pi$
$863$	14.6873	+	14.6873i	0.499961	+	0.499961i	−0.411464	+	0.911426i	$0.634983\pi$
$864$		0			0
$865$	0.333238	+	1.24366i	0.0113304	+	0.0422858i
$866$	69.1933	+	69.1933i	2.35128	+	2.35128i
$867$		0			0
$868$	0.403746	+	56.1074i	0.0137040	+	1.90441i
$869$	−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
$875$	3.22522	−	1.89315i	0.109032	−	0.0640003i
$876$		0			0
$877$	16.7227	−	4.48084i	0.564687	−	0.151307i	0.0348281	−	0.999393i	$-0.488912\pi$
$877$	16.7227	−	4.48084i	0.564687	−	0.151307i	0.529859	+	0.848086i	$0.322245\pi$
$878$	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	$-0.315583\pi$
$881$	−13.3851	−	23.1836i	−0.450955	−	0.781076i	−0.998446	+	0.0557352i	$0.982250\pi$
$882$		0			0
$883$			41.2346i			1.38766i	0.720141	+	0.693828i	$0.244077\pi$
$883$			41.2346i			1.38766i	−0.720141	+	0.693828i	$0.755923\pi$
$884$	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	$-0.514946\pi$
$887$	23.6672	−	13.6643i	0.794668	−	0.458802i	0.841603	+	0.540096i	$0.181612\pi$
$888$		0			0
$889$	−6.75884	−	24.5173i	−0.226684	−	0.822283i
$890$	−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	−0.0244850	−	0.999700i	$-0.507795\pi$
$907$	24.9677	−	14.4151i	0.829038	−	0.478645i	0.853523	+	0.521055i	$0.174461\pi$
$908$	21.7955	−	81.3418i	0.723308	−	2.69942i
$909$		0			0
$910$	37.1019	−	71.3907i	1.22992	−	2.36658i
$911$	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
$917$	−39.9574	−	10.3990i	−1.31951	−	0.343405i
$918$		0			0
$919$	12.4821	−	21.6196i	0.411745	−	0.713164i	−0.583336	−	0.812231i	$-0.698253\pi$
$919$	12.4821	−	21.6196i	0.411745	−	0.713164i	0.995081	+	0.0990678i	$0.0315861\pi$
$920$	−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	−0.991690	−	0.128651i	$-0.958935\pi$
$929$	−6.01016	−	22.4302i	−0.197187	−	0.735911i	0.794503	−	0.607260i	$-0.207731\pi$
$930$		0			0
$931$	−10.0576	+	39.8190i	−0.329624	+	1.30502i
$932$	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	$0.945762\pi$
$938$	42.5762	−	43.1934i	1.39016	−	1.41031i
$939$		0			0
$940$	−135.212	−	78.0649i	−4.41014	−	2.54620i
$941$	−21.0506	+	21.0506i	−0.686232	+	0.686232i	−0.961397	−	0.275165i	$-0.911267\pi$
$941$	−21.0506	+	21.0506i	−0.686232	+	0.686232i	0.275165	+	0.961397i	$0.411267\pi$
$942$		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	0.0423224	−	0.999104i	$-0.486524\pi$
$947$	−12.9426	−	3.46795i	−0.420577	−	0.112693i	−0.462900	+	0.886411i	$0.653191\pi$
$948$		0			0
$949$	12.4314	−	0.461641i	0.403541	−	0.0149855i
$950$			72.7643i			2.36079i
$951$		0			0
$952$	56.9631	−	0.409903i	1.84618	−	0.0132850i
$953$	13.8070	+	7.97146i	0.447252	+	0.258221i	0.706669	−	0.707544i	$-0.250197\pi$
$953$	13.8070	+	7.97146i	0.447252	+	0.258221i	−0.259417	+	0.965765i	$0.583530\pi$
$954$		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
$959$	−51.4580	+	0.370288i	−1.66166	+	0.0119572i
$960$		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	0.824104	−	0.566439i	$-0.191679\pi$
$967$	8.01251	+	8.01251i	0.257665	+	0.257665i	−0.566439	+	0.824104i	$0.691679\pi$
$968$	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	$-0.582364\pi$
$971$	−38.0478	−	21.9669i	−1.22101	−	0.704951i	−0.965134	+	0.261758i	$0.915698\pi$
$972$		0			0
$973$	10.4041	−	10.5549i	0.333539	−	0.338374i
$974$		−	34.0126i		−	1.08984i
$975$		0			0
$976$			9.49003i			0.303768i
$977$	9.68314	−	36.1380i	0.309791	−	1.15616i	−0.618951	−	0.785430i	$-0.712442\pi$
$977$	9.68314	−	36.1380i	0.309791	−	1.15616i	0.928742	−	0.370727i	$-0.120891\pi$
$978$		0			0
$979$	0.331885	−	0.574842i	0.0106071	−	0.0183720i
$980$	114.354	+	28.8839i	3.65291	+	0.922662i
$981$		0			0
$982$	−13.6993	−	51.1264i	−0.437162	−	1.63151i
$983$	−24.9501	−	24.9501i	−0.795786	−	0.795786i	0.186642	−	0.982428i	$-0.440239\pi$
$983$	−24.9501	−	24.9501i	−0.795786	−	0.795786i	−0.982428	+	0.186642i	$0.940239\pi$
$984$		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	0.790247	−	0.612788i	$-0.209952\pi$
$991$	−4.26766	−	7.39180i	−0.135567	−	0.234808i	−0.925814	+	0.377980i	$0.876619\pi$
$992$	42.1090	−	72.9350i	1.33696	−	2.31569i
$993$		0			0
$994$	−15.4585	−	4.02310i	−0.490314	−	0.127605i
$995$	2.38763	+	8.91077i	0.0756931	+	0.282490i
$996$		0			0
$997$	−30.8124	−	17.7895i	−0.975837	−	0.563400i	−0.0748264	−	0.997197i	$-0.523840\pi$
$997$	−30.8124	−	17.7895i	−0.975837	−	0.563400i	−0.901011	+	0.433797i	$0.857174\pi$
$998$	−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.e.622.8		32
3.2	odd	2		273.2.by.d.76.1	yes	32
7.6	odd	2		819.2.fm.f.622.8		32
13.6	odd	12		819.2.fm.f.370.8		32
21.20	even	2		273.2.by.c.76.1	✓	32
39.32	even	12		273.2.by.c.97.1	yes	32
91.6	even	12	inner	819.2.fm.e.370.8		32
273.188	odd	12		273.2.by.d.97.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.1	✓	32	21.20	even	2
273.2.by.c.97.1	yes	32	39.32	even	12
273.2.by.d.76.1	yes	32	3.2	odd	2
273.2.by.d.97.1	yes	32	273.188	odd	12
819.2.fm.e.370.8		32	91.6	even	12	inner
819.2.fm.e.622.8		32	1.1	even	1	trivial
819.2.fm.f.370.8		32	13.6	odd	12
819.2.fm.f.622.8		32	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.706652 - 2.63726i) q^{2} +(-4.72373 - 2.72725i) q^{4} +(2.18431 - 2.18431i) q^{5} +(0.666364 - 2.56046i) q^{7} +(-6.66928 + 6.66928i) q^{8} +O(q^{10})\)	\(q+(0.706652 - 2.63726i) q^{2} +(-4.72373 - 2.72725i) q^{4} +(2.18431 - 2.18431i) q^{5} +(0.666364 - 2.56046i) q^{7} +(-6.66928 + 6.66928i) q^{8} +(-4.21705 - 7.30414i) q^{10} +(0.456585 + 0.122342i) q^{11} +(-2.45314 + 2.64236i) q^{13} +(-6.28171 - 3.56673i) q^{14} +(7.42128 + 12.8540i) q^{16} +(1.14138 - 1.97693i) q^{17} +(-1.51851 - 5.66717i) q^{19} +(-16.2753 + 4.36094i) q^{20} +(0.645294 - 1.11768i) q^{22} +(-0.481898 + 0.278224i) q^{23} -4.54242i q^{25} +(5.23509 + 8.33681i) q^{26} +(-10.1307 + 10.2776i) q^{28} +(3.64605 + 6.31515i) q^{29} +(2.74924 - 2.74924i) q^{31} +(20.9229 - 5.60626i) q^{32} +(-4.40713 - 4.40713i) q^{34} +(-4.13729 - 7.04838i) q^{35} +(-6.41041 - 1.71767i) q^{37} -16.0189 q^{38} +29.1356i q^{40} +(1.49535 + 0.400678i) q^{41} +(5.08624 + 2.93654i) q^{43} +(-1.82313 - 1.82313i) q^{44} +(0.393215 + 1.46750i) q^{46} +(6.55220 + 6.55220i) q^{47} +(-6.11192 - 3.41240i) q^{49} +(-11.9795 - 3.20991i) q^{50} +(18.7944 - 5.79150i) q^{52} -4.17698 q^{53} +(1.26456 - 0.730092i) q^{55} +(12.6323 + 21.5206i) q^{56} +(19.2312 - 5.15298i) q^{58} +(14.2781 - 3.82579i) q^{59} +(0.553719 + 0.319690i) q^{61} +(-5.30771 - 9.19322i) q^{62} -29.4556i q^{64} +(0.413319 + 11.1302i) q^{65} +(-2.17304 + 8.10989i) q^{67} +(-10.7832 + 6.22567i) q^{68} +(-21.5120 + 5.93037i) q^{70} +(2.13591 - 0.572316i) q^{71} +(-2.43968 - 2.43968i) q^{73} +(-9.05986 + 15.6921i) q^{74} +(-8.28273 + 30.9116i) q^{76} +(0.617503 - 1.08755i) q^{77} -11.8014 q^{79} +(44.2876 + 11.8668i) q^{80} +(2.11339 - 3.66049i) q^{82} +(1.80810 - 1.80810i) q^{83} +(-1.82510 - 6.81137i) q^{85} +(11.3386 - 11.3386i) q^{86} +(-3.86103 + 2.22917i) q^{88} +(0.363443 - 1.35639i) q^{89} +(5.13099 + 8.04195i) q^{91} +3.03514 q^{92} +(21.9100 - 12.6497i) q^{94} +(-15.6957 - 9.06194i) q^{95} +(-3.25005 - 12.1294i) q^{97} +(-13.3184 + 13.7073i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 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 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * 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 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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