LMFDB - Embedded newform 820.2.y.a.137.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			137.12
Character	$\chi$	$=$	820.137
Dual form			820.2.y.a.413.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.124058 + 0.0513864i) q^{3} +(-0.0384730 - 2.23574i) q^{5} +(-1.97802 + 4.77536i) q^{7} +(-2.10857 - 2.10857i) q^{9} +(1.44680 - 0.599283i) q^{11} +(2.66954 + 1.10576i) q^{13} +(0.110114 - 0.279338i) q^{15} +(3.55865 - 1.47404i) q^{17} +(7.04336 + 2.91746i) q^{19} +(-0.490777 + 0.490777i) q^{21} +(3.15426 + 3.15426i) q^{23} +(-4.99704 + 0.172031i) q^{25} +(-0.307392 - 0.742110i) q^{27} +(8.72309 - 3.61322i) q^{29} +0.581838i q^{31} +0.210282 q^{33} +(10.7525 + 4.23861i) q^{35} +(3.55128 + 3.55128i) q^{37} +(0.274356 + 0.274356i) q^{39} +(3.07916 - 5.61416i) q^{41} -7.84817 q^{43} +(-4.63309 + 4.79533i) q^{45} +(2.27624 - 0.942851i) q^{47} +(-13.9418 - 13.9418i) q^{49} +0.517223 q^{51} +(-1.76450 + 4.25988i) q^{53} +(-1.39550 - 3.21160i) q^{55} +(0.723866 + 0.723866i) q^{57} +2.23104i q^{59} +(2.78581 + 2.78581i) q^{61} +(14.2400 - 5.89839i) q^{63} +(2.36948 - 6.01092i) q^{65} +(1.81373 - 0.751271i) q^{67} +(0.229224 + 0.553397i) q^{69} +(-3.41502 - 8.24458i) q^{71} +6.77830 q^{73} +(-0.628762 - 0.235438i) q^{75} +8.09438i q^{77} +(3.17162 + 7.65698i) q^{79} +8.83805i q^{81} +(-2.19939 + 2.19939i) q^{83} +(-3.43248 - 7.89948i) q^{85} +1.26784 q^{87} +(-10.7228 + 4.44154i) q^{89} +(-10.5608 + 10.5608i) q^{91} +(-0.0298985 + 0.0721815i) q^{93} +(6.25169 - 15.8594i) q^{95} +(6.98542 + 16.8643i) q^{97} +(-4.31431 - 1.78704i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.124058	+	0.0513864i	0.0716248	+	0.0296680i	0.418208	−	0.908351i	$-0.362658\pi$
$3$	0.124058	+	0.0513864i	0.0716248	+	0.0296680i	−0.346583	+	0.938019i	$0.612658\pi$
$4$		0			0
$5$	−0.0384730	−	2.23574i	−0.0172057	−	0.999852i
$5$	−0.0384730	−	2.23574i	−0.0172057	−	0.999852i
$6$		0			0
$7$	−1.97802	+	4.77536i	−0.747621	+	1.80492i	−0.176016	+	0.984387i	$0.556321\pi$
$7$	−1.97802	+	4.77536i	−0.747621	+	1.80492i	−0.571605	+	0.820529i	$0.693679\pi$
$8$		0			0
$9$	−2.10857	−	2.10857i	−0.702857	−	0.702857i
$10$		0			0
$11$	1.44680	−	0.599283i	0.436226	−	0.180691i	−0.153753	−	0.988109i	$-0.549136\pi$
$11$	1.44680	−	0.599283i	0.436226	−	0.180691i	0.589979	+	0.807419i	$0.299136\pi$
$12$		0			0
$13$	2.66954	+	1.10576i	0.740396	+	0.306682i	0.720816	−	0.693126i	$-0.243767\pi$
$13$	2.66954	+	1.10576i	0.740396	+	0.306682i	0.0195797	+	0.999808i	$0.493767\pi$
$14$		0			0
$15$	0.110114	−	0.279338i	0.0284312	−	0.0721246i
$16$		0			0
$17$	3.55865	−	1.47404i	0.863098	−	0.357507i	0.0931799	−	0.995649i	$-0.470297\pi$
$17$	3.55865	−	1.47404i	0.863098	−	0.357507i	0.769918	+	0.638142i	$0.220297\pi$
$18$		0			0
$19$	7.04336	+	2.91746i	1.61586	+	0.669311i	0.993543	−	0.113456i	$-0.0361921\pi$
$19$	7.04336	+	2.91746i	1.61586	+	0.669311i	0.622316	+	0.782767i	$0.286192\pi$
$20$		0			0
$21$	−0.490777	+	0.490777i	−0.107096	+	0.107096i
$22$		0			0
$23$	3.15426	+	3.15426i	0.657709	+	0.657709i	0.954837	−	0.297129i	$-0.0960290\pi$
$23$	3.15426	+	3.15426i	0.657709	+	0.657709i	−0.297129	+	0.954837i	$0.596029\pi$
$24$		0			0
$25$	−4.99704	+	0.172031i	−0.999408	+	0.0344062i
$26$		0			0
$27$	−0.307392	−	0.742110i	−0.0591576	−	0.142819i
$28$		0			0
$29$	8.72309	−	3.61322i	1.61984	−	0.670959i	0.625798	−	0.779985i	$-0.284773\pi$
$29$	8.72309	−	3.61322i	1.61984	−	0.670959i	0.994039	+	0.109026i	$0.0347733\pi$
$30$		0			0
$31$			0.581838i			0.104501i	0.998634	+	0.0522506i	$0.0166394\pi$
$31$			0.581838i			0.104501i	−0.998634	+	0.0522506i	$0.983361\pi$
$32$		0			0
$33$	0.210282			0.0366053
$34$		0			0
$35$	10.7525	+	4.23861i	1.81751	+	0.716455i
$36$		0			0
$37$	3.55128	+	3.55128i	0.583827	+	0.583827i	0.935953	−	0.352126i	$-0.114541\pi$
$37$	3.55128	+	3.55128i	0.583827	+	0.583827i	−0.352126	+	0.935953i	$0.614541\pi$
$38$		0			0
$39$	0.274356	+	0.274356i	0.0439321	+	0.0439321i
$40$		0			0
$41$	3.07916	−	5.61416i	0.480885	−	0.876784i
$41$	3.07916	−	5.61416i	0.480885	−	0.876784i
$42$		0			0
$43$	−7.84817			−1.19683			−0.598417	−	0.801185i	$-0.704203\pi$
$43$	−7.84817			−1.19683			−0.598417	+	0.801185i	$0.704203\pi$
$44$		0			0
$45$	−4.63309	+	4.79533i	−0.690660	+	0.714846i
$46$		0			0
$47$	2.27624	−	0.942851i	0.332024	−	0.137529i	−0.210442	−	0.977606i	$-0.567490\pi$
$47$	2.27624	−	0.942851i	0.332024	−	0.137529i	0.542467	+	0.840077i	$0.317490\pi$
$48$		0			0
$49$	−13.9418	−	13.9418i	−1.99168	−	1.99168i
$50$		0			0
$51$	0.517223			0.0724257
$52$		0			0
$53$	−1.76450	+	4.25988i	−0.242373	+	0.585139i	−0.997518	−	0.0704187i	$-0.977566\pi$
$53$	−1.76450	+	4.25988i	−0.242373	+	0.585139i	0.755145	+	0.655558i	$0.227566\pi$
$54$		0			0
$55$	−1.39550	−	3.21160i	−0.188170	−	0.433053i
$56$		0			0
$57$	0.723866	+	0.723866i	0.0958784	+	0.0958784i
$58$		0			0
$59$			2.23104i			0.290456i	0.989398	+	0.145228i	$0.0463916\pi$
$59$			2.23104i			0.290456i	−0.989398	+	0.145228i	$0.953608\pi$
$60$		0			0
$61$	2.78581	+	2.78581i	0.356687	+	0.356687i	0.862590	−	0.505904i	$-0.168841\pi$
$61$	2.78581	+	2.78581i	0.356687	+	0.356687i	−0.505904	+	0.862590i	$0.668841\pi$
$62$		0			0
$63$	14.2400	−	5.89839i	1.79407	−	0.743127i
$64$		0			0
$65$	2.36948	−	6.01092i	0.293898	−	0.745563i
$66$		0			0
$67$	1.81373	−	0.751271i	0.221582	−	0.0917823i	−0.269131	−	0.963104i	$-0.586736\pi$
$67$	1.81373	−	0.751271i	0.221582	−	0.0917823i	0.490713	+	0.871321i	$0.336736\pi$
$68$		0			0
$69$	0.229224	+	0.553397i	0.0275954	+	0.0666211i
$70$		0			0
$71$	−3.41502	−	8.24458i	−0.405288	−	0.978452i	−0.986360	−	0.164600i	$-0.947367\pi$
$71$	−3.41502	−	8.24458i	−0.405288	−	0.978452i	0.581072	−	0.813852i	$-0.302633\pi$
$72$		0			0
$73$	6.77830			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$73$	6.77830			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$74$		0			0
$75$	−0.628762	−	0.235438i	−0.0726031	−	0.0271861i
$76$		0			0
$77$			8.09438i			0.922440i
$78$		0			0
$79$	3.17162	+	7.65698i	0.356836	+	0.861477i	0.995741	+	0.0921922i	$0.0293874\pi$
$79$	3.17162	+	7.65698i	0.356836	+	0.861477i	−0.638906	+	0.769285i	$0.720613\pi$
$80$		0			0
$81$			8.83805i			0.982005i
$82$		0			0
$83$	−2.19939	+	2.19939i	−0.241415	+	0.241415i	−0.817435	−	0.576020i	$-0.804605\pi$
$83$	−2.19939	+	2.19939i	−0.241415	+	0.241415i	0.576020	+	0.817435i	$0.304605\pi$
$84$		0			0
$85$	−3.43248	−	7.89948i	−0.372304	−	0.856819i
$86$		0			0
$87$	1.26784			0.135926
$88$		0			0
$89$	−10.7228	+	4.44154i	−1.13662	+	0.470802i	−0.870025	−	0.493008i	$-0.835898\pi$
$89$	−10.7228	+	4.44154i	−1.13662	+	0.470802i	−0.266592	+	0.963810i	$0.585898\pi$
$90$		0			0
$91$	−10.5608	+	10.5608i	−1.10707	+	1.10707i
$92$		0			0
$93$	−0.0298985	+	0.0721815i	−0.00310034	+	0.00748487i
$94$		0			0
$95$	6.25169	−	15.8594i	0.641410	−	1.62714i
$96$		0			0
$97$	6.98542	+	16.8643i	0.709262	+	1.71231i	0.701837	+	0.712338i	$0.252364\pi$
$97$	6.98542	+	16.8643i	0.709262	+	1.71231i	0.00742554	+	0.999972i	$0.497636\pi$
$98$		0			0
$99$	−4.31431	−	1.78704i	−0.433604	−	0.179605i
$100$		0			0
$101$	−4.83064	+	11.6622i	−0.480667	+	1.16043i	0.478626	+	0.878019i	$0.341135\pi$
$101$	−4.83064	+	11.6622i	−0.480667	+	1.16043i	−0.959293	+	0.282413i	$0.908865\pi$
$102$		0			0
$103$			1.93720i			0.190878i	0.995435	+	0.0954391i	$0.0304255\pi$
$103$			1.93720i			0.190878i	−0.995435	+	0.0954391i	$0.969574\pi$
$104$		0			0
$105$	1.11613	+	1.07837i	0.108923	+	0.105238i
$106$		0			0
$107$	8.75910	−	8.75910i	0.846774	−	0.846774i	−0.142955	−	0.989729i	$-0.545660\pi$
$107$	8.75910	−	8.75910i	0.846774	−	0.846774i	0.989729	+	0.142955i	$0.0456603\pi$
$108$		0			0
$109$	2.53161	−	6.11185i	0.242484	−	0.585409i	−0.755044	−	0.655674i	$-0.772385\pi$
$109$	2.53161	−	6.11185i	0.242484	−	0.585409i	0.997528	+	0.0702651i	$0.0223845\pi$
$110$		0			0
$111$	0.258076	+	0.623051i	0.0244955	+	0.0591374i
$112$		0			0
$113$	−7.53604	−	7.53604i	−0.708931	−	0.708931i	0.257379	−	0.966311i	$-0.417141\pi$
$113$	−7.53604	−	7.53604i	−0.708931	−	0.708931i	−0.966311	+	0.257379i	$0.917141\pi$
$114$		0			0
$115$	6.93075	−	7.17345i	0.646295	−	0.668928i
$116$		0			0
$117$	−3.29734	−	7.96047i	−0.304839	−	0.735946i
$118$		0			0
$119$			19.9095i			1.82510i
$120$		0			0
$121$	−6.04409	+	6.04409i	−0.549463	+	0.549463i
$122$		0			0
$123$	0.670485	−	0.538253i	0.0604556	−	0.0485326i
$124$		0			0
$125$	0.576867	+	11.1654i	0.0515966	+	0.998668i
$126$		0			0
$127$	5.23641	−	5.23641i	0.464656	−	0.464656i	−0.435522	−	0.900178i	$-0.643436\pi$
$127$	5.23641	−	5.23641i	0.464656	−	0.464656i	0.900178	+	0.435522i	$0.143436\pi$
$128$		0			0
$129$	−0.973626	−	0.403289i	−0.0857230	−	0.0355076i
$130$		0			0
$131$	−2.28279	+	2.28279i	−0.199448	+	0.199448i	−0.799764	−	0.600315i	$-0.795042\pi$
$131$	−2.28279	+	2.28279i	−0.199448	+	0.199448i	0.600315	+	0.799764i	$0.295042\pi$
$132$		0			0
$133$	−27.8638	+	27.8638i	−2.41610	+	2.41610i
$134$		0			0
$135$	−1.64734	+	0.715799i	−0.141780	+	0.0616061i
$136$		0			0
$137$	15.0682	−	6.24145i	1.28736	−	0.533243i	0.369164	−	0.929364i	$-0.379644\pi$
$137$	15.0682	−	6.24145i	1.28736	−	0.533243i	0.918198	+	0.396121i	$0.129644\pi$
$138$		0			0
$139$		−	18.6315i		−	1.58030i	−0.612913	−	0.790151i	$-0.710002\pi$
$139$		−	18.6315i		−	1.58030i	0.612913	−	0.790151i	$-0.289998\pi$
$140$		0			0
$141$	0.330835			0.0278614
$142$		0			0
$143$	4.52494			0.378395
$144$		0			0
$145$	−8.41382	−	19.3635i	−0.698730	−	1.60805i
$146$		0			0
$147$	−1.01317	−	2.44600i	−0.0835646	−	0.201743i
$148$		0			0
$149$	−11.6445	−	4.82329i	−0.953951	−	0.395140i	−0.149237	−	0.988801i	$-0.547682\pi$
$149$	−11.6445	−	4.82329i	−0.953951	−	0.395140i	−0.804715	+	0.593662i	$0.797682\pi$
$150$		0			0
$151$	−1.10497	+	0.457695i	−0.0899215	+	0.0372467i	−0.427191	−	0.904162i	$-0.640497\pi$
$151$	−1.10497	+	0.457695i	−0.0899215	+	0.0372467i	0.337269	+	0.941408i	$0.390497\pi$
$152$		0			0
$153$	−10.6118	−	4.39554i	−0.857911	−	0.355358i
$154$		0			0
$155$	1.30084	−	0.0223850i	0.104486	−	0.00179801i
$156$		0			0
$157$	5.84494	+	2.42105i	0.466477	+	0.193221i	0.603526	−	0.797343i	$-0.293762\pi$
$157$	5.84494	+	2.42105i	0.466477	+	0.193221i	−0.137049	+	0.990564i	$0.543762\pi$
$158$		0			0
$159$	−0.437800	+	0.437800i	−0.0347198	+	0.0347198i
$160$		0			0
$161$	−21.3019	+	8.82355i	−1.67883	+	0.695393i
$162$		0			0
$163$	−10.0081	−	10.0081i	−0.783896	−	0.783896i	0.196590	−	0.980486i	$-0.437013\pi$
$163$	−10.0081	−	10.0081i	−0.783896	−	0.783896i	−0.980486	+	0.196590i	$0.937013\pi$
$164$		0			0
$165$	−0.00809016	−	0.470134i	−0.000629818	−	0.0365999i
$166$		0			0
$167$	−3.93896	+	9.50948i	−0.304806	+	0.735866i	0.695052	+	0.718960i	$0.255382\pi$
$167$	−3.93896	+	9.50948i	−0.304806	+	0.735866i	−0.999857	+	0.0169058i	$0.994618\pi$
$168$		0			0
$169$	−3.28867	−	3.28867i	−0.252975	−	0.252975i
$170$		0			0
$171$	−8.69977	−	21.0031i	−0.665288	−	1.60615i
$172$		0			0
$173$		−	19.0543i		−	1.44867i	−0.689449	−	0.724334i	$-0.742147\pi$
$173$		−	19.0543i		−	1.44867i	0.689449	−	0.724334i	$-0.257853\pi$
$174$		0			0
$175$	9.06273	−	24.2029i	0.685078	−	1.82957i
$176$		0			0
$177$	−0.114645	+	0.276777i	−0.00861724	+	0.0208039i
$178$		0			0
$179$	−7.03366	+	16.9808i	−0.525721	+	1.26920i	0.408582	+	0.912721i	$0.366023\pi$
$179$	−7.03366	+	16.9808i	−0.525721	+	1.26920i	−0.934303	+	0.356480i	$0.883977\pi$
$180$		0			0
$181$	2.19045	−	5.28821i	0.162815	−	0.393070i	−0.821326	−	0.570459i	$-0.806765\pi$
$181$	2.19045	−	5.28821i	0.162815	−	0.393070i	0.984141	+	0.177390i	$0.0567653\pi$
$182$		0			0
$183$	0.202449	+	0.488754i	0.0149654	+	0.0361298i
$184$		0			0
$185$	7.80310	−	8.07635i	0.573695	−	0.593785i
$186$		0			0
$187$	4.26527	−	4.26527i	0.311908	−	0.311908i
$188$		0			0
$189$	4.15187			0.302004
$190$		0			0
$191$	−11.6232	−	4.81450i	−0.841027	−	0.348365i	−0.0797686	−	0.996813i	$-0.525418\pi$
$191$	−11.6232	−	4.81450i	−0.841027	−	0.348365i	−0.761258	+	0.648449i	$0.775418\pi$
$192$		0			0
$193$	−5.50875	−	2.28180i	−0.396528	−	0.164247i	0.175504	−	0.984479i	$-0.443845\pi$
$193$	−5.50875	−	2.28180i	−0.396528	−	0.164247i	−0.572032	+	0.820231i	$0.693845\pi$
$194$		0			0
$195$	0.602832	−	0.623942i	0.0431697	−	0.0446814i
$196$		0			0
$197$		−	9.70195i		−	0.691235i	−0.938375	−	0.345618i	$-0.887669\pi$
$197$		−	9.70195i		−	0.691235i	0.938375	−	0.345618i	$-0.112331\pi$
$198$		0			0
$199$	9.74422	−	23.5246i	0.690749	−	1.66762i	−0.0525160	−	0.998620i	$-0.516724\pi$
$199$	9.74422	−	23.5246i	0.690749	−	1.66762i	0.743265	−	0.668997i	$-0.233276\pi$
$200$		0			0
$201$	0.263612			0.0185938
$202$		0			0
$203$			48.8029i			3.42529i
$204$		0			0
$205$	−12.6702	−	6.66821i	−0.884928	−	0.465728i
$206$		0			0
$207$		−	13.3020i		−	0.924551i
$208$		0			0
$209$	11.9387			0.825818
$210$		0			0
$211$	−9.05819	+	21.8684i	−0.623591	+	1.50548i	0.223867	+	0.974620i	$0.428132\pi$
$211$	−9.05819	+	21.8684i	−0.623591	+	1.50548i	−0.847458	+	0.530863i	$0.821868\pi$
$212$		0			0
$213$		−	1.19829i		−	0.0821055i
$214$		0			0
$215$	0.301943	+	17.5464i	0.0205923	+	1.19666i
$216$		0			0
$217$	−2.77848	−	1.15089i	−0.188616	−	0.0781272i
$218$		0			0
$219$	0.840901	+	0.348313i	0.0568228	+	0.0235368i
$220$		0			0
$221$	11.1299			0.748675
$222$		0			0
$223$	−6.90096	+	6.90096i	−0.462122	+	0.462122i	−0.899351	−	0.437228i	$-0.855960\pi$
$223$	−6.90096	+	6.90096i	−0.462122	+	0.462122i	0.437228	+	0.899351i	$0.355960\pi$
$224$		0			0
$225$	10.8994	+	10.1739i	0.726623	+	0.678258i
$226$		0			0
$227$	7.29338	+	17.6078i	0.484079	+	1.16867i	0.957655	+	0.287917i	$0.0929626\pi$
$227$	7.29338	+	17.6078i	0.484079	+	1.16867i	−0.473577	+	0.880753i	$0.657037\pi$
$228$		0			0
$229$	5.79728	−	13.9959i	0.383095	−	0.924873i	−0.608269	−	0.793731i	$-0.708136\pi$
$229$	5.79728	−	13.9959i	0.383095	−	0.924873i	0.991364	−	0.131142i	$-0.0418643\pi$
$230$		0			0
$231$	−0.415941	+	1.00417i	−0.0273669	+	0.0660695i
$232$		0			0
$233$	−4.05421	+	9.78773i	−0.265600	+	0.641216i	−0.999267	−	0.0382943i	$-0.987808\pi$
$233$	−4.05421	+	9.78773i	−0.265600	+	0.641216i	0.733666	+	0.679510i	$0.237808\pi$
$234$		0			0
$235$	−2.19554	−	5.05281i	−0.143221	−	0.329609i
$236$		0			0
$237$			1.11289i			0.0722897i
$238$		0			0
$239$	−4.54233	−	10.9662i	−0.293819	−	0.709342i	−0.999999	−	0.00130963i	$-0.999583\pi$
$239$	−4.54233	−	10.9662i	−0.293819	−	0.709342i	0.706180	−	0.708032i	$-0.250417\pi$
$240$		0			0
$241$	−0.769654	−	0.769654i	−0.0495778	−	0.0495778i	0.681883	−	0.731461i	$-0.261161\pi$
$241$	−0.769654	−	0.769654i	−0.0495778	−	0.0495778i	−0.731461	+	0.681883i	$0.761161\pi$
$242$		0			0
$243$	−1.37633	+	3.32276i	−0.0882917	+	0.213155i
$244$		0			0
$245$	−30.6337	+	31.7065i	−1.95712	+	2.02565i
$246$		0			0
$247$	15.5765	+	15.5765i	0.991110	+	0.991110i
$248$		0			0
$249$	−0.385871	+	0.159833i	−0.0244536	+	0.0101290i
$250$		0			0
$251$	−0.221906	+	0.221906i	−0.0140066	+	0.0140066i	−0.714075	−	0.700069i	$-0.753153\pi$
$251$	−0.221906	+	0.221906i	−0.0140066	+	0.0140066i	0.700069	+	0.714075i	$0.253153\pi$
$252$		0			0
$253$	6.45388	+	2.67328i	0.405752	+	0.168068i
$254$		0			0
$255$	−0.0198991	−	1.15638i	−0.00124613	−	0.0724150i
$256$		0			0
$257$	−21.1679	−	8.76802i	−1.32042	−	0.546934i	−0.392510	−	0.919748i	$-0.628393\pi$
$257$	−21.1679	−	8.76802i	−1.32042	−	0.546934i	−0.927906	+	0.372813i	$0.878393\pi$
$258$		0			0
$259$	−23.9831	+	9.93414i	−1.49024	+	0.617277i
$260$		0			0
$261$	−26.0120	−	10.7745i	−1.61010	−	0.666926i
$262$		0			0
$263$	4.00664	+	9.67289i	0.247060	+	0.596456i	0.997952	−	0.0639695i	$-0.0203760\pi$
$263$	4.00664	+	9.67289i	0.247060	+	0.596456i	−0.750892	+	0.660425i	$0.770376\pi$
$264$		0			0
$265$	9.59185	+	3.78107i	0.589223	+	0.232269i
$266$		0			0
$267$	−1.55848			−0.0953777
$268$		0			0
$269$	19.6796			1.19989			0.599944	−	0.800042i	$-0.295190\pi$
$269$	19.6796			1.19989			0.599944	+	0.800042i	$0.295190\pi$
$270$		0			0
$271$		−	0.451821i		−	0.0274462i	−0.999906	−	0.0137231i	$-0.995632\pi$
$271$		−	0.451821i		−	0.0274462i	0.999906	−	0.0137231i	$-0.00436834\pi$
$272$		0			0
$273$	−1.85283	+	0.767466i	−0.112138	+	0.0464492i
$274$		0			0
$275$	−7.12661	+	3.24354i	−0.429751	+	0.195593i
$276$		0			0
$277$	−3.27930	+	3.27930i	−0.197034	+	0.197034i	−0.798727	−	0.601693i	$-0.794493\pi$
$277$	−3.27930	+	3.27930i	−0.197034	+	0.197034i	0.601693	+	0.798727i	$0.294493\pi$
$278$		0			0
$279$	1.22685	−	1.22685i	0.0734493	−	0.0734493i
$280$		0			0
$281$	−1.04096	−	0.431179i	−0.0620984	−	0.0257220i	0.351418	−	0.936219i	$-0.385700\pi$
$281$	−1.04096	−	0.431179i	−0.0620984	−	0.0257220i	−0.413516	+	0.910497i	$0.635700\pi$
$282$		0			0
$283$	−8.48943	+	8.48943i	−0.504644	+	0.504644i	−0.912878	−	0.408234i	$-0.866145\pi$
$283$	−8.48943	+	8.48943i	−0.504644	+	0.504644i	0.408234	+	0.912878i	$0.366145\pi$
$284$		0			0
$285$	1.59053	−	1.64622i	0.0942146	−	0.0975139i
$286$		0			0
$287$	20.7190	+	25.8090i	1.22300	+	1.52346i
$288$		0			0
$289$	−1.52965	+	1.52965i	−0.0899793	+	0.0899793i
$290$		0			0
$291$			2.45110i			0.143686i
$292$		0			0
$293$	0.463834	+	1.11979i	0.0270975	+	0.0654191i	0.936849	−	0.349734i	$-0.113728\pi$
$293$	0.463834	+	1.11979i	0.0270975	+	0.0654191i	−0.909752	+	0.415153i	$0.863728\pi$
$294$		0			0
$295$	4.98801	−	0.0858347i	0.290413	−	0.00499749i
$296$		0			0
$297$	−0.889468	−	0.889468i	−0.0516122	−	0.0516122i
$298$		0			0
$299$	4.93256	+	11.9083i	0.285258	+	0.688673i
$300$		0			0
$301$	15.5238	−	37.4778i	0.894778	−	2.16019i
$302$		0			0
$303$	−1.19856	+	1.19856i	−0.0688553	+	0.0688553i
$304$		0			0
$305$	6.12116	−	6.33552i	0.350497	−	0.362771i
$306$		0			0
$307$		−	1.60008i		−	0.0913215i	−0.998957	−	0.0456607i	$-0.985461\pi$
$307$		−	1.60008i		−	0.0913215i	0.998957	−	0.0456607i	$-0.0145393\pi$
$308$		0			0
$309$	−0.0995458	+	0.240325i	−0.00566297	+	0.0136716i
$310$		0			0
$311$	13.7665	+	5.70228i	0.780628	+	0.323347i	0.737169	−	0.675708i	$-0.236162\pi$
$311$	13.7665	+	5.70228i	0.780628	+	0.323347i	0.0434593	+	0.999055i	$0.486162\pi$
$312$		0			0
$313$	−0.326936	−	0.789294i	−0.0184795	−	0.0446135i	0.914370	−	0.404879i	$-0.132686\pi$
$313$	−0.326936	−	0.789294i	−0.0184795	−	0.0446135i	−0.932850	+	0.360265i	$0.882686\pi$
$314$		0			0
$315$	−13.7351	−	31.6099i	−0.773886	−	1.78102i
$316$		0			0
$317$	3.45993	−	8.35302i	0.194329	−	0.469152i	−0.796439	−	0.604719i	$-0.793286\pi$
$317$	3.45993	−	8.35302i	0.194329	−	0.469152i	0.990768	+	0.135567i	$0.0432855\pi$
$318$		0			0
$319$	10.4552	−	10.4552i	0.585379	−	0.585379i
$320$		0			0
$321$	1.53673	−	0.636536i	0.0857721	−	0.0355280i
$322$		0			0
$323$	29.3653			1.63393
$324$		0			0
$325$	−13.5300	−	5.06627i	−0.750509	−	0.281026i
$326$		0			0
$327$	0.628132	−	0.628132i	0.0347358	−	0.0347358i
$328$		0			0
$329$			12.7349i			0.702095i
$330$		0			0
$331$	−9.36169	−	22.6011i	−0.514565	−	1.24227i	−0.941201	−	0.337847i	$-0.890302\pi$
$331$	−9.36169	−	22.6011i	−0.514565	−	1.24227i	0.426636	−	0.904423i	$-0.359698\pi$
$332$		0			0
$333$		−	14.9762i		−	0.820693i
$334$		0			0
$335$	−1.74942	−	4.02612i	−0.0955812	−	0.219970i
$336$		0			0
$337$	−13.5956			−0.740598			−0.370299	−	0.928913i	$-0.620745\pi$
$337$	−13.5956			−0.740598			−0.370299	+	0.928913i	$0.620745\pi$
$338$		0			0
$339$	−0.547655	−	1.32216i	−0.0297445	−	0.0718096i
$340$		0			0
$341$	0.348686	+	0.841802i	0.0188824	+	0.0455861i
$342$		0			0
$343$	60.7264	−	25.1537i	3.27892	−	1.35817i
$344$		0			0
$345$	1.22843	−	0.533776i	0.0661365	−	0.0287376i
$346$		0			0
$347$	25.7053	−	10.6475i	1.37993	−	0.571587i	0.435469	−	0.900204i	$-0.356582\pi$
$347$	25.7053	−	10.6475i	1.37993	−	0.571587i	0.944463	+	0.328617i	$0.106582\pi$
$348$		0			0
$349$	−1.05562	−	1.05562i	−0.0565061	−	0.0565061i	0.678289	−	0.734795i	$-0.262722\pi$
$349$	−1.05562	−	1.05562i	−0.0565061	−	0.0565061i	−0.734795	+	0.678289i	$0.762722\pi$
$350$		0			0
$351$		−	2.32099i		−	0.123885i
$352$		0			0
$353$	−16.9283	−	16.9283i	−0.901000	−	0.901000i	0.0945227	−	0.995523i	$-0.469868\pi$
$353$	−16.9283	−	16.9283i	−0.901000	−	0.901000i	−0.995523	+	0.0945227i	$0.969868\pi$
$354$		0			0
$355$	−18.3013	+	7.95228i	−0.971334	+	0.422063i
$356$		0			0
$357$	−1.02308	+	2.46993i	−0.0541470	+	0.130722i
$358$		0			0
$359$	1.28422			0.0677783			0.0338892	−	0.999426i	$-0.489211\pi$
$359$	1.28422			0.0677783			0.0338892	+	0.999426i	$0.489211\pi$
$360$		0			0
$361$	27.6624	+	27.6624i	1.45592	+	1.45592i
$362$		0			0
$363$	−1.06040	+	0.439232i	−0.0556566	+	0.0230537i
$364$		0			0
$365$	−0.260782	−	15.1545i	−0.0136499	−	0.793223i
$366$		0			0
$367$	−24.4450			−1.27602			−0.638008	−	0.770029i	$-0.720242\pi$
$367$	−24.4450			−1.27602			−0.638008	+	0.770029i	$0.720242\pi$
$368$		0			0
$369$	−18.3305	+	5.34521i	−0.954247	+	0.278261i
$370$		0			0
$371$	−16.8522	−	16.8522i	−0.874925	−	0.874925i
$372$		0			0
$373$	14.3400	+	14.3400i	0.742495	+	0.742495i	0.973058	−	0.230562i	$-0.0740565\pi$
$373$	14.3400	+	14.3400i	0.742495	+	0.742495i	−0.230562	+	0.973058i	$0.574057\pi$
$374$		0			0
$375$	−0.502187	+	1.41480i	−0.0259328	+	0.0730601i
$376$		0			0
$377$	27.2819			1.40509
$378$		0			0
$379$		−	13.6541i		−	0.701364i	−0.936495	−	0.350682i	$-0.885950\pi$
$379$		−	13.6541i		−	0.701364i	0.936495	−	0.350682i	$-0.114050\pi$
$380$		0			0
$381$	0.918697	−	0.380537i	0.0470663	−	0.0194955i
$382$		0			0
$383$	5.30558	+	12.8088i	0.271102	+	0.654499i	0.999531	−	0.0306228i	$-0.00974906\pi$
$383$	5.30558	+	12.8088i	0.271102	+	0.654499i	−0.728429	+	0.685122i	$0.759749\pi$
$384$		0			0
$385$	18.0969	−	0.311415i	0.922303	−	0.0158712i
$386$		0			0
$387$	16.5484	+	16.5484i	0.841203	+	0.841203i
$388$		0			0
$389$	−5.02196	+	5.02196i	−0.254623	+	0.254623i	−0.822863	−	0.568240i	$-0.807625\pi$
$389$	−5.02196	+	5.02196i	−0.254623	+	0.254623i	0.568240	+	0.822863i	$0.307625\pi$
$390$		0			0
$391$	15.8744	+	6.57539i	0.802803	+	0.332532i
$392$		0			0
$393$	−0.400503	+	0.165894i	−0.0202027	+	0.00836822i
$394$		0			0
$395$	16.9970	−	7.38550i	0.855210	−	0.371605i
$396$		0			0
$397$	−30.4977	−	12.6326i	−1.53064	−	0.634010i	−0.550948	−	0.834540i	$-0.685734\pi$
$397$	−30.4977	−	12.6326i	−1.53064	−	0.634010i	−0.979688	+	0.200530i	$0.935734\pi$
$398$		0			0
$399$	−4.88854	+	2.02490i	−0.244733	+	0.101372i
$400$		0			0
$401$	−0.412704	−	0.412704i	−0.0206095	−	0.0206095i	0.696727	−	0.717336i	$-0.254639\pi$
$401$	−0.412704	−	0.412704i	−0.0206095	−	0.0206095i	−0.717336	+	0.696727i	$0.754639\pi$
$402$		0			0
$403$	−0.643372	+	1.55324i	−0.0320486	+	0.0773722i
$404$		0			0
$405$	19.7595	−	0.340026i	0.981860	−	0.0168960i
$406$		0			0
$407$	7.26621	+	3.00976i	0.360173	+	0.149188i
$408$		0			0
$409$	23.7886			1.17627			0.588136	−	0.808762i	$-0.299862\pi$
$409$	23.7886			1.17627			0.588136	+	0.808762i	$0.299862\pi$
$410$		0			0
$411$	2.19005			0.108027
$412$		0			0
$413$	−10.6540	−	4.41303i	−0.524249	−	0.217151i
$414$		0			0
$415$	5.00188	+	4.83265i	0.245533	+	0.237225i
$416$		0			0
$417$	0.957405	−	2.31138i	0.0468843	−	0.113189i
$418$		0			0
$419$	−20.5497	−	20.5497i	−1.00392	−	1.00392i	−0.999992	−	0.00392531i	$-0.998751\pi$
$419$	−20.5497	−	20.5497i	−1.00392	−	1.00392i	−0.00392531	−	0.999992i	$-0.501249\pi$
$420$		0			0
$421$	33.4635	−	13.8611i	1.63091	−	0.675547i	0.635580	−	0.772035i	$-0.280761\pi$
$421$	33.4635	−	13.8611i	1.63091	−	0.675547i	0.995334	+	0.0964889i	$0.0307612\pi$
$422$		0			0
$423$	−6.78769	−	2.81155i	−0.330029	−	0.136702i
$424$		0			0
$425$	−17.5291	+	7.97803i	−0.850287	+	0.386991i
$426$		0			0
$427$	−18.8136	+	7.79286i	−0.910456	+	0.377123i
$428$		0			0
$429$	0.561354	+	0.232520i	0.0271024	+	0.0112262i
$430$		0			0
$431$	−2.47624	+	2.47624i	−0.119276	+	0.119276i	−0.764225	−	0.644949i	$-0.776878\pi$
$431$	−2.47624	+	2.47624i	−0.119276	+	0.119276i	0.644949	+	0.764225i	$0.276878\pi$
$432$		0			0
$433$	19.2809	+	19.2809i	0.926579	+	0.926579i	0.997483	−	0.0709037i	$-0.0225883\pi$
$433$	19.2809	+	19.2809i	0.926579	+	0.926579i	−0.0709037	+	0.997483i	$0.522588\pi$
$434$		0			0
$435$	−0.0487775	−	2.83455i	−0.00233870	−	0.135906i
$436$		0			0
$437$	13.0142	+	31.4190i	0.622553	+	1.50298i
$438$		0			0
$439$	−4.72164	+	1.95577i	−0.225352	+	0.0933438i	−0.492503	−	0.870311i	$-0.663918\pi$
$439$	−4.72164	+	1.95577i	−0.225352	+	0.0933438i	0.267151	+	0.963655i	$0.413918\pi$
$440$		0			0
$441$			58.7944i			2.79973i
$442$		0			0
$443$	−21.8037			−1.03593			−0.517963	−	0.855403i	$-0.673309\pi$
$443$	−21.8037			−1.03593			−0.517963	+	0.855403i	$0.673309\pi$
$444$		0			0
$445$	10.3426	+	23.8025i	0.490289	+	1.12835i
$446$		0			0
$447$	−1.19673	−	1.19673i	−0.0566036	−	0.0566036i
$448$		0			0
$449$	13.3094	+	13.3094i	0.628110	+	0.628110i	0.947592	−	0.319482i	$-0.103509\pi$
$449$	13.3094	+	13.3094i	0.628110	+	0.628110i	−0.319482	+	0.947592i	$0.603509\pi$
$450$		0			0
$451$	1.09046	−	9.96784i	0.0513476	−	0.469367i
$452$		0			0
$453$	−0.160600			−0.00754564
$454$		0			0
$455$	24.0174	+	23.2048i	1.12595	+	1.08786i
$456$		0			0
$457$	−0.465744	+	0.192918i	−0.0217866	+	0.00902430i	−0.393550	−	0.919303i	$-0.628753\pi$
$457$	−0.465744	+	0.192918i	−0.0217866	+	0.00902430i	0.371764	+	0.928327i	$0.378753\pi$
$458$		0			0
$459$	−2.18780	−	2.18780i	−0.102118	−	0.102118i
$460$		0			0
$461$	−13.3263			−0.620666			−0.310333	−	0.950628i	$-0.600441\pi$
$461$	−13.3263			−0.620666			−0.310333	+	0.950628i	$0.600441\pi$
$462$		0			0
$463$	10.7686	−	25.9976i	0.500458	−	1.20821i	−0.448777	−	0.893644i	$-0.648140\pi$
$463$	10.7686	−	25.9976i	0.500458	−	1.20821i	0.949235	−	0.314568i	$-0.101860\pi$
$464$		0			0
$465$	0.162529	+	0.0640683i	0.00753711	+	0.00297109i
$466$		0			0
$467$	−23.2661	−	23.2661i	−1.07663	−	1.07663i	−0.996810	−	0.0798168i	$-0.974566\pi$
$467$	−23.2661	−	23.2661i	−1.07663	−	1.07663i	−0.0798168	−	0.996810i	$-0.525434\pi$
$468$		0			0
$469$			10.1472i			0.468556i
$470$		0			0
$471$	0.600701	+	0.600701i	0.0276788	+	0.0276788i
$472$		0			0
$473$	−11.3547	+	4.70328i	−0.522090	+	0.216257i
$474$		0			0
$475$	−35.6979	−	13.3670i	−1.63793	−	0.613319i
$476$		0			0
$477$	12.7028	−	5.26168i	0.581622	−	0.240916i
$478$		0			0
$479$	10.2878	+	24.8368i	0.470059	+	1.13482i	0.964137	+	0.265406i	$0.0855060\pi$
$479$	10.2878	+	24.8368i	0.470059	+	1.13482i	−0.494077	+	0.869418i	$0.664494\pi$
$480$		0			0
$481$	5.55341	+	13.4071i	0.253214	+	0.611312i
$482$		0			0
$483$	−3.09608			−0.140876
$484$		0			0
$485$	37.4354	−	16.2664i	1.69985	−	0.738619i
$486$		0			0
$487$			38.5942i			1.74887i	0.485143	+	0.874435i	$0.338768\pi$
$487$			38.5942i			1.74887i	−0.485143	+	0.874435i	$0.661232\pi$
$488$		0			0
$489$	−0.727303	−	1.75587i	−0.0328898	−	0.0794030i
$490$		0			0
$491$			19.6407i			0.886374i	0.896429	+	0.443187i	$0.146152\pi$
$491$			19.6407i			0.886374i	−0.896429	+	0.443187i	$0.853848\pi$
$492$		0			0
$493$	25.7164	−	25.7164i	1.15821	−	1.15821i
$494$		0			0
$495$	−3.82938	+	9.71441i	−0.172118	+	0.436630i
$496$		0			0
$497$	46.1258			2.06903
$498$		0			0
$499$	11.9164	−	4.93593i	0.533451	−	0.220963i	−0.0996627	−	0.995021i	$-0.531776\pi$
$499$	11.9164	−	4.93593i	0.533451	−	0.220963i	0.633114	+	0.774058i	$0.281776\pi$
$500$		0			0
$501$	−0.977316	+	0.977316i	−0.0436633	+	0.0436633i
$502$		0			0
$503$	0.440178	−	1.06268i	0.0196266	−	0.0473828i	−0.913762	−	0.406249i	$-0.866837\pi$
$503$	0.440178	−	1.06268i	0.0196266	−	0.0473828i	0.933389	+	0.358866i	$0.116837\pi$
$504$		0			0
$505$	26.2595	+	10.3514i	1.16853	+	0.460630i
$506$		0			0
$507$	−0.238992	−	0.576978i	−0.0106140	−	0.0256245i
$508$		0			0
$509$	6.71011	+	2.77942i	0.297421	+	0.123196i	0.526404	−	0.850235i	$-0.323540\pi$
$509$	6.71011	+	2.77942i	0.297421	+	0.123196i	−0.228983	+	0.973430i	$0.573540\pi$
$510$		0			0
$511$	−13.4076	+	32.3688i	−0.593118	+	1.43191i
$512$		0			0
$513$		−	6.12375i		−	0.270370i
$514$		0			0
$515$	4.33107	−	0.0745300i	0.190850	−	0.00328418i
$516$		0			0
$517$	2.72823	−	2.72823i	0.119987	−	0.119987i
$518$		0			0
$519$	0.979130	−	2.36383i	0.0429790	−	0.103761i
$520$		0			0
$521$	−4.68228	−	11.3040i	−0.205135	−	0.495239i	0.787510	−	0.616302i	$-0.211370\pi$
$521$	−4.68228	−	11.3040i	−0.205135	−	0.495239i	−0.992645	+	0.121063i	$0.961370\pi$
$522$		0			0
$523$	−13.6458	−	13.6458i	−0.596690	−	0.596690i	0.342740	−	0.939430i	$-0.388645\pi$
$523$	−13.6458	−	13.6458i	−0.596690	−	0.596690i	−0.939430	+	0.342740i	$0.888645\pi$
$524$		0			0
$525$	2.36800	−	2.53686i	0.103348	−	0.110718i
$526$		0			0
$527$	0.857652	+	2.07055i	0.0373599	+	0.0901948i
$528$		0			0
$529$		−	3.10127i		−	0.134838i
$530$		0			0
$531$	4.70430	−	4.70430i	0.204149	−	0.204149i
$532$		0			0
$533$	14.4278	−	11.5824i	0.624939	−	0.501689i
$534$		0			0
$535$	−19.9200	−	19.2461i	−0.861218	−	0.832080i
$536$		0			0
$537$	−1.74516	+	1.74516i	−0.0753092	+	0.0753092i
$538$		0			0
$539$	−28.5260	−	11.8158i	−1.22870	−	0.508944i
$540$		0			0
$541$	−23.9623	+	23.9623i	−1.03022	+	1.03022i	−0.0306898	+	0.999529i	$0.509770\pi$
$541$	−23.9623	+	23.9623i	−1.03022	+	1.03022i	−0.999529	+	0.0306898i	$0.990230\pi$
$542$		0			0
$543$	0.543484	−	0.543484i	0.0233231	−	0.0233231i
$544$		0			0
$545$	−13.7619	−	5.42488i	−0.589495	−	0.232376i
$546$		0			0
$547$	−36.4014	+	15.0780i	−1.55641	+	0.644687i	−0.984461	−	0.175601i	$-0.943813\pi$
$547$	−36.4014	+	15.0780i	−1.55641	+	0.644687i	−0.571951	+	0.820288i	$0.693813\pi$
$548$		0			0
$549$		−	11.7482i		−	0.501399i
$550$		0			0
$551$	71.9813			3.06651
$552$		0			0
$553$	−42.8384			−1.82167
$554$		0			0
$555$	1.38305	−	0.600961i	0.0587072	−	0.0255094i
$556$		0			0
$557$	5.31276	+	12.8261i	0.225109	+	0.543460i	0.995570	−	0.0940267i	$-0.0299739\pi$
$557$	5.31276	+	12.8261i	0.225109	+	0.543460i	−0.770461	+	0.637487i	$0.779974\pi$
$558$		0			0
$559$	−20.9510	−	8.67817i	−0.886131	−	0.367048i
$560$		0			0
$561$	0.748318	−	0.309963i	0.0315940	−	0.0130867i
$562$		0			0
$563$	17.1985	+	7.12385i	0.724830	+	0.300234i	0.714426	−	0.699711i	$-0.246688\pi$
$563$	17.1985	+	7.12385i	0.724830	+	0.300234i	0.0104044	+	0.999946i	$0.496688\pi$
$564$		0			0
$565$	−16.5587	+	17.1385i	−0.696629	+	0.721024i
$566$		0			0
$567$	−42.2049	−	17.4818i	−1.77244	−	0.734168i
$568$		0			0
$569$	19.6719	−	19.6719i	0.824688	−	0.824688i	−0.162088	−	0.986776i	$-0.551823\pi$
$569$	19.6719	−	19.6719i	0.824688	−	0.824688i	0.986776	+	0.162088i	$0.0518229\pi$
$570$		0			0
$571$	21.4792	−	8.89696i	0.898875	−	0.372326i	0.115088	−	0.993355i	$-0.463285\pi$
$571$	21.4792	−	8.89696i	0.898875	−	0.372326i	0.783788	+	0.621029i	$0.213285\pi$
$572$		0			0
$573$	−1.19455	−	1.19455i	−0.0499031	−	0.0499031i
$574$		0			0
$575$	−16.3046	−	15.2193i	−0.679949	−	0.634690i
$576$		0			0
$577$	6.70482	−	16.1869i	0.279125	−	0.673868i	−0.720687	−	0.693261i	$-0.756173\pi$
$577$	6.70482	−	16.1869i	0.279125	−	0.673868i	0.999812	+	0.0193927i	$0.00617329\pi$
$578$		0			0
$579$	−0.566150	−	0.566150i	−0.0235284	−	0.0235284i
$580$		0			0
$581$	−6.15245	−	14.8533i	−0.255247	−	0.616220i
$582$		0			0
$583$			7.22062i			0.299047i
$584$		0			0
$585$	−17.6707	+	7.67824i	−0.730592	+	0.317456i
$586$		0			0
$587$	9.34917	−	22.5709i	0.385882	−	0.931601i	−0.604921	−	0.796286i	$-0.706795\pi$
$587$	9.34917	−	22.5709i	0.385882	−	0.931601i	0.990803	−	0.135315i	$-0.0432047\pi$
$588$		0			0
$589$	−1.69749	+	4.09809i	−0.0699437	+	0.168859i
$590$		0			0
$591$	0.498548	−	1.20360i	0.0205075	−	0.0495096i
$592$		0			0
$593$	−14.7840	−	35.6916i	−0.607105	−	1.46568i	−0.866135	−	0.499811i	$-0.833403\pi$
$593$	−14.7840	−	35.6916i	−0.607105	−	1.46568i	0.259030	−	0.965869i	$-0.416597\pi$
$594$		0			0
$595$	44.5124	−	0.765978i	1.82483	−	0.0314020i
$596$		0			0
$597$	2.41769	−	2.41769i	0.0989496	−	0.0989496i
$598$		0			0
$599$	15.0603			0.615348			0.307674	−	0.951492i	$-0.400449\pi$
$599$	15.0603			0.615348			0.307674	+	0.951492i	$0.400449\pi$
$600$		0			0
$601$	−38.3446	−	15.8828i	−1.56411	−	0.647874i	−0.578310	−	0.815817i	$-0.696288\pi$
$601$	−38.3446	−	15.8828i	−1.56411	−	0.647874i	−0.985797	+	0.167942i	$0.946288\pi$
$602$		0			0
$603$	−5.40848	−	2.24027i	−0.220250	−	0.0912307i
$604$		0			0
$605$	13.7455	+	13.2805i	0.558835	+	0.539928i
$606$		0			0
$607$		−	20.5003i		−	0.832080i	−0.909346	−	0.416040i	$-0.863418\pi$
$607$		−	20.5003i		−	0.832080i	0.909346	−	0.416040i	$-0.136582\pi$
$608$		0			0
$609$	−2.50781	+	6.05438i	−0.101621	+	0.245336i
$610$		0			0
$611$	7.11908			0.288007
$612$		0			0
$613$		−	11.0998i		−	0.448315i	−0.974553	−	0.224157i	$-0.928037\pi$
$613$		−	11.0998i		−	0.448315i	0.974553	−	0.224157i	$-0.0719630\pi$
$614$		0			0
$615$	−1.22919	−	1.47832i	−0.0495656	−	0.0596117i
$616$		0			0
$617$		−	21.4931i		−	0.865280i	−0.901567	−	0.432640i	$-0.857582\pi$
$617$		−	21.4931i		−	0.865280i	0.901567	−	0.432640i	$-0.142418\pi$
$618$		0			0
$619$	−2.11090			−0.0848441			−0.0424221	−	0.999100i	$-0.513507\pi$
$619$	−2.11090			−0.0848441			−0.0424221	+	0.999100i	$0.513507\pi$
$620$		0			0
$621$	1.37121	−	3.31040i	0.0550249	−	0.132842i
$622$		0			0
$623$		−	59.9908i		−	2.40348i
$624$		0			0
$625$	24.9408	−	1.71929i	0.997632	−	0.0687717i
$626$		0			0
$627$	1.48109	+	0.613487i	0.0591490	+	0.0245003i
$628$		0			0
$629$	17.8725	+	7.40302i	0.712622	+	0.295178i
$630$		0			0
$631$	2.74593			0.109314			0.0546569	−	0.998505i	$-0.482593\pi$
$631$	2.74593			0.109314			0.0546569	+	0.998505i	$0.482593\pi$
$632$		0			0
$633$	−2.24748	+	2.24748i	−0.0893292	+	0.0893292i
$634$		0			0
$635$	−11.9087	−	11.5058i	−0.472582	−	0.456592i
$636$		0			0
$637$	−21.8018	−	52.6342i	−0.863819	−	2.08544i
$638$		0			0
$639$	−10.1835	+	24.5851i	−0.402852	+	0.972571i
$640$		0			0
$641$	−7.05347	+	17.0286i	−0.278595	+	0.672588i	−0.999797	−	0.0201364i	$-0.993590\pi$
$641$	−7.05347	+	17.0286i	−0.278595	+	0.672588i	0.721202	+	0.692725i	$0.243590\pi$
$642$		0			0
$643$	−14.3276	+	34.5900i	−0.565027	+	1.36409i	0.340676	+	0.940181i	$0.389344\pi$
$643$	−14.3276	+	34.5900i	−0.565027	+	1.36409i	−0.905702	+	0.423914i	$0.860656\pi$
$644$		0			0
$645$	−0.864190	+	2.19229i	−0.0340275	+	0.0863212i
$646$		0			0
$647$			40.3011i			1.58440i	0.610263	+	0.792199i	$0.291064\pi$
$647$			40.3011i			1.58440i	−0.610263	+	0.792199i	$0.708936\pi$
$648$		0			0
$649$	1.33702	+	3.22786i	0.0524827	+	0.126705i
$650$		0			0
$651$	−0.285553	−	0.285553i	−0.0111917	−	0.0111917i
$652$		0			0
$653$	−18.1784	+	43.8865i	−0.711374	+	1.71741i	−0.0148365	+	0.999890i	$0.504723\pi$
$653$	−18.1784	+	43.8865i	−0.711374	+	1.71741i	−0.696538	+	0.717520i	$0.745277\pi$
$654$		0			0
$655$	5.19155	+	5.01590i	0.202851	+	0.195987i
$656$		0			0
$657$	−14.2925	−	14.2925i	−0.557605	−	0.557605i
$658$		0			0
$659$	−1.31316	+	0.543928i	−0.0511534	+	0.0211884i	−0.408113	−	0.912931i	$-0.633813\pi$
$659$	−1.31316	+	0.543928i	−0.0511534	+	0.0211884i	0.356960	+	0.934120i	$0.383813\pi$
$660$		0			0
$661$	15.1836	−	15.1836i	0.590575	−	0.590575i	−0.347212	−	0.937787i	$-0.612871\pi$
$661$	15.1836	−	15.1836i	0.590575	−	0.590575i	0.937787	+	0.347212i	$0.112871\pi$
$662$		0			0
$663$	1.38075	+	0.571924i	0.0536237	+	0.0222117i
$664$		0			0
$665$	63.3682	+	61.2242i	2.45731	+	2.37417i
$666$		0			0
$667$	38.9120	+	16.1179i	1.50668	+	0.624086i
$668$		0			0
$669$	−1.21073	+	0.501502i	−0.0468096	+	0.0193892i
$670$		0			0
$671$	5.70000	+	2.36102i	0.220046	+	0.0911460i
$672$		0			0
$673$	8.69970	+	21.0029i	0.335349	+	0.809604i	0.998149	+	0.0608080i	$0.0193677\pi$
$673$	8.69970	+	21.0029i	0.335349	+	0.809604i	−0.662801	+	0.748796i	$0.730632\pi$
$674$		0			0
$675$	1.66372	+	3.65547i	0.0640364	+	0.140699i
$676$		0			0
$677$	−18.4225			−0.708036			−0.354018	−	0.935239i	$-0.615185\pi$
$677$	−18.4225			−0.708036			−0.354018	+	0.935239i	$0.615185\pi$
$678$		0			0
$679$	−94.3504			−3.62084
$680$		0			0
$681$			2.55916i			0.0980673i
$682$		0			0
$683$	−20.9447	+	8.67559i	−0.801428	+	0.331962i	−0.745528	−	0.666474i	$-0.767803\pi$
$683$	−20.9447	+	8.67559i	−0.801428	+	0.331962i	−0.0558995	+	0.998436i	$0.517803\pi$
$684$		0			0
$685$	−14.5340	−	33.4484i	−0.555314	−	1.27800i
$686$		0			0
$687$	1.43839	−	1.43839i	0.0548782	−	0.0548782i
$688$		0			0
$689$	−9.42079	+	9.42079i	−0.358903	+	0.358903i
$690$		0			0
$691$	−39.9296	−	16.5394i	−1.51899	−	0.629187i	−0.541603	−	0.840634i	$-0.682183\pi$
$691$	−39.9296	−	16.5394i	−1.51899	−	0.629187i	−0.977390	+	0.211447i	$0.932183\pi$
$692$		0			0
$693$	17.0676	−	17.0676i	0.648343	−	0.648343i
$694$		0			0
$695$	−41.6551	+	0.716809i	−1.58007	+	0.0271901i
$696$		0			0
$697$	2.68216	−	24.5176i	0.101594	−	0.928670i
$698$		0			0
$699$	−1.00591	+	1.00591i	−0.0380471	+	0.0380471i
$700$		0			0
$701$		−	5.18584i		−	0.195867i	−0.995193	−	0.0979333i	$-0.968777\pi$
$701$		−	5.18584i		−	0.195867i	0.995193	−	0.0979333i	$-0.0312232\pi$
$702$		0			0
$703$	14.6522	+	35.3737i	0.552620	+	1.33414i
$704$		0			0
$705$	−0.0127282	−	0.739661i	−0.000479373	−	0.0278572i
$706$		0			0
$707$	−46.1361	−	46.1361i	−1.73513	−	1.73513i
$708$		0			0
$709$	7.63909	+	18.4424i	0.286892	+	0.692619i	0.999964	−	0.00847206i	$-0.00269677\pi$
$709$	7.63909	+	18.4424i	0.286892	+	0.692619i	−0.713072	+	0.701091i	$0.752697\pi$
$710$		0			0
$711$	9.45768	−	22.8329i	0.354691	−	0.856300i
$712$		0			0
$713$	−1.83527	+	1.83527i	−0.0687313	+	0.0687313i
$714$		0			0
$715$	−0.174088	−	10.1166i	−0.00651053	−	0.378339i
$716$		0			0
$717$		−	1.59385i		−	0.0595235i
$718$		0			0
$719$	2.75049	−	6.64026i	0.102576	−	0.247640i	−0.864257	−	0.503051i	$-0.832211\pi$
$719$	2.75049	−	6.64026i	0.102576	−	0.247640i	0.966833	+	0.255411i	$0.0822108\pi$
$720$		0			0
$721$	−9.25084	−	3.83182i	−0.344519	−	0.142705i
$722$		0			0
$723$	−0.0559318	−	0.135031i	−0.00208013	−	0.00502187i
$724$		0			0
$725$	−42.9680	+	19.5561i	−1.59579	+	0.726294i
$726$		0			0
$727$	−18.9775	+	45.8158i	−0.703838	+	1.69921i	0.0110146	+	0.999939i	$0.496494\pi$
$727$	−18.9775	+	45.8158i	−0.703838	+	1.69921i	−0.714852	+	0.699275i	$0.753506\pi$
$728$		0			0
$729$	18.4068	−	18.4068i	0.681735	−	0.681735i
$730$		0			0
$731$	−27.9288	+	11.5685i	−1.03299	+	0.427877i
$732$		0			0
$733$	14.1493			0.522615			0.261307	−	0.965256i	$-0.415846\pi$
$733$	14.1493			0.522615			0.261307	+	0.965256i	$0.415846\pi$
$734$		0			0
$735$	−5.42963	+	2.35928i	−0.200275	+	0.0870233i
$736$		0			0
$737$	2.17387	−	2.17387i	0.0800757	−	0.0800757i
$738$		0			0
$739$			38.0109i			1.39825i	0.714998	+	0.699127i	$0.246428\pi$
$739$			38.0109i			1.39825i	−0.714998	+	0.699127i	$0.753572\pi$
$740$		0			0
$741$	1.13197	+	2.73281i	0.0415838	+	0.100392i
$742$		0			0
$743$		−	26.4012i		−	0.968564i	−0.874912	−	0.484282i	$-0.839081\pi$
$743$		−	26.4012i		−	0.968564i	0.874912	−	0.484282i	$-0.160919\pi$
$744$		0			0
$745$	−10.3356	+	26.2195i	−0.378668	+	0.960609i
$746$		0			0
$747$	9.27515			0.339360
$748$		0			0
$749$	24.5022	+	59.1535i	0.895291	+	2.16142i
$750$		0			0
$751$	7.58678	+	18.3161i	0.276846	+	0.668364i	0.999745	−	0.0225890i	$-0.00719092\pi$
$751$	7.58678	+	18.3161i	0.276846	+	0.668364i	−0.722899	+	0.690954i	$0.757191\pi$
$752$		0			0
$753$	−0.0389322	+	0.0161262i	−0.00141877	+	0.000587673i
$754$		0			0
$755$	1.06580	+	2.45282i	0.0387884	+	0.0892673i
$756$		0			0
$757$	−10.6777	+	4.42285i	−0.388088	+	0.160751i	−0.568191	−	0.822896i	$-0.692357\pi$
$757$	−10.6777	+	4.42285i	−0.388088	+	0.160751i	0.180104	+	0.983648i	$0.442357\pi$
$758$		0			0
$759$	0.663283	+	0.663283i	0.0240756	+	0.0240756i
$760$		0			0
$761$		−	51.5226i		−	1.86769i	−0.357676	−	0.933846i	$-0.616431\pi$
$761$		−	51.5226i		−	1.86769i	0.357676	−	0.933846i	$-0.383569\pi$
$762$		0			0
$763$	24.1787	+	24.1787i	0.875328	+	0.875328i
$764$		0			0
$765$	−9.41900	+	23.8942i	−0.340545	+	0.863898i
$766$		0			0
$767$	−2.46699	+	5.95583i	−0.0890777	+	0.215053i
$768$		0			0
$769$	−4.24770			−0.153176			−0.0765879	−	0.997063i	$-0.524403\pi$
$769$	−4.24770			−0.153176			−0.0765879	+	0.997063i	$0.524403\pi$
$770$		0			0
$771$	−2.17548	−	2.17548i	−0.0783481	−	0.0783481i
$772$		0			0
$773$	−27.3395	+	11.3244i	−0.983335	+	0.407311i	−0.815660	−	0.578532i	$-0.803626\pi$
$773$	−27.3395	+	11.3244i	−0.983335	+	0.407311i	−0.167675	+	0.985842i	$0.553626\pi$
$774$		0			0
$775$	−0.100094	−	2.90747i	−0.00359549	−	0.104439i
$776$		0			0
$777$	−3.48577			−0.125051
$778$		0			0
$779$	38.0667	−	30.5592i	1.36388	−	1.09490i
$780$		0			0
$781$	−9.88168	−	9.88168i	−0.353594	−	0.353594i
$782$		0			0
$783$	−5.36281	−	5.36281i	−0.191651	−	0.191651i
$784$		0			0
$785$	5.18796	−	13.1609i	0.185166	−	0.469732i
$786$		0			0
$787$	4.01912			0.143266			0.0716330	−	0.997431i	$-0.477179\pi$
$787$	4.01912			0.143266			0.0716330	+	0.997431i	$0.477179\pi$
$788$		0			0
$789$			1.40588i			0.0500508i
$790$		0			0
$791$	50.8938	−	21.0809i	1.80957	−	0.749550i
$792$		0			0
$793$	4.35639	+	10.5173i	0.154700	+	0.373479i
$794$		0			0
$795$	0.995648	+	0.961961i	0.0353120	+	0.0341173i
$796$		0			0
$797$	−19.5782	−	19.5782i	−0.693494	−	0.693494i	0.269505	−	0.962999i	$-0.413140\pi$
$797$	−19.5782	−	19.5782i	−0.693494	−	0.693494i	−0.962999	+	0.269505i	$0.913140\pi$
$798$		0			0
$799$	6.71054	−	6.71054i	0.237402	−	0.237402i
$800$		0			0
$801$	31.9751	+	13.2445i	1.12979	+	0.467972i
$802$		0			0
$803$	9.80683	−	4.06212i	0.346076	−	0.143349i
$804$		0			0
$805$	20.5467	+	47.2860i	0.724175	+	1.66661i
$806$		0			0
$807$	2.44141	+	1.01127i	0.0859417	+	0.0355982i
$808$		0			0
$809$	42.0230	−	17.4065i	1.47745	−	0.611980i	0.508906	−	0.860822i	$-0.330050\pi$
$809$	42.0230	−	17.4065i	1.47745	−	0.611980i	0.968544	+	0.248842i	$0.0800500\pi$
$810$		0			0
$811$	−21.1865	−	21.1865i	−0.743960	−	0.743960i	0.229378	−	0.973338i	$-0.426331\pi$
$811$	−21.1865	−	21.1865i	−0.743960	−	0.743960i	−0.973338	+	0.229378i	$0.926331\pi$
$812$		0			0
$813$	0.0232175	−	0.0560520i	0.000814273	−	0.00196583i
$814$		0			0
$815$	−21.9905	+	22.7606i	−0.770293	+	0.797267i
$816$		0			0
$817$	−55.2775	−	22.8967i	−1.93392	−	0.801054i
$818$		0			0
$819$	44.5363			1.55622
$820$		0			0
$821$	−21.0312			−0.733995			−0.366998	−	0.930222i	$-0.619614\pi$
$821$	−21.0312			−0.733995			−0.366998	+	0.930222i	$0.619614\pi$
$822$		0			0
$823$	−21.6103	−	8.95128i	−0.753287	−	0.312022i	−0.0272053	−	0.999630i	$-0.508661\pi$
$823$	−21.6103	−	8.95128i	−0.753287	−	0.312022i	−0.726082	+	0.687608i	$0.758661\pi$
$824$		0			0
$825$	−1.05079	+	0.0361750i	−0.0365836	+	0.00125945i
$826$		0			0
$827$	−9.05968	+	21.8720i	−0.315036	+	0.760564i	0.684467	+	0.729044i	$0.260035\pi$
$827$	−9.05968	+	21.8720i	−0.315036	+	0.760564i	−0.999503	+	0.0315203i	$0.989965\pi$
$828$		0			0
$829$	−12.4962	−	12.4962i	−0.434010	−	0.434010i	0.455980	−	0.889990i	$-0.349289\pi$
$829$	−12.4962	−	12.4962i	−0.434010	−	0.434010i	−0.889990	+	0.455980i	$0.849289\pi$
$830$		0			0
$831$	−0.575335	+	0.238312i	−0.0199581	+	0.00826694i
$832$		0			0
$833$	−70.1645	−	29.0631i	−2.43105	−	1.00698i
$834$		0			0
$835$	21.4122	+	8.44061i	0.741001	+	0.292099i
$836$		0			0
$837$	0.431787	−	0.178852i	0.0149248	−	0.00618204i
$838$		0			0
$839$	−20.8139	−	8.62142i	−0.718577	−	0.297644i	−0.00672867	−	0.999977i	$-0.502142\pi$
$839$	−20.8139	−	8.62142i	−0.718577	−	0.297644i	−0.711849	+	0.702333i	$0.752142\pi$
$840$		0			0
$841$	42.5308	−	42.5308i	1.46658	−	1.46658i
$842$		0			0
$843$	−0.106982	−	0.106982i	−0.00368467	−	0.00368467i
$844$		0			0
$845$	−7.22607	+	7.47912i	−0.248585	+	0.257290i
$846$		0			0
$847$	−16.9074	−	40.8180i	−0.580945	−	1.40252i
$848$		0			0
$849$	−1.48942	+	0.616938i	−0.0511168	+	0.0211733i
$850$		0			0
$851$			22.4033i			0.767976i
$852$		0			0
$853$	−37.3672			−1.27943			−0.639714	−	0.768613i	$-0.720947\pi$
$853$	−37.3672			−1.27943			−0.639714	+	0.768613i	$0.720947\pi$
$854$		0			0
$855$	−46.6227	+	20.2584i	−1.59446	+	0.692824i
$856$		0			0
$857$	−30.3210	−	30.3210i	−1.03574	−	1.03574i	−0.999337	−	0.0364072i	$-0.988409\pi$
$857$	−30.3210	−	30.3210i	−1.03574	−	1.03574i	−0.0364072	−	0.999337i	$-0.511591\pi$
$858$		0			0
$859$	−31.0175	−	31.0175i	−1.05830	−	1.05830i	−0.998192	−	0.0601110i	$-0.980855\pi$
$859$	−31.0175	−	31.0175i	−1.05830	−	1.05830i	−0.0601110	−	0.998192i	$-0.519145\pi$
$860$		0			0
$861$	1.24412	+	4.26648i	0.0423994	+	0.145401i
$862$		0			0
$863$	39.2347			1.33557			0.667783	−	0.744356i	$-0.267243\pi$
$863$	39.2347			1.33557			0.667783	+	0.744356i	$0.267243\pi$
$864$		0			0
$865$	−42.6003	+	0.733075i	−1.44845	+	0.0249253i
$866$		0			0
$867$	−0.268368	+	0.111162i	−0.00911425	+	0.00377525i
$868$		0			0
$869$	9.17740	+	9.17740i	0.311322	+	0.311322i
$870$		0			0
$871$	5.67254			0.192207
$872$		0			0
$873$	20.8303	−	50.2888i	0.704999	−	1.70202i
$874$		0			0
$875$	−54.4601	−	19.3307i	−1.84109	−	0.653498i
$876$		0			0
$877$	31.3625	+	31.3625i	1.05903	+	1.05903i	0.998144	+	0.0608905i	$0.0193940\pi$
$877$	31.3625	+	31.3625i	1.05903	+	1.05903i	0.0608905	+	0.998144i	$0.480606\pi$
$878$		0			0
$879$			0.162754i			0.00548956i
$880$		0			0
$881$	27.4019	+	27.4019i	0.923195	+	0.923195i	0.997254	−	0.0740592i	$-0.0235954\pi$
$881$	27.4019	+	27.4019i	0.923195	+	0.923195i	−0.0740592	+	0.997254i	$0.523595\pi$
$882$		0			0
$883$	−21.0081	+	8.70184i	−0.706979	+	0.292840i	−0.707054	−	0.707160i	$-0.749976\pi$
$883$	−21.0081	+	8.70184i	−0.706979	+	0.292840i	7.49254e−5		1.00000i	$0.499976\pi$
$884$		0			0
$885$	0.623212	+	0.245667i	0.0209490	+	0.00825802i
$886$		0			0
$887$	−35.3713	+	14.6513i	−1.18765	+	0.491941i	−0.886989	−	0.461790i	$-0.847207\pi$
$887$	−35.3713	+	14.6513i	−1.18765	+	0.491941i	−0.300662	+	0.953731i	$0.597207\pi$
$888$		0			0
$889$	14.6480	+	35.3634i	0.491279	+	1.18605i
$890$		0			0
$891$	5.29649	+	12.7869i	0.177439	+	0.428376i
$892$		0			0
$893$	18.7831			0.628554
$894$		0			0
$895$	38.2351	+	15.0721i	1.27806	+	0.503805i
$896$		0			0
$897$			1.73078i			0.0577890i
$898$		0			0
$899$	2.10231	+	5.07542i	0.0701159	+	0.169275i
$900$		0			0
$901$			17.7603i			0.591683i
$902$		0			0
$903$	3.85170	−	3.85170i	0.128177	−	0.128177i
$904$		0			0
$905$	−11.9073	−	4.69381i	−0.395813	−	0.156028i
$906$		0			0
$907$	−18.0756			−0.600192			−0.300096	−	0.953909i	$-0.597019\pi$
$907$	−18.0756			−0.600192			−0.300096	+	0.953909i	$0.597019\pi$
$908$		0			0
$909$	34.7763	−	14.4048i	1.15346	−	0.477778i
$910$		0			0
$911$	−15.5601	+	15.5601i	−0.515528	+	0.515528i	−0.916215	−	0.400687i	$-0.868772\pi$
$911$	−15.5601	+	15.5601i	−0.515528	+	0.515528i	0.400687	+	0.916215i	$0.368772\pi$
$912$		0			0
$913$	−1.86402	+	4.50014i	−0.0616900	+	0.148933i
$914$		0			0
$915$	1.08494	−	0.471426i	0.0358669	−	0.0155849i
$916$		0			0
$917$	−6.38575	−	15.4166i	−0.210876	−	0.509100i
$918$		0			0
$919$	41.5468	+	17.2093i	1.37050	+	0.567681i	0.941925	−	0.335823i	$-0.109014\pi$
$919$	41.5468	+	17.2093i	1.37050	+	0.567681i	0.428579	+	0.903504i	$0.359014\pi$
$920$		0			0
$921$	0.0822225	−	0.198503i	0.00270932	−	0.00654088i
$922$		0			0
$923$		−	25.7854i		−	0.848737i
$924$		0			0
$925$	−18.3568	−	17.1350i	−0.603568	−	0.563394i
$926$		0			0
$927$	4.08473	−	4.08473i	0.134160	−	0.134160i
$928$		0			0
$929$	9.68203	−	23.3745i	0.317657	−	0.766892i	−0.681720	−	0.731613i	$-0.738768\pi$
$929$	9.68203	−	23.3745i	0.317657	−	0.766892i	0.999377	−	0.0352793i	$-0.0112321\pi$
$930$		0			0
$931$	−57.5224	−	138.871i	−1.88522	−	4.55132i
$932$		0			0
$933$	1.41483	+	1.41483i	0.0463193	+	0.0463193i
$934$		0			0
$935$	−9.70013	−	9.37193i	−0.317228	−	0.306495i
$936$		0			0
$937$	8.90697	+	21.5033i	0.290978	+	0.702483i	0.999996	−	0.00270675i	$-0.000861586\pi$
$937$	8.90697	+	21.5033i	0.290978	+	0.702483i	−0.709018	+	0.705190i	$0.750862\pi$
$938$		0			0
$939$		−	0.114718i		−	0.00374369i
$940$		0			0
$941$	12.0967	−	12.0967i	0.394342	−	0.394342i	−0.481890	−	0.876232i	$-0.660049\pi$
$941$	12.0967	−	12.0967i	0.394342	−	0.394342i	0.876232	+	0.481890i	$0.160049\pi$
$942$		0			0
$943$	27.4210	−	7.99603i	0.892951	−	0.260387i
$944$		0			0
$945$	−0.159735	−	9.28248i	−0.00519618	−	0.301959i
$946$		0			0
$947$	−21.3941	+	21.3941i	−0.695214	+	0.695214i	−0.963374	−	0.268161i	$-0.913584\pi$
$947$	−21.3941	+	21.3941i	−0.695214	+	0.695214i	0.268161	+	0.963374i	$0.413584\pi$
$948$		0			0
$949$	18.0949	+	7.49516i	0.587386	+	0.243303i
$950$		0			0
$951$	0.858463	−	0.858463i	0.0278376	−	0.0278376i
$952$		0			0
$953$	19.9985	−	19.9985i	0.647816	−	0.647816i	−0.304649	−	0.952465i	$-0.598539\pi$
$953$	19.9985	−	19.9985i	0.647816	−	0.647816i	0.952465	+	0.304649i	$0.0985391\pi$
$954$		0			0
$955$	−10.3168	+	26.1717i	−0.333843	+	0.846896i
$956$		0			0
$957$	1.83431	−	0.759794i	0.0592947	−	0.0245607i
$958$		0			0
$959$			84.3017i			2.72225i
$960$		0			0
$961$	30.6615			0.989080
$962$		0			0
$963$	−36.9384			−1.19032
$964$		0			0
$965$	−4.88956	+	12.4039i	−0.157401	+	0.399296i
$966$		0			0
$967$	−18.1289	−	43.7670i	−0.582985	−	1.40745i	−0.890094	−	0.455776i	$-0.849362\pi$
$967$	−18.1289	−	43.7670i	−0.582985	−	1.40745i	0.307109	−	0.951674i	$-0.400638\pi$
$968$		0			0
$969$	3.64299	+	1.50898i	0.117030	+	0.0484753i
$970$		0			0
$971$	−8.17341	+	3.38554i	−0.262297	+	0.108647i	−0.509957	−	0.860200i	$-0.670339\pi$
$971$	−8.17341	+	3.38554i	−0.262297	+	0.108647i	0.247660	+	0.968847i	$0.420339\pi$
$972$		0			0
$973$	88.9720	+	36.8534i	2.85231	+	1.18147i
$974$		0			0
$975$	−1.41816	−	1.32377i	−0.0454176	−	0.0423945i
$976$		0			0
$977$	36.9215	+	15.2934i	1.18122	+	0.489279i	0.884888	−	0.465804i	$-0.154235\pi$
$977$	36.9215	+	15.2934i	1.18122	+	0.489279i	0.296337	+	0.955083i	$0.404235\pi$
$978$		0			0
$979$	−12.8520	+	12.8520i	−0.410752	+	0.410752i
$980$		0			0
$981$	−18.2253	+	7.54919i	−0.581891	+	0.241027i
$982$		0			0
$983$	24.4923	+	24.4923i	0.781184	+	0.781184i	0.980031	−	0.198846i	$-0.0637195\pi$
$983$	24.4923	+	24.4923i	0.781184	+	0.781184i	−0.198846	+	0.980031i	$0.563719\pi$
$984$		0			0
$985$	−21.6910	+	0.373263i	−0.691133	+	0.0118932i
$986$		0			0
$987$	−0.654399	+	1.57986i	−0.0208297	+	0.0502874i
$988$		0			0
$989$	−24.7552	−	24.7552i	−0.787169	−	0.787169i
$990$		0			0
$991$	−19.7674	−	47.7227i	−0.627932	−	1.51596i	−0.842188	−	0.539183i	$-0.818733\pi$
$991$	−19.7674	−	47.7227i	−0.627932	−	1.51596i	0.214257	−	0.976777i	$-0.431267\pi$
$992$		0			0
$993$		−	3.28491i		−	0.104243i
$994$		0			0
$995$	−52.9698	−	20.8805i	−1.67925	−	0.661955i
$996$		0			0
$997$	2.49277	−	6.01807i	0.0789467	−	0.190594i	−0.879478	−	0.475939i	$-0.842108\pi$
$997$	2.49277	−	6.01807i	0.0789467	−	0.190594i	0.958425	+	0.285345i	$0.0921082\pi$
$998$		0			0
$999$	1.54380	−	3.72707i	0.0488438	−	0.117919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.137.12	yes	84
5.3	odd	4		820.2.x.a.793.10	yes	84
41.3	odd	8		820.2.x.a.577.10	✓	84
205.3	even	8	inner	820.2.y.a.413.12	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.10	✓	84	41.3	odd	8
820.2.x.a.793.10	yes	84	5.3	odd	4
820.2.y.a.137.12	yes	84	1.1	even	1	trivial
820.2.y.a.413.12	yes	84	205.3	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.124058 + 0.0513864i) q^{3} +(-0.0384730 - 2.23574i) q^{5} +(-1.97802 + 4.77536i) q^{7} +(-2.10857 - 2.10857i) q^{9} +(1.44680 - 0.599283i) q^{11} +(2.66954 + 1.10576i) q^{13} +(0.110114 - 0.279338i) q^{15} +(3.55865 - 1.47404i) q^{17} +(7.04336 + 2.91746i) q^{19} +(-0.490777 + 0.490777i) q^{21} +(3.15426 + 3.15426i) q^{23} +(-4.99704 + 0.172031i) q^{25} +(-0.307392 - 0.742110i) q^{27} +(8.72309 - 3.61322i) q^{29} +0.581838i q^{31} +0.210282 q^{33} +(10.7525 + 4.23861i) q^{35} +(3.55128 + 3.55128i) q^{37} +(0.274356 + 0.274356i) q^{39} +(3.07916 - 5.61416i) q^{41} -7.84817 q^{43} +(-4.63309 + 4.79533i) q^{45} +(2.27624 - 0.942851i) q^{47} +(-13.9418 - 13.9418i) q^{49} +0.517223 q^{51} +(-1.76450 + 4.25988i) q^{53} +(-1.39550 - 3.21160i) q^{55} +(0.723866 + 0.723866i) q^{57} +2.23104i q^{59} +(2.78581 + 2.78581i) q^{61} +(14.2400 - 5.89839i) q^{63} +(2.36948 - 6.01092i) q^{65} +(1.81373 - 0.751271i) q^{67} +(0.229224 + 0.553397i) q^{69} +(-3.41502 - 8.24458i) q^{71} +6.77830 q^{73} +(-0.628762 - 0.235438i) q^{75} +8.09438i q^{77} +(3.17162 + 7.65698i) q^{79} +8.83805i q^{81} +(-2.19939 + 2.19939i) q^{83} +(-3.43248 - 7.89948i) q^{85} +1.26784 q^{87} +(-10.7228 + 4.44154i) q^{89} +(-10.5608 + 10.5608i) q^{91} +(-0.0298985 + 0.0721815i) q^{93} +(6.25169 - 15.8594i) q^{95} +(6.98542 + 16.8643i) q^{97} +(-4.31431 - 1.78704i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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