LMFDB - Embedded newform 891.2.f.c.487.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(82,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.1
Character	$\chi$	$=$	891.487
Dual form			891.2.f.c.730.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.12715 + 1.54546i) q^{2} +(1.51827 - 4.67274i) q^{4} +(0.193808 + 0.140810i) q^{5} +(-0.366442 + 1.12779i) q^{7} +(2.36698 + 7.28482i) q^{8} -0.629874 q^{10} +(2.93952 + 1.53597i) q^{11} +(4.88403 - 3.54845i) q^{13} +(-0.963487 - 2.96531i) q^{14} +(-8.34358 - 6.06197i) q^{16} +(1.48403 + 1.07821i) q^{17} +(-1.00736 - 3.10034i) q^{19} +(0.952219 - 0.691827i) q^{20} +(-8.62659 + 1.27568i) q^{22} -5.55040 q^{23} +(-1.52735 - 4.70070i) q^{25} +(-4.90504 + 15.0962i) q^{26} +(4.71353 + 3.42458i) q^{28} +(1.92367 - 5.92043i) q^{29} +(-3.20168 + 2.32616i) q^{31} +11.7972 q^{32} -4.82307 q^{34} +(-0.229824 + 0.166977i) q^{35} +(-1.67897 + 5.16733i) q^{37} +(6.93427 + 5.03804i) q^{38} +(-0.567033 + 1.74515i) q^{40} +(-3.29583 - 10.1435i) q^{41} +12.1439 q^{43} +(11.6402 - 11.4036i) q^{44} +(11.8065 - 8.57795i) q^{46} +(0.511346 + 1.57376i) q^{47} +(4.52548 + 3.28795i) q^{49} +(10.5137 + 7.63862i) q^{50} +(-9.16576 - 28.2093i) q^{52} +(6.99142 - 5.07956i) q^{53} +(0.353422 + 0.711596i) q^{55} -9.08313 q^{56} +(5.05789 + 15.5666i) q^{58} +(-1.21376 + 3.73558i) q^{59} +(8.67742 + 6.30451i) q^{61} +(3.21546 - 9.89616i) q^{62} +(-8.40715 + 6.10815i) q^{64} +1.44622 q^{65} +9.22102 q^{67} +(7.29134 - 5.29747i) q^{68} +(0.230812 - 0.710368i) q^{70} +(-5.77707 - 4.19728i) q^{71} +(-0.172710 + 0.531546i) q^{73} +(-4.41451 - 13.5865i) q^{74} -16.0165 q^{76} +(-2.80943 + 2.75233i) q^{77} +(-3.57826 + 2.59976i) q^{79} +(-0.763468 - 2.34971i) q^{80} +(22.6872 + 16.4832i) q^{82} +(12.4742 + 9.06302i) q^{83} +(0.135794 + 0.417930i) q^{85} +(-25.8319 + 18.7680i) q^{86} +(-4.23151 + 25.0495i) q^{88} -0.0625956 q^{89} +(2.21221 + 6.80848i) q^{91} +(-8.42699 + 25.9356i) q^{92} +(-3.51990 - 2.55735i) q^{94} +(0.241323 - 0.742716i) q^{95} +(-4.92941 + 3.58143i) q^{97} -14.7078 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 8 q^{4} + 4 q^{5} + 7 q^{7} + 10 q^{8} - 16 q^{10} + 5 q^{11} + 7 q^{13} + 13 q^{14} + 2 q^{16} - 5 q^{17} + 4 q^{19} + 27 q^{20} - 2 q^{22} + 6 q^{23} - 2 q^{25} - 34 q^{26} - 9 q^{28}+ \cdots + 68 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 - 8 * q^4 + 4 * q^5 + 7 * q^7 + 10 * q^8 - 16 * q^10 + 5 * q^11 + 7 * q^13 + 13 * q^14 + 2 * q^16 - 5 * q^17 + 4 * q^19 + 27 * q^20 - 2 * q^22 + 6 * q^23 - 2 * q^25 - 34 * q^26 - 9 * q^28 + 22 * q^29 + 2 * q^31 + 18 * q^32 - 42 * q^34 + 6 * q^37 - 5 * q^38 + 53 * q^40 + 10 * q^41 - 30 * q^43 + 59 * q^44 + 31 * q^46 + 4 * q^47 - 3 * q^49 + 9 * q^50 - 26 * q^52 + 17 * q^53 + 12 * q^55 - 48 * q^56 + 53 * q^58 + 11 * q^59 + 3 * q^61 - 2 * q^62 + 38 * q^64 - 68 * q^65 - 14 * q^67 + 22 * q^68 - 20 * q^70 - 36 * q^71 + 35 * q^73 + 3 * q^74 - 102 * q^76 - 88 * q^77 - 9 * q^79 - 37 * q^80 - 6 * q^82 + 32 * q^83 - 45 * q^85 - 110 * q^86 + 54 * q^88 + 34 * q^89 + 13 * q^91 - q^92 - 25 * q^94 - 84 * q^95 + 15 * q^97 + 68 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−2.12715	+	1.54546i	−1.50412	+	1.09281i	−0.535417	+	0.844588i	$0.679845\pi$
$2$	−2.12715	+	1.54546i	−1.50412	+	1.09281i	−0.968704	+	0.248219i	$0.920155\pi$
$3$		0			0
$3$		0			0
$4$	1.51827	−	4.67274i	0.759133	−	2.33637i
$5$	0.193808	+	0.140810i	0.0866735	+	0.0629720i	0.630278	−	0.776369i	$-0.282941\pi$
$5$	0.193808	+	0.140810i	0.0866735	+	0.0629720i	−0.543605	+	0.839341i	$0.682941\pi$
$6$		0			0
$7$	−0.366442	+	1.12779i	−0.138502	+	0.426266i	−0.996118	−	0.0880245i	$-0.971945\pi$
$7$	−0.366442	+	1.12779i	−0.138502	+	0.426266i	0.857616	+	0.514290i	$0.171945\pi$
$8$	2.36698	+	7.28482i	0.836854	+	2.57557i
$9$		0			0
$10$	−0.629874			−0.199184
$11$	2.93952	+	1.53597i	0.886299	+	0.463114i
$11$	2.93952	+	1.53597i	0.886299	+	0.463114i
$12$		0			0
$13$	4.88403	−	3.54845i	1.35459	−	0.984164i	0.355816	−	0.934556i	$-0.384203\pi$
$13$	4.88403	−	3.54845i	1.35459	−	0.984164i	0.998769	−	0.0496079i	$-0.0157972\pi$
$14$	−0.963487	−	2.96531i	−0.257503	−	0.792512i
$15$		0			0
$16$	−8.34358	−	6.06197i	−2.08590	−	1.51549i
$17$	1.48403	+	1.07821i	0.359929	+	0.261504i	0.753023	−	0.657995i	$-0.228595\pi$
$17$	1.48403	+	1.07821i	0.359929	+	0.261504i	−0.393093	+	0.919499i	$0.628595\pi$
$18$		0			0
$19$	−1.00736	−	3.10034i	−0.231105	−	0.711267i	−0.997614	−	0.0690339i	$-0.978008\pi$
$19$	−1.00736	−	3.10034i	−0.231105	−	0.711267i	0.766510	−	0.642233i	$-0.221992\pi$
$20$	0.952219	−	0.691827i	0.212923	−	0.154697i
$21$		0			0
$22$	−8.62659	+	1.27568i	−1.83919	+	0.271975i
$23$	−5.55040			−1.15734			−0.578670	−	0.815562i	$-0.696428\pi$
$23$	−5.55040			−1.15734			−0.578670	+	0.815562i	$0.696428\pi$
$24$		0			0
$25$	−1.52735	−	4.70070i	−0.305470	−	0.940141i
$26$	−4.90504	+	15.0962i	−0.961958	+	2.96060i
$27$		0			0
$28$	4.71353	+	3.42458i	0.890774	+	0.647185i
$29$	1.92367	−	5.92043i	0.357216	−	1.09940i	−0.597498	−	0.801870i	$-0.703838\pi$
$29$	1.92367	−	5.92043i	0.357216	−	1.09940i	0.954714	−	0.297526i	$-0.0961616\pi$
$30$		0			0
$31$	−3.20168	+	2.32616i	−0.575039	+	0.417790i	−0.836932	−	0.547307i	$-0.815653\pi$
$31$	−3.20168	+	2.32616i	−0.575039	+	0.417790i	0.261893	+	0.965097i	$0.415653\pi$
$32$	11.7972			2.08546
$33$		0			0
$34$	−4.82307			−0.827150
$35$	−0.229824	+	0.166977i	−0.0388473	+	0.0282242i
$36$		0			0
$37$	−1.67897	+	5.16733i	−0.276020	+	0.849504i	0.712927	+	0.701238i	$0.247369\pi$
$37$	−1.67897	+	5.16733i	−0.276020	+	0.849504i	−0.988948	+	0.148265i	$0.952631\pi$
$38$	6.93427	+	5.03804i	1.12489	+	0.817278i
$39$		0			0
$40$	−0.567033	+	1.74515i	−0.0896557	+	0.275932i
$41$	−3.29583	−	10.1435i	−0.514722	−	1.58415i	−0.783787	−	0.621030i	$-0.786715\pi$
$41$	−3.29583	−	10.1435i	−0.514722	−	1.58415i	0.269065	−	0.963122i	$-0.413285\pi$
$42$		0			0
$43$	12.1439			1.85193			0.925964	−	0.377612i	$-0.123255\pi$
$43$	12.1439			1.85193			0.925964	+	0.377612i	$0.123255\pi$
$44$	11.6402	−	11.4036i	1.75482	−	1.71916i
$45$		0			0
$46$	11.8065	−	8.57795i	1.74078	−	1.26475i
$47$	0.511346	+	1.57376i	0.0745874	+	0.229557i	0.981399	−	0.191980i	$-0.0614909\pi$
$47$	0.511346	+	1.57376i	0.0745874	+	0.229557i	−0.906811	+	0.421537i	$0.861491\pi$
$48$		0			0
$49$	4.52548	+	3.28795i	0.646497	+	0.469708i
$50$	10.5137	+	7.63862i	1.48686	+	1.08026i
$51$		0			0
$52$	−9.16576	−	28.2093i	−1.27106	−	3.91193i
$53$	6.99142	−	5.07956i	0.960345	−	0.697732i	0.00711436	−	0.999975i	$-0.497735\pi$
$53$	6.99142	−	5.07956i	0.960345	−	0.697732i	0.953231	+	0.302243i	$0.0977354\pi$
$54$		0			0
$55$	0.353422	+	0.711596i	0.0476554	+	0.0959516i
$56$	−9.08313			−1.21378
$57$		0			0
$58$	5.05789	+	15.5666i	0.664134	+	2.04399i
$59$	−1.21376	+	3.73558i	−0.158019	+	0.486332i	−0.998454	−	0.0555800i	$-0.982299\pi$
$59$	−1.21376	+	3.73558i	−0.158019	+	0.486332i	0.840436	+	0.541912i	$0.182299\pi$
$60$		0			0
$61$	8.67742	+	6.30451i	1.11103	+	0.807210i	0.982825	−	0.184538i	$-0.0590787\pi$
$61$	8.67742	+	6.30451i	1.11103	+	0.807210i	0.128204	+	0.991748i	$0.459079\pi$
$62$	3.21546	−	9.89616i	0.408364	−	1.25681i
$63$		0			0
$64$	−8.40715	+	6.10815i	−1.05089	+	0.763519i
$65$	1.44622			0.179381
$66$		0			0
$67$	9.22102			1.12653			0.563263	−	0.826277i	$-0.309546\pi$
$67$	9.22102			1.12653			0.563263	+	0.826277i	$0.309546\pi$
$68$	7.29134	−	5.29747i	0.884205	−	0.642412i
$69$		0			0
$70$	0.230812	−	0.710368i	0.0275874	−	0.0849052i
$71$	−5.77707	−	4.19728i	−0.685612	−	0.498126i	0.189603	−	0.981861i	$-0.439280\pi$
$71$	−5.77707	−	4.19728i	−0.685612	−	0.498126i	−0.875215	+	0.483735i	$0.839280\pi$
$72$		0			0
$73$	−0.172710	+	0.531546i	−0.0202141	+	0.0622127i	−0.960655	−	0.277745i	$-0.910413\pi$
$73$	−0.172710	+	0.531546i	−0.0202141	+	0.0622127i	0.940441	+	0.339958i	$0.110413\pi$
$74$	−4.41451	−	13.5865i	−0.513176	−	1.57939i
$75$		0			0
$76$	−16.0165			−1.83722
$77$	−2.80943	+	2.75233i	−0.320164	+	0.313657i
$78$		0			0
$79$	−3.57826	+	2.59976i	−0.402585	+	0.292495i	−0.770593	−	0.637327i	$-0.780040\pi$
$79$	−3.57826	+	2.59976i	−0.402585	+	0.292495i	0.368008	+	0.929823i	$0.380040\pi$
$80$	−0.763468	−	2.34971i	−0.0853583	−	0.262706i
$81$		0			0
$82$	22.6872	+	16.4832i	2.50538	+	1.82026i
$83$	12.4742	+	9.06302i	1.36922	+	0.994795i	0.997798	+	0.0663309i	$0.0211293\pi$
$83$	12.4742	+	9.06302i	1.36922	+	0.994795i	0.371421	+	0.928465i	$0.378871\pi$
$84$		0			0
$85$	0.135794	+	0.417930i	0.0147289	+	0.0453309i
$86$	−25.8319	+	18.7680i	−2.78552	+	2.02380i
$87$		0			0
$88$	−4.23151	+	25.0495i	−0.451080	+	2.67028i
$89$	−0.0625956			−0.00663512			−0.00331756	−	0.999994i	$-0.501056\pi$
$89$	−0.0625956			−0.00663512			−0.00331756	+	0.999994i	$0.501056\pi$
$90$		0			0
$91$	2.21221	+	6.80848i	0.231902	+	0.713722i
$92$	−8.42699	+	25.9356i	−0.878575	+	2.70397i
$93$		0			0
$94$	−3.51990	−	2.55735i	−0.363050	−	0.263771i
$95$	0.241323	−	0.742716i	0.0247592	−	0.0762010i
$96$		0			0
$97$	−4.92941	+	3.58143i	−0.500506	+	0.363639i	−0.809210	−	0.587519i	$-0.800105\pi$
$97$	−4.92941	+	3.58143i	−0.500506	+	0.363639i	0.308704	+	0.951158i	$0.400105\pi$
$98$	−14.7078			−1.48571
$99$		0			0
$100$	−24.2841			−2.42841
$101$	12.3436	−	8.96815i	1.22823	−	0.892365i	0.231478	−	0.972840i	$-0.425644\pi$
$101$	12.3436	−	8.96815i	1.22823	−	0.892365i	0.996757	+	0.0804755i	$0.0256439\pi$
$102$		0			0
$103$	3.86162	−	11.8849i	0.380497	−	1.17105i	−0.559198	−	0.829034i	$-0.688891\pi$
$103$	3.86162	−	11.8849i	0.380497	−	1.17105i	0.939695	−	0.342015i	$-0.111109\pi$
$104$	37.4102	+	27.1801i	3.66837	+	2.66523i
$105$		0			0
$106$	−7.02150	+	21.6100i	−0.681989	+	2.09894i
$107$	3.33446	+	10.2624i	0.322354	+	0.992105i	0.972621	+	0.232399i	$0.0746574\pi$
$107$	3.33446	+	10.2624i	0.322354	+	0.992105i	−0.650266	+	0.759706i	$0.725343\pi$
$108$		0			0
$109$	−5.16947			−0.495146			−0.247573	−	0.968869i	$-0.579633\pi$
$109$	−5.16947			−0.495146			−0.247573	+	0.968869i	$0.579633\pi$
$110$	−1.85153	−	0.967470i	−0.176536	−	0.0922447i
$111$		0			0
$112$	9.89409	−	7.18848i	0.934904	−	0.679247i
$113$	0.629758	+	1.93820i	0.0592427	+	0.182330i	0.976298	−	0.216429i	$-0.0694410\pi$
$113$	0.629758	+	1.93820i	0.0592427	+	0.182330i	−0.917056	+	0.398759i	$0.869441\pi$
$114$		0			0
$115$	−1.07571	−	0.781550i	−0.100311	−	0.0728799i
$116$	−24.7440	−	17.9776i	−2.29743	−	1.66918i
$117$		0			0
$118$	−3.19135	−	9.82197i	−0.293788	−	0.904185i
$119$	−1.75981	+	1.27857i	−0.161321	+	0.117207i
$120$		0			0
$121$	6.28156	+	9.03006i	0.571051	+	0.820914i
$122$	−28.2015			−2.55325
$123$		0			0
$124$	6.00853	+	18.4924i	0.539582	+	1.66066i
$125$	0.736031	−	2.26527i	0.0658326	−	0.202612i
$126$		0			0
$127$	0.969141	+	0.704122i	0.0859974	+	0.0624808i	0.629953	−	0.776633i	$-0.283074\pi$
$127$	0.969141	+	0.704122i	0.0859974	+	0.0624808i	−0.543956	+	0.839114i	$0.683074\pi$
$128$	1.15227	−	3.54633i	0.101847	−	0.313454i
$129$		0			0
$130$	−3.07632	+	2.23508i	−0.269811	+	0.196029i
$131$	−5.76699			−0.503864			−0.251932	−	0.967745i	$-0.581066\pi$
$131$	−5.76699			−0.503864			−0.251932	+	0.967745i	$0.581066\pi$
$132$		0			0
$133$	3.86568			0.335197
$134$	−19.6145	+	14.2507i	−1.69443	+	1.23108i
$135$		0			0
$136$	−4.34189	+	13.3630i	−0.372314	+	1.14586i
$137$	−0.108211	−	0.0786196i	−0.00924505	−	0.00671693i	0.583153	−	0.812362i	$-0.301819\pi$
$137$	−0.108211	−	0.0786196i	−0.00924505	−	0.00671693i	−0.592398	+	0.805645i	$0.701819\pi$
$138$		0			0
$139$	3.44404	−	10.5997i	0.292120	−	0.899053i	−0.692054	−	0.721846i	$-0.743294\pi$
$139$	3.44404	−	10.5997i	0.292120	−	0.899053i	0.984174	−	0.177207i	$-0.0567061\pi$
$140$	0.431305	+	1.32742i	0.0364519	+	0.112188i
$141$		0			0
$142$	18.7754			1.57560
$143$	19.8070	−	2.92901i	1.65635	−	0.244936i
$144$		0			0
$145$	1.20647	−	0.876555i	0.100192	−	0.0727939i
$146$	−0.454106	−	1.39759i	−0.0375820	−	0.115666i
$147$		0			0
$148$	21.5965	+	15.6908i	1.77522	+	1.28977i
$149$	−3.19148	−	2.31875i	−0.261456	−	0.189959i	0.449333	−	0.893365i	$-0.351662\pi$
$149$	−3.19148	−	2.31875i	−0.261456	−	0.189959i	−0.710789	+	0.703406i	$0.751662\pi$
$150$		0			0
$151$	−0.827284	−	2.54612i	−0.0673235	−	0.207200i	0.911735	−	0.410778i	$-0.134743\pi$
$151$	−0.827284	−	2.54612i	−0.0673235	−	0.207200i	−0.979059	+	0.203578i	$0.934743\pi$
$152$	20.2010	−	14.6769i	1.63852	−	1.19045i
$153$		0			0
$154$	1.72245	−	10.1965i	0.138799	−	0.821655i
$155$	−0.948056			−0.0761497
$156$		0			0
$157$	−3.29874	−	10.1525i	−0.263268	−	0.810257i	−0.992087	−	0.125550i	$-0.959930\pi$
$157$	−3.29874	−	10.1525i	−0.263268	−	0.810257i	0.728819	−	0.684706i	$-0.240070\pi$
$158$	3.59365	−	11.0601i	0.285896	−	0.879896i
$159$		0			0
$160$	2.28638	+	1.66115i	0.180754	+	0.131326i
$161$	2.03390	−	6.25971i	0.160294	−	0.493334i
$162$		0			0
$163$	−5.97347	+	4.33998i	−0.467878	+	0.339933i	−0.796614	−	0.604489i	$-0.793378\pi$
$163$	−5.97347	+	4.33998i	−0.467878	+	0.339933i	0.328736	+	0.944422i	$0.393378\pi$
$164$	−52.4020			−4.09191
$165$		0			0
$166$	−40.5410			−3.14659
$167$	8.35056	−	6.06704i	0.646186	−	0.469481i	−0.215784	−	0.976441i	$-0.569231\pi$
$167$	8.35056	−	6.06704i	0.646186	−	0.469481i	0.861970	+	0.506960i	$0.169231\pi$
$168$		0			0
$169$	7.24498	−	22.2977i	0.557306	−	1.71521i
$170$	−0.934749	−	0.679135i	−0.0716920	−	0.0520873i
$171$		0			0
$172$	18.4377	−	56.7454i	1.40586	−	4.32679i
$173$	4.96625	+	15.2845i	0.377577	+	1.16206i	0.941724	+	0.336388i	$0.109205\pi$
$173$	4.96625	+	15.2845i	0.377577	+	1.16206i	−0.564147	+	0.825675i	$0.690795\pi$
$174$		0			0
$175$	5.86111			0.443058
$176$	−15.2151	−	30.6348i	−1.14688	−	2.30919i
$177$		0			0
$178$	0.133150	−	0.0967392i	0.00998002	−	0.00725091i
$179$	−1.14818	−	3.53374i	−0.0858191	−	0.264124i	0.898933	−	0.438085i	$-0.144343\pi$
$179$	−1.14818	−	3.53374i	−0.0858191	−	0.264124i	−0.984752	+	0.173961i	$0.944343\pi$
$180$		0			0
$181$	12.2247	+	8.88174i	0.908652	+	0.660174i	0.940674	−	0.339313i	$-0.110195\pi$
$181$	12.2247	+	8.88174i	0.908652	+	0.660174i	−0.0320216	+	0.999487i	$0.510195\pi$
$182$	−15.2279	−	11.0637i	−1.12877	−	0.820100i
$183$		0			0
$184$	−13.1377	−	40.4337i	−0.968524	−	2.98081i
$185$	−1.05301	+	0.765054i	−0.0774185	+	0.0562479i
$186$		0			0
$187$	2.70623	+	5.44884i	0.197899	+	0.398459i
$188$	8.13014			0.592951
$189$		0			0
$190$	0.634510	+	1.95282i	0.0460322	+	0.141673i
$191$	3.70323	−	11.3974i	0.267956	−	0.824685i	−0.723041	−	0.690805i	$-0.757256\pi$
$191$	3.70323	−	11.3974i	0.267956	−	0.824685i	0.990998	−	0.133880i	$-0.0427437\pi$
$192$		0			0
$193$	18.2299	+	13.2448i	1.31221	+	0.953379i	0.999994	+	0.00336958i	$0.00107257\pi$
$193$	18.2299	+	13.2448i	1.31221	+	0.953379i	0.312220	+	0.950010i	$0.398927\pi$
$194$	4.95062	−	15.2364i	0.355434	−	1.09391i
$195$		0			0
$196$	22.2347	−	16.1544i	1.58819	−	1.15389i
$197$	−9.95308			−0.709127			−0.354564	−	0.935032i	$-0.615371\pi$
$197$	−9.95308			−0.709127			−0.354564	+	0.935032i	$0.615371\pi$
$198$		0			0
$199$	−15.5617			−1.10314			−0.551570	−	0.834128i	$-0.685971\pi$
$199$	−15.5617			−1.10314			−0.551570	+	0.834128i	$0.685971\pi$
$200$	30.6285	−	22.2529i	2.16577	−	1.57352i
$201$		0			0
$202$	−12.3967	+	38.1532i	−0.872230	+	2.68445i
$203$	5.97211	+	4.33899i	0.419160	+	0.304538i
$204$		0			0
$205$	0.789548	−	2.42998i	0.0551444	−	0.169717i
$206$	10.1534	+	31.2488i	0.707418	+	2.17721i
$207$		0			0
$208$	−62.2609			−4.31702
$209$	1.80088	−	10.6608i	0.124570	−	0.737422i
$210$		0			0
$211$	1.93750	−	1.40768i	0.133383	−	0.0969084i	−0.519093	−	0.854718i	$-0.673730\pi$
$211$	1.93750	−	1.40768i	0.133383	−	0.0969084i	0.652476	+	0.757809i	$0.273730\pi$
$212$	−13.1207	−	40.3812i	−0.901131	−	2.77339i
$213$		0			0
$214$	−22.9531	−	16.6764i	−1.56904	−	1.13997i
$215$	2.35358	+	1.70998i	0.160513	+	0.116620i
$216$		0			0
$217$	−1.45019	−	4.46324i	−0.0984456	−	0.302984i
$218$	10.9962	−	7.98923i	0.744759	−	0.541099i
$219$		0			0
$220$	3.86170	−	0.571057i	0.260356	−	0.0385007i
$221$	11.0740			0.744918
$222$		0			0
$223$	4.01224	+	12.3484i	0.268679	+	0.826910i	0.990823	+	0.135167i	$0.0431570\pi$
$223$	4.01224	+	12.3484i	0.268679	+	0.826910i	−0.722144	+	0.691743i	$0.756843\pi$
$224$	−4.32298	+	13.3048i	−0.288841	+	0.888962i
$225$		0			0
$226$	−4.33500	−	3.14956i	−0.288360	−	0.209506i
$227$	5.70156	−	17.5476i	0.378426	−	1.16467i	−0.562712	−	0.826653i	$-0.690242\pi$
$227$	5.70156	−	17.5476i	0.378426	−	1.16467i	0.941138	−	0.338022i	$-0.109758\pi$
$228$		0			0
$229$	−16.2934	+	11.8379i	−1.07670	+	0.782267i	−0.977104	−	0.212761i	$-0.931755\pi$
$229$	−16.2934	+	11.8379i	−1.07670	+	0.782267i	−0.0995945	+	0.995028i	$0.531755\pi$
$230$	3.49605			0.230523
$231$		0			0
$232$	47.6825			3.13051
$233$	5.95367	−	4.32560i	0.390038	−	0.283379i	−0.375433	−	0.926850i	$-0.622506\pi$
$233$	5.95367	−	4.32560i	0.390038	−	0.283379i	0.765471	+	0.643470i	$0.222506\pi$
$234$		0			0
$235$	−0.122498	+	0.377009i	−0.00799087	+	0.0245934i
$236$	15.6126	+	11.3432i	1.01629	+	0.738381i
$237$		0			0
$238$	1.76738	−	5.43943i	0.114562	−	0.352586i
$239$	2.97454	+	9.15470i	0.192407	+	0.592168i	0.999997	+	0.00242388i	$0.000771547\pi$
$239$	2.97454	+	9.15470i	0.192407	+	0.592168i	−0.807590	+	0.589744i	$0.799228\pi$
$240$		0			0
$241$	−26.5631			−1.71108			−0.855540	−	0.517736i	$-0.826775\pi$
$241$	−26.5631			−1.71108			−0.855540	+	0.517736i	$0.826775\pi$
$242$	−27.3174	−	9.50034i	−1.75603	−	0.610705i
$243$		0			0
$244$	42.6340	−	30.9754i	2.72936	−	1.98300i
$245$	0.414098	+	1.27446i	0.0264557	+	0.0814224i
$246$		0			0
$247$	−15.9214	−	11.5676i	−1.01305	−	0.736026i
$248$	−24.5239	−	17.8177i	−1.55727	−	1.13142i
$249$		0			0
$250$	1.93525	+	5.95608i	0.122396	+	0.376695i
$251$	−20.1137	+	14.6135i	−1.26957	+	0.922394i	−0.999185	−	0.0403590i	$-0.987150\pi$
$251$	−20.1137	+	14.6135i	−1.26957	+	0.922394i	−0.270382	+	0.962753i	$0.587150\pi$
$252$		0			0
$253$	−16.3155	−	8.52528i	−1.02575	−	0.535980i
$254$	−3.14970			−0.197630
$255$		0			0
$256$	−3.39282	−	10.4420i	−0.212051	−	0.652627i
$257$	4.14394	−	12.7537i	0.258492	−	0.795556i	−0.734630	−	0.678468i	$-0.762644\pi$
$257$	4.14394	−	12.7537i	0.258492	−	0.795556i	0.993122	−	0.117088i	$-0.0373559\pi$
$258$		0			0
$259$	−5.21244	−	3.78706i	−0.323885	−	0.235316i
$260$	2.19574	−	6.75781i	0.136174	−	0.419101i
$261$		0			0
$262$	12.2672	−	8.91267i	0.757873	−	0.550627i
$263$	−0.781901			−0.0482141			−0.0241071	−	0.999709i	$-0.507674\pi$
$263$	−0.781901			−0.0482141			−0.0241071	+	0.999709i	$0.507674\pi$
$264$		0			0
$265$	2.07024			0.127174
$266$	−8.22288	+	5.97427i	−0.504177	+	0.366306i
$267$		0			0
$268$	14.0000	−	43.0875i	0.855184	−	2.63199i
$269$	8.62814	+	6.26871i	0.526067	+	0.382210i	0.818884	−	0.573958i	$-0.194593\pi$
$269$	8.62814	+	6.26871i	0.526067	+	0.382210i	−0.292818	+	0.956168i	$0.594593\pi$
$270$		0			0
$271$	−7.60141	+	23.3947i	−0.461753	+	1.42113i	0.401268	+	0.915961i	$0.368570\pi$
$271$	−7.60141	+	23.3947i	−0.461753	+	1.42113i	−0.863021	+	0.505168i	$0.831430\pi$
$272$	−5.84603	−	17.9922i	−0.354468	−	1.09094i
$273$		0			0
$274$	0.351684			0.0212460
$275$	2.73048	−	16.1638i	0.164654	−	0.974713i
$276$		0			0
$277$	7.25869	−	5.27374i	0.436132	−	0.316869i	−0.347964	−	0.937508i	$-0.613127\pi$
$277$	7.25869	−	5.27374i	0.436132	−	0.316869i	0.784096	+	0.620639i	$0.213127\pi$
$278$	9.05542	+	27.8697i	0.543108	+	1.67151i
$279$		0			0
$280$	−1.76038	−	1.27899i	−0.105203	−	0.0764344i
$281$	−13.5317	−	9.83136i	−0.807234	−	0.586490i	0.105794	−	0.994388i	$-0.466262\pi$
$281$	−13.5317	−	9.83136i	−0.807234	−	0.586490i	−0.913027	+	0.407898i	$0.866262\pi$
$282$		0			0
$283$	−1.80836	−	5.56556i	−0.107496	−	0.330838i	0.882812	−	0.469726i	$-0.155647\pi$
$283$	−1.80836	−	5.56556i	−0.107496	−	0.330838i	−0.990308	+	0.138888i	$0.955647\pi$
$284$	−28.3840	+	20.6221i	−1.68428	+	1.22370i
$285$		0			0
$286$	−37.6058	+	36.8415i	−2.22368	+	2.17848i
$287$	12.6475			0.746560
$288$		0			0
$289$	−4.21349	−	12.9678i	−0.247852	−	0.762811i
$290$	−1.21167	+	3.72912i	−0.0711515	+	0.218982i
$291$		0			0
$292$	2.22156	+	1.61406i	0.130007	+	0.0944555i
$293$	4.62996	−	14.2495i	0.270485	−	0.832467i	−0.719894	−	0.694084i	$-0.755810\pi$
$293$	4.62996	−	14.2495i	0.270485	−	0.832467i	0.990379	−	0.138383i	$-0.0441905\pi$
$294$		0			0
$295$	−0.761243	+	0.553075i	−0.0443213	+	0.0322013i
$296$	−41.6171			−2.41895
$297$		0			0
$298$	10.3723			0.600850
$299$	−27.1083	+	19.6953i	−1.56771	+	1.13901i
$300$		0			0
$301$	−4.45004	+	13.6958i	−0.256496	+	0.789414i
$302$	5.69469	+	4.13743i	0.327693	+	0.238083i
$303$		0			0
$304$	−10.3892	+	31.9745i	−0.595859	+	1.83387i
$305$	0.794015	+	2.44373i	0.0454652	+	0.139927i
$306$		0			0
$307$	6.52424			0.372358			0.186179	−	0.982516i	$-0.440390\pi$
$307$	6.52424			0.372358			0.186179	+	0.982516i	$0.440390\pi$
$308$	8.59546	+	17.3065i	0.489772	+	0.986129i
$309$		0			0
$310$	2.01665	−	1.46519i	0.114538	−	0.0832169i
$311$	4.45446	+	13.7094i	0.252589	+	0.777390i	0.994295	+	0.106664i	$0.0340170\pi$
$311$	4.45446	+	13.7094i	0.252589	+	0.777390i	−0.741706	+	0.670725i	$0.765983\pi$
$312$		0			0
$313$	−12.7327	−	9.25081i	−0.719692	−	0.522887i	0.166594	−	0.986026i	$-0.446723\pi$
$313$	−12.7327	−	9.25081i	−0.719692	−	0.522887i	−0.886286	+	0.463139i	$0.846723\pi$
$314$	22.7072	+	16.4978i	1.28144	+	0.931022i
$315$		0			0
$316$	6.71524	+	20.6674i	0.377762	+	1.16263i
$317$	−23.7184	+	17.2325i	−1.33216	+	0.967871i	−0.332466	+	0.943115i	$0.607881\pi$
$317$	−23.7184	+	17.2325i	−1.33216	+	0.967871i	−0.999694	+	0.0247558i	$0.992119\pi$
$318$		0			0
$319$	14.7483	−	14.4485i	0.825746	−	0.808962i
$320$	−2.48946			−0.139165
$321$		0			0
$322$	5.34774	+	16.4587i	0.298018	+	0.917205i
$323$	1.84786	−	5.68713i	0.102818	−	0.316440i
$324$		0			0
$325$	−24.1398	−	17.5386i	−1.33904	−	0.972868i
$326$	5.99917	−	18.4636i	0.332263	−	1.02260i
$327$		0			0
$328$	66.0925	−	48.0190i	3.64935	−	2.65141i
$329$	−1.96226			−0.108183
$330$		0			0
$331$	13.4116			0.737169			0.368584	−	0.929594i	$-0.379843\pi$
$331$	13.4116			0.737169			0.368584	+	0.929594i	$0.379843\pi$
$332$	61.2883	−	44.5285i	3.36363	−	2.44382i
$333$		0			0
$334$	−8.38649	+	25.8110i	−0.458888	+	1.41231i
$335$	1.78711	+	1.29841i	0.0976400	+	0.0709396i
$336$		0			0
$337$	3.99318	−	12.2897i	0.217522	−	0.669465i	−0.781443	−	0.623977i	$-0.785516\pi$
$337$	3.99318	−	12.2897i	0.217522	−	0.669465i	0.998965	−	0.0454877i	$-0.0144842\pi$
$338$	19.0492	+	58.6274i	1.03614	+	3.18891i
$339$		0			0
$340$	2.15905			0.117091
$341$	−12.9843	+	1.92009i	−0.703141	+	0.103979i
$342$		0			0
$343$	−12.0820	+	8.77807i	−0.652365	+	0.473971i
$344$	28.7444	+	88.4661i	1.54979	+	4.76977i
$345$		0			0
$346$	−34.1856	−	24.8373i	−1.83783	−	1.33526i
$347$	28.2314	+	20.5113i	1.51554	+	1.10111i	0.963643	+	0.267195i	$0.0860968\pi$
$347$	28.2314	+	20.5113i	1.51554	+	1.10111i	0.551899	+	0.833911i	$0.313903\pi$
$348$		0			0
$349$	−1.14963	−	3.53819i	−0.0615382	−	0.189395i	0.915561	−	0.402179i	$-0.131747\pi$
$349$	−1.14963	−	3.53819i	−0.0615382	−	0.189395i	−0.977099	+	0.212784i	$0.931747\pi$
$350$	−12.4674	+	9.05813i	−0.666413	+	0.484177i
$351$		0			0
$352$	34.6780	+	18.1202i	1.84834	+	0.965807i
$353$	−3.95252			−0.210371			−0.105186	−	0.994453i	$-0.533544\pi$
$353$	−3.95252			−0.210371			−0.105186	+	0.994453i	$0.533544\pi$
$354$		0			0
$355$	−0.528622	−	1.62693i	−0.0280564	−	0.0863486i
$356$	−0.0950368	+	0.292493i	−0.00503694	+	0.0155021i
$357$		0			0
$358$	7.90361	+	5.74231i	0.417719	+	0.303491i
$359$	−2.28796	+	7.04162i	−0.120754	+	0.371643i	−0.993104	−	0.117240i	$-0.962595\pi$
$359$	−2.28796	+	7.04162i	−0.120754	+	0.371643i	0.872350	+	0.488883i	$0.162595\pi$
$360$		0			0
$361$	6.77400	−	4.92160i	0.356526	−	0.259031i
$362$	−39.7301			−2.08817
$363$		0			0
$364$	35.1730			1.84357
$365$	−0.108319	+	0.0786985i	−0.00566969	+	0.00411927i
$366$		0			0
$367$	−7.85395	+	24.1720i	−0.409973	+	1.26177i	0.506698	+	0.862123i	$0.330866\pi$
$367$	−7.85395	+	24.1720i	−0.409973	+	1.26177i	−0.916671	+	0.399643i	$0.869134\pi$
$368$	46.3103	+	33.6464i	2.41409	+	1.75394i
$369$		0			0
$370$	1.05754	−	3.25476i	0.0549787	−	0.169207i
$371$	3.16675	+	9.74624i	0.164409	+	0.506000i
$372$		0			0
$373$	−4.77475			−0.247227			−0.123614	−	0.992330i	$-0.539448\pi$
$373$	−4.77475			−0.247227			−0.123614	+	0.992330i	$0.539448\pi$
$374$	−14.1775	−	7.40812i	−0.733102	−	0.383065i
$375$		0			0
$376$	−10.2542	+	7.45012i	−0.528820	+	0.384211i
$377$	−11.6131	−	35.7416i	−0.598107	−	1.84079i
$378$		0			0
$379$	14.1162	+	10.2560i	0.725100	+	0.526816i	0.888009	−	0.459825i	$-0.152088\pi$
$379$	14.1162	+	10.2560i	0.725100	+	0.526816i	−0.162910	+	0.986641i	$0.552088\pi$
$380$	−3.10413	−	2.25528i	−0.159238	−	0.115693i
$381$		0			0
$382$	9.73690	+	29.9671i	0.498183	+	1.53325i
$383$	−2.74105	+	1.99149i	−0.140061	+	0.101760i	−0.655610	−	0.755100i	$-0.727588\pi$
$383$	−2.74105	+	1.99149i	−0.140061	+	0.101760i	0.515548	+	0.856861i	$0.327588\pi$
$384$		0			0
$385$	−0.932043	+	0.137828i	−0.0475013	+	0.00702436i
$386$	−59.2469			−3.01559
$387$		0			0
$388$	9.25093	+	28.4714i	0.469645	+	1.44542i
$389$	5.79538	−	17.8363i	0.293837	−	0.904339i	−0.689772	−	0.724027i	$-0.742289\pi$
$389$	5.79538	−	17.8363i	0.293837	−	0.904339i	0.983609	−	0.180312i	$-0.0577108\pi$
$390$		0			0
$391$	−8.23695	−	5.98449i	−0.416560	−	0.302649i
$392$	−13.2404	+	40.7498i	−0.668742	+	2.05818i
$393$		0			0
$394$	21.1717	−	15.3821i	1.06661	−	0.774940i
$395$	−1.05956			−0.0533125
$396$		0			0
$397$	10.7157			0.537806			0.268903	−	0.963167i	$-0.413339\pi$
$397$	10.7157			0.537806			0.268903	+	0.963167i	$0.413339\pi$
$398$	33.1021	−	24.0501i	1.65926	−	1.20552i
$399$		0			0
$400$	−15.7519	+	48.4795i	−0.787597	+	2.42397i
$401$	−2.29166	−	1.66499i	−0.114440	−	0.0831457i	0.529093	−	0.848564i	$-0.322532\pi$
$401$	−2.29166	−	1.66499i	−0.114440	−	0.0831457i	−0.643533	+	0.765418i	$0.722532\pi$
$402$		0			0
$403$	−7.38284	+	22.7220i	−0.367765	+	1.13186i
$404$	−23.1650	−	71.2945i	−1.15250	−	3.54704i
$405$		0			0
$406$	−19.4093			−0.963268
$407$	−12.8722	+	12.6106i	−0.638053	+	0.625085i
$408$		0			0
$409$	−19.0473	+	13.8387i	−0.941827	+	0.684278i	−0.948860	−	0.315698i	$-0.897761\pi$
$409$	−19.0473	+	13.8387i	−0.941827	+	0.684278i	0.00703246	+	0.999975i	$0.497761\pi$
$410$	2.07596	+	6.38914i	0.102524	+	0.315537i
$411$		0			0
$412$	−49.6719	−	36.0887i	−2.44716	−	1.77796i
$413$	−3.76819	−	2.73775i	−0.185421	−	0.134716i
$414$		0			0
$415$	1.14143	+	3.51297i	0.0560307	+	0.172445i
$416$	57.6177	−	41.8617i	2.82494	−	2.05244i
$417$		0			0
$418$	12.6451	+	25.4603i	0.618493	+	1.24530i
$419$	21.1174			1.03165			0.515826	−	0.856693i	$-0.327485\pi$
$419$	21.1174			1.03165			0.515826	+	0.856693i	$0.327485\pi$
$420$		0			0
$421$	−7.26722	−	22.3662i	−0.354183	−	1.09006i	−0.956482	−	0.291792i	$-0.905748\pi$
$421$	−7.26722	−	22.3662i	−0.354183	−	1.09006i	0.602299	−	0.798271i	$-0.294252\pi$
$422$	−1.94584	+	5.98867i	−0.0947218	+	0.291524i
$423$		0			0
$424$	53.5522	+	38.9080i	2.60073	+	1.88954i
$425$	2.80171	−	8.62277i	0.135903	−	0.418266i
$426$		0			0
$427$	−10.2900	+	7.47610i	−0.497966	+	0.361794i
$428$	53.0162			2.56264
$429$		0			0
$430$	−7.64913			−0.368874
$431$	4.02881	−	2.92710i	0.194061	−	0.140994i	−0.486512	−	0.873674i	$-0.661731\pi$
$431$	4.02881	−	2.92710i	0.194061	−	0.140994i	0.680573	+	0.732680i	$0.261731\pi$
$432$		0			0
$433$	−7.90629	+	24.3331i	−0.379952	+	1.16937i	0.560124	+	0.828409i	$0.310753\pi$
$433$	−7.90629	+	24.3331i	−0.379952	+	1.16937i	−0.940076	+	0.340964i	$0.889247\pi$
$434$	9.98255	+	7.25274i	0.479178	+	0.348143i
$435$		0			0
$436$	−7.84863	+	24.1556i	−0.375881	+	1.15684i
$437$	5.59126	+	17.2081i	0.267466	+	0.823177i
$438$		0			0
$439$	−4.66005			−0.222412			−0.111206	−	0.993797i	$-0.535471\pi$
$439$	−4.66005			−0.222412			−0.111206	+	0.993797i	$0.535471\pi$
$440$	−4.34731	+	4.25895i	−0.207250	+	0.203037i
$441$		0			0
$442$	−23.5560	+	17.1145i	−1.12045	+	0.814052i
$443$	−7.14563	−	21.9920i	−0.339499	−	1.04487i	−0.964463	−	0.264217i	$-0.914886\pi$
$443$	−7.14563	−	21.9920i	−0.339499	−	1.04487i	0.624964	−	0.780653i	$-0.285114\pi$
$444$		0			0
$445$	−0.0121315	−	0.00881406i	−0.000575089	−	0.000417827i
$446$	−27.6186	−	20.0661i	−1.30778	−	0.950157i
$447$		0			0
$448$	−3.80800	−	11.7198i	−0.179911	−	0.553709i
$449$	−11.1354	+	8.09035i	−0.525512	+	0.381807i	−0.818676	−	0.574255i	$-0.805292\pi$
$449$	−11.1354	+	8.09035i	−0.525512	+	0.381807i	0.293164	+	0.956062i	$0.405292\pi$
$450$		0			0
$451$	5.89203	−	34.8794i	0.277445	−	1.64241i
$452$	10.0128			0.470964
$453$		0			0
$454$	14.9911	+	46.1379i	0.703567	+	2.16536i
$455$	−0.529956	+	1.63104i	−0.0248447	+	0.0764641i
$456$		0			0
$457$	−8.76935	−	6.37131i	−0.410213	−	0.298037i	0.363475	−	0.931604i	$-0.381590\pi$
$457$	−8.76935	−	6.37131i	−0.410213	−	0.298037i	−0.773688	+	0.633567i	$0.781590\pi$
$458$	16.3635	−	50.3617i	0.764617	−	2.35325i
$459$		0			0
$460$	−5.28520	+	3.83992i	−0.246424	+	0.179037i
$461$	2.92792			0.136367			0.0681833	−	0.997673i	$-0.478280\pi$
$461$	2.92792			0.136367			0.0681833	+	0.997673i	$0.478280\pi$
$462$		0			0
$463$	−27.0835			−1.25867			−0.629337	−	0.777132i	$-0.716674\pi$
$463$	−27.0835			−1.25867			−0.629337	+	0.777132i	$0.716674\pi$
$464$	−51.9397	+	37.7364i	−2.41124	+	1.75187i
$465$		0			0
$466$	−5.97929	+	18.4024i	−0.276985	+	0.852473i
$467$	9.14721	+	6.64584i	0.423282	+	0.307533i	0.778957	−	0.627077i	$-0.215749\pi$
$467$	9.14721	+	6.64584i	0.423282	+	0.307533i	−0.355675	+	0.934610i	$0.615749\pi$
$468$		0			0
$469$	−3.37897	+	10.3994i	−0.156026	+	0.480200i
$470$	−0.322083	−	0.991270i	−0.0148566	−	0.0457239i
$471$		0			0
$472$	−30.0860			−1.38482
$473$	35.6973	+	18.6527i	1.64136	+	0.857654i
$474$		0			0
$475$	−13.0352	+	9.47061i	−0.598095	+	0.434541i
$476$	3.30259	+	10.1643i	0.151374	+	0.465882i
$477$		0			0
$478$	−20.4755	−	14.8764i	−0.936530	−	0.680429i
$479$	24.5826	+	17.8603i	1.12321	+	0.816059i	0.984692	−	0.174302i	$-0.0557668\pi$
$479$	24.5826	+	17.8603i	1.12321	+	0.816059i	0.138516	+	0.990360i	$0.455767\pi$
$480$		0			0
$481$	10.1359	+	31.1951i	0.462157	+	1.42237i
$482$	56.5037	−	41.0523i	2.57367	−	1.86988i
$483$		0			0
$484$	51.7322	−	15.6421i	2.35147	−	0.711004i
$485$	−1.45966			−0.0662796
$486$		0			0
$487$	−0.988742	−	3.04303i	−0.0448042	−	0.137893i	0.926152	−	0.377150i	$-0.123096\pi$
$487$	−0.988742	−	3.04303i	−0.0448042	−	0.137893i	−0.970956	+	0.239257i	$0.923096\pi$
$488$	−25.3879	+	78.1361i	−1.14926	+	3.53705i
$489$		0			0
$490$	−2.85048	−	2.07100i	−0.128772	−	0.0935581i
$491$	−1.84843	+	5.68887i	−0.0834183	+	0.256735i	−0.984063	−	0.177822i	$-0.943095\pi$
$491$	−1.84843	+	5.68887i	−0.0834183	+	0.256735i	0.900644	+	0.434557i	$0.143095\pi$
$492$		0			0
$493$	9.23823	−	6.71197i	0.416069	−	0.302292i
$494$	51.7444			2.32809
$495$		0			0
$496$	40.8146			1.83263
$497$	6.85063	−	4.97727i	0.307293	−	0.223261i
$498$		0			0
$499$	9.07808	−	27.9395i	0.406391	−	1.25074i	−0.513338	−	0.858187i	$-0.671591\pi$
$499$	9.07808	−	27.9395i	0.406391	−	1.25074i	0.919728	−	0.392555i	$-0.128409\pi$
$500$	−9.46754	−	6.87857i	−0.423401	−	0.307619i
$501$		0			0
$502$	20.2003	−	62.1700i	0.901582	−	2.77478i
$503$	−4.45188	−	13.7015i	−0.198500	−	0.610919i	−0.999918	−	0.0128145i	$-0.995921\pi$
$503$	−4.45188	−	13.7015i	−0.198500	−	0.610919i	0.801418	−	0.598104i	$-0.204079\pi$
$504$		0			0
$505$	3.65509			0.162649
$506$	47.8810	−	7.08052i	2.12857	−	0.314767i
$507$		0			0
$508$	4.76160	−	3.45950i	0.211262	−	0.153491i
$509$	−13.5477	−	41.6956i	−0.600492	−	1.84812i	−0.525230	−	0.850961i	$-0.676021\pi$
$509$	−13.5477	−	41.6956i	−0.600492	−	1.84812i	−0.0752625	−	0.997164i	$-0.523979\pi$
$510$		0			0
$511$	−0.536186	−	0.389562i	−0.0237195	−	0.0172332i
$512$	29.3882	+	21.3518i	1.29879	+	0.943624i
$513$		0			0
$514$	10.8957	+	33.5334i	0.480587	+	1.47909i
$515$	2.42191	−	1.75962i	0.106722	−	0.0775382i
$516$		0			0
$517$	−0.914145	+	5.41151i	−0.0402040	+	0.237998i
$518$	16.9404			0.744317
$519$		0			0
$520$	3.42317	+	10.5354i	0.150116	+	0.462009i
$521$	6.23122	−	19.1777i	0.272995	−	0.840191i	−0.716748	−	0.697332i	$-0.754370\pi$
$521$	6.23122	−	19.1777i	0.272995	−	0.840191i	0.989743	−	0.142859i	$-0.0456296\pi$
$522$		0			0
$523$	−31.6906	−	23.0245i	−1.38573	−	1.00679i	−0.996318	−	0.0857293i	$-0.972678\pi$
$523$	−31.6906	−	23.0245i	−1.38573	−	1.00679i	−0.389413	−	0.921063i	$-0.627322\pi$
$524$	−8.75583	+	26.9477i	−0.382500	+	1.17721i
$525$		0			0
$526$	1.66322	−	1.20840i	0.0725198	−	0.0526887i
$527$	−7.25946			−0.316227
$528$		0			0
$529$	7.80699			0.339434
$530$	−4.40371	+	3.19948i	−0.191285	+	0.138977i
$531$		0			0
$532$	5.86914	−	18.0633i	0.254459	−	0.783145i
$533$	−52.0907	−	37.8461i	−2.25630	−	1.63930i
$534$		0			0
$535$	−0.798802	+	2.45846i	−0.0345352	+	0.106288i
$536$	21.8260	+	67.1734i	0.942738	+	2.90145i
$537$		0			0
$538$	−28.0414			−1.20895
$539$	8.25253	+	16.6160i	0.355462	+	0.715703i
$540$		0			0
$541$	−14.5837	+	10.5957i	−0.627002	+	0.455544i	−0.855360	−	0.518034i	$-0.826664\pi$
$541$	−14.5837	+	10.5957i	−0.627002	+	0.455544i	0.228358	+	0.973577i	$0.426664\pi$
$542$	−19.9864	−	61.5118i	−0.858489	−	2.64216i
$543$		0			0
$544$	17.5073	+	12.7198i	0.750620	+	0.545357i
$545$	−1.00188	−	0.727911i	−0.0429160	−	0.0311803i
$546$		0			0
$547$	−0.0276786	−	0.0851858i	−0.00118345	−	0.00364228i	0.950463	−	0.310838i	$-0.100610\pi$
$547$	−0.0276786	−	0.0851858i	−0.00118345	−	0.00364228i	−0.951646	+	0.307195i	$0.900610\pi$
$548$	−0.531662	+	0.386275i	−0.0227115	+	0.0165008i
$549$		0			0
$550$	19.1724	+	38.6026i	0.817514	+	1.64602i
$551$	−20.2932			−0.864518
$552$		0			0
$553$	−1.62076	−	4.98819i	−0.0689218	−	0.212120i
$554$	−7.28992	+	22.4361i	−0.309719	+	0.953217i
$555$		0			0
$556$	−44.3006	−	32.1863i	−1.87876	−	1.36500i
$557$	−0.950270	+	2.92463i	−0.0402642	+	0.123921i	−0.969168	−	0.246400i	$-0.920752\pi$
$557$	−0.950270	+	2.92463i	−0.0402642	+	0.123921i	0.928904	+	0.370321i	$0.120752\pi$
$558$		0			0
$559$	59.3112	−	43.0921i	2.50859	−	1.82260i
$560$	2.92976			0.123805
$561$		0			0
$562$	43.9779			1.85510
$563$	−14.4119	+	10.4709i	−0.607390	+	0.441294i	−0.848494	−	0.529205i	$-0.822490\pi$
$563$	−14.4119	+	10.4709i	−0.607390	+	0.441294i	0.241105	+	0.970499i	$0.422490\pi$
$564$		0			0
$565$	−0.150865	+	0.464313i	−0.00634692	+	0.0195338i
$566$	12.4480	+	9.04401i	0.523229	+	0.380148i
$567$		0			0
$568$	16.9022	−	52.0197i	0.709202	−	2.18270i
$569$	−1.31301	−	4.04103i	−0.0550442	−	0.169409i	0.919755	−	0.392493i	$-0.128387\pi$
$569$	−1.31301	−	4.04103i	−0.0550442	−	0.169409i	−0.974799	+	0.223085i	$0.928387\pi$
$570$		0			0
$571$	−45.0573			−1.88559			−0.942795	−	0.333373i	$-0.891813\pi$
$571$	−45.0573			−1.88559			−0.942795	+	0.333373i	$0.891813\pi$
$572$	16.3858	−	97.0002i	0.685126	−	4.05578i
$573$		0			0
$574$	−26.9032	+	19.5463i	−1.12292	+	0.815846i
$575$	8.47741	+	26.0908i	0.353533	+	1.08806i
$576$		0			0
$577$	12.3578	+	8.97845i	0.514461	+	0.373778i	0.814513	−	0.580145i	$-0.197004\pi$
$577$	12.3578	+	8.97845i	0.514461	+	0.373778i	−0.300052	+	0.953923i	$0.597004\pi$
$578$	29.0039	+	21.0726i	1.20640	+	0.876504i
$579$		0			0
$580$	−2.26417	−	6.96839i	−0.0940144	−	0.289347i
$581$	−14.7923	+	10.7472i	−0.613687	+	0.445870i
$582$		0			0
$583$	28.3535	−	4.19284i	1.17428	−	0.173650i
$584$	−4.28101			−0.177150
$585$		0			0
$586$	12.1735	+	37.4663i	0.502884	+	1.54772i
$587$	−13.1598	+	40.5017i	−0.543163	+	1.67168i	0.182154	+	0.983270i	$0.441693\pi$
$587$	−13.1598	+	40.5017i	−0.543163	+	1.67168i	−0.725318	+	0.688414i	$0.758307\pi$
$588$		0			0
$589$	10.4371	+	7.58302i	0.430054	+	0.312453i
$590$	0.764518	−	2.35295i	0.0314747	−	0.0968692i
$591$		0			0
$592$	45.3328	−	32.9362i	1.86317	−	1.35367i
$593$	−10.6230			−0.436236			−0.218118	−	0.975922i	$-0.569992\pi$
$593$	−10.6230			−0.436236			−0.218118	+	0.975922i	$0.569992\pi$
$594$		0			0
$595$	−0.521100			−0.0213630
$596$	−15.6804	+	11.3925i	−0.642295	+	0.466655i
$597$		0			0
$598$	27.2250	−	83.7898i	1.11331	−	3.42642i
$599$	−28.1278	−	20.4360i	−1.14927	−	0.834994i	−0.160887	−	0.986973i	$-0.551436\pi$
$599$	−28.1278	−	20.4360i	−1.14927	−	0.834994i	−0.988384	+	0.151978i	$0.951436\pi$
$600$		0			0
$601$	2.80823	−	8.64285i	0.114550	−	0.352549i	−0.877303	−	0.479937i	$-0.840659\pi$
$601$	2.80823	−	8.64285i	0.114550	−	0.352549i	0.991853	+	0.127388i	$0.0406594\pi$
$602$	−11.7005	−	36.0104i	−0.476876	−	1.46767i
$603$		0			0
$604$	−13.1534			−0.535204
$605$	−0.0541032	+	2.63460i	−0.00219961	+	0.107112i
$606$		0			0
$607$	12.6176	−	9.16720i	0.512131	−	0.372085i	−0.301500	−	0.953466i	$-0.597487\pi$
$607$	12.6176	−	9.16720i	0.512131	−	0.372085i	0.813631	+	0.581381i	$0.197487\pi$
$608$	−11.8840	−	36.5752i	−0.481960	−	1.48332i
$609$		0			0
$610$	−5.46568	−	3.97105i	−0.221299	−	0.160783i
$611$	8.08184	+	5.87180i	0.326956	+	0.237548i
$612$		0			0
$613$	−8.59141	−	26.4417i	−0.347004	−	1.06797i	−0.960502	−	0.278272i	$-0.910238\pi$
$613$	−8.59141	−	26.4417i	−0.347004	−	1.06797i	0.613498	−	0.789696i	$-0.289762\pi$
$614$	−13.8780	+	10.0830i	−0.560071	+	0.406916i
$615$		0			0
$616$	−26.7000	−	13.9515i	−1.07578	−	0.562120i
$617$	−8.03380			−0.323428			−0.161714	−	0.986838i	$-0.551702\pi$
$617$	−8.03380			−0.323428			−0.161714	+	0.986838i	$0.551702\pi$
$618$		0			0
$619$	1.11249	+	3.42391i	0.0447149	+	0.137618i	0.970922	−	0.239398i	$-0.0769501\pi$
$619$	1.11249	+	3.42391i	0.0447149	+	0.137618i	−0.926207	+	0.377016i	$0.876950\pi$
$620$	−1.43940	+	4.43002i	−0.0578078	+	0.177914i
$621$		0			0
$622$	−30.6627	−	22.2777i	−1.22946	−	0.893256i
$623$	0.0229377	−	0.0705949i	0.000918979	−	0.00282833i
$624$		0			0
$625$	−19.5317	+	14.1906i	−0.781266	+	0.567623i
$626$	41.3810			1.65392
$627$		0			0
$628$	−52.4483			−2.09292
$629$	−8.06309	+	5.85818i	−0.321496	+	0.233581i
$630$		0			0
$631$	−6.25432	+	19.2488i	−0.248981	+	0.766283i	0.745976	+	0.665973i	$0.231984\pi$
$631$	−6.25432	+	19.2488i	−0.248981	+	0.766283i	−0.994956	+	0.100310i	$0.968016\pi$
$632$	−27.4084	−	19.9134i	−1.09025	−	0.792111i
$633$		0			0
$634$	23.8205	−	73.3119i	0.946033	−	2.91159i
$635$	0.0886799	+	0.272929i	0.00351916	+	0.0108308i
$636$		0			0
$637$	33.7697			1.33800
$638$	−9.04211	+	53.5271i	−0.357981	+	2.11916i
$639$		0			0
$640$	0.722676	−	0.525055i	0.0285663	−	0.0207546i
$641$	8.61501	+	26.5143i	0.340272	+	1.04725i	0.964066	+	0.265662i	$0.0855904\pi$
$641$	8.61501	+	26.5143i	0.340272	+	1.04725i	−0.623794	+	0.781589i	$0.714410\pi$
$642$		0			0
$643$	−0.0723797	−	0.0525869i	−0.00285437	−	0.00207382i	0.586357	−	0.810053i	$-0.300562\pi$
$643$	−0.0723797	−	0.0525869i	−0.00285437	−	0.00207382i	−0.589212	+	0.807979i	$0.700562\pi$
$644$	−26.1620	−	19.0078i	−1.03093	−	0.749013i
$645$		0			0
$646$	4.85858	+	14.9532i	0.191158	+	0.588324i
$647$	−38.1698	+	27.7320i	−1.50061	+	1.09026i	−0.530473	+	0.847702i	$0.677986\pi$
$647$	−38.1698	+	27.7320i	−1.50061	+	1.09026i	−0.970137	+	0.242556i	$0.922014\pi$
$648$		0			0
$649$	−9.30565	+	9.11651i	−0.365279	+	0.357854i
$650$	78.4543			3.07723
$651$		0			0
$652$	11.2103	+	34.5017i	0.439029	+	1.35119i
$653$	−5.34005	+	16.4350i	−0.208972	+	0.643151i	0.790554	+	0.612392i	$0.209792\pi$
$653$	−5.34005	+	16.4350i	−0.208972	+	0.643151i	−0.999527	+	0.0307590i	$0.990208\pi$
$654$		0			0
$655$	−1.11769	−	0.812048i	−0.0436717	−	0.0317293i
$656$	−33.9907	+	104.613i	−1.32711	+	4.08443i
$657$		0			0
$658$	4.17401	−	3.03259i	0.162720	−	0.118223i
$659$	12.0864			0.470818			0.235409	−	0.971896i	$-0.424357\pi$
$659$	12.0864			0.470818			0.235409	+	0.971896i	$0.424357\pi$
$660$		0			0
$661$	38.5830			1.50071			0.750353	−	0.661037i	$-0.229884\pi$
$661$	38.5830			1.50071			0.750353	+	0.661037i	$0.229884\pi$
$662$	−28.5285	+	20.7271i	−1.10879	+	0.805583i
$663$		0			0
$664$	−36.4963	+	112.324i	−1.41633	+	4.35902i
$665$	0.749199	+	0.544325i	0.0290527	+	0.0211080i
$666$		0			0
$667$	−10.6771	+	32.8608i	−0.413420	+	1.27237i
$668$	−15.6713	−	48.2314i	−0.606342	−	1.86613i
$669$		0			0
$670$	−5.80808			−0.224386
$671$	15.8239	+	31.8605i	0.610874	+	1.22996i
$672$		0			0
$673$	−23.3342	+	16.9533i	−0.899466	+	0.653500i	−0.938329	−	0.345745i	$-0.887626\pi$
$673$	−23.3342	+	16.9533i	−0.899466	+	0.653500i	0.0388631	+	0.999245i	$0.487626\pi$
$674$	10.4993	+	32.3134i	0.404416	+	1.24467i
$675$		0			0
$676$	−93.1918	−	67.7078i	−3.58430	−	2.60415i
$677$	−5.70123	−	4.14218i	−0.219116	−	0.159197i	0.472813	−	0.881163i	$-0.343239\pi$
$677$	−5.70123	−	4.14218i	−0.219116	−	0.159197i	−0.691929	+	0.721966i	$0.743239\pi$
$678$		0			0
$679$	−2.23277	−	6.87174i	−0.0856857	−	0.263713i
$680$	−2.72312	+	1.97847i	−0.104427	+	0.0758707i
$681$		0			0
$682$	24.6522	−	24.1511i	0.943980	−	0.924794i
$683$	−32.5733			−1.24638			−0.623191	−	0.782070i	$-0.714164\pi$
$683$	−32.5733			−1.24638			−0.623191	+	0.782070i	$0.714164\pi$
$684$		0			0
$685$	−0.00990166	−	0.0304742i	−0.000378323	−	0.00116436i
$686$	12.1340	−	37.3445i	0.463277	−	1.42582i
$687$		0			0
$688$	−101.324	−	73.6160i	−3.86293	−	2.80658i
$689$	16.1217	−	49.6174i	0.614187	−	1.89027i
$690$		0			0
$691$	−34.9341	+	25.3811i	−1.32895	+	0.965542i	−0.329181	+	0.944267i	$0.606772\pi$
$691$	−34.9341	+	25.3811i	−1.32895	+	0.965542i	−0.999774	+	0.0212748i	$0.993228\pi$
$692$	78.9608			3.00164
$693$		0			0
$694$	−91.7519			−3.48285
$695$	2.16002	−	1.56935i	0.0819342	−	0.0595287i
$696$		0			0
$697$	6.04573	−	18.6068i	0.228998	−	0.704784i
$698$	7.91357	+	5.74955i	0.299533	+	0.217624i
$699$		0			0
$700$	8.89872	−	27.3875i	0.336340	−	1.03515i
$701$	−8.39620	−	25.8408i	−0.317120	−	0.975995i	−0.974873	−	0.222761i	$-0.928493\pi$
$701$	−8.39620	−	25.8408i	−0.317120	−	0.975995i	0.657753	−	0.753234i	$-0.271507\pi$
$702$		0			0
$703$	17.7118			0.668013
$704$	−34.0949	+	5.04187i	−1.28500	+	0.190023i
$705$		0			0
$706$	8.40759	−	6.10847i	0.316424	−	0.229895i
$707$	5.59101	+	17.2073i	0.210271	+	0.647149i
$708$		0			0
$709$	17.3625	+	12.6146i	0.652063	+	0.473751i	0.863973	−	0.503538i	$-0.167969\pi$
$709$	17.3625	+	12.6146i	0.652063	+	0.473751i	−0.211911	+	0.977289i	$0.567969\pi$
$710$	3.63882	+	2.64376i	0.136563	+	0.0992185i
$711$		0			0
$712$	−0.148163	−	0.455998i	−0.00555263	−	0.0170892i
$713$	17.7706	−	12.9111i	0.665515	−	0.483525i
$714$		0			0
$715$	4.25119	+	2.22135i	0.158985	+	0.0830740i
$716$	−18.2555			−0.682240
$717$		0			0
$718$	−6.01574	−	18.5145i	−0.224505	−	0.690956i
$719$	−5.61293	+	17.2748i	−0.209327	+	0.644242i	0.790181	+	0.612874i	$0.209987\pi$
$719$	−5.61293	+	17.2748i	−0.209327	+	0.644242i	−0.999508	+	0.0313684i	$0.990013\pi$
$720$		0			0
$721$	11.9886	+	8.71023i	0.446479	+	0.324386i
$722$	−6.80314	+	20.9379i	−0.253187	+	0.779229i
$723$		0			0
$724$	60.0624	−	43.6379i	2.23220	−	1.62179i
$725$	−30.7683			−1.14271
$726$		0			0
$727$	−25.5506			−0.947619			−0.473810	−	0.880627i	$-0.657122\pi$
$727$	−25.5506			−0.947619			−0.473810	+	0.880627i	$0.657122\pi$
$728$	−44.3622	+	32.2311i	−1.64417	+	1.19456i
$729$		0			0
$730$	0.108785	−	0.334807i	0.00402633	−	0.0123918i
$731$	18.0219	+	13.0937i	0.666563	+	0.484287i
$732$		0			0
$733$	−12.5884	+	38.7430i	−0.464962	+	1.43101i	0.394068	+	0.919081i	$0.371067\pi$
$733$	−12.5884	+	38.7430i	−0.464962	+	1.43101i	−0.859030	+	0.511925i	$0.828933\pi$
$734$	−20.6504	−	63.5553i	−0.762219	−	2.34587i
$735$		0			0
$736$	−65.4790			−2.41359
$737$	27.1054	+	14.1633i	0.998439	+	0.521710i
$738$		0			0
$739$	25.9774	−	18.8737i	0.955596	−	0.694281i	0.00347186	−	0.999994i	$-0.498895\pi$
$739$	25.9774	−	18.8737i	0.955596	−	0.694281i	0.952124	+	0.305713i	$0.0988949\pi$
$740$	1.97616	+	6.08198i	0.0726449	+	0.223578i
$741$		0			0
$742$	−21.7986	−	15.8376i	−0.800252	−	0.581417i
$743$	−14.5318	−	10.5580i	−0.533121	−	0.387335i	0.288403	−	0.957509i	$-0.406876\pi$
$743$	−14.5318	−	10.5580i	−0.533121	−	0.387335i	−0.821524	+	0.570174i	$0.806876\pi$
$744$		0			0
$745$	−0.292032	−	0.898782i	−0.0106992	−	0.0329288i
$746$	10.1566	−	7.37920i	0.371859	−	0.270172i
$747$		0			0
$748$	29.5698	−	4.37270i	1.08118	−	0.159882i
$749$	−12.7958			−0.467547
$750$		0			0
$751$	−7.68948	−	23.6658i	−0.280593	−	0.863577i	−0.987685	−	0.156455i	$-0.949993\pi$
$751$	−7.68948	−	23.6658i	−0.280593	−	0.863577i	0.707092	−	0.707122i	$-0.250007\pi$
$752$	5.27363	−	16.2306i	0.192309	−	0.591868i
$753$		0			0
$754$	79.9402	+	58.0799i	2.91125	+	2.11515i
$755$	0.198184	−	0.609947i	0.00721265	−	0.0221983i
$756$		0			0
$757$	26.3079	−	19.1138i	0.956178	−	0.694704i	0.00391833	−	0.999992i	$-0.498753\pi$
$757$	26.3079	−	19.1138i	0.956178	−	0.694704i	0.952260	+	0.305288i	$0.0987528\pi$
$758$	−45.8775			−1.66635
$759$		0			0
$760$	5.98175			0.216981
$761$	7.13808	−	5.18612i	0.258755	−	0.187997i	−0.450843	−	0.892603i	$-0.648877\pi$
$761$	7.13808	−	5.18612i	0.258755	−	0.187997i	0.709598	+	0.704607i	$0.248877\pi$
$762$		0			0
$763$	1.89431	−	5.83010i	0.0685787	−	0.211064i
$764$	−47.6345	−	34.6085i	−1.72336	−	1.25209i
$765$		0			0
$766$	2.75285	−	8.47239i	0.0994644	−	0.306120i
$767$	7.32748	+	22.5517i	0.264580	+	0.814294i
$768$		0			0
$769$	−26.9649			−0.972378			−0.486189	−	0.873854i	$-0.661613\pi$
$769$	−26.9649			−0.972378			−0.486189	+	0.873854i	$0.661613\pi$
$770$	1.76958	−	1.73362i	0.0637714	−	0.0624753i
$771$		0			0
$772$	89.5672	−	65.0744i	3.22359	−	2.34208i
$773$	−8.24081	−	25.3626i	−0.296401	−	0.912230i	−0.982747	−	0.184954i	$-0.940786\pi$
$773$	−8.24081	−	25.3626i	−0.296401	−	0.912230i	0.686346	−	0.727276i	$-0.259214\pi$
$774$		0			0
$775$	15.8247	+	11.4973i	0.568439	+	0.412995i
$776$	−37.7579	−	27.4327i	−1.35543	−	0.984776i
$777$		0			0
$778$	15.2378	+	46.8971i	0.546301	+	1.68134i
$779$	−28.1283	+	20.4364i	−1.00780	+	0.732209i
$780$		0			0
$781$	−10.5349	−	21.2114i	−0.376968	−	0.759005i
$782$	26.7700			0.957294
$783$		0			0
$784$	−17.8273	−	54.8666i	−0.636688	−	1.95952i
$785$	0.790245	−	2.43213i	0.0282051	−	0.0868063i
$786$		0			0
$787$	13.3855	+	9.72517i	0.477143	+	0.346665i	0.800219	−	0.599708i	$-0.204717\pi$
$787$	13.3855	+	9.72517i	0.477143	+	0.346665i	−0.323075	+	0.946373i	$0.604717\pi$
$788$	−15.1114	+	46.5082i	−0.538322	+	1.65679i
$789$		0			0
$790$	2.25385	−	1.63752i	0.0801884	−	0.0582603i
$791$	−2.41666			−0.0859264
$792$		0			0
$793$	64.7520			2.29941
$794$	−22.7939	+	16.5607i	−0.808924	+	0.587718i
$795$		0			0
$796$	−23.6268	+	72.7159i	−0.837431	+	2.57735i
$797$	−36.0162	−	26.1673i	−1.27576	−	0.926894i	−0.276344	−	0.961059i	$-0.589123\pi$
$797$	−36.0162	−	26.1673i	−1.27576	−	0.926894i	−0.999416	+	0.0341648i	$0.989123\pi$
$798$		0			0
$799$	−0.937991	+	2.88684i	−0.0331837	+	0.102129i
$800$	−18.0184	−	55.4550i	−0.637047	−	1.96063i
$801$		0			0
$802$	7.44789			0.262994
$803$	−1.32412	+	1.29721i	−0.0467274	+	0.0457776i
$804$		0			0
$805$	1.27561	−	0.926787i	0.0449595	−	0.0326650i
$806$	−19.4117	−	59.7430i	−0.683747	−	2.10436i
$807$		0			0
$808$	94.5484	+	68.6934i	3.32620	+	2.41663i
$809$	39.7013	+	28.8447i	1.39582	+	1.01413i	0.995198	+	0.0978851i	$0.0312078\pi$
$809$	39.7013	+	28.8447i	1.39582	+	1.01413i	0.400627	+	0.916241i	$0.368792\pi$
$810$		0			0
$811$	−13.2047	−	40.6400i	−0.463681	−	1.42706i	−0.860634	−	0.509224i	$-0.829933\pi$
$811$	−13.2047	−	40.6400i	−0.463681	−	1.42706i	0.396953	−	0.917839i	$-0.370067\pi$
$812$	29.3423	−	21.3184i	1.02971	−	0.748129i
$813$		0			0
$814$	7.89192	−	46.7182i	0.276612	−	1.63747i
$815$	−1.76882			−0.0619589
$816$		0			0
$817$	−12.2333	−	37.6502i	−0.427989	−	1.31721i
$818$	19.1292	−	58.8737i	0.668838	−	2.05847i
$819$		0			0
$820$	−10.1559	−	7.37871i	−0.354660	−	0.257676i
$821$	8.95439	−	27.5588i	0.312510	−	0.961808i	−0.664257	−	0.747504i	$-0.731252\pi$
$821$	8.95439	−	27.5588i	0.312510	−	0.961808i	0.976767	−	0.214303i	$-0.0687481\pi$
$822$		0			0
$823$	−15.5570	+	11.3028i	−0.542282	+	0.393991i	−0.824932	−	0.565232i	$-0.808787\pi$
$823$	−15.5570	+	11.3028i	−0.542282	+	0.393991i	0.282650	+	0.959223i	$0.408787\pi$
$824$	95.7193			3.33454
$825$		0			0
$826$	12.2466			0.426114
$827$	35.2773	−	25.6305i	1.22671	−	0.891259i	0.230074	−	0.973173i	$-0.426103\pi$
$827$	35.2773	−	25.6305i	1.22671	−	0.891259i	0.996639	+	0.0819138i	$0.0261032\pi$
$828$		0			0
$829$	6.68209	−	20.5654i	0.232078	−	0.714264i	−0.765417	−	0.643535i	$-0.777467\pi$
$829$	6.68209	−	20.5654i	0.232078	−	0.714264i	0.997496	−	0.0707296i	$-0.0225327\pi$
$830$	−7.85715	−	5.70856i	−0.272726	−	0.198147i
$831$		0			0
$832$	−19.3862	+	59.6647i	−0.672097	+	2.06850i
$833$	3.17083	+	9.75882i	0.109863	+	0.338123i
$834$		0			0
$835$	2.47270			0.0855713
$836$	−47.0809	−	24.6010i	−1.62833	−	0.850843i
$837$		0			0
$838$	−44.9198	+	32.6361i	−1.55173	+	1.12740i
$839$	6.86129	+	21.1169i	0.236878	+	0.729036i	0.996867	+	0.0790995i	$0.0252045\pi$
$839$	6.86129	+	21.1169i	0.236878	+	0.729036i	−0.759989	+	0.649936i	$0.774796\pi$
$840$		0			0
$841$	−7.88954	−	5.73208i	−0.272053	−	0.197658i
$842$	50.0246	+	36.3450i	1.72396	+	1.25253i
$843$		0			0
$844$	−3.63607	−	11.1907i	−0.125159	−	0.385199i
$845$	4.54387	−	3.30131i	0.156314	−	0.113569i
$846$		0			0
$847$	−12.4859	+	3.77531i	−0.429020	+	0.129721i
$848$	−89.1256			−3.06059
$849$		0			0
$850$	7.36653	+	22.6718i	0.252670	+	0.777638i
$851$	9.31894	−	28.6808i	0.319449	−	0.983164i
$852$		0			0
$853$	−21.2902	−	15.4682i	−0.728962	−	0.529622i	0.160273	−	0.987073i	$-0.448763\pi$
$853$	−21.2902	−	15.4682i	−0.728962	−	0.529622i	−0.889235	+	0.457451i	$0.848763\pi$
$854$	10.3342	−	31.8055i	0.353630	−	1.08836i
$855$		0			0
$856$	−66.8672	+	48.5819i	−2.28547	+	1.66049i
$857$	27.9702			0.955442			0.477721	−	0.878512i	$-0.341463\pi$
$857$	27.9702			0.955442			0.477721	+	0.878512i	$0.341463\pi$
$858$		0			0
$859$	15.3807			0.524784			0.262392	−	0.964961i	$-0.415489\pi$
$859$	15.3807			0.524784			0.262392	+	0.964961i	$0.415489\pi$
$860$	11.5637	−	8.40149i	0.394317	−	0.286488i
$861$		0			0
$862$	−4.04615	+	12.4528i	−0.137812	+	0.424143i
$863$	−26.5699	−	19.3041i	−0.904449	−	0.657121i	0.0351559	−	0.999382i	$-0.488807\pi$
$863$	−26.5699	−	19.3041i	−0.904449	−	0.657121i	−0.939605	+	0.342261i	$0.888807\pi$
$864$		0			0
$865$	−1.18971	+	3.66156i	−0.0404514	+	0.124497i
$866$	−20.7880	−	63.9789i	−0.706405	−	2.17409i
$867$		0			0
$868$	−23.0573			−0.782617
$869$	−14.5115	+	2.14592i	−0.492269	+	0.0727954i
$870$		0			0
$871$	45.0357	−	32.7204i	1.52598	−	1.10869i
$872$	−12.2360	−	37.6586i	−0.414364	−	1.27528i
$873$		0			0
$874$	−38.4880	−	27.9632i	−1.30188	−	0.945868i
$875$	2.28505	+	1.66018i	0.0772486	+	0.0561244i
$876$		0			0
$877$	15.4562	+	47.5693i	0.521919	+	1.60630i	0.770330	+	0.637646i	$0.220092\pi$
$877$	15.4562	+	47.5693i	0.521919	+	1.60630i	−0.248411	+	0.968655i	$0.579908\pi$
$878$	9.91262	−	7.20194i	0.334535	−	0.243054i
$879$		0			0
$880$	1.36487	−	8.07970i	0.0460098	−	0.272367i
$881$	32.0798			1.08080			0.540399	−	0.841409i	$-0.318273\pi$
$881$	32.0798			1.08080			0.540399	+	0.841409i	$0.318273\pi$
$882$		0			0
$883$	14.4035	+	44.3294i	0.484716	+	1.49180i	0.832392	+	0.554188i	$0.186971\pi$
$883$	14.4035	+	44.3294i	0.484716	+	1.49180i	−0.347676	+	0.937615i	$0.613029\pi$
$884$	16.8133	−	51.7459i	0.565492	−	1.74040i
$885$		0			0
$886$	49.1876	+	35.7369i	1.65249	+	1.20060i
$887$	−9.06966	+	27.9136i	−0.304530	+	0.937245i	0.675323	+	0.737522i	$0.264004\pi$
$887$	−9.06966	+	27.9136i	−0.304530	+	0.937245i	−0.979852	+	0.199723i	$0.935996\pi$
$888$		0			0
$889$	−1.14924	+	0.834971i	−0.0385442	+	0.0280040i
$890$	0.0394273			0.00132161
$891$		0			0
$892$	63.7925			2.13593
$893$	4.36408	−	3.17069i	0.146038	−	0.106103i
$894$		0			0
$895$	0.275058	−	0.846541i	0.00919417	−	0.0282967i
$896$	3.57729	+	2.59905i	0.119509	+	0.0868282i
$897$		0			0
$898$	11.1833	−	34.4187i	0.373192	−	1.14857i
$899$	7.61290	+	23.4301i	0.253904	+	0.781437i
$900$		0			0
$901$	15.8523			0.528116
$902$	41.3716	+	83.2996i	1.37752	+	2.77357i
$903$		0			0
$904$	−12.6288	+	9.17534i	−0.420027	+	0.305167i
$905$	1.11860	+	3.44270i	0.0371835	+	0.114439i
$906$		0			0
$907$	20.3221	+	14.7649i	0.674786	+	0.490260i	0.871624	−	0.490176i	$-0.163067\pi$
$907$	20.3221	+	14.7649i	0.674786	+	0.490260i	−0.196838	+	0.980436i	$0.563067\pi$
$908$	−73.3389	−	53.2838i	−2.43384	−	1.76829i
$909$		0			0
$910$	−1.39341	−	4.28848i	−0.0461912	−	0.142162i
$911$	2.24012	−	1.62754i	0.0742186	−	0.0539230i	−0.550057	−	0.835127i	$-0.685394\pi$
$911$	2.24012	−	1.62754i	0.0742186	−	0.0539230i	0.624276	+	0.781204i	$0.285394\pi$
$912$		0			0
$913$	22.7475	+	45.8009i	0.752833	+	1.51579i
$914$	28.5003			0.942707
$915$		0			0
$916$	30.5775	+	94.1079i	1.01031	+	3.10941i
$917$	2.11327	−	6.50398i	0.0697863	−	0.214780i
$918$		0			0
$919$	−9.58156	−	6.96141i	−0.316066	−	0.229636i	0.418429	−	0.908250i	$-0.362581\pi$
$919$	−9.58156	−	6.96141i	−0.316066	−	0.229636i	−0.734495	+	0.678614i	$0.762581\pi$
$920$	3.14726	−	9.68627i	0.103762	−	0.319347i
$921$		0			0
$922$	−6.22811	+	4.52499i	−0.205112	+	0.149022i
$923$	−43.1092			−1.41896
$924$		0			0
$925$	26.8544			0.882969
$926$	57.6105	−	41.8565i	1.89320	−	1.37549i
$927$		0			0
$928$	22.6938	−	69.8443i	0.744960	−	2.29275i
$929$	9.10833	+	6.61759i	0.298835	+	0.217116i	0.727091	−	0.686541i	$-0.240872\pi$
$929$	9.10833	+	6.61759i	0.298835	+	0.217116i	−0.428256	+	0.903657i	$0.640872\pi$
$930$		0			0
$931$	5.63498	−	17.3427i	0.184679	−	0.568383i
$932$	−11.1731	−	34.3874i	−0.365988	−	1.12640i
$933$		0			0
$934$	−29.7284			−0.972742
$935$	−0.242762	+	1.43709i	−0.00793916	+	0.0469979i
$936$		0			0
$937$	25.6860	−	18.6619i	0.839123	−	0.609659i	−0.0830022	−	0.996549i	$-0.526451\pi$
$937$	25.6860	−	18.6619i	0.839123	−	0.609659i	0.922126	+	0.386891i	$0.126451\pi$
$938$	−8.88433	−	27.3431i	−0.290084	−	0.892785i
$939$		0			0
$940$	1.57568	+	1.14480i	0.0513931	+	0.0373393i
$941$	10.2016	+	7.41190i	0.332563	+	0.241621i	0.741517	−	0.670934i	$-0.234106\pi$
$941$	10.2016	+	7.41190i	0.332563	+	0.241621i	−0.408954	+	0.912555i	$0.634106\pi$
$942$		0			0
$943$	18.2932	+	56.3006i	0.595708	+	1.83340i
$944$	32.7721	−	23.8104i	1.06664	−	0.774961i
$945$		0			0
$946$	−104.760	+	15.4917i	−3.40606	+	0.503678i
$947$	0.369770			0.0120159			0.00600796	−	0.999982i	$-0.498088\pi$
$947$	0.369770			0.0120159			0.00600796	+	0.999982i	$0.498088\pi$
$948$		0			0
$949$	1.04265	+	3.20894i	0.0338457	+	0.104166i
$950$	13.0913	−	40.2908i	0.424737	−	1.30721i
$951$		0			0
$952$	−13.4796	−	9.79351i	−0.436877	−	0.317409i
$953$	−5.23478	+	16.1110i	−0.169571	+	0.521886i	−0.999344	−	0.0362151i	$-0.988470\pi$
$953$	−5.23478	+	16.1110i	−0.169571	+	0.521886i	0.829773	+	0.558101i	$0.188470\pi$
$954$		0			0
$955$	2.32257	−	1.68745i	0.0751567	−	0.0546046i
$956$	47.2937			1.52959
$957$		0			0
$958$	−79.8933			−2.58124
$959$	0.128320	−	0.0932297i	0.00414366	−	0.00301054i
$960$		0			0
$961$	−4.73977	+	14.5875i	−0.152896	+	0.470565i
$962$	−69.7714	−	50.6919i	−2.24952	−	1.63437i
$963$		0			0
$964$	−40.3299	+	124.123i	−1.29894	+	3.99772i
$965$	1.66810	+	5.13388i	0.0536980	+	0.165265i
$966$		0			0
$967$	24.8161			0.798031			0.399016	−	0.916944i	$-0.369352\pi$
$967$	24.8161			0.798031			0.399016	+	0.916944i	$0.369352\pi$
$968$	−50.9140	+	67.1340i	−1.63644	+	2.15777i
$969$		0			0
$970$	3.10491	−	2.25585i	0.0996925	−	0.0724309i
$971$	−3.75006	−	11.5415i	−0.120345	−	0.370384i	0.872679	−	0.488294i	$-0.162381\pi$
$971$	−3.75006	−	11.5415i	−0.120345	−	0.370384i	−0.993024	+	0.117910i	$0.962381\pi$
$972$		0			0
$973$	10.6922	+	7.76834i	0.342776	+	0.249042i
$974$	6.80610	+	4.94492i	0.218081	+	0.158445i
$975$		0			0
$976$	−34.1830	−	105.204i	−1.09417	−	3.36751i
$977$	−28.6201	+	20.7937i	−0.915639	+	0.665251i	−0.942435	−	0.334390i	$-0.891470\pi$
$977$	−28.6201	+	20.7937i	−0.915639	+	0.665251i	0.0267954	+	0.999641i	$0.491470\pi$
$978$		0			0
$979$	−0.184001	−	0.0961453i	−0.00588070	−	0.00307282i
$980$	6.58394			0.210316
$981$		0			0
$982$	−4.86006	−	14.9577i	−0.155091	−	0.477321i
$983$	6.94854	−	21.3854i	0.221624	−	0.682088i	−0.776993	−	0.629509i	$-0.783256\pi$
$983$	6.94854	−	21.3854i	0.221624	−	0.682088i	0.998617	−	0.0525789i	$-0.0167441\pi$
$984$		0			0
$985$	−1.92898	−	1.40149i	−0.0614625	−	0.0446551i
$986$	−9.27798	+	28.5547i	−0.295471	+	0.909366i
$987$		0			0
$988$	−78.2252	+	56.8339i	−2.48867	+	1.80813i
$989$	−67.4036			−2.14331
$990$		0			0
$991$	16.2761			0.517028			0.258514	−	0.966008i	$-0.416767\pi$
$991$	16.2761			0.517028			0.258514	+	0.966008i	$0.416767\pi$
$992$	−37.7708	+	27.4421i	−1.19922	+	0.871287i
$993$		0			0
$994$	−6.88011	+	21.1748i	−0.218224	+	0.671624i
$995$	−3.01598	−	2.19124i	−0.0956130	−	0.0694669i
$996$		0			0
$997$	1.42895	−	4.39786i	0.0452553	−	0.139282i	−0.925876	−	0.377828i	$-0.876671\pi$
$997$	1.42895	−	4.39786i	0.0452553	−	0.139282i	0.971131	+	0.238547i	$0.0766710\pi$
$998$	23.8690	+	73.4612i	0.755560	+	2.32537i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.c.487.1	✓	24
3.2	odd	2		891.2.f.d.487.6	yes	24
9.2	odd	6		891.2.n.j.190.1		48
9.4	even	3		891.2.n.k.784.1		48
9.5	odd	6		891.2.n.j.784.6		48
9.7	even	3		891.2.n.k.190.6		48
11.2	odd	10		9801.2.a.cl.1.1		12
11.4	even	5	inner	891.2.f.c.730.1	yes	24
11.9	even	5		9801.2.a.cg.1.12		12
33.2	even	10		9801.2.a.cf.1.12		12
33.20	odd	10		9801.2.a.ck.1.1		12
33.26	odd	10		891.2.f.d.730.6	yes	24
99.4	even	15		891.2.n.k.136.6		48
99.59	odd	30		891.2.n.j.136.1		48
99.70	even	15		891.2.n.k.433.1		48
99.92	odd	30		891.2.n.j.433.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.c.487.1	✓	24	1.1	even	1	trivial
891.2.f.c.730.1	yes	24	11.4	even	5	inner
891.2.f.d.487.6	yes	24	3.2	odd	2
891.2.f.d.730.6	yes	24	33.26	odd	10
891.2.n.j.136.1		48	99.59	odd	30
891.2.n.j.190.1		48	9.2	odd	6
891.2.n.j.433.6		48	99.92	odd	30
891.2.n.j.784.6		48	9.5	odd	6
891.2.n.k.136.6		48	99.4	even	15
891.2.n.k.190.6		48	9.7	even	3
891.2.n.k.433.1		48	99.70	even	15
891.2.n.k.784.1		48	9.4	even	3
9801.2.a.cf.1.12		12	33.2	even	10
9801.2.a.cg.1.12		12	11.9	even	5
9801.2.a.ck.1.1		12	33.20	odd	10
9801.2.a.cl.1.1		12	11.2	odd	10

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12715 + 1.54546i) q^{2} +(1.51827 - 4.67274i) q^{4} +(0.193808 + 0.140810i) q^{5} +(-0.366442 + 1.12779i) q^{7} +(2.36698 + 7.28482i) q^{8} -0.629874 q^{10} +(2.93952 + 1.53597i) q^{11} +(4.88403 - 3.54845i) q^{13} +(-0.963487 - 2.96531i) q^{14} +(-8.34358 - 6.06197i) q^{16} +(1.48403 + 1.07821i) q^{17} +(-1.00736 - 3.10034i) q^{19} +(0.952219 - 0.691827i) q^{20} +(-8.62659 + 1.27568i) q^{22} -5.55040 q^{23} +(-1.52735 - 4.70070i) q^{25} +(-4.90504 + 15.0962i) q^{26} +(4.71353 + 3.42458i) q^{28} +(1.92367 - 5.92043i) q^{29} +(-3.20168 + 2.32616i) q^{31} +11.7972 q^{32} -4.82307 q^{34} +(-0.229824 + 0.166977i) q^{35} +(-1.67897 + 5.16733i) q^{37} +(6.93427 + 5.03804i) q^{38} +(-0.567033 + 1.74515i) q^{40} +(-3.29583 - 10.1435i) q^{41} +12.1439 q^{43} +(11.6402 - 11.4036i) q^{44} +(11.8065 - 8.57795i) q^{46} +(0.511346 + 1.57376i) q^{47} +(4.52548 + 3.28795i) q^{49} +(10.5137 + 7.63862i) q^{50} +(-9.16576 - 28.2093i) q^{52} +(6.99142 - 5.07956i) q^{53} +(0.353422 + 0.711596i) q^{55} -9.08313 q^{56} +(5.05789 + 15.5666i) q^{58} +(-1.21376 + 3.73558i) q^{59} +(8.67742 + 6.30451i) q^{61} +(3.21546 - 9.89616i) q^{62} +(-8.40715 + 6.10815i) q^{64} +1.44622 q^{65} +9.22102 q^{67} +(7.29134 - 5.29747i) q^{68} +(0.230812 - 0.710368i) q^{70} +(-5.77707 - 4.19728i) q^{71} +(-0.172710 + 0.531546i) q^{73} +(-4.41451 - 13.5865i) q^{74} -16.0165 q^{76} +(-2.80943 + 2.75233i) q^{77} +(-3.57826 + 2.59976i) q^{79} +(-0.763468 - 2.34971i) q^{80} +(22.6872 + 16.4832i) q^{82} +(12.4742 + 9.06302i) q^{83} +(0.135794 + 0.417930i) q^{85} +(-25.8319 + 18.7680i) q^{86} +(-4.23151 + 25.0495i) q^{88} -0.0625956 q^{89} +(2.21221 + 6.80848i) q^{91} +(-8.42699 + 25.9356i) q^{92} +(-3.51990 - 2.55735i) q^{94} +(0.241323 - 0.742716i) q^{95} +(-4.92941 + 3.58143i) q^{97} -14.7078 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 8 q^{4} + 4 q^{5} + 7 q^{7} + 10 q^{8} - 16 q^{10} + 5 q^{11} + 7 q^{13} + 13 q^{14} + 2 q^{16} - 5 q^{17} + 4 q^{19} + 27 q^{20} - 2 q^{22} + 6 q^{23} - 2 q^{25} - 34 q^{26} - 9 q^{28}+ \cdots + 68 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 - 8 * q^4 + 4 * q^5 + 7 * q^7 + 10 * q^8 - 16 * q^10 + 5 * q^11 + 7 * q^13 + 13 * q^14 + 2 * q^16 - 5 * q^17 + 4 * q^19 + 27 * q^20 - 2 * q^22 + 6 * q^23 - 2 * q^25 - 34 * q^26 - 9 * q^28 + 22 * q^29 + 2 * q^31 + 18 * q^32 - 42 * q^34 + 6 * q^37 - 5 * q^38 + 53 * q^40 + 10 * q^41 - 30 * q^43 + 59 * q^44 + 31 * q^46 + 4 * q^47 - 3 * q^49 + 9 * q^50 - 26 * q^52 + 17 * q^53 + 12 * q^55 - 48 * q^56 + 53 * q^58 + 11 * q^59 + 3 * q^61 - 2 * q^62 + 38 * q^64 - 68 * q^65 - 14 * q^67 + 22 * q^68 - 20 * q^70 - 36 * q^71 + 35 * q^73 + 3 * q^74 - 102 * q^76 - 88 * q^77 - 9 * q^79 - 37 * q^80 - 6 * q^82 + 32 * q^83 - 45 * q^85 - 110 * q^86 + 54 * q^88 + 34 * q^89 + 13 * q^91 - q^92 - 25 * q^94 - 84 * q^95 + 15 * q^97 + 68 * q^98

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