LMFDB - Embedded newform 936.2.dg.f.829.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 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("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.21
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.f.901.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03161 - 0.967362i) q^{2} +(0.128423 - 1.99587i) q^{4} -1.39452 q^{5} +(2.60703 + 1.50517i) q^{7} +(-1.79825 - 2.18319i) q^{8} +(-1.43859 + 1.34900i) q^{10} +(-1.67760 - 2.90570i) q^{11} +(3.25027 - 1.56068i) q^{13} +(4.14547 - 0.969197i) q^{14} +(-3.96701 - 0.512632i) q^{16} +(1.30140 - 2.25409i) q^{17} +(1.73878 - 3.01165i) q^{19} +(-0.179088 + 2.78328i) q^{20} +(-4.54148 - 1.37468i) q^{22} +(-0.413673 - 0.716502i) q^{23} -3.05532 q^{25} +(1.84326 - 4.75420i) q^{26} +(3.33893 - 5.00999i) q^{28} +(1.52087 - 0.878073i) q^{29} -3.22258i q^{31} +(-4.58830 + 3.30870i) q^{32} +(-0.837987 - 3.58425i) q^{34} +(-3.63555 - 2.09898i) q^{35} +(-1.69186 - 2.93038i) q^{37} +(-1.11962 - 4.78887i) q^{38} +(2.50769 + 3.04449i) q^{40} +(0.270962 - 0.156440i) q^{41} +(6.10602 + 3.52531i) q^{43} +(-6.01484 + 2.97513i) q^{44} +(-1.11986 - 0.338977i) q^{46} -9.27654i q^{47} +(1.03106 + 1.78585i) q^{49} +(-3.15188 + 2.95560i) q^{50} +(-2.69751 - 6.68756i) q^{52} -0.507221i q^{53} +(2.33945 + 4.05205i) q^{55} +(-1.40202 - 8.39829i) q^{56} +(0.719522 - 2.37705i) q^{58} +(-6.95782 + 12.0513i) q^{59} +(7.47996 + 4.31856i) q^{61} +(-3.11740 - 3.32443i) q^{62} +(-1.53261 + 7.85182i) q^{64} +(-4.53257 + 2.17640i) q^{65} +(0.361505 + 0.626146i) q^{67} +(-4.33174 - 2.88690i) q^{68} +(-5.78093 + 1.35156i) q^{70} +(4.51882 + 2.60894i) q^{71} +13.8454i q^{73} +(-4.58007 - 1.38636i) q^{74} +(-5.78758 - 3.85715i) q^{76} -10.1003i q^{77} -1.78577 q^{79} +(5.53208 + 0.714876i) q^{80} +(0.128192 - 0.423503i) q^{82} -7.28881 q^{83} +(-1.81482 + 3.14337i) q^{85} +(9.70926 - 2.26999i) q^{86} +(-3.32693 + 8.88768i) q^{88} +(10.3020 - 5.94787i) q^{89} +(10.8226 + 0.823461i) q^{91} +(-1.48317 + 0.733623i) q^{92} +(-8.97377 - 9.56973i) q^{94} +(-2.42476 + 4.19981i) q^{95} +(-1.96079 - 1.13206i) q^{97} +(2.79120 + 0.844883i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) $ 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	1.03161	−	0.967362i	0.729456	−	0.684028i
$2$	1.03161	−	0.967362i	0.729456	−	0.684028i
$3$		0			0
$3$		0			0
$4$	0.128423	−	1.99587i	0.0642116	−	0.997936i
$5$	−1.39452			−0.623648			−0.311824	−	0.950140i	$-0.600940\pi$
$5$	−1.39452			−0.623648			−0.311824	+	0.950140i	$0.600940\pi$
$6$		0			0
$7$	2.60703	+	1.50517i	0.985363	+	0.568900i	0.903885	−	0.427775i	$-0.140703\pi$
$7$	2.60703	+	1.50517i	0.985363	+	0.568900i	0.0814783	+	0.996675i	$0.474036\pi$
$8$	−1.79825	−	2.18319i	−0.635777	−	0.771873i
$9$		0			0
$10$	−1.43859	+	1.34900i	−0.454924	+	0.426593i
$11$	−1.67760	−	2.90570i	−0.505817	−	0.876100i	−0.999977	−	0.00672953i	$-0.997858\pi$
$11$	−1.67760	−	2.90570i	−0.505817	−	0.876100i	0.494161	−	0.869371i	$-0.335475\pi$
$12$		0			0
$13$	3.25027	−	1.56068i	0.901463	−	0.432856i
$13$	3.25027	−	1.56068i	0.901463	−	0.432856i
$14$	4.14547	−	0.969197i	1.10792	−	0.259029i
$15$		0			0
$16$	−3.96701	−	0.512632i	−0.991754	−	0.128158i
$17$	1.30140	−	2.25409i	0.315635	−	0.546696i	−0.663937	−	0.747788i	$-0.731116\pi$
$17$	1.30140	−	2.25409i	0.315635	−	0.546696i	0.979572	+	0.201092i	$0.0644491\pi$
$18$		0			0
$19$	1.73878	−	3.01165i	0.398903	−	0.690921i	−0.594688	−	0.803957i	$-0.702724\pi$
$19$	1.73878	−	3.01165i	0.398903	−	0.690921i	0.993591	+	0.113036i	$0.0360576\pi$
$20$	−0.179088	+	2.78328i	−0.0400454	+	0.622361i
$21$		0			0
$22$	−4.54148	−	1.37468i	−0.968248	−	0.293084i
$23$	−0.413673	−	0.716502i	−0.0862568	−	0.149401i	0.819669	−	0.572837i	$-0.194157\pi$
$23$	−0.413673	−	0.716502i	−0.0862568	−	0.149401i	−0.905926	+	0.423436i	$0.860824\pi$
$24$		0			0
$25$	−3.05532			−0.611063
$26$	1.84326	−	4.75420i	0.361492	−	0.932375i
$27$		0			0
$28$	3.33893	−	5.00999i	0.630998	−	0.946800i
$29$	1.52087	−	0.878073i	0.282418	−	0.163054i	−0.352100	−	0.935963i	$-0.614532\pi$
$29$	1.52087	−	0.878073i	0.282418	−	0.163054i	0.634518	+	0.772908i	$0.281199\pi$
$30$		0			0
$31$		−	3.22258i		−	0.578792i	−0.957209	−	0.289396i	$-0.906546\pi$
$31$		−	3.22258i		−	0.578792i	0.957209	−	0.289396i	$-0.0934545\pi$
$32$	−4.58830	+	3.30870i	−0.811104	+	0.584902i
$33$		0			0
$34$	−0.837987	−	3.58425i	−0.143714	−	0.614694i
$35$	−3.63555	−	2.09898i	−0.614520	−	0.354793i
$36$		0			0
$37$	−1.69186	−	2.93038i	−0.278139	−	0.481751i	0.692783	−	0.721146i	$-0.256384\pi$
$37$	−1.69186	−	2.93038i	−0.278139	−	0.481751i	−0.970922	+	0.239395i	$0.923051\pi$
$38$	−1.11962	−	4.78887i	−0.181627	−	0.776857i
$39$		0			0
$40$	2.50769	+	3.04449i	0.396501	+	0.481377i
$41$	0.270962	−	0.156440i	0.0423172	−	0.0244318i	−0.478692	−	0.877983i	$-0.658889\pi$
$41$	0.270962	−	0.156440i	0.0423172	−	0.0244318i	0.521009	+	0.853551i	$0.325556\pi$
$42$		0			0
$43$	6.10602	+	3.52531i	0.931159	+	0.537605i	0.887178	−	0.461427i	$-0.152662\pi$
$43$	6.10602	+	3.52531i	0.931159	+	0.537605i	0.0439812	+	0.999032i	$0.485996\pi$
$44$	−6.01484	+	2.97513i	−0.906771	+	0.448517i
$45$		0			0
$46$	−1.11986	−	0.338977i	−0.165115	−	0.0499795i
$47$		−	9.27654i		−	1.35312i	−0.736387	−	0.676561i	$-0.763470\pi$
$47$		−	9.27654i		−	1.35312i	0.736387	−	0.676561i	$-0.236530\pi$
$48$		0			0
$49$	1.03106	+	1.78585i	0.147294	+	0.255121i
$50$	−3.15188	+	2.95560i	−0.445744	+	0.417984i
$51$		0			0
$52$	−2.69751	−	6.68756i	−0.374078	−	0.927397i
$53$		−	0.507221i		−	0.0696721i	−0.999393	−	0.0348361i	$-0.988909\pi$
$53$		−	0.507221i		−	0.0696721i	0.999393	−	0.0348361i	$-0.0110909\pi$
$54$		0			0
$55$	2.33945	+	4.05205i	0.315451	+	0.546378i
$56$	−1.40202	−	8.39829i	−0.187353	−	1.12227i
$57$		0			0
$58$	0.719522	−	2.37705i	0.0944779	−	0.312122i
$59$	−6.95782	+	12.0513i	−0.905831	+	1.56895i	−0.0860327	+	0.996292i	$0.527419\pi$
$59$	−6.95782	+	12.0513i	−0.905831	+	1.56895i	−0.819798	+	0.572653i	$0.805914\pi$
$60$		0			0
$61$	7.47996	+	4.31856i	0.957711	+	0.552935i	0.895468	−	0.445126i	$-0.146841\pi$
$61$	7.47996	+	4.31856i	0.957711	+	0.552935i	0.0622432	+	0.998061i	$0.480175\pi$
$62$	−3.11740	−	3.32443i	−0.395910	−	0.422203i
$63$		0			0
$64$	−1.53261	+	7.85182i	−0.191576	+	0.981478i
$65$	−4.53257	+	2.17640i	−0.562196	+	0.269949i
$66$		0			0
$67$	0.361505	+	0.626146i	0.0441649	+	0.0764959i	0.887263	−	0.461264i	$-0.152604\pi$
$67$	0.361505	+	0.626146i	0.0441649	+	0.0764959i	−0.843098	+	0.537760i	$0.819271\pi$
$68$	−4.33174	−	2.88690i	−0.525301	−	0.350088i
$69$		0			0
$70$	−5.78093	+	1.35156i	−0.690953	+	0.161543i
$71$	4.51882	+	2.60894i	0.536285	+	0.309624i	0.743572	−	0.668656i	$-0.233130\pi$
$71$	4.51882	+	2.60894i	0.536285	+	0.309624i	−0.207287	+	0.978280i	$0.566463\pi$
$72$		0			0
$73$			13.8454i			1.62048i	0.586095	+	0.810242i	$0.300664\pi$
$73$			13.8454i			1.62048i	−0.586095	+	0.810242i	$0.699336\pi$
$74$	−4.58007	−	1.38636i	−0.532422	−	0.161161i
$75$		0			0
$76$	−5.78758	−	3.85715i	−0.663880	−	0.442445i
$77$		−	10.1003i		−	1.15104i
$78$		0			0
$79$	−1.78577			−0.200915			−0.100458	−	0.994941i	$-0.532031\pi$
$79$	−1.78577			−0.200915			−0.100458	+	0.994941i	$0.532031\pi$
$80$	5.53208	+	0.714876i	0.618505	+	0.0799255i
$81$		0			0
$82$	0.128192	−	0.423503i	0.0141564	−	0.0467681i
$83$	−7.28881			−0.800051			−0.400026	−	0.916504i	$-0.630999\pi$
$83$	−7.28881			−0.800051			−0.400026	+	0.916504i	$0.630999\pi$
$84$		0			0
$85$	−1.81482	+	3.14337i	−0.196845	+	0.340946i
$86$	9.70926	−	2.26999i	1.04698	−	0.244780i
$87$		0			0
$88$	−3.32693	+	8.88768i	−0.354651	+	0.947430i
$89$	10.3020	−	5.94787i	1.09201	−	0.630473i	0.157900	−	0.987455i	$-0.449527\pi$
$89$	10.3020	−	5.94787i	1.09201	−	0.630473i	0.934111	+	0.356982i	$0.116194\pi$
$90$		0			0
$91$	10.8226	+	0.823461i	1.13452	+	0.0863222i
$92$	−1.48317	+	0.733623i	−0.154631	+	0.0764855i
$93$		0			0
$94$	−8.97377	−	9.56973i	−0.925573	−	0.987043i
$95$	−2.42476	+	4.19981i	−0.248775	+	0.430891i
$96$		0			0
$97$	−1.96079	−	1.13206i	−0.199088	−	0.114944i	0.397142	−	0.917757i	$-0.370002\pi$
$97$	−1.96079	−	1.13206i	−0.199088	−	0.114944i	−0.596230	+	0.802814i	$0.703335\pi$
$98$	2.79120	+	0.844883i	0.281954	+	0.0853461i
$99$		0			0
$100$	−0.392373	+	6.09802i	−0.0392373	+	0.609802i
$101$	15.5789	−	8.99451i	1.55016	−	0.894987i	0.552035	−	0.833821i	$-0.313851\pi$
$101$	15.5789	−	8.99451i	1.55016	−	0.894987i	0.998128	−	0.0611664i	$-0.0194820\pi$
$102$		0			0
$103$	−8.79966			−0.867056			−0.433528	−	0.901140i	$-0.642732\pi$
$103$	−8.79966			−0.867056			−0.433528	+	0.901140i	$0.642732\pi$
$104$	−9.25206	−	4.28945i	−0.907239	−	0.420616i
$105$		0			0
$106$	−0.490666	−	0.523252i	−0.0476577	−	0.0508227i
$107$	−10.1957	+	5.88648i	−0.985653	+	0.569067i	−0.903972	−	0.427591i	$-0.859362\pi$
$107$	−10.1957	+	5.88648i	−0.985653	+	0.569067i	−0.0816811	+	0.996659i	$0.526029\pi$
$108$		0			0
$109$	14.5156			1.39034			0.695169	−	0.718846i	$-0.255329\pi$
$109$	14.5156			1.39034			0.695169	+	0.718846i	$0.255329\pi$
$110$	6.33319	+	1.91702i	0.603846	+	0.182781i
$111$		0			0
$112$	−9.57052	−	7.30747i	−0.904329	−	0.690491i
$113$	−5.35991	+	9.28364i	−0.504218	+	0.873331i	0.495770	+	0.868454i	$0.334886\pi$
$113$	−5.35991	+	9.28364i	−0.504218	+	0.873331i	−0.999988	+	0.00487747i	$0.998447\pi$
$114$		0			0
$115$	0.576875	+	0.999176i	0.0537938	+	0.0931737i
$116$	−1.55721	−	3.14822i	−0.144583	−	0.292305i
$117$		0			0
$118$	4.48023	+	19.1629i	0.412439	+	1.76409i
$119$	6.78556	−	3.91764i	0.622031	−	0.359130i
$120$		0			0
$121$	−0.128710	+	0.222932i	−0.0117009	+	0.0202666i
$122$	11.8940	−	2.78078i	1.07683	−	0.251760i
$123$		0			0
$124$	−6.43186	−	0.413854i	−0.577598	−	0.0371652i
$125$	11.2333			1.00474
$126$		0			0
$127$	2.69249	+	4.66353i	0.238920	+	0.413821i	0.960405	−	0.278609i	$-0.0898734\pi$
$127$	2.69249	+	4.66353i	0.238920	+	0.413821i	−0.721485	+	0.692430i	$0.756540\pi$
$128$	6.01451	+	9.58257i	0.531612	+	0.846988i
$129$		0			0
$130$	−2.57046	+	6.62982i	−0.225444	+	0.581474i
$131$			14.2718i			1.24694i	0.781849	+	0.623468i	$0.214277\pi$
$131$			14.2718i			1.24694i	−0.781849	+	0.623468i	$0.785723\pi$
$132$		0			0
$133$	9.06608	−	5.23431i	0.786129	−	0.453872i
$134$	0.978641	+	0.296230i	0.0845417	+	0.0255903i
$135$		0			0
$136$	−7.26133	+	1.21221i	−0.622654	+	0.103947i
$137$	14.3160	+	8.26537i	1.22310	+	0.706158i	0.965578	−	0.260114i	$-0.0837602\pi$
$137$	14.3160	+	8.26537i	1.22310	+	0.706158i	0.257524	+	0.966272i	$0.417094\pi$
$138$		0			0
$139$	3.08627	+	1.78186i	0.261774	+	0.151135i	0.625143	−	0.780510i	$-0.285040\pi$
$139$	3.08627	+	1.78186i	0.261774	+	0.151135i	−0.363370	+	0.931645i	$0.618374\pi$
$140$	−4.65619	+	6.98653i	−0.393520	+	0.590470i
$141$		0			0
$142$	7.18543	−	1.67993i	0.602988	−	0.140977i
$143$	−9.98754	−	6.82609i	−0.835200	−	0.570826i
$144$		0			0
$145$	−2.12088	+	1.22449i	−0.176129	+	0.101688i
$146$	13.3935	+	14.2830i	1.10846	+	1.18207i
$147$		0			0
$148$	−6.06594	+	3.00040i	−0.498617	+	0.246631i
$149$	10.1172	−	17.5236i	0.828836	−	1.43559i	−0.0701151	−	0.997539i	$-0.522337\pi$
$149$	10.1172	−	17.5236i	0.828836	−	1.43559i	0.898952	−	0.438048i	$-0.144330\pi$
$150$		0			0
$151$			22.9213i			1.86531i	0.360769	+	0.932655i	$0.382514\pi$
$151$			22.9213i			1.86531i	−0.360769	+	0.932655i	$0.617486\pi$
$152$	−9.70175	+	1.61962i	−0.786916	+	0.131369i
$153$		0			0
$154$	−9.77064	−	10.4195i	−0.787341	−	0.839630i
$155$			4.49395i			0.360963i
$156$		0			0
$157$			6.04864i			0.482734i	0.970434	+	0.241367i	$0.0775957\pi$
$157$			6.04864i			0.482734i	−0.970434	+	0.241367i	$0.922404\pi$
$158$	−1.84221	+	1.72749i	−0.146559	+	0.137432i
$159$		0			0
$160$	6.39847	−	4.61405i	0.505843	−	0.364773i
$161$		−	2.49059i		−	0.196286i
$162$		0			0
$163$	10.2755	−	17.7978i	0.804843	−	1.39403i	−0.111554	−	0.993758i	$-0.535583\pi$
$163$	10.2755	−	17.7978i	0.804843	−	1.39403i	0.916397	−	0.400270i	$-0.131084\pi$
$164$	−0.277437	−	0.560896i	−0.0216642	−	0.0437986i
$165$		0			0
$166$	−7.51919	+	7.05092i	−0.583602	+	0.547257i
$167$	−16.8550	+	9.73122i	−1.30428	+	0.753024i	−0.981134	−	0.193326i	$-0.938072\pi$
$167$	−16.8550	+	9.73122i	−1.30428	+	0.753024i	−0.323142	+	0.946351i	$0.604739\pi$
$168$		0			0
$169$	8.12854	−	10.1453i	0.625272	−	0.780407i
$170$	1.16859	+	4.99831i	0.0896267	+	0.383353i
$171$		0			0
$172$	7.82023	−	11.7341i	0.596287	−	0.894717i
$173$	8.41311	+	4.85731i	0.639637	+	0.369295i	0.784475	−	0.620161i	$-0.212933\pi$
$173$	8.41311	+	4.85731i	0.639637	+	0.369295i	−0.144838	+	0.989455i	$0.546266\pi$
$174$		0			0
$175$	−7.96529	−	4.59876i	−0.602120	−	0.347634i
$176$	5.16553	+	12.3869i	0.389366	+	0.933700i
$177$		0			0
$178$	4.87388	−	16.1016i	0.365313	−	1.20687i
$179$	−8.77002	+	5.06337i	−0.655502	+	0.378454i	−0.790561	−	0.612383i	$-0.790211\pi$
$179$	−8.77002	+	5.06337i	−0.655502	+	0.378454i	0.135059	+	0.990838i	$0.456878\pi$
$180$		0			0
$181$		−	8.20352i		−	0.609763i	−0.952390	−	0.304882i	$-0.901383\pi$
$181$		−	8.20352i		−	0.609763i	0.952390	−	0.304882i	$-0.0986169\pi$
$182$	11.9613	−	9.61991i	0.886629	−	0.713075i
$183$		0			0
$184$	−0.820372	+	2.19157i	−0.0604786	+	0.161565i
$185$	2.35932	+	4.08647i	0.173461	+	0.300443i
$186$		0			0
$187$	−8.73292			−0.638614
$188$	−18.5148	−	1.19132i	−1.35033	−	0.0868861i
$189$		0			0
$190$	1.56133	+	6.67817i	0.113271	+	0.484485i
$191$	−1.95382	+	3.38412i	−0.141374	+	0.244866i	−0.928014	−	0.372545i	$-0.878485\pi$
$191$	−1.95382	+	3.38412i	−0.141374	+	0.244866i	0.786640	+	0.617411i	$0.211819\pi$
$192$		0			0
$193$	9.29572	−	5.36689i	0.669121	−	0.386317i	−0.126623	−	0.991951i	$-0.540414\pi$
$193$	9.29572	−	5.36689i	0.669121	−	0.386317i	0.795743	+	0.605634i	$0.207080\pi$
$194$	−3.11788	+	0.728951i	−0.223851	+	0.0523356i
$195$		0			0
$196$	3.69673	−	1.82852i	0.264052	−	0.130608i
$197$	8.26574	+	14.3167i	0.588909	+	1.02002i	0.994376	+	0.105911i	$0.0337758\pi$
$197$	8.26574	+	14.3167i	0.588909	+	1.02002i	−0.405466	+	0.914110i	$0.632891\pi$
$198$		0			0
$199$	0.916505	−	1.58743i	0.0649693	−	0.112530i	−0.831711	−	0.555209i	$-0.812638\pi$
$199$	0.916505	−	1.58743i	0.0649693	−	0.112530i	0.896680	+	0.442679i	$0.145972\pi$
$200$	5.49422	+	6.67033i	0.388500	+	0.471663i
$201$		0			0
$202$	7.37040	−	24.3493i	0.518579	−	1.71321i
$203$	5.28659			0.371046
$204$		0			0
$205$	−0.377862	+	0.218159i	−0.0263910	+	0.0152369i
$206$	−9.07779	+	8.51245i	−0.632479	+	0.593091i
$207$		0			0
$208$	−13.6939	+	4.52506i	−0.949504	+	0.313756i
$209$	−11.6679			−0.807087
$210$		0			0
$211$	−13.6854	+	7.90126i	−0.942140	+	0.543945i	−0.890631	−	0.454728i	$-0.849737\pi$
$211$	−13.6854	+	7.90126i	−0.942140	+	0.543945i	−0.0515097	+	0.998672i	$0.516403\pi$
$212$	−1.01235	−	0.0651389i	−0.0695284	−	0.00447376i
$213$		0			0
$214$	−4.82357	+	15.9354i	−0.329733	+	1.08932i
$215$	−8.51496	−	4.91611i	−0.580715	−	0.335276i
$216$		0			0
$217$	4.85052	−	8.40135i	0.329275	−	0.570321i
$218$	14.9743	−	14.0418i	1.01419	−	0.951030i
$219$		0			0
$220$	8.38781	−	4.14887i	0.565506	−	0.279717i
$221$	0.711981	−	9.35746i	0.0478930	−	0.629451i
$222$		0			0
$223$	10.8683	−	6.27482i	0.727795	−	0.420193i	−0.0898197	−	0.995958i	$-0.528629\pi$
$223$	10.8683	−	6.27482i	0.727795	−	0.420193i	0.817615	+	0.575765i	$0.195296\pi$
$224$	−16.9420	+	1.71972i	−1.13198	+	0.114904i
$225$		0			0
$226$	3.45132	+	14.7620i	0.229578	+	0.981956i
$227$	1.99719	−	3.45924i	0.132558	−	0.229598i	−0.792104	−	0.610386i	$-0.791014\pi$
$227$	1.99719	−	3.45924i	0.132558	−	0.229598i	0.924662	+	0.380789i	$0.124348\pi$
$228$		0			0
$229$	−28.4156			−1.87775			−0.938877	−	0.344252i	$-0.888133\pi$
$229$	−28.4156			−1.87775			−0.938877	+	0.344252i	$0.888133\pi$
$230$	1.56167	+	0.472710i	0.102974	+	0.0311696i
$231$		0			0
$232$	−4.65189	−	1.74134i	−0.305412	−	0.114325i
$233$	−24.7808			−1.62344			−0.811721	−	0.584046i	$-0.801469\pi$
$233$	−24.7808			−1.62344			−0.811721	+	0.584046i	$0.801469\pi$
$234$		0			0
$235$			12.9363i			0.843872i
$236$	23.1593	+	15.4346i	1.50754	+	1.00471i
$237$		0			0
$238$	3.21025	−	10.6056i	0.208089	−	0.687456i
$239$		−	6.99266i		−	0.452317i	−0.974090	−	0.226159i	$-0.927383\pi$
$239$		−	6.99266i		−	0.452317i	0.974090	−	0.226159i	$-0.0726168\pi$
$240$		0			0
$241$	−8.67485	−	5.00842i	−0.558796	−	0.322621i	0.193866	−	0.981028i	$-0.437897\pi$
$241$	−8.67485	−	5.00842i	−0.558796	−	0.322621i	−0.752662	+	0.658407i	$0.771231\pi$
$242$	0.0828781	+	0.354487i	0.00532760	+	0.0227873i
$243$		0			0
$244$	9.57989	−	14.3744i	0.613290	−	0.920230i
$245$	−1.43783	−	2.49040i	−0.0918596	−	0.159106i
$246$		0			0
$247$	0.951267	−	12.5024i	0.0605277	−	0.795507i
$248$	−7.03549	+	5.79500i	−0.446754	+	0.367983i
$249$		0			0
$250$	11.5883	−	10.8667i	0.732911	−	0.687268i
$251$	−6.05507	−	3.49590i	−0.382193	−	0.220659i	0.296579	−	0.955008i	$-0.404154\pi$
$251$	−6.05507	−	3.49590i	−0.382193	−	0.220659i	−0.678772	+	0.734349i	$0.737488\pi$
$252$		0			0
$253$	−1.38796	+	2.40401i	−0.0872602	+	0.151139i
$254$	7.28891	+	2.20631i	0.457347	+	0.138437i
$255$		0			0
$256$	15.4744	+	4.06724i	0.967151	+	0.254203i
$257$	4.97845	+	8.62293i	0.310547	+	0.537883i	0.978481	−	0.206337i	$-0.0661544\pi$
$257$	4.97845	+	8.62293i	0.310547	+	0.537883i	−0.667934	+	0.744221i	$0.732821\pi$
$258$		0			0
$259$		−	10.1861i		−	0.632934i
$260$	3.76174	+	9.32592i	0.233293	+	0.578369i
$261$		0			0
$262$	13.8060	+	14.7229i	0.852938	+	0.909584i
$263$	13.2725	+	22.9886i	0.818417	+	1.41754i	0.906848	+	0.421458i	$0.138481\pi$
$263$	13.2725	+	22.9886i	0.818417	+	1.41754i	−0.0884309	+	0.996082i	$0.528185\pi$
$264$		0			0
$265$			0.707329i			0.0434509i
$266$	4.28916	−	14.1699i	0.262985	−	0.868814i
$267$		0			0
$268$	1.29613	−	0.641107i	0.0791739	−	0.0391619i
$269$	7.86858	+	4.54293i	0.479756	+	0.276987i	0.720315	−	0.693647i	$-0.243997\pi$
$269$	7.86858	+	4.54293i	0.479756	+	0.276987i	−0.240559	+	0.970635i	$0.577331\pi$
$270$		0			0
$271$	−2.90301	+	1.67605i	−0.176345	+	0.101813i	−0.585574	−	0.810619i	$-0.699131\pi$
$271$	−2.90301	+	1.67605i	−0.176345	+	0.101813i	0.409229	+	0.912432i	$0.365798\pi$
$272$	−6.31818	+	8.27486i	−0.383096	+	0.501737i
$273$		0			0
$274$	22.7641	−	5.32218i	1.37523	−	0.321525i
$275$	5.12561	+	8.87782i	0.309086	+	0.535353i
$276$		0			0
$277$	−12.3436	−	7.12656i	−0.741653	−	0.428193i	0.0810172	−	0.996713i	$-0.474183\pi$
$277$	−12.3436	−	7.12656i	−0.741653	−	0.428193i	−0.822670	+	0.568519i	$0.807516\pi$
$278$	4.90751	−	1.14736i	0.294333	−	0.0688141i
$279$		0			0
$280$	1.95514	+	11.7116i	0.116842	+	0.699900i
$281$			27.8007i			1.65845i	0.558913	+	0.829226i	$0.311218\pi$
$281$			27.8007i			1.65845i	−0.558913	+	0.829226i	$0.688782\pi$
$282$		0			0
$283$	−9.56257	+	5.52095i	−0.568435	+	0.328186i	−0.756524	−	0.653966i	$-0.773104\pi$
$283$	−9.56257	+	5.52095i	−0.568435	+	0.328186i	0.188089	+	0.982152i	$0.439771\pi$
$284$	5.78744	−	8.68394i	0.343421	−	0.515297i
$285$		0			0
$286$	−16.9065	+	2.61972i	−0.999703	+	0.154907i
$287$	0.941874			0.0555970
$288$		0			0
$289$	5.11273	+	8.85551i	0.300749	+	0.520912i
$290$	−1.00339	+	3.31485i	−0.0589209	+	0.194655i
$291$		0			0
$292$	27.6337	+	1.77807i	1.61714	+	0.104054i
$293$	−6.33493	+	10.9724i	−0.370091	+	0.641016i	−0.989579	−	0.143990i	$-0.954007\pi$
$293$	−6.33493	+	10.9724i	−0.370091	+	0.641016i	0.619488	+	0.785006i	$0.287340\pi$
$294$		0			0
$295$	9.70281	−	16.8058i	0.564919	−	0.978469i
$296$	−3.35519	+	8.96319i	−0.195016	+	0.520975i
$297$		0			0
$298$	−6.51462	−	27.8645i	−0.377382	−	1.61414i
$299$	−2.46278	−	1.68322i	−0.142426	−	0.0973429i
$300$		0			0
$301$	10.6124	+	18.3812i	0.611687	+	1.05947i
$302$	22.1732	+	23.6458i	1.27592	+	1.36066i
$303$		0			0
$304$	−8.44163	+	11.0559i	−0.484161	+	0.634100i
$305$	−10.4309	−	6.02231i	−0.597274	−	0.344837i
$306$		0			0
$307$	−28.5408			−1.62891			−0.814455	−	0.580227i	$-0.802964\pi$
$307$	−28.5408			−1.62891			−0.814455	+	0.580227i	$0.802964\pi$
$308$	−20.1589	−	1.29711i	−1.14866	−	0.0739098i
$309$		0			0
$310$	4.34727	+	4.63598i	0.246908	+	0.263306i
$311$	28.1190			1.59448			0.797241	−	0.603661i	$-0.206292\pi$
$311$	28.1190			1.59448			0.797241	+	0.603661i	$0.206292\pi$
$312$		0			0
$313$	−7.36544			−0.416320			−0.208160	−	0.978095i	$-0.566747\pi$
$313$	−7.36544			−0.416320			−0.208160	+	0.978095i	$0.566747\pi$
$314$	5.85122	+	6.23981i	0.330203	+	0.352133i
$315$		0			0
$316$	−0.229335	+	3.56417i	−0.0129011	+	0.200500i
$317$	20.5016			1.15149			0.575743	−	0.817630i	$-0.304713\pi$
$317$	20.5016			1.15149			0.575743	+	0.817630i	$0.304713\pi$
$318$		0			0
$319$	−5.10283	−	2.94612i	−0.285703	−	0.164951i
$320$	2.13725	−	10.9495i	0.119476	−	0.612097i
$321$		0			0
$322$	−2.40930	−	2.56931i	−0.134265	−	0.143182i
$323$	−4.52568	−	7.83871i	−0.251816	−	0.436158i
$324$		0			0
$325$	−9.93061	+	4.76838i	−0.550851	+	0.264502i
$326$	−6.61656	−	28.3005i	−0.366457	−	1.56742i
$327$		0			0
$328$	−0.828795	−	0.310243i	−0.0457625	−	0.0171303i
$329$	13.9627	−	24.1842i	0.769791	−	1.33332i
$330$		0			0
$331$	7.94086	−	13.7540i	0.436469	−	0.755987i	−0.560945	−	0.827853i	$-0.689562\pi$
$331$	7.94086	−	13.7540i	0.436469	−	0.755987i	0.997414	+	0.0718660i	$0.0228954\pi$
$332$	−0.936052	+	14.5475i	−0.0513725	+	0.798400i
$333$		0			0
$334$	−7.97408	+	26.3436i	−0.436322	+	1.44146i
$335$	−0.504126	−	0.873172i	−0.0275434	−	0.0477065i
$336$		0			0
$337$	−4.25797			−0.231946			−0.115973	−	0.993252i	$-0.536999\pi$
$337$	−4.25797			−0.231946			−0.115973	+	0.993252i	$0.536999\pi$
$338$	−1.42872	−	18.3292i	−0.0777119	−	0.996976i
$339$		0			0
$340$	6.04069	+	4.02584i	0.327603	+	0.218332i
$341$	−9.36383	+	5.40621i	−0.507080	+	0.292763i
$342$		0			0
$343$		−	14.8647i		−	0.802617i
$344$	−3.28373	−	19.6700i	−0.177047	−	1.06053i
$345$		0			0
$346$	13.3778	−	3.12769i	0.719195	−	0.168145i
$347$	3.58974	+	2.07254i	0.192708	+	0.111260i	0.593249	−	0.805019i	$-0.297845\pi$
$347$	3.58974	+	2.07254i	0.192708	+	0.111260i	−0.400542	+	0.916278i	$0.631178\pi$
$348$		0			0
$349$	−14.1312	−	24.4759i	−0.756425	−	1.31017i	−0.944663	−	0.328043i	$-0.893611\pi$
$349$	−14.1312	−	24.4759i	−0.756425	−	1.31017i	0.188238	−	0.982123i	$-0.439722\pi$
$350$	−12.6657	+	2.96120i	−0.677011	+	0.158283i
$351$		0			0
$352$	17.3114	+	7.78150i	0.922702	+	0.414756i
$353$	22.2772	−	12.8618i	1.18570	−	0.684563i	0.228372	−	0.973574i	$-0.426660\pi$
$353$	22.2772	−	12.8618i	1.18570	−	0.684563i	0.957326	+	0.289011i	$0.0933263\pi$
$354$		0			0
$355$	−6.30158	−	3.63822i	−0.334453	−	0.193097i
$356$	−10.5482	−	21.3254i	−0.559052	−	1.13024i
$357$		0			0
$358$	−4.14909	+	13.7072i	−0.219286	+	0.724447i
$359$		−	23.8199i		−	1.25717i	−0.777742	−	0.628584i	$-0.783635\pi$
$359$		−	23.8199i		−	1.25717i	0.777742	−	0.628584i	$-0.216365\pi$
$360$		0			0
$361$	3.45330	+	5.98129i	0.181753	+	0.314805i
$362$	−7.93577	−	8.46281i	−0.417095	−	0.444795i
$363$		0			0
$364$	3.03340	−	21.4948i	0.158993	−	1.12664i
$365$		−	19.3077i		−	1.01061i
$366$		0			0
$367$	0.240863	+	0.417186i	0.0125729	+	0.0217769i	0.872243	−	0.489072i	$-0.162664\pi$
$367$	0.240863	+	0.417186i	0.0125729	+	0.0217769i	−0.859670	+	0.510849i	$0.829331\pi$
$368$	1.27374	+	3.05444i	0.0663985	+	0.159224i
$369$		0			0
$370$	6.38699	+	1.93331i	0.332044	+	0.100508i
$371$	0.763452	−	1.32234i	0.0396365	−	0.0686524i
$372$		0			0
$373$	4.06977	+	2.34968i	0.210725	+	0.121662i	0.601648	−	0.798761i	$-0.294511\pi$
$373$	4.06977	+	2.34968i	0.210725	+	0.121662i	−0.390923	+	0.920423i	$0.627844\pi$
$374$	−9.00893	+	8.44789i	−0.465841	+	0.436830i
$375$		0			0
$376$	−20.2524	+	16.6815i	−1.04444	+	0.860284i
$377$	3.57284	−	5.22757i	0.184011	−	0.269233i
$378$		0			0
$379$	8.08676	+	14.0067i	0.415389	+	0.719475i	0.995469	−	0.0950847i	$-0.0303122\pi$
$379$	8.08676	+	14.0067i	0.415389	+	0.719475i	−0.580080	+	0.814559i	$0.696979\pi$
$380$	8.07088	+	5.37886i	0.414028	+	0.275930i
$381$		0			0
$382$	1.25809	+	5.38113i	0.0643696	+	0.275323i
$383$	−16.3259	−	9.42576i	−0.834214	−	0.481634i	0.0210792	−	0.999778i	$-0.493290\pi$
$383$	−16.3259	−	9.42576i	−0.834214	−	0.481634i	−0.855293	+	0.518144i	$0.826623\pi$
$384$		0			0
$385$			14.0851i			0.717841i
$386$	4.39781	−	14.5288i	0.223842	−	0.739499i
$387$		0			0
$388$	−2.51127	+	3.76811i	−0.127490	+	0.191297i
$389$		−	16.5912i		−	0.841205i	−0.907245	−	0.420603i	$-0.861819\pi$
$389$		−	16.5912i		−	0.841205i	0.907245	−	0.420603i	$-0.138181\pi$
$390$		0			0
$391$	−2.15341			−0.108903
$392$	2.04473	−	5.46239i	0.103275	−	0.275892i
$393$		0			0
$394$	22.3764	+	6.77322i	1.12731	+	0.341230i
$395$	2.49029			0.125300
$396$		0			0
$397$	−1.91914	+	3.32405i	−0.0963189	+	0.166829i	−0.910158	−	0.414261i	$-0.864040\pi$
$397$	−1.91914	+	3.32405i	−0.0963189	+	0.166829i	0.813839	+	0.581090i	$0.197374\pi$
$398$	−0.590150	−	2.52420i	−0.0295815	−	0.126527i
$399$		0			0
$400$	12.1205	+	1.56625i	0.606024	+	0.0783127i
$401$	10.0269	−	5.78906i	0.500721	−	0.289092i	−0.228290	−	0.973593i	$-0.573313\pi$
$401$	10.0269	−	5.78906i	0.500721	−	0.289092i	0.729011	+	0.684501i	$0.239980\pi$
$402$		0			0
$403$	−5.02942	−	10.4743i	−0.250534	−	0.521760i
$404$	−15.9512	−	32.2487i	−0.793602	−	1.60443i
$405$		0			0
$406$	5.45368	−	5.11404i	0.270661	−	0.253806i
$407$	−5.67653	+	9.83203i	−0.281375	+	0.487356i
$408$		0			0
$409$	−32.1730	−	18.5751i	−1.59085	−	0.918480i	−0.993161	−	0.116755i	$-0.962751\pi$
$409$	−32.1730	−	18.5751i	−1.59085	−	0.918480i	−0.597693	−	0.801725i	$-0.703916\pi$
$410$	−0.178766	+	0.590583i	−0.00882864	+	0.0291668i
$411$		0			0
$412$	−1.13008	+	17.5630i	−0.0556750	+	0.865267i
$413$	−36.2784	+	20.9454i	−1.78515	+	1.03065i
$414$		0			0
$415$	10.1644			0.498950
$416$	−9.74938	+	17.9151i	−0.478003	+	0.878358i
$417$		0			0
$418$	−12.0367	+	11.2871i	−0.588735	+	0.552070i
$419$	−26.3097	+	15.1899i	−1.28531	+	0.742075i	−0.977814	−	0.209474i	$-0.932825\pi$
$419$	−26.3097	+	15.1899i	−1.28531	+	0.742075i	−0.307497	+	0.951549i	$0.599491\pi$
$420$		0			0
$421$	5.99236			0.292050			0.146025	−	0.989281i	$-0.453352\pi$
$421$	5.99236			0.292050			0.146025	+	0.989281i	$0.453352\pi$
$422$	−6.47455	+	21.3897i	−0.315176	+	1.04123i
$423$		0			0
$424$	−1.10736	+	0.912109i	−0.0537780	+	0.0442959i
$425$	−3.97618	+	6.88695i	−0.192873	+	0.334066i
$426$		0			0
$427$	13.0003	+	22.5172i	0.629129	+	1.08968i
$428$	10.4393	+	21.1052i	0.504602	+	1.02016i
$429$		0			0
$430$	−13.5397	+	3.16555i	−0.652945	+	0.152656i
$431$	25.4435	−	14.6898i	1.22557	−	0.707582i	0.259469	−	0.965752i	$-0.416453\pi$
$431$	25.4435	−	14.6898i	1.22557	−	0.707582i	0.966100	+	0.258169i	$0.0831193\pi$
$432$		0			0
$433$	−7.83461	+	13.5699i	−0.376508	+	0.652130i	−0.990551	−	0.137142i	$-0.956208\pi$
$433$	−7.83461	+	13.5699i	−0.376508	+	0.652130i	0.614044	+	0.789272i	$0.289542\pi$
$434$	−3.12331	−	13.3591i	−0.149924	−	0.641257i
$435$		0			0
$436$	1.86413	−	28.9712i	0.0892758	−	1.38747i
$437$	−2.87714			−0.137632
$438$		0			0
$439$	3.93162	+	6.80976i	0.187646	+	0.325012i	0.944465	−	0.328612i	$-0.106581\pi$
$439$	3.93162	+	6.80976i	0.187646	+	0.325012i	−0.756819	+	0.653624i	$0.773248\pi$
$440$	4.63946	−	12.3940i	0.221178	−	0.590863i
$441$		0			0
$442$	−8.31757	−	10.3420i	−0.395626	−	0.491917i
$443$		−	24.0190i		−	1.14118i	−0.821236	−	0.570589i	$-0.806715\pi$
$443$		−	24.0190i		−	1.14118i	0.821236	−	0.570589i	$-0.193285\pi$
$444$		0			0
$445$	−14.3664	+	8.29442i	−0.681031	+	0.393193i
$446$	5.14179	−	16.9867i	0.243471	−	0.804345i
$447$		0			0
$448$	−15.8139	+	18.1631i	−0.747134	+	0.858125i
$449$	19.9175	+	11.4994i	0.939963	+	0.542688i	0.889949	−	0.456061i	$-0.150740\pi$
$449$	19.9175	+	11.4994i	0.939963	+	0.542688i	0.0500144	+	0.998748i	$0.484073\pi$
$450$		0			0
$451$	−0.909134	−	0.524889i	−0.0428094	−	0.0247160i
$452$	17.8406	+	11.8899i	0.839152	+	0.559255i
$453$		0			0
$454$	−1.28602	−	5.50058i	−0.0603558	−	0.258155i
$455$	−15.0924	−	1.14833i	−0.707541	−	0.0538346i
$456$		0			0
$457$	30.8485	−	17.8104i	1.44303	−	0.833135i	0.444981	−	0.895540i	$-0.353211\pi$
$457$	30.8485	−	17.8104i	1.44303	−	0.833135i	0.998051	+	0.0624055i	$0.0198772\pi$
$458$	−29.3137	+	27.4881i	−1.36974	+	1.28444i
$459$		0			0
$460$	2.06831	−	1.02305i	0.0964356	−	0.0477000i
$461$	−0.848560	+	1.46975i	−0.0395214	+	0.0684530i	−0.885109	−	0.465383i	$-0.845917\pi$
$461$	−0.848560	+	1.46975i	−0.0395214	+	0.0684530i	0.845588	+	0.533836i	$0.179250\pi$
$462$		0			0
$463$		−	1.17416i		−	0.0545677i	−0.999628	−	0.0272838i	$-0.991314\pi$
$463$		−	1.17416i		−	0.0545677i	0.999628	−	0.0272838i	$-0.00868580\pi$
$464$	−6.48343	+	2.70368i	−0.300986	+	0.125515i
$465$		0			0
$466$	−25.5640	+	23.9720i	−1.18423	+	1.11048i
$467$		−	5.69837i		−	0.263689i	−0.991270	−	0.131845i	$-0.957910\pi$
$467$		−	5.69837i		−	0.263689i	0.991270	−	0.131845i	$-0.0420900\pi$
$468$		0			0
$469$			2.17651i			0.100502i
$470$	12.5141	+	13.3452i	0.577232	+	0.615567i
$471$		0			0
$472$	38.8221	−	6.48101i	1.78693	−	0.298313i
$473$		−	23.6563i		−	1.08772i
$474$		0			0
$475$	−5.31252	+	9.20155i	−0.243755	+	0.422196i
$476$	−6.94769	−	14.0462i	−0.318447	−	0.643808i
$477$		0			0
$478$	−6.76443	−	7.21367i	−0.309398	−	0.329946i
$479$	−22.0832	+	12.7498i	−1.00901	+	0.582552i	−0.910901	−	0.412624i	$-0.864612\pi$
$479$	−22.0832	+	12.7498i	−1.00901	+	0.582552i	−0.0981078	+	0.995176i	$0.531279\pi$
$480$		0			0
$481$	−10.0724	−	6.88408i	−0.459261	−	0.313887i
$482$	−13.7940	+	3.22499i	−0.628299	+	0.146894i
$483$		0			0
$484$	0.428415	+	0.285518i	0.0194734	+	0.0129781i
$485$	2.73436	+	1.57868i	0.124161	+	0.0716844i
$486$		0			0
$487$	−22.0022	−	12.7030i	−0.997016	−	0.575627i	−0.0896517	−	0.995973i	$-0.528575\pi$
$487$	−22.0022	−	12.7030i	−0.997016	−	0.575627i	−0.907364	+	0.420346i	$0.861909\pi$
$488$	−4.02261	−	24.0960i	−0.182095	−	1.09077i
$489$		0			0
$490$	−3.89239	−	1.17821i	−0.175840	−	0.0532259i
$491$	−10.8324	+	6.25412i	−0.488861	+	0.282244i	−0.724102	−	0.689693i	$-0.757746\pi$
$491$	−10.8324	+	6.25412i	−0.488861	+	0.282244i	0.235241	+	0.971937i	$0.424412\pi$
$492$		0			0
$493$		−	4.57089i		−	0.205862i
$494$	−11.1130	−	13.8177i	−0.499997	−	0.621690i
$495$		0			0
$496$	−1.65200	+	12.7840i	−0.0741769	+	0.574019i
$497$	7.85379	+	13.6032i	0.352291	+	0.610185i
$498$		0			0
$499$	−34.1916			−1.53063			−0.765313	−	0.643658i	$-0.777416\pi$
$499$	−34.1916			−1.53063			−0.765313	+	0.643658i	$0.777416\pi$
$500$	1.44261	−	22.4202i	0.0645157	−	1.00266i
$501$		0			0
$502$	−9.62825	+	2.25106i	−0.429730	+	0.100470i
$503$	−4.00439	+	6.93580i	−0.178547	+	0.309252i	−0.941383	−	0.337340i	$-0.890473\pi$
$503$	−4.00439	+	6.93580i	−0.178547	+	0.309252i	0.762836	+	0.646592i	$0.223806\pi$
$504$		0			0
$505$	−21.7251	+	12.5430i	−0.966756	+	0.558157i
$506$	0.893725	+	3.82265i	0.0397309	+	0.169938i
$507$		0			0
$508$	9.65359	−	4.77496i	0.428309	−	0.211855i
$509$	−13.0201	−	22.5515i	−0.577107	−	0.999579i	−0.995809	−	0.0914551i	$-0.970848\pi$
$509$	−13.0201	−	22.5515i	−0.577107	−	0.999579i	0.418702	−	0.908124i	$-0.362485\pi$
$510$		0			0
$511$	−20.8397	+	36.0954i	−0.921893	+	1.59677i
$512$	19.8980	−	10.7736i	0.879376	−	0.476129i
$513$		0			0
$514$	13.4773	+	4.07950i	0.594458	+	0.179939i
$515$	12.2713			0.540738
$516$		0			0
$517$	−26.9548	+	15.5624i	−1.18547	+	0.684432i
$518$	−9.85365	−	10.5080i	−0.432944	−	0.461697i
$519$		0			0
$520$	12.9022	+	5.98172i	0.565798	+	0.262316i
$521$	−40.3000			−1.76557			−0.882787	−	0.469773i	$-0.844336\pi$
$521$	−40.3000			−1.76557			−0.882787	+	0.469773i	$0.844336\pi$
$522$		0			0
$523$	−2.28594	+	1.31979i	−0.0999571	+	0.0577103i	−0.549145	−	0.835727i	$-0.685047\pi$
$523$	−2.28594	+	1.31979i	−0.0999571	+	0.0577103i	0.449188	+	0.893437i	$0.351713\pi$
$524$	28.4847	+	1.83283i	1.24436	+	0.0800677i
$525$		0			0
$526$	35.9303	+	10.8759i	1.56664	+	0.474213i
$527$	−7.26397	−	4.19386i	−0.316424	−	0.182687i
$528$		0			0
$529$	11.1577	−	19.3258i	0.485120	−	0.840252i
$530$	0.684243	+	0.729685i	0.0297216	+	0.0316955i
$531$		0			0
$532$	−9.28271	−	18.7670i	−0.402457	−	0.813651i
$533$	0.636547	−	0.931358i	0.0275719	−	0.0403416i
$534$		0			0
$535$	14.2181	−	8.20880i	0.614701	−	0.354898i
$536$	0.716916	−	1.91520i	0.0309661	−	0.0827240i
$537$		0			0
$538$	12.5119	−	2.92525i	0.539428	−	0.126117i
$539$	3.45942	−	5.99188i	0.149008	−	0.258089i
$540$		0			0
$541$	−3.53693			−0.152065			−0.0760324	−	0.997105i	$-0.524225\pi$
$541$	−3.53693			−0.152065			−0.0760324	+	0.997105i	$0.524225\pi$
$542$	−1.37341	+	4.53729i	−0.0589932	+	0.194893i
$543$		0			0
$544$	1.48690	+	14.6484i	0.0637504	+	0.628043i
$545$	−20.2422			−0.867082
$546$		0			0
$547$		−	37.3193i		−	1.59566i	−0.602885	−	0.797828i	$-0.705982\pi$
$547$		−	37.3193i		−	1.59566i	0.602885	−	0.797828i	$-0.294018\pi$
$548$	18.3351	−	27.5115i	0.783238	−	1.17523i
$549$		0			0
$550$	13.8757	+	4.20010i	0.591661	+	0.179093i
$551$		−	6.10710i		−	0.260171i
$552$		0			0
$553$	−4.65556	−	2.68789i	−0.197974	−	0.114301i
$554$	−19.6277	+	4.58888i	−0.833899	+	0.194963i
$555$		0			0
$556$	3.95271	−	5.93096i	0.167632	−	0.251529i
$557$	1.99339	+	3.45265i	0.0844626	+	0.146294i	0.905162	−	0.425067i	$-0.139749\pi$
$557$	1.99339	+	3.45265i	0.0844626	+	0.146294i	−0.820699	+	0.571360i	$0.806416\pi$
$558$		0			0
$559$	25.3481	+	1.92866i	1.07211	+	0.0815736i
$560$	13.3463	+	10.1904i	0.563983	+	0.430623i
$561$		0			0
$562$	26.8933	+	28.6794i	1.13443	+	1.20977i
$563$	15.8682	+	9.16148i	0.668763	+	0.386110i	0.795608	−	0.605812i	$-0.207152\pi$
$563$	15.8682	+	9.16148i	0.668763	+	0.386110i	−0.126845	+	0.991923i	$0.540485\pi$
$564$		0			0
$565$	7.47450	−	12.9462i	0.314455	−	0.544651i
$566$	−4.52405	+	14.9459i	−0.190160	+	0.628223i
$567$		0			0
$568$	−2.43015	−	14.5570i	−0.101967	−	0.610796i
$569$	−8.79566	−	15.2345i	−0.368733	−	0.638665i	0.620634	−	0.784100i	$-0.286875\pi$
$569$	−8.79566	−	15.2345i	−0.368733	−	0.638665i	−0.989368	+	0.145435i	$0.953542\pi$
$570$		0			0
$571$			42.8062i			1.79139i	0.444674	+	0.895693i	$0.353320\pi$
$571$			42.8062i			1.79139i	−0.444674	+	0.895693i	$0.646680\pi$
$572$	−14.9066	+	19.0572i	−0.623278	+	0.796823i
$573$		0			0
$574$	0.971643	−	0.911132i	0.0405556	−	0.0380299i
$575$	1.26390	+	2.18914i	0.0527083	+	0.0912935i
$576$		0			0
$577$		−	31.7922i		−	1.32353i	−0.749713	−	0.661763i	$-0.769808\pi$
$577$		−	31.7922i		−	1.32353i	0.749713	−	0.661763i	$-0.230192\pi$
$578$	13.8408	+	4.18954i	0.575701	+	0.174262i
$579$		0			0
$580$	2.17156	+	4.39025i	0.0901689	+	0.182295i
$581$	−19.0021	−	10.9709i	−0.788341	−	0.455149i
$582$		0			0
$583$	−1.47383	+	0.850916i	−0.0610398	+	0.0352413i
$584$	30.2271	−	24.8975i	1.25081	−	1.03027i
$585$		0			0
$586$	4.07915	+	17.4474i	0.168508	+	0.720745i
$587$	11.5920	+	20.0779i	0.478453	+	0.828705i	0.999695	−	0.0247044i	$-0.00786445\pi$
$587$	11.5920	+	20.0779i	0.478453	+	0.828705i	−0.521242	+	0.853409i	$0.674531\pi$
$588$		0			0
$589$	−9.70529	−	5.60335i	−0.399899	−	0.230882i
$590$	−6.24777	−	26.7231i	−0.257216	−	1.10017i
$591$		0			0
$592$	5.20941	+	12.4922i	0.214105	+	0.513425i
$593$			2.17000i			0.0891111i	0.999007	+	0.0445555i	$0.0141872\pi$
$593$			2.17000i			0.0891111i	−0.999007	+	0.0445555i	$0.985813\pi$
$594$		0			0
$595$	−9.46259	+	5.46323i	−0.387928	+	0.223970i
$596$	−33.6755	−	22.4432i	−1.37940	−	0.919307i
$597$		0			0
$598$	−4.16890	+	0.645986i	−0.170479	+	0.0264163i
$599$	14.4334			0.589731			0.294865	−	0.955539i	$-0.404725\pi$
$599$	14.4334			0.589731			0.294865	+	0.955539i	$0.404725\pi$
$600$		0			0
$601$	2.98263	+	5.16607i	0.121664	+	0.210728i	0.920424	−	0.390922i	$-0.127844\pi$
$601$	2.98263	+	5.16607i	0.121664	+	0.210728i	−0.798760	+	0.601650i	$0.794510\pi$
$602$	28.7290	+	8.69613i	1.17091	+	0.354428i
$603$		0			0
$604$	45.7480	+	2.94363i	1.86146	+	0.119775i
$605$	0.179489	−	0.310883i	0.00729725	−	0.0126392i
$606$		0			0
$607$	−0.844631	+	1.46294i	−0.0342825	+	0.0593791i	−0.882658	−	0.470017i	$-0.844248\pi$
$607$	−0.844631	+	1.46294i	−0.0342825	+	0.0593791i	0.848375	+	0.529396i	$0.177581\pi$
$608$	1.98663	+	19.5715i	0.0805685	+	0.793728i
$609$		0			0
$610$	−16.5864	+	3.87784i	−0.671563	+	0.157009i
$611$	−14.4777	−	30.1513i	−0.585706	−	1.21979i
$612$		0			0
$613$	3.26462	+	5.65449i	0.131857	+	0.228383i	0.924392	−	0.381443i	$-0.124573\pi$
$613$	3.26462	+	5.65449i	0.131857	+	0.228383i	−0.792536	+	0.609826i	$0.791239\pi$
$614$	−29.4429	+	27.6093i	−1.18822	+	1.11422i
$615$		0			0
$616$	−22.0508	+	18.1628i	−0.888454	+	0.731802i
$617$	3.07220	+	1.77374i	0.123682	+	0.0714079i	0.560565	−	0.828111i	$-0.310584\pi$
$617$	3.07220	+	1.77374i	0.123682	+	0.0714079i	−0.436883	+	0.899519i	$0.643917\pi$
$618$		0			0
$619$	−3.20378			−0.128771			−0.0643854	−	0.997925i	$-0.520509\pi$
$619$	−3.20378			−0.128771			−0.0643854	+	0.997925i	$0.520509\pi$
$620$	8.96935	+	0.577127i	0.360218	+	0.0231780i
$621$		0			0
$622$	29.0077	−	27.2012i	1.16310	−	1.09067i
$623$	35.8102			1.43470
$624$		0			0
$625$	−0.388454			−0.0155381
$626$	−7.59824	+	7.12505i	−0.303687	+	0.284774i
$627$		0			0
$628$	12.0723	+	0.776785i	0.481738	+	0.0309971i
$629$	−8.80711			−0.351162
$630$		0			0
$631$	−24.3730	−	14.0718i	−0.970274	−	0.560188i	−0.0709541	−	0.997480i	$-0.522604\pi$
$631$	−24.3730	−	14.0718i	−0.970274	−	0.560188i	−0.899320	+	0.437292i	$0.855938\pi$
$632$	3.21126	+	3.89867i	0.127737	+	0.155081i
$633$		0			0
$634$	21.1496	−	19.8325i	0.839959	−	0.787649i
$635$	−3.75473	−	6.50338i	−0.149002	−	0.258079i
$636$		0			0
$637$	6.13836	+	4.19533i	0.243211	+	0.166225i
$638$	−8.11407	+	1.89704i	−0.321239	+	0.0751047i
$639$		0			0
$640$	−8.38734	−	13.3631i	−0.331539	−	0.528222i
$641$	17.9287	−	31.0534i	0.708140	−	1.22653i	−0.257407	−	0.966303i	$-0.582868\pi$
$641$	17.9287	−	31.0534i	0.708140	−	1.22653i	0.965546	−	0.260231i	$-0.0837987\pi$
$642$		0			0
$643$	12.5211	−	21.6872i	0.493785	−	0.855261i	−0.506189	−	0.862422i	$-0.668946\pi$
$643$	12.5211	−	21.6872i	0.493785	−	0.855261i	0.999974	+	0.00716140i	$0.00227956\pi$
$644$	−4.97090	−	0.319849i	−0.195881	−	0.0126038i
$645$		0			0
$646$	−12.2516	−	3.70849i	−0.482033	−	0.145909i
$647$	13.5526	+	23.4737i	0.532806	+	0.922847i	0.999266	+	0.0383048i	$0.0121958\pi$
$647$	13.5526	+	23.4737i	0.532806	+	0.922847i	−0.466460	+	0.884542i	$0.654471\pi$
$648$		0			0
$649$	46.6899			1.83274
$650$	−5.63173	+	14.5256i	−0.220895	+	0.569740i
$651$		0			0
$652$	−34.2025	−	22.7943i	−1.33947	−	0.892695i
$653$	−35.2712	+	20.3638i	−1.38027	+	0.796898i	−0.992191	−	0.124729i	$-0.960194\pi$
$653$	−35.2712	+	20.3638i	−1.38027	+	0.796898i	−0.388077	+	0.921627i	$0.626861\pi$
$654$		0			0
$655$		−	19.9023i		−	0.777648i
$656$	−1.15511	+	0.481696i	−0.0450993	+	0.0188071i
$657$		0			0
$658$	−8.99079	−	38.4556i	−0.350498	−	1.49915i
$659$	2.20901	+	1.27537i	0.0860507	+	0.0496814i	0.542408	−	0.840115i	$-0.317513\pi$
$659$	2.20901	+	1.27537i	0.0860507	+	0.0496814i	−0.456357	+	0.889797i	$0.650846\pi$
$660$		0			0
$661$	16.9110	+	29.2907i	0.657761	+	1.13927i	0.981194	+	0.193024i	$0.0618295\pi$
$661$	16.9110	+	29.2907i	0.657761	+	1.13927i	−0.323433	+	0.946251i	$0.604837\pi$
$662$	−5.11323	−	21.8704i	−0.198731	−	0.850016i
$663$		0			0
$664$	13.1071	+	15.9128i	0.508654	+	0.617538i
$665$	−12.6428	+	7.29934i	−0.490268	+	0.283056i
$666$		0			0
$667$	−1.25828	−	0.726470i	−0.0487209	−	0.0281290i
$668$	17.2577	+	34.8901i	0.667721	+	1.34994i
$669$		0			0
$670$	−1.36473	−	0.413098i	−0.0527242	−	0.0159594i
$671$		−	28.9793i		−	1.11873i
$672$		0			0
$673$	17.7278	+	30.7055i	0.683358	+	1.18361i	0.973950	+	0.226764i	$0.0728145\pi$
$673$	17.7278	+	30.7055i	0.683358	+	1.18361i	−0.290592	+	0.956847i	$0.593852\pi$
$674$	−4.39254	+	4.11899i	−0.169194	+	0.158658i
$675$		0			0
$676$	−19.2048	−	17.5264i	−0.738647	−	0.674093i
$677$			9.66173i			0.371331i	0.982613	+	0.185665i	$0.0594440\pi$
$677$			9.66173i			0.371331i	−0.982613	+	0.185665i	$0.940556\pi$
$678$		0			0
$679$	−3.40789	−	5.90264i	−0.130783	−	0.226523i
$680$	10.1261	−	1.69046i	0.388317	−	0.0648260i
$681$		0			0
$682$	−4.43003	+	14.6353i	−0.169635	+	0.560414i
$683$	20.1053	−	34.8234i	0.769308	−	1.33248i	−0.168630	−	0.985679i	$-0.553934\pi$
$683$	20.1053	−	34.8234i	0.769308	−	1.33248i	0.937939	−	0.346802i	$-0.112732\pi$
$684$		0			0
$685$	−19.9640	−	11.5262i	−0.762785	−	0.440394i
$686$	−14.3795	−	15.3345i	−0.549013	−	0.585474i
$687$		0			0
$688$	−22.4155	−	17.1151i	−0.854582	−	0.652507i
$689$	−0.791611	−	1.64861i	−0.0301580	−	0.0628069i
$690$		0			0
$691$	−14.4864	−	25.0911i	−0.551087	−	0.954511i	−0.998196	−	0.0600319i	$-0.980880\pi$
$691$	−14.4864	−	25.0911i	−0.551087	−	0.954511i	0.447109	−	0.894479i	$-0.352454\pi$
$692$	10.7750	−	16.1677i	0.409605	−	0.614604i
$693$		0			0
$694$	5.70810	−	1.33454i	0.216676	−	0.0506583i
$695$	−4.30386	−	2.48483i	−0.163255	−	0.0942551i
$696$		0			0
$697$		−	0.814362i		−	0.0308462i
$698$	−38.2549	−	11.5796i	−1.44797	−	0.438293i
$699$		0			0
$700$	−10.2015	+	15.3071i	−0.385579	+	0.578555i
$701$			35.4685i			1.33963i	0.742529	+	0.669814i	$0.233626\pi$
$701$			35.4685i			1.33963i	−0.742529	+	0.669814i	$0.766374\pi$
$702$		0			0
$703$	−11.7670			−0.443803
$704$	25.3861	−	8.71896i	0.956775	−	0.328608i
$705$		0			0
$706$	10.5394	−	34.8184i	0.396654	−	1.31041i
$707$	54.1530			2.03663
$708$		0			0
$709$	9.45321	−	16.3734i	0.355023	−	0.614917i	−0.632099	−	0.774888i	$-0.717806\pi$
$709$	9.45321	−	16.3734i	0.355023	−	0.614917i	0.987122	+	0.159970i	$0.0511398\pi$
$710$	−10.0202	+	2.34270i	−0.376052	+	0.0879198i
$711$		0			0
$712$	−31.5109	−	11.7955i	−1.18092	−	0.442054i
$713$	−2.30899	+	1.33309i	−0.0864722	+	0.0499247i
$714$		0			0
$715$	13.9278	+	9.51911i	0.520871	+	0.355995i
$716$	8.97957	+	18.1541i	0.335582	+	0.678450i
$717$		0			0
$718$	−23.0425	−	24.5728i	−0.859938	−	0.917048i
$719$	8.07721	−	13.9901i	0.301229	−	0.521744i	−0.675185	−	0.737648i	$-0.735936\pi$
$719$	8.07721	−	13.9901i	0.301229	−	0.521744i	0.976415	+	0.215904i	$0.0692697\pi$
$720$		0			0
$721$	−22.9409	−	13.2450i	−0.854366	−	0.493268i
$722$	9.34851	+	2.82975i	0.347916	+	0.105312i
$723$		0			0
$724$	−16.3732	−	1.05352i	−0.608505	−	0.0391538i
$725$	−4.64673	+	2.68279i	−0.172575	+	0.0996364i
$726$		0			0
$727$	39.4524			1.46321			0.731605	−	0.681729i	$-0.238772\pi$
$727$	39.4524			1.46321			0.731605	+	0.681729i	$0.238772\pi$
$728$	−17.6640	−	25.1086i	−0.654672	−	0.930587i
$729$		0			0
$730$	−18.6775	−	19.9179i	−0.691286	−	0.737196i
$731$	15.8927	−	9.17566i	0.587813	−	0.339374i
$732$		0			0
$733$	5.87587			0.217030			0.108515	−	0.994095i	$-0.465390\pi$
$733$	5.87587			0.217030			0.108515	+	0.994095i	$0.465390\pi$
$734$	0.652045	+	0.197371i	0.0240674	+	0.00728509i
$735$		0			0
$736$	4.26875	+	1.91881i	0.157348	+	0.0707281i
$737$	1.21293	−	2.10085i	0.0446787	−	0.0773858i
$738$		0			0
$739$	−22.0371	−	38.1694i	−0.810648	−	1.40408i	−0.912411	−	0.409275i	$-0.865782\pi$
$739$	−22.0371	−	38.1694i	−0.810648	−	1.40408i	0.101763	−	0.994809i	$-0.467552\pi$
$740$	8.45907	−	4.18411i	0.310961	−	0.153811i
$741$		0			0
$742$	−0.491597	−	2.10267i	−0.0180471	−	0.0771913i
$743$	12.8577	−	7.42341i	0.471704	−	0.272338i	−0.245249	−	0.969460i	$-0.578870\pi$
$743$	12.8577	−	7.42341i	0.471704	−	0.272338i	0.716953	+	0.697122i	$0.245536\pi$
$744$		0			0
$745$	−14.1087	+	24.4370i	−0.516902	+	0.895301i
$746$	6.47139	−	1.51299i	0.236935	−	0.0553946i
$747$		0			0
$748$	−1.12151	+	17.4298i	−0.0410064	+	0.637296i
$749$	−35.4405			−1.29497
$750$		0			0
$751$	11.5133	+	19.9416i	0.420126	+	0.727680i	0.995951	−	0.0898929i	$-0.0286525\pi$
$751$	11.5133	+	19.9416i	0.420126	+	0.727680i	−0.575825	+	0.817573i	$0.695319\pi$
$752$	−4.75545	+	36.8002i	−0.173414	+	1.34196i
$753$		0			0
$754$	−1.37119	−	8.84902i	−0.0499357	−	0.322262i
$755$		−	31.9642i		−	1.16330i
$756$		0			0
$757$	34.5605	−	19.9535i	1.25612	−	0.725223i	0.283804	−	0.958882i	$-0.408403\pi$
$757$	34.5605	−	19.9535i	1.25612	−	0.725223i	0.972318	+	0.233659i	$0.0750701\pi$
$758$	21.8919	+	6.62656i	0.795149	+	0.240687i
$759$		0			0
$760$	13.5293	−	2.25859i	0.490759	−	0.0819278i
$761$	14.0376	+	8.10461i	0.508862	+	0.293792i	0.732366	−	0.680911i	$-0.238416\pi$
$761$	14.0376	+	8.10461i	0.508862	+	0.293792i	−0.223504	+	0.974703i	$0.571749\pi$
$762$		0			0
$763$	37.8425	+	21.8484i	1.36999	+	0.790963i
$764$	6.50336	+	4.33418i	0.235283	+	0.156805i
$765$		0			0
$766$	−25.9600	+	6.06937i	−0.937973	+	0.219295i
$767$	−3.80655	+	50.0289i	−0.137446	+	1.80644i
$768$		0			0
$769$	7.15236	−	4.12942i	0.257921	−	0.148911i	−0.365465	−	0.930825i	$-0.619090\pi$
$769$	7.15236	−	4.12942i	0.257921	−	0.148911i	0.623386	+	0.781914i	$0.285757\pi$
$770$	13.6253	+	14.5302i	0.491023	+	0.523633i
$771$		0			0
$772$	−9.51784	−	19.2423i	−0.342555	−	0.692546i
$773$	−22.2426	+	38.5253i	−0.800010	+	1.38566i	0.119598	+	0.992822i	$0.461839\pi$
$773$	−22.2426	+	38.5253i	−0.800010	+	1.38566i	−0.919609	+	0.392836i	$0.871494\pi$
$774$		0			0
$775$			9.84600i			0.353679i
$776$	1.05449	+	6.31651i	0.0378538	+	0.226749i
$777$		0			0
$778$	−16.0497	−	17.1155i	−0.575408	−	0.613622i
$779$		−	1.08806i		−	0.0389837i
$780$		0			0
$781$		−	17.5071i		−	0.626453i
$782$	−2.22147	+	2.08313i	−0.0794397	+	0.0744925i
$783$		0			0
$784$	−3.17474	−	7.61303i	−0.113384	−	0.271894i
$785$		−	8.43494i		−	0.301056i
$786$		0			0
$787$	−0.323566	+	0.560432i	−0.0115339	+	0.0199772i	−0.871735	−	0.489978i	$-0.837005\pi$
$787$	−0.323566	+	0.560432i	−0.0115339	+	0.0199772i	0.860201	+	0.509955i	$0.170338\pi$
$788$	29.6358	−	14.6588i	1.05573	−	0.522197i
$789$		0			0
$790$	2.56900	−	2.40901i	0.0914010	−	0.0857089i
$791$	−27.9469	+	16.1351i	−0.993676	+	0.573699i
$792$		0			0
$793$	31.0518	+	2.36264i	1.10268	+	0.0838997i
$794$	1.23576	+	5.28561i	0.0438555	+	0.187579i
$795$		0			0
$796$	−3.05062	−	2.03309i	−0.108126	−	0.0720610i
$797$	42.8073	+	24.7148i	1.51631	+	0.875443i	0.999817	+	0.0191525i	$0.00609680\pi$
$797$	42.8073	+	24.7148i	1.51631	+	0.875443i	0.516495	+	0.856290i	$0.327237\pi$
$798$		0			0
$799$	−20.9101	−	12.0725i	−0.739747	−	0.427093i
$800$	14.0187	−	10.1091i	0.495636	−	0.357412i
$801$		0			0
$802$	4.74374	−	15.6717i	0.167507	−	0.553387i
$803$	40.2306	−	23.2271i	1.41971	−	0.819668i
$804$		0			0
$805$			3.47317i			0.122413i
$806$	−15.3208	−	5.94004i	−0.539652	−	0.209229i
$807$		0			0
$808$	−47.6515	−	17.8374i	−1.67637	−	0.627517i
$809$	26.5322	+	45.9551i	0.932822	+	1.61569i	0.778473	+	0.627678i	$0.215994\pi$
$809$	26.5322	+	45.9551i	0.932822	+	1.61569i	0.154348	+	0.988016i	$0.450672\pi$
$810$		0			0
$811$	51.6547			1.81384			0.906921	−	0.421301i	$-0.138426\pi$
$811$	51.6547			1.81384			0.906921	+	0.421301i	$0.138426\pi$
$812$	0.678920	−	10.5514i	0.0238254	−	0.370280i
$813$		0			0
$814$	3.65519	+	15.6340i	0.128114	+	0.547973i
$815$	−14.3294	+	24.8193i	−0.501939	+	0.869383i
$816$		0			0
$817$	21.2340	−	12.2595i	0.742885	−	0.428905i
$818$	−51.1587	+	11.9608i	−1.78872	+	0.418198i
$819$		0			0
$820$	0.386890	+	0.782180i	0.0135108	+	0.0273149i
$821$	11.4785	+	19.8813i	0.400602	+	0.693864i	0.993799	−	0.111194i	$-0.0354675\pi$
$821$	11.4785	+	19.8813i	0.400602	+	0.693864i	−0.593196	+	0.805058i	$0.702134\pi$
$822$		0			0
$823$	−20.2415	+	35.0593i	−0.705574	+	1.22209i	0.260910	+	0.965363i	$0.415977\pi$
$823$	−20.2415	+	35.0593i	−0.705574	+	1.22209i	−0.966484	+	0.256727i	$0.917356\pi$
$824$	15.8240	+	19.2113i	0.551254	+	0.669257i
$825$		0			0
$826$	−17.1633	+	56.7017i	−0.597188	+	1.97291i
$827$	30.9590			1.07655			0.538275	−	0.842770i	$-0.319076\pi$
$827$	30.9590			1.07655			0.538275	+	0.842770i	$0.319076\pi$
$828$		0			0
$829$	−23.9582	+	13.8323i	−0.832103	+	0.480415i	−0.854572	−	0.519333i	$-0.826181\pi$
$829$	−23.9582	+	13.8323i	−0.832103	+	0.480415i	0.0224693	+	0.999748i	$0.492847\pi$
$830$	10.4856	−	9.83264i	0.363962	−	0.341296i
$831$		0			0
$832$	7.27282	+	27.9125i	0.252140	+	0.967691i
$833$	5.36727			0.185965
$834$		0			0
$835$	23.5046	−	13.5704i	0.813409	−	0.469622i
$836$	−1.49843	+	23.2877i	−0.0518243	+	0.805422i
$837$		0			0
$838$	−12.4471	+	41.1209i	−0.429978	+	1.42050i
$839$	3.52348	+	2.03428i	0.121644	+	0.0702312i	0.559587	−	0.828771i	$-0.310960\pi$
$839$	3.52348	+	2.03428i	0.121644	+	0.0702312i	−0.437943	+	0.899003i	$0.644293\pi$
$840$		0			0
$841$	−12.9580	+	22.4439i	−0.446827	+	0.773927i
$842$	6.18176	−	5.79678i	0.213038	−	0.199770i
$843$		0			0
$844$	14.0124	+	28.3290i	0.482326	+	0.975124i
$845$	−11.3354	+	14.1478i	−0.389950	+	0.486699i
$846$		0			0
$847$	−0.671101	+	0.387460i	−0.0230593	+	0.0133133i
$848$	−0.260018	+	2.01215i	−0.00892905	+	0.0690976i
$849$		0			0
$850$	2.56032	+	10.9510i	0.0878181	+	0.375617i
$851$	−1.39975	+	2.42444i	−0.0479828	+	0.0831086i
$852$		0			0
$853$	44.1481			1.51160			0.755801	−	0.654801i	$-0.227248\pi$
$853$	44.1481			1.51160			0.755801	+	0.654801i	$0.227248\pi$
$854$	35.1935	+	10.6529i	1.20430	+	0.364534i
$855$		0			0
$856$	31.1856	+	11.6737i	1.06590	+	0.398999i
$857$	−42.2555			−1.44342			−0.721711	−	0.692195i	$-0.756644\pi$
$857$	−42.2555			−1.44342			−0.721711	+	0.692195i	$0.756644\pi$
$858$		0			0
$859$			15.8242i			0.539915i	0.962872	+	0.269957i	$0.0870096\pi$
$859$			15.8242i			0.539915i	−0.962872	+	0.269957i	$0.912990\pi$
$860$	−10.9055	+	16.3634i	−0.371873	+	0.557988i
$861$		0			0
$862$	12.0373	−	39.7671i	0.409992	−	1.35447i
$863$			27.8210i			0.947037i	0.880784	+	0.473518i	$0.157016\pi$
$863$			27.8210i			0.947037i	−0.880784	+	0.473518i	$0.842984\pi$
$864$		0			0
$865$	−11.7322	−	6.77361i	−0.398908	−	0.230310i
$866$	5.04481	+	21.5778i	0.171430	+	0.733242i
$867$		0			0
$868$	−16.1451	−	10.7599i	−0.548001	−	0.365216i
$869$	2.99582	+	5.18891i	0.101626	+	0.176022i
$870$		0			0
$871$	2.15221	+	1.47095i	0.0729247	+	0.0498412i
$872$	−26.1026	−	31.6902i	−0.883945	−	1.07316i
$873$		0			0
$874$	−2.96808	+	2.78324i	−0.100397	+	0.0941444i
$875$	29.2855	+	16.9080i	0.990030	+	0.571594i
$876$		0			0
$877$	18.8441	−	32.6389i	0.636320	−	1.10214i	−0.349914	−	0.936782i	$-0.613789\pi$
$877$	18.8441	−	32.6389i	0.636320	−	1.10214i	0.986234	−	0.165357i	$-0.0528776\pi$
$878$	10.6434	+	3.22170i	0.359197	+	0.108727i
$879$		0			0
$880$	−7.20342	−	17.2738i	−0.242827	−	0.582300i
$881$	−14.3408	−	24.8389i	−0.483152	−	0.836844i	0.516661	−	0.856190i	$-0.327175\pi$
$881$	−14.3408	−	24.8389i	−0.483152	−	0.836844i	−0.999813	+	0.0193461i	$0.993842\pi$
$882$		0			0
$883$			22.8091i			0.767586i	0.923419	+	0.383793i	$0.125382\pi$
$883$			22.8091i			0.767586i	−0.923419	+	0.383793i	$0.874618\pi$
$884$	−18.5849	−	2.62274i	−0.625077	−	0.0882122i
$885$		0			0
$886$	−23.2351	−	24.7782i	−0.780597	−	0.832439i
$887$	−8.49750	−	14.7181i	−0.285318	−	0.494185i	0.687368	−	0.726309i	$-0.258766\pi$
$887$	−8.49750	−	14.7181i	−0.285318	−	0.494185i	−0.972686	+	0.232124i	$0.925433\pi$
$888$		0			0
$889$			16.2106i			0.543686i
$890$	−6.79672	+	22.4540i	−0.227827	+	0.752661i
$891$		0			0
$892$	−11.1280	−	22.4976i	−0.372593	−	0.753275i
$893$	−27.9377	−	16.1298i	−0.934900	−	0.539765i
$894$		0			0
$895$	12.2300	−	7.06097i	0.408802	−	0.236022i
$896$	1.25660	+	34.0349i	0.0419800	+	1.13702i
$897$		0			0
$898$	31.6710	−	7.40458i	1.05688	−	0.247094i
$899$	−2.82966	−	4.90111i	−0.0943744	−	0.163461i
$900$		0			0
$901$	−1.14332	−	0.660096i	−0.0380895	−	0.0219910i
$902$	−1.44563	+	0.337983i	−0.0481341	+	0.0112536i
$903$		0			0
$904$	29.9064	−	4.99260i	0.994671	−	0.166052i
$905$			11.4400i			0.380277i
$906$		0			0
$907$	25.2984	−	14.6060i	0.840019	−	0.484985i	−0.0172519	−	0.999851i	$-0.505492\pi$
$907$	25.2984	−	14.6060i	0.840019	−	0.484985i	0.857271	+	0.514866i	$0.172158\pi$
$908$	−6.64771	−	4.43039i	−0.220612	−	0.147028i
$909$		0			0
$910$	−16.6802	+	13.4152i	−0.552944	+	0.444708i
$911$	−27.4869			−0.910680			−0.455340	−	0.890318i	$-0.650482\pi$
$911$	−27.4869			−0.910680			−0.455340	+	0.890318i	$0.650482\pi$
$912$		0			0
$913$	12.2277	+	21.1791i	0.404679	+	0.700925i
$914$	14.5944	−	48.2150i	0.482740	−	1.59481i
$915$		0			0
$916$	−3.64922	+	56.7139i	−0.120574	+	1.87388i
$917$	−21.4815	+	37.2070i	−0.709381	+	1.22868i
$918$		0			0
$919$	1.46485	−	2.53719i	0.0483209	−	0.0836942i	−0.840853	−	0.541263i	$-0.817946\pi$
$919$	1.46485	−	2.53719i	0.0483209	−	0.0836942i	0.889174	+	0.457569i	$0.151280\pi$
$920$	1.14402	−	3.05619i	0.0377174	−	0.100760i
$921$		0			0
$922$	0.546399	+	2.33707i	0.0179947	+	0.0769672i
$923$	18.7591	+	1.42732i	0.617464	+	0.0469809i
$924$		0			0
$925$	5.16915	+	8.95324i	0.169961	+	0.294381i
$926$	−1.13583	−	1.21127i	−0.0373258	−	0.0398047i
$927$		0			0
$928$	−4.07291	+	9.06096i	−0.133700	+	0.297441i
$929$	15.9378	+	9.20171i	0.522903	+	0.301898i	0.738122	−	0.674668i	$-0.235713\pi$
$929$	15.9378	+	9.20171i	0.522903	+	0.301898i	−0.215218	+	0.976566i	$0.569046\pi$
$930$		0			0
$931$	7.17113			0.235024
$932$	−3.18242	+	49.4592i	−0.104244	+	1.62009i
$933$		0			0
$934$	−5.51239	−	5.87848i	−0.180371	−	0.192350i
$935$	12.1782			0.398270
$936$		0			0
$937$	−44.9730			−1.46921			−0.734603	−	0.678498i	$-0.762631\pi$
$937$	−44.9730			−1.46921			−0.734603	+	0.678498i	$0.762631\pi$
$938$	2.10547	+	2.24530i	0.0687460	+	0.0733115i
$939$		0			0
$940$	25.8192	+	1.66132i	0.842130	+	0.0541863i
$941$	15.4993			0.505264			0.252632	−	0.967562i	$-0.418704\pi$
$941$	15.4993			0.505264			0.252632	+	0.967562i	$0.418704\pi$
$942$		0			0
$943$	−0.224179	−	0.129430i	−0.00730028	−	0.00421482i
$944$	33.7797	−	44.2409i	1.09943	−	1.43992i
$945$		0			0
$946$	−22.8842	−	24.4040i	−0.744030	−	0.793442i
$947$	0.289949	+	0.502206i	0.00942207	+	0.0163195i	0.870698	−	0.491818i	$-0.163667\pi$
$947$	0.289949	+	0.502206i	0.00942207	+	0.0163195i	−0.861276	+	0.508138i	$0.830334\pi$
$948$		0			0
$949$	21.6083	+	45.0014i	0.701436	+	1.46081i
$950$	3.42080	+	14.6315i	0.110985	+	0.474709i
$951$		0			0
$952$	−20.7551	−	7.76924i	−0.672675	−	0.251802i
$953$	6.73143	−	11.6592i	0.218052	−	0.377678i	−0.736160	−	0.676807i	$-0.763363\pi$
$953$	6.73143	−	11.6592i	0.218052	−	0.377678i	0.954212	+	0.299130i	$0.0966963\pi$
$954$		0			0
$955$	2.72464	−	4.71922i	0.0881674	−	0.152710i
$956$	−13.9565	−	0.898019i	−0.451384	−	0.0290440i
$957$		0			0
$958$	−10.4476	+	34.5152i	−0.337546	+	1.11514i
$959$	24.8815	+	43.0961i	0.803466	+	1.39164i
$960$		0			0
$961$	20.6150			0.665000
$962$	−17.0501	+	2.64198i	−0.549718	+	0.0851808i
$963$		0			0
$964$	−11.1102	+	16.6707i	−0.357836	+	0.536927i
$965$	−12.9631	+	7.48423i	−0.417296	+	0.240926i
$966$		0			0
$967$			38.3159i			1.23216i	0.787686	+	0.616078i	$0.211279\pi$
$967$			38.3159i			1.23216i	−0.787686	+	0.616078i	$0.788721\pi$
$968$	0.718155	−	0.119890i	0.0230824	−	0.00385340i
$969$		0			0
$970$	4.34794	−	1.01654i	0.139604	−	0.0326390i
$971$	−11.6662	−	6.73549i	−0.374386	−	0.216152i	0.300987	−	0.953628i	$-0.402684\pi$
$971$	−11.6662	−	6.73549i	−0.374386	−	0.216152i	−0.675373	+	0.737476i	$0.736017\pi$
$972$		0			0
$973$	5.36399	+	9.29069i	0.171961	+	0.297846i
$974$	−34.9860	+	8.17962i	−1.12102	+	0.262092i
$975$		0			0
$976$	−27.4593	−	20.9663i	−0.878950	−	0.671113i
$977$	−47.5102	+	27.4300i	−1.51999	+	0.877564i	−0.520263	+	0.854006i	$0.674166\pi$
$977$	−47.5102	+	27.4300i	−1.51999	+	0.877564i	−0.999722	+	0.0235584i	$0.992500\pi$
$978$		0			0
$979$	−34.5654	−	19.9564i	−1.10472	−	0.637808i
$980$	−5.15516	+	2.54990i	−0.164676	+	0.0814536i
$981$		0			0
$982$	−5.12483	+	16.9307i	−0.163540	+	0.540280i
$983$		−	56.9126i		−	1.81523i	−0.419803	−	0.907615i	$-0.637901\pi$
$983$		−	56.9126i		−	1.81523i	0.419803	−	0.907615i	$-0.362099\pi$
$984$		0			0
$985$	−11.5267	−	19.9649i	−0.367272	−	0.636134i
$986$	−4.42170	−	4.71536i	−0.140816	−	0.150168i
$987$		0			0
$988$	−24.8310	−	3.50420i	−0.789979	−	0.111484i
$989$		−	5.83330i		−	0.185488i
$990$		0			0
$991$	8.93539	+	15.4765i	0.283842	+	0.491629i	0.972328	−	0.233621i	$-0.0750576\pi$
$991$	8.93539	+	15.4765i	0.283842	+	0.491629i	−0.688486	+	0.725250i	$0.741724\pi$
$992$	10.6626	+	14.7862i	0.338537	+	0.469461i
$993$		0			0
$994$	21.2612	+	6.43565i	0.674364	+	0.204127i
$995$	−1.27808	+	2.21371i	−0.0405180	+	0.0701792i
$996$		0			0
$997$	5.15008	+	2.97340i	0.163105	+	0.0941686i	0.579331	−	0.815093i	$-0.303314\pi$
$997$	5.15008	+	2.97340i	0.163105	+	0.0941686i	−0.416226	+	0.909261i	$0.636647\pi$
$998$	−35.2723	+	33.0756i	−1.11652	+	1.04699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.f.829.21	yes	56
3.2	odd	2	inner	936.2.dg.f.829.8	yes	56
8.5	even	2	inner	936.2.dg.f.829.26	yes	56
13.4	even	6	inner	936.2.dg.f.901.26	yes	56
24.5	odd	2	inner	936.2.dg.f.829.3	✓	56
39.17	odd	6	inner	936.2.dg.f.901.3	yes	56
104.69	even	6	inner	936.2.dg.f.901.21	yes	56
312.173	odd	6	inner	936.2.dg.f.901.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dg.f.829.3	✓	56	24.5	odd	2	inner
936.2.dg.f.829.8	yes	56	3.2	odd	2	inner
936.2.dg.f.829.21	yes	56	1.1	even	1	trivial
936.2.dg.f.829.26	yes	56	8.5	even	2	inner
936.2.dg.f.901.3	yes	56	39.17	odd	6	inner
936.2.dg.f.901.8	yes	56	312.173	odd	6	inner
936.2.dg.f.901.21	yes	56	104.69	even	6	inner
936.2.dg.f.901.26	yes	56	13.4	even	6	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03161 - 0.967362i) q^{2} +(0.128423 - 1.99587i) q^{4} -1.39452 q^{5} +(2.60703 + 1.50517i) q^{7} +(-1.79825 - 2.18319i) q^{8} +(-1.43859 + 1.34900i) q^{10} +(-1.67760 - 2.90570i) q^{11} +(3.25027 - 1.56068i) q^{13} +(4.14547 - 0.969197i) q^{14} +(-3.96701 - 0.512632i) q^{16} +(1.30140 - 2.25409i) q^{17} +(1.73878 - 3.01165i) q^{19} +(-0.179088 + 2.78328i) q^{20} +(-4.54148 - 1.37468i) q^{22} +(-0.413673 - 0.716502i) q^{23} -3.05532 q^{25} +(1.84326 - 4.75420i) q^{26} +(3.33893 - 5.00999i) q^{28} +(1.52087 - 0.878073i) q^{29} -3.22258i q^{31} +(-4.58830 + 3.30870i) q^{32} +(-0.837987 - 3.58425i) q^{34} +(-3.63555 - 2.09898i) q^{35} +(-1.69186 - 2.93038i) q^{37} +(-1.11962 - 4.78887i) q^{38} +(2.50769 + 3.04449i) q^{40} +(0.270962 - 0.156440i) q^{41} +(6.10602 + 3.52531i) q^{43} +(-6.01484 + 2.97513i) q^{44} +(-1.11986 - 0.338977i) q^{46} -9.27654i q^{47} +(1.03106 + 1.78585i) q^{49} +(-3.15188 + 2.95560i) q^{50} +(-2.69751 - 6.68756i) q^{52} -0.507221i q^{53} +(2.33945 + 4.05205i) q^{55} +(-1.40202 - 8.39829i) q^{56} +(0.719522 - 2.37705i) q^{58} +(-6.95782 + 12.0513i) q^{59} +(7.47996 + 4.31856i) q^{61} +(-3.11740 - 3.32443i) q^{62} +(-1.53261 + 7.85182i) q^{64} +(-4.53257 + 2.17640i) q^{65} +(0.361505 + 0.626146i) q^{67} +(-4.33174 - 2.88690i) q^{68} +(-5.78093 + 1.35156i) q^{70} +(4.51882 + 2.60894i) q^{71} +13.8454i q^{73} +(-4.58007 - 1.38636i) q^{74} +(-5.78758 - 3.85715i) q^{76} -10.1003i q^{77} -1.78577 q^{79} +(5.53208 + 0.714876i) q^{80} +(0.128192 - 0.423503i) q^{82} -7.28881 q^{83} +(-1.81482 + 3.14337i) q^{85} +(9.70926 - 2.26999i) q^{86} +(-3.32693 + 8.88768i) q^{88} +(10.3020 - 5.94787i) q^{89} +(10.8226 + 0.823461i) q^{91} +(-1.48317 + 0.733623i) q^{92} +(-8.97377 - 9.56973i) q^{94} +(-2.42476 + 4.19981i) q^{95} +(-1.96079 - 1.13206i) q^{97} +(2.79120 + 0.844883i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Introduction

L-functions

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