LMFDB - Embedded newform 820.2.x.a.273.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			273.6
Character	$\chi$	$=$	820.273
Dual form			820.2.x.a.817.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30072 - 0.538776i) q^{3} +(1.59126 + 1.57096i) q^{5} +(-0.188362 + 0.454747i) q^{7} +(-0.719728 - 0.719728i) q^{9} +(-0.189669 - 0.457901i) q^{11} +(1.98169 + 0.820844i) q^{13} +(-1.22338 - 2.90070i) q^{15} +(5.85122 - 2.42365i) q^{17} +(0.0217955 - 0.0526190i) q^{19} +(0.490013 - 0.490013i) q^{21} +(-2.81893 + 2.81893i) q^{23} +(0.0641897 + 4.99959i) q^{25} +(2.16472 + 5.22610i) q^{27} +(0.996646 + 2.40612i) q^{29} +10.5037i q^{31} +0.697789i q^{33} +(-1.01412 + 0.427710i) q^{35} +(4.54494 - 4.54494i) q^{37} +(-2.13538 - 2.13538i) q^{39} +(5.37057 - 3.48669i) q^{41} -11.9827i q^{43} +(-0.0146097 - 2.27593i) q^{45} +(8.60362 - 3.56374i) q^{47} +(4.77843 + 4.77843i) q^{49} -8.91660 q^{51} +(-3.08766 + 7.45426i) q^{53} +(0.417531 - 1.02660i) q^{55} +(-0.0566997 + 0.0566997i) q^{57} +9.71888i q^{59} +(6.46086 + 6.46086i) q^{61} +(0.462864 - 0.191724i) q^{63} +(1.86387 + 4.41933i) q^{65} +(14.4796 - 5.99766i) q^{67} +(5.18540 - 2.14786i) q^{69} +(-5.71563 + 2.36749i) q^{71} -6.53797i q^{73} +(2.61016 - 6.53765i) q^{75} +0.243955 q^{77} +(-6.06436 + 2.51194i) q^{79} -4.91043i q^{81} +(1.32027 + 1.32027i) q^{83} +(13.1182 + 5.33536i) q^{85} -3.66665i q^{87} +(2.35851 + 5.69395i) q^{89} +(-0.746553 + 0.746553i) q^{91} +(5.65915 - 13.6624i) q^{93} +(0.117344 - 0.0494905i) q^{95} +(4.68468 + 11.3098i) q^{97} +(-0.193054 + 0.466074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.30072	−	0.538776i	−0.750971	−	0.311062i	−0.0258332	−	0.999666i	$-0.508224\pi$
$3$	−1.30072	−	0.538776i	−0.750971	−	0.311062i	−0.725138	+	0.688604i	$0.758224\pi$
$4$		0			0
$5$	1.59126	+	1.57096i	0.711631	+	0.702553i
$5$	1.59126	+	1.57096i	0.711631	+	0.702553i
$6$		0			0
$7$	−0.188362	+	0.454747i	−0.0711943	+	0.171878i	−0.955471	−	0.295085i	$-0.904652\pi$
$7$	−0.188362	+	0.454747i	−0.0711943	+	0.171878i	0.884277	+	0.466963i	$0.154652\pi$
$8$		0			0
$9$	−0.719728	−	0.719728i	−0.239909	−	0.239909i
$10$		0			0
$11$	−0.189669	−	0.457901i	−0.0571872	−	0.138062i	0.892703	−	0.450645i	$-0.148806\pi$
$11$	−0.189669	−	0.457901i	−0.0571872	−	0.138062i	−0.949891	+	0.312583i	$0.898806\pi$
$12$		0			0
$13$	1.98169	+	0.820844i	0.549623	+	0.227661i	0.640173	−	0.768231i	$-0.278863\pi$
$13$	1.98169	+	0.820844i	0.549623	+	0.227661i	−0.0905504	+	0.995892i	$0.528863\pi$
$14$		0			0
$15$	−1.22338	−	2.90070i	−0.315876	−	0.748959i
$16$		0			0
$17$	5.85122	−	2.42365i	1.41913	−	0.587822i	0.464487	−	0.885580i	$-0.346239\pi$
$17$	5.85122	−	2.42365i	1.41913	−	0.587822i	0.954641	+	0.297758i	$0.0962388\pi$
$18$		0			0
$19$	0.0217955	−	0.0526190i	0.00500023	−	0.0120716i	−0.921360	−	0.388711i	$-0.872920\pi$
$19$	0.0217955	−	0.0526190i	0.00500023	−	0.0120716i	0.926360	+	0.376639i	$0.122920\pi$
$20$		0			0
$21$	0.490013	−	0.490013i	0.106930	−	0.106930i
$22$		0			0
$23$	−2.81893	+	2.81893i	−0.587787	+	0.587787i	−0.937031	−	0.349245i	$-0.886438\pi$
$23$	−2.81893	+	2.81893i	−0.587787	+	0.587787i	0.349245	+	0.937031i	$0.386438\pi$
$24$		0			0
$25$	0.0641897	+	4.99959i	0.0128379	+	0.999918i
$26$		0			0
$27$	2.16472	+	5.22610i	0.416600	+	1.00576i
$28$		0			0
$29$	0.996646	+	2.40612i	0.185073	+	0.446805i	0.988999	−	0.147925i	$-0.0472593\pi$
$29$	0.996646	+	2.40612i	0.185073	+	0.446805i	−0.803926	+	0.594729i	$0.797259\pi$
$30$		0			0
$31$			10.5037i			1.88652i	0.332049	+	0.943262i	$0.392260\pi$
$31$			10.5037i			1.88652i	−0.332049	+	0.943262i	$0.607740\pi$
$32$		0			0
$33$			0.697789i			0.121469i
$34$		0			0
$35$	−1.01412	+	0.427710i	−0.171418	+	0.0722961i
$36$		0			0
$37$	4.54494	−	4.54494i	0.747183	−	0.747183i	−0.226766	−	0.973949i	$-0.572815\pi$
$37$	4.54494	−	4.54494i	0.747183	−	0.747183i	0.973949	+	0.226766i	$0.0728154\pi$
$38$		0			0
$39$	−2.13538	−	2.13538i	−0.341934	−	0.341934i
$40$		0			0
$41$	5.37057	−	3.48669i	0.838741	−	0.544530i
$41$	5.37057	−	3.48669i	0.838741	−	0.544530i
$42$		0			0
$43$		−	11.9827i		−	1.82734i	−0.406457	−	0.913670i	$-0.633236\pi$
$43$		−	11.9827i		−	1.82734i	0.406457	−	0.913670i	$-0.366764\pi$
$44$		0			0
$45$	−0.0146097	−	2.27593i	−0.00217789	−	0.339276i
$46$		0			0
$47$	8.60362	−	3.56374i	1.25497	−	0.519824i	0.346606	−	0.938011i	$-0.387334\pi$
$47$	8.60362	−	3.56374i	1.25497	−	0.519824i	0.908361	+	0.418186i	$0.137334\pi$
$48$		0			0
$49$	4.77843	+	4.77843i	0.682633	+	0.682633i
$50$		0			0
$51$	−8.91660			−1.24857
$52$		0			0
$53$	−3.08766	+	7.45426i	−0.424122	+	1.02392i	0.556996	+	0.830515i	$0.311954\pi$
$53$	−3.08766	+	7.45426i	−0.424122	+	1.02392i	−0.981119	+	0.193407i	$0.938046\pi$
$54$		0			0
$55$	0.417531	−	1.02660i	0.0562998	−	0.138426i
$56$		0			0
$57$	−0.0566997	+	0.0566997i	−0.00751005	+	0.00751005i
$58$		0			0
$59$			9.71888i			1.26529i	0.774442	+	0.632645i	$0.218031\pi$
$59$			9.71888i			1.26529i	−0.774442	+	0.632645i	$0.781969\pi$
$60$		0			0
$61$	6.46086	+	6.46086i	0.827228	+	0.827228i	0.987132	−	0.159905i	$-0.0511187\pi$
$61$	6.46086	+	6.46086i	0.827228	+	0.827228i	−0.159905	+	0.987132i	$0.551119\pi$
$62$		0			0
$63$	0.462864	−	0.191724i	0.0583154	−	0.0241550i
$64$		0			0
$65$	1.86387	+	4.41933i	0.231185	+	0.548150i
$66$		0			0
$67$	14.4796	−	5.99766i	1.76897	−	0.732730i	0.773925	−	0.633277i	$-0.218291\pi$
$67$	14.4796	−	5.99766i	1.76897	−	0.732730i	0.995042	−	0.0994529i	$-0.0317093\pi$
$68$		0			0
$69$	5.18540	−	2.14786i	0.624249	−	0.258572i
$70$		0			0
$71$	−5.71563	+	2.36749i	−0.678321	+	0.280970i	−0.695125	−	0.718889i	$-0.744651\pi$
$71$	−5.71563	+	2.36749i	−0.678321	+	0.280970i	0.0168040	+	0.999859i	$0.494651\pi$
$72$		0			0
$73$		−	6.53797i		−	0.765211i	−0.923912	−	0.382605i	$-0.875027\pi$
$73$		−	6.53797i		−	0.765211i	0.923912	−	0.382605i	$-0.124973\pi$
$74$		0			0
$75$	2.61016	−	6.53765i	0.301396	−	0.754902i
$76$		0			0
$77$	0.243955			0.0278013
$78$		0			0
$79$	−6.06436	+	2.51194i	−0.682293	+	0.282615i	−0.696785	−	0.717280i	$-0.745387\pi$
$79$	−6.06436	+	2.51194i	−0.682293	+	0.282615i	0.0144919	+	0.999895i	$0.495387\pi$
$80$		0			0
$81$		−	4.91043i		−	0.545604i
$82$		0			0
$83$	1.32027	+	1.32027i	0.144918	+	0.144918i	0.775844	−	0.630925i	$-0.217325\pi$
$83$	1.32027	+	1.32027i	0.144918	+	0.144918i	−0.630925	+	0.775844i	$0.717325\pi$
$84$		0			0
$85$	13.1182	+	5.33536i	1.42287	+	0.578701i
$86$		0			0
$87$		−	3.66665i		−	0.393106i
$88$		0			0
$89$	2.35851	+	5.69395i	0.250002	+	0.603557i	0.998204	−	0.0599137i	$-0.0190826\pi$
$89$	2.35851	+	5.69395i	0.250002	+	0.603557i	−0.748202	+	0.663471i	$0.769083\pi$
$90$		0			0
$91$	−0.746553	+	0.746553i	−0.0782600	+	0.0782600i
$92$		0			0
$93$	5.65915	−	13.6624i	0.586826	−	1.41672i
$94$		0			0
$95$	0.117344	−	0.0494905i	0.0120393	−	0.00507762i
$96$		0			0
$97$	4.68468	+	11.3098i	0.475657	+	1.14834i	0.961626	+	0.274362i	$0.0884666\pi$
$97$	4.68468	+	11.3098i	0.475657	+	1.14834i	−0.485969	+	0.873976i	$0.661533\pi$
$98$		0			0
$99$	−0.193054	+	0.466074i	−0.0194027	+	0.0468422i
$100$		0			0
$101$	−2.96526	−	1.22825i	−0.295055	−	0.122216i	0.230246	−	0.973133i	$-0.426047\pi$
$101$	−2.96526	−	1.22825i	−0.295055	−	0.122216i	−0.525300	+	0.850917i	$0.676047\pi$
$102$		0			0
$103$	−13.3057			−1.31105			−0.655527	−	0.755172i	$-0.727554\pi$
$103$	−13.3057			−1.31105			−0.655527	+	0.755172i	$0.727554\pi$
$104$		0			0
$105$	1.54953	−	0.00994677i	0.151218	−	0.000970705i
$106$		0			0
$107$	−7.17591	−	7.17591i	−0.693721	−	0.693721i	0.269327	−	0.963049i	$-0.413199\pi$
$107$	−7.17591	−	7.17591i	−0.693721	−	0.693721i	−0.963049	+	0.269327i	$0.913199\pi$
$108$		0			0
$109$	−16.8126	−	6.96403i	−1.61036	−	0.667033i	−0.617527	−	0.786550i	$-0.711865\pi$
$109$	−16.8126	−	6.96403i	−1.61036	−	0.667033i	−0.992832	+	0.119517i	$0.961865\pi$
$110$		0			0
$111$	−8.36039	+	3.46299i	−0.793533	+	0.328692i
$112$		0			0
$113$	7.75944	−	7.75944i	0.729947	−	0.729947i	−0.240662	−	0.970609i	$-0.577365\pi$
$113$	7.75944	−	7.75944i	0.729947	−	0.729947i	0.970609	+	0.240662i	$0.0773646\pi$
$114$		0			0
$115$	−8.91404	+	0.0572213i	−0.831239	+	0.00533591i
$116$		0			0
$117$	−0.835495	−	2.01706i	−0.0772416	−	0.186478i
$118$		0			0
$119$			3.11735i			0.285767i
$120$		0			0
$121$	7.60448	−	7.60448i	0.691316	−	0.691316i
$122$		0			0
$123$	−8.86415	+	1.64168i	−0.799253	+	0.148025i
$124$		0			0
$125$	−7.75199	+	8.05646i	−0.693359	+	0.720592i
$126$		0			0
$127$	−0.911552	−	0.911552i	−0.0808871	−	0.0808871i	0.665506	−	0.746393i	$-0.268216\pi$
$127$	−0.911552	−	0.911552i	−0.0808871	−	0.0808871i	−0.746393	+	0.665506i	$0.768216\pi$
$128$		0			0
$129$	−6.45597	+	15.5861i	−0.568417	+	1.37228i
$130$		0			0
$131$	8.94315	−	8.94315i	0.781367	−	0.781367i	−0.198695	−	0.980061i	$-0.563670\pi$
$131$	8.94315	−	8.94315i	0.781367	−	0.781367i	0.980061	+	0.198695i	$0.0636703\pi$
$132$		0			0
$133$	0.0198229	+	0.0198229i	0.00171886	+	0.00171886i
$134$		0			0
$135$	−4.76535	+	11.7167i	−0.410136	+	1.00842i
$136$		0			0
$137$	−0.351496	+	0.145594i	−0.0300303	+	0.0124390i	−0.397648	−	0.917538i	$-0.630173\pi$
$137$	−0.351496	+	0.145594i	−0.0300303	+	0.0124390i	0.367618	+	0.929977i	$0.380173\pi$
$138$		0			0
$139$		−	16.4127i		−	1.39210i	−0.717992	−	0.696052i	$-0.754938\pi$
$139$		−	16.4127i		−	1.39210i	0.717992	−	0.696052i	$-0.245062\pi$
$140$		0			0
$141$	−13.1110			−1.10414
$142$		0			0
$143$		−	1.06311i		−	0.0889014i
$144$		0			0
$145$	−2.19399	+	5.39443i	−0.182201	+	0.447983i
$146$		0			0
$147$	−3.64090	−	8.78991i	−0.300296	−	0.724979i
$148$		0			0
$149$	−7.15737	+	17.2794i	−0.586355	+	1.41559i	0.300609	+	0.953747i	$0.402810\pi$
$149$	−7.15737	+	17.2794i	−0.586355	+	1.41559i	−0.886964	+	0.461838i	$0.847190\pi$
$150$		0			0
$151$	−2.76918	−	6.68540i	−0.225353	−	0.544050i	0.770248	−	0.637744i	$-0.220132\pi$
$151$	−2.76918	−	6.68540i	−0.225353	−	0.544050i	−0.995601	+	0.0936942i	$0.970132\pi$
$152$		0			0
$153$	−5.95566	−	2.46691i	−0.481486	−	0.199438i
$154$		0			0
$155$	−16.5009	+	16.7141i	−1.32538	+	1.34251i
$156$		0			0
$157$	−10.2939	−	4.26387i	−0.821542	−	0.340294i	−0.0679933	−	0.997686i	$-0.521660\pi$
$157$	−10.2939	−	4.26387i	−0.821542	−	0.340294i	−0.753549	+	0.657392i	$0.771660\pi$
$158$		0			0
$159$	8.03235	−	8.03235i	0.637007	−	0.637007i
$160$		0			0
$161$	−0.750918	−	1.81288i	−0.0591807	−	0.142875i
$162$		0			0
$163$	−6.31580	+	6.31580i	−0.494692	+	0.494692i	−0.909781	−	0.415089i	$-0.863750\pi$
$163$	−6.31580	+	6.31580i	−0.494692	+	0.494692i	0.415089	+	0.909781i	$0.363750\pi$
$164$		0			0
$165$	−1.09620	+	1.11036i	−0.0853388	+	0.0864415i
$166$		0			0
$167$	1.51616	−	3.66034i	0.117324	−	0.283246i	−0.854298	−	0.519783i	$-0.826013\pi$
$167$	1.51616	−	3.66034i	0.117324	−	0.283246i	0.971622	+	0.236538i	$0.0760126\pi$
$168$		0			0
$169$	−5.93907	−	5.93907i	−0.456851	−	0.456851i
$170$		0			0
$171$	−0.0535582	+	0.0221845i	−0.00409570	+	0.00169649i
$172$		0			0
$173$	−11.9549			−0.908917			−0.454459	−	0.890768i	$-0.650167\pi$
$173$	−11.9549			−0.908917			−0.454459	+	0.890768i	$0.650167\pi$
$174$		0			0
$175$	−2.28564	−	0.912544i	−0.172778	−	0.0689819i
$176$		0			0
$177$	5.23630	−	12.6415i	0.393584	−	0.950197i
$178$		0			0
$179$	8.40792	+	3.48267i	0.628437	+	0.260307i	0.674089	−	0.738650i	$-0.264536\pi$
$179$	8.40792	+	3.48267i	0.628437	+	0.260307i	−0.0456517	+	0.998957i	$0.514536\pi$
$180$		0			0
$181$	−19.9999	−	8.28422i	−1.48658	−	0.615761i	−0.516010	−	0.856583i	$-0.672583\pi$
$181$	−19.9999	−	8.28422i	−1.48658	−	0.615761i	−0.970569	+	0.240821i	$0.922583\pi$
$182$		0			0
$183$	−4.92281	−	11.8847i	−0.363905	−	0.878543i
$184$		0			0
$185$	14.3721	−	0.0922575i	1.05665	−	0.00678291i
$186$		0			0
$187$	−2.21958	−	2.21958i	−0.162312	−	0.162312i
$188$		0			0
$189$	−2.78430			−0.202528
$190$		0			0
$191$	−2.07967	+	5.02076i	−0.150479	+	0.363290i	−0.981087	−	0.193569i	$-0.937994\pi$
$191$	−2.07967	+	5.02076i	−0.150479	+	0.363290i	0.830607	+	0.556859i	$0.187994\pi$
$192$		0			0
$193$	14.0879	+	5.83539i	1.01407	+	0.420040i	0.826937	−	0.562295i	$-0.190081\pi$
$193$	14.0879	+	5.83539i	1.01407	+	0.420040i	0.187130	+	0.982335i	$0.440081\pi$
$194$		0			0
$195$	−0.0433459	−	6.75251i	−0.00310407	−	0.483557i
$196$		0			0
$197$	−17.5199			−1.24824			−0.624122	−	0.781327i	$-0.714543\pi$
$197$	−17.5199			−1.24824			−0.624122	+	0.781327i	$0.714543\pi$
$198$		0			0
$199$	10.8383	+	4.48936i	0.768304	+	0.318242i	0.732185	−	0.681105i	$-0.238500\pi$
$199$	10.8383	+	4.48936i	0.768304	+	0.318242i	0.0361190	+	0.999347i	$0.488500\pi$
$200$		0			0
$201$	−22.0653			−1.55637
$202$		0			0
$203$	−1.28190			−0.0899721
$204$		0			0
$205$	14.0234	+	2.88871i	0.979436	+	0.201756i
$206$		0			0
$207$	4.05772			0.282031
$208$		0			0
$209$	−0.0282282			−0.00195258
$210$		0			0
$211$	−17.0929	−	7.08012i	−1.17673	−	0.487416i	−0.293315	−	0.956016i	$-0.594758\pi$
$211$	−17.0929	−	7.08012i	−1.17673	−	0.487416i	−0.883410	+	0.468600i	$0.844758\pi$
$212$		0			0
$213$	8.70998			0.596798
$214$		0			0
$215$	18.8243	−	19.0675i	1.28380	−	1.30039i
$216$		0			0
$217$	−4.77654	−	1.97851i	−0.324252	−	0.134310i
$218$		0			0
$219$	−3.52250	+	8.50406i	−0.238028	+	0.574651i
$220$		0			0
$221$	13.5848			0.913809
$222$		0			0
$223$	5.85628	+	5.85628i	0.392166	+	0.392166i	0.875459	−	0.483293i	$-0.160559\pi$
$223$	5.85628	+	5.85628i	0.392166	+	0.392166i	−0.483293	+	0.875459i	$0.660559\pi$
$224$		0			0
$225$	3.55215	−	3.64454i	0.236810	−	0.242970i
$226$		0			0
$227$	2.94037	+	7.09869i	0.195159	+	0.471156i	0.990920	−	0.134455i	$-0.0429285\pi$
$227$	2.94037	+	7.09869i	0.195159	+	0.471156i	−0.795760	+	0.605612i	$0.792928\pi$
$228$		0			0
$229$	5.31111	+	2.19993i	0.350968	+	0.145376i	0.551201	−	0.834373i	$-0.314170\pi$
$229$	5.31111	+	2.19993i	0.350968	+	0.145376i	−0.200233	+	0.979748i	$0.564170\pi$
$230$		0			0
$231$	−0.317317	−	0.131437i	−0.0208780	−	0.00864793i
$232$		0			0
$233$	1.86028	−	4.49111i	0.121871	−	0.294222i	−0.851157	−	0.524912i	$-0.824098\pi$
$233$	1.86028	−	4.49111i	0.121871	−	0.294222i	0.973027	+	0.230690i	$0.0740983\pi$
$234$		0			0
$235$	19.2890	+	7.84510i	1.25828	+	0.511758i
$236$		0			0
$237$	9.24140			0.600293
$238$		0			0
$239$	−7.97443	+	3.30312i	−0.515823	+	0.213661i	−0.625381	−	0.780319i	$-0.715056\pi$
$239$	−7.97443	+	3.30312i	−0.515823	+	0.213661i	0.109558	+	0.993980i	$0.465056\pi$
$240$		0			0
$241$	−12.1579	−	12.1579i	−0.783158	−	0.783158i	0.197205	−	0.980362i	$-0.436814\pi$
$241$	−12.1579	−	12.1579i	−0.783158	−	0.783158i	−0.980362	+	0.197205i	$0.936814\pi$
$242$		0			0
$243$	3.84854	−	9.29119i	0.246884	−	0.596030i
$244$		0			0
$245$	0.0969973	+	15.1104i	0.00619693	+	0.965369i
$246$		0			0
$247$	0.0863839	−	0.0863839i	0.00549648	−	0.00549648i
$248$		0			0
$249$	−1.00597	−	2.42863i	−0.0637508	−	0.153908i
$250$		0			0
$251$	−5.31667	+	5.31667i	−0.335585	+	0.335585i	−0.854703	−	0.519118i	$-0.826261\pi$
$251$	−5.31667	+	5.31667i	−0.335585	+	0.335585i	0.519118	+	0.854703i	$0.326261\pi$
$252$		0			0
$253$	1.82545	+	0.756126i	0.114765	+	0.0475372i
$254$		0			0
$255$	−14.1886	−	14.0076i	−0.888524	−	0.877189i
$256$		0			0
$257$	22.9273	+	9.49681i	1.43017	+	0.592395i	0.957393	−	0.288789i	$-0.0932526\pi$
$257$	22.9273	+	9.49681i	1.43017	+	0.592395i	0.472774	+	0.881184i	$0.343253\pi$
$258$		0			0
$259$	1.21070	+	2.92289i	0.0752293	+	0.181620i
$260$		0			0
$261$	1.01444	−	2.44906i	0.0627920	−	0.151593i
$262$		0			0
$263$	3.79530	+	9.16267i	0.234028	+	0.564994i	0.996644	−	0.0818574i	$-0.0260852\pi$
$263$	3.79530	+	9.16267i	0.234028	+	0.564994i	−0.762616	+	0.646852i	$0.776085\pi$
$264$		0			0
$265$	−16.6236	+	7.01106i	−1.02118	+	0.430686i
$266$		0			0
$267$		−	8.67694i		−	0.531020i
$268$		0			0
$269$	0.579557			0.0353362			0.0176681	−	0.999844i	$-0.494376\pi$
$269$	0.579557			0.0353362			0.0176681	+	0.999844i	$0.494376\pi$
$270$		0			0
$271$		−	2.11139i		−	0.128258i	−0.997942	−	0.0641288i	$-0.979573\pi$
$271$		−	2.11139i		−	0.128258i	0.997942	−	0.0641288i	$-0.0204268\pi$
$272$		0			0
$273$	1.37328	−	0.568831i	0.0831147	−	0.0344272i
$274$		0			0
$275$	2.27714	−	0.977657i	0.137317	−	0.0589550i
$276$		0			0
$277$	4.32839	+	4.32839i	0.260068	+	0.260068i	0.825081	−	0.565014i	$-0.191129\pi$
$277$	4.32839	+	4.32839i	0.260068	+	0.260068i	−0.565014	+	0.825081i	$0.691129\pi$
$278$		0			0
$279$	7.55982	−	7.55982i	0.452595	−	0.452595i
$280$		0			0
$281$	−4.40245	+	10.6285i	−0.262628	+	0.634041i	−0.999100	−	0.0424280i	$-0.986491\pi$
$281$	−4.40245	+	10.6285i	−0.262628	+	0.634041i	0.736471	+	0.676469i	$0.236491\pi$
$282$		0			0
$283$	−14.2991	−	14.2991i	−0.849996	−	0.849996i	0.140136	−	0.990132i	$-0.455246\pi$
$283$	−14.2991	−	14.2991i	−0.849996	−	0.849996i	−0.990132	+	0.140136i	$0.955246\pi$
$284$		0			0
$285$	−0.179296	+	0.00115094i	−0.0106206	+	6.81761e-5i
$286$		0			0
$287$	0.573951	+	3.09901i	0.0338792	+	0.182929i
$288$		0			0
$289$	16.3418	−	16.3418i	0.961283	−	0.961283i
$290$		0			0
$291$		−	17.2349i		−	1.01033i
$292$		0			0
$293$	1.81364	+	4.37852i	0.105954	+	0.255796i	0.967961	−	0.251101i	$-0.0807925\pi$
$293$	1.81364	+	4.37852i	0.105954	+	0.255796i	−0.862007	+	0.506897i	$0.830793\pi$
$294$		0			0
$295$	−15.2679	+	15.4652i	−0.888934	+	0.900421i
$296$		0			0
$297$	1.98245	−	1.98245i	0.115034	−	0.115034i
$298$		0			0
$299$	−7.90014	+	3.27235i	−0.456877	+	0.189245i
$300$		0			0
$301$	5.44908	+	2.25708i	0.314080	+	0.130096i
$302$		0			0
$303$	3.19522	+	3.19522i	0.183561	+	0.183561i
$304$		0			0
$305$	0.131149	+	20.4306i	0.00750956	+	1.16985i
$306$		0			0
$307$	14.4264			0.823361			0.411680	−	0.911328i	$-0.364942\pi$
$307$	14.4264			0.823361			0.411680	+	0.911328i	$0.364942\pi$
$308$		0			0
$309$	17.3070	+	7.16881i	0.984563	+	0.407820i
$310$		0			0
$311$	5.53375	−	13.3596i	0.313790	−	0.757556i	−0.685768	−	0.727820i	$-0.740533\pi$
$311$	5.53375	−	13.3596i	0.313790	−	0.757556i	0.999558	−	0.0297355i	$-0.00946651\pi$
$312$		0			0
$313$	−5.85254	−	14.1293i	−0.330805	−	0.798634i	−0.998529	−	0.0542251i	$-0.982731\pi$
$313$	−5.85254	−	14.1293i	−0.330805	−	0.798634i	0.667724	−	0.744409i	$-0.267269\pi$
$314$		0			0
$315$	1.03773	+	0.422056i	0.0584692	+	0.0237802i
$316$		0			0
$317$	4.37125	−	10.5531i	0.245514	−	0.592723i	−0.752299	−	0.658822i	$-0.771055\pi$
$317$	4.37125	−	10.5531i	0.245514	−	0.592723i	0.997813	+	0.0660987i	$0.0210552\pi$
$318$		0			0
$319$	0.912730	−	0.912730i	0.0511030	−	0.0511030i
$320$		0			0
$321$	5.46764	+	13.2001i	0.305174	+	0.736755i
$322$		0			0
$323$		−	0.360710i		−	0.0200704i
$324$		0			0
$325$	−3.97668	+	9.96034i	−0.220586	+	0.552500i
$326$		0			0
$327$	18.1165	+	18.1165i	1.00184	+	1.00184i
$328$		0			0
$329$			4.58375i			0.252710i
$330$		0			0
$331$	−13.0248	+	5.39503i	−0.715906	+	0.296538i	−0.710746	−	0.703449i	$-0.751642\pi$
$331$	−13.0248	+	5.39503i	−0.715906	+	0.296538i	−0.00515976	+	0.999987i	$0.501642\pi$
$332$		0			0
$333$	−6.54224			−0.358512
$334$		0			0
$335$	32.4628	+	13.2031i	1.77363	+	0.721360i
$336$		0			0
$337$		−	30.2100i		−	1.64564i	−0.568300	−	0.822821i	$-0.692399\pi$
$337$		−	30.2100i		−	1.64564i	0.568300	−	0.822821i	$-0.307601\pi$
$338$		0			0
$339$	−14.2735	+	5.91226i	−0.775228	+	0.321110i
$340$		0			0
$341$	4.80966	−	1.99223i	0.260458	−	0.107885i
$342$		0			0
$343$	−6.25628	+	2.59144i	−0.337808	+	0.139924i
$344$		0			0
$345$	11.6255	+	4.72824i	0.625896	+	0.254560i
$346$		0			0
$347$	−28.8006	+	11.9296i	−1.54610	+	0.640414i	−0.982605	−	0.185709i	$-0.940542\pi$
$347$	−28.8006	+	11.9296i	−1.54610	+	0.640414i	−0.563491	+	0.826122i	$0.690542\pi$
$348$		0			0
$349$	−25.4667	−	25.4667i	−1.36320	−	1.36320i	−0.869802	−	0.493401i	$-0.835753\pi$
$349$	−25.4667	−	25.4667i	−1.36320	−	1.36320i	−0.493401	−	0.869802i	$-0.664247\pi$
$350$		0			0
$351$			12.1334i			0.647634i
$352$		0			0
$353$	−4.64880	+	4.64880i	−0.247431	+	0.247431i	−0.819915	−	0.572485i	$-0.805980\pi$
$353$	−4.64880	+	4.64880i	−0.247431	+	0.247431i	0.572485	+	0.819915i	$0.305980\pi$
$354$		0			0
$355$	−12.8143	−	5.21172i	−0.680110	−	0.276610i
$356$		0			0
$357$	1.67955	−	4.05480i	0.0888913	−	0.214603i
$358$		0			0
$359$	32.4231			1.71123			0.855614	−	0.517614i	$-0.173180\pi$
$359$	32.4231			1.71123			0.855614	+	0.517614i	$0.173180\pi$
$360$		0			0
$361$	13.4327	+	13.4327i	0.706986	+	0.706986i
$362$		0			0
$363$	−13.9884	+	5.79418i	−0.734200	+	0.304116i
$364$		0			0
$365$	10.2709	−	10.4036i	0.537601	−	0.544548i
$366$		0			0
$367$		−	8.13367i		−	0.424574i	−0.977207	−	0.212287i	$-0.931909\pi$
$367$		−	8.13367i		−	0.424574i	0.977207	−	0.212287i	$-0.0680912\pi$
$368$		0			0
$369$	−6.37482	−	1.35588i	−0.331860	−	0.0705841i
$370$		0			0
$371$	−2.80821	−	2.80821i	−0.145795	−	0.145795i
$372$		0			0
$373$	12.1598	−	12.1598i	0.629611	−	0.629611i	−0.318359	−	0.947970i	$-0.603132\pi$
$373$	12.1598	−	12.1598i	0.629611	−	0.629611i	0.947970	+	0.318359i	$0.103132\pi$
$374$		0			0
$375$	14.4238	−	6.30261i	0.744842	−	0.325465i
$376$		0			0
$377$			5.58627i			0.287708i
$378$		0			0
$379$		−	19.0663i		−	0.979371i	−0.871899	−	0.489685i	$-0.837112\pi$
$379$		−	19.0663i		−	0.979371i	0.871899	−	0.489685i	$-0.162888\pi$
$380$		0			0
$381$	0.694551	+	1.67679i	0.0355829	+	0.0859048i
$382$		0			0
$383$	12.4975	+	30.1716i	0.638591	+	1.54169i	0.828557	+	0.559904i	$0.189162\pi$
$383$	12.4975	+	30.1716i	0.638591	+	1.54169i	−0.189967	+	0.981791i	$0.560838\pi$
$384$		0			0
$385$	0.388195	+	0.383243i	0.0197843	+	0.0195319i
$386$		0			0
$387$	−8.62426	+	8.62426i	−0.438396	+	0.438396i
$388$		0			0
$389$	0.725677	−	0.725677i	0.0367933	−	0.0367933i	−0.688471	−	0.725264i	$-0.741718\pi$
$389$	0.725677	−	0.725677i	0.0367933	−	0.0367933i	0.725264	+	0.688471i	$0.241718\pi$
$390$		0			0
$391$	−9.66204	+	23.3262i	−0.488631	+	1.17966i
$392$		0			0
$393$	−16.4509	+	6.81418i	−0.829837	+	0.343730i
$394$		0			0
$395$	−13.5961	−	5.52970i	−0.684093	−	0.278230i
$396$		0			0
$397$	−10.9657	−	4.54215i	−0.550354	−	0.227964i	0.0901374	−	0.995929i	$-0.471269\pi$
$397$	−10.9657	−	4.54215i	−0.550354	−	0.227964i	−0.640492	+	0.767965i	$0.721269\pi$
$398$		0			0
$399$	−0.0151039	−	0.0364641i	−0.000756142	−	0.00182549i
$400$		0			0
$401$	27.2714	+	27.2714i	1.36187	+	1.36187i	0.871532	+	0.490338i	$0.163127\pi$
$401$	27.2714	+	27.2714i	1.36187	+	1.36187i	0.490338	+	0.871532i	$0.336873\pi$
$402$		0			0
$403$	−8.62192	+	20.8151i	−0.429488	+	1.03688i
$404$		0			0
$405$	7.71408	−	7.81376i	0.383316	−	0.388269i
$406$		0			0
$407$	−2.94316	−	1.21910i	−0.145887	−	0.0604284i
$408$		0			0
$409$	−3.49897			−0.173013			−0.0865065	−	0.996251i	$-0.527570\pi$
$409$	−3.49897			−0.173013			−0.0865065	+	0.996251i	$0.527570\pi$
$410$		0			0
$411$	0.535640			0.0264212
$412$		0			0
$413$	−4.41963	−	1.83067i	−0.217476	−	0.0900815i
$414$		0			0
$415$	0.0268001	+	4.17497i	0.00131557	+	0.204941i
$416$		0			0
$417$	−8.84274	+	21.3483i	−0.433031	+	1.04543i
$418$		0			0
$419$	−2.28049	−	2.28049i	−0.111409	−	0.111409i	0.649205	−	0.760614i	$-0.275102\pi$
$419$	−2.28049	−	2.28049i	−0.111409	−	0.111409i	−0.760614	+	0.649205i	$0.775102\pi$
$420$		0			0
$421$	−12.3379	−	29.7863i	−0.601313	−	1.45170i	−0.872231	−	0.489094i	$-0.837327\pi$
$421$	−12.3379	−	29.7863i	−0.601313	−	1.45170i	0.270918	−	0.962602i	$-0.412673\pi$
$422$		0			0
$423$	−8.75719	−	3.62735i	−0.425789	−	0.176368i
$424$		0			0
$425$	12.4929	+	29.0981i	0.605992	+	1.41146i
$426$		0			0
$427$	−4.15504	+	1.72107i	−0.201076	+	0.0832885i
$428$		0			0
$429$	−0.572776	+	1.38280i	−0.0276539	+	0.0667624i
$430$		0			0
$431$	9.43862	−	9.43862i	0.454642	−	0.454642i	−0.442250	−	0.896892i	$-0.645820\pi$
$431$	9.43862	−	9.43862i	0.454642	−	0.454642i	0.896892	+	0.442250i	$0.145820\pi$
$432$		0			0
$433$	18.6791	−	18.6791i	0.897659	−	0.897659i	−0.0975699	−	0.995229i	$-0.531107\pi$
$433$	18.6791	−	18.6791i	0.897659	−	0.897659i	0.995229	+	0.0975699i	$0.0311070\pi$
$434$		0			0
$435$	5.76015	−	5.83458i	0.276178	−	0.279747i
$436$		0			0
$437$	0.0868891	+	0.209769i	0.00415647	+	0.0100346i
$438$		0			0
$439$	3.16437	+	7.63947i	0.151027	+	0.364612i	0.981228	−	0.192853i	$-0.0617740\pi$
$439$	3.16437	+	7.63947i	0.151027	+	0.364612i	−0.830200	+	0.557465i	$0.811774\pi$
$440$		0			0
$441$		−	6.87835i		−	0.327540i
$442$		0			0
$443$		−	5.94830i		−	0.282612i	−0.989966	−	0.141306i	$-0.954870\pi$
$443$		−	5.94830i		−	0.282612i	0.989966	−	0.141306i	$-0.0451302\pi$
$444$		0			0
$445$	−5.19195	+	12.7656i	−0.246122	+	0.605150i
$446$		0			0
$447$	18.6195	−	18.6195i	0.880671	−	0.880671i
$448$		0			0
$449$	−23.5285	−	23.5285i	−1.11038	−	1.11038i	−0.993099	−	0.117280i	$-0.962582\pi$
$449$	−23.5285	−	23.5285i	−1.11038	−	1.11038i	−0.117280	−	0.993099i	$-0.537418\pi$
$450$		0			0
$451$	−2.61519	−	1.79787i	−0.123144	−	0.0846583i
$452$		0			0
$453$			10.1878i			0.478665i
$454$		0			0
$455$	−2.36076	+	0.0151543i	−0.110674	+	0.000710442i
$456$		0			0
$457$	3.90481	−	1.61743i	0.182659	−	0.0756600i	−0.289479	−	0.957184i	$-0.593482\pi$
$457$	3.90481	−	1.61743i	0.182659	−	0.0756600i	0.472139	+	0.881524i	$0.343482\pi$
$458$		0			0
$459$	25.3325	+	25.3325i	1.18242	+	1.18242i
$460$		0			0
$461$	8.14853			0.379515			0.189757	−	0.981831i	$-0.439230\pi$
$461$	8.14853			0.379515			0.189757	+	0.981831i	$0.439230\pi$
$462$		0			0
$463$	4.29904	−	10.3788i	0.199794	−	0.482344i	−0.791949	−	0.610587i	$-0.790934\pi$
$463$	4.29904	−	10.3788i	0.199794	−	0.482344i	0.991743	+	0.128243i	$0.0409336\pi$
$464$		0			0
$465$	30.4682	−	12.8501i	1.41293	−	0.595908i
$466$		0			0
$467$	14.5791	−	14.5791i	0.674639	−	0.674639i	−0.284143	−	0.958782i	$-0.591709\pi$
$467$	14.5791	−	14.5791i	0.674639	−	0.674639i	0.958782	+	0.284143i	$0.0917089\pi$
$468$		0			0
$469$			7.71430i			0.356213i
$470$		0			0
$471$	11.0922	+	11.0922i	0.511102	+	0.511102i
$472$		0			0
$473$	−5.48687	+	2.27274i	−0.252287	+	0.104501i
$474$		0			0
$475$	0.264472	+	0.105591i	0.0121348	+	0.00484484i
$476$		0			0
$477$	7.58732	−	3.14277i	0.347399	−	0.143898i
$478$		0			0
$479$	9.13378	−	3.78334i	0.417333	−	0.172865i	−0.164128	−	0.986439i	$-0.552481\pi$
$479$	9.13378	−	3.78334i	0.417333	−	0.172865i	0.581461	+	0.813574i	$0.302481\pi$
$480$		0			0
$481$	12.7373	−	5.27598i	0.580773	−	0.240564i
$482$		0			0
$483$			2.76262i			0.125704i
$484$		0			0
$485$	−10.3127	+	25.3562i	−0.468276	+	1.15137i
$486$		0			0
$487$	17.5304			0.794379			0.397190	−	0.917737i	$-0.369986\pi$
$487$	17.5304			0.794379			0.397190	+	0.917737i	$0.369986\pi$
$488$		0			0
$489$	11.6179	−	4.81229i	0.525379	−	0.217619i
$490$		0			0
$491$		−	9.83918i		−	0.444036i	−0.975043	−	0.222018i	$-0.928736\pi$
$491$		−	9.83918i		−	0.444036i	0.975043	−	0.222018i	$-0.0712644\pi$
$492$		0			0
$493$	11.6632	+	11.6632i	0.525283	+	0.525283i
$494$		0			0
$495$	−1.03938	+	0.438363i	−0.0467167	+	0.0197029i
$496$		0			0
$497$		−	3.04511i		−	0.136592i
$498$		0			0
$499$	3.52346	+	8.50639i	0.157732	+	0.380798i	0.982913	−	0.184069i	$-0.0589271\pi$
$499$	3.52346	+	8.50639i	0.157732	+	0.380798i	−0.825181	+	0.564868i	$0.808927\pi$
$500$		0			0
$501$	−3.94421	+	3.94421i	−0.176214	+	0.176214i
$502$		0			0
$503$	3.60463	−	8.70234i	0.160722	−	0.388018i	−0.822918	−	0.568160i	$-0.807656\pi$
$503$	3.60463	−	8.70234i	0.160722	−	0.388018i	0.983641	+	0.180142i	$0.0576556\pi$
$504$		0			0
$505$	−2.78896	−	6.61276i	−0.124107	−	0.294264i
$506$		0			0
$507$	4.52524	+	10.9249i	0.200973	+	0.485191i
$508$		0			0
$509$	−0.0578167	+	0.139582i	−0.00256268	+	0.00618686i	−0.925156	−	0.379588i	$-0.876066\pi$
$509$	−0.0578167	+	0.139582i	−0.00256268	+	0.00618686i	0.922593	+	0.385775i	$0.126066\pi$
$510$		0			0
$511$	2.97312	+	1.23151i	0.131523	+	0.0544786i
$512$		0			0
$513$	0.322173			0.0142243
$514$		0			0
$515$	−21.1728	−	20.9028i	−0.932987	−	0.921085i
$516$		0			0
$517$	−3.26367	−	3.26367i	−0.143536	−	0.143536i
$518$		0			0
$519$	15.5500	+	6.44103i	0.682570	+	0.282730i
$520$		0			0
$521$	−32.1222	+	13.3054i	−1.40730	+	0.582922i	−0.951635	−	0.307230i	$-0.900598\pi$
$521$	−32.1222	+	13.3054i	−1.40730	+	0.582922i	−0.455663	+	0.890152i	$0.650598\pi$
$522$		0			0
$523$	8.60500	−	8.60500i	0.376270	−	0.376270i	−0.493484	−	0.869755i	$-0.664277\pi$
$523$	8.60500	−	8.60500i	0.376270	−	0.376270i	0.869755	+	0.493484i	$0.164277\pi$
$524$		0			0
$525$	2.48132	+	2.41841i	0.108294	+	0.105548i
$526$		0			0
$527$	25.4574	+	61.4595i	1.10894	+	2.67722i
$528$		0			0
$529$			7.10732i			0.309014i
$530$		0			0
$531$	6.99495	−	6.99495i	0.303555	−	0.303555i
$532$		0			0
$533$	13.5048	−	2.50116i	0.584960	−	0.108337i
$534$		0			0
$535$	−0.145664	−	22.6917i	−0.00629759	−	0.981050i
$536$		0			0
$537$	−9.05996	−	9.05996i	−0.390966	−	0.390966i
$538$		0			0
$539$	1.28173	−	3.09437i	0.0552079	−	0.133284i
$540$		0			0
$541$	−12.9488	+	12.9488i	−0.556712	+	0.556712i	−0.928370	−	0.371658i	$-0.878789\pi$
$541$	−12.9488	+	12.9488i	−0.556712	+	0.556712i	0.371658	+	0.928370i	$0.378789\pi$
$542$		0			0
$543$	21.5509	+	21.5509i	0.924837	+	0.924837i
$544$		0			0
$545$	−15.8130	−	37.4935i	−0.677356	−	1.60604i
$546$		0			0
$547$	0.614192	−	0.254407i	0.0262610	−	0.0108776i	−0.369514	−	0.929225i	$-0.620476\pi$
$547$	0.614192	−	0.254407i	0.0262610	−	0.0108776i	0.395775	+	0.918347i	$0.370476\pi$
$548$		0			0
$549$		−	9.30012i		−	0.396919i
$550$		0			0
$551$	0.148330			0.00631906
$552$		0			0
$553$		−	3.23090i		−	0.137392i
$554$		0			0
$555$	−18.7437	−	7.62331i	−0.795627	−	0.323592i
$556$		0			0
$557$	8.53239	+	20.5990i	0.361529	+	0.872808i	0.995077	+	0.0991045i	$0.0315978\pi$
$557$	8.53239	+	20.5990i	0.361529	+	0.872808i	−0.633548	+	0.773703i	$0.718402\pi$
$558$		0			0
$559$	9.83590	−	23.7460i	0.416014	−	1.00435i
$560$		0			0
$561$	1.69120	+	4.08291i	0.0714025	+	0.172381i
$562$		0			0
$563$	16.1470	+	6.68831i	0.680516	+	0.281879i	0.696042	−	0.718001i	$-0.254943\pi$
$563$	16.1470	+	6.68831i	0.680516	+	0.281879i	−0.0155269	+	0.999879i	$0.504943\pi$
$564$		0			0
$565$	24.5370	−	0.157509i	1.03228	−	0.00662644i
$566$		0			0
$567$	2.23301	+	0.924941i	0.0937774	+	0.0388439i
$568$		0			0
$569$	−24.2186	+	24.2186i	−1.01529	+	1.01529i	−0.0154134	+	0.999881i	$0.504906\pi$
$569$	−24.2186	+	24.2186i	−1.01529	+	1.01529i	−0.999881	+	0.0154134i	$0.995094\pi$
$570$		0			0
$571$	4.32752	+	10.4476i	0.181101	+	0.437217i	0.988194	−	0.153208i	$-0.0489604\pi$
$571$	4.32752	+	10.4476i	0.181101	+	0.437217i	−0.807093	+	0.590424i	$0.798960\pi$
$572$		0			0
$573$	5.41013	−	5.41013i	0.226011	−	0.226011i
$574$		0			0
$575$	−14.2744	−	13.9125i	−0.595284	−	0.580192i
$576$		0			0
$577$	−1.62569	+	3.92477i	−0.0676786	+	0.163391i	−0.954100	−	0.299489i	$-0.903184\pi$
$577$	−1.62569	+	3.92477i	−0.0676786	+	0.163391i	0.886421	+	0.462880i	$0.153184\pi$
$578$		0			0
$579$	−15.1804	−	15.1804i	−0.630876	−	0.630876i
$580$		0			0
$581$	−0.849078	+	0.351700i	−0.0352257	+	0.0145910i
$582$		0			0
$583$	3.99894			0.165619
$584$		0			0
$585$	1.83923	−	4.52219i	0.0760430	−	0.186970i
$586$		0			0
$587$	2.75273	−	6.64568i	0.113617	−	0.274297i	−0.856834	−	0.515592i	$-0.827572\pi$
$587$	2.75273	−	6.64568i	0.113617	−	0.274297i	0.970452	+	0.241295i	$0.0775722\pi$
$588$		0			0
$589$	0.552695	+	0.228934i	0.0227734	+	0.00943305i
$590$		0			0
$591$	22.7885	+	9.43931i	0.937394	+	0.388281i
$592$		0			0
$593$	−9.95206	−	24.0264i	−0.408682	−	0.986646i	−0.985485	−	0.169762i	$-0.945700\pi$
$593$	−9.95206	−	24.0264i	−0.408682	−	0.986646i	0.576803	−	0.816883i	$-0.304300\pi$
$594$		0			0
$595$	−4.89722	+	4.96050i	−0.200766	+	0.203361i
$596$		0			0
$597$	−11.6788	−	11.6788i	−0.477981	−	0.477981i
$598$		0			0
$599$	−28.7206			−1.17349			−0.586746	−	0.809771i	$-0.699591\pi$
$599$	−28.7206			−1.17349			−0.586746	+	0.809771i	$0.699591\pi$
$600$		0			0
$601$	−3.20865	+	7.74638i	−0.130884	+	0.315981i	−0.975712	−	0.219056i	$-0.929702\pi$
$601$	−3.20865	+	7.74638i	−0.130884	+	0.315981i	0.844829	+	0.535037i	$0.179702\pi$
$602$		0			0
$603$	−14.7381	−	6.10471i	−0.600181	−	0.248603i
$604$		0			0
$605$	24.0470	−	0.154363i	0.977648	−	0.00627575i
$606$		0			0
$607$	−27.2423			−1.10573			−0.552866	−	0.833270i	$-0.686466\pi$
$607$	−27.2423			−1.10573			−0.552866	+	0.833270i	$0.686466\pi$
$608$		0			0
$609$	1.66740	+	0.690659i	0.0675664	+	0.0279869i
$610$		0			0
$611$	19.9750			0.808102
$612$		0			0
$613$	−13.4945			−0.545039			−0.272519	−	0.962150i	$-0.587857\pi$
$613$	−13.4945			−0.545039			−0.272519	+	0.962150i	$0.587857\pi$
$614$		0			0
$615$	−16.6841	−	11.3129i	−0.672769	−	0.456178i
$616$		0			0
$617$	−42.6063			−1.71527			−0.857633	−	0.514262i	$-0.828066\pi$
$617$	−42.6063			−1.71527			−0.857633	+	0.514262i	$0.828066\pi$
$618$		0			0
$619$	6.13111			0.246430			0.123215	−	0.992380i	$-0.460679\pi$
$619$	6.13111			0.246430			0.123215	+	0.992380i	$0.460679\pi$
$620$		0			0
$621$	−20.8342	−	8.62979i	−0.836046	−	0.346302i
$622$		0			0
$623$	−3.03356			−0.121537
$624$		0			0
$625$	−24.9918	+	0.641844i	−0.999670	+	0.0256738i
$626$		0			0
$627$	0.0367170	+	0.0152087i	0.00146633	+	0.000607375i
$628$		0			0
$629$	15.5781	−	37.6087i	0.621138	−	1.49956i
$630$		0			0
$631$	28.4846			1.13395			0.566977	−	0.823734i	$-0.308113\pi$
$631$	28.4846			1.13395			0.566977	+	0.823734i	$0.308113\pi$
$632$		0			0
$633$	18.4185	+	18.4185i	0.732070	+	0.732070i
$634$		0			0
$635$	−0.0185036	−	2.88252i	−0.000734291	−	0.114389i
$636$		0			0
$637$	5.54704	+	13.3917i	0.219782	+	0.530600i
$638$		0			0
$639$	5.81765	+	2.40975i	0.230143	+	0.0953282i
$640$		0			0
$641$	45.5367	+	18.8619i	1.79859	+	0.745002i	0.986988	+	0.160796i	$0.0514063\pi$
$641$	45.5367	+	18.8619i	1.79859	+	0.745002i	0.811606	+	0.584205i	$0.198594\pi$
$642$		0			0
$643$	1.47720	−	3.56628i	0.0582551	−	0.140640i	−0.892072	−	0.451893i	$-0.850749\pi$
$643$	1.47720	−	3.56628i	0.0582551	−	0.140640i	0.950327	+	0.311253i	$0.100749\pi$
$644$		0			0
$645$	−34.7582	+	14.6594i	−1.36860	+	0.577214i
$646$		0			0
$647$	−15.9302			−0.626281			−0.313141	−	0.949707i	$-0.601381\pi$
$647$	−15.9302			−0.626281			−0.313141	+	0.949707i	$0.601381\pi$
$648$		0			0
$649$	4.45028	−	1.84337i	0.174689	−	0.0723585i
$650$		0			0
$651$	5.14696	+	5.14696i	0.201725	+	0.201725i
$652$		0			0
$653$	−6.57203	+	15.8663i	−0.257183	+	0.620896i	−0.998750	−	0.0499835i	$-0.984083\pi$
$653$	−6.57203	+	15.8663i	−0.257183	+	0.620896i	0.741567	+	0.670879i	$0.234083\pi$
$654$		0			0
$655$	28.2801	−	0.181537i	1.10500	−	0.00709323i
$656$		0			0
$657$	−4.70556	+	4.70556i	−0.183581	+	0.183581i
$658$		0			0
$659$	16.3545	+	39.4832i	0.637079	+	1.53805i	0.830553	+	0.556940i	$0.188025\pi$
$659$	16.3545	+	39.4832i	0.637079	+	1.53805i	−0.193474	+	0.981105i	$0.561975\pi$
$660$		0			0
$661$	3.09190	−	3.09190i	0.120261	−	0.120261i	−0.644415	−	0.764676i	$-0.722899\pi$
$661$	3.09190	−	3.09190i	0.120261	−	0.120261i	0.764676	+	0.644415i	$0.222899\pi$
$662$		0			0
$663$	−17.6700	−	7.31913i	−0.686244	−	0.284252i
$664$		0			0
$665$	0.000402384		0.0626841i	1.56038e−5		0.00243079i
$666$		0			0
$667$	−9.59213	−	3.97319i	−0.371409	−	0.153843i
$668$		0			0
$669$	−4.46216	−	10.7726i	−0.172517	−	0.416493i
$670$		0			0
$671$	1.73301	−	4.18385i	0.0669020	−	0.161516i
$672$		0			0
$673$	4.59408	+	11.0911i	0.177089	+	0.427530i	0.987354	−	0.158534i	$-0.0506767\pi$
$673$	4.59408	+	11.0911i	0.177089	+	0.427530i	−0.810265	+	0.586064i	$0.800677\pi$
$674$		0			0
$675$	−25.9894	+	11.1582i	−1.00033	+	0.429478i
$676$		0			0
$677$		−	21.3868i		−	0.821962i	−0.911644	−	0.410981i	$-0.865186\pi$
$677$		−	21.3868i		−	0.821962i	0.911644	−	0.410981i	$-0.134814\pi$
$678$		0			0
$679$	−6.02552			−0.231238
$680$		0			0
$681$		−	10.8176i		−	0.414531i
$682$		0			0
$683$	−19.9368	+	8.25810i	−0.762861	+	0.315987i	−0.729977	−	0.683472i	$-0.760469\pi$
$683$	−19.9368	+	8.25810i	−0.762861	+	0.315987i	−0.0328840	+	0.999459i	$0.510469\pi$
$684$		0			0
$685$	−0.788042	−	0.320507i	−0.0301095	−	0.0122459i
$686$		0			0
$687$	−5.72299	−	5.72299i	−0.218346	−	0.218346i
$688$		0			0
$689$	−12.2376	+	12.2376i	−0.466214	+	0.466214i
$690$		0			0
$691$	−10.3927	+	25.0902i	−0.395357	+	0.954476i	0.593395	+	0.804912i	$0.297787\pi$
$691$	−10.3927	+	25.0902i	−0.395357	+	0.954476i	−0.988752	+	0.149565i	$0.952213\pi$
$692$		0			0
$693$	−0.175582	−	0.175582i	−0.00666979	−	0.00666979i
$694$		0			0
$695$	25.7836	−	26.1167i	0.978027	−	0.990664i
$696$		0			0
$697$	22.9738	−	33.4178i	0.870195	−	1.26579i
$698$		0			0
$699$	−4.83940	+	4.83940i	−0.183043	+	0.183043i
$700$		0			0
$701$		−	17.5094i		−	0.661321i	−0.943750	−	0.330661i	$-0.892728\pi$
$701$		−	17.5094i		−	0.661321i	0.943750	−	0.330661i	$-0.107272\pi$
$702$		0			0
$703$	−0.140091	−	0.338209i	−0.00528362	−	0.0127558i
$704$		0			0
$705$	−20.8629	−	20.5967i	−0.785742	−	0.775718i
$706$		0			0
$707$	1.11709	−	1.11709i	0.0420124	−	0.0420124i
$708$		0			0
$709$	−22.6567	+	9.38470i	−0.850889	+	0.352450i	−0.765138	−	0.643867i	$-0.777329\pi$
$709$	−22.6567	+	9.38470i	−0.850889	+	0.352450i	−0.0857516	+	0.996317i	$0.527329\pi$
$710$		0			0
$711$	6.17260	+	2.55677i	0.231491	+	0.0958865i
$712$		0			0
$713$	−29.6092	−	29.6092i	−1.10887	−	1.10887i
$714$		0			0
$715$	1.67009	−	1.69167i	0.0624580	−	0.0632650i
$716$		0			0
$717$	12.1521			0.453830
$718$		0			0
$719$	7.56563	+	3.13379i	0.282150	+	0.116871i	0.519271	−	0.854610i	$-0.326204\pi$
$719$	7.56563	+	3.13379i	0.282150	+	0.116871i	−0.237120	+	0.971480i	$0.576204\pi$
$720$		0			0
$721$	2.50630	−	6.05075i	0.0933396	−	0.225342i
$722$		0			0
$723$	9.26362	+	22.3644i	0.344518	+	0.831739i
$724$		0			0
$725$	−11.9656	+	5.13727i	−0.444392	+	0.190793i
$726$		0			0
$727$	−16.1652	+	39.0262i	−0.599533	+	1.44740i	0.274526	+	0.961580i	$0.411479\pi$
$727$	−16.1652	+	39.0262i	−0.599533	+	1.44740i	−0.874059	+	0.485820i	$0.838521\pi$
$728$		0			0
$729$	−20.4283	+	20.4283i	−0.756605	+	0.756605i
$730$		0			0
$731$	−29.0418	−	70.1132i	−1.07415	−	2.59323i
$732$		0			0
$733$		−	9.21987i		−	0.340544i	−0.985397	−	0.170272i	$-0.945535\pi$
$733$		−	9.21987i		−	0.340544i	0.985397	−	0.170272i	$-0.0544646\pi$
$734$		0			0
$735$	8.01496	−	19.7067i	0.295636	−	0.726892i
$736$		0			0
$737$	−5.49266	−	5.49266i	−0.202325	−	0.202325i
$738$		0			0
$739$			53.4210i			1.96512i	0.185939	+	0.982561i	$0.440467\pi$
$739$			53.4210i			1.96512i	−0.185939	+	0.982561i	$0.559533\pi$
$740$		0			0
$741$	−0.158903	+	0.0658197i	−0.00583744	+	0.00241795i
$742$		0			0
$743$	−18.6850			−0.685487			−0.342743	−	0.939429i	$-0.611356\pi$
$743$	−18.6850			−0.685487			−0.342743	+	0.939429i	$0.611356\pi$
$744$		0			0
$745$	−38.5344	+	16.2521i	−1.41179	+	0.595429i
$746$		0			0
$747$		−	1.90047i		−	0.0695346i
$748$		0			0
$749$	4.61489	−	1.91155i	0.168625	−	0.0698466i
$750$		0			0
$751$	43.6824	−	18.0939i	1.59399	−	0.660254i	0.603444	−	0.797405i	$-0.293795\pi$
$751$	43.6824	−	18.0939i	1.59399	−	0.660254i	0.990550	+	0.137151i	$0.0437945\pi$
$752$		0			0
$753$	9.77999	−	4.05101i	0.356403	−	0.147627i
$754$		0			0
$755$	6.09600	−	14.9884i	0.221856	−	0.545486i
$756$		0			0
$757$	−39.9980	+	16.5677i	−1.45375	+	0.602164i	−0.963089	−	0.269185i	$-0.913246\pi$
$757$	−39.9980	+	16.5677i	−1.45375	+	0.602164i	−0.490664	+	0.871349i	$0.663246\pi$
$758$		0			0
$759$	−1.96702	−	1.96702i	−0.0713981	−	0.0713981i
$760$		0			0
$761$			20.3747i			0.738583i	0.929314	+	0.369292i	$0.120400\pi$
$761$			20.3747i			0.738583i	−0.929314	+	0.369292i	$0.879600\pi$
$762$		0			0
$763$	6.33374	−	6.33374i	0.229297	−	0.229297i
$764$		0			0
$765$	−5.60156	−	13.2816i	−0.202525	−	0.480196i
$766$		0			0
$767$	−7.97769	+	19.2598i	−0.288058	+	0.695433i
$768$		0			0
$769$	−45.3351			−1.63482			−0.817412	−	0.576054i	$-0.804592\pi$
$769$	−45.3351			−1.63482			−0.817412	+	0.576054i	$0.804592\pi$
$770$		0			0
$771$	−24.7054	−	24.7054i	−0.889742	−	0.889742i
$772$		0			0
$773$	22.5290	−	9.33183i	0.810313	−	0.335643i	0.0612340	−	0.998123i	$-0.480496\pi$
$773$	22.5290	−	9.33183i	0.810313	−	0.335643i	0.749079	+	0.662481i	$0.230496\pi$
$774$		0			0
$775$	−52.5143	+	0.674230i	−1.88637	+	0.0242191i
$776$		0			0
$777$		−	4.45416i		−	0.159792i
$778$		0			0
$779$	−0.0664121	−	0.358588i	−0.00237946	−	0.0128477i
$780$		0			0
$781$	2.16815	+	2.16815i	0.0775826	+	0.0775826i
$782$		0			0
$783$	−10.4171	+	10.4171i	−0.372278	+	0.372278i
$784$		0			0
$785$	−9.68186	−	22.9562i	−0.345560	−	0.819341i
$786$		0			0
$787$		−	19.6523i		−	0.700530i	−0.936651	−	0.350265i	$-0.886092\pi$
$787$		−	19.6523i		−	0.700530i	0.936651	−	0.350265i	$-0.113908\pi$
$788$		0			0
$789$		−	13.9629i		−	0.497092i
$790$		0			0
$791$	2.06700	+	4.99017i	0.0734939	+	0.177430i
$792$		0			0
$793$	7.50008	+	18.1068i	0.266335	+	0.642991i
$794$		0			0
$795$	25.4000	−	0.163049i	0.900845	−	0.00578274i
$796$		0			0
$797$	−26.9802	+	26.9802i	−0.955688	+	0.955688i	−0.999059	−	0.0433713i	$-0.986190\pi$
$797$	−26.9802	+	26.9802i	−0.955688	+	0.955688i	0.0433713	+	0.999059i	$0.486190\pi$
$798$		0			0
$799$	41.7044	−	41.7044i	1.47540	−	1.47540i
$800$		0			0
$801$	2.40061	−	5.79558i	0.0848213	−	0.204777i
$802$		0			0
$803$	−2.99374	+	1.24005i	−0.105647	+	0.0437603i
$804$		0			0
$805$	1.65305	−	4.06441i	0.0582623	−	0.143252i
$806$		0			0
$807$	−0.753841	−	0.312251i	−0.0265365	−	0.0109918i
$808$		0			0
$809$	−10.4186	−	25.1526i	−0.366297	−	0.884319i	−0.994350	−	0.106149i	$-0.966148\pi$
$809$	−10.4186	−	25.1526i	−0.366297	−	0.884319i	0.628053	−	0.778170i	$-0.283852\pi$
$810$		0			0
$811$	−11.9717	−	11.9717i	−0.420383	−	0.420383i	0.464952	−	0.885336i	$-0.346071\pi$
$811$	−11.9717	−	11.9717i	−0.420383	−	0.420383i	−0.885336	+	0.464952i	$0.846071\pi$
$812$		0			0
$813$	−1.13756	+	2.74632i	−0.0398961	+	0.0963176i
$814$		0			0
$815$	−19.9719	+	0.128204i	−0.699586	+	0.00449080i
$816$		0			0
$817$	−0.630516	−	0.261168i	−0.0220590	−	0.00913712i
$818$		0			0
$819$	1.07463			0.0375506
$820$		0			0
$821$	14.4027			0.502657			0.251328	−	0.967902i	$-0.419133\pi$
$821$	14.4027			0.502657			0.251328	+	0.967902i	$0.419133\pi$
$822$		0			0
$823$	46.7166	+	19.3507i	1.62844	+	0.674522i	0.995056	−	0.0993163i	$-0.0316656\pi$
$823$	46.7166	+	19.3507i	1.62844	+	0.674522i	0.633384	+	0.773838i	$0.281666\pi$
$824$		0			0
$825$	−3.48866	+	0.0447909i	−0.121459	+	0.00155942i
$826$		0			0
$827$	−2.30520	+	5.56524i	−0.0801596	+	0.193522i	−0.958878	−	0.283818i	$-0.908399\pi$
$827$	−2.30520	+	5.56524i	−0.0801596	+	0.193522i	0.878719	+	0.477340i	$0.158399\pi$
$828$		0			0
$829$	−29.8583	−	29.8583i	−1.03702	−	1.03702i	−0.999288	−	0.0377321i	$-0.987987\pi$
$829$	−29.8583	−	29.8583i	−1.03702	−	1.03702i	−0.0377321	−	0.999288i	$-0.512013\pi$
$830$		0			0
$831$	−3.29799	−	7.96205i	−0.114406	−	0.276200i
$832$		0			0
$833$	39.5409	+	16.3784i	1.37001	+	0.567477i
$834$		0			0
$835$	8.16285	−	3.44272i	0.282487	−	0.119140i
$836$		0			0
$837$	−54.8934	+	22.7376i	−1.89740	+	0.785927i
$838$		0			0
$839$	−7.88791	+	19.0431i	−0.272321	+	0.657441i	−0.999582	−	0.0289202i	$-0.990793\pi$
$839$	−7.88791	+	19.0431i	−0.272321	+	0.657441i	0.727261	+	0.686361i	$0.240793\pi$
$840$		0			0
$841$	15.7100	−	15.7100i	0.541724	−	0.541724i
$842$		0			0
$843$	11.4527	−	11.4527i	0.394452	−	0.394452i
$844$		0			0
$845$	−0.120557	−	18.7806i	−0.00414729	−	0.646072i
$846$		0			0
$847$	2.02572	+	4.89051i	0.0696044	+	0.168040i
$848$		0			0
$849$	10.8951	+	26.3032i	0.373921	+	0.902724i
$850$		0			0
$851$			25.6237i			0.878368i
$852$		0			0
$853$		−	16.7045i		−	0.571951i	−0.958237	−	0.285976i	$-0.907682\pi$
$853$		−	16.7045i		−	0.571951i	0.958237	−	0.285976i	$-0.0923176\pi$
$854$		0			0
$855$	−0.120076	−	0.0488363i	−0.00410650	−	0.00167017i
$856$		0			0
$857$	−8.21752	+	8.21752i	−0.280705	+	0.280705i	−0.833390	−	0.552685i	$-0.813603\pi$
$857$	−8.21752	+	8.21752i	−0.280705	+	0.280705i	0.552685	+	0.833390i	$0.313603\pi$
$858$		0			0
$859$	−20.3198	−	20.3198i	−0.693302	−	0.693302i	0.269655	−	0.962957i	$-0.413090\pi$
$859$	−20.3198	−	20.3198i	−0.693302	−	0.693302i	−0.962957	+	0.269655i	$0.913090\pi$
$860$		0			0
$861$	0.923122	−	4.34017i	0.0314599	−	0.147913i
$862$		0			0
$863$			11.7246i			0.399109i	0.979887	+	0.199555i	$0.0639495\pi$
$863$			11.7246i			0.399109i	−0.979887	+	0.199555i	$0.936050\pi$
$864$		0			0
$865$	−19.0234	−	18.7807i	−0.646814	−	0.638563i
$866$		0			0
$867$	−30.0607	+	12.4515i	−1.02091	+	0.422877i
$868$		0			0
$869$	2.30044	+	2.30044i	0.0780369	+	0.0780369i
$870$		0			0
$871$	33.6173			1.13908
$872$		0			0
$873$	4.76830	−	11.5117i	0.161382	−	0.389612i
$874$		0			0
$875$	−2.20347	−	5.04273i	−0.0744908	−	0.170475i
$876$		0			0
$877$	29.6735	−	29.6735i	1.00200	−	1.00200i	0.00200576	−	0.999998i	$-0.499362\pi$
$877$	29.6735	−	29.6735i	1.00200	−	1.00200i	0.999998	−	0.00200576i	$-0.000638453\pi$
$878$		0			0
$879$		−	6.67238i		−	0.225054i
$880$		0			0
$881$	14.6196	+	14.6196i	0.492548	+	0.492548i	0.909108	−	0.416560i	$-0.136765\pi$
$881$	14.6196	+	14.6196i	0.492548	+	0.492548i	−0.416560	+	0.909108i	$0.636765\pi$
$882$		0			0
$883$	19.5686	−	8.10559i	0.658537	−	0.272775i	−0.0282859	−	0.999600i	$-0.509005\pi$
$883$	19.5686	−	8.10559i	0.658537	−	0.272775i	0.686823	+	0.726825i	$0.259005\pi$
$884$		0			0
$885$	28.1916	−	11.8899i	0.947651	−	0.399676i
$886$		0			0
$887$	−16.8765	+	6.99048i	−0.566658	+	0.234717i	−0.647573	−	0.762004i	$-0.724216\pi$
$887$	−16.8765	+	6.99048i	−0.566658	+	0.234717i	0.0809149	+	0.996721i	$0.474216\pi$
$888$		0			0
$889$	0.586227	−	0.242823i	0.0196614	−	0.00814403i
$890$		0			0
$891$	−2.24849	+	0.931355i	−0.0753273	+	0.0312016i
$892$		0			0
$893$		−	0.530387i		−	0.0177487i
$894$		0			0
$895$	7.90802	+	18.7503i	0.264336	+	0.626753i
$896$		0			0
$897$	12.0389			0.401968
$898$		0			0
$899$	−25.2732	+	10.4685i	−0.842908	+	0.349144i
$900$		0			0
$901$			51.0999i			1.70239i
$902$		0			0
$903$	−5.87167	−	5.87167i	−0.195397	−	0.195397i
$904$		0			0
$905$	−18.8108	−	44.6013i	−0.625291	−	1.48260i
$906$		0			0
$907$			32.9754i			1.09493i	0.836828	+	0.547466i	$0.184407\pi$
$907$			32.9754i			1.09493i	−0.836828	+	0.547466i	$0.815593\pi$
$908$		0			0
$909$	1.25018	+	3.01819i	0.0414657	+	0.100107i
$910$		0			0
$911$	24.3773	−	24.3773i	0.807657	−	0.807657i	−0.176622	−	0.984279i	$-0.556517\pi$
$911$	24.3773	−	24.3773i	0.807657	−	0.807657i	0.984279	+	0.176622i	$0.0565170\pi$
$912$		0			0
$913$	0.354138	−	0.854966i	0.0117203	−	0.0282952i
$914$		0			0
$915$	10.8369	−	26.6451i	0.358258	−	0.880861i
$916$		0			0
$917$	2.38232	+	5.75142i	0.0786710	+	0.189929i
$918$		0			0
$919$	6.05214	−	14.6111i	0.199642	−	0.481977i	−0.792075	−	0.610424i	$-0.790999\pi$
$919$	6.05214	−	14.6111i	0.199642	−	0.481977i	0.991716	+	0.128447i	$0.0409991\pi$
$920$		0			0
$921$	−18.7648	−	7.77262i	−0.618320	−	0.256116i
$922$		0			0
$923$	−13.2700			−0.436786
$924$		0			0
$925$	23.0145	+	22.4311i	0.756714	+	0.737529i
$926$		0			0
$927$	9.57652	+	9.57652i	0.314534	+	0.314534i
$928$		0			0
$929$	15.3041	+	6.33917i	0.502112	+	0.207981i	0.619339	−	0.785124i	$-0.287401\pi$
$929$	15.3041	+	6.33917i	0.502112	+	0.207981i	−0.117227	+	0.993105i	$0.537401\pi$
$930$		0			0
$931$	0.355585	−	0.147288i	0.0116538	−	0.00482717i
$932$		0			0
$933$	−14.3957	+	14.3957i	−0.471294	+	0.471294i
$934$		0			0
$935$	−0.0450553	−	7.01880i	−0.00147347	−	0.229539i
$936$		0			0
$937$	−7.60698	−	18.3649i	−0.248509	−	0.599955i	0.749569	−	0.661927i	$-0.230261\pi$
$937$	−7.60698	−	18.3649i	−0.248509	−	0.599955i	−0.998078	+	0.0619722i	$0.980261\pi$
$938$		0			0
$939$			21.5314i			0.702652i
$940$		0			0
$941$	−30.0763	+	30.0763i	−0.980459	+	0.980459i	−0.999813	−	0.0193535i	$-0.993839\pi$
$941$	−30.0763	+	30.0763i	−0.980459	+	0.980459i	0.0193535	+	0.999813i	$0.493839\pi$
$942$		0			0
$943$	−5.31050	+	24.9680i	−0.172934	+	0.813068i
$944$		0			0
$945$	−4.43054	−	4.37402i	−0.144125	−	0.142287i
$946$		0			0
$947$	−35.4467	−	35.4467i	−1.15186	−	1.15186i	−0.986179	−	0.165684i	$-0.947017\pi$
$947$	−35.4467	−	35.4467i	−1.15186	−	1.15186i	−0.165684	−	0.986179i	$-0.552983\pi$
$948$		0			0
$949$	5.36665	−	12.9562i	0.174209	−	0.420577i
$950$		0			0
$951$	−11.3715	+	11.3715i	−0.368748	+	0.368748i
$952$		0			0
$953$	−29.9917	−	29.9917i	−0.971527	−	0.971527i	0.0280786	−	0.999606i	$-0.491061\pi$
$953$	−29.9917	−	29.9917i	−0.971527	−	0.971527i	−0.999606	+	0.0280786i	$0.991061\pi$
$954$		0			0
$955$	−11.1967	+	4.72225i	−0.362316	+	0.152808i
$956$		0			0
$957$	−1.67896	+	0.695449i	−0.0542731	+	0.0224807i
$958$		0			0
$959$		−	0.187266i		−	0.00604714i
$960$		0			0
$961$	−79.3282			−2.55897
$962$		0			0
$963$			10.3294i			0.332861i
$964$		0			0
$965$	13.2503	+	31.4170i	0.426541	+	1.01135i
$966$		0			0
$967$	−11.8697	−	28.6559i	−0.381703	−	0.921512i	−0.991637	−	0.129060i	$-0.958804\pi$
$967$	−11.8697	−	28.6559i	−0.381703	−	0.921512i	0.609934	−	0.792452i	$-0.291196\pi$
$968$		0			0
$969$	−0.194342	+	0.469182i	−0.00624315	+	0.0150723i
$970$		0			0
$971$	−19.7791	−	47.7510i	−0.634742	−	1.53240i	−0.833597	−	0.552373i	$-0.813722\pi$
$971$	−19.7791	−	47.7510i	−0.634742	−	1.53240i	0.198855	−	0.980029i	$-0.436278\pi$
$972$		0			0
$973$	7.46360	+	3.09153i	0.239272	+	0.0991098i
$974$		0			0
$975$	10.5389	−	10.8131i	0.337516	−	0.346295i
$976$		0			0
$977$	−23.1937	−	9.60714i	−0.742032	−	0.307360i	−0.0205461	−	0.999789i	$-0.506540\pi$
$977$	−23.1937	−	9.60714i	−0.742032	−	0.307360i	−0.721486	+	0.692429i	$0.756540\pi$
$978$		0			0
$979$	2.15993	−	2.15993i	0.0690316	−	0.0690316i
$980$		0			0
$981$	7.08833	+	17.1127i	0.226313	+	0.546368i
$982$		0			0
$983$	−29.7720	+	29.7720i	−0.949579	+	0.949579i	−0.998788	−	0.0492099i	$-0.984330\pi$
$983$	−29.7720	+	29.7720i	−0.949579	+	0.949579i	0.0492099	+	0.998788i	$0.484330\pi$
$984$		0			0
$985$	−27.8787	−	27.5231i	−0.888289	−	0.876957i
$986$		0			0
$987$	2.46961	−	5.96217i	0.0786086	−	0.189778i
$988$		0			0
$989$	33.7783	+	33.7783i	1.07409	+	1.07409i
$990$		0			0
$991$	19.1637	−	7.93785i	0.608754	−	0.252154i	−0.0569418	−	0.998378i	$-0.518135\pi$
$991$	19.1637	−	7.93785i	0.608754	−	0.252154i	0.665696	+	0.746223i	$0.268135\pi$
$992$		0			0
$993$	19.8483			0.629866
$994$		0			0
$995$	10.1939	+	24.1702i	0.323167	+	0.766246i
$996$		0			0
$997$	8.91965	−	21.5340i	0.282488	−	0.681987i	−0.717404	−	0.696657i	$-0.754670\pi$
$997$	8.91965	−	21.5340i	0.282488	−	0.681987i	0.999892	+	0.0146702i	$0.00466985\pi$
$998$		0			0
$999$	33.5908	+	13.9138i	1.06277	+	0.440212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.273.6	✓	84
5.2	odd	4		820.2.y.a.437.6	yes	84
41.38	odd	8		820.2.y.a.653.6	yes	84
205.202	even	8	inner	820.2.x.a.817.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.6	✓	84	1.1	even	1	trivial
820.2.x.a.817.6	yes	84	205.202	even	8	inner
820.2.y.a.437.6	yes	84	5.2	odd	4
820.2.y.a.653.6	yes	84	41.38	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.30072 - 0.538776i) q^{3} +(1.59126 + 1.57096i) q^{5} +(-0.188362 + 0.454747i) q^{7} +(-0.719728 - 0.719728i) q^{9} +(-0.189669 - 0.457901i) q^{11} +(1.98169 + 0.820844i) q^{13} +(-1.22338 - 2.90070i) q^{15} +(5.85122 - 2.42365i) q^{17} +(0.0217955 - 0.0526190i) q^{19} +(0.490013 - 0.490013i) q^{21} +(-2.81893 + 2.81893i) q^{23} +(0.0641897 + 4.99959i) q^{25} +(2.16472 + 5.22610i) q^{27} +(0.996646 + 2.40612i) q^{29} +10.5037i q^{31} +0.697789i q^{33} +(-1.01412 + 0.427710i) q^{35} +(4.54494 - 4.54494i) q^{37} +(-2.13538 - 2.13538i) q^{39} +(5.37057 - 3.48669i) q^{41} -11.9827i q^{43} +(-0.0146097 - 2.27593i) q^{45} +(8.60362 - 3.56374i) q^{47} +(4.77843 + 4.77843i) q^{49} -8.91660 q^{51} +(-3.08766 + 7.45426i) q^{53} +(0.417531 - 1.02660i) q^{55} +(-0.0566997 + 0.0566997i) q^{57} +9.71888i q^{59} +(6.46086 + 6.46086i) q^{61} +(0.462864 - 0.191724i) q^{63} +(1.86387 + 4.41933i) q^{65} +(14.4796 - 5.99766i) q^{67} +(5.18540 - 2.14786i) q^{69} +(-5.71563 + 2.36749i) q^{71} -6.53797i q^{73} +(2.61016 - 6.53765i) q^{75} +0.243955 q^{77} +(-6.06436 + 2.51194i) q^{79} -4.91043i q^{81} +(1.32027 + 1.32027i) q^{83} +(13.1182 + 5.33536i) q^{85} -3.66665i q^{87} +(2.35851 + 5.69395i) q^{89} +(-0.746553 + 0.746553i) q^{91} +(5.65915 - 13.6624i) q^{93} +(0.117344 - 0.0494905i) q^{95} +(4.68468 + 11.3098i) q^{97} +(-0.193054 + 0.466074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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