LMFDB - Embedded newform 920.2.bv.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.16592 + 1.18268i) q^{3} +(-1.96360 - 1.06972i) q^{5} +(0.350713 + 0.468498i) q^{7} +(1.67054 - 2.59942i) q^{9} +(5.54914 - 2.53421i) q^{11} +(-2.22491 - 1.66555i) q^{13} +(5.51812 - 0.00538709i) q^{15} +(0.520071 + 7.27155i) q^{17} +(3.45019 + 3.98174i) q^{19} +(-1.31370 - 0.599946i) q^{21} +(-4.53719 - 1.55366i) q^{23} +(2.71141 + 4.20098i) q^{25} +(-0.0158327 + 0.221370i) q^{27} +(-4.83131 - 4.18635i) q^{29} +(-1.95159 + 0.573039i) q^{31} +(-9.02182 + 12.0517i) q^{33} +(-0.187499 - 1.29510i) q^{35} +(-5.39542 + 1.17370i) q^{37} +(6.78878 + 0.976079i) q^{39} +(-10.6281 + 6.83025i) q^{41} +(-1.29547 - 2.37248i) q^{43} +(-6.06091 + 3.31719i) q^{45} +(-1.31669 - 1.31669i) q^{47} +(1.87564 - 6.38783i) q^{49} +(-9.72635 - 15.1345i) q^{51} +(0.488117 - 0.365400i) q^{53} +(-13.6071 - 0.959851i) q^{55} +(-12.1820 - 4.54364i) q^{57} +(2.62745 - 0.377771i) q^{59} +(2.84942 + 9.70424i) q^{61} +(1.80370 - 0.129003i) q^{63} +(2.58716 + 5.65048i) q^{65} +(4.62955 + 12.4123i) q^{67} +(11.6647 - 2.00095i) q^{69} +(-5.57231 + 12.2017i) q^{71} +(-9.46161 - 0.676708i) q^{73} +(-10.8411 - 5.89225i) q^{75} +(3.13343 + 1.71098i) q^{77} +(0.0759873 + 0.528503i) q^{79} +(3.62330 + 7.93391i) q^{81} +(-0.122202 - 0.561752i) q^{83} +(6.75729 - 14.8347i) q^{85} +(15.4153 + 3.35340i) q^{87} +(1.01298 + 0.297438i) q^{89} -1.62649i q^{91} +(3.54926 - 3.54926i) q^{93} +(-2.51545 - 11.5092i) q^{95} +(-3.06193 + 14.0755i) q^{97} +(2.68262 - 18.6580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.16592	+	1.18268i	−1.25049	+	0.682821i	−0.961578	−	0.274534i	$-0.911477\pi$
$3$	−2.16592	+	1.18268i	−1.25049	+	0.682821i	−0.288916	+	0.957355i	$0.593295\pi$
$4$		0			0
$5$	−1.96360	−	1.06972i	−0.878146	−	0.478392i
$5$	−1.96360	−	1.06972i	−0.878146	−	0.478392i
$6$		0			0
$7$	0.350713	+	0.468498i	0.132557	+	0.177076i	0.861909	−	0.507063i	$-0.169269\pi$
$7$	0.350713	+	0.468498i	0.132557	+	0.177076i	−0.729352	+	0.684139i	$0.760178\pi$
$8$		0			0
$9$	1.67054	−	2.59942i	0.556848	−	0.866472i
$10$		0			0
$11$	5.54914	−	2.53421i	1.67313	−	0.764092i	0.673437	−	0.739245i	$-0.264817\pi$
$11$	5.54914	−	2.53421i	1.67313	−	0.764092i	0.999691	−	0.0248475i	$-0.00791003\pi$
$12$		0			0
$13$	−2.22491	−	1.66555i	−0.617079	−	0.461939i	0.244441	−	0.969664i	$-0.421396\pi$
$13$	−2.22491	−	1.66555i	−0.617079	−	0.461939i	−0.861519	+	0.507725i	$0.830487\pi$
$14$		0			0
$15$	5.51812	−	0.00538709i	1.42477	−	0.00139094i
$16$		0			0
$17$	0.520071	+	7.27155i	0.126136	+	1.76361i	0.529256	+	0.848462i	$0.322471\pi$
$17$	0.520071	+	7.27155i	0.126136	+	1.76361i	−0.403120	+	0.915147i	$0.632074\pi$
$18$		0			0
$19$	3.45019	+	3.98174i	0.791529	+	0.913473i	0.997885	−	0.0650040i	$-0.0207060\pi$
$19$	3.45019	+	3.98174i	0.791529	+	0.913473i	−0.206356	+	0.978477i	$0.566161\pi$
$20$		0			0
$21$	−1.31370	−	0.599946i	−0.286673	−	0.130919i
$22$		0			0
$23$	−4.53719	−	1.55366i	−0.946070	−	0.323961i
$23$	−4.53719	−	1.55366i	−0.946070	−	0.323961i
$24$		0			0
$25$	2.71141	+	4.20098i	0.542282	+	0.840196i
$26$		0			0
$27$	−0.0158327	+	0.221370i	−0.00304700	+	0.0426027i
$28$		0			0
$29$	−4.83131	−	4.18635i	−0.897151	−	0.777386i	0.0784539	−	0.996918i	$-0.475002\pi$
$29$	−4.83131	−	4.18635i	−0.897151	−	0.777386i	−0.975605	+	0.219532i	$0.929547\pi$
$30$		0			0
$31$	−1.95159	+	0.573039i	−0.350516	+	0.102921i	−0.452251	−	0.891891i	$-0.649379\pi$
$31$	−1.95159	+	0.573039i	−0.350516	+	0.102921i	0.101735	+	0.994812i	$0.467561\pi$
$32$		0			0
$33$	−9.02182	+	12.0517i	−1.57050	+	2.09794i
$34$		0			0
$35$	−0.187499	−	1.29510i	−0.0316930	−	0.218913i
$36$		0			0
$37$	−5.39542	+	1.17370i	−0.887002	+	0.192955i	−0.632911	−	0.774225i	$-0.718140\pi$
$37$	−5.39542	+	1.17370i	−0.887002	+	0.192955i	−0.254091	+	0.967180i	$0.581776\pi$
$38$		0			0
$39$	6.78878	+	0.976079i	1.08707	+	0.156298i
$40$		0			0
$41$	−10.6281	+	6.83025i	−1.65983	+	1.06671i	−0.741442	+	0.671017i	$0.765858\pi$
$41$	−10.6281	+	6.83025i	−1.65983	+	1.06671i	−0.918385	+	0.395689i	$0.870506\pi$
$42$		0			0
$43$	−1.29547	−	2.37248i	−0.197558	−	0.361800i	0.760055	−	0.649859i	$-0.225172\pi$
$43$	−1.29547	−	2.37248i	−0.197558	−	0.361800i	−0.957613	+	0.288059i	$0.906990\pi$
$44$		0			0
$45$	−6.06091	+	3.31719i	−0.903508	+	0.494498i
$46$		0			0
$47$	−1.31669	−	1.31669i	−0.192059	−	0.192059i	0.604526	−	0.796585i	$-0.293362\pi$
$47$	−1.31669	−	1.31669i	−0.192059	−	0.192059i	−0.796585	+	0.604526i	$0.793362\pi$
$48$		0			0
$49$	1.87564	−	6.38783i	0.267948	−	0.912548i
$50$		0			0
$51$	−9.72635	−	15.1345i	−1.36196	−	2.11925i
$52$		0			0
$53$	0.488117	−	0.365400i	0.0670481	−	0.0501916i	−0.565228	−	0.824935i	$-0.691212\pi$
$53$	0.488117	−	0.365400i	0.0670481	−	0.0501916i	0.632276	+	0.774743i	$0.282121\pi$
$54$		0			0
$55$	−13.6071	−	0.959851i	−1.83479	−	0.129426i
$56$		0			0
$57$	−12.1820	−	4.54364i	−1.61354	−	0.601819i
$58$		0			0
$59$	2.62745	−	0.377771i	0.342065	−	0.0491816i	0.0308585	−	0.999524i	$-0.490176\pi$
$59$	2.62745	−	0.377771i	0.342065	−	0.0491816i	0.311207	+	0.950342i	$0.399267\pi$
$60$		0			0
$61$	2.84942	+	9.70424i	0.364831	+	1.24250i	0.913630	+	0.406546i	$0.133267\pi$
$61$	2.84942	+	9.70424i	0.364831	+	1.24250i	−0.548799	+	0.835954i	$0.684915\pi$
$62$		0			0
$63$	1.80370	−	0.129003i	0.227245	−	0.0162529i
$64$		0			0
$65$	2.58716	+	5.65048i	0.320897	+	0.700856i
$66$		0			0
$67$	4.62955	+	12.4123i	0.565590	+	1.51641i	0.833252	+	0.552893i	$0.186476\pi$
$67$	4.62955	+	12.4123i	0.565590	+	1.51641i	−0.267662	+	0.963513i	$0.586251\pi$
$68$		0			0
$69$	11.6647	−	2.00095i	1.40426	−	0.240886i
$70$		0			0
$71$	−5.57231	+	12.2017i	−0.661312	+	1.44807i	0.219983	+	0.975504i	$0.429400\pi$
$71$	−5.57231	+	12.2017i	−0.661312	+	1.44807i	−0.881295	+	0.472567i	$0.843328\pi$
$72$		0			0
$73$	−9.46161	−	0.676708i	−1.10740	−	0.0792027i	−0.494361	−	0.869257i	$-0.664598\pi$
$73$	−9.46161	−	0.676708i	−1.10740	−	0.0792027i	−0.613037	+	0.790054i	$0.710052\pi$
$74$		0			0
$75$	−10.8411	−	5.89225i	−1.25182	−	0.680378i
$76$		0			0
$77$	3.13343	+	1.71098i	0.357087	+	0.194984i
$78$		0			0
$79$	0.0759873	+	0.528503i	0.00854924	+	0.0594613i	0.993649	−	0.112520i	$-0.0358922\pi$
$79$	0.0759873	+	0.528503i	0.00854924	+	0.0594613i	−0.985100	+	0.171981i	$0.944983\pi$
$80$		0			0
$81$	3.62330	+	7.93391i	0.402588	+	0.881546i
$82$		0			0
$83$	−0.122202	−	0.561752i	−0.0134134	−	0.0616603i	0.969954	−	0.243290i	$-0.0782265\pi$
$83$	−0.122202	−	0.561752i	−0.0134134	−	0.0616603i	−0.983367	+	0.181629i	$0.941863\pi$
$84$		0			0
$85$	6.75729	−	14.8347i	0.732931	−	1.60905i
$86$		0			0
$87$	15.4153	+	3.35340i	1.65270	+	0.359522i
$88$		0			0
$89$	1.01298	+	0.297438i	0.107376	+	0.0315284i	0.334979	−	0.942226i	$-0.391271\pi$
$89$	1.01298	+	0.297438i	0.107376	+	0.0315284i	−0.227603	+	0.973754i	$0.573089\pi$
$90$		0			0
$91$		−	1.62649i		−	0.170503i
$92$		0			0
$93$	3.54926	−	3.54926i	0.368042	−	0.368042i
$94$		0			0
$95$	−2.51545	−	11.5092i	−0.258080	−	1.18082i
$96$		0			0
$97$	−3.06193	+	14.0755i	−0.310892	+	1.42915i	0.511037	+	0.859558i	$0.329261\pi$
$97$	−3.06193	+	14.0755i	−0.310892	+	1.42915i	−0.821929	+	0.569589i	$0.807102\pi$
$98$		0			0
$99$	2.68262	−	18.6580i	0.269613	−	1.87520i
$100$		0			0
$101$	−11.5402	−	7.41644i	−1.14829	−	0.737963i	−0.178995	−	0.983850i	$-0.557285\pi$
$101$	−11.5402	−	7.41644i	−1.14829	−	0.737963i	−0.969299	+	0.245887i	$0.920921\pi$
$102$		0			0
$103$	−4.91213	+	13.1699i	−0.484007	+	1.29767i	0.433930	+	0.900947i	$0.357127\pi$
$103$	−4.91213	+	13.1699i	−0.484007	+	1.29767i	−0.917937	+	0.396726i	$0.870146\pi$
$104$		0			0
$105$	1.93780	+	2.58334i	0.189110	+	0.252108i
$106$		0			0
$107$	3.62685	−	6.64208i	0.350621	−	0.642114i	−0.641539	−	0.767091i	$-0.721704\pi$
$107$	3.62685	−	6.64208i	0.350621	−	0.642114i	0.992160	+	0.124976i	$0.0398855\pi$
$108$		0			0
$109$	−10.6912	+	12.3383i	−1.02403	+	1.18180i	−0.0408506	+	0.999165i	$0.513007\pi$
$109$	−10.6912	+	12.3383i	−1.02403	+	1.18180i	−0.983182	+	0.182631i	$0.941539\pi$
$110$		0			0
$111$	10.2979	−	8.92320i	0.977436	−	0.846953i
$112$		0			0
$113$	−1.67821	+	0.625940i	−0.157873	+	0.0588835i	−0.427158	−	0.904177i	$-0.640485\pi$
$113$	−1.67821	+	0.625940i	−0.157873	+	0.0588835i	0.269285	+	0.963060i	$0.413213\pi$
$114$		0			0
$115$	7.24723	+	7.90428i	0.675808	+	0.737078i
$116$		0			0
$117$	−8.04625	+	3.00110i	−0.743877	+	0.277452i
$118$		0			0
$119$	−3.22431	+	2.79388i	−0.295572	+	0.256115i
$120$		0			0
$121$	17.1673	−	19.8121i	1.56066	−	1.80110i
$122$		0			0
$123$	14.9415	−	27.3634i	1.34723	−	2.46727i
$124$		0			0
$125$	−0.830254	−	11.1495i	−0.0742602	−	0.997239i
$126$		0			0
$127$	−2.72980	+	7.31887i	−0.242230	+	0.649445i	−0.999995	−	0.00308290i	$-0.999019\pi$
$127$	−2.72980	+	7.31887i	−0.242230	+	0.649445i	0.757765	+	0.652528i	$0.226291\pi$
$128$		0			0
$129$	5.61177	+	3.60647i	0.494089	+	0.317532i
$130$		0			0
$131$	0.404796	−	2.81542i	0.0353672	−	0.245984i	−0.964467	−	0.264204i	$-0.914891\pi$
$131$	0.404796	−	2.81542i	0.0353672	−	0.245984i	0.999834	+	0.0182197i	$0.00579983\pi$
$132$		0			0
$133$	−0.655407	+	3.01286i	−0.0568310	+	0.261248i
$134$		0			0
$135$	0.267892	−	0.417744i	0.0230565	−	0.0359537i
$136$		0			0
$137$	7.48167	−	7.48167i	0.639202	−	0.639202i	−0.311156	−	0.950359i	$-0.600716\pi$
$137$	7.48167	−	7.48167i	0.639202	−	0.639202i	0.950359	+	0.311156i	$0.100716\pi$
$138$		0			0
$139$			3.16283i			0.268268i	0.990963	+	0.134134i	$0.0428253\pi$
$139$			3.16283i			0.268268i	−0.990963	+	0.134134i	$0.957175\pi$
$140$		0			0
$141$	4.40906	+	1.29462i	0.371310	+	0.109026i
$142$		0			0
$143$	−16.5672	−	3.60397i	−1.38542	−	0.301379i
$144$		0			0
$145$	5.00852	+	13.3884i	0.415935	+	1.11185i
$146$		0			0
$147$	3.49229	+	16.0538i	0.288039	+	1.32410i
$148$		0			0
$149$	−1.93768	−	4.24292i	−0.158741	−	0.347594i	0.813504	−	0.581559i	$-0.197557\pi$
$149$	−1.93768	−	4.24292i	−0.158741	−	0.347594i	−0.972245	+	0.233965i	$0.924830\pi$
$150$		0			0
$151$	1.72430	+	11.9928i	0.140322	+	0.975958i	0.931336	+	0.364161i	$0.118644\pi$
$151$	1.72430	+	11.9928i	0.140322	+	0.975958i	−0.791015	+	0.611797i	$0.790447\pi$
$152$		0			0
$153$	19.7706	+	10.7956i	1.59836	+	0.872769i
$154$		0			0
$155$	4.44512	+	0.962434i	0.357041	+	0.0773045i
$156$		0			0
$157$	−14.8328	−	1.06086i	−1.18379	−	0.0846660i	−0.534472	−	0.845186i	$-0.679489\pi$
$157$	−14.8328	−	1.06086i	−1.18379	−	0.0846660i	−0.649314	+	0.760520i	$0.724944\pi$
$158$		0			0
$159$	−0.625071	+	1.36871i	−0.0495713	+	0.108546i
$160$		0			0
$161$	−0.863366	−	2.67056i	−0.0680428	−	0.210469i
$162$		0			0
$163$	2.96097	+	7.93867i	0.231921	+	0.621804i	0.999824	−	0.0187619i	$-0.00597244\pi$
$163$	2.96097	+	7.93867i	0.231921	+	0.621804i	−0.767903	+	0.640566i	$0.778700\pi$
$164$		0			0
$165$	30.6072	−	14.0139i	2.38276	−	1.09098i
$166$		0			0
$167$	0.334715	−	0.0239393i	0.0259010	−	0.00185248i	−0.0583827	−	0.998294i	$-0.518594\pi$
$167$	0.334715	−	0.0239393i	0.0259010	−	0.00185248i	0.0842837	+	0.996442i	$0.473140\pi$
$168$		0			0
$169$	−1.48635	−	5.06204i	−0.114334	−	0.389387i
$170$		0			0
$171$	16.1139	−	2.31683i	1.23226	−	0.177172i
$172$		0			0
$173$	13.2004	+	4.92348i	1.00361	+	0.374326i	0.796922	−	0.604082i	$-0.206460\pi$
$173$	13.2004	+	4.92348i	1.00361	+	0.374326i	0.206684	+	0.978408i	$0.433733\pi$
$174$		0			0
$175$	−1.01722	+	2.74363i	−0.0768949	+	0.207399i
$176$		0			0
$177$	−5.24407	+	3.92566i	−0.394168	+	0.295071i
$178$		0			0
$179$	−14.1797	−	22.0641i	−1.05984	−	1.64915i	−0.696612	−	0.717448i	$-0.745310\pi$
$179$	−14.1797	−	22.0641i	−1.05984	−	1.64915i	−0.363231	−	0.931699i	$-0.618326\pi$
$180$		0			0
$181$	−1.04562	+	3.56107i	−0.0777207	+	0.264692i	−0.989182	−	0.146693i	$-0.953137\pi$
$181$	−1.04562	+	3.56107i	−0.0777207	+	0.264692i	0.911461	+	0.411386i	$0.134955\pi$
$182$		0			0
$183$	−17.6486	−	17.6486i	−1.30462	−	1.30462i
$184$		0			0
$185$	11.8500	+	3.46690i	0.871226	+	0.254891i
$186$		0			0
$187$	21.3136	+	39.0329i	1.55860	+	2.85437i
$188$		0			0
$189$	−0.109264	+	0.0702198i	−0.00794779	+	0.00510774i
$190$		0			0
$191$	16.7799	+	2.41259i	1.21415	+	0.174569i	0.719481	−	0.694512i	$-0.244380\pi$
$191$	16.7799	+	2.41259i	1.21415	+	0.174569i	0.494670	+	0.869081i	$0.335289\pi$
$192$		0			0
$193$	−8.07943	+	1.75757i	−0.581570	+	0.126513i	−0.493720	−	0.869621i	$-0.664363\pi$
$193$	−8.07943	+	1.75757i	−0.581570	+	0.126513i	−0.0878501	+	0.996134i	$0.528000\pi$
$194$		0			0
$195$	−12.2863	−	9.17869i	−0.879839	−	0.657300i
$196$		0			0
$197$	−0.412624	+	0.551201i	−0.0293982	+	0.0392714i	−0.815000	−	0.579462i	$-0.803263\pi$
$197$	−0.412624	+	0.551201i	−0.0293982	+	0.0392714i	0.785601	+	0.618733i	$0.212354\pi$
$198$		0			0
$199$	15.1332	−	4.44350i	1.07276	−	0.314991i	0.302782	−	0.953060i	$-0.402085\pi$
$199$	15.1332	−	4.44350i	1.07276	−	0.314991i	0.769979	+	0.638069i	$0.220267\pi$
$200$		0			0
$201$	−24.7070	−	21.4088i	−1.74270	−	1.51006i
$202$		0			0
$203$	0.266894	−	3.73167i	0.0187323	−	0.261912i
$204$		0			0
$205$	28.1757	−	2.04281i	1.96787	−	0.142676i
$206$		0			0
$207$	−11.6182	+	9.19860i	−0.807521	+	0.639347i
$208$		0			0
$209$	29.2361	+	13.3517i	2.02231	+	0.923557i
$210$		0			0
$211$	−0.0816244	−	0.0941996i	−0.00561926	−	0.00648497i	0.752933	−	0.658097i	$-0.228638\pi$
$211$	−0.0816244	−	0.0941996i	−0.00561926	−	0.00648497i	−0.758552	+	0.651612i	$0.774093\pi$
$212$		0			0
$213$	−2.36150	−	33.0181i	−0.161807	−	2.26236i
$214$		0			0
$215$	0.00590086	+	6.04438i	0.000402435	+	0.412223i
$216$		0			0
$217$	−0.952916	−	0.713344i	−0.0646882	−	0.0484250i
$218$		0			0
$219$	21.2934	−	9.72437i	1.43888	−	0.657112i
$220$		0			0
$221$	10.9540	−	17.0447i	0.736845	−	1.14655i
$222$		0			0
$223$	4.91957	+	6.57178i	0.329439	+	0.440079i	0.934427	−	0.356156i	$-0.115913\pi$
$223$	4.91957	+	6.57178i	0.329439	+	0.440079i	−0.604988	+	0.796235i	$0.706822\pi$
$224$		0			0
$225$	15.4496	−	0.0301656i	1.02998	−	0.00201104i
$226$		0			0
$227$	1.07898	−	0.589170i	0.0716147	−	0.0391046i	−0.443043	−	0.896501i	$-0.646101\pi$
$227$	1.07898	−	0.589170i	0.0716147	−	0.0391046i	0.514657	+	0.857396i	$0.327919\pi$
$228$		0			0
$229$	−8.65661			−0.572045			−0.286022	−	0.958223i	$-0.592333\pi$
$229$	−8.65661			−0.572045			−0.286022	+	0.958223i	$0.592333\pi$
$230$		0			0
$231$	−8.81029			−0.579674
$232$		0			0
$233$	−5.42465	+	2.96208i	−0.355380	+	0.194052i	−0.647015	−	0.762478i	$-0.723983\pi$
$233$	−5.42465	+	2.96208i	−0.355380	+	0.194052i	0.291634	+	0.956530i	$0.405801\pi$
$234$		0			0
$235$	1.17696	+	3.99392i	0.0767763	+	0.260535i
$236$		0			0
$237$	−0.789633	−	1.05483i	−0.0512922	−	0.0685183i
$238$		0			0
$239$	−0.966001	+	1.50313i	−0.0624854	+	0.0972292i	−0.871090	−	0.491123i	$-0.836587\pi$
$239$	−0.966001	+	1.50313i	−0.0624854	+	0.0972292i	0.808605	+	0.588352i	$0.200223\pi$
$240$		0			0
$241$	6.62482	−	3.02545i	0.426742	−	0.194887i	−0.190454	−	0.981696i	$-0.560996\pi$
$241$	6.62482	−	3.02545i	0.426742	−	0.194887i	0.617196	+	0.786810i	$0.288269\pi$
$242$		0			0
$243$	−17.7641	−	13.2980i	−1.13956	−	0.853067i
$244$		0			0
$245$	−10.5162	+	10.5367i	−0.671853	+	0.673166i
$246$		0			0
$247$	−1.04460	−	14.6055i	−0.0664665	−	0.929323i
$248$		0			0
$249$	0.929053	+	1.07218i	0.0588763	+	0.0679469i
$250$		0			0
$251$	−24.1662	−	11.0363i	−1.52536	−	0.696607i	−0.536284	−	0.844038i	$-0.680172\pi$
$251$	−24.1662	−	11.0363i	−1.52536	−	0.696607i	−0.989072	+	0.147431i	$0.952900\pi$
$252$		0			0
$253$	−29.1148	+	2.87670i	−1.83043	+	0.180857i
$254$		0			0
$255$	2.90899	+	40.1225i	0.182168	+	2.51257i
$256$		0			0
$257$	−0.324592	+	4.53838i	−0.0202475	+	0.283097i	0.977234	+	0.212166i	$0.0680516\pi$
$257$	−0.324592	+	4.53838i	−0.0202475	+	0.283097i	−0.997481	+	0.0709311i	$0.977403\pi$
$258$		0			0
$259$	−2.44212	−	2.11611i	−0.151746	−	0.131489i
$260$		0			0
$261$	−18.9530	+	5.56510i	−1.17316	+	0.344471i
$262$		0			0
$263$	16.1954	−	21.6345i	0.998652	−	1.33404i	0.0566648	−	0.998393i	$-0.481953\pi$
$263$	16.1954	−	21.6345i	0.998652	−	1.33404i	0.941987	−	0.335649i	$-0.108956\pi$
$264$		0			0
$265$	−1.34934	+	0.195350i	−0.0828893	+	0.0120003i
$266$		0			0
$267$	−2.54581	+	0.553807i	−0.155801	+	0.0338924i
$268$		0			0
$269$	8.67544	+	1.24734i	0.528951	+	0.0760516i	0.401616	−	0.915808i	$-0.368449\pi$
$269$	8.67544	+	1.24734i	0.528951	+	0.0760516i	0.127335	+	0.991860i	$0.459358\pi$
$270$		0			0
$271$	−4.14079	+	2.66112i	−0.251535	+	0.161652i	−0.660332	−	0.750973i	$-0.729585\pi$
$271$	−4.14079	+	2.66112i	−0.251535	+	0.161652i	0.408798	+	0.912625i	$0.365948\pi$
$272$		0			0
$273$	1.92362	+	3.52285i	0.116423	+	0.213213i
$274$		0			0
$275$	25.6922	+	16.4406i	1.54930	+	0.991403i
$276$		0			0
$277$	−12.3692	−	12.3692i	−0.743191	−	0.743191i	0.229999	−	0.973191i	$-0.426128\pi$
$277$	−12.3692	−	12.3692i	−0.743191	−	0.743191i	−0.973191	+	0.229999i	$0.926128\pi$
$278$		0			0
$279$	−1.77065	+	6.03029i	−0.106006	+	0.361024i
$280$		0			0
$281$	−4.91460	−	7.64726i	−0.293180	−	0.456197i	0.663150	−	0.748487i	$-0.269219\pi$
$281$	−4.91460	−	7.64726i	−0.293180	−	0.456197i	−0.956330	+	0.292289i	$0.905583\pi$
$282$		0			0
$283$	2.94705	−	2.20614i	0.175184	−	0.131141i	−0.508088	−	0.861305i	$-0.669647\pi$
$283$	2.94705	−	2.20614i	0.175184	−	0.131141i	0.683272	+	0.730164i	$0.260556\pi$
$284$		0			0
$285$	19.0600	+	21.9531i	1.12902	+	1.30039i
$286$		0			0
$287$	−6.92737	−	2.58377i	−0.408909	−	0.152515i
$288$		0			0
$289$	−35.7780	+	5.14409i	−2.10459	+	0.302594i
$290$		0			0
$291$	−10.0149	−	34.1076i	−0.587084	−	1.99942i
$292$		0			0
$293$	12.8294	−	0.917579i	0.749503	−	0.0536055i	0.308639	−	0.951179i	$-0.400126\pi$
$293$	12.8294	−	0.917579i	0.749503	−	0.0536055i	0.440864	+	0.897574i	$0.354672\pi$
$294$		0			0
$295$	−5.56336	−	2.06884i	−0.323912	−	0.120453i
$296$		0			0
$297$	0.473139	+	1.26854i	0.0274543	+	0.0736079i
$298$		0			0
$299$	7.50715	+	11.0137i	0.434149	+	0.636936i
$300$		0			0
$301$	0.657163	−	1.43899i	0.0378782	−	0.0829418i
$302$		0			0
$303$	33.7664	+	2.41502i	1.93983	+	0.138739i
$304$		0			0
$305$	4.78568	−	22.1033i	0.274027	−	1.26563i
$306$		0			0
$307$	−7.24588	−	3.95655i	−0.413544	−	0.225812i	0.258987	−	0.965881i	$-0.416611\pi$
$307$	−7.24588	−	3.95655i	−0.413544	−	0.225812i	−0.672531	+	0.740069i	$0.734793\pi$
$308$		0			0
$309$	−4.93656	−	34.3345i	−0.280831	−	1.95322i
$310$		0			0
$311$	8.97715	+	19.6572i	0.509047	+	1.11466i	0.973422	+	0.229019i	$0.0735519\pi$
$311$	8.97715	+	19.6572i	0.509047	+	1.11466i	−0.464375	+	0.885639i	$0.653721\pi$
$312$		0			0
$313$	−0.545990	−	2.50988i	−0.0308612	−	0.141867i	0.959138	−	0.282938i	$-0.0913090\pi$
$313$	−0.545990	−	2.50988i	−0.0308612	−	0.141867i	−0.989999	+	0.141071i	$0.954945\pi$
$314$		0			0
$315$	−3.67974	−	1.67614i	−0.207330	−	0.0944399i
$316$		0			0
$317$	−5.44435	−	1.18435i	−0.305785	−	0.0665195i	0.0570545	−	0.998371i	$-0.481829\pi$
$317$	−5.44435	−	1.18435i	−0.305785	−	0.0665195i	−0.362840	+	0.931852i	$0.618193\pi$
$318$		0			0
$319$	−37.4187	−	10.9871i	−2.09504	−	0.615160i
$320$		0			0
$321$			18.6756i			1.04237i
$322$		0			0
$323$	−27.1590	+	27.1590i	−1.51117	+	1.51117i
$324$		0			0
$325$	0.964284	−	13.8628i	0.0534888	−	0.768969i
$326$		0			0
$327$	8.56400	−	39.3681i	0.473590	−	2.17706i
$328$		0			0
$329$	0.155086	−	1.07864i	0.00855015	−	0.0594676i
$330$		0			0
$331$	−1.09924	−	0.706441i	−0.0604199	−	0.0388295i	0.510082	−	0.860126i	$-0.329615\pi$
$331$	−1.09924	−	0.706441i	−0.0604199	−	0.0388295i	−0.570502	+	0.821296i	$0.693251\pi$
$332$		0			0
$333$	−5.96235	+	15.9857i	−0.326735	+	0.876009i
$334$		0			0
$335$	4.18709	−	29.3251i	0.228765	−	1.60220i
$336$		0			0
$337$	−0.720548	+	1.31959i	−0.0392508	+	0.0718824i	−0.896568	−	0.442906i	$-0.853948\pi$
$337$	−0.720548	+	1.31959i	−0.0392508	+	0.0718824i	0.857317	+	0.514788i	$0.172129\pi$
$338$		0			0
$339$	2.89458	−	3.34052i	0.157212	−	0.181432i
$340$		0			0
$341$	−9.37745	+	8.12561i	−0.507818	+	0.440026i
$342$		0			0
$343$	7.48879	−	2.79318i	0.404357	−	0.150817i
$344$		0			0
$345$	−25.0451	−	8.54885i	−1.34839	−	0.460255i
$346$		0			0
$347$	−7.30823	+	2.72583i	−0.392326	+	0.146330i	−0.537882	−	0.843020i	$-0.680776\pi$
$347$	−7.30823	+	2.72583i	−0.392326	+	0.146330i	0.145556	+	0.989350i	$0.453503\pi$
$348$		0			0
$349$	−15.4886	+	13.4210i	−0.829087	+	0.718408i	−0.962097	−	0.272706i	$-0.912081\pi$
$349$	−15.4886	+	13.4210i	−0.829087	+	0.718408i	0.133010	+	0.991115i	$0.457536\pi$
$350$		0			0
$351$	0.403928	−	0.466158i	0.0215601	−	0.0248817i
$352$		0			0
$353$	6.88369	−	12.6065i	0.366382	−	0.670978i	−0.627838	−	0.778344i	$-0.716060\pi$
$353$	6.88369	−	12.6065i	0.366382	−	0.670978i	0.994220	+	0.107366i	$0.0342417\pi$
$354$		0			0
$355$	23.9941	−	17.9983i	1.27347	−	0.955252i
$356$		0			0
$357$	3.67932	−	9.86464i	0.194730	−	0.522092i
$358$		0			0
$359$	−0.256860	−	0.165074i	−0.0135566	−	0.00871227i	0.533845	−	0.845582i	$-0.320747\pi$
$359$	−0.256860	−	0.165074i	−0.0135566	−	0.00871227i	−0.547402	+	0.836870i	$0.684383\pi$
$360$		0			0
$361$	−1.24640	+	8.66892i	−0.0656001	+	0.456259i
$362$		0			0
$363$	−13.7515	+	63.2147i	−0.721768	+	3.31791i
$364$		0			0
$365$	17.8549	+	11.4500i	0.934568	+	0.599322i
$366$		0			0
$367$	4.77352	−	4.77352i	0.249176	−	0.249176i	−0.571456	−	0.820632i	$-0.693621\pi$
$367$	4.77352	−	4.77352i	0.249176	−	0.249176i	0.820632	+	0.571456i	$0.193621\pi$
$368$		0			0
$369$			39.0370i			2.03219i
$370$		0			0
$371$	0.342378	+	0.100531i	0.0177754	+	0.00521933i
$372$		0			0
$373$	−0.453037	−	0.0985521i	−0.0234573	−	0.00510283i	0.200821	−	0.979628i	$-0.435639\pi$
$373$	−0.453037	−	0.0985521i	−0.0234573	−	0.00510283i	−0.224279	+	0.974525i	$0.572003\pi$
$374$		0			0
$375$	14.9845	+	23.1669i	0.773797	+	1.19633i
$376$		0			0
$377$	3.77666	+	17.3610i	0.194508	+	0.894138i
$378$		0			0
$379$	9.31366	+	20.3941i	0.478410	+	1.04757i	0.982897	+	0.184153i	$0.0589543\pi$
$379$	9.31366	+	20.3941i	0.478410	+	1.04757i	−0.504487	+	0.863419i	$0.668318\pi$
$380$		0			0
$381$	−2.74337	−	19.0806i	−0.140547	−	0.977526i
$382$		0			0
$383$	8.76676	+	4.78701i	0.447960	+	0.244605i	0.687361	−	0.726316i	$-0.258769\pi$
$383$	8.76676	+	4.78701i	0.447960	+	0.244605i	−0.239401	+	0.970921i	$0.576951\pi$
$384$		0			0
$385$	−4.32252	−	6.71155i	−0.220296	−	0.342052i
$386$		0			0
$387$	−8.33121	−	0.595860i	−0.423499	−	0.0302893i
$388$		0			0
$389$	−15.4015	+	33.7245i	−0.780886	+	1.70990i	−0.0798147	+	0.996810i	$0.525433\pi$
$389$	−15.4015	+	33.7245i	−0.780886	+	1.70990i	−0.701071	+	0.713091i	$0.747294\pi$
$390$		0			0
$391$	8.93786	−	33.8004i	0.452007	−	1.70936i
$392$		0			0
$393$	2.45299	+	6.57671i	0.123737	+	0.331751i
$394$		0			0
$395$	0.416141	−	1.11905i	0.0209383	−	0.0563056i
$396$		0			0
$397$	29.4796	−	2.10842i	1.47954	−	0.105819i	0.691917	−	0.721977i	$-0.256766\pi$
$397$	29.4796	−	2.10842i	1.47954	−	0.105819i	0.787622	+	0.616158i	$0.211312\pi$
$398$		0			0
$399$	−2.14369	−	7.30074i	−0.107319	−	0.365494i
$400$		0			0
$401$	−23.3215	+	3.35312i	−1.16462	+	0.167447i	−0.697391	−	0.716691i	$-0.745656\pi$
$401$	−23.3215	+	3.35312i	−1.16462	+	0.167447i	−0.467227	+	0.884137i	$0.654747\pi$
$402$		0			0
$403$	5.29653	+	1.97551i	0.263839	+	0.0984069i
$404$		0			0
$405$	1.37235	−	19.4549i	0.0681928	−	0.966721i
$406$		0			0
$407$	−26.9655	+	20.1861i	−1.33663	+	1.00059i
$408$		0			0
$409$	19.3633	+	30.1299i	0.957454	+	1.48983i	0.869637	+	0.493691i	$0.164353\pi$
$409$	19.3633	+	30.1299i	0.957454	+	1.48983i	0.0878166	+	0.996137i	$0.472011\pi$
$410$		0			0
$411$	−7.35626	+	25.0531i	−0.362857	+	1.23578i
$412$		0			0
$413$	1.09847	+	1.09847i	0.0540521	+	0.0540521i
$414$		0			0
$415$	−0.360961	+	1.23378i	−0.0177189	+	0.0605637i
$416$		0			0
$417$	−3.74062	−	6.85044i	−0.183179	−	0.335467i
$418$		0			0
$419$	−22.1894	+	14.2603i	−1.08402	+	0.696660i	−0.955484	−	0.295044i	$-0.904666\pi$
$419$	−22.1894	+	14.2603i	−1.08402	+	0.696660i	−0.128541	+	0.991704i	$0.541029\pi$
$420$		0			0
$421$	11.2502	+	1.61753i	0.548299	+	0.0788335i	0.410897	−	0.911682i	$-0.365216\pi$
$421$	11.2502	+	1.61753i	0.548299	+	0.0788335i	0.137402	+	0.990515i	$0.456125\pi$
$422$		0			0
$423$	−5.62220	+	1.22304i	−0.273361	+	0.0594660i
$424$		0			0
$425$	−29.1375	+	21.9010i	−1.41338	+	1.06235i
$426$		0			0
$427$	−3.54709	+	4.73835i	−0.171655	+	0.229305i
$428$		0			0
$429$	40.1454	−	11.7878i	1.93824	−	0.569119i
$430$		0			0
$431$	−6.91198	−	5.98926i	−0.332938	−	0.288493i	0.472308	−	0.881434i	$-0.343421\pi$
$431$	−6.91198	−	5.98926i	−0.332938	−	0.288493i	−0.805246	+	0.592941i	$0.797967\pi$
$432$		0			0
$433$	1.48457	−	20.7570i	0.0713440	−	0.997520i	−0.828127	−	0.560540i	$-0.810594\pi$
$433$	1.48457	−	20.7570i	0.0713440	−	0.997520i	0.899471	−	0.436980i	$-0.143952\pi$
$434$		0			0
$435$	−26.6823	−	23.0748i	−1.27932	−	1.10635i
$436$		0			0
$437$	−9.46793	−	23.4263i	−0.452912	−	1.12063i
$438$		0			0
$439$	10.3001	+	4.70390i	0.491597	+	0.224505i	0.645760	−	0.763541i	$-0.276541\pi$
$439$	10.3001	+	4.70390i	0.491597	+	0.224505i	−0.154163	+	0.988045i	$0.549268\pi$
$440$		0			0
$441$	−13.4713	−	15.5467i	−0.641491	−	0.740320i
$442$		0			0
$443$	−0.398726	−	5.57492i	−0.0189440	−	0.264872i	−0.998093	−	0.0617286i	$-0.980339\pi$
$443$	−0.398726	−	5.57492i	−0.0189440	−	0.264872i	0.979149	−	0.203144i	$-0.0651159\pi$
$444$		0			0
$445$	−1.67091	−	1.66765i	−0.0792088	−	0.0790543i
$446$		0			0
$447$	9.21488	+	6.89817i	0.435849	+	0.326272i
$448$		0			0
$449$	2.43292	−	1.11108i	0.114817	−	0.0524350i	−0.357179	−	0.934036i	$-0.616261\pi$
$449$	2.43292	−	1.11108i	0.114817	−	0.0524350i	0.471995	+	0.881601i	$0.343534\pi$
$450$		0			0
$451$	−41.6674	+	64.8358i	−1.96204	+	3.05300i
$452$		0			0
$453$	−17.9183	−	23.9361i	−0.841876	−	1.12461i
$454$		0			0
$455$	−1.73989	+	3.19378i	−0.0815672	+	0.149726i
$456$		0			0
$457$	19.2181	−	10.4939i	0.898985	−	0.490883i	0.0378640	−	0.999283i	$-0.487945\pi$
$457$	19.2181	−	10.4939i	0.898985	−	0.490883i	0.861121	+	0.508400i	$0.169763\pi$
$458$		0			0
$459$	−1.61794			−0.0755188
$460$		0			0
$461$	26.4648			1.23259			0.616295	−	0.787516i	$-0.288633\pi$
$461$	26.4648			1.23259			0.616295	+	0.787516i	$0.288633\pi$
$462$		0			0
$463$	−11.3204	+	6.18140i	−0.526103	+	0.287274i	−0.720269	−	0.693695i	$-0.755982\pi$
$463$	−11.3204	+	6.18140i	−0.526103	+	0.287274i	0.194166	+	0.980969i	$0.437800\pi$
$464$		0			0
$465$	−10.7660	+	3.17261i	−0.499263	+	0.147126i
$466$		0			0
$467$	8.94270	+	11.9460i	0.413819	+	0.552797i	0.958222	−	0.286027i	$-0.0923347\pi$
$467$	8.94270	+	11.9460i	0.413819	+	0.552797i	−0.544403	+	0.838824i	$0.683244\pi$
$468$		0			0
$469$	−4.19150	+	6.52210i	−0.193545	+	0.301163i
$470$		0			0
$471$	33.3813	−	15.2447i	1.53813	−	0.702439i
$472$		0			0
$473$	−13.2011	−	9.88223i	−0.606988	−	0.454385i
$474$		0			0
$475$	−7.37230	+	25.2903i	−0.338265	+	1.16040i
$476$		0			0
$477$	−0.134406	−	1.87924i	−0.00615402	−	0.0860444i
$478$		0			0
$479$	−11.7709	−	13.5844i	−0.537827	−	0.620686i	0.420176	−	0.907443i	$-0.361968\pi$
$479$	−11.7709	−	13.5844i	−0.537827	−	0.620686i	−0.958003	+	0.286757i	$0.907423\pi$
$480$		0			0
$481$	13.9592	+	6.37494i	0.636483	+	0.290672i
$482$		0			0
$483$	5.02840	+	4.76312i	0.228800	+	0.216729i
$484$		0			0
$485$	21.0692	−	24.3631i	0.956701	−	1.10627i
$486$		0			0
$487$	1.53035	−	21.3971i	0.0693468	−	0.969595i	−0.837039	−	0.547144i	$-0.815715\pi$
$487$	1.53035	−	21.3971i	0.0693468	−	0.969595i	0.906386	−	0.422452i	$-0.138830\pi$
$488$		0			0
$489$	−15.8021	−	13.6926i	−0.714597	−	0.619202i
$490$		0			0
$491$	11.5074	−	3.37887i	0.519320	−	0.152486i	−0.0115597	−	0.999933i	$-0.503680\pi$
$491$	11.5074	−	3.37887i	0.519320	−	0.152486i	0.530880	+	0.847447i	$0.321861\pi$
$492$		0			0
$493$	27.9286	−	37.3083i	1.25784	−	1.68028i
$494$		0			0
$495$	−25.2264	+	33.7672i	−1.13384	+	1.51772i
$496$		0			0
$497$	−7.67074	+	1.66867i	−0.344080	+	0.0748499i
$498$		0			0
$499$	−11.3364	−	1.62993i	−0.507487	−	0.0729656i	−0.116184	−	0.993228i	$-0.537066\pi$
$499$	−11.3364	−	1.62993i	−0.507487	−	0.0729656i	−0.391303	+	0.920262i	$0.627975\pi$
$500$		0			0
$501$	−0.696652	+	0.447711i	−0.0311241	+	0.0200023i
$502$		0			0
$503$	11.5725	+	21.1934i	0.515990	+	0.944966i	0.997644	+	0.0686041i	$0.0218545\pi$
$503$	11.5725	+	21.1934i	0.515990	+	0.944966i	−0.481654	+	0.876362i	$0.659964\pi$
$504$		0			0
$505$	14.7268	+	26.9076i	0.655334	+	1.19737i
$506$		0			0
$507$	9.20608	+	9.20608i	0.408856	+	0.408856i
$508$		0			0
$509$	−8.31384	+	28.3143i	−0.368504	+	1.25501i	0.541602	+	0.840635i	$0.317818\pi$
$509$	−8.31384	+	28.3143i	−0.368504	+	1.25501i	−0.910106	+	0.414375i	$0.864000\pi$
$510$		0			0
$511$	−3.00128	−	4.67008i	−0.132769	−	0.206592i
$512$		0			0
$513$	−0.936063	+	0.700728i	−0.0413282	+	0.0309379i
$514$		0			0
$515$	23.7336	−	20.6058i	1.04583	−	0.908002i
$516$		0			0
$517$	−10.6432	−	3.96972i	−0.468089	−	0.174588i
$518$		0			0
$519$	−34.4138	+	4.94796i	−1.51060	+	0.217191i
$520$		0			0
$521$	1.38239	+	4.70797i	0.0605634	+	0.206260i	0.984216	−	0.176970i	$-0.0566297\pi$
$521$	1.38239	+	4.70797i	0.0605634	+	0.206260i	−0.923653	+	0.383230i	$0.874812\pi$
$522$		0			0
$523$	−30.2071	+	2.16045i	−1.32086	+	0.0944700i	−0.713893	−	0.700255i	$-0.753070\pi$
$523$	−30.2071	+	2.16045i	−1.32086	+	0.0944700i	−0.606970	+	0.794725i	$0.707615\pi$
$524$		0			0
$525$	−1.04162	−	7.14553i	−0.0454599	−	0.311856i
$526$		0			0
$527$	−5.18185	−	13.8931i	−0.225725	−	0.605192i
$528$		0			0
$529$	18.1723	+	14.0985i	0.790099	+	0.612980i
$530$		0			0
$531$	3.40729	−	7.46093i	0.147864	−	0.323777i
$532$		0			0
$533$	35.0226	+	2.50486i	1.51700	+	0.108498i
$534$		0			0
$535$	−14.2268	+	9.16265i	−0.615079	+	0.396136i
$536$		0			0
$537$	56.8069	+	31.0189i	2.45140	+	1.33856i
$538$		0			0
$539$	−5.77992	−	40.2002i	−0.248959	−	1.73155i
$540$		0			0
$541$	2.39503	+	5.24438i	0.102970	+	0.225473i	0.954104	−	0.299476i	$-0.0968117\pi$
$541$	2.39503	+	5.24438i	0.102970	+	0.225473i	−0.851134	+	0.524949i	$0.824084\pi$
$542$		0			0
$543$	−1.94687	−	8.94963i	−0.0835483	−	0.384065i
$544$		0			0
$545$	34.1917	−	12.7909i	1.46461	−	0.547901i
$546$		0			0
$547$	27.9207	+	6.07377i	1.19380	+	0.259696i	0.765197	−	0.643797i	$-0.222642\pi$
$547$	27.9207	+	6.07377i	1.19380	+	0.259696i	0.428605	+	0.903492i	$0.359005\pi$
$548$		0			0
$549$	29.9854	+	8.80452i	1.27975	+	0.375768i
$550$		0			0
$551$		−	33.6807i		−	1.43485i
$552$		0			0
$553$	−0.220953	+	0.220953i	−0.00939588	+	0.00939588i
$554$		0			0
$555$	−29.7663	+	6.50569i	−1.26351	+	0.276151i
$556$		0			0
$557$	6.24512	−	28.7084i	0.264614	−	1.21641i	−0.632481	−	0.774576i	$-0.717963\pi$
$557$	6.24512	−	28.7084i	0.264614	−	1.21641i	0.897095	−	0.441837i	$-0.145673\pi$
$558$		0			0
$559$	−1.06917	+	7.43622i	−0.0452209	+	0.314519i
$560$		0			0
$561$	−92.3268	−	59.3348i	−3.89804	−	2.50512i
$562$		0			0
$563$	−9.35111	+	25.0713i	−0.394102	+	1.05663i	0.576744	+	0.816925i	$0.304323\pi$
$563$	−9.35111	+	25.0713i	−0.394102	+	1.05663i	−0.970846	+	0.239704i	$0.922950\pi$
$564$		0			0
$565$	3.96490	+	0.566117i	0.166805	+	0.0238167i
$566$		0			0
$567$	−2.44628	+	4.48003i	−0.102734	+	0.188144i
$568$		0			0
$569$	13.5648	−	15.6546i	0.568664	−	0.656274i	−0.396464	−	0.918050i	$-0.629763\pi$
$569$	13.5648	−	15.6546i	0.568664	−	0.656274i	0.965129	+	0.261776i	$0.0843083\pi$
$570$		0			0
$571$	−12.8616	+	11.1447i	−0.538242	+	0.466390i	−0.881055	−	0.473014i	$-0.843166\pi$
$571$	−12.8616	+	11.1447i	−0.538242	+	0.466390i	0.342813	+	0.939404i	$0.388620\pi$
$572$		0			0
$573$	−39.1972	+	14.6198i	−1.63749	+	0.610751i
$574$		0			0
$575$	−5.77529	−	23.2733i	−0.240846	−	0.970563i
$576$		0			0
$577$	25.1288	−	9.37255i	1.04612	−	0.390184i	0.233124	−	0.972447i	$-0.425105\pi$
$577$	25.1288	−	9.37255i	1.04612	−	0.390184i	0.813001	+	0.582263i	$0.197832\pi$
$578$		0			0
$579$	15.4207	−	13.3621i	0.640864	−	0.555312i
$580$		0			0
$581$	0.220322	−	0.254265i	0.00914050	−	0.0105487i
$582$		0			0
$583$	1.78263	−	3.26465i	0.0738291	−	0.135208i
$584$		0			0
$585$	19.0099	+	2.71427i	0.785963	+	0.112221i
$586$		0			0
$587$	−4.78981	+	12.8420i	−0.197697	+	0.530046i	−0.997535	−	0.0701700i	$-0.977646\pi$
$587$	−4.78981	+	12.8420i	−0.197697	+	0.530046i	0.799838	+	0.600216i	$0.204919\pi$
$588$		0			0
$589$	−9.01506	−	5.79363i	−0.371459	−	0.238722i
$590$		0			0
$591$	0.241815	−	1.68186i	0.00994693	−	0.0691824i
$592$		0			0
$593$	0.926807	−	4.26046i	0.0380594	−	0.174956i	−0.954194	−	0.299190i	$-0.903284\pi$
$593$	0.926807	−	4.26046i	0.0380594	−	0.174956i	0.992253	+	0.124234i	$0.0396472\pi$
$594$		0			0
$595$	9.31990	−	2.03695i	0.382079	−	0.0835069i
$596$		0			0
$597$	−27.5219	+	27.5219i	−1.12640	+	1.12640i
$598$		0			0
$599$		−	36.3876i		−	1.48676i	−0.668870	−	0.743379i	$-0.733222\pi$
$599$		−	36.3876i		−	1.48676i	0.668870	−	0.743379i	$-0.266778\pi$
$600$		0			0
$601$	6.96665	+	2.04559i	0.284176	+	0.0834415i	0.420714	−	0.907193i	$-0.361780\pi$
$601$	6.96665	+	2.04559i	0.284176	+	0.0834415i	−0.136538	+	0.990635i	$0.543598\pi$
$602$		0			0
$603$	39.9987	+	8.70118i	1.62887	+	0.354339i
$604$		0			0
$605$	−54.9029	+	20.5388i	−2.23212	+	0.835021i
$606$		0			0
$607$	6.82420	+	31.3704i	0.276986	+	1.27328i	0.879778	+	0.475385i	$0.157691\pi$
$607$	6.82420	+	31.3704i	0.276986	+	1.27328i	−0.602792	+	0.797899i	$0.705945\pi$
$608$		0			0
$609$	3.83530	+	8.39814i	0.155414	+	0.340310i
$610$		0			0
$611$	0.736506	+	5.12251i	0.0297958	+	0.207235i
$612$		0			0
$613$	28.7172	+	15.6808i	1.15988	+	0.633341i	0.939660	−	0.342110i	$-0.111141\pi$
$613$	28.7172	+	15.6808i	1.15988	+	0.633341i	0.220218	+	0.975451i	$0.429323\pi$
$614$		0			0
$615$	−58.6102	+	37.7474i	−2.36339	+	1.52212i
$616$		0			0
$617$	−11.7374	−	0.839479i	−0.472532	−	0.0337961i	−0.166957	−	0.985964i	$-0.553394\pi$
$617$	−11.7374	−	0.839479i	−0.472532	−	0.0337961i	−0.305575	+	0.952168i	$0.598849\pi$
$618$		0			0
$619$	−5.28776	+	11.5786i	−0.212533	+	0.465382i	−0.985633	−	0.168902i	$-0.945978\pi$
$619$	−5.28776	+	11.5786i	−0.212533	+	0.465382i	0.773100	+	0.634284i	$0.218705\pi$
$620$		0			0
$621$	0.415770	−	0.979800i	0.0166843	−	0.0393180i
$622$		0			0
$623$	0.215917	+	0.578895i	0.00865052	+	0.0231929i
$624$		0			0
$625$	−10.2965	+	22.7812i	−0.411860	+	0.911247i
$626$		0			0
$627$	−79.1139	+	5.65834i	−3.15950	+	0.225972i
$628$		0			0
$629$	−11.3406	−	38.6226i	−0.452181	−	1.53999i
$630$		0			0
$631$	5.98043	−	0.859856i	0.238077	−	0.0342303i	−0.0222433	−	0.999753i	$-0.507081\pi$
$631$	5.98043	−	0.859856i	0.238077	−	0.0342303i	0.260321	+	0.965522i	$0.416172\pi$
$632$		0			0
$633$	0.288200	+	0.107493i	0.0114549	+	0.00427246i
$634$		0			0
$635$	13.1893	−	11.4512i	0.523403	−	0.454427i
$636$		0			0
$637$	−14.8123	+	11.0884i	−0.586887	+	0.439338i
$638$		0			0
$639$	22.4084	+	34.8682i	0.886463	+	1.37936i
$640$		0			0
$641$	−3.78356	+	12.8856i	−0.149442	+	0.508952i	−0.999853	−	0.0171674i	$-0.994535\pi$
$641$	−3.78356	+	12.8856i	−0.149442	+	0.508952i	0.850411	+	0.526119i	$0.176353\pi$
$642$		0			0
$643$	−35.1625	−	35.1625i	−1.38667	−	1.38667i	−0.832206	−	0.554467i	$-0.812922\pi$
$643$	−35.1625	−	35.1625i	−1.38667	−	1.38667i	−0.554467	−	0.832206i	$-0.687078\pi$
$644$		0			0
$645$	−7.16135	−	13.0846i	−0.281978	−	0.515208i
$646$		0			0
$647$	−13.8623	−	25.3870i	−0.544985	−	0.998065i	−0.994494	−	0.104789i	$-0.966583\pi$
$647$	−13.8623	−	25.3870i	−0.544985	−	0.998065i	0.449510	−	0.893275i	$-0.351599\pi$
$648$		0			0
$649$	13.6228	−	8.75481i	0.534740	−	0.343656i
$650$		0			0
$651$	2.90760	+	0.418049i	0.113958	+	0.0163846i
$652$		0			0
$653$	−35.4879	+	7.71993i	−1.38875	+	0.302104i	−0.843932	−	0.536450i	$-0.819765\pi$
$653$	−35.4879	+	7.71993i	−1.38875	+	0.302104i	−0.544819	+	0.838554i	$0.683401\pi$
$654$		0			0
$655$	−3.80656	+	5.09533i	−0.148735	+	0.199091i
$656$		0			0
$657$	−17.5651	+	23.4642i	−0.685279	+	0.915426i
$658$		0			0
$659$	30.3891	−	8.92305i	1.18379	−	0.347593i	0.370158	−	0.928969i	$-0.379304\pi$
$659$	30.3891	−	8.92305i	1.18379	−	0.347593i	0.813635	+	0.581376i	$0.197485\pi$
$660$		0			0
$661$	14.1857	+	12.2920i	0.551759	+	0.478102i	0.885549	−	0.464546i	$-0.153782\pi$
$661$	14.1857	+	12.2920i	0.551759	+	0.478102i	−0.333790	+	0.942647i	$0.608328\pi$
$662$		0			0
$663$	−3.56695	+	49.8725i	−0.138529	+	1.93689i
$664$		0			0
$665$	4.50986	−	5.21493i	0.174885	−	0.202226i
$666$		0			0
$667$	15.4164	+	26.5005i	0.596926	+	1.02610i
$668$		0			0
$669$	−18.4277	−	8.41565i	−0.712456	−	0.325368i
$670$		0			0
$671$	40.4044	+	46.6291i	1.55979	+	1.80010i
$672$		0			0
$673$	0.856176	+	11.9709i	0.0330032	+	0.461445i	0.986902	+	0.161318i	$0.0515744\pi$
$673$	0.856176	+	11.9709i	0.0330032	+	0.461445i	−0.953899	+	0.300127i	$0.902971\pi$
$674$		0			0
$675$	−0.972900	+	0.533712i	−0.0374469	+	0.0205426i
$676$		0			0
$677$	−28.7133	−	21.4945i	−1.10354	−	0.826101i	−0.117579	−	0.993064i	$-0.537513\pi$
$677$	−28.7133	−	21.4945i	−1.10354	−	0.826101i	−0.985963	+	0.166962i	$0.946604\pi$
$678$		0			0
$679$	−7.66819	+	3.50195i	−0.294278	+	0.134392i
$680$		0			0
$681$	−1.64019	+	2.55219i	−0.0628523	+	0.0978000i
$682$		0			0
$683$	−7.35313	−	9.82263i	−0.281360	−	0.375853i	0.637491	−	0.770458i	$-0.279972\pi$
$683$	−7.35313	−	9.82263i	−0.281360	−	0.375853i	−0.918851	+	0.394605i	$0.870881\pi$
$684$		0			0
$685$	−22.6942	+	6.68770i	−0.867102	+	0.255524i
$686$		0			0
$687$	18.7495	−	10.2380i	0.715338	−	0.390604i
$688$		0			0
$689$	−1.69461			−0.0645594
$690$		0			0
$691$	−3.29595			−0.125384			−0.0626918	−	0.998033i	$-0.519969\pi$
$691$	−3.29595			−0.125384			−0.0626918	+	0.998033i	$0.519969\pi$
$692$		0			0
$693$	9.68208	−	5.28682i	0.367792	−	0.200830i
$694$		0			0
$695$	3.38334	−	6.21053i	0.128337	−	0.235579i
$696$		0			0
$697$	−55.1938	−	73.7303i	−2.09062	−	2.79274i
$698$		0			0
$699$	8.24614	−	12.8312i	0.311898	−	0.485322i
$700$		0			0
$701$	13.0017	−	5.93769i	0.491068	−	0.224263i	−0.154461	−	0.987999i	$-0.549364\pi$
$701$	13.0017	−	5.93769i	0.491068	−	0.224263i	0.645529	+	0.763736i	$0.276637\pi$
$702$		0			0
$703$	−23.2886	−	17.4336i	−0.878347	−	0.657522i
$704$		0			0
$705$	−7.27273	−	7.25854i	−0.273907	−	0.273373i
$706$		0			0
$707$	−0.572715	−	8.00761i	−0.0215392	−	0.301157i
$708$		0			0
$709$	−2.51448	−	2.90186i	−0.0944333	−	0.108982i	0.706566	−	0.707647i	$-0.250243\pi$
$709$	−2.51448	−	2.90186i	−0.0944333	−	0.108982i	−0.800999	+	0.598665i	$0.795698\pi$
$710$		0			0
$711$	1.50074	+	0.685366i	0.0562822	+	0.0257032i
$712$		0			0
$713$	9.74506	+	0.432125i	0.364955	+	0.0161832i
$714$		0			0
$715$	28.6760	+	24.7989i	1.07242	+	0.927426i
$716$		0			0
$717$	0.314560	−	4.39812i	0.0117475	−	0.164251i
$718$		0			0
$719$	−0.997963	−	0.864740i	−0.0372178	−	0.0322494i	0.636053	−	0.771645i	$-0.280566\pi$
$719$	−0.997963	−	0.864740i	−0.0372178	−	0.0322494i	−0.673271	+	0.739396i	$0.735111\pi$
$720$		0			0
$721$	−7.89284	+	2.31755i	−0.293945	+	0.0863100i
$722$		0			0
$723$	−10.7707	+	14.3879i	−0.400565	+	0.535093i
$724$		0			0
$725$	4.48712	−	31.6472i	0.166648	−	1.17535i
$726$		0			0
$727$	−1.85403	+	0.403320i	−0.0687623	+	0.0149583i	−0.246815	−	0.969063i	$-0.579384\pi$
$727$	−1.85403	+	0.403320i	−0.0687623	+	0.0149583i	0.178053	+	0.984021i	$0.443020\pi$
$728$		0			0
$729$	28.3028	+	4.06932i	1.04825	+	0.150716i
$730$		0			0
$731$	16.5779	−	10.6539i	0.613154	−	0.394050i
$732$		0			0
$733$	−21.5089	−	39.3905i	−0.794448	−	1.45492i	−0.888264	−	0.459333i	$-0.848088\pi$
$733$	−21.5089	−	39.3905i	−0.794448	−	1.45492i	0.0938162	−	0.995590i	$-0.470093\pi$
$734$		0			0
$735$	10.3156	−	35.2589i	0.380496	−	1.30055i
$736$		0			0
$737$	57.1454	+	57.1454i	2.10498	+	2.10498i
$738$		0			0
$739$	12.4822	−	42.5105i	0.459165	−	1.56377i	−0.326547	−	0.945181i	$-0.605885\pi$
$739$	12.4822	−	42.5105i	0.459165	−	1.56377i	0.785712	−	0.618592i	$-0.212297\pi$
$740$		0			0
$741$	19.5361	+	30.3988i	0.717677	+	1.11673i
$742$		0			0
$743$	33.0788	−	24.7624i	1.21354	−	0.908446i	0.215855	−	0.976425i	$-0.430746\pi$
$743$	33.0788	−	24.7624i	1.21354	−	0.908446i	0.997687	+	0.0679795i	$0.0216553\pi$
$744$		0			0
$745$	−0.733911	+	10.4042i	−0.0268884	+	0.381179i
$746$		0			0
$747$	−1.66437	−	0.620779i	−0.0608962	−	0.0227131i
$748$		0			0
$749$	4.38379	−	0.630293i	0.160180	−	0.0230304i
$750$		0			0
$751$	11.3150	+	38.5353i	0.412890	+	1.40617i	0.859358	+	0.511375i	$0.170864\pi$
$751$	11.3150	+	38.5353i	0.412890	+	1.40617i	−0.446468	+	0.894800i	$0.647318\pi$
$752$		0			0
$753$	65.3944	−	4.67710i	2.38311	−	0.170443i
$754$		0			0
$755$	9.44304	−	25.3935i	0.343667	−	0.924162i
$756$		0			0
$757$	7.74217	+	20.7576i	0.281394	+	0.754447i	0.998355	+	0.0573335i	$0.0182598\pi$
$757$	7.74217	+	20.7576i	0.281394	+	0.754447i	−0.716961	+	0.697113i	$0.754467\pi$
$758$		0			0
$759$	59.6581	−	40.6642i	2.16545	−	1.47602i
$760$		0			0
$761$	−11.9022	+	26.0622i	−0.431455	+	0.944756i	0.561633	+	0.827387i	$0.310173\pi$
$761$	−11.9022	+	26.0622i	−0.431455	+	0.944756i	−0.993088	+	0.117369i	$0.962554\pi$
$762$		0			0
$763$	−9.53002	−	0.681601i	−0.345010	−	0.0246756i
$764$		0			0
$765$	−27.2732	−	42.3470i	−0.986066	−	1.53106i
$766$		0			0
$767$	−6.47504	−	3.53564i	−0.233800	−	0.127664i
$768$		0			0
$769$	4.94583	+	34.3990i	0.178351	+	1.24046i	0.860578	+	0.509318i	$0.170102\pi$
$769$	4.94583	+	34.3990i	0.178351	+	1.24046i	−0.682227	+	0.731140i	$0.738988\pi$
$770$		0			0
$771$	−4.66442	−	10.2137i	−0.167985	−	0.367836i
$772$		0			0
$773$	7.66220	+	35.2226i	0.275590	+	1.26687i	0.881823	+	0.471581i	$0.156316\pi$
$773$	7.66220	+	35.2226i	0.275590	+	1.26687i	−0.606233	+	0.795287i	$0.707320\pi$
$774$		0			0
$775$	−7.69889	−	6.64486i	−0.276552	−	0.238690i
$776$		0			0
$777$	7.79212	+	1.69507i	0.279541	+	0.0608104i
$778$		0			0
$779$	−63.8652	−	18.7525i	−2.28821	−	0.671878i
$780$		0			0
$781$			81.8301i			2.92811i
$782$		0			0
$783$	1.00323	−	1.00323i	0.0358523	−	0.0358523i
$784$		0			0
$785$	27.9908	+	17.9500i	0.999033	+	0.640663i
$786$		0			0
$787$	8.48652	−	39.0119i	0.302512	−	1.39062i	−0.535299	−	0.844663i	$-0.679801\pi$
$787$	8.48652	−	39.0119i	0.302512	−	1.39062i	0.837811	−	0.545961i	$-0.183835\pi$
$788$		0			0
$789$	−9.49118	+	66.0126i	−0.337895	+	2.35011i
$790$		0			0
$791$	−0.881822	−	0.566713i	−0.0313540	−	0.0201500i
$792$		0			0
$793$	9.82315	−	26.3369i	0.348830	−	0.935250i
$794$		0			0
$795$	2.69152	−	2.01895i	0.0954584	−	0.0716048i
$796$		0			0
$797$	19.3139	−	35.3708i	0.684133	−	1.25290i	−0.272655	−	0.962112i	$-0.587902\pi$
$797$	19.3139	−	35.3708i	0.684133	−	1.25290i	0.956789	−	0.290785i	$-0.0939163\pi$
$798$		0			0
$799$	8.88958	−	10.2591i	0.314491	−	0.362942i
$800$		0			0
$801$	2.46540	−	2.13628i	0.0871105	−	0.0754817i
$802$		0			0
$803$	−54.2187	+	20.2225i	−1.91334	+	0.713638i
$804$		0			0
$805$	−1.16144	+	6.16745i	−0.0409353	+	0.217374i
$806$		0			0
$807$	−20.2655	+	7.55864i	−0.713379	+	0.266077i
$808$		0			0
$809$	−27.1854	+	23.5563i	−0.955787	+	0.828195i	−0.985206	−	0.171373i	$-0.945180\pi$
$809$	−27.1854	+	23.5563i	−0.955787	+	0.828195i	0.0294188	+	0.999567i	$0.490634\pi$
$810$		0			0
$811$	30.9089	−	35.6707i	1.08536	−	1.25257i	0.119683	−	0.992812i	$-0.461812\pi$
$811$	30.9089	−	35.6707i	1.08536	−	1.25257i	0.965674	−	0.259757i	$-0.0836424\pi$
$812$		0			0
$813$	5.82135	−	10.6610i	0.204164	−	0.373898i
$814$		0			0
$815$	2.67798	−	18.7557i	0.0938055	−	0.656984i
$816$		0			0
$817$	4.97696	−	13.3437i	0.174122	−	0.466839i
$818$		0			0
$819$	−4.22794	−	2.71713i	−0.147736	−	0.0949442i
$820$		0			0
$821$	1.87800	−	13.0618i	0.0655428	−	0.455860i	−0.930449	−	0.366420i	$-0.880583\pi$
$821$	1.87800	−	13.0618i	0.0655428	−	0.455860i	0.995992	−	0.0894399i	$-0.0285077\pi$
$822$		0			0
$823$	−4.30536	+	19.7914i	−0.150076	+	0.689886i	0.839200	+	0.543823i	$0.183024\pi$
$823$	−4.30536	+	19.7914i	−0.150076	+	0.689886i	−0.989275	+	0.146063i	$0.953340\pi$
$824$		0			0
$825$	−75.0910	−	5.22327i	−2.61433	−	0.181851i
$826$		0			0
$827$	12.4601	−	12.4601i	0.433279	−	0.433279i	−0.456463	−	0.889742i	$-0.650884\pi$
$827$	12.4601	−	12.4601i	0.433279	−	0.433279i	0.889742	+	0.456463i	$0.150884\pi$
$828$		0			0
$829$		−	51.8642i		−	1.80132i	−0.434526	−	0.900659i	$-0.643084\pi$
$829$		−	51.8642i		−	1.80132i	0.434526	−	0.900659i	$-0.356916\pi$
$830$		0			0
$831$	41.4194	+	12.1618i	1.43682	+	0.421889i
$832$		0			0
$833$	47.4249	+	10.3167i	1.64318	+	0.357451i
$834$		0			0
$835$	−0.682853	−	0.311043i	−0.0236311	−	0.0107641i
$836$		0			0
$837$	−0.0959547	−	0.441096i	−0.00331668	−	0.0152465i
$838$		0			0
$839$	−18.0076	−	39.4311i	−0.621691	−	1.36131i	−0.914283	−	0.405077i	$-0.867245\pi$
$839$	−18.0076	−	39.4311i	−0.621691	−	1.36131i	0.292591	−	0.956238i	$-0.405482\pi$
$840$		0			0
$841$	1.68886	+	11.7463i	0.0582367	+	0.405045i
$842$		0			0
$843$	19.6889	+	10.7509i	0.678121	+	0.370282i
$844$		0			0
$845$	−2.49636	+	11.5298i	−0.0858774	+	0.396636i
$846$		0			0
$847$	15.3027	+	1.09447i	0.525807	+	0.0376065i
$848$		0			0
$849$	−3.77392	+	8.26373i	−0.129521	+	0.283610i
$850$		0			0
$851$	26.3036	+	3.05735i	0.901676	+	0.104805i
$852$		0			0
$853$	−14.9475	−	40.0757i	−0.511791	−	1.37217i	−0.893991	−	0.448085i	$-0.852106\pi$
$853$	−14.9475	−	40.0757i	−0.511791	−	1.37217i	0.382200	−	0.924080i	$-0.375167\pi$
$854$		0			0
$855$	−34.1195	−	12.6880i	−1.16686	−	0.433920i
$856$		0			0
$857$	−19.3347	+	1.38284i	−0.660460	+	0.0472370i	−0.397546	−	0.917582i	$-0.630138\pi$
$857$	−19.3347	+	1.38284i	−0.660460	+	0.0472370i	−0.262914	+	0.964819i	$0.584684\pi$
$858$		0			0
$859$	3.29477	+	11.2210i	0.112416	+	0.382854i	0.996411	−	0.0846416i	$-0.0269745\pi$
$859$	3.29477	+	11.2210i	0.112416	+	0.382854i	−0.883995	+	0.467496i	$0.845156\pi$
$860$		0			0
$861$	18.0599	−	2.59662i	0.615479	−	0.0884925i
$862$		0			0
$863$	−12.7025	−	4.73780i	−0.432399	−	0.161276i	0.123834	−	0.992303i	$-0.460481\pi$
$863$	−12.7025	−	4.73780i	−0.432399	−	0.161276i	−0.556233	+	0.831026i	$0.687754\pi$
$864$		0			0
$865$	−20.6535	−	23.7884i	−0.702238	−	0.808829i
$866$		0			0
$867$	71.4083	−	53.4556i	2.42515	−	1.81545i
$868$		0			0
$869$	1.76100	+	2.74017i	0.0597379	+	0.0929539i
$870$		0			0
$871$	10.3729	−	35.3270i	0.351474	−	1.19701i
$872$		0			0
$873$	31.4729	+	31.4729i	1.06520	+	1.06520i
$874$		0			0
$875$	4.93232	−	4.29924i	0.166743	−	0.145341i
$876$		0			0
$877$	14.5416	+	26.6309i	0.491034	+	0.899262i	0.999276	+	0.0380474i	$0.0121138\pi$
$877$	14.5416	+	26.6309i	0.491034	+	0.899262i	−0.508242	+	0.861214i	$0.669704\pi$
$878$		0			0
$879$	−26.7023	+	17.1605i	−0.900646	+	0.578810i
$880$		0			0
$881$	25.2859	+	3.63557i	0.851904	+	0.122485i	0.554415	−	0.832240i	$-0.312942\pi$
$881$	25.2859	+	3.63557i	0.851904	+	0.122485i	0.297489	+	0.954725i	$0.403851\pi$
$882$		0			0
$883$	0.952292	−	0.207158i	0.0320472	−	0.00697143i	−0.196513	−	0.980501i	$-0.562962\pi$
$883$	0.952292	−	0.207158i	0.0320472	−	0.00697143i	0.228560	+	0.973530i	$0.426598\pi$
$884$		0			0
$885$	14.4966	−	2.09874i	0.487297	−	0.0705483i
$886$		0			0
$887$	10.8533	−	14.4984i	0.364420	−	0.486808i	−0.580431	−	0.814310i	$-0.697116\pi$
$887$	10.8533	−	14.4984i	0.364420	−	0.486808i	0.944851	+	0.327502i	$0.106207\pi$
$888$		0			0
$889$	−4.38625	+	1.28792i	−0.147110	+	0.0431954i
$890$		0			0
$891$	40.2123	+	34.8442i	1.34716	+	1.16732i
$892$		0			0
$893$	0.699875	−	9.78553i	0.0234204	−	0.327460i
$894$		0			0
$895$	4.24092	+	58.4932i	0.141758	+	1.95521i
$896$		0			0
$897$	−29.2855	−	14.9761i	−0.977814	−	0.500038i
$898$		0			0
$899$	11.8277	+	5.40152i	0.394475	+	0.180151i
$900$		0			0
$901$	2.91088	+	3.35933i	0.0969755	+	0.111916i
$902$		0			0
$903$	0.278500	+	3.89394i	0.00926790	+	0.129582i
$904$		0			0
$905$	5.86252	−	5.87398i	0.194877	−	0.195258i
$906$		0			0
$907$	20.9547	+	15.6865i	0.695789	+	0.520861i	0.887625	−	0.460566i	$-0.152354\pi$
$907$	20.9547	+	15.6865i	0.695789	+	0.520861i	−0.191837	+	0.981427i	$0.561444\pi$
$908$		0			0
$909$	−38.5569	+	17.6083i	−1.27885	+	0.584031i
$910$		0			0
$911$	9.95502	−	15.4903i	0.329825	−	0.513217i	−0.636249	−	0.771484i	$-0.719515\pi$
$911$	9.95502	−	15.4903i	0.329825	−	0.513217i	0.966074	+	0.258267i	$0.0831513\pi$
$912$		0			0
$913$	−2.10171	−	2.80756i	−0.0695565	−	0.0929166i
$914$		0			0
$915$	15.7757	+	53.5338i	0.521529	+	1.76977i
$916$		0			0
$917$	1.46099	−	0.797759i	0.0482460	−	0.0263443i
$918$		0			0
$919$	31.6830			1.04513			0.522563	−	0.852601i	$-0.324976\pi$
$919$	31.6830			1.04513			0.522563	+	0.852601i	$0.324976\pi$
$920$		0			0
$921$	20.3733			0.671323
$922$		0			0
$923$	32.7203	−	17.8666i	1.07700	−	0.588087i
$924$		0			0
$925$	−19.5599	−	19.4837i	−0.643126	−	0.640619i
$926$		0			0
$927$	26.0282	+	34.7697i	0.854880	+	1.14199i
$928$		0			0
$929$	−6.35665	+	9.89114i	−0.208555	+	0.324518i	−0.929735	−	0.368230i	$-0.879964\pi$
$929$	−6.35665	+	9.89114i	−0.208555	+	0.324518i	0.721180	+	0.692748i	$0.243600\pi$
$930$		0			0
$931$	31.9060	−	14.5710i	1.04568	−	0.477544i
$932$		0			0
$933$	−42.6920	−	31.9588i	−1.39767	−	1.04628i
$934$		0			0
$935$	−0.0970829	−	99.4442i	−0.00317495	−	3.25217i
$936$		0			0
$937$	−0.264036	−	3.69170i	−0.00862567	−	0.120603i	0.991315	−	0.131510i	$-0.0419826\pi$
$937$	−0.264036	−	3.69170i	−0.00862567	−	0.120603i	−0.999941	+	0.0109074i	$0.996528\pi$
$938$		0			0
$939$	4.15095	+	4.79045i	0.135461	+	0.156331i
$940$		0			0
$941$	24.1096	+	11.0105i	0.785950	+	0.358931i	0.767624	−	0.640901i	$-0.221439\pi$
$941$	24.1096	+	11.0105i	0.785950	+	0.358931i	0.0183261	+	0.999832i	$0.494166\pi$
$942$		0			0
$943$	58.8336	−	14.4777i	1.91588	−	0.471460i
$944$		0			0
$945$	0.289666	−	0.0210016i	0.00942283	−	0.000683181i
$946$		0			0
$947$	2.04168	−	28.5464i	0.0663456	−	0.927632i	−0.849882	−	0.526973i	$-0.823327\pi$
$947$	2.04168	−	28.5464i	0.0663456	−	0.927632i	0.916227	−	0.400659i	$-0.131219\pi$
$948$		0			0
$949$	19.9241	+	17.2644i	0.646765	+	0.560425i
$950$		0			0
$951$	13.1927	−	3.87373i	0.427803	−	0.125614i
$952$		0			0
$953$	−5.52325	+	7.37820i	−0.178916	+	0.239003i	−0.881029	−	0.473061i	$-0.843149\pi$
$953$	−5.52325	+	7.37820i	−0.178916	+	0.239003i	0.702114	+	0.712065i	$0.252240\pi$
$954$		0			0
$955$	−30.3682	−	22.6871i	−0.982691	−	0.734137i
$956$		0			0
$957$	94.0400	−	20.4572i	3.03988	−	0.661286i
$958$		0			0
$959$	6.12907	+	0.881227i	0.197918	+	0.0284563i
$960$		0			0
$961$	−22.5985	+	14.5232i	−0.728985	+	0.468490i
$962$		0			0
$963$	−11.2067	−	20.5236i	−0.361132	−	0.661363i
$964$		0			0
$965$	17.7448	+	5.19154i	0.571227	+	0.167122i
$966$		0			0
$967$	−4.62611	−	4.62611i	−0.148766	−	0.148766i	0.628801	−	0.777566i	$-0.283546\pi$
$967$	−4.62611	−	4.62611i	−0.148766	−	0.148766i	−0.777566	+	0.628801i	$0.783546\pi$
$968$		0			0
$969$	26.7038	−	90.9447i	0.857849	−	2.92156i
$970$		0			0
$971$	18.8871	+	29.3889i	0.606116	+	0.943134i	0.999715	+	0.0238525i	$0.00759320\pi$
$971$	18.8871	+	29.3889i	0.606116	+	0.943134i	−0.393600	+	0.919282i	$0.628770\pi$
$972$		0			0
$973$	−1.48178	+	1.10925i	−0.0475037	+	0.0355609i
$974$		0			0
$975$	14.3067	+	31.1661i	0.458180	+	0.998113i
$976$		0			0
$977$	−19.5043	−	7.27475i	−0.623999	−	0.232740i	0.0175200	−	0.999847i	$-0.494423\pi$
$977$	−19.5043	−	7.27475i	−0.623999	−	0.232740i	−0.641519	+	0.767107i	$0.721696\pi$
$978$		0			0
$979$	6.37494	−	0.916579i	0.203744	−	0.0292940i
$980$		0			0
$981$	14.2123	+	48.4026i	0.453763	+	1.54538i
$982$		0			0
$983$	55.0315	−	3.93593i	1.75523	−	0.125537i	0.843713	−	0.536795i	$-0.180365\pi$
$983$	55.0315	−	3.93593i	1.75523	−	0.125537i	0.911519	+	0.411259i	$0.134911\pi$
$984$		0			0
$985$	1.39985	−	0.640945i	0.0446031	−	0.0204222i
$986$		0			0
$987$	0.939789	+	2.51967i	0.0299138	+	0.0802021i
$988$		0			0
$989$	2.19178	+	12.7771i	0.0696944	+	0.406289i
$990$		0			0
$991$	13.2315	−	28.9730i	0.420313	−	0.920357i	−0.574487	−	0.818513i	$-0.694799\pi$
$991$	13.2315	−	28.9730i	0.420313	−	0.920357i	0.994800	−	0.101844i	$-0.0324742\pi$
$992$		0			0
$993$	3.21636	+	0.230039i	0.102068	+	0.00730006i
$994$		0			0
$995$	−34.4687	−	7.46297i	−1.09273	−	0.236592i
$996$		0			0
$997$	4.82934	+	2.63702i	0.152947	+	0.0835153i	0.553900	−	0.832583i	$-0.313139\pi$
$997$	4.82934	+	2.63702i	0.152947	+	0.0835153i	−0.400953	+	0.916099i	$0.631321\pi$
$998$		0			0
$999$	−0.174398	−	1.21297i	−0.00551772	−	0.0383766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.5	✓	720
5.3	odd	4	inner	920.2.bv.a.753.5	yes	720
23.19	odd	22	inner	920.2.bv.a.617.5	yes	720
115.88	even	44	inner	920.2.bv.a.433.5	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.5	✓	720	1.1	even	1	trivial
920.2.bv.a.433.5	yes	720	115.88	even	44	inner
920.2.bv.a.617.5	yes	720	23.19	odd	22	inner
920.2.bv.a.753.5	yes	720	5.3	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16592 + 1.18268i) q^{3} +(-1.96360 - 1.06972i) q^{5} +(0.350713 + 0.468498i) q^{7} +(1.67054 - 2.59942i) q^{9} +(5.54914 - 2.53421i) q^{11} +(-2.22491 - 1.66555i) q^{13} +(5.51812 - 0.00538709i) q^{15} +(0.520071 + 7.27155i) q^{17} +(3.45019 + 3.98174i) q^{19} +(-1.31370 - 0.599946i) q^{21} +(-4.53719 - 1.55366i) q^{23} +(2.71141 + 4.20098i) q^{25} +(-0.0158327 + 0.221370i) q^{27} +(-4.83131 - 4.18635i) q^{29} +(-1.95159 + 0.573039i) q^{31} +(-9.02182 + 12.0517i) q^{33} +(-0.187499 - 1.29510i) q^{35} +(-5.39542 + 1.17370i) q^{37} +(6.78878 + 0.976079i) q^{39} +(-10.6281 + 6.83025i) q^{41} +(-1.29547 - 2.37248i) q^{43} +(-6.06091 + 3.31719i) q^{45} +(-1.31669 - 1.31669i) q^{47} +(1.87564 - 6.38783i) q^{49} +(-9.72635 - 15.1345i) q^{51} +(0.488117 - 0.365400i) q^{53} +(-13.6071 - 0.959851i) q^{55} +(-12.1820 - 4.54364i) q^{57} +(2.62745 - 0.377771i) q^{59} +(2.84942 + 9.70424i) q^{61} +(1.80370 - 0.129003i) q^{63} +(2.58716 + 5.65048i) q^{65} +(4.62955 + 12.4123i) q^{67} +(11.6647 - 2.00095i) q^{69} +(-5.57231 + 12.2017i) q^{71} +(-9.46161 - 0.676708i) q^{73} +(-10.8411 - 5.89225i) q^{75} +(3.13343 + 1.71098i) q^{77} +(0.0759873 + 0.528503i) q^{79} +(3.62330 + 7.93391i) q^{81} +(-0.122202 - 0.561752i) q^{83} +(6.75729 - 14.8347i) q^{85} +(15.4153 + 3.35340i) q^{87} +(1.01298 + 0.297438i) q^{89} -1.62649i q^{91} +(3.54926 - 3.54926i) q^{93} +(-2.51545 - 11.5092i) q^{95} +(-3.06193 + 14.0755i) q^{97} +(2.68262 - 18.6580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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