LMFDB - Embedded newform 820.2.x.a.817.15

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)

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);

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")

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			817.15
Character	$\chi$	$=$	820.817
Dual form			820.2.x.a.273.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17715 - 0.487592i) q^{3} +(2.02779 + 0.942363i) q^{5} +(-0.0522617 - 0.126171i) q^{7} +(-0.973380 + 0.973380i) q^{9} +(-1.39412 + 3.36569i) q^{11} +(2.67998 - 1.11008i) q^{13} +(2.84651 + 0.120567i) q^{15} +(4.97519 + 2.06079i) q^{17} +(-1.09138 - 2.63482i) q^{19} +(-0.123040 - 0.123040i) q^{21} +(3.63902 + 3.63902i) q^{23} +(3.22390 + 3.82184i) q^{25} +(-2.13398 + 5.15188i) q^{27} +(0.0765437 - 0.184793i) q^{29} -3.53619i q^{31} +4.64169i q^{33} +(0.0129228 - 0.305098i) q^{35} +(-2.65667 - 2.65667i) q^{37} +(2.61348 - 2.61348i) q^{39} +(0.722911 - 6.36219i) q^{41} -1.71177i q^{43} +(-2.89109 + 1.05654i) q^{45} +(-6.26338 - 2.59438i) q^{47} +(4.93656 - 4.93656i) q^{49} +6.86138 q^{51} +(-0.857011 - 2.06901i) q^{53} +(-5.99869 + 5.51117i) q^{55} +(-2.56943 - 2.56943i) q^{57} +10.3918i q^{59} +(0.729392 - 0.729392i) q^{61} +(0.173683 + 0.0719417i) q^{63} +(6.48055 + 0.274492i) q^{65} +(-5.82842 - 2.41421i) q^{67} +(6.05804 + 2.50932i) q^{69} +(-1.08593 - 0.449805i) q^{71} +2.01433i q^{73} +(5.65852 + 2.92693i) q^{75} +0.497511 q^{77} +(-2.96500 - 1.22814i) q^{79} +2.97536i q^{81} +(8.37256 - 8.37256i) q^{83} +(8.14665 + 8.86730i) q^{85} -0.254851i q^{87} +(-2.94049 + 7.09896i) q^{89} +(-0.280121 - 0.280121i) q^{91} +(-1.72422 - 4.16263i) q^{93} +(0.269866 - 6.37134i) q^{95} +(-0.859610 + 2.07528i) q^{97} +(-1.91909 - 4.63310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.17715	−	0.487592i	0.679629	−	0.281512i	−0.0160429	−	0.999871i	$-0.505107\pi$
$3$	1.17715	−	0.487592i	0.679629	−	0.281512i	0.695672	+	0.718360i	$0.255107\pi$
$4$		0			0
$5$	2.02779	+	0.942363i	0.906857	+	0.421438i
$5$	2.02779	+	0.942363i	0.906857	+	0.421438i
$6$		0			0
$7$	−0.0522617	−	0.126171i	−0.0197531	−	0.0476881i	0.913695	−	0.406400i	$-0.133216\pi$
$7$	−0.0522617	−	0.126171i	−0.0197531	−	0.0476881i	−0.933448	+	0.358712i	$0.883216\pi$
$8$		0			0
$9$	−0.973380	+	0.973380i	−0.324460	+	0.324460i
$10$		0			0
$11$	−1.39412	+	3.36569i	−0.420342	+	1.01479i	0.561905	+	0.827202i	$0.310069\pi$
$11$	−1.39412	+	3.36569i	−0.420342	+	1.01479i	−0.982247	+	0.187593i	$0.939931\pi$
$12$		0			0
$13$	2.67998	−	1.11008i	0.743293	−	0.307882i	0.0212912	−	0.999773i	$-0.493222\pi$
$13$	2.67998	−	1.11008i	0.743293	−	0.307882i	0.722002	+	0.691891i	$0.243222\pi$
$14$		0			0
$15$	2.84651	+	0.120567i	0.734966	+	0.0311304i
$16$		0			0
$17$	4.97519	+	2.06079i	1.20666	+	0.499816i	0.893146	−	0.449767i	$-0.148493\pi$
$17$	4.97519	+	2.06079i	1.20666	+	0.499816i	0.313516	+	0.949583i	$0.398493\pi$
$18$		0			0
$19$	−1.09138	−	2.63482i	−0.250379	−	0.604468i	0.747856	−	0.663861i	$-0.231083\pi$
$19$	−1.09138	−	2.63482i	−0.250379	−	0.604468i	−0.998235	+	0.0593932i	$0.981083\pi$
$20$		0			0
$21$	−0.123040	−	0.123040i	−0.0268495	−	0.0268495i
$22$		0			0
$23$	3.63902	+	3.63902i	0.758789	+	0.758789i	0.976102	−	0.217313i	$-0.0697292\pi$
$23$	3.63902	+	3.63902i	0.758789	+	0.758789i	−0.217313	+	0.976102i	$0.569729\pi$
$24$		0			0
$25$	3.22390	+	3.82184i	0.644781	+	0.764368i
$26$		0			0
$27$	−2.13398	+	5.15188i	−0.410685	+	0.991481i
$28$		0			0
$29$	0.0765437	−	0.184793i	0.0142138	−	0.0343152i	−0.916613	−	0.399775i	$-0.869088\pi$
$29$	0.0765437	−	0.184793i	0.0142138	−	0.0343152i	0.930827	+	0.365460i	$0.119088\pi$
$30$		0			0
$31$		−	3.53619i		−	0.635119i	−0.948238	−	0.317559i	$-0.897137\pi$
$31$		−	3.53619i		−	0.635119i	0.948238	−	0.317559i	$-0.102863\pi$
$32$		0			0
$33$			4.64169i			0.808015i
$34$		0			0
$35$	0.0129228	−	0.305098i	0.00218435	−	0.0515710i
$36$		0			0
$37$	−2.65667	−	2.65667i	−0.436754	−	0.436754i	0.454164	−	0.890918i	$-0.349938\pi$
$37$	−2.65667	−	2.65667i	−0.436754	−	0.436754i	−0.890918	+	0.454164i	$0.849938\pi$
$38$		0			0
$39$	2.61348	−	2.61348i	0.418491	−	0.418491i
$40$		0			0
$41$	0.722911	−	6.36219i	0.112900	−	0.993606i
$41$	0.722911	−	6.36219i	0.112900	−	0.993606i
$42$		0			0
$43$		−	1.71177i		−	0.261042i	−0.991446	−	0.130521i	$-0.958335\pi$
$43$		−	1.71177i		−	0.261042i	0.991446	−	0.130521i	$-0.0416650\pi$
$44$		0			0
$45$	−2.89109	+	1.05654i	−0.430979	+	0.157499i
$46$		0			0
$47$	−6.26338	−	2.59438i	−0.913607	−	0.378429i	−0.124171	−	0.992261i	$-0.539627\pi$
$47$	−6.26338	−	2.59438i	−0.913607	−	0.378429i	−0.789436	+	0.613832i	$0.789627\pi$
$48$		0			0
$49$	4.93656	−	4.93656i	0.705223	−	0.705223i
$50$		0			0
$51$	6.86138			0.960786
$52$		0			0
$53$	−0.857011	−	2.06901i	−0.117719	−	0.284200i	0.854026	−	0.520230i	$-0.174154\pi$
$53$	−0.857011	−	2.06901i	−0.117719	−	0.284200i	−0.971746	+	0.236030i	$0.924154\pi$
$54$		0			0
$55$	−5.99869	+	5.51117i	−0.808863	+	0.743126i
$56$		0			0
$57$	−2.56943	−	2.56943i	−0.340329	−	0.340329i
$58$		0			0
$59$			10.3918i			1.35290i	0.736487	+	0.676452i	$0.236483\pi$
$59$			10.3918i			1.35290i	−0.736487	+	0.676452i	$0.763517\pi$
$60$		0			0
$61$	0.729392	−	0.729392i	0.0933891	−	0.0933891i	−0.658869	−	0.752258i	$-0.728965\pi$
$61$	0.729392	−	0.729392i	0.0933891	−	0.0933891i	0.752258	+	0.658869i	$0.228965\pi$
$62$		0			0
$63$	0.173683	+	0.0719417i	0.0218820	+	0.00906381i
$64$		0			0
$65$	6.48055	+	0.274492i	0.803814	+	0.0340465i
$66$		0			0
$67$	−5.82842	−	2.41421i	−0.712055	−	0.294943i	−0.00290043	−	0.999996i	$-0.500923\pi$
$67$	−5.82842	−	2.41421i	−0.712055	−	0.294943i	−0.709155	+	0.705053i	$0.750923\pi$
$68$		0			0
$69$	6.05804	+	2.50932i	0.729303	+	0.302087i
$70$		0			0
$71$	−1.08593	−	0.449805i	−0.128876	−	0.0533820i	0.317314	−	0.948321i	$-0.397219\pi$
$71$	−1.08593	−	0.449805i	−0.128876	−	0.0533820i	−0.446189	+	0.894939i	$0.647219\pi$
$72$		0			0
$73$			2.01433i			0.235759i	0.993028	+	0.117880i	$0.0376097\pi$
$73$			2.01433i			0.235759i	−0.993028	+	0.117880i	$0.962390\pi$
$74$		0			0
$75$	5.65852	+	2.92693i	0.653390	+	0.337973i
$76$		0			0
$77$	0.497511			0.0566967
$78$		0			0
$79$	−2.96500	−	1.22814i	−0.333588	−	0.138177i	0.209601	−	0.977787i	$-0.432783\pi$
$79$	−2.96500	−	1.22814i	−0.333588	−	0.138177i	−0.543189	+	0.839610i	$0.682783\pi$
$80$		0			0
$81$			2.97536i			0.330596i
$82$		0			0
$83$	8.37256	−	8.37256i	0.919008	−	0.919008i	−0.0779496	−	0.996957i	$-0.524837\pi$
$83$	8.37256	−	8.37256i	0.919008	−	0.919008i	0.996957	+	0.0779496i	$0.0248373\pi$
$84$		0			0
$85$	8.14665	+	8.86730i	0.883629	+	0.961794i
$86$		0			0
$87$		−	0.254851i		−	0.0273229i
$88$		0			0
$89$	−2.94049	+	7.09896i	−0.311691	+	0.752489i	0.687952	+	0.725757i	$0.258510\pi$
$89$	−2.94049	+	7.09896i	−0.311691	+	0.752489i	−0.999643	+	0.0267321i	$0.991490\pi$
$90$		0			0
$91$	−0.280121	−	0.280121i	−0.0293646	−	0.0293646i
$92$		0			0
$93$	−1.72422	−	4.16263i	−0.178793	−	0.431645i
$94$		0			0
$95$	0.269866	−	6.37134i	0.0276876	−	0.653685i
$96$		0			0
$97$	−0.859610	+	2.07528i	−0.0872801	+	0.210713i	−0.961493	−	0.274831i	$-0.911378\pi$
$97$	−0.859610	+	2.07528i	−0.0872801	+	0.210713i	0.874213	+	0.485543i	$0.161378\pi$
$98$		0			0
$99$	−1.91909	−	4.63310i	−0.192876	−	0.465645i
$100$		0			0
$101$	16.6155	−	6.88236i	1.65330	−	0.684820i	0.655765	−	0.754965i	$-0.272346\pi$
$101$	16.6155	−	6.88236i	1.65330	−	0.684820i	0.997537	+	0.0701445i	$0.0223460\pi$
$102$		0			0
$103$	−2.51098			−0.247414			−0.123707	−	0.992319i	$-0.539478\pi$
$103$	−2.51098			−0.247414			−0.123707	+	0.992319i	$0.539478\pi$
$104$		0			0
$105$	−0.133551	−	0.365448i	−0.0130333	−	0.0356641i
$106$		0			0
$107$	−3.63299	+	3.63299i	−0.351215	+	0.351215i	−0.860561	−	0.509347i	$-0.829887\pi$
$107$	−3.63299	+	3.63299i	−0.351215	+	0.351215i	0.509347	+	0.860561i	$0.329887\pi$
$108$		0			0
$109$	−1.97303	+	0.817254i	−0.188982	+	0.0782787i	−0.475167	−	0.879895i	$-0.657613\pi$
$109$	−1.97303	+	0.817254i	−0.188982	+	0.0782787i	0.286186	+	0.958174i	$0.407613\pi$
$110$		0			0
$111$	−4.42267	−	1.83193i	−0.419782	−	0.173879i
$112$		0			0
$113$	−15.0019	−	15.0019i	−1.41126	−	1.41126i	−0.751305	−	0.659956i	$-0.770575\pi$
$113$	−15.0019	−	15.0019i	−1.41126	−	1.41126i	−0.659956	−	0.751305i	$-0.729425\pi$
$114$		0			0
$115$	3.94991	+	10.8085i	0.368331	+	1.00790i
$116$		0			0
$117$	−1.52811	+	3.68917i	−0.141273	+	0.341064i
$118$		0			0
$119$		−	0.735425i		−	0.0674163i
$120$		0			0
$121$	−1.60616	−	1.60616i	−0.146015	−	0.146015i
$122$		0			0
$123$	−2.25118	−	7.84174i	−0.202982	−	0.707066i
$124$		0			0
$125$	2.93586	+	10.7880i	0.262591	+	0.964907i
$126$		0			0
$127$	−4.45241	+	4.45241i	−0.395088	+	0.395088i	−0.876496	−	0.481409i	$-0.840125\pi$
$127$	−4.45241	+	4.45241i	−0.395088	+	0.395088i	0.481409	+	0.876496i	$0.340125\pi$
$128$		0			0
$129$	−0.834643	−	2.01501i	−0.0734863	−	0.177412i
$130$		0			0
$131$	−13.8556	−	13.8556i	−1.21057	−	1.21057i	−0.970838	−	0.239735i	$-0.922939\pi$
$131$	−13.8556	−	13.8556i	−1.21057	−	1.21057i	−0.239735	−	0.970838i	$-0.577061\pi$
$132$		0			0
$133$	−0.275400	+	0.275400i	−0.0238802	+	0.0238802i
$134$		0			0
$135$	−9.18222	+	8.43598i	−0.790280	+	0.726054i
$136$		0			0
$137$	−2.63440	−	1.09120i	−0.225072	−	0.0932278i	0.267298	−	0.963614i	$-0.413869\pi$
$137$	−2.63440	−	1.09120i	−0.225072	−	0.0932278i	−0.492370	+	0.870386i	$0.663869\pi$
$138$		0			0
$139$		−	8.89978i		−	0.754869i	−0.926036	−	0.377435i	$-0.876806\pi$
$139$		−	8.89978i		−	0.754869i	0.926036	−	0.377435i	$-0.123194\pi$
$140$		0			0
$141$	−8.63794			−0.727446
$142$		0			0
$143$			10.5676i			0.883705i
$144$		0			0
$145$	0.329357	−	0.302590i	0.0273516	−	0.0251287i
$146$		0			0
$147$	3.40405	−	8.21811i	0.280761	−	0.677818i
$148$		0			0
$149$	5.37439	+	12.9749i	0.440287	+	1.06295i	0.975848	+	0.218450i	$0.0701001\pi$
$149$	5.37439	+	12.9749i	0.440287	+	1.06295i	−0.535561	+	0.844496i	$0.679900\pi$
$150$		0			0
$151$	0.893869	−	2.15799i	0.0727421	−	0.175615i	−0.883326	−	0.468759i	$-0.844701\pi$
$151$	0.893869	−	2.15799i	0.0727421	−	0.175615i	0.956068	+	0.293144i	$0.0947014\pi$
$152$		0			0
$153$	−6.84869	+	2.83682i	−0.553684	+	0.229343i
$154$		0			0
$155$	3.33238	−	7.17067i	0.267663	−	0.575962i
$156$		0			0
$157$	2.63529	−	1.09157i	0.210319	−	0.0871171i	−0.275037	−	0.961434i	$-0.588690\pi$
$157$	2.63529	−	1.09157i	0.210319	−	0.0871171i	0.485356	+	0.874317i	$0.338690\pi$
$158$		0			0
$159$	−2.01766	−	2.01766i	−0.160011	−	0.160011i
$160$		0			0
$161$	0.268957	−	0.649320i	0.0211968	−	0.0511736i
$162$		0			0
$163$	−11.9357	−	11.9357i	−0.934872	−	0.934872i	0.0631327	−	0.998005i	$-0.479891\pi$
$163$	−11.9357	−	11.9357i	−0.934872	−	0.934872i	−0.998005	+	0.0631327i	$0.979891\pi$
$164$		0			0
$165$	−4.37416	+	9.41240i	−0.340528	+	0.732754i
$166$		0			0
$167$	2.50027	+	6.03619i	0.193477	+	0.467094i	0.990611	−	0.136707i	$-0.0436520\pi$
$167$	2.50027	+	6.03619i	0.193477	+	0.467094i	−0.797135	+	0.603801i	$0.793652\pi$
$168$		0			0
$169$	−3.24238	+	3.24238i	−0.249414	+	0.249414i
$170$		0			0
$171$	3.62700	+	1.50235i	0.277364	+	0.114888i
$172$		0			0
$173$	3.62675			0.275737			0.137868	−	0.990451i	$-0.455975\pi$
$173$	3.62675			0.275737			0.137868	+	0.990451i	$0.455975\pi$
$174$		0			0
$175$	0.313718	−	0.606498i	0.0237149	−	0.0458470i
$176$		0			0
$177$	5.06698	+	12.2328i	0.380858	+	0.919472i
$178$		0			0
$179$	−3.53799	+	1.46548i	−0.264441	+	0.109535i	−0.510965	−	0.859602i	$-0.670712\pi$
$179$	−3.53799	+	1.46548i	−0.264441	+	0.109535i	0.246523	+	0.969137i	$0.420712\pi$
$180$		0			0
$181$	13.8304	−	5.72875i	1.02801	−	0.425815i	0.196015	−	0.980601i	$-0.437200\pi$
$181$	13.8304	−	5.72875i	1.02801	−	0.425815i	0.831993	+	0.554786i	$0.187200\pi$
$182$		0			0
$183$	0.502959	−	1.21425i	0.0371798	−	0.0897600i
$184$		0			0
$185$	−2.88363	−	7.89073i	−0.212009	−	0.580138i
$186$		0			0
$187$	−13.8720	+	13.8720i	−1.01442	+	1.01442i
$188$		0			0
$189$	0.761543			0.0553941
$190$		0			0
$191$	−9.72673	−	23.4824i	−0.703801	−	1.69913i	−0.714938	−	0.699188i	$-0.753545\pi$
$191$	−9.72673	−	23.4824i	−0.703801	−	1.69913i	0.0111364	−	0.999938i	$-0.496455\pi$
$192$		0			0
$193$	−22.9203	+	9.49392i	−1.64984	+	0.683387i	−0.997235	−	0.0743096i	$-0.976325\pi$
$193$	−22.9203	+	9.49392i	−1.64984	+	0.683387i	−0.652607	+	0.757697i	$0.726325\pi$
$194$		0			0
$195$	7.76244	−	2.83675i	0.555880	−	0.203144i
$196$		0			0
$197$	−17.6946			−1.26069			−0.630344	−	0.776316i	$-0.717086\pi$
$197$	−17.6946			−1.26069			−0.630344	+	0.776316i	$0.717086\pi$
$198$		0			0
$199$	−6.20314	+	2.56942i	−0.439729	+	0.182142i	−0.591553	−	0.806266i	$-0.701485\pi$
$199$	−6.20314	+	2.56942i	−0.439729	+	0.182142i	0.151825	+	0.988407i	$0.451485\pi$
$200$		0			0
$201$	−8.03809			−0.566963
$202$		0			0
$203$	−0.0273158			−0.00191719
$204$		0			0
$205$	7.46140	−	12.2200i	0.521127	−	0.853479i
$206$		0			0
$207$	−7.08431			−0.492393
$208$		0			0
$209$	10.3895			0.718656
$210$		0			0
$211$	−10.1221	+	4.19272i	−0.696836	+	0.288639i	−0.702845	−	0.711343i	$-0.748087\pi$
$211$	−10.1221	+	4.19272i	−0.696836	+	0.288639i	0.00600904	+	0.999982i	$0.498087\pi$
$212$		0			0
$213$	−1.49762			−0.102615
$214$		0			0
$215$	1.61310	−	3.47111i	0.110013	−	0.236728i
$216$		0			0
$217$	−0.446164	+	0.184807i	−0.0302876	+	0.0125455i
$218$		0			0
$219$	0.982170	+	2.37117i	0.0663689	+	0.160229i
$220$		0			0
$221$	15.6211			1.05079
$222$		0			0
$223$	10.1606	−	10.1606i	0.680404	−	0.680404i	−0.279687	−	0.960091i	$-0.590231\pi$
$223$	10.1606	−	10.1606i	0.680404	−	0.680404i	0.960091	+	0.279687i	$0.0902307\pi$
$224$		0			0
$225$	−6.85819	−	0.582017i	−0.457212	−	0.0388012i
$226$		0			0
$227$	−1.99103	+	4.80678i	−0.132149	+	0.319037i	−0.976079	−	0.217417i	$-0.930237\pi$
$227$	−1.99103	+	4.80678i	−0.132149	+	0.319037i	0.843929	+	0.536455i	$0.180237\pi$
$228$		0			0
$229$	−10.6187	+	4.39839i	−0.701700	+	0.290654i	−0.704865	−	0.709341i	$-0.748993\pi$
$229$	−10.6187	+	4.39839i	−0.701700	+	0.290654i	0.00316489	+	0.999995i	$0.498993\pi$
$230$		0			0
$231$	0.585646	−	0.242583i	0.0385327	−	0.0159608i
$232$		0			0
$233$	0.113484	+	0.273974i	0.00743456	+	0.0179486i	0.927553	−	0.373691i	$-0.121908\pi$
$233$	0.113484	+	0.273974i	0.00743456	+	0.0179486i	−0.920119	+	0.391640i	$0.871908\pi$
$234$		0			0
$235$	−10.2560	−	11.1632i	−0.669028	−	0.728209i
$236$		0			0
$237$	−4.08908			−0.265615
$238$		0			0
$239$	7.25697	+	3.00594i	0.469414	+	0.194438i	0.604836	−	0.796350i	$-0.293239\pi$
$239$	7.25697	+	3.00594i	0.469414	+	0.194438i	−0.135421	+	0.990788i	$0.543239\pi$
$240$		0			0
$241$	19.9707	−	19.9707i	1.28642	−	1.28642i	0.349482	−	0.936943i	$-0.386358\pi$
$241$	19.9707	−	19.9707i	1.28642	−	1.28642i	0.936943	−	0.349482i	$-0.113642\pi$
$242$		0			0
$243$	−4.95118	−	11.9532i	−0.317618	−	0.766798i
$244$		0			0
$245$	14.6624	−	5.35830i	0.936744	−	0.342329i
$246$		0			0
$247$	−5.84973	−	5.84973i	−0.372210	−	0.372210i
$248$		0			0
$249$	5.77338	−	13.9382i	0.365873	−	0.883295i
$250$		0			0
$251$	−16.6541	−	16.6541i	−1.05120	−	1.05120i	−0.998617	−	0.0525807i	$-0.983255\pi$
$251$	−16.6541	−	16.6541i	−1.05120	−	1.05120i	−0.0525807	−	0.998617i	$-0.516745\pi$
$252$		0			0
$253$	−17.3211	+	7.17462i	−1.08897	+	0.451064i
$254$		0			0
$255$	13.9135	+	6.46591i	0.871296	+	0.404911i
$256$		0			0
$257$	23.2565	−	9.63318i	1.45070	−	0.600901i	0.488337	−	0.872655i	$-0.337604\pi$
$257$	23.2565	−	9.63318i	1.45070	−	0.600901i	0.962367	+	0.271754i	$0.0876038\pi$
$258$		0			0
$259$	−0.196352	+	0.474036i	−0.0122007	+	0.0294552i
$260$		0			0
$261$	0.105368	+	0.254380i	0.00652209	+	0.0157457i
$262$		0			0
$263$	3.30155	−	7.97066i	0.203583	−	0.491492i	−0.788805	−	0.614643i	$-0.789300\pi$
$263$	3.30155	−	7.97066i	0.203583	−	0.491492i	0.992388	+	0.123151i	$0.0393000\pi$
$264$		0			0
$265$	0.211914	−	5.00314i	0.0130178	−	0.307340i
$266$		0			0
$267$			9.79032i			0.599158i
$268$		0			0
$269$	24.2413			1.47802			0.739010	−	0.673694i	$-0.235293\pi$
$269$	24.2413			1.47802			0.739010	+	0.673694i	$0.235293\pi$
$270$		0			0
$271$			21.5717i			1.31039i	0.755461	+	0.655194i	$0.227413\pi$
$271$			21.5717i			1.31039i	−0.755461	+	0.655194i	$0.772587\pi$
$272$		0			0
$273$	−0.466329	−	0.193160i	−0.0282235	−	0.0116906i
$274$		0			0
$275$	−17.3576	+	5.52259i	−1.04670	+	0.333025i
$276$		0			0
$277$	−17.6302	+	17.6302i	−1.05930	+	1.05930i	−0.0611676	+	0.998128i	$0.519482\pi$
$277$	−17.6302	+	17.6302i	−1.05930	+	1.05930i	−0.998128	+	0.0611676i	$0.980518\pi$
$278$		0			0
$279$	3.44206	+	3.44206i	0.206071	+	0.206071i
$280$		0			0
$281$	1.24749	+	3.01171i	0.0744192	+	0.179664i	0.956711	−	0.291038i	$-0.0940007\pi$
$281$	1.24749	+	3.01171i	0.0744192	+	0.179664i	−0.882292	+	0.470702i	$0.844001\pi$
$282$		0			0
$283$	−2.17743	+	2.17743i	−0.129435	+	0.129435i	−0.768856	−	0.639422i	$-0.779174\pi$
$283$	−2.17743	+	2.17743i	−0.129435	+	0.129435i	0.639422	+	0.768856i	$0.279174\pi$
$284$		0			0
$285$	−2.78894	−	7.63161i	−0.165203	−	0.452058i
$286$		0			0
$287$	−0.840503	+	0.241288i	−0.0496133	+	0.0142428i
$288$		0			0
$289$	8.48486	+	8.48486i	0.499109	+	0.499109i
$290$		0			0
$291$			2.86206i			0.167777i
$292$		0			0
$293$	−4.05129	+	9.78067i	−0.236679	+	0.571393i	−0.996935	−	0.0782300i	$-0.975073\pi$
$293$	−4.05129	+	9.78067i	−0.236679	+	0.571393i	0.760257	+	0.649623i	$0.225073\pi$
$294$		0			0
$295$	−9.79289	+	21.0725i	−0.570164	+	1.22689i
$296$		0			0
$297$	−14.3646	−	14.3646i	−0.833521	−	0.833521i
$298$		0			0
$299$	13.7921	+	5.71289i	0.797620	+	0.330385i
$300$		0			0
$301$	−0.215975	+	0.0894597i	−0.0124486	+	0.00515637i
$302$		0			0
$303$	16.2032	−	16.2032i	0.930847	−	0.930847i
$304$		0			0
$305$	2.16641	−	0.791705i	0.124048	−	0.0453329i
$306$		0			0
$307$	−29.6900			−1.69450			−0.847248	−	0.531197i	$-0.821742\pi$
$307$	−29.6900			−1.69450			−0.847248	+	0.531197i	$0.821742\pi$
$308$		0			0
$309$	−2.95581	+	1.22434i	−0.168150	+	0.0696500i
$310$		0			0
$311$	4.04831	+	9.77348i	0.229558	+	0.554203i	0.996124	−	0.0879632i	$-0.0280358\pi$
$311$	4.04831	+	9.77348i	0.229558	+	0.554203i	−0.766565	+	0.642166i	$0.778036\pi$
$312$		0			0
$313$	2.07688	−	5.01403i	0.117392	−	0.283410i	−0.854251	−	0.519860i	$-0.825984\pi$
$313$	2.07688	−	5.01403i	0.117392	−	0.283410i	0.971644	+	0.236450i	$0.0759841\pi$
$314$		0			0
$315$	0.284398	+	0.309555i	0.0160240	+	0.0174415i
$316$		0			0
$317$	0.308161	+	0.743966i	0.0173080	+	0.0417853i	0.932297	−	0.361693i	$-0.117801\pi$
$317$	0.308161	+	0.743966i	0.0173080	+	0.0417853i	−0.914989	+	0.403478i	$0.867801\pi$
$318$		0			0
$319$	0.515246	+	0.515246i	0.0288482	+	0.0288482i
$320$		0			0
$321$	−2.50517	+	6.04800i	−0.139825	+	0.337567i
$322$		0			0
$323$		−	15.3578i		−	0.854531i
$324$		0			0
$325$	12.8826	+	6.66365i	0.714596	+	0.369633i
$326$		0			0
$327$	−1.92406	+	1.92406i	−0.106401	+	0.106401i
$328$		0			0
$329$			0.925842i			0.0510433i
$330$		0			0
$331$	−18.8782	−	7.81961i	−1.03764	−	0.429805i	−0.202176	−	0.979349i	$-0.564801\pi$
$331$	−18.8782	−	7.81961i	−1.03764	−	0.429805i	−0.835465	+	0.549544i	$0.814801\pi$
$332$		0			0
$333$	5.17190			0.283418
$334$		0			0
$335$	−9.54378	−	10.3880i	−0.521432	−	0.567558i
$336$		0			0
$337$			4.10336i			0.223524i	0.993735	+	0.111762i	$0.0356494\pi$
$337$			4.10336i			0.223524i	−0.993735	+	0.111762i	$0.964351\pi$
$338$		0			0
$339$	−24.9743	−	10.3447i	−1.35642	−	0.561847i
$340$		0			0
$341$	11.9017	+	4.92986i	0.644515	+	0.266967i
$342$		0			0
$343$	−1.76404	−	0.730689i	−0.0952492	−	0.0394535i
$344$		0			0
$345$	9.91977	+	10.7973i	0.534063	+	0.581305i
$346$		0			0
$347$	27.0874	+	11.2200i	1.45413	+	0.602320i	0.963177	−	0.268868i	$-0.0866495\pi$
$347$	27.0874	+	11.2200i	1.45413	+	0.602320i	0.490951	+	0.871187i	$0.336649\pi$
$348$		0			0
$349$	18.6691	−	18.6691i	0.999333	−	0.999333i	−0.000667260	−	1.00000i	$-0.500212\pi$
$349$	18.6691	−	18.6691i	0.999333	−	0.999333i	1.00000		0.000667260i	$0.000212395\pi$
$350$		0			0
$351$			16.1758i			0.863403i
$352$		0			0
$353$	17.3875	+	17.3875i	0.925444	+	0.925444i	0.997407	−	0.0719631i	$-0.0229264\pi$
$353$	17.3875	+	17.3875i	0.925444	+	0.925444i	−0.0719631	+	0.997407i	$0.522926\pi$
$354$		0			0
$355$	−1.77815	−	1.93545i	−0.0943746	−	0.102723i
$356$		0			0
$357$	−0.358587	−	0.865707i	−0.0189785	−	0.0458181i
$358$		0			0
$359$	27.5526			1.45417			0.727086	−	0.686546i	$-0.240874\pi$
$359$	27.5526			1.45417			0.727086	+	0.686546i	$0.240874\pi$
$360$		0			0
$361$	7.68388	−	7.68388i	0.404415	−	0.404415i
$362$		0			0
$363$	−2.67384	−	1.10754i	−0.140340	−	0.0581309i
$364$		0			0
$365$	−1.89823	+	4.08464i	−0.0993577	+	0.213800i
$366$		0			0
$367$			2.34363i			0.122336i	0.998127	+	0.0611682i	$0.0194826\pi$
$367$			2.34363i			0.122336i	−0.998127	+	0.0611682i	$0.980517\pi$
$368$		0			0
$369$	5.48916	+	6.89649i	0.285754	+	0.359017i
$370$		0			0
$371$	−0.216260	+	0.216260i	−0.0112276	+	0.0112276i
$372$		0			0
$373$	10.2660	+	10.2660i	0.531552	+	0.531552i	0.921034	−	0.389482i	$-0.127346\pi$
$373$	10.2660	+	10.2660i	0.531552	+	0.531552i	−0.389482	+	0.921034i	$0.627346\pi$
$374$		0			0
$375$	8.71609	+	11.2676i	0.450097	+	0.581856i
$376$		0			0
$377$		−	0.580212i		−	0.0298824i
$378$		0			0
$379$		−	0.360110i		−	0.0184976i	−0.999957	−	0.00924881i	$-0.997056\pi$
$379$		−	0.360110i		−	0.0184976i	0.999957	−	0.00924881i	$-0.00294403\pi$
$380$		0			0
$381$	−3.07020	+	7.41212i	−0.157291	+	0.379735i
$382$		0			0
$383$	8.94022	−	21.5836i	0.456824	−	1.10287i	−0.512852	−	0.858477i	$-0.671411\pi$
$383$	8.94022	−	21.5836i	0.456824	−	1.10287i	0.969676	−	0.244393i	$-0.0785888\pi$
$384$		0			0
$385$	1.00885	+	0.468836i	0.0514158	+	0.0238941i
$386$		0			0
$387$	1.66620	+	1.66620i	0.0846976	+	0.0846976i
$388$		0			0
$389$	3.69311	+	3.69311i	0.187248	+	0.187248i	0.794505	−	0.607257i	$-0.207730\pi$
$389$	3.69311	+	3.69311i	0.187248	+	0.187248i	−0.607257	+	0.794505i	$0.707730\pi$
$390$		0			0
$391$	10.6056	+	25.6041i	0.536347	+	1.29486i
$392$		0			0
$393$	−23.0661	−	9.55429i	−1.16353	−	0.481950i
$394$		0			0
$395$	−4.85505	−	5.28452i	−0.244284	−	0.265893i
$396$		0			0
$397$	−29.3365	+	12.1516i	−1.47236	+	0.609871i	−0.967396	−	0.253270i	$-0.918494\pi$
$397$	−29.3365	+	12.1516i	−1.47236	+	0.609871i	−0.504963	+	0.863141i	$0.668494\pi$
$398$		0			0
$399$	−0.189905	+	0.458470i	−0.00950712	+	0.0229522i
$400$		0			0
$401$	16.8775	−	16.8775i	0.842820	−	0.842820i	−0.146405	−	0.989225i	$-0.546770\pi$
$401$	16.8775	−	16.8775i	0.842820	−	0.842820i	0.989225	+	0.146405i	$0.0467702\pi$
$402$		0			0
$403$	−3.92547	−	9.47693i	−0.195542	−	0.472079i
$404$		0			0
$405$	−2.80387	+	6.03342i	−0.139325	+	0.299803i
$406$		0			0
$407$	12.6452	−	5.23783i	0.626801	−	0.259630i
$408$		0			0
$409$	−23.9966			−1.18656			−0.593279	−	0.804997i	$-0.702167\pi$
$409$	−23.9966			−1.18656			−0.593279	+	0.804997i	$0.702167\pi$
$410$		0			0
$411$	−3.63315			−0.179210
$412$		0			0
$413$	1.31115	−	0.543095i	0.0645174	−	0.0267240i
$414$		0			0
$415$	24.8678	−	9.08784i	1.22071	−	0.446105i
$416$		0			0
$417$	−4.33946	−	10.4764i	−0.212504	−	0.513031i
$418$		0			0
$419$	15.9566	−	15.9566i	0.779533	−	0.779533i	−0.200218	−	0.979751i	$-0.564165\pi$
$419$	15.9566	−	15.9566i	0.779533	−	0.779533i	0.979751	+	0.200218i	$0.0641651\pi$
$420$		0			0
$421$	−8.96845	+	21.6518i	−0.437096	+	1.05524i	0.539851	+	0.841760i	$0.318480\pi$
$421$	−8.96845	+	21.6518i	−0.437096	+	1.05524i	−0.976947	+	0.213482i	$0.931520\pi$
$422$		0			0
$423$	8.62196	−	3.57133i	0.419214	−	0.173644i
$424$		0			0
$425$	8.16353	+	25.6582i	0.395989	+	1.24460i
$426$		0			0
$427$	−0.130147	−	0.0539088i	−0.00629827	−	0.00260883i
$428$		0			0
$429$	5.15267	+	12.4396i	0.248773	+	0.600592i
$430$		0			0
$431$	12.4486	+	12.4486i	0.599628	+	0.599628i	0.940213	−	0.340586i	$-0.110625\pi$
$431$	12.4486	+	12.4486i	0.599628	+	0.599628i	−0.340586	+	0.940213i	$0.610625\pi$
$432$		0			0
$433$	17.3716	+	17.3716i	0.834827	+	0.834827i	0.988173	−	0.153345i	$-0.0490046\pi$
$433$	17.3716	+	17.3716i	0.834827	+	0.834827i	−0.153345	+	0.988173i	$0.549005\pi$
$434$		0			0
$435$	0.240163	−	0.516787i	0.0115149	−	0.0247780i
$436$		0			0
$437$	5.61661	−	13.5597i	0.268679	−	0.648648i
$438$		0			0
$439$	4.85410	−	11.7188i	0.231674	−	0.559310i	−0.764701	−	0.644386i	$-0.777113\pi$
$439$	4.85410	−	11.7188i	0.231674	−	0.559310i	0.996374	+	0.0850758i	$0.0271132\pi$
$440$		0			0
$441$			9.61030i			0.457633i
$442$		0			0
$443$			4.63283i			0.220112i	0.993925	+	0.110056i	$0.0351031\pi$
$443$			4.63283i			0.220112i	−0.993925	+	0.110056i	$0.964897\pi$
$444$		0			0
$445$	−12.6525	+	11.6242i	−0.599786	+	0.551042i
$446$		0			0
$447$	12.6529	+	12.6529i	0.598463	+	0.598463i
$448$		0			0
$449$	16.3537	−	16.3537i	0.771780	−	0.771780i	−0.206637	−	0.978418i	$-0.566252\pi$
$449$	16.3537	−	16.3537i	0.771780	−	0.771780i	0.978418	+	0.206637i	$0.0662520\pi$
$450$		0			0
$451$	20.4053	+	11.3027i	0.960850	+	0.532224i
$452$		0			0
$453$		−	2.97613i		−	0.139831i
$454$		0			0
$455$	−0.304052	−	0.832002i	−0.0142542	−	0.0390049i
$456$		0			0
$457$	−19.1719	−	7.94128i	−0.896825	−	0.371477i	−0.113827	−	0.993501i	$-0.536311\pi$
$457$	−19.1719	−	7.94128i	−0.896825	−	0.371477i	−0.782999	+	0.622023i	$0.786311\pi$
$458$		0			0
$459$	−21.2339	+	21.2339i	−0.991115	+	0.991115i
$460$		0			0
$461$	28.0939			1.30846			0.654232	−	0.756294i	$-0.272992\pi$
$461$	28.0939			1.30846			0.654232	+	0.756294i	$0.272992\pi$
$462$		0			0
$463$	16.4064	+	39.6084i	0.762468	+	1.84076i	0.461569	+	0.887104i	$0.347287\pi$
$463$	16.4064	+	39.6084i	0.762468	+	1.84076i	0.300899	+	0.953656i	$0.402713\pi$
$464$		0			0
$465$	0.426349	−	10.0658i	0.0197715	−	0.466791i
$466$		0			0
$467$	8.61010	+	8.61010i	0.398428	+	0.398428i	0.877678	−	0.479250i	$-0.159091\pi$
$467$	8.61010	+	8.61010i	0.398428	+	0.398428i	−0.479250	+	0.877678i	$0.659091\pi$
$468$		0			0
$469$			0.861548i			0.0397826i
$470$		0			0
$471$	2.56990	−	2.56990i	0.118415	−	0.118415i
$472$		0			0
$473$	5.76128	+	2.38640i	0.264904	+	0.109727i
$474$		0			0
$475$	6.55134	−	12.6655i	0.300596	−	0.581131i
$476$		0			0
$477$	2.84813	+	1.17973i	0.130407	+	0.0540163i
$478$		0			0
$479$	3.58956	+	1.48684i	0.164011	+	0.0679357i	0.463179	−	0.886265i	$-0.346709\pi$
$479$	3.58956	+	1.48684i	0.164011	+	0.0679357i	−0.299167	+	0.954201i	$0.596709\pi$
$480$		0			0
$481$	−10.0689	−	4.17069i	−0.459105	−	0.190167i
$482$		0			0
$483$		−	0.895490i		−	0.0407462i
$484$		0			0
$485$	−3.69878	+	3.39818i	−0.167953	+	0.154303i
$486$		0			0
$487$	19.3884			0.878570			0.439285	−	0.898348i	$-0.355232\pi$
$487$	19.3884			0.878570			0.439285	+	0.898348i	$0.355232\pi$
$488$		0			0
$489$	−19.8698	−	8.23034i	−0.898544	−	0.372189i
$490$		0			0
$491$		−	7.82643i		−	0.353202i	−0.984283	−	0.176601i	$-0.943490\pi$
$491$		−	7.82643i		−	0.353202i	0.984283	−	0.176601i	$-0.0565102\pi$
$492$		0			0
$493$	0.761640	−	0.761640i	0.0343025	−	0.0343025i
$494$		0			0
$495$	0.474536	−	11.2035i	0.0213288	−	0.503558i
$496$		0			0
$497$			0.160520i			0.00720029i
$498$		0			0
$499$	−1.98918	+	4.80230i	−0.0890478	+	0.214980i	−0.962129	−	0.272594i	$-0.912118\pi$
$499$	−1.98918	+	4.80230i	−0.0890478	+	0.214980i	0.873081	+	0.487575i	$0.162118\pi$
$500$		0			0
$501$	5.88640	+	5.88640i	0.262985	+	0.262985i
$502$		0			0
$503$	16.6926	+	40.2995i	0.744286	+	1.79687i	0.587484	+	0.809235i	$0.300118\pi$
$503$	16.6926	+	40.2995i	0.744286	+	1.79687i	0.156802	+	0.987630i	$0.449882\pi$
$504$		0			0
$505$	40.1785	+	1.70181i	1.78792	+	0.0757294i
$506$		0			0
$507$	−2.23581	+	5.39773i	−0.0992959	+	0.239722i
$508$		0			0
$509$	−14.2039	−	34.2914i	−0.629579	−	1.51994i	−0.840147	−	0.542358i	$-0.817532\pi$
$509$	−14.2039	−	34.2914i	−0.629579	−	1.51994i	0.210569	−	0.977579i	$-0.432468\pi$
$510$		0			0
$511$	0.254149	−	0.105272i	0.0112429	−	0.00465696i
$512$		0			0
$513$	15.9032			0.702145
$514$		0			0
$515$	−5.09176	−	2.36626i	−0.224370	−	0.104270i
$516$		0			0
$517$	17.4637	−	17.4637i	0.768055	−	0.768055i
$518$		0			0
$519$	4.26923	−	1.76837i	0.187399	−	0.0776230i
$520$		0			0
$521$	−20.9244	−	8.66718i	−0.916716	−	0.379716i	−0.126092	−	0.992019i	$-0.540244\pi$
$521$	−20.9244	−	8.66718i	−0.916716	−	0.379716i	−0.790624	+	0.612302i	$0.790244\pi$
$522$		0			0
$523$	8.36722	+	8.36722i	0.365873	+	0.365873i	0.865970	−	0.500097i	$-0.166702\pi$
$523$	8.36722	+	8.36722i	0.365873	+	0.365873i	−0.500097	+	0.865970i	$0.666702\pi$
$524$		0			0
$525$	0.0735698	−	0.866907i	0.00321085	−	0.0378349i
$526$		0			0
$527$	7.28736	−	17.5932i	0.317442	−	0.766373i
$528$		0			0
$529$			3.48499i			0.151521i
$530$		0			0
$531$	−10.1152	−	10.1152i	−0.438963	−	0.438963i
$532$		0			0
$533$	−5.12517	−	17.8530i	−0.221996	−	0.773300i
$534$		0			0
$535$	−10.7906	+	3.94337i	−0.466517	+	0.170487i
$536$		0			0
$537$	−3.45019	+	3.45019i	−0.148887	+	0.148887i
$538$		0			0
$539$	9.73281	+	23.4971i	0.419222	+	1.01209i
$540$		0			0
$541$	−14.3332	−	14.3332i	−0.616231	−	0.616231i	0.328332	−	0.944562i	$-0.393514\pi$
$541$	−14.3332	−	14.3332i	−0.616231	−	0.616231i	−0.944562	+	0.328332i	$0.893514\pi$
$542$		0			0
$543$	13.4872	−	13.4872i	0.578792	−	0.578792i
$544$		0			0
$545$	−4.77104	−	0.202083i	−0.204369	−	0.00865629i
$546$		0			0
$547$	15.0179	+	6.22063i	0.642120	+	0.265975i	0.679893	−	0.733311i	$-0.262026\pi$
$547$	15.0179	+	6.22063i	0.642120	+	0.265975i	−0.0377725	+	0.999286i	$0.512026\pi$
$548$		0			0
$549$			1.41995i			0.0606020i
$550$		0			0
$551$	−0.570433			−0.0243013
$552$		0			0
$553$			0.438281i			0.0186376i
$554$		0			0
$555$	−7.24193	−	7.88255i	−0.307403	−	0.334595i
$556$		0			0
$557$	2.50478	−	6.04707i	0.106131	−	0.256222i	−0.861889	−	0.507098i	$-0.830718\pi$
$557$	2.50478	−	6.04707i	0.106131	−	0.256222i	0.968019	+	0.250875i	$0.0807184\pi$
$558$		0			0
$559$	−1.90020	−	4.58750i	−0.0803701	−	0.194030i
$560$		0			0
$561$	−9.56556	+	23.0933i	−0.403858	+	0.975000i
$562$		0			0
$563$	−33.7102	+	13.9632i	−1.42072	+	0.588480i	−0.955041	−	0.296475i	$-0.904189\pi$
$563$	−33.7102	+	13.9632i	−1.42072	+	0.588480i	−0.465676	+	0.884955i	$0.654189\pi$
$564$		0			0
$565$	−16.2835	−	44.5580i	−0.685054	−	1.87457i
$566$		0			0
$567$	0.375404	−	0.155497i	0.0157655	−	0.00653027i
$568$		0			0
$569$	−4.26563	−	4.26563i	−0.178825	−	0.178825i	0.612019	−	0.790843i	$-0.290358\pi$
$569$	−4.26563	−	4.26563i	−0.178825	−	0.178825i	−0.790843	+	0.612019i	$0.790358\pi$
$570$		0			0
$571$	17.6909	−	42.7095i	0.740339	−	1.78734i	0.135841	−	0.990731i	$-0.456626\pi$
$571$	17.6909	−	42.7095i	0.740339	−	1.78734i	0.604498	−	0.796606i	$-0.293374\pi$
$572$		0			0
$573$	−22.8997	−	22.8997i	−0.956647	−	0.956647i
$574$		0			0
$575$	−2.17590	+	25.6396i	−0.0907412	+	1.06925i
$576$		0			0
$577$	1.84842	+	4.46249i	0.0769509	+	0.185776i	0.957674	−	0.287856i	$-0.0929426\pi$
$577$	1.84842	+	4.46249i	0.0769509	+	0.185776i	−0.880723	+	0.473632i	$0.842943\pi$
$578$		0			0
$579$	−22.3516	+	22.3516i	−0.928899	+	0.928899i
$580$		0			0
$581$	−1.49394	−	0.618809i	−0.0619790	−	0.0256725i
$582$		0			0
$583$	8.15842			0.337887
$584$		0			0
$585$	−6.57523	+	6.04086i	−0.271852	+	0.249759i
$586$		0			0
$587$	−2.03978	−	4.92446i	−0.0841906	−	0.203254i	0.876178	−	0.481988i	$-0.160085\pi$
$587$	−2.03978	−	4.92446i	−0.0841906	−	0.203254i	−0.960368	+	0.278734i	$0.910085\pi$
$588$		0			0
$589$	−9.31721	+	3.85932i	−0.383909	+	0.159020i
$590$		0			0
$591$	−20.8292	+	8.62775i	−0.856801	+	0.354898i
$592$		0			0
$593$	−5.14339	+	12.4172i	−0.211214	+	0.509915i	−0.993610	−	0.112865i	$-0.963997\pi$
$593$	−5.14339	+	12.4172i	−0.211214	+	0.509915i	0.782396	+	0.622781i	$0.213997\pi$
$594$		0			0
$595$	0.693037	−	1.49129i	0.0284118	−	0.0611370i
$596$		0			0
$597$	−6.04920	+	6.04920i	−0.247577	+	0.247577i
$598$		0			0
$599$	−5.14350			−0.210158			−0.105079	−	0.994464i	$-0.533509\pi$
$599$	−5.14350			−0.210158			−0.105079	+	0.994464i	$0.533509\pi$
$600$		0			0
$601$	−3.85646	−	9.31032i	−0.157308	−	0.379776i	0.825501	−	0.564401i	$-0.190893\pi$
$601$	−3.85646	−	9.31032i	−0.157308	−	0.379776i	−0.982809	+	0.184625i	$0.940893\pi$
$602$		0			0
$603$	8.02322	−	3.32333i	0.326731	−	0.135336i
$604$		0			0
$605$	−1.74338	−	4.77055i	−0.0708783	−	0.193950i
$606$		0			0
$607$	15.9525			0.647491			0.323746	−	0.946144i	$-0.395058\pi$
$607$	15.9525			0.647491			0.323746	+	0.946144i	$0.395058\pi$
$608$		0			0
$609$	−0.0321548	+	0.0133190i	−0.00130298	+	0.000539712i
$610$		0			0
$611$	−19.6657			−0.795589
$612$		0			0
$613$	−32.1295			−1.29770			−0.648849	−	0.760917i	$-0.724749\pi$
$613$	−32.1295			−1.29770			−0.648849	+	0.760917i	$0.724749\pi$
$614$		0			0
$615$	2.82485	−	18.0229i	0.113909	−	0.726752i
$616$		0			0
$617$	−24.1103			−0.970646			−0.485323	−	0.874335i	$-0.661298\pi$
$617$	−24.1103			−0.970646			−0.485323	+	0.874335i	$0.661298\pi$
$618$		0			0
$619$	43.9636			1.76705			0.883523	−	0.468388i	$-0.155165\pi$
$619$	43.9636			1.76705			0.883523	+	0.468388i	$0.155165\pi$
$620$		0			0
$621$	−26.5134	+	10.9822i	−1.06395	+	0.440701i
$622$		0			0
$623$	1.04936			0.0420416
$624$		0			0
$625$	−4.21289	+	24.6425i	−0.168516	+	0.985699i
$626$		0			0
$627$	12.2300	−	5.06583i	0.488419	−	0.202310i
$628$		0			0
$629$	−7.74260	−	18.6923i	−0.308718	−	0.745310i
$630$		0			0
$631$	4.20212			0.167284			0.0836418	−	0.996496i	$-0.473345\pi$
$631$	4.20212			0.167284			0.0836418	+	0.996496i	$0.473345\pi$
$632$		0			0
$633$	−9.87094	+	9.87094i	−0.392335	+	0.392335i
$634$		0			0
$635$	−13.2244	+	4.83279i	−0.524793	+	0.191783i
$636$		0			0
$637$	7.74989	−	18.7099i	0.307062	−	0.741313i
$638$		0			0
$639$	1.49485	−	0.619187i	0.0591353	−	0.0244947i
$640$		0			0
$641$	−21.7477	+	9.00821i	−0.858984	+	0.355803i	−0.768310	−	0.640078i	$-0.778902\pi$
$641$	−21.7477	+	9.00821i	−0.858984	+	0.355803i	−0.0906741	+	0.995881i	$0.528902\pi$
$642$		0			0
$643$	17.9984	+	43.4520i	0.709788	+	1.71358i	0.700530	+	0.713623i	$0.252947\pi$
$643$	17.9984	+	43.4520i	0.709788	+	1.71358i	0.00925848	+	0.999957i	$0.497053\pi$
$644$		0			0
$645$	0.206383	−	4.87256i	0.00812632	−	0.191857i
$646$		0			0
$647$	48.1647			1.89355			0.946774	−	0.321899i	$-0.104321\pi$
$647$	48.1647			1.89355			0.946774	+	0.321899i	$0.104321\pi$
$648$		0			0
$649$	−34.9758	−	14.4874i	−1.37292	−	0.568682i
$650$		0			0
$651$	−0.435093	+	0.435093i	−0.0170526	+	0.0170526i
$652$		0			0
$653$	−5.68337	−	13.7209i	−0.222408	−	0.536939i	0.772808	−	0.634639i	$-0.218851\pi$
$653$	−5.68337	−	13.7209i	−0.222408	−	0.536939i	−0.995216	+	0.0977002i	$0.968851\pi$
$654$		0			0
$655$	−15.0394	−	41.1535i	−0.587636	−	1.60800i
$656$		0			0
$657$	−1.96071	−	1.96071i	−0.0764944	−	0.0764944i
$658$		0			0
$659$	−15.9583	+	38.5268i	−0.621648	+	1.50079i	0.228120	+	0.973633i	$0.426742\pi$
$659$	−15.9583	+	38.5268i	−0.621648	+	1.50079i	−0.849768	+	0.527157i	$0.823258\pi$
$660$		0			0
$661$	−0.425721	−	0.425721i	−0.0165586	−	0.0165586i	0.698779	−	0.715338i	$-0.253727\pi$
$661$	−0.425721	−	0.425721i	−0.0165586	−	0.0165586i	−0.715338	+	0.698779i	$0.753727\pi$
$662$		0			0
$663$	18.3884	−	7.61671i	0.714145	−	0.295809i
$664$		0			0
$665$	−0.817981	+	0.298928i	−0.0317199	+	0.0115919i
$666$		0			0
$667$	0.951010	−	0.393921i	0.0368233	−	0.0152527i
$668$		0			0
$669$	7.00634	−	16.9148i	0.270881	−	0.653964i
$670$		0			0
$671$	1.43805	+	3.47177i	0.0555154	+	0.134026i
$672$		0			0
$673$	−8.17483	+	19.7358i	−0.315117	+	0.760759i	0.684383	+	0.729123i	$0.260072\pi$
$673$	−8.17483	+	19.7358i	−0.315117	+	0.760759i	−0.999499	+	0.0316358i	$0.989928\pi$
$674$		0			0
$675$	−26.5694	+	8.45345i	−1.02266	+	0.325373i
$676$		0			0
$677$		−	28.3686i		−	1.09029i	−0.838341	−	0.545147i	$-0.816474\pi$
$677$		−	28.3686i		−	1.09029i	0.838341	−	0.545147i	$-0.183526\pi$
$678$		0			0
$679$	0.306765			0.0117726
$680$		0			0
$681$			6.62912i			0.254028i
$682$		0			0
$683$	−21.0204	−	8.70693i	−0.804323	−	0.333162i	−0.0576366	−	0.998338i	$-0.518356\pi$
$683$	−21.0204	−	8.70693i	−0.804323	−	0.333162i	−0.746687	+	0.665176i	$0.768356\pi$
$684$		0			0
$685$	−4.31371	−	4.69530i	−0.164818	−	0.179398i
$686$		0			0
$687$	−10.3551	+	10.3551i	−0.395073	+	0.395073i
$688$		0			0
$689$	−4.59355	−	4.59355i	−0.175000	−	0.175000i
$690$		0			0
$691$	−8.59161	−	20.7420i	−0.326840	−	0.789062i	−0.998823	−	0.0484957i	$-0.984557\pi$
$691$	−8.59161	−	20.7420i	−0.326840	−	0.789062i	0.671983	−	0.740566i	$-0.265443\pi$
$692$		0			0
$693$	−0.484268	+	0.484268i	−0.0183958	+	0.0183958i
$694$		0			0
$695$	8.38682	−	18.0469i	0.318130	−	0.684559i
$696$		0			0
$697$	16.7078	−	30.1633i	0.632852	−	1.14252i
$698$		0			0
$699$	0.267175	+	0.267175i	0.0101055	+	0.0101055i
$700$		0			0
$701$			34.4894i			1.30265i	0.758800	+	0.651324i	$0.225786\pi$
$701$			34.4894i			1.30265i	−0.758800	+	0.651324i	$0.774214\pi$
$702$		0			0
$703$	−4.10041	+	9.89926i	−0.154650	+	0.373358i
$704$		0			0
$705$	−17.5160	−	8.14008i	−0.659690	−	0.306573i
$706$		0			0
$707$	−1.73671	−	1.73671i	−0.0653156	−	0.0653156i
$708$		0			0
$709$	−13.9091	−	5.76133i	−0.522366	−	0.216371i	0.105890	−	0.994378i	$-0.466231\pi$
$709$	−13.9091	−	5.76133i	−0.522366	−	0.216371i	−0.628256	+	0.778007i	$0.716231\pi$
$710$		0			0
$711$	4.08152	−	1.69062i	0.153069	−	0.0634032i
$712$		0			0
$713$	12.8683	−	12.8683i	0.481921	−	0.481921i
$714$		0			0
$715$	−9.95850	+	21.4289i	−0.372427	+	0.801395i
$716$		0			0
$717$	10.0082			0.373764
$718$		0			0
$719$	−41.6838	+	17.2660i	−1.55454	+	0.643913i	−0.984131	−	0.177445i	$-0.943217\pi$
$719$	−41.6838	+	17.2660i	−1.55454	+	0.643913i	−0.570413	+	0.821358i	$0.693217\pi$
$720$		0			0
$721$	0.131228	+	0.316813i	0.00488719	+	0.0117987i
$722$		0			0
$723$	13.7710	−	33.2461i	0.512148	−	1.23643i
$724$		0			0
$725$	0.953018	−	0.303217i	0.0353942	−	0.0112612i
$726$		0			0
$727$	3.83585	+	9.26056i	0.142264	+	0.343455i	0.978911	−	0.204287i	$-0.0654876\pi$
$727$	3.83585	+	9.26056i	0.142264	+	0.343455i	−0.836647	+	0.547742i	$0.815488\pi$
$728$		0			0
$729$	−17.9683	−	17.9683i	−0.665491	−	0.665491i
$730$		0			0
$731$	3.52759	−	8.51636i	0.130473	−	0.314989i
$732$		0			0
$733$			13.4057i			0.495151i	0.968869	+	0.247575i	$0.0796338\pi$
$733$			13.4057i			0.495151i	−0.968869	+	0.247575i	$0.920366\pi$
$734$		0			0
$735$	14.6472	−	13.4568i	0.540269	−	0.496361i
$736$		0			0
$737$	16.2510	−	16.2510i	0.598613	−	0.598613i
$738$		0			0
$739$			13.5812i			0.499593i	0.968298	+	0.249796i	$0.0803637\pi$
$739$			13.5812i			0.499593i	−0.968298	+	0.249796i	$0.919636\pi$
$740$		0			0
$741$	−9.73831	−	4.03374i	−0.357746	−	0.148183i
$742$		0			0
$743$	22.5559			0.827497			0.413748	−	0.910391i	$-0.364219\pi$
$743$	22.5559			0.827497			0.413748	+	0.910391i	$0.364219\pi$
$744$		0			0
$745$	−1.32893	+	31.3751i	−0.0486882	+	1.14949i
$746$		0			0
$747$			16.2994i			0.596363i
$748$		0			0
$749$	0.648244	+	0.268512i	0.0236863	+	0.00981120i
$750$		0			0
$751$	26.2895	+	10.8895i	0.959319	+	0.397363i	0.806726	−	0.590926i	$-0.201238\pi$
$751$	26.2895	+	10.8895i	0.959319	+	0.397363i	0.152593	+	0.988289i	$0.451238\pi$
$752$		0			0
$753$	−27.7248	−	11.4840i	−1.01035	−	0.418500i
$754$		0			0
$755$	3.84619	−	3.53361i	0.139977	−	0.128601i
$756$		0			0
$757$	−17.0468	−	7.06101i	−0.619576	−	0.256637i	0.0507409	−	0.998712i	$-0.483842\pi$
$757$	−17.0468	−	7.06101i	−0.619576	−	0.256637i	−0.670317	+	0.742075i	$0.733842\pi$
$758$		0			0
$759$	−16.8912	+	16.8912i	−0.613113	+	0.613113i
$760$		0			0
$761$			23.1561i			0.839406i	0.907661	+	0.419703i	$0.137866\pi$
$761$			23.1561i			0.839406i	−0.907661	+	0.419703i	$0.862134\pi$
$762$		0			0
$763$	0.206227	+	0.206227i	0.00746593	+	0.00746593i
$764$		0			0
$765$	−16.5610	−	0.701463i	−0.598766	−	0.0253614i
$766$		0			0
$767$	11.5358	+	27.8499i	0.416535	+	1.00560i
$768$		0			0
$769$	−20.0750			−0.723922			−0.361961	−	0.932193i	$-0.617893\pi$
$769$	−20.0750			−0.723922			−0.361961	+	0.932193i	$0.617893\pi$
$770$		0			0
$771$	22.6794	−	22.6794i	0.816779	−	0.816779i
$772$		0			0
$773$	−34.9607	−	14.4812i	−1.25745	−	0.520852i	−0.348323	−	0.937375i	$-0.613249\pi$
$773$	−34.9607	−	14.4812i	−1.25745	−	0.520852i	−0.909125	+	0.416523i	$0.863249\pi$
$774$		0			0
$775$	13.5148	−	11.4003i	0.485464	−	0.409512i
$776$		0			0
$777$			0.653752i			0.0234532i
$778$		0			0
$779$	−17.5521	+	5.03880i	−0.628871	+	0.180534i
$780$		0			0
$781$	3.02781	−	3.02781i	0.108344	−	0.108344i
$782$		0			0
$783$	0.788689	+	0.788689i	0.0281854	+	0.0281854i
$784$		0			0
$785$	6.37250	+	0.269915i	0.227444	+	0.00963367i
$786$		0			0
$787$		−	24.1385i		−	0.860445i	−0.902723	−	0.430222i	$-0.858435\pi$
$787$		−	24.1385i		−	0.860445i	0.902723	−	0.430222i	$-0.141565\pi$
$788$		0			0
$789$		−	10.9925i		−	0.391343i
$790$		0			0
$791$	−1.10878	+	2.67683i	−0.0394236	+	0.0951770i
$792$		0			0
$793$	1.14507	−	2.76444i	0.0406626	−	0.0981682i
$794$		0			0
$795$	−2.19004	−	5.99278i	−0.0776726	−	0.212542i
$796$		0			0
$797$	28.3880	+	28.3880i	1.00556	+	1.00556i	0.999984	+	0.00557171i	$0.00177354\pi$
$797$	28.3880	+	28.3880i	1.00556	+	1.00556i	0.00557171	+	0.999984i	$0.498226\pi$
$798$		0			0
$799$	−25.8150	−	25.8150i	−0.913270	−	0.913270i
$800$		0			0
$801$	−4.04778	−	9.77220i	−0.143021	−	0.345284i
$802$		0			0
$803$	−6.77961	−	2.80820i	−0.239247	−	0.0990994i
$804$		0			0
$805$	1.15729	−	1.06323i	0.0407890	−	0.0374740i
$806$		0			0
$807$	28.5357	−	11.8199i	1.00451	−	0.416080i
$808$		0			0
$809$	−1.70266	+	4.11060i	−0.0598625	+	0.144521i	−0.950981	−	0.309251i	$-0.899922\pi$
$809$	−1.70266	+	4.11060i	−0.0598625	+	0.144521i	0.891118	+	0.453772i	$0.149922\pi$
$810$		0			0
$811$	10.8882	−	10.8882i	0.382337	−	0.382337i	−0.489606	−	0.871944i	$-0.662859\pi$
$811$	10.8882	−	10.8882i	0.382337	−	0.382337i	0.871944	+	0.489606i	$0.162859\pi$
$812$		0			0
$813$	10.5182	+	25.3932i	0.368889	+	0.890577i
$814$		0			0
$815$	−12.9553	−	35.4508i	−0.453806	−	1.24179i
$816$		0			0
$817$	−4.51018	+	1.86818i	−0.157791	+	0.0653593i
$818$		0			0
$819$	0.545328			0.0190553
$820$		0			0
$821$	16.0582			0.560436			0.280218	−	0.959936i	$-0.409593\pi$
$821$	16.0582			0.560436			0.280218	+	0.959936i	$0.409593\pi$
$822$		0			0
$823$	16.3749	−	6.78273i	0.570795	−	0.236431i	−0.0785692	−	0.996909i	$-0.525035\pi$
$823$	16.3749	−	6.78273i	0.570795	−	0.236431i	0.649364	+	0.760478i	$0.275035\pi$
$824$		0			0
$825$	−17.7398	+	14.9644i	−0.617620	+	0.520992i
$826$		0			0
$827$	−16.7861	−	40.5253i	−0.583711	−	1.40920i	−0.889425	−	0.457080i	$-0.848895\pi$
$827$	−16.7861	−	40.5253i	−0.583711	−	1.40920i	0.305714	−	0.952123i	$-0.401105\pi$
$828$		0			0
$829$	25.4294	−	25.4294i	0.883198	−	0.883198i	−0.110660	−	0.993858i	$-0.535296\pi$
$829$	25.4294	−	25.4294i	0.883198	−	0.883198i	0.993858	+	0.110660i	$0.0352964\pi$
$830$		0			0
$831$	−12.1571	+	29.3497i	−0.421724	+	1.01813i
$832$		0			0
$833$	34.7336	−	14.3871i	1.20345	−	0.498484i
$834$		0			0
$835$	−0.618244	+	14.5963i	−0.0213952	+	0.505126i
$836$		0			0
$837$	18.2181	+	7.54616i	0.629708	+	0.260834i
$838$		0			0
$839$	12.5334	+	30.2583i	0.432701	+	1.04463i	0.978413	+	0.206660i	$0.0662592\pi$
$839$	12.5334	+	30.2583i	0.432701	+	1.04463i	−0.545712	+	0.837973i	$0.683741\pi$
$840$		0			0
$841$	20.4778	+	20.4778i	0.706131	+	0.706131i
$842$		0			0
$843$	2.93698	+	2.93698i	0.101155	+	0.101155i
$844$		0			0
$845$	−9.63038	+	3.51938i	−0.331295	+	0.121070i
$846$		0			0
$847$	−0.118710	+	0.286591i	−0.00407892	+	0.00984739i
$848$		0			0
$849$	−1.50147	+	3.62486i	−0.0515302	+	0.124405i
$850$		0			0
$851$		−	19.3354i		−	0.662808i
$852$		0			0
$853$			32.1199i			1.09977i	0.835242	+	0.549883i	$0.185328\pi$
$853$			32.1199i			1.09977i	−0.835242	+	0.549883i	$0.814672\pi$
$854$		0			0
$855$	5.93905	+	6.46441i	0.203111	+	0.221078i
$856$		0			0
$857$	−14.1050	−	14.1050i	−0.481817	−	0.481817i	0.423895	−	0.905711i	$-0.360663\pi$
$857$	−14.1050	−	14.1050i	−0.481817	−	0.481817i	−0.905711	+	0.423895i	$0.860663\pi$
$858$		0			0
$859$	−21.7100	+	21.7100i	−0.740734	+	0.740734i	−0.972719	−	0.231985i	$-0.925478\pi$
$859$	−21.7100	+	21.7100i	−0.740734	+	0.740734i	0.231985	+	0.972719i	$0.425478\pi$
$860$		0			0
$861$	−0.871749	+	0.693856i	−0.0297091	+	0.0236465i
$862$		0			0
$863$			24.4641i			0.832769i	0.909189	+	0.416385i	$0.136703\pi$
$863$			24.4641i			0.832769i	−0.909189	+	0.416385i	$0.863297\pi$
$864$		0			0
$865$	7.35430	+	3.41771i	0.250054	+	0.116206i
$866$		0			0
$867$	14.1251	+	5.85082i	0.479714	+	0.198704i
$868$		0			0
$869$	8.26710	−	8.26710i	0.280442	−	0.280442i
$870$		0			0
$871$	−18.3000			−0.620073
$872$		0			0
$873$	−1.18331	−	2.85677i	−0.0400490	−	0.0966868i
$874$		0			0
$875$	1.20770	−	0.934218i	0.0408276	−	0.0315823i
$876$		0			0
$877$	−25.6976	−	25.6976i	−0.867746	−	0.867746i	0.124476	−	0.992223i	$-0.460275\pi$
$877$	−25.6976	−	25.6976i	−0.867746	−	0.867746i	−0.992223	+	0.124476i	$0.960275\pi$
$878$		0			0
$879$			13.4887i			0.454963i
$880$		0			0
$881$	15.4359	−	15.4359i	0.520049	−	0.520049i	−0.397537	−	0.917586i	$-0.630135\pi$
$881$	15.4359	−	15.4359i	0.520049	−	0.520049i	0.917586	+	0.397537i	$0.130135\pi$
$882$		0			0
$883$	−27.5548	−	11.4136i	−0.927292	−	0.384097i	−0.132642	−	0.991164i	$-0.542346\pi$
$883$	−27.5548	−	11.4136i	−0.927292	−	0.384097i	−0.794651	+	0.607067i	$0.792346\pi$
$884$		0			0
$885$	−1.25292	+	29.5805i	−0.0421164	+	0.994338i
$886$		0			0
$887$	−6.45462	−	2.67359i	−0.216725	−	0.0897704i	0.271680	−	0.962388i	$-0.412421\pi$
$887$	−6.45462	−	2.67359i	−0.216725	−	0.0897704i	−0.488404	+	0.872617i	$0.662421\pi$
$888$		0			0
$889$	0.794455	+	0.329074i	0.0266452	+	0.0110368i
$890$		0			0
$891$	−10.0141	−	4.14800i	−0.335487	−	0.138963i
$892$		0			0
$893$			19.3343i			0.646997i
$894$		0			0
$895$	−8.55532	−	0.362371i	−0.285973	−	0.0121127i
$896$		0			0
$897$	19.0210			0.635093
$898$		0			0
$899$	−0.653463	−	0.270673i	−0.0217942	−	0.00902746i
$900$		0			0
$901$		−	12.0598i		−	0.401771i
$902$		0			0
$903$	−0.210615	+	0.210615i	−0.00700884	+	0.00700884i
$904$		0			0
$905$	33.4438	+	1.41655i	1.11171	+	0.0470878i
$906$		0			0
$907$			1.35625i			0.0450337i	0.999746	+	0.0225168i	$0.00716793\pi$
$907$			1.35625i			0.0450337i	−0.999746	+	0.0225168i	$0.992832\pi$
$908$		0			0
$909$	−9.47403	+	22.8723i	−0.314234	+	0.758627i
$910$		0			0
$911$	−20.5044	−	20.5044i	−0.679340	−	0.679340i	0.280511	−	0.959851i	$-0.409496\pi$
$911$	−20.5044	−	20.5044i	−0.679340	−	0.679340i	−0.959851	+	0.280511i	$0.909496\pi$
$912$		0			0
$913$	16.5071	+	39.8518i	0.546307	+	1.31890i
$914$		0			0
$915$	2.16416	−	1.98828i	0.0715450	−	0.0657305i
$916$		0			0
$917$	−1.02406	+	2.47230i	−0.0338174	+	0.0816425i
$918$		0			0
$919$	5.80964	+	14.0257i	0.191642	+	0.462665i	0.990270	−	0.139160i	$-0.0444403\pi$
$919$	5.80964	+	14.0257i	0.191642	+	0.462665i	−0.798628	+	0.601825i	$0.794440\pi$
$920$		0			0
$921$	−34.9496	+	14.4766i	−1.15163	+	0.477020i
$922$		0			0
$923$	−3.40958			−0.112228
$924$		0			0
$925$	1.58851	−	18.7182i	0.0522300	−	0.615451i
$926$		0			0
$927$	2.44414	−	2.44414i	0.0802761	−	0.0802761i
$928$		0			0
$929$	−13.5502	+	5.61266i	−0.444567	+	0.184145i	−0.593725	−	0.804668i	$-0.702343\pi$
$929$	−13.5502	+	5.61266i	−0.444567	+	0.184145i	0.149159	+	0.988813i	$0.452343\pi$
$930$		0			0
$931$	−18.3946	−	7.61928i	−0.602858	−	0.249712i
$932$		0			0
$933$	9.53095	+	9.53095i	0.312029	+	0.312029i
$934$		0			0
$935$	−41.2020	+	15.0571i	−1.34745	+	0.492420i
$936$		0			0
$937$	2.36304	−	5.70489i	0.0771972	−	0.186371i	−0.880569	−	0.473917i	$-0.842840\pi$
$937$	2.36304	−	5.70489i	0.0771972	−	0.186371i	0.957767	+	0.287547i	$0.0928396\pi$
$938$		0			0
$939$		−	6.91495i		−	0.225661i
$940$		0			0
$941$	0.141295	+	0.141295i	0.00460609	+	0.00460609i	0.709406	−	0.704800i	$-0.248963\pi$
$941$	0.141295	+	0.141295i	0.00460609	+	0.00460609i	−0.704800	+	0.709406i	$0.748963\pi$
$942$		0			0
$943$	25.7828	−	20.5215i	0.839605	−	0.668270i
$944$		0			0
$945$	1.54425	+	0.717650i	0.0502346	+	0.0233452i
$946$		0			0
$947$	3.31720	−	3.31720i	0.107794	−	0.107794i	−0.651152	−	0.758947i	$-0.725714\pi$
$947$	3.31720	−	3.31720i	0.107794	−	0.107794i	0.758947	+	0.651152i	$0.225714\pi$
$948$		0			0
$949$	2.23607	+	5.39836i	0.0725860	+	0.175238i
$950$		0			0
$951$	0.725504	+	0.725504i	0.0235261	+	0.0235261i
$952$		0			0
$953$	9.03395	−	9.03395i	0.292638	−	0.292638i	−0.545483	−	0.838122i	$-0.683654\pi$
$953$	9.03395	−	9.03395i	0.292638	−	0.292638i	0.838122	+	0.545483i	$0.183654\pi$
$954$		0			0
$955$	2.40514	−	56.7836i	0.0778284	−	1.83747i
$956$		0			0
$957$	0.857752	+	0.355293i	0.0277272	+	0.0114850i
$958$		0			0
$959$			0.389413i			0.0125748i
$960$		0			0
$961$	18.4953			0.596624
$962$		0			0
$963$		−	7.07257i		−	0.227910i
$964$		0			0
$965$	−55.4245	−	2.34757i	−1.78418	−	0.0755709i
$966$		0			0
$967$	−0.910974	+	2.19929i	−0.0292949	+	0.0707243i	−0.937850	−	0.347041i	$-0.887187\pi$
$967$	−0.910974	+	2.19929i	−0.0292949	+	0.0707243i	0.908555	+	0.417765i	$0.137187\pi$
$968$		0			0
$969$	−7.48835	−	18.0785i	−0.240560	−	0.580764i
$970$		0			0
$971$	−10.2061	+	24.6396i	−0.327528	+	0.790724i	0.671246	+	0.741234i	$0.265759\pi$
$971$	−10.2061	+	24.6396i	−0.327528	+	0.790724i	−0.998775	+	0.0494891i	$0.984241\pi$
$972$		0			0
$973$	−1.12289	+	0.465117i	−0.0359983	+	0.0149110i
$974$		0			0
$975$	18.4139	+	1.56269i	0.589716	+	0.0500460i
$976$		0			0
$977$	39.6514	−	16.4242i	1.26856	−	0.525455i	0.356035	−	0.934473i	$-0.384129\pi$
$977$	39.6514	−	16.4242i	1.26856	−	0.525455i	0.912526	+	0.409018i	$0.134129\pi$
$978$		0			0
$979$	−19.7936	−	19.7936i	−0.632605	−	0.632605i
$980$		0			0
$981$	1.12501	−	2.71600i	0.0359187	−	0.0867153i
$982$		0			0
$983$	−13.0026	−	13.0026i	−0.414720	−	0.414720i	0.468659	−	0.883379i	$-0.344737\pi$
$983$	−13.0026	−	13.0026i	−0.414720	−	0.414720i	−0.883379	+	0.468659i	$0.844737\pi$
$984$		0			0
$985$	−35.8810	−	16.6747i	−1.14326	−	0.531302i
$986$		0			0
$987$	0.451433	+	1.08986i	0.0143693	+	0.0346905i
$988$		0			0
$989$	6.22915	−	6.22915i	0.198076	−	0.198076i
$990$		0			0
$991$	17.0114	+	7.04634i	0.540384	+	0.223834i	0.636144	−	0.771570i	$-0.280528\pi$
$991$	17.0114	+	7.04634i	0.540384	+	0.223834i	−0.0957603	+	0.995404i	$0.530528\pi$
$992$		0			0
$993$	−26.0353			−0.826206
$994$		0			0
$995$	−15.0000	−	0.635344i	−0.475532	−	0.0201417i
$996$		0			0
$997$	−11.2964	−	27.2718i	−0.357759	−	0.863707i	−0.995615	−	0.0935508i	$-0.970178\pi$
$997$	−11.2964	−	27.2718i	−0.357759	−	0.863707i	0.637855	−	0.770156i	$-0.279822\pi$
$998$		0			0
$999$	19.3561	−	8.01757i	0.612401	−	0.253665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.817.15	yes	84
5.3	odd	4		820.2.y.a.653.15	yes	84
41.27	odd	8		820.2.y.a.437.15	yes	84
205.68	even	8	inner	820.2.x.a.273.15	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.15	✓	84	205.68	even	8	inner
820.2.x.a.817.15	yes	84	1.1	even	1	trivial
820.2.y.a.437.15	yes	84	41.27	odd	8
820.2.y.a.653.15	yes	84	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(1.17715 - 0.487592i) q^{3} +(2.02779 + 0.942363i) q^{5} +(-0.0522617 - 0.126171i) q^{7} +(-0.973380 + 0.973380i) q^{9} +(-1.39412 + 3.36569i) q^{11} +(2.67998 - 1.11008i) q^{13} +(2.84651 + 0.120567i) q^{15} +(4.97519 + 2.06079i) q^{17} +(-1.09138 - 2.63482i) q^{19} +(-0.123040 - 0.123040i) q^{21} +(3.63902 + 3.63902i) q^{23} +(3.22390 + 3.82184i) q^{25} +(-2.13398 + 5.15188i) q^{27} +(0.0765437 - 0.184793i) q^{29} -3.53619i q^{31} +4.64169i q^{33} +(0.0129228 - 0.305098i) q^{35} +(-2.65667 - 2.65667i) q^{37} +(2.61348 - 2.61348i) q^{39} +(0.722911 - 6.36219i) q^{41} -1.71177i q^{43} +(-2.89109 + 1.05654i) q^{45} +(-6.26338 - 2.59438i) q^{47} +(4.93656 - 4.93656i) q^{49} +6.86138 q^{51} +(-0.857011 - 2.06901i) q^{53} +(-5.99869 + 5.51117i) q^{55} +(-2.56943 - 2.56943i) q^{57} +10.3918i q^{59} +(0.729392 - 0.729392i) q^{61} +(0.173683 + 0.0719417i) q^{63} +(6.48055 + 0.274492i) q^{65} +(-5.82842 - 2.41421i) q^{67} +(6.05804 + 2.50932i) q^{69} +(-1.08593 - 0.449805i) q^{71} +2.01433i q^{73} +(5.65852 + 2.92693i) q^{75} +0.497511 q^{77} +(-2.96500 - 1.22814i) q^{79} +2.97536i q^{81} +(8.37256 - 8.37256i) q^{83} +(8.14665 + 8.86730i) q^{85} -0.254851i q^{87} +(-2.94049 + 7.09896i) q^{89} +(-0.280121 - 0.280121i) q^{91} +(-1.72422 - 4.16263i) q^{93} +(0.269866 - 6.37134i) q^{95} +(-0.859610 + 2.07528i) q^{97} +(-1.91909 - 4.63310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 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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Representations

Groups

Database

Properties

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