LMFDB - Embedded newform 432.2.be.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	432.47
Dual form			432.2.be.b.239.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939092 + 1.45537i) q^{3} +(-1.07086 + 0.188822i) q^{5} +(-0.0466102 + 0.0555478i) q^{7} +(-1.23621 - 2.73346i) q^{9} +O(q^{10})$	\(q+(-0.939092 + 1.45537i) q^{3} +(-1.07086 + 0.188822i) q^{5} +(-0.0466102 + 0.0555478i) q^{7} +(-1.23621 - 2.73346i) q^{9} +(-0.889704 + 5.04576i) q^{11} +(-5.31632 - 1.93498i) q^{13} +(0.730832 - 1.73582i) q^{15} +(3.79605 - 2.19165i) q^{17} +(-4.96707 - 2.86774i) q^{19} +(-0.0370715 - 0.120000i) q^{21} +(-3.14687 + 2.64054i) q^{23} +(-3.58737 + 1.30570i) q^{25} +(5.13911 + 0.767820i) q^{27} +(-1.30353 - 3.58141i) q^{29} +(-2.61088 - 3.11153i) q^{31} +(-6.50794 - 6.03328i) q^{33} +(0.0394244 - 0.0682850i) q^{35} +(-1.14643 - 1.98567i) q^{37} +(7.80863 - 5.92009i) q^{39} +(-0.494495 + 1.35861i) q^{41} +(0.128831 + 0.0227164i) q^{43} +(1.83995 + 2.69373i) q^{45} +(-4.26138 - 3.57572i) q^{47} +(1.21462 + 6.88848i) q^{49} +(-0.375176 + 7.58283i) q^{51} +10.4743i q^{53} -5.57130i q^{55} +(8.83817 - 4.53586i) q^{57} +(1.69171 + 9.59417i) q^{59} +(4.96656 + 4.16744i) q^{61} +(0.209458 + 0.0587379i) q^{63} +(6.05841 + 1.06826i) q^{65} +(-2.28472 + 6.27722i) q^{67} +(-0.887762 - 7.05957i) q^{69} +(3.47730 + 6.02286i) q^{71} +(2.77130 - 4.80004i) q^{73} +(1.46860 - 6.44713i) q^{75} +(-0.238812 - 0.284605i) q^{77} +(-4.83670 - 13.2887i) q^{79} +(-5.94356 + 6.75826i) q^{81} +(-3.77579 + 1.37428i) q^{83} +(-3.65122 + 3.06373i) q^{85} +(6.43641 + 1.46616i) q^{87} +(14.4547 + 8.34541i) q^{89} +(0.355279 - 0.205120i) q^{91} +(6.98029 - 0.877792i) q^{93} +(5.86054 + 2.13306i) q^{95} +(-2.74888 + 15.5897i) q^{97} +(14.8922 - 3.80566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{18}\right)$

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
$3$	−0.939092	+	1.45537i	−0.542185	+	0.840259i
$3$	−0.939092	+	1.45537i	−0.542185	+	0.840259i
$4$		0			0
$5$	−1.07086	+	0.188822i	−0.478904	+	0.0844436i	−0.407889	−	0.913032i	$-0.633735\pi$
$5$	−1.07086	+	0.188822i	−0.478904	+	0.0844436i	−0.0710149	+	0.997475i	$0.522624\pi$
$6$		0			0
$7$	−0.0466102	+	0.0555478i	−0.0176170	+	0.0209951i	−0.774781	−	0.632230i	$-0.782140\pi$
$7$	−0.0466102	+	0.0555478i	−0.0176170	+	0.0209951i	0.757164	+	0.653225i	$0.226584\pi$
$8$		0			0
$9$	−1.23621	−	2.73346i	−0.412071	−	0.911152i
$10$		0			0
$11$	−0.889704	+	5.04576i	−0.268256	+	1.52135i	0.491346	+	0.870965i	$0.336505\pi$
$11$	−0.889704	+	5.04576i	−0.268256	+	1.52135i	−0.759601	+	0.650389i	$0.774606\pi$
$12$		0			0
$13$	−5.31632	−	1.93498i	−1.47448	−	0.536668i	−0.525168	−	0.850998i	$-0.675998\pi$
$13$	−5.31632	−	1.93498i	−1.47448	−	0.536668i	−0.949314	+	0.314331i	$0.898220\pi$
$14$		0			0
$15$	0.730832	−	1.73582i	0.188700	−	0.448187i
$16$		0			0
$17$	3.79605	−	2.19165i	0.920678	−	0.531554i	0.0368269	−	0.999322i	$-0.488275\pi$
$17$	3.79605	−	2.19165i	0.920678	−	0.531554i	0.883851	+	0.467768i	$0.154942\pi$
$18$		0			0
$19$	−4.96707	−	2.86774i	−1.13952	−	0.657905i	−0.193212	−	0.981157i	$-0.561890\pi$
$19$	−4.96707	−	2.86774i	−1.13952	−	0.657905i	−0.946313	+	0.323252i	$0.895224\pi$
$20$		0			0
$21$	−0.0370715	−	0.120000i	−0.00808966	−	0.0261861i
$22$		0			0
$23$	−3.14687	+	2.64054i	−0.656168	+	0.550590i	−0.908935	−	0.416937i	$-0.863104\pi$
$23$	−3.14687	+	2.64054i	−0.656168	+	0.550590i	0.252768	+	0.967527i	$0.418659\pi$
$24$		0			0
$25$	−3.58737	+	1.30570i	−0.717475	+	0.261139i
$26$		0			0
$27$	5.13911	+	0.767820i	0.989022	+	0.147767i
$28$		0			0
$29$	−1.30353	−	3.58141i	−0.242059	−	0.665051i	−0.999920	−	0.0126352i	$-0.995978\pi$
$29$	−1.30353	−	3.58141i	−0.242059	−	0.665051i	0.757862	−	0.652415i	$-0.226244\pi$
$30$		0			0
$31$	−2.61088	−	3.11153i	−0.468929	−	0.558847i	0.478800	−	0.877924i	$-0.341072\pi$
$31$	−2.61088	−	3.11153i	−0.468929	−	0.558847i	−0.947729	+	0.319076i	$0.896627\pi$
$32$		0			0
$33$	−6.50794	−	6.03328i	−1.13289	−	1.05026i
$34$		0			0
$35$	0.0394244	−	0.0682850i	0.00666394	−	0.0115423i
$36$		0			0
$37$	−1.14643	−	1.98567i	−0.188471	−	0.326442i	0.756269	−	0.654260i	$-0.227020\pi$
$37$	−1.14643	−	1.98567i	−0.188471	−	0.326442i	−0.944741	+	0.327818i	$0.893687\pi$
$38$		0			0
$39$	7.80863	−	5.92009i	1.25038	−	0.947974i
$40$		0			0
$41$	−0.494495	+	1.35861i	−0.0772271	+	0.212180i	−0.972298	−	0.233744i	$-0.924902\pi$
$41$	−0.494495	+	1.35861i	−0.0772271	+	0.212180i	0.895071	+	0.445923i	$0.147125\pi$
$42$		0			0
$43$	0.128831	+	0.0227164i	0.0196466	+	0.00346422i	0.183463	−	0.983027i	$-0.441269\pi$
$43$	0.128831	+	0.0227164i	0.0196466	+	0.00346422i	−0.163816	+	0.986491i	$0.552380\pi$
$44$		0			0
$45$	1.83995	+	2.69373i	0.274283	+	0.401557i
$46$		0			0
$47$	−4.26138	−	3.57572i	−0.621586	−	0.521573i	0.276716	−	0.960952i	$-0.410754\pi$
$47$	−4.26138	−	3.57572i	−0.621586	−	0.521573i	−0.898302	+	0.439379i	$0.855198\pi$
$48$		0			0
$49$	1.21462	+	6.88848i	0.173518	+	0.984068i
$50$		0			0
$51$	−0.375176	+	7.58283i	−0.0525351	+	1.06181i
$52$		0			0
$53$			10.4743i			1.43876i	0.694619	+	0.719378i	$0.255573\pi$
$53$			10.4743i			1.43876i	−0.694619	+	0.719378i	$0.744427\pi$
$54$		0			0
$55$		−	5.57130i		−	0.751234i
$56$		0			0
$57$	8.83817	−	4.53586i	1.17064	−	0.600790i
$58$		0			0
$59$	1.69171	+	9.59417i	0.220242	+	1.24905i	0.871575	+	0.490262i	$0.163099\pi$
$59$	1.69171	+	9.59417i	0.220242	+	1.24905i	−0.651333	+	0.758792i	$0.725790\pi$
$60$		0			0
$61$	4.96656	+	4.16744i	0.635903	+	0.533586i	0.902757	−	0.430151i	$-0.141540\pi$
$61$	4.96656	+	4.16744i	0.635903	+	0.533586i	−0.266854	+	0.963737i	$0.585984\pi$
$62$		0			0
$63$	0.209458	+	0.0587379i	0.0263892	+	0.00740029i
$64$		0			0
$65$	6.05841	+	1.06826i	0.751453	+	0.132501i
$66$		0			0
$67$	−2.28472	+	6.27722i	−0.279123	+	0.766885i	0.718339	+	0.695693i	$0.244903\pi$
$67$	−2.28472	+	6.27722i	−0.279123	+	0.766885i	−0.997463	+	0.0711921i	$0.977320\pi$
$68$		0			0
$69$	−0.887762	−	7.05957i	−0.106874	−	0.849873i
$70$		0			0
$71$	3.47730	+	6.02286i	0.412680	+	0.714782i	0.995182	−	0.0980471i	$-0.0312596\pi$
$71$	3.47730	+	6.02286i	0.412680	+	0.714782i	−0.582502	+	0.812829i	$0.697926\pi$
$72$		0			0
$73$	2.77130	−	4.80004i	0.324356	−	0.561802i	−0.657026	−	0.753868i	$-0.728186\pi$
$73$	2.77130	−	4.80004i	0.324356	−	0.561802i	0.981382	+	0.192067i	$0.0615190\pi$
$74$		0			0
$75$	1.46860	−	6.44713i	0.169579	−	0.744450i
$76$		0			0
$77$	−0.238812	−	0.284605i	−0.0272151	−	0.0324337i
$78$		0			0
$79$	−4.83670	−	13.2887i	−0.544171	−	1.49510i	−0.841465	−	0.540312i	$-0.818306\pi$
$79$	−4.83670	−	13.2887i	−0.544171	−	1.49510i	0.297294	−	0.954786i	$-0.403916\pi$
$80$		0			0
$81$	−5.94356	+	6.75826i	−0.660396	+	0.750918i
$82$		0			0
$83$	−3.77579	+	1.37428i	−0.414447	+	0.150846i	−0.540824	−	0.841136i	$-0.681887\pi$
$83$	−3.77579	+	1.37428i	−0.414447	+	0.150846i	0.126377	+	0.991982i	$0.459665\pi$
$84$		0			0
$85$	−3.65122	+	3.06373i	−0.396030	+	0.332309i
$86$		0			0
$87$	6.43641	+	1.46616i	0.690055	+	0.157189i
$88$		0			0
$89$	14.4547	+	8.34541i	1.53219	+	0.884612i	0.999260	+	0.0384538i	$0.0122432\pi$
$89$	14.4547	+	8.34541i	1.53219	+	0.884612i	0.532932	+	0.846158i	$0.321090\pi$
$90$		0			0
$91$	0.355279	−	0.205120i	0.0372433	−	0.0215024i
$92$		0			0
$93$	6.98029	−	0.877792i	0.723823	−	0.0910228i
$94$		0			0
$95$	5.86054	+	2.13306i	0.601278	+	0.218847i
$96$		0			0
$97$	−2.74888	+	15.5897i	−0.279106	+	1.58289i	0.446502	+	0.894783i	$0.352670\pi$
$97$	−2.74888	+	15.5897i	−0.279106	+	1.58289i	−0.725608	+	0.688108i	$0.758442\pi$
$98$		0			0
$99$	14.8922	−	3.80566i	1.49672	−	0.382483i
$100$		0			0
$101$	5.40951	−	6.44680i	0.538266	−	0.641481i	−0.426532	−	0.904473i	$-0.640265\pi$
$101$	5.40951	−	6.44680i	0.538266	−	0.641481i	0.964798	+	0.262992i	$0.0847092\pi$
$102$		0			0
$103$	−0.918166	+	0.161897i	−0.0904696	+	0.0159522i	−0.218700	−	0.975792i	$-0.570182\pi$
$103$	−0.918166	+	0.161897i	−0.0904696	+	0.0159522i	0.128230	+	0.991744i	$0.459070\pi$
$104$		0			0
$105$	0.0623569	+	0.121503i	0.00608541	+	0.0118575i
$106$		0			0
$107$	−11.2973			−1.09215			−0.546076	−	0.837736i	$-0.683879\pi$
$107$	−11.2973			−1.09215			−0.546076	+	0.837736i	$0.683879\pi$
$108$		0			0
$109$	7.80915			0.747981			0.373991	−	0.927433i	$-0.377989\pi$
$109$	7.80915			0.747981			0.373991	+	0.927433i	$0.377989\pi$
$110$		0			0
$111$	3.96649	+	0.196250i	0.376482	+	0.0186272i
$112$		0			0
$113$	−8.09837	+	1.42796i	−0.761830	+	0.134331i	−0.541048	−	0.840992i	$-0.681972\pi$
$113$	−8.09837	+	1.42796i	−0.761830	+	0.134331i	−0.220782	+	0.975323i	$0.570861\pi$
$114$		0			0
$115$	2.87127	−	3.42185i	0.267747	−	0.319089i
$116$		0			0
$117$	1.28291	+	16.9240i	0.118605	+	1.56462i
$118$		0			0
$119$	−0.0551931	+	0.313016i	−0.00505955	+	0.0286941i
$120$		0			0
$121$	−14.3315	−	5.21624i	−1.30286	−	0.474203i
$122$		0			0
$123$	−1.51291	−	1.99554i	−0.136415	−	0.179931i
$124$		0			0
$125$	8.30353	−	4.79405i	0.742690	−	0.428793i
$126$		0			0
$127$	−4.34261	−	2.50721i	−0.385344	−	0.222479i	0.294797	−	0.955560i	$-0.404748\pi$
$127$	−4.34261	−	2.50721i	−0.385344	−	0.222479i	−0.680141	+	0.733081i	$0.738081\pi$
$128$		0			0
$129$	−0.154045	+	0.166164i	−0.0135629	+	0.0146300i
$130$		0			0
$131$	1.94960	−	1.63591i	0.170337	−	0.142930i	−0.553634	−	0.832760i	$-0.686759\pi$
$131$	1.94960	−	1.63591i	0.170337	−	0.142930i	0.723971	+	0.689830i	$0.242315\pi$
$132$		0			0
$133$	0.390813	−	0.142244i	0.0338878	−	0.0123341i
$134$		0			0
$135$	−5.64825	+	0.148147i	−0.486124	+	0.0127505i
$136$		0			0
$137$	−3.44548	−	9.46638i	−0.294367	−	0.808767i	−0.995415	−	0.0956528i	$-0.969506\pi$
$137$	−3.44548	−	9.46638i	−0.294367	−	0.808767i	0.701048	−	0.713115i	$-0.252716\pi$
$138$		0			0
$139$	2.17758	+	2.59514i	0.184700	+	0.220117i	0.850447	−	0.526060i	$-0.176331\pi$
$139$	2.17758	+	2.59514i	0.184700	+	0.220117i	−0.665747	+	0.746178i	$0.731887\pi$
$140$		0			0
$141$	9.20583	−	2.84396i	0.775271	−	0.239504i
$142$		0			0
$143$	14.4934	−	25.1033i	1.21200	−	2.09924i
$144$		0			0
$145$	2.07214	+	3.58906i	0.172082	+	0.298055i
$146$		0			0
$147$	−11.1659	−	4.70118i	−0.920951	−	0.387747i
$148$		0			0
$149$	−7.17252	+	19.7063i	−0.587596	+	1.61441i	0.187290	+	0.982305i	$0.440030\pi$
$149$	−7.17252	+	19.7063i	−0.587596	+	1.61441i	−0.774886	+	0.632101i	$0.782193\pi$
$150$		0			0
$151$	20.2553	+	3.57156i	1.64835	+	0.290649i	0.919227	−	0.393728i	$-0.128815\pi$
$151$	20.2553	+	3.57156i	1.64835	+	0.290649i	0.729128	+	0.684377i	$0.239926\pi$
$152$		0			0
$153$	−10.6835	−	7.66700i	−0.863711	−	0.619840i
$154$		0			0
$155$	3.38342	+	2.83903i	0.271763	+	0.228036i
$156$		0			0
$157$	−4.28433	−	24.2976i	−0.341927	−	1.93916i	−0.343470	−	0.939164i	$-0.611602\pi$
$157$	−4.28433	−	24.2976i	−0.341927	−	1.93916i	0.00154349	−	0.999999i	$-0.499509\pi$
$158$		0			0
$159$	−15.2440	−	9.83633i	−1.20893	−	0.780072i
$160$		0			0
$161$		−	0.297878i		−	0.0234761i
$162$		0			0
$163$		−	12.2188i		−	0.957048i	−0.878074	−	0.478524i	$-0.841172\pi$
$163$		−	12.2188i		−	0.957048i	0.878074	−	0.478524i	$-0.158828\pi$
$164$		0			0
$165$	8.10832	+	5.23197i	0.631231	+	0.407308i
$166$		0			0
$167$	0.673297	+	3.81846i	0.0521013	+	0.295481i	0.999713	−	0.0239425i	$-0.00762187\pi$
$167$	0.673297	+	3.81846i	0.0521013	+	0.295481i	−0.947612	+	0.319423i	$0.896511\pi$
$168$		0			0
$169$	14.5605	+	12.2177i	1.12004	+	0.939826i
$170$		0			0
$171$	−1.69849	+	17.1224i	−0.129887	+	1.30938i
$172$		0			0
$173$	−15.4083	−	2.71690i	−1.17147	−	0.206562i	−0.446141	−	0.894963i	$-0.647202\pi$
$173$	−15.4083	−	2.71690i	−1.17147	−	0.206562i	−0.725330	+	0.688401i	$0.758313\pi$
$174$		0			0
$175$	0.0946794	−	0.260130i	0.00715709	−	0.0196639i
$176$		0			0
$177$	−15.5518	−	6.54774i	−1.16894	−	0.492158i
$178$		0			0
$179$	6.03273	+	10.4490i	0.450907	+	0.780994i	0.998443	−	0.0557882i	$-0.0177671\pi$
$179$	6.03273	+	10.4490i	0.450907	+	0.780994i	−0.547535	+	0.836783i	$0.684434\pi$
$180$		0			0
$181$	10.1241	−	17.5354i	0.752515	−	1.30339i	−0.194085	−	0.980985i	$-0.562174\pi$
$181$	10.1241	−	17.5354i	0.752515	−	1.30339i	0.946600	−	0.322410i	$-0.104493\pi$
$182$		0			0
$183$	−10.7292	+	3.31458i	−0.793127	+	0.245021i
$184$		0			0
$185$	1.60260	+	1.90991i	0.117826	+	0.140419i
$186$		0			0
$187$	7.68119	+	21.1039i	0.561704	+	1.54327i
$188$		0			0
$189$	−0.282186	+	0.249678i	−0.0205260	+	0.0181614i
$190$		0			0
$191$	−23.5661	+	8.57737i	−1.70518	+	0.620636i	−0.996399	−	0.0847874i	$-0.972979\pi$
$191$	−23.5661	+	8.57737i	−1.70518	+	0.620636i	−0.708786	+	0.705424i	$0.750757\pi$
$192$		0			0
$193$	−11.3801	+	9.54906i	−0.819160	+	0.687357i	−0.952775	−	0.303677i	$-0.901786\pi$
$193$	−11.3801	+	9.54906i	−0.819160	+	0.687357i	0.133615	+	0.991033i	$0.457341\pi$
$194$		0			0
$195$	−7.24412	+	7.81404i	−0.518762	+	0.559575i
$196$		0			0
$197$	−14.3982	−	8.31282i	−1.02583	−	0.592264i	−0.110043	−	0.993927i	$-0.535099\pi$
$197$	−14.3982	−	8.31282i	−1.02583	−	0.592264i	−0.915788	+	0.401663i	$0.868432\pi$
$198$		0			0
$199$	−17.6909	+	10.2138i	−1.25407	+	0.724039i	−0.971916	−	0.235329i	$-0.924383\pi$
$199$	−17.6909	+	10.2138i	−1.25407	+	0.724039i	−0.282157	+	0.959368i	$0.591050\pi$
$200$		0			0
$201$	−6.99013	−	9.22001i	−0.493046	−	0.650330i
$202$		0			0
$203$	0.259697	+	0.0945220i	0.0182272	+	0.00663414i
$204$		0			0
$205$	0.272999	−	1.54826i	0.0190671	−	0.108135i
$206$		0			0
$207$	11.1080	+	5.33757i	0.772059	+	0.370987i
$208$		0			0
$209$	18.8892	−	22.5112i	1.30659	−	1.55713i
$210$		0			0
$211$	−17.6769	+	3.11691i	−1.21693	+	0.214577i	−0.745002	−	0.667062i	$-0.767552\pi$
$211$	−17.6769	+	3.11691i	−1.21693	+	0.214577i	−0.471924	+	0.881639i	$0.656441\pi$
$212$		0			0
$213$	−12.0310	−	0.595258i	−0.824351	−	0.0407864i
$214$		0			0
$215$	−0.142250			−0.00970134
$216$		0			0
$217$	0.294533			0.0199942
$218$		0			0
$219$	4.38333	+	8.54095i	0.296198	+	0.577144i
$220$		0			0
$221$	−24.4218	+	4.30623i	−1.64279	+	0.289668i
$222$		0			0
$223$	0.193902	−	0.231084i	0.0129846	−	0.0154745i	−0.759513	−	0.650492i	$-0.774563\pi$
$223$	0.193902	−	0.231084i	0.0129846	−	0.0154745i	0.772498	+	0.635018i	$0.219007\pi$
$224$		0			0
$225$	8.00382	+	8.19181i	0.533588	+	0.546121i
$226$		0			0
$227$	3.55254	−	20.1475i	0.235790	−	1.33723i	−0.605152	−	0.796110i	$-0.706888\pi$
$227$	3.55254	−	20.1475i	0.235790	−	1.33723i	0.840943	−	0.541124i	$-0.182001\pi$
$228$		0			0
$229$	6.31957	+	2.30013i	0.417609	+	0.151997i	0.542274	−	0.840202i	$-0.317563\pi$
$229$	6.31957	+	2.30013i	0.417609	+	0.151997i	−0.124665	+	0.992199i	$0.539786\pi$
$230$		0			0
$231$	0.638472	−	0.0802897i	0.0420084	−	0.00528267i
$232$		0			0
$233$	5.00964	−	2.89232i	0.328193	−	0.189482i	−0.326846	−	0.945078i	$-0.605986\pi$
$233$	5.00964	−	2.89232i	0.328193	−	0.189482i	0.655038	+	0.755596i	$0.272652\pi$
$234$		0			0
$235$	5.23852	+	3.02446i	0.341723	+	0.197294i
$236$		0			0
$237$	23.8821	+	5.44014i	1.55131	+	0.353375i
$238$		0			0
$239$	−1.92638	+	1.61642i	−0.124607	+	0.104558i	−0.702962	−	0.711228i	$-0.748139\pi$
$239$	−1.92638	+	1.61642i	−0.124607	+	0.104558i	0.578355	+	0.815785i	$0.303695\pi$
$240$		0			0
$241$	0.855851	−	0.311504i	0.0551302	−	0.0200657i	−0.314308	−	0.949321i	$-0.601772\pi$
$241$	0.855851	−	0.311504i	0.0551302	−	0.0200657i	0.369438	+	0.929255i	$0.379550\pi$
$242$		0			0
$243$	−4.25423	−	14.9967i	−0.272909	−	0.962040i
$244$		0			0
$245$	−2.60139	−	7.14725i	−0.166197	−	0.456621i
$246$		0			0
$247$	20.8575	+	24.8570i	1.32713	+	1.58161i
$248$		0			0
$249$	1.54573	−	6.78575i	0.0979569	−	0.430029i
$250$		0			0
$251$	9.85499	−	17.0693i	0.622041	−	1.07741i	−0.367064	−	0.930196i	$-0.619637\pi$
$251$	9.85499	−	17.0693i	0.622041	−	1.07741i	0.989105	−	0.147212i	$-0.0470298\pi$
$252$		0			0
$253$	−10.5237	−	18.2276i	−0.661622	−	1.14596i
$254$		0			0
$255$	−1.03004	−	8.19100i	−0.0645037	−	0.512940i
$256$		0			0
$257$	3.84779	−	10.5717i	0.240018	−	0.659445i	−0.759937	−	0.649997i	$-0.774770\pi$
$257$	3.84779	−	10.5717i	0.240018	−	0.659445i	0.999955	−	0.00944810i	$-0.00300747\pi$
$258$		0			0
$259$	0.163735	+	0.0288709i	0.0101740	+	0.00179395i
$260$		0			0
$261$	−8.17818	+	7.99051i	−0.506217	+	0.494600i
$262$		0			0
$263$	−8.08262	−	6.78213i	−0.498396	−	0.418204i	0.358628	−	0.933481i	$-0.383245\pi$
$263$	−8.08262	−	6.78213i	−0.498396	−	0.418204i	−0.857024	+	0.515277i	$0.827689\pi$
$264$		0			0
$265$	−1.97778	−	11.2165i	−0.121494	−	0.689025i
$266$		0			0
$267$	−25.7199	+	13.1998i	−1.57404	+	0.807815i
$268$		0			0
$269$			28.9612i			1.76580i	0.469564	+	0.882898i	$0.344411\pi$
$269$			28.9612i			1.76580i	−0.469564	+	0.882898i	$0.655589\pi$
$270$		0			0
$271$			29.5660i			1.79600i	0.439991	+	0.898002i	$0.354982\pi$
$271$			29.5660i			1.79600i	−0.439991	+	0.898002i	$0.645018\pi$
$272$		0			0
$273$	−0.0351133	+	0.709689i	−0.00212515	+	0.0429523i
$274$		0			0
$275$	−3.39653	−	19.2627i	−0.204819	−	1.16158i
$276$		0			0
$277$	−1.54306	−	1.29478i	−0.0927134	−	0.0777958i	0.595253	−	0.803538i	$-0.297052\pi$
$277$	−1.54306	−	1.29478i	−0.0927134	−	0.0777958i	−0.687966	+	0.725743i	$0.741496\pi$
$278$		0			0
$279$	−5.27763	+	10.9832i	−0.315963	+	0.657550i
$280$		0			0
$281$	−4.06067	−	0.716005i	−0.242239	−	0.0427133i	0.0512103	−	0.998688i	$-0.483692\pi$
$281$	−4.06067	−	0.716005i	−0.242239	−	0.0427133i	−0.293449	+	0.955975i	$0.594803\pi$
$282$		0			0
$283$	−2.21065	+	6.07372i	−0.131410	+	0.361045i	−0.987895	−	0.155127i	$-0.950421\pi$
$283$	−2.21065	+	6.07372i	−0.131410	+	0.361045i	0.856485	+	0.516172i	$0.172644\pi$
$284$		0			0
$285$	−8.60798	+	6.52612i	−0.509893	+	0.386574i
$286$		0			0
$287$	−0.0524195	−	0.0907933i	−0.00309423	−	0.00535936i
$288$		0			0
$289$	1.10668	−	1.91683i	0.0650990	−	0.112755i
$290$		0			0
$291$	−20.1073	−	18.6408i	−1.17871	−	1.09274i
$292$		0			0
$293$	−19.8278	−	23.6299i	−1.15835	−	1.38047i	−0.911439	−	0.411435i	$-0.865028\pi$
$293$	−19.8278	−	23.6299i	−1.15835	−	1.38047i	−0.246915	−	0.969037i	$-0.579417\pi$
$294$		0			0
$295$	−3.62318	−	9.95459i	−0.210949	−	0.579579i
$296$		0			0
$297$	−8.44652	+	25.2476i	−0.490117	+	1.46501i
$298$		0			0
$299$	21.8392	−	7.94881i	1.26299	−	0.459691i
$300$		0			0
$301$	−0.00726669	+	0.00609748i	−0.000418845	+	0.000351453i
$302$		0			0
$303$	4.30246	+	13.9270i	0.247170	+	0.800084i
$304$		0			0
$305$	−6.10540	−	3.52495i	−0.349594	−	0.201838i
$306$		0			0
$307$	27.5367	−	15.8983i	1.57160	−	0.907364i	0.575628	−	0.817712i	$-0.304758\pi$
$307$	27.5367	−	15.8983i	1.57160	−	0.907364i	0.995973	−	0.0896520i	$-0.0285755\pi$
$308$		0			0
$309$	0.626622	−	1.48831i	0.0356473	−	0.0846670i
$310$		0			0
$311$	13.5550	+	4.93361i	0.768633	+	0.279759i	0.696424	−	0.717630i	$-0.254773\pi$
$311$	13.5550	+	4.93361i	0.768633	+	0.279759i	0.0722083	+	0.997390i	$0.476995\pi$
$312$		0			0
$313$	0.513567	−	2.91258i	0.0290285	−	0.164629i	−0.966847	−	0.255355i	$-0.917808\pi$
$313$	0.513567	−	2.91258i	0.0290285	−	0.164629i	0.995876	+	0.0907261i	$0.0289188\pi$
$314$		0			0
$315$	−0.235391	−	0.0233501i	−0.0132628	−	0.00131563i
$316$		0			0
$317$	−14.9386	+	17.8031i	−0.839035	+	0.999923i	0.160881	+	0.986974i	$0.448567\pi$
$317$	−14.9386	+	17.8031i	−0.839035	+	0.999923i	−0.999916	+	0.0129495i	$0.995878\pi$
$318$		0			0
$319$	19.2307	−	3.39089i	1.07671	−	0.189853i
$320$		0			0
$321$	10.6092	−	16.4418i	0.592148	−	0.917690i
$322$		0			0
$323$	−25.1404			−1.39885
$324$		0			0
$325$	21.5981			1.19805
$326$		0			0
$327$	−7.33351	+	11.3652i	−0.405544	+	0.628498i
$328$		0			0
$329$	0.397247	−	0.0700454i	0.0219010	−	0.00386173i
$330$		0			0
$331$	4.74589	−	5.65593i	0.260857	−	0.310878i	−0.619680	−	0.784855i	$-0.712738\pi$
$331$	4.74589	−	5.65593i	0.260857	−	0.310878i	0.880537	+	0.473977i	$0.157182\pi$
$332$		0			0
$333$	−4.01051	+	5.58842i	−0.219775	+	0.306243i
$334$		0			0
$335$	1.26134	−	7.15344i	0.0689146	−	0.390834i
$336$		0			0
$337$	8.45078	+	3.07583i	0.460343	+	0.167551i	0.561773	−	0.827292i	$-0.310119\pi$
$337$	8.45078	+	3.07583i	0.460343	+	0.167551i	−0.101430	+	0.994843i	$0.532342\pi$
$338$		0			0
$339$	5.52690	−	13.1271i	0.300180	−	0.712967i
$340$		0			0
$341$	18.0230	−	10.4056i	0.975997	−	0.563492i
$342$		0			0
$343$	−0.878838	−	0.507397i	−0.0474528	−	0.0273969i
$344$		0			0
$345$	2.28367	+	7.39219i	0.122949	+	0.397982i
$346$		0			0
$347$	11.3234	−	9.50146i	0.607872	−	0.510065i	−0.286093	−	0.958202i	$-0.592357\pi$
$347$	11.3234	−	9.50146i	0.607872	−	0.510065i	0.893965	+	0.448137i	$0.147912\pi$
$348$		0			0
$349$	6.57893	−	2.39453i	0.352162	−	0.128176i	−0.159881	−	0.987136i	$-0.551111\pi$
$349$	6.57893	−	2.39453i	0.352162	−	0.128176i	0.512043	+	0.858960i	$0.328889\pi$
$350$		0			0
$351$	−25.8354	−	14.0261i	−1.37899	−	0.748656i
$352$		0			0
$353$	−3.61218	−	9.92437i	−0.192257	−	0.528221i	0.805685	−	0.592344i	$-0.201797\pi$
$353$	−3.61218	−	9.92437i	−0.192257	−	0.528221i	−0.997942	+	0.0641228i	$0.979575\pi$
$354$		0			0
$355$	−4.86095	−	5.79306i	−0.257993	−	0.307464i
$356$		0			0
$357$	−0.403723	−	0.374277i	−0.0213673	−	0.0198089i
$358$		0			0
$359$	12.6210	−	21.8603i	0.666112	−	1.15374i	−0.312871	−	0.949796i	$-0.601291\pi$
$359$	12.6210	−	21.8603i	0.666112	−	1.15374i	0.978983	−	0.203944i	$-0.0653761\pi$
$360$		0			0
$361$	6.94788	+	12.0341i	0.365678	+	0.633373i
$362$		0			0
$363$	21.0502	−	15.9591i	1.10485	−	0.837637i
$364$		0			0
$365$	−2.06133	+	5.66345i	−0.107895	+	0.296439i
$366$		0			0
$367$	−11.2545	−	1.98448i	−0.587483	−	0.103589i	−0.127997	−	0.991774i	$-0.540855\pi$
$367$	−11.2545	−	1.98448i	−0.587483	−	0.103589i	−0.459485	+	0.888185i	$0.651966\pi$
$368$		0			0
$369$	4.32501	−	0.327854i	0.225151	−	0.0170674i
$370$		0			0
$371$	−0.581825	−	0.488209i	−0.0302068	−	0.0253465i
$372$		0			0
$373$	2.86274	+	16.2354i	0.148227	+	0.840639i	0.964719	+	0.263282i	$0.0848048\pi$
$373$	2.86274	+	16.2354i	0.148227	+	0.840639i	−0.816492	+	0.577357i	$0.804084\pi$
$374$		0			0
$375$	−0.820664	+	16.5868i	−0.0423789	+	0.856537i
$376$		0			0
$377$			21.5622i			1.11051i
$378$		0			0
$379$		−	15.7412i		−	0.808572i	−0.914633	−	0.404286i	$-0.867520\pi$
$379$		−	15.7412i		−	0.808572i	0.914633	−	0.404286i	$-0.132480\pi$
$380$		0			0
$381$	7.72703	−	3.96561i	0.395868	−	0.203164i
$382$		0			0
$383$	5.45535	+	30.9388i	0.278756	+	1.58090i	0.726774	+	0.686877i	$0.241019\pi$
$383$	5.45535	+	30.9388i	0.278756	+	1.58090i	−0.448018	+	0.894024i	$0.647870\pi$
$384$		0			0
$385$	0.309474	+	0.259679i	0.0157722	+	0.0132345i
$386$		0			0
$387$	−0.0971683	−	0.380237i	−0.00493934	−	0.0193285i
$388$		0			0
$389$	10.4122	+	1.83595i	0.527918	+	0.0930862i	0.431253	−	0.902231i	$-0.358071\pi$
$389$	10.4122	+	1.83595i	0.527918	+	0.0930862i	0.0966646	+	0.995317i	$0.469183\pi$
$390$		0			0
$391$	−6.15855	+	16.9205i	−0.311451	+	0.855705i
$392$		0			0
$393$	0.550001	+	4.37366i	0.0277439	+	0.220622i
$394$		0			0
$395$	7.68863	+	13.3171i	0.386857	+	0.670056i
$396$		0			0
$397$	2.12129	−	3.67419i	0.106465	−	0.184402i	−0.807871	−	0.589359i	$-0.799380\pi$
$397$	2.12129	−	3.67419i	0.106465	−	0.184402i	0.914336	+	0.404957i	$0.132714\pi$
$398$		0			0
$399$	−0.159991	+	0.702358i	−0.00800957	+	0.0351619i
$400$		0			0
$401$	17.6057	+	20.9817i	0.879189	+	1.04778i	0.998491	+	0.0549188i	$0.0174900\pi$
$401$	17.6057	+	20.9817i	0.879189	+	1.04778i	−0.119302	+	0.992858i	$0.538066\pi$
$402$		0			0
$403$	7.85954	+	21.5939i	0.391512	+	1.07567i
$404$		0			0
$405$	5.08862	−	8.35943i	0.252856	−	0.415384i
$406$		0			0
$407$	11.0392	−	4.01794i	0.547193	−	0.199162i
$408$		0			0
$409$	0.397716	−	0.333723i	0.0196658	−	0.0165016i	−0.632902	−	0.774232i	$-0.718136\pi$
$409$	0.397716	−	0.333723i	0.0196658	−	0.0165016i	0.652568	+	0.757731i	$0.273692\pi$
$410$		0			0
$411$	17.0127	+	3.87535i	0.839176	+	0.191157i
$412$		0			0
$413$	−0.611786	−	0.353215i	−0.0301040	−	0.0173806i
$414$		0			0
$415$	3.78385	−	2.18461i	0.185742	−	0.107238i
$416$		0			0
$417$	−5.82185	+	0.732114i	−0.285097	+	0.0358518i
$418$		0			0
$419$	−11.8567	−	4.31547i	−0.579236	−	0.210825i	0.0357528	−	0.999361i	$-0.488617\pi$
$419$	−11.8567	−	4.31547i	−0.579236	−	0.210825i	−0.614988	+	0.788536i	$0.710839\pi$
$420$		0			0
$421$	−2.43676	+	13.8196i	−0.118760	+	0.673524i	0.866059	+	0.499942i	$0.166645\pi$
$421$	−2.43676	+	13.8196i	−0.118760	+	0.673524i	−0.984819	+	0.173582i	$0.944466\pi$
$422$		0			0
$423$	−4.50611	+	16.0686i	−0.219095	+	0.781284i
$424$		0			0
$425$	−10.7562	+	12.8188i	−0.521754	+	0.621802i
$426$		0			0
$427$	−0.462984	+	0.0816366i	−0.0224054	+	0.00395067i
$428$		0			0
$429$	22.9240	+	44.6676i	1.10678	+	2.15657i
$430$		0			0
$431$	−4.28837			−0.206564			−0.103282	−	0.994652i	$-0.532934\pi$
$431$	−4.28837			−0.206564			−0.103282	+	0.994652i	$0.532934\pi$
$432$		0			0
$433$	5.60769			0.269488			0.134744	−	0.990880i	$-0.456979\pi$
$433$	5.60769			0.269488			0.134744	+	0.990880i	$0.456979\pi$
$434$		0			0
$435$	−7.16934	−	0.354718i	−0.343744	−	0.0170074i
$436$		0			0
$437$	23.2031	−	4.09133i	1.10996	−	0.195715i
$438$		0			0
$439$	4.51341	−	5.37887i	0.215413	−	0.256719i	−0.647507	−	0.762059i	$-0.724188\pi$
$439$	4.51341	−	5.37887i	0.215413	−	0.256719i	0.862920	+	0.505340i	$0.168633\pi$
$440$		0			0
$441$	17.3278	−	11.8357i	0.825134	−	0.563606i
$442$		0			0
$443$	−5.26637	+	29.8670i	−0.250213	+	1.41903i	0.557856	+	0.829938i	$0.311624\pi$
$443$	−5.26637	+	29.8670i	−0.250213	+	1.41903i	−0.808069	+	0.589088i	$0.799487\pi$
$444$		0			0
$445$	−17.0547	−	6.20742i	−0.808472	−	0.294260i
$446$		0			0
$447$	−21.9444	−	28.9447i	−1.03793	−	1.36904i
$448$		0			0
$449$	24.7669	−	14.2991i	1.16882	−	0.674819i	0.215418	−	0.976522i	$-0.430889\pi$
$449$	24.7669	−	14.2991i	1.16882	−	0.674819i	0.953402	+	0.301703i	$0.0975552\pi$
$450$		0			0
$451$	−6.41528	−	3.70386i	−0.302084	−	0.174408i
$452$		0			0
$453$	−24.2196	+	26.1250i	−1.13793	+	1.22746i
$454$		0			0
$455$	−0.341723	+	0.286740i	−0.0160202	+	0.0134426i
$456$		0			0
$457$	−0.676715	+	0.246304i	−0.0316554	+	0.0115216i	−0.357799	−	0.933799i	$-0.616473\pi$
$457$	−0.676715	+	0.246304i	−0.0316554	+	0.0115216i	0.326144	+	0.945320i	$0.394251\pi$
$458$		0			0
$459$	21.1911	−	8.34846i	0.989117	−	0.389673i
$460$		0			0
$461$	0.907267	+	2.49269i	0.0422556	+	0.116096i	0.959026	−	0.283319i	$-0.0914354\pi$
$461$	0.907267	+	2.49269i	0.0422556	+	0.116096i	−0.916770	+	0.399415i	$0.869213\pi$
$462$		0			0
$463$	−6.24403	−	7.44135i	−0.290185	−	0.345829i	0.601181	−	0.799113i	$-0.294697\pi$
$463$	−6.24403	−	7.44135i	−0.290185	−	0.345829i	−0.891366	+	0.453284i	$0.850252\pi$
$464$		0			0
$465$	−7.30918	+	2.25802i	−0.338955	+	0.104713i
$466$		0			0
$467$	9.87482	−	17.1037i	0.456952	−	0.791464i	−0.541846	−	0.840478i	$-0.682274\pi$
$467$	9.87482	−	17.1037i	0.456952	−	0.791464i	0.998798	+	0.0490137i	$0.0156078\pi$
$468$		0			0
$469$	−0.242195	−	0.419494i	−0.0111835	−	0.0193704i
$470$		0			0
$471$	39.3855	+	16.5824i	1.81479	+	0.764078i
$472$		0			0
$473$	−0.229243	+	0.629840i	−0.0105406	+	0.0289601i
$474$		0			0
$475$	21.5631	+	3.80216i	0.989385	+	0.174455i
$476$		0			0
$477$	28.6310	−	12.9485i	1.31093	−	0.592869i
$478$		0			0
$479$	−15.2243	−	12.7747i	−0.695616	−	0.583691i	0.224906	−	0.974380i	$-0.427792\pi$
$479$	−15.2243	−	12.7747i	−0.695616	−	0.583691i	−0.920523	+	0.390689i	$0.872237\pi$
$480$		0			0
$481$	2.25254	+	12.7748i	0.102707	+	0.582480i
$482$		0			0
$483$	0.433523	+	0.279735i	0.0197260	+	0.0127284i
$484$		0			0
$485$		−	17.2134i		−	0.781621i
$486$		0			0
$487$		−	3.34369i		−	0.151517i	−0.997126	−	0.0757584i	$-0.975862\pi$
$487$		−	3.34369i		−	0.151517i	0.997126	−	0.0757584i	$-0.0241378\pi$
$488$		0			0
$489$	17.7829	+	11.4746i	0.804169	+	0.518897i
$490$		0			0
$491$	−6.46183	−	36.6468i	−0.291618	−	1.65385i	−0.680638	−	0.732620i	$-0.738297\pi$
$491$	−6.46183	−	36.6468i	−0.291618	−	1.65385i	0.389020	−	0.921229i	$-0.372814\pi$
$492$		0			0
$493$	−12.7975	−	10.7383i	−0.576368	−	0.483630i
$494$		0			0
$495$	−15.2289	+	6.88731i	−0.684489	+	0.309562i
$496$		0			0
$497$	−0.496634	−	0.0875700i	−0.0222771	−	0.00392805i
$498$		0			0
$499$	6.25828	−	17.1945i	0.280159	−	0.769731i	−0.717184	−	0.696884i	$-0.754569\pi$
$499$	6.25828	−	17.1945i	0.280159	−	0.769731i	0.997343	−	0.0728472i	$-0.0232085\pi$
$500$		0			0
$501$	−6.18956	−	2.60599i	−0.276529	−	0.116427i
$502$		0			0
$503$	19.9327	+	34.5244i	0.888754	+	1.53937i	0.841350	+	0.540491i	$0.181761\pi$
$503$	19.9327	+	34.5244i	0.888754	+	1.53937i	0.0474040	+	0.998876i	$0.484905\pi$
$504$		0			0
$505$	−4.57554	+	7.92506i	−0.203609	+	0.352661i
$506$		0			0
$507$	−31.4550	+	9.71740i	−1.39697	+	0.431565i
$508$		0			0
$509$	0.228853	+	0.272736i	0.0101437	+	0.0120888i	0.771092	−	0.636723i	$-0.219711\pi$
$509$	0.228853	+	0.272736i	0.0101437	+	0.0120888i	−0.760949	+	0.648812i	$0.775266\pi$
$510$		0			0
$511$	0.137461	+	0.377670i	0.00608091	+	0.0167072i
$512$		0			0
$513$	−23.3244	−	18.5515i	−1.02980	−	0.819067i
$514$		0			0
$515$	0.952659	−	0.346739i	0.0419792	−	0.0152792i
$516$		0			0
$517$	21.8336	−	18.3206i	0.960241	−	0.805738i
$518$		0			0
$519$	18.4239	−	19.8734i	0.808720	−	0.872344i
$520$		0			0
$521$	−23.3668	−	13.4908i	−1.02372	−	0.591044i	−0.108539	−	0.994092i	$-0.534617\pi$
$521$	−23.3668	−	13.4908i	−1.02372	−	0.591044i	−0.915179	+	0.403049i	$0.867951\pi$
$522$		0			0
$523$	−24.8958	+	14.3736i	−1.08862	+	0.628513i	−0.933208	−	0.359337i	$-0.883003\pi$
$523$	−24.8958	+	14.3736i	−1.08862	+	0.628513i	−0.155408	+	0.987850i	$0.549669\pi$
$524$		0			0
$525$	0.289672	+	0.382079i	0.0126423	+	0.0166753i
$526$		0			0
$527$	−16.7305	−	6.08939i	−0.728790	−	0.265258i
$528$		0			0
$529$	−1.06356	+	6.03172i	−0.0462415	+	0.262249i
$530$		0			0
$531$	24.1339	−	16.4846i	1.04732	−	0.715373i
$532$		0			0
$533$	5.25778	−	6.26598i	0.227740	−	0.271410i
$534$		0			0
$535$	12.0978	−	2.13318i	0.523035	−	0.0922253i
$536$		0			0
$537$	−20.8725	−	1.03271i	−0.900713	−	0.0445646i
$538$		0			0
$539$	−35.8382			−1.54366
$540$		0			0
$541$	−21.2500			−0.913608			−0.456804	−	0.889567i	$-0.651006\pi$
$541$	−21.2500			−0.913608			−0.456804	+	0.889567i	$0.651006\pi$
$542$		0			0
$543$	16.0131	+	31.2016i	0.687186	+	1.33899i
$544$		0			0
$545$	−8.36252	+	1.47454i	−0.358211	+	0.0631622i
$546$		0			0
$547$	−8.82124	+	10.5127i	−0.377169	+	0.449492i	−0.920919	−	0.389755i	$-0.872560\pi$
$547$	−8.82124	+	10.5127i	−0.377169	+	0.449492i	0.543750	+	0.839247i	$0.317004\pi$
$548$		0			0
$549$	5.25179	−	18.7277i	0.224141	−	0.799279i
$550$		0			0
$551$	−3.79584	+	21.5273i	−0.161708	+	0.917093i
$552$		0			0
$553$	0.963599	+	0.350721i	0.0409764	+	0.0149142i
$554$		0			0
$555$	−4.28461	+	0.538803i	−0.181872	+	0.0228709i
$556$		0			0
$557$	−29.8867	+	17.2551i	−1.26634	+	0.731121i	−0.974293	−	0.225283i	$-0.927669\pi$
$557$	−29.8867	+	17.2551i	−1.26634	+	0.731121i	−0.292046	+	0.956404i	$0.594336\pi$
$558$		0			0
$559$	−0.640952	−	0.370054i	−0.0271094	−	0.0156516i
$560$		0			0
$561$	−37.9274	−	8.63952i	−1.60129	−	0.364761i
$562$		0			0
$563$	−7.90869	+	6.63618i	−0.333312	+	0.279682i	−0.794048	−	0.607856i	$-0.792030\pi$
$563$	−7.90869	+	6.63618i	−0.333312	+	0.279682i	0.460736	+	0.887537i	$0.347586\pi$
$564$		0			0
$565$	8.40260	−	3.05830i	0.353500	−	0.128663i
$566$		0			0
$567$	−0.0983763	−	0.645156i	−0.00413142	−	0.0270940i
$568$		0			0
$569$	10.3576	+	28.4573i	0.434214	+	1.19299i	0.943202	+	0.332219i	$0.107797\pi$
$569$	10.3576	+	28.4573i	0.434214	+	1.19299i	−0.508989	+	0.860773i	$0.669981\pi$
$570$		0			0
$571$	−23.6804	−	28.2212i	−0.990992	−	1.18102i	−0.983475	−	0.181047i	$-0.942051\pi$
$571$	−23.6804	−	28.2212i	−0.990992	−	1.18102i	−0.00751760	−	0.999972i	$-0.502393\pi$
$572$		0			0
$573$	9.64751	−	42.3524i	0.403030	−	1.76930i
$574$		0			0
$575$	7.84125	−	13.5815i	0.327003	−	0.566386i
$576$		0			0
$577$	5.46070	+	9.45821i	0.227332	+	0.393750i	0.957016	−	0.290034i	$-0.0936665\pi$
$577$	5.46070	+	9.45821i	0.227332	+	0.393750i	−0.729685	+	0.683784i	$0.760333\pi$
$578$		0			0
$579$	−3.21044	−	25.5298i	−0.133421	−	1.06098i
$580$		0			0
$581$	0.0996522	−	0.273792i	0.00413427	−	0.0113588i
$582$		0			0
$583$	−52.8508	−	9.31902i	−2.18886	−	0.385954i
$584$		0			0
$585$	−4.56943	−	17.8810i	−0.188923	−	0.739288i
$586$		0			0
$587$	25.8588	+	21.6981i	1.06730	+	0.895575i	0.994806	−	0.101793i	$-0.0324580\pi$
$587$	25.8588	+	21.6981i	1.06730	+	0.895575i	0.0724993	+	0.997368i	$0.476902\pi$
$588$		0			0
$589$	4.04539	+	22.9425i	0.166687	+	0.945331i
$590$		0			0
$591$	25.6195	−	13.1483i	1.05385	−	0.540847i
$592$		0			0
$593$			1.65720i			0.0680529i	0.999421	+	0.0340265i	$0.0108330\pi$
$593$			1.65720i			0.0680529i	−0.999421	+	0.0340265i	$0.989167\pi$
$594$		0			0
$595$		−	0.345618i		−	0.0141690i
$596$		0			0
$597$	1.74845	−	35.3385i	0.0715591	−	1.44631i
$598$		0			0
$599$	2.97543	+	16.8745i	0.121573	+	0.689474i	0.983285	+	0.182076i	$0.0582816\pi$
$599$	2.97543	+	16.8745i	0.121573	+	0.689474i	−0.861712	+	0.507398i	$0.830607\pi$
$600$		0			0
$601$	−24.6454	−	20.6799i	−1.00531	−	0.843552i	−0.0175950	−	0.999845i	$-0.505601\pi$
$601$	−24.6454	−	20.6799i	−1.00531	−	0.843552i	−0.987711	+	0.156294i	$0.950045\pi$
$602$		0			0
$603$	19.9829	−	1.51479i	0.813767	−	0.0616870i
$604$		0			0
$605$	16.3320	+	2.87977i	0.663990	+	0.117079i
$606$		0			0
$607$	11.5382	−	31.7008i	0.468319	−	1.28670i	−0.450768	−	0.892641i	$-0.648850\pi$
$607$	11.5382	−	31.7008i	0.468319	−	1.28670i	0.919087	−	0.394055i	$-0.128928\pi$
$608$		0			0
$609$	−0.381444	+	0.289191i	−0.0154569	+	0.0117186i
$610$		0			0
$611$	15.7359	+	27.2554i	0.636606	+	1.10263i
$612$		0			0
$613$	−21.7069	+	37.5975i	−0.876734	+	1.51855i	−0.0218308	+	0.999762i	$0.506949\pi$
$613$	−21.7069	+	37.5975i	−0.876734	+	1.51855i	−0.854904	+	0.518787i	$0.826384\pi$
$614$		0			0
$615$	1.99692	+	1.85127i	0.0805235	+	0.0746505i
$616$		0			0
$617$	−4.65341	−	5.54572i	−0.187339	−	0.223262i	0.664198	−	0.747557i	$-0.268773\pi$
$617$	−4.65341	−	5.54572i	−0.187339	−	0.223262i	−0.851537	+	0.524295i	$0.824329\pi$
$618$		0			0
$619$	−8.37729	−	23.0164i	−0.336712	−	0.925108i	−0.986320	−	0.164839i	$-0.947289\pi$
$619$	−8.37729	−	23.0164i	−0.336712	−	0.925108i	0.649609	−	0.760269i	$-0.274933\pi$
$620$		0			0
$621$	−18.1996	+	11.1538i	−0.730324	+	0.447586i
$622$		0			0
$623$	−1.13730	+	0.413945i	−0.0455651	+	0.0165844i
$624$		0			0
$625$	6.63556	−	5.56789i	0.265422	−	0.222716i
$626$		0			0
$627$	15.0235	+	48.6308i	0.599982	+	1.94213i
$628$		0			0
$629$	−8.70380	−	5.02514i	−0.347043	−	0.200365i
$630$		0			0
$631$	−9.68103	+	5.58935i	−0.385396	+	0.222508i	−0.680163	−	0.733061i	$-0.738091\pi$
$631$	−9.68103	+	5.58935i	−0.385396	+	0.222508i	0.294768	+	0.955569i	$0.404758\pi$
$632$		0			0
$633$	12.0640	−	28.6535i	0.479499	−	1.13887i
$634$		0			0
$635$	5.12375	+	1.86489i	0.203330	+	0.0740060i
$636$		0			0
$637$	6.87175	−	38.9716i	0.272269	−	1.54411i
$638$		0			0
$639$	12.1645	−	16.9506i	0.481222	−	0.670554i
$640$		0			0
$641$	−7.72355	+	9.20457i	−0.305062	+	0.363559i	−0.896695	−	0.442649i	$-0.854039\pi$
$641$	−7.72355	+	9.20457i	−0.305062	+	0.363559i	0.591633	+	0.806207i	$0.298483\pi$
$642$		0			0
$643$	−7.71839	+	1.36096i	−0.304384	+	0.0536711i	−0.323754	−	0.946141i	$-0.604945\pi$
$643$	−7.71839	+	1.36096i	−0.304384	+	0.0536711i	0.0193702	+	0.999812i	$0.493834\pi$
$644$		0			0
$645$	0.133586	−	0.207026i	0.00525992	−	0.00815164i
$646$		0			0
$647$	−44.0555			−1.73200			−0.866000	−	0.500044i	$-0.833317\pi$
$647$	−44.0555			−1.73200			−0.866000	+	0.500044i	$0.833317\pi$
$648$		0			0
$649$	−49.9150			−1.95933
$650$		0			0
$651$	−0.276593	+	0.428654i	−0.0108405	+	0.0168003i
$652$		0			0
$653$	39.0561	−	6.88664i	1.52838	−	0.269495i	0.654661	−	0.755923i	$-0.272811\pi$
$653$	39.0561	−	6.88664i	1.52838	−	0.269495i	0.873721	+	0.486428i	$0.161700\pi$
$654$		0			0
$655$	−1.77886	+	2.11996i	−0.0695057	+	0.0828336i
$656$		0			0
$657$	−16.5466	−	1.64137i	−0.645544	−	0.0640360i
$658$		0			0
$659$	−1.66439	+	9.43924i	−0.0648355	+	0.367701i	0.935077	+	0.354446i	$0.115330\pi$
$659$	−1.66439	+	9.43924i	−0.0648355	+	0.367701i	−0.999912	+	0.0132549i	$0.995781\pi$
$660$		0			0
$661$	−10.0924	−	3.67332i	−0.392547	−	0.142876i	0.138203	−	0.990404i	$-0.455867\pi$
$661$	−10.0924	−	3.67332i	−0.392547	−	0.142876i	−0.530750	+	0.847528i	$0.678090\pi$
$662$		0			0
$663$	16.6672	−	39.5868i	0.647301	−	1.53742i
$664$		0			0
$665$	−0.391648	+	0.226118i	−0.0151874	+	0.00876847i
$666$		0			0
$667$	13.5589	+	7.82821i	0.525001	+	0.303110i
$668$		0			0
$669$	0.154220	+	0.499208i	0.00596250	+	0.0193005i
$670$		0			0
$671$	−25.4467	+	21.3523i	−0.982357	+	0.824296i
$672$		0			0
$673$	−0.534095	+	0.194395i	−0.0205878	+	0.00749336i	−0.352294	−	0.935890i	$-0.614598\pi$
$673$	−0.534095	+	0.194395i	−0.0205878	+	0.00749336i	0.331706	+	0.943383i	$0.392376\pi$
$674$		0			0
$675$	−19.4384	+	3.95566i	−0.748186	+	0.152254i
$676$		0			0
$677$	2.40412	+	6.60528i	0.0923980	+	0.253861i	0.977279	−	0.211955i	$-0.0679830\pi$
$677$	2.40412	+	6.60528i	0.0923980	+	0.253861i	−0.884881	+	0.465816i	$0.845761\pi$
$678$		0			0
$679$	−0.737846	−	0.879331i	−0.0283159	−	0.0337456i
$680$		0			0
$681$	25.9859	+	24.0906i	0.995781	+	0.923153i
$682$		0			0
$683$	−24.1061	+	41.7529i	−0.922393	+	1.59763i	−0.126693	+	0.991942i	$0.540436\pi$
$683$	−24.1061	+	41.7529i	−0.922393	+	1.59763i	−0.795701	+	0.605690i	$0.792897\pi$
$684$		0			0
$685$	5.47709	+	9.48660i	0.209269	+	0.362464i
$686$		0			0
$687$	−9.28220	+	7.03728i	−0.354138	+	0.268489i
$688$		0			0
$689$	20.2676	−	55.6847i	0.772134	−	2.12142i
$690$		0			0
$691$	−21.0430	−	3.71046i	−0.800515	−	0.141152i	−0.241599	−	0.970376i	$-0.577672\pi$
$691$	−21.0430	−	3.71046i	−0.800515	−	0.141152i	−0.558917	+	0.829224i	$0.688783\pi$
$692$		0			0
$693$	−0.482733	+	1.00461i	−0.0183375	+	0.0381621i
$694$		0			0
$695$	−2.82191	−	2.36786i	−0.107041	−	0.0898182i
$696$		0			0
$697$	1.10048	+	6.24113i	0.0416836	+	0.236400i
$698$		0			0
$699$	−0.495119	+	10.0070i	−0.0187271	+	0.378501i
$700$		0			0
$701$		−	12.4157i		−	0.468935i	−0.972124	−	0.234468i	$-0.924665\pi$
$701$		−	12.4157i		−	0.468935i	0.972124	−	0.234468i	$-0.0753347\pi$
$702$		0			0
$703$			13.1506i			0.495985i
$704$		0			0
$705$	−9.32117	+	4.78375i	−0.351056	+	0.180166i
$706$		0			0
$707$	0.105968	+	0.600973i	0.00398533	+	0.0226019i
$708$		0			0
$709$	−0.976912	−	0.819726i	−0.0366887	−	0.0307855i	0.624259	−	0.781218i	$-0.285401\pi$
$709$	−0.976912	−	0.819726i	−0.0366887	−	0.0307855i	−0.660948	+	0.750432i	$0.729845\pi$
$710$		0			0
$711$	−30.3449	+	29.6486i	−1.13802	+	1.11191i
$712$		0			0
$713$	16.4322	+	2.89745i	0.615392	+	0.108510i
$714$		0			0
$715$	−10.7804	+	29.6188i	−0.403163	+	1.10768i
$716$		0			0
$717$	−0.543449	−	4.32157i	−0.0202955	−	0.161392i
$718$		0			0
$719$	14.5684	+	25.2332i	0.543310	+	0.941041i	0.998711	+	0.0507546i	$0.0161627\pi$
$719$	14.5684	+	25.2332i	0.543310	+	0.941041i	−0.455401	+	0.890287i	$0.650504\pi$
$720$		0			0
$721$	0.0338028	−	0.0585482i	0.00125888	−	0.00218045i
$722$		0			0
$723$	−0.350368	+	1.53811i	−0.0130303	+	0.0572030i
$724$		0			0
$725$	9.35246	+	11.1458i	0.347342	+	0.413946i
$726$		0			0
$727$	−2.73821	−	7.52317i	−0.101555	−	0.279019i	0.878502	−	0.477739i	$-0.158544\pi$
$727$	−2.73821	−	7.52317i	−0.101555	−	0.279019i	−0.980056	+	0.198720i	$0.936321\pi$
$728$		0			0
$729$	25.8209	+	7.89182i	0.956330	+	0.292290i
$730$		0			0
$731$	0.538836	−	0.196120i	0.0199296	−	0.00725378i
$732$		0			0
$733$	2.12619	−	1.78409i	0.0785326	−	0.0658967i	−0.602676	−	0.797986i	$-0.705899\pi$
$733$	2.12619	−	1.78409i	0.0785326	−	0.0658967i	0.681209	+	0.732089i	$0.261455\pi$
$734$		0			0
$735$	12.8449	+	2.92595i	0.473790	+	0.107925i
$736$		0			0
$737$	−29.6406	−	17.1130i	−1.09183	−	0.630367i
$738$		0			0
$739$	22.0458	−	12.7281i	0.810967	−	0.468212i	−0.0363245	−	0.999340i	$-0.511565\pi$
$739$	22.0458	−	12.7281i	0.810967	−	0.468212i	0.847292	+	0.531128i	$0.178232\pi$
$740$		0			0
$741$	−55.7634	+	7.01240i	−2.04852	+	0.257607i
$742$		0			0
$743$	−2.02834	−	0.738257i	−0.0744127	−	0.0270840i	0.304546	−	0.952498i	$-0.401495\pi$
$743$	−2.02834	−	0.738257i	−0.0744127	−	0.0270840i	−0.378958	+	0.925414i	$0.623718\pi$
$744$		0			0
$745$	3.95979	−	22.4571i	0.145075	−	0.822764i
$746$		0			0
$747$	8.42420	+	8.62206i	0.308225	+	0.315465i
$748$		0			0
$749$	0.526569	−	0.627541i	0.0192404	−	0.0229298i
$750$		0			0
$751$	3.26718	−	0.576092i	0.119221	−	0.0210219i	−0.113719	−	0.993513i	$-0.536276\pi$
$751$	3.26718	−	0.576092i	0.119221	−	0.0210219i	0.232940	+	0.972491i	$0.425165\pi$
$752$		0			0
$753$	15.5875	+	30.3724i	0.568040	+	1.10683i
$754$		0			0
$755$	−22.3650			−0.813947
$756$		0			0
$757$	−21.4846			−0.780869			−0.390435	−	0.920631i	$-0.627675\pi$
$757$	−21.4846			−0.780869			−0.390435	+	0.920631i	$0.627675\pi$
$758$		0			0
$759$	36.4108	+	1.80150i	1.32163	+	0.0653901i
$760$		0			0
$761$	−6.57062	+	1.15858i	−0.238185	+	0.0419984i	−0.291466	−	0.956581i	$-0.594143\pi$
$761$	−6.57062	+	1.15858i	−0.238185	+	0.0419984i	0.0532815	+	0.998580i	$0.483032\pi$
$762$		0			0
$763$	−0.363986	+	0.433781i	−0.0131772	+	0.0157039i
$764$		0			0
$765$	12.8883	+	6.19301i	0.465976	+	0.223909i
$766$		0			0
$767$	9.57087	−	54.2791i	0.345584	−	1.95991i
$768$		0			0
$769$	37.8560	+	13.7784i	1.36512	+	0.496863i	0.917634	−	0.397427i	$-0.130097\pi$
$769$	37.8560	+	13.7784i	1.36512	+	0.496863i	0.447487	+	0.894290i	$0.352319\pi$
$770$		0			0
$771$	11.7723	+	15.5278i	0.423970	+	0.559219i
$772$		0			0
$773$	15.8074	−	9.12640i	0.568552	−	0.328254i	−0.188019	−	0.982165i	$-0.560207\pi$
$773$	15.8074	−	9.12640i	0.568552	−	0.328254i	0.756571	+	0.653912i	$0.226873\pi$
$774$		0			0
$775$	13.4289	+	7.75320i	0.482382	+	0.278503i
$776$		0			0
$777$	−0.195780	+	0.211183i	−0.00702357	+	0.00757613i
$778$		0			0
$779$	6.35234	−	5.33025i	0.227596	−	0.190976i
$780$		0			0
$781$	−33.4837	+	12.1871i	−1.19814	+	0.436087i
$782$		0			0
$783$	−3.94909	−	19.4061i	−0.141129	−	0.693518i
$784$		0			0
$785$	9.17584	+	25.2104i	0.327500	+	0.899798i
$786$		0			0
$787$	−12.4720	−	14.8636i	−0.444580	−	0.529830i	0.496490	−	0.868043i	$-0.334622\pi$
$787$	−12.4720	−	14.8636i	−0.444580	−	0.529830i	−0.941070	+	0.338213i	$0.890178\pi$
$788$		0			0
$789$	17.4608	−	5.39418i	0.621622	−	0.192038i
$790$		0			0
$791$	0.298146	−	0.516404i	0.0106009	−	0.0183612i
$792$		0			0
$793$	−18.3399	−	31.7656i	−0.651269	−	1.12803i
$794$		0			0
$795$	18.1815	+	7.65495i	0.644832	+	0.271493i
$796$		0			0
$797$	−3.34972	+	9.20329i	−0.118653	+	0.325997i	−0.984774	−	0.173837i	$-0.944383\pi$
$797$	−3.34972	+	9.20329i	−0.118653	+	0.325997i	0.866121	+	0.499834i	$0.166606\pi$
$798$		0			0
$799$	−24.0132	−	4.23417i	−0.849525	−	0.149794i
$800$		0			0
$801$	4.94277	−	49.8279i	0.174644	−	1.76058i
$802$		0			0
$803$	21.7542	+	18.2539i	0.767689	+	0.644167i
$804$		0			0
$805$	0.0562458	+	0.318986i	0.00198240	+	0.0112428i
$806$		0			0
$807$	−42.1493	−	27.1973i	−1.48373	−	0.957389i
$808$		0			0
$809$			25.9021i			0.910671i	0.890320	+	0.455336i	$0.150481\pi$
$809$			25.9021i			0.910671i	−0.890320	+	0.455336i	$0.849519\pi$
$810$		0			0
$811$		−	28.6572i		−	1.00629i	−0.864202	−	0.503145i	$-0.832176\pi$
$811$		−	28.6572i		−	1.00629i	0.864202	−	0.503145i	$-0.167824\pi$
$812$		0			0
$813$	−43.0295	−	27.7652i	−1.50911	−	0.973767i
$814$		0			0
$815$	2.30717	+	13.0846i	0.0808166	+	0.458334i
$816$		0			0
$817$	−0.574769	−	0.482288i	−0.0201086	−	0.0168731i
$818$		0			0
$819$	−0.999887	−	0.717566i	−0.0349389	−	0.0250738i
$820$		0			0
$821$	−28.2292	−	4.97757i	−0.985205	−	0.173718i	−0.342239	−	0.939613i	$-0.611185\pi$
$821$	−28.2292	−	4.97757i	−0.985205	−	0.173718i	−0.642966	+	0.765895i	$0.722296\pi$
$822$		0			0
$823$	7.22536	−	19.8515i	0.251860	−	0.691980i	−0.747748	−	0.663983i	$-0.768865\pi$
$823$	7.22536	−	19.8515i	0.251860	−	0.691980i	0.999608	−	0.0279972i	$-0.00891296\pi$
$824$		0			0
$825$	31.2240	+	13.1462i	1.08708	+	0.457693i
$826$		0			0
$827$	9.73569	+	16.8627i	0.338543	+	0.586374i	0.984159	−	0.177288i	$-0.0567325\pi$
$827$	9.73569	+	16.8627i	0.338543	+	0.586374i	−0.645616	+	0.763662i	$0.723399\pi$
$828$		0			0
$829$	−20.1430	+	34.8887i	−0.699595	+	1.21173i	0.269012	+	0.963137i	$0.413303\pi$
$829$	−20.1430	+	34.8887i	−0.699595	+	1.21173i	−0.968607	+	0.248597i	$0.920031\pi$
$830$		0			0
$831$	3.33346	−	1.02981i	0.115636	−	0.0357236i
$832$		0			0
$833$	19.7079	+	23.4870i	0.682839	+	0.813776i
$834$		0			0
$835$	−1.44201	−	3.96190i	−0.0499030	−	0.137107i
$836$		0			0
$837$	−11.0285	−	17.9952i	−0.381202	−	0.622005i
$838$		0			0
$839$	−23.3185	+	8.48725i	−0.805045	+	0.293012i	−0.711575	−	0.702610i	$-0.752018\pi$
$839$	−23.3185	+	8.48725i	−0.805045	+	0.293012i	−0.0934694	+	0.995622i	$0.529796\pi$
$840$		0			0
$841$	11.0880	−	9.30393i	0.382345	−	0.320825i
$842$		0			0
$843$	4.85540	−	5.23739i	0.167229	−	0.180385i
$844$		0			0
$845$	−17.8993	−	10.3342i	−0.615754	−	0.355506i
$846$		0			0
$847$	0.957744	−	0.552954i	0.0329085	−	0.0189997i
$848$		0			0
$849$	−6.76351	−	8.92110i	−0.232123	−	0.306171i
$850$		0			0
$851$	8.85089	+	3.22146i	0.303405	+	0.110430i
$852$		0			0
$853$	−4.33230	+	24.5697i	−0.148335	+	0.841250i	0.816294	+	0.577637i	$0.196025\pi$
$853$	−4.33230	+	24.5697i	−0.148335	+	0.841250i	−0.964629	+	0.263613i	$0.915086\pi$
$854$		0			0
$855$	−1.41424	−	18.6564i	−0.0483659	−	0.638037i
$856$		0			0
$857$	−20.1320	+	23.9924i	−0.687696	+	0.819564i	−0.991075	−	0.133306i	$-0.957441\pi$
$857$	−20.1320	+	23.9924i	−0.687696	+	0.819564i	0.303379	+	0.952870i	$0.401885\pi$
$858$		0			0
$859$	−42.8494	+	7.55550i	−1.46200	+	0.257790i	−0.847361	−	0.531017i	$-0.821810\pi$
$859$	−42.8494	+	7.55550i	−1.46200	+	0.257790i	−0.614640	+	0.788808i	$0.710699\pi$
$860$		0			0
$861$	0.181365	+	0.00897338i	0.00618089	+	0.000305812i
$862$		0			0
$863$	16.1195			0.548714			0.274357	−	0.961628i	$-0.411535\pi$
$863$	16.1195			0.548714			0.274357	+	0.961628i	$0.411535\pi$
$864$		0			0
$865$	17.0132			0.578465
$866$		0			0
$867$	1.75042	+	3.41072i	0.0594475	+	0.115834i
$868$		0			0
$869$	71.3549	−	12.5818i	2.42055	−	0.426808i
$870$		0			0
$871$	24.2926	−	28.9508i	0.823125	−	0.980962i
$872$		0			0
$873$	46.0118	−	11.7582i	1.55727	−	0.397954i
$874$		0			0
$875$	−0.120730	+	0.684695i	−0.00408142	+	0.0231469i
$876$		0			0
$877$	52.9396	+	19.2684i	1.78764	+	0.650649i	0.999376	+	0.0353144i	$0.0112432\pi$
$877$	52.9396	+	19.2684i	1.78764	+	0.650649i	0.788266	+	0.615334i	$0.210979\pi$
$878$		0			0
$879$	53.0104	−	6.66621i	1.78800	−	0.224846i
$880$		0			0
$881$	20.5381	−	11.8577i	0.691946	−	0.399495i	−0.112394	−	0.993664i	$-0.535852\pi$
$881$	20.5381	−	11.8577i	0.691946	−	0.399495i	0.804341	+	0.594168i	$0.202519\pi$
$882$		0			0
$883$	11.3285	+	6.54053i	0.381235	+	0.220106i	0.678356	−	0.734734i	$-0.262693\pi$
$883$	11.3285	+	6.54053i	0.381235	+	0.220106i	−0.297120	+	0.954840i	$0.596026\pi$
$884$		0			0
$885$	17.8901	+	4.07521i	0.601370	+	0.136987i
$886$		0			0
$887$	25.2454	−	21.1834i	0.847659	−	0.711270i	−0.111614	−	0.993752i	$-0.535602\pi$
$887$	25.2454	−	21.1834i	0.847659	−	0.711270i	0.959273	+	0.282482i	$0.0911576\pi$
$888$		0			0
$889$	0.341680	−	0.124361i	0.0114596	−	0.00417094i
$890$		0			0
$891$	−28.8125	−	36.0026i	−0.965257	−	1.20613i
$892$		0			0
$893$	10.9123	+	29.9814i	0.365168	+	1.00329i
$894$		0			0
$895$	−8.43321	−	10.0503i	−0.281891	−	0.335945i
$896$		0			0
$897$	−8.94052	+	39.2488i	−0.298515	+	1.31048i
$898$		0			0
$899$	−7.74030	+	13.4066i	−0.258154	+	0.447135i
$900$		0			0
$901$	22.9560	+	39.7610i	0.764776	+	1.32463i
$902$		0			0
$903$	−0.00205000	−	0.0163018i	−6.82198e−5	−	0.000542491i
$904$		0			0
$905$	−7.53040	+	20.6896i	−0.250319	+	0.687746i
$906$		0			0
$907$	38.1995	+	6.73561i	1.26839	+	0.223652i	0.767045	−	0.641593i	$-0.221726\pi$
$907$	38.1995	+	6.73561i	1.26839	+	0.223652i	0.501349	+	0.865245i	$0.332837\pi$
$908$		0			0
$909$	−24.3093	−	6.81704i	−0.806290	−	0.226107i
$910$		0			0
$911$	21.4658	+	18.0119i	0.711192	+	0.596761i	0.924933	−	0.380129i	$-0.124120\pi$
$911$	21.4658	+	18.0119i	0.711192	+	0.596761i	−0.213741	+	0.976890i	$0.568565\pi$
$912$		0			0
$913$	−3.57493	−	20.2744i	−0.118313	−	0.670986i
$914$		0			0
$915$	10.8636	−	5.57537i	0.359141	−	0.184316i
$916$		0			0
$917$			0.184546i			0.00609425i
$918$		0			0
$919$			1.63307i			0.0538701i	0.999637	+	0.0269351i	$0.00857473\pi$
$919$			1.63307i			0.0538701i	−0.999637	+	0.0269351i	$0.991425\pi$
$920$		0			0
$921$	−2.72154	+	55.0061i	−0.0896776	+	1.81251i
$922$		0			0
$923$	−6.83231	−	38.7480i	−0.224888	−	1.27540i
$924$		0			0
$925$	6.70535	+	5.62645i	0.220470	+	0.184997i
$926$		0			0
$927$	1.57759	+	2.30963i	0.0518148	+	0.0758581i
$928$		0			0
$929$	−13.8733	−	2.44623i	−0.455167	−	0.0802582i	−0.0586356	−	0.998279i	$-0.518675\pi$
$929$	−13.8733	−	2.44623i	−0.455167	−	0.0802582i	−0.396531	+	0.918021i	$0.629786\pi$
$930$		0			0
$931$	13.7212	−	37.6988i	0.449695	−	1.23553i
$932$		0			0
$933$	−19.9096	+	15.0944i	−0.651812	+	0.494169i
$934$		0			0
$935$	−12.2104	−	21.1490i	−0.399322	−	0.691645i
$936$		0			0
$937$	9.05418	−	15.6823i	0.295787	−	0.512318i	−0.679381	−	0.733786i	$-0.737751\pi$
$937$	9.05418	−	15.6823i	0.295787	−	0.512318i	0.975168	+	0.221468i	$0.0710847\pi$
$938$		0			0
$939$	3.75660	+	3.48261i	0.122592	+	0.113651i
$940$		0			0
$941$	5.18751	+	6.18223i	0.169108	+	0.201535i	0.843942	−	0.536435i	$-0.180229\pi$
$941$	5.18751	+	6.18223i	0.169108	+	0.201535i	−0.674834	+	0.737970i	$0.735785\pi$
$942$		0			0
$943$	−2.03136	−	5.58111i	−0.0661501	−	0.181746i
$944$		0			0
$945$	0.255037	−	0.320653i	0.00829635	−	0.0104309i
$946$		0			0
$947$	3.27726	−	1.19283i	0.106497	−	0.0387617i	−0.288222	−	0.957564i	$-0.593064\pi$
$947$	3.27726	−	1.19283i	0.106497	−	0.0387617i	0.394719	+	0.918802i	$0.370842\pi$
$948$		0			0
$949$	−24.0211	+	20.1561i	−0.779758	+	0.654295i
$950$		0			0
$951$	−11.8814	−	38.4600i	−0.385282	−	1.24715i
$952$		0			0
$953$	−44.9114	−	25.9296i	−1.45482	−	0.839942i	−0.456073	−	0.889942i	$-0.650744\pi$
$953$	−44.9114	−	25.9296i	−1.45482	−	0.839942i	−0.998749	+	0.0500006i	$0.984078\pi$
$954$		0			0
$955$	23.6165	−	13.6350i	0.764210	−	0.441217i
$956$		0			0
$957$	−13.1244	+	31.1721i	−0.424251	+	1.00765i
$958$		0			0
$959$	0.686431	+	0.249841i	0.0221660	+	0.00806777i
$960$		0			0
$961$	2.51819	−	14.2813i	0.0812318	−	0.460688i
$962$		0			0
$963$	13.9659	+	30.8807i	0.450044	+	0.995116i
$964$		0			0
$965$	10.3835	−	12.3745i	0.334256	−	0.398350i
$966$		0			0
$967$	51.8699	−	9.14607i	1.66802	−	0.294118i	0.741669	−	0.670766i	$-0.234035\pi$
$967$	51.8699	−	9.14607i	1.66802	−	0.294118i	0.926356	+	0.376649i	$0.122924\pi$
$968$		0			0
$969$	23.6091	−	36.5886i	0.758434	−	1.17539i
$970$		0			0
$971$	−32.1045			−1.03028			−0.515142	−	0.857105i	$-0.672261\pi$
$971$	−32.1045			−1.03028			−0.515142	+	0.857105i	$0.672261\pi$
$972$		0			0
$973$	−0.245652			−0.00787525
$974$		0			0
$975$	−20.2826	+	31.4333i	−0.649564	+	1.00667i
$976$		0			0
$977$	−23.4436	+	4.13374i	−0.750028	+	0.132250i	−0.535579	−	0.844485i	$-0.679907\pi$
$977$	−23.4436	+	4.13374i	−0.750028	+	0.132250i	−0.214449	+	0.976735i	$0.568796\pi$
$978$		0			0
$979$	−54.9693	+	65.5099i	−1.75683	+	2.09370i
$980$		0			0
$981$	−9.65377	−	21.3460i	−0.308221	−	0.681524i
$982$		0			0
$983$	0.141641	−	0.803287i	0.00451765	−	0.0256209i	−0.982466	−	0.186444i	$-0.940304\pi$
$983$	0.141641	−	0.803287i	0.00451765	−	0.0256209i	0.986983	+	0.160823i	$0.0514148\pi$
$984$		0			0
$985$	16.9881	+	6.18318i	0.541287	+	0.197012i
$986$		0			0
$987$	−0.271110	+	0.643921i	−0.00862952	+	0.0204962i
$988$		0			0
$989$	−0.465398	+	0.268698i	−0.0147988	+	0.00854410i
$990$		0			0
$991$	−21.2917	−	12.2928i	−0.676353	−	0.390492i	0.122127	−	0.992515i	$-0.461029\pi$
$991$	−21.2917	−	12.2928i	−0.676353	−	0.390492i	−0.798479	+	0.602022i	$0.794362\pi$
$992$		0			0
$993$	3.77465	+	12.2185i	0.119785	+	0.387741i
$994$		0			0
$995$	17.0159	−	14.2780i	0.539440	−	0.452644i
$996$		0			0
$997$	28.0212	−	10.1989i	0.887440	−	0.323002i	0.142232	−	0.989833i	$-0.454572\pi$
$997$	28.0212	−	10.1989i	0.887440	−	0.323002i	0.745208	+	0.666832i	$0.232350\pi$
$998$		0			0
$999$	−4.36698	−	11.0848i	−0.138165	−	0.350708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.47.3	✓	36
4.3	odd	2		432.2.be.c.47.4	yes	36
27.23	odd	18		432.2.be.c.239.4	yes	36
108.23	even	18	inner	432.2.be.b.239.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.47.3	✓	36	1.1	even	1	trivial
432.2.be.b.239.3	yes	36	108.23	even	18	inner
432.2.be.c.47.4	yes	36	4.3	odd	2
432.2.be.c.239.4	yes	36	27.23	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939092 + 1.45537i) q^{3} +(-1.07086 + 0.188822i) q^{5} +(-0.0466102 + 0.0555478i) q^{7} +(-1.23621 - 2.73346i) q^{9} +O(q^{10})\)	\(q+(-0.939092 + 1.45537i) q^{3} +(-1.07086 + 0.188822i) q^{5} +(-0.0466102 + 0.0555478i) q^{7} +(-1.23621 - 2.73346i) q^{9} +(-0.889704 + 5.04576i) q^{11} +(-5.31632 - 1.93498i) q^{13} +(0.730832 - 1.73582i) q^{15} +(3.79605 - 2.19165i) q^{17} +(-4.96707 - 2.86774i) q^{19} +(-0.0370715 - 0.120000i) q^{21} +(-3.14687 + 2.64054i) q^{23} +(-3.58737 + 1.30570i) q^{25} +(5.13911 + 0.767820i) q^{27} +(-1.30353 - 3.58141i) q^{29} +(-2.61088 - 3.11153i) q^{31} +(-6.50794 - 6.03328i) q^{33} +(0.0394244 - 0.0682850i) q^{35} +(-1.14643 - 1.98567i) q^{37} +(7.80863 - 5.92009i) q^{39} +(-0.494495 + 1.35861i) q^{41} +(0.128831 + 0.0227164i) q^{43} +(1.83995 + 2.69373i) q^{45} +(-4.26138 - 3.57572i) q^{47} +(1.21462 + 6.88848i) q^{49} +(-0.375176 + 7.58283i) q^{51} +10.4743i q^{53} -5.57130i q^{55} +(8.83817 - 4.53586i) q^{57} +(1.69171 + 9.59417i) q^{59} +(4.96656 + 4.16744i) q^{61} +(0.209458 + 0.0587379i) q^{63} +(6.05841 + 1.06826i) q^{65} +(-2.28472 + 6.27722i) q^{67} +(-0.887762 - 7.05957i) q^{69} +(3.47730 + 6.02286i) q^{71} +(2.77130 - 4.80004i) q^{73} +(1.46860 - 6.44713i) q^{75} +(-0.238812 - 0.284605i) q^{77} +(-4.83670 - 13.2887i) q^{79} +(-5.94356 + 6.75826i) q^{81} +(-3.77579 + 1.37428i) q^{83} +(-3.65122 + 3.06373i) q^{85} +(6.43641 + 1.46616i) q^{87} +(14.4547 + 8.34541i) q^{89} +(0.355279 - 0.205120i) q^{91} +(6.98029 - 0.877792i) q^{93} +(5.86054 + 2.13306i) q^{95} +(-2.74888 + 15.5897i) q^{97} +(14.8922 - 3.80566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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