LMFDB - Embedded newform 432.2.be.c.47.4

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			47.4
Character	$\chi$	$=$	432.47
Dual form			432.2.be.c.239.4

$q$-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	−0.757164	−	0.653225i	$-0.773416\pi$
$7$	0.0466102	−	0.0555478i	0.0176170	−	0.0209951i	0.774781	+	0.632230i	$0.217860\pi$
$8$		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	$-0.663495\pi$
$11$	0.889704	−	5.04576i	0.268256	−	1.52135i	0.759601	−	0.650389i	$-0.225394\pi$
$12$		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	0.946313	−	0.323252i	$-0.104776\pi$
$19$	4.96707	+	2.86774i	1.13952	+	0.657905i	0.193212	+	0.981157i	$0.438110\pi$
$20$		0			0
$21$	−0.0370715	−	0.120000i	−0.00808966	−	0.0261861i
$22$		0			0
$23$	3.14687	−	2.64054i	0.656168	−	0.550590i	−0.252768	−	0.967527i	$-0.581341\pi$
$23$	3.14687	−	2.64054i	0.656168	−	0.550590i	0.908935	+	0.416937i	$0.136896\pi$
$24$		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	0.947729	−	0.319076i	$-0.103373\pi$
$31$	2.61088	+	3.11153i	0.468929	+	0.558847i	−0.478800	+	0.877924i	$0.658928\pi$
$32$		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	0.163816	−	0.986491i	$-0.447620\pi$
$43$	−0.128831	−	0.0227164i	−0.0196466	−	0.00346422i	−0.183463	+	0.983027i	$0.558731\pi$
$44$		0			0
$45$	1.83995	+	2.69373i	0.274283	+	0.401557i
$46$		0			0
$47$	4.26138	+	3.57572i	0.621586	+	0.521573i	0.898302	−	0.439379i	$-0.144802\pi$
$47$	4.26138	+	3.57572i	0.621586	+	0.521573i	−0.276716	+	0.960952i	$0.589246\pi$
$48$		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	$-0.836901\pi$
$59$	−1.69171	−	9.59417i	−0.220242	−	1.24905i	0.651333	−	0.758792i	$-0.274210\pi$
$60$		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	$-0.755097\pi$
$67$	2.28472	−	6.27722i	0.279123	−	0.766885i	0.997463	−	0.0711921i	$-0.0226803\pi$
$68$		0			0
$69$	−0.887762	−	7.05957i	−0.106874	−	0.849873i
$70$		0			0
$71$	−3.47730	−	6.02286i	−0.412680	−	0.714782i	0.582502	−	0.812829i	$-0.302074\pi$
$71$	−3.47730	−	6.02286i	−0.412680	−	0.714782i	−0.995182	+	0.0980471i	$0.968740\pi$
$72$		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	$0.181694\pi$
$79$	4.83670	+	13.2887i	0.544171	+	1.49510i	−0.297294	+	0.954786i	$0.596084\pi$
$80$		0			0
$81$	−5.94356	+	6.75826i	−0.660396	+	0.750918i
$82$		0			0
$83$	3.77579	−	1.37428i	0.414447	−	0.150846i	−0.126377	−	0.991982i	$-0.540335\pi$
$83$	3.77579	−	1.37428i	0.414447	−	0.150846i	0.540824	+	0.841136i	$0.318113\pi$
$84$		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	−0.128230	−	0.991744i	$-0.540930\pi$
$103$	0.918166	−	0.161897i	0.0904696	−	0.0159522i	0.218700	+	0.975792i	$0.429818\pi$
$104$		0			0
$105$	0.0623569	+	0.121503i	0.00608541	+	0.0118575i
$106$		0			0
$107$	11.2973			1.09215			0.546076	−	0.837736i	$-0.316121\pi$
$107$	11.2973			1.09215			0.546076	+	0.837736i	$0.316121\pi$
$108$		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	0.680141	−	0.733081i	$-0.261919\pi$
$127$	4.34261	+	2.50721i	0.385344	+	0.222479i	−0.294797	+	0.955560i	$0.595252\pi$
$128$		0			0
$129$	−0.154045	+	0.166164i	−0.0135629	+	0.0146300i
$130$		0			0
$131$	−1.94960	+	1.63591i	−0.170337	+	0.142930i	−0.723971	−	0.689830i	$-0.757685\pi$
$131$	−1.94960	+	1.63591i	−0.170337	+	0.142930i	0.553634	+	0.832760i	$0.313241\pi$
$132$		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	0.665747	−	0.746178i	$-0.268113\pi$
$139$	−2.17758	−	2.59514i	−0.184700	−	0.220117i	−0.850447	+	0.526060i	$0.823669\pi$
$140$		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	−0.729128	−	0.684377i	$-0.760074\pi$
$151$	−20.2553	−	3.57156i	−1.64835	−	0.290649i	−0.919227	+	0.393728i	$0.871185\pi$
$152$		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	$0.158828\pi$
$163$			12.2188i			0.957048i	−0.878074	+	0.478524i	$0.841172\pi$
$164$		0			0
$165$	8.10832	+	5.23197i	0.631231	+	0.407308i
$166$		0			0
$167$	−0.673297	−	3.81846i	−0.0521013	−	0.295481i	0.947612	−	0.319423i	$-0.103489\pi$
$167$	−0.673297	−	3.81846i	−0.0521013	−	0.295481i	−0.999713	+	0.0239425i	$0.992378\pi$
$168$		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	0.547535	−	0.836783i	$-0.315566\pi$
$179$	−6.03273	−	10.4490i	−0.450907	−	0.780994i	−0.998443	+	0.0557882i	$0.982233\pi$
$180$		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	0.708786	−	0.705424i	$-0.249243\pi$
$191$	23.5661	−	8.57737i	1.70518	−	0.620636i	0.996399	+	0.0847874i	$0.0270211\pi$
$192$		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	0.282157	−	0.959368i	$-0.408950\pi$
$199$	17.6909	−	10.2138i	1.25407	−	0.724039i	0.971916	+	0.235329i	$0.0756167\pi$
$200$		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	0.471924	−	0.881639i	$-0.343559\pi$
$211$	17.6769	−	3.11691i	1.21693	−	0.214577i	0.745002	+	0.667062i	$0.232448\pi$
$212$		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	−0.772498	−	0.635018i	$-0.780993\pi$
$223$	−0.193902	+	0.231084i	−0.0129846	+	0.0154745i	0.759513	+	0.650492i	$0.225437\pi$
$224$		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	$0.293112\pi$
$227$	−3.55254	+	20.1475i	−0.235790	+	1.33723i	−0.840943	+	0.541124i	$0.817999\pi$
$228$		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	−0.578355	−	0.815785i	$-0.696305\pi$
$239$	1.92638	−	1.61642i	0.124607	−	0.104558i	0.702962	+	0.711228i	$0.251861\pi$
$240$		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	$0.380363\pi$
$251$	−9.85499	+	17.0693i	−0.622041	+	1.07741i	−0.989105	+	0.147212i	$0.952970\pi$
$252$		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	0.857024	−	0.515277i	$-0.172311\pi$
$263$	8.08262	+	6.78213i	0.498396	+	0.418204i	−0.358628	+	0.933481i	$0.616755\pi$
$264$		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	$-0.645018\pi$
$271$		−	29.5660i		−	1.79600i	0.439991	−	0.898002i	$-0.354982\pi$
$272$		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	−0.856485	−	0.516172i	$-0.827356\pi$
$283$	2.21065	−	6.07372i	0.131410	−	0.361045i	0.987895	+	0.155127i	$0.0495787\pi$
$284$		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	$0.695242\pi$
$307$	−27.5367	+	15.8983i	−1.57160	+	0.907364i	−0.995973	+	0.0896520i	$0.971425\pi$
$308$		0			0
$309$	0.626622	−	1.48831i	0.0356473	−	0.0846670i
$310$		0			0
$311$	−13.5550	−	4.93361i	−0.768633	−	0.279759i	−0.0722083	−	0.997390i	$-0.523005\pi$
$311$	−13.5550	−	4.93361i	−0.768633	−	0.279759i	−0.696424	+	0.717630i	$0.745227\pi$
$312$		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	−0.880537	−	0.473977i	$-0.842818\pi$
$331$	−4.74589	+	5.65593i	−0.260857	+	0.310878i	0.619680	+	0.784855i	$0.287262\pi$
$332$		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	−0.893965	−	0.448137i	$-0.852088\pi$
$347$	−11.3234	+	9.50146i	−0.607872	+	0.510065i	0.286093	+	0.958202i	$0.407643\pi$
$348$		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	$0.398709\pi$
$359$	−12.6210	+	21.8603i	−0.666112	+	1.15374i	−0.978983	+	0.203944i	$0.934624\pi$
$360$		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	0.459485	−	0.888185i	$-0.348034\pi$
$367$	11.2545	+	1.98448i	0.587483	+	0.103589i	0.127997	+	0.991774i	$0.459145\pi$
$368$		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	$0.132480\pi$
$379$			15.7412i			0.808572i	−0.914633	+	0.404286i	$0.867520\pi$
$380$		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	$-0.758981\pi$
$383$	−5.45535	−	30.9388i	−0.278756	−	1.58090i	0.448018	−	0.894024i	$-0.352130\pi$
$384$		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	0.614988	−	0.788536i	$-0.289161\pi$
$419$	11.8567	+	4.31547i	0.579236	+	0.210825i	−0.0357528	+	0.999361i	$0.511383\pi$
$420$		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	$-0.467066\pi$
$431$	4.28837			0.206564			0.103282	+	0.994652i	$0.467066\pi$
$432$		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	−0.862920	−	0.505340i	$-0.831367\pi$
$439$	−4.51341	+	5.37887i	−0.215413	+	0.256719i	0.647507	+	0.762059i	$0.275812\pi$
$440$		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	$-0.688376\pi$
$443$	5.26637	−	29.8670i	0.250213	−	1.41903i	0.808069	−	0.589088i	$-0.200513\pi$
$444$		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	0.891366	−	0.453284i	$-0.149748\pi$
$463$	6.24403	+	7.44135i	0.290185	+	0.345829i	−0.601181	+	0.799113i	$0.705303\pi$
$464$		0			0
$465$	−7.30918	+	2.25802i	−0.338955	+	0.104713i
$466$		0			0
$467$	−9.87482	+	17.1037i	−0.456952	+	0.791464i	−0.998798	−	0.0490137i	$-0.984392\pi$
$467$	−9.87482	+	17.1037i	−0.456952	+	0.791464i	0.541846	+	0.840478i	$0.317726\pi$
$468$		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	0.920523	−	0.390689i	$-0.127763\pi$
$479$	15.2243	+	12.7747i	0.695616	+	0.583691i	−0.224906	+	0.974380i	$0.572208\pi$
$480$		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	$0.0241378\pi$
$487$			3.34369i			0.151517i	−0.997126	+	0.0757584i	$0.975862\pi$
$488$		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	$0.261703\pi$
$491$	6.46183	+	36.6468i	0.291618	+	1.65385i	−0.389020	+	0.921229i	$0.627186\pi$
$492$		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	$0.245431\pi$
$499$	−6.25828	+	17.1945i	−0.280159	+	0.769731i	−0.997343	+	0.0728472i	$0.976791\pi$
$500$		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	$-0.818239\pi$
$503$	−19.9327	−	34.5244i	−0.888754	−	1.53937i	−0.0474040	−	0.998876i	$-0.515095\pi$
$504$		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	0.155408	−	0.987850i	$-0.450331\pi$
$523$	24.8958	−	14.3736i	1.08862	−	0.628513i	0.933208	+	0.359337i	$0.116997\pi$
$524$		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	−0.543750	−	0.839247i	$-0.682996\pi$
$547$	8.82124	−	10.5127i	0.377169	−	0.449492i	0.920919	+	0.389755i	$0.127440\pi$
$548$		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	−0.460736	−	0.887537i	$-0.652414\pi$
$563$	7.90869	−	6.63618i	0.333312	−	0.279682i	0.794048	+	0.607856i	$0.207970\pi$
$564$		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	$0.0579485\pi$
$571$	23.6804	+	28.2212i	0.990992	+	1.18102i	0.00751760	+	0.999972i	$0.497607\pi$
$572$		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	−0.0724993	−	0.997368i	$-0.523098\pi$
$587$	−25.8588	−	21.6981i	−1.06730	−	0.895575i	−0.994806	+	0.101793i	$0.967542\pi$
$588$		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	$-0.941718\pi$
$599$	−2.97543	−	16.8745i	−0.121573	−	0.689474i	0.861712	−	0.507398i	$-0.169393\pi$
$600$		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	$0.351150\pi$
$607$	−11.5382	+	31.7008i	−0.468319	+	1.28670i	−0.919087	+	0.394055i	$0.871072\pi$
$608$		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	$0.0527105\pi$
$619$	8.37729	+	23.0164i	0.336712	+	0.925108i	−0.649609	+	0.760269i	$0.725067\pi$
$620$		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	−0.294768	−	0.955569i	$-0.595242\pi$
$631$	9.68103	−	5.58935i	0.385396	−	0.222508i	0.680163	+	0.733061i	$0.261909\pi$
$632$		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	−0.0193702	−	0.999812i	$-0.506166\pi$
$643$	7.71839	−	1.36096i	0.304384	−	0.0536711i	0.323754	+	0.946141i	$0.395055\pi$
$644$		0			0
$645$	0.133586	−	0.207026i	0.00525992	−	0.00815164i
$646$		0			0
$647$	44.0555			1.73200			0.866000	−	0.500044i	$-0.166683\pi$
$647$	44.0555			1.73200			0.866000	+	0.500044i	$0.166683\pi$
$648$		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	$-0.884670\pi$
$659$	1.66439	−	9.43924i	0.0648355	−	0.367701i	0.999912	−	0.0132549i	$-0.00421930\pi$
$660$		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	$-0.459564\pi$
$683$	24.1061	−	41.7529i	0.922393	−	1.59763i	0.795701	−	0.605690i	$-0.207103\pi$
$684$		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	0.558917	−	0.829224i	$-0.311217\pi$
$691$	21.0430	+	3.71046i	0.800515	+	0.141152i	0.241599	+	0.970376i	$0.422328\pi$
$692$		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	$-0.983837\pi$
$719$	−14.5684	−	25.2332i	−0.543310	−	0.941041i	0.455401	−	0.890287i	$-0.349496\pi$
$720$		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	0.980056	−	0.198720i	$-0.0636786\pi$
$727$	2.73821	+	7.52317i	0.101555	+	0.279019i	−0.878502	+	0.477739i	$0.841456\pi$
$728$		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	−0.847292	−	0.531128i	$-0.821768\pi$
$739$	−22.0458	+	12.7281i	−0.810967	+	0.468212i	0.0363245	+	0.999340i	$0.488435\pi$
$740$		0			0
$741$	−55.7634	+	7.01240i	−2.04852	+	0.257607i
$742$		0			0
$743$	2.02834	+	0.738257i	0.0744127	+	0.0270840i	0.378958	−	0.925414i	$-0.376282\pi$
$743$	2.02834	+	0.738257i	0.0744127	+	0.0270840i	−0.304546	+	0.952498i	$0.598505\pi$
$744$		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	−0.232940	−	0.972491i	$-0.574835\pi$
$751$	−3.26718	+	0.576092i	−0.119221	+	0.0210219i	0.113719	+	0.993513i	$0.463724\pi$
$752$		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	0.941070	−	0.338213i	$-0.109822\pi$
$787$	12.4720	+	14.8636i	0.444580	+	0.529830i	−0.496490	+	0.868043i	$0.665378\pi$
$788$		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	$0.167824\pi$
$811$			28.6572i			1.00629i	−0.864202	+	0.503145i	$0.832176\pi$
$812$		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	$0.231135\pi$
$823$	−7.22536	+	19.8515i	−0.251860	+	0.691980i	−0.999608	+	0.0279972i	$0.991087\pi$
$824$		0			0
$825$	31.2240	+	13.1462i	1.08708	+	0.457693i
$826$		0			0
$827$	−9.73569	−	16.8627i	−0.338543	−	0.586374i	0.645616	−	0.763662i	$-0.276601\pi$
$827$	−9.73569	−	16.8627i	−0.338543	−	0.586374i	−0.984159	+	0.177288i	$0.943267\pi$
$828$		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	0.0934694	−	0.995622i	$-0.470204\pi$
$839$	23.3185	−	8.48725i	0.805045	−	0.293012i	0.711575	+	0.702610i	$0.247982\pi$
$840$		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	0.614640	−	0.788808i	$-0.289301\pi$
$859$	42.8494	−	7.55550i	1.46200	−	0.257790i	0.847361	+	0.531017i	$0.178190\pi$
$860$		0			0
$861$	0.181365	+	0.00897338i	0.00618089	+	0.000305812i
$862$		0			0
$863$	−16.1195			−0.548714			−0.274357	−	0.961628i	$-0.588465\pi$
$863$	−16.1195			−0.548714			−0.274357	+	0.961628i	$0.588465\pi$
$864$		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	0.297120	−	0.954840i	$-0.403974\pi$
$883$	−11.3285	−	6.54053i	−0.381235	−	0.220106i	−0.678356	+	0.734734i	$0.737307\pi$
$884$		0			0
$885$	17.8901	+	4.07521i	0.601370	+	0.136987i
$886$		0			0
$887$	−25.2454	+	21.1834i	−0.847659	+	0.711270i	−0.959273	−	0.282482i	$-0.908842\pi$
$887$	−25.2454	+	21.1834i	−0.847659	+	0.711270i	0.111614	+	0.993752i	$0.464398\pi$
$888$		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	−0.501349	−	0.865245i	$-0.667163\pi$
$907$	−38.1995	−	6.73561i	−1.26839	−	0.223652i	−0.767045	+	0.641593i	$0.778274\pi$
$908$		0			0
$909$	−24.3093	−	6.81704i	−0.806290	−	0.226107i
$910$		0			0
$911$	−21.4658	−	18.0119i	−0.711192	−	0.596761i	0.213741	−	0.976890i	$-0.431435\pi$
$911$	−21.4658	−	18.0119i	−0.711192	−	0.596761i	−0.924933	+	0.380129i	$0.875880\pi$
$912$		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	$-0.991425\pi$
$919$		−	1.63307i		−	0.0538701i	0.999637	−	0.0269351i	$-0.00857473\pi$
$920$		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	−0.394719	−	0.918802i	$-0.629158\pi$
$947$	−3.27726	+	1.19283i	−0.106497	+	0.0387617i	0.288222	+	0.957564i	$0.406936\pi$
$948$		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	−0.926356	−	0.376649i	$-0.877076\pi$
$967$	−51.8699	+	9.14607i	−1.66802	+	0.294118i	−0.741669	+	0.670766i	$0.765965\pi$
$968$		0			0
$969$	23.6091	−	36.5886i	0.758434	−	1.17539i
$970$		0			0
$971$	32.1045			1.03028			0.515142	−	0.857105i	$-0.327739\pi$
$971$	32.1045			1.03028			0.515142	+	0.857105i	$0.327739\pi$
$972$		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	−0.986983	−	0.160823i	$-0.948585\pi$
$983$	−0.141641	+	0.803287i	−0.00451765	+	0.0256209i	0.982466	+	0.186444i	$0.0596963\pi$
$984$		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	0.798479	−	0.602022i	$-0.205638\pi$
$991$	21.2917	+	12.2928i	0.676353	+	0.390492i	−0.122127	+	0.992515i	$0.538971\pi$
$992$		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.c.47.4	yes	36
4.3	odd	2		432.2.be.b.47.3	✓	36
27.23	odd	18		432.2.be.b.239.3	yes	36
108.23	even	18	inner	432.2.be.c.239.4	yes	36

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
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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