LMFDB - Embedded newform 432.2.y.e.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$432 = 2^{4} \cdot 3^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	432.y (of order $12$ , degree $4$ , not 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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	432.37
Dual form			432.2.y.e.397.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30266 - 0.550520i) q^{2} +(1.39386 + 1.43428i) q^{4} +(-2.73721 + 0.733432i) q^{5} +(-1.14487 + 0.660988i) q^{7} +(-1.02612 - 2.63573i) q^{8} +(3.96942 + 0.551472i) q^{10} +(0.343957 - 1.28367i) q^{11} +(-0.902174 - 3.36696i) q^{13} +(1.85526 - 0.230773i) q^{14} +(-0.114331 + 3.99837i) q^{16} +7.60772 q^{17} +(4.32297 - 4.32297i) q^{19} +(-4.86722 - 2.90363i) q^{20} +(-1.15474 + 1.48283i) q^{22} +(3.46087 + 1.99814i) q^{23} +(2.62424 - 1.51511i) q^{25} +(-0.678350 + 4.88267i) q^{26} +(-2.54382 - 0.720737i) q^{28} +(3.54658 + 0.950303i) q^{29} +(0.569129 - 0.985760i) q^{31} +(2.35011 - 5.14558i) q^{32} +(-9.91029 - 4.18820i) q^{34} +(2.64894 - 2.64894i) q^{35} +(2.26014 + 2.26014i) q^{37} +(-8.01124 + 3.25149i) q^{38} +(4.74184 + 6.46194i) q^{40} +(1.42311 + 0.821634i) q^{41} +(1.65438 - 6.17424i) q^{43} +(2.32057 - 1.29591i) q^{44} +(-3.40833 - 4.50817i) q^{46} +(-4.58731 - 7.94546i) q^{47} +(-2.62619 + 4.54869i) q^{49} +(-4.25260 + 0.528975i) q^{50} +(3.57167 - 5.98703i) q^{52} +(-7.72215 - 7.72215i) q^{53} +3.76593i q^{55} +(2.91696 + 2.33930i) q^{56} +(-4.09683 - 3.19038i) q^{58} +(4.80982 - 1.28879i) q^{59} +(9.92979 + 2.66068i) q^{61} +(-1.28406 + 0.970795i) q^{62} +(-5.89415 + 5.40916i) q^{64} +(4.93887 + 8.55438i) q^{65} +(-3.73189 - 13.9276i) q^{67} +(10.6041 + 10.9116i) q^{68} +(-4.90897 + 1.99238i) q^{70} -7.87498i q^{71} +0.577222i q^{73} +(-1.69995 - 4.18846i) q^{74} +(12.2259 + 0.174761i) q^{76} +(0.454704 + 1.69698i) q^{77} +(0.716890 + 1.24169i) q^{79} +(-2.61958 - 11.0282i) q^{80} +(-1.40151 - 1.85376i) q^{82} +(-3.30414 - 0.885341i) q^{83} +(-20.8239 + 5.57975i) q^{85} +(-5.55414 + 7.13218i) q^{86} +(-3.73634 + 0.410620i) q^{88} +16.2114i q^{89} +(3.25839 + 3.25839i) q^{91} +(1.95807 + 7.74898i) q^{92} +(1.60159 + 12.8757i) q^{94} +(-8.66225 + 15.0035i) q^{95} +(-0.648931 - 1.12398i) q^{97} +(5.92518 - 4.47964i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32}+ \cdots - 88 q^{98}+O(q^{100})$ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−1.30266	−	0.550520i	−0.921121	−	0.389276i
$2$	−1.30266	−	0.550520i	−0.921121	−	0.389276i
$3$		0			0
$3$		0			0
$4$	1.39386	+	1.43428i	0.696928	+	0.717141i
$5$	−2.73721	+	0.733432i	−1.22412	+	0.328001i	−0.812286	−	0.583260i	$-0.801777\pi$
$5$	−2.73721	+	0.733432i	−1.22412	+	0.328001i	−0.411830	+	0.911261i	$0.635110\pi$
$6$		0			0
$7$	−1.14487	+	0.660988i	−0.432718	+	0.249830i	−0.700504	−	0.713648i	$-0.747041\pi$
$7$	−1.14487	+	0.660988i	−0.432718	+	0.249830i	0.267786	+	0.963479i	$0.413708\pi$
$8$	−1.02612	−	2.63573i	−0.362789	−	0.931871i
$9$		0			0
$10$	3.96942	+	0.551472i	1.25524	+	0.174391i
$11$	0.343957	−	1.28367i	0.103707	−	0.387040i	−0.894488	−	0.447092i	$-0.852460\pi$
$11$	0.343957	−	1.28367i	0.103707	−	0.387040i	0.998195	+	0.0600515i	$0.0191265\pi$
$12$		0			0
$13$	−0.902174	−	3.36696i	−0.250218	−	0.933827i	−0.970689	−	0.240341i	$-0.922741\pi$
$13$	−0.902174	−	3.36696i	−0.250218	−	0.933827i	0.720470	−	0.693486i	$-0.243926\pi$
$14$	1.85526	−	0.230773i	0.495839	−	0.0616768i
$15$		0			0
$16$	−0.114331	+	3.99837i	−0.0285827	+	0.999591i
$17$	7.60772			1.84514			0.922572	−	0.385825i	$-0.126083\pi$
$17$	7.60772			1.84514			0.922572	+	0.385825i	$0.126083\pi$
$18$		0			0
$19$	4.32297	−	4.32297i	0.991757	−	0.991757i	−0.00820954	−	0.999966i	$-0.502613\pi$
$19$	4.32297	−	4.32297i	0.991757	−	0.991757i	0.999966	+	0.00820954i	$0.00261321\pi$
$20$	−4.86722	−	2.90363i	−1.08834	−	0.649271i
$21$		0			0
$22$	−1.15474	+	1.48283i	−0.246192	+	0.316140i
$23$	3.46087	+	1.99814i	0.721642	+	0.416640i	0.815357	−	0.578959i	$-0.196541\pi$
$23$	3.46087	+	1.99814i	0.721642	+	0.416640i	−0.0937148	+	0.995599i	$0.529874\pi$
$24$		0			0
$25$	2.62424	−	1.51511i	0.524849	−	0.303021i
$26$	−0.678350	+	4.88267i	−0.133035	+	0.957571i
$27$		0			0
$28$	−2.54382	−	0.720737i	−0.480737	−	0.136207i
$29$	3.54658	+	0.950303i	0.658583	+	0.176467i	0.572606	−	0.819830i	$-0.305932\pi$
$29$	3.54658	+	0.950303i	0.658583	+	0.176467i	0.0859765	+	0.996297i	$0.472599\pi$
$30$		0			0
$31$	0.569129	−	0.985760i	0.102219	−	0.177048i	−0.810380	−	0.585905i	$-0.800739\pi$
$31$	0.569129	−	0.985760i	0.102219	−	0.177048i	0.912598	+	0.408857i	$0.134073\pi$
$32$	2.35011	−	5.14558i	0.415445	−	0.909618i
$33$		0			0
$34$	−9.91029	−	4.18820i	−1.69960	−	0.718271i
$35$	2.64894	−	2.64894i	0.447753	−	0.447753i
$36$		0			0
$37$	2.26014	+	2.26014i	0.371565	+	0.371565i	0.868047	−	0.496482i	$-0.165375\pi$
$37$	2.26014	+	2.26014i	0.371565	+	0.371565i	−0.496482	+	0.868047i	$0.665375\pi$
$38$	−8.01124	+	3.25149i	−1.29960	+	0.527461i
$39$		0			0
$40$	4.74184	+	6.46194i	0.749750	+	1.02172i
$41$	1.42311	+	0.821634i	0.222253	+	0.128318i	0.606993	−	0.794707i	$-0.292376\pi$
$41$	1.42311	+	0.821634i	0.222253	+	0.128318i	−0.384740	+	0.923025i	$0.625709\pi$
$42$		0			0
$43$	1.65438	−	6.17424i	0.252291	−	0.941563i	−0.717287	−	0.696778i	$-0.754616\pi$
$43$	1.65438	−	6.17424i	0.252291	−	0.941563i	0.969578	−	0.244784i	$-0.0787172\pi$
$44$	2.32057	−	1.29591i	0.349839	−	0.195366i
$45$		0			0
$46$	−3.40833	−	4.50817i	−0.502531	−	0.664694i
$47$	−4.58731	−	7.94546i	−0.669129	−	1.15896i	−0.978148	−	0.207909i	$-0.933334\pi$
$47$	−4.58731	−	7.94546i	−0.669129	−	1.15896i	0.309020	−	0.951056i	$-0.399999\pi$
$48$		0			0
$49$	−2.62619	+	4.54869i	−0.375170	+	0.649813i
$50$	−4.25260	+	0.528975i	−0.601408	+	0.0748084i
$51$		0			0
$52$	3.57167	−	5.98703i	0.495301	−	0.830252i
$53$	−7.72215	−	7.72215i	−1.06072	−	1.06072i	−0.998033	−	0.0626852i	$-0.980034\pi$
$53$	−7.72215	−	7.72215i	−1.06072	−	1.06072i	−0.0626852	−	0.998033i	$-0.519966\pi$
$54$		0			0
$55$			3.76593i			0.507798i
$56$	2.91696	+	2.33930i	0.389795	+	0.312602i
$57$		0			0
$58$	−4.09683	−	3.19038i	−0.537940	−	0.418918i
$59$	4.80982	−	1.28879i	0.626185	−	0.167786i	0.0682473	−	0.997668i	$-0.478259\pi$
$59$	4.80982	−	1.28879i	0.626185	−	0.167786i	0.557938	+	0.829883i	$0.311593\pi$
$60$		0			0
$61$	9.92979	+	2.66068i	1.27138	+	0.340665i	0.830559	−	0.556931i	$-0.188021\pi$
$61$	9.92979	+	2.66068i	1.27138	+	0.340665i	0.440820	+	0.897596i	$0.354688\pi$
$62$	−1.28406	+	0.970795i	−0.163076	+	0.123291i
$63$		0			0
$64$	−5.89415	+	5.40916i	−0.736768	+	0.676145i
$65$	4.93887	+	8.55438i	0.612592	+	1.06104i
$66$		0			0
$67$	−3.73189	−	13.9276i	−0.455923	−	1.70153i	−0.685359	−	0.728205i	$-0.740355\pi$
$67$	−3.73189	−	13.9276i	−0.455923	−	1.70153i	0.229436	−	0.973324i	$-0.426312\pi$
$68$	10.6041	+	10.9116i	1.28593	+	1.32323i
$69$		0			0
$70$	−4.90897	+	1.99238i	−0.586734	+	0.238135i
$71$		−	7.87498i		−	0.934588i	−0.884102	−	0.467294i	$-0.845229\pi$
$71$		−	7.87498i		−	0.934588i	0.884102	−	0.467294i	$-0.154771\pi$
$72$		0			0
$73$			0.577222i			0.0675588i	0.999429	+	0.0337794i	$0.0107544\pi$
$73$			0.577222i			0.0675588i	−0.999429	+	0.0337794i	$0.989246\pi$
$74$	−1.69995	−	4.18846i	−0.197615	−	0.486898i
$75$		0			0
$76$	12.2259	+	0.174761i	1.40241	+	0.0200464i
$77$	0.454704	+	1.69698i	0.0518183	+	0.193389i
$78$		0			0
$79$	0.716890	+	1.24169i	0.0806564	+	0.139701i	0.903532	−	0.428521i	$-0.140965\pi$
$79$	0.716890	+	1.24169i	0.0806564	+	0.139701i	−0.822876	+	0.568221i	$0.807632\pi$
$80$	−2.61958	−	11.0282i	−0.292878	−	1.23299i
$81$		0			0
$82$	−1.40151	−	1.85376i	−0.154771	−	0.204714i
$83$	−3.30414	−	0.885341i	−0.362676	−	0.0971788i	0.0728790	−	0.997341i	$-0.476781\pi$
$83$	−3.30414	−	0.885341i	−0.362676	−	0.0971788i	−0.435555	+	0.900162i	$0.643448\pi$
$84$		0			0
$85$	−20.8239	+	5.57975i	−2.25867	+	0.605208i
$86$	−5.55414	+	7.13218i	−0.598919	+	0.769082i
$87$		0			0
$88$	−3.73634	+	0.410620i	−0.398295	+	0.0437723i
$89$			16.2114i			1.71841i	0.511635	+	0.859203i	$0.329040\pi$
$89$			16.2114i			1.71841i	−0.511635	+	0.859203i	$0.670960\pi$
$90$		0			0
$91$	3.25839	+	3.25839i	0.341572	+	0.341572i
$92$	1.95807	+	7.74898i	0.204143	+	0.807887i
$93$		0			0
$94$	1.60159	+	12.8757i	0.165191	+	1.32802i
$95$	−8.66225	+	15.0035i	−0.888728	+	1.53932i
$96$		0			0
$97$	−0.648931	−	1.12398i	−0.0658889	−	0.114123i	0.831199	−	0.555975i	$-0.187655\pi$
$97$	−0.648931	−	1.12398i	−0.0658889	−	0.114123i	−0.897088	+	0.441852i	$0.854322\pi$
$98$	5.92518	−	4.47964i	0.598534	−	0.452512i
$99$		0			0
$100$	5.83091	+	1.65206i	0.583091	+	0.165206i
$101$	−2.60956	+	9.73900i	−0.259661	+	0.969067i	0.705777	+	0.708434i	$0.250598\pi$
$101$	−2.60956	+	9.73900i	−0.259661	+	0.969067i	−0.965438	+	0.260633i	$0.916069\pi$
$102$		0			0
$103$	8.04850	+	4.64680i	0.793042	+	0.457863i	0.841033	−	0.540985i	$-0.181948\pi$
$103$	8.04850	+	4.64680i	0.793042	+	0.457863i	−0.0479901	+	0.998848i	$0.515282\pi$
$104$	−7.94866	+	5.83280i	−0.779430	+	0.571953i
$105$		0			0
$106$	5.80815	+	14.3105i	0.564138	+	1.38996i
$107$	−1.89502	−	1.89502i	−0.183199	−	0.183199i	0.609549	−	0.792748i	$-0.291350\pi$
$107$	−1.89502	−	1.89502i	−0.183199	−	0.183199i	−0.792748	+	0.609549i	$0.791350\pi$
$108$		0			0
$109$	−8.63272	+	8.63272i	−0.826864	+	0.826864i	−0.987082	−	0.160217i	$-0.948780\pi$
$109$	−8.63272	+	8.63272i	−0.826864	+	0.826864i	0.160217	+	0.987082i	$0.448780\pi$
$110$	2.07322	−	4.90573i	0.197674	−	0.467743i
$111$		0			0
$112$	−2.51198	−	4.65316i	−0.237360	−	0.439682i
$113$	1.70180	−	2.94761i	0.160092	−	0.277288i	−0.774809	−	0.632195i	$-0.782154\pi$
$113$	1.70180	−	2.94761i	0.160092	−	0.277288i	0.934902	+	0.354907i	$0.115488\pi$
$114$		0			0
$115$	−10.9386	−	2.93099i	−1.02003	−	0.273317i
$116$	3.58042	+	6.41138i	0.332433	+	0.595281i
$117$		0			0
$118$	−6.97507	−	0.969047i	−0.642108	−	0.0892080i
$119$	−8.70982	+	5.02862i	−0.798428	+	0.460972i
$120$		0			0
$121$	7.99679	+	4.61695i	0.726981	+	0.419722i
$122$	−11.4704	−	8.93251i	−1.03848	−	0.808711i
$123$		0			0
$124$	2.20714	−	0.557716i	0.198207	−	0.0500844i
$125$	3.94700	−	3.94700i	0.353031	−	0.353031i
$126$		0			0
$127$	−5.24504			−0.465422			−0.232711	−	0.972546i	$-0.574760\pi$
$127$	−5.24504			−0.465422			−0.232711	+	0.972546i	$0.574760\pi$
$128$	10.6559	−	3.80147i	0.941860	−	0.336006i
$129$		0			0
$130$	−1.72433	−	13.8624i	−0.151233	−	1.21581i
$131$	−1.68026	−	6.27080i	−0.146805	−	0.547883i	−0.999668	−	0.0257490i	$-0.991803\pi$
$131$	−1.68026	−	6.27080i	−0.146805	−	0.547883i	0.852864	−	0.522134i	$-0.174864\pi$
$132$		0			0
$133$	−2.09178	+	7.80665i	−0.181381	+	0.676922i
$134$	−2.80603	+	20.1975i	−0.242404	+	1.74479i
$135$		0			0
$136$	−7.80646	−	20.0519i	−0.669398	−	1.71944i
$137$	6.16622	−	3.56007i	0.526816	−	0.304157i	−0.212903	−	0.977073i	$-0.568292\pi$
$137$	6.16622	−	3.56007i	0.526816	−	0.304157i	0.739719	+	0.672916i	$0.234958\pi$
$138$		0			0
$139$	4.07133	−	1.09091i	0.345326	−	0.0925298i	−0.0819876	−	0.996633i	$-0.526127\pi$
$139$	4.07133	−	1.09091i	0.345326	−	0.0925298i	0.427313	+	0.904104i	$0.359460\pi$
$140$	7.49157	+	0.107086i	0.633154	+	0.00905045i
$141$		0			0
$142$	−4.33533	+	10.2584i	−0.363813	+	0.860869i
$143$	−4.63236			−0.387378
$144$		0			0
$145$	−10.4047			−0.864063
$146$	0.317772	−	0.751925i	0.0262990	−	0.0622298i
$147$		0			0
$148$	−0.0913688	+	6.39200i	−0.00751047	+	0.525419i
$149$	8.40971	−	2.25338i	0.688950	−	0.184604i	0.102674	−	0.994715i	$-0.467260\pi$
$149$	8.40971	−	2.25338i	0.688950	−	0.184604i	0.586276	+	0.810111i	$0.300593\pi$
$150$		0			0
$151$	17.8103	−	10.2828i	1.44938	−	0.836803i	0.450940	−	0.892554i	$-0.351089\pi$
$151$	17.8103	−	10.2828i	1.44938	−	0.836803i	0.998445	+	0.0557515i	$0.0177554\pi$
$152$	−15.8301	−	6.95828i	−1.28399	−	0.564391i
$153$		0			0
$154$	0.341894	−	2.46091i	0.0275506	−	0.198306i
$155$	−0.834834	+	3.11564i	−0.0670555	+	0.250255i
$156$		0			0
$157$	−2.38710	−	8.90879i	−0.190512	−	0.710999i	−0.993383	−	0.114847i	$-0.963362\pi$
$157$	−2.38710	−	8.90879i	−0.190512	−	0.710999i	0.802872	−	0.596152i	$-0.203304\pi$
$158$	−0.250290	−	2.01216i	−0.0199120	−	0.160079i
$159$		0			0
$160$	−2.65881	+	15.8081i	−0.210198	+	1.24974i
$161$	−5.28298			−0.416357
$162$		0			0
$163$	−10.4053	+	10.4053i	−0.815004	+	0.815004i	−0.985379	−	0.170375i	$-0.945502\pi$
$163$	−10.4053	+	10.4053i	−0.815004	+	0.815004i	0.170375	+	0.985379i	$0.445502\pi$
$164$	0.805158	+	3.18638i	0.0628723	+	0.248815i
$165$		0			0
$166$	3.81678	+	2.97229i	0.296239	+	0.230695i
$167$	5.95392	+	3.43750i	0.460728	+	0.266001i	0.712350	−	0.701824i	$-0.247631\pi$
$167$	5.95392	+	3.43750i	0.460728	+	0.266001i	−0.251622	+	0.967826i	$0.580964\pi$
$168$		0			0
$169$	0.735830	−	0.424832i	0.0566023	−	0.0326794i
$170$	30.1983	+	4.19544i	2.31610	+	0.321776i
$171$		0			0
$172$	11.1616	−	6.23315i	0.851062	−	0.475273i
$173$	3.07494	+	0.823927i	0.233783	+	0.0626420i	0.373808	−	0.927506i	$-0.378052\pi$
$173$	3.07494	+	0.823927i	0.233783	+	0.0626420i	−0.140025	+	0.990148i	$0.544718\pi$
$174$		0			0
$175$	−2.00294	+	3.46919i	−0.151408	+	0.262246i
$176$	5.09324	+	1.52203i	0.383918	+	0.114727i
$177$		0			0
$178$	8.92470	−	21.1180i	0.668934	−	1.58286i
$179$	3.73648	−	3.73648i	0.279278	−	0.279278i	−0.553543	−	0.832821i	$-0.686725\pi$
$179$	3.73648	−	3.73648i	0.279278	−	0.279278i	0.832821	+	0.553543i	$0.186725\pi$
$180$		0			0
$181$	0.169132	+	0.169132i	0.0125715	+	0.0125715i	0.713365	−	0.700793i	$-0.247170\pi$
$181$	0.169132	+	0.169132i	0.0125715	+	0.0125715i	−0.700793	+	0.713365i	$0.747170\pi$
$182$	−2.45077	−	6.03839i	−0.181663	−	0.447595i
$183$		0			0
$184$	1.71527	−	11.1723i	0.126451	−	0.823630i
$185$	−7.84414	−	4.52882i	−0.576713	−	0.332965i
$186$		0			0
$187$	2.61673	−	9.76578i	0.191354	−	0.714145i
$188$	5.00198	−	17.6543i	0.364807	−	1.28757i
$189$		0			0
$190$	19.5437	−	14.7757i	1.41785	−	1.07194i
$191$	−11.0451	−	19.1306i	−0.799194	−	1.38424i	−0.920142	−	0.391586i	$-0.871927\pi$
$191$	−11.0451	−	19.1306i	−0.799194	−	1.38424i	0.120947	−	0.992659i	$-0.461407\pi$
$192$		0			0
$193$	7.90683	−	13.6950i	0.569146	−	0.985790i	−0.427505	−	0.904013i	$-0.640607\pi$
$193$	7.90683	−	13.6950i	0.569146	−	0.985790i	0.996651	−	0.0817767i	$-0.0260594\pi$
$194$	0.226564	+	1.82142i	0.0162663	+	0.130770i
$195$		0			0
$196$	−10.1846	+	2.57353i	−0.727474	+	0.183823i
$197$	−1.19611	−	1.19611i	−0.0852196	−	0.0852196i	0.663212	−	0.748432i	$-0.269193\pi$
$197$	−1.19611	−	1.19611i	−0.0852196	−	0.0852196i	−0.748432	+	0.663212i	$0.769193\pi$
$198$		0			0
$199$			6.39170i			0.453095i	0.974000	+	0.226548i	$0.0727439\pi$
$199$			6.39170i			0.453095i	−0.974000	+	0.226548i	$0.927256\pi$
$200$	−6.68621	−	5.36211i	−0.472786	−	0.379158i
$201$		0			0
$202$	8.76088	−	11.2500i	0.616414	−	0.791548i
$203$	−4.68849	+	1.25628i	−0.329068	+	0.0881734i
$204$		0			0
$205$	−4.49796	−	1.20523i	−0.314151	−	0.0841766i
$206$	−7.92632	−	10.4841i	−0.552253	−	0.730460i
$207$		0			0
$208$	13.5655	−	3.22228i	0.940597	−	0.223425i
$209$	−4.06233	−	7.03617i	−0.280997	−	0.486702i
$210$		0			0
$211$	0.539586	+	2.01376i	0.0371466	+	0.138633i	0.982009	−	0.188835i	$-0.0604712\pi$
$211$	0.539586	+	2.01376i	0.0371466	+	0.138633i	−0.944862	+	0.327468i	$0.893805\pi$
$212$	0.312176	−	21.8393i	0.0214404	−	1.49993i
$213$		0			0
$214$	1.42533	+	3.51182i	0.0974333	+	0.240063i
$215$			18.1135i			1.23533i
$216$		0			0
$217$			1.50475i			0.102149i
$218$	15.9980	−	6.49303i	1.08352	−	0.439764i
$219$		0			0
$220$	−5.40140	+	5.24916i	−0.364163	+	0.353898i
$221$	−6.86349	−	25.6149i	−0.461688	−	1.72304i
$222$		0			0
$223$	13.6496	+	23.6417i	0.914042	+	1.58317i	0.808297	+	0.588775i	$0.200389\pi$
$223$	13.6496	+	23.6417i	0.914042	+	1.58317i	0.105745	+	0.994393i	$0.466277\pi$
$224$	0.710603	+	7.44439i	0.0474792	+	0.497399i
$225$		0			0
$226$	−3.83959	+	2.90286i	−0.255406	+	0.193095i
$227$	−2.80787	−	0.752368i	−0.186365	−	0.0499364i	0.164429	−	0.986389i	$-0.447422\pi$
$227$	−2.80787	−	0.752368i	−0.186365	−	0.0499364i	−0.350794	+	0.936452i	$0.614088\pi$
$228$		0			0
$229$	−6.48583	+	1.73787i	−0.428596	+	0.114842i	−0.466667	−	0.884433i	$-0.654545\pi$
$229$	−6.48583	+	1.73787i	−0.428596	+	0.114842i	0.0380710	+	0.999275i	$0.487879\pi$
$230$	12.6357	+	9.84002i	0.833177	+	0.648832i
$231$		0			0
$232$	−1.13448	−	10.3229i	−0.0744824	−	0.677735i
$233$			11.8159i			0.774086i	0.922062	+	0.387043i	$0.126503\pi$
$233$			11.8159i			0.774086i	−0.922062	+	0.387043i	$0.873497\pi$
$234$		0			0
$235$	18.3839	+	18.3839i	1.19923	+	1.19923i
$236$	8.55268	+	5.10226i	0.556732	+	0.332129i
$237$		0			0
$238$	14.1143	−	1.75566i	0.914894	−	0.113803i
$239$	1.75364	−	3.03739i	0.113433	−	0.196472i	−0.803719	−	0.595009i	$-0.797148\pi$
$239$	1.75364	−	3.03739i	0.113433	−	0.196472i	0.917152	+	0.398537i	$0.130482\pi$
$240$		0			0
$241$	−4.35635	−	7.54543i	−0.280617	−	0.486044i	0.690920	−	0.722932i	$-0.257206\pi$
$241$	−4.35635	−	7.54543i	−0.280617	−	0.486044i	−0.971537	+	0.236888i	$0.923873\pi$
$242$	−7.87539	−	10.4167i	−0.506249	−	0.669611i
$243$		0			0
$244$	10.0245	+	17.9507i	0.641755	+	1.14918i
$245$	3.85226	−	14.3768i	0.246112	−	0.918502i
$246$		0			0
$247$	−18.4553	−	10.6552i	−1.17428	−	0.677973i
$248$	−3.18219	−	0.488559i	−0.202069	−	0.0310235i
$249$		0			0
$250$	−7.31451	+	2.96871i	−0.462610	+	0.187758i
$251$	9.70213	+	9.70213i	0.612393	+	0.612393i	0.943569	−	0.331176i	$-0.107445\pi$
$251$	9.70213	+	9.70213i	0.612393	+	0.612393i	−0.331176	+	0.943569i	$0.607445\pi$
$252$		0			0
$253$	3.75533	−	3.75533i	0.236096	−	0.236096i
$254$	6.83251	+	2.88750i	0.428710	+	0.181178i
$255$		0			0
$256$	−15.9739	−	0.914271i	−0.998366	−	0.0571420i
$257$	9.26857	−	16.0536i	0.578158	−	1.00140i	−0.417533	−	0.908662i	$-0.637105\pi$
$257$	9.26857	−	16.0536i	0.578158	−	1.00140i	0.995691	−	0.0927366i	$-0.0295615\pi$
$258$		0			0
$259$	−4.08149	−	1.09363i	−0.253611	−	0.0679550i
$260$	−5.38531	+	19.0073i	−0.333983	+	1.17878i
$261$		0			0
$262$	−1.26339	+	9.09375i	−0.0780528	+	0.561814i
$263$	−3.42692	+	1.97853i	−0.211313	+	0.122002i	−0.601922	−	0.798555i	$-0.705598\pi$
$263$	−3.42692	+	1.97853i	−0.211313	+	0.122002i	0.390608	+	0.920557i	$0.372265\pi$
$264$		0			0
$265$	26.8008	+	15.4734i	1.64636	+	0.950525i
$266$	7.02260	−	9.01785i	0.430583	−	0.552920i
$267$		0			0
$268$	14.7744	−	24.7657i	0.902491	−	1.51280i
$269$	−17.6742	+	17.6742i	−1.07762	+	1.07762i	−0.0808951	+	0.996723i	$0.525778\pi$
$269$	−17.6742	+	17.6742i	−1.07762	+	1.07762i	−0.996723	+	0.0808951i	$0.974222\pi$
$270$		0			0
$271$	−26.9563			−1.63748			−0.818738	−	0.574167i	$-0.805326\pi$
$271$	−26.9563			−1.63748			−0.818738	+	0.574167i	$0.805326\pi$
$272$	−0.869796	+	30.4185i	−0.0527391	+	1.84439i
$273$		0			0
$274$	−9.99239	+	1.24294i	−0.603662	+	0.0750888i
$275$	−1.04226	−	3.88979i	−0.0628509	−	0.234563i
$276$		0			0
$277$	2.47723	−	9.24514i	0.148842	−	0.555487i	−0.850712	−	0.525632i	$-0.823829\pi$
$277$	2.47723	−	9.24514i	0.148842	−	0.555487i	0.999554	−	0.0298548i	$-0.00950449\pi$
$278$	−5.90414	−	0.820261i	−0.354107	−	0.0491960i
$279$		0			0
$280$	−9.70003	−	4.26376i	−0.579688	−	0.254808i
$281$	−8.51476	+	4.91600i	−0.507948	+	0.293264i	−0.731990	−	0.681316i	$-0.761408\pi$
$281$	−8.51476	+	4.91600i	−0.507948	+	0.293264i	0.224042	+	0.974580i	$0.428075\pi$
$282$		0			0
$283$	−30.0988	+	8.06496i	−1.78919	+	0.479412i	−0.992208	−	0.124591i	$-0.960238\pi$
$283$	−30.0988	+	8.06496i	−1.78919	+	0.479412i	−0.796982	+	0.604003i	$0.793572\pi$
$284$	11.2949	−	10.9766i	0.670231	−	0.651341i
$285$		0			0
$286$	6.03440	+	2.55021i	0.356822	+	0.150797i
$287$	−2.17236			−0.128231
$288$		0			0
$289$	40.8774			2.40456
$290$	13.5538	+	5.72799i	0.795906	+	0.336359i
$291$		0			0
$292$	−0.827900	+	0.804565i	−0.0484492	+	0.0470836i
$293$	−30.6204	+	8.20472i	−1.78886	+	0.479325i	−0.992152	−	0.125035i	$-0.960096\pi$
$293$	−30.6204	+	8.20472i	−1.78886	+	0.479325i	−0.796711	+	0.604360i	$0.793429\pi$
$294$		0			0
$295$	−12.2202	+	7.05535i	−0.711489	+	0.410778i
$296$	3.63794	−	8.27631i	0.211451	−	0.481051i
$297$		0			0
$298$	−12.1955	−	1.69433i	−0.706468	−	0.0981496i
$299$	3.60533	−	13.4553i	0.208502	−	0.778139i
$300$		0			0
$301$	2.18706	+	8.16220i	0.126060	+	0.470462i
$302$	−28.8617	+	3.59007i	−1.66081	+	0.206586i
$303$		0			0
$304$	16.7906	+	17.7791i	0.963005	+	1.01970i
$305$	−29.1313			−1.66805
$306$		0			0
$307$	17.2513	−	17.2513i	0.984581	−	0.984581i	−0.0153018	−	0.999883i	$-0.504871\pi$
$307$	17.2513	−	17.2513i	0.984581	−	0.984581i	0.999883	+	0.0153018i	$0.00487090\pi$
$308$	−1.80015	+	3.01752i	−0.102573	+	0.171939i
$309$		0			0
$310$	2.80273	−	3.59904i	0.159184	−	0.204412i
$311$	8.53625	+	4.92841i	0.484046	+	0.279464i	0.722101	−	0.691787i	$-0.243176\pi$
$311$	8.53625	+	4.92841i	0.484046	+	0.279464i	−0.238055	+	0.971252i	$0.576510\pi$
$312$		0			0
$313$	−8.45774	+	4.88308i	−0.478060	+	0.276008i	−0.719608	−	0.694381i	$-0.755678\pi$
$313$	−8.45774	+	4.88308i	−0.478060	+	0.276008i	0.241548	+	0.970389i	$0.422345\pi$
$314$	−1.79488	+	12.9193i	−0.101291	+	0.729078i
$315$		0			0
$316$	−0.781692	+	2.75896i	−0.0439736	+	0.155204i
$317$	12.8098	+	3.43237i	0.719469	+	0.192781i	0.599935	−	0.800049i	$-0.295193\pi$
$317$	12.8098	+	3.43237i	0.719469	+	0.192781i	0.119534	+	0.992830i	$0.461860\pi$
$318$		0			0
$319$	2.43974	−	4.22576i	0.136599	−	0.236597i
$320$	12.1662	−	19.1289i	0.680113	−	1.06934i
$321$		0			0
$322$	6.88194	+	2.90838i	0.383515	+	0.162078i
$323$	32.8879	−	32.8879i	1.82993	−	1.82993i
$324$		0			0
$325$	−7.46883	−	7.46883i	−0.414296	−	0.414296i
$326$	19.2829	−	7.82624i	1.06798	−	0.433456i
$327$		0			0
$328$	0.705318	−	4.59404i	0.0389447	−	0.253663i
$329$	10.5037	+	6.06432i	0.579089	+	0.334337i
$330$		0			0
$331$	0.274151	−	1.02314i	0.0150687	−	0.0562371i	−0.957982	−	0.286828i	$-0.907399\pi$
$331$	0.274151	−	1.02314i	0.0150687	−	0.0562371i	0.973051	+	0.230591i	$0.0740659\pi$
$332$	−3.33566	−	5.97311i	−0.183068	−	0.327817i
$333$		0			0
$334$	−5.86353	−	7.75565i	−0.320838	−	0.424370i
$335$	20.4299	+	35.3857i	1.11621	+	1.93332i
$336$		0			0
$337$	−2.50387	+	4.33683i	−0.136395	+	0.236242i	−0.926129	−	0.377206i	$-0.876885\pi$
$337$	−2.50387	+	4.33683i	−0.136395	+	0.236242i	0.789735	+	0.613448i	$0.210218\pi$
$338$	−1.19242	+	0.148323i	−0.0648589	+	0.00806771i
$339$		0			0
$340$	−37.0284	−	22.0900i	−2.00815	−	1.19800i
$341$	−1.06963	−	1.06963i	−0.0579238	−	0.0579238i
$342$		0			0
$343$		−	16.1974i		−	0.874575i
$344$	−17.9712	+	1.97502i	−0.968944	+	0.106486i
$345$		0			0
$346$	−3.55201	−	2.76611i	−0.190958	−	0.148707i
$347$	−5.88711	+	1.57745i	−0.316036	+	0.0846817i	−0.413350	−	0.910572i	$-0.635642\pi$
$347$	−5.88711	+	1.57745i	−0.316036	+	0.0846817i	0.0973140	+	0.995254i	$0.468975\pi$
$348$		0			0
$349$	−5.42227	−	1.45289i	−0.290247	−	0.0777715i	0.110758	−	0.993847i	$-0.464672\pi$
$349$	−5.42227	−	1.45289i	−0.290247	−	0.0777715i	−0.401005	+	0.916076i	$0.631339\pi$
$350$	4.51901	−	3.41652i	0.241551	−	0.182621i
$351$		0			0
$352$	−5.79687	−	4.78662i	−0.308974	−	0.255128i
$353$	5.06146	+	8.76671i	0.269395	+	0.466605i	0.968706	−	0.248212i	$-0.0798431\pi$
$353$	5.06146	+	8.76671i	0.269395	+	0.466605i	−0.699311	+	0.714817i	$0.746510\pi$
$354$		0			0
$355$	5.77576	+	21.5554i	0.306546	+	1.14404i
$356$	−23.2517	+	22.5964i	−1.23234	+	1.19761i
$357$		0			0
$358$	−6.92438	+	2.81037i	−0.365965	+	0.148532i
$359$			5.28081i			0.278710i	0.990242	+	0.139355i	$0.0445030\pi$
$359$			5.28081i			0.278710i	−0.990242	+	0.139355i	$0.955497\pi$
$360$		0			0
$361$		−	18.3761i		−	0.967163i
$362$	−0.127212	−	0.313433i	−0.00668610	−	0.0164737i
$363$		0			0
$364$	−0.131724	+	9.21518i	−0.00690421	+	0.483006i
$365$	−0.423353	−	1.57998i	−0.0221593	−	0.0826997i
$366$		0			0
$367$	5.01941	+	8.69388i	0.262011	+	0.453817i	0.966776	−	0.255624i	$-0.0822810\pi$
$367$	5.01941	+	8.69388i	0.262011	+	0.453817i	−0.704765	+	0.709441i	$0.748948\pi$
$368$	−8.38496	+	13.6094i	−0.437096	+	0.709438i
$369$		0			0
$370$	7.72506	+	10.2179i	0.401607	+	0.531202i
$371$	13.9451	+	3.73657i	0.723992	+	0.193993i
$372$		0			0
$373$	25.1865	−	6.74869i	1.30411	−	0.349434i	0.461105	−	0.887346i	$-0.347453\pi$
$373$	25.1865	−	6.74869i	1.30411	−	0.349434i	0.843001	+	0.537912i	$0.180787\pi$
$374$	−8.78497	+	11.2809i	−0.454260	+	0.583324i
$375$		0			0
$376$	−16.2349	+	20.2439i	−0.837253	+	1.04400i
$377$		−	12.7985i		−	0.659157i
$378$		0			0
$379$	−11.3259	−	11.3259i	−0.581771	−	0.581771i	0.353619	−	0.935390i	$-0.384951\pi$
$379$	−11.3259	−	11.3259i	−0.581771	−	0.581771i	−0.935390	+	0.353619i	$0.884951\pi$
$380$	−33.5931	+	8.48855i	−1.72329	+	0.435453i
$381$		0			0
$382$	3.85621	+	31.0013i	0.197301	+	1.58616i
$383$	−2.50076	+	4.33145i	−0.127783	+	0.221327i	−0.922817	−	0.385238i	$-0.874119\pi$
$383$	−2.50076	+	4.33145i	−0.127783	+	0.221327i	0.795034	+	0.606564i	$0.207453\pi$
$384$		0			0
$385$	−2.48924	−	4.31148i	−0.126863	−	0.219733i
$386$	−17.8393	+	13.4871i	−0.907997	+	0.686477i
$387$		0			0
$388$	0.707590	−	2.49742i	0.0359224	−	0.126787i
$389$	3.45749	−	12.9035i	0.175302	−	0.654235i	−0.821198	−	0.570643i	$-0.806694\pi$
$389$	3.45749	−	12.9035i	0.175302	−	0.654235i	0.996500	−	0.0835921i	$-0.0266393\pi$
$390$		0			0
$391$	26.3294	+	15.2013i	1.33153	+	0.768761i
$392$	14.6839	+	2.25441i	0.741650	+	0.113865i
$393$		0			0
$394$	0.899647	+	2.21662i	0.0453236	+	0.111671i
$395$	−2.87297	−	2.87297i	−0.144555	−	0.144555i
$396$		0			0
$397$	−18.7165	+	18.7165i	−0.939356	+	0.939356i	−0.998263	−	0.0589078i	$-0.981238\pi$
$397$	−18.7165	+	18.7165i	−0.939356	+	0.939356i	0.0589078	+	0.998263i	$0.481238\pi$
$398$	3.51876	−	8.32622i	0.176379	−	0.417356i
$399$		0			0
$400$	5.75792	+	10.6659i	0.287896	+	0.533295i
$401$	−6.66124	+	11.5376i	−0.332647	+	0.576161i	−0.983030	−	0.183445i	$-0.941275\pi$
$401$	−6.66124	+	11.5376i	−0.332647	+	0.576161i	0.650383	+	0.759606i	$0.274608\pi$
$402$		0			0
$403$	−3.83247	−	1.02691i	−0.190909	−	0.0511538i
$404$	−17.6058	+	9.83193i	−0.875923	+	0.489157i
$405$		0			0
$406$	6.79913	+	0.944602i	0.337435	+	0.0468798i
$407$	3.67866	−	2.12388i	0.182345	−	0.105277i
$408$		0			0
$409$	−10.6037	−	6.12206i	−0.524320	−	0.302717i	0.214380	−	0.976750i	$-0.431227\pi$
$409$	−10.6037	−	6.12206i	−0.524320	−	0.302717i	−0.738701	+	0.674034i	$0.764560\pi$
$410$	5.19582	+	4.04622i	0.256604	+	0.199829i
$411$		0			0
$412$	4.55362	+	18.0208i	0.224341	+	0.887821i
$413$	−4.65472	+	4.65472i	−0.229044	+	0.229044i
$414$		0			0
$415$	9.69344			0.475832
$416$	−19.4452	−	3.27053i	−0.953378	−	0.160351i
$417$		0			0
$418$	1.41830	+	11.4021i	0.0693712	+	0.557697i
$419$	8.58573	+	32.0424i	0.419440	+	1.56537i	0.775772	+	0.631013i	$0.217361\pi$
$419$	8.58573	+	32.0424i	0.419440	+	1.56537i	−0.356332	+	0.934360i	$0.615973\pi$
$420$		0			0
$421$	6.61930	−	24.7035i	0.322605	−	1.20398i	−0.594093	−	0.804396i	$-0.702489\pi$
$421$	6.61930	−	24.7035i	0.322605	−	1.20398i	0.916698	−	0.399581i	$-0.130844\pi$
$422$	0.405718	−	2.92030i	0.0197500	−	0.142158i
$423$		0			0
$424$	−12.4296	+	28.2774i	−0.603636	+	1.37327i
$425$	19.9645	−	11.5265i	0.968421	−	0.559118i
$426$		0			0
$427$	−13.1269	+	3.51736i	−0.635258	+	0.170217i
$428$	0.0766084	−	5.35938i	0.00370300	−	0.259056i
$429$		0			0
$430$	9.97186	−	23.5958i	0.480886	−	1.13789i
$431$	10.3041			0.496332			0.248166	−	0.968717i	$-0.420172\pi$
$431$	10.3041			0.496332			0.248166	+	0.968717i	$0.420172\pi$
$432$		0			0
$433$	−11.7692			−0.565591			−0.282795	−	0.959180i	$-0.591262\pi$
$433$	−11.7692			−0.565591			−0.282795	+	0.959180i	$0.591262\pi$
$434$	0.828394	−	1.96018i	0.0397642	−	0.0940916i
$435$		0			0
$436$	−24.4145	−	0.348987i	−1.16924	−	0.0167135i
$437$	23.5991	−	6.32337i	1.12890	−	0.302488i
$438$		0			0
$439$	−23.9893	+	13.8502i	−1.14494	+	0.661034i	−0.947650	−	0.319310i	$-0.896549\pi$
$439$	−23.9893	+	13.8502i	−1.14494	+	0.661034i	−0.197294	+	0.980344i	$0.563215\pi$
$440$	9.92597	−	3.86430i	0.473202	−	0.184223i
$441$		0			0
$442$	−5.16070	+	37.1460i	−0.245469	+	1.76686i
$443$	−6.50677	+	24.2836i	−0.309146	+	1.15375i	0.620172	+	0.784466i	$0.287063\pi$
$443$	−6.50677	+	24.2836i	−0.309146	+	1.15375i	−0.929317	+	0.369282i	$0.879604\pi$
$444$		0			0
$445$	−11.8900	−	44.3739i	−0.563638	−	2.10353i
$446$	−4.76552	−	38.3115i	−0.225654	−	1.81410i
$447$		0			0
$448$	3.17261	−	10.0887i	0.149892	−	0.476648i
$449$	20.0988			0.948522			0.474261	−	0.880384i	$-0.342715\pi$
$449$	20.0988			0.948522			0.474261	+	0.880384i	$0.342715\pi$
$450$		0			0
$451$	1.54419	−	1.54419i	0.0727133	−	0.0727133i
$452$	6.59977	−	1.66768i	0.310427	−	0.0784409i
$453$		0			0
$454$	3.24352	+	2.52587i	0.152226	+	0.118545i
$455$	−11.3087	−	6.52907i	−0.530159	−	0.306088i
$456$		0			0
$457$	−20.8270	+	12.0245i	−0.974244	+	0.562480i	−0.900527	−	0.434799i	$-0.856819\pi$
$457$	−20.8270	+	12.0245i	−0.974244	+	0.562480i	−0.0737167	+	0.997279i	$0.523486\pi$
$458$	9.40558	+	1.30672i	0.439494	+	0.0610589i
$459$		0			0
$460$	−11.0430	−	19.7744i	−0.514882	−	0.921988i
$461$	3.90967	+	1.04759i	0.182092	+	0.0487913i	0.348713	−	0.937230i	$-0.386619\pi$
$461$	3.90967	+	1.04759i	0.182092	+	0.0487913i	−0.166621	+	0.986021i	$0.553286\pi$
$462$		0			0
$463$	5.16489	−	8.94585i	0.240033	−	0.415749i	−0.720691	−	0.693257i	$-0.756175\pi$
$463$	5.16489	−	8.94585i	0.240033	−	0.415749i	0.960723	+	0.277508i	$0.0895085\pi$
$464$	−4.20514	+	14.0719i	−0.195219	+	0.653270i
$465$		0			0
$466$	6.50489	−	15.3921i	0.301333	−	0.713027i
$467$	−11.8966	+	11.8966i	−0.550509	+	0.550509i	−0.926588	−	0.376079i	$-0.877272\pi$
$467$	−11.8966	+	11.8966i	−0.550509	+	0.550509i	0.376079	+	0.926588i	$0.377272\pi$
$468$		0			0
$469$	13.4785	+	13.4785i	0.622380	+	0.622380i
$470$	−13.8273	−	34.0687i	−0.637805	−	1.57147i
$471$		0			0
$472$	−8.33236	−	11.3549i	−0.383528	−	0.522653i
$473$	−7.35663	−	4.24735i	−0.338258	−	0.195293i
$474$		0			0
$475$	4.79476	−	17.8943i	0.219999	−	0.821046i
$476$	−19.3527	−	5.48317i	−0.887029	−	0.251321i
$477$		0			0
$478$	−3.95654	+	2.99128i	−0.180968	+	0.136818i
$479$	7.47878	+	12.9536i	0.341714	+	0.591866i	0.984751	−	0.173969i	$-0.0556593\pi$
$479$	7.47878	+	12.9536i	0.341714	+	0.591866i	−0.643037	+	0.765835i	$0.722326\pi$
$480$		0			0
$481$	5.57077	−	9.64886i	0.254005	−	0.439950i
$482$	1.52095	+	12.2274i	0.0692774	+	0.556943i
$483$		0			0
$484$	4.52436	+	17.9050i	0.205653	+	0.813864i
$485$	2.60062	+	2.60062i	0.118088	+	0.118088i
$486$		0			0
$487$		−	27.0362i		−	1.22513i	−0.790420	−	0.612565i	$-0.790138\pi$
$487$		−	27.0362i		−	1.22513i	0.790420	−	0.612565i	$-0.209862\pi$
$488$	−3.17635	−	28.9024i	−0.143787	−	1.30835i
$489$		0			0
$490$	−12.9329	+	16.6074i	−0.584250	+	0.750246i
$491$	−5.41853	+	1.45189i	−0.244535	+	0.0655229i	−0.379005	−	0.925395i	$-0.623734\pi$
$491$	−5.41853	+	1.45189i	−0.244535	+	0.0655229i	0.134470	+	0.990918i	$0.457067\pi$
$492$		0			0
$493$	26.9814	+	7.22964i	1.21518	+	0.325607i
$494$	18.1752	+	24.0401i	0.817739	+	1.08162i
$495$		0			0
$496$	3.87636	+	2.38829i	0.174054	+	0.107237i
$497$	5.20527	+	9.01579i	0.233488	+	0.404413i
$498$		0			0
$499$	5.68146	+	21.2035i	0.254337	+	0.949198i	0.968458	+	0.249176i	$0.0801598\pi$
$499$	5.68146	+	21.2035i	0.254337	+	0.949198i	−0.714121	+	0.700022i	$0.753174\pi$
$500$	11.1627	+	0.159562i	0.499210	+	0.00713583i
$501$		0			0
$502$	−7.29738	−	17.9798i	−0.325698	−	0.802478i
$503$		−	23.1955i		−	1.03423i	−0.855915	−	0.517117i	$-0.827005\pi$
$503$		−	23.1955i		−	1.03423i	0.855915	−	0.517117i	$-0.172995\pi$
$504$		0			0
$505$		−	28.5716i		−	1.27142i
$506$	−6.95932	+	2.82454i	−0.309379	+	0.125566i
$507$		0			0
$508$	−7.31083	−	7.52286i	−0.324366	−	0.333773i
$509$	3.37049	+	12.5788i	0.149394	+	0.557547i	0.999520	+	0.0309681i	$0.00985902\pi$
$509$	3.37049	+	12.5788i	0.149394	+	0.557547i	−0.850126	+	0.526579i	$0.823474\pi$
$510$		0			0
$511$	−0.381537	−	0.660842i	−0.0168782	−	0.0292339i
$512$	20.3052	+	9.98491i	0.897372	+	0.441275i
$513$		0			0
$514$	−20.9117	+	15.8099i	−0.922374	+	0.697346i
$515$	−25.4385	−	6.81623i	−1.12095	−	0.300359i
$516$		0			0
$517$	−11.7772	+	3.15568i	−0.517959	+	0.138787i
$518$	4.71473	+	3.67157i	0.207154	+	0.161320i
$519$		0			0
$520$	17.4791	−	21.7954i	0.766511	−	0.955790i
$521$		−	21.4547i		−	0.939949i	−0.882680	−	0.469974i	$-0.844263\pi$
$521$		−	21.4547i		−	0.939949i	0.882680	−	0.469974i	$-0.155737\pi$
$522$		0			0
$523$	2.07495	+	2.07495i	0.0907314	+	0.0907314i	0.751016	−	0.660284i	$-0.229564\pi$
$523$	2.07495	+	2.07495i	0.0907314	+	0.0907314i	−0.660284	+	0.751016i	$0.729564\pi$
$524$	6.65206	−	11.1506i	0.290597	−	0.487114i
$525$		0			0
$526$	5.55334	−	0.690773i	0.242137	−	0.0301191i
$527$	4.32977	−	7.49939i	0.188608	−	0.326678i
$528$		0			0
$529$	−3.51490	−	6.08799i	−0.152822	−	0.264695i
$530$	−26.3939	−	34.9110i	−1.14648	−	1.51644i
$531$		0			0
$532$	−14.1126	+	7.88113i	−0.611858	+	0.341690i
$533$	1.48251	−	5.53282i	0.0642148	−	0.239653i
$534$		0			0
$535$	6.57693	+	3.79719i	0.284346	+	0.164167i
$536$	−32.8801	+	24.1277i	−1.42020	+	1.04216i
$537$		0			0
$538$	32.7536	−	13.2935i	1.41211	−	0.573125i
$539$	4.93571	+	4.93571i	0.212596	+	0.212596i
$540$		0			0
$541$	22.7947	−	22.7947i	0.980022	−	0.980022i	−0.0197819	−	0.999804i	$-0.506297\pi$
$541$	22.7947	−	22.7947i	0.980022	−	0.980022i	0.999804	+	0.0197819i	$0.00629719\pi$
$542$	35.1149	+	14.8399i	1.50831	+	0.637430i
$543$		0			0
$544$	17.8790	−	39.1461i	0.766556	−	1.67838i
$545$	17.2980	−	29.9610i	0.740965	−	1.28339i
$546$		0			0
$547$	13.3804	+	3.58528i	0.572106	+	0.153295i	0.533262	−	0.845950i	$-0.320966\pi$
$547$	13.3804	+	3.58528i	0.572106	+	0.153295i	0.0388438	+	0.999245i	$0.487633\pi$
$548$	13.7010	+	3.88188i	0.585276	+	0.165826i
$549$		0			0
$550$	−0.783685	+	5.64086i	−0.0334164	+	0.240527i
$551$	19.4399	−	11.2236i	0.828166	−	0.478142i
$552$		0			0
$553$	−1.64148	−	0.947711i	−0.0698030	−	0.0403008i
$554$	−8.31663	+	10.6795i	−0.353340	+	0.453730i
$555$		0			0
$556$	7.23952	+	4.31887i	0.307024	+	0.183161i
$557$	8.62660	−	8.62660i	0.365521	−	0.365521i	−0.500320	−	0.865841i	$-0.666784\pi$
$557$	8.62660	−	8.62660i	0.365521	−	0.365521i	0.865841	+	0.500320i	$0.166784\pi$
$558$		0			0
$559$	−22.2810			−0.942384
$560$	10.2886	+	10.8943i	0.434772	+	0.460368i
$561$		0			0
$562$	13.7982	−	1.71634i	0.582042	−	0.0723995i
$563$	5.46409	+	20.3923i	0.230284	+	0.859432i	0.980218	+	0.197920i	$0.0634185\pi$
$563$	5.46409	+	20.3923i	0.230284	+	0.859432i	−0.749934	+	0.661513i	$0.769915\pi$
$564$		0			0
$565$	−2.49631	+	9.31636i	−0.105021	+	0.391942i
$566$	43.6485	+	6.06409i	1.83468	+	0.254893i
$567$		0			0
$568$	−20.7563	+	8.08069i	−0.870916	+	0.339058i
$569$	−21.4776	+	12.4001i	−0.900389	+	0.519840i	−0.877326	−	0.479894i	$-0.840675\pi$
$569$	−21.4776	+	12.4001i	−0.900389	+	0.519840i	−0.0230625	+	0.999734i	$0.507342\pi$
$570$		0			0
$571$	17.7063	−	4.74438i	0.740985	−	0.198546i	0.131469	−	0.991320i	$-0.458031\pi$
$571$	17.7063	−	4.74438i	0.740985	−	0.198546i	0.609516	+	0.792774i	$0.291364\pi$
$572$	−6.45685	−	6.64412i	−0.269974	−	0.277804i
$573$		0			0
$574$	2.82985	+	1.19593i	0.118116	+	0.0499171i
$575$	12.1096			0.505004
$576$		0			0
$577$	−23.4462			−0.976078			−0.488039	−	0.872822i	$-0.662288\pi$
$577$	−23.4462			−0.976078			−0.488039	+	0.872822i	$0.662288\pi$
$578$	−53.2495	−	22.5038i	−2.21489	−	0.936036i
$579$		0			0
$580$	−14.5026	−	14.9233i	−0.602189	−	0.619655i
$581$	4.36800	−	1.17040i	0.181215	−	0.0485564i
$582$		0			0
$583$	−12.5688	+	7.25657i	−0.520545	+	0.300537i
$584$	1.52140	−	0.592301i	0.0629561	−	0.0245096i
$585$		0			0
$586$	44.4049	+	6.16917i	1.83435	+	0.254846i
$587$	−4.33159	+	16.1657i	−0.178784	+	0.667230i	0.817092	+	0.576507i	$0.195585\pi$
$587$	−4.33159	+	16.1657i	−0.178784	+	0.667230i	−0.995876	+	0.0907235i	$0.971082\pi$
$588$		0			0
$589$	−1.80108	−	6.72173i	−0.0742123	−	0.276964i
$590$	19.8029	−	2.46326i	0.815274	−	0.101411i
$591$		0			0
$592$	−9.29528	+	8.77848i	−0.382034	+	0.360793i
$593$	−6.18675			−0.254059			−0.127030	−	0.991899i	$-0.540544\pi$
$593$	−6.18675			−0.254059			−0.127030	+	0.991899i	$0.540544\pi$
$594$		0			0
$595$	20.1524	−	20.1524i	0.826168	−	0.826168i
$596$	14.9539	+	8.92102i	0.612536	+	0.365419i
$597$		0			0
$598$	−12.1039	+	15.5429i	−0.494967	+	0.635596i
$599$	−7.98730	−	4.61147i	−0.326352	−	0.188420i	0.327868	−	0.944723i	$-0.393670\pi$
$599$	−7.98730	−	4.61147i	−0.326352	−	0.188420i	−0.654220	+	0.756304i	$0.727003\pi$
$600$		0			0
$601$	−15.0097	+	8.66586i	−0.612259	+	0.353488i	−0.773849	−	0.633370i	$-0.781671\pi$
$601$	−15.0097	+	8.66586i	−0.612259	+	0.353488i	0.161590	+	0.986858i	$0.448338\pi$
$602$	1.64446	−	11.8366i	0.0670232	−	0.482424i
$603$		0			0
$604$	39.5735	+	11.2123i	1.61022	+	0.456222i
$605$	−25.2751	−	6.77243i	−1.02758	−	0.275339i
$606$		0			0
$607$	11.8418	−	20.5106i	0.480643	−	0.832498i	−0.519110	−	0.854707i	$-0.673737\pi$
$607$	11.8418	−	20.5106i	0.480643	−	0.832498i	0.999753	+	0.0222090i	$0.00706992\pi$
$608$	−12.0847	−	32.4036i	−0.490099	−	1.31414i
$609$		0			0
$610$	37.9482	+	16.0374i	1.53648	+	0.649333i
$611$	−22.6135	+	22.6135i	−0.914844	+	0.914844i
$612$		0			0
$613$	15.4110	+	15.4110i	0.622445	+	0.622445i	0.946156	−	0.323711i	$-0.104930\pi$
$613$	15.4110	+	15.4110i	0.622445	+	0.622445i	−0.323711	+	0.946156i	$0.604930\pi$
$614$	−31.9697	+	12.9754i	−1.29019	+	0.523644i
$615$		0			0
$616$	4.00619	−	2.93978i	0.161414	−	0.118447i
$617$	11.9979	+	6.92700i	0.483018	+	0.278870i	0.721673	−	0.692234i	$-0.243373\pi$
$617$	11.9979	+	6.92700i	0.483018	+	0.278870i	−0.238655	+	0.971104i	$0.576707\pi$
$618$		0			0
$619$	−10.3518	+	38.6333i	−0.416072	+	1.55280i	0.366606	+	0.930376i	$0.380520\pi$
$619$	−10.3518	+	38.6333i	−0.416072	+	1.55280i	−0.782678	+	0.622427i	$0.786147\pi$
$620$	−5.63235	+	3.14537i	−0.226201	+	0.126321i
$621$		0			0
$622$	−8.40666	−	11.1194i	−0.337076	−	0.445848i
$623$	−10.7156	−	18.5599i	−0.429310	−	0.743586i
$624$		0			0
$625$	−15.4844	+	26.8198i	−0.619377	+	1.07279i
$626$	13.7058	−	1.70485i	0.547794	−	0.0681394i
$627$		0			0
$628$	9.45044	−	15.8414i	0.377114	−	0.632139i
$629$	17.1945	+	17.1945i	0.685591	+	0.685591i
$630$		0			0
$631$			16.7956i			0.668624i	0.942462	+	0.334312i	$0.108504\pi$
$631$			16.7956i			0.668624i	−0.942462	+	0.334312i	$0.891496\pi$
$632$	2.53714	−	3.16365i	0.100922	−	0.125843i
$633$		0			0
$634$	−14.7972	−	11.5233i	−0.587673	−	0.457647i
$635$	14.3567	−	3.84688i	0.569730	−	0.152659i
$636$		0			0
$637$	17.6845	+	4.73856i	0.700687	+	0.187749i
$638$	−5.50452	+	4.16161i	−0.217926	+	0.164760i
$639$		0			0
$640$	−26.3793	+	18.2208i	−1.04274	+	0.720240i
$641$	−20.0246	−	34.6837i	−0.790925	−	1.36992i	−0.925395	−	0.379005i	$-0.876266\pi$
$641$	−20.0246	−	34.6837i	−0.790925	−	1.36992i	0.134470	−	0.990918i	$-0.457067\pi$
$642$		0			0
$643$	−0.289008	−	1.07859i	−0.0113974	−	0.0425356i	0.959993	−	0.280024i	$-0.0903425\pi$
$643$	−0.289008	−	1.07859i	−0.0113974	−	0.0425356i	−0.971390	+	0.237489i	$0.923676\pi$
$644$	−7.36371	−	7.57728i	−0.290171	−	0.298587i
$645$		0			0
$646$	−60.9473	+	24.7364i	−2.39794	+	0.973241i
$647$		−	31.9272i		−	1.25519i	−0.778541	−	0.627594i	$-0.784040\pi$
$647$		−	31.9272i		−	1.25519i	0.778541	−	0.627594i	$-0.215960\pi$
$648$		0			0
$649$		−	6.61750i		−	0.259759i
$650$	5.61762	+	13.8411i	0.220341	+	0.542893i
$651$		0			0
$652$	−29.4275	−	0.420645i	−1.15247	−	0.0164737i
$653$	3.36682	+	12.5651i	0.131754	+	0.491712i	0.999990	−	0.00443888i	$-0.00141294\pi$
$653$	3.36682	+	12.5651i	0.131754	+	0.491712i	−0.868236	+	0.496151i	$0.834746\pi$
$654$		0			0
$655$	9.19841	+	15.9321i	0.359412	+	0.622519i
$656$	−3.44790	+	5.59619i	−0.134618	+	0.218494i
$657$		0			0
$658$	−10.3443	−	13.6823i	−0.403261	−	0.533390i
$659$	−15.4883	−	4.15007i	−0.603337	−	0.161664i	−0.0557954	−	0.998442i	$-0.517769\pi$
$659$	−15.4883	−	4.15007i	−0.603337	−	0.161664i	−0.547541	+	0.836779i	$0.684436\pi$
$660$		0			0
$661$	21.9923	−	5.89283i	0.855403	−	0.229204i	0.195637	−	0.980676i	$-0.437322\pi$
$661$	21.9923	−	5.89283i	0.855403	−	0.229204i	0.659765	+	0.751472i	$0.270656\pi$
$662$	−0.920387	+	1.18189i	−0.0357719	+	0.0459353i
$663$		0			0
$664$	1.05693	+	9.61729i	0.0410169	+	0.373223i
$665$		−	22.9026i		−	0.888124i
$666$		0			0
$667$	10.3754	+	10.3754i	0.401738	+	0.401738i
$668$	3.36857	+	13.3310i	0.130334	+	0.515791i
$669$		0			0
$670$	−7.13277	−	57.3426i	−0.275563	−	2.21534i
$671$	6.83085	−	11.8314i	0.263702	−	0.456745i
$672$		0			0
$673$	16.3212	+	28.2692i	0.629136	+	1.08970i	0.987725	+	0.156201i	$0.0499246\pi$
$673$	16.3212	+	28.2692i	0.629136	+	1.08970i	−0.358589	+	0.933496i	$0.616742\pi$
$674$	5.64921	−	4.27100i	0.217599	−	0.164513i
$675$		0			0
$676$	1.63497	+	0.463234i	0.0628835	+	0.0178167i
$677$	−3.84993	+	14.3681i	−0.147965	+	0.552212i	0.851641	+	0.524126i	$0.175608\pi$
$677$	−3.84993	+	14.3681i	−0.147965	+	0.552212i	−0.999606	+	0.0280861i	$0.991059\pi$
$678$		0			0
$679$	1.48588	+	0.857871i	0.0570227	+	0.0329221i
$680$	36.0746	+	49.1607i	1.38340	+	1.88523i
$681$		0			0
$682$	0.804514	+	1.98222i	0.0308065	+	0.0759031i
$683$	−21.4912	−	21.4912i	−0.822338	−	0.822338i	0.164105	−	0.986443i	$-0.447526\pi$
$683$	−21.4912	−	21.4912i	−0.822338	−	0.822338i	−0.986443	+	0.164105i	$0.947526\pi$
$684$		0			0
$685$	−14.2671	+	14.2671i	−0.545120	+	0.545120i
$686$	−8.91697	+	21.0997i	−0.340451	+	0.805590i
$687$		0			0
$688$	24.4977	+	7.32073i	0.933967	+	0.279100i
$689$	−19.0334	+	32.9669i	−0.725116	+	1.25594i
$690$		0			0
$691$	−8.83775	−	2.36807i	−0.336204	−	0.0900855i	0.0867676	−	0.996229i	$-0.472346\pi$
$691$	−8.83775	−	2.36807i	−0.336204	−	0.0900855i	−0.422971	+	0.906143i	$0.639013\pi$
$692$	3.10428	+	5.55876i	0.118007	+	0.211312i
$693$		0			0
$694$	8.53733	+	1.18609i	0.324072	+	0.0450234i
$695$	−10.3440	+	5.97209i	−0.392369	+	0.226534i
$696$		0			0
$697$	10.8266	+	6.25077i	0.410088	+	0.236765i
$698$	6.26354	+	4.87769i	0.237078	+	0.184623i
$699$		0			0
$700$	−7.76760	+	1.96277i	−0.293588	+	0.0741858i
$701$	4.05144	−	4.05144i	0.153021	−	0.153021i	−0.626445	−	0.779466i	$-0.715491\pi$
$701$	4.05144	−	4.05144i	0.153021	−	0.153021i	0.779466	+	0.626445i	$0.215491\pi$
$702$		0			0
$703$	19.5411			0.737005
$704$	4.91623	+	9.42664i	0.185287	+	0.355280i
$705$		0			0
$706$	−1.76713	−	14.2065i	−0.0665067	−	0.534669i
$707$	−3.44978	−	12.8747i	−0.129742	−	0.484204i
$708$		0			0
$709$	−1.00775	+	3.76098i	−0.0378469	+	0.141247i	−0.982264	−	0.187503i	$-0.939961\pi$
$709$	−1.00775	+	3.76098i	−0.0378469	+	0.141247i	0.944417	+	0.328750i	$0.106627\pi$
$710$	4.34283	−	31.2591i	0.162983	−	1.17313i
$711$		0			0
$712$	42.7289	−	16.6349i	1.60133	−	0.623419i
$713$	3.93936	−	2.27439i	0.147530	−	0.0851767i
$714$		0			0
$715$	12.6797	−	3.39752i	0.474195	−	0.127060i
$716$	10.5673	+	0.151051i	0.394918	+	0.00564506i
$717$		0			0
$718$	2.90719	−	6.87911i	0.108495	−	0.256726i
$719$	37.0063			1.38010			0.690050	−	0.723761i	$-0.257588\pi$
$719$	37.0063			1.38010			0.690050	+	0.723761i	$0.257588\pi$
$720$		0			0
$721$	−12.2859			−0.457552
$722$	−10.1164	+	23.9378i	−0.376494	+	0.890874i
$723$		0			0
$724$	−0.00683737	+	0.478330i	−0.000254109	+	0.0177770i
$725$	10.7469	−	2.87962i	0.399129	−	0.106946i
$726$		0			0
$727$	28.4066	−	16.4006i	1.05354	−	0.608264i	0.129905	−	0.991526i	$-0.458533\pi$
$727$	28.4066	−	16.4006i	1.05354	−	0.608264i	0.923640	+	0.383262i	$0.125199\pi$
$728$	5.24473	−	11.9317i	0.194383	−	0.442220i
$729$		0			0
$730$	−0.318322	+	2.29124i	−0.0117816	+	0.0848025i
$731$	12.5861	−	46.9719i	0.465513	−	1.73732i
$732$		0			0
$733$	10.9743	+	40.9566i	0.405345	+	1.51277i	0.803419	+	0.595413i	$0.203012\pi$
$733$	10.9743	+	40.9566i	0.405345	+	1.51277i	−0.398075	+	0.917353i	$0.630322\pi$
$734$	−1.75245	−	14.0885i	−0.0646840	−	0.520015i
$735$		0			0
$736$	18.4150	−	13.1123i	0.678786	−	0.483327i
$737$	−19.1620			−0.705842
$738$		0			0
$739$	−15.3761	+	15.3761i	−0.565620	+	0.565620i	−0.930898	−	0.365278i	$-0.880974\pi$
$739$	−15.3761	+	15.3761i	−0.565620	+	0.565620i	0.365278	+	0.930898i	$0.380974\pi$
$740$	−4.43800	−	17.5632i	−0.163144	−	0.645637i
$741$		0			0
$742$	−16.1087	−	12.5445i	−0.591367	−	0.460524i
$743$	−40.4824	−	23.3725i	−1.48516	−	0.857456i	−0.485299	−	0.874348i	$-0.661289\pi$
$743$	−40.4824	−	23.3725i	−1.48516	−	0.857456i	−0.999857	+	0.0168926i	$0.994623\pi$
$744$		0			0
$745$	−21.3664	+	12.3359i	−0.782805	+	0.451952i
$746$	−36.5247	−	5.07438i	−1.33727	−	0.185786i
$747$		0			0
$748$	17.6542	−	9.85896i	0.645503	−	0.360479i
$749$	3.42213	+	0.916958i	0.125042	+	0.0335049i
$750$		0			0
$751$	25.7074	−	44.5265i	0.938077	−	1.62480i	0.169023	−	0.985612i	$-0.445939\pi$
$751$	25.7074	−	44.5265i	0.938077	−	1.62480i	0.769054	−	0.639184i	$-0.220728\pi$
$752$	32.2933	−	17.4334i	1.17762	−	0.635729i
$753$		0			0
$754$	−7.04584	+	16.6721i	−0.256594	+	0.607164i
$755$	−41.2088	+	41.2088i	−1.49974	+	1.49974i
$756$		0			0
$757$	25.4143	+	25.4143i	0.923698	+	0.923698i	0.997289	−	0.0735910i	$-0.0234459\pi$
$757$	25.4143	+	25.4143i	0.923698	+	0.923698i	−0.0735910	+	0.997289i	$0.523446\pi$
$758$	8.51866	+	20.9889i	0.309412	+	0.762351i
$759$		0			0
$760$	48.4336	+	7.43596i	1.75687	+	0.269731i
$761$	−20.2336	−	11.6819i	−0.733467	−	0.423467i	0.0862220	−	0.996276i	$-0.472521\pi$
$761$	−20.2336	−	11.6819i	−0.733467	−	0.423467i	−0.819689	+	0.572808i	$0.805854\pi$
$762$		0			0
$763$	4.17717	−	15.5894i	0.151224	−	0.564375i
$764$	12.0435	−	42.5071i	0.435718	−	1.53785i
$765$		0			0
$766$	5.64219	−	4.26569i	0.203861	−	0.154126i
$767$	−8.67859	−	15.0318i	−0.313366	−	0.542765i
$768$		0			0
$769$	−12.7645	+	22.1087i	−0.460299	+	0.797261i	−0.998976	−	0.0452513i	$-0.985591\pi$
$769$	−12.7645	+	22.1087i	−0.460299	+	0.797261i	0.538677	+	0.842513i	$0.318924\pi$
$770$	0.869076	+	6.98678i	0.0313193	+	0.251786i
$771$		0			0
$772$	30.6635	−	7.74828i	1.10360	−	0.278867i
$773$	19.2256	+	19.2256i	0.691496	+	0.691496i	0.962561	−	0.271065i	$-0.0873758\pi$
$773$	19.2256	+	19.2256i	0.691496	+	0.691496i	−0.271065	+	0.962561i	$0.587376\pi$
$774$		0			0
$775$		−	3.44916i		−	0.123898i
$776$	−2.29663	+	2.86375i	−0.0824441	+	0.102803i
$777$		0			0
$778$	−11.6076	+	14.9055i	−0.416152	+	0.534389i
$779$	9.70397	−	2.60017i	0.347681	−	0.0931608i
$780$		0			0
$781$	−10.1088	−	2.70866i	−0.361723	−	0.0969234i
$782$	−25.9297	−	34.2969i	−0.927243	−	1.22646i
$783$		0			0
$784$	−17.8871	−	11.0205i	−0.638824	−	0.393590i
$785$	13.0680	+	22.6344i	0.466416	+	0.807857i
$786$		0			0
$787$	5.16260	+	19.2671i	0.184027	+	0.686797i	0.994837	+	0.101488i	$0.0323603\pi$
$787$	5.16260	+	19.2671i	0.184027	+	0.686797i	−0.810810	+	0.585309i	$0.800973\pi$
$788$	0.0483542	−	3.38277i	0.00172255	−	0.120506i
$789$		0			0
$790$	2.16088	+	5.32413i	0.0768807	+	0.189424i
$791$			4.49949i			0.159983i
$792$		0			0
$793$		−	35.8336i		−	1.27249i
$794$	34.6851	−	14.0775i	1.23093	−	0.499591i
$795$		0			0
$796$	−9.16750	+	8.90911i	−0.324933	+	0.315775i
$797$	3.02171	+	11.2772i	0.107035	+	0.399458i	0.998568	−	0.0534965i	$-0.0170366\pi$
$797$	3.02171	+	11.2772i	0.107035	+	0.399458i	−0.891534	+	0.452955i	$0.850370\pi$
$798$		0			0
$799$	−34.8990	−	60.4469i	−1.23464	−	2.13846i
$800$	−1.62883	−	17.0639i	−0.0575880	−	0.603301i
$801$		0			0
$802$	15.0290	−	11.3625i	0.530694	−	0.401222i
$803$	0.740961	+	0.198540i	0.0261479	+	0.00700632i
$804$		0			0
$805$	14.4606	−	3.87471i	0.509669	−	0.136565i
$806$	4.42708	+	3.44756i	0.155937	+	0.121435i
$807$		0			0
$808$	28.3471	−	3.11532i	0.997248	−	0.109597i
$809$			13.1110i			0.460958i	0.973077	+	0.230479i	$0.0740292\pi$
$809$			13.1110i			0.460958i	−0.973077	+	0.230479i	$0.925971\pi$
$810$		0			0
$811$	−34.1945	−	34.1945i	−1.20073	−	1.20073i	−0.973944	−	0.226789i	$-0.927177\pi$
$811$	−34.1945	−	34.1945i	−1.20073	−	1.20073i	−0.226789	−	0.973944i	$-0.572823\pi$
$812$	−8.33694	−	4.97355i	−0.292569	−	0.174537i
$813$		0			0
$814$	−5.96129	+	0.741517i	−0.208943	+	0.0259902i
$815$	20.8498	−	36.1129i	0.730337	−	1.26498i
$816$		0			0
$817$	−19.5392	−	33.8429i	−0.683590	−	1.18401i
$818$	10.4428	+	13.8125i	0.365122	+	0.482944i
$819$		0			0
$820$	−4.54088	−	8.13126i	−0.158574	−	0.283956i
$821$	−6.39631	+	23.8714i	−0.223233	+	0.833116i	0.759872	+	0.650073i	$0.225262\pi$
$821$	−6.39631	+	23.8714i	−0.223233	+	0.833116i	−0.983105	+	0.183044i	$0.941405\pi$
$822$		0			0
$823$	−16.2152	−	9.36184i	−0.565226	−	0.326333i	0.190014	−	0.981781i	$-0.439147\pi$
$823$	−16.2152	−	9.36184i	−0.565226	−	0.326333i	−0.755240	+	0.655448i	$0.772480\pi$
$824$	3.98897	−	25.9819i	0.138962	−	0.905121i
$825$		0			0
$826$	8.62605	−	3.50101i	0.300139	−	0.121816i
$827$	24.1212	+	24.1212i	0.838775	+	0.838775i	0.988698	−	0.149923i	$-0.0479025\pi$
$827$	24.1212	+	24.1212i	0.838775	+	0.838775i	−0.149923	+	0.988698i	$0.547902\pi$
$828$		0			0
$829$	−20.8683	+	20.8683i	−0.724787	+	0.724787i	−0.969576	−	0.244789i	$-0.921281\pi$
$829$	−20.8683	+	20.8683i	−0.724787	+	0.724787i	0.244789	+	0.969576i	$0.421281\pi$
$830$	−12.6273	−	5.33643i	−0.438299	−	0.185230i
$831$		0			0
$832$	23.5300	+	14.9653i	0.815755	+	0.518830i
$833$	−19.9793	+	34.6052i	−0.692242	+	1.19900i
$834$		0			0
$835$	−18.8183	−	5.04234i	−0.651233	−	0.174497i
$836$	4.42954	−	15.6339i	0.153199	−	0.540711i
$837$		0			0
$838$	6.45566	−	46.4670i	0.223007	−	1.60518i
$839$	5.01977	−	2.89816i	0.173302	−	0.100056i	−0.410840	−	0.911707i	$-0.634765\pi$
$839$	5.01977	−	2.89816i	0.173302	−	0.100056i	0.584142	+	0.811652i	$0.301431\pi$
$840$		0			0
$841$	−13.4396	−	7.75936i	−0.463435	−	0.267564i
$842$	−22.2225	+	28.5363i	−0.765838	+	0.983426i
$843$		0			0
$844$	−2.13620	+	3.58081i	−0.0735309	+	0.123257i
$845$	−1.70253	+	1.70253i	−0.0585689	+	0.0585689i
$846$		0			0
$847$	−12.2070			−0.419437
$848$	31.7588	−	29.9931i	1.09060	−	1.02997i
$849$		0			0
$850$	−32.3526	+	4.02430i	−1.10968	+	0.138032i
$851$	3.30600	+	12.3381i	0.113328	+	0.422946i
$852$		0			0
$853$	−0.461332	+	1.72171i	−0.0157957	+	0.0589504i	−0.973374	−	0.229223i	$-0.926381\pi$
$853$	−0.461332	+	1.72171i	−0.0157957	+	0.0589504i	0.957578	+	0.288174i	$0.0930481\pi$
$854$	19.0363	+	2.64472i	0.651410	+	0.0905004i
$855$		0			0
$856$	−3.05024	+	6.93929i	−0.104255	+	0.237180i
$857$	−12.6918	+	7.32760i	−0.433543	+	0.250306i	−0.700855	−	0.713304i	$-0.747198\pi$
$857$	−12.6918	+	7.32760i	−0.433543	+	0.250306i	0.267312	+	0.963610i	$0.413865\pi$
$858$		0			0
$859$	−51.3859	+	13.7688i	−1.75327	+	0.469786i	−0.985318	−	0.170727i	$-0.945388\pi$
$859$	−51.3859	+	13.7688i	−1.75327	+	0.469786i	−0.767947	+	0.640513i	$0.778722\pi$
$860$	−25.9799	+	25.2477i	−0.885908	+	0.860938i
$861$		0			0
$862$	−13.4228	−	5.67262i	−0.457182	−	0.193210i
$863$	−23.9467			−0.815157			−0.407578	−	0.913170i	$-0.633627\pi$
$863$	−23.9467			−0.815157			−0.407578	+	0.913170i	$0.633627\pi$
$864$		0			0
$865$	−9.02103			−0.306724
$866$	15.3313	+	6.47917i	0.520978	+	0.220171i
$867$		0			0
$868$	−2.15824	+	2.09740i	−0.0732553	+	0.0711905i
$869$	1.84049	−	0.493159i	0.0624345	−	0.0167293i
$870$		0			0
$871$	−43.5269	+	25.1303i	−1.47485	+	0.851507i
$872$	31.6117	+	13.8953i	1.07051	+	0.470554i
$873$		0			0
$874$	−34.2228	−	4.75457i	−1.15760	−	0.160826i
$875$	−1.90986	+	7.12771i	−0.0645652	+	0.240961i
$876$		0			0
$877$	10.6447	+	39.7266i	0.359446	+	1.34147i	0.874796	+	0.484492i	$0.160996\pi$
$877$	10.6447	+	39.7266i	0.359446	+	1.34147i	−0.515349	+	0.856980i	$0.672338\pi$
$878$	38.8747	−	4.83557i	1.31196	−	0.163193i
$879$		0			0
$880$	−15.0576	−	0.430561i	−0.507590	−	0.0145142i
$881$	41.2335			1.38919			0.694597	−	0.719399i	$-0.255583\pi$
$881$	41.2335			1.38919			0.694597	+	0.719399i	$0.255583\pi$
$882$		0			0
$883$	−11.9719	+	11.9719i	−0.402885	+	0.402885i	−0.879248	−	0.476364i	$-0.841955\pi$
$883$	−11.9719	+	11.9719i	−0.402885	+	0.402885i	0.476364	+	0.879248i	$0.341955\pi$
$884$	27.1723	−	45.5477i	0.913902	−	1.53193i
$885$		0			0
$886$	21.8447	−	28.0512i	0.733887	−	0.942398i
$887$	26.7452	+	15.4413i	0.898016	+	0.518470i	0.876556	−	0.481300i	$-0.159835\pi$
$887$	26.7452	+	15.4413i	0.898016	+	0.518470i	0.0214599	+	0.999770i	$0.493169\pi$
$888$		0			0
$889$	6.00486	−	3.46691i	0.201397	−	0.116276i
$890$	−8.94013	+	64.3499i	−0.299674	+	2.15701i
$891$		0			0
$892$	−14.8834	+	52.5305i	−0.498333	+	1.75885i
$893$	−54.1788	−	14.5172i	−1.81302	−	0.485798i
$894$		0			0
$895$	−7.48706	+	12.9680i	−0.250265	+	0.433471i
$896$	−9.68688	+	11.3956i	−0.323616	+	0.380701i
$897$		0			0
$898$	−26.1820	−	11.0648i	−0.873704	−	0.369237i
$899$	2.95523	−	2.95523i	0.0985624	−	0.0985624i
$900$		0			0
$901$	−58.7480	−	58.7480i	−1.95718	−	1.95718i
$902$	−2.86167	+	1.16145i	−0.0952833	+	0.0386722i
$903$		0			0
$904$	−9.51536	−	1.46088i	−0.316476	−	0.0485883i
$905$	−0.586997	−	0.338903i	−0.0195125	−	0.0112655i
$906$		0			0
$907$	7.16365	−	26.7351i	0.237865	−	0.887725i	−0.738971	−	0.673737i	$-0.764688\pi$
$907$	7.16365	−	26.7351i	0.237865	−	0.887725i	0.976836	−	0.213988i	$-0.0686453\pi$
$908$	−2.83466	−	5.07598i	−0.0940717	−	0.168452i
$909$		0			0
$910$	11.1370	+	14.7308i	0.369188	+	0.488322i
$911$	4.83009	+	8.36596i	0.160028	+	0.277177i	0.934878	−	0.354968i	$-0.115508\pi$
$911$	4.83009	+	8.36596i	0.160028	+	0.277177i	−0.774850	+	0.632145i	$0.782175\pi$
$912$		0			0
$913$	−2.27297	+	3.93689i	−0.0752242	+	0.130292i
$914$	33.7502	−	4.19814i	1.11636	−	0.138862i
$915$		0			0
$916$	−11.5329	−	6.88017i	−0.381058	−	0.227327i
$917$	6.06859	+	6.06859i	0.200403	+	0.200403i
$918$		0			0
$919$			12.5574i			0.414229i	0.978317	+	0.207115i	$0.0664073\pi$
$919$			12.5574i			0.414229i	−0.978317	+	0.207115i	$0.933593\pi$
$920$	3.49905	+	31.8388i	0.115360	+	1.04969i
$921$		0			0
$922$	−4.51626	−	3.51701i	−0.148735	−	0.115827i
$923$	−26.5147	+	7.10460i	−0.872743	+	0.233851i
$924$		0			0
$925$	9.35553	+	2.50681i	0.307608	+	0.0824233i
$926$	−11.6530	+	8.81005i	−0.382941	+	0.289516i
$927$		0			0
$928$	13.2247	−	16.0159i	0.434122	−	0.525747i
$929$	−4.50031	−	7.79477i	−0.147650	−	0.255738i	0.782708	−	0.622389i	$-0.213838\pi$
$929$	−4.50031	−	7.79477i	−0.147650	−	0.255738i	−0.930359	+	0.366651i	$0.880504\pi$
$930$		0			0
$931$	8.31092	+	31.0168i	0.272379	+	1.01653i
$932$	−16.9473	+	16.4697i	−0.555129	+	0.539482i
$933$		0			0
$934$	22.0466	−	8.94793i	0.721385	−	0.292785i
$935$			28.6501i			0.936960i
$936$		0			0
$937$			59.2265i			1.93485i	0.253166	+	0.967423i	$0.418528\pi$
$937$			59.2265i			1.93485i	−0.253166	+	0.967423i	$0.581472\pi$
$938$	−10.1378	−	24.9781i	−0.331009	−	0.815565i
$939$		0			0
$940$	−0.743188	+	51.9921i	−0.0242401	+	1.69580i
$941$	2.95446	+	11.0262i	0.0963126	+	0.359443i	0.997215	−	0.0745778i	$-0.0237609\pi$
$941$	2.95446	+	11.0262i	0.0963126	+	0.359443i	−0.900903	+	0.434021i	$0.857094\pi$
$942$		0			0
$943$	3.28347	+	5.68714i	0.106925	+	0.185199i
$944$	4.60313	+	19.3788i	0.149819	+	0.630725i
$945$		0			0
$946$	7.24495	+	9.58283i	0.235554	+	0.311565i
$947$	−8.32058	−	2.22949i	−0.270382	−	0.0724488i	0.121080	−	0.992643i	$-0.461364\pi$
$947$	−8.32058	−	2.22949i	−0.270382	−	0.0724488i	−0.391463	+	0.920194i	$0.628031\pi$
$948$		0			0
$949$	1.94348	−	0.520755i	0.0630882	−	0.0169044i
$950$	−16.0971	+	20.6706i	−0.522259	+	0.670642i
$951$		0			0
$952$	22.1914	+	17.7968i	0.719228	+	0.576796i
$953$		−	43.5260i		−	1.40995i	−0.709234	−	0.704973i	$-0.750959\pi$
$953$		−	43.5260i		−	1.40995i	0.709234	−	0.704973i	$-0.249041\pi$
$954$		0			0
$955$	44.2637	+	44.2637i	1.43234	+	1.43234i
$956$	6.80079	−	1.71847i	0.219953	−	0.0555794i
$957$		0			0
$958$	−2.61109	−	20.9914i	−0.0843606	−	0.678201i
$959$	−4.70633	+	8.15160i	−0.151975	+	0.263229i
$960$		0			0
$961$	14.8522	+	25.7247i	0.479103	+	0.829830i
$962$	−12.5687	+	9.50238i	−0.405232	+	0.306369i
$963$		0			0
$964$	4.75014	−	16.7655i	0.152992	−	0.539980i
$965$	−11.5982	+	43.2852i	−0.373361	+	1.39340i
$966$		0			0
$967$	−26.2267	−	15.1420i	−0.843393	−	0.486933i	0.0150229	−	0.999887i	$-0.495218\pi$
$967$	−26.2267	−	15.1420i	−0.843393	−	0.486933i	−0.858416	+	0.512954i	$0.828551\pi$
$968$	3.96334	−	25.8149i	0.127387	−	0.829723i
$969$		0			0
$970$	−1.95604	−	4.81942i	−0.0628045	−	0.154742i
$971$	−9.06755	−	9.06755i	−0.290992	−	0.290992i	0.546480	−	0.837472i	$-0.315967\pi$
$971$	−9.06755	−	9.06755i	−0.290992	−	0.290992i	−0.837472	+	0.546480i	$0.815967\pi$
$972$		0			0
$973$	−3.94005	+	3.94005i	−0.126312	+	0.126312i
$974$	−14.8840	+	35.2191i	−0.476914	+	1.12849i
$975$		0			0
$976$	−11.7736	+	39.3987i	−0.376865	+	1.26112i
$977$	−10.4475	+	18.0956i	−0.334246	+	0.578931i	−0.983340	−	0.181778i	$-0.941815\pi$
$977$	−10.4475	+	18.0956i	−0.334246	+	0.578931i	0.649094	+	0.760708i	$0.275148\pi$
$978$		0			0
$979$	20.8100	+	5.57603i	0.665092	+	0.178211i
$980$	25.9899	−	14.5140i	0.830218	−	0.463633i
$981$		0			0
$982$	7.85781	+	1.09168i	0.250753	+	0.0348371i
$983$	1.14158	−	0.659092i	0.0364108	−	0.0210218i	−0.481684	−	0.876345i	$-0.659975\pi$
$983$	1.14158	−	0.659092i	0.0364108	−	0.0210218i	0.518095	+	0.855323i	$0.326641\pi$
$984$		0			0
$985$	4.15128	+	2.39674i	0.132271	+	0.0763665i
$986$	−31.1676	−	24.2716i	−0.992577	−	0.772964i
$987$		0			0
$988$	−10.4415	−	41.3219i	−0.332189	−	1.31463i
$989$	18.0626	−	18.0626i	0.574357	−	0.574357i
$990$		0			0
$991$	2.51185			0.0797914			0.0398957	−	0.999204i	$-0.487297\pi$
$991$	2.51185			0.0797914			0.0398957	+	0.999204i	$0.487297\pi$
$992$	−3.73479	−	5.24514i	−0.118580	−	0.166533i
$993$		0			0
$994$	−1.81734	−	14.6101i	−0.0576424	−	0.463405i
$995$	−4.68788	−	17.4954i	−0.148616	−	0.554641i
$996$		0			0
$997$	11.9030	−	44.4227i	0.376973	−	1.40688i	−0.473468	−	0.880811i	$-0.656998\pi$
$997$	11.9030	−	44.4227i	0.376973	−	1.40688i	0.850441	−	0.526071i	$-0.176335\pi$
$998$	4.27192	−	30.7487i	0.135225	−	0.973334i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.37.2		72
3.2	odd	2		144.2.x.e.85.17	yes	72
4.3	odd	2		1728.2.bc.e.1009.5		72
9.2	odd	6		144.2.x.e.133.7	yes	72
9.7	even	3	inner	432.2.y.e.181.12		72
12.11	even	2		576.2.bb.e.49.18		72
16.3	odd	4		1728.2.bc.e.145.14		72
16.13	even	4	inner	432.2.y.e.253.12		72
36.7	odd	6		1728.2.bc.e.1585.14		72
36.11	even	6		576.2.bb.e.241.11		72
48.29	odd	4		144.2.x.e.13.7	✓	72
48.35	even	4		576.2.bb.e.337.11		72
144.29	odd	12		144.2.x.e.61.17	yes	72
144.61	even	12	inner	432.2.y.e.397.2		72
144.83	even	12		576.2.bb.e.529.18		72
144.115	odd	12		1728.2.bc.e.721.5		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.7	✓	72	48.29	odd	4
144.2.x.e.61.17	yes	72	144.29	odd	12
144.2.x.e.85.17	yes	72	3.2	odd	2
144.2.x.e.133.7	yes	72	9.2	odd	6
432.2.y.e.37.2		72	1.1	even	1	trivial
432.2.y.e.181.12		72	9.7	even	3	inner
432.2.y.e.253.12		72	16.13	even	4	inner
432.2.y.e.397.2		72	144.61	even	12	inner
576.2.bb.e.49.18		72	12.11	even	2
576.2.bb.e.241.11		72	36.11	even	6
576.2.bb.e.337.11		72	48.35	even	4
576.2.bb.e.529.18		72	144.83	even	12
1728.2.bc.e.145.14		72	16.3	odd	4
1728.2.bc.e.721.5		72	144.115	odd	12
1728.2.bc.e.1009.5		72	4.3	odd	2
1728.2.bc.e.1585.14		72	36.7	odd	6

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	432.2.y.e.37.2

Level	$432$
Weight	$2$
Character	432.37
Analytic conductor	$3.450$
Analytic rank	$0$
Dimension	$72$
Inner twists	$4$