LMFDB - Embedded newform 804.2.y.a.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	804.157
Dual form			804.2.y.a.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(0.336386 + 0.736583i) q^{5} +(-0.860971 + 0.820934i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(0.336386 + 0.736583i) q^{5} +(-0.860971 + 0.820934i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-6.29895 - 0.601476i) q^{11} +(-1.18997 - 0.229348i) q^{13} +(-0.776959 + 0.228136i) q^{15} +(0.338723 + 0.174624i) q^{17} +(-5.52620 - 5.26922i) q^{19} +(-0.690049 - 0.969038i) q^{21} +(2.28586 - 0.915120i) q^{23} +(2.84490 - 3.28319i) q^{25} +(0.415415 - 0.909632i) q^{27} +(-4.30380 + 7.45439i) q^{29} +(-1.70014 + 0.327675i) q^{31} +(1.49179 - 6.14923i) q^{33} +(-0.894305 - 0.358026i) q^{35} +(1.87912 + 3.25473i) q^{37} +(0.396364 - 1.14522i) q^{39} +(-0.0769909 - 1.61624i) q^{41} +(1.67464 - 1.07623i) q^{43} +(-0.115241 - 0.801517i) q^{45} +(-2.15399 - 1.69392i) q^{47} +(-0.265735 + 5.57847i) q^{49} +(-0.221052 + 0.310424i) q^{51} +(-8.63650 - 5.55034i) q^{53} +(-1.67584 - 4.84203i) q^{55} +(6.00205 - 4.72006i) q^{57} +(-0.628805 - 0.725680i) q^{59} +(-2.52726 + 0.241324i) q^{61} +(1.05738 - 0.545117i) q^{63} +(-0.231356 - 0.953661i) q^{65} +(-2.35790 - 7.83839i) q^{67} +(0.580494 + 2.39283i) q^{69} +(-8.85676 + 4.56598i) q^{71} +(-1.71735 + 0.163987i) q^{73} +(2.84490 + 3.28319i) q^{75} +(5.91698 - 4.65316i) q^{77} +(0.687180 + 1.98548i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-7.45985 + 10.4759i) q^{83} +(-0.0146832 + 0.308239i) q^{85} +(-6.76602 - 5.32086i) q^{87} +(1.71692 + 11.9415i) q^{89} +(1.21281 - 0.779424i) q^{91} +(-0.0823847 - 1.72947i) q^{93} +(2.02228 - 5.84300i) q^{95} +(-6.15956 - 10.6687i) q^{97} +(5.87434 + 2.35173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{14}{33}\right)$	$1$

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
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	0.336386	+	0.736583i	0.150437	+	0.329410i	0.969815	−	0.243843i	$-0.0784083\pi$
$5$	0.336386	+	0.736583i	0.150437	+	0.329410i	−0.819378	+	0.573253i	$0.805681\pi$
$6$		0			0
$7$	−0.860971	+	0.820934i	−0.325416	+	0.310284i	−0.835122	−	0.550065i	$-0.814603\pi$
$7$	−0.860971	+	0.820934i	−0.325416	+	0.310284i	0.509705	+	0.860349i	$0.329754\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	−6.29895	−	0.601476i	−1.89920	−	0.181352i	−0.921079	−	0.389375i	$-0.872691\pi$
$11$	−6.29895	−	0.601476i	−1.89920	−	0.181352i	−0.978124	+	0.208023i	$0.933297\pi$
$12$		0			0
$13$	−1.18997	−	0.229348i	−0.330038	−	0.0636096i	0.0215406	−	0.999768i	$-0.493143\pi$
$13$	−1.18997	−	0.229348i	−0.330038	−	0.0636096i	−0.351579	+	0.936158i	$0.614355\pi$
$14$		0			0
$15$	−0.776959	+	0.228136i	−0.200610	+	0.0589044i
$16$		0			0
$17$	0.338723	+	0.174624i	0.0821524	+	0.0423525i	0.498813	−	0.866710i	$-0.333769\pi$
$17$	0.338723	+	0.174624i	0.0821524	+	0.0423525i	−0.416661	+	0.909062i	$0.636800\pi$
$18$		0			0
$19$	−5.52620	−	5.26922i	−1.26780	−	1.20884i	−0.966891	−	0.255189i	$-0.917862\pi$
$19$	−5.52620	−	5.26922i	−1.26780	−	1.20884i	−0.300907	−	0.953654i	$-0.597289\pi$
$20$		0			0
$21$	−0.690049	−	0.969038i	−0.150581	−	0.211461i
$22$		0			0
$23$	2.28586	−	0.915120i	0.476634	−	0.190816i	−0.120891	−	0.992666i	$-0.538575\pi$
$23$	2.28586	−	0.915120i	0.476634	−	0.190816i	0.597525	+	0.801850i	$0.296151\pi$
$24$		0			0
$25$	2.84490	−	3.28319i	0.568981	−	0.656639i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	−4.30380	+	7.45439i	−0.799195	+	1.38425i	0.120946	+	0.992659i	$0.461407\pi$
$29$	−4.30380	+	7.45439i	−0.799195	+	1.38425i	−0.920141	+	0.391587i	$0.871926\pi$
$30$		0			0
$31$	−1.70014	+	0.327675i	−0.305354	+	0.0588522i	−0.339627	−	0.940560i	$-0.610301\pi$
$31$	−1.70014	+	0.327675i	−0.305354	+	0.0588522i	0.0342726	+	0.999413i	$0.489089\pi$
$32$		0			0
$33$	1.49179	−	6.14923i	0.259687	−	1.07044i
$34$		0			0
$35$	−0.894305	−	0.358026i	−0.151165	−	0.0605174i
$36$		0			0
$37$	1.87912	+	3.25473i	0.308926	+	0.535075i	0.978128	−	0.208006i	$-0.0666972\pi$
$37$	1.87912	+	3.25473i	0.308926	+	0.535075i	−0.669202	+	0.743081i	$0.733364\pi$
$38$		0			0
$39$	0.396364	−	1.14522i	0.0634690	−	0.183382i
$40$		0			0
$41$	−0.0769909	−	1.61624i	−0.0120240	−	0.252414i	−0.996874	−	0.0790065i	$-0.974825\pi$
$41$	−0.0769909	−	1.61624i	−0.0120240	−	0.252414i	0.984850	−	0.173408i	$-0.0554778\pi$
$42$		0			0
$43$	1.67464	−	1.07623i	0.255380	−	0.164123i	−0.406687	−	0.913568i	$-0.633316\pi$
$43$	1.67464	−	1.07623i	0.255380	−	0.164123i	0.662067	+	0.749445i	$0.269680\pi$
$44$		0			0
$45$	−0.115241	−	0.801517i	−0.0171791	−	0.119483i
$46$		0			0
$47$	−2.15399	−	1.69392i	−0.314192	−	0.247083i	0.448592	−	0.893737i	$-0.351926\pi$
$47$	−2.15399	−	1.69392i	−0.314192	−	0.247083i	−0.762784	+	0.646653i	$0.776168\pi$
$48$		0			0
$49$	−0.265735	+	5.57847i	−0.0379622	+	0.796925i
$50$		0			0
$51$	−0.221052	+	0.310424i	−0.0309535	+	0.0434680i
$52$		0			0
$53$	−8.63650	−	5.55034i	−1.18631	−	0.762398i	−0.209777	−	0.977749i	$-0.567274\pi$
$53$	−8.63650	−	5.55034i	−1.18631	−	0.762398i	−0.976537	+	0.215352i	$0.930910\pi$
$54$		0			0
$55$	−1.67584	−	4.84203i	−0.225970	−	0.652899i
$56$		0			0
$57$	6.00205	−	4.72006i	0.794991	−	0.625188i
$58$		0			0
$59$	−0.628805	−	0.725680i	−0.0818635	−	0.0944755i	0.713340	−	0.700818i	$-0.247182\pi$
$59$	−0.628805	−	0.725680i	−0.0818635	−	0.0944755i	−0.795204	+	0.606343i	$0.792636\pi$
$60$		0			0
$61$	−2.52726	+	0.241324i	−0.323582	+	0.0308983i	−0.255583	−	0.966787i	$-0.582267\pi$
$61$	−2.52726	+	0.241324i	−0.323582	+	0.0308983i	−0.0679988	+	0.997685i	$0.521661\pi$
$62$		0			0
$63$	1.05738	−	0.545117i	0.133217	−	0.0686783i
$64$		0			0
$65$	−0.231356	−	0.953661i	−0.0286961	−	0.118287i
$66$		0			0
$67$	−2.35790	−	7.83839i	−0.288063	−	0.957612i
$67$	−2.35790	−	7.83839i	−0.288063	−	0.957612i
$68$		0			0
$69$	0.580494	+	2.39283i	0.0698832	+	0.288062i
$70$		0			0
$71$	−8.85676	+	4.56598i	−1.05110	+	0.541882i	−0.895096	−	0.445874i	$-0.852893\pi$
$71$	−8.85676	+	4.56598i	−1.05110	+	0.541882i	−0.156008	+	0.987756i	$0.549863\pi$
$72$		0			0
$73$	−1.71735	+	0.163987i	−0.201001	+	0.0191933i	−0.195071	−	0.980789i	$-0.562494\pi$
$73$	−1.71735	+	0.163987i	−0.201001	+	0.0191933i	−0.00593009	+	0.999982i	$0.501888\pi$
$74$		0			0
$75$	2.84490	+	3.28319i	0.328501	+	0.379111i
$76$		0			0
$77$	5.91698	−	4.65316i	0.674302	−	0.530277i
$78$		0			0
$79$	0.687180	+	1.98548i	0.0773138	+	0.223384i	0.977034	−	0.213084i	$-0.0683507\pi$
$79$	0.687180	+	1.98548i	0.0773138	+	0.223384i	−0.899720	+	0.436467i	$0.856229\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	−7.45985	+	10.4759i	−0.818825	+	1.14988i	0.167630	+	0.985850i	$0.446389\pi$
$83$	−7.45985	+	10.4759i	−0.818825	+	1.14988i	−0.986455	+	0.164029i	$0.947551\pi$
$84$		0			0
$85$	−0.0146832	+	0.308239i	−0.00159262	+	0.0334332i
$86$		0			0
$87$	−6.76602	−	5.32086i	−0.725394	−	0.570456i
$88$		0			0
$89$	1.71692	+	11.9415i	0.181993	+	1.26579i	0.852041	+	0.523474i	$0.175364\pi$
$89$	1.71692	+	11.9415i	0.181993	+	1.26579i	−0.670048	+	0.742318i	$0.733727\pi$
$90$		0			0
$91$	1.21281	−	0.779424i	0.127137	−	0.0817059i
$92$		0			0
$93$	−0.0823847	−	1.72947i	−0.00854289	−	0.179337i
$94$		0			0
$95$	2.02228	−	5.84300i	0.207482	−	0.599479i
$96$		0			0
$97$	−6.15956	−	10.6687i	−0.625409	−	1.08324i	−0.988462	−	0.151471i	$-0.951599\pi$
$97$	−6.15956	−	10.6687i	−0.625409	−	1.08324i	0.363053	−	0.931768i	$-0.381734\pi$
$98$		0			0
$99$	5.87434	+	2.35173i	0.590393	+	0.236358i
$100$		0			0
$101$	−2.71070	+	11.1737i	−0.269725	+	1.11182i	0.662246	+	0.749287i	$0.269604\pi$
$101$	−2.71070	+	11.1737i	−0.269725	+	1.11182i	−0.931970	+	0.362534i	$0.881912\pi$
$102$		0			0
$103$	7.77542	−	1.49859i	0.766135	−	0.147660i	0.208811	−	0.977956i	$-0.433041\pi$
$103$	7.77542	−	1.49859i	0.766135	−	0.147660i	0.557323	+	0.830296i	$0.311828\pi$
$104$		0			0
$105$	0.481654	−	0.834250i	0.0470046	−	0.0814144i
$106$		0			0
$107$	−2.71631	+	5.94790i	−0.262596	+	0.575005i	−0.994300	−	0.106617i	$-0.965998\pi$
$107$	−2.71631	+	5.94790i	−0.262596	+	0.575005i	0.731704	+	0.681622i	$0.238725\pi$
$108$		0			0
$109$	12.6661	−	14.6175i	1.21320	−	1.40010i	0.321845	−	0.946792i	$-0.395697\pi$
$109$	12.6661	−	14.6175i	1.21320	−	1.40010i	0.891352	−	0.453312i	$-0.149757\pi$
$110$		0			0
$111$	−3.48903	+	1.39680i	−0.331164	+	0.132578i
$112$		0			0
$113$	3.19914	+	4.49256i	0.300950	+	0.422625i	0.937165	−	0.348887i	$-0.113440\pi$
$113$	3.19914	+	4.49256i	0.300950	+	0.422625i	−0.636215	+	0.771512i	$0.719501\pi$
$114$		0			0
$115$	1.44299	+	1.37589i	0.134560	+	0.128303i
$116$		0			0
$117$	1.07715	+	0.555311i	0.0995828	+	0.0513385i
$118$		0			0
$119$	−0.434985	+	0.127723i	−0.0398750	+	0.0117084i
$120$		0			0
$121$	28.5137	+	5.49557i	2.59216	+	0.499597i
$122$		0			0
$123$	1.61074	+	0.153807i	0.145236	+	0.0138684i
$124$		0			0
$125$	7.26013	+	2.13177i	0.649365	+	0.190671i
$126$		0			0
$127$	−8.47022	+	8.07634i	−0.751611	+	0.716659i	−0.965559	−	0.260186i	$-0.916216\pi$
$127$	−8.47022	+	8.07634i	−0.751611	+	0.716659i	0.213948	+	0.976845i	$0.431368\pi$
$128$		0			0
$129$	0.826945	+	1.81076i	0.0728084	+	0.159428i
$130$		0			0
$131$	−0.748388	+	5.20516i	−0.0653870	+	0.454777i	0.930655	+	0.365897i	$0.119238\pi$
$131$	−0.748388	+	5.20516i	−0.0653870	+	0.454777i	−0.996042	+	0.0888797i	$0.971671\pi$
$132$		0			0
$133$	9.08358			0.787646
$134$		0			0
$135$	0.809760			0.0696930
$136$		0			0
$137$	−2.72824	+	18.9753i	−0.233089	+	1.62117i	0.451522	+	0.892260i	$0.350881\pi$
$137$	−2.72824	+	18.9753i	−0.233089	+	1.62117i	−0.684611	+	0.728909i	$0.740028\pi$
$138$		0			0
$139$	−6.23645	−	13.6559i	−0.528969	−	1.15828i	−0.965931	−	0.258800i	$-0.916673\pi$
$139$	−6.23645	−	13.6559i	−0.528969	−	1.15828i	0.436962	−	0.899480i	$-0.356054\pi$
$140$		0			0
$141$	1.98322	−	1.89100i	0.167017	−	0.159251i
$142$		0			0
$143$	7.35760	+	2.16039i	0.615274	+	0.180661i
$144$		0			0
$145$	−6.93852	−	0.662548i	−0.576213	−	0.0550216i
$146$		0			0
$147$	−5.48387	−	1.05693i	−0.452302	−	0.0871741i
$148$		0			0
$149$	−9.22891	+	2.70985i	−0.756062	+	0.222000i	−0.636976	−	0.770884i	$-0.719815\pi$
$149$	−9.22891	+	2.70985i	−0.756062	+	0.222000i	−0.119087	+	0.992884i	$0.537997\pi$
$150$		0			0
$151$	2.97063	+	1.53146i	0.241746	+	0.124629i	0.574843	−	0.818264i	$-0.305063\pi$
$151$	2.97063	+	1.53146i	0.241746	+	0.124629i	−0.333097	+	0.942893i	$0.608094\pi$
$152$		0			0
$153$	−0.275805	−	0.262980i	−0.0222975	−	0.0212607i
$154$		0			0
$155$	−0.813263	−	1.14207i	−0.0653229	−	0.0917332i
$156$		0			0
$157$	8.51067	−	3.40716i	0.679225	−	0.271921i	−0.00628872	−	0.999980i	$-0.502002\pi$
$157$	8.51067	−	3.40716i	0.679225	−	0.271921i	0.685514	+	0.728059i	$0.259578\pi$
$158$		0			0
$159$	6.72295	−	7.75869i	0.533164	−	0.615304i
$160$		0			0
$161$	−1.21680	+	2.66443i	−0.0958976	+	0.209986i
$162$		0			0
$163$	−10.8598	+	18.8097i	−0.850606	+	1.47329i	0.0300562	+	0.999548i	$0.490431\pi$
$163$	−10.8598	+	18.8097i	−0.850606	+	1.47329i	−0.880662	+	0.473745i	$0.842902\pi$
$164$		0			0
$165$	5.03124	−	0.969692i	0.391681	−	0.0754904i
$166$		0			0
$167$	−0.645125	+	2.65924i	−0.0499213	+	0.205778i	−0.991310	−	0.131545i	$-0.958006\pi$
$167$	−0.645125	+	2.65924i	−0.0499213	+	0.205778i	0.941389	+	0.337323i	$0.109521\pi$
$168$		0			0
$169$	−10.7054	−	4.28578i	−0.823489	−	0.329675i
$170$		0			0
$171$	3.81784	+	6.61269i	0.291958	+	0.505685i
$172$		0			0
$173$	2.70448	−	7.81407i	0.205617	−	0.594093i	−0.794292	−	0.607536i	$-0.792158\pi$
$173$	2.70448	−	7.81407i	0.205617	−	0.594093i	0.999910	+	0.0134434i	$0.00427928\pi$
$174$		0			0
$175$	0.245906	+	5.16221i	0.0185888	+	0.390227i
$176$		0			0
$177$	0.807782	−	0.519130i	0.0607166	−	0.0390202i
$178$		0			0
$179$	−0.818405	−	5.69213i	−0.0611704	−	0.425450i	−0.997278	−	0.0737355i	$-0.976508\pi$
$179$	−0.818405	−	5.69213i	−0.0611704	−	0.425450i	0.936107	−	0.351714i	$-0.114401\pi$
$180$		0			0
$181$	6.47812	+	5.09445i	0.481515	+	0.378668i	0.829207	−	0.558941i	$-0.188792\pi$
$181$	6.47812	+	5.09445i	0.481515	+	0.378668i	−0.347692	+	0.937609i	$0.613035\pi$
$182$		0			0
$183$	0.120799	−	2.53588i	0.00892969	−	0.187457i
$184$		0			0
$185$	−1.76527	+	2.47898i	−0.129785	+	0.182258i
$186$		0			0
$187$	−2.02857	−	1.30368i	−0.148343	−	0.0953346i
$188$		0			0
$189$	0.389088	+	1.12419i	0.0283020	+	0.0817731i
$190$		0			0
$191$	13.4275	−	10.5595i	0.971581	−	0.764060i	−0.000186207	−	1.00000i	$-0.500059\pi$
$191$	13.4275	−	10.5595i	0.971581	−	0.764060i	0.971768	+	0.235940i	$0.0758168\pi$
$192$		0			0
$193$	7.06020	+	8.14791i	0.508204	+	0.586499i	0.950638	−	0.310302i	$-0.100430\pi$
$193$	7.06020	+	8.14791i	0.508204	+	0.586499i	−0.442434	+	0.896801i	$0.645885\pi$
$194$		0			0
$195$	0.976879	−	0.0932807i	0.0699558	−	0.00667997i
$196$		0			0
$197$	13.2887	−	6.85079i	0.946780	−	0.488099i	0.0855607	−	0.996333i	$-0.472732\pi$
$197$	13.2887	−	6.85079i	0.946780	−	0.488099i	0.861219	+	0.508234i	$0.169702\pi$
$198$		0			0
$199$	5.66843	+	23.3656i	0.401825	+	1.65634i	0.709390	+	0.704817i	$0.248971\pi$
$199$	5.66843	+	23.3656i	0.401825	+	1.65634i	−0.307565	+	0.951527i	$0.599514\pi$
$200$		0			0
$201$	8.09417	−	1.21838i	0.570919	−	0.0859376i
$202$		0			0
$203$	−2.41412	−	9.95114i	−0.169438	−	0.698433i
$204$		0			0
$205$	1.16460	−	0.600391i	0.0813389	−	0.0419331i
$206$		0			0
$207$	−2.45108	+	0.234050i	−0.170362	+	0.0162676i
$208$		0			0
$209$	31.6399	+	36.5144i	2.18858	+	2.52576i
$210$		0			0
$211$	2.52314	−	1.98422i	0.173700	−	0.136599i	−0.527524	−	0.849540i	$-0.676880\pi$
$211$	2.52314	−	1.98422i	0.173700	−	0.136599i	0.701224	+	0.712941i	$0.252637\pi$
$212$		0			0
$213$	−3.25905	−	9.41642i	−0.223307	−	0.645202i
$214$		0			0
$215$	1.35606	+	0.871484i	0.0924822	+	0.0594347i
$216$		0			0
$217$	1.19477	−	1.67782i	0.0811063	−	0.113898i
$218$		0			0
$219$	0.0820866	−	1.72321i	0.00554690	−	0.116444i
$220$		0			0
$221$	−0.363021	−	0.285483i	−0.0244194	−	0.0192036i
$222$		0			0
$223$	2.63875	+	18.3529i	0.176704	+	1.22900i	0.864326	+	0.502932i	$0.167745\pi$
$223$	2.63875	+	18.3529i	0.176704	+	1.22900i	−0.687623	+	0.726068i	$0.741346\pi$
$224$		0			0
$225$	−3.65465	+	2.34870i	−0.243643	+	0.156580i
$226$		0			0
$227$	−0.353565	−	7.42223i	−0.0234669	−	0.492631i	−0.979754	−	0.200203i	$-0.935840\pi$
$227$	−0.353565	−	7.42223i	−0.0234669	−	0.492631i	0.956288	−	0.292428i	$-0.0944632\pi$
$228$		0			0
$229$	6.10521	−	17.6399i	0.403444	−	1.16567i	−0.542138	−	0.840290i	$-0.682385\pi$
$229$	6.10521	−	17.6399i	0.403444	−	1.16567i	0.945582	−	0.325385i	$-0.105494\pi$
$230$		0			0
$231$	3.76373	+	6.51897i	0.247635	+	0.428916i
$232$		0			0
$233$	−25.3376	−	10.1436i	−1.65992	−	0.664531i	−0.663428	−	0.748240i	$-0.730899\pi$
$233$	−25.3376	−	10.1436i	−1.65992	−	0.664531i	−0.996490	+	0.0837087i	$0.973323\pi$
$234$		0			0
$235$	0.523138	−	2.15641i	0.0341258	−	0.140668i
$236$		0			0
$237$	−2.06306	+	0.397623i	−0.134010	+	0.0258284i
$238$		0			0
$239$	4.71959	−	8.17458i	0.305285	−	0.528769i	−0.672040	−	0.740515i	$-0.734582\pi$
$239$	4.71959	−	8.17458i	0.305285	−	0.528769i	0.977325	+	0.211746i	$0.0679149\pi$
$240$		0			0
$241$	5.97270	−	13.0784i	0.384735	−	0.842453i	−0.613857	−	0.789417i	$-0.710383\pi$
$241$	5.97270	−	13.0784i	0.384735	−	0.842453i	0.998593	−	0.0530359i	$-0.0168898\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	−4.19840	+	1.68079i	−0.268226	+	0.107381i
$246$		0			0
$247$	5.36753	+	7.53764i	0.341528	+	0.479608i
$248$		0			0
$249$	−9.30762	−	8.87480i	−0.589847	−	0.562418i
$250$		0			0
$251$	−8.90936	−	4.59309i	−0.562354	−	0.289913i	0.153517	−	0.988146i	$-0.450940\pi$
$251$	−8.90936	−	4.59309i	−0.562354	−	0.289913i	−0.715871	+	0.698233i	$0.753970\pi$
$252$		0			0
$253$	−14.9489	+	4.38940i	−0.939831	+	0.275959i
$254$		0			0
$255$	−0.303012	−	0.0584008i	−0.0189753	−	0.00365720i
$256$		0			0
$257$	13.1534	+	1.25599i	0.820484	+	0.0783467i	0.496851	−	0.867836i	$-0.334490\pi$
$257$	13.1534	+	1.25599i	0.820484	+	0.0783467i	0.323633	+	0.946183i	$0.395096\pi$
$258$		0			0
$259$	−4.28979	−	1.25960i	−0.266554	−	0.0782675i
$260$		0			0
$261$	6.22961	−	5.93992i	0.385603	−	0.367672i
$262$		0			0
$263$	−6.90007	−	15.1091i	−0.425477	−	0.931664i	−0.994039	−	0.109024i	$-0.965227\pi$
$263$	−6.90007	−	15.1091i	−0.425477	−	0.931664i	0.568562	−	0.822640i	$-0.307500\pi$
$264$		0			0
$265$	1.18309	−	8.22856i	0.0726765	−	0.505476i
$266$		0			0
$267$	−12.0643			−0.738320
$268$		0			0
$269$	14.3928			0.877542			0.438771	−	0.898599i	$-0.355414\pi$
$269$	14.3928			0.877542			0.438771	+	0.898599i	$0.355414\pi$
$270$		0			0
$271$	0.709884	−	4.93735i	0.0431224	−	0.299923i	−0.956834	−	0.290633i	$-0.906134\pi$
$271$	0.709884	−	4.93735i	0.0431224	−	0.299923i	0.999957	−	0.00928935i	$-0.00295694\pi$
$272$		0			0
$273$	0.598890	+	1.31139i	0.0362465	+	0.0793687i
$274$		0			0
$275$	−19.8947	+	18.9695i	−1.19969	+	1.14391i
$276$		0			0
$277$	7.61320	+	2.23544i	0.457433	+	0.134314i	0.502328	−	0.864677i	$-0.332477\pi$
$277$	7.61320	+	2.23544i	0.457433	+	0.134314i	−0.0448948	+	0.998992i	$0.514295\pi$
$278$		0			0
$279$	1.72359	+	0.164583i	0.103189	+	0.00985331i
$280$		0			0
$281$	−6.37963	−	1.22957i	−0.380577	−	0.0733502i	−0.00462479	−	0.999989i	$-0.501472\pi$
$281$	−6.37963	−	1.22957i	−0.380577	−	0.0733502i	−0.375952	+	0.926639i	$0.622684\pi$
$282$		0			0
$283$	−2.20532	+	0.647542i	−0.131093	+	0.0384923i	−0.346621	−	0.938005i	$-0.612671\pi$
$283$	−2.20532	+	0.647542i	−0.131093	+	0.0384923i	0.215528	+	0.976498i	$0.430853\pi$
$284$		0			0
$285$	5.49573	+	2.83324i	0.325539	+	0.167827i
$286$		0			0
$287$	1.39311	+	1.32833i	0.0822328	+	0.0784088i
$288$		0			0
$289$	−9.77673	−	13.7295i	−0.575102	−	0.807617i
$290$		0			0
$291$	11.4367	−	4.57855i	0.670430	−	0.268400i
$292$		0			0
$293$	−17.0034	+	19.6230i	−0.993348	+	1.14639i	−0.00412184	+	0.999992i	$0.501312\pi$
$293$	−17.0034	+	19.6230i	−0.993348	+	1.14639i	−0.989226	+	0.146394i	$0.953233\pi$
$294$		0			0
$295$	0.323002	−	0.707276i	0.0188059	−	0.0411792i
$296$		0			0
$297$	−3.16380	+	5.47986i	−0.183582	+	0.317974i
$298$		0			0
$299$	−2.92998	+	0.564708i	−0.169445	+	0.0326579i
$300$		0			0
$301$	−0.558305	+	2.30137i	−0.0321802	+	0.132649i
$302$		0			0
$303$	−10.6742	−	4.27329i	−0.613214	−	0.245494i
$304$		0			0
$305$	−1.02789	−	1.78036i	−0.0588568	−	0.101943i
$306$		0			0
$307$	−10.0176	+	28.9440i	−0.571736	+	1.65192i	0.173278	+	0.984873i	$0.444564\pi$
$307$	−10.0176	+	28.9440i	−0.571736	+	1.65192i	−0.745014	+	0.667049i	$0.767557\pi$
$308$		0			0
$309$	0.376778	+	7.90955i	0.0214342	+	0.449958i
$310$		0			0
$311$	12.4160	−	7.97928i	0.704047	−	0.452463i	−0.139008	−	0.990291i	$-0.544391\pi$
$311$	12.4160	−	7.97928i	0.704047	−	0.452463i	0.843055	+	0.537828i	$0.180755\pi$
$312$		0			0
$313$	0.581834	+	4.04675i	0.0328872	+	0.228736i	0.999636	−	0.0269938i	$-0.00859344\pi$
$313$	0.581834	+	4.04675i	0.0328872	+	0.228736i	−0.966748	+	0.255730i	$0.917684\pi$
$314$		0			0
$315$	0.757212	+	0.595478i	0.0426640	+	0.0335514i
$316$		0			0
$317$	1.16779	−	24.5149i	0.0655897	−	1.37690i	−0.690928	−	0.722923i	$-0.742798\pi$
$317$	1.16779	−	24.5149i	0.0655897	−	1.37690i	0.756518	−	0.653973i	$-0.226899\pi$
$318$		0			0
$319$	31.5930	−	44.3662i	1.76887	−	2.48403i
$320$		0			0
$321$	−5.50079	−	3.53514i	−0.307024	−	0.197312i
$322$		0			0
$323$	−0.951720	−	2.74982i	−0.0529551	−	0.153004i
$324$		0			0
$325$	−4.13834	+	3.25443i	−0.229554	+	0.180523i
$326$		0			0
$327$	12.6661	+	14.6175i	0.700440	+	0.808350i
$328$		0			0
$329$	3.24512	−	0.309871i	0.178909	−	0.0170838i
$330$		0			0
$331$	−6.74970	+	3.47971i	−0.370997	+	0.191262i	−0.633635	−	0.773632i	$-0.718438\pi$
$331$	−6.74970	+	3.47971i	−0.370997	+	0.191262i	0.262638	+	0.964895i	$0.415408\pi$
$332$		0			0
$333$	−0.886039	−	3.65230i	−0.0485547	−	0.200145i
$334$		0			0
$335$	4.98046	−	4.37351i	0.272112	−	0.238950i
$336$		0			0
$337$	−7.05556	−	29.0834i	−0.384341	−	1.58428i	−0.755141	−	0.655562i	$-0.772432\pi$
$337$	−7.05556	−	29.0834i	−0.384341	−	1.58428i	0.370800	−	0.928713i	$-0.379084\pi$
$338$		0			0
$339$	−4.90212	+	2.52722i	−0.266247	+	0.137260i
$340$		0			0
$341$	10.9062	−	1.04141i	0.590602	−	0.0563957i
$342$		0			0
$343$	−9.80403	−	11.3144i	−0.529368	−	0.610923i
$344$		0			0
$345$	−1.56725	+	1.23250i	−0.0843777	+	0.0663553i
$346$		0			0
$347$	1.38673	+	4.00671i	0.0744438	+	0.215091i	0.976083	−	0.217397i	$-0.0697568\pi$
$347$	1.38673	+	4.00671i	0.0744438	+	0.215091i	−0.901639	+	0.432489i	$0.857636\pi$
$348$		0			0
$349$	−21.2267	−	13.6416i	−1.13624	−	0.730215i	−0.169385	−	0.985550i	$-0.554178\pi$
$349$	−21.2267	−	13.6416i	−1.13624	−	0.730215i	−0.966853	+	0.255335i	$0.917814\pi$
$350$		0			0
$351$	−0.702953	+	0.987160i	−0.0375209	+	0.0526907i
$352$		0			0
$353$	0.0651100	−	1.36683i	0.00346545	−	0.0727488i	−0.996472	−	0.0839248i	$-0.973254\pi$
$353$	0.0651100	−	1.36683i	0.00346545	−	0.0727488i	0.999938	+	0.0111759i	$0.00355748\pi$
$354$		0			0
$355$	−6.34252	−	4.98781i	−0.336626	−	0.264725i
$356$		0			0
$357$	−0.0645183	−	0.448735i	−0.00341467	−	0.0237496i
$358$		0			0
$359$	−20.8058	+	13.3711i	−1.09809	+	0.705698i	−0.958666	−	0.284535i	$-0.908161\pi$
$359$	−20.8058	+	13.3711i	−1.09809	+	0.705698i	−0.139422	+	0.990233i	$0.544524\pi$
$360$		0			0
$361$	1.87014	+	39.2591i	0.0984285	+	2.06627i
$362$		0			0
$363$	−9.49756	+	27.4414i	−0.498492	+	1.44030i
$364$		0			0
$365$	−0.698484	−	1.20981i	−0.0365603	−	0.0633244i
$366$		0			0
$367$	27.5657	+	11.0357i	1.43892	+	0.576057i	0.954349	−	0.298695i	$-0.0965514\pi$
$367$	27.5657	+	11.0357i	1.43892	+	0.576057i	0.484571	+	0.874752i	$0.338976\pi$
$368$		0			0
$369$	−0.381475	+	1.57246i	−0.0198588	+	0.0818590i
$370$		0			0
$371$	11.9922	−	2.31131i	0.622605	−	0.119997i
$372$		0			0
$373$	−13.8168	+	23.9313i	−0.715405	+	1.23912i	0.247399	+	0.968914i	$0.420424\pi$
$373$	−13.8168	+	23.9313i	−0.715405	+	1.23912i	−0.962803	+	0.270203i	$0.912909\pi$
$374$		0			0
$375$	−3.14329	+	6.88285i	−0.162319	+	0.355429i
$376$		0			0
$377$	6.83103	−	7.88343i	0.351816	−	0.406017i
$378$		0			0
$379$	−8.46016	+	3.38694i	−0.434569	+	0.173975i	−0.578624	−	0.815594i	$-0.696410\pi$
$379$	−8.46016	+	3.38694i	−0.434569	+	0.173975i	0.144055	+	0.989570i	$0.453986\pi$
$380$		0			0
$381$	−6.78870	−	9.53339i	−0.347795	−	0.488410i
$382$		0			0
$383$	−19.0948	−	18.2069i	−0.975701	−	0.930329i	0.0218856	−	0.999760i	$-0.493033\pi$
$383$	−19.0948	−	18.2069i	−0.975701	−	0.930329i	−0.997587	+	0.0694313i	$0.977882\pi$
$384$		0			0
$385$	5.41783	+	2.79309i	0.276118	+	0.142349i
$386$		0			0
$387$	−1.91001	+	0.560830i	−0.0970914	+	0.0285086i
$388$		0			0
$389$	−23.0684	−	4.44607i	−1.16962	−	0.225425i	−0.432782	−	0.901499i	$-0.642468\pi$
$389$	−23.0684	−	4.44607i	−1.16962	−	0.225425i	−0.736834	+	0.676074i	$0.763680\pi$
$390$		0			0
$391$	0.934075	+	0.0891934i	0.0472382	+	0.00451070i
$392$		0			0
$393$	−5.04567	−	1.48154i	−0.254520	−	0.0747339i
$394$		0			0
$395$	−1.23131	+	1.17405i	−0.0619540	+	0.0590730i
$396$		0			0
$397$	−3.90667	−	8.55442i	−0.196070	−	0.429334i	0.785904	−	0.618349i	$-0.212198\pi$
$397$	−3.90667	−	8.55442i	−0.196070	−	0.429334i	−0.981974	+	0.189014i	$0.939471\pi$
$398$		0			0
$399$	−1.29273	+	8.99112i	−0.0647174	+	0.450119i
$400$		0			0
$401$	13.3908			0.668706			0.334353	−	0.942448i	$-0.391482\pi$
$401$	13.3908			0.668706			0.334353	+	0.942448i	$0.391482\pi$
$402$		0			0
$403$	2.09826			0.104522
$404$		0			0
$405$	−0.115241	+	0.801517i	−0.00572636	+	0.0398277i
$406$		0			0
$407$	−9.87884	−	21.6316i	−0.489676	−	1.07224i
$408$		0			0
$409$	−11.3066	+	10.7808i	−0.559076	+	0.533078i	−0.916065	−	0.401031i	$-0.868652\pi$
$409$	−11.3066	+	10.7808i	−0.559076	+	0.533078i	0.356988	+	0.934109i	$0.383804\pi$
$410$		0			0
$411$	−18.3939	−	5.40093i	−0.907304	−	0.266408i
$412$		0			0
$413$	1.13712	+	0.108582i	0.0559539	+	0.00534295i
$414$		0			0
$415$	−10.2258	−	1.97085i	−0.501963	−	0.0967454i
$416$		0			0
$417$	14.4045	−	4.22953i	0.705390	−	0.207121i
$418$		0			0
$419$	10.4643	+	5.39470i	0.511213	+	0.263548i	0.694477	−	0.719515i	$-0.255636\pi$
$419$	10.4643	+	5.39470i	0.511213	+	0.263548i	−0.183264	+	0.983064i	$0.558666\pi$
$420$		0			0
$421$	7.67835	+	7.32129i	0.374220	+	0.356818i	0.853728	−	0.520720i	$-0.174336\pi$
$421$	7.67835	+	7.32129i	0.374220	+	0.356818i	−0.479508	+	0.877538i	$0.659185\pi$
$422$		0			0
$423$	1.58951	+	2.23215i	0.0772846	+	0.108531i
$424$		0			0
$425$	1.53696	−	0.615306i	0.0745535	−	0.0298467i
$426$		0			0
$427$	1.97778	−	2.28248i	0.0957116	−	0.110457i
$428$		0			0
$429$	−3.18549	+	6.97526i	−0.153797	+	0.336769i
$430$		0			0
$431$	17.9207	−	31.0396i	0.863210	−	1.49512i	−0.00560396	−	0.999984i	$-0.501784\pi$
$431$	17.9207	−	31.0396i	0.863210	−	1.49512i	0.868814	−	0.495139i	$-0.164883\pi$
$432$		0			0
$433$	−12.5703	+	2.42272i	−0.604088	+	0.116428i	−0.482120	−	0.876105i	$-0.660133\pi$
$433$	−12.5703	+	2.42272i	−0.604088	+	0.116428i	−0.121969	+	0.992534i	$0.538921\pi$
$434$		0			0
$435$	1.64326	−	6.77360i	0.0787882	−	0.324769i
$436$		0			0
$437$	−17.4541	−	6.98756i	−0.834942	−	0.334260i
$438$		0			0
$439$	−17.1465	−	29.6986i	−0.818359	−	1.41744i	−0.906891	−	0.421366i	$-0.861551\pi$
$439$	−17.1465	−	29.6986i	−0.818359	−	1.41744i	0.0885319	−	0.996073i	$-0.471782\pi$
$440$		0			0
$441$	1.82661	−	5.27764i	0.0869814	−	0.251316i
$442$		0			0
$443$	0.00369572	+	0.0775827i	0.000175589	+	0.00368606i	0.998953	−	0.0457388i	$-0.0145642\pi$
$443$	0.00369572	+	0.0775827i	0.000175589	+	0.00368606i	−0.998778	+	0.0494249i	$0.984261\pi$
$444$		0			0
$445$	−8.21833	+	5.28160i	−0.389586	+	0.250372i
$446$		0			0
$447$	−1.36886	−	9.52063i	−0.0647449	−	0.450310i
$448$		0			0
$449$	−3.95295	−	3.10863i	−0.186551	−	0.146705i	0.520516	−	0.853852i	$-0.325740\pi$
$449$	−3.95295	−	3.10863i	−0.186551	−	0.146705i	−0.707067	+	0.707147i	$0.749982\pi$
$450$		0			0
$451$	−0.487168	+	10.2269i	−0.0229398	+	0.481566i
$452$		0			0
$453$	−1.93864	+	2.72244i	−0.0910853	+	0.127911i
$454$		0			0
$455$	0.982083	+	0.631146i	0.0460407	+	0.0295886i
$456$		0			0
$457$	−4.60482	−	13.3048i	−0.215404	−	0.622370i	−0.999997	−	0.00235891i	$-0.999249\pi$
$457$	−4.60482	−	13.3048i	−0.215404	−	0.622370i	0.784593	−	0.620011i	$-0.212872\pi$
$458$		0			0
$459$	0.299554	−	0.235572i	0.0139820	−	0.0109956i
$460$		0			0
$461$	−11.7176	−	13.5229i	−0.545745	−	0.629823i	0.414142	−	0.910212i	$-0.364082\pi$
$461$	−11.7176	−	13.5229i	−0.545745	−	0.629823i	−0.959886	+	0.280390i	$0.909536\pi$
$462$		0			0
$463$	−34.2621	+	3.27163i	−1.59229	+	0.152046i	−0.853210	−	0.521568i	$-0.825347\pi$
$463$	−34.2621	+	3.27163i	−1.59229	+	0.152046i	−0.739084	+	0.673614i	$0.764741\pi$
$464$		0			0
$465$	1.24618	−	0.642452i	0.0577904	−	0.0297930i
$466$		0			0
$467$	0.160839	+	0.662986i	0.00744273	+	0.0306793i	0.975412	−	0.220390i	$-0.0707330\pi$
$467$	0.160839	+	0.662986i	0.00744273	+	0.0306793i	−0.967969	+	0.251069i	$0.919218\pi$
$468$		0			0
$469$	8.46488	+	4.81295i	0.390872	+	0.222241i
$470$		0			0
$471$	2.16128	+	8.90893i	0.0995867	+	0.410502i
$472$		0			0
$473$	−11.1958	+	5.77183i	−0.514783	+	0.265389i
$474$		0			0
$475$	−33.0214	+	3.15316i	−1.51513	+	0.144677i
$476$		0			0
$477$	6.72295	+	7.75869i	0.307823	+	0.355246i
$478$		0			0
$479$	20.0188	−	15.7430i	0.914683	−	0.719315i	−0.0454180	−	0.998968i	$-0.514462\pi$
$479$	20.0188	−	15.7430i	0.914683	−	0.719315i	0.960101	+	0.279653i	$0.0902195\pi$
$480$		0			0
$481$	−1.48963	−	4.30401i	−0.0679213	−	0.196246i
$482$		0			0
$483$	−2.46414	−	1.58361i	−0.112122	−	0.0720566i
$484$		0			0
$485$	5.78637	−	8.12582i	0.262746	−	0.368975i
$486$		0			0
$487$	−0.411109	+	8.63024i	−0.0186291	+	0.391073i	0.970227	+	0.242198i	$0.0778684\pi$
$487$	−0.411109	+	8.63024i	−0.0186291	+	0.391073i	−0.988856	+	0.148875i	$0.952435\pi$
$488$		0			0
$489$	−17.0728	−	13.4262i	−0.772058	−	0.607153i
$490$		0			0
$491$	3.30072	+	22.9570i	0.148959	+	1.03603i	0.917928	+	0.396747i	$0.129861\pi$
$491$	3.30072	+	22.9570i	0.148959	+	1.03603i	−0.768969	+	0.639287i	$0.779230\pi$
$492$		0			0
$493$	−2.75951	+	1.77343i	−0.124282	+	0.0798713i
$494$		0			0
$495$	0.243802	+	5.11803i	0.0109581	+	0.230038i
$496$		0			0
$497$	3.87705	−	11.2020i	0.173909	−	0.502478i
$498$		0			0
$499$	11.9172	+	20.6412i	0.533487	+	0.924026i	0.999235	+	0.0391088i	$0.0124519\pi$
$499$	11.9172	+	20.6412i	0.533487	+	0.924026i	−0.465748	+	0.884917i	$0.654215\pi$
$500$		0			0
$501$	−2.54036	−	1.01701i	−0.113495	−	0.0454366i
$502$		0			0
$503$	−4.32733	+	17.8375i	−0.192946	+	0.795335i	0.790250	+	0.612784i	$0.209951\pi$
$503$	−4.32733	+	17.8375i	−0.192946	+	0.795335i	−0.983196	+	0.182551i	$0.941565\pi$
$504$		0			0
$505$	−9.14218	+	1.76201i	−0.406821	+	0.0784084i
$506$		0			0
$507$	5.76569	−	9.98646i	0.256063	−	0.443514i
$508$		0			0
$509$	−6.38983	+	13.9918i	−0.283224	+	0.620175i	−0.996759	−	0.0804450i	$-0.974366\pi$
$509$	−6.38983	+	13.9918i	−0.283224	+	0.620175i	0.713535	+	0.700620i	$0.247093\pi$
$510$		0			0
$511$	1.34397	−	1.55102i	0.0594536	−	0.0686131i
$512$		0			0
$513$	−7.08872	+	2.83790i	−0.312975	+	0.125296i
$514$		0			0
$515$	3.71938	+	5.22314i	0.163895	+	0.230159i
$516$		0			0
$517$	12.5490	+	11.9655i	0.551906	+	0.526241i
$518$		0			0
$519$	7.34964	+	3.78901i	0.322614	+	0.166319i
$520$		0			0
$521$	21.8181	−	6.40638i	0.955869	−	0.280668i	0.233641	−	0.972323i	$-0.424936\pi$
$521$	21.8181	−	6.40638i	0.955869	−	0.280668i	0.722228	+	0.691655i	$0.243118\pi$
$522$		0			0
$523$	−23.1050	−	4.45312i	−1.01031	−	0.194721i	−0.342868	−	0.939384i	$-0.611398\pi$
$523$	−23.1050	−	4.45312i	−1.01031	−	0.194721i	−0.667441	+	0.744662i	$0.732611\pi$
$524$		0			0
$525$	−5.14466	−	0.491256i	−0.224532	−	0.0214402i
$526$		0			0
$527$	−0.633096	−	0.185894i	−0.0275781	−	0.00809767i
$528$		0			0
$529$	−12.2582	+	11.6881i	−0.532964	+	0.508180i
$530$		0			0
$531$	0.398887	+	0.873440i	0.0173102	+	0.0379041i
$532$		0			0
$533$	−0.279064	+	1.94093i	−0.0120876	+	0.0840711i
$534$		0			0
$535$	−5.29485			−0.228916
$536$		0			0
$537$	5.75066			0.248159
$538$		0			0
$539$	5.02917	−	34.9787i	0.216622	−	1.50664i
$540$		0			0
$541$	−11.0009	−	24.0886i	−0.472965	−	1.03565i	−0.984338	−	0.176290i	$-0.943590\pi$
$541$	−11.0009	−	24.0886i	−0.472965	−	1.03565i	0.511373	−	0.859359i	$-0.329137\pi$
$542$		0			0
$543$	−5.96453	+	5.68717i	−0.255963	+	0.244060i
$544$		0			0
$545$	15.0277	+	4.41254i	0.643717	+	0.189012i
$546$		0			0
$547$	5.31855	+	0.507860i	0.227405	+	0.0217145i	0.208136	−	0.978100i	$-0.433260\pi$
$547$	5.31855	+	0.507860i	0.227405	+	0.0217145i	0.0192685	+	0.999814i	$0.493866\pi$
$548$		0			0
$549$	2.49287	+	0.480462i	0.106393	+	0.0205056i
$550$		0			0
$551$	63.0625	−	18.5168i	2.68655	−	0.788843i
$552$		0			0
$553$	−2.22159	−	1.14531i	−0.0944715	−	0.0487034i
$554$		0			0
$555$	−2.20252	−	2.10010i	−0.0934918	−	0.0891442i
$556$		0			0
$557$	−4.38400	−	6.15646i	−0.185756	−	0.260858i	0.711188	−	0.703002i	$-0.248157\pi$
$557$	−4.38400	−	6.15646i	−0.185756	−	0.260858i	−0.896944	+	0.442144i	$0.854218\pi$
$558$		0			0
$559$	−2.23960	+	0.896600i	−0.0947249	+	0.0379221i
$560$		0			0
$561$	1.57911	−	1.82239i	0.0666699	−	0.0769412i
$562$		0			0
$563$	14.3982	−	31.5277i	0.606812	−	1.32873i	−0.317922	−	0.948117i	$-0.602985\pi$
$563$	14.3982	−	31.5277i	0.606812	−	1.32873i	0.924733	−	0.380615i	$-0.124288\pi$
$564$		0			0
$565$	−2.23300	+	3.86767i	−0.0939430	+	0.162714i
$566$		0			0
$567$	−1.16812	+	0.225138i	−0.0490566	+	0.00945489i
$568$		0			0
$569$	−4.43245	+	18.2708i	−0.185818	+	0.765952i	0.800258	+	0.599656i	$0.204696\pi$
$569$	−4.43245	+	18.2708i	−0.185818	+	0.765952i	−0.986076	+	0.166296i	$0.946819\pi$
$570$		0			0
$571$	9.60831	+	3.84659i	0.402095	+	0.160975i	0.563890	−	0.825850i	$-0.309304\pi$
$571$	9.60831	+	3.84659i	0.402095	+	0.160975i	−0.161795	+	0.986824i	$0.551728\pi$
$572$		0			0
$573$	8.54110	+	14.7936i	0.356810	+	0.618013i
$574$		0			0
$575$	3.49853	−	10.1083i	0.145899	−	0.421547i
$576$		0			0
$577$	−1.55099	−	32.5593i	−0.0645686	−	1.35546i	−0.766053	−	0.642777i	$-0.777782\pi$
$577$	−1.55099	−	32.5593i	−0.0645686	−	1.35546i	0.701485	−	0.712685i	$-0.252521\pi$
$578$		0			0
$579$	−9.06974	+	5.82877i	−0.376926	+	0.242235i
$580$		0			0
$581$	−2.17730	−	15.1435i	−0.0903298	−	0.628258i
$582$		0			0
$583$	51.0624	+	40.1559i	2.11479	+	1.66309i
$584$		0			0
$585$	−0.0466932	+	0.980211i	−0.00193053	+	0.0405267i
$586$		0			0
$587$	18.1345	−	25.4664i	0.748492	−	1.05111i	−0.248110	−	0.968732i	$-0.579809\pi$
$587$	18.1345	−	25.4664i	0.748492	−	1.05111i	0.996601	−	0.0823775i	$-0.0262513\pi$
$588$		0			0
$589$	11.1219	+	7.14761i	0.458270	+	0.294512i
$590$		0			0
$591$	4.88988	+	14.1284i	0.201143	+	0.581165i
$592$		0			0
$593$	−12.3238	+	9.69158i	−0.506080	+	0.397985i	−0.838294	−	0.545219i	$-0.816447\pi$
$593$	−12.3238	+	9.69158i	−0.506080	+	0.397985i	0.332214	+	0.943204i	$0.392204\pi$
$594$		0			0
$595$	−0.240402	−	0.277439i	−0.00985552	−	0.0113739i
$596$		0			0
$597$	−23.9345	+	2.28547i	−0.979573	+	0.0935379i
$598$		0			0
$599$	−9.93728	+	5.12303i	−0.406026	+	0.209321i	−0.649127	−	0.760680i	$-0.724866\pi$
$599$	−9.93728	+	5.12303i	−0.406026	+	0.209321i	0.243101	+	0.970001i	$0.421835\pi$
$600$		0			0
$601$	7.70622	+	31.7655i	0.314343	+	1.29574i	0.881521	+	0.472145i	$0.156520\pi$
$601$	7.70622	+	31.7655i	0.314343	+	1.29574i	−0.567178	+	0.823595i	$0.691965\pi$
$602$		0			0
$603$	0.0540547	+	8.18517i	0.00220128	+	0.333326i
$604$		0			0
$605$	5.54368	+	22.8514i	0.225383	+	0.929040i
$606$		0			0
$607$	33.5727	−	17.3079i	1.36267	−	0.702508i	0.387072	−	0.922050i	$-0.373487\pi$
$607$	33.5727	−	17.3079i	1.36267	−	0.702508i	0.975603	+	0.219542i	$0.0704563\pi$
$608$		0			0
$609$	10.1934	−	0.973354i	0.413058	−	0.0394423i
$610$		0			0
$611$	2.17469	+	2.50972i	0.0879785	+	0.101533i
$612$		0			0
$613$	−23.3586	+	18.3694i	−0.943445	+	0.741934i	−0.966196	−	0.257808i	$-0.917000\pi$
$613$	−23.3586	+	18.3694i	−0.943445	+	0.741934i	0.0227509	+	0.999741i	$0.492758\pi$
$614$		0			0
$615$	0.428540	+	1.23819i	0.0172804	+	0.0499285i
$616$		0			0
$617$	−31.5005	−	20.2441i	−1.26816	−	0.814998i	−0.278782	−	0.960354i	$-0.589931\pi$
$617$	−31.5005	−	20.2441i	−1.26816	−	0.814998i	−0.989379	+	0.145356i	$0.953567\pi$
$618$		0			0
$619$	12.9712	−	18.2155i	0.521356	−	0.732143i	−0.467007	−	0.884254i	$-0.654668\pi$
$619$	12.9712	−	18.2155i	0.521356	−	0.732143i	0.988363	+	0.152111i	$0.0486071\pi$
$620$		0			0
$621$	0.117158	−	2.45944i	0.00470138	−	0.0986941i
$622$		0			0
$623$	−11.2814	−	8.87176i	−0.451978	−	0.355440i
$624$		0			0
$625$	−2.21930	−	15.4356i	−0.0887720	−	0.617423i
$626$		0			0
$627$	−40.6456	+	26.1213i	−1.62323	+	1.04319i
$628$		0			0
$629$	0.0681476	+	1.43059i	0.00271722	+	0.0570415i
$630$		0			0
$631$	7.72714	−	22.3261i	0.307613	−	0.888788i	−0.680184	−	0.733041i	$-0.738100\pi$
$631$	7.72714	−	22.3261i	0.307613	−	0.888788i	0.987797	−	0.155747i	$-0.0497785\pi$
$632$		0			0
$633$	1.60494	+	2.77984i	0.0637908	+	0.110489i
$634$		0			0
$635$	−8.79816	−	3.52225i	−0.349144	−	0.139776i
$636$		0			0
$637$	1.59563	−	6.57726i	0.0632210	−	0.260601i
$638$		0			0
$639$	9.78439	−	1.88579i	0.387064	−	0.0746005i
$640$		0			0
$641$	−3.38739	+	5.86713i	−0.133794	+	0.231738i	−0.925136	−	0.379636i	$-0.876049\pi$
$641$	−3.38739	+	5.86713i	−0.133794	+	0.231738i	0.791342	+	0.611373i	$0.209383\pi$
$642$		0			0
$643$	8.72701	−	19.1095i	0.344160	−	0.753605i	−0.655839	−	0.754901i	$-0.727685\pi$
$643$	8.72701	−	19.1095i	0.344160	−	0.753605i	0.999999	+	0.00129559i	$0.000412398\pi$
$644$		0			0
$645$	−1.05560	+	1.21823i	−0.0415642	+	0.0479677i
$646$		0			0
$647$	33.9314	−	13.5841i	1.33398	−	0.534046i	0.408473	−	0.912770i	$-0.366061\pi$
$647$	33.9314	−	13.5841i	1.33398	−	0.534046i	0.925510	+	0.378724i	$0.123637\pi$
$648$		0			0
$649$	3.52433	+	4.94923i	0.138342	+	0.194274i
$650$		0			0
$651$	1.49071	+	1.42139i	0.0584255	+	0.0557086i
$652$		0			0
$653$	−8.36429	−	4.31209i	−0.327320	−	0.168745i	0.286732	−	0.958011i	$-0.407431\pi$
$653$	−8.36429	−	4.31209i	−0.327320	−	0.168745i	−0.614052	+	0.789266i	$0.710461\pi$
$654$		0			0
$655$	−4.08578	+	1.19969i	−0.159645	+	0.0468759i
$656$		0			0
$657$	1.69399	+	0.326490i	0.0660888	+	0.0127376i
$658$		0			0
$659$	0.103438	+	0.00987716i	0.00402939	+	0.000384760i	0.0970705	−	0.995278i	$-0.469053\pi$
$659$	0.103438	+	0.00987716i	0.00402939	+	0.000384760i	−0.0930412	+	0.995662i	$0.529659\pi$
$660$		0			0
$661$	7.62636	+	2.23930i	0.296631	+	0.0870988i	0.426662	−	0.904411i	$-0.359689\pi$
$661$	7.62636	+	2.23930i	0.296631	+	0.0870988i	−0.130031	+	0.991510i	$0.541508\pi$
$662$		0			0
$663$	0.334240	−	0.318697i	0.0129808	−	0.0123772i
$664$		0			0
$665$	3.05559	+	6.69081i	0.118491	+	0.259459i
$666$		0			0
$667$	−3.01621	+	20.9782i	−0.116788	+	0.812278i
$668$		0			0
$669$	−18.5416			−0.716860
$670$		0			0
$671$	16.0642			0.620151
$672$		0			0
$673$	0.970654	−	6.75105i	0.0374160	−	0.260234i	−0.962524	−	0.271197i	$-0.912581\pi$
$673$	0.970654	−	6.75105i	0.0374160	−	0.260234i	0.999940	+	0.0109630i	$0.00348971\pi$
$674$		0			0
$675$	−1.80468	−	3.95170i	−0.0694623	−	0.152101i
$676$		0			0
$677$	−13.9264	+	13.2788i	−0.535235	+	0.510345i	−0.908785	−	0.417265i	$-0.862989\pi$
$677$	−13.9264	+	13.2788i	−0.535235	+	0.510345i	0.373550	+	0.927610i	$0.378140\pi$
$678$		0			0
$679$	14.0615	+	4.12882i	0.539630	+	0.158450i
$680$		0			0
$681$	7.39700	+	0.706328i	0.283454	+	0.0270666i
$682$		0			0
$683$	−19.5423	−	3.76648i	−0.747767	−	0.144120i	−0.198888	−	0.980022i	$-0.563733\pi$
$683$	−19.5423	−	3.76648i	−0.747767	−	0.144120i	−0.548879	+	0.835902i	$0.684945\pi$
$684$		0			0
$685$	−14.8946	+	4.37346i	−0.569094	+	0.167101i
$686$		0			0
$687$	16.5914	+	8.55348i	0.633003	+	0.326336i
$688$		0			0
$689$	9.00421	+	8.58549i	0.343033	+	0.327081i
$690$		0			0
$691$	6.31117	+	8.86280i	0.240088	+	0.337157i	0.916985	−	0.398921i	$-0.130615\pi$
$691$	6.31117	+	8.86280i	0.240088	+	0.337157i	−0.676897	+	0.736078i	$0.736676\pi$
$692$		0			0
$693$	−6.98825	+	2.79767i	−0.265462	+	0.106275i
$694$		0			0
$695$	7.96087	−	9.18733i	0.301973	−	0.348495i
$696$		0			0
$697$	0.256155	−	0.560902i	0.00970258	−	0.0212457i
$698$		0			0
$699$	13.6463	−	23.6361i	0.516150	−	0.893998i
$700$		0			0
$701$	24.5322	−	4.72820i	0.926569	−	0.178582i	0.296422	−	0.955057i	$-0.404207\pi$
$701$	24.5322	−	4.72820i	0.926569	−	0.178582i	0.630147	+	0.776476i	$0.282994\pi$
$702$		0			0
$703$	6.76551	−	27.8878i	0.255166	−	1.05181i
$704$		0			0
$705$	2.06001	+	0.824702i	0.0775843	+	0.0310601i
$706$		0			0
$707$	−6.83900	−	11.8455i	−0.257207	−	0.445496i
$708$		0			0
$709$	6.41017	−	18.5210i	0.240739	−	0.695570i	−0.758307	−	0.651898i	$-0.773973\pi$
$709$	6.41017	−	18.5210i	0.240739	−	0.695570i	0.999046	−	0.0436719i	$-0.0139056\pi$
$710$		0			0
$711$	−0.0999711	−	2.09865i	−0.00374921	−	0.0787056i
$712$		0			0
$713$	−3.58642	+	2.30485i	−0.134312	+	0.0863173i
$714$		0			0
$715$	0.883692	+	6.14621i	0.0330482	+	0.229855i
$716$		0			0
$717$	7.41970	+	5.83492i	0.277094	+	0.217909i
$718$		0			0
$719$	−0.696506	+	14.6215i	−0.0259753	+	0.545288i	0.947950	+	0.318419i	$0.103152\pi$
$719$	−0.696506	+	14.6215i	−0.0259753	+	0.545288i	−0.973925	+	0.226869i	$0.927151\pi$
$720$		0			0
$721$	−5.46416	+	7.67334i	−0.203496	+	0.285770i
$722$		0			0
$723$	12.0953	+	7.77315i	0.449828	+	0.289087i
$724$		0			0
$725$	12.2303	+	35.3372i	0.454223	+	1.31239i
$726$		0			0
$727$	−0.587367	+	0.461911i	−0.0217842	+	0.0171313i	−0.628992	−	0.777412i	$-0.716532\pi$
$727$	−0.587367	+	0.461911i	−0.0217842	+	0.0171313i	0.607208	+	0.794543i	$0.292290\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	0.755174	−	0.0721104i	0.0279311	−	0.00266710i
$732$		0			0
$733$	−21.9888	+	11.3360i	−0.812175	+	0.418706i	−0.813694	−	0.581293i	$-0.802547\pi$
$733$	−21.9888	+	11.3360i	−0.812175	+	0.418706i	0.00151869	+	0.999999i	$0.499517\pi$
$734$		0			0
$735$	−1.06618	−	4.39487i	−0.0393267	−	0.162107i
$736$		0			0
$737$	10.1376	+	50.7918i	0.373425	+	1.87094i
$738$		0			0
$739$	9.78994	+	40.3547i	0.360129	+	1.48447i	0.807363	+	0.590055i	$0.200894\pi$
$739$	9.78994	+	40.3547i	0.360129	+	1.48447i	−0.447234	+	0.894417i	$0.647591\pi$
$740$		0			0
$741$	−8.22479	+	4.24018i	−0.302145	+	0.155767i
$742$		0			0
$743$	45.5855	−	4.35289i	1.67237	−	0.159692i	0.784607	−	0.619993i	$-0.212865\pi$
$743$	45.5855	−	4.35289i	1.67237	−	0.159692i	0.887763	+	0.460301i	$0.152259\pi$
$744$		0			0
$745$	−5.10051	−	5.88631i	−0.186868	−	0.215658i
$746$		0			0
$747$	10.1091	−	7.94987i	0.369872	−	0.290870i
$748$		0			0
$749$	−2.54416	−	7.35088i	−0.0929617	−	0.268595i
$750$		0			0
$751$	20.5540	+	13.2093i	0.750026	+	0.482013i	0.858964	−	0.512036i	$-0.171109\pi$
$751$	20.5540	+	13.2093i	0.750026	+	0.482013i	−0.108938	+	0.994049i	$0.534745\pi$
$752$		0			0
$753$	5.81427	−	8.16501i	0.211884	−	0.297549i
$754$		0			0
$755$	−0.128773	+	2.70328i	−0.00468653	+	0.0983823i
$756$		0			0
$757$	18.3308	+	14.4155i	0.666243	+	0.523940i	0.893026	−	0.450006i	$-0.148578\pi$
$757$	18.3308	+	14.4155i	0.666243	+	0.523940i	−0.226782	+	0.973945i	$0.572821\pi$
$758$		0			0
$759$	−2.21727	−	15.4214i	−0.0804817	−	0.559763i
$760$		0			0
$761$	−8.35355	+	5.36850i	−0.302816	+	0.194608i	−0.683220	−	0.730212i	$-0.739421\pi$
$761$	−8.35355	+	5.36850i	−0.302816	+	0.194608i	0.380404	+	0.924820i	$0.375785\pi$
$762$		0			0
$763$	1.09483	+	22.9833i	0.0396355	+	0.832052i
$764$		0			0
$765$	0.100929	−	0.291616i	0.00364911	−	0.0105434i
$766$		0			0
$767$	0.581826	+	1.00775i	0.0210085	+	0.0363878i
$768$		0			0
$769$	5.39333	+	2.15916i	0.194489	+	0.0778615i	0.466862	−	0.884330i	$-0.345384\pi$
$769$	5.39333	+	2.15916i	0.194489	+	0.0778615i	−0.272374	+	0.962192i	$0.587809\pi$
$770$		0			0
$771$	−3.11513	+	12.8407i	−0.112189	+	0.462448i
$772$		0			0
$773$	−32.1062	+	6.18797i	−1.15478	+	0.222566i	−0.730466	−	0.682949i	$-0.760697\pi$
$773$	−32.1062	+	6.18797i	−1.15478	+	0.222566i	−0.424315	+	0.905515i	$0.639485\pi$
$774$		0			0
$775$	−3.76091	+	6.51409i	−0.135096	+	0.233993i
$776$		0			0
$777$	1.85728	−	4.06687i	0.0666294	−	0.145898i
$778$		0			0
$779$	−8.09086	+	9.33735i	−0.289885	+	0.334545i
$780$		0			0
$781$	58.5346	−	23.4337i	2.09453	−	0.838524i
$782$		0			0
$783$	4.99289	+	7.01154i	0.178431	+	0.250572i
$784$		0			0
$785$	5.37253	+	5.12269i	0.191754	+	0.182837i
$786$		0			0
$787$	29.5585	+	15.2385i	1.05365	+	0.543192i	0.895886	−	0.444285i	$-0.146542\pi$
$787$	29.5585	+	15.2385i	1.05365	+	0.543192i	0.157761	+	0.987477i	$0.449573\pi$
$788$		0			0
$789$	15.9372	−	4.67960i	0.567381	−	0.166598i
$790$		0			0
$791$	−6.44246	−	1.24168i	−0.229068	−	0.0441491i
$792$		0			0
$793$	3.06270	+	0.292453i	0.108760	+	0.0103853i
$794$		0			0
$795$	7.97643	+	2.34209i	0.282895	+	0.0830654i
$796$		0			0
$797$	38.6778	−	36.8793i	1.37004	−	1.30633i	0.462344	−	0.886701i	$-0.347009\pi$
$797$	38.6778	−	36.8793i	1.37004	−	1.30633i	0.907696	−	0.419629i	$-0.137840\pi$
$798$		0			0
$799$	−0.433809	−	0.949908i	−0.0153470	−	0.0336053i
$800$		0			0
$801$	1.71692	−	11.9415i	0.0606645	−	0.421931i
$802$		0			0
$803$	10.9161			0.385222
$804$		0			0
$805$	−2.37189			−0.0835981
$806$		0			0
$807$	−2.04830	+	14.2463i	−0.0721037	+	0.501492i
$808$		0			0
$809$	15.9353	+	34.8934i	0.560255	+	1.22679i	0.951826	+	0.306639i	$0.0992043\pi$
$809$	15.9353	+	34.8934i	0.560255	+	1.22679i	−0.391571	+	0.920148i	$0.628068\pi$
$810$		0			0
$811$	−25.7367	+	24.5399i	−0.903738	+	0.861713i	−0.990916	−	0.134480i	$-0.957064\pi$
$811$	−25.7367	+	24.5399i	−0.903738	+	0.861713i	0.0871779	+	0.996193i	$0.472215\pi$
$812$		0			0
$813$	4.78607	+	1.40532i	0.167855	+	0.0492866i
$814$		0			0
$815$	−17.5080	−	1.67181i	−0.613280	−	0.0585611i
$816$		0			0
$817$	−14.9253	−	2.87661i	−0.522169	−	0.100640i
$818$		0			0
$819$	−1.38327	+	0.406165i	−0.0483354	+	0.0141925i
$820$		0			0
$821$	−1.56116	−	0.804832i	−0.0544847	−	0.0280888i	0.430769	−	0.902462i	$-0.358242\pi$
$821$	−1.56116	−	0.804832i	−0.0544847	−	0.0280888i	−0.485254	+	0.874373i	$0.661273\pi$
$822$		0			0
$823$	−24.7095	−	23.5605i	−0.861320	−	0.821267i	0.123947	−	0.992289i	$-0.460445\pi$
$823$	−24.7095	−	23.5605i	−0.861320	−	0.821267i	−0.985267	+	0.171022i	$0.945293\pi$
$824$		0			0
$825$	−15.9451	−	22.3918i	−0.555138	−	0.779583i
$826$		0			0
$827$	−27.2315	+	10.9018i	−0.946930	+	0.379094i	−0.793160	−	0.609013i	$-0.791566\pi$
$827$	−27.2315	+	10.9018i	−0.946930	+	0.379094i	−0.153770	+	0.988107i	$0.549142\pi$
$828$		0			0
$829$	−29.9275	+	34.5381i	−1.03942	+	1.19956i	−0.0599060	+	0.998204i	$0.519080\pi$
$829$	−29.9275	+	34.5381i	−1.03942	+	1.19956i	−0.979518	+	0.201355i	$0.935465\pi$
$830$		0			0
$831$	−3.29616	+	7.21757i	−0.114342	+	0.250375i
$832$		0			0
$833$	−1.06415	+	1.84315i	−0.0368705	+	0.0638615i
$834$		0			0
$835$	−2.17576	+	0.419344i	−0.0752954	+	0.0145120i
$836$		0			0
$837$	−0.408200	+	1.68262i	−0.0141094	+	0.0581599i
$838$		0			0
$839$	6.85956	+	2.74616i	0.236818	+	0.0948078i	0.487036	−	0.873382i	$-0.338078\pi$
$839$	6.85956	+	2.74616i	0.236818	+	0.0948078i	−0.250218	+	0.968190i	$0.580502\pi$
$840$		0			0
$841$	−22.5453	−	39.0496i	−0.777425	−	1.34654i
$842$		0			0
$843$	2.12497	−	6.13971i	0.0731880	−	0.211463i
$844$		0			0
$845$	−0.444303	−	9.32706i	−0.0152845	−	0.320861i
$846$		0			0
$847$	−29.0610	+	18.6764i	−0.998547	+	0.641727i
$848$		0			0
$849$	−0.327100	−	2.27503i	−0.0112260	−	0.0780789i
$850$		0			0
$851$	7.27388	+	5.72024i	0.249345	+	0.196087i
$852$		0			0
$853$	−0.573325	+	12.0356i	−0.0196303	+	0.412090i	0.967570	+	0.252604i	$0.0812869\pi$
$853$	−0.573325	+	12.0356i	−0.0196303	+	0.412090i	−0.987200	+	0.159486i	$0.949016\pi$
$854$		0			0
$855$	−3.58653	+	5.03658i	−0.122657	+	0.172247i
$856$		0			0
$857$	−9.80443	−	6.30093i	−0.334913	−	0.215236i	0.362365	−	0.932036i	$-0.381969\pi$
$857$	−9.80443	−	6.30093i	−0.334913	−	0.215236i	−0.697278	+	0.716801i	$0.745606\pi$
$858$		0			0
$859$	17.0530	+	49.2715i	0.581842	+	1.68112i	0.722760	+	0.691100i	$0.242873\pi$
$859$	17.0530	+	49.2715i	0.581842	+	1.68112i	−0.140918	+	0.990021i	$0.545005\pi$
$860$		0			0
$861$	−1.51307	+	1.18989i	−0.0515653	+	0.0405514i
$862$		0			0
$863$	10.6856	+	12.3319i	0.363744	+	0.419783i	0.907890	−	0.419207i	$-0.137692\pi$
$863$	10.6856	+	12.3319i	0.363744	+	0.419783i	−0.544147	+	0.838990i	$0.683147\pi$
$864$		0			0
$865$	6.66546	−	0.636474i	0.226632	−	0.0216408i
$866$		0			0
$867$	14.9811	−	7.72330i	0.508786	−	0.262297i
$868$		0			0
$869$	−3.13429	−	12.9197i	−0.106324	−	0.438272i
$870$		0			0
$871$	1.00811	+	9.86822i	0.0341584	+	0.334372i
$872$		0			0
$873$	2.90434	+	11.9719i	0.0982971	+	0.405186i
$874$		0			0
$875$	−8.00079	+	4.12470i	−0.270476	+	0.139440i
$876$		0			0
$877$	−6.18377	+	0.590478i	−0.208811	+	0.0199390i	−0.198937	−	0.980012i	$-0.563749\pi$
$877$	−6.18377	+	0.590478i	−0.208811	+	0.0199390i	−0.00987367	+	0.999951i	$0.503143\pi$
$878$		0			0
$879$	−17.0034	−	19.6230i	−0.573510	−	0.661866i
$880$		0			0
$881$	16.8681	−	13.2652i	0.568300	−	0.446916i	−0.292207	−	0.956355i	$-0.594390\pi$
$881$	16.8681	−	13.2652i	0.568300	−	0.446916i	0.860507	+	0.509439i	$0.170147\pi$
$882$		0			0
$883$	10.9142	+	31.5344i	0.367291	+	1.06122i	0.965618	+	0.259965i	$0.0837110\pi$
$883$	10.9142	+	31.5344i	0.367291	+	1.06122i	−0.598327	+	0.801252i	$0.704168\pi$
$884$		0			0
$885$	0.654109	+	0.420371i	0.0219876	+	0.0141306i
$886$		0			0
$887$	15.0949	−	21.1978i	0.506837	−	0.711753i	−0.479307	−	0.877647i	$-0.659112\pi$
$887$	15.0949	−	21.1978i	0.506837	−	0.711753i	0.986143	+	0.165895i	$0.0530513\pi$
$888$		0			0
$889$	0.662471	−	13.9070i	0.0222186	−	0.466425i
$890$		0			0
$891$	−4.97383	−	3.91146i	−0.166629	−	0.131039i
$892$		0			0
$893$	2.97776	+	20.7108i	0.0996471	+	0.693061i
$894$		0			0
$895$	3.91743	−	2.51758i	0.130945	−	0.0841533i
$896$		0			0
$897$	−0.141980	−	2.98053i	−0.00474057	−	0.0995168i
$898$		0			0
$899$	4.87443	−	14.0838i	0.162571	−	0.469719i
$900$		0			0
$901$	−1.95616	−	3.38817i	−0.0651691	−	0.112876i
$902$		0			0
$903$	−2.19849	−	0.880141i	−0.0731610	−	0.0292893i
$904$		0			0
$905$	−1.57334	+	6.48538i	−0.0522995	+	0.215581i
$906$		0			0
$907$	−40.0208	+	7.71338i	−1.32887	+	0.256119i	−0.803779	−	0.594928i	$-0.797181\pi$
$907$	−40.0208	+	7.71338i	−1.32887	+	0.256119i	−0.525091	+	0.851046i	$0.675969\pi$
$908$		0			0
$909$	5.74888	−	9.95736i	0.190678	−	0.330265i
$910$		0			0
$911$	−22.5738	+	49.4296i	−0.747902	+	1.63768i	0.0221979	+	0.999754i	$0.492934\pi$
$911$	−22.5738	+	49.4296i	−0.747902	+	1.63768i	−0.770100	+	0.637923i	$0.779794\pi$
$912$		0			0
$913$	53.2902	−	61.5002i	1.76365	−	2.03536i
$914$		0			0
$915$	1.90852	−	0.764056i	0.0630937	−	0.0252589i
$916$		0			0
$917$	−3.62875	−	5.09586i	−0.119832	−	0.168280i
$918$		0			0
$919$	22.5002	+	21.4539i	0.742213	+	0.707699i	0.963559	−	0.267497i	$-0.0861965\pi$
$919$	22.5002	+	21.4539i	0.742213	+	0.707699i	−0.221346	+	0.975195i	$0.571045\pi$
$920$		0			0
$921$	−27.2237	−	14.0348i	−0.897053	−	0.462463i
$922$		0			0
$923$	11.5865	−	3.40210i	0.381373	−	0.111981i
$924$		0			0
$925$	16.0318	+	3.08988i	0.527124	+	0.101595i
$926$		0			0
$927$	−7.88266	−	0.752703i	−0.258901	−	0.0247220i
$928$		0			0
$929$	−2.72764	−	0.800907i	−0.0894909	−	0.0262769i	0.236681	−	0.971588i	$-0.423941\pi$
$929$	−2.72764	−	0.800907i	−0.0894909	−	0.0262769i	−0.326171	+	0.945311i	$0.605759\pi$
$930$		0			0
$931$	30.8627	−	29.4275i	1.01148	−	0.964449i
$932$		0			0
$933$	6.13108	+	13.4252i	0.200722	+	0.439521i
$934$		0			0
$935$	0.277887	−	1.93275i	0.00908789	−	0.0632076i
$936$		0			0
$937$	−9.32656			−0.304685			−0.152343	−	0.988328i	$-0.548682\pi$
$937$	−9.32656			−0.304685			−0.152343	+	0.988328i	$0.548682\pi$
$938$		0			0
$939$	−4.08836			−0.133419
$940$		0			0
$941$	2.93981	−	20.4468i	0.0958351	−	0.666548i	−0.884110	−	0.467279i	$-0.845234\pi$
$941$	2.93981	−	20.4468i	0.0958351	−	0.666548i	0.979945	−	0.199269i	$-0.0638566\pi$
$942$		0			0
$943$	−1.65504	−	3.62404i	−0.0538956	−	0.118015i
$944$		0			0
$945$	−0.697179	+	0.664759i	−0.0226792	+	0.0216246i
$946$		0			0
$947$	−13.6476	−	4.00731i	−0.443489	−	0.130220i	0.0523613	−	0.998628i	$-0.483325\pi$
$947$	−13.6476	−	4.00731i	−0.443489	−	0.130220i	−0.495850	+	0.868408i	$0.665143\pi$
$948$		0			0
$949$	2.08121	+	0.198731i	0.0675588	+	0.00645109i
$950$		0			0
$951$	24.0992	+	4.64474i	0.781471	+	0.150616i
$952$		0			0
$953$	−11.8550	+	3.48093i	−0.384020	+	0.112758i	−0.468044	−	0.883705i	$-0.655041\pi$
$953$	−11.8550	+	3.48093i	−0.384020	+	0.112758i	0.0840238	+	0.996464i	$0.473223\pi$
$954$		0			0
$955$	12.2948	+	6.33841i	0.397850	+	0.205106i
$956$		0			0
$957$	39.4184	+	37.5854i	1.27422	+	1.21496i
$958$		0			0
$959$	−13.2285	−	18.5769i	−0.427172	−	0.599879i
$960$		0			0
$961$	−25.9963	+	10.4074i	−0.838590	+	0.335721i
$962$		0			0
$963$	4.28200	−	4.94169i	0.137986	−	0.159244i
$964$		0			0
$965$	−3.62666	+	7.94127i	−0.116746	+	0.255638i
$966$		0			0
$967$	−5.15811	+	8.93410i	−0.165874	+	0.287301i	−0.936965	−	0.349423i	$-0.886378\pi$
$967$	−5.15811	+	8.93410i	−0.165874	+	0.287301i	0.771092	+	0.636724i	$0.219711\pi$
$968$		0			0
$969$	2.85727	−	0.550694i	0.0917887	−	0.0176908i
$970$		0			0
$971$	9.95860	−	41.0499i	0.319587	−	1.31735i	−0.554743	−	0.832022i	$-0.687183\pi$
$971$	9.95860	−	41.0499i	0.319587	−	1.31735i	0.874329	−	0.485333i	$-0.161302\pi$
$972$		0			0
$973$	16.5800	+	6.63763i	0.531531	+	0.212793i
$974$		0			0
$975$	−2.63236	−	4.55937i	−0.0843029	−	0.146017i
$976$		0			0
$977$	11.4454	−	33.0692i	0.366169	−	1.05798i	−0.599985	−	0.800011i	$-0.704827\pi$
$977$	11.4454	−	33.0692i	0.366169	−	1.05798i	0.966154	−	0.257965i	$-0.0830520\pi$
$978$		0			0
$979$	−3.63230	−	76.2513i	−0.116089	−	2.43700i
$980$		0			0
$981$	−16.2713	+	10.4569i	−0.519503	+	0.333864i
$982$		0			0
$983$	−3.20843	−	22.3151i	−0.102333	−	0.711741i	−0.974802	−	0.223072i	$-0.928392\pi$
$983$	−3.20843	−	22.3151i	−0.102333	−	0.711741i	0.872469	−	0.488669i	$-0.162518\pi$
$984$		0			0
$985$	9.51631	+	7.48371i	0.303215	+	0.238451i
$986$		0			0
$987$	−0.155111	+	3.25619i	−0.00493725	+	0.103646i
$988$		0			0
$989$	2.84311	−	3.99259i	0.0904057	−	0.126957i
$990$		0			0
$991$	−38.9093	−	25.0055i	−1.23599	−	0.794325i	−0.251180	−	0.967940i	$-0.580819\pi$
$991$	−38.9093	−	25.0055i	−1.23599	−	0.794325i	−0.984814	+	0.173615i	$0.944455\pi$
$992$		0			0
$993$	−2.48371	−	7.17622i	−0.0788182	−	0.227730i
$994$		0			0
$995$	−15.3039	+	12.0351i	−0.485167	+	0.381540i
$996$		0			0
$997$	16.3590	+	18.8793i	0.518096	+	0.597914i	0.953153	−	0.302489i	$-0.0978174\pi$
$997$	16.3590	+	18.8793i	0.518096	+	0.597914i	−0.435057	+	0.900403i	$0.643272\pi$
$998$		0			0
$999$	3.74122	−	0.357244i	0.118367	−	0.0113027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.157.3	✓	100
67.35	even	33	inner	804.2.y.a.169.3	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.157.3	✓	100	1.1	even	1	trivial
804.2.y.a.169.3	yes	100	67.35	even	33	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(0.336386 + 0.736583i) q^{5} +(-0.860971 + 0.820934i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(0.336386 + 0.736583i) q^{5} +(-0.860971 + 0.820934i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-6.29895 - 0.601476i) q^{11} +(-1.18997 - 0.229348i) q^{13} +(-0.776959 + 0.228136i) q^{15} +(0.338723 + 0.174624i) q^{17} +(-5.52620 - 5.26922i) q^{19} +(-0.690049 - 0.969038i) q^{21} +(2.28586 - 0.915120i) q^{23} +(2.84490 - 3.28319i) q^{25} +(0.415415 - 0.909632i) q^{27} +(-4.30380 + 7.45439i) q^{29} +(-1.70014 + 0.327675i) q^{31} +(1.49179 - 6.14923i) q^{33} +(-0.894305 - 0.358026i) q^{35} +(1.87912 + 3.25473i) q^{37} +(0.396364 - 1.14522i) q^{39} +(-0.0769909 - 1.61624i) q^{41} +(1.67464 - 1.07623i) q^{43} +(-0.115241 - 0.801517i) q^{45} +(-2.15399 - 1.69392i) q^{47} +(-0.265735 + 5.57847i) q^{49} +(-0.221052 + 0.310424i) q^{51} +(-8.63650 - 5.55034i) q^{53} +(-1.67584 - 4.84203i) q^{55} +(6.00205 - 4.72006i) q^{57} +(-0.628805 - 0.725680i) q^{59} +(-2.52726 + 0.241324i) q^{61} +(1.05738 - 0.545117i) q^{63} +(-0.231356 - 0.953661i) q^{65} +(-2.35790 - 7.83839i) q^{67} +(0.580494 + 2.39283i) q^{69} +(-8.85676 + 4.56598i) q^{71} +(-1.71735 + 0.163987i) q^{73} +(2.84490 + 3.28319i) q^{75} +(5.91698 - 4.65316i) q^{77} +(0.687180 + 1.98548i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-7.45985 + 10.4759i) q^{83} +(-0.0146832 + 0.308239i) q^{85} +(-6.76602 - 5.32086i) q^{87} +(1.71692 + 11.9415i) q^{89} +(1.21281 - 0.779424i) q^{91} +(-0.0823847 - 1.72947i) q^{93} +(2.02228 - 5.84300i) q^{95} +(-6.15956 - 10.6687i) q^{97} +(5.87434 + 2.35173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more