LMFDB - Embedded newform 1134.2.k.d.647.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.1
Root			$0.500000 + 1.12119i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.d.971.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.58481 - 2.74498i) q^{5} +(-0.457557 + 2.60589i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.58481 - 2.74498i) q^{5} +(-0.457557 + 2.60589i) q^{7} +1.00000i q^{8} +(2.74498 + 1.58481i) q^{10} +(0.578334 + 0.333901i) q^{11} +0.359503i q^{13} +(-0.906687 - 2.48554i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.03017 - 3.51637i) q^{17} +(0.692392 - 0.399753i) q^{19} -3.16963 q^{20} -0.667803 q^{22} +(-1.55729 + 0.899104i) q^{23} +(-2.52326 + 4.37042i) q^{25} +(-0.179752 - 0.311339i) q^{26} +(2.02798 + 1.69920i) q^{28} -7.25212i q^{29} +(5.80953 + 3.35413i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.06035i q^{34} +(7.87824 - 2.87386i) q^{35} +(-3.94496 - 6.83287i) q^{37} +(-0.399753 + 0.692392i) q^{38} +(2.74498 - 1.58481i) q^{40} -1.92698 q^{41} -11.3128 q^{43} +(0.578334 - 0.333901i) q^{44} +(0.899104 - 1.55729i) q^{46} +(-4.08888 - 7.08214i) q^{47} +(-6.58128 - 2.38468i) q^{49} -5.04653i q^{50} +(0.311339 + 0.179752i) q^{52} +(-11.5572 - 6.67257i) q^{53} -2.11668i q^{55} +(-2.60589 - 0.457557i) q^{56} +(3.62606 + 6.28052i) q^{58} +(-7.00197 + 12.1278i) q^{59} +(-10.4977 + 6.06088i) q^{61} -6.70827 q^{62} -1.00000 q^{64} +(0.986828 - 0.569746i) q^{65} +(5.76606 - 9.98712i) q^{67} +(-2.03017 - 3.51637i) q^{68} +(-5.38583 + 6.42795i) q^{70} -1.98690i q^{71} +(7.99132 + 4.61379i) q^{73} +(6.83287 + 3.94496i) q^{74} -0.799506i q^{76} +(-1.13473 + 1.35429i) q^{77} +(-1.70943 - 2.96082i) q^{79} +(-1.58481 + 2.74498i) q^{80} +(1.66882 - 0.963492i) q^{82} -10.0952 q^{83} -12.8698 q^{85} +(9.79714 - 5.65638i) q^{86} +(-0.333901 + 0.578334i) q^{88} +(1.29352 + 2.24044i) q^{89} +(-0.936825 - 0.164493i) q^{91} +1.79821i q^{92} +(7.08214 + 4.08888i) q^{94} +(-2.19462 - 1.26707i) q^{95} -18.3910i q^{97} +(6.89190 - 1.22544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^7	$ 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.58481	−	2.74498i	−0.708750	−	1.22759i	−0.965321	−	0.261065i	$-0.915926\pi$
$5$	−1.58481	−	2.74498i	−0.708750	−	1.22759i	0.256571	−	0.966525i	$-0.417407\pi$
$6$		0			0
$7$	−0.457557	+	2.60589i	−0.172940	+	0.984932i
$7$	−0.457557	+	2.60589i	−0.172940	+	0.984932i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.74498	+	1.58481i	0.868038	+	0.501162i
$11$	0.578334	+	0.333901i	0.174374	+	0.100675i	0.584647	−	0.811288i	$-0.301233\pi$
$11$	0.578334	+	0.333901i	0.174374	+	0.100675i	−0.410273	+	0.911963i	$0.634566\pi$
$12$		0			0
$13$			0.359503i			0.0997083i	0.998757	+	0.0498542i	$0.0158757\pi$
$13$			0.359503i			0.0997083i	−0.998757	+	0.0498542i	$0.984124\pi$
$14$	−0.906687	−	2.48554i	−0.242322	−	0.664289i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.03017	−	3.51637i	0.492390	−	0.852844i	−0.507572	−	0.861609i	$-0.669457\pi$
$17$	2.03017	−	3.51637i	0.492390	−	0.852844i	0.999962	+	0.00876540i	$0.00279015\pi$
$18$		0			0
$19$	0.692392	−	0.399753i	0.158846	−	0.0917096i	−0.418470	−	0.908231i	$-0.637434\pi$
$19$	0.692392	−	0.399753i	0.158846	−	0.0917096i	0.577316	+	0.816521i	$0.304100\pi$
$20$	−3.16963			−0.708750
$21$		0			0
$22$	−0.667803			−0.142376
$23$	−1.55729	+	0.899104i	−0.324718	+	0.187476i	−0.653494	−	0.756932i	$-0.726697\pi$
$23$	−1.55729	+	0.899104i	−0.324718	+	0.187476i	0.328776	+	0.944408i	$0.393364\pi$
$24$		0			0
$25$	−2.52326	+	4.37042i	−0.504653	+	0.874084i
$26$	−0.179752	−	0.311339i	−0.0352522	−	0.0610586i
$27$		0			0
$28$	2.02798	+	1.69920i	0.383253	+	0.321118i
$29$		−	7.25212i		−	1.34669i	−0.739331	−	0.673343i	$-0.764858\pi$
$29$		−	7.25212i		−	1.34669i	0.739331	−	0.673343i	$-0.235142\pi$
$30$		0			0
$31$	5.80953	+	3.35413i	1.04342	+	0.602420i	0.920801	−	0.390033i	$-0.127537\pi$
$31$	5.80953	+	3.35413i	1.04342	+	0.602420i	0.122621	+	0.992454i	$0.460870\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			4.06035i			0.696344i
$35$	7.87824	−	2.87386i	1.33167	−	0.485771i
$36$		0			0
$37$	−3.94496	−	6.83287i	−0.648548	−	1.12332i	−0.983470	−	0.181072i	$-0.942043\pi$
$37$	−3.94496	−	6.83287i	−0.648548	−	1.12332i	0.334922	−	0.942246i	$-0.391290\pi$
$38$	−0.399753	+	0.692392i	−0.0648485	+	0.112321i
$39$		0			0
$40$	2.74498	−	1.58481i	0.434019	−	0.250581i
$41$	−1.92698			−0.300944			−0.150472	−	0.988614i	$-0.548079\pi$
$41$	−1.92698			−0.300944			−0.150472	+	0.988614i	$0.548079\pi$
$42$		0			0
$43$	−11.3128			−1.72518			−0.862590	−	0.505904i	$-0.831159\pi$
$43$	−11.3128			−1.72518			−0.862590	+	0.505904i	$0.831159\pi$
$44$	0.578334	−	0.333901i	0.0871871	−	0.0503375i
$45$		0			0
$46$	0.899104	−	1.55729i	0.132566	−	0.229610i
$47$	−4.08888	−	7.08214i	−0.596424	−	1.03304i	−0.993344	−	0.115184i	$-0.963254\pi$
$47$	−4.08888	−	7.08214i	−0.596424	−	1.03304i	0.396920	−	0.917853i	$-0.370079\pi$
$48$		0			0
$49$	−6.58128	−	2.38468i	−0.940183	−	0.340669i
$50$		−	5.04653i		−	0.713687i
$51$		0			0
$52$	0.311339	+	0.179752i	0.0431750	+	0.0249271i
$53$	−11.5572	−	6.67257i	−1.58751	−	0.916548i	−0.993716	−	0.111928i	$-0.964297\pi$
$53$	−11.5572	−	6.67257i	−1.58751	−	0.916548i	−0.593791	−	0.804619i	$-0.702369\pi$
$54$		0			0
$55$		−	2.11668i		−	0.285414i
$56$	−2.60589	−	0.457557i	−0.348226	−	0.0611437i
$57$		0			0
$58$	3.62606	+	6.28052i	0.476125	+	0.824673i
$59$	−7.00197	+	12.1278i	−0.911579	+	1.57890i	−0.0997451	+	0.995013i	$0.531803\pi$
$59$	−7.00197	+	12.1278i	−0.911579	+	1.57890i	−0.811834	+	0.583888i	$0.801531\pi$
$60$		0			0
$61$	−10.4977	+	6.06088i	−1.34410	+	0.776016i	−0.987406	−	0.158206i	$-0.949429\pi$
$61$	−10.4977	+	6.06088i	−1.34410	+	0.776016i	−0.356693	+	0.934222i	$0.616096\pi$
$62$	−6.70827			−0.851951
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.986828	−	0.569746i	0.122401	−	0.0706682i
$66$		0			0
$67$	5.76606	−	9.98712i	0.704437	−	1.22012i	−0.262458	−	0.964944i	$-0.584533\pi$
$67$	5.76606	−	9.98712i	0.704437	−	1.22012i	0.966894	−	0.255177i	$-0.0821337\pi$
$68$	−2.03017	−	3.51637i	−0.246195	−	0.426422i
$69$		0			0
$70$	−5.38583	+	6.42795i	−0.643729	+	0.768287i
$71$		−	1.98690i		−	0.235801i	−0.993025	−	0.117901i	$-0.962384\pi$
$71$		−	1.98690i		−	0.235801i	0.993025	−	0.117901i	$-0.0376164\pi$
$72$		0			0
$73$	7.99132	+	4.61379i	0.935314	+	0.540004i	0.888488	−	0.458900i	$-0.151756\pi$
$73$	7.99132	+	4.61379i	0.935314	+	0.540004i	0.0468255	+	0.998903i	$0.485090\pi$
$74$	6.83287	+	3.94496i	0.794305	+	0.458592i
$75$		0			0
$76$		−	0.799506i		−	0.0917096i
$77$	−1.13473	+	1.35429i	−0.129314	+	0.154336i
$78$		0			0
$79$	−1.70943	−	2.96082i	−0.192326	−	0.333118i	0.753695	−	0.657225i	$-0.228270\pi$
$79$	−1.70943	−	2.96082i	−0.192326	−	0.333118i	−0.946021	+	0.324106i	$0.894936\pi$
$80$	−1.58481	+	2.74498i	−0.177187	+	0.306898i
$81$		0			0
$82$	1.66882	−	0.963492i	0.184290	−	0.106400i
$83$	−10.0952			−1.10809			−0.554046	−	0.832486i	$-0.686917\pi$
$83$	−10.0952			−1.10809			−0.554046	+	0.832486i	$0.686917\pi$
$84$		0			0
$85$	−12.8698			−1.39592
$86$	9.79714	−	5.65638i	1.05645	−	0.609943i
$87$		0			0
$88$	−0.333901	+	0.578334i	−0.0355940	+	0.0616506i
$89$	1.29352	+	2.24044i	0.137113	+	0.237486i	0.926402	−	0.376535i	$-0.122884\pi$
$89$	1.29352	+	2.24044i	0.137113	+	0.237486i	−0.789290	+	0.614021i	$0.789551\pi$
$90$		0			0
$91$	−0.936825	−	0.164493i	−0.0982059	−	0.0172436i
$92$			1.79821i			0.187476i
$93$		0			0
$94$	7.08214	+	4.08888i	0.730467	+	0.421736i
$95$	−2.19462	−	1.26707i	−0.225164	−	0.129998i
$96$		0			0
$97$		−	18.3910i		−	1.86732i	−0.358156	−	0.933662i	$-0.616595\pi$
$97$		−	18.3910i		−	1.86732i	0.358156	−	0.933662i	$-0.383405\pi$
$98$	6.89190	−	1.22544i	0.696187	−	0.123789i
$99$		0			0
$100$	2.52326	+	4.37042i	0.252326	+	0.437042i
$101$	1.34350	−	2.32701i	0.133683	−	0.231546i	−0.791410	−	0.611285i	$-0.790653\pi$
$101$	1.34350	−	2.32701i	0.133683	−	0.231546i	0.925094	+	0.379739i	$0.123986\pi$
$102$		0			0
$103$	11.2447	−	6.49215i	1.10798	−	0.639690i	0.169672	−	0.985501i	$-0.445729\pi$
$103$	11.2447	−	6.49215i	1.10798	−	0.639690i	0.938304	+	0.345810i	$0.112396\pi$
$104$	−0.359503			−0.0352522
$105$		0			0
$106$	13.3451			1.29619
$107$	−10.9941	+	6.34743i	−1.06284	+	0.613629i	−0.926216	−	0.376994i	$-0.876958\pi$
$107$	−10.9941	+	6.34743i	−1.06284	+	0.613629i	−0.136621	+	0.990623i	$0.543624\pi$
$108$		0			0
$109$	2.74463	−	4.75384i	0.262888	−	0.455335i	−0.704120	−	0.710081i	$-0.748658\pi$
$109$	2.74463	−	4.75384i	0.262888	−	0.455335i	0.967008	+	0.254746i	$0.0819917\pi$
$110$	1.05834	+	1.83310i	0.100909	+	0.174779i
$111$		0			0
$112$	2.48554	−	0.906687i	0.234862	−	0.0856738i
$113$		−	12.2390i		−	1.15135i	−0.817679	−	0.575675i	$-0.804739\pi$
$113$		−	12.2390i		−	1.15135i	0.817679	−	0.575675i	$-0.195261\pi$
$114$		0			0
$115$	4.93604	+	2.84982i	0.460288	+	0.265747i
$116$	−6.28052	−	3.62606i	−0.583132	−	0.336671i
$117$		0			0
$118$		−	14.0039i		−	1.28917i
$119$	8.23433	+	6.89934i	0.754840	+	0.632462i
$120$		0			0
$121$	−5.27702	−	9.14007i	−0.479729	−	0.830915i
$122$	6.06088	−	10.4977i	0.548726	−	0.950421i
$123$		0			0
$124$	5.80953	−	3.35413i	0.521711	−	0.301210i
$125$	0.147471			0.0131903
$126$		0			0
$127$	11.6308			1.03207			0.516035	−	0.856568i	$-0.327408\pi$
$127$	11.6308			1.03207			0.516035	+	0.856568i	$0.327408\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.569746	+	0.986828i	−0.0499700	+	0.0865506i
$131$	5.99707	+	10.3872i	0.523966	+	0.907536i	0.999611	+	0.0278986i	$0.00888156\pi$
$131$	5.99707	+	10.3872i	0.523966	+	0.907536i	−0.475644	+	0.879638i	$0.657785\pi$
$132$		0			0
$133$	0.724901	+	1.98720i	0.0628569	+	0.172312i
$134$			11.5321i			0.996224i
$135$		0			0
$136$	3.51637	+	2.03017i	0.301526	+	0.174086i
$137$	15.5148	+	8.95748i	1.32552	+	0.765289i	0.984603	−	0.174805i	$-0.0559295\pi$
$137$	15.5148	+	8.95748i	1.32552	+	0.765289i	0.340916	+	0.940094i	$0.389263\pi$
$138$		0			0
$139$			9.70788i			0.823412i	0.911317	+	0.411706i	$0.135067\pi$
$139$			9.70788i			0.823412i	−0.911317	+	0.411706i	$0.864933\pi$
$140$	1.45029	−	8.25968i	0.122571	−	0.698071i
$141$		0			0
$142$	0.993449	+	1.72070i	0.0833684	+	0.144398i
$143$	−0.120039	+	0.207913i	−0.0100381	+	0.0173866i
$144$		0			0
$145$	−19.9069	+	11.4933i	−1.65318	+	0.954463i
$146$	−9.22759			−0.763680
$147$		0			0
$148$	−7.88992			−0.648548
$149$	2.79687	−	1.61477i	0.229128	−	0.132287i	−0.381042	−	0.924558i	$-0.624435\pi$
$149$	2.79687	−	1.61477i	0.229128	−	0.132287i	0.610170	+	0.792271i	$0.291101\pi$
$150$		0			0
$151$	0.108309	−	0.187596i	0.00881403	−	0.0152663i	−0.861585	−	0.507614i	$-0.830528\pi$
$151$	0.108309	−	0.187596i	0.00881403	−	0.0152663i	0.870399	+	0.492347i	$0.163861\pi$
$152$	0.399753	+	0.692392i	0.0324242	+	0.0561604i
$153$		0			0
$154$	0.305558	−	1.74022i	0.0246226	−	0.140231i
$155$		−	21.2627i		−	1.70786i
$156$		0			0
$157$	0.475769	+	0.274685i	0.0379705	+	0.0219223i	0.518865	−	0.854856i	$-0.326355\pi$
$157$	0.475769	+	0.274685i	0.0379705	+	0.0219223i	−0.480895	+	0.876778i	$0.659688\pi$
$158$	2.96082	+	1.70943i	0.235550	+	0.135995i
$159$		0			0
$160$		−	3.16963i		−	0.250581i
$161$	−1.63041	−	4.46952i	−0.128494	−	0.352248i
$162$		0			0
$163$	−8.20005	−	14.2029i	−0.642277	−	1.11246i	−0.984923	−	0.172992i	$-0.944656\pi$
$163$	−8.20005	−	14.2029i	−0.642277	−	1.11246i	0.342646	−	0.939465i	$-0.388677\pi$
$164$	−0.963492	+	1.66882i	−0.0752361	+	0.130313i
$165$		0			0
$166$	8.74269	−	5.04760i	0.678564	−	0.391769i
$167$	−0.249203			−0.0192839			−0.00964196	−	0.999954i	$-0.503069\pi$
$167$	−0.249203			−0.0192839			−0.00964196	+	0.999954i	$0.503069\pi$
$168$		0			0
$169$	12.8708			0.990058
$170$	11.1456	−	6.43489i	0.854826	−	0.493534i
$171$		0			0
$172$	−5.65638	+	9.79714i	−0.431295	+	0.747025i
$173$	3.78735	+	6.55988i	0.287947	+	0.498739i	0.973320	−	0.229454i	$-0.0736940\pi$
$173$	3.78735	+	6.55988i	0.287947	+	0.498739i	−0.685373	+	0.728193i	$0.740361\pi$
$174$		0			0
$175$	−10.2343	−	8.57505i	−0.773639	−	0.648213i
$176$		−	0.667803i		−	0.0503375i
$177$		0			0
$178$	−2.24044	−	1.29352i	−0.167928	−	0.0969532i
$179$	1.31716	+	0.760465i	0.0984495	+	0.0568398i	0.548416	−	0.836205i	$-0.315231\pi$
$179$	1.31716	+	0.760465i	0.0984495	+	0.0568398i	−0.449967	+	0.893045i	$0.648564\pi$
$180$		0			0
$181$		−	6.12414i		−	0.455204i	−0.973754	−	0.227602i	$-0.926911\pi$
$181$		−	6.12414i		−	0.455204i	0.973754	−	0.227602i	$-0.0730885\pi$
$182$	0.893561	−	0.325957i	0.0662351	−	0.0241615i
$183$		0			0
$184$	−0.899104	−	1.55729i	−0.0662828	−	0.114805i
$185$	−12.5040	+	21.6576i	−0.919316	+	1.59230i
$186$		0			0
$187$	2.34824	−	1.35576i	0.171720	−	0.0991427i
$188$	−8.17775			−0.596424
$189$		0			0
$190$	2.53413			0.183845
$191$	1.45018	−	0.837265i	0.104932	−	0.0605823i	−0.446616	−	0.894726i	$-0.647371\pi$
$191$	1.45018	−	0.837265i	0.104932	−	0.0605823i	0.551547	+	0.834144i	$0.314038\pi$
$192$		0			0
$193$	−12.0244	+	20.8268i	−0.865532	+	1.49915i	0.000985697		1.00000i	$0.499686\pi$
$193$	−12.0244	+	20.8268i	−0.865532	+	1.49915i	−0.866518	+	0.499146i	$0.833647\pi$
$194$	9.19550	+	15.9271i	0.660198	+	1.14350i
$195$		0			0
$196$	−5.35584	+	4.50722i	−0.382560	+	0.321944i
$197$		−	25.2476i		−	1.79881i	−0.437111	−	0.899407i	$-0.643998\pi$
$197$		−	25.2476i		−	1.79881i	0.437111	−	0.899407i	$-0.356002\pi$
$198$		0			0
$199$	−8.35598	−	4.82433i	−0.592340	−	0.341988i	0.173682	−	0.984802i	$-0.444433\pi$
$199$	−8.35598	−	4.82433i	−0.592340	−	0.341988i	−0.766022	+	0.642814i	$0.777767\pi$
$200$	−4.37042	−	2.52326i	−0.309035	−	0.178422i
$201$		0			0
$202$			2.68700i			0.189057i
$203$	18.8982	+	3.31826i	1.32639	+	0.232896i
$204$		0			0
$205$	3.05391	+	5.28953i	0.213294	+	0.369437i
$206$	−6.49215	+	11.2447i	−0.452329	+	0.783457i
$207$		0			0
$208$	0.311339	−	0.179752i	0.0215875	−	0.0124635i
$209$	0.533912			0.0369315
$210$		0			0
$211$	−14.8478			−1.02216			−0.511082	−	0.859532i	$-0.670755\pi$
$211$	−14.8478			−1.02216			−0.511082	+	0.859532i	$0.670755\pi$
$212$	−11.5572	+	6.67257i	−0.793754	+	0.458274i
$213$		0			0
$214$	6.34743	−	10.9941i	0.433901	−	0.751539i
$215$	17.9286	+	31.0533i	1.22272	+	2.11782i
$216$		0			0
$217$	−11.3987	+	13.6043i	−0.773793	+	0.923517i
$218$			5.48926i			0.371780i
$219$		0			0
$220$	−1.83310	−	1.05834i	−0.123588	−	0.0713534i
$221$	1.26415	+	0.729855i	0.0850356	+	0.0490953i
$222$		0			0
$223$		−	25.2014i		−	1.68761i	−0.536652	−	0.843804i	$-0.680311\pi$
$223$		−	25.2014i		−	1.68761i	0.536652	−	0.843804i	$-0.319689\pi$
$224$	−1.69920	+	2.02798i	−0.113533	+	0.135500i
$225$		0			0
$226$	6.11951	+	10.5993i	0.407064	+	0.705055i
$227$	3.45101	−	5.97732i	0.229051	−	0.396729i	−0.728476	−	0.685071i	$-0.759771\pi$
$227$	3.45101	−	5.97732i	0.229051	−	0.396729i	0.957527	+	0.288343i	$0.0931043\pi$
$228$		0			0
$229$	9.54074	−	5.50835i	0.630470	−	0.364002i	−0.150464	−	0.988615i	$-0.548077\pi$
$229$	9.54074	−	5.50835i	0.630470	−	0.364002i	0.780934	+	0.624613i	$0.214743\pi$
$230$	−5.69964			−0.375823
$231$		0			0
$232$	7.25212			0.476125
$233$	7.12863	−	4.11572i	0.467012	−	0.269630i	−0.247976	−	0.968766i	$-0.579765\pi$
$233$	7.12863	−	4.11572i	0.467012	−	0.269630i	0.714988	+	0.699137i	$0.246432\pi$
$234$		0			0
$235$	−12.9602	+	22.4477i	−0.845431	+	1.46433i
$236$	7.00197	+	12.1278i	0.455790	+	0.789451i
$237$		0			0
$238$	−10.5808	−	1.85784i	−0.685852	−	0.120426i
$239$			12.7821i			0.826807i	0.910548	+	0.413404i	$0.135660\pi$
$239$			12.7821i			0.826807i	−0.910548	+	0.413404i	$0.864340\pi$
$240$		0			0
$241$	−3.07823	−	1.77722i	−0.198286	−	0.114481i	0.397570	−	0.917572i	$-0.369854\pi$
$241$	−3.07823	−	1.77722i	−0.198286	−	0.114481i	−0.595856	+	0.803091i	$0.703187\pi$
$242$	9.14007	+	5.27702i	0.587546	+	0.339220i
$243$		0			0
$244$			12.1218i			0.776016i
$245$	3.88420	+	21.8447i	0.248152	+	1.39561i
$246$		0			0
$247$	0.143712	+	0.248917i	0.00914421	+	0.0158382i
$248$	−3.35413	+	5.80953i	−0.212988	+	0.368905i
$249$		0			0
$250$	−0.127714	+	0.0737357i	−0.00807735	+	0.00466346i
$251$	12.3111			0.777068			0.388534	−	0.921434i	$-0.372982\pi$
$251$	12.3111			0.777068			0.388534	+	0.921434i	$0.372982\pi$
$252$		0			0
$253$	−1.20085			−0.0754966
$254$	−10.0726	+	5.81542i	−0.632011	+	0.364892i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.90151	+	8.48966i	0.305748	+	0.529571i	0.977428	−	0.211271i	$-0.0677603\pi$
$257$	4.90151	+	8.48966i	0.305748	+	0.529571i	−0.671680	+	0.740842i	$0.734427\pi$
$258$		0			0
$259$	19.6107	−	7.15369i	1.21855	−	0.444508i
$260$		−	1.13949i		−	0.0706682i
$261$		0			0
$262$	−10.3872	−	5.99707i	−0.641725	−	0.370500i
$263$	−5.08677	−	2.93685i	−0.313664	−	0.181094i	0.334901	−	0.942253i	$-0.391297\pi$
$263$	−5.08677	−	2.93685i	−0.313664	−	0.181094i	−0.648565	+	0.761160i	$0.724630\pi$
$264$		0			0
$265$			42.2991i			2.59841i
$266$	−1.62138	−	1.35852i	−0.0994135	−	0.0832962i
$267$		0			0
$268$	−5.76606	−	9.98712i	−0.352218	−	0.610060i
$269$	−10.7526	+	18.6240i	−0.655597	+	1.13553i	0.326146	+	0.945319i	$0.394250\pi$
$269$	−10.7526	+	18.6240i	−0.655597	+	1.13553i	−0.981744	+	0.190209i	$0.939084\pi$
$270$		0			0
$271$	5.98353	−	3.45459i	0.363473	−	0.209851i	−0.307130	−	0.951668i	$-0.599369\pi$
$271$	5.98353	−	3.45459i	0.363473	−	0.209851i	0.670603	+	0.741816i	$0.266035\pi$
$272$	−4.06035			−0.246195
$273$		0			0
$274$	−17.9150			−1.08228
$275$	−2.91858	+	1.68504i	−0.175997	+	0.101612i
$276$		0			0
$277$	−9.95298	+	17.2391i	−0.598016	+	1.03579i	0.395097	+	0.918639i	$0.370711\pi$
$277$	−9.95298	+	17.2391i	−0.598016	+	1.03579i	−0.993114	+	0.117155i	$0.962622\pi$
$278$	−4.85394	−	8.40727i	−0.291120	−	0.504235i
$279$		0			0
$280$	2.87386	+	7.87824i	0.171746	+	0.470815i
$281$			16.4847i			0.983394i	0.870766	+	0.491697i	$0.163623\pi$
$281$			16.4847i			0.983394i	−0.870766	+	0.491697i	$0.836377\pi$
$282$		0			0
$283$	15.8991	+	9.17933i	0.945101	+	0.545654i	0.891556	−	0.452911i	$-0.149615\pi$
$283$	15.8991	+	9.17933i	0.945101	+	0.545654i	0.0535453	+	0.998565i	$0.482948\pi$
$284$	−1.72070	−	0.993449i	−0.102105	−	0.0589503i
$285$		0			0
$286$		−	0.240077i		−	0.0141961i
$287$	0.881706	−	5.02150i	0.0520455	−	0.296410i
$288$		0			0
$289$	0.256780	+	0.444756i	0.0151047	+	0.0261621i
$290$	11.4933	−	19.9069i	0.674907	−	1.16897i
$291$		0			0
$292$	7.99132	−	4.61379i	0.467657	−	0.270002i
$293$	−21.4347			−1.25223			−0.626115	−	0.779731i	$-0.715356\pi$
$293$	−21.4347			−1.25223			−0.626115	+	0.779731i	$0.715356\pi$
$294$		0			0
$295$	44.3873			2.58433
$296$	6.83287	−	3.94496i	0.397153	−	0.229296i
$297$		0			0
$298$	−1.61477	+	2.79687i	−0.0935412	+	0.162018i
$299$	−0.323231	−	0.559852i	−0.0186929	−	0.0323771i
$300$		0			0
$301$	5.17624	−	29.4798i	0.298353	−	1.69919i
$302$			0.216617i			0.0124649i
$303$		0			0
$304$	−0.692392	−	0.399753i	−0.0397114	−	0.0229274i
$305$	33.2739	+	19.2107i	1.90526	+	1.10000i
$306$		0			0
$307$		−	4.75321i		−	0.271280i	−0.990758	−	0.135640i	$-0.956691\pi$
$307$		−	4.75321i		−	0.271280i	0.990758	−	0.135640i	$-0.0433091\pi$
$308$	0.605488	+	1.65985i	0.0345009	+	0.0945788i
$309$		0			0
$310$	10.6313	+	18.4140i	0.603820	+	1.04585i
$311$	13.2314	−	22.9174i	0.750283	−	1.29953i	−0.197403	−	0.980322i	$-0.563251\pi$
$311$	13.2314	−	22.9174i	0.750283	−	1.29953i	0.947686	−	0.319205i	$-0.103416\pi$
$312$		0			0
$313$	−3.07935	+	1.77786i	−0.174055	+	0.100491i	−0.584496	−	0.811396i	$-0.698708\pi$
$313$	−3.07935	+	1.77786i	−0.174055	+	0.100491i	0.410442	+	0.911887i	$0.365375\pi$
$314$	−0.549371			−0.0310028
$315$		0			0
$316$	−3.41886			−0.192326
$317$	−4.10604	+	2.37062i	−0.230618	+	0.133147i	−0.610857	−	0.791741i	$-0.709175\pi$
$317$	−4.10604	+	2.37062i	−0.230618	+	0.133147i	0.380239	+	0.924888i	$0.375842\pi$
$318$		0			0
$319$	2.42149	−	4.19415i	0.135578	−	0.234827i
$320$	1.58481	+	2.74498i	0.0885937	+	0.153449i
$321$		0			0
$322$	3.64674	+	3.05551i	0.203225	+	0.170277i
$323$		−	3.24627i		−	0.180627i
$324$		0			0
$325$	−1.57118	−	0.907122i	−0.0871534	−	0.0503181i
$326$	14.2029	+	8.20005i	0.786626	+	0.454159i
$327$		0			0
$328$		−	1.92698i		−	0.106400i
$329$	20.3262	−	7.41466i	1.12062	−	0.408784i
$330$		0			0
$331$	−7.13919	−	12.3654i	−0.392406	−	0.679666i	0.600361	−	0.799729i	$-0.295024\pi$
$331$	−7.13919	−	12.3654i	−0.392406	−	0.679666i	−0.992766	+	0.120063i	$0.961690\pi$
$332$	−5.04760	+	8.74269i	−0.277023	+	0.479818i
$333$		0			0
$334$	0.215816	−	0.124602i	0.0118089	−	0.00681790i
$335$	−36.5525			−1.99708
$336$		0			0
$337$	4.89010			0.266381			0.133190	−	0.991090i	$-0.457478\pi$
$337$	4.89010			0.266381			0.133190	+	0.991090i	$0.457478\pi$
$338$	−11.1464	+	6.43538i	−0.606284	+	0.350038i
$339$		0			0
$340$	−6.43489	+	11.1456i	−0.348981	+	0.604453i
$341$	2.23990	+	3.87962i	0.121297	+	0.210093i
$342$		0			0
$343$	9.22553	−	16.0589i	0.498132	−	0.867101i
$344$		−	11.3128i		−	0.609943i
$345$		0			0
$346$	−6.55988	−	3.78735i	−0.352661	−	0.203609i
$347$	−3.78158	−	2.18330i	−0.203006	−	0.117206i	0.395051	−	0.918659i	$-0.370727\pi$
$347$	−3.78158	−	2.18330i	−0.203006	−	0.117206i	−0.598057	+	0.801454i	$0.704060\pi$
$348$		0			0
$349$			5.94382i			0.318166i	0.987265	+	0.159083i	$0.0508537\pi$
$349$			5.94382i			0.318166i	−0.987265	+	0.159083i	$0.949146\pi$
$350$	13.1507	+	2.30908i	0.702933	+	0.123425i
$351$		0			0
$352$	0.333901	+	0.578334i	0.0177970	+	0.0308253i
$353$	−12.7152	+	22.0234i	−0.676764	+	1.17219i	0.299187	+	0.954195i	$0.403285\pi$
$353$	−12.7152	+	22.0234i	−0.676764	+	1.17219i	−0.975950	+	0.217994i	$0.930049\pi$
$354$		0			0
$355$	−5.45399	+	3.14886i	−0.289468	+	0.167124i
$356$	2.58703			0.137113
$357$		0			0
$358$	−1.52093			−0.0803837
$359$	−8.82521	+	5.09523i	−0.465777	+	0.268916i	−0.714470	−	0.699666i	$-0.753332\pi$
$359$	−8.82521	+	5.09523i	−0.465777	+	0.268916i	0.248694	+	0.968582i	$0.419999\pi$
$360$		0			0
$361$	−9.18040	+	15.9009i	−0.483179	+	0.836890i
$362$	3.06207	+	5.30366i	0.160939	+	0.278754i
$363$		0			0
$364$	−0.610868	+	0.729067i	−0.0320182	+	0.0382135i
$365$		−	29.2480i		−	1.53091i
$366$		0			0
$367$	15.8165	+	9.13169i	0.825617	+	0.476670i	0.852350	−	0.522972i	$-0.175177\pi$
$367$	15.8165	+	9.13169i	0.825617	+	0.476670i	−0.0267326	+	0.999643i	$0.508510\pi$
$368$	1.55729	+	0.899104i	0.0811795	+	0.0468690i
$369$		0			0
$370$		−	25.0081i		−	1.30011i
$371$	22.6760	−	27.0637i	1.17728	−	1.40508i
$372$		0			0
$373$	5.84571	+	10.1251i	0.302679	+	0.524256i	0.976742	−	0.214418i	$-0.0687856\pi$
$373$	5.84571	+	10.1251i	0.302679	+	0.524256i	−0.674063	+	0.738674i	$0.735452\pi$
$374$	−1.35576	+	2.34824i	−0.0701045	+	0.121425i
$375$		0			0
$376$	7.08214	−	4.08888i	0.365234	−	0.210868i
$377$	2.60716			0.134276
$378$		0			0
$379$	37.9048			1.94704			0.973519	−	0.228608i	$-0.0734173\pi$
$379$	37.9048			1.94704			0.973519	+	0.228608i	$0.0734173\pi$
$380$	−2.19462	+	1.26707i	−0.112582	+	0.0649991i
$381$		0			0
$382$	−0.837265	+	1.45018i	−0.0428382	+	0.0741979i
$383$	−7.39368	−	12.8062i	−0.377799	−	0.654368i	0.612942	−	0.790128i	$-0.289986\pi$
$383$	−7.39368	−	12.8062i	−0.377799	−	0.654368i	−0.990742	+	0.135760i	$0.956652\pi$
$384$		0			0
$385$	5.51584	+	0.968504i	0.281113	+	0.0493596i
$386$		−	24.0487i		−	1.22405i
$387$		0			0
$388$	−15.9271	−	9.19550i	−0.808575	−	0.466831i
$389$	19.6080	+	11.3207i	0.994164	+	0.573981i	0.906516	−	0.422171i	$-0.138732\pi$
$389$	19.6080	+	11.3207i	0.994164	+	0.573981i	0.0876475	+	0.996152i	$0.472065\pi$
$390$		0			0
$391$			7.30135i			0.369245i
$392$	2.38468	−	6.58128i	0.120445	−	0.332405i
$393$		0			0
$394$	12.6238	+	21.8650i	0.635977	+	1.10154i
$395$	−5.41826	+	9.38469i	−0.272622	+	0.472195i
$396$		0			0
$397$	−11.3805	+	6.57052i	−0.571170	+	0.329765i	−0.757616	−	0.652700i	$-0.773636\pi$
$397$	−11.3805	+	6.57052i	−0.571170	+	0.329765i	0.186447	+	0.982465i	$0.440303\pi$
$398$	9.64866			0.483643
$399$		0			0
$400$	5.04653			0.252326
$401$	0.0453074	−	0.0261582i	0.00226254	−	0.00130628i	−0.498868	−	0.866678i	$-0.666251\pi$
$401$	0.0453074	−	0.0261582i	0.00226254	−	0.00130628i	0.501131	+	0.865372i	$0.332918\pi$
$402$		0			0
$403$	−1.20582	+	2.08855i	−0.0600663	+	0.104038i
$404$	−1.34350	−	2.32701i	−0.0668416	−	0.115773i
$405$		0			0
$406$	−18.0255	+	6.57540i	−0.894588	+	0.326332i
$407$		−	5.26891i		−	0.261170i
$408$		0			0
$409$	7.88089	+	4.55003i	0.389685	+	0.224985i	0.682024	−	0.731330i	$-0.261100\pi$
$409$	7.88089	+	4.55003i	0.389685	+	0.224985i	−0.292339	+	0.956315i	$0.594433\pi$
$410$	−5.28953	−	3.05391i	−0.261231	−	0.150822i
$411$		0			0
$412$		−	12.9843i		−	0.639690i
$413$	−28.3998	−	23.7955i	−1.39746	−	1.17090i
$414$		0			0
$415$	15.9990	+	27.7111i	0.785359	+	1.36028i
$416$	−0.179752	+	0.311339i	−0.00881305	+	0.0152647i
$417$		0			0
$418$	−0.462381	+	0.266956i	−0.0226158	+	0.0130572i
$419$	4.69603			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$419$	4.69603			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$420$		0			0
$421$	−1.17675			−0.0573512			−0.0286756	−	0.999589i	$-0.509129\pi$
$421$	−1.17675			−0.0573512			−0.0286756	+	0.999589i	$0.509129\pi$
$422$	12.8586	−	7.42389i	0.625945	−	0.361389i
$423$		0			0
$424$	6.67257	−	11.5572i	0.324049	−	0.561269i
$425$	10.2453	+	17.7454i	0.496972	+	0.860780i
$426$		0			0
$427$	−10.9906	−	30.1291i	−0.531874	−	1.45805i
$428$			12.6949i			0.613629i
$429$		0			0
$430$	−31.0533	−	17.9286i	−1.49752	−	0.864594i
$431$	7.29448	+	4.21147i	0.351363	+	0.202859i	0.665285	−	0.746589i	$-0.268310\pi$
$431$	7.29448	+	4.21147i	0.351363	+	0.202859i	−0.313922	+	0.949449i	$0.601643\pi$
$432$		0			0
$433$			2.26665i			0.108928i	0.998516	+	0.0544642i	$0.0173451\pi$
$433$			2.26665i			0.108928i	−0.998516	+	0.0544642i	$0.982655\pi$
$434$	3.06942	−	17.4810i	0.147337	−	0.839114i
$435$		0			0
$436$	−2.74463	−	4.75384i	−0.131444	−	0.227668i
$437$	−0.718838	+	1.24506i	−0.0343867	+	0.0595595i
$438$		0			0
$439$	−14.5691	+	8.41149i	−0.695347	+	0.401459i	−0.805612	−	0.592444i	$-0.798163\pi$
$439$	−14.5691	+	8.41149i	−0.695347	+	0.401459i	0.110265	+	0.993902i	$0.464830\pi$
$440$	2.11668			0.100909
$441$		0			0
$442$	−1.45971			−0.0694313
$443$	−27.3481	+	15.7894i	−1.29935	+	0.750179i	−0.980291	−	0.197557i	$-0.936699\pi$
$443$	−27.3481	+	15.7894i	−1.29935	+	0.750179i	−0.319057	+	0.947736i	$0.603366\pi$
$444$		0			0
$445$	4.09997	−	7.10135i	0.194357	−	0.336636i
$446$	12.6007	+	21.8250i	0.596659	+	1.03344i
$447$		0			0
$448$	0.457557	−	2.60589i	0.0216176	−	0.123117i
$449$		−	23.6374i		−	1.11552i	−0.830002	−	0.557760i	$-0.811661\pi$
$449$		−	23.6374i		−	1.11552i	0.830002	−	0.557760i	$-0.188339\pi$
$450$		0			0
$451$	−1.11444	−	0.643423i	−0.0524770	−	0.0302976i
$452$	−10.5993	−	6.11951i	−0.498549	−	0.287838i
$453$		0			0
$454$			6.90201i			0.323927i
$455$	1.03316	+	2.83225i	0.0484354	+	0.132778i
$456$		0			0
$457$	−8.42929	−	14.6000i	−0.394306	−	0.682958i	0.598707	−	0.800968i	$-0.295682\pi$
$457$	−8.42929	−	14.6000i	−0.394306	−	0.682958i	−0.993012	+	0.118011i	$0.962348\pi$
$458$	−5.50835	+	9.54074i	−0.257388	+	0.445810i
$459$		0			0
$460$	4.93604	−	2.84982i	0.230144	−	0.132874i
$461$	−1.49416			−0.0695899			−0.0347949	−	0.999394i	$-0.511078\pi$
$461$	−1.49416			−0.0695899			−0.0347949	+	0.999394i	$0.511078\pi$
$462$		0			0
$463$	−32.5896			−1.51457			−0.757284	−	0.653086i	$-0.773474\pi$
$463$	−32.5896			−1.51457			−0.757284	+	0.653086i	$0.773474\pi$
$464$	−6.28052	+	3.62606i	−0.291566	+	0.168336i
$465$		0			0
$466$	−4.11572	+	7.12863i	−0.190657	+	0.330228i
$467$	2.54500	+	4.40808i	0.117769	+	0.203982i	0.918883	−	0.394530i	$-0.129092\pi$
$467$	2.54500	+	4.40808i	0.117769	+	0.203982i	−0.801114	+	0.598511i	$0.795759\pi$
$468$		0			0
$469$	23.3870	+	19.5954i	1.07991	+	0.904831i
$470$		−	25.9204i		−	1.19562i
$471$		0			0
$472$	−12.1278	−	7.00197i	−0.558226	−	0.322292i
$473$	−6.54256	−	3.77735i	−0.300827	−	0.173683i
$474$		0			0
$475$			4.03473i			0.185126i
$476$	10.0922	−	3.68147i	0.462574	−	0.168740i
$477$		0			0
$478$	−6.39107	−	11.0696i	−0.292321	−	0.506314i
$479$	14.2483	−	24.6788i	0.651022	−	1.12760i	−0.331853	−	0.943331i	$-0.607674\pi$
$479$	14.2483	−	24.6788i	0.651022	−	1.12760i	0.982875	−	0.184272i	$-0.0589928\pi$
$480$		0			0
$481$	2.45644	−	1.41823i	0.112004	−	0.0646656i
$482$	3.55444			0.161900
$483$		0			0
$484$	−10.5540			−0.479729
$485$	−50.4829	+	29.1463i	−2.29231	+	1.32346i
$486$		0			0
$487$	6.32071	−	10.9478i	0.286419	−	0.496091i	−0.686534	−	0.727098i	$-0.740869\pi$
$487$	6.32071	−	10.9478i	0.286419	−	0.496091i	0.972952	+	0.231007i	$0.0742019\pi$
$488$	−6.06088	−	10.4977i	−0.274363	−	0.475211i
$489$		0			0
$490$	−14.2862	−	16.9760i	−0.645384	−	0.766898i
$491$			14.6396i			0.660676i	0.943863	+	0.330338i	$0.107163\pi$
$491$			14.6396i			0.660676i	−0.943863	+	0.330338i	$0.892837\pi$
$492$		0			0
$493$	−25.5011	−	14.7231i	−1.14851	−	0.663094i
$494$	−0.248917	−	0.143712i	−0.0111993	−	0.00646593i
$495$		0			0
$496$		−	6.70827i		−	0.301210i
$497$	5.17763	+	0.909119i	0.232248	+	0.0407796i
$498$		0			0
$499$	−2.86102	−	4.95543i	−0.128077	−	0.221836i	0.794855	−	0.606800i	$-0.207547\pi$
$499$	−2.86102	−	4.95543i	−0.128077	−	0.221836i	−0.922931	+	0.384964i	$0.874214\pi$
$500$	0.0737357	−	0.127714i	0.00329756	−	0.00571155i
$501$		0			0
$502$	−10.6617	+	6.15553i	−0.475855	+	0.274735i
$503$	−32.6206			−1.45448			−0.727241	−	0.686382i	$-0.759198\pi$
$503$	−32.6206			−1.45448			−0.727241	+	0.686382i	$0.759198\pi$
$504$		0			0
$505$	−8.51678			−0.378992
$506$	1.03996	−	0.600424i	0.0462321	−	0.0266921i
$507$		0			0
$508$	5.81542	−	10.0726i	0.258017	−	0.446899i
$509$	6.07886	+	10.5289i	0.269441	+	0.466685i	0.968718	−	0.248166i	$-0.0798278\pi$
$509$	6.07886	+	10.5289i	0.269441	+	0.466685i	−0.699277	+	0.714851i	$0.746494\pi$
$510$		0			0
$511$	−15.6795	+	18.7134i	−0.693620	+	0.827832i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−8.48966	−	4.90151i	−0.374463	−	0.216196i
$515$	−35.6416	−	20.5777i	−1.57056	−	0.906761i
$516$		0			0
$517$		−	5.46113i		−	0.240180i
$518$	−13.4065	+	16.0006i	−0.589050	+	0.703028i
$519$		0			0
$520$	0.569746	+	0.986828i	0.0249850	+	0.0432753i
$521$	11.2859	−	19.5477i	0.494443	−	0.856400i	−0.505537	−	0.862805i	$-0.668706\pi$
$521$	11.2859	−	19.5477i	0.494443	−	0.856400i	0.999979	+	0.00640532i	$0.00203889\pi$
$522$		0			0
$523$	18.9578	−	10.9453i	0.828969	−	0.478605i	−0.0245307	−	0.999699i	$-0.507809\pi$
$523$	18.9578	−	10.9453i	0.828969	−	0.478605i	0.853499	+	0.521094i	$0.174476\pi$
$524$	11.9941			0.523966
$525$		0			0
$526$	5.87369			0.256105
$527$	23.5887	−	13.6190i	1.02754	−	0.593251i
$528$		0			0
$529$	−9.88323	+	17.1182i	−0.429705	+	0.744272i
$530$	−21.1495	−	36.6321i	−0.918677	−	1.59120i
$531$		0			0
$532$	2.08342	+	0.365820i	0.0903277	+	0.0158603i
$533$		−	0.692758i		−	0.0300067i
$534$		0			0
$535$	34.8471	+	20.1190i	1.50657	+	0.869819i
$536$	9.98712	+	5.76606i	0.431378	+	0.249056i
$537$		0			0
$538$		−	21.5052i		−	0.927155i
$539$	−3.00993	−	3.57664i	−0.129647	−	0.154057i
$540$		0			0
$541$	−14.5676	−	25.2319i	−0.626311	−	1.08480i	−0.988286	−	0.152614i	$-0.951231\pi$
$541$	−14.5676	−	25.2319i	−0.626311	−	1.08480i	0.361975	−	0.932188i	$-0.382103\pi$
$542$	−3.45459	+	5.98353i	−0.148387	+	0.257014i
$543$		0			0
$544$	3.51637	−	2.03017i	0.150763	−	0.0870430i
$545$	−17.3989			−0.745287
$546$		0			0
$547$	1.03000			0.0440396			0.0220198	−	0.999758i	$-0.492990\pi$
$547$	1.03000			0.0440396			0.0220198	+	0.999758i	$0.492990\pi$
$548$	15.5148	−	8.95748i	0.662760	−	0.382644i
$549$		0			0
$550$	1.68504	−	2.91858i	0.0718504	−	0.124449i
$551$	−2.89906	−	5.02131i	−0.123504	−	0.213915i
$552$		0			0
$553$	8.49772	−	3.09984i	0.361360	−	0.131818i
$554$		−	19.9060i		−	0.845723i
$555$		0			0
$556$	8.40727	+	4.85394i	0.356548	+	0.205853i
$557$	−15.2159	−	8.78490i	−0.644718	−	0.372228i	0.141711	−	0.989908i	$-0.454739\pi$
$557$	−15.2159	−	8.78490i	−0.644718	−	0.372228i	−0.786430	+	0.617680i	$0.788073\pi$
$558$		0			0
$559$		−	4.06698i		−	0.172015i
$560$	−6.42795	−	5.38583i	−0.271631	−	0.227593i
$561$		0			0
$562$	−8.24234	−	14.2762i	−0.347682	−	0.602203i
$563$	8.10910	−	14.0454i	0.341758	−	0.591942i	−0.643002	−	0.765865i	$-0.722311\pi$
$563$	8.10910	−	14.0454i	0.341758	−	0.591942i	0.984759	+	0.173923i	$0.0556445\pi$
$564$		0			0
$565$	−33.5958	+	19.3966i	−1.41339	+	0.816019i
$566$	−18.3587			−0.771672
$567$		0			0
$568$	1.98690			0.0833684
$569$	23.6741	−	13.6683i	0.992471	−	0.573003i	0.0864588	−	0.996255i	$-0.472445\pi$
$569$	23.6741	−	13.6683i	0.992471	−	0.573003i	0.906012	+	0.423252i	$0.139112\pi$
$570$		0			0
$571$	20.3164	−	35.1890i	0.850213	−	1.47261i	−0.0308033	−	0.999525i	$-0.509807\pi$
$571$	20.3164	−	35.1890i	0.850213	−	1.47261i	0.881016	−	0.473086i	$-0.156860\pi$
$572$	0.120039	+	0.207913i	0.00501907	+	0.00869328i
$573$		0			0
$574$	1.74717	+	4.78960i	0.0729255	+	0.199914i
$575$		−	9.07470i		−	0.378441i
$576$		0			0
$577$	8.57355	+	4.94994i	0.356922	+	0.206069i	0.667730	−	0.744404i	$-0.267266\pi$
$577$	8.57355	+	4.94994i	0.356922	+	0.206069i	−0.310808	+	0.950473i	$0.600600\pi$
$578$	−0.444756	−	0.256780i	−0.0184994	−	0.0106806i
$579$		0			0
$580$			22.9865i			0.954463i
$581$	4.61913	−	26.3069i	0.191634	−	1.09139i
$582$		0			0
$583$	−4.45596	−	7.71795i	−0.184547	−	0.319645i
$584$	−4.61379	+	7.99132i	−0.190920	+	0.330683i
$585$		0			0
$586$	18.5630	−	10.7174i	0.766831	−	0.442730i
$587$	1.64613			0.0679431			0.0339715	−	0.999423i	$-0.489184\pi$
$587$	1.64613			0.0679431			0.0339715	+	0.999423i	$0.489184\pi$
$588$		0			0
$589$	5.36330			0.220991
$590$	−38.4405	+	22.1936i	−1.58257	+	0.913697i
$591$		0			0
$592$	−3.94496	+	6.83287i	−0.162137	+	0.280829i
$593$	14.5720	+	25.2395i	0.598401	+	1.03646i	0.993057	+	0.117632i	$0.0375305\pi$
$593$	14.5720	+	25.2395i	0.598401	+	1.03646i	−0.394656	+	0.918829i	$0.629136\pi$
$594$		0			0
$595$	5.88867	−	33.5372i	0.241412	−	1.37489i
$596$		−	3.22954i		−	0.132287i
$597$		0			0
$598$	0.559852	+	0.323231i	0.0228941	+	0.0132179i
$599$	−5.06696	−	2.92541i	−0.207030	−	0.119529i	0.392900	−	0.919581i	$-0.371472\pi$
$599$	−5.06696	−	2.92541i	−0.207030	−	0.119529i	−0.599931	+	0.800052i	$0.704805\pi$
$600$		0			0
$601$			37.6966i			1.53768i	0.639444	+	0.768838i	$0.279165\pi$
$601$			37.6966i			1.53768i	−0.639444	+	0.768838i	$0.720835\pi$
$602$	10.2571	+	28.1183i	0.418049	+	1.14602i
$603$		0			0
$604$	−0.108309	−	0.187596i	−0.00440701	−	0.00763317i
$605$	−16.7262	+	28.9706i	−0.680016	+	1.17782i
$606$		0			0
$607$	33.3511	−	19.2553i	1.35368	−	0.781547i	0.364917	−	0.931040i	$-0.381097\pi$
$607$	33.3511	−	19.2553i	1.35368	−	0.781547i	0.988763	+	0.149493i	$0.0477641\pi$
$608$	0.799506			0.0324242
$609$		0			0
$610$	−38.4214			−1.55564
$611$	2.54605	−	1.46997i	0.103002	−	0.0594684i
$612$		0			0
$613$	10.9890	−	19.0335i	0.443841	−	0.768756i	−0.554129	−	0.832431i	$-0.686949\pi$
$613$	10.9890	−	19.0335i	0.443841	−	0.768756i	0.997971	+	0.0636748i	$0.0202821\pi$
$614$	2.37661	+	4.11640i	0.0959120	+	0.166125i
$615$		0			0
$616$	−1.35429	−	1.13473i	−0.0545660	−	0.0457196i
$617$		−	34.8709i		−	1.40385i	−0.712251	−	0.701925i	$-0.752324\pi$
$617$		−	34.8709i		−	1.40385i	0.712251	−	0.701925i	$-0.247676\pi$
$618$		0			0
$619$	12.5198	+	7.22830i	0.503213	+	0.290530i	0.730039	−	0.683405i	$-0.239502\pi$
$619$	12.5198	+	7.22830i	0.503213	+	0.290530i	−0.226827	+	0.973935i	$0.572835\pi$
$620$	−18.4140	−	10.6313i	−0.739525	−	0.426965i
$621$		0			0
$622$			26.4628i			1.06106i
$623$	−6.43018	+	2.34563i	−0.257620	+	0.0939757i
$624$		0			0
$625$	12.3826	+	21.4473i	0.495304	+	0.857892i
$626$	1.77786	−	3.07935i	0.0710577	−	0.123075i
$627$		0			0
$628$	0.475769	−	0.274685i	0.0189853	−	0.0109611i
$629$	−32.0358			−1.27735
$630$		0			0
$631$	10.6492			0.423940			0.211970	−	0.977276i	$-0.432012\pi$
$631$	10.6492			0.423940			0.211970	+	0.977276i	$0.432012\pi$
$632$	2.96082	−	1.70943i	0.117775	−	0.0679975i
$633$		0			0
$634$	2.37062	−	4.10604i	0.0941495	−	0.163072i
$635$	−18.4327	−	31.9264i	−0.731479	−	1.26696i
$636$		0			0
$637$	0.857302	−	2.36599i	0.0339675	−	0.0937441i
$638$			4.84299i			0.191736i
$639$		0			0
$640$	−2.74498	−	1.58481i	−0.108505	−	0.0626452i
$641$	1.35659	+	0.783228i	0.0535821	+	0.0309356i	0.526552	−	0.850143i	$-0.323485\pi$
$641$	1.35659	+	0.783228i	0.0535821	+	0.0309356i	−0.472970	+	0.881079i	$0.656818\pi$
$642$		0			0
$643$			48.1820i			1.90011i	0.312081	+	0.950056i	$0.398974\pi$
$643$			48.1820i			1.90011i	−0.312081	+	0.950056i	$0.601026\pi$
$644$	−4.68592	−	0.822783i	−0.184651	−	0.0324222i
$645$		0			0
$646$	1.62314	+	2.81135i	0.0638614	+	0.110611i
$647$	22.1466	−	38.3591i	0.870673	−	1.50805i	0.00937171	−	0.999956i	$-0.497017\pi$
$647$	22.1466	−	38.3591i	0.870673	−	1.50805i	0.861302	−	0.508094i	$-0.169650\pi$
$648$		0			0
$649$	−8.09896	+	4.67594i	−0.317912	+	0.183547i
$650$	1.81424			0.0711605
$651$		0			0
$652$	−16.4001			−0.642277
$653$	28.6373	−	16.5338i	1.12067	−	0.647017i	0.179095	−	0.983832i	$-0.442683\pi$
$653$	28.6373	−	16.5338i	1.12067	−	0.647017i	0.941571	+	0.336815i	$0.109350\pi$
$654$		0			0
$655$	19.0085	−	32.9236i	0.742722	−	1.28643i
$656$	0.963492	+	1.66882i	0.0376181	+	0.0651564i
$657$		0			0
$658$	−13.8956	+	16.5844i	−0.541708	+	0.646526i
$659$		−	6.37371i		−	0.248284i	−0.992264	−	0.124142i	$-0.960382\pi$
$659$		−	6.37371i		−	0.248284i	0.992264	−	0.124142i	$-0.0396179\pi$
$660$		0			0
$661$	−20.6041	−	11.8958i	−0.801407	−	0.462693i	0.0425557	−	0.999094i	$-0.486450\pi$
$661$	−20.6041	−	11.8958i	−0.801407	−	0.462693i	−0.843963	+	0.536401i	$0.819783\pi$
$662$	12.3654	+	7.13919i	0.480597	+	0.277473i
$663$		0			0
$664$		−	10.0952i		−	0.391769i
$665$	4.30600	−	5.13918i	0.166979	−	0.199289i
$666$		0			0
$667$	6.52041	+	11.2937i	0.252471	+	0.437293i
$668$	−0.124602	+	0.215816i	−0.00482098	+	0.00835018i
$669$		0			0
$670$	31.6554	−	18.2763i	1.22296	−	0.706074i
$671$	−8.09494			−0.312502
$672$		0			0
$673$	27.6774			1.06688			0.533442	−	0.845836i	$-0.320898\pi$
$673$	27.6774			1.06688			0.533442	+	0.845836i	$0.320898\pi$
$674$	−4.23495	+	2.44505i	−0.163124	+	0.0941797i
$675$		0			0
$676$	6.43538	−	11.1464i	0.247515	−	0.428708i
$677$	−0.796340	−	1.37930i	−0.0306058	−	0.0530108i	0.850317	−	0.526271i	$-0.176410\pi$
$677$	−0.796340	−	1.37930i	−0.0306058	−	0.0530108i	−0.880923	+	0.473260i	$0.843077\pi$
$678$		0			0
$679$	47.9248	+	8.41494i	1.83919	+	0.322936i
$680$		−	12.8698i		−	0.493534i
$681$		0			0
$682$	−3.87962	−	2.23990i	−0.148558	−	0.0857702i
$683$	−0.00267350	−	0.00154355i	−0.000102299	−	5.90622e-5i	0.499949	−	0.866055i	$-0.333352\pi$
$683$	−0.00267350	−	0.00154355i	−0.000102299	−	5.90622e-5i	−0.500051	+	0.865996i	$0.666685\pi$
$684$		0			0
$685$		−	56.7837i		−	2.16959i
$686$	0.0399286	+	18.5202i	0.00152448	+	0.707105i
$687$		0			0
$688$	5.65638	+	9.79714i	0.215648	+	0.373512i
$689$	2.39881	−	4.15486i	0.0913874	−	0.158288i
$690$		0			0
$691$	−10.3385	+	5.96896i	−0.393296	+	0.227070i	−0.683587	−	0.729869i	$-0.739581\pi$
$691$	−10.3385	+	5.96896i	−0.393296	+	0.227070i	0.290291	+	0.956938i	$0.406248\pi$
$692$	7.57470			0.287947
$693$		0			0
$694$	4.36660			0.165754
$695$	26.6479	−	15.3852i	1.01081	−	0.583593i
$696$		0			0
$697$	−3.91212	+	6.77598i	−0.148182	+	0.256659i
$698$	−2.97191	−	5.14750i	−0.112489	−	0.194836i
$699$		0			0
$700$	−12.5434	+	4.57562i	−0.474094	+	0.172942i
$701$			15.2404i			0.575621i	0.957687	+	0.287811i	$0.0929274\pi$
$701$			15.2404i			0.575621i	−0.957687	+	0.287811i	$0.907073\pi$
$702$		0			0
$703$	−5.46292	−	3.15402i	−0.206038	−	0.118956i
$704$	−0.578334	−	0.333901i	−0.0217968	−	0.0125844i
$705$		0			0
$706$		−	25.4305i		−	0.957088i
$707$	5.44919	+	4.56575i	0.204938	+	0.171713i
$708$		0			0
$709$	−8.36636	−	14.4910i	−0.314205	−	0.544219i	0.665063	−	0.746787i	$-0.268405\pi$
$709$	−8.36636	−	14.4910i	−0.314205	−	0.544219i	−0.979268	+	0.202568i	$0.935071\pi$
$710$	3.14886	−	5.45399i	0.118175	−	0.204684i
$711$		0			0
$712$	−2.24044	+	1.29352i	−0.0839639	+	0.0484766i
$713$	−12.0629			−0.451757
$714$		0			0
$715$	0.760955			0.0284581
$716$	1.31716	−	0.760465i	0.0492247	−	0.0284199i
$717$		0			0
$718$	5.09523	−	8.82521i	0.190152	−	0.329354i
$719$	20.2756	+	35.1184i	0.756153	+	1.30970i	0.944799	+	0.327651i	$0.106257\pi$
$719$	20.2756	+	35.1184i	0.756153	+	1.30970i	−0.188645	+	0.982045i	$0.560410\pi$
$720$		0			0
$721$	11.7727	+	32.2730i	0.438438	+	1.20191i
$722$		−	18.3608i		−	0.683318i
$723$		0			0
$724$	−5.30366	−	3.06207i	−0.197109	−	0.113801i
$725$	31.6948	+	18.2990i	1.17712	+	0.679608i
$726$		0			0
$727$			43.7610i			1.62300i	0.584350	+	0.811502i	$0.301350\pi$
$727$			43.7610i			1.62300i	−0.584350	+	0.811502i	$0.698650\pi$
$728$	0.164493	−	0.936825i	0.00609653	−	0.0347210i
$729$		0			0
$730$	14.6240	+	25.3295i	0.541258	+	0.937487i
$731$	−22.9669	+	39.7798i	−0.849461	+	1.47131i
$732$		0			0
$733$	−17.1301	+	9.89007i	−0.632715	+	0.365298i	−0.781803	−	0.623526i	$-0.785700\pi$
$733$	−17.1301	+	9.89007i	−0.632715	+	0.365298i	0.149088	+	0.988824i	$0.452366\pi$
$734$	−18.2634			−0.674113
$735$		0			0
$736$	−1.79821			−0.0662828
$737$	6.66942	−	3.85059i	0.245671	−	0.141838i
$738$		0			0
$739$	6.64246	−	11.5051i	0.244347	−	0.423221i	−0.717601	−	0.696454i	$-0.754760\pi$
$739$	6.64246	−	11.5051i	0.244347	−	0.423221i	0.961948	+	0.273233i	$0.0880932\pi$
$740$	12.5040	+	21.6576i	0.459658	+	0.796151i
$741$		0			0
$742$	−6.10616	+	34.7759i	−0.224164	+	1.27666i
$743$			7.45642i			0.273549i	0.990602	+	0.136775i	$0.0436736\pi$
$743$			7.45642i			0.273549i	−0.990602	+	0.136775i	$0.956326\pi$
$744$		0			0
$745$	−8.86502	−	5.11822i	−0.324789	−	0.187517i
$746$	−10.1251	−	5.84571i	−0.370705	−	0.214027i
$747$		0			0
$748$		−	2.71151i		−	0.0991427i
$749$	−11.5103	−	31.5536i	−0.420576	−	1.15294i
$750$		0			0
$751$	−23.3592	−	40.4593i	−0.852390	−	1.47638i	−0.879046	−	0.476737i	$-0.841819\pi$
$751$	−23.3592	−	40.4593i	−0.852390	−	1.47638i	0.0266562	−	0.999645i	$-0.491514\pi$
$752$	−4.08888	+	7.08214i	−0.149106	+	0.258259i
$753$		0			0
$754$	−2.25787	+	1.30358i	−0.0822267	+	0.0474736i
$755$	−0.686595			−0.0249878
$756$		0			0
$757$	−6.88544			−0.250255			−0.125128	−	0.992141i	$-0.539934\pi$
$757$	−6.88544			−0.250255			−0.125128	+	0.992141i	$0.539934\pi$
$758$	−32.8265	+	18.9524i	−1.19231	+	0.688382i
$759$		0			0
$760$	1.26707	−	2.19462i	0.0459613	−	0.0796074i
$761$	−18.5403	−	32.1128i	−0.672086	−	1.16409i	−0.977311	−	0.211807i	$-0.932065\pi$
$761$	−18.5403	−	32.1128i	−0.672086	−	1.16409i	0.305225	−	0.952280i	$-0.401268\pi$
$762$		0			0
$763$	11.1321	+	9.32735i	0.403010	+	0.337673i
$764$		−	1.67453i		−	0.0605823i
$765$		0			0
$766$	12.8062	+	7.39368i	0.462708	+	0.267144i
$767$	−4.35997	−	2.51723i	−0.157430	−	0.0908920i
$768$		0			0
$769$		−	24.7826i		−	0.893682i	−0.894613	−	0.446841i	$-0.852549\pi$
$769$		−	24.7826i		−	0.893682i	0.894613	−	0.446841i	$-0.147451\pi$
$770$	−5.26111	+	1.91917i	−0.189597	+	0.0691621i
$771$		0			0
$772$	12.0244	+	20.8268i	0.432766	+	0.749573i
$773$	14.5338	−	25.1732i	0.522743	−	0.905418i	−0.476907	−	0.878954i	$-0.658242\pi$
$773$	14.5338	−	25.1732i	0.522743	−	0.905418i	0.999650	−	0.0264637i	$-0.00842464\pi$
$774$		0			0
$775$	−29.3179	+	16.9267i	−1.05313	+	0.608026i
$776$	18.3910			0.660198
$777$		0			0
$778$	−22.6413			−0.811731
$779$	−1.33423	+	0.770318i	−0.0478037	+	0.0275995i
$780$		0			0
$781$	0.663428	−	1.14909i	0.0237393	−	0.0411177i
$782$	−3.65068	−	6.32315i	−0.130548	−	0.226116i
$783$		0			0
$784$	1.22544	+	6.89190i	0.0437659	+	0.246139i
$785$		−	1.74130i		−	0.0621497i
$786$		0			0
$787$	25.2734	+	14.5916i	0.900899	+	0.520134i	0.877492	−	0.479592i	$-0.159215\pi$
$787$	25.2734	+	14.5916i	0.900899	+	0.520134i	0.0234069	+	0.999726i	$0.492549\pi$
$788$	−21.8650	−	12.6238i	−0.778910	−	0.449704i
$789$		0			0
$790$		−	10.8365i		−	0.385546i
$791$	31.8935	+	5.60005i	1.13400	+	0.199115i
$792$		0			0
$793$	−2.17891	−	3.77398i	−0.0773752	−	0.134018i
$794$	6.57052	−	11.3805i	0.233179	−	0.403878i
$795$		0			0
$796$	−8.35598	+	4.82433i	−0.296170	+	0.170994i
$797$	−25.7700			−0.912820			−0.456410	−	0.889770i	$-0.650865\pi$
$797$	−25.7700			−0.912820			−0.456410	+	0.889770i	$0.650865\pi$
$798$		0			0
$799$	−33.2045			−1.17469
$800$	−4.37042	+	2.52326i	−0.154518	+	0.0892108i
$801$		0			0
$802$	−0.0261582	+	0.0453074i	−0.000923679	+	0.00159986i
$803$	3.08110	+	5.33663i	0.108730	+	0.188325i
$804$		0			0
$805$	−9.68483	+	11.5588i	−0.341345	+	0.407394i
$806$		−	2.41164i		−	0.0849465i
$807$		0			0
$808$	2.32701	+	1.34350i	0.0818639	+	0.0472642i
$809$	−1.94380	−	1.12225i	−0.0683405	−	0.0394564i	0.465440	−	0.885079i	$-0.345896\pi$
$809$	−1.94380	−	1.12225i	−0.0683405	−	0.0394564i	−0.533781	+	0.845623i	$0.679229\pi$
$810$		0			0
$811$			51.0753i			1.79350i	0.442541	+	0.896748i	$0.354077\pi$
$811$			51.0753i			1.79350i	−0.442541	+	0.896748i	$0.645923\pi$
$812$	12.3228	−	14.7072i	0.432445	−	0.516121i
$813$		0			0
$814$	2.63446	+	4.56301i	0.0923376	+	0.159933i
$815$	−25.9911	+	45.0179i	−0.910428	+	1.57691i
$816$		0			0
$817$	−7.83287	+	4.52231i	−0.274037	+	0.158216i
$818$	−9.10006			−0.318176
$819$		0			0
$820$	6.10782			0.213294
$821$	34.6286	−	19.9928i	1.20855	−	0.697754i	0.246104	−	0.969243i	$-0.420850\pi$
$821$	34.6286	−	19.9928i	1.20855	−	0.697754i	0.962441	+	0.271489i	$0.0875162\pi$
$822$		0			0
$823$	−15.8292	+	27.4171i	−0.551773	+	0.955699i	0.446374	+	0.894847i	$0.352715\pi$
$823$	−15.8292	+	27.4171i	−0.551773	+	0.955699i	−0.998147	+	0.0608520i	$0.980618\pi$
$824$	6.49215	+	11.2447i	0.226165	+	0.391729i
$825$		0			0
$826$	36.4927	+	6.40761i	1.26974	+	0.222949i
$827$			20.1221i			0.699715i	0.936803	+	0.349858i	$0.113770\pi$
$827$			20.1221i			0.699715i	−0.936803	+	0.349858i	$0.886230\pi$
$828$		0			0
$829$	38.7539	+	22.3745i	1.34598	+	0.777100i	0.987677	−	0.156506i	$-0.0500232\pi$
$829$	38.7539	+	22.3745i	1.34598	+	0.777100i	0.358300	+	0.933607i	$0.383357\pi$
$830$	−27.7111	−	15.9990i	−0.961865	−	0.555333i
$831$		0			0
$832$		−	0.359503i		−	0.0124635i
$833$	−21.7466	+	18.3009i	−0.753474	+	0.634088i
$834$		0			0
$835$	0.394940	+	0.684057i	0.0136675	+	0.0236728i
$836$	0.266956	−	0.462381i	0.00923287	−	0.0159918i
$837$		0			0
$838$	−4.06688	+	2.34802i	−0.140488	+	0.0811109i
$839$	−29.5513			−1.02023			−0.510113	−	0.860108i	$-0.670396\pi$
$839$	−29.5513			−1.02023			−0.510113	+	0.860108i	$0.670396\pi$
$840$		0			0
$841$	−23.5933			−0.813561
$842$	1.01909	−	0.588375i	0.0351203	−	0.0202767i
$843$		0			0
$844$	−7.42389	+	12.8586i	−0.255541	+	0.442610i
$845$	−20.3977	−	35.3299i	−0.701704	−	1.21539i
$846$		0			0
$847$	26.2325	−	9.56921i	0.901360	−	0.328802i
$848$			13.3451i			0.458274i
$849$		0			0
$850$	−17.7454	−	10.2453i	−0.608663	−	0.351412i
$851$	12.2869	+	7.09386i	0.421190	+	0.243174i
$852$		0			0
$853$		−	38.0995i		−	1.30450i	−0.758003	−	0.652251i	$-0.773825\pi$
$853$		−	38.0995i		−	1.30450i	0.758003	−	0.652251i	$-0.226175\pi$
$854$	24.5827	+	20.5973i	0.841204	+	0.704824i
$855$		0			0
$856$	−6.34743	−	10.9941i	−0.216951	−	0.375770i
$857$	−12.1638	+	21.0683i	−0.415507	+	0.719679i	−0.995482	−	0.0949553i	$-0.969729\pi$
$857$	−12.1638	+	21.0683i	−0.415507	+	0.719679i	0.579974	+	0.814635i	$0.303063\pi$
$858$		0			0
$859$	−8.16908	+	4.71642i	−0.278725	+	0.160922i	−0.632846	−	0.774278i	$-0.718113\pi$
$859$	−8.16908	+	4.71642i	−0.278725	+	0.160922i	0.354121	+	0.935200i	$0.384780\pi$
$860$	35.8572			1.22272
$861$		0			0
$862$	−8.42294			−0.286887
$863$	−16.5943	+	9.58074i	−0.564877	+	0.326132i	−0.755101	−	0.655609i	$-0.772412\pi$
$863$	−16.5943	+	9.58074i	−0.564877	+	0.326132i	0.190223	+	0.981741i	$0.439079\pi$
$864$		0			0
$865$	12.0045	−	20.7924i	0.408165	−	0.706962i
$866$	−1.13333	−	1.96298i	−0.0385120	−	0.0667047i
$867$		0			0
$868$	6.08230	+	16.6737i	0.206447	+	0.565941i
$869$		−	2.28312i		−	0.0774497i
$870$		0			0
$871$	3.59040	+	2.07292i	0.121656	+	0.0702382i
$872$	4.75384	+	2.74463i	0.160985	+	0.0929449i
$873$		0			0
$874$		−	1.43768i		−	0.0486301i
$875$	−0.0674767	+	0.384294i	−0.00228113	+	0.0129915i
$876$		0			0
$877$	−17.4869	−	30.2882i	−0.590491	−	1.02276i	−0.994166	−	0.107858i	$-0.965601\pi$
$877$	−17.4869	−	30.2882i	−0.590491	−	1.02276i	0.403675	−	0.914902i	$-0.367733\pi$
$878$	8.41149	−	14.5691i	0.283874	−	0.491684i
$879$		0			0
$880$	−1.83310	+	1.05834i	−0.0617939	+	0.0356767i
$881$	49.8295			1.67880			0.839400	−	0.543515i	$-0.182907\pi$
$881$	49.8295			1.67880			0.839400	+	0.543515i	$0.182907\pi$
$882$		0			0
$883$	−45.7673			−1.54019			−0.770096	−	0.637928i	$-0.779792\pi$
$883$	−45.7673			−1.54019			−0.770096	+	0.637928i	$0.779792\pi$
$884$	1.26415	−	0.729855i	0.0425178	−	0.0245477i
$885$		0			0
$886$	15.7894	−	27.3481i	0.530457	−	0.918778i
$887$	24.5833	+	42.5796i	0.825427	+	1.42968i	0.901592	+	0.432587i	$0.142399\pi$
$887$	24.5833	+	42.5796i	0.825427	+	1.42968i	−0.0761651	+	0.997095i	$0.524268\pi$
$888$		0			0
$889$	−5.32177	+	30.3086i	−0.178487	+	1.01652i
$890$			8.19993i			0.274862i
$891$		0			0
$892$	−21.8250	−	12.6007i	−0.730756	−	0.421902i
$893$	−5.66221	−	3.26908i	−0.189479	−	0.109396i
$894$		0			0
$895$		−	4.82078i		−	0.161141i
$896$	0.906687	+	2.48554i	0.0302903	+	0.0830361i
$897$		0			0
$898$	11.8187	+	20.4706i	0.394396	+	0.683113i
$899$	24.3246	−	42.1314i	0.811270	−	1.40516i
$900$		0			0
$901$	−46.9264	+	27.0930i	−1.56334	+	0.902597i
$902$	1.28685			0.0428473
$903$		0			0
$904$	12.2390			0.407064
$905$	−16.8106	+	9.70562i	−0.558804	+	0.322626i
$906$		0			0
$907$	17.6978	−	30.6535i	0.587646	−	1.01783i	−0.406894	−	0.913475i	$-0.633388\pi$
$907$	17.6978	−	30.6535i	0.587646	−	1.01783i	0.994540	−	0.104357i	$-0.0332784\pi$
$908$	−3.45101	−	5.97732i	−0.114526	−	0.198364i
$909$		0			0
$910$	−2.31087	−	1.93622i	−0.0766046	−	0.0641851i
$911$			0.358549i			0.0118793i	0.999982	+	0.00593963i	$0.00189066\pi$
$911$			0.358549i			0.0118793i	−0.999982	+	0.00593963i	$0.998109\pi$
$912$		0			0
$913$	−5.83839	−	3.37080i	−0.193223	−	0.111557i
$914$	14.6000	+	8.42929i	0.482924	+	0.278816i
$915$		0			0
$916$		−	11.0167i		−	0.364002i
$917$	−29.8119	+	10.8749i	−0.984477	+	0.359122i
$918$		0			0
$919$	−11.9204	−	20.6468i	−0.393219	−	0.681075i	0.599653	−	0.800260i	$-0.295305\pi$
$919$	−11.9204	−	20.6468i	−0.393219	−	0.681075i	−0.992872	+	0.119185i	$0.961972\pi$
$920$	−2.84982	+	4.93604i	−0.0939558	+	0.162736i
$921$		0			0
$922$	1.29398	−	0.747079i	0.0426149	−	0.0246037i
$923$	0.714296			0.0235114
$924$		0			0
$925$	39.8167			1.30916
$926$	28.2234	−	16.2948i	0.927480	−	0.535481i
$927$		0			0
$928$	3.62606	−	6.28052i	0.119031	−	0.206168i
$929$	−23.0731	−	39.9638i	−0.757004	−	1.31117i	−0.944372	−	0.328880i	$-0.893329\pi$
$929$	−23.0731	−	39.9638i	−0.757004	−	1.31117i	0.187368	−	0.982290i	$-0.440004\pi$
$930$		0			0
$931$	−5.51011	+	0.979749i	−0.180587	+	0.0321100i
$932$		−	8.23144i		−	0.269630i
$933$		0			0
$934$	−4.40808	−	2.54500i	−0.144237	−	0.0832751i
$935$	−7.44304	−	4.29724i	−0.243413	−	0.140535i
$936$		0			0
$937$			40.0103i			1.30708i	0.756892	+	0.653540i	$0.226717\pi$
$937$			40.0103i			1.30708i	−0.756892	+	0.653540i	$0.773283\pi$
$938$	−30.0514	−	5.27661i	−0.981213	−	0.172287i
$939$		0			0
$940$	12.9602	+	22.4477i	0.422715	+	0.732165i
$941$	−11.1295	+	19.2769i	−0.362811	+	0.628408i	−0.988422	−	0.151727i	$-0.951516\pi$
$941$	−11.1295	+	19.2769i	−0.362811	+	0.628408i	0.625611	+	0.780135i	$0.284850\pi$
$942$		0			0
$943$	3.00088	−	1.73256i	0.0977221	−	0.0564199i
$944$	14.0039			0.455790
$945$		0			0
$946$	7.55469			0.245624
$947$	26.8280	−	15.4891i	0.871792	−	0.503329i	0.00384870	−	0.999993i	$-0.498775\pi$
$947$	26.8280	−	15.4891i	0.871792	−	0.503329i	0.867943	+	0.496663i	$0.165442\pi$
$948$		0			0
$949$	−1.65867	+	2.87291i	−0.0538428	+	0.0932585i
$950$	−2.01736	−	3.49417i	−0.0654519	−	0.113366i
$951$		0			0
$952$	−6.89934	+	8.23433i	−0.223609	+	0.266876i
$953$			26.4488i			0.856761i	0.903598	+	0.428380i	$0.140916\pi$
$953$			26.4488i			0.856761i	−0.903598	+	0.428380i	$0.859084\pi$
$954$		0			0
$955$	−4.59654	−	2.65382i	−0.148741	−	0.0858755i
$956$	11.0696	+	6.39107i	0.358018	+	0.206702i
$957$		0			0
$958$			28.4966i			0.920684i
$959$	−30.4411	+	36.3312i	−0.982993	+	1.17320i
$960$		0			0
$961$	7.00041	+	12.1251i	0.225820	+	0.391131i
$962$	−1.41823	+	2.45644i	−0.0457255	+	0.0791988i
$963$		0			0
$964$	−3.07823	+	1.77722i	−0.0991432	+	0.0572404i
$965$	76.2254			2.45378
$966$		0			0
$967$	−24.4562			−0.786459			−0.393230	−	0.919440i	$-0.628642\pi$
$967$	−24.4562			−0.786459			−0.393230	+	0.919440i	$0.628642\pi$
$968$	9.14007	−	5.27702i	0.293773	−	0.169610i
$969$		0			0
$970$	29.1463	−	50.4829i	0.935831	−	1.62091i
$971$	19.7198	+	34.1556i	0.632837	+	1.09611i	0.986969	+	0.160911i	$0.0514431\pi$
$971$	19.7198	+	34.1556i	0.632837	+	1.09611i	−0.354132	+	0.935196i	$0.615224\pi$
$972$		0			0
$973$	−25.2976	−	4.44191i	−0.811005	−	0.142401i
$974$			12.6414i			0.405057i
$975$		0			0
$976$	10.4977	+	6.06088i	0.336025	+	0.194004i
$977$	21.1701	+	12.2226i	0.677291	+	0.391034i	0.798834	−	0.601552i	$-0.205451\pi$
$977$	21.1701	+	12.2226i	0.677291	+	0.391034i	−0.121542	+	0.992586i	$0.538784\pi$
$978$		0			0
$979$			1.72763i			0.0552152i
$980$	20.8602	+	7.55856i	0.666355	+	0.241449i
$981$		0			0
$982$	−7.31980	−	12.6783i	−0.233584	−	0.404580i
$983$	−7.49038	+	12.9737i	−0.238906	+	0.413798i	−0.960401	−	0.278623i	$-0.910122\pi$
$983$	−7.49038	+	12.9737i	−0.238906	+	0.413798i	0.721495	+	0.692420i	$0.243455\pi$
$984$		0			0
$985$	−69.3040	+	40.0127i	−2.20821	+	1.27491i
$986$	29.4462			0.937757
$987$		0			0
$988$	0.287425			0.00914421
$989$	17.6173	−	10.1713i	0.560197	−	0.323430i
$990$		0			0
$991$	−23.3185	+	40.3887i	−0.740735	+	1.28299i	0.211426	+	0.977394i	$0.432189\pi$
$991$	−23.3185	+	40.3887i	−0.740735	+	1.28299i	−0.952161	+	0.305597i	$0.901144\pi$
$992$	3.35413	+	5.80953i	0.106494	+	0.184453i
$993$		0			0
$994$	−4.93852	+	1.80149i	−0.156640	+	0.0571399i
$995$			30.5826i			0.969535i
$996$		0			0
$997$	16.8646	+	9.73679i	0.534108	+	0.308367i	0.742687	−	0.669638i	$-0.233551\pi$
$997$	16.8646	+	9.73679i	0.534108	+	0.308367i	−0.208580	+	0.978005i	$0.566884\pi$
$998$	4.95543	+	2.86102i	0.156861	+	0.0905640i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.d.647.1	yes	16
3.2	odd	2		1134.2.k.c.647.8	✓	16
7.5	odd	6		1134.2.k.c.971.8	yes	16
9.2	odd	6		1134.2.t.h.1025.1		16
9.4	even	3		1134.2.l.g.269.1		16
9.5	odd	6		1134.2.l.h.269.8		16
9.7	even	3		1134.2.t.g.1025.8		16
21.5	even	6	inner	1134.2.k.d.971.1	yes	16
63.5	even	6		1134.2.t.g.593.8		16
63.40	odd	6		1134.2.t.h.593.1		16
63.47	even	6		1134.2.l.g.215.5		16
63.61	odd	6		1134.2.l.h.215.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.8	✓	16	3.2	odd	2
1134.2.k.c.971.8	yes	16	7.5	odd	6
1134.2.k.d.647.1	yes	16	1.1	even	1	trivial
1134.2.k.d.971.1	yes	16	21.5	even	6	inner
1134.2.l.g.215.5		16	63.47	even	6
1134.2.l.g.269.1		16	9.4	even	3
1134.2.l.h.215.4		16	63.61	odd	6
1134.2.l.h.269.8		16	9.5	odd	6
1134.2.t.g.593.8		16	63.5	even	6
1134.2.t.g.1025.8		16	9.7	even	3
1134.2.t.h.593.1		16	63.40	odd	6
1134.2.t.h.1025.1		16	9.2	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.58481 - 2.74498i) q^{5} +(-0.457557 + 2.60589i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.58481 - 2.74498i) q^{5} +(-0.457557 + 2.60589i) q^{7} +1.00000i q^{8} +(2.74498 + 1.58481i) q^{10} +(0.578334 + 0.333901i) q^{11} +0.359503i q^{13} +(-0.906687 - 2.48554i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.03017 - 3.51637i) q^{17} +(0.692392 - 0.399753i) q^{19} -3.16963 q^{20} -0.667803 q^{22} +(-1.55729 + 0.899104i) q^{23} +(-2.52326 + 4.37042i) q^{25} +(-0.179752 - 0.311339i) q^{26} +(2.02798 + 1.69920i) q^{28} -7.25212i q^{29} +(5.80953 + 3.35413i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.06035i q^{34} +(7.87824 - 2.87386i) q^{35} +(-3.94496 - 6.83287i) q^{37} +(-0.399753 + 0.692392i) q^{38} +(2.74498 - 1.58481i) q^{40} -1.92698 q^{41} -11.3128 q^{43} +(0.578334 - 0.333901i) q^{44} +(0.899104 - 1.55729i) q^{46} +(-4.08888 - 7.08214i) q^{47} +(-6.58128 - 2.38468i) q^{49} -5.04653i q^{50} +(0.311339 + 0.179752i) q^{52} +(-11.5572 - 6.67257i) q^{53} -2.11668i q^{55} +(-2.60589 - 0.457557i) q^{56} +(3.62606 + 6.28052i) q^{58} +(-7.00197 + 12.1278i) q^{59} +(-10.4977 + 6.06088i) q^{61} -6.70827 q^{62} -1.00000 q^{64} +(0.986828 - 0.569746i) q^{65} +(5.76606 - 9.98712i) q^{67} +(-2.03017 - 3.51637i) q^{68} +(-5.38583 + 6.42795i) q^{70} -1.98690i q^{71} +(7.99132 + 4.61379i) q^{73} +(6.83287 + 3.94496i) q^{74} -0.799506i q^{76} +(-1.13473 + 1.35429i) q^{77} +(-1.70943 - 2.96082i) q^{79} +(-1.58481 + 2.74498i) q^{80} +(1.66882 - 0.963492i) q^{82} -10.0952 q^{83} -12.8698 q^{85} +(9.79714 - 5.65638i) q^{86} +(-0.333901 + 0.578334i) q^{88} +(1.29352 + 2.24044i) q^{89} +(-0.936825 - 0.164493i) q^{91} +1.79821i q^{92} +(7.08214 + 4.08888i) q^{94} +(-2.19462 - 1.26707i) q^{95} -18.3910i q^{97} +(6.89190 - 1.22544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^7	\( 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

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