LMFDB - Embedded newform 819.2.bm.h.478.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			478.7
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.h.550.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.16108i q^{2} +0.651901 q^{4} +(-3.43209 - 1.98152i) q^{5} +(-2.10943 - 1.59697i) q^{7} -3.07906i q^{8} +O(q^{10})$	\(q-1.16108i q^{2} +0.651901 q^{4} +(-3.43209 - 1.98152i) q^{5} +(-2.10943 - 1.59697i) q^{7} -3.07906i q^{8} +(-2.30069 + 3.98492i) q^{10} +(-0.144951 - 0.0836874i) q^{11} +(-0.211584 + 3.59934i) q^{13} +(-1.85420 + 2.44921i) q^{14} -2.27122 q^{16} +1.81120 q^{17} +(-3.45252 + 1.99331i) q^{19} +(-2.23738 - 1.29175i) q^{20} +(-0.0971674 + 0.168299i) q^{22} -3.60847 q^{23} +(5.35282 + 9.27135i) q^{25} +(4.17911 + 0.245665i) q^{26} +(-1.37514 - 1.04106i) q^{28} +(2.60277 + 4.50812i) q^{29} +(1.95252 - 1.12729i) q^{31} -3.52106i q^{32} -2.10295i q^{34} +(4.07533 + 9.66080i) q^{35} +1.31601i q^{37} +(2.31439 + 4.00864i) q^{38} +(-6.10121 + 10.5676i) q^{40} +(-9.53289 + 5.50381i) q^{41} +(4.64123 - 8.03885i) q^{43} +(-0.0944936 - 0.0545559i) q^{44} +4.18971i q^{46} +(-8.62959 - 4.98230i) q^{47} +(1.89939 + 6.73738i) q^{49} +(10.7647 - 6.21503i) q^{50} +(-0.137932 + 2.34641i) q^{52} +(-3.26454 - 5.65434i) q^{53} +(0.331656 + 0.574445i) q^{55} +(-4.91716 + 6.49506i) q^{56} +(5.23428 - 3.02201i) q^{58} +4.11001i q^{59} +(-6.50404 - 11.2653i) q^{61} +(-1.30887 - 2.26703i) q^{62} -8.63066 q^{64} +(7.85832 - 11.9340i) q^{65} +(-10.3145 - 5.95509i) q^{67} +1.18073 q^{68} +(11.2169 - 4.73177i) q^{70} +(3.62344 + 2.09199i) q^{71} +(-9.65972 + 5.57704i) q^{73} +1.52799 q^{74} +(-2.25070 + 1.29944i) q^{76} +(0.172118 + 0.408014i) q^{77} +(-0.727082 + 1.25934i) q^{79} +(7.79503 + 4.50047i) q^{80} +(6.39035 + 11.0684i) q^{82} +3.67555i q^{83} +(-6.21621 - 3.58893i) q^{85} +(-9.33372 - 5.38883i) q^{86} +(-0.257678 + 0.446312i) q^{88} -7.80832i q^{89} +(6.19434 - 7.25466i) q^{91} -2.35236 q^{92} +(-5.78483 + 10.0196i) q^{94} +15.7991 q^{95} +(9.81792 + 5.66838i) q^{97} +(7.82262 - 2.20534i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) $ 36 * q - 44 * q^4 + 8 * q^7	$ 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) $ 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		−	1.16108i		−	0.821005i	−0.911859	−	0.410503i	$-0.865353\pi$
$2$		−	1.16108i		−	0.821005i	0.911859	−	0.410503i	$-0.134647\pi$
$3$		0			0
$3$		0			0
$4$	0.651901			0.325951
$5$	−3.43209	−	1.98152i	−1.53488	−	0.886161i	−0.999127	−	0.0417842i	$-0.986696\pi$
$5$	−3.43209	−	1.98152i	−1.53488	−	0.886161i	−0.535749	−	0.844377i	$-0.679971\pi$
$6$		0			0
$7$	−2.10943	−	1.59697i	−0.797290	−	0.603597i
$7$	−2.10943	−	1.59697i	−0.797290	−	0.603597i
$8$		−	3.07906i		−	1.08861i
$9$		0			0
$10$	−2.30069	+	3.98492i	−0.727543	+	1.26014i
$11$	−0.144951	−	0.0836874i	−0.0437043	−	0.0252327i	0.477989	−	0.878366i	$-0.341366\pi$
$11$	−0.144951	−	0.0836874i	−0.0437043	−	0.0252327i	−0.521693	+	0.853133i	$0.674699\pi$
$12$		0			0
$13$	−0.211584	+	3.59934i	−0.0586828	+	0.998277i
$13$	−0.211584	+	3.59934i	−0.0586828	+	0.998277i
$14$	−1.85420	+	2.44921i	−0.495556	+	0.654579i
$15$		0			0
$16$	−2.27122			−0.567806
$17$	1.81120			0.439281			0.219641	−	0.975581i	$-0.429512\pi$
$17$	1.81120			0.439281			0.219641	+	0.975581i	$0.429512\pi$
$18$		0			0
$19$	−3.45252	+	1.99331i	−0.792063	+	0.457298i	−0.840688	−	0.541519i	$-0.817849\pi$
$19$	−3.45252	+	1.99331i	−0.792063	+	0.457298i	0.0486255	+	0.998817i	$0.484516\pi$
$20$	−2.23738	−	1.29175i	−0.500294	−	0.288845i
$21$		0			0
$22$	−0.0971674	+	0.168299i	−0.0207162	+	0.0358815i
$23$	−3.60847			−0.752418			−0.376209	−	0.926535i	$-0.622772\pi$
$23$	−3.60847			−0.752418			−0.376209	+	0.926535i	$0.622772\pi$
$24$		0			0
$25$	5.35282	+	9.27135i	1.07056	+	1.85427i
$26$	4.17911	+	0.245665i	0.819590	+	0.0481789i
$27$		0			0
$28$	−1.37514	−	1.04106i	−0.259877	−	0.196743i
$29$	2.60277	+	4.50812i	0.483322	+	0.837138i	0.999817	−	0.0191526i	$-0.00609683\pi$
$29$	2.60277	+	4.50812i	0.483322	+	0.837138i	−0.516495	+	0.856290i	$0.672763\pi$
$30$		0			0
$31$	1.95252	−	1.12729i	0.350683	−	0.202467i	−0.314303	−	0.949323i	$-0.601771\pi$
$31$	1.95252	−	1.12729i	0.350683	−	0.202467i	0.664986	+	0.746856i	$0.268437\pi$
$32$		−	3.52106i		−	0.622441i
$33$		0			0
$34$		−	2.10295i		−	0.360652i
$35$	4.07533	+	9.66080i	0.688857	+	1.63297i
$36$		0			0
$37$			1.31601i			0.216351i	0.994132	+	0.108176i	$0.0345009\pi$
$37$			1.31601i			0.216351i	−0.994132	+	0.108176i	$0.965499\pi$
$38$	2.31439	+	4.00864i	0.375444	+	0.650288i
$39$		0			0
$40$	−6.10121	+	10.5676i	−0.964686	+	1.67088i
$41$	−9.53289	+	5.50381i	−1.48879	+	0.859551i	−0.999918	−	0.0128059i	$-0.995924\pi$
$41$	−9.53289	+	5.50381i	−1.48879	+	0.859551i	−0.488869	+	0.872357i	$0.662590\pi$
$42$		0			0
$43$	4.64123	−	8.03885i	0.707781	−	1.22591i	−0.257897	−	0.966172i	$-0.583030\pi$
$43$	4.64123	−	8.03885i	0.707781	−	1.22591i	0.965678	−	0.259741i	$-0.0836371\pi$
$44$	−0.0944936	−	0.0545559i	−0.0142454	−	0.00822461i
$45$		0			0
$46$			4.18971i			0.617739i
$47$	−8.62959	−	4.98230i	−1.25876	−	0.726743i	−0.285923	−	0.958253i	$-0.592300\pi$
$47$	−8.62959	−	4.98230i	−1.25876	−	0.726743i	−0.972833	+	0.231510i	$0.925633\pi$
$48$		0			0
$49$	1.89939	+	6.73738i	0.271342	+	0.962483i
$50$	10.7647	−	6.21503i	1.52237	−	0.878938i
$51$		0			0
$52$	−0.137932	+	2.34641i	−0.0191277	+	0.325389i
$53$	−3.26454	−	5.65434i	−0.448419	−	0.776684i	0.549865	−	0.835254i	$-0.314679\pi$
$53$	−3.26454	−	5.65434i	−0.448419	−	0.776684i	−0.998283	+	0.0585700i	$0.981346\pi$
$54$		0			0
$55$	0.331656	+	0.574445i	0.0447205	+	0.0774581i
$56$	−4.91716	+	6.49506i	−0.657083	+	0.867939i
$57$		0			0
$58$	5.23428	−	3.02201i	0.687294	−	0.396810i
$59$			4.11001i			0.535078i	0.963547	+	0.267539i	$0.0862104\pi$
$59$			4.11001i			0.535078i	−0.963547	+	0.267539i	$0.913790\pi$
$60$		0			0
$61$	−6.50404	−	11.2653i	−0.832757	−	1.44238i	−0.895843	−	0.444370i	$-0.853428\pi$
$61$	−6.50404	−	11.2653i	−0.832757	−	1.44238i	0.0630863	−	0.998008i	$-0.479906\pi$
$62$	−1.30887	−	2.26703i	−0.166226	−	0.287913i
$63$		0			0
$64$	−8.63066			−1.07883
$65$	7.85832	−	11.9340i	0.974705	−	1.48023i
$66$		0			0
$67$	−10.3145	−	5.95509i	−1.26012	−	0.727531i	−0.287022	−	0.957924i	$-0.592665\pi$
$67$	−10.3145	−	5.95509i	−1.26012	−	0.727531i	−0.973098	+	0.230393i	$0.925999\pi$
$68$	1.18073			0.143184
$69$		0			0
$70$	11.2169	−	4.73177i	1.34068	−	0.565555i
$71$	3.62344	+	2.09199i	0.430023	+	0.248274i	0.699356	−	0.714773i	$-0.253470\pi$
$71$	3.62344	+	2.09199i	0.430023	+	0.248274i	−0.269333	+	0.963047i	$0.586803\pi$
$72$		0			0
$73$	−9.65972	+	5.57704i	−1.13058	+	0.652744i	−0.944082	−	0.329711i	$-0.893049\pi$
$73$	−9.65972	+	5.57704i	−1.13058	+	0.652744i	−0.186503	+	0.982454i	$0.559715\pi$
$74$	1.52799			0.177626
$75$		0			0
$76$	−2.25070	+	1.29944i	−0.258173	+	0.149056i
$77$	0.172118	+	0.408014i	0.0196146	+	0.0464975i
$78$		0			0
$79$	−0.727082	+	1.25934i	−0.0818031	+	0.141687i	−0.904024	−	0.427481i	$-0.859401\pi$
$79$	−0.727082	+	1.25934i	−0.0818031	+	0.141687i	0.822221	+	0.569168i	$0.192735\pi$
$80$	7.79503	+	4.50047i	0.871511	+	0.503167i
$81$		0			0
$82$	6.39035	+	11.0684i	0.705696	+	1.22230i
$83$			3.67555i			0.403444i	0.979443	+	0.201722i	$0.0646538\pi$
$83$			3.67555i			0.403444i	−0.979443	+	0.201722i	$0.935346\pi$
$84$		0			0
$85$	−6.21621	−	3.58893i	−0.674242	−	0.389274i
$86$	−9.33372	−	5.38883i	−1.00648	−	0.581092i
$87$		0			0
$88$	−0.257678	+	0.446312i	−0.0274686	+	0.0475770i
$89$		−	7.80832i		−	0.827680i	−0.910350	−	0.413840i	$-0.864187\pi$
$89$		−	7.80832i		−	0.827680i	0.910350	−	0.413840i	$-0.135813\pi$
$90$		0			0
$91$	6.19434	−	7.25466i	0.649344	−	0.760495i
$92$	−2.35236			−0.245251
$93$		0			0
$94$	−5.78483	+	10.0196i	−0.596660	+	1.03344i
$95$	15.7991			1.62096
$96$		0			0
$97$	9.81792	+	5.66838i	0.996859	+	0.575537i	0.907317	−	0.420446i	$-0.138127\pi$
$97$	9.81792	+	5.66838i	0.996859	+	0.575537i	0.0895414	+	0.995983i	$0.471460\pi$
$98$	7.82262	−	2.20534i	0.790203	−	0.222773i
$99$		0			0
$100$	3.48951	+	6.04400i	0.348951	+	0.604400i
$101$	5.28784	−	9.15881i	0.526160	−	0.911336i	−0.473375	−	0.880861i	$-0.656965\pi$
$101$	5.28784	−	9.15881i	0.526160	−	0.911336i	0.999536	−	0.0304753i	$-0.00970210\pi$
$102$		0			0
$103$	3.18620	−	5.51867i	0.313946	−	0.543770i	−0.665267	−	0.746606i	$-0.731682\pi$
$103$	3.18620	−	5.51867i	0.313946	−	0.543770i	0.979213	+	0.202835i	$0.0650156\pi$
$104$	11.0826	+	0.651480i	1.08674	+	0.0638828i
$105$		0			0
$106$	−6.56512	+	3.79038i	−0.637661	+	0.368154i
$107$	5.01592			0.484908			0.242454	−	0.970163i	$-0.422048\pi$
$107$	5.01592			0.484908			0.242454	+	0.970163i	$0.422048\pi$
$108$		0			0
$109$	8.48515	−	4.89890i	0.812730	−	0.469230i	−0.0351731	−	0.999381i	$-0.511198\pi$
$109$	8.48515	−	4.89890i	0.812730	−	0.469230i	0.847903	+	0.530151i	$0.177865\pi$
$110$	0.666974	−	0.385078i	0.0635935	−	0.0367157i
$111$		0			0
$112$	4.79099	+	3.62707i	0.452706	+	0.342726i
$113$	−9.38349	+	16.2527i	−0.882725	+	1.52892i	−0.0344256	+	0.999407i	$0.510960\pi$
$113$	−9.38349	+	16.2527i	−0.882725	+	1.52892i	−0.848299	+	0.529517i	$0.822373\pi$
$114$		0			0
$115$	12.3846	+	7.15024i	1.15487	+	0.666763i
$116$	1.69675	+	2.93885i	0.157539	+	0.272866i
$117$		0			0
$118$	4.77204			0.439302
$119$	−3.82061	−	2.89243i	−0.350235	−	0.265149i
$120$		0			0
$121$	−5.48599	−	9.50202i	−0.498727	−	0.863820i
$122$	−13.0799	+	7.55169i	−1.18420	+	0.683698i
$123$		0			0
$124$	1.27285	−	0.734881i	0.114305	−	0.0659943i
$125$		−	22.6116i		−	2.02244i
$126$		0			0
$127$	−7.71676	−	13.3658i	−0.684752	−	1.18603i	−0.973515	−	0.228624i	$-0.926577\pi$
$127$	−7.71676	−	13.3658i	−0.684752	−	1.18603i	0.288763	−	0.957401i	$-0.406756\pi$
$128$			2.97875i			0.263286i
$129$		0			0
$130$	−13.8563	−	9.12411i	−1.21528	−	0.800238i
$131$	−7.50248	+	12.9947i	−0.655495	+	1.13535i	0.326274	+	0.945275i	$0.394207\pi$
$131$	−7.50248	+	12.9947i	−0.655495	+	1.13535i	−0.981769	+	0.190076i	$0.939127\pi$
$132$		0			0
$133$	10.4661	+	1.30880i	0.907527	+	0.113488i
$134$	−6.91432	+	11.9760i	−0.597306	+	1.03456i
$135$		0			0
$136$		−	5.57680i		−	0.478207i
$137$		−	11.2959i		−	0.965074i	−0.875876	−	0.482537i	$-0.839715\pi$
$137$		−	11.2959i		−	0.965074i	0.875876	−	0.482537i	$-0.160285\pi$
$138$		0			0
$139$	−0.161548	+	0.279809i	−0.0137023	+	0.0237331i	−0.872795	−	0.488087i	$-0.837695\pi$
$139$	−0.161548	+	0.279809i	−0.0137023	+	0.0237331i	0.859093	+	0.511820i	$0.171028\pi$
$140$	2.65671	+	6.29789i	0.224533	+	0.532269i
$141$		0			0
$142$	2.42896	−	4.20709i	0.203834	−	0.353051i
$143$	0.331888	−	0.504020i	0.0277539	−	0.0421483i
$144$		0			0
$145$		−	20.6297i		−	1.71320i
$146$	6.47537	+	11.2157i	0.535906	+	0.928216i
$147$		0			0
$148$			0.857911i			0.0705198i
$149$	−1.41702	+	0.818117i	−0.116087	+	0.0670228i	−0.556919	−	0.830567i	$-0.688017\pi$
$149$	−1.41702	+	0.818117i	−0.116087	+	0.0670228i	0.440832	+	0.897589i	$0.354683\pi$
$150$		0			0
$151$	2.95194	−	1.70430i	0.240225	−	0.138694i	−0.375055	−	0.927003i	$-0.622376\pi$
$151$	2.95194	−	1.70430i	0.240225	−	0.138694i	0.615280	+	0.788308i	$0.289043\pi$
$152$	6.13753	+	10.6305i	0.497820	+	0.862249i
$153$		0			0
$154$	0.473736	−	0.199842i	0.0381747	−	0.0161037i
$155$	−8.93497			−0.717674
$156$		0			0
$157$	2.61046	+	4.52145i	0.208338	+	0.360851i	0.951191	−	0.308603i	$-0.0998614\pi$
$157$	2.61046	+	4.52145i	0.208338	+	0.360851i	−0.742853	+	0.669454i	$0.766528\pi$
$158$	1.46219	+	0.844198i	0.116326	+	0.0671608i
$159$		0			0
$160$	−6.97703	+	12.0846i	−0.551583	+	0.955370i
$161$	7.61181	+	5.76260i	0.599895	+	0.454157i
$162$		0			0
$163$	19.4460	−	11.2271i	1.52312	−	0.879376i	0.523499	−	0.852027i	$-0.324627\pi$
$163$	19.4460	−	11.2271i	1.52312	−	0.879376i	0.999626	−	0.0273499i	$-0.00870682\pi$
$164$	−6.21450	+	3.58794i	−0.485271	+	0.280171i
$165$		0			0
$166$	4.26760			0.331230
$167$	−1.65134	+	0.953400i	−0.127784	+	0.0737763i	−0.562530	−	0.826777i	$-0.690172\pi$
$167$	−1.65134	+	0.953400i	−0.127784	+	0.0737763i	0.434745	+	0.900553i	$0.356838\pi$
$168$		0			0
$169$	−12.9105	−	1.52312i	−0.993113	−	0.117163i
$170$	−4.16702	+	7.21749i	−0.319596	+	0.553556i
$171$		0			0
$172$	3.02562	−	5.24054i	0.230702	−	0.399587i
$173$	−10.8349	−	18.7667i	−0.823765	−	1.42680i	−0.902860	−	0.429935i	$-0.858536\pi$
$173$	−10.8349	−	18.7667i	−0.823765	−	1.42680i	0.0790951	−	0.996867i	$-0.474797\pi$
$174$		0			0
$175$	3.51464	−	28.1055i	0.265682	−	2.12458i
$176$	0.329215	+	0.190073i	0.0248156	+	0.0143273i
$177$		0			0
$178$	−9.06606			−0.679530
$179$	−5.22832	+	9.05572i	−0.390783	+	0.676856i	−0.992553	−	0.121813i	$-0.961129\pi$
$179$	−5.22832	+	9.05572i	−0.390783	+	0.676856i	0.601770	+	0.798669i	$0.294462\pi$
$180$		0			0
$181$	−5.63442			−0.418803			−0.209401	−	0.977830i	$-0.567152\pi$
$181$	−5.63442			−0.418803			−0.209401	+	0.977830i	$0.567152\pi$
$182$	−8.42322	−	7.19211i	−0.624370	−	0.533115i
$183$		0			0
$184$			11.1107i			0.819091i
$185$	2.60770	−	4.51667i	0.191722	−	0.332072i
$186$		0			0
$187$	−0.262535	−	0.151575i	−0.0191985	−	0.0110843i
$188$	−5.62564	−	3.24797i	−0.410292	−	0.236882i
$189$		0			0
$190$		−	18.3440i		−	1.33081i
$191$	4.15904	+	7.20367i	0.300938	+	0.521240i	0.976349	−	0.216202i	$-0.0693670\pi$
$191$	4.15904	+	7.20367i	0.300938	+	0.521240i	−0.675411	+	0.737442i	$0.736034\pi$
$192$		0			0
$193$	−2.39343	−	1.38185i	−0.172283	−	0.0994676i	0.411379	−	0.911464i	$-0.365047\pi$
$193$	−2.39343	−	1.38185i	−0.172283	−	0.0994676i	−0.583662	+	0.811997i	$0.698381\pi$
$194$	6.58142	−	11.3994i	0.472519	−	0.818426i
$195$		0			0
$196$	1.23822	+	4.39211i	0.0884441	+	0.313722i
$197$	−0.0747038	+	0.0431303i	−0.00532243	+	0.00307291i	−0.502659	−	0.864485i	$-0.667645\pi$
$197$	−0.0747038	+	0.0431303i	−0.00532243	+	0.00307291i	0.497336	+	0.867558i	$0.334311\pi$
$198$		0			0
$199$	−21.5843			−1.53007			−0.765036	−	0.643988i	$-0.777279\pi$
$199$	−21.5843			−1.53007			−0.765036	+	0.643988i	$0.777279\pi$
$200$	28.5470	−	16.4816i	2.01858	−	1.16543i
$201$		0			0
$202$	−10.6341	−	6.13959i	−0.748212	−	0.431980i
$203$	1.70897	−	13.6661i	0.119946	−	0.959173i
$204$		0			0
$205$	43.6236			3.04680
$206$	−6.40760	−	3.69943i	−0.446438	−	0.257751i
$207$		0			0
$208$	0.480554	−	8.17490i	0.0333204	−	0.566827i
$209$	0.667261			0.0461554
$210$		0			0
$211$	−7.37251	−	12.7696i	−0.507544	−	0.879093i	−0.999962	−	0.00873343i	$-0.997220\pi$
$211$	−7.37251	−	12.7696i	−0.507544	−	0.879093i	0.492418	−	0.870359i	$-0.336113\pi$
$212$	−2.12815	−	3.68607i	−0.146162	−	0.253160i
$213$		0			0
$214$		−	5.82387i		−	0.398112i
$215$	−31.8582	+	18.3934i	−2.17271	+	1.25442i
$216$		0			0
$217$	−5.91895	−	0.740175i	−0.401805	−	0.0502463i
$218$	−5.68800	−	9.85191i	−0.385240	−	0.667255i
$219$		0			0
$220$	0.216207	+	0.374481i	0.0145767	+	0.0252475i
$221$	−0.383221	+	6.51913i	−0.0257783	+	0.438524i
$222$		0			0
$223$	21.4978	−	12.4117i	1.43960	−	0.831152i	0.441776	−	0.897125i	$-0.354349\pi$
$223$	21.4978	−	12.4117i	1.43960	−	0.831152i	0.997821	+	0.0659732i	$0.0210152\pi$
$224$	−5.62301	+	7.42743i	−0.375703	+	0.496266i
$225$		0			0
$226$	18.8706	+	10.8950i	1.25525	+	0.724722i
$227$		−	0.904181i		−	0.0600126i	−0.999550	−	0.0300063i	$-0.990447\pi$
$227$		−	0.904181i		−	0.0600126i	0.999550	−	0.0300063i	$-0.00955274\pi$
$228$		0			0
$229$	−1.69713	−	0.979838i	−0.112149	−	0.0647495i	0.442876	−	0.896583i	$-0.353958\pi$
$229$	−1.69713	−	0.979838i	−0.112149	−	0.0647495i	−0.555025	+	0.831833i	$0.687292\pi$
$230$	8.30198	−	14.3794i	0.547416	−	0.948152i
$231$		0			0
$232$	13.8808	−	8.01408i	0.911318	−	0.526150i
$233$	−5.83603	+	10.1083i	−0.382331	+	0.662217i	−0.991395	−	0.130904i	$-0.958212\pi$
$233$	−5.83603	+	10.1083i	−0.382331	+	0.662217i	0.609064	+	0.793121i	$0.291545\pi$
$234$		0			0
$235$	19.7450	+	34.1994i	1.28802	+	2.23092i
$236$			2.67932i			0.174409i
$237$		0			0
$238$	−3.35833	+	4.43602i	−0.217689	+	0.287544i
$239$			17.8732i			1.15612i	0.815993	+	0.578062i	$0.196191\pi$
$239$			17.8732i			1.15612i	−0.815993	+	0.578062i	$0.803809\pi$
$240$		0			0
$241$			3.42885i			0.220871i	0.993883	+	0.110436i	$0.0352246\pi$
$241$			3.42885i			0.220871i	−0.993883	+	0.110436i	$0.964775\pi$
$242$	−11.0326	+	6.36966i	−0.709201	+	0.409457i
$243$		0			0
$244$	−4.23999	−	7.34388i	−0.271438	−	0.470144i
$245$	6.83135	−	26.8870i	0.436439	−	1.71774i
$246$		0			0
$247$	−6.44411	−	12.8485i	−0.410029	−	0.817533i
$248$	−3.47099	−	6.01193i	−0.220408	−	0.381758i
$249$		0			0
$250$	−26.2538			−1.66044
$251$	15.2493	−	26.4126i	0.962527	−	1.66715i	0.246410	−	0.969166i	$-0.420749\pi$
$251$	15.2493	−	26.4126i	0.962527	−	1.66715i	0.716117	−	0.697980i	$-0.245918\pi$
$252$		0			0
$253$	0.523050	+	0.301983i	0.0328839	+	0.0189855i
$254$	−15.5187	+	8.95975i	−0.973733	+	0.562185i
$255$		0			0
$256$	−13.8028			−0.862673
$257$	3.43176			0.214067			0.107034	−	0.994255i	$-0.465865\pi$
$257$	3.43176			0.214067			0.107034	+	0.994255i	$0.465865\pi$
$258$		0			0
$259$	2.10163	−	2.77604i	0.130589	−	0.172495i
$260$	5.12285	−	7.77978i	0.317706	−	0.482481i
$261$		0			0
$262$	15.0878	+	8.71096i	0.932129	+	0.538165i
$263$	11.4321	−	19.8010i	0.704935	−	1.22098i	−0.261781	−	0.965127i	$-0.584310\pi$
$263$	11.4321	−	19.8010i	0.704935	−	1.22098i	0.966715	−	0.255855i	$-0.0823570\pi$
$264$		0			0
$265$			25.8749i			1.58948i
$266$	1.51962	−	12.1520i	0.0931740	−	0.745084i
$267$		0			0
$268$	−6.72405	−	3.88213i	−0.410737	−	0.237139i
$269$	−18.7212			−1.14145			−0.570724	−	0.821142i	$-0.693338\pi$
$269$	−18.7212			−1.14145			−0.570724	+	0.821142i	$0.693338\pi$
$270$		0			0
$271$			23.7981i			1.44563i	0.691040	+	0.722816i	$0.257153\pi$
$271$			23.7981i			1.44563i	−0.691040	+	0.722816i	$0.742847\pi$
$272$	−4.11365			−0.249426
$273$		0			0
$274$	−13.1154			−0.792331
$275$		−	1.79185i		−	0.108053i
$276$		0			0
$277$	−7.42576			−0.446171			−0.223085	−	0.974799i	$-0.571613\pi$
$277$	−7.42576			−0.446171			−0.223085	+	0.974799i	$0.571613\pi$
$278$	0.324880	+	0.187569i	0.0194850	+	0.0112497i
$279$		0			0
$280$	29.7462	−	12.5482i	1.77767	−	0.749898i
$281$			3.75352i			0.223916i	0.993713	+	0.111958i	$0.0357122\pi$
$281$			3.75352i			0.223916i	−0.993713	+	0.111958i	$0.964288\pi$
$282$		0			0
$283$	10.4173	−	18.0433i	0.619246	−	1.07257i	−0.370378	−	0.928881i	$-0.620772\pi$
$283$	10.4173	−	18.0433i	0.619246	−	1.07257i	0.989624	−	0.143684i	$-0.0458949\pi$
$284$	2.36212	+	1.36377i	0.140166	+	0.0809250i
$285$		0			0
$286$	−0.585206	−	0.385348i	−0.0346039	−	0.0227861i
$287$	28.8984	+	3.61379i	1.70582	+	0.213315i
$288$		0			0
$289$	−13.7195			−0.807032
$290$	−23.9527			−1.40655
$291$		0			0
$292$	−6.29718	+	3.63568i	−0.368515	+	0.212762i
$293$	−14.8913	−	8.59747i	−0.869956	−	0.502270i	−0.00262263	−	0.999997i	$-0.500835\pi$
$293$	−14.8913	−	8.59747i	−0.869956	−	0.502270i	−0.867334	+	0.497727i	$0.834168\pi$
$294$		0			0
$295$	8.14406	−	14.1059i	0.474165	−	0.821278i
$296$	4.05209			0.235523
$297$		0			0
$298$	0.949897	+	1.64527i	0.0550260	+	0.0953079i
$299$	0.763494	−	12.9881i	0.0441540	−	0.751121i
$300$		0			0
$301$	−22.6281	+	9.54550i	−1.30426	+	0.550194i
$302$	−1.97883	−	3.42743i	−0.113869	−	0.197226i
$303$		0			0
$304$	7.84145	−	4.52726i	0.449738	−	0.259656i
$305$			51.5515i			2.95183i
$306$		0			0
$307$			3.70213i			0.211292i	0.994404	+	0.105646i	$0.0336910\pi$
$307$			3.70213i			0.211292i	−0.994404	+	0.105646i	$0.966309\pi$
$308$	0.112204	+	0.265985i	0.00639340	+	0.0151559i
$309$		0			0
$310$			10.3742i			0.589214i
$311$	−10.4053	−	18.0225i	−0.590031	−	1.02196i	−0.994228	−	0.107291i	$-0.965782\pi$
$311$	−10.4053	−	18.0225i	−0.590031	−	1.02196i	0.404197	−	0.914672i	$-0.367551\pi$
$312$		0			0
$313$	−6.66145	+	11.5380i	−0.376527	+	0.652164i	−0.990554	−	0.137121i	$-0.956215\pi$
$313$	−6.66145	+	11.5380i	−0.376527	+	0.652164i	0.614027	+	0.789285i	$0.289549\pi$
$314$	5.24975	−	3.03095i	0.296261	−	0.171046i
$315$		0			0
$316$	−0.473986	+	0.820967i	−0.0266638	+	0.0461830i
$317$	18.1799	+	10.4961i	1.02108	+	0.589522i	0.914417	−	0.404773i	$-0.132649\pi$
$317$	18.1799	+	10.4961i	1.02108	+	0.589522i	0.106665	+	0.994295i	$0.465983\pi$
$318$		0			0
$319$		−	0.871275i		−	0.0487820i
$320$	29.6212	+	17.1018i	1.65587	+	0.956020i
$321$		0			0
$322$	6.69082	−	8.83790i	0.372865	−	0.492517i
$323$	−6.25322	+	3.61030i	−0.347938	+	0.200882i
$324$		0			0
$325$	−34.5033	+	17.3049i	−1.91390	+	0.959904i
$326$	−13.0356	−	22.5782i	−0.721973	−	1.25049i
$327$		0			0
$328$	16.9466	+	29.3523i	0.935718	+	1.62071i
$329$	10.2470	+	24.2910i	0.564933	+	1.33921i
$330$		0			0
$331$	−10.2997	+	5.94654i	−0.566123	+	0.326851i	−0.755599	−	0.655034i	$-0.772654\pi$
$331$	−10.2997	+	5.94654i	−0.566123	+	0.326851i	0.189476	+	0.981885i	$0.439321\pi$
$332$			2.39610i			0.131503i
$333$		0			0
$334$	1.10697	+	1.91733i	0.0605707	+	0.104912i
$335$	23.6002	+	40.8768i	1.28942	+	2.23334i
$336$		0			0
$337$	−12.0035			−0.653874			−0.326937	−	0.945046i	$-0.606017\pi$
$337$	−12.0035			−0.653874			−0.326937	+	0.945046i	$0.606017\pi$
$338$	−1.76846	+	14.9900i	−0.0961917	+	0.815351i
$339$		0			0
$340$	−4.05235	−	2.33963i	−0.219770	−	0.126884i
$341$	−0.377359			−0.0204352
$342$		0			0
$343$	6.75274	−	17.2453i	0.364613	−	0.931159i
$344$	−24.7521	−	14.2906i	−1.33454	−	0.770499i
$345$		0			0
$346$	−21.7895	+	12.5802i	−1.17141	+	0.676315i
$347$	−12.6353			−0.678301			−0.339150	−	0.940732i	$-0.610140\pi$
$347$	−12.6353			−0.678301			−0.339150	+	0.940732i	$0.610140\pi$
$348$		0			0
$349$	24.7055	−	14.2637i	1.32246	−	0.763520i	0.338335	−	0.941026i	$-0.390136\pi$
$349$	24.7055	−	14.2637i	1.32246	−	0.763520i	0.984120	+	0.177506i	$0.0568028\pi$
$350$	−32.6327	−	4.08077i	−1.74429	−	0.218126i
$351$		0			0
$352$	−0.294668	+	0.510380i	−0.0157059	+	0.0272033i
$353$	0.146041	+	0.0843167i	0.00777297	+	0.00448772i	0.503881	−	0.863773i	$-0.331905\pi$
$353$	0.146041	+	0.0843167i	0.00777297	+	0.00448772i	−0.496108	+	0.868261i	$0.665238\pi$
$354$		0			0
$355$	−8.29064	−	14.3598i	−0.440021	−	0.762139i
$356$		−	5.09025i		−	0.269783i
$357$		0			0
$358$	10.5144	+	6.07048i	0.555702	+	0.320835i
$359$	14.7729	+	8.52914i	0.779684	+	0.450151i	0.836318	−	0.548244i	$-0.184703\pi$
$359$	14.7729	+	8.52914i	0.779684	+	0.450151i	−0.0566341	+	0.998395i	$0.518037\pi$
$360$		0			0
$361$	−1.55340	+	2.69056i	−0.0817577	+	0.141609i
$362$			6.54199i			0.343839i
$363$		0			0
$364$	4.03810	−	4.72932i	0.211654	−	0.247884i
$365$	44.2040			2.31374
$366$		0			0
$367$	−8.48838	+	14.7023i	−0.443090	+	0.767454i	−0.997917	−	0.0645113i	$-0.979451\pi$
$367$	−8.48838	+	14.7023i	−0.443090	+	0.767454i	0.554827	+	0.831966i	$0.312784\pi$
$368$	8.19563			0.427227
$369$		0			0
$370$	−5.24420	−	3.02774i	−0.272633	−	0.157405i
$371$	−2.14349	+	17.1408i	−0.111284	+	0.889906i
$372$		0			0
$373$	3.67899	+	6.37220i	0.190491	+	0.329940i	0.945413	−	0.325875i	$-0.105659\pi$
$373$	3.67899	+	6.37220i	0.190491	+	0.329940i	−0.754922	+	0.655814i	$0.772325\pi$
$374$	−0.175990	+	0.304824i	−0.00910023	+	0.0157621i
$375$		0			0
$376$	−15.3408	+	26.5710i	−0.791141	+	1.37030i
$377$	−16.7770	+	8.41439i	−0.864058	+	0.433363i
$378$		0			0
$379$	6.99388	−	4.03792i	0.359252	−	0.207414i	−0.309501	−	0.950899i	$-0.600162\pi$
$379$	6.99388	−	4.03792i	0.359252	−	0.207414i	0.668752	+	0.743485i	$0.266829\pi$
$380$	10.2995			0.528352
$381$		0			0
$382$	8.36402	−	4.82897i	0.427940	−	0.247072i
$383$	19.8165	−	11.4411i	1.01258	−	0.584612i	0.100633	−	0.994924i	$-0.467913\pi$
$383$	19.8165	−	11.4411i	1.01258	−	0.584612i	0.911945	+	0.410311i	$0.134580\pi$
$384$		0			0
$385$	0.217764	−	1.74139i	0.0110983	−	0.0887497i
$386$	−1.60443	+	2.77896i	−0.0816634	+	0.141445i
$387$		0			0
$388$	6.40031	+	3.69522i	0.324927	+	0.187597i
$389$	19.0363	+	32.9719i	0.965180	+	1.67174i	0.709130	+	0.705078i	$0.249088\pi$
$389$	19.0363	+	32.9719i	0.965180	+	1.67174i	0.256051	+	0.966663i	$0.417579\pi$
$390$		0			0
$391$	−6.53567			−0.330523
$392$	20.7448	−	5.84835i	1.04777	−	0.295386i
$393$		0			0
$394$	0.0500776	+	0.0867369i	0.00252287	+	0.00436974i
$395$	4.99082	−	2.88145i	0.251115	−	0.144982i
$396$		0			0
$397$	−7.58482	+	4.37910i	−0.380671	+	0.219781i	−0.678110	−	0.734960i	$-0.737201\pi$
$397$	−7.58482	+	4.37910i	−0.380671	+	0.219781i	0.297439	+	0.954741i	$0.403867\pi$
$398$			25.0610i			1.25620i
$399$		0			0
$400$	−12.1574	−	21.0573i	−0.607872	−	1.05286i
$401$			18.6648i			0.932078i	0.884764	+	0.466039i	$0.154319\pi$
$401$			18.6648i			0.932078i	−0.884764	+	0.466039i	$0.845681\pi$
$402$		0			0
$403$	3.64437	+	7.26630i	0.181539	+	0.361960i
$404$	3.44715	−	5.97064i	0.171502	−	0.297051i
$405$		0			0
$406$	−15.8674	−	1.98424i	−0.787486	−	0.0984764i
$407$	0.110134	−	0.190757i	0.00545913	−	0.00945548i
$408$		0			0
$409$			21.2759i			1.05203i	0.850476	+	0.526013i	$0.176314\pi$
$409$			21.2759i			1.05203i	−0.850476	+	0.526013i	$0.823686\pi$
$410$		−	50.6503i		−	2.50144i
$411$		0			0
$412$	2.07709	−	3.59763i	0.102331	−	0.177242i
$413$	6.56355	−	8.66978i	0.322971	−	0.426612i
$414$		0			0
$415$	7.28317	−	12.6148i	0.357517	−	0.619237i
$416$	12.6735	+	0.744999i	0.621368	+	0.0365266i
$417$		0			0
$418$		−	0.774741i		−	0.0378938i
$419$	8.15625	+	14.1270i	0.398459	+	0.690151i	0.993536	−	0.113517i	$-0.0362118\pi$
$419$	8.15625	+	14.1270i	0.398459	+	0.690151i	−0.595077	+	0.803669i	$0.702878\pi$
$420$		0			0
$421$		−	27.0449i		−	1.31809i	−0.752104	−	0.659045i	$-0.770961\pi$
$421$		−	27.0449i		−	1.31809i	0.752104	−	0.659045i	$-0.229039\pi$
$422$	−14.8264	+	8.56005i	−0.721739	+	0.416696i
$423$		0			0
$424$	−17.4101	+	10.0517i	−0.845507	+	0.488154i
$425$	9.69504	+	16.7923i	0.470278	+	0.814546i
$426$		0			0
$427$	−4.27054	+	34.1502i	−0.206666	+	1.65264i
$428$	3.26989			0.158056
$429$		0			0
$430$	21.3561	+	36.9898i	1.02988	+	1.78381i
$431$	−22.0663	−	12.7400i	−1.06290	−	0.613664i	−0.136665	−	0.990617i	$-0.543638\pi$
$431$	−22.0663	−	12.7400i	−1.06290	−	0.613664i	−0.926232	+	0.376954i	$0.876972\pi$
$432$		0			0
$433$	13.1549	−	22.7849i	0.632184	−	1.09497i	−0.354921	−	0.934896i	$-0.615492\pi$
$433$	13.1549	−	22.7849i	0.632184	−	1.09497i	0.987104	−	0.160078i	$-0.0511745\pi$
$434$	−0.859400	+	6.87236i	−0.0412525	+	0.329884i
$435$		0			0
$436$	5.53148	−	3.19360i	0.264910	−	0.152946i
$437$	12.4583	−	7.19281i	0.595962	−	0.344079i
$438$		0			0
$439$	6.20384			0.296093			0.148047	−	0.988980i	$-0.452701\pi$
$439$	6.20384			0.296093			0.148047	+	0.988980i	$0.452701\pi$
$440$	1.76875	−	1.02119i	0.0843219	−	0.0486832i
$441$		0			0
$442$	7.56921	+	0.444949i	0.360031	+	0.0211641i
$443$	19.7524	−	34.2122i	0.938467	−	1.62547i	0.170136	−	0.985421i	$-0.445579\pi$
$443$	19.7524	−	34.2122i	0.938467	−	1.62547i	0.768331	−	0.640052i	$-0.221087\pi$
$444$		0			0
$445$	−15.4723	+	26.7988i	−0.733458	+	1.27039i
$446$	−14.4110	−	24.9606i	−0.682380	−	1.18192i
$447$		0			0
$448$	18.2058	+	13.7829i	0.860142	+	0.651180i
$449$	12.7890	+	7.38371i	0.603548	+	0.348459i	0.770436	−	0.637517i	$-0.220038\pi$
$449$	12.7890	+	7.38371i	0.603548	+	0.348459i	−0.166888	+	0.985976i	$0.553372\pi$
$450$		0			0
$451$	1.84240			0.0867552
$452$	−6.11711	+	10.5951i	−0.287725	+	0.498354i
$453$		0			0
$454$	−1.04982			−0.0492707
$455$	−35.6348	+	12.6244i	−1.67058	+	0.591842i
$456$		0			0
$457$			25.1713i			1.17746i	0.808329	+	0.588732i	$0.200372\pi$
$457$			25.1713i			1.17746i	−0.808329	+	0.588732i	$0.799628\pi$
$458$	−1.13767	+	1.97050i	−0.0531597	+	0.0920753i
$459$		0			0
$460$	8.07352	+	4.66125i	0.376430	+	0.217332i
$461$	−12.7870	−	7.38256i	−0.595549	−	0.343840i	0.171740	−	0.985142i	$-0.445061\pi$
$461$	−12.7870	−	7.38256i	−0.595549	−	0.343840i	−0.767288	+	0.641302i	$0.778394\pi$
$462$		0			0
$463$			33.9012i			1.57552i	0.615980	+	0.787762i	$0.288760\pi$
$463$			33.9012i			1.57552i	−0.615980	+	0.787762i	$0.711240\pi$
$464$	−5.91146	−	10.2390i	−0.274433	−	0.475332i
$465$		0			0
$466$	11.7365	+	6.77608i	0.543684	+	0.313896i
$467$	8.16938	−	14.1498i	0.378034	−	0.654773i	−0.612742	−	0.790283i	$-0.709934\pi$
$467$	8.16938	−	14.1498i	0.378034	−	0.654773i	0.990776	+	0.135509i	$0.0432670\pi$
$468$		0			0
$469$	12.2477	+	29.0338i	0.565546	+	1.34066i
$470$	39.7081	−	22.9255i	1.83160	−	1.05747i
$471$		0			0
$472$	12.6550			0.582492
$473$	−1.34550	+	0.776825i	−0.0618662	+	0.0357185i
$474$		0			0
$475$	−36.9614	−	21.3397i	−1.69591	−	0.979132i
$476$	−2.49066	−	1.88558i	−0.114159	−	0.0864254i
$477$		0			0
$478$	20.7522			0.949183
$479$	2.82226	+	1.62944i	0.128953	+	0.0744508i	0.563089	−	0.826397i	$-0.309613\pi$
$479$	2.82226	+	1.62944i	0.128953	+	0.0744508i	−0.434136	+	0.900847i	$0.642946\pi$
$480$		0			0
$481$	−4.73678	−	0.278447i	−0.215978	−	0.0126961i
$482$	3.98115			0.181337
$483$		0			0
$484$	−3.57633	−	6.19438i	−0.162560	−	0.281563i
$485$	−22.4640	−	38.9087i	−1.02004	−	1.76675i
$486$		0			0
$487$		−	13.8512i		−	0.627658i	−0.949480	−	0.313829i	$-0.898388\pi$
$487$		−	13.8512i		−	0.627658i	0.949480	−	0.313829i	$-0.101612\pi$
$488$	−34.6866	+	20.0263i	−1.57019	+	0.906550i
$489$		0			0
$490$	−31.2178	−	7.93172i	−1.41028	−	0.358318i
$491$	−12.6207	−	21.8597i	−0.569565	−	0.986516i	−0.996609	−	0.0822850i	$-0.973778\pi$
$491$	−12.6207	−	21.8597i	−0.569565	−	0.986516i	0.427044	−	0.904231i	$-0.359555\pi$
$492$		0			0
$493$	4.71414	+	8.16513i	0.212314	+	0.367739i
$494$	−14.9181	+	7.48211i	−0.671199	+	0.336636i
$495$		0			0
$496$	−4.43461	+	2.56032i	−0.199120	+	0.114962i
$497$	−4.30255	−	10.1994i	−0.192996	−	0.457507i
$498$		0			0
$499$	15.8541	+	9.15338i	0.709727	+	0.409761i	0.810960	−	0.585101i	$-0.198945\pi$
$499$	15.8541	+	9.15338i	0.709727	+	0.409761i	−0.101233	+	0.994863i	$0.532279\pi$
$500$		−	14.7405i		−	0.659217i
$501$		0			0
$502$	−30.6670	−	17.7056i	−1.36874	−	0.790240i
$503$	9.61697	−	16.6571i	0.428799	−	0.742702i	−0.567967	−	0.823051i	$-0.692270\pi$
$503$	9.61697	−	16.6571i	0.428799	−	0.742702i	0.996767	+	0.0803487i	$0.0256034\pi$
$504$		0			0
$505$	−36.2967	+	20.9559i	−1.61518	+	0.932525i
$506$	0.350626	−	0.607301i	0.0155872	−	0.0269978i
$507$		0			0
$508$	−5.03057	−	8.71320i	−0.223195	−	0.386586i
$509$		−	5.20276i		−	0.230608i	−0.993330	−	0.115304i	$-0.963216\pi$
$509$		−	5.20276i		−	0.230608i	0.993330	−	0.115304i	$-0.0367843\pi$
$510$		0			0
$511$	29.2829	+	3.66187i	1.29540	+	0.161992i
$512$			21.9836i			0.971546i
$513$		0			0
$514$		−	3.98454i		−	0.175751i
$515$	−21.8707	+	12.6270i	−0.963736	+	0.556414i
$516$		0			0
$517$	0.833911	+	1.44438i	0.0366754	+	0.0635236i
$518$	−3.22319	−	2.44015i	−0.141619	−	0.107214i
$519$		0			0
$520$	−36.7455	−	24.1962i	−1.61139	−	1.06108i
$521$	16.1236	+	27.9270i	0.706389	+	1.22350i	0.966188	+	0.257840i	$0.0830106\pi$
$521$	16.1236	+	27.9270i	0.706389	+	1.22350i	−0.259798	+	0.965663i	$0.583656\pi$
$522$		0			0
$523$	−7.00324			−0.306230			−0.153115	−	0.988208i	$-0.548931\pi$
$523$	−7.00324			−0.306230			−0.153115	+	0.988208i	$0.548931\pi$
$524$	−4.89088	+	8.47125i	−0.213659	+	0.370068i
$525$		0			0
$526$	−22.9905	−	13.2736i	−1.00243	−	0.578755i
$527$	3.53641	−	2.04175i	0.154049	−	0.0889400i
$528$		0			0
$529$	−9.97896			−0.433868
$530$	30.0428			1.30497
$531$		0			0
$532$	6.82287	+	0.853211i	0.295809	+	0.0369914i
$533$	−17.7931	−	35.4766i	−0.770704	−	1.53666i
$534$		0			0
$535$	−17.2151	−	9.93914i	−0.744273	−	0.429706i
$536$	−18.3361	+	31.7590i	−0.791999	+	1.37178i
$537$		0			0
$538$			21.7367i			0.937135i
$539$	0.288515	−	1.13554i	0.0124272	−	0.0489113i
$540$		0			0
$541$	−6.07149	−	3.50538i	−0.261034	−	0.150708i	0.363772	−	0.931488i	$-0.381489\pi$
$541$	−6.07149	−	3.50538i	−0.261034	−	0.150708i	−0.624806	+	0.780780i	$0.714822\pi$
$542$	27.6314			1.18687
$543$		0			0
$544$		−	6.37735i		−	0.273427i
$545$	−38.8290			−1.66325
$546$		0			0
$547$	−25.4150			−1.08667			−0.543333	−	0.839518i	$-0.682838\pi$
$547$	−25.4150			−1.08667			−0.543333	+	0.839518i	$0.682838\pi$
$548$		−	7.36381i		−	0.314566i
$549$		0			0
$550$	−2.08048			−0.0887119
$551$	−17.9722	−	10.3763i	−0.765642	−	0.442044i
$552$		0			0
$553$	3.54486	−	1.49537i	0.150743	−	0.0635896i
$554$			8.62187i			0.366308i
$555$		0			0
$556$	−0.105313	+	0.182408i	−0.00446627	+	0.00773581i
$557$	−25.9200	−	14.9649i	−1.09826	−	0.634083i	−0.162500	−	0.986709i	$-0.551956\pi$
$557$	−25.9200	−	14.9649i	−1.09826	−	0.634083i	−0.935764	+	0.352626i	$0.885289\pi$
$558$		0			0
$559$	27.9525	+	18.4063i	1.18227	+	0.778502i
$560$	−9.25599	−	21.9418i	−0.391137	−	0.927212i
$561$		0			0
$562$	4.35812			0.183836
$563$	28.1607			1.18683			0.593415	−	0.804897i	$-0.297779\pi$
$563$	28.1607			1.18683			0.593415	+	0.804897i	$0.297779\pi$
$564$		0			0
$565$	64.4099	−	37.1871i	2.70975	−	1.56447i
$566$	−20.9497	−	12.0953i	−0.880582	−	0.508404i
$567$		0			0
$568$	6.44137	−	11.1568i	0.270274	−	0.468128i
$569$	13.7042			0.574509			0.287255	−	0.957854i	$-0.407257\pi$
$569$	13.7042			0.574509			0.287255	+	0.957854i	$0.407257\pi$
$570$		0			0
$571$	19.9141	+	34.4923i	0.833381	+	1.44346i	0.895342	+	0.445380i	$0.146931\pi$
$571$	19.9141	+	34.4923i	0.833381	+	1.44346i	−0.0619609	+	0.998079i	$0.519735\pi$
$572$	0.216358	−	0.328571i	0.00904640	−	0.0137383i
$573$		0			0
$574$	4.19589	−	33.5532i	0.175133	−	1.40048i
$575$	−19.3155	−	33.4554i	−0.805511	−	1.39519i
$576$		0			0
$577$	14.9924	−	8.65589i	0.624144	−	0.360349i	−0.154337	−	0.988018i	$-0.549324\pi$
$577$	14.9924	−	8.65589i	0.624144	−	0.360349i	0.778480	+	0.627669i	$0.215991\pi$
$578$			15.9294i			0.662577i
$579$		0			0
$580$		−	13.4485i		−	0.558420i
$581$	5.86974	−	7.75332i	0.243518	−	0.321662i
$582$		0			0
$583$			1.09280i			0.0452592i
$584$	17.1721	+	29.7429i	0.710585	+	1.23077i
$585$		0			0
$586$	−9.98232	+	17.2899i	−0.412366	+	0.714239i
$587$	−22.2152	+	12.8259i	−0.916919	+	0.529383i	−0.882651	−	0.470030i	$-0.844243\pi$
$587$	−22.2152	+	12.8259i	−0.916919	+	0.529383i	−0.0342678	+	0.999413i	$0.510910\pi$
$588$		0			0
$589$	−4.49408	+	7.78398i	−0.185175	+	0.320733i
$590$	−16.3781	−	9.45587i	−0.674274	−	0.389292i
$591$		0			0
$592$		−	2.98896i		−	0.122846i
$593$	36.1840	+	20.8908i	1.48590	+	0.857884i	0.999871	−	0.0160601i	$-0.00511230\pi$
$593$	36.1840	+	20.8908i	1.48590	+	0.857884i	0.486027	+	0.873944i	$0.338446\pi$
$594$		0			0
$595$	7.38126	+	17.4977i	0.302602	+	0.717335i
$596$	−0.923757	+	0.533332i	−0.0378386	+	0.0218461i
$597$		0			0
$598$	−15.0802	−	0.886475i	−0.616674	−	0.0362506i
$599$	−11.2111	−	19.4181i	−0.458072	−	0.793403i	0.540787	−	0.841159i	$-0.318126\pi$
$599$	−11.2111	−	19.4181i	−0.458072	−	0.793403i	−0.998859	+	0.0477560i	$0.984793\pi$
$600$		0			0
$601$	2.82545	+	4.89383i	0.115253	+	0.199623i	0.917881	−	0.396856i	$-0.129899\pi$
$601$	2.82545	+	4.89383i	0.115253	+	0.199623i	−0.802628	+	0.596480i	$0.796566\pi$
$602$	11.0831	+	26.2730i	0.451712	+	1.07081i
$603$		0			0
$604$	1.92437	−	1.11104i	0.0783016	−	0.0452074i
$605$			43.4823i			1.76781i
$606$		0			0
$607$	−13.6690	−	23.6754i	−0.554807	−	0.960954i	−0.997919	−	0.0644877i	$-0.979459\pi$
$607$	−13.6690	−	23.6754i	−0.554807	−	0.960954i	0.443111	−	0.896467i	$-0.353875\pi$
$608$	7.01857	+	12.1565i	0.284641	+	0.493012i
$609$		0			0
$610$	59.8552			2.42347
$611$	19.7589	−	30.0066i	0.799358	−	1.21394i
$612$		0			0
$613$	−17.6432	−	10.1863i	−0.712603	−	0.411421i	0.0994212	−	0.995045i	$-0.468301\pi$
$613$	−17.6432	−	10.1863i	−0.712603	−	0.411421i	−0.812024	+	0.583624i	$0.801634\pi$
$614$	4.29845			0.173471
$615$		0			0
$616$	1.25630	−	0.529961i	0.0506178	−	0.0213527i
$617$	−4.93620	−	2.84992i	−0.198724	−	0.114733i	0.397336	−	0.917673i	$-0.369935\pi$
$617$	−4.93620	−	2.84992i	−0.198724	−	0.114733i	−0.596060	+	0.802940i	$0.703268\pi$
$618$		0			0
$619$	11.0877	−	6.40151i	0.445654	−	0.257298i	−0.260339	−	0.965517i	$-0.583834\pi$
$619$	11.0877	−	6.40151i	0.445654	−	0.257298i	0.705993	+	0.708219i	$0.250501\pi$
$620$	−5.82471			−0.233926
$621$		0			0
$622$	−20.9255	+	12.0814i	−0.839037	+	0.484418i
$623$	−12.4696	+	16.4711i	−0.499585	+	0.659901i
$624$		0			0
$625$	−18.0412	+	31.2483i	−0.721648	+	1.24993i
$626$	13.3965	+	7.73445i	0.535430	+	0.309131i
$627$		0			0
$628$	1.70176	+	2.94754i	0.0679078	+	0.117620i
$629$			2.38357i			0.0950391i
$630$		0			0
$631$	−33.1493	−	19.1388i	−1.31965	−	0.761903i	−0.335981	−	0.941869i	$-0.609068\pi$
$631$	−33.1493	−	19.1388i	−1.31965	−	0.761903i	−0.983673	+	0.179966i	$0.942401\pi$
$632$	3.87759	+	2.23873i	0.154242	+	0.0890519i
$633$		0			0
$634$	12.1868	−	21.1082i	0.484001	−	0.838314i
$635$			61.1636i			2.42720i
$636$		0			0
$637$	−24.6520	+	5.41104i	−0.976747	+	0.214393i
$638$	−1.01162			−0.0400503
$639$		0			0
$640$	5.90243	−	10.2233i	0.233314	−	0.404112i
$641$	36.8740			1.45644			0.728218	−	0.685346i	$-0.240349\pi$
$641$	36.8740			1.45644			0.728218	+	0.685346i	$0.240349\pi$
$642$		0			0
$643$	−2.08911	−	1.20615i	−0.0823864	−	0.0475658i	0.458241	−	0.888828i	$-0.348480\pi$
$643$	−2.08911	−	1.20615i	−0.0823864	−	0.0475658i	−0.540627	+	0.841262i	$0.681813\pi$
$644$	4.96215	+	3.75665i	0.195536	+	0.148033i
$645$		0			0
$646$	4.19183	+	7.26047i	0.164925	+	0.285659i
$647$	24.8787	−	43.0912i	0.978083	−	1.69409i	0.308721	−	0.951152i	$-0.400099\pi$
$647$	24.8787	−	43.0912i	0.978083	−	1.69409i	0.669361	−	0.742937i	$-0.266568\pi$
$648$		0			0
$649$	0.343956	−	0.595749i	0.0135015	−	0.0233852i
$650$	20.0923	+	40.0610i	0.788087	+	1.57132i
$651$		0			0
$652$	12.6768	−	7.31898i	0.496463	−	0.286633i
$653$	−45.4278			−1.77773			−0.888863	−	0.458173i	$-0.848504\pi$
$653$	−45.4278			−1.77773			−0.888863	+	0.458173i	$0.848504\pi$
$654$		0			0
$655$	51.4984	−	29.7326i	2.01221	−	1.16175i
$656$	21.6513	−	12.5004i	0.845342	−	0.488058i
$657$		0			0
$658$	28.2037	−	11.8975i	1.09949	−	0.463813i
$659$	−4.73832	+	8.20701i	−0.184579	+	0.319700i	−0.943435	−	0.331559i	$-0.892425\pi$
$659$	−4.73832	+	8.20701i	−0.184579	+	0.319700i	0.758856	+	0.651259i	$0.225759\pi$
$660$		0			0
$661$	−12.4070	−	7.16318i	−0.482576	−	0.278616i	0.238913	−	0.971041i	$-0.423209\pi$
$661$	−12.4070	−	7.16318i	−0.482576	−	0.278616i	−0.721490	+	0.692425i	$0.756542\pi$
$662$	6.90439	+	11.9588i	0.268347	+	0.464790i
$663$		0			0
$664$	11.3172			0.439194
$665$	−33.3272	−	25.2307i	−1.29237	−	0.978405i
$666$		0			0
$667$	−9.39200	−	16.2674i	−0.363660	−	0.629877i
$668$	−1.07651	+	0.621522i	−0.0416514	+	0.0240474i
$669$		0			0
$670$	47.4611	−	27.4017i	1.83358	−	1.05862i
$671$			2.17722i			0.0840508i
$672$		0			0
$673$	15.3521	+	26.5906i	0.591779	+	1.02499i	0.993993	+	0.109445i	$0.0349073\pi$
$673$	15.3521	+	26.5906i	0.591779	+	1.02499i	−0.402214	+	0.915546i	$0.631759\pi$
$674$			13.9370i			0.536834i
$675$		0			0
$676$	−8.41635	−	0.992926i	−0.323706	−	0.0381895i
$677$	−14.0675	+	24.3656i	−0.540658	+	0.936447i	0.458208	+	0.888845i	$0.348491\pi$
$677$	−14.0675	+	24.3656i	−0.540658	+	0.936447i	−0.998866	+	0.0476025i	$0.984842\pi$
$678$		0			0
$679$	−11.6580	−	27.6359i	−0.447393	−	1.06057i
$680$	−11.0505	+	19.1401i	−0.423768	+	0.733989i
$681$		0			0
$682$			0.438143i			0.0167774i
$683$		−	26.7398i		−	1.02317i	−0.859233	−	0.511585i	$-0.829059\pi$
$683$		−	26.7398i		−	1.02317i	0.859233	−	0.511585i	$-0.170941\pi$
$684$		0			0
$685$	−22.3830	+	38.7685i	−0.855211	+	1.48127i
$686$	−20.0231	−	7.84044i	−0.764486	−	0.299350i
$687$		0			0
$688$	−10.5413	+	18.2580i	−0.401882	+	0.696080i
$689$	21.0426	−	10.5538i	0.801660	−	0.402068i
$690$		0			0
$691$			8.13595i			0.309506i	0.987953	+	0.154753i	$0.0494582\pi$
$691$			8.13595i			0.309506i	−0.987953	+	0.154753i	$0.950542\pi$
$692$	−7.06330	−	12.2340i	−0.268507	−	0.465067i
$693$		0			0
$694$			14.6706i			0.556888i
$695$	1.10889	−	0.640219i	0.0420627	−	0.0242849i
$696$		0			0
$697$	−17.2660	+	9.96853i	−0.653996	+	0.377585i
$698$	−16.5613	−	28.6850i	−0.626854	−	1.08574i
$699$		0			0
$700$	2.29120	−	18.3220i	0.0865992	−	0.692508i
$701$	−5.23317			−0.197654			−0.0988271	−	0.995105i	$-0.531509\pi$
$701$	−5.23317			−0.197654			−0.0988271	+	0.995105i	$0.531509\pi$
$702$		0			0
$703$	−2.62323	−	4.54357i	−0.0989370	−	0.171364i
$704$	1.25102	+	0.722277i	0.0471496	+	0.0272219i
$705$		0			0
$706$	0.0978981	−	0.169565i	0.00368444	−	0.00638165i
$707$	−25.7807	+	10.8754i	−0.969582	+	0.409010i
$708$		0			0
$709$	0.102071	−	0.0589307i	0.00383335	−	0.00221319i	−0.498082	−	0.867130i	$-0.665962\pi$
$709$	0.102071	−	0.0589307i	0.00383335	−	0.00221319i	0.501915	+	0.864917i	$0.332629\pi$
$710$	−16.6728	+	9.62607i	−0.625720	+	0.361260i
$711$		0			0
$712$	−24.0423			−0.901023
$713$	−7.04561	+	4.06779i	−0.263860	+	0.152340i
$714$		0			0
$715$	−2.13779	+	1.07220i	−0.0799490	+	0.0400979i
$716$	−3.40835	+	5.90343i	−0.127376	+	0.220622i
$717$		0			0
$718$	9.90299	−	17.1525i	0.369576	−	0.640125i
$719$	−9.16359	−	15.8718i	−0.341744	−	0.591918i	0.643013	−	0.765856i	$-0.277684\pi$
$719$	−9.16359	−	15.8718i	−0.341744	−	0.591918i	−0.984757	+	0.173937i	$0.944351\pi$
$720$		0			0
$721$	−15.5342	+	6.55298i	−0.578524	+	0.244046i
$722$	3.12395	+	1.80361i	0.116261	+	0.0671235i
$723$		0			0
$724$	−3.67308			−0.136509
$725$	−27.8643	+	48.2623i	−1.03485	+	1.79242i
$726$		0			0
$727$	−12.7190			−0.471723			−0.235861	−	0.971787i	$-0.575791\pi$
$727$	−12.7190			−0.471723			−0.235861	+	0.971787i	$0.575791\pi$
$728$	−22.3375	−	19.0728i	−0.827884	−	0.706884i
$729$		0			0
$730$		−	51.3242i		−	1.89960i
$731$	8.40621	−	14.5600i	0.310915	−	0.538521i
$732$		0			0
$733$	14.3625	+	8.29218i	0.530490	+	0.306279i	0.741216	−	0.671266i	$-0.234249\pi$
$733$	14.3625	+	8.29218i	0.530490	+	0.306279i	−0.210726	+	0.977545i	$0.567583\pi$
$734$	17.0705	+	9.85566i	0.630084	+	0.363779i
$735$		0			0
$736$			12.7056i			0.468335i
$737$	0.996732	+	1.72639i	0.0367151	+	0.0635924i
$738$		0			0
$739$	1.34662	+	0.777474i	0.0495364	+	0.0285998i	0.524564	−	0.851371i	$-0.324228\pi$
$739$	1.34662	+	0.777474i	0.0495364	+	0.0285998i	−0.475027	+	0.879971i	$0.657562\pi$
$740$	1.69996	−	2.94443i	0.0624919	−	0.108239i
$741$		0			0
$742$	19.9018	+	2.48875i	0.730617	+	0.0913649i
$743$	11.0846	−	6.39972i	0.406656	−	0.234783i	−0.282696	−	0.959210i	$-0.591229\pi$
$743$	11.0846	−	6.39972i	0.406656	−	0.234783i	0.689352	+	0.724427i	$0.257895\pi$
$744$		0			0
$745$	6.48445			0.237572
$746$	7.39861	−	4.27159i	0.270882	−	0.156394i
$747$		0			0
$748$	−0.171147	−	0.0988118i	−0.00625776	−	0.00361292i
$749$	−10.5807	−	8.01027i	−0.386612	−	0.292689i
$750$		0			0
$751$	−16.8987			−0.616642			−0.308321	−	0.951282i	$-0.599767\pi$
$751$	−16.8987			−0.616642			−0.308321	+	0.951282i	$0.599767\pi$
$752$	19.5997	+	11.3159i	0.714728	+	0.412649i
$753$		0			0
$754$	9.76975	+	19.4793i	0.355793	+	0.709396i
$755$	−13.5084			−0.491622
$756$		0			0
$757$	16.0054	+	27.7222i	0.581727	+	1.00758i	0.995275	+	0.0970988i	$0.0309563\pi$
$757$	16.0054	+	27.7222i	0.581727	+	1.00758i	−0.413547	+	0.910483i	$0.635710\pi$
$758$	−4.68833	−	8.12043i	−0.170288	−	0.294947i
$759$		0			0
$760$		−	48.6465i		−	1.76459i
$761$	33.8923	−	19.5677i	1.22859	−	0.709329i	0.261858	−	0.965106i	$-0.415665\pi$
$761$	33.8923	−	19.5677i	1.22859	−	0.709329i	0.966736	+	0.255777i	$0.0823313\pi$
$762$		0			0
$763$	−25.7222	−	3.21661i	−0.931207	−	0.116449i
$764$	2.71129	+	4.69608i	0.0980909	+	0.169898i
$765$		0			0
$766$	−13.2840	−	23.0085i	−0.479970	−	0.831332i
$767$	−14.7933	−	0.869612i	−0.534156	−	0.0313999i
$768$		0			0
$769$	1.12749	−	0.650958i	0.0406584	−	0.0234742i	−0.479533	−	0.877524i	$-0.659194\pi$
$769$	1.12749	−	0.650958i	0.0406584	−	0.0234742i	0.520191	+	0.854050i	$0.325861\pi$
$770$	−2.02189	−	0.252841i	−0.0728639	−	0.00911176i
$771$		0			0
$772$	−1.56028	−	0.900828i	−0.0561557	−	0.0324215i
$773$		−	33.6000i		−	1.20851i	−0.796792	−	0.604254i	$-0.793471\pi$
$773$		−	33.6000i		−	1.20851i	0.796792	−	0.604254i	$-0.206529\pi$
$774$		0			0
$775$	20.9030	+	12.0683i	0.750857	+	0.433508i
$776$	17.4533	−	30.2300i	0.626536	−	1.08519i
$777$		0			0
$778$	38.2829	−	22.1026i	1.37251	−	0.792418i
$779$	21.9417	−	38.0041i	0.786142	−	1.36164i
$780$		0			0
$781$	−0.350147	−	0.606472i	−0.0125292	−	0.0217013i
$782$			7.58841i			0.271361i
$783$		0			0
$784$	−4.31395	−	15.3021i	−0.154069	−	0.546503i
$785$		−	20.6907i		−	0.738483i
$786$		0			0
$787$		−	19.3540i		−	0.689894i	−0.938622	−	0.344947i	$-0.887897\pi$
$787$		−	19.3540i		−	0.689894i	0.938622	−	0.344947i	$-0.112103\pi$
$788$	−0.0486995	+	0.0281167i	−0.00173485	+	0.00100162i
$789$		0			0
$790$	−3.34559	−	5.79472i	−0.119031	−	0.206167i
$791$	45.7488	−	19.2988i	1.62664	−	0.686186i
$792$		0			0
$793$	41.9239	−	21.0267i	1.48876	−	0.746679i
$794$	5.08447	+	8.80656i	0.180441	+	0.312533i
$795$		0			0
$796$	−14.0708			−0.498728
$797$	7.54012	−	13.0599i	0.267085	−	0.462605i	−0.701023	−	0.713139i	$-0.747273\pi$
$797$	7.54012	−	13.0599i	0.267085	−	0.462605i	0.968108	+	0.250534i	$0.0806063\pi$
$798$		0			0
$799$	−15.6299	−	9.02395i	−0.552948	−	0.319245i
$800$	32.6450	−	18.8476i	1.15417	−	0.666362i
$801$		0			0
$802$	21.6713			0.765241
$803$	1.86691			0.0658819
$804$		0			0
$805$	−14.7057	−	34.8607i	−0.518308	−	1.22868i
$806$	8.43673	−	4.23139i	0.297171	−	0.149045i
$807$		0			0
$808$	−28.2005	−	16.2816i	−0.992092	−	0.572784i
$809$	−17.3829	+	30.1081i	−0.611152	+	1.05855i	0.379895	+	0.925030i	$0.375960\pi$
$809$	−17.3829	+	30.1081i	−0.611152	+	1.05855i	−0.991047	+	0.133516i	$0.957373\pi$
$810$		0			0
$811$		−	28.0062i		−	0.983431i	−0.870756	−	0.491716i	$-0.836370\pi$
$811$		−	28.0062i		−	0.983431i	0.870756	−	0.491716i	$-0.163630\pi$
$812$	1.11408	−	8.90895i	0.0390965	−	0.312643i
$813$		0			0
$814$	−0.221484	−	0.127874i	−0.00776300	−	0.00448197i
$815$	−88.9869			−3.11708
$816$		0			0
$817$			37.0057i			1.29467i
$818$	24.7030			0.863719
$819$		0			0
$820$	28.4383			0.993108
$821$			14.2030i			0.495688i	0.968800	+	0.247844i	$0.0797220\pi$
$821$			14.2030i			0.495688i	−0.968800	+	0.247844i	$0.920278\pi$
$822$		0			0
$823$	−2.56761			−0.0895013			−0.0447506	−	0.998998i	$-0.514249\pi$
$823$	−2.56761			−0.0895013			−0.0447506	+	0.998998i	$0.514249\pi$
$824$	−16.9923	−	9.81051i	−0.591955	−	0.341765i
$825$		0			0
$826$	−10.0663	−	7.62079i	−0.350251	−	0.265161i
$827$		−	43.5833i		−	1.51554i	−0.652522	−	0.757770i	$-0.726289\pi$
$827$		−	43.5833i		−	1.51554i	0.652522	−	0.757770i	$-0.273711\pi$
$828$		0			0
$829$	23.2377	−	40.2489i	0.807079	−	1.39790i	−0.107800	−	0.994173i	$-0.534381\pi$
$829$	23.2377	−	40.2489i	0.807079	−	1.39790i	0.914879	−	0.403729i	$-0.132286\pi$
$830$	−14.6468	−	8.45632i	−0.508397	−	0.293523i
$831$		0			0
$832$	1.82611	−	31.0647i	0.0633089	−	1.07697i
$833$	3.44019	+	12.2028i	0.119195	+	0.422801i
$834$		0			0
$835$	7.55671			0.261511
$836$	0.434988			0.0150444
$837$		0			0
$838$	16.4026	−	9.47003i	0.566618	−	0.327137i
$839$	14.5988	+	8.42862i	0.504006	+	0.290988i	0.730367	−	0.683055i	$-0.239349\pi$
$839$	14.5988	+	8.42862i	0.504006	+	0.290988i	−0.226360	+	0.974044i	$0.572683\pi$
$840$		0			0
$841$	0.951210	−	1.64754i	0.0328003	−	0.0568119i
$842$	−31.4012			−1.08216
$843$		0			0
$844$	−4.80615	−	8.32449i	−0.165434	−	0.286541i
$845$	41.2917	+	30.8098i	1.42048	+	1.05989i
$846$		0			0
$847$	−3.60209	+	28.8048i	−0.123769	+	0.989744i
$848$	7.41449	+	12.8423i	0.254615	+	0.441005i
$849$		0			0
$850$	19.4971	−	11.2567i	0.668747	−	0.386101i
$851$		−	4.74879i		−	0.162787i
$852$		0			0
$853$			8.49697i			0.290931i	0.989363	+	0.145465i	$0.0464679\pi$
$853$			8.49697i			0.290931i	−0.989363	+	0.145465i	$0.953532\pi$
$854$	39.6510	+	4.95842i	1.35683	+	0.169674i
$855$		0			0
$856$		−	15.4443i		−	0.527876i
$857$	20.1410	+	34.8852i	0.688002	+	1.19165i	0.972483	+	0.232973i	$0.0748454\pi$
$857$	20.1410	+	34.8852i	0.688002	+	1.19165i	−0.284481	+	0.958682i	$0.591821\pi$
$858$		0			0
$859$	−5.55680	+	9.62465i	−0.189595	+	0.328389i	−0.945115	−	0.326737i	$-0.894051\pi$
$859$	−5.55680	+	9.62465i	−0.189595	+	0.328389i	0.755520	+	0.655126i	$0.227384\pi$
$860$	−20.7684	+	11.9907i	−0.708197	+	0.408878i
$861$		0			0
$862$	−14.7921	+	25.6207i	−0.503821	+	0.872644i
$863$	11.7498	+	6.78378i	0.399969	+	0.230922i	0.686471	−	0.727157i	$-0.259159\pi$
$863$	11.7498	+	6.78378i	0.399969	+	0.230922i	−0.286501	+	0.958080i	$0.592492\pi$
$864$		0			0
$865$			85.8784i			2.91995i
$866$	−26.4551	−	15.2738i	−0.898980	−	0.519026i
$867$		0			0
$868$	−3.85857	−	0.482521i	−0.130968	−	0.0163778i
$869$	0.210782	−	0.121695i	0.00715030	−	0.00412823i
$870$		0			0
$871$	23.6168	−	35.8655i	0.800224	−	1.21525i
$872$	−15.0840	−	26.1263i	−0.510809	−	0.884748i
$873$		0			0
$874$	−8.35140	−	14.4651i	−0.282490	−	0.489288i
$875$	−36.1100	+	47.6976i	−1.22074	+	1.61247i
$876$		0			0
$877$	13.6469	−	7.87903i	0.460822	−	0.266056i	−0.251568	−	0.967840i	$-0.580946\pi$
$877$	13.6469	−	7.87903i	0.460822	−	0.266056i	0.712390	+	0.701784i	$0.247613\pi$
$878$		−	7.20313i		−	0.243094i
$879$		0			0
$880$	−0.753264	−	1.30469i	−0.0253925	−	0.0439812i
$881$	−2.18226	−	3.77978i	−0.0735220	−	0.127344i	0.826921	−	0.562319i	$-0.190091\pi$
$881$	−2.18226	−	3.77978i	−0.0735220	−	0.127344i	−0.900443	+	0.434975i	$0.856757\pi$
$882$		0			0
$883$	6.56947			0.221080			0.110540	−	0.993872i	$-0.464742\pi$
$883$	6.56947			0.221080			0.110540	+	0.993872i	$0.464742\pi$
$884$	−0.249822	+	4.24983i	−0.00840244	+	0.142937i
$885$		0			0
$886$	−39.7230	−	22.9341i	−1.33452	−	0.770486i
$887$	35.4419			1.19002			0.595011	−	0.803717i	$-0.297148\pi$
$887$	35.4419			1.19002			0.595011	+	0.803717i	$0.297148\pi$
$888$		0			0
$889$	−5.06680	+	40.5177i	−0.169935	+	1.35892i
$890$	31.1155	+	17.9645i	1.04299	+	0.602173i
$891$		0			0
$892$	14.0144	−	8.09123i	0.469238	−	0.270914i
$893$	39.7251			1.32935
$894$		0			0
$895$	35.8881	−	20.7200i	1.19961	−	0.692593i
$896$	4.75696	−	6.28346i	0.158919	−	0.209916i
$897$		0			0
$898$	8.57305	−	14.8490i	0.286086	−	0.495516i
$899$	10.1639	+	5.86814i	0.338986	+	0.195713i
$900$		0			0
$901$	−5.91274	−	10.2412i	−0.196982	−	0.341183i
$902$		−	2.13917i		−	0.0712265i
$903$		0			0
$904$	50.0430	+	28.8923i	1.66441	+	0.960945i
$905$	19.3378	+	11.1647i	0.642810	+	0.371127i
$906$		0			0
$907$	20.1674	−	34.9310i	0.669649	−	1.15987i	−0.308354	−	0.951272i	$-0.599778\pi$
$907$	20.1674	−	34.9310i	0.669649	−	1.15987i	0.978002	−	0.208594i	$-0.0668886\pi$
$908$		−	0.589437i		−	0.0195611i
$909$		0			0
$910$	14.6579	+	41.3747i	0.485906	+	1.37156i
$911$	−35.3287			−1.17049			−0.585246	−	0.810856i	$-0.699002\pi$
$911$	−35.3287			−1.17049			−0.585246	+	0.810856i	$0.699002\pi$
$912$		0			0
$913$	0.307597	−	0.532774i	0.0101800	−	0.0176323i
$914$	29.2258			0.966703
$915$		0			0
$916$	−1.10636	−	0.638757i	−0.0365552	−	0.0211051i
$917$	36.5780	−	15.4302i	1.20791	−	0.509549i
$918$		0			0
$919$	−23.6041	−	40.8835i	−0.778627	−	1.34862i	−0.932733	−	0.360568i	$-0.882583\pi$
$919$	−23.6041	−	40.8835i	−0.778627	−	1.34862i	0.154106	−	0.988054i	$-0.450750\pi$
$920$	22.0160	−	38.1329i	0.725847	−	1.25720i
$921$		0			0
$922$	−8.57172	+	14.8467i	−0.282295	+	0.488948i
$923$	−8.29645	+	12.5993i	−0.273081	+	0.414713i
$924$		0			0
$925$	−12.2012	+	7.04438i	−0.401174	+	0.231618i
$926$	39.3619			1.29351
$927$		0			0
$928$	15.8734	−	9.16449i	0.521069	−	0.300839i
$929$	−0.921498	+	0.532027i	−0.0302334	+	0.0174552i	−0.515041	−	0.857166i	$-0.672223\pi$
$929$	−0.921498	+	0.532027i	−0.0302334	+	0.0174552i	0.484807	+	0.874621i	$0.338890\pi$
$930$		0			0
$931$	−19.9874	−	19.4749i	−0.655061	−	0.638263i
$932$	−3.80452	+	6.58962i	−0.124621	+	0.215850i
$933$		0			0
$934$	−16.4290	−	9.48527i	−0.537572	−	0.310368i
$935$	0.600696	+	1.04044i	0.0196449	+	0.0340259i
$936$		0			0
$937$	−12.7545			−0.416672			−0.208336	−	0.978057i	$-0.566805\pi$
$937$	−12.7545			−0.416672			−0.208336	+	0.978057i	$0.566805\pi$
$938$	33.7105	−	14.2205i	1.10069	−	0.464316i
$939$		0			0
$940$	12.8718	+	22.2946i	0.419832	+	0.727170i
$941$	−17.0165	+	9.82449i	−0.554722	+	0.320269i	−0.751025	−	0.660274i	$-0.770440\pi$
$941$	−17.0165	+	9.82449i	−0.554722	+	0.320269i	0.196302	+	0.980543i	$0.437107\pi$
$942$		0			0
$943$	34.3991	−	19.8603i	1.12019	−	0.646742i
$944$		−	9.33475i		−	0.303820i
$945$		0			0
$946$	0.901953	+	1.56223i	0.0293250	+	0.0507924i
$947$			19.5891i			0.636561i	0.947997	+	0.318280i	$0.103105\pi$
$947$			19.5891i			0.636561i	−0.947997	+	0.318280i	$0.896895\pi$
$948$		0			0
$949$	−18.0298	−	35.9486i	−0.585273	−	1.16694i
$950$	−24.7770	+	42.9150i	−0.803872	+	1.39235i
$951$		0			0
$952$	−8.90597	+	11.7639i	−0.288644	+	0.381270i
$953$	−14.5265	+	25.1607i	−0.470560	+	0.815034i	−0.999433	−	0.0336667i	$-0.989282\pi$
$953$	−14.5265	+	25.1607i	−0.470560	+	0.815034i	0.528873	+	0.848701i	$0.322615\pi$
$954$		0			0
$955$		−	32.9649i		−	1.06672i
$956$			11.6516i			0.376839i
$957$		0			0
$958$	1.89190	−	3.27686i	0.0611245	−	0.105871i
$959$	−18.0392	+	23.8279i	−0.582515	+	0.769444i
$960$		0			0
$961$	−12.9584	+	22.4447i	−0.418014	+	0.724022i
$962$	−0.323299	+	5.49976i	−0.0104236	+	0.177319i
$963$		0			0
$964$			2.23527i			0.0719931i
$965$	5.47631	+	9.48524i	0.176289	+	0.305341i
$966$		0			0
$967$			30.9934i			0.996681i	0.866981	+	0.498340i	$0.166057\pi$
$967$			30.9934i			0.996681i	−0.866981	+	0.498340i	$0.833943\pi$
$968$	−29.2573	+	16.8917i	−0.940365	+	0.542920i
$969$		0			0
$970$	−45.1760	+	26.0824i	−1.45051	+	0.837455i
$971$	3.75460	+	6.50316i	0.120491	+	0.208696i	0.919961	−	0.392009i	$-0.128220\pi$
$971$	3.75460	+	6.50316i	0.120491	+	0.208696i	−0.799470	+	0.600705i	$0.794886\pi$
$972$		0			0
$973$	0.787619	−	0.332251i	0.0252499	−	0.0106515i
$974$	−16.0823			−0.515310
$975$		0			0
$976$	14.7721	+	25.5861i	0.472844	+	0.818990i
$977$	−33.1128	−	19.1177i	−1.05937	−	0.611629i	−0.134114	−	0.990966i	$-0.542819\pi$
$977$	−33.1128	−	19.1177i	−1.05937	−	0.611629i	−0.925259	+	0.379337i	$0.876152\pi$
$978$		0			0
$979$	−0.653458	+	1.13182i	−0.0208846	+	0.0361732i
$980$	4.45336	−	17.5276i	0.142257	−	0.559900i
$981$		0			0
$982$	−25.3808	+	14.6536i	−0.809935	+	0.467616i
$983$	−24.3101	+	14.0354i	−0.775371	+	0.447661i	−0.834787	−	0.550573i	$-0.814409\pi$
$983$	−24.3101	+	14.0354i	−0.775371	+	0.447661i	0.0594163	+	0.998233i	$0.481076\pi$
$984$		0			0
$985$	0.341853			0.0108924
$986$	9.48034	−	5.47348i	0.301916	−	0.174311i
$987$		0			0
$988$	−4.20092	−	8.37598i	−0.133649	−	0.266475i
$989$	−16.7477	+	29.0079i	−0.532547	+	0.922399i
$990$		0			0
$991$	3.13172	−	5.42429i	0.0994822	−	0.172308i	−0.811988	−	0.583674i	$-0.801615\pi$
$991$	3.13172	−	5.42429i	0.0994822	−	0.172308i	0.911470	+	0.411366i	$0.134948\pi$
$992$	−3.96925	−	6.87494i	−0.126024	−	0.218280i
$993$		0			0
$994$	−11.8423	+	4.99559i	−0.375615	+	0.158450i
$995$	74.0792	+	42.7697i	2.34847	+	1.35589i
$996$		0			0
$997$	−50.5444			−1.60076			−0.800378	−	0.599495i	$-0.795368\pi$
$997$	−50.5444			−1.60076			−0.800378	+	0.599495i	$0.795368\pi$
$998$	10.6278	−	18.4078i	0.336416	−	0.582690i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.h.478.7	✓	36
3.2	odd	2	inner	819.2.bm.h.478.12	yes	36
7.4	even	3		819.2.do.h.361.12	yes	36
13.4	even	6		819.2.do.h.667.12	yes	36
21.11	odd	6		819.2.do.h.361.7	yes	36
39.17	odd	6		819.2.do.h.667.7	yes	36
91.4	even	6	inner	819.2.bm.h.550.12	yes	36
273.95	odd	6	inner	819.2.bm.h.550.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bm.h.478.7	✓	36	1.1	even	1	trivial
819.2.bm.h.478.12	yes	36	3.2	odd	2	inner
819.2.bm.h.550.7	yes	36	273.95	odd	6	inner
819.2.bm.h.550.12	yes	36	91.4	even	6	inner
819.2.do.h.361.7	yes	36	21.11	odd	6
819.2.do.h.361.12	yes	36	7.4	even	3
819.2.do.h.667.7	yes	36	39.17	odd	6
819.2.do.h.667.12	yes	36	13.4	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.16108i q^{2} +0.651901 q^{4} +(-3.43209 - 1.98152i) q^{5} +(-2.10943 - 1.59697i) q^{7} -3.07906i q^{8} +O(q^{10})\)	\(q-1.16108i q^{2} +0.651901 q^{4} +(-3.43209 - 1.98152i) q^{5} +(-2.10943 - 1.59697i) q^{7} -3.07906i q^{8} +(-2.30069 + 3.98492i) q^{10} +(-0.144951 - 0.0836874i) q^{11} +(-0.211584 + 3.59934i) q^{13} +(-1.85420 + 2.44921i) q^{14} -2.27122 q^{16} +1.81120 q^{17} +(-3.45252 + 1.99331i) q^{19} +(-2.23738 - 1.29175i) q^{20} +(-0.0971674 + 0.168299i) q^{22} -3.60847 q^{23} +(5.35282 + 9.27135i) q^{25} +(4.17911 + 0.245665i) q^{26} +(-1.37514 - 1.04106i) q^{28} +(2.60277 + 4.50812i) q^{29} +(1.95252 - 1.12729i) q^{31} -3.52106i q^{32} -2.10295i q^{34} +(4.07533 + 9.66080i) q^{35} +1.31601i q^{37} +(2.31439 + 4.00864i) q^{38} +(-6.10121 + 10.5676i) q^{40} +(-9.53289 + 5.50381i) q^{41} +(4.64123 - 8.03885i) q^{43} +(-0.0944936 - 0.0545559i) q^{44} +4.18971i q^{46} +(-8.62959 - 4.98230i) q^{47} +(1.89939 + 6.73738i) q^{49} +(10.7647 - 6.21503i) q^{50} +(-0.137932 + 2.34641i) q^{52} +(-3.26454 - 5.65434i) q^{53} +(0.331656 + 0.574445i) q^{55} +(-4.91716 + 6.49506i) q^{56} +(5.23428 - 3.02201i) q^{58} +4.11001i q^{59} +(-6.50404 - 11.2653i) q^{61} +(-1.30887 - 2.26703i) q^{62} -8.63066 q^{64} +(7.85832 - 11.9340i) q^{65} +(-10.3145 - 5.95509i) q^{67} +1.18073 q^{68} +(11.2169 - 4.73177i) q^{70} +(3.62344 + 2.09199i) q^{71} +(-9.65972 + 5.57704i) q^{73} +1.52799 q^{74} +(-2.25070 + 1.29944i) q^{76} +(0.172118 + 0.408014i) q^{77} +(-0.727082 + 1.25934i) q^{79} +(7.79503 + 4.50047i) q^{80} +(6.39035 + 11.0684i) q^{82} +3.67555i q^{83} +(-6.21621 - 3.58893i) q^{85} +(-9.33372 - 5.38883i) q^{86} +(-0.257678 + 0.446312i) q^{88} -7.80832i q^{89} +(6.19434 - 7.25466i) q^{91} -2.35236 q^{92} +(-5.78483 + 10.0196i) q^{94} +15.7991 q^{95} +(9.81792 + 5.66838i) q^{97} +(7.82262 - 2.20534i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) \) 36 * q - 44 * q^4 + 8 * q^7	\( 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) \) 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

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