LMFDB - Embedded newform 864.2.bh.b.47.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(47,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 7]))

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

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

chi := DirichletCharacter("864.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.13
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.459797 + 1.66991i) q^{3} +(-0.221850 - 1.25817i) q^{5} +(0.0241545 - 0.0287862i) q^{7} +(-2.57717 - 1.53564i) q^{9} +O(q^{10})$	\(q+(-0.459797 + 1.66991i) q^{3} +(-0.221850 - 1.25817i) q^{5} +(0.0241545 - 0.0287862i) q^{7} +(-2.57717 - 1.53564i) q^{9} +(3.96591 + 0.699297i) q^{11} +(1.52273 - 4.18367i) q^{13} +(2.20304 + 0.208036i) q^{15} +(-0.960657 + 0.554636i) q^{17} +(-1.54631 + 2.67828i) q^{19} +(0.0369640 + 0.0535715i) q^{21} +(1.78597 - 1.49861i) q^{23} +(3.16468 - 1.15185i) q^{25} +(3.74934 - 3.59756i) q^{27} +(8.19341 - 2.98216i) q^{29} +(-0.991533 - 1.18166i) q^{31} +(-2.99127 + 6.30116i) q^{33} +(-0.0415766 - 0.0240043i) q^{35} +(-0.0149964 + 0.00865816i) q^{37} +(6.28618 + 4.46645i) q^{39} +(-0.470758 + 1.29340i) q^{41} +(0.0865581 - 0.490896i) q^{43} +(-1.36035 + 3.58321i) q^{45} +(7.19227 + 6.03503i) q^{47} +(1.21529 + 6.89226i) q^{49} +(-0.484482 - 1.85923i) q^{51} +14.3897 q^{53} -5.14494i q^{55} +(-3.76149 - 3.81365i) q^{57} +(-1.54236 + 0.271959i) q^{59} +(-9.01061 + 10.7384i) q^{61} +(-0.106455 + 0.0370945i) q^{63} +(-5.60159 - 0.987712i) q^{65} +(-7.92365 - 2.88397i) q^{67} +(1.68135 + 3.67146i) q^{69} +(-4.72079 - 8.17664i) q^{71} +(6.64650 - 11.5121i) q^{73} +(0.468370 + 5.81434i) q^{75} +(0.115924 - 0.0972722i) q^{77} +(-3.05388 - 8.39047i) q^{79} +(4.28364 + 7.91520i) q^{81} +(4.13336 + 11.3563i) q^{83} +(0.910949 + 1.08563i) q^{85} +(1.21262 + 15.0534i) q^{87} +(6.90026 + 3.98387i) q^{89} +(-0.0836510 - 0.144888i) q^{91} +(2.42917 - 1.11244i) q^{93} +(3.71279 + 1.35134i) q^{95} +(-0.0961922 + 0.545533i) q^{97} +(-9.14697 - 7.89240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) $ 192 * q + 12 * q^3 - 12 * q^9	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.459797	+	1.66991i	−0.265464	+	0.964121i
$3$	−0.459797	+	1.66991i	−0.265464	+	0.964121i
$4$		0			0
$5$	−0.221850	−	1.25817i	−0.0992142	−	0.562672i	−0.993374	−	0.114924i	$-0.963337\pi$
$5$	−0.221850	−	1.25817i	−0.0992142	−	0.562672i	0.894160	−	0.447748i	$-0.147774\pi$
$6$		0			0
$7$	0.0241545	−	0.0287862i	0.00912953	−	0.0108801i	−0.761460	−	0.648211i	$-0.775517\pi$
$7$	0.0241545	−	0.0287862i	0.00912953	−	0.0108801i	0.770590	+	0.637331i	$0.219962\pi$
$8$		0			0
$9$	−2.57717	−	1.53564i	−0.859058	−	0.511879i
$10$		0			0
$11$	3.96591	+	0.699297i	1.19577	+	0.210846i	0.735868	−	0.677125i	$-0.236775\pi$
$11$	3.96591	+	0.699297i	1.19577	+	0.210846i	0.459899	+	0.887971i	$0.347886\pi$
$12$		0			0
$13$	1.52273	−	4.18367i	0.422329	−	1.16034i	−0.528041	−	0.849219i	$-0.677073\pi$
$13$	1.52273	−	4.18367i	0.422329	−	1.16034i	0.950370	−	0.311121i	$-0.100705\pi$
$14$		0			0
$15$	2.20304	+	0.208036i	0.568821	+	0.0537146i
$16$		0			0
$17$	−0.960657	+	0.554636i	−0.232994	+	0.134519i	−0.611952	−	0.790895i	$-0.709616\pi$
$17$	−0.960657	+	0.554636i	−0.232994	+	0.134519i	0.378959	+	0.925414i	$0.376282\pi$
$18$		0			0
$19$	−1.54631	+	2.67828i	−0.354747	+	0.614439i	−0.987075	−	0.160261i	$-0.948766\pi$
$19$	−1.54631	+	2.67828i	−0.354747	+	0.614439i	0.632328	+	0.774701i	$0.282100\pi$
$20$		0			0
$21$	0.0369640	+	0.0535715i	0.00806622	+	0.0116903i
$22$		0			0
$23$	1.78597	−	1.49861i	0.372400	−	0.312481i	−0.437310	−	0.899311i	$-0.644069\pi$
$23$	1.78597	−	1.49861i	0.372400	−	0.312481i	0.809710	+	0.586830i	$0.199624\pi$
$24$		0			0
$25$	3.16468	−	1.15185i	0.632936	−	0.230370i
$26$		0			0
$27$	3.74934	−	3.59756i	0.721562	−	0.692350i
$28$		0			0
$29$	8.19341	−	2.98216i	1.52148	−	0.553772i	0.559961	−	0.828519i	$-0.310816\pi$
$29$	8.19341	−	2.98216i	1.52148	−	0.553772i	0.961517	+	0.274747i	$0.0885941\pi$
$30$		0			0
$31$	−0.991533	−	1.18166i	−0.178085	−	0.212233i	0.669617	−	0.742707i	$-0.266458\pi$
$31$	−0.991533	−	1.18166i	−0.178085	−	0.212233i	−0.847701	+	0.530474i	$0.822014\pi$
$32$		0			0
$33$	−2.99127	+	6.30116i	−0.520714	+	1.09689i
$34$		0			0
$35$	−0.0415766	−	0.0240043i	−0.00702773	−	0.00405746i
$36$		0			0
$37$	−0.0149964	+	0.00865816i	−0.00246539	+	0.00142339i	−0.501232	−	0.865313i	$-0.667120\pi$
$37$	−0.0149964	+	0.00865816i	−0.00246539	+	0.00142339i	0.498767	+	0.866736i	$0.333786\pi$
$38$		0			0
$39$	6.28618	+	4.46645i	1.00660	+	0.715205i
$40$		0			0
$41$	−0.470758	+	1.29340i	−0.0735200	+	0.201995i	−0.971009	−	0.239042i	$-0.923167\pi$
$41$	−0.470758	+	1.29340i	−0.0735200	+	0.201995i	0.897489	+	0.441036i	$0.145389\pi$
$42$		0			0
$43$	0.0865581	−	0.490896i	0.0132000	−	0.0748609i	−0.977496	−	0.210953i	$-0.932343\pi$
$43$	0.0865581	−	0.490896i	0.0132000	−	0.0748609i	0.990696	+	0.136092i	$0.0434544\pi$
$44$		0			0
$45$	−1.36035	+	3.58321i	−0.202789	+	0.534153i
$46$		0			0
$47$	7.19227	+	6.03503i	1.04910	+	0.880300i	0.992999	−	0.118125i	$-0.0376885\pi$
$47$	7.19227	+	6.03503i	1.04910	+	0.880300i	0.0561017	+	0.998425i	$0.482133\pi$
$48$		0			0
$49$	1.21529	+	6.89226i	0.173613	+	0.984609i
$50$		0			0
$51$	−0.484482	−	1.85923i	−0.0678411	−	0.260344i
$52$		0			0
$53$	14.3897			1.97657			0.988287	−	0.152609i	$-0.0487674\pi$
$53$	14.3897			1.97657			0.988287	+	0.152609i	$0.0487674\pi$
$54$		0			0
$55$		−	5.14494i		−	0.693743i
$56$		0			0
$57$	−3.76149	−	3.81365i	−0.498221	−	0.505130i
$58$		0			0
$59$	−1.54236	+	0.271959i	−0.200798	+	0.0354060i	−0.273142	−	0.961974i	$-0.588063\pi$
$59$	−1.54236	+	0.271959i	−0.200798	+	0.0354060i	0.0723446	+	0.997380i	$0.476952\pi$
$60$		0			0
$61$	−9.01061	+	10.7384i	−1.15369	+	1.37491i	−0.238870	+	0.971052i	$0.576777\pi$
$61$	−9.01061	+	10.7384i	−1.15369	+	1.37491i	−0.914820	+	0.403862i	$0.867667\pi$
$62$		0			0
$63$	−0.106455	+	0.0370945i	−0.0134121	+	0.00467347i
$64$		0			0
$65$	−5.60159	−	0.987712i	−0.694792	−	0.122511i
$66$		0			0
$67$	−7.92365	−	2.88397i	−0.968028	−	0.352333i	−0.190853	−	0.981619i	$-0.561125\pi$
$67$	−7.92365	−	2.88397i	−0.968028	−	0.352333i	−0.777174	+	0.629285i	$0.783348\pi$
$68$		0			0
$69$	1.68135	+	3.67146i	0.202411	+	0.441991i
$70$		0			0
$71$	−4.72079	−	8.17664i	−0.560254	−	0.970389i	−0.997474	−	0.0710340i	$-0.977370\pi$
$71$	−4.72079	−	8.17664i	−0.560254	−	0.970389i	0.437220	−	0.899355i	$-0.355963\pi$
$72$		0			0
$73$	6.64650	−	11.5121i	0.777914	−	1.34739i	−0.155229	−	0.987879i	$-0.549611\pi$
$73$	6.64650	−	11.5121i	0.777914	−	1.34739i	0.933142	−	0.359507i	$-0.117055\pi$
$74$		0			0
$75$	0.468370	+	5.81434i	0.0540827	+	0.671382i
$76$		0			0
$77$	0.115924	−	0.0972722i	0.0132108	−	0.0110852i
$78$		0			0
$79$	−3.05388	−	8.39047i	−0.343589	−	0.944002i	−0.984344	−	0.176257i	$-0.943601\pi$
$79$	−3.05388	−	8.39047i	−0.343589	−	0.944002i	0.640756	−	0.767745i	$-0.278621\pi$
$80$		0			0
$81$	4.28364	+	7.91520i	0.475961	+	0.879467i
$82$		0			0
$83$	4.13336	+	11.3563i	0.453696	+	1.24652i	0.930105	+	0.367295i	$0.119716\pi$
$83$	4.13336	+	11.3563i	0.453696	+	1.24652i	−0.476409	+	0.879224i	$0.658062\pi$
$84$		0			0
$85$	0.910949	+	1.08563i	0.0988063	+	0.117753i
$86$		0			0
$87$	1.21262	+	15.0534i	0.130006	+	1.61389i
$88$		0			0
$89$	6.90026	+	3.98387i	0.731426	+	0.422289i	0.818944	−	0.573874i	$-0.194560\pi$
$89$	6.90026	+	3.98387i	0.731426	+	0.422289i	−0.0875175	+	0.996163i	$0.527893\pi$
$90$		0			0
$91$	−0.0836510	−	0.144888i	−0.00876901	−	0.0151884i
$92$		0			0
$93$	2.42917	−	1.11244i	0.251893	−	0.115355i
$94$		0			0
$95$	3.71279	+	1.35134i	0.380924	+	0.138645i
$96$		0			0
$97$	−0.0961922	+	0.545533i	−0.00976684	+	0.0553905i	−0.989302	−	0.145884i	$-0.953397\pi$
$97$	−0.0961922	+	0.545533i	−0.00976684	+	0.0553905i	0.979535	+	0.201275i	$0.0645084\pi$
$98$		0			0
$99$	−9.14697	−	7.89240i	−0.919305	−	0.793216i
$100$		0			0
$101$	0.735978	+	0.617559i	0.0732325	+	0.0614494i	0.678669	−	0.734444i	$-0.262557\pi$
$101$	0.735978	+	0.617559i	0.0732325	+	0.0614494i	−0.605437	+	0.795894i	$0.707001\pi$
$102$		0			0
$103$	5.44272	−	0.959698i	0.536287	−	0.0945618i	0.101056	−	0.994881i	$-0.467778\pi$
$103$	5.44272	−	0.959698i	0.536287	−	0.0945618i	0.435231	+	0.900319i	$0.356667\pi$
$104$		0			0
$105$	0.0592017	−	0.0583920i	0.00577749	−	0.00569847i
$106$		0			0
$107$			13.8930i			1.34309i	0.740966	+	0.671543i	$0.234368\pi$
$107$			13.8930i			1.34309i	−0.740966	+	0.671543i	$0.765632\pi$
$108$		0			0
$109$		−	13.3583i		−	1.27949i	−0.768586	−	0.639746i	$-0.779039\pi$
$109$		−	13.3583i		−	1.27949i	0.768586	−	0.639746i	$-0.220961\pi$
$110$		0			0
$111$	−0.00756303	−	0.0290235i	−0.000717851	−	0.00275479i
$112$		0			0
$113$	6.47027	−	1.14088i	0.608672	−	0.107325i	0.139187	−	0.990266i	$-0.455551\pi$
$113$	6.47027	−	1.14088i	0.608672	−	0.107325i	0.469484	+	0.882941i	$0.344440\pi$
$114$		0			0
$115$	−2.28172	−	1.91459i	−0.212772	−	0.178537i
$116$		0			0
$117$	−10.3489	+	8.44368i	−0.956759	+	0.780618i
$118$		0			0
$119$	−0.00723832	+	0.0410506i	−0.000663536	+	0.00376310i
$120$		0			0
$121$	4.90280	+	1.78447i	0.445709	+	0.162225i
$122$		0			0
$123$	−1.94340	−	1.38082i	−0.175230	−	0.124504i
$124$		0			0
$125$	−5.34527	−	9.25827i	−0.478095	−	0.828085i
$126$		0			0
$127$	−15.5376	−	8.97063i	−1.37874	−	0.796015i	−0.386730	−	0.922193i	$-0.626396\pi$
$127$	−15.5376	−	8.97063i	−1.37874	−	0.796015i	−0.992008	+	0.126178i	$0.959729\pi$
$128$		0			0
$129$	0.779950	+	0.370256i	0.0686708	+	0.0325993i
$130$		0			0
$131$	−9.77701	−	11.6518i	−0.854221	−	1.01802i	−0.999590	−	0.0286439i	$-0.990881\pi$
$131$	−9.77701	−	11.6518i	−0.854221	−	1.01802i	0.145368	−	0.989378i	$-0.453563\pi$
$132$		0			0
$133$	0.0397472	+	0.109205i	0.00344652	+	0.00946924i
$134$		0			0
$135$	−5.35814	−	3.91921i	−0.461155	−	0.337312i
$136$		0			0
$137$	−3.50778	−	9.63755i	−0.299690	−	0.823391i	−0.994551	−	0.104248i	$-0.966757\pi$
$137$	−3.50778	−	9.63755i	−0.299690	−	0.823391i	0.694861	−	0.719144i	$-0.255466\pi$
$138$		0			0
$139$	16.5421	−	13.8805i	1.40308	−	1.17733i	0.443370	−	0.896339i	$-0.353783\pi$
$139$	16.5421	−	13.8805i	1.40308	−	1.17733i	0.959712	−	0.280987i	$-0.0906616\pi$
$140$		0			0
$141$	−13.3849	+	9.23553i	−1.12721	+	0.777772i
$142$		0			0
$143$	8.96463	−	15.5272i	0.749660	−	1.29845i
$144$		0			0
$145$	−5.56977	−	9.64713i	−0.462544	−	0.801150i
$146$		0			0
$147$	−12.0682	−	1.13962i	−0.995370	−	0.0939942i
$148$		0			0
$149$	−11.6387	−	4.23616i	−0.953483	−	0.347039i	−0.182007	−	0.983297i	$-0.558259\pi$
$149$	−11.6387	−	4.23616i	−0.953483	−	0.347039i	−0.771476	+	0.636258i	$0.780481\pi$
$150$		0			0
$151$	−8.22863	−	1.45093i	−0.669637	−	0.118075i	−0.171514	−	0.985182i	$-0.554866\pi$
$151$	−8.22863	−	1.45093i	−0.669637	−	0.118075i	−0.498123	+	0.867107i	$0.665977\pi$
$152$		0			0
$153$	3.32750	+	0.0458274i	0.269012	+	0.00370493i
$154$		0			0
$155$	−1.26677	+	1.50967i	−0.101749	+	0.121260i
$156$		0			0
$157$	−7.33700	+	1.29371i	−0.585556	+	0.103249i	−0.458575	−	0.888656i	$-0.651640\pi$
$157$	−7.33700	+	1.29371i	−0.585556	+	0.103249i	−0.126981	+	0.991905i	$0.540529\pi$
$158$		0			0
$159$	−6.61633	+	24.0294i	−0.524709	+	1.90566i
$160$		0			0
$161$		−	0.0876093i		−	0.00690458i
$162$		0			0
$163$	8.72750			0.683591			0.341795	−	0.939774i	$-0.388965\pi$
$163$	8.72750			0.683591			0.341795	+	0.939774i	$0.388965\pi$
$164$		0			0
$165$	8.59156	+	2.36563i	0.668852	+	0.184164i
$166$		0			0
$167$	1.28634	+	7.29522i	0.0995404	+	0.564521i	0.993261	+	0.115898i	$0.0369745\pi$
$167$	1.28634	+	7.29522i	0.0995404	+	0.564521i	−0.893721	+	0.448624i	$0.851914\pi$
$168$		0			0
$169$	−5.22578	−	4.38495i	−0.401983	−	0.337304i
$170$		0			0
$171$	8.09796	−	4.52783i	0.619266	−	0.346252i
$172$		0			0
$173$	−1.10221	+	6.25096i	−0.0837996	+	0.475251i	0.913810	+	0.406143i	$0.133127\pi$
$173$	−1.10221	+	6.25096i	−0.0837996	+	0.475251i	−0.997609	+	0.0691084i	$0.977985\pi$
$174$		0			0
$175$	0.0432838	−	0.118921i	0.00327195	−	0.00898961i
$176$		0			0
$177$	0.255025	−	2.70064i	0.0191688	−	0.202992i
$178$		0			0
$179$	10.8244	−	6.24945i	0.809051	−	0.467106i	−0.0375750	−	0.999294i	$-0.511963\pi$
$179$	10.8244	−	6.24945i	0.809051	−	0.467106i	0.846626	+	0.532188i	$0.178630\pi$
$180$		0			0
$181$	−19.6860	−	11.3657i	−1.46325	−	0.844807i	−0.464088	−	0.885789i	$-0.653618\pi$
$181$	−19.6860	−	11.3657i	−1.46325	−	0.844807i	−0.999160	+	0.0409826i	$0.986951\pi$
$182$		0			0
$183$	−13.7891	−	19.9844i	−1.01932	−	1.47729i
$184$		0			0
$185$	0.0142204	+	0.0169472i	0.00104550	+	0.00124598i
$186$		0			0
$187$	−4.19773	+	1.52785i	−0.306969	+	0.111727i
$188$		0			0
$189$	−0.0129965	−	0.194826i	−0.000945354	−	0.0141715i
$190$		0			0
$191$	3.53137	−	1.28531i	0.255521	−	0.0930020i	−0.211084	−	0.977468i	$-0.567699\pi$
$191$	3.53137	−	1.28531i	0.255521	−	0.0930020i	0.466605	+	0.884466i	$0.345477\pi$
$192$		0			0
$193$	−18.9554	+	15.9055i	−1.36444	+	1.14490i	−0.389857	+	0.920876i	$0.627475\pi$
$193$	−18.9554	+	15.9055i	−1.36444	+	1.14490i	−0.974583	+	0.224025i	$0.928080\pi$
$194$		0			0
$195$	4.22498	−	8.89999i	0.302557	−	0.637341i
$196$		0			0
$197$	2.31882	−	4.01631i	0.165209	−	0.286150i	−0.771521	−	0.636204i	$-0.780504\pi$
$197$	2.31882	−	4.01631i	0.165209	−	0.286150i	0.936729	+	0.350054i	$0.113837\pi$
$198$		0			0
$199$	−12.8167	+	7.39975i	−0.908555	+	0.524554i	−0.879966	−	0.475037i	$-0.842435\pi$
$199$	−12.8167	+	7.39975i	−0.908555	+	0.524554i	−0.0285887	+	0.999591i	$0.509101\pi$
$200$		0			0
$201$	8.45923	−	11.9057i	0.596668	−	0.839764i
$202$		0			0
$203$	0.112062	−	0.307889i	0.00786524	−	0.0216096i
$204$		0			0
$205$	1.73175	+	0.305355i	0.120951	+	0.0213269i
$206$		0			0
$207$	−6.90407	+	1.11957i	−0.479866	+	0.0778155i
$208$		0			0
$209$	−8.00542	+	9.54049i	−0.553746	+	0.659929i
$210$		0			0
$211$	2.04564	+	11.6014i	0.140828	+	0.798673i	0.970623	+	0.240606i	$0.0773460\pi$
$211$	2.04564	+	11.6014i	0.140828	+	0.798673i	−0.829795	+	0.558068i	$0.811543\pi$
$212$		0			0
$213$	15.8248	−	4.12367i	1.08430	−	0.282549i
$214$		0			0
$215$	−0.636834			−0.0434317
$216$		0			0
$217$	−0.0579655			−0.00393496
$218$		0			0
$219$	16.1680	+	16.3922i	1.09253	+	1.10768i
$220$		0			0
$221$	0.857589	+	4.86363i	0.0576877	+	0.327163i
$222$		0			0
$223$	−13.5037	+	16.0931i	−0.904277	+	1.07768i	0.0923592	+	0.995726i	$0.470559\pi$
$223$	−13.5037	+	16.0931i	−0.904277	+	1.07768i	−0.996636	+	0.0819499i	$0.973885\pi$
$224$		0			0
$225$	−9.92476	−	1.89128i	−0.661650	−	0.126085i
$226$		0			0
$227$	2.94969	+	0.520110i	0.195778	+	0.0345209i	0.270677	−	0.962670i	$-0.412752\pi$
$227$	2.94969	+	0.520110i	0.195778	+	0.0345209i	−0.0748993	+	0.997191i	$0.523864\pi$
$228$		0			0
$229$	2.32907	−	6.39908i	0.153910	−	0.422863i	−0.838643	−	0.544682i	$-0.816650\pi$
$229$	2.32907	−	6.39908i	0.153910	−	0.422863i	0.992552	+	0.121819i	$0.0388727\pi$
$230$		0			0
$231$	0.109134	+	0.238308i	0.00718047	+	0.0156795i
$232$		0			0
$233$	9.35687	−	5.40219i	0.612989	−	0.353909i	−0.161145	−	0.986931i	$-0.551519\pi$
$233$	9.35687	−	5.40219i	0.612989	−	0.353909i	0.774134	+	0.633021i	$0.218185\pi$
$234$		0			0
$235$	5.99751	−	10.3880i	0.391234	−	0.677638i
$236$		0			0
$237$	15.4155	−	1.24178i	1.00134	−	0.0806624i
$238$		0			0
$239$	−6.88390	+	5.77628i	−0.445282	+	0.373636i	−0.837682	−	0.546159i	$-0.816090\pi$
$239$	−6.88390	+	5.77628i	−0.445282	+	0.373636i	0.392399	+	0.919795i	$0.371645\pi$
$240$		0			0
$241$	7.68472	−	2.79701i	0.495016	−	0.180171i	−0.0824349	−	0.996596i	$-0.526270\pi$
$241$	7.68472	−	2.79701i	0.495016	−	0.180171i	0.577451	+	0.816425i	$0.304047\pi$
$242$		0			0
$243$	−15.1872	+	3.51390i	−0.974262	+	0.225417i
$244$		0			0
$245$	8.40205	−	3.05809i	0.536787	−	0.195374i
$246$		0			0
$247$	8.85042	+	10.5475i	0.563139	+	0.671123i
$248$		0			0
$249$	−20.8645	+	1.68073i	−1.32223	+	0.106512i
$250$		0			0
$251$	−16.1945	−	9.34989i	−1.02219	−	0.590160i	−0.107450	−	0.994210i	$-0.534269\pi$
$251$	−16.1945	−	9.34989i	−1.02219	−	0.590160i	−0.914737	+	0.404051i	$0.867602\pi$
$252$		0			0
$253$	8.13096	−	4.69441i	0.511189	−	0.295135i
$254$		0			0
$255$	−2.23175	+	1.02203i	−0.139757	+	0.0640021i
$256$		0			0
$257$	−4.78002	+	13.1330i	−0.298170	+	0.819214i	0.696636	+	0.717424i	$0.254679\pi$
$257$	−4.78002	+	13.1330i	−0.298170	+	0.819214i	−0.994806	+	0.101790i	$0.967543\pi$
$258$		0			0
$259$	−0.000112994	0	0.000640821i	−7.02111e−6	0	3.98187e-5i
$260$		0			0
$261$	−25.6953	−	4.89656i	−1.59050	−	0.303089i
$262$		0			0
$263$	14.3635	+	12.0524i	0.885694	+	0.743186i	0.967342	−	0.253475i	$-0.0815737\pi$
$263$	14.3635	+	12.0524i	0.885694	+	0.743186i	−0.0816475	+	0.996661i	$0.526018\pi$
$264$		0			0
$265$	−3.19235	−	18.1047i	−0.196104	−	1.11216i
$266$		0			0
$267$	−9.82540	+	9.69102i	−0.601305	+	0.593081i
$268$		0			0
$269$	1.60260			0.0977123			0.0488561	−	0.998806i	$-0.484442\pi$
$269$	1.60260			0.0977123			0.0488561	+	0.998806i	$0.484442\pi$
$270$		0			0
$271$		−	1.09029i		−	0.0662304i	−0.999452	−	0.0331152i	$-0.989457\pi$
$271$		−	1.09029i		−	0.0662304i	0.999452	−	0.0331152i	$-0.0105428\pi$
$272$		0			0
$273$	0.280411	−	0.0730703i	0.0169713	−	0.00442242i
$274$		0			0
$275$	13.3563	−	2.35508i	0.805417	−	0.142017i
$276$		0			0
$277$	−15.6324	+	18.6300i	−0.939260	+	1.11937i	0.0534180	+	0.998572i	$0.482988\pi$
$277$	−15.6324	+	18.6300i	−0.939260	+	1.11937i	−0.992678	+	0.120794i	$0.961456\pi$
$278$		0			0
$279$	0.740749	+	4.56799i	0.0443475	+	0.273478i
$280$		0			0
$281$	−1.76346	−	0.310946i	−0.105199	−	0.0185495i	0.120801	−	0.992677i	$-0.461454\pi$
$281$	−1.76346	−	0.310946i	−0.105199	−	0.0185495i	−0.226000	+	0.974127i	$0.572565\pi$
$282$		0			0
$283$	3.16461	+	1.15182i	0.188117	+	0.0684688i	0.434361	−	0.900739i	$-0.356974\pi$
$283$	3.16461	+	1.15182i	0.188117	+	0.0684688i	−0.246244	+	0.969208i	$0.579197\pi$
$284$		0			0
$285$	−3.96374	+	5.57866i	−0.234792	+	0.330451i
$286$		0			0
$287$	0.0258610	+	0.0447926i	0.00152653	+	0.00264402i
$288$		0			0
$289$	−7.88476	+	13.6568i	−0.463809	+	0.803341i
$290$		0			0
$291$	−0.866760	−	0.411466i	−0.0508104	−	0.0241206i
$292$		0			0
$293$	−19.4842	+	16.3492i	−1.13828	+	0.955130i	−0.999381	−	0.0351766i	$-0.988801\pi$
$293$	−19.4842	+	16.3492i	−1.13828	+	0.955130i	−0.138898	+	0.990307i	$0.544356\pi$
$294$		0			0
$295$	0.684343	+	1.88022i	0.0398440	+	0.109470i
$296$		0			0
$297$	17.3853	−	11.6457i	1.00880	−	0.675751i
$298$		0			0
$299$	−3.55012	−	9.75388i	−0.205309	−	0.564081i
$300$		0			0
$301$	−0.0120402	−	0.0143490i	−0.000693988	−	0.000827062i
$302$		0			0
$303$	−1.36967	+	0.945062i	−0.0786852	+	0.0542924i
$304$		0			0
$305$	15.5098	+	8.95458i	0.888088	+	0.512738i
$306$		0			0
$307$	13.4800	+	23.3481i	0.769346	+	1.33255i	0.937918	+	0.346857i	$0.112751\pi$
$307$	13.4800	+	23.3481i	0.769346	+	1.33255i	−0.168572	+	0.985689i	$0.553916\pi$
$308$		0			0
$309$	−0.899940	+	9.53009i	−0.0511958	+	0.542148i
$310$		0			0
$311$	−23.0984	−	8.40714i	−1.30979	−	0.476725i	−0.409618	−	0.912257i	$-0.634338\pi$
$311$	−23.0984	−	8.40714i	−1.30979	−	0.476725i	−0.900173	+	0.435532i	$0.856560\pi$
$312$		0			0
$313$	0.589807	−	3.34496i	0.0333379	−	0.189069i	−0.963591	−	0.267381i	$-0.913842\pi$
$313$	0.589807	−	3.34496i	0.0333379	−	0.189069i	0.996929	+	0.0783120i	$0.0249530\pi$
$314$		0			0
$315$	0.0702883	+	0.125710i	0.00396030	+	0.00708294i
$316$		0			0
$317$	16.0239	+	13.4456i	0.899991	+	0.755182i	0.970189	−	0.242351i	$-0.0779184\pi$
$317$	16.0239	+	13.4456i	0.899991	+	0.755182i	−0.0701973	+	0.997533i	$0.522363\pi$
$318$		0			0
$319$	34.5797	−	6.09734i	1.93609	−	0.341385i
$320$		0			0
$321$	−23.2000	−	6.38795i	−1.29490	−	0.356541i
$322$		0			0
$323$		−	3.43054i		−	0.190881i
$324$		0			0
$325$		−	14.9939i		−	0.831714i
$326$		0			0
$327$	22.3071	+	6.14210i	1.23359	+	0.339659i
$328$		0			0
$329$	0.347451	−	0.0612650i	0.0191556	−	0.00337765i
$330$		0			0
$331$	−21.5215	−	18.0587i	−1.18293	−	0.992594i	−0.999955	−	0.00947543i	$-0.996984\pi$
$331$	−21.5215	−	18.0587i	−1.18293	−	0.992594i	−0.182972	−	0.983118i	$-0.558572\pi$
$332$		0			0
$333$	0.0519440		0.000715390i	0.00284652		3.92032e-5i
$334$		0			0
$335$	−1.87067	+	10.6091i	−0.102206	+	0.579638i
$336$		0			0
$337$	16.1167	+	5.86598i	0.877930	+	0.319540i	0.741374	−	0.671092i	$-0.234174\pi$
$337$	16.1167	+	5.86598i	0.877930	+	0.319540i	0.136556	+	0.990632i	$0.456397\pi$
$338$		0			0
$339$	−1.06984	+	11.3293i	−0.0581059	+	0.615324i
$340$		0			0
$341$	−3.10600	−	5.37975i	−0.168199	−	0.291330i
$342$		0			0
$343$	0.455559	+	0.263017i	0.0245979	+	0.0142016i
$344$		0			0
$345$	4.24632	−	2.92994i	0.228614	−	0.157743i
$346$		0			0
$347$	−3.20624	−	3.82105i	−0.172120	−	0.205125i	0.673087	−	0.739563i	$-0.264968\pi$
$347$	−3.20624	−	3.82105i	−0.172120	−	0.205125i	−0.845208	+	0.534438i	$0.820523\pi$
$348$		0			0
$349$	−0.573161	−	1.57475i	−0.0306806	−	0.0842943i	0.923407	−	0.383823i	$-0.125393\pi$
$349$	−0.573161	−	1.57475i	−0.0306806	−	0.0842943i	−0.954087	+	0.299529i	$0.903171\pi$
$350$		0			0
$351$	−9.34174	−	21.1641i	−0.498625	−	1.12966i
$352$		0			0
$353$	10.7094	+	29.4240i	0.570006	+	1.56608i	0.804495	+	0.593960i	$0.202436\pi$
$353$	10.7094	+	29.4240i	0.570006	+	1.56608i	−0.234489	+	0.972119i	$0.575342\pi$
$354$		0			0
$355$	−9.24032	+	7.75355i	−0.490425	+	0.411516i
$356$		0			0
$357$	−0.0652224	−	0.0309622i	−0.00345194	−	0.00163870i
$358$		0			0
$359$	14.7790	−	25.5979i	0.780004	−	1.35101i	−0.151934	−	0.988391i	$-0.548550\pi$
$359$	14.7790	−	25.5979i	0.780004	−	1.35101i	0.931938	−	0.362617i	$-0.118117\pi$
$360$		0			0
$361$	4.71788	+	8.17161i	0.248309	+	0.430085i
$362$		0			0
$363$	−5.23419	+	7.36672i	−0.274724	+	0.386652i
$364$		0			0
$365$	−15.9587	−	5.80849i	−0.835316	−	0.304030i
$366$		0			0
$367$	19.6688	+	3.46814i	1.02670	+	0.181035i	0.661541	−	0.749909i	$-0.269903\pi$
$367$	19.6688	+	3.46814i	1.02670	+	0.181035i	0.365162	+	0.930944i	$0.381014\pi$
$368$		0			0
$369$	3.19941	−	2.61039i	0.166555	−	0.135892i
$370$		0			0
$371$	0.347575	−	0.414223i	0.0180452	−	0.0215054i
$372$		0			0
$373$	29.7847	−	5.25185i	1.54219	−	0.271930i	0.663082	−	0.748546i	$-0.269248\pi$
$373$	29.7847	−	5.25185i	1.54219	−	0.271930i	0.879112	+	0.476616i	$0.158137\pi$
$374$		0			0
$375$	17.9182	−	4.66917i	0.925291	−	0.241115i
$376$		0			0
$377$		−	38.8195i		−	1.99931i
$378$		0			0
$379$	2.37587			0.122040			0.0610201	−	0.998137i	$-0.480565\pi$
$379$	2.37587			0.122040			0.0610201	+	0.998137i	$0.480565\pi$
$380$		0			0
$381$	22.1242	−	21.8216i	1.13346	−	1.11796i
$382$		0			0
$383$	−2.35543	−	13.3583i	−0.120357	−	0.682578i	−0.983958	−	0.178402i	$-0.942907\pi$
$383$	−2.35543	−	13.3583i	−0.120357	−	0.682578i	0.863601	−	0.504176i	$-0.168204\pi$
$384$		0			0
$385$	−0.148103	−	0.124273i	−0.00754803	−	0.00633355i
$386$		0			0
$387$	−0.976912	+	1.13220i	−0.0496592	+	0.0575530i
$388$		0			0
$389$	0.151459	−	0.858969i	0.00767929	−	0.0435514i	−0.980727	−	0.195381i	$-0.937406\pi$
$389$	0.151459	−	0.858969i	0.00767929	−	0.0435514i	0.988407	+	0.151830i	$0.0485166\pi$
$390$		0			0
$391$	−0.884524	+	2.43021i	−0.0447323	+	0.122901i
$392$		0			0
$393$	23.9528	−	10.9692i	1.20826	−	0.553325i
$394$		0			0
$395$	−9.87916	+	5.70374i	−0.497074	+	0.286986i
$396$		0			0
$397$	14.0922	+	8.13615i	0.707269	+	0.408342i	0.810049	−	0.586362i	$-0.199440\pi$
$397$	14.0922	+	8.13615i	0.707269	+	0.408342i	−0.102780	+	0.994704i	$0.532774\pi$
$398$		0			0
$399$	−0.200637	+	0.0161622i	−0.0100444	+	0.000809121i
$400$		0			0
$401$	−3.43727	−	4.09638i	−0.171649	−	0.204563i	0.673361	−	0.739314i	$-0.264850\pi$
$401$	−3.43727	−	4.09638i	−0.171649	−	0.204563i	−0.845010	+	0.534751i	$0.820406\pi$
$402$		0			0
$403$	−6.45352	+	2.34889i	−0.321473	+	0.117007i
$404$		0			0
$405$	9.00836	−	7.14555i	0.447629	−	0.355065i
$406$		0			0
$407$	−0.0655289	+	0.0238506i	−0.00324815	+	0.00118223i
$408$		0			0
$409$	−3.30579	+	2.77389i	−0.163461	+	0.137160i	−0.720849	−	0.693092i	$-0.756248\pi$
$409$	−3.30579	+	2.77389i	−0.163461	+	0.137160i	0.557388	+	0.830252i	$0.311803\pi$
$410$		0			0
$411$	17.7067	−	1.42635i	0.873406	−	0.0703566i
$412$		0			0
$413$	−0.0294261	+	0.0509675i	−0.00144796	+	0.00250795i
$414$		0			0
$415$	13.3712	−	7.71988i	0.656368	−	0.378954i
$416$		0			0
$417$	15.5731	+	34.0059i	0.762616	+	1.66528i
$418$		0			0
$419$	7.20187	−	19.7870i	0.351834	−	0.966657i	−0.629946	−	0.776639i	$-0.716923\pi$
$419$	7.20187	−	19.7870i	0.351834	−	0.966657i	0.981781	−	0.190018i	$-0.0608547\pi$
$420$		0			0
$421$	14.9273	+	2.63209i	0.727513	+	0.128280i	0.525125	−	0.851025i	$-0.324019\pi$
$421$	14.9273	+	2.63209i	0.727513	+	0.128280i	0.202388	+	0.979305i	$0.435130\pi$
$422$		0			0
$423$	−9.26812	−	26.5980i	−0.450631	−	1.29324i
$424$		0			0
$425$	−2.40132	+	2.86178i	−0.116481	+	0.138817i
$426$		0			0
$427$	0.0914717	+	0.518762i	0.00442662	+	0.0251046i
$428$		0			0
$429$	21.8071	+	22.1095i	1.05285	+	1.06745i
$430$		0			0
$431$	−17.8689			−0.860714			−0.430357	−	0.902659i	$-0.641612\pi$
$431$	−17.8689			−0.860714			−0.430357	+	0.902659i	$0.641612\pi$
$432$		0			0
$433$	6.59150			0.316767			0.158384	−	0.987378i	$-0.449372\pi$
$433$	6.59150			0.316767			0.158384	+	0.987378i	$0.449372\pi$
$434$		0			0
$435$	18.6708	−	4.86528i	0.895195	−	0.233272i
$436$		0			0
$437$	1.25203	+	7.10063i	0.0598928	+	0.339669i
$438$		0			0
$439$	−24.6051	+	29.3233i	−1.17434	+	1.39952i	−0.275468	+	0.961310i	$0.588833\pi$
$439$	−24.6051	+	29.3233i	−1.17434	+	1.39952i	−0.898871	+	0.438213i	$0.855612\pi$
$440$		0			0
$441$	7.45199	−	19.6288i	0.354857	−	0.934705i
$442$		0			0
$443$	−25.9385	−	4.57366i	−1.23237	−	0.217301i	−0.480730	−	0.876869i	$-0.659628\pi$
$443$	−25.9385	−	4.57366i	−1.23237	−	0.217301i	−0.751645	+	0.659568i	$0.770739\pi$
$444$		0			0
$445$	3.48157	−	9.56554i	0.165042	−	0.453450i
$446$		0			0
$447$	12.4254	−	17.4878i	0.587703	−	0.827146i
$448$		0			0
$449$	−25.4654	+	14.7025i	−1.20179	+	0.693852i	−0.960952	−	0.276714i	$-0.910755\pi$
$449$	−25.4654	+	14.7025i	−1.20179	+	0.693852i	−0.240835	+	0.970566i	$0.577421\pi$
$450$		0			0
$451$	−2.77145	+	4.80029i	−0.130503	+	0.226037i
$452$		0			0
$453$	6.20642	−	13.0739i	0.291603	−	0.614266i
$454$		0			0
$455$	−0.163736	+	0.137391i	−0.00767606	+	0.00644098i
$456$		0			0
$457$	−11.4536	+	4.16878i	−0.535778	+	0.195007i	−0.595717	−	0.803195i	$-0.703132\pi$
$457$	−11.4536	+	4.16878i	−0.535778	+	0.195007i	0.0599382	+	0.998202i	$0.480910\pi$
$458$		0			0
$459$	−1.60650	+	5.53554i	−0.0749851	+	0.258377i
$460$		0			0
$461$	3.68812	−	1.34237i	0.171773	−	0.0625203i	−0.254702	−	0.967020i	$-0.581977\pi$
$461$	3.68812	−	1.34237i	0.171773	−	0.0625203i	0.426475	+	0.904499i	$0.359755\pi$
$462$		0			0
$463$	3.95108	+	4.70872i	0.183622	+	0.218833i	0.850001	−	0.526781i	$-0.176601\pi$
$463$	3.95108	+	4.70872i	0.183622	+	0.218833i	−0.666379	+	0.745613i	$0.732157\pi$
$464$		0			0
$465$	−1.93856	−	2.80952i	−0.0898984	−	0.130288i
$466$		0			0
$467$	17.5858	+	10.1531i	0.813772	+	0.469832i	0.848264	−	0.529573i	$-0.177648\pi$
$467$	17.5858	+	10.1531i	0.813772	+	0.469832i	−0.0344919	+	0.999405i	$0.510981\pi$
$468$		0			0
$469$	−0.274410	+	0.158431i	−0.0126711	+	0.00731565i
$470$		0			0
$471$	1.21315	−	12.8469i	0.0558992	−	0.591956i
$472$		0			0
$473$	0.686563	−	1.88632i	0.0315682	−	0.0867330i
$474$		0			0
$475$	−1.80859	+	10.2570i	−0.0829837	+	0.470624i
$476$		0			0
$477$	−37.0847	−	22.0973i	−1.69799	−	1.01177i
$478$		0			0
$479$	−0.0276350	−	0.0231885i	−0.00126268	−	0.00105951i	0.642156	−	0.766574i	$-0.278040\pi$
$479$	−0.0276350	−	0.0231885i	−0.00126268	−	0.00105951i	−0.643419	+	0.765514i	$0.722485\pi$
$480$		0			0
$481$	0.0133874	+	0.0759239i	0.000610414	+	0.00346183i
$482$		0			0
$483$	0.146299	+	0.0402825i	0.00665685	+	0.00183292i
$484$		0			0
$485$	0.707715			0.0321357
$486$		0			0
$487$		−	27.8804i		−	1.26338i	−0.775220	−	0.631692i	$-0.782361\pi$
$487$		−	27.8804i		−	1.26338i	0.775220	−	0.631692i	$-0.217639\pi$
$488$		0			0
$489$	−4.01288	+	14.5741i	−0.181469	+	0.659064i
$490$		0			0
$491$	−4.20879	+	0.742123i	−0.189940	+	0.0334916i	−0.267809	−	0.963472i	$-0.586300\pi$
$491$	−4.20879	+	0.742123i	−0.189940	+	0.0334916i	0.0778688	+	0.996964i	$0.475188\pi$
$492$		0			0
$493$	−6.21704	+	7.40918i	−0.280002	+	0.333693i
$494$		0			0
$495$	−7.90075	+	13.2594i	−0.355112	+	0.595965i
$496$		0			0
$497$	−0.349402	−	0.0616090i	−0.0156728	−	0.00276354i
$498$		0			0
$499$	16.1486	+	5.87762i	0.722912	+	0.263119i	0.677162	−	0.735834i	$-0.263210\pi$
$499$	16.1486	+	5.87762i	0.722912	+	0.263119i	0.0457508	+	0.998953i	$0.485432\pi$
$500$		0			0
$501$	−12.7738	−	1.20625i	−0.570691	−	0.0538912i
$502$		0			0
$503$	13.1215	+	22.7271i	0.585059	+	1.01335i	0.994868	+	0.101180i	$0.0322619\pi$
$503$	13.1215	+	22.7271i	0.585059	+	1.01335i	−0.409809	+	0.912171i	$0.634405\pi$
$504$		0			0
$505$	0.613719	−	1.06299i	0.0273101	−	0.0473025i
$506$		0			0
$507$	9.72526	−	6.71038i	0.431914	−	0.298018i
$508$		0			0
$509$	−16.9060	+	14.1858i	−0.749347	+	0.628777i	−0.935330	−	0.353776i	$-0.884897\pi$
$509$	−16.9060	+	14.1858i	−0.749347	+	0.628777i	0.185983	+	0.982553i	$0.440453\pi$
$510$		0			0
$511$	−0.170846	−	0.469395i	−0.00755777	−	0.0207648i
$512$		0			0
$513$	3.83763	+	15.6047i	0.169436	+	0.688965i
$514$		0			0
$515$	−2.41493	−	6.63497i	−0.106415	−	0.292372i
$516$		0			0
$517$	24.3036	+	28.9639i	1.06887	+	1.27383i
$518$		0			0
$519$	−9.93172	−	4.71476i	−0.435954	−	0.206955i
$520$		0			0
$521$	22.9164	+	13.2308i	1.00399	+	0.579652i	0.909426	−	0.415867i	$-0.136522\pi$
$521$	22.9164	+	13.2308i	1.00399	+	0.579652i	0.0945615	+	0.995519i	$0.469855\pi$
$522$		0			0
$523$	−17.4375	−	30.2027i	−0.762490	−	1.32067i	−0.941564	−	0.336835i	$-0.890643\pi$
$523$	−17.4375	−	30.2027i	−0.762490	−	1.32067i	0.179074	−	0.983836i	$-0.442690\pi$
$524$		0			0
$525$	0.178686	+	0.126960i	0.00779849	+	0.00554097i
$526$		0			0
$527$	1.60792	+	0.585234i	0.0700419	+	0.0254932i
$528$		0			0
$529$	−3.05004	+	17.2976i	−0.132611	+	0.752072i
$530$		0			0
$531$	4.39255	+	1.66761i	0.190620	+	0.0723682i
$532$		0			0
$533$	4.69430	+	3.93899i	0.203333	+	0.170617i
$534$		0			0
$535$	17.4798	−	3.08216i	0.755716	−	0.133253i
$536$		0			0
$537$	5.45899	+	20.9492i	0.235573	+	0.904023i
$538$		0			0
$539$			28.1839i			1.21397i
$540$		0			0
$541$			23.3686i			1.00469i	0.864666	+	0.502347i	$0.167530\pi$
$541$			23.3686i			1.00469i	−0.864666	+	0.502347i	$0.832470\pi$
$542$		0			0
$543$	28.0312	−	27.6478i	1.20294	−	1.18648i
$544$		0			0
$545$	−16.8070	+	2.96353i	−0.719935	+	0.126944i
$546$		0			0
$547$	−2.47846	−	2.07967i	−0.105971	−	0.0889204i	0.588263	−	0.808670i	$-0.299812\pi$
$547$	−2.47846	−	2.07967i	−0.105971	−	0.0889204i	−0.694234	+	0.719750i	$0.744257\pi$
$548$		0			0
$549$	39.7122	−	13.8378i	1.69488	−	0.590581i
$550$		0			0
$551$	−4.68246	+	26.5556i	−0.199480	+	1.13130i
$552$		0			0
$553$	−0.315294	−	0.114758i	−0.0134077	−	0.00488000i
$554$		0			0
$555$	−0.0348388	+	0.0159545i	−0.00147882	+	0.000677229i
$556$		0			0
$557$	−14.4176	−	24.9721i	−0.610894	−	1.05810i	−0.991090	−	0.133194i	$-0.957477\pi$
$557$	−14.4176	−	24.9721i	−0.610894	−	1.05810i	0.380196	−	0.924906i	$-0.375857\pi$
$558$		0			0
$559$	−1.92194	−	1.10963i	−0.0812894	−	0.0469324i
$560$		0			0
$561$	−0.621261	−	7.71232i	−0.0262296	−	0.325614i
$562$		0			0
$563$	11.4121	+	13.6005i	0.480964	+	0.573191i	0.950895	−	0.309512i	$-0.100166\pi$
$563$	11.4121	+	13.6005i	0.480964	+	0.573191i	−0.469931	+	0.882703i	$0.655721\pi$
$564$		0			0
$565$	−2.87086	−	7.88761i	−0.120778	−	0.331834i
$566$		0			0
$567$	0.331317	+	0.0678777i	0.0139140	+	0.00285059i
$568$		0			0
$569$	−8.74755	−	24.0337i	−0.366716	−	1.00754i	−0.976602	−	0.215055i	$-0.931007\pi$
$569$	−8.74755	−	24.0337i	−0.366716	−	1.00754i	0.609886	−	0.792490i	$-0.291215\pi$
$570$		0			0
$571$	−12.8608	+	10.7915i	−0.538209	+	0.451611i	−0.870925	−	0.491416i	$-0.836480\pi$
$571$	−12.8608	+	10.7915i	−0.538209	+	0.451611i	0.332716	+	0.943027i	$0.392035\pi$
$572$		0			0
$573$	0.522639	+	6.48804i	0.0218336	+	0.271042i
$574$		0			0
$575$	3.92586	−	6.79978i	0.163720	−	0.283571i
$576$		0			0
$577$	−4.28264	−	7.41775i	−0.178289	−	0.308805i	0.763006	−	0.646392i	$-0.223723\pi$
$577$	−4.28264	−	7.41775i	−0.178289	−	0.308805i	−0.941294	+	0.337587i	$0.890389\pi$
$578$		0			0
$579$	−17.8450	−	38.9670i	−0.741613	−	1.61941i
$580$		0			0
$581$	0.426744	+	0.155322i	0.0177043	+	0.00644385i
$582$		0			0
$583$	57.0681	+	10.0627i	2.36352	+	0.416752i
$584$		0			0
$585$	12.9195	+	11.1475i	0.534156	+	0.460893i
$586$		0			0
$587$	−21.1215	+	25.1716i	−0.871778	+	1.03894i	0.127115	+	0.991888i	$0.459428\pi$
$587$	−21.1215	+	25.1716i	−0.871778	+	1.03894i	−0.998892	+	0.0470560i	$0.985016\pi$
$588$		0			0
$589$	4.69804	−	0.828391i	0.193579	−	0.0341333i
$590$		0			0
$591$	5.64067	+	5.71889i	0.232026	+	0.235244i
$592$		0			0
$593$		−	12.9354i		−	0.531195i	−0.964084	−	0.265597i	$-0.914431\pi$
$593$		−	12.9354i		−	0.531195i	0.964084	−	0.265597i	$-0.0855692\pi$
$594$		0			0
$595$	0.0532545			0.00218322
$596$		0			0
$597$	−6.46379	−	24.8051i	−0.264545	−	1.01521i
$598$		0			0
$599$	3.81637	+	21.6437i	0.155932	+	0.884337i	0.957928	+	0.287007i	$0.0926604\pi$
$599$	3.81637	+	21.6437i	0.155932	+	0.884337i	−0.801996	+	0.597330i	$0.796228\pi$
$600$		0			0
$601$	−12.7487	−	10.6974i	−0.520030	−	0.436357i	0.344612	−	0.938745i	$-0.388010\pi$
$601$	−12.7487	−	10.6974i	−0.520030	−	0.436357i	−0.864642	+	0.502388i	$0.832455\pi$
$602$		0			0
$603$	15.9919	+	19.6003i	0.651240	+	0.798187i
$604$		0			0
$605$	1.15749	−	6.56445i	0.0470587	−	0.266883i
$606$		0			0
$607$	−5.65521	+	15.5376i	−0.229538	+	0.630650i	−0.999976	−	0.00686394i	$-0.997815\pi$
$607$	−5.65521	+	15.5376i	−0.229538	+	0.630650i	0.770438	+	0.637514i	$0.220037\pi$
$608$		0			0
$609$	0.462620	+	0.328700i	0.0187463	+	0.0133196i
$610$		0			0
$611$	36.2004	−	20.9003i	1.46451	−	0.845537i
$612$		0			0
$613$	8.59588	+	4.96283i	0.347184	+	0.200447i	0.663444	−	0.748226i	$-0.269094\pi$
$613$	8.59588	+	4.96283i	0.347184	+	0.200447i	−0.316260	+	0.948672i	$0.602427\pi$
$614$		0			0
$615$	−1.30617	+	2.75147i	−0.0526698	+	0.110950i
$616$		0			0
$617$	−16.0619	−	19.1418i	−0.646626	−	0.770619i	0.338775	−	0.940867i	$-0.389987\pi$
$617$	−16.0619	−	19.1418i	−0.646626	−	0.770619i	−0.985401	+	0.170248i	$0.945543\pi$
$618$		0			0
$619$	21.8055	−	7.93656i	0.876437	−	0.318997i	0.135666	−	0.990755i	$-0.456683\pi$
$619$	21.8055	−	7.93656i	0.876437	−	0.318997i	0.740771	+	0.671757i	$0.234460\pi$
$620$		0			0
$621$	1.30489	−	12.0439i	0.0523636	−	0.483306i
$622$		0			0
$623$	0.281352	−	0.102404i	0.0112721	−	0.00410273i
$624$		0			0
$625$	2.43670	−	2.04464i	0.0974682	−	0.0817855i
$626$		0			0
$627$	−12.2508	−	17.7550i	−0.489252	−	0.709066i
$628$		0			0
$629$	0.00960425	−	0.0166350i	0.000382946	−	0.000663283i
$630$		0			0
$631$	8.21645	−	4.74377i	0.327092	−	0.188847i	−0.327457	−	0.944866i	$-0.606192\pi$
$631$	8.21645	−	4.74377i	0.327092	−	0.188847i	0.654549	+	0.756019i	$0.272858\pi$
$632$		0			0
$633$	−20.3138	−	1.91826i	−0.807402	−	0.0762441i
$634$		0			0
$635$	−7.83959	+	21.5391i	−0.311105	+	0.854753i
$636$		0			0
$637$	30.6855	+	5.41068i	1.21580	+	0.214379i
$638$		0			0
$639$	−0.390060	+	28.3220i	−0.0154305	+	1.12040i
$640$		0			0
$641$	7.44194	−	8.86896i	0.293939	−	0.350303i	−0.598783	−	0.800912i	$-0.704349\pi$
$641$	7.44194	−	8.86896i	0.293939	−	0.350303i	0.892721	+	0.450609i	$0.148793\pi$
$642$		0			0
$643$	5.63647	+	31.9660i	0.222281	+	1.26062i	0.867816	+	0.496886i	$0.165523\pi$
$643$	5.63647	+	31.9660i	0.222281	+	1.26062i	−0.645535	+	0.763731i	$0.723365\pi$
$644$		0			0
$645$	0.292815	−	1.06345i	0.0115296	−	0.0418734i
$646$		0			0
$647$	−40.5576			−1.59448			−0.797242	−	0.603660i	$-0.793708\pi$
$647$	−40.5576			−1.59448			−0.797242	+	0.603660i	$0.793708\pi$
$648$		0			0
$649$	−6.30702			−0.247572
$650$		0			0
$651$	0.0266524	−	0.0967970i	0.00104459	−	0.00379377i
$652$		0			0
$653$	1.89217	+	10.7310i	0.0740463	+	0.419937i	0.999187	+	0.0403132i	$0.0128356\pi$
$653$	1.89217	+	10.7310i	0.0740463	+	0.419937i	−0.925141	+	0.379624i	$0.876053\pi$
$654$		0			0
$655$	−12.4909	+	14.8861i	−0.488061	+	0.581649i
$656$		0			0
$657$	−34.8075	+	19.4620i	−1.35797	+	0.759285i
$658$		0			0
$659$	15.6898	+	2.76653i	0.611187	+	0.107769i	0.470670	−	0.882309i	$-0.344012\pi$
$659$	15.6898	+	2.76653i	0.611187	+	0.107769i	0.140517	+	0.990078i	$0.455123\pi$
$660$		0			0
$661$	−3.94900	+	10.8498i	−0.153598	+	0.422008i	−0.992495	−	0.122282i	$-0.960979\pi$
$661$	−3.94900	+	10.8498i	−0.153598	+	0.422008i	0.838897	+	0.544290i	$0.183201\pi$
$662$		0			0
$663$	−8.51612	−	0.804189i	−0.330739	−	0.0312321i
$664$		0			0
$665$	0.128580	−	0.0742359i	0.00498613	−	0.00287874i
$666$		0			0
$667$	10.1641	−	17.6047i	0.393555	−	0.681658i
$668$		0			0
$669$	−20.6650	−	29.9496i	−0.798956	−	1.15792i
$670$		0			0
$671$	−43.2446	+	36.2865i	−1.66944	+	1.40083i
$672$		0			0
$673$	11.8463	−	4.31169i	0.456640	−	0.166203i	−0.103451	−	0.994635i	$-0.532988\pi$
$673$	11.8463	−	4.31169i	0.456640	−	0.166203i	0.560091	+	0.828431i	$0.310766\pi$
$674$		0			0
$675$	7.72164	−	15.7038i	0.297206	−	0.604440i
$676$		0			0
$677$	−35.2718	+	12.8379i	−1.35560	+	0.493399i	−0.914692	−	0.404151i	$-0.867567\pi$
$677$	−35.2718	+	12.8379i	−1.35560	+	0.493399i	−0.440912	+	0.897551i	$0.645345\pi$
$678$		0			0
$679$	0.0133803	+	0.0159461i	0.000513490	+	0.000611954i
$680$		0			0
$681$	−2.22479	+	4.68656i	−0.0852543	+	0.179589i
$682$		0			0
$683$	−24.5827	−	14.1928i	−0.940631	−	0.543073i	−0.0504727	−	0.998725i	$-0.516073\pi$
$683$	−24.5827	−	14.1928i	−0.940631	−	0.543073i	−0.890158	+	0.455652i	$0.849406\pi$
$684$		0			0
$685$	−11.3475	+	6.55148i	−0.433566	+	0.250319i
$686$		0			0
$687$	9.61496	+	6.83161i	0.366833	+	0.260642i
$688$		0			0
$689$	21.9116	−	60.2016i	0.834765	−	2.29350i
$690$		0			0
$691$	−5.71664	+	32.4207i	−0.217471	+	1.23334i	0.659095	+	0.752060i	$0.270940\pi$
$691$	−5.71664	+	32.4207i	−0.217471	+	1.23334i	−0.876566	+	0.481281i	$0.840172\pi$
$692$		0			0
$693$	−0.448132	+	0.0726695i	−0.0170231	+	0.00276049i
$694$		0			0
$695$	−21.1339	−	17.7334i	−0.801654	−	0.672667i
$696$		0			0
$697$	−0.265127	−	1.50361i	−0.0100424	−	0.0569533i
$698$		0			0
$699$	4.71889	+	18.1090i	0.178485	+	0.684946i
$700$		0			0
$701$	−2.58326			−0.0975684			−0.0487842	−	0.998809i	$-0.515535\pi$
$701$	−2.58326			−0.0975684			−0.0487842	+	0.998809i	$0.515535\pi$
$702$		0			0
$703$		−	0.0535526i		−	0.00201978i
$704$		0			0
$705$	14.5893	+	14.7916i	0.549466	+	0.557085i
$706$		0			0
$707$	0.0355543	−	0.00626918i	0.00133716	−	0.000235777i
$708$		0			0
$709$	−25.7394	+	30.6751i	−0.966665	+	1.15203i	0.0216755	+	0.999765i	$0.493100\pi$
$709$	−25.7394	+	30.6751i	−0.966665	+	1.15203i	−0.988340	+	0.152261i	$0.951345\pi$
$710$		0			0
$711$	−5.01433	+	26.3134i	−0.188052	+	0.986828i
$712$		0			0
$713$	−3.54170	−	0.624497i	−0.132638	−	0.0233876i
$714$		0			0
$715$	−21.5247	−	7.83435i	−0.804978	−	0.292988i
$716$		0			0
$717$	−6.48064	−	14.1514i	−0.242024	−	0.528493i
$718$		0			0
$719$	1.78773	+	3.09644i	0.0666710	+	0.115478i	0.897434	−	0.441149i	$-0.145429\pi$
$719$	1.78773	+	3.09644i	0.0666710	+	0.115478i	−0.830763	+	0.556626i	$0.812096\pi$
$720$		0			0
$721$	0.103840	−	0.179856i	0.00386720	−	0.00669818i
$722$		0			0
$723$	1.13733	+	14.1188i	0.0422978	+	0.525084i
$724$		0			0
$725$	22.4945	−	18.8751i	0.835426	−	0.701005i
$726$		0			0
$727$	−11.0625	−	30.3940i	−0.410285	−	1.12725i	−0.957040	−	0.289956i	$-0.906359\pi$
$727$	−11.0625	−	30.3940i	−0.410285	−	1.12725i	0.546755	−	0.837293i	$-0.315863\pi$
$728$		0			0
$729$	1.11517	−	26.9770i	0.0413026	−	0.999147i
$730$		0			0
$731$	0.189115	+	0.519591i	0.00699469	+	0.0192177i
$732$		0			0
$733$	19.2878	+	22.9862i	0.712409	+	0.849016i	0.993870	−	0.110556i	$-0.0352633\pi$
$733$	19.2878	+	22.9862i	0.712409	+	0.849016i	−0.281460	+	0.959573i	$0.590819\pi$
$734$		0			0
$735$	1.24349	+	15.4367i	0.0458670	+	0.569392i
$736$		0			0
$737$	−29.4077	−	16.9785i	−1.08325	−	0.625413i
$738$		0			0
$739$	−6.60975	−	11.4484i	−0.243143	−	0.421137i	0.718465	−	0.695564i	$-0.244845\pi$
$739$	−6.60975	−	11.4484i	−0.243143	−	0.421137i	−0.961608	+	0.274427i	$0.911512\pi$
$740$		0			0
$741$	−21.6828	+	9.92966i	−0.796537	+	0.364775i
$742$		0			0
$743$	−24.1121	−	8.77610i	−0.884588	−	0.321964i	−0.140528	−	0.990077i	$-0.544880\pi$
$743$	−24.1121	−	8.77610i	−0.884588	−	0.321964i	−0.744060	+	0.668113i	$0.767102\pi$
$744$		0			0
$745$	−2.74776	+	15.5833i	−0.100670	+	0.570929i
$746$		0			0
$747$	6.78678	−	35.6146i	0.248315	−	1.30307i
$748$		0			0
$749$	0.399926	+	0.335578i	0.0146130	+	0.0122617i
$750$		0			0
$751$	−24.9654	+	4.40207i	−0.911000	+	0.160634i	−0.609458	−	0.792819i	$-0.708613\pi$
$751$	−24.9654	+	4.40207i	−0.911000	+	0.160634i	−0.301543	+	0.953453i	$0.597502\pi$
$752$		0			0
$753$	23.0596	−	22.7442i	0.840339	−	0.828845i
$754$		0			0
$755$			10.6749i			0.388500i
$756$		0			0
$757$		−	7.76347i		−	0.282168i	−0.989998	−	0.141084i	$-0.954941\pi$
$757$		−	7.76347i		−	0.282168i	0.989998	−	0.141084i	$-0.0450588\pi$
$758$		0			0
$759$	4.10064	+	15.7364i	0.148844	+	0.571196i
$760$		0			0
$761$	−9.22102	+	1.62592i	−0.334262	+	0.0589394i	−0.338260	−	0.941053i	$-0.609838\pi$
$761$	−9.22102	+	1.62592i	−0.334262	+	0.0589394i	0.00399834	+	0.999992i	$0.498727\pi$
$762$		0			0
$763$	−0.384534	−	0.322662i	−0.0139211	−	0.0116812i
$764$		0			0
$765$	−0.680546	−	4.19673i	−0.0246052	−	0.151733i
$766$		0			0
$767$	−1.21081	+	6.86682i	−0.0437197	+	0.247947i
$768$		0			0
$769$	−25.0021	−	9.10003i	−0.901600	−	0.328156i	−0.150706	−	0.988579i	$-0.548155\pi$
$769$	−25.0021	−	9.10003i	−0.901600	−	0.328156i	−0.750894	+	0.660423i	$0.770377\pi$
$770$		0			0
$771$	−19.7330	−	14.0207i	−0.710668	−	0.504943i
$772$		0			0
$773$	−8.90177	−	15.4183i	−0.320174	−	0.554558i	0.660349	−	0.750959i	$-0.270408\pi$
$773$	−8.90177	−	15.4183i	−0.320174	−	0.554558i	−0.980524	+	0.196400i	$0.937075\pi$
$774$		0			0
$775$	−4.49899	−	2.59749i	−0.161608	−	0.0933047i
$776$		0			0
$777$	−0.00101816		0.000483337i	−3.65262e−5		1.73396e-5i
$778$		0			0
$779$	−2.73614	−	3.26081i	−0.0980325	−	0.116831i
$780$		0			0
$781$	−13.0043	−	35.7290i	−0.465331	−	1.27849i
$782$		0			0
$783$	19.9914	−	40.6574i	0.714435	−	1.45298i
$784$		0			0
$785$	3.25542	+	8.94420i	0.116191	+	0.319232i
$786$		0			0
$787$	−16.8309	+	14.1228i	−0.599957	+	0.503424i	−0.891432	−	0.453155i	$-0.850299\pi$
$787$	−16.8309	+	14.1228i	−0.599957	+	0.503424i	0.291475	+	0.956579i	$0.405854\pi$
$788$		0			0
$789$	−26.7308	+	18.4441i	−0.951641	+	0.656627i
$790$		0			0
$791$	0.123444	−	0.213812i	0.00438917	−	0.00760227i
$792$		0			0
$793$	31.2053	+	54.0491i	1.10813	+	1.91934i
$794$		0			0
$795$	31.7010	+	2.99357i	1.12432	+	0.106171i
$796$		0			0
$797$	14.4147	+	5.24652i	0.510595	+	0.185841i	0.584453	−	0.811427i	$-0.301309\pi$
$797$	14.4147	+	5.24652i	0.510595	+	0.185841i	−0.0738582	+	0.997269i	$0.523531\pi$
$798$		0			0
$799$	−10.2565	−	1.80851i	−0.362851	−	0.0639803i
$800$		0			0
$801$	−11.6654	−	20.8634i	−0.412177	−	0.737172i
$802$		0			0
$803$	34.4098	−	41.0079i	1.21429	−	1.44714i
$804$		0			0
$805$	−0.110228	+	0.0194361i	−0.00388501	+	0.000685032i
$806$		0			0
$807$	−0.736871	+	2.67619i	−0.0259391	+	0.0942064i
$808$		0			0
$809$			38.3503i			1.34832i	0.738584	+	0.674162i	$0.235495\pi$
$809$			38.3503i			1.34832i	−0.738584	+	0.674162i	$0.764505\pi$
$810$		0			0
$811$	−2.84191			−0.0997928			−0.0498964	−	0.998754i	$-0.515889\pi$
$811$	−2.84191			−0.0997928			−0.0498964	+	0.998754i	$0.515889\pi$
$812$		0			0
$813$	1.82068	+	0.501312i	0.0638541	+	0.0175818i
$814$		0			0
$815$	−1.93619	−	10.9807i	−0.0678219	−	0.384637i
$816$		0			0
$817$	1.18091	+	0.990901i	0.0413148	+	0.0346673i
$818$		0			0
$819$	−0.00691176	+	0.501858i	−0.000241516	+	0.0175364i
$820$		0			0
$821$	−6.41903	+	36.4041i	−0.224026	+	1.27051i	0.640514	+	0.767947i	$0.278721\pi$
$821$	−6.41903	+	36.4041i	−0.224026	+	1.27051i	−0.864539	+	0.502565i	$0.832390\pi$
$822$		0			0
$823$	17.0571	−	46.8639i	0.594572	−	1.63357i	−0.167346	−	0.985898i	$-0.553520\pi$
$823$	17.0571	−	46.8639i	0.594572	−	1.63357i	0.761918	−	0.647674i	$-0.224258\pi$
$824$		0			0
$825$	−2.20844	+	23.3867i	−0.0768879	+	0.814219i
$826$		0			0
$827$	25.4053	−	14.6677i	0.883428	−	0.510047i	0.0116409	−	0.999932i	$-0.496295\pi$
$827$	25.4053	−	14.6677i	0.883428	−	0.510047i	0.871787	+	0.489885i	$0.162961\pi$
$828$		0			0
$829$	−35.7709	−	20.6523i	−1.24237	−	0.717285i	−0.272797	−	0.962072i	$-0.587949\pi$
$829$	−35.7709	−	20.6523i	−1.24237	−	0.717285i	−0.969577	+	0.244786i	$0.921282\pi$
$830$		0			0
$831$	−23.9226	−	34.6706i	−0.829864	−	1.20271i
$832$		0			0
$833$	−4.99017	−	5.94706i	−0.172899	−	0.206053i
$834$		0			0
$835$	8.89328	−	3.23689i	0.307765	−	0.112017i
$836$		0			0
$837$	−7.96870	−	0.863366i	−0.275439	−	0.0298423i
$838$		0			0
$839$	19.7178	−	7.17669i	0.680734	−	0.247767i	0.0215712	−	0.999767i	$-0.493133\pi$
$839$	19.7178	−	7.17669i	0.680734	−	0.247767i	0.659163	+	0.752001i	$0.270911\pi$
$840$		0			0
$841$	36.0233	−	30.2272i	1.24218	−	1.04232i
$842$		0			0
$843$	1.33008	−	2.80184i	0.0458106	−	0.0965006i
$844$		0			0
$845$	−4.35769	+	7.54774i	−0.149909	+	0.259650i
$846$		0			0
$847$	0.169793	−	0.0980298i	0.00583414	−	0.00336834i
$848$		0			0
$849$	−3.37852	+	4.75500i	−0.115950	+	0.163191i
$850$		0			0
$851$	−0.0138079	+	0.0379369i	−0.000473329	+	0.00130046i
$852$		0			0
$853$	23.5698	+	4.15599i	0.807015	+	0.142299i	0.561910	−	0.827198i	$-0.310067\pi$
$853$	23.5698	+	4.15599i	0.807015	+	0.142299i	0.245105	+	0.969497i	$0.421178\pi$
$854$		0			0
$855$	−7.49332	−	9.18413i	−0.256266	−	0.314091i
$856$		0			0
$857$	11.8477	−	14.1196i	0.404710	−	0.482315i	−0.524740	−	0.851263i	$-0.675837\pi$
$857$	11.8477	−	14.1196i	0.404710	−	0.482315i	0.929450	+	0.368948i	$0.120282\pi$
$858$		0			0
$859$	−4.54416	−	25.7712i	−0.155045	−	0.879303i	−0.958745	−	0.284268i	$-0.908249\pi$
$859$	−4.54416	−	25.7712i	−0.155045	−	0.879303i	0.803700	−	0.595035i	$-0.202862\pi$
$860$		0			0
$861$	−0.0866903	+	0.0225900i	−0.00295440	+	0.000769864i
$862$		0			0
$863$	16.7507			0.570199			0.285100	−	0.958498i	$-0.407973\pi$
$863$	16.7507			0.570199			0.285100	+	0.958498i	$0.407973\pi$
$864$		0			0
$865$	8.10931			0.275725
$866$		0			0
$867$	−19.1802	−	19.4462i	−0.651393	−	0.660426i
$868$		0			0
$869$	−6.24399	−	35.4114i	−0.211813	−	1.20125i
$870$		0			0
$871$	−24.1312	+	28.7584i	−0.817653	+	0.974441i
$872$		0			0
$873$	1.08564	−	1.25822i	0.0367435	−	0.0425842i
$874$		0			0
$875$	−0.395622	−	0.0697589i	−0.0133745	−	0.00235828i
$876$		0			0
$877$	−11.8079	+	32.4419i	−0.398724	+	1.09549i	0.564183	+	0.825650i	$0.309191\pi$
$877$	−11.8079	+	32.4419i	−0.398724	+	1.09549i	−0.962907	+	0.269835i	$0.913031\pi$
$878$		0			0
$879$	−18.3428	−	40.0541i	−0.618688	−	1.35099i
$880$		0			0
$881$	−26.4274	+	15.2579i	−0.890362	+	0.514050i	−0.874061	−	0.485817i	$-0.838522\pi$
$881$	−26.4274	+	15.2579i	−0.890362	+	0.514050i	−0.0163008	+	0.999867i	$0.505189\pi$
$882$		0			0
$883$	−16.0187	+	27.7452i	−0.539073	+	0.933701i	0.459882	+	0.887980i	$0.347892\pi$
$883$	−16.0187	+	27.7452i	−0.539073	+	0.933701i	−0.998954	+	0.0457210i	$0.985441\pi$
$884$		0			0
$885$	−3.45444	+	0.278270i	−0.116120	+	0.00935395i
$886$		0			0
$887$	0.309940	−	0.260070i	0.0104068	−	0.00873231i	−0.637569	−	0.770393i	$-0.720060\pi$
$887$	0.309940	−	0.260070i	0.0104068	−	0.00873231i	0.647976	+	0.761661i	$0.275616\pi$
$888$		0			0
$889$	−0.633532	+	0.230587i	−0.0212480	+	0.00773363i
$890$		0			0
$891$	11.4535	+	34.3865i	0.383706	+	1.15199i
$892$		0			0
$893$	−27.2849	+	9.93091i	−0.913056	+	0.332325i
$894$		0			0
$895$	−10.2643	−	12.2325i	−0.343097	−	0.408887i
$896$		0			0
$897$	17.9204	−	1.44356i	0.598345	−	0.0481992i
$898$		0			0
$899$	−11.6479	−	6.72494i	−0.388481	−	0.224289i
$900$		0			0
$901$	−13.8235	+	7.98102i	−0.460529	+	0.265886i
$902$		0			0
$903$	0.0294975	−	0.0135084i	0.000981617	−	0.000449533i
$904$		0			0
$905$	−9.93269	+	27.2898i	−0.330174	+	0.907145i
$906$		0			0
$907$	6.48461	−	36.7760i	0.215318	−	1.22113i	−0.665036	−	0.746811i	$-0.731584\pi$
$907$	6.48461	−	36.7760i	0.215318	−	1.22113i	0.880354	−	0.474317i	$-0.157305\pi$
$908$		0			0
$909$	−0.948397	−	2.72175i	−0.0314563	−	0.0902748i
$910$		0			0
$911$	−12.5899	−	10.5642i	−0.417122	−	0.350007i	0.409945	−	0.912110i	$-0.365548\pi$
$911$	−12.5899	−	10.5642i	−0.417122	−	0.350007i	−0.827067	+	0.562103i	$0.809992\pi$
$912$		0			0
$913$	8.45110	+	47.9286i	0.279691	+	1.58620i
$914$		0			0
$915$	−22.0847	+	21.7826i	−0.730097	+	0.720111i
$916$		0			0
$917$	−0.571569			−0.0188749
$918$		0			0
$919$			37.7169i			1.24417i	0.782951	+	0.622084i	$0.213714\pi$
$919$			37.7169i			1.24417i	−0.782951	+	0.622084i	$0.786286\pi$
$920$		0			0
$921$	−45.1872	+	11.7750i	−1.48897	+	0.387999i
$922$		0			0
$923$	−41.3968	+	7.29938i	−1.36259	+	0.240262i
$924$		0			0
$925$	−0.0374859	+	0.0446739i	−0.00123253	+	0.00146887i
$926$		0			0
$927$	−15.5006	−	5.88472i	−0.509105	−	0.193280i
$928$		0			0
$929$	35.1367	+	6.19555i	1.15280	+	0.203270i	0.717197	−	0.696870i	$-0.245425\pi$
$929$	35.1367	+	6.19555i	1.15280	+	0.203270i	0.435601	+	0.900140i	$0.356536\pi$
$930$		0			0
$931$	−20.3386	−	7.40265i	−0.666571	−	0.242612i
$932$		0			0
$933$	24.6597	−	34.7066i	0.807323	−	1.13624i
$934$		0			0
$935$	2.85357	+	4.94252i	0.0933216	+	0.161638i
$936$		0			0
$937$	17.8075	−	30.8434i	0.581744	−	1.00761i	−0.413529	−	0.910491i	$-0.635704\pi$
$937$	17.8075	−	30.8434i	0.581744	−	1.00761i	0.995273	−	0.0971193i	$-0.0309628\pi$
$938$		0			0
$939$	5.31458	+	2.52293i	0.173435	+	0.0823326i
$940$		0			0
$941$	2.81572	−	2.36267i	0.0917898	−	0.0770208i	−0.595738	−	0.803179i	$-0.703140\pi$
$941$	2.81572	−	2.36267i	0.0917898	−	0.0770208i	0.687528	+	0.726158i	$0.258696\pi$
$942$		0			0
$943$	1.09753	+	3.01545i	0.0357406	+	0.0981965i
$944$		0			0
$945$	−0.242242	+	0.0595740i	−0.00788013	+	0.00193794i
$946$		0			0
$947$	1.54304	+	4.23946i	0.0501420	+	0.137764i	0.962236	−	0.272218i	$-0.0877572\pi$
$947$	1.54304	+	4.23946i	0.0501420	+	0.137764i	−0.912094	+	0.409982i	$0.865535\pi$
$948$		0			0
$949$	−38.0418	−	45.3365i	−1.23489	−	1.47169i
$950$		0			0
$951$	−29.8207	+	20.5761i	−0.967002	+	0.667227i
$952$		0			0
$953$	11.2227	+	6.47942i	0.363538	+	0.209889i	0.670632	−	0.741790i	$-0.266023\pi$
$953$	11.2227	+	6.47942i	0.363538	+	0.209889i	−0.307093	+	0.951679i	$0.599356\pi$
$954$		0			0
$955$	−2.40058	−	4.15793i	−0.0776809	−	0.134547i
$956$		0			0
$957$	−5.71767	+	60.5484i	−0.184826	+	1.95725i
$958$		0			0
$959$	−0.362157	−	0.131814i	−0.0116946	−	0.00425650i
$960$		0			0
$961$	4.96990	−	28.1857i	0.160319	−	0.909217i
$962$		0			0
$963$	21.3346	−	35.8046i	0.687497	−	1.15379i
$964$		0			0
$965$	24.2171	+	20.3205i	0.779575	+	0.654141i
$966$		0			0
$967$	−53.8023	+	9.48680i	−1.73017	+	0.305075i	−0.948065	−	0.318076i	$-0.896963\pi$
$967$	−53.8023	+	9.48680i	−1.73017	+	0.305075i	−0.782101	+	0.623151i	$0.785852\pi$
$968$		0			0
$969$	5.72869	+	1.57735i	0.184032	+	0.0506719i
$970$		0			0
$971$		−	42.8083i		−	1.37378i	−0.726760	−	0.686892i	$-0.758975\pi$
$971$		−	42.8083i		−	1.37378i	0.726760	−	0.686892i	$-0.241025\pi$
$972$		0			0
$973$		−	0.811458i		−	0.0260142i
$974$		0			0
$975$	25.0385	+	6.89417i	0.801872	+	0.220790i
$976$		0			0
$977$	33.9041	−	5.97821i	1.08469	−	0.191260i	0.397400	−	0.917645i	$-0.369912\pi$
$977$	33.9041	−	5.97821i	1.08469	−	0.191260i	0.687287	+	0.726386i	$0.258801\pi$
$978$		0			0
$979$	24.5799	+	20.6250i	0.785577	+	0.659177i
$980$		0			0
$981$	−20.5135	+	34.4266i	−0.654945	+	1.09916i
$982$		0			0
$983$	7.45500	−	42.2794i	0.237778	−	1.34850i	−0.598907	−	0.800819i	$-0.704398\pi$
$983$	7.45500	−	42.2794i	0.237778	−	1.34850i	0.836684	−	0.547685i	$-0.184491\pi$
$984$		0			0
$985$	−5.56764	−	2.02646i	−0.177400	−	0.0645682i
$986$		0			0
$987$	−0.0574501	+	0.608380i	−0.00182866	+	0.0193649i
$988$		0			0
$989$	−0.581069	−	1.00644i	−0.0184769	−	0.0320030i
$990$		0			0
$991$	34.3889	+	19.8544i	1.09240	+	0.630697i	0.934214	−	0.356713i	$-0.116103\pi$
$991$	34.3889	+	19.8544i	1.09240	+	0.630697i	0.158185	+	0.987410i	$0.449436\pi$
$992$		0			0
$993$	40.0518	−	27.6355i	1.27100	−	0.876987i
$994$		0			0
$995$	12.1536	+	14.4840i	0.385293	+	0.459175i
$996$		0			0
$997$	−3.81126	−	10.4713i	−0.120704	−	0.331631i	0.864595	−	0.502469i	$-0.167575\pi$
$997$	−3.81126	−	10.4713i	−0.120704	−	0.331631i	−0.985299	+	0.170838i	$0.945353\pi$
$998$		0			0
$999$	−0.0250784	+	0.0864127i	−0.000793444	+	0.00273398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.47.13		192
4.3	odd	2		216.2.v.b.155.7	yes	192
8.3	odd	2	inner	864.2.bh.b.47.14		192
8.5	even	2		216.2.v.b.155.32	yes	192
12.11	even	2		648.2.v.b.467.26		192
24.5	odd	2		648.2.v.b.467.1		192
27.23	odd	18	inner	864.2.bh.b.239.14		192
108.23	even	18		216.2.v.b.131.32	yes	192
108.31	odd	18		648.2.v.b.179.1		192
216.77	odd	18		216.2.v.b.131.7	✓	192
216.85	even	18		648.2.v.b.179.26		192
216.131	even	18	inner	864.2.bh.b.239.13		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.7	✓	192	216.77	odd	18
216.2.v.b.131.32	yes	192	108.23	even	18
216.2.v.b.155.7	yes	192	4.3	odd	2
216.2.v.b.155.32	yes	192	8.5	even	2
648.2.v.b.179.1		192	108.31	odd	18
648.2.v.b.179.26		192	216.85	even	18
648.2.v.b.467.1		192	24.5	odd	2
648.2.v.b.467.26		192	12.11	even	2
864.2.bh.b.47.13		192	1.1	even	1	trivial
864.2.bh.b.47.14		192	8.3	odd	2	inner
864.2.bh.b.239.13		192	216.131	even	18	inner
864.2.bh.b.239.14		192	27.23	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.459797 + 1.66991i) q^{3} +(-0.221850 - 1.25817i) q^{5} +(0.0241545 - 0.0287862i) q^{7} +(-2.57717 - 1.53564i) q^{9} +O(q^{10})\)	\(q+(-0.459797 + 1.66991i) q^{3} +(-0.221850 - 1.25817i) q^{5} +(0.0241545 - 0.0287862i) q^{7} +(-2.57717 - 1.53564i) q^{9} +(3.96591 + 0.699297i) q^{11} +(1.52273 - 4.18367i) q^{13} +(2.20304 + 0.208036i) q^{15} +(-0.960657 + 0.554636i) q^{17} +(-1.54631 + 2.67828i) q^{19} +(0.0369640 + 0.0535715i) q^{21} +(1.78597 - 1.49861i) q^{23} +(3.16468 - 1.15185i) q^{25} +(3.74934 - 3.59756i) q^{27} +(8.19341 - 2.98216i) q^{29} +(-0.991533 - 1.18166i) q^{31} +(-2.99127 + 6.30116i) q^{33} +(-0.0415766 - 0.0240043i) q^{35} +(-0.0149964 + 0.00865816i) q^{37} +(6.28618 + 4.46645i) q^{39} +(-0.470758 + 1.29340i) q^{41} +(0.0865581 - 0.490896i) q^{43} +(-1.36035 + 3.58321i) q^{45} +(7.19227 + 6.03503i) q^{47} +(1.21529 + 6.89226i) q^{49} +(-0.484482 - 1.85923i) q^{51} +14.3897 q^{53} -5.14494i q^{55} +(-3.76149 - 3.81365i) q^{57} +(-1.54236 + 0.271959i) q^{59} +(-9.01061 + 10.7384i) q^{61} +(-0.106455 + 0.0370945i) q^{63} +(-5.60159 - 0.987712i) q^{65} +(-7.92365 - 2.88397i) q^{67} +(1.68135 + 3.67146i) q^{69} +(-4.72079 - 8.17664i) q^{71} +(6.64650 - 11.5121i) q^{73} +(0.468370 + 5.81434i) q^{75} +(0.115924 - 0.0972722i) q^{77} +(-3.05388 - 8.39047i) q^{79} +(4.28364 + 7.91520i) q^{81} +(4.13336 + 11.3563i) q^{83} +(0.910949 + 1.08563i) q^{85} +(1.21262 + 15.0534i) q^{87} +(6.90026 + 3.98387i) q^{89} +(-0.0836510 - 0.144888i) q^{91} +(2.42917 - 1.11244i) q^{93} +(3.71279 + 1.35134i) q^{95} +(-0.0961922 + 0.545533i) q^{97} +(-9.14697 - 7.89240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 192 * q + 12 * q^3 - 12 * q^9	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more