LMFDB - Embedded newform 864.2.bh.b.47.14

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			47.14
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.14

$q$-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	$0.0366626\pi$
$5$	0.221850	+	1.25817i	0.0992142	+	0.562672i	−0.894160	+	0.447748i	$0.852226\pi$
$6$		0			0
$7$	−0.0241545	+	0.0287862i	−0.00912953	+	0.0108801i	−0.770590	−	0.637331i	$-0.780038\pi$
$7$	−0.0241545	+	0.0287862i	−0.00912953	+	0.0108801i	0.761460	+	0.648211i	$0.224483\pi$
$8$		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	$0.322927\pi$
$13$	−1.52273	+	4.18367i	−0.422329	+	1.16034i	−0.950370	+	0.311121i	$0.899295\pi$
$14$		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	−0.809710	−	0.586830i	$-0.800376\pi$
$23$	−1.78597	+	1.49861i	−0.372400	+	0.312481i	0.437310	+	0.899311i	$0.355931\pi$
$24$		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	−0.961517	−	0.274747i	$-0.911406\pi$
$29$	−8.19341	+	2.98216i	−1.52148	+	0.553772i	−0.559961	+	0.828519i	$0.689184\pi$
$30$		0			0
$31$	0.991533	+	1.18166i	0.178085	+	0.212233i	0.847701	−	0.530474i	$-0.177986\pi$
$31$	0.991533	+	1.18166i	0.178085	+	0.212233i	−0.669617	+	0.742707i	$0.733542\pi$
$32$		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	−0.498767	−	0.866736i	$-0.666214\pi$
$37$	0.0149964	−	0.00865816i	0.00246539	−	0.00142339i	0.501232	+	0.865313i	$0.332880\pi$
$38$		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	−0.0561017	−	0.998425i	$-0.517867\pi$
$47$	−7.19227	−	6.03503i	−1.04910	−	0.880300i	−0.992999	+	0.118125i	$0.962312\pi$
$48$		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	$-0.951233\pi$
$53$	−14.3897			−1.97657			−0.988287	+	0.152609i	$0.951233\pi$
$54$		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	$-0.423223\pi$
$61$	9.01061	−	10.7384i	1.15369	−	1.37491i	0.914820	−	0.403862i	$-0.132333\pi$
$62$		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	$0.0226299\pi$
$71$	4.72079	+	8.17664i	0.560254	+	0.970389i	−0.437220	+	0.899355i	$0.644037\pi$
$72$		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	$0.0563990\pi$
$79$	3.05388	+	8.39047i	0.343589	+	0.944002i	−0.640756	+	0.767745i	$0.721379\pi$
$80$		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	0.605437	−	0.795894i	$-0.292999\pi$
$101$	−0.735978	−	0.617559i	−0.0732325	−	0.0614494i	−0.678669	+	0.734444i	$0.737443\pi$
$102$		0			0
$103$	−5.44272	+	0.959698i	−0.536287	+	0.0945618i	−0.435231	−	0.900319i	$-0.643333\pi$
$103$	−5.44272	+	0.959698i	−0.536287	+	0.0945618i	−0.101056	+	0.994881i	$0.532222\pi$
$104$		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	$0.220961\pi$
$109$			13.3583i			1.27949i	−0.768586	+	0.639746i	$0.779039\pi$
$110$		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	0.992008	−	0.126178i	$-0.0402711\pi$
$127$	15.5376	+	8.97063i	1.37874	+	0.796015i	0.386730	+	0.922193i	$0.373604\pi$
$128$		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	0.771476	−	0.636258i	$-0.219519\pi$
$149$	11.6387	+	4.23616i	0.953483	+	0.347039i	0.182007	+	0.983297i	$0.441741\pi$
$150$		0			0
$151$	8.22863	+	1.45093i	0.669637	+	0.118075i	0.498123	−	0.867107i	$-0.334023\pi$
$151$	8.22863	+	1.45093i	0.669637	+	0.118075i	0.171514	+	0.985182i	$0.445134\pi$
$152$		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	0.126981	−	0.991905i	$-0.459471\pi$
$157$	7.33700	−	1.29371i	0.585556	−	0.103249i	0.458575	+	0.888656i	$0.348360\pi$
$158$		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	$-0.963025\pi$
$167$	−1.28634	−	7.29522i	−0.0995404	−	0.564521i	0.893721	−	0.448624i	$-0.148086\pi$
$168$		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	$-0.866873\pi$
$173$	1.10221	−	6.25096i	0.0837996	−	0.475251i	0.997609	−	0.0691084i	$-0.0220154\pi$
$174$		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	0.999160	−	0.0409826i	$-0.0130488\pi$
$181$	19.6860	+	11.3657i	1.46325	+	0.844807i	0.464088	+	0.885789i	$0.346382\pi$
$182$		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	−0.466605	−	0.884466i	$-0.654523\pi$
$191$	−3.53137	+	1.28531i	−0.255521	+	0.0930020i	0.211084	+	0.977468i	$0.432301\pi$
$192$		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	−0.936729	−	0.350054i	$-0.886163\pi$
$197$	−2.31882	+	4.01631i	−0.165209	+	0.286150i	0.771521	+	0.636204i	$0.219496\pi$
$198$		0			0
$199$	12.8167	−	7.39975i	0.908555	−	0.524554i	0.0285887	−	0.999591i	$-0.490899\pi$
$199$	12.8167	−	7.39975i	0.908555	−	0.524554i	0.879966	+	0.475037i	$0.157565\pi$
$200$		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	$-0.529441\pi$
$223$	13.5037	−	16.0931i	0.904277	−	1.07768i	0.996636	−	0.0819499i	$-0.0261148\pi$
$224$		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	−0.992552	−	0.121819i	$-0.961127\pi$
$229$	−2.32907	+	6.39908i	−0.153910	+	0.422863i	0.838643	+	0.544682i	$0.183350\pi$
$230$		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	−0.392399	−	0.919795i	$-0.628355\pi$
$239$	6.88390	−	5.77628i	0.445282	−	0.373636i	0.837682	+	0.546159i	$0.183910\pi$
$240$		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	0.0816475	−	0.996661i	$-0.473982\pi$
$263$	−14.3635	−	12.0524i	−0.885694	−	0.743186i	−0.967342	+	0.253475i	$0.918426\pi$
$264$		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	$-0.515558\pi$
$269$	−1.60260			−0.0977123			−0.0488561	+	0.998806i	$0.515558\pi$
$270$		0			0
$271$			1.09029i			0.0662304i	0.999452	+	0.0331152i	$0.0105428\pi$
$271$			1.09029i			0.0662304i	−0.999452	+	0.0331152i	$0.989457\pi$
$272$		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	$-0.517012\pi$
$277$	15.6324	−	18.6300i	0.939260	−	1.11937i	0.992678	−	0.120794i	$-0.0385440\pi$
$278$		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	0.138898	−	0.990307i	$-0.455644\pi$
$293$	19.4842	−	16.3492i	1.13828	−	0.955130i	0.999381	+	0.0351766i	$0.0111994\pi$
$294$		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	0.900173	−	0.435532i	$-0.143440\pi$
$311$	23.0984	+	8.40714i	1.30979	+	0.476725i	0.409618	+	0.912257i	$0.365662\pi$
$312$		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	0.0701973	−	0.997533i	$-0.477637\pi$
$317$	−16.0239	−	13.4456i	−0.899991	−	0.755182i	−0.970189	+	0.242351i	$0.922082\pi$
$318$		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	0.954087	−	0.299529i	$-0.0968295\pi$
$349$	0.573161	+	1.57475i	0.0306806	+	0.0842943i	−0.923407	+	0.383823i	$0.874607\pi$
$350$		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	$0.451450\pi$
$359$	−14.7790	+	25.5979i	−0.780004	+	1.35101i	−0.931938	+	0.362617i	$0.881883\pi$
$360$		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	−0.365162	−	0.930944i	$-0.618986\pi$
$367$	−19.6688	−	3.46814i	−1.02670	−	0.181035i	−0.661541	+	0.749909i	$0.730097\pi$
$368$		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	−0.879112	−	0.476616i	$-0.841863\pi$
$373$	−29.7847	+	5.25185i	−1.54219	+	0.271930i	−0.663082	+	0.748546i	$0.730752\pi$
$374$		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	$0.0570926\pi$
$383$	2.35543	+	13.3583i	0.120357	+	0.682578i	−0.863601	+	0.504176i	$0.831796\pi$
$384$		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	−0.988407	−	0.151830i	$-0.951483\pi$
$389$	−0.151459	+	0.858969i	−0.00767929	+	0.0435514i	0.980727	+	0.195381i	$0.0625945\pi$
$390$		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	0.102780	−	0.994704i	$-0.467226\pi$
$397$	−14.0922	−	8.13615i	−0.707269	−	0.408342i	−0.810049	+	0.586362i	$0.800560\pi$
$398$		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	−0.202388	−	0.979305i	$-0.564870\pi$
$421$	−14.9273	−	2.63209i	−0.727513	−	0.128280i	−0.525125	+	0.851025i	$0.675981\pi$
$422$		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	$-0.358388\pi$
$431$	17.8689			0.860714			0.430357	+	0.902659i	$0.358388\pi$
$432$		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	$-0.411167\pi$
$439$	24.6051	−	29.3233i	1.17434	−	1.39952i	0.898871	−	0.438213i	$-0.144388\pi$
$440$		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	−0.426475	−	0.904499i	$-0.640245\pi$
$461$	−3.68812	+	1.34237i	−0.171773	+	0.0625203i	0.254702	+	0.967020i	$0.418023\pi$
$462$		0			0
$463$	−3.95108	−	4.70872i	−0.183622	−	0.218833i	0.666379	−	0.745613i	$-0.267843\pi$
$463$	−3.95108	−	4.70872i	−0.183622	−	0.218833i	−0.850001	+	0.526781i	$0.823399\pi$
$464$		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	0.643419	−	0.765514i	$-0.277515\pi$
$479$	0.0276350	+	0.0231885i	0.00126268	+	0.00105951i	−0.642156	+	0.766574i	$0.721960\pi$
$480$		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	$0.217639\pi$
$487$			27.8804i			1.26338i	−0.775220	+	0.631692i	$0.782361\pi$
$488$		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	$-0.967738\pi$
$503$	−13.1215	−	22.7271i	−0.585059	−	1.01335i	0.409809	−	0.912171i	$-0.365595\pi$
$504$		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	−0.185983	−	0.982553i	$-0.559547\pi$
$509$	16.9060	−	14.1858i	0.749347	−	0.628777i	0.935330	+	0.353776i	$0.115103\pi$
$510$		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	$-0.832470\pi$
$541$		−	23.3686i		−	1.00469i	0.864666	−	0.502347i	$-0.167530\pi$
$542$		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	$0.0425234\pi$
$557$	14.4176	+	24.9721i	0.610894	+	1.05810i	−0.380196	+	0.924906i	$0.624143\pi$
$558$		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	$-0.907340\pi$
$599$	−3.81637	−	21.6437i	−0.155932	−	0.884337i	0.801996	−	0.597330i	$-0.203772\pi$
$600$		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	−0.770438	−	0.637514i	$-0.779963\pi$
$607$	5.65521	−	15.5376i	0.229538	−	0.630650i	0.999976	+	0.00686394i	$0.00218488\pi$
$608$		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	0.316260	−	0.948672i	$-0.397573\pi$
$613$	−8.59588	−	4.96283i	−0.347184	−	0.200447i	−0.663444	+	0.748226i	$0.730906\pi$
$614$		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	−0.654549	−	0.756019i	$-0.727142\pi$
$631$	−8.21645	+	4.74377i	−0.327092	+	0.188847i	0.327457	+	0.944866i	$0.393808\pi$
$632$		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	$-0.206292\pi$
$647$	40.5576			1.59448			0.797242	+	0.603660i	$0.206292\pi$
$648$		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	$-0.987164\pi$
$653$	−1.89217	−	10.7310i	−0.0740463	−	0.419937i	0.925141	−	0.379624i	$-0.123947\pi$
$654$		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	−0.838897	−	0.544290i	$-0.816799\pi$
$661$	3.94900	−	10.8498i	0.153598	−	0.422008i	0.992495	+	0.122282i	$0.0390212\pi$
$662$		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	0.440912	−	0.897551i	$-0.354655\pi$
$677$	35.2718	−	12.8379i	1.35560	−	0.493399i	0.914692	+	0.404151i	$0.132433\pi$
$678$		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	$-0.484465\pi$
$701$	2.58326			0.0975684			0.0487842	+	0.998809i	$0.484465\pi$
$702$		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	$-0.506900\pi$
$709$	25.7394	−	30.6751i	0.966665	−	1.15203i	0.988340	−	0.152261i	$-0.0486555\pi$
$710$		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	0.830763	−	0.556626i	$-0.187904\pi$
$719$	−1.78773	−	3.09644i	−0.0666710	−	0.115478i	−0.897434	+	0.441149i	$0.854571\pi$
$720$		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	$0.0936408\pi$
$727$	11.0625	+	30.3940i	0.410285	+	1.12725i	−0.546755	+	0.837293i	$0.684137\pi$
$728$		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	0.281460	−	0.959573i	$-0.409181\pi$
$733$	−19.2878	−	22.9862i	−0.712409	−	0.849016i	−0.993870	+	0.110556i	$0.964737\pi$
$734$		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	0.744060	−	0.668113i	$-0.232898\pi$
$743$	24.1121	+	8.77610i	0.884588	+	0.321964i	0.140528	+	0.990077i	$0.455120\pi$
$744$		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	0.301543	−	0.953453i	$-0.402498\pi$
$751$	24.9654	−	4.40207i	0.911000	−	0.160634i	0.609458	+	0.792819i	$0.291387\pi$
$752$		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	$0.0450588\pi$
$757$			7.76347i			0.282168i	−0.989998	+	0.141084i	$0.954941\pi$
$758$		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	0.980524	−	0.196400i	$-0.0629251\pi$
$773$	8.90177	+	15.4183i	0.320174	+	0.554558i	−0.660349	+	0.750959i	$0.729592\pi$
$774$		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	0.0738582	−	0.997269i	$-0.476469\pi$
$797$	−14.4147	−	5.24652i	−0.510595	−	0.185841i	−0.584453	+	0.811427i	$0.698691\pi$
$798$		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	$-0.721279\pi$
$821$	6.41903	−	36.4041i	0.224026	−	1.27051i	0.864539	−	0.502565i	$-0.167610\pi$
$822$		0			0
$823$	−17.0571	+	46.8639i	−0.594572	+	1.63357i	0.167346	+	0.985898i	$0.446480\pi$
$823$	−17.0571	+	46.8639i	−0.594572	+	1.63357i	−0.761918	+	0.647674i	$0.775742\pi$
$824$		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	0.969577	−	0.244786i	$-0.0787178\pi$
$829$	35.7709	+	20.6523i	1.24237	+	0.717285i	0.272797	+	0.962072i	$0.412051\pi$
$830$		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	−0.659163	−	0.752001i	$-0.729089\pi$
$839$	−19.7178	+	7.17669i	−0.680734	+	0.247767i	−0.0215712	+	0.999767i	$0.506867\pi$
$840$		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	−0.245105	−	0.969497i	$-0.578822\pi$
$853$	−23.5698	−	4.15599i	−0.807015	−	0.142299i	−0.561910	+	0.827198i	$0.689933\pi$
$854$		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	$-0.592027\pi$
$863$	−16.7507			−0.570199			−0.285100	+	0.958498i	$0.592027\pi$
$864$		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	$-0.690809\pi$
$877$	11.8079	−	32.4419i	0.398724	−	1.09549i	0.962907	−	0.269835i	$-0.0869692\pi$
$878$		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	−0.647976	−	0.761661i	$-0.724384\pi$
$887$	−0.309940	+	0.260070i	−0.0104068	+	0.00873231i	0.637569	+	0.770393i	$0.279940\pi$
$888$		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	0.827067	−	0.562103i	$-0.190008\pi$
$911$	12.5899	+	10.5642i	0.417122	+	0.350007i	−0.409945	+	0.912110i	$0.634452\pi$
$912$		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	$-0.786286\pi$
$919$		−	37.7169i		−	1.24417i	0.782951	−	0.622084i	$-0.213714\pi$
$920$		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	−0.687528	−	0.726158i	$-0.741304\pi$
$941$	−2.81572	+	2.36267i	−0.0917898	+	0.0770208i	0.595738	+	0.803179i	$0.296860\pi$
$942$		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	0.782101	−	0.623151i	$-0.214148\pi$
$967$	53.8023	−	9.48680i	1.73017	−	0.305075i	0.948065	+	0.318076i	$0.103037\pi$
$968$		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	$0.295602\pi$
$983$	−7.45500	+	42.2794i	−0.237778	+	1.34850i	−0.836684	+	0.547685i	$0.815509\pi$
$984$		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	−0.158185	−	0.987410i	$-0.550564\pi$
$991$	−34.3889	−	19.8544i	−1.09240	−	0.630697i	−0.934214	+	0.356713i	$0.883897\pi$
$992$		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	0.985299	−	0.170838i	$-0.0546474\pi$
$997$	3.81126	+	10.4713i	0.120704	+	0.331631i	−0.864595	+	0.502469i	$0.832425\pi$
$998$		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.47.14		192
4.3	odd	2		216.2.v.b.155.32	yes	192
8.3	odd	2	inner	864.2.bh.b.47.13		192
8.5	even	2		216.2.v.b.155.7	yes	192
12.11	even	2		648.2.v.b.467.1		192
24.5	odd	2		648.2.v.b.467.26		192
27.23	odd	18	inner	864.2.bh.b.239.13		192
108.23	even	18		216.2.v.b.131.7	✓	192
108.31	odd	18		648.2.v.b.179.26		192
216.77	odd	18		216.2.v.b.131.32	yes	192
216.85	even	18		648.2.v.b.179.1		192
216.131	even	18	inner	864.2.bh.b.239.14		192

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

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