LMFDB - Embedded newform 819.2.n.e.100.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(100,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.100"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-6,0,0,1,-12,0,8,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.7
Root			$-1.02737 - 1.77946i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.e.172.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02737 + 1.77946i) q^{2} +(-1.11098 + 1.92428i) q^{4} +(0.274662 - 0.475728i) q^{5} +(-0.839752 + 2.50895i) q^{7} -0.456078 q^{8} +1.12872 q^{10} -4.69824 q^{11} +(-0.663964 + 3.54389i) q^{13} +(-5.32730 + 1.08331i) q^{14} +(1.75340 + 3.03698i) q^{16} +(-0.301806 + 0.522743i) q^{17} +0.561110 q^{19} +(0.610289 + 1.05705i) q^{20} +(-4.82684 - 8.36033i) q^{22} +(0.188350 + 0.326231i) q^{23} +(2.34912 + 4.06880i) q^{25} +(-6.98834 + 2.45939i) q^{26} +(-3.89496 - 4.40331i) q^{28} +(-2.09200 + 3.62344i) q^{29} +(-0.577330 - 0.999965i) q^{31} +(-4.05887 + 7.03016i) q^{32} -1.24027 q^{34} +(0.962929 + 1.08861i) q^{35} +(4.40116 + 7.62304i) q^{37} +(0.576468 + 0.998472i) q^{38} +(-0.125267 + 0.216969i) q^{40} +(3.96001 - 6.85894i) q^{41} +(-0.747200 - 1.29419i) q^{43} +(5.21966 - 9.04072i) q^{44} +(-0.387010 + 0.670321i) q^{46} +(1.09885 - 1.90326i) q^{47} +(-5.58963 - 4.21379i) q^{49} +(-4.82684 + 8.36033i) q^{50} +(-6.08177 - 5.21485i) q^{52} +(-4.52338 - 7.83473i) q^{53} +(-1.29043 + 2.23509i) q^{55} +(0.382993 - 1.14428i) q^{56} -8.59702 q^{58} +(4.26827 - 7.39286i) q^{59} +7.42424 q^{61} +(1.18626 - 2.05467i) q^{62} -9.66624 q^{64} +(1.50356 + 1.28924i) q^{65} -9.59873 q^{67} +(-0.670602 - 1.16152i) q^{68} +(-0.947844 + 2.83190i) q^{70} +(-2.88877 - 5.00350i) q^{71} +(7.24668 + 12.5516i) q^{73} +(-9.04325 + 15.6634i) q^{74} +(-0.623383 + 1.07973i) q^{76} +(3.94536 - 11.7876i) q^{77} +(7.31102 - 12.6631i) q^{79} +1.92637 q^{80} +16.2736 q^{82} +14.8750 q^{83} +(0.165789 + 0.287155i) q^{85} +(1.53530 - 2.65922i) q^{86} +2.14277 q^{88} +(4.59177 + 7.95317i) q^{89} +(-8.33387 - 4.64184i) q^{91} -0.837013 q^{92} +4.51569 q^{94} +(0.154115 - 0.266936i) q^{95} +(3.15034 + 5.45655i) q^{97} +(1.75564 - 14.2756i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31}+ \cdots + 3 q^{98}+O(q^{100}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.02737	+	1.77946i	0.726461	+	1.25827i	0.958370	+	0.285530i	$0.0921695\pi$
$2$	1.02737	+	1.77946i	0.726461	+	1.25827i	−0.231909	+	0.972738i	$0.574497\pi$
$3$		0			0
$3$		0			0
$4$	−1.11098	+	1.92428i	−0.555491	+	0.962139i
$5$	0.274662	−	0.475728i	0.122833	−	0.212752i	−0.798051	−	0.602590i	$-0.794136\pi$
$5$	0.274662	−	0.475728i	0.122833	−	0.212752i	0.920884	+	0.389838i	$0.127469\pi$
$6$		0			0
$7$	−0.839752	+	2.50895i	−0.317397	+	0.948293i
$7$	−0.839752	+	2.50895i	−0.317397	+	0.948293i
$8$	−0.456078			−0.161248
$9$		0			0
$10$	1.12872			0.356932
$11$	−4.69824			−1.41657			−0.708287	−	0.705925i	$-0.750532\pi$
$11$	−4.69824			−1.41657			−0.708287	+	0.705925i	$0.750532\pi$
$12$		0			0
$13$	−0.663964	+	3.54389i	−0.184150	+	0.982898i
$13$	−0.663964	+	3.54389i	−0.184150	+	0.982898i
$14$	−5.32730	+	1.08331i	−1.42378	+	0.289528i
$15$		0			0
$16$	1.75340	+	3.03698i	0.438351	+	0.759245i
$17$	−0.301806	+	0.522743i	−0.0731987	+	0.126784i	−0.900302	−	0.435267i	$-0.856654\pi$
$17$	−0.301806	+	0.522743i	−0.0731987	+	0.126784i	0.827103	+	0.562051i	$0.189987\pi$
$18$		0			0
$19$	0.561110			0.128727			0.0643637	−	0.997927i	$-0.479498\pi$
$19$	0.561110			0.128727			0.0643637	+	0.997927i	$0.479498\pi$
$20$	0.610289	+	1.05705i	0.136465	+	0.236364i
$21$		0			0
$22$	−4.82684	−	8.36033i	−1.02909	−	1.78243i
$23$	0.188350	+	0.326231i	0.0392736	+	0.0680239i	0.884994	−	0.465602i	$-0.154162\pi$
$23$	0.188350	+	0.326231i	0.0392736	+	0.0680239i	−0.845720	+	0.533626i	$0.820829\pi$
$24$		0			0
$25$	2.34912	+	4.06880i	0.469824	+	0.813760i
$26$	−6.98834	+	2.45939i	−1.37053	+	0.482327i
$27$		0			0
$28$	−3.89496	−	4.40331i	−0.736078	−	0.832148i
$29$	−2.09200	+	3.62344i	−0.388474	+	0.672856i	−0.992244	−	0.124302i	$-0.960331\pi$
$29$	−2.09200	+	3.62344i	−0.388474	+	0.672856i	0.603771	+	0.797158i	$0.293664\pi$
$30$		0			0
$31$	−0.577330	−	0.999965i	−0.103691	−	0.179599i	0.809511	−	0.587104i	$-0.199732\pi$
$31$	−0.577330	−	0.999965i	−0.103691	−	0.179599i	−0.913203	+	0.407505i	$0.866399\pi$
$32$	−4.05887	+	7.03016i	−0.717513	+	1.24277i
$33$		0			0
$34$	−1.24027			−0.212704
$35$	0.962929	+	1.08861i	0.162765	+	0.184008i
$36$		0			0
$37$	4.40116	+	7.62304i	0.723547	+	1.25322i	0.959569	+	0.281472i	$0.0908227\pi$
$37$	4.40116	+	7.62304i	0.723547	+	1.25322i	−0.236023	+	0.971748i	$0.575844\pi$
$38$	0.576468	+	0.998472i	0.0935154	+	0.161973i
$39$		0			0
$40$	−0.125267	+	0.216969i	−0.0198065	+	0.0343059i
$41$	3.96001	−	6.85894i	0.618450	−	1.07119i	−0.371319	−	0.928506i	$-0.621094\pi$
$41$	3.96001	−	6.85894i	0.618450	−	1.07119i	0.989769	−	0.142681i	$-0.0455724\pi$
$42$		0			0
$43$	−0.747200	−	1.29419i	−0.113947	−	0.197362i	0.803411	−	0.595424i	$-0.203016\pi$
$43$	−0.747200	−	1.29419i	−0.113947	−	0.197362i	−0.917358	+	0.398062i	$0.869683\pi$
$44$	5.21966	−	9.04072i	0.786894	−	1.36294i
$45$		0			0
$46$	−0.387010	+	0.670321i	−0.0570615	+	0.0988334i
$47$	1.09885	−	1.90326i	0.160283	−	0.277619i	−0.774687	−	0.632345i	$-0.782093\pi$
$47$	1.09885	−	1.90326i	0.160283	−	0.277619i	0.934970	+	0.354726i	$0.115426\pi$
$48$		0			0
$49$	−5.58963	−	4.21379i	−0.798519	−	0.601970i
$50$	−4.82684	+	8.36033i	−0.682618	+	1.18233i
$51$		0			0
$52$	−6.08177	−	5.21485i	−0.843390	−	0.723169i
$53$	−4.52338	−	7.83473i	−0.621334	−	1.07618i	−0.989238	−	0.146318i	$-0.953258\pi$
$53$	−4.52338	−	7.83473i	−0.621334	−	1.07618i	0.367903	−	0.929864i	$-0.380076\pi$
$54$		0			0
$55$	−1.29043	+	2.23509i	−0.174001	+	0.301379i
$56$	0.382993	−	1.14428i	0.0511796	−	0.152910i
$57$		0			0
$58$	−8.59702			−1.12884
$59$	4.26827	−	7.39286i	0.555681	−	0.962468i	−0.442169	−	0.896932i	$-0.645791\pi$
$59$	4.26827	−	7.39286i	0.555681	−	0.962468i	0.997850	−	0.0655364i	$-0.0208758\pi$
$60$		0			0
$61$	7.42424			0.950576			0.475288	−	0.879830i	$-0.342344\pi$
$61$	7.42424			0.950576			0.475288	+	0.879830i	$0.342344\pi$
$62$	1.18626	−	2.05467i	0.150656	−	0.260943i
$63$		0			0
$64$	−9.66624			−1.20828
$65$	1.50356	+	1.28924i	0.186494	+	0.159910i
$66$		0			0
$67$	−9.59873			−1.17267			−0.586336	−	0.810068i	$-0.699430\pi$
$67$	−9.59873			−1.17267			−0.586336	+	0.810068i	$0.699430\pi$
$68$	−0.670602	−	1.16152i	−0.0813224	−	0.140855i
$69$		0			0
$70$	−0.947844	+	2.83190i	−0.113289	+	0.338476i
$71$	−2.88877	−	5.00350i	−0.342834	−	0.593806i	0.642124	−	0.766601i	$-0.278053\pi$
$71$	−2.88877	−	5.00350i	−0.342834	−	0.593806i	−0.984958	+	0.172795i	$0.944720\pi$
$72$		0			0
$73$	7.24668	+	12.5516i	0.848160	+	1.46906i	0.882849	+	0.469657i	$0.155623\pi$
$73$	7.24668	+	12.5516i	0.848160	+	1.46906i	−0.0346892	+	0.999398i	$0.511044\pi$
$74$	−9.04325	+	15.6634i	−1.05126	+	1.82083i
$75$		0			0
$76$	−0.623383	+	1.07973i	−0.0715069	+	0.123854i
$77$	3.94536	−	11.7876i	0.449616	−	1.34333i
$78$		0			0
$79$	7.31102	−	12.6631i	0.822554	−	1.42471i	−0.0812206	−	0.996696i	$-0.525882\pi$
$79$	7.31102	−	12.6631i	0.822554	−	1.42471i	0.903774	−	0.428009i	$-0.140785\pi$
$80$	1.92637			0.215375
$81$		0			0
$82$	16.2736			1.79712
$83$	14.8750			1.63274			0.816371	−	0.577528i	$-0.195983\pi$
$83$	14.8750			1.63274			0.816371	+	0.577528i	$0.195983\pi$
$84$		0			0
$85$	0.165789	+	0.287155i	0.0179824	+	0.0311464i
$86$	1.53530	−	2.65922i	0.165556	−	0.286751i
$87$		0			0
$88$	2.14277			0.228420
$89$	4.59177	+	7.95317i	0.486726	+	0.843035i	0.999884	−	0.0152600i	$-0.00485760\pi$
$89$	4.59177	+	7.95317i	0.486726	+	0.843035i	−0.513157	+	0.858295i	$0.671524\pi$
$90$		0			0
$91$	−8.33387	−	4.64184i	−0.873627	−	0.486597i
$92$	−0.837013			−0.0872646
$93$		0			0
$94$	4.51569			0.465758
$95$	0.154115	−	0.266936i	0.0158119	−	0.0273870i
$96$		0			0
$97$	3.15034	+	5.45655i	0.319869	+	0.554029i	0.980460	−	0.196717i	$-0.0630279\pi$
$97$	3.15034	+	5.45655i	0.319869	+	0.554029i	−0.660592	+	0.750745i	$0.729695\pi$
$98$	1.75564	−	14.2756i	0.177346	−	1.44206i
$99$		0			0
$100$	−10.4393			−1.04393
$101$	−4.44387			−0.442182			−0.221091	−	0.975253i	$-0.570962\pi$
$101$	−4.44387			−0.442182			−0.221091	+	0.975253i	$0.570962\pi$
$102$		0			0
$103$	8.31431	−	14.4008i	0.819234	−	1.41895i	−0.0870141	−	0.996207i	$-0.527733\pi$
$103$	8.31431	−	14.4008i	0.819234	−	1.41895i	0.906248	−	0.422747i	$-0.138934\pi$
$104$	0.302820	−	1.61629i	0.0296939	−	0.158490i
$105$		0			0
$106$	9.29438	−	16.0983i	0.902750	−	1.56361i
$107$	8.93605	+	15.4777i	0.863881	+	1.49629i	0.868154	+	0.496295i	$0.165306\pi$
$107$	8.93605	+	15.4777i	0.863881	+	1.49629i	−0.00427332	+	0.999991i	$0.501360\pi$
$108$		0			0
$109$	−5.07774	−	8.79490i	−0.486359	−	0.842399i	0.513518	−	0.858079i	$-0.328342\pi$
$109$	−5.07774	−	8.79490i	−0.486359	−	0.842399i	−0.999877	+	0.0156799i	$0.995009\pi$
$110$	−5.30299			−0.505621
$111$		0			0
$112$	−9.09205	+	1.84888i	−0.859118	+	0.174703i
$113$	3.74505	+	6.48662i	0.352305	+	0.610210i	0.986653	−	0.162838i	$-0.0520647\pi$
$113$	3.74505	+	6.48662i	0.352305	+	0.610210i	−0.634348	+	0.773048i	$0.718731\pi$
$114$		0			0
$115$	0.206930			0.0192963
$116$	−4.64834	−	8.05116i	−0.431587	−	0.747531i
$117$		0			0
$118$	17.5404			1.61472
$119$	−1.05809	−	1.19619i	−0.0969952	−	0.109655i
$120$		0			0
$121$	11.0735			1.00668
$122$	7.62745	+	13.2111i	0.690557	+	1.19608i
$123$		0			0
$124$	2.56561			0.230399
$125$	5.32748			0.476504
$126$		0			0
$127$	2.36612	−	4.09824i	0.209959	−	0.363660i	−0.741742	−	0.670685i	$-0.766000\pi$
$127$	2.36612	−	4.09824i	0.209959	−	0.363660i	0.951702	+	0.307025i	$0.0993335\pi$
$128$	−1.81308	−	3.14034i	−0.160255	−	0.277570i
$129$		0			0
$130$	−0.749428	+	4.00005i	−0.0657292	+	0.350828i
$131$	1.78705	−	3.09527i	0.156136	−	0.270435i	−0.777336	−	0.629085i	$-0.783430\pi$
$131$	1.78705	−	3.09527i	0.156136	−	0.270435i	0.933472	+	0.358650i	$0.116763\pi$
$132$		0			0
$133$	−0.471193	+	1.40779i	−0.0408576	+	0.122071i
$134$	−9.86145	−	17.0805i	−0.851900	−	1.47553i
$135$		0			0
$136$	0.137647	−	0.238412i	0.0118031	−	0.0204437i
$137$	−9.62880	+	16.6776i	−0.822644	+	1.42486i	0.0810628	+	0.996709i	$0.474169\pi$
$137$	−9.62880	+	16.6776i	−0.822644	+	1.42486i	−0.903707	+	0.428152i	$0.859165\pi$
$138$		0			0
$139$	−4.83155	−	8.36849i	−0.409807	−	0.709806i	0.585061	−	0.810989i	$-0.301070\pi$
$139$	−4.83155	−	8.36849i	−0.409807	−	0.709806i	−0.994868	+	0.101183i	$0.967737\pi$
$140$	−3.16458	+	0.643521i	−0.267456	+	0.0543875i
$141$		0			0
$142$	5.93568	−	10.2809i	0.498111	−	0.862753i
$143$	3.11946	−	16.6501i	0.260863	−	1.39235i
$144$		0			0
$145$	1.14918	+	1.99044i	0.0954344	+	0.165297i
$146$	−14.8901	+	25.7903i	−1.23231	+	2.13442i
$147$		0			0
$148$	−19.5584			−1.60769
$149$	−7.12496			−0.583699			−0.291850	−	0.956464i	$-0.594271\pi$
$149$	−7.12496			−0.583699			−0.291850	+	0.956464i	$0.594271\pi$
$150$		0			0
$151$	9.82744	+	17.0216i	0.799746	+	1.38520i	0.919781	+	0.392431i	$0.128366\pi$
$151$	9.82744	+	17.0216i	0.799746	+	1.38520i	−0.120036	+	0.992770i	$0.538301\pi$
$152$	−0.255910			−0.0207570
$153$		0			0
$154$	25.0290	−	5.08968i	2.01689	−	0.410138i
$155$	−0.634282			−0.0509468
$156$		0			0
$157$	2.60509	+	4.51215i	0.207909	+	0.360109i	0.951056	−	0.309020i	$-0.100001\pi$
$157$	2.60509	+	4.51215i	0.207909	+	0.360109i	−0.743147	+	0.669129i	$0.766668\pi$
$158$	30.0445			2.39021
$159$		0			0
$160$	2.22963	+	3.86184i	0.176268	+	0.305305i
$161$	−0.976664	+	0.198606i	−0.0769719	+	0.0156523i
$162$		0			0
$163$	−4.17379			−0.326917			−0.163458	−	0.986550i	$-0.552265\pi$
$163$	−4.17379			−0.326917			−0.163458	+	0.986550i	$0.552265\pi$
$164$	8.79901	+	15.2403i	0.687087	+	1.19007i
$165$		0			0
$166$	15.2821	+	26.4694i	1.18612	+	2.05442i
$167$	2.52335	−	4.37058i	0.195263	−	0.338205i	−0.751724	−	0.659478i	$-0.770777\pi$
$167$	2.52335	−	4.37058i	0.195263	−	0.338205i	0.946987	+	0.321273i	$0.104111\pi$
$168$		0			0
$169$	−12.1183	−	4.70603i	−0.932177	−	0.362002i
$170$	−0.340654	+	0.590030i	−0.0261270	+	0.0452532i
$171$		0			0
$172$	3.32050			0.253186
$173$	−2.73897			−0.208240			−0.104120	−	0.994565i	$-0.533203\pi$
$173$	−2.73897			−0.208240			−0.104120	+	0.994565i	$0.533203\pi$
$174$		0			0
$175$	−12.1811	+	2.47704i	−0.920803	+	0.187247i
$176$	−8.23791	−	14.2685i	−0.620956	−	1.07553i
$177$		0			0
$178$	−9.43489	+	16.3417i	−0.707175	+	1.22486i
$179$	12.6956			0.948917			0.474459	−	0.880278i	$-0.342644\pi$
$179$	12.6956			0.948917			0.474459	+	0.880278i	$0.342644\pi$
$180$		0			0
$181$	7.95691			0.591432			0.295716	−	0.955276i	$-0.404442\pi$
$181$	7.95691			0.591432			0.295716	+	0.955276i	$0.404442\pi$
$182$	−0.302011	−	19.5987i	−0.0223866	−	1.45275i
$183$		0			0
$184$	−0.0859023	−	0.148787i	−0.00633280	−	0.0109687i
$185$	4.83533			0.355500
$186$		0			0
$187$	1.41796	−	2.45597i	0.103691	−	0.179599i
$188$	2.44160	+	4.22897i	0.178072	+	0.308429i
$189$		0			0
$190$	0.633335			0.0459469
$191$	−3.07979			−0.222846			−0.111423	−	0.993773i	$-0.535541\pi$
$191$	−3.07979			−0.222846			−0.111423	+	0.993773i	$0.535541\pi$
$192$		0			0
$193$	−3.39175			−0.244143			−0.122072	−	0.992521i	$-0.538954\pi$
$193$	−3.39175			−0.244143			−0.122072	+	0.992521i	$0.538954\pi$
$194$	−6.47314	+	11.2118i	−0.464744	+	0.804961i
$195$		0			0
$196$	14.3185	−	6.07456i	1.02275	−	0.433897i
$197$	−2.06163	+	3.57085i	−0.146885	+	0.254413i	−0.930075	−	0.367370i	$-0.880258\pi$
$197$	−2.06163	+	3.57085i	−0.146885	+	0.254413i	0.783189	+	0.621783i	$0.213591\pi$
$198$		0			0
$199$	0.574142	−	0.994443i	0.0406998	−	0.0704942i	−0.844958	−	0.534833i	$-0.820375\pi$
$199$	0.574142	−	0.994443i	0.0406998	−	0.0704942i	0.885658	+	0.464339i	$0.153708\pi$
$200$	−1.07138	−	1.85569i	−0.0757583	−	0.131217i
$201$		0			0
$202$	−4.56551	−	7.90769i	−0.321228	−	0.556383i
$203$	−7.33427	−	8.29150i	−0.514765	−	0.581949i
$204$		0			0
$205$	−2.17533	−	3.76778i	−0.151932	−	0.263153i
$206$	34.1675			2.38056
$207$		0			0
$208$	−11.9269	+	4.19742i	−0.826983	+	0.291039i
$209$	−2.63623			−0.182352
$210$		0			0
$211$	−2.28300	+	3.95427i	−0.157168	+	0.272223i	−0.933846	−	0.357674i	$-0.883570\pi$
$211$	−2.28300	+	3.95427i	−0.157168	+	0.272223i	0.776678	+	0.629898i	$0.216903\pi$
$212$	20.1016			1.38058
$213$		0			0
$214$	−18.3613	+	31.8027i	−1.25515	+	2.17399i
$215$	−0.820910			−0.0559856
$216$		0			0
$217$	2.99367	−	0.608768i	0.203224	−	0.0413258i
$218$	10.4334	−	18.0713i	0.706642	−	1.22394i
$219$		0			0
$220$	−2.86729	−	4.96628i	−0.193312	−	0.334827i
$221$	−1.65216	−	1.41665i	−0.111136	−	0.0952941i
$222$		0			0
$223$	8.42312	−	14.5893i	0.564054	−	0.976970i	−0.433083	−	0.901354i	$-0.642574\pi$
$223$	8.42312	−	14.5893i	0.564054	−	0.976970i	0.997137	−	0.0756163i	$-0.0240924\pi$
$224$	−14.2299	−	16.0871i	−0.950773	−	1.07486i
$225$		0			0
$226$	−7.69512	+	13.3283i	−0.511872	+	0.886588i
$227$	−14.2365	+	24.6583i	−0.944909	+	1.63663i	−0.188976	+	0.981982i	$0.560517\pi$
$227$	−14.2365	+	24.6583i	−0.944909	+	1.63663i	−0.755933	+	0.654649i	$0.772816\pi$
$228$		0			0
$229$	−13.1373	+	22.7545i	−0.868137	+	1.50366i	−0.00423787	+	0.999991i	$0.501349\pi$
$229$	−13.1373	+	22.7545i	−0.868137	+	1.50366i	−0.863899	+	0.503666i	$0.831984\pi$
$230$	0.212594	+	0.368223i	0.0140180	+	0.0242799i
$231$		0			0
$232$	0.954114	−	1.65257i	0.0626406	−	0.108497i
$233$	11.0974	−	19.2212i	0.727014	−	1.25922i	−0.231126	−	0.972924i	$-0.574241\pi$
$233$	11.0974	−	19.2212i	0.727014	−	1.25922i	0.958140	−	0.286301i	$-0.0924257\pi$
$234$		0			0
$235$	−0.603622	−	1.04550i	−0.0393760	−	0.0682012i
$236$	9.48394	+	16.4267i	0.617352	+	1.06928i
$237$		0			0
$238$	1.04152	−	3.11176i	0.0675115	−	0.201706i
$239$	−27.3213			−1.76727			−0.883633	−	0.468180i	$-0.844910\pi$
$239$	−27.3213			−1.76727			−0.883633	+	0.468180i	$0.844910\pi$
$240$		0			0
$241$	11.8915	−	20.5967i	0.766001	−	1.32675i	−0.173715	−	0.984796i	$-0.555577\pi$
$241$	11.8915	−	20.5967i	0.766001	−	1.32675i	0.939716	−	0.341957i	$-0.111090\pi$
$242$	11.3766	+	19.7048i	0.731314	+	1.26667i
$243$		0			0
$244$	−8.24820	+	14.2863i	−0.528037	+	0.914586i
$245$	−3.53988	+	1.50178i	−0.226154	+	0.0959452i
$246$		0			0
$247$	−0.372557	+	1.98851i	−0.0237052	+	0.126526i
$248$	0.263308	+	0.456062i	0.0167201	+	0.0289600i
$249$		0			0
$250$	5.47329	+	9.48002i	0.346161	+	0.599569i
$251$	−4.16795	−	7.21910i	−0.263079	−	0.455666i	0.703980	−	0.710220i	$-0.251405\pi$
$251$	−4.16795	−	7.21910i	−0.263079	−	0.455666i	−0.967058	+	0.254554i	$0.918071\pi$
$252$		0			0
$253$	−0.884913	−	1.53271i	−0.0556340	−	0.0963609i
$254$	9.72354			0.610109
$255$		0			0
$256$	−5.94083	+	10.2898i	−0.371302	+	0.643114i
$257$	−6.88712	−	11.9288i	−0.429607	−	0.744101i	0.567231	−	0.823558i	$-0.308015\pi$
$257$	−6.88712	−	11.9288i	−0.429607	−	0.744101i	−0.996838	+	0.0794576i	$0.974681\pi$
$258$		0			0
$259$	−22.8217	+	4.64082i	−1.41807	+	0.288367i
$260$	−4.15128	+	1.46095i	−0.257452	+	0.0906044i
$261$		0			0
$262$	7.34387			0.453706
$263$	9.04564			0.557778			0.278889	−	0.960323i	$-0.410034\pi$
$263$	9.04564			0.557778			0.278889	+	0.960323i	$0.410034\pi$
$264$		0			0
$265$	−4.96960			−0.305280
$266$	−2.98920	+	0.607859i	−0.183280	+	0.0372702i
$267$		0			0
$268$	10.6640	−	18.4706i	0.651408	−	1.12827i
$269$	1.14428	−	1.98196i	0.0697681	−	0.120842i	−0.829031	−	0.559203i	$-0.811107\pi$
$269$	1.14428	−	1.98196i	0.0697681	−	0.120842i	0.898799	+	0.438361i	$0.144441\pi$
$270$		0			0
$271$	−1.99057	−	3.44778i	−0.120919	−	0.209437i	0.799211	−	0.601050i	$-0.205251\pi$
$271$	−1.99057	−	3.44778i	−0.120919	−	0.209437i	−0.920130	+	0.391612i	$0.871917\pi$
$272$	−2.11675			−0.128347
$273$		0			0
$274$	−39.5694			−2.39047
$275$	−11.0367	−	19.1162i	−0.665541	−	1.15275i
$276$		0			0
$277$	4.19999	−	7.27460i	0.252353	−	0.437089i	−0.711820	−	0.702362i	$-0.752129\pi$
$277$	4.19999	−	7.27460i	0.252353	−	0.437089i	0.964173	+	0.265273i	$0.0854622\pi$
$278$	9.92758	−	17.1951i	0.595417	−	1.03129i
$279$		0			0
$280$	−0.439171	−	0.496490i	−0.0262455	−	0.0296709i
$281$	12.9559			0.772884			0.386442	−	0.922314i	$-0.373704\pi$
$281$	12.9559			0.772884			0.386442	+	0.922314i	$0.373704\pi$
$282$		0			0
$283$	25.6051			1.52207			0.761033	−	0.648713i	$-0.224692\pi$
$283$	25.6051			1.52207			0.761033	+	0.648713i	$0.224692\pi$
$284$	12.8375			0.761765
$285$		0			0
$286$	32.8329	−	11.5548i	1.94145	−	0.683251i
$287$	13.8833	+	15.6953i	0.819505	+	0.926463i
$288$		0			0
$289$	8.31783	+	14.4069i	0.489284	+	0.847465i
$290$	−2.36127	+	4.08985i	−0.138659	+	0.240164i
$291$		0			0
$292$	−32.2037			−1.88458
$293$	12.3943	+	21.4675i	0.724081	+	1.25415i	0.959351	+	0.282215i	$0.0910692\pi$
$293$	12.3943	+	21.4675i	0.724081	+	1.25415i	−0.235270	+	0.971930i	$0.575597\pi$
$294$		0			0
$295$	−2.34466	−	4.06107i	−0.136511	−	0.236445i
$296$	−2.00728	−	3.47670i	−0.116671	−	0.202079i
$297$		0			0
$298$	−7.31997	−	12.6786i	−0.424035	−	0.734450i
$299$	−1.28118	+	0.450885i	−0.0740928	+	0.0260753i
$300$		0			0
$301$	3.87451	−	0.787888i	0.223323	−	0.0454131i
$302$	−20.1929	+	34.9751i	−1.16197	+	2.01259i
$303$		0			0
$304$	0.983851	+	1.70408i	0.0564277	+	0.0977357i
$305$	2.03916	−	3.53192i	0.116762	−	0.202237i
$306$		0			0
$307$	−25.2086			−1.43873			−0.719365	−	0.694632i	$-0.755567\pi$
$307$	−25.2086			−1.43873			−0.719365	+	0.694632i	$0.755567\pi$
$308$	18.2995	+	20.6878i	1.04271	+	1.17880i
$309$		0			0
$310$	−0.651643	−	1.12868i	−0.0370108	−	0.0641046i
$311$	2.06640	+	3.57911i	0.117175	+	0.202953i	0.918647	−	0.395079i	$-0.129283\pi$
$311$	2.06640	+	3.57911i	0.117175	+	0.202953i	−0.801472	+	0.598032i	$0.795950\pi$
$312$		0			0
$313$	15.0691	−	26.1005i	0.851758	−	1.47529i	−0.0278626	−	0.999612i	$-0.508870\pi$
$313$	15.0691	−	26.1005i	0.851758	−	1.47529i	0.879620	−	0.475676i	$-0.157797\pi$
$314$	−5.35279	+	9.27131i	−0.302076	+	0.523210i
$315$		0			0
$316$	16.2448	+	28.1369i	0.913843	+	1.58282i
$317$	5.76330	−	9.98233i	0.323699	−	0.560663i	−0.657549	−	0.753412i	$-0.728407\pi$
$317$	5.76330	−	9.98233i	0.323699	−	0.560663i	0.981248	+	0.192748i	$0.0617401\pi$
$318$		0			0
$319$	9.82870	−	17.0238i	0.550302	−	0.953150i
$320$	−2.65495	+	4.59850i	−0.148416	+	0.257064i
$321$		0			0
$322$	−1.35681	−	1.53389i	−0.0756119	−	0.0854804i
$323$	−0.169346	+	0.293316i	−0.00942268	+	0.0163206i
$324$		0			0
$325$	−15.9791	+	5.62349i	−0.886361	+	0.311935i
$326$	−4.28803	−	7.42709i	−0.237492	−	0.411348i
$327$		0			0
$328$	−1.80608	+	3.12822i	−0.0997239	+	0.172727i
$329$	3.85241	+	4.35521i	0.212390	+	0.240110i
$330$		0			0
$331$	−1.13539			−0.0624067			−0.0312033	−	0.999513i	$-0.509934\pi$
$331$	−1.13539			−0.0624067			−0.0312033	+	0.999513i	$0.509934\pi$
$332$	−16.5258	+	28.6236i	−0.906973	+	1.57092i
$333$		0			0
$334$	10.3697			0.567404
$335$	−2.63640	+	4.56639i	−0.144042	+	0.249488i
$336$		0			0
$337$	23.3181			1.27022			0.635110	−	0.772421i	$-0.280955\pi$
$337$	23.3181			1.27022			0.635110	+	0.772421i	$0.280955\pi$
$338$	−4.07581	−	26.3989i	−0.221695	−	1.43591i
$339$		0			0
$340$	−0.736755			−0.0399562
$341$	2.71244	+	4.69808i	0.146887	+	0.254415i
$342$		0			0
$343$	15.2661	−	10.4856i	0.824291	−	0.566167i
$344$	0.340782	+	0.590252i	0.0183737	+	0.0318242i
$345$		0			0
$346$	−2.81394	−	4.87389i	−0.151279	−	0.262022i
$347$	1.26911	−	2.19816i	0.0681294	−	0.118004i	−0.829948	−	0.557840i	$-0.811630\pi$
$347$	1.26911	−	2.19816i	0.0681294	−	0.118004i	0.898078	+	0.439836i	$0.144964\pi$
$348$		0			0
$349$	−5.34353	+	9.25527i	−0.286033	+	0.495423i	−0.972859	−	0.231398i	$-0.925670\pi$
$349$	−5.34353	+	9.25527i	−0.286033	+	0.495423i	0.686826	+	0.726822i	$0.259003\pi$
$350$	−16.9223	−	19.1309i	−0.904534	−	1.02259i
$351$		0			0
$352$	19.0695	−	33.0294i	1.01641	−	1.76047i
$353$	−22.2407			−1.18375			−0.591875	−	0.806030i	$-0.701612\pi$
$353$	−22.2407			−1.18375			−0.591875	+	0.806030i	$0.701612\pi$
$354$		0			0
$355$	−3.17374			−0.168445
$356$	−20.4055			−1.08149
$357$		0			0
$358$	13.0431	+	22.5914i	0.689351	+	1.19399i
$359$	−8.38142	+	14.5170i	−0.442354	+	0.766180i	−0.997864	−	0.0653300i	$-0.979190\pi$
$359$	−8.38142	+	14.5170i	−0.442354	+	0.766180i	0.555509	+	0.831510i	$0.312523\pi$
$360$		0			0
$361$	−18.6852			−0.983429
$362$	8.17470	+	14.1590i	0.429653	+	0.744180i
$363$		0			0
$364$	18.1910	−	10.8797i	0.953465	−	0.570250i
$365$	7.96155			0.416726
$366$		0			0
$367$	−4.68194			−0.244395			−0.122198	−	0.992506i	$-0.538994\pi$
$367$	−4.68194			−0.244395			−0.122198	+	0.992506i	$0.538994\pi$
$368$	−0.660506	+	1.14403i	−0.0344312	+	0.0596366i
$369$		0			0
$370$	4.96767	+	8.60426i	0.258257	+	0.447314i
$371$	23.4554	−	4.76970i	1.21775	−	0.247630i
$372$		0			0
$373$	−6.76172			−0.350109			−0.175054	−	0.984559i	$-0.556010\pi$
$373$	−6.76172			−0.350109			−0.175054	+	0.984559i	$0.556010\pi$
$374$	5.82707			0.301311
$375$		0			0
$376$	−0.501160	+	0.868034i	−0.0258453	+	0.0447655i
$377$	−11.4521	−	9.81963i	−0.589811	−	0.505737i
$378$		0			0
$379$	9.62497	−	16.6709i	0.494402	−	0.856329i	−0.505578	−	0.862781i	$-0.668721\pi$
$379$	9.62497	−	16.6709i	0.494402	−	0.856329i	0.999979	+	0.00645256i	$0.00205393\pi$
$380$	0.342439	+	0.593122i	0.0175667	+	0.0304265i
$381$		0			0
$382$	−3.16408	−	5.48036i	−0.161889	−	0.280399i
$383$	−13.4851			−0.689055			−0.344528	−	0.938776i	$-0.611961\pi$
$383$	−13.4851			−0.689055			−0.344528	+	0.938776i	$0.611961\pi$
$384$		0			0
$385$	−4.52408	−	5.11454i	−0.230568	−	0.260661i
$386$	−3.48458	−	6.03547i	−0.177361	−	0.307198i
$387$		0			0
$388$	−13.9999			−0.710737
$389$	−16.4229	−	28.4453i	−0.832675	−	1.44224i	−0.895909	−	0.444238i	$-0.853475\pi$
$389$	−16.4229	−	28.4453i	−0.832675	−	1.44224i	0.0632336	−	0.997999i	$-0.479859\pi$
$390$		0			0
$391$	−0.227380			−0.0114991
$392$	2.54931	+	1.92182i	0.128760	+	0.0970665i
$393$		0			0
$394$	−8.47225			−0.426826
$395$	−4.01612	−	6.95612i	−0.202073	−	0.350000i
$396$		0			0
$397$	−26.6109			−1.33556			−0.667781	−	0.744358i	$-0.732756\pi$
$397$	−26.6109			−1.33556			−0.667781	+	0.744358i	$0.732756\pi$
$398$	2.35943			0.118267
$399$		0			0
$400$	−8.23791	+	14.2685i	−0.411895	+	0.713424i
$401$	−11.5558	−	20.0153i	−0.577071	−	0.999517i	−0.995813	−	0.0914115i	$-0.970862\pi$
$401$	−11.5558	−	20.0153i	−0.577071	−	0.999517i	0.418742	−	0.908105i	$-0.362471\pi$
$402$		0			0
$403$	3.92709	−	1.38205i	0.195622	−	0.0688450i
$404$	4.93706	−	8.55124i	0.245628	−	0.425440i
$405$		0			0
$406$	7.21937	−	21.5695i	0.358291	−	1.07047i
$407$	−20.6777	−	35.8149i	−1.02496	−	1.77528i
$408$		0			0
$409$	3.62073	−	6.27129i	0.179034	−	0.310096i	−0.762516	−	0.646969i	$-0.776036\pi$
$409$	3.62073	−	6.27129i	0.179034	−	0.310096i	0.941550	+	0.336874i	$0.109370\pi$
$410$	4.46974	−	7.74182i	0.220745	−	0.382341i
$411$		0			0
$412$	18.4741	+	31.9981i	0.910154	+	1.57643i
$413$	14.9640	+	16.9170i	0.736330	+	0.832433i
$414$		0			0
$415$	4.08559	−	7.07645i	0.200554	−	0.347369i
$416$	−22.2192	−	19.0520i	−1.08939	−	0.934099i
$417$		0			0
$418$	−2.70839	−	4.69106i	−0.132471	−	0.229447i
$419$	17.5550	−	30.4062i	0.857618	−	1.48544i	−0.0165759	−	0.999863i	$-0.505277\pi$
$419$	17.5550	−	30.4062i	0.857618	−	1.48544i	0.874194	−	0.485576i	$-0.161390\pi$
$420$		0			0
$421$	25.2731			1.23174			0.615868	−	0.787849i	$-0.288805\pi$
$421$	25.2731			1.23174			0.615868	+	0.787849i	$0.288805\pi$
$422$	−9.38195			−0.456706
$423$		0			0
$424$	2.06302	+	3.57325i	0.100189	+	0.173532i
$425$	−2.83592			−0.137562
$426$		0			0
$427$	−6.23452	+	18.6270i	−0.301710	+	0.901425i
$428$	−39.7112			−1.91951
$429$		0			0
$430$	−0.843379	−	1.46077i	−0.0406713	−	0.0704448i
$431$	−17.5693			−0.846285			−0.423142	−	0.906063i	$-0.639073\pi$
$431$	−17.5693			−0.846285			−0.423142	+	0.906063i	$0.639073\pi$
$432$		0			0
$433$	−3.02011	−	5.23098i	−0.145137	−	0.251385i	0.784287	−	0.620398i	$-0.213029\pi$
$433$	−3.02011	−	5.23098i	−0.145137	−	0.251385i	−0.929424	+	0.369013i	$0.879696\pi$
$434$	4.15889	+	4.70169i	0.199633	+	0.225688i
$435$		0			0
$436$	22.5651			1.08067
$437$	0.105685	+	0.183052i	0.00505559	+	0.00875654i
$438$		0			0
$439$	−12.4282	−	21.5262i	−0.593164	−	1.02739i	−0.993803	−	0.111155i	$-0.964545\pi$
$439$	−12.4282	−	21.5262i	−0.593164	−	1.02739i	0.400639	−	0.916236i	$-0.368788\pi$
$440$	0.588537	−	1.01938i	0.0280574	−	0.0485968i
$441$		0			0
$442$	0.823492	−	4.39537i	0.0391695	−	0.209066i
$443$	−15.8094	+	27.3826i	−0.751126	+	1.30099i	0.196152	+	0.980574i	$0.437155\pi$
$443$	−15.8094	+	27.3826i	−0.751126	+	1.30099i	−0.947278	+	0.320414i	$0.896178\pi$
$444$		0			0
$445$	5.04473			0.239143
$446$	34.6147			1.63905
$447$		0			0
$448$	8.11725	−	24.2521i	0.383504	−	1.14580i
$449$	2.63384	+	4.56194i	0.124298	+	0.215291i	0.921459	−	0.388477i	$-0.126999\pi$
$449$	2.63384	+	4.56194i	0.124298	+	0.215291i	−0.797160	+	0.603768i	$0.793665\pi$
$450$		0			0
$451$	−18.6051	+	32.2250i	−0.876080	+	1.51742i
$452$	−16.6427			−0.782809
$453$		0			0
$454$	−58.5046			−2.74576
$455$	−4.49725	+	2.68972i	−0.210834	+	0.126096i
$456$		0			0
$457$	9.24474	+	16.0124i	0.432451	+	0.749027i	0.997084	−	0.0763154i	$-0.0243156\pi$
$457$	9.24474	+	16.0124i	0.432451	+	0.749027i	−0.564633	+	0.825342i	$0.690982\pi$
$458$	−53.9875			−2.52267
$459$		0			0
$460$	−0.229895	+	0.398191i	−0.0107189	+	0.0185657i
$461$	−4.79101	−	8.29827i	−0.223140	−	0.386489i	0.732620	−	0.680638i	$-0.238297\pi$
$461$	−4.79101	−	8.29827i	−0.223140	−	0.386489i	−0.955760	+	0.294149i	$0.904964\pi$
$462$		0			0
$463$	2.22178			0.103255			0.0516275	−	0.998666i	$-0.483559\pi$
$463$	2.22178			0.103255			0.0516275	+	0.998666i	$0.483559\pi$
$464$	−14.6724			−0.681151
$465$		0			0
$466$	45.6045			2.11259
$467$	−6.76331	+	11.7144i	−0.312969	+	0.542078i	−0.979004	−	0.203843i	$-0.934657\pi$
$467$	−6.76331	+	11.7144i	−0.312969	+	0.542078i	0.666035	+	0.745921i	$0.267990\pi$
$468$		0			0
$469$	8.06055	−	24.0827i	0.372202	−	1.11204i
$470$	1.24029	−	2.14824i	0.0572102	−	0.0990910i
$471$		0			0
$472$	−1.94667	+	3.37172i	−0.0896025	+	0.155196i
$473$	3.51053	+	6.08041i	0.161414	+	0.279578i
$474$		0			0
$475$	1.31812	+	2.28304i	0.0604793	+	0.104753i
$476$	3.47732	−	0.707119i	0.159383	−	0.0324107i
$477$		0			0
$478$	−28.0691	−	48.6171i	−1.28385	−	2.22369i
$479$	14.5871			0.666501			0.333251	−	0.942838i	$-0.391854\pi$
$479$	14.5871			0.666501			0.333251	+	0.942838i	$0.391854\pi$
$480$		0			0
$481$	−29.9374	+	10.5358i	−1.36503	+	0.480392i
$482$	48.8681			2.22588
$483$		0			0
$484$	−12.3024	+	21.3085i	−0.559202	+	0.968567i
$485$	3.46111			0.157161
$486$		0			0
$487$	0.750628	−	1.30013i	0.0340142	−	0.0589143i	−0.848517	−	0.529168i	$-0.822504\pi$
$487$	0.750628	−	1.30013i	0.0340142	−	0.0589143i	0.882531	+	0.470254i	$0.155838\pi$
$488$	−3.38604			−0.153279
$489$		0			0
$490$	−6.30912	−	4.75618i	−0.285017	−	0.214862i
$491$	−14.1980	+	24.5917i	−0.640748	+	1.10981i	0.344518	+	0.938780i	$0.388042\pi$
$491$	−14.1980	+	24.5917i	−0.640748	+	1.10981i	−0.985266	+	0.171028i	$0.945291\pi$
$492$		0			0
$493$	−1.26275	−	2.18715i	−0.0568715	−	0.0985044i
$494$	−3.92123	+	1.37999i	−0.176424	+	0.0620886i
$495$		0			0
$496$	2.02458	−	3.50668i	0.0909064	−	0.157455i
$497$	14.9794	−	3.04607i	0.671916	−	0.136635i
$498$		0			0
$499$	−10.5569	+	18.2851i	−0.472593	+	0.818554i	−0.999508	−	0.0313633i	$-0.990015\pi$
$499$	−10.5569	+	18.2851i	−0.472593	+	0.818554i	0.526915	+	0.849918i	$0.323348\pi$
$500$	−5.91873	+	10.2515i	−0.264694	+	0.458463i
$501$		0			0
$502$	8.56406	−	14.8334i	0.382233	−	0.662046i
$503$	−14.2618	−	24.7022i	−0.635903	−	1.10142i	−0.986323	−	0.164824i	$-0.947294\pi$
$503$	−14.2618	−	24.7022i	−0.635903	−	1.10142i	0.350420	−	0.936593i	$-0.386039\pi$
$504$		0			0
$505$	−1.22056	+	2.11408i	−0.0543143	+	0.0940752i
$506$	1.81827	−	3.14933i	0.0808318	−	0.140005i
$507$		0			0
$508$	5.25744	+	9.10615i	0.233261	+	0.404020i
$509$	17.1295	+	29.6691i	0.759250	+	1.31506i	0.943234	+	0.332130i	$0.107767\pi$
$509$	17.1295	+	29.6691i	0.759250	+	1.31506i	−0.183984	+	0.982929i	$0.558900\pi$
$510$		0			0
$511$	−37.5768	+	7.64129i	−1.66230	+	0.338031i
$512$	−31.6661			−1.39946
$513$		0			0
$514$	14.1513	−	24.5107i	0.624185	−	1.08112i
$515$	−4.56725	−	7.91071i	−0.201257	−	0.348587i
$516$		0			0
$517$	−5.16264	+	8.94196i	−0.227053	+	0.393267i
$518$	−31.7045	−	35.8424i	−1.39302	−	1.57482i
$519$		0			0
$520$	−0.685743	−	0.587994i	−0.0300718	−	0.0257852i
$521$	17.2434	+	29.8665i	0.755448	+	1.30847i	0.945151	+	0.326633i	$0.105914\pi$
$521$	17.2434	+	29.8665i	0.755448	+	1.30847i	−0.189703	+	0.981841i	$0.560753\pi$
$522$		0			0
$523$	−15.6948	−	27.1842i	−0.686285	−	1.18868i	−0.973031	−	0.230674i	$-0.925907\pi$
$523$	−15.6948	−	27.1842i	−0.686285	−	1.18868i	0.286746	−	0.958007i	$-0.407427\pi$
$524$	3.97077	+	6.87757i	0.173464	+	0.300448i
$525$		0			0
$526$	9.29323	+	16.0963i	0.405204	+	0.701834i
$527$	0.696966			0.0303603
$528$		0			0
$529$	11.4290	−	19.7957i	0.496915	−	0.860682i
$530$	−5.10562	−	8.84320i	−0.221774	−	0.384124i
$531$		0			0
$532$	−2.18550	−	2.47074i	−0.0947534	−	0.107120i
$533$	21.6780	+	18.5879i	0.938980	+	0.805133i
$534$		0			0
$535$	9.81757			0.424451
$536$	4.37777			0.189091
$537$		0			0
$538$	4.70241			0.202735
$539$	26.2615	+	19.7974i	1.13116	+	0.852734i
$540$		0			0
$541$	−4.55013	+	7.88106i	−0.195626	+	0.338833i	−0.947105	−	0.320923i	$-0.896007\pi$
$541$	−4.55013	+	7.88106i	−0.195626	+	0.338833i	0.751480	+	0.659756i	$0.229340\pi$
$542$	4.09012	−	7.08429i	0.175685	−	0.304296i
$543$		0			0
$544$	−2.44998	−	4.24349i	−0.105042	−	0.181938i
$545$	−5.57865			−0.238963
$546$		0			0
$547$	−35.9950			−1.53903			−0.769517	−	0.638626i	$-0.779503\pi$
$547$	−35.9950			−1.53903			−0.769517	+	0.638626i	$0.779503\pi$
$548$	−21.3948	−	37.0570i	−0.913943	−	1.58299i
$549$		0			0
$550$	22.6777	−	39.2789i	0.966979	−	1.67486i
$551$	−1.17384	+	2.03315i	−0.0500072	+	0.0866150i
$552$		0			0
$553$	25.6315	+	28.9768i	1.08996	+	1.23222i
$554$	17.2598			0.733299
$555$		0			0
$556$	21.4710			0.910575
$557$	15.9142			0.674304			0.337152	−	0.941450i	$-0.390536\pi$
$557$	15.9142			0.674304			0.337152	+	0.941450i	$0.390536\pi$
$558$		0			0
$559$	5.08257	−	1.78870i	0.214970	−	0.0756540i
$560$	−1.61767	+	4.83316i	−0.0683592	+	0.204238i
$561$		0			0
$562$	13.3105	+	23.0545i	0.561470	+	0.972495i
$563$	−12.6124	+	21.8453i	−0.531548	+	0.920668i	0.467774	+	0.883848i	$0.345056\pi$
$563$	−12.6124	+	21.8453i	−0.531548	+	0.920668i	−0.999322	+	0.0368201i	$0.988277\pi$
$564$		0			0
$565$	4.11449			0.173098
$566$	26.3059	+	45.5632i	1.10572	+	1.91517i
$567$		0			0
$568$	1.31751	+	2.28199i	0.0552813	+	0.0957501i
$569$	17.0842	+	29.5908i	0.716208	+	1.24051i	0.962492	+	0.271311i	$0.0874573\pi$
$569$	17.0842	+	29.5908i	0.716208	+	1.24051i	−0.246283	+	0.969198i	$0.579209\pi$
$570$		0			0
$571$	−7.15867	−	12.3992i	−0.299581	−	0.518889i	0.676459	−	0.736480i	$-0.263514\pi$
$571$	−7.15867	−	12.3992i	−0.299581	−	0.518889i	−0.976040	+	0.217591i	$0.930180\pi$
$572$	28.5737	+	24.5006i	1.19472	+	1.02442i
$573$		0			0
$574$	−13.6658	+	40.8296i	−0.570399	+	1.70420i
$575$	−0.884913	+	1.53271i	−0.0369034	+	0.0639186i
$576$		0			0
$577$	5.34662	+	9.26061i	0.222583	+	0.385524i	0.955591	−	0.294695i	$-0.0952180\pi$
$577$	5.34662	+	9.26061i	0.222583	+	0.385524i	−0.733009	+	0.680219i	$0.761885\pi$
$578$	−17.0910	+	29.6025i	−0.710891	+	1.23130i
$579$		0			0
$580$	−5.10688			−0.212052
$581$	−12.4913	+	37.3205i	−0.518226	+	1.54832i
$582$		0			0
$583$	21.2519	+	36.8095i	0.880166	+	1.52449i
$584$	−3.30505	−	5.72452i	−0.136764	−	0.236882i
$585$		0			0
$586$	−25.4670	+	44.1102i	−1.05203	+	1.82217i
$587$	21.3592	−	36.9951i	0.881587	−	1.52695i	0.0320103	−	0.999488i	$-0.489809\pi$
$587$	21.3592	−	36.9951i	0.881587	−	1.52695i	0.849576	−	0.527465i	$-0.176858\pi$
$588$		0			0
$589$	−0.323945	−	0.561090i	−0.0133479	−	0.0231193i
$590$	4.81767	−	8.34446i	0.198341	−	0.343536i
$591$		0			0
$592$	−15.4340	+	26.7325i	−0.634334	+	1.09870i
$593$	−14.0922	+	24.4084i	−0.578697	+	1.00233i	0.416932	+	0.908938i	$0.363105\pi$
$593$	−14.0922	+	24.4084i	−0.578697	+	1.00233i	−0.995629	+	0.0933948i	$0.970228\pi$
$594$		0			0
$595$	−0.859679	+	0.174817i	−0.0352434	+	0.00716680i
$596$	7.91570	−	13.7104i	0.324240	−	0.561599i
$597$		0			0
$598$	−2.11858	−	1.81659i	−0.0866353	−	0.0742859i
$599$	−15.7857	−	27.3417i	−0.644987	−	1.11715i	−0.984304	−	0.176479i	$-0.943529\pi$
$599$	−15.7857	−	27.3417i	−0.644987	−	1.11715i	0.339317	−	0.940672i	$-0.389804\pi$
$600$		0			0
$601$	16.0445	−	27.7899i	0.654469	−	1.13357i	−0.327558	−	0.944831i	$-0.606226\pi$
$601$	16.0445	−	27.7899i	0.654469	−	1.13357i	0.982027	−	0.188742i	$-0.0604409\pi$
$602$	5.38258	+	6.08508i	0.219377	+	0.248009i
$603$		0			0
$604$	−43.6724			−1.77701
$605$	3.04147	−	5.26797i	0.123653	−	0.214174i
$606$		0			0
$607$	−18.6665			−0.757649			−0.378825	−	0.925468i	$-0.623672\pi$
$607$	−18.6665			−0.757649			−0.378825	+	0.925468i	$0.623672\pi$
$608$	−2.27747	+	3.94469i	−0.0923636	+	0.159978i
$609$		0			0
$610$	8.37988			0.339291
$611$	6.01534	+	5.15788i	0.243354	+	0.208666i
$612$		0			0
$613$	17.9314			0.724241			0.362121	−	0.932131i	$-0.382053\pi$
$613$	17.9314			0.724241			0.362121	+	0.932131i	$0.382053\pi$
$614$	−25.8986	−	44.8576i	−1.04518	−	1.81031i
$615$		0			0
$616$	−1.79939	+	5.37609i	−0.0724997	+	0.216609i
$617$	15.8059	+	27.3765i	0.636320	+	1.10214i	0.986234	+	0.165356i	$0.0528774\pi$
$617$	15.8059	+	27.3765i	0.636320	+	1.10214i	−0.349914	+	0.936782i	$0.613789\pi$
$618$		0			0
$619$	16.3184	+	28.2644i	0.655894	+	1.13604i	0.981669	+	0.190594i	$0.0610413\pi$
$619$	16.3184	+	28.2644i	0.655894	+	1.13604i	−0.325775	+	0.945447i	$0.605625\pi$
$620$	0.704676	−	1.22053i	0.0283005	−	0.0490178i
$621$		0			0
$622$	−4.24592	+	7.35415i	−0.170246	+	0.294875i
$623$	−23.8100	+	4.84180i	−0.953929	+	0.193983i
$624$		0			0
$625$	−10.2824	+	17.8096i	−0.411294	+	0.712382i
$626$	61.9264			2.47508
$627$		0			0
$628$	−11.5768			−0.461966
$629$	−5.31319			−0.211851
$630$		0			0
$631$	12.7985	+	22.1676i	0.509500	+	0.882480i	0.999939	+	0.0110045i	$0.00350290\pi$
$631$	12.7985	+	22.1676i	0.509500	+	0.882480i	−0.490440	+	0.871475i	$0.663164\pi$
$632$	−3.33440	+	5.77535i	−0.132635	+	0.229731i
$633$		0			0
$634$	23.6842			0.940619
$635$	−1.29977	−	2.25126i	−0.0515797	−	0.0893387i
$636$		0			0
$637$	18.6445	−	17.0112i	0.738722	−	0.674010i
$638$	40.3909			1.59909
$639$		0			0
$640$	−1.99193			−0.0787381
$641$	21.6208	−	37.4483i	0.853969	−	1.47912i	−0.0236292	−	0.999721i	$-0.507522\pi$
$641$	21.6208	−	37.4483i	0.853969	−	1.47912i	0.877598	−	0.479397i	$-0.159145\pi$
$642$		0			0
$643$	2.25709	+	3.90939i	0.0890108	+	0.154171i	0.907093	−	0.420930i	$-0.138296\pi$
$643$	2.25709	+	3.90939i	0.0890108	+	0.154171i	−0.818082	+	0.575101i	$0.804963\pi$
$644$	0.702883	−	2.10002i	0.0276975	−	0.0827524i
$645$		0			0
$646$	−0.695926			−0.0273808
$647$	11.4404			0.449769			0.224884	−	0.974385i	$-0.427800\pi$
$647$	11.4404			0.449769			0.224884	+	0.974385i	$0.427800\pi$
$648$		0			0
$649$	−20.0534	+	34.7334i	−0.787163	+	1.36341i
$650$	−26.4232	−	22.6567i	−1.03640	−	0.888670i
$651$		0			0
$652$	4.63701	−	8.03153i	0.181599	−	0.314539i
$653$	−10.8757	−	18.8373i	−0.425600	−	0.737162i	0.570876	−	0.821036i	$-0.306604\pi$
$653$	−10.8757	−	18.8373i	−0.425600	−	0.737162i	−0.996476	+	0.0838748i	$0.973270\pi$
$654$		0			0
$655$	−0.981671	−	1.70030i	−0.0383571	−	0.0664364i
$656$	27.7740			1.08439
$657$		0			0
$658$	−3.79206	+	11.3296i	−0.147830	+	0.441675i
$659$	−3.28320	−	5.68668i	−0.127895	−	0.221521i	0.794966	−	0.606655i	$-0.207489\pi$
$659$	−3.28320	−	5.68668i	−0.127895	−	0.221521i	−0.922861	+	0.385133i	$0.874156\pi$
$660$		0			0
$661$	−46.1554			−1.79524			−0.897619	−	0.440772i	$-0.854705\pi$
$661$	−46.1554			−1.79524			−0.897619	+	0.440772i	$0.854705\pi$
$662$	−1.16647	−	2.02038i	−0.0453360	−	0.0785243i
$663$		0			0
$664$	−6.78416			−0.263276
$665$	0.540309	+	0.610828i	0.0209523	+	0.0236869i
$666$		0			0
$667$	−1.57611			−0.0610271
$668$	5.60680	+	9.71127i	0.216934	+	0.375740i
$669$		0			0
$670$	−10.8343			−0.418564
$671$	−34.8809			−1.34656
$672$		0			0
$673$	−5.50174	+	9.52930i	−0.212077	+	0.367327i	−0.952364	−	0.304963i	$-0.901356\pi$
$673$	−5.50174	+	9.52930i	−0.212077	+	0.367327i	0.740288	+	0.672290i	$0.234689\pi$
$674$	23.9564	+	41.4937i	0.922766	+	1.59828i
$675$		0			0
$676$	22.5189	−	18.0907i	0.866112	−	0.695795i
$677$	11.0575	−	19.1522i	0.424976	−	0.736080i	−0.571442	−	0.820642i	$-0.693616\pi$
$677$	11.0575	−	19.1522i	0.424976	−	0.736080i	0.996418	+	0.0845623i	$0.0269492\pi$
$678$		0			0
$679$	−16.3357	+	3.32189i	−0.626907	+	0.127482i
$680$	−0.0756129	−	0.130965i	−0.00289962	−	0.00502229i
$681$		0			0
$682$	−5.57336	+	9.65334i	−0.213415	+	0.369645i
$683$	−4.23809	+	7.34059i	−0.162166	+	0.280880i	−0.935645	−	0.352942i	$-0.885181\pi$
$683$	−4.23809	+	7.34059i	−0.162166	+	0.280880i	0.773479	+	0.633822i	$0.218515\pi$
$684$		0			0
$685$	5.28933	+	9.16139i	0.202095	+	0.350039i
$686$	34.3425	+	16.3928i	1.31120	+	0.625880i
$687$		0			0
$688$	2.62028	−	4.53847i	0.0998974	−	0.173027i
$689$	30.7688	−	10.8284i	1.17220	−	0.412529i
$690$		0			0
$691$	−0.959714	−	1.66227i	−0.0365092	−	0.0632359i	0.847193	−	0.531285i	$-0.178291\pi$
$691$	−0.959714	−	1.66227i	−0.0365092	−	0.0632359i	−0.883703	+	0.468049i	$0.844957\pi$
$692$	3.04295	−	5.27055i	0.115676	−	0.200356i
$693$		0			0
$694$	5.21539			0.197973
$695$	−5.30817			−0.201350
$696$		0			0
$697$	2.39031	+	4.14014i	0.0905395	+	0.156819i
$698$	−21.9592			−0.831166
$699$		0			0
$700$	8.76645	−	26.1917i	0.331341	−	0.989954i
$701$	18.1080			0.683929			0.341965	−	0.939713i	$-0.388908\pi$
$701$	18.1080			0.683929			0.341965	+	0.939713i	$0.388908\pi$
$702$		0			0
$703$	2.46953	+	4.27736i	0.0931403	+	0.161324i
$704$	45.4143			1.71162
$705$		0			0
$706$	−22.8494	−	39.5763i	−0.859948	−	1.48947i
$707$	3.73175	−	11.1494i	0.140347	−	0.419318i
$708$		0			0
$709$	−28.3768			−1.06571			−0.532857	−	0.846205i	$-0.678882\pi$
$709$	−28.3768			−1.06571			−0.532857	+	0.846205i	$0.678882\pi$
$710$	−3.26061	−	5.64754i	−0.122368	−	0.211948i
$711$		0			0
$712$	−2.09421	−	3.62727i	−0.0784837	−	0.135938i
$713$	0.217480	−	0.376686i	0.00814468	−	0.0141070i
$714$		0			0
$715$	−7.06411	−	6.05715i	−0.264183	−	0.226525i
$716$	−14.1046	+	24.4299i	−0.527115	+	0.912990i
$717$		0			0
$718$	−34.4433			−1.28541
$719$	−44.3482			−1.65391			−0.826955	−	0.562269i	$-0.809929\pi$
$719$	−44.3482			−1.65391			−0.826955	+	0.562269i	$0.809929\pi$
$720$		0			0
$721$	29.1489	+	32.9533i	1.08556	+	1.22724i
$722$	−19.1966	−	33.2495i	−0.714423	−	1.23742i
$723$		0			0
$724$	−8.83998	+	15.3113i	−0.328535	+	0.569040i
$725$	−19.6574			−0.730058
$726$		0			0
$727$	24.1298			0.894924			0.447462	−	0.894303i	$-0.352328\pi$
$727$	24.1298			0.894924			0.447462	+	0.894303i	$0.352328\pi$
$728$	3.80090	+	2.11704i	0.140871	+	0.0784628i
$729$		0			0
$730$	8.17946	+	14.1672i	0.302735	+	0.524353i
$731$	0.902038			0.0333631
$732$		0			0
$733$	16.7734	−	29.0524i	0.619540	−	1.07308i	−0.370029	−	0.929020i	$-0.620652\pi$
$733$	16.7734	−	29.0524i	0.619540	−	1.07308i	0.989570	−	0.144055i	$-0.0460143\pi$
$734$	−4.81009	−	8.33132i	−0.177544	−	0.307515i
$735$		0			0
$736$	−3.05795			−0.112717
$737$	45.0972			1.66118
$738$		0			0
$739$	−16.8221			−0.618811			−0.309405	−	0.950930i	$-0.600130\pi$
$739$	−16.8221			−0.618811			−0.309405	+	0.950930i	$0.600130\pi$
$740$	−5.37196	+	9.30451i	−0.197477	+	0.342041i
$741$		0			0
$742$	32.5849	+	36.8377i	1.19623	+	1.35236i
$743$	16.5645	−	28.6906i	0.607694	−	1.05256i	−0.383926	−	0.923364i	$-0.625428\pi$
$743$	16.5645	−	28.6906i	0.607694	−	1.05256i	0.991620	−	0.129192i	$-0.0412385\pi$
$744$		0			0
$745$	−1.95695	+	3.38954i	−0.0716972	+	0.124183i
$746$	−6.94680	−	12.0322i	−0.254340	−	0.440530i
$747$		0			0
$748$	3.15065	+	5.45709i	0.115199	+	0.199531i
$749$	−46.3368	+	9.42265i	−1.69311	+	0.344296i
$750$		0			0
$751$	14.8975	+	25.8032i	0.543616	+	0.941571i	0.998693	+	0.0511187i	$0.0162787\pi$
$751$	14.8975	+	25.8032i	0.543616	+	0.941571i	−0.455076	+	0.890453i	$0.650388\pi$
$752$	7.70687			0.281041
$753$		0			0
$754$	5.70811	−	30.4669i	0.207877	−	1.10954i
$755$	10.7969			0.392939
$756$		0			0
$757$	−11.0742	+	19.1810i	−0.402498	+	0.697147i	−0.994027	−	0.109137i	$-0.965191\pi$
$757$	−11.0742	+	19.1810i	−0.402498	+	0.697147i	0.591529	+	0.806284i	$0.298525\pi$
$758$	39.5537			1.43665
$759$		0			0
$760$	−0.0702887	+	0.121744i	−0.00254964	+	0.00441611i
$761$	−42.8934			−1.55489			−0.777443	−	0.628954i	$-0.783483\pi$
$761$	−42.8934			−1.55489			−0.777443	+	0.628954i	$0.783483\pi$
$762$		0			0
$763$	26.3300	−	5.35424i	0.953210	−	0.193837i
$764$	3.42159	−	5.92637i	0.123789	−	0.214408i
$765$		0			0
$766$	−13.8542	−	23.9961i	−0.500572	−	0.867016i
$767$	23.3655	+	20.0349i	0.843679	+	0.723417i
$768$		0			0
$769$	25.5865	−	44.3171i	0.922671	−	1.59811i	0.127407	−	0.991850i	$-0.459334\pi$
$769$	25.5865	−	44.3171i	0.922671	−	1.59811i	0.795264	−	0.606263i	$-0.207332\pi$
$770$	4.45320	−	13.3049i	0.160482	−	0.479477i
$771$		0			0
$772$	3.76817	−	6.52666i	0.135619	−	0.234900i
$773$	−18.1625	+	31.4583i	−0.653259	+	1.13148i	0.329069	+	0.944306i	$0.393265\pi$
$773$	−18.1625	+	31.4583i	−0.653259	+	1.13148i	−0.982327	+	0.187171i	$0.940068\pi$
$774$		0			0
$775$	2.71244	−	4.69808i	0.0974336	−	0.168760i
$776$	−1.43680	−	2.48862i	−0.0515782	−	0.0893361i
$777$		0			0
$778$	33.7449	−	58.4478i	1.20981	−	2.09546i
$779$	2.22200	−	3.84862i	0.0796115	−	0.137891i
$780$		0			0
$781$	13.5721	+	23.5076i	0.485650	+	0.841170i
$782$	−0.233604	−	0.404614i	−0.00835366	−	0.0144690i
$783$		0			0
$784$	2.99632	−	24.3641i	0.107012	−	0.870146i
$785$	2.86208			0.102152
$786$		0			0
$787$	27.1974	−	47.1072i	0.969482	−	1.67919i	0.272424	−	0.962177i	$-0.412175\pi$
$787$	27.1974	−	47.1072i	0.969482	−	1.67919i	0.697058	−	0.717015i	$-0.254492\pi$
$788$	−4.58087	−	7.93431i	−0.163187	−	0.282648i
$789$		0			0
$790$	8.25208	−	14.2930i	0.293596	−	0.508523i
$791$	−19.4195	+	3.94898i	−0.690478	+	0.140410i
$792$		0			0
$793$	−4.92943	+	26.3107i	−0.175049	+	0.934320i
$794$	−27.3392	−	47.3529i	−0.970233	−	1.68049i
$795$		0			0
$796$	1.27572	+	2.20962i	0.0452168	+	0.0783178i
$797$	−15.9900	−	27.6955i	−0.566396	−	0.981026i	−0.996918	−	0.0784465i	$-0.975004\pi$
$797$	−15.9900	−	27.6955i	−0.566396	−	0.981026i	0.430522	−	0.902580i	$-0.358329\pi$
$798$		0			0
$799$	0.663276	+	1.14883i	0.0234650	+	0.0406426i
$800$	−38.1391			−1.34842
$801$		0			0
$802$	23.7443	−	41.1263i	0.838440	−	1.45222i
$803$	−34.0467	−	58.9705i	−1.20148	−	2.08103i
$804$		0			0
$805$	−0.173770	+	0.519176i	−0.00612458	+	0.0182986i
$806$	6.49388	+	5.56821i	0.228737	+	0.196132i
$807$		0			0
$808$	2.02675			0.0713010
$809$	0.0847866			0.00298094			0.00149047	−	0.999999i	$-0.499526\pi$
$809$	0.0847866			0.00298094			0.00149047	+	0.999999i	$0.499526\pi$
$810$		0			0
$811$	2.81654			0.0989019			0.0494510	−	0.998777i	$-0.484253\pi$
$811$	2.81654			0.0989019			0.0494510	+	0.998777i	$0.484253\pi$
$812$	24.1034	−	4.90146i	0.845863	−	0.172007i
$813$		0			0
$814$	42.4874	−	73.5903i	1.48918	−	2.57934i
$815$	−1.14638	+	1.98559i	−0.0401560	+	0.0695522i
$816$		0			0
$817$	−0.419261	−	0.726182i	−0.0146681	−	0.0254059i
$818$	14.8793			0.520244
$819$		0			0
$820$	9.66701			0.337586
$821$	8.35156	+	14.4653i	0.291471	+	0.504843i	0.974158	−	0.225868i	$-0.0725219\pi$
$821$	8.35156	+	14.4653i	0.291471	+	0.504843i	−0.682687	+	0.730711i	$0.739189\pi$
$822$		0			0
$823$	13.1869	−	22.8405i	0.459668	−	0.796168i	−0.539275	−	0.842130i	$-0.681302\pi$
$823$	13.1869	−	22.8405i	0.459668	−	0.796168i	0.998943	+	0.0459612i	$0.0146351\pi$
$824$	−3.79198	+	6.56790i	−0.132100	+	0.228804i
$825$		0			0
$826$	−14.7296	+	44.0079i	−0.512507	+	1.53123i
$827$	36.8372			1.28095			0.640477	−	0.767977i	$-0.278737\pi$
$827$	36.8372			1.28095			0.640477	+	0.767977i	$0.278737\pi$
$828$		0			0
$829$	24.8055			0.861530			0.430765	−	0.902464i	$-0.358244\pi$
$829$	24.8055			0.861530			0.430765	+	0.902464i	$0.358244\pi$
$830$	16.7897			0.582778
$831$		0			0
$832$	6.41803	−	34.2561i	0.222505	−	1.18762i
$833$	3.88971	−	1.65020i	0.134771	−	0.0571759i
$834$		0			0
$835$	−1.38614	−	2.40086i	−0.0479693	−	0.0830853i
$836$	2.92880	−	5.07284i	0.101295	−	0.175448i
$837$		0			0
$838$	72.1420			2.49211
$839$	11.4460	+	19.8250i	0.395159	+	0.684435i	0.993121	−	0.117089i	$-0.0373562\pi$
$839$	11.4460	+	19.8250i	0.395159	+	0.684435i	−0.597963	+	0.801524i	$0.704023\pi$
$840$		0			0
$841$	5.74711	+	9.95429i	0.198176	+	0.343251i
$842$	25.9649	+	44.9725i	0.894808	+	1.54985i
$843$		0			0
$844$	−5.07274	−	8.78625i	−0.174611	−	0.302435i
$845$	−5.56723	+	4.47245i	−0.191518	+	0.153857i
$846$		0			0
$847$	−9.29899	+	27.7828i	−0.319517	+	0.954628i
$848$	15.8626	−	27.4749i	0.544724	−	0.943490i
$849$		0			0
$850$	−2.91354	−	5.04639i	−0.0999335	−	0.173090i
$851$	−1.65792	+	2.87159i	−0.0568326	+	0.0984370i
$852$		0			0
$853$	0.727097			0.0248953			0.0124477	−	0.999923i	$-0.496038\pi$
$853$	0.727097			0.0248953			0.0124477	+	0.999923i	$0.496038\pi$
$854$	−39.5512	+	8.04279i	−1.35341	+	0.275219i
$855$		0			0
$856$	−4.07554	−	7.05904i	−0.139299	−	0.241273i
$857$	−6.16106	−	10.6713i	−0.210458	−	0.364524i	0.741400	−	0.671063i	$-0.234162\pi$
$857$	−6.16106	−	10.6713i	−0.210458	−	0.364524i	−0.951858	+	0.306540i	$0.900829\pi$
$858$		0			0
$859$	−17.1581	+	29.7187i	−0.585427	+	1.01399i	0.409395	+	0.912357i	$0.365740\pi$
$859$	−17.1581	+	29.7187i	−0.585427	+	1.01399i	−0.994822	+	0.101632i	$0.967594\pi$
$860$	0.912016	−	1.57966i	0.0310995	−	0.0538659i
$861$		0			0
$862$	−18.0502	−	31.2639i	−0.614793	−	1.06485i
$863$	−17.8997	+	31.0032i	−0.609313	+	1.05536i	0.382041	+	0.924146i	$0.375221\pi$
$863$	−17.8997	+	31.0032i	−0.609313	+	1.05536i	−0.991354	+	0.131216i	$0.958112\pi$
$864$		0			0
$865$	−0.752292	+	1.30301i	−0.0255787	+	0.0443036i
$866$	6.20554	−	10.7483i	0.210873	−	0.365242i
$867$		0			0
$868$	−2.15448	+	6.43699i	−0.0731278	+	0.218486i
$869$	−34.3489	+	59.4941i	−1.16521	+	2.01820i
$870$		0			0
$871$	6.37321	−	34.0168i	0.215948	−	1.15262i
$872$	2.31585	+	4.01117i	0.0784245	+	0.135835i
$873$		0			0
$874$	−0.217155	+	0.376124i	−0.00734538	+	0.0127226i
$875$	−4.47376	+	13.3664i	−0.151241	+	0.451865i
$876$		0			0
$877$	29.8080			1.00654			0.503272	−	0.864128i	$-0.332129\pi$
$877$	29.8080			1.00654			0.503272	+	0.864128i	$0.332129\pi$
$878$	25.5367	−	44.2308i	0.861821	−	1.49272i
$879$		0			0
$880$	−9.05056			−0.305094
$881$	−11.3524	+	19.6629i	−0.382470	+	0.662458i	−0.991415	−	0.130755i	$-0.958260\pi$
$881$	−11.3524	+	19.6629i	−0.382470	+	0.662458i	0.608944	+	0.793213i	$0.291593\pi$
$882$		0			0
$883$	51.4418			1.73115			0.865577	−	0.500776i	$-0.166952\pi$
$883$	51.4418			1.73115			0.865577	+	0.500776i	$0.166952\pi$
$884$	4.56154	−	1.60533i	0.153421	−	0.0539932i
$885$		0			0
$886$	−64.9683			−2.18265
$887$	7.40385	+	12.8238i	0.248597	+	0.430583i	0.963137	−	0.269012i	$-0.0866972\pi$
$887$	7.40385	+	12.8238i	0.248597	+	0.430583i	−0.714540	+	0.699595i	$0.753364\pi$
$888$		0			0
$889$	8.29532	+	9.37799i	0.278216	+	0.314528i
$890$	5.18281	+	8.97689i	0.173728	+	0.300906i
$891$		0			0
$892$	18.7159	+	32.4169i	0.626654	+	1.08540i
$893$	0.616573	−	1.06794i	0.0206328	−	0.0357371i
$894$		0			0
$895$	3.48701	−	6.03968i	0.116558	−	0.201884i
$896$	9.40150	−	1.91181i	0.314082	−	0.0638690i
$897$		0			0
$898$	−5.41186	+	9.37361i	−0.180596	+	0.312801i
$899$	4.83108			0.161126
$900$		0			0
$901$	5.46073			0.181923
$902$	−76.4574			−2.54575
$903$		0			0
$904$	−1.70804	−	2.95841i	−0.0568085	−	0.0983952i
$905$	2.18546	−	3.78533i	0.0726471	−	0.125829i
$906$		0			0
$907$	−2.22350			−0.0738303			−0.0369151	−	0.999318i	$-0.511753\pi$
$907$	−2.22350			−0.0738303			−0.0369151	+	0.999318i	$0.511753\pi$
$908$	−31.6330	−	54.7899i	−1.04978	−	1.81827i
$909$		0			0
$910$	−9.40659	−	5.23933i	−0.311825	−	0.173682i
$911$	29.3786			0.973355			0.486678	−	0.873582i	$-0.338209\pi$
$911$	29.3786			0.973355			0.486678	+	0.873582i	$0.338209\pi$
$912$		0			0
$913$	−69.8863			−2.31290
$914$	−18.9956	+	32.9013i	−0.628317	+	1.08828i
$915$		0			0
$916$	−29.1906	−	50.5596i	−0.964484	−	1.67054i
$917$	6.26518	+	7.08288i	0.206895	+	0.233897i
$918$		0			0
$919$	−21.6911			−0.715522			−0.357761	−	0.933813i	$-0.616460\pi$
$919$	−21.6911			−0.715522			−0.357761	+	0.933813i	$0.616460\pi$
$920$	−0.0943763			−0.00311149
$921$		0			0
$922$	9.84429	−	17.0508i	0.324204	−	0.561538i
$923$	19.6499	−	6.91534i	0.646784	−	0.227621i
$924$		0			0
$925$	−20.6777	+	35.8149i	−0.679880	+	1.17759i
$926$	2.28259	+	3.95357i	0.0750107	+	0.129922i
$927$		0			0
$928$	−16.9823	−	29.4141i	−0.557470	−	0.965566i
$929$	31.1231			1.02111			0.510557	−	0.859844i	$-0.329439\pi$
$929$	31.1231			1.02111			0.510557	+	0.859844i	$0.329439\pi$
$930$		0			0
$931$	−3.13640	−	2.36440i	−0.102791	−	0.0774900i
$932$	24.6580	+	42.7089i	0.807699	+	1.39898i
$933$		0			0
$934$	−27.7937			−0.909439
$935$	−0.778918	−	1.34913i	−0.0254733	−	0.0441211i
$936$		0			0
$937$	13.1250			0.428777			0.214388	−	0.976749i	$-0.431224\pi$
$937$	13.1250			0.428777			0.214388	+	0.976749i	$0.431224\pi$
$938$	51.1354	−	10.3984i	1.66963	−	0.339521i
$939$		0			0
$940$	2.68245			0.0874920
$941$	23.5806	+	40.8428i	0.768705	+	1.33144i	0.938265	+	0.345917i	$0.112432\pi$
$941$	23.5806	+	40.8428i	0.768705	+	1.33144i	−0.169560	+	0.985520i	$0.554235\pi$
$942$		0			0
$943$	2.98347			0.0971551
$944$	29.9360			0.974333
$945$		0			0
$946$	−7.21323	+	12.4937i	−0.234522	+	0.406204i
$947$	2.15742	+	3.73676i	0.0701068	+	0.121429i	0.898948	−	0.438055i	$-0.144333\pi$
$947$	2.15742	+	3.73676i	0.0701068	+	0.121429i	−0.828841	+	0.559484i	$0.810999\pi$
$948$		0			0
$949$	−49.2931	+	17.3476i	−1.60012	+	0.563127i
$950$	−2.70839	+	4.69106i	−0.0878716	+	0.152198i
$951$		0			0
$952$	0.482573	+	0.545556i	0.0156403	+	0.0176816i
$953$	5.09812	+	8.83020i	0.165144	+	0.286038i	0.936707	−	0.350116i	$-0.113858\pi$
$953$	5.09812	+	8.83020i	0.165144	+	0.286038i	−0.771562	+	0.636154i	$0.780524\pi$
$954$		0			0
$955$	−0.845901	+	1.46514i	−0.0273727	+	0.0474109i
$956$	30.3534	−	52.5737i	0.981700	−	1.70035i
$957$		0			0
$958$	14.9864	+	25.9571i	0.484187	+	0.838637i
$959$	−33.7573	−	38.1632i	−1.09008	−	1.23235i
$960$		0			0
$961$	14.8334	−	25.6922i	0.478496	−	0.828780i
$962$	−49.5049	−	42.4482i	−1.59610	−	1.36858i
$963$		0			0
$964$	26.4226	+	45.7652i	0.851013	+	1.47400i
$965$	−0.931584	+	1.61355i	−0.0299887	+	0.0519420i
$966$		0			0
$967$	14.3246			0.460649			0.230324	−	0.973114i	$-0.426021\pi$
$967$	14.3246			0.460649			0.230324	+	0.973114i	$0.426021\pi$
$968$	−5.05038			−0.162325
$969$		0			0
$970$	3.55585	+	6.15891i	0.114171	+	0.197751i
$971$	17.0859			0.548312			0.274156	−	0.961685i	$-0.411602\pi$
$971$	17.0859			0.548312			0.274156	+	0.961685i	$0.411602\pi$
$972$		0			0
$973$	25.0534	−	5.09464i	0.803175	−	0.163327i
$974$	3.08469			0.0988400
$975$		0			0
$976$	13.0177	+	22.5473i	0.416686	+	0.721721i
$977$	50.0570			1.60147			0.800733	−	0.599021i	$-0.204443\pi$
$977$	50.0570			1.60147			0.800733	+	0.599021i	$0.204443\pi$
$978$		0			0
$979$	−21.5732	−	37.3659i	−0.689484	−	1.19422i
$980$	1.04290	−	8.48016i	0.0333142	−	0.270889i
$981$		0			0
$982$	−58.3465			−1.86191
$983$	−20.6067	−	35.6919i	−0.657252	−	1.13839i	−0.981324	−	0.192362i	$-0.938385\pi$
$983$	−20.6067	−	35.6919i	−0.657252	−	1.13839i	0.324072	−	0.946032i	$-0.394948\pi$
$984$		0			0
$985$	1.13250	+	1.96155i	0.0360846	+	0.0625003i
$986$	2.59463	−	4.49403i	0.0826299	−	0.143119i
$987$		0			0
$988$	−3.41254	−	2.92610i	−0.108567	−	0.0930917i
$989$	0.281470	−	0.487520i	0.00895022	−	0.0155022i
$990$		0			0
$991$	10.0248			0.318449			0.159225	−	0.987242i	$-0.449101\pi$
$991$	10.0248			0.318449			0.159225	+	0.987242i	$0.449101\pi$
$992$	9.37322			0.297600
$993$		0			0
$994$	20.8097	+	23.5257i	0.660044	+	0.746190i
$995$	−0.315390	−	0.546271i	−0.00999853	−	0.0173180i
$996$		0			0
$997$	21.9259	−	37.9768i	0.694401	−	1.20274i	−0.275982	−	0.961163i	$-0.589003\pi$
$997$	21.9259	−	37.9768i	0.694401	−	1.20274i	0.970382	−	0.241574i	$-0.0776638\pi$
$998$	−43.3835			−1.37328
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.e.100.7		16
3.2	odd	2		273.2.j.b.100.2	✓	16
7.4	even	3		819.2.s.e.802.2		16
13.3	even	3		819.2.s.e.289.2		16
21.11	odd	6		273.2.l.b.256.7	yes	16
39.29	odd	6		273.2.l.b.16.7	yes	16
91.81	even	3	inner	819.2.n.e.172.7		16
273.263	odd	6		273.2.j.b.172.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.2	✓	16	3.2	odd	2
273.2.j.b.172.2	yes	16	273.263	odd	6
273.2.l.b.16.7	yes	16	39.29	odd	6
273.2.l.b.256.7	yes	16	21.11	odd	6
819.2.n.e.100.7		16	1.1	even	1	trivial
819.2.n.e.172.7		16	91.81	even	3	inner
819.2.s.e.289.2		16	13.3	even	3
819.2.s.e.802.2		16	7.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02737 + 1.77946i) q^{2} +(-1.11098 + 1.92428i) q^{4} +(0.274662 - 0.475728i) q^{5} +(-0.839752 + 2.50895i) q^{7} -0.456078 q^{8} +1.12872 q^{10} -4.69824 q^{11} +(-0.663964 + 3.54389i) q^{13} +(-5.32730 + 1.08331i) q^{14} +(1.75340 + 3.03698i) q^{16} +(-0.301806 + 0.522743i) q^{17} +0.561110 q^{19} +(0.610289 + 1.05705i) q^{20} +(-4.82684 - 8.36033i) q^{22} +(0.188350 + 0.326231i) q^{23} +(2.34912 + 4.06880i) q^{25} +(-6.98834 + 2.45939i) q^{26} +(-3.89496 - 4.40331i) q^{28} +(-2.09200 + 3.62344i) q^{29} +(-0.577330 - 0.999965i) q^{31} +(-4.05887 + 7.03016i) q^{32} -1.24027 q^{34} +(0.962929 + 1.08861i) q^{35} +(4.40116 + 7.62304i) q^{37} +(0.576468 + 0.998472i) q^{38} +(-0.125267 + 0.216969i) q^{40} +(3.96001 - 6.85894i) q^{41} +(-0.747200 - 1.29419i) q^{43} +(5.21966 - 9.04072i) q^{44} +(-0.387010 + 0.670321i) q^{46} +(1.09885 - 1.90326i) q^{47} +(-5.58963 - 4.21379i) q^{49} +(-4.82684 + 8.36033i) q^{50} +(-6.08177 - 5.21485i) q^{52} +(-4.52338 - 7.83473i) q^{53} +(-1.29043 + 2.23509i) q^{55} +(0.382993 - 1.14428i) q^{56} -8.59702 q^{58} +(4.26827 - 7.39286i) q^{59} +7.42424 q^{61} +(1.18626 - 2.05467i) q^{62} -9.66624 q^{64} +(1.50356 + 1.28924i) q^{65} -9.59873 q^{67} +(-0.670602 - 1.16152i) q^{68} +(-0.947844 + 2.83190i) q^{70} +(-2.88877 - 5.00350i) q^{71} +(7.24668 + 12.5516i) q^{73} +(-9.04325 + 15.6634i) q^{74} +(-0.623383 + 1.07973i) q^{76} +(3.94536 - 11.7876i) q^{77} +(7.31102 - 12.6631i) q^{79} +1.92637 q^{80} +16.2736 q^{82} +14.8750 q^{83} +(0.165789 + 0.287155i) q^{85} +(1.53530 - 2.65922i) q^{86} +2.14277 q^{88} +(4.59177 + 7.95317i) q^{89} +(-8.33387 - 4.64184i) q^{91} -0.837013 q^{92} +4.51569 q^{94} +(0.154115 - 0.266936i) q^{95} +(3.15034 + 5.45655i) q^{97} +(1.75564 - 14.2756i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31}+ \cdots + 3 q^{98}+O(q^{100}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

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