LMFDB - Embedded newform 819.2.ct.a.127.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(127,819)] 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("819.127"); 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, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ct (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.4
Root			$1.34408 + 0.439820i$ of defining polynomial
Character	$\chi$	$=$	819.127
Dual form			819.2.ct.a.316.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.104235 - 0.0601799i) q^{2} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.866025 + 0.500000i) q^{7} +0.479696i q^{8} +(-0.101594 - 0.175965i) q^{10} +(0.315769 - 0.182309i) q^{11} +(1.80124 - 3.12338i) q^{13} +0.120360 q^{14} +(-1.95665 - 3.38901i) q^{16} +(1.59277 - 2.75877i) q^{17} +(1.25046 + 0.721954i) q^{19} +(2.90281 + 1.67594i) q^{20} +(0.0219427 - 0.0380059i) q^{22} +(2.54161 + 4.40219i) q^{23} +2.15010 q^{25} +(-0.000212944 - 0.433964i) q^{26} +(-1.71951 + 0.992757i) q^{28} +(4.09831 + 7.09848i) q^{29} +4.69775i q^{31} +(-1.23876 - 0.715198i) q^{32} -0.383412i q^{34} +(0.844083 - 1.46199i) q^{35} +(5.46967 - 3.15792i) q^{37} +0.173789 q^{38} +0.809806 q^{40} +(5.04661 - 2.91366i) q^{41} +(-0.386561 + 0.669543i) q^{43} +0.723954i q^{44} +(0.529847 + 0.305907i) q^{46} -12.7905i q^{47} +(0.500000 + 0.866025i) q^{49} +(0.224115 - 0.129393i) q^{50} +(3.58248 + 6.19801i) q^{52} -1.37110 q^{53} +(-0.307768 - 0.533070i) q^{55} +(-0.239848 + 0.415429i) q^{56} +(0.854372 + 0.493272i) q^{58} +(8.10770 + 4.68098i) q^{59} +(4.51242 - 7.81574i) q^{61} +(0.282711 + 0.489669i) q^{62} +7.65442 q^{64} +(-5.27279 - 3.04080i) q^{65} +(-11.6705 + 6.73797i) q^{67} +(3.16247 + 5.47757i) q^{68} -0.203187i q^{70} +(6.13246 + 3.54058i) q^{71} -2.16083i q^{73} +(0.380087 - 0.658329i) q^{74} +(-2.48281 + 1.43345i) q^{76} +0.364618 q^{77} -6.88781 q^{79} +(-5.72121 + 3.30314i) q^{80} +(0.350688 - 0.607409i) q^{82} +0.567380i q^{83} +(-4.65725 - 2.68887i) q^{85} +0.0930528i q^{86} +(0.0874529 + 0.151473i) q^{88} +(0.986346 - 0.569467i) q^{89} +(3.12161 - 1.80431i) q^{91} -10.0928 q^{92} +(-0.769734 - 1.33322i) q^{94} +(1.21878 - 2.11098i) q^{95} +(6.86572 + 3.96393i) q^{97} +(0.104235 + 0.0601799i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40}+ \cdots + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 12 * q^10 - 6 * q^11 + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 + 12 * q^23 - 20 * q^25 + 42 * q^26 - 8 * q^29 - 36 * q^32 - 6 * q^35 - 42 * q^37 - 4 * q^38 + 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 6 * q^49 + 18 * q^50 + 2 * q^52 + 44 * q^53 - 6 * q^55 + 12 * q^56 - 12 * q^58 - 18 * q^59 + 14 * q^61 + 4 * q^62 - 52 * q^64 - 60 * q^65 - 24 * q^67 + 8 * q^68 + 24 * q^71 - 6 * q^74 - 18 * q^76 - 8 * q^77 - 56 * q^79 + 72 * q^80 + 14 * q^82 - 48 * q^85 - 14 * q^88 + 12 * q^89 + 14 * q^91 - 24 * q^92 + 4 * q^94 + 22 * q^95 + 6 * q^97

Character values

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

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

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 $

$2$	0.104235	−	0.0601799i	0.0737051	−	0.0425536i	−0.462695	−	0.886518i	$-0.653117\pi$
$2$	0.104235	−	0.0601799i	0.0737051	−	0.0425536i	0.536400	+	0.843964i	$0.319784\pi$
$3$		0			0
$3$		0			0
$4$	−0.992757	+	1.71951i	−0.496378	+	0.859753i
$5$		−	1.68817i		−	0.754971i	−0.926016	−	0.377485i	$-0.876789\pi$
$5$		−	1.68817i		−	0.754971i	0.926016	−	0.377485i	$-0.123211\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			0.479696i			0.169598i
$9$		0			0
$10$	−0.101594	−	0.175965i	−0.0321267	−	0.0556452i
$11$	0.315769	−	0.182309i	0.0952078	−	0.0549682i	−0.451640	−	0.892200i	$-0.649161\pi$
$11$	0.315769	−	0.182309i	0.0952078	−	0.0549682i	0.546848	+	0.837232i	$0.315828\pi$
$12$		0			0
$13$	1.80124	−	3.12338i	0.499575	−	0.866271i
$13$	1.80124	−	3.12338i	0.499575	−	0.866271i
$14$	0.120360			0.0321675
$15$		0			0
$16$	−1.95665	−	3.38901i	−0.489161	−	0.847252i
$17$	1.59277	−	2.75877i	0.386304	−	0.669099i	−0.605645	−	0.795735i	$-0.707085\pi$
$17$	1.59277	−	2.75877i	0.386304	−	0.669099i	0.991949	+	0.126636i	$0.0404181\pi$
$18$		0			0
$19$	1.25046	+	0.721954i	0.286875	+	0.165628i	0.636532	−	0.771250i	$-0.280368\pi$
$19$	1.25046	+	0.721954i	0.286875	+	0.165628i	−0.349657	+	0.936878i	$0.613702\pi$
$20$	2.90281	+	1.67594i	0.649088	+	0.374751i
$21$		0			0
$22$	0.0219427	−	0.0380059i	0.00467820	−	0.00810288i
$23$	2.54161	+	4.40219i	0.529962	+	0.917920i	0.999389	+	0.0349493i	$0.0111270\pi$
$23$	2.54161	+	4.40219i	0.529962	+	0.917920i	−0.469428	+	0.882971i	$0.655540\pi$
$24$		0			0
$25$	2.15010			0.430020
$26$	−0.000212944	−	0.433964i	−4.17617e−5	−	0.0851073i
$27$		0			0
$28$	−1.71951	+	0.992757i	−0.324956	+	0.187613i
$29$	4.09831	+	7.09848i	0.761037	+	1.31815i	0.942317	+	0.334723i	$0.108643\pi$
$29$	4.09831	+	7.09848i	0.761037	+	1.31815i	−0.181280	+	0.983432i	$0.558024\pi$
$30$		0			0
$31$			4.69775i			0.843742i	0.906656	+	0.421871i	$0.138626\pi$
$31$			4.69775i			0.843742i	−0.906656	+	0.421871i	$0.861374\pi$
$32$	−1.23876	−	0.715198i	−0.218984	−	0.126430i
$33$		0			0
$34$		−	0.383412i		−	0.0657546i
$35$	0.844083	−	1.46199i	0.142676	−	0.247122i
$36$		0			0
$37$	5.46967	−	3.15792i	0.899209	−	0.519159i	0.0222655	−	0.999752i	$-0.492912\pi$
$37$	5.46967	−	3.15792i	0.899209	−	0.519159i	0.876943	+	0.480594i	$0.159579\pi$
$38$	0.173789			0.0281922
$39$		0			0
$40$	0.809806			0.128042
$41$	5.04661	−	2.91366i	0.788148	−	0.455037i	−0.0511624	−	0.998690i	$-0.516293\pi$
$41$	5.04661	−	2.91366i	0.788148	−	0.455037i	0.839310	+	0.543653i	$0.182959\pi$
$42$		0			0
$43$	−0.386561	+	0.669543i	−0.0589500	+	0.102104i	−0.893994	−	0.448078i	$-0.852109\pi$
$43$	−0.386561	+	0.669543i	−0.0589500	+	0.102104i	0.835044	+	0.550183i	$0.185442\pi$
$44$			0.723954i			0.109140i
$45$		0			0
$46$	0.529847	+	0.305907i	0.0781217	+	0.0451036i
$47$		−	12.7905i		−	1.86569i	−0.360275	−	0.932846i	$-0.617317\pi$
$47$		−	12.7905i		−	1.86569i	0.360275	−	0.932846i	$-0.382683\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	0.224115	−	0.129393i	0.0316946	−	0.0182989i
$51$		0			0
$52$	3.58248	+	6.19801i	0.496800	+	0.859509i
$53$	−1.37110			−0.188334			−0.0941672	−	0.995556i	$-0.530019\pi$
$53$	−1.37110			−0.188334			−0.0941672	+	0.995556i	$0.530019\pi$
$54$		0			0
$55$	−0.307768	−	0.533070i	−0.0414994	−	0.0718791i
$56$	−0.239848	+	0.415429i	−0.0320510	+	0.0555140i
$57$		0			0
$58$	0.854372	+	0.493272i	0.112185	+	0.0647698i
$59$	8.10770	+	4.68098i	1.05553	+	0.609412i	0.924193	−	0.381925i	$-0.124739\pi$
$59$	8.10770	+	4.68098i	1.05553	+	0.609412i	0.131340	+	0.991337i	$0.458072\pi$
$60$		0			0
$61$	4.51242	−	7.81574i	0.577756	−	1.00070i	−0.417980	−	0.908456i	$-0.637262\pi$
$61$	4.51242	−	7.81574i	0.577756	−	1.00070i	0.995736	−	0.0922469i	$-0.0294049\pi$
$62$	0.282711	+	0.489669i	0.0359043	+	0.0621880i
$63$		0			0
$64$	7.65442			0.956802
$65$	−5.27279	−	3.04080i	−0.654009	−	0.377164i
$66$		0			0
$67$	−11.6705	+	6.73797i	−1.42578	+	0.823174i	−0.996784	−	0.0801330i	$-0.974466\pi$
$67$	−11.6705	+	6.73797i	−1.42578	+	0.823174i	−0.428995	+	0.903307i	$0.641132\pi$
$68$	3.16247	+	5.47757i	0.383506	+	0.664252i
$69$		0			0
$70$		−	0.203187i		−	0.0242855i
$71$	6.13246	+	3.54058i	0.727789	+	0.420189i	0.817613	−	0.575769i	$-0.195297\pi$
$71$	6.13246	+	3.54058i	0.727789	+	0.420189i	−0.0898239	+	0.995958i	$0.528630\pi$
$72$		0			0
$73$		−	2.16083i		−	0.252906i	−0.991973	−	0.126453i	$-0.959641\pi$
$73$		−	2.16083i		−	0.252906i	0.991973	−	0.126453i	$-0.0403592\pi$
$74$	0.380087	−	0.658329i	0.0441842	−	0.0765292i
$75$		0			0
$76$	−2.48281	+	1.43345i	−0.284797	+	0.164428i
$77$	0.364618			0.0415521
$78$		0			0
$79$	−6.88781			−0.774940			−0.387470	−	0.921882i	$-0.626651\pi$
$79$	−6.88781			−0.774940			−0.387470	+	0.921882i	$0.626651\pi$
$80$	−5.72121	+	3.30314i	−0.639651	+	0.369302i
$81$		0			0
$82$	0.350688	−	0.607409i	0.0387270	−	0.0670771i
$83$			0.567380i			0.0622780i	0.999515	+	0.0311390i	$0.00991345\pi$
$83$			0.567380i			0.0622780i	−0.999515	+	0.0311390i	$0.990087\pi$
$84$		0			0
$85$	−4.65725	−	2.68887i	−0.505150	−	0.291648i
$86$			0.0930528i			0.0100341i
$87$		0			0
$88$	0.0874529	+	0.151473i	0.00932251	+	0.0161471i
$89$	0.986346	−	0.569467i	0.104553	−	0.0603634i	−0.446812	−	0.894628i	$-0.647441\pi$
$89$	0.986346	−	0.569467i	0.104553	−	0.0603634i	0.551364	+	0.834264i	$0.314107\pi$
$90$		0			0
$91$	3.12161	−	1.80431i	0.327234	−	0.189143i
$92$	−10.0928			−1.05225
$93$		0			0
$94$	−0.769734	−	1.33322i	−0.0793920	−	0.137511i
$95$	1.21878	−	2.11098i	0.125044	−	0.216582i
$96$		0			0
$97$	6.86572	+	3.96393i	0.697109	+	0.402476i	0.806270	−	0.591548i	$-0.201483\pi$
$97$	6.86572	+	3.96393i	0.697109	+	0.402476i	−0.109161	+	0.994024i	$0.534816\pi$
$98$	0.104235	+	0.0601799i	0.0105293	+	0.00607909i
$99$		0			0
$100$	−2.13452	+	3.69710i	−0.213452	+	0.369710i
$101$	7.77322	+	13.4636i	0.773465	+	1.33968i	0.935653	+	0.352920i	$0.114811\pi$
$101$	7.77322	+	13.4636i	0.773465	+	1.33968i	−0.162189	+	0.986760i	$0.551855\pi$
$102$		0			0
$103$	−10.2982			−1.01471			−0.507354	−	0.861738i	$-0.669376\pi$
$103$	−10.2982			−1.01471			−0.507354	+	0.861738i	$0.669376\pi$
$104$	1.49827	+	0.864049i	0.146918	+	0.0847270i
$105$		0			0
$106$	−0.142916	+	0.0825124i	−0.0138812	+	0.00801432i
$107$	−6.56220	−	11.3661i	−0.634391	−	1.09880i	−0.986644	−	0.162893i	$-0.947917\pi$
$107$	−6.56220	−	11.3661i	−0.634391	−	1.09880i	0.352252	−	0.935905i	$-0.385416\pi$
$108$		0			0
$109$		−	10.4459i		−	1.00054i	−0.865871	−	0.500268i	$-0.833235\pi$
$109$		−	10.4459i		−	1.00054i	0.865871	−	0.500268i	$-0.166765\pi$
$110$	−0.0641602	−	0.0370429i	−0.00611743	−	0.00353190i
$111$		0			0
$112$		−	3.91329i		−	0.369771i
$113$	2.47631	−	4.28909i	0.232952	−	0.403484i	−0.725724	−	0.687986i	$-0.758495\pi$
$113$	2.47631	−	4.28909i	0.232952	−	0.403484i	0.958675	+	0.284502i	$0.0918283\pi$
$114$		0			0
$115$	7.43163	−	4.29065i	0.693003	−	0.400105i
$116$	−16.2745			−1.51105
$117$		0			0
$118$	1.12681			0.103731
$119$	2.75877	−	1.59277i	0.252896	−	0.146009i
$120$		0			0
$121$	−5.43353	+	9.41114i	−0.493957	+	0.855559i
$122$		−	1.08623i		−	0.0983425i
$123$		0			0
$124$	−8.07781	−	4.66373i	−0.725409	−	0.418815i
$125$		−	12.0705i		−	1.07962i
$126$		0			0
$127$	4.03366	+	6.98650i	0.357929	+	0.619951i	0.987615	−	0.156899i	$-0.0501496\pi$
$127$	4.03366	+	6.98650i	0.357929	+	0.619951i	−0.629686	+	0.776850i	$0.716816\pi$
$128$	3.27537	−	1.89104i	0.289505	−	0.167146i
$129$		0			0
$130$	−0.732603		0.000359484i	−0.0642535		3.15288e-5i
$131$	−18.9039			−1.65164			−0.825820	−	0.563934i	$-0.809287\pi$
$131$	−18.9039			−1.65164			−0.825820	+	0.563934i	$0.809287\pi$
$132$		0			0
$133$	0.721954	+	1.25046i	0.0626013	+	0.108429i
$134$	−0.810981	+	1.40466i	−0.0700581	+	0.121344i
$135$		0			0
$136$	1.32337	+	0.764047i	0.113478	+	0.0655165i
$137$	−15.7837	−	9.11274i	−1.34850	−	0.778554i	−0.360459	−	0.932775i	$-0.617380\pi$
$137$	−15.7837	−	9.11274i	−1.34850	−	0.778554i	−0.988036	+	0.154221i	$0.950713\pi$
$138$		0			0
$139$	−2.62542	+	4.54737i	−0.222686	+	0.385703i	−0.955623	−	0.294594i	$-0.904816\pi$
$139$	−2.62542	+	4.54737i	−0.222686	+	0.385703i	0.732937	+	0.680297i	$0.238149\pi$
$140$	1.67594	+	2.90281i	0.141643	+	0.245332i
$141$		0			0
$142$	0.852287			0.0715223
$143$	−0.000645091	−	1.31465i	−5.39452e−5	−	0.109936i
$144$		0			0
$145$	11.9834	−	6.91862i	0.995167	−	0.574560i
$146$	−0.130038	−	0.225233i	−0.0107621	−	0.0186404i
$147$		0			0
$148$			12.5402i			1.03080i
$149$	−8.03073	−	4.63654i	−0.657903	−	0.379841i	0.133574	−	0.991039i	$-0.457354\pi$
$149$	−8.03073	−	4.63654i	−0.657903	−	0.379841i	−0.791478	+	0.611198i	$0.790688\pi$
$150$		0			0
$151$		−	14.0132i		−	1.14038i	−0.821513	−	0.570189i	$-0.806870\pi$
$151$		−	14.0132i		−	1.14038i	0.821513	−	0.570189i	$-0.193130\pi$
$152$	−0.346318	+	0.599841i	−0.0280901	+	0.0486535i
$153$		0			0
$154$	0.0380059	−	0.0219427i	0.00306260	−	0.00176819i
$155$	7.93059			0.637000
$156$		0			0
$157$	−17.1825			−1.37131			−0.685656	−	0.727925i	$-0.740485\pi$
$157$	−17.1825			−1.37131			−0.685656	+	0.727925i	$0.740485\pi$
$158$	−0.717949	+	0.414508i	−0.0571170	+	0.0329765i
$159$		0			0
$160$	−1.20737	+	2.09123i	−0.0954511	+	0.165326i
$161$			5.08321i			0.400613i
$162$		0			0
$163$	10.2128	+	5.89637i	0.799930	+	0.461840i	0.843447	−	0.537213i	$-0.180523\pi$
$163$	10.2128	+	5.89637i	0.799930	+	0.461840i	−0.0435169	+	0.999053i	$0.513856\pi$
$164$			11.5702i			0.903482i
$165$		0			0
$166$	0.0341449	+	0.0591407i	0.00265016	+	0.00459021i
$167$	−3.73852	+	2.15843i	−0.289295	+	0.167025i	−0.637624	−	0.770348i	$-0.720083\pi$
$167$	−3.73852	+	2.15843i	−0.289295	+	0.167025i	0.348329	+	0.937372i	$0.386749\pi$
$168$		0			0
$169$	−6.51105	−	11.2519i	−0.500850	−	0.865534i
$170$	−0.647263			−0.0496428
$171$		0			0
$172$	−0.767522	−	1.32939i	−0.0585230	−	0.101365i
$173$	−6.25985	+	10.8424i	−0.475928	+	0.824331i	−0.999620	−	0.0275769i	$-0.991221\pi$
$173$	−6.25985	+	10.8424i	−0.475928	+	0.824331i	0.523692	+	0.851908i	$0.324554\pi$
$174$		0			0
$175$	1.86204	+	1.07505i	0.140757	+	0.0812660i
$176$	−1.23569	−	0.713428i	−0.0931440	−	0.0537767i
$177$		0			0
$178$	0.0685410	−	0.118717i	0.00513737	−	0.00889818i
$179$	3.29767	+	5.71173i	0.246479	+	0.426915i	0.962547	−	0.271117i	$-0.0873929\pi$
$179$	3.29767	+	5.71173i	0.246479	+	0.426915i	−0.716067	+	0.698031i	$0.754060\pi$
$180$		0			0
$181$	−11.0157			−0.818791			−0.409395	−	0.912357i	$-0.634260\pi$
$181$	−11.0157			−0.818791			−0.409395	+	0.912357i	$0.634260\pi$
$182$	0.216797	−	0.375930i	0.0160701	−	0.0278658i
$183$		0			0
$184$	−2.11171	+	1.21920i	−0.155678	+	0.0898805i
$185$	−5.33109	−	9.23371i	−0.391949	−	0.678876i
$186$		0			0
$187$		−	1.16151i		−	0.0849379i
$188$	21.9934	+	12.6979i	1.60403	+	0.926089i
$189$		0			0
$190$		−	0.293384i		−	0.0212843i
$191$	2.96606	−	5.13737i	0.214617	−	0.371727i	−0.738537	−	0.674213i	$-0.764483\pi$
$191$	2.96606	−	5.13737i	0.214617	−	0.371727i	0.953154	+	0.302486i	$0.0978164\pi$
$192$		0			0
$193$	3.63380	−	2.09798i	0.261567	−	0.151016i	−0.363482	−	0.931601i	$-0.618412\pi$
$193$	3.63380	−	2.09798i	0.261567	−	0.151016i	0.625049	+	0.780586i	$0.285079\pi$
$194$	0.954196			0.0685073
$195$		0			0
$196$	−1.98551			−0.141822
$197$	−5.00990	+	2.89247i	−0.356941	+	0.206080i	−0.667738	−	0.744396i	$-0.732737\pi$
$197$	−5.00990	+	2.89247i	−0.356941	+	0.206080i	0.310797	+	0.950476i	$0.399404\pi$
$198$		0			0
$199$	5.97988	−	10.3575i	0.423903	−	0.734221i	−0.572415	−	0.819964i	$-0.693993\pi$
$199$	5.97988	−	10.3575i	0.423903	−	0.734221i	0.996317	+	0.0857435i	$0.0273266\pi$
$200$			1.03139i			0.0729305i
$201$		0			0
$202$	1.62048	+	0.935584i	0.114017	+	0.0658275i
$203$			8.19662i			0.575290i
$204$		0			0
$205$	−4.91874	−	8.51951i	−0.343540	−	0.595028i
$206$	−1.07343	+	0.619743i	−0.0747891	+	0.0431795i
$207$		0			0
$208$	−14.1096	+	0.00692349i	−0.978323	+	0.000480057i
$209$	0.526475			0.0364170
$210$		0			0
$211$	4.11795	+	7.13251i	0.283492	+	0.491022i	0.972242	−	0.233976i	$-0.0751738\pi$
$211$	4.11795	+	7.13251i	0.283492	+	0.491022i	−0.688751	+	0.724998i	$0.741840\pi$
$212$	1.36116	−	2.35761i	0.0934851	−	0.161921i
$213$		0			0
$214$	−1.36802	−	0.789825i	−0.0935157	−	0.0539913i
$215$	1.13030	+	0.652579i	0.0770858	+	0.0445055i
$216$		0			0
$217$	−2.34888	+	4.06838i	−0.159452	+	0.276179i
$218$	−0.628633	−	1.08882i	−0.0425764	−	0.0737445i
$219$		0			0
$220$	1.22215			0.0823976
$221$	−5.74771	−	9.94405i	−0.386633	−	0.668909i
$222$		0			0
$223$	13.2515	−	7.65073i	0.887383	−	0.512331i	0.0142977	−	0.999898i	$-0.495449\pi$
$223$	13.2515	−	7.65073i	0.887383	−	0.512331i	0.873086	+	0.487567i	$0.162115\pi$
$224$	−0.715198	−	1.23876i	−0.0477861	−	0.0827680i
$225$		0			0
$226$		−	0.596097i		−	0.0396518i
$227$	6.02292	+	3.47733i	0.399755	+	0.230799i	0.686378	−	0.727245i	$-0.259199\pi$
$227$	6.02292	+	3.47733i	0.399755	+	0.230799i	−0.286623	+	0.958043i	$0.592533\pi$
$228$		0			0
$229$			27.4219i			1.81209i	0.423180	+	0.906045i	$0.360914\pi$
$229$			27.4219i			1.81209i	−0.423180	+	0.906045i	$0.639086\pi$
$230$	0.516422	−	0.894470i	0.0340519	−	0.0589796i
$231$		0			0
$232$	−3.40511	+	1.96594i	−0.223556	+	0.129070i
$233$	−6.85333			−0.448976			−0.224488	−	0.974477i	$-0.572071\pi$
$233$	−6.85333			−0.448976			−0.224488	+	0.974477i	$0.572071\pi$
$234$		0			0
$235$	−21.5926			−1.40854
$236$	−16.0980	+	9.29416i	−1.04789	+	0.604998i
$237$		0			0
$238$	0.191706	−	0.332045i	0.0124265	−	0.0215233i
$239$			22.0754i			1.42794i	0.700177	+	0.713970i	$0.253105\pi$
$239$			22.0754i			1.42794i	−0.700177	+	0.713970i	$0.746895\pi$
$240$		0			0
$241$	13.6807	+	7.89855i	0.881251	+	0.508790i	0.871071	−	0.491158i	$-0.163426\pi$
$241$	13.6807	+	7.89855i	0.881251	+	0.508790i	0.0101802	+	0.999948i	$0.496759\pi$
$242$			1.30796i			0.0840787i
$243$		0			0
$244$	8.95947	+	15.5183i	0.573571	+	0.993455i
$245$	1.46199	−	0.844083i	0.0934034	−	0.0539265i
$246$		0			0
$247$	4.50732	−	2.60525i	0.286794	−	0.165768i
$248$	−2.25349			−0.143097
$249$		0			0
$250$	−0.726405	−	1.25817i	−0.0459419	−	0.0795737i
$251$	−11.2783	+	19.5346i	−0.711882	+	1.23302i	0.252268	+	0.967658i	$0.418824\pi$
$251$	−11.2783	+	19.5346i	−0.711882	+	1.23302i	−0.964150	+	0.265359i	$0.914510\pi$
$252$		0			0
$253$	1.60512	+	0.926716i	0.100913	+	0.0582621i
$254$	0.840894	+	0.485490i	0.0527624	+	0.0304624i
$255$		0			0
$256$	−7.42681	+	12.8636i	−0.464176	+	0.803976i
$257$	−10.2064	−	17.6781i	−0.636660	−	1.10273i	−0.986161	−	0.165791i	$-0.946982\pi$
$257$	−10.2064	−	17.6781i	−0.636660	−	1.10273i	0.349501	−	0.936936i	$-0.386351\pi$
$258$		0			0
$259$	6.31584			0.392447
$260$	10.4633	−	6.04781i	0.648904	−	0.375069i
$261$		0			0
$262$	−1.97044	+	1.13763i	−0.121734	+	0.0702833i
$263$	−14.7701	−	25.5826i	−0.910764	−	1.57749i	−0.812987	−	0.582281i	$-0.802160\pi$
$263$	−14.7701	−	25.5826i	−0.910764	−	1.57749i	−0.0977768	−	0.995208i	$-0.531173\pi$
$264$		0			0
$265$			2.31464i			0.142187i
$266$	0.150505	+	0.0868943i	0.00922807	+	0.00532783i
$267$		0			0
$268$		−	26.7567i		−	1.63442i
$269$	13.9581	−	24.1762i	0.851043	−	1.47405i	−0.0292252	−	0.999573i	$-0.509304\pi$
$269$	13.9581	−	24.1762i	0.851043	−	1.47405i	0.880268	−	0.474477i	$-0.157363\pi$
$270$		0			0
$271$	−25.5036	+	14.7245i	−1.54924	+	0.894451i	−0.551035	+	0.834482i	$0.685767\pi$
$271$	−25.5036	+	14.7245i	−1.54924	+	0.894451i	−0.998200	+	0.0599690i	$0.980900\pi$
$272$	−12.4660			−0.755861
$273$		0			0
$274$	−2.19362			−0.132521
$275$	0.678933	−	0.391982i	0.0409412	−	0.0236374i
$276$		0			0
$277$	3.42927	−	5.93967i	0.206045	−	0.356880i	−0.744420	−	0.667711i	$-0.767274\pi$
$277$	3.42927	−	5.93967i	0.206045	−	0.356880i	0.950465	+	0.310831i	$0.100607\pi$
$278$			0.631992i			0.0379043i
$279$		0			0
$280$	0.701313	+	0.404903i	0.0419114	+	0.0241976i
$281$		−	29.0940i		−	1.73561i	−0.496909	−	0.867803i	$-0.665532\pi$
$281$		−	29.0940i		−	1.73561i	0.496909	−	0.867803i	$-0.334468\pi$
$282$		0			0
$283$	5.80511	+	10.0547i	0.345078	+	0.597692i	0.985368	−	0.170441i	$-0.0545192\pi$
$283$	5.80511	+	10.0547i	0.345078	+	0.597692i	−0.640290	+	0.768133i	$0.721186\pi$
$284$	−12.1761	+	7.02986i	−0.722517	+	0.417146i
$285$		0			0
$286$	−0.0791828	−	0.136993i	−0.00468217	−	0.00810058i
$287$	5.82732			0.343976
$288$		0			0
$289$	3.42614	+	5.93425i	0.201538	+	0.349074i
$290$	0.832724	−	1.44232i	0.0488993	−	0.0846960i
$291$		0			0
$292$	3.71555	+	2.14517i	0.217436	+	0.125537i
$293$	15.4054	+	8.89430i	0.899992	+	0.519610i	0.877197	−	0.480130i	$-0.159410\pi$
$293$	15.4054	+	8.89430i	0.899992	+	0.519610i	0.0227942	+	0.999740i	$0.492744\pi$
$294$		0			0
$295$	7.90228	−	13.6871i	0.460088	−	0.796896i
$296$	1.51484	+	2.62378i	0.0880483	+	0.152504i
$297$		0			0
$298$	−1.11611			−0.0646544
$299$	18.3278	−	0.00899334i	1.05992	−	0.000520098i
$300$		0			0
$301$	−0.669543	+	0.386561i	−0.0385918	+	0.0222810i
$302$	−0.843314	−	1.46066i	−0.0485273	−	0.0840517i
$303$		0			0
$304$		−	5.65043i		−	0.324074i
$305$	−13.1943	−	7.61771i	−0.755501	−	0.436189i
$306$		0			0
$307$		−	9.07966i		−	0.518204i	−0.965850	−	0.259102i	$-0.916573\pi$
$307$		−	9.07966i		−	0.518204i	0.965850	−	0.259102i	$-0.0834265\pi$
$308$	−0.361977	+	0.626963i	−0.0206256	+	0.0357245i
$309$		0			0
$310$	0.826643	−	0.477262i	0.0469501	−	0.0271067i
$311$	1.57073			0.0890677			0.0445338	−	0.999008i	$-0.485820\pi$
$311$	1.57073			0.0890677			0.0445338	+	0.999008i	$0.485820\pi$
$312$		0			0
$313$	20.6232			1.16569			0.582846	−	0.812582i	$-0.301939\pi$
$313$	20.6232			1.16569			0.582846	+	0.812582i	$0.301939\pi$
$314$	−1.79101	+	1.03404i	−0.101073	+	0.0583544i
$315$		0			0
$316$	6.83792	−	11.8436i	0.384663	−	0.666256i
$317$			30.5435i			1.71549i	0.514072	+	0.857747i	$0.328137\pi$
$317$			30.5435i			1.71549i	−0.514072	+	0.857747i	$0.671863\pi$
$318$		0			0
$319$	2.58823	+	1.49432i	0.144913	+	0.0836657i
$320$		−	12.9219i		−	0.722358i
$321$		0			0
$322$	0.305907	+	0.529847i	0.0170476	+	0.0295272i
$323$	3.98340	−	2.29982i	0.221642	−	0.127965i
$324$		0			0
$325$	3.87285	−	6.71558i	0.214827	−	0.372513i
$326$	1.41937			0.0786118
$327$		0			0
$328$	1.39767	+	2.42084i	0.0771735	+	0.133668i
$329$	6.39527	−	11.0769i	0.352583	−	0.610691i
$330$		0			0
$331$	−22.3894	−	12.9265i	−1.23063	−	0.710507i	−0.263472	−	0.964667i	$-0.584868\pi$
$331$	−22.3894	−	12.9265i	−1.23063	−	0.710507i	−0.967162	+	0.254161i	$0.918201\pi$
$332$	−0.975612	−	0.563270i	−0.0535437	−	0.0309135i
$333$		0			0
$334$	−0.259789	+	0.449967i	−0.0142150	+	0.0246211i
$335$	11.3748	+	19.7017i	0.621472	+	1.07642i
$336$		0			0
$337$	−21.3954			−1.16548			−0.582742	−	0.812657i	$-0.698020\pi$
$337$	−21.3954			−1.16548			−0.582742	+	0.812657i	$0.698020\pi$
$338$	−1.35582	−	0.781009i	−0.0737468	−	0.0424813i
$339$		0			0
$340$	9.24704	−	5.33878i	0.501491	−	0.289536i
$341$	0.856443	+	1.48340i	0.0463790	+	0.0803308i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−0.321177	−	0.185432i	−0.0173167	−	0.00999781i
$345$		0			0
$346$			1.50687i			0.0810098i
$347$	1.10442	−	1.91291i	0.0592882	−	0.102690i	−0.834858	−	0.550466i	$-0.814450\pi$
$347$	1.10442	−	1.91291i	0.0592882	−	0.102690i	0.894146	+	0.447775i	$0.147784\pi$
$348$		0			0
$349$	−9.77843	+	5.64558i	−0.523427	+	0.302201i	−0.738336	−	0.674433i	$-0.764388\pi$
$349$	−9.77843	+	5.64558i	−0.523427	+	0.302201i	0.214908	+	0.976634i	$0.431055\pi$
$350$	0.258786			0.0138327
$351$		0			0
$352$	−0.521548			−0.0277986
$353$	30.8680	−	17.8217i	1.64294	−	0.948552i	0.663158	−	0.748479i	$-0.269216\pi$
$353$	30.8680	−	17.8217i	1.64294	−	0.948552i	0.979781	−	0.200072i	$-0.0641177\pi$
$354$		0			0
$355$	5.97708	−	10.3526i	0.317230	−	0.549459i
$356$			2.26137i			0.119852i
$357$		0			0
$358$	0.687464	+	0.396907i	0.0363336	+	0.0209772i
$359$			19.3218i			1.01976i	0.860244	+	0.509882i	$0.170311\pi$
$359$			19.3218i			1.01976i	−0.860244	+	0.509882i	$0.829689\pi$
$360$		0			0
$361$	−8.45757	−	14.6489i	−0.445135	−	0.770997i
$362$	−1.14822	+	0.662924i	−0.0603490	+	0.0348425i
$363$		0			0
$364$	0.00351282	+	7.15887i	0.000184122	+	0.375227i
$365$	−3.64783			−0.190936
$366$		0			0
$367$	1.86032	+	3.22218i	0.0971082	+	0.168196i	0.910487	−	0.413539i	$-0.135707\pi$
$367$	1.86032	+	3.22218i	0.0971082	+	0.168196i	−0.813378	+	0.581735i	$0.802374\pi$
$368$	9.94604	−	17.2271i	0.518473	−	0.898022i
$369$		0			0
$370$	−1.11137	−	0.641649i	−0.0577773	−	0.0333578i
$371$	−1.18740	−	0.685548i	−0.0616469	−	0.0355919i
$372$		0			0
$373$	1.75638	−	3.04214i	0.0909420	−	0.157516i	−0.816966	−	0.576686i	$-0.804346\pi$
$373$	1.75638	−	3.04214i	0.0909420	−	0.157516i	0.907908	+	0.419170i	$0.137679\pi$
$374$	−0.0698995	−	0.121070i	−0.00361442	−	0.00626035i
$375$		0			0
$376$	6.13557			0.316418
$377$	29.5533	−	0.0145016i	1.52207	−	0.000746873i
$378$		0			0
$379$	21.6647	−	12.5081i	1.11284	−	0.642500i	0.173279	−	0.984873i	$-0.444564\pi$
$379$	21.6647	−	12.5081i	1.11284	−	0.642500i	0.939564	+	0.342373i	$0.111230\pi$
$380$	2.41990	+	4.19139i	0.124138	+	0.215014i
$381$		0			0
$382$		−	0.713990i		−	0.0365309i
$383$	19.4556	+	11.2327i	0.994134	+	0.573964i	0.906507	−	0.422190i	$-0.138738\pi$
$383$	19.4556	+	11.2327i	0.994134	+	0.573964i	0.0876266	+	0.996153i	$0.472072\pi$
$384$		0			0
$385$		−	0.615536i		−	0.0313706i
$386$	0.252512	−	0.437364i	0.0128525	−	0.0222612i
$387$		0			0
$388$	−13.6320	+	7.87043i	−0.692059	+	0.399561i
$389$	−13.3364			−0.676184			−0.338092	−	0.941113i	$-0.609781\pi$
$389$	−13.3364			−0.676184			−0.338092	+	0.941113i	$0.609781\pi$
$390$		0			0
$391$	16.1928			0.818906
$392$	−0.415429	+	0.239848i	−0.0209823	+	0.0121142i
$393$		0			0
$394$	−0.348137	+	0.602991i	−0.0175389	+	0.0303783i
$395$			11.6278i			0.585057i
$396$		0			0
$397$	−22.3723	−	12.9166i	−1.12283	−	0.648268i	−0.180710	−	0.983536i	$-0.557840\pi$
$397$	−22.3723	−	12.9166i	−1.12283	−	0.648268i	−0.942123	+	0.335268i	$0.891173\pi$
$398$		−	1.43948i		−	0.0721544i
$399$		0			0
$400$	−4.20698	−	7.28670i	−0.210349	−	0.364335i
$401$	−15.2078	+	8.78025i	−0.759443	+	0.438465i	−0.829096	−	0.559106i	$-0.811144\pi$
$401$	−15.2078	+	8.78025i	−0.759443	+	0.438465i	0.0696524	+	0.997571i	$0.477811\pi$
$402$		0			0
$403$	14.6729	+	8.46180i	0.730909	+	0.421512i
$404$	−30.8677			−1.53572
$405$		0			0
$406$	0.493272	+	0.854372i	0.0244807	+	0.0424018i
$407$	1.15143	−	1.99434i	0.0570745	−	0.0988559i
$408$		0			0
$409$	12.5818	+	7.26410i	0.622129	+	0.359186i	0.777698	−	0.628639i	$-0.216388\pi$
$409$	12.5818	+	7.26410i	0.622129	+	0.359186i	−0.155568	+	0.987825i	$0.549721\pi$
$410$	−1.02541	−	0.592019i	−0.0506412	−	0.0292377i
$411$		0			0
$412$	10.2236	−	17.7077i	0.503679	−	0.872398i
$413$	4.68098	+	8.10770i	0.230336	+	0.398954i
$414$		0			0
$415$	0.957831			0.0470181
$416$	−4.46514	+	2.58087i	−0.218922	+	0.126538i
$417$		0			0
$418$	0.0548769	−	0.0316832i	0.00268412	−	0.00154968i
$419$	−2.30096	−	3.98538i	−0.112409	−	0.194699i	0.804332	−	0.594180i	$-0.202523\pi$
$419$	−2.30096	−	3.98538i	−0.112409	−	0.194699i	−0.916741	+	0.399482i	$0.869190\pi$
$420$		0			0
$421$			19.2645i			0.938895i	0.882960	+	0.469447i	$0.155547\pi$
$421$			19.2645i			0.938895i	−0.882960	+	0.469447i	$0.844453\pi$
$422$	0.858468	+	0.495637i	0.0417896	+	0.0241272i
$423$		0			0
$424$		−	0.657709i		−	0.0319412i
$425$	3.42462	−	5.93161i	0.166118	−	0.287726i
$426$		0			0
$427$	7.81574	−	4.51242i	0.378230	−	0.218371i
$428$	26.0587			1.25959
$429$		0			0
$430$	0.157089			0.00757548
$431$	24.5649	−	14.1825i	1.18325	−	0.683149i	0.226485	−	0.974015i	$-0.427277\pi$
$431$	24.5649	−	14.1825i	1.18325	−	0.683149i	0.956764	+	0.290865i	$0.0939432\pi$
$432$		0			0
$433$	−6.26014	+	10.8429i	−0.300843	+	0.521076i	−0.976327	−	0.216299i	$-0.930601\pi$
$433$	−6.26014	+	10.8429i	−0.300843	+	0.521076i	0.675484	+	0.737375i	$0.263935\pi$
$434$			0.565421i			0.0271411i
$435$		0			0
$436$	17.9618	+	10.3702i	0.860213	+	0.496644i
$437$			7.33969i			0.351105i
$438$		0			0
$439$	15.8637	+	27.4767i	0.757132	+	1.31139i	0.944307	+	0.329064i	$0.106733\pi$
$439$	15.8637	+	27.4767i	0.757132	+	1.31139i	−0.187176	+	0.982326i	$0.559933\pi$
$440$	0.255711	−	0.147635i	0.0121906	−	0.00703822i
$441$		0			0
$442$	−1.19754	−	0.690619i	−0.0569613	−	0.0328494i
$443$	−1.73048			−0.0822177			−0.0411088	−	0.999155i	$-0.513089\pi$
$443$	−1.73048			−0.0822177			−0.0411088	+	0.999155i	$0.513089\pi$
$444$		0			0
$445$	−0.961355	−	1.66512i	−0.0455726	−	0.0789341i
$446$	0.920842	−	1.59494i	0.0436031	−	0.0755228i
$447$		0			0
$448$	6.62892	+	3.82721i	0.313187	+	0.180819i
$449$	9.14208	+	5.27818i	0.431442	+	0.249093i	0.699961	−	0.714181i	$-0.253201\pi$
$449$	9.14208	+	5.27818i	0.431442	+	0.249093i	−0.268519	+	0.963274i	$0.586534\pi$
$450$		0			0
$451$	1.06237	−	1.84008i	0.0500252	−	0.0866462i
$452$	4.91675	+	8.51605i	0.231264	+	0.400561i
$453$		0			0
$454$	0.837063			0.0392853
$455$	−3.04597	−	5.26980i	−0.142797	−	0.247052i
$456$		0			0
$457$	−6.88399	+	3.97447i	−0.322019	+	0.185918i	−0.652292	−	0.757968i	$-0.726193\pi$
$457$	−6.88399	+	3.97447i	−0.322019	+	0.185918i	0.330273	+	0.943885i	$0.392859\pi$
$458$	1.65025	+	2.85832i	0.0771111	+	0.133560i
$459$		0			0
$460$			17.0383i			0.794415i
$461$	−9.43262	−	5.44592i	−0.439321	−	0.253642i	0.263989	−	0.964526i	$-0.414962\pi$
$461$	−9.43262	−	5.44592i	−0.439321	−	0.253642i	−0.703309	+	0.710884i	$0.748295\pi$
$462$		0			0
$463$			35.8227i			1.66482i	0.554158	+	0.832411i	$0.313040\pi$
$463$			35.8227i			1.66482i	−0.554158	+	0.832411i	$0.686960\pi$
$464$	16.0379	−	27.7784i	0.744539	−	1.28958i
$465$		0			0
$466$	−0.714355	+	0.412433i	−0.0330918	+	0.0191056i
$467$	19.8983			0.920785			0.460393	−	0.887715i	$-0.347709\pi$
$467$	19.8983			0.920785			0.460393	+	0.887715i	$0.347709\pi$
$468$		0			0
$469$	−13.4759			−0.622261
$470$	−2.25069	+	1.29944i	−0.103817	+	0.0599386i
$471$		0			0
$472$	−2.24545	+	3.88923i	−0.103355	+	0.179016i
$473$			0.281894i			0.0129615i
$474$		0			0
$475$	2.68861	+	1.55227i	0.123362	+	0.0712231i
$476$			6.32495i			0.289904i
$477$		0			0
$478$	1.32850	+	2.30102i	0.0607640	+	0.105246i
$479$	−22.7680	+	13.1451i	−1.04030	+	0.600615i	−0.919917	−	0.392113i	$-0.871744\pi$
$479$	−22.7680	+	13.1451i	−1.04030	+	0.600615i	−0.120379	+	0.992728i	$0.538411\pi$
$480$		0			0
$481$	−0.0111741	−	22.7721i	−0.000509496	−	1.03832i
$482$	1.90134			0.0866035
$483$		0			0
$484$	−10.7883	−	18.6860i	−0.490379	−	0.849362i
$485$	6.69177	−	11.5905i	0.303857	−	0.526296i
$486$		0			0
$487$	5.52491	+	3.18981i	0.250358	+	0.144544i	0.619928	−	0.784659i	$-0.287162\pi$
$487$	5.52491	+	3.18981i	0.250358	+	0.144544i	−0.369570	+	0.929203i	$0.620495\pi$
$488$	3.74918	+	2.16459i	0.169717	+	0.0979864i
$489$		0			0
$490$	0.101594	−	0.175965i	0.00458954	−	0.00794931i
$491$	1.48384	+	2.57008i	0.0669647	+	0.115986i	0.897564	−	0.440885i	$-0.145335\pi$
$491$	1.48384	+	2.57008i	0.0669647	+	0.115986i	−0.830599	+	0.556871i	$0.812002\pi$
$492$		0			0
$493$	26.1107			1.17597
$494$	0.313035	−	0.542808i	0.0140841	−	0.0244221i
$495$		0			0
$496$	15.9207	−	9.19184i	0.714862	−	0.412726i
$497$	3.54058	+	6.13246i	0.158817	+	0.275078i
$498$		0			0
$499$			28.1331i			1.25941i	0.776835	+	0.629704i	$0.216824\pi$
$499$			28.1331i			1.25941i	−0.776835	+	0.629704i	$0.783176\pi$
$500$	20.7554	+	11.9831i	0.928208	+	0.535901i
$501$		0			0
$502$			2.71492i			0.121173i
$503$	−15.7688	+	27.3124i	−0.703097	+	1.21780i	0.264277	+	0.964447i	$0.414867\pi$
$503$	−15.7688	+	27.3124i	−0.703097	+	1.21780i	−0.967374	+	0.253353i	$0.918467\pi$
$504$		0			0
$505$	22.7288	−	13.1225i	1.01142	−	0.583943i
$506$	0.223079			0.00991706
$507$		0			0
$508$	−16.0178			−0.710673
$509$	−11.7731	+	6.79719i	−0.521832	+	0.301280i	−0.737684	−	0.675146i	$-0.764081\pi$
$509$	−11.7731	+	6.79719i	−0.521832	+	0.301280i	0.215852	+	0.976426i	$0.430747\pi$
$510$		0			0
$511$	1.08041	−	1.87133i	0.0477947	−	0.0827828i
$512$			9.35193i			0.413301i
$513$		0			0
$514$	−2.12773	−	1.22845i	−0.0938502	−	0.0541844i
$515$			17.3850i			0.766074i
$516$		0			0
$517$	−2.33183	−	4.03885i	−0.102554	−	0.177628i
$518$	0.658329	−	0.380087i	0.0289253	−	0.0167000i
$519$		0			0
$520$	1.45866	−	2.52933i	0.0639664	−	0.110919i
$521$	−8.78344			−0.384810			−0.192405	−	0.981316i	$-0.561629\pi$
$521$	−8.78344			−0.384810			−0.192405	+	0.981316i	$0.561629\pi$
$522$		0			0
$523$	−16.2849	−	28.2063i	−0.712088	−	1.23337i	−0.964072	−	0.265642i	$-0.914416\pi$
$523$	−16.2849	−	28.2063i	−0.712088	−	1.23337i	0.251983	−	0.967732i	$-0.418917\pi$
$524$	18.7670	−	32.5053i	0.819838	−	1.42000i
$525$		0			0
$526$	−3.07912	−	1.77773i	−0.134256	−	0.0775127i
$527$	12.9600	+	7.48246i	0.564547	+	0.325941i
$528$		0			0
$529$	−1.41953	+	2.45869i	−0.0617185	+	0.106900i
$530$	0.139295	+	0.241265i	0.00605057	+	0.0104799i
$531$		0			0
$532$	−2.86690			−0.124296
$533$	−0.0103098	−	21.0107i	−0.000446568	−	0.910074i
$534$		0			0
$535$	−19.1878	+	11.0781i	−0.829560	+	0.478947i
$536$	−3.23218	−	5.59829i	−0.139609	−	0.241809i
$537$		0			0
$538$		−	3.36000i		−	0.144860i
$539$	0.315769	+	0.182309i	0.0136011	+	0.00785261i
$540$		0			0
$541$			6.94870i			0.298748i	0.988781	+	0.149374i	$0.0477258\pi$
$541$			6.94870i			0.298748i	−0.988781	+	0.149374i	$0.952274\pi$
$542$	−1.77224	+	3.06961i	−0.0761243	+	0.131851i
$543$		0			0
$544$	−3.94612	+	2.27830i	−0.169189	+	0.0976811i
$545$	−17.6344			−0.755375
$546$		0			0
$547$	10.9095			0.466457			0.233229	−	0.972422i	$-0.425071\pi$
$547$	10.9095			0.466457			0.233229	+	0.972422i	$0.425071\pi$
$548$	31.3388	−	18.0935i	1.33873	−	0.772915i
$549$		0			0
$550$	0.0471789	−	0.0817163i	0.00201172	−	0.00348440i
$551$			11.8352i			0.504194i
$552$		0			0
$553$	−5.96502	−	3.44391i	−0.253659	−	0.146450i
$554$		−	0.825493i		−	0.0350718i
$555$		0			0
$556$	−5.21282	−	9.02886i	−0.221073	−	0.382909i
$557$	−29.9901	+	17.3148i	−1.27072	+	0.733650i	−0.975123	−	0.221662i	$-0.928852\pi$
$557$	−29.9901	+	17.3148i	−1.27072	+	0.733650i	−0.295596	+	0.955313i	$0.595518\pi$
$558$		0			0
$559$	1.39495	+	2.41339i	0.0590001	+	0.102075i
$560$	−6.60628			−0.279166
$561$		0			0
$562$	−1.75088	−	3.03261i	−0.0738563	−	0.127923i
$563$	−4.56839	+	7.91269i	−0.192535	+	0.333480i	−0.946090	−	0.323905i	$-0.895004\pi$
$563$	−4.56839	+	7.91269i	−0.192535	+	0.333480i	0.753555	+	0.657385i	$0.228338\pi$
$564$		0			0
$565$	−7.24070	−	4.18042i	−0.304618	−	0.175872i
$566$	1.21019	+	0.698702i	0.0508680	+	0.0293686i
$567$		0			0
$568$	−1.69840	+	2.94172i	−0.0712633	+	0.123432i
$569$	−9.15000	−	15.8483i	−0.383588	−	0.664394i	0.607984	−	0.793949i	$-0.291978\pi$
$569$	−9.15000	−	15.8483i	−0.383588	−	0.664394i	−0.991572	+	0.129555i	$0.958645\pi$
$570$		0			0
$571$	−10.1791			−0.425981			−0.212990	−	0.977054i	$-0.568320\pi$
$571$	−10.1791			−0.425981			−0.212990	+	0.977054i	$0.568320\pi$
$572$	2.26119	+	1.30402i	0.0945450	+	0.0545237i
$573$		0			0
$574$	0.607409	−	0.350688i	0.0253528	−	0.0146374i
$575$	5.46470	+	9.46514i	0.227894	+	0.394724i
$576$		0			0
$577$		−	19.5165i		−	0.812482i	−0.913766	−	0.406241i	$-0.866839\pi$
$577$		−	19.5165i		−	0.812482i	0.913766	−	0.406241i	$-0.133161\pi$
$578$	0.714246	+	0.412370i	0.0297087	+	0.0171523i
$579$		0			0
$580$			27.4740i			1.14080i
$581$	−0.283690	+	0.491365i	−0.0117694	+	0.0203853i
$582$		0			0
$583$	−0.432949	+	0.249963i	−0.0179309	+	0.0103524i
$584$	1.03654			0.0428923
$585$		0			0
$586$	2.14103			0.0884453
$587$	30.6486	−	17.6950i	1.26501	−	0.730351i	0.290967	−	0.956733i	$-0.406023\pi$
$587$	30.6486	−	17.6950i	1.26501	−	0.730351i	0.974039	+	0.226382i	$0.0726898\pi$
$588$		0			0
$589$	−3.39156	+	5.87436i	−0.139747	+	0.242049i
$590$		−	1.90223i		−	0.0783137i
$591$		0			0
$592$	−21.4044	−	12.3579i	−0.879716	−	0.507905i
$593$		−	18.0881i		−	0.742790i	−0.928475	−	0.371395i	$-0.878880\pi$
$593$		−	18.0881i		−	0.742790i	0.928475	−	0.371395i	$-0.121120\pi$
$594$		0			0
$595$	−2.68887	−	4.65725i	−0.110233	−	0.190929i
$596$	15.9451	−	9.20592i	0.653138	−	0.377089i
$597$		0			0
$598$	1.90985	−	1.10390i	0.0780996	−	0.0451419i
$599$	−9.05992			−0.370178			−0.185089	−	0.982722i	$-0.559257\pi$
$599$	−9.05992			−0.370178			−0.185089	+	0.982722i	$0.559257\pi$
$600$		0			0
$601$	−14.6440	−	25.3642i	−0.597343	−	1.03463i	−0.993212	−	0.116321i	$-0.962890\pi$
$601$	−14.6440	−	25.3642i	−0.597343	−	1.03463i	0.395869	−	0.918307i	$-0.370444\pi$
$602$	−0.0465264	+	0.0805861i	−0.00189628	+	0.00328444i
$603$		0			0
$604$	24.0958	+	13.9117i	0.980444	+	0.566059i
$605$	15.8876	+	9.17269i	0.645922	+	0.372923i
$606$		0			0
$607$	19.6825	−	34.0911i	0.798887	−	1.38371i	−0.121454	−	0.992597i	$-0.538756\pi$
$607$	19.6825	−	34.0911i	0.798887	−	1.38371i	0.920341	−	0.391116i	$-0.127911\pi$
$608$	−1.03268	−	1.78865i	−0.0418807	−	0.0725394i
$609$		0			0
$610$	−1.83373			−0.0742457
$611$	−39.9498	−	23.0389i	−1.61619	−	0.932053i
$612$		0			0
$613$	4.79186	−	2.76658i	0.193541	−	0.111741i	−0.400098	−	0.916472i	$-0.631024\pi$
$613$	4.79186	−	2.76658i	0.193541	−	0.111741i	0.593639	+	0.804731i	$0.297691\pi$
$614$	−0.546413	−	0.946416i	−0.0220514	−	0.0381942i
$615$		0			0
$616$			0.174906i			0.00704716i
$617$	−10.8959	−	6.29077i	−0.438654	−	0.253257i	0.264373	−	0.964421i	$-0.414835\pi$
$617$	−10.8959	−	6.29077i	−0.438654	−	0.253257i	−0.703026	+	0.711164i	$0.748168\pi$
$618$		0			0
$619$		−	22.3955i		−	0.900149i	−0.892991	−	0.450075i	$-0.851397\pi$
$619$		−	22.3955i		−	0.900149i	0.892991	−	0.450075i	$-0.148603\pi$
$620$	−7.87314	+	13.6367i	−0.316193	+	0.547662i
$621$		0			0
$622$	0.163724	−	0.0945262i	0.00656474	−	0.00379015i
$623$	1.13893			0.0456305
$624$		0			0
$625$	−9.62659			−0.385064
$626$	2.14965	−	1.24110i	0.0859175	−	0.0496045i
$627$		0			0
$628$	17.0580	−	29.5454i	0.680690	−	1.17899i
$629$		−	20.1194i		−	0.802213i
$630$		0			0
$631$	1.68778	+	0.974439i	0.0671894	+	0.0387918i	0.533218	−	0.845978i	$-0.320982\pi$
$631$	1.68778	+	0.974439i	0.0671894	+	0.0387918i	−0.466029	+	0.884769i	$0.654316\pi$
$632$		−	3.30406i		−	0.131428i
$633$		0			0
$634$	1.83811	+	3.18369i	0.0730005	+	0.126441i
$635$	11.7944	−	6.80948i	0.468045	−	0.270226i
$636$		0			0
$637$	3.60555	−	0.00176922i	0.142857	−	7.00992e-5i
$638$	0.359712			0.0142411
$639$		0			0
$640$	−3.19238	−	5.52937i	−0.126190	−	0.218568i
$641$	−5.21051	+	9.02487i	−0.205803	+	0.356461i	−0.950388	−	0.311066i	$-0.899314\pi$
$641$	−5.21051	+	9.02487i	−0.205803	+	0.356461i	0.744585	+	0.667527i	$0.232647\pi$
$642$		0			0
$643$	13.2247	+	7.63531i	0.521533	+	0.301107i	0.737562	−	0.675280i	$-0.235977\pi$
$643$	13.2247	+	7.63531i	0.521533	+	0.301107i	−0.216029	+	0.976387i	$0.569310\pi$
$644$	−8.74061	−	5.04639i	−0.344428	−	0.198856i
$645$		0			0
$646$	0.276806	−	0.479442i	0.0108908	−	0.0188634i
$647$	−8.75328	−	15.1611i	−0.344127	−	0.596045i	0.641068	−	0.767484i	$-0.278492\pi$
$647$	−8.75328	−	15.1611i	−0.344127	−	0.596045i	−0.985195	+	0.171439i	$0.945158\pi$
$648$		0			0
$649$	3.41354			0.133993
$650$	−0.000457849	−	0.933064i	−1.79583e−5	−	0.0365978i
$651$		0			0
$652$	−20.2777	+	11.7073i	−0.794136	+	0.458494i
$653$	−5.09169	−	8.81906i	−0.199253	−	0.345117i	0.749033	−	0.662532i	$-0.230518\pi$
$653$	−5.09169	−	8.81906i	−0.199253	−	0.345117i	−0.948287	+	0.317416i	$0.897185\pi$
$654$		0			0
$655$			31.9129i			1.24694i
$656$	−19.7488	−	11.4020i	−0.771063	−	0.445173i
$657$		0			0
$658$		−	1.53947i		−	0.0600147i
$659$	−21.9294	+	37.9828i	−0.854247	+	1.47960i	0.0230945	+	0.999733i	$0.492648\pi$
$659$	−21.9294	+	37.9828i	−0.854247	+	1.47960i	−0.877342	+	0.479866i	$0.840685\pi$
$660$		0			0
$661$	−28.5156	+	16.4635i	−1.10913	+	0.640356i	−0.938604	−	0.344997i	$-0.887880\pi$
$661$	−28.5156	+	16.4635i	−1.10913	+	0.640356i	−0.170526	+	0.985353i	$0.554547\pi$
$662$	−3.11167			−0.120939
$663$		0			0
$664$	−0.272170			−0.0105622
$665$	2.11098	−	1.21878i	0.0818604	−	0.0472621i
$666$		0			0
$667$	−20.8326	+	36.0831i	−0.806640	+	1.39714i
$668$		−	8.57120i		−	0.331630i
$669$		0			0
$670$	2.37130	+	1.36907i	0.0916113	+	0.0528918i
$671$		−	3.29062i		−	0.127033i
$672$		0			0
$673$	13.3423	+	23.1095i	0.514307	+	0.890806i	0.999862	+	0.0165997i	$0.00528409\pi$
$673$	13.3423	+	23.1095i	0.514307	+	0.890806i	−0.485555	+	0.874206i	$0.661383\pi$
$674$	−2.23015	+	1.28758i	−0.0859021	+	0.0495956i
$675$		0			0
$676$	25.8117	−	0.0253313i	0.992756	−	0.000974280i
$677$	−29.5328			−1.13504			−0.567519	−	0.823361i	$-0.692096\pi$
$677$	−29.5328			−1.13504			−0.567519	+	0.823361i	$0.692096\pi$
$678$		0			0
$679$	3.96393	+	6.86572i	0.152122	+	0.263482i
$680$	1.28984	−	2.23406i	0.0494630	−	0.0856725i
$681$		0			0
$682$	0.178542	+	0.103081i	0.00683674	+	0.00394719i
$683$	15.8379	+	9.14400i	0.606019	+	0.349885i	0.771406	−	0.636343i	$-0.219554\pi$
$683$	15.8379	+	9.14400i	0.606019	+	0.349885i	−0.165387	+	0.986229i	$0.552887\pi$
$684$		0			0
$685$	−15.3838	+	26.6456i	−0.587786	+	1.01807i
$686$	0.0601799	+	0.104235i	0.00229768	+	0.00397970i
$687$		0			0
$688$	3.02545			0.115344
$689$	−2.46968	+	4.28246i	−0.0940872	+	0.163149i
$690$		0			0
$691$	−8.95525	+	5.17031i	−0.340674	+	0.196688i	−0.660570	−	0.750765i	$-0.729685\pi$
$691$	−8.95525	+	5.17031i	−0.340674	+	0.196688i	0.319896	+	0.947453i	$0.396352\pi$
$692$	−12.4290	−	21.5277i	−0.472480	−	0.818360i
$693$		0			0
$694$		−	0.265855i		−	0.0100917i
$695$	7.67671	+	4.43215i	0.291194	+	0.168121i
$696$		0			0
$697$		−	18.5632i		−	0.703131i
$698$	−0.679501	+	1.17693i	−0.0257195	+	0.0445475i
$699$		0			0
$700$	−3.69710	+	2.13452i	−0.139737	+	0.0806774i
$701$	−41.6959			−1.57483			−0.787415	−	0.616423i	$-0.788581\pi$
$701$	−41.6959			−1.57483			−0.787415	+	0.616423i	$0.788581\pi$
$702$		0			0
$703$	9.11948			0.343948
$704$	2.41702	−	1.39547i	0.0910951	−	0.0525938i
$705$		0			0
$706$	2.14501	−	3.71527i	0.0807287	−	0.139826i
$707$			15.5464i			0.584684i
$708$		0			0
$709$	0.00947974	+	0.00547313i	0.000356019	+	0.000205548i	0.500178	−	0.865923i	$-0.333268\pi$
$709$	0.00947974	+	0.00547313i	0.000356019	+	0.000205548i	−0.499822	+	0.866128i	$0.666601\pi$
$710$		−	1.43880i		−	0.0539972i
$711$		0			0
$712$	0.273171	+	0.473146i	0.0102375	+	0.0177319i
$713$	−20.6804	+	11.9398i	−0.774488	+	0.447151i
$714$		0			0
$715$	−2.21935	+	0.00108902i	−0.0829988	+	4.07271e-5i
$716$	−13.0951			−0.489388
$717$		0			0
$718$	1.16278	+	2.01400i	0.0433947	+	0.0751618i
$719$	12.7330	−	22.0542i	0.474861	−	0.822484i	−0.524724	−	0.851272i	$-0.675832\pi$
$719$	12.7330	−	22.0542i	0.474861	−	0.822484i	0.999586	+	0.0287885i	$0.00916494\pi$
$720$		0			0
$721$	−8.91847	−	5.14908i	−0.332141	−	0.191762i
$722$	−1.76314	−	1.01795i	−0.0656174	−	0.0378842i
$723$		0			0
$724$	10.9359	−	18.9416i	0.406430	−	0.703957i
$725$	8.81176	+	15.2624i	0.327261	+	0.566832i
$726$		0			0
$727$	−23.5565			−0.873663			−0.436831	−	0.899543i	$-0.643899\pi$
$727$	−23.5565			−0.873663			−0.436831	+	0.899543i	$0.643899\pi$
$728$	0.865519	+	1.49743i	0.0320783	+	0.0554983i
$729$		0			0
$730$	−0.380231	+	0.219526i	−0.0140730	+	0.00812503i
$731$	1.23141	+	2.13286i	0.0455453	+	0.0788867i
$732$		0			0
$733$		−	6.23249i		−	0.230202i	−0.993354	−	0.115101i	$-0.963281\pi$
$733$		−	6.23249i		−	0.230202i	0.993354	−	0.115101i	$-0.0367192\pi$
$734$	0.387821	+	0.223909i	0.0143147	+	0.00826461i
$735$		0			0
$736$		−	7.27100i		−	0.268013i
$737$	−2.45679	+	4.25528i	−0.0904969	+	0.156745i
$738$		0			0
$739$	1.12339	−	0.648588i	0.0413244	−	0.0238587i	−0.479195	−	0.877708i	$-0.659071\pi$
$739$	1.12339	−	0.648588i	0.0413244	−	0.0238587i	0.520520	+	0.853850i	$0.325738\pi$
$740$	21.1699			0.778221
$741$		0			0
$742$	−0.165025			−0.00605825
$743$	−5.25627	+	3.03471i	−0.192834	+	0.111333i	−0.593309	−	0.804975i	$-0.702179\pi$
$743$	−5.25627	+	3.03471i	−0.192834	+	0.111333i	0.400475	+	0.916308i	$0.368845\pi$
$744$		0			0
$745$	−7.82725	+	13.5572i	−0.286768	+	0.496697i
$746$		−	0.422796i		−	0.0154797i
$747$		0			0
$748$	1.99722	+	1.15310i	0.0730256	+	0.0421613i
$749$		−	13.1244i		−	0.479555i
$750$		0			0
$751$	−18.3023	−	31.7005i	−0.667860	−	1.15677i	−0.978501	−	0.206241i	$-0.933877\pi$
$751$	−18.3023	−	31.7005i	−0.667860	−	1.15677i	0.310641	−	0.950527i	$-0.399456\pi$
$752$	−43.3473	+	25.0266i	−1.58071	+	0.912625i
$753$		0			0
$754$	3.07961	−	1.78003i	0.112153	−	0.0648248i
$755$	−23.6566			−0.860952
$756$		0			0
$757$	−5.83991	−	10.1150i	−0.212255	−	0.367636i	0.740165	−	0.672425i	$-0.234747\pi$
$757$	−5.83991	−	10.1150i	−0.212255	−	0.367636i	−0.952420	+	0.304789i	$0.901414\pi$
$758$	1.50548	−	2.60757i	0.0546815	−	0.0947111i
$759$		0			0
$760$	1.01263	+	0.584642i	0.0367320	+	0.0212072i
$761$	34.4408	+	19.8844i	1.24848	+	0.720810i	0.970806	−	0.239866i	$-0.0771035\pi$
$761$	34.4408	+	19.8844i	1.24848	+	0.720810i	0.277673	+	0.960676i	$0.410437\pi$
$762$		0			0
$763$	5.22295	−	9.04641i	0.189083	−	0.327502i
$764$	5.88916	+	10.2003i	0.213062	+	0.369035i
$765$		0			0
$766$	2.70393			0.0976970
$767$	29.2245	−	16.8919i	1.05523	−	0.609930i
$768$		0			0
$769$	−8.62507	+	4.97969i	−0.311028	+	0.179572i	−0.647386	−	0.762162i	$-0.724138\pi$
$769$	−8.62507	+	4.97969i	−0.311028	+	0.179572i	0.336358	+	0.941734i	$0.390805\pi$
$770$	−0.0370429	−	0.0641602i	−0.00133493	−	0.00231217i
$771$		0			0
$772$			8.33112i			0.299843i
$773$	−11.0433	−	6.37588i	−0.397201	−	0.229324i	0.288074	−	0.957608i	$-0.406985\pi$
$773$	−11.0433	−	6.37588i	−0.397201	−	0.229324i	−0.685276	+	0.728284i	$0.740318\pi$
$774$		0			0
$775$			10.1006i			0.362825i
$776$	−1.90148	+	3.29346i	−0.0682592	+	0.118228i
$777$		0			0
$778$	−1.39012	+	0.802586i	−0.0498382	+	0.0287741i
$779$	8.41411			0.301467
$780$		0			0
$781$	2.58192			0.0923882
$782$	1.68785	−	0.974483i	0.0603575	−	0.0348474i
$783$		0			0
$784$	1.95665	−	3.38901i	0.0698802	−	0.121036i
$785$			29.0069i			1.03530i
$786$		0			0
$787$	7.52380	+	4.34387i	0.268194	+	0.154842i	0.628067	−	0.778159i	$-0.283846\pi$
$787$	7.52380	+	4.34387i	0.268194	+	0.154842i	−0.359872	+	0.933002i	$0.617180\pi$
$788$		−	11.4861i		−	0.409174i
$789$		0			0
$790$	0.699759	+	1.21202i	0.0248963	+	0.0431216i
$791$	4.28909	−	2.47631i	0.152503	−	0.0880474i
$792$		0			0
$793$	−16.2836	−	28.1721i	−0.578247	−	1.00042i
$794$	−3.10929			−0.110345
$795$		0			0
$796$	11.8731	+	20.5649i	0.420832	+	0.728903i
$797$	−19.3719	+	33.5531i	−0.686187	+	1.18851i	0.286875	+	0.957968i	$0.407384\pi$
$797$	−19.3719	+	33.5531i	−0.686187	+	1.18851i	−0.973062	+	0.230543i	$0.925950\pi$
$798$		0			0
$799$	−35.2861	−	20.3724i	−1.24833	−	0.720725i
$800$	−2.66345	−	1.53774i	−0.0941672	−	0.0543675i
$801$		0			0
$802$	−1.05679	+	1.83041i	−0.0373166	+	0.0646342i
$803$	−0.393938	−	0.682321i	−0.0139018	−	0.0240786i
$804$		0			0
$805$	8.58130			0.302451
$806$	2.03866	−	0.00100036i	0.0718086	−	3.52361e-5i
$807$		0			0
$808$	−6.45844	+	3.72878i	−0.227207	+	0.131178i
$809$	14.4275	+	24.9892i	0.507244	+	0.878573i	0.999965	+	0.00838530i	$0.00266915\pi$
$809$	14.4275	+	24.9892i	0.507244	+	0.878573i	−0.492721	+	0.870188i	$0.663998\pi$
$810$		0			0
$811$			12.3917i			0.435131i	0.976046	+	0.217566i	$0.0698116\pi$
$811$			12.3917i			0.435131i	−0.976046	+	0.217566i	$0.930188\pi$
$812$	−14.0941	−	8.13725i	−0.494607	−	0.285561i
$813$		0			0
$814$		−	0.277173i		−	0.00971491i
$815$	9.95405	−	17.2409i	0.348675	−	0.603923i
$816$		0			0
$817$	−0.966758	+	0.558158i	−0.0338226	+	0.0195275i
$818$	1.74861			0.0611388
$819$		0			0
$820$	19.5324			0.682103
$821$	−35.5277	+	20.5119i	−1.23992	+	0.715870i	−0.969079	−	0.246753i	$-0.920636\pi$
$821$	−35.5277	+	20.5119i	−1.23992	+	0.715870i	−0.270845	+	0.962623i	$0.587303\pi$
$822$		0			0
$823$	−1.06806	+	1.84994i	−0.0372304	+	0.0644849i	−0.884040	−	0.467411i	$-0.845187\pi$
$823$	−1.06806	+	1.84994i	−0.0372304	+	0.0644849i	0.846810	+	0.531896i	$0.178520\pi$
$824$		−	4.93999i		−	0.172093i
$825$		0			0
$826$	0.975842	+	0.563403i	0.0339539	+	0.0196033i
$827$			8.54938i			0.297291i	0.988891	+	0.148645i	$0.0474913\pi$
$827$			8.54938i			0.297291i	−0.988891	+	0.148645i	$0.952509\pi$
$828$		0			0
$829$	−7.37844	−	12.7798i	−0.256264	−	0.443862i	0.708974	−	0.705234i	$-0.249158\pi$
$829$	−7.37844	−	12.7798i	−0.256264	−	0.443862i	−0.965238	+	0.261373i	$0.915825\pi$
$830$	0.0998392	−	0.0576422i	0.00346547	−	0.00200079i
$831$		0			0
$832$	13.7875	−	23.9077i	0.477995	−	0.828850i
$833$	3.18555			0.110373
$834$		0			0
$835$	3.64379	+	6.31123i	0.126099	+	0.218409i
$836$	−0.522661	+	0.905276i	−0.0180766	+	0.0313096i
$837$		0			0
$838$	−0.479680	−	0.276943i	−0.0165703	−	0.00956685i
$839$	−23.3581	−	13.4858i	−0.806411	−	0.465582i	0.0392968	−	0.999228i	$-0.487488\pi$
$839$	−23.3581	−	13.4858i	−0.806411	−	0.465582i	−0.845708	+	0.533646i	$0.820822\pi$
$840$		0			0
$841$	−19.0923	+	33.0687i	−0.658353	+	1.14030i
$842$	1.15934	+	2.00803i	0.0399534	+	0.0692013i
$843$		0			0
$844$	−16.3525			−0.562877
$845$	−18.9951	+	10.9917i	−0.653453	+	0.378127i
$846$		0			0
$847$	−9.41114	+	5.43353i	−0.323371	+	0.186698i
$848$	2.68275	+	4.64665i	0.0921259	+	0.159567i
$849$		0			0
$850$		−	0.824374i		−	0.0282758i
$851$	27.8035	+	16.0524i	0.953092	+	0.550268i
$852$		0			0
$853$		−	25.6332i		−	0.877665i	−0.898569	−	0.438832i	$-0.855392\pi$
$853$		−	25.6332i		−	0.877665i	0.898569	−	0.438832i	$-0.144608\pi$
$854$	0.543114	−	0.940702i	0.0185850	−	0.0321902i
$855$		0			0
$856$	5.45225	−	3.14786i	0.186354	−	0.107592i
$857$	11.7653			0.401894			0.200947	−	0.979602i	$-0.435598\pi$
$857$	11.7653			0.401894			0.200947	+	0.979602i	$0.435598\pi$
$858$		0			0
$859$	−21.7761			−0.742992			−0.371496	−	0.928435i	$-0.621155\pi$
$859$	−21.7761			−0.742992			−0.371496	+	0.928435i	$0.621155\pi$
$860$	−2.24422	+	1.29570i	−0.0765274	+	0.0441831i
$861$		0			0
$862$	1.70701	−	2.95663i	0.0581410	−	0.100703i
$863$			41.0575i			1.39761i	0.715310	+	0.698807i	$0.246285\pi$
$863$			41.0575i			1.39761i	−0.715310	+	0.698807i	$0.753715\pi$
$864$		0			0
$865$	18.3037	+	10.5677i	0.622345	+	0.359311i
$866$			1.50694i			0.0512079i
$867$		0			0
$868$	−4.66373	−	8.07781i	−0.158297	−	0.274179i
$869$	−2.17496	+	1.25571i	−0.0737803	+	0.0425971i
$870$		0			0
$871$	0.0238420	+	48.5882i	0.000807854	+	1.64635i
$872$	5.01085			0.169689
$873$		0			0
$874$	0.441702	+	0.765050i	0.0149408	+	0.0258782i
$875$	6.03527	−	10.4534i	0.204029	−	0.353389i
$876$		0			0
$877$	5.96788	+	3.44556i	0.201521	+	0.116348i	0.597365	−	0.801970i	$-0.296214\pi$
$877$	5.96788	+	3.44556i	0.201521	+	0.116348i	−0.395844	+	0.918318i	$0.629548\pi$
$878$	3.30709	+	1.90935i	0.111609	+	0.0644374i
$879$		0			0
$880$	−1.20439	+	2.08606i	−0.0405998	+	0.0703209i
$881$	5.32288	+	9.21950i	0.179332	+	0.310613i	0.941652	−	0.336588i	$-0.109273\pi$
$881$	5.32288	+	9.21950i	0.179332	+	0.310613i	−0.762320	+	0.647201i	$0.775940\pi$
$882$		0			0
$883$	21.3844			0.719641			0.359821	−	0.933022i	$-0.382838\pi$
$883$	21.3844			0.719641			0.359821	+	0.933022i	$0.382838\pi$
$884$	22.8049	−	0.0111902i	0.767012	−	0.000376369i
$885$		0			0
$886$	−0.180376	+	0.104140i	−0.00605986	+	0.00349866i
$887$	−17.0575	−	29.5445i	−0.572735	−	0.992007i	−0.996284	−	0.0861333i	$-0.972549\pi$
$887$	−17.0575	−	29.5445i	−0.572735	−	0.992007i	0.423548	−	0.905874i	$-0.360784\pi$
$888$		0			0
$889$			8.06731i			0.270569i
$890$	−0.200413	−	0.115709i	−0.00671786	−	0.00387856i
$891$		0			0
$892$			30.3813i			1.01724i
$893$	9.23418	−	15.9941i	0.309010	−	0.535221i
$894$		0			0
$895$	9.64235	−	5.56701i	0.322308	−	0.186085i
$896$	3.78208			0.126350
$897$		0			0
$898$	1.27056			0.0423992
$899$	−33.3469	+	19.2528i	−1.11218	+	0.642118i
$900$		0			0
$901$	−2.18384	+	3.78253i	−0.0727544	+	0.126014i
$902$		−	0.255734i		−	0.00851502i
$903$		0			0
$904$	2.05746	+	1.18788i	0.0684301	+	0.0395081i
$905$			18.5963i			0.618163i
$906$		0			0
$907$	21.0758	+	36.5043i	0.699810	+	1.21211i	0.968532	+	0.248888i	$0.0800652\pi$
$907$	21.0758	+	36.5043i	0.699810	+	1.21211i	−0.268723	+	0.963218i	$0.586601\pi$
$908$	−11.9586	+	6.90429i	−0.396860	+	0.229127i
$909$		0			0
$910$	−0.634632	−	0.365990i	−0.0210379	−	0.0121324i
$911$	−20.9947			−0.695584			−0.347792	−	0.937572i	$-0.613068\pi$
$911$	−20.9947			−0.695584			−0.347792	+	0.937572i	$0.613068\pi$
$912$		0			0
$913$	0.103438	+	0.179161i	0.00342331	+	0.00592935i
$914$	−0.478367	+	0.828556i	−0.0158230	+	0.0274062i
$915$		0			0
$916$	−47.1521	−	27.2233i	−1.55795	−	0.899483i
$917$	−16.3712	−	9.45194i	−0.540626	−	0.312131i
$918$		0			0
$919$	7.14699	−	12.3789i	0.235757	−	0.408344i	−0.723735	−	0.690078i	$-0.757576\pi$
$919$	7.14699	−	12.3789i	0.235757	−	0.408344i	0.959493	+	0.281734i	$0.0909096\pi$
$920$	2.05821	+	3.56492i	0.0678571	+	0.117532i
$921$		0			0
$922$	−1.31094			−0.0431736
$923$	22.1046	−	12.7766i	0.727583	−	0.420546i
$924$		0			0
$925$	11.7603	−	6.78983i	0.386677	−	0.223248i
$926$	2.15581	+	3.73397i	0.0708443	+	0.122706i
$927$		0			0
$928$		−	11.7244i		−	0.384872i
$929$	−5.89524	−	3.40362i	−0.193416	−	0.111669i	0.400164	−	0.916443i	$-0.368953\pi$
$929$	−5.89524	−	3.40362i	−0.193416	−	0.111669i	−0.593581	+	0.804774i	$0.702286\pi$
$930$		0			0
$931$			1.44391i			0.0473221i
$932$	6.80369	−	11.7843i	0.222862	−	0.386009i
$933$		0			0
$934$	2.07410	−	1.19748i	0.0678666	−	0.0391828i
$935$	−1.96082			−0.0641256
$936$		0			0
$937$	−5.22890			−0.170821			−0.0854104	−	0.996346i	$-0.527220\pi$
$937$	−5.22890			−0.170821			−0.0854104	+	0.996346i	$0.527220\pi$
$938$	−1.40466	+	0.810981i	−0.0458638	+	0.0264795i
$939$		0			0
$940$	21.4362	−	37.1285i	0.699170	−	1.21100i
$941$		−	56.4403i		−	1.83990i	−0.392033	−	0.919951i	$-0.628228\pi$
$941$		−	56.4403i		−	1.83990i	0.392033	−	0.919951i	$-0.371772\pi$
$942$		0			0
$943$	25.6530	+	14.8108i	0.835376	+	0.482304i
$944$		−	36.6361i		−	1.19240i
$945$		0			0
$946$	0.0169644	+	0.0293832i	0.000551559	+	0.000955329i
$947$	5.06648	−	2.92513i	0.164639	−	0.0950541i	−0.415417	−	0.909631i	$-0.636364\pi$
$947$	5.06648	−	2.92513i	0.164639	−	0.0950541i	0.580055	+	0.814577i	$0.303031\pi$
$948$		0			0
$949$	−6.74909	−	3.89217i	−0.219085	−	0.126345i
$950$	0.373662			0.0121232
$951$		0			0
$952$	0.764047	+	1.32337i	0.0247629	+	0.0428906i
$953$	10.8742	−	18.8346i	0.352249	−	0.610114i	−0.634394	−	0.773010i	$-0.718750\pi$
$953$	10.8742	−	18.8346i	0.352249	−	0.610114i	0.986643	+	0.162896i	$0.0520836\pi$
$954$		0			0
$955$	−8.67273	−	5.00720i	−0.280643	−	0.162029i
$956$	−37.9588	−	21.9155i	−1.22767	−	0.708798i
$957$		0			0
$958$	−1.58214	+	2.74035i	−0.0511167	+	0.0885368i
$959$	−9.11274	−	15.7837i	−0.294266	−	0.509683i
$960$		0			0
$961$	8.93110			0.288100
$962$	−1.37159	−	2.37297i	−0.0442217	−	0.0765075i
$963$		0			0
$964$	−27.1632	+	15.6827i	−0.874868	+	0.505105i
$965$	−3.54173	−	6.13446i	−0.114012	−	0.197475i
$966$		0			0
$967$		−	13.3251i		−	0.428507i	−0.976778	−	0.214253i	$-0.931268\pi$
$967$		−	13.3251i		−	0.428507i	0.976778	−	0.214253i	$-0.0687318\pi$
$968$	−4.51449	−	2.60644i	−0.145101	−	0.0837742i
$969$		0			0
$970$		−	1.61084i		−	0.0517210i
$971$	3.73092	−	6.46215i	0.119731	−	0.207380i	−0.799930	−	0.600093i	$-0.795130\pi$
$971$	3.73092	−	6.46215i	0.119731	−	0.207380i	0.919661	+	0.392713i	$0.128463\pi$
$972$		0			0
$973$	−4.54737	+	2.62542i	−0.145782	+	0.0841673i
$974$	0.767850			0.0246035
$975$		0			0
$976$	−35.3168			−1.13046
$977$	9.49204	−	5.48023i	0.303677	−	0.175328i	−0.340416	−	0.940275i	$-0.610568\pi$
$977$	9.49204	−	5.48023i	0.303677	−	0.175328i	0.644094	+	0.764947i	$0.277235\pi$
$978$		0			0
$979$	0.207638	−	0.359640i	0.00663614	−	0.0114941i
$980$			3.35188i			0.107072i
$981$		0			0
$982$	0.309335	+	0.178595i	0.00987127	+	0.00569918i
$983$			16.1441i			0.514918i	0.966289	+	0.257459i	$0.0828852\pi$
$983$			16.1441i			0.514918i	−0.966289	+	0.257459i	$0.917115\pi$
$984$		0			0
$985$	4.88296	+	8.45754i	0.155584	+	0.269480i
$986$	2.72164	−	1.57134i	0.0866747	−	0.0500417i
$987$		0			0
$988$	0.00507218	+	10.3367i	0.000161368	+	0.328856i
$989$	−3.92994			−0.124965
$990$		0			0
$991$	−3.35748	−	5.81533i	−0.106654	−	0.184730i	0.807759	−	0.589513i	$-0.200680\pi$
$991$	−3.35748	−	5.81533i	−0.106654	−	0.184730i	−0.914413	+	0.404783i	$0.867347\pi$
$992$	3.35982	−	5.81938i	0.106674	−	0.184766i
$993$		0			0
$994$	0.738102	+	0.426143i	0.0234112	+	0.0135164i
$995$	−17.4851	−	10.0950i	−0.554315	−	0.320034i
$996$		0			0
$997$	9.22057	−	15.9705i	0.292018	−	0.505791i	−0.682269	−	0.731102i	$-0.739007\pi$
$997$	9.22057	−	15.9705i	0.292018	−	0.505791i	0.974287	+	0.225311i	$0.0723399\pi$
$998$	1.69305	+	2.93244i	0.0535924	+	0.0928248i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ct.a.127.4		12
3.2	odd	2		91.2.q.a.36.3	✓	12
12.11	even	2		1456.2.cc.c.673.3		12
13.4	even	6	inner	819.2.ct.a.316.4		12
21.2	odd	6		637.2.u.h.361.4		12
21.5	even	6		637.2.u.i.361.4		12
21.11	odd	6		637.2.k.h.569.3		12
21.17	even	6		637.2.k.g.569.3		12
21.20	even	2		637.2.q.h.491.3		12
39.2	even	12		1183.2.a.m.1.4		6
39.11	even	12		1183.2.a.p.1.3		6
39.17	odd	6		91.2.q.a.43.3	yes	12
39.23	odd	6		1183.2.c.i.337.7		12
39.29	odd	6		1183.2.c.i.337.6		12
156.95	even	6		1456.2.cc.c.225.3		12
273.17	even	6		637.2.u.i.30.4		12
273.41	odd	12		8281.2.a.by.1.4		6
273.95	odd	6		637.2.u.h.30.4		12
273.167	odd	12		8281.2.a.ch.1.3		6
273.173	even	6		637.2.k.g.459.4		12
273.212	odd	6		637.2.k.h.459.4		12
273.251	even	6		637.2.q.h.589.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	3.2	odd	2
91.2.q.a.43.3	yes	12	39.17	odd	6
637.2.k.g.459.4		12	273.173	even	6
637.2.k.g.569.3		12	21.17	even	6
637.2.k.h.459.4		12	273.212	odd	6
637.2.k.h.569.3		12	21.11	odd	6
637.2.q.h.491.3		12	21.20	even	2
637.2.q.h.589.3		12	273.251	even	6
637.2.u.h.30.4		12	273.95	odd	6
637.2.u.h.361.4		12	21.2	odd	6
637.2.u.i.30.4		12	273.17	even	6
637.2.u.i.361.4		12	21.5	even	6
819.2.ct.a.127.4		12	1.1	even	1	trivial
819.2.ct.a.316.4		12	13.4	even	6	inner
1183.2.a.m.1.4		6	39.2	even	12
1183.2.a.p.1.3		6	39.11	even	12
1183.2.c.i.337.6		12	39.29	odd	6
1183.2.c.i.337.7		12	39.23	odd	6
1456.2.cc.c.225.3		12	156.95	even	6
1456.2.cc.c.673.3		12	12.11	even	2
8281.2.a.by.1.4		6	273.41	odd	12
8281.2.a.ch.1.3		6	273.167	odd	12

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.ct (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104235 - 0.0601799i) q^{2} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.866025 + 0.500000i) q^{7} +0.479696i q^{8} +(-0.101594 - 0.175965i) q^{10} +(0.315769 - 0.182309i) q^{11} +(1.80124 - 3.12338i) q^{13} +0.120360 q^{14} +(-1.95665 - 3.38901i) q^{16} +(1.59277 - 2.75877i) q^{17} +(1.25046 + 0.721954i) q^{19} +(2.90281 + 1.67594i) q^{20} +(0.0219427 - 0.0380059i) q^{22} +(2.54161 + 4.40219i) q^{23} +2.15010 q^{25} +(-0.000212944 - 0.433964i) q^{26} +(-1.71951 + 0.992757i) q^{28} +(4.09831 + 7.09848i) q^{29} +4.69775i q^{31} +(-1.23876 - 0.715198i) q^{32} -0.383412i q^{34} +(0.844083 - 1.46199i) q^{35} +(5.46967 - 3.15792i) q^{37} +0.173789 q^{38} +0.809806 q^{40} +(5.04661 - 2.91366i) q^{41} +(-0.386561 + 0.669543i) q^{43} +0.723954i q^{44} +(0.529847 + 0.305907i) q^{46} -12.7905i q^{47} +(0.500000 + 0.866025i) q^{49} +(0.224115 - 0.129393i) q^{50} +(3.58248 + 6.19801i) q^{52} -1.37110 q^{53} +(-0.307768 - 0.533070i) q^{55} +(-0.239848 + 0.415429i) q^{56} +(0.854372 + 0.493272i) q^{58} +(8.10770 + 4.68098i) q^{59} +(4.51242 - 7.81574i) q^{61} +(0.282711 + 0.489669i) q^{62} +7.65442 q^{64} +(-5.27279 - 3.04080i) q^{65} +(-11.6705 + 6.73797i) q^{67} +(3.16247 + 5.47757i) q^{68} -0.203187i q^{70} +(6.13246 + 3.54058i) q^{71} -2.16083i q^{73} +(0.380087 - 0.658329i) q^{74} +(-2.48281 + 1.43345i) q^{76} +0.364618 q^{77} -6.88781 q^{79} +(-5.72121 + 3.30314i) q^{80} +(0.350688 - 0.607409i) q^{82} +0.567380i q^{83} +(-4.65725 - 2.68887i) q^{85} +0.0930528i q^{86} +(0.0874529 + 0.151473i) q^{88} +(0.986346 - 0.569467i) q^{89} +(3.12161 - 1.80431i) q^{91} -10.0928 q^{92} +(-0.769734 - 1.33322i) q^{94} +(1.21878 - 2.11098i) q^{95} +(6.86572 + 3.96393i) q^{97} +(0.104235 + 0.0601799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40}+ \cdots + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 12 * q^10 - 6 * q^11 + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 + 12 * q^23 - 20 * q^25 + 42 * q^26 - 8 * q^29 - 36 * q^32 - 6 * q^35 - 42 * q^37 - 4 * q^38 + 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 6 * q^49 + 18 * q^50 + 2 * q^52 + 44 * q^53 - 6 * q^55 + 12 * q^56 - 12 * q^58 - 18 * q^59 + 14 * q^61 + 4 * q^62 - 52 * q^64 - 60 * q^65 - 24 * q^67 + 8 * q^68 + 24 * q^71 - 6 * q^74 - 18 * q^76 - 8 * q^77 - 56 * q^79 + 72 * q^80 + 14 * q^82 - 48 * q^85 - 14 * q^88 + 12 * q^89 + 14 * q^91 - 24 * q^92 + 4 * q^94 + 22 * q^95 + 6 * q^97

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