LMFDB - Embedded newform 819.2.ct.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(127,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
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			127.1
Root			$-1.30089 + 0.554694i$ of defining polynomial
Character	$\chi$	$=$	819.127
Dual form			819.2.ct.a.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82678 + 1.05469i) q^{2} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(-0.866025 - 0.500000i) q^{7} +0.948212i q^{8} +O(q^{10})$	\(q+(-1.82678 + 1.05469i) q^{2} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(-0.866025 - 0.500000i) q^{7} +0.948212i q^{8} +(3.79878 + 6.57967i) q^{10} +(-0.767631 + 0.443192i) q^{11} +(-1.17349 - 3.40924i) q^{13} +2.10939 q^{14} +(1.44945 + 2.51051i) q^{16} +(2.48008 - 4.29563i) q^{17} +(2.06008 + 1.18939i) q^{19} +(-7.64062 - 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +(1.92926 + 3.34157i) q^{23} -7.97282 q^{25} +(5.73942 + 4.99028i) q^{26} +(-2.12135 + 1.22476i) q^{28} +(0.640986 + 1.11022i) q^{29} -8.46921i q^{31} +(-6.93800 - 4.00566i) q^{32} +10.4629i q^{34} +(-1.80089 + 3.11923i) q^{35} +(-8.34686 + 4.81906i) q^{37} -5.01776 q^{38} +3.41525 q^{40} +(-10.4652 + 6.04207i) q^{41} +(-1.82125 + 3.15450i) q^{43} +2.17122i q^{44} +(-7.04867 - 4.06955i) q^{46} -2.98229i q^{47} +(0.500000 + 0.866025i) q^{49} +(14.5646 - 8.40888i) q^{50} +(-8.66942 - 1.68613i) q^{52} -4.92032 q^{53} +(1.59628 + 2.76484i) q^{55} +(0.474106 - 0.821175i) q^{56} +(-2.34189 - 1.35209i) q^{58} +(-6.34577 - 3.66373i) q^{59} +(0.769632 - 1.33304i) q^{61} +(8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(-12.2793 + 4.22664i) q^{65} +(7.29756 - 4.21325i) q^{67} +(-6.07501 - 10.5222i) q^{68} -7.59755i q^{70} +(5.58490 + 3.22444i) q^{71} -7.14859i q^{73} +(10.1653 - 17.6068i) q^{74} +(5.04621 - 2.91343i) q^{76} +0.886384 q^{77} +0.757551 q^{79} +(9.04232 - 5.22059i) q^{80} +(12.7451 - 22.0751i) q^{82} -4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} -7.68344i q^{86} +(-0.420240 - 0.727877i) q^{88} +(-3.13400 + 1.80942i) q^{89} +(-0.688351 + 3.53923i) q^{91} +9.45150 q^{92} +(3.14541 + 5.44800i) q^{94} +(4.28391 - 7.41995i) q^{95} +(-0.401229 - 0.231650i) q^{97} +(-1.82678 - 1.05469i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4}+O(q^{10}) $ 12 * q + 4 * q^4	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.82678	+	1.05469i	−1.29173	+	0.745781i	−0.978961	−	0.204047i	$-0.934590\pi$
$2$	−1.82678	+	1.05469i	−1.29173	+	0.745781i	−0.312770	+	0.949829i	$0.601257\pi$
$3$		0			0
$3$		0			0
$4$	1.22476	−	2.12135i	0.612380	−	1.06067i
$5$		−	3.60178i		−	1.61076i	−0.592756	−	0.805382i	$-0.701960\pi$
$5$		−	3.60178i		−	1.61076i	0.592756	−	0.805382i	$-0.298040\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			0.948212i			0.335243i
$9$		0			0
$10$	3.79878	+	6.57967i	1.20128	+	2.08068i
$11$	−0.767631	+	0.443192i	−0.231450	+	0.133627i	−0.611241	−	0.791445i	$-0.709329\pi$
$11$	−0.767631	+	0.443192i	−0.231450	+	0.133627i	0.379791	+	0.925072i	$0.375996\pi$
$12$		0			0
$13$	−1.17349	−	3.40924i	−0.325467	−	0.945553i
$13$	−1.17349	−	3.40924i	−0.325467	−	0.945553i
$14$	2.10939			0.563758
$15$		0			0
$16$	1.44945	+	2.51051i	0.362362	+	0.627629i
$17$	2.48008	−	4.29563i	0.601508	−	1.04184i	−0.391085	−	0.920355i	$-0.627900\pi$
$17$	2.48008	−	4.29563i	0.601508	−	1.04184i	0.992593	−	0.121488i	$-0.0387665\pi$
$18$		0			0
$19$	2.06008	+	1.18939i	0.472615	+	0.272864i	0.717334	−	0.696730i	$-0.245362\pi$
$19$	2.06008	+	1.18939i	0.472615	+	0.272864i	−0.244719	+	0.969594i	$0.578696\pi$
$20$	−7.64062	−	4.41132i	−1.70849	−	0.986400i
$21$		0			0
$22$	0.934864	−	1.61923i	0.199314	−	0.345222i
$23$	1.92926	+	3.34157i	0.402278	+	0.696765i	0.994000	−	0.109376i	$-0.0348853\pi$
$23$	1.92926	+	3.34157i	0.402278	+	0.696765i	−0.591723	+	0.806142i	$0.701552\pi$
$24$		0			0
$25$	−7.97282			−1.59456
$26$	5.73942	+	4.99028i	1.12559	+	0.978674i
$27$		0			0
$28$	−2.12135	+	1.22476i	−0.400897	+	0.231458i
$29$	0.640986	+	1.11022i	0.119028	+	0.206163i	0.919383	−	0.393364i	$-0.128689\pi$
$29$	0.640986	+	1.11022i	0.119028	+	0.206163i	−0.800355	+	0.599527i	$0.795355\pi$
$30$		0			0
$31$		−	8.46921i		−	1.52111i	−0.649271	−	0.760557i	$-0.724926\pi$
$31$		−	8.46921i		−	1.52111i	0.649271	−	0.760557i	$-0.275074\pi$
$32$	−6.93800	−	4.00566i	−1.22648	−	0.708107i
$33$		0			0
$34$			10.4629i			1.79437i
$35$	−1.80089	+	3.11923i	−0.304406	+	0.527247i
$36$		0			0
$37$	−8.34686	+	4.81906i	−1.37222	+	0.792249i	−0.991207	−	0.132323i	$-0.957757\pi$
$37$	−8.34686	+	4.81906i	−1.37222	+	0.792249i	−0.381009	+	0.924571i	$0.624423\pi$
$38$	−5.01776			−0.813988
$39$		0			0
$40$	3.41525			0.539998
$41$	−10.4652	+	6.04207i	−1.63438	+	0.943612i	−0.651666	+	0.758506i	$0.725929\pi$
$41$	−10.4652	+	6.04207i	−1.63438	+	0.943612i	−0.982719	+	0.185106i	$0.940737\pi$
$42$		0			0
$43$	−1.82125	+	3.15450i	−0.277738	+	0.481056i	−0.970822	−	0.239800i	$-0.922918\pi$
$43$	−1.82125	+	3.15450i	−0.277738	+	0.481056i	0.693084	+	0.720856i	$0.256251\pi$
$44$			2.17122i			0.327323i
$45$		0			0
$46$	−7.04867	−	4.06955i	−1.03927	−	0.600022i
$47$		−	2.98229i		−	0.435012i	−0.976059	−	0.217506i	$-0.930208\pi$
$47$		−	2.98229i		−	0.435012i	0.976059	−	0.217506i	$-0.0697922\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	14.5646	−	8.40888i	2.05975	−	1.18920i
$51$		0			0
$52$	−8.66942	−	1.68613i	−1.20223	−	0.233824i
$53$	−4.92032			−0.675858			−0.337929	−	0.941172i	$-0.609726\pi$
$53$	−4.92032			−0.675858			−0.337929	+	0.941172i	$0.609726\pi$
$54$		0			0
$55$	1.59628	+	2.76484i	0.215242	+	0.372811i
$56$	0.474106	−	0.821175i	0.0633551	−	0.109734i
$57$		0			0
$58$	−2.34189	−	1.35209i	−0.307505	−	0.177538i
$59$	−6.34577	−	3.66373i	−0.826148	−	0.476977i	0.0263837	−	0.999652i	$-0.491601\pi$
$59$	−6.34577	−	3.66373i	−0.826148	−	0.476977i	−0.852532	+	0.522675i	$0.824934\pi$
$60$		0			0
$61$	0.769632	−	1.33304i	0.0985412	−	0.170678i	−0.812540	−	0.582906i	$-0.801916\pi$
$61$	0.769632	−	1.33304i	0.0985412	−	0.170678i	0.911081	+	0.412227i	$0.135249\pi$
$62$	8.93242	+	15.4714i	1.13442	+	1.96487i
$63$		0			0
$64$	11.1012			1.38765
$65$	−12.2793	+	4.22664i	−1.52306	+	0.524250i
$66$		0			0
$67$	7.29756	−	4.21325i	0.891539	−	0.514730i	0.0170931	−	0.999854i	$-0.494559\pi$
$67$	7.29756	−	4.21325i	0.891539	−	0.514730i	0.874445	+	0.485124i	$0.161225\pi$
$68$	−6.07501	−	10.5222i	−0.736703	−	1.27601i
$69$		0			0
$70$		−	7.59755i		−	0.908081i
$71$	5.58490	+	3.22444i	0.662805	+	0.382671i	0.793345	−	0.608772i	$-0.208338\pi$
$71$	5.58490	+	3.22444i	0.662805	+	0.382671i	−0.130540	+	0.991443i	$0.541671\pi$
$72$		0			0
$73$		−	7.14859i		−	0.836679i	−0.908291	−	0.418340i	$-0.862612\pi$
$73$		−	7.14859i		−	0.836679i	0.908291	−	0.418340i	$-0.137388\pi$
$74$	10.1653	−	17.6068i	1.18169	−	2.04675i
$75$		0			0
$76$	5.04621	−	2.91343i	0.578840	−	0.334193i
$77$	0.886384			0.101013
$78$		0			0
$79$	0.757551			0.0852311			0.0426156	−	0.999092i	$-0.486431\pi$
$79$	0.757551			0.0852311			0.0426156	+	0.999092i	$0.486431\pi$
$80$	9.04232	−	5.22059i	1.01096	−	0.583679i
$81$		0			0
$82$	12.7451	−	22.0751i	1.40746	−	2.43779i
$83$		−	4.76766i		−	0.523319i	−0.965160	−	0.261659i	$-0.915730\pi$
$83$		−	4.76766i		−	0.523319i	0.965160	−	0.261659i	$-0.0842697\pi$
$84$		0			0
$85$	−15.4719	−	8.93270i	−1.67816	−	0.968888i
$86$		−	7.68344i		−	0.828527i
$87$		0			0
$88$	−0.420240	−	0.727877i	−0.0447977	−	0.0775919i
$89$	−3.13400	+	1.80942i	−0.332204	+	0.191798i	−0.656819	−	0.754048i	$-0.728098\pi$
$89$	−3.13400	+	1.80942i	−0.332204	+	0.191798i	0.324615	+	0.945846i	$0.394765\pi$
$90$		0			0
$91$	−0.688351	+	3.53923i	−0.0721588	+	0.371012i
$92$	9.45150			0.985387
$93$		0			0
$94$	3.14541	+	5.44800i	0.324424	+	0.561919i
$95$	4.28391	−	7.41995i	0.439520	−	0.761271i
$96$		0			0
$97$	−0.401229	−	0.231650i	−0.0407386	−	0.0235205i	0.479492	−	0.877546i	$-0.340821\pi$
$97$	−0.401229	−	0.231650i	−0.0407386	−	0.0235205i	−0.520231	+	0.854026i	$0.674154\pi$
$98$	−1.82678	−	1.05469i	−0.184533	−	0.106540i
$99$		0			0
$100$	−9.76479	+	16.9131i	−0.976479	+	1.69131i
$101$	−2.91152	−	5.04289i	−0.289707	−	0.501787i	0.684033	−	0.729451i	$-0.260224\pi$
$101$	−2.91152	−	5.04289i	−0.289707	−	0.501787i	−0.973740	+	0.227664i	$0.926891\pi$
$102$		0			0
$103$	−8.23888			−0.811801			−0.405901	−	0.913917i	$-0.633042\pi$
$103$	−8.23888			−0.811801			−0.405901	+	0.913917i	$0.633042\pi$
$104$	3.23268	−	1.11271i	0.316991	−	0.109111i
$105$		0			0
$106$	8.98837	−	5.18944i	0.873027	−	0.504043i
$107$	−1.91630	−	3.31913i	−0.185256	−	0.320872i	0.758407	−	0.651781i	$-0.225978\pi$
$107$	−1.91630	−	3.31913i	−0.185256	−	0.320872i	−0.943663	+	0.330909i	$0.892645\pi$
$108$		0			0
$109$			10.4180i			0.997867i	0.866640	+	0.498934i	$0.166275\pi$
$109$			10.4180i			0.997867i	−0.866640	+	0.498934i	$0.833725\pi$
$110$	−5.83212	−	3.36718i	−0.556071	−	0.321048i
$111$		0			0
$112$		−	2.89889i		−	0.273920i
$113$	−2.45505	+	4.25228i	−0.230952	+	0.400021i	−0.958089	−	0.286472i	$-0.907517\pi$
$113$	−2.45505	+	4.25228i	−0.230952	+	0.400021i	0.727136	+	0.686493i	$0.240851\pi$
$114$		0			0
$115$	12.0356	−	6.94875i	1.12233	−	0.647975i
$116$	3.14022			0.291562
$117$		0			0
$118$	15.4565			1.42288
$119$	−4.29563	+	2.48008i	−0.393779	+	0.227349i
$120$		0			0
$121$	−5.10716	+	8.84586i	−0.464287	+	0.804169i
$122$			3.24690i			0.293961i
$123$		0			0
$124$	−17.9661	−	10.3727i	−1.61341	−	0.931500i
$125$			10.7074i			0.957702i
$126$		0			0
$127$	−6.15508	−	10.6609i	−0.546175	−	0.946003i	−0.998532	−	0.0541658i	$-0.982750\pi$
$127$	−6.15508	−	10.6609i	−0.546175	−	0.946003i	0.452357	−	0.891837i	$-0.350583\pi$
$128$	−6.40347	+	3.69704i	−0.565992	+	0.326776i
$129$		0			0
$130$	17.9739	−	20.6721i	1.57641	−	1.81306i
$131$	8.20265			0.716669			0.358335	−	0.933593i	$-0.383345\pi$
$131$	8.20265			0.716669			0.358335	+	0.933593i	$0.383345\pi$
$132$		0			0
$133$	−1.18939	−	2.06008i	−0.103133	−	0.178632i
$134$	−8.88737	+	15.3934i	−0.767752	+	1.32979i
$135$		0			0
$136$	4.07316	+	2.35164i	0.349271	+	0.201652i
$137$	−6.45670	−	3.72778i	−0.551633	−	0.318485i	0.198147	−	0.980172i	$-0.436508\pi$
$137$	−6.45670	−	3.72778i	−0.551633	−	0.318485i	−0.749780	+	0.661687i	$0.769841\pi$
$138$		0			0
$139$	−8.34028	+	14.4458i	−0.707413	+	1.22528i	0.258400	+	0.966038i	$0.416805\pi$
$139$	−8.34028	+	14.4458i	−0.707413	+	1.22528i	−0.965813	+	0.259238i	$0.916529\pi$
$140$	4.41132	+	7.64062i	0.372824	+	0.645750i
$141$		0			0
$142$	−13.6032			−1.14156
$143$	2.41175	+	2.09696i	0.201681	+	0.175357i
$144$		0			0
$145$	3.99877	−	2.30869i	0.332080	−	0.191726i
$146$	7.53958	+	13.0589i	0.623980	+	1.08076i
$147$		0			0
$148$			23.6088i			1.94063i
$149$	2.18380	+	1.26082i	0.178904	+	0.103290i	0.586777	−	0.809748i	$-0.300396\pi$
$149$	2.18380	+	1.26082i	0.178904	+	0.103290i	−0.407874	+	0.913038i	$0.633730\pi$
$150$		0			0
$151$		−	15.8972i		−	1.29370i	−0.762618	−	0.646849i	$-0.776086\pi$
$151$		−	15.8972i		−	1.29370i	0.762618	−	0.646849i	$-0.223914\pi$
$152$	−1.12779	+	1.95339i	−0.0914760	+	0.158441i
$153$		0			0
$154$	−1.61923	+	0.934864i	−0.130481	+	0.0753335i
$155$	−30.5042			−2.45016
$156$		0			0
$157$	12.9831			1.03616			0.518082	−	0.855331i	$-0.326646\pi$
$157$	12.9831			1.03616			0.518082	+	0.855331i	$0.326646\pi$
$158$	−1.38388	+	0.798985i	−0.110096	+	0.0635638i
$159$		0			0
$160$	−14.4275	+	24.9892i	−1.14059	+	1.97557i
$161$		−	3.85851i		−	0.304093i
$162$		0			0
$163$	−2.00873	−	1.15974i	−0.157336	−	0.0908378i	0.419265	−	0.907864i	$-0.362288\pi$
$163$	−2.00873	−	1.15974i	−0.157336	−	0.0908378i	−0.576601	+	0.817026i	$0.695621\pi$
$164$			29.6003i			2.31140i
$165$		0			0
$166$	5.02843	+	8.70949i	0.390282	+	0.675987i
$167$	11.9441	−	6.89591i	0.924260	−	0.533622i	0.0392682	−	0.999229i	$-0.487497\pi$
$167$	11.9441	−	6.89591i	0.924260	−	0.533622i	0.884992	+	0.465607i	$0.154164\pi$
$168$		0			0
$169$	−10.2459	+	8.00140i	−0.788143	+	0.615493i
$170$	37.6851			2.89031
$171$		0			0
$172$	4.46118	+	7.72700i	0.340162	+	0.589178i
$173$	1.84216	−	3.19071i	0.140057	−	0.242585i	−0.787461	−	0.616364i	$-0.788605\pi$
$173$	1.84216	−	3.19071i	0.140057	−	0.242585i	0.927518	+	0.373779i	$0.121938\pi$
$174$		0			0
$175$	6.90466	+	3.98641i	0.521943	+	0.301344i
$176$	−2.22528	−	1.28477i	−0.167737	−	0.0968429i
$177$		0			0
$178$	3.81677	−	6.61083i	0.286079	−	0.495503i
$179$	2.94638	+	5.10328i	0.220223	+	0.381437i	0.954876	−	0.297006i	$-0.0959882\pi$
$179$	2.94638	+	5.10328i	0.220223	+	0.381437i	−0.734653	+	0.678443i	$0.762655\pi$
$180$		0			0
$181$	−2.11543			−0.157239			−0.0786193	−	0.996905i	$-0.525051\pi$
$181$	−2.11543			−0.157239			−0.0786193	+	0.996905i	$0.525051\pi$
$182$	−2.47534	−	7.19141i	−0.183484	−	0.533063i
$183$		0			0
$184$	−3.16851	+	1.82934i	−0.233586	+	0.134861i
$185$	17.3572	+	30.0635i	1.27613	+	2.21032i
$186$		0			0
$187$			4.39661i			0.321512i
$188$	−6.32647	−	3.65259i	−0.461406	−	0.266393i
$189$		0			0
$190$			18.0729i			1.31114i
$191$	−5.68333	+	9.84381i	−0.411231	+	0.712273i	−0.995025	−	0.0996290i	$-0.968234\pi$
$191$	−5.68333	+	9.84381i	−0.411231	+	0.712273i	0.583794	+	0.811902i	$0.301568\pi$
$192$		0			0
$193$	12.2017	−	7.04468i	0.878301	−	0.507087i	0.00820314	−	0.999966i	$-0.497389\pi$
$193$	12.2017	−	7.04468i	0.878301	−	0.507087i	0.870098	+	0.492879i	$0.164055\pi$
$194$	0.977279			0.0701645
$195$		0			0
$196$	2.44952			0.174966
$197$	19.8815	−	11.4786i	1.41650	−	0.817814i	0.420507	−	0.907289i	$-0.361852\pi$
$197$	19.8815	−	11.4786i	1.41650	−	0.817814i	0.995989	+	0.0894753i	$0.0285190\pi$
$198$		0			0
$199$	−1.57492	+	2.72785i	−0.111643	+	0.193372i	−0.916433	−	0.400188i	$-0.868945\pi$
$199$	−1.57492	+	2.72785i	−0.111643	+	0.193372i	0.804790	+	0.593560i	$0.202278\pi$
$200$		−	7.55992i		−	0.534567i
$201$		0			0
$202$	10.6374	+	6.14152i	0.748446	+	0.432116i
$203$		−	1.28197i		−	0.0899768i
$204$		0			0
$205$	21.7622	+	37.6932i	1.51994	+	2.63261i
$206$	15.0507	−	8.68950i	1.04863	−	0.605426i
$207$		0			0
$208$	6.85804	−	7.88757i	0.475520	−	0.546905i
$209$	−2.10851			−0.145849
$210$		0			0
$211$	7.43191	+	12.8725i	0.511634	+	0.886176i	0.999909	+	0.0134864i	$0.00429298\pi$
$211$	7.43191	+	12.8725i	0.511634	+	0.886176i	−0.488275	+	0.872690i	$0.662374\pi$
$212$	−6.02621	+	10.4377i	−0.413882	+	0.716865i
$213$		0			0
$214$	7.00133	+	4.04222i	0.478601	+	0.276321i
$215$	11.3618	+	6.55974i	0.774868	+	0.447370i
$216$		0			0
$217$	−4.23460	+	7.33455i	−0.287464	+	0.497902i
$218$	−10.9878	−	19.0315i	−0.744191	−	1.28898i
$219$		0			0
$220$	7.82024			0.527241
$221$	−17.5552	−	3.41433i	−1.18089	−	0.229673i
$222$		0			0
$223$	3.79396	−	2.19044i	0.254062	−	0.146683i	−0.367561	−	0.930000i	$-0.619807\pi$
$223$	3.79396	−	2.19044i	0.254062	−	0.146683i	0.621623	+	0.783317i	$0.286474\pi$
$224$	4.00566	+	6.93800i	0.267639	+	0.463565i
$225$		0			0
$226$		−	10.3573i		−	0.688959i
$227$	−11.7488	−	6.78316i	−0.779793	−	0.450214i	0.0565636	−	0.998399i	$-0.481986\pi$
$227$	−11.7488	−	6.78316i	−0.779793	−	0.450214i	−0.836357	+	0.548185i	$0.815319\pi$
$228$		0			0
$229$			16.5180i			1.09154i	0.837935	+	0.545770i	$0.183763\pi$
$229$			16.5180i			1.09154i	−0.837935	+	0.545770i	$0.816237\pi$
$230$	−14.6576	+	25.3877i	−0.966495	+	1.67402i
$231$		0			0
$232$	−1.05272	+	0.607791i	−0.0691147	+	0.0399034i
$233$	−16.5026			−1.08112			−0.540561	−	0.841305i	$-0.681788\pi$
$233$	−16.5026			−1.08112			−0.540561	+	0.841305i	$0.681788\pi$
$234$		0			0
$235$	−10.7416			−0.700702
$236$	−15.5441	+	8.97438i	−1.01183	+	0.584182i
$237$		0			0
$238$	5.23145	−	9.06114i	0.339105	−	0.587347i
$239$			30.4210i			1.96777i	0.178796	+	0.983886i	$0.442780\pi$
$239$			30.4210i			1.96777i	−0.178796	+	0.983886i	$0.557220\pi$
$240$		0			0
$241$	−25.5602	−	14.7572i	−1.64648	−	0.950593i	−0.978458	−	0.206448i	$-0.933810\pi$
$241$	−25.5602	−	14.7572i	−1.64648	−	0.950593i	−0.668018	−	0.744145i	$-0.732857\pi$
$242$		−	21.5460i		−	1.38503i
$243$		0			0
$244$	−1.88523	−	3.26531i	−0.120689	−	0.209040i
$245$	3.11923	−	1.80089i	0.199280	−	0.115055i
$246$		0			0
$247$	1.63743	−	8.41904i	0.104187	−	0.535691i
$248$	8.03060			0.509944
$249$		0			0
$250$	−11.2931	−	19.5602i	−0.714236	−	1.23709i
$251$	6.49134	−	11.2433i	0.409730	−	0.709673i	−0.585130	−	0.810940i	$-0.698956\pi$
$251$	6.49134	−	11.2433i	0.409730	−	0.709673i	0.994859	+	0.101267i	$0.0322897\pi$
$252$		0			0
$253$	−2.96191	−	1.71006i	−0.186214	−	0.107511i
$254$	22.4880	+	12.9835i	1.41102	+	0.814654i
$255$		0			0
$256$	−3.30268	+	5.72042i	−0.206418	+	0.357526i
$257$	2.29261	+	3.97091i	0.143009	+	0.247698i	0.928628	−	0.371011i	$-0.120989\pi$
$257$	2.29261	+	3.97091i	0.143009	+	0.247698i	−0.785620	+	0.618710i	$0.787656\pi$
$258$		0			0
$259$	9.63812			0.598884
$260$	−6.07307	+	31.2253i	−0.376636	+	1.93651i
$261$		0			0
$262$	−14.9845	+	8.65129i	−0.925744	+	0.534479i
$263$	−1.33250	−	2.30795i	−0.0821652	−	0.142314i	0.822015	−	0.569466i	$-0.192850\pi$
$263$	−1.33250	−	2.30795i	−0.0821652	−	0.142314i	−0.904180	+	0.427152i	$0.859517\pi$
$264$		0			0
$265$			17.7219i			1.08865i
$266$	4.34551	+	2.50888i	0.266440	+	0.153829i
$267$		0			0
$268$		−	20.6409i		−	1.26084i
$269$	5.96282	−	10.3279i	0.363559	−	0.629703i	−0.624984	−	0.780637i	$-0.714895\pi$
$269$	5.96282	−	10.3279i	0.363559	−	0.629703i	0.988544	+	0.150934i	$0.0482280\pi$
$270$		0			0
$271$	−11.2828	+	6.51416i	−0.685384	+	0.395707i	−0.801881	−	0.597484i	$-0.796167\pi$
$271$	−11.2828	+	6.51416i	−0.685384	+	0.395707i	0.116496	+	0.993191i	$0.462834\pi$
$272$	14.3790			0.871853
$273$		0			0
$274$	15.7267			0.950082
$275$	6.12018	−	3.53349i	0.369061	−	0.213077i
$276$		0			0
$277$	10.6824	−	18.5025i	0.641846	−	1.11171i	−0.343174	−	0.939272i	$-0.611502\pi$
$277$	10.6824	−	18.5025i	0.641846	−	1.11171i	0.985020	−	0.172438i	$-0.0551646\pi$
$278$		−	35.1858i		−	2.11030i
$279$		0			0
$280$	−2.95769	−	1.70762i	−0.176756	−	0.102050i
$281$		−	17.2678i		−	1.03011i	−0.857158	−	0.515054i	$-0.827772\pi$
$281$		−	17.2678i		−	1.03011i	0.857158	−	0.515054i	$-0.172228\pi$
$282$		0			0
$283$	−10.6201	−	18.3946i	−0.631299	−	1.09344i	−0.987286	−	0.158952i	$-0.949189\pi$
$283$	−10.6201	−	18.3946i	−0.631299	−	1.09344i	0.355987	−	0.934491i	$-0.384145\pi$
$284$	13.6803	−	7.89833i	0.811777	−	0.468680i
$285$		0			0
$286$	−6.61741	−	1.28703i	−0.391295	−	0.0761037i
$287$	12.0841			0.713304
$288$		0			0
$289$	−3.80160	−	6.58457i	−0.223624	−	0.387327i
$290$	−4.86993	+	8.43496i	−0.285972	+	0.495318i
$291$		0			0
$292$	−15.1646	−	8.75531i	−0.887443	−	0.512366i
$293$	0.363782	+	0.210030i	0.0212524	+	0.0122701i	0.510589	−	0.859825i	$-0.329428\pi$
$293$	0.363782	+	0.210030i	0.0212524	+	0.0122701i	−0.489336	+	0.872095i	$0.662761\pi$
$294$		0			0
$295$	−13.1959	+	22.8561i	−0.768298	+	1.33073i
$296$	−4.56949	−	7.91459i	−0.265596	−	0.460026i
$297$		0			0
$298$	−5.31910			−0.308127
$299$	9.12826	−	10.4986i	0.527901	−	0.607149i
$300$		0			0
$301$	3.15450	−	1.82125i	0.181822	−	0.104975i
$302$	16.7667	+	29.0408i	0.964817	+	1.67111i
$303$		0			0
$304$			6.89581i			0.395502i
$305$	−4.80132	−	2.77204i	−0.274923	−	0.158727i
$306$		0			0
$307$		−	14.0807i		−	0.803628i	−0.915721	−	0.401814i	$-0.868380\pi$
$307$		−	14.0807i		−	0.803628i	0.915721	−	0.401814i	$-0.131620\pi$
$308$	1.08561	−	1.88033i	0.0618583	−	0.107142i
$309$		0			0
$310$	55.7246	−	32.1726i	3.16495	−	1.82728i
$311$	10.3848			0.588867			0.294434	−	0.955672i	$-0.404869\pi$
$311$	10.3848			0.588867			0.294434	+	0.955672i	$0.404869\pi$
$312$		0			0
$313$	6.84759			0.387048			0.193524	−	0.981096i	$-0.438008\pi$
$313$	6.84759			0.387048			0.193524	+	0.981096i	$0.438008\pi$
$314$	−23.7173	+	13.6932i	−1.33845	+	0.772752i
$315$		0			0
$316$	0.927818	−	1.60703i	0.0521938	−	0.0904024i
$317$		−	0.701249i		−	0.0393861i	−0.999806	−	0.0196930i	$-0.993731\pi$
$317$		−	0.701249i		−	0.0393861i	0.999806	−	0.0196930i	$-0.00626889\pi$
$318$		0			0
$319$	−0.984082	−	0.568160i	−0.0550980	−	0.0318109i
$320$		−	39.9840i		−	2.23518i
$321$		0			0
$322$	4.06955	+	7.04867i	0.226787	+	0.392807i
$323$	10.2183	−	5.89956i	0.568563	−	0.328260i
$324$		0			0
$325$	9.35600	+	27.1813i	0.518977	+	1.50774i
$326$	4.89268			0.270980
$327$		0			0
$328$	−5.72916	−	9.92319i	−0.316340	−	0.547917i
$329$	−1.49115	+	2.58274i	−0.0822095	+	0.142391i
$330$		0			0
$331$	3.63613	+	2.09932i	0.199860	+	0.115389i	0.596590	−	0.802546i	$-0.296522\pi$
$331$	3.63613	+	2.09932i	0.199860	+	0.115389i	−0.396730	+	0.917935i	$0.629855\pi$
$332$	−10.1139	−	5.83924i	−0.555070	−	0.320470i
$333$		0			0
$334$	−14.5462	+	25.1947i	−0.795930	+	1.37859i
$335$	−15.1752	−	26.2842i	−0.829109	−	1.43606i
$336$		0			0
$337$	−20.4278			−1.11278			−0.556388	−	0.830923i	$-0.687813\pi$
$337$	−20.4278			−1.11278			−0.556388	+	0.830923i	$0.687813\pi$
$338$	10.2779	−	25.4231i	0.559046	−	1.38283i
$339$		0			0
$340$	−37.8987	+	21.8808i	−2.05535	+	1.18665i
$341$	3.75349	+	6.50123i	0.203263	+	0.352061i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−2.99113	−	1.72693i	−0.161271	−	0.0931098i
$345$		0			0
$346$			7.77165i			0.417807i
$347$	3.98500	−	6.90222i	0.213926	−	0.370531i	−0.739014	−	0.673690i	$-0.764708\pi$
$347$	3.98500	−	6.90222i	0.213926	−	0.370531i	0.952940	+	0.303160i	$0.0980415\pi$
$348$		0			0
$349$	18.7038	−	10.7986i	1.00119	−	0.578037i	0.0925892	−	0.995704i	$-0.470486\pi$
$349$	18.7038	−	10.7986i	1.00119	−	0.578037i	0.908600	+	0.417668i	$0.137152\pi$
$350$	−16.8178			−0.898947
$351$		0			0
$352$	7.10110			0.378490
$353$	−18.7214	+	10.8088i	−0.996439	+	0.575295i	−0.907193	−	0.420715i	$-0.861779\pi$
$353$	−18.7214	+	10.8088i	−0.996439	+	0.575295i	−0.0892465	+	0.996010i	$0.528446\pi$
$354$		0			0
$355$	11.6137	−	20.1156i	0.616393	−	1.06762i
$356$			8.86441i			0.469813i
$357$		0			0
$358$	−10.7648	−	6.21507i	−0.568938	−	0.328476i
$359$		−	13.6834i		−	0.722180i	−0.932531	−	0.361090i	$-0.882405\pi$
$359$		−	13.6834i		−	0.722180i	0.932531	−	0.361090i	$-0.117595\pi$
$360$		0			0
$361$	−6.67071	−	11.5540i	−0.351090	−	0.608106i
$362$	3.86443	−	2.23113i	0.203110	−	0.117266i
$363$		0			0
$364$	6.66487	+	5.79494i	0.349334	+	0.303737i
$365$	−25.7477			−1.34769
$366$		0			0
$367$	5.70638	+	9.88374i	0.297871	+	0.515927i	0.975649	−	0.219339i	$-0.0703902\pi$
$367$	5.70638	+	9.88374i	0.297871	+	0.515927i	−0.677778	+	0.735267i	$0.737057\pi$
$368$	−5.59271	+	9.68685i	−0.291540	+	0.504962i
$369$		0			0
$370$	−63.4157	−	36.6131i	−3.29683	−	1.90342i
$371$	4.26112	+	2.46016i	0.221227	+	0.127725i
$372$		0			0
$373$	15.6404	−	27.0900i	0.809830	−	1.40267i	−0.103151	−	0.994666i	$-0.532892\pi$
$373$	15.6404	−	27.0900i	0.809830	−	1.40267i	0.912981	−	0.408002i	$-0.133774\pi$
$374$	−4.63708	−	8.03166i	−0.239778	−	0.415307i
$375$		0			0
$376$	2.82784			0.145835
$377$	3.03282	−	3.48811i	0.156198	−	0.179647i
$378$		0			0
$379$	23.7421	−	13.7075i	1.21955	−	0.704108i	0.254729	−	0.967012i	$-0.418014\pi$
$379$	23.7421	−	13.7075i	1.21955	−	0.704108i	0.964822	+	0.262904i	$0.0846803\pi$
$380$	−10.4935	−	18.1753i	−0.538307	−	0.932374i
$381$		0			0
$382$		−	23.9767i		−	1.22675i
$383$	−13.9436	−	8.05032i	−0.712483	−	0.411352i	0.0994967	−	0.995038i	$-0.468277\pi$
$383$	−13.9436	−	8.05032i	−0.712483	−	0.411352i	−0.811980	+	0.583686i	$0.801610\pi$
$384$		0			0
$385$		−	3.19256i		−	0.162708i
$386$	−14.8600	+	25.7382i	−0.756353	+	1.31004i
$387$		0			0
$388$	−0.982819	+	0.567431i	−0.0498951	+	0.0288069i
$389$	21.1380			1.07174			0.535870	−	0.844301i	$-0.319984\pi$
$389$	21.1380			1.07174			0.535870	+	0.844301i	$0.319984\pi$
$390$		0			0
$391$	19.1388			0.967893
$392$	−0.821175	+	0.474106i	−0.0414756	+	0.0239460i
$393$		0			0
$394$	−24.2128	+	41.9377i	−1.21982	+	2.11279i
$395$		−	2.72853i		−	0.137287i
$396$		0			0
$397$	11.3436	+	6.54921i	0.569317	+	0.328695i	0.756876	−	0.653558i	$-0.226724\pi$
$397$	11.3436	+	6.54921i	0.569317	+	0.328695i	−0.187560	+	0.982253i	$0.560058\pi$
$398$		−	6.64426i		−	0.333046i
$399$		0			0
$400$	−11.5562	−	20.0159i	−0.577808	−	1.00079i
$401$	−16.8396	+	9.72236i	−0.840930	+	0.485511i	−0.857580	−	0.514350i	$-0.828033\pi$
$401$	−16.8396	+	9.72236i	−0.840930	+	0.485511i	0.0166501	+	0.999861i	$0.494700\pi$
$402$		0			0
$403$	−28.8736	+	9.93851i	−1.43830	+	0.495072i
$404$	−14.2636			−0.709642
$405$		0			0
$406$	1.35209	+	2.34189i	0.0671031	+	0.116226i
$407$	4.27154	−	7.39853i	0.211732	−	0.366731i
$408$		0			0
$409$	20.8330	+	12.0279i	1.03013	+	0.594743i	0.917020	−	0.398840i	$-0.130587\pi$
$409$	20.8330	+	12.0279i	1.03013	+	0.594743i	0.113105	+	0.993583i	$0.463921\pi$
$410$	−79.5096	−	45.9049i	−3.92670	−	2.26708i
$411$		0			0
$412$	−10.0907	+	17.4775i	−0.497131	+	0.861056i
$413$	3.66373	+	6.34577i	0.180280	+	0.312255i
$414$		0			0
$415$	−17.1721			−0.842944
$416$	−5.51460	+	28.3539i	−0.270375	+	1.39016i
$417$		0			0
$418$	3.85179	−	2.22383i	0.188397	−	0.108771i
$419$	19.5119	+	33.7956i	0.953218	+	1.65102i	0.738394	+	0.674370i	$0.235585\pi$
$419$	19.5119	+	33.7956i	0.953218	+	1.65102i	0.214825	+	0.976653i	$0.431082\pi$
$420$		0			0
$421$		−	22.0284i		−	1.07360i	−0.843710	−	0.536799i	$-0.819633\pi$
$421$		−	22.0284i		−	1.07360i	0.843710	−	0.536799i	$-0.180367\pi$
$422$	−27.1530	−	15.6768i	−1.32179	−	0.763134i
$423$		0			0
$424$		−	4.66551i		−	0.226577i
$425$	−19.7732	+	34.2482i	−0.959142	+	1.66128i
$426$		0			0
$427$	−1.33304	+	0.769632i	−0.0645104	+	0.0372451i
$428$	−9.38803			−0.453787
$429$		0			0
$430$	−27.6741			−1.33456
$431$	31.0727	−	17.9398i	1.49672	−	0.864131i	0.496726	−	0.867907i	$-0.334535\pi$
$431$	31.0727	−	17.9398i	1.49672	−	0.864131i	0.999993	+	0.00377645i	$0.00120209\pi$
$432$		0			0
$433$	6.10678	−	10.5773i	0.293473	−	0.508310i	−0.681155	−	0.732139i	$-0.738522\pi$
$433$	6.10678	−	10.5773i	0.293473	−	0.508310i	0.974629	+	0.223828i	$0.0718555\pi$
$434$		−	17.8648i		−	0.857540i
$435$		0			0
$436$	22.1003	+	12.7596i	1.05841	+	0.611074i
$437$			9.17853i			0.439069i
$438$		0			0
$439$	−7.87765	−	13.6445i	−0.375980	−	0.651216i	0.614493	−	0.788922i	$-0.289361\pi$
$439$	−7.87765	−	13.6445i	−0.375980	−	0.651216i	−0.990473	+	0.137706i	$0.956027\pi$
$440$	−2.62165	+	1.51361i	−0.124982	+	0.0721586i
$441$		0			0
$442$	35.6706	−	12.2781i	1.69668	−	0.584009i
$443$	15.0706			0.716028			0.358014	−	0.933716i	$-0.383454\pi$
$443$	15.0706			0.716028			0.358014	+	0.933716i	$0.383454\pi$
$444$		0			0
$445$	6.51712	+	11.2880i	0.308941	+	0.535102i
$446$	−4.62050	+	8.00293i	−0.218787	+	0.378950i
$447$		0			0
$448$	−9.61391	−	5.55059i	−0.454215	−	0.262241i
$449$	−26.6585	−	15.3913i	−1.25809	−	0.726360i	−0.285388	−	0.958412i	$-0.592123\pi$
$449$	−26.6585	−	15.3913i	−1.25809	−	0.726360i	−0.972703	+	0.232052i	$0.925456\pi$
$450$		0			0
$451$	5.35559	−	9.27616i	0.252185	−	0.436797i
$452$	6.01371	+	10.4160i	0.282861	+	0.489929i
$453$		0			0
$454$	28.6166			1.34304
$455$	12.7475	+	2.47929i	0.597614	+	0.116231i
$456$		0			0
$457$	−6.71687	+	3.87799i	−0.314202	+	0.181405i	−0.648805	−	0.760955i	$-0.724731\pi$
$457$	−6.71687	+	3.87799i	−0.314202	+	0.181405i	0.334603	+	0.942359i	$0.391398\pi$
$458$	−17.4214	−	30.1748i	−0.814050	−	1.40998i
$459$		0			0
$460$		−	34.0422i		−	1.58723i
$461$	−1.27498	−	0.736110i	−0.0593817	−	0.0342840i	0.470015	−	0.882658i	$-0.344248\pi$
$461$	−1.27498	−	0.736110i	−0.0593817	−	0.0342840i	−0.529397	+	0.848374i	$0.677582\pi$
$462$		0			0
$463$		−	14.0366i		−	0.652335i	−0.945312	−	0.326168i	$-0.894243\pi$
$463$		−	14.0366i		−	0.652335i	0.945312	−	0.326168i	$-0.105757\pi$
$464$	−1.85815	+	3.21841i	−0.0862625	+	0.149411i
$465$		0			0
$466$	30.1467	−	17.4052i	1.39652	−	0.806281i
$467$	31.3806			1.45212			0.726060	−	0.687631i	$-0.241349\pi$
$467$	31.3806			1.45212			0.726060	+	0.687631i	$0.241349\pi$
$468$		0			0
$469$	−8.42649			−0.389099
$470$	19.6225	−	11.3291i	0.905119	−	0.522571i
$471$		0			0
$472$	3.47399	−	6.01713i	0.159903	−	0.276961i
$473$		−	3.22865i		−	0.148454i
$474$		0			0
$475$	−16.4246	−	9.48277i	−0.753614	−	0.435099i
$476$			12.1500i			0.556895i
$477$		0			0
$478$	−32.0849	−	55.5726i	−1.46753	−	2.54183i
$479$	−35.6760	+	20.5975i	−1.63008	+	0.941125i	−0.646009	+	0.763330i	$0.723563\pi$
$479$	−35.6760	+	20.5975i	−1.63008	+	0.941125i	−0.984068	+	0.177795i	$0.943104\pi$
$480$		0			0
$481$	26.2243	+	22.8014i	1.19572	+	1.03965i
$482$	62.2572			2.83574
$483$		0			0
$484$	12.5101	+	21.6681i	0.568641	+	0.984914i
$485$	−0.834351	+	1.44514i	−0.0378859	+	0.0656204i
$486$		0			0
$487$	24.5314	+	14.1632i	1.11163	+	0.641798i	0.939250	−	0.343234i	$-0.111522\pi$
$487$	24.5314	+	14.1632i	1.11163	+	0.641798i	0.172376	+	0.985031i	$0.444856\pi$
$488$	1.26400	+	0.729774i	0.0572188	+	0.0330353i
$489$		0			0
$490$	−3.79878	+	6.57967i	−0.171611	+	0.297239i
$491$	−17.3931	−	30.1258i	−0.784941	−	1.35956i	−0.929034	−	0.369993i	$-0.879360\pi$
$491$	−17.3931	−	30.1258i	−0.784941	−	1.35956i	0.144094	−	0.989564i	$-0.453973\pi$
$492$		0			0
$493$	6.35879			0.286386
$494$	5.88828	+	17.1068i	0.264926	+	0.769670i
$495$		0			0
$496$	21.2621	−	12.2757i	0.954695	−	0.551194i
$497$	−3.22444	−	5.58490i	−0.144636	−	0.250517i
$498$		0			0
$499$		−	0.0694885i		−	0.00311073i	−0.999999	−	0.00155537i	$-0.999505\pi$
$499$		−	0.0694885i		−	0.00311073i	0.999999	−	0.00155537i	$-0.000495089\pi$
$500$	22.7142	+	13.1140i	1.01581	+	0.586477i
$501$		0			0
$502$			27.3855i			1.22228i
$503$	12.8686	−	22.2891i	0.573782	−	0.993820i	−0.422391	−	0.906414i	$-0.638809\pi$
$503$	12.8686	−	22.2891i	0.573782	−	0.993820i	0.996173	−	0.0874060i	$-0.0278578\pi$
$504$		0			0
$505$	−18.1634	+	10.4866i	−0.808260	+	0.466649i
$506$	7.21437			0.320718
$507$		0			0
$508$	−30.1540			−1.33787
$509$	6.09682	−	3.52000i	0.270237	−	0.156021i	−0.358759	−	0.933430i	$-0.616800\pi$
$509$	6.09682	−	3.52000i	0.270237	−	0.156021i	0.628995	+	0.777409i	$0.283467\pi$
$510$		0			0
$511$	−3.57430	+	6.19086i	−0.158118	+	0.273868i
$512$		−	28.7215i		−	1.26932i
$513$		0			0
$514$	−8.37619	−	4.83599i	−0.369458	−	0.213307i
$515$			29.6746i			1.30762i
$516$		0			0
$517$	1.32173	+	2.28930i	0.0581295	+	0.100683i
$518$	−17.6068	+	10.1653i	−0.773597	+	0.446636i
$519$		0			0
$520$	−4.00775	−	11.6434i	−0.175752	−	0.510597i
$521$	−16.3253			−0.715225			−0.357613	−	0.933870i	$-0.616409\pi$
$521$	−16.3253			−0.715225			−0.357613	+	0.933870i	$0.616409\pi$
$522$		0			0
$523$	3.54473	+	6.13965i	0.155000	+	0.268468i	0.933059	−	0.359723i	$-0.117129\pi$
$523$	3.54473	+	6.13965i	0.155000	+	0.268468i	−0.778059	+	0.628191i	$0.783796\pi$
$524$	10.0463	−	17.4007i	0.438874	−	0.760152i
$525$		0			0
$526$	4.86836	+	2.81075i	0.212271	+	0.122555i
$527$	−36.3805	−	21.0043i	−1.58476	−	0.914963i
$528$		0			0
$529$	4.05594	−	7.02510i	0.176345	−	0.305439i
$530$	−18.6912	−	32.3741i	−0.811894	−	1.40624i
$531$		0			0
$532$	−5.82686			−0.252626
$533$	32.8796	+	28.5880i	1.42417	+	1.23828i
$534$		0			0
$535$	−11.9548	+	6.90209i	−0.516850	+	0.298403i
$536$	3.99505	+	6.91963i	0.172560	+	0.298882i
$537$		0			0
$538$			25.1558i			1.08454i
$539$	−0.767631	−	0.443192i	−0.0330642	−	0.0190896i
$540$		0			0
$541$		−	25.5162i		−	1.09703i	−0.836141	−	0.548515i	$-0.815194\pi$
$541$		−	25.5162i		−	1.09703i	0.836141	−	0.548515i	$-0.184806\pi$
$542$	13.7409	−	23.7999i	0.590222	−	1.02229i
$543$		0			0
$544$	−34.4136	+	19.8687i	−1.47547	+	0.851864i
$545$	37.5235			1.60733
$546$		0			0
$547$	−13.3073			−0.568978			−0.284489	−	0.958679i	$-0.591824\pi$
$547$	−13.3073			−0.568978			−0.284489	+	0.958679i	$0.591824\pi$
$548$	−15.8158	+	9.13126i	−0.675618	+	0.390068i
$549$		0			0
$550$	−7.45350	+	12.9098i	−0.317818	+	0.550478i
$551$			3.04952i			0.129914i
$552$		0			0
$553$	−0.656058	−	0.378775i	−0.0278984	−	0.0161072i
$554$			45.0669i			1.91471i
$555$		0			0
$556$	20.4297	+	35.3852i	0.866412	+	1.50067i
$557$	14.7285	−	8.50353i	0.624069	−	0.360306i	−0.154383	−	0.988011i	$-0.549339\pi$
$557$	14.7285	−	8.50353i	0.624069	−	0.360306i	0.778451	+	0.627705i	$0.216006\pi$
$558$		0			0
$559$	12.8916	+	2.50732i	0.545259	+	0.106048i
$560$	−10.4412			−0.441220
$561$		0			0
$562$	18.2122	+	31.5445i	0.768235	+	1.33062i
$563$	12.4596	−	21.5807i	0.525111	−	0.909519i	−0.474461	−	0.880276i	$-0.657357\pi$
$563$	12.4596	−	21.5807i	0.525111	−	0.909519i	0.999572	−	0.0292428i	$-0.00930961\pi$
$564$		0			0
$565$	15.3158	+	8.84257i	0.644340	+	0.372010i
$566$	38.8013	+	22.4019i	1.63094	+	0.941623i
$567$		0			0
$568$	−3.05745	+	5.29566i	−0.128288	+	0.222201i
$569$	−2.94065	−	5.09335i	−0.123278	−	0.213524i	0.797780	−	0.602948i	$-0.206007\pi$
$569$	−2.94065	−	5.09335i	−0.123278	−	0.213524i	−0.921059	+	0.389424i	$0.872674\pi$
$570$		0			0
$571$	−8.92622			−0.373551			−0.186775	−	0.982403i	$-0.559804\pi$
$571$	−8.92622			−0.373551			−0.186775	+	0.982403i	$0.559804\pi$
$572$	7.40220	−	2.54789i	0.309501	−	0.106533i
$573$		0			0
$574$	−22.0751	+	12.7451i	−0.921397	+	0.531969i
$575$	−15.3816	−	26.6417i	−0.641457	−	1.11104i
$576$		0			0
$577$			36.1933i			1.50675i	0.657592	+	0.753374i	$0.271575\pi$
$577$			36.1933i			1.50675i	−0.657592	+	0.753374i	$0.728425\pi$
$578$	13.8894	+	8.01905i	0.577723	+	0.333549i
$579$		0			0
$580$		−	11.3104i		−	0.469638i
$581$	−2.38383	+	4.12892i	−0.0988980	+	0.171296i
$582$		0			0
$583$	3.77699	−	2.18065i	0.156427	−	0.0903132i
$584$	6.77838			0.280491
$585$		0			0
$586$	−0.886069			−0.0366032
$587$	−31.6008	+	18.2447i	−1.30431	+	0.753041i	−0.981139	−	0.193301i	$-0.938080\pi$
$587$	−31.6008	+	18.2447i	−1.30431	+	0.753041i	−0.323166	+	0.946342i	$0.604747\pi$
$588$		0			0
$589$	10.0732	−	17.4472i	0.415058	−	0.718901i
$590$		−	55.6708i		−	2.29193i
$591$		0			0
$592$	−24.1967	−	13.9699i	−0.994476	−	0.574161i
$593$			34.9930i			1.43699i	0.695533	+	0.718495i	$0.255168\pi$
$593$			34.9930i			1.43699i	−0.695533	+	0.718495i	$0.744832\pi$
$594$		0			0
$595$	8.93270	+	15.4719i	0.366205	+	0.634286i
$596$	5.34926	−	3.08839i	0.219114	−	0.126506i
$597$		0			0
$598$	−5.60256	+	28.8062i	−0.229106	+	1.17797i
$599$	32.5052			1.32812			0.664062	−	0.747677i	$-0.268831\pi$
$599$	32.5052			1.32812			0.664062	+	0.747677i	$0.268831\pi$
$600$		0			0
$601$	−10.0390	−	17.3881i	−0.409500	−	0.709275i	0.585334	−	0.810792i	$-0.300963\pi$
$601$	−10.0390	−	17.3881i	−0.409500	−	0.709275i	−0.994834	+	0.101518i	$0.967630\pi$
$602$	−3.84172	+	6.65406i	−0.156577	+	0.271199i
$603$		0			0
$604$	−33.7235	−	19.4703i	−1.37219	−	0.792235i
$605$	31.8608	+	18.3949i	1.29533	+	0.747858i
$606$		0			0
$607$	−4.85800	+	8.41431i	−0.197180	+	0.341526i	−0.947613	−	0.319420i	$-0.896512\pi$
$607$	−4.85800	+	8.41431i	−0.197180	+	0.341526i	0.750433	+	0.660947i	$0.229845\pi$
$608$	−9.52856	−	16.5039i	−0.386434	−	0.669323i
$609$		0			0
$610$	11.6946			0.473502
$611$	−10.1674	+	3.49968i	−0.411327	+	0.141582i
$612$		0			0
$613$	−10.2898	+	5.94080i	−0.415600	+	0.239947i	−0.693193	−	0.720752i	$-0.743797\pi$
$613$	−10.2898	+	5.94080i	−0.415600	+	0.239947i	0.277593	+	0.960699i	$0.410463\pi$
$614$	14.8508	+	25.7224i	0.599331	+	1.03807i
$615$		0			0
$616$			0.840480i			0.0338639i
$617$	17.3105	+	9.99422i	0.696895	+	0.402352i	0.806190	−	0.591657i	$-0.201526\pi$
$617$	17.3105	+	9.99422i	0.696895	+	0.402352i	−0.109295	+	0.994009i	$0.534859\pi$
$618$		0			0
$619$		−	41.7176i		−	1.67677i	−0.545078	−	0.838386i	$-0.683500\pi$
$619$		−	41.7176i		−	1.67677i	0.545078	−	0.838386i	$-0.316500\pi$
$620$	−37.3603	+	64.7100i	−1.50043	+	2.59882i
$621$		0			0
$622$	−18.9708	+	10.9528i	−0.760659	+	0.439166i
$623$	3.61884			0.144986
$624$		0			0
$625$	−1.29828			−0.0519312
$626$	−12.5091	+	7.22211i	−0.499963	+	0.288654i
$627$		0			0
$628$	15.9012	−	27.5416i	0.634526	−	1.09903i
$629$			47.8066i			1.90618i
$630$		0			0
$631$	15.2780	+	8.82074i	0.608206	+	0.351148i	0.772263	−	0.635303i	$-0.219125\pi$
$631$	15.2780	+	8.82074i	0.608206	+	0.351148i	−0.164057	+	0.986451i	$0.552458\pi$
$632$			0.718319i			0.0285732i
$633$		0			0
$634$	0.739603	+	1.28103i	0.0293734	+	0.0508762i
$635$	−38.3982	+	22.1692i	−1.52379	+	0.879759i
$636$		0			0
$637$	2.36575	−	2.72089i	0.0937343	−	0.107806i
$638$	2.39694			0.0948958
$639$		0			0
$640$	13.3159	+	23.0639i	0.526359	+	0.911680i
$641$	5.46012	−	9.45721i	0.215662	−	0.373537i	−0.737815	−	0.675003i	$-0.764142\pi$
$641$	5.46012	−	9.45721i	0.215662	−	0.373537i	0.953477	+	0.301465i	$0.0974758\pi$
$642$		0			0
$643$	15.2725	+	8.81757i	0.602288	+	0.347731i	0.769941	−	0.638115i	$-0.220286\pi$
$643$	15.2725	+	8.81757i	0.602288	+	0.347731i	−0.167653	+	0.985846i	$0.553619\pi$
$644$	−8.18524	−	4.72575i	−0.322544	−	0.186221i
$645$		0			0
$646$	−12.4445	+	21.5544i	−0.489620	+	0.848048i
$647$	−8.33632	−	14.4389i	−0.327735	−	0.567653i	0.654327	−	0.756211i	$-0.272952\pi$
$647$	−8.33632	−	14.4389i	−0.327735	−	0.567653i	−0.982062	+	0.188558i	$0.939619\pi$
$648$		0			0
$649$	6.49495			0.254949
$650$	−45.7593	−	39.7866i	−1.79483	−	1.56056i
$651$		0			0
$652$	−4.92042	+	2.84080i	−0.192698	+	0.111254i
$653$	−3.38664	−	5.86584i	−0.132530	−	0.229548i	0.792121	−	0.610364i	$-0.208977\pi$
$653$	−3.38664	−	5.86584i	−0.132530	−	0.229548i	−0.924651	+	0.380816i	$0.875643\pi$
$654$		0			0
$655$		−	29.5441i		−	1.15439i
$656$	−30.3374	−	17.5153i	−1.18448	−	0.683858i
$657$		0			0
$658$		−	6.29081i		−	0.245241i
$659$	16.7680	−	29.0431i	0.653190	−	1.13136i	−0.329154	−	0.944276i	$-0.606764\pi$
$659$	16.7680	−	29.0431i	0.653190	−	1.13136i	0.982344	−	0.187082i	$-0.0599031\pi$
$660$		0			0
$661$	−21.7945	+	12.5830i	−0.847707	+	0.489424i	−0.859876	−	0.510502i	$-0.829460\pi$
$661$	−21.7945	+	12.5830i	−0.847707	+	0.489424i	0.0121696	+	0.999926i	$0.496126\pi$
$662$	−8.85657			−0.344221
$663$		0			0
$664$	4.52075			0.175439
$665$	−7.41995	+	4.28391i	−0.287733	+	0.166123i
$666$		0			0
$667$	−2.47325	+	4.28380i	−0.0957647	+	0.165869i
$668$		−	33.7833i		−	1.30712i
$669$		0			0
$670$	55.4436	+	32.0104i	2.14197	+	1.23667i
$671$			1.36438i			0.0526713i
$672$		0			0
$673$	−0.927341	−	1.60620i	−0.0357464	−	0.0619145i	0.847599	−	0.530638i	$-0.178048\pi$
$673$	−0.927341	−	1.60620i	−0.0357464	−	0.0619145i	−0.883345	+	0.468723i	$0.844714\pi$
$674$	37.3172	−	21.5451i	1.43741	−	0.829887i
$675$		0			0
$676$	4.42503	+	31.5348i	0.170194	+	1.21288i
$677$	14.7209			0.565770			0.282885	−	0.959154i	$-0.408709\pi$
$677$	14.7209			0.565770			0.282885	+	0.959154i	$0.408709\pi$
$678$		0			0
$679$	0.231650	+	0.401229i	0.00888990	+	0.0153978i
$680$	8.47009	−	14.6706i	0.324813	−	0.562593i
$681$		0			0
$682$	−13.7136	−	7.91756i	−0.525122	−	0.303179i
$683$	−6.87930	−	3.97177i	−0.263229	−	0.151975i	0.362578	−	0.931954i	$-0.381897\pi$
$683$	−6.87930	−	3.97177i	−0.263229	−	0.151975i	−0.625807	+	0.779978i	$0.715230\pi$
$684$		0			0
$685$	−13.4266	+	23.2556i	−0.513005	+	0.888551i
$686$	1.05469	+	1.82678i	0.0402684	+	0.0697469i
$687$		0			0
$688$	−10.5592			−0.402566
$689$	5.77394	+	16.7746i	0.219969	+	0.639060i
$690$		0			0
$691$	8.86002	−	5.11534i	0.337051	−	0.194597i	−0.321916	−	0.946768i	$-0.604327\pi$
$691$	8.86002	−	5.11534i	0.337051	−	0.194597i	0.658967	+	0.752172i	$0.270994\pi$
$692$	−4.51240	−	7.81571i	−0.171536	−	0.297109i
$693$		0			0
$694$			16.8118i			0.638168i
$695$	52.0306	+	30.0399i	1.97363	+	1.13948i
$696$		0			0
$697$			59.9392i			2.27036i
$698$	−22.7785	+	39.4535i	−0.862178	+	1.49334i
$699$		0			0
$700$	16.9131	−	9.76479i	0.639255	−	0.369074i
$701$	16.5978			0.626891			0.313445	−	0.949606i	$-0.398517\pi$
$701$	16.5978			0.626891			0.313445	+	0.949606i	$0.398517\pi$
$702$		0			0
$703$	−22.9269			−0.864706
$704$	−8.52162	+	4.91996i	−0.321171	+	0.185428i
$705$		0			0
$706$	22.8000	−	39.4907i	0.858088	−	1.48625i
$707$			5.82303i			0.218998i
$708$		0			0
$709$	41.4531	+	23.9329i	1.55680	+	0.898820i	0.997560	+	0.0698158i	$0.0222412\pi$
$709$	41.4531	+	23.9329i	1.55680	+	0.898820i	0.559242	+	0.829004i	$0.311092\pi$
$710$			48.9957i			1.83878i
$711$		0			0
$712$	−1.71571	−	2.97170i	−0.0642990	−	0.111369i
$713$	28.3004	−	16.3393i	1.05986	−	0.611910i
$714$		0			0
$715$	7.55279	−	8.68661i	0.282458	−	0.324861i
$716$	14.4344			0.539441
$717$		0			0
$718$	14.4318	+	24.9965i	0.538588	+	0.932862i
$719$	19.0461	−	32.9888i	0.710300	−	1.23028i	−0.254444	−	0.967087i	$-0.581893\pi$
$719$	19.0461	−	32.9888i	0.710300	−	1.23028i	0.964744	−	0.263188i	$-0.0847741\pi$
$720$		0			0
$721$	7.13508	+	4.11944i	0.265724	+	0.153416i
$722$	24.3719	+	14.0711i	0.907028	+	0.523673i
$723$		0			0
$724$	−2.59089	+	4.48756i	−0.0962898	+	0.166779i
$725$	−5.11047	−	8.85159i	−0.189798	−	0.328740i
$726$		0			0
$727$	15.4059			0.571374			0.285687	−	0.958323i	$-0.407778\pi$
$727$	15.4059			0.571374			0.285687	+	0.958323i	$0.407778\pi$
$728$	−3.35594	−	0.652702i	−0.124379	−	0.0241908i
$729$		0			0
$730$	47.0354	−	27.1559i	1.74086	−	1.00508i
$731$	9.03369	+	15.6468i	0.334123	+	0.578718i
$732$		0			0
$733$		−	11.6298i		−	0.429557i	−0.976663	−	0.214778i	$-0.931097\pi$
$733$		−	11.6298i		−	0.429557i	0.976663	−	0.214778i	$-0.0689029\pi$
$734$	−20.8487	−	12.0370i	−0.769538	−	0.444293i
$735$		0			0
$736$		−	30.9117i		−	1.13942i
$737$	−3.73456	+	6.46844i	−0.137564	+	0.238268i
$738$		0			0
$739$	2.32875	−	1.34451i	0.0856645	−	0.0494584i	−0.456556	−	0.889695i	$-0.650917\pi$
$739$	2.32875	−	1.34451i	0.0856645	−	0.0494584i	0.542220	+	0.840236i	$0.317584\pi$
$740$	85.0336			3.12590
$741$		0			0
$742$	−10.3789			−0.381020
$743$	2.13665	−	1.23360i	0.0783862	−	0.0452563i	−0.460295	−	0.887766i	$-0.652256\pi$
$743$	2.13665	−	1.23360i	0.0783862	−	0.0452563i	0.538681	+	0.842510i	$0.318923\pi$
$744$		0			0
$745$	4.54118	−	7.86556i	0.166376	−	0.288172i
$746$			65.9835i			2.41583i
$747$		0			0
$748$	9.32673	+	5.38479i	0.341019	+	0.196887i
$749$			3.83260i			0.140040i
$750$		0			0
$751$	−18.9592	−	32.8383i	−0.691832	−	1.19829i	−0.971237	−	0.238115i	$-0.923471\pi$
$751$	−18.9592	−	32.8383i	−0.691832	−	1.19829i	0.279405	−	0.960173i	$-0.409863\pi$
$752$	7.48709	−	4.32267i	0.273026	−	0.157632i
$753$		0			0
$754$	−1.86142	+	9.57072i	−0.0677890	+	0.348545i
$755$	−57.2583			−2.08384
$756$		0			0
$757$	−17.3225	−	30.0035i	−0.629598	−	1.09050i	−0.987632	−	0.156788i	$-0.949886\pi$
$757$	−17.3225	−	30.0035i	−0.629598	−	1.09050i	0.358034	−	0.933709i	$-0.383447\pi$
$758$	−28.9145	+	50.0814i	−1.05022	+	1.81904i
$759$		0			0
$760$	7.03569	+	4.06206i	0.255211	+	0.147346i
$761$	−19.7969	−	11.4297i	−0.717636	−	0.414328i	0.0962458	−	0.995358i	$-0.469317\pi$
$761$	−19.7969	−	11.4297i	−0.717636	−	0.414328i	−0.813882	+	0.581030i	$0.802650\pi$
$762$		0			0
$763$	5.20902	−	9.02229i	0.188579	−	0.326629i
$764$	13.9214	+	24.1126i	0.503659	+	0.872363i
$765$		0			0
$766$	33.9625			1.22712
$767$	−5.04386	+	25.9336i	−0.182123	+	0.936408i
$768$		0			0
$769$	−44.8839	+	25.9137i	−1.61855	+	0.934473i	−0.631260	+	0.775571i	$0.717462\pi$
$769$	−44.8839	+	25.9137i	−1.61855	+	0.934473i	−0.987294	+	0.158902i	$0.949205\pi$
$770$	3.36718	+	5.83212i	0.121345	+	0.210175i
$771$		0			0
$772$		−	34.5122i		−	1.24212i
$773$	4.93605	+	2.84983i	0.177538	+	0.102501i	0.586135	−	0.810213i	$-0.300649\pi$
$773$	4.93605	+	2.84983i	0.177538	+	0.102501i	−0.408598	+	0.912715i	$0.633982\pi$
$774$		0			0
$775$			67.5234i			2.42551i
$776$	0.219653	−	0.380450i	0.00788508	−	0.0136574i
$777$		0			0
$778$	−38.6146	+	22.2941i	−1.38440	+	0.799283i
$779$	−28.7454			−1.02991
$780$		0			0
$781$	−5.71619			−0.204541
$782$	−34.9625	+	20.1856i	−1.25026	+	0.721836i
$783$		0			0
$784$	−1.44945	+	2.51051i	−0.0517659	+	0.0896612i
$785$		−	46.7622i		−	1.66902i
$786$		0			0
$787$	−14.5614	−	8.40705i	−0.519059	−	0.299679i	0.217490	−	0.976062i	$-0.430213\pi$
$787$	−14.5614	−	8.40705i	−0.519059	−	0.299679i	−0.736550	+	0.676384i	$0.763546\pi$
$788$		−	56.2340i		−	2.00325i
$789$		0			0
$790$	2.87777	+	4.98444i	0.102386	+	0.177338i
$791$	4.25228	−	2.45505i	0.151194	−	0.0872917i
$792$		0			0
$793$	−5.44781	−	1.05955i	−0.193457	−	0.0376258i
$794$	−27.6296			−0.980539
$795$		0			0
$796$	3.85781	+	6.68192i	0.136736	+	0.236834i
$797$	−21.0651	+	36.4858i	−0.746163	+	1.29239i	0.203487	+	0.979078i	$0.434773\pi$
$797$	−21.0651	+	36.4858i	−0.746163	+	1.29239i	−0.949650	+	0.313314i	$0.898561\pi$
$798$		0			0
$799$	−12.8108	−	7.39632i	−0.453214	−	0.261663i
$800$	55.3154	+	31.9364i	1.95570	+	1.12912i
$801$		0			0
$802$	20.5082	−	35.5213i	0.724171	−	1.25430i
$803$	3.16820	+	5.48748i	0.111803	+	0.193649i
$804$		0			0
$805$	−13.8975			−0.489823
$806$	42.2637	−	48.6083i	1.48868	−	1.71215i
$807$		0			0
$808$	4.78173	−	2.76073i	0.168221	−	0.0971223i
$809$	−15.0843	−	26.1268i	−0.530336	−	0.918569i	−0.999374	−	0.0353910i	$-0.988732\pi$
$809$	−15.0843	−	26.1268i	−0.530336	−	0.918569i	0.469037	−	0.883178i	$-0.344601\pi$
$810$		0			0
$811$			23.7929i			0.835480i	0.908567	+	0.417740i	$0.137178\pi$
$811$			23.7929i			0.835480i	−0.908567	+	0.417740i	$0.862822\pi$
$812$	−2.71951	−	1.57011i	−0.0954360	−	0.0551000i
$813$		0			0
$814$			18.0207i			0.631624i
$815$	−4.17712	+	7.23499i	−0.146318	+	0.253431i
$816$		0			0
$817$	−7.50384	+	4.33234i	−0.262526	+	0.151569i
$818$	−50.7432			−1.77419
$819$		0			0
$820$	106.614			3.72312
$821$	31.0771	−	17.9424i	1.08460	−	0.626193i	0.152465	−	0.988309i	$-0.451279\pi$
$821$	31.0771	−	17.9424i	1.08460	−	0.626193i	0.932133	+	0.362116i	$0.117946\pi$
$822$		0			0
$823$	−6.11728	+	10.5954i	−0.213235	+	0.369334i	−0.952725	−	0.303833i	$-0.901733\pi$
$823$	−6.11728	+	10.5954i	−0.213235	+	0.369334i	0.739490	+	0.673167i	$0.235067\pi$
$824$		−	7.81220i		−	0.272151i
$825$		0			0
$826$	−13.3857	−	7.72823i	−0.465748	−	0.268900i
$827$			27.3474i			0.950962i	0.879726	+	0.475481i	$0.157726\pi$
$827$			27.3474i			0.950962i	−0.879726	+	0.475481i	$0.842274\pi$
$828$		0			0
$829$	11.7869	+	20.4155i	0.409376	+	0.709060i	0.994820	−	0.101653i	$-0.0324132\pi$
$829$	11.7869	+	20.4155i	0.409376	+	0.709060i	−0.585444	+	0.810713i	$0.699080\pi$
$830$	31.3697	−	18.1113i	1.08886	−	0.628652i
$831$		0			0
$832$	−13.0271	−	37.8466i	−0.451634	−	1.31210i
$833$	4.96016			0.171859
$834$		0			0
$835$	−24.8376	−	43.0199i	−0.859539	−	1.48877i
$836$	−2.58242	+	4.47288i	−0.0893148	+	0.154698i
$837$		0			0
$838$	−71.2880	−	41.1582i	−2.46260	−	1.42179i
$839$	−9.16975	−	5.29416i	−0.316575	−	0.182775i	0.333290	−	0.942824i	$-0.391841\pi$
$839$	−9.16975	−	5.29416i	−0.316575	−	0.182775i	−0.649865	+	0.760050i	$0.725175\pi$
$840$		0			0
$841$	13.6783	−	23.6915i	0.471665	−	0.816947i
$842$	23.2332	+	40.2411i	0.800669	+	1.38680i
$843$		0			0
$844$	36.4092			1.25326
$845$	28.8193	+	36.9033i	0.991414	+	1.26951i
$846$		0			0
$847$	8.84586	−	5.10716i	0.303947	−	0.175484i
$848$	−7.13174	−	12.3525i	−0.244905	−	0.424188i
$849$		0			0
$850$		−	83.4188i		−	2.86124i
$851$	−32.2065	−	18.5944i	−1.10402	−	0.637408i
$852$		0			0
$853$		−	21.3925i		−	0.732464i	−0.930524	−	0.366232i	$-0.880648\pi$
$853$		−	21.3925i		−	0.732464i	0.930524	−	0.366232i	$-0.119352\pi$
$854$	1.62345	−	2.81190i	0.0555534	−	0.0962213i
$855$		0			0
$856$	3.14724	−	1.81706i	0.107570	−	0.0621058i
$857$	7.22129			0.246675			0.123337	−	0.992365i	$-0.460640\pi$
$857$	7.22129			0.246675			0.123337	+	0.992365i	$0.460640\pi$
$858$		0			0
$859$	57.1073			1.94848			0.974238	−	0.225524i	$-0.0724095\pi$
$859$	57.1073			1.94848			0.974238	+	0.225524i	$0.0724095\pi$
$860$	27.8309	−	16.0682i	0.949027	−	0.547921i
$861$		0			0
$862$	−37.8421	+	65.5444i	−1.28891	+	2.23245i
$863$		−	51.3361i		−	1.74750i	−0.486374	−	0.873751i	$-0.661681\pi$
$863$		−	51.3361i		−	1.74750i	0.486374	−	0.873751i	$-0.338319\pi$
$864$		0			0
$865$	−11.4922	−	6.63505i	−0.390748	−	0.225598i
$866$			25.7631i			0.875467i
$867$		0			0
$868$	10.3727	+	17.9661i	0.352074	+	0.609810i
$869$	−0.581520	+	0.335741i	−0.0197267	+	0.0113892i
$870$		0			0
$871$	−22.9276	−	19.9349i	−0.776871	−	0.675470i
$872$	−9.87851			−0.334528
$873$		0			0
$874$	−9.68055	−	16.7672i	−0.327449	−	0.567159i
$875$	5.35371	−	9.27291i	0.180989	−	0.313481i
$876$		0			0
$877$	−18.5570	−	10.7139i	−0.626624	−	0.361781i	0.152820	−	0.988254i	$-0.451165\pi$
$877$	−18.5570	−	10.7139i	−0.626624	−	0.361781i	−0.779443	+	0.626473i	$0.784498\pi$
$878$	28.7815	+	16.6170i	0.971330	+	0.560798i
$879$		0			0
$880$	−4.62745	+	8.01497i	−0.155991	+	0.270185i
$881$	−14.5309	−	25.1683i	−0.489560	−	0.847943i	0.510368	−	0.859956i	$-0.329509\pi$
$881$	−14.5309	−	25.1683i	−0.489560	−	0.847943i	−0.999928	+	0.0120134i	$0.996176\pi$
$882$		0			0
$883$	4.83594			0.162742			0.0813711	−	0.996684i	$-0.474070\pi$
$883$	4.83594			0.162742			0.0813711	+	0.996684i	$0.474070\pi$
$884$	−28.7438	+	33.0589i	−0.966760	+	1.11189i
$885$		0			0
$886$	−27.5308	+	15.8949i	−0.924916	+	0.534000i
$887$	−12.4949	−	21.6418i	−0.419538	−	0.726660i	0.576355	−	0.817199i	$-0.304474\pi$
$887$	−12.4949	−	21.6418i	−0.419538	−	0.726660i	−0.995893	+	0.0905387i	$0.971141\pi$
$888$		0			0
$889$			12.3102i			0.412869i
$890$	−23.8108	−	13.7471i	−0.798138	−	0.460805i
$891$		0			0
$892$		−	10.7311i		−	0.359303i
$893$	3.54710	−	6.14376i	0.118699	−	0.205593i
$894$		0			0
$895$	18.3809	−	10.6122i	0.614406	−	0.354727i
$896$	7.39409			0.247019
$897$		0			0
$898$	64.9324			2.16682
$899$	9.40269	−	5.42865i	0.313597	−	0.181055i
$900$		0			0
$901$	−12.2028	+	21.1359i	−0.406534	+	0.704138i
$902$			22.5940i			0.752300i
$903$		0			0
$904$	−4.03206	−	2.32791i	−0.134104	−	0.0774252i
$905$			7.61931i			0.253274i
$906$		0			0
$907$	7.52060	+	13.0261i	0.249717	+	0.432523i	0.963447	−	0.267898i	$-0.0863290\pi$
$907$	7.52060	+	13.0261i	0.249717	+	0.432523i	−0.713730	+	0.700421i	$0.752996\pi$
$908$	−28.7789	+	16.6155i	−0.955060	+	0.551404i
$909$		0			0
$910$	−25.9019	+	8.91563i	−0.858639	+	0.295550i
$911$	9.22150			0.305522			0.152761	−	0.988263i	$-0.451184\pi$
$911$	9.22150			0.305522			0.152761	+	0.988263i	$0.451184\pi$
$912$		0			0
$913$	2.11299	+	3.65981i	0.0699298	+	0.121122i
$914$	8.18018	−	14.1685i	0.270576	−	0.468652i
$915$		0			0
$916$	35.0404	+	20.2306i	1.15777	+	0.668437i
$917$	−7.10371	−	4.10133i	−0.234585	−	0.135438i
$918$		0			0
$919$	22.5402	−	39.0407i	0.743531	−	1.28783i	−0.207346	−	0.978268i	$-0.566483\pi$
$919$	22.5402	−	39.0407i	0.743531	−	1.28783i	0.950878	−	0.309567i	$-0.100184\pi$
$920$	6.58889	+	11.4123i	0.217229	+	0.376252i
$921$		0			0
$922$	3.10548			0.102274
$923$	4.43910	−	22.8241i	0.146115	−	0.751265i
$924$		0			0
$925$	66.5480	−	38.4215i	2.18808	−	1.26329i
$926$	14.8043	+	25.6418i	0.486499	+	0.842642i
$927$		0			0
$928$		−	10.2703i		−	0.337139i
$929$	40.6313	+	23.4585i	1.33307	+	0.769647i	0.985769	−	0.168107i	$-0.0537654\pi$
$929$	40.6313	+	23.4585i	1.33307	+	0.769647i	0.347300	+	0.937754i	$0.387099\pi$
$930$		0			0
$931$			2.37878i			0.0779612i
$932$	−20.2117	+	35.0078i	−0.662058	+	1.14672i
$933$		0			0
$934$	−57.3256	+	33.0969i	−1.87575	+	1.08296i
$935$	15.8356			0.517880
$936$		0			0
$937$	−28.3912			−0.927501			−0.463750	−	0.885966i	$-0.653497\pi$
$937$	−28.3912			−0.927501			−0.463750	+	0.885966i	$0.653497\pi$
$938$	15.3934	−	8.88737i	0.502612	−	0.290183i
$939$		0			0
$940$	−13.1558	+	22.7866i	−0.429096	+	0.743216i
$941$		−	17.8718i		−	0.582603i	−0.956631	−	0.291302i	$-0.905912\pi$
$941$		−	17.8718i		−	0.582603i	0.956631	−	0.291302i	$-0.0940883\pi$
$942$		0			0
$943$	−40.3800	−	23.3134i	−1.31495	−	0.759188i
$944$		−	21.2415i		−	0.691353i
$945$		0			0
$946$	3.40524	+	5.89805i	0.110714	+	0.191762i
$947$	−8.24659	+	4.76117i	−0.267978	+	0.154717i	−0.627969	−	0.778239i	$-0.716113\pi$
$947$	−8.24659	+	4.76117i	−0.267978	+	0.154717i	0.359990	+	0.932956i	$0.382780\pi$
$948$		0			0
$949$	−24.3713	+	8.38878i	−0.791125	+	0.272311i
$950$	40.0057			1.29796
$951$		0			0
$952$	−2.35164	−	4.07316i	−0.0762171	−	0.132012i
$953$	6.70900	−	11.6203i	0.217326	−	0.376419i	−0.736664	−	0.676259i	$-0.763600\pi$
$953$	6.70900	−	11.6203i	0.217326	−	0.376419i	0.953990	+	0.299840i	$0.0969333\pi$
$954$		0			0
$955$	35.4552	+	20.4701i	1.14730	+	0.662397i
$956$	64.5335	+	37.2584i	2.08716	+	1.20502i
$957$		0			0
$958$	43.4482	−	75.2545i	1.40375	−	2.43136i
$959$	3.72778	+	6.45670i	0.120376	+	0.208498i
$960$		0			0
$961$	−40.7275			−1.31379
$962$	−71.9545	−	13.9946i	−2.31991	−	0.451202i
$963$		0			0
$964$	−62.6102	+	36.1480i	−2.01654	+	1.16425i
$965$	−25.3734	−	43.9480i	−0.816798	−	1.41474i
$966$		0			0
$967$		−	12.9316i		−	0.415851i	−0.978145	−	0.207926i	$-0.933329\pi$
$967$		−	12.9316i		−	0.415851i	0.978145	−	0.207926i	$-0.0666712\pi$
$968$	−8.38775	−	4.84267i	−0.269593	−	0.155649i
$969$		0			0
$970$		−	3.51994i		−	0.113019i
$971$	23.7607	−	41.1547i	0.762516	−	1.32072i	−0.179034	−	0.983843i	$-0.557297\pi$
$971$	23.7607	−	41.1547i	0.762516	−	1.32072i	0.941550	−	0.336874i	$-0.109370\pi$
$972$		0			0
$973$	14.4458	−	8.34028i	0.463111	−	0.267377i
$974$	−59.7515			−1.91456
$975$		0			0
$976$	4.46216			0.142830
$977$	−31.6049	+	18.2471i	−1.01113	+	0.583776i	−0.911522	−	0.411251i	$-0.865092\pi$
$977$	−31.6049	+	18.2471i	−1.01113	+	0.583776i	−0.0996074	+	0.995027i	$0.531759\pi$
$978$		0			0
$979$	1.60384	−	2.77793i	0.0512589	−	0.0887831i
$980$		−	8.82263i		−	0.281829i
$981$		0			0
$982$	63.5470	+	36.6889i	2.02787	+	1.17079i
$983$		−	44.1843i		−	1.40926i	−0.709576	−	0.704629i	$-0.751113\pi$
$983$		−	44.1843i		−	1.40926i	0.709576	−	0.704629i	$-0.248887\pi$
$984$		0			0
$985$	−41.3433	−	71.6087i	−1.31731	−	2.28164i
$986$	−11.6161	+	6.70658i	−0.369933	+	0.213581i
$987$		0			0
$988$	−15.8542	−	13.7849i	−0.504391	−	0.438555i
$989$	−14.0546			−0.446911
$990$		0			0
$991$	25.3549	+	43.9159i	0.805424	+	1.39504i	0.916005	+	0.401168i	$0.131396\pi$
$991$	25.3549	+	43.9159i	0.805424	+	1.39504i	−0.110581	+	0.993867i	$0.535271\pi$
$992$	−33.9247	+	58.7594i	−1.07711	+	1.86561i
$993$		0			0
$994$	11.7807	+	6.80160i	0.373662	+	0.215734i
$995$	9.82511	+	5.67253i	0.311477	+	0.179831i
$996$		0			0
$997$	25.1384	−	43.5410i	0.796141	−	1.37896i	−0.125971	−	0.992034i	$-0.540205\pi$
$997$	25.1384	−	43.5410i	0.796141	−	1.37896i	0.922112	−	0.386923i	$-0.126462\pi$
$998$	0.0732891	+	0.126940i	0.00231993	+	0.00401823i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ct.a.127.1		12
3.2	odd	2		91.2.q.a.36.6	✓	12
12.11	even	2		1456.2.cc.c.673.5		12
13.4	even	6	inner	819.2.ct.a.316.1		12
21.2	odd	6		637.2.u.h.361.1		12
21.5	even	6		637.2.u.i.361.1		12
21.11	odd	6		637.2.k.h.569.6		12
21.17	even	6		637.2.k.g.569.6		12
21.20	even	2		637.2.q.h.491.6		12
39.2	even	12		1183.2.a.p.1.5		6
39.11	even	12		1183.2.a.m.1.2		6
39.17	odd	6		91.2.q.a.43.6	yes	12
39.23	odd	6		1183.2.c.i.337.2		12
39.29	odd	6		1183.2.c.i.337.11		12
156.95	even	6		1456.2.cc.c.225.5		12
273.17	even	6		637.2.u.i.30.1		12
273.41	odd	12		8281.2.a.ch.1.5		6
273.95	odd	6		637.2.u.h.30.1		12
273.167	odd	12		8281.2.a.by.1.2		6
273.173	even	6		637.2.k.g.459.1		12
273.212	odd	6		637.2.k.h.459.1		12
273.251	even	6		637.2.q.h.589.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.6	✓	12	3.2	odd	2
91.2.q.a.43.6	yes	12	39.17	odd	6
637.2.k.g.459.1		12	273.173	even	6
637.2.k.g.569.6		12	21.17	even	6
637.2.k.h.459.1		12	273.212	odd	6
637.2.k.h.569.6		12	21.11	odd	6
637.2.q.h.491.6		12	21.20	even	2
637.2.q.h.589.6		12	273.251	even	6
637.2.u.h.30.1		12	273.95	odd	6
637.2.u.h.361.1		12	21.2	odd	6
637.2.u.i.30.1		12	273.17	even	6
637.2.u.i.361.1		12	21.5	even	6
819.2.ct.a.127.1		12	1.1	even	1	trivial
819.2.ct.a.316.1		12	13.4	even	6	inner
1183.2.a.m.1.2		6	39.11	even	12
1183.2.a.p.1.5		6	39.2	even	12
1183.2.c.i.337.2		12	39.23	odd	6
1183.2.c.i.337.11		12	39.29	odd	6
1456.2.cc.c.225.5		12	156.95	even	6
1456.2.cc.c.673.5		12	12.11	even	2
8281.2.a.by.1.2		6	273.167	odd	12
8281.2.a.ch.1.5		6	273.41	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.82678 + 1.05469i) q^{2} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(-0.866025 - 0.500000i) q^{7} +0.948212i q^{8} +O(q^{10})\)	\(q+(-1.82678 + 1.05469i) q^{2} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(-0.866025 - 0.500000i) q^{7} +0.948212i q^{8} +(3.79878 + 6.57967i) q^{10} +(-0.767631 + 0.443192i) q^{11} +(-1.17349 - 3.40924i) q^{13} +2.10939 q^{14} +(1.44945 + 2.51051i) q^{16} +(2.48008 - 4.29563i) q^{17} +(2.06008 + 1.18939i) q^{19} +(-7.64062 - 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +(1.92926 + 3.34157i) q^{23} -7.97282 q^{25} +(5.73942 + 4.99028i) q^{26} +(-2.12135 + 1.22476i) q^{28} +(0.640986 + 1.11022i) q^{29} -8.46921i q^{31} +(-6.93800 - 4.00566i) q^{32} +10.4629i q^{34} +(-1.80089 + 3.11923i) q^{35} +(-8.34686 + 4.81906i) q^{37} -5.01776 q^{38} +3.41525 q^{40} +(-10.4652 + 6.04207i) q^{41} +(-1.82125 + 3.15450i) q^{43} +2.17122i q^{44} +(-7.04867 - 4.06955i) q^{46} -2.98229i q^{47} +(0.500000 + 0.866025i) q^{49} +(14.5646 - 8.40888i) q^{50} +(-8.66942 - 1.68613i) q^{52} -4.92032 q^{53} +(1.59628 + 2.76484i) q^{55} +(0.474106 - 0.821175i) q^{56} +(-2.34189 - 1.35209i) q^{58} +(-6.34577 - 3.66373i) q^{59} +(0.769632 - 1.33304i) q^{61} +(8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(-12.2793 + 4.22664i) q^{65} +(7.29756 - 4.21325i) q^{67} +(-6.07501 - 10.5222i) q^{68} -7.59755i q^{70} +(5.58490 + 3.22444i) q^{71} -7.14859i q^{73} +(10.1653 - 17.6068i) q^{74} +(5.04621 - 2.91343i) q^{76} +0.886384 q^{77} +0.757551 q^{79} +(9.04232 - 5.22059i) q^{80} +(12.7451 - 22.0751i) q^{82} -4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} -7.68344i q^{86} +(-0.420240 - 0.727877i) q^{88} +(-3.13400 + 1.80942i) q^{89} +(-0.688351 + 3.53923i) q^{91} +9.45150 q^{92} +(3.14541 + 5.44800i) q^{94} +(4.28391 - 7.41995i) q^{95} +(-0.401229 - 0.231650i) q^{97} +(-1.82678 - 1.05469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4}+O(q^{10}) \) 12 * q + 4 * q^4	\( 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 6 q^{49} + 18 q^{50} + 2 q^{52} + 44 q^{53} - 6 q^{55} + 12 q^{56} - 12 q^{58} - 18 q^{59} + 14 q^{61} + 4 q^{62} - 52 q^{64} - 60 q^{65} - 24 q^{67} + 8 q^{68} + 24 q^{71} - 6 q^{74} - 18 q^{76} - 8 q^{77} - 56 q^{79} + 72 q^{80} + 14 q^{82} - 48 q^{85} - 14 q^{88} + 12 q^{89} + 14 q^{91} - 24 q^{92} + 4 q^{94} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 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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