LMFDB - Embedded newform 684.2.r.b.559.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(487,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 2 x^{17} + x^{16} + 3 x^{14} - 12 x^{13} + 28 x^{12} - 24 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 2x^17 + x^16 + 3x^14 - 12x^13 + 28x^12 - 24x^11 + 40x^10 - 48x^9 + 112x^8 - 96x^7 + 48x^6 + 64x^4 - 256x^3 + 768x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.6
Root			$-1.34963 + 0.422503i$ of defining polynomial
Character	$\chi$	$=$	684.559
Dual form			684.2.r.b.487.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.308915 - 1.38006i) q^{2} +(-1.80914 - 0.852645i) q^{4} +(-0.984694 + 1.70554i) q^{5} +0.355075i q^{7} +(-1.73557 + 2.23333i) q^{8} +(2.04956 + 1.88581i) q^{10} +1.34327i q^{11} +(5.75562 - 3.32301i) q^{13} +(0.490026 + 0.109688i) q^{14} +(2.54599 + 3.08511i) q^{16} +(1.91321 - 3.31378i) q^{17} +(2.96616 - 3.19404i) q^{19} +(3.23567 - 2.24597i) q^{20} +(1.85379 + 0.414956i) q^{22} +(2.43262 - 1.40448i) q^{23} +(0.560757 + 0.971259i) q^{25} +(-2.80796 - 8.96963i) q^{26} +(0.302753 - 0.642382i) q^{28} +(4.28481 - 2.47383i) q^{29} -1.76220 q^{31} +(5.04414 - 2.56059i) q^{32} +(-3.98220 - 3.66403i) q^{34} +(-0.605595 - 0.349640i) q^{35} +8.49598i q^{37} +(-3.49169 - 5.08017i) q^{38} +(-2.10003 - 5.15924i) q^{40} +(5.63122 + 3.25119i) q^{41} +(-4.14089 - 2.39074i) q^{43} +(1.14533 - 2.43016i) q^{44} +(-1.18679 - 3.79103i) q^{46} +(-6.83062 + 3.94366i) q^{47} +6.87392 q^{49} +(1.51362 - 0.473842i) q^{50} +(-13.2461 + 1.10430i) q^{52} +(2.89136 - 1.66933i) q^{53} +(-2.29100 - 1.32271i) q^{55} +(-0.793001 - 0.616259i) q^{56} +(-2.09040 - 6.67750i) q^{58} +(-1.83715 + 3.18204i) q^{59} +(1.98919 + 3.44537i) q^{61} +(-0.544372 + 2.43195i) q^{62} +(-1.97556 - 7.75223i) q^{64} +13.0886i q^{65} +(-1.05161 - 1.82144i) q^{67} +(-6.28675 + 4.36381i) q^{68} +(-0.669603 + 0.727749i) q^{70} +(7.80349 - 13.5160i) q^{71} +(0.435445 - 0.754212i) q^{73} +(11.7250 + 2.62454i) q^{74} +(-8.08958 + 3.24941i) q^{76} -0.476961 q^{77} +(-8.37212 + 14.5009i) q^{79} +(-7.76880 + 1.30440i) q^{80} +(6.22641 - 6.76709i) q^{82} -8.44752i q^{83} +(3.76786 + 6.52612i) q^{85} +(-4.57856 + 4.97615i) q^{86} +(-2.99997 - 2.33134i) q^{88} +(-1.83862 + 1.06153i) q^{89} +(1.17992 + 2.04368i) q^{91} +(-5.59848 + 0.466734i) q^{92} +(3.33241 + 10.6449i) q^{94} +(2.52682 + 8.20405i) q^{95} +(-13.7139 - 7.91774i) q^{97} +(2.12346 - 9.48644i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{4} - 4 q^{8} + 6 q^{10} + 6 q^{13} - 9 q^{14} - 11 q^{16} + 12 q^{19} + 14 q^{20} + 8 q^{22} - 10 q^{25} + 7 q^{28} + 12 q^{31} + 29 q^{32} - 6 q^{34} - 25 q^{38} - 46 q^{40} - 12 q^{41}+ \cdots - 12 q^{97}+O(q^{100}) $ 20 * q - q^2 + q^4 - 4 * q^8 + 6 * q^10 + 6 * q^13 - 9 * q^14 - 11 * q^16 + 12 * q^19 + 14 * q^20 + 8 * q^22 - 10 * q^25 + 7 * q^28 + 12 * q^31 + 29 * q^32 - 6 * q^34 - 25 * q^38 - 46 * q^40 - 12 * q^41 - 18 * q^43 + 12 * q^44 - 32 * q^46 + 36 * q^47 - 24 * q^49 + 34 * q^50 + 3 * q^52 + 12 * q^53 - 38 * q^56 + 16 * q^58 + 10 * q^61 + 55 * q^62 - 14 * q^64 + 14 * q^67 - 40 * q^68 + 26 * q^70 - 8 * q^71 - 6 * q^73 - 45 * q^74 - 69 * q^76 + 32 * q^77 - 6 * q^79 - 22 * q^80 + 24 * q^82 + 8 * q^85 - 7 * q^86 + 44 * q^88 + 24 * q^89 + 26 * q^91 + 18 * q^92 - 52 * q^94 - 4 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	0.308915	−	1.38006i	0.218436	−	0.975851i
$2$	0.308915	−	1.38006i	0.218436	−	0.975851i
$3$		0			0
$3$		0			0
$4$	−1.80914	−	0.852645i	−0.904571	−	0.426322i
$5$	−0.984694	+	1.70554i	−0.440368	+	0.762740i	−0.997717	−	0.0675384i	$-0.978485\pi$
$5$	−0.984694	+	1.70554i	−0.440368	+	0.762740i	0.557348	+	0.830279i	$0.311819\pi$
$6$		0			0
$7$			0.355075i			0.134206i	0.997746	+	0.0671029i	$0.0213756\pi$
$7$			0.355075i			0.134206i	−0.997746	+	0.0671029i	$0.978624\pi$
$8$	−1.73557	+	2.23333i	−0.613618	+	0.789603i
$9$		0			0
$10$	2.04956	+	1.88581i	0.648129	+	0.596344i
$11$			1.34327i			0.405011i	0.979281	+	0.202505i	$0.0649084\pi$
$11$			1.34327i			0.405011i	−0.979281	+	0.202505i	$0.935092\pi$
$12$		0			0
$13$	5.75562	−	3.32301i	1.59632	−	0.921636i	0.604133	−	0.796884i	$-0.293520\pi$
$13$	5.75562	−	3.32301i	1.59632	−	0.921636i	0.992188	−	0.124752i	$-0.0398137\pi$
$14$	0.490026	+	0.109688i	0.130965	+	0.0293154i
$15$		0			0
$16$	2.54599	+	3.08511i	0.636499	+	0.771278i
$17$	1.91321	−	3.31378i	0.464022	−	0.803710i	−0.535134	−	0.844767i	$-0.679739\pi$
$17$	1.91321	−	3.31378i	0.464022	−	0.803710i	0.999157	+	0.0410566i	$0.0130724\pi$
$18$		0			0
$19$	2.96616	−	3.19404i	0.680483	−	0.732764i
$19$	2.96616	−	3.19404i	0.680483	−	0.732764i
$20$	3.23567	−	2.24597i	0.723518	−	0.502214i
$21$		0			0
$22$	1.85379	+	0.414956i	0.395230	+	0.0884690i
$23$	2.43262	−	1.40448i	0.507237	−	0.292853i	−0.224460	−	0.974483i	$-0.572062\pi$
$23$	2.43262	−	1.40448i	0.507237	−	0.292853i	0.731697	+	0.681630i	$0.238729\pi$
$24$		0			0
$25$	0.560757	+	0.971259i	0.112151	+	0.194252i
$26$	−2.80796	−	8.96963i	−0.550686	−	1.75909i
$27$		0			0
$28$	0.302753	−	0.642382i	0.0572149	−	0.121399i
$29$	4.28481	−	2.47383i	0.795669	−	0.459380i	−0.0462857	−	0.998928i	$-0.514738\pi$
$29$	4.28481	−	2.47383i	0.795669	−	0.459380i	0.841954	+	0.539549i	$0.181405\pi$
$30$		0			0
$31$	−1.76220			−0.316501			−0.158251	−	0.987399i	$-0.550585\pi$
$31$	−1.76220			−0.316501			−0.158251	+	0.987399i	$0.550585\pi$
$32$	5.04414	−	2.56059i	0.891687	−	0.452653i
$33$		0			0
$34$	−3.98220	−	3.66403i	−0.682942	−	0.628376i
$35$	−0.605595	−	0.349640i	−0.102364	−	0.0591000i
$36$		0			0
$37$			8.49598i			1.39673i	0.715742	+	0.698365i	$0.246089\pi$
$37$			8.49598i			1.39673i	−0.715742	+	0.698365i	$0.753911\pi$
$38$	−3.49169	−	5.08017i	−0.566427	−	0.824112i
$39$		0			0
$40$	−2.10003	−	5.15924i	−0.332044	−	0.815748i
$41$	5.63122	+	3.25119i	0.879449	+	0.507750i	0.870477	−	0.492210i	$-0.163811\pi$
$41$	5.63122	+	3.25119i	0.879449	+	0.507750i	0.00897225	+	0.999960i	$0.497144\pi$
$42$		0			0
$43$	−4.14089	−	2.39074i	−0.631479	−	0.364585i	0.149845	−	0.988709i	$-0.452122\pi$
$43$	−4.14089	−	2.39074i	−0.631479	−	0.364585i	−0.781325	+	0.624125i	$0.785456\pi$
$44$	1.14533	−	2.43016i	0.172665	−	0.366361i
$45$		0			0
$46$	−1.18679	−	3.79103i	−0.174982	−	0.558957i
$47$	−6.83062	+	3.94366i	−0.996348	+	0.575242i	−0.907166	−	0.420774i	$-0.861759\pi$
$47$	−6.83062	+	3.94366i	−0.996348	+	0.575242i	−0.0891820	+	0.996015i	$0.528425\pi$
$48$		0			0
$49$	6.87392			0.981989
$50$	1.51362	−	0.473842i	0.214059	−	0.0670114i
$51$		0			0
$52$	−13.2461	+	1.10430i	−1.83690	+	0.153139i
$53$	2.89136	−	1.66933i	0.397159	−	0.229300i	−0.288098	−	0.957601i	$-0.593023\pi$
$53$	2.89136	−	1.66933i	0.397159	−	0.229300i	0.685257	+	0.728301i	$0.259690\pi$
$54$		0			0
$55$	−2.29100	−	1.32271i	−0.308918	−	0.178354i
$56$	−0.793001	−	0.616259i	−0.105969	−	0.0823511i
$57$		0			0
$58$	−2.09040	−	6.67750i	−0.274483	−	0.876799i
$59$	−1.83715	+	3.18204i	−0.239177	+	0.414266i	−0.960478	−	0.278355i	$-0.910211\pi$
$59$	−1.83715	+	3.18204i	−0.239177	+	0.414266i	0.721302	+	0.692621i	$0.243544\pi$
$60$		0			0
$61$	1.98919	+	3.44537i	0.254689	+	0.441135i	0.964811	−	0.262944i	$-0.0846935\pi$
$61$	1.98919	+	3.44537i	0.254689	+	0.441135i	−0.710122	+	0.704079i	$0.751360\pi$
$62$	−0.544372	+	2.43195i	−0.0691353	+	0.308858i
$63$		0			0
$64$	−1.97556	−	7.75223i	−0.246946	−	0.969029i
$65$			13.0886i			1.62344i
$66$		0			0
$67$	−1.05161	−	1.82144i	−0.128475	−	0.222525i	0.794611	−	0.607119i	$-0.207675\pi$
$67$	−1.05161	−	1.82144i	−0.128475	−	0.222525i	−0.923086	+	0.384594i	$0.874341\pi$
$68$	−6.28675	+	4.36381i	−0.762381	+	0.529190i
$69$		0			0
$70$	−0.669603	+	0.727749i	−0.0800328	+	0.0869826i
$71$	7.80349	−	13.5160i	0.926104	−	1.60406i	0.136327	−	0.990664i	$-0.456470\pi$
$71$	7.80349	−	13.5160i	0.926104	−	1.60406i	0.789776	−	0.613395i	$-0.210197\pi$
$72$		0			0
$73$	0.435445	−	0.754212i	0.0509649	−	0.0882739i	−0.839417	−	0.543487i	$-0.817104\pi$
$73$	0.435445	−	0.754212i	0.0509649	−	0.0882739i	0.890382	+	0.455213i	$0.150437\pi$
$74$	11.7250	+	2.62454i	1.36300	+	0.305096i
$75$		0			0
$76$	−8.08958	+	3.24941i	−0.927939	+	0.372733i
$77$	−0.476961			−0.0543548
$78$		0			0
$79$	−8.37212	+	14.5009i	−0.941937	+	1.63148i	−0.180165	+	0.983636i	$0.557663\pi$
$79$	−8.37212	+	14.5009i	−0.941937	+	1.63148i	−0.761771	+	0.647846i	$0.775670\pi$
$80$	−7.76880	+	1.30440i	−0.868579	+	0.145837i
$81$		0			0
$82$	6.22641	−	6.76709i	0.687592	−	0.747300i
$83$		−	8.44752i		−	0.927235i	−0.886035	−	0.463618i	$-0.846551\pi$
$83$		−	8.44752i		−	0.927235i	0.886035	−	0.463618i	$-0.153449\pi$
$84$		0			0
$85$	3.76786	+	6.52612i	0.408682	+	0.707857i
$86$	−4.57856	+	4.97615i	−0.493718	+	0.536592i
$87$		0			0
$88$	−2.99997	−	2.33134i	−0.319798	−	0.248522i
$89$	−1.83862	+	1.06153i	−0.194894	+	0.112522i	−0.594271	−	0.804265i	$-0.702560\pi$
$89$	−1.83862	+	1.06153i	−0.194894	+	0.112522i	0.399378	+	0.916786i	$0.369226\pi$
$90$		0			0
$91$	1.17992	+	2.04368i	0.123689	+	0.214235i
$92$	−5.59848	+	0.466734i	−0.583682	+	0.0486604i
$93$		0			0
$94$	3.33241	+	10.6449i	0.343712	+	1.09794i
$95$	2.52682	+	8.20405i	0.259246	+	0.841718i
$96$		0			0
$97$	−13.7139	−	7.91774i	−1.39244	−	0.803924i	−0.398853	−	0.917015i	$-0.630592\pi$
$97$	−13.7139	−	7.91774i	−1.39244	−	0.803924i	−0.993585	+	0.113090i	$0.963925\pi$
$98$	2.12346	−	9.48644i	0.214502	−	0.958275i
$99$		0			0
$100$	−0.186350	−	2.23527i	−0.0186350	−	0.223527i
$101$	−2.81400	−	4.87399i	−0.280004	−	0.484980i	0.691382	−	0.722490i	$-0.257002\pi$
$101$	−2.81400	−	4.87399i	−0.280004	−	0.484980i	−0.971385	+	0.237509i	$0.923669\pi$
$102$		0			0
$103$	17.9755			1.77118			0.885590	−	0.464469i	$-0.153755\pi$
$103$	17.9755			1.77118			0.885590	+	0.464469i	$0.153755\pi$
$104$	−2.56791	+	18.6215i	−0.251805	+	1.82599i
$105$		0			0
$106$	−1.41059	−	4.50594i	−0.137009	−	0.437655i
$107$	−10.4128			−1.00664			−0.503322	−	0.864099i	$-0.667889\pi$
$107$	−10.4128			−1.00664			−0.503322	+	0.864099i	$0.667889\pi$
$108$		0			0
$109$	−0.0517777	−	0.0298939i	−0.00495940	−	0.00286331i	0.497518	−	0.867454i	$-0.334245\pi$
$109$	−0.0517777	−	0.0298939i	−0.00495940	−	0.00286331i	−0.502478	+	0.864590i	$0.667578\pi$
$110$	−2.53314	+	2.75311i	−0.241526	+	0.262499i
$111$		0			0
$112$	−1.09545	+	0.904019i	−0.103510	+	0.0854218i
$113$		−	0.272476i		−	0.0256324i	−0.999918	−	0.0128162i	$-0.995920\pi$
$113$		−	0.272476i		−	0.0256324i	0.999918	−	0.0128162i	$-0.00407963\pi$
$114$		0			0
$115$			5.53191i			0.515853i
$116$	−9.86113	+	0.822102i	−0.915583	+	0.0763303i
$117$		0			0
$118$	3.82389	+	3.51836i	0.352017	+	0.323891i
$119$	1.17664	+	0.679334i	0.107863	+	0.0622745i
$120$		0			0
$121$	9.19563			0.835966
$122$	5.36932	−	1.68087i	0.486115	−	0.152179i
$123$		0			0
$124$	3.18808	+	1.50253i	0.286298	+	0.134932i
$125$	−12.0556			−1.07829
$126$		0			0
$127$	6.44881	+	11.1697i	0.572239	+	0.991148i	0.996336	+	0.0855306i	$0.0272585\pi$
$127$	6.44881	+	11.1697i	0.572239	+	0.991148i	−0.424096	+	0.905617i	$0.639408\pi$
$128$	−11.3088	+	0.331618i	−0.999570	+	0.0293112i
$129$		0			0
$130$	18.0630	+	4.04326i	1.58423	+	0.354617i
$131$	−9.18456	−	5.30271i	−0.802459	−	0.463300i	0.0418713	−	0.999123i	$-0.486668\pi$
$131$	−9.18456	−	5.30271i	−0.802459	−	0.463300i	−0.844330	+	0.535823i	$0.820001\pi$
$132$		0			0
$133$	1.13413	+	1.05321i	0.0983412	+	0.0913247i
$134$	−2.83856	+	0.888617i	−0.245215	+	0.0767648i
$135$		0			0
$136$	4.08026	+	10.0242i	0.349879	+	0.859565i
$137$	2.79679	+	4.84418i	0.238946	+	0.413866i	0.960412	−	0.278583i	$-0.0898649\pi$
$137$	2.79679	+	4.84418i	0.238946	+	0.413866i	−0.721466	+	0.692449i	$0.756532\pi$
$138$		0			0
$139$	−9.39468	+	5.42402i	−0.796846	+	0.460060i	−0.842367	−	0.538904i	$-0.818839\pi$
$139$	−9.39468	+	5.42402i	−0.796846	+	0.460060i	0.0455208	+	0.998963i	$0.485505\pi$
$140$	0.797488	+	1.14891i	0.0674001	+	0.0971003i
$141$		0			0
$142$	−16.2424	−	14.9446i	−1.36303	−	1.25412i
$143$	4.46369	+	7.73134i	0.373273	+	0.646527i
$144$		0			0
$145$			9.74388i			0.809185i
$146$	−0.906344	−	0.833928i	−0.0750096	−	0.0690164i
$147$		0			0
$148$	7.24405	−	15.3704i	0.595457	−	1.26344i
$149$	9.13332	−	15.8194i	0.748230	−	1.29597i	−0.200440	−	0.979706i	$-0.564237\pi$
$149$	9.13332	−	15.8194i	0.748230	−	1.29597i	0.948670	−	0.316267i	$-0.102430\pi$
$150$		0			0
$151$	−1.59192			−0.129549			−0.0647743	−	0.997900i	$-0.520633\pi$
$151$	−1.59192			−0.129549			−0.0647743	+	0.997900i	$0.520633\pi$
$152$	1.98539	+	12.1679i	0.161036	+	0.986949i
$153$		0			0
$154$	−0.147341	+	0.658236i	−0.0118730	+	0.0530422i
$155$	1.73523	−	3.00551i	0.139377	−	0.241408i
$156$		0			0
$157$	0.00391076	−	0.00677364i	0.000312113	−	0.000540595i	−0.865869	−	0.500270i	$-0.833234\pi$
$157$	0.00391076	−	0.00677364i	0.000312113	−	0.000540595i	0.866181	+	0.499730i	$0.166567\pi$
$158$	17.4259	+	16.0336i	1.38633	+	1.27556i
$159$		0			0
$160$	−0.599742	+	11.1244i	−0.0474138	+	0.879460i
$161$	0.498694	+	0.863764i	0.0393026	+	0.0680741i
$162$		0			0
$163$		−	17.5559i		−	1.37509i	−0.726143	−	0.687544i	$-0.758689\pi$
$163$		−	17.5559i		−	1.37509i	0.726143	−	0.687544i	$-0.241311\pi$
$164$	−7.41558	−	10.6833i	−0.579059	−	0.834225i
$165$		0			0
$166$	−11.6581	−	2.60957i	−0.904844	−	0.202542i
$167$	11.2272	+	19.4461i	0.868787	+	1.50478i	0.863238	+	0.504798i	$0.168433\pi$
$167$	11.2272	+	19.4461i	0.868787	+	1.50478i	0.00554910	+	0.999985i	$0.498234\pi$
$168$		0			0
$169$	15.5847	−	26.9936i	1.19883	−	2.07643i
$170$	10.1704	−	3.18386i	0.780034	−	0.244191i
$171$		0			0
$172$	5.45300	+	7.85590i	0.415788	+	0.599007i
$173$	6.61142	+	3.81710i	0.502657	+	0.290209i	0.729810	−	0.683650i	$-0.239609\pi$
$173$	6.61142	+	3.81710i	0.502657	+	0.290209i	−0.227153	+	0.973859i	$0.572942\pi$
$174$		0			0
$175$	−0.344870	+	0.199111i	−0.0260697	+	0.0150514i
$176$	−4.14413	+	3.41995i	−0.312376	+	0.257789i
$177$		0			0
$178$	0.896998	+	2.86534i	0.0672329	+	0.214766i
$179$	12.2234			0.913619			0.456809	−	0.889565i	$-0.348992\pi$
$179$	12.2234			0.913619			0.456809	+	0.889565i	$0.348992\pi$
$180$		0			0
$181$	−9.15093	+	5.28329i	−0.680183	+	0.392704i	−0.799924	−	0.600101i	$-0.795127\pi$
$181$	−9.15093	+	5.28329i	−0.680183	+	0.392704i	0.119741	+	0.992805i	$0.461794\pi$
$182$	3.18489	−	0.997036i	0.236080	−	0.0739052i
$183$		0			0
$184$	−1.08533	+	7.87043i	−0.0800119	+	0.580216i
$185$	−14.4902	−	8.36594i	−1.06534	−	0.615076i
$186$		0			0
$187$	4.45130	+	2.56996i	0.325511	+	0.187934i
$188$	15.7201	−	1.31055i	1.14651	−	0.0955819i
$189$		0			0
$190$	12.1027	−	0.952805i	0.878020	−	0.0691238i
$191$			15.0979i			1.09244i	0.837641	+	0.546222i	$0.183934\pi$
$191$			15.0979i			1.09244i	−0.837641	+	0.546222i	$0.816066\pi$
$192$		0			0
$193$	−19.1330	−	11.0464i	−1.37722	−	0.795141i	−0.385400	−	0.922750i	$-0.625936\pi$
$193$	−19.1330	−	11.0464i	−1.37722	−	0.795141i	−0.991825	+	0.127609i	$0.959270\pi$
$194$	−15.1634	+	16.4802i	−1.08867	+	1.18321i
$195$		0			0
$196$	−12.4359	−	5.86101i	−0.888279	−	0.418644i
$197$	−11.7097			−0.834278			−0.417139	−	0.908843i	$-0.636967\pi$
$197$	−11.7097			−0.834278			−0.417139	+	0.908843i	$0.636967\pi$
$198$		0			0
$199$	−0.153604	+	0.0886834i	−0.0108887	+	0.00628660i	−0.505434	−	0.862865i	$-0.668668\pi$
$199$	−0.153604	+	0.0886834i	−0.0108887	+	0.00628660i	0.494546	+	0.869152i	$0.335334\pi$
$200$	−3.14238	−	0.433335i	−0.222200	−	0.0306414i
$201$		0			0
$202$	−7.59570	+	2.37785i	−0.534432	+	0.167305i
$203$	0.878397	+	1.52143i	0.0616514	+	0.106783i
$204$		0			0
$205$	−11.0901	+	6.40285i	−0.774563	+	0.447194i
$206$	5.55291	−	24.8073i	0.386889	−	1.72841i
$207$		0			0
$208$	24.9056	+	9.29636i	1.72689	+	0.644586i
$209$	4.29046	+	3.98434i	0.296777	+	0.275603i
$210$		0			0
$211$	−6.51477	+	11.2839i	−0.448495	+	0.776817i	−0.998288	−	0.0584842i	$-0.981373\pi$
$211$	−6.51477	+	11.2839i	−0.448495	+	0.776817i	0.549793	+	0.835301i	$0.314707\pi$
$212$	−6.65423	+	0.554749i	−0.457014	+	0.0381003i
$213$		0			0
$214$	−3.21667	+	14.3703i	−0.219887	+	0.982334i
$215$	8.15501	−	4.70830i	0.556167	−	0.321103i
$216$		0			0
$217$		−	0.625715i		−	0.0424763i
$218$	−0.0572503	+	0.0622218i	−0.00387748	+	0.00421419i
$219$		0			0
$220$	3.01694	+	4.34637i	0.203402	+	0.293032i
$221$		−	25.4305i		−	1.71064i
$222$		0			0
$223$	2.15498	−	3.73253i	0.144308	−	0.249949i	−0.784807	−	0.619741i	$-0.787238\pi$
$223$	2.15498	−	3.73253i	0.144308	−	0.249949i	0.929115	+	0.369792i	$0.120571\pi$
$224$	0.909203	+	1.79105i	0.0607487	+	0.119670i
$225$		0			0
$226$	−0.376034	−	0.0841719i	−0.0250134	−	0.00559903i
$227$	−21.1194			−1.40175			−0.700873	−	0.713286i	$-0.747206\pi$
$227$	−21.1194			−1.40175			−0.700873	+	0.713286i	$0.747206\pi$
$228$		0			0
$229$	−4.17703			−0.276026			−0.138013	−	0.990430i	$-0.544072\pi$
$229$	−4.17703			−0.276026			−0.138013	+	0.990430i	$0.544072\pi$
$230$	7.63438	+	1.70889i	0.503396	+	0.112681i
$231$		0			0
$232$	−1.91170	+	13.8629i	−0.125509	+	0.910146i
$233$	−14.2716	+	24.7192i	−0.934964	+	1.61941i	−0.160267	+	0.987074i	$0.551236\pi$
$233$	−14.2716	+	24.7192i	−0.934964	+	1.61941i	−0.774697	+	0.632332i	$0.782098\pi$
$234$		0			0
$235$		−	15.5332i		−	1.01327i
$236$	6.03681	−	4.19032i	0.392963	−	0.272767i
$237$		0			0
$238$	1.30101	−	1.41398i	0.0843317	−	0.0916548i
$239$			0.705254i			0.0456191i	0.999740	+	0.0228095i	$0.00726113\pi$
$239$			0.705254i			0.0456191i	−0.999740	+	0.0228095i	$0.992739\pi$
$240$		0			0
$241$	−4.95189	+	2.85897i	−0.318979	+	0.184163i	−0.650937	−	0.759131i	$-0.725624\pi$
$241$	−4.95189	+	2.85897i	−0.318979	+	0.184163i	0.331958	+	0.943294i	$0.392291\pi$
$242$	2.84067	−	12.6905i	0.182605	−	0.815779i
$243$		0			0
$244$	−0.661044	−	7.92924i	−0.0423190	−	0.507617i
$245$	−6.76871	+	11.7237i	−0.432437	+	0.749003i
$246$		0			0
$247$	6.45822	−	28.2402i	0.410927	−	1.79688i
$248$	3.05844	−	3.93559i	0.194211	−	0.249910i
$249$		0			0
$250$	−3.72417	+	16.6375i	−0.235537	+	1.05225i
$251$	−14.2589	+	8.23237i	−0.900013	+	0.519623i	−0.877204	−	0.480117i	$-0.840594\pi$
$251$	−14.2589	+	8.23237i	−0.900013	+	0.519623i	−0.0228086	+	0.999740i	$0.507261\pi$
$252$		0			0
$253$	1.88659	+	3.26767i	0.118609	+	0.205436i
$254$	17.4070	−	5.44928i	1.09221	−	0.341918i
$255$		0			0
$256$	−3.03582	+	15.7094i	−0.189739	+	0.981835i
$257$	13.2604	−	7.65590i	0.827161	−	0.477562i	−0.0257185	−	0.999669i	$-0.508187\pi$
$257$	13.2604	−	7.65590i	0.827161	−	0.477562i	0.852880	+	0.522107i	$0.174854\pi$
$258$		0			0
$259$	−3.01671			−0.187449
$260$	11.1599	−	23.6791i	0.692108	−	1.46852i
$261$		0			0
$262$	−10.1553	+	11.0372i	−0.627398	+	0.681879i
$263$	12.0977	+	6.98462i	0.745977	+	0.430690i	0.824238	−	0.566243i	$-0.191604\pi$
$263$	12.0977	+	6.98462i	0.745977	+	0.430690i	−0.0782616	+	0.996933i	$0.524937\pi$
$264$		0			0
$265$			6.57511i			0.403905i
$266$	1.80384	−	1.23981i	0.110601	−	0.0760178i
$267$		0			0
$268$	0.349470	+	4.19190i	0.0213473	+	0.256061i
$269$	17.7199	+	10.2306i	1.08040	+	0.623770i	0.931004	−	0.365008i	$-0.118934\pi$
$269$	17.7199	+	10.2306i	1.08040	+	0.623770i	0.149396	+	0.988777i	$0.452267\pi$
$270$		0			0
$271$	7.40043	+	4.27264i	0.449544	+	0.259544i	0.707638	−	0.706576i	$-0.249761\pi$
$271$	7.40043	+	4.27264i	0.449544	+	0.259544i	−0.258094	+	0.966120i	$0.583094\pi$
$272$	15.0944	−	2.53440i	0.915234	−	0.153670i
$273$		0			0
$274$	7.54924	−	2.36330i	0.456066	−	0.142772i
$275$	−1.30466	+	0.753247i	−0.0786741	+	0.0454225i
$276$		0			0
$277$	−10.4223			−0.626213			−0.313107	−	0.949718i	$-0.601370\pi$
$277$	−10.4223			−0.626213			−0.313107	+	0.949718i	$0.601370\pi$
$278$	4.58333	+	14.6408i	0.274890	+	0.878097i
$279$		0			0
$280$	1.83192	−	0.745669i	0.109478	−	0.0445622i
$281$	−12.0512	+	6.95777i	−0.718915	+	0.415066i	−0.814353	−	0.580370i	$-0.802908\pi$
$281$	−12.0512	+	6.95777i	−0.718915	+	0.415066i	0.0954384	+	0.995435i	$0.469575\pi$
$282$		0			0
$283$	−13.1484	−	7.59120i	−0.781588	−	0.451250i	0.0554045	−	0.998464i	$-0.482355\pi$
$283$	−13.1484	−	7.59120i	−0.781588	−	0.451250i	−0.836993	+	0.547214i	$0.815688\pi$
$284$	−25.6420	+	17.7988i	−1.52157	+	1.05617i
$285$		0			0
$286$	12.0486	−	3.77184i	0.712450	−	0.223034i
$287$	−1.15442	+	1.99951i	−0.0681430	+	0.118027i
$288$		0			0
$289$	1.17923	+	2.04249i	0.0693665	+	0.120146i
$290$	13.4472	+	3.01003i	0.789644	+	0.176755i
$291$		0			0
$292$	−1.43086	+	0.993198i	−0.0837346	+	0.0581225i
$293$		−	15.3923i		−	0.899229i	−0.893223	−	0.449614i	$-0.851561\pi$
$293$		−	15.3923i		−	0.899229i	0.893223	−	0.449614i	$-0.148439\pi$
$294$		0			0
$295$	−3.61806	−	6.26666i	−0.210652	−	0.364859i
$296$	−18.9744	−	14.7454i	−1.10286	−	0.857059i
$297$		0			0
$298$	−19.0103	−	17.4914i	−1.10124	−	1.01325i
$299$	9.33416	−	16.1672i	0.539808	−	0.934976i
$300$		0			0
$301$	0.848893	−	1.47033i	0.0489294	−	0.0847482i
$302$	−0.491769	+	2.19695i	−0.0282981	+	0.126420i
$303$		0			0
$304$	17.4058	+	1.01890i	0.998291	+	0.0584378i
$305$	−7.83496			−0.448628
$306$		0			0
$307$	16.2895	−	28.2143i	0.929692	−	1.61027i	0.145856	−	0.989306i	$-0.453406\pi$
$307$	16.2895	−	28.2143i	0.929692	−	1.61027i	0.783836	−	0.620968i	$-0.213260\pi$
$308$	0.862891	+	0.406678i	0.0491678	+	0.0231727i
$309$		0			0
$310$	−3.61175	−	3.32317i	−0.205134	−	0.188744i
$311$		−	23.4521i		−	1.32984i	−0.746913	−	0.664922i	$-0.768465\pi$
$311$		−	23.4521i		−	1.32984i	0.746913	−	0.664922i	$-0.231535\pi$
$312$		0			0
$313$	0.505863	+	0.876180i	0.0285930	+	0.0495246i	0.879968	−	0.475033i	$-0.157564\pi$
$313$	0.505863	+	0.876180i	0.0285930	+	0.0495246i	−0.851375	+	0.524558i	$0.824231\pi$
$314$	−0.00813995	−	0.00748958i	−0.000459364	−	0.000422661i
$315$		0			0
$316$	27.5105	−	19.0958i	1.54759	−	1.07422i
$317$	−26.9491	+	15.5591i	−1.51361	+	0.873885i	−0.513740	+	0.857946i	$0.671741\pi$
$317$	−26.9491	+	15.5591i	−1.51361	+	0.873885i	−0.999873	+	0.0159394i	$0.994926\pi$
$318$		0			0
$319$	3.32302	+	5.75565i	0.186054	+	0.322254i
$320$	15.1671	+	4.26417i	0.847865	+	0.238375i
$321$		0			0
$322$	1.34610	−	0.421399i	0.0750153	−	0.0234837i
$323$	−4.90948	−	15.9401i	−0.273171	−	0.886930i
$324$		0			0
$325$	6.45500	+	3.72680i	0.358059	+	0.206725i
$326$	−24.2283	−	5.42330i	−1.34188	−	0.300369i
$327$		0			0
$328$	−17.0344	+	6.93372i	−0.940567	+	0.382851i
$329$	−1.40029	−	2.42538i	−0.0772007	−	0.133716i
$330$		0			0
$331$	−33.1040			−1.81956			−0.909781	−	0.415089i	$-0.863750\pi$
$331$	−33.1040			−1.81956			−0.909781	+	0.415089i	$0.863750\pi$
$332$	−7.20273	+	15.2828i	−0.395301	+	0.838750i
$333$		0			0
$334$	30.3050	−	9.48704i	1.65822	−	0.519108i
$335$	4.14206			0.226305
$336$		0			0
$337$	−26.3761	−	15.2282i	−1.43680	−	0.829535i	−0.439171	−	0.898404i	$-0.644728\pi$
$337$	−26.3761	−	15.2282i	−1.43680	−	0.829535i	−0.997626	+	0.0688690i	$0.978061\pi$
$338$	−32.4384	−	29.8466i	−1.76442	−	1.62344i
$339$		0			0
$340$	−1.25213	−	15.0193i	−0.0679063	−	0.814537i
$341$		−	2.36711i		−	0.128186i
$342$		0			0
$343$			4.92628i			0.265994i
$344$	12.5261	−	5.09868i	0.675365	−	0.274902i
$345$		0			0
$346$	7.31021	−	7.94500i	0.392999	−	0.427126i
$347$	0.161858	+	0.0934487i	0.00868898	+	0.00501659i	0.504338	−	0.863506i	$-0.331736\pi$
$347$	0.161858	+	0.0934487i	0.00868898	+	0.00501659i	−0.495649	+	0.868523i	$0.665070\pi$
$348$		0			0
$349$	5.01843			0.268631			0.134315	−	0.990939i	$-0.457116\pi$
$349$	5.01843			0.268631			0.134315	+	0.990939i	$0.457116\pi$
$350$	0.168250	+	0.537450i	0.00899332	+	0.0287279i
$351$		0			0
$352$	3.43956	+	6.77564i	0.183329	+	0.361143i
$353$	29.7351			1.58264			0.791319	−	0.611404i	$-0.209395\pi$
$353$	29.7351			1.58264			0.791319	+	0.611404i	$0.209395\pi$
$354$		0			0
$355$	15.3681	+	26.6183i	0.815654	+	1.41275i
$356$	4.23144	−	0.352767i	0.224266	−	0.0186966i
$357$		0			0
$358$	3.77599	−	16.8690i	0.199567	−	0.891556i
$359$	−13.1403	−	7.58655i	−0.693518	−	0.400403i	0.111411	−	0.993774i	$-0.464463\pi$
$359$	−13.1403	−	7.58655i	−0.693518	−	0.400403i	−0.804929	+	0.593372i	$0.797796\pi$
$360$		0			0
$361$	−1.40385	−	18.9481i	−0.0738866	−	0.997267i
$362$	4.46441	+	14.2609i	0.234644	+	0.749538i
$363$		0			0
$364$	−0.392109	−	4.70335i	−0.0205521	−	0.246523i
$365$	0.857559	+	1.48534i	0.0448867	+	0.0777461i
$366$		0			0
$367$	12.4274	−	7.17495i	0.648704	−	0.374530i	−0.139255	−	0.990257i	$-0.544471\pi$
$367$	12.4274	−	7.17495i	0.648704	−	0.374530i	0.787960	+	0.615727i	$0.211138\pi$
$368$	10.5264	+	3.92912i	0.548727	+	0.204820i
$369$		0			0
$370$	−16.0218	+	17.4130i	−0.832932	+	0.905261i
$371$	0.592737	+	1.02665i	0.0307734	+	0.0533010i
$372$		0			0
$373$			1.28645i			0.0666099i	0.999445	+	0.0333050i	$0.0106033\pi$
$373$			1.28645i			0.0666099i	−0.999445	+	0.0333050i	$0.989397\pi$
$374$	4.92178	−	5.34917i	0.254499	−	0.276599i
$375$		0			0
$376$	3.04753	−	22.0996i	0.157165	−	1.13970i
$377$	16.4411	−	28.4769i	0.846762	−	1.46663i
$378$		0			0
$379$	−1.85939			−0.0955106			−0.0477553	−	0.998859i	$-0.515207\pi$
$379$	−1.85939			−0.0955106			−0.0477553	+	0.998859i	$0.515207\pi$
$380$	2.42377	−	16.9968i	0.124337	−	0.871916i
$381$		0			0
$382$	20.8360	+	4.66396i	1.06606	+	0.238629i
$383$	14.5822	−	25.2572i	0.745118	−	1.29058i	−0.205022	−	0.978757i	$-0.565727\pi$
$383$	14.5822	−	25.2572i	0.745118	−	1.29058i	0.950140	−	0.311824i	$-0.100940\pi$
$384$		0			0
$385$	0.469661	−	0.813476i	0.0239361	−	0.0414586i
$386$	−21.1553	+	22.9923i	−1.07677	+	1.17028i
$387$		0			0
$388$	18.0594	+	26.0174i	0.916829	+	1.32083i
$389$	2.67844	+	4.63919i	0.135802	+	0.235216i	0.925904	−	0.377760i	$-0.123305\pi$
$389$	2.67844	+	4.63919i	0.135802	+	0.235216i	−0.790101	+	0.612976i	$0.789972\pi$
$390$		0			0
$391$		−	10.7482i		−	0.543562i
$392$	−11.9302	+	15.3518i	−0.602566	+	0.775381i
$393$		0			0
$394$	−3.61729	+	16.1601i	−0.182236	+	0.814132i
$395$	−16.4879	−	28.5580i	−0.829598	−	1.43691i
$396$		0			0
$397$	13.0057	−	22.5266i	0.652738	−	1.13058i	−0.329718	−	0.944080i	$-0.606954\pi$
$397$	13.0057	−	22.5266i	0.652738	−	1.13058i	0.982456	−	0.186496i	$-0.0597131\pi$
$398$	0.0749380	+	0.239379i	0.00375630	+	0.0119990i
$399$		0			0
$400$	−1.56876	+	4.20282i	−0.0784379	+	0.210141i
$401$	−19.4940	−	11.2548i	−0.973482	−	0.562040i	−0.0731860	−	0.997318i	$-0.523317\pi$
$401$	−19.4940	−	11.2548i	−0.973482	−	0.562040i	−0.900296	+	0.435278i	$0.856650\pi$
$402$		0			0
$403$	−10.1426	+	5.85582i	−0.505237	+	0.291699i
$404$	0.935146	+	11.2171i	0.0465253	+	0.558071i
$405$		0			0
$406$	2.37102	−	0.742250i	0.117672	−	0.0368372i
$407$	−11.4124			−0.565691
$408$		0			0
$409$	−17.7553	+	10.2510i	−0.877945	+	0.506882i	−0.869980	−	0.493087i	$-0.835869\pi$
$409$	−17.7553	+	10.2510i	−0.877945	+	0.506882i	−0.00796465	+	0.999968i	$0.502535\pi$
$410$	5.41044	+	17.2829i	0.267202	+	0.853542i
$411$		0			0
$412$	−32.5203	−	15.3267i	−1.60216	−	0.755093i
$413$	−1.12986	−	0.652326i	−0.0555969	−	0.0320989i
$414$		0			0
$415$	14.4076	+	8.31821i	0.707240	+	0.408325i
$416$	20.5233	−	31.4995i	1.00624	−	1.54439i
$417$		0			0
$418$	6.82403	−	4.69028i	0.333774	−	0.229409i
$419$		−	12.8954i		−	0.629984i	−0.949094	−	0.314992i	$-0.897998\pi$
$419$		−	12.8954i		−	0.629984i	0.949094	−	0.314992i	$-0.102002\pi$
$420$		0			0
$421$	−16.5038	−	9.52845i	−0.804344	−	0.464388i	0.0406439	−	0.999174i	$-0.487059\pi$
$421$	−16.5038	−	9.52845i	−0.804344	−	0.464388i	−0.844988	+	0.534785i	$0.820392\pi$
$422$	13.5600	+	12.4766i	0.660090	+	0.607350i
$423$		0			0
$424$	−1.29000	+	9.35462i	−0.0626481	+	0.454300i
$425$	4.29139			0.208163
$426$		0			0
$427$	−1.22337	+	0.706310i	−0.0592028	+	0.0341808i
$428$	18.8382	+	8.87842i	0.910581	+	0.429154i
$429$		0			0
$430$	−3.97854	−	12.7089i	−0.191862	−	0.612877i
$431$	9.21153	+	15.9548i	0.443704	+	0.768517i	0.997961	−	0.0638282i	$-0.0203310\pi$
$431$	9.21153	+	15.9548i	0.443704	+	0.768517i	−0.554257	+	0.832345i	$0.686998\pi$
$432$		0			0
$433$	−7.50721	+	4.33429i	−0.360774	+	0.208293i	−0.669420	−	0.742884i	$-0.733457\pi$
$433$	−7.50721	+	4.33429i	−0.360774	+	0.208293i	0.308646	+	0.951177i	$0.400124\pi$
$434$	−0.863525	−	0.193293i	−0.0414505	−	0.00927835i
$435$		0			0
$436$	0.0681844	+	0.0982302i	0.00326544	+	0.00470438i
$437$	2.72958	−	11.9358i	0.130573	−	0.570967i
$438$		0			0
$439$	−15.6506	+	27.1077i	−0.746963	+	1.29378i	0.202309	+	0.979322i	$0.435156\pi$
$439$	−15.6506	+	27.1077i	−0.746963	+	1.29378i	−0.949272	+	0.314456i	$0.898178\pi$
$440$	6.93025	−	2.82091i	0.330387	−	0.134481i
$441$		0			0
$442$	−35.0956	−	7.85586i	−1.66933	−	0.373665i
$443$	2.99719	−	1.73043i	0.142401	−	0.0822152i	−0.427107	−	0.904201i	$-0.640467\pi$
$443$	2.99719	−	1.73043i	0.142401	−	0.0822152i	0.569508	+	0.821986i	$0.307134\pi$
$444$		0			0
$445$		−	4.18113i		−	0.198204i
$446$	−4.48542	−	4.12704i	−0.212391	−	0.195421i
$447$		0			0
$448$	2.75263	−	0.701474i	0.130049	−	0.0331415i
$449$		−	17.3513i		−	0.818858i	−0.912342	−	0.409429i	$-0.865728\pi$
$449$		−	17.3513i		−	0.818858i	0.912342	−	0.409429i	$-0.134272\pi$
$450$		0			0
$451$	−4.36722	+	7.56424i	−0.205644	+	0.356186i
$452$	−0.232325	+	0.492948i	−0.0109276	+	0.0231863i
$453$		0			0
$454$	−6.52412	+	29.1461i	−0.306192	+	1.36790i
$455$	−4.64743			−0.217875
$456$		0			0
$457$	−2.05680			−0.0962131			−0.0481065	−	0.998842i	$-0.515319\pi$
$457$	−2.05680			−0.0962131			−0.0481065	+	0.998842i	$0.515319\pi$
$458$	−1.29035	+	5.76456i	−0.0602940	+	0.269360i
$459$		0			0
$460$	4.71675	−	10.0080i	0.219920	−	0.466626i
$461$	−9.26074	+	16.0401i	−0.431316	+	0.747061i	−0.996987	−	0.0775700i	$-0.975284\pi$
$461$	−9.26074	+	16.0401i	−0.431316	+	0.747061i	0.565671	+	0.824631i	$0.308617\pi$
$462$		0			0
$463$		−	14.7319i		−	0.684649i	−0.939582	−	0.342325i	$-0.888786\pi$
$463$		−	14.7319i		−	0.684649i	0.939582	−	0.342325i	$-0.111214\pi$
$464$	18.5412	+	6.92074i	0.860751	+	0.321287i
$465$		0			0
$466$	29.7053	+	27.3318i	1.37607	+	1.26612i
$467$			28.5370i			1.32054i	0.751030	+	0.660268i	$0.229557\pi$
$467$			28.5370i			1.32054i	−0.751030	+	0.660268i	$0.770443\pi$
$468$		0			0
$469$	0.646749	−	0.373401i	0.0298641	−	0.0172421i
$470$	−21.4368	−	4.79844i	−0.988804	−	0.221335i
$471$		0			0
$472$	−3.91804	−	9.62563i	−0.180343	−	0.443056i
$473$	3.21141	−	5.56232i	0.147661	−	0.255756i
$474$		0			0
$475$	4.76554	+	1.08982i	0.218658	+	0.0500045i
$476$	−1.54948	−	2.23227i	−0.0710204	−	0.102316i
$477$		0			0
$478$	0.973294	+	0.217864i	0.0445174	+	0.00996485i
$479$	−2.12263	+	1.22550i	−0.0969857	+	0.0559947i	−0.547708	−	0.836669i	$-0.684500\pi$
$479$	−2.12263	+	1.22550i	−0.0969857	+	0.0559947i	0.450723	+	0.892664i	$0.351166\pi$
$480$		0			0
$481$	28.2322	+	48.8996i	1.28728	+	2.22963i
$482$	2.41585	+	7.71709i	0.110039	+	0.351504i
$483$		0			0
$484$	−16.6362	−	7.84060i	−0.756191	−	0.356391i
$485$	27.0080	−	15.5931i	1.22637	−	0.708046i
$486$		0			0
$487$	8.18323			0.370817			0.185409	−	0.982661i	$-0.440639\pi$
$487$	8.18323			0.370817			0.185409	+	0.982661i	$0.440639\pi$
$488$	−11.1470	−	1.53718i	−0.504603	−	0.0695849i
$489$		0			0
$490$	14.0885	+	12.9629i	0.636455	+	0.585603i
$491$	−0.994013	−	0.573893i	−0.0448592	−	0.0258994i	0.477403	−	0.878685i	$-0.341578\pi$
$491$	−0.994013	−	0.573893i	−0.0448592	−	0.0258994i	−0.522262	+	0.852785i	$0.674912\pi$
$492$		0			0
$493$		−	18.9319i		−	0.852649i
$494$	−36.9783	−	17.6366i	−1.66373	−	0.793508i
$495$		0			0
$496$	−4.48656	−	5.43660i	−0.201453	−	0.244110i
$497$	4.79921	+	2.77082i	0.215274	+	0.124288i
$498$		0			0
$499$	22.8813	+	13.2105i	1.02431	+	0.591385i	0.915349	−	0.402662i	$-0.131915\pi$
$499$	22.8813	+	13.2105i	1.02431	+	0.591385i	0.108959	+	0.994046i	$0.465248\pi$
$500$	21.8104	+	10.2792i	0.975389	+	0.459698i
$501$		0			0
$502$	6.95640	+	22.2213i	0.310479	+	0.991783i
$503$	33.7105	−	19.4628i	1.50308	−	0.867802i	0.503084	−	0.864238i	$-0.332199\pi$
$503$	33.7105	−	19.4628i	1.50308	−	0.867802i	0.999994	−	0.00356422i	$-0.00113453\pi$
$504$		0			0
$505$	11.0837			0.493219
$506$	5.09238	−	1.59418i	0.226384	−	0.0708698i
$507$		0			0
$508$	−2.14306	−	25.7061i	−0.0950830	−	1.14052i
$509$	−27.6426	+	15.9594i	−1.22524	+	0.707390i	−0.966029	−	0.258432i	$-0.916794\pi$
$509$	−27.6426	+	15.9594i	−1.22524	+	0.707390i	−0.259206	+	0.965822i	$0.583461\pi$
$510$		0			0
$511$	0.267802	+	0.154616i	0.0118469	+	0.00683979i
$512$	20.7421	+	9.04248i	0.916679	+	0.399625i
$513$		0			0
$514$	−6.46927	−	20.6652i	−0.285347	−	0.911503i
$515$	−17.7004	+	30.6579i	−0.779971	+	1.35095i
$516$		0			0
$517$	−5.29739	−	9.17535i	−0.232979	−	0.403531i
$518$	−0.931908	+	4.16325i	−0.0409457	+	0.182923i
$519$		0			0
$520$	−29.2312	−	22.7162i	−1.28187	−	0.996171i
$521$			38.3269i			1.67913i	0.543259	+	0.839565i	$0.317190\pi$
$521$			38.3269i			1.67913i	−0.543259	+	0.839565i	$0.682810\pi$
$522$		0			0
$523$	12.2460	+	21.2106i	0.535478	+	0.927475i	0.999140	+	0.0414632i	$0.0132019\pi$
$523$	12.2460	+	21.2106i	0.535478	+	0.927475i	−0.463662	+	0.886012i	$0.653465\pi$
$524$	12.0949	+	17.4245i	0.528366	+	0.761194i
$525$		0			0
$526$	13.3764	−	14.5379i	0.583238	−	0.633884i
$527$	−3.37147	+	5.83956i	−0.146864	+	0.254375i
$528$		0			0
$529$	−7.55490	+	13.0855i	−0.328474	+	0.568933i
$530$	9.07405	+	2.03115i	0.394152	+	0.0882275i
$531$		0			0
$532$	−1.15378	−	2.87241i	−0.0500229	−	0.124535i
$533$	43.2149			1.87184
$534$		0			0
$535$	10.2534	−	17.7594i	0.443294	−	0.767807i
$536$	5.89304	+	0.812652i	0.254541	+	0.0351012i
$537$		0			0
$538$	19.5928	−	21.2942i	0.844705	−	0.918056i
$539$			9.23352i			0.397716i
$540$		0			0
$541$	15.0480	+	26.0639i	0.646964	+	1.12058i	0.983844	+	0.179027i	$0.0572951\pi$
$541$	15.0480	+	26.0639i	0.646964	+	1.12058i	−0.336880	+	0.941548i	$0.609372\pi$
$542$	8.18261	−	8.89317i	0.351473	−	0.381994i
$543$		0			0
$544$	1.16527	−	21.6141i	0.0499606	−	0.926699i
$545$	0.101970	−	0.0588726i	0.00436793	−	0.00252183i
$546$		0			0
$547$	−1.94265	−	3.36477i	−0.0830619	−	0.143867i	0.821502	−	0.570206i	$-0.193137\pi$
$547$	−1.94265	−	3.36477i	−0.0830619	−	0.143867i	−0.904564	+	0.426339i	$0.859803\pi$
$548$	−0.929426	−	11.1485i	−0.0397031	−	0.476239i
$549$		0			0
$550$	0.636498	+	2.03320i	0.0271403	+	0.0866961i
$551$	4.80786	−	21.0236i	0.204822	−	0.895637i
$552$		0			0
$553$	−5.14892	−	2.97273i	−0.218954	−	0.126413i
$554$	−3.21960	+	14.3834i	−0.136788	+	0.611091i
$555$		0			0
$556$	21.6211	−	1.80251i	0.916938	−	0.0764433i
$557$	−9.25647	−	16.0327i	−0.392209	−	0.679326i	0.600531	−	0.799601i	$-0.294956\pi$
$557$	−9.25647	−	16.0327i	−0.392209	−	0.679326i	−0.992741	+	0.120275i	$0.961622\pi$
$558$		0			0
$559$	−31.7778			−1.34406
$560$	−0.463162	−	2.75851i	−0.0195722	−	0.116568i
$561$		0			0
$562$	5.87935	+	18.7808i	0.248005	+	0.792219i
$563$	37.3030			1.57213			0.786067	−	0.618141i	$-0.212114\pi$
$563$	37.3030			1.57213			0.786067	+	0.618141i	$0.212114\pi$
$564$		0			0
$565$	0.464718	+	0.268305i	0.0195508	+	0.0112877i
$566$	−14.5381	+	15.8005i	−0.611080	+	0.664145i
$567$		0			0
$568$	16.6423	+	40.8859i	0.698295	+	1.71553i
$569$			35.1981i			1.47558i	0.675030	+	0.737791i	$0.264131\pi$
$569$			35.1981i			1.47558i	−0.675030	+	0.737791i	$0.735869\pi$
$570$		0			0
$571$			22.9289i			0.959544i	0.877393	+	0.479772i	$0.159281\pi$
$571$			22.9289i			0.959544i	−0.877393	+	0.479772i	$0.840719\pi$
$572$	−1.48337	−	17.7930i	−0.0620228	−	0.743964i
$573$		0			0
$574$	2.40283	+	2.21084i	0.100292	+	0.0922788i
$575$	2.72822	+	1.57514i	0.113775	+	0.0656878i
$576$		0			0
$577$	34.9147			1.45352			0.726759	−	0.686892i	$-0.241026\pi$
$577$	34.9147			1.45352			0.726759	+	0.686892i	$0.241026\pi$
$578$	3.18304	−	0.996456i	0.132397	−	0.0414471i
$579$		0			0
$580$	8.30806	−	17.6281i	0.344974	−	0.731965i
$581$	2.99950			0.124440
$582$		0			0
$583$	2.24236	+	3.88387i	0.0928689	+	0.160854i
$584$	0.928662	+	2.28149i	0.0384283	+	0.0944085i
$585$		0			0
$586$	−21.2424	−	4.75492i	−0.877514	−	0.196424i
$587$	−8.39604	−	4.84746i	−0.346542	−	0.200076i	0.316619	−	0.948553i	$-0.397452\pi$
$587$	−8.39604	−	4.84746i	−0.346542	−	0.200076i	−0.663161	+	0.748477i	$0.730786\pi$
$588$		0			0
$589$	−5.22697	+	5.62856i	−0.215374	+	0.231921i
$590$	−9.76606	+	3.05728i	−0.402062	+	0.125866i
$591$		0			0
$592$	−26.2110	+	21.6307i	−1.07727	+	0.889017i
$593$	5.45069	+	9.44088i	0.223833	+	0.387690i	0.955969	−	0.293469i	$-0.0948096\pi$
$593$	5.45069	+	9.44088i	0.223833	+	0.387690i	−0.732136	+	0.681159i	$0.761476\pi$
$594$		0			0
$595$	−2.31726	+	1.33787i	−0.0949985	+	0.0548474i
$596$	−30.0118	+	20.8320i	−1.22933	+	0.853313i
$597$		0			0
$598$	−19.4283	−	17.8760i	−0.794484	−	0.731005i
$599$	21.1928	+	36.7070i	0.865915	+	1.49981i	0.866136	+	0.499808i	$0.166596\pi$
$599$	21.1928	+	36.7070i	0.865915	+	1.49981i	−0.000221764		1.00000i	$0.500071\pi$
$600$		0			0
$601$			5.82413i			0.237571i	0.992920	+	0.118786i	$0.0379001\pi$
$601$			5.82413i			0.237571i	−0.992920	+	0.118786i	$0.962100\pi$
$602$	−1.76691	−	1.62573i	−0.0720137	−	0.0662599i
$603$		0			0
$604$	2.88001	+	1.35734i	0.117186	+	0.0552295i
$605$	−9.05488	+	15.6835i	−0.368133	+	0.637625i
$606$		0			0
$607$	−32.3172			−1.31172			−0.655858	−	0.754884i	$-0.727693\pi$
$607$	−32.3172			−1.31172			−0.655858	+	0.754884i	$0.727693\pi$
$608$	6.78306	−	23.7063i	0.275089	−	0.961419i
$609$		0			0
$610$	−2.42034	+	10.8127i	−0.0979966	+	0.437794i
$611$	−26.2096	+	45.3964i	−1.06033	+	1.83654i
$612$		0			0
$613$	−7.57118	+	13.1137i	−0.305797	+	0.529656i	−0.977438	−	0.211220i	$-0.932256\pi$
$613$	−7.57118	+	13.1137i	−0.305797	+	0.529656i	0.671641	+	0.740876i	$0.265590\pi$
$614$	−33.9054	−	31.1964i	−1.36831	−	1.25898i
$615$		0			0
$616$	0.827802	−	1.06521i	0.0333531	−	0.0429187i
$617$	−17.9959	−	31.1699i	−0.724489	−	1.25485i	−0.959184	−	0.282782i	$-0.908743\pi$
$617$	−17.9959	−	31.1699i	−0.724489	−	1.25485i	0.234696	−	0.972069i	$-0.424591\pi$
$618$		0			0
$619$		−	18.3315i		−	0.736806i	−0.929666	−	0.368403i	$-0.879905\pi$
$619$		−	18.3315i		−	0.736806i	0.929666	−	0.368403i	$-0.120095\pi$
$620$	−5.70191	+	3.95786i	−0.228994	+	0.158951i
$621$		0			0
$622$	−32.3653	−	7.24470i	−1.29773	−	0.290486i
$623$	−0.376923	−	0.652850i	−0.0151011	−	0.0261559i
$624$		0			0
$625$	9.06732	−	15.7051i	0.362693	−	0.628202i
$626$	1.36545	−	0.427457i	0.0545744	−	0.0170846i
$627$		0			0
$628$	−0.0128506	+	0.00891999i	−0.000512796	+	0.000355946i
$629$	28.1538	+	16.2546i	1.12257	+	0.648114i
$630$		0			0
$631$	2.13172	−	1.23075i	0.0848624	−	0.0489953i	−0.456968	−	0.889483i	$-0.651065\pi$
$631$	2.13172	−	1.23075i	0.0848624	−	0.0489953i	0.541831	+	0.840488i	$0.317731\pi$
$632$	−17.8550	−	43.8652i	−0.710234	−	1.74486i
$633$		0			0
$634$	13.1475	+	41.9979i	0.522154	+	1.66795i
$635$	−25.4004			−1.00798
$636$		0			0
$637$	39.5637	−	22.8421i	1.56757	−	0.905036i
$638$	8.96968	−	2.80797i	0.355113	−	0.111169i
$639$		0			0
$640$	10.5702	−	19.6142i	0.417822	−	0.775320i
$641$	−36.7475	−	21.2162i	−1.45144	−	0.837988i	−0.452875	−	0.891574i	$-0.649601\pi$
$641$	−36.7475	−	21.2162i	−1.45144	−	0.837988i	−0.998563	+	0.0535862i	$0.982935\pi$
$642$		0			0
$643$	−18.1691	−	10.4899i	−0.716519	−	0.413682i	0.0969511	−	0.995289i	$-0.469091\pi$
$643$	−18.1691	−	10.4899i	−0.716519	−	0.413682i	−0.813470	+	0.581607i	$0.802424\pi$
$644$	−0.165726	−	1.98788i	−0.00653050	−	0.0783335i
$645$		0			0
$646$	−23.5149	+	1.85126i	−0.925182	+	0.0728367i
$647$			41.3586i			1.62597i	0.582282	+	0.812987i	$0.302160\pi$
$647$			41.3586i			1.62597i	−0.582282	+	0.812987i	$0.697840\pi$
$648$		0			0
$649$	−4.27433	−	2.46779i	−0.167782	−	0.0968691i
$650$	7.13726	−	7.75704i	0.279946	−	0.304256i
$651$		0			0
$652$	−14.9690	+	31.7612i	−0.586230	+	1.24386i
$653$	−21.1062			−0.825950			−0.412975	−	0.910742i	$-0.635510\pi$
$653$	−21.1062			−0.825950			−0.412975	+	0.910742i	$0.635510\pi$
$654$		0			0
$655$	18.0880	−	10.4431i	0.706755	−	0.408045i
$656$	4.30678	+	25.6504i	0.168152	+	1.00148i
$657$		0			0
$658$	−3.77975	+	1.18326i	−0.147350	+	0.0461281i
$659$	−10.9192	−	18.9126i	−0.425351	−	0.736730i	0.571102	−	0.820879i	$-0.306516\pi$
$659$	−10.9192	−	18.9126i	−0.425351	−	0.736730i	−0.996453	+	0.0841494i	$0.973183\pi$
$660$		0			0
$661$	−7.76653	+	4.48401i	−0.302083	+	0.174408i	−0.643378	−	0.765548i	$-0.722468\pi$
$661$	−7.76653	+	4.48401i	−0.302083	+	0.174408i	0.341295	+	0.939956i	$0.389134\pi$
$662$	−10.2263	+	45.6856i	−0.397458	+	1.77562i
$663$		0			0
$664$	18.8661	+	14.6613i	0.732148	+	0.568968i
$665$	−2.91305	+	0.897209i	−0.112963	+	0.0347923i
$666$		0			0
$667$	6.94888	−	12.0358i	0.269062	−	0.466028i
$668$	−3.73101	−	44.7535i	−0.144357	−	1.73157i
$669$		0			0
$670$	1.27955	−	5.71630i	0.0494331	−	0.220840i
$671$	−4.62806	+	2.67201i	−0.178664	+	0.103152i
$672$		0			0
$673$			3.65151i			0.140756i	0.997520	+	0.0703778i	$0.0224205\pi$
$673$			3.65151i			0.140756i	−0.997520	+	0.0703778i	$0.977580\pi$
$674$	−29.1639	+	31.6964i	−1.12335	+	1.22090i
$675$		0			0
$676$	−51.2109	+	35.5470i	−1.96965	+	1.36719i
$677$			12.3206i			0.473520i	0.971568	+	0.236760i	$0.0760855\pi$
$677$			12.3206i			0.473520i	−0.971568	+	0.236760i	$0.923915\pi$
$678$		0			0
$679$	2.81139	−	4.86947i	0.107891	−	0.186873i
$680$	−21.1144	−	2.91168i	−0.809701	−	0.111658i
$681$		0			0
$682$	−3.26676	−	0.731238i	−0.125091	−	0.0280005i
$683$	−34.1567			−1.30697			−0.653486	−	0.756939i	$-0.726694\pi$
$683$	−34.1567			−1.30697			−0.653486	+	0.756939i	$0.726694\pi$
$684$		0			0
$685$	−11.0159			−0.420896
$686$	6.79858	+	1.52180i	0.259571	+	0.0581028i
$687$		0			0
$688$	−3.16697	−	18.8619i	−0.120740	−	0.719104i
$689$	11.0944	−	19.2160i	0.422662	−	0.732072i
$690$		0			0
$691$			10.5938i			0.403008i	0.979488	+	0.201504i	$0.0645830\pi$
$691$			10.5938i			0.403008i	−0.979488	+	0.201504i	$0.935417\pi$
$692$	−8.70636	−	12.5429i	−0.330966	−	0.476808i
$693$		0			0
$694$	0.178965	−	0.194506i	0.00679343	−	0.00738335i
$695$		−	21.3640i		−	0.810383i
$696$		0			0
$697$	21.5475	−	12.4404i	0.816168	−	0.471215i
$698$	1.55027	−	6.92575i	0.0586786	−	0.262144i
$699$		0			0
$700$	0.793690	−	0.0661683i	0.0299987	−	0.00250093i
$701$	−5.91254	+	10.2408i	−0.223314	+	0.386791i	−0.955812	−	0.293978i	$-0.905021\pi$
$701$	−5.91254	+	10.2408i	−0.223314	+	0.386791i	0.732498	+	0.680769i	$0.238354\pi$
$702$		0			0
$703$	27.1365	+	25.2004i	1.02347	+	0.950451i
$704$	10.4133	−	2.65371i	0.392467	−	0.100016i
$705$		0			0
$706$	9.18561	−	41.0362i	0.345705	−	1.54442i
$707$	1.73063	−	0.999182i	0.0650872	−	0.0375781i
$708$		0			0
$709$	−3.70068	−	6.40977i	−0.138982	−	0.240724i	0.788130	−	0.615509i	$-0.211050\pi$
$709$	−3.70068	−	6.40977i	−0.138982	−	0.240724i	−0.927112	+	0.374786i	$0.877716\pi$
$710$	41.4824	−	12.9861i	1.55681	−	0.487360i
$711$		0			0
$712$	0.820317	−	5.94863i	0.0307427	−	0.222934i
$713$	−4.28678	+	2.47497i	−0.160541	+	0.0926884i
$714$		0			0
$715$	−17.5815			−0.657510
$716$	−22.1139	−	10.4222i	−0.826433	−	0.389496i
$717$		0			0
$718$	−14.5291	+	15.7908i	−0.542223	+	0.589308i
$719$	28.7145	+	16.5783i	1.07087	+	0.618268i	0.928419	−	0.371534i	$-0.121168\pi$
$719$	28.7145	+	16.5783i	1.07087	+	0.618268i	0.142452	+	0.989802i	$0.454501\pi$
$720$		0			0
$721$			6.38265i			0.237702i
$722$	−26.5832	−	3.91595i	−0.989323	−	0.145737i
$723$		0			0
$724$	21.0601	−	1.75574i	0.782692	−	0.0652515i
$725$	4.80547	+	2.77444i	0.178471	+	0.103040i
$726$		0			0
$727$	30.3035	+	17.4957i	1.12390	+	0.648881i	0.942393	−	0.334509i	$-0.108570\pi$
$727$	30.3035	+	17.4957i	1.12390	+	0.648881i	0.181503	+	0.983390i	$0.441904\pi$
$728$	−6.61204	−	0.911802i	−0.245059	−	0.0337936i
$729$		0			0
$730$	2.31477	−	0.724642i	0.0856735	−	0.0268202i
$731$	−15.8448	+	9.14800i	−0.586041	+	0.338351i
$732$		0			0
$733$	4.06091			0.149993			0.0749966	−	0.997184i	$-0.476105\pi$
$733$	4.06091			0.149993			0.0749966	+	0.997184i	$0.476105\pi$
$734$	−6.06287	−	19.3670i	−0.223785	−	0.714850i
$735$		0			0
$736$	8.67420	−	13.3133i	0.319735	−	0.490736i
$737$	2.44669	−	1.41260i	0.0901249	−	0.0520336i
$738$		0			0
$739$	−37.7065	−	21.7699i	−1.38706	−	0.800817i	−0.394074	−	0.919079i	$-0.628935\pi$
$739$	−37.7065	−	21.7699i	−1.38706	−	0.800817i	−0.992982	+	0.118261i	$0.962268\pi$
$740$	19.0817	+	27.4902i	0.701458	+	1.01056i
$741$		0			0
$742$	1.59995	−	0.500866i	0.0587359	−	0.0183874i
$743$	1.52131	−	2.63499i	0.0558115	−	0.0966683i	−0.836770	−	0.547555i	$-0.815559\pi$
$743$	1.52131	−	2.63499i	0.0558115	−	0.0966683i	0.892581	+	0.450887i	$0.148892\pi$
$744$		0			0
$745$	17.9870	+	31.1545i	0.658994	+	1.14141i
$746$	1.77538	+	0.397405i	0.0650014	+	0.0145500i
$747$		0			0
$748$	−5.86178	−	8.44480i	−0.214328	−	0.308772i
$749$		−	3.69733i		−	0.135097i
$750$		0			0
$751$	−13.9706	−	24.1977i	−0.509794	−	0.882988i	−0.999936	−	0.0113458i	$-0.996388\pi$
$751$	−13.9706	−	24.1977i	−0.509794	−	0.882988i	0.490142	−	0.871643i	$-0.336945\pi$
$752$	−29.5573	−	11.0327i	−1.07785	−	0.402320i
$753$		0			0
$754$	−34.2209	−	31.4867i	−1.24625	−	1.14668i
$755$	1.56755	−	2.71508i	0.0570492	−	0.0988120i
$756$		0			0
$757$	6.64342	−	11.5067i	0.241459	−	0.418219i	−0.719671	−	0.694315i	$-0.755707\pi$
$757$	6.64342	−	11.5067i	0.241459	−	0.418219i	0.961130	+	0.276096i	$0.0890407\pi$
$758$	−0.574395	+	2.56608i	−0.0208630	+	0.0932041i
$759$		0			0
$760$	−22.7079	−	8.59552i	−0.823701	−	0.311792i
$761$	−0.108264			−0.00392458			−0.00196229	−	0.999998i	$-0.500625\pi$
$761$	−0.108264			−0.00392458			−0.00196229	+	0.999998i	$0.500625\pi$
$762$		0			0
$763$	0.0106146	−	0.0183850i	0.000384273	−	0.000665581i
$764$	12.8731	−	27.3142i	0.465733	−	0.988193i
$765$		0			0
$766$	−30.3518	−	27.9267i	−1.09665	−	1.00903i
$767$			24.4194i			0.881735i
$768$		0			0
$769$	16.3034	+	28.2383i	0.587916	+	1.01830i	0.994505	+	0.104689i	$0.0333847\pi$
$769$	16.3034	+	28.2383i	0.587916	+	1.01830i	−0.406589	+	0.913611i	$0.633282\pi$
$770$	−0.977562	−	0.899456i	−0.0352289	−	0.0324142i
$771$		0			0
$772$	25.1957	+	36.2983i	0.906811	+	1.30640i
$773$	−23.4972	+	13.5661i	−0.845135	+	0.487939i	−0.859006	−	0.511965i	$-0.828918\pi$
$773$	−23.4972	+	13.5661i	−0.845135	+	0.487939i	0.0138713	+	0.999904i	$0.495584\pi$
$774$		0			0
$775$	−0.988168	−	1.71156i	−0.0354960	−	0.0614809i
$776$	41.4845	−	16.8860i	1.48921	−	0.606170i
$777$		0			0
$778$	7.22979	−	2.26329i	0.259200	−	0.0811431i
$779$	27.0875	−	8.34285i	0.970511	−	0.298914i
$780$		0			0
$781$	18.1557	+	10.4822i	0.649661	+	0.375082i
$782$	−14.8332	−	3.32030i	−0.530436	−	0.118734i
$783$		0			0
$784$	17.5010	+	21.2068i	0.625035	+	0.757386i
$785$	0.00770181	+	0.0133399i	0.000274889	+	0.000476122i
$786$		0			0
$787$	21.3735			0.761882			0.380941	−	0.924599i	$-0.375600\pi$
$787$	21.3735			0.761882			0.380941	+	0.924599i	$0.375600\pi$
$788$	21.1844	+	9.98417i	0.754664	+	0.355671i
$789$		0			0
$790$	−44.5051	+	13.9324i	−1.58342	+	0.495692i
$791$	0.0967494			0.00344001
$792$		0			0
$793$	22.8980	+	13.2202i	0.813131	+	0.469461i
$794$	−27.0704	−	24.9075i	−0.960692	−	0.883934i
$795$		0			0
$796$	0.353507	−	0.0294712i	0.0125297	−	0.00104458i
$797$		−	16.8176i		−	0.595709i	−0.954611	−	0.297854i	$-0.903729\pi$
$797$		−	16.8176i		−	0.595709i	0.954611	−	0.297854i	$-0.0962710\pi$
$798$		0			0
$799$			30.1802i			1.06770i
$800$	5.31554	+	3.46330i	0.187933	+	0.122446i
$801$		0			0
$802$	−21.5544	+	23.4261i	−0.761111	+	0.827204i
$803$	1.01311	+	0.584919i	0.0357519	+	0.0206414i
$804$		0			0
$805$	−1.96424			−0.0692305
$806$	4.94819	+	15.8063i	0.174293	+	0.556754i
$807$		0			0
$808$	15.7692	+	2.17457i	0.554757	+	0.0765011i
$809$	−2.57747			−0.0906191			−0.0453095	−	0.998973i	$-0.514427\pi$
$809$	−2.57747			−0.0906191			−0.0453095	+	0.998973i	$0.514427\pi$
$810$		0			0
$811$	−3.04330	−	5.27116i	−0.106865	−	0.185095i	0.807634	−	0.589684i	$-0.200748\pi$
$811$	−3.04330	−	5.27116i	−0.106865	−	0.185095i	−0.914499	+	0.404589i	$0.867415\pi$
$812$	−0.291908	−	3.50144i	−0.0102440	−	0.122877i
$813$		0			0
$814$	−3.52546	+	15.7498i	−0.123567	+	0.552030i
$815$	29.9424	+	17.2872i	1.04883	+	0.605545i
$816$		0			0
$817$	−19.9187	+	6.13487i	−0.696866	+	0.214632i
$818$	8.66219	+	27.6702i	0.302866	+	0.967465i
$819$		0			0
$820$	25.5228	−	2.12779i	0.891296	−	0.0743056i
$821$	8.28986	+	14.3585i	0.289318	+	0.501114i	0.973647	−	0.228060i	$-0.0732382\pi$
$821$	8.28986	+	14.3585i	0.289318	+	0.501114i	−0.684329	+	0.729173i	$0.739905\pi$
$822$		0			0
$823$	−0.808864	+	0.466998i	−0.0281952	+	0.0162785i	−0.514031	−	0.857771i	$-0.671849\pi$
$823$	−0.808864	+	0.466998i	−0.0281952	+	0.0162785i	0.485836	+	0.874050i	$0.338515\pi$
$824$	−31.1978	+	40.1453i	−1.08683	+	1.39853i
$825$		0			0
$826$	−1.24928	+	1.35777i	−0.0434681	+	0.0472427i
$827$	−23.7237	−	41.0907i	−0.824954	−	1.42886i	−0.901954	−	0.431831i	$-0.857868\pi$
$827$	−23.7237	−	41.0907i	−0.824954	−	1.42886i	0.0770002	−	0.997031i	$-0.475466\pi$
$828$		0			0
$829$		−	47.7375i		−	1.65799i	−0.559254	−	0.828997i	$-0.688912\pi$
$829$		−	47.7375i		−	1.65799i	0.559254	−	0.828997i	$-0.311088\pi$
$830$	15.9304	−	17.3137i	0.552951	−	0.600968i
$831$		0			0
$832$	−37.1313	−	38.0541i	−1.28730	−	1.31929i
$833$	13.1513	−	22.7787i	0.455665	−	0.789235i
$834$		0			0
$835$	−44.2214			−1.53034
$836$	−4.36483	−	10.8665i	−0.150961	−	0.375825i
$837$		0			0
$838$	−17.7965	−	3.98360i	−0.614771	−	0.137611i
$839$	−7.37906	+	12.7809i	−0.254754	+	0.441246i	−0.964829	−	0.262880i	$-0.915328\pi$
$839$	−7.37906	+	12.7809i	−0.254754	+	0.441246i	0.710075	+	0.704126i	$0.248661\pi$
$840$		0			0
$841$	−2.26029	+	3.91493i	−0.0779409	+	0.134998i
$842$	−18.2481	+	19.8327i	−0.628872	+	0.683481i
$843$		0			0
$844$	21.4073	−	14.8594i	0.736870	−	0.511483i
$845$	30.6924	+	53.1608i	1.05585	+	1.82879i
$846$		0			0
$847$			3.26514i			0.112192i
$848$	12.5114	+	4.67007i	0.429645	+	0.160371i
$849$		0			0
$850$	1.32568	−	5.92238i	0.0454703	−	0.203136i
$851$	11.9324	+	20.6675i	0.409037	+	0.708473i
$852$		0			0
$853$	−17.8909	+	30.9879i	−0.612573	+	1.06101i	0.378232	+	0.925711i	$0.376532\pi$
$853$	−17.8909	+	30.9879i	−0.612573	+	1.06101i	−0.990805	+	0.135296i	$0.956801\pi$
$854$	0.596836	+	1.90651i	0.0204233	+	0.0652394i
$855$		0			0
$856$	18.0722	−	23.2553i	0.617695	−	0.794848i
$857$	11.1696	+	6.44877i	0.381546	+	0.220286i	0.678491	−	0.734609i	$-0.262634\pi$
$857$	11.1696	+	6.44877i	0.381546	+	0.220286i	−0.296945	+	0.954895i	$0.595968\pi$
$858$		0			0
$859$	−24.0984	+	13.9132i	−0.822225	+	0.474712i	−0.851183	−	0.524869i	$-0.824114\pi$
$859$	−24.0984	+	13.9132i	−0.822225	+	0.474712i	0.0289579	+	0.999581i	$0.490781\pi$
$860$	−18.7681	+	1.56466i	−0.639986	+	0.0533544i
$861$		0			0
$862$	24.8642	−	7.78379i	0.846879	−	0.265117i
$863$	13.5990			0.462917			0.231458	−	0.972845i	$-0.425650\pi$
$863$	13.5990			0.462917			0.231458	+	0.972845i	$0.425650\pi$
$864$		0			0
$865$	−13.0204	+	7.51735i	−0.442708	+	0.255598i
$866$	3.66250	+	11.6993i	0.124457	+	0.397560i
$867$		0			0
$868$	−0.533512	+	1.13201i	−0.0181086	+	0.0384228i
$869$	−19.4786	−	11.2460i	−0.660768	−	0.381494i
$870$		0			0
$871$	−12.1053	−	6.98902i	−0.410174	−	0.236814i
$872$	0.156627	−	0.0637539i	0.00530406	−	0.00215898i
$873$		0			0
$874$	−15.6289	−	7.45414i	−0.528657	−	0.252140i
$875$		−	4.28065i		−	0.144713i
$876$		0			0
$877$	0.579383	+	0.334507i	0.0195644	+	0.0112955i	0.509750	−	0.860322i	$-0.329738\pi$
$877$	0.579383	+	0.334507i	0.0195644	+	0.0112955i	−0.490186	+	0.871618i	$0.663071\pi$
$878$	32.5755	+	29.9728i	1.09937	+	1.01153i
$879$		0			0
$880$	−1.75217	−	10.4356i	−0.0590655	−	0.351784i
$881$	44.4036			1.49600			0.747998	−	0.663701i	$-0.231015\pi$
$881$	44.4036			1.49600			0.747998	+	0.663701i	$0.231015\pi$
$882$		0			0
$883$	37.7133	−	21.7738i	1.26915	−	0.732747i	0.294326	−	0.955705i	$-0.404905\pi$
$883$	37.7133	−	21.7738i	1.26915	−	0.732747i	0.974828	+	0.222958i	$0.0715714\pi$
$884$	−21.6832	+	46.0074i	−0.729284	+	1.54740i
$885$		0			0
$886$	−1.46222	−	4.67087i	−0.0491243	−	0.156921i
$887$	−6.59049	−	11.4151i	−0.221287	−	0.383280i	0.733912	−	0.679245i	$-0.237692\pi$
$887$	−6.59049	−	11.4151i	−0.221287	−	0.383280i	−0.955199	+	0.295964i	$0.904359\pi$
$888$		0			0
$889$	−3.96607	+	2.28981i	−0.133018	+	0.0767978i
$890$	−5.77022	−	1.29161i	−0.193418	−	0.0432950i
$891$		0			0
$892$	−7.08119	+	4.91525i	−0.237096	+	0.164575i
$893$	−7.66445	+	33.5148i	−0.256481	+	1.12153i
$894$		0			0
$895$	−12.0363	+	20.8475i	−0.402329	+	0.696854i
$896$	−0.117749	−	4.01549i	−0.00393373	−	0.134148i
$897$		0			0
$898$	−23.9459	−	5.36008i	−0.799084	−	0.178868i
$899$	−7.55070	+	4.35940i	−0.251830	+	0.145394i
$900$		0			0
$901$		−	12.7751i		−	0.425601i
$902$	9.09002	+	8.36374i	0.302665	+	0.278482i
$903$		0			0
$904$	0.608530	+	0.472902i	0.0202394	+	0.0157285i
$905$		−	20.8097i		−	0.691737i
$906$		0			0
$907$	26.1929	−	45.3674i	0.869720	−	1.50640i	0.00743704	−	0.999972i	$-0.497633\pi$
$907$	26.1929	−	45.3674i	0.869720	−	1.50640i	0.862283	−	0.506427i	$-0.169034\pi$
$908$	38.2081	+	18.0074i	1.26798	+	0.597596i
$909$		0			0
$910$	−1.43566	+	6.41374i	−0.0475917	+	0.212613i
$911$	19.4053			0.642925			0.321462	−	0.946922i	$-0.395826\pi$
$911$	19.4053			0.642925			0.321462	+	0.946922i	$0.395826\pi$
$912$		0			0
$913$	11.3473			0.375540
$914$	−0.635377	+	2.83851i	−0.0210164	+	0.0938897i
$915$		0			0
$916$	7.55684	+	3.56152i	0.249685	+	0.117676i
$917$	1.88286	−	3.26121i	0.0621775	−	0.107695i
$918$		0			0
$919$			16.2385i			0.535660i	0.963466	+	0.267830i	$0.0863065\pi$
$919$			16.2385i			0.535660i	−0.963466	+	0.267830i	$0.913693\pi$
$920$	−12.3546	−	9.60104i	−0.407319	−	0.316537i
$921$		0			0
$922$	19.2755	+	17.7354i	0.634805	+	0.584085i
$923$		−	103.724i		−	3.41412i
$924$		0			0
$925$	−8.25180	+	4.76418i	−0.271317	+	0.156645i
$926$	−20.3309	−	4.55091i	−0.668116	−	0.149552i
$927$		0			0
$928$	15.2787	−	23.4500i	0.501548	−	0.769785i
$929$	14.8773	−	25.7682i	0.488108	−	0.845429i	−0.511798	−	0.859106i	$-0.671020\pi$
$929$	14.8773	−	25.7682i	0.488108	−	0.845429i	0.999906	+	0.0136771i	$0.00435370\pi$
$930$		0			0
$931$	20.3891	−	21.9556i	0.668226	−	0.719566i
$932$	46.8960	−	32.5519i	1.53613	−	1.06627i
$933$		0			0
$934$	39.3829	+	8.81553i	1.28865	+	0.288453i
$935$	−8.76633	+	5.06125i	−0.286690	+	0.165520i
$936$		0			0
$937$	−5.96068	−	10.3242i	−0.194727	−	0.337277i	0.752084	−	0.659067i	$-0.229049\pi$
$937$	−5.96068	−	10.3242i	−0.194727	−	0.337277i	−0.946811	+	0.321790i	$0.895715\pi$
$938$	−0.315526	−	1.00790i	−0.0103023	−	0.0329092i
$939$		0			0
$940$	−13.2443	+	28.1017i	−0.431981	+	0.916578i
$941$	39.8041	−	22.9809i	1.29758	−	0.749156i	0.317592	−	0.948228i	$-0.397126\pi$
$941$	39.8041	−	22.9809i	1.29758	−	0.749156i	0.979985	+	0.199071i	$0.0637925\pi$
$942$		0			0
$943$	18.2648			0.594785
$944$	−14.4943	+	2.43364i	−0.471750	+	0.0792082i
$945$		0			0
$946$	−6.68430	−	6.15023i	−0.217325	−	0.199961i
$947$	−12.3615	−	7.13691i	−0.401695	−	0.231918i	0.285520	−	0.958373i	$-0.407834\pi$
$947$	−12.3615	−	7.13691i	−0.401695	−	0.231918i	−0.687215	+	0.726454i	$0.741167\pi$
$948$		0			0
$949$		−	5.78794i		−	0.187885i
$950$	2.97617	−	6.24007i	0.0965597	−	0.202455i
$951$		0			0
$952$	−3.55933	+	1.44880i	−0.115359	+	0.0469558i
$953$	−42.9569	−	24.8012i	−1.39151	−	0.803389i	−0.398028	−	0.917373i	$-0.630305\pi$
$953$	−42.9569	−	24.8012i	−1.39151	−	0.803389i	−0.993483	+	0.113985i	$0.963639\pi$
$954$		0			0
$955$	−25.7500	−	14.8668i	−0.833251	−	0.481078i
$956$	0.601331	−	1.27590i	0.0194484	−	0.0412657i
$957$		0			0
$958$	1.03556	+	3.30794i	0.0334573	+	0.106875i
$959$	−1.72005	+	0.993069i	−0.0555432	+	0.0320679i
$960$		0			0
$961$	−27.8946			−0.899827
$962$	76.2058	−	23.8563i	2.45697	−	0.769160i
$963$		0			0
$964$	11.3964	−	0.950091i	0.367052	−	0.0306004i
$965$	37.6803	−	21.7547i	1.21297	−	0.700310i
$966$		0			0
$967$	33.2407	+	19.1915i	1.06895	+	0.617157i	0.927894	−	0.372845i	$-0.121618\pi$
$967$	33.2407	+	19.1915i	1.06895	+	0.617157i	0.141054	+	0.990002i	$0.454951\pi$
$968$	−15.9597	+	20.5369i	−0.512964	+	0.660081i
$969$		0			0
$970$	−13.1762	−	42.0897i	−0.423064	−	1.35142i
$971$	−2.90903	+	5.03859i	−0.0933552	+	0.161696i	−0.908921	−	0.416968i	$-0.863093\pi$
$971$	−2.90903	+	5.03859i	−0.0933552	+	0.161696i	0.815566	+	0.578664i	$0.196426\pi$
$972$		0			0
$973$	−1.92594	−	3.33582i	−0.0617426	−	0.106941i
$974$	2.52792	−	11.2934i	0.0809999	−	0.361863i
$975$		0			0
$976$	−5.56490	+	14.9088i	−0.178128	+	0.477218i
$977$		−	44.4183i		−	1.42107i	−0.703663	−	0.710533i	$-0.748454\pi$
$977$		−	44.4183i		−	1.42107i	0.703663	−	0.710533i	$-0.251546\pi$
$978$		0			0
$979$	−1.42592	−	2.46977i	−0.0455726	−	0.0789341i
$980$	22.2417	−	15.4386i	0.710486	−	0.493169i
$981$		0			0
$982$	−1.09907	+	1.19451i	−0.0350729	+	0.0381185i
$983$	−4.00137	+	6.93057i	−0.127624	+	0.221051i	−0.922755	−	0.385386i	$-0.874068\pi$
$983$	−4.00137	+	6.93057i	−0.127624	+	0.221051i	0.795132	+	0.606437i	$0.207402\pi$
$984$		0			0
$985$	11.5304	−	19.9713i	0.367390	−	0.636338i
$986$	−26.1272	−	5.84835i	−0.832059	−	0.186249i
$987$		0			0
$988$	−35.7627	+	45.5841i	−1.13776	+	1.45022i
$989$	−13.4310			−0.427080
$990$		0			0
$991$	−9.93799	+	17.2131i	−0.315691	+	0.546792i	−0.979584	−	0.201035i	$-0.935570\pi$
$991$	−9.93799	+	17.2131i	−0.315691	+	0.546792i	0.663893	+	0.747827i	$0.268903\pi$
$992$	−8.88881	+	4.51229i	−0.282220	+	0.143265i
$993$		0			0
$994$	5.30646	−	5.76726i	0.168311	−	0.182926i
$995$		−	0.349304i		−	0.0110737i
$996$		0			0
$997$	−1.78001	−	3.08307i	−0.0563736	−	0.0976419i	0.836461	−	0.548026i	$-0.184620\pi$
$997$	−1.78001	−	3.08307i	−0.0563736	−	0.0976419i	−0.892835	+	0.450384i	$0.851287\pi$
$998$	25.2997	−	27.4967i	0.800849	−	0.870393i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.r.b.559.6		20
3.2	odd	2		228.2.k.b.103.5	yes	20
4.3	odd	2		684.2.r.c.559.3		20
12.11	even	2		228.2.k.a.103.8	yes	20
19.12	odd	6		684.2.r.c.487.3		20
57.50	even	6		228.2.k.a.31.8	✓	20
76.31	even	6	inner	684.2.r.b.487.6		20
228.107	odd	6		228.2.k.b.31.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.k.a.31.8	✓	20	57.50	even	6
228.2.k.a.103.8	yes	20	12.11	even	2
228.2.k.b.31.5	yes	20	228.107	odd	6
228.2.k.b.103.5	yes	20	3.2	odd	2
684.2.r.b.487.6		20	76.31	even	6	inner
684.2.r.b.559.6		20	1.1	even	1	trivial
684.2.r.c.487.3		20	19.12	odd	6
684.2.r.c.559.3		20	4.3	odd	2

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.308915 - 1.38006i) q^{2} +(-1.80914 - 0.852645i) q^{4} +(-0.984694 + 1.70554i) q^{5} +0.355075i q^{7} +(-1.73557 + 2.23333i) q^{8} +(2.04956 + 1.88581i) q^{10} +1.34327i q^{11} +(5.75562 - 3.32301i) q^{13} +(0.490026 + 0.109688i) q^{14} +(2.54599 + 3.08511i) q^{16} +(1.91321 - 3.31378i) q^{17} +(2.96616 - 3.19404i) q^{19} +(3.23567 - 2.24597i) q^{20} +(1.85379 + 0.414956i) q^{22} +(2.43262 - 1.40448i) q^{23} +(0.560757 + 0.971259i) q^{25} +(-2.80796 - 8.96963i) q^{26} +(0.302753 - 0.642382i) q^{28} +(4.28481 - 2.47383i) q^{29} -1.76220 q^{31} +(5.04414 - 2.56059i) q^{32} +(-3.98220 - 3.66403i) q^{34} +(-0.605595 - 0.349640i) q^{35} +8.49598i q^{37} +(-3.49169 - 5.08017i) q^{38} +(-2.10003 - 5.15924i) q^{40} +(5.63122 + 3.25119i) q^{41} +(-4.14089 - 2.39074i) q^{43} +(1.14533 - 2.43016i) q^{44} +(-1.18679 - 3.79103i) q^{46} +(-6.83062 + 3.94366i) q^{47} +6.87392 q^{49} +(1.51362 - 0.473842i) q^{50} +(-13.2461 + 1.10430i) q^{52} +(2.89136 - 1.66933i) q^{53} +(-2.29100 - 1.32271i) q^{55} +(-0.793001 - 0.616259i) q^{56} +(-2.09040 - 6.67750i) q^{58} +(-1.83715 + 3.18204i) q^{59} +(1.98919 + 3.44537i) q^{61} +(-0.544372 + 2.43195i) q^{62} +(-1.97556 - 7.75223i) q^{64} +13.0886i q^{65} +(-1.05161 - 1.82144i) q^{67} +(-6.28675 + 4.36381i) q^{68} +(-0.669603 + 0.727749i) q^{70} +(7.80349 - 13.5160i) q^{71} +(0.435445 - 0.754212i) q^{73} +(11.7250 + 2.62454i) q^{74} +(-8.08958 + 3.24941i) q^{76} -0.476961 q^{77} +(-8.37212 + 14.5009i) q^{79} +(-7.76880 + 1.30440i) q^{80} +(6.22641 - 6.76709i) q^{82} -8.44752i q^{83} +(3.76786 + 6.52612i) q^{85} +(-4.57856 + 4.97615i) q^{86} +(-2.99997 - 2.33134i) q^{88} +(-1.83862 + 1.06153i) q^{89} +(1.17992 + 2.04368i) q^{91} +(-5.59848 + 0.466734i) q^{92} +(3.33241 + 10.6449i) q^{94} +(2.52682 + 8.20405i) q^{95} +(-13.7139 - 7.91774i) q^{97} +(2.12346 - 9.48644i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} - 4 q^{8} + 6 q^{10} + 6 q^{13} - 9 q^{14} - 11 q^{16} + 12 q^{19} + 14 q^{20} + 8 q^{22} - 10 q^{25} + 7 q^{28} + 12 q^{31} + 29 q^{32} - 6 q^{34} - 25 q^{38} - 46 q^{40} - 12 q^{41}+ \cdots - 12 q^{97}+O(q^{100}) \) 20 * q - q^2 + q^4 - 4 * q^8 + 6 * q^10 + 6 * q^13 - 9 * q^14 - 11 * q^16 + 12 * q^19 + 14 * q^20 + 8 * q^22 - 10 * q^25 + 7 * q^28 + 12 * q^31 + 29 * q^32 - 6 * q^34 - 25 * q^38 - 46 * q^40 - 12 * q^41 - 18 * q^43 + 12 * q^44 - 32 * q^46 + 36 * q^47 - 24 * q^49 + 34 * q^50 + 3 * q^52 + 12 * q^53 - 38 * q^56 + 16 * q^58 + 10 * q^61 + 55 * q^62 - 14 * q^64 + 14 * q^67 - 40 * q^68 + 26 * q^70 - 8 * q^71 - 6 * q^73 - 45 * q^74 - 69 * q^76 + 32 * q^77 - 6 * q^79 - 22 * q^80 + 24 * q^82 + 8 * q^85 - 7 * q^86 + 44 * q^88 + 24 * q^89 + 26 * q^91 + 18 * q^92 - 52 * q^94 - 4 * q^95 - 12 * q^97

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