LMFDB - Embedded newform 864.2.bh.b.47.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(47,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 7]))

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

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

chi := DirichletCharacter("864.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.9
Character	$\chi$	$=$	864.47
Dual form			864.2.bh.b.239.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967099 + 1.43691i) q^{3} +(-0.586059 - 3.32370i) q^{5} +(1.89356 - 2.25666i) q^{7} +(-1.12944 - 2.77927i) q^{9} +O(q^{10})$	\(q+(-0.967099 + 1.43691i) q^{3} +(-0.586059 - 3.32370i) q^{5} +(1.89356 - 2.25666i) q^{7} +(-1.12944 - 2.77927i) q^{9} +(-3.51297 - 0.619431i) q^{11} +(-0.204490 + 0.561832i) q^{13} +(5.34265 + 2.37223i) q^{15} +(-1.97627 + 1.14100i) q^{17} +(-2.72623 + 4.72197i) q^{19} +(1.41136 + 4.90330i) q^{21} +(-6.69233 + 5.61553i) q^{23} +(-6.00508 + 2.18567i) q^{25} +(5.08586 + 1.06492i) q^{27} +(-4.86478 + 1.77064i) q^{29} +(0.468156 + 0.557926i) q^{31} +(4.28745 - 4.44878i) q^{33} +(-8.61021 - 4.97111i) q^{35} +(-0.422340 + 0.243838i) q^{37} +(-0.609542 - 0.837181i) q^{39} +(0.645850 - 1.77446i) q^{41} +(1.01523 - 5.75766i) q^{43} +(-8.57557 + 5.38274i) q^{45} +(-3.87524 - 3.25171i) q^{47} +(-0.291398 - 1.65260i) q^{49} +(0.271731 - 3.94320i) q^{51} +13.0806 q^{53} +12.0391i q^{55} +(-4.14853 - 8.48397i) q^{57} +(-7.04866 + 1.24287i) q^{59} +(5.74555 - 6.84728i) q^{61} +(-8.41054 - 2.71397i) q^{63} +(1.98721 + 0.350398i) q^{65} +(-2.79254 - 1.01640i) q^{67} +(-1.59689 - 15.0471i) q^{69} +(1.67775 + 2.90596i) q^{71} +(-5.59255 + 9.68658i) q^{73} +(2.66689 - 10.7425i) q^{75} +(-8.04987 + 6.75464i) q^{77} +(-5.79167 - 15.9125i) q^{79} +(-6.44873 + 6.27805i) q^{81} +(-2.75916 - 7.58072i) q^{83} +(4.95057 + 5.89986i) q^{85} +(2.16047 - 8.70265i) q^{87} +(-13.3509 - 7.70815i) q^{89} +(0.880649 + 1.52533i) q^{91} +(-1.25444 + 0.133129i) q^{93} +(17.2922 + 6.29383i) q^{95} +(-1.67485 + 9.49852i) q^{97} +(2.24612 + 10.4631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) $ 192 * q + 12 * q^3 - 12 * q^9	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.967099	+	1.43691i	−0.558355	+	0.829602i
$3$	−0.967099	+	1.43691i	−0.558355	+	0.829602i
$4$		0			0
$5$	−0.586059	−	3.32370i	−0.262093	−	1.48641i	−0.777186	−	0.629271i	$-0.783354\pi$
$5$	−0.586059	−	3.32370i	−0.262093	−	1.48641i	0.515092	−	0.857135i	$-0.327758\pi$
$6$		0			0
$7$	1.89356	−	2.25666i	0.715700	−	0.852937i	−0.278506	−	0.960435i	$-0.589839\pi$
$7$	1.89356	−	2.25666i	0.715700	−	0.852937i	0.994205	+	0.107497i	$0.0342836\pi$
$8$		0			0
$9$	−1.12944	−	2.77927i	−0.376480	−	0.926425i
$10$		0			0
$11$	−3.51297	−	0.619431i	−1.05920	−	0.186765i	−0.383198	−	0.923666i	$-0.625177\pi$
$11$	−3.51297	−	0.619431i	−1.05920	−	0.186765i	−0.676001	+	0.736901i	$0.736289\pi$
$12$		0			0
$13$	−0.204490	+	0.561832i	−0.0567153	+	0.155824i	−0.964815	−	0.262930i	$-0.915311\pi$
$13$	−0.204490	+	0.561832i	−0.0567153	+	0.155824i	0.908099	+	0.418755i	$0.137533\pi$
$14$		0			0
$15$	5.34265	+	2.37223i	1.37947	+	0.612508i
$16$		0			0
$17$	−1.97627	+	1.14100i	−0.479317	+	0.276734i	−0.720132	−	0.693837i	$-0.755919\pi$
$17$	−1.97627	+	1.14100i	−0.479317	+	0.276734i	0.240815	+	0.970571i	$0.422585\pi$
$18$		0			0
$19$	−2.72623	+	4.72197i	−0.625440	+	1.08329i	0.363016	+	0.931783i	$0.381747\pi$
$19$	−2.72623	+	4.72197i	−0.625440	+	1.08329i	−0.988456	+	0.151511i	$0.951586\pi$
$20$		0			0
$21$	1.41136	+	4.90330i	0.307985	+	1.06999i
$22$		0			0
$23$	−6.69233	+	5.61553i	−1.39545	+	1.17092i	−0.432368	+	0.901697i	$0.642322\pi$
$23$	−6.69233	+	5.61553i	−1.39545	+	1.17092i	−0.963078	+	0.269222i	$0.913234\pi$
$24$		0			0
$25$	−6.00508	+	2.18567i	−1.20102	+	0.437134i
$26$		0			0
$27$	5.08586	+	1.06492i	0.978774	+	0.204945i
$28$		0			0
$29$	−4.86478	+	1.77064i	−0.903368	+	0.328799i	−0.751601	−	0.659618i	$-0.770718\pi$
$29$	−4.86478	+	1.77064i	−0.903368	+	0.328799i	−0.151766	+	0.988416i	$0.548496\pi$
$30$		0			0
$31$	0.468156	+	0.557926i	0.0840832	+	0.100206i	0.806446	−	0.591308i	$-0.201388\pi$
$31$	0.468156	+	0.557926i	0.0840832	+	0.100206i	−0.722363	+	0.691515i	$0.756944\pi$
$32$		0			0
$33$	4.28745	−	4.44878i	0.746350	−	0.774433i
$34$		0			0
$35$	−8.61021	−	4.97111i	−1.45539	−	0.840271i
$36$		0			0
$37$	−0.422340	+	0.243838i	−0.0694322	+	0.0400867i	−0.534314	−	0.845286i	$-0.679430\pi$
$37$	−0.422340	+	0.243838i	−0.0694322	+	0.0400867i	0.464882	+	0.885373i	$0.346097\pi$
$38$		0			0
$39$	−0.609542	−	0.837181i	−0.0976048	−	0.134056i
$40$		0			0
$41$	0.645850	−	1.77446i	0.100865	−	0.277124i	−0.878988	−	0.476843i	$-0.841781\pi$
$41$	0.645850	−	1.77446i	0.100865	−	0.277124i	0.979853	+	0.199720i	$0.0640031\pi$
$42$		0			0
$43$	1.01523	−	5.75766i	0.154821	−	0.878035i	−0.804128	−	0.594456i	$-0.797367\pi$
$43$	1.01523	−	5.75766i	0.154821	−	0.878035i	0.958949	−	0.283578i	$-0.0915216\pi$
$44$		0			0
$45$	−8.57557	+	5.38274i	−1.27837	+	0.802412i
$46$		0			0
$47$	−3.87524	−	3.25171i	−0.565262	−	0.474311i	0.314808	−	0.949155i	$-0.398060\pi$
$47$	−3.87524	−	3.25171i	−0.565262	−	0.474311i	−0.880070	+	0.474844i	$0.842504\pi$
$48$		0			0
$49$	−0.291398	−	1.65260i	−0.0416284	−	0.236086i
$50$		0			0
$51$	0.271731	−	3.94320i	0.0380499	−	0.552158i
$52$		0			0
$53$	13.0806			1.79676			0.898380	−	0.439220i	$-0.144745\pi$
$53$	13.0806			1.79676			0.898380	+	0.439220i	$0.144745\pi$
$54$		0			0
$55$			12.0391i			1.62335i
$56$		0			0
$57$	−4.14853	−	8.48397i	−0.549486	−	1.12373i
$58$		0			0
$59$	−7.04866	+	1.24287i	−0.917658	+	0.161808i	−0.612479	−	0.790487i	$-0.709827\pi$
$59$	−7.04866	+	1.24287i	−0.917658	+	0.161808i	−0.305179	+	0.952295i	$0.598716\pi$
$60$		0			0
$61$	5.74555	−	6.84728i	0.735642	−	0.876705i	−0.260408	−	0.965499i	$-0.583857\pi$
$61$	5.74555	−	6.84728i	0.735642	−	0.876705i	0.996050	+	0.0887943i	$0.0283014\pi$
$62$		0			0
$63$	−8.41054	−	2.71397i	−1.05963	−	0.341928i
$64$		0			0
$65$	1.98721	+	0.350398i	0.246483	+	0.0434615i
$66$		0			0
$67$	−2.79254	−	1.01640i	−0.341163	−	0.124173i	0.165756	−	0.986167i	$-0.446994\pi$
$67$	−2.79254	−	1.01640i	−0.341163	−	0.124173i	−0.506919	+	0.861994i	$0.669216\pi$
$68$		0			0
$69$	−1.59689	−	15.0471i	−0.192243	−	1.81145i
$70$		0			0
$71$	1.67775	+	2.90596i	0.199113	+	0.344873i	0.948241	−	0.317552i	$-0.102861\pi$
$71$	1.67775	+	2.90596i	0.199113	+	0.344873i	−0.749128	+	0.662425i	$0.769527\pi$
$72$		0			0
$73$	−5.59255	+	9.68658i	−0.654558	+	1.13373i	0.327446	+	0.944870i	$0.393812\pi$
$73$	−5.59255	+	9.68658i	−0.654558	+	1.13373i	−0.982004	+	0.188858i	$0.939521\pi$
$74$		0			0
$75$	2.66689	−	10.7425i	0.307946	−	1.24044i
$76$		0			0
$77$	−8.04987	+	6.75464i	−0.917368	+	0.769763i
$78$		0			0
$79$	−5.79167	−	15.9125i	−0.651614	−	1.79030i	−0.611696	−	0.791093i	$-0.709513\pi$
$79$	−5.79167	−	15.9125i	−0.651614	−	1.79030i	−0.0399179	−	0.999203i	$-0.512710\pi$
$80$		0			0
$81$	−6.44873	+	6.27805i	−0.716526	+	0.697561i
$82$		0			0
$83$	−2.75916	−	7.58072i	−0.302857	−	0.832092i	−0.994001	−	0.109375i	$-0.965115\pi$
$83$	−2.75916	−	7.58072i	−0.302857	−	0.832092i	0.691144	−	0.722717i	$-0.257107\pi$
$84$		0			0
$85$	4.95057	+	5.89986i	0.536965	+	0.639929i
$86$		0			0
$87$	2.16047	−	8.70265i	0.231627	−	0.933022i
$88$		0			0
$89$	−13.3509	−	7.70815i	−1.41519	−	0.817063i	−0.419323	−	0.907837i	$-0.637732\pi$
$89$	−13.3509	−	7.70815i	−1.41519	−	0.817063i	−0.995871	+	0.0907747i	$0.971066\pi$
$90$		0			0
$91$	0.880649	+	1.52533i	0.0923171	+	0.159898i
$92$		0			0
$93$	−1.25444	+	0.133129i	−0.130080	+	0.0138049i
$94$		0			0
$95$	17.2922	+	6.29383i	1.77414	+	0.645733i
$96$		0			0
$97$	−1.67485	+	9.49852i	−0.170055	+	0.964429i	0.773643	+	0.633621i	$0.218432\pi$
$97$	−1.67485	+	9.49852i	−0.170055	+	0.964429i	−0.943698	+	0.330807i	$0.892679\pi$
$98$		0			0
$99$	2.24612	+	10.4631i	0.225743	+	1.05158i
$100$		0			0
$101$	−1.58712	−	1.33175i	−0.157924	−	0.132514i	0.560402	−	0.828221i	$-0.310647\pi$
$101$	−1.58712	−	1.33175i	−0.157924	−	0.132514i	−0.718326	+	0.695707i	$0.755091\pi$
$102$		0			0
$103$	5.47205	−	0.964870i	0.539177	−	0.0950715i	0.102573	−	0.994725i	$-0.467292\pi$
$103$	5.47205	−	0.964870i	0.539177	−	0.0950715i	0.436604	+	0.899654i	$0.356181\pi$
$104$		0			0
$105$	15.4700	−	7.56458i	1.50972	−	0.738227i
$106$		0			0
$107$		−	11.8518i		−	1.14576i	−0.819640	−	0.572879i	$-0.805826\pi$
$107$		−	11.8518i		−	1.14576i	0.819640	−	0.572879i	$-0.194174\pi$
$108$		0			0
$109$			5.60849i			0.537196i	0.963252	+	0.268598i	$0.0865603\pi$
$109$			5.60849i			0.537196i	−0.963252	+	0.268598i	$0.913440\pi$
$110$		0			0
$111$	0.0580702	−	0.842681i	0.00551178	−	0.0799837i
$112$		0			0
$113$	1.25678	−	0.221604i	0.118228	−	0.0208467i	−0.114221	−	0.993455i	$-0.536437\pi$
$113$	1.25678	−	0.221604i	0.118228	−	0.0208467i	0.232449	+	0.972609i	$0.425326\pi$
$114$		0			0
$115$	22.5865	+	18.9523i	2.10620	+	1.76731i
$116$		0			0
$117$	1.79244	−	0.0662214i	0.165712	−	0.00612217i
$118$		0			0
$119$	−1.16734	+	6.62034i	−0.107010	+	0.606886i
$120$		0			0
$121$	1.62062	+	0.589859i	0.147329	+	0.0536235i
$122$		0			0
$123$	1.92514	+	2.64411i	0.173584	+	0.238411i
$124$		0			0
$125$	2.34641	+	4.06411i	0.209870	+	0.363505i
$126$		0			0
$127$	−5.76339	−	3.32750i	−0.511419	−	0.295268i	0.221998	−	0.975047i	$-0.428742\pi$
$127$	−5.76339	−	3.32750i	−0.511419	−	0.295268i	−0.733417	+	0.679779i	$0.762075\pi$
$128$		0			0
$129$	7.29143	+	7.02702i	0.641975	+	0.618695i
$130$		0			0
$131$	10.6613	+	12.7057i	0.931486	+	1.11010i	0.993704	+	0.112040i	$0.0357384\pi$
$131$	10.6613	+	12.7057i	0.931486	+	1.11010i	−0.0622173	+	0.998063i	$0.519817\pi$
$132$		0			0
$133$	5.49359	+	15.0935i	0.476355	+	1.30877i
$134$		0			0
$135$	0.558885	−	17.5280i	0.0481012	−	1.50857i
$136$		0			0
$137$	−6.41579	−	17.6272i	−0.548138	−	1.50600i	−0.836222	−	0.548391i	$-0.815241\pi$
$137$	−6.41579	−	17.6272i	−0.548138	−	1.50600i	0.288085	−	0.957605i	$-0.406982\pi$
$138$		0			0
$139$	0.589031	−	0.494256i	0.0499610	−	0.0419223i	−0.617465	−	0.786598i	$-0.711840\pi$
$139$	0.589031	−	0.494256i	0.0499610	−	0.0419223i	0.667426	+	0.744676i	$0.267396\pi$
$140$		0			0
$141$	8.42017	−	2.42366i	0.709106	−	0.204109i
$142$		0			0
$143$	1.06638	−	1.84703i	0.0891754	−	0.154456i
$144$		0			0
$145$	8.73612	+	15.1314i	0.725495	+	1.25659i
$146$		0			0
$147$	2.65646	+	1.17952i	0.219101	+	0.0972848i
$148$		0			0
$149$	2.83808	+	1.03298i	0.232504	+	0.0846246i	0.455645	−	0.890162i	$-0.349409\pi$
$149$	2.83808	+	1.03298i	0.232504	+	0.0846246i	−0.223141	+	0.974786i	$0.571631\pi$
$150$		0			0
$151$	2.11341	+	0.372652i	0.171987	+	0.0303260i	0.258978	−	0.965883i	$-0.416614\pi$
$151$	2.11341	+	0.372652i	0.171987	+	0.0303260i	−0.0869913	+	0.996209i	$0.527725\pi$
$152$		0			0
$153$	5.40324	+	4.20391i	0.436826	+	0.339866i
$154$		0			0
$155$	1.58001	−	1.88299i	0.126910	−	0.151245i
$156$		0			0
$157$	−7.69184	+	1.35628i	−0.613876	+	0.108243i	−0.471936	−	0.881633i	$-0.656445\pi$
$157$	−7.69184	+	1.35628i	−0.613876	+	0.108243i	−0.141939	+	0.989875i	$0.545334\pi$
$158$		0			0
$159$	−12.6502	+	18.7957i	−1.00323	+	1.49060i
$160$		0			0
$161$			25.7357i			2.02825i
$162$		0			0
$163$	−12.9106			−1.01124			−0.505620	−	0.862756i	$-0.668736\pi$
$163$	−12.9106			−1.01124			−0.505620	+	0.862756i	$0.668736\pi$
$164$		0			0
$165$	−17.2991	−	11.6430i	−1.34674	−	0.906405i
$166$		0			0
$167$	−2.62966	−	14.9135i	−0.203489	−	1.15404i	−0.899800	−	0.436304i	$-0.856287\pi$
$167$	−2.62966	−	14.9135i	−0.203489	−	1.15404i	0.696310	−	0.717741i	$-0.254824\pi$
$168$		0			0
$169$	9.68474	+	8.12646i	0.744980	+	0.625112i
$170$		0			0
$171$	16.2028	+	2.24376i	1.23906	+	0.171585i
$172$		0			0
$173$	3.13725	−	17.7922i	0.238521	−	1.35272i	−0.596551	−	0.802576i	$-0.703462\pi$
$173$	3.13725	−	17.7922i	0.238521	−	1.35272i	0.835071	−	0.550142i	$-0.185426\pi$
$174$		0			0
$175$	−6.43868	+	17.6901i	−0.486719	+	1.33725i
$176$		0			0
$177$	5.03086	−	11.3303i	0.378142	−	0.851637i
$178$		0			0
$179$	−5.86858	+	3.38823i	−0.438638	+	0.253248i	−0.703020	−	0.711170i	$-0.748166\pi$
$179$	−5.86858	+	3.38823i	−0.438638	+	0.253248i	0.264381	+	0.964418i	$0.414832\pi$
$180$		0			0
$181$	−8.33722	−	4.81350i	−0.619701	−	0.357784i	0.157052	−	0.987590i	$-0.449801\pi$
$181$	−8.33722	−	4.81350i	−0.619701	−	0.357784i	−0.776753	+	0.629806i	$0.783134\pi$
$182$		0			0
$183$	4.28243	+	14.8779i	0.316567	+	1.09980i
$184$		0			0
$185$	1.05796	+	1.26083i	0.0777828	+	0.0926980i
$186$		0			0
$187$	7.64936	−	2.78414i	0.559377	−	0.203596i
$188$		0			0
$189$	12.0336	−	9.46055i	0.875313	−	0.688154i
$190$		0			0
$191$	0.938669	−	0.341648i	0.0679197	−	0.0247208i	−0.307837	−	0.951439i	$-0.599605\pi$
$191$	0.938669	−	0.341648i	0.0679197	−	0.0247208i	0.375757	+	0.926718i	$0.377383\pi$
$192$		0			0
$193$	−0.369507	+	0.310054i	−0.0265977	+	0.0223181i	−0.655990	−	0.754770i	$-0.727748\pi$
$193$	−0.369507	+	0.310054i	−0.0265977	+	0.0223181i	0.629392	+	0.777088i	$0.283304\pi$
$194$		0			0
$195$	−2.42532	+	2.51657i	−0.173681	+	0.180216i
$196$		0			0
$197$	−6.10771	+	10.5789i	−0.435157	+	0.753713i	−0.997308	−	0.0733207i	$-0.976640\pi$
$197$	−6.10771	+	10.5789i	−0.435157	+	0.753713i	0.562152	+	0.827034i	$0.309974\pi$
$198$		0			0
$199$	11.7431	−	6.77986i	0.832444	−	0.480612i	−0.0222449	−	0.999753i	$-0.507081\pi$
$199$	11.7431	−	6.77986i	0.832444	−	0.480612i	0.854689	+	0.519141i	$0.173748\pi$
$200$		0			0
$201$	4.16114	−	3.02968i	0.293504	−	0.213697i
$202$		0			0
$203$	−5.21605	+	14.3310i	−0.366095	+	1.00584i
$204$		0			0
$205$	−6.27628	−	1.10668i	−0.438355	−	0.0772937i
$206$		0			0
$207$	23.1657	+	12.2574i	1.61013	+	0.851949i
$208$		0			0
$209$	12.5021	−	14.8994i	0.864788	−	1.03061i
$210$		0			0
$211$	2.37424	+	13.4650i	0.163449	+	0.926968i	0.950649	+	0.310269i	$0.100419\pi$
$211$	2.37424	+	13.4650i	0.163449	+	0.926968i	−0.787199	+	0.616699i	$0.788470\pi$
$212$		0			0
$213$	−5.79816	−	0.399558i	−0.397283	−	0.0273773i
$214$		0			0
$215$	−19.7317			−1.34569
$216$		0			0
$217$	2.14553			0.145648
$218$		0			0
$219$	−8.51023	−	17.4039i	−0.575068	−	1.17605i
$220$		0			0
$221$	−0.236923	−	1.34366i	−0.0159372	−	0.0903842i
$222$		0			0
$223$	3.52036	−	4.19541i	0.235741	−	0.280945i	−0.635184	−	0.772361i	$-0.719076\pi$
$223$	3.52036	−	4.19541i	0.235741	−	0.280945i	0.870925	+	0.491415i	$0.163520\pi$
$224$		0			0
$225$	12.8570	+	14.2212i	0.857131	+	0.948079i
$226$		0			0
$227$	−10.8215	−	1.90812i	−0.718247	−	0.126646i	−0.197433	−	0.980316i	$-0.563261\pi$
$227$	−10.8215	−	1.90812i	−0.718247	−	0.126646i	−0.520814	+	0.853670i	$0.674372\pi$
$228$		0			0
$229$	9.00757	−	24.7481i	0.595237	−	1.63540i	−0.165403	−	0.986226i	$-0.552892\pi$
$229$	9.00757	−	24.7481i	0.595237	−	1.63540i	0.760640	−	0.649174i	$-0.224885\pi$
$230$		0			0
$231$	−1.92082	−	18.0994i	−0.126381	−	1.19085i
$232$		0			0
$233$	−8.32478	+	4.80631i	−0.545374	+	0.314872i	−0.747254	−	0.664538i	$-0.768628\pi$
$233$	−8.32478	+	4.80631i	−0.545374	+	0.314872i	0.201880	+	0.979410i	$0.435295\pi$
$234$		0			0
$235$	−8.53661	+	14.7858i	−0.556867	+	0.964522i
$236$		0			0
$237$	28.4660	+	7.06682i	1.84907	+	0.459039i
$238$		0			0
$239$	11.0157	−	9.24328i	0.712547	−	0.597898i	−0.212765	−	0.977103i	$-0.568247\pi$
$239$	11.0157	−	9.24328i	0.712547	−	0.597898i	0.925313	+	0.379205i	$0.123803\pi$
$240$		0			0
$241$	12.6743	−	4.61308i	0.816426	−	0.297155i	0.100150	−	0.994972i	$-0.468068\pi$
$241$	12.6743	−	4.61308i	0.816426	−	0.297155i	0.716276	+	0.697818i	$0.245845\pi$
$242$		0			0
$243$	−2.78445	−	15.3378i	−0.178623	−	0.983918i
$244$		0			0
$245$	−5.32199	+	1.93704i	−0.340009	+	0.123753i
$246$		0			0
$247$	−2.09547	−	2.49728i	−0.133331	−	0.158898i
$248$		0			0
$249$	13.5612	+	3.36664i	0.859407	+	0.213352i
$250$		0			0
$251$	12.4670	+	7.19782i	0.786910	+	0.454323i	0.838874	−	0.544326i	$-0.183215\pi$
$251$	12.4670	+	7.19782i	0.786910	+	0.454323i	−0.0519636	+	0.998649i	$0.516548\pi$
$252$		0			0
$253$	26.9884	−	15.5817i	1.69674	−	0.979615i
$254$		0			0
$255$	−13.2653	+	1.40779i	−0.830704	+	0.0881594i
$256$		0			0
$257$	1.76587	−	4.85170i	0.110152	−	0.302641i	−0.872353	−	0.488877i	$-0.837407\pi$
$257$	1.76587	−	4.85170i	0.110152	−	0.302641i	0.982505	+	0.186236i	$0.0596289\pi$
$258$		0			0
$259$	−0.249467	+	1.41480i	−0.0155011	+	0.0879113i
$260$		0			0
$261$	10.4156	+	11.5207i	0.644707	+	0.713116i
$262$		0			0
$263$	0.180828	+	0.151733i	0.0111503	+	0.00935624i	0.648346	−	0.761346i	$-0.275461\pi$
$263$	0.180828	+	0.151733i	0.0111503	+	0.00935624i	−0.637195	+	0.770702i	$0.719906\pi$
$264$		0			0
$265$	−7.66600	−	43.4761i	−0.470919	−	2.67071i
$266$		0			0
$267$	23.9876	−	11.7296i	1.46802	−	0.717837i
$268$		0			0
$269$	−18.1431			−1.10620			−0.553102	−	0.833114i	$-0.686556\pi$
$269$	−18.1431			−1.10620			−0.553102	+	0.833114i	$0.686556\pi$
$270$		0			0
$271$		−	7.29313i		−	0.443026i	−0.975157	−	0.221513i	$-0.928900\pi$
$271$		−	7.29313i		−	0.443026i	0.975157	−	0.221513i	$-0.0710995\pi$
$272$		0			0
$273$	−3.04344	−	0.209727i	−0.184197	−	0.0126933i
$274$		0			0
$275$	22.4495	−	3.95846i	1.35376	−	0.238704i
$276$		0			0
$277$	−8.65619	+	10.3160i	−0.520100	+	0.619831i	−0.960604	−	0.277920i	$-0.910355\pi$
$277$	−8.65619	+	10.3160i	−0.520100	+	0.619831i	0.440505	+	0.897750i	$0.354800\pi$
$278$		0			0
$279$	1.02188	−	1.93128i	0.0611781	−	0.115623i
$280$		0			0
$281$	8.48774	+	1.49662i	0.506336	+	0.0892807i	0.420980	−	0.907070i	$-0.361686\pi$
$281$	8.48774	+	1.49662i	0.506336	+	0.0892807i	0.0853558	+	0.996351i	$0.472797\pi$
$282$		0			0
$283$	−25.0099	−	9.10286i	−1.48668	−	0.541109i	−0.534110	−	0.845415i	$-0.679353\pi$
$283$	−25.0099	−	9.10286i	−1.48668	−	0.541109i	−0.952574	+	0.304306i	$0.901575\pi$
$284$		0			0
$285$	−25.7669	+	18.7606i	−1.52630	+	1.11128i
$286$		0			0
$287$	−2.78139	−	4.81751i	−0.164180	−	0.284369i
$288$		0			0
$289$	−5.89623	+	10.2126i	−0.346837	+	0.600739i
$290$		0			0
$291$	−12.0288	−	11.5926i	−0.705141	−	0.679571i
$292$		0			0
$293$	−5.26423	+	4.41721i	−0.307540	+	0.258056i	−0.783474	−	0.621424i	$-0.786554\pi$
$293$	−5.26423	+	4.41721i	−0.307540	+	0.258056i	0.475935	+	0.879481i	$0.342110\pi$
$294$		0			0
$295$	8.26186	+	22.6993i	0.481024	+	1.32160i
$296$		0			0
$297$	−17.2068	−	6.89138i	−0.998440	−	0.399879i
$298$		0			0
$299$	−1.78647	−	4.90828i	−0.103314	−	0.283853i
$300$		0			0
$301$	−11.0707	−	13.1935i	−0.638103	−	0.760462i
$302$		0			0
$303$	3.44851	−	0.992616i	0.198111	−	0.0570243i
$304$		0			0
$305$	−26.1256	−	15.0836i	−1.49595	−	0.863685i
$306$		0			0
$307$	−2.12558	−	3.68162i	−0.121314	−	0.210121i	0.798972	−	0.601368i	$-0.205377\pi$
$307$	−2.12558	−	3.68162i	−0.121314	−	0.210121i	−0.920286	+	0.391247i	$0.872044\pi$
$308$		0			0
$309$	−3.90558	+	8.79598i	−0.222181	+	0.500386i
$310$		0			0
$311$	−1.79911	−	0.654823i	−0.102018	−	0.0371316i	0.290507	−	0.956873i	$-0.406176\pi$
$311$	−1.79911	−	0.654823i	−0.102018	−	0.0371316i	−0.392525	+	0.919741i	$0.628398\pi$
$312$		0			0
$313$	3.78761	−	21.4806i	0.214088	−	1.21415i	−0.668393	−	0.743808i	$-0.733018\pi$
$313$	3.78761	−	21.4806i	0.214088	−	1.21415i	0.882482	−	0.470347i	$-0.155871\pi$
$314$		0			0
$315$	−4.09135	+	29.5447i	−0.230522	+	1.66466i
$316$		0			0
$317$	−0.457251	−	0.383679i	−0.0256818	−	0.0215496i	0.629856	−	0.776712i	$-0.283114\pi$
$317$	−0.457251	−	0.383679i	−0.0256818	−	0.0215496i	−0.655538	+	0.755162i	$0.727558\pi$
$318$		0			0
$319$	18.1866	−	3.20679i	1.01825	−	0.179546i
$320$		0			0
$321$	17.0300	+	11.4619i	0.950524	+	0.639740i
$322$		0			0
$323$		−	12.4425i		−	0.692322i
$324$		0			0
$325$		−	3.82080i		−	0.211940i
$326$		0			0
$327$	−8.05892	−	5.42397i	−0.445659	−	0.299946i
$328$		0			0
$329$	−14.6760	+	2.58778i	−0.809115	+	0.142669i
$330$		0			0
$331$	3.25579	+	2.73193i	0.178954	+	0.150161i	0.727865	−	0.685721i	$-0.240513\pi$
$331$	3.25579	+	2.73193i	0.178954	+	0.150161i	−0.548911	+	0.835881i	$0.684957\pi$
$332$		0			0
$333$	1.15470	+	0.898397i	0.0632771	+	0.0492319i
$334$		0			0
$335$	−1.74163	+	9.87725i	−0.0951552	+	0.539652i
$336$		0			0
$337$	4.55155	+	1.65663i	0.247939	+	0.0902424i	0.463000	−	0.886358i	$-0.346773\pi$
$337$	4.55155	+	1.65663i	0.247939	+	0.0902424i	−0.215061	+	0.976601i	$0.568995\pi$
$338$		0			0
$339$	−0.897003	+	2.02019i	−0.0487185	+	0.109722i
$340$		0			0
$341$	−1.29902	−	2.24997i	−0.0703458	−	0.121842i
$342$		0			0
$343$	13.5772	+	7.83879i	0.733099	+	0.423255i
$344$		0			0
$345$	−49.0761	+	14.1260i	−2.64217	+	0.760521i
$346$		0			0
$347$	13.5458	+	16.1432i	0.727176	+	0.866615i	0.995307	−	0.0967678i	$-0.0308504\pi$
$347$	13.5458	+	16.1432i	0.727176	+	0.866615i	−0.268131	+	0.963382i	$0.586406\pi$
$348$		0			0
$349$	−6.80166	−	18.6874i	−0.364084	−	1.00031i	−0.977571	−	0.210608i	$-0.932456\pi$
$349$	−6.80166	−	18.6874i	−0.364084	−	1.00031i	0.613486	−	0.789705i	$-0.289767\pi$
$350$		0			0
$351$	−1.63832	+	2.63963i	−0.0874468	+	0.140893i
$352$		0			0
$353$	7.96814	+	21.8923i	0.424101	+	1.16521i	0.949339	+	0.314253i	$0.101754\pi$
$353$	7.96814	+	21.8923i	0.424101	+	1.16521i	−0.525238	+	0.850955i	$0.676024\pi$
$354$		0			0
$355$	8.67527	−	7.27942i	0.460436	−	0.386351i
$356$		0			0
$357$	−8.38392	−	8.07990i	−0.443724	−	0.427633i
$358$		0			0
$359$	−5.84236	+	10.1193i	−0.308348	+	0.534075i	−0.978001	−	0.208599i	$-0.933110\pi$
$359$	−5.84236	+	10.1193i	−0.308348	+	0.534075i	0.669653	+	0.742674i	$0.266443\pi$
$360$		0			0
$361$	−5.36466	−	9.29186i	−0.282351	−	0.489045i
$362$		0			0
$363$	−2.41488	+	1.75824i	−0.126748	+	0.0922839i
$364$		0			0
$365$	35.4729	+	12.9111i	1.85674	+	0.675797i
$366$		0			0
$367$	−3.28119	−	0.578562i	−0.171277	−	0.0302007i	0.0873521	−	0.996178i	$-0.472159\pi$
$367$	−3.28119	−	0.578562i	−0.171277	−	0.0302007i	−0.258629	+	0.965977i	$0.583271\pi$
$368$		0			0
$369$	−5.66116	+	0.209150i	−0.294708	+	0.0108879i
$370$		0			0
$371$	24.7689	−	29.5185i	1.28594	−	1.53252i
$372$		0			0
$373$	−34.7339	+	6.12453i	−1.79845	+	0.317116i	−0.970030	−	0.242985i	$-0.921874\pi$
$373$	−34.7339	+	6.12453i	−1.79845	+	0.317116i	−0.828425	+	0.560101i	$0.810762\pi$
$374$		0			0
$375$	−8.10898	−	0.558800i	−0.418746	−	0.0288563i
$376$		0			0
$377$		−	3.09527i		−	0.159414i
$378$		0			0
$379$	−15.7785			−0.810486			−0.405243	−	0.914209i	$-0.632813\pi$
$379$	−15.7785			−0.810486			−0.405243	+	0.914209i	$0.632813\pi$
$380$		0			0
$381$	10.3551	−	5.06348i	0.530508	−	0.259410i
$382$		0			0
$383$	−1.89462	−	10.7449i	−0.0968106	−	0.549040i	−0.994177	−	0.107755i	$-0.965634\pi$
$383$	−1.89462	−	10.7449i	−0.0968106	−	0.549040i	0.897367	−	0.441285i	$-0.145477\pi$
$384$		0			0
$385$	27.1681	+	22.7968i	1.38462	+	1.16183i
$386$		0			0
$387$	−17.1488	+	3.68133i	−0.871720	+	0.187132i
$388$		0			0
$389$	−4.60469	+	26.1145i	−0.233467	+	1.32406i	0.612352	+	0.790586i	$0.290224\pi$
$389$	−4.60469	+	26.1145i	−0.233467	+	1.32406i	−0.845818	+	0.533471i	$0.820887\pi$
$390$		0			0
$391$	6.81854	−	18.7338i	0.344828	−	0.947408i
$392$		0			0
$393$	−28.5676	+	3.03177i	−1.44104	+	0.152932i
$394$		0			0
$395$	−49.4942	+	28.5755i	−2.49032	+	1.43779i
$396$		0			0
$397$	21.7835	+	12.5767i	1.09328	+	0.631208i	0.934449	−	0.356098i	$-0.115893\pi$
$397$	21.7835	+	12.5767i	1.09328	+	0.631208i	0.158835	+	0.987305i	$0.449226\pi$
$398$		0			0
$399$	−27.0009	−	6.70311i	−1.35174	−	0.335575i
$400$		0			0
$401$	13.8988	+	16.5639i	0.694071	+	0.827162i	0.991842	−	0.127475i	$-0.0406874\pi$
$401$	13.8988	+	16.5639i	0.694071	+	0.827162i	−0.297770	+	0.954638i	$0.596243\pi$
$402$		0			0
$403$	−0.409194	+	0.148934i	−0.0203834	+	0.00741895i
$404$		0			0
$405$	24.6457	+	17.7544i	1.22466	+	0.882222i
$406$		0			0
$407$	1.63471	−	0.594984i	0.0810293	−	0.0294923i
$408$		0			0
$409$	11.4354	−	9.59540i	0.565442	−	0.474462i	−0.314688	−	0.949195i	$-0.601900\pi$
$409$	11.4354	−	9.59540i	0.565442	−	0.474462i	0.880130	+	0.474733i	$0.157455\pi$
$410$		0			0
$411$	31.5335	+	7.82834i	1.55543	+	0.386144i
$412$		0			0
$413$	−10.5424	+	18.2599i	−0.518755	+	0.898510i
$414$		0			0
$415$	−23.5791	+	13.6134i	−1.15745	+	0.668254i
$416$		0			0
$417$	0.140552	+	1.32438i	0.00688284	+	0.0648552i
$418$		0			0
$419$	5.14629	−	14.1393i	0.251413	−	0.690751i	−0.748214	−	0.663457i	$-0.769089\pi$
$419$	5.14629	−	14.1393i	0.251413	−	0.690751i	0.999627	−	0.0272945i	$-0.00868919\pi$
$420$		0			0
$421$	5.74293	+	1.01263i	0.279893	+	0.0493527i	0.311832	−	0.950137i	$-0.399057\pi$
$421$	5.74293	+	1.01263i	0.279893	+	0.0493527i	−0.0319393	+	0.999490i	$0.510168\pi$
$422$		0			0
$423$	−4.66055	+	14.4430i	−0.226604	+	0.702241i
$424$		0			0
$425$	9.37384	−	11.1713i	0.454698	−	0.541888i
$426$		0			0
$427$	−4.57243	−	25.9315i	−0.221275	−	1.25491i
$428$		0			0
$429$	1.62272	+	3.31856i	0.0783458	+	0.160222i
$430$		0			0
$431$	−2.52134			−0.121449			−0.0607244	−	0.998155i	$-0.519341\pi$
$431$	−2.52134			−0.121449			−0.0607244	+	0.998155i	$0.519341\pi$
$432$		0			0
$433$	−32.6249			−1.56785			−0.783927	−	0.620854i	$-0.786786\pi$
$433$	−32.6249			−1.56785			−0.783927	+	0.620854i	$0.786786\pi$
$434$		0			0
$435$	−30.1912	−	2.08051i	−1.44756	−	0.0997530i
$436$		0			0
$437$	−8.27153	−	46.9102i	−0.395681	−	2.24402i
$438$		0			0
$439$	−6.25287	+	7.45188i	−0.298433	+	0.355659i	−0.894335	−	0.447399i	$-0.852350\pi$
$439$	−6.25287	+	7.45188i	−0.298433	+	0.355659i	0.595901	+	0.803058i	$0.296795\pi$
$440$		0			0
$441$	−4.26392	+	2.67639i	−0.203044	+	0.127447i
$442$		0			0
$443$	17.6810	+	3.11764i	0.840050	+	0.148123i	0.577087	−	0.816683i	$-0.304189\pi$
$443$	17.6810	+	3.11764i	0.840050	+	0.148123i	0.262963	+	0.964806i	$0.415300\pi$
$444$		0			0
$445$	−17.7952	+	48.8919i	−0.843574	+	2.31770i
$446$		0			0
$447$	−4.22900	+	3.07908i	−0.200025	+	0.145635i
$448$		0			0
$449$	−5.44960	+	3.14633i	−0.257182	+	0.148484i	−0.623049	−	0.782183i	$-0.714106\pi$
$449$	−5.44960	+	3.14633i	−0.257182	+	0.148484i	0.365866	+	0.930667i	$0.380773\pi$
$450$		0			0
$451$	−3.36801	+	5.83356i	−0.158593	+	0.274691i
$452$		0			0
$453$	−2.57935	+	2.67640i	−0.121188	+	0.125748i
$454$		0			0
$455$	4.55363	−	3.82095i	0.213477	−	0.179129i
$456$		0			0
$457$	−26.0970	+	9.49851i	−1.22076	+	0.444322i	−0.870425	−	0.492301i	$-0.836156\pi$
$457$	−26.0970	+	9.49851i	−1.22076	+	0.444322i	−0.350339	+	0.936623i	$0.613934\pi$
$458$		0			0
$459$	−11.2661	+	3.69839i	−0.525858	+	0.172626i
$460$		0			0
$461$	31.8699	−	11.5997i	1.48433	−	0.540251i	0.532379	−	0.846506i	$-0.321298\pi$
$461$	31.8699	−	11.5997i	1.48433	−	0.540251i	0.951950	+	0.306255i	$0.0990759\pi$
$462$		0			0
$463$	−24.5141	−	29.2148i	−1.13927	−	1.35773i	−0.924555	−	0.381049i	$-0.875563\pi$
$463$	−24.5141	−	29.2148i	−1.13927	−	1.35773i	−0.214712	−	0.976677i	$-0.568881\pi$
$464$		0			0
$465$	1.17766	+	4.09138i	0.0546127	+	0.189733i
$466$		0			0
$467$	13.7803	+	7.95604i	0.637674	+	0.368161i	0.783718	−	0.621117i	$-0.213321\pi$
$467$	13.7803	+	7.95604i	0.637674	+	0.368161i	−0.146044	+	0.989278i	$0.546654\pi$
$468$		0			0
$469$	−7.58152	+	4.37719i	−0.350082	+	0.202120i
$470$		0			0
$471$	5.48991	−	12.3642i	0.252962	−	0.569711i
$472$		0			0
$473$	−7.13294	+	19.5976i	−0.327973	+	0.901099i
$474$		0			0
$475$	6.05057	−	34.3145i	0.277619	−	1.57446i
$476$		0			0
$477$	−14.7738	−	36.3546i	−0.676444	−	1.66456i
$478$		0			0
$479$	9.67464	+	8.11798i	0.442045	+	0.370920i	0.836474	−	0.548006i	$-0.184613\pi$
$479$	9.67464	+	8.11798i	0.442045	+	0.370920i	−0.394429	+	0.918927i	$0.629058\pi$
$480$		0			0
$481$	−0.0506316	−	0.287146i	−0.00230860	−	0.0130927i
$482$		0			0
$483$	−36.9799	−	24.8889i	−1.68264	−	1.13249i
$484$		0			0
$485$	32.5518			1.47810
$486$		0			0
$487$			0.979490i			0.0443849i	0.999754	+	0.0221925i	$0.00706466\pi$
$487$			0.979490i			0.0443849i	−0.999754	+	0.0221925i	$0.992935\pi$
$488$		0			0
$489$	12.4859	−	18.5515i	0.564631	−	0.838927i
$490$		0			0
$491$	2.99103	−	0.527400i	0.134983	−	0.0238012i	−0.105748	−	0.994393i	$-0.533724\pi$
$491$	2.99103	−	0.527400i	0.134983	−	0.0238012i	0.240732	+	0.970592i	$0.422613\pi$
$492$		0			0
$493$	7.59385	−	9.04999i	0.342010	−	0.407591i
$494$		0			0
$495$	33.4599	−	13.5974i	1.50391	−	0.611159i
$496$		0			0
$497$	9.73469	+	1.71649i	0.436660	+	0.0769950i
$498$		0			0
$499$	11.5067	+	4.18808i	0.515109	+	0.187484i	0.586477	−	0.809966i	$-0.300514\pi$
$499$	11.5067	+	4.18808i	0.515109	+	0.187484i	−0.0713684	+	0.997450i	$0.522737\pi$
$500$		0			0
$501$	23.9726	+	10.6443i	1.07102	+	0.475551i
$502$		0			0
$503$	18.8493	+	32.6480i	0.840450	+	1.45570i	0.889515	+	0.456906i	$0.151042\pi$
$503$	18.8493	+	32.6480i	0.840450	+	1.45570i	−0.0490653	+	0.998796i	$0.515624\pi$
$504$		0			0
$505$	−3.49620	+	6.05559i	−0.155579	+	0.269470i
$506$		0			0
$507$	−21.0431	+	6.05704i	−0.934558	+	0.269003i
$508$		0			0
$509$	5.48541	−	4.60281i	0.243137	−	0.204016i	−0.513074	−	0.858345i	$-0.671493\pi$
$509$	5.48541	−	4.60281i	0.243137	−	0.204016i	0.756210	+	0.654329i	$0.227049\pi$
$510$		0			0
$511$	11.2695	+	30.9626i	0.498532	+	1.36971i
$512$		0			0
$513$	−18.8938	+	21.1120i	−0.834180	+	0.932119i
$514$		0			0
$515$	−6.41388	−	17.6220i	−0.282630	−	0.776518i
$516$		0			0
$517$	11.5994	+	13.8236i	0.510140	+	0.607961i
$518$		0			0
$519$	22.5319	+	21.7148i	0.989038	+	0.953173i
$520$		0			0
$521$	11.2996	+	6.52385i	0.495046	+	0.285815i	0.726665	−	0.686992i	$-0.241069\pi$
$521$	11.2996	+	6.52385i	0.495046	+	0.285815i	−0.231619	+	0.972806i	$0.574402\pi$
$522$		0			0
$523$	−9.72356	−	16.8417i	−0.425181	−	0.736436i	0.571256	−	0.820772i	$-0.306456\pi$
$523$	−9.72356	−	16.8417i	−0.425181	−	0.736436i	−0.996437	+	0.0843361i	$0.973123\pi$
$524$		0			0
$525$	−19.1924	−	26.3599i	−0.837623	−	1.15044i
$526$		0			0
$527$	−1.56180	−	0.568448i	−0.0680330	−	0.0247620i
$528$		0			0
$529$	9.25917	−	52.5113i	0.402572	−	2.28310i
$530$		0			0
$531$	11.4153	+	18.1864i	0.495383	+	0.789223i
$532$		0			0
$533$	0.864878	+	0.725718i	0.0374620	+	0.0314344i
$534$		0			0
$535$	−39.3919	+	6.94586i	−1.70306	+	0.300296i
$536$		0			0
$537$	0.806909	−	11.7094i	0.0348207	−	0.505298i
$538$		0			0
$539$			5.98604i			0.257837i
$540$		0			0
$541$			8.91838i			0.383431i	0.981451	+	0.191716i	$0.0614051\pi$
$541$			8.91838i			0.383431i	−0.981451	+	0.191716i	$0.938595\pi$
$542$		0			0
$543$	14.9795	−	7.32474i	0.642832	−	0.314335i
$544$		0			0
$545$	18.6410	−	3.28691i	0.798491	−	0.140796i
$546$		0			0
$547$	10.8502	+	9.10444i	0.463923	+	0.389278i	0.844572	−	0.535442i	$-0.179855\pi$
$547$	10.8502	+	9.10444i	0.463923	+	0.389278i	−0.380649	+	0.924720i	$0.624299\pi$
$548$		0			0
$549$	−25.5197	−	8.23487i	−1.08916	−	0.351456i
$550$		0			0
$551$	4.90163	−	27.7985i	0.208816	−	1.18426i
$552$		0			0
$553$	−46.8760	−	17.0615i	−1.99337	−	0.725527i
$554$		0			0
$555$	−2.83485	+	0.300852i	−0.120333	+	0.0127705i
$556$		0			0
$557$	−14.2671	−	24.7114i	−0.604517	−	1.04705i	−0.992128	−	0.125231i	$-0.960033\pi$
$557$	−14.2671	−	24.7114i	−0.604517	−	1.04705i	0.387611	−	0.921823i	$-0.373300\pi$
$558$		0			0
$559$	3.02723	+	1.74777i	0.128038	+	0.0739229i
$560$		0			0
$561$	−3.39712	+	13.6840i	−0.143426	+	0.577739i
$562$		0			0
$563$	−3.67507	−	4.37978i	−0.154886	−	0.184586i	0.683022	−	0.730398i	$-0.260666\pi$
$563$	−3.67507	−	4.37978i	−0.154886	−	0.184586i	−0.837907	+	0.545813i	$0.816221\pi$
$564$		0			0
$565$	−1.47309	−	4.04728i	−0.0619734	−	0.170271i
$566$		0			0
$567$	1.95634	+	26.4405i	0.0821588	+	1.11040i
$568$		0			0
$569$	−11.0377	−	30.3258i	−0.462723	−	1.27132i	−0.923429	−	0.383769i	$-0.874626\pi$
$569$	−11.0377	−	30.3258i	−0.462723	−	1.27132i	0.460706	−	0.887553i	$-0.347596\pi$
$570$		0			0
$571$	3.60436	−	3.02442i	0.150838	−	0.126568i	−0.564246	−	0.825607i	$-0.690833\pi$
$571$	3.60436	−	3.02442i	0.150838	−	0.126568i	0.715084	+	0.699039i	$0.246389\pi$
$572$		0			0
$573$	−0.416868	+	1.67919i	−0.0174149	+	0.0701493i
$574$		0			0
$575$	27.9143	−	48.3489i	1.16411	−	2.01629i
$576$		0			0
$577$	−5.60346	−	9.70547i	−0.233275	−	0.404044i	0.725495	−	0.688227i	$-0.241611\pi$
$577$	−5.60346	−	9.70547i	−0.233275	−	0.404044i	−0.958770	+	0.284183i	$0.908278\pi$
$578$		0			0
$579$	−0.0881699	−	0.830803i	−0.00366422	−	0.0345270i
$580$		0			0
$581$	−22.3318	−	8.12809i	−0.926477	−	0.337210i
$582$		0			0
$583$	−45.9517	−	8.10253i	−1.90313	−	0.335573i
$584$		0			0
$585$	−1.27058	−	5.91874i	−0.0525319	−	0.244710i
$586$		0			0
$587$	−24.7159	+	29.4553i	−1.02013	+	1.21575i	−0.0438990	+	0.999036i	$0.513978\pi$
$587$	−24.7159	+	29.4553i	−1.02013	+	1.21575i	−0.976235	+	0.216713i	$0.930466\pi$
$588$		0			0
$589$	−3.91081	+	0.689581i	−0.161142	+	0.0284137i
$590$		0			0
$591$	−9.29416	−	19.0071i	−0.382311	−	0.781846i
$592$		0			0
$593$		−	13.0127i		−	0.534370i	−0.963645	−	0.267185i	$-0.913907\pi$
$593$		−	13.0127i		−	0.534370i	0.963645	−	0.267185i	$-0.0860934\pi$
$594$		0			0
$595$	22.6882			0.930125
$596$		0			0
$597$	−1.61463	+	23.4306i	−0.0660824	+	0.958949i
$598$		0			0
$599$	−1.26632	−	7.18164i	−0.0517403	−	0.293434i	0.947947	−	0.318427i	$-0.103155\pi$
$599$	−1.26632	−	7.18164i	−0.0517403	−	0.293434i	−0.999688	+	0.0249933i	$0.992044\pi$
$600$		0			0
$601$	24.0699	+	20.1971i	0.981833	+	0.823856i	0.984365	−	0.176141i	$-0.0563614\pi$
$601$	24.0699	+	20.1971i	0.981833	+	0.823856i	−0.00253165	+	0.999997i	$0.500806\pi$
$602$		0			0
$603$	0.329148	+	8.90920i	0.0134040	+	0.362811i
$604$		0			0
$605$	1.01074	−	5.73217i	0.0410923	−	0.233046i
$606$		0			0
$607$	−9.22172	+	25.3365i	−0.374298	+	1.02838i	0.599383	+	0.800462i	$0.295412\pi$
$607$	−9.22172	+	25.3365i	−0.374298	+	1.02838i	−0.973681	+	0.227913i	$0.926810\pi$
$608$		0			0
$609$	−15.5479	−	21.3545i	−0.630034	−	0.865327i
$610$		0			0
$611$	2.61936	−	1.51229i	0.105968	−	0.0611807i
$612$		0			0
$613$	3.01282	+	1.73945i	0.121687	+	0.0702559i	0.559608	−	0.828758i	$-0.310952\pi$
$613$	3.01282	+	1.73945i	0.121687	+	0.0702559i	−0.437921	+	0.899013i	$0.644285\pi$
$614$		0			0
$615$	7.65999	−	7.94821i	0.308880	−	0.320503i
$616$		0			0
$617$	23.1805	+	27.6254i	0.933210	+	1.11216i	0.993484	+	0.113975i	$0.0363584\pi$
$617$	23.1805	+	27.6254i	0.933210	+	1.11216i	−0.0602731	+	0.998182i	$0.519197\pi$
$618$		0			0
$619$	−20.9325	+	7.61881i	−0.841349	+	0.306226i	−0.726508	−	0.687158i	$-0.758858\pi$
$619$	−20.9325	+	7.61881i	−0.841349	+	0.306226i	−0.114841	+	0.993384i	$0.536636\pi$
$620$		0			0
$621$	−40.0163	+	21.4329i	−1.60580	+	0.860075i
$622$		0			0
$623$	−42.6755	+	15.5326i	−1.70976	+	0.622301i
$624$		0			0
$625$	−12.3442	+	10.3580i	−0.493768	+	0.414320i
$626$		0			0
$627$	9.31841	+	32.3736i	0.372141	+	1.29288i
$628$		0			0
$629$	0.556439	−	0.963781i	0.0221867	−	0.0384285i
$630$		0			0
$631$	8.28573	−	4.78377i	0.329850	−	0.190439i	−0.325925	−	0.945396i	$-0.605676\pi$
$631$	8.28573	−	4.78377i	0.329850	−	0.190439i	0.655774	+	0.754957i	$0.272342\pi$
$632$		0			0
$633$	−21.6441	−	9.61039i	−0.860278	−	0.381979i
$634$		0			0
$635$	−7.68193	+	21.1059i	−0.304848	+	0.837563i
$636$		0			0
$637$	0.988073	+	0.174224i	0.0391489	+	0.00690300i
$638$		0			0
$639$	6.18152	−	7.94504i	0.244537	−	0.314301i
$640$		0			0
$641$	1.06709	−	1.27171i	0.0421477	−	0.0502297i	−0.744559	−	0.667557i	$-0.767340\pi$
$641$	1.06709	−	1.27171i	0.0421477	−	0.0502297i	0.786706	+	0.617327i	$0.211785\pi$
$642$		0			0
$643$	−5.71286	−	32.3993i	−0.225293	−	1.27770i	−0.862124	−	0.506698i	$-0.830866\pi$
$643$	−5.71286	−	32.3993i	−0.225293	−	1.27770i	0.636830	−	0.771004i	$-0.280245\pi$
$644$		0			0
$645$	19.0825	−	28.3528i	0.751374	−	1.11639i
$646$		0			0
$647$	25.6189			1.00718			0.503592	−	0.863942i	$-0.332012\pi$
$647$	25.6189			1.00718			0.503592	+	0.863942i	$0.332012\pi$
$648$		0			0
$649$	25.5316			1.00220
$650$		0			0
$651$	−2.07494	+	3.08294i	−0.0813233	+	0.120830i
$652$		0			0
$653$	7.68220	+	43.5679i	0.300628	+	1.70495i	0.643403	+	0.765528i	$0.277522\pi$
$653$	7.68220	+	43.5679i	0.300628	+	1.70495i	−0.342775	+	0.939417i	$0.611367\pi$
$654$		0			0
$655$	35.9818	−	42.8815i	1.40593	−	1.67552i
$656$		0			0
$657$	33.2381	+	4.60282i	1.29674	+	0.179573i
$658$		0			0
$659$	28.0225	+	4.94113i	1.09160	+	0.192479i	0.690341	−	0.723484i	$-0.257461\pi$
$659$	28.0225	+	4.94113i	1.09160	+	0.192479i	0.401262	+	0.915963i	$0.368572\pi$
$660$		0			0
$661$	10.5767	−	29.0592i	0.411385	−	1.13027i	−0.545069	−	0.838391i	$-0.683497\pi$
$661$	10.5767	−	29.0592i	0.411385	−	1.13027i	0.956455	−	0.291881i	$-0.0942811\pi$
$662$		0			0
$663$	2.15985	+	0.959012i	0.0838815	+	0.0372449i
$664$		0			0
$665$	46.9468	−	27.1048i	1.82052	−	1.05108i
$666$		0			0
$667$	22.6137	−	39.1680i	0.875604	−	1.51659i
$668$		0			0
$669$	2.62390	+	9.11583i	0.101446	+	0.352438i
$670$		0			0
$671$	−24.4253	+	20.4953i	−0.942930	+	0.791212i
$672$		0			0
$673$	−5.42191	+	1.97341i	−0.208999	+	0.0760695i	−0.444398	−	0.895829i	$-0.646583\pi$
$673$	−5.42191	+	1.97341i	−0.208999	+	0.0760695i	0.235399	+	0.971899i	$0.424360\pi$
$674$		0			0
$675$	−32.8686	+	4.72105i	−1.26511	+	0.181713i
$676$		0			0
$677$	−38.0136	+	13.8358i	−1.46098	+	0.531754i	−0.945635	−	0.325229i	$-0.894559\pi$
$677$	−38.0136	+	13.8358i	−1.46098	+	0.531754i	−0.515346	+	0.856982i	$0.672336\pi$
$678$		0			0
$679$	18.2635	+	21.7656i	0.700889	+	0.835287i
$680$		0			0
$681$	13.2073	−	13.7042i	0.506103	−	0.525146i
$682$		0			0
$683$	6.34298	+	3.66212i	0.242707	+	0.140127i	0.616420	−	0.787417i	$-0.288582\pi$
$683$	6.34298	+	3.66212i	0.242707	+	0.140127i	−0.373713	+	0.927544i	$0.621916\pi$
$684$		0			0
$685$	−54.8277	+	31.6548i	−2.09486	+	1.20947i
$686$		0			0
$687$	26.8497	+	36.8770i	1.02438	+	1.40694i
$688$		0			0
$689$	−2.67485	+	7.34910i	−0.101904	+	0.279978i
$690$		0			0
$691$	4.43476	−	25.1508i	0.168706	−	0.956781i	−0.776454	−	0.630174i	$-0.782984\pi$
$691$	4.43476	−	25.1508i	0.168706	−	0.956781i	0.945160	−	0.326607i	$-0.105905\pi$
$692$		0			0
$693$	27.8648	+	14.7438i	1.05850	+	0.560072i
$694$		0			0
$695$	−1.98797	−	1.66810i	−0.0754079	−	0.0632748i
$696$		0			0
$697$	0.748285	+	4.24373i	0.0283433	+	0.160743i
$698$		0			0
$699$	1.14463	−	16.6102i	0.0432938	−	0.628254i
$700$		0			0
$701$	−19.0555			−0.719715			−0.359857	−	0.933007i	$-0.617175\pi$
$701$	−19.0555			−0.719715			−0.359857	+	0.933007i	$0.617175\pi$
$702$		0			0
$703$		−	2.65903i		−	0.100287i
$704$		0			0
$705$	−12.9902	−	26.5657i	−0.489240	−	1.00052i
$706$		0			0
$707$	−6.01061	+	1.05983i	−0.226052	+	0.0398591i
$708$		0			0
$709$	20.4893	−	24.4183i	0.769494	−	0.917047i	−0.228915	−	0.973447i	$-0.573518\pi$
$709$	20.4893	−	24.4183i	0.769494	−	0.917047i	0.998408	+	0.0563997i	$0.0179621\pi$
$710$		0			0
$711$	−37.6838	+	34.0689i	−1.41325	+	1.27768i
$712$		0			0
$713$	−6.26610	−	1.10488i	−0.234667	−	0.0413782i
$714$		0			0
$715$	−6.76394	−	2.46187i	−0.252957	−	0.0920689i
$716$		0			0
$717$	2.62851	+	24.7678i	0.0981636	+	0.924970i
$718$		0			0
$719$	16.9767	+	29.4045i	0.633124	+	1.09660i	0.986909	+	0.161277i	$0.0515611\pi$
$719$	16.9767	+	29.4045i	0.633124	+	1.09660i	−0.353785	+	0.935327i	$0.615106\pi$
$720$		0			0
$721$	8.18429	−	14.1756i	0.304799	−	0.527927i
$722$		0			0
$723$	−5.62874	+	22.6732i	−0.209335	+	0.843227i
$724$		0			0
$725$	25.3434	−	21.2656i	0.941230	−	0.789786i
$726$		0			0
$727$	−17.7280	−	48.7074i	−0.657497	−	1.80646i	−0.587979	−	0.808876i	$-0.700076\pi$
$727$	−17.7280	−	48.7074i	−0.657497	−	1.80646i	−0.0695178	−	0.997581i	$-0.522146\pi$
$728$		0			0
$729$	24.7319	+	10.8321i	0.915995	+	0.401189i
$730$		0			0
$731$	4.56313	+	12.5371i	0.168773	+	0.463701i
$732$		0			0
$733$	2.97953	+	3.55086i	0.110051	+	0.131154i	0.818258	−	0.574851i	$-0.194940\pi$
$733$	2.97953	+	3.55086i	0.110051	+	0.131154i	−0.708207	+	0.706005i	$0.750496\pi$
$734$		0			0
$735$	2.36352	−	9.52055i	0.0871798	−	0.351171i
$736$		0			0
$737$	9.18051	+	5.30037i	0.338168	+	0.195242i
$738$		0			0
$739$	25.0295	+	43.3524i	0.920726	+	1.59474i	0.798295	+	0.602266i	$0.205736\pi$
$739$	25.0295	+	43.3524i	0.920726	+	1.59474i	0.122430	+	0.992477i	$0.460931\pi$
$740$		0			0
$741$	5.61490	−	0.595888i	0.206268	−	0.0218905i
$742$		0			0
$743$	−11.2170	−	4.08266i	−0.411512	−	0.149778i	0.127964	−	0.991779i	$-0.459156\pi$
$743$	−11.2170	−	4.08266i	−0.411512	−	0.149778i	−0.539477	+	0.842000i	$0.681378\pi$
$744$		0			0
$745$	1.77002	−	10.0383i	0.0648487	−	0.367775i
$746$		0			0
$747$	−17.9526	+	16.2304i	−0.656851	+	0.593840i
$748$		0			0
$749$	−26.7455	−	22.4422i	−0.977260	−	0.820019i
$750$		0			0
$751$	19.4858	−	3.43587i	0.711046	−	0.125377i	0.193585	−	0.981083i	$-0.437988\pi$
$751$	19.4858	−	3.43587i	0.711046	−	0.125377i	0.517461	+	0.855707i	$0.326877\pi$
$752$		0			0
$753$	−22.3995	+	10.9530i	−0.816282	+	0.399149i
$754$		0			0
$755$		−	7.24276i		−	0.263591i
$756$		0			0
$757$		−	16.3318i		−	0.593590i	−0.954941	−	0.296795i	$-0.904082\pi$
$757$		−	16.3318i		−	0.593590i	0.954941	−	0.296795i	$-0.0959178\pi$
$758$		0			0
$759$	−3.71080	+	53.8490i	−0.134694	+	1.95460i
$760$		0			0
$761$	40.2204	−	7.09194i	1.45799	−	0.257082i	0.612242	−	0.790670i	$-0.290268\pi$
$761$	40.2204	−	7.09194i	1.45799	−	0.257082i	0.845745	+	0.533588i	$0.179157\pi$
$762$		0			0
$763$	12.6565	+	10.6200i	0.458195	+	0.384471i
$764$		0			0
$765$	10.8060	−	20.4225i	0.390690	−	0.738378i
$766$		0			0
$767$	0.743098	−	4.21432i	0.0268317	−	0.152170i
$768$		0			0
$769$	23.2382	+	8.45800i	0.837989	+	0.305003i	0.725134	−	0.688608i	$-0.241778\pi$
$769$	23.2382	+	8.45800i	0.837989	+	0.305003i	0.112856	+	0.993611i	$0.464000\pi$
$770$		0			0
$771$	5.26370	+	7.22948i	0.189567	+	0.260363i
$772$		0			0
$773$	−9.22148	−	15.9721i	−0.331674	−	0.574475i	0.651167	−	0.758935i	$-0.274280\pi$
$773$	−9.22148	−	15.9721i	−0.331674	−	0.574475i	−0.982840	+	0.184459i	$0.940947\pi$
$774$		0			0
$775$	−4.03076	−	2.32716i	−0.144789	−	0.0835940i
$776$		0			0
$777$	−1.79168	−	1.72671i	−0.0642763	−	0.0619455i
$778$		0			0
$779$	6.61820	+	7.88727i	0.237122	+	0.282591i
$780$		0			0
$781$	−4.09386	−	11.2478i	−0.146490	−	0.402477i
$782$		0			0
$783$	−26.6272	+	3.82457i	−0.951578	+	0.136679i
$784$		0			0
$785$	9.01574	+	24.7705i	0.321786	+	0.884099i
$786$		0			0
$787$	25.2598	−	21.1955i	0.900415	−	0.755538i	−0.0698563	−	0.997557i	$-0.522254\pi$
$787$	25.2598	−	21.1955i	0.900415	−	0.755538i	0.970272	+	0.242019i	$0.0778096\pi$
$788$		0			0
$789$	−0.392905	+	0.113094i	−0.0139878	+	0.00402624i
$790$		0			0
$791$	1.87970	−	3.25574i	0.0668345	−	0.115761i
$792$		0			0
$793$	2.67211	+	4.62823i	0.0948895	+	0.164353i
$794$		0			0
$795$	69.8851	+	31.0303i	2.47857	+	1.10053i
$796$		0			0
$797$	−24.1141	−	8.77682i	−0.854166	−	0.310891i	−0.122428	−	0.992477i	$-0.539068\pi$
$797$	−24.1141	−	8.77682i	−0.854166	−	0.310891i	−0.731738	+	0.681586i	$0.761290\pi$
$798$		0			0
$799$	11.3687	+	2.00462i	0.402197	+	0.0709182i
$800$		0			0
$801$	−6.34402	+	45.8117i	−0.224155	+	1.61868i
$802$		0			0
$803$	25.6466	−	30.5644i	0.905049	−	1.07860i
$804$		0			0
$805$	85.5378	−	15.0826i	3.01481	−	0.531592i
$806$		0			0
$807$	17.5462	−	26.0701i	0.617654	−	0.917709i
$808$		0			0
$809$			35.5723i			1.25066i	0.780362	+	0.625328i	$0.215035\pi$
$809$			35.5723i			1.25066i	−0.780362	+	0.625328i	$0.784965\pi$
$810$		0			0
$811$	−5.98290			−0.210088			−0.105044	−	0.994468i	$-0.533498\pi$
$811$	−5.98290			−0.210088			−0.105044	+	0.994468i	$0.533498\pi$
$812$		0			0
$813$	10.4796	+	7.05318i	0.367535	+	0.247366i
$814$		0			0
$815$	7.56640	+	42.9112i	0.265039	+	1.50311i
$816$		0			0
$817$	24.4197	+	20.4906i	0.854338	+	0.716875i
$818$		0			0
$819$	3.24467	−	4.17033i	0.113378	−	0.145723i
$820$		0			0
$821$	1.31505	−	7.45804i	0.0458957	−	0.260287i	−0.953223	−	0.302269i	$-0.902256\pi$
$821$	1.31505	−	7.45804i	0.0458957	−	0.260287i	0.999118	+	0.0419816i	$0.0133671\pi$
$822$		0			0
$823$	8.60702	−	23.6476i	0.300022	−	0.824303i	−0.694473	−	0.719519i	$-0.744363\pi$
$823$	8.60702	−	23.6476i	0.300022	−	0.824303i	0.994495	−	0.104784i	$-0.0334152\pi$
$824$		0			0
$825$	−16.0230	+	36.0863i	−0.557848	+	1.25636i
$826$		0			0
$827$	−2.17911	+	1.25811i	−0.0757749	+	0.0437487i	−0.537409	−	0.843322i	$-0.680597\pi$
$827$	−2.17911	+	1.25811i	−0.0757749	+	0.0437487i	0.461634	+	0.887071i	$0.347263\pi$
$828$		0			0
$829$	23.0116	+	13.2858i	0.799227	+	0.461434i	0.843201	−	0.537599i	$-0.180668\pi$
$829$	23.0116	+	13.2858i	0.799227	+	0.461434i	−0.0439737	+	0.999033i	$0.514002\pi$
$830$		0			0
$831$	−6.45187	−	22.4148i	−0.223813	−	0.777562i
$832$		0			0
$833$	2.46151	+	2.93351i	0.0852862	+	0.101640i
$834$		0			0
$835$	−48.0271	+	17.4804i	−1.66205	+	0.604935i
$836$		0			0
$837$	1.78682	+	3.33608i	0.0617616	+	0.115312i
$838$		0			0
$839$	20.0868	−	7.31100i	0.693473	−	0.252404i	0.0288517	−	0.999584i	$-0.490815\pi$
$839$	20.0868	−	7.31100i	0.693473	−	0.252404i	0.664622	+	0.747180i	$0.268593\pi$
$840$		0			0
$841$	−1.68433	+	1.41332i	−0.0580803	+	0.0487351i
$842$		0			0
$843$	−10.3590	+	10.7488i	−0.356783	+	0.370207i
$844$		0			0
$845$	21.3341	−	36.9518i	0.733916	−	1.27118i
$846$		0			0
$847$	4.39987	−	2.54026i	0.151181	−	0.0872845i
$848$		0			0
$849$	37.2671	−	27.1337i	1.27900	−	0.931226i
$850$		0			0
$851$	1.45716	−	4.00350i	0.0499507	−	0.137238i
$852$		0			0
$853$	−10.2340	−	1.80454i	−0.350407	−	0.0617861i	−0.00432523	−	0.999991i	$-0.501377\pi$
$853$	−10.2340	−	1.80454i	−0.350407	−	0.0617861i	−0.346081	+	0.938205i	$0.612488\pi$
$854$		0			0
$855$	−2.03818	−	55.1682i	−0.0697041	−	1.88671i
$856$		0			0
$857$	−18.8893	+	22.5114i	−0.645245	+	0.768973i	−0.985189	−	0.171472i	$-0.945148\pi$
$857$	−18.8893	+	22.5114i	−0.645245	+	0.768973i	0.339944	+	0.940446i	$0.389592\pi$
$858$		0			0
$859$	−2.76131	−	15.6602i	−0.0942148	−	0.534319i	−0.994985	−	0.100023i	$-0.968108\pi$
$859$	−2.76131	−	15.6602i	−0.0942148	−	0.534319i	0.900770	−	0.434296i	$-0.143003\pi$
$860$		0			0
$861$	9.61223	+	0.662391i	0.327584	+	0.0225742i
$862$		0			0
$863$	−25.8291			−0.879233			−0.439617	−	0.898185i	$-0.644886\pi$
$863$	−25.8291			−0.879233			−0.439617	+	0.898185i	$0.644886\pi$
$864$		0			0
$865$	−60.9747			−2.07320
$866$		0			0
$867$	−8.97234	−	18.3489i	−0.304717	−	0.623162i
$868$		0			0
$869$	10.4893	+	59.4876i	0.355824	+	2.01798i
$870$		0			0
$871$	1.14209	−	1.36109i	0.0386984	−	0.0461189i
$872$		0			0
$873$	28.2906	−	6.07315i	0.957493	−	0.205545i
$874$		0			0
$875$	13.6144	+	2.40058i	0.460250	+	0.0811546i
$876$		0			0
$877$	4.98502	−	13.6962i	0.168332	−	0.462489i	−0.826629	−	0.562747i	$-0.809745\pi$
$877$	4.98502	−	13.6962i	0.168332	−	0.462489i	0.994961	+	0.100258i	$0.0319668\pi$
$878$		0			0
$879$	−1.25612	−	11.8361i	−0.0423680	−	0.399223i
$880$		0			0
$881$	−10.8614	+	6.27081i	−0.365929	+	0.211269i	−0.671678	−	0.740843i	$-0.734426\pi$
$881$	−10.8614	+	6.27081i	−0.365929	+	0.211269i	0.305750	+	0.952112i	$0.401093\pi$
$882$		0			0
$883$	−14.5195	+	25.1485i	−0.488620	+	0.846315i	−0.999914	−	0.0130911i	$-0.995833\pi$
$883$	−14.5195	+	25.1485i	−0.488620	+	0.846315i	0.511294	+	0.859406i	$0.329166\pi$
$884$		0			0
$885$	−40.6069	−	10.0809i	−1.36499	−	0.338865i
$886$		0			0
$887$	16.1110	−	13.5188i	0.540955	−	0.453915i	−0.330909	−	0.943663i	$-0.607355\pi$
$887$	16.1110	−	13.5188i	0.540955	−	0.453915i	0.871864	+	0.489747i	$0.162911\pi$
$888$		0			0
$889$	−18.4224	+	6.70520i	−0.617867	+	0.224885i
$890$		0			0
$891$	26.5430	−	18.0600i	0.889224	−	0.605034i
$892$		0			0
$893$	25.9193	−	9.43384i	0.867355	−	0.315692i
$894$		0			0
$895$	14.7008	+	17.5197i	0.491394	+	0.585620i
$896$		0			0
$897$	8.78047	+	2.17979i	0.293171	+	0.0727812i
$898$		0			0
$899$	−3.26536	−	1.88526i	−0.108906	−	0.0628768i
$900$		0			0
$901$	−25.8509	+	14.9250i	−0.861217	+	0.497224i
$902$		0			0
$903$	29.6644	−	3.14817i	0.987169	−	0.104765i
$904$		0			0
$905$	−11.1125	+	30.5315i	−0.369393	+	1.01490i
$906$		0			0
$907$	1.09570	−	6.21403i	0.0363822	−	0.206333i	−0.961198	−	0.275859i	$-0.911038\pi$
$907$	1.09570	−	6.21403i	0.0363822	−	0.206333i	0.997580	+	0.0695260i	$0.0221487\pi$
$908$		0			0
$909$	−1.90874	+	5.91516i	−0.0633090	+	0.196194i
$910$		0			0
$911$	−30.4836	−	25.5788i	−1.00997	−	0.847463i	−0.0216332	−	0.999766i	$-0.506887\pi$
$911$	−30.4836	−	25.5788i	−1.00997	−	0.847463i	−0.988334	+	0.152303i	$0.951331\pi$
$912$		0			0
$913$	4.99710	+	28.3399i	0.165380	+	0.937915i
$914$		0			0
$915$	46.9398	−	22.9528i	1.55178	−	0.758798i
$916$		0			0
$917$	48.8604			1.61351
$918$		0			0
$919$		−	43.2414i		−	1.42640i	−0.700960	−	0.713201i	$-0.747245\pi$
$919$		−	43.2414i		−	1.42640i	0.700960	−	0.713201i	$-0.252755\pi$
$920$		0			0
$921$	7.34582	+	0.506210i	0.242053	+	0.0166802i
$922$		0			0
$923$	−1.97574	+	0.348377i	−0.0650324	+	0.0114670i
$924$		0			0
$925$	2.00323	−	2.38736i	0.0658659	−	0.0784960i
$926$		0			0
$927$	−8.86199	−	14.1186i	−0.291066	−	0.463714i
$928$		0			0
$929$	−4.34064	−	0.765372i	−0.142412	−	0.0251111i	0.101988	−	0.994786i	$-0.467480\pi$
$929$	−4.34064	−	0.765372i	−0.142412	−	0.0251111i	−0.244400	+	0.969675i	$0.578591\pi$
$930$		0			0
$931$	8.59796	+	3.12940i	0.281787	+	0.102562i
$932$		0			0
$933$	2.68084	−	1.95189i	0.0877668	−	0.0639020i
$934$		0			0
$935$	−13.7366	−	23.7925i	−0.449236	−	0.778099i
$936$		0			0
$937$	0.581707	−	1.00755i	0.0190035	−	0.0329151i	−0.856367	−	0.516367i	$-0.827284\pi$
$937$	0.581707	−	1.00755i	0.0190035	−	0.0329151i	0.875371	+	0.483452i	$0.160617\pi$
$938$		0			0
$939$	27.2028	+	26.2163i	0.887728	+	0.855537i
$940$		0			0
$941$	24.6581	−	20.6906i	0.803833	−	0.674496i	−0.145295	−	0.989388i	$-0.546413\pi$
$941$	24.6581	−	20.6906i	0.803833	−	0.674496i	0.949127	+	0.314893i	$0.101969\pi$
$942$		0			0
$943$	5.64228	+	15.5021i	0.183738	+	0.504816i
$944$		0			0
$945$	−38.4964	−	34.4516i	−1.25229	−	1.12071i
$946$		0			0
$947$	9.21146	+	25.3083i	0.299332	+	0.822408i	0.994612	+	0.103669i	$0.0330583\pi$
$947$	9.21146	+	25.3083i	0.299332	+	0.822408i	−0.695280	+	0.718739i	$0.744719\pi$
$948$		0			0
$949$	−4.29861	−	5.12288i	−0.139539	−	0.166296i
$950$		0			0
$951$	0.993520	−	0.285974i	0.0322171	−	0.00927335i
$952$		0			0
$953$	−24.2787	−	14.0173i	−0.786465	−	0.454066i	0.0522513	−	0.998634i	$-0.483360\pi$
$953$	−24.2787	−	14.0173i	−0.786465	−	0.454066i	−0.838717	+	0.544568i	$0.816694\pi$
$954$		0			0
$955$	−1.68565	−	2.91963i	−0.0545464	−	0.0944771i
$956$		0			0
$957$	−12.9804	+	29.2339i	−0.419596	+	0.944997i
$958$		0			0
$959$	−51.9274	−	18.9000i	−1.67682	−	0.610313i
$960$		0			0
$961$	5.29098	−	30.0066i	0.170677	−	0.967956i
$962$		0			0
$963$	−32.9395	+	13.3859i	−1.06146	+	0.431355i
$964$		0			0
$965$	1.24708	+	1.04642i	0.0401449	+	0.0336856i
$966$		0			0
$967$	−46.5149	+	8.20184i	−1.49582	+	0.263753i	−0.860880	−	0.508809i	$-0.830086\pi$
$967$	−46.5149	+	8.20184i	−1.49582	+	0.263753i	−0.634940	+	0.772562i	$0.718975\pi$
$968$		0			0
$969$	17.8789	+	12.0332i	0.574352	+	0.386561i
$970$		0			0
$971$			3.24802i			0.104234i	0.998641	+	0.0521170i	$0.0165969\pi$
$971$			3.24802i			0.104234i	−0.998641	+	0.0521170i	$0.983403\pi$
$972$		0			0
$973$		−	2.26515i		−	0.0726173i
$974$		0			0
$975$	5.49015	+	3.69509i	0.175826	+	0.118337i
$976$		0			0
$977$	25.4482	−	4.48720i	0.814160	−	0.143558i	0.248962	−	0.968513i	$-0.419911\pi$
$977$	25.4482	−	4.48720i	0.814160	−	0.143558i	0.565198	+	0.824955i	$0.308800\pi$
$978$		0			0
$979$	42.1267	+	35.3485i	1.34637	+	1.12974i
$980$		0			0
$981$	15.5875	−	6.33446i	0.497672	−	0.202244i
$982$		0			0
$983$	5.64306	−	32.0034i	0.179986	−	1.02075i	−0.752244	−	0.658884i	$-0.771029\pi$
$983$	5.64306	−	32.0034i	0.179986	−	1.02075i	0.932230	−	0.361866i	$-0.117860\pi$
$984$		0			0
$985$	38.7405	+	14.1004i	1.23438	+	0.449276i
$986$		0			0
$987$	10.4747	−	23.5908i	0.333415	−	0.750904i
$988$		0			0
$989$	25.5381	+	44.2332i	0.812063	+	1.40653i
$990$		0			0
$991$	4.42071	+	2.55230i	0.140429	+	0.0810765i	0.568568	−	0.822636i	$-0.307498\pi$
$991$	4.42071	+	2.55230i	0.140429	+	0.0810765i	−0.428140	+	0.903713i	$0.640831\pi$
$992$		0			0
$993$	−7.07422	+	2.03624i	−0.224494	+	0.0646181i
$994$		0			0
$995$	−29.4164	−	35.0571i	−0.932562	−	1.11138i
$996$		0			0
$997$	11.4461	+	31.4478i	0.362501	+	0.995963i	0.978142	+	0.207937i	$0.0666748\pi$
$997$	11.4461	+	31.4478i	0.362501	+	0.995963i	−0.615641	+	0.788026i	$0.711103\pi$
$998$		0			0
$999$	−2.40763	+	0.790364i	−0.0761740	+	0.0250060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.47.9		192
4.3	odd	2		216.2.v.b.155.17	yes	192
8.3	odd	2	inner	864.2.bh.b.47.10		192
8.5	even	2		216.2.v.b.155.10	yes	192
12.11	even	2		648.2.v.b.467.16		192
24.5	odd	2		648.2.v.b.467.23		192
27.23	odd	18	inner	864.2.bh.b.239.10		192
108.23	even	18		216.2.v.b.131.10	✓	192
108.31	odd	18		648.2.v.b.179.23		192
216.77	odd	18		216.2.v.b.131.17	yes	192
216.85	even	18		648.2.v.b.179.16		192
216.131	even	18	inner	864.2.bh.b.239.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.10	✓	192	108.23	even	18
216.2.v.b.131.17	yes	192	216.77	odd	18
216.2.v.b.155.10	yes	192	8.5	even	2
216.2.v.b.155.17	yes	192	4.3	odd	2
648.2.v.b.179.16		192	216.85	even	18
648.2.v.b.179.23		192	108.31	odd	18
648.2.v.b.467.16		192	12.11	even	2
648.2.v.b.467.23		192	24.5	odd	2
864.2.bh.b.47.9		192	1.1	even	1	trivial
864.2.bh.b.47.10		192	8.3	odd	2	inner
864.2.bh.b.239.9		192	216.131	even	18	inner
864.2.bh.b.239.10		192	27.23	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.967099 + 1.43691i) q^{3} +(-0.586059 - 3.32370i) q^{5} +(1.89356 - 2.25666i) q^{7} +(-1.12944 - 2.77927i) q^{9} +O(q^{10})\)	\(q+(-0.967099 + 1.43691i) q^{3} +(-0.586059 - 3.32370i) q^{5} +(1.89356 - 2.25666i) q^{7} +(-1.12944 - 2.77927i) q^{9} +(-3.51297 - 0.619431i) q^{11} +(-0.204490 + 0.561832i) q^{13} +(5.34265 + 2.37223i) q^{15} +(-1.97627 + 1.14100i) q^{17} +(-2.72623 + 4.72197i) q^{19} +(1.41136 + 4.90330i) q^{21} +(-6.69233 + 5.61553i) q^{23} +(-6.00508 + 2.18567i) q^{25} +(5.08586 + 1.06492i) q^{27} +(-4.86478 + 1.77064i) q^{29} +(0.468156 + 0.557926i) q^{31} +(4.28745 - 4.44878i) q^{33} +(-8.61021 - 4.97111i) q^{35} +(-0.422340 + 0.243838i) q^{37} +(-0.609542 - 0.837181i) q^{39} +(0.645850 - 1.77446i) q^{41} +(1.01523 - 5.75766i) q^{43} +(-8.57557 + 5.38274i) q^{45} +(-3.87524 - 3.25171i) q^{47} +(-0.291398 - 1.65260i) q^{49} +(0.271731 - 3.94320i) q^{51} +13.0806 q^{53} +12.0391i q^{55} +(-4.14853 - 8.48397i) q^{57} +(-7.04866 + 1.24287i) q^{59} +(5.74555 - 6.84728i) q^{61} +(-8.41054 - 2.71397i) q^{63} +(1.98721 + 0.350398i) q^{65} +(-2.79254 - 1.01640i) q^{67} +(-1.59689 - 15.0471i) q^{69} +(1.67775 + 2.90596i) q^{71} +(-5.59255 + 9.68658i) q^{73} +(2.66689 - 10.7425i) q^{75} +(-8.04987 + 6.75464i) q^{77} +(-5.79167 - 15.9125i) q^{79} +(-6.44873 + 6.27805i) q^{81} +(-2.75916 - 7.58072i) q^{83} +(4.95057 + 5.89986i) q^{85} +(2.16047 - 8.70265i) q^{87} +(-13.3509 - 7.70815i) q^{89} +(0.880649 + 1.52533i) q^{91} +(-1.25444 + 0.133129i) q^{93} +(17.2922 + 6.29383i) q^{95} +(-1.67485 + 9.49852i) q^{97} +(2.24612 + 10.4631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 192 * q + 12 * q^3 - 12 * q^9	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more