LMFDB - Embedded newform 864.2.y.a.193.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, 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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.7
Character	$\chi$	$=$	864.193
Dual form			864.2.y.a.385.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46485 + 0.924244i) q^{3} +(-0.217354 + 1.23268i) q^{5} +(2.00770 - 1.68466i) q^{7} +(1.29155 + 2.70775i) q^{9} +O(q^{10})$	\(q+(1.46485 + 0.924244i) q^{3} +(-0.217354 + 1.23268i) q^{5} +(2.00770 - 1.68466i) q^{7} +(1.29155 + 2.70775i) q^{9} +(-0.0755572 - 0.428506i) q^{11} +(0.140798 - 0.0512461i) q^{13} +(-1.45769 + 1.60480i) q^{15} +(2.14919 - 3.72251i) q^{17} +(3.46096 + 5.99456i) q^{19} +(4.49801 - 0.612165i) q^{21} +(1.58087 + 1.32651i) q^{23} +(3.22621 + 1.17424i) q^{25} +(-0.610701 + 5.16014i) q^{27} +(-8.62346 - 3.13868i) q^{29} +(0.439495 + 0.368780i) q^{31} +(0.285364 - 0.697529i) q^{33} +(1.64026 + 2.84102i) q^{35} +(1.47714 - 2.55848i) q^{37} +(0.253611 + 0.0550635i) q^{39} +(-4.70068 + 1.71091i) q^{41} +(0.773643 + 4.38755i) q^{43} +(-3.61851 + 1.00352i) q^{45} +(5.17552 - 4.34278i) q^{47} +(-0.0227557 + 0.129054i) q^{49} +(6.58874 - 3.46653i) q^{51} -7.31935 q^{53} +0.544633 q^{55} +(-0.470659 + 11.9799i) q^{57} +(-1.82524 + 10.3515i) q^{59} +(6.60685 - 5.54381i) q^{61} +(7.15469 + 3.26053i) q^{63} +(0.0325670 + 0.184697i) q^{65} +(3.27428 - 1.19174i) q^{67} +(1.08972 + 3.40424i) q^{69} +(-1.25942 + 2.18139i) q^{71} +(-5.40834 - 9.36752i) q^{73} +(3.64061 + 4.70189i) q^{75} +(-0.873584 - 0.733024i) q^{77} +(-13.9853 - 5.09023i) q^{79} +(-5.66381 + 6.99437i) q^{81} +(3.90853 + 1.42259i) q^{83} +(4.12152 + 3.45837i) q^{85} +(-9.73114 - 12.5679i) q^{87} +(-2.90527 - 5.03208i) q^{89} +(0.196347 - 0.340083i) q^{91} +(0.302950 + 0.946407i) q^{93} +(-8.14162 + 2.96331i) q^{95} +(-2.44135 - 13.8456i) q^{97} +(1.06270 - 0.758026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{9}+O(q^{10}) $ 48 * q - 12 * q^9	$ 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) $ 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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
$3$	1.46485	+	0.924244i	0.845729	+	0.533612i
$3$	1.46485	+	0.924244i	0.845729	+	0.533612i
$4$		0			0
$5$	−0.217354	+	1.23268i	−0.0972038	+	0.551270i	0.896846	+	0.442343i	$0.145853\pi$
$5$	−0.217354	+	1.23268i	−0.0972038	+	0.551270i	−0.994050	+	0.108927i	$0.965258\pi$
$6$		0			0
$7$	2.00770	−	1.68466i	0.758840	−	0.636742i	−0.178985	−	0.983852i	$-0.557281\pi$
$7$	2.00770	−	1.68466i	0.758840	−	0.636742i	0.937825	+	0.347109i	$0.112837\pi$
$8$		0			0
$9$	1.29155	+	2.70775i	0.430516	+	0.902583i
$10$		0			0
$11$	−0.0755572	−	0.428506i	−0.0227813	−	0.129199i	0.971296	−	0.237874i	$-0.0764505\pi$
$11$	−0.0755572	−	0.428506i	−0.0227813	−	0.129199i	−0.994077	+	0.108674i	$0.965339\pi$
$12$		0			0
$13$	0.140798	−	0.0512461i	0.0390502	−	0.0142131i	−0.322421	−	0.946596i	$-0.604497\pi$
$13$	0.140798	−	0.0512461i	0.0390502	−	0.0142131i	0.361471	+	0.932383i	$0.382275\pi$
$14$		0			0
$15$	−1.45769	+	1.60480i	−0.376373	+	0.414356i
$16$		0			0
$17$	2.14919	−	3.72251i	0.521256	−	0.902841i	−0.478439	−	0.878121i	$-0.658797\pi$
$17$	2.14919	−	3.72251i	0.521256	−	0.902841i	0.999694	−	0.0247203i	$-0.00786951\pi$
$18$		0			0
$19$	3.46096	+	5.99456i	0.793999	+	1.37525i	0.923473	+	0.383664i	$0.125338\pi$
$19$	3.46096	+	5.99456i	0.793999	+	1.37525i	−0.129473	+	0.991583i	$0.541329\pi$
$20$		0			0
$21$	4.49801	−	0.612165i	0.981547	−	0.133585i
$22$		0			0
$23$	1.58087	+	1.32651i	0.329634	+	0.276596i	0.792551	−	0.609806i	$-0.208753\pi$
$23$	1.58087	+	1.32651i	0.329634	+	0.276596i	−0.462916	+	0.886402i	$0.653197\pi$
$24$		0			0
$25$	3.22621	+	1.17424i	0.645242	+	0.234849i
$26$		0			0
$27$	−0.610701	+	5.16014i	−0.117529	+	0.993069i
$28$		0			0
$29$	−8.62346	−	3.13868i	−1.60134	−	0.582839i	−0.621637	−	0.783306i	$-0.713532\pi$
$29$	−8.62346	−	3.13868i	−1.60134	−	0.582839i	−0.979701	+	0.200467i	$0.935754\pi$
$30$		0			0
$31$	0.439495	+	0.368780i	0.0789357	+	0.0662349i	0.681402	−	0.731910i	$-0.261371\pi$
$31$	0.439495	+	0.368780i	0.0789357	+	0.0662349i	−0.602466	+	0.798145i	$0.705815\pi$
$32$		0			0
$33$	0.285364	−	0.697529i	0.0496755	−	0.121424i
$34$		0			0
$35$	1.64026	+	2.84102i	0.277255	+	0.480220i
$36$		0			0
$37$	1.47714	−	2.55848i	0.242841	−	0.420612i	−0.718682	−	0.695339i	$-0.755254\pi$
$37$	1.47714	−	2.55848i	0.242841	−	0.420612i	0.961522	+	0.274727i	$0.0885875\pi$
$38$		0			0
$39$	0.253611	+	0.0550635i	0.0406102	+	0.00881722i
$40$		0			0
$41$	−4.70068	+	1.71091i	−0.734123	+	0.267199i	−0.681909	−	0.731437i	$-0.738850\pi$
$41$	−4.70068	+	1.71091i	−0.734123	+	0.267199i	−0.0522140	+	0.998636i	$0.516628\pi$
$42$		0			0
$43$	0.773643	+	4.38755i	0.117980	+	0.669095i	0.985232	+	0.171226i	$0.0547728\pi$
$43$	0.773643	+	4.38755i	0.117980	+	0.669095i	−0.867252	+	0.497869i	$0.834116\pi$
$44$		0			0
$45$	−3.61851	+	1.00352i	−0.539415	+	0.149596i
$46$		0			0
$47$	5.17552	−	4.34278i	0.754927	−	0.633459i	−0.181874	−	0.983322i	$-0.558216\pi$
$47$	5.17552	−	4.34278i	0.754927	−	0.633459i	0.936801	+	0.349863i	$0.113772\pi$
$48$		0			0
$49$	−0.0227557	+	0.129054i	−0.00325082	+	0.0184363i
$50$		0			0
$51$	6.58874	−	3.46653i	0.922608	−	0.485411i
$52$		0			0
$53$	−7.31935			−1.00539			−0.502695	−	0.864464i	$-0.667658\pi$
$53$	−7.31935			−1.00539			−0.502695	+	0.864464i	$0.667658\pi$
$54$		0			0
$55$	0.544633			0.0734383
$56$		0			0
$57$	−0.470659	+	11.9799i	−0.0623403	+	1.58677i
$58$		0			0
$59$	−1.82524	+	10.3515i	−0.237627	+	1.34765i	0.599384	+	0.800461i	$0.295412\pi$
$59$	−1.82524	+	10.3515i	−0.237627	+	1.34765i	−0.837011	+	0.547186i	$0.815699\pi$
$60$		0			0
$61$	6.60685	−	5.54381i	0.845921	−	0.709812i	−0.112966	−	0.993599i	$-0.536035\pi$
$61$	6.60685	−	5.54381i	0.845921	−	0.709812i	0.958887	+	0.283787i	$0.0915908\pi$
$62$		0			0
$63$	7.15469	+	3.26053i	0.901406	+	0.410788i
$64$		0			0
$65$	0.0325670	+	0.184697i	0.00403944	+	0.0229088i
$66$		0			0
$67$	3.27428	−	1.19174i	0.400018	−	0.145594i	−0.134174	−	0.990958i	$-0.542838\pi$
$67$	3.27428	−	1.19174i	0.400018	−	0.145594i	0.534192	+	0.845363i	$0.320616\pi$
$68$		0			0
$69$	1.08972	+	3.40424i	0.131186	+	0.409822i
$70$		0			0
$71$	−1.25942	+	2.18139i	−0.149466	+	0.258883i	−0.931030	−	0.364942i	$-0.881089\pi$
$71$	−1.25942	+	2.18139i	−0.149466	+	0.258883i	0.781564	+	0.623825i	$0.214422\pi$
$72$		0			0
$73$	−5.40834	−	9.36752i	−0.632999	−	1.09639i	−0.986935	−	0.161116i	$-0.948491\pi$
$73$	−5.40834	−	9.36752i	−0.632999	−	1.09639i	0.353937	−	0.935269i	$-0.384843\pi$
$74$		0			0
$75$	3.64061	+	4.70189i	0.420382	+	0.542928i
$76$		0			0
$77$	−0.873584	−	0.733024i	−0.0995542	−	0.0835359i
$78$		0			0
$79$	−13.9853	−	5.09023i	−1.57347	−	0.572696i	−0.599698	−	0.800226i	$-0.704713\pi$
$79$	−13.9853	−	5.09023i	−1.57347	−	0.572696i	−0.973771	+	0.227530i	$0.926935\pi$
$80$		0			0
$81$	−5.66381	+	6.99437i	−0.629312	+	0.777153i
$82$		0			0
$83$	3.90853	+	1.42259i	0.429017	+	0.156149i	0.547498	−	0.836807i	$-0.315580\pi$
$83$	3.90853	+	1.42259i	0.429017	+	0.156149i	−0.118481	+	0.992956i	$0.537803\pi$
$84$		0			0
$85$	4.12152	+	3.45837i	0.447042	+	0.375112i
$86$		0			0
$87$	−9.73114	−	12.5679i	−1.04329	−	1.34742i
$88$		0			0
$89$	−2.90527	−	5.03208i	−0.307958	−	0.533399i	0.669957	−	0.742400i	$-0.266312\pi$
$89$	−2.90527	−	5.03208i	−0.307958	−	0.533399i	−0.977916	+	0.209000i	$0.932979\pi$
$90$		0			0
$91$	0.196347	−	0.340083i	0.0205828	−	0.0356504i
$92$		0			0
$93$	0.302950	+	0.946407i	0.0314145	+	0.0981379i
$94$		0			0
$95$	−8.14162	+	2.96331i	−0.835313	+	0.304029i
$96$		0			0
$97$	−2.44135	−	13.8456i	−0.247881	−	1.40580i	−0.813705	−	0.581278i	$-0.802553\pi$
$97$	−2.44135	−	13.8456i	−0.247881	−	1.40580i	0.565824	−	0.824526i	$-0.308558\pi$
$98$		0			0
$99$	1.06270	−	0.758026i	0.106805	−	0.0761845i
$100$		0			0
$101$	−2.91700	+	2.44766i	−0.290253	+	0.243551i	−0.776273	−	0.630396i	$-0.782892\pi$
$101$	−2.91700	+	2.44766i	−0.290253	+	0.243551i	0.486021	+	0.873947i	$0.338448\pi$
$102$		0			0
$103$	0.915423	−	5.19162i	0.0901993	−	0.511546i	−0.905914	−	0.423462i	$-0.860815\pi$
$103$	0.915423	−	5.19162i	0.0901993	−	0.511546i	0.996113	−	0.0880835i	$-0.0280742\pi$
$104$		0			0
$105$	−0.223061	+	5.67766i	−0.0217685	+	0.554083i
$106$		0			0
$107$	13.3087			1.28660			0.643300	−	0.765614i	$-0.277565\pi$
$107$	13.3087			1.28660			0.643300	+	0.765614i	$0.277565\pi$
$108$		0			0
$109$	5.92489			0.567502			0.283751	−	0.958898i	$-0.408421\pi$
$109$	5.92489			0.567502			0.283751	+	0.958898i	$0.408421\pi$
$110$		0			0
$111$	4.52845	−	2.38255i	0.429821	−	0.226141i
$112$		0			0
$113$	1.95040	−	11.0613i	0.183478	−	1.04056i	−0.744416	−	0.667716i	$-0.767272\pi$
$113$	1.95040	−	11.0613i	0.183478	−	1.04056i	0.927895	−	0.372842i	$-0.121617\pi$
$114$		0			0
$115$	−1.97877	+	1.66038i	−0.184521	+	0.154831i
$116$		0			0
$117$	0.320608	+	0.315058i	0.0296402	+	0.0291271i
$118$		0			0
$119$	−1.95623	−	11.0944i	−0.179328	−	1.01702i
$120$		0			0
$121$	10.1587	−	3.69747i	0.923519	−	0.336133i
$122$		0			0
$123$	−8.46707	−	1.83836i	−0.763450	−	0.165759i
$124$		0			0
$125$	−5.27793	+	9.14165i	−0.472073	+	0.817654i
$126$		0			0
$127$	9.82310	+	17.0141i	0.871659	+	1.50976i	0.860279	+	0.509823i	$0.170289\pi$
$127$	9.82310	+	17.0141i	0.871659	+	1.50976i	0.0113799	+	0.999935i	$0.496378\pi$
$128$		0			0
$129$	−2.92190	+	7.14212i	−0.257259	+	0.628829i
$130$		0			0
$131$	−9.54637	−	8.01035i	−0.834070	−	0.699868i	0.122152	−	0.992511i	$-0.461021\pi$
$131$	−9.54637	−	8.01035i	−0.834070	−	0.699868i	−0.956222	+	0.292644i	$0.905465\pi$
$132$		0			0
$133$	17.0474	+	6.20475i	1.47820	+	0.538020i
$134$		0			0
$135$	−6.22805	−	1.87438i	−0.536025	−	0.161321i
$136$		0			0
$137$	−2.04197	−	0.743217i	−0.174457	−	0.0634973i	0.253315	−	0.967384i	$-0.418479\pi$
$137$	−2.04197	−	0.743217i	−0.174457	−	0.0634973i	−0.427772	+	0.903887i	$0.640701\pi$
$138$		0			0
$139$	−2.96384	−	2.48696i	−0.251390	−	0.210941i	0.508381	−	0.861132i	$-0.330244\pi$
$139$	−2.96384	−	2.48696i	−0.251390	−	0.210941i	−0.759771	+	0.650191i	$0.774689\pi$
$140$		0			0
$141$	11.5951	−	1.57806i	0.976485	−	0.132896i
$142$		0			0
$143$	−0.0325975	−	0.0564606i	−0.00272594	−	0.00472147i
$144$		0			0
$145$	5.74334	−	9.94775i	0.476958	−	0.826116i
$146$		0			0
$147$	−0.152611	+	0.168012i	−0.0125871	+	0.0138574i
$148$		0			0
$149$	−13.5703	+	4.93919i	−1.11172	+	0.404634i	−0.831626	−	0.555337i	$-0.812589\pi$
$149$	−13.5703	+	4.93919i	−1.11172	+	0.404634i	−0.280098	+	0.959971i	$0.590367\pi$
$150$		0			0
$151$	−3.06746	−	17.3964i	−0.249626	−	1.41570i	−0.809499	−	0.587121i	$-0.800261\pi$
$151$	−3.06746	−	17.3964i	−0.249626	−	1.41570i	0.559873	−	0.828578i	$-0.310850\pi$
$152$		0			0
$153$	12.8554	+	1.01167i	1.03930	+	0.0817889i
$154$		0			0
$155$	−0.550114	+	0.461600i	−0.0441862	+	0.0370766i
$156$		0			0
$157$	2.35174	−	13.3374i	0.187690	−	1.06444i	−0.734761	−	0.678326i	$-0.762706\pi$
$157$	2.35174	−	13.3374i	0.187690	−	1.06444i	0.922451	−	0.386115i	$-0.126183\pi$
$158$		0			0
$159$	−10.7217	−	6.76486i	−0.850288	−	0.536489i
$160$		0			0
$161$	5.40864			0.426260
$162$		0			0
$163$	−12.0254			−0.941901			−0.470950	−	0.882160i	$-0.656089\pi$
$163$	−12.0254			−0.941901			−0.470950	+	0.882160i	$0.656089\pi$
$164$		0			0
$165$	0.797803	+	0.503373i	0.0621089	+	0.0391876i
$166$		0			0
$167$	0.603470	−	3.42245i	0.0466979	−	0.264837i	−0.952516	−	0.304490i	$-0.901514\pi$
$167$	0.603470	−	3.42245i	0.0466979	−	0.264837i	0.999214	+	0.0396527i	$0.0126252\pi$
$168$		0			0
$169$	−9.94138	+	8.34181i	−0.764722	+	0.641678i
$170$		0			0
$171$	−11.7618	+	17.1137i	−0.899445	+	1.30872i
$172$		0			0
$173$	−0.814505	−	4.61929i	−0.0619257	−	0.351198i	−0.999989	−	0.00473354i	$-0.998493\pi$
$173$	−0.814505	−	4.61929i	−0.0619257	−	0.351198i	0.938063	−	0.346464i	$-0.112618\pi$
$174$		0			0
$175$	8.45548	−	3.07754i	0.639174	−	0.232640i
$176$		0			0
$177$	−12.2410	+	13.4764i	−0.920089	+	1.01294i
$178$		0			0
$179$	3.38084	−	5.85579i	0.252696	−	0.437682i	−0.711571	−	0.702614i	$-0.752016\pi$
$179$	3.38084	−	5.85579i	0.252696	−	0.437682i	0.964267	+	0.264932i	$0.0853494\pi$
$180$		0			0
$181$	11.2936	+	19.5611i	0.839449	+	1.45397i	0.890356	+	0.455265i	$0.150456\pi$
$181$	11.2936	+	19.5611i	0.839449	+	1.45397i	−0.0509068	+	0.998703i	$0.516211\pi$
$182$		0			0
$183$	14.8019	−	2.01448i	1.09418	−	0.148915i
$184$		0			0
$185$	2.83272	+	2.37694i	0.208266	+	0.174756i
$186$		0			0
$187$	−1.75750	−	0.639679i	−0.128521	−	0.0467780i
$188$		0			0
$189$	7.46699	+	11.3888i	0.543143	+	0.828417i
$190$		0			0
$191$	−19.2482	−	7.00576i	−1.39275	−	0.506919i	−0.466731	−	0.884399i	$-0.654568\pi$
$191$	−19.2482	−	7.00576i	−1.39275	−	0.506919i	−0.926018	+	0.377480i	$0.876791\pi$
$192$		0			0
$193$	−9.21604	−	7.73318i	−0.663385	−	0.556646i	0.247714	−	0.968833i	$-0.420321\pi$
$193$	−9.21604	−	7.73318i	−0.663385	−	0.556646i	−0.911099	+	0.412187i	$0.864765\pi$
$194$		0			0
$195$	−0.122999	+	0.300652i	−0.00880814	+	0.0215301i
$196$		0			0
$197$	−6.04818	−	10.4758i	−0.430915	−	0.746367i	0.566037	−	0.824380i	$-0.308476\pi$
$197$	−6.04818	−	10.4758i	−0.430915	−	0.746367i	−0.996952	+	0.0780129i	$0.975142\pi$
$198$		0			0
$199$	1.22573	−	2.12302i	0.0868895	−	0.150497i	−0.819305	−	0.573357i	$-0.805641\pi$
$199$	1.22573	−	2.12302i	0.0868895	−	0.150497i	0.906195	+	0.422860i	$0.138974\pi$
$200$		0			0
$201$	5.89778	+	1.28052i	0.415998	+	0.0903207i
$202$		0			0
$203$	−22.6010	+	8.22608i	−1.58628	+	0.577358i
$204$		0			0
$205$	−1.08728	−	6.16630i	−0.0759393	−	0.430673i
$206$		0			0
$207$	−1.55008	+	5.99385i	−0.107738	+	0.416601i
$208$		0			0
$209$	2.30721	−	1.93598i	0.159593	−	0.133914i
$210$		0			0
$211$	4.62980	−	26.2569i	0.318728	−	1.80760i	−0.231780	−	0.972768i	$-0.574455\pi$
$211$	4.62980	−	26.2569i	0.318728	−	1.80760i	0.550508	−	0.834830i	$-0.314434\pi$
$212$		0			0
$213$	−3.86099	+	2.03138i	−0.264551	+	0.139188i
$214$		0			0
$215$	−5.57659			−0.380320
$216$		0			0
$217$	1.50365			0.102074
$218$		0			0
$219$	0.735485	−	18.7206i	0.0496994	−	1.26502i
$220$		0			0
$221$	0.111837	−	0.634258i	0.00752296	−	0.0426648i
$222$		0			0
$223$	−17.2166	+	14.4464i	−1.15291	+	0.967406i	−0.999784	−	0.0208011i	$-0.993378\pi$
$223$	−17.2166	+	14.4464i	−1.15291	+	0.967406i	−0.153125	+	0.988207i	$0.548934\pi$
$224$		0			0
$225$	0.987246	+	10.2524i	0.0658164	+	0.683491i
$226$		0			0
$227$	−5.16159	−	29.2728i	−0.342587	−	1.94291i	−0.332926	−	0.942953i	$-0.608036\pi$
$227$	−5.16159	−	29.2728i	−0.342587	−	1.94291i	−0.00966119	−	0.999953i	$-0.503075\pi$
$228$		0			0
$229$	5.19975	−	1.89255i	0.343609	−	0.125063i	−0.164451	−	0.986385i	$-0.552585\pi$
$229$	5.19975	−	1.89255i	0.343609	−	0.125063i	0.508060	+	0.861322i	$0.330363\pi$
$230$		0			0
$231$	−0.602173	−	1.88117i	−0.0396201	−	0.123772i
$232$		0			0
$233$	−2.65354	+	4.59607i	−0.173839	+	0.301099i	−0.939759	−	0.341838i	$-0.888951\pi$
$233$	−2.65354	+	4.59607i	−0.173839	+	0.301099i	0.765920	+	0.642936i	$0.222284\pi$
$234$		0			0
$235$	4.22832	+	7.32367i	0.275825	+	0.477743i
$236$		0			0
$237$	−15.7817	−	20.3822i	−1.02513	−	1.32397i
$238$		0			0
$239$	7.34432	+	6.16261i	0.475064	+	0.398626i	0.848638	−	0.528974i	$-0.177423\pi$
$239$	7.34432	+	6.16261i	0.475064	+	0.398626i	−0.373574	+	0.927601i	$0.621868\pi$
$240$		0			0
$241$	−8.99311	−	3.27322i	−0.579297	−	0.210847i	0.0357185	−	0.999362i	$-0.488628\pi$
$241$	−8.99311	−	3.27322i	−0.579297	−	0.210847i	−0.615015	+	0.788515i	$0.710850\pi$
$242$		0			0
$243$	−14.7611	+	5.01094i	−0.946926	+	0.321452i
$244$		0			0
$245$	−0.154136	−	0.0561009i	−0.00984739	−	0.00358416i
$246$		0			0
$247$	0.794493	+	0.666659i	0.0505524	+	0.0424185i
$248$		0			0
$249$	4.41057	+	5.69630i	0.279509	+	0.360989i
$250$		0			0
$251$	10.4773	+	18.1472i	0.661322	+	1.14544i	0.980269	+	0.197671i	$0.0633376\pi$
$251$	10.4773	+	18.1472i	0.661322	+	1.14544i	−0.318947	+	0.947773i	$0.603329\pi$
$252$		0			0
$253$	0.448971	−	0.777640i	0.0282265	−	0.0488898i
$254$		0			0
$255$	2.84102	+	8.87526i	0.177912	+	0.555790i
$256$		0			0
$257$	−2.50778	+	0.912758i	−0.156431	+	0.0569363i	−0.419049	−	0.907964i	$-0.637636\pi$
$257$	−2.50778	+	0.912758i	−0.156431	+	0.0569363i	0.262618	+	0.964900i	$0.415414\pi$
$258$		0			0
$259$	−1.34452	−	7.62516i	−0.0835445	−	0.473804i
$260$		0			0
$261$	−2.63885	−	27.4039i	−0.163341	−	1.69626i
$262$		0			0
$263$	19.4608	−	16.3295i	1.20000	−	1.00692i	0.200371	−	0.979720i	$-0.435785\pi$
$263$	19.4608	−	16.3295i	1.20000	−	1.00692i	0.999630	−	0.0272008i	$-0.00865934\pi$
$264$		0			0
$265$	1.59089	−	9.02241i	0.0977278	−	0.554242i
$266$		0			0
$267$	0.395090	−	10.0564i	0.0241791	−	0.615442i
$268$		0			0
$269$	−12.1250			−0.739271			−0.369636	−	0.929177i	$-0.620518\pi$
$269$	−12.1250			−0.739271			−0.369636	+	0.929177i	$0.620518\pi$
$270$		0			0
$271$	7.48386			0.454612			0.227306	−	0.973823i	$-0.427008\pi$
$271$	7.48386			0.454612			0.227306	+	0.973823i	$0.427008\pi$
$272$		0			0
$273$	0.601938	−	0.316697i	0.0364309	−	0.0191674i
$274$		0			0
$275$	0.259408	−	1.47117i	0.0156429	−	0.0887151i
$276$		0			0
$277$	−20.3515	+	17.0769i	−1.22280	+	1.02605i	−0.224128	+	0.974560i	$0.571953\pi$
$277$	−20.3515	+	17.0769i	−1.22280	+	1.02605i	−0.998673	+	0.0514928i	$0.983602\pi$
$278$		0			0
$279$	−0.430936	+	1.66634i	−0.0257994	+	0.0997612i
$280$		0			0
$281$	−1.31454	−	7.45511i	−0.0784187	−	0.444735i	−0.998584	−	0.0532038i	$-0.983057\pi$
$281$	−1.31454	−	7.45511i	−0.0784187	−	0.444735i	0.920165	−	0.391531i	$-0.128054\pi$
$282$		0			0
$283$	20.8522	−	7.58959i	1.23954	−	0.451154i	0.362683	−	0.931913i	$-0.381861\pi$
$283$	20.8522	−	7.58959i	1.23954	−	0.451154i	0.876853	+	0.480758i	$0.159639\pi$
$284$		0			0
$285$	−14.6650	−	3.18405i	−0.868682	−	0.188607i
$286$		0			0
$287$	−6.55527	+	11.3541i	−0.386945	+	0.670209i
$288$		0			0
$289$	−0.738052	−	1.27834i	−0.0434148	−	0.0751966i
$290$		0			0
$291$	9.22048	−	22.5380i	0.540514	−	1.32120i
$292$		0			0
$293$	−15.5524	−	13.0501i	−0.908584	−	0.762392i	0.0632654	−	0.997997i	$-0.479849\pi$
$293$	−15.5524	−	13.0501i	−0.908584	−	0.762392i	−0.971849	+	0.235605i	$0.924293\pi$
$294$		0			0
$295$	−12.3633	−	4.49988i	−0.719820	−	0.261993i
$296$		0			0
$297$	2.25729	−	0.128197i	0.130981	−	0.00743872i
$298$		0			0
$299$	0.290561	+	0.105756i	0.0168036	+	0.00611600i
$300$		0			0
$301$	8.94478	+	7.50557i	0.515569	+	0.432614i
$302$		0			0
$303$	−6.53519	+	0.889418i	−0.375437	+	0.0510958i
$304$		0			0
$305$	5.39770	+	9.34910i	0.309072	+	0.535328i
$306$		0			0
$307$	−7.06387	+	12.2350i	−0.403156	+	0.698287i	−0.994105	−	0.108422i	$-0.965420\pi$
$307$	−7.06387	+	12.2350i	−0.403156	+	0.698287i	0.590949	+	0.806709i	$0.298754\pi$
$308$		0			0
$309$	6.13928	−	6.75885i	0.349251	−	0.384498i
$310$		0			0
$311$	1.60764	−	0.585132i	0.0911607	−	0.0331798i	−0.296037	−	0.955176i	$-0.595665\pi$
$311$	1.60764	−	0.585132i	0.0911607	−	0.0331798i	0.387198	+	0.921997i	$0.373443\pi$
$312$		0			0
$313$	−1.34795	−	7.64463i	−0.0761909	−	0.432100i	−0.998912	−	0.0466321i	$-0.985151\pi$
$313$	−1.34795	−	7.64463i	−0.0761909	−	0.432100i	0.922721	−	0.385468i	$-0.125960\pi$
$314$		0			0
$315$	−5.57429	+	8.11073i	−0.314076	+	0.456988i
$316$		0			0
$317$	−10.7336	+	9.00657i	−0.602860	+	0.505859i	−0.892363	−	0.451318i	$-0.850954\pi$
$317$	−10.7336	+	9.00657i	−0.602860	+	0.505859i	0.289504	+	0.957177i	$0.406510\pi$
$318$		0			0
$319$	−0.693381	+	3.93236i	−0.0388219	+	0.220170i
$320$		0			0
$321$	19.4952	+	12.3005i	1.08812	+	0.686546i
$322$		0			0
$323$	29.7531			1.65551
$324$		0			0
$325$	0.514418			0.0285348
$326$		0			0
$327$	8.67906	+	5.47604i	0.479953	+	0.302826i
$328$		0			0
$329$	3.07479	−	17.4380i	0.169519	−	0.961388i
$330$		0			0
$331$	−21.0418	+	17.6562i	−1.15656	+	0.970470i	−0.999853	−	0.0171747i	$-0.994533\pi$
$331$	−21.0418	+	17.6562i	−1.15656	+	0.970470i	−0.156709	+	0.987645i	$0.550088\pi$
$332$		0			0
$333$	8.83553	+	0.695324i	0.484184	+	0.0381035i
$334$		0			0
$335$	0.757354	+	4.29517i	0.0413787	+	0.234670i
$336$		0			0
$337$	−14.5611	+	5.29982i	−0.793196	+	0.288700i	−0.706664	−	0.707549i	$-0.749801\pi$
$337$	−14.5611	+	5.29982i	−0.793196	+	0.288700i	−0.0865320	+	0.996249i	$0.527578\pi$
$338$		0			0
$339$	13.0804	−	14.4004i	0.710427	−	0.782124i
$340$		0			0
$341$	0.124818	−	0.216190i	0.00675925	−	0.0117074i
$342$		0			0
$343$	9.34477	+	16.1856i	0.504570	+	0.873941i
$344$		0			0
$345$	−4.43319	+	0.603342i	−0.238675	+	0.0324829i
$346$		0			0
$347$	−20.5878	−	17.2752i	−1.10521	−	0.927383i	−0.107447	−	0.994211i	$-0.534268\pi$
$347$	−20.5878	−	17.2752i	−1.10521	−	0.927383i	−0.997765	+	0.0668278i	$0.978712\pi$
$348$		0			0
$349$	15.2051	+	5.53421i	0.813911	+	0.296239i	0.715238	−	0.698881i	$-0.246318\pi$
$349$	15.2051	+	5.53421i	0.813911	+	0.296239i	0.0986726	+	0.995120i	$0.468540\pi$
$350$		0			0
$351$	0.178452	+	0.757831i	0.00952506	+	0.0404500i
$352$		0			0
$353$	28.3394	+	10.3147i	1.50835	+	0.548996i	0.958208	−	0.286072i	$-0.0923497\pi$
$353$	28.3394	+	10.3147i	1.50835	+	0.548996i	0.550146	+	0.835068i	$0.314572\pi$
$354$		0			0
$355$	−2.41521	−	2.02660i	−0.128186	−	0.107561i
$356$		0			0
$357$	7.38830	−	18.0596i	0.391030	−	0.955813i
$358$		0			0
$359$	18.3168	+	31.7257i	0.966725	+	1.67442i	0.704908	+	0.709299i	$0.250988\pi$
$359$	18.3168	+	31.7257i	0.966725	+	1.67442i	0.261817	+	0.965118i	$0.415678\pi$
$360$		0			0
$361$	−14.4565	+	25.0394i	−0.760870	+	1.31787i
$362$		0			0
$363$	18.2983	+	3.97290i	0.960412	+	0.208523i
$364$		0			0
$365$	12.7227	−	4.63067i	0.665935	−	0.242380i
$366$		0			0
$367$	−1.08778	−	6.16912i	−0.0567818	−	0.322026i	0.943165	−	0.332324i	$-0.107833\pi$
$367$	−1.08778	−	6.16912i	−0.0567818	−	0.322026i	−0.999947	+	0.0102988i	$0.996722\pi$
$368$		0			0
$369$	−10.7039	−	10.5185i	−0.557221	−	0.547574i
$370$		0			0
$371$	−14.6951	+	12.3306i	−0.762931	+	0.640175i
$372$		0			0
$373$	−5.77652	+	32.7603i	−0.299097	+	1.69626i	0.350970	+	0.936387i	$0.385852\pi$
$373$	−5.77652	+	32.7603i	−0.299097	+	1.69626i	−0.650067	+	0.759877i	$0.725259\pi$
$374$		0			0
$375$	−16.1805	+	8.51301i	−0.835556	+	0.439610i
$376$		0			0
$377$	−1.37501			−0.0708165
$378$		0			0
$379$	−8.45211			−0.434156			−0.217078	−	0.976154i	$-0.569653\pi$
$379$	−8.45211			−0.434156			−0.217078	+	0.976154i	$0.569653\pi$
$380$		0			0
$381$	−1.33585	+	34.0020i	−0.0684377	+	1.74197i
$382$		0			0
$383$	−6.74904	+	38.2757i	−0.344860	+	1.95580i	−0.0559842	+	0.998432i	$0.517830\pi$
$383$	−6.74904	+	38.2757i	−0.344860	+	1.95580i	−0.288876	+	0.957367i	$0.593281\pi$
$384$		0			0
$385$	1.09346	−	0.917522i	0.0557279	−	0.0467613i
$386$		0			0
$387$	−10.8812	+	7.76156i	−0.553122	+	0.394542i
$388$		0			0
$389$	1.03961	+	5.89591i	0.0527102	+	0.298935i	0.999754	−	0.0221692i	$-0.00705725\pi$
$389$	1.03961	+	5.89591i	0.0527102	+	0.298935i	−0.947044	+	0.321104i	$0.895946\pi$
$390$		0			0
$391$	8.33553	−	3.03389i	0.421546	−	0.153430i
$392$		0			0
$393$	−6.58044	−	20.5571i	−0.331939	−	1.03697i
$394$		0			0
$395$	9.31439	−	16.1330i	0.468658	−	0.811739i
$396$		0			0
$397$	−8.17528	−	14.1600i	−0.410306	−	0.710670i	0.584617	−	0.811309i	$-0.301245\pi$
$397$	−8.17528	−	14.1600i	−0.410306	−	0.710670i	−0.994923	+	0.100639i	$0.967911\pi$
$398$		0			0
$399$	19.2371	+	24.8449i	0.963060	+	1.24380i
$400$		0			0
$401$	26.0792	+	21.8831i	1.30233	+	1.09279i	0.989737	+	0.142902i	$0.0456435\pi$
$401$	26.0792	+	21.8831i	1.30233	+	1.09279i	0.312597	+	0.949886i	$0.398801\pi$
$402$		0			0
$403$	0.0807784	+	0.0294009i	0.00402386	+	0.00146457i
$404$		0			0
$405$	−7.39076	−	8.50191i	−0.367250	−	0.422463i
$406$		0			0
$407$	−1.20793	−	0.439652i	−0.0598751	−	0.0217927i
$408$		0			0
$409$	−3.99535	−	3.35250i	−0.197557	−	0.165770i	0.538643	−	0.842534i	$-0.318937\pi$
$409$	−3.99535	−	3.35250i	−0.197557	−	0.165770i	−0.736200	+	0.676764i	$0.763382\pi$
$410$		0			0
$411$	−2.30426	−	2.97598i	−0.113661	−	0.146794i
$412$		0			0
$413$	13.7742	+	23.8576i	0.677784	+	1.17396i
$414$		0			0
$415$	−2.60313	+	4.50875i	−0.127783	+	0.221326i
$416$		0			0
$417$	−2.04302	−	6.38233i	−0.100047	−	0.312544i
$418$		0			0
$419$	−16.8905	+	6.14764i	−0.825155	+	0.300332i	−0.719869	−	0.694110i	$-0.755798\pi$
$419$	−16.8905	+	6.14764i	−0.825155	+	0.300332i	−0.105286	+	0.994442i	$0.533576\pi$
$420$		0			0
$421$	−3.92389	−	22.2535i	−0.191239	−	1.08457i	−0.917674	−	0.397334i	$-0.869936\pi$
$421$	−3.92389	−	22.2535i	−0.191239	−	1.08457i	0.726436	−	0.687235i	$-0.241176\pi$
$422$		0			0
$423$	18.4436	+	8.40510i	0.896757	+	0.408670i
$424$		0			0
$425$	11.3049	−	9.48592i	0.548367	−	0.460135i
$426$		0			0
$427$	3.92515	−	22.2606i	0.189951	−	1.07727i
$428$		0			0
$429$	0.00443296	−	0.112834i	0.000214025	−	0.00544768i
$430$		0			0
$431$	31.5534			1.51987			0.759937	−	0.649997i	$-0.225230\pi$
$431$	31.5534			1.51987			0.759937	+	0.649997i	$0.225230\pi$
$432$		0			0
$433$	−6.48155			−0.311483			−0.155742	−	0.987798i	$-0.549777\pi$
$433$	−6.48155			−0.311483			−0.155742	+	0.987798i	$0.549777\pi$
$434$		0			0
$435$	17.6072	−	9.26368i	0.844203	−	0.444159i
$436$		0			0
$437$	−2.48050	+	14.0676i	−0.118659	+	0.672946i
$438$		0			0
$439$	0.866103	−	0.726747i	0.0413369	−	0.0346857i	−0.621885	−	0.783108i	$-0.713633\pi$
$439$	0.866103	−	0.726747i	0.0413369	−	0.0346857i	0.663222	+	0.748423i	$0.269189\pi$
$440$		0			0
$441$	−0.378836	+	0.105063i	−0.0180398	+	0.00500299i
$442$		0			0
$443$	4.32165	+	24.5093i	0.205328	+	1.16447i	0.896923	+	0.442187i	$0.145797\pi$
$443$	4.32165	+	24.5093i	0.205328	+	1.16447i	−0.691595	+	0.722285i	$0.743092\pi$
$444$		0			0
$445$	6.83441	−	2.48752i	0.323982	−	0.117920i
$446$		0			0
$447$	−24.4434	−	5.30712i	−1.15614	−	0.251018i
$448$		0			0
$449$	11.9582	−	20.7122i	0.564342	−	0.977469i	−0.432769	−	0.901505i	$-0.642463\pi$
$449$	11.9582	−	20.7122i	0.564342	−	0.977469i	0.997111	−	0.0759636i	$-0.0242033\pi$
$450$		0			0
$451$	1.08830	+	1.88500i	0.0512463	+	0.0887611i
$452$		0			0
$453$	11.5852	−	28.3181i	0.544318	−	1.33050i
$454$		0			0
$455$	0.376536	+	0.315951i	0.0176523	+	0.0148120i
$456$		0			0
$457$	29.5749	+	10.7644i	1.38346	+	0.503537i	0.923225	−	0.384261i	$-0.125544\pi$
$457$	29.5749	+	10.7644i	1.38346	+	0.503537i	0.460233	+	0.887798i	$0.347766\pi$
$458$		0			0
$459$	17.8962	+	13.3635i	0.835321	+	0.623753i
$460$		0			0
$461$	22.8426	+	8.31404i	1.06389	+	0.387223i	0.813887	−	0.581023i	$-0.197347\pi$
$461$	22.8426	+	8.31404i	1.06389	+	0.387223i	0.250000	+	0.968246i	$0.419569\pi$
$462$		0			0
$463$	23.5795	+	19.7856i	1.09583	+	0.919514i	0.997138	−	0.0756034i	$-0.0240883\pi$
$463$	23.5795	+	19.7856i	1.09583	+	0.919514i	0.0986964	+	0.995118i	$0.468533\pi$
$464$		0			0
$465$	−1.23246	+	0.167734i	−0.0571541	+	0.00777849i
$466$		0			0
$467$	−5.11571	−	8.86067i	−0.236727	−	0.410023i	0.723046	−	0.690800i	$-0.242741\pi$
$467$	−5.11571	−	8.86067i	−0.236727	−	0.410023i	−0.959773	+	0.280777i	$0.909408\pi$
$468$		0			0
$469$	4.56611	−	7.90873i	0.210843	−	0.365191i
$470$		0			0
$471$	15.7720	−	17.3637i	0.726733	−	0.800075i
$472$		0			0
$473$	1.82164	−	0.663022i	0.0837590	−	0.0304858i
$474$		0			0
$475$	4.12671	+	23.4037i	0.189347	+	1.07384i
$476$		0			0
$477$	−9.45329	−	19.8190i	−0.432837	−	0.907448i
$478$		0			0
$479$	16.0279	−	13.4490i	0.732333	−	0.614500i	−0.198434	−	0.980114i	$-0.563585\pi$
$479$	16.0279	−	13.4490i	0.732333	−	0.614500i	0.930767	+	0.365614i	$0.119141\pi$
$480$		0			0
$481$	0.0768655	−	0.435926i	0.00350477	−	0.0198765i
$482$		0			0
$483$	7.92282	+	4.99890i	0.360501	+	0.227458i
$484$		0			0
$485$	17.5978			0.799073
$486$		0			0
$487$	38.3549			1.73803			0.869014	−	0.494787i	$-0.164754\pi$
$487$	38.3549			1.73803			0.869014	+	0.494787i	$0.164754\pi$
$488$		0			0
$489$	−17.6153	−	11.1144i	−0.796593	−	0.502610i
$490$		0			0
$491$	4.06155	−	23.0342i	0.183295	−	1.03952i	−0.744831	−	0.667254i	$-0.767470\pi$
$491$	4.06155	−	23.0342i	0.183295	−	1.03952i	0.928126	−	0.372266i	$-0.121419\pi$
$492$		0			0
$493$	−30.2173	+	25.3553i	−1.36092	+	1.14195i
$494$		0			0
$495$	0.703419	+	1.47473i	0.0316163	+	0.0662841i
$496$		0			0
$497$	1.14635	+	6.50128i	0.0514209	+	0.291622i
$498$		0			0
$499$	29.6850	−	10.8045i	1.32888	−	0.483674i	0.422590	−	0.906321i	$-0.361121\pi$
$499$	29.6850	−	10.8045i	1.32888	−	0.483674i	0.906295	+	0.422647i	$0.138899\pi$
$500$		0			0
$501$	4.04717	−	4.45561i	0.180814	−	0.199062i
$502$		0			0
$503$	−7.21779	+	12.5016i	−0.321825	+	0.557417i	−0.980865	−	0.194691i	$-0.937630\pi$
$503$	−7.21779	+	12.5016i	−0.321825	+	0.557417i	0.659040	+	0.752108i	$0.270963\pi$
$504$		0			0
$505$	−2.38315	−	4.12774i	−0.106049	−	0.183682i
$506$		0			0
$507$	−22.2725	+	3.03121i	−0.989154	+	0.134621i
$508$		0			0
$509$	15.1218	+	12.6887i	0.670263	+	0.562417i	0.913143	−	0.407639i	$-0.133648\pi$
$509$	15.1218	+	12.6887i	0.670263	+	0.562417i	−0.242880	+	0.970056i	$0.578092\pi$
$510$		0			0
$511$	−26.6395	−	9.69597i	−1.17846	−	0.428924i
$512$		0			0
$513$	−33.0464	+	14.1982i	−1.45903	+	0.626864i
$514$		0			0
$515$	6.20063	+	2.25684i	0.273232	+	0.0994484i
$516$		0			0
$517$	−2.25195	−	1.88961i	−0.0990408	−	0.0831051i
$518$		0			0
$519$	3.07622	−	7.51935i	0.135031	−	0.330063i
$520$		0			0
$521$	2.20290	+	3.81554i	0.0965110	+	0.167162i	0.910238	−	0.414085i	$-0.135898\pi$
$521$	2.20290	+	3.81554i	0.0965110	+	0.167162i	−0.813727	+	0.581247i	$0.802565\pi$
$522$		0			0
$523$	−14.3769	+	24.9015i	−0.628657	+	1.08887i	0.359164	+	0.933274i	$0.383062\pi$
$523$	−14.3769	+	24.9015i	−0.628657	+	1.08887i	−0.987821	+	0.155592i	$0.950271\pi$
$524$		0			0
$525$	15.2304	+	3.30679i	0.664708	+	0.144320i
$526$		0			0
$527$	2.31735	−	0.843446i	0.100945	−	0.0367411i
$528$		0			0
$529$	−3.25438	−	18.4565i	−0.141495	−	0.802457i
$530$		0			0
$531$	−30.3866	+	8.42712i	−1.31867	+	0.365706i
$532$		0			0
$533$	−0.574167	+	0.481783i	−0.0248699	+	0.0208683i
$534$		0			0
$535$	−2.89270	+	16.4053i	−0.125063	+	0.709265i
$536$		0			0
$537$	10.3646	−	5.45311i	0.447265	−	0.235319i
$538$		0			0
$539$	0.0570198			0.00245602
$540$		0			0
$541$	−25.4458			−1.09400			−0.547000	−	0.837132i	$-0.684230\pi$
$541$	−25.4458			−1.09400			−0.547000	+	0.837132i	$0.684230\pi$
$542$		0			0
$543$	−1.53583	+	39.0921i	−0.0659088	+	1.67760i
$544$		0			0
$545$	−1.28780	+	7.30348i	−0.0551634	+	0.312847i
$546$		0			0
$547$	10.4534	−	8.77145i	0.446955	−	0.375040i	−0.391349	−	0.920242i	$-0.627992\pi$
$547$	10.4534	−	8.77145i	0.446955	−	0.375040i	0.838305	+	0.545202i	$0.183547\pi$
$548$		0			0
$549$	23.5443	+	10.7296i	1.00485	+	0.457929i
$550$		0			0
$551$	−11.0304	−	62.5568i	−0.469913	−	2.66501i
$552$		0			0
$553$	−36.6536	+	13.3408i	−1.55867	+	0.567310i
$554$		0			0
$555$	1.95263	+	6.09997i	0.0828847	+	0.258929i
$556$		0			0
$557$	11.3352	−	19.6331i	0.480287	−	0.831882i	−0.519457	−	0.854497i	$-0.673866\pi$
$557$	11.3352	−	19.6331i	0.480287	−	0.831882i	0.999744	+	0.0226145i	$0.00719902\pi$
$558$		0			0
$559$	0.333772	+	0.578110i	0.0141170	+	0.0244514i
$560$		0			0
$561$	−1.98325	−	2.56139i	−0.0837331	−	0.108142i
$562$		0			0
$563$	14.3128	+	12.0098i	0.603211	+	0.506154i	0.892476	−	0.451095i	$-0.148966\pi$
$563$	14.3128	+	12.0098i	0.603211	+	0.506154i	−0.289265	+	0.957249i	$0.593411\pi$
$564$		0			0
$565$	13.2111	+	4.80844i	0.555794	+	0.202292i
$566$		0			0
$567$	0.411916	+	23.5842i	0.0172989	+	0.990444i
$568$		0			0
$569$	−38.7414	−	14.1007i	−1.62412	−	0.591132i	−0.639961	−	0.768407i	$-0.721050\pi$
$569$	−38.7414	−	14.1007i	−1.62412	−	0.591132i	−0.984161	+	0.177275i	$0.943272\pi$
$570$		0			0
$571$	3.25271	+	2.72935i	0.136122	+	0.114220i	0.708306	−	0.705905i	$-0.249460\pi$
$571$	3.25271	+	2.72935i	0.136122	+	0.114220i	−0.572185	+	0.820125i	$0.693904\pi$
$572$		0			0
$573$	−21.7206	−	28.0524i	−0.907390	−	1.17190i
$574$		0			0
$575$	3.54258	+	6.13592i	0.147736	+	0.255886i
$576$		0			0
$577$	−9.12159	+	15.7991i	−0.379737	+	0.657723i	−0.991024	−	0.133686i	$-0.957319\pi$
$577$	−9.12159	+	15.7991i	−0.379737	+	0.657723i	0.611287	+	0.791409i	$0.290652\pi$
$578$		0			0
$579$	−6.35274	−	19.8458i	−0.264011	−	0.824763i
$580$		0			0
$581$	10.2437	−	3.72842i	0.424982	−	0.154681i
$582$		0			0
$583$	0.553030	+	3.13639i	0.0229041	+	0.129896i
$584$		0			0
$585$	−0.458050	+	0.326728i	−0.0189380	+	0.0135085i
$586$		0			0
$587$	5.82918	−	4.89126i	0.240596	−	0.201884i	−0.514514	−	0.857482i	$-0.672028\pi$
$587$	5.82918	−	4.89126i	0.240596	−	0.201884i	0.755110	+	0.655598i	$0.227583\pi$
$588$		0			0
$589$	−0.689600	+	3.91092i	−0.0284145	+	0.161147i
$590$		0			0
$591$	0.822497	−	20.9354i	0.0338330	−	0.861166i
$592$		0			0
$593$	22.2158			0.912292			0.456146	−	0.889905i	$-0.349230\pi$
$593$	22.2158			0.912292			0.456146	+	0.889905i	$0.349230\pi$
$594$		0			0
$595$	14.1010			0.578083
$596$		0			0
$597$	3.75769	−	1.97703i	0.153792	−	0.0809144i
$598$		0			0
$599$	−3.92770	+	22.2751i	−0.160481	+	0.910135i	0.793121	+	0.609065i	$0.208455\pi$
$599$	−3.92770	+	22.2751i	−0.160481	+	0.910135i	−0.953602	+	0.301070i	$0.902656\pi$
$600$		0			0
$601$	−32.4503	+	27.2290i	−1.32367	+	1.11070i	−0.338163	+	0.941087i	$0.609806\pi$
$601$	−32.4503	+	27.2290i	−1.32367	+	1.11070i	−0.985512	+	0.169608i	$0.945750\pi$
$602$		0			0
$603$	7.45583	+	7.32675i	0.303625	+	0.298368i
$604$		0			0
$605$	2.34975	+	13.3261i	0.0955308	+	0.541782i
$606$		0			0
$607$	−15.0612	+	5.48184i	−0.611317	+	0.222501i	−0.629079	−	0.777341i	$-0.716568\pi$
$607$	−15.0612	+	5.48184i	−0.611317	+	0.222501i	0.0177626	+	0.999842i	$0.494346\pi$
$608$		0			0
$609$	−40.7098	−	8.83886i	−1.64965	−	0.358169i
$610$		0			0
$611$	0.506150	−	0.876677i	0.0204766	−	0.0354666i
$612$		0			0
$613$	6.81926	+	11.8113i	0.275427	+	0.477054i	0.970243	−	0.242134i	$-0.0778473\pi$
$613$	6.81926	+	11.8113i	0.275427	+	0.477054i	−0.694816	+	0.719188i	$0.744514\pi$
$614$		0			0
$615$	4.10646	−	10.0376i	0.165588	−	0.404755i
$616$		0			0
$617$	18.7328	+	15.7187i	0.754154	+	0.632810i	0.936598	−	0.350406i	$-0.113956\pi$
$617$	18.7328	+	15.7187i	0.754154	+	0.632810i	−0.182444	+	0.983216i	$0.558401\pi$
$618$		0			0
$619$	−10.2632	−	3.73551i	−0.412514	−	0.150143i	0.127423	−	0.991848i	$-0.459329\pi$
$619$	−10.2632	−	3.73551i	−0.412514	−	0.150143i	−0.539936	+	0.841706i	$0.681552\pi$
$620$		0			0
$621$	−7.81041	+	7.34742i	−0.313421	+	0.294842i
$622$		0			0
$623$	−14.3103	−	5.20851i	−0.573329	−	0.208675i
$624$		0			0
$625$	3.02863	+	2.54132i	0.121145	+	0.101653i
$626$		0			0
$627$	5.16901	−	0.703486i	0.206431	−	0.0280945i
$628$		0			0
$629$	−6.34932	−	10.9973i	−0.253164	−	0.438493i
$630$		0			0
$631$	−2.56965	+	4.45077i	−0.102296	+	0.177182i	−0.912630	−	0.408786i	$-0.865952\pi$
$631$	−2.56965	+	4.45077i	−0.102296	+	0.177182i	0.810334	+	0.585968i	$0.199286\pi$
$632$		0			0
$633$	31.0497	−	34.1832i	1.23411	−	1.35866i
$634$		0			0
$635$	−23.1080	+	8.41063i	−0.917014	+	0.333766i
$636$		0			0
$637$	0.00340957	+	0.0193366i	0.000135092	+	0.000766145i
$638$		0			0
$639$	−7.53325	−	0.592839i	−0.298011	−	0.0234524i
$640$		0			0
$641$	4.47254	−	3.75291i	0.176655	−	0.148231i	−0.550173	−	0.835051i	$-0.685438\pi$
$641$	4.47254	−	3.75291i	0.176655	−	0.148231i	0.726828	+	0.686820i	$0.240994\pi$
$642$		0			0
$643$	5.49213	−	31.1474i	0.216589	−	1.22833i	−0.661540	−	0.749910i	$-0.730097\pi$
$643$	5.49213	−	31.1474i	0.216589	−	1.22833i	0.878128	−	0.478425i	$-0.158792\pi$
$644$		0			0
$645$	−8.16885	−	5.15413i	−0.321648	−	0.202944i
$646$		0			0
$647$	−40.1682			−1.57917			−0.789587	−	0.613639i	$-0.789705\pi$
$647$	−40.1682			−1.57917			−0.789587	+	0.613639i	$0.789705\pi$
$648$		0			0
$649$	4.57358			0.179529
$650$		0			0
$651$	2.20261	+	1.38974i	0.0863271	+	0.0544680i
$652$		0			0
$653$	−6.56762	+	37.2468i	−0.257011	+	1.45758i	0.533848	+	0.845581i	$0.320746\pi$
$653$	−6.56762	+	37.2468i	−0.257011	+	1.45758i	−0.790858	+	0.611999i	$0.790365\pi$
$654$		0			0
$655$	11.9491	−	10.0265i	0.466891	−	0.391768i
$656$		0			0
$657$	18.3798	−	26.7430i	0.717063	−	1.04335i
$658$		0			0
$659$	−0.0662537	−	0.375744i	−0.00258088	−	0.0146369i	0.983490	−	0.180962i	$-0.0579210\pi$
$659$	−0.0662537	−	0.375744i	−0.00258088	−	0.0146369i	−0.986071	+	0.166325i	$0.946810\pi$
$660$		0			0
$661$	−16.6867	+	6.07345i	−0.649036	+	0.236230i	−0.645496	−	0.763764i	$-0.723349\pi$
$661$	−16.6867	+	6.07345i	−0.649036	+	0.236230i	−0.00354036	+	0.999994i	$0.501127\pi$
$662$		0			0
$663$	0.750032	−	0.825726i	0.0291288	−	0.0320685i
$664$		0			0
$665$	−11.3538	+	19.6653i	−0.440281	+	0.762589i
$666$		0			0
$667$	−9.46909	−	16.4010i	−0.366645	−	0.635047i
$668$		0			0
$669$	−38.5717	+	5.24948i	−1.49127	+	0.202957i
$670$		0			0
$671$	−2.87475	−	2.41220i	−0.110979	−	0.0931220i
$672$		0			0
$673$	20.7306	+	7.54531i	0.799105	+	0.290850i	0.709115	−	0.705092i	$-0.249095\pi$
$673$	20.7306	+	7.54531i	0.799105	+	0.290850i	0.0899892	+	0.995943i	$0.471317\pi$
$674$		0			0
$675$	−8.02952	+	15.9306i	−0.309056	+	0.613169i
$676$		0			0
$677$	−26.3402	−	9.58706i	−1.01234	−	0.368461i	−0.218007	−	0.975947i	$-0.569956\pi$
$677$	−26.3402	−	9.58706i	−1.01234	−	0.368461i	−0.794330	+	0.607486i	$0.792178\pi$
$678$		0			0
$679$	−28.2266	−	23.6849i	−1.08324	−	0.908944i
$680$		0			0
$681$	19.4943	−	47.6508i	0.747023	−	1.82598i
$682$		0			0
$683$	8.46217	+	14.6569i	0.323796	+	0.560831i	0.981268	−	0.192648i	$-0.0617076\pi$
$683$	8.46217	+	14.6569i	0.323796	+	0.560831i	−0.657472	+	0.753479i	$0.728374\pi$
$684$		0			0
$685$	1.35998	−	2.35555i	0.0519621	−	0.0900010i
$686$		0			0
$687$	9.36601	+	2.03353i	0.357336	+	0.0775842i
$688$		0			0
$689$	−1.03055	+	0.375088i	−0.0392607	+	0.0142897i
$690$		0			0
$691$	0.149708	+	0.849035i	0.00569515	+	0.0322988i	0.987523	−	0.157475i	$-0.0503355\pi$
$691$	0.149708	+	0.849035i	0.00569515	+	0.0322988i	−0.981828	+	0.189774i	$0.939224\pi$
$692$		0			0
$693$	0.856570	−	3.31218i	0.0325384	−	0.125819i
$694$		0			0
$695$	3.70983	−	3.11291i	0.140722	−	0.118080i
$696$		0			0
$697$	−3.73379	+	21.1754i	−0.141428	+	0.802075i
$698$		0			0
$699$	−8.13492	+	4.28002i	−0.307691	+	0.161885i
$700$		0			0
$701$	40.8711			1.54368			0.771840	−	0.635816i	$-0.219336\pi$
$701$	40.8711			1.54368			0.771840	+	0.635816i	$0.219336\pi$
$702$		0			0
$703$	20.4493			0.771261
$704$		0			0
$705$	−0.575013	+	14.6360i	−0.0216562	+	0.551225i
$706$		0			0
$707$	−1.73300	+	9.82833i	−0.0651762	+	0.369632i
$708$		0			0
$709$	−11.9287	+	10.0094i	−0.447992	+	0.375910i	−0.838690	−	0.544609i	$-0.816678\pi$
$709$	−11.9287	+	10.0094i	−0.447992	+	0.375910i	0.390698	+	0.920519i	$0.372234\pi$
$710$		0			0
$711$	−4.27961	−	44.4430i	−0.160498	−	1.66674i
$712$		0			0
$713$	0.205595	+	1.16599i	0.00769960	+	0.0436666i
$714$		0			0
$715$	0.0766829	−	0.0279103i	0.00286778	−	0.00104379i
$716$		0			0
$717$	5.06254	+	15.8152i	0.189064	+	0.590630i
$718$		0			0
$719$	−3.13113	+	5.42328i	−0.116772	+	0.202254i	−0.918487	−	0.395452i	$-0.870588\pi$
$719$	−3.13113	+	5.42328i	−0.116772	+	0.202254i	0.801715	+	0.597707i	$0.203921\pi$
$720$		0			0
$721$	−6.90823	−	11.9654i	−0.257276	−	0.445615i
$722$		0			0
$723$	−10.1483	−	13.1066i	−0.377418	−	0.487439i
$724$		0			0
$725$	−24.1355	−	20.2521i	−0.896371	−	0.752145i
$726$		0			0
$727$	−16.2260	−	5.90578i	−0.601789	−	0.219033i	0.0231176	−	0.999733i	$-0.492641\pi$
$727$	−16.2260	−	5.90578i	−0.601789	−	0.219033i	−0.624907	+	0.780699i	$0.714863\pi$
$728$		0			0
$729$	−26.2541	−	6.30260i	−0.972374	−	0.233430i
$730$		0			0
$731$	17.9954	+	6.54979i	0.665584	+	0.242253i
$732$		0			0
$733$	−23.0253	−	19.3205i	−0.850459	−	0.713620i	0.109431	−	0.993994i	$-0.465097\pi$
$733$	−23.0253	−	19.3205i	−0.850459	−	0.713620i	−0.959891	+	0.280374i	$0.909541\pi$
$734$		0			0
$735$	−0.173935	−	0.224638i	−0.00641567	−	0.00828591i
$736$		0			0
$737$	−0.758064	−	1.31301i	−0.0279237	−	0.0483652i
$738$		0			0
$739$	−23.5616	+	40.8099i	−0.866727	+	1.50122i	−0.00140498	+	0.999999i	$0.500447\pi$
$739$	−23.5616	+	40.8099i	−0.866727	+	1.50122i	−0.865322	+	0.501216i	$0.832886\pi$
$740$		0			0
$741$	0.547655	+	1.71086i	0.0201186	+	0.0628499i
$742$		0			0
$743$	12.6329	−	4.59802i	0.463458	−	0.168685i	−0.0997287	−	0.995015i	$-0.531797\pi$
$743$	12.6329	−	4.59802i	0.463458	−	0.168685i	0.563186	+	0.826330i	$0.309575\pi$
$744$		0			0
$745$	−3.13887	−	17.8014i	−0.114999	−	0.652193i
$746$		0			0
$747$	1.19604	+	12.4207i	0.0437608	+	0.454448i
$748$		0			0
$749$	26.7199	−	22.4207i	0.976324	−	0.819233i
$750$		0			0
$751$	−0.601741	+	3.41265i	−0.0219579	+	0.124529i	−0.993816	−	0.111036i	$-0.964583\pi$
$751$	−0.601741	+	3.41265i	−0.0219579	+	0.124529i	0.971859	+	0.235565i	$0.0756942\pi$
$752$		0			0
$753$	−1.42482	+	36.2665i	−0.0519232	+	1.32162i
$754$		0			0
$755$	22.1109			0.804698
$756$		0			0
$757$	−10.5644			−0.383969			−0.191985	−	0.981398i	$-0.561492\pi$
$757$	−10.5644			−0.383969			−0.191985	+	0.981398i	$0.561492\pi$
$758$		0			0
$759$	1.37640	−	0.724165i	0.0499602	−	0.0262855i
$760$		0			0
$761$	3.97579	−	22.5478i	0.144122	−	0.817358i	−0.823945	−	0.566669i	$-0.808232\pi$
$761$	3.97579	−	22.5478i	0.144122	−	0.817358i	0.968068	−	0.250689i	$-0.0806571\pi$
$762$		0			0
$763$	11.8954	−	9.98144i	0.430643	−	0.361352i
$764$		0			0
$765$	−4.04125	+	15.6267i	−0.146112	+	0.564984i
$766$		0			0
$767$	0.273483	+	1.55100i	0.00987490	+	0.0560033i
$768$		0			0
$769$	24.6854	−	8.98475i	0.890178	−	0.323998i	0.143868	−	0.989597i	$-0.454046\pi$
$769$	24.6854	−	8.98475i	0.890178	−	0.323998i	0.746310	+	0.665599i	$0.231824\pi$
$770$		0			0
$771$	−4.51713	−	0.980751i	−0.162680	−	0.0353209i
$772$		0			0
$773$	−2.84371	+	4.92545i	−0.102281	+	0.177156i	−0.912624	−	0.408800i	$-0.865947\pi$
$773$	−2.84371	+	4.92545i	−0.102281	+	0.177156i	0.810343	+	0.585956i	$0.199281\pi$
$774$		0			0
$775$	0.984866	+	1.70584i	0.0353774	+	0.0612755i
$776$		0			0
$777$	5.07799	−	12.4123i	0.182172	−	0.445290i
$778$		0			0
$779$	−26.5250	−	22.2571i	−0.950358	−	0.797445i
$780$		0			0
$781$	1.02990	+	0.374851i	0.0368526	+	0.0134132i
$782$		0			0
$783$	21.4624	−	42.5815i	0.767004	−	1.52174i
$784$		0			0
$785$	15.9296	+	5.79789i	0.568551	+	0.206936i
$786$		0			0
$787$	−25.9361	−	21.7630i	−0.924523	−	0.775767i	0.0503033	−	0.998734i	$-0.483981\pi$
$787$	−25.9361	−	21.7630i	−0.924523	−	0.775767i	−0.974826	+	0.222967i	$0.928426\pi$
$788$		0			0
$789$	43.5995	−	5.93374i	1.55218	−	0.211247i
$790$		0			0
$791$	−14.7187	−	25.4935i	−0.523336	−	0.906445i
$792$		0			0
$793$	0.646130	−	1.11913i	0.0229448	−	0.0397415i
$794$		0			0
$795$	10.6693	−	11.7461i	0.378402	−	0.416590i
$796$		0			0
$797$	46.9450	−	17.0866i	1.66288	−	0.605238i	0.672066	−	0.740492i	$-0.265407\pi$
$797$	46.9450	−	17.0866i	1.66288	−	0.605238i	0.990811	+	0.135254i	$0.0431850\pi$
$798$		0			0
$799$	−5.04284	−	28.5994i	−0.178403	−	1.01177i
$800$		0			0
$801$	9.87331	−	14.3659i	0.348856	−	0.507595i
$802$		0			0
$803$	−3.60540	+	3.02529i	−0.127232	+	0.106760i
$804$		0			0
$805$	−1.17559	+	6.66711i	−0.0414341	+	0.234985i
$806$		0			0
$807$	−17.7612	−	11.2064i	−0.625223	−	0.394484i
$808$		0			0
$809$	−16.4595			−0.578685			−0.289343	−	0.957226i	$-0.593437\pi$
$809$	−16.4595			−0.578685			−0.289343	+	0.957226i	$0.593437\pi$
$810$		0			0
$811$	−26.9173			−0.945194			−0.472597	−	0.881279i	$-0.656683\pi$
$811$	−26.9173			−0.945194			−0.472597	+	0.881279i	$0.656683\pi$
$812$		0			0
$813$	10.9627	+	6.91691i	0.384479	+	0.242586i
$814$		0			0
$815$	2.61377	−	14.8234i	0.0915564	−	0.519242i
$816$		0			0
$817$	−23.6239	+	19.8228i	−0.826495	+	0.693512i
$818$		0			0
$819$	1.17445	+	0.0924250i	0.0410387	+	0.00322959i
$820$		0			0
$821$	2.24040	+	12.7059i	0.0781904	+	0.443440i	0.998619	+	0.0525299i	$0.0167285\pi$
$821$	2.24040	+	12.7059i	0.0781904	+	0.443440i	−0.920429	+	0.390910i	$0.872160\pi$
$822$		0			0
$823$	−45.0091	+	16.3820i	−1.56892	+	0.571040i	−0.972758	−	0.231824i	$-0.925531\pi$
$823$	−45.0091	+	16.3820i	−1.56892	+	0.571040i	−0.596162	+	0.802864i	$0.703308\pi$
$824$		0			0
$825$	1.73971	−	1.91529i	0.0605691	−	0.0666817i
$826$		0			0
$827$	13.5643	−	23.4940i	0.471676	−	0.816967i	−0.527799	−	0.849370i	$-0.676982\pi$
$827$	13.5643	−	23.4940i	0.471676	−	0.816967i	0.999475	+	0.0324022i	$0.0103157\pi$
$828$		0			0
$829$	−5.27491	−	9.13640i	−0.183205	−	0.317320i	0.759765	−	0.650198i	$-0.225314\pi$
$829$	−5.27491	−	9.13640i	−0.183205	−	0.317320i	−0.942970	+	0.332877i	$0.891981\pi$
$830$		0			0
$831$	−45.5950	+	6.20533i	−1.58167	+	0.215261i
$832$		0			0
$833$	0.431498	+	0.362070i	0.0149505	+	0.0125450i
$834$		0			0
$835$	4.08761	+	1.48777i	0.141458	+	0.0514864i
$836$		0			0
$837$	−2.17136	+	2.04264i	−0.0750531	+	0.0706041i
$838$		0			0
$839$	−15.8164	−	5.75670i	−0.546043	−	0.198743i	0.0542444	−	0.998528i	$-0.482725\pi$
$839$	−15.8164	−	5.75670i	−0.546043	−	0.198743i	−0.600288	+	0.799784i	$0.704947\pi$
$840$		0			0
$841$	42.2975	+	35.4918i	1.45853	+	1.22386i
$842$		0			0
$843$	4.96474	−	12.1355i	0.170995	−	0.417970i
$844$		0			0
$845$	−8.12196	−	14.0676i	−0.279404	−	0.483942i
$846$		0			0
$847$	14.1667	−	24.5374i	0.486773	−	0.843115i
$848$		0			0
$849$	37.5599	+	8.15495i	1.28905	+	0.279877i
$850$		0			0
$851$	5.72902	−	2.08519i	0.196388	−	0.0714795i
$852$		0			0
$853$	−4.38376	−	24.8616i	−0.150097	−	0.851244i	−0.963132	−	0.269029i	$-0.913297\pi$
$853$	−4.38376	−	24.8616i	−0.150097	−	0.851244i	0.813035	−	0.582215i	$-0.197814\pi$
$854$		0			0
$855$	−18.5392	−	18.2182i	−0.634027	−	0.623050i
$856$		0			0
$857$	−14.0872	+	11.8205i	−0.481209	+	0.403782i	−0.850863	−	0.525387i	$-0.823921\pi$
$857$	−14.0872	+	11.8205i	−0.481209	+	0.403782i	0.369654	+	0.929169i	$0.379476\pi$
$858$		0			0
$859$	−3.23196	+	18.3294i	−0.110273	+	0.625390i	0.878709	+	0.477357i	$0.158405\pi$
$859$	−3.23196	+	18.3294i	−0.110273	+	0.625390i	−0.988982	+	0.148033i	$0.952706\pi$
$860$		0			0
$861$	−20.0964	+	10.5733i	−0.684882	+	0.360336i
$862$		0			0
$863$	−25.0726			−0.853481			−0.426740	−	0.904374i	$-0.640338\pi$
$863$	−25.0726			−0.853481			−0.426740	+	0.904374i	$0.640338\pi$
$864$		0			0
$865$	5.87113			0.199624
$866$		0			0
$867$	0.100368	−	2.55472i	0.00340868	−	0.0867627i
$868$		0			0
$869$	−1.12451	+	6.37739i	−0.0381462	+	0.216338i
$870$		0			0
$871$	0.399939	−	0.335589i	0.0135514	−	0.0113710i
$872$		0			0
$873$	34.3372	−	24.4928i	1.16214	−	0.828954i
$874$		0			0
$875$	4.80407	+	27.2452i	0.162407	+	0.921057i
$876$		0			0
$877$	−3.92469	+	1.42847i	−0.132527	+	0.0482360i	−0.407432	−	0.913235i	$-0.633576\pi$
$877$	−3.92469	+	1.42847i	−0.132527	+	0.0482360i	0.274905	+	0.961471i	$0.411354\pi$
$878$		0			0
$879$	−10.7205	−	33.4906i	−0.361594	−	1.12961i
$880$		0			0
$881$	−15.7167	+	27.2222i	−0.529511	+	0.917139i	0.469897	+	0.882721i	$0.344291\pi$
$881$	−15.7167	+	27.2222i	−0.529511	+	0.917139i	−0.999408	+	0.0344179i	$0.989042\pi$
$882$		0			0
$883$	4.16699	+	7.21744i	0.140230	+	0.242886i	0.927583	−	0.373616i	$-0.121882\pi$
$883$	4.16699	+	7.21744i	0.140230	+	0.242886i	−0.787353	+	0.616503i	$0.788549\pi$
$884$		0			0
$885$	−13.9514	−	18.0183i	−0.468970	−	0.605680i
$886$		0			0
$887$	24.3887	+	20.4645i	0.818892	+	0.687132i	0.952712	−	0.303873i	$-0.0982800\pi$
$887$	24.3887	+	20.4645i	0.818892	+	0.687132i	−0.133820	+	0.991006i	$0.542724\pi$
$888$		0			0
$889$	48.3849	+	17.6107i	1.62278	+	0.590643i
$890$		0			0
$891$	3.42507	+	1.89850i	0.114744	+	0.0636022i
$892$		0			0
$893$	43.9453	+	15.9948i	1.47057	+	0.535245i
$894$		0			0
$895$	6.48346	+	5.44027i	0.216718	+	0.181848i
$896$		0			0
$897$	0.327883	+	0.423465i	0.0109477	+	0.0141391i
$898$		0			0
$899$	−2.63249	−	4.55960i	−0.0877984	−	0.152071i
$900$		0			0
$901$	−15.7307	+	27.2464i	−0.524065	+	0.907708i
$902$		0			0
$903$	6.16576	+	19.2617i	0.205184	+	0.640988i
$904$		0			0
$905$	−26.5673	+	9.66971i	−0.883127	+	0.321432i
$906$		0			0
$907$	1.06494	+	6.03956i	0.0353607	+	0.200540i	0.997370	−	0.0724755i	$-0.0230899\pi$
$907$	1.06494	+	6.03956i	0.0353607	+	0.200540i	−0.962010	+	0.273016i	$0.911979\pi$
$908$		0			0
$909$	−10.3951	−	4.73725i	−0.344783	−	0.157125i
$910$		0			0
$911$	7.54121	−	6.32783i	0.249852	−	0.209650i	−0.509257	−	0.860615i	$-0.670080\pi$
$911$	7.54121	−	6.32783i	0.249852	−	0.209650i	0.759108	+	0.650964i	$0.225635\pi$
$912$		0			0
$913$	0.314270	−	1.78231i	0.0104008	−	0.0589860i
$914$		0			0
$915$	−0.734038	+	18.6838i	−0.0242665	+	0.617667i
$916$		0			0
$917$	−32.6610			−1.07856
$918$		0			0
$919$	2.78907			0.0920028			0.0460014	−	0.998941i	$-0.485352\pi$
$919$	2.78907			0.0920028			0.0460014	+	0.998941i	$0.485352\pi$
$920$		0			0
$921$	−21.6556	+	11.3936i	−0.713576	+	0.375433i
$922$		0			0
$923$	−0.0655362	+	0.371674i	−0.00215715	+	0.0122338i
$924$		0			0
$925$	7.76986	−	6.51968i	0.255471	−	0.214366i
$926$		0			0
$927$	15.2399	−	4.22649i	0.500545	−	0.138816i
$928$		0			0
$929$	2.43301	+	13.7983i	0.0798246	+	0.452708i	0.998354	+	0.0573548i	$0.0182666\pi$
$929$	2.43301	+	13.7983i	0.0798246	+	0.452708i	−0.918529	+	0.395353i	$0.870622\pi$
$930$		0			0
$931$	−0.852379	+	0.310241i	−0.0279356	+	0.0101677i
$932$		0			0
$933$	2.89574	+	0.628719i	0.0948024	+	0.0205834i
$934$		0			0
$935$	1.17052	−	2.02740i	0.0382801	−	0.0663031i
$936$		0			0
$937$	27.2804	+	47.2510i	0.891211	+	1.54362i	0.838425	+	0.545018i	$0.183477\pi$
$937$	27.2804	+	47.2510i	0.891211	+	1.54362i	0.0527867	+	0.998606i	$0.483190\pi$
$938$		0			0
$939$	5.09095	−	12.4440i	0.166137	−	0.406096i
$940$		0			0
$941$	−33.6466	−	28.2328i	−1.09685	−	0.920364i	−0.0996380	−	0.995024i	$-0.531768\pi$
$941$	−33.6466	−	28.2328i	−1.09685	−	0.920364i	−0.997209	+	0.0746598i	$0.976213\pi$
$942$		0			0
$943$	−9.70070	−	3.53077i	−0.315898	−	0.114978i
$944$		0			0
$945$	−15.6618	+	6.72897i	−0.509477	+	0.218894i
$946$		0			0
$947$	−10.4622	−	3.80793i	−0.339975	−	0.123741i	0.166390	−	0.986060i	$-0.446789\pi$
$947$	−10.4622	−	3.80793i	−0.339975	−	0.123741i	−0.506365	+	0.862319i	$0.669011\pi$
$948$		0			0
$949$	−1.24153	−	1.04177i	−0.0403018	−	0.0338172i
$950$		0			0
$951$	−24.0473	+	3.27277i	−0.779789	+	0.106127i
$952$		0			0
$953$	0.662493	+	1.14747i	0.0214603	+	0.0371703i	0.876556	−	0.481300i	$-0.159835\pi$
$953$	0.662493	+	1.14747i	0.0214603	+	0.0371703i	−0.855096	+	0.518470i	$0.826502\pi$
$954$		0			0
$955$	12.8195	−	22.2041i	0.414830	−	0.718507i
$956$		0			0
$957$	−4.65015	+	5.11944i	−0.150318	+	0.165488i
$958$		0			0
$959$	−5.35174	+	1.94787i	−0.172817	+	0.0629001i
$960$		0			0
$961$	−5.32594	−	30.2049i	−0.171804	−	0.974351i
$962$		0			0
$963$	17.1888	+	36.0366i	0.553902	+	1.16126i
$964$		0			0
$965$	11.5357	−	9.67957i	0.371346	−	0.311596i
$966$		0			0
$967$	−0.0123738	+	0.0701752i	−0.000397914	+	0.00225668i	−0.985006	−	0.172520i	$-0.944809\pi$
$967$	−0.0123738	+	0.0701752i	−0.000397914	+	0.00225668i	0.984608	+	0.174776i	$0.0559203\pi$
$968$		0			0
$969$	43.5837	+	27.4991i	1.40011	+	0.883399i
$970$		0			0
$971$	−7.28612			−0.233823			−0.116911	−	0.993142i	$-0.537299\pi$
$971$	−7.28612			−0.233823			−0.116911	+	0.993142i	$0.537299\pi$
$972$		0			0
$973$	−10.1402			−0.325080
$974$		0			0
$975$	0.753543	+	0.475447i	0.0241327	+	0.0152265i
$976$		0			0
$977$	0.881098	−	4.99696i	0.0281888	−	0.159867i	−0.967464	−	0.253009i	$-0.918580\pi$
$977$	0.881098	−	4.99696i	0.0281888	−	0.159867i	0.995653	+	0.0931418i	$0.0296910\pi$
$978$		0			0
$979$	−1.93676	+	1.62514i	−0.0618992	+	0.0519396i
$980$		0			0
$981$	7.65228	+	16.0431i	0.244319	+	0.512217i
$982$		0			0
$983$	−2.41684	−	13.7066i	−0.0770852	−	0.437172i	−0.998786	−	0.0492693i	$-0.984311\pi$
$983$	−2.41684	−	13.7066i	−0.0770852	−	0.437172i	0.921700	−	0.387903i	$-0.126800\pi$
$984$		0			0
$985$	14.2278	−	5.17851i	0.453336	−	0.165001i
$986$		0			0
$987$	20.6211	−	22.7021i	0.656375	−	0.722617i
$988$		0			0
$989$	−4.59709	+	7.96239i	−0.146179	+	0.253189i
$990$		0			0
$991$	−26.3753	−	45.6833i	−0.837839	−	1.45118i	−0.891698	−	0.452630i	$-0.850486\pi$
$991$	−26.3753	−	45.6833i	−0.837839	−	1.45118i	0.0538597	−	0.998549i	$-0.482848\pi$
$992$		0			0
$993$	−47.1416	+	6.41581i	−1.49599	+	0.203600i
$994$		0			0
$995$	2.35058	+	1.97237i	0.0745185	+	0.0625285i
$996$		0			0
$997$	11.4626	+	4.17204i	0.363024	+	0.132130i	0.517091	−	0.855930i	$-0.327015\pi$
$997$	11.4626	+	4.17204i	0.363024	+	0.132130i	−0.154067	+	0.988060i	$0.549237\pi$
$998$		0			0
$999$	12.3000	+	9.18472i	0.389156	+	0.290592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.a.193.7	yes	48
4.3	odd	2	inner	864.2.y.a.193.2	✓	48
27.7	even	9	inner	864.2.y.a.385.7	yes	48
108.7	odd	18	inner	864.2.y.a.385.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.193.2	✓	48	4.3	odd	2	inner
864.2.y.a.193.7	yes	48	1.1	even	1	trivial
864.2.y.a.385.2	yes	48	108.7	odd	18	inner
864.2.y.a.385.7	yes	48	27.7	even	9	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.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46485 + 0.924244i) q^{3} +(-0.217354 + 1.23268i) q^{5} +(2.00770 - 1.68466i) q^{7} +(1.29155 + 2.70775i) q^{9} +O(q^{10})\)	\(q+(1.46485 + 0.924244i) q^{3} +(-0.217354 + 1.23268i) q^{5} +(2.00770 - 1.68466i) q^{7} +(1.29155 + 2.70775i) q^{9} +(-0.0755572 - 0.428506i) q^{11} +(0.140798 - 0.0512461i) q^{13} +(-1.45769 + 1.60480i) q^{15} +(2.14919 - 3.72251i) q^{17} +(3.46096 + 5.99456i) q^{19} +(4.49801 - 0.612165i) q^{21} +(1.58087 + 1.32651i) q^{23} +(3.22621 + 1.17424i) q^{25} +(-0.610701 + 5.16014i) q^{27} +(-8.62346 - 3.13868i) q^{29} +(0.439495 + 0.368780i) q^{31} +(0.285364 - 0.697529i) q^{33} +(1.64026 + 2.84102i) q^{35} +(1.47714 - 2.55848i) q^{37} +(0.253611 + 0.0550635i) q^{39} +(-4.70068 + 1.71091i) q^{41} +(0.773643 + 4.38755i) q^{43} +(-3.61851 + 1.00352i) q^{45} +(5.17552 - 4.34278i) q^{47} +(-0.0227557 + 0.129054i) q^{49} +(6.58874 - 3.46653i) q^{51} -7.31935 q^{53} +0.544633 q^{55} +(-0.470659 + 11.9799i) q^{57} +(-1.82524 + 10.3515i) q^{59} +(6.60685 - 5.54381i) q^{61} +(7.15469 + 3.26053i) q^{63} +(0.0325670 + 0.184697i) q^{65} +(3.27428 - 1.19174i) q^{67} +(1.08972 + 3.40424i) q^{69} +(-1.25942 + 2.18139i) q^{71} +(-5.40834 - 9.36752i) q^{73} +(3.64061 + 4.70189i) q^{75} +(-0.873584 - 0.733024i) q^{77} +(-13.9853 - 5.09023i) q^{79} +(-5.66381 + 6.99437i) q^{81} +(3.90853 + 1.42259i) q^{83} +(4.12152 + 3.45837i) q^{85} +(-9.73114 - 12.5679i) q^{87} +(-2.90527 - 5.03208i) q^{89} +(0.196347 - 0.340083i) q^{91} +(0.302950 + 0.946407i) q^{93} +(-8.14162 + 2.96331i) q^{95} +(-2.44135 - 13.8456i) q^{97} +(1.06270 - 0.758026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{9}+O(q^{10}) \) 48 * q - 12 * q^9	\( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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