LMFDB - Embedded newform 864.2.y.a.193.2

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			193.2
Character	$\chi$	$=$	864.193
Dual form			864.2.y.a.385.2

$q$-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	−0.937825	−	0.347109i	$-0.887163\pi$
$7$	−2.00770	+	1.68466i	−0.758840	+	0.636742i	0.178985	+	0.983852i	$0.442719\pi$
$8$		0			0
$9$	1.29155	+	2.70775i	0.430516	+	0.902583i
$10$		0			0
$11$	0.0755572	+	0.428506i	0.0227813	+	0.129199i	0.994077	−	0.108674i	$-0.0346606\pi$
$11$	0.0755572	+	0.428506i	0.0227813	+	0.129199i	−0.971296	+	0.237874i	$0.923550\pi$
$12$		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	$-0.874662\pi$
$19$	−3.46096	−	5.99456i	−0.793999	−	1.37525i	0.129473	−	0.991583i	$-0.458671\pi$
$20$		0			0
$21$	4.49801	−	0.612165i	0.981547	−	0.133585i
$22$		0			0
$23$	−1.58087	−	1.32651i	−0.329634	−	0.276596i	0.462916	−	0.886402i	$-0.346803\pi$
$23$	−1.58087	−	1.32651i	−0.329634	−	0.276596i	−0.792551	+	0.609806i	$0.791247\pi$
$24$		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	0.602466	−	0.798145i	$-0.294185\pi$
$31$	−0.439495	−	0.368780i	−0.0789357	−	0.0662349i	−0.681402	+	0.731910i	$0.738629\pi$
$32$		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	$-0.945227\pi$
$43$	−0.773643	−	4.38755i	−0.117980	−	0.669095i	0.867252	−	0.497869i	$-0.165884\pi$
$44$		0			0
$45$	−3.61851	+	1.00352i	−0.539415	+	0.149596i
$46$		0			0
$47$	−5.17552	+	4.34278i	−0.754927	+	0.633459i	−0.936801	−	0.349863i	$-0.886228\pi$
$47$	−5.17552	+	4.34278i	−0.754927	+	0.633459i	0.181874	+	0.983322i	$0.441784\pi$
$48$		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	$-0.704588\pi$
$59$	1.82524	−	10.3515i	0.237627	−	1.34765i	0.837011	−	0.547186i	$-0.184301\pi$
$60$		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	−0.534192	−	0.845363i	$-0.679384\pi$
$67$	−3.27428	+	1.19174i	−0.400018	+	0.145594i	0.134174	+	0.990958i	$0.457162\pi$
$68$		0			0
$69$	1.08972	+	3.40424i	0.131186	+	0.409822i
$70$		0			0
$71$	1.25942	−	2.18139i	0.149466	−	0.258883i	−0.781564	−	0.623825i	$-0.785578\pi$
$71$	1.25942	−	2.18139i	0.149466	−	0.258883i	0.931030	+	0.364942i	$0.118911\pi$
$72$		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	0.973771	−	0.227530i	$-0.0730650\pi$
$79$	13.9853	+	5.09023i	1.57347	+	0.572696i	0.599698	+	0.800226i	$0.295287\pi$
$80$		0			0
$81$	−5.66381	+	6.99437i	−0.629312	+	0.777153i
$82$		0			0
$83$	−3.90853	−	1.42259i	−0.429017	−	0.156149i	0.118481	−	0.992956i	$-0.462197\pi$
$83$	−3.90853	−	1.42259i	−0.429017	−	0.156149i	−0.547498	+	0.836807i	$0.684420\pi$
$84$		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	$0.139185\pi$
$103$	−0.915423	+	5.19162i	−0.0901993	+	0.511546i	−0.996113	+	0.0880835i	$0.971926\pi$
$104$		0			0
$105$	−0.223061	+	5.67766i	−0.0217685	+	0.554083i
$106$		0			0
$107$	−13.3087			−1.28660			−0.643300	−	0.765614i	$-0.722435\pi$
$107$	−13.3087			−1.28660			−0.643300	+	0.765614i	$0.722435\pi$
$108$		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	$-0.829711\pi$
$127$	−9.82310	−	17.0141i	−0.871659	−	1.50976i	−0.0113799	−	0.999935i	$-0.503622\pi$
$128$		0			0
$129$	−2.92190	+	7.14212i	−0.257259	+	0.628829i
$130$		0			0
$131$	9.54637	+	8.01035i	0.834070	+	0.699868i	0.956222	−	0.292644i	$-0.0945349\pi$
$131$	9.54637	+	8.01035i	0.834070	+	0.699868i	−0.122152	+	0.992511i	$0.538979\pi$
$132$		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	0.759771	−	0.650191i	$-0.225311\pi$
$139$	2.96384	+	2.48696i	0.251390	+	0.210941i	−0.508381	+	0.861132i	$0.669756\pi$
$140$		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	$0.199739\pi$
$151$	3.06746	+	17.3964i	0.249626	+	1.41570i	−0.559873	+	0.828578i	$0.689150\pi$
$152$		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	$-0.343911\pi$
$163$	12.0254			0.941901			0.470950	+	0.882160i	$0.343911\pi$
$164$		0			0
$165$	0.797803	+	0.503373i	0.0621089	+	0.0391876i
$166$		0			0
$167$	−0.603470	+	3.42245i	−0.0466979	+	0.264837i	−0.999214	−	0.0396527i	$-0.987375\pi$
$167$	−0.603470	+	3.42245i	−0.0466979	+	0.264837i	0.952516	+	0.304490i	$0.0984859\pi$
$168$		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	−0.964267	−	0.264932i	$-0.914651\pi$
$179$	−3.38084	+	5.85579i	−0.252696	+	0.437682i	0.711571	+	0.702614i	$0.247984\pi$
$180$		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	0.926018	−	0.377480i	$-0.123209\pi$
$191$	19.2482	+	7.00576i	1.39275	+	0.506919i	0.466731	+	0.884399i	$0.345432\pi$
$192$		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	−0.906195	−	0.422860i	$-0.861026\pi$
$199$	−1.22573	+	2.12302i	−0.0868895	+	0.150497i	0.819305	+	0.573357i	$0.194359\pi$
$200$		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	$0.425545\pi$
$211$	−4.62980	+	26.2569i	−0.318728	+	1.80760i	−0.550508	+	0.834830i	$0.685566\pi$
$212$		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	0.153125	−	0.988207i	$-0.451066\pi$
$223$	17.2166	−	14.4464i	1.15291	−	0.967406i	0.999784	+	0.0208011i	$0.00662168\pi$
$224$		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	$0.391964\pi$
$227$	5.16159	+	29.2728i	0.342587	+	1.94291i	0.00966119	+	0.999953i	$0.496925\pi$
$228$		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	0.373574	−	0.927601i	$-0.378132\pi$
$239$	−7.34432	−	6.16261i	−0.475064	−	0.398626i	−0.848638	+	0.528974i	$0.822577\pi$
$240$		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	$-0.936662\pi$
$251$	−10.4773	−	18.1472i	−0.661322	−	1.14544i	0.318947	−	0.947773i	$-0.396671\pi$
$252$		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	$0.564215\pi$
$263$	−19.4608	+	16.3295i	−1.20000	+	1.00692i	−0.999630	+	0.0272008i	$0.991341\pi$
$264$		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	$-0.572992\pi$
$271$	−7.48386			−0.454612			−0.227306	+	0.973823i	$0.572992\pi$
$272$		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	−0.876853	−	0.480758i	$-0.840361\pi$
$283$	−20.8522	+	7.58959i	−1.23954	+	0.451154i	−0.362683	+	0.931913i	$0.618139\pi$
$284$		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	−0.590949	−	0.806709i	$-0.701246\pi$
$307$	7.06387	−	12.2350i	0.403156	−	0.698287i	0.994105	+	0.108422i	$0.0345797\pi$
$308$		0			0
$309$	6.13928	−	6.75885i	0.349251	−	0.384498i
$310$		0			0
$311$	−1.60764	+	0.585132i	−0.0911607	+	0.0331798i	−0.387198	−	0.921997i	$-0.626557\pi$
$311$	−1.60764	+	0.585132i	−0.0911607	+	0.0331798i	0.296037	+	0.955176i	$0.404335\pi$
$312$		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	0.156709	−	0.987645i	$-0.449912\pi$
$331$	21.0418	−	17.6562i	1.15656	−	0.970470i	0.999853	+	0.0171747i	$0.00546715\pi$
$332$		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	0.997765	−	0.0668278i	$-0.0212878\pi$
$347$	20.5878	+	17.2752i	1.10521	+	0.927383i	0.107447	+	0.994211i	$0.465732\pi$
$348$		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	$-0.749012\pi$
$359$	−18.3168	−	31.7257i	−0.966725	−	1.67442i	−0.261817	−	0.965118i	$-0.584322\pi$
$360$		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	0.999947	−	0.0102988i	$-0.00327826\pi$
$367$	1.08778	+	6.16912i	0.0567818	+	0.322026i	−0.943165	+	0.332324i	$0.892167\pi$
$368$		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	$-0.430347\pi$
$379$	8.45211			0.434156			0.217078	+	0.976154i	$0.430347\pi$
$380$		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	$-0.482170\pi$
$383$	6.74904	−	38.2757i	0.344860	−	1.95580i	0.288876	−	0.957367i	$-0.406719\pi$
$384$		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	0.105286	−	0.994442i	$-0.466424\pi$
$419$	16.8905	−	6.14764i	0.825155	−	0.300332i	0.719869	+	0.694110i	$0.244202\pi$
$420$		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	$-0.774770\pi$
$431$	−31.5534			−1.51987			−0.759937	+	0.649997i	$0.774770\pi$
$432$		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	−0.663222	−	0.748423i	$-0.730811\pi$
$439$	−0.866103	+	0.726747i	−0.0413369	+	0.0346857i	0.621885	+	0.783108i	$0.286367\pi$
$440$		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	$-0.854203\pi$
$443$	−4.32165	−	24.5093i	−0.205328	−	1.16447i	0.691595	−	0.722285i	$-0.256908\pi$
$444$		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	−0.0986964	−	0.995118i	$-0.531467\pi$
$463$	−23.5795	−	19.7856i	−1.09583	−	0.919514i	−0.997138	+	0.0756034i	$0.975912\pi$
$464$		0			0
$465$	−1.23246	+	0.167734i	−0.0571541	+	0.00777849i
$466$		0			0
$467$	5.11571	+	8.86067i	0.236727	+	0.410023i	0.959773	−	0.280777i	$-0.0905920\pi$
$467$	5.11571	+	8.86067i	0.236727	+	0.410023i	−0.723046	+	0.690800i	$0.757259\pi$
$468$		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	−0.930767	−	0.365614i	$-0.880859\pi$
$479$	−16.0279	+	13.4490i	−0.732333	+	0.614500i	0.198434	+	0.980114i	$0.436415\pi$
$480$		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	$-0.835246\pi$
$487$	−38.3549			−1.73803			−0.869014	+	0.494787i	$0.835246\pi$
$488$		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	$0.232530\pi$
$491$	−4.06155	+	23.0342i	−0.183295	+	1.03952i	−0.928126	+	0.372266i	$0.878581\pi$
$492$		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	−0.906295	−	0.422647i	$-0.861101\pi$
$499$	−29.6850	+	10.8045i	−1.32888	+	0.483674i	−0.422590	+	0.906321i	$0.638879\pi$
$500$		0			0
$501$	4.04717	−	4.45561i	0.180814	−	0.199062i
$502$		0			0
$503$	7.21779	−	12.5016i	0.321825	−	0.557417i	−0.659040	−	0.752108i	$-0.729037\pi$
$503$	7.21779	−	12.5016i	0.321825	−	0.557417i	0.980865	+	0.194691i	$0.0623704\pi$
$504$		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	$-0.616938\pi$
$523$	14.3769	−	24.9015i	0.628657	−	1.08887i	0.987821	−	0.155592i	$-0.0497285\pi$
$524$		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	−0.838305	−	0.545202i	$-0.816453\pi$
$547$	−10.4534	+	8.77145i	−0.446955	+	0.375040i	0.391349	+	0.920242i	$0.372008\pi$
$548$		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	0.289265	−	0.957249i	$-0.406589\pi$
$563$	−14.3128	−	12.0098i	−0.603211	−	0.506154i	−0.892476	+	0.451095i	$0.851034\pi$
$564$		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	0.572185	−	0.820125i	$-0.306096\pi$
$571$	−3.25271	−	2.72935i	−0.136122	−	0.114220i	−0.708306	+	0.705905i	$0.750540\pi$
$572$		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	−0.755110	−	0.655598i	$-0.772417\pi$
$587$	−5.82918	+	4.89126i	−0.240596	+	0.201884i	0.514514	+	0.857482i	$0.327972\pi$
$588$		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	$-0.791545\pi$
$599$	3.92770	−	22.2751i	0.160481	−	0.910135i	0.953602	−	0.301070i	$-0.0973439\pi$
$600$		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	−0.0177626	−	0.999842i	$-0.505654\pi$
$607$	15.0612	−	5.48184i	0.611317	−	0.222501i	0.629079	+	0.777341i	$0.283432\pi$
$608$		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	0.539936	−	0.841706i	$-0.318448\pi$
$619$	10.2632	+	3.73551i	0.412514	+	0.150143i	−0.127423	+	0.991848i	$0.540671\pi$
$620$		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	−0.810334	−	0.585968i	$-0.800714\pi$
$631$	2.56965	−	4.45077i	0.102296	−	0.177182i	0.912630	+	0.408786i	$0.134048\pi$
$632$		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	$0.269903\pi$
$643$	−5.49213	+	31.1474i	−0.216589	+	1.22833i	−0.878128	+	0.478425i	$0.841208\pi$
$644$		0			0
$645$	−8.16885	−	5.15413i	−0.321648	−	0.202944i
$646$		0			0
$647$	40.1682			1.57917			0.789587	−	0.613639i	$-0.210295\pi$
$647$	40.1682			1.57917			0.789587	+	0.613639i	$0.210295\pi$
$648$		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	0.986071	−	0.166325i	$-0.0531901\pi$
$659$	0.0662537	+	0.375744i	0.00258088	+	0.0146369i	−0.983490	+	0.180962i	$0.942079\pi$
$660$		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	0.657472	−	0.753479i	$-0.271626\pi$
$683$	−8.46217	−	14.6569i	−0.323796	−	0.560831i	−0.981268	+	0.192648i	$0.938292\pi$
$684$		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	0.981828	−	0.189774i	$-0.0607756\pi$
$691$	−0.149708	−	0.849035i	−0.00569515	−	0.0322988i	−0.987523	+	0.157475i	$0.949664\pi$
$692$		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	−0.801715	−	0.597707i	$-0.796079\pi$
$719$	3.13113	−	5.42328i	0.116772	−	0.202254i	0.918487	+	0.395452i	$0.129412\pi$
$720$		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	0.624907	−	0.780699i	$-0.285137\pi$
$727$	16.2260	+	5.90578i	0.601789	+	0.219033i	−0.0231176	+	0.999733i	$0.507359\pi$
$728$		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	$-0.499553\pi$
$739$	23.5616	−	40.8099i	0.866727	−	1.50122i	0.865322	−	0.501216i	$-0.167114\pi$
$740$		0			0
$741$	0.547655	+	1.71086i	0.0201186	+	0.0628499i
$742$		0			0
$743$	−12.6329	+	4.59802i	−0.463458	+	0.168685i	−0.563186	−	0.826330i	$-0.690425\pi$
$743$	−12.6329	+	4.59802i	−0.463458	+	0.168685i	0.0997287	+	0.995015i	$0.468203\pi$
$744$		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	−0.971859	−	0.235565i	$-0.924306\pi$
$751$	0.601741	−	3.41265i	0.0219579	−	0.124529i	0.993816	+	0.111036i	$0.0354169\pi$
$752$		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	0.974826	−	0.222967i	$-0.0715743\pi$
$787$	25.9361	+	21.7630i	0.924523	+	0.775767i	−0.0503033	+	0.998734i	$0.516019\pi$
$788$		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	$-0.343317\pi$
$811$	26.9173			0.945194			0.472597	+	0.881279i	$0.343317\pi$
$812$		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	0.596162	−	0.802864i	$-0.296692\pi$
$823$	45.0091	−	16.3820i	1.56892	−	0.571040i	0.972758	+	0.231824i	$0.0744694\pi$
$824$		0			0
$825$	1.73971	−	1.91529i	0.0605691	−	0.0666817i
$826$		0			0
$827$	−13.5643	+	23.4940i	−0.471676	+	0.816967i	−0.999475	−	0.0324022i	$-0.989684\pi$
$827$	−13.5643	+	23.4940i	−0.471676	+	0.816967i	0.527799	+	0.849370i	$0.323018\pi$
$828$		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	0.600288	−	0.799784i	$-0.295053\pi$
$839$	15.8164	+	5.75670i	0.546043	+	0.198743i	−0.0542444	+	0.998528i	$0.517275\pi$
$840$		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	$-0.841595\pi$
$859$	3.23196	−	18.3294i	0.110273	−	0.625390i	0.988982	−	0.148033i	$-0.0472941\pi$
$860$		0			0
$861$	−20.0964	+	10.5733i	−0.684882	+	0.360336i
$862$		0			0
$863$	25.0726			0.853481			0.426740	−	0.904374i	$-0.359662\pi$
$863$	25.0726			0.853481			0.426740	+	0.904374i	$0.359662\pi$
$864$		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	0.787353	−	0.616503i	$-0.211451\pi$
$883$	−4.16699	−	7.21744i	−0.140230	−	0.242886i	−0.927583	+	0.373616i	$0.878118\pi$
$884$		0			0
$885$	−13.9514	−	18.0183i	−0.468970	−	0.605680i
$886$		0			0
$887$	−24.3887	−	20.4645i	−0.818892	−	0.687132i	0.133820	−	0.991006i	$-0.457276\pi$
$887$	−24.3887	−	20.4645i	−0.818892	−	0.687132i	−0.952712	+	0.303873i	$0.901720\pi$
$888$		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	0.962010	−	0.273016i	$-0.0880212\pi$
$907$	−1.06494	−	6.03956i	−0.0353607	−	0.200540i	−0.997370	+	0.0724755i	$0.976910\pi$
$908$		0			0
$909$	−10.3951	−	4.73725i	−0.344783	−	0.157125i
$910$		0			0
$911$	−7.54121	+	6.32783i	−0.249852	+	0.209650i	−0.759108	−	0.650964i	$-0.774365\pi$
$911$	−7.54121	+	6.32783i	−0.249852	+	0.209650i	0.509257	+	0.860615i	$0.329920\pi$
$912$		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	$-0.514648\pi$
$919$	−2.78907			−0.0920028			−0.0460014	+	0.998941i	$0.514648\pi$
$920$		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	0.506365	−	0.862319i	$-0.330989\pi$
$947$	10.4622	+	3.80793i	0.339975	+	0.123741i	−0.166390	+	0.986060i	$0.553211\pi$
$948$		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	−0.984608	−	0.174776i	$-0.944080\pi$
$967$	0.0123738	−	0.0701752i	0.000397914	−	0.00225668i	0.985006	+	0.172520i	$0.0551909\pi$
$968$		0			0
$969$	43.5837	+	27.4991i	1.40011	+	0.883399i
$970$		0			0
$971$	7.28612			0.233823			0.116911	−	0.993142i	$-0.462701\pi$
$971$	7.28612			0.233823			0.116911	+	0.993142i	$0.462701\pi$
$972$		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	$0.0156892\pi$
$983$	2.41684	+	13.7066i	0.0770852	+	0.437172i	−0.921700	+	0.387903i	$0.873200\pi$
$984$		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	$0.149514\pi$
$991$	26.3753	+	45.6833i	0.837839	+	1.45118i	−0.0538597	+	0.998549i	$0.517152\pi$
$992$		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.193.2	✓	48
4.3	odd	2	inner	864.2.y.a.193.7	yes	48
27.7	even	9	inner	864.2.y.a.385.2	yes	48
108.7	odd	18	inner	864.2.y.a.385.7	yes	48

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