LMFDB - Embedded newform 1764.2.bm.a.1697.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1697.4
Root			$-0.811340 - 1.53027i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.a.1685.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.478402 - 1.66467i) q^{3} -2.74332 q^{5} +(-2.54226 + 1.59276i) q^{9} +O(q^{10})$	\(q+(-0.478402 - 1.66467i) q^{3} -2.74332 q^{5} +(-2.54226 + 1.59276i) q^{9} +0.418355i q^{11} +(1.32512 + 0.765056i) q^{13} +(1.31241 + 4.56672i) q^{15} +(-1.95291 + 3.38253i) q^{17} +(5.11994 - 2.95600i) q^{19} +8.92450i q^{23} +2.52579 q^{25} +(3.86765 + 3.47005i) q^{27} +(6.00378 - 3.46629i) q^{29} +(3.05626 - 1.76453i) q^{31} +(0.696424 - 0.200142i) q^{33} +(-4.54861 - 7.87842i) q^{37} +(0.639629 - 2.57189i) q^{39} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(6.97424 - 4.36946i) q^{45} +(0.885373 - 1.53351i) q^{47} +(6.56508 + 1.63274i) q^{51} +(3.39526 + 1.96025i) q^{53} -1.14768i q^{55} +(-7.37015 - 7.10886i) q^{57} +(2.02728 + 3.51135i) q^{59} +(1.61459 + 0.932184i) q^{61} +(-3.63521 - 2.09879i) q^{65} +(6.38441 + 11.0581i) q^{67} +(14.8564 - 4.26950i) q^{69} -8.51021i q^{71} +(-1.65059 - 0.952971i) q^{73} +(-1.20834 - 4.20462i) q^{75} +(0.433633 - 0.751074i) q^{79} +(3.92620 - 8.09845i) q^{81} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(-8.64245 - 8.33605i) q^{87} +(-4.88864 - 8.46738i) q^{89} +(-4.39949 - 4.24351i) q^{93} +(-14.0456 + 8.10924i) q^{95} +(0.200411 - 0.115707i) q^{97} +(-0.666342 - 1.06357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.478402	−	1.66467i	−0.276205	−	0.961099i
$3$	−0.478402	−	1.66467i	−0.276205	−	0.961099i
$4$		0			0
$5$	−2.74332			−1.22685			−0.613425	−	0.789753i	$-0.710209\pi$
$5$	−2.74332			−1.22685			−0.613425	+	0.789753i	$0.710209\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.54226	+	1.59276i	−0.847421	+	0.530921i
$10$		0			0
$11$			0.418355i			0.126139i	0.998009	+	0.0630695i	$0.0200890\pi$
$11$			0.418355i			0.126139i	−0.998009	+	0.0630695i	$0.979911\pi$
$12$		0			0
$13$	1.32512	+	0.765056i	0.367521	+	0.212188i	0.672375	−	0.740211i	$-0.265274\pi$
$13$	1.32512	+	0.765056i	0.367521	+	0.212188i	−0.304854	+	0.952399i	$0.598608\pi$
$14$		0			0
$15$	1.31241	+	4.56672i	0.338862	+	1.17912i
$16$		0			0
$17$	−1.95291	+	3.38253i	−0.473649	+	0.820385i	−0.999545	−	0.0301645i	$-0.990397\pi$
$17$	−1.95291	+	3.38253i	−0.473649	+	0.820385i	0.525896	+	0.850549i	$0.323730\pi$
$18$		0			0
$19$	5.11994	−	2.95600i	1.17459	−	0.678152i	0.219836	−	0.975537i	$-0.429448\pi$
$19$	5.11994	−	2.95600i	1.17459	−	0.678152i	0.954758	+	0.297385i	$0.0961144\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			8.92450i			1.86089i	0.366436	+	0.930443i	$0.380578\pi$
$23$			8.92450i			1.86089i	−0.366436	+	0.930443i	$0.619422\pi$
$24$		0			0
$25$	2.52579			0.505159
$26$		0			0
$27$	3.86765	+	3.47005i	0.744330	+	0.667812i
$28$		0			0
$29$	6.00378	−	3.46629i	1.11487	−	0.643673i	0.174787	−	0.984606i	$-0.444076\pi$
$29$	6.00378	−	3.46629i	1.11487	−	0.643673i	0.940088	+	0.340933i	$0.110743\pi$
$30$		0			0
$31$	3.05626	−	1.76453i	0.548921	−	0.316920i	−0.199766	−	0.979844i	$-0.564018\pi$
$31$	3.05626	−	1.76453i	0.548921	−	0.316920i	0.748687	+	0.662924i	$0.230685\pi$
$32$		0			0
$33$	0.696424	−	0.200142i	0.121232	−	0.0348403i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.54861	−	7.87842i	−0.747787	−	1.29520i	−0.948881	−	0.315633i	$-0.897783\pi$
$37$	−4.54861	−	7.87842i	−0.747787	−	1.29520i	0.201095	−	0.979572i	$-0.435550\pi$
$38$		0			0
$39$	0.639629	−	2.57189i	0.102423	−	0.411832i
$40$		0			0
$41$	1.06236	−	1.84006i	0.165913	−	0.287370i	−0.771066	−	0.636755i	$-0.780276\pi$
$41$	1.06236	−	1.84006i	0.165913	−	0.287370i	0.936979	+	0.349385i	$0.113610\pi$
$42$		0			0
$43$	−5.77846	−	10.0086i	−0.881208	−	1.52630i	−0.850000	−	0.526783i	$-0.823398\pi$
$43$	−5.77846	−	10.0086i	−0.881208	−	1.52630i	−0.0312079	−	0.999513i	$-0.509935\pi$
$44$		0			0
$45$	6.97424	−	4.36946i	1.03966	−	0.651360i
$46$		0			0
$47$	0.885373	−	1.53351i	0.129145	−	0.223686i	−0.794201	−	0.607656i	$-0.792110\pi$
$47$	0.885373	−	1.53351i	0.129145	−	0.223686i	0.923346	+	0.383970i	$0.125443\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	6.56508	+	1.63274i	0.919295	+	0.228629i
$52$		0			0
$53$	3.39526	+	1.96025i	0.466374	+	0.269261i	0.714721	−	0.699410i	$-0.246554\pi$
$53$	3.39526	+	1.96025i	0.466374	+	0.269261i	−0.248346	+	0.968671i	$0.579887\pi$
$54$		0			0
$55$		−	1.14768i		−	0.154753i
$56$		0			0
$57$	−7.37015	−	7.10886i	−0.976200	−	0.941591i
$58$		0			0
$59$	2.02728	+	3.51135i	0.263929	+	0.457139i	0.967283	−	0.253702i	$-0.0816481\pi$
$59$	2.02728	+	3.51135i	0.263929	+	0.457139i	−0.703353	+	0.710840i	$0.748315\pi$
$60$		0			0
$61$	1.61459	+	0.932184i	0.206727	+	0.119354i	0.599789	−	0.800158i	$-0.295251\pi$
$61$	1.61459	+	0.932184i	0.206727	+	0.119354i	−0.393062	+	0.919512i	$0.628584\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.63521	−	2.09879i	−0.450893	−	0.260323i
$66$		0			0
$67$	6.38441	+	11.0581i	0.779979	+	1.35096i	0.931953	+	0.362579i	$0.118104\pi$
$67$	6.38441	+	11.0581i	0.779979	+	1.35096i	−0.151974	+	0.988385i	$0.548563\pi$
$68$		0			0
$69$	14.8564	−	4.26950i	1.78850	−	0.513987i
$70$		0			0
$71$		−	8.51021i		−	1.00998i	−0.863126	−	0.504988i	$-0.831497\pi$
$71$		−	8.51021i		−	1.00998i	0.863126	−	0.504988i	$-0.168503\pi$
$72$		0			0
$73$	−1.65059	−	0.952971i	−0.193187	−	0.111537i	0.400286	−	0.916390i	$-0.368911\pi$
$73$	−1.65059	−	0.952971i	−0.193187	−	0.111537i	−0.593474	+	0.804853i	$0.702244\pi$
$74$		0			0
$75$	−1.20834	−	4.20462i	−0.139528	−	0.485507i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.433633	−	0.751074i	0.0487875	−	0.0845024i	−0.840600	−	0.541656i	$-0.817798\pi$
$79$	0.433633	−	0.751074i	0.0487875	−	0.0845024i	0.889388	+	0.457153i	$0.151131\pi$
$80$		0			0
$81$	3.92620	−	8.09845i	0.436245	−	0.899828i
$82$		0			0
$83$	3.45880	+	5.99082i	0.379653	+	0.657578i	0.991012	−	0.133775i	$-0.0427100\pi$
$83$	3.45880	+	5.99082i	0.379653	+	0.657578i	−0.611359	+	0.791354i	$0.709377\pi$
$84$		0			0
$85$	5.35744	−	9.27936i	0.581096	−	1.00649i
$86$		0			0
$87$	−8.64245	−	8.33605i	−0.926568	−	0.893718i
$88$		0			0
$89$	−4.88864	−	8.46738i	−0.518195	−	0.897540i	−0.999777	−	0.0211389i	$-0.993271\pi$
$89$	−4.88864	−	8.46738i	−0.518195	−	0.897540i	0.481581	−	0.876401i	$-0.340063\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.39949	−	4.24351i	−0.456206	−	0.440032i
$94$		0			0
$95$	−14.0456	+	8.10924i	−1.44105	+	0.831990i
$96$		0			0
$97$	0.200411	−	0.115707i	0.0203486	−	0.0117483i	−0.489791	−	0.871840i	$-0.662927\pi$
$97$	0.200411	−	0.115707i	0.0203486	−	0.0117483i	0.510140	+	0.860091i	$0.329594\pi$
$98$		0			0
$99$	−0.666342	−	1.06357i	−0.0669699	−	0.106893i
$100$		0			0
$101$	14.2806			1.42097			0.710487	−	0.703710i	$-0.248475\pi$
$101$	14.2806			1.42097			0.710487	+	0.703710i	$0.248475\pi$
$102$		0			0
$103$		−	10.7458i		−	1.05882i	−0.848366	−	0.529410i	$-0.822413\pi$
$103$		−	10.7458i		−	1.05882i	0.848366	−	0.529410i	$-0.177587\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.50534	−	3.17851i	0.532221	−	0.307278i	−0.209699	−	0.977766i	$-0.567249\pi$
$107$	5.50534	−	3.17851i	0.532221	−	0.307278i	0.741920	+	0.670488i	$0.233915\pi$
$108$		0			0
$109$	2.58036	−	4.46932i	0.247154	−	0.428083i	−0.715581	−	0.698530i	$-0.753838\pi$
$109$	2.58036	−	4.46932i	0.247154	−	0.428083i	0.962735	+	0.270447i	$0.0871714\pi$
$110$		0			0
$111$	−10.9389	+	11.3410i	−1.03828	+	1.07644i
$112$		0			0
$113$	9.19186	+	5.30692i	0.864697	+	0.499233i	0.865582	−	0.500766i	$-0.166948\pi$
$113$	9.19186	+	5.30692i	0.864697	+	0.499233i	−0.000885276		1.00000i	$0.500282\pi$
$114$		0			0
$115$		−	24.4827i		−	2.28303i
$116$		0			0
$117$	−4.58735	+	0.165624i	−0.424100	+	0.0153119i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.8250			0.984089
$122$		0			0
$123$	−3.57134	−	0.888193i	−0.322017	−	0.0800856i
$124$		0			0
$125$	6.78753			0.607096
$126$		0			0
$127$	10.2909			0.913169			0.456584	−	0.889680i	$-0.349073\pi$
$127$	10.2909			0.913169			0.456584	+	0.889680i	$0.349073\pi$
$128$		0			0
$129$	−13.8966	+	14.4074i	−1.22353	+	1.26850i
$130$		0			0
$131$	−19.6610			−1.71779			−0.858893	−	0.512155i	$-0.828847\pi$
$131$	−19.6610			−1.71779			−0.858893	+	0.512155i	$0.828847\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−10.6102	−	9.51946i	−0.913181	−	0.819304i
$136$		0			0
$137$			5.38565i			0.460127i	0.973176	+	0.230063i	$0.0738933\pi$
$137$			5.38565i			0.460127i	−0.973176	+	0.230063i	$0.926107\pi$
$138$		0			0
$139$	14.7839	+	8.53549i	1.25395	+	0.723971i	0.971892	−	0.235425i	$-0.0756484\pi$
$139$	14.7839	+	8.53549i	1.25395	+	0.723971i	0.282062	+	0.959396i	$0.408982\pi$
$140$		0			0
$141$	−2.97636	−	0.740221i	−0.250655	−	0.0623379i
$142$		0			0
$143$	−0.320065	+	0.554369i	−0.0267652	+	0.0463587i
$144$		0			0
$145$	−16.4703	+	9.50912i	−1.36778	+	0.789690i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			10.7521i			0.880849i	0.897790	+	0.440425i	$0.145172\pi$
$149$			10.7521i			0.880849i	−0.897790	+	0.440425i	$0.854828\pi$
$150$		0			0
$151$	7.56447			0.615588			0.307794	−	0.951453i	$-0.400409\pi$
$151$	7.56447			0.615588			0.307794	+	0.951453i	$0.400409\pi$
$152$		0			0
$153$	−0.422776	−	11.7098i	−0.0341794	−	0.946682i
$154$		0			0
$155$	−8.38430	+	4.84068i	−0.673443	+	0.388812i
$156$		0			0
$157$	10.6317	−	6.13820i	0.848500	−	0.489882i	−0.0116445	−	0.999932i	$-0.503707\pi$
$157$	10.6317	−	6.13820i	0.848500	−	0.489882i	0.860144	+	0.510051i	$0.170373\pi$
$158$		0			0
$159$	1.63888	−	6.58978i	0.129972	−	0.522603i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	5.91745	+	10.2493i	0.463490	+	0.802789i	0.999132	−	0.0416566i	$-0.0132635\pi$
$163$	5.91745	+	10.2493i	0.463490	+	0.802789i	−0.535642	+	0.844445i	$0.679930\pi$
$164$		0			0
$165$	−1.91051	+	0.549053i	−0.148733	+	0.0427437i
$166$		0			0
$167$	6.78854	−	11.7581i	0.525313	−	0.909869i	−0.474252	−	0.880389i	$-0.657282\pi$
$167$	6.78854	−	11.7581i	0.525313	−	0.909869i	0.999565	−	0.0294798i	$-0.00938508\pi$
$168$		0			0
$169$	−5.32938	−	9.23075i	−0.409952	−	0.710058i
$170$		0			0
$171$	−8.30802	+	15.6698i	−0.635330	+	1.19830i
$172$		0			0
$173$	8.31085	−	14.3948i	0.631862	−	1.09442i	−0.355308	−	0.934749i	$-0.615624\pi$
$173$	8.31085	−	14.3948i	0.631862	−	1.09442i	0.987171	−	0.159668i	$-0.0510425\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.87539	−	5.05459i	0.366457	−	0.379926i
$178$		0			0
$179$	−14.8080	−	8.54942i	−1.10680	−	0.639014i	−0.168805	−	0.985650i	$-0.553991\pi$
$179$	−14.8080	−	8.54942i	−1.10680	−	0.639014i	−0.938000	+	0.346636i	$0.887324\pi$
$180$		0			0
$181$		−	18.2171i		−	1.35407i	−0.735952	−	0.677034i	$-0.763265\pi$
$181$		−	18.2171i		−	1.35407i	0.735952	−	0.677034i	$-0.236735\pi$
$182$		0			0
$183$	0.779357	−	3.13372i	0.0576117	−	0.231651i
$184$		0			0
$185$	12.4783	+	21.6130i	0.917422	+	1.58902i
$186$		0			0
$187$	−1.41510	−	0.817009i	−0.103482	−	0.0597456i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.1860	−	10.4997i	−1.31589	−	0.759730i	−0.332826	−	0.942988i	$-0.608002\pi$
$191$	−18.1860	−	10.4997i	−1.31589	−	0.759730i	−0.983065	+	0.183258i	$0.941336\pi$
$192$		0			0
$193$	3.48741	+	6.04038i	0.251030	+	0.434796i	0.963810	−	0.266592i	$-0.0858975\pi$
$193$	3.48741	+	6.04038i	0.251030	+	0.434796i	−0.712780	+	0.701388i	$0.752564\pi$
$194$		0			0
$195$	−1.75471	+	7.05550i	−0.125657	+	0.505255i
$196$		0			0
$197$			16.0756i			1.14534i	0.819786	+	0.572670i	$0.194092\pi$
$197$			16.0756i			1.14534i	−0.819786	+	0.572670i	$0.805908\pi$
$198$		0			0
$199$	5.44956	+	3.14630i	0.386309	+	0.223036i	0.680560	−	0.732693i	$-0.261737\pi$
$199$	5.44956	+	3.14630i	0.386309	+	0.223036i	−0.294251	+	0.955728i	$0.595070\pi$
$200$		0			0
$201$	15.3538	−	15.9182i	1.08297	−	1.12278i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.91440	+	5.04788i	−0.203550	+	0.352559i
$206$		0			0
$207$	−14.2146	−	22.6884i	−0.987984	−	1.57695i
$208$		0			0
$209$	1.23666	+	2.14195i	0.0855414	+	0.148162i
$210$		0			0
$211$	−1.29814	+	2.24844i	−0.0893674	+	0.154789i	−0.907244	−	0.420605i	$-0.861818\pi$
$211$	−1.29814	+	2.24844i	−0.0893674	+	0.154789i	0.817876	+	0.575394i	$0.195151\pi$
$212$		0			0
$213$	−14.1667	+	4.07130i	−0.970687	+	0.278961i
$214$		0			0
$215$	15.8522	+	27.4568i	1.08111	+	1.87254i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−0.796736	+	3.20360i	−0.0538385	+	0.216479i
$220$		0			0
$221$	−5.17565	+	2.98816i	−0.348152	+	0.201006i
$222$		0			0
$223$	−20.7215	+	11.9636i	−1.38762	+	0.801141i	−0.993046	−	0.117725i	$-0.962440\pi$
$223$	−20.7215	+	11.9636i	−1.38762	+	0.801141i	−0.394571	+	0.918866i	$0.629107\pi$
$224$		0			0
$225$	−6.42123	+	4.02299i	−0.428082	+	0.268200i
$226$		0			0
$227$	3.73218			0.247713			0.123857	−	0.992300i	$-0.460474\pi$
$227$	3.73218			0.247713			0.123857	+	0.992300i	$0.460474\pi$
$228$		0			0
$229$			21.0681i			1.39222i	0.717935	+	0.696111i	$0.245088\pi$
$229$			21.0681i			1.39222i	−0.717935	+	0.696111i	$0.754912\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.0542	−	6.38215i	0.724186	−	0.418109i	−0.0921057	−	0.995749i	$-0.529360\pi$
$233$	11.0542	−	6.38215i	0.724186	−	0.418109i	0.816291	+	0.577640i	$0.196026\pi$
$234$		0			0
$235$	−2.42886	+	4.20691i	−0.158441	+	0.274429i
$236$		0			0
$237$	−1.45774	−	0.362541i	−0.0946905	−	0.0235496i
$238$		0			0
$239$	11.0521	+	6.38091i	0.714899	+	0.412747i	0.812872	−	0.582442i	$-0.197903\pi$
$239$	11.0521	+	6.38091i	0.714899	+	0.412747i	−0.0979736	+	0.995189i	$0.531236\pi$
$240$		0			0
$241$			3.04192i			0.195947i	0.995189	+	0.0979737i	$0.0312361\pi$
$241$			3.04192i			0.195947i	−0.995189	+	0.0979737i	$0.968764\pi$
$242$		0			0
$243$	−15.3596	−	2.66152i	−0.985317	−	0.170737i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.04601			0.575584
$248$		0			0
$249$	8.31806	−	8.62379i	0.527135	−	0.546511i
$250$		0			0
$251$	−6.32067			−0.398957			−0.199478	−	0.979902i	$-0.563925\pi$
$251$	−6.32067			−0.398957			−0.199478	+	0.979902i	$0.563925\pi$
$252$		0			0
$253$	−3.73361			−0.234730
$254$		0			0
$255$	−18.0101	−	4.47912i	−1.12784	−	0.280493i
$256$		0			0
$257$	24.5076			1.52874			0.764372	−	0.644776i	$-0.223049\pi$
$257$	24.5076			1.52874			0.764372	+	0.644776i	$0.223049\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−9.74222	+	18.3748i	−0.603028	+	1.13737i
$262$		0			0
$263$			24.3830i			1.50352i	0.659438	+	0.751759i	$0.270794\pi$
$263$			24.3830i			1.50352i	−0.659438	+	0.751759i	$0.729206\pi$
$264$		0			0
$265$	−9.31427	−	5.37760i	−0.572171	−	0.330343i
$266$		0			0
$267$	−11.7567	+	12.1888i	−0.719496	+	0.745942i
$268$		0			0
$269$	4.94525	−	8.56542i	0.301517	−	0.522243i	−0.674963	−	0.737852i	$-0.735840\pi$
$269$	4.94525	−	8.56542i	0.301517	−	0.522243i	0.976480	+	0.215609i	$0.0691737\pi$
$270$		0			0
$271$	5.10505	−	2.94740i	0.310110	−	0.179042i	−0.336866	−	0.941553i	$-0.609367\pi$
$271$	5.10505	−	2.94740i	0.310110	−	0.179042i	0.646976	+	0.762511i	$0.276034\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			1.05668i			0.0637202i
$276$		0			0
$277$	23.2939			1.39959			0.699796	−	0.714343i	$-0.253274\pi$
$277$	23.2939			1.39959			0.699796	+	0.714343i	$0.253274\pi$
$278$		0			0
$279$	−4.95933	+	9.35381i	−0.296908	+	0.559998i
$280$		0			0
$281$	21.7962	−	12.5840i	1.30025	−	0.750700i	0.319803	−	0.947484i	$-0.396383\pi$
$281$	21.7962	−	12.5840i	1.30025	−	0.750700i	0.980447	+	0.196784i	$0.0630499\pi$
$282$		0			0
$283$	8.62942	−	4.98220i	0.512966	−	0.296161i	−0.221086	−	0.975254i	$-0.570960\pi$
$283$	8.62942	−	4.98220i	0.512966	−	0.296161i	0.734052	+	0.679093i	$0.237627\pi$
$284$		0			0
$285$	20.2187	+	19.5019i	1.19765	+	1.15519i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.872317	+	1.51090i	0.0513128	+	0.0888764i
$290$		0			0
$291$	−0.288492	−	0.278264i	−0.0169117	−	0.0163121i
$292$		0			0
$293$	−6.79065	+	11.7618i	−0.396714	+	0.687129i	−0.993318	−	0.115406i	$-0.963183\pi$
$293$	−6.79065	+	11.7618i	−0.396714	+	0.687129i	0.596604	+	0.802536i	$0.296516\pi$
$294$		0			0
$295$	−5.56147	−	9.63275i	−0.323801	−	0.560841i
$296$		0			0
$297$	−1.45172	+	1.61805i	−0.0842371	+	0.0938890i
$298$		0			0
$299$	−6.82774	+	11.8260i	−0.394858	+	0.683915i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.83187	−	23.7725i	−0.392481	−	1.36570i
$304$		0			0
$305$	−4.42933	−	2.55728i	−0.253623	−	0.146429i
$306$		0			0
$307$			16.9849i			0.969381i	0.874686	+	0.484691i	$0.161068\pi$
$307$			16.9849i			0.969381i	−0.874686	+	0.484691i	$0.838932\pi$
$308$		0			0
$309$	−17.8883	+	5.14083i	−1.01763	+	0.292452i
$310$		0			0
$311$	−0.00148940	−	0.00257972i	−8.44563e−5	−	0.000146283i	0.865983	−	0.500073i	$-0.166694\pi$
$311$	−0.00148940	−	0.00257972i	−8.44563e−5	−	0.000146283i	−0.866068	+	0.499927i	$0.833360\pi$
$312$		0			0
$313$	10.6154	+	6.12878i	0.600015	+	0.346419i	0.769048	−	0.639191i	$-0.220731\pi$
$313$	10.6154	+	6.12878i	0.600015	+	0.346419i	−0.169032	+	0.985611i	$0.554064\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.0008	+	11.5475i	1.12336	+	0.648571i	0.942256	−	0.334894i	$-0.108700\pi$
$317$	20.0008	+	11.5475i	1.12336	+	0.648571i	0.181102	+	0.983464i	$0.442034\pi$
$318$		0			0
$319$	1.45014	+	2.51172i	0.0811922	+	0.140629i
$320$		0			0
$321$	−7.92494	−	7.64397i	−0.442327	−	0.426645i
$322$		0			0
$323$			23.0911i			1.28482i
$324$		0			0
$325$	3.34697	+	1.93237i	0.185656	+	0.107189i
$326$		0			0
$327$	−8.67440	−	2.15732i	−0.479695	−	0.119300i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.73106	−	2.99829i	0.0951479	−	0.164801i	−0.814522	−	0.580132i	$-0.803001\pi$
$331$	1.73106	−	2.99829i	0.0951479	−	0.164801i	0.909670	+	0.415331i	$0.136334\pi$
$332$		0			0
$333$	24.1122	+	12.7842i	1.32134	+	0.700568i
$334$		0			0
$335$	−17.5145	−	30.3359i	−0.956917	−	1.65743i
$336$		0			0
$337$	−9.13018	+	15.8139i	−0.497352	+	0.861440i	−0.999995	−	0.00305455i	$-0.999028\pi$
$337$	−9.13018	+	15.8139i	−0.497352	+	0.861440i	0.502643	+	0.864494i	$0.332361\pi$
$338$		0			0
$339$	4.43688	−	17.8403i	0.240978	−	0.968950i
$340$		0			0
$341$	0.738202	+	1.27860i	0.0399759	+	0.0692403i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−40.7557	+	11.7126i	−2.19421	+	0.630584i
$346$		0			0
$347$	−4.62386	+	2.66959i	−0.248222	+	0.143311i	−0.618950	−	0.785431i	$-0.712442\pi$
$347$	−4.62386	+	2.66959i	−0.248222	+	0.143311i	0.370728	+	0.928741i	$0.379108\pi$
$348$		0			0
$349$	−0.0136817	+	0.00789914i	−0.000732365	+	0.000422831i	−0.500366	−	0.865814i	$-0.666801\pi$
$349$	−0.0136817	+	0.00789914i	−0.000732365	+	0.000422831i	0.499634	+	0.866237i	$0.333468\pi$
$350$		0			0
$351$	2.47030	+	7.55719i	0.131855	+	0.403373i
$352$		0			0
$353$	−34.3085			−1.82606			−0.913029	−	0.407894i	$-0.866263\pi$
$353$	−34.3085			−1.82606			−0.913029	+	0.407894i	$0.866263\pi$
$354$		0			0
$355$			23.3462i			1.23909i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.42754	−	3.13359i	0.286454	−	0.165385i	−0.349887	−	0.936792i	$-0.613780\pi$
$359$	5.42754	−	3.13359i	0.286454	−	0.165385i	0.636342	+	0.771407i	$0.280447\pi$
$360$		0			0
$361$	7.97583	−	13.8145i	0.419781	−	0.727081i
$362$		0			0
$363$	−5.17869	−	18.0200i	−0.271811	−	0.945807i
$364$		0			0
$365$	4.52811	+	2.61430i	0.237012	+	0.136839i
$366$		0			0
$367$		−	19.0397i		−	0.993863i	−0.867790	−	0.496931i	$-0.834460\pi$
$367$		−	19.0397i		−	0.993863i	0.867790	−	0.496931i	$-0.165540\pi$
$368$		0			0
$369$	0.229986	+	6.37002i	0.0119726	+	0.331610i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.8380			0.561172			0.280586	−	0.959829i	$-0.409471\pi$
$373$	10.8380			0.561172			0.280586	+	0.959829i	$0.409471\pi$
$374$		0			0
$375$	−3.24717	−	11.2990i	−0.167683	−	0.583479i
$376$		0			0
$377$	10.6076			0.546320
$378$		0			0
$379$	0.700312			0.0359726			0.0179863	−	0.999838i	$-0.494274\pi$
$379$	0.700312			0.0359726			0.0179863	+	0.999838i	$0.494274\pi$
$380$		0			0
$381$	−4.92318	−	17.1310i	−0.252222	−	0.877645i
$382$		0			0
$383$	−38.0470			−1.94411			−0.972056	−	0.234749i	$-0.924573\pi$
$383$	−38.0470			−1.94411			−0.972056	+	0.234749i	$0.924573\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	30.6317	+	16.2407i	1.55710	+	0.825564i
$388$		0			0
$389$		−	19.2787i		−	0.977468i	−0.872433	−	0.488734i	$-0.837459\pi$
$389$		−	19.2787i		−	0.977468i	0.872433	−	0.488734i	$-0.162541\pi$
$390$		0			0
$391$	−30.1874	−	17.4287i	−1.52664	−	0.881407i
$392$		0			0
$393$	9.40584	+	32.7290i	0.474462	+	1.65096i
$394$		0			0
$395$	−1.18959	+	2.06044i	−0.0598549	+	0.103672i
$396$		0			0
$397$	17.3610	−	10.0234i	0.871325	−	0.503059i	0.00353639	−	0.999994i	$-0.498874\pi$
$397$	17.3610	−	10.0234i	0.871325	−	0.503059i	0.867788	+	0.496934i	$0.165541\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			30.5109i			1.52364i	0.647789	+	0.761820i	$0.275694\pi$
$401$			30.5109i			1.52364i	−0.647789	+	0.761820i	$0.724306\pi$
$402$		0			0
$403$	5.39987			0.268987
$404$		0			0
$405$	−10.7708	+	22.2166i	−0.535207	+	1.10395i
$406$		0			0
$407$	3.29598	−	1.90294i	0.163376	−	0.0943250i
$408$		0			0
$409$	0.150631	−	0.0869667i	0.00744821	−	0.00430023i	−0.496271	−	0.868168i	$-0.665298\pi$
$409$	0.150631	−	0.0869667i	0.00744821	−	0.00430023i	0.503719	+	0.863867i	$0.331965\pi$
$410$		0			0
$411$	8.96533	−	2.57650i	0.442227	−	0.127090i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−9.48860	−	16.4347i	−0.465777	−	0.806749i
$416$		0			0
$417$	7.13614	−	28.6937i	0.349458	−	1.40514i
$418$		0			0
$419$	−14.0690	+	24.3682i	−0.687316	+	1.19047i	0.285387	+	0.958412i	$0.407878\pi$
$419$	−14.0690	+	24.3682i	−0.687316	+	1.19047i	−0.972703	+	0.232054i	$0.925455\pi$
$420$		0			0
$421$	−1.56130	−	2.70424i	−0.0760929	−	0.131797i	0.825468	−	0.564449i	$-0.190911\pi$
$421$	−1.56130	−	2.70424i	−0.0760929	−	0.131797i	−0.901561	+	0.432652i	$0.857578\pi$
$422$		0			0
$423$	0.191671	+	5.30878i	0.00931934	+	0.258122i
$424$		0			0
$425$	−4.93264	+	8.54358i	−0.239268	+	0.414424i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.07596	+	0.267592i	0.0519480	+	0.0129195i
$430$		0			0
$431$	−8.58876	−	4.95872i	−0.413706	−	0.238853i	0.278675	−	0.960385i	$-0.410105\pi$
$431$	−8.58876	−	4.95872i	−0.413706	−	0.238853i	−0.692381	+	0.721532i	$0.743438\pi$
$432$		0			0
$433$			17.1274i			0.823092i	0.911389	+	0.411546i	$0.135011\pi$
$433$			17.1274i			0.823092i	−0.911389	+	0.411546i	$0.864989\pi$
$434$		0			0
$435$	23.7090	+	22.8684i	1.13676	+	1.09646i
$436$		0			0
$437$	26.3808	+	45.6929i	1.26196	+	2.18579i
$438$		0			0
$439$	18.5795	+	10.7269i	0.886750	+	0.511965i	0.872878	−	0.487938i	$-0.162251\pi$
$439$	18.5795	+	10.7269i	0.886750	+	0.511965i	0.0138721	+	0.999904i	$0.495584\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.84340	−	3.37369i	−0.277628	−	0.160289i	0.354721	−	0.934972i	$-0.384576\pi$
$443$	−5.84340	−	3.37369i	−0.277628	−	0.160289i	−0.632349	+	0.774683i	$0.717909\pi$
$444$		0			0
$445$	13.4111	+	23.2287i	0.635747	+	1.10115i
$446$		0			0
$447$	17.8988	−	5.14384i	0.846583	−	0.243295i
$448$		0			0
$449$			5.81624i			0.274485i	0.990537	+	0.137243i	$0.0438240\pi$
$449$			5.81624i			0.274485i	−0.990537	+	0.137243i	$0.956176\pi$
$450$		0			0
$451$	0.769801	+	0.444445i	0.0362485	+	0.0209281i
$452$		0			0
$453$	−3.61886	−	12.5924i	−0.170029	−	0.591640i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.6949	−	28.9164i	0.780954	−	1.35265i	−0.150432	−	0.988620i	$-0.548066\pi$
$457$	16.6949	−	28.9164i	0.780954	−	1.35265i	0.931386	−	0.364032i	$-0.118600\pi$
$458$		0			0
$459$	−19.2907	+	6.30578i	−0.900414	+	0.294328i
$460$		0			0
$461$	−18.5154	−	32.0696i	−0.862347	−	1.49363i	−0.869657	−	0.493656i	$-0.835660\pi$
$461$	−18.5154	−	32.0696i	−0.862347	−	1.49363i	0.00730959	−	0.999973i	$-0.497673\pi$
$462$		0			0
$463$	10.5618	−	18.2935i	0.490848	−	0.850173i	−0.509097	−	0.860709i	$-0.670020\pi$
$463$	10.5618	−	18.2935i	0.490848	−	0.850173i	0.999944	+	0.0105362i	$0.00335383\pi$
$464$		0			0
$465$	12.0692	+	11.6413i	0.559696	+	0.539853i
$466$		0			0
$467$	9.30470	+	16.1162i	0.430570	+	0.745770i	0.996922	−	0.0783937i	$-0.0249791\pi$
$467$	9.30470	+	16.1162i	0.430570	+	0.745770i	−0.566352	+	0.824163i	$0.691646\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−15.3043	−	14.7617i	−0.705185	−	0.680184i
$472$		0			0
$473$	4.18715	−	2.41745i	0.192525	−	0.111155i
$474$		0			0
$475$	12.9319	−	7.46624i	0.593356	−	0.342574i
$476$		0			0
$477$	−11.7539	+	0.424366i	−0.538172	+	0.0194304i
$478$		0			0
$479$	−14.3341			−0.654940			−0.327470	−	0.944862i	$-0.606196\pi$
$479$	−14.3341			−0.654940			−0.327470	+	0.944862i	$0.606196\pi$
$480$		0			0
$481$		−	13.9198i		−	0.634687i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.549791	+	0.317422i	−0.0249647	+	0.0144134i
$486$		0			0
$487$	−5.64829	+	9.78313i	−0.255949	+	0.443316i	−0.965153	−	0.261687i	$-0.915721\pi$
$487$	−5.64829	+	9.78313i	−0.255949	+	0.443316i	0.709204	+	0.705003i	$0.249054\pi$
$488$		0			0
$489$	14.2308	−	14.7539i	0.643541	−	0.667195i
$490$		0			0
$491$	−8.84097	−	5.10434i	−0.398988	−	0.230356i	0.287059	−	0.957913i	$-0.407322\pi$
$491$	−8.84097	−	5.10434i	−0.398988	−	0.230356i	−0.686047	+	0.727557i	$0.740656\pi$
$492$		0			0
$493$			27.0773i			1.21950i
$494$		0			0
$495$	1.82799	+	2.91771i	0.0821619	+	0.131141i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.1334			−0.856531			−0.428265	−	0.903653i	$-0.640875\pi$
$499$	−19.1334			−0.856531			−0.428265	+	0.903653i	$0.640875\pi$
$500$		0			0
$501$	−22.8210	−	5.67559i	−1.01957	−	0.253567i
$502$		0			0
$503$	0.268917			0.0119904			0.00599520	−	0.999982i	$-0.498092\pi$
$503$	0.268917			0.0119904			0.00599520	+	0.999982i	$0.498092\pi$
$504$		0			0
$505$	−39.1763			−1.74332
$506$		0			0
$507$	−12.8166	+	13.2877i	−0.569205	+	0.590126i
$508$		0			0
$509$	−21.8877			−0.970157			−0.485079	−	0.874471i	$-0.661209\pi$
$509$	−21.8877			−0.970157			−0.485079	+	0.874471i	$0.661209\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	30.0596	+	6.33367i	1.32716	+	0.279639i
$514$		0			0
$515$			29.4793i			1.29901i
$516$		0			0
$517$	0.641553	+	0.370401i	0.0282155	+	0.0162902i
$518$		0			0
$519$	−27.9386	−	6.94833i	−1.22637	−	0.304998i
$520$		0			0
$521$	0.856074	−	1.48276i	0.0375053	−	0.0649610i	−0.846663	−	0.532129i	$-0.821392\pi$
$521$	0.856074	−	1.48276i	0.0375053	−	0.0649610i	0.884169	+	0.467168i	$0.154726\pi$
$522$		0			0
$523$	−7.16320	+	4.13568i	−0.313225	+	0.180841i	−0.648369	−	0.761326i	$-0.724548\pi$
$523$	−7.16320	+	4.13568i	−0.313225	+	0.180841i	0.335144	+	0.942167i	$0.391215\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			13.7839i			0.600435i
$528$		0			0
$529$	−56.6466			−2.46290
$530$		0			0
$531$	−10.7466	−	5.69780i	−0.466364	−	0.247263i
$532$		0			0
$533$	2.81550	−	1.62553i	0.121953	−	0.0704096i
$534$		0			0
$535$	−15.1029	+	8.71966i	−0.652955	+	0.376984i
$536$		0			0
$537$	−7.14779	+	28.7406i	−0.308450	+	1.24025i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.1997	−	17.6664i	−0.438518	−	0.759536i	0.559057	−	0.829129i	$-0.311163\pi$
$541$	−10.1997	−	17.6664i	−0.438518	−	0.759536i	−0.997575	+	0.0695932i	$0.977830\pi$
$542$		0			0
$543$	−30.3255	+	8.71510i	−1.30139	+	0.374001i
$544$		0			0
$545$	−7.07875	+	12.2608i	−0.303220	+	0.525193i
$546$		0			0
$547$	18.9630	+	32.8449i	0.810801	+	1.40435i	0.912304	+	0.409513i	$0.134301\pi$
$547$	18.9630	+	32.8449i	0.810801	+	1.40435i	−0.101503	+	0.994835i	$0.532365\pi$
$548$		0			0
$549$	−5.58946	+	0.201804i	−0.238552	+	0.00861280i
$550$		0			0
$551$	20.4927	−	35.4943i	0.873017	−	1.51211i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	30.0089	−	31.1120i	1.27381	−	1.32063i
$556$		0			0
$557$	−14.5919	−	8.42463i	−0.618278	−	0.356963i	0.157920	−	0.987452i	$-0.449521\pi$
$557$	−14.5919	−	8.42463i	−0.618278	−	0.356963i	−0.776198	+	0.630489i	$0.782854\pi$
$558$		0			0
$559$		−	17.6834i		−	0.747928i
$560$		0			0
$561$	−0.683064	+	2.74654i	−0.0288390	+	0.115959i
$562$		0			0
$563$	8.28035	+	14.3420i	0.348975	+	0.604443i	0.986068	−	0.166345i	$-0.0531965\pi$
$563$	8.28035	+	14.3420i	0.348975	+	0.604443i	−0.637093	+	0.770787i	$0.719863\pi$
$564$		0			0
$565$	−25.2162	−	14.5586i	−1.06085	−	0.612484i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.49856	−	3.17460i	−0.230512	−	0.133086i	0.380296	−	0.924865i	$-0.375822\pi$
$569$	−5.49856	−	3.17460i	−0.230512	−	0.133086i	−0.610808	+	0.791779i	$0.709155\pi$
$570$		0			0
$571$	−22.8703	−	39.6125i	−0.957092	−	1.65773i	−0.729507	−	0.683973i	$-0.760250\pi$
$571$	−22.8703	−	39.6125i	−0.957092	−	1.65773i	−0.227585	−	0.973758i	$-0.573083\pi$
$572$		0			0
$573$	−8.77831	+	35.2967i	−0.366719	+	1.47454i
$574$		0			0
$575$			22.5414i			0.940043i
$576$		0			0
$577$	−15.3719	−	8.87497i	−0.639940	−	0.369470i	0.144651	−	0.989483i	$-0.453794\pi$
$577$	−15.3719	−	8.87497i	−0.639940	−	0.369470i	−0.784592	+	0.620013i	$0.787127\pi$
$578$		0			0
$579$	8.38686	−	8.69513i	0.348546	−	0.361357i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.820082	+	1.42042i	−0.0339643	+	0.0588280i
$584$		0			0
$585$	12.5846	−	0.454358i	0.520307	−	0.0187854i
$586$		0			0
$587$	4.41148	+	7.64091i	0.182081	+	0.315374i	0.942589	−	0.333955i	$-0.108383\pi$
$587$	4.41148	+	7.64091i	0.182081	+	0.315374i	−0.760508	+	0.649329i	$0.775050\pi$
$588$		0			0
$589$	10.4319	−	18.0686i	0.429839	−	0.744503i
$590$		0			0
$591$	26.7606	−	7.69061i	1.10079	−	0.316349i
$592$		0			0
$593$	4.24849	+	7.35860i	0.174465	+	0.302181i	0.939976	−	0.341241i	$-0.110847\pi$
$593$	4.24849	+	7.35860i	0.174465	+	0.302181i	−0.765511	+	0.643422i	$0.777514\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.63048	−	10.5769i	0.107658	−	0.432885i
$598$		0			0
$599$	−3.21158	+	1.85421i	−0.131222	+	0.0757609i	−0.564174	−	0.825656i	$-0.690805\pi$
$599$	−3.21158	+	1.85421i	−0.131222	+	0.0757609i	0.432952	+	0.901417i	$0.357472\pi$
$600$		0			0
$601$	6.14043	−	3.54518i	0.250473	−	0.144611i	−0.369508	−	0.929228i	$-0.620474\pi$
$601$	6.14043	−	3.54518i	0.250473	−	0.144611i	0.619981	+	0.784617i	$0.287140\pi$
$602$		0			0
$603$	−33.8438	−	17.9438i	−1.37823	−	0.730727i
$604$		0			0
$605$	−29.6964			−1.20733
$606$		0			0
$607$		−	33.9940i		−	1.37977i	−0.723918	−	0.689886i	$-0.757661\pi$
$607$		−	33.9940i		−	1.37977i	0.723918	−	0.689886i	$-0.242339\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.34644	−	1.35472i	0.0949270	−	0.0548061i
$612$		0			0
$613$	−11.6761	+	20.2237i	−0.471595	+	0.816827i	−0.999472	−	0.0324944i	$-0.989655\pi$
$613$	−11.6761	+	20.2237i	−0.471595	+	0.816827i	0.527877	+	0.849321i	$0.322988\pi$
$614$		0			0
$615$	9.79732	+	2.43659i	0.395066	+	0.0982530i
$616$		0			0
$617$	−39.0817	−	22.5638i	−1.57337	−	0.908386i	−0.995752	−	0.0920787i	$-0.970649\pi$
$617$	−39.0817	−	22.5638i	−1.57337	−	0.908386i	−0.577618	−	0.816307i	$-0.696018\pi$
$618$		0			0
$619$			9.21352i			0.370323i	0.982708	+	0.185161i	$0.0592808\pi$
$619$			9.21352i			0.370323i	−0.982708	+	0.185161i	$0.940719\pi$
$620$		0			0
$621$	−30.9685	+	34.5169i	−1.24272	+	1.38511i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−31.2493			−1.24997
$626$		0			0
$627$	2.97403	−	3.08334i	0.118771	−	0.123137i
$628$		0			0
$629$	35.5320			1.41675
$630$		0			0
$631$	17.6136			0.701188			0.350594	−	0.936528i	$-0.385980\pi$
$631$	17.6136			0.701188			0.350594	+	0.936528i	$0.385980\pi$
$632$		0			0
$633$	4.36394	+	1.08531i	0.173451	+	0.0431374i
$634$		0			0
$635$	−28.2312			−1.12032
$636$		0			0
$637$		0			0
$638$		0			0
$639$	13.5548	+	21.6352i	0.536218	+	0.855875i
$640$		0			0
$641$		−	19.1402i		−	0.755991i	−0.925807	−	0.377996i	$-0.876613\pi$
$641$		−	19.1402i		−	0.755991i	0.925807	−	0.377996i	$-0.123387\pi$
$642$		0			0
$643$	−2.01129	−	1.16122i	−0.0793177	−	0.0457941i	0.459817	−	0.888014i	$-0.347915\pi$
$643$	−2.01129	−	1.16122i	−0.0793177	−	0.0457941i	−0.539134	+	0.842220i	$0.681248\pi$
$644$		0			0
$645$	38.1228	−	39.5240i	1.50108	−	1.55626i
$646$		0			0
$647$	12.9310	−	22.3971i	0.508370	−	0.880522i	−0.491583	−	0.870831i	$-0.663582\pi$
$647$	12.9310	−	22.3971i	0.508370	−	0.880522i	0.999953	−	0.00969167i	$-0.00308500\pi$
$648$		0			0
$649$	−1.46899	+	0.848123i	−0.0576630	+	0.0332918i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	23.2257i		−	0.908891i	−0.890774	−	0.454446i	$-0.849837\pi$
$653$		−	23.2257i		−	0.908891i	0.890774	−	0.454446i	$-0.150163\pi$
$654$		0			0
$655$	53.9363			2.10746
$656$		0			0
$657$	5.71410	−	0.206305i	0.222928	−	0.00804871i
$658$		0			0
$659$	13.7002	−	7.90981i	0.533684	−	0.308122i	−0.208832	−	0.977952i	$-0.566966\pi$
$659$	13.7002	−	7.90981i	0.533684	−	0.308122i	0.742515	+	0.669829i	$0.233633\pi$
$660$		0			0
$661$	15.8006	−	9.12248i	0.614572	−	0.354823i	−0.160181	−	0.987088i	$-0.551208\pi$
$661$	15.8006	−	9.12248i	0.614572	−	0.354823i	0.774753	+	0.632264i	$0.217874\pi$
$662$		0			0
$663$	7.45036	+	7.18622i	0.289348	+	0.279090i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	30.9349	+	53.5807i	1.19780	+	2.07465i
$668$		0			0
$669$	29.8287	+	28.7712i	1.15324	+	1.11236i
$670$		0			0
$671$	−0.389984	+	0.675472i	−0.0150552	+	0.0260763i
$672$		0			0
$673$	14.4184	+	24.9733i	0.555787	+	0.962651i	0.997842	+	0.0656633i	$0.0209163\pi$
$673$	14.4184	+	24.9733i	0.555787	+	0.962651i	−0.442055	+	0.896988i	$0.645750\pi$
$674$		0			0
$675$	9.76889	+	8.76463i	0.376005	+	0.337351i
$676$		0			0
$677$	16.7668	−	29.0409i	0.644400	−	1.11613i	−0.340040	−	0.940411i	$-0.610441\pi$
$677$	16.7668	−	29.0409i	0.644400	−	1.11613i	0.984440	−	0.175722i	$-0.0562261\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.78548	−	6.21285i	−0.0684198	−	0.238077i
$682$		0			0
$683$	19.0943	+	11.0241i	0.730621	+	0.421824i	0.818649	−	0.574294i	$-0.194723\pi$
$683$	19.0943	+	11.0241i	0.730621	+	0.421824i	−0.0880282	+	0.996118i	$0.528057\pi$
$684$		0			0
$685$		−	14.7745i		−	0.564506i
$686$		0			0
$687$	35.0715	−	10.0790i	1.33806	−	0.384539i
$688$		0			0
$689$	2.99941	+	5.19512i	0.114268	+	0.197918i
$690$		0			0
$691$	22.8662	+	13.2018i	0.869869	+	0.502219i	0.867305	−	0.497777i	$-0.165850\pi$
$691$	22.8662	+	13.2018i	0.869869	+	0.502219i	0.00256453	+	0.999997i	$0.499184\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−40.5569	−	23.4156i	−1.53841	−	0.888203i
$696$		0			0
$697$	4.14938	+	7.18694i	0.157169	+	0.272225i
$698$		0			0
$699$	−15.9125	−	15.3484i	−0.601868	−	0.580530i
$700$		0			0
$701$		−	20.5140i		−	0.774804i	−0.921911	−	0.387402i	$-0.873373\pi$
$701$		−	20.5140i		−	0.774804i	0.921911	−	0.387402i	$-0.126627\pi$
$702$		0			0
$703$	−46.5772	−	26.8913i	−1.75669	−	1.01423i
$704$		0			0
$705$	8.16510	+	2.03066i	0.307515	+	0.0764791i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.13054	−	5.42226i	0.117570	−	0.203637i	−0.801234	−	0.598351i	$-0.795823\pi$
$709$	3.13054	−	5.42226i	0.117570	−	0.203637i	0.918804	+	0.394714i	$0.129156\pi$
$710$		0			0
$711$	0.0938752	+	2.60010i	0.00352060	+	0.0975115i
$712$		0			0
$713$	15.7476	+	27.2756i	0.589751	+	1.02148i
$714$		0			0
$715$	0.878041	−	1.52081i	0.0328369	−	0.0568751i
$716$		0			0
$717$	5.33479	−	21.4507i	0.199232	−	0.801091i
$718$		0			0
$719$	−11.6111	−	20.1111i	−0.433023	−	0.750017i	0.564109	−	0.825700i	$-0.309220\pi$
$719$	−11.6111	−	20.1111i	−0.433023	−	0.750017i	−0.997132	+	0.0756828i	$0.975886\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.06380	−	1.45526i	0.188325	−	0.0541218i
$724$		0			0
$725$	15.1643	−	8.75512i	0.563189	−	0.325157i
$726$		0			0
$727$	2.50999	−	1.44914i	0.0930903	−	0.0537457i	−0.452732	−	0.891647i	$-0.649551\pi$
$727$	2.50999	−	1.44914i	0.0930903	−	0.0537457i	0.545822	+	0.837901i	$0.316217\pi$
$728$		0			0
$729$	2.91748	+	26.8419i	0.108055	+	0.994145i
$730$		0			0
$731$	45.1392			1.66953
$732$		0			0
$733$			11.8891i			0.439135i	0.975597	+	0.219568i	$0.0704647\pi$
$733$			11.8891i			0.439135i	−0.975597	+	0.219568i	$0.929535\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.62622	+	2.67095i	−0.170409	+	0.0983858i
$738$		0			0
$739$	17.2254	−	29.8354i	0.633648	−	1.09751i	−0.353151	−	0.935566i	$-0.614890\pi$
$739$	17.2254	−	29.8354i	0.633648	−	1.09751i	0.986800	−	0.161945i	$-0.0517767\pi$
$740$		0			0
$741$	−4.32763	−	15.0586i	−0.158979	−	0.553193i
$742$		0			0
$743$	−2.44069	−	1.40913i	−0.0895401	−	0.0516960i	0.454561	−	0.890715i	$-0.349796\pi$
$743$	−2.44069	−	1.40913i	−0.0895401	−	0.0516960i	−0.544101	+	0.839019i	$0.683129\pi$
$744$		0			0
$745$		−	29.4965i		−	1.08067i
$746$		0			0
$747$	−18.3352	−	9.72119i	−0.670848	−	0.355680i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.72089			0.281739			0.140870	−	0.990028i	$-0.455010\pi$
$751$	7.72089			0.281739			0.140870	+	0.990028i	$0.455010\pi$
$752$		0			0
$753$	3.02382	+	10.5218i	0.110194	+	0.383437i
$754$		0			0
$755$	−20.7517			−0.755233
$756$		0			0
$757$	1.17924			0.0428603			0.0214302	−	0.999770i	$-0.493178\pi$
$757$	1.17924			0.0428603			0.0214302	+	0.999770i	$0.493178\pi$
$758$		0			0
$759$	1.78617	+	6.21524i	0.0648338	+	0.225599i
$760$		0			0
$761$	3.13289			0.113567			0.0567835	−	0.998387i	$-0.481916\pi$
$761$	3.13289			0.113567			0.0567835	+	0.998387i	$0.481916\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.15981	+	32.1237i	0.0419330	+	1.16144i
$766$		0			0
$767$			6.20393i			0.224011i
$768$		0			0
$769$	5.53497	+	3.19562i	0.199596	+	0.115237i	0.596467	−	0.802637i	$-0.296571\pi$
$769$	5.53497	+	3.19562i	0.199596	+	0.115237i	−0.396871	+	0.917874i	$0.629904\pi$
$770$		0			0
$771$	−11.7245	−	40.7971i	−0.422247	−	1.46927i
$772$		0			0
$773$	23.9779	−	41.5309i	0.862425	−	1.49376i	−0.00715621	−	0.999974i	$-0.502278\pi$
$773$	23.9779	−	41.5309i	0.862425	−	1.49376i	0.869581	−	0.493790i	$-0.164389\pi$
$774$		0			0
$775$	7.71948	−	4.45685i	0.277292	−	0.160095i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	12.5613i		−	0.450057i
$780$		0			0
$781$	3.56029			0.127397
$782$		0			0
$783$	35.2487	+	7.42705i	1.25969	+	0.265421i
$784$		0			0
$785$	−29.1661	+	16.8390i	−1.04098	+	0.601011i
$786$		0			0
$787$	−5.23136	+	3.02033i	−0.186478	+	0.107663i	−0.590333	−	0.807160i	$-0.701003\pi$
$787$	−5.23136	+	3.02033i	−0.186478	+	0.107663i	0.403855	+	0.914823i	$0.367670\pi$
$788$		0			0
$789$	40.5896	−	11.6649i	1.44503	−	0.415280i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.42635	+	2.47050i	0.0506510	+	0.0877301i
$794$		0			0
$795$	−4.49597	+	18.0779i	−0.159455	+	0.641155i
$796$		0			0
$797$	0.782501	−	1.35533i	0.0277176	−	0.0480083i	−0.851834	−	0.523812i	$-0.824509\pi$
$797$	0.782501	−	1.35533i	0.0277176	−	0.0480083i	0.879551	+	0.475804i	$0.157843\pi$
$798$		0			0
$799$	3.45810	+	5.98961i	0.122339	+	0.211897i
$800$		0			0
$801$	25.9148	+	13.7398i	0.915653	+	0.485474i
$802$		0			0
$803$	0.398681	−	0.690535i	0.0140691	−	0.0243685i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−16.6244	−	4.13450i	−0.585207	−	0.145541i
$808$		0			0
$809$	15.3445	+	8.85918i	0.539485	+	0.311472i	0.744870	−	0.667209i	$-0.232511\pi$
$809$	15.3445	+	8.85918i	0.539485	+	0.311472i	−0.205385	+	0.978681i	$0.565845\pi$
$810$		0			0
$811$			27.5261i			0.966571i	0.875463	+	0.483285i	$0.160557\pi$
$811$			27.5261i			0.966571i	−0.875463	+	0.483285i	$0.839443\pi$
$812$		0			0
$813$	−7.34872	−	7.08819i	−0.257731	−	0.248594i
$814$		0			0
$815$	−16.2334	−	28.1171i	−0.568633	−	0.984901i
$816$		0			0
$817$	−59.1707	−	34.1622i	−2.07012	−	1.19519i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	23.0343	+	13.2989i	0.803903	+	0.464134i	0.844834	−	0.535028i	$-0.179699\pi$
$821$	23.0343	+	13.2989i	0.803903	+	0.464134i	−0.0409311	+	0.999162i	$0.513032\pi$
$822$		0			0
$823$	−12.0797	−	20.9227i	−0.421073	−	0.729319i	0.574972	−	0.818173i	$-0.305013\pi$
$823$	−12.0797	−	20.9227i	−0.421073	−	0.729319i	−0.996045	+	0.0888537i	$0.971680\pi$
$824$		0			0
$825$	1.75902	−	0.505518i	0.0612414	−	0.0175999i
$826$		0			0
$827$		−	9.64923i		−	0.335537i	−0.985826	−	0.167768i	$-0.946344\pi$
$827$		−	9.64923i		−	0.335537i	0.985826	−	0.167768i	$-0.0536561\pi$
$828$		0			0
$829$	25.1481	+	14.5193i	0.873430	+	0.504275i	0.868486	−	0.495713i	$-0.165093\pi$
$829$	25.1481	+	14.5193i	0.873430	+	0.504275i	0.00494329	+	0.999988i	$0.498426\pi$
$830$		0			0
$831$	−11.1438	−	38.7766i	−0.386575	−	1.34515i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.6231	+	32.2562i	−0.644480	+	1.11627i
$836$		0			0
$837$	17.9436	+	3.78078i	0.620221	+	0.130683i
$838$		0			0
$839$	6.84383	+	11.8539i	0.236275	+	0.409241i	0.959642	−	0.281223i	$-0.0907400\pi$
$839$	6.84383	+	11.8539i	0.236275	+	0.409241i	−0.723367	+	0.690463i	$0.757407\pi$
$840$		0			0
$841$	9.53027	−	16.5069i	0.328630	−	0.569204i
$842$		0			0
$843$	−31.3756	−	30.2632i	−1.08063	−	1.04232i
$844$		0			0
$845$	14.6202	+	25.3229i	0.502949	+	0.871134i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−12.4221	−	11.9817i	−0.426324	−	0.411209i
$850$		0			0
$851$	70.3110	−	40.5941i	2.41023	−	1.39155i
$852$		0			0
$853$	40.5184	−	23.3933i	1.38732	−	0.800972i	0.394310	−	0.918977i	$-0.370983\pi$
$853$	40.5184	−	23.3933i	1.38732	−	0.800972i	0.993013	+	0.118006i	$0.0376501\pi$
$854$		0			0
$855$	22.7915	−	42.9872i	0.779454	−	1.47013i
$856$		0			0
$857$	−31.7960			−1.08613			−0.543065	−	0.839691i	$-0.682736\pi$
$857$	−31.7960			−1.08613			−0.543065	+	0.839691i	$0.682736\pi$
$858$		0			0
$859$			25.2885i			0.862832i	0.902153	+	0.431416i	$0.141986\pi$
$859$			25.2885i			0.862832i	−0.902153	+	0.431416i	$0.858014\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.9513	+	9.20946i	−0.542987	+	0.313494i	−0.746289	−	0.665622i	$-0.768166\pi$
$863$	−15.9513	+	9.20946i	−0.542987	+	0.313494i	0.203302	+	0.979116i	$0.434833\pi$
$864$		0			0
$865$	−22.7993	+	39.4896i	−0.775200	+	1.34269i
$866$		0			0
$867$	2.09783	−	2.17494i	0.0712461	−	0.0738648i
$868$		0			0
$869$	0.314216	+	0.181413i	0.0106590	+	0.00615400i
$870$		0			0
$871$			19.5377i			0.662010i
$872$		0			0
$873$	−0.325203	+	0.613366i	−0.0110064	+	0.0207593i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.89389			−0.300325			−0.150163	−	0.988661i	$-0.547980\pi$
$877$	−8.89389			−0.300325			−0.150163	+	0.988661i	$0.547980\pi$
$878$		0			0
$879$	22.8281	+	5.67736i	0.769974	+	0.191493i
$880$		0			0
$881$	13.1721			0.443780			0.221890	−	0.975072i	$-0.428777\pi$
$881$	13.1721			0.443780			0.221890	+	0.975072i	$0.428777\pi$
$882$		0			0
$883$	12.6729			0.426477			0.213239	−	0.977000i	$-0.431599\pi$
$883$	12.6729			0.426477			0.213239	+	0.977000i	$0.431599\pi$
$884$		0			0
$885$	−13.3748	+	13.8664i	−0.449587	+	0.466112i
$886$		0			0
$887$	33.3983			1.12141			0.560703	−	0.828017i	$-0.310531\pi$
$887$	33.3983			1.12141			0.560703	+	0.828017i	$0.310531\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	3.38803	+	1.64255i	0.113503	+	0.0550275i
$892$		0			0
$893$		−	10.4686i		−	0.350320i
$894$		0			0
$895$	40.6231	+	23.4538i	1.35788	+	0.783974i
$896$		0			0
$897$	22.9528	+	5.70837i	0.766372	+	0.190597i
$898$		0			0
$899$	12.2328	−	21.1877i	0.407985	−	0.706651i
$900$		0			0
$901$	−13.2612	+	7.65638i	−0.441796	+	0.255071i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			49.9753i			1.66124i
$906$		0			0
$907$	−29.3127			−0.973311			−0.486655	−	0.873594i	$-0.661783\pi$
$907$	−29.3127			−0.973311			−0.486655	+	0.873594i	$0.661783\pi$
$908$		0			0
$909$	−36.3051	+	22.7457i	−1.20416	+	0.754426i
$910$		0			0
$911$	1.72555	−	0.996246i	0.0571700	−	0.0330071i	−0.471143	−	0.882057i	$-0.656158\pi$
$911$	1.72555	−	0.996246i	0.0571700	−	0.0330071i	0.528313	+	0.849050i	$0.322825\pi$
$912$		0			0
$913$	−2.50629	+	1.44701i	−0.0829462	+	0.0478890i
$914$		0			0
$915$	−2.13802	+	8.59679i	−0.0706809	+	0.284201i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.897678	−	1.55482i	−0.0296117	−	0.0512889i	0.850840	−	0.525425i	$-0.176094\pi$
$919$	−0.897678	−	1.55482i	−0.0296117	−	0.0512889i	−0.880451	+	0.474136i	$0.842760\pi$
$920$		0			0
$921$	28.2743	−	8.12562i	0.931671	−	0.267748i
$922$		0			0
$923$	6.51079	−	11.2770i	0.214305	−	0.371188i
$924$		0			0
$925$	−11.4889	−	19.8993i	−0.377751	−	0.654284i
$926$		0			0
$927$	17.1156	+	27.3188i	0.562150	+	0.897266i
$928$		0			0
$929$	12.4178	−	21.5083i	0.407415	−	0.705664i	−0.587184	−	0.809453i	$-0.699763\pi$
$929$	12.4178	−	21.5083i	0.407415	−	0.705664i	0.994599	+	0.103789i	$0.0330968\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.00358186	+	0.00371351i	−0.000117265	+	0.000121575i
$934$		0			0
$935$	3.88207	+	2.24132i	0.126957	+	0.0732988i
$936$		0			0
$937$			27.9046i			0.911605i	0.890081	+	0.455802i	$0.150648\pi$
$937$			27.9046i			0.911605i	−0.890081	+	0.455802i	$0.849352\pi$
$938$		0			0
$939$	5.12400	−	20.6031i	0.167215	−	0.672357i
$940$		0			0
$941$	−26.2537	−	45.4728i	−0.855847	−	1.48237i	−0.875857	−	0.482571i	$-0.839703\pi$
$941$	−26.2537	−	45.4728i	−0.855847	−	1.48237i	0.0200094	−	0.999800i	$-0.493630\pi$
$942$		0			0
$943$	16.4216	+	9.48104i	0.534762	+	0.308745i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−37.3591	−	21.5693i	−1.21401	−	0.700907i	−0.250377	−	0.968148i	$-0.580555\pi$
$947$	−37.3591	−	21.5693i	−1.21401	−	0.700907i	−0.963630	+	0.267241i	$0.913888\pi$
$948$		0			0
$949$	−1.45815	−	2.52559i	−0.0473336	−	0.0819843i
$950$		0			0
$951$	9.65433	−	38.8191i	0.313063	−	1.25880i
$952$		0			0
$953$		−	59.9829i		−	1.94304i	−0.236965	−	0.971518i	$-0.576153\pi$
$953$		−	59.9829i		−	1.94304i	0.236965	−	0.971518i	$-0.423847\pi$
$954$		0			0
$955$	49.8899	+	28.8040i	1.61440	+	0.932074i
$956$		0			0
$957$	3.48743	−	3.61562i	0.112733	−	0.116876i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9.27285	+	16.0610i	−0.299124	+	0.518098i
$962$		0			0
$963$	−8.93340	+	16.8493i	−0.287875	+	0.542961i
$964$		0			0
$965$	−9.56709	−	16.5707i	−0.307975	−	0.533429i
$966$		0			0
$967$	−26.6398	+	46.1414i	−0.856677	+	1.48381i	0.0184029	+	0.999831i	$0.494142\pi$
$967$	−26.6398	+	46.1414i	−0.856677	+	1.48381i	−0.875080	+	0.483978i	$0.839191\pi$
$968$		0			0
$969$	38.4392	−	11.0468i	1.23484	−	0.354876i
$970$		0			0
$971$	28.1556	+	48.7669i	0.903555	+	1.56500i	0.822845	+	0.568266i	$0.192385\pi$
$971$	28.1556	+	48.7669i	0.903555	+	1.56500i	0.0807100	+	0.996738i	$0.474281\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.61557	−	6.49606i	0.0517397	−	0.208040i
$976$		0			0
$977$	−22.5755	+	13.0340i	−0.722254	+	0.416994i	−0.815582	−	0.578642i	$-0.803583\pi$
$977$	−22.5755	+	13.0340i	−0.722254	+	0.416994i	0.0933275	+	0.995635i	$0.470250\pi$
$978$		0			0
$979$	3.54237	−	2.04519i	0.113215	−	0.0653646i
$980$		0			0
$981$	0.558611	+	15.4721i	0.0178351	+	0.493986i
$982$		0			0
$983$	−38.0505			−1.21362			−0.606811	−	0.794846i	$-0.707551\pi$
$983$	−38.0505			−1.21362			−0.606811	+	0.794846i	$0.707551\pi$
$984$		0			0
$985$		−	44.1005i		−	1.40516i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	89.3217	−	51.5699i	2.84026	−	1.63983i
$990$		0			0
$991$	−5.68758	+	9.85118i	−0.180672	+	0.312933i	−0.942110	−	0.335305i	$-0.891161\pi$
$991$	−5.68758	+	9.85118i	−0.180672	+	0.312933i	0.761438	+	0.648238i	$0.224494\pi$
$992$		0			0
$993$	−5.81931	−	1.44726i	−0.184670	−	0.0459276i
$994$		0			0
$995$	−14.9499	−	8.63131i	−0.473943	−	0.273631i
$996$		0			0
$997$			50.9904i			1.61488i	0.589948	+	0.807441i	$0.299148\pi$
$997$			50.9904i			1.61488i	−0.589948	+	0.807441i	$0.700852\pi$
$998$		0			0
$999$	9.74609	−	46.2549i	0.308353	−	1.46344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.bm.a.1697.4		16
3.2	odd	2		5292.2.bm.a.2285.7		16
7.2	even	3		252.2.w.a.5.7	✓	16
7.3	odd	6		1764.2.x.b.293.7		16
7.4	even	3		1764.2.x.a.293.2		16
7.5	odd	6		1764.2.w.b.509.2		16
7.6	odd	2		252.2.bm.a.185.5	yes	16
9.2	odd	6		1764.2.w.b.1109.2		16
9.7	even	3		5292.2.w.b.521.7		16
21.2	odd	6		756.2.w.a.341.2		16
21.5	even	6		5292.2.w.b.1097.7		16
21.11	odd	6		5292.2.x.a.881.2		16
21.17	even	6		5292.2.x.b.881.7		16
21.20	even	2		756.2.bm.a.17.2		16
28.23	odd	6		1008.2.ca.d.257.2		16
28.27	even	2		1008.2.df.d.689.4		16
63.2	odd	6		252.2.bm.a.173.5	yes	16
63.11	odd	6		1764.2.x.b.1469.7		16
63.13	odd	6		2268.2.t.a.1781.2		16
63.16	even	3		756.2.bm.a.89.2		16
63.20	even	6		252.2.w.a.101.7	yes	16
63.23	odd	6		2268.2.t.a.2105.2		16
63.25	even	3		5292.2.x.b.4409.7		16
63.34	odd	6		756.2.w.a.521.2		16
63.38	even	6		1764.2.x.a.1469.2		16
63.41	even	6		2268.2.t.b.1781.7		16
63.47	even	6	inner	1764.2.bm.a.1685.4		16
63.52	odd	6		5292.2.x.a.4409.2		16
63.58	even	3		2268.2.t.b.2105.7		16
63.61	odd	6		5292.2.bm.a.4625.7		16
84.23	even	6		3024.2.ca.d.2609.2		16
84.83	odd	2		3024.2.df.d.17.2		16
252.79	odd	6		3024.2.df.d.1601.2		16
252.83	odd	6		1008.2.ca.d.353.2		16
252.191	even	6		1008.2.df.d.929.4		16
252.223	even	6		3024.2.ca.d.2033.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	7.2	even	3
252.2.w.a.101.7	yes	16	63.20	even	6
252.2.bm.a.173.5	yes	16	63.2	odd	6
252.2.bm.a.185.5	yes	16	7.6	odd	2
756.2.w.a.341.2		16	21.2	odd	6
756.2.w.a.521.2		16	63.34	odd	6
756.2.bm.a.17.2		16	21.20	even	2
756.2.bm.a.89.2		16	63.16	even	3
1008.2.ca.d.257.2		16	28.23	odd	6
1008.2.ca.d.353.2		16	252.83	odd	6
1008.2.df.d.689.4		16	28.27	even	2
1008.2.df.d.929.4		16	252.191	even	6
1764.2.w.b.509.2		16	7.5	odd	6
1764.2.w.b.1109.2		16	9.2	odd	6
1764.2.x.a.293.2		16	7.4	even	3
1764.2.x.a.1469.2		16	63.38	even	6
1764.2.x.b.293.7		16	7.3	odd	6
1764.2.x.b.1469.7		16	63.11	odd	6
1764.2.bm.a.1685.4		16	63.47	even	6	inner
1764.2.bm.a.1697.4		16	1.1	even	1	trivial
2268.2.t.a.1781.2		16	63.13	odd	6
2268.2.t.a.2105.2		16	63.23	odd	6
2268.2.t.b.1781.7		16	63.41	even	6
2268.2.t.b.2105.7		16	63.58	even	3
3024.2.ca.d.2033.2		16	252.223	even	6
3024.2.ca.d.2609.2		16	84.23	even	6
3024.2.df.d.17.2		16	84.83	odd	2
3024.2.df.d.1601.2		16	252.79	odd	6
5292.2.w.b.521.7		16	9.7	even	3
5292.2.w.b.1097.7		16	21.5	even	6
5292.2.x.a.881.2		16	21.11	odd	6
5292.2.x.a.4409.2		16	63.52	odd	6
5292.2.x.b.881.7		16	21.17	even	6
5292.2.x.b.4409.7		16	63.25	even	3
5292.2.bm.a.2285.7		16	3.2	odd	2
5292.2.bm.a.4625.7		16	63.61	odd	6

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.478402 - 1.66467i) q^{3} -2.74332 q^{5} +(-2.54226 + 1.59276i) q^{9} +O(q^{10})\)	\(q+(-0.478402 - 1.66467i) q^{3} -2.74332 q^{5} +(-2.54226 + 1.59276i) q^{9} +0.418355i q^{11} +(1.32512 + 0.765056i) q^{13} +(1.31241 + 4.56672i) q^{15} +(-1.95291 + 3.38253i) q^{17} +(5.11994 - 2.95600i) q^{19} +8.92450i q^{23} +2.52579 q^{25} +(3.86765 + 3.47005i) q^{27} +(6.00378 - 3.46629i) q^{29} +(3.05626 - 1.76453i) q^{31} +(0.696424 - 0.200142i) q^{33} +(-4.54861 - 7.87842i) q^{37} +(0.639629 - 2.57189i) q^{39} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(6.97424 - 4.36946i) q^{45} +(0.885373 - 1.53351i) q^{47} +(6.56508 + 1.63274i) q^{51} +(3.39526 + 1.96025i) q^{53} -1.14768i q^{55} +(-7.37015 - 7.10886i) q^{57} +(2.02728 + 3.51135i) q^{59} +(1.61459 + 0.932184i) q^{61} +(-3.63521 - 2.09879i) q^{65} +(6.38441 + 11.0581i) q^{67} +(14.8564 - 4.26950i) q^{69} -8.51021i q^{71} +(-1.65059 - 0.952971i) q^{73} +(-1.20834 - 4.20462i) q^{75} +(0.433633 - 0.751074i) q^{79} +(3.92620 - 8.09845i) q^{81} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(-8.64245 - 8.33605i) q^{87} +(-4.88864 - 8.46738i) q^{89} +(-4.39949 - 4.24351i) q^{93} +(-14.0456 + 8.10924i) q^{95} +(0.200411 - 0.115707i) q^{97} +(-0.666342 - 1.06357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

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