LMFDB - Embedded newform 252.2.w.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, 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:	$2.01223013094$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.7
Root			$-0.811340 + 1.53027i$ of defining polynomial
Character	$\chi$	$=$	252.5
Dual form			252.2.w.a.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68085 + 0.418028i) q^{3} +(1.37166 + 2.37578i) q^{5} +(-2.60476 + 0.463945i) q^{7} +(2.65051 + 1.40528i) q^{9} +O(q^{10})$	\(q+(1.68085 + 0.418028i) q^{3} +(1.37166 + 2.37578i) q^{5} +(-2.60476 + 0.463945i) q^{7} +(2.65051 + 1.40528i) q^{9} +(-0.362306 - 0.209178i) q^{11} +(1.32512 + 0.765056i) q^{13} +(1.31241 + 4.56672i) q^{15} +(-1.95291 - 3.38253i) q^{17} +(-5.11994 - 2.95600i) q^{19} +(-4.57214 - 0.309039i) q^{21} +(7.72884 - 4.46225i) q^{23} +(-1.26290 + 2.18740i) q^{25} +(3.86765 + 3.47005i) q^{27} +(6.00378 - 3.46629i) q^{29} +3.52907i q^{31} +(-0.521540 - 0.503050i) q^{33} +(-4.67507 - 5.55196i) q^{35} +(-4.54861 + 7.87842i) q^{37} +(1.90751 + 1.83988i) q^{39} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(0.296944 + 8.22460i) q^{45} -1.77075 q^{47} +(6.56951 - 2.41692i) q^{49} +(-1.86855 - 6.50189i) q^{51} +(-3.39526 + 1.96025i) q^{53} -1.14768i q^{55} +(-7.37015 - 7.10886i) q^{57} -4.05456 q^{59} -1.86437i q^{61} +(-7.55590 - 2.43073i) q^{63} +4.19758i q^{65} -12.7688 q^{67} +(14.8564 - 4.26950i) q^{69} -8.51021i q^{71} +(1.65059 - 0.952971i) q^{73} +(-3.03713 + 3.14877i) q^{75} +(1.04077 + 0.376767i) q^{77} -0.867266 q^{79} +(5.05036 + 7.44942i) q^{81} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(11.5405 - 3.31656i) q^{87} +(-4.88864 + 8.46738i) q^{89} +(-3.80655 - 1.37800i) q^{91} +(-1.47525 + 5.93183i) q^{93} -16.2185i q^{95} +(0.200411 - 0.115707i) q^{97} +(-0.666342 - 1.06357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{9}+O(q^{10}) $ 16 * q - q^7 + 6 * q^9	$ 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.68085	+	0.418028i	0.970439	+	0.241348i
$3$	1.68085	+	0.418028i	0.970439	+	0.241348i
$4$		0			0
$5$	1.37166	+	2.37578i	0.613425	+	1.06248i	0.990659	+	0.136365i	$0.0435419\pi$
$5$	1.37166	+	2.37578i	0.613425	+	1.06248i	−0.377234	+	0.926118i	$0.623125\pi$
$6$		0			0
$7$	−2.60476	+	0.463945i	−0.984505	+	0.175355i
$7$	−2.60476	+	0.463945i	−0.984505	+	0.175355i
$8$		0			0
$9$	2.65051	+	1.40528i	0.883502	+	0.468427i
$10$		0			0
$11$	−0.362306	−	0.209178i	−0.109240	−	0.0630695i	0.444385	−	0.895836i	$-0.353422\pi$
$11$	−0.362306	−	0.209178i	−0.109240	−	0.0630695i	−0.553624	+	0.832767i	$0.686756\pi$
$12$		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	0.525896	−	0.850549i	$-0.323730\pi$
$17$	−1.95291	−	3.38253i	−0.473649	−	0.820385i	−0.999545	+	0.0301645i	$0.990397\pi$
$18$		0			0
$19$	−5.11994	−	2.95600i	−1.17459	−	0.678152i	−0.219836	−	0.975537i	$-0.570552\pi$
$19$	−5.11994	−	2.95600i	−1.17459	−	0.678152i	−0.954758	+	0.297385i	$0.903886\pi$
$20$		0			0
$21$	−4.57214	−	0.309039i	−0.997723	−	0.0674379i
$22$		0			0
$23$	7.72884	−	4.46225i	1.61157	−	0.930443i	0.622569	−	0.782565i	$-0.286089\pi$
$23$	7.72884	−	4.46225i	1.61157	−	0.930443i	0.989006	−	0.147878i	$-0.0472444\pi$
$24$		0			0
$25$	−1.26290	+	2.18740i	−0.252579	+	0.437480i
$26$		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
$31$			3.52907i			0.633839i	0.948452	+	0.316920i	$0.102649\pi$
$31$			3.52907i			0.633839i	−0.948452	+	0.316920i	$0.897351\pi$
$32$		0			0
$33$	−0.521540	−	0.503050i	−0.0907885	−	0.0875698i
$34$		0			0
$35$	−4.67507	−	5.55196i	−0.790231	−	0.938453i
$36$		0			0
$37$	−4.54861	+	7.87842i	−0.747787	+	1.29520i	0.201095	+	0.979572i	$0.435550\pi$
$37$	−4.54861	+	7.87842i	−0.747787	+	1.29520i	−0.948881	+	0.315633i	$0.897783\pi$
$38$		0			0
$39$	1.90751	+	1.83988i	0.305445	+	0.294616i
$40$		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
$45$	0.296944	+	8.22460i	0.0442659	+	1.22605i
$46$		0			0
$47$	−1.77075			−0.258290			−0.129145	−	0.991626i	$-0.541223\pi$
$47$	−1.77075			−0.258290			−0.129145	+	0.991626i	$0.541223\pi$
$48$		0			0
$49$	6.56951	−	2.41692i	0.938502	−	0.345275i
$50$		0			0
$51$	−1.86855	−	6.50189i	−0.261649	−	0.910447i
$52$		0			0
$53$	−3.39526	+	1.96025i	−0.466374	+	0.269261i	−0.714721	−	0.699410i	$-0.753446\pi$
$53$	−3.39526	+	1.96025i	−0.466374	+	0.269261i	0.248346	+	0.968671i	$0.420113\pi$
$54$		0			0
$55$		−	1.14768i		−	0.154753i
$56$		0			0
$57$	−7.37015	−	7.10886i	−0.976200	−	0.941591i
$58$		0			0
$59$	−4.05456			−0.527859			−0.263929	−	0.964542i	$-0.585019\pi$
$59$	−4.05456			−0.527859			−0.263929	+	0.964542i	$0.585019\pi$
$60$		0			0
$61$		−	1.86437i		−	0.238708i	−0.992852	−	0.119354i	$-0.961918\pi$
$61$		−	1.86437i		−	0.238708i	0.992852	−	0.119354i	$-0.0380823\pi$
$62$		0			0
$63$	−7.55590	−	2.43073i	−0.951953	−	0.306243i
$64$		0			0
$65$			4.19758i			0.520646i
$66$		0			0
$67$	−12.7688			−1.55996			−0.779979	−	0.625805i	$-0.784770\pi$
$67$	−12.7688			−1.55996			−0.779979	+	0.625805i	$0.784770\pi$
$68$		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	$-0.631089\pi$
$73$	1.65059	−	0.952971i	0.193187	−	0.111537i	0.593474	+	0.804853i	$0.297756\pi$
$74$		0			0
$75$	−3.03713	+	3.14877i	−0.350698	+	0.363588i
$76$		0			0
$77$	1.04077	+	0.376767i	0.118606	+	0.0429366i
$78$		0			0
$79$	−0.867266			−0.0975750			−0.0487875	−	0.998809i	$-0.515536\pi$
$79$	−0.867266			−0.0975750			−0.0487875	+	0.998809i	$0.515536\pi$
$80$		0			0
$81$	5.05036	+	7.44942i	0.561151	+	0.827713i
$82$		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
$87$	11.5405	−	3.31656i	1.23727	−	0.355572i
$88$		0			0
$89$	−4.88864	+	8.46738i	−0.518195	+	0.897540i	0.481581	+	0.876401i	$0.340063\pi$
$89$	−4.88864	+	8.46738i	−0.518195	+	0.897540i	−0.999777	+	0.0211389i	$0.993271\pi$
$90$		0			0
$91$	−3.80655	−	1.37800i	−0.399035	−	0.144454i
$92$		0			0
$93$	−1.47525	+	5.93183i	−0.152976	+	0.615102i
$94$		0			0
$95$		−	16.2185i		−	1.66398i
$96$		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
$101$	−7.14031	+	12.3674i	−0.710487	+	1.23060i	0.254187	+	0.967155i	$0.418192\pi$
$101$	−7.14031	+	12.3674i	−0.710487	+	1.23060i	−0.964674	+	0.263445i	$0.915141\pi$
$102$		0			0
$103$	−9.30617	+	5.37292i	−0.916964	+	0.529410i	−0.882665	−	0.470002i	$-0.844253\pi$
$103$	−9.30617	+	5.37292i	−0.916964	+	0.529410i	−0.0342991	+	0.999412i	$0.510920\pi$
$104$		0			0
$105$	−5.53721	−	11.2863i	−0.540376	−	1.10143i
$106$		0			0
$107$	−5.50534	−	3.17851i	−0.532221	−	0.307278i	0.209699	−	0.977766i	$-0.432751\pi$
$107$	−5.50534	−	3.17851i	−0.532221	−	0.307278i	−0.741920	+	0.670488i	$0.766085\pi$
$108$		0			0
$109$	2.58036	+	4.46932i	0.247154	+	0.428083i	0.962735	−	0.270447i	$-0.0871714\pi$
$109$	2.58036	+	4.46932i	0.247154	+	0.428083i	−0.715581	+	0.698530i	$0.753838\pi$
$110$		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
$115$	21.2027	+	12.2414i	1.97716	+	1.14151i
$116$		0			0
$117$	2.43711	+	3.88995i	0.225311	+	0.359626i
$118$		0			0
$119$	6.65615	+	7.90463i	0.610168	+	0.724616i
$120$		0			0
$121$	−5.41249	−	9.37471i	−0.492044	−	0.852246i
$122$		0			0
$123$	2.55487	−	2.64877i	0.230365	−	0.238832i
$124$		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
$129$	−5.52886	−	19.2385i	−0.486789	−	1.69385i
$130$		0			0
$131$	9.83048	+	17.0269i	0.858893	+	1.48765i	0.872986	+	0.487746i	$0.162181\pi$
$131$	9.83048	+	17.0269i	0.858893	+	1.48765i	−0.0140928	+	0.999901i	$0.504486\pi$
$132$		0			0
$133$	14.7076	+	5.32428i	1.27531	+	0.461674i
$134$		0			0
$135$	−2.93899	+	13.9484i	−0.252948	+	1.20049i
$136$		0			0
$137$	−4.66411	−	2.69282i	−0.398481	−	0.230063i	0.287347	−	0.957827i	$-0.407227\pi$
$137$	−4.66411	−	2.69282i	−0.398481	−	0.230063i	−0.685829	+	0.727763i	$0.740560\pi$
$138$		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
$147$	12.0527	−	1.31625i	0.994090	−	0.108562i
$148$		0			0
$149$	9.31162	−	5.37607i	0.762838	−	0.440425i	−0.0674758	−	0.997721i	$-0.521495\pi$
$149$	9.31162	−	5.37607i	0.762838	−	0.440425i	0.830314	+	0.557296i	$0.188161\pi$
$150$		0			0
$151$	−3.78223	+	6.55102i	−0.307794	+	0.533115i	−0.977879	−	0.209169i	$-0.932924\pi$
$151$	−3.78223	+	6.55102i	−0.307794	+	0.533115i	0.670086	+	0.742284i	$0.266257\pi$
$152$		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
$157$			12.2764i			0.979763i	0.871789	+	0.489882i	$0.162960\pi$
$157$			12.2764i			0.979763i	−0.871789	+	0.489882i	$0.837040\pi$
$158$		0			0
$159$	−6.52635	+	1.87558i	−0.517573	+	0.148743i
$160$		0			0
$161$	−18.0615	+	15.2088i	−1.42345	+	1.19862i
$162$		0			0
$163$	5.91745	−	10.2493i	0.463490	−	0.802789i	−0.535642	−	0.844445i	$-0.679930\pi$
$163$	5.91745	−	10.2493i	0.463490	−	0.802789i	0.999132	+	0.0416566i	$0.0132635\pi$
$164$		0			0
$165$	0.479763	−	1.92908i	0.0373495	−	0.150179i
$166$		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
$171$	−9.41641	−	15.0298i	−0.720091	−	1.14936i
$172$		0			0
$173$	−16.6217			−1.26372			−0.631862	−	0.775081i	$-0.717709\pi$
$173$	−16.6217			−1.26372			−0.631862	+	0.775081i	$0.717709\pi$
$174$		0			0
$175$	2.27471	−	6.28356i	0.171952	−	0.474993i
$176$		0			0
$177$	−6.81510	−	1.69492i	−0.512254	−	0.127398i
$178$		0			0
$179$	14.8080	−	8.54942i	1.10680	−	0.639014i	0.168805	−	0.985650i	$-0.446009\pi$
$179$	14.8080	−	8.54942i	1.10680	−	0.639014i	0.938000	+	0.346636i	$0.112676\pi$
$180$		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
$185$	−24.9566			−1.83484
$186$		0			0
$187$			1.63402i			0.119491i
$188$		0			0
$189$	−11.6842	−	7.24426i	−0.849901	−	0.526943i
$190$		0			0
$191$			20.9994i			1.51946i	0.650239	+	0.759730i	$0.274669\pi$
$191$			20.9994i			1.51946i	−0.650239	+	0.759730i	$0.725331\pi$
$192$		0			0
$193$	−6.97483			−0.502059			−0.251030	−	0.967979i	$-0.580769\pi$
$193$	−6.97483			−0.502059			−0.251030	+	0.967979i	$0.580769\pi$
$194$		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	$-0.738263\pi$
$199$	−5.44956	+	3.14630i	−0.386309	+	0.223036i	0.294251	+	0.955728i	$0.404930\pi$
$200$		0			0
$201$	−21.4624	−	5.33772i	−1.51384	−	0.376493i
$202$		0			0
$203$	−14.0302	+	11.8143i	−0.984729	+	0.829198i
$204$		0			0
$205$	5.82879			0.407100
$206$		0			0
$207$	26.7561	−	0.966012i	1.85967	−	0.0671425i
$208$		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
$213$	3.55750	−	14.3044i	0.243756	−	0.980120i
$214$		0			0
$215$	15.8522	−	27.4568i	1.08111	−	1.87254i
$216$		0			0
$217$	−1.63729	−	9.19236i	−0.111147	−	0.624018i
$218$		0			0
$219$	3.17277	−	0.911807i	0.214396	−	0.0616142i
$220$		0			0
$221$		−	5.97633i		−	0.402011i
$222$		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
$227$	−1.86609	+	3.23216i	−0.123857	+	0.214526i	−0.921285	−	0.388887i	$-0.872860\pi$
$227$	−1.86609	+	3.23216i	−0.123857	+	0.214526i	0.797429	+	0.603413i	$0.206193\pi$
$228$		0			0
$229$	18.2455	−	10.5341i	1.20570	−	0.696111i	0.243882	−	0.969805i	$-0.421579\pi$
$229$	18.2455	−	10.5341i	1.20570	−	0.696111i	0.961817	+	0.273694i	$0.0882457\pi$
$230$		0			0
$231$	1.59187	+	1.06836i	0.104738	+	0.0702928i
$232$		0			0
$233$	−11.0542	−	6.38215i	−0.724186	−	0.418109i	0.0921057	−	0.995749i	$-0.470640\pi$
$233$	−11.0542	−	6.38215i	−0.724186	−	0.418109i	−0.816291	+	0.577640i	$0.803974\pi$
$234$		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
$241$	−2.63438	−	1.52096i	−0.169695	−	0.0979737i	0.412747	−	0.910846i	$-0.364569\pi$
$241$	−2.63438	−	1.52096i	−0.169695	−	0.0979737i	−0.582442	+	0.812872i	$0.697903\pi$
$242$		0			0
$243$	5.37484	+	14.6325i	0.344796	+	0.938678i
$244$		0			0
$245$	14.7532	+	12.2925i	0.942549	+	0.785341i
$246$		0			0
$247$	−4.52301	−	7.83408i	−0.287792	−	0.498470i
$248$		0			0
$249$	3.30940	+	11.5155i	0.209725	+	0.729768i
$250$		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
$255$	12.8841	−	13.3576i	0.806832	−	0.836488i
$256$		0			0
$257$	−12.2538	−	21.2242i	−0.764372	−	1.32393i	−0.940578	−	0.339577i	$-0.889716\pi$
$257$	−12.2538	−	21.2242i	−0.764372	−	1.32393i	0.176206	−	0.984353i	$-0.443617\pi$
$258$		0			0
$259$	8.19287	−	22.6317i	0.509080	−	1.40626i
$260$		0			0
$261$	20.7842	−	0.750401i	1.28651	−	0.0464486i
$262$		0			0
$263$	−21.1163	−	12.1915i	−1.30208	−	0.751759i	−0.321323	−	0.946970i	$-0.604128\pi$
$263$	−21.1163	−	12.1915i	−1.30208	−	0.751759i	−0.980761	+	0.195211i	$0.937461\pi$
$264$		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	0.976480	−	0.215609i	$-0.0691737\pi$
$269$	4.94525	+	8.56542i	0.301517	+	0.522243i	−0.674963	+	0.737852i	$0.735840\pi$
$270$		0			0
$271$	−5.10505	−	2.94740i	−0.310110	−	0.179042i	0.336866	−	0.941553i	$-0.390633\pi$
$271$	−5.10505	−	2.94740i	−0.310110	−	0.179042i	−0.646976	+	0.762511i	$0.723966\pi$
$272$		0			0
$273$	−5.82219	−	3.90746i	−0.352375	−	0.236490i
$274$		0			0
$275$	0.915111	−	0.528340i	0.0551833	−	0.0318601i
$276$		0			0
$277$	−11.6469	+	20.1731i	−0.699796	+	1.21208i	0.268741	+	0.963213i	$0.413392\pi$
$277$	−11.6469	+	20.1731i	−0.699796	+	1.21208i	−0.968537	+	0.248870i	$0.919941\pi$
$278$		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
$283$			9.96439i			0.592322i	0.955138	+	0.296161i	$0.0957064\pi$
$283$			9.96439i			0.592322i	−0.955138	+	0.296161i	$0.904294\pi$
$284$		0			0
$285$	6.77977	−	27.2608i	0.401599	−	1.61479i
$286$		0			0
$287$	−1.91350	+	5.28579i	−0.112951	+	0.312011i
$288$		0			0
$289$	0.872317	−	1.51090i	0.0513128	−	0.0888764i
$290$		0			0
$291$	0.385229	−	0.110709i	0.0225825	−	0.00648989i
$292$		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
$297$	−0.675418	−	2.06625i	−0.0391917	−	0.119896i
$298$		0			0
$299$	13.6555			0.789717
$300$		0			0
$301$	19.6949	+	23.3891i	1.13520	+	1.34812i
$302$		0			0
$303$	−17.1717	+	17.8028i	−0.986487	+	1.02275i
$304$		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
$311$	0.00297881			0.000168913			8.44563e−5	−	1.00000i	$-0.499973\pi$
$311$	0.00297881			0.000168913			8.44563e−5		1.00000i	$0.499973\pi$
$312$		0			0
$313$		−	12.2576i		−	0.692838i	−0.938080	−	0.346419i	$-0.887398\pi$
$313$		−	12.2576i		−	0.692838i	0.938080	−	0.346419i	$-0.112602\pi$
$314$		0			0
$315$	−4.58922	−	21.2853i	−0.258573	−	1.19929i
$316$		0			0
$317$		−	23.0950i		−	1.29714i	−0.761154	−	0.648571i	$-0.775367\pi$
$317$		−	23.0950i		−	1.29714i	0.761154	−	0.648571i	$-0.224633\pi$
$318$		0			0
$319$	−2.90028			−0.162384
$320$		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
$327$	2.46890	+	8.59091i	0.136530	+	0.475078i
$328$		0			0
$329$	4.61236	−	0.821528i	0.254288	−	0.0452923i
$330$		0			0
$331$	−3.46213			−0.190296			−0.0951479	−	0.995463i	$-0.530332\pi$
$331$	−3.46213			−0.190296			−0.0951479	+	0.995463i	$0.530332\pi$
$332$		0			0
$333$	−23.1275	+	14.4897i	−1.26738	+	0.794032i
$334$		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
$339$	13.2317	+	12.7626i	0.718646	+	0.693168i
$340$		0			0
$341$	0.738202	−	1.27860i	0.0399759	−	0.0692403i
$342$		0			0
$343$	−15.9907	+	9.34339i	−0.863414	+	0.504496i
$344$		0			0
$345$	30.5213	+	29.4392i	1.64321	+	1.58495i
$346$		0			0
$347$		−	5.33917i		−	0.286622i	−0.989678	−	0.143311i	$-0.954225\pi$
$347$		−	5.33917i		−	0.286622i	0.989678	−	0.143311i	$-0.0457749\pi$
$348$		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
$353$	17.1543	−	29.7121i	0.913029	−	1.58141i	0.103268	−	0.994654i	$-0.467070\pi$
$353$	17.1543	−	29.7121i	0.913029	−	1.58141i	0.809761	−	0.586760i	$-0.199597\pi$
$354$		0			0
$355$	20.2184	−	11.6731i	1.07308	−	0.619544i
$356$		0			0
$357$	7.88363	+	16.0689i	0.417246	+	0.850459i
$358$		0			0
$359$	−5.42754	−	3.13359i	−0.286454	−	0.165385i	0.349887	−	0.936792i	$-0.386220\pi$
$359$	−5.42754	−	3.13359i	−0.286454	−	0.165385i	−0.636342	+	0.771407i	$0.719553\pi$
$360$		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
$367$	16.4888	+	9.51984i	0.860711	+	0.496931i	0.864250	−	0.503062i	$-0.167793\pi$
$367$	16.4888	+	9.51984i	0.860711	+	0.496931i	−0.00353959	+	0.999994i	$0.501127\pi$
$368$		0			0
$369$	5.40160	−	3.38418i	0.281196	−	0.176174i
$370$		0			0
$371$	7.93437	−	6.68119i	0.411932	−	0.346870i
$372$		0			0
$373$	−5.41901	−	9.38600i	−0.280586	−	0.485989i	0.690943	−	0.722909i	$-0.257195\pi$
$373$	−5.41901	−	9.38600i	−0.280586	−	0.485989i	−0.971529	+	0.236920i	$0.923862\pi$
$374$		0			0
$375$	11.4088	+	2.83738i	0.589149	+	0.146521i
$376$		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
$381$	17.2974	+	4.30188i	0.886174	+	0.220392i
$382$		0			0
$383$	19.0235	+	32.9497i	0.972056	+	1.68365i	0.689327	+	0.724451i	$0.257906\pi$
$383$	19.0235	+	32.9497i	0.972056	+	1.68365i	0.282729	+	0.959200i	$0.408760\pi$
$384$		0			0
$385$	0.532461	+	2.98943i	0.0271367	+	0.152356i
$386$		0			0
$387$	−1.25095	−	34.6482i	−0.0635896	−	1.76127i
$388$		0			0
$389$	16.6958	+	9.63934i	0.846512	+	0.488734i	0.859473	−	0.511182i	$-0.170792\pi$
$389$	16.6958	+	9.63934i	0.846512	+	0.488734i	−0.0129603	+	0.999916i	$0.504125\pi$
$390$		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	$-0.501126\pi$
$397$	−17.3610	−	10.0234i	−0.871325	−	0.503059i	−0.867788	+	0.496934i	$0.834459\pi$
$398$		0			0
$399$	22.4956	+	15.0975i	1.12619	+	0.755820i
$400$		0			0
$401$	26.4232	−	15.2554i	1.31951	−	0.761820i	0.335861	−	0.941912i	$-0.390973\pi$
$401$	26.4232	−	15.2554i	1.31951	−	0.761820i	0.983650	+	0.180092i	$0.0576395\pi$
$402$		0			0
$403$	−2.69993	+	4.67642i	−0.134493	+	0.232949i
$404$		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
$409$			0.173933i			0.00860045i	0.999991	+	0.00430023i	$0.00136881\pi$
$409$			0.173933i			0.00860045i	−0.999991	+	0.00430023i	$0.998631\pi$
$410$		0			0
$411$	−6.71398	−	6.47595i	−0.331176	−	0.319435i
$412$		0			0
$413$	10.5611	−	1.88109i	0.519680	−	0.0925624i
$414$		0			0
$415$	−9.48860	+	16.4347i	−0.465777	+	0.806749i
$416$		0			0
$417$	21.2814	+	20.5269i	1.04216	+	1.00521i
$418$		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
$423$	−4.69337	−	2.48840i	−0.228200	−	0.120990i
$424$		0			0
$425$	9.86527			0.478536
$426$		0			0
$427$	0.864963	+	4.85622i	0.0418585	+	0.235009i
$428$		0			0
$429$	−0.306240	−	1.06561i	−0.0147854	−	0.0514480i
$430$		0			0
$431$	8.58876	−	4.95872i	0.413706	−	0.238853i	−0.278675	−	0.960385i	$-0.589895\pi$
$431$	8.58876	−	4.95872i	0.413706	−	0.238853i	0.692381	+	0.721532i	$0.256562\pi$
$432$		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
$437$	−52.7616			−2.52393
$438$		0			0
$439$		−	21.4537i		−	1.02393i	−0.859006	−	0.511965i	$-0.828918\pi$
$439$		−	21.4537i		−	1.02393i	0.859006	−	0.511965i	$-0.171082\pi$
$440$		0			0
$441$	20.8090	+	2.82594i	0.990904	+	0.134569i
$442$		0			0
$443$			6.74738i			0.320578i	0.987070	+	0.160289i	$0.0512425\pi$
$443$			6.74738i			0.320578i	−0.987070	+	0.160289i	$0.948757\pi$
$444$		0			0
$445$	−26.8222			−1.27149
$446$		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
$453$	−9.09587	+	9.43020i	−0.427361	+	0.443069i
$454$		0			0
$455$	−1.94745	−	10.9337i	−0.0912977	−	0.512579i
$456$		0			0
$457$	−33.3898			−1.56191			−0.780954	−	0.624588i	$-0.785267\pi$
$457$	−33.3898			−1.56191			−0.780954	+	0.624588i	$0.785267\pi$
$458$		0			0
$459$	4.18440	−	19.8591i	0.195311	−	0.926946i
$460$		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
$465$	−16.1163	+	4.63158i	−0.747374	+	0.214784i
$466$		0			0
$467$	9.30470	−	16.1162i	0.430570	−	0.745770i	−0.566352	−	0.824163i	$-0.691646\pi$
$467$	9.30470	−	16.1162i	0.430570	−	0.745770i	0.996922	+	0.0783937i	$0.0249791\pi$
$468$		0			0
$469$	33.2596	−	5.92402i	1.53579	−	0.273546i
$470$		0			0
$471$	−5.13187	+	20.6348i	−0.236464	+	0.950800i
$472$		0			0
$473$			4.83490i			0.222309i
$474$		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
$479$	7.16703	−	12.4137i	0.327470	−	0.567194i	−0.654539	−	0.756028i	$-0.727137\pi$
$479$	7.16703	−	12.4137i	0.327470	−	0.567194i	0.982009	+	0.188834i	$0.0604707\pi$
$480$		0			0
$481$	−12.0549	+	6.95988i	−0.549655	+	0.317343i
$482$		0			0
$483$	−36.7164	+	18.0135i	−1.67065	+	0.819644i
$484$		0			0
$485$	0.549791	+	0.317422i	0.0249647	+	0.0144134i
$486$		0			0
$487$	−5.64829	−	9.78313i	−0.255949	−	0.443316i	0.709204	−	0.705003i	$-0.249054\pi$
$487$	−5.64829	−	9.78313i	−0.255949	−	0.443316i	−0.965153	+	0.261687i	$0.915721\pi$
$488$		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
$493$	−23.4496	−	13.5387i	−1.05612	−	0.609751i
$494$		0			0
$495$	1.61282	−	3.04194i	0.0724907	−	0.136725i
$496$		0			0
$497$	3.94827	+	22.1670i	0.177104	+	0.994327i
$498$		0			0
$499$	9.56672	+	16.5701i	0.428265	+	0.741777i	0.996719	−	0.0809379i	$-0.0257915\pi$
$499$	9.56672	+	16.5701i	0.428265	+	0.741777i	−0.568454	+	0.822715i	$0.692458\pi$
$500$		0			0
$501$	16.3257	−	16.9258i	0.729379	−	0.756188i
$502$		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
$507$	−5.09917	−	17.7433i	−0.226462	−	0.788009i
$508$		0			0
$509$	10.9439	+	18.9553i	0.485079	+	0.840181i	0.999853	−	0.0171449i	$-0.00545767\pi$
$509$	10.9439	+	18.9553i	0.485079	+	0.840181i	−0.514774	+	0.857326i	$0.672124\pi$
$510$		0			0
$511$	−3.85727	+	3.24804i	−0.170636	+	0.143685i
$512$		0			0
$513$	−9.54468	−	29.1992i	−0.421408	−	1.28918i
$514$		0			0
$515$	−25.5298	−	14.7396i	−1.12498	−	0.649506i
$516$		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	0.884169	−	0.467168i	$-0.154726\pi$
$521$	0.856074	+	1.48276i	0.0375053	+	0.0649610i	−0.846663	+	0.532129i	$0.821392\pi$
$522$		0			0
$523$	7.16320	+	4.13568i	0.313225	+	0.180841i	0.648369	−	0.761326i	$-0.275452\pi$
$523$	7.16320	+	4.13568i	0.313225	+	0.180841i	−0.335144	+	0.942167i	$0.608785\pi$
$524$		0			0
$525$	6.45014	−	9.61083i	0.281507	−	0.419451i
$526$		0			0
$527$	11.9372	−	6.89193i	0.519992	−	0.300217i
$528$		0			0
$529$	28.3233	−	49.0574i	1.23145	−	2.13293i
$530$		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
$535$		−	17.4393i		−	0.753967i
$536$		0			0
$537$	28.4640	−	8.18012i	1.22831	−	0.352998i
$538$		0			0
$539$	−2.88574	−	0.498528i	−0.124298	−	0.0214731i
$540$		0			0
$541$	−10.1997	+	17.6664i	−0.438518	+	0.759536i	−0.997575	−	0.0695932i	$-0.977830\pi$
$541$	−10.1997	+	17.6664i	−0.438518	+	0.759536i	0.559057	+	0.829129i	$0.311163\pi$
$542$		0			0
$543$	7.61526	−	30.6202i	0.326802	−	1.31404i
$544$		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
$549$	2.61996	−	4.94152i	0.111817	−	0.210899i
$550$		0			0
$551$	−40.9853			−1.74603
$552$		0			0
$553$	2.25902	−	0.402363i	0.0960631	−	0.0171102i
$554$		0			0
$555$	−41.9482	−	10.4325i	−1.78060	−	0.442836i
$556$		0			0
$557$	14.5919	−	8.42463i	0.618278	−	0.356963i	−0.157920	−	0.987452i	$-0.550479\pi$
$557$	14.5919	−	8.42463i	0.618278	−	0.356963i	0.776198	+	0.630489i	$0.217146\pi$
$558$		0			0
$559$		−	17.6834i		−	0.747928i
$560$		0			0
$561$	−0.683064	+	2.74654i	−0.0288390	+	0.115959i
$562$		0			0
$563$	−16.5607			−0.697950			−0.348975	−	0.937132i	$-0.613470\pi$
$563$	−16.5607			−0.697950			−0.348975	+	0.937132i	$0.613470\pi$
$564$		0			0
$565$			29.1171i			1.22497i
$566$		0			0
$567$	−16.6111	−	17.0608i	−0.697600	−	0.716488i
$568$		0			0
$569$			6.34919i			0.266172i	0.991104	+	0.133086i	$0.0424886\pi$
$569$			6.34919i			0.266172i	−0.991104	+	0.133086i	$0.957511\pi$
$570$		0			0
$571$	45.7406			1.91418			0.957092	−	0.289785i	$-0.0935838\pi$
$571$	45.7406			1.91418			0.957092	+	0.289785i	$0.0935838\pi$
$572$		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	$-0.546206\pi$
$577$	15.3719	−	8.87497i	0.639940	−	0.369470i	0.784592	+	0.620013i	$0.212873\pi$
$578$		0			0
$579$	−11.7236	−	2.91567i	−0.487218	−	0.121171i
$580$		0			0
$581$	−11.7888	−	13.9999i	−0.489080	−	0.580815i
$582$		0			0
$583$	1.64016			0.0679287
$584$		0			0
$585$	−5.89879	+	11.1257i	−0.243885	+	0.459992i
$586$		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
$591$	−6.72005	+	27.0207i	−0.276426	+	1.11148i
$592$		0			0
$593$	4.24849	−	7.35860i	0.174465	−	0.302181i	−0.765511	−	0.643422i	$-0.777514\pi$
$593$	4.24849	−	7.35860i	0.174465	−	0.302181i	0.939976	+	0.341241i	$0.110847\pi$
$594$		0			0
$595$	−9.64972	+	26.6560i	−0.395600	+	1.09279i
$596$		0			0
$597$	−10.4751	+	3.01040i	−0.428718	+	0.123207i
$598$		0			0
$599$		−	3.70842i		−	0.151522i	−0.997126	−	0.0757609i	$-0.975861\pi$
$599$		−	3.70842i		−	0.151522i	0.997126	−	0.0757609i	$-0.0241386\pi$
$600$		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
$605$	14.8482	−	25.7178i	0.603664	−	1.04558i
$606$		0			0
$607$	−29.4396	+	16.9970i	−1.19492	+	0.689886i	−0.959418	−	0.281988i	$-0.909006\pi$
$607$	−29.4396	+	16.9970i	−1.19492	+	0.689886i	−0.235500	+	0.971874i	$0.575673\pi$
$608$		0			0
$609$	−28.5214	+	13.9930i	−1.15574	+	0.567023i
$610$		0			0
$611$	−2.34644	−	1.35472i	−0.0949270	−	0.0548061i
$612$		0			0
$613$	−11.6761	−	20.2237i	−0.471595	−	0.816827i	0.527877	−	0.849321i	$-0.322988\pi$
$613$	−11.6761	−	20.2237i	−0.471595	−	0.816827i	−0.999472	+	0.0324944i	$0.989655\pi$
$614$		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
$619$	−7.97914	−	4.60676i	−0.320709	−	0.185161i	0.331000	−	0.943631i	$-0.392614\pi$
$619$	−7.97914	−	4.60676i	−0.320709	−	0.185161i	−0.651708	+	0.758470i	$0.725947\pi$
$620$		0			0
$621$	45.3767	+	9.56105i	1.82090	+	0.383672i
$622$		0			0
$623$	8.80533	−	24.3235i	0.352778	−	0.974501i
$624$		0			0
$625$	15.6247	+	27.0627i	0.624987	+	1.08251i
$626$		0			0
$627$	1.18324	+	4.11726i	0.0472540	+	0.164427i
$628$		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
$633$	−3.12188	+	3.23663i	−0.124084	+	0.128644i
$634$		0			0
$635$	14.1156	+	24.4489i	0.560160	+	0.970226i
$636$		0			0
$637$	10.5544	+	1.82334i	0.418182	+	0.0722433i
$638$		0			0
$639$	11.9593	−	22.5564i	0.473101	−	0.892316i
$640$		0			0
$641$	16.5759	+	9.57009i	0.654708	+	0.377996i	0.790258	−	0.612775i	$-0.209947\pi$
$641$	16.5759	+	9.57009i	0.654708	+	0.377996i	−0.135550	+	0.990771i	$0.543280\pi$
$642$		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	0.999953	+	0.00969167i	$0.00308500\pi$
$647$	12.9310	+	22.3971i	0.508370	+	0.880522i	−0.491583	+	0.870831i	$0.663582\pi$
$648$		0			0
$649$	1.46899	+	0.848123i	0.0576630	+	0.0332918i
$650$		0			0
$651$	1.09062	−	16.1354i	0.0427448	−	0.632396i
$652$		0			0
$653$	−20.1140	+	11.6128i	−0.787123	+	0.454446i	−0.838949	−	0.544211i	$-0.816829\pi$
$653$	−20.1140	+	11.6128i	−0.787123	+	0.454446i	0.0518258	+	0.998656i	$0.483496\pi$
$654$		0			0
$655$	−26.9681	+	46.7102i	−1.05373	+	1.82512i
$656$		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
$661$			18.2450i			0.709647i	0.934933	+	0.354823i	$0.115459\pi$
$661$			18.2450i			0.709647i	−0.934933	+	0.354823i	$0.884541\pi$
$662$		0			0
$663$	2.49827	−	10.0453i	0.0970248	−	0.390127i
$664$		0			0
$665$	7.52447	+	42.2452i	0.291787	+	1.63820i
$666$		0			0
$667$	30.9349	−	53.5807i	1.19780	−	2.07465i
$668$		0			0
$669$	−39.8309	+	11.4468i	−1.53995	+	0.442559i
$670$		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
$675$	−12.4748	+	4.07779i	−0.480157	+	0.156954i
$676$		0			0
$677$	−33.5336			−1.28880			−0.644400	−	0.764689i	$-0.722893\pi$
$677$	−33.5336			−1.28880			−0.644400	+	0.764689i	$0.722893\pi$
$678$		0			0
$679$	−0.468340	+	0.394369i	−0.0179732	+	0.0151345i
$680$		0			0
$681$	−4.48775	+	4.65270i	−0.171971	+	0.178292i
$682$		0			0
$683$	−19.0943	+	11.0241i	−0.730621	+	0.421824i	−0.818649	−	0.574294i	$-0.805277\pi$
$683$	−19.0943	+	11.0241i	−0.730621	+	0.421824i	0.0880282	+	0.996118i	$0.471943\pi$
$684$		0			0
$685$		−	14.7745i		−	0.564506i
$686$		0			0
$687$	35.0715	−	10.0790i	1.33806	−	0.384539i
$688$		0			0
$689$	−5.99881			−0.228537
$690$		0			0
$691$		−	26.4036i		−	1.00444i	−0.864740	−	0.502219i	$-0.832517\pi$
$691$		−	26.4036i		−	1.00444i	0.864740	−	0.502219i	$-0.167483\pi$
$692$		0			0
$693$	2.22910	+	2.46119i	0.0846763	+	0.0934930i
$694$		0			0
$695$			46.8311i			1.77641i
$696$		0			0
$697$	−8.29877			−0.314338
$698$		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
$705$	−2.32394	−	8.08651i	−0.0875248	−	0.304556i
$706$		0			0
$707$	12.8610	−	35.5267i	0.483687	−	1.33612i
$708$		0			0
$709$	−6.26109			−0.235140			−0.117570	−	0.993065i	$-0.537510\pi$
$709$	−6.26109			−0.235140			−0.117570	+	0.993065i	$0.537510\pi$
$710$		0			0
$711$	−2.29869	−	1.21875i	−0.0862077	−	0.0457068i
$712$		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
$717$	15.9095	+	15.3454i	0.594149	+	0.573085i
$718$		0			0
$719$	−11.6111	+	20.1111i	−0.433023	+	0.750017i	−0.997132	−	0.0756828i	$-0.975886\pi$
$719$	−11.6111	+	20.1111i	−0.433023	+	0.750017i	0.564109	+	0.825700i	$0.309220\pi$
$720$		0			0
$721$	21.7476	−	18.3127i	0.809922	−	0.682001i
$722$		0			0
$723$	−3.79220	−	3.65775i	−0.141033	−	0.136033i
$724$		0			0
$725$			17.5102i			0.650314i
$726$		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
$731$	−22.5696	+	39.0917i	−0.834767	+	1.44586i
$732$		0			0
$733$	10.2963	−	5.94457i	0.380302	−	0.219568i	−0.297647	−	0.954676i	$-0.596202\pi$
$733$	10.2963	−	5.94457i	0.380302	−	0.219568i	0.677950	+	0.735108i	$0.262869\pi$
$734$		0			0
$735$	19.6593	+	26.8291i	0.725145	+	0.989608i
$736$		0			0
$737$	4.62622	+	2.67095i	0.170409	+	0.0983858i
$738$		0			0
$739$	17.2254	+	29.8354i	0.633648	+	1.09751i	0.986800	+	0.161945i	$0.0517767\pi$
$739$	17.2254	+	29.8354i	0.633648	+	1.09751i	−0.353151	+	0.935566i	$0.614890\pi$
$740$		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
$745$	25.5447	+	14.7483i	0.935887	+	0.540335i
$746$		0			0
$747$	0.748781	+	20.7393i	0.0273965	+	0.758812i
$748$		0			0
$749$	15.8147	+	5.72507i	0.577857	+	0.209189i
$750$		0			0
$751$	−3.86045	−	6.68649i	−0.140870	−	0.243993i	0.786955	−	0.617011i	$-0.211657\pi$
$751$	−3.86045	−	6.68649i	−0.140870	−	0.243993i	−0.927824	+	0.373017i	$0.878323\pi$
$752$		0			0
$753$	−10.6241	−	2.64221i	−0.387163	−	0.0962876i
$754$		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
$759$	−6.27564	−	1.56075i	−0.227791	−	0.0566517i
$760$		0			0
$761$	−1.56644	−	2.71316i	−0.0567835	−	0.0983520i	0.836236	−	0.548369i	$-0.184751\pi$
$761$	−1.56644	−	2.71316i	−0.0567835	−	0.0983520i	−0.893020	+	0.450017i	$0.851418\pi$
$762$		0			0
$763$	−8.79473	−	10.4443i	−0.318391	−	0.378110i
$764$		0			0
$765$	27.2401	−	17.0663i	0.984866	−	0.617033i
$766$		0			0
$767$	−5.37276	−	3.10196i	−0.193999	−	0.112005i
$768$		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	0.869581	+	0.493790i	$0.164389\pi$
$773$	23.9779	+	41.5309i	0.862425	+	1.49376i	−0.00715621	+	0.999974i	$0.502278\pi$
$774$		0			0
$775$	−7.71948	−	4.45685i	−0.277292	−	0.160095i
$776$		0			0
$777$	23.2316	−	34.6156i	0.833430	−	1.24183i
$778$		0			0
$779$	−10.8784	+	6.28067i	−0.389761	+	0.225028i
$780$		0			0
$781$	−1.78015	+	3.08331i	−0.0636987	+	0.110329i
$782$		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
$787$		−	6.04066i		−	0.215326i	−0.994187	−	0.107663i	$-0.965663\pi$
$787$		−	6.04066i		−	0.215326i	0.994187	−	0.107663i	$-0.0343368\pi$
$788$		0			0
$789$	−30.3969	−	29.3192i	−1.08216	−	1.04379i
$790$		0			0
$791$	−26.4047	−	9.55872i	−0.938842	−	0.339869i
$792$		0			0
$793$	1.42635	−	2.47050i	0.0506510	−	0.0877301i
$794$		0			0
$795$	−13.4079	−	12.9325i	−0.475529	−	0.458670i
$796$		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
$801$	−24.8564	+	15.5729i	−0.878259	+	0.550242i
$802$		0			0
$803$	−0.797361			−0.0281383
$804$		0			0
$805$	−60.9071	−	22.0489i	−2.14669	−	0.777122i
$806$		0			0
$807$	4.73163	+	16.4644i	0.166561	+	0.579575i
$808$		0			0
$809$	−15.3445	+	8.85918i	−0.539485	+	0.311472i	−0.744870	−	0.667209i	$-0.767489\pi$
$809$	−15.3445	+	8.85918i	−0.539485	+	0.311472i	0.205385	+	0.978681i	$0.434155\pi$
$810$		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
$815$	32.4669			1.13727
$816$		0			0
$817$			68.3245i			2.39037i
$818$		0			0
$819$	−8.15279	−	9.00168i	−0.284882	−	0.314544i
$820$		0			0
$821$		−	26.5977i		−	0.928267i	−0.885765	−	0.464134i	$-0.846366\pi$
$821$		−	26.5977i		−	0.928267i	0.885765	−	0.464134i	$-0.153634\pi$
$822$		0			0
$823$	24.1595			0.842146			0.421073	−	0.907027i	$-0.361654\pi$
$823$	24.1595			0.842146			0.421073	+	0.907027i	$0.361654\pi$
$824$		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	$-0.834907\pi$
$829$	−25.1481	+	14.5193i	−0.873430	+	0.504275i	−0.00494329	+	0.999988i	$0.501574\pi$
$830$		0			0
$831$	−28.0096	+	29.0391i	−0.971643	+	1.00736i
$832$		0			0
$833$	−21.0050	−	17.5016i	−0.727779	−	0.606393i
$834$		0			0
$835$	37.2462			1.28896
$836$		0			0
$837$	−12.2460	+	13.6492i	−0.423285	+	0.471786i
$838$		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
$843$	41.8965	−	12.0404i	1.44299	−	0.414695i
$844$		0			0
$845$	14.6202	−	25.3229i	0.502949	−	0.871134i
$846$		0			0
$847$	18.4476	+	21.9077i	0.633866	+	0.752759i
$848$		0			0
$849$	−4.16539	+	16.7486i	−0.142956	+	0.574812i
$850$		0			0
$851$			81.1881i			2.78309i
$852$		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
$857$	15.8980	−	27.5361i	0.543065	−	0.940616i	−0.455661	−	0.890153i	$-0.650597\pi$
$857$	15.8980	−	27.5361i	0.543065	−	0.940616i	0.998726	−	0.0504623i	$-0.0160695\pi$
$858$		0			0
$859$	21.9005	−	12.6442i	0.747235	−	0.431416i	−0.0774592	−	0.996996i	$-0.524681\pi$
$859$	21.9005	−	12.6442i	0.747235	−	0.431416i	0.824694	+	0.565579i	$0.191347\pi$
$860$		0			0
$861$	−5.42592	+	8.08472i	−0.184915	+	0.275527i
$862$		0			0
$863$	15.9513	+	9.20946i	0.542987	+	0.313494i	0.746289	−	0.665622i	$-0.231834\pi$
$863$	15.9513	+	9.20946i	0.542987	+	0.313494i	−0.203302	+	0.979116i	$0.565167\pi$
$864$		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
$871$	−16.9202	−	9.76886i	−0.573318	−	0.331005i
$872$		0			0
$873$	0.693792	−	0.0250490i	0.0234813	−	0.000847779i
$874$		0			0
$875$	−17.6799	+	3.14904i	−0.597689	+	0.106457i
$876$		0			0
$877$	4.44695	+	7.70234i	0.150163	+	0.260089i	0.931287	−	0.364286i	$-0.118687\pi$
$877$	4.44695	+	7.70234i	0.150163	+	0.260089i	−0.781124	+	0.624375i	$0.785354\pi$
$878$		0			0
$879$	−16.3308	+	16.9311i	−0.550824	+	0.571070i
$880$		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
$885$	−5.32124	−	18.5160i	−0.178871	−	0.622410i
$886$		0			0
$887$	−16.6991	−	28.9238i	−0.560703	−	0.971165i	−0.997435	−	0.0715740i	$-0.977198\pi$
$887$	−16.6991	−	28.9238i	−0.560703	−	0.971165i	0.436733	−	0.899591i	$-0.356136\pi$
$888$		0			0
$889$	−26.8053	+	4.77440i	−0.899019	+	0.160128i
$890$		0			0
$891$	−0.271527	−	3.75540i	−0.00909649	−	0.125810i
$892$		0			0
$893$	9.06611	+	5.23432i	0.303386	+	0.175160i
$894$		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
$903$	23.3269	+	47.5465i	0.776271	+	1.58225i
$904$		0			0
$905$	43.2799	−	24.9877i	1.43867	−	0.830618i
$906$		0			0
$907$	14.6563	−	25.3855i	0.486655	−	0.842912i	−0.513227	−	0.858253i	$-0.671550\pi$
$907$	14.6563	−	25.3855i	0.486655	−	0.842912i	0.999882	+	0.0153411i	$0.00488340\pi$
$908$		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
$913$		−	2.89402i		−	0.0957780i
$914$		0			0
$915$	8.51405	−	2.44681i	0.281466	−	0.0808891i
$916$		0			0
$917$	−33.5055	−	39.7901i	−1.10645	−	1.31398i
$918$		0			0
$919$	−0.897678	+	1.55482i	−0.0296117	+	0.0512889i	−0.880451	−	0.474136i	$-0.842760\pi$
$919$	−0.897678	+	1.55482i	−0.0296117	+	0.0512889i	0.850840	+	0.525425i	$0.176094\pi$
$920$		0			0
$921$	−7.10017	+	28.5491i	−0.233958	+	0.940725i
$922$		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
$927$	−32.2165	+	1.16316i	−1.05813	+	0.0382032i
$928$		0			0
$929$	−24.8356			−0.814831			−0.407415	−	0.913243i	$-0.633570\pi$
$929$	−24.8356			−0.814831			−0.407415	+	0.913243i	$0.633570\pi$
$930$		0			0
$931$	−40.7799	−	7.04495i	−1.33651	−	0.230889i
$932$		0			0
$933$	0.00500692	+	0.00124522i	0.000163919	+	4.07668e-5i
$934$		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
$941$	52.5075			1.71169			0.855847	−	0.517229i	$-0.173036\pi$
$941$	52.5075			1.71169			0.855847	+	0.517229i	$0.173036\pi$
$942$		0			0
$943$		−	18.9621i		−	0.617490i
$944$		0			0
$945$	1.18405	−	37.6958i	0.0385172	−	1.22624i
$946$		0			0
$947$			43.1385i			1.40181i	0.713253	+	0.700907i	$0.247221\pi$
$947$			43.1385i			1.40181i	−0.713253	+	0.700907i	$0.752779\pi$
$948$		0			0
$949$	2.91631			0.0946673
$950$		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
$957$	−4.87493	−	1.21240i	−0.157584	−	0.0391912i
$958$		0			0
$959$	13.3982	+	4.85026i	0.432650	+	0.156623i
$960$		0			0
$961$	18.5457			0.598248
$962$		0			0
$963$	−10.1252	−	16.1612i	−0.326281	−	0.520788i
$964$		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
$969$	−9.65273	+	38.8127i	−0.310090	+	1.24684i
$970$		0			0
$971$	28.1556	−	48.7669i	0.903555	−	1.56500i	0.0807100	−	0.996738i	$-0.474281\pi$
$971$	28.1556	−	48.7669i	0.903555	−	1.56500i	0.822845	−	0.568266i	$-0.192385\pi$
$972$		0			0
$973$	−42.4685	−	15.3740i	−1.36148	−	0.492867i
$974$		0			0
$975$	−6.43354	+	1.84890i	−0.206038	+	0.0592123i
$976$		0			0
$977$		−	26.0679i		−	0.833988i	−0.908909	−	0.416994i	$-0.863084\pi$
$977$		−	26.0679i		−	0.833988i	0.908909	−	0.416994i	$-0.136916\pi$
$978$		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
$983$	19.0252	−	32.9527i	0.606811	−	1.05103i	−0.384952	−	0.922937i	$-0.625782\pi$
$983$	19.0252	−	32.9527i	0.606811	−	1.05103i	0.991763	−	0.128090i	$-0.0408848\pi$
$984$		0			0
$985$	−38.1922	+	22.0503i	−1.21690	+	0.702580i
$986$		0			0
$987$	8.09611	+	0.547230i	0.257702	+	0.0174185i
$988$		0			0
$989$	−89.3217	−	51.5699i	−2.84026	−	1.63983i
$990$		0			0
$991$	−5.68758	−	9.85118i	−0.180672	−	0.312933i	0.761438	−	0.648238i	$-0.224494\pi$
$991$	−5.68758	−	9.85118i	−0.180672	−	0.312933i	−0.942110	+	0.335305i	$0.891161\pi$
$992$		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
$997$	−44.1590	−	25.4952i	−1.39853	−	0.807441i	−0.404290	−	0.914631i	$-0.632482\pi$
$997$	−44.1590	−	25.4952i	−1.39853	−	0.807441i	−0.994239	+	0.107189i	$0.965815\pi$
$998$		0			0
$999$	−44.9310	+	14.6871i	−1.42155	+	0.464679i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	1.1	even	1	trivial
252.2.w.a.101.7	yes	16	63.38	even	6	inner
252.2.bm.a.173.5	yes	16	9.2	odd	6
252.2.bm.a.185.5	yes	16	7.3	odd	6
756.2.w.a.341.2		16	3.2	odd	2
756.2.w.a.521.2		16	63.52	odd	6
756.2.bm.a.17.2		16	21.17	even	6
756.2.bm.a.89.2		16	9.7	even	3
1008.2.ca.d.257.2		16	4.3	odd	2
1008.2.ca.d.353.2		16	252.227	odd	6
1008.2.df.d.689.4		16	28.3	even	6
1008.2.df.d.929.4		16	36.11	even	6
1764.2.w.b.509.2		16	7.6	odd	2
1764.2.w.b.1109.2		16	63.11	odd	6
1764.2.x.a.293.2		16	7.2	even	3
1764.2.x.a.1469.2		16	63.47	even	6
1764.2.x.b.293.7		16	7.5	odd	6
1764.2.x.b.1469.7		16	63.2	odd	6
1764.2.bm.a.1685.4		16	63.20	even	6
1764.2.bm.a.1697.4		16	7.4	even	3
2268.2.t.a.1781.2		16	63.31	odd	6
2268.2.t.a.2105.2		16	9.5	odd	6
2268.2.t.b.1781.7		16	63.59	even	6
2268.2.t.b.2105.7		16	9.4	even	3
3024.2.ca.d.2033.2		16	252.115	even	6
3024.2.ca.d.2609.2		16	12.11	even	2
3024.2.df.d.17.2		16	84.59	odd	6
3024.2.df.d.1601.2		16	36.7	odd	6
5292.2.w.b.521.7		16	63.25	even	3
5292.2.w.b.1097.7		16	21.20	even	2
5292.2.x.a.881.2		16	21.2	odd	6
5292.2.x.a.4409.2		16	63.61	odd	6
5292.2.x.b.881.7		16	21.5	even	6
5292.2.x.b.4409.7		16	63.16	even	3
5292.2.bm.a.2285.7		16	21.11	odd	6
5292.2.bm.a.4625.7		16	63.34	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68085 + 0.418028i) q^{3} +(1.37166 + 2.37578i) q^{5} +(-2.60476 + 0.463945i) q^{7} +(2.65051 + 1.40528i) q^{9} +O(q^{10})\)	\(q+(1.68085 + 0.418028i) q^{3} +(1.37166 + 2.37578i) q^{5} +(-2.60476 + 0.463945i) q^{7} +(2.65051 + 1.40528i) q^{9} +(-0.362306 - 0.209178i) q^{11} +(1.32512 + 0.765056i) q^{13} +(1.31241 + 4.56672i) q^{15} +(-1.95291 - 3.38253i) q^{17} +(-5.11994 - 2.95600i) q^{19} +(-4.57214 - 0.309039i) q^{21} +(7.72884 - 4.46225i) q^{23} +(-1.26290 + 2.18740i) q^{25} +(3.86765 + 3.47005i) q^{27} +(6.00378 - 3.46629i) q^{29} +3.52907i q^{31} +(-0.521540 - 0.503050i) q^{33} +(-4.67507 - 5.55196i) q^{35} +(-4.54861 + 7.87842i) q^{37} +(1.90751 + 1.83988i) q^{39} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(0.296944 + 8.22460i) q^{45} -1.77075 q^{47} +(6.56951 - 2.41692i) q^{49} +(-1.86855 - 6.50189i) q^{51} +(-3.39526 + 1.96025i) q^{53} -1.14768i q^{55} +(-7.37015 - 7.10886i) q^{57} -4.05456 q^{59} -1.86437i q^{61} +(-7.55590 - 2.43073i) q^{63} +4.19758i q^{65} -12.7688 q^{67} +(14.8564 - 4.26950i) q^{69} -8.51021i q^{71} +(1.65059 - 0.952971i) q^{73} +(-3.03713 + 3.14877i) q^{75} +(1.04077 + 0.376767i) q^{77} -0.867266 q^{79} +(5.05036 + 7.44942i) q^{81} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(11.5405 - 3.31656i) q^{87} +(-4.88864 + 8.46738i) q^{89} +(-3.80655 - 1.37800i) q^{91} +(-1.47525 + 5.93183i) q^{93} -16.2185i q^{95} +(0.200411 - 0.115707i) q^{97} +(-0.666342 - 1.06357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{9}+O(q^{10}) \) 16 * q - q^7 + 6 * q^9	\( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

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