LMFDB - Embedded newform 252.2.w.a.101.7

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			101.7
Root			$-0.811340 - 1.53027i$ of defining polynomial
Character	$\chi$	$=$	252.101
Dual form			252.2.w.a.5.7

$q$-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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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	−0.377234	−	0.926118i	$-0.623125\pi$
$5$	1.37166	−	2.37578i	0.613425	−	1.06248i	0.990659	−	0.136365i	$-0.0435419\pi$
$6$		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	−0.553624	−	0.832767i	$-0.686756\pi$
$11$	−0.362306	+	0.209178i	−0.109240	+	0.0630695i	0.444385	+	0.895836i	$0.353422\pi$
$12$		0			0
$13$	1.32512	−	0.765056i	0.367521	−	0.212188i	−0.304854	−	0.952399i	$-0.598608\pi$
$13$	1.32512	−	0.765056i	0.367521	−	0.212188i	0.672375	+	0.740211i	$0.265274\pi$
$14$		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	−0.954758	−	0.297385i	$-0.903886\pi$
$19$	−5.11994	+	2.95600i	−1.17459	+	0.678152i	−0.219836	+	0.975537i	$0.570552\pi$
$20$		0			0
$21$	−4.57214	+	0.309039i	−0.997723	+	0.0674379i
$22$		0			0
$23$	7.72884	+	4.46225i	1.61157	+	0.930443i	0.989006	+	0.147878i	$0.0472444\pi$
$23$	7.72884	+	4.46225i	1.61157	+	0.930443i	0.622569	+	0.782565i	$0.286089\pi$
$24$		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	0.940088	−	0.340933i	$-0.110743\pi$
$29$	6.00378	+	3.46629i	1.11487	+	0.643673i	0.174787	+	0.984606i	$0.444076\pi$
$30$		0			0
$31$		−	3.52907i		−	0.633839i	−0.948452	−	0.316920i	$-0.897351\pi$
$31$		−	3.52907i		−	0.633839i	0.948452	−	0.316920i	$-0.102649\pi$
$32$		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	−0.948881	−	0.315633i	$-0.897783\pi$
$37$	−4.54861	−	7.87842i	−0.747787	−	1.29520i	0.201095	−	0.979572i	$-0.435550\pi$
$38$		0			0
$39$	1.90751	−	1.83988i	0.305445	−	0.294616i
$40$		0			0
$41$	1.06236	+	1.84006i	0.165913	+	0.287370i	0.936979	−	0.349385i	$-0.113610\pi$
$41$	1.06236	+	1.84006i	0.165913	+	0.287370i	−0.771066	+	0.636755i	$0.780276\pi$
$42$		0			0
$43$	−5.77846	+	10.0086i	−0.881208	+	1.52630i	−0.0312079	+	0.999513i	$0.509935\pi$
$43$	−5.77846	+	10.0086i	−0.881208	+	1.52630i	−0.850000	+	0.526783i	$0.823398\pi$
$44$		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	0.248346	−	0.968671i	$-0.420113\pi$
$53$	−3.39526	−	1.96025i	−0.466374	−	0.269261i	−0.714721	+	0.699410i	$0.753446\pi$
$54$		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	$0.0380823\pi$
$61$			1.86437i			0.238708i	−0.992852	+	0.119354i	$0.961918\pi$
$62$		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	$0.168503\pi$
$71$			8.51021i			1.00998i	−0.863126	+	0.504988i	$0.831497\pi$
$72$		0			0
$73$	1.65059	+	0.952971i	0.193187	+	0.111537i	0.593474	−	0.804853i	$-0.297756\pi$
$73$	1.65059	+	0.952971i	0.193187	+	0.111537i	−0.400286	+	0.916390i	$0.631089\pi$
$74$		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	−0.611359	−	0.791354i	$-0.709377\pi$
$83$	3.45880	−	5.99082i	0.379653	−	0.657578i	0.991012	+	0.133775i	$0.0427100\pi$
$84$		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	−0.999777	−	0.0211389i	$-0.993271\pi$
$89$	−4.88864	−	8.46738i	−0.518195	−	0.897540i	0.481581	−	0.876401i	$-0.340063\pi$
$90$		0			0
$91$	−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	0.510140	−	0.860091i	$-0.329594\pi$
$97$	0.200411	+	0.115707i	0.0203486	+	0.0117483i	−0.489791	+	0.871840i	$0.662927\pi$
$98$		0			0
$99$	−0.666342	+	1.06357i	−0.0669699	+	0.106893i
$100$		0			0
$101$	−7.14031	−	12.3674i	−0.710487	−	1.23060i	−0.964674	−	0.263445i	$-0.915141\pi$
$101$	−7.14031	−	12.3674i	−0.710487	−	1.23060i	0.254187	−	0.967155i	$-0.418192\pi$
$102$		0			0
$103$	−9.30617	−	5.37292i	−0.916964	−	0.529410i	−0.0342991	−	0.999412i	$-0.510920\pi$
$103$	−9.30617	−	5.37292i	−0.916964	−	0.529410i	−0.882665	+	0.470002i	$0.844253\pi$
$104$		0			0
$105$	−5.53721	+	11.2863i	−0.540376	+	1.10143i
$106$		0			0
$107$	−5.50534	+	3.17851i	−0.532221	+	0.307278i	−0.741920	−	0.670488i	$-0.766085\pi$
$107$	−5.50534	+	3.17851i	−0.532221	+	0.307278i	0.209699	+	0.977766i	$0.432751\pi$
$108$		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	−0.000885276	−	1.00000i	$-0.500282\pi$
$113$	9.19186	−	5.30692i	0.864697	−	0.499233i	0.865582	+	0.500766i	$0.166948\pi$
$114$		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	−0.0140928	−	0.999901i	$-0.504486\pi$
$131$	9.83048	−	17.0269i	0.858893	−	1.48765i	0.872986	−	0.487746i	$-0.162181\pi$
$132$		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	−0.685829	−	0.727763i	$-0.740560\pi$
$137$	−4.66411	+	2.69282i	−0.398481	+	0.230063i	0.287347	+	0.957827i	$0.407227\pi$
$138$		0			0
$139$	14.7839	−	8.53549i	1.25395	−	0.723971i	0.282062	−	0.959396i	$-0.408982\pi$
$139$	14.7839	−	8.53549i	1.25395	−	0.723971i	0.971892	+	0.235425i	$0.0756484\pi$
$140$		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	0.830314	−	0.557296i	$-0.188161\pi$
$149$	9.31162	+	5.37607i	0.762838	+	0.440425i	−0.0674758	+	0.997721i	$0.521495\pi$
$150$		0			0
$151$	−3.78223	−	6.55102i	−0.307794	−	0.533115i	0.670086	−	0.742284i	$-0.266257\pi$
$151$	−3.78223	−	6.55102i	−0.307794	−	0.533115i	−0.977879	+	0.209169i	$0.932924\pi$
$152$		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	$-0.837040\pi$
$157$		−	12.2764i		−	0.979763i	0.871789	−	0.489882i	$-0.162960\pi$
$158$		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	0.999132	−	0.0416566i	$-0.0132635\pi$
$163$	5.91745	+	10.2493i	0.463490	+	0.802789i	−0.535642	+	0.844445i	$0.679930\pi$
$164$		0			0
$165$	0.479763	+	1.92908i	0.0373495	+	0.150179i
$166$		0			0
$167$	6.78854	+	11.7581i	0.525313	+	0.909869i	0.999565	+	0.0294798i	$0.00938508\pi$
$167$	6.78854	+	11.7581i	0.525313	+	0.909869i	−0.474252	+	0.880389i	$0.657282\pi$
$168$		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	0.938000	−	0.346636i	$-0.112676\pi$
$179$	14.8080	+	8.54942i	1.10680	+	0.639014i	0.168805	+	0.985650i	$0.446009\pi$
$180$		0			0
$181$			18.2171i			1.35407i	0.735952	+	0.677034i	$0.236735\pi$
$181$			18.2171i			1.35407i	−0.735952	+	0.677034i	$0.763265\pi$
$182$		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	$-0.725331\pi$
$191$		−	20.9994i		−	1.51946i	0.650239	−	0.759730i	$-0.274669\pi$
$192$		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	$-0.805908\pi$
$197$		−	16.0756i		−	1.14534i	0.819786	−	0.572670i	$-0.194092\pi$
$198$		0			0
$199$	−5.44956	−	3.14630i	−0.386309	−	0.223036i	0.294251	−	0.955728i	$-0.404930\pi$
$199$	−5.44956	−	3.14630i	−0.386309	−	0.223036i	−0.680560	+	0.732693i	$0.738263\pi$
$200$		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	0.817876	−	0.575394i	$-0.195151\pi$
$211$	−1.29814	−	2.24844i	−0.0893674	−	0.154789i	−0.907244	+	0.420605i	$0.861818\pi$
$212$		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	−0.394571	−	0.918866i	$-0.629107\pi$
$223$	−20.7215	−	11.9636i	−1.38762	−	0.801141i	−0.993046	+	0.117725i	$0.962440\pi$
$224$		0			0
$225$	−6.42123	−	4.02299i	−0.428082	−	0.268200i
$226$		0			0
$227$	−1.86609	−	3.23216i	−0.123857	−	0.214526i	0.797429	−	0.603413i	$-0.206193\pi$
$227$	−1.86609	−	3.23216i	−0.123857	−	0.214526i	−0.921285	+	0.388887i	$0.872860\pi$
$228$		0			0
$229$	18.2455	+	10.5341i	1.20570	+	0.696111i	0.961817	−	0.273694i	$-0.0882457\pi$
$229$	18.2455	+	10.5341i	1.20570	+	0.696111i	0.243882	+	0.969805i	$0.421579\pi$
$230$		0			0
$231$	1.59187	−	1.06836i	0.104738	−	0.0702928i
$232$		0			0
$233$	−11.0542	+	6.38215i	−0.724186	+	0.418109i	−0.816291	−	0.577640i	$-0.803974\pi$
$233$	−11.0542	+	6.38215i	−0.724186	+	0.418109i	0.0921057	+	0.995749i	$0.470640\pi$
$234$		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	−0.0979736	−	0.995189i	$-0.531236\pi$
$239$	11.0521	−	6.38091i	0.714899	−	0.412747i	0.812872	+	0.582442i	$0.197903\pi$
$240$		0			0
$241$	−2.63438	+	1.52096i	−0.169695	+	0.0979737i	−0.582442	−	0.812872i	$-0.697903\pi$
$241$	−2.63438	+	1.52096i	−0.169695	+	0.0979737i	0.412747	+	0.910846i	$0.364569\pi$
$242$		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	0.176206	+	0.984353i	$0.443617\pi$
$257$	−12.2538	+	21.2242i	−0.764372	+	1.32393i	−0.940578	+	0.339577i	$0.889716\pi$
$258$		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	−0.980761	−	0.195211i	$-0.937461\pi$
$263$	−21.1163	+	12.1915i	−1.30208	+	0.751759i	−0.321323	+	0.946970i	$0.604128\pi$
$264$		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	−0.646976	−	0.762511i	$-0.723966\pi$
$271$	−5.10505	+	2.94740i	−0.310110	+	0.179042i	0.336866	+	0.941553i	$0.390633\pi$
$272$		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	−0.968537	−	0.248870i	$-0.919941\pi$
$277$	−11.6469	−	20.1731i	−0.699796	−	1.21208i	0.268741	−	0.963213i	$-0.413392\pi$
$278$		0			0
$279$	−4.95933	−	9.35381i	−0.296908	−	0.559998i
$280$		0			0
$281$	21.7962	+	12.5840i	1.30025	+	0.750700i	0.980447	−	0.196784i	$-0.0630499\pi$
$281$	21.7962	+	12.5840i	1.30025	+	0.750700i	0.319803	+	0.947484i	$0.396383\pi$
$282$		0			0
$283$		−	9.96439i		−	0.592322i	−0.955138	−	0.296161i	$-0.904294\pi$
$283$		−	9.96439i		−	0.592322i	0.955138	−	0.296161i	$-0.0957064\pi$
$284$		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	0.596604	−	0.802536i	$-0.296516\pi$
$293$	−6.79065	−	11.7618i	−0.396714	−	0.687129i	−0.993318	+	0.115406i	$0.963183\pi$
$294$		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	$-0.838932\pi$
$307$		−	16.9849i		−	0.969381i	0.874686	−	0.484691i	$-0.161068\pi$
$308$		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	$0.112602\pi$
$313$			12.2576i			0.692838i	−0.938080	+	0.346419i	$0.887398\pi$
$314$		0			0
$315$	−4.58922	+	21.2853i	−0.258573	+	1.19929i
$316$		0			0
$317$			23.0950i			1.29714i	0.761154	+	0.648571i	$0.224633\pi$
$317$			23.0950i			1.29714i	−0.761154	+	0.648571i	$0.775367\pi$
$318$		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	0.502643	−	0.864494i	$-0.332361\pi$
$337$	−9.13018	−	15.8139i	−0.497352	−	0.861440i	−0.999995	+	0.00305455i	$0.999028\pi$
$338$		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	$0.0457749\pi$
$347$			5.33917i			0.286622i	−0.989678	+	0.143311i	$0.954225\pi$
$348$		0			0
$349$	−0.0136817	−	0.00789914i	−0.000732365	−	0.000422831i	0.499634	−	0.866237i	$-0.333468\pi$
$349$	−0.0136817	−	0.00789914i	−0.000732365	−	0.000422831i	−0.500366	+	0.865814i	$0.666801\pi$
$350$		0			0
$351$	2.47030	−	7.55719i	0.131855	−	0.403373i
$352$		0			0
$353$	17.1543	+	29.7121i	0.913029	+	1.58141i	0.809761	+	0.586760i	$0.199597\pi$
$353$	17.1543	+	29.7121i	0.913029	+	1.58141i	0.103268	+	0.994654i	$0.467070\pi$
$354$		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	−0.636342	−	0.771407i	$-0.719553\pi$
$359$	−5.42754	+	3.13359i	−0.286454	+	0.165385i	0.349887	+	0.936792i	$0.386220\pi$
$360$		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	−0.00353959	−	0.999994i	$-0.501127\pi$
$367$	16.4888	−	9.51984i	0.860711	−	0.496931i	0.864250	+	0.503062i	$0.167793\pi$
$368$		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	−0.971529	−	0.236920i	$-0.923862\pi$
$373$	−5.41901	+	9.38600i	−0.280586	+	0.485989i	0.690943	+	0.722909i	$0.257195\pi$
$374$		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	0.282729	−	0.959200i	$-0.408760\pi$
$383$	19.0235	−	32.9497i	0.972056	−	1.68365i	0.689327	−	0.724451i	$-0.257906\pi$
$384$		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	−0.0129603	−	0.999916i	$-0.504125\pi$
$389$	16.6958	−	9.63934i	0.846512	−	0.488734i	0.859473	+	0.511182i	$0.170792\pi$
$390$		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	−0.867788	−	0.496934i	$-0.834459\pi$
$397$	−17.3610	+	10.0234i	−0.871325	+	0.503059i	−0.00353639	+	0.999994i	$0.501126\pi$
$398$		0			0
$399$	22.4956	−	15.0975i	1.12619	−	0.755820i
$400$		0			0
$401$	26.4232	+	15.2554i	1.31951	+	0.761820i	0.983650	−	0.180092i	$-0.0576395\pi$
$401$	26.4232	+	15.2554i	1.31951	+	0.761820i	0.335861	+	0.941912i	$0.390973\pi$
$402$		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	$-0.998631\pi$
$409$		−	0.173933i		−	0.00860045i	0.999991	−	0.00430023i	$-0.00136881\pi$
$410$		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	−0.972703	−	0.232054i	$-0.925455\pi$
$419$	−14.0690	−	24.3682i	−0.687316	−	1.19047i	0.285387	−	0.958412i	$-0.407878\pi$
$420$		0			0
$421$	−1.56130	+	2.70424i	−0.0760929	+	0.131797i	−0.901561	−	0.432652i	$-0.857578\pi$
$421$	−1.56130	+	2.70424i	−0.0760929	+	0.131797i	0.825468	+	0.564449i	$0.190911\pi$
$422$		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	0.692381	−	0.721532i	$-0.256562\pi$
$431$	8.58876	+	4.95872i	0.413706	+	0.238853i	−0.278675	+	0.960385i	$0.589895\pi$
$432$		0			0
$433$		−	17.1274i		−	0.823092i	−0.911389	−	0.411546i	$-0.864989\pi$
$433$		−	17.1274i		−	0.823092i	0.911389	−	0.411546i	$-0.135011\pi$
$434$		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	$0.171082\pi$
$439$			21.4537i			1.02393i	−0.859006	+	0.511965i	$0.828918\pi$
$440$		0			0
$441$	20.8090	−	2.82594i	0.990904	−	0.134569i
$442$		0			0
$443$		−	6.74738i		−	0.320578i	−0.987070	−	0.160289i	$-0.948757\pi$
$443$		−	6.74738i		−	0.320578i	0.987070	−	0.160289i	$-0.0512425\pi$
$444$		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	$-0.956176\pi$
$449$		−	5.81624i		−	0.274485i	0.990537	−	0.137243i	$-0.0438240\pi$
$450$		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	0.00730959	+	0.999973i	$0.497673\pi$
$461$	−18.5154	+	32.0696i	−0.862347	+	1.49363i	−0.869657	+	0.493656i	$0.835660\pi$
$462$		0			0
$463$	10.5618	+	18.2935i	0.490848	+	0.850173i	0.999944	−	0.0105362i	$-0.00335383\pi$
$463$	10.5618	+	18.2935i	0.490848	+	0.850173i	−0.509097	+	0.860709i	$0.670020\pi$
$464$		0			0
$465$	−16.1163	−	4.63158i	−0.747374	−	0.214784i
$466$		0			0
$467$	9.30470	+	16.1162i	0.430570	+	0.745770i	0.996922	−	0.0783937i	$-0.0249791\pi$
$467$	9.30470	+	16.1162i	0.430570	+	0.745770i	−0.566352	+	0.824163i	$0.691646\pi$
$468$		0			0
$469$	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	0.982009	−	0.188834i	$-0.0604707\pi$
$479$	7.16703	+	12.4137i	0.327470	+	0.567194i	−0.654539	+	0.756028i	$0.727137\pi$
$480$		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	−0.965153	−	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	−0.686047	−	0.727557i	$-0.740656\pi$
$491$	−8.84097	+	5.10434i	−0.398988	+	0.230356i	0.287059	+	0.957913i	$0.407322\pi$
$492$		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	−0.568454	−	0.822715i	$-0.692458\pi$
$499$	9.56672	−	16.5701i	0.428265	−	0.741777i	0.996719	+	0.0809379i	$0.0257915\pi$
$500$		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	−0.514774	−	0.857326i	$-0.672124\pi$
$509$	10.9439	−	18.9553i	0.485079	−	0.840181i	0.999853	+	0.0171449i	$0.00545767\pi$
$510$		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	−0.846663	−	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	−0.335144	−	0.942167i	$-0.608785\pi$
$523$	7.16320	−	4.13568i	0.313225	−	0.180841i	0.648369	+	0.761326i	$0.275452\pi$
$524$		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	0.559057	−	0.829129i	$-0.311163\pi$
$541$	−10.1997	−	17.6664i	−0.438518	−	0.759536i	−0.997575	+	0.0695932i	$0.977830\pi$
$542$		0			0
$543$	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	−0.101503	−	0.994835i	$-0.532365\pi$
$547$	18.9630	−	32.8449i	0.810801	−	1.40435i	0.912304	−	0.409513i	$-0.134301\pi$
$548$		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	0.776198	−	0.630489i	$-0.217146\pi$
$557$	14.5919	+	8.42463i	0.618278	+	0.356963i	−0.157920	+	0.987452i	$0.550479\pi$
$558$		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	$-0.957511\pi$
$569$		−	6.34919i		−	0.266172i	0.991104	−	0.133086i	$-0.0424886\pi$
$570$		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	0.784592	−	0.620013i	$-0.212873\pi$
$577$	15.3719	+	8.87497i	0.639940	+	0.369470i	−0.144651	+	0.989483i	$0.546206\pi$
$578$		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	−0.760508	−	0.649329i	$-0.775050\pi$
$587$	4.41148	−	7.64091i	0.182081	−	0.315374i	0.942589	+	0.333955i	$0.108383\pi$
$588$		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	0.939976	−	0.341241i	$-0.110847\pi$
$593$	4.24849	+	7.35860i	0.174465	+	0.302181i	−0.765511	+	0.643422i	$0.777514\pi$
$594$		0			0
$595$	−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	$0.0241386\pi$
$599$			3.70842i			0.151522i	−0.997126	+	0.0757609i	$0.975861\pi$
$600$		0			0
$601$	6.14043	+	3.54518i	0.250473	+	0.144611i	0.619981	−	0.784617i	$-0.287140\pi$
$601$	6.14043	+	3.54518i	0.250473	+	0.144611i	−0.369508	+	0.929228i	$0.620474\pi$
$602$		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	−0.235500	−	0.971874i	$-0.575673\pi$
$607$	−29.4396	−	16.9970i	−1.19492	−	0.689886i	−0.959418	+	0.281988i	$0.909006\pi$
$608$		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	−0.999472	−	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	−0.577618	+	0.816307i	$0.696018\pi$
$617$	−39.0817	+	22.5638i	−1.57337	+	0.908386i	−0.995752	+	0.0920787i	$0.970649\pi$
$618$		0			0
$619$	−7.97914	+	4.60676i	−0.320709	+	0.185161i	−0.651708	−	0.758470i	$-0.725947\pi$
$619$	−7.97914	+	4.60676i	−0.320709	+	0.185161i	0.331000	+	0.943631i	$0.392614\pi$
$620$		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	−0.135550	−	0.990771i	$-0.543280\pi$
$641$	16.5759	−	9.57009i	0.654708	−	0.377996i	0.790258	+	0.612775i	$0.209947\pi$
$642$		0			0
$643$	−2.01129	+	1.16122i	−0.0793177	+	0.0457941i	−0.539134	−	0.842220i	$-0.681248\pi$
$643$	−2.01129	+	1.16122i	−0.0793177	+	0.0457941i	0.459817	+	0.888014i	$0.347915\pi$
$644$		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
$651$	1.09062	+	16.1354i	0.0427448	+	0.632396i
$652$		0			0
$653$	−20.1140	−	11.6128i	−0.787123	−	0.454446i	0.0518258	−	0.998656i	$-0.483496\pi$
$653$	−20.1140	−	11.6128i	−0.787123	−	0.454446i	−0.838949	+	0.544211i	$0.816829\pi$
$654$		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	0.742515	−	0.669829i	$-0.233633\pi$
$659$	13.7002	+	7.90981i	0.533684	+	0.308122i	−0.208832	+	0.977952i	$0.566966\pi$
$660$		0			0
$661$		−	18.2450i		−	0.709647i	−0.934933	−	0.354823i	$-0.884541\pi$
$661$		−	18.2450i		−	0.709647i	0.934933	−	0.354823i	$-0.115459\pi$
$662$		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	−0.442055	−	0.896988i	$-0.645750\pi$
$673$	14.4184	−	24.9733i	0.555787	−	0.962651i	0.997842	−	0.0656633i	$-0.0209163\pi$
$674$		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	0.0880282	−	0.996118i	$-0.471943\pi$
$683$	−19.0943	−	11.0241i	−0.730621	−	0.421824i	−0.818649	+	0.574294i	$0.805277\pi$
$684$		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	$0.167483\pi$
$691$			26.4036i			1.00444i	−0.864740	+	0.502219i	$0.832517\pi$
$692$		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	$0.126627\pi$
$701$			20.5140i			0.774804i	−0.921911	+	0.387402i	$0.873373\pi$
$702$		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	0.564109	−	0.825700i	$-0.309220\pi$
$719$	−11.6111	−	20.1111i	−0.433023	−	0.750017i	−0.997132	+	0.0756828i	$0.975886\pi$
$720$		0			0
$721$	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	0.545822	−	0.837901i	$-0.316217\pi$
$727$	2.50999	+	1.44914i	0.0930903	+	0.0537457i	−0.452732	+	0.891647i	$0.649551\pi$
$728$		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	0.677950	−	0.735108i	$-0.262869\pi$
$733$	10.2963	+	5.94457i	0.380302	+	0.219568i	−0.297647	+	0.954676i	$0.596202\pi$
$734$		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	−0.353151	−	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	−0.544101	−	0.839019i	$-0.683129\pi$
$743$	−2.44069	+	1.40913i	−0.0895401	+	0.0516960i	0.454561	+	0.890715i	$0.349796\pi$
$744$		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	−0.927824	−	0.373017i	$-0.878323\pi$
$751$	−3.86045	+	6.68649i	−0.140870	+	0.243993i	0.786955	+	0.617011i	$0.211657\pi$
$752$		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	−0.893020	−	0.450017i	$-0.851418\pi$
$761$	−1.56644	+	2.71316i	−0.0567835	+	0.0983520i	0.836236	+	0.548369i	$0.184751\pi$
$762$		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	−0.396871	−	0.917874i	$-0.629904\pi$
$769$	5.53497	−	3.19562i	0.199596	−	0.115237i	0.596467	+	0.802637i	$0.296571\pi$
$770$		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
$777$	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	$0.0343368\pi$
$787$			6.04066i			0.215326i	−0.994187	+	0.107663i	$0.965663\pi$
$788$		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	0.879551	−	0.475804i	$-0.157843\pi$
$797$	0.782501	+	1.35533i	0.0277176	+	0.0480083i	−0.851834	+	0.523812i	$0.824509\pi$
$798$		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	0.205385	−	0.978681i	$-0.434155\pi$
$809$	−15.3445	−	8.85918i	−0.539485	−	0.311472i	−0.744870	+	0.667209i	$0.767489\pi$
$810$		0			0
$811$		−	27.5261i		−	0.966571i	−0.875463	−	0.483285i	$-0.839443\pi$
$811$		−	27.5261i		−	0.966571i	0.875463	−	0.483285i	$-0.160557\pi$
$812$		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	$0.153634\pi$
$821$			26.5977i			0.928267i	−0.885765	+	0.464134i	$0.846366\pi$
$822$		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	$0.0536561\pi$
$827$			9.64923i			0.335537i	−0.985826	+	0.167768i	$0.946344\pi$
$828$		0			0
$829$	−25.1481	−	14.5193i	−0.873430	−	0.504275i	−0.00494329	−	0.999988i	$-0.501574\pi$
$829$	−25.1481	−	14.5193i	−0.873430	−	0.504275i	−0.868486	+	0.495713i	$0.834907\pi$
$830$		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	−0.723367	−	0.690463i	$-0.757407\pi$
$839$	6.84383	−	11.8539i	0.236275	−	0.409241i	0.959642	+	0.281223i	$0.0907400\pi$
$840$		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	0.993013	−	0.118006i	$-0.0376501\pi$
$853$	40.5184	+	23.3933i	1.38732	+	0.800972i	0.394310	+	0.918977i	$0.370983\pi$
$854$		0			0
$855$	22.7915	+	42.9872i	0.779454	+	1.47013i
$856$		0			0
$857$	15.8980	+	27.5361i	0.543065	+	0.940616i	0.998726	+	0.0504623i	$0.0160695\pi$
$857$	15.8980	+	27.5361i	0.543065	+	0.940616i	−0.455661	+	0.890153i	$0.650597\pi$
$858$		0			0
$859$	21.9005	+	12.6442i	0.747235	+	0.431416i	0.824694	−	0.565579i	$-0.191347\pi$
$859$	21.9005	+	12.6442i	0.747235	+	0.431416i	−0.0774592	+	0.996996i	$0.524681\pi$
$860$		0			0
$861$	−5.42592	−	8.08472i	−0.184915	−	0.275527i
$862$		0			0
$863$	15.9513	−	9.20946i	0.542987	−	0.313494i	−0.203302	−	0.979116i	$-0.565167\pi$
$863$	15.9513	−	9.20946i	0.542987	−	0.313494i	0.746289	+	0.665622i	$0.231834\pi$
$864$		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	−0.781124	−	0.624375i	$-0.785354\pi$
$877$	4.44695	−	7.70234i	0.150163	−	0.260089i	0.931287	+	0.364286i	$0.118687\pi$
$878$		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	0.436733	+	0.899591i	$0.356136\pi$
$887$	−16.6991	+	28.9238i	−0.560703	+	0.971165i	−0.997435	+	0.0715740i	$0.977198\pi$
$888$		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	0.999882	−	0.0153411i	$-0.00488340\pi$
$907$	14.6563	+	25.3855i	0.486655	+	0.842912i	−0.513227	+	0.858253i	$0.671550\pi$
$908$		0			0
$909$	−36.3051	−	22.7457i	−1.20416	−	0.754426i
$910$		0			0
$911$	1.72555	+	0.996246i	0.0571700	+	0.0330071i	0.528313	−	0.849050i	$-0.322825\pi$
$911$	1.72555	+	0.996246i	0.0571700	+	0.0330071i	−0.471143	+	0.882057i	$0.656158\pi$
$912$		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	0.850840	−	0.525425i	$-0.176094\pi$
$919$	−0.897678	−	1.55482i	−0.0296117	−	0.0512889i	−0.880451	+	0.474136i	$0.842760\pi$
$920$		0			0
$921$	−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	$-0.849352\pi$
$937$		−	27.9046i		−	0.911605i	0.890081	−	0.455802i	$-0.150648\pi$
$938$		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	$-0.752779\pi$
$947$		−	43.1385i		−	1.40181i	0.713253	−	0.700907i	$-0.247221\pi$
$948$		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	$0.423847\pi$
$953$			59.9829i			1.94304i	−0.236965	+	0.971518i	$0.576153\pi$
$954$		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	−0.875080	−	0.483978i	$-0.839191\pi$
$967$	−26.6398	−	46.1414i	−0.856677	−	1.48381i	0.0184029	−	0.999831i	$-0.494142\pi$
$968$		0			0
$969$	−9.65273	−	38.8127i	−0.310090	−	1.24684i
$970$		0			0
$971$	28.1556	+	48.7669i	0.903555	+	1.56500i	0.822845	+	0.568266i	$0.192385\pi$
$971$	28.1556	+	48.7669i	0.903555	+	1.56500i	0.0807100	+	0.996738i	$0.474281\pi$
$972$		0			0
$973$	−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	$0.136916\pi$
$977$			26.0679i			0.833988i	−0.908909	+	0.416994i	$0.863084\pi$
$978$		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	0.991763	+	0.128090i	$0.0408848\pi$
$983$	19.0252	+	32.9527i	0.606811	+	1.05103i	−0.384952	+	0.922937i	$0.625782\pi$
$984$		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	−0.942110	−	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
$997$	−44.1590	+	25.4952i	−1.39853	+	0.807441i	−0.994239	−	0.107189i	$-0.965815\pi$
$997$	−44.1590	+	25.4952i	−1.39853	+	0.807441i	−0.404290	+	0.914631i	$0.632482\pi$
$998$		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.101.7	yes	16
3.2	odd	2		756.2.w.a.521.2		16
4.3	odd	2		1008.2.ca.d.353.2		16
7.2	even	3		1764.2.bm.a.1685.4		16
7.3	odd	6		1764.2.x.b.1469.7		16
7.4	even	3		1764.2.x.a.1469.2		16
7.5	odd	6		252.2.bm.a.173.5	yes	16
7.6	odd	2		1764.2.w.b.1109.2		16
9.2	odd	6		2268.2.t.a.1781.2		16
9.4	even	3		756.2.bm.a.17.2		16
9.5	odd	6		252.2.bm.a.185.5	yes	16
9.7	even	3		2268.2.t.b.1781.7		16
12.11	even	2		3024.2.ca.d.2033.2		16
21.2	odd	6		5292.2.bm.a.4625.7		16
21.5	even	6		756.2.bm.a.89.2		16
21.11	odd	6		5292.2.x.a.4409.2		16
21.17	even	6		5292.2.x.b.4409.7		16
21.20	even	2		5292.2.w.b.521.7		16
28.19	even	6		1008.2.df.d.929.4		16
36.23	even	6		1008.2.df.d.689.4		16
36.31	odd	6		3024.2.df.d.17.2		16
63.4	even	3		5292.2.x.b.881.7		16
63.5	even	6	inner	252.2.w.a.5.7	✓	16
63.13	odd	6		5292.2.bm.a.2285.7		16
63.23	odd	6		1764.2.w.b.509.2		16
63.31	odd	6		5292.2.x.a.881.2		16
63.32	odd	6		1764.2.x.b.293.7		16
63.40	odd	6		756.2.w.a.341.2		16
63.41	even	6		1764.2.bm.a.1697.4		16
63.47	even	6		2268.2.t.b.2105.7		16
63.58	even	3		5292.2.w.b.1097.7		16
63.59	even	6		1764.2.x.a.293.2		16
63.61	odd	6		2268.2.t.a.2105.2		16
84.47	odd	6		3024.2.df.d.1601.2		16
252.103	even	6		3024.2.ca.d.2609.2		16
252.131	odd	6		1008.2.ca.d.257.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	63.5	even	6	inner
252.2.w.a.101.7	yes	16	1.1	even	1	trivial
252.2.bm.a.173.5	yes	16	7.5	odd	6
252.2.bm.a.185.5	yes	16	9.5	odd	6
756.2.w.a.341.2		16	63.40	odd	6
756.2.w.a.521.2		16	3.2	odd	2
756.2.bm.a.17.2		16	9.4	even	3
756.2.bm.a.89.2		16	21.5	even	6
1008.2.ca.d.257.2		16	252.131	odd	6
1008.2.ca.d.353.2		16	4.3	odd	2
1008.2.df.d.689.4		16	36.23	even	6
1008.2.df.d.929.4		16	28.19	even	6
1764.2.w.b.509.2		16	63.23	odd	6
1764.2.w.b.1109.2		16	7.6	odd	2
1764.2.x.a.293.2		16	63.59	even	6
1764.2.x.a.1469.2		16	7.4	even	3
1764.2.x.b.293.7		16	63.32	odd	6
1764.2.x.b.1469.7		16	7.3	odd	6
1764.2.bm.a.1685.4		16	7.2	even	3
1764.2.bm.a.1697.4		16	63.41	even	6
2268.2.t.a.1781.2		16	9.2	odd	6
2268.2.t.a.2105.2		16	63.61	odd	6
2268.2.t.b.1781.7		16	9.7	even	3
2268.2.t.b.2105.7		16	63.47	even	6
3024.2.ca.d.2033.2		16	12.11	even	2
3024.2.ca.d.2609.2		16	252.103	even	6
3024.2.df.d.17.2		16	36.31	odd	6
3024.2.df.d.1601.2		16	84.47	odd	6
5292.2.w.b.521.7		16	21.20	even	2
5292.2.w.b.1097.7		16	63.58	even	3
5292.2.x.a.881.2		16	63.31	odd	6
5292.2.x.a.4409.2		16	21.11	odd	6
5292.2.x.b.881.7		16	63.4	even	3
5292.2.x.b.4409.7		16	21.17	even	6
5292.2.bm.a.2285.7		16	63.13	odd	6
5292.2.bm.a.4625.7		16	21.2	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

Introduction

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