LMFDB - Embedded newform 1764.2.l.e.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(949,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("1764.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1764.961
Dual form			1764.2.l.e.949.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09097 + 1.34528i) q^{3} +0.239123 q^{5} +(-0.619562 + 2.93533i) q^{9} +O(q^{10})$	\(q+(1.09097 + 1.34528i) q^{3} +0.239123 q^{5} +(-0.619562 + 2.93533i) q^{9} -5.12476 q^{11} +(2.44282 + 4.23109i) q^{13} +(0.260877 + 0.321688i) q^{15} +(-1.85185 - 3.20750i) q^{17} +(-1.83009 + 3.16982i) q^{19} +7.42107 q^{23} -4.94282 q^{25} +(-4.62476 + 2.36887i) q^{27} +(-1.73229 + 3.00041i) q^{29} +(0.358685 - 0.621261i) q^{31} +(-5.59097 - 6.89425i) q^{33} +(-2.30150 + 3.98632i) q^{37} +(-3.02696 + 7.90228i) q^{39} +(-2.80150 - 4.85235i) q^{41} +(-6.24433 + 10.8155i) q^{43} +(-0.148152 + 0.701905i) q^{45} +(-2.16991 - 3.75839i) q^{47} +(2.29467 - 5.99054i) q^{51} +(0.471410 + 0.816506i) q^{53} -1.22545 q^{55} +(-6.26088 + 0.996189i) q^{57} +(-3.78947 + 6.56355i) q^{59} +(-2.75404 - 4.77014i) q^{61} +(0.584135 + 1.01175i) q^{65} +(0.330095 - 0.571741i) q^{67} +(8.09617 + 9.98342i) q^{69} +13.7414 q^{71} +(1.83009 + 3.16982i) q^{73} +(-5.39248 - 6.64948i) q^{75} +(3.11273 + 5.39140i) q^{79} +(-8.23229 - 3.63723i) q^{81} +(-4.85185 + 8.40365i) q^{83} +(-0.442820 - 0.766987i) q^{85} +(-5.92627 + 0.942948i) q^{87} +(3.74433 - 6.48536i) q^{89} +(1.22708 - 0.195246i) q^{93} +(-0.437618 + 0.757977i) q^{95} +(8.57442 - 14.8513i) q^{97} +(3.17511 - 15.0429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} + 2 q^{5} - 4 q^{9}+O(q^{10}) $ 6 * q - 2 * q^3 + 2 * q^5 - 4 * q^9	$ 6 q - 2 q^{3} + 2 q^{5} - 4 q^{9} + 4 q^{11} - 3 q^{13} + q^{15} - 2 q^{17} - 3 q^{19} + 28 q^{23} - 12 q^{25} + 7 q^{27} - q^{29} + 3 q^{31} - 25 q^{33} + 3 q^{37} + 18 q^{39} - 3 q^{43} - 10 q^{45} - 21 q^{47} - 13 q^{51} - 6 q^{53} + 12 q^{55} - 37 q^{57} - 31 q^{59} - 6 q^{61} - 15 q^{65} - 6 q^{67} + 5 q^{69} + 34 q^{71} + 3 q^{73} - 7 q^{75} + 9 q^{79} - 40 q^{81} - 20 q^{83} + 15 q^{85} + 16 q^{87} - 12 q^{89} + 33 q^{93} - 20 q^{95} + 9 q^{97} - 8 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 + 2 * q^5 - 4 * q^9 + 4 * q^11 - 3 * q^13 + q^15 - 2 * q^17 - 3 * q^19 + 28 * q^23 - 12 * q^25 + 7 * q^27 - q^29 + 3 * q^31 - 25 * q^33 + 3 * q^37 + 18 * q^39 - 3 * q^43 - 10 * q^45 - 21 * q^47 - 13 * q^51 - 6 * q^53 + 12 * q^55 - 37 * q^57 - 31 * q^59 - 6 * q^61 - 15 * q^65 - 6 * q^67 + 5 * q^69 + 34 * q^71 + 3 * q^73 - 7 * q^75 + 9 * q^79 - 40 * q^81 - 20 * q^83 + 15 * q^85 + 16 * q^87 - 12 * q^89 + 33 * q^93 - 20 * q^95 + 9 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.09097	+	1.34528i	0.629873	+	0.776698i
$3$	1.09097	+	1.34528i	0.629873	+	0.776698i
$4$		0			0
$5$	0.239123			0.106939			0.0534696	−	0.998569i	$-0.482972\pi$
$5$	0.239123			0.106939			0.0534696	+	0.998569i	$0.482972\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.619562	+	2.93533i	−0.206521	+	0.978442i
$10$		0			0
$11$	−5.12476			−1.54517			−0.772587	−	0.634909i	$-0.781038\pi$
$11$	−5.12476			−1.54517			−0.772587	+	0.634909i	$0.781038\pi$
$12$		0			0
$13$	2.44282	+	4.23109i	0.677516	+	1.17349i	0.975727	+	0.218993i	$0.0702770\pi$
$13$	2.44282	+	4.23109i	0.677516	+	1.17349i	−0.298210	+	0.954500i	$0.596390\pi$
$14$		0			0
$15$	0.260877	+	0.321688i	0.0673581	+	0.0830595i
$16$		0			0
$17$	−1.85185	−	3.20750i	−0.449139	−	0.777932i	0.549191	−	0.835697i	$-0.314936\pi$
$17$	−1.85185	−	3.20750i	−0.449139	−	0.777932i	−0.998330	+	0.0577649i	$0.981603\pi$
$18$		0			0
$19$	−1.83009	+	3.16982i	−0.419853	+	0.727206i	−0.995924	−	0.0901932i	$-0.971252\pi$
$19$	−1.83009	+	3.16982i	−0.419853	+	0.727206i	0.576072	+	0.817399i	$0.304585\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.42107			1.54740			0.773700	−	0.633553i	$-0.218404\pi$
$23$	7.42107			1.54740			0.773700	+	0.633553i	$0.218404\pi$
$24$		0			0
$25$	−4.94282			−0.988564
$26$		0			0
$27$	−4.62476	+	2.36887i	−0.890036	+	0.455890i
$28$		0			0
$29$	−1.73229	+	3.00041i	−0.321678	+	0.557162i	−0.980834	−	0.194844i	$-0.937580\pi$
$29$	−1.73229	+	3.00041i	−0.321678	+	0.557162i	0.659157	+	0.752006i	$0.270913\pi$
$30$		0			0
$31$	0.358685	−	0.621261i	0.0644217	−	0.111582i	−0.832016	−	0.554752i	$-0.812813\pi$
$31$	0.358685	−	0.621261i	0.0644217	−	0.111582i	0.896437	+	0.443171i	$0.146146\pi$
$32$		0			0
$33$	−5.59097	−	6.89425i	−0.973263	−	1.20013i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.30150	+	3.98632i	−0.378365	+	0.655348i	−0.990825	−	0.135154i	$-0.956847\pi$
$37$	−2.30150	+	3.98632i	−0.378365	+	0.655348i	0.612459	+	0.790502i	$0.290180\pi$
$38$		0			0
$39$	−3.02696	+	7.90228i	−0.484701	+	1.26538i
$40$		0			0
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	0.559976	−	0.828509i	$-0.310810\pi$
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	−0.997498	+	0.0706992i	$0.977477\pi$
$42$		0			0
$43$	−6.24433	+	10.8155i	−0.952251	+	1.64935i	−0.211713	+	0.977332i	$0.567904\pi$
$43$	−6.24433	+	10.8155i	−0.952251	+	1.64935i	−0.740538	+	0.672015i	$0.765429\pi$
$44$		0			0
$45$	−0.148152	+	0.701905i	−0.0220851	+	0.104634i
$46$		0			0
$47$	−2.16991	−	3.75839i	−0.316513	−	0.548217i	0.663245	−	0.748403i	$-0.269179\pi$
$47$	−2.16991	−	3.75839i	−0.316513	−	0.548217i	−0.979758	+	0.200186i	$0.935845\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.29467	−	5.99054i	0.321318	−	0.838844i
$52$		0			0
$53$	0.471410	+	0.816506i	0.0647531	+	0.112156i	0.896584	−	0.442873i	$-0.146041\pi$
$53$	0.471410	+	0.816506i	0.0647531	+	0.112156i	−0.831831	+	0.555029i	$0.812707\pi$
$54$		0			0
$55$	−1.22545			−0.165240
$56$		0			0
$57$	−6.26088	+	0.996189i	−0.829273	+	0.131948i
$58$		0			0
$59$	−3.78947	+	6.56355i	−0.493347	+	0.854501i	−0.999971	−	0.00766579i	$-0.997560\pi$
$59$	−3.78947	+	6.56355i	−0.493347	+	0.854501i	0.506624	+	0.862167i	$0.330893\pi$
$60$		0			0
$61$	−2.75404	−	4.77014i	−0.352619	−	0.610754i	0.634089	−	0.773260i	$-0.281375\pi$
$61$	−2.75404	−	4.77014i	−0.352619	−	0.610754i	−0.986707	+	0.162507i	$0.948042\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.584135	+	1.01175i	0.0724530	+	0.125492i
$66$		0			0
$67$	0.330095	−	0.571741i	0.0403275	−	0.0698493i	−0.845157	−	0.534518i	$-0.820493\pi$
$67$	0.330095	−	0.571741i	0.0403275	−	0.0698493i	0.885485	+	0.464669i	$0.153827\pi$
$68$		0			0
$69$	8.09617	+	9.98342i	0.974665	+	1.20186i
$70$		0			0
$71$	13.7414			1.63081			0.815405	−	0.578891i	$-0.196514\pi$
$71$	13.7414			1.63081			0.815405	+	0.578891i	$0.196514\pi$
$72$		0			0
$73$	1.83009	+	3.16982i	0.214196	+	0.370999i	0.953024	−	0.302896i	$-0.0979534\pi$
$73$	1.83009	+	3.16982i	0.214196	+	0.370999i	−0.738827	+	0.673895i	$0.764620\pi$
$74$		0			0
$75$	−5.39248	−	6.64948i	−0.622670	−	0.767816i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.11273	+	5.39140i	0.350209	+	0.606580i	0.986286	−	0.165046i	$-0.0527772\pi$
$79$	3.11273	+	5.39140i	0.350209	+	0.606580i	−0.636077	+	0.771626i	$0.719444\pi$
$80$		0			0
$81$	−8.23229	−	3.63723i	−0.914699	−	0.404137i
$82$		0			0
$83$	−4.85185	+	8.40365i	−0.532560	+	0.922420i	0.466718	+	0.884406i	$0.345436\pi$
$83$	−4.85185	+	8.40365i	−0.532560	+	0.922420i	−0.999277	+	0.0380138i	$0.987897\pi$
$84$		0			0
$85$	−0.442820	−	0.766987i	−0.0480306	−	0.0831914i
$86$		0			0
$87$	−5.92627	+	0.942948i	−0.635363	+	0.101095i
$88$		0			0
$89$	3.74433	−	6.48536i	0.396898	−	0.687447i	−0.596444	−	0.802655i	$-0.703420\pi$
$89$	3.74433	−	6.48536i	0.396898	−	0.687447i	0.993341	+	0.115208i	$0.0367535\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.22708	−	0.195246i	0.127243	−	0.0202460i
$94$		0			0
$95$	−0.437618	+	0.757977i	−0.0448987	+	0.0777668i
$96$		0			0
$97$	8.57442	−	14.8513i	0.870600	−	1.50792i	0.00922376	−	0.999957i	$-0.497064\pi$
$97$	8.57442	−	14.8513i	0.870600	−	1.50792i	0.861377	−	0.507967i	$-0.169603\pi$
$98$		0			0
$99$	3.17511	−	15.0429i	0.319110	−	1.51186i
$100$		0			0
$101$	7.18194			0.714630			0.357315	−	0.933984i	$-0.383692\pi$
$101$	7.18194			0.714630			0.357315	+	0.933984i	$0.383692\pi$
$102$		0			0
$103$	−12.8285			−1.26403			−0.632013	−	0.774958i	$-0.717771\pi$
$103$	−12.8285			−1.26403			−0.632013	+	0.774958i	$0.717771\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.78263	+	6.55171i	−0.365681	+	0.633377i	−0.988885	−	0.148681i	$-0.952497\pi$
$107$	−3.78263	+	6.55171i	−0.365681	+	0.633377i	0.623204	+	0.782059i	$0.285830\pi$
$108$		0			0
$109$	3.49028	+	6.04535i	0.334309	+	0.579040i	0.983352	−	0.181712i	$-0.0581639\pi$
$109$	3.49028	+	6.04535i	0.334309	+	0.579040i	−0.649043	+	0.760752i	$0.724831\pi$
$110$		0			0
$111$	−7.87360	+	1.25280i	−0.747329	+	0.118910i
$112$		0			0
$113$	9.78495	+	16.9480i	0.920491	+	1.59434i	0.798657	+	0.601787i	$0.205544\pi$
$113$	9.78495	+	16.9480i	0.920491	+	1.59434i	0.121834	+	0.992550i	$0.461122\pi$
$114$		0			0
$115$	1.77455			0.165478
$116$		0			0
$117$	−13.9331	+	4.54906i	−1.28812	+	0.420560i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	15.2632			1.38756
$122$		0			0
$123$	3.47141	−	9.06259i	0.313007	−	0.817146i
$124$		0			0
$125$	−2.37756			−0.212655
$126$		0			0
$127$	−16.8090			−1.49156			−0.745780	−	0.666192i	$-0.767923\pi$
$127$	−16.8090			−1.49156			−0.745780	+	0.666192i	$0.767923\pi$
$128$		0			0
$129$	−21.3623	+	3.39902i	−1.88084	+	0.299267i
$130$		0			0
$131$	4.89931			0.428055			0.214027	−	0.976828i	$-0.431342\pi$
$131$	4.89931			0.428055			0.214027	+	0.976828i	$0.431342\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.10589	+	0.566453i	−0.0951797	+	0.0487525i
$136$		0			0
$137$	5.44514			0.465210			0.232605	−	0.972571i	$-0.425275\pi$
$137$	5.44514			0.465210			0.232605	+	0.972571i	$0.425275\pi$
$138$		0			0
$139$	−2.83009	−	4.90187i	−0.240046	−	0.415771i	0.720681	−	0.693266i	$-0.243829\pi$
$139$	−2.83009	−	4.90187i	−0.240046	−	0.415771i	−0.960727	+	0.277495i	$0.910496\pi$
$140$		0			0
$141$	2.68878	−	7.01942i	0.226436	−	0.591142i
$142$		0			0
$143$	−12.5189	−	21.6833i	−1.04688	−	1.81325i
$144$		0			0
$145$	−0.414230	+	0.717468i	−0.0343999	+	0.0595824i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.28263			0.187000			0.0935002	−	0.995619i	$-0.470194\pi$
$149$	2.28263			0.187000			0.0935002	+	0.995619i	$0.470194\pi$
$150$		0			0
$151$	11.2632			0.916586			0.458293	−	0.888801i	$-0.348461\pi$
$151$	11.2632			0.916586			0.458293	+	0.888801i	$0.348461\pi$
$152$		0			0
$153$	10.5624	−	3.44854i	0.853918	−	0.278798i
$154$		0			0
$155$	0.0857699	−	0.148558i	0.00688921	−	0.0119325i
$156$		0			0
$157$	−2.77292	+	4.80283i	−0.221303	+	0.383308i	−0.955204	−	0.295949i	$-0.904364\pi$
$157$	−2.77292	+	4.80283i	−0.221303	+	0.383308i	0.733901	+	0.679256i	$0.237698\pi$
$158$		0			0
$159$	−0.584135	+	1.52496i	−0.0463249	+	0.120938i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.33009	+	5.76789i	−0.260833	+	0.451776i	−0.966464	−	0.256804i	$-0.917331\pi$
$163$	−3.33009	+	5.76789i	−0.260833	+	0.451776i	0.705630	+	0.708580i	$0.250664\pi$
$164$		0			0
$165$	−1.33693	−	1.64857i	−0.104080	−	0.128341i
$166$		0			0
$167$	−2.20370	−	3.81691i	−0.170527	−	0.295362i	0.768077	−	0.640357i	$-0.221214\pi$
$167$	−2.20370	−	3.81691i	−0.170527	−	0.295362i	−0.938604	+	0.344996i	$0.887880\pi$
$168$		0			0
$169$	−5.43474	+	9.41325i	−0.418057	+	0.724096i
$170$		0			0
$171$	−8.17059	−	7.33582i	−0.624821	−	0.560984i
$172$		0			0
$173$	−12.6654	−	21.9371i	−0.962932	−	1.66785i	−0.715072	−	0.699051i	$-0.753606\pi$
$173$	−12.6654	−	21.9371i	−0.962932	−	1.66785i	−0.247860	−	0.968796i	$-0.579727\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.9640	+	2.06275i	−0.974435	+	0.155046i
$178$		0			0
$179$	−4.77292	−	8.26693i	−0.356744	−	0.617899i	0.630670	−	0.776051i	$-0.282780\pi$
$179$	−4.77292	−	8.26693i	−0.356744	−	0.617899i	−0.987415	+	0.158151i	$0.949447\pi$
$180$		0			0
$181$	12.3743			0.919774			0.459887	−	0.887978i	$-0.347890\pi$
$181$	12.3743			0.919774			0.459887	+	0.887978i	$0.347890\pi$
$182$		0			0
$183$	3.41260	−	8.90904i	0.252266	−	0.658575i
$184$		0			0
$185$	−0.550343	+	0.953223i	−0.0404621	+	0.0700823i
$186$		0			0
$187$	9.49028	+	16.4377i	0.693998	+	1.20204i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.58414	−	11.4041i	−0.476411	−	0.825169i	0.523223	−	0.852196i	$-0.324729\pi$
$191$	−6.58414	−	11.4041i	−0.476411	−	0.825169i	−0.999635	+	0.0270270i	$0.991396\pi$
$192$		0			0
$193$	−5.57442	+	9.65518i	−0.401256	+	0.694995i	−0.993878	−	0.110486i	$-0.964759\pi$
$193$	−5.57442	+	9.65518i	−0.401256	+	0.694995i	0.592622	+	0.805481i	$0.298093\pi$
$194$		0			0
$195$	−0.723815	+	1.88962i	−0.0518335	+	0.135318i
$196$		0			0
$197$	−0.144194			−0.0102734			−0.00513669	−	0.999987i	$-0.501635\pi$
$197$	−0.144194			−0.0102734			−0.00513669	+	0.999987i	$0.501635\pi$
$198$		0			0
$199$	9.73461	+	16.8608i	0.690068	+	1.19523i	0.971815	+	0.235744i	$0.0757528\pi$
$199$	9.73461	+	16.8608i	0.690068	+	1.19523i	−0.281747	+	0.959489i	$0.590914\pi$
$200$		0			0
$201$	1.12928	−	0.179683i	0.0796530	−	0.0126739i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.669905	−	1.16031i	−0.0467882	−	0.0810395i
$206$		0			0
$207$	−4.59781	+	21.7833i	−0.319570	+	1.51404i
$208$		0			0
$209$	9.37880	−	16.2446i	0.648745	−	1.12366i
$210$		0			0
$211$	1.61436	+	2.79615i	0.111137	+	0.192495i	0.916229	−	0.400655i	$-0.131217\pi$
$211$	1.61436	+	2.79615i	0.111137	+	0.192495i	−0.805092	+	0.593150i	$0.797884\pi$
$212$		0			0
$213$	14.9915	+	18.4861i	1.02720	+	1.26665i
$214$		0			0
$215$	−1.49316	+	2.58623i	−0.101833	+	0.176380i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2.26771	+	5.92017i	−0.153238	+	0.400048i
$220$		0			0
$221$	9.04746	−	15.6707i	0.608598	−	1.05412i
$222$		0			0
$223$	−10.3856	+	17.9885i	−0.695474	+	1.20460i	0.274547	+	0.961574i	$0.411472\pi$
$223$	−10.3856	+	17.9885i	−0.695474	+	1.20460i	−0.970021	+	0.243022i	$0.921861\pi$
$224$		0			0
$225$	3.06238	−	14.5088i	0.204159	−	0.967253i
$226$		0			0
$227$	21.9428			1.45640			0.728198	−	0.685367i	$-0.240358\pi$
$227$	21.9428			1.45640			0.728198	+	0.685367i	$0.240358\pi$
$228$		0			0
$229$	22.7713			1.50477			0.752384	−	0.658724i	$-0.228904\pi$
$229$	22.7713			1.50477			0.752384	+	0.658724i	$0.228904\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.8908	−	22.3276i	0.844507	−	1.46273i	−0.0415414	−	0.999137i	$-0.513227\pi$
$233$	12.8908	−	22.3276i	0.844507	−	1.46273i	0.886049	−	0.463592i	$-0.153440\pi$
$234$		0			0
$235$	−0.518875	−	0.898718i	−0.0338477	−	0.0586259i
$236$		0			0
$237$	−3.85705	+	10.0694i	−0.250542	+	0.654075i
$238$		0			0
$239$	13.6488	+	23.6405i	0.882870	+	1.52918i	0.848136	+	0.529779i	$0.177725\pi$
$239$	13.6488	+	23.6405i	0.882870	+	1.52918i	0.0347345	+	0.999397i	$0.488941\pi$
$240$		0			0
$241$	10.0345			0.646378			0.323189	−	0.946334i	$-0.395245\pi$
$241$	10.0345			0.646378			0.323189	+	0.946334i	$0.395245\pi$
$242$		0			0
$243$	−4.08809	−	15.0429i	−0.262251	−	0.965000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−17.8824			−1.13783
$248$		0			0
$249$	−16.5985	+	2.64104i	−1.05189	+	0.167369i
$250$		0			0
$251$	−28.3171			−1.78736			−0.893680	−	0.448705i	$-0.851885\pi$
$251$	−28.3171			−1.78736			−0.893680	+	0.448705i	$0.851885\pi$
$252$		0			0
$253$	−38.0312			−2.39100
$254$		0			0
$255$	0.548709	−	1.43248i	0.0343615	−	0.0897053i
$256$		0			0
$257$	28.8629			1.80042			0.900210	−	0.435455i	$-0.143413\pi$
$257$	28.8629			1.80042			0.900210	+	0.435455i	$0.143413\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−7.73392	−	6.94377i	−0.478718	−	0.429808i
$262$		0			0
$263$	−1.20929			−0.0745680			−0.0372840	−	0.999305i	$-0.511871\pi$
$263$	−1.20929			−0.0745680			−0.0372840	+	0.999305i	$0.511871\pi$
$264$		0			0
$265$	0.112725	+	0.195246i	0.00692465	+	0.0119938i
$266$		0			0
$267$	12.8096	−	2.03818i	0.783934	−	0.124734i
$268$		0			0
$269$	−4.50684	−	7.80607i	−0.274787	−	0.475944i	0.695295	−	0.718725i	$-0.255274\pi$
$269$	−4.50684	−	7.80607i	−0.274787	−	0.475944i	−0.970081	+	0.242780i	$0.921941\pi$
$270$		0			0
$271$	−8.80150	+	15.2447i	−0.534653	+	0.926047i	0.464527	+	0.885559i	$0.346224\pi$
$271$	−8.80150	+	15.2447i	−0.534653	+	0.926047i	−0.999180	+	0.0404876i	$0.987109\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	25.3308			1.52750
$276$		0			0
$277$	1.45417			0.0873726			0.0436863	−	0.999045i	$-0.486090\pi$
$277$	1.45417			0.0873726			0.0436863	+	0.999045i	$0.486090\pi$
$278$		0			0
$279$	1.60138	+	1.43777i	0.0958718	+	0.0860768i
$280$		0			0
$281$	10.1482	−	17.5771i	0.605388	−	1.04856i	−0.386602	−	0.922247i	$-0.626351\pi$
$281$	10.1482	−	17.5771i	0.605388	−	1.04856i	0.991990	−	0.126316i	$-0.0403154\pi$
$282$		0			0
$283$	2.30150	−	3.98632i	0.136810	−	0.236962i	−0.789477	−	0.613780i	$-0.789648\pi$
$283$	2.30150	−	3.98632i	0.136810	−	0.236962i	0.926288	+	0.376817i	$0.122982\pi$
$284$		0			0
$285$	−1.49712	+	0.238212i	−0.0886818	+	0.0141105i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.64132	−	2.84284i	0.0965479	−	0.167226i
$290$		0			0
$291$	29.3337	−	4.66738i	1.71957	−	0.273607i
$292$		0			0
$293$	3.53667	+	6.12569i	0.206614	+	0.357867i	0.950646	−	0.310278i	$-0.100422\pi$
$293$	3.53667	+	6.12569i	0.206614	+	0.357867i	−0.744031	+	0.668145i	$0.767089\pi$
$294$		0			0
$295$	−0.906150	+	1.56950i	−0.0527581	+	0.0913797i
$296$		0			0
$297$	23.7008	−	12.1399i	1.37526	−	0.704430i
$298$		0			0
$299$	18.1283	+	31.3992i	1.04839	+	1.81586i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	7.83530	+	9.66173i	0.450126	+	0.555052i
$304$		0			0
$305$	−0.658555	−	1.14065i	−0.0377088	−	0.0653135i
$306$		0			0
$307$	15.7518			0.899006			0.449503	−	0.893279i	$-0.351601\pi$
$307$	15.7518			0.899006			0.449503	+	0.893279i	$0.351601\pi$
$308$		0			0
$309$	−13.9955	−	17.2579i	−0.796175	−	0.981767i
$310$		0			0
$311$	9.81191	−	16.9947i	0.556382	−	0.963682i	−0.441412	−	0.897304i	$-0.645522\pi$
$311$	9.81191	−	16.9947i	0.556382	−	0.963682i	0.997795	−	0.0663780i	$-0.0211443\pi$
$312$		0			0
$313$	12.7427	+	22.0710i	0.720259	+	1.24753i	0.960896	+	0.276911i	$0.0893106\pi$
$313$	12.7427	+	22.0710i	0.720259	+	1.24753i	−0.240636	+	0.970615i	$0.577356\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.14132	−	7.17297i	−0.232599	−	0.402874i	0.725973	−	0.687723i	$-0.241390\pi$
$317$	−4.14132	−	7.17297i	−0.232599	−	0.402874i	−0.958572	+	0.284849i	$0.908056\pi$
$318$		0			0
$319$	8.87756	−	15.3764i	0.497048	−	0.860912i
$320$		0			0
$321$	−12.9406	+	2.05903i	−0.722276	+	0.114924i
$322$		0			0
$323$	13.5562			0.754289
$324$		0			0
$325$	−12.0744	−	20.9135i	−0.669768	−	1.16007i
$326$		0			0
$327$	−4.32489	+	11.2907i	−0.239167	+	0.624378i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	5.99028	+	10.3755i	0.329256	+	0.570288i	0.982364	−	0.186976i	$-0.0598688\pi$
$331$	5.99028	+	10.3755i	0.329256	+	0.570288i	−0.653109	+	0.757264i	$0.726535\pi$
$332$		0			0
$333$	−10.2752	−	9.22544i	−0.563080	−	0.505551i
$334$		0			0
$335$	0.0789334	−	0.136717i	0.00431259	−	0.00746963i
$336$		0			0
$337$	6.46006	+	11.1892i	0.351902	+	0.609512i	0.986583	−	0.163262i	$-0.0522017\pi$
$337$	6.46006	+	11.1892i	0.351902	+	0.609512i	−0.634681	+	0.772774i	$0.718868\pi$
$338$		0			0
$339$	−12.1248	+	31.6533i	−0.658527	+	1.71917i
$340$		0			0
$341$	−1.83818	+	3.18381i	−0.0995428	+	0.172413i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.93598	+	2.38727i	0.104230	+	0.128526i
$346$		0			0
$347$	−8.09329	+	14.0180i	−0.434471	+	0.752526i	−0.997252	−	0.0740802i	$-0.976398\pi$
$347$	−8.09329	+	14.0180i	−0.434471	+	0.752526i	0.562781	+	0.826606i	$0.309731\pi$
$348$		0			0
$349$	9.05718	−	15.6875i	0.484820	−	0.839732i	−0.515028	−	0.857173i	$-0.672219\pi$
$349$	9.05718	−	15.6875i	0.484820	−	0.839732i	0.999848	+	0.0174409i	$0.00555188\pi$
$350$		0			0
$351$	−21.3204	−	13.7811i	−1.13800	−	0.735578i
$352$		0			0
$353$	−11.6979			−0.622618			−0.311309	−	0.950309i	$-0.600767\pi$
$353$	−11.6979			−0.622618			−0.311309	+	0.950309i	$0.600767\pi$
$354$		0			0
$355$	3.28590			0.174397
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−17.8623	+	30.9383i	−0.942734	+	1.63286i	−0.182507	+	0.983205i	$0.558421\pi$
$359$	−17.8623	+	30.9383i	−0.942734	+	1.63286i	−0.760227	+	0.649658i	$0.774912\pi$
$360$		0			0
$361$	2.80150	+	4.85235i	0.147448	+	0.255387i
$362$		0			0
$363$	16.6517	+	20.5333i	0.873989	+	1.07772i
$364$		0			0
$365$	0.437618	+	0.757977i	0.0229060	+	0.0396743i
$366$		0			0
$367$	17.0539			0.890207			0.445103	−	0.895479i	$-0.353167\pi$
$367$	17.0539			0.890207			0.445103	+	0.895479i	$0.353167\pi$
$368$		0			0
$369$	15.9789	−	5.21700i	0.831830	−	0.271586i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−25.9234			−1.34226			−0.671131	−	0.741339i	$-0.734191\pi$
$373$	−25.9234			−1.34226			−0.671131	+	0.741339i	$0.734191\pi$
$374$		0			0
$375$	−2.59385	−	3.19849i	−0.133946	−	0.165169i
$376$		0			0
$377$	−16.9267			−0.871767
$378$		0			0
$379$	26.8446			1.37892			0.689458	−	0.724326i	$-0.257849\pi$
$379$	26.8446			1.37892			0.689458	+	0.724326i	$0.257849\pi$
$380$		0			0
$381$	−18.3382	−	22.6129i	−0.939493	−	1.15849i
$382$		0			0
$383$	24.8525			1.26991			0.634953	−	0.772551i	$-0.281020\pi$
$383$	24.8525			1.26991			0.634953	+	0.772551i	$0.281020\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−27.8782	−	25.0300i	−1.41713	−	1.27235i
$388$		0			0
$389$	−18.2528			−0.925454			−0.462727	−	0.886501i	$-0.653129\pi$
$389$	−18.2528			−0.925454			−0.462727	+	0.886501i	$0.653129\pi$
$390$		0			0
$391$	−13.7427	−	23.8030i	−0.694998	−	1.20377i
$392$		0			0
$393$	5.34501	+	6.59095i	0.269620	+	0.332470i
$394$		0			0
$395$	0.744325	+	1.28921i	0.0374511	+	0.0648671i
$396$		0			0
$397$	−6.18715	+	10.7164i	−0.310524	+	0.537843i	−0.978476	−	0.206361i	$-0.933838\pi$
$397$	−6.18715	+	10.7164i	−0.310524	+	0.537843i	0.667952	+	0.744204i	$0.267171\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.9623			−0.547429			−0.273714	−	0.961811i	$-0.588252\pi$
$401$	−10.9623			−0.547429			−0.273714	+	0.961811i	$0.588252\pi$
$402$		0			0
$403$	3.50481			0.174587
$404$		0			0
$405$	−1.96853	−	0.869747i	−0.0978171	−	0.0432181i
$406$		0			0
$407$	11.7947	−	20.4290i	0.584640	−	1.01263i
$408$		0			0
$409$	6.66019	−	11.5358i	0.329325	−	0.570408i	−0.653053	−	0.757312i	$-0.726512\pi$
$409$	6.66019	−	11.5358i	0.329325	−	0.570408i	0.982378	+	0.186904i	$0.0598454\pi$
$410$		0			0
$411$	5.94050	+	7.32525i	0.293023	+	0.361328i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.16019	+	2.00951i	−0.0569515	+	0.0986429i
$416$		0			0
$417$	3.50684	−	9.15507i	0.171731	−	0.448326i
$418$		0			0
$419$	−2.35705	−	4.08253i	−0.115149	−	0.199445i	0.802690	−	0.596396i	$-0.203401\pi$
$419$	−2.35705	−	4.08253i	−0.115149	−	0.199445i	−0.917839	+	0.396952i	$0.870068\pi$
$420$		0			0
$421$	−9.65856	+	16.7291i	−0.470729	+	0.815327i	−0.999440	−	0.0334755i	$-0.989342\pi$
$421$	−9.65856	+	16.7291i	−0.470729	+	0.815327i	0.528710	+	0.848802i	$0.322676\pi$
$422$		0			0
$423$	12.3765	−	4.04083i	0.601765	−	0.196472i
$424$		0			0
$425$	9.15335	+	15.8541i	0.444003	+	0.769036i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	15.5124	−	40.4973i	0.748947	−	1.95523i
$430$		0			0
$431$	15.1397	+	26.2227i	0.729253	+	1.26310i	0.957199	+	0.289429i	$0.0934655\pi$
$431$	15.1397	+	26.2227i	0.729253	+	1.26310i	−0.227947	+	0.973674i	$0.573201\pi$
$432$		0			0
$433$	34.2060			1.64384			0.821918	−	0.569606i	$-0.192904\pi$
$433$	34.2060			1.64384			0.821918	+	0.569606i	$0.192904\pi$
$434$		0			0
$435$	−1.41711	+	0.225481i	−0.0679452	+	0.0108110i
$436$		0			0
$437$	−13.5813	+	23.5234i	−0.649680	+	1.12528i
$438$		0			0
$439$	0.311220	+	0.539049i	0.0148537	+	0.0257274i	0.873357	−	0.487081i	$-0.161938\pi$
$439$	0.311220	+	0.539049i	0.0148537	+	0.0257274i	−0.858503	+	0.512809i	$0.828605\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.58934	+	4.48486i	0.123023	+	0.213082i	0.920958	−	0.389661i	$-0.127408\pi$
$443$	2.58934	+	4.48486i	0.123023	+	0.213082i	−0.797935	+	0.602743i	$0.794074\pi$
$444$		0			0
$445$	0.895355	−	1.55080i	0.0424439	−	0.0735150i
$446$		0			0
$447$	2.49028	+	3.07078i	0.117786	+	0.145243i
$448$		0			0
$449$	−10.4977			−0.495416			−0.247708	−	0.968835i	$-0.579677\pi$
$449$	−10.4977			−0.495416			−0.247708	+	0.968835i	$0.579677\pi$
$450$		0			0
$451$	14.3571	+	24.8671i	0.676047	+	1.17095i
$452$		0			0
$453$	12.2878	+	15.1522i	0.577333	+	0.711911i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.60464	+	2.77933i	0.0750621	+	0.130011i	0.901113	−	0.433584i	$-0.142751\pi$
$457$	1.60464	+	2.77933i	0.0750621	+	0.130011i	−0.826051	+	0.563595i	$0.809418\pi$
$458$		0			0
$459$	16.1625	+	10.4471i	0.754402	+	0.487629i
$460$		0			0
$461$	18.1150	−	31.3762i	0.843702	−	1.46133i	−0.0430418	−	0.999073i	$-0.513705\pi$
$461$	18.1150	−	31.3762i	0.843702	−	1.46133i	0.886744	−	0.462261i	$-0.152962\pi$
$462$		0			0
$463$	−14.5253	−	25.1586i	−0.675049	−	1.16922i	−0.976455	−	0.215723i	$-0.930789\pi$
$463$	−14.5253	−	25.1586i	−0.675049	−	1.16922i	0.301406	−	0.953496i	$-0.402544\pi$
$464$		0			0
$465$	0.293425	−	0.0466878i	0.0136072	−	0.00216509i
$466$		0			0
$467$	18.7466	−	32.4701i	0.867491	−	1.50254i	0.00293952	−	0.999996i	$-0.499064\pi$
$467$	18.7466	−	32.4701i	0.867491	−	1.50254i	0.864552	−	0.502544i	$-0.167602\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−9.48633	+	1.50940i	−0.437107	+	0.0695495i
$472$		0			0
$473$	32.0007	−	55.4268i	1.47139	−	2.54853i
$474$		0			0
$475$	9.04583	−	15.6678i	0.415051	−	0.718890i
$476$		0			0
$477$	−2.68878	+	0.877867i	−0.123111	+	0.0401948i
$478$		0			0
$479$	29.9097			1.36661			0.683305	−	0.730133i	$-0.260542\pi$
$479$	29.9097			1.36661			0.683305	+	0.730133i	$0.260542\pi$
$480$		0			0
$481$	−22.4887			−1.02539
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.05034	−	3.55130i	0.0931013	−	0.161256i
$486$		0			0
$487$	−10.6316	−	18.4145i	−0.481764	−	0.834439i	0.518017	−	0.855370i	$-0.326670\pi$
$487$	−10.6316	−	18.4145i	−0.481764	−	0.834439i	−0.999781	+	0.0209309i	$0.993337\pi$
$488$		0			0
$489$	−11.3925	+	1.81270i	−0.515186	+	0.0819729i
$490$		0			0
$491$	10.6985	+	18.5303i	0.482816	+	0.836262i	0.999805	−	0.0197296i	$-0.00628054\pi$
$491$	10.6985	+	18.5303i	0.482816	+	0.836262i	−0.516989	+	0.855992i	$0.672947\pi$
$492$		0			0
$493$	12.8317			0.577912
$494$		0			0
$495$	0.759242	−	3.59710i	0.0341254	−	0.161677i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.5653			0.652031			0.326015	−	0.945364i	$-0.394294\pi$
$499$	14.5653			0.652031			0.326015	+	0.945364i	$0.394294\pi$
$500$		0			0
$501$	2.73065	−	7.12874i	0.121997	−	0.318488i
$502$		0			0
$503$	2.92339			0.130348			0.0651738	−	0.997874i	$-0.479240\pi$
$503$	2.92339			0.130348			0.0651738	+	0.997874i	$0.479240\pi$
$504$		0			0
$505$	1.71737			0.0764220
$506$		0			0
$507$	−18.5926	+	2.95833i	−0.825727	+	0.131384i
$508$		0			0
$509$	−19.2405			−0.852820			−0.426410	−	0.904530i	$-0.640222\pi$
$509$	−19.2405			−0.852820			−0.426410	+	0.904530i	$0.640222\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.954858	−	18.9949i	0.0421580	−	0.838646i
$514$		0			0
$515$	−3.06758			−0.135174
$516$		0			0
$517$	11.1202	+	19.2608i	0.489068	+	0.847091i
$518$		0			0
$519$	15.6940	−	40.9713i	0.688889	−	1.79844i
$520$		0			0
$521$	−13.8743	−	24.0310i	−0.607844	−	1.05282i	−0.991595	−	0.129380i	$-0.958701\pi$
$521$	−13.8743	−	24.0310i	−0.607844	−	1.05282i	0.383751	−	0.923436i	$-0.374632\pi$
$522$		0			0
$523$	1.36840	−	2.37014i	0.0598360	−	0.103639i	−0.834556	−	0.550924i	$-0.814276\pi$
$523$	1.36840	−	2.37014i	0.0598360	−	0.103639i	0.894392	+	0.447285i	$0.147609\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.65692			−0.115737
$528$		0			0
$529$	32.0722			1.39444
$530$		0			0
$531$	−16.9184	−	15.1898i	−0.734194	−	0.659183i
$532$		0			0
$533$	13.6871	−	23.7068i	0.592856	−	1.02686i
$534$		0			0
$535$	−0.904515	+	1.56667i	−0.0391056	+	0.0677329i
$536$		0			0
$537$	5.91423	−	15.4399i	0.255218	−	0.666281i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	5.98865	−	10.3726i	0.257472	−	0.445955i	−0.708092	−	0.706120i	$-0.750444\pi$
$541$	5.98865	−	10.3726i	0.257472	−	0.445955i	0.965564	+	0.260165i	$0.0837771\pi$
$542$		0			0
$543$	13.5000	+	16.6469i	0.579340	+	0.714387i
$544$		0			0
$545$	0.834608	+	1.44558i	0.0357507	+	0.0619220i
$546$		0			0
$547$	10.7346	−	18.5929i	0.458979	−	0.794975i	−0.539928	−	0.841711i	$-0.681549\pi$
$547$	10.7346	−	18.5929i	0.458979	−	0.794975i	0.998907	+	0.0467363i	$0.0148821\pi$
$548$		0			0
$549$	15.7082	−	5.12861i	0.670410	−	0.218884i
$550$		0			0
$551$	−6.34050	−	10.9821i	−0.270114	−	0.467852i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.88276	+	0.299573i	−0.0799188	+	0.0127161i
$556$		0			0
$557$	15.9246	+	27.5823i	0.674748	+	1.16870i	0.976542	+	0.215325i	$0.0690812\pi$
$557$	15.9246	+	27.5823i	0.674748	+	1.16870i	−0.301794	+	0.953373i	$0.597585\pi$
$558$		0			0
$559$	−61.0150			−2.58066
$560$		0			0
$561$	−11.7596	+	30.7001i	−0.496492	+	1.29616i
$562$		0			0
$563$	−17.7742	+	30.7857i	−0.749091	+	1.29746i	0.199167	+	0.979966i	$0.436176\pi$
$563$	−17.7742	+	30.7857i	−0.749091	+	1.29746i	−0.948259	+	0.317499i	$0.897157\pi$
$564$		0			0
$565$	2.33981	+	4.05267i	0.0984366	+	0.170497i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.8743	−	18.8348i	−0.455874	−	0.789597i	0.542864	−	0.839821i	$-0.317340\pi$
$569$	−10.8743	−	18.8348i	−0.455874	−	0.789597i	−0.998738	+	0.0502237i	$0.984007\pi$
$570$		0			0
$571$	4.79987	−	8.31362i	0.200868	−	0.347914i	−0.747940	−	0.663766i	$-0.768957\pi$
$571$	4.79987	−	8.31362i	0.200868	−	0.347914i	0.948808	+	0.315852i	$0.102290\pi$
$572$		0			0
$573$	8.15856	−	21.2990i	0.340829	−	0.889779i
$574$		0			0
$575$	−36.6810			−1.52970
$576$		0			0
$577$	−6.50916	−	11.2742i	−0.270980	−	0.469351i	0.698133	−	0.715968i	$-0.254014\pi$
$577$	−6.50916	−	11.2742i	−0.270980	−	0.469351i	−0.969113	+	0.246617i	$0.920681\pi$
$578$		0			0
$579$	−19.0705	+	3.03437i	−0.792541	+	0.126104i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.41586	−	4.18440i	−0.100055	−	0.173300i
$584$		0			0
$585$	−3.33173	+	1.08778i	−0.137750	+	0.0449744i
$586$		0			0
$587$	−8.64364	+	14.9712i	−0.356761	+	0.617928i	−0.987418	−	0.158134i	$-0.949452\pi$
$587$	−8.64364	+	14.9712i	−0.356761	+	0.617928i	0.630657	+	0.776062i	$0.282786\pi$
$588$		0			0
$589$	1.31285	+	2.27393i	0.0540952	+	0.0936957i
$590$		0			0
$591$	−0.157311	−	0.193981i	−0.00647092	−	0.00797931i
$592$		0			0
$593$	−6.20765	+	10.7520i	−0.254918	+	0.441531i	−0.964873	−	0.262716i	$-0.915382\pi$
$593$	−6.20765	+	10.7520i	−0.254918	+	0.441531i	0.709955	+	0.704247i	$0.248715\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.0624	+	31.4905i	−0.493680	+	1.28882i
$598$		0			0
$599$	3.94282	−	6.82916i	0.161099	−	0.279032i	−0.774164	−	0.632985i	$-0.781829\pi$
$599$	3.94282	−	6.82916i	0.161099	−	0.279032i	0.935263	+	0.353953i	$0.115163\pi$
$600$		0			0
$601$	−11.1413	+	19.2973i	−0.454464	+	0.787154i	−0.998657	−	0.0518055i	$-0.983502\pi$
$601$	−11.1413	+	19.2973i	−0.454464	+	0.787154i	0.544193	+	0.838960i	$0.316836\pi$
$602$		0			0
$603$	1.47373	+	1.32317i	0.0600151	+	0.0538835i
$604$		0			0
$605$	3.64979			0.148385
$606$		0			0
$607$	22.0917			0.896673			0.448336	−	0.893865i	$-0.352017\pi$
$607$	22.0917			0.896673			0.448336	+	0.893865i	$0.352017\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	10.6014	−	18.3621i	0.428886	−	0.742852i
$612$		0			0
$613$	14.7632	+	25.5706i	0.596280	+	1.03279i	0.993365	+	0.115005i	$0.0366885\pi$
$613$	14.7632	+	25.5706i	0.596280	+	1.03279i	−0.397085	+	0.917782i	$0.629978\pi$
$614$		0			0
$615$	0.830095	−	2.16708i	0.0334727	−	0.0873849i
$616$		0			0
$617$	5.01655	+	8.68892i	0.201959	+	0.349803i	0.949159	−	0.314796i	$-0.101936\pi$
$617$	5.01655	+	8.68892i	0.201959	+	0.349803i	−0.747201	+	0.664598i	$0.768603\pi$
$618$		0			0
$619$	−38.2567			−1.53767			−0.768833	−	0.639450i	$-0.779162\pi$
$619$	−38.2567			−1.53767			−0.768833	+	0.639450i	$0.779162\pi$
$620$		0			0
$621$	−34.3207	+	17.5796i	−1.37724	+	0.705444i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.1456			0.965823
$626$		0			0
$627$	32.0855	−	5.10523i	1.28137	−	0.203883i
$628$		0			0
$629$	17.0482			0.679754
$630$		0			0
$631$	−23.0377			−0.917118			−0.458559	−	0.888664i	$-0.651634\pi$
$631$	−23.0377			−0.917118			−0.458559	+	0.888664i	$0.651634\pi$
$632$		0			0
$633$	−2.00039	+	5.22229i	−0.0795084	+	0.207567i
$634$		0			0
$635$	−4.01943			−0.159506
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−8.51367	+	40.3356i	−0.336796	+	1.59565i
$640$		0			0
$641$	−17.3729			−0.686189			−0.343094	−	0.939301i	$-0.611475\pi$
$641$	−17.3729			−0.686189			−0.343094	+	0.939301i	$0.611475\pi$
$642$		0			0
$643$	9.47949	+	16.4190i	0.373835	+	0.647501i	0.990152	−	0.139997i	$-0.0447094\pi$
$643$	9.47949	+	16.4190i	0.373835	+	0.647501i	−0.616317	+	0.787498i	$0.711376\pi$
$644$		0			0
$645$	−5.10821	+	0.812785i	−0.201136	+	0.0320034i
$646$		0			0
$647$	−9.50972	−	16.4713i	−0.373865	−	0.647554i	0.616291	−	0.787518i	$-0.288634\pi$
$647$	−9.50972	−	16.4713i	−0.373865	−	0.647554i	−0.990157	+	0.139964i	$0.955301\pi$
$648$		0			0
$649$	19.4201	−	33.6366i	0.762306	−	1.32035i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.18659			−0.281233			−0.140616	−	0.990064i	$-0.544908\pi$
$653$	−7.18659			−0.281233			−0.140616	+	0.990064i	$0.544908\pi$
$654$		0			0
$655$	1.17154			0.0457758
$656$		0			0
$657$	−10.4383	+	3.40803i	−0.407237	+	0.132960i
$658$		0			0
$659$	−12.7261	+	22.0423i	−0.495740	+	0.858647i	−0.999988	−	0.00491209i	$-0.998436\pi$
$659$	−12.7261	+	22.0423i	−0.495740	+	0.858647i	0.504248	+	0.863559i	$0.331770\pi$
$660$		0			0
$661$	−4.14295	+	7.17580i	−0.161142	+	0.279106i	−0.935279	−	0.353912i	$-0.884851\pi$
$661$	−4.14295	+	7.17580i	−0.161142	+	0.279106i	0.774136	+	0.633019i	$0.218184\pi$
$662$		0			0
$663$	30.9520	−	4.92487i	1.20208	−	0.191266i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12.8554	+	22.2662i	−0.497764	+	0.862152i
$668$		0			0
$669$	−35.5300	+	5.65329i	−1.37367	+	0.218569i
$670$		0			0
$671$	14.1138	+	24.4458i	0.544857	+	0.943721i
$672$		0			0
$673$	5.91586	−	10.2466i	0.228040	−	0.394977i	−0.729187	−	0.684314i	$-0.760102\pi$
$673$	5.91586	−	10.2466i	0.228040	−	0.394977i	0.957227	+	0.289338i	$0.0934350\pi$
$674$		0			0
$675$	22.8594	−	11.7089i	0.879858	−	0.450676i
$676$		0			0
$677$	−6.80314	−	11.7834i	−0.261466	−	0.452872i	0.705166	−	0.709042i	$-0.250873\pi$
$677$	−6.80314	−	11.7834i	−0.261466	−	0.452872i	−0.966632	+	0.256170i	$0.917539\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	23.9390	+	29.5193i	0.917344	+	1.13118i
$682$		0			0
$683$	−1.79071	−	3.10160i	−0.0685196	−	0.118679i	0.829730	−	0.558165i	$-0.188494\pi$
$683$	−1.79071	−	3.10160i	−0.0685196	−	0.118679i	−0.898250	+	0.439485i	$0.855161\pi$
$684$		0			0
$685$	1.30206			0.0497492
$686$		0			0
$687$	24.8428	+	30.6338i	0.947813	+	1.16875i
$688$		0			0
$689$	−2.30314	+	3.98916i	−0.0877426	+	0.151975i
$690$		0			0
$691$	−5.85868	−	10.1475i	−0.222875	−	0.386031i	0.732805	−	0.680439i	$-0.238211\pi$
$691$	−5.85868	−	10.1475i	−0.222875	−	0.386031i	−0.955680	+	0.294408i	$0.904877\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.676742	−	1.17215i	−0.0256703	−	0.0444622i
$696$		0			0
$697$	−10.3759	+	17.9716i	−0.393016	+	0.680724i
$698$		0			0
$699$	44.1004	−	7.01697i	1.66803	−	0.265406i
$700$		0			0
$701$	−10.5926			−0.400077			−0.200039	−	0.979788i	$-0.564107\pi$
$701$	−10.5926			−0.400077			−0.200039	+	0.979788i	$0.564107\pi$
$702$		0			0
$703$	−8.42395	−	14.5907i	−0.317715	−	0.550299i
$704$		0			0
$705$	0.642950	−	1.67851i	0.0242149	−	0.0632163i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.1488	−	33.1668i	−0.719150	−	1.24560i	−0.961337	−	0.275374i	$-0.911198\pi$
$709$	−19.1488	−	33.1668i	−0.719150	−	1.24560i	0.242187	−	0.970230i	$-0.422135\pi$
$710$		0			0
$711$	−17.7540	+	5.79656i	−0.665829	+	0.217388i
$712$		0			0
$713$	2.66182	−	4.61042i	0.0996861	−	0.172661i
$714$		0			0
$715$	−2.99355	−	5.18499i	−0.111953	−	0.193908i
$716$		0			0
$717$	−16.9126	+	44.1526i	−0.631612	+	1.64891i
$718$		0			0
$719$	−20.8376	+	36.0918i	−0.777112	+	1.34600i	0.156488	+	0.987680i	$0.449983\pi$
$719$	−20.8376	+	36.0918i	−0.777112	+	1.34600i	−0.933600	+	0.358318i	$0.883350\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	10.9473	+	13.4992i	0.407136	+	0.502040i
$724$		0			0
$725$	8.56238	−	14.8305i	0.317999	−	0.550790i
$726$		0			0
$727$	16.4126	−	28.4274i	0.608709	−	1.05432i	−0.382744	−	0.923854i	$-0.625021\pi$
$727$	16.4126	−	28.4274i	0.608709	−	1.05432i	0.991453	−	0.130461i	$-0.0416458\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$		0			0
$731$	46.2542			1.71077
$732$		0			0
$733$	9.29768			0.343418			0.171709	−	0.985148i	$-0.445071\pi$
$733$	9.29768			0.343418			0.171709	+	0.985148i	$0.445071\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.69166	+	2.93004i	−0.0623130	+	0.107929i
$738$		0			0
$739$	−5.68878	−	9.85326i	−0.209265	−	0.362458i	0.742218	−	0.670158i	$-0.233774\pi$
$739$	−5.68878	−	9.85326i	−0.209265	−	0.362458i	−0.951483	+	0.307701i	$0.900441\pi$
$740$		0			0
$741$	−19.5092	−	24.0568i	−0.716687	−	0.883749i
$742$		0			0
$743$	1.16182	+	2.01234i	0.0426232	+	0.0738256i	0.886550	−	0.462633i	$-0.153095\pi$
$743$	1.16182	+	2.01234i	0.0426232	+	0.0738256i	−0.843927	+	0.536458i	$0.819762\pi$
$744$		0			0
$745$	0.545830			0.0199977
$746$		0			0
$747$	−21.6614	−	19.4483i	−0.792550	−	0.711577i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−11.1338			−0.406278			−0.203139	−	0.979150i	$-0.565114\pi$
$751$	−11.1338			−0.406278			−0.203139	+	0.979150i	$0.565114\pi$
$752$		0			0
$753$	−30.8932	−	38.0945i	−1.12581	−	1.38824i
$754$		0			0
$755$	2.69329			0.0980190
$756$		0			0
$757$	52.1639			1.89593			0.947964	−	0.318376i	$-0.103138\pi$
$757$	52.1639			1.89593			0.947964	+	0.318376i	$0.103138\pi$
$758$		0			0
$759$	−41.4910	−	51.1627i	−1.50603	−	1.85709i
$760$		0			0
$761$	−47.0255			−1.70467			−0.852336	−	0.522995i	$-0.824815\pi$
$761$	−47.0255			−1.70467			−0.852336	+	0.522995i	$0.824815\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.52571	−	0.824626i	0.0913173	−	0.0298144i
$766$		0			0
$767$	−37.0279			−1.33700
$768$		0			0
$769$	3.30314	+	5.72121i	0.119114	+	0.206312i	0.919417	−	0.393284i	$-0.128661\pi$
$769$	3.30314	+	5.72121i	0.119114	+	0.206312i	−0.800303	+	0.599596i	$0.795328\pi$
$770$		0			0
$771$	31.4887	+	38.8288i	1.13404	+	1.39838i
$772$		0			0
$773$	−9.54351	−	16.5298i	−0.343256	−	0.594537i	0.641779	−	0.766889i	$-0.278197\pi$
$773$	−9.54351	−	16.5298i	−0.343256	−	0.594537i	−0.985035	+	0.172352i	$0.944863\pi$
$774$		0			0
$775$	−1.77292	+	3.07078i	−0.0636850	+	0.110306i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	20.5081			0.734778
$780$		0			0
$781$	−70.4217			−2.51989
$782$		0			0
$783$	0.903827	−	17.9797i	0.0323001	−	0.642544i
$784$		0			0
$785$	−0.663069	+	1.14847i	−0.0236659	+	0.0409906i
$786$		0			0
$787$	−25.4503	+	44.0813i	−0.907207	+	1.57133i	−0.0892796	+	0.996007i	$0.528456\pi$
$787$	−25.4503	+	44.0813i	−0.907207	+	1.57133i	−0.817927	+	0.575322i	$0.804877\pi$
$788$		0			0
$789$	−1.31930	−	1.62683i	−0.0469683	−	0.0579168i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	13.4552	−	23.3052i	0.477810	−	0.827591i
$794$		0			0
$795$	−0.139680	+	0.364654i	−0.00495395	+	0.0129330i
$796$		0			0
$797$	−4.38727	−	7.59898i	−0.155405	−	0.269170i	0.777801	−	0.628510i	$-0.216335\pi$
$797$	−4.38727	−	7.59898i	−0.155405	−	0.269170i	−0.933207	+	0.359341i	$0.883002\pi$
$798$		0			0
$799$	−8.03667	+	13.9199i	−0.284317	+	0.492451i
$800$		0			0
$801$	16.7168	+	15.0089i	0.590660	+	0.530313i
$802$		0			0
$803$	−9.37880	−	16.2446i	−0.330971	−	0.573258i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.58453	−	14.5792i	0.196585	−	0.513211i
$808$		0			0
$809$	4.75692	+	8.23923i	0.167244	+	0.289676i	0.937450	−	0.348120i	$-0.113180\pi$
$809$	4.75692	+	8.23923i	0.167244	+	0.289676i	−0.770206	+	0.637796i	$0.779846\pi$
$810$		0			0
$811$	−25.0118			−0.878282			−0.439141	−	0.898418i	$-0.644717\pi$
$811$	−25.0118			−0.878282			−0.439141	+	0.898418i	$0.644717\pi$
$812$		0			0
$813$	−30.1105	+	4.79099i	−1.05602	+	0.168027i
$814$		0			0
$815$	−0.796303	+	1.37924i	−0.0278933	+	0.0483126i
$816$		0			0
$817$	−22.8554	−	39.5867i	−0.799610	−	1.38496i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.7970	+	30.8253i	0.621119	+	1.07581i	0.989278	+	0.146047i	$0.0466551\pi$
$821$	17.7970	+	30.8253i	0.621119	+	1.07581i	−0.368158	+	0.929763i	$0.620012\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		0			0
$825$	27.6352	+	34.0770i	0.962133	+	1.18641i
$826$		0			0
$827$	−25.4531			−0.885090			−0.442545	−	0.896746i	$-0.645924\pi$
$827$	−25.4531			−0.885090			−0.442545	+	0.896746i	$0.645924\pi$
$828$		0			0
$829$	8.77292	+	15.1951i	0.304696	+	0.527749i	0.977194	−	0.212350i	$-0.0681118\pi$
$829$	8.77292	+	15.1951i	0.304696	+	0.527749i	−0.672498	+	0.740099i	$0.734778\pi$
$830$		0			0
$831$	1.58646	+	1.95627i	0.0550336	+	0.0678622i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.526955	−	0.912713i	−0.0182360	−	0.0315857i
$836$		0			0
$837$	−0.187145	+	3.72286i	−0.00646868	+	0.128681i
$838$		0			0
$839$	−12.0562	+	20.8820i	−0.416227	+	0.720927i	−0.995556	−	0.0941668i	$-0.969981\pi$
$839$	−12.0562	+	20.8820i	−0.416227	+	0.720927i	0.579329	+	0.815094i	$0.303315\pi$
$840$		0			0
$841$	8.49837	+	14.7196i	0.293047	+	0.507572i
$842$		0			0
$843$	34.7175	−	5.52402i	1.19573	−	0.190257i
$844$		0			0
$845$	−1.29957	+	2.25093i	−0.0447067	+	0.0774342i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	7.87360	−	1.25280i	0.270221	−	0.0429958i
$850$		0			0
$851$	−17.0796	+	29.5828i	−0.585482	+	1.01408i
$852$		0			0
$853$	−16.2616	+	28.1659i	−0.556785	+	0.964381i	0.440977	+	0.897518i	$0.354632\pi$
$853$	−16.2616	+	28.1659i	−0.556785	+	0.964381i	−0.997762	+	0.0668621i	$0.978701\pi$
$854$		0			0
$855$	−1.95378	−	1.75417i	−0.0668178	−	0.0599912i
$856$		0			0
$857$	−0.599740			−0.0204867			−0.0102434	−	0.999948i	$-0.503261\pi$
$857$	−0.599740			−0.0204867			−0.0102434	+	0.999948i	$0.503261\pi$
$858$		0			0
$859$	−26.4347			−0.901942			−0.450971	−	0.892539i	$-0.648922\pi$
$859$	−26.4347			−0.901942			−0.450971	+	0.892539i	$0.648922\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.92270	+	17.1866i	−0.337773	+	0.585039i	−0.984013	−	0.178094i	$-0.943007\pi$
$863$	−9.92270	+	17.1866i	−0.337773	+	0.585039i	0.646241	+	0.763134i	$0.276340\pi$
$864$		0			0
$865$	−3.02859	−	5.24567i	−0.102975	−	0.178358i
$866$		0			0
$867$	5.61505	−	0.893429i	0.190697	−	0.0303424i
$868$		0			0
$869$	−15.9520	−	27.6296i	−0.541134	−	0.937271i
$870$		0			0
$871$	3.22545			0.109290
$872$		0			0
$873$	38.2811	+	34.3700i	1.29562	+	1.16325i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	20.4703			0.691234			0.345617	−	0.938376i	$-0.387670\pi$
$877$	20.4703			0.691234			0.345617	+	0.938376i	$0.387670\pi$
$878$		0			0
$879$	−4.38237	+	11.4408i	−0.147814	+	0.385888i
$880$		0			0
$881$	−31.1683			−1.05009			−0.525043	−	0.851076i	$-0.675951\pi$
$881$	−31.1683			−1.05009			−0.525043	+	0.851076i	$0.675951\pi$
$882$		0			0
$883$	−2.64187			−0.0889060			−0.0444530	−	0.999011i	$-0.514154\pi$
$883$	−2.64187			−0.0889060			−0.0444530	+	0.999011i	$0.514154\pi$
$884$		0			0
$885$	−3.10000	+	0.493251i	−0.104205	+	0.0165805i
$886$		0			0
$887$	−23.1650			−0.777805			−0.388902	−	0.921279i	$-0.627146\pi$
$887$	−23.1650			−0.777805			−0.388902	+	0.921279i	$0.627146\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	42.1885	+	18.6400i	1.41337	+	0.624462i
$892$		0			0
$893$	15.8845			0.531555
$894$		0			0
$895$	−1.14132	−	1.97682i	−0.0381500	−	0.0660777i
$896$		0			0
$897$	−22.4632	+	58.6433i	−0.750026	+	1.95804i
$898$		0			0
$899$	1.24269	+	2.15240i	0.0414460	+	0.0717866i
$900$		0			0
$901$	1.74596	−	3.02409i	0.0581664	−	0.100747i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.95898			0.0983599
$906$		0			0
$907$	−50.0528			−1.66198			−0.830988	−	0.556290i	$-0.812224\pi$
$907$	−50.0528			−1.66198			−0.830988	+	0.556290i	$0.812224\pi$
$908$		0			0
$909$	−4.44966	+	21.0814i	−0.147586	+	0.699224i
$910$		0			0
$911$	5.42231	−	9.39172i	0.179649	−	0.311161i	−0.762111	−	0.647446i	$-0.775837\pi$
$911$	5.42231	−	9.39172i	0.179649	−	0.311161i	0.941760	+	0.336285i	$0.109170\pi$
$912$		0			0
$913$	24.8646	−	43.0667i	0.822897	−	1.42530i
$914$		0			0
$915$	0.816031	−	2.13036i	0.0269772	−	0.0704275i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−5.59549	+	9.69166i	−0.184578	+	0.319699i	−0.943434	−	0.331560i	$-0.892425\pi$
$919$	−5.59549	+	9.69166i	−0.184578	+	0.319699i	0.758856	+	0.651258i	$0.225759\pi$
$920$		0			0
$921$	17.1848	+	21.1907i	0.566259	+	0.698256i
$922$		0			0
$923$	33.5679	+	58.1413i	1.10490	+	1.91374i
$924$		0			0
$925$	11.3759	−	19.7037i	0.374038	−	0.647853i
$926$		0			0
$927$	7.94802	−	37.6557i	0.261047	−	1.23678i
$928$		0			0
$929$	−20.6478	−	35.7630i	−0.677431	−	1.17335i	−0.975752	−	0.218879i	$-0.929760\pi$
$929$	−20.6478	−	35.7630i	−0.677431	−	1.17335i	0.298321	−	0.954466i	$-0.403573\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	33.5672	−	5.34099i	1.09894	−	0.174856i
$934$		0			0
$935$	2.26935	+	3.93063i	0.0742156	+	0.128545i
$936$		0			0
$937$	−33.5620			−1.09642			−0.548211	−	0.836340i	$-0.684691\pi$
$937$	−33.5620			−1.09642			−0.548211	+	0.836340i	$0.684691\pi$
$938$		0			0
$939$	−15.7898	+	41.2213i	−0.515279	+	1.34521i
$940$		0			0
$941$	−25.2112	+	43.6671i	−0.821862	+	1.42351i	0.0824315	+	0.996597i	$0.473731\pi$
$941$	−25.2112	+	43.6671i	−0.821862	+	1.42351i	−0.904294	+	0.426911i	$0.859602\pi$
$942$		0			0
$943$	−20.7902	−	36.0096i	−0.677021	−	1.17263i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.1212	−	17.5304i	−0.328895	−	0.569662i	0.653398	−	0.757014i	$-0.273343\pi$
$947$	−10.1212	−	17.5304i	−0.328895	−	0.569662i	−0.982293	+	0.187352i	$0.940009\pi$
$948$		0			0
$949$	−8.94119	+	15.4866i	−0.290243	+	0.502716i
$950$		0			0
$951$	5.13160	−	13.3967i	0.166404	−	0.434419i
$952$		0			0
$953$	−29.3685			−0.951340			−0.475670	−	0.879624i	$-0.657794\pi$
$953$	−29.3685			−0.951340			−0.475670	+	0.879624i	$0.657794\pi$
$954$		0			0
$955$	−1.57442	−	2.72698i	−0.0509470	−	0.0882429i
$956$		0			0
$957$	30.3707	−	4.83239i	0.981746	−	0.156209i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.2427	+	26.4011i	0.491700	+	0.851649i
$962$		0			0
$963$	−16.8878	−	15.1624i	−0.544203	−	0.488603i
$964$		0			0
$965$	−1.33297	+	2.30878i	−0.0429099	+	0.0743222i
$966$		0			0
$967$	15.2157	+	26.3544i	0.489305	+	0.847501i	0.999924	−	0.0123057i	$-0.00391714\pi$
$967$	15.2157	+	26.3544i	0.489305	+	0.847501i	−0.510619	+	0.859807i	$0.670584\pi$
$968$		0			0
$969$	14.7895	+	18.2369i	0.475106	+	0.585855i
$970$		0			0
$971$	−3.59329	+	6.22377i	−0.115314	+	0.199730i	−0.917905	−	0.396799i	$-0.870121\pi$
$971$	−3.59329	+	6.22377i	−0.115314	+	0.199730i	0.802591	+	0.596530i	$0.203454\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	14.9617	−	39.0595i	0.479158	−	1.25091i
$976$		0			0
$977$	−14.2713	+	24.7186i	−0.456579	+	0.790818i	−0.998777	−	0.0494328i	$-0.984259\pi$
$977$	−14.2713	+	24.7186i	−0.456579	+	0.790818i	0.542199	+	0.840250i	$0.317592\pi$
$978$		0			0
$979$	−19.1888	+	33.2359i	−0.613276	+	1.06223i
$980$		0			0
$981$	−19.9075	+	6.49966i	−0.635598	+	0.207518i
$982$		0			0
$983$	4.41642			0.140862			0.0704310	−	0.997517i	$-0.477563\pi$
$983$	4.41642			0.140862			0.0704310	+	0.997517i	$0.477563\pi$
$984$		0			0
$985$	−0.0344801			−0.00109863
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−46.3396	+	80.2625i	−1.47351	+	2.55220i
$990$		0			0
$991$	2.90671	+	5.03456i	0.0923345	+	0.159928i	0.908493	−	0.417900i	$-0.137234\pi$
$991$	2.90671	+	5.03456i	0.0923345	+	0.159928i	−0.816159	+	0.577828i	$0.803900\pi$
$992$		0			0
$993$	−7.42270	+	19.3780i	−0.235552	+	0.614941i
$994$		0			0
$995$	2.32777	+	4.03182i	0.0737953	+	0.127817i
$996$		0			0
$997$	−52.6408			−1.66715			−0.833575	−	0.552407i	$-0.813710\pi$
$997$	−52.6408			−1.66715			−0.833575	+	0.552407i	$0.813710\pi$
$998$		0			0
$999$	1.20082	−	23.8878i	0.0379922	−	0.755776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.l.e.961.3		6
3.2	odd	2		5292.2.l.e.3313.2		6
7.2	even	3		252.2.j.a.169.1	yes	6
7.3	odd	6		1764.2.i.d.1537.2		6
7.4	even	3		1764.2.i.g.1537.2		6
7.5	odd	6		1764.2.j.e.1177.3		6
7.6	odd	2		1764.2.l.f.961.1		6
9.4	even	3		1764.2.i.g.373.2		6
9.5	odd	6		5292.2.i.f.1549.2		6
21.2	odd	6		756.2.j.b.505.2		6
21.5	even	6		5292.2.j.d.3529.2		6
21.11	odd	6		5292.2.i.f.2125.2		6
21.17	even	6		5292.2.i.e.2125.2		6
21.20	even	2		5292.2.l.f.3313.2		6
28.23	odd	6		1008.2.r.j.673.3		6
63.2	odd	6		2268.2.a.h.1.2		3
63.4	even	3	inner	1764.2.l.e.949.3		6
63.5	even	6		5292.2.j.d.1765.2		6
63.13	odd	6		1764.2.i.d.373.2		6
63.16	even	3		2268.2.a.i.1.2		3
63.23	odd	6		756.2.j.b.253.2		6
63.31	odd	6		1764.2.l.f.949.1		6
63.32	odd	6		5292.2.l.e.361.2		6
63.40	odd	6		1764.2.j.e.589.3		6
63.41	even	6		5292.2.i.e.1549.2		6
63.58	even	3		252.2.j.a.85.1	✓	6
63.59	even	6		5292.2.l.f.361.2		6
84.23	even	6		3024.2.r.j.2017.2		6
252.23	even	6		3024.2.r.j.1009.2		6
252.79	odd	6		9072.2.a.by.1.2		3
252.191	even	6		9072.2.a.bv.1.2		3
252.247	odd	6		1008.2.r.j.337.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.1	✓	6	63.58	even	3
252.2.j.a.169.1	yes	6	7.2	even	3
756.2.j.b.253.2		6	63.23	odd	6
756.2.j.b.505.2		6	21.2	odd	6
1008.2.r.j.337.3		6	252.247	odd	6
1008.2.r.j.673.3		6	28.23	odd	6
1764.2.i.d.373.2		6	63.13	odd	6
1764.2.i.d.1537.2		6	7.3	odd	6
1764.2.i.g.373.2		6	9.4	even	3
1764.2.i.g.1537.2		6	7.4	even	3
1764.2.j.e.589.3		6	63.40	odd	6
1764.2.j.e.1177.3		6	7.5	odd	6
1764.2.l.e.949.3		6	63.4	even	3	inner
1764.2.l.e.961.3		6	1.1	even	1	trivial
1764.2.l.f.949.1		6	63.31	odd	6
1764.2.l.f.961.1		6	7.6	odd	2
2268.2.a.h.1.2		3	63.2	odd	6
2268.2.a.i.1.2		3	63.16	even	3
3024.2.r.j.1009.2		6	252.23	even	6
3024.2.r.j.2017.2		6	84.23	even	6
5292.2.i.e.1549.2		6	63.41	even	6
5292.2.i.e.2125.2		6	21.17	even	6
5292.2.i.f.1549.2		6	9.5	odd	6
5292.2.i.f.2125.2		6	21.11	odd	6
5292.2.j.d.1765.2		6	63.5	even	6
5292.2.j.d.3529.2		6	21.5	even	6
5292.2.l.e.361.2		6	63.32	odd	6
5292.2.l.e.3313.2		6	3.2	odd	2
5292.2.l.f.361.2		6	63.59	even	6
5292.2.l.f.3313.2		6	21.20	even	2
9072.2.a.bv.1.2		3	252.191	even	6
9072.2.a.by.1.2		3	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.09097 + 1.34528i) q^{3} +0.239123 q^{5} +(-0.619562 + 2.93533i) q^{9} +O(q^{10})\)	\(q+(1.09097 + 1.34528i) q^{3} +0.239123 q^{5} +(-0.619562 + 2.93533i) q^{9} -5.12476 q^{11} +(2.44282 + 4.23109i) q^{13} +(0.260877 + 0.321688i) q^{15} +(-1.85185 - 3.20750i) q^{17} +(-1.83009 + 3.16982i) q^{19} +7.42107 q^{23} -4.94282 q^{25} +(-4.62476 + 2.36887i) q^{27} +(-1.73229 + 3.00041i) q^{29} +(0.358685 - 0.621261i) q^{31} +(-5.59097 - 6.89425i) q^{33} +(-2.30150 + 3.98632i) q^{37} +(-3.02696 + 7.90228i) q^{39} +(-2.80150 - 4.85235i) q^{41} +(-6.24433 + 10.8155i) q^{43} +(-0.148152 + 0.701905i) q^{45} +(-2.16991 - 3.75839i) q^{47} +(2.29467 - 5.99054i) q^{51} +(0.471410 + 0.816506i) q^{53} -1.22545 q^{55} +(-6.26088 + 0.996189i) q^{57} +(-3.78947 + 6.56355i) q^{59} +(-2.75404 - 4.77014i) q^{61} +(0.584135 + 1.01175i) q^{65} +(0.330095 - 0.571741i) q^{67} +(8.09617 + 9.98342i) q^{69} +13.7414 q^{71} +(1.83009 + 3.16982i) q^{73} +(-5.39248 - 6.64948i) q^{75} +(3.11273 + 5.39140i) q^{79} +(-8.23229 - 3.63723i) q^{81} +(-4.85185 + 8.40365i) q^{83} +(-0.442820 - 0.766987i) q^{85} +(-5.92627 + 0.942948i) q^{87} +(3.74433 - 6.48536i) q^{89} +(1.22708 - 0.195246i) q^{93} +(-0.437618 + 0.757977i) q^{95} +(8.57442 - 14.8513i) q^{97} +(3.17511 - 15.0429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} + 2 q^{5} - 4 q^{9}+O(q^{10}) \) 6 * q - 2 * q^3 + 2 * q^5 - 4 * q^9	\( 6 q - 2 q^{3} + 2 q^{5} - 4 q^{9} + 4 q^{11} - 3 q^{13} + q^{15} - 2 q^{17} - 3 q^{19} + 28 q^{23} - 12 q^{25} + 7 q^{27} - q^{29} + 3 q^{31} - 25 q^{33} + 3 q^{37} + 18 q^{39} - 3 q^{43} - 10 q^{45} - 21 q^{47} - 13 q^{51} - 6 q^{53} + 12 q^{55} - 37 q^{57} - 31 q^{59} - 6 q^{61} - 15 q^{65} - 6 q^{67} + 5 q^{69} + 34 q^{71} + 3 q^{73} - 7 q^{75} + 9 q^{79} - 40 q^{81} - 20 q^{83} + 15 q^{85} + 16 q^{87} - 12 q^{89} + 33 q^{93} - 20 q^{95} + 9 q^{97} - 8 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 + 2 * q^5 - 4 * q^9 + 4 * q^11 - 3 * q^13 + q^15 - 2 * q^17 - 3 * q^19 + 28 * q^23 - 12 * q^25 + 7 * q^27 - q^29 + 3 * q^31 - 25 * q^33 + 3 * q^37 + 18 * q^39 - 3 * q^43 - 10 * q^45 - 21 * q^47 - 13 * q^51 - 6 * q^53 + 12 * q^55 - 37 * q^57 - 31 * q^59 - 6 * q^61 - 15 * q^65 - 6 * q^67 + 5 * q^69 + 34 * q^71 + 3 * q^73 - 7 * q^75 + 9 * q^79 - 40 * q^81 - 20 * q^83 + 15 * q^85 + 16 * q^87 - 12 * q^89 + 33 * q^93 - 20 * q^95 + 9 * q^97 - 8 * q^99

Introduction

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