LMFDB - Embedded newform 1764.2.i.d.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(373,1764)]

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, 2]))

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

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

chi := DirichletCharacter("1764.373");

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.i (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1764.373
Dual form			1764.2.i.d.1537.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.619562 - 1.61745i) q^{3} +(0.119562 + 0.207087i) q^{5} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})$	\(q+(-0.619562 - 1.61745i) q^{3} +(0.119562 + 0.207087i) q^{5} +(-2.23229 + 2.00422i) q^{9} +(2.56238 - 4.43818i) q^{11} +(-2.44282 + 4.23109i) q^{13} +(0.260877 - 0.321688i) q^{15} +(1.85185 + 3.20750i) q^{17} +(1.83009 - 3.16982i) q^{19} +(-3.71053 - 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(4.62476 + 2.36887i) q^{27} +(-1.73229 - 3.00041i) q^{29} +0.717370 q^{31} +(-8.76608 - 1.39480i) q^{33} +(-2.30150 + 3.98632i) q^{37} +(8.35705 + 1.32972i) q^{39} +(2.80150 - 4.85235i) q^{41} +(-6.24433 - 10.8155i) q^{43} +(-0.681943 - 0.222649i) q^{45} -4.33981 q^{47} +(4.04063 - 4.98251i) q^{51} +(0.471410 + 0.816506i) q^{53} +1.22545 q^{55} +(-6.26088 - 0.996189i) q^{57} -7.57893 q^{59} -5.50808 q^{61} -1.16827 q^{65} -0.660190 q^{67} +(-8.09617 + 9.98342i) q^{69} +13.7414 q^{71} +(-1.83009 - 3.16982i) q^{73} +(-8.45486 - 1.34528i) q^{75} -6.22545 q^{79} +(0.966208 - 8.94799i) q^{81} +(4.85185 + 8.40365i) q^{83} +(-0.442820 + 0.766987i) q^{85} +(-3.77975 + 4.66082i) q^{87} +(-3.74433 + 6.48536i) q^{89} +(-0.444455 - 1.16031i) q^{93} +0.875237 q^{95} +(-8.57442 - 14.8513i) q^{97} +(3.17511 + 15.0429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} + q^{5} - 4 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 + q^5 - 4 * q^9	$ 6 q - 4 q^{3} + q^{5} - 4 q^{9} - 2 q^{11} + 3 q^{13} + q^{15} + 2 q^{17} + 3 q^{19} - 14 q^{23} + 6 q^{25} - 7 q^{27} - q^{29} + 6 q^{31} - 17 q^{33} + 3 q^{37} + 6 q^{39} - 3 q^{43} + 13 q^{45} - 42 q^{47} + 8 q^{51} - 6 q^{53} - 12 q^{55} - 37 q^{57} - 62 q^{59} - 12 q^{61} + 30 q^{65} + 12 q^{67} - 5 q^{69} + 34 q^{71} - 3 q^{73} - 8 q^{75} - 18 q^{79} + 32 q^{81} + 20 q^{83} + 15 q^{85} - 7 q^{87} + 12 q^{89} - 30 q^{93} + 40 q^{95} - 9 q^{97} - 8 q^{99}+O(q^{100}) $ 6 * q - 4 * q^3 + q^5 - 4 * q^9 - 2 * q^11 + 3 * q^13 + q^15 + 2 * q^17 + 3 * q^19 - 14 * q^23 + 6 * q^25 - 7 * q^27 - q^29 + 6 * q^31 - 17 * q^33 + 3 * q^37 + 6 * q^39 - 3 * q^43 + 13 * q^45 - 42 * q^47 + 8 * q^51 - 6 * q^53 - 12 * q^55 - 37 * q^57 - 62 * q^59 - 12 * q^61 + 30 * q^65 + 12 * q^67 - 5 * q^69 + 34 * q^71 - 3 * q^73 - 8 * q^75 - 18 * q^79 + 32 * q^81 + 20 * q^83 + 15 * q^85 - 7 * q^87 + 12 * q^89 - 30 * q^93 + 40 * q^95 - 9 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.619562	−	1.61745i	−0.357704	−	0.933835i
$3$	−0.619562	−	1.61745i	−0.357704	−	0.933835i
$4$		0			0
$5$	0.119562	+	0.207087i	0.0534696	+	0.0926120i	0.891521	−	0.452979i	$-0.149639\pi$
$5$	0.119562	+	0.207087i	0.0534696	+	0.0926120i	−0.838052	+	0.545591i	$0.816305\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.23229	+	2.00422i	−0.744096	+	0.668073i
$10$		0			0
$11$	2.56238	−	4.43818i	0.772587	−	1.33816i	−0.163554	−	0.986534i	$-0.552296\pi$
$11$	2.56238	−	4.43818i	0.772587	−	1.33816i	0.936141	−	0.351626i	$-0.114371\pi$
$12$		0			0
$13$	−2.44282	+	4.23109i	−0.677516	+	1.17349i	0.298210	+	0.954500i	$0.403610\pi$
$13$	−2.44282	+	4.23109i	−0.677516	+	1.17349i	−0.975727	+	0.218993i	$0.929723\pi$
$14$		0			0
$15$	0.260877	−	0.321688i	0.0673581	−	0.0830595i
$16$		0			0
$17$	1.85185	+	3.20750i	0.449139	+	0.777932i	0.998330	−	0.0577649i	$-0.0183974\pi$
$17$	1.85185	+	3.20750i	0.449139	+	0.777932i	−0.549191	+	0.835697i	$0.685064\pi$
$18$		0			0
$19$	1.83009	−	3.16982i	0.419853	−	0.727206i	−0.576072	−	0.817399i	$-0.695415\pi$
$19$	1.83009	−	3.16982i	0.419853	−	0.727206i	0.995924	+	0.0901932i	$0.0287484\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.71053	−	6.42683i	−0.773700	−	1.34009i	−0.935522	−	0.353267i	$-0.885071\pi$
$23$	−3.71053	−	6.42683i	−0.773700	−	1.34009i	0.161823	−	0.986820i	$-0.448263\pi$
$24$		0			0
$25$	2.47141	−	4.28061i	0.494282	−	0.856122i
$26$		0			0
$27$	4.62476	+	2.36887i	0.890036	+	0.455890i
$28$		0			0
$29$	−1.73229	−	3.00041i	−0.321678	−	0.557162i	0.659157	−	0.752006i	$-0.270913\pi$
$29$	−1.73229	−	3.00041i	−0.321678	−	0.557162i	−0.980834	+	0.194844i	$0.937580\pi$
$30$		0			0
$31$	0.717370			0.128843			0.0644217	−	0.997923i	$-0.479480\pi$
$31$	0.717370			0.128843			0.0644217	+	0.997923i	$0.479480\pi$
$32$		0			0
$33$	−8.76608	−	1.39480i	−1.52598	−	0.242804i
$34$		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
$39$	8.35705	+	1.32972i	1.33820	+	0.212925i
$40$		0			0
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	−0.559976	−	0.828509i	$-0.689190\pi$
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	0.997498	+	0.0706992i	$0.0225230\pi$
$42$		0			0
$43$	−6.24433	−	10.8155i	−0.952251	−	1.64935i	−0.740538	−	0.672015i	$-0.765429\pi$
$43$	−6.24433	−	10.8155i	−0.952251	−	1.64935i	−0.211713	−	0.977332i	$-0.567904\pi$
$44$		0			0
$45$	−0.681943	−	0.222649i	−0.101658	−	0.0331906i
$46$		0			0
$47$	−4.33981			−0.633026			−0.316513	−	0.948588i	$-0.602512\pi$
$47$	−4.33981			−0.633026			−0.316513	+	0.948588i	$0.602512\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	4.04063	−	4.98251i	0.565801	−	0.697691i
$52$		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
$59$	−7.57893			−0.986693			−0.493347	−	0.869833i	$-0.664227\pi$
$59$	−7.57893			−0.986693			−0.493347	+	0.869833i	$0.664227\pi$
$60$		0			0
$61$	−5.50808			−0.705237			−0.352619	−	0.935767i	$-0.614709\pi$
$61$	−5.50808			−0.705237			−0.352619	+	0.935767i	$0.614709\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.16827			−0.144906
$66$		0			0
$67$	−0.660190			−0.0806550			−0.0403275	−	0.999187i	$-0.512840\pi$
$67$	−0.660190			−0.0806550			−0.0403275	+	0.999187i	$0.512840\pi$
$68$		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	0.738827	−	0.673895i	$-0.235380\pi$
$73$	−1.83009	−	3.16982i	−0.214196	−	0.370999i	−0.953024	+	0.302896i	$0.902047\pi$
$74$		0			0
$75$	−8.45486	−	1.34528i	−0.976283	−	0.155340i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.22545			−0.700418			−0.350209	−	0.936672i	$-0.613889\pi$
$79$	−6.22545			−0.700418			−0.350209	+	0.936672i	$0.613889\pi$
$80$		0			0
$81$	0.966208	−	8.94799i	0.107356	−	0.994221i
$82$		0			0
$83$	4.85185	+	8.40365i	0.532560	+	0.922420i	0.999277	+	0.0380138i	$0.0121031\pi$
$83$	4.85185	+	8.40365i	0.532560	+	0.922420i	−0.466718	+	0.884406i	$0.654564\pi$
$84$		0			0
$85$	−0.442820	+	0.766987i	−0.0480306	+	0.0831914i
$86$		0			0
$87$	−3.77975	+	4.66082i	−0.405232	+	0.499693i
$88$		0			0
$89$	−3.74433	+	6.48536i	−0.396898	+	0.687447i	−0.993341	−	0.115208i	$-0.963247\pi$
$89$	−3.74433	+	6.48536i	−0.396898	+	0.687447i	0.596444	+	0.802655i	$0.296580\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.444455	−	1.16031i	−0.0460878	−	0.120318i
$94$		0			0
$95$	0.875237			0.0897974
$96$		0			0
$97$	−8.57442	−	14.8513i	−0.870600	−	1.50792i	−0.861377	−	0.507967i	$-0.830397\pi$
$97$	−8.57442	−	14.8513i	−0.870600	−	1.50792i	−0.00922376	−	0.999957i	$-0.502936\pi$
$98$		0			0
$99$	3.17511	+	15.0429i	0.319110	+	1.51186i
$100$		0			0
$101$	3.59097	−	6.21975i	0.357315	−	0.618888i	−0.630196	−	0.776436i	$-0.717026\pi$
$101$	3.59097	−	6.21975i	0.357315	−	0.618888i	0.987511	+	0.157548i	$0.0503589\pi$
$102$		0			0
$103$	−6.41423	−	11.1098i	−0.632013	−	1.09468i	−0.987140	−	0.159860i	$-0.948896\pi$
$103$	−6.41423	−	11.1098i	−0.632013	−	1.09468i	0.355127	−	0.934818i	$-0.384438\pi$
$104$		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	0.121834	−	0.992550i	$-0.461122\pi$
$113$	9.78495	−	16.9480i	0.920491	−	1.59434i	0.798657	−	0.601787i	$-0.205544\pi$
$114$		0			0
$115$	0.887275	−	1.53681i	0.0827388	−	0.143308i
$116$		0			0
$117$	−3.02696	−	14.3410i	−0.279842	−	1.32582i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.63160	−	13.2183i	−0.693782	−	1.20167i
$122$		0			0
$123$	−9.58414	−	1.52496i	−0.864172	−	0.137501i
$124$		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
$129$	−13.6248	+	16.8007i	−1.19959	+	1.47922i
$130$		0			0
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	0.952971	−	0.303061i	$-0.0980085\pi$
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	−0.738944	+	0.673767i	$0.764675\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.0623817	+	1.24095i	0.00536896	+	0.106804i
$136$		0			0
$137$	−2.72257	+	4.71563i	−0.232605	+	0.402884i	−0.958574	−	0.284844i	$-0.908058\pi$
$137$	−2.72257	+	4.71563i	−0.232605	+	0.402884i	0.725969	+	0.687727i	$0.241392\pi$
$138$		0			0
$139$	2.83009	−	4.90187i	0.240046	−	0.415771i	−0.720681	−	0.693266i	$-0.756171\pi$
$139$	2.83009	−	4.90187i	0.240046	−	0.415771i	0.960727	+	0.277495i	$0.0895043\pi$
$140$		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
$149$	−1.14132	−	1.97682i	−0.0935002	−	0.161947i	0.815481	−	0.578783i	$-0.196472\pi$
$149$	−1.14132	−	1.97682i	−0.0935002	−	0.161947i	−0.908982	+	0.416836i	$0.863139\pi$
$150$		0			0
$151$	−5.63160	+	9.75422i	−0.458293	+	0.793787i	−0.998871	−	0.0475071i	$-0.984872\pi$
$151$	−5.63160	+	9.75422i	−0.458293	+	0.793787i	0.540578	+	0.841294i	$0.318206\pi$
$152$		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
$157$	−5.54583			−0.442605			−0.221303	−	0.975205i	$-0.571031\pi$
$157$	−5.54583			−0.442605			−0.221303	+	0.975205i	$0.571031\pi$
$158$		0			0
$159$	1.02859	−	1.26836i	0.0815725	−	0.100587i
$160$		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
$165$	−0.759242	−	1.98210i	−0.0591069	−	0.154307i
$166$		0			0
$167$	2.20370	−	3.81691i	0.170527	−	0.295362i	−0.768077	−	0.640357i	$-0.778786\pi$
$167$	2.20370	−	3.81691i	0.170527	−	0.295362i	0.938604	+	0.344996i	$0.112120\pi$
$168$		0			0
$169$	−5.43474	−	9.41325i	−0.418057	−	0.724096i
$170$		0			0
$171$	2.26771	+	10.7439i	0.173416	+	0.821603i
$172$		0			0
$173$	−25.3308			−1.92586			−0.962932	−	0.269745i	$-0.913061\pi$
$173$	−25.3308			−1.92586			−0.962932	+	0.269745i	$0.913061\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.69562	+	12.2585i	0.352944	+	0.921409i
$178$		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	$-0.652110\pi$
$181$	−12.3743			−0.919774			−0.459887	+	0.887978i	$0.652110\pi$
$182$		0			0
$183$	3.41260	+	8.90904i	0.252266	+	0.658575i
$184$		0			0
$185$	−1.10069			−0.0809241
$186$		0			0
$187$	18.9806			1.38800
$188$		0			0
$189$		0			0
$190$		0			0
$191$	13.1683			0.952823			0.476411	−	0.879223i	$-0.341937\pi$
$191$	13.1683			0.952823			0.476411	+	0.879223i	$0.341937\pi$
$192$		0			0
$193$	11.1488			0.802511			0.401256	−	0.915966i	$-0.368574\pi$
$193$	11.1488			0.802511			0.401256	+	0.915966i	$0.368574\pi$
$194$		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	$-0.924247\pi$
$199$	−9.73461	−	16.8608i	−0.690068	−	1.19523i	0.281747	−	0.959489i	$-0.409086\pi$
$200$		0			0
$201$	0.409028	+	1.06782i	0.0288506	+	0.0753185i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.33981			0.0935764
$206$		0			0
$207$	21.1638	+	6.90981i	1.47098	+	0.480265i
$208$		0			0
$209$	−9.37880	−	16.2446i	−0.648745	−	1.12366i
$210$		0			0
$211$	1.61436	−	2.79615i	0.111137	−	0.192495i	−0.805092	−	0.593150i	$-0.797884\pi$
$211$	1.61436	−	2.79615i	0.111137	−	0.192495i	0.916229	+	0.400655i	$0.131217\pi$
$212$		0			0
$213$	−8.51367	−	22.2261i	−0.583347	−	1.52291i
$214$		0			0
$215$	1.49316	−	2.58623i	0.101833	−	0.176380i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.99316	+	4.92398i	−0.269833	+	0.332732i
$220$		0			0
$221$	−18.0949			−1.21720
$222$		0			0
$223$	10.3856	+	17.9885i	0.695474	+	1.20460i	0.970021	+	0.243022i	$0.0781389\pi$
$223$	10.3856	+	17.9885i	0.695474	+	1.20460i	−0.274547	+	0.961574i	$0.588528\pi$
$224$		0			0
$225$	3.06238	+	14.5088i	0.204159	+	0.967253i
$226$		0			0
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	−0.229446	−	0.973321i	$-0.573691\pi$
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	0.957644	−	0.287955i	$-0.0929752\pi$
$228$		0			0
$229$	11.3856	+	19.7205i	0.752384	+	1.30317i	0.946664	+	0.322222i	$0.104430\pi$
$229$	11.3856	+	19.7205i	0.752384	+	1.30317i	−0.194280	+	0.980946i	$0.562237\pi$
$230$		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	0.0347345	−	0.999397i	$-0.488941\pi$
$239$	13.6488	−	23.6405i	0.882870	−	1.52918i	0.848136	−	0.529779i	$-0.177725\pi$
$240$		0			0
$241$	5.01724	−	8.69011i	0.323189	−	0.559779i	−0.657955	−	0.753057i	$-0.728578\pi$
$241$	5.01724	−	8.69011i	0.323189	−	0.559779i	0.981144	+	0.193277i	$0.0619118\pi$
$242$		0			0
$243$	−15.0715	+	3.98104i	−0.966840	+	0.255384i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.94119	+	15.4866i	0.568914	+	0.985388i
$248$		0			0
$249$	10.5865	−	13.0542i	0.670890	−	0.827276i
$250$		0			0
$251$	28.3171			1.78736			0.893680	−	0.448705i	$-0.148115\pi$
$251$	28.3171			1.78736			0.893680	+	0.448705i	$0.148115\pi$
$252$		0			0
$253$	−38.0312			−2.39100
$254$		0			0
$255$	1.51492	+	0.241044i	0.0948678	+	0.0150947i
$256$		0			0
$257$	14.4315	+	24.9960i	0.900210	+	1.55921i	0.827221	+	0.561877i	$0.189921\pi$
$257$	14.4315	+	24.9960i	0.900210	+	1.55921i	0.0729899	+	0.997333i	$0.476746\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	9.88044	+	3.22589i	0.611584	+	0.199678i
$262$		0			0
$263$	0.604645	−	1.04728i	0.0372840	−	0.0645778i	−0.846781	−	0.531941i	$-0.821463\pi$
$263$	0.604645	−	1.04728i	0.0372840	−	0.0645778i	0.884065	+	0.467363i	$0.154796\pi$
$264$		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	0.970081	−	0.242780i	$-0.0780594\pi$
$269$	4.50684	+	7.80607i	0.274787	+	0.475944i	−0.695295	+	0.718725i	$0.744726\pi$
$270$		0			0
$271$	8.80150	−	15.2447i	0.534653	−	0.926047i	−0.464527	−	0.885559i	$-0.653776\pi$
$271$	8.80150	−	15.2447i	0.534653	−	0.926047i	0.999180	−	0.0404876i	$-0.0128911\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.6654	−	21.9371i	−0.763752	−	1.32286i
$276$		0			0
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	−0.887042	−	0.461689i	$-0.847244\pi$
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	0.843355	+	0.537356i	$0.180577\pi$
$278$		0			0
$279$	−1.60138	+	1.43777i	−0.0958718	+	0.0860768i
$280$		0			0
$281$	10.1482	+	17.5771i	0.605388	+	1.04856i	0.991990	+	0.126316i	$0.0403154\pi$
$281$	10.1482	+	17.5771i	0.605388	+	1.04856i	−0.386602	+	0.922247i	$0.626351\pi$
$282$		0			0
$283$	4.60301			0.273621			0.136810	−	0.990597i	$-0.456315\pi$
$283$	4.60301			0.273621			0.136810	+	0.990597i	$0.456315\pi$
$284$		0			0
$285$	−0.542263	−	1.41565i	−0.0321209	−	0.0838559i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.64132	−	2.84284i	0.0965479	−	0.167226i
$290$		0			0
$291$	−18.7089	+	23.0700i	−1.09674	+	1.35239i
$292$		0			0
$293$	−3.53667	+	6.12569i	−0.206614	+	0.357867i	−0.950646	−	0.310278i	$-0.899578\pi$
$293$	−3.53667	+	6.12569i	−0.206614	+	0.357867i	0.744031	+	0.668145i	$0.232911\pi$
$294$		0			0
$295$	−0.906150	−	1.56950i	−0.0527581	−	0.0913797i
$296$		0			0
$297$	22.3639	−	14.4556i	1.29768	−	0.838796i
$298$		0			0
$299$	36.2567			2.09678
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−12.2850	−	1.95470i	−0.705752	−	0.112295i
$304$		0			0
$305$	−0.658555	−	1.14065i	−0.0377088	−	0.0653135i
$306$		0			0
$307$	−15.7518			−0.899006			−0.449503	−	0.893279i	$-0.648399\pi$
$307$	−15.7518			−0.899006			−0.449503	+	0.893279i	$0.648399\pi$
$308$		0			0
$309$	−13.9955	+	17.2579i	−0.796175	+	0.981767i
$310$		0			0
$311$	19.6238			1.11276			0.556382	−	0.830926i	$-0.312189\pi$
$311$	19.6238			1.11276			0.556382	+	0.830926i	$0.312189\pi$
$312$		0			0
$313$	25.4854			1.44052			0.720259	−	0.693705i	$-0.244023\pi$
$313$	25.4854			1.44052			0.720259	+	0.693705i	$0.244023\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.28263			0.465199			0.232599	−	0.972573i	$-0.425277\pi$
$317$	8.28263			0.465199			0.232599	+	0.972573i	$0.425277\pi$
$318$		0			0
$319$	−17.7551			−0.994096
$320$		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
$327$	7.61560	−	9.39083i	0.421144	−	0.519314i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−11.9806			−0.658512			−0.329256	−	0.944241i	$-0.606798\pi$
$331$	−11.9806			−0.658512			−0.329256	+	0.944241i	$0.606798\pi$
$332$		0			0
$333$	−2.85185	−	13.5113i	−0.156280	−	0.740417i
$334$		0			0
$335$	−0.0789334	−	0.136717i	−0.00431259	−	0.00746963i
$336$		0			0
$337$	6.46006	−	11.1892i	0.351902	−	0.609512i	−0.634681	−	0.772774i	$-0.718868\pi$
$337$	6.46006	−	11.1892i	0.351902	−	0.609512i	0.986583	+	0.163262i	$0.0522017\pi$
$338$		0			0
$339$	−33.4750	−	5.32632i	−1.81811	−	0.289286i
$340$		0			0
$341$	1.83818	−	3.18381i	0.0995428	−	0.172413i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.03543	−	0.482977i	−0.163422	−	0.0260026i
$346$		0			0
$347$	16.1866			0.868942			0.434471	−	0.900686i	$-0.356935\pi$
$347$	16.1866			0.868942			0.434471	+	0.900686i	$0.356935\pi$
$348$		0			0
$349$	−9.05718	−	15.6875i	−0.484820	−	0.839732i	0.515028	−	0.857173i	$-0.327781\pi$
$349$	−9.05718	−	15.6875i	−0.484820	−	0.839732i	−0.999848	+	0.0174409i	$0.994448\pi$
$350$		0			0
$351$	−21.3204	+	13.7811i	−1.13800	+	0.735578i
$352$		0			0
$353$	−5.84897	+	10.1307i	−0.311309	+	0.539203i	−0.978646	−	0.205553i	$-0.934101\pi$
$353$	−5.84897	+	10.1307i	−0.311309	+	0.539203i	0.667337	+	0.744756i	$0.267434\pi$
$354$		0			0
$355$	1.64295	+	2.84567i	0.0871987	+	0.151033i
$356$		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
$367$	8.52696	−	14.7691i	0.445103	−	0.770942i	−0.552956	−	0.833210i	$-0.686500\pi$
$367$	8.52696	−	14.7691i	0.445103	−	0.770942i	0.998059	+	0.0622687i	$0.0198336\pi$
$368$		0			0
$369$	3.47141	+	16.4467i	0.180714	+	0.856179i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	0.977584	+	0.210547i	$0.0675246\pi$
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	−0.306453	+	0.951886i	$0.599142\pi$
$374$		0			0
$375$	−1.47304	−	3.84558i	−0.0760677	−	0.198585i
$376$		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
$381$	10.4142	+	27.1878i	0.533537	+	1.39287i
$382$		0			0
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	0.986525	+	0.163610i	$0.0523137\pi$
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	−0.351573	+	0.936161i	$0.614353\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	35.6157	+	11.6283i	1.81045	+	0.591098i
$388$		0			0
$389$	9.12640	−	15.8074i	0.462727	−	0.801466i	−0.536369	−	0.843984i	$-0.680204\pi$
$389$	9.12640	−	15.8074i	0.462727	−	0.801466i	0.999096	+	0.0425174i	$0.0135378\pi$
$390$		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	−0.667952	−	0.744204i	$-0.732829\pi$
$397$	6.18715	−	10.7164i	0.310524	−	0.537843i	0.978476	+	0.206361i	$0.0661622\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.48113	+	9.49359i	0.273714	+	0.474087i	0.969810	−	0.243862i	$-0.0784144\pi$
$401$	5.48113	+	9.49359i	0.273714	+	0.474087i	−0.696096	+	0.717949i	$0.745081\pi$
$402$		0			0
$403$	−1.75241	+	3.03526i	−0.0872935	+	0.151197i
$404$		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
$409$	13.3204			0.658650			0.329325	−	0.944217i	$-0.393179\pi$
$409$	13.3204			0.658650			0.329325	+	0.944217i	$0.393179\pi$
$410$		0			0
$411$	9.31410	+	1.48200i	0.459431	+	0.0731015i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.16019	+	2.00951i	−0.0569515	+	0.0986429i
$416$		0			0
$417$	−9.68194	−	1.54053i	−0.474127	−	0.0754399i
$418$		0			0
$419$	2.35705	−	4.08253i	0.115149	−	0.199445i	−0.802690	−	0.596396i	$-0.796599\pi$
$419$	2.35705	−	4.08253i	0.115149	−	0.199445i	0.917839	+	0.396952i	$0.129932\pi$
$420$		0			0
$421$	−9.65856	−	16.7291i	−0.470729	−	0.815327i	0.528710	−	0.848802i	$-0.322676\pi$
$421$	−9.65856	−	16.7291i	−0.470729	−	0.815327i	−0.999440	+	0.0334755i	$0.989342\pi$
$422$		0			0
$423$	9.68770	−	8.69793i	0.471032	−	0.422908i
$424$		0			0
$425$	18.3067			0.888006
$426$		0			0
$427$		0			0
$428$		0			0
$429$	27.3155	−	33.6828i	1.31880	−	1.62622i
$430$		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	$-0.807096\pi$
$433$	−34.2060			−1.64384			−0.821918	+	0.569606i	$0.807096\pi$
$434$		0			0
$435$	−1.41711	−	0.225481i	−0.0679452	−	0.0108110i
$436$		0			0
$437$	−27.1625			−1.29936
$438$		0			0
$439$	0.622440			0.0297075			0.0148537	−	0.999890i	$-0.495272\pi$
$439$	0.622440			0.0297075			0.0148537	+	0.999890i	$0.495272\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.17867			−0.246046			−0.123023	−	0.992404i	$-0.539259\pi$
$443$	−5.17867			−0.246046			−0.123023	+	0.992404i	$0.539259\pi$
$444$		0			0
$445$	−1.79071			−0.0848878
$446$		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
$453$	19.2661	+	3.06549i	0.905199	+	0.144029i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.20929			−0.150124			−0.0750621	−	0.997179i	$-0.523916\pi$
$457$	−3.20929			−0.150124			−0.0750621	+	0.997179i	$0.523916\pi$
$458$		0			0
$459$	0.966208	+	19.2207i	0.0450987	+	0.897146i
$460$		0			0
$461$	−18.1150	−	31.3762i	−0.843702	−	1.46133i	−0.886744	−	0.462261i	$-0.847038\pi$
$461$	−18.1150	−	31.3762i	−0.843702	−	1.46133i	0.0430418	−	0.999073i	$-0.486295\pi$
$462$		0			0
$463$	−14.5253	+	25.1586i	−0.675049	+	1.16922i	0.301406	+	0.953496i	$0.402544\pi$
$463$	−14.5253	+	25.1586i	−0.675049	+	1.16922i	−0.976455	+	0.215723i	$0.930789\pi$
$464$		0			0
$465$	0.187145	−	0.230769i	0.00867865	−	0.0107017i
$466$		0			0
$467$	−18.7466	+	32.4701i	−0.867491	+	1.50254i	−0.00293952	+	0.999996i	$0.500936\pi$
$467$	−18.7466	+	32.4701i	−0.867491	+	1.50254i	−0.864552	+	0.502544i	$0.832398\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.43598	+	8.97010i	0.158322	+	0.413320i
$472$		0			0
$473$	−64.0014			−2.94279
$474$		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
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	−0.290661	−	0.956826i	$-0.593875\pi$
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	0.973966	−	0.226693i	$-0.0727914\pi$
$480$		0			0
$481$	−11.2443	−	19.4757i	−0.512697	−	0.888017i
$482$		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	−0.516989	−	0.855992i	$-0.672947\pi$
$491$	10.6985	−	18.5303i	0.482816	−	0.836262i	0.999805	+	0.0197296i	$0.00628054\pi$
$492$		0			0
$493$	6.41586	−	11.1126i	0.288956	−	0.500487i
$494$		0			0
$495$	−2.73556	+	2.45607i	−0.122954	+	0.110392i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−7.28263	−	12.6139i	−0.326015	−	0.564675i	0.655702	−	0.755020i	$-0.272373\pi$
$499$	−7.28263	−	12.6139i	−0.326015	−	0.564675i	−0.981717	+	0.190345i	$0.939039\pi$
$500$		0			0
$501$	−7.53899	−	1.19955i	−0.336817	−	0.0535921i
$502$		0			0
$503$	−2.92339			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$503$	−2.92339			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$504$		0			0
$505$	1.71737			0.0764220
$506$		0			0
$507$	−11.8583	+	14.6225i	−0.526645	+	0.649408i
$508$		0			0
$509$	−9.62025	−	16.6628i	−0.426410	−	0.738564i	0.570141	−	0.821547i	$-0.306889\pi$
$509$	−9.62025	−	16.6628i	−0.426410	−	0.738564i	−0.996551	+	0.0829830i	$0.973555\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	15.9727	−	10.3244i	0.705210	−	0.455833i
$514$		0			0
$515$	1.53379	−	2.65661i	0.0675869	−	0.117064i
$516$		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	$0.0412986\pi$
$521$	13.8743	+	24.0310i	0.607844	+	1.05282i	−0.383751	+	0.923436i	$0.625368\pi$
$522$		0			0
$523$	−1.36840	+	2.37014i	−0.0598360	+	0.103639i	−0.894392	−	0.447285i	$-0.852391\pi$
$523$	−1.36840	+	2.37014i	−0.0598360	+	0.103639i	0.834556	+	0.550924i	$0.185724\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.32846	+	2.30096i	0.0578686	+	0.100231i
$528$		0			0
$529$	−16.0361	+	27.7754i	−0.697222	+	1.20762i
$530$		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
$535$	−1.80903			−0.0782112
$536$		0			0
$537$	−10.4142	+	12.8418i	−0.449407	+	0.554166i
$538$		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
$543$	7.66664	+	20.0148i	0.329007	+	0.858917i
$544$		0			0
$545$	−0.834608	+	1.44558i	−0.0357507	+	0.0619220i
$546$		0			0
$547$	10.7346	+	18.5929i	0.458979	+	0.794975i	0.998907	−	0.0467363i	$-0.0148821\pi$
$547$	10.7346	+	18.5929i	0.458979	+	0.794975i	−0.539928	+	0.841711i	$0.681549\pi$
$548$		0			0
$549$	12.2956	−	11.0394i	0.524764	−	0.471150i
$550$		0			0
$551$	−12.6810			−0.540229
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.681943	+	1.78031i	0.0289469	+	0.0755698i
$556$		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
$563$	−35.5483			−1.49818			−0.749091	−	0.662467i	$-0.769510\pi$
$563$	−35.5483			−1.49818			−0.749091	+	0.662467i	$0.769510\pi$
$564$		0			0
$565$	4.67962			0.196873
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.7486			0.911748			0.455874	−	0.890044i	$-0.349327\pi$
$569$	21.7486			0.911748			0.455874	+	0.890044i	$0.349327\pi$
$570$		0			0
$571$	−9.59974			−0.401737			−0.200868	−	0.979618i	$-0.564376\pi$
$571$	−9.59974			−0.401737			−0.200868	+	0.979618i	$0.564376\pi$
$572$		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	0.969113	−	0.246617i	$-0.0793190\pi$
$577$	6.50916	+	11.2742i	0.270980	+	0.469351i	−0.698133	+	0.715968i	$0.745986\pi$
$578$		0			0
$579$	−6.90739	−	18.0327i	−0.287061	−	0.749413i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.83173			0.200110
$584$		0			0
$585$	2.60791	−	2.34147i	0.107824	−	0.0968079i
$586$		0			0
$587$	8.64364	+	14.9712i	0.356761	+	0.617928i	0.987418	−	0.158134i	$-0.0505477\pi$
$587$	8.64364	+	14.9712i	0.356761	+	0.617928i	−0.630657	+	0.776062i	$0.717214\pi$
$588$		0			0
$589$	1.31285	−	2.27393i	0.0540952	−	0.0936957i
$590$		0			0
$591$	0.0893369	+	0.233226i	0.00367483	+	0.00959364i
$592$		0			0
$593$	6.20765	−	10.7520i	0.254918	−	0.441531i	−0.709955	−	0.704247i	$-0.751285\pi$
$593$	6.20765	−	10.7520i	0.254918	−	0.441531i	0.964873	+	0.262716i	$0.0846182\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−21.2404	+	26.1916i	−0.869310	+	1.07195i
$598$		0			0
$599$	−7.88564			−0.322199			−0.161099	−	0.986938i	$-0.551504\pi$
$599$	−7.88564			−0.322199			−0.161099	+	0.986938i	$0.551504\pi$
$600$		0			0
$601$	11.1413	+	19.2973i	0.454464	+	0.787154i	0.998657	−	0.0518055i	$-0.0164976\pi$
$601$	11.1413	+	19.2973i	0.454464	+	0.787154i	−0.544193	+	0.838960i	$0.683164\pi$
$602$		0			0
$603$	1.47373	−	1.32317i	0.0600151	−	0.0538835i
$604$		0			0
$605$	1.82489	−	3.16081i	0.0741925	−	0.128505i
$606$		0			0
$607$	11.0458	+	19.1319i	0.448336	+	0.776541i	0.998278	−	0.0586617i	$-0.0186833\pi$
$607$	11.0458	+	19.1319i	0.448336	+	0.776541i	−0.549942	+	0.835203i	$0.685350\pi$
$608$		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	−0.747201	−	0.664598i	$-0.768603\pi$
$617$	5.01655	−	8.68892i	0.201959	−	0.349803i	0.949159	+	0.314796i	$0.101936\pi$
$618$		0			0
$619$	−19.1283	+	33.1312i	−0.768833	+	1.33166i	0.169364	+	0.985554i	$0.445829\pi$
$619$	−19.1283	+	33.1312i	−0.768833	+	1.33166i	−0.938196	+	0.346103i	$0.887505\pi$
$620$		0			0
$621$	−1.93598	−	38.5124i	−0.0776883	−	1.54545i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.0728	−	20.9107i	−0.482911	−	0.836427i
$626$		0			0
$627$	−20.4640	+	25.2343i	−0.817254	+	1.00776i
$628$		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
$633$	−5.52283	−	0.878756i	−0.219513	−	0.0349274i
$634$		0			0
$635$	−2.00972	−	3.48093i	−0.0797531	−	0.138136i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−30.6748	+	27.5409i	−1.21348	+	1.08950i
$640$		0			0
$641$	8.68646	−	15.0454i	0.343094	−	0.594257i	−0.641911	−	0.766779i	$-0.721858\pi$
$641$	8.68646	−	15.0454i	0.343094	−	0.594257i	0.985006	+	0.172522i	$0.0551916\pi$
$642$		0			0
$643$	−9.47949	+	16.4190i	−0.373835	+	0.647501i	−0.990152	−	0.139997i	$-0.955291\pi$
$643$	−9.47949	+	16.4190i	−0.373835	+	0.647501i	0.616317	+	0.787498i	$0.288624\pi$
$644$		0			0
$645$	−5.10821	−	0.812785i	−0.201136	−	0.0320034i
$646$		0			0
$647$	9.50972	+	16.4713i	0.373865	+	0.647554i	0.990157	−	0.139964i	$-0.0446988\pi$
$647$	9.50972	+	16.4713i	0.373865	+	0.647554i	−0.616291	+	0.787518i	$0.711366\pi$
$648$		0			0
$649$	−19.4201	+	33.6366i	−0.762306	+	1.32035i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.59329	+	6.22377i	0.140616	+	0.243555i	0.927729	−	0.373255i	$-0.121758\pi$
$653$	3.59329	+	6.22377i	0.140616	+	0.243555i	−0.787112	+	0.616810i	$0.788425\pi$
$654$		0			0
$655$	−0.585770	+	1.01458i	−0.0228879	+	0.0396430i
$656$		0			0
$657$	10.4383	+	3.40803i	0.407237	+	0.132960i
$658$		0			0
$659$	−12.7261	−	22.0423i	−0.495740	−	0.858647i	0.504248	−	0.863559i	$-0.331770\pi$
$659$	−12.7261	−	22.0423i	−0.495740	−	0.858647i	−0.999988	+	0.00491209i	$0.998436\pi$
$660$		0			0
$661$	−8.28590			−0.322284			−0.161142	−	0.986931i	$-0.551518\pi$
$661$	−8.28590			−0.322284			−0.161142	+	0.986931i	$0.551518\pi$
$662$		0			0
$663$	11.2109	+	29.2676i	0.435396	+	1.13666i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12.8554	+	22.2662i	−0.497764	+	0.862152i
$668$		0			0
$669$	22.6609	−	27.9432i	0.876120	−	1.08035i
$670$		0			0
$671$	−14.1138	+	24.4458i	−0.544857	+	0.943721i
$672$		0			0
$673$	5.91586	+	10.2466i	0.228040	+	0.394977i	0.957227	−	0.289338i	$-0.0934350\pi$
$673$	5.91586	+	10.2466i	0.228040	+	0.394977i	−0.729187	+	0.684314i	$0.760102\pi$
$674$		0			0
$675$	21.5699	−	13.9423i	0.830226	−	0.536641i
$676$		0			0
$677$	−13.6063			−0.522932			−0.261466	−	0.965213i	$-0.584206\pi$
$677$	−13.6063			−0.522932			−0.261466	+	0.965213i	$0.584206\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−37.5339	−	5.97215i	−1.43830	−	0.228853i
$682$		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
$689$	−4.60628			−0.175485
$690$		0			0
$691$	−11.7174			−0.445750			−0.222875	−	0.974847i	$-0.571544\pi$
$691$	−11.7174			−0.445750			−0.222875	+	0.974847i	$0.571544\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.35348			0.0513405
$696$		0			0
$697$	20.7518			0.786032
$698$		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
$705$	−1.13216	+	1.39606i	−0.0426394	+	0.0525788i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	38.2977			1.43830			0.719150	−	0.694855i	$-0.244532\pi$
$709$	38.2977			1.43830			0.719150	+	0.694855i	$0.244532\pi$
$710$		0			0
$711$	13.8970	−	12.4772i	0.521178	−	0.467930i
$712$		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
$717$	−46.6936	−	7.42957i	−1.74380	−	0.277463i
$718$		0			0
$719$	20.8376	−	36.0918i	0.777112	−	1.34600i	−0.156488	−	0.987680i	$-0.550017\pi$
$719$	20.8376	−	36.0918i	0.777112	−	1.34600i	0.933600	−	0.358318i	$-0.116650\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−17.1643	−	2.73107i	−0.638348	−	0.101570i
$724$		0			0
$725$	−17.1248			−0.635998
$726$		0			0
$727$	−16.4126	−	28.4274i	−0.608709	−	1.05432i	−0.991453	−	0.130461i	$-0.958354\pi$
$727$	−16.4126	−	28.4274i	−0.608709	−	1.05432i	0.382744	−	0.923854i	$-0.374979\pi$
$728$		0			0
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$		0			0
$731$	23.1271	−	40.0573i	0.855386	−	1.48157i
$732$		0			0
$733$	4.64884	+	8.05203i	0.171709	+	0.297408i	0.939017	−	0.343870i	$-0.111738\pi$
$733$	4.64884	+	8.05203i	0.171709	+	0.297408i	−0.767309	+	0.641278i	$0.778405\pi$
$734$		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	−0.843927	−	0.536458i	$-0.819762\pi$
$743$	1.16182	−	2.01234i	0.0426232	−	0.0738256i	0.886550	+	0.462633i	$0.153095\pi$
$744$		0			0
$745$	0.272915	−	0.472703i	0.00999883	−	0.0173185i
$746$		0			0
$747$	−27.6735	−	9.03518i	−1.01252	−	0.330580i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	5.56690	+	9.64215i	0.203139	+	0.351847i	0.949538	−	0.313652i	$-0.101552\pi$
$751$	5.56690	+	9.64215i	0.203139	+	0.351847i	−0.746399	+	0.665498i	$0.768219\pi$
$752$		0			0
$753$	−17.5442	−	45.8015i	−0.639346	−	1.66910i
$754$		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
$759$	23.5627	+	61.5136i	0.855271	+	2.23280i
$760$		0			0
$761$	−23.5127	−	40.7252i	−0.852336	−	1.47629i	−0.879095	−	0.476647i	$-0.841852\pi$
$761$	−23.5127	−	40.7252i	−0.852336	−	1.47629i	0.0267592	−	0.999642i	$-0.491481\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.548709	−	2.59964i	−0.0198386	−	0.0939903i
$766$		0			0
$767$	18.5140	−	32.0671i	0.668501	−	1.15788i
$768$		0			0
$769$	−3.30314	+	5.72121i	−0.119114	+	0.206312i	−0.919417	−	0.393284i	$-0.871339\pi$
$769$	−3.30314	+	5.72121i	−0.119114	+	0.206312i	0.800303	+	0.599596i	$0.204672\pi$
$770$		0			0
$771$	31.4887	−	38.8288i	1.13404	−	1.39838i
$772$		0			0
$773$	9.54351	+	16.5298i	0.343256	+	0.594537i	0.985035	−	0.172352i	$-0.0551368\pi$
$773$	9.54351	+	16.5298i	0.343256	+	0.594537i	−0.641779	+	0.766889i	$0.721803\pi$
$774$		0			0
$775$	1.77292	−	3.07078i	0.0636850	−	0.110306i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.2540	−	17.7605i	−0.367389	−	0.636337i
$780$		0			0
$781$	35.2108	−	60.9869i	1.25994	−	2.18228i
$782$		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
$787$	−50.9007			−1.81441			−0.907207	−	0.420685i	$-0.861790\pi$
$787$	−50.9007			−1.81441			−0.907207	+	0.420685i	$0.861790\pi$
$788$		0			0
$789$	−2.06853	−	0.329131i	−0.0736416	−	0.0117174i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	13.4552	−	23.3052i	0.477810	−	0.827591i
$794$		0			0
$795$	0.385640	+	0.0613605i	0.0136772	+	0.00217623i
$796$		0			0
$797$	4.38727	−	7.59898i	0.155405	−	0.269170i	−0.777801	−	0.628510i	$-0.783665\pi$
$797$	4.38727	−	7.59898i	0.155405	−	0.269170i	0.933207	+	0.359341i	$0.116998\pi$
$798$		0			0
$799$	−8.03667	−	13.9199i	−0.284317	−	0.492451i
$800$		0			0
$801$	−4.63968	−	21.9816i	−0.163935	−	0.776683i
$802$		0			0
$803$	−18.7576			−0.661942
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.83366	−	12.1259i	0.346161	−	0.426853i
$808$		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	$-0.355283\pi$
$811$	25.0118			0.878282			0.439141	+	0.898418i	$0.355283\pi$
$812$		0			0
$813$	−30.1105	−	4.79099i	−1.05602	−	0.168027i
$814$		0			0
$815$	−1.59261			−0.0557866
$816$		0			0
$817$	−45.7108			−1.59922
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−35.5940			−1.24224			−0.621119	−	0.783716i	$-0.713322\pi$
$821$	−35.5940			−1.24224			−0.621119	+	0.783716i	$0.713322\pi$
$822$		0			0
$823$	16.0000			0.557725			0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000			0.557725			0.278862	+	0.960331i	$0.410043\pi$
$824$		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	0.672498	−	0.740099i	$-0.265222\pi$
$829$	−8.77292	−	15.1951i	−0.304696	−	0.527749i	−0.977194	+	0.212350i	$0.931888\pi$
$830$		0			0
$831$	2.48741	+	0.395780i	0.0862872	+	0.0137294i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.05391			0.0364721
$836$		0			0
$837$	3.31767	+	1.69936i	0.114675	+	0.0587384i
$838$		0			0
$839$	12.0562	+	20.8820i	0.416227	+	0.720927i	0.995556	−	0.0941668i	$-0.0300187\pi$
$839$	12.0562	+	20.8820i	0.416227	+	0.720927i	−0.579329	+	0.815094i	$0.696685\pi$
$840$		0			0
$841$	8.49837	−	14.7196i	0.293047	−	0.507572i
$842$		0			0
$843$	22.1427	−	27.3042i	0.762635	−	0.940408i
$844$		0			0
$845$	1.29957	−	2.25093i	0.0447067	−	0.0774342i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.85185	−	7.44514i	−0.0978752	−	0.255516i
$850$		0			0
$851$	34.1592			1.17096
$852$		0			0
$853$	16.2616	+	28.1659i	0.556785	+	0.964381i	0.997762	+	0.0668621i	$0.0212988\pi$
$853$	16.2616	+	28.1659i	0.556785	+	0.964381i	−0.440977	+	0.897518i	$0.645368\pi$
$854$		0			0
$855$	−1.95378	+	1.75417i	−0.0668178	+	0.0599912i
$856$		0			0
$857$	−0.299870	+	0.519390i	−0.0102434	+	0.0177420i	−0.871102	−	0.491103i	$-0.836594\pi$
$857$	−0.299870	+	0.519390i	−0.0102434	+	0.0177420i	0.860858	+	0.508845i	$0.169927\pi$
$858$		0			0
$859$	−13.2174	−	22.8932i	−0.450971	−	0.781104i	0.547476	−	0.836822i	$-0.315589\pi$
$859$	−13.2174	−	22.8932i	−0.450971	−	0.781104i	−0.998447	+	0.0557171i	$0.982255\pi$
$860$		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
$871$	1.61273	−	2.79332i	0.0546451	−	0.0946481i
$872$		0			0
$873$	48.9059	+	15.9674i	1.65521	+	0.540415i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	0.639849	−	0.768501i	$-0.278997\pi$
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	−0.985466	+	0.169875i	$0.945664\pi$
$878$		0			0
$879$	12.0992	+	1.92514i	0.408095	+	0.0649334i
$880$		0			0
$881$	31.1683			1.05009			0.525043	−	0.851076i	$-0.324049\pi$
$881$	31.1683			1.05009			0.525043	+	0.851076i	$0.324049\pi$
$882$		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
$885$	−1.97717	+	2.43805i	−0.0664618	+	0.0819542i
$886$		0			0
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	0.603400	−	0.797439i	$-0.293812\pi$
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	−0.992302	+	0.123840i	$0.960479\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−37.2369	−	27.2164i	−1.24748	−	0.911782i
$892$		0			0
$893$	−7.94226	+	13.7564i	−0.265778	+	0.460341i
$894$		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
$905$	−1.47949	−	2.56255i	−0.0491799	−	0.0851821i
$906$		0			0
$907$	25.0264	−	43.3470i	0.830988	−	1.43931i	−0.0662676	−	0.997802i	$-0.521109\pi$
$907$	25.0264	−	43.3470i	0.830988	−	1.43931i	0.897256	−	0.441511i	$-0.145558\pi$
$908$		0			0
$909$	4.44966	+	21.0814i	0.147586	+	0.699224i
$910$		0			0
$911$	5.42231	+	9.39172i	0.179649	+	0.311161i	0.941760	−	0.336285i	$-0.109170\pi$
$911$	5.42231	+	9.39172i	0.179649	+	0.311161i	−0.762111	+	0.647446i	$0.775837\pi$
$912$		0			0
$913$	49.7292			1.64579
$914$		0			0
$915$	−1.43693	+	1.77188i	−0.0475034	+	0.0585767i
$916$		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
$921$	9.75924	+	25.4778i	0.321578	+	0.839523i
$922$		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
$927$	36.5848	+	11.9447i	1.20160	+	0.392315i
$928$		0			0
$929$	−41.2955			−1.35486			−0.677431	−	0.735586i	$-0.736907\pi$
$929$	−41.2955			−1.35486			−0.677431	+	0.735586i	$0.736907\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−12.1582	−	31.7405i	−0.398040	−	1.03914i
$934$		0			0
$935$	2.26935	+	3.93063i	0.0742156	+	0.128545i
$936$		0			0
$937$	33.5620			1.09642			0.548211	−	0.836340i	$-0.315309\pi$
$937$	33.5620			1.09642			0.548211	+	0.836340i	$0.315309\pi$
$938$		0			0
$939$	−15.7898	−	41.2213i	−0.515279	−	1.34521i
$940$		0			0
$941$	−50.4224			−1.64372			−0.821862	−	0.569686i	$-0.807065\pi$
$941$	−50.4224			−1.64372			−0.821862	+	0.569686i	$0.807065\pi$
$942$		0			0
$943$	−41.5803			−1.35404
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.2424			0.657789			0.328895	−	0.944367i	$-0.393324\pi$
$947$	20.2424			0.657789			0.328895	+	0.944367i	$0.393324\pi$
$948$		0			0
$949$	17.8824			0.580486
$950$		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
$957$	11.0004	+	28.7180i	0.355592	+	0.928321i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−30.4854			−0.983399
$962$		0			0
$963$	−4.68715	−	22.2065i	−0.151041	−	0.715595i
$964$		0			0
$965$	1.33297	+	2.30878i	0.0429099	+	0.0743222i
$966$		0			0
$967$	15.2157	−	26.3544i	0.489305	−	0.847501i	−0.510619	−	0.859807i	$-0.670584\pi$
$967$	15.2157	−	26.3544i	0.489305	−	0.847501i	0.999924	+	0.0123057i	$0.00391714\pi$
$968$		0			0
$969$	−8.39892	−	21.9265i	−0.269812	−	0.704381i
$970$		0			0
$971$	3.59329	−	6.22377i	0.115314	−	0.199730i	−0.802591	−	0.596530i	$-0.796546\pi$
$971$	3.59329	−	6.22377i	0.115314	−	0.199730i	0.917905	+	0.396799i	$0.129879\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	26.3457	−	32.4870i	0.843738	−	1.04042i
$976$		0			0
$977$	28.5426			0.913157			0.456579	−	0.889683i	$-0.349075\pi$
$977$	28.5426			0.913157			0.456579	+	0.889683i	$0.349075\pi$
$978$		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
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	−0.828659	−	0.559753i	$-0.810896\pi$
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	0.899090	+	0.437763i	$0.144229\pi$
$984$		0			0
$985$	−0.0172400	−	0.0298606i	−0.000549313	−	0.000951438i
$986$		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
$997$	−26.3204	+	45.5882i	−0.833575	+	1.44379i	0.0616108	+	0.998100i	$0.480376\pi$
$997$	−26.3204	+	45.5882i	−0.833575	+	1.44379i	−0.895186	+	0.445694i	$0.852957\pi$
$998$		0			0
$999$	−20.0870	+	12.9838i	−0.635525	+	0.410790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.i.d.373.2		6
3.2	odd	2		5292.2.i.e.1549.2		6
7.2	even	3		1764.2.j.e.589.3		6
7.3	odd	6		1764.2.l.e.949.3		6
7.4	even	3		1764.2.l.f.949.1		6
7.5	odd	6		252.2.j.a.85.1	✓	6
7.6	odd	2		1764.2.i.g.373.2		6
9.2	odd	6		5292.2.l.f.3313.2		6
9.7	even	3		1764.2.l.f.961.1		6
21.2	odd	6		5292.2.j.d.1765.2		6
21.5	even	6		756.2.j.b.253.2		6
21.11	odd	6		5292.2.l.f.361.2		6
21.17	even	6		5292.2.l.e.361.2		6
21.20	even	2		5292.2.i.f.1549.2		6
28.19	even	6		1008.2.r.j.337.3		6
63.2	odd	6		5292.2.j.d.3529.2		6
63.5	even	6		2268.2.a.h.1.2		3
63.11	odd	6		5292.2.i.e.2125.2		6
63.16	even	3		1764.2.j.e.1177.3		6
63.20	even	6		5292.2.l.e.3313.2		6
63.25	even	3	inner	1764.2.i.d.1537.2		6
63.34	odd	6		1764.2.l.e.961.3		6
63.38	even	6		5292.2.i.f.2125.2		6
63.40	odd	6		2268.2.a.i.1.2		3
63.47	even	6		756.2.j.b.505.2		6
63.52	odd	6		1764.2.i.g.1537.2		6
63.61	odd	6		252.2.j.a.169.1	yes	6
84.47	odd	6		3024.2.r.j.1009.2		6
252.47	odd	6		3024.2.r.j.2017.2		6
252.103	even	6		9072.2.a.by.1.2		3
252.131	odd	6		9072.2.a.bv.1.2		3
252.187	even	6		1008.2.r.j.673.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.1	✓	6	7.5	odd	6
252.2.j.a.169.1	yes	6	63.61	odd	6
756.2.j.b.253.2		6	21.5	even	6
756.2.j.b.505.2		6	63.47	even	6
1008.2.r.j.337.3		6	28.19	even	6
1008.2.r.j.673.3		6	252.187	even	6
1764.2.i.d.373.2		6	1.1	even	1	trivial
1764.2.i.d.1537.2		6	63.25	even	3	inner
1764.2.i.g.373.2		6	7.6	odd	2
1764.2.i.g.1537.2		6	63.52	odd	6
1764.2.j.e.589.3		6	7.2	even	3
1764.2.j.e.1177.3		6	63.16	even	3
1764.2.l.e.949.3		6	7.3	odd	6
1764.2.l.e.961.3		6	63.34	odd	6
1764.2.l.f.949.1		6	7.4	even	3
1764.2.l.f.961.1		6	9.7	even	3
2268.2.a.h.1.2		3	63.5	even	6
2268.2.a.i.1.2		3	63.40	odd	6
3024.2.r.j.1009.2		6	84.47	odd	6
3024.2.r.j.2017.2		6	252.47	odd	6
5292.2.i.e.1549.2		6	3.2	odd	2
5292.2.i.e.2125.2		6	63.11	odd	6
5292.2.i.f.1549.2		6	21.20	even	2
5292.2.i.f.2125.2		6	63.38	even	6
5292.2.j.d.1765.2		6	21.2	odd	6
5292.2.j.d.3529.2		6	63.2	odd	6
5292.2.l.e.361.2		6	21.17	even	6
5292.2.l.e.3313.2		6	63.20	even	6
5292.2.l.f.361.2		6	21.11	odd	6
5292.2.l.f.3313.2		6	9.2	odd	6
9072.2.a.bv.1.2		3	252.131	odd	6
9072.2.a.by.1.2		3	252.103	even	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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.619562 - 1.61745i) q^{3} +(0.119562 + 0.207087i) q^{5} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})\)	\(q+(-0.619562 - 1.61745i) q^{3} +(0.119562 + 0.207087i) q^{5} +(-2.23229 + 2.00422i) q^{9} +(2.56238 - 4.43818i) q^{11} +(-2.44282 + 4.23109i) q^{13} +(0.260877 - 0.321688i) q^{15} +(1.85185 + 3.20750i) q^{17} +(1.83009 - 3.16982i) q^{19} +(-3.71053 - 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(4.62476 + 2.36887i) q^{27} +(-1.73229 - 3.00041i) q^{29} +0.717370 q^{31} +(-8.76608 - 1.39480i) q^{33} +(-2.30150 + 3.98632i) q^{37} +(8.35705 + 1.32972i) q^{39} +(2.80150 - 4.85235i) q^{41} +(-6.24433 - 10.8155i) q^{43} +(-0.681943 - 0.222649i) q^{45} -4.33981 q^{47} +(4.04063 - 4.98251i) q^{51} +(0.471410 + 0.816506i) q^{53} +1.22545 q^{55} +(-6.26088 - 0.996189i) q^{57} -7.57893 q^{59} -5.50808 q^{61} -1.16827 q^{65} -0.660190 q^{67} +(-8.09617 + 9.98342i) q^{69} +13.7414 q^{71} +(-1.83009 - 3.16982i) q^{73} +(-8.45486 - 1.34528i) q^{75} -6.22545 q^{79} +(0.966208 - 8.94799i) q^{81} +(4.85185 + 8.40365i) q^{83} +(-0.442820 + 0.766987i) q^{85} +(-3.77975 + 4.66082i) q^{87} +(-3.74433 + 6.48536i) q^{89} +(-0.444455 - 1.16031i) q^{93} +0.875237 q^{95} +(-8.57442 - 14.8513i) q^{97} +(3.17511 + 15.0429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} + q^{5} - 4 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 + q^5 - 4 * q^9	\( 6 q - 4 q^{3} + q^{5} - 4 q^{9} - 2 q^{11} + 3 q^{13} + q^{15} + 2 q^{17} + 3 q^{19} - 14 q^{23} + 6 q^{25} - 7 q^{27} - q^{29} + 6 q^{31} - 17 q^{33} + 3 q^{37} + 6 q^{39} - 3 q^{43} + 13 q^{45} - 42 q^{47} + 8 q^{51} - 6 q^{53} - 12 q^{55} - 37 q^{57} - 62 q^{59} - 12 q^{61} + 30 q^{65} + 12 q^{67} - 5 q^{69} + 34 q^{71} - 3 q^{73} - 8 q^{75} - 18 q^{79} + 32 q^{81} + 20 q^{83} + 15 q^{85} - 7 q^{87} + 12 q^{89} - 30 q^{93} + 40 q^{95} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 6 * q - 4 * q^3 + q^5 - 4 * q^9 - 2 * q^11 + 3 * q^13 + q^15 + 2 * q^17 + 3 * q^19 - 14 * q^23 + 6 * q^25 - 7 * q^27 - q^29 + 6 * q^31 - 17 * q^33 + 3 * q^37 + 6 * q^39 - 3 * q^43 + 13 * q^45 - 42 * q^47 + 8 * q^51 - 6 * q^53 - 12 * q^55 - 37 * q^57 - 62 * q^59 - 12 * q^61 + 30 * q^65 + 12 * q^67 - 5 * q^69 + 34 * q^71 - 3 * q^73 - 8 * q^75 - 18 * q^79 + 32 * q^81 + 20 * q^83 + 15 * q^85 - 7 * q^87 + 12 * q^89 - 30 * q^93 + 40 * q^95 - 9 * q^97 - 8 * q^99

Introduction

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