LMFDB - Embedded newform 1386.2.r.c.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(89,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("1386.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1386.89
Dual form			1386.2.r.c.1277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.0340742 - 0.0590182i) q^{5} +(-2.19067 - 1.48356i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.0340742 - 0.0590182i) q^{5} +(-2.19067 - 1.48356i) q^{7} -1.00000i q^{8} +(-0.0590182 + 0.0340742i) q^{10} +(-0.866025 + 0.500000i) q^{11} +2.44949i q^{13} +(1.15539 + 2.38014i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.817837 - 1.41654i) q^{17} +(6.28497 + 3.62863i) q^{19} +0.0681483 q^{20} +1.00000 q^{22} +(-0.405083 - 0.233875i) q^{23} +(2.49768 + 4.32611i) q^{25} +(1.22474 - 2.12132i) q^{26} +(0.189469 - 2.63896i) q^{28} -7.23143i q^{29} +(-0.201501 + 0.116337i) q^{31} +(0.866025 - 0.500000i) q^{32} +1.63567i q^{34} +(-0.162203 + 0.0787382i) q^{35} +(2.74496 - 4.75442i) q^{37} +(-3.62863 - 6.28497i) q^{38} +(-0.0590182 - 0.0340742i) q^{40} -5.38891 q^{41} +9.64100 q^{43} +(-0.866025 - 0.500000i) q^{44} +(0.233875 + 0.405083i) q^{46} +(4.31199 - 7.46859i) q^{47} +(2.59808 + 6.50000i) q^{49} -4.99536i q^{50} +(-2.12132 + 1.22474i) q^{52} +(7.34278 - 4.23936i) q^{53} +0.0681483i q^{55} +(-1.48356 + 2.19067i) q^{56} +(-3.61571 + 6.26260i) q^{58} +(-0.439158 - 0.760643i) q^{59} +(-8.63223 - 4.98382i) q^{61} +0.232673 q^{62} -1.00000 q^{64} +(0.144564 + 0.0834643i) q^{65} +(1.52993 + 2.64991i) q^{67} +(0.817837 - 1.41654i) q^{68} +(0.179841 + 0.0129120i) q^{70} +15.8771i q^{71} +(6.76696 - 3.90691i) q^{73} +(-4.75442 + 2.74496i) q^{74} +7.25725i q^{76} +(2.63896 + 0.189469i) q^{77} +(5.76612 - 9.98722i) q^{79} +(0.0340742 + 0.0590182i) q^{80} +(4.66693 + 2.69445i) q^{82} +17.1270 q^{83} -0.111469 q^{85} +(-8.34935 - 4.82050i) q^{86} +(0.500000 + 0.866025i) q^{88} +(5.33814 - 9.24592i) q^{89} +(3.63397 - 5.36603i) q^{91} -0.467750i q^{92} +(-7.46859 + 4.31199i) q^{94} +(0.428310 - 0.247285i) q^{95} +9.99876i q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 8 q^{5}+O(q^{10}) $ 8 * q + 4 * q^4 + 8 * q^5	$ 8 q + 4 q^{4} + 8 q^{5} - 4 q^{16} - 4 q^{17} + 24 q^{19} + 16 q^{20} + 8 q^{22} + 24 q^{23} - 4 q^{25} + 12 q^{31} + 16 q^{35} + 12 q^{37} - 8 q^{38} + 16 q^{41} - 32 q^{43} + 8 q^{46} + 48 q^{53} - 4 q^{58} + 16 q^{59} + 24 q^{62} - 8 q^{64} - 12 q^{65} - 24 q^{67} + 4 q^{68} - 20 q^{70} - 24 q^{73} - 12 q^{74} + 40 q^{79} + 8 q^{80} + 12 q^{82} + 72 q^{83} - 32 q^{85} - 24 q^{86} + 4 q^{88} - 16 q^{89} + 36 q^{91} + 24 q^{95} + 8 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 8 * q^5 - 4 * q^16 - 4 * q^17 + 24 * q^19 + 16 * q^20 + 8 * q^22 + 24 * q^23 - 4 * q^25 + 12 * q^31 + 16 * q^35 + 12 * q^37 - 8 * q^38 + 16 * q^41 - 32 * q^43 + 8 * q^46 + 48 * q^53 - 4 * q^58 + 16 * q^59 + 24 * q^62 - 8 * q^64 - 12 * q^65 - 24 * q^67 + 4 * q^68 - 20 * q^70 - 24 * q^73 - 12 * q^74 + 40 * q^79 + 8 * q^80 + 12 * q^82 + 72 * q^83 - 32 * q^85 - 24 * q^86 + 4 * q^88 - 16 * q^89 + 36 * q^91 + 24 * q^95 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.0340742	−	0.0590182i	0.0152384	−	0.0263937i	−0.858306	−	0.513139i	$-0.828483\pi$
$5$	0.0340742	−	0.0590182i	0.0152384	−	0.0263937i	0.873544	+	0.486745i	$0.161816\pi$
$6$		0			0
$7$	−2.19067	−	1.48356i	−0.827996	−	0.560734i
$7$	−2.19067	−	1.48356i	−0.827996	−	0.560734i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.0590182	+	0.0340742i	−0.0186632	+	0.0107752i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$		0			0
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$	1.15539	+	2.38014i	0.308792	+	0.636119i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.817837	−	1.41654i	−0.198355	−	0.343560i	0.749640	−	0.661845i	$-0.230226\pi$
$17$	−0.817837	−	1.41654i	−0.198355	−	0.343560i	−0.947995	+	0.318285i	$0.896893\pi$
$18$		0			0
$19$	6.28497	+	3.62863i	1.44187	+	0.832464i	0.997975	−	0.0636147i	$-0.0202629\pi$
$19$	6.28497	+	3.62863i	1.44187	+	0.832464i	0.443895	+	0.896079i	$0.353596\pi$
$20$	0.0681483			0.0152384
$21$		0			0
$22$	1.00000			0.213201
$23$	−0.405083	−	0.233875i	−0.0844657	−	0.0487663i	0.457172	−	0.889378i	$-0.348862\pi$
$23$	−0.405083	−	0.233875i	−0.0844657	−	0.0487663i	−0.541638	+	0.840612i	$0.682196\pi$
$24$		0			0
$25$	2.49768	+	4.32611i	0.499536	+	0.865221i
$26$	1.22474	−	2.12132i	0.240192	−	0.416025i
$27$		0			0
$28$	0.189469	−	2.63896i	0.0358062	−	0.498716i
$29$		−	7.23143i		−	1.34284i	−0.741076	−	0.671421i	$-0.765684\pi$
$29$		−	7.23143i		−	1.34284i	0.741076	−	0.671421i	$-0.234316\pi$
$30$		0			0
$31$	−0.201501	+	0.116337i	−0.0361906	+	0.0208947i	−0.517986	−	0.855389i	$-0.673318\pi$
$31$	−0.201501	+	0.116337i	−0.0361906	+	0.0208947i	0.481796	+	0.876284i	$0.339985\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			1.63567i			0.280516i
$35$	−0.162203	+	0.0787382i	−0.0274172	+	0.0133092i
$36$		0			0
$37$	2.74496	−	4.75442i	0.451269	−	0.781621i	−0.547196	−	0.837004i	$-0.684305\pi$
$37$	2.74496	−	4.75442i	0.451269	−	0.781621i	0.998465	+	0.0553835i	$0.0176381\pi$
$38$	−3.62863	−	6.28497i	−0.588641	−	1.01956i
$39$		0			0
$40$	−0.0590182	−	0.0340742i	−0.00933160	−	0.00538760i
$41$	−5.38891			−0.841606			−0.420803	−	0.907152i	$-0.638252\pi$
$41$	−5.38891			−0.841606			−0.420803	+	0.907152i	$0.638252\pi$
$42$		0			0
$43$	9.64100			1.47024			0.735119	−	0.677938i	$-0.237126\pi$
$43$	9.64100			1.47024			0.735119	+	0.677938i	$0.237126\pi$
$44$	−0.866025	−	0.500000i	−0.130558	−	0.0753778i
$45$		0			0
$46$	0.233875	+	0.405083i	0.0344830	+	0.0597263i
$47$	4.31199	−	7.46859i	0.628969	−	1.08941i	−0.358791	−	0.933418i	$-0.616811\pi$
$47$	4.31199	−	7.46859i	0.628969	−	1.08941i	0.987759	−	0.155987i	$-0.0498559\pi$
$48$		0			0
$49$	2.59808	+	6.50000i	0.371154	+	0.928571i
$50$		−	4.99536i		−	0.706450i
$51$		0			0
$52$	−2.12132	+	1.22474i	−0.294174	+	0.169842i
$53$	7.34278	−	4.23936i	1.00861	−	0.582320i	0.0978246	−	0.995204i	$-0.468812\pi$
$53$	7.34278	−	4.23936i	1.00861	−	0.582320i	0.910784	+	0.412883i	$0.135478\pi$
$54$		0			0
$55$			0.0681483i			0.00918912i
$56$	−1.48356	+	2.19067i	−0.198250	+	0.292741i
$57$		0			0
$58$	−3.61571	+	6.26260i	−0.474767	+	0.822320i
$59$	−0.439158	−	0.760643i	−0.0571734	−	0.0990273i	0.836022	−	0.548696i	$-0.184875\pi$
$59$	−0.439158	−	0.760643i	−0.0571734	−	0.0990273i	−0.893196	+	0.449668i	$0.851542\pi$
$60$		0			0
$61$	−8.63223	−	4.98382i	−1.10524	−	0.638113i	−0.167651	−	0.985846i	$-0.553618\pi$
$61$	−8.63223	−	4.98382i	−1.10524	−	0.638113i	−0.937593	+	0.347733i	$0.886951\pi$
$62$	0.232673			0.0295495
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.144564	+	0.0834643i	0.0179310	+	0.0103525i
$66$		0			0
$67$	1.52993	+	2.64991i	0.186910	+	0.323738i	0.944219	−	0.329319i	$-0.106819\pi$
$67$	1.52993	+	2.64991i	0.186910	+	0.323738i	−0.757308	+	0.653058i	$0.773486\pi$
$68$	0.817837	−	1.41654i	0.0991773	−	0.171780i
$69$		0			0
$70$	0.179841	+	0.0129120i	0.0214951	+	0.00154328i
$71$			15.8771i			1.88426i	0.335245	+	0.942131i	$0.391181\pi$
$71$			15.8771i			1.88426i	−0.335245	+	0.942131i	$0.608819\pi$
$72$		0			0
$73$	6.76696	−	3.90691i	0.792013	−	0.457269i	−0.0486577	−	0.998816i	$-0.515494\pi$
$73$	6.76696	−	3.90691i	0.792013	−	0.457269i	0.840671	+	0.541547i	$0.182161\pi$
$74$	−4.75442	+	2.74496i	−0.552690	+	0.319095i
$75$		0			0
$76$			7.25725i			0.832464i
$77$	2.63896	+	0.189469i	0.300737	+	0.0215920i
$78$		0			0
$79$	5.76612	−	9.98722i	0.648740	−	1.12365i	−0.334684	−	0.942330i	$-0.608630\pi$
$79$	5.76612	−	9.98722i	0.648740	−	1.12365i	0.983424	−	0.181320i	$-0.0580370\pi$
$80$	0.0340742	+	0.0590182i	0.00380961	+	0.00659844i
$81$		0			0
$82$	4.66693	+	2.69445i	0.515376	+	0.297553i
$83$	17.1270			1.87993			0.939967	−	0.341266i	$-0.110856\pi$
$83$	17.1270			1.87993			0.939967	+	0.341266i	$0.110856\pi$
$84$		0			0
$85$	−0.111469			−0.0120905
$86$	−8.34935	−	4.82050i	−0.900333	−	0.519808i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	5.33814	−	9.24592i	0.565841	−	0.980066i	−0.431129	−	0.902290i	$-0.641885\pi$
$89$	5.33814	−	9.24592i	0.565841	−	0.980066i	0.996971	−	0.0777760i	$-0.0247819\pi$
$90$		0			0
$91$	3.63397	−	5.36603i	0.380944	−	0.562512i
$92$		−	0.467750i		−	0.0487663i
$93$		0			0
$94$	−7.46859	+	4.31199i	−0.770326	+	0.444748i
$95$	0.428310	−	0.247285i	0.0439437	−	0.0253709i
$96$		0			0
$97$			9.99876i			1.01522i	0.861587	+	0.507610i	$0.169471\pi$
$97$			9.99876i			1.01522i	−0.861587	+	0.507610i	$0.830529\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$		0			0
$100$	−2.49768	+	4.32611i	−0.249768	+	0.432611i
$101$	1.76028	+	3.04889i	0.175154	+	0.303376i	0.940215	−	0.340582i	$-0.110624\pi$
$101$	1.76028	+	3.04889i	0.175154	+	0.303376i	−0.765060	+	0.643959i	$0.777291\pi$
$102$		0			0
$103$	13.8471	+	7.99465i	1.36440	+	0.787736i	0.990206	−	0.139614i	$-0.0445862\pi$
$103$	13.8471	+	7.99465i	1.36440	+	0.787736i	0.374194	+	0.927351i	$0.377920\pi$
$104$	2.44949			0.240192
$105$		0			0
$106$	−8.47871			−0.823525
$107$	−5.25201	−	3.03225i	−0.507731	−	0.293139i	0.224169	−	0.974550i	$-0.428033\pi$
$107$	−5.25201	−	3.03225i	−0.507731	−	0.293139i	−0.731901	+	0.681412i	$0.761366\pi$
$108$		0			0
$109$	−9.00877	−	15.6036i	−0.862883	−	1.49456i	−0.869134	−	0.494577i	$-0.835323\pi$
$109$	−9.00877	−	15.6036i	−0.862883	−	1.49456i	0.00625046	−	0.999980i	$-0.498010\pi$
$110$	0.0340742	−	0.0590182i	0.00324884	−	0.00562716i
$111$		0			0
$112$	2.38014	−	1.15539i	0.224902	−	0.109175i
$113$			7.05521i			0.663698i	0.943332	+	0.331849i	$0.107673\pi$
$113$			7.05521i			0.663698i	−0.943332	+	0.331849i	$0.892327\pi$
$114$		0			0
$115$	−0.0276058	+	0.0159382i	−0.00257425	+	0.00148624i
$116$	6.26260	−	3.61571i	0.581468	−	0.335711i
$117$		0			0
$118$			0.878315i			0.0808555i
$119$	−0.309909	+	4.31648i	−0.0284093	+	0.395691i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	4.98382	+	8.63223i	0.451214	+	0.781526i
$123$		0			0
$124$	−0.201501	−	0.116337i	−0.0180953	−	0.0104473i
$125$	0.681167			0.0609254
$126$		0			0
$127$	6.83939			0.606898			0.303449	−	0.952848i	$-0.401862\pi$
$127$	6.83939			0.606898			0.303449	+	0.952848i	$0.401862\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.0834643	−	0.144564i	−0.00732031	−	0.0126791i
$131$	0.757359	−	1.31178i	0.0661708	−	0.114611i	−0.831042	−	0.556210i	$-0.812255\pi$
$131$	0.757359	−	1.31178i	0.0661708	−	0.114611i	0.897213	+	0.441599i	$0.145588\pi$
$132$		0			0
$133$	−8.38499	−	17.2733i	−0.727071	−	1.49778i
$134$		−	3.05986i		−	0.264331i
$135$		0			0
$136$	−1.41654	+	0.817837i	−0.121467	+	0.0701290i
$137$	4.27427	−	2.46775i	0.365175	−	0.210834i	−0.306173	−	0.951976i	$-0.599049\pi$
$137$	4.27427	−	2.46775i	0.365175	−	0.210834i	0.671349	+	0.741142i	$0.265715\pi$
$138$		0			0
$139$			1.10583i			0.0937952i	0.998900	+	0.0468976i	$0.0149334\pi$
$139$			1.10583i			0.0937952i	−0.998900	+	0.0468976i	$0.985067\pi$
$140$	−0.149291	−	0.101102i	−0.0126174	−	0.00854471i
$141$		0			0
$142$	7.93854	−	13.7499i	0.666187	−	1.15387i
$143$	−1.22474	−	2.12132i	−0.102418	−	0.177394i
$144$		0			0
$145$	−0.426786	−	0.246405i	−0.0354426	−	0.0204628i
$146$	−7.81382			−0.646676
$147$		0			0
$148$	5.48993			0.451269
$149$	−0.275702	−	0.159176i	−0.0225863	−	0.0130402i	0.488664	−	0.872472i	$-0.337484\pi$
$149$	−0.275702	−	0.159176i	−0.0225863	−	0.0130402i	−0.511251	+	0.859432i	$0.670818\pi$
$150$		0			0
$151$	−1.76941	−	3.06471i	−0.143992	−	0.249402i	0.785004	−	0.619491i	$-0.212661\pi$
$151$	−1.76941	−	3.06471i	−0.143992	−	0.249402i	−0.928997	+	0.370088i	$0.879327\pi$
$152$	3.62863	−	6.28497i	0.294320	−	0.509778i
$153$		0			0
$154$	−2.19067	−	1.48356i	−0.176529	−	0.119549i
$155$			0.0158563i			0.00127361i
$156$		0			0
$157$	−5.64589	+	3.25966i	−0.450591	+	0.260149i	−0.708080	−	0.706132i	$-0.750438\pi$
$157$	−5.64589	+	3.25966i	−0.450591	+	0.260149i	0.257489	+	0.966281i	$0.417105\pi$
$158$	−9.98722	+	5.76612i	−0.794541	+	0.458728i
$159$		0			0
$160$		−	0.0681483i		−	0.00538760i
$161$	0.540436	+	1.11331i	0.0425923	+	0.0877411i
$162$		0			0
$163$	0.553536	−	0.958753i	0.0433563	−	0.0750954i	−0.843533	−	0.537078i	$-0.819528\pi$
$163$	0.553536	−	0.958753i	0.0433563	−	0.0750954i	0.886889	+	0.461982i	$0.152862\pi$
$164$	−2.69445	−	4.66693i	−0.210401	−	0.364426i
$165$		0			0
$166$	−14.8324	−	8.56350i	−1.15122	−	0.664657i
$167$	9.93426			0.768736			0.384368	−	0.923180i	$-0.374419\pi$
$167$	9.93426			0.768736			0.384368	+	0.923180i	$0.374419\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	0.0965346	+	0.0557343i	0.00740386	+	0.00427462i
$171$		0			0
$172$	4.82050	+	8.34935i	0.367560	+	0.636632i
$173$	6.61107	−	11.4507i	0.502630	−	0.870581i	−0.497365	−	0.867541i	$-0.665699\pi$
$173$	6.61107	−	11.4507i	0.502630	−	0.870581i	0.999995	−	0.00303994i	$-0.000967644\pi$
$174$		0			0
$175$	0.946464	−	13.1825i	0.0715459	−	0.996506i
$176$		−	1.00000i		−	0.0753778i
$177$		0			0
$178$	−9.24592	+	5.33814i	−0.693011	+	0.400110i
$179$	−9.79227	+	5.65357i	−0.731909	+	0.422568i	−0.819120	−	0.573622i	$-0.805538\pi$
$179$	−9.79227	+	5.65357i	−0.731909	+	0.422568i	0.0872113	+	0.996190i	$0.472204\pi$
$180$		0			0
$181$			8.26670i			0.614459i	0.951635	+	0.307230i	$0.0994020\pi$
$181$			8.26670i			0.614459i	−0.951635	+	0.307230i	$0.900598\pi$
$182$	−5.83013	+	2.83013i	−0.432158	+	0.209783i
$183$		0			0
$184$	−0.233875	+	0.405083i	−0.0172415	+	0.0298631i
$185$	−0.187065	−	0.324006i	−0.0137533	−	0.0238214i
$186$		0			0
$187$	1.41654	+	0.817837i	0.103587	+	0.0598062i
$188$	8.62398			0.628969
$189$		0			0
$190$	−0.494570			−0.0358799
$191$	−10.3133	−	5.95439i	−0.746245	−	0.430845i	0.0780906	−	0.996946i	$-0.475118\pi$
$191$	−10.3133	−	5.95439i	−0.746245	−	0.430845i	−0.824335	+	0.566102i	$0.808451\pi$
$192$		0			0
$193$	−12.7134	−	22.0203i	−0.915132	−	1.58506i	−0.806707	−	0.590951i	$-0.798753\pi$
$193$	−12.7134	−	22.0203i	−0.915132	−	1.58506i	−0.108425	−	0.994105i	$-0.534581\pi$
$194$	4.99938	−	8.65918i	0.358934	−	0.621693i
$195$		0			0
$196$	−4.33013	+	5.50000i	−0.309295	+	0.392857i
$197$		−	8.37821i		−	0.596923i	−0.954422	−	0.298461i	$-0.903527\pi$
$197$		−	8.37821i		−	0.596923i	0.954422	−	0.298461i	$-0.0964734\pi$
$198$		0			0
$199$	17.3736	−	10.0306i	1.23158	−	0.711053i	0.264220	−	0.964462i	$-0.414885\pi$
$199$	17.3736	−	10.0306i	1.23158	−	0.711053i	0.967359	+	0.253410i	$0.0815521\pi$
$200$	4.32611	−	2.49768i	0.305902	−	0.176612i
$201$		0			0
$202$		−	3.52056i		−	0.247706i
$203$	−10.7283	+	15.8417i	−0.752978	+	1.11187i
$204$		0			0
$205$	−0.183622	+	0.318043i	−0.0128248	+	0.0222131i
$206$	−7.99465	−	13.8471i	−0.557014	−	0.964776i
$207$		0			0
$208$	−2.12132	−	1.22474i	−0.147087	−	0.0849208i
$209$	−7.25725			−0.501995
$210$		0			0
$211$	2.96399			0.204050			0.102025	−	0.994782i	$-0.467468\pi$
$211$	2.96399			0.204050			0.102025	+	0.994782i	$0.467468\pi$
$212$	7.34278	+	4.23936i	0.504304	+	0.291160i
$213$		0			0
$214$	3.03225	+	5.25201i	0.207280	+	0.359020i
$215$	0.328509	−	0.568994i	0.0224041	−	0.0388051i
$216$		0			0
$217$	0.614014	+	0.0440843i	0.0416820	+	0.00299263i
$218$			18.0175i			1.22030i
$219$		0			0
$220$	−0.0590182	+	0.0340742i	−0.00397901	+	0.00229728i
$221$	3.46979	−	2.00328i	0.233403	−	0.134755i
$222$		0			0
$223$			13.8238i			0.925709i	0.886434	+	0.462854i	$0.153175\pi$
$223$			13.8238i			0.925709i	−0.886434	+	0.462854i	$0.846825\pi$
$224$	−2.63896	−	0.189469i	−0.176323	−	0.0126594i
$225$		0			0
$226$	3.52761	−	6.10999i	0.234653	−	0.406431i
$227$	11.1257	+	19.2702i	0.738437	+	1.27901i	0.953199	+	0.302345i	$0.0977693\pi$
$227$	11.1257	+	19.2702i	0.738437	+	1.27901i	−0.214761	+	0.976667i	$0.568897\pi$
$228$		0			0
$229$	12.3195	+	7.11269i	0.814098	+	0.470020i	0.848377	−	0.529393i	$-0.177580\pi$
$229$	12.3195	+	7.11269i	0.814098	+	0.470020i	−0.0342790	+	0.999412i	$0.510913\pi$
$230$	0.0318764			0.00210187
$231$		0			0
$232$	−7.23143			−0.474767
$233$	0.445759	+	0.257359i	0.0292027	+	0.0168602i	0.514530	−	0.857472i	$-0.327966\pi$
$233$	0.445759	+	0.257359i	0.0292027	+	0.0168602i	−0.485328	+	0.874332i	$0.661300\pi$
$234$		0			0
$235$	−0.293855	−	0.508972i	−0.0191690	−	0.0332017i
$236$	0.439158	−	0.760643i	0.0285867	−	0.0495137i
$237$		0			0
$238$	2.42663	−	3.58322i	0.157295	−	0.232266i
$239$			21.8238i			1.41166i	0.708380	+	0.705832i	$0.249426\pi$
$239$			21.8238i			1.41166i	−0.708380	+	0.705832i	$0.750574\pi$
$240$		0			0
$241$	−7.95439	+	4.59247i	−0.512387	+	0.295827i	−0.733814	−	0.679350i	$-0.762262\pi$
$241$	−7.95439	+	4.59247i	−0.512387	+	0.295827i	0.221427	+	0.975177i	$0.428929\pi$
$242$	−0.866025	+	0.500000i	−0.0556702	+	0.0321412i
$243$		0			0
$244$		−	9.96764i		−	0.638113i
$245$	0.472146	+	0.0681483i	0.0301643	+	0.00435384i
$246$		0			0
$247$	−8.88828	+	15.3950i	−0.565548	+	0.979558i
$248$	0.116337	+	0.201501i	0.00738738	+	0.0127953i
$249$		0			0
$250$	−0.589908	−	0.340583i	−0.0373091	−	0.0215404i
$251$	−31.3044			−1.97592			−0.987959	−	0.154718i	$-0.950553\pi$
$251$	−31.3044			−1.97592			−0.987959	+	0.154718i	$0.950553\pi$
$252$		0			0
$253$	0.467750			0.0294072
$254$	−5.92309	−	3.41970i	−0.371647	−	0.214571i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.01033	−	3.48200i	0.125401	−	0.217201i	−0.796489	−	0.604654i	$-0.793312\pi$
$257$	2.01033	−	3.48200i	0.125401	−	0.217201i	0.921890	+	0.387453i	$0.126645\pi$
$258$		0			0
$259$	−13.0668	+	6.34303i	−0.811931	+	0.394137i
$260$			0.166929i			0.0103525i
$261$		0			0
$262$	−1.31178	+	0.757359i	−0.0810423	+	0.0467898i
$263$	11.6746	−	6.74032i	0.719885	−	0.415626i	−0.0948253	−	0.995494i	$-0.530229\pi$
$263$	11.6746	−	6.74032i	0.719885	−	0.415626i	0.814710	+	0.579868i	$0.196896\pi$
$264$		0			0
$265$		−	0.577810i		−	0.0354946i
$266$	−1.37502	+	19.1516i	−0.0843080	+	1.17426i
$267$		0			0
$268$	−1.52993	+	2.64991i	−0.0934552	+	0.161869i
$269$	15.7399	+	27.2624i	0.959681	+	1.66222i	0.723273	+	0.690562i	$0.242637\pi$
$269$	15.7399	+	27.2624i	0.959681	+	1.66222i	0.236408	+	0.971654i	$0.424030\pi$
$270$		0			0
$271$	−4.89157	−	2.82415i	−0.297142	−	0.171555i	0.344017	−	0.938964i	$-0.388212\pi$
$271$	−4.89157	−	2.82415i	−0.297142	−	0.171555i	−0.641158	+	0.767409i	$0.721546\pi$
$272$	1.63567			0.0991773
$273$		0			0
$274$	−4.93550			−0.298164
$275$	−4.32611	−	2.49768i	−0.260874	−	0.150616i
$276$		0			0
$277$	−3.45982	−	5.99259i	−0.207881	−	0.360060i	0.743166	−	0.669107i	$-0.233323\pi$
$277$	−3.45982	−	5.99259i	−0.207881	−	0.360060i	−0.951047	+	0.309047i	$0.899990\pi$
$278$	0.552914	−	0.957676i	0.0331616	−	0.0574376i
$279$		0			0
$280$	0.0787382	+	0.162203i	0.00470551	+	0.00969346i
$281$			30.4582i			1.81698i	0.417902	+	0.908492i	$0.362766\pi$
$281$			30.4582i			1.81698i	−0.417902	+	0.908492i	$0.637234\pi$
$282$		0			0
$283$	−22.8490	+	13.1919i	−1.35823	+	0.784175i	−0.989385	−	0.145315i	$-0.953580\pi$
$283$	−22.8490	+	13.1919i	−1.35823	+	0.784175i	−0.368846	+	0.929490i	$0.620247\pi$
$284$	−13.7499	+	7.93854i	−0.815909	+	0.471065i
$285$		0			0
$286$			2.44949i			0.144841i
$287$	11.8053	+	7.99479i	0.696846	+	0.471917i
$288$		0			0
$289$	7.16228	−	12.4054i	0.421311	−	0.729732i
$290$	0.246405	+	0.426786i	0.0144694	+	0.0250617i
$291$		0			0
$292$	6.76696	+	3.90691i	0.396007	+	0.228634i
$293$	−15.0095			−0.876862			−0.438431	−	0.898765i	$-0.644466\pi$
$293$	−15.0095			−0.876862			−0.438431	+	0.898765i	$0.644466\pi$
$294$		0			0
$295$	−0.0598557			−0.00348494
$296$	−4.75442	−	2.74496i	−0.276345	−	0.159548i
$297$		0			0
$298$	0.159176	+	0.275702i	0.00922084	+	0.0159710i
$299$	0.572874	−	0.992248i	0.0331302	−	0.0573832i
$300$		0			0
$301$	−21.1203	−	14.3030i	−1.21735	−	0.824413i
$302$			3.53882i			0.203636i
$303$		0			0
$304$	−6.28497	+	3.62863i	−0.360467	+	0.208116i
$305$	−0.588272	+	0.339639i	−0.0336844	+	0.0194477i
$306$		0			0
$307$		−	15.0711i		−	0.860151i	−0.902793	−	0.430076i	$-0.858487\pi$
$307$		−	15.0711i		−	0.860151i	0.902793	−	0.430076i	$-0.141513\pi$
$308$	1.15539	+	2.38014i	0.0658347	+	0.135621i
$309$		0			0
$310$	0.00792814	−	0.0137319i	0.000450288	−	0.000779922i
$311$	9.93645	+	17.2104i	0.563445	+	0.975915i	0.997193	+	0.0748804i	$0.0238575\pi$
$311$	9.93645	+	17.2104i	0.563445	+	0.975915i	−0.433748	+	0.901034i	$0.642809\pi$
$312$		0			0
$313$	−7.81257	−	4.51059i	−0.441593	−	0.254954i	0.262680	−	0.964883i	$-0.415394\pi$
$313$	−7.81257	−	4.51059i	−0.441593	−	0.254954i	−0.704273	+	0.709929i	$0.748727\pi$
$314$	6.51931			0.367906
$315$		0			0
$316$	11.5322			0.648740
$317$	−10.2958	−	5.94427i	−0.578268	−	0.333863i	0.182177	−	0.983266i	$-0.441686\pi$
$317$	−10.2958	−	5.94427i	−0.578268	−	0.333863i	−0.760445	+	0.649403i	$0.775019\pi$
$318$		0			0
$319$	3.61571	+	6.26260i	0.202441	+	0.350638i
$320$	−0.0340742	+	0.0590182i	−0.00190480	+	0.00329922i
$321$		0			0
$322$	0.0886240	−	1.23437i	0.00493882	−	0.0687889i
$323$		−	11.8705i		−	0.660492i
$324$		0			0
$325$	−10.5967	+	6.11804i	−0.587802	+	0.339368i
$326$	−0.958753	+	0.553536i	−0.0531004	+	0.0306575i
$327$		0			0
$328$			5.38891i			0.297553i
$329$	−20.5263	+	9.96410i	−1.13165	+	0.549339i
$330$		0			0
$331$	−11.5175	+	19.9489i	−0.633061	+	1.09649i	0.353862	+	0.935298i	$0.384868\pi$
$331$	−11.5175	+	19.9489i	−0.633061	+	1.09649i	−0.986922	+	0.161196i	$0.948465\pi$
$332$	8.56350	+	14.8324i	0.469983	+	0.814035i
$333$		0			0
$334$	−8.60332	−	4.96713i	−0.470753	−	0.271789i
$335$	0.208524			0.0113929
$336$		0			0
$337$	−20.8191			−1.13409			−0.567045	−	0.823687i	$-0.691914\pi$
$337$	−20.8191			−1.13409			−0.567045	+	0.823687i	$0.691914\pi$
$338$	−6.06218	−	3.50000i	−0.329739	−	0.190375i
$339$		0			0
$340$	−0.0557343	−	0.0965346i	−0.00302261	−	0.00523532i
$341$	0.116337	−	0.201501i	0.00629998	−	0.0109119i
$342$		0			0
$343$	3.95164	−	18.0938i	0.213368	−	0.976972i
$344$		−	9.64100i		−	0.519808i
$345$		0			0
$346$	−11.4507	+	6.61107i	−0.615594	+	0.355413i
$347$	6.30751	−	3.64165i	0.338605	−	0.195494i	−0.321050	−	0.947062i	$-0.604036\pi$
$347$	6.30751	−	3.64165i	0.338605	−	0.195494i	0.659655	+	0.751569i	$0.270702\pi$
$348$		0			0
$349$			33.7366i			1.80588i	0.429767	+	0.902940i	$0.358596\pi$
$349$			33.7366i			1.80588i	−0.429767	+	0.902940i	$0.641404\pi$
$350$	−7.41093	+	10.9432i	−0.396131	+	0.584938i
$351$		0			0
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	8.71467	+	15.0943i	0.463835	+	0.803386i	0.999148	−	0.0412678i	$-0.0131397\pi$
$353$	8.71467	+	15.0943i	0.463835	+	0.803386i	−0.535313	+	0.844654i	$0.679806\pi$
$354$		0			0
$355$	0.937036	+	0.540998i	0.0497327	+	0.0287132i
$356$	10.6763			0.565841
$357$		0			0
$358$	11.3071			0.597601
$359$	−22.6722	−	13.0898i	−1.19659	−	0.690852i	−0.236798	−	0.971559i	$-0.576098\pi$
$359$	−22.6722	−	13.0898i	−1.19659	−	0.690852i	−0.959794	+	0.280707i	$0.909431\pi$
$360$		0			0
$361$	16.8339	+	29.1571i	0.885992	+	1.53458i
$362$	4.13335	−	7.15918i	0.217244	−	0.376278i
$363$		0			0
$364$	6.46410	+	0.464102i	0.338811	+	0.0243255i
$365$		−	0.532499i		−	0.0278723i
$366$		0			0
$367$	9.91510	−	5.72449i	0.517564	−	0.298816i	−0.218373	−	0.975865i	$-0.570075\pi$
$367$	9.91510	−	5.72449i	0.517564	−	0.298816i	0.735937	+	0.677050i	$0.236742\pi$
$368$	0.405083	−	0.233875i	0.0211164	−	0.0121916i
$369$		0			0
$370$			0.374129i			0.0194501i
$371$	−22.3750	−	1.60645i	−1.16165	−	0.0834028i
$372$		0			0
$373$	14.1189	−	24.4546i	0.731048	−	1.26621i	−0.225388	−	0.974269i	$-0.572365\pi$
$373$	14.1189	−	24.4546i	0.731048	−	1.26621i	0.956436	−	0.291943i	$-0.0943016\pi$
$374$	−0.817837	−	1.41654i	−0.0422894	−	0.0732473i
$375$		0			0
$376$	−7.46859	−	4.31199i	−0.385163	−	0.222374i
$377$	17.7133			0.912282
$378$		0			0
$379$	9.93550			0.510352			0.255176	−	0.966895i	$-0.417867\pi$
$379$	9.93550			0.510352			0.255176	+	0.966895i	$0.417867\pi$
$380$	0.428310	+	0.247285i	0.0219718	+	0.0126854i
$381$		0			0
$382$	5.95439	+	10.3133i	0.304653	+	0.527675i
$383$	−6.97381	+	12.0790i	−0.356345	+	0.617208i	−0.987347	−	0.158573i	$-0.949311\pi$
$383$	−6.97381	+	12.0790i	−0.356345	+	0.617208i	0.631002	+	0.775781i	$0.282644\pi$
$384$		0			0
$385$	0.101102	−	0.149291i	0.00515266	−	0.00760855i
$386$			25.4269i			1.29419i
$387$		0			0
$388$	−8.65918	+	4.99938i	−0.439603	+	0.253805i
$389$	1.53141	−	0.884161i	0.0776457	−	0.0448288i	−0.460674	−	0.887569i	$-0.652392\pi$
$389$	1.53141	−	0.884161i	0.0776457	−	0.0448288i	0.538320	+	0.842740i	$0.319059\pi$
$390$		0			0
$391$			0.765087i			0.0386921i
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$		0			0
$394$	−4.18910	+	7.25574i	−0.211044	+	0.365539i
$395$	−0.392952	−	0.680613i	−0.0197716	−	0.0342453i
$396$		0			0
$397$	−1.04114	−	0.601102i	−0.0522533	−	0.0301685i	0.473646	−	0.880715i	$-0.342938\pi$
$397$	−1.04114	−	0.601102i	−0.0522533	−	0.0301685i	−0.525899	+	0.850547i	$0.676271\pi$
$398$	−20.0613			−1.00558
$399$		0			0
$400$	−4.99536			−0.249768
$401$	−15.4934	−	8.94510i	−0.773702	−	0.446697i	0.0604915	−	0.998169i	$-0.480733\pi$
$401$	−15.4934	−	8.94510i	−0.773702	−	0.446697i	−0.834194	+	0.551472i	$0.814067\pi$
$402$		0			0
$403$	−0.284965	−	0.493574i	−0.0141951	−	0.0245867i
$404$	−1.76028	+	3.04889i	−0.0875771	+	0.151688i
$405$		0			0
$406$	17.2118	−	8.35515i	0.854208	−	0.414659i
$407$			5.48993i			0.272126i
$408$		0			0
$409$	−1.35436	+	0.781939i	−0.0669687	+	0.0386644i	−0.533110	−	0.846046i	$-0.678977\pi$
$409$	−1.35436	+	0.781939i	−0.0669687	+	0.0386644i	0.466142	+	0.884710i	$0.345644\pi$
$410$	0.318043	−	0.183622i	0.0157070	−	0.00906847i
$411$		0			0
$412$			15.9893i			0.787736i
$413$	−0.166413	+	2.31784i	−0.00818866	+	0.114053i
$414$		0			0
$415$	0.583589	−	1.01081i	0.0286472	−	0.0496185i
$416$	1.22474	+	2.12132i	0.0600481	+	0.104006i
$417$		0			0
$418$	6.28497	+	3.62863i	0.307408	+	0.177482i
$419$	4.99020			0.243787			0.121894	−	0.992543i	$-0.461103\pi$
$419$	4.99020			0.243787			0.121894	+	0.992543i	$0.461103\pi$
$420$		0			0
$421$	−37.0235			−1.80441			−0.902207	−	0.431302i	$-0.858054\pi$
$421$	−37.0235			−1.80441			−0.902207	+	0.431302i	$0.858054\pi$
$422$	−2.56689	−	1.48200i	−0.124954	−	0.0721425i
$423$		0			0
$424$	−4.23936	−	7.34278i	−0.205881	−	0.356597i
$425$	4.08539	−	7.07610i	0.198170	−	0.343241i
$426$		0			0
$427$	11.5166	+	23.7244i	0.557325	+	1.14810i
$428$		−	6.06450i		−	0.293139i
$429$		0			0
$430$	−0.568994	+	0.328509i	−0.0274393	+	0.0158421i
$431$	11.4567	−	6.61453i	0.551850	−	0.318611i	−0.198018	−	0.980198i	$-0.563450\pi$
$431$	11.4567	−	6.61453i	0.551850	−	0.318611i	0.749868	+	0.661588i	$0.230117\pi$
$432$		0			0
$433$		−	12.5794i		−	0.604527i	−0.953224	−	0.302263i	$-0.902258\pi$
$433$		−	12.5794i		−	0.604527i	0.953224	−	0.302263i	$-0.0977422\pi$
$434$	−0.509710	−	0.345185i	−0.0244669	−	0.0165694i
$435$		0			0
$436$	9.00877	−	15.6036i	0.431442	−	0.747279i
$437$	−1.69729	−	2.93979i	−0.0811924	−	0.140629i
$438$		0			0
$439$	−15.2358	−	8.79639i	−0.727165	−	0.419829i	0.0902191	−	0.995922i	$-0.471243\pi$
$439$	−15.2358	−	8.79639i	−0.727165	−	0.419829i	−0.817384	+	0.576093i	$0.804577\pi$
$440$	0.0681483			0.00324884
$441$		0			0
$442$	−4.00657			−0.190573
$443$	−23.4746	−	13.5531i	−1.11531	−	0.643926i	−0.175112	−	0.984549i	$-0.556029\pi$
$443$	−23.4746	−	13.5531i	−1.11531	−	0.643926i	−0.940200	+	0.340623i	$0.889362\pi$
$444$		0			0
$445$	−0.363785	−	0.630094i	−0.0172451	−	0.0298693i
$446$	6.91189	−	11.9717i	0.327288	−	0.566879i
$447$		0			0
$448$	2.19067	+	1.48356i	0.103499	+	0.0700918i
$449$		−	14.9950i		−	0.707658i	−0.935310	−	0.353829i	$-0.884879\pi$
$449$		−	14.9950i		−	0.707658i	0.935310	−	0.353829i	$-0.115121\pi$
$450$		0			0
$451$	4.66693	−	2.69445i	0.219757	−	0.126877i
$452$	−6.10999	+	3.52761i	−0.287390	+	0.165925i
$453$		0			0
$454$		−	22.2514i		−	1.04431i
$455$	−0.192868	−	0.397314i	−0.00904181	−	0.0186263i
$456$		0			0
$457$	0.475430	−	0.823468i	0.0222397	−	0.0385202i	−0.854691	−	0.519136i	$-0.826254\pi$
$457$	0.475430	−	0.823468i	0.0222397	−	0.0385202i	0.876931	+	0.480616i	$0.159587\pi$
$458$	−7.11269	−	12.3195i	−0.332354	−	0.575654i
$459$		0			0
$460$	−0.0276058	−	0.0159382i	−0.00128713	−	0.000743122i
$461$	17.7698			0.827621			0.413810	−	0.910363i	$-0.364198\pi$
$461$	17.7698			0.827621			0.413810	+	0.910363i	$0.364198\pi$
$462$		0			0
$463$	1.21592			0.0565088			0.0282544	−	0.999601i	$-0.491005\pi$
$463$	1.21592			0.0565088			0.0282544	+	0.999601i	$0.491005\pi$
$464$	6.26260	+	3.61571i	0.290734	+	0.167855i
$465$		0			0
$466$	−0.257359	−	0.445759i	−0.0119219	−	0.0206494i
$467$	−4.45982	+	7.72464i	−0.206376	+	0.357454i	−0.950570	−	0.310510i	$-0.899500\pi$
$467$	−4.45982	+	7.72464i	−0.206376	+	0.357454i	0.744194	+	0.667963i	$0.232834\pi$
$468$		0			0
$469$	0.579747	−	8.07483i	0.0267702	−	0.372861i
$470$			0.587710i			0.0271090i
$471$		0			0
$472$	−0.760643	+	0.439158i	−0.0350114	+	0.0202139i
$473$	−8.34935	+	4.82050i	−0.383903	+	0.221647i
$474$		0			0
$475$			36.2526i			1.66338i
$476$	−3.89313	+	1.88985i	−0.178441	+	0.0866211i
$477$		0			0
$478$	10.9119	−	18.9000i	0.499098	−	0.864464i
$479$	10.3161	+	17.8680i	0.471355	+	0.816411i	0.999463	−	0.0327661i	$-0.0104317\pi$
$479$	10.3161	+	17.8680i	0.471355	+	0.816411i	−0.528108	+	0.849177i	$0.677098\pi$
$480$		0			0
$481$	11.6459	+	6.72376i	0.531007	+	0.306577i
$482$	9.18494			0.418363
$483$		0			0
$484$	1.00000			0.0454545
$485$	0.590109	+	0.340699i	0.0267954	+	0.0154704i
$486$		0			0
$487$	−0.0189644	−	0.0328473i	−0.000859360	−	0.00148845i	0.865595	−	0.500744i	$-0.166940\pi$
$487$	−0.0189644	−	0.0328473i	−0.000859360	−	0.00148845i	−0.866455	+	0.499256i	$0.833607\pi$
$488$	−4.98382	+	8.63223i	−0.225607	+	0.390763i
$489$		0			0
$490$	−0.374816	−	0.295091i	−0.0169325	−	0.0133309i
$491$			34.6919i			1.56562i	0.622258	+	0.782812i	$0.286215\pi$
$491$			34.6919i			1.56562i	−0.622258	+	0.782812i	$0.713785\pi$
$492$		0			0
$493$	−10.2436	+	5.91413i	−0.461347	+	0.266359i
$494$	15.3950	−	8.88828i	0.692652	−	0.399903i
$495$		0			0
$496$		−	0.232673i		−	0.0104473i
$497$	23.5546	−	34.7814i	1.05657	−	1.56016i
$498$		0			0
$499$	10.2268	−	17.7133i	0.457814	−	0.792957i	−0.541031	−	0.841002i	$-0.681966\pi$
$499$	10.2268	−	17.7133i	0.457814	−	0.792957i	0.998845	+	0.0480457i	$0.0152993\pi$
$500$	0.340583	+	0.589908i	0.0152314	+	0.0263815i
$501$		0			0
$502$	27.1104	+	15.6522i	1.21000	+	0.698592i
$503$	−31.4660			−1.40300			−0.701501	−	0.712669i	$-0.747486\pi$
$503$	−31.4660			−1.40300			−0.701501	+	0.712669i	$0.747486\pi$
$504$		0			0
$505$	0.239920			0.0106763
$506$	−0.405083	−	0.233875i	−0.0180082	−	0.0103970i
$507$		0			0
$508$	3.41970	+	5.92309i	0.151724	+	0.262794i
$509$	−4.97798	+	8.62211i	−0.220645	+	0.382168i	−0.955004	−	0.296593i	$-0.904150\pi$
$509$	−4.97798	+	8.62211i	−0.220645	+	0.382168i	0.734359	+	0.678761i	$0.237483\pi$
$510$		0			0
$511$	−20.6203	−	1.48047i	−0.912190	−	0.0654923i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−3.48200	+	2.01033i	−0.153584	+	0.0886720i
$515$	0.943660	−	0.544822i	0.0415826	−	0.0240077i
$516$		0			0
$517$			8.62398i			0.379282i
$518$	14.4877	+	1.04017i	0.636552	+	0.0457024i
$519$		0			0
$520$	0.0834643	−	0.144564i	0.00366015	−	0.00633957i
$521$	−20.4947	−	35.4979i	−0.897891	−	1.55519i	−0.830186	−	0.557487i	$-0.811766\pi$
$521$	−20.4947	−	35.4979i	−0.897891	−	1.55519i	−0.0677047	−	0.997705i	$-0.521568\pi$
$522$		0			0
$523$	32.0347	+	18.4952i	1.40078	+	0.808741i	0.994473	−	0.104996i	$-0.0334829\pi$
$523$	32.0347	+	18.4952i	1.40078	+	0.808741i	0.406307	+	0.913736i	$0.366816\pi$
$524$	1.51472			0.0661708
$525$		0			0
$526$	−13.4806			−0.587784
$527$	0.329590	+	0.190289i	0.0143571	+	0.00828910i
$528$		0			0
$529$	−11.3906	−	19.7291i	−0.495244	−	0.857787i
$530$	−0.288905	+	0.500398i	−0.0125492	+	0.0217359i
$531$		0			0
$532$	10.7666	−	15.8983i	0.466791	−	0.689277i
$533$		−	13.2001i		−	0.571758i
$534$		0			0
$535$	−0.357916	+	0.206643i	−0.0154741	+	0.00893395i
$536$	2.64991	−	1.52993i	0.114459	−	0.0660828i
$537$		0			0
$538$		−	31.4799i		−	1.35719i
$539$	−5.50000	−	4.33013i	−0.236902	−	0.186512i
$540$		0			0
$541$	17.7301	−	30.7095i	0.762277	−	1.32030i	−0.179397	−	0.983777i	$-0.557415\pi$
$541$	17.7301	−	30.7095i	0.762277	−	1.32030i	0.941674	−	0.336526i	$-0.109252\pi$
$542$	2.82415	+	4.89157i	0.121308	+	0.210111i
$543$		0			0
$544$	−1.41654	−	0.817837i	−0.0607335	−	0.0350645i
$545$	−1.22786			−0.0525960
$546$		0			0
$547$	33.2066			1.41981			0.709907	−	0.704296i	$-0.248737\pi$
$547$	33.2066			1.41981			0.709907	+	0.704296i	$0.248737\pi$
$548$	4.27427	+	2.46775i	0.182588	+	0.105417i
$549$		0			0
$550$	2.49768	+	4.32611i	0.106501	+	0.184466i
$551$	26.2402	−	45.4493i	1.11787	−	1.93620i
$552$		0			0
$553$	−27.4484	+	13.3243i	−1.16722	+	0.566607i
$554$			6.91964i			0.293987i
$555$		0			0
$556$	−0.957676	+	0.552914i	−0.0406145	+	0.0234488i
$557$	1.95592	−	1.12925i	0.0828748	−	0.0478478i	−0.457990	−	0.888957i	$-0.651430\pi$
$557$	1.95592	−	1.12925i	0.0828748	−	0.0478478i	0.540865	+	0.841110i	$0.318097\pi$
$558$		0			0
$559$			23.6155i			0.998830i
$560$	0.0129120	−	0.179841i	0.000545631	−	0.00759965i
$561$		0			0
$562$	15.2291	−	26.3776i	0.642401	−	1.11267i
$563$	4.02066	+	6.96399i	0.169451	+	0.293497i	0.938227	−	0.346021i	$-0.112467\pi$
$563$	4.02066	+	6.96399i	0.169451	+	0.293497i	−0.768776	+	0.639518i	$0.779134\pi$
$564$		0			0
$565$	0.416386	+	0.240401i	0.0175175	+	0.0101137i
$566$	26.3837			1.10899
$567$		0			0
$568$	15.8771			0.666187
$569$	−15.6841	−	9.05521i	−0.657511	−	0.379614i	0.133817	−	0.991006i	$-0.457277\pi$
$569$	−15.6841	−	9.05521i	−0.657511	−	0.379614i	−0.791328	+	0.611392i	$0.790610\pi$
$570$		0			0
$571$	−7.15006	−	12.3843i	−0.299221	−	0.518266i	0.676737	−	0.736225i	$-0.263393\pi$
$571$	−7.15006	−	12.3843i	−0.299221	−	0.518266i	−0.975958	+	0.217959i	$0.930060\pi$
$572$	1.22474	−	2.12132i	0.0512092	−	0.0886969i
$573$		0			0
$574$	−6.22631	−	12.8263i	−0.259881	−	0.535361i
$575$		−	2.33658i		−	0.0974420i
$576$		0			0
$577$	−27.3960	+	15.8171i	−1.14051	+	0.658475i	−0.946557	−	0.322536i	$-0.895465\pi$
$577$	−27.3960	+	15.8171i	−1.14051	+	0.658475i	−0.193955	+	0.981011i	$0.562131\pi$
$578$	−12.4054	+	7.16228i	−0.515998	+	0.297912i
$579$		0			0
$580$		−	0.492810i		−	0.0204628i
$581$	−37.5196	−	25.4090i	−1.55658	−	1.05414i
$582$		0			0
$583$	−4.23936	+	7.34278i	−0.175576	+	0.304107i
$584$	−3.90691	−	6.76696i	−0.161669	−	0.280019i
$585$		0			0
$586$	12.9986	+	7.50473i	0.536966	+	0.310017i
$587$	25.9909			1.07276			0.536381	−	0.843976i	$-0.319791\pi$
$587$	25.9909			1.07276			0.536381	+	0.843976i	$0.319791\pi$
$588$		0			0
$589$	−1.68857			−0.0695762
$590$	0.0518366	+	0.0299279i	0.00213408	+	0.00123211i
$591$		0			0
$592$	2.74496	+	4.75442i	0.112817	+	0.195405i
$593$	15.0260	−	26.0258i	0.617043	−	1.06875i	−0.372979	−	0.927840i	$-0.621664\pi$
$593$	15.0260	−	26.0258i	0.617043	−	1.06875i	0.990022	−	0.140911i	$-0.0450030\pi$
$594$		0			0
$595$	0.244191	+	0.165371i	0.0100108	+	0.00677954i
$596$		−	0.318353i		−	0.0130402i
$597$		0			0
$598$	−0.992248	+	0.572874i	−0.0405760	+	0.0234266i
$599$	−8.18991	+	4.72844i	−0.334631	+	0.193199i	−0.657895	−	0.753110i	$-0.728553\pi$
$599$	−8.18991	+	4.72844i	−0.334631	+	0.193199i	0.323265	+	0.946309i	$0.395220\pi$
$600$		0			0
$601$			2.30182i			0.0938931i	0.998897	+	0.0469465i	$0.0149490\pi$
$601$			2.30182i			0.0938931i	−0.998897	+	0.0469465i	$0.985051\pi$
$602$	11.1392	+	22.9469i	0.453998	+	0.935247i
$603$		0			0
$604$	1.76941	−	3.06471i	0.0719962	−	0.124701i
$605$	−0.0340742	−	0.0590182i	−0.00138531	−	0.00239943i
$606$		0			0
$607$	−3.13710	−	1.81121i	−0.127331	−	0.0735145i	0.434982	−	0.900439i	$-0.356755\pi$
$607$	−3.13710	−	1.81121i	−0.127331	−	0.0735145i	−0.562313	+	0.826925i	$0.690088\pi$
$608$	7.25725			0.294320
$609$		0			0
$610$	0.679278			0.0275032
$611$	18.2942	+	10.5622i	0.740105	+	0.427300i
$612$		0			0
$613$	4.97209	+	8.61192i	0.200821	+	0.347832i	0.948793	−	0.315898i	$-0.102306\pi$
$613$	4.97209	+	8.61192i	0.200821	+	0.347832i	−0.747972	+	0.663730i	$0.768972\pi$
$614$	−7.53553	+	13.0519i	−0.304109	+	0.526733i
$615$		0			0
$616$	0.189469	−	2.63896i	0.00763391	−	0.106327i
$617$		−	5.20936i		−	0.209721i	−0.994487	−	0.104860i	$-0.966560\pi$
$617$		−	5.20936i		−	0.209721i	0.994487	−	0.104860i	$-0.0334396\pi$
$618$		0			0
$619$	10.6324	−	6.13859i	0.427350	−	0.246731i	−0.270867	−	0.962617i	$-0.587310\pi$
$619$	10.6324	−	6.13859i	0.427350	−	0.246731i	0.698217	+	0.715886i	$0.253977\pi$
$620$	−0.0137319	+	0.00792814i	−0.000551488	+	0.000318402i
$621$		0			0
$622$		−	19.8729i		−	0.796831i
$623$	−25.4110	+	12.3353i	−1.01807	+	0.494204i
$624$		0			0
$625$	−12.4652	+	21.5903i	−0.498607	+	0.863613i
$626$	4.51059	+	7.81257i	0.180279	+	0.312253i
$627$		0			0
$628$	−5.64589	−	3.25966i	−0.225296	−	0.130074i
$629$	−8.97973			−0.358045
$630$		0			0
$631$	1.18708			0.0472568			0.0236284	−	0.999721i	$-0.492478\pi$
$631$	1.18708			0.0472568			0.0236284	+	0.999721i	$0.492478\pi$
$632$	−9.98722	−	5.76612i	−0.397270	−	0.229364i
$633$		0			0
$634$	5.94427	+	10.2958i	0.236077	+	0.408897i
$635$	0.233047	−	0.403649i	0.00924817	−	0.0160183i
$636$		0			0
$637$	−15.9217	+	6.36396i	−0.630840	+	0.252149i
$638$		−	7.23143i		−	0.286295i
$639$		0			0
$640$	0.0590182	−	0.0340742i	0.00233290	−	0.00134690i
$641$	32.2791	−	18.6364i	1.27495	−	0.736092i	0.299033	−	0.954243i	$-0.403336\pi$
$641$	32.2791	−	18.6364i	1.27495	−	0.736092i	0.975915	+	0.218151i	$0.0700025\pi$
$642$		0			0
$643$			2.75684i			0.108719i	0.998521	+	0.0543597i	$0.0173117\pi$
$643$			2.75684i			0.108719i	−0.998521	+	0.0543597i	$0.982688\pi$
$644$	−0.693937	+	1.02469i	−0.0273450	+	0.0403783i
$645$		0			0
$646$	−5.93525	+	10.2802i	−0.233519	+	0.404467i
$647$	15.2508	+	26.4151i	0.599570	+	1.03849i	0.992884	+	0.119081i	$0.0379950\pi$
$647$	15.2508	+	26.4151i	0.599570	+	1.03849i	−0.393315	+	0.919404i	$0.628672\pi$
$648$		0			0
$649$	0.760643	+	0.439158i	0.0298579	+	0.0172384i
$650$	12.2361			0.479938
$651$		0			0
$652$	1.10707			0.0433563
$653$	−9.77473	−	5.64344i	−0.382515	−	0.220845i	0.296397	−	0.955065i	$-0.404215\pi$
$653$	−9.77473	−	5.64344i	−0.382515	−	0.220845i	−0.678912	+	0.734220i	$0.737548\pi$
$654$		0			0
$655$	−0.0516128	−	0.0893960i	−0.00201668	−	0.00349299i
$656$	2.69445	−	4.66693i	0.105201	−	0.182213i
$657$		0			0
$658$	22.7583	+	1.63397i	0.887212	+	0.0636990i
$659$			10.2338i			0.398652i	0.979933	+	0.199326i	$0.0638753\pi$
$659$			10.2338i			0.398652i	−0.979933	+	0.199326i	$0.936125\pi$
$660$		0			0
$661$	−19.6739	+	11.3587i	−0.765226	+	0.441803i	−0.831169	−	0.556020i	$-0.812328\pi$
$661$	−19.6739	+	11.3587i	−0.765226	+	0.441803i	0.0659431	+	0.997823i	$0.478994\pi$
$662$	19.9489	−	11.5175i	0.775338	−	0.447642i
$663$		0			0
$664$		−	17.1270i		−	0.664657i
$665$	−1.30515	−	0.0937055i	−0.0506115	−	0.00363374i
$666$		0			0
$667$	−1.69125	+	2.92933i	−0.0654855	+	0.113424i
$668$	4.96713	+	8.60332i	0.192184	+	0.332872i
$669$		0			0
$670$	−0.180587	−	0.104262i	−0.00697669	−	0.00402799i
$671$	9.96764			0.384797
$672$		0			0
$673$	−28.2268			−1.08806			−0.544031	−	0.839065i	$-0.683103\pi$
$673$	−28.2268			−1.08806			−0.544031	+	0.839065i	$0.683103\pi$
$674$	18.0299	+	10.4096i	0.694486	+	0.400962i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	8.40665	−	14.5607i	0.323094	−	0.559615i	−0.658031	−	0.752991i	$-0.728610\pi$
$677$	8.40665	−	14.5607i	0.323094	−	0.559615i	0.981125	+	0.193376i	$0.0619437\pi$
$678$		0			0
$679$	14.8338	−	21.9040i	0.569269	−	0.840598i
$680$			0.111469i			0.00427462i
$681$		0			0
$682$	−0.201501	+	0.116337i	−0.00771586	+	0.00445476i
$683$	17.9178	−	10.3448i	0.685604	−	0.395834i	−0.116359	−	0.993207i	$-0.537122\pi$
$683$	17.9178	−	10.3448i	0.685604	−	0.395834i	0.801963	+	0.597374i	$0.203789\pi$
$684$		0			0
$685$		−	0.336346i		−	0.0128511i
$686$	−12.4691	+	13.6938i	−0.476073	+	0.522834i
$687$		0			0
$688$	−4.82050	+	8.34935i	−0.183780	+	0.318316i
$689$	10.3843	+	17.9861i	0.395609	+	0.685215i
$690$		0			0
$691$	40.3537	+	23.2982i	1.53513	+	0.886306i	0.999114	+	0.0420972i	$0.0134039\pi$
$691$	40.3537	+	23.2982i	1.53513	+	0.886306i	0.536014	+	0.844209i	$0.319929\pi$
$692$	13.2221			0.502630
$693$		0			0
$694$	−7.28329			−0.276470
$695$	0.0652640	+	0.0376802i	0.00247561	+	0.00142929i
$696$		0			0
$697$	4.40725	+	7.63358i	0.166936	+	0.289142i
$698$	16.8683	−	29.2168i	0.638475	−	1.10587i
$699$		0			0
$700$	11.8896	−	5.77161i	0.449386	−	0.218146i
$701$		−	25.8612i		−	0.976765i	−0.872630	−	0.488382i	$-0.837587\pi$
$701$		−	25.8612i		−	0.976765i	0.872630	−	0.488382i	$-0.162413\pi$
$702$		0			0
$703$	34.5040	−	19.9209i	1.30134	−	0.751331i
$704$	0.866025	−	0.500000i	0.0326396	−	0.0188445i
$705$		0			0
$706$		−	17.4293i		−	0.655962i
$707$	0.667035	−	9.29061i	0.0250864	−	0.349409i
$708$		0			0
$709$	−10.3750	+	17.9700i	−0.389641	+	0.674878i	−0.992401	−	0.123044i	$-0.960734\pi$
$709$	−10.3750	+	17.9700i	−0.389641	+	0.674878i	0.602760	+	0.797923i	$0.294068\pi$
$710$	−0.540998	−	0.937036i	−0.0203033	−	0.0351663i
$711$		0			0
$712$	−9.24592	−	5.33814i	−0.346506	−	0.200055i
$713$	0.108833			0.00407582
$714$		0			0
$715$	−0.166929			−0.00624278
$716$	−9.79227	−	5.65357i	−0.365954	−	0.211284i
$717$		0			0
$718$	13.0898	+	22.6722i	0.488506	+	0.846118i
$719$	12.4722	−	21.6025i	0.465136	−	0.805639i	−0.534072	−	0.845439i	$-0.679339\pi$
$719$	12.4722	−	21.6025i	0.465136	−	0.805639i	0.999208	+	0.0398001i	$0.0126721\pi$
$720$		0			0
$721$	−18.4740	−	38.0568i	−0.688006	−	1.41731i
$722$		−	33.6677i		−	1.25298i
$723$		0			0
$724$	−7.15918	+	4.13335i	−0.266069	+	0.153615i
$725$	31.2839	−	18.0618i	1.16186	−	0.670798i
$726$		0			0
$727$		−	19.4534i		−	0.721487i	−0.932665	−	0.360743i	$-0.882523\pi$
$727$		−	19.4534i		−	0.721487i	0.932665	−	0.360743i	$-0.117477\pi$
$728$	−5.36603	−	3.63397i	−0.198878	−	0.134684i
$729$		0			0
$730$	−0.266249	+	0.461157i	−0.00985433	+	0.0170682i
$731$	−7.88477	−	13.6568i	−0.291629	−	0.505116i
$732$		0			0
$733$	2.02326	+	1.16813i	0.0747309	+	0.0431459i	0.536900	−	0.843646i	$-0.319595\pi$
$733$	2.02326	+	1.16813i	0.0747309	+	0.0431459i	−0.462169	+	0.886792i	$0.652929\pi$
$734$	−11.4490			−0.422589
$735$		0			0
$736$	−0.467750			−0.0172415
$737$	−2.64991	−	1.52993i	−0.0976108	−	0.0563556i
$738$		0			0
$739$	−18.2066	−	31.5348i	−0.669742	−	1.16003i	−0.977976	−	0.208717i	$-0.933071\pi$
$739$	−18.2066	−	31.5348i	−0.669742	−	1.16003i	0.308234	−	0.951310i	$-0.400262\pi$
$740$	0.187065	−	0.324006i	0.00687663	−	0.0119107i
$741$		0			0
$742$	18.5741	+	12.5787i	0.681876	+	0.461779i
$743$		−	52.1166i		−	1.91197i	−0.293409	−	0.955987i	$-0.594790\pi$
$743$		−	52.1166i		−	1.91197i	0.293409	−	0.955987i	$-0.405210\pi$
$744$		0			0
$745$	−0.0187886	+	0.0108476i	−0.000688361	+	0.000397425i
$746$	−24.4546	+	14.1189i	−0.895347	+	0.516929i
$747$		0			0
$748$			1.63567i			0.0598062i
$749$	7.00689	+	14.4344i	0.256026	+	0.527420i
$750$		0			0
$751$	4.88661	−	8.46385i	0.178315	−	0.308850i	−0.762989	−	0.646412i	$-0.776269\pi$
$751$	4.88661	−	8.46385i	0.178315	−	0.308850i	0.941303	+	0.337562i	$0.109602\pi$
$752$	4.31199	+	7.46859i	0.157242	+	0.272351i
$753$		0			0
$754$	−15.3402	−	8.85666i	−0.558656	−	0.322540i
$755$	−0.241165			−0.00877688
$756$		0			0
$757$	27.6251			1.00405			0.502026	−	0.864852i	$-0.332588\pi$
$757$	27.6251			1.00405			0.502026	+	0.864852i	$0.332588\pi$
$758$	−8.60440	−	4.96775i	−0.312526	−	0.180437i
$759$		0			0
$760$	−0.247285	−	0.428310i	−0.00896997	−	0.0155364i
$761$	10.0318	−	17.3755i	0.363651	−	0.629863i	−0.624907	−	0.780699i	$-0.714863\pi$
$761$	10.0318	−	17.3755i	0.363651	−	0.629863i	0.988559	+	0.150836i	$0.0481966\pi$
$762$		0			0
$763$	−3.41376	+	47.5475i	−0.123586	+	1.72134i
$764$		−	11.9088i		−	0.430845i
$765$		0			0
$766$	12.0790	−	6.97381i	0.436432	−	0.251974i
$767$	1.86319	−	1.07571i	0.0672758	−	0.0388417i
$768$		0			0
$769$		−	31.4568i		−	1.13436i	−0.823593	−	0.567181i	$-0.808034\pi$
$769$		−	31.4568i		−	1.13436i	0.823593	−	0.567181i	$-0.191966\pi$
$770$	−0.162203	+	0.0787382i	−0.00584537	+	0.00283753i
$771$		0			0
$772$	12.7134	−	22.0203i	0.457566	−	0.792528i
$773$	−3.56548	−	6.17559i	−0.128241	−	0.222121i	0.794754	−	0.606932i	$-0.207600\pi$
$773$	−3.56548	−	6.17559i	−0.128241	−	0.222121i	−0.922995	+	0.384811i	$0.874267\pi$
$774$		0			0
$775$	−1.00657	−	0.581142i	−0.0361570	−	0.0208752i
$776$	9.99876			0.358934
$777$		0			0
$778$	−1.76832			−0.0633974
$779$	−33.8691	−	19.5543i	−1.21349	−	0.700606i
$780$		0			0
$781$	−7.93854	−	13.7499i	−0.284063	−	0.492012i
$782$	0.382543	−	0.662585i	0.0136797	−	0.0236940i
$783$		0			0
$784$	−6.92820	−	1.00000i	−0.247436	−	0.0357143i
$785$			0.444280i			0.0158570i
$786$		0			0
$787$	20.7613	−	11.9865i	0.740061	−	0.427274i	−0.0820306	−	0.996630i	$-0.526141\pi$
$787$	20.7613	−	11.9865i	0.740061	−	0.427274i	0.822091	+	0.569356i	$0.192807\pi$
$788$	7.25574	−	4.18910i	0.258475	−	0.149231i
$789$		0			0
$790$			0.785904i			0.0279612i
$791$	10.4669	−	15.4556i	0.372159	−	0.549539i
$792$		0			0
$793$	12.2078	−	21.1446i	0.433512	−	0.750866i
$794$	0.601102	+	1.04114i	0.0213323	+	0.0369487i
$795$		0			0
$796$	17.3736	+	10.0306i	0.615790	+	0.355526i
$797$	−7.65551			−0.271172			−0.135586	−	0.990766i	$-0.543292\pi$
$797$	−7.65551			−0.271172			−0.135586	+	0.990766i	$0.543292\pi$
$798$		0			0
$799$	−14.1060			−0.499035
$800$	4.32611	+	2.49768i	0.152951	+	0.0883062i
$801$		0			0
$802$	8.94510	+	15.4934i	0.315863	+	0.547090i
$803$	−3.90691	+	6.76696i	−0.137872	+	0.238801i
$804$		0			0
$805$	0.0841205	+	0.00603958i	0.00296486	+	0.000212867i
$806$			0.569930i			0.0200749i
$807$		0			0
$808$	3.04889	−	1.76028i	0.107260	−	0.0619264i
$809$	−22.9383	+	13.2434i	−0.806467	+	0.465614i	−0.845728	−	0.533615i	$-0.820833\pi$
$809$	−22.9383	+	13.2434i	−0.806467	+	0.465614i	0.0392603	+	0.999229i	$0.487500\pi$
$810$		0			0
$811$			50.2759i			1.76543i	0.469911	+	0.882714i	$0.344286\pi$
$811$			50.2759i			1.76543i	−0.469911	+	0.882714i	$0.655714\pi$
$812$	−19.0834	−	1.37013i	−0.669697	−	0.0480821i
$813$		0			0
$814$	2.74496	−	4.75442i	0.0962109	−	0.166642i
$815$	−0.0377226	−	0.0653375i	−0.00132136	−	0.00228867i
$816$		0			0
$817$	60.5933	+	34.9836i	2.11989	+	1.22392i
$818$	1.56388			0.0546797
$819$		0			0
$820$	−0.367245			−0.0128248
$821$	5.84233	+	3.37307i	0.203899	+	0.117721i	0.598473	−	0.801143i	$-0.295774\pi$
$821$	5.84233	+	3.37307i	0.203899	+	0.117721i	−0.394574	+	0.918864i	$0.629108\pi$
$822$		0			0
$823$	15.5276	+	26.8946i	0.541258	+	0.937487i	0.998832	+	0.0483153i	$0.0153852\pi$
$823$	15.5276	+	26.8946i	0.541258	+	0.937487i	−0.457574	+	0.889172i	$0.651281\pi$
$824$	7.99465	−	13.8471i	0.278507	−	0.482388i
$825$		0			0
$826$	1.30304	−	1.92410i	0.0453384	−	0.0669480i
$827$			17.0506i			0.592906i	0.955047	+	0.296453i	$0.0958039\pi$
$827$			17.0506i			0.592906i	−0.955047	+	0.296453i	$0.904196\pi$
$828$		0			0
$829$	30.5417	−	17.6332i	1.06076	−	0.612428i	0.135115	−	0.990830i	$-0.456860\pi$
$829$	30.5417	−	17.6332i	1.06076	−	0.612428i	0.925641	+	0.378402i	$0.123526\pi$
$830$	−1.01081	+	0.583589i	−0.0350856	+	0.0202567i
$831$		0			0
$832$		−	2.44949i		−	0.0849208i
$833$	7.08268	−	8.99621i	0.245400	−	0.311700i
$834$		0			0
$835$	0.338502	−	0.586302i	0.0117143	−	0.0202898i
$836$	−3.62863	−	6.28497i	−0.125499	−	0.217370i
$837$		0			0
$838$	−4.32164	−	2.49510i	−0.149288	−	0.0861917i
$839$	−20.8253			−0.718969			−0.359484	−	0.933151i	$-0.617047\pi$
$839$	−20.8253			−0.718969			−0.359484	+	0.933151i	$0.617047\pi$
$840$		0			0
$841$	−23.2936			−0.803226
$842$	32.0633	+	18.5117i	1.10497	+	0.637957i
$843$		0			0
$844$	1.48200	+	2.56689i	0.0510125	+	0.0883562i
$845$	0.238519	−	0.413127i	0.00820531	−	0.0142120i
$846$		0			0
$847$	−2.38014	+	1.15539i	−0.0817826	+	0.0396998i
$848$			8.47871i			0.291160i
$849$		0			0
$850$	−7.07610	+	4.08539i	−0.242708	+	0.140128i
$851$	−2.22388	+	1.28396i	−0.0762335	+	0.0440135i
$852$		0			0
$853$			15.3869i			0.526837i	0.964682	+	0.263419i	$0.0848501\pi$
$853$			15.3869i			0.526837i	−0.964682	+	0.263419i	$0.915150\pi$
$854$	1.88856	−	26.3042i	0.0646251	−	0.900111i
$855$		0			0
$856$	−3.03225	+	5.25201i	−0.103640	+	0.179510i
$857$	21.0768	+	36.5061i	0.719969	+	1.24702i	0.961011	+	0.276509i	$0.0891775\pi$
$857$	21.0768	+	36.5061i	0.719969	+	1.24702i	−0.241042	+	0.970515i	$0.577489\pi$
$858$		0			0
$859$	−6.86724	−	3.96481i	−0.234307	−	0.135277i	0.378250	−	0.925703i	$-0.376526\pi$
$859$	−6.86724	−	3.96481i	−0.234307	−	0.135277i	−0.612558	+	0.790426i	$0.709859\pi$
$860$	0.657018			0.0224041
$861$		0			0
$862$	−13.2291			−0.450584
$863$	20.6857	+	11.9429i	0.704150	+	0.406541i	0.808891	−	0.587958i	$-0.200068\pi$
$863$	20.6857	+	11.9429i	0.704150	+	0.406541i	−0.104741	+	0.994500i	$0.533401\pi$
$864$		0			0
$865$	−0.450534	−	0.780347i	−0.0153186	−	0.0265326i
$866$	−6.28969	+	10.8941i	−0.213732	+	0.370195i
$867$		0			0
$868$	0.268829	+	0.553794i	0.00912465	+	0.0187970i
$869$			11.5322i			0.391205i
$870$		0			0
$871$	−6.49093	+	3.74754i	−0.219937	+	0.126981i
$872$	−15.6036	+	9.00877i	−0.528406	+	0.305075i
$873$		0			0
$874$			3.39458i			0.114823i
$875$	−1.49221	−	1.01055i	−0.0504460	−	0.0341630i
$876$		0			0
$877$	−14.3033	+	24.7741i	−0.482989	+	0.836562i	−0.999809	−	0.0195322i	$-0.993782\pi$
$877$	−14.3033	+	24.7741i	−0.482989	+	0.836562i	0.516820	+	0.856094i	$0.327116\pi$
$878$	8.79639	+	15.2358i	0.296864	+	0.514183i
$879$		0			0
$880$	−0.0590182	−	0.0340742i	−0.00198950	−	0.00114864i
$881$	−10.9836			−0.370048			−0.185024	−	0.982734i	$-0.559236\pi$
$881$	−10.9836			−0.370048			−0.185024	+	0.982734i	$0.559236\pi$
$882$		0			0
$883$	6.61872			0.222738			0.111369	−	0.993779i	$-0.464477\pi$
$883$	6.61872			0.222738			0.111369	+	0.993779i	$0.464477\pi$
$884$	3.46979	+	2.00328i	0.116702	+	0.0673777i
$885$		0			0
$886$	13.5531	+	23.4746i	0.455324	+	0.788645i
$887$	−13.1198	+	22.7241i	−0.440519	+	0.763001i	−0.997728	−	0.0673712i	$-0.978539\pi$
$887$	−13.1198	+	22.7241i	−0.440519	+	0.763001i	0.557209	+	0.830372i	$0.311872\pi$
$888$		0			0
$889$	−14.9829	−	10.1467i	−0.502509	−	0.340308i
$890$			0.727570i			0.0243882i
$891$		0			0
$892$	−11.9717	+	6.91189i	−0.400844	+	0.231427i
$893$	54.2014	−	31.2932i	1.81378	−	1.04719i
$894$		0			0
$895$			0.770563i			0.0257571i
$896$	−1.15539	−	2.38014i	−0.0385990	−	0.0795149i
$897$		0			0
$898$	−7.49750	+	12.9861i	−0.250195	+	0.433350i
$899$	0.841279	+	1.45714i	0.0280582	+	0.0485983i
$900$		0			0
$901$	−12.0104	−	6.93421i	−0.400124	−	0.231012i
$902$	−5.38891			−0.179431
$903$		0			0
$904$	7.05521			0.234653
$905$	0.487886	+	0.281681i	0.0162179	+	0.00936340i
$906$		0			0
$907$	2.03536	+	3.52534i	0.0675830	+	0.117057i	0.897837	−	0.440328i	$-0.145138\pi$
$907$	2.03536	+	3.52534i	0.0675830	+	0.117057i	−0.830254	+	0.557385i	$0.811805\pi$
$908$	−11.1257	+	19.2702i	−0.369219	+	0.639506i
$909$		0			0
$910$	−0.0316278	+	0.440518i	−0.00104845	+	0.0146030i
$911$		−	48.6470i		−	1.61175i	−0.592089	−	0.805873i	$-0.701696\pi$
$911$		−	48.6470i		−	1.61175i	0.592089	−	0.805873i	$-0.298304\pi$
$912$		0			0
$913$	−14.8324	+	8.56350i	−0.490882	+	0.283411i
$914$	−0.823468	+	0.475430i	−0.0272379	+	0.0157258i
$915$		0			0
$916$			14.2254i			0.470020i
$917$	−3.60524	+	1.75010i	−0.119056	+	0.0577933i
$918$		0			0
$919$	15.5377	−	26.9121i	0.512542	−	0.887750i	−0.487352	−	0.873206i	$-0.662037\pi$
$919$	15.5377	−	26.9121i	0.512542	−	0.887750i	0.999894	−	0.0145439i	$-0.00462962\pi$
$920$	0.0159382	+	0.0276058i	0.000525467	+	0.000910135i
$921$		0			0
$922$	−15.3891	−	8.88488i	−0.506812	−	0.292608i
$923$	−38.8907			−1.28010
$924$		0			0
$925$	27.4241			0.901700
$926$	−1.05302	−	0.607962i	−0.0346044	−	0.0199789i
$927$		0			0
$928$	−3.61571	−	6.26260i	−0.118692	−	0.205580i
$929$	−23.7632	+	41.1591i	−0.779645	+	1.35039i	0.152501	+	0.988303i	$0.451267\pi$
$929$	−23.7632	+	41.1591i	−0.779645	+	1.35039i	−0.932146	+	0.362082i	$0.882066\pi$
$930$		0			0
$931$	−7.25725	+	50.2797i	−0.237847	+	1.64785i
$932$			0.514719i			0.0168602i
$933$		0			0
$934$	7.72464	−	4.45982i	0.252758	−	0.145930i
$935$	0.0965346	−	0.0557343i	0.00315702	−	0.00182271i
$936$		0			0
$937$		−	40.0691i		−	1.30900i	−0.756062	−	0.654500i	$-0.772879\pi$
$937$		−	40.0691i		−	1.30900i	0.756062	−	0.654500i	$-0.227121\pi$
$938$	−4.53949	+	6.70314i	−0.148220	+	0.218865i
$939$		0			0
$940$	0.293855	−	0.508972i	0.00958450	−	0.0166008i
$941$	−13.3932	−	23.1977i	−0.436606	−	0.756223i	0.560819	−	0.827938i	$-0.310486\pi$
$941$	−13.3932	−	23.1977i	−0.436606	−	0.756223i	−0.997425	+	0.0717148i	$0.977153\pi$
$942$		0			0
$943$	2.18296	+	1.26033i	0.0710868	+	0.0410420i
$944$	0.878315			0.0285867
$945$		0			0
$946$	9.64100			0.313456
$947$	7.02383	+	4.05521i	0.228244	+	0.131777i	0.609762	−	0.792585i	$-0.291265\pi$
$947$	7.02383	+	4.05521i	0.228244	+	0.131777i	−0.381518	+	0.924362i	$0.624598\pi$
$948$		0			0
$949$	9.56993	+	16.5756i	0.310653	+	0.538067i
$950$	18.1263	−	31.3956i	0.588094	−	1.01861i
$951$		0			0
$952$	4.31648	+	0.309909i	0.139898	+	0.0100442i
$953$			1.34315i			0.0435088i	0.999763	+	0.0217544i	$0.00692518\pi$
$953$			1.34315i			0.0435088i	−0.999763	+	0.0217544i	$0.993075\pi$
$954$		0			0
$955$	−0.702835	+	0.405782i	−0.0227432	+	0.0131308i
$956$	−18.9000	+	10.9119i	−0.611268	+	0.352916i
$957$		0			0
$958$		−	20.6322i		−	0.666597i
$959$	−13.0246	−	0.935123i	−0.420586	−	0.0301967i
$960$		0			0
$961$	−15.4729	+	26.7999i	−0.499127	+	0.864513i
$962$	−6.72376	−	11.6459i	−0.216783	−	0.375479i
$963$		0			0
$964$	−7.95439	−	4.59247i	−0.256194	−	0.147914i
$965$	−1.73280			−0.0557807
$966$		0			0
$967$	−33.5361			−1.07845			−0.539224	−	0.842162i	$-0.681282\pi$
$967$	−33.5361			−1.07845			−0.539224	+	0.842162i	$0.681282\pi$
$968$	−0.866025	−	0.500000i	−0.0278351	−	0.0160706i
$969$		0			0
$970$	−0.340699	−	0.590109i	−0.0109392	−	0.0189472i
$971$	−26.6106	+	46.0910i	−0.853976	+	1.47913i	0.0236161	+	0.999721i	$0.492482\pi$
$971$	−26.6106	+	46.0910i	−0.853976	+	1.47913i	−0.877592	+	0.479408i	$0.840851\pi$
$972$		0			0
$973$	1.64057	−	2.42251i	0.0525942	−	0.0776620i
$974$			0.0379288i			0.00121532i
$975$		0			0
$976$	8.63223	−	4.98382i	0.276311	−	0.159528i
$977$	−0.171724	+	0.0991448i	−0.00549393	+	0.00317192i	−0.502744	−	0.864435i	$-0.667676\pi$
$977$	−0.171724	+	0.0991448i	−0.00549393	+	0.00317192i	0.497251	+	0.867607i	$0.334343\pi$
$978$		0			0
$979$			10.6763i			0.341215i
$980$	0.177055	+	0.442964i	0.00565580	+	0.0141500i
$981$		0			0
$982$	17.3460	−	30.0441i	0.553532	−	0.958745i
$983$	13.7122	+	23.7503i	0.437352	+	0.757516i	0.997484	−	0.0708872i	$-0.0225830\pi$
$983$	13.7122	+	23.7503i	0.437352	+	0.757516i	−0.560132	+	0.828403i	$0.689250\pi$
$984$		0			0
$985$	−0.494467	−	0.285481i	−0.0157550	−	0.00909617i
$986$	11.8283			0.376689
$987$		0			0
$988$	−17.7766			−0.565548
$989$	−3.90541	−	2.25479i	−0.124185	−	0.0716981i
$990$		0			0
$991$	−10.4729	−	18.1396i	−0.332682	−	0.576222i	0.650355	−	0.759631i	$-0.274620\pi$
$991$	−10.4729	−	18.1396i	−0.332682	−	0.576222i	−0.983037	+	0.183408i	$0.941287\pi$
$992$	−0.116337	+	0.201501i	−0.00369369	+	0.00639765i
$993$		0			0
$994$	−37.7896	+	18.3443i	−1.19861	+	0.581845i
$995$		−	1.36714i		−	0.0433413i
$996$		0			0
$997$	−18.8774	+	10.8989i	−0.597853	+	0.345170i	−0.768196	−	0.640214i	$-0.778846\pi$
$997$	−18.8774	+	10.8989i	−0.597853	+	0.345170i	0.170344	+	0.985385i	$0.445512\pi$
$998$	−17.7133	+	10.2268i	−0.560705	+	0.323723i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.r.c.89.1	yes	8
3.2	odd	2		1386.2.r.a.89.4	✓	8
7.3	odd	6		1386.2.r.a.1277.4	yes	8
21.17	even	6	inner	1386.2.r.c.1277.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.a.89.4	✓	8	3.2	odd	2
1386.2.r.a.1277.4	yes	8	7.3	odd	6
1386.2.r.c.89.1	yes	8	1.1	even	1	trivial
1386.2.r.c.1277.1	yes	8	21.17	even	6	inner

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.0340742 - 0.0590182i) q^{5} +(-2.19067 - 1.48356i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.0340742 - 0.0590182i) q^{5} +(-2.19067 - 1.48356i) q^{7} -1.00000i q^{8} +(-0.0590182 + 0.0340742i) q^{10} +(-0.866025 + 0.500000i) q^{11} +2.44949i q^{13} +(1.15539 + 2.38014i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.817837 - 1.41654i) q^{17} +(6.28497 + 3.62863i) q^{19} +0.0681483 q^{20} +1.00000 q^{22} +(-0.405083 - 0.233875i) q^{23} +(2.49768 + 4.32611i) q^{25} +(1.22474 - 2.12132i) q^{26} +(0.189469 - 2.63896i) q^{28} -7.23143i q^{29} +(-0.201501 + 0.116337i) q^{31} +(0.866025 - 0.500000i) q^{32} +1.63567i q^{34} +(-0.162203 + 0.0787382i) q^{35} +(2.74496 - 4.75442i) q^{37} +(-3.62863 - 6.28497i) q^{38} +(-0.0590182 - 0.0340742i) q^{40} -5.38891 q^{41} +9.64100 q^{43} +(-0.866025 - 0.500000i) q^{44} +(0.233875 + 0.405083i) q^{46} +(4.31199 - 7.46859i) q^{47} +(2.59808 + 6.50000i) q^{49} -4.99536i q^{50} +(-2.12132 + 1.22474i) q^{52} +(7.34278 - 4.23936i) q^{53} +0.0681483i q^{55} +(-1.48356 + 2.19067i) q^{56} +(-3.61571 + 6.26260i) q^{58} +(-0.439158 - 0.760643i) q^{59} +(-8.63223 - 4.98382i) q^{61} +0.232673 q^{62} -1.00000 q^{64} +(0.144564 + 0.0834643i) q^{65} +(1.52993 + 2.64991i) q^{67} +(0.817837 - 1.41654i) q^{68} +(0.179841 + 0.0129120i) q^{70} +15.8771i q^{71} +(6.76696 - 3.90691i) q^{73} +(-4.75442 + 2.74496i) q^{74} +7.25725i q^{76} +(2.63896 + 0.189469i) q^{77} +(5.76612 - 9.98722i) q^{79} +(0.0340742 + 0.0590182i) q^{80} +(4.66693 + 2.69445i) q^{82} +17.1270 q^{83} -0.111469 q^{85} +(-8.34935 - 4.82050i) q^{86} +(0.500000 + 0.866025i) q^{88} +(5.33814 - 9.24592i) q^{89} +(3.63397 - 5.36603i) q^{91} -0.467750i q^{92} +(-7.46859 + 4.31199i) q^{94} +(0.428310 - 0.247285i) q^{95} +9.99876i q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 8 q^{5}+O(q^{10}) \) 8 * q + 4 * q^4 + 8 * q^5	\( 8 q + 4 q^{4} + 8 q^{5} - 4 q^{16} - 4 q^{17} + 24 q^{19} + 16 q^{20} + 8 q^{22} + 24 q^{23} - 4 q^{25} + 12 q^{31} + 16 q^{35} + 12 q^{37} - 8 q^{38} + 16 q^{41} - 32 q^{43} + 8 q^{46} + 48 q^{53} - 4 q^{58} + 16 q^{59} + 24 q^{62} - 8 q^{64} - 12 q^{65} - 24 q^{67} + 4 q^{68} - 20 q^{70} - 24 q^{73} - 12 q^{74} + 40 q^{79} + 8 q^{80} + 12 q^{82} + 72 q^{83} - 32 q^{85} - 24 q^{86} + 4 q^{88} - 16 q^{89} + 36 q^{91} + 24 q^{95} + 8 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 + 8 * q^5 - 4 * q^16 - 4 * q^17 + 24 * q^19 + 16 * q^20 + 8 * q^22 + 24 * q^23 - 4 * q^25 + 12 * q^31 + 16 * q^35 + 12 * q^37 - 8 * q^38 + 16 * q^41 - 32 * q^43 + 8 * q^46 + 48 * q^53 - 4 * q^58 + 16 * q^59 + 24 * q^62 - 8 * q^64 - 12 * q^65 - 24 * q^67 + 4 * q^68 - 20 * q^70 - 24 * q^73 - 12 * q^74 + 40 * q^79 + 8 * q^80 + 12 * q^82 + 72 * q^83 - 32 * q^85 - 24 * q^86 + 4 * q^88 - 16 * q^89 + 36 * q^91 + 24 * q^95 + 8 * q^98

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