LMFDB - Embedded newform 1386.2.r.a.89.4

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			89.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1386.89
Dual form			1386.2.r.a.1277.4

$q$-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	−0.873544	−	0.486745i	$-0.838184\pi$
$5$	−0.0340742	+	0.0590182i	−0.0152384	+	0.0263937i	0.858306	+	0.513139i	$0.171517\pi$
$6$		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	0.947995	−	0.318285i	$-0.103107\pi$
$17$	0.817837	+	1.41654i	0.198355	+	0.343560i	−0.749640	+	0.661845i	$0.769774\pi$
$18$		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	0.541638	−	0.840612i	$-0.317804\pi$
$23$	0.405083	+	0.233875i	0.0844657	+	0.0487663i	−0.457172	+	0.889378i	$0.651138\pi$
$24$		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	$0.234316\pi$
$29$			7.23143i			1.34284i	−0.741076	+	0.671421i	$0.765684\pi$
$30$		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	$-0.361748\pi$
$41$	5.38891			0.841606			0.420803	+	0.907152i	$0.361748\pi$
$42$		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	$0.383189\pi$
$47$	−4.31199	+	7.46859i	−0.628969	+	1.08941i	−0.987759	+	0.155987i	$0.950144\pi$
$48$		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	−0.910784	−	0.412883i	$-0.864522\pi$
$53$	−7.34278	+	4.23936i	−1.00861	+	0.582320i	−0.0978246	+	0.995204i	$0.531188\pi$
$54$		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	0.893196	−	0.449668i	$-0.148458\pi$
$59$	0.439158	+	0.760643i	0.0571734	+	0.0990273i	−0.836022	+	0.548696i	$0.815125\pi$
$60$		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	$-0.608819\pi$
$71$		−	15.8771i		−	1.88426i	0.335245	−	0.942131i	$-0.391181\pi$
$72$		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	$-0.889144\pi$
$83$	−17.1270			−1.87993			−0.939967	+	0.341266i	$0.889144\pi$
$84$		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	$0.358115\pi$
$89$	−5.33814	+	9.24592i	−0.565841	+	0.980066i	−0.996971	+	0.0777760i	$0.975218\pi$
$90$		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	0.765060	−	0.643959i	$-0.222709\pi$
$101$	−1.76028	−	3.04889i	−0.175154	−	0.303376i	−0.940215	+	0.340582i	$0.889376\pi$
$102$		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	0.731901	−	0.681412i	$-0.238634\pi$
$107$	5.25201	+	3.03225i	0.507731	+	0.293139i	−0.224169	+	0.974550i	$0.571967\pi$
$108$		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	$-0.892327\pi$
$113$		−	7.05521i		−	0.663698i	0.943332	−	0.331849i	$-0.107673\pi$
$114$		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	−0.897213	−	0.441599i	$-0.854412\pi$
$131$	−0.757359	+	1.31178i	−0.0661708	+	0.114611i	0.831042	+	0.556210i	$0.187745\pi$
$132$		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	−0.671349	−	0.741142i	$-0.734285\pi$
$137$	−4.27427	+	2.46775i	−0.365175	+	0.210834i	0.306173	+	0.951976i	$0.400951\pi$
$138$		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	0.511251	−	0.859432i	$-0.329182\pi$
$149$	0.275702	+	0.159176i	0.0225863	+	0.0130402i	−0.488664	+	0.872472i	$0.662516\pi$
$150$		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	$-0.625581\pi$
$167$	−9.93426			−0.768736			−0.384368	+	0.923180i	$0.625581\pi$
$168$		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	$0.334301\pi$
$173$	−6.61107	+	11.4507i	−0.502630	+	0.870581i	−0.999995	+	0.00303994i	$0.999032\pi$
$174$		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	−0.0872113	−	0.996190i	$-0.527796\pi$
$179$	9.79227	−	5.65357i	0.731909	−	0.422568i	0.819120	+	0.573622i	$0.194462\pi$
$180$		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	0.824335	−	0.566102i	$-0.191549\pi$
$191$	10.3133	+	5.95439i	0.746245	+	0.430845i	−0.0780906	+	0.996946i	$0.524882\pi$
$192$		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	$0.0964734\pi$
$197$			8.37821i			0.596923i	−0.954422	+	0.298461i	$0.903527\pi$
$198$		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	$-0.902231\pi$
$227$	−11.1257	−	19.2702i	−0.738437	−	1.27901i	0.214761	−	0.976667i	$-0.431103\pi$
$228$		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	0.485328	−	0.874332i	$-0.338700\pi$
$233$	−0.445759	−	0.257359i	−0.0292027	−	0.0168602i	−0.514530	+	0.857472i	$0.672034\pi$
$234$		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	$-0.750574\pi$
$239$		−	21.8238i		−	1.41166i	0.708380	−	0.705832i	$-0.249426\pi$
$240$		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	$-0.0494468\pi$
$251$	31.3044			1.97592			0.987959	+	0.154718i	$0.0494468\pi$
$252$		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	−0.921890	−	0.387453i	$-0.873355\pi$
$257$	−2.01033	+	3.48200i	−0.125401	+	0.217201i	0.796489	+	0.604654i	$0.206688\pi$
$258$		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	−0.814710	−	0.579868i	$-0.803104\pi$
$263$	−11.6746	+	6.74032i	−0.719885	+	0.415626i	0.0948253	+	0.995494i	$0.469771\pi$
$264$		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	$-0.757363\pi$
$269$	−15.7399	−	27.2624i	−0.959681	−	1.66222i	−0.236408	−	0.971654i	$-0.575970\pi$
$270$		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	$-0.637234\pi$
$281$		−	30.4582i		−	1.81698i	0.417902	−	0.908492i	$-0.362766\pi$
$282$		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	$-0.355534\pi$
$293$	15.0095			0.876862			0.438431	+	0.898765i	$0.355534\pi$
$294$		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	$-0.976143\pi$
$311$	−9.93645	−	17.2104i	−0.563445	−	0.975915i	0.433748	−	0.901034i	$-0.357191\pi$
$312$		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	0.760445	−	0.649403i	$-0.224981\pi$
$317$	10.2958	+	5.94427i	0.578268	+	0.333863i	−0.182177	+	0.983266i	$0.558314\pi$
$318$		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	−0.659655	−	0.751569i	$-0.729298\pi$
$347$	−6.30751	+	3.64165i	−0.338605	+	0.195494i	0.321050	+	0.947062i	$0.395964\pi$
$348$		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	0.535313	−	0.844654i	$-0.320194\pi$
$353$	−8.71467	−	15.0943i	−0.463835	−	0.803386i	−0.999148	+	0.0412678i	$0.986860\pi$
$354$		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	0.959794	−	0.280707i	$-0.0905688\pi$
$359$	22.6722	+	13.0898i	1.19659	+	0.690852i	0.236798	+	0.971559i	$0.423902\pi$
$360$		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	−0.631002	−	0.775781i	$-0.717356\pi$
$383$	6.97381	−	12.0790i	0.356345	−	0.617208i	0.987347	+	0.158573i	$0.0506894\pi$
$384$		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	−0.538320	−	0.842740i	$-0.680941\pi$
$389$	−1.53141	+	0.884161i	−0.0776457	+	0.0448288i	0.460674	+	0.887569i	$0.347608\pi$
$390$		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	0.834194	−	0.551472i	$-0.185933\pi$
$401$	15.4934	+	8.94510i	0.773702	+	0.446697i	−0.0604915	+	0.998169i	$0.519267\pi$
$402$		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	$-0.538897\pi$
$419$	−4.99020			−0.243787			−0.121894	+	0.992543i	$0.538897\pi$
$420$		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	−0.749868	−	0.661588i	$-0.769883\pi$
$431$	−11.4567	+	6.61453i	−0.551850	+	0.318611i	0.198018	+	0.980198i	$0.436550\pi$
$432$		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	0.940200	−	0.340623i	$-0.110638\pi$
$443$	23.4746	+	13.5531i	1.11531	+	0.643926i	0.175112	+	0.984549i	$0.443971\pi$
$444$		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	$0.115121\pi$
$449$			14.9950i			0.707658i	−0.935310	+	0.353829i	$0.884879\pi$
$450$		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	$-0.635802\pi$
$461$	−17.7698			−0.827621			−0.413810	+	0.910363i	$0.635802\pi$
$462$		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	−0.744194	−	0.667963i	$-0.767166\pi$
$467$	4.45982	−	7.72464i	0.206376	−	0.357454i	0.950570	+	0.310510i	$0.100500\pi$
$468$		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	0.528108	−	0.849177i	$-0.322902\pi$
$479$	−10.3161	−	17.8680i	−0.471355	−	0.816411i	−0.999463	+	0.0327661i	$0.989568\pi$
$480$		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	$-0.713785\pi$
$491$		−	34.6919i		−	1.56562i	0.622258	−	0.782812i	$-0.286215\pi$
$492$		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	$-0.252514\pi$
$503$	31.4660			1.40300			0.701501	+	0.712669i	$0.252514\pi$
$504$		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	−0.734359	−	0.678761i	$-0.762517\pi$
$509$	4.97798	−	8.62211i	0.220645	−	0.382168i	0.955004	+	0.296593i	$0.0958505\pi$
$510$		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	$0.188234\pi$
$521$	20.4947	+	35.4979i	0.897891	+	1.55519i	0.0677047	+	0.997705i	$0.478432\pi$
$522$		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	−0.540865	−	0.841110i	$-0.681903\pi$
$557$	−1.95592	+	1.12925i	−0.0828748	+	0.0478478i	0.457990	+	0.888957i	$0.348570\pi$
$558$		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	0.768776	−	0.639518i	$-0.220866\pi$
$563$	−4.02066	−	6.96399i	−0.169451	−	0.293497i	−0.938227	+	0.346021i	$0.887533\pi$
$564$		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	0.791328	−	0.611392i	$-0.209390\pi$
$569$	15.6841	+	9.05521i	0.657511	+	0.379614i	−0.133817	+	0.991006i	$0.542723\pi$
$570$		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	$-0.680209\pi$
$587$	−25.9909			−1.07276			−0.536381	+	0.843976i	$0.680209\pi$
$588$		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	$0.378336\pi$
$593$	−15.0260	+	26.0258i	−0.617043	+	1.06875i	−0.990022	+	0.140911i	$0.954997\pi$
$594$		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	−0.323265	−	0.946309i	$-0.604780\pi$
$599$	8.18991	−	4.72844i	0.334631	−	0.193199i	0.657895	+	0.753110i	$0.271447\pi$
$600$		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	$0.0334396\pi$
$617$			5.20936i			0.209721i	−0.994487	+	0.104860i	$0.966560\pi$
$618$		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	−0.975915	−	0.218151i	$-0.929997\pi$
$641$	−32.2791	+	18.6364i	−1.27495	+	0.736092i	−0.299033	+	0.954243i	$0.596664\pi$
$642$		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	$-0.962005\pi$
$647$	−15.2508	−	26.4151i	−0.599570	−	1.03849i	0.393315	−	0.919404i	$-0.371328\pi$
$648$		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	0.678912	−	0.734220i	$-0.262452\pi$
$653$	9.77473	+	5.64344i	0.382515	+	0.220845i	−0.296397	+	0.955065i	$0.595785\pi$
$654$		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	$-0.936125\pi$
$659$		−	10.2338i		−	0.398652i	0.979933	−	0.199326i	$-0.0638753\pi$
$660$		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	−0.981125	−	0.193376i	$-0.938056\pi$
$677$	−8.40665	+	14.5607i	−0.323094	+	0.559615i	0.658031	+	0.752991i	$0.271390\pi$
$678$		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	−0.801963	−	0.597374i	$-0.796211\pi$
$683$	−17.9178	+	10.3448i	−0.685604	+	0.395834i	0.116359	+	0.993207i	$0.462878\pi$
$684$		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	$0.162413\pi$
$701$			25.8612i			0.976765i	−0.872630	+	0.488382i	$0.837587\pi$
$702$		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	−0.999208	−	0.0398001i	$-0.987328\pi$
$719$	−12.4722	+	21.6025i	−0.465136	+	0.805639i	0.534072	+	0.845439i	$0.320661\pi$
$720$		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	$0.405210\pi$
$743$			52.1166i			1.91197i	−0.293409	+	0.955987i	$0.594790\pi$
$744$		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	−0.988559	−	0.150836i	$-0.951803\pi$
$761$	−10.0318	+	17.3755i	−0.363651	+	0.629863i	0.624907	+	0.780699i	$0.285137\pi$
$762$		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	0.922995	−	0.384811i	$-0.125733\pi$
$773$	3.56548	+	6.17559i	0.128241	+	0.222121i	−0.794754	+	0.606932i	$0.792400\pi$
$774$		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	$-0.456708\pi$
$797$	7.65551			0.271172			0.135586	+	0.990766i	$0.456708\pi$
$798$		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	−0.0392603	−	0.999229i	$-0.512500\pi$
$809$	22.9383	−	13.2434i	0.806467	−	0.465614i	0.845728	+	0.533615i	$0.179167\pi$
$810$		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	0.394574	−	0.918864i	$-0.370892\pi$
$821$	−5.84233	−	3.37307i	−0.203899	−	0.117721i	−0.598473	+	0.801143i	$0.704226\pi$
$822$		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	$-0.904196\pi$
$827$		−	17.0506i		−	0.592906i	0.955047	−	0.296453i	$-0.0958039\pi$
$828$		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	$-0.382953\pi$
$839$	20.8253			0.718969			0.359484	+	0.933151i	$0.382953\pi$
$840$		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	$-0.910822\pi$
$857$	−21.0768	−	36.5061i	−0.719969	−	1.24702i	0.241042	−	0.970515i	$-0.422511\pi$
$858$		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	0.104741	−	0.994500i	$-0.466599\pi$
$863$	−20.6857	−	11.9429i	−0.704150	−	0.406541i	−0.808891	+	0.587958i	$0.799932\pi$
$864$		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	$-0.440764\pi$
$881$	10.9836			0.370048			0.185024	+	0.982734i	$0.440764\pi$
$882$		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	−0.557209	−	0.830372i	$-0.688128\pi$
$887$	13.1198	−	22.7241i	0.440519	−	0.763001i	0.997728	+	0.0673712i	$0.0214612\pi$
$888$		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	$0.298304\pi$
$911$			48.6470i			1.61175i	−0.592089	+	0.805873i	$0.701696\pi$
$912$		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	$-0.548733\pi$
$929$	23.7632	−	41.1591i	0.779645	−	1.35039i	0.932146	−	0.362082i	$-0.117934\pi$
$930$		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	0.997425	−	0.0717148i	$-0.0228471\pi$
$941$	13.3932	+	23.1977i	0.436606	+	0.756223i	−0.560819	+	0.827938i	$0.689514\pi$
$942$		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	0.381518	−	0.924362i	$-0.375402\pi$
$947$	−7.02383	−	4.05521i	−0.228244	−	0.131777i	−0.609762	+	0.792585i	$0.708735\pi$
$948$		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	$-0.993075\pi$
$953$		−	1.34315i		−	0.0435088i	0.999763	−	0.0217544i	$-0.00692518\pi$
$954$		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	$-0.507518\pi$
$971$	26.6106	−	46.0910i	0.853976	−	1.47913i	0.877592	−	0.479408i	$-0.159149\pi$
$972$		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	−0.497251	−	0.867607i	$-0.665657\pi$
$977$	0.171724	−	0.0991448i	0.00549393	−	0.00317192i	0.502744	+	0.864435i	$0.332324\pi$
$978$		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	0.560132	−	0.828403i	$-0.310750\pi$
$983$	−13.7122	−	23.7503i	−0.437352	−	0.757516i	−0.997484	+	0.0708872i	$0.977417\pi$
$984$		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.a.89.4	✓	8
3.2	odd	2		1386.2.r.c.89.1	yes	8
7.3	odd	6		1386.2.r.c.1277.1	yes	8
21.17	even	6	inner	1386.2.r.a.1277.4	yes	8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
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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