LMFDB - Embedded newform 1134.2.f.n.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(379,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.379
Dual form			1134.2.f.n.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} -1.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.50000 - 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{28} +(2.00000 - 3.46410i) q^{29} +(4.50000 + 7.79423i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +1.00000 q^{35} +5.00000 q^{37} +(-0.500000 + 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} -5.00000 q^{44} -1.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} -12.0000 q^{53} +5.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(-7.00000 - 12.1244i) q^{59} +9.00000 q^{62} +1.00000 q^{64} +(4.00000 + 6.92820i) q^{67} +(1.00000 + 1.73205i) q^{68} +(0.500000 - 0.866025i) q^{70} +13.0000 q^{71} -2.00000 q^{73} +(2.50000 - 4.33013i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-2.50000 - 4.33013i) q^{77} +(-3.00000 + 5.19615i) q^{79} -1.00000 q^{80} -9.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-1.00000 - 1.73205i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(-2.50000 + 4.33013i) q^{88} +9.00000 q^{89} +(-0.500000 + 0.866025i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(-8.00000 + 13.8564i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} + 2 q^{10} + 5 q^{11} - q^{14} - q^{16} - 4 q^{17} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} + 4 q^{25} - 2 q^{28} + 4 q^{29} + 9 q^{31} + q^{32} - 2 q^{34} + 2 q^{35} + 10 q^{37} - q^{38} - q^{40} - 9 q^{41} + 10 q^{43} - 10 q^{44} - 2 q^{46} + 6 q^{47} - q^{49} - 4 q^{50} - 24 q^{53} + 10 q^{55} - q^{56} - 4 q^{58} - 14 q^{59} + 18 q^{62} + 2 q^{64} + 8 q^{67} + 2 q^{68} + q^{70} + 26 q^{71} - 4 q^{73} + 5 q^{74} + q^{76} - 5 q^{77} - 6 q^{79} - 2 q^{80} - 18 q^{82} - 4 q^{83} - 2 q^{85} - 10 q^{86} - 5 q^{88} + 18 q^{89} - q^{92} - 6 q^{94} - q^{95} - 16 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 + 2 * q^10 + 5 * q^11 - q^14 - q^16 - 4 * q^17 - 2 * q^19 + q^20 - 5 * q^22 - q^23 + 4 * q^25 - 2 * q^28 + 4 * q^29 + 9 * q^31 + q^32 - 2 * q^34 + 2 * q^35 + 10 * q^37 - q^38 - q^40 - 9 * q^41 + 10 * q^43 - 10 * q^44 - 2 * q^46 + 6 * q^47 - q^49 - 4 * q^50 - 24 * q^53 + 10 * q^55 - q^56 - 4 * q^58 - 14 * q^59 + 18 * q^62 + 2 * q^64 + 8 * q^67 + 2 * q^68 + q^70 + 26 * q^71 - 4 * q^73 + 5 * q^74 + q^76 - 5 * q^77 - 6 * q^79 - 2 * q^80 - 18 * q^82 - 4 * q^83 - 2 * q^85 - 10 * q^86 - 5 * q^88 + 18 * q^89 - q^92 - 6 * q^94 - q^95 - 16 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.00000			0.316228
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$13$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−2.50000	−	4.33013i	−0.533002	−	0.923186i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$	−1.00000			−0.188982
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$		0			0
$31$	4.50000	+	7.79423i	0.808224	+	1.39988i	0.914093	+	0.405505i	$0.132904\pi$
$31$	4.50000	+	7.79423i	0.808224	+	1.39988i	−0.105869	+	0.994380i	$0.533762\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	1.00000			0.169031
$36$		0			0
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$	−5.00000			−0.753778
$45$		0			0
$46$	−1.00000			−0.147442
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$		0			0
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−2.00000	−	3.46410i	−0.262613	−	0.454859i
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.812198	−	0.583382i	$-0.801729\pi$
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.0991242	−	0.995075i	$-0.531604\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	9.00000			1.14300
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	0.999915	−	0.0130248i	$-0.00414604\pi$
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	−0.511237	+	0.859440i	$0.670813\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$		0			0
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	13.0000			1.54282			0.771408	−	0.636341i	$-0.219553\pi$
$71$	13.0000			1.54282			0.771408	+	0.636341i	$0.219553\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	2.50000	−	4.33013i	0.290619	−	0.503367i
$75$		0			0
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$	−2.50000	−	4.33013i	−0.284901	−	0.493464i
$78$		0			0
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	−0.983967	−	0.178352i	$-0.942924\pi$
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	0.646440	+	0.762964i	$0.276257\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	−9.00000			−0.993884
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	−0.954664	−	0.297686i	$-0.903785\pi$
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	0.735135	+	0.677920i	$0.237119\pi$
$84$		0			0
$85$	−1.00000	−	1.73205i	−0.108465	−	0.187867i
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$		0			0
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$		0			0
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−8.00000	+	13.8564i	−0.812277	+	1.40690i	0.0989899	+	0.995088i	$0.468439\pi$
$97$	−8.00000	+	13.8564i	−0.812277	+	1.40690i	−0.911267	+	0.411816i	$0.864894\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−4.00000			−0.400000
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$		0			0
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$		0			0
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$	2.50000	−	4.33013i	0.238366	−	0.412861i
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	0.815149	−	0.579252i	$-0.196655\pi$
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	−0.909221	+	0.416314i	$0.863322\pi$
$114$		0			0
$115$	0.500000	−	0.866025i	0.0466252	−	0.0807573i
$116$	−4.00000			−0.371391
$117$		0			0
$118$	−14.0000			−1.28880
$119$	−1.00000	+	1.73205i	−0.0916698	+	0.158777i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$		0			0
$123$		0			0
$124$	4.50000	−	7.79423i	0.404112	−	0.699942i
$125$	9.00000			0.804984
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	11.0000	+	19.0526i	0.961074	+	1.66463i	0.719811	+	0.694170i	$0.244228\pi$
$131$	11.0000	+	19.0526i	0.961074	+	1.66463i	0.241264	+	0.970460i	$0.422438\pi$
$132$		0			0
$133$	−0.500000	+	0.866025i	−0.0433555	+	0.0750939i
$134$	8.00000			0.691095
$135$		0			0
$136$	2.00000			0.171499
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	0.973910	−	0.226935i	$-0.0728704\pi$
$138$		0			0
$139$	10.0000	+	17.3205i	0.848189	+	1.46911i	0.882823	+	0.469706i	$0.155640\pi$
$139$	10.0000	+	17.3205i	0.848189	+	1.46911i	−0.0346338	+	0.999400i	$0.511026\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$		0			0
$142$	6.50000	−	11.2583i	0.545468	−	0.944778i
$143$		0			0
$144$		0			0
$145$	4.00000			0.332182
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$		0			0
$148$	−2.50000	−	4.33013i	−0.205499	−	0.355934i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	1.00000			0.0811107
$153$		0			0
$154$	−5.00000			−0.402911
$155$	−4.50000	+	7.79423i	−0.361449	+	0.626048i
$156$		0			0
$157$	−4.00000	−	6.92820i	−0.319235	−	0.552931i	0.661094	−	0.750303i	$-0.270093\pi$
$157$	−4.00000	−	6.92820i	−0.319235	−	0.552931i	−0.980329	+	0.197372i	$0.936759\pi$
$158$	3.00000	+	5.19615i	0.238667	+	0.413384i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−1.00000			−0.0788110
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	2.00000	+	3.46410i	0.155230	+	0.268866i
$167$	5.00000	+	8.66025i	0.386912	+	0.670151i	0.992032	−	0.125983i	$-0.0402085\pi$
$167$	5.00000	+	8.66025i	0.386912	+	0.670151i	−0.605121	+	0.796134i	$0.706875\pi$
$168$		0			0
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$	−2.00000			−0.153393
$171$		0			0
$172$	−10.0000			−0.762493
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	−0.701751	−	0.712422i	$-0.747598\pi$
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	0.967851	+	0.251523i	$0.0809315\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	2.50000	+	4.33013i	0.188445	+	0.326396i
$177$		0			0
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	−24.0000			−1.79384			−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000			−1.79384			−0.896922	+	0.442189i	$0.854202\pi$
$180$		0			0
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		0			0
$183$		0			0
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	2.50000	+	4.33013i	0.183804	+	0.318357i
$186$		0			0
$187$	−5.00000	+	8.66025i	−0.365636	+	0.633300i
$188$	−6.00000			−0.437595
$189$		0			0
$190$	−1.00000			−0.0725476
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$		0			0
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	8.00000	+	13.8564i	0.574367	+	0.994832i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$		0			0
$199$	−13.0000			−0.921546			−0.460773	−	0.887518i	$-0.652428\pi$
$199$	−13.0000			−0.921546			−0.460773	+	0.887518i	$0.652428\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	−2.00000	−	3.46410i	−0.140372	−	0.243132i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	1.00000			0.0696733
$207$		0			0
$208$		0			0
$209$	−2.50000	+	4.33013i	−0.172929	+	0.299521i
$210$		0			0
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	10.0000			0.681994
$216$		0			0
$217$	9.00000			0.610960
$218$	3.50000	−	6.06218i	0.237050	−	0.410582i
$219$		0			0
$220$	−2.50000	−	4.33013i	−0.168550	−	0.291937i
$221$		0			0
$222$		0			0
$223$	−2.50000	+	4.33013i	−0.167412	+	0.289967i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−2.50000	+	4.33013i	−0.167412	+	0.289967i	0.770097	+	0.637927i	$0.220208\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−2.00000			−0.133038
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$		0			0
$229$	−14.0000	−	24.2487i	−0.925146	−	1.60240i	−0.791326	−	0.611394i	$-0.790609\pi$
$229$	−14.0000	−	24.2487i	−0.925146	−	1.60240i	−0.133820	−	0.991006i	$-0.542724\pi$
$230$	−0.500000	−	0.866025i	−0.0329690	−	0.0571040i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$		0			0
$235$	6.00000			0.391397
$236$	−7.00000	+	12.1244i	−0.455661	+	0.789228i
$237$		0			0
$238$	1.00000	+	1.73205i	0.0648204	+	0.112272i
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	0.934109	+	0.356988i	$0.116196\pi$
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	−0.157893	+	0.987456i	$0.550470\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	−14.0000			−0.899954
$243$		0			0
$244$		0			0
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$		0			0
$247$		0			0
$248$	−4.50000	−	7.79423i	−0.285750	−	0.494934i
$249$		0			0
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$	−5.00000			−0.314347
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	0.888110	+	0.459631i	$0.152018\pi$
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	−0.0460033	+	0.998941i	$0.514648\pi$
$258$		0			0
$259$	2.50000	−	4.33013i	0.155342	−	0.269061i
$260$		0			0
$261$		0			0
$262$	22.0000			1.35916
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$		0			0
$265$	−6.00000	−	10.3923i	−0.368577	−	0.638394i
$266$	0.500000	+	0.866025i	0.0306570	+	0.0530994i
$267$		0			0
$268$	4.00000	−	6.92820i	0.244339	−	0.423207i
$269$	−13.0000			−0.792624			−0.396312	−	0.918116i	$-0.629710\pi$
$269$	−13.0000			−0.792624			−0.396312	+	0.918116i	$0.629710\pi$
$270$		0			0
$271$	24.0000			1.45790			0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000			1.45790			0.728948	+	0.684569i	$0.240010\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$		0			0
$274$	−8.00000	−	13.8564i	−0.483298	−	0.837096i
$275$	−10.0000	−	17.3205i	−0.603023	−	1.04447i
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$	20.0000			1.19952
$279$		0			0
$280$	−1.00000			−0.0597614
$281$	−5.00000	+	8.66025i	−0.298275	+	0.516627i	−0.975741	−	0.218926i	$-0.929745\pi$
$281$	−5.00000	+	8.66025i	−0.298275	+	0.516627i	0.677466	+	0.735554i	$0.263078\pi$
$282$		0			0
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	0.993626	+	0.112728i	$0.0359589\pi$
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	−0.399188	+	0.916869i	$0.630708\pi$
$284$	−6.50000	−	11.2583i	−0.385704	−	0.668059i
$285$		0			0
$286$		0			0
$287$	−9.00000			−0.531253
$288$		0			0
$289$	−13.0000			−0.764706
$290$	2.00000	−	3.46410i	0.117444	−	0.203419i
$291$		0			0
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	0.999549	+	0.0300351i	$0.00956192\pi$
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	−0.473763	+	0.880652i	$0.657105\pi$
$294$		0			0
$295$	7.00000	−	12.1244i	0.407556	−	0.705907i
$296$	−5.00000			−0.290619
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$		0			0
$301$	−5.00000	−	8.66025i	−0.288195	−	0.499169i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$		0			0
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$		0			0
$306$		0			0
$307$	−5.00000			−0.285365			−0.142683	−	0.989769i	$-0.545573\pi$
$307$	−5.00000			−0.285365			−0.142683	+	0.989769i	$0.545573\pi$
$308$	−2.50000	+	4.33013i	−0.142451	+	0.246732i
$309$		0			0
$310$	4.50000	+	7.79423i	0.255583	+	0.442682i
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$		0			0
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$	−8.00000			−0.451466
$315$		0			0
$316$	6.00000			0.337526
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	−10.0000	−	17.3205i	−0.559893	−	0.969762i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−0.500000	+	0.866025i	−0.0278639	+	0.0482617i
$323$	2.00000			0.111283
$324$		0			0
$325$		0			0
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	4.00000			0.219529
$333$		0			0
$334$	10.0000			0.547176
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$		0			0
$337$	−13.5000	−	23.3827i	−0.735392	−	1.27374i	−0.954551	−	0.298047i	$-0.903665\pi$
$337$	−13.5000	−	23.3827i	−0.735392	−	1.27374i	0.219159	−	0.975689i	$-0.429669\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$		0			0
$340$	−1.00000	+	1.73205i	−0.0542326	+	0.0939336i
$341$	45.0000			2.43689
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−5.00000	+	8.66025i	−0.269582	+	0.466930i
$345$		0			0
$346$	−3.50000	−	6.06218i	−0.188161	−	0.325905i
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	0.822951	−	0.568112i	$-0.192326\pi$
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	−0.903475	+	0.428640i	$0.858993\pi$
$348$		0			0
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	−0.274011	−	0.961727i	$-0.588351\pi$
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	0.969885	−	0.243563i	$-0.0783162\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	5.00000			0.266501
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$		0			0
$355$	6.50000	+	11.2583i	0.344984	+	0.597530i
$356$	−4.50000	−	7.79423i	−0.238500	−	0.413093i
$357$		0			0
$358$	−12.0000	+	20.7846i	−0.634220	+	1.09850i
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$	9.00000	−	15.5885i	0.473029	−	0.819311i
$363$		0			0
$364$		0			0
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$		0			0
$367$	−17.5000	+	30.3109i	−0.913493	+	1.58222i	−0.104399	+	0.994535i	$0.533292\pi$
$367$	−17.5000	+	30.3109i	−0.913493	+	1.58222i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	1.00000			0.0521286
$369$		0			0
$370$	5.00000			0.259938
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$		0			0
$373$	8.50000	+	14.7224i	0.440113	+	0.762299i	0.997697	−	0.0678218i	$-0.0216049\pi$
$373$	8.50000	+	14.7224i	0.440113	+	0.762299i	−0.557584	+	0.830120i	$0.688272\pi$
$374$	5.00000	+	8.66025i	0.258544	+	0.447811i
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$		0			0
$378$		0			0
$379$	−14.0000			−0.719132			−0.359566	−	0.933120i	$-0.617075\pi$
$379$	−14.0000			−0.719132			−0.359566	+	0.933120i	$0.617075\pi$
$380$	−0.500000	+	0.866025i	−0.0256495	+	0.0444262i
$381$		0			0
$382$	1.50000	+	2.59808i	0.0767467	+	0.132929i
$383$	−5.00000	−	8.66025i	−0.255488	−	0.442518i	0.709540	−	0.704665i	$-0.248903\pi$
$383$	−5.00000	−	8.66025i	−0.255488	−	0.442518i	−0.965028	+	0.262147i	$0.915569\pi$
$384$		0			0
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$	10.0000			0.508987
$387$		0			0
$388$	16.0000			0.812277
$389$	−10.0000	+	17.3205i	−0.507020	+	0.878185i	0.492947	+	0.870059i	$0.335920\pi$
$389$	−10.0000	+	17.3205i	−0.507020	+	0.878185i	−0.999967	+	0.00812520i	$0.997414\pi$
$390$		0			0
$391$	1.00000	+	1.73205i	0.0505722	+	0.0875936i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	5.00000	−	8.66025i	0.251896	−	0.436297i
$395$	−6.00000			−0.301893
$396$		0			0
$397$	−30.0000			−1.50566			−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000			−1.50566			−0.752828	+	0.658217i	$0.771311\pi$
$398$	−6.50000	+	11.2583i	−0.325816	+	0.564329i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	0.676425	−	0.736512i	$-0.263528\pi$
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	−0.976050	+	0.217545i	$0.930195\pi$
$402$		0			0
$403$		0			0
$404$	14.0000			0.696526
$405$		0			0
$406$	−4.00000			−0.198517
$407$	12.5000	−	21.6506i	0.619602	−	1.07318i
$408$		0			0
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$		0			0
$412$	0.500000	−	0.866025i	0.0246332	−	0.0426660i
$413$	−14.0000			−0.688895
$414$		0			0
$415$	−4.00000			−0.196352
$416$		0			0
$417$		0			0
$418$	2.50000	+	4.33013i	0.122279	+	0.211793i
$419$	3.00000	+	5.19615i	0.146560	+	0.253849i	0.929954	−	0.367677i	$-0.119847\pi$
$419$	3.00000	+	5.19615i	0.146560	+	0.253849i	−0.783394	+	0.621525i	$0.786513\pi$
$420$		0			0
$421$	13.5000	−	23.3827i	0.657950	−	1.13960i	−0.323196	−	0.946332i	$-0.604757\pi$
$421$	13.5000	−	23.3827i	0.657950	−	1.13960i	0.981146	−	0.193270i	$-0.0619094\pi$
$422$	22.0000			1.07094
$423$		0			0
$424$	12.0000			0.582772
$425$	−4.00000	+	6.92820i	−0.194029	+	0.336067i
$426$		0			0
$427$		0			0
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$		0			0
$430$	5.00000	−	8.66025i	0.241121	−	0.417635i
$431$	15.0000			0.722525			0.361262	−	0.932464i	$-0.382346\pi$
$431$	15.0000			0.722525			0.361262	+	0.932464i	$0.382346\pi$
$432$		0			0
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$	4.50000	−	7.79423i	0.216007	−	0.374135i
$435$		0			0
$436$	−3.50000	−	6.06218i	−0.167620	−	0.290326i
$437$	0.500000	+	0.866025i	0.0239182	+	0.0414276i
$438$		0			0
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$	−5.00000			−0.238366
$441$		0			0
$442$		0			0
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$		0			0
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$	2.50000	+	4.33013i	0.118378	+	0.205037i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$		0			0
$451$	−45.0000			−2.11897
$452$	−1.00000	+	1.73205i	−0.0470360	+	0.0814688i
$453$		0			0
$454$	−3.00000	−	5.19615i	−0.140797	−	0.243868i
$455$		0			0
$456$		0			0
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	−0.977051	−	0.213006i	$-0.931675\pi$
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	0.672994	+	0.739648i	$0.265008\pi$
$458$	−28.0000			−1.30835
$459$		0			0
$460$	−1.00000			−0.0466252
$461$	15.5000	−	26.8468i	0.721907	−	1.25038i	−0.238328	−	0.971185i	$-0.576599\pi$
$461$	15.5000	−	26.8468i	0.721907	−	1.25038i	0.960235	−	0.279195i	$-0.0900675\pi$
$462$		0			0
$463$	7.00000	+	12.1244i	0.325318	+	0.563467i	0.981577	−	0.191069i	$-0.0611955\pi$
$463$	7.00000	+	12.1244i	0.325318	+	0.563467i	−0.656259	+	0.754536i	$0.727862\pi$
$464$	2.00000	+	3.46410i	0.0928477	+	0.160817i
$465$		0			0
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$	3.00000	−	5.19615i	0.138380	−	0.239681i
$471$		0			0
$472$	7.00000	+	12.1244i	0.322201	+	0.558069i
$473$	−25.0000	−	43.3013i	−1.14950	−	1.99099i
$474$		0			0
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$	2.00000			0.0916698
$477$		0			0
$478$	24.0000			1.09773
$479$	16.0000	−	27.7128i	0.731059	−	1.26623i	−0.225372	−	0.974273i	$-0.572360\pi$
$479$	16.0000	−	27.7128i	0.731059	−	1.26623i	0.956431	−	0.291958i	$-0.0943068\pi$
$480$		0			0
$481$		0			0
$482$	7.00000	+	12.1244i	0.318841	+	0.552249i
$483$		0			0
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	−16.0000			−0.726523
$486$		0			0
$487$	26.0000			1.17817			0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000			1.17817			0.589086	+	0.808070i	$0.299488\pi$
$488$		0			0
$489$		0			0
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	0.949520	−	0.313707i	$-0.101571\pi$
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	−0.746438	+	0.665455i	$0.768237\pi$
$492$		0			0
$493$	−4.00000	+	6.92820i	−0.180151	+	0.312031i
$494$		0			0
$495$		0			0
$496$	−9.00000			−0.404112
$497$	6.50000	−	11.2583i	0.291565	−	0.505005i
$498$		0			0
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$		0			0
$502$	12.0000	−	20.7846i	0.535586	−	0.927663i
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$	−14.0000			−0.622992
$506$	−2.50000	+	4.33013i	−0.111139	+	0.192498i
$507$		0			0
$508$		0			0
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	27.0000			1.19092
$515$	−0.500000	+	0.866025i	−0.0220326	+	0.0381616i
$516$		0			0
$517$	−15.0000	−	25.9808i	−0.659699	−	1.14263i
$518$	−2.50000	−	4.33013i	−0.109844	−	0.190255i
$519$		0			0
$520$		0			0
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$		0			0
$523$	11.0000			0.480996			0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000			0.480996			0.240498	+	0.970650i	$0.422689\pi$
$524$	11.0000	−	19.0526i	0.480537	−	0.832315i
$525$		0			0
$526$	10.5000	+	18.1865i	0.457822	+	0.792971i
$527$	−9.00000	−	15.5885i	−0.392046	−	0.679044i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−12.0000			−0.521247
$531$		0			0
$532$	1.00000			0.0433555
$533$		0			0
$534$		0			0
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$		0			0
$538$	−6.50000	+	11.2583i	−0.280235	+	0.485381i
$539$	−5.00000			−0.215365
$540$		0			0
$541$	−3.00000			−0.128980			−0.0644900	−	0.997918i	$-0.520542\pi$
$541$	−3.00000			−0.128980			−0.0644900	+	0.997918i	$0.520542\pi$
$542$	12.0000	−	20.7846i	0.515444	−	0.892775i
$543$		0			0
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	3.50000	+	6.06218i	0.149924	+	0.259675i
$546$		0			0
$547$	−6.00000	+	10.3923i	−0.256541	+	0.444343i	−0.965313	−	0.261095i	$-0.915916\pi$
$547$	−6.00000	+	10.3923i	−0.256541	+	0.444343i	0.708772	+	0.705438i	$0.249250\pi$
$548$	−16.0000			−0.683486
$549$		0			0
$550$	−20.0000			−0.852803
$551$	−2.00000	+	3.46410i	−0.0852029	+	0.147576i
$552$		0			0
$553$	3.00000	+	5.19615i	0.127573	+	0.220963i
$554$	−9.50000	−	16.4545i	−0.403616	−	0.699084i
$555$		0			0
$556$	10.0000	−	17.3205i	0.424094	−	0.734553i
$557$	−22.0000			−0.932170			−0.466085	−	0.884740i	$-0.654336\pi$
$557$	−22.0000			−0.932170			−0.466085	+	0.884740i	$0.654336\pi$
$558$		0			0
$559$		0			0
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$		0			0
$562$	5.00000	+	8.66025i	0.210912	+	0.365311i
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		0			0
$565$	1.00000	−	1.73205i	0.0420703	−	0.0728679i
$566$	20.0000			0.840663
$567$		0			0
$568$	−13.0000			−0.545468
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	0.613933	−	0.789359i	$-0.289587\pi$
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	−0.990571	+	0.137002i	$0.956253\pi$
$572$		0			0
$573$		0			0
$574$	−4.50000	+	7.79423i	−0.187826	+	0.325325i
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−14.0000			−0.582828			−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000			−0.582828			−0.291414	+	0.956597i	$0.594126\pi$
$578$	−6.50000	+	11.2583i	−0.270364	+	0.468285i
$579$		0			0
$580$	−2.00000	−	3.46410i	−0.0830455	−	0.143839i
$581$	2.00000	+	3.46410i	0.0829740	+	0.143715i
$582$		0			0
$583$	−30.0000	+	51.9615i	−1.24247	+	2.15203i
$584$	2.00000			0.0827606
$585$		0			0
$586$	18.0000			0.743573
$587$	7.00000	−	12.1244i	0.288921	−	0.500426i	−0.684632	−	0.728889i	$-0.740037\pi$
$587$	7.00000	−	12.1244i	0.288921	−	0.500426i	0.973552	+	0.228464i	$0.0733702\pi$
$588$		0			0
$589$	−4.50000	−	7.79423i	−0.185419	−	0.321156i
$590$	−7.00000	−	12.1244i	−0.288185	−	0.499152i
$591$		0			0
$592$	−2.50000	+	4.33013i	−0.102749	+	0.177967i
$593$	−9.00000			−0.369586			−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000			−0.369586			−0.184793	+	0.982777i	$0.559161\pi$
$594$		0			0
$595$	−2.00000			−0.0819920
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$		0			0
$599$	−13.5000	−	23.3827i	−0.551595	−	0.955391i	−0.998160	−	0.0606393i	$-0.980686\pi$
$599$	−13.5000	−	23.3827i	−0.551595	−	0.955391i	0.446565	−	0.894751i	$-0.352647\pi$
$600$		0			0
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	−0.936002	−	0.351996i	$-0.885503\pi$
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	0.772838	+	0.634603i	$0.218836\pi$
$602$	−10.0000			−0.407570
$603$		0			0
$604$	10.0000			0.406894
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	−6.00000	−	10.3923i	−0.243532	−	0.421811i	0.718186	−	0.695852i	$-0.244973\pi$
$607$	−6.00000	−	10.3923i	−0.243532	−	0.421811i	−0.961718	+	0.274041i	$0.911640\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−15.0000			−0.605844			−0.302922	−	0.953015i	$-0.597962\pi$
$613$	−15.0000			−0.605844			−0.302922	+	0.953015i	$0.597962\pi$
$614$	−2.50000	+	4.33013i	−0.100892	+	0.174750i
$615$		0			0
$616$	2.50000	+	4.33013i	0.100728	+	0.174466i
$617$	7.00000	+	12.1244i	0.281809	+	0.488108i	0.971830	−	0.235681i	$-0.0757321\pi$
$617$	7.00000	+	12.1244i	0.281809	+	0.488108i	−0.690021	+	0.723789i	$0.742399\pi$
$618$		0			0
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$	9.00000			0.361449
$621$		0			0
$622$	−8.00000			−0.320771
$623$	4.50000	−	7.79423i	0.180289	−	0.312269i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$		0			0
$628$	−4.00000	+	6.92820i	−0.159617	+	0.276465i
$629$	−10.0000			−0.398726
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	3.00000	−	5.19615i	0.119334	−	0.206692i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−20.0000			−0.791808
$639$		0			0
$640$	1.00000			0.0395285
$641$	−11.0000	+	19.0526i	−0.434474	+	0.752531i	−0.997253	−	0.0740768i	$-0.976399\pi$
$641$	−11.0000	+	19.0526i	−0.434474	+	0.752531i	0.562779	+	0.826608i	$0.309732\pi$
$642$		0			0
$643$	6.50000	+	11.2583i	0.256335	+	0.443985i	0.965257	−	0.261301i	$-0.0841516\pi$
$643$	6.50000	+	11.2583i	0.256335	+	0.443985i	−0.708922	+	0.705287i	$0.750818\pi$
$644$	0.500000	+	0.866025i	0.0197028	+	0.0341262i
$645$		0			0
$646$	1.00000	−	1.73205i	0.0393445	−	0.0681466i
$647$	−42.0000			−1.65119			−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000			−1.65119			−0.825595	+	0.564263i	$0.809160\pi$
$648$		0			0
$649$	−70.0000			−2.74774
$650$		0			0
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$		0			0
$655$	−11.0000	+	19.0526i	−0.429806	+	0.744445i
$656$	9.00000			0.351391
$657$		0			0
$658$	−6.00000			−0.233904
$659$	8.50000	−	14.7224i	0.331113	−	0.573505i	−0.651617	−	0.758548i	$-0.725909\pi$
$659$	8.50000	−	14.7224i	0.331113	−	0.573505i	0.982730	+	0.185043i	$0.0592425\pi$
$660$		0			0
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	−0.998636	−	0.0522143i	$-0.983372\pi$
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	0.454099	−	0.890951i	$-0.349961\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	2.00000	−	3.46410i	0.0776151	−	0.134433i
$665$	−1.00000			−0.0387783
$666$		0			0
$667$	−4.00000			−0.154881
$668$	5.00000	−	8.66025i	0.193456	−	0.335075i
$669$		0			0
$670$	4.00000	+	6.92820i	0.154533	+	0.267660i
$671$		0			0
$672$		0			0
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	0.498886	+	0.866668i	$0.333743\pi$
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$	−27.0000			−1.04000
$675$		0			0
$676$	−13.0000			−0.500000
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$		0			0
$679$	8.00000	+	13.8564i	0.307012	+	0.531760i
$680$	1.00000	+	1.73205i	0.0383482	+	0.0664211i
$681$		0			0
$682$	22.5000	−	38.9711i	0.861570	−	1.49228i
$683$	9.00000			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$684$		0			0
$685$	16.0000			0.611329
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$		0			0
$690$		0			0
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	−0.825473	−	0.564441i	$-0.809092\pi$
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	0.901557	+	0.432660i	$0.142425\pi$
$692$	−7.00000			−0.266100
$693$		0			0
$694$	−3.00000			−0.113878
$695$	−10.0000	+	17.3205i	−0.379322	+	0.657004i
$696$		0			0
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$		0			0
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	20.0000			0.755390			0.377695	−	0.925930i	$-0.376717\pi$
$701$	20.0000			0.755390			0.377695	+	0.925930i	$0.376717\pi$
$702$		0			0
$703$	−5.00000			−0.188579
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$		0			0
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$	7.00000	+	12.1244i	0.263262	+	0.455983i
$708$		0			0
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$	13.0000			0.487881
$711$		0			0
$712$	−9.00000			−0.337289
$713$	4.50000	−	7.79423i	0.168526	−	0.291896i
$714$		0			0
$715$		0			0
$716$	12.0000	+	20.7846i	0.448461	+	0.776757i
$717$		0			0
$718$	−2.00000	+	3.46410i	−0.0746393	+	0.129279i
$719$	30.0000			1.11881			0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000			1.11881			0.559406	+	0.828894i	$0.311029\pi$
$720$		0			0
$721$	1.00000			0.0372419
$722$	−9.00000	+	15.5885i	−0.334945	+	0.580142i
$723$		0			0
$724$	−9.00000	−	15.5885i	−0.334482	−	0.579340i
$725$	−8.00000	−	13.8564i	−0.297113	−	0.514614i
$726$		0			0
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	−0.400362	−	0.916357i	$-0.631116\pi$
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	0.993770	−	0.111454i	$-0.0355509\pi$
$728$		0			0
$729$		0			0
$730$	−2.00000			−0.0740233
$731$	−10.0000	+	17.3205i	−0.369863	+	0.640622i
$732$		0			0
$733$	9.00000	+	15.5885i	0.332423	+	0.575773i	0.982986	−	0.183679i	$-0.0588007\pi$
$733$	9.00000	+	15.5885i	0.332423	+	0.575773i	−0.650564	+	0.759452i	$0.725467\pi$
$734$	17.5000	+	30.3109i	0.645937	+	1.11880i
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	40.0000			1.47342
$738$		0			0
$739$	18.0000			0.662141			0.331070	−	0.943606i	$-0.392590\pi$
$739$	18.0000			0.662141			0.331070	+	0.943606i	$0.392590\pi$
$740$	2.50000	−	4.33013i	0.0919018	−	0.159179i
$741$		0			0
$742$	6.00000	+	10.3923i	0.220267	+	0.381514i
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	0.606590	−	0.795015i	$-0.292537\pi$
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	−0.991798	+	0.127815i	$0.959204\pi$
$744$		0			0
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$	17.0000			0.622414
$747$		0			0
$748$	10.0000			0.365636
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		0			0
$751$	−9.00000	−	15.5885i	−0.328415	−	0.568831i	0.653783	−	0.756682i	$-0.273181\pi$
$751$	−9.00000	−	15.5885i	−0.328415	−	0.568831i	−0.982197	+	0.187851i	$0.939848\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$		0			0
$755$	−10.0000			−0.363937
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$	−7.00000	+	12.1244i	−0.254251	+	0.440376i
$759$		0			0
$760$	0.500000	+	0.866025i	0.0181369	+	0.0314140i
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	0.594822	−	0.803857i	$-0.297222\pi$
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	−0.993572	+	0.113203i	$0.963889\pi$
$762$		0			0
$763$	3.50000	−	6.06218i	0.126709	−	0.219466i
$764$	3.00000			0.108536
$765$		0			0
$766$	−10.0000			−0.361315
$767$		0			0
$768$		0			0
$769$	−20.0000	−	34.6410i	−0.721218	−	1.24919i	−0.960512	−	0.278240i	$-0.910249\pi$
$769$	−20.0000	−	34.6410i	−0.721218	−	1.24919i	0.239293	−	0.970947i	$-0.423084\pi$
$770$	−2.50000	−	4.33013i	−0.0900937	−	0.156047i
$771$		0			0
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$	−19.0000			−0.683383			−0.341691	−	0.939812i	$-0.611000\pi$
$773$	−19.0000			−0.683383			−0.341691	+	0.939812i	$0.611000\pi$
$774$		0			0
$775$	36.0000			1.29316
$776$	8.00000	−	13.8564i	0.287183	−	0.497416i
$777$		0			0
$778$	10.0000	+	17.3205i	0.358517	+	0.620970i
$779$	4.50000	+	7.79423i	0.161229	+	0.279257i
$780$		0			0
$781$	32.5000	−	56.2917i	1.16294	−	2.01427i
$782$	2.00000			0.0715199
$783$		0			0
$784$	1.00000			0.0357143
$785$	4.00000	−	6.92820i	0.142766	−	0.247278i
$786$		0			0
$787$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$787$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$788$	−5.00000	−	8.66025i	−0.178118	−	0.308509i
$789$		0			0
$790$	−3.00000	+	5.19615i	−0.106735	+	0.184871i
$791$	−2.00000			−0.0711118
$792$		0			0
$793$		0			0
$794$	−15.0000	+	25.9808i	−0.532330	+	0.922023i
$795$		0			0
$796$	6.50000	+	11.2583i	0.230386	+	0.399041i
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$	4.00000			0.141421
$801$		0			0
$802$	−12.0000			−0.423735
$803$	−5.00000	+	8.66025i	−0.176446	+	0.305614i
$804$		0			0
$805$	−0.500000	−	0.866025i	−0.0176227	−	0.0305234i
$806$		0			0
$807$		0			0
$808$	7.00000	−	12.1244i	0.246259	−	0.426533i
$809$	20.0000			0.703163			0.351581	−	0.936157i	$-0.385644\pi$
$809$	20.0000			0.703163			0.351581	+	0.936157i	$0.385644\pi$
$810$		0			0
$811$	1.00000			0.0351147			0.0175574	−	0.999846i	$-0.494411\pi$
$811$	1.00000			0.0351147			0.0175574	+	0.999846i	$0.494411\pi$
$812$	−2.00000	+	3.46410i	−0.0701862	+	0.121566i
$813$		0			0
$814$	−12.5000	−	21.6506i	−0.438125	−	0.758854i
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$		0			0
$817$	−5.00000	+	8.66025i	−0.174928	+	0.302984i
$818$	10.0000			0.349642
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	−0.939989	−	0.341206i	$-0.889165\pi$
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	0.765487	+	0.643451i	$0.222498\pi$
$822$		0			0
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	−0.993883	−	0.110437i	$-0.964775\pi$
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	0.401300	−	0.915947i	$-0.368558\pi$
$824$	−0.500000	−	0.866025i	−0.0174183	−	0.0301694i
$825$		0			0
$826$	−7.00000	+	12.1244i	−0.243561	+	0.421860i
$827$	33.0000			1.14752			0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000			1.14752			0.573761	+	0.819023i	$0.305484\pi$
$828$		0			0
$829$	10.0000			0.347314			0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000			0.347314			0.173657	+	0.984806i	$0.444442\pi$
$830$	−2.00000	+	3.46410i	−0.0694210	+	0.120241i
$831$		0			0
$832$		0			0
$833$	1.00000	+	1.73205i	0.0346479	+	0.0600120i
$834$		0			0
$835$	−5.00000	+	8.66025i	−0.173032	+	0.299700i
$836$	5.00000			0.172929
$837$		0			0
$838$	6.00000			0.207267
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	−0.898482	−	0.439010i	$-0.855329\pi$
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	0.829435	+	0.558604i	$0.188663\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−13.5000	−	23.3827i	−0.465241	−	0.805821i
$843$		0			0
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$	13.0000			0.447214
$846$		0			0
$847$	−14.0000			−0.481046
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$		0			0
$850$	4.00000	+	6.92820i	0.137199	+	0.237635i
$851$	−2.50000	−	4.33013i	−0.0856989	−	0.148435i
$852$		0			0
$853$	8.00000	−	13.8564i	0.273915	−	0.474434i	−0.695946	−	0.718094i	$-0.745015\pi$
$853$	8.00000	−	13.8564i	0.273915	−	0.474434i	0.969861	+	0.243660i	$0.0783480\pi$
$854$		0			0
$855$		0			0
$856$	12.0000			0.410152
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	−0.839268	−	0.543718i	$-0.817016\pi$
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	0.890507	+	0.454969i	$0.150350\pi$
$858$		0			0
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	0.996559	−	0.0828900i	$-0.0264150\pi$
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	−0.570064	+	0.821600i	$0.693082\pi$
$860$	−5.00000	−	8.66025i	−0.170499	−	0.295312i
$861$		0			0
$862$	7.50000	−	12.9904i	0.255451	−	0.442454i
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$	7.00000			0.238007
$866$	−2.00000	+	3.46410i	−0.0679628	+	0.117715i
$867$		0			0
$868$	−4.50000	−	7.79423i	−0.152740	−	0.264553i
$869$	15.0000	+	25.9808i	0.508840	+	0.881337i
$870$		0			0
$871$		0			0
$872$	−7.00000			−0.237050
$873$		0			0
$874$	1.00000			0.0338255
$875$	4.50000	−	7.79423i	0.152128	−	0.263493i
$876$		0			0
$877$	25.0000	+	43.3013i	0.844190	+	1.46218i	0.886323	+	0.463068i	$0.153251\pi$
$877$	25.0000	+	43.3013i	0.844190	+	1.46218i	−0.0421327	+	0.999112i	$0.513415\pi$
$878$	12.0000	+	20.7846i	0.404980	+	0.701447i
$879$		0			0
$880$	−2.50000	+	4.33013i	−0.0842750	+	0.145969i
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$		0			0
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$		0			0
$885$		0			0
$886$	−5.50000	−	9.52628i	−0.184776	−	0.320042i
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$		0			0
$890$	9.00000			0.301681
$891$		0			0
$892$	5.00000			0.167412
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$		0			0
$895$	−12.0000	−	20.7846i	−0.401116	−	0.694753i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	−5.00000	+	8.66025i	−0.166852	+	0.288996i
$899$	36.0000			1.20067
$900$		0			0
$901$	24.0000			0.799556
$902$	−22.5000	+	38.9711i	−0.749168	+	1.29760i
$903$		0			0
$904$	1.00000	+	1.73205i	0.0332595	+	0.0576072i
$905$	9.00000	+	15.5885i	0.299170	+	0.518178i
$906$		0			0
$907$	−15.0000	+	25.9808i	−0.498067	+	0.862677i	−0.999998	−	0.00223080i	$-0.999290\pi$
$907$	−15.0000	+	25.9808i	−0.498067	+	0.862677i	0.501931	+	0.864908i	$0.332623\pi$
$908$	−6.00000			−0.199117
$909$		0			0
$910$		0			0
$911$	−12.0000	+	20.7846i	−0.397578	+	0.688625i	−0.993426	−	0.114472i	$-0.963482\pi$
$911$	−12.0000	+	20.7846i	−0.397578	+	0.688625i	0.595849	+	0.803097i	$0.296816\pi$
$912$		0			0
$913$	10.0000	+	17.3205i	0.330952	+	0.573225i
$914$	6.50000	+	11.2583i	0.215001	+	0.372392i
$915$		0			0
$916$	−14.0000	+	24.2487i	−0.462573	+	0.801200i
$917$	22.0000			0.726504
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$	−0.500000	+	0.866025i	−0.0164845	+	0.0285520i
$921$		0			0
$922$	−15.5000	−	26.8468i	−0.510465	−	0.884152i
$923$		0			0
$924$		0			0
$925$	10.0000	−	17.3205i	0.328798	−	0.569495i
$926$	14.0000			0.460069
$927$		0			0
$928$	4.00000			0.131306
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	0.283178	+	0.959067i	$0.408611\pi$
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$930$		0			0
$931$	0.500000	+	0.866025i	0.0163868	+	0.0283828i
$932$	7.00000	+	12.1244i	0.229293	+	0.397146i
$933$		0			0
$934$	13.0000	−	22.5167i	0.425373	−	0.736768i
$935$	−10.0000			−0.327035
$936$		0			0
$937$	−28.0000			−0.914720			−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000			−0.914720			−0.457360	+	0.889282i	$0.651205\pi$
$938$	4.00000	−	6.92820i	0.130605	−	0.226214i
$939$		0			0
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	6.50000	+	11.2583i	0.211894	+	0.367011i	0.952307	−	0.305141i	$-0.0987035\pi$
$941$	6.50000	+	11.2583i	0.211894	+	0.367011i	−0.740413	+	0.672152i	$0.765370\pi$
$942$		0			0
$943$	−4.50000	+	7.79423i	−0.146540	+	0.253815i
$944$	14.0000			0.455661
$945$		0			0
$946$	−50.0000			−1.62564
$947$	−8.50000	+	14.7224i	−0.276213	+	0.478415i	−0.970440	−	0.241341i	$-0.922413\pi$
$947$	−8.50000	+	14.7224i	−0.276213	+	0.478415i	0.694228	+	0.719756i	$0.255746\pi$
$948$		0			0
$949$		0			0
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$		0			0
$952$	1.00000	−	1.73205i	0.0324102	−	0.0561361i
$953$	−44.0000			−1.42530			−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000			−1.42530			−0.712650	+	0.701520i	$0.752505\pi$
$954$		0			0
$955$	−3.00000			−0.0970777
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$		0			0
$958$	−16.0000	−	27.7128i	−0.516937	−	0.895360i
$959$	−8.00000	−	13.8564i	−0.258333	−	0.447447i
$960$		0			0
$961$	−25.0000	+	43.3013i	−0.806452	+	1.39682i
$962$		0			0
$963$		0			0
$964$	14.0000			0.450910
$965$	−5.00000	+	8.66025i	−0.160956	+	0.278783i
$966$		0			0
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	0.849499	−	0.527591i	$-0.176905\pi$
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	−0.881656	+	0.471892i	$0.843571\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$		0			0
$970$	−8.00000	+	13.8564i	−0.256865	+	0.444902i
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$		0			0
$973$	20.0000			0.641171
$974$	13.0000	−	22.5167i	0.416547	−	0.721480i
$975$		0			0
$976$		0			0
$977$	30.0000	+	51.9615i	0.959785	+	1.66240i	0.723017	+	0.690830i	$0.242755\pi$
$977$	30.0000	+	51.9615i	0.959785	+	1.66240i	0.236768	+	0.971566i	$0.423912\pi$
$978$		0			0
$979$	22.5000	−	38.9711i	0.719103	−	1.24552i
$980$	−1.00000			−0.0319438
$981$		0			0
$982$	9.00000			0.287202
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	−0.999694	−	0.0247352i	$-0.992126\pi$
$983$	−15.0000	+	25.9808i	−0.478426	+	0.828658i	0.521268	+	0.853393i	$0.325459\pi$
$984$		0			0
$985$	5.00000	+	8.66025i	0.159313	+	0.275939i
$986$	4.00000	+	6.92820i	0.127386	+	0.220639i
$987$		0			0
$988$		0			0
$989$	−10.0000			−0.317982
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−4.50000	+	7.79423i	−0.142875	+	0.247467i
$993$		0			0
$994$	−6.50000	−	11.2583i	−0.206167	−	0.357093i
$995$	−6.50000	−	11.2583i	−0.206064	−	0.356913i
$996$		0			0
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	0.390822	+	0.920466i	$0.372191\pi$
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	−0.992558	+	0.121771i	$0.961143\pi$
$998$	−10.0000			−0.316544
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.n.379.1		2
3.2	odd	2		1134.2.f.c.379.1		2
9.2	odd	6		378.2.a.f.1.1	yes	1
9.4	even	3	inner	1134.2.f.n.757.1		2
9.5	odd	6		1134.2.f.c.757.1		2
9.7	even	3		378.2.a.c.1.1	✓	1
36.7	odd	6		3024.2.a.m.1.1		1
36.11	even	6		3024.2.a.t.1.1		1
45.29	odd	6		9450.2.a.bx.1.1		1
45.34	even	6		9450.2.a.dc.1.1		1
63.20	even	6		2646.2.a.v.1.1		1
63.34	odd	6		2646.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.a.c.1.1	✓	1	9.7	even	3
378.2.a.f.1.1	yes	1	9.2	odd	6
1134.2.f.c.379.1		2	3.2	odd	2
1134.2.f.c.757.1		2	9.5	odd	6
1134.2.f.n.379.1		2	1.1	even	1	trivial
1134.2.f.n.757.1		2	9.4	even	3	inner
2646.2.a.i.1.1		1	63.34	odd	6
2646.2.a.v.1.1		1	63.20	even	6
3024.2.a.m.1.1		1	36.7	odd	6
3024.2.a.t.1.1		1	36.11	even	6
9450.2.a.bx.1.1		1	45.29	odd	6
9450.2.a.dc.1.1		1	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(2.50000 - 4.33013i) q^{11} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} -1.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-2.50000 - 4.33013i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{28} +(2.00000 - 3.46410i) q^{29} +(4.50000 + 7.79423i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +1.00000 q^{35} +5.00000 q^{37} +(-0.500000 + 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} -5.00000 q^{44} -1.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} -12.0000 q^{53} +5.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(-7.00000 - 12.1244i) q^{59} +9.00000 q^{62} +1.00000 q^{64} +(4.00000 + 6.92820i) q^{67} +(1.00000 + 1.73205i) q^{68} +(0.500000 - 0.866025i) q^{70} +13.0000 q^{71} -2.00000 q^{73} +(2.50000 - 4.33013i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-2.50000 - 4.33013i) q^{77} +(-3.00000 + 5.19615i) q^{79} -1.00000 q^{80} -9.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(-1.00000 - 1.73205i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(-2.50000 + 4.33013i) q^{88} +9.00000 q^{89} +(-0.500000 + 0.866025i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(-8.00000 + 13.8564i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} + 2 q^{10} + 5 q^{11} - q^{14} - q^{16} - 4 q^{17} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} + 4 q^{25} - 2 q^{28} + 4 q^{29} + 9 q^{31} + q^{32} - 2 q^{34} + 2 q^{35} + 10 q^{37} - q^{38} - q^{40} - 9 q^{41} + 10 q^{43} - 10 q^{44} - 2 q^{46} + 6 q^{47} - q^{49} - 4 q^{50} - 24 q^{53} + 10 q^{55} - q^{56} - 4 q^{58} - 14 q^{59} + 18 q^{62} + 2 q^{64} + 8 q^{67} + 2 q^{68} + q^{70} + 26 q^{71} - 4 q^{73} + 5 q^{74} + q^{76} - 5 q^{77} - 6 q^{79} - 2 q^{80} - 18 q^{82} - 4 q^{83} - 2 q^{85} - 10 q^{86} - 5 q^{88} + 18 q^{89} - q^{92} - 6 q^{94} - q^{95} - 16 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 + 2 * q^10 + 5 * q^11 - q^14 - q^16 - 4 * q^17 - 2 * q^19 + q^20 - 5 * q^22 - q^23 + 4 * q^25 - 2 * q^28 + 4 * q^29 + 9 * q^31 + q^32 - 2 * q^34 + 2 * q^35 + 10 * q^37 - q^38 - q^40 - 9 * q^41 + 10 * q^43 - 10 * q^44 - 2 * q^46 + 6 * q^47 - q^49 - 4 * q^50 - 24 * q^53 + 10 * q^55 - q^56 - 4 * q^58 - 14 * q^59 + 18 * q^62 + 2 * q^64 + 8 * q^67 + 2 * q^68 + q^70 + 26 * q^71 - 4 * q^73 + 5 * q^74 + q^76 - 5 * q^77 - 6 * q^79 - 2 * q^80 - 18 * q^82 - 4 * q^83 - 2 * q^85 - 10 * q^86 - 5 * q^88 + 18 * q^89 - q^92 - 6 * q^94 - q^95 - 16 * q^97 - 2 * q^98

Introduction

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