LMFDB - Embedded newform 819.2.j.c.352.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(235,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	819.352
Dual form			819.2.j.c.235.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30902 + 2.26728i) q^{2} +(-2.42705 - 4.20378i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-2.00000 - 1.73205i) q^{7} +7.47214 q^{8} +(2.92705 + 5.06980i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +(6.54508 - 2.26728i) q^{14} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +(-1.50000 + 2.59808i) q^{19} -10.8541 q^{20} +7.85410 q^{22} +(-4.11803 + 7.13264i) q^{23} +(1.30902 - 2.26728i) q^{26} +(-2.42705 + 12.6113i) q^{28} -4.47214 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-5.42705 - 9.39993i) q^{32} -3.85410 q^{34} +(-5.59017 + 1.93649i) q^{35} +(-2.35410 + 4.07742i) q^{37} +(-3.92705 - 6.80185i) q^{38} +(8.35410 - 14.4697i) q^{40} +4.47214 q^{41} -8.00000 q^{43} +(-7.28115 + 12.6113i) q^{44} +(-10.7812 - 18.6735i) q^{46} +(-3.73607 + 6.47106i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.42705 + 4.20378i) q^{52} +(-3.73607 - 6.47106i) q^{53} -6.70820 q^{55} +(-14.9443 - 12.9421i) q^{56} +(5.85410 - 10.1396i) q^{58} +(-0.736068 - 1.27491i) q^{59} +(-1.50000 + 2.59808i) q^{61} +13.0902 q^{62} +8.70820 q^{64} +(-1.11803 + 1.93649i) q^{65} +(1.50000 + 2.59808i) q^{67} +(3.57295 - 6.18853i) q^{68} +(2.92705 - 15.2094i) q^{70} +8.94427 q^{71} +(1.35410 + 2.34537i) q^{73} +(-6.16312 - 10.6748i) q^{74} +14.5623 q^{76} +(-1.50000 + 7.79423i) q^{77} +(1.35410 - 2.34537i) q^{79} +(11.0172 + 19.0824i) q^{80} +(-5.85410 + 10.1396i) q^{82} +3.29180 q^{85} +(10.4721 - 18.1383i) q^{86} +(-11.2082 - 19.4132i) q^{88} +(1.11803 - 1.93649i) q^{89} +(2.00000 + 1.73205i) q^{91} +39.9787 q^{92} +(-9.78115 - 16.9415i) q^{94} +(3.35410 + 5.80948i) q^{95} +9.41641 q^{97} +(-17.0172 - 6.80185i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + 5 q^{10} - 6 q^{11} - 4 q^{13} + 15 q^{14} - 13 q^{16} - 6 q^{17} - 6 q^{19} - 30 q^{20} + 18 q^{22} - 12 q^{23} + 3 q^{26} - 3 q^{28} - 10 q^{31} - 15 q^{32}+ \cdots - 39 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 - 3 * q^4 - 8 * q^7 + 12 * q^8 + 5 * q^10 - 6 * q^11 - 4 * q^13 + 15 * q^14 - 13 * q^16 - 6 * q^17 - 6 * q^19 - 30 * q^20 + 18 * q^22 - 12 * q^23 + 3 * q^26 - 3 * q^28 - 10 * q^31 - 15 * q^32 - 2 * q^34 + 4 * q^37 - 9 * q^38 + 20 * q^40 - 32 * q^43 - 9 * q^44 - 23 * q^46 - 6 * q^47 + 4 * q^49 + 3 * q^52 - 6 * q^53 - 24 * q^56 + 10 * q^58 + 6 * q^59 - 6 * q^61 + 30 * q^62 + 8 * q^64 + 6 * q^67 + 21 * q^68 + 5 * q^70 - 8 * q^73 - 9 * q^74 + 18 * q^76 - 6 * q^77 - 8 * q^79 + 15 * q^80 - 10 * q^82 + 40 * q^85 + 24 * q^86 - 18 * q^88 + 8 * q^91 + 66 * q^92 - 19 * q^94 - 16 * q^97 - 39 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.30902	+	2.26728i	−0.925615	+	1.60321i	−0.135045	+	0.990839i	$0.543118\pi$
$2$	−1.30902	+	2.26728i	−0.925615	+	1.60321i	−0.790569	+	0.612372i	$0.790215\pi$
$3$		0			0
$3$		0			0
$4$	−2.42705	−	4.20378i	−1.21353	−	2.10189i
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	1.00000			$0$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	7.47214			2.64180
$9$		0			0
$10$	2.92705	+	5.06980i	0.925615	+	1.60321i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	6.54508	−	2.26728i	1.74925	−	0.605957i
$15$		0			0
$16$	−4.92705	+	8.53390i	−1.23176	+	2.13348i
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	0.941375	−	0.337363i	$-0.109535\pi$
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	−0.762852	+	0.646573i	$0.776202\pi$
$18$		0			0
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$	−10.8541			−2.42705
$21$		0			0
$22$	7.85410			1.67450
$23$	−4.11803	+	7.13264i	−0.858669	+	1.48726i	0.0145291	+	0.999894i	$0.495375\pi$
$23$	−4.11803	+	7.13264i	−0.858669	+	1.48726i	−0.873199	+	0.487365i	$0.837958\pi$
$24$		0			0
$25$		0			0
$26$	1.30902	−	2.26728i	0.256719	−	0.444651i
$27$		0			0
$28$	−2.42705	+	12.6113i	−0.458670	+	2.38332i
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−5.42705	−	9.39993i	−0.959376	−	1.66169i
$33$		0			0
$34$	−3.85410			−0.660973
$35$	−5.59017	+	1.93649i	−0.944911	+	0.327327i
$36$		0			0
$37$	−2.35410	+	4.07742i	−0.387012	+	0.670324i	−0.992046	−	0.125875i	$-0.959826\pi$
$37$	−2.35410	+	4.07742i	−0.387012	+	0.670324i	0.605034	+	0.796200i	$0.293159\pi$
$38$	−3.92705	−	6.80185i	−0.637052	−	1.10341i
$39$		0			0
$40$	8.35410	−	14.4697i	1.32090	−	2.28787i
$41$	4.47214			0.698430			0.349215	−	0.937043i	$-0.386448\pi$
$41$	4.47214			0.698430			0.349215	+	0.937043i	$0.386448\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−7.28115	+	12.6113i	−1.09768	+	1.90123i
$45$		0			0
$46$	−10.7812	−	18.6735i	−1.58959	−	2.75326i
$47$	−3.73607	+	6.47106i	−0.544962	+	0.943901i	0.453648	+	0.891181i	$0.350122\pi$
$47$	−3.73607	+	6.47106i	−0.544962	+	0.943901i	−0.998609	+	0.0527200i	$0.983211\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$	2.42705	+	4.20378i	0.336571	+	0.582959i
$53$	−3.73607	−	6.47106i	−0.513188	−	0.888868i	−0.999883	−	0.0152962i	$-0.995131\pi$
$53$	−3.73607	−	6.47106i	−0.513188	−	0.888868i	0.486695	−	0.873572i	$-0.338202\pi$
$54$		0			0
$55$	−6.70820			−0.904534
$56$	−14.9443	−	12.9421i	−1.99701	−	1.72946i
$57$		0			0
$58$	5.85410	−	10.1396i	0.768681	−	1.33139i
$59$	−0.736068	−	1.27491i	−0.0958279	−	0.165979i	0.814126	−	0.580688i	$-0.197217\pi$
$59$	−0.736068	−	1.27491i	−0.0958279	−	0.165979i	−0.909954	+	0.414710i	$0.863883\pi$
$60$		0			0
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	−0.945931	−	0.324367i	$-0.894849\pi$
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	0.753876	+	0.657017i	$0.228182\pi$
$62$	13.0902			1.66245
$63$		0			0
$64$	8.70820			1.08853
$65$	−1.11803	+	1.93649i	−0.138675	+	0.240192i
$66$		0			0
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$	3.57295	−	6.18853i	0.433284	−	0.750469i
$69$		0			0
$70$	2.92705	−	15.2094i	0.349850	−	1.81787i
$71$	8.94427			1.06149			0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427			1.06149			0.530745	+	0.847532i	$0.321912\pi$
$72$		0			0
$73$	1.35410	+	2.34537i	0.158486	+	0.274505i	0.934323	−	0.356428i	$-0.116006\pi$
$73$	1.35410	+	2.34537i	0.158486	+	0.274505i	−0.775837	+	0.630933i	$0.782672\pi$
$74$	−6.16312	−	10.6748i	−0.716448	−	1.24092i
$75$		0			0
$76$	14.5623			1.67041
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$		0			0
$79$	1.35410	−	2.34537i	0.152348	−	0.263875i	−0.779742	−	0.626101i	$-0.784650\pi$
$79$	1.35410	−	2.34537i	0.152348	−	0.263875i	0.932090	+	0.362226i	$0.117983\pi$
$80$	11.0172	+	19.0824i	1.23176	+	2.13348i
$81$		0			0
$82$	−5.85410	+	10.1396i	−0.646477	+	1.11973i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	3.29180			0.357045
$86$	10.4721	−	18.1383i	1.12924	−	1.95590i
$87$		0			0
$88$	−11.2082	−	19.4132i	−1.19480	−	2.06945i
$89$	1.11803	−	1.93649i	0.118511	−	0.205268i	−0.800667	−	0.599110i	$-0.795521\pi$
$89$	1.11803	−	1.93649i	0.118511	−	0.205268i	0.919178	+	0.393842i	$0.128854\pi$
$90$		0			0
$91$	2.00000	+	1.73205i	0.209657	+	0.181568i
$92$	39.9787			4.16807
$93$		0			0
$94$	−9.78115	−	16.9415i	−1.00885	−	1.74738i
$95$	3.35410	+	5.80948i	0.344124	+	0.596040i
$96$		0			0
$97$	9.41641			0.956091			0.478046	−	0.878335i	$-0.341345\pi$
$97$	9.41641			0.956091			0.478046	+	0.878335i	$0.341345\pi$
$98$	−17.0172	−	6.80185i	−1.71900	−	0.687091i
$99$		0			0
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	1.35410	−	2.34537i	0.133424	−	0.231097i	−0.791571	−	0.611078i	$-0.790736\pi$
$103$	1.35410	−	2.34537i	0.133424	−	0.231097i	0.924994	+	0.379981i	$0.124070\pi$
$104$	−7.47214			−0.732703
$105$		0			0
$106$	19.5623			1.90006
$107$	−4.88197	+	8.45581i	−0.471957	+	0.817454i	−0.999485	−	0.0320835i	$-0.989786\pi$
$107$	−4.88197	+	8.45581i	−0.471957	+	0.817454i	0.527528	+	0.849538i	$0.323119\pi$
$108$		0			0
$109$	1.35410	+	2.34537i	0.129699	+	0.224646i	0.923560	−	0.383454i	$-0.125265\pi$
$109$	1.35410	+	2.34537i	0.129699	+	0.224646i	−0.793861	+	0.608100i	$0.791932\pi$
$110$	8.78115	−	15.2094i	0.837250	−	1.45016i
$111$		0			0
$112$	24.6353	−	8.53390i	2.32781	−	0.806378i
$113$	−2.94427			−0.276974			−0.138487	−	0.990364i	$-0.544224\pi$
$113$	−2.94427			−0.276974			−0.138487	+	0.990364i	$0.544224\pi$
$114$		0			0
$115$	9.20820	+	15.9491i	0.858669	+	1.48726i
$116$	10.8541	+	18.7999i	1.00778	+	1.74552i
$117$		0			0
$118$	3.85410			0.354799
$119$	0.736068	−	3.82472i	0.0674752	−	0.350612i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−3.92705	−	6.80185i	−0.355538	−	0.615811i
$123$		0			0
$124$	−12.1353	+	21.0189i	−1.08978	+	1.88755i
$125$	11.1803			1.00000
$126$		0			0
$127$	−11.4164			−1.01304			−0.506521	−	0.862228i	$-0.669069\pi$
$127$	−11.4164			−1.01304			−0.506521	+	0.862228i	$0.669069\pi$
$128$	−0.545085	+	0.944115i	−0.0481792	+	0.0834488i
$129$		0			0
$130$	−2.92705	−	5.06980i	−0.256719	−	0.444651i
$131$	−4.11803	+	7.13264i	−0.359794	+	0.623182i	−0.987926	−	0.154925i	$-0.950486\pi$
$131$	−4.11803	+	7.13264i	−0.359794	+	0.623182i	0.628132	+	0.778107i	$0.283820\pi$
$132$		0			0
$133$	7.50000	−	2.59808i	0.650332	−	0.225282i
$134$	−7.85410			−0.678491
$135$		0			0
$136$	5.50000	+	9.52628i	0.471621	+	0.816872i
$137$	−4.11803	−	7.13264i	−0.351827	−	0.609383i	0.634742	−	0.772724i	$-0.281106\pi$
$137$	−4.11803	−	7.13264i	−0.351827	−	0.609383i	−0.986570	+	0.163341i	$0.947773\pi$
$138$		0			0
$139$	−23.4164			−1.98615			−0.993077	−	0.117466i	$-0.962523\pi$
$139$	−23.4164			−1.98615			−0.993077	+	0.117466i	$0.962523\pi$
$140$	21.7082	+	18.7999i	1.83468	+	1.58888i
$141$		0			0
$142$	−11.7082	+	20.2792i	−0.982531	+	1.70179i
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	−5.00000	+	8.66025i	−0.415227	+	0.719195i
$146$	−7.09017			−0.586787
$147$		0			0
$148$	22.8541			1.87860
$149$	0.354102	−	0.613323i	0.0290092	−	0.0502453i	−0.851156	−	0.524912i	$-0.824098\pi$
$149$	0.354102	−	0.613323i	0.0290092	−	0.0502453i	0.880166	+	0.474667i	$0.157431\pi$
$150$		0			0
$151$	−10.2082	−	17.6811i	−0.830732	−	1.43887i	−0.897459	−	0.441098i	$-0.854589\pi$
$151$	−10.2082	−	17.6811i	−0.830732	−	1.43887i	0.0667268	−	0.997771i	$-0.478744\pi$
$152$	−11.2082	+	19.4132i	−0.909105	+	1.57462i
$153$		0			0
$154$	−15.7082	−	13.6037i	−1.26580	−	1.09622i
$155$	−11.1803			−0.898027
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	3.54508	+	6.14027i	0.282032	+	0.488493i
$159$		0			0
$160$	−24.2705			−1.91875
$161$	20.5902	−	7.13264i	1.62273	−	0.562131i
$162$		0			0
$163$	8.20820	−	14.2170i	0.642916	−	1.11356i	−0.341862	−	0.939750i	$-0.611058\pi$
$163$	8.20820	−	14.2170i	0.642916	−	1.11356i	0.984779	−	0.173813i	$-0.0556090\pi$
$164$	−10.8541	−	18.7999i	−0.847563	−	1.46802i
$165$		0			0
$166$		0			0
$167$	−22.4721			−1.73895			−0.869473	−	0.493980i	$-0.835541\pi$
$167$	−22.4721			−1.73895			−0.869473	+	0.493980i	$0.835541\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−4.30902	+	7.46344i	−0.330487	+	0.572419i
$171$		0			0
$172$	19.4164	+	33.6302i	1.48049	+	2.56428i
$173$	−8.20820	+	14.2170i	−0.624058	+	1.08090i	0.364664	+	0.931139i	$0.381184\pi$
$173$	−8.20820	+	14.2170i	−0.624058	+	1.08090i	−0.988722	+	0.149761i	$0.952149\pi$
$174$		0			0
$175$		0			0
$176$	29.5623			2.22834
$177$		0			0
$178$	2.92705	+	5.06980i	0.219392	+	0.379998i
$179$	−10.0623	−	17.4284i	−0.752092	−	1.30266i	−0.946807	−	0.321802i	$-0.895712\pi$
$179$	−10.0623	−	17.4284i	−0.752092	−	1.30266i	0.194715	−	0.980860i	$-0.437622\pi$
$180$		0			0
$181$	−25.4164			−1.88919			−0.944593	−	0.328243i	$-0.893544\pi$
$181$	−25.4164			−1.88919			−0.944593	+	0.328243i	$0.893544\pi$
$182$	−6.54508	+	2.26728i	−0.485154	+	0.168062i
$183$		0			0
$184$	−30.7705	+	53.2961i	−2.26843	+	3.92904i
$185$	5.26393	+	9.11740i	0.387012	+	0.670324i
$186$		0			0
$187$	2.20820	−	3.82472i	0.161480	−	0.279691i
$188$	36.2705			2.64530
$189$		0			0
$190$	−17.5623			−1.27410
$191$	5.59017	−	9.68246i	0.404491	−	0.700598i	−0.589772	−	0.807570i	$-0.700782\pi$
$191$	5.59017	−	9.68246i	0.404491	−	0.700598i	0.994262	+	0.106972i	$0.0341155\pi$
$192$		0			0
$193$	−0.354102	−	0.613323i	−0.0254888	−	0.0441479i	0.853000	−	0.521912i	$-0.174781\pi$
$193$	−0.354102	−	0.613323i	−0.0254888	−	0.0441479i	−0.878488	+	0.477764i	$0.841448\pi$
$194$	−12.3262	+	21.3497i	−0.884972	+	1.53282i
$195$		0			0
$196$	26.6976	−	21.0189i	1.90697	−	1.50135i
$197$	9.05573			0.645194			0.322597	−	0.946536i	$-0.395444\pi$
$197$	9.05573			0.645194			0.322597	+	0.946536i	$0.395444\pi$
$198$		0			0
$199$	10.3541	+	17.9338i	0.733983	+	1.27130i	0.955168	+	0.296064i	$0.0956741\pi$
$199$	10.3541	+	17.9338i	0.733983	+	1.27130i	−0.221185	+	0.975232i	$0.570993\pi$
$200$		0			0
$201$		0			0
$202$	23.5623			1.65784
$203$	8.94427	+	7.74597i	0.627765	+	0.543660i
$204$		0			0
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$	3.54508	+	6.14027i	0.246998	+	0.427813i
$207$		0			0
$208$	4.92705	−	8.53390i	0.341630	−	0.591720i
$209$	9.00000			0.622543
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−18.1353	+	31.4112i	−1.24553	+	2.15733i
$213$		0			0
$214$	−12.7812	−	22.1376i	−0.873702	−	1.51330i
$215$	−8.94427	+	15.4919i	−0.609994	+	1.05654i
$216$		0			0
$217$	−2.50000	+	12.9904i	−0.169711	+	0.881845i
$218$	−7.09017			−0.480207
$219$		0			0
$220$	16.2812	+	28.1998i	1.09768	+	1.90123i
$221$	−0.736068	−	1.27491i	−0.0495133	−	0.0857595i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	−5.42705	+	28.1998i	−0.362610	+	1.88418i
$225$		0			0
$226$	3.85410	−	6.67550i	0.256371	−	0.444048i
$227$	2.97214	+	5.14789i	0.197268	+	0.341677i	0.947642	−	0.319336i	$-0.103460\pi$
$227$	2.97214	+	5.14789i	0.197268	+	0.341677i	−0.750374	+	0.661014i	$0.770127\pi$
$228$		0			0
$229$	−12.0623	+	20.8925i	−0.797100	+	1.38062i	0.124398	+	0.992232i	$0.460300\pi$
$229$	−12.0623	+	20.8925i	−0.797100	+	1.38062i	−0.921497	+	0.388385i	$0.873033\pi$
$230$	−48.2148			−3.17919
$231$		0			0
$232$	−33.4164			−2.19389
$233$	5.97214	−	10.3440i	0.391248	−	0.677661i	−0.601367	−	0.798973i	$-0.705377\pi$
$233$	5.97214	−	10.3440i	0.391248	−	0.677661i	0.992614	+	0.121312i	$0.0387103\pi$
$234$		0			0
$235$	8.35410	+	14.4697i	0.544962	+	0.943901i
$236$	−3.57295	+	6.18853i	−0.232579	+	0.402839i
$237$		0			0
$238$	7.70820	+	6.67550i	0.499649	+	0.432708i
$239$	−19.4164			−1.25594			−0.627972	−	0.778236i	$-0.716115\pi$
$239$	−19.4164			−1.25594			−0.627972	+	0.778236i	$0.716115\pi$
$240$		0			0
$241$	−2.35410	−	4.07742i	−0.151641	−	0.262650i	0.780190	−	0.625543i	$-0.215122\pi$
$241$	−2.35410	−	4.07742i	−0.151641	−	0.262650i	−0.931831	+	0.362893i	$0.881789\pi$
$242$	2.61803	+	4.53457i	0.168294	+	0.291493i
$243$		0			0
$244$	14.5623			0.932256
$245$	14.5344	+	5.80948i	0.928571	+	0.371154i
$246$		0			0
$247$	1.50000	−	2.59808i	0.0954427	−	0.165312i
$248$	−18.6803	−	32.3553i	−1.18620	−	2.05456i
$249$		0			0
$250$	−14.6353	+	25.3490i	−0.925615	+	1.60321i
$251$	−1.52786			−0.0964379			−0.0482190	−	0.998837i	$-0.515355\pi$
$251$	−1.52786			−0.0964379			−0.0482190	+	0.998837i	$0.515355\pi$
$252$		0			0
$253$	24.7082			1.55339
$254$	14.9443	−	25.8842i	0.937687	−	1.62412i
$255$		0			0
$256$	7.28115	+	12.6113i	0.455072	+	0.788208i
$257$	−0.0278640	+	0.0482619i	−0.00173811	+	0.00301050i	−0.866893	−	0.498494i	$-0.833887\pi$
$257$	−0.0278640	+	0.0482619i	−0.00173811	+	0.00301050i	0.865155	+	0.501504i	$0.167220\pi$
$258$		0			0
$259$	11.7705	−	4.07742i	0.731384	−	0.253359i
$260$	10.8541			0.673143
$261$		0			0
$262$	−10.7812	−	18.6735i	−0.666062	−	1.15365i
$263$	13.0623	+	22.6246i	0.805456	+	1.39509i	0.915983	+	0.401218i	$0.131413\pi$
$263$	13.0623	+	22.6246i	0.805456	+	1.39509i	−0.110526	+	0.993873i	$0.535254\pi$
$264$		0			0
$265$	−16.7082			−1.02638
$266$	−3.92705	+	20.4056i	−0.240783	+	1.25114i
$267$		0			0
$268$	7.28115	−	12.6113i	0.444767	−	0.770359i
$269$	6.73607	+	11.6672i	0.410705	+	0.711362i	0.994967	−	0.100203i	$-0.0319492\pi$
$269$	6.73607	+	11.6672i	0.410705	+	0.711362i	−0.584262	+	0.811565i	$0.698616\pi$
$270$		0			0
$271$	10.2082	−	17.6811i	0.620104	−	1.07405i	−0.369362	−	0.929286i	$-0.620424\pi$
$271$	10.2082	−	17.6811i	0.620104	−	1.07405i	0.989466	−	0.144766i	$-0.0462430\pi$
$272$	−14.5066			−0.879590
$273$		0			0
$274$	21.5623			1.30263
$275$		0			0
$276$		0			0
$277$	0.208204	+	0.360620i	0.0125098	+	0.0216675i	0.872213	−	0.489127i	$-0.162685\pi$
$277$	0.208204	+	0.360620i	0.0125098	+	0.0216675i	−0.859703	+	0.510795i	$0.829351\pi$
$278$	30.6525	−	53.0916i	1.83841	−	3.18423i
$279$		0			0
$280$	−41.7705	+	14.4697i	−2.49627	+	0.864732i
$281$	−26.9443			−1.60736			−0.803680	−	0.595061i	$-0.797128\pi$
$281$	−26.9443			−1.60736			−0.803680	+	0.595061i	$0.797128\pi$
$282$		0			0
$283$	−13.0623	−	22.6246i	−0.776473	−	1.34489i	−0.933963	−	0.357371i	$-0.883673\pi$
$283$	−13.0623	−	22.6246i	−0.776473	−	1.34489i	0.157489	−	0.987521i	$-0.449660\pi$
$284$	−21.7082	−	37.5997i	−1.28814	−	2.23113i
$285$		0			0
$286$	−7.85410			−0.464423
$287$	−8.94427	−	7.74597i	−0.527964	−	0.457230i
$288$		0			0
$289$	7.41641	−	12.8456i	0.436259	−	0.755623i
$290$	−13.0902	−	22.6728i	−0.768681	−	1.33139i
$291$		0			0
$292$	6.57295	−	11.3847i	0.384653	−	0.666238i
$293$	14.9443			0.873054			0.436527	−	0.899691i	$-0.356208\pi$
$293$	14.9443			0.873054			0.436527	+	0.899691i	$0.356208\pi$
$294$		0			0
$295$	−3.29180			−0.191656
$296$	−17.5902	+	30.4671i	−1.02241	+	1.77086i
$297$		0			0
$298$	0.927051	+	1.60570i	0.0537026	+	0.0930157i
$299$	4.11803	−	7.13264i	0.238152	−	0.412491i
$300$		0			0
$301$	16.0000	+	13.8564i	0.922225	+	0.798670i
$302$	53.4508			3.07575
$303$		0			0
$304$	−14.7812	−	25.6017i	−0.847757	−	1.46836i
$305$	3.35410	+	5.80948i	0.192055	+	0.332650i
$306$		0			0
$307$	19.4164			1.10815			0.554076	−	0.832466i	$-0.313072\pi$
$307$	19.4164			1.10815			0.554076	+	0.832466i	$0.313072\pi$
$308$	36.4058	−	12.6113i	2.07441	−	0.718597i
$309$		0			0
$310$	14.6353	−	25.3490i	0.831227	−	1.43973i
$311$	−13.8820	−	24.0443i	−0.787174	−	1.36343i	−0.927692	−	0.373347i	$-0.878210\pi$
$311$	−13.8820	−	24.0443i	−0.787174	−	1.36343i	0.140518	−	0.990078i	$-0.455123\pi$
$312$		0			0
$313$	2.79180	−	4.83553i	0.157802	−	0.273320i	−0.776274	−	0.630396i	$-0.782893\pi$
$313$	2.79180	−	4.83553i	0.157802	−	0.273320i	0.934076	+	0.357075i	$0.116226\pi$
$314$	18.3262			1.03421
$315$		0			0
$316$	−13.1459			−0.739515
$317$	−4.11803	+	7.13264i	−0.231292	+	0.400609i	−0.958189	−	0.286138i	$-0.907629\pi$
$317$	−4.11803	+	7.13264i	−0.231292	+	0.400609i	0.726897	+	0.686747i	$0.240962\pi$
$318$		0			0
$319$	6.70820	+	11.6190i	0.375587	+	0.650536i
$320$	9.73607	−	16.8634i	0.544263	−	0.942691i
$321$		0			0
$322$	−10.7812	+	56.0205i	−0.600810	+	3.12190i
$323$	−4.41641			−0.245736
$324$		0			0
$325$		0			0
$326$	21.4894	+	37.2207i	1.19019	+	2.06146i
$327$		0			0
$328$	33.4164			1.84511
$329$	18.6803	−	6.47106i	1.02988	−	0.356761i
$330$		0			0
$331$	0.791796	−	1.37143i	0.0435210	−	0.0753807i	−0.843444	−	0.537217i	$-0.819476\pi$
$331$	0.791796	−	1.37143i	0.0435210	−	0.0753807i	0.886965	+	0.461836i	$0.152809\pi$
$332$		0			0
$333$		0			0
$334$	29.4164	−	50.9507i	1.60959	−	2.78790i
$335$	6.70820			0.366508
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	−1.30902	+	2.26728i	−0.0712011	+	0.123324i
$339$		0			0
$340$	−7.98936	−	13.8380i	−0.433284	−	0.750469i
$341$	−7.50000	+	12.9904i	−0.406148	+	0.703469i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−59.7771			−3.22296
$345$		0			0
$346$	−21.4894	−	37.2207i	−1.15527	−	2.00099i
$347$	11.5344	+	19.9782i	0.619201	+	1.07249i	0.989632	+	0.143628i	$0.0458768\pi$
$347$	11.5344	+	19.9782i	0.619201	+	1.07249i	−0.370430	+	0.928860i	$0.620790\pi$
$348$		0			0
$349$	−29.4164			−1.57462			−0.787312	−	0.616555i	$-0.788528\pi$
$349$	−29.4164			−1.57462			−0.787312	+	0.616555i	$0.788528\pi$
$350$		0			0
$351$		0			0
$352$	−16.2812	+	28.1998i	−0.867788	+	1.50305i
$353$	8.64590	+	14.9751i	0.460175	+	0.797046i	0.998969	−	0.0453912i	$-0.0144534\pi$
$353$	8.64590	+	14.9751i	0.460175	+	0.797046i	−0.538795	+	0.842437i	$0.681120\pi$
$354$		0			0
$355$	10.0000	−	17.3205i	0.530745	−	0.919277i
$356$	−10.8541			−0.575266
$357$		0			0
$358$	52.6869			2.78459
$359$	5.97214	−	10.3440i	0.315197	−	0.545938i	−0.664282	−	0.747482i	$-0.731263\pi$
$359$	5.97214	−	10.3440i	0.315197	−	0.545938i	0.979479	+	0.201544i	$0.0645960\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	33.2705	−	57.6262i	1.74866	−	3.02877i
$363$		0			0
$364$	2.42705	−	12.6113i	0.127212	−	0.661013i
$365$	6.05573			0.316971
$366$		0			0
$367$	6.35410	+	11.0056i	0.331681	+	0.574489i	0.982842	−	0.184451i	$-0.0590508\pi$
$367$	6.35410	+	11.0056i	0.331681	+	0.574489i	−0.651160	+	0.758940i	$0.725717\pi$
$368$	−40.5795	−	70.2858i	−2.11535	−	3.66390i
$369$		0			0
$370$	−27.5623			−1.43290
$371$	−3.73607	+	19.4132i	−0.193967	+	1.00788i
$372$		0			0
$373$	0.791796	−	1.37143i	0.0409976	−	0.0710100i	−0.844798	−	0.535085i	$-0.820280\pi$
$373$	0.791796	−	1.37143i	0.0409976	−	0.0710100i	0.885796	+	0.464075i	$0.153613\pi$
$374$	5.78115	+	10.0133i	0.298936	+	0.517773i
$375$		0			0
$376$	−27.9164	+	48.3526i	−1.43968	+	2.49360i
$377$	4.47214			0.230327
$378$		0			0
$379$	−15.4164			−0.791888			−0.395944	−	0.918275i	$-0.629583\pi$
$379$	−15.4164			−0.791888			−0.395944	+	0.918275i	$0.629583\pi$
$380$	16.2812	−	28.1998i	0.835206	−	1.44662i
$381$		0			0
$382$	14.6353	+	25.3490i	0.748805	+	1.29697i
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$	13.4164	+	11.6190i	0.683763	+	0.592157i
$386$	1.85410			0.0943713
$387$		0			0
$388$	−22.8541	−	39.5845i	−1.16024	−	2.00960i
$389$	0.736068	+	1.27491i	0.0373201	+	0.0646404i	0.884082	−	0.467332i	$-0.154785\pi$
$389$	0.736068	+	1.27491i	0.0373201	+	0.0646404i	−0.846762	+	0.531972i	$0.821451\pi$
$390$		0			0
$391$	−12.1246			−0.613168
$392$	7.47214	+	51.7685i	0.377400	+	2.61470i
$393$		0			0
$394$	−11.8541	+	20.5319i	−0.597201	+	1.03438i
$395$	−3.02786	−	5.24441i	−0.152348	−	0.263875i
$396$		0			0
$397$	13.0623	−	22.6246i	0.655578	−	1.13549i	−0.326170	−	0.945311i	$-0.605758\pi$
$397$	13.0623	−	22.6246i	0.655578	−	1.13549i	0.981748	−	0.190184i	$-0.0609084\pi$
$398$	−54.2148			−2.71754
$399$		0			0
$400$		0			0
$401$	7.11803	−	12.3288i	0.355458	−	0.615671i	−0.631739	−	0.775182i	$-0.717658\pi$
$401$	7.11803	−	12.3288i	0.355458	−	0.615671i	0.987196	+	0.159511i	$0.0509917\pi$
$402$		0			0
$403$	2.50000	+	4.33013i	0.124534	+	0.215699i
$404$	−21.8435	+	37.8340i	−1.08675	+	1.88231i
$405$		0			0
$406$	−29.2705	+	10.1396i	−1.45267	+	0.503220i
$407$	14.1246			0.700131
$408$		0			0
$409$	−4.35410	−	7.54153i	−0.215296	−	0.372904i	0.738068	−	0.674727i	$-0.235738\pi$
$409$	−4.35410	−	7.54153i	−0.215296	−	0.372904i	−0.953364	+	0.301822i	$0.902405\pi$
$410$	13.0902	+	22.6728i	0.646477	+	1.11973i
$411$		0			0
$412$	−13.1459			−0.647652
$413$	−0.736068	+	3.82472i	−0.0362195	+	0.188202i
$414$		0			0
$415$		0			0
$416$	5.42705	+	9.39993i	0.266083	+	0.460869i
$417$		0			0
$418$	−11.7812	+	20.4056i	−0.576235	+	0.998068i
$419$	−32.9443			−1.60943			−0.804717	−	0.593659i	$-0.797683\pi$
$419$	−32.9443			−1.60943			−0.804717	+	0.593659i	$0.797683\pi$
$420$		0			0
$421$	13.4164			0.653876			0.326938	−	0.945046i	$-0.393983\pi$
$421$	13.4164			0.653876			0.326938	+	0.945046i	$0.393983\pi$
$422$	−5.23607	+	9.06914i	−0.254888	+	0.441479i
$423$		0			0
$424$	−27.9164	−	48.3526i	−1.35574	−	2.34821i
$425$		0			0
$426$		0			0
$427$	7.50000	−	2.59808i	0.362950	−	0.125730i
$428$	47.3951			2.29093
$429$		0			0
$430$	−23.4164	−	40.5584i	−1.12924	−	1.95590i
$431$	−15.6803	−	27.1591i	−0.755295	−	1.30821i	−0.945227	−	0.326413i	$-0.894160\pi$
$431$	−15.6803	−	27.1591i	−0.755295	−	1.30821i	0.189932	−	0.981797i	$-0.439173\pi$
$432$		0			0
$433$	29.4164			1.41366			0.706831	−	0.707382i	$-0.250124\pi$
$433$	29.4164			1.41366			0.706831	+	0.707382i	$0.250124\pi$
$434$	−26.1803	−	22.6728i	−1.25670	−	1.08833i
$435$		0			0
$436$	6.57295	−	11.3847i	0.314787	−	0.545227i
$437$	−12.3541	−	21.3979i	−0.590977	−	1.02360i
$438$		0			0
$439$	−12.0623	+	20.8925i	−0.575702	+	0.997146i	0.420262	+	0.907403i	$0.361938\pi$
$439$	−12.0623	+	20.8925i	−0.575702	+	0.997146i	−0.995965	+	0.0897433i	$0.971395\pi$
$440$	−50.1246			−2.38960
$441$		0			0
$442$	3.85410			0.183321
$443$	1.11803	−	1.93649i	0.0531194	−	0.0920055i	−0.838243	−	0.545297i	$-0.816417\pi$
$443$	1.11803	−	1.93649i	0.0531194	−	0.0920055i	0.891362	+	0.453291i	$0.149750\pi$
$444$		0			0
$445$	−2.50000	−	4.33013i	−0.118511	−	0.205268i
$446$	5.23607	−	9.06914i	0.247935	−	0.429436i
$447$		0			0
$448$	−17.4164	−	15.0831i	−0.822848	−	0.712607i
$449$	34.3607			1.62158			0.810790	−	0.585337i	$-0.199038\pi$
$449$	34.3607			1.62158			0.810790	+	0.585337i	$0.199038\pi$
$450$		0			0
$451$	−6.70820	−	11.6190i	−0.315877	−	0.547115i
$452$	7.14590	+	12.3771i	0.336115	+	0.582168i
$453$		0			0
$454$	−15.5623			−0.730375
$455$	5.59017	−	1.93649i	0.262071	−	0.0907841i
$456$		0			0
$457$	3.06231	−	5.30407i	0.143249	−	0.248114i	−0.785470	−	0.618900i	$-0.787578\pi$
$457$	3.06231	−	5.30407i	0.143249	−	0.248114i	0.928718	+	0.370786i	$0.120912\pi$
$458$	−31.5795	−	54.6973i	−1.47561	−	2.55584i
$459$		0			0
$460$	44.6976	−	77.4184i	2.08403	−	3.60965i
$461$	−34.3607			−1.60034			−0.800168	−	0.599776i	$-0.795256\pi$
$461$	−34.3607			−1.60034			−0.800168	+	0.599776i	$0.795256\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	22.0344	−	38.1648i	1.02292	−	1.77176i
$465$		0			0
$466$	15.6353	+	27.0811i	0.724289	+	1.25451i
$467$	4.82624	−	8.35929i	0.223332	−	0.386822i	−0.732486	−	0.680782i	$-0.761640\pi$
$467$	4.82624	−	8.35929i	0.223332	−	0.386822i	0.955818	+	0.293960i	$0.0949734\pi$
$468$		0			0
$469$	1.50000	−	7.79423i	0.0692636	−	0.359904i
$470$	−43.7426			−2.01770
$471$		0			0
$472$	−5.50000	−	9.52628i	−0.253158	−	0.438483i
$473$	12.0000	+	20.7846i	0.551761	+	0.955677i
$474$		0			0
$475$		0			0
$476$	−17.8647	+	6.18853i	−0.818829	+	0.283651i
$477$		0			0
$478$	25.4164	−	44.0225i	1.16252	−	2.01354i
$479$	11.9164	+	20.6398i	0.544475	+	0.943058i	0.998640	+	0.0521401i	$0.0166043\pi$
$479$	11.9164	+	20.6398i	0.544475	+	0.943058i	−0.454165	+	0.890917i	$0.650062\pi$
$480$		0			0
$481$	2.35410	−	4.07742i	0.107338	−	0.185915i
$482$	12.3262			0.561445
$483$		0			0
$484$	−9.70820			−0.441282
$485$	10.5279	−	18.2348i	0.478046	−	0.827999i
$486$		0			0
$487$	10.9164	+	18.9078i	0.494670	+	0.856793i	0.999981	−	0.00614405i	$-0.00195572\pi$
$487$	10.9164	+	18.9078i	0.494670	+	0.856793i	−0.505311	+	0.862937i	$0.668622\pi$
$488$	−11.2082	+	19.4132i	−0.507372	+	0.878793i
$489$		0			0
$490$	−32.1976	+	25.3490i	−1.45454	+	1.14515i
$491$	25.5279			1.15206			0.576028	−	0.817430i	$-0.304602\pi$
$491$	25.5279			1.15206			0.576028	+	0.817430i	$0.304602\pi$
$492$		0			0
$493$	−3.29180	−	5.70156i	−0.148255	−	0.256785i
$494$	3.92705	+	6.80185i	0.176686	+	0.306030i
$495$		0			0
$496$	49.2705			2.21231
$497$	−17.8885	−	15.4919i	−0.802411	−	0.694908i
$498$		0			0
$499$	−13.2082	+	22.8773i	−0.591280	+	1.02413i	0.402780	+	0.915297i	$0.368044\pi$
$499$	−13.2082	+	22.8773i	−0.591280	+	1.02413i	−0.994060	+	0.108831i	$0.965289\pi$
$500$	−27.1353	−	46.9996i	−1.21353	−	2.10189i
$501$		0			0
$502$	2.00000	−	3.46410i	0.0892644	−	0.154610i
$503$	−20.9443			−0.933859			−0.466929	−	0.884295i	$-0.654640\pi$
$503$	−20.9443			−0.933859			−0.466929	+	0.884295i	$0.654640\pi$
$504$		0			0
$505$	−20.1246			−0.895533
$506$	−32.3435	+	56.0205i	−1.43784	+	2.49042i
$507$		0			0
$508$	27.7082	+	47.9920i	1.22935	+	2.12930i
$509$	−10.1180	+	17.5249i	−0.448474	+	0.776780i	−0.998287	−	0.0585081i	$-0.981366\pi$
$509$	−10.1180	+	17.5249i	−0.448474	+	0.776780i	0.549813	+	0.835288i	$0.314699\pi$
$510$		0			0
$511$	1.35410	−	7.03612i	0.0599019	−	0.311260i
$512$	−40.3050			−1.78124
$513$		0			0
$514$	−0.0729490	−	0.126351i	−0.00321764	−	0.00557312i
$515$	−3.02786	−	5.24441i	−0.133424	−	0.231097i
$516$		0			0
$517$	22.4164			0.985872
$518$	−6.16312	+	32.0245i	−0.270792	+	1.40708i
$519$		0			0
$520$	−8.35410	+	14.4697i	−0.366352	+	0.634540i
$521$	−8.97214	−	15.5402i	−0.393076	−	0.680828i	0.599777	−	0.800167i	$-0.295256\pi$
$521$	−8.97214	−	15.5402i	−0.393076	−	0.680828i	−0.992854	+	0.119339i	$0.961923\pi$
$522$		0			0
$523$	−16.3541	+	28.3261i	−0.715115	+	1.23862i	0.247800	+	0.968811i	$0.420292\pi$
$523$	−16.3541	+	28.3261i	−0.715115	+	1.23862i	−0.962915	+	0.269804i	$0.913041\pi$
$524$	39.9787			1.74648
$525$		0			0
$526$	−68.3951			−2.98217
$527$	3.68034	−	6.37454i	0.160318	−	0.277679i
$528$		0			0
$529$	−22.4164	−	38.8264i	−0.974626	−	1.68810i
$530$	21.8713	−	37.8822i	0.950030	−	1.64550i
$531$		0			0
$532$	−29.1246	−	25.2227i	−1.26271	−	1.09354i
$533$	−4.47214			−0.193710
$534$		0			0
$535$	10.9164	+	18.9078i	0.471957	+	0.817454i
$536$	11.2082	+	19.4132i	0.484121	+	0.838522i
$537$		0			0
$538$	−35.2705			−1.52062
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	−0.645898	+	1.11873i	−0.0277693	+	0.0480979i	−0.879576	−	0.475758i	$-0.842174\pi$
$541$	−0.645898	+	1.11873i	−0.0277693	+	0.0480979i	0.851807	+	0.523856i	$0.175507\pi$
$542$	26.7254	+	46.2898i	1.14796	+	1.98832i
$543$		0			0
$544$	7.98936	−	13.8380i	0.342541	−	0.593298i
$545$	6.05573			0.259399
$546$		0			0
$547$	−4.58359			−0.195980			−0.0979901	−	0.995187i	$-0.531241\pi$
$547$	−4.58359			−0.195980			−0.0979901	+	0.995187i	$0.531241\pi$
$548$	−19.9894	+	34.6226i	−0.853903	+	1.47900i
$549$		0			0
$550$		0			0
$551$	6.70820	−	11.6190i	0.285779	−	0.494984i
$552$		0			0
$553$	−6.77051	+	2.34537i	−0.287911	+	0.0997354i
$554$	−1.09017			−0.0463169
$555$		0			0
$556$	56.8328	+	98.4373i	2.41025	+	4.17467i
$557$	−9.35410	−	16.2018i	−0.396346	−	0.686491i	0.596926	−	0.802296i	$-0.296389\pi$
$557$	−9.35410	−	16.2018i	−0.396346	−	0.686491i	−0.993272	+	0.115805i	$0.963055\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	11.0172	−	57.2472i	0.465563	−	2.41913i
$561$		0			0
$562$	35.2705	−	61.0903i	1.48780	−	2.57694i
$563$	6.29837	+	10.9091i	0.265445	+	0.459764i	0.967680	−	0.252181i	$-0.0811479\pi$
$563$	6.29837	+	10.9091i	0.265445	+	0.459764i	−0.702235	+	0.711945i	$0.747815\pi$
$564$		0			0
$565$	−3.29180	+	5.70156i	−0.138487	+	0.239866i
$566$	68.3951			2.87486
$567$		0			0
$568$	66.8328			2.80424
$569$	12.7361	−	22.0595i	0.533924	−	0.924783i	−0.465291	−	0.885158i	$-0.654050\pi$
$569$	12.7361	−	22.0595i	0.533924	−	0.924783i	0.999215	−	0.0396252i	$-0.0126164\pi$
$570$		0			0
$571$	18.0623	+	31.2848i	0.755884	+	1.30923i	0.944934	+	0.327262i	$0.106126\pi$
$571$	18.0623	+	31.2848i	0.755884	+	1.30923i	−0.189050	+	0.981968i	$0.560541\pi$
$572$	7.28115	−	12.6113i	0.304440	−	0.527306i
$573$		0			0
$574$	29.2705	−	10.1396i	1.22173	−	0.423219i
$575$		0			0
$576$		0			0
$577$	9.64590	+	16.7072i	0.401564	+	0.695529i	0.993915	−	0.110151i	$-0.0351334\pi$
$577$	9.64590	+	16.7072i	0.401564	+	0.695529i	−0.592351	+	0.805680i	$0.701800\pi$
$578$	19.4164	+	33.6302i	0.807616	+	1.39883i
$579$		0			0
$580$	48.5410			2.01556
$581$		0			0
$582$		0			0
$583$	−11.2082	+	19.4132i	−0.464196	+	0.804012i
$584$	10.1180	+	17.5249i	0.418687	+	0.725188i
$585$		0			0
$586$	−19.5623	+	33.8829i	−0.808111	+	1.39969i
$587$	6.11146			0.252247			0.126123	−	0.992015i	$-0.459746\pi$
$587$	6.11146			0.252247			0.126123	+	0.992015i	$0.459746\pi$
$588$		0			0
$589$	15.0000			0.618064
$590$	4.30902	−	7.46344i	0.177399	−	0.307265i
$591$		0			0
$592$	−23.1976	−	40.1794i	−0.953414	−	1.65136i
$593$	13.8820	−	24.0443i	0.570064	−	0.987380i	−0.426495	−	0.904490i	$-0.640252\pi$
$593$	13.8820	−	24.0443i	0.570064	−	0.987380i	0.996559	−	0.0828898i	$-0.0264149\pi$
$594$		0			0
$595$	−6.58359	−	5.70156i	−0.269901	−	0.233741i
$596$	−3.43769			−0.140813
$597$		0			0
$598$	10.7812	+	18.6735i	0.440874	+	0.763616i
$599$	−8.53444	−	14.7821i	−0.348708	−	0.603980i	0.637312	−	0.770606i	$-0.280046\pi$
$599$	−8.53444	−	14.7821i	−0.348708	−	0.603980i	−0.986020	+	0.166626i	$0.946713\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−52.3607	+	18.1383i	−2.13406	+	0.739261i
$603$		0			0
$604$	−49.5517	+	85.8260i	−2.01623	+	3.49221i
$605$	−2.23607	−	3.87298i	−0.0909091	−	0.157459i
$606$		0			0
$607$	−12.0623	+	20.8925i	−0.489594	+	0.848001i	−0.999928	−	0.0119745i	$-0.996188\pi$
$607$	−12.0623	+	20.8925i	−0.489594	+	0.848001i	0.510334	+	0.859976i	$0.329522\pi$
$608$	32.5623			1.32058
$609$		0			0
$610$	−17.5623			−0.711077
$611$	3.73607	−	6.47106i	0.151145	−	0.261791i
$612$		0			0
$613$	9.06231	+	15.6964i	0.366023	+	0.633971i	0.988940	−	0.148318i	$-0.0473858\pi$
$613$	9.06231	+	15.6964i	0.366023	+	0.633971i	−0.622917	+	0.782288i	$0.714052\pi$
$614$	−25.4164	+	44.0225i	−1.02572	+	1.77660i
$615$		0			0
$616$	−11.2082	+	58.2395i	−0.451591	+	2.34654i
$617$	4.47214			0.180041			0.0900207	−	0.995940i	$-0.471307\pi$
$617$	4.47214			0.180041			0.0900207	+	0.995940i	$0.471307\pi$
$618$		0			0
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	0.643094	−	0.765787i	$-0.277650\pi$
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	−0.984738	+	0.174042i	$0.944317\pi$
$620$	27.1353	+	46.9996i	1.08978	+	1.88755i
$621$		0			0
$622$	72.6869			2.91448
$623$	−5.59017	+	1.93649i	−0.223965	+	0.0775839i
$624$		0			0
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	7.30902	+	12.6596i	0.292127	+	0.505979i
$627$		0			0
$628$	−16.9894	+	29.4264i	−0.677949	+	1.17424i
$629$	−6.93112			−0.276362
$630$		0			0
$631$	22.8328			0.908960			0.454480	−	0.890757i	$-0.349825\pi$
$631$	22.8328			0.908960			0.454480	+	0.890757i	$0.349825\pi$
$632$	10.1180	−	17.5249i	0.402474	−	0.697105i
$633$		0			0
$634$	−10.7812	−	18.6735i	−0.428174	−	0.741620i
$635$	−12.7639	+	22.1078i	−0.506521	+	0.877320i
$636$		0			0
$637$	−1.00000	−	6.92820i	−0.0396214	−	0.274505i
$638$	−35.1246			−1.39060
$639$		0			0
$640$	1.21885	+	2.11111i	0.0481792	+	0.0834488i
$641$	5.97214	+	10.3440i	0.235885	+	0.408565i	0.959530	−	0.281608i	$-0.0908677\pi$
$641$	5.97214	+	10.3440i	0.235885	+	0.408565i	−0.723644	+	0.690173i	$0.757534\pi$
$642$		0			0
$643$	34.8328			1.37367			0.686836	−	0.726812i	$-0.258999\pi$
$643$	34.8328			1.37367			0.686836	+	0.726812i	$0.258999\pi$
$644$	−79.9574	−	69.2452i	−3.15076	−	2.72864i
$645$		0			0
$646$	5.78115	−	10.0133i	0.227456	−	0.393966i
$647$	10.1180	+	17.5249i	0.397781	+	0.688977i	0.993452	−	0.114252i	$-0.0364471\pi$
$647$	10.1180	+	17.5249i	0.397781	+	0.688977i	−0.595671	+	0.803229i	$0.703114\pi$
$648$		0			0
$649$	−2.20820	+	3.82472i	−0.0866796	+	0.150133i
$650$		0			0
$651$		0			0
$652$	−79.6869			−3.12078
$653$	2.26393	−	3.92125i	0.0885945	−	0.153450i	−0.818323	−	0.574759i	$-0.805096\pi$
$653$	2.26393	−	3.92125i	0.0885945	−	0.153450i	0.906917	+	0.421309i	$0.138429\pi$
$654$		0			0
$655$	9.20820	+	15.9491i	0.359794	+	0.623182i
$656$	−22.0344	+	38.1648i	−0.860300	+	1.49008i
$657$		0			0
$658$	−9.78115	+	50.8244i	−0.381309	+	1.98134i
$659$	8.94427			0.348419			0.174210	−	0.984709i	$-0.444263\pi$
$659$	8.94427			0.348419			0.174210	+	0.984709i	$0.444263\pi$
$660$		0			0
$661$	3.35410	+	5.80948i	0.130459	+	0.225962i	0.923854	−	0.382746i	$-0.125021\pi$
$661$	3.35410	+	5.80948i	0.130459	+	0.225962i	−0.793394	+	0.608708i	$0.791688\pi$
$662$	2.07295	+	3.59045i	0.0805675	+	0.139547i
$663$		0			0
$664$		0			0
$665$	3.35410	−	17.4284i	0.130066	−	0.675845i
$666$		0			0
$667$	18.4164	−	31.8982i	0.713086	−	1.23510i
$668$	54.5410	+	94.4678i	2.11026	+	3.65507i
$669$		0			0
$670$	−8.78115	+	15.2094i	−0.339246	+	0.587591i
$671$	9.00000			0.347441
$672$		0			0
$673$	−9.41641			−0.362976			−0.181488	−	0.983393i	$-0.558091\pi$
$673$	−9.41641			−0.362976			−0.181488	+	0.983393i	$0.558091\pi$
$674$	−23.5623	+	40.8111i	−0.907586	+	1.57199i
$675$		0			0
$676$	−2.42705	−	4.20378i	−0.0933481	−	0.161684i
$677$	−1.44427	+	2.50155i	−0.0555079	+	0.0961425i	−0.892444	−	0.451158i	$-0.851011\pi$
$677$	−1.44427	+	2.50155i	−0.0555079	+	0.0961425i	0.836936	+	0.547300i	$0.184344\pi$
$678$		0			0
$679$	−18.8328	−	16.3097i	−0.722737	−	0.625909i
$680$	24.5967			0.943242
$681$		0			0
$682$	−19.6353	−	34.0093i	−0.751873	−	1.30228i
$683$	−6.73607	−	11.6672i	−0.257748	−	0.446433i	0.707890	−	0.706323i	$-0.249647\pi$
$683$	−6.73607	−	11.6672i	−0.257748	−	0.446433i	−0.965638	+	0.259889i	$0.916314\pi$
$684$		0			0
$685$	−18.4164			−0.703655
$686$	22.2533	+	43.0784i	0.849635	+	1.64474i
$687$		0			0
$688$	39.4164	−	68.2712i	1.50274	−	2.60282i
$689$	3.73607	+	6.47106i	0.142333	+	0.246528i
$690$		0			0
$691$	25.9164	−	44.8885i	0.985907	−	1.70764i	0.348070	−	0.937468i	$-0.386837\pi$
$691$	25.9164	−	44.8885i	0.985907	−	1.70764i	0.637836	−	0.770172i	$-0.279830\pi$
$692$	79.6869			3.02924
$693$		0			0
$694$	−60.3951			−2.29257
$695$	−26.1803	+	45.3457i	−0.993077	+	1.72006i
$696$		0			0
$697$	3.29180	+	5.70156i	0.124686	+	0.215962i
$698$	38.5066	−	66.6953i	1.45750	−	2.52446i
$699$		0			0
$700$		0			0
$701$	22.3607			0.844551			0.422276	−	0.906467i	$-0.361231\pi$
$701$	22.3607			0.844551			0.422276	+	0.906467i	$0.361231\pi$
$702$		0			0
$703$	−7.06231	−	12.2323i	−0.266360	−	0.461349i
$704$	−13.0623	−	22.6246i	−0.492304	−	0.852696i
$705$		0			0
$706$	−45.2705			−1.70378
$707$	−4.50000	+	23.3827i	−0.169240	+	0.879396i
$708$		0			0
$709$	25.0623	−	43.4092i	0.941235	−	1.63027i	0.178114	−	0.984010i	$-0.443000\pi$
$709$	25.0623	−	43.4092i	0.941235	−	1.63027i	0.763120	−	0.646256i	$-0.223666\pi$
$710$	26.1803	+	45.3457i	0.982531	+	1.70179i
$711$		0			0
$712$	8.35410	−	14.4697i	0.313083	−	0.542276i
$713$	41.1803			1.54222
$714$		0			0
$715$	6.70820			0.250873
$716$	−48.8435	+	84.5994i	−1.82537	+	3.16163i
$717$		0			0
$718$	15.6353	+	27.0811i	0.583503	+	1.01066i
$719$	12.3541	−	21.3979i	0.460730	−	0.798008i	−0.538267	−	0.842774i	$-0.680921\pi$
$719$	12.3541	−	21.3979i	0.460730	−	0.798008i	0.998998	+	0.0447660i	$0.0142542\pi$
$720$		0			0
$721$	−6.77051	+	2.34537i	−0.252147	+	0.0873463i
$722$	−26.1803			−0.974331
$723$		0			0
$724$	61.6869	+	106.845i	2.29258	+	3.97086i
$725$		0			0
$726$		0			0
$727$	−38.8328			−1.44023			−0.720115	−	0.693855i	$-0.755911\pi$
$727$	−38.8328			−1.44023			−0.720115	+	0.693855i	$0.755911\pi$
$728$	14.9443	+	12.9421i	0.553872	+	0.479667i
$729$		0			0
$730$	−7.92705	+	13.7301i	−0.293393	+	0.508172i
$731$	−5.88854	−	10.1993i	−0.217796	−	0.377233i
$732$		0			0
$733$	−14.3541	+	24.8620i	−0.530181	+	0.918300i	0.469199	+	0.883092i	$0.344543\pi$
$733$	−14.3541	+	24.8620i	−0.530181	+	0.918300i	−0.999380	+	0.0352078i	$0.988791\pi$
$734$	−33.2705			−1.22804
$735$		0			0
$736$	89.3951			3.29515
$737$	4.50000	−	7.79423i	0.165760	−	0.287104i
$738$		0			0
$739$	8.91641	+	15.4437i	0.327995	+	0.568105i	0.982114	−	0.188287i	$-0.0602936\pi$
$739$	8.91641	+	15.4437i	0.327995	+	0.568105i	−0.654119	+	0.756392i	$0.726960\pi$
$740$	25.5517	−	44.2568i	0.939298	−	1.62691i
$741$		0			0
$742$	−39.1246	−	33.8829i	−1.43631	−	1.24388i
$743$	−32.9443			−1.20861			−0.604304	−	0.796754i	$-0.706549\pi$
$743$	−32.9443			−1.20861			−0.604304	+	0.796754i	$0.706549\pi$
$744$		0			0
$745$	−0.791796	−	1.37143i	−0.0290092	−	0.0502453i
$746$	2.07295	+	3.59045i	0.0758961	+	0.131456i
$747$		0			0
$748$	−21.4377			−0.783840
$749$	24.4098	−	8.45581i	0.891916	−	0.308969i
$750$		0			0
$751$	5.06231	−	8.76817i	0.184726	−	0.319955i	−0.758758	−	0.651373i	$-0.774194\pi$
$751$	5.06231	−	8.76817i	0.184726	−	0.319955i	0.943484	+	0.331417i	$0.107527\pi$
$752$	−36.8156	−	63.7665i	−1.34253	−	2.32532i
$753$		0			0
$754$	−5.85410	+	10.1396i	−0.213194	+	0.369263i
$755$	−45.6525			−1.66146
$756$		0			0
$757$	−52.8328			−1.92024			−0.960121	−	0.279586i	$-0.909803\pi$
$757$	−52.8328			−1.92024			−0.960121	+	0.279586i	$0.909803\pi$
$758$	20.1803	−	34.9534i	0.732983	−	1.26956i
$759$		0			0
$760$	25.0623	+	43.4092i	0.909105	+	1.57462i
$761$	−16.7705	+	29.0474i	−0.607931	+	1.05297i	0.383650	+	0.923478i	$0.374667\pi$
$761$	−16.7705	+	29.0474i	−0.607931	+	1.05297i	−0.991581	+	0.129488i	$0.958667\pi$
$762$		0			0
$763$	1.35410	−	7.03612i	0.0490218	−	0.254725i
$764$	−54.2705			−1.96344
$765$		0			0
$766$	19.6353	+	34.0093i	0.709451	+	1.22880i
$767$	0.736068	+	1.27491i	0.0265779	+	0.0460342i
$768$		0			0
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$	−43.9058	+	15.2094i	−1.58225	+	0.548109i
$771$		0			0
$772$	−1.71885	+	2.97713i	−0.0618627	+	0.107149i
$773$	−23.5344	−	40.7628i	−0.846475	−	1.46614i	−0.884334	−	0.466855i	$-0.845387\pi$
$773$	−23.5344	−	40.7628i	−0.846475	−	1.46614i	0.0378590	−	0.999283i	$-0.487946\pi$
$774$		0			0
$775$		0			0
$776$	70.3607			2.52580
$777$		0			0
$778$	−3.85410			−0.138176
$779$	−6.70820	+	11.6190i	−0.240346	+	0.416292i
$780$		0			0
$781$	−13.4164	−	23.2379i	−0.480077	−	0.831517i
$782$	15.8713	−	27.4899i	0.567557	−	0.983038i
$783$		0			0
$784$	−64.0517	−	25.6017i	−2.28756	−	0.914347i
$785$	−15.6525			−0.558661
$786$		0			0
$787$	−10.2082	−	17.6811i	−0.363883	−	0.630264i	0.624713	−	0.780854i	$-0.285216\pi$
$787$	−10.2082	−	17.6811i	−0.363883	−	0.630264i	−0.988596	+	0.150590i	$0.951883\pi$
$788$	−21.9787	−	38.0682i	−0.782959	−	1.35613i
$789$		0			0
$790$	15.8541			0.564064
$791$	5.88854	+	5.09963i	0.209373	+	0.181322i
$792$		0			0
$793$	1.50000	−	2.59808i	0.0532666	−	0.0922604i
$794$	34.1976	+	59.2319i	1.21363	+	2.10206i
$795$		0			0
$796$	50.2599	−	87.0526i	1.78141	−	3.08550i
$797$	−9.05573			−0.320770			−0.160385	−	0.987055i	$-0.551274\pi$
$797$	−9.05573			−0.320770			−0.160385	+	0.987055i	$0.551274\pi$
$798$		0			0
$799$	−11.0000			−0.389152
$800$		0			0
$801$		0			0
$802$	18.6353	+	32.2772i	0.658034	+	1.13975i
$803$	4.06231	−	7.03612i	0.143356	−	0.248299i
$804$		0			0
$805$	9.20820	−	47.8472i	0.324547	−	1.68639i
$806$	−13.0902			−0.461082
$807$		0			0
$808$	−33.6246	−	58.2395i	−1.18291	−	2.04886i
$809$	11.2082	+	19.4132i	0.394059	+	0.682531i	0.992981	−	0.118277i	$-0.0377371\pi$
$809$	11.2082	+	19.4132i	0.394059	+	0.682531i	−0.598921	+	0.800808i	$0.704404\pi$
$810$		0			0
$811$	−14.8328			−0.520851			−0.260425	−	0.965494i	$-0.583863\pi$
$811$	−14.8328			−0.520851			−0.260425	+	0.965494i	$0.583863\pi$
$812$	10.8541	−	56.3996i	0.380904	−	1.97924i
$813$		0			0
$814$	−18.4894	+	32.0245i	−0.648052	+	1.12246i
$815$	−18.3541	−	31.7902i	−0.642916	−	1.11356i
$816$		0			0
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$	22.7984			0.797126
$819$		0			0
$820$	−48.5410			−1.69513
$821$	19.1180	−	33.1134i	0.667224	−	1.15567i	−0.311453	−	0.950261i	$-0.600816\pi$
$821$	19.1180	−	33.1134i	0.667224	−	1.15567i	0.978677	−	0.205404i	$-0.0658509\pi$
$822$		0			0
$823$	−17.0623	−	29.5528i	−0.594755	−	1.03015i	−0.993581	−	0.113119i	$-0.963916\pi$
$823$	−17.0623	−	29.5528i	−0.594755	−	1.03015i	0.398827	−	0.917026i	$-0.369417\pi$
$824$	10.1180	−	17.5249i	0.352478	−	0.610511i
$825$		0			0
$826$	−7.70820	−	6.67550i	−0.268203	−	0.232270i
$827$	−26.8328			−0.933068			−0.466534	−	0.884503i	$-0.654498\pi$
$827$	−26.8328			−0.933068			−0.466534	+	0.884503i	$0.654498\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$		0			0
$832$	−8.70820			−0.301903
$833$	−8.09675	+	6.37454i	−0.280536	+	0.220865i
$834$		0			0
$835$	−25.1246	+	43.5171i	−0.869473	+	1.50597i
$836$	−21.8435	−	37.8340i	−0.755472	−	1.30852i
$837$		0			0
$838$	43.1246	−	74.6940i	1.48971	−	2.58026i
$839$	5.88854			0.203295			0.101648	−	0.994820i	$-0.467589\pi$
$839$	5.88854			0.203295			0.101648	+	0.994820i	$0.467589\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$	−17.5623	+	30.4188i	−0.605237	+	1.04830i
$843$		0			0
$844$	−9.70820	−	16.8151i	−0.334170	−	0.578800i
$845$	1.11803	−	1.93649i	0.0384615	−	0.0666173i
$846$		0			0
$847$	−5.00000	+	1.73205i	−0.171802	+	0.0595140i
$848$	73.6312			2.52851
$849$		0			0
$850$		0			0
$851$	−19.3885	−	33.5819i	−0.664631	−	1.15117i
$852$		0			0
$853$	−52.2492			−1.78898			−0.894490	−	0.447089i	$-0.852461\pi$
$853$	−52.2492			−1.78898			−0.894490	+	0.447089i	$0.852461\pi$
$854$	−3.92705	+	20.4056i	−0.134381	+	0.698264i
$855$		0			0
$856$	−36.4787	+	63.1830i	−1.24682	+	2.15955i
$857$	−0.680340	−	1.17838i	−0.0232400	−	0.0402528i	0.854172	−	0.519991i	$-0.174065\pi$
$857$	−0.680340	−	1.17838i	−0.0232400	−	0.0402528i	−0.877411	+	0.479739i	$0.840732\pi$
$858$		0			0
$859$	−10.3541	+	17.9338i	−0.353277	+	0.611894i	−0.986822	−	0.161812i	$-0.948266\pi$
$859$	−10.3541	+	17.9338i	−0.353277	+	0.611894i	0.633544	+	0.773707i	$0.281599\pi$
$860$	86.8328			2.96097
$861$		0			0
$862$	82.1033			2.79645
$863$	11.9721	−	20.7363i	0.407536	−	0.705873i	−0.587077	−	0.809531i	$-0.699721\pi$
$863$	11.9721	−	20.7363i	0.407536	−	0.705873i	0.994613	+	0.103658i	$0.0330547\pi$
$864$		0			0
$865$	18.3541	+	31.7902i	0.624058	+	1.08090i
$866$	−38.5066	+	66.6953i	−1.30851	+	2.26640i
$867$		0			0
$868$	60.6763	−	21.0189i	2.05949	−	0.713427i
$869$	−8.12461			−0.275609
$870$		0			0
$871$	−1.50000	−	2.59808i	−0.0508256	−	0.0880325i
$872$	10.1180	+	17.5249i	0.342640	+	0.593470i
$873$		0			0
$874$	64.6869			2.18807
$875$	−22.3607	−	19.3649i	−0.755929	−	0.654654i
$876$		0			0
$877$	−16.0623	+	27.8207i	−0.542386	+	0.939439i	0.456381	+	0.889785i	$0.349145\pi$
$877$	−16.0623	+	27.8207i	−0.542386	+	0.939439i	−0.998766	+	0.0496548i	$0.984188\pi$
$878$	−31.5795	−	54.6973i	−1.06576	−	1.84595i
$879$		0			0
$880$	33.0517	−	57.2472i	1.11417	−	1.92980i
$881$	−43.3050			−1.45898			−0.729490	−	0.683991i	$-0.760243\pi$
$881$	−43.3050			−1.45898			−0.729490	+	0.683991i	$0.760243\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−3.57295	+	6.18853i	−0.120171	+	0.208143i
$885$		0			0
$886$	2.92705	+	5.06980i	0.0983362	+	0.170323i
$887$	−10.1180	+	17.5249i	−0.339730	+	0.588430i	−0.984382	−	0.176046i	$-0.943669\pi$
$887$	−10.1180	+	17.5249i	−0.339730	+	0.588430i	0.644652	+	0.764477i	$0.277002\pi$
$888$		0			0
$889$	22.8328	+	19.7738i	0.765788	+	0.663192i
$890$	13.0902			0.438783
$891$		0			0
$892$	9.70820	+	16.8151i	0.325055	+	0.563011i
$893$	−11.2082	−	19.4132i	−0.375068	−	0.649637i
$894$		0			0
$895$	−45.0000			−1.50418
$896$	2.72542	−	0.944115i	0.0910501	−	0.0315407i
$897$		0			0
$898$	−44.9787	+	77.9054i	−1.50096	+	2.59974i
$899$	11.1803	+	19.3649i	0.372885	+	0.645856i
$900$		0			0
$901$	5.50000	−	9.52628i	0.183232	−	0.317366i
$902$	35.1246			1.16952
$903$		0			0
$904$	−22.0000			−0.731709
$905$	−28.4164	+	49.2187i	−0.944593	+	1.63608i
$906$		0			0
$907$	−9.35410	−	16.2018i	−0.310598	−	0.537971i	0.667894	−	0.744256i	$-0.267196\pi$
$907$	−9.35410	−	16.2018i	−0.310598	−	0.537971i	−0.978492	+	0.206285i	$0.933863\pi$
$908$	14.4271	−	24.9884i	0.478779	−	0.829269i
$909$		0			0
$910$	−2.92705	+	15.2094i	−0.0970308	+	0.504187i
$911$	34.2492			1.13473			0.567364	−	0.823467i	$-0.307963\pi$
$911$	34.2492			1.13473			0.567364	+	0.823467i	$0.307963\pi$
$912$		0			0
$913$		0			0
$914$	8.01722	+	13.8862i	0.265186	+	0.459316i
$915$		0			0
$916$	117.103			3.86920
$917$	20.5902	−	7.13264i	0.679947	−	0.235541i
$918$		0			0
$919$	−10.0623	+	17.4284i	−0.331925	+	0.574911i	−0.982889	−	0.184198i	$-0.941031\pi$
$919$	−10.0623	+	17.4284i	−0.331925	+	0.574911i	0.650964	+	0.759108i	$0.274365\pi$
$920$	68.8050	+	119.174i	2.26843	+	3.92904i
$921$		0			0
$922$	44.9787	−	77.9054i	1.48130	−	2.56568i
$923$	−8.94427			−0.294404
$924$		0			0
$925$		0			0
$926$	31.4164	−	54.4148i	1.03241	−	1.78818i
$927$		0			0
$928$	24.2705	+	42.0378i	0.796719	+	1.37996i
$929$	−12.4098	+	21.4945i	−0.407153	+	0.705210i	−0.994569	−	0.104075i	$-0.966812\pi$
$929$	−12.4098	+	21.4945i	−0.407153	+	0.705210i	0.587416	+	0.809285i	$0.300145\pi$
$930$		0			0
$931$	−19.5000	−	7.79423i	−0.639087	−	0.255446i
$932$	−57.9787			−1.89916
$933$		0			0
$934$	12.6353	+	21.8849i	0.413438	+	0.716096i
$935$	−4.93769	−	8.55234i	−0.161480	−	0.279691i
$936$		0			0
$937$	25.4164			0.830318			0.415159	−	0.909749i	$-0.363726\pi$
$937$	25.4164			0.830318			0.415159	+	0.909749i	$0.363726\pi$
$938$	15.7082	+	13.6037i	0.512891	+	0.444177i
$939$		0			0
$940$	40.5517	−	70.2375i	1.32265	−	2.29090i
$941$	25.1180	+	43.5057i	0.818825	+	1.41825i	0.906549	+	0.422101i	$0.138707\pi$
$941$	25.1180	+	43.5057i	0.818825	+	1.41825i	−0.0877244	+	0.996145i	$0.527959\pi$
$942$		0			0
$943$	−18.4164	+	31.8982i	−0.599721	+	1.03875i
$944$	14.5066			0.472149
$945$		0			0
$946$	−62.8328			−2.04287
$947$	−11.2639	+	19.5097i	−0.366029	+	0.633980i	−0.988941	−	0.148312i	$-0.952616\pi$
$947$	−11.2639	+	19.5097i	−0.366029	+	0.633980i	0.622912	+	0.782292i	$0.285949\pi$
$948$		0			0
$949$	−1.35410	−	2.34537i	−0.0439560	−	0.0761340i
$950$		0			0
$951$		0			0
$952$	5.50000	−	28.5788i	0.178256	−	0.926245i
$953$	41.7771			1.35329			0.676646	−	0.736308i	$-0.263433\pi$
$953$	41.7771			1.35329			0.676646	+	0.736308i	$0.263433\pi$
$954$		0			0
$955$	−12.5000	−	21.6506i	−0.404491	−	0.700598i
$956$	47.1246	+	81.6222i	1.52412	+	2.63985i
$957$		0			0
$958$	−62.3951			−2.01589
$959$	−4.11803	+	21.3979i	−0.132978	+	0.690975i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	6.16312	+	10.6748i	0.198707	+	0.344170i
$963$		0			0
$964$	−11.4271	+	19.7922i	−0.368041	+	0.637465i
$965$	−1.58359			−0.0509776
$966$		0			0
$967$	16.5836			0.533292			0.266646	−	0.963794i	$-0.414084\pi$
$967$	16.5836			0.533292			0.266646	+	0.963794i	$0.414084\pi$
$968$	7.47214	−	12.9421i	0.240164	−	0.415975i
$969$		0			0
$970$	27.5623	+	47.7393i	0.884972	+	1.53282i
$971$	−5.64590	+	9.77898i	−0.181185	+	0.313822i	−0.942285	−	0.334813i	$-0.891327\pi$
$971$	−5.64590	+	9.77898i	−0.181185	+	0.313822i	0.761099	+	0.648636i	$0.224660\pi$
$972$		0			0
$973$	46.8328	+	40.5584i	1.50139	+	1.30024i
$974$	−57.1591			−1.83149
$975$		0			0
$976$	−14.7812	−	25.6017i	−0.473133	−	0.819491i
$977$	−1.17376	−	2.03302i	−0.0375520	−	0.0650419i	0.846639	−	0.532168i	$-0.178623\pi$
$977$	−1.17376	−	2.03302i	−0.0375520	−	0.0650419i	−0.884191	+	0.467126i	$0.845289\pi$
$978$		0			0
$979$	−6.70820			−0.214395
$980$	−10.8541	−	75.1994i	−0.346722	−	2.40216i
$981$		0			0
$982$	−33.4164	+	57.8789i	−1.06636	+	1.84699i
$983$	3.73607	+	6.47106i	0.119162	+	0.206395i	0.919436	−	0.393240i	$-0.128646\pi$
$983$	3.73607	+	6.47106i	0.119162	+	0.206395i	−0.800274	+	0.599635i	$0.795313\pi$
$984$		0			0
$985$	10.1246	−	17.5363i	0.322597	−	0.558754i
$986$	17.2361			0.548908
$987$		0			0
$988$	−14.5623			−0.463289
$989$	32.9443	−	57.0612i	1.04757	−	1.81444i
$990$		0			0
$991$	−15.3541	−	26.5941i	−0.487739	−	0.844789i	0.512161	−	0.858889i	$-0.328845\pi$
$991$	−15.3541	−	26.5941i	−0.487739	−	0.844789i	−0.999901	+	0.0141002i	$0.995512\pi$
$992$	−27.1353	+	46.9996i	−0.861545	+	1.49224i
$993$		0			0
$994$	58.5410	−	20.2792i	1.85681	−	0.643217i
$995$	46.3050			1.46797
$996$		0			0
$997$	−13.2082	−	22.8773i	−0.418308	−	0.724531i	0.577461	−	0.816418i	$-0.304043\pi$
$997$	−13.2082	−	22.8773i	−0.418308	−	0.724531i	−0.995769	+	0.0918873i	$0.970710\pi$
$998$	−34.5795	−	59.8935i	−1.09460	−	1.89590i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.c.352.1		4
3.2	odd	2		91.2.e.b.79.2	yes	4
7.2	even	3		5733.2.a.v.1.2		2
7.4	even	3	inner	819.2.j.c.235.1		4
7.5	odd	6		5733.2.a.w.1.2		2
12.11	even	2		1456.2.r.j.625.1		4
21.2	odd	6		637.2.a.f.1.1		2
21.5	even	6		637.2.a.e.1.1		2
21.11	odd	6		91.2.e.b.53.2	✓	4
21.17	even	6		637.2.e.h.508.2		4
21.20	even	2		637.2.e.h.79.2		4
39.38	odd	2		1183.2.e.d.170.1		4
84.11	even	6		1456.2.r.j.417.1		4
273.116	odd	6		1183.2.e.d.508.1		4
273.194	even	6		8281.2.a.ba.1.2		2
273.233	odd	6		8281.2.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.b.53.2	✓	4	21.11	odd	6
91.2.e.b.79.2	yes	4	3.2	odd	2
637.2.a.e.1.1		2	21.5	even	6
637.2.a.f.1.1		2	21.2	odd	6
637.2.e.h.79.2		4	21.20	even	2
637.2.e.h.508.2		4	21.17	even	6
819.2.j.c.235.1		4	7.4	even	3	inner
819.2.j.c.352.1		4	1.1	even	1	trivial
1183.2.e.d.170.1		4	39.38	odd	2
1183.2.e.d.508.1		4	273.116	odd	6
1456.2.r.j.417.1		4	84.11	even	6
1456.2.r.j.625.1		4	12.11	even	2
5733.2.a.v.1.2		2	7.2	even	3
5733.2.a.w.1.2		2	7.5	odd	6
8281.2.a.z.1.2		2	273.233	odd	6
8281.2.a.ba.1.2		2	273.194	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 2.26728i) q^{2} +(-2.42705 - 4.20378i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-2.00000 - 1.73205i) q^{7} +7.47214 q^{8} +(2.92705 + 5.06980i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +(6.54508 - 2.26728i) q^{14} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +(-1.50000 + 2.59808i) q^{19} -10.8541 q^{20} +7.85410 q^{22} +(-4.11803 + 7.13264i) q^{23} +(1.30902 - 2.26728i) q^{26} +(-2.42705 + 12.6113i) q^{28} -4.47214 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-5.42705 - 9.39993i) q^{32} -3.85410 q^{34} +(-5.59017 + 1.93649i) q^{35} +(-2.35410 + 4.07742i) q^{37} +(-3.92705 - 6.80185i) q^{38} +(8.35410 - 14.4697i) q^{40} +4.47214 q^{41} -8.00000 q^{43} +(-7.28115 + 12.6113i) q^{44} +(-10.7812 - 18.6735i) q^{46} +(-3.73607 + 6.47106i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.42705 + 4.20378i) q^{52} +(-3.73607 - 6.47106i) q^{53} -6.70820 q^{55} +(-14.9443 - 12.9421i) q^{56} +(5.85410 - 10.1396i) q^{58} +(-0.736068 - 1.27491i) q^{59} +(-1.50000 + 2.59808i) q^{61} +13.0902 q^{62} +8.70820 q^{64} +(-1.11803 + 1.93649i) q^{65} +(1.50000 + 2.59808i) q^{67} +(3.57295 - 6.18853i) q^{68} +(2.92705 - 15.2094i) q^{70} +8.94427 q^{71} +(1.35410 + 2.34537i) q^{73} +(-6.16312 - 10.6748i) q^{74} +14.5623 q^{76} +(-1.50000 + 7.79423i) q^{77} +(1.35410 - 2.34537i) q^{79} +(11.0172 + 19.0824i) q^{80} +(-5.85410 + 10.1396i) q^{82} +3.29180 q^{85} +(10.4721 - 18.1383i) q^{86} +(-11.2082 - 19.4132i) q^{88} +(1.11803 - 1.93649i) q^{89} +(2.00000 + 1.73205i) q^{91} +39.9787 q^{92} +(-9.78115 - 16.9415i) q^{94} +(3.35410 + 5.80948i) q^{95} +9.41641 q^{97} +(-17.0172 - 6.80185i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + 5 q^{10} - 6 q^{11} - 4 q^{13} + 15 q^{14} - 13 q^{16} - 6 q^{17} - 6 q^{19} - 30 q^{20} + 18 q^{22} - 12 q^{23} + 3 q^{26} - 3 q^{28} - 10 q^{31} - 15 q^{32}+ \cdots - 39 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^4 - 8 * q^7 + 12 * q^8 + 5 * q^10 - 6 * q^11 - 4 * q^13 + 15 * q^14 - 13 * q^16 - 6 * q^17 - 6 * q^19 - 30 * q^20 + 18 * q^22 - 12 * q^23 + 3 * q^26 - 3 * q^28 - 10 * q^31 - 15 * q^32 - 2 * q^34 + 4 * q^37 - 9 * q^38 + 20 * q^40 - 32 * q^43 - 9 * q^44 - 23 * q^46 - 6 * q^47 + 4 * q^49 + 3 * q^52 - 6 * q^53 - 24 * q^56 + 10 * q^58 + 6 * q^59 - 6 * q^61 + 30 * q^62 + 8 * q^64 + 6 * q^67 + 21 * q^68 + 5 * q^70 - 8 * q^73 - 9 * q^74 + 18 * q^76 - 6 * q^77 - 8 * q^79 + 15 * q^80 - 10 * q^82 + 40 * q^85 + 24 * q^86 - 18 * q^88 + 8 * q^91 + 66 * q^92 - 19 * q^94 - 16 * q^97 - 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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