LMFDB - Embedded newform 819.2.j.j.352.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(235,819)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} + 214 x^{16} + 1450 x^{14} + 7087 x^{12} + 20465 x^{10} + 42361 x^{8} + 50535 x^{6} + \cdots + 3969 $ x^20 + 18x^18 + 214x^16 + 1450x^14 + 7087x^12 + 20465x^10 + 42361x^8 + 50535x^6 + 42354x^4 + 15309*x^2 + 3969
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.4
Root			$-0.563413 - 0.975859i$ of defining polynomial
Character	$\chi$	$=$	819.352
Dual form			819.2.j.j.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.563413 + 0.975859i) q^{2} +(0.365133 + 0.632428i) q^{4} +(-1.71089 + 2.96335i) q^{5} +(-2.13253 - 1.56598i) q^{7} -3.07653 q^{8} +(-1.92787 - 3.33917i) q^{10} +(3.11435 + 5.39421i) q^{11} +1.00000 q^{13} +(2.72967 - 1.19876i) q^{14} +(1.00309 - 1.73741i) q^{16} +(-0.301314 - 0.521891i) q^{17} +(-2.64962 + 4.58928i) q^{19} -2.49881 q^{20} -7.01866 q^{22} +(2.35766 - 4.08359i) q^{23} +(-3.35428 - 5.80979i) q^{25} +(-0.563413 + 0.975859i) q^{26} +(0.211714 - 1.92047i) q^{28} -6.48608 q^{29} +(-5.35737 - 9.27924i) q^{31} +(-1.94622 - 3.37096i) q^{32} +0.679056 q^{34} +(8.28908 - 3.64021i) q^{35} +(-0.134867 + 0.233597i) q^{37} +(-2.98566 - 5.17131i) q^{38} +(5.26360 - 9.11683i) q^{40} -0.266816 q^{41} +12.0187 q^{43} +(-2.27430 + 3.93921i) q^{44} +(2.65667 + 4.60149i) q^{46} +(-4.37598 + 7.57942i) q^{47} +(2.09540 + 6.67902i) q^{49} +7.55938 q^{50} +(0.365133 + 0.632428i) q^{52} +(-1.81893 - 3.15048i) q^{53} -21.3132 q^{55} +(6.56081 + 4.81779i) q^{56} +(3.65434 - 6.32950i) q^{58} +(-2.14089 - 3.70814i) q^{59} +(1.78991 - 3.10022i) q^{61} +12.0736 q^{62} +8.39847 q^{64} +(-1.71089 + 2.96335i) q^{65} +(-0.687573 - 1.19091i) q^{67} +(0.220039 - 0.381119i) q^{68} +(-1.11783 + 10.1399i) q^{70} +0.740276 q^{71} +(-2.09231 - 3.62398i) q^{73} +(-0.151972 - 0.263223i) q^{74} -3.86985 q^{76} +(1.80579 - 16.3804i) q^{77} +(-4.21779 + 7.30542i) q^{79} +(3.43236 + 5.94501i) q^{80} +(0.150327 - 0.260374i) q^{82} +0.116941 q^{83} +2.06206 q^{85} +(-6.77146 + 11.7285i) q^{86} +(-9.58140 - 16.5955i) q^{88} +(-4.93800 + 8.55286i) q^{89} +(-2.13253 - 1.56598i) q^{91} +3.44344 q^{92} +(-4.93096 - 8.54068i) q^{94} +(-9.06641 - 15.7035i) q^{95} +10.8465 q^{97} +(-7.69836 - 1.71823i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{4} - 4 q^{7} + 4 q^{10} + 20 q^{13} - 32 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 8 q^{28} - 12 q^{31} + 68 q^{34} - 26 q^{37} + 70 q^{40} + 80 q^{43} + 6 q^{46} - 28 q^{49} - 16 q^{52}+ \cdots + 36 q^{97}+O(q^{100}) $ 20 * q - 16 * q^4 - 4 * q^7 + 4 * q^10 + 20 * q^13 - 32 * q^16 - 6 * q^19 + 20 * q^22 - 24 * q^25 + 8 * q^28 - 12 * q^31 + 68 * q^34 - 26 * q^37 + 70 * q^40 + 80 * q^43 + 6 * q^46 - 28 * q^49 - 16 * q^52 - 48 * q^55 - 36 * q^58 + 22 * q^61 + 156 * q^64 - 26 * q^67 - 130 * q^70 - 24 * q^73 + 8 * q^76 - 28 * q^79 + 28 * q^82 - 40 * q^85 - 12 * q^88 - 4 * q^91 - 4 * q^94 + 36 * q^97

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 $

$2$	−0.563413	+	0.975859i	−0.398393	+	0.690037i	−0.993528	−	0.113589i	$-0.963765\pi$
$2$	−0.563413	+	0.975859i	−0.398393	+	0.690037i	0.595135	+	0.803626i	$0.297099\pi$
$3$		0			0
$3$		0			0
$4$	0.365133	+	0.632428i	0.182566	+	0.316214i
$5$	−1.71089	+	2.96335i	−0.765133	+	1.32525i	0.175044	+	0.984561i	$0.443993\pi$
$5$	−1.71089	+	2.96335i	−0.765133	+	1.32525i	−0.940176	+	0.340688i	$0.889340\pi$
$6$		0			0
$7$	−2.13253	−	1.56598i	−0.806022	−	0.591886i
$7$	−2.13253	−	1.56598i	−0.806022	−	0.591886i
$8$	−3.07653			−1.08772
$9$		0			0
$10$	−1.92787	−	3.33917i	−0.609647	−	1.05594i
$11$	3.11435	+	5.39421i	0.939012	+	1.62642i	0.767319	+	0.641266i	$0.221591\pi$
$11$	3.11435	+	5.39421i	0.939012	+	1.62642i	0.171693	+	0.985150i	$0.445076\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	2.72967	−	1.19876i	0.729536	−	0.320382i
$15$		0			0
$16$	1.00309	−	1.73741i	0.250773	−	0.434351i
$17$	−0.301314	−	0.521891i	−0.0730794	−	0.126577i	0.827170	−	0.561952i	$-0.189949\pi$
$17$	−0.301314	−	0.521891i	−0.0730794	−	0.126577i	−0.900249	+	0.435374i	$0.856616\pi$
$18$		0			0
$19$	−2.64962	+	4.58928i	−0.607865	+	1.05285i	0.383727	+	0.923447i	$0.374640\pi$
$19$	−2.64962	+	4.58928i	−0.607865	+	1.05285i	−0.991592	+	0.129406i	$0.958693\pi$
$20$	−2.49881			−0.558750
$21$		0			0
$22$	−7.01866			−1.49638
$23$	2.35766	−	4.08359i	0.491607	−	0.851488i	−0.508346	−	0.861153i	$-0.669743\pi$
$23$	2.35766	−	4.08359i	0.491607	−	0.851488i	0.999953	+	0.00966467i	$0.00307641\pi$
$24$		0			0
$25$	−3.35428	−	5.80979i	−0.670856	−	1.16196i
$26$	−0.563413	+	0.975859i	−0.110494	+	0.191382i
$27$		0			0
$28$	0.211714	−	1.92047i	0.0400102	−	0.362934i
$29$	−6.48608			−1.20444			−0.602218	−	0.798332i	$-0.705716\pi$
$29$	−6.48608			−1.20444			−0.602218	+	0.798332i	$0.705716\pi$
$30$		0			0
$31$	−5.35737	−	9.27924i	−0.962213	−	1.66660i	−0.716924	−	0.697151i	$-0.754451\pi$
$31$	−5.35737	−	9.27924i	−0.962213	−	1.66660i	−0.245288	−	0.969450i	$-0.578883\pi$
$32$	−1.94622	−	3.37096i	−0.344047	−	0.595907i
$33$		0			0
$34$	0.679056			0.116457
$35$	8.28908	−	3.64021i	1.40111	−	0.615308i
$36$		0			0
$37$	−0.134867	+	0.233597i	−0.0221721	+	0.0384032i	−0.876899	−	0.480676i	$-0.840392\pi$
$37$	−0.134867	+	0.233597i	−0.0221721	+	0.0384032i	0.854726	+	0.519079i	$0.173725\pi$
$38$	−2.98566	−	5.17131i	−0.484338	−	0.838898i
$39$		0			0
$40$	5.26360	−	9.11683i	0.832249	−	1.44150i
$41$	−0.266816			−0.0416696			−0.0208348	−	0.999783i	$-0.506632\pi$
$41$	−0.266816			−0.0416696			−0.0208348	+	0.999783i	$0.506632\pi$
$42$		0			0
$43$	12.0187			1.83283			0.916414	−	0.400232i	$-0.131070\pi$
$43$	12.0187			1.83283			0.916414	+	0.400232i	$0.131070\pi$
$44$	−2.27430	+	3.93921i	−0.342864	+	0.593858i
$45$		0			0
$46$	2.65667	+	4.60149i	0.391705	+	0.678453i
$47$	−4.37598	+	7.57942i	−0.638302	+	1.10557i	0.347503	+	0.937679i	$0.387030\pi$
$47$	−4.37598	+	7.57942i	−0.638302	+	1.10557i	−0.985805	+	0.167893i	$0.946304\pi$
$48$		0			0
$49$	2.09540	+	6.67902i	0.299343	+	0.954146i
$50$	7.55938			1.06906
$51$		0			0
$52$	0.365133	+	0.632428i	0.0506348	+	0.0877020i
$53$	−1.81893	−	3.15048i	−0.249849	−	0.432751i	0.713635	−	0.700518i	$-0.247048\pi$
$53$	−1.81893	−	3.15048i	−0.249849	−	0.432751i	−0.963484	+	0.267767i	$0.913714\pi$
$54$		0			0
$55$	−21.3132			−2.87388
$56$	6.56081	+	4.81779i	0.876725	+	0.643805i
$57$		0			0
$58$	3.65434	−	6.32950i	0.479838	−	0.831104i
$59$	−2.14089	−	3.70814i	−0.278721	−	0.482758i	0.692346	−	0.721565i	$-0.256577\pi$
$59$	−2.14089	−	3.70814i	−0.278721	−	0.482758i	−0.971067	+	0.238807i	$0.923244\pi$
$60$		0			0
$61$	1.78991	−	3.10022i	0.229175	−	0.396943i	−0.728389	−	0.685164i	$-0.759731\pi$
$61$	1.78991	−	3.10022i	0.229175	−	0.396943i	0.957564	+	0.288221i	$0.0930639\pi$
$62$	12.0736			1.53335
$63$		0			0
$64$	8.39847			1.04981
$65$	−1.71089	+	2.96335i	−0.212210	+	0.367558i
$66$		0			0
$67$	−0.687573	−	1.19091i	−0.0840004	−	0.145493i	0.820964	−	0.570979i	$-0.193436\pi$
$67$	−0.687573	−	1.19091i	−0.0840004	−	0.145493i	−0.904965	+	0.425486i	$0.860103\pi$
$68$	0.220039	−	0.381119i	0.0266837	−	0.0462175i
$69$		0			0
$70$	−1.11783	+	10.1399i	−0.133607	+	1.21195i
$71$	0.740276			0.0878546			0.0439273	−	0.999035i	$-0.486013\pi$
$71$	0.740276			0.0878546			0.0439273	+	0.999035i	$0.486013\pi$
$72$		0			0
$73$	−2.09231	−	3.62398i	−0.244886	−	0.424155i	0.717214	−	0.696853i	$-0.245417\pi$
$73$	−2.09231	−	3.62398i	−0.244886	−	0.424155i	−0.962100	+	0.272699i	$0.912084\pi$
$74$	−0.151972	−	0.263223i	−0.0176664	−	0.0305991i
$75$		0			0
$76$	−3.86985			−0.443902
$77$	1.80579	−	16.3804i	0.205789	−	1.86672i
$78$		0			0
$79$	−4.21779	+	7.30542i	−0.474538	+	0.821924i	−0.999575	−	0.0291555i	$-0.990718\pi$
$79$	−4.21779	+	7.30542i	−0.474538	+	0.821924i	0.525037	+	0.851080i	$0.324052\pi$
$80$	3.43236	+	5.94501i	0.383749	+	0.664673i
$81$		0			0
$82$	0.150327	−	0.260374i	0.0166009	−	0.0287535i
$83$	0.116941			0.0128359			0.00641795	−	0.999979i	$-0.497957\pi$
$83$	0.116941			0.0128359			0.00641795	+	0.999979i	$0.497957\pi$
$84$		0			0
$85$	2.06206			0.223662
$86$	−6.77146	+	11.7285i	−0.730186	+	1.26472i
$87$		0			0
$88$	−9.58140	−	16.5955i	−1.02138	−	1.76908i
$89$	−4.93800	+	8.55286i	−0.523427	+	0.906601i	0.476202	+	0.879336i	$0.342013\pi$
$89$	−4.93800	+	8.55286i	−0.523427	+	0.906601i	−0.999628	+	0.0272653i	$0.991320\pi$
$90$		0			0
$91$	−2.13253	−	1.56598i	−0.223550	−	0.164160i
$92$	3.44344			0.359003
$93$		0			0
$94$	−4.93096	−	8.54068i	−0.508590	−	0.880904i
$95$	−9.06641	−	15.7035i	−0.930195	−	1.61114i
$96$		0			0
$97$	10.8465			1.10130			0.550649	−	0.834737i	$-0.314380\pi$
$97$	10.8465			1.10130			0.550649	+	0.834737i	$0.314380\pi$
$98$	−7.69836	−	1.71823i	−0.777651	−	0.173568i
$99$		0			0
$100$	2.44952	−	4.24268i	0.244952	−	0.424268i
$101$	−2.23509	−	3.87128i	−0.222399	−	0.385207i	0.733137	−	0.680081i	$-0.238056\pi$
$101$	−2.23509	−	3.87128i	−0.222399	−	0.385207i	−0.955536	+	0.294874i	$0.904722\pi$
$102$		0			0
$103$	−5.86361	+	10.1561i	−0.577759	+	1.00071i	0.417977	+	0.908458i	$0.362739\pi$
$103$	−5.86361	+	10.1561i	−0.577759	+	1.00071i	−0.995736	+	0.0922499i	$0.970594\pi$
$104$	−3.07653			−0.301679
$105$		0			0
$106$	4.09923			0.398152
$107$	−1.75504	+	3.03981i	−0.169666	+	0.293870i	−0.938302	−	0.345816i	$-0.887602\pi$
$107$	−1.75504	+	3.03981i	−0.169666	+	0.293870i	0.768637	+	0.639686i	$0.220935\pi$
$108$		0			0
$109$	6.21166	+	10.7589i	0.594969	+	1.03052i	0.993551	+	0.113384i	$0.0361689\pi$
$109$	6.21166	+	10.7589i	0.594969	+	1.03052i	−0.398583	+	0.917132i	$0.630498\pi$
$110$	12.0081	−	20.7987i	1.14493	−	1.98308i
$111$		0			0
$112$	−4.85987	+	2.13425i	−0.459215	+	0.201668i
$113$	−5.31516			−0.500008			−0.250004	−	0.968245i	$-0.580432\pi$
$113$	−5.31516			−0.500008			−0.250004	+	0.968245i	$0.580432\pi$
$114$		0			0
$115$	8.06740	+	13.9731i	0.752289	+	1.30300i
$116$	−2.36828	−	4.10198i	−0.219889	−	0.380859i
$117$		0			0
$118$	4.82483			0.444161
$119$	−0.174710	+	1.58480i	−0.0160157	+	0.145279i
$120$		0			0
$121$	−13.8984	+	24.0727i	−1.26349	+	2.18842i
$122$	2.01692	+	3.49341i	0.182603	+	0.316278i
$123$		0			0
$124$	3.91230	−	6.77631i	0.351335	−	0.608530i
$125$	5.84633			0.522911
$126$		0			0
$127$	−6.42331			−0.569977			−0.284988	−	0.958531i	$-0.591990\pi$
$127$	−6.42331			−0.569977			−0.284988	+	0.958531i	$0.591990\pi$
$128$	−0.839358	+	1.45381i	−0.0741895	+	0.128500i
$129$		0			0
$130$	−1.92787	−	3.33917i	−0.169086	−	0.292865i
$131$	−8.82899	+	15.2923i	−0.771393	+	1.33609i	0.165407	+	0.986225i	$0.447106\pi$
$131$	−8.82899	+	15.2923i	−0.771393	+	1.33609i	−0.936800	+	0.349866i	$0.886227\pi$
$132$		0			0
$133$	12.8371	−	5.63753i	1.11312	−	0.488836i
$134$	1.54955			0.133861
$135$		0			0
$136$	0.927002	+	1.60561i	0.0794898	+	0.137680i
$137$	3.08946	+	5.35110i	0.263950	+	0.457175i	0.967288	−	0.253680i	$-0.0816412\pi$
$137$	3.08946	+	5.35110i	0.263950	+	0.457175i	−0.703338	+	0.710856i	$0.748308\pi$
$138$		0			0
$139$	−7.82775			−0.663941			−0.331971	−	0.943290i	$-0.607713\pi$
$139$	−7.82775			−0.663941			−0.331971	+	0.943290i	$0.607713\pi$
$140$	5.32879	+	3.91308i	0.450365	+	0.330716i
$141$		0			0
$142$	−0.417081	+	0.722405i	−0.0350007	+	0.0606229i
$143$	3.11435	+	5.39421i	0.260435	+	0.451087i
$144$		0			0
$145$	11.0970	−	19.2205i	0.921553	−	1.59618i
$146$	4.71533			0.390243
$147$		0			0
$148$	−0.196978			−0.0161915
$149$	4.16205	−	7.20889i	0.340969	−	0.590575i	−0.643644	−	0.765325i	$-0.722578\pi$
$149$	4.16205	−	7.20889i	0.340969	−	0.590575i	0.984613	+	0.174750i	$0.0559116\pi$
$150$		0			0
$151$	10.1844	+	17.6398i	0.828792	+	1.43551i	0.898987	+	0.437976i	$0.144305\pi$
$151$	10.1844	+	17.6398i	0.828792	+	1.43551i	−0.0701948	+	0.997533i	$0.522362\pi$
$152$	8.15164	−	14.1191i	0.661186	−	1.14521i
$153$		0			0
$154$	14.9675	+	10.9911i	1.20612	+	0.885688i
$155$	36.6635			2.94488
$156$		0			0
$157$	−2.28840	−	3.96362i	−0.182634	−	0.316331i	0.760143	−	0.649756i	$-0.225129\pi$
$157$	−2.28840	−	3.96362i	−0.182634	−	0.316331i	−0.942777	+	0.333425i	$0.891796\pi$
$158$	−4.75271	−	8.23193i	−0.378105	−	0.654897i
$159$		0			0
$160$	13.3191			1.05297
$161$	−11.4226	+	5.01634i	−0.900229	+	0.395343i
$162$		0			0
$163$	−4.55731	+	7.89350i	−0.356956	+	0.618267i	−0.987451	−	0.157927i	$-0.949519\pi$
$163$	−4.55731	+	7.89350i	−0.356956	+	0.618267i	0.630494	+	0.776194i	$0.282852\pi$
$164$	−0.0974230	−	0.168742i	−0.00760746	−	0.0131765i
$165$		0			0
$166$	−0.0658859	+	0.114118i	−0.00511373	+	0.00885725i
$167$	−13.9793			−1.08175			−0.540874	−	0.841104i	$-0.681906\pi$
$167$	−13.9793			−1.08175			−0.540874	+	0.841104i	$0.681906\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−1.16179	+	2.01228i	−0.0891052	+	0.154335i
$171$		0			0
$172$	4.38840	+	7.60094i	0.334613	+	0.579566i
$173$	6.63403	−	11.4905i	0.504376	−	0.873605i	−0.495611	−	0.868544i	$-0.665056\pi$
$173$	6.63403	−	11.4905i	0.504376	−	0.873605i	0.999987	−	0.00506015i	$-0.00161070\pi$
$174$		0			0
$175$	−1.94491	+	17.6423i	−0.147021	+	1.33363i
$176$	12.4959			0.941915
$177$		0			0
$178$	−5.56426	−	9.63758i	−0.417059	−	0.722367i
$179$	−9.84939	−	17.0596i	−0.736178	−	1.27510i	−0.954205	−	0.299155i	$-0.903295\pi$
$179$	−9.84939	−	17.0596i	−0.736178	−	1.27510i	0.218027	−	0.975943i	$-0.430038\pi$
$180$		0			0
$181$	−5.10682			−0.379587			−0.189794	−	0.981824i	$-0.560782\pi$
$181$	−5.10682			−0.379587			−0.189794	+	0.981824i	$0.560782\pi$
$182$	2.72967	−	1.19876i	0.202337	−	0.0888579i
$183$		0			0
$184$	−7.25343	+	12.5633i	−0.534730	+	0.926179i
$185$	−0.461486	−	0.799318i	−0.0339292	−	0.0587670i
$186$		0			0
$187$	1.87679	−	3.25070i	0.137245	−	0.237715i
$188$	−6.39125			−0.466130
$189$		0			0
$190$	20.4325			1.48233
$191$	−8.93725	+	15.4798i	−0.646677	+	1.12008i	0.337235	+	0.941420i	$0.390508\pi$
$191$	−8.93725	+	15.4798i	−0.646677	+	1.12008i	−0.983912	+	0.178656i	$0.942825\pi$
$192$		0			0
$193$	0.307628	+	0.532827i	0.0221435	+	0.0383537i	0.876885	−	0.480701i	$-0.159618\pi$
$193$	0.307628	+	0.532827i	0.0221435	+	0.0383537i	−0.854741	+	0.519054i	$0.826284\pi$
$194$	−6.11106	+	10.5847i	−0.438749	+	0.759935i
$195$		0			0
$196$	−3.45890	+	3.76392i	−0.247064	+	0.268851i
$197$	2.01129			0.143298			0.0716492	−	0.997430i	$-0.477174\pi$
$197$	2.01129			0.143298			0.0716492	+	0.997430i	$0.477174\pi$
$198$		0			0
$199$	9.02080	+	15.6245i	0.639468	+	1.10759i	0.985550	+	0.169386i	$0.0541785\pi$
$199$	9.02080	+	15.6245i	0.639468	+	1.10759i	−0.346082	+	0.938204i	$0.612488\pi$
$200$	10.3196	+	17.8740i	0.729703	+	1.26388i
$201$		0			0
$202$	5.03710			0.354409
$203$	13.8318	+	10.1571i	0.970801	+	0.712888i
$204$		0			0
$205$	0.456492	−	0.790667i	0.0318828	−	0.0552226i
$206$	−6.60726	−	11.4441i	−0.460350	−	0.797349i
$207$		0			0
$208$	1.00309	−	1.73741i	0.0695519	−	0.120467i
$209$	−33.0074			−2.28317
$210$		0			0
$211$	18.9585			1.30516			0.652578	−	0.757721i	$-0.273687\pi$
$211$	18.9585			1.30516			0.652578	+	0.757721i	$0.273687\pi$
$212$	1.32830	−	2.30068i	0.0912280	−	0.158012i
$213$		0			0
$214$	−1.97762	−	3.42533i	−0.135187	−	0.234151i
$215$	−20.5626	+	35.6154i	−1.40236	+	2.42895i
$216$		0			0
$217$	−3.10635	+	28.1778i	−0.210873	+	1.91284i
$218$	−13.9989			−0.948125
$219$		0			0
$220$	−7.78215	−	13.4791i	−0.524673	−	0.908760i
$221$	−0.301314	−	0.521891i	−0.0202686	−	0.0351062i
$222$		0			0
$223$	−17.7722			−1.19012			−0.595059	−	0.803682i	$-0.702871\pi$
$223$	−17.7722			−1.19012			−0.595059	+	0.803682i	$0.702871\pi$
$224$	−1.12847	+	10.2364i	−0.0753993	+	0.683950i
$225$		0			0
$226$	2.99463	−	5.18685i	0.199200	−	0.345024i
$227$	11.3015	+	19.5748i	0.750107	+	1.29922i	0.947770	+	0.318953i	$0.103331\pi$
$227$	11.3015	+	19.5748i	0.750107	+	1.29922i	−0.197663	+	0.980270i	$0.563335\pi$
$228$		0			0
$229$	−7.23550	+	12.5323i	−0.478135	+	0.828155i	−0.999686	−	0.0250657i	$-0.992020\pi$
$229$	−7.23550	+	12.5323i	−0.478135	+	0.828155i	0.521550	+	0.853220i	$0.325354\pi$
$230$	−18.1811			−1.19883
$231$		0			0
$232$	19.9546			1.31009
$233$	11.4239	−	19.7867i	0.748402	−	1.29627i	−0.200186	−	0.979758i	$-0.564155\pi$
$233$	11.4239	−	19.7867i	0.748402	−	1.29627i	0.948588	−	0.316513i	$-0.102512\pi$
$234$		0			0
$235$	−14.9736	−	25.9351i	−0.976772	−	1.69182i
$236$	1.56342	−	2.70792i	0.101770	−	0.176271i
$237$		0			0
$238$	−1.44811	−	1.06339i	−0.0938671	−	0.0689294i
$239$	−5.37010			−0.347363			−0.173682	−	0.984802i	$-0.555566\pi$
$239$	−5.37010			−0.347363			−0.173682	+	0.984802i	$0.555566\pi$
$240$		0			0
$241$	−2.97144	−	5.14668i	−0.191407	−	0.331527i	0.754310	−	0.656519i	$-0.227972\pi$
$241$	−2.97144	−	5.14668i	−0.191407	−	0.331527i	−0.945717	+	0.324992i	$0.894638\pi$
$242$	−15.6610	−	27.1257i	−1.00673	−	1.74370i
$243$		0			0
$244$	2.61422			0.167359
$245$	−23.3772	−	5.21767i	−1.49352	−	0.333345i
$246$		0			0
$247$	−2.64962	+	4.58928i	−0.168591	+	0.292009i
$248$	16.4821	+	28.5479i	1.04662	+	1.81279i
$249$		0			0
$250$	−3.29389	+	5.70519i	−0.208324	+	0.360828i
$251$	−8.52086			−0.537832			−0.268916	−	0.963164i	$-0.586665\pi$
$251$	−8.52086			−0.537832			−0.268916	+	0.963164i	$0.586665\pi$
$252$		0			0
$253$	29.3704			1.84650
$254$	3.61897	−	6.26825i	0.227075	−	0.393305i
$255$		0			0
$256$	7.45266	+	12.9084i	0.465791	+	0.806774i
$257$	−8.33602	+	14.4384i	−0.519986	+	0.900643i	0.479744	+	0.877409i	$0.340730\pi$
$257$	−8.33602	+	14.4384i	−0.519986	+	0.900643i	−0.999730	+	0.0232341i	$0.992604\pi$
$258$		0			0
$259$	0.653419	−	0.286954i	0.0406015	−	0.0178304i
$260$	−2.49881			−0.154969
$261$		0			0
$262$	−9.94873	−	17.2317i	−0.614635	−	1.06458i
$263$	13.8924	+	24.0623i	0.856640	+	1.48374i	0.875116	+	0.483914i	$0.160785\pi$
$263$	13.8924	+	24.0623i	0.856640	+	1.48374i	−0.0184759	+	0.999829i	$0.505881\pi$
$264$		0			0
$265$	12.4479			0.764671
$266$	−1.73117	+	15.7035i	−0.106145	+	0.962843i
$267$		0			0
$268$	0.502111	−	0.869681i	0.0306713	−	0.0531242i
$269$	−1.17500	−	2.03516i	−0.0716409	−	0.124086i	0.827980	−	0.560758i	$-0.189490\pi$
$269$	−1.17500	−	2.03516i	−0.0716409	−	0.124086i	−0.899621	+	0.436672i	$0.856157\pi$
$270$		0			0
$271$	3.52194	−	6.10018i	0.213942	−	0.370559i	−0.739002	−	0.673703i	$-0.764703\pi$
$271$	3.52194	−	6.10018i	0.213942	−	0.370559i	0.952945	+	0.303143i	$0.0980361\pi$
$272$	−1.20898			−0.0733053
$273$		0			0
$274$	−6.96256			−0.420624
$275$	20.8928	−	36.1874i	1.25988	−	2.18218i
$276$		0			0
$277$	8.15415	+	14.1234i	0.489935	+	0.848593i	0.999933	−	0.0115828i	$-0.00368702\pi$
$277$	8.15415	+	14.1234i	0.489935	+	0.848593i	−0.509997	+	0.860176i	$0.670354\pi$
$278$	4.41025	−	7.63878i	0.264509	−	0.458144i
$279$		0			0
$280$	−25.5016	+	11.1992i	−1.52401	+	0.669282i
$281$	22.5518			1.34533			0.672665	−	0.739947i	$-0.265150\pi$
$281$	22.5518			1.34533			0.672665	+	0.739947i	$0.265150\pi$
$282$		0			0
$283$	−12.4284	−	21.5267i	−0.738794	−	1.27963i	−0.953039	−	0.302849i	$-0.902062\pi$
$283$	−12.4284	−	21.5267i	−0.738794	−	1.27963i	0.214245	−	0.976780i	$-0.431271\pi$
$284$	0.270299	+	0.468171i	0.0160393	+	0.0277809i
$285$		0			0
$286$	−7.01866			−0.415022
$287$	0.568993	+	0.417828i	0.0335866	+	0.0246636i
$288$		0			0
$289$	8.31842	−	14.4079i	0.489319	−	0.847525i
$290$	12.5043	+	21.6582i	0.734280	+	1.27181i
$291$		0			0
$292$	1.52794	−	2.64647i	0.0894158	−	0.154873i
$293$	24.2328			1.41569			0.707847	−	0.706365i	$-0.249666\pi$
$293$	24.2328			1.41569			0.707847	+	0.706365i	$0.249666\pi$
$294$		0			0
$295$	14.6513			0.853033
$296$	0.414924	−	0.718669i	0.0241170	−	0.0417718i
$297$		0			0
$298$	4.68991	+	8.12316i	0.271679	+	0.470562i
$299$	2.35766	−	4.08359i	0.136347	−	0.236160i
$300$		0			0
$301$	−25.6302	−	18.8210i	−1.47730	−	1.08482i
$302$	−22.9520			−1.32074
$303$		0			0
$304$	5.31562	+	9.20693i	0.304872	+	0.528054i
$305$	6.12469	+	10.6083i	0.350699	+	0.607428i
$306$		0			0
$307$	−14.9020			−0.850503			−0.425252	−	0.905075i	$-0.639814\pi$
$307$	−14.9020			−0.850503			−0.425252	+	0.905075i	$0.639814\pi$
$308$	11.0188	−	4.83897i	0.627852	−	0.275726i
$309$		0			0
$310$	−20.6567	+	35.7784i	−1.17322	+	2.03208i
$311$	−8.84894	−	15.3268i	−0.501777	−	0.869104i	−0.999998	−	0.00205350i	$-0.999346\pi$
$311$	−8.84894	−	15.3268i	−0.501777	−	0.869104i	0.498221	−	0.867050i	$-0.333987\pi$
$312$		0			0
$313$	−9.33353	+	16.1661i	−0.527562	+	0.913765i	0.471922	+	0.881640i	$0.343560\pi$
$313$	−9.33353	+	16.1661i	−0.527562	+	0.913765i	−0.999484	+	0.0321240i	$0.989773\pi$
$314$	5.15724			0.291040
$315$		0			0
$316$	−6.16020			−0.346539
$317$	−0.00139638	+	0.00241860i	−7.84284e−5	+	0.000135842i	−0.866065	−	0.499932i	$-0.833358\pi$
$317$	−0.00139638	+	0.00241860i	−7.84284e−5	+	0.000135842i	0.865986	+	0.500068i	$0.166692\pi$
$318$		0			0
$319$	−20.1999	−	34.9873i	−1.13098	−	1.95891i
$320$	−14.3689	+	24.8876i	−0.803243	+	1.39126i
$321$		0			0
$322$	1.54041	−	13.9731i	0.0858439	−	0.778693i
$323$	3.19347			0.177690
$324$		0			0
$325$	−3.35428	−	5.80979i	−0.186062	−	0.322269i
$326$	−5.13530	−	8.89460i	−0.284418	−	0.492626i
$327$		0			0
$328$	0.820866			0.0453248
$329$	21.2012	−	9.31066i	1.16886	−	0.513313i
$330$		0			0
$331$	−16.7977	+	29.0944i	−0.923283	+	1.59917i	−0.128984	+	0.991647i	$0.541172\pi$
$331$	−16.7977	+	29.0944i	−0.923283	+	1.59917i	−0.794299	+	0.607527i	$0.792162\pi$
$332$	0.0426989	+	0.0739566i	0.00234340	+	0.00405889i
$333$		0			0
$334$	7.87609	−	13.6418i	0.430960	−	0.746445i
$335$	4.70544			0.257086
$336$		0			0
$337$	4.38767			0.239012			0.119506	−	0.992833i	$-0.461869\pi$
$337$	4.38767			0.239012			0.119506	+	0.992833i	$0.461869\pi$
$338$	−0.563413	+	0.975859i	−0.0306456	+	0.0530797i
$339$		0			0
$340$	0.752925	+	1.30410i	0.0408331	+	0.0707250i
$341$	33.3695	−	57.7976i	1.80706	−	3.12992i
$342$		0			0
$343$	5.99072	−	17.5246i	0.323469	−	0.946239i
$344$	−36.9758			−1.99360
$345$		0			0
$346$	7.47539	+	12.9478i	0.401879	+	0.696076i
$347$	−0.0356658	−	0.0617749i	−0.00191464	−	0.00331625i	0.865066	−	0.501657i	$-0.167276\pi$
$347$	−0.0356658	−	0.0617749i	−0.00191464	−	0.00331625i	−0.866981	+	0.498341i	$0.833943\pi$
$348$		0			0
$349$	3.77491			0.202066			0.101033	−	0.994883i	$-0.467785\pi$
$349$	3.77491			0.202066			0.101033	+	0.994883i	$0.467785\pi$
$350$	−16.1206	−	11.8379i	−0.861684	−	0.632760i
$351$		0			0
$352$	12.1224	−	20.9967i	0.646128	−	1.11913i
$353$	−3.32688	−	5.76232i	−0.177072	−	0.306698i	0.763804	−	0.645448i	$-0.223329\pi$
$353$	−3.32688	−	5.76232i	−0.177072	−	0.306698i	−0.940876	+	0.338750i	$0.889996\pi$
$354$		0			0
$355$	−1.26653	+	2.19369i	−0.0672204	+	0.116429i
$356$	−7.21209			−0.382240
$357$		0			0
$358$	22.1971			1.17315
$359$	9.40817	−	16.2954i	0.496544	−	0.860040i	−0.503448	−	0.864026i	$-0.667935\pi$
$359$	9.40817	−	16.2954i	0.496544	−	0.860040i	0.999992	+	0.00398593i	$0.00126876\pi$
$360$		0			0
$361$	−4.54098	−	7.86522i	−0.238999	−	0.413959i
$362$	2.87725	−	4.98354i	0.151225	−	0.261929i
$363$		0			0
$364$	0.211714	−	1.92047i	0.0110968	−	0.100660i
$365$	14.3188			0.749481
$366$		0			0
$367$	−11.4969	−	19.9132i	−0.600133	−	1.03946i	−0.992800	−	0.119781i	$-0.961781\pi$
$367$	−11.4969	−	19.9132i	−0.600133	−	1.03946i	0.392667	−	0.919681i	$-0.371552\pi$
$368$	−4.72990	−	8.19243i	−0.246563	−	0.427060i
$369$		0			0
$370$	1.04003			0.0540685
$371$	−1.05467	+	9.56691i	−0.0547555	+	0.496689i
$372$		0			0
$373$	9.01928	−	15.6219i	0.467001	−	0.808869i	−0.532289	−	0.846563i	$-0.678668\pi$
$373$	9.01928	−	15.6219i	0.467001	−	0.808869i	0.999289	+	0.0376939i	$0.0120012\pi$
$374$	2.11482	+	3.66298i	0.109355	+	0.189408i
$375$		0			0
$376$	13.4628	−	23.3183i	0.694293	−	1.20255i
$377$	−6.48608			−0.334050
$378$		0			0
$379$	−9.99684			−0.513503			−0.256752	−	0.966477i	$-0.582652\pi$
$379$	−9.99684			−0.513503			−0.256752	+	0.966477i	$0.582652\pi$
$380$	6.62089	−	11.4677i	0.339644	−	0.588281i
$381$		0			0
$382$	−10.0707	−	17.4430i	−0.515263	−	0.892461i
$383$	5.07629	−	8.79240i	0.259386	−	0.449271i	−0.706691	−	0.707522i	$-0.749813\pi$
$383$	5.07629	−	8.79240i	0.259386	−	0.449271i	0.966078	+	0.258252i	$0.0831463\pi$
$384$		0			0
$385$	45.4512	+	33.3761i	2.31641	+	1.70101i
$386$	−0.693286			−0.0352873
$387$		0			0
$388$	3.96042	+	6.85964i	0.201060	+	0.348246i
$389$	15.6584	+	27.1212i	0.793914	+	1.37510i	0.923526	+	0.383535i	$0.125294\pi$
$389$	15.6584	+	27.1212i	0.793914	+	1.37510i	−0.129612	+	0.991565i	$0.541373\pi$
$390$		0			0
$391$	−2.84159			−0.143705
$392$	−6.44656	−	20.5482i	−0.325600	−	1.03784i
$393$		0			0
$394$	−1.13319	+	1.96273i	−0.0570890	+	0.0988811i
$395$	−14.4323	−	24.9975i	−0.726169	−	1.25776i
$396$		0			0
$397$	−11.4615	+	19.8519i	−0.575235	+	0.996336i	0.420781	+	0.907162i	$0.361756\pi$
$397$	−11.4615	+	19.8519i	−0.575235	+	0.996336i	−0.996016	+	0.0891738i	$0.971577\pi$
$398$	−20.3297			−1.01904
$399$		0			0
$400$	−13.4586			−0.672930
$401$	9.16131	−	15.8679i	0.457494	−	0.792403i	−0.541334	−	0.840808i	$-0.682080\pi$
$401$	9.16131	−	15.8679i	0.457494	−	0.792403i	0.998828	+	0.0484048i	$0.0154137\pi$
$402$		0			0
$403$	−5.35737	−	9.27924i	−0.266870	−	0.462232i
$404$	1.63221	−	2.82706i	0.0812053	−	0.140652i
$405$		0			0
$406$	−17.7049	+	7.77524i	−0.878679	+	0.385879i
$407$	−1.68010			−0.0832794
$408$		0			0
$409$	−2.46042	−	4.26157i	−0.121660	−	0.210721i	0.798762	−	0.601647i	$-0.205488\pi$
$409$	−2.46042	−	4.26157i	−0.121660	−	0.210721i	−0.920422	+	0.390925i	$0.872155\pi$
$410$	0.514386	+	0.890943i	0.0254037	+	0.0440006i
$411$		0			0
$412$	−8.56398			−0.421917
$413$	−1.24135	+	11.2603i	−0.0610828	+	0.554084i
$414$		0			0
$415$	−0.200073	+	0.346536i	−0.00982117	+	0.0170108i
$416$	−1.94622	−	3.37096i	−0.0954214	−	0.165275i
$417$		0			0
$418$	18.5968	−	32.2106i	0.909598	−	1.57547i
$419$	19.6349			0.959230			0.479615	−	0.877479i	$-0.340776\pi$
$419$	19.6349			0.959230			0.479615	+	0.877479i	$0.340776\pi$
$420$		0			0
$421$	−4.93028			−0.240287			−0.120144	−	0.992757i	$-0.538335\pi$
$421$	−4.93028			−0.240287			−0.120144	+	0.992757i	$0.538335\pi$
$422$	−10.6815	+	18.5008i	−0.519965	+	0.900606i
$423$		0			0
$424$	5.59599	+	9.69254i	0.271765	+	0.470711i
$425$	−2.02138	+	3.50114i	−0.0980515	+	0.169830i
$426$		0			0
$427$	−8.67194	+	3.80835i	−0.419665	+	0.184299i
$428$	−2.56328			−0.123901
$429$		0			0
$430$	−23.1704	−	40.1324i	−1.11738	−	1.93536i
$431$	−16.5274	−	28.6262i	−0.796094	−	1.37888i	−0.922142	−	0.386852i	$-0.873562\pi$
$431$	−16.5274	−	28.6262i	−0.796094	−	1.37888i	0.126047	−	0.992024i	$-0.459771\pi$
$432$		0			0
$433$	6.62761			0.318503			0.159251	−	0.987238i	$-0.449092\pi$
$433$	6.62761			0.318503			0.159251	+	0.987238i	$0.449092\pi$
$434$	−25.7475	−	18.9071i	−1.23592	−	0.907571i
$435$		0			0
$436$	−4.53616	+	7.85685i	−0.217242	+	0.376275i
$437$	12.4938	+	21.6399i	0.597661	+	1.03518i
$438$		0			0
$439$	10.7822	−	18.6753i	0.514607	−	0.891325i	−0.485250	−	0.874376i	$-0.661271\pi$
$439$	10.7822	−	18.6753i	0.514607	−	0.891325i	0.999856	−	0.0169492i	$-0.00539535\pi$
$440$	65.5708			3.12597
$441$		0			0
$442$	0.679056			0.0322994
$443$	−6.57363	+	11.3859i	−0.312323	+	0.540958i	−0.978865	−	0.204509i	$-0.934440\pi$
$443$	−6.57363	+	11.3859i	−0.312323	+	0.540958i	0.666542	+	0.745467i	$0.267774\pi$
$444$		0			0
$445$	−16.8967	−	29.2660i	−0.800982	−	1.38734i
$446$	10.0131	−	17.3432i	0.474134	−	0.821225i
$447$		0			0
$448$	−17.9100	−	13.1519i	−0.846169	−	0.621367i
$449$	−18.5922			−0.877422			−0.438711	−	0.898628i	$-0.644565\pi$
$449$	−18.5922			−0.877422			−0.438711	+	0.898628i	$0.644565\pi$
$450$		0			0
$451$	−0.830957	−	1.43926i	−0.0391282	−	0.0677721i
$452$	−1.94074	−	3.36146i	−0.0912847	−	0.158110i
$453$		0			0
$454$	−25.4696			−1.19535
$455$	8.28908	−	3.64021i	0.388598	−	0.170656i
$456$		0			0
$457$	2.90763	−	5.03617i	0.136013	−	0.235582i	−0.789971	−	0.613145i	$-0.789904\pi$
$457$	2.90763	−	5.03617i	0.136013	−	0.235582i	0.925984	+	0.377562i	$0.123238\pi$
$458$	−8.15314	−	14.1217i	−0.380971	−	0.659862i
$459$		0			0
$460$	−5.89134	+	10.2041i	−0.274685	+	0.475769i
$461$	−3.87560			−0.180505			−0.0902523	−	0.995919i	$-0.528767\pi$
$461$	−3.87560			−0.180505			−0.0902523	+	0.995919i	$0.528767\pi$
$462$		0			0
$463$	−12.3411			−0.573540			−0.286770	−	0.957999i	$-0.592582\pi$
$463$	−12.3411			−0.573540			−0.286770	+	0.957999i	$0.592582\pi$
$464$	−6.50613	+	11.2690i	−0.302040	+	0.523148i
$465$		0			0
$466$	12.8727	+	22.2962i	0.596316	+	1.03285i
$467$	−15.0283	+	26.0298i	−0.695427	+	1.20451i	0.274610	+	0.961556i	$0.411451\pi$
$467$	−15.0283	+	26.0298i	−0.695427	+	1.20451i	−0.970037	+	0.242959i	$0.921882\pi$
$468$		0			0
$469$	−0.398674	+	3.61639i	−0.0184091	+	0.166989i
$470$	33.7453			1.55656
$471$		0			0
$472$	6.58653	+	11.4082i	0.303169	+	0.525105i
$473$	37.4303	+	64.8312i	1.72105	+	2.98094i
$474$		0			0
$475$	35.5503			1.63116
$476$	−1.06607	+	0.468171i	−0.0488631	+	0.0214586i
$477$		0			0
$478$	3.02558	−	5.24046i	0.138387	−	0.239693i
$479$	−5.86167	−	10.1527i	−0.267827	−	0.463890i	0.700474	−	0.713678i	$-0.252972\pi$
$479$	−5.86167	−	10.1527i	−0.267827	−	0.463890i	−0.968300	+	0.249789i	$0.919639\pi$
$480$		0			0
$481$	−0.134867	+	0.233597i	−0.00614943	+	0.0106511i
$482$	6.69658			0.305021
$483$		0			0
$484$	−20.2990			−0.922681
$485$	−18.5572	+	32.1420i	−0.842638	+	1.45949i
$486$		0			0
$487$	−10.7409	−	18.6038i	−0.486718	−	0.843020i	0.513166	−	0.858290i	$-0.328473\pi$
$487$	−10.7409	−	18.6038i	−0.486718	−	0.843020i	−0.999883	+	0.0152696i	$0.995139\pi$
$488$	−5.50673	+	9.53793i	−0.249278	+	0.431762i
$489$		0			0
$490$	18.2627	−	19.8732i	0.825027	−	0.897779i
$491$	−4.33221			−0.195510			−0.0977549	−	0.995211i	$-0.531166\pi$
$491$	−4.33221			−0.195510			−0.0977549	+	0.995211i	$0.531166\pi$
$492$		0			0
$493$	1.95435	+	3.38503i	0.0880194	+	0.152454i
$494$	−2.98566	−	5.17131i	−0.134331	−	0.232668i
$495$		0			0
$496$	−21.4957			−0.965187
$497$	−1.57866	−	1.15926i	−0.0708127	−	0.0519999i
$498$		0			0
$499$	−18.9118	+	32.7563i	−0.846610	+	1.46637i	0.0376058	+	0.999293i	$0.488027\pi$
$499$	−18.9118	+	32.7563i	−0.846610	+	1.46637i	−0.884216	+	0.467079i	$0.845306\pi$
$500$	2.13468	+	3.69738i	0.0954660	+	0.165352i
$501$		0			0
$502$	4.80076	−	8.31516i	0.214268	−	0.371124i
$503$	37.2173			1.65944			0.829718	−	0.558182i	$-0.188501\pi$
$503$	37.2173			1.65944			0.829718	+	0.558182i	$0.188501\pi$
$504$		0			0
$505$	15.2959			0.680660
$506$	−16.5476	+	28.6613i	−0.735632	+	1.27415i
$507$		0			0
$508$	−2.34536	−	4.06228i	−0.104059	−	0.180235i
$509$	4.22616	−	7.31993i	0.187321	−	0.324450i	−0.757035	−	0.653374i	$-0.773353\pi$
$509$	4.22616	−	7.31993i	0.187321	−	0.324450i	0.944356	+	0.328924i	$0.106686\pi$
$510$		0			0
$511$	−1.21318	+	11.0048i	−0.0536678	+	0.486823i
$512$	−20.1531			−0.890651
$513$		0			0
$514$	−9.39323	−	16.2696i	−0.414318	−	0.717619i
$515$	−20.0640	−	34.7518i	−0.884124	−	1.53135i
$516$		0			0
$517$	−54.5133			−2.39749
$518$	−0.0881176	+	0.799318i	−0.00387167	+	0.0351200i
$519$		0			0
$520$	5.26360	−	9.11683i	0.230824	−	0.399799i
$521$	13.7821	+	23.8712i	0.603803	+	1.04582i	0.992239	+	0.124342i	$0.0396820\pi$
$521$	13.7821	+	23.8712i	0.603803	+	1.04582i	−0.388436	+	0.921476i	$0.626985\pi$
$522$		0			0
$523$	8.75484	−	15.1638i	0.382823	−	0.663068i	−0.608642	−	0.793445i	$-0.708285\pi$
$523$	8.75484	−	15.1638i	0.382823	−	0.663068i	0.991465	+	0.130377i	$0.0416187\pi$
$524$	−12.8950			−0.563321
$525$		0			0
$526$	−31.3085			−1.36512
$527$	−3.22850	+	5.59193i	−0.140636	+	0.243588i
$528$		0			0
$529$	0.382847	+	0.663110i	0.0166455	+	0.0288309i
$530$	−7.01332	+	12.1474i	−0.304639	+	0.527651i
$531$		0			0
$532$	8.25259	+	6.06012i	0.357795	+	0.262740i
$533$	−0.266816			−0.0115571
$534$		0			0
$535$	−6.00534	−	10.4016i	−0.259634	−	0.449698i
$536$	2.11534	+	3.66388i	0.0913688	+	0.158255i
$537$		0			0
$538$	2.64803			0.114165
$539$	−29.5023	+	32.1038i	−1.27075	+	1.38281i
$540$		0			0
$541$	15.7752	−	27.3235i	0.678230	−	1.17473i	−0.297283	−	0.954789i	$-0.596081\pi$
$541$	15.7752	−	27.3235i	0.678230	−	1.17473i	0.975513	−	0.219940i	$-0.0705861\pi$
$542$	3.96861	+	6.87383i	0.170466	+	0.295256i
$543$		0			0
$544$	−1.17285	+	2.03143i	−0.0502855	+	0.0870970i
$545$	−42.5098			−1.82092
$546$		0			0
$547$	10.3525			0.442639			0.221319	−	0.975201i	$-0.428964\pi$
$547$	10.3525			0.442639			0.221319	+	0.975201i	$0.428964\pi$
$548$	−2.25612	+	3.90772i	−0.0963768	+	0.166930i
$549$		0			0
$550$	23.5426	+	40.7769i	1.00386	+	1.73873i
$551$	17.1857	−	29.7664i	0.732134	−	1.26809i
$552$		0			0
$553$	20.4347	−	8.97407i	0.868973	−	0.381616i
$554$	−18.3766			−0.780747
$555$		0			0
$556$	−2.85817	−	4.95049i	−0.121213	−	0.209948i
$557$	13.9175	+	24.1058i	0.589704	+	1.02140i	0.994271	+	0.106889i	$0.0340889\pi$
$557$	13.9175	+	24.1058i	0.589704	+	1.02140i	−0.404567	+	0.914508i	$0.632578\pi$
$558$		0			0
$559$	12.0187			0.508335
$560$	1.99018	−	18.0530i	0.0841003	−	0.762876i
$561$		0			0
$562$	−12.7060	+	22.0074i	−0.535970	+	0.928327i
$563$	−13.8917	−	24.0611i	−0.585466	−	1.01406i	−0.994817	−	0.101680i	$-0.967578\pi$
$563$	−13.8917	−	24.0611i	−0.585466	−	1.01406i	0.409351	−	0.912377i	$-0.365755\pi$
$564$		0			0
$565$	9.09365	−	15.7507i	0.382573	−	0.662636i
$566$	28.0094			1.17732
$567$		0			0
$568$	−2.27748			−0.0955611
$569$	−19.2451	+	33.3335i	−0.806797	+	1.39741i	0.108274	+	0.994121i	$0.465468\pi$
$569$	−19.2451	+	33.3335i	−0.806797	+	1.39741i	−0.915071	+	0.403293i	$0.867866\pi$
$570$		0			0
$571$	16.6707	+	28.8744i	0.697646	+	1.20836i	0.969281	+	0.245957i	$0.0791023\pi$
$571$	16.6707	+	28.8744i	0.697646	+	1.20836i	−0.271635	+	0.962400i	$0.587564\pi$
$572$	−2.27430	+	3.93921i	−0.0950933	+	0.164706i
$573$		0			0
$574$	−0.728320	+	0.319847i	−0.0303995	+	0.0133502i
$575$	−31.6331			−1.31919
$576$		0			0
$577$	1.17754	+	2.03956i	0.0490216	+	0.0849079i	0.889495	−	0.456945i	$-0.151056\pi$
$577$	1.17754	+	2.03956i	0.0490216	+	0.0849079i	−0.840473	+	0.541853i	$0.817723\pi$
$578$	9.37340	+	16.2352i	0.389882	+	0.675296i
$579$		0			0
$580$	16.2075			0.672978
$581$	−0.249380	−	0.183127i	−0.0103460	−	0.00759739i
$582$		0			0
$583$	11.3296	−	19.6234i	0.469222	−	0.812717i
$584$	6.43705	+	11.1493i	0.266367	+	0.461361i
$585$		0			0
$586$	−13.6531	+	23.6478i	−0.564003	+	0.976881i
$587$	20.8410			0.860202			0.430101	−	0.902781i	$-0.358478\pi$
$587$	20.8410			0.860202			0.430101	+	0.902781i	$0.358478\pi$
$588$		0			0
$589$	56.7800			2.33958
$590$	−8.25474	+	14.2976i	−0.339842	+	0.588624i
$591$		0			0
$592$	0.270569	+	0.468639i	0.0111203	+	0.0192609i
$593$	−4.21249	+	7.29624i	−0.172986	+	0.299621i	−0.939462	−	0.342652i	$-0.888675\pi$
$593$	−4.21249	+	7.29624i	−0.172986	+	0.299621i	0.766476	+	0.642272i	$0.222008\pi$
$594$		0			0
$595$	−4.39741	−	3.22915i	−0.180276	−	0.132382i
$596$	6.07881			0.248998
$597$		0			0
$598$	2.65667	+	4.60149i	0.108639	+	0.188169i
$599$	−11.3372	−	19.6366i	−0.463225	−	0.802329i	0.535895	−	0.844285i	$-0.319974\pi$
$599$	−11.3372	−	19.6366i	−0.463225	−	0.802329i	−0.999119	+	0.0419561i	$0.986641\pi$
$600$		0			0
$601$	12.9905			0.529895			0.264948	−	0.964263i	$-0.414645\pi$
$601$	12.9905			0.529895			0.264948	+	0.964263i	$0.414645\pi$
$602$	32.8070	−	14.4075i	1.33711	−	0.587204i
$603$		0			0
$604$	−7.43729	+	12.8818i	−0.302619	+	0.524151i
$605$	−47.5571	−	82.3713i	−1.93347	−	3.34887i
$606$		0			0
$607$	−16.1643	+	27.9974i	−0.656089	+	1.13638i	0.325530	+	0.945532i	$0.394457\pi$
$607$	−16.1643	+	27.9974i	−0.656089	+	1.13638i	−0.981620	+	0.190848i	$0.938876\pi$
$608$	20.6270			0.836536
$609$		0			0
$610$	−13.8029			−0.558863
$611$	−4.37598	+	7.57942i	−0.177033	+	0.306630i
$612$		0			0
$613$	−15.5161	−	26.8747i	−0.626691	−	1.08546i	−0.988211	−	0.153096i	$-0.951076\pi$
$613$	−15.5161	−	26.8747i	−0.626691	−	1.08546i	0.361521	−	0.932364i	$-0.382258\pi$
$614$	8.39599	−	14.5423i	0.338834	−	0.586879i
$615$		0			0
$616$	−5.55556	+	50.3947i	−0.223840	+	2.03046i
$617$	−27.2587			−1.09739			−0.548697	−	0.836022i	$-0.684876\pi$
$617$	−27.2587			−1.09739			−0.548697	+	0.836022i	$0.684876\pi$
$618$		0			0
$619$	−0.720416	−	1.24780i	−0.0289560	−	0.0501532i	0.851184	−	0.524867i	$-0.175885\pi$
$619$	−0.720416	−	1.24780i	−0.0289560	−	0.0501532i	−0.880140	+	0.474714i	$0.842552\pi$
$620$	13.3870	+	23.1870i	0.537636	+	0.931213i
$621$		0			0
$622$	19.9424			0.799618
$623$	23.9241	−	10.5064i	0.958498	−	0.420932i
$624$		0			0
$625$	6.76900	−	11.7242i	0.270760	−	0.468970i
$626$	−10.5173	−	18.2164i	−0.420354	−	0.728074i
$627$		0			0
$628$	1.67114	−	2.89449i	0.0666856	−	0.115503i
$629$	0.162550			0.00648129
$630$		0			0
$631$	−19.3826			−0.771610			−0.385805	−	0.922580i	$-0.626076\pi$
$631$	−19.3826			−0.771610			−0.385805	+	0.922580i	$0.626076\pi$
$632$	12.9762	−	22.4754i	0.516164	−	0.894022i
$633$		0			0
$634$	−0.00157347	−	0.00272534i	−6.24906e−5	−	0.000108237i
$635$	10.9896	−	19.0345i	0.436108	−	0.755361i
$636$		0			0
$637$	2.09540	+	6.67902i	0.0830227	+	0.264632i
$638$	45.5236			1.80230
$639$		0			0
$640$	−2.87210	−	4.97462i	−0.113530	−	0.196639i
$641$	0.481498	+	0.833979i	0.0190180	+	0.0329402i	0.875378	−	0.483439i	$-0.160613\pi$
$641$	0.481498	+	0.833979i	0.0190180	+	0.0329402i	−0.856360	+	0.516380i	$0.827279\pi$
$642$		0			0
$643$	5.51311			0.217416			0.108708	−	0.994074i	$-0.465329\pi$
$643$	5.51311			0.217416			0.108708	+	0.994074i	$0.465329\pi$
$644$	−7.34325	−	5.39236i	−0.289365	−	0.212489i
$645$		0			0
$646$	−1.79924	+	3.11638i	−0.0707902	+	0.122612i
$647$	−2.87275	−	4.97574i	−0.112939	−	0.195617i	0.804015	−	0.594609i	$-0.202693\pi$
$647$	−2.87275	−	4.97574i	−0.112939	−	0.195617i	−0.916954	+	0.398993i	$0.869360\pi$
$648$		0			0
$649$	13.3350	−	23.0969i	0.523444	−	0.906632i
$650$	7.55938			0.296503
$651$		0			0
$652$	−6.65610			−0.260673
$653$	3.17807	−	5.50458i	0.124368	−	0.215411i	−0.797118	−	0.603824i	$-0.793643\pi$
$653$	3.17807	−	5.50458i	0.124368	−	0.215411i	0.921486	+	0.388413i	$0.126976\pi$
$654$		0			0
$655$	−30.2109	−	52.3267i	−1.18044	−	2.04457i
$656$	−0.267640	+	0.463567i	−0.0104496	+	0.0180992i
$657$		0			0
$658$	−2.85911	+	25.9351i	−0.111460	+	1.01106i
$659$	−18.7092			−0.728806			−0.364403	−	0.931241i	$-0.618727\pi$
$659$	−18.7092			−0.728806			−0.364403	+	0.931241i	$0.618727\pi$
$660$		0			0
$661$	18.4125	+	31.8913i	0.716162	+	1.24043i	0.962510	+	0.271247i	$0.0874360\pi$
$661$	18.4125	+	31.8913i	0.716162	+	1.24043i	−0.246348	+	0.969181i	$0.579231\pi$
$662$	−18.9280	−	32.7843i	−0.735659	−	1.27420i
$663$		0			0
$664$	−0.359772			−0.0139618
$665$	−5.25696	+	47.6861i	−0.203856	+	1.84919i
$666$		0			0
$667$	−15.2920	+	26.4865i	−0.592109	+	1.02556i
$668$	−5.10428	−	8.84088i	−0.197491	−	0.342064i
$669$		0			0
$670$	−2.65111	+	4.59185i	−0.102421	+	0.177399i
$671$	22.2977			0.860792
$672$		0			0
$673$	40.4024			1.55740			0.778699	−	0.627397i	$-0.215880\pi$
$673$	40.4024			1.55740			0.778699	+	0.627397i	$0.215880\pi$
$674$	−2.47207	+	4.28175i	−0.0952205	+	0.164927i
$675$		0			0
$676$	0.365133	+	0.632428i	0.0140436	+	0.0243242i
$677$	1.00827	−	1.74638i	0.0387511	−	0.0671189i	−0.845999	−	0.533184i	$-0.820995\pi$
$677$	1.00827	−	1.74638i	0.0387511	−	0.0671189i	0.884750	+	0.466065i	$0.154329\pi$
$678$		0			0
$679$	−23.1306	−	16.9855i	−0.887670	−	0.651842i
$680$	−6.34399			−0.243281
$681$		0			0
$682$	37.6016	+	65.1278i	1.43984	+	2.49387i
$683$	6.95073	+	12.0390i	0.265962	+	0.460660i	0.967815	−	0.251662i	$-0.0809770\pi$
$683$	6.95073	+	12.0390i	0.265962	+	0.460660i	−0.701853	+	0.712322i	$0.747644\pi$
$684$		0			0
$685$	−21.1429			−0.807828
$686$	13.7263	+	15.7197i	0.524072	+	0.600180i
$687$		0			0
$688$	12.0558	−	20.8813i	0.459623	−	0.796091i
$689$	−1.81893	−	3.15048i	−0.0692957	−	0.120024i
$690$		0			0
$691$	−11.9023	+	20.6154i	−0.452785	+	0.784247i	−0.998558	−	0.0536861i	$-0.982903\pi$
$691$	−11.9023	+	20.6154i	−0.452785	+	0.784247i	0.545772	+	0.837933i	$0.316236\pi$
$692$	9.68920			0.368328
$693$		0			0
$694$	0.0803782			0.00305111
$695$	13.3924	−	23.1963i	0.508003	−	0.879887i
$696$		0			0
$697$	0.0803953	+	0.139249i	0.00304519	+	0.00527442i
$698$	−2.12683	+	3.68378i	−0.0805018	+	0.139433i
$699$		0			0
$700$	−11.8676	+	5.21177i	−0.448555	+	0.196986i
$701$	15.6607			0.591498			0.295749	−	0.955266i	$-0.404431\pi$
$701$	15.6607			0.591498			0.295749	+	0.955266i	$0.404431\pi$
$702$		0			0
$703$	−0.714695	−	1.23789i	−0.0269552	−	0.0466878i
$704$	26.1558	+	45.3031i	0.985783	+	1.70743i
$705$		0			0
$706$	7.49762			0.282177
$707$	−1.29597	+	11.7557i	−0.0487398	+	0.442120i
$708$		0			0
$709$	11.8412	−	20.5096i	0.444707	−	0.770255i	−0.553325	−	0.832965i	$-0.686641\pi$
$709$	11.8412	−	20.5096i	0.444707	−	0.770255i	0.998032	+	0.0627109i	$0.0199746\pi$
$710$	−1.42716	−	2.47191i	−0.0535603	−	0.0927691i
$711$		0			0
$712$	15.1919	−	26.3131i	0.569340	−	0.986127i
$713$	−50.5235			−1.89212
$714$		0			0
$715$	−21.3132			−0.797070
$716$	7.19267	−	12.4581i	0.268803	−	0.465580i
$717$		0			0
$718$	10.6014	+	18.3621i	0.395639	+	0.685267i
$719$	−19.0793	+	33.0463i	−0.711538	+	1.23242i	0.252742	+	0.967534i	$0.418668\pi$
$719$	−19.0793	+	33.0463i	−0.711538	+	1.23242i	−0.964280	+	0.264886i	$0.914666\pi$
$720$		0			0
$721$	28.4086	−	12.4758i	1.05799	−	0.464625i
$722$	10.2338			0.380862
$723$		0			0
$724$	−1.86467	−	3.22970i	−0.0692998	−	0.120031i
$725$	21.7561	+	37.6828i	0.808003	+	1.39950i
$726$		0			0
$727$	−41.6980			−1.54649			−0.773246	−	0.634106i	$-0.781368\pi$
$727$	−41.6980			−1.54649			−0.773246	+	0.634106i	$0.781368\pi$
$728$	6.56081	+	4.81779i	0.243160	+	0.178559i
$729$		0			0
$730$	−8.06740	+	13.9731i	−0.298588	+	0.517169i
$731$	−3.62139	−	6.27243i	−0.133942	−	0.231994i
$732$		0			0
$733$	10.1023	−	17.4977i	0.373137	−	0.646293i	−0.616909	−	0.787034i	$-0.711615\pi$
$733$	10.1023	−	17.4977i	0.373137	−	0.646293i	0.990046	+	0.140742i	$0.0449487\pi$
$734$	25.9100			0.956355
$735$		0			0
$736$	−18.3542			−0.676543
$737$	4.28269	−	7.41783i	0.157755	−	0.273239i
$738$		0			0
$739$	7.01305	+	12.1470i	0.257979	+	0.446833i	0.965700	−	0.259659i	$-0.0836101\pi$
$739$	7.01305	+	12.1470i	0.257979	+	0.446833i	−0.707721	+	0.706492i	$0.750277\pi$
$740$	0.337007	−	0.583714i	0.0123886	−	0.0214578i
$741$		0			0
$742$	−8.74174	−	6.41932i	−0.320919	−	0.235661i
$743$	−37.7853			−1.38621			−0.693103	−	0.720838i	$-0.743757\pi$
$743$	−37.7853			−1.38621			−0.693103	+	0.720838i	$0.743757\pi$
$744$		0			0
$745$	14.2416	+	24.6672i	0.521773	+	0.903737i
$746$	10.1632	+	17.6031i	0.372100	+	0.644495i
$747$		0			0
$748$	2.74112			0.100225
$749$	8.50296	−	3.73414i	0.310691	−	0.136443i
$750$		0			0
$751$	3.57055	−	6.18438i	0.130291	−	0.225671i	−0.793498	−	0.608573i	$-0.791742\pi$
$751$	3.57055	−	6.18438i	0.130291	−	0.225671i	0.923789	+	0.382902i	$0.125075\pi$
$752$	8.77901	+	15.2057i	0.320138	+	0.554495i
$753$		0			0
$754$	3.65434	−	6.32950i	0.133083	−	0.230507i
$755$	−69.6973			−2.53654
$756$		0			0
$757$	−17.9270			−0.651568			−0.325784	−	0.945444i	$-0.605628\pi$
$757$	−17.9270			−0.651568			−0.325784	+	0.945444i	$0.605628\pi$
$758$	5.63234	−	9.75551i	0.204576	−	0.354336i
$759$		0			0
$760$	27.8931	+	48.3123i	1.01179	+	1.75247i
$761$	6.01264	−	10.4142i	0.217958	−	0.377514i	−0.736226	−	0.676736i	$-0.763394\pi$
$761$	6.01264	−	10.4142i	0.217958	−	0.377514i	0.954184	+	0.299222i	$0.0967271\pi$
$762$		0			0
$763$	3.60169	−	32.6711i	0.130390	−	1.18277i
$764$	−13.0531			−0.472245
$765$		0			0
$766$	5.72010	+	9.90750i	0.206675	+	0.357972i
$767$	−2.14089	−	3.70814i	−0.0773032	−	0.133893i
$768$		0			0
$769$	−0.871602			−0.0314308			−0.0157154	−	0.999877i	$-0.505003\pi$
$769$	−0.871602			−0.0314308			−0.0157154	+	0.999877i	$0.505003\pi$
$770$	−58.1782	+	25.5494i	−2.09660	+	0.920737i
$771$		0			0
$772$	−0.224650	+	0.389105i	−0.00808533	+	0.0140042i
$773$	−7.11923	−	12.3309i	−0.256061	−	0.443511i	0.709122	−	0.705086i	$-0.249091\pi$
$773$	−7.11923	−	12.3309i	−0.256061	−	0.443511i	−0.965183	+	0.261575i	$0.915758\pi$
$774$		0			0
$775$	−35.9403	+	62.2504i	−1.29101	+	2.23610i
$776$	−33.3697			−1.19790
$777$		0			0
$778$	−35.2886			−1.26516
$779$	0.706960	−	1.22449i	0.0253295	−	0.0438719i
$780$		0			0
$781$	2.30548	+	3.99321i	0.0824965	+	0.142888i
$782$	1.60099	−	2.77299i	0.0572512	−	0.0991619i
$783$		0			0
$784$	13.7060	+	3.05911i	0.489501	+	0.109254i
$785$	15.6608			0.558957
$786$		0			0
$787$	17.8883	+	30.9834i	0.637648	+	1.10444i	0.985948	+	0.167055i	$0.0534258\pi$
$787$	17.8883	+	30.9834i	0.637648	+	1.10444i	−0.348300	+	0.937383i	$0.613241\pi$
$788$	0.734387	+	1.27200i	0.0261614	+	0.0453130i
$789$		0			0
$790$	32.5254			1.15720
$791$	11.3348	+	8.32345i	0.403018	+	0.295948i
$792$		0			0
$793$	1.78991	−	3.10022i	0.0635617	−	0.110092i
$794$	−12.9151	−	22.3696i	−0.458339	−	0.793866i
$795$		0			0
$796$	−6.58758	+	11.4100i	−0.233490	+	0.404417i
$797$	18.8290			0.666958			0.333479	−	0.942758i	$-0.391777\pi$
$797$	18.8290			0.666958			0.333479	+	0.942758i	$0.391777\pi$
$798$		0			0
$799$	5.27418			0.186587
$800$	−13.0564	+	22.6143i	−0.461612	+	0.799536i
$801$		0			0
$802$	10.3232	+	17.8803i	0.364525	+	0.631375i
$803$	13.0324	−	22.5727i	0.459902	−	0.796573i
$804$		0			0
$805$	4.67770	−	42.4316i	0.164867	−	1.49552i
$806$	12.0736			0.425276
$807$		0			0
$808$	6.87631	+	11.9101i	0.241908	+	0.418997i
$809$	23.0269	+	39.8837i	0.809582	+	1.40224i	0.913153	+	0.407616i	$0.133640\pi$
$809$	23.0269	+	39.8837i	0.809582	+	1.40224i	−0.103571	+	0.994622i	$0.533027\pi$
$810$		0			0
$811$	45.8404			1.60968			0.804838	−	0.593495i	$-0.202252\pi$
$811$	45.8404			1.60968			0.804838	+	0.593495i	$0.202252\pi$
$812$	−1.37319	+	12.4563i	−0.0481897	+	0.437130i
$813$		0			0
$814$	0.946588	−	1.63954i	0.0331779	−	0.0574658i
$815$	−15.5941	−	27.0098i	−0.546238	−	0.946112i
$816$		0			0
$817$	−31.8449	+	55.1570i	−1.11411	+	1.92970i
$818$	5.54493			0.193874
$819$		0			0
$820$	0.666720			0.0232829
$821$	−13.0337	+	22.5751i	−0.454880	+	0.787876i	−0.998681	−	0.0513383i	$-0.983651\pi$
$821$	−13.0337	+	22.5751i	−0.454880	+	0.787876i	0.543801	+	0.839214i	$0.316985\pi$
$822$		0			0
$823$	12.5040	+	21.6575i	0.435861	+	0.754934i	0.997365	−	0.0725401i	$-0.0231105\pi$
$823$	12.5040	+	21.6575i	0.435861	+	0.754934i	−0.561504	+	0.827474i	$0.689777\pi$
$824$	18.0396	−	31.2455i	0.628439	−	1.08849i
$825$		0			0
$826$	−10.2891	−	7.55559i	−0.358004	−	0.262893i
$827$	32.1098			1.11657			0.558284	−	0.829650i	$-0.311460\pi$
$827$	32.1098			1.11657			0.558284	+	0.829650i	$0.311460\pi$
$828$		0			0
$829$	−5.93772	−	10.2844i	−0.206225	−	0.357193i	0.744297	−	0.667849i	$-0.232785\pi$
$829$	−5.93772	−	10.2844i	−0.206225	−	0.357193i	−0.950522	+	0.310656i	$0.899451\pi$
$830$	−0.225447	−	0.390485i	−0.00782537	−	0.0135539i
$831$		0			0
$832$	8.39847			0.291165
$833$	2.85435	−	3.10605i	0.0988973	−	0.107618i
$834$		0			0
$835$	23.9170	−	41.4254i	0.827680	−	1.43358i
$836$	−12.0521	−	20.8748i	−0.416830	−	0.721970i
$837$		0			0
$838$	−11.0626	+	19.1609i	−0.382150	+	0.661904i
$839$	11.7957			0.407232			0.203616	−	0.979051i	$-0.434731\pi$
$839$	11.7957			0.407232			0.203616	+	0.979051i	$0.434731\pi$
$840$		0			0
$841$	13.0693			0.450664
$842$	2.77778	−	4.81126i	0.0957287	−	0.165807i
$843$		0			0
$844$	6.92236	+	11.9899i	0.238278	+	0.412709i
$845$	−1.71089	+	2.96335i	−0.0588564	+	0.101942i
$846$		0			0
$847$	67.3361	−	29.5712i	2.31370	−	1.01608i
$848$	−7.29821			−0.250621
$849$		0			0
$850$	−2.27775	−	3.94517i	−0.0781261	−	0.135318i
$851$	0.635944	+	1.10149i	0.0217999	+	0.0377585i
$852$		0			0
$853$	30.7053			1.05133			0.525665	−	0.850692i	$-0.323817\pi$
$853$	30.7053			1.05133			0.525665	+	0.850692i	$0.323817\pi$
$854$	1.16947	−	10.6083i	0.0400183	−	0.363008i
$855$		0			0
$856$	5.39942	−	9.35207i	0.184548	−	0.319647i
$857$	18.3991	+	31.8682i	0.628502	+	1.08860i	0.987853	+	0.155394i	$0.0496648\pi$
$857$	18.3991	+	31.8682i	0.628502	+	1.08860i	−0.359351	+	0.933203i	$0.617002\pi$
$858$		0			0
$859$	2.91404	−	5.04726i	0.0994256	−	0.172210i	−0.812021	−	0.583628i	$-0.801633\pi$
$859$	2.91404	−	5.04726i	0.0994256	−	0.172210i	0.911447	+	0.411417i	$0.134966\pi$
$860$	−30.0323			−1.02409
$861$		0			0
$862$	37.2469			1.26863
$863$	20.5440	−	35.5833i	0.699327	−	1.21127i	−0.269373	−	0.963036i	$-0.586816\pi$
$863$	20.5440	−	35.5833i	0.699327	−	1.21127i	0.968700	−	0.248234i	$-0.0798503\pi$
$864$		0			0
$865$	22.7002	+	39.3178i	0.771829	+	1.33685i
$866$	−3.73408	+	6.46762i	−0.126889	+	0.219779i
$867$		0			0
$868$	−18.9547	+	8.32410i	−0.643364	+	0.282538i
$869$	−52.5427			−1.78239
$870$		0			0
$871$	−0.687573	−	1.19091i	−0.0232975	−	0.0403525i
$872$	−19.1104	−	33.1001i	−0.647158	−	1.12091i
$873$		0			0
$874$	−28.1567			−0.952415
$875$	−12.4675	−	9.15524i	−0.421478	−	0.309504i
$876$		0			0
$877$	5.78069	−	10.0125i	0.195200	−	0.338096i	−0.751766	−	0.659430i	$-0.770798\pi$
$877$	5.78069	−	10.0125i	0.195200	−	0.338096i	0.946966	+	0.321334i	$0.104131\pi$
$878$	12.1497	+	21.0438i	0.410031	+	0.710195i
$879$		0			0
$880$	−21.3791	+	37.0297i	−0.720690	+	1.24827i
$881$	18.8516			0.635125			0.317563	−	0.948237i	$-0.397136\pi$
$881$	18.8516			0.635125			0.317563	+	0.948237i	$0.397136\pi$
$882$		0			0
$883$	−0.0238069			−0.000801165			−0.000400582	−	1.00000i	$-0.500128\pi$
$883$	−0.0238069			−0.000801165			−0.000400582		1.00000i	$0.500128\pi$
$884$	0.220039	−	0.381119i	0.00740072	−	0.0128184i
$885$		0			0
$886$	−7.40733	−	12.8299i	−0.248854	−	0.431028i
$887$	7.59392	−	13.1530i	0.254979	−	0.441636i	−0.709911	−	0.704291i	$-0.751265\pi$
$887$	7.59392	−	13.1530i	0.254979	−	0.441636i	0.964890	+	0.262655i	$0.0845982\pi$
$888$		0			0
$889$	13.6979	+	10.0588i	0.459414	+	0.337361i
$890$	38.0793			1.27642
$891$		0			0
$892$	−6.48923	−	11.2397i	−0.217275	−	0.376332i
$893$	−23.1894	−	40.1652i	−0.776003	−	1.34408i
$894$		0			0
$895$	67.4048			2.25310
$896$	4.06660	−	1.78588i	0.135856	−	0.0596621i
$897$		0			0
$898$	10.4751	−	18.1434i	0.349559	−	0.605453i
$899$	34.7484	+	60.1859i	1.15892	+	2.00731i
$900$		0			0
$901$	−1.09614	+	1.89857i	−0.0365176	+	0.0632504i
$902$	1.87269			0.0623536
$903$		0			0
$904$	16.3523			0.543868
$905$	8.73721	−	15.1333i	0.290435	−	0.503048i
$906$		0			0
$907$	−4.31162	−	7.46794i	−0.143165	−	0.247969i	0.785522	−	0.618834i	$-0.212395\pi$
$907$	−4.31162	−	7.46794i	−0.143165	−	0.247969i	−0.928687	+	0.370865i	$0.879061\pi$
$908$	−8.25309	+	14.2948i	−0.273888	+	0.474389i
$909$		0			0
$910$	−1.11783	+	10.1399i	−0.0370558	+	0.336135i
$911$	10.5379			0.349135			0.174568	−	0.984645i	$-0.444147\pi$
$911$	10.5379			0.349135			0.174568	+	0.984645i	$0.444147\pi$
$912$		0			0
$913$	0.364194	+	0.630803i	0.0120531	+	0.0208765i
$914$	3.27640	+	5.67488i	0.108374	+	0.187708i
$915$		0			0
$916$	−10.5677			−0.349166
$917$	42.7755	−	18.7852i	1.41257	−	0.620343i
$918$		0			0
$919$	−1.41911	+	2.45797i	−0.0468122	+	0.0810811i	−0.888482	−	0.458911i	$-0.848240\pi$
$919$	−1.41911	+	2.45797i	−0.0468122	+	0.0810811i	0.841670	+	0.539992i	$0.181573\pi$
$920$	−24.8196	−	42.9888i	−0.818278	−	1.41730i
$921$		0			0
$922$	2.18356	−	3.78204i	0.0719117	−	0.124555i
$923$	0.740276			0.0243665
$924$		0			0
$925$	1.80953			0.0594971
$926$	6.95314	−	12.0432i	0.228494	−	0.395764i
$927$		0			0
$928$	12.6234	+	21.8643i	0.414382	+	0.717731i
$929$	28.6027	−	49.5413i	0.938425	−	1.62540i	0.170014	−	0.985442i	$-0.445619\pi$
$929$	28.6027	−	49.5413i	0.938425	−	1.62540i	0.768410	−	0.639957i	$-0.221048\pi$
$930$		0			0
$931$	−36.2039	−	8.08051i	−1.18653	−	0.264828i
$932$	16.6849			0.546532
$933$		0			0
$934$	−16.9343	−	29.3310i	−0.554106	−	0.959740i
$935$	6.42198	+	11.1232i	0.210021	+	0.363767i
$936$		0			0
$937$	−3.71475			−0.121355			−0.0606777	−	0.998157i	$-0.519326\pi$
$937$	−3.71475			−0.121355			−0.0606777	+	0.998157i	$0.519326\pi$
$938$	−3.30447	−	2.42657i	−0.107895	−	0.0792302i
$939$		0			0
$940$	10.9347	−	18.9395i	0.356651	−	0.617738i
$941$	20.8884	+	36.1797i	0.680941	+	1.17942i	0.974694	+	0.223543i	$0.0717625\pi$
$941$	20.8884	+	36.1797i	0.680941	+	1.17942i	−0.293753	+	0.955881i	$0.594904\pi$
$942$		0			0
$943$	−0.629061	+	1.08957i	−0.0204851	+	0.0354812i
$944$	−8.59005			−0.279582
$945$		0			0
$946$	−84.3548			−2.74261
$947$	5.90368	−	10.2255i	0.191844	−	0.332283i	−0.754018	−	0.656854i	$-0.771887\pi$
$947$	5.90368	−	10.2255i	0.191844	−	0.332283i	0.945861	+	0.324571i	$0.105220\pi$
$948$		0			0
$949$	−2.09231	−	3.62398i	−0.0679191	−	0.117639i
$950$	−20.0295	+	34.6921i	−0.649842	+	1.12556i
$951$		0			0
$952$	0.537502	−	4.87570i	0.0174205	−	0.158022i
$953$	−17.1436			−0.555334			−0.277667	−	0.960677i	$-0.589561\pi$
$953$	−17.1436			−0.555334			−0.277667	+	0.960677i	$0.589561\pi$
$954$		0			0
$955$	−30.5813	−	52.9683i	−0.989587	−	1.71401i
$956$	−1.96080	−	3.39620i	−0.0634168	−	0.109841i
$957$		0			0
$958$	13.2102			0.426801
$959$	1.79135	−	16.2494i	0.0578458	−	0.524722i
$960$		0			0
$961$	−41.9029	+	72.5779i	−1.35171	+	2.34122i
$962$	−0.151972	−	0.263223i	−0.00489977	−	0.00848666i
$963$		0			0
$964$	2.16994	−	3.75844i	0.0698889	−	0.121051i
$965$	−2.10527			−0.0677710
$966$		0			0
$967$	14.7591			0.474622			0.237311	−	0.971434i	$-0.423734\pi$
$967$	14.7591			0.474622			0.237311	+	0.971434i	$0.423734\pi$
$968$	42.7587	−	74.0603i	1.37432	−	2.38039i
$969$		0			0
$970$	−20.9107	−	36.2184i	−0.671402	−	1.16290i
$971$	−15.3435	+	26.5756i	−0.492395	+	0.852853i	−0.999962	−	0.00875959i	$-0.997212\pi$
$971$	−15.3435	+	26.5756i	−0.492395	+	0.852853i	0.507567	+	0.861612i	$0.330545\pi$
$972$		0			0
$973$	16.6929	+	12.2581i	0.535151	+	0.392977i
$974$	24.2063			0.775620
$975$		0			0
$976$	−3.59089	−	6.21961i	−0.114942	−	0.199085i
$977$	−18.0720	−	31.3016i	−0.578175	−	1.00143i	−0.995689	−	0.0927576i	$-0.970432\pi$
$977$	−18.0720	−	31.3016i	−0.578175	−	1.00143i	0.417514	−	0.908671i	$-0.362902\pi$
$978$		0			0
$979$	−61.5146			−1.96602
$980$	−5.23599	−	16.6896i	−0.167258	−	0.533129i
$981$		0			0
$982$	2.44082	−	4.22763i	0.0778897	−	0.134909i
$983$	23.0569	+	39.9357i	0.735401	+	1.27375i	0.954547	+	0.298059i	$0.0963393\pi$
$983$	23.0569	+	39.9357i	0.735401	+	1.27375i	−0.219147	+	0.975692i	$0.570327\pi$
$984$		0			0
$985$	−3.44109	+	5.96014i	−0.109642	+	0.189906i
$986$	−4.40442			−0.140265
$987$		0			0
$988$	−3.86985			−0.123116
$989$	28.3359	−	49.0793i	0.901031	−	1.56063i
$990$		0			0
$991$	14.1119	+	24.4425i	0.448278	+	0.776440i	0.998274	−	0.0587271i	$-0.0187042\pi$
$991$	14.1119	+	24.4425i	0.448278	+	0.776440i	−0.549996	+	0.835167i	$0.685371\pi$
$992$	−20.8533	+	36.1189i	−0.662092	+	1.14678i
$993$		0			0
$994$	2.02071	−	0.887412i	0.0640931	−	0.0281470i
$995$	−61.7344			−1.95711
$996$		0			0
$997$	3.18006	+	5.50802i	0.100713	+	0.174441i	0.911979	−	0.410237i	$-0.134554\pi$
$997$	3.18006	+	5.50802i	0.100713	+	0.174441i	−0.811265	+	0.584678i	$0.801221\pi$
$998$	−21.3103	−	36.9106i	−0.674567	−	1.16838i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.j.352.4	yes	20
3.2	odd	2	inner	819.2.j.j.352.7	yes	20
7.2	even	3		5733.2.a.by.1.7		10
7.4	even	3	inner	819.2.j.j.235.4	✓	20
7.5	odd	6		5733.2.a.bz.1.7		10
21.2	odd	6		5733.2.a.by.1.4		10
21.5	even	6		5733.2.a.bz.1.4		10
21.11	odd	6	inner	819.2.j.j.235.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.j.j.235.4	✓	20	7.4	even	3	inner
819.2.j.j.235.7	yes	20	21.11	odd	6	inner
819.2.j.j.352.4	yes	20	1.1	even	1	trivial
819.2.j.j.352.7	yes	20	3.2	odd	2	inner
5733.2.a.by.1.4		10	21.2	odd	6
5733.2.a.by.1.7		10	7.2	even	3
5733.2.a.bz.1.4		10	21.5	even	6
5733.2.a.bz.1.7		10	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.563413 + 0.975859i) q^{2} +(0.365133 + 0.632428i) q^{4} +(-1.71089 + 2.96335i) q^{5} +(-2.13253 - 1.56598i) q^{7} -3.07653 q^{8} +(-1.92787 - 3.33917i) q^{10} +(3.11435 + 5.39421i) q^{11} +1.00000 q^{13} +(2.72967 - 1.19876i) q^{14} +(1.00309 - 1.73741i) q^{16} +(-0.301314 - 0.521891i) q^{17} +(-2.64962 + 4.58928i) q^{19} -2.49881 q^{20} -7.01866 q^{22} +(2.35766 - 4.08359i) q^{23} +(-3.35428 - 5.80979i) q^{25} +(-0.563413 + 0.975859i) q^{26} +(0.211714 - 1.92047i) q^{28} -6.48608 q^{29} +(-5.35737 - 9.27924i) q^{31} +(-1.94622 - 3.37096i) q^{32} +0.679056 q^{34} +(8.28908 - 3.64021i) q^{35} +(-0.134867 + 0.233597i) q^{37} +(-2.98566 - 5.17131i) q^{38} +(5.26360 - 9.11683i) q^{40} -0.266816 q^{41} +12.0187 q^{43} +(-2.27430 + 3.93921i) q^{44} +(2.65667 + 4.60149i) q^{46} +(-4.37598 + 7.57942i) q^{47} +(2.09540 + 6.67902i) q^{49} +7.55938 q^{50} +(0.365133 + 0.632428i) q^{52} +(-1.81893 - 3.15048i) q^{53} -21.3132 q^{55} +(6.56081 + 4.81779i) q^{56} +(3.65434 - 6.32950i) q^{58} +(-2.14089 - 3.70814i) q^{59} +(1.78991 - 3.10022i) q^{61} +12.0736 q^{62} +8.39847 q^{64} +(-1.71089 + 2.96335i) q^{65} +(-0.687573 - 1.19091i) q^{67} +(0.220039 - 0.381119i) q^{68} +(-1.11783 + 10.1399i) q^{70} +0.740276 q^{71} +(-2.09231 - 3.62398i) q^{73} +(-0.151972 - 0.263223i) q^{74} -3.86985 q^{76} +(1.80579 - 16.3804i) q^{77} +(-4.21779 + 7.30542i) q^{79} +(3.43236 + 5.94501i) q^{80} +(0.150327 - 0.260374i) q^{82} +0.116941 q^{83} +2.06206 q^{85} +(-6.77146 + 11.7285i) q^{86} +(-9.58140 - 16.5955i) q^{88} +(-4.93800 + 8.55286i) q^{89} +(-2.13253 - 1.56598i) q^{91} +3.44344 q^{92} +(-4.93096 - 8.54068i) q^{94} +(-9.06641 - 15.7035i) q^{95} +10.8465 q^{97} +(-7.69836 - 1.71823i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{4} - 4 q^{7} + 4 q^{10} + 20 q^{13} - 32 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 8 q^{28} - 12 q^{31} + 68 q^{34} - 26 q^{37} + 70 q^{40} + 80 q^{43} + 6 q^{46} - 28 q^{49} - 16 q^{52}+ \cdots + 36 q^{97}+O(q^{100}) \) 20 * q - 16 * q^4 - 4 * q^7 + 4 * q^10 + 20 * q^13 - 32 * q^16 - 6 * q^19 + 20 * q^22 - 24 * q^25 + 8 * q^28 - 12 * q^31 + 68 * q^34 - 26 * q^37 + 70 * q^40 + 80 * q^43 + 6 * q^46 - 28 * q^49 - 16 * q^52 - 48 * q^55 - 36 * q^58 + 22 * q^61 + 156 * q^64 - 26 * q^67 - 130 * q^70 - 24 * q^73 + 8 * q^76 - 28 * q^79 + 28 * q^82 - 40 * q^85 - 12 * q^88 - 4 * q^91 - 4 * q^94 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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