LMFDB - Embedded newform 819.2.n.g.172.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(100,819)] 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("819.100"); 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, 2, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [36,0,0,-22,0,0,-8,0,0,-16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.17
Character	$\chi$	$=$	819.172
Dual form			819.2.n.g.100.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18650 - 2.05508i) q^{2} +(-1.81558 - 3.14468i) q^{4} +(0.794473 + 1.37607i) q^{5} +(0.440507 - 2.60882i) q^{7} -3.87075 q^{8} +3.77058 q^{10} +3.28228 q^{11} +(3.29459 + 1.46482i) q^{13} +(-4.83869 - 4.00066i) q^{14} +(-0.961502 + 1.66537i) q^{16} +(-2.97659 - 5.15561i) q^{17} -7.15042 q^{19} +(2.88486 - 4.99672i) q^{20} +(3.89444 - 6.74536i) q^{22} +(2.77149 - 4.80037i) q^{23} +(1.23763 - 2.14363i) q^{25} +(6.91937 - 5.03263i) q^{26} +(-9.00368 + 3.35127i) q^{28} +(3.68065 + 6.37507i) q^{29} +(-4.24807 + 7.35787i) q^{31} +(-1.58910 - 2.75241i) q^{32} -14.1269 q^{34} +(3.93989 - 1.46647i) q^{35} +(1.27742 - 2.21255i) q^{37} +(-8.48399 + 14.6947i) q^{38} +(-3.07521 - 5.32642i) q^{40} +(-1.54466 - 2.67543i) q^{41} +(-5.36917 + 9.29968i) q^{43} +(-5.95924 - 10.3217i) q^{44} +(-6.57677 - 11.3913i) q^{46} +(4.29375 + 7.43700i) q^{47} +(-6.61191 - 2.29841i) q^{49} +(-2.93690 - 5.08685i) q^{50} +(-1.37519 - 13.0199i) q^{52} +(5.97827 - 10.3547i) q^{53} +(2.60768 + 4.51664i) q^{55} +(-1.70510 + 10.0981i) q^{56} +17.4684 q^{58} +(0.607697 + 1.05256i) q^{59} +0.638454 q^{61} +(10.0807 + 17.4603i) q^{62} -11.3879 q^{64} +(0.601765 + 5.69733i) q^{65} +1.36416 q^{67} +(-10.8085 + 18.7208i) q^{68} +(1.66097 - 9.83677i) q^{70} +(1.19321 - 2.06670i) q^{71} +(-0.309169 + 0.535496i) q^{73} +(-3.03132 - 5.25041i) q^{74} +(12.9822 + 22.4858i) q^{76} +(1.44587 - 8.56288i) q^{77} +(7.41828 + 12.8488i) q^{79} -3.05555 q^{80} -7.33099 q^{82} +10.1913 q^{83} +(4.72964 - 8.19198i) q^{85} +(12.7411 + 22.0682i) q^{86} -12.7049 q^{88} +(-4.13859 + 7.16824i) q^{89} +(5.27275 - 7.94972i) q^{91} -20.1275 q^{92} +20.3782 q^{94} +(-5.68081 - 9.83945i) q^{95} +(0.831568 - 1.44032i) q^{97} +(-12.5685 + 10.8610i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 22 q^{4} - 8 q^{7} - 16 q^{10} - 10 q^{16} - 8 q^{19} - 10 q^{22} - 22 q^{25} - 14 q^{28} - 18 q^{31} + 8 q^{34} + 10 q^{37} + 14 q^{40} + 20 q^{43} - 4 q^{46} - 48 q^{49} + 22 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) $ 36 * q - 22 * q^4 - 8 * q^7 - 16 * q^10 - 10 * q^16 - 8 * q^19 - 10 * q^22 - 22 * q^25 - 14 * q^28 - 18 * q^31 + 8 * q^34 + 10 * q^37 + 14 * q^40 + 20 * q^43 - 4 * q^46 - 48 * q^49 + 22 * q^52 + 42 * q^55 + 24 * q^58 - 28 * q^61 - 12 * q^64 - 24 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 - 76 * q^82 + 28 * q^85 + 24 * q^88 + 26 * q^91 - 56 * q^94 + 28 * q^97

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.18650	−	2.05508i	0.838985	−	1.45316i	−0.0517600	−	0.998660i	$-0.516483\pi$
$2$	1.18650	−	2.05508i	0.838985	−	1.45316i	0.890745	−	0.454504i	$-0.150184\pi$
$3$		0			0
$3$		0			0
$4$	−1.81558	−	3.14468i	−0.907790	−	1.57234i
$5$	0.794473	+	1.37607i	0.355299	+	0.615396i	0.987169	−	0.159678i	$-0.0510457\pi$
$5$	0.794473	+	1.37607i	0.355299	+	0.615396i	−0.631870	+	0.775074i	$0.717712\pi$
$6$		0			0
$7$	0.440507	−	2.60882i	0.166496	−	0.986042i
$7$	0.440507	−	2.60882i	0.166496	−	0.986042i
$8$	−3.87075			−1.36852
$9$		0			0
$10$	3.77058			1.19236
$11$	3.28228			0.989645			0.494822	−	0.868994i	$-0.335233\pi$
$11$	3.28228			0.989645			0.494822	+	0.868994i	$0.335233\pi$
$12$		0			0
$13$	3.29459	+	1.46482i	0.913754	+	0.406269i
$13$	3.29459	+	1.46482i	0.913754	+	0.406269i
$14$	−4.83869	−	4.00066i	−1.29319	−	1.06922i
$15$		0			0
$16$	−0.961502	+	1.66537i	−0.240376	+	0.416343i
$17$	−2.97659	−	5.15561i	−0.721929	−	1.25042i	−0.960225	−	0.279226i	$-0.909922\pi$
$17$	−2.97659	−	5.15561i	−0.721929	−	1.25042i	0.238296	−	0.971193i	$-0.423411\pi$
$18$		0			0
$19$	−7.15042			−1.64042			−0.820209	−	0.572064i	$-0.806143\pi$
$19$	−7.15042			−1.64042			−0.820209	+	0.572064i	$0.806143\pi$
$20$	2.88486	−	4.99672i	0.645074	−	1.11730i
$21$		0			0
$22$	3.89444	−	6.74536i	0.830296	−	1.43812i
$23$	2.77149	−	4.80037i	0.577896	−	1.00095i	−0.417824	−	0.908528i	$-0.637207\pi$
$23$	2.77149	−	4.80037i	0.577896	−	1.00095i	0.995720	−	0.0924177i	$-0.0294595\pi$
$24$		0			0
$25$	1.23763	−	2.14363i	0.247525	−	0.428726i
$26$	6.91937	−	5.03263i	1.35700	−	0.986981i
$27$		0			0
$28$	−9.00368	+	3.35127i	−1.70154	+	0.633331i
$29$	3.68065	+	6.37507i	0.683479	+	1.18382i	0.973912	+	0.226925i	$0.0728672\pi$
$29$	3.68065	+	6.37507i	0.683479	+	1.18382i	−0.290433	+	0.956895i	$0.593799\pi$
$30$		0			0
$31$	−4.24807	+	7.35787i	−0.762976	+	1.32151i	0.178335	+	0.983970i	$0.442929\pi$
$31$	−4.24807	+	7.35787i	−0.762976	+	1.32151i	−0.941310	+	0.337542i	$0.890404\pi$
$32$	−1.58910	−	2.75241i	−0.280916	−	0.486561i
$33$		0			0
$34$	−14.1269			−2.42275
$35$	3.93989	−	1.46647i	0.665962	−	0.247879i
$36$		0			0
$37$	1.27742	−	2.21255i	0.210006	−	0.363742i	−0.741710	−	0.670721i	$-0.765985\pi$
$37$	1.27742	−	2.21255i	0.210006	−	0.363742i	0.951716	+	0.306979i	$0.0993182\pi$
$38$	−8.48399	+	14.6947i	−1.37629	+	2.38380i
$39$		0			0
$40$	−3.07521	−	5.32642i	−0.486233	−	0.842181i
$41$	−1.54466	−	2.67543i	−0.241236	−	0.417832i	0.719831	−	0.694149i	$-0.244219\pi$
$41$	−1.54466	−	2.67543i	−0.241236	−	0.417832i	−0.961067	+	0.276317i	$0.910886\pi$
$42$		0			0
$43$	−5.36917	+	9.29968i	−0.818791	+	1.41819i	0.0877830	+	0.996140i	$0.472022\pi$
$43$	−5.36917	+	9.29968i	−0.818791	+	1.41819i	−0.906574	+	0.422048i	$0.861312\pi$
$44$	−5.95924	−	10.3217i	−0.898390	−	1.55606i
$45$		0			0
$46$	−6.57677	−	11.3913i	−0.969692	−	1.67956i
$47$	4.29375	+	7.43700i	0.626308	+	1.08480i	0.988286	+	0.152611i	$0.0487681\pi$
$47$	4.29375	+	7.43700i	0.626308	+	1.08480i	−0.361978	+	0.932186i	$0.617899\pi$
$48$		0			0
$49$	−6.61191	−	2.29841i	−0.944558	−	0.328344i
$50$	−2.93690	−	5.08685i	−0.415340	−	0.719389i
$51$		0			0
$52$	−1.37519	−	13.0199i	−0.190705	−	1.80554i
$53$	5.97827	−	10.3547i	0.821179	−	1.42232i	−0.0836255	−	0.996497i	$-0.526650\pi$
$53$	5.97827	−	10.3547i	0.821179	−	1.42232i	0.904805	−	0.425827i	$-0.140017\pi$
$54$		0			0
$55$	2.60768	+	4.51664i	0.351620	+	0.609023i
$56$	−1.70510	+	10.0981i	−0.227853	+	1.34942i
$57$		0			0
$58$	17.4684			2.29371
$59$	0.607697	+	1.05256i	0.0791154	+	0.137032i	0.902869	−	0.429917i	$-0.141457\pi$
$59$	0.607697	+	1.05256i	0.0791154	+	0.137032i	−0.823753	+	0.566949i	$0.808124\pi$
$60$		0			0
$61$	0.638454			0.0817457			0.0408728	−	0.999164i	$-0.486986\pi$
$61$	0.638454			0.0817457			0.0408728	+	0.999164i	$0.486986\pi$
$62$	10.0807	+	17.4603i	1.28025	+	2.21746i
$63$		0			0
$64$	−11.3879			−1.42349
$65$	0.601765	+	5.69733i	0.0746398	+	0.706667i
$66$		0			0
$67$	1.36416			0.166658			0.0833291	−	0.996522i	$-0.473445\pi$
$67$	1.36416			0.166658			0.0833291	+	0.996522i	$0.473445\pi$
$68$	−10.8085	+	18.7208i	−1.31072	+	2.27023i
$69$		0			0
$70$	1.66097	−	9.83677i	0.198524	−	1.17572i
$71$	1.19321	−	2.06670i	0.141608	−	0.245272i	−0.786494	−	0.617598i	$-0.788106\pi$
$71$	1.19321	−	2.06670i	0.141608	−	0.245272i	0.928102	+	0.372325i	$0.121439\pi$
$72$		0			0
$73$	−0.309169	+	0.535496i	−0.0361855	+	0.0626751i	−0.883551	−	0.468335i	$-0.844854\pi$
$73$	−0.309169	+	0.535496i	−0.0361855	+	0.0626751i	0.847366	+	0.531010i	$0.178187\pi$
$74$	−3.03132	−	5.25041i	−0.352384	−	0.610347i
$75$		0			0
$76$	12.9822	+	22.4858i	1.48916	+	2.57929i
$77$	1.44587	−	8.56288i	0.164772	−	0.975831i
$78$		0			0
$79$	7.41828	+	12.8488i	0.834622	+	1.44561i	0.894338	+	0.447392i	$0.147647\pi$
$79$	7.41828	+	12.8488i	0.834622	+	1.44561i	−0.0597162	+	0.998215i	$0.519020\pi$
$80$	−3.05555			−0.341621
$81$		0			0
$82$	−7.33099			−0.809572
$83$	10.1913			1.11864			0.559319	−	0.828953i	$-0.311063\pi$
$83$	10.1913			1.11864			0.559319	+	0.828953i	$0.311063\pi$
$84$		0			0
$85$	4.72964	−	8.19198i	0.513002	−	0.888545i
$86$	12.7411	+	22.0682i	1.37391	+	2.37967i
$87$		0			0
$88$	−12.7049			−1.35435
$89$	−4.13859	+	7.16824i	−0.438689	+	0.759832i	−0.997589	−	0.0694034i	$-0.977890\pi$
$89$	−4.13859	+	7.16824i	−0.438689	+	0.759832i	0.558899	+	0.829235i	$0.311224\pi$
$90$		0			0
$91$	5.27275	−	7.94972i	0.552734	−	0.833357i
$92$	−20.1275			−2.09843
$93$		0			0
$94$	20.3782			2.10185
$95$	−5.68081	−	9.83945i	−0.582839	−	1.00951i
$96$		0			0
$97$	0.831568	−	1.44032i	0.0844329	−	0.146242i	−0.820717	−	0.571336i	$-0.806425\pi$
$97$	0.831568	−	1.44032i	0.0844329	−	0.146242i	0.905149	+	0.425094i	$0.139759\pi$
$98$	−12.5685	+	10.8610i	−1.26961	+	1.09712i
$99$		0			0
$100$	−8.98804			−0.898804
$101$	0.193821			0.0192859			0.00964296	−	0.999954i	$-0.496931\pi$
$101$	0.193821			0.0192859			0.00964296	+	0.999954i	$0.496931\pi$
$102$		0			0
$103$	1.31879	+	2.28421i	0.129944	+	0.225070i	0.923655	−	0.383225i	$-0.125187\pi$
$103$	1.31879	+	2.28421i	0.129944	+	0.225070i	−0.793710	+	0.608296i	$0.791853\pi$
$104$	−12.7525	−	5.66997i	−1.25049	−	0.555986i
$105$		0			0
$106$	−14.1865	−	24.5717i	−1.37791	−	2.38662i
$107$	−1.80814	+	3.13179i	−0.174800	+	0.302762i	−0.940092	−	0.340921i	$-0.889261\pi$
$107$	−1.80814	+	3.13179i	−0.174800	+	0.302762i	0.765292	+	0.643683i	$0.222594\pi$
$108$		0			0
$109$	−0.193567	+	0.335267i	−0.0185403	+	0.0321128i	−0.875147	−	0.483858i	$-0.839235\pi$
$109$	−0.193567	+	0.335267i	−0.0185403	+	0.0321128i	0.856606	+	0.515970i	$0.172569\pi$
$110$	12.3761			1.18001
$111$		0			0
$112$	3.92111	+	3.24200i	0.370510	+	0.306340i
$113$	−5.11211	+	8.85443i	−0.480907	+	0.832955i	−0.999760	−	0.0219083i	$-0.993026\pi$
$113$	−5.11211	+	8.85443i	−0.480907	+	0.832955i	0.518853	+	0.854863i	$0.326359\pi$
$114$		0			0
$115$	8.80750			0.821304
$116$	13.3650	−	23.1489i	1.24091	−	2.14932i
$117$		0			0
$118$	2.88414			0.265507
$119$	−14.7613	+	5.49431i	−1.35316	+	0.503663i
$120$		0			0
$121$	−0.226640			−0.0206036
$122$	0.757528	−	1.31208i	0.0685833	−	0.118790i
$123$		0			0
$124$	30.8508			2.77049
$125$	11.8778			1.06238
$126$		0			0
$127$	2.95916	+	5.12542i	0.262583	+	0.454807i	0.966928	−	0.255051i	$-0.0820923\pi$
$127$	2.95916	+	5.12542i	0.262583	+	0.454807i	−0.704345	+	0.709858i	$0.748759\pi$
$128$	−10.3336	+	17.8983i	−0.913369	+	1.58200i
$129$		0			0
$130$	12.4225	+	5.52323i	1.08952	+	0.484419i
$131$	−0.623862	−	1.08056i	−0.0545071	−	0.0944090i	0.837484	−	0.546461i	$-0.184025\pi$
$131$	−0.623862	−	1.08056i	−0.0545071	−	0.0944090i	−0.891991	+	0.452052i	$0.850692\pi$
$132$		0			0
$133$	−3.14981	+	18.6542i	−0.273123	+	1.61752i
$134$	1.61858	−	2.80346i	0.139824	−	0.242182i
$135$		0			0
$136$	11.5217	+	19.9561i	0.987974	+	1.71122i
$137$	0.524726	+	0.908852i	0.0448304	+	0.0776485i	0.887570	−	0.460673i	$-0.152392\pi$
$137$	0.524726	+	0.908852i	0.0448304	+	0.0776485i	−0.842740	+	0.538322i	$0.819059\pi$
$138$		0			0
$139$	−1.79256	+	3.10480i	−0.152043	+	0.263346i	−0.931978	−	0.362514i	$-0.881918\pi$
$139$	−1.79256	+	3.10480i	−0.152043	+	0.263346i	0.779936	+	0.625860i	$0.215252\pi$
$140$	−11.7648	−	9.72717i	−0.994303	−	0.822096i
$141$		0			0
$142$	−2.83149	−	4.90429i	−0.237614	−	0.411559i
$143$	10.8138	+	4.80796i	0.904291	+	0.402061i
$144$		0			0
$145$	−5.84835	+	10.1296i	−0.485679	+	0.841220i
$146$	0.733659	+	1.27074i	0.0607181	+	0.105167i
$147$		0			0
$148$	−9.27702			−0.762567
$149$	22.5530			1.84761			0.923806	−	0.382861i	$-0.125061\pi$
$149$	22.5530			1.84761			0.923806	+	0.382861i	$0.125061\pi$
$150$		0			0
$151$	−7.36849	+	12.7626i	−0.599639	+	1.03861i	0.393235	+	0.919438i	$0.371356\pi$
$151$	−7.36849	+	12.7626i	−0.599639	+	1.03861i	−0.992874	+	0.119167i	$0.961977\pi$
$152$	27.6775			2.24494
$153$		0			0
$154$	−15.8819	−	13.1313i	−1.27980	−	1.05815i
$155$	−13.4999			−1.08434
$156$		0			0
$157$	6.63722	−	11.4960i	0.529708	−	0.917481i	−0.469691	−	0.882831i	$-0.655635\pi$
$157$	6.63722	−	11.4960i	0.529708	−	0.917481i	0.999399	−	0.0346506i	$-0.0110318\pi$
$158$	35.2073			2.80094
$159$		0			0
$160$	2.52500	−	4.37342i	0.199619	−	0.345750i
$161$	−11.3024	−	9.34493i	−0.890757	−	0.736484i
$162$		0			0
$163$	−4.81929			−0.377476			−0.188738	−	0.982028i	$-0.560440\pi$
$163$	−4.81929			−0.377476			−0.188738	+	0.982028i	$0.560440\pi$
$164$	−5.60892	+	9.71493i	−0.437983	+	0.758608i
$165$		0			0
$166$	12.0920	−	20.9439i	0.938520	−	1.62556i
$167$	4.56029	+	7.89865i	0.352886	+	0.611216i	0.986754	−	0.162225i	$-0.0518671\pi$
$167$	4.56029	+	7.89865i	0.352886	+	0.611216i	−0.633868	+	0.773441i	$0.718534\pi$
$168$		0			0
$169$	8.70859	+	9.65197i	0.669892	+	0.742459i
$170$	−11.2235	−	19.4396i	−0.860801	−	1.49095i
$171$		0			0
$172$	38.9926			2.97316
$173$	15.6807			1.19218			0.596092	−	0.802916i	$-0.296719\pi$
$173$	15.6807			1.19218			0.596092	+	0.802916i	$0.296719\pi$
$174$		0			0
$175$	−5.04717	−	4.17303i	−0.381530	−	0.315452i
$176$	−3.15592	+	5.46621i	−0.237886	+	0.412031i
$177$		0			0
$178$	9.82089	+	17.0103i	0.736107	+	1.27497i
$179$	−10.1114			−0.755759			−0.377879	−	0.925855i	$-0.623347\pi$
$179$	−10.1114			−0.755759			−0.377879	+	0.925855i	$0.623347\pi$
$180$		0			0
$181$	−16.7897			−1.24797			−0.623983	−	0.781438i	$-0.714487\pi$
$181$	−16.7897			−1.24797			−0.623983	+	0.781438i	$0.714487\pi$
$182$	−10.0812	−	20.2683i	−0.747269	−	1.50239i
$183$		0			0
$184$	−10.7278	+	18.5810i	−0.790862	+	1.36981i
$185$	4.05950			0.298460
$186$		0			0
$187$	−9.77000	−	16.9221i	−0.714453	−	1.23747i
$188$	15.5913	−	27.0049i	1.13711	−	1.96954i
$189$		0			0
$190$	−26.9612			−1.95597
$191$	18.9076			1.36811			0.684055	−	0.729431i	$-0.260215\pi$
$191$	18.9076			1.36811			0.684055	+	0.729431i	$0.260215\pi$
$192$		0			0
$193$	−7.85016			−0.565067			−0.282534	−	0.959257i	$-0.591175\pi$
$193$	−7.85016			−0.565067			−0.282534	+	0.959257i	$0.591175\pi$
$194$	−1.97332	−	3.41788i	−0.141676	−	0.245390i
$195$		0			0
$196$	4.77669	+	24.9653i	0.341192	+	1.78323i
$197$	−12.5419	−	21.7232i	−0.893572	−	1.54771i	−0.835562	−	0.549396i	$-0.814858\pi$
$197$	−12.5419	−	21.7232i	−0.893572	−	1.54771i	−0.0580100	−	0.998316i	$-0.518476\pi$
$198$		0			0
$199$	3.89191	+	6.74099i	0.275890	+	0.477856i	0.970359	−	0.241667i	$-0.0776940\pi$
$199$	3.89191	+	6.74099i	0.275890	+	0.477856i	−0.694469	+	0.719523i	$0.744361\pi$
$200$	−4.79055	+	8.29747i	−0.338743	+	0.586720i
$201$		0			0
$202$	0.229969	−	0.398319i	0.0161806	−	0.0280256i
$203$	18.2528	−	6.79389i	1.28109	−	0.476837i
$204$		0			0
$205$	2.45438	−	4.25112i	0.171422	−	0.296911i
$206$	6.25900			0.436085
$207$		0			0
$208$	−5.60722	+	4.07828i	−0.388791	+	0.282778i
$209$	−23.4697			−1.62343
$210$		0			0
$211$	1.17458	+	2.03443i	0.0808614	+	0.140056i	0.903620	−	0.428335i	$-0.140900\pi$
$211$	1.17458	+	2.03443i	0.0808614	+	0.140056i	−0.822759	+	0.568391i	$0.807566\pi$
$212$	−43.4161			−2.98183
$213$		0			0
$214$	4.29073	+	7.43177i	0.293309	+	0.508025i
$215$	−17.0626			−1.16366
$216$		0			0
$217$	17.3241	+	14.3236i	1.17603	+	0.972353i
$218$	0.459335	+	0.795591i	0.0311101	+	0.0538842i
$219$		0			0
$220$	9.46891	−	16.4006i	0.638394	−	1.10573i
$221$	−2.25459	−	21.3458i	−0.151660	−	1.43587i
$222$		0			0
$223$	−5.78913	−	10.0271i	−0.387669	−	0.671462i	0.604467	−	0.796630i	$-0.293386\pi$
$223$	−5.78913	−	10.0271i	−0.387669	−	0.671462i	−0.992136	+	0.125168i	$0.960053\pi$
$224$	−7.88055	+	2.93323i	−0.526541	+	0.195985i
$225$		0			0
$226$	12.1311	+	21.0116i	0.806947	+	1.39767i
$227$	6.48974	+	11.2406i	0.430739	+	0.746062i	0.996937	−	0.0782070i	$-0.0249195\pi$
$227$	6.48974	+	11.2406i	0.430739	+	0.746062i	−0.566198	+	0.824269i	$0.691586\pi$
$228$		0			0
$229$	9.63048	+	16.6805i	0.636400	+	1.10228i	0.986217	+	0.165459i	$0.0529105\pi$
$229$	9.63048	+	16.6805i	0.636400	+	1.10228i	−0.349817	+	0.936818i	$0.613756\pi$
$230$	10.4501	−	18.1002i	0.689061	−	1.19349i
$231$		0			0
$232$	−14.2469	−	24.6763i	−0.935353	−	1.62008i
$233$	−6.25233	−	10.8294i	−0.409604	−	0.709454i	0.585242	−	0.810859i	$-0.301000\pi$
$233$	−6.25233	−	10.8294i	−0.409604	−	0.709454i	−0.994845	+	0.101405i	$0.967666\pi$
$234$		0			0
$235$	−6.82254	+	11.8170i	−0.445053	+	0.770855i
$236$	2.20665	−	3.82202i	0.143640	−	0.248793i
$237$		0			0
$238$	−6.22302	+	36.8547i	−0.403378	+	2.38893i
$239$	−29.7431			−1.92392			−0.961961	−	0.273187i	$-0.911922\pi$
$239$	−29.7431			−1.92392			−0.961961	+	0.273187i	$0.911922\pi$
$240$		0			0
$241$	−8.07397	−	13.9845i	−0.520090	−	0.900822i	−0.999727	−	0.0233553i	$-0.992565\pi$
$241$	−8.07397	−	13.9845i	−0.520090	−	0.900822i	0.479637	−	0.877467i	$-0.340768\pi$
$242$	−0.268909	+	0.465764i	−0.0172861	+	0.0299404i
$243$		0			0
$244$	−1.15916	−	2.00773i	−0.0742079	−	0.128532i
$245$	−2.09021	−	10.9245i	−0.133539	−	0.697938i
$246$		0			0
$247$	−23.5577	−	10.4741i	−1.49894	−	0.666450i
$248$	16.4432	−	28.4805i	1.04415	−	1.80851i
$249$		0			0
$250$	14.0930	−	24.4098i	0.891320	−	1.54381i
$251$	−9.80082	+	16.9755i	−0.618622	+	1.07149i	0.371115	+	0.928587i	$0.378976\pi$
$251$	−9.80082	+	16.9755i	−0.618622	+	1.07149i	−0.989737	+	0.142898i	$0.954358\pi$
$252$		0			0
$253$	9.09682	−	15.7561i	0.571912	−	0.990580i
$254$	14.0442			0.881212
$255$		0			0
$256$	13.1338	+	22.7483i	0.820860	+	1.42177i
$257$	−2.98951	+	5.17798i	−0.186481	+	0.322994i	−0.944074	−	0.329732i	$-0.893041\pi$
$257$	−2.98951	+	5.17798i	−0.186481	+	0.322994i	0.757594	+	0.652726i	$0.226375\pi$
$258$		0			0
$259$	−5.20945	−	4.30720i	−0.323699	−	0.267637i
$260$	16.8237	−	12.2363i	1.04336	−	0.758864i
$261$		0			0
$262$	−2.96086			−0.182922
$263$	−14.9922			−0.924461			−0.462231	−	0.886760i	$-0.652951\pi$
$263$	−14.9922			−0.924461			−0.462231	+	0.886760i	$0.652951\pi$
$264$		0			0
$265$	18.9983			1.16706
$266$	34.5986	+	28.6064i	2.12138	+	1.75397i
$267$		0			0
$268$	−2.47674	−	4.28983i	−0.151291	−	0.262043i
$269$	−5.10294	−	8.83854i	−0.311131	−	0.538896i	0.667476	−	0.744631i	$-0.267375\pi$
$269$	−5.10294	−	8.83854i	−0.311131	−	0.538896i	−0.978608	+	0.205736i	$0.934041\pi$
$270$		0			0
$271$	−2.96662	+	5.13834i	−0.180209	+	0.312132i	−0.941952	−	0.335748i	$-0.891011\pi$
$271$	−2.96662	+	5.13834i	−0.180209	+	0.312132i	0.761742	+	0.647880i	$0.224344\pi$
$272$	11.4480			0.694137
$273$		0			0
$274$	2.49036			0.150448
$275$	4.06224	−	7.03600i	0.244962	−	0.424287i
$276$		0			0
$277$	−4.18766	−	7.25325i	−0.251612	−	0.435805i	0.712358	−	0.701817i	$-0.247627\pi$
$277$	−4.18766	−	7.25325i	−0.251612	−	0.435805i	−0.963970	+	0.266011i	$0.914294\pi$
$278$	4.25375	+	7.36771i	0.255123	+	0.441886i
$279$		0			0
$280$	−15.2503	+	5.67635i	−0.911381	+	0.339227i
$281$	13.9797			0.833958			0.416979	−	0.908916i	$-0.363089\pi$
$281$	13.9797			0.833958			0.416979	+	0.908916i	$0.363089\pi$
$282$		0			0
$283$	−16.8820			−1.00353			−0.501766	−	0.865003i	$-0.667316\pi$
$283$	−16.8820			−1.00353			−0.501766	+	0.865003i	$0.667316\pi$
$284$	−8.66547			−0.514201
$285$		0			0
$286$	22.7113	−	16.5185i	1.34295	−	0.976760i
$287$	−7.66016	+	2.85120i	−0.452165	+	0.168301i
$288$		0			0
$289$	−9.22019	+	15.9698i	−0.542364	+	0.939402i
$290$	13.8782	+	24.0377i	0.814954	+	1.41154i
$291$		0			0
$292$	2.24528			0.131395
$293$	−14.2012	+	24.5972i	−0.829643	+	1.43698i	0.0686755	+	0.997639i	$0.478123\pi$
$293$	−14.2012	+	24.5972i	−0.829643	+	1.43698i	−0.898319	+	0.439345i	$0.855211\pi$
$294$		0			0
$295$	−0.965598	+	1.67246i	−0.0562193	+	0.0973746i
$296$	−4.94457	+	8.56425i	−0.287398	+	0.497787i
$297$		0			0
$298$	26.7592	−	46.3483i	1.55012	−	2.68488i
$299$	16.1626	−	11.7555i	0.934708	−	0.679837i
$300$		0			0
$301$	21.8960	+	18.1038i	1.26207	+	1.04348i
$302$	17.4855	+	30.2857i	1.00618	+	1.74275i
$303$		0			0
$304$	6.87514	−	11.9081i	0.394317	−	0.682976i
$305$	0.507234	+	0.878556i	0.0290441	+	0.0503059i
$306$		0			0
$307$	23.5914			1.34643			0.673217	−	0.739445i	$-0.264912\pi$
$307$	23.5914			1.34643			0.673217	+	0.739445i	$0.264912\pi$
$308$	−29.5526	+	10.9998i	−1.68392	+	0.626773i
$309$		0			0
$310$	−16.0177	+	27.7434i	−0.909743	+	1.57572i
$311$	−3.26084	+	5.64795i	−0.184905	+	0.320266i	−0.943545	−	0.331245i	$-0.892531\pi$
$311$	−3.26084	+	5.64795i	−0.184905	+	0.320266i	0.758639	+	0.651511i	$0.225865\pi$
$312$		0			0
$313$	−7.81661	−	13.5388i	−0.441821	−	0.765256i	0.556004	−	0.831180i	$-0.312334\pi$
$313$	−7.81661	−	13.5388i	−0.441821	−	0.765256i	−0.997825	+	0.0659236i	$0.979001\pi$
$314$	−15.7502	−	27.2801i	−0.888834	−	1.53951i
$315$		0			0
$316$	26.9370	−	46.6562i	1.51532	−	2.62462i
$317$	8.89819	+	15.4121i	0.499772	+	0.865631i	1.00000		0.000262972i	$-8.37067e-5\pi$
$317$	8.89819	+	15.4121i	0.499772	+	0.865631i	−0.500228	+	0.865894i	$0.666750\pi$
$318$		0			0
$319$	12.0809	+	20.9247i	0.676401	+	1.17156i
$320$	−9.04739	−	15.6705i	−0.505764	−	0.876009i
$321$		0			0
$322$	−32.6150	+	12.1397i	−1.81756	+	0.676518i
$323$	21.2839	+	36.8647i	1.18427	+	2.05121i
$324$		0			0
$325$	7.21750	−	5.24948i	0.400355	−	0.291189i
$326$	−5.71810	+	9.90404i	−0.316696	+	0.548534i
$327$		0			0
$328$	5.97901	+	10.3559i	0.330135	+	0.571811i
$329$	21.2932	−	7.92558i	1.17393	−	0.436952i
$330$		0			0
$331$	1.64183			0.0902429			0.0451215	−	0.998982i	$-0.485633\pi$
$331$	1.64183			0.0902429			0.0451215	+	0.998982i	$0.485633\pi$
$332$	−18.5031	−	32.0483i	−1.01549	−	1.75888i
$333$		0			0
$334$	21.6432			1.18426
$335$	1.08379	+	1.87717i	0.0592135	+	0.102561i
$336$		0			0
$337$	7.89772			0.430216			0.215108	−	0.976590i	$-0.430990\pi$
$337$	7.89772			0.430216			0.215108	+	0.976590i	$0.430990\pi$
$338$	30.1684	−	6.44480i	1.64094	−	0.350551i
$339$		0			0
$340$	−34.3482			−1.86279
$341$	−13.9433	+	24.1506i	−0.755075	+	1.30783i
$342$		0			0
$343$	−8.90874	+	16.2368i	−0.481027	+	0.876706i
$344$	20.7827	−	35.9968i	1.12053	−	1.94082i
$345$		0			0
$346$	18.6052	−	32.2252i	1.00022	−	1.73244i
$347$	2.76200	+	4.78393i	0.148272	+	0.256815i	0.930589	−	0.366066i	$-0.119296\pi$
$347$	2.76200	+	4.78393i	0.148272	+	0.256815i	−0.782317	+	0.622881i	$0.785962\pi$
$348$		0			0
$349$	−4.98919	−	8.64153i	−0.267065	−	0.462570i	0.701037	−	0.713124i	$-0.252721\pi$
$349$	−4.98919	−	8.64153i	−0.267065	−	0.462570i	−0.968103	+	0.250554i	$0.919387\pi$
$350$	−14.5644	+	5.42104i	−0.778501	+	0.289767i
$351$		0			0
$352$	−5.21588	−	9.03417i	−0.278007	−	0.481523i
$353$	10.5928			0.563798			0.281899	−	0.959444i	$-0.409036\pi$
$353$	10.5928			0.563798			0.281899	+	0.959444i	$0.409036\pi$
$354$		0			0
$355$	3.79189			0.201253
$356$	30.0557			1.59295
$357$		0			0
$358$	−11.9972	+	20.7797i	−0.634070	+	1.09824i
$359$	−10.4330	−	18.0706i	−0.550635	−	0.953728i	−0.998229	−	0.0594908i	$-0.981052\pi$
$359$	−10.4330	−	18.0706i	−0.550635	−	0.953728i	0.447594	−	0.894237i	$-0.352281\pi$
$360$		0			0
$361$	32.1285			1.69097
$362$	−19.9210	+	34.5042i	−1.04702	+	1.81350i
$363$		0			0
$364$	−34.5724	−	2.14773i	−1.81209	−	0.112572i
$365$	−0.982504			−0.0514266
$366$		0			0
$367$	−9.69370			−0.506007			−0.253003	−	0.967465i	$-0.581418\pi$
$367$	−9.69370			−0.506007			−0.253003	+	0.967465i	$0.581418\pi$
$368$	5.32959	+	9.23113i	0.277824	+	0.481206i
$369$		0			0
$370$	4.81661	−	8.34261i	0.250403	−	0.433712i
$371$	−24.3800	−	20.1576i	−1.26575	−	1.04653i
$372$		0			0
$373$	−12.4318			−0.643693			−0.321847	−	0.946792i	$-0.604304\pi$
$373$	−12.4318			−0.643693			−0.321847	+	0.946792i	$0.604304\pi$
$374$	−46.3686			−2.39766
$375$		0			0
$376$	−16.6201	−	28.7868i	−0.857114	−	1.48456i
$377$	2.78787	+	26.3947i	0.143582	+	1.35940i
$378$		0			0
$379$	−13.3427	−	23.1102i	−0.685368	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$379$	−13.3427	−	23.1102i	−0.685368	−	1.18709i	0.287953	−	0.957644i	$-0.407025\pi$
$380$	−20.6279	+	35.7286i	−1.05819	+	1.83284i
$381$		0			0
$382$	22.4340	−	38.8568i	1.14782	−	1.98809i
$383$	−2.56082			−0.130852			−0.0654260	−	0.997857i	$-0.520841\pi$
$383$	−2.56082			−0.130852			−0.0654260	+	0.997857i	$0.520841\pi$
$384$		0			0
$385$	12.9318	−	4.81337i	0.659066	−	0.245312i
$386$	−9.31424	+	16.1327i	−0.474083	+	0.821135i
$387$		0			0
$388$	−6.03911			−0.306589
$389$	−10.0916	+	17.4792i	−0.511664	+	0.886228i	0.488244	+	0.872707i	$0.337637\pi$
$389$	−10.0916	+	17.4792i	−0.511664	+	0.886228i	−0.999909	+	0.0135213i	$0.995696\pi$
$390$		0			0
$391$	−32.9984			−1.66880
$392$	25.5931	+	8.89658i	1.29265	+	0.449345i
$393$		0			0
$394$	−59.5239			−2.99877
$395$	−11.7872	+	20.4161i	−0.593081	+	1.02725i
$396$		0			0
$397$	−5.70253			−0.286202			−0.143101	−	0.989708i	$-0.545707\pi$
$397$	−5.70253			−0.286202			−0.143101	+	0.989708i	$0.545707\pi$
$398$	18.4711			0.925871
$399$		0			0
$400$	2.37996	+	4.12221i	0.118998	+	0.206111i
$401$	−2.66435	+	4.61480i	−0.133051	+	0.230452i	−0.924851	−	0.380329i	$-0.875811\pi$
$401$	−2.66435	+	4.61480i	−0.133051	+	0.230452i	0.791800	+	0.610781i	$0.209144\pi$
$402$		0			0
$403$	−24.7736	+	18.0185i	−1.23406	+	0.897564i
$404$	−0.351898	−	0.609505i	−0.0175076	−	0.0303240i
$405$		0			0
$406$	7.69496	−	45.5719i	0.381894	−	2.26170i
$407$	4.19285	−	7.26222i	0.207832	−	0.359975i
$408$		0			0
$409$	10.8443	+	18.7829i	0.536216	+	0.928753i	0.999103	+	0.0423360i	$0.0134800\pi$
$409$	10.8443	+	18.7829i	0.536216	+	0.928753i	−0.462888	+	0.886417i	$0.653187\pi$
$410$	−5.82427	−	10.0879i	−0.287640	−	0.498207i
$411$		0			0
$412$	4.78874	−	8.29435i	0.235924	−	0.408633i
$413$	3.01364	−	1.12171i	0.148292	−	0.0551959i
$414$		0			0
$415$	8.09669	+	14.0239i	0.397451	+	0.688405i
$416$	−1.20365	−	11.3958i	−0.0590137	−	0.558725i
$417$		0			0
$418$	−27.8468	+	48.2321i	−1.36203	+	2.35911i
$419$	−18.0347	−	31.2369i	−0.881050	−	1.52602i	−0.850175	−	0.526501i	$-0.823504\pi$
$419$	−18.0347	−	31.2369i	−0.881050	−	1.52602i	−0.0308759	−	0.999523i	$-0.509830\pi$
$420$		0			0
$421$	17.4314			0.849552			0.424776	−	0.905298i	$-0.360353\pi$
$421$	17.4314			0.849552			0.424776	+	0.905298i	$0.360353\pi$
$422$	5.57457			0.271366
$423$		0			0
$424$	−23.1404	+	40.0804i	−1.12380	+	1.94648i
$425$	−14.7356			−0.714783
$426$		0			0
$427$	0.281244	−	1.66561i	0.0136103	−	0.0806047i
$428$	13.1313			0.634726
$429$		0			0
$430$	−20.2449	+	35.0652i	−0.976295	+	1.69099i
$431$	−0.674855			−0.0325066			−0.0162533	−	0.999868i	$-0.505174\pi$
$431$	−0.674855			−0.0325066			−0.0162533	+	0.999868i	$0.505174\pi$
$432$		0			0
$433$	9.80271	−	16.9788i	0.471088	−	0.815948i	−0.528365	−	0.849017i	$-0.677195\pi$
$433$	9.80271	−	16.9788i	0.471088	−	0.815948i	0.999453	+	0.0330689i	$0.0105281\pi$
$434$	49.9914	−	18.6074i	2.39966	−	0.893182i
$435$		0			0
$436$	1.40574			0.0673228
$437$	−19.8173	+	34.3246i	−0.947992	+	1.64197i
$438$		0			0
$439$	16.0125	−	27.7345i	0.764236	−	1.32370i	−0.176414	−	0.984316i	$-0.556450\pi$
$439$	16.0125	−	27.7345i	0.764236	−	1.32370i	0.940650	−	0.339379i	$-0.110217\pi$
$440$	−10.0937	−	17.4828i	−0.481198	−	0.833459i
$441$		0			0
$442$	−46.5424	−	20.6935i	−2.21380	−	0.984287i
$443$	−8.77986	−	15.2072i	−0.417144	−	0.722514i	0.578507	−	0.815677i	$-0.303636\pi$
$443$	−8.77986	−	15.2072i	−0.417144	−	0.722514i	−0.995651	+	0.0931630i	$0.970302\pi$
$444$		0			0
$445$	−13.1520			−0.623463
$446$	−27.4753			−1.30099
$447$		0			0
$448$	−5.01646	+	29.7090i	−0.237005	+	1.40362i
$449$	−2.82841	+	4.89895i	−0.133481	+	0.231196i	−0.925016	−	0.379928i	$-0.875949\pi$
$449$	−2.82841	+	4.89895i	−0.133481	+	0.231196i	0.791535	+	0.611123i	$0.209282\pi$
$450$		0			0
$451$	−5.07001	−	8.78152i	−0.238738	−	0.413506i
$452$	37.1258			1.74625
$453$		0			0
$454$	30.8004			1.44553
$455$	15.1284	+	0.939819i	0.709231	+	0.0440594i
$456$		0			0
$457$	2.95432	−	5.11703i	0.138197	−	0.239365i	−0.788617	−	0.614885i	$-0.789203\pi$
$457$	2.95432	−	5.11703i	0.138197	−	0.239365i	0.926814	+	0.375520i	$0.122536\pi$
$458$	45.7064			2.13572
$459$		0			0
$460$	−15.9907	−	27.6968i	−0.745571	−	1.29137i
$461$	−19.0332	+	32.9664i	−0.886463	+	1.53540i	−0.0424358	+	0.999099i	$0.513512\pi$
$461$	−19.0332	+	32.9664i	−0.886463	+	1.53540i	−0.844027	+	0.536300i	$0.819822\pi$
$462$		0			0
$463$	−35.4984			−1.64975			−0.824876	−	0.565314i	$-0.808755\pi$
$463$	−35.4984			−1.64975			−0.824876	+	0.565314i	$0.808755\pi$
$464$	−14.1558			−0.657167
$465$		0			0
$466$	−29.6736			−1.37460
$467$	−0.127466	−	0.220777i	−0.00589842	−	0.0102164i	0.863061	−	0.505099i	$-0.168544\pi$
$467$	−0.127466	−	0.220777i	−0.00589842	−	0.0102164i	−0.868960	+	0.494883i	$0.835211\pi$
$468$		0			0
$469$	0.600921	−	3.55884i	0.0277480	−	0.164332i
$470$	16.1899	+	28.0418i	0.746786	+	1.29347i
$471$		0			0
$472$	−2.35225	−	4.07421i	−0.108271	−	0.187531i
$473$	−17.6231	+	30.5241i	−0.810312	+	1.40350i
$474$		0			0
$475$	−8.84954	+	15.3279i	−0.406045	+	0.703290i
$476$	44.0781	+	36.4441i	2.02032	+	1.67041i
$477$		0			0
$478$	−35.2903	+	61.1246i	−1.61414	+	2.79577i
$479$	15.1983			0.694426			0.347213	−	0.937786i	$-0.387128\pi$
$479$	15.1983			0.694426			0.347213	+	0.937786i	$0.387128\pi$
$480$		0			0
$481$	7.44956	−	5.41826i	0.339671	−	0.247051i
$482$	−38.3192			−1.74539
$483$		0			0
$484$	0.411483	+	0.712709i	0.0187038	+	0.0323959i
$485$	2.64263			0.119996
$486$		0			0
$487$	−0.114540	−	0.198389i	−0.00519030	−	0.00898986i	0.863419	−	0.504488i	$-0.168319\pi$
$487$	−0.114540	−	0.198389i	−0.00519030	−	0.00898986i	−0.868609	+	0.495498i	$0.834985\pi$
$488$	−2.47130			−0.111870
$489$		0			0
$490$	−24.9307	−	8.66634i	−1.12625	−	0.391505i
$491$	7.19778	+	12.4669i	0.324831	+	0.562624i	0.981478	−	0.191574i	$-0.0613591\pi$
$491$	7.19778	+	12.4669i	0.324831	+	0.562624i	−0.656647	+	0.754198i	$0.728026\pi$
$492$		0			0
$493$	21.9116	−	37.9519i	0.986847	−	1.70927i
$494$	−49.4764	+	35.9854i	−2.22605	+	1.61906i
$495$		0			0
$496$	−8.16906	−	14.1492i	−0.366801	−	0.635319i
$497$	−4.86604	−	4.02327i	−0.218272	−	0.180468i
$498$		0			0
$499$	−6.68657	−	11.5815i	−0.299332	−	0.518458i	0.676651	−	0.736304i	$-0.263430\pi$
$499$	−6.68657	−	11.5815i	−0.299332	−	0.518458i	−0.975983	+	0.217845i	$0.930097\pi$
$500$	−21.5650	−	37.3517i	−0.964418	−	1.67042i
$501$		0			0
$502$	23.2574	+	40.2830i	1.03803	+	1.79792i
$503$	5.78251	−	10.0156i	0.257829	−	0.446574i	−0.707831	−	0.706382i	$-0.750326\pi$
$503$	5.78251	−	10.0156i	0.257829	−	0.446574i	0.965660	+	0.259808i	$0.0836594\pi$
$504$		0			0
$505$	0.153986	+	0.266711i	0.00685227	+	0.0118685i
$506$	−21.5868	−	37.3894i	−0.959650	−	1.66216i
$507$		0			0
$508$	10.7452	−	18.6112i	0.476740	−	0.825739i
$509$	14.7718	−	25.5855i	0.654748	−	1.13406i	−0.327209	−	0.944952i	$-0.606108\pi$
$509$	14.7718	−	25.5855i	0.654748	−	1.13406i	0.981957	−	0.189104i	$-0.0605584\pi$
$510$		0			0
$511$	1.26082	+	1.04246i	0.0557755	+	0.0461155i
$512$	20.9987			0.928019
$513$		0			0
$514$	7.09413	+	12.2874i	0.312909	+	0.541974i
$515$	−2.09549	+	3.62949i	−0.0923382	+	0.159935i
$516$		0			0
$517$	14.0933	+	24.4103i	0.619822	+	1.07356i
$518$	−15.0327	+	5.59534i	−0.660499	+	0.245845i
$519$		0			0
$520$	−2.32928	−	22.0530i	−0.102146	−	0.967087i
$521$	8.38685	−	14.5265i	0.367435	−	0.636416i	−0.621729	−	0.783233i	$-0.713569\pi$
$521$	8.38685	−	14.5265i	0.367435	−	0.636416i	0.989164	+	0.146817i	$0.0469028\pi$
$522$		0			0
$523$	20.1394	−	34.8824i	0.880633	−	1.52530i	0.0299941	−	0.999550i	$-0.490451\pi$
$523$	20.1394	−	34.8824i	0.880633	−	1.52530i	0.850639	−	0.525751i	$-0.176216\pi$
$524$	−2.26534	+	3.92369i	−0.0989619	+	0.171407i
$525$		0			0
$526$	−17.7883	+	30.8103i	−0.775609	+	1.34339i
$527$	50.5790			2.20326
$528$		0			0
$529$	−3.86235	−	6.68978i	−0.167928	−	0.290860i
$530$	22.5416	−	39.0431i	0.979142	−	1.69592i
$531$		0			0
$532$	64.3801	−	23.9630i	2.79123	−	1.03893i
$533$	−1.16999	−	11.0771i	−0.0506778	−	0.479802i
$534$		0			0
$535$	−5.74608			−0.248425
$536$	−5.28032			−0.228075
$537$		0			0
$538$	−24.2186			−1.04414
$539$	−21.7021	−	7.54403i	−0.934777	−	0.324944i
$540$		0			0
$541$	2.65491	+	4.59844i	0.114144	+	0.197702i	0.917437	−	0.397881i	$-0.130254\pi$
$541$	2.65491	+	4.59844i	0.114144	+	0.197702i	−0.803294	+	0.595583i	$0.796921\pi$
$542$	7.03981	+	12.1933i	0.302386	+	0.523747i
$543$		0			0
$544$	−9.46022	+	16.3856i	−0.405603	+	0.702526i
$545$	−0.615133			−0.0263494
$546$		0			0
$547$	28.9584			1.23817			0.619085	−	0.785324i	$-0.287504\pi$
$547$	28.9584			1.23817			0.619085	+	0.785324i	$0.287504\pi$
$548$	1.90536	−	3.30019i	0.0813931	−	0.140977i
$549$		0			0
$550$	−9.63971	−	16.6965i	−0.411039	−	0.711940i
$551$	−26.3182	−	45.5844i	−1.12119	−	1.94196i
$552$		0			0
$553$	36.7881	−	13.6930i	1.56439	−	0.582284i
$554$	−19.8747			−0.844395
$555$		0			0
$556$	13.0181			0.552092
$557$	11.5392			0.488931			0.244466	−	0.969658i	$-0.421387\pi$
$557$	11.5392			0.488931			0.244466	+	0.969658i	$0.421387\pi$
$558$		0			0
$559$	−31.3116	+	22.7737i	−1.32434	+	0.963225i
$560$	−1.34599	+	7.97139i	−0.0568785	+	0.336853i
$561$		0			0
$562$	16.5869	−	28.7294i	0.699678	−	1.21188i
$563$	−11.9812	−	20.7521i	−0.504949	−	0.874597i	−0.999984	−	0.00572413i	$-0.998178\pi$
$563$	−11.9812	−	20.7521i	−0.504949	−	0.874597i	0.495035	−	0.868873i	$-0.335155\pi$
$564$		0			0
$565$	−16.2457			−0.683463
$566$	−20.0306	+	34.6940i	−0.841948	+	1.45830i
$567$		0			0
$568$	−4.61862	+	7.99969i	−0.193793	+	0.335659i
$569$	−0.316091	+	0.547485i	−0.0132512	+	0.0229518i	−0.872575	−	0.488480i	$-0.837551\pi$
$569$	−0.316091	+	0.547485i	−0.0132512	+	0.0229518i	0.859324	+	0.511432i	$0.170885\pi$
$570$		0			0
$571$	−1.82039	+	3.15301i	−0.0761810	+	0.131949i	−0.901599	−	0.432572i	$-0.857606\pi$
$571$	−1.82039	+	3.15301i	−0.0761810	+	0.131949i	0.825418	+	0.564522i	$0.190939\pi$
$572$	−4.51376	−	42.7350i	−0.188730	−	1.78684i
$573$		0			0
$574$	−3.22935	+	19.1252i	−0.134791	+	0.798272i
$575$	−6.86014	−	11.8821i	−0.286088	−	0.495519i
$576$		0			0
$577$	2.63632	−	4.56623i	0.109751	−	0.190095i	−0.805918	−	0.592027i	$-0.798328\pi$
$577$	2.63632	−	4.56623i	0.109751	−	0.190095i	0.915669	+	0.401932i	$0.131661\pi$
$578$	21.8796	+	37.8965i	0.910070	+	1.57629i
$579$		0			0
$580$	42.4726			1.76358
$581$	4.48933	−	26.5872i	0.186249	−	1.10302i
$582$		0			0
$583$	19.6224	−	33.9869i	0.812676	−	1.40760i
$584$	1.19672	−	2.07277i	0.0495205	−	0.0857720i
$585$		0			0
$586$	33.6995	+	58.3693i	1.39212	+	2.41121i
$587$	1.40954	+	2.44139i	0.0581779	+	0.100767i	0.893648	−	0.448770i	$-0.148138\pi$
$587$	1.40954	+	2.44139i	0.0581779	+	0.100767i	−0.835470	+	0.549537i	$0.814804\pi$
$588$		0			0
$589$	30.3755	−	52.6118i	1.25160	−	2.16783i
$590$	2.29137	+	3.96877i	0.0943342	+	0.163392i
$591$		0			0
$592$	2.45648	+	4.25475i	0.100961	+	0.174869i
$593$	−7.65704	−	13.2624i	−0.314437	−	0.544621i	0.664881	−	0.746949i	$-0.268482\pi$
$593$	−7.65704	−	13.2624i	−0.314437	−	0.544621i	−0.979318	+	0.202329i	$0.935149\pi$
$594$		0			0
$595$	−19.2880	−	15.9474i	−0.790730	−	0.653780i
$596$	−40.9467	−	70.9218i	−1.67724	−	2.90507i
$597$		0			0
$598$	−4.98151	−	47.1634i	−0.203709	−	1.92866i
$599$	4.16303	−	7.21058i	0.170097	−	0.294616i	−0.768357	−	0.640022i	$-0.778925\pi$
$599$	4.16303	−	7.21058i	0.170097	−	0.294616i	0.938453	+	0.345406i	$0.112259\pi$
$600$		0			0
$601$	−8.31185	−	14.3965i	−0.339047	−	0.587247i	0.645207	−	0.764008i	$-0.276771\pi$
$601$	−8.31185	−	14.3965i	−0.339047	−	0.587247i	−0.984254	+	0.176761i	$0.943438\pi$
$602$	63.1845	−	23.5180i	2.57521	−	0.958522i
$603$		0			0
$604$	53.5123			2.17739
$605$	−0.180059	−	0.311872i	−0.00732045	−	0.0126794i
$606$		0			0
$607$	−34.7311			−1.40969			−0.704846	−	0.709360i	$-0.748984\pi$
$607$	−34.7311			−1.40969			−0.704846	+	0.709360i	$0.748984\pi$
$608$	11.3627	+	19.6809i	0.460820	+	0.798164i
$609$		0			0
$610$	2.40734			0.0974704
$611$	3.25226	+	30.7914i	0.131572	+	1.24569i
$612$		0			0
$613$	2.25257			0.0909804			0.0454902	−	0.998965i	$-0.485515\pi$
$613$	2.25257			0.0909804			0.0454902	+	0.998965i	$0.485515\pi$
$614$	27.9913	−	48.4823i	1.12964	−	1.95659i
$615$		0			0
$616$	−5.59660	+	33.1448i	−0.225493	+	1.33544i
$617$	13.5484	−	23.4666i	0.545439	−	0.944729i	−0.453140	−	0.891440i	$-0.649696\pi$
$617$	13.5484	−	23.4666i	0.545439	−	0.944729i	0.998579	−	0.0532893i	$-0.0169706\pi$
$618$		0			0
$619$	16.6208	−	28.7880i	0.668045	−	1.15709i	−0.310405	−	0.950604i	$-0.600465\pi$
$619$	16.6208	−	28.7880i	0.668045	−	1.15709i	0.978450	−	0.206484i	$-0.0662020\pi$
$620$	24.5101	+	42.4528i	0.984351	+	1.70495i
$621$		0			0
$622$	7.73800	+	13.4026i	0.310266	+	0.537396i
$623$	16.8776	+	13.9545i	0.676186	+	0.559075i
$624$		0			0
$625$	3.24843	+	5.62645i	0.129937	+	0.225058i
$626$	−37.0977			−1.48272
$627$		0			0
$628$	−48.2016			−1.92345
$629$	−15.2094			−0.606439
$630$		0			0
$631$	−20.6922	+	35.8399i	−0.823743	+	1.42677i	0.0791326	+	0.996864i	$0.474785\pi$
$631$	−20.6922	+	35.8399i	−0.823743	+	1.42677i	−0.902876	+	0.429901i	$0.858548\pi$
$632$	−28.7143	−	49.7347i	−1.14220	−	1.97834i
$633$		0			0
$634$	42.2309			1.67720
$635$	−4.70194	+	8.14401i	−0.186591	+	0.323185i
$636$		0			0
$637$	−18.4167	−	17.2576i	−0.729697	−	0.683770i
$638$	57.3362			2.26996
$639$		0			0
$640$	−32.8390			−1.29808
$641$	−23.0317	−	39.8920i	−0.909695	−	1.57564i	−0.814487	−	0.580181i	$-0.802982\pi$
$641$	−23.0317	−	39.8920i	−0.909695	−	1.57564i	−0.0952082	−	0.995457i	$-0.530352\pi$
$642$		0			0
$643$	−16.6181	+	28.7834i	−0.655353	+	1.13510i	0.326452	+	0.945214i	$0.394147\pi$
$643$	−16.6181	+	28.7834i	−0.655353	+	1.13510i	−0.981805	+	0.189891i	$0.939187\pi$
$644$	−8.86630	+	52.5090i	−0.349381	+	2.06914i
$645$		0			0
$646$	101.014			3.97432
$647$	5.97709			0.234984			0.117492	−	0.993074i	$-0.462515\pi$
$647$	5.97709			0.234984			0.117492	+	0.993074i	$0.462515\pi$
$648$		0			0
$649$	1.99463	+	3.45480i	0.0782962	+	0.135613i
$650$	−2.22452	−	21.0611i	−0.0872529	−	0.826084i
$651$		0			0
$652$	8.74980	+	15.1551i	0.342669	+	0.593520i
$653$	11.9276	−	20.6592i	0.466764	−	0.808458i	−0.532516	−	0.846420i	$-0.678753\pi$
$653$	11.9276	−	20.6592i	0.466764	−	0.808458i	0.999279	+	0.0379620i	$0.0120866\pi$
$654$		0			0
$655$	0.991282	−	1.71695i	0.0387326	−	0.0670868i
$656$	5.94078			0.231949
$657$		0			0
$658$	8.97675	−	53.1631i	0.349950	−	2.07251i
$659$	13.1153	−	22.7163i	0.510899	−	0.884902i	−0.489022	−	0.872272i	$-0.662646\pi$
$659$	13.1153	−	22.7163i	0.510899	−	0.884902i	0.999920	−	0.0126308i	$-0.00402061\pi$
$660$		0			0
$661$	−16.6208			−0.646474			−0.323237	−	0.946318i	$-0.604771\pi$
$661$	−16.6208			−0.646474			−0.323237	+	0.946318i	$0.604771\pi$
$662$	1.94803	−	3.37409i	0.0757124	−	0.131138i
$663$		0			0
$664$	−39.4479			−1.53088
$665$	−28.1718	+	10.4859i	−1.09246	+	0.406625i
$666$		0			0
$667$	40.8035			1.57992
$668$	16.5591	−	28.6813i	0.640692	−	1.10971i
$669$		0			0
$670$	5.14366			0.198717
$671$	2.09558			0.0808991
$672$		0			0
$673$	21.2726	+	36.8451i	0.819997	+	1.42028i	0.905684	+	0.423954i	$0.139358\pi$
$673$	21.2726	+	36.8451i	0.819997	+	1.42028i	−0.0856874	+	0.996322i	$0.527309\pi$
$674$	9.37068	−	16.2305i	0.360945	−	0.625175i
$675$		0			0
$676$	14.5412	−	44.9096i	0.559276	−	1.72729i
$677$	5.90158	+	10.2218i	0.226816	+	0.392857i	0.956863	−	0.290540i	$-0.0938350\pi$
$677$	5.90158	+	10.2218i	0.226816	+	0.392857i	−0.730047	+	0.683397i	$0.760502\pi$
$678$		0			0
$679$	−3.39122	−	2.80388i	−0.130143	−	0.107603i
$680$	−18.3073	+	31.7091i	−0.702052	+	1.21599i
$681$		0			0
$682$	33.0877	+	57.3095i	1.26699	+	2.19449i
$683$	10.3451	+	17.9182i	0.395843	+	0.685619i	0.993208	−	0.116349i	$-0.0371193\pi$
$683$	10.3451	+	17.9182i	0.395843	+	0.685619i	−0.597366	+	0.801969i	$0.703786\pi$
$684$		0			0
$685$	−0.833761	+	1.44412i	−0.0318564	+	0.0551768i
$686$	22.7978	+	37.5732i	0.870424	+	1.43455i
$687$		0			0
$688$	−10.3249	−	17.8833i	−0.393635	−	0.681795i
$689$	34.8637	−	25.3573i	1.32820	−	0.966035i
$690$		0			0
$691$	−6.21052	+	10.7569i	−0.236259	+	0.409213i	−0.959638	−	0.281238i	$-0.909255\pi$
$691$	−6.21052	+	10.7569i	−0.236259	+	0.409213i	0.723379	+	0.690452i	$0.242588\pi$
$692$	−28.4696	−	49.3108i	−1.08225	−	1.87452i
$693$		0			0
$694$	13.1085			0.497592
$695$	−5.69655			−0.216083
$696$		0			0
$697$	−9.19565	+	15.9273i	−0.348310	+	0.603291i
$698$	−23.6788			−0.896254
$699$		0			0
$700$	−3.95930	+	23.4482i	−0.149647	+	0.886258i
$701$	−35.6900			−1.34799			−0.673996	−	0.738735i	$-0.735423\pi$
$701$	−35.6900			−1.34799			−0.673996	+	0.738735i	$0.735423\pi$
$702$		0			0
$703$	−9.13408	+	15.8207i	−0.344498	+	0.596688i
$704$	−37.3783			−1.40875
$705$		0			0
$706$	12.5684	−	21.7691i	0.473018	−	0.819291i
$707$	0.0853796	−	0.505645i	0.00321103	−	0.0190167i
$708$		0			0
$709$	−31.0123			−1.16469			−0.582346	−	0.812941i	$-0.697865\pi$
$709$	−31.0123			−1.16469			−0.582346	+	0.812941i	$0.697865\pi$
$710$	4.49909	−	7.79265i	0.168848	−	0.292453i
$711$		0			0
$712$	16.0195	−	27.7465i	0.600354	−	1.03984i
$713$	23.5470	+	40.7846i	0.881841	+	1.52739i
$714$		0			0
$715$	1.97516	+	18.7002i	0.0738668	+	0.699349i
$716$	18.3580	+	31.7970i	0.686070	+	1.18831i
$717$		0			0
$718$	−49.5154			−1.84790
$719$	−27.1417			−1.01222			−0.506108	−	0.862470i	$-0.668916\pi$
$719$	−27.1417			−1.01222			−0.506108	+	0.862470i	$0.668916\pi$
$720$		0			0
$721$	6.54005	−	2.43428i	0.243564	−	0.0906573i
$722$	38.1205	−	66.0267i	1.41870	−	2.45726i
$723$		0			0
$724$	30.4830	+	52.7981i	1.13289	+	1.96222i
$725$	18.2211			0.676713
$726$		0			0
$727$	−21.0336			−0.780095			−0.390047	−	0.920795i	$-0.627541\pi$
$727$	−21.0336			−0.780095			−0.390047	+	0.920795i	$0.627541\pi$
$728$	−20.4095	+	30.7714i	−0.756427	+	1.14047i
$729$		0			0
$730$	−1.16574	+	2.01913i	−0.0431461	+	0.0747313i
$731$	63.9273			2.36444
$732$		0			0
$733$	4.49198	+	7.78034i	0.165915	+	0.287373i	0.936980	−	0.349383i	$-0.113609\pi$
$733$	4.49198	+	7.78034i	0.165915	+	0.287373i	−0.771065	+	0.636757i	$0.780276\pi$
$734$	−11.5016	+	19.9214i	−0.424532	+	0.735311i
$735$		0			0
$736$	−17.6167			−0.649362
$737$	4.47754			0.164932
$738$		0			0
$739$	11.9334			0.438979			0.219489	−	0.975615i	$-0.429561\pi$
$739$	11.9334			0.438979			0.219489	+	0.975615i	$0.429561\pi$
$740$	−7.37034	−	12.7658i	−0.270939	−	0.469280i
$741$		0			0
$742$	−70.3525	+	26.1860i	−2.58272	+	0.961318i
$743$	7.76713	+	13.4531i	0.284948	+	0.493545i	0.972597	−	0.232499i	$-0.0746902\pi$
$743$	7.76713	+	13.4531i	0.284948	+	0.493545i	−0.687648	+	0.726044i	$0.741357\pi$
$744$		0			0
$745$	17.9177	+	31.0344i	0.656455	+	1.13701i
$746$	−14.7504	+	25.5484i	−0.540049	+	0.935392i
$747$		0			0
$748$	−35.4765	+	61.4470i	−1.29715	+	2.24673i
$749$	7.37380	+	6.09670i	0.269433	+	0.222769i
$750$		0			0
$751$	18.3109	−	31.7153i	0.668173	−	1.15731i	−0.310242	−	0.950658i	$-0.600410\pi$
$751$	18.3109	−	31.7153i	0.668173	−	1.15731i	0.978415	−	0.206652i	$-0.0662567\pi$
$752$	−16.5138			−0.602197
$753$		0			0
$754$	57.5511	+	25.5881i	2.09589	+	0.931863i
$755$	−23.4163			−0.852205
$756$		0			0
$757$	−9.66722	−	16.7441i	−0.351361	−	0.608575i	0.635127	−	0.772408i	$-0.280948\pi$
$757$	−9.66722	−	16.7441i	−0.351361	−	0.608575i	−0.986488	+	0.163832i	$0.947614\pi$
$758$	−63.3246			−2.30005
$759$		0			0
$760$	21.9890	+	38.0861i	0.797626	+	1.38153i
$761$	22.0990			0.801087			0.400543	−	0.916278i	$-0.368821\pi$
$761$	22.0990			0.801087			0.400543	+	0.916278i	$0.368821\pi$
$762$		0			0
$763$	0.789385	+	0.652668i	0.0285776	+	0.0236282i
$764$	−34.3283	−	59.4584i	−1.24196	−	2.15113i
$765$		0			0
$766$	−3.03843	+	5.26271i	−0.109783	+	0.190149i
$767$	0.460294	+	4.35793i	0.0166202	+	0.157356i
$768$		0			0
$769$	−8.04717	−	13.9381i	−0.290188	−	0.502621i	0.683666	−	0.729795i	$-0.260385\pi$
$769$	−8.04717	−	13.9381i	−0.290188	−	0.502621i	−0.973854	+	0.227174i	$0.927051\pi$
$770$	5.45176	−	32.2870i	0.196468	−	1.16354i
$771$		0			0
$772$	14.2526	+	24.6862i	0.512962	+	0.888477i
$773$	11.9883	+	20.7643i	0.431188	+	0.746839i	0.996976	−	0.0777116i	$-0.0247613\pi$
$773$	11.9883	+	20.7643i	0.431188	+	0.746839i	−0.565788	+	0.824551i	$0.691428\pi$
$774$		0			0
$775$	10.5150	+	18.2126i	0.377711	+	0.654215i
$776$	−3.21879	+	5.57511i	−0.115548	+	0.200135i
$777$		0			0
$778$	23.9474	+	41.4781i	0.858557	+	1.48706i
$779$	11.0450	+	19.1305i	0.395727	+	0.685420i
$780$		0			0
$781$	3.91645	−	6.78349i	0.140142	−	0.242732i
$782$	−39.1527	+	67.8145i	−1.40010	+	2.42504i
$783$		0			0
$784$	10.1851	−	8.80135i	0.363753	−	0.314334i
$785$	21.0924			0.752819
$786$		0			0
$787$	19.2452	+	33.3337i	0.686019	+	1.18822i	0.973115	+	0.230318i	$0.0739766\pi$
$787$	19.2452	+	33.3337i	0.686019	+	1.18822i	−0.287097	+	0.957902i	$0.592690\pi$
$788$	−45.5416	+	78.8803i	−1.62235	+	2.81000i
$789$		0			0
$790$	27.9712	+	48.4476i	0.995171	+	1.72369i
$791$	20.8477	+	17.2370i	0.741260	+	0.612878i
$792$		0			0
$793$	2.10344	+	0.935222i	0.0746954	+	0.0332107i
$794$	−6.76607	+	11.7192i	−0.240119	+	0.415898i
$795$		0			0
$796$	14.1322	−	24.4776i	0.500901	−	0.867586i
$797$	22.8007	−	39.4919i	0.807641	−	1.39888i	−0.106853	−	0.994275i	$-0.534077\pi$
$797$	22.8007	−	39.4919i	0.807641	−	1.39888i	0.914494	−	0.404600i	$-0.132589\pi$
$798$		0			0
$799$	25.5615	−	44.2738i	0.904300	−	1.56629i
$800$	−7.86686			−0.278136
$801$		0			0
$802$	6.32253	+	10.9509i	0.223256	+	0.386691i
$803$	−1.01478	+	1.75765i	−0.0358107	+	0.0620260i
$804$		0			0
$805$	3.87977	−	22.9772i	0.136744	−	0.809840i
$806$	7.63551	+	72.2908i	0.268950	+	2.54633i
$807$		0			0
$808$	−0.750234			−0.0263931
$809$	−24.9225			−0.876228			−0.438114	−	0.898919i	$-0.644353\pi$
$809$	−24.9225			−0.876228			−0.438114	+	0.898919i	$0.644353\pi$
$810$		0			0
$811$	−23.7418			−0.833689			−0.416844	−	0.908978i	$-0.636864\pi$
$811$	−23.7418			−0.833689			−0.416844	+	0.908978i	$0.636864\pi$
$812$	−54.5039	−	45.0642i	−1.91271	−	1.58144i
$813$		0			0
$814$	−9.94965	−	17.2333i	−0.348735	−	0.604027i
$815$	−3.82879	−	6.63166i	−0.134117	−	0.232297i
$816$		0			0
$817$	38.3918	−	66.4966i	1.34316	−	2.32642i
$818$	51.4672			1.79951
$819$		0			0
$820$	−17.8245			−0.622459
$821$	14.4778	−	25.0762i	0.505278	−	0.875166i	−0.494704	−	0.869062i	$-0.664723\pi$
$821$	14.4778	−	25.0762i	0.505278	−	0.875166i	0.999981	−	0.00610476i	$-0.00194322\pi$
$822$		0			0
$823$	−18.6438	−	32.2919i	−0.649880	−	1.12563i	−0.983151	−	0.182795i	$-0.941486\pi$
$823$	−18.6438	−	32.2919i	−0.649880	−	1.12563i	0.333271	−	0.942831i	$-0.391848\pi$
$824$	−5.10472	−	8.84163i	−0.177831	−	0.308013i
$825$		0			0
$826$	1.27048	−	7.52421i	0.0442058	−	0.261801i
$827$	20.7885			0.722888			0.361444	−	0.932394i	$-0.382284\pi$
$827$	20.7885			0.722888			0.361444	+	0.932394i	$0.382284\pi$
$828$		0			0
$829$	−55.8295			−1.93904			−0.969520	−	0.245014i	$-0.921208\pi$
$829$	−55.8295			−1.93904			−0.969520	+	0.245014i	$0.921208\pi$
$830$	38.4270			1.33382
$831$		0			0
$832$	−37.5185	−	16.6813i	−1.30072	−	0.578319i
$833$	7.83124	+	40.9298i	0.271336	+	1.41813i
$834$		0			0
$835$	−7.24605	+	12.5505i	−0.250760	+	0.434329i
$836$	42.6111	+	73.8045i	1.47373	+	2.55258i
$837$		0			0
$838$	−85.5927			−2.95675
$839$	11.2275	−	19.4465i	0.387615	−	0.671369i	−0.604513	−	0.796595i	$-0.706632\pi$
$839$	11.2275	−	19.4465i	0.387615	−	0.671369i	0.992128	+	0.125226i	$0.0399656\pi$
$840$		0			0
$841$	−12.5943	+	21.8140i	−0.434287	+	0.752206i
$842$	20.6824	−	35.8229i	0.712761	−	1.23454i
$843$		0			0
$844$	4.26509	−	7.38735i	0.146810	−	0.254283i
$845$	−6.36301	+	19.6518i	−0.218894	+	0.676044i
$846$		0			0
$847$	−0.0998365	+	0.591263i	−0.00343042	+	0.0203160i
$848$	11.4963	+	19.9121i	0.394783	+	0.683784i
$849$		0			0
$850$	−17.4839	+	30.2830i	−0.599692	+	1.03870i
$851$	−7.08071	−	12.2642i	−0.242724	−	0.420410i
$852$		0			0
$853$	10.8150			0.370298			0.185149	−	0.982710i	$-0.440723\pi$
$853$	10.8150			0.370298			0.185149	+	0.982710i	$0.440723\pi$
$854$	−3.08928	−	2.55423i	−0.105713	−	0.0874041i
$855$		0			0
$856$	6.99888	−	12.1224i	0.239217	−	0.414335i
$857$	−17.7262	+	30.7026i	−0.605514	+	1.04878i	0.386456	+	0.922308i	$0.373699\pi$
$857$	−17.7262	+	30.7026i	−0.605514	+	1.04878i	−0.991970	+	0.126474i	$0.959634\pi$
$858$		0			0
$859$	−24.0734	−	41.6963i	−0.821373	−	1.42266i	−0.904660	−	0.426134i	$-0.859875\pi$
$859$	−24.0734	−	41.6963i	−0.821373	−	1.42266i	0.0832873	−	0.996526i	$-0.473458\pi$
$860$	30.9786	+	53.6565i	1.05636	+	1.82967i
$861$		0			0
$862$	−0.800718	+	1.38688i	−0.0272726	+	0.0472375i
$863$	−2.06142	−	3.57048i	−0.0701714	−	0.121540i	0.828805	−	0.559538i	$-0.189021\pi$
$863$	−2.06142	−	3.57048i	−0.0701714	−	0.121540i	−0.898976	+	0.437997i	$0.855688\pi$
$864$		0			0
$865$	12.4579	+	21.5777i	0.423582	+	0.733665i
$866$	−23.2619	−	40.2908i	−0.790471	−	1.36914i
$867$		0			0
$868$	13.5900	−	80.4843i	0.461275	−	2.73182i
$869$	24.3489	+	42.1735i	0.825979	+	1.43064i
$870$		0			0
$871$	4.49433	+	1.99825i	0.152285	+	0.0677080i
$872$	0.749248	−	1.29774i	0.0253728	−	0.0439469i
$873$		0			0
$874$	47.0267	+	81.4526i	1.59070	+	2.75517i
$875$	5.23224	−	30.9870i	0.176882	−	1.04755i
$876$		0			0
$877$	28.9796			0.978572			0.489286	−	0.872124i	$-0.337258\pi$
$877$	28.9796			0.978572			0.489286	+	0.872124i	$0.337258\pi$
$878$	−37.9978	−	65.8142i	−1.28236	−	2.22112i
$879$		0			0
$880$	−10.0292			−0.338083
$881$	7.56041	+	13.0950i	0.254717	+	0.441182i	0.964819	−	0.262917i	$-0.0846845\pi$
$881$	7.56041	+	13.0950i	0.254717	+	0.441182i	−0.710102	+	0.704099i	$0.751351\pi$
$882$		0			0
$883$	−31.9151			−1.07403			−0.537014	−	0.843573i	$-0.680448\pi$
$883$	−31.9151			−1.07403			−0.537014	+	0.843573i	$0.680448\pi$
$884$	−63.0322	+	45.8449i	−2.12000	+	1.54193i
$885$		0			0
$886$	−41.6693			−1.39991
$887$	−24.3422	+	42.1619i	−0.817330	+	1.41566i	0.0903126	+	0.995913i	$0.471213\pi$
$887$	−24.3422	+	42.1619i	−0.817330	+	1.41566i	−0.907643	+	0.419744i	$0.862120\pi$
$888$		0			0
$889$	14.6748	−	5.46214i	0.492178	−	0.183194i
$890$	−15.6049	+	27.0284i	−0.523076	+	0.905995i
$891$		0			0
$892$	−21.0213	+	36.4099i	−0.703844	+	1.21909i
$893$	−30.7021	−	53.1776i	−1.02741	−	1.77952i
$894$		0			0
$895$	−8.03320	−	13.9139i	−0.268520	−	0.465091i
$896$	42.1415	+	34.8428i	1.40785	+	1.16402i
$897$		0			0
$898$	6.71183	+	11.6252i	0.223977	+	0.387939i
$899$	−62.5425			−2.08591
$900$		0			0
$901$	−71.1795			−2.37133
$902$	−24.0623			−0.801189
$903$		0			0
$904$	19.7877	−	34.2733i	0.658130	−	1.13991i
$905$	−13.3389	−	23.1037i	−0.443401	−	0.767993i
$906$		0			0
$907$	−41.4369			−1.37589			−0.687945	−	0.725763i	$-0.741487\pi$
$907$	−41.4369			−1.37589			−0.687945	+	0.725763i	$0.741487\pi$
$908$	23.5653	−	40.8163i	0.782042	−	1.35454i
$909$		0			0
$910$	19.8813	−	29.9751i	0.659059	−	0.993663i
$911$	55.6403			1.84344			0.921722	−	0.387851i	$-0.126782\pi$
$911$	55.6403			1.84344			0.921722	+	0.387851i	$0.126782\pi$
$912$		0			0
$913$	33.4506			1.10705
$914$	−7.01062	−	12.1427i	−0.231891	−	0.401646i
$915$		0			0
$916$	34.9698	−	60.5695i	1.15544	−	2.00127i
$917$	−3.09381	+	1.15155i	−0.102166	+	0.0380275i
$918$		0			0
$919$	2.31981			0.0765233			0.0382617	−	0.999268i	$-0.487818\pi$
$919$	2.31981			0.0765233			0.0382617	+	0.999268i	$0.487818\pi$
$920$	−34.0917			−1.12397
$921$		0			0
$922$	45.1658	+	78.2295i	1.48746	+	2.57635i
$923$	6.95848	−	5.06108i	0.229041	−	0.166588i
$924$		0			0
$925$	−3.16193	−	5.47663i	−0.103964	−	0.180070i
$926$	−42.1190	+	72.9523i	−1.38412	+	2.39736i
$927$		0			0
$928$	11.6978	−	20.2613i	0.384001	−	0.665109i
$929$	−45.2481			−1.48454			−0.742270	−	0.670101i	$-0.766251\pi$
$929$	−45.2481			−1.48454			−0.742270	+	0.670101i	$0.766251\pi$
$930$		0			0
$931$	47.2779	+	16.4346i	1.54947	+	0.538622i
$932$	−22.7032	+	39.3231i	−0.743668	+	1.28807i
$933$		0			0
$934$	−0.604955			−0.0197947
$935$	15.5240	−	26.8884i	0.507689	−	0.879343i
$936$		0			0
$937$	23.7899			0.777181			0.388590	−	0.921411i	$-0.372962\pi$
$937$	23.7899			0.777181			0.388590	+	0.921411i	$0.372962\pi$
$938$	−6.60073	−	5.45752i	−0.215521	−	0.178194i
$939$		0			0
$940$	49.5475			1.61606
$941$	15.7112	−	27.2127i	0.512172	−	0.887107i	−0.487729	−	0.872995i	$-0.662175\pi$
$941$	15.7112	−	27.2127i	0.512172	−	0.887107i	0.999900	−	0.0141120i	$-0.00449213\pi$
$942$		0			0
$943$	−17.1241			−0.557637
$944$	−2.33721			−0.0760697
$945$		0			0
$946$	41.8198	+	72.4340i	1.35968	+	2.35503i
$947$	8.88848	−	15.3953i	0.288837	−	0.500280i	−0.684695	−	0.728829i	$-0.740065\pi$
$947$	8.88848	−	15.3953i	0.288837	−	0.500280i	0.973532	+	0.228549i	$0.0733981\pi$
$948$		0			0
$949$	−1.80299	+	1.31136i	−0.0585275	+	0.0425685i
$950$	21.0000	+	36.3731i	0.681331	+	1.18010i
$951$		0			0
$952$	57.1373	−	21.2671i	1.85183	−	0.689272i
$953$	−0.457510	+	0.792431i	−0.0148202	+	0.0256694i	−0.873340	−	0.487110i	$-0.838051\pi$
$953$	−0.457510	+	0.792431i	−0.0148202	+	0.0256694i	0.858520	+	0.512780i	$0.171384\pi$
$954$		0			0
$955$	15.0216	+	26.0182i	0.486088	+	0.841929i
$956$	54.0010	+	93.5325i	1.74652	+	3.02506i
$957$		0			0
$958$	18.0328	−	31.2337i	0.582613	−	1.00911i
$959$	2.60218	−	0.968561i	0.0840287	−	0.0312765i
$960$		0			0
$961$	−20.5922	−	35.6667i	−0.664263	−	1.15054i
$962$	−2.29604	−	21.7383i	−0.0740274	−	0.700870i
$963$		0			0
$964$	−29.3179	+	50.7800i	−0.944265	+	1.63551i
$965$	−6.23674	−	10.8024i	−0.200768	−	0.347740i
$966$		0			0
$967$	48.9250			1.57332			0.786660	−	0.617386i	$-0.211808\pi$
$967$	48.9250			1.57332			0.786660	+	0.617386i	$0.211808\pi$
$968$	0.877267			0.0281964
$969$		0			0
$970$	3.13549	−	5.43083i	0.100675	−	0.174373i
$971$	29.1907			0.936774			0.468387	−	0.883523i	$-0.344835\pi$
$971$	29.1907			0.936774			0.468387	+	0.883523i	$0.344835\pi$
$972$		0			0
$973$	7.31024	+	6.04415i	0.234355	+	0.193767i
$974$	−0.543608			−0.0174183
$975$		0			0
$976$	−0.613875	+	1.06326i	−0.0196497	+	0.0340342i
$977$	27.6168			0.883539			0.441770	−	0.897128i	$-0.354351\pi$
$977$	27.6168			0.883539			0.441770	+	0.897128i	$0.354351\pi$
$978$		0			0
$979$	−13.5840	+	23.5282i	−0.434146	+	0.751964i
$980$	−30.5589	+	26.4073i	−0.976169	+	0.843549i
$981$		0			0
$982$	34.1608			1.09011
$983$	−6.29829	+	10.9090i	−0.200884	+	0.347942i	−0.948814	−	0.315836i	$-0.897715\pi$
$983$	−6.29829	+	10.9090i	−0.200884	+	0.347942i	0.747929	+	0.663778i	$0.231048\pi$
$984$		0			0
$985$	19.9284	−	34.5169i	0.634970	−	1.09980i
$986$	−51.9963	−	90.0602i	−1.65590	−	2.86810i
$987$		0			0
$988$	9.83320	+	93.0978i	0.312836	+	2.96184i
$989$	29.7612	+	51.5480i	0.946352	+	1.63913i
$990$		0			0
$991$	4.08461			0.129752			0.0648760	−	0.997893i	$-0.479335\pi$
$991$	4.08461			0.129752			0.0648760	+	0.997893i	$0.479335\pi$
$992$	27.0025			0.857329
$993$		0			0
$994$	−14.0417	+	5.22649i	−0.445376	+	0.165774i
$995$	−6.18403	+	10.7111i	−0.196047	+	0.339563i
$996$		0			0
$997$	−21.0442	−	36.4497i	−0.666478	−	1.15437i	−0.978882	−	0.204424i	$-0.934468\pi$
$997$	−21.0442	−	36.4497i	−0.666478	−	1.15437i	0.312405	−	0.949949i	$-0.398865\pi$
$998$	−31.7346			−1.00454
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.g.172.17	yes	36
3.2	odd	2	inner	819.2.n.g.172.2	yes	36
7.2	even	3		819.2.s.g.289.2	yes	36
13.9	even	3		819.2.s.g.802.2	yes	36
21.2	odd	6		819.2.s.g.289.17	yes	36
39.35	odd	6		819.2.s.g.802.17	yes	36
91.9	even	3	inner	819.2.n.g.100.17	yes	36
273.191	odd	6	inner	819.2.n.g.100.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.n.g.100.2	✓	36	273.191	odd	6	inner
819.2.n.g.100.17	yes	36	91.9	even	3	inner
819.2.n.g.172.2	yes	36	3.2	odd	2	inner
819.2.n.g.172.17	yes	36	1.1	even	1	trivial
819.2.s.g.289.2	yes	36	7.2	even	3
819.2.s.g.289.17	yes	36	21.2	odd	6
819.2.s.g.802.2	yes	36	13.9	even	3
819.2.s.g.802.17	yes	36	39.35	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.18650 - 2.05508i) q^{2} +(-1.81558 - 3.14468i) q^{4} +(0.794473 + 1.37607i) q^{5} +(0.440507 - 2.60882i) q^{7} -3.87075 q^{8} +3.77058 q^{10} +3.28228 q^{11} +(3.29459 + 1.46482i) q^{13} +(-4.83869 - 4.00066i) q^{14} +(-0.961502 + 1.66537i) q^{16} +(-2.97659 - 5.15561i) q^{17} -7.15042 q^{19} +(2.88486 - 4.99672i) q^{20} +(3.89444 - 6.74536i) q^{22} +(2.77149 - 4.80037i) q^{23} +(1.23763 - 2.14363i) q^{25} +(6.91937 - 5.03263i) q^{26} +(-9.00368 + 3.35127i) q^{28} +(3.68065 + 6.37507i) q^{29} +(-4.24807 + 7.35787i) q^{31} +(-1.58910 - 2.75241i) q^{32} -14.1269 q^{34} +(3.93989 - 1.46647i) q^{35} +(1.27742 - 2.21255i) q^{37} +(-8.48399 + 14.6947i) q^{38} +(-3.07521 - 5.32642i) q^{40} +(-1.54466 - 2.67543i) q^{41} +(-5.36917 + 9.29968i) q^{43} +(-5.95924 - 10.3217i) q^{44} +(-6.57677 - 11.3913i) q^{46} +(4.29375 + 7.43700i) q^{47} +(-6.61191 - 2.29841i) q^{49} +(-2.93690 - 5.08685i) q^{50} +(-1.37519 - 13.0199i) q^{52} +(5.97827 - 10.3547i) q^{53} +(2.60768 + 4.51664i) q^{55} +(-1.70510 + 10.0981i) q^{56} +17.4684 q^{58} +(0.607697 + 1.05256i) q^{59} +0.638454 q^{61} +(10.0807 + 17.4603i) q^{62} -11.3879 q^{64} +(0.601765 + 5.69733i) q^{65} +1.36416 q^{67} +(-10.8085 + 18.7208i) q^{68} +(1.66097 - 9.83677i) q^{70} +(1.19321 - 2.06670i) q^{71} +(-0.309169 + 0.535496i) q^{73} +(-3.03132 - 5.25041i) q^{74} +(12.9822 + 22.4858i) q^{76} +(1.44587 - 8.56288i) q^{77} +(7.41828 + 12.8488i) q^{79} -3.05555 q^{80} -7.33099 q^{82} +10.1913 q^{83} +(4.72964 - 8.19198i) q^{85} +(12.7411 + 22.0682i) q^{86} -12.7049 q^{88} +(-4.13859 + 7.16824i) q^{89} +(5.27275 - 7.94972i) q^{91} -20.1275 q^{92} +20.3782 q^{94} +(-5.68081 - 9.83945i) q^{95} +(0.831568 - 1.44032i) q^{97} +(-12.5685 + 10.8610i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 22 q^{4} - 8 q^{7} - 16 q^{10} - 10 q^{16} - 8 q^{19} - 10 q^{22} - 22 q^{25} - 14 q^{28} - 18 q^{31} + 8 q^{34} + 10 q^{37} + 14 q^{40} + 20 q^{43} - 4 q^{46} - 48 q^{49} + 22 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) \) 36 * q - 22 * q^4 - 8 * q^7 - 16 * q^10 - 10 * q^16 - 8 * q^19 - 10 * q^22 - 22 * q^25 - 14 * q^28 - 18 * q^31 + 8 * q^34 + 10 * q^37 + 14 * q^40 + 20 * q^43 - 4 * q^46 - 48 * q^49 + 22 * q^52 + 42 * q^55 + 24 * q^58 - 28 * q^61 - 12 * q^64 - 24 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 - 76 * q^82 + 28 * q^85 + 24 * q^88 + 26 * q^91 - 56 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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