LMFDB - Embedded newform 1998.2.t.a.307.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1998,2,Mod(307,1998)] 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("1998.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1998, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1998 = 2 \cdot 3^{3} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1998.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$15.9541103239$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 666)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.5
Character	$\chi$	$=$	1998.307
Dual form			1998.2.t.a.397.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.07358 + 0.619834i) q^{5} +2.74469 q^{7} -1.00000i q^{8} +1.23967 q^{10} +(1.41594 + 2.45249i) q^{11} +(1.66758 - 0.962778i) q^{13} +(-2.37697 - 1.37235i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.21619 + 0.702166i) q^{17} +(1.19640 + 0.690743i) q^{19} +(-1.07358 - 0.619834i) q^{20} -2.83189i q^{22} +(2.66127 + 1.53649i) q^{23} +(-1.73161 + 2.99924i) q^{25} -1.92556 q^{26} +(1.37235 + 2.37697i) q^{28} +(4.11863 - 2.37789i) q^{29} +(-0.786366 - 0.454008i) q^{31} +(0.866025 - 0.500000i) q^{32} +1.40433 q^{34} +(-2.94666 + 1.70126i) q^{35} +(-0.296493 - 6.07553i) q^{37} +(-0.690743 - 1.19640i) q^{38} +(0.619834 + 1.07358i) q^{40} +(5.78225 + 10.0151i) q^{41} +(-3.06264 + 1.76822i) q^{43} +(-1.41594 + 2.45249i) q^{44} +(-1.53649 - 2.66127i) q^{46} +(-2.53796 - 4.39587i) q^{47} +0.533346 q^{49} +(2.99924 - 1.73161i) q^{50} +(1.66758 + 0.962778i) q^{52} +(-5.02762 - 8.70809i) q^{53} +(-3.04027 - 1.75530i) q^{55} -2.74469i q^{56} -4.75579 q^{58} +10.1954i q^{59} -2.20608i q^{61} +(0.454008 + 0.786366i) q^{62} -1.00000 q^{64} +(-1.19353 + 2.06725i) q^{65} +(6.32487 + 10.9550i) q^{67} +(-1.21619 - 0.702166i) q^{68} +3.40251 q^{70} +(-0.513569 + 0.889528i) q^{71} -2.71210 q^{73} +(-2.78100 + 5.40981i) q^{74} +1.38149i q^{76} +(3.88633 + 6.73132i) q^{77} +2.26276i q^{79} -1.23967i q^{80} -11.5645i q^{82} +(1.72363 - 2.98542i) q^{83} +(0.870453 - 1.50767i) q^{85} +3.53643 q^{86} +(2.45249 - 1.41594i) q^{88} +(6.58592 - 3.80239i) q^{89} +(4.57700 - 2.64253i) q^{91} +3.07298i q^{92} +5.07591i q^{94} -1.71259 q^{95} +(3.60285 - 2.08011i) q^{97} +(-0.461891 - 0.266673i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) $ 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1998\mathbb{Z}\right)^\times$.

$n$	$1297$	$1703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.07358	+	0.619834i	−0.480121	+	0.277198i	−0.720467	−	0.693489i	$-0.756073\pi$
$5$	−1.07358	+	0.619834i	−0.480121	+	0.277198i	0.240346	+	0.970687i	$0.422739\pi$
$6$		0			0
$7$	2.74469			1.03740			0.518698	−	0.854957i	$-0.326417\pi$
$7$	2.74469			1.03740			0.518698	+	0.854957i	$0.326417\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.23967			0.392018
$11$	1.41594	+	2.45249i	0.426923	+	0.739452i	0.996598	−	0.0824179i	$-0.0262642\pi$
$11$	1.41594	+	2.45249i	0.426923	+	0.739452i	−0.569675	+	0.821870i	$0.692931\pi$
$12$		0			0
$13$	1.66758	−	0.962778i	0.462504	−	0.267027i	−0.250593	−	0.968093i	$-0.580626\pi$
$13$	1.66758	−	0.962778i	0.462504	−	0.267027i	0.713096	+	0.701066i	$0.247292\pi$
$14$	−2.37697	−	1.37235i	−0.635273	−	0.366775i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.21619	+	0.702166i	−0.294969	+	0.170300i	−0.640180	−	0.768225i	$-0.721140\pi$
$17$	−1.21619	+	0.702166i	−0.294969	+	0.170300i	0.345212	+	0.938525i	$0.387807\pi$
$18$		0			0
$19$	1.19640	+	0.690743i	0.274474	+	0.158467i	0.630919	−	0.775849i	$-0.282678\pi$
$19$	1.19640	+	0.690743i	0.274474	+	0.158467i	−0.356445	+	0.934316i	$0.616011\pi$
$20$	−1.07358	−	0.619834i	−0.240061	−	0.138599i
$21$		0			0
$22$		−	2.83189i		−	0.603760i
$23$	2.66127	+	1.53649i	0.554914	+	0.320380i	0.751102	−	0.660187i	$-0.229523\pi$
$23$	2.66127	+	1.53649i	0.554914	+	0.320380i	−0.196188	+	0.980566i	$0.562856\pi$
$24$		0			0
$25$	−1.73161	+	2.99924i	−0.346322	+	0.599848i
$26$	−1.92556			−0.377633
$27$		0			0
$28$	1.37235	+	2.37697i	0.259349	+	0.449206i
$29$	4.11863	−	2.37789i	0.764811	−	0.441564i	−0.0662092	−	0.997806i	$-0.521090\pi$
$29$	4.11863	−	2.37789i	0.764811	−	0.441564i	0.831021	+	0.556242i	$0.187757\pi$
$30$		0			0
$31$	−0.786366	−	0.454008i	−0.141235	−	0.0815423i	0.427717	−	0.903913i	$-0.359318\pi$
$31$	−0.786366	−	0.454008i	−0.141235	−	0.0815423i	−0.568953	+	0.822370i	$0.692651\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	1.40433			0.240841
$35$	−2.94666	+	1.70126i	−0.498077	+	0.287565i
$36$		0			0
$37$	−0.296493	−	6.07553i	−0.0487431	−	0.998811i
$37$	−0.296493	−	6.07553i	−0.0487431	−	0.998811i
$38$	−0.690743	−	1.19640i	−0.112053	−	0.194082i
$39$		0			0
$40$	0.619834	+	1.07358i	0.0980044	+	0.169749i
$41$	5.78225	+	10.0151i	0.903035	+	1.56410i	0.823533	+	0.567269i	$0.192000\pi$
$41$	5.78225	+	10.0151i	0.903035	+	1.56410i	0.0795026	+	0.996835i	$0.474667\pi$
$42$		0			0
$43$	−3.06264	+	1.76822i	−0.467049	+	0.269651i	−0.715003	−	0.699121i	$-0.753575\pi$
$43$	−3.06264	+	1.76822i	−0.467049	+	0.269651i	0.247955	+	0.968772i	$0.420242\pi$
$44$	−1.41594	+	2.45249i	−0.213461	+	0.369726i
$45$		0			0
$46$	−1.53649	−	2.66127i	−0.226543	−	0.392384i
$47$	−2.53796	−	4.39587i	−0.370199	−	0.641204i	0.619397	−	0.785078i	$-0.287377\pi$
$47$	−2.53796	−	4.39587i	−0.370199	−	0.641204i	−0.989596	+	0.143874i	$0.954044\pi$
$48$		0			0
$49$	0.533346			0.0761923
$50$	2.99924	−	1.73161i	0.424156	−	0.244887i
$51$		0			0
$52$	1.66758	+	0.962778i	0.231252	+	0.133513i
$53$	−5.02762	−	8.70809i	−0.690596	−	1.19615i	−0.971643	−	0.236454i	$-0.924015\pi$
$53$	−5.02762	−	8.70809i	−0.690596	−	1.19615i	0.281046	−	0.959694i	$-0.409319\pi$
$54$		0			0
$55$	−3.04027	−	1.75530i	−0.409950	−	0.236685i
$56$		−	2.74469i		−	0.366775i
$57$		0			0
$58$	−4.75579			−0.624466
$59$			10.1954i			1.32732i	0.748033	+	0.663662i	$0.230999\pi$
$59$			10.1954i			1.32732i	−0.748033	+	0.663662i	$0.769001\pi$
$60$		0			0
$61$		−	2.20608i		−	0.282460i	−0.989977	−	0.141230i	$-0.954894\pi$
$61$		−	2.20608i		−	0.282460i	0.989977	−	0.141230i	$-0.0451057\pi$
$62$	0.454008	+	0.786366i	0.0576591	+	0.0998685i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.19353	+	2.06725i	−0.148039	+	0.256410i
$66$		0			0
$67$	6.32487	+	10.9550i	0.772705	+	1.33836i	0.936075	+	0.351800i	$0.114430\pi$
$67$	6.32487	+	10.9550i	0.772705	+	1.33836i	−0.163370	+	0.986565i	$0.552236\pi$
$68$	−1.21619	−	0.702166i	−0.147484	−	0.0851501i
$69$		0			0
$70$	3.40251			0.406678
$71$	−0.513569	+	0.889528i	−0.0609494	+	0.105568i	−0.894890	−	0.446287i	$-0.852746\pi$
$71$	−0.513569	+	0.889528i	−0.0609494	+	0.105568i	0.833941	+	0.551854i	$0.186080\pi$
$72$		0			0
$73$	−2.71210			−0.317427			−0.158714	−	0.987325i	$-0.550735\pi$
$73$	−2.71210			−0.317427			−0.158714	+	0.987325i	$0.550735\pi$
$74$	−2.78100	+	5.40981i	−0.323284	+	0.628878i
$75$		0			0
$76$			1.38149i			0.158467i
$77$	3.88633	+	6.73132i	0.442889	+	0.767105i
$78$		0			0
$79$			2.26276i			0.254580i	0.991866	+	0.127290i	$0.0406279\pi$
$79$			2.26276i			0.254580i	−0.991866	+	0.127290i	$0.959372\pi$
$80$		−	1.23967i		−	0.138599i
$81$		0			0
$82$		−	11.5645i		−	1.27708i
$83$	1.72363	−	2.98542i	0.189193	−	0.327692i	−0.755788	−	0.654816i	$-0.772746\pi$
$83$	1.72363	−	2.98542i	0.189193	−	0.327692i	0.944981	+	0.327124i	$0.106079\pi$
$84$		0			0
$85$	0.870453	−	1.50767i	0.0944139	−	0.163530i
$86$	3.53643			0.381344
$87$		0			0
$88$	2.45249	−	1.41594i	0.261436	−	0.150940i
$89$	6.58592	−	3.80239i	0.698107	−	0.403052i	−0.108535	−	0.994093i	$-0.534616\pi$
$89$	6.58592	−	3.80239i	0.698107	−	0.403052i	0.806642	+	0.591041i	$0.201283\pi$
$90$		0			0
$91$	4.57700	−	2.64253i	0.479800	−	0.277013i
$92$			3.07298i			0.320380i
$93$		0			0
$94$			5.07591i			0.523541i
$95$	−1.71259			−0.175708
$96$		0			0
$97$	3.60285	−	2.08011i	0.365814	−	0.211203i	−0.305814	−	0.952091i	$-0.598929\pi$
$97$	3.60285	−	2.08011i	0.365814	−	0.211203i	0.671628	+	0.740888i	$0.265595\pi$
$98$	−0.461891	−	0.266673i	−0.0466581	−	0.0269380i
$99$		0			0
$100$	−3.46322			−0.346322
$101$	7.80416	+	13.5172i	0.776543	+	1.34501i	0.933923	+	0.357474i	$0.116362\pi$
$101$	7.80416	+	13.5172i	0.776543	+	1.34501i	−0.157380	+	0.987538i	$0.550305\pi$
$102$		0			0
$103$	5.43389	+	3.13726i	0.535417	+	0.309123i	0.743220	−	0.669048i	$-0.233298\pi$
$103$	5.43389	+	3.13726i	0.535417	+	0.309123i	−0.207802	+	0.978171i	$0.566631\pi$
$104$	−0.962778	−	1.66758i	−0.0944082	−	0.163520i
$105$		0			0
$106$			10.0552i			0.976651i
$107$	−5.52174	+	9.56393i	−0.533806	+	0.924580i	0.465414	+	0.885093i	$0.345906\pi$
$107$	−5.52174	+	9.56393i	−0.533806	+	0.924580i	−0.999220	+	0.0394865i	$0.987428\pi$
$108$		0			0
$109$	2.86780	−	1.65572i	0.274685	−	0.158590i	−0.356330	−	0.934360i	$-0.615972\pi$
$109$	2.86780	−	1.65572i	0.274685	−	0.158590i	0.631015	+	0.775771i	$0.282639\pi$
$110$	1.75530	+	3.04027i	0.167361	+	0.289878i
$111$		0			0
$112$	−1.37235	+	2.37697i	−0.129675	+	0.224603i
$113$			15.6543i			1.47264i	0.676635	+	0.736318i	$0.263437\pi$
$113$			15.6543i			1.47264i	−0.676635	+	0.736318i	$0.736563\pi$
$114$		0			0
$115$	−3.80947			−0.355235
$116$	4.11863	+	2.37789i	0.382406	+	0.220782i
$117$		0			0
$118$	5.09768	−	8.82945i	0.469280	−	0.812817i
$119$	−3.33806	+	1.92723i	−0.306000	+	0.176669i
$120$		0			0
$121$	1.49021	−	2.58112i	0.135474	−	0.234647i
$122$	−1.10304	+	1.91052i	−0.0998647	+	0.172971i
$123$		0			0
$124$		−	0.908017i		−	0.0815423i
$125$		−	10.4916i		−	0.938396i
$126$		0			0
$127$	4.12507	+	7.14483i	0.366040	+	0.634001i	0.988943	−	0.148299i	$-0.0473798\pi$
$127$	4.12507	+	7.14483i	0.366040	+	0.634001i	−0.622902	+	0.782300i	$0.714046\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	2.06725	−	1.19353i	0.181310	−	0.104679i
$131$			9.78730i			0.855121i	0.903987	+	0.427560i	$0.140627\pi$
$131$			9.78730i			0.855121i	−0.903987	+	0.427560i	$0.859373\pi$
$132$		0			0
$133$	3.28376	+	1.89588i	0.284738	+	0.164394i
$134$		−	12.6497i		−	1.09277i
$135$		0			0
$136$	0.702166	+	1.21619i	0.0602102	+	0.104287i
$137$	0.345628	+	0.598646i	0.0295290	+	0.0511458i	0.880412	−	0.474209i	$-0.157266\pi$
$137$	0.345628	+	0.598646i	0.0295290	+	0.0511458i	−0.850883	+	0.525355i	$0.823933\pi$
$138$		0			0
$139$	20.6904			1.75493			0.877466	−	0.479638i	$-0.159232\pi$
$139$	20.6904			1.75493			0.877466	+	0.479638i	$0.159232\pi$
$140$	−2.94666	−	1.70126i	−0.249038	−	0.143782i
$141$		0			0
$142$	0.889528	−	0.513569i	0.0746475	−	0.0430978i
$143$	4.72240	+	2.72648i	0.394907	+	0.228000i
$144$		0			0
$145$	−2.94780	+	5.10574i	−0.244802	+	0.424009i
$146$	2.34875	+	1.35605i	0.194384	+	0.112227i
$147$		0			0
$148$	5.11332	−	3.29454i	0.420312	−	0.270809i
$149$	6.26380	−	10.8492i	0.513150	−	0.888802i	−0.486733	−	0.873551i	$-0.661812\pi$
$149$	6.26380	−	10.8492i	0.513150	−	0.888802i	0.999884	−	0.0152518i	$-0.00485497\pi$
$150$		0			0
$151$	−1.83012			−0.148933			−0.0744663	−	0.997224i	$-0.523725\pi$
$151$	−1.83012			−0.148933			−0.0744663	+	0.997224i	$0.523725\pi$
$152$	0.690743	−	1.19640i	0.0560267	−	0.0970411i
$153$		0			0
$154$		−	7.77266i		−	0.626339i
$155$	1.12564			0.0904135
$156$		0			0
$157$	−4.52223			−0.360913			−0.180457	−	0.983583i	$-0.557758\pi$
$157$	−4.52223			−0.360913			−0.180457	+	0.983583i	$0.557758\pi$
$158$	1.13138	−	1.95960i	0.0900076	−	0.155898i
$159$		0			0
$160$	−0.619834	+	1.07358i	−0.0490022	+	0.0848743i
$161$	7.30438	+	4.21719i	0.575666	+	0.332361i
$162$		0			0
$163$	12.1660	−	7.02404i	0.952914	−	0.550165i	0.0589293	−	0.998262i	$-0.481231\pi$
$163$	12.1660	−	7.02404i	0.952914	−	0.550165i	0.893985	+	0.448097i	$0.147898\pi$
$164$	−5.78225	+	10.0151i	−0.451518	+	0.782052i
$165$		0			0
$166$	−2.98542	+	1.72363i	−0.231713	+	0.133780i
$167$	−9.59165	+	5.53774i	−0.742224	+	0.428523i	−0.822878	−	0.568219i	$-0.807633\pi$
$167$	−9.59165	+	5.53774i	−0.742224	+	0.428523i	0.0806532	+	0.996742i	$0.474299\pi$
$168$		0			0
$169$	−4.64612	+	8.04731i	−0.357394	+	0.619024i
$170$	−1.50767	+	0.870453i	−0.115633	+	0.0667607i
$171$		0			0
$172$	−3.06264	−	1.76822i	−0.233524	−	0.134825i
$173$	−3.28490	+	5.68961i	−0.249746	+	0.432573i	−0.963455	−	0.267869i	$-0.913680\pi$
$173$	−3.28490	+	5.68961i	−0.249746	+	0.432573i	0.713709	+	0.700442i	$0.247014\pi$
$174$		0			0
$175$	−4.75274	+	8.23199i	−0.359274	+	0.622280i
$176$	−2.83189			−0.213461
$177$		0			0
$178$	−7.60477			−0.570002
$179$		−	0.338286i		−	0.0252847i	−0.999920	−	0.0126424i	$-0.995976\pi$
$179$		−	0.338286i		−	0.0252847i	0.999920	−	0.0126424i	$-0.00402429\pi$
$180$		0			0
$181$	−1.25459	+	2.17301i	−0.0932529	+	0.161519i	−0.908878	−	0.417062i	$-0.863060\pi$
$181$	−1.25459	+	2.17301i	−0.0932529	+	0.161519i	0.815625	+	0.578581i	$0.196393\pi$
$182$	−5.28506			−0.391755
$183$		0			0
$184$	1.53649	−	2.66127i	0.113271	−	0.196192i
$185$	4.08413	+	6.33882i	0.300271	+	0.466039i
$186$		0			0
$187$	−3.44410	−	1.98845i	−0.251858	−	0.145410i
$188$	2.53796	−	4.39587i	0.185100	−	0.320602i
$189$		0			0
$190$	1.48314	+	0.856293i	0.107598	+	0.0621220i
$191$	9.28198	−	5.35895i	0.671621	−	0.387760i	−0.125070	−	0.992148i	$-0.539915\pi$
$191$	9.28198	−	5.35895i	0.671621	−	0.387760i	0.796690	+	0.604388i	$0.206582\pi$
$192$		0			0
$193$	−0.763709	−	0.440928i	−0.0549730	−	0.0317387i	0.472262	−	0.881458i	$-0.343438\pi$
$193$	−0.763709	−	0.440928i	−0.0549730	−	0.0317387i	−0.527235	+	0.849720i	$0.676771\pi$
$194$	−4.16021			−0.298686
$195$		0			0
$196$	0.266673	+	0.461891i	0.0190481	+	0.0329922i
$197$	10.0925	+	17.4808i	0.719062	+	1.24545i	0.961372	+	0.275253i	$0.0887618\pi$
$197$	10.0925	+	17.4808i	0.719062	+	1.24545i	−0.242309	+	0.970199i	$0.577905\pi$
$198$		0			0
$199$		−	20.7170i		−	1.46859i	−0.678831	−	0.734295i	$-0.737513\pi$
$199$		−	20.7170i		−	1.46859i	0.678831	−	0.734295i	$-0.262487\pi$
$200$	2.99924	+	1.73161i	0.212078	+	0.122443i
$201$		0			0
$202$		−	15.6083i		−	1.09820i
$203$	11.3044	−	6.52659i	0.793413	−	0.458077i
$204$		0			0
$205$	−12.4155	−	7.16807i	−0.867133	−	0.500640i
$206$	−3.13726	−	5.43389i	−0.218583	−	0.378597i
$207$		0			0
$208$			1.92556i			0.133513i
$209$			3.91221i			0.270613i
$210$		0			0
$211$	−8.79114	+	15.2267i	−0.605207	+	1.04825i	0.386812	+	0.922159i	$0.373576\pi$
$211$	−8.79114	+	15.2267i	−0.605207	+	1.04825i	−0.992019	+	0.126090i	$0.959757\pi$
$212$	5.02762	−	8.70809i	0.345298	−	0.598074i
$213$		0			0
$214$	9.56393	−	5.52174i	0.653777	−	0.377458i
$215$	2.19200	−	3.79666i	0.149493	−	0.258930i
$216$		0			0
$217$	−2.15833	−	1.24611i	−0.146517	−	0.0845917i
$218$	−3.31145			−0.224280
$219$		0			0
$220$		−	3.51060i		−	0.236685i
$221$	−1.35206	+	2.34184i	−0.0909494	+	0.157529i
$222$		0			0
$223$	6.17989	+	10.7039i	0.413836	+	0.716786i	0.995306	−	0.0967829i	$-0.0308552\pi$
$223$	6.17989	+	10.7039i	0.413836	+	0.716786i	−0.581469	+	0.813568i	$0.697522\pi$
$224$	2.37697	−	1.37235i	0.158818	−	0.0916938i
$225$		0			0
$226$	7.82717	−	13.5571i	0.520656	−	0.901802i
$227$		−	25.7519i		−	1.70921i	−0.519276	−	0.854607i	$-0.673798\pi$
$227$		−	25.7519i		−	1.70921i	0.519276	−	0.854607i	$-0.326202\pi$
$228$		0			0
$229$	9.25384	+	16.0281i	0.611511	+	1.05917i	0.990986	+	0.133966i	$0.0427714\pi$
$229$	9.25384	+	16.0281i	0.611511	+	1.05917i	−0.379475	+	0.925202i	$0.623895\pi$
$230$	3.29910	+	1.90473i	0.217536	+	0.125594i
$231$		0			0
$232$	−2.37789	−	4.11863i	−0.156116	−	0.270402i
$233$	4.45679			0.291974			0.145987	−	0.989287i	$-0.453364\pi$
$233$	4.45679			0.291974			0.145987	+	0.989287i	$0.453364\pi$
$234$		0			0
$235$	5.44942	+	3.14623i	0.355481	+	0.205237i
$236$	−8.82945	+	5.09768i	−0.574748	+	0.331831i
$237$		0			0
$238$	3.85446			0.249848
$239$		−	10.7475i		−	0.695201i	−0.937643	−	0.347600i	$-0.886997\pi$
$239$		−	10.7475i		−	0.695201i	0.937643	−	0.347600i	$-0.113003\pi$
$240$		0			0
$241$			3.80759i			0.245269i	0.992452	+	0.122634i	$0.0391342\pi$
$241$			3.80759i			0.245269i	−0.992452	+	0.122634i	$0.960866\pi$
$242$	−2.58112	+	1.49021i	−0.165921	+	0.0957943i
$243$		0			0
$244$	1.91052	−	1.10304i	0.122309	−	0.0706150i
$245$	−0.572592	+	0.330586i	−0.0365816	+	0.0211204i
$246$		0			0
$247$	2.66013			0.169260
$248$	−0.454008	+	0.786366i	−0.0288296	+	0.0499343i
$249$		0			0
$250$	−5.24579	+	9.08598i	−0.331773	+	0.574648i
$251$		−	10.4606i		−	0.660265i	−0.943935	−	0.330133i	$-0.892907\pi$
$251$		−	10.4606i		−	0.660265i	0.943935	−	0.330133i	$-0.107093\pi$
$252$		0			0
$253$			8.70232i			0.547110i
$254$		−	8.25013i		−	0.517659i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	24.0846i		−	1.50236i	−0.660099	−	0.751179i	$-0.729486\pi$
$257$		−	24.0846i		−	1.50236i	0.660099	−	0.751179i	$-0.270514\pi$
$258$		0			0
$259$	−0.813782	−	16.6755i	−0.0505660	−	1.03616i
$260$	−2.38705			−0.148039
$261$		0			0
$262$	4.89365	−	8.47605i	0.302331	−	0.523652i
$263$	0.511138			0.0315181			0.0157591	−	0.999876i	$-0.494984\pi$
$263$	0.511138			0.0315181			0.0157591	+	0.999876i	$0.494984\pi$
$264$		0			0
$265$	10.7951	+	6.23258i	0.663140	+	0.382864i
$266$	−1.89588	−	3.28376i	−0.116244	−	0.201340i
$267$		0			0
$268$	−6.32487	+	10.9550i	−0.386353	+	0.669182i
$269$	5.35280			0.326366			0.163183	−	0.986596i	$-0.447824\pi$
$269$	5.35280			0.326366			0.163183	+	0.986596i	$0.447824\pi$
$270$		0			0
$271$	−10.0119	−	17.3411i	−0.608180	−	1.05340i	−0.991540	−	0.129799i	$-0.958567\pi$
$271$	−10.0119	−	17.3411i	−0.608180	−	1.05340i	0.383361	−	0.923599i	$-0.374767\pi$
$272$		−	1.40433i		−	0.0851501i
$273$		0			0
$274$		−	0.691256i		−	0.0417603i
$275$	−9.80745			−0.591412
$276$		0			0
$277$			29.1131i			1.74924i	0.484812	+	0.874618i	$0.338888\pi$
$277$			29.1131i			1.74924i	−0.484812	+	0.874618i	$0.661112\pi$
$278$	−17.9184	−	10.3452i	−1.07467	−	0.620462i
$279$		0			0
$280$	1.70126	+	2.94666i	0.101669	+	0.176097i
$281$	12.6314	+	7.29275i	0.753527	+	0.435049i	0.826967	−	0.562250i	$-0.190064\pi$
$281$	12.6314	+	7.29275i	0.753527	+	0.435049i	−0.0734397	+	0.997300i	$0.523398\pi$
$282$		0			0
$283$	9.30175	−	5.37037i	0.552931	−	0.319235i	−0.197372	−	0.980329i	$-0.563241\pi$
$283$	9.30175	−	5.37037i	0.552931	−	0.319235i	0.750304	+	0.661094i	$0.229907\pi$
$284$	−1.02714			−0.0609494
$285$		0			0
$286$	−2.72648	−	4.72240i	−0.161220	−	0.279241i
$287$	15.8705	+	27.4885i	0.936806	+	1.62260i
$288$		0			0
$289$	−7.51393	+	13.0145i	−0.441996	+	0.765559i
$290$	5.10574	−	2.94780i	0.299819	−	0.173101i
$291$		0			0
$292$	−1.35605	−	2.34875i	−0.0793568	−	0.137450i
$293$	−6.06109	−	10.4981i	−0.354093	−	0.613307i	0.632869	−	0.774259i	$-0.281877\pi$
$293$	−6.06109	−	10.4981i	−0.354093	−	0.613307i	−0.986962	+	0.160952i	$0.948544\pi$
$294$		0			0
$295$	−6.31944	−	10.9456i	−0.367932	−	0.637277i
$296$	−6.07553	+	0.296493i	−0.353133	+	0.0172333i
$297$		0			0
$298$	−10.8492	+	6.26380i	−0.628478	+	0.362852i
$299$	5.91719			0.342200
$300$		0			0
$301$	−8.40602	+	4.85322i	−0.484515	+	0.279735i
$302$	1.58493	+	0.915058i	0.0912023	+	0.0526557i
$303$		0			0
$304$	−1.19640	+	0.690743i	−0.0686184	+	0.0396169i
$305$	1.36741	+	2.36842i	0.0782975	+	0.135615i
$306$		0			0
$307$	−11.1732			−0.637687			−0.318844	−	0.947807i	$-0.603294\pi$
$307$	−11.1732			−0.637687			−0.318844	+	0.947807i	$0.603294\pi$
$308$	−3.88633	+	6.73132i	−0.221444	+	0.383553i
$309$		0			0
$310$	−0.974832	−	0.562820i	−0.0553668	−	0.0319660i
$311$			0.366735i			0.0207957i	0.999946	+	0.0103978i	$0.00330979\pi$
$311$			0.366735i			0.0207957i	−0.999946	+	0.0103978i	$0.996690\pi$
$312$		0			0
$313$	4.29901	+	2.48203i	0.242994	+	0.140293i	0.616552	−	0.787314i	$-0.288529\pi$
$313$	4.29901	+	2.48203i	0.242994	+	0.140293i	−0.373558	+	0.927607i	$0.621862\pi$
$314$	3.91637	+	2.26112i	0.221013	+	0.127602i
$315$		0			0
$316$	−1.95960	+	1.13138i	−0.110236	+	0.0636450i
$317$	14.6694	−	25.4082i	0.823918	−	1.42707i	−0.0788249	−	0.996888i	$-0.525117\pi$
$317$	14.6694	−	25.4082i	0.823918	−	1.42707i	0.902743	−	0.430180i	$-0.141550\pi$
$318$		0			0
$319$	11.6635	+	6.73393i	0.653031	+	0.377028i
$320$	1.07358	−	0.619834i	0.0600152	−	0.0346498i
$321$		0			0
$322$	−4.21719	−	7.30438i	−0.235015	−	0.407057i
$323$	−1.94007			−0.107948
$324$		0			0
$325$			6.66863i			0.369909i
$326$	−14.0481			−0.778051
$327$		0			0
$328$	10.0151	−	5.78225i	0.552994	−	0.319271i
$329$	−6.96592	−	12.0653i	−0.384043	−	0.665183i
$330$		0			0
$331$	21.5217	+	12.4255i	1.18294	+	0.682970i	0.956692	−	0.291101i	$-0.0940214\pi$
$331$	21.5217	+	12.4255i	1.18294	+	0.682970i	0.226246	+	0.974070i	$0.427355\pi$
$332$	3.44726			0.189193
$333$		0			0
$334$	11.0755			0.606024
$335$	−13.5806	−	7.84074i	−0.741985	−	0.428385i
$336$		0			0
$337$	−8.67709	−	15.0292i	−0.472671	−	0.818690i	0.526840	−	0.849965i	$-0.323377\pi$
$337$	−8.67709	−	15.0292i	−0.472671	−	0.818690i	−0.999511	+	0.0312742i	$0.990043\pi$
$338$	8.04731	−	4.64612i	0.437716	−	0.252715i
$339$		0			0
$340$	1.74091			0.0944139
$341$		−	2.57140i		−	0.139249i
$342$		0			0
$343$	−17.7490			−0.958355
$344$	1.76822	+	3.06264i	0.0953359	+	0.165127i
$345$		0			0
$346$	5.68961	−	3.28490i	0.305875	−	0.176597i
$347$	2.29310	+	1.32392i	0.123100	+	0.0710717i	0.560286	−	0.828300i	$-0.310691\pi$
$347$	2.29310	+	1.32392i	0.123100	+	0.0710717i	−0.437186	+	0.899371i	$0.644025\pi$
$348$		0			0
$349$	−14.7822	+	25.6036i	−0.791274	+	1.37053i	0.133904	+	0.990994i	$0.457249\pi$
$349$	−14.7822	+	25.6036i	−0.791274	+	1.37053i	−0.925178	+	0.379533i	$0.876085\pi$
$350$	8.23199	−	4.75274i	0.440019	−	0.254045i
$351$		0			0
$352$	2.45249	+	1.41594i	0.130718	+	0.0754700i
$353$	−27.2261	−	15.7190i	−1.44910	−	0.836637i	−0.450671	−	0.892690i	$-0.648815\pi$
$353$	−27.2261	−	15.7190i	−1.44910	−	0.836637i	−0.998428	+	0.0560529i	$0.982148\pi$
$354$		0			0
$355$		−	1.27331i		−	0.0675803i
$356$	6.58592	+	3.80239i	0.349053	+	0.201526i
$357$		0			0
$358$	−0.169143	+	0.292965i	−0.00893949	+	0.0154837i
$359$	1.58279			0.0835365			0.0417683	−	0.999127i	$-0.486701\pi$
$359$	1.58279			0.0835365			0.0417683	+	0.999127i	$0.486701\pi$
$360$		0			0
$361$	−8.54575	−	14.8017i	−0.449776	−	0.779035i
$362$	2.17301	−	1.25459i	0.114211	−	0.0659398i
$363$		0			0
$364$	4.57700	+	2.64253i	0.239900	+	0.138506i
$365$	2.91167	−	1.68105i	0.152404	−	0.0879903i
$366$		0			0
$367$	−14.5904			−0.761615			−0.380808	−	0.924654i	$-0.624354\pi$
$367$	−14.5904			−0.761615			−0.380808	+	0.924654i	$0.624354\pi$
$368$	−2.66127	+	1.53649i	−0.138729	+	0.0800949i
$369$		0			0
$370$	−0.367553	−	7.53164i	−0.0191082	−	0.391552i
$371$	−13.7993	−	23.9010i	−0.716422	−	1.24088i
$372$		0			0
$373$	−7.23418	−	12.5300i	−0.374572	−	0.648777i	0.615691	−	0.787988i	$-0.288877\pi$
$373$	−7.23418	−	12.5300i	−0.374572	−	0.648777i	−0.990263	+	0.139210i	$0.955544\pi$
$374$	1.98845	+	3.44410i	0.102821	+	0.178090i
$375$		0			0
$376$	−4.39587	+	2.53796i	−0.226700	+	0.130885i
$377$	4.57877	−	7.93066i	0.235819	−	0.408450i
$378$		0			0
$379$	13.6059	+	23.5661i	0.698889	+	1.21051i	0.968852	+	0.247640i	$0.0796551\pi$
$379$	13.6059	+	23.5661i	0.698889	+	1.21051i	−0.269963	+	0.962871i	$0.587012\pi$
$380$	−0.856293	−	1.48314i	−0.0439269	−	0.0760836i
$381$		0			0
$382$	−10.7179			−0.548376
$383$	−12.7826	+	7.38004i	−0.653161	+	0.377103i	−0.789666	−	0.613537i	$-0.789746\pi$
$383$	−12.7826	+	7.38004i	−0.653161	+	0.377103i	0.136505	+	0.990639i	$0.456413\pi$
$384$		0			0
$385$	−8.34461	−	4.81776i	−0.425281	−	0.245536i
$386$	0.440928	+	0.763709i	0.0224426	+	0.0388718i
$387$		0			0
$388$	3.60285	+	2.08011i	0.182907	+	0.105601i
$389$			18.3809i			0.931949i	0.884798	+	0.465975i	$0.154296\pi$
$389$			18.3809i			0.931949i	−0.884798	+	0.465975i	$0.845704\pi$
$390$		0			0
$391$	−4.31548			−0.218243
$392$		−	0.533346i		−	0.0269380i
$393$		0			0
$394$		−	20.1850i		−	1.01691i
$395$	−1.40253	−	2.42926i	−0.0705691	−	0.122229i
$396$		0			0
$397$	−5.51580			−0.276830			−0.138415	−	0.990374i	$-0.544201\pi$
$397$	−5.51580			−0.276830			−0.138415	+	0.990374i	$0.544201\pi$
$398$	−10.3585	+	17.9415i	−0.519225	+	0.899324i
$399$		0			0
$400$	−1.73161	−	2.99924i	−0.0865806	−	0.149962i
$401$	−9.38853	−	5.42047i	−0.468841	−	0.270686i	0.246913	−	0.969038i	$-0.420584\pi$
$401$	−9.38853	−	5.42047i	−0.468841	−	0.270686i	−0.715754	+	0.698352i	$0.753917\pi$
$402$		0			0
$403$	−1.74844			−0.0870959
$404$	−7.80416	+	13.5172i	−0.388272	+	0.672506i
$405$		0			0
$406$	−13.0532			−0.647819
$407$	14.4803	−	9.32975i	0.717764	−	0.462459i
$408$		0			0
$409$			5.54739i			0.274301i	0.990550	+	0.137150i	$0.0437944\pi$
$409$			5.54739i			0.274301i	−0.990550	+	0.137150i	$0.956206\pi$
$410$	7.16807	+	12.4155i	0.354006	+	0.613156i
$411$		0			0
$412$			6.27452i			0.309123i
$413$			27.9832i			1.37696i
$414$		0			0
$415$			4.27346i			0.209776i
$416$	0.962778	−	1.66758i	0.0472041	−	0.0817599i
$417$		0			0
$418$	1.95611	−	3.38808i	0.0956763	−	0.165716i
$419$	−6.29800			−0.307677			−0.153839	−	0.988096i	$-0.549164\pi$
$419$	−6.29800			−0.307677			−0.153839	+	0.988096i	$0.549164\pi$
$420$		0			0
$421$	−29.7804	+	17.1937i	−1.45141	+	0.837972i	−0.998562	−	0.0536160i	$-0.982925\pi$
$421$	−29.7804	+	17.1937i	−1.45141	+	0.837972i	−0.452848	+	0.891588i	$0.649592\pi$
$422$	15.2267	−	8.79114i	0.741224	−	0.427946i
$423$		0			0
$424$	−8.70809	+	5.02762i	−0.422902	+	0.244163i
$425$		−	4.86351i		−	0.235915i
$426$		0			0
$427$		−	6.05503i		−	0.293023i
$428$	−11.0435			−0.533806
$429$		0			0
$430$	−3.79666	+	2.19200i	−0.183091	+	0.105708i
$431$	−20.9067	−	12.0705i	−1.00704	−	0.581416i	−0.0967181	−	0.995312i	$-0.530835\pi$
$431$	−20.9067	−	12.0705i	−1.00704	−	0.581416i	−0.910324	+	0.413896i	$0.864168\pi$
$432$		0			0
$433$	−17.3086			−0.831800			−0.415900	−	0.909410i	$-0.636533\pi$
$433$	−17.3086			−0.831800			−0.415900	+	0.909410i	$0.636533\pi$
$434$	1.24611	+	2.15833i	0.0598154	+	0.103603i
$435$		0			0
$436$	2.86780	+	1.65572i	0.137343	+	0.0792948i
$437$	2.12264	+	3.67652i	0.101540	+	0.175872i
$438$		0			0
$439$		−	8.66800i		−	0.413701i	−0.978373	−	0.206850i	$-0.933679\pi$
$439$		−	8.66800i		−	0.413701i	0.978373	−	0.206850i	$-0.0663214\pi$
$440$	−1.75530	+	3.04027i	−0.0836806	+	0.144939i
$441$		0			0
$442$	2.34184	−	1.35206i	0.111390	−	0.0643109i
$443$	−5.95484	−	10.3141i	−0.282923	−	0.490037i	0.689180	−	0.724590i	$-0.257971\pi$
$443$	−5.95484	−	10.3141i	−0.282923	−	0.490037i	−0.972103	+	0.234553i	$0.924637\pi$
$444$		0			0
$445$	−4.71370	+	8.16436i	−0.223451	+	0.387028i
$446$		−	12.3598i		−	0.585253i
$447$		0			0
$448$	−2.74469			−0.129675
$449$	−8.54656	−	4.93436i	−0.403337	−	0.232867i	0.284586	−	0.958651i	$-0.408144\pi$
$449$	−8.54656	−	4.93436i	−0.403337	−	0.232867i	−0.687923	+	0.725784i	$0.741477\pi$
$450$		0			0
$451$	−16.3747	+	28.3618i	−0.771053	+	1.33550i
$452$	−13.5571	+	7.82717i	−0.637670	+	0.368159i
$453$		0			0
$454$	−12.8759	+	22.3018i	−0.604298	+	1.04668i
$455$	−3.27586	+	5.67396i	−0.153575	+	0.265999i
$456$		0			0
$457$		−	5.30951i		−	0.248368i	−0.992259	−	0.124184i	$-0.960369\pi$
$457$		−	5.30951i		−	0.248368i	0.992259	−	0.124184i	$-0.0396314\pi$
$458$		−	18.5077i		−	0.864807i
$459$		0			0
$460$	−1.90473	−	3.29910i	−0.0888087	−	0.153821i
$461$	10.9264	+	6.30837i	0.508894	+	0.293810i	0.732379	−	0.680897i	$-0.238410\pi$
$461$	10.9264	+	6.30837i	0.508894	+	0.293810i	−0.223485	+	0.974707i	$0.571743\pi$
$462$		0			0
$463$	32.7382	−	18.9014i	1.52147	−	0.878422i	0.521794	−	0.853072i	$-0.325263\pi$
$463$	32.7382	−	18.9014i	1.52147	−	0.878422i	0.999679	−	0.0253507i	$-0.00807023\pi$
$464$			4.75579i			0.220782i
$465$		0			0
$466$	−3.85969	−	2.22839i	−0.178797	−	0.103228i
$467$		−	22.3889i		−	1.03603i	−0.855370	−	0.518017i	$-0.826670\pi$
$467$		−	22.3889i		−	1.03603i	0.855370	−	0.518017i	$-0.173330\pi$
$468$		0			0
$469$	17.3598	+	30.0681i	0.801602	+	1.38842i
$470$	−3.14623	−	5.44942i	−0.145125	−	0.251363i
$471$		0			0
$472$	10.1954			0.469280
$473$	−8.67305	−	5.00739i	−0.398787	−	0.230240i
$474$		0			0
$475$	−4.14341	+	2.39220i	−0.190113	+	0.109762i
$476$	−3.33806	−	1.92723i	−0.153000	−	0.0883345i
$477$		0			0
$478$	−5.37377	+	9.30764i	−0.245791	+	0.425722i
$479$	−11.5287	−	6.65609i	−0.526759	−	0.304124i	0.212937	−	0.977066i	$-0.431697\pi$
$479$	−11.5287	−	6.65609i	−0.526759	−	0.304124i	−0.739696	+	0.672942i	$0.765031\pi$
$480$		0			0
$481$	−6.34382	−	9.84598i	−0.289253	−	0.448938i
$482$	1.90380	−	3.29747i	0.0867156	−	0.150196i
$483$		0			0
$484$	2.98042			0.135474
$485$	−2.57864	+	4.46634i	−0.117090	+	0.202806i
$486$		0			0
$487$		−	40.6102i		−	1.84022i	−0.391656	−	0.920112i	$-0.628098\pi$
$487$		−	40.6102i		−	1.84022i	0.391656	−	0.920112i	$-0.371902\pi$
$488$	−2.20608			−0.0998647
$489$		0			0
$490$	0.661172			0.0298687
$491$	2.21150	−	3.83043i	0.0998037	−	0.172865i	−0.811800	−	0.583936i	$-0.801512\pi$
$491$	2.21150	−	3.83043i	0.0998037	−	0.172865i	0.911603	+	0.411071i	$0.134845\pi$
$492$		0			0
$493$	−3.33935	+	5.78393i	−0.150397	+	0.260495i
$494$	−2.30374	−	1.33007i	−0.103650	−	0.0598425i
$495$		0			0
$496$	0.786366	−	0.454008i	0.0353089	−	0.0203856i
$497$	−1.40959	+	2.44148i	−0.0632287	+	0.109515i
$498$		0			0
$499$	16.3906	−	9.46311i	0.733743	−	0.423627i	−0.0860468	−	0.996291i	$-0.527423\pi$
$499$	16.3906	−	9.46311i	0.733743	−	0.423627i	0.819790	+	0.572664i	$0.194090\pi$
$500$	9.08598	−	5.24579i	0.406337	−	0.234599i
$501$		0			0
$502$	−5.23028	+	9.05912i	−0.233439	+	0.404328i
$503$	19.8574	−	11.4647i	0.885397	−	0.511184i	0.0129626	−	0.999916i	$-0.495874\pi$
$503$	19.8574	−	11.4647i	0.885397	−	0.511184i	0.872434	+	0.488732i	$0.162540\pi$
$504$		0			0
$505$	−16.7568	−	9.67457i	−0.745670	−	0.430513i
$506$	4.35116	−	7.53643i	0.193433	−	0.335035i
$507$		0			0
$508$	−4.12507	+	7.14483i	−0.183020	+	0.317000i
$509$	2.67326			0.118490			0.0592450	−	0.998243i	$-0.481131\pi$
$509$	2.67326			0.118490			0.0592450	+	0.998243i	$0.481131\pi$
$510$		0			0
$511$	−7.44388			−0.329298
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.0423	+	20.8579i	−0.531164	+	0.920002i
$515$	−7.77832			−0.342754
$516$		0			0
$517$	7.18721	−	12.4486i	0.316093	−	0.547489i
$518$	−7.63298	+	14.8483i	−0.335374	+	0.652396i
$519$		0			0
$520$	2.06725	+	1.19353i	0.0906548	+	0.0523396i
$521$	−18.0698	+	31.2978i	−0.791653	+	1.37118i	0.133290	+	0.991077i	$0.457446\pi$
$521$	−18.0698	+	31.2978i	−0.791653	+	1.37118i	−0.924943	+	0.380106i	$0.875888\pi$
$522$		0			0
$523$	5.60689	+	3.23714i	0.245172	+	0.141550i	0.617552	−	0.786530i	$-0.288125\pi$
$523$	5.60689	+	3.23714i	0.245172	+	0.141550i	−0.372379	+	0.928081i	$0.621458\pi$
$524$	−8.47605	+	4.89365i	−0.370278	+	0.213780i
$525$		0			0
$526$	−0.442658	−	0.255569i	−0.0193008	−	0.0111433i
$527$	1.27516			0.0555467
$528$		0			0
$529$	−6.77841	−	11.7406i	−0.294714	−	0.510459i
$530$	−6.23258	−	10.7951i	−0.270726	−	0.468911i
$531$		0			0
$532$			3.79176i			0.164394i
$533$	19.2847	+	11.1340i	0.835314	+	0.482269i
$534$		0			0
$535$		−	13.6902i		−	0.591881i
$536$	10.9550	−	6.32487i	0.473183	−	0.273193i
$537$		0			0
$538$	−4.63566	−	2.67640i	−0.199857	−	0.115388i
$539$	0.755188	+	1.30802i	0.0325282	+	0.0563406i
$540$		0			0
$541$		−	43.5596i		−	1.87277i	−0.350972	−	0.936386i	$-0.614149\pi$
$541$		−	43.5596i		−	1.87277i	0.350972	−	0.936386i	$-0.385851\pi$
$542$			20.0238i			0.860096i
$543$		0			0
$544$	−0.702166	+	1.21619i	−0.0301051	+	0.0521436i
$545$	−2.05255	+	3.55512i	−0.0879215	+	0.152285i
$546$		0			0
$547$	14.6318	−	8.44768i	0.625611	−	0.361197i	−0.153439	−	0.988158i	$-0.549035\pi$
$547$	14.6318	−	8.44768i	0.625611	−	0.361197i	0.779050	+	0.626961i	$0.215702\pi$
$548$	−0.345628	+	0.598646i	−0.0147645	+	0.0255729i
$549$		0			0
$550$	8.49350	+	4.90373i	0.362164	+	0.209096i
$551$	6.57006			0.279894
$552$		0			0
$553$			6.21058i			0.264101i
$554$	14.5566	−	25.2127i	0.618449	−	1.07118i
$555$		0			0
$556$	10.3452	+	17.9184i	0.438733	+	0.759908i
$557$	−13.6854	+	7.90127i	−0.579869	+	0.334787i	−0.761081	−	0.648657i	$-0.775331\pi$
$557$	−13.6854	+	7.90127i	−0.579869	+	0.334787i	0.181212	+	0.983444i	$0.441998\pi$
$558$		0			0
$559$	−3.40480	+	5.89729i	−0.144008	+	0.249429i
$560$		−	3.40251i		−	0.143782i
$561$		0			0
$562$	−7.29275	−	12.6314i	−0.307626	−	0.532824i
$563$	−37.4367	−	21.6141i	−1.57777	−	0.910924i	−0.995170	−	0.0981628i	$-0.968703\pi$
$563$	−37.4367	−	21.6141i	−1.57777	−	0.910924i	−0.582597	−	0.812761i	$-0.697963\pi$
$564$		0			0
$565$	−9.70310	−	16.8063i	−0.408212	−	0.707045i
$566$	−10.7407			−0.451467
$567$		0			0
$568$	0.889528	+	0.513569i	0.0373237	+	0.0215489i
$569$	−20.0195	+	11.5582i	−0.839260	+	0.484547i	−0.857013	−	0.515295i	$-0.827682\pi$
$569$	−20.0195	+	11.5582i	−0.839260	+	0.484547i	0.0177527	+	0.999842i	$0.494349\pi$
$570$		0			0
$571$	−13.8827			−0.580974			−0.290487	−	0.956879i	$-0.593817\pi$
$571$	−13.8827			−0.580974			−0.290487	+	0.956879i	$0.593817\pi$
$572$			5.45296i			0.228000i
$573$		0			0
$574$		−	31.7410i		−	1.32484i
$575$	−9.21659	+	5.32120i	−0.384358	+	0.221909i
$576$		0			0
$577$	−6.48754	+	3.74558i	−0.270080	+	0.155931i	−0.628924	−	0.777467i	$-0.716504\pi$
$577$	−6.48754	+	3.74558i	−0.270080	+	0.155931i	0.358844	+	0.933398i	$0.383171\pi$
$578$	13.0145	−	7.51393i	0.541332	−	0.312538i
$579$		0			0
$580$	−5.89560			−0.244802
$581$	4.73084	−	8.19405i	0.196268	−	0.339947i
$582$		0			0
$583$	14.2376	−	24.6603i	0.589663	−	1.02133i
$584$			2.71210i			0.112227i
$585$		0			0
$586$			12.1222i			0.500763i
$587$		−	14.7877i		−	0.610355i	−0.952295	−	0.305177i	$-0.901284\pi$
$587$		−	14.7877i		−	0.610355i	0.952295	−	0.305177i	$-0.0987158\pi$
$588$		0			0
$589$	−0.627207	−	1.08635i	−0.0258436	−	0.0447624i
$590$			12.6389i			0.520334i
$591$		0			0
$592$	5.40981	+	2.78100i	0.222342	+	0.114298i
$593$	−26.6675			−1.09510			−0.547552	−	0.836772i	$-0.684440\pi$
$593$	−26.6675			−1.09510			−0.547552	+	0.836772i	$0.684440\pi$
$594$		0			0
$595$	2.38913	−	4.13809i	0.0979446	−	0.169645i
$596$	12.5276			0.513150
$597$		0			0
$598$	−5.12443	−	2.95859i	−0.209554	−	0.120986i
$599$	−18.2443	−	31.6000i	−0.745440	−	1.29114i	−0.949989	−	0.312284i	$-0.898906\pi$
$599$	−18.2443	−	31.6000i	−0.745440	−	1.29114i	0.204549	−	0.978856i	$-0.434427\pi$
$600$		0			0
$601$	−6.34775	+	10.9946i	−0.258930	+	0.448480i	−0.965956	−	0.258708i	$-0.916703\pi$
$601$	−6.34775	+	10.9946i	−0.258930	+	0.448480i	0.707025	+	0.707188i	$0.250037\pi$
$602$	9.70643			0.395605
$603$		0			0
$604$	−0.915058	−	1.58493i	−0.0372332	−	0.0644897i
$605$			3.69473i			0.150212i
$606$		0			0
$607$		−	14.1668i		−	0.575014i	−0.957778	−	0.287507i	$-0.907173\pi$
$607$		−	14.1668i		−	0.575014i	0.957778	−	0.287507i	$-0.0928265\pi$
$608$	1.38149			0.0560267
$609$		0			0
$610$		−	2.73481i		−	0.110729i
$611$	−8.46450	−	4.88698i	−0.342437	−	0.197706i
$612$		0			0
$613$	−23.9113	−	41.4155i	−0.965767	−	1.67276i	−0.707541	−	0.706672i	$-0.750196\pi$
$613$	−23.9113	−	41.4155i	−0.965767	−	1.67276i	−0.258225	−	0.966085i	$-0.583138\pi$
$614$	9.67626	+	5.58659i	0.390502	+	0.225456i
$615$		0			0
$616$	6.73132	−	3.88633i	0.271213	−	0.156585i
$617$	1.03978			0.0418598			0.0209299	−	0.999781i	$-0.493337\pi$
$617$	1.03978			0.0418598			0.0209299	+	0.999781i	$0.493337\pi$
$618$		0			0
$619$	−17.8366	−	30.8940i	−0.716915	−	1.24173i	−0.962216	−	0.272287i	$-0.912220\pi$
$619$	−17.8366	−	30.8940i	−0.716915	−	1.24173i	0.245301	−	0.969447i	$-0.421113\pi$
$620$	0.562820	+	0.974832i	0.0226034	+	0.0391502i
$621$		0			0
$622$	0.183368	−	0.317602i	0.00735238	−	0.0127347i
$623$	18.0763	−	10.4364i	0.724214	−	0.418125i
$624$		0			0
$625$	−2.15501	−	3.73259i	−0.0862005	−	0.149304i
$626$	−2.48203	−	4.29901i	−0.0992020	−	0.171823i
$627$		0			0
$628$	−2.26112	−	3.91637i	−0.0902283	−	0.156280i
$629$	4.62662	+	7.18080i	0.184476	+	0.286317i
$630$		0			0
$631$	1.39099	−	0.803091i	0.0553746	−	0.0319705i	−0.472057	−	0.881568i	$-0.656488\pi$
$631$	1.39099	−	0.803091i	0.0553746	−	0.0319705i	0.527432	+	0.849597i	$0.323155\pi$
$632$	2.26276			0.0900076
$633$		0			0
$634$	−25.4082	+	14.6694i	−1.00909	+	0.582598i
$635$	−8.85721	−	5.11371i	−0.351488	−	0.202932i
$636$		0			0
$637$	0.889398	−	0.513494i	0.0352392	−	0.0203454i
$638$	−6.73393	−	11.6635i	−0.266599	−	0.461763i
$639$		0			0
$640$	−1.23967			−0.0490022
$641$	−15.0018	+	25.9839i	−0.592535	+	1.02630i	0.401354	+	0.915923i	$0.368540\pi$
$641$	−15.0018	+	25.9839i	−0.592535	+	1.02630i	−0.993890	+	0.110378i	$0.964794\pi$
$642$		0			0
$643$	22.8805	+	13.2100i	0.902317	+	0.520953i	0.877951	−	0.478750i	$-0.158910\pi$
$643$	22.8805	+	13.2100i	0.902317	+	0.520953i	0.0243658	+	0.999703i	$0.492243\pi$
$644$			8.43438i			0.332361i
$645$		0			0
$646$	1.68015	+	0.970033i	0.0661045	+	0.0381654i
$647$	33.6835	+	19.4472i	1.32424	+	0.764548i	0.984401	−	0.175937i	$-0.0562956\pi$
$647$	33.6835	+	19.4472i	1.32424	+	0.764548i	0.339835	+	0.940485i	$0.389629\pi$
$648$		0			0
$649$	−25.0040	+	14.4361i	−0.981493	+	0.566665i
$650$	3.33431	−	5.77520i	0.130783	−	0.226522i
$651$		0			0
$652$	12.1660	+	7.02404i	0.476457	+	0.275083i
$653$	18.5354	−	10.7014i	0.725345	−	0.418778i	−0.0913717	−	0.995817i	$-0.529125\pi$
$653$	18.5354	−	10.7014i	0.725345	−	0.418778i	0.816717	+	0.577039i	$0.195792\pi$
$654$		0			0
$655$	−6.06651	−	10.5075i	−0.237038	−	0.410562i
$656$	−11.5645			−0.451518
$657$		0			0
$658$			13.9318i			0.543119i
$659$	10.5331			0.410310			0.205155	−	0.978729i	$-0.434230\pi$
$659$	10.5331			0.410310			0.205155	+	0.978729i	$0.434230\pi$
$660$		0			0
$661$	−22.9872	+	13.2716i	−0.894097	+	0.516207i	−0.875280	−	0.483616i	$-0.839323\pi$
$661$	−22.9872	+	13.2716i	−0.894097	+	0.516207i	−0.0188163	+	0.999823i	$0.505990\pi$
$662$	−12.4255	−	21.5217i	−0.482932	−	0.836464i
$663$		0			0
$664$	−2.98542	−	1.72363i	−0.115857	−	0.0668898i
$665$	−4.70052			−0.182278
$666$		0			0
$667$	14.6144			0.565873
$668$	−9.59165	−	5.53774i	−0.371112	−	0.214262i
$669$		0			0
$670$	7.84074	+	13.5806i	0.302914	+	0.524663i
$671$	5.41039	−	3.12369i	0.208866	−	0.120589i
$672$		0			0
$673$	−13.9001			−0.535809			−0.267905	−	0.963445i	$-0.586331\pi$
$673$	−13.9001			−0.535809			−0.267905	+	0.963445i	$0.586331\pi$
$674$			17.3542i			0.668458i
$675$		0			0
$676$	−9.29223			−0.357394
$677$	12.7769	+	22.1302i	0.491055	+	0.850533i	0.999947	−	0.0102977i	$-0.00327793\pi$
$677$	12.7769	+	22.1302i	0.491055	+	0.850533i	−0.508892	+	0.860831i	$0.669945\pi$
$678$		0			0
$679$	9.88872	−	5.70925i	0.379494	−	0.219101i
$680$	−1.50767	−	0.870453i	−0.0578164	−	0.0333803i
$681$		0			0
$682$	−1.28570	+	2.22690i	−0.0492320	+	0.0852723i
$683$	24.3837	−	14.0780i	0.933018	−	0.538678i	0.0452530	−	0.998976i	$-0.485591\pi$
$683$	24.3837	−	14.0780i	0.933018	−	0.538678i	0.887765	+	0.460298i	$0.152257\pi$
$684$		0			0
$685$	−0.742122	−	0.428464i	−0.0283550	−	0.0163708i
$686$	15.3711	+	8.87449i	0.586870	+	0.338830i
$687$		0			0
$688$		−	3.53643i		−	0.134825i
$689$	−16.7679	−	9.68096i	−0.638807	−	0.368815i
$690$		0			0
$691$	−15.8596	+	27.4696i	−0.603327	+	1.04499i	0.388986	+	0.921244i	$0.372825\pi$
$691$	−15.8596	+	27.4696i	−0.603327	+	1.04499i	−0.992313	+	0.123750i	$0.960508\pi$
$692$	−6.56979			−0.249746
$693$		0			0
$694$	−1.32392	−	2.29310i	−0.0502553	−	0.0870447i
$695$	−22.2128	+	12.8246i	−0.842581	+	0.486464i
$696$		0			0
$697$	−14.0646	−	8.12019i	−0.532734	−	0.307574i
$698$	25.6036	−	14.7822i	0.969109	−	0.559515i
$699$		0			0
$700$	−9.50549			−0.359274
$701$	9.75364	−	5.63127i	0.368390	−	0.212690i	−0.304365	−	0.952556i	$-0.598444\pi$
$701$	9.75364	−	5.63127i	0.368390	−	0.212690i	0.672755	+	0.739865i	$0.265111\pi$
$702$		0			0
$703$	3.84191	−	7.47358i	0.144900	−	0.281872i
$704$	−1.41594	−	2.45249i	−0.0533654	−	0.0924315i
$705$		0			0
$706$	15.7190	+	27.2261i	0.591592	+	1.02467i
$707$	21.4200	+	37.1006i	0.805583	+	1.39531i
$708$		0			0
$709$	26.4971	−	15.2981i	0.995118	−	0.574532i	0.0883182	−	0.996092i	$-0.471851\pi$
$709$	26.4971	−	15.2981i	0.995118	−	0.574532i	0.906800	+	0.421560i	$0.138517\pi$
$710$	−0.636655	+	1.10272i	−0.0238932	+	0.0413843i
$711$		0			0
$712$	−3.80239	−	6.58592i	−0.142500	−	0.246818i
$713$	−1.39516	−	2.41648i	−0.0522490	−	0.0904980i
$714$		0			0
$715$	−6.75986			−0.252804
$716$	0.292965	−	0.169143i	0.0109486	−	0.00632118i
$717$		0			0
$718$	−1.37074	−	0.791396i	−0.0511555	−	0.0295346i
$719$	−8.23394	−	14.2616i	−0.307074	−	0.531868i	0.670647	−	0.741777i	$-0.266017\pi$
$719$	−8.23394	−	14.2616i	−0.307074	−	0.531868i	−0.977721	+	0.209909i	$0.932683\pi$
$720$		0			0
$721$	14.9144	+	8.61081i	0.555440	+	0.320683i
$722$			17.0915i			0.636080i
$723$		0			0
$724$	−2.50918			−0.0932529
$725$			16.4704i			0.611694i
$726$		0			0
$727$		−	51.2617i		−	1.90119i	−0.310433	−	0.950595i	$-0.600474\pi$
$727$		−	51.2617i		−	1.90119i	0.310433	−	0.950595i	$-0.399526\pi$
$728$	−2.64253	−	4.57700i	−0.0979387	−	0.169635i
$729$		0			0
$730$	−3.36210			−0.124437
$731$	2.48316	−	4.30097i	0.0918431	−	0.159077i
$732$		0			0
$733$	4.17357	+	7.22884i	0.154154	+	0.267003i	0.932751	−	0.360522i	$-0.117401\pi$
$733$	4.17357	+	7.22884i	0.154154	+	0.267003i	−0.778596	+	0.627525i	$0.784068\pi$
$734$	12.6357	+	7.29522i	0.466392	+	0.269272i
$735$		0			0
$736$	3.07298			0.113271
$737$	−17.9113	+	31.0233i	−0.659771	+	1.14276i
$738$		0			0
$739$	50.5573			1.85978			0.929891	−	0.367836i	$-0.119901\pi$
$739$	50.5573			1.85978			0.929891	+	0.367836i	$0.119901\pi$
$740$	−3.44751	+	6.70637i	−0.126733	+	0.246531i
$741$		0			0
$742$			27.5985i			1.01317i
$743$	7.67532	+	13.2940i	0.281580	+	0.487711i	0.971774	−	0.235913i	$-0.0758082\pi$
$743$	7.67532	+	13.2940i	0.281580	+	0.487711i	−0.690194	+	0.723624i	$0.742475\pi$
$744$		0			0
$745$			15.5301i			0.568977i
$746$			14.4684i			0.529725i
$747$		0			0
$748$		−	3.97691i		−	0.145410i
$749$	−15.1555	+	26.2501i	−0.553769	+	0.959156i
$750$		0			0
$751$	−15.8638	+	27.4769i	−0.578877	+	1.00264i	0.416731	+	0.909030i	$0.363176\pi$
$751$	−15.8638	+	27.4769i	−0.578877	+	1.00264i	−0.995608	+	0.0936151i	$0.970158\pi$
$752$	5.07591			0.185100
$753$		0			0
$754$	−7.93066	+	4.57877i	−0.288818	+	0.166749i
$755$	1.96478	−	1.13437i	0.0715058	−	0.0412839i
$756$		0			0
$757$	−7.64086	+	4.41145i	−0.277712	+	0.160337i	−0.632387	−	0.774653i	$-0.717925\pi$
$757$	−7.64086	+	4.41145i	−0.277712	+	0.160337i	0.354675	+	0.934990i	$0.384591\pi$
$758$		−	27.2118i		−	0.988378i
$759$		0			0
$760$			1.71259i			0.0621220i
$761$	−53.2098			−1.92886			−0.964428	−	0.264347i	$-0.914844\pi$
$761$	−53.2098			−1.92886			−0.964428	+	0.264347i	$0.914844\pi$
$762$		0			0
$763$	7.87123	−	4.54446i	0.284958	−	0.164520i
$764$	9.28198	+	5.35895i	0.335810	+	0.193880i
$765$		0			0
$766$	14.7601			0.533303
$767$	9.81588	+	17.0016i	0.354431	+	0.613892i
$768$		0			0
$769$	−28.4605	−	16.4317i	−1.02631	−	0.592542i	−0.110386	−	0.993889i	$-0.535209\pi$
$769$	−28.4605	−	16.4317i	−1.02631	−	0.592542i	−0.915926	+	0.401347i	$0.868542\pi$
$770$	4.81776	+	8.34461i	0.173620	+	0.300719i
$771$		0			0
$772$		−	0.881856i		−	0.0317387i
$773$	14.5634	−	25.2246i	0.523811	−	0.907267i	−0.475805	−	0.879551i	$-0.657843\pi$
$773$	14.5634	−	25.2246i	0.523811	−	0.907267i	0.999616	−	0.0277160i	$-0.00882340\pi$
$774$		0			0
$775$	2.72336	−	1.57233i	0.0978259	−	0.0564798i
$776$	−2.08011	−	3.60285i	−0.0746715	−	0.129335i
$777$		0			0
$778$	9.19046	−	15.9183i	0.329494	−	0.570700i
$779$			15.9762i			0.572407i
$780$		0			0
$781$	−2.90874			−0.104083
$782$	3.73731	+	2.15774i	0.133646	+	0.0771606i
$783$		0			0
$784$	−0.266673	+	0.461891i	−0.00952404	+	0.0164961i
$785$	4.85500	−	2.80303i	0.173282	−	0.100045i
$786$		0			0
$787$	23.9599	−	41.4998i	0.854078	−	1.47931i	−0.0234194	−	0.999726i	$-0.507455\pi$
$787$	23.9599	−	41.4998i	0.854078	−	1.47931i	0.877498	−	0.479581i	$-0.159211\pi$
$788$	−10.0925	+	17.4808i	−0.359531	+	0.622726i
$789$		0			0
$790$			2.80507i			0.0997998i
$791$			42.9664i			1.52771i
$792$		0			0
$793$	−2.12397	−	3.67882i	−0.0754244	−	0.130639i
$794$	4.77682	+	2.75790i	0.169523	+	0.0978742i
$795$		0			0
$796$	17.9415	−	10.3585i	0.635918	−	0.367147i
$797$		−	20.2379i		−	0.716862i	−0.933556	−	0.358431i	$-0.883312\pi$
$797$		−	20.2379i		−	0.716862i	0.933556	−	0.358431i	$-0.116688\pi$
$798$		0			0
$799$	6.17326	+	3.56413i	0.218394	+	0.126090i
$800$			3.46322i			0.122443i
$801$		0			0
$802$	5.42047	+	9.38853i	0.191404	+	0.331521i
$803$	−3.84018	−	6.65139i	−0.135517	−	0.234722i
$804$		0			0
$805$	−10.4558			−0.368520
$806$	1.51419	+	0.874219i	0.0533351	+	0.0307930i
$807$		0			0
$808$	13.5172	−	7.80416i	0.475534	−	0.274549i
$809$	36.5839	+	21.1217i	1.28622	+	0.742600i	0.977978	−	0.208707i	$-0.0669255\pi$
$809$	36.5839	+	21.1217i	1.28622	+	0.742600i	0.308244	+	0.951307i	$0.400259\pi$
$810$		0			0
$811$	−3.98436	+	6.90111i	−0.139910	+	0.242331i	−0.927462	−	0.373917i	$-0.878015\pi$
$811$	−3.98436	+	6.90111i	−0.139910	+	0.242331i	0.787553	+	0.616247i	$0.211348\pi$
$812$	11.3044	+	6.52659i	0.396706	+	0.229039i
$813$		0			0
$814$	−17.2052	+	0.839634i	−0.603043	+	0.0294292i
$815$	−8.70748	+	15.0818i	−0.305010	+	0.528292i
$816$		0			0
$817$	−4.88554			−0.170923
$818$	2.77369	−	4.80418i	0.0969800	−	0.167974i
$819$		0			0
$820$		−	14.3361i		−	0.500640i
$821$	13.8133			0.482088			0.241044	−	0.970514i	$-0.422510\pi$
$821$	13.8133			0.482088			0.241044	+	0.970514i	$0.422510\pi$
$822$		0			0
$823$	−14.1193			−0.492167			−0.246083	−	0.969249i	$-0.579144\pi$
$823$	−14.1193			−0.492167			−0.246083	+	0.969249i	$0.579144\pi$
$824$	3.13726	−	5.43389i	0.109292	−	0.189299i
$825$		0			0
$826$	13.9916	−	24.2341i	0.486829	−	0.843213i
$827$	17.4898	+	10.0977i	0.608179	+	0.351132i	0.772252	−	0.635316i	$-0.219130\pi$
$827$	17.4898	+	10.0977i	0.608179	+	0.351132i	−0.164074	+	0.986448i	$0.552463\pi$
$828$		0			0
$829$	41.7968	−	24.1314i	1.45166	−	0.838118i	0.453087	−	0.891466i	$-0.350323\pi$
$829$	41.7968	−	24.1314i	1.45166	−	0.838118i	0.998576	+	0.0533481i	$0.0169893\pi$
$830$	2.13673	−	3.70092i	0.0741670	−	0.128461i
$831$		0			0
$832$	−1.66758	+	0.962778i	−0.0578130	+	0.0333783i
$833$	−0.648649	+	0.374497i	−0.0224743	+	0.0129756i
$834$		0			0
$835$	6.86496	−	11.8905i	0.237572	−	0.411487i
$836$	−3.38808	+	1.95611i	−0.117179	+	0.0676534i
$837$		0			0
$838$	5.45422	+	3.14900i	0.188413	+	0.108780i
$839$	13.7503	−	23.8162i	0.474713	−	0.822226i	−0.524868	−	0.851184i	$-0.675885\pi$
$839$	13.7503	−	23.8162i	0.474713	−	0.822226i	0.999581	+	0.0289573i	$0.00921869\pi$
$840$		0			0
$841$	−3.19123	+	5.52738i	−0.110042	+	0.190599i
$842$	34.3875			1.18507
$843$		0			0
$844$	−17.5823			−0.605207
$845$		−	11.5193i		−	0.396276i
$846$		0			0
$847$	4.09017	−	7.08438i	0.140540	−	0.243422i
$848$	10.0552			0.345298
$849$		0			0
$850$	−2.43176	+	4.21193i	−0.0834086	+	0.144468i
$851$	8.54593	−	16.6242i	0.292951	−	0.569871i
$852$		0			0
$853$	41.7596	+	24.1099i	1.42982	+	0.825507i	0.997106	−	0.0760245i	$-0.0242227\pi$
$853$	41.7596	+	24.1099i	1.42982	+	0.825507i	0.432714	+	0.901531i	$0.357556\pi$
$854$	−3.02751	+	5.24381i	−0.103599	+	0.179439i
$855$		0			0
$856$	9.56393	+	5.52174i	0.326888	+	0.188729i
$857$	−1.11957	+	0.646384i	−0.0382438	+	0.0220801i	−0.519000	−	0.854774i	$-0.673696\pi$
$857$	−1.11957	+	0.646384i	−0.0382438	+	0.0220801i	0.480756	+	0.876854i	$0.340362\pi$
$858$		0			0
$859$	36.3089	+	20.9629i	1.23884	+	0.715246i	0.968858	−	0.247619i	$-0.0796480\pi$
$859$	36.3089	+	20.9629i	1.23884	+	0.715246i	0.269985	+	0.962865i	$0.412981\pi$
$860$	4.38401			0.149493
$861$		0			0
$862$	12.0705	+	20.9067i	0.411123	+	0.712087i
$863$	12.6948	+	21.9880i	0.432136	+	0.748481i	0.997057	−	0.0766639i	$-0.0244268\pi$
$863$	12.6948	+	21.9880i	0.432136	+	0.748481i	−0.564921	+	0.825145i	$0.691093\pi$
$864$		0			0
$865$		−	8.14436i		−	0.276917i
$866$	14.9897	+	8.65431i	0.509371	+	0.294086i
$867$		0			0
$868$		−	2.49223i		−	0.0845917i
$869$	−5.54938	+	3.20394i	−0.188250	+	0.108686i
$870$		0			0
$871$	21.0944	+	12.1789i	0.714758	+	0.412666i
$872$	−1.65572	−	2.86780i	−0.0560699	−	0.0971159i
$873$		0			0
$874$		−	4.24527i		−	0.143599i
$875$		−	28.7962i		−	0.973489i
$876$		0			0
$877$	−5.78085	+	10.0127i	−0.195205	+	0.338106i	−0.946968	−	0.321328i	$-0.895871\pi$
$877$	−5.78085	+	10.0127i	−0.195205	+	0.338106i	0.751762	+	0.659434i	$0.229204\pi$
$878$	−4.33400	+	7.50670i	−0.146265	+	0.253339i
$879$		0			0
$880$	3.04027	−	1.75530i	0.102487	−	0.0591711i
$881$	15.2766	−	26.4598i	0.514681	−	0.891453i	−0.485174	−	0.874418i	$-0.661244\pi$
$881$	15.2766	−	26.4598i	0.514681	−	0.891453i	0.999855	−	0.0170357i	$-0.00542290\pi$
$882$		0			0
$883$	34.8864	+	20.1417i	1.17402	+	0.677821i	0.954624	−	0.297815i	$-0.0962579\pi$
$883$	34.8864	+	20.1417i	1.17402	+	0.677821i	0.219396	+	0.975636i	$0.429591\pi$
$884$	−2.70412			−0.0909494
$885$		0			0
$886$			11.9097i			0.400114i
$887$	9.33434	−	16.1675i	0.313416	−	0.542853i	−0.665683	−	0.746234i	$-0.731860\pi$
$887$	9.33434	−	16.1675i	0.313416	−	0.542853i	0.979100	+	0.203381i	$0.0651931\pi$
$888$		0			0
$889$	11.3220	+	19.6104i	0.379729	+	0.657710i
$890$	8.16436	−	4.71370i	0.273670	−	0.158003i
$891$		0			0
$892$	−6.17989	+	10.7039i	−0.206918	+	0.358393i
$893$		−	7.01231i		−	0.234658i
$894$		0			0
$895$	0.209681	+	0.363179i	0.00700888	+	0.0121397i
$896$	2.37697	+	1.37235i	0.0794092	+	0.0458469i
$897$		0			0
$898$	4.93436	+	8.54656i	0.164662	+	0.285202i
$899$	−4.31834			−0.144025
$900$		0			0
$901$	12.2290	+	7.06044i	0.407409	+	0.235217i
$902$	28.3618	−	16.3747i	0.944343	−	0.545217i
$903$		0			0
$904$	15.6543			0.520656
$905$		−	3.11055i		−	0.103398i
$906$		0			0
$907$			36.6702i			1.21761i	0.793319	+	0.608807i	$0.208352\pi$
$907$			36.6702i			1.21761i	−0.793319	+	0.608807i	$0.791648\pi$
$908$	22.3018	−	12.8759i	0.740111	−	0.427303i
$909$		0			0
$910$	5.67396	−	3.27586i	0.188090	−	0.108594i
$911$	7.08375	−	4.08980i	0.234695	−	0.135501i	−0.378041	−	0.925789i	$-0.623402\pi$
$911$	7.08375	−	4.08980i	0.234695	−	0.135501i	0.612736	+	0.790288i	$0.290069\pi$
$912$		0			0
$913$	9.76225			0.323083
$914$	−2.65476	+	4.59817i	−0.0878115	+	0.152094i
$915$		0			0
$916$	−9.25384	+	16.0281i	−0.305756	+	0.529584i
$917$			26.8632i			0.887100i
$918$		0			0
$919$		−	14.9852i		−	0.494317i	−0.968975	−	0.247158i	$-0.920503\pi$
$919$		−	14.9852i		−	0.494317i	0.968975	−	0.247158i	$-0.0794968\pi$
$920$			3.80947i			0.125594i
$921$		0			0
$922$	−6.30837	−	10.9264i	−0.207755	−	0.359842i
$923$			1.97781i			0.0651005i
$924$		0			0
$925$	18.7354	+	9.63121i	0.616016	+	0.316672i
$926$	−37.8028			−1.24228
$927$		0			0
$928$	2.37789	−	4.11863i	0.0780582	−	0.135201i
$929$	8.20071			0.269057			0.134528	−	0.990910i	$-0.457048\pi$
$929$	8.20071			0.269057			0.134528	+	0.990910i	$0.457048\pi$
$930$		0			0
$931$	0.638097	+	0.368405i	0.0209128	+	0.0120740i
$932$	2.22839	+	3.85969i	0.0729935	+	0.126428i
$933$		0			0
$934$	−11.1944	+	19.3893i	−0.366293	+	0.634439i
$935$	4.93005			0.161230
$936$		0			0
$937$	15.5944	+	27.0103i	0.509447	+	0.882389i	0.999940	+	0.0109436i	$0.00348352\pi$
$937$	15.5944	+	27.0103i	0.509447	+	0.882389i	−0.490493	+	0.871445i	$0.663183\pi$
$938$		−	34.7196i		−	1.13364i
$939$		0			0
$940$			6.29245i			0.205237i
$941$	−9.67245			−0.315313			−0.157656	−	0.987494i	$-0.550394\pi$
$941$	−9.67245			−0.315313			−0.157656	+	0.987494i	$0.550394\pi$
$942$		0			0
$943$			35.5374i			1.15726i
$944$	−8.82945	−	5.09768i	−0.287374	−	0.165915i
$945$		0			0
$946$	5.00739	+	8.67305i	0.162804	+	0.281985i
$947$	41.4975	+	23.9586i	1.34849	+	0.778550i	0.988035	−	0.154227i	$-0.0492887\pi$
$947$	41.4975	+	23.9586i	1.34849	+	0.778550i	0.360453	+	0.932777i	$0.382622\pi$
$948$		0			0
$949$	−4.52265	+	2.61115i	−0.146811	+	0.0847615i
$950$	4.78440			0.155226
$951$		0			0
$952$	1.92723	+	3.33806i	0.0624619	+	0.108187i
$953$	−5.68521	−	9.84707i	−0.184162	−	0.318978i	0.759132	−	0.650937i	$-0.225624\pi$
$953$	−5.68521	−	9.84707i	−0.184162	−	0.318978i	−0.943294	+	0.331959i	$0.892290\pi$
$954$		0			0
$955$	−6.64333	+	11.5066i	−0.214973	+	0.372344i
$956$	9.30764	−	5.37377i	0.301031	−	0.173800i
$957$		0			0
$958$	6.65609	+	11.5287i	0.215048	+	0.372475i
$959$	0.948644	+	1.64310i	0.0306333	+	0.0530584i
$960$		0			0
$961$	−15.0878	−	26.1328i	−0.486702	−	0.842992i
$962$	0.570914	+	11.6988i	0.0184070	+	0.377184i
$963$		0			0
$964$	−3.29747	+	1.90380i	−0.106204	+	0.0613172i
$965$	1.09321			0.0351916
$966$		0			0
$967$	−25.3595	+	14.6413i	−0.815506	+	0.470833i	−0.848864	−	0.528611i	$-0.822713\pi$
$967$	−25.3595	+	14.6413i	−0.815506	+	0.470833i	0.0333580	+	0.999443i	$0.489380\pi$
$968$	−2.58112	−	1.49021i	−0.0829603	−	0.0478972i
$969$		0			0
$970$	4.46634	−	2.57864i	0.143405	−	0.0827952i
$971$	−26.3852	−	45.7005i	−0.846741	−	1.46660i	−0.884100	−	0.467297i	$-0.845228\pi$
$971$	−26.3852	−	45.7005i	−0.846741	−	1.46660i	0.0373590	−	0.999302i	$-0.488105\pi$
$972$		0			0
$973$	56.7887			1.82056
$974$	−20.3051	+	35.1695i	−0.650617	+	1.12690i
$975$		0			0
$976$	1.91052	+	1.10304i	0.0611544	+	0.0353075i
$977$			36.7331i			1.17520i	0.809153	+	0.587598i	$0.199926\pi$
$977$			36.7331i			1.17520i	−0.809153	+	0.587598i	$0.800074\pi$
$978$		0			0
$979$	18.6506	+	10.7679i	0.596075	+	0.344144i
$980$	−0.572592	−	0.330586i	−0.0182908	−	0.0105602i
$981$		0			0
$982$	−3.83043	+	2.21150i	−0.122234	+	0.0705719i
$983$	5.64502	−	9.77747i	0.180048	−	0.311853i	−0.761848	−	0.647755i	$-0.775708\pi$
$983$	5.64502	−	9.77747i	0.180048	−	0.311853i	0.941897	+	0.335903i	$0.109041\pi$
$984$		0			0
$985$	−21.6703	−	12.5114i	−0.690475	−	0.398646i
$986$	5.78393	−	3.33935i	0.184198	−	0.106347i
$987$		0			0
$988$	1.33007	+	2.30374i	0.0423150	+	0.0732917i
$989$	−10.8674			−0.345562
$990$		0			0
$991$		−	23.3231i		−	0.740882i	−0.928856	−	0.370441i	$-0.879207\pi$
$991$		−	23.3231i		−	0.740882i	0.928856	−	0.370441i	$-0.120793\pi$
$992$	−0.908017			−0.0288296
$993$		0			0
$994$	2.44148	−	1.40959i	0.0774391	−	0.0447095i
$995$	12.8411	+	22.2414i	0.407090	+	0.705101i
$996$		0			0
$997$	8.79770	+	5.07935i	0.278626	+	0.160865i	0.632801	−	0.774314i	$-0.281905\pi$
$997$	8.79770	+	5.07935i	0.278626	+	0.160865i	−0.354175	+	0.935179i	$0.615238\pi$
$998$	−18.9262			−0.599099
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1998.2.t.a.307.5		76
3.2	odd	2		666.2.t.a.85.33	yes	76
9.2	odd	6		666.2.k.a.529.1	yes	76
9.7	even	3		1998.2.k.a.1639.29		76
37.27	even	6		1998.2.k.a.1063.10		76
111.101	odd	6		666.2.k.a.175.20	✓	76
333.101	odd	6		666.2.t.a.619.33	yes	76
333.286	even	6	inner	1998.2.t.a.397.5		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.20	✓	76	111.101	odd	6
666.2.k.a.529.1	yes	76	9.2	odd	6
666.2.t.a.85.33	yes	76	3.2	odd	2
666.2.t.a.619.33	yes	76	333.101	odd	6
1998.2.k.a.1063.10		76	37.27	even	6
1998.2.k.a.1639.29		76	9.7	even	3
1998.2.t.a.307.5		76	1.1	even	1	trivial
1998.2.t.a.397.5		76	333.286	even	6	inner

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:	\( N \)	\(=\)	\( 1998 = 2 \cdot 3^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1998.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.07358 + 0.619834i) q^{5} +2.74469 q^{7} -1.00000i q^{8} +1.23967 q^{10} +(1.41594 + 2.45249i) q^{11} +(1.66758 - 0.962778i) q^{13} +(-2.37697 - 1.37235i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.21619 + 0.702166i) q^{17} +(1.19640 + 0.690743i) q^{19} +(-1.07358 - 0.619834i) q^{20} -2.83189i q^{22} +(2.66127 + 1.53649i) q^{23} +(-1.73161 + 2.99924i) q^{25} -1.92556 q^{26} +(1.37235 + 2.37697i) q^{28} +(4.11863 - 2.37789i) q^{29} +(-0.786366 - 0.454008i) q^{31} +(0.866025 - 0.500000i) q^{32} +1.40433 q^{34} +(-2.94666 + 1.70126i) q^{35} +(-0.296493 - 6.07553i) q^{37} +(-0.690743 - 1.19640i) q^{38} +(0.619834 + 1.07358i) q^{40} +(5.78225 + 10.0151i) q^{41} +(-3.06264 + 1.76822i) q^{43} +(-1.41594 + 2.45249i) q^{44} +(-1.53649 - 2.66127i) q^{46} +(-2.53796 - 4.39587i) q^{47} +0.533346 q^{49} +(2.99924 - 1.73161i) q^{50} +(1.66758 + 0.962778i) q^{52} +(-5.02762 - 8.70809i) q^{53} +(-3.04027 - 1.75530i) q^{55} -2.74469i q^{56} -4.75579 q^{58} +10.1954i q^{59} -2.20608i q^{61} +(0.454008 + 0.786366i) q^{62} -1.00000 q^{64} +(-1.19353 + 2.06725i) q^{65} +(6.32487 + 10.9550i) q^{67} +(-1.21619 - 0.702166i) q^{68} +3.40251 q^{70} +(-0.513569 + 0.889528i) q^{71} -2.71210 q^{73} +(-2.78100 + 5.40981i) q^{74} +1.38149i q^{76} +(3.88633 + 6.73132i) q^{77} +2.26276i q^{79} -1.23967i q^{80} -11.5645i q^{82} +(1.72363 - 2.98542i) q^{83} +(0.870453 - 1.50767i) q^{85} +3.53643 q^{86} +(2.45249 - 1.41594i) q^{88} +(6.58592 - 3.80239i) q^{89} +(4.57700 - 2.64253i) q^{91} +3.07298i q^{92} +5.07591i q^{94} -1.71259 q^{95} +(3.60285 - 2.08011i) q^{97} +(-0.461891 - 0.266673i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 4 q^{7} + 4 q^{11} + 6 q^{13} - 38 q^{16} + 12 q^{23} + 50 q^{25} + 24 q^{26} + 2 q^{28} + 18 q^{29} - 6 q^{31} + 18 q^{35} + 10 q^{37} - 12 q^{38} + 36 q^{41} - 6 q^{43} - 4 q^{44} + 20 q^{47}+ \cdots + 24 q^{98}+O(q^{100}) \) 76 * q + 38 * q^4 + 4 * q^7 + 4 * q^11 + 6 * q^13 - 38 * q^16 + 12 * q^23 + 50 * q^25 + 24 * q^26 + 2 * q^28 + 18 * q^29 - 6 * q^31 + 18 * q^35 + 10 * q^37 - 12 * q^38 + 36 * q^41 - 6 * q^43 - 4 * q^44 + 20 * q^47 + 72 * q^49 + 6 * q^52 - 14 * q^53 + 16 * q^62 - 76 * q^64 + 16 * q^65 - 20 * q^67 - 2 * q^71 + 28 * q^73 + 20 * q^74 - 12 * q^77 - 32 * q^83 - 12 * q^85 + 8 * q^86 - 60 * q^89 + 42 * q^91 - 28 * q^95 + 12 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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