LMFDB - Embedded newform 270.2.p.a.259.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [270,2,Mod(49,270)] 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("270.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(270, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.p (of order $18$, degree $6$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			259.3
Character	$\chi$	$=$	270.259
Dual form			270.2.p.a.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 + 0.766044i) q^{2} +(-1.28397 - 1.16251i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.993869 - 2.00305i) q^{5} +(1.71585 - 0.236329i) q^{6} +(-3.46311 - 0.610640i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.297144 + 2.98525i) q^{9} +(0.895581 + 2.04889i) q^{10} +(-5.10364 + 1.85757i) q^{11} +(-0.921890 + 1.46633i) q^{12} +(2.59740 + 3.09546i) q^{13} +(2.69382 - 2.26039i) q^{14} +(-3.60466 + 1.41647i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-4.88082 + 2.81794i) q^{17} +(-2.47783 - 1.69125i) q^{18} +(2.74408 - 4.75289i) q^{19} +(-2.14521 - 0.630943i) q^{20} +(3.73665 + 4.80994i) q^{21} +(1.85757 - 5.10364i) q^{22} +(-5.55998 + 0.980374i) q^{23} +(-0.530694 - 1.64875i) q^{24} +(-3.02445 - 3.98155i) q^{25} -4.04083 q^{26} +(3.08886 - 4.17839i) q^{27} +3.51653i q^{28} +(-3.89133 - 3.26521i) q^{29} +(1.23195 - 3.67182i) q^{30} +(-0.162152 - 0.919611i) q^{31} +(0.342020 - 0.939693i) q^{32} +(8.71235 + 3.54796i) q^{33} +(0.978660 - 5.55026i) q^{34} +(-4.66502 + 6.32990i) q^{35} +(2.88830 - 0.811013i) q^{36} +(-1.52496 + 0.880434i) q^{37} +(1.87706 + 5.15719i) q^{38} +(0.263525 - 6.99396i) q^{39} +(1.86224 - 1.23776i) q^{40} +(-1.39959 + 1.17440i) q^{41} +(-6.08650 - 0.229333i) q^{42} +(0.251653 + 0.691411i) q^{43} +(2.71559 + 4.70354i) q^{44} +(6.27493 + 2.37175i) q^{45} +(2.82287 - 4.88936i) q^{46} +(8.06173 + 1.42150i) q^{47} +(1.60414 + 0.653259i) q^{48} +(5.04241 + 1.83529i) q^{49} +(4.99412 + 0.242427i) q^{50} +(9.54269 + 2.05585i) q^{51} +(2.59740 - 3.09546i) q^{52} -11.3915i q^{53} +(1.21536 + 5.05202i) q^{54} +(-1.35153 + 12.0690i) q^{55} +(-2.69382 - 2.26039i) q^{56} +(-9.04859 + 2.91253i) q^{57} +(5.00260 - 0.882093i) q^{58} +(-6.59417 - 2.40008i) q^{59} +(2.02090 + 3.30393i) q^{60} +(-0.372365 + 2.11179i) q^{61} +(0.808692 + 0.466899i) q^{62} +(0.793868 - 10.5197i) q^{63} +(0.500000 + 0.866025i) q^{64} +(8.78183 - 2.12624i) q^{65} +(-8.31809 + 4.39346i) q^{66} +(3.83285 + 4.56782i) q^{67} +(3.62267 + 4.31733i) q^{68} +(8.27852 + 5.20476i) q^{69} +(-1.85037 - 7.64240i) q^{70} +(-0.545952 - 0.945616i) q^{71} +(-1.23529 + 2.73387i) q^{72} +(-8.00992 - 4.62453i) q^{73} +(0.305771 - 1.73412i) q^{74} +(-0.745292 + 8.62812i) q^{75} +(-5.15719 - 1.87706i) q^{76} +(18.8088 - 3.31649i) q^{77} +(5.18829 + 4.69750i) q^{78} +(-2.33332 - 1.95789i) q^{79} +(-0.248847 + 2.22218i) q^{80} +(-8.82341 + 1.77410i) q^{81} -1.82704i q^{82} +(-3.55626 + 4.23818i) q^{83} +(4.08800 - 4.51512i) q^{84} +(0.793593 + 12.5772i) q^{85} +(-0.691411 - 0.251653i) q^{86} +(1.20050 + 8.71614i) q^{87} +(-5.34867 - 0.943114i) q^{88} +(4.29096 - 7.43216i) q^{89} +(-5.85032 + 3.28235i) q^{90} +(-7.10486 - 12.3060i) q^{91} +(1.93096 + 5.30527i) q^{92} +(-0.860858 + 1.36925i) q^{93} +(-6.27091 + 5.26192i) q^{94} +(-6.79303 - 10.2203i) q^{95} +(-1.53154 + 0.808933i) q^{96} +(-4.34698 - 11.9432i) q^{97} +(-4.64711 + 2.68301i) q^{98} +(-7.06183 - 14.6837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41}+ \cdots - 36 q^{99}+O(q^{100}) $ 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	−1.28397	−	1.16251i	−0.741299	−	0.671175i
$3$	−1.28397	−	1.16251i	−0.741299	−	0.671175i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	0.993869	−	2.00305i	0.444472	−	0.895793i
$5$	0.993869	−	2.00305i	0.444472	−	0.895793i
$6$	1.71585	−	0.236329i	0.700494	−	0.0964811i
$7$	−3.46311	−	0.610640i	−1.30893	−	0.230800i	−0.524711	−	0.851281i	$-0.675827\pi$
$7$	−3.46311	−	0.610640i	−1.30893	−	0.230800i	−0.784222	+	0.620480i	$0.786938\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	0.297144	+	2.98525i	0.0990481	+	0.995083i
$10$	0.895581	+	2.04889i	0.283208	+	0.647915i
$11$	−5.10364	+	1.85757i	−1.53880	+	0.560079i	−0.965758	−	0.259444i	$-0.916461\pi$
$11$	−5.10364	+	1.85757i	−1.53880	+	0.560079i	−0.573046	+	0.819523i	$0.694239\pi$
$12$	−0.921890	+	1.46633i	−0.266127	+	0.423293i
$13$	2.59740	+	3.09546i	0.720388	+	0.858525i	0.994668	−	0.103125i	$-0.0328841\pi$
$13$	2.59740	+	3.09546i	0.720388	+	0.858525i	−0.274281	+	0.961650i	$0.588440\pi$
$14$	2.69382	−	2.26039i	0.719954	−	0.604113i
$15$	−3.60466	+	1.41647i	−0.930720	+	0.365732i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−4.88082	+	2.81794i	−1.18377	+	0.683451i	−0.956884	−	0.290470i	$-0.906188\pi$
$17$	−4.88082	+	2.81794i	−1.18377	+	0.683451i	−0.226887	+	0.973921i	$0.572855\pi$
$18$	−2.47783	−	1.69125i	−0.584031	−	0.398633i
$19$	2.74408	−	4.75289i	0.629536	−	1.09039i	−0.358109	−	0.933680i	$-0.616578\pi$
$19$	2.74408	−	4.75289i	0.629536	−	1.09039i	0.987645	−	0.156708i	$-0.0500882\pi$
$20$	−2.14521	−	0.630943i	−0.479683	−	0.141083i
$21$	3.73665	+	4.80994i	0.815403	+	1.04961i
$22$	1.85757	−	5.10364i	0.396036	−	1.08810i
$23$	−5.55998	+	0.980374i	−1.15934	+	0.204422i	−0.720048	−	0.693925i	$-0.755880\pi$
$23$	−5.55998	+	0.980374i	−1.15934	+	0.204422i	−0.439287	+	0.898347i	$0.644769\pi$
$24$	−0.530694	−	1.64875i	−0.108327	−	0.336549i
$25$	−3.02445	−	3.98155i	−0.604890	−	0.796309i
$26$	−4.04083			−0.792472
$27$	3.08886	−	4.17839i	0.594450	−	0.804132i
$28$			3.51653i			0.664563i
$29$	−3.89133	−	3.26521i	−0.722602	−	0.606335i	0.205502	−	0.978657i	$-0.434117\pi$
$29$	−3.89133	−	3.26521i	−0.722602	−	0.606335i	−0.928104	+	0.372322i	$0.878562\pi$
$30$	1.23195	−	3.67182i	0.224923	−	0.670380i
$31$	−0.162152	−	0.919611i	−0.0291234	−	0.165167i	0.966777	−	0.255620i	$-0.0822796\pi$
$31$	−0.162152	−	0.919611i	−0.0291234	−	0.165167i	−0.995901	+	0.0904531i	$0.971168\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	8.71235	+	3.54796i	1.51663	+	0.617621i
$34$	0.978660	−	5.55026i	0.167839	−	0.951861i
$35$	−4.66502	+	6.32990i	−0.788533	+	1.06995i
$36$	2.88830	−	0.811013i	0.481383	−	0.135169i
$37$	−1.52496	+	0.880434i	−0.250701	+	0.144742i	−0.620085	−	0.784534i	$-0.712902\pi$
$37$	−1.52496	+	0.880434i	−0.250701	+	0.144742i	0.369384	+	0.929277i	$0.379569\pi$
$38$	1.87706	+	5.15719i	0.304500	+	0.836606i
$39$	0.263525	−	6.99396i	0.0421977	−	1.11993i
$40$	1.86224	−	1.23776i	0.294446	−	0.195707i
$41$	−1.39959	+	1.17440i	−0.218580	+	0.183410i	−0.745502	−	0.666503i	$-0.767790\pi$
$41$	−1.39959	+	1.17440i	−0.218580	+	0.183410i	0.526922	+	0.849913i	$0.323346\pi$
$42$	−6.08650	−	0.229333i	−0.939167	−	0.0353868i
$43$	0.251653	+	0.691411i	0.0383767	+	0.105439i	0.957401	−	0.288762i	$-0.0932436\pi$
$43$	0.251653	+	0.691411i	0.0383767	+	0.105439i	−0.919024	+	0.394201i	$0.871021\pi$
$44$	2.71559	+	4.70354i	0.409390	+	0.709085i
$45$	6.27493	+	2.37175i	0.935412	+	0.353560i
$46$	2.82287	−	4.88936i	0.416210	−	0.720897i
$47$	8.06173	+	1.42150i	1.17592	+	0.207347i	0.727265	−	0.686356i	$-0.240791\pi$
$47$	8.06173	+	1.42150i	1.17592	+	0.207347i	0.448658	+	0.893703i	$0.351902\pi$
$48$	1.60414	+	0.653259i	0.231537	+	0.0942898i
$49$	5.04241	+	1.83529i	0.720344	+	0.262184i
$50$	4.99412	+	0.242427i	0.706275	+	0.0342844i
$51$	9.54269	+	2.05585i	1.33624	+	0.287877i
$52$	2.59740	−	3.09546i	0.360194	−	0.429262i
$53$		−	11.3915i		−	1.56475i	−0.622809	−	0.782374i	$-0.714009\pi$
$53$		−	11.3915i		−	1.56475i	0.622809	−	0.782374i	$-0.285991\pi$
$54$	1.21536	+	5.05202i	0.165389	+	0.687493i
$55$	−1.35153	+	12.0690i	−0.182240	+	1.62739i
$56$	−2.69382	−	2.26039i	−0.359977	−	0.302057i
$57$	−9.04859	+	2.91253i	−1.19852	+	0.385775i
$58$	5.00260	−	0.882093i	0.656873	−	0.115825i
$59$	−6.59417	−	2.40008i	−0.858488	−	0.312464i	−0.124992	−	0.992158i	$-0.539890\pi$
$59$	−6.59417	−	2.40008i	−0.858488	−	0.312464i	−0.733496	+	0.679694i	$0.762113\pi$
$60$	2.02090	+	3.30393i	0.260897	+	0.426536i
$61$	−0.372365	+	2.11179i	−0.0476765	+	0.270387i	−0.999322	−	0.0368107i	$-0.988280\pi$
$61$	−0.372365	+	2.11179i	−0.0476765	+	0.270387i	0.951646	+	0.307198i	$0.0993913\pi$
$62$	0.808692	+	0.466899i	0.102704	+	0.0592962i
$63$	0.793868	−	10.5197i	0.100018	−	1.32536i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	8.78183	−	2.12624i	1.08925	−	0.263728i
$66$	−8.31809	+	4.39346i	−1.02389	+	0.540797i
$67$	3.83285	+	4.56782i	0.468257	+	0.558047i	0.947550	−	0.319608i	$-0.103551\pi$
$67$	3.83285	+	4.56782i	0.468257	+	0.558047i	−0.479292	+	0.877655i	$0.659107\pi$
$68$	3.62267	+	4.31733i	0.439314	+	0.523554i
$69$	8.27852	+	5.20476i	0.996617	+	0.626579i
$70$	−1.85037	−	7.64240i	−0.221161	−	0.913441i
$71$	−0.545952	−	0.945616i	−0.0647926	−	0.112224i	0.831809	−	0.555061i	$-0.187305\pi$
$71$	−0.545952	−	0.945616i	−0.0647926	−	0.112224i	−0.896602	+	0.442837i	$0.853972\pi$
$72$	−1.23529	+	2.73387i	−0.145580	+	0.322190i
$73$	−8.00992	−	4.62453i	−0.937491	−	0.541260i	−0.0483177	−	0.998832i	$-0.515386\pi$
$73$	−8.00992	−	4.62453i	−0.937491	−	0.541260i	−0.889173	+	0.457572i	$0.848719\pi$
$74$	0.305771	−	1.73412i	0.0355452	−	0.201587i
$75$	−0.745292	+	8.62812i	−0.0860589	+	0.996290i
$76$	−5.15719	−	1.87706i	−0.591570	−	0.215314i
$77$	18.8088	−	3.31649i	2.14346	−	0.377950i
$78$	5.18829	+	4.69750i	0.587459	+	0.531887i
$79$	−2.33332	−	1.95789i	−0.262519	−	0.220279i	0.502022	−	0.864855i	$-0.332590\pi$
$79$	−2.33332	−	1.95789i	−0.262519	−	0.220279i	−0.764541	+	0.644576i	$0.777034\pi$
$80$	−0.248847	+	2.22218i	−0.0278219	+	0.248447i
$81$	−8.82341	+	1.77410i	−0.980379	+	0.197122i
$82$		−	1.82704i		−	0.201763i
$83$	−3.55626	+	4.23818i	−0.390350	+	0.465201i	−0.925052	−	0.379839i	$-0.875979\pi$
$83$	−3.55626	+	4.23818i	−0.390350	+	0.465201i	0.534703	+	0.845040i	$0.320424\pi$
$84$	4.08800	−	4.51512i	0.446038	−	0.492640i
$85$	0.793593	+	12.5772i	0.0860773	+	1.36419i
$86$	−0.691411	−	0.251653i	−0.0745567	−	0.0271364i
$87$	1.20050	+	8.71614i	0.128707	+	0.934468i
$88$	−5.34867	−	0.943114i	−0.570170	−	0.100536i
$89$	4.29096	−	7.43216i	0.454841	−	0.787807i	−0.543838	−	0.839190i	$-0.683029\pi$
$89$	4.29096	−	7.43216i	0.454841	−	0.787807i	0.998679	+	0.0513827i	$0.0163628\pi$
$90$	−5.85032	+	3.28235i	−0.616677	+	0.345990i
$91$	−7.10486	−	12.3060i	−0.744792	−	1.29002i
$92$	1.93096	+	5.30527i	0.201316	+	0.553112i
$93$	−0.860858	+	1.36925i	−0.0892668	+	0.141985i
$94$	−6.27091	+	5.26192i	−0.646795	+	0.542725i
$95$	−6.79303	−	10.2203i	−0.696951	−	1.04858i
$96$	−1.53154	+	0.808933i	−0.156313	+	0.0825614i
$97$	−4.34698	−	11.9432i	−0.441368	−	1.21265i	−0.938592	−	0.345028i	$-0.887870\pi$
$97$	−4.34698	−	11.9432i	−0.441368	−	1.21265i	0.497224	−	0.867622i	$-0.334353\pi$
$98$	−4.64711	+	2.68301i	−0.469429	+	0.271025i
$99$	−7.06183	−	14.6837i	−0.709741	−	1.47576i
$100$	−3.39587	+	3.66989i	−0.339587	+	0.366989i
$101$	−2.66665	+	15.1233i	−0.265342	+	1.50483i	0.502719	+	0.864450i	$0.332333\pi$
$101$	−2.66665	+	15.1233i	−0.265342	+	1.50483i	−0.768061	+	0.640377i	$0.778778\pi$
$102$	−7.70879	+	5.98865i	−0.763284	+	0.592965i
$103$	4.56373	−	12.5388i	0.449678	−	1.23548i	−0.483271	−	0.875471i	$-0.660551\pi$
$103$	4.56373	−	12.5388i	0.449678	−	1.23548i	0.932949	−	0.360009i	$-0.117226\pi$
$104$	0.701683	+	3.97944i	0.0688057	+	0.390216i
$105$	13.3483	−	2.70425i	1.30266	−	0.263908i
$106$	8.72642	+	7.32234i	0.847585	+	0.711208i
$107$			5.43123i			0.525056i	0.964924	+	0.262528i	$0.0845563\pi$
$107$			5.43123i			0.525056i	−0.964924	+	0.262528i	$0.915444\pi$
$108$	−4.65129	−	2.31636i	−0.447570	−	0.222892i
$109$	9.42494			0.902746			0.451373	−	0.892335i	$-0.350934\pi$
$109$	9.42494			0.902746			0.451373	+	0.892335i	$0.350934\pi$
$110$	−8.37668	−	8.79316i	−0.798685	−	0.838395i
$111$	2.98151	+	0.642327i	0.282992	+	0.0609670i
$112$	3.46311	−	0.610640i	0.327233	−	0.0577000i
$113$	4.93920	−	13.5703i	0.464641	−	1.27659i	−0.457318	−	0.889303i	$-0.651190\pi$
$113$	4.93920	−	13.5703i	0.464641	−	1.27659i	0.921959	−	0.387287i	$-0.126588\pi$
$114$	3.58519	−	8.80376i	0.335784	−	0.824548i
$115$	−3.56215	+	12.1113i	−0.332172	+	1.12938i
$116$	−2.53989	+	4.39921i	−0.235823	+	0.408457i
$117$	−8.46890	+	8.67367i	−0.782950	+	0.801881i
$118$	6.07722	−	3.50868i	0.559453	−	0.323001i
$119$	18.6236	−	6.77842i	1.70722	−	0.621377i
$120$	−3.82997	−	0.575630i	−0.349627	−	0.0525476i
$121$	14.1701	−	11.8901i	1.28819	−	1.08092i
$122$	−1.37837	−	1.64268i	−0.124792	−	0.148721i
$123$	3.16228	+	0.119151i	0.285133	+	0.0107435i
$124$	−0.877482	+	0.319377i	−0.0788002	+	0.0286809i
$125$	−10.9812	+	2.10100i	−0.982185	+	0.187919i
$126$	7.54826	+	7.37007i	0.672453	+	0.656578i
$127$	−0.871965	−	0.503429i	−0.0773744	−	0.0446721i	0.460814	−	0.887497i	$-0.347558\pi$
$127$	−0.871965	−	0.503429i	−0.0773744	−	0.0446721i	−0.538188	+	0.842825i	$0.680891\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	0.480657	−	1.18030i	0.0423195	−	0.103919i
$130$	−4.01606	+	8.09400i	−0.352231	+	0.709891i
$131$	−0.227390	−	1.28959i	−0.0198671	−	0.112672i	0.973262	−	0.229700i	$-0.0737745\pi$
$131$	−0.227390	−	1.28959i	−0.0198671	−	0.112672i	−0.993129	+	0.117028i	$0.962663\pi$
$132$	1.98118	−	9.19609i	0.172440	−	0.800417i
$133$	−12.4054	+	14.7841i	−1.07568	+	1.28195i
$134$	−5.96286			−0.515113
$135$	−5.29963	−	10.3399i	−0.456119	−	0.889919i
$136$	−5.63588			−0.483273
$137$	−7.52051	+	8.96259i	−0.642520	+	0.765726i	−0.984766	−	0.173884i	$-0.944368\pi$
$137$	−7.52051	+	8.96259i	−0.642520	+	0.765726i	0.342246	+	0.939611i	$0.388813\pi$
$138$	−9.30840	+	2.99616i	−0.792384	+	0.255050i
$139$	−0.820876	−	4.65542i	−0.0696258	−	0.394868i	−0.999627	−	0.0273111i	$-0.991306\pi$
$139$	−0.820876	−	4.65542i	−0.0696258	−	0.394868i	0.930001	−	0.367557i	$-0.119806\pi$
$140$	7.04381	+	3.49498i	0.595310	+	0.295379i
$141$	−8.69849	−	11.1970i	−0.732545	−	0.942957i
$142$	1.07532	+	0.189607i	0.0902384	+	0.0159115i
$143$	−19.0062	−	10.9732i	−1.58938	−	0.917628i
$144$	−1.30024	−	2.70359i	−0.108353	−	0.225299i
$145$	−10.4079	+	4.54935i	−0.864327	+	0.377803i
$146$	8.69128	−	3.16337i	0.719295	−	0.261802i
$147$	−4.34075	−	8.21829i	−0.358019	−	0.677833i
$148$	1.13186	+	1.34890i	0.0930386	+	0.110879i
$149$	3.36115	−	2.82034i	0.275356	−	0.231051i	−0.494643	−	0.869096i	$-0.664701\pi$
$149$	3.36115	−	2.82034i	0.275356	−	0.231051i	0.769999	+	0.638045i	$0.220257\pi$
$150$	−6.13046	−	6.11698i	−0.500550	−	0.499449i
$151$	−11.6928	+	4.25583i	−0.951547	+	0.346335i	−0.770716	−	0.637179i	$-0.780101\pi$
$151$	−11.6928	+	4.25583i	−0.951547	+	0.346335i	−0.180831	+	0.983514i	$0.557879\pi$
$152$	4.75289	−	2.74408i	0.385510	−	0.222574i
$153$	−9.86256	−	13.7331i	−0.797340	−	1.11026i
$154$	−9.54946	+	16.5402i	−0.769518	+	1.33284i
$155$	−2.00319	−	0.589173i	−0.160900	−	0.0473235i
$156$	−6.93347	+	0.954967i	−0.555122	+	0.0764586i
$157$	2.42928	−	6.67440i	0.193878	−	0.532675i	−0.804219	−	0.594332i	$-0.797416\pi$
$157$	2.42928	−	6.67440i	0.193878	−	0.532675i	0.998097	+	0.0616573i	$0.0196386\pi$
$158$	2.99965	−	0.528920i	0.238640	−	0.0420786i
$159$	−13.2428	+	14.6264i	−1.05022	+	1.15995i
$160$	−1.54233	−	1.61902i	−0.121932	−	0.127994i
$161$	19.8535			1.56467
$162$	4.31254	−	7.89949i	0.338825	−	0.620643i
$163$			20.0999i			1.57434i	0.616734	+	0.787172i	$0.288456\pi$
$163$			20.0999i			1.57434i	−0.616734	+	0.787172i	$0.711544\pi$
$164$	1.39959	+	1.17440i	0.109290	+	0.0917051i
$165$	15.7657	−	13.9251i	1.22736	−	1.08407i
$166$	−0.960718	−	5.44850i	−0.0745662	−	0.422886i
$167$	−0.926560	+	2.54570i	−0.0716993	+	0.196992i	−0.970366	−	0.241640i	$-0.922315\pi$
$167$	−0.926560	+	2.54570i	−0.0716993	+	0.196992i	0.898667	+	0.438632i	$0.144537\pi$
$168$	0.831061	+	6.03385i	0.0641177	+	0.465522i
$169$	−0.577954	+	3.27774i	−0.0444580	+	0.252134i
$170$	−10.1448	−	7.47654i	−0.778071	−	0.573424i
$171$	15.0039	+	6.77947i	1.14738	+	0.518439i
$172$	0.637208	−	0.367892i	0.0485866	−	0.0280515i
$173$	0.601954	+	1.65386i	0.0457658	+	0.125740i	0.960470	−	0.278384i	$-0.0897987\pi$
$173$	0.601954	+	1.65386i	0.0457658	+	0.125740i	−0.914704	+	0.404124i	$0.867576\pi$
$174$	−7.44862	−	4.68299i	−0.564678	−	0.355017i
$175$	8.04271	+	15.6354i	0.607972	+	1.18192i
$176$	4.16052	−	3.49109i	0.313611	−	0.263151i
$177$	5.67658	+	10.7474i	0.426678	+	0.807825i
$178$	2.93519	+	8.06437i	0.220002	+	0.604450i
$179$	−4.49872	−	7.79201i	−0.336250	−	0.582402i	0.647474	−	0.762087i	$-0.275825\pi$
$179$	−4.49872	−	7.79201i	−0.336250	−	0.582402i	−0.983724	+	0.179685i	$0.942492\pi$
$180$	1.24609	−	6.59145i	0.0928778	−	0.491298i
$181$	−10.2809	+	17.8070i	−0.764171	+	1.32358i	0.176513	+	0.984298i	$0.443518\pi$
$181$	−10.2809	+	17.8070i	−0.764171	+	1.32358i	−0.940684	+	0.339284i	$0.889815\pi$
$182$	13.9938	+	2.46749i	1.03729	+	0.182903i
$183$	2.93308	−	2.27859i	0.216819	−	0.168438i
$184$	−5.30527	−	1.93096i	−0.391109	−	0.142352i
$185$	0.247949	+	3.92961i	0.0182296	+	0.288910i
$186$	−0.495560	−	1.53959i	−0.0363362	−	0.112889i
$187$	19.6754	−	23.4482i	1.43881	−	1.71470i
$188$		−	8.18609i		−	0.597032i
$189$	−13.2485	+	12.5841i	−0.963690	+	0.915356i
$190$	12.1957	+	1.36571i	0.884767	+	0.0990792i
$191$	−0.365379	−	0.306590i	−0.0264379	−	0.0221841i	0.629473	−	0.777022i	$-0.283271\pi$
$191$	−0.365379	−	0.306590i	−0.0264379	−	0.0221841i	−0.655911	+	0.754838i	$0.727715\pi$
$192$	0.364779	−	1.69320i	0.0263257	−	0.122196i
$193$	−8.86275	+	1.56274i	−0.637955	+	0.112489i	−0.483265	−	0.875474i	$-0.660549\pi$
$193$	−8.86275	+	1.56274i	−0.637955	+	0.112489i	−0.154690	+	0.987963i	$0.549438\pi$
$194$	11.9432	+	4.34698i	0.857473	+	0.312095i
$195$	−13.7474	−	7.47893i	−0.984469	−	0.535578i
$196$	0.931799	−	5.28450i	0.0665571	−	0.377464i
$197$	0.991092	+	0.572207i	0.0706124	+	0.0407681i	0.534891	−	0.844921i	$-0.320353\pi$
$197$	0.991092	+	0.572207i	0.0706124	+	0.0407681i	−0.464278	+	0.885689i	$0.653686\pi$
$198$	15.7876	+	4.02880i	1.12198	+	0.286314i
$199$	6.60760	+	11.4447i	0.468400	+	0.811293i	0.999348	−	0.0361116i	$-0.0114972\pi$
$199$	6.60760	+	11.4447i	0.468400	+	0.811293i	−0.530947	+	0.847405i	$0.678164\pi$
$200$	−0.628476	−	4.96034i	−0.0444399	−	0.350749i
$201$	0.388871	−	10.3207i	0.0274288	−	0.727963i
$202$	−9.87105	−	11.7639i	−0.694524	−	0.827702i
$203$	11.4822	+	13.6840i	0.805895	+	0.960429i
$204$	0.367547	−	9.75471i	0.0257334	−	0.682966i
$205$	0.961370	+	3.97066i	0.0671450	+	0.277323i
$206$	6.67173	+	11.5558i	0.464841	+	0.805129i
$207$	−4.57877	−	16.3066i	−0.318247	−	1.13339i
$208$	−3.49946	−	2.02041i	−0.242644	−	0.140091i
$209$	−5.17597	+	29.3544i	−0.358029	+	2.03048i
$210$	−6.50855	+	11.9637i	−0.449132	+	0.825571i
$211$	9.94339	+	3.61910i	0.684531	+	0.249149i	0.660792	−	0.750569i	$-0.270221\pi$
$211$	9.94339	+	3.61910i	0.684531	+	0.249149i	0.0237394	+	0.999718i	$0.492443\pi$
$212$	−11.2185	+	1.97812i	−0.770488	+	0.135858i
$213$	−0.398303	+	1.84881i	−0.0272913	+	0.126679i
$214$	−4.16056	−	3.49112i	−0.284410	−	0.238648i
$215$	1.63504	+	0.183097i	0.111509	+	0.0124871i
$216$	4.76422	−	2.07417i	0.324164	−	0.141129i
$217$			3.28373i			0.222914i
$218$	−6.05824	+	7.21993i	−0.410316	+	0.488995i
$219$	4.90842	+	15.2494i	0.331680	+	1.03046i
$220$	12.1204	−	0.764769i	0.817156	−	0.0515607i
$221$	−21.4002	−	7.78904i	−1.43953	−	0.523948i
$222$	−2.40853	+	1.87109i	−0.161650	+	0.125579i
$223$	2.39964	+	0.423122i	0.160692	+	0.0283343i	0.253415	−	0.967358i	$-0.418446\pi$
$223$	2.39964	+	0.423122i	0.160692	+	0.0283343i	−0.0927233	+	0.995692i	$0.529557\pi$
$224$	−1.75827	+	3.04541i	−0.117479	+	0.203480i
$225$	10.9872	−	10.2118i	0.732480	−	0.680788i
$226$	7.22063	+	12.5065i	0.480309	+	0.831920i
$227$	4.73521	+	13.0099i	0.314287	+	0.863497i	0.991779	+	0.127966i	$0.0408449\pi$
$227$	4.73521	+	13.0099i	0.314287	+	0.863497i	−0.677491	+	0.735531i	$0.736933\pi$
$228$	4.43956	+	8.40537i	0.294017	+	0.556659i
$229$	−20.2647	+	17.0041i	−1.33913	+	1.12366i	−0.357278	+	0.933998i	$0.616295\pi$
$229$	−20.2647	+	17.0041i	−1.33913	+	1.12366i	−0.981849	+	0.189663i	$0.939260\pi$
$230$	−6.98808	−	10.5138i	−0.460781	−	0.693256i
$231$	−28.0053	−	17.6071i	−1.84261	−	1.15846i
$232$	−1.73738	−	4.77342i	−0.114065	−	0.313391i
$233$	16.6209	−	9.59607i	1.08887	−	0.628660i	0.155595	−	0.987821i	$-0.450270\pi$
$233$	16.6209	−	9.59607i	1.08887	−	0.628660i	0.933276	+	0.359161i	$0.116937\pi$
$234$	−1.20071	−	12.0629i	−0.0784928	−	0.788575i
$235$	10.8596	−	14.7353i	0.708405	−	0.961224i
$236$	−1.21855	+	6.91076i	−0.0793211	+	0.449852i
$237$	0.719843	+	5.22636i	0.0467588	+	0.339489i
$238$	−6.77842	+	18.6236i	−0.439380	+	1.20719i
$239$	0.114604	+	0.649954i	0.00741314	+	0.0420420i	0.988290	−	0.152588i	$-0.0487606\pi$
$239$	0.114604	+	0.649954i	0.00741314	+	0.0420420i	−0.980877	+	0.194630i	$0.937650\pi$
$240$	2.90281	−	2.56392i	0.187376	−	0.165500i
$241$	6.42764	+	5.39343i	0.414041	+	0.347422i	0.825891	−	0.563830i	$-0.190673\pi$
$241$	6.42764	+	5.39343i	0.414041	+	0.347422i	−0.411850	+	0.911252i	$0.635117\pi$
$242$			18.4977i			1.18908i
$243$	13.3914	+	7.97941i	0.859057	+	0.511880i
$244$	2.14437			0.137279
$245$	8.68767	−	8.27618i	0.555035	−	0.528746i
$246$	−2.12395	+	2.34586i	−0.135418	+	0.149567i
$247$	21.8398	−	3.85095i	1.38963	−	0.245030i
$248$	0.319377	−	0.877482i	0.0202805	−	0.0557202i
$249$	9.49304	−	1.30751i	0.601597	−	0.0828598i
$250$	5.44910	−	9.76255i	0.344631	−	0.617438i
$251$	12.6104	−	21.8419i	0.795963	−	1.37865i	−0.126262	−	0.991997i	$-0.540298\pi$
$251$	12.6104	−	21.8419i	0.795963	−	1.37865i	0.922226	−	0.386652i	$-0.126369\pi$
$252$	−10.4977	+	1.04492i	−0.661295	+	0.0658236i
$253$	26.5550	−	15.3315i	1.66950	−	0.963885i
$254$	0.946137	−	0.344366i	0.0593659	−	0.0216074i
$255$	13.6022	−	17.0713i	0.851800	−	1.06904i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	3.94258	+	4.69858i	0.245931	+	0.293089i	0.874862	−	0.484372i	$-0.160952\pi$
$257$	3.94258	+	4.69858i	0.245931	+	0.293089i	−0.628931	+	0.777461i	$0.716507\pi$
$258$	0.595200	+	1.12689i	0.0370555	+	0.0701568i
$259$	5.81872	−	2.11784i	0.361558	−	0.131596i
$260$	−3.61889	−	8.27920i	−0.224434	−	0.513454i
$261$	8.59119	−	12.5868i	0.531781	−	0.779105i
$262$	1.13405	+	0.654743i	0.0700617	+	0.0404501i
$263$	−12.8317	−	2.26257i	−0.791236	−	0.139516i	−0.236598	−	0.971608i	$-0.576032\pi$
$263$	−12.8317	−	2.26257i	−0.791236	−	0.139516i	−0.554639	+	0.832091i	$0.687143\pi$
$264$	5.77113	+	7.42880i	0.355189	+	0.457211i
$265$	−22.8179	−	11.3217i	−1.40169	−	0.695486i
$266$	−3.35129	−	19.0061i	−0.205481	−	1.16534i
$267$	−14.1494	+	4.55437i	−0.865930	+	0.278723i
$268$	3.83285	−	4.56782i	0.234129	−	0.279024i
$269$	−0.490553			−0.0299095			−0.0149548	−	0.999888i	$-0.504760\pi$
$269$	−0.490553			−0.0299095			−0.0149548	+	0.999888i	$0.504760\pi$
$270$	11.3274	+	2.58662i	0.689362	+	0.157417i
$271$	−26.5846			−1.61490			−0.807448	−	0.589938i	$-0.799152\pi$
$271$	−26.5846			−1.61490			−0.807448	+	0.589938i	$0.799152\pi$
$272$	3.62267	−	4.31733i	0.219657	−	0.261777i
$273$	−5.18341	+	24.0599i	−0.313714	+	1.45617i
$274$	−2.03166	−	11.5221i	−0.122737	−	0.696075i
$275$	22.8317	+	14.7022i	1.37680	+	0.886578i
$276$	3.68813	−	9.05655i	0.222000	−	0.545140i
$277$	−10.7409	−	1.89391i	−0.645359	−	0.113794i	−0.158617	−	0.987340i	$-0.550704\pi$
$277$	−10.7409	−	1.89391i	−0.645359	−	0.113794i	−0.486742	+	0.873546i	$0.661815\pi$
$278$	4.09391	+	2.36362i	0.245536	+	0.141760i
$279$	2.69708	−	0.757321i	0.161470	−	0.0453396i
$280$	−7.20498	+	3.14934i	−0.430580	+	0.188209i
$281$	20.3451	−	7.40501i	1.21369	−	0.441746i	0.345706	−	0.938343i	$-0.387639\pi$
$281$	20.3451	−	7.40501i	1.21369	−	0.441746i	0.867981	+	0.496597i	$0.165417\pi$
$282$	14.1687	+	0.533860i	0.843732	+	0.0317909i
$283$	−11.1028	−	13.2318i	−0.659994	−	0.786550i	0.327391	−	0.944889i	$-0.393831\pi$
$283$	−11.1028	−	13.2318i	−0.659994	−	0.786550i	−0.987385	+	0.158339i	$0.949386\pi$
$284$	−0.836447	+	0.701862i	−0.0496340	+	0.0416479i
$285$	−3.15915	+	21.0195i	−0.187132	+	1.24509i
$286$	20.6229	−	7.50613i	1.21946	−	0.443847i
$287$	5.56408	−	3.21242i	0.328437	−	0.189623i
$288$	2.90684	+	0.741791i	0.171287	+	0.0437104i
$289$	7.38157	−	12.7853i	0.434210	−	0.752074i
$290$	3.20505	−	10.8972i	0.188207	−	0.639903i
$291$	−8.30273	+	20.3881i	−0.486714	+	1.19517i
$292$	−3.16337	+	8.69128i	−0.185122	+	0.508618i
$293$	−5.25521	+	0.926636i	−0.307013	+	0.0541346i	−0.325032	−	0.945703i	$-0.605375\pi$
$293$	−5.25521	+	0.926636i	−0.307013	+	0.0541346i	0.0180193	+	0.999838i	$0.494264\pi$
$294$	9.08576	+	1.95741i	0.529892	+	0.114158i
$295$	−11.3612	+	10.8231i	−0.661477	+	0.630146i
$296$	−1.76087			−0.102348
$297$	−8.00273	+	27.0628i	−0.464365	+	1.57034i
$298$			4.38766i			0.254171i
$299$	−17.4762	−	14.6642i	−1.01067	−	0.848055i
$300$	8.62646	−	0.764289i	0.498049	−	0.0441262i
$301$	−0.449299	−	2.54810i	−0.0258972	−	0.146870i
$302$	4.25583	−	11.6928i	0.244896	−	0.672845i
$303$	21.0049	−	16.3178i	1.20670	−	0.937436i
$304$	−0.953010	+	5.40479i	−0.0546589	+	0.309986i
$305$	3.85994	+	2.84471i	0.221020	+	0.162888i
$306$	16.8597	+	1.27232i	0.963805	+	0.0727335i
$307$	0.787087	−	0.454425i	0.0449214	−	0.0259354i	−0.477371	−	0.878702i	$-0.658410\pi$
$307$	0.787087	−	0.454425i	0.0449214	−	0.0259354i	0.522293	+	0.852766i	$0.325077\pi$
$308$	−6.53222	−	17.9471i	−0.372208	−	1.02263i
$309$	−20.4361	+	10.7940i	−1.16257	+	0.614047i
$310$	1.73896	−	1.15582i	0.0987661	−	0.0656460i
$311$	−17.5519	+	14.7278i	−0.995274	+	0.835134i	−0.986323	−	0.164826i	$-0.947294\pi$
$311$	−17.5519	+	14.7278i	−0.995274	+	0.835134i	−0.00895145	+	0.999960i	$0.502849\pi$
$312$	3.72520	−	5.92518i	0.210898	−	0.335448i
$313$	−3.44829	−	9.47411i	−0.194909	−	0.535508i	0.803284	−	0.595596i	$-0.203084\pi$
$313$	−3.44829	−	9.47411i	−0.194909	−	0.535508i	−0.998193	+	0.0600878i	$0.980862\pi$
$314$	3.55137	+	6.15116i	0.200416	+	0.347130i
$315$	−20.2825	−	12.0454i	−1.14279	−	0.678679i
$316$	−1.52296	+	2.63785i	−0.0856734	+	0.148391i
$317$	4.99561	+	0.880860i	0.280581	+	0.0494740i	0.312168	−	0.950027i	$-0.398945\pi$
$317$	4.99561	+	0.880860i	0.280581	+	0.0494740i	−0.0315866	+	0.999501i	$0.510056\pi$
$318$	−2.69216	−	19.5462i	−0.150969	−	1.09610i
$319$	25.9253	+	9.43604i	1.45154	+	0.528317i
$320$	2.23163	−	0.140811i	0.124752	−	0.00787157i
$321$	6.31385	−	6.97352i	0.352405	−	0.389224i
$322$	−12.7616	+	15.2086i	−0.711174	+	0.847544i
$323$			30.9306i			1.72103i
$324$	3.27931	+	8.38129i	0.182184	+	0.465627i
$325$	4.46901	−	19.7037i	0.247896	−	1.09296i
$326$	−15.3974	−	12.9199i	−0.852783	−	0.715570i
$327$	−12.1013	−	10.9566i	−0.669204	−	0.605900i
$328$	−1.79928	+	0.317262i	−0.0993488	+	0.0175179i
$329$	−27.0506	−	9.84562i	−1.49135	−	0.542807i
$330$	0.533243	+	21.0281i	0.0293541	+	1.15756i
$331$	−3.15260	+	17.8793i	−0.173282	+	0.982734i	0.766825	+	0.641856i	$0.221835\pi$
$331$	−3.15260	+	17.8793i	−0.173282	+	0.982734i	−0.940108	+	0.340878i	$0.889276\pi$
$332$	4.79133	+	2.76628i	0.262958	+	0.151819i
$333$	−3.08145	−	4.29076i	−0.168862	−	0.235132i
$334$	−1.35454	−	2.34613i	−0.0741171	−	0.128375i
$335$	12.9589	−	3.13760i	0.708022	−	0.171425i
$336$	−5.15640	−	3.24186i	−0.281304	−	0.176858i
$337$	2.32809	+	2.77451i	0.126819	+	0.151137i	0.825718	−	0.564084i	$-0.190770\pi$
$337$	2.32809	+	2.77451i	0.126819	+	0.151137i	−0.698898	+	0.715221i	$0.746326\pi$
$338$	−2.13939	−	2.54963i	−0.116368	−	0.138682i
$339$	−22.1174	+	11.6820i	−1.20125	+	0.634480i
$340$	12.2483	−	2.96554i	0.664258	−	0.160829i
$341$	2.53581	+	4.39215i	0.137322	+	0.237848i
$342$	−14.8377	+	7.13593i	−0.802332	+	0.385867i
$343$	4.97614	+	2.87298i	0.268687	+	0.155126i
$344$	−0.127768	+	0.724606i	−0.00688876	+	0.0390681i
$345$	18.6532	−	11.4095i	1.00425	−	0.614265i
$346$	−1.65386	−	0.601954i	−0.0889119	−	0.0323613i
$347$	−6.61930	+	1.16716i	−0.355342	+	0.0626565i	−0.348470	−	0.937320i	$-0.613299\pi$
$347$	−6.61930	+	1.16716i	−0.355342	+	0.0626565i	−0.00687244	+	0.999976i	$0.502188\pi$
$348$	8.37526	−	2.69580i	0.448961	−	0.144510i
$349$	1.27399	+	1.06900i	0.0681951	+	0.0572225i	0.676248	−	0.736674i	$-0.263605\pi$
$349$	1.27399	+	1.06900i	0.0681951	+	0.0572225i	−0.608053	+	0.793896i	$0.708049\pi$
$350$	−17.1472	−	3.88916i	−0.916554	−	0.207884i
$351$	20.9570	−	1.29153i	1.11860	−	0.0689367i
$352$			5.43118i			0.289483i
$353$	7.69684	−	9.17274i	0.409662	−	0.488216i	−0.521279	−	0.853386i	$-0.674545\pi$
$353$	7.69684	−	9.17274i	0.409662	−	0.488216i	0.930941	+	0.365171i	$0.118989\pi$
$354$	−11.8818	−	2.55979i	−0.631512	−	0.136051i
$355$	−2.43672	+	0.153752i	−0.129328	+	0.00816031i
$356$	−8.06437	−	2.93519i	−0.427411	−	0.155565i
$357$	−31.7920	−	12.9468i	−1.68261	−	0.685216i
$358$	8.86075	+	1.56239i	0.468305	+	0.0825748i
$359$	−11.4660	+	19.8596i	−0.605151	+	1.04815i	0.386877	+	0.922131i	$0.373554\pi$
$359$	−11.4660	+	19.8596i	−0.605151	+	1.04815i	−0.992028	+	0.126020i	$0.959780\pi$
$360$	4.24838	+	5.19146i	0.223909	+	0.273614i
$361$	−5.55997	−	9.63016i	−0.292630	−	0.506850i
$362$	−7.03253	−	19.3217i	−0.369621	−	1.01553i
$363$	−32.0162	−	1.20634i	−1.68042	−	0.0633162i
$364$	−10.8853	+	9.13383i	−0.570543	+	0.478743i
$365$	−17.2240	+	11.4481i	−0.901545	+	0.599222i
$366$	−0.139846	+	3.71152i	−0.00730987	+	0.194004i
$367$	5.15961	+	14.1759i	0.269330	+	0.739977i	0.998453	+	0.0555953i	$0.0177057\pi$
$367$	5.15961	+	14.1759i	0.269330	+	0.739977i	−0.729124	+	0.684382i	$0.760072\pi$
$368$	4.88936	−	2.82287i	0.254876	−	0.147152i
$369$	−3.92175	−	3.82917i	−0.204158	−	0.199339i
$370$	−3.16963	−	2.33596i	−0.164781	−	0.121441i
$371$	−6.95612	+	39.4501i	−0.361144	+	2.04815i
$372$	1.49794	+	0.610011i	0.0776644	+	0.0316276i
$373$	−3.31306	+	9.10256i	−0.171544	+	0.471313i	−0.995436	−	0.0954341i	$-0.969576\pi$
$373$	−3.31306	+	9.10256i	−0.171544	+	0.471313i	0.823892	+	0.566747i	$0.191798\pi$
$374$	5.31528	+	30.1444i	0.274846	+	1.55873i
$375$	16.5419	+	10.0681i	0.854219	+	0.519914i
$376$	6.27091	+	5.26192i	0.323397	+	0.271363i
$377$		−	20.5265i		−	1.05717i
$378$	−1.12395	−	18.2379i	−0.0578099	−	0.938054i
$379$	−5.56826			−0.286022			−0.143011	−	0.989721i	$-0.545678\pi$
$379$	−5.56826			−0.286022			−0.143011	+	0.989721i	$0.545678\pi$
$380$	−8.88543	+	8.46457i	−0.455813	+	0.434223i
$381$	0.534333	+	1.66005i	0.0273747	+	0.0850472i
$382$	0.469723	−	0.0828248i	0.0240331	−	0.00423769i
$383$	−5.14423	+	14.1337i	−0.262858	+	0.722197i	0.736114	+	0.676858i	$0.236659\pi$
$383$	−5.14423	+	14.1337i	−0.262858	+	0.722197i	−0.998972	+	0.0453387i	$0.985563\pi$
$384$	1.06259	+	1.36781i	0.0542252	+	0.0698006i
$385$	12.0503	−	40.9711i	0.614142	−	2.08808i
$386$	4.49974	−	7.79377i	0.229031	−	0.396693i
$387$	−1.98926	+	0.956695i	−0.101120	+	0.0486315i
$388$	−11.0069	+	6.35485i	−0.558792	+	0.322619i
$389$	−1.64772	+	0.599721i	−0.0835428	+	0.0304071i	−0.383453	−	0.923560i	$-0.625265\pi$
$389$	−1.64772	+	0.599721i	−0.0835428	+	0.0304071i	0.299911	+	0.953967i	$0.403043\pi$
$390$	14.5658	−	5.72373i	0.737570	−	0.289832i
$391$	24.3746	−	20.4527i	1.23268	−	1.03434i
$392$	3.44921	+	4.11061i	0.174211	+	0.207617i
$393$	−1.20720	+	1.92014i	−0.0608952	+	0.0968580i
$394$	−1.07540	+	0.391413i	−0.0541778	+	0.0197191i
$395$	−6.24076	+	2.72788i	−0.314007	+	0.137254i
$396$	−13.2343	+	9.50434i	−0.665049	+	0.477611i
$397$	−30.1903	−	17.4304i	−1.51521	−	0.874806i	−0.999841	−	0.0178373i	$-0.994322\pi$
$397$	−30.1903	−	17.4304i	−1.51521	−	0.874806i	−0.515368	−	0.856969i	$-0.672345\pi$
$398$	−13.0144	−	2.29480i	−0.652354	−	0.115028i
$399$	33.1148	−	4.56100i	1.65781	−	0.228336i
$400$	4.20382	+	2.70701i	0.210191	+	0.135350i
$401$	−6.17563	−	35.0238i	−0.308396	−	1.74900i	−0.607070	−	0.794648i	$-0.707655\pi$
$401$	−6.17563	−	35.0238i	−0.308396	−	1.74900i	0.298674	−	0.954355i	$-0.403456\pi$
$402$	7.65612	+	6.93188i	0.381852	+	0.345731i
$403$	2.42544	−	2.89053i	0.120820	−	0.143987i
$404$	15.3566			0.764020
$405$	−5.21570	+	19.4370i	−0.259170	+	0.965832i
$406$	−17.8632			−0.886536
$407$	6.14735	−	7.32613i	0.304713	−	0.363143i
$408$	7.23629	+	6.55176i	0.358250	+	0.324361i
$409$	−0.724502	−	4.10886i	−0.0358243	−	0.203170i	0.961642	−	0.274307i	$-0.0884484\pi$
$409$	−0.724502	−	4.10886i	−0.0358243	−	0.203170i	−0.997467	+	0.0711370i	$0.977337\pi$
$410$	−3.65966	−	1.81584i	−0.180738	−	0.0896779i
$411$	20.0752	−	2.76502i	0.990236	−	0.136388i
$412$	−13.1407	−	2.31707i	−0.647398	−	0.114154i
$413$	21.3708	+	12.3384i	1.05159	+	0.607133i
$414$	15.4348	+	6.97413i	0.758577	+	0.342760i
$415$	4.95485	+	11.3356i	0.243224	+	0.556441i
$416$	3.79714	−	1.38205i	0.186170	−	0.0677603i
$417$	−4.35799	+	6.93168i	−0.213412	+	0.339446i
$418$	−19.1597	−	22.8336i	−0.937131	−	1.11683i
$419$	−1.56057	+	1.30947i	−0.0762389	+	0.0639720i	−0.680111	−	0.733109i	$-0.738068\pi$
$419$	−1.56057	+	1.30947i	−0.0762389	+	0.0639720i	0.603872	+	0.797081i	$0.293624\pi$
$420$	−4.98108	−	12.6759i	−0.243052	−	0.618522i
$421$	−6.23377	+	2.26891i	−0.303816	+	0.110580i	−0.489429	−	0.872043i	$-0.662795\pi$
$421$	−6.23377	+	2.26891i	−0.303816	+	0.110580i	0.185614	+	0.982623i	$0.440573\pi$
$422$	−9.16388	+	5.29077i	−0.446091	+	0.257551i
$423$	−1.84803	+	24.4886i	−0.0898545	+	1.19068i
$424$	5.69577	−	9.86536i	0.276611	−	0.479104i
$425$	25.9815	+	10.9105i	1.26029	+	0.529236i
$426$	−1.16025	−	1.49351i	−0.0562143	−	0.0723609i
$427$	2.57909	−	7.08598i	0.124811	−	0.342915i
$428$	5.34871	−	0.943122i	0.258540	−	0.0455875i
$429$	11.6468	+	36.1842i	0.562315	+	1.74699i
$430$	−1.19125	+	1.13482i	−0.0574470	+	0.0547260i
$431$	7.07523			0.340802			0.170401	−	0.985375i	$-0.445494\pi$
$431$	7.07523			0.340802			0.170401	+	0.985375i	$0.445494\pi$
$432$	−1.47348	+	4.98286i	−0.0708928	+	0.239738i
$433$		−	5.11571i		−	0.245845i	−0.992416	−	0.122923i	$-0.960773\pi$
$433$		−	5.11571i		−	0.245845i	0.992416	−	0.122923i	$-0.0392267\pi$
$434$	−2.51548	−	2.11074i	−0.120747	−	0.101319i
$435$	18.6520	+	6.25803i	0.894296	+	0.300050i
$436$	−1.63662	−	9.28176i	−0.0783801	−	0.444516i
$437$	−10.5974	+	29.1162i	−0.506943	+	1.39282i
$438$	−14.8368	−	6.04203i	−0.708928	−	0.288699i
$439$	2.18336	−	12.3825i	0.104206	−	0.590983i	−0.887328	−	0.461139i	$-0.847441\pi$
$439$	2.18336	−	12.3825i	0.104206	−	0.590983i	0.991534	−	0.129845i	$-0.0414478\pi$
$440$	−7.20498	+	9.77633i	−0.343484	+	0.466068i
$441$	−3.98046	+	15.5982i	−0.189546	+	0.742770i
$442$	19.7225	−	11.3868i	0.938106	−	0.541616i
$443$	−10.5047	−	28.8614i	−0.499092	−	1.37124i	−0.892154	−	0.451732i	$-0.850806\pi$
$443$	−10.5047	−	28.8614i	−0.499092	−	1.37124i	0.393062	−	0.919512i	$-0.371416\pi$
$444$	0.114836	−	3.04775i	0.00544987	−	0.144640i
$445$	−10.6224	−	15.9816i	−0.503548	−	0.757601i
$446$	−1.86659	+	1.56626i	−0.0883857	+	0.0741644i
$447$	−7.59427	−	0.286144i	−0.359197	−	0.0135341i
$448$	−1.20273	−	3.30446i	−0.0568235	−	0.156121i
$449$	−13.2721	−	22.9880i	−0.626351	−	1.08487i	−0.988278	−	0.152665i	$-0.951215\pi$
$449$	−13.2721	−	22.9880i	−0.626351	−	1.08487i	0.361927	−	0.932206i	$-0.382119\pi$
$450$	0.760269	+	14.9807i	0.0358394	+	0.706198i
$451$	4.96149	−	8.59355i	0.233627	−	0.404655i
$452$	−14.2219	−	2.50770i	−0.668940	−	0.117952i
$453$	19.9606	+	8.12864i	0.937832	+	0.381917i
$454$	−13.0099	−	4.73521i	−0.610584	−	0.222235i
$455$	−31.7108	+	2.00088i	−1.48663	+	0.0938029i
$456$	−9.29258	−	2.00197i	−0.435165	−	0.0937507i
$457$	5.39729	−	6.43224i	0.252474	−	0.300887i	−0.624889	−	0.780714i	$-0.714856\pi$
$457$	5.39729	−	6.43224i	0.252474	−	0.300887i	0.877364	+	0.479826i	$0.159300\pi$
$458$		−	26.4537i		−	1.23610i
$459$	−3.30167	+	29.0982i	−0.154109	+	1.35819i
$460$	12.5459	+	1.40493i	0.584954	+	0.0655050i
$461$	9.67490	+	8.11821i	0.450605	+	0.378103i	0.839660	−	0.543112i	$-0.182754\pi$
$461$	9.67490	+	8.11821i	0.450605	+	0.378103i	−0.389055	+	0.921214i	$0.627198\pi$
$462$	31.4893	−	10.1357i	1.46501	−	0.471554i
$463$	−37.9626	+	6.69384i	−1.76427	+	0.311089i	−0.959335	−	0.282269i	$-0.908913\pi$
$463$	−37.9626	+	6.69384i	−1.76427	+	0.311089i	−0.804938	+	0.593358i	$0.797802\pi$
$464$	4.77342	+	1.73738i	0.221601	+	0.0806560i
$465$	1.88711	+	3.08520i	0.0875125	+	0.143073i
$466$	−3.33268	+	18.9006i	−0.154384	+	0.875552i
$467$	17.3860	+	10.0378i	0.804528	+	0.464495i	0.845052	−	0.534684i	$-0.179569\pi$
$467$	17.3860	+	10.0378i	0.804528	+	0.464495i	−0.0405238	+	0.999179i	$0.512903\pi$
$468$	10.0125	+	6.83407i	0.462828	+	0.315905i
$469$	−10.4843	−	18.1593i	−0.484120	−	0.838521i
$470$	4.30744	+	17.7906i	0.198687	+	0.820620i
$471$	−10.8782	+	5.74565i	−0.501240	+	0.264745i
$472$	−4.51068	−	5.37562i	−0.207621	−	0.247433i
$473$	−2.56869	−	3.06125i	−0.118109	−	0.140756i
$474$	−4.46633	−	2.80801i	−0.205145	−	0.128976i
$475$	−27.2232	+	3.44918i	−1.24909	+	0.158259i
$476$	−9.90938	−	17.1636i	−0.454196	−	0.786690i
$477$	34.0066	−	3.38493i	1.55705	−	0.154985i
$478$	−0.571560	−	0.329990i	−0.0261425	−	0.0150934i
$479$	4.45579	−	25.2701i	0.203590	−	1.15462i	−0.696052	−	0.717991i	$-0.745062\pi$
$479$	4.45579	−	25.2701i	0.203590	−	1.15462i	0.899643	−	0.436627i	$-0.143827\pi$
$480$	0.0981819	+	3.87174i	0.00448137	+	0.176720i
$481$	−6.68626	−	2.43360i	−0.304867	−	0.110963i
$482$	−8.26322	+	1.45703i	−0.376379	+	0.0663658i
$483$	−25.4912	−	23.0798i	−1.15989	−	1.05017i
$484$	−14.1701	−	11.8901i	−0.644093	−	0.540458i
$485$	−28.2432	−	3.16277i	−1.28246	−	0.143614i
$486$	−14.7204	+	5.12932i	−0.667731	+	0.232671i
$487$		−	35.0685i		−	1.58910i	−0.607196	−	0.794552i	$-0.707706\pi$
$487$		−	35.0685i		−	1.58910i	0.607196	−	0.794552i	$-0.292294\pi$
$488$	−1.37837	+	1.64268i	−0.0623960	+	0.0743606i
$489$	23.3663	−	25.8076i	1.05666	−	1.16706i
$490$	0.755594	+	11.9750i	0.0341343	+	0.540974i
$491$	29.4943	+	10.7351i	1.33106	+	0.484466i	0.906986	−	0.421161i	$-0.138377\pi$
$491$	29.4943	+	10.7351i	1.33106	+	0.484466i	0.424074	+	0.905627i	$0.360600\pi$
$492$	−0.431783	−	3.13493i	−0.0194663	−	0.141334i
$493$	28.1940	+	4.97137i	1.26980	+	0.223899i
$494$	−11.0884	+	19.2056i	−0.498889	+	0.864102i
$495$	−36.4307	−	0.448409i	−1.63744	−	0.0201545i
$496$	0.466899	+	0.808692i	0.0209644	+	0.0363113i
$497$	1.31326	+	3.60815i	0.0589078	+	0.161848i
$498$	−5.10040	+	8.11254i	−0.228555	+	0.363532i
$499$	21.4974	−	18.0385i	0.962358	−	0.807514i	−0.0189771	−	0.999820i	$-0.506041\pi$
$499$	21.4974	−	18.0385i	0.962358	−	0.807514i	0.981335	+	0.192306i	$0.0615965\pi$
$500$	3.97594	+	10.4495i	0.177809	+	0.467316i
$501$	4.14907	−	2.19146i	0.185367	−	0.0979074i
$502$	8.62604	+	23.6999i	0.384999	+	1.05778i
$503$	−4.78321	+	2.76159i	−0.213273	+	0.123133i	−0.602832	−	0.797869i	$-0.705961\pi$
$503$	−4.78321	+	2.76159i	−0.213273	+	0.123133i	0.389559	+	0.921002i	$0.372628\pi$
$504$	5.94736	−	8.71339i	0.264916	−	0.388125i
$505$	27.6425	+	20.3720i	1.23008	+	0.906544i
$506$	−5.32458	+	30.1972i	−0.236707	+	1.34243i
$507$	4.55248	−	3.53664i	0.202183	−	0.157067i
$508$	−0.344366	+	0.946137i	−0.0152788	+	0.0419781i
$509$	4.69976	+	26.6536i	0.208313	+	1.18140i	0.892140	+	0.451758i	$0.149203\pi$
$509$	4.69976	+	26.6536i	0.208313	+	1.18140i	−0.683827	+	0.729644i	$0.739686\pi$
$510$	4.33405	+	21.3931i	0.191915	+	0.947301i
$511$	24.9153	+	20.9064i	1.10219	+	0.924846i
$512$			1.00000i			0.0441942i
$513$	−11.3834	−	26.1468i	−0.502588	−	1.15441i
$514$	−6.13356			−0.270540
$515$	−20.5800	−	21.6033i	−0.906865	−	0.951954i
$516$	−1.24583	−	0.268398i	−0.0548447	−	0.0118156i
$517$	−43.7847	+	7.72042i	−1.92565	+	0.339544i
$518$	−2.11784	+	5.81872i	−0.0930526	+	0.255660i
$519$	1.14973	−	2.82328i	0.0504677	−	0.123928i
$520$	8.66841	+	2.54953i	0.380135	+	0.111805i
$521$	17.4971	−	30.3059i	0.766562	−	1.32772i	−0.172855	−	0.984947i	$-0.555299\pi$
$521$	17.4971	−	30.3059i	0.766562	−	1.32772i	0.939417	−	0.342777i	$-0.111367\pi$
$522$	4.11976	+	14.6719i	0.180317	+	0.642171i
$523$	33.5940	−	19.3955i	1.46896	−	0.848107i	0.469569	−	0.882896i	$-0.344409\pi$
$523$	33.5940	−	19.3955i	1.46896	−	0.848107i	0.999395	+	0.0347889i	$0.0110759\pi$
$524$	−1.23051	+	0.447870i	−0.0537552	+	0.0195653i
$525$	7.84971	−	29.4250i	0.342589	−	1.28421i
$526$	9.98129	−	8.37529i	0.435205	−	0.365180i
$527$	3.38284	+	4.03151i	0.147359	+	0.175616i
$528$	−9.40041	−	0.354197i	−0.409100	−	0.0154144i
$529$	8.33926	−	3.03524i	0.362577	−	0.131967i
$530$	23.3400	−	10.2020i	1.01382	−	0.443149i
$531$	5.20542	−	20.3984i	0.225896	−	0.885215i
$532$	16.7137	+	9.64966i	0.724631	+	0.418366i
$533$	−7.27060	−	1.28200i	−0.314924	−	0.0555297i
$534$	5.60621	−	13.7666i	0.242605	−	0.595738i
$535$	10.8790	+	5.39793i	0.470342	+	0.233373i
$536$	1.03544	+	5.87227i	0.0447242	+	0.253643i
$537$	−3.28208	+	15.2345i	−0.141632	+	0.657417i
$538$	0.315321	−	0.375785i	0.0135945	−	0.0162013i
$539$	−29.1438			−1.25531
$540$	−9.26256	+	7.01462i	−0.398597	+	0.301861i
$541$	18.4926			0.795057			0.397529	−	0.917590i	$-0.369868\pi$
$541$	18.4926			0.795057			0.397529	+	0.917590i	$0.369868\pi$
$542$	17.0882	−	20.3649i	0.734002	−	0.874749i
$543$	33.9011	−	10.9120i	1.45483	−	0.468278i
$544$	0.978660	+	5.55026i	0.0419597	+	0.237965i
$545$	9.36716	−	18.8787i	0.401245	−	0.808673i
$546$	−15.0992	−	19.4361i	−0.646184	−	0.831790i
$547$	23.5111	+	4.14564i	1.00526	+	0.177255i	0.651959	−	0.758254i	$-0.273947\pi$
$547$	23.5111	+	4.14564i	1.00526	+	0.177255i	0.353303	+	0.935509i	$0.385058\pi$
$548$	10.1324	+	5.84992i	0.432833	+	0.249896i
$549$	−6.41486	−	0.484097i	−0.273780	−	0.0206608i
$550$	−25.9385	+	8.03968i	−1.10602	+	0.342813i
$551$	−26.1973	+	9.53505i	−1.11604	+	0.406207i
$552$	4.56703	+	8.64671i	0.194386	+	0.368028i
$553$	6.88497	+	8.20519i	0.292779	+	0.348920i
$554$	8.35495	−	7.01063i	0.354968	−	0.297853i
$555$	4.24984	−	5.33373i	0.180396	−	0.226404i
$556$	−4.44215	+	1.61681i	−0.188389	+	0.0685680i
$557$	1.51084	−	0.872285i	0.0640165	−	0.0369599i	−0.467650	−	0.883914i	$-0.654899\pi$
$557$	1.51084	−	0.872285i	0.0640165	−	0.0369599i	0.531667	+	0.846954i	$0.321566\pi$
$558$	−1.15351	+	2.55288i	−0.0488320	+	0.108072i
$559$	−1.48659	+	2.57485i	−0.0628760	+	0.108904i
$560$	2.21873	−	7.54369i	0.0937586	−	0.318779i
$561$	−52.5213	+	7.23392i	−2.21745	+	0.305416i
$562$	−7.40501	+	20.3451i	−0.312362	+	0.858206i
$563$	25.9452	−	4.57485i	1.09346	−	0.192807i	0.402301	−	0.915508i	$-0.368211\pi$
$563$	25.9452	−	4.57485i	1.09346	−	0.192807i	0.691161	+	0.722701i	$0.257100\pi$
$564$	−9.51641	+	10.5107i	−0.400713	+	0.442579i
$565$	−22.2732	−	23.3806i	−0.937041	−	0.983631i
$566$	17.2729			0.726035
$567$	31.6398	−	0.755972i	1.32875	−	0.0317479i
$568$		−	1.09190i		−	0.0458153i
$569$	−19.5668	−	16.4185i	−0.820284	−	0.688300i	0.132754	−	0.991149i	$-0.457618\pi$
$569$	−19.5668	−	16.4185i	−0.820284	−	0.688300i	−0.953039	+	0.302849i	$0.902062\pi$
$570$	−14.0712	−	15.9311i	−0.589378	−	0.667281i
$571$	−2.02367	−	11.4768i	−0.0846879	−	0.480289i	−0.997424	−	0.0717381i	$-0.977145\pi$
$571$	−2.02367	−	11.4768i	−0.0846879	−	0.480289i	0.912736	−	0.408551i	$-0.133966\pi$
$572$	−7.50613	+	20.6229i	−0.313847	+	0.862288i
$573$	0.112722	+	0.818408i	0.00470902	+	0.0341895i
$574$	−1.11566	+	6.32724i	−0.0465669	+	0.264094i
$575$	20.7193	+	19.1722i	0.864053	+	0.799536i
$576$	−2.43673	+	1.74996i	−0.101530	+	0.0729149i
$577$	−28.3260	+	16.3540i	−1.17923	+	0.680827i	−0.955836	−	0.293901i	$-0.905046\pi$
$577$	−28.3260	+	16.3540i	−1.17923	+	0.680827i	−0.223392	+	0.974729i	$0.571713\pi$
$578$	5.04929	+	13.8728i	0.210023	+	0.577033i
$579$	13.1962	+	8.29652i	0.548415	+	0.344792i
$580$	6.28754	+	9.45977i	0.261076	+	0.392796i
$581$	14.9037	−	12.5057i	0.618310	−	0.518824i
$582$	−10.2813	−	19.4655i	−0.426174	−	0.806870i
$583$	21.1606	+	58.1383i	0.876382	+	2.40784i
$584$	−4.62453	−	8.00992i	−0.191364	−	0.331453i
$585$	8.95684	+	25.5842i	0.370320	+	1.05777i
$586$	2.66814	−	4.62136i	0.110220	−	0.190906i
$587$	−28.5008	−	5.02547i	−1.17636	−	0.207423i	−0.448903	−	0.893581i	$-0.648185\pi$
$587$	−28.5008	−	5.02547i	−1.17636	−	0.207423i	−0.727453	+	0.686157i	$0.759296\pi$
$588$	−7.33967	+	5.70189i	−0.302683	+	0.235142i
$589$	−4.81577	−	1.75280i	−0.198430	−	0.0722227i
$590$	−0.988122	−	15.6602i	−0.0406803	−	0.644719i
$591$	−0.607333	−	1.88685i	−0.0249824	−	0.0776146i
$592$	1.13186	−	1.34890i	0.0465193	−	0.0554396i
$593$			16.5893i			0.681241i	0.940201	+	0.340621i	$0.110637\pi$
$593$			16.5893i			0.681241i	−0.940201	+	0.340621i	$0.889363\pi$
$594$	−15.5872	−	23.5261i	−0.639552	−	0.965286i
$595$	4.93184	−	44.0408i	0.202186	−	1.80550i
$596$	−3.36115	−	2.82034i	−0.137678	−	0.115525i
$597$	4.82063	−	22.3760i	0.197295	−	0.915789i
$598$	22.4669	−	3.96152i	0.918740	−	0.161999i
$599$	20.2166	+	7.35824i	0.826028	+	0.300650i	0.720228	−	0.693738i	$-0.244037\pi$
$599$	20.2166	+	7.35824i	0.826028	+	0.300650i	0.105800	+	0.994387i	$0.466260\pi$
$600$	−4.95950	+	7.09953i	−0.202471	+	0.289837i
$601$	−5.92816	+	33.6203i	−0.241815	+	1.37140i	0.585961	+	0.810339i	$0.300717\pi$
$601$	−5.92816	+	33.6203i	−0.241815	+	1.37140i	−0.827775	+	0.561060i	$0.810394\pi$
$602$	2.24076	+	1.29370i	0.0913267	+	0.0527275i
$603$	−12.4972	+	12.7993i	−0.508923	+	0.521228i
$604$	6.22161	+	10.7761i	0.253154	+	0.438475i
$605$	−9.73330	−	40.2006i	−0.395715	−	1.63439i
$606$	−1.00149	+	26.5796i	−0.0406827	+	1.07972i
$607$	29.1556	+	34.7463i	1.18339	+	1.41031i	0.890995	+	0.454013i	$0.150008\pi$
$607$	29.1556	+	34.7463i	1.18339	+	1.41031i	0.292396	+	0.956297i	$0.405547\pi$
$608$	−3.52772	−	4.20418i	−0.143068	−	0.170502i
$609$	1.16496	−	30.9180i	0.0472065	−	1.25286i
$610$	−4.66030	+	1.12834i	−0.188690	+	0.0456853i
$611$	16.5393	+	28.6469i	0.669108	+	1.15893i
$612$	−11.8119	+	12.0975i	−0.477466	+	0.489010i
$613$	−5.01203	−	2.89370i	−0.202434	−	0.116875i	0.395356	−	0.918528i	$-0.370621\pi$
$613$	−5.01203	−	2.89370i	−0.202434	−	0.116875i	−0.597790	+	0.801652i	$0.703954\pi$
$614$	−0.157820	+	0.895042i	−0.00636910	+	0.0361210i
$615$	3.38156	−	6.21580i	0.136358	−	0.250645i
$616$	17.9471	+	6.53222i	0.723110	+	0.263191i
$617$	−9.01576	+	1.58972i	−0.362961	+	0.0639998i	−0.352155	−	0.935942i	$-0.614551\pi$
$617$	−9.01576	+	1.58972i	−0.362961	+	0.0639998i	−0.0108061	+	0.999942i	$0.503440\pi$
$618$	4.86741	−	22.5932i	0.195796	−	0.908831i
$619$	−3.71314	−	3.11570i	−0.149244	−	0.125230i	0.565109	−	0.825016i	$-0.308834\pi$
$619$	−3.71314	−	3.11570i	−0.149244	−	0.125230i	−0.714352	+	0.699786i	$0.753279\pi$
$620$	−0.232372	+	2.07506i	−0.00933230	+	0.0833365i
$621$	−13.0776	+	26.2600i	−0.524785	+	1.05378i
$622$		−	22.9123i		−	0.918700i
$623$	−19.3984	+	23.1182i	−0.777182	+	0.926210i
$624$	2.14444	+	6.66230i	0.0858464	+	0.266706i
$625$	−6.70543	+	24.0840i	−0.268217	+	0.963359i
$626$	9.47411	+	3.44829i	0.378662	+	0.137822i
$627$	40.7705	−	31.6729i	1.62822	−	1.26489i
$628$	−6.99484	−	1.23338i	−0.279125	−	0.0492172i
$629$	4.96202	−	8.59447i	0.197849	−	0.342684i
$630$	22.2646	−	7.79470i	0.887044	−	0.310548i
$631$	−21.5515	−	37.3284i	−0.857953	−	1.48602i	−0.873878	−	0.486145i	$-0.838403\pi$
$631$	−21.5515	−	37.3284i	−0.857953	−	1.48602i	0.0159249	−	0.999873i	$-0.494931\pi$
$632$	−1.04177	−	2.86224i	−0.0414393	−	0.113854i
$633$	−8.55975	−	16.2061i	−0.340220	−	0.644134i
$634$	−3.88589	+	3.26065i	−0.154328	+	0.129497i
$635$	−1.87501	+	1.24625i	−0.0744077	+	0.0494559i
$636$	16.7037	+	10.5017i	0.662346	+	0.416421i
$637$	7.41608	+	20.3755i	0.293836	+	0.807307i
$638$	−23.8929	+	13.7946i	−0.945929	+	0.546132i
$639$	2.66067	−	1.91079i	0.105255	−	0.0755895i
$640$	−1.32660	+	1.80004i	−0.0524383	+	0.0711528i
$641$	−1.97759	+	11.2155i	−0.0781100	+	0.442984i	0.920522	+	0.390691i	$0.127764\pi$
$641$	−1.97759	+	11.2155i	−0.0781100	+	0.442984i	−0.998632	+	0.0522927i	$0.983347\pi$
$642$	1.28356	+	9.31918i	0.0506580	+	0.367799i
$643$	5.87723	−	16.1476i	0.231775	−	0.636798i	−0.768219	−	0.640187i	$-0.778857\pi$
$643$	5.87723	−	16.1476i	0.231775	−	0.636798i	0.999994	+	0.00338958i	$0.00107894\pi$
$644$	−3.44752	−	19.5518i	−0.135851	−	0.770451i
$645$	−1.88649	−	2.13584i	−0.0742804	−	0.0840988i
$646$	−23.6942	−	19.8818i	−0.932237	−	0.782240i
$647$		−	24.7071i		−	0.971337i	−0.874143	−	0.485669i	$-0.838576\pi$
$647$		−	24.7071i		−	0.971337i	0.874143	−	0.485669i	$-0.161424\pi$
$648$	−8.52835	−	2.87529i	−0.335025	−	0.112952i
$649$	38.1126			1.49605
$650$	12.2213	+	16.0888i	0.479358	+	0.631053i
$651$	3.81737	−	4.21620i	0.149614	−	0.165246i
$652$	19.7945	−	3.49031i	0.775213	−	0.136691i
$653$	−15.9807	+	43.9067i	−0.625375	+	1.71820i	0.0680570	+	0.997681i	$0.478320\pi$
$653$	−15.9807	+	43.9067i	−0.625375	+	1.71820i	−0.693432	+	0.720522i	$0.743902\pi$
$654$	16.1718	−	2.22739i	0.632368	−	0.0870979i
$655$	−2.80912	−	0.826211i	−0.109761	−	0.0322827i
$656$	0.913520	−	1.58226i	0.0356670	−	0.0617770i
$657$	11.4253	−	25.2858i	0.445742	−	0.986491i
$658$	24.9300	−	14.3933i	0.971872	−	0.561111i
$659$	42.7170	−	15.5477i	1.66402	−	0.605653i	0.673032	−	0.739614i	$-0.264992\pi$
$659$	42.7170	−	15.5477i	1.66402	−	0.605653i	0.990987	+	0.133960i	$0.0427695\pi$
$660$	−16.4512	−	13.1081i	−0.640363	−	0.510233i
$661$	−36.3646	+	30.5135i	−1.41442	+	1.18684i	−0.460168	+	0.887832i	$0.652211\pi$
$661$	−36.3646	+	30.5135i	−1.41442	+	1.18684i	−0.954251	+	0.299007i	$0.903345\pi$
$662$	−11.6699	−	13.9076i	−0.453562	−	0.540534i
$663$	18.4223	+	34.8788i	0.715464	+	1.35458i
$664$	−5.19890	+	1.89224i	−0.201756	+	0.0734333i
$665$	17.2841	+	39.5421i	0.670249	+	1.53338i
$666$	5.26763	+	0.397521i	0.204116	+	0.0154036i
$667$	24.8368	+	14.3396i	0.961686	+	0.555230i
$668$	2.66792	+	0.470427i	0.103225	+	0.0182014i
$669$	−2.58918	−	3.33288i	−0.100104	−	0.128857i
$670$	−5.92630	+	11.9439i	−0.228953	+	0.461434i
$671$	−2.02238	−	11.4695i	−0.0780732	−	0.442775i
$672$	5.79787	−	1.86620i	0.223658	−	0.0719903i
$673$	−7.48676	+	8.92238i	−0.288594	+	0.343932i	−0.890790	−	0.454416i	$-0.849848\pi$
$673$	−7.48676	+	8.92238i	−0.288594	+	0.343932i	0.602196	+	0.798348i	$0.294292\pi$
$674$	−3.62187			−0.139509
$675$	−25.9786	+	0.338915i	−0.999915	+	0.0130449i
$676$	3.32831			0.128012
$677$	−2.46088	+	2.93277i	−0.0945794	+	0.112715i	−0.811258	−	0.584688i	$-0.801217\pi$
$677$	−2.46088	+	2.93277i	−0.0945794	+	0.112715i	0.716679	+	0.697403i	$0.245661\pi$
$678$	5.26787	−	24.4520i	0.202311	−	0.939073i
$679$	7.76105	+	44.0151i	0.297842	+	1.68915i
$680$	−5.60133	+	11.2890i	−0.214801	+	0.432912i
$681$	9.04426	−	22.2090i	0.346577	−	0.851051i
$682$	−4.99457	−	0.880677i	−0.191252	−	0.0337229i
$683$	6.92956	+	4.00079i	0.265152	+	0.153086i	0.626683	−	0.779275i	$-0.284412\pi$
$683$	6.92956	+	4.00079i	0.265152	+	0.153086i	−0.361530	+	0.932360i	$0.617746\pi$
$684$	4.07107	−	15.9532i	0.155661	−	0.609987i
$685$	10.4782	+	23.9716i	0.400350	+	0.915909i
$686$	−5.39943	+	1.96523i	−0.206151	+	0.0750329i
$687$	45.7866	+	1.72519i	1.74687	+	0.0658200i
$688$	−0.472953	−	0.563643i	−0.0180312	−	0.0214887i
$689$	35.2620	−	29.5883i	1.34337	−	1.12723i
$690$	−3.24986	+	21.6230i	−0.123720	+	0.823175i
$691$	34.1170	−	12.4176i	1.29787	−	0.472386i	0.401568	−	0.915829i	$-0.368465\pi$
$691$	34.1170	−	12.4176i	1.29787	−	0.472386i	0.896303	+	0.443443i	$0.146243\pi$
$692$	1.52420	−	0.879999i	0.0579415	−	0.0334525i
$693$	15.4895	+	55.1634i	0.588396	+	2.09548i
$694$	3.36071	−	5.82091i	0.127571	−	0.220959i
$695$	−10.1409	−	2.98262i	−0.384666	−	0.113137i
$696$	−3.31841	+	8.14865i	−0.125784	+	0.308874i
$697$	3.52177	−	9.67599i	0.133397	−	0.366504i
$698$	−1.63781	+	0.288790i	−0.0619920	+	0.0109309i
$699$	−32.4962	−	7.00089i	−1.22912	−	0.264798i
$700$	14.0012	−	10.6356i	0.529197	−	0.401987i
$701$	37.4904			1.41599			0.707997	−	0.706215i	$-0.249599\pi$
$701$	37.4904			1.41599			0.707997	+	0.706215i	$0.249599\pi$
$702$	−12.4815	+	16.8842i	−0.471085	+	0.637252i
$703$			9.66393i			0.364482i
$704$	−4.16052	−	3.49109i	−0.156806	−	0.131576i
$705$	−31.0733	+	6.29519i	−1.17029	+	0.237091i
$706$	2.07929	+	11.7922i	0.0782551	+	0.443807i
$707$	18.4698	−	50.7454i	0.694628	−	1.90848i
$708$	9.59840	−	7.45661i	0.360730	−	0.280237i
$709$	7.48114	−	42.4276i	0.280960	−	1.59340i	−0.438409	−	0.898776i	$-0.644458\pi$
$709$	7.48114	−	42.4276i	0.280960	−	1.59340i	0.719369	−	0.694628i	$-0.244431\pi$
$710$	1.44852	−	1.96547i	0.0543618	−	0.0737627i
$711$	5.15144	−	7.54730i	0.193194	−	0.283046i
$712$	7.43216	−	4.29096i	0.278532	−	0.160811i
$713$	1.80312	+	4.95404i	0.0675275	+	0.185530i
$714$	30.3533	−	16.0321i	1.13594	−	0.599985i
$715$	−40.8696	+	27.1645i	−1.52844	+	1.01589i
$716$	−6.89244	+	5.78344i	−0.257583	+	0.216137i
$717$	0.608429	−	0.967748i	0.0227222	−	0.0361412i
$718$	−7.84319	−	21.5490i	−0.292705	−	0.804201i
$719$	15.7723	+	27.3183i	0.588206	+	1.01880i	0.994467	+	0.105046i	$0.0334988\pi$
$719$	15.7723	+	27.3183i	0.588206	+	1.01880i	−0.406262	+	0.913757i	$0.633168\pi$
$720$	−6.70770	−	0.0825620i	−0.249981	−	0.00307691i
$721$	−23.4614	+	40.6363i	−0.873747	+	1.51337i
$722$	10.9510	+	1.93096i	0.407554	+	0.0718628i
$723$	−1.98297	−	14.3972i	−0.0737474	−	0.535437i
$724$	19.3217	+	7.03253i	0.718085	+	0.261362i
$725$	−1.23147	+	25.3690i	−0.0457358	+	0.942181i
$726$	21.5037	−	23.7504i	0.798079	−	0.881461i
$727$	−10.4723	+	12.4804i	−0.388395	+	0.462872i	−0.924445	−	0.381315i	$-0.875471\pi$
$727$	−10.4723	+	12.4804i	−0.388395	+	0.462872i	0.536050	+	0.844186i	$0.319916\pi$
$728$		−	14.2097i		−	0.526647i
$729$	−7.91795	−	25.8129i	−0.293257	−	0.956034i
$730$	2.30160	−	20.5531i	0.0851860	−	0.760703i
$731$	−3.17663	−	2.66551i	−0.117492	−	0.0985873i
$732$	−2.75330	−	2.49285i	−0.101765	−	0.0921383i
$733$	−5.43736	+	0.958754i	−0.200834	+	0.0354124i	−0.273160	−	0.961969i	$-0.588069\pi$
$733$	−5.43736	+	0.958754i	−0.200834	+	0.0354124i	0.0723263	+	0.997381i	$0.476958\pi$
$734$	−14.1759	−	5.15961i	−0.523243	−	0.190445i
$735$	−20.7758	+	0.526846i	−0.766328	+	0.0194330i
$736$	−0.980374	+	5.55998i	−0.0361371	+	0.204943i
$737$	−28.0465	−	16.1927i	−1.03311	−	0.596465i
$738$	5.45417	−	0.542894i	0.200771	−	0.0199842i
$739$	4.68981	+	8.12298i	0.172517	+	0.298809i	0.939299	−	0.343099i	$-0.111477\pi$
$739$	4.68981	+	8.12298i	0.172517	+	0.298809i	−0.766782	+	0.641908i	$0.778143\pi$
$740$	3.82685	−	0.926551i	0.140678	−	0.0340607i
$741$	−32.5184	−	20.4445i	−1.19459	−	0.751048i
$742$	−25.7493	−	30.6868i	−0.945285	−	1.12655i
$743$	−15.0919	−	17.9858i	−0.553669	−	0.659836i	0.414525	−	0.910038i	$-0.363948\pi$
$743$	−15.0919	−	17.9858i	−0.553669	−	0.659836i	−0.968194	+	0.250201i	$0.919503\pi$
$744$	−1.43015	+	0.755379i	−0.0524319	+	0.0276935i
$745$	−2.30875	−	9.53560i	−0.0845859	−	0.349357i
$746$	−4.84337	−	8.38897i	−0.177328	−	0.307142i
$747$	−13.7087	−	9.35696i	−0.501577	−	0.342353i
$748$	−26.5086	−	15.3047i	−0.969249	−	0.559596i
$749$	3.31652	−	18.8089i	0.121183	−	0.687264i
$750$	−18.3455	+	6.20017i	−0.669883	+	0.226398i
$751$	−23.5033	−	8.55451i	−0.857648	−	0.312158i	−0.124493	−	0.992220i	$-0.539731\pi$
$751$	−23.5033	−	8.55451i	−0.857648	−	0.312158i	−0.733155	+	0.680062i	$0.761953\pi$
$752$	−8.06173	+	1.42150i	−0.293981	+	0.0518368i
$753$	−41.5828	+	13.3846i	−1.51536	+	0.487760i
$754$	15.7242	+	13.1942i	0.572642	+	0.480504i
$755$	−3.09646	+	27.6511i	−0.112692	+	1.00632i
$756$	14.6935	+	10.8621i	0.534396	+	0.395050i
$757$			24.1936i			0.879330i	0.898162	+	0.439665i	$0.144903\pi$
$757$			24.1936i			0.879330i	−0.898162	+	0.439665i	$0.855097\pi$
$758$	3.57921	−	4.26554i	0.130003	−	0.154931i
$759$	−51.9188	−	11.1852i	−1.88453	−	0.405998i
$760$	−0.772793	−	12.2476i	−0.0280322	−	0.444265i
$761$	−50.1467	−	18.2519i	−1.81782	−	0.661631i	−0.995735	−	0.0922626i	$-0.970590\pi$
$761$	−50.1467	−	18.2519i	−1.81782	−	0.661631i	−0.822082	−	0.569369i	$-0.807188\pi$
$762$	−1.61514	−	0.657739i	−0.0585103	−	0.0238274i
$763$	−32.6396	−	5.75525i	−1.18163	−	0.208354i
$764$	−0.238485	+	0.413067i	−0.00862807	+	0.0149442i
$765$	−37.3102	+	6.10631i	−1.34895	+	0.220774i
$766$	−7.52037	−	13.0257i	−0.271722	−	0.470636i
$767$	−9.69832	−	26.6459i	−0.350186	−	0.962128i
$768$	−1.73082	−	0.0652155i	−0.0624557	−	0.00235326i
$769$	1.41090	−	1.18389i	0.0508784	−	0.0426920i	−0.616994	−	0.786968i	$-0.711650\pi$
$769$	1.41090	−	1.18389i	0.0508784	−	0.0426920i	0.667872	+	0.744276i	$0.267205\pi$
$770$	23.6399	+	35.5668i	0.851923	+	1.28174i
$771$	0.400003	−	10.6161i	0.0144058	−	0.382330i
$772$	3.07800	+	8.45674i	0.110780	+	0.304365i
$773$	31.1134	−	17.9633i	1.11907	−	0.646096i	0.177907	−	0.984047i	$-0.443067\pi$
$773$	31.1134	−	17.9633i	1.11907	−	0.646096i	0.941163	+	0.337952i	$0.109734\pi$
$774$	0.545798	−	2.13881i	0.0196183	−	0.0768779i
$775$	−3.17105	+	3.42693i	−0.113908	+	0.123099i
$776$	2.20702	−	12.5166i	0.0792273	−	0.449320i
$777$	−9.93306	−	4.04508i	−0.356346	−	0.145116i
$778$	0.599721	−	1.64772i	0.0215011	−	0.0590737i
$779$	1.74119	+	9.87476i	0.0623845	+	0.353800i
$780$	−4.97811	+	14.8372i	−0.178245	+	0.531258i
$781$	4.54289	+	3.81194i	0.162557	+	0.136402i
$782$			31.8188i			1.13784i
$783$	−25.6631	+	6.17374i	−0.917125	+	0.220631i
$784$	−5.36602			−0.191643
$785$	−10.9548	−	11.4995i	−0.390993	−	0.410434i
$786$	−0.694936	−	2.15901i	−0.0247875	−	0.0770093i
$787$	−48.1986	+	8.49871i	−1.71809	+	0.302946i	−0.943956	−	0.330071i	$-0.892927\pi$
$787$	−48.1986	+	8.49871i	−1.71809	+	0.302946i	−0.774138	+	0.633017i	$0.781816\pi$
$788$	0.391413	−	1.07540i	0.0139435	−	0.0383095i
$789$	13.8452	+	17.8220i	0.492903	+	0.634481i
$790$	1.92181	−	6.53415i	0.0683749	−	0.232474i
$791$	−25.3916	+	43.9795i	−0.902821	+	1.56373i
$792$	1.22610	−	16.2473i	0.0435677	−	0.577324i
$793$	−7.50413	+	4.33251i	−0.266479	+	0.153852i
$794$	32.7584	−	11.9231i	1.16255	−	0.423135i
$795$	16.1358	+	41.0627i	0.572278	+	1.45634i
$796$	10.1234	−	8.49457i	0.358815	−	0.301082i
$797$	−17.1972	−	20.4949i	−0.609157	−	0.725965i	0.370008	−	0.929028i	$-0.379355\pi$
$797$	−17.1972	−	20.4949i	−0.609157	−	0.725965i	−0.979166	+	0.203063i	$0.934910\pi$
$798$	−17.7918	+	28.2991i	−0.629824	+	1.00178i
$799$	−43.3535	+	15.7794i	−1.53374	+	0.558234i
$800$	−4.77585	+	1.48028i	−0.168852	+	0.0523359i
$801$	23.4619	+	10.6012i	0.828985	+	0.374573i
$802$	30.7994	+	17.7820i	1.08756	+	0.627905i
$803$	49.4701	+	8.72292i	1.74576	+	0.307825i
$804$	−10.2314	+	1.40920i	−0.360833	+	0.0496986i
$805$	19.7317	−	39.7676i	0.695453	−	1.40162i
$806$	0.655229	+	3.71599i	0.0230795	+	0.130890i
$807$	0.629854	+	0.570272i	0.0221719	+	0.0200745i
$808$	−9.87105	+	11.7639i	−0.347262	+	0.413851i
$809$	4.07349			0.143216			0.0716081	−	0.997433i	$-0.477187\pi$
$809$	4.07349			0.143216			0.0716081	+	0.997433i	$0.477187\pi$
$810$	−11.5370	−	16.4893i	−0.405369	−	0.579375i
$811$	−41.3275			−1.45120			−0.725602	−	0.688114i	$-0.758439\pi$
$811$	−41.3275			−1.45120			−0.725602	+	0.688114i	$0.758439\pi$
$812$	11.4822	−	13.6840i	0.402948	−	0.480214i
$813$	34.1337	+	30.9048i	1.19712	+	1.08388i
$814$	1.66070	+	9.41829i	0.0582075	+	0.330111i
$815$	40.2611	+	19.9766i	1.41029	+	0.699751i
$816$	−9.67034	+	1.33192i	−0.338529	+	0.0466267i
$817$	3.97676	+	0.701209i	0.139129	+	0.0245322i
$818$	3.61327	+	2.08612i	0.126335	+	0.0729395i
$819$	34.6252	−	24.8664i	1.20990	−	0.868903i
$820$	3.74340	−	1.63626i	0.130725	−	0.0571408i
$821$	−28.3970	+	10.3357i	−0.991063	+	0.360717i	−0.786132	−	0.618059i	$-0.787919\pi$
$821$	−28.3970	+	10.3357i	−0.991063	+	0.360717i	−0.204931	+	0.978776i	$0.565697\pi$
$822$	−10.7860	+	17.1558i	−0.376203	+	0.598377i
$823$	12.9035	+	15.3778i	0.449788	+	0.536037i	0.942522	−	0.334143i	$-0.108447\pi$
$823$	12.9035	+	15.3778i	0.449788	+	0.536037i	−0.492734	+	0.870180i	$0.664002\pi$
$824$	10.2217	−	8.57701i	0.356089	−	0.298794i
$825$	−12.2237	−	45.4193i	−0.425573	−	1.58130i
$826$	−23.1886	+	8.43997i	−0.806836	+	0.293664i
$827$	11.7743	−	6.79787i	0.409431	−	0.236385i	−0.281114	−	0.959674i	$-0.590704\pi$
$827$	11.7743	−	6.79787i	0.409431	−	0.236385i	0.690545	+	0.723289i	$0.257371\pi$
$828$	−15.2638	+	7.34082i	−0.530452	+	0.255111i
$829$	3.94419	−	6.83154i	0.136987	−	0.237269i	−0.789367	−	0.613921i	$-0.789591\pi$
$829$	3.94419	−	6.83154i	0.136987	−	0.237269i	0.926355	+	0.376652i	$0.122925\pi$
$830$	−11.8685	−	3.49073i	−0.411961	−	0.121165i
$831$	11.5893	+	14.9181i	0.402028	+	0.517504i
$832$	−1.38205	+	3.79714i	−0.0479138	+	0.131642i
$833$	−29.7828	+	5.25151i	−1.03191	+	0.181954i
$834$	−2.50872	−	7.79402i	−0.0868697	−	0.269885i
$835$	4.17830	+	4.38604i	0.144596	+	0.151785i
$836$	29.8072			1.03090
$837$	−4.34336	−	2.16301i	−0.150128	−	0.0747645i
$838$		−	2.03718i		−	0.0703732i
$839$	−8.53630	−	7.16280i	−0.294706	−	0.247287i	0.483431	−	0.875383i	$-0.339390\pi$
$839$	−8.53630	−	7.16280i	−0.294706	−	0.247287i	−0.778137	+	0.628095i	$0.783835\pi$
$840$	12.9121	+	4.33220i	0.445510	+	0.149475i
$841$	−0.554964	−	3.14736i	−0.0191367	−	0.108530i
$842$	2.26891	−	6.23377i	0.0781917	−	0.214830i
$843$	−34.7308	−	14.1436i	−1.19619	−	0.487131i
$844$	1.83746	−	10.4208i	0.0632481	−	0.358698i
$845$	5.99108	+	4.41532i	0.206099	+	0.151892i
$846$	−17.5715	−	17.1567i	−0.604120	−	0.589858i
$847$	−56.3330	+	32.5239i	−1.93563	+	1.11753i
$848$	3.89613	+	10.7045i	0.133794	+	0.367595i
$849$	−1.12646	+	29.8963i	−0.0386601	+	1.02604i
$850$	−25.0585	+	12.8899i	−0.859500	+	0.442119i
$851$	7.61557	−	6.39022i	0.261058	−	0.219054i
$852$	1.88989	+	0.0712090i	0.0647466	+	0.00243958i
$853$	−14.9374	−	41.0402i	−0.511447	−	1.40519i	−0.879729	−	0.475476i	$-0.842276\pi$
$853$	−14.9374	−	41.0402i	−0.511447	−	1.40519i	0.368281	−	0.929714i	$-0.379946\pi$
$854$	3.77037	+	6.53047i	0.129019	+	0.223468i
$855$	28.4916	−	23.3158i	0.974392	−	0.797383i
$856$	−2.71561	+	4.70358i	−0.0928177	+	0.160765i
$857$	−26.1326	−	4.60788i	−0.892672	−	0.157402i	−0.291547	−	0.956557i	$-0.594170\pi$
$857$	−26.1326	−	4.60788i	−0.892672	−	0.157402i	−0.601126	+	0.799154i	$0.705281\pi$
$858$	−35.2051	−	14.3367i	−1.20188	−	0.489448i
$859$	−23.0434	−	8.38711i	−0.786230	−	0.286164i	−0.0824622	−	0.996594i	$-0.526278\pi$
$859$	−23.0434	−	8.38711i	−0.786230	−	0.286164i	−0.703768	+	0.710430i	$0.748501\pi$
$860$	−0.103606	−	1.64200i	−0.00353295	−	0.0559917i
$861$	−10.8786	−	2.34365i	−0.370741	−	0.0798714i
$862$	−4.54787	+	5.41994i	−0.154901	+	0.184604i
$863$		−	36.8069i		−	1.25292i	−0.779453	−	0.626460i	$-0.784503\pi$
$863$		−	36.8069i		−	1.25292i	0.779453	−	0.626460i	$-0.215497\pi$
$864$	−2.86996	−	4.33167i	−0.0976379	−	0.147366i
$865$	3.91103	+	0.437970i	0.132979	+	0.0148914i
$866$	3.91886	+	3.28831i	0.133168	+	0.111741i
$867$	−24.3407	+	7.83471i	−0.826653	+	0.266081i
$868$	3.23384	−	0.570214i	0.109764	−	0.0193543i
$869$	15.5453	+	5.65803i	0.527339	+	0.191936i
$870$	−16.7832	+	10.2657i	−0.569005	+	0.348040i
$871$	−4.18404	+	23.7288i	−0.141771	+	0.804021i
$872$	8.16224	+	4.71247i	0.276408	+	0.159584i
$873$	34.3618	−	16.5257i	1.16297	−	0.559309i
$874$	−15.4924	−	26.8336i	−0.524038	−	0.907660i
$875$	39.3119	−	0.570450i	1.32899	−	0.0192847i
$876$	14.1653	−	7.48187i	0.478603	−	0.252789i
$877$	23.2217	+	27.6746i	0.784142	+	0.934505i	0.999113	−	0.0421160i	$-0.0134099\pi$
$877$	23.2217	+	27.6746i	0.784142	+	0.934505i	−0.214970	+	0.976621i	$0.568965\pi$
$878$	8.08209	+	9.63186i	0.272757	+	0.325059i
$879$	7.82474	+	4.91946i	0.263922	+	0.165929i
$880$	−2.85783	−	11.8034i	−0.0963375	−	0.397894i
$881$	−6.38299	−	11.0557i	−0.215048	−	0.372475i	0.738239	−	0.674539i	$-0.235658\pi$
$881$	−6.38299	−	11.0557i	−0.215048	−	0.372475i	−0.953288	+	0.302064i	$0.902324\pi$
$882$	−9.39031	−	13.0755i	−0.316188	−	0.440276i
$883$	−37.4558	−	21.6251i	−1.26049	−	0.727742i	−0.287318	−	0.957835i	$-0.592764\pi$
$883$	−37.4558	−	21.6251i	−1.26049	−	0.727742i	−0.973169	+	0.230093i	$0.926097\pi$
$884$	−3.95460	+	22.4276i	−0.133008	+	0.754323i
$885$	27.1694	−	0.688978i	0.913290	−	0.0231598i
$886$	28.8614	+	10.5047i	0.969616	+	0.352911i
$887$	1.81575	−	0.320165i	0.0609668	−	0.0107501i	−0.143082	−	0.989711i	$-0.545701\pi$
$887$	1.81575	−	0.320165i	0.0609668	−	0.0107501i	0.204048	+	0.978961i	$0.434590\pi$
$888$	2.26090	+	2.04703i	0.0758707	+	0.0686937i
$889$	2.71230	+	2.27589i	0.0909675	+	0.0763308i
$890$	19.0706	+	2.13558i	0.639246	+	0.0715849i
$891$	41.7360	−	25.4445i	1.39821	−	0.852422i
$892$		−	2.43666i		−	0.0815855i
$893$	28.8783	−	34.4158i	0.966374	−	1.15168i
$894$	5.10070	−	5.63362i	0.170593	−	0.188416i
$895$	−20.0790	+	1.26694i	−0.671165	+	0.0423491i
$896$	3.30446	+	1.20273i	0.110394	+	0.0401802i
$897$	5.39150	+	39.1446i	0.180017	+	1.30700i
$898$	26.1410	+	4.60936i	0.872336	+	0.153816i
$899$	−2.37174	+	4.10797i	−0.0791019	+	0.137009i
$900$	−11.9646	−	9.04702i	−0.398820	−	0.301567i
$901$	32.1007	+	55.6000i	1.06943	+	1.85230i
$902$	3.39386	+	9.32455i	0.113003	+	0.310474i
$903$	−2.38531	+	3.79399i	−0.0793780	+	0.126256i
$904$	11.0626	−	9.28266i	0.367938	−	0.308737i
$905$	25.4505	+	38.2909i	0.846003	+	1.27283i
$906$	−19.0573	+	10.0657i	−0.633138	+	0.334412i
$907$	−12.5758	−	34.5516i	−0.417571	−	1.14727i	−0.953075	−	0.302735i	$-0.902100\pi$
$907$	−12.5758	−	34.5516i	−0.417571	−	1.14727i	0.535504	−	0.844533i	$-0.320122\pi$
$908$	11.9900	−	6.92242i	0.397902	−	0.229729i
$909$	−45.9392	−	3.46680i	−1.52371	−	0.114987i
$910$	18.8506	−	25.5781i	0.624890	−	0.847904i
$911$	5.42726	−	30.7795i	0.179813	−	1.01977i	−0.752627	−	0.658447i	$-0.771214\pi$
$911$	5.42726	−	30.7795i	0.179813	−	1.01977i	0.932440	−	0.361324i	$-0.117675\pi$
$912$	7.50675	−	5.83169i	0.248573	−	0.193106i
$913$	10.2771	−	28.2361i	0.340123	−	0.934480i
$914$	1.45807	+	8.26912i	0.0482287	+	0.273518i
$915$	−1.64904	−	8.13974i	−0.0545156	−	0.269091i
$916$	20.2647	+	17.0041i	0.669564	+	0.561831i
$917$			4.60485i			0.152066i
$918$	−20.1682	−	21.2332i	−0.665651	−	0.700799i
$919$	−26.7135			−0.881197			−0.440599	−	0.897704i	$-0.645234\pi$
$919$	−26.7135			−0.881197			−0.440599	+	0.897704i	$0.645234\pi$
$920$	−9.14056	+	8.70761i	−0.301355	+	0.287082i
$921$	−1.53887	−	0.331529i	−0.0507074	−	0.0109243i
$922$	−12.4378	+	2.19312i	−0.409618	+	0.0722267i
$923$	1.50906	−	4.14611i	0.0496713	−	0.136471i
$924$	−12.4765	+	30.6373i	−0.410448	+	1.00789i
$925$	8.11764	+	3.40886i	0.266906	+	0.112083i
$926$	19.2741	−	33.3838i	0.633388	−	1.09706i
$927$	38.7874	+	9.89805i	1.27394	+	0.325095i
$928$	−4.39921	+	2.53989i	−0.144411	+	0.0833758i
$929$	−47.6545	+	17.3448i	−1.56349	+	0.569065i	−0.971533	−	0.236903i	$-0.923868\pi$
$929$	−47.6545	+	17.3448i	−1.56349	+	0.569065i	−0.591960	+	0.805968i	$0.701646\pi$
$930$	−3.57641	−	0.537522i	−0.117275	−	0.0176260i
$931$	22.5597	−	18.9298i	0.739364	−	0.620400i
$932$	−12.3365	−	14.7020i	−0.404095	−	0.481581i
$933$	39.6572	+	1.49424i	1.29832	+	0.0489192i
$934$	−18.8649	+	6.86627i	−0.617279	+	0.224671i
$935$	−27.4133	−	62.7153i	−0.896510	−	2.05101i
$936$	−11.6711	+	3.27716i	−0.381482	+	0.107117i
$937$	49.8732	+	28.7943i	1.62929	+	0.940669i	0.984306	+	0.176471i	$0.0564682\pi$
$937$	49.8732	+	28.7943i	1.62929	+	0.940669i	0.644981	+	0.764198i	$0.276865\pi$
$938$	20.6500	+	3.64116i	0.674248	+	0.118888i
$939$	−6.58624	+	16.1731i	−0.214934	+	0.527790i
$940$	−16.3972	−	8.13590i	−0.534817	−	0.265364i
$941$	−2.72603	−	15.4601i	−0.0888661	−	0.503985i	−0.996455	−	0.0841253i	$-0.973190\pi$
$941$	−2.72603	−	15.4601i	−0.0888661	−	0.503985i	0.907589	−	0.419860i	$-0.137921\pi$
$942$	2.59093	−	12.0264i	0.0844172	−	0.391841i
$943$	6.63036	−	7.90175i	0.215914	−	0.257316i
$944$	7.01737			0.228396
$945$	12.0392	+	39.0445i	0.391636	+	1.27012i
$946$	3.99617			0.129927
$947$	−32.1498	+	38.3147i	−1.04473	+	1.24506i	−0.0759555	+	0.997111i	$0.524201\pi$
$947$	−32.1498	+	38.3147i	−1.04473	+	1.24506i	−0.968773	+	0.247948i	$0.920244\pi$
$948$	5.02196	−	1.61646i	0.163106	−	0.0525000i
$949$	−6.48991	−	36.8061i	−0.210671	−	1.19478i
$950$	14.8565	−	23.0713i	0.482009	−	0.748531i
$951$	−5.39019	−	6.93843i	−0.174789	−	0.224994i
$952$	19.5177	+	3.44149i	0.632572	+	0.111539i
$953$	−27.8592	−	16.0845i	−0.902447	−	0.521028i	−0.0244534	−	0.999701i	$-0.507785\pi$
$953$	−27.8592	−	16.0845i	−0.902447	−	0.521028i	−0.877993	+	0.478673i	$0.841118\pi$
$954$	−19.2660	+	28.2263i	−0.623759	+	0.913861i
$955$	−0.977255	+	0.427165i	−0.0316232	+	0.0138227i
$956$	0.620178	−	0.225726i	0.0200580	−	0.00730052i
$957$	−22.3178	−	42.2540i	−0.721431	−	1.36588i
$958$	16.4939	+	19.6566i	0.532892	+	0.635076i
$959$	31.5173	−	26.4461i	1.01775	−	0.853990i
$960$	−3.02903	−	2.41349i	−0.0977617	−	0.0778952i
$961$	28.3111	−	10.3044i	0.913261	−	0.332400i
$962$	6.16209	−	3.55768i	0.198674	−	0.114704i
$963$	−16.2136	+	1.61386i	−0.522474	+	0.0520058i
$964$	4.19535	−	7.26655i	0.135123	−	0.234040i
$965$	−5.67816	+	19.3057i	−0.182786	+	0.621474i
$966$	34.0656	−	4.69196i	1.09604	−	0.150961i
$967$	−10.3943	+	28.5581i	−0.334258	+	0.918366i	0.652733	+	0.757588i	$0.273623\pi$
$967$	−10.3943	+	28.5581i	−0.334258	+	0.918366i	−0.986991	+	0.160778i	$0.948600\pi$
$968$	18.2167	−	3.21209i	0.585506	−	0.103240i
$969$	35.9572	−	39.7139i	1.15511	−	1.27580i
$970$	20.5772	−	19.6026i	0.660695	−	0.629401i
$971$	−55.3803			−1.77724			−0.888619	−	0.458646i	$-0.848335\pi$
$971$	−55.3803			−1.77724			−0.888619	+	0.458646i	$0.848335\pi$
$972$	5.53280	−	14.5735i	0.177465	−	0.467447i
$973$			16.6235i			0.532925i
$974$	26.8640	+	22.5416i	0.860779	+	0.722279i
$975$	−28.6438	+	20.1036i	−0.917336	+	0.643832i
$976$	−0.372365	−	2.11179i	−0.0119191	−	0.0675967i
$977$	6.25930	−	17.1973i	0.200253	−	0.550190i	−0.798397	−	0.602131i	$-0.794319\pi$
$977$	6.25930	−	17.1973i	0.200253	−	0.550190i	0.998650	+	0.0519408i	$0.0165407\pi$
$978$	4.75019	+	34.4884i	0.151894	+	1.10282i
$979$	−8.09373	+	45.9018i	−0.258677	+	1.46703i
$980$	−9.65904	−	7.11854i	−0.308547	−	0.227393i
$981$	2.80057	+	28.1358i	0.0894152	+	0.898307i
$982$	−27.1821	+	15.6936i	−0.867416	+	0.500803i
$983$	10.2946	+	28.2841i	0.328346	+	0.902122i	0.988531	+	0.151019i	$0.0482556\pi$
$983$	10.2946	+	28.2841i	0.328346	+	0.902122i	−0.660185	+	0.751103i	$0.729522\pi$
$984$	2.67904	+	1.68433i	0.0854047	+	0.0536944i
$985$	2.13118	−	1.41651i	0.0679050	−	0.0451338i
$986$	−21.9311	+	18.4024i	−0.698428	+	0.586050i
$987$	23.2865	+	44.0881i	0.741217	+	1.40334i
$988$	−7.58489	−	20.8393i	−0.241308	−	0.662987i
$989$	−2.07703	−	3.59751i	−0.0660456	−	0.114394i
$990$	23.7607	−	27.6193i	0.755164	−	0.877799i
$991$	20.2291	−	35.0378i	0.642598	−	1.11301i	−0.342252	−	0.939608i	$-0.611190\pi$
$991$	20.2291	−	35.0378i	0.642598	−	1.11301i	0.984851	−	0.173405i	$-0.0554769\pi$
$992$	−0.919611	−	0.162152i	−0.0291977	−	0.00514834i
$993$	24.8327	−	19.2915i	0.788041	−	0.612197i
$994$	−3.60815	−	1.31326i	−0.114444	−	0.0416541i
$995$	29.4914	−	1.86084i	0.934941	−	0.0589927i
$996$	−2.93609	−	9.12178i	−0.0930336	−	0.289035i
$997$	−10.3907	+	12.3832i	−0.329077	+	0.392179i	−0.905061	−	0.425282i	$-0.860175\pi$
$997$	−10.3907	+	12.3832i	−0.329077	+	0.392179i	0.575983	+	0.817461i	$0.304619\pi$
$998$			28.0629i			0.888316i
$999$	−1.03157	+	9.09140i	−0.0326374	+	0.287639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.p.a.259.3	yes	108
3.2	odd	2		810.2.p.a.289.12		108
5.4	even	2	inner	270.2.p.a.259.16	yes	108
15.14	odd	2		810.2.p.a.289.6		108
27.5	odd	18		810.2.p.a.199.6		108
27.22	even	9	inner	270.2.p.a.49.16	yes	108
135.49	even	18	inner	270.2.p.a.49.3	✓	108
135.59	odd	18		810.2.p.a.199.12		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.p.a.49.3	✓	108	135.49	even	18	inner
270.2.p.a.49.16	yes	108	27.22	even	9	inner
270.2.p.a.259.3	yes	108	1.1	even	1	trivial
270.2.p.a.259.16	yes	108	5.4	even	2	inner
810.2.p.a.199.6		108	27.5	odd	18
810.2.p.a.199.12		108	135.59	odd	18
810.2.p.a.289.6		108	15.14	odd	2
810.2.p.a.289.12		108	3.2	odd	2

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-1.28397 - 1.16251i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.993869 - 2.00305i) q^{5} +(1.71585 - 0.236329i) q^{6} +(-3.46311 - 0.610640i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.297144 + 2.98525i) q^{9} +(0.895581 + 2.04889i) q^{10} +(-5.10364 + 1.85757i) q^{11} +(-0.921890 + 1.46633i) q^{12} +(2.59740 + 3.09546i) q^{13} +(2.69382 - 2.26039i) q^{14} +(-3.60466 + 1.41647i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-4.88082 + 2.81794i) q^{17} +(-2.47783 - 1.69125i) q^{18} +(2.74408 - 4.75289i) q^{19} +(-2.14521 - 0.630943i) q^{20} +(3.73665 + 4.80994i) q^{21} +(1.85757 - 5.10364i) q^{22} +(-5.55998 + 0.980374i) q^{23} +(-0.530694 - 1.64875i) q^{24} +(-3.02445 - 3.98155i) q^{25} -4.04083 q^{26} +(3.08886 - 4.17839i) q^{27} +3.51653i q^{28} +(-3.89133 - 3.26521i) q^{29} +(1.23195 - 3.67182i) q^{30} +(-0.162152 - 0.919611i) q^{31} +(0.342020 - 0.939693i) q^{32} +(8.71235 + 3.54796i) q^{33} +(0.978660 - 5.55026i) q^{34} +(-4.66502 + 6.32990i) q^{35} +(2.88830 - 0.811013i) q^{36} +(-1.52496 + 0.880434i) q^{37} +(1.87706 + 5.15719i) q^{38} +(0.263525 - 6.99396i) q^{39} +(1.86224 - 1.23776i) q^{40} +(-1.39959 + 1.17440i) q^{41} +(-6.08650 - 0.229333i) q^{42} +(0.251653 + 0.691411i) q^{43} +(2.71559 + 4.70354i) q^{44} +(6.27493 + 2.37175i) q^{45} +(2.82287 - 4.88936i) q^{46} +(8.06173 + 1.42150i) q^{47} +(1.60414 + 0.653259i) q^{48} +(5.04241 + 1.83529i) q^{49} +(4.99412 + 0.242427i) q^{50} +(9.54269 + 2.05585i) q^{51} +(2.59740 - 3.09546i) q^{52} -11.3915i q^{53} +(1.21536 + 5.05202i) q^{54} +(-1.35153 + 12.0690i) q^{55} +(-2.69382 - 2.26039i) q^{56} +(-9.04859 + 2.91253i) q^{57} +(5.00260 - 0.882093i) q^{58} +(-6.59417 - 2.40008i) q^{59} +(2.02090 + 3.30393i) q^{60} +(-0.372365 + 2.11179i) q^{61} +(0.808692 + 0.466899i) q^{62} +(0.793868 - 10.5197i) q^{63} +(0.500000 + 0.866025i) q^{64} +(8.78183 - 2.12624i) q^{65} +(-8.31809 + 4.39346i) q^{66} +(3.83285 + 4.56782i) q^{67} +(3.62267 + 4.31733i) q^{68} +(8.27852 + 5.20476i) q^{69} +(-1.85037 - 7.64240i) q^{70} +(-0.545952 - 0.945616i) q^{71} +(-1.23529 + 2.73387i) q^{72} +(-8.00992 - 4.62453i) q^{73} +(0.305771 - 1.73412i) q^{74} +(-0.745292 + 8.62812i) q^{75} +(-5.15719 - 1.87706i) q^{76} +(18.8088 - 3.31649i) q^{77} +(5.18829 + 4.69750i) q^{78} +(-2.33332 - 1.95789i) q^{79} +(-0.248847 + 2.22218i) q^{80} +(-8.82341 + 1.77410i) q^{81} -1.82704i q^{82} +(-3.55626 + 4.23818i) q^{83} +(4.08800 - 4.51512i) q^{84} +(0.793593 + 12.5772i) q^{85} +(-0.691411 - 0.251653i) q^{86} +(1.20050 + 8.71614i) q^{87} +(-5.34867 - 0.943114i) q^{88} +(4.29096 - 7.43216i) q^{89} +(-5.85032 + 3.28235i) q^{90} +(-7.10486 - 12.3060i) q^{91} +(1.93096 + 5.30527i) q^{92} +(-0.860858 + 1.36925i) q^{93} +(-6.27091 + 5.26192i) q^{94} +(-6.79303 - 10.2203i) q^{95} +(-1.53154 + 0.808933i) q^{96} +(-4.34698 - 11.9432i) q^{97} +(-4.64711 + 2.68301i) q^{98} +(-7.06183 - 14.6837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41}+ \cdots - 36 q^{99}+O(q^{100}) \) 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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