LMFDB - Embedded newform 460.2.e.b.91.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [460,2,Mod(91,460)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(460, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("460.91"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$460 = 2^{2} \cdot 5 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	460.e (of order $2$ , degree $1$ , minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	460.91
Dual form			460.2.e.b.91.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39466 + 0.234385i) q^{2} +1.37989i q^{3} +(1.89013 - 0.653773i) q^{4} -1.00000i q^{5} +(-0.323424 - 1.92446i) q^{6} +2.31854 q^{7} +(-2.48284 + 1.35481i) q^{8} +1.09592 q^{9} +(0.234385 + 1.39466i) q^{10} +1.65400 q^{11} +(0.902131 + 2.60816i) q^{12} -3.48270 q^{13} +(-3.23356 + 0.543431i) q^{14} +1.37989 q^{15} +(3.14516 - 2.47143i) q^{16} -5.56745i q^{17} +(-1.52843 + 0.256867i) q^{18} +6.63011 q^{19} +(-0.653773 - 1.89013i) q^{20} +3.19932i q^{21} +(-2.30676 + 0.387673i) q^{22} +(-0.716404 - 4.74202i) q^{23} +(-1.86948 - 3.42604i) q^{24} -1.00000 q^{25} +(4.85717 - 0.816294i) q^{26} +5.65189i q^{27} +(4.38233 - 1.51580i) q^{28} +4.94862 q^{29} +(-1.92446 + 0.323424i) q^{30} +3.53020i q^{31} +(-3.80715 + 4.18397i) q^{32} +2.28233i q^{33} +(1.30493 + 7.76468i) q^{34} -2.31854i q^{35} +(2.07142 - 0.716481i) q^{36} +9.38162i q^{37} +(-9.24672 + 1.55400i) q^{38} -4.80573i q^{39} +(1.35481 + 2.48284i) q^{40} -6.37131 q^{41} +(-0.749872 - 4.46194i) q^{42} +12.8813 q^{43} +(3.12628 - 1.08134i) q^{44} -1.09592i q^{45} +(2.11060 + 6.44557i) q^{46} +8.60850i q^{47} +(3.41029 + 4.33996i) q^{48} -1.62438 q^{49} +(1.39466 - 0.234385i) q^{50} +7.68244 q^{51} +(-6.58275 + 2.27690i) q^{52} +2.04707i q^{53} +(-1.32472 - 7.88245i) q^{54} -1.65400i q^{55} +(-5.75656 + 3.14117i) q^{56} +9.14879i q^{57} +(-6.90162 + 1.15988i) q^{58} -9.50571i q^{59} +(2.60816 - 0.902131i) q^{60} -3.86641i q^{61} +(-0.827425 - 4.92341i) q^{62} +2.54093 q^{63} +(4.32901 - 6.72753i) q^{64} +3.48270i q^{65} +(-0.534945 - 3.18307i) q^{66} +4.67720 q^{67} +(-3.63985 - 10.5232i) q^{68} +(6.54344 - 0.988556i) q^{69} +(0.543431 + 3.23356i) q^{70} +10.9401i q^{71} +(-2.72099 + 1.48475i) q^{72} +6.51430 q^{73} +(-2.19891 - 13.0841i) q^{74} -1.37989i q^{75} +(12.5318 - 4.33459i) q^{76} +3.83487 q^{77} +(1.12639 + 6.70234i) q^{78} -4.23483 q^{79} +(-2.47143 - 3.14516i) q^{80} -4.51121 q^{81} +(8.88578 - 1.49334i) q^{82} -5.44089 q^{83} +(2.09163 + 6.04711i) q^{84} -5.56745 q^{85} +(-17.9649 + 3.01918i) q^{86} +6.82852i q^{87} +(-4.10663 + 2.24085i) q^{88} -7.48765i q^{89} +(0.256867 + 1.52843i) q^{90} -8.07478 q^{91} +(-4.45430 - 8.49466i) q^{92} -4.87126 q^{93} +(-2.01770 - 12.0059i) q^{94} -6.63011i q^{95} +(-5.77340 - 5.25343i) q^{96} -19.0123i q^{97} +(2.26545 - 0.380731i) q^{98} +1.81265 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48}+ \cdots + 62 q^{98}+O(q^{100})$ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$ .

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$-1$

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

)

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

$2$	−1.39466	+	0.234385i	−0.986170	+	0.165735i
$2$	−1.39466	+	0.234385i	−0.986170	+	0.165735i
$3$			1.37989i			0.796677i	0.917238	+	0.398339i	$0.130413\pi$
$3$			1.37989i			0.796677i	−0.917238	+	0.398339i	$0.869587\pi$
$4$	1.89013	−	0.653773i	0.945064	−	0.326886i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.323424	−	1.92446i	−0.132037	−	0.785659i
$7$	2.31854			0.876325			0.438162	−	0.898896i	$-0.355629\pi$
$7$	2.31854			0.876325			0.438162	+	0.898896i	$0.355629\pi$
$8$	−2.48284	+	1.35481i	−0.877817	+	0.478996i
$9$	1.09592			0.365306
$10$	0.234385	+	1.39466i	0.0741191	+	0.441029i
$11$	1.65400			0.498701			0.249350	−	0.968413i	$-0.419783\pi$
$11$	1.65400			0.498701			0.249350	+	0.968413i	$0.419783\pi$
$12$	0.902131	+	2.60816i	0.260423	+	0.752910i
$13$	−3.48270			−0.965928			−0.482964	−	0.875640i	$-0.660440\pi$
$13$	−3.48270			−0.965928			−0.482964	+	0.875640i	$0.660440\pi$
$14$	−3.23356	+	0.543431i	−0.864206	+	0.145238i
$15$	1.37989			0.356285
$16$	3.14516	−	2.47143i	0.786291	−	0.617857i
$17$		−	5.56745i		−	1.35031i	−0.737678	−	0.675153i	$-0.764078\pi$
$17$		−	5.56745i		−	1.35031i	0.737678	−	0.675153i	$-0.235922\pi$
$18$	−1.52843	+	0.256867i	−0.360254	+	0.0605440i
$19$	6.63011			1.52105			0.760526	−	0.649307i	$-0.224941\pi$
$19$	6.63011			1.52105			0.760526	+	0.649307i	$0.224941\pi$
$20$	−0.653773	−	1.89013i	−0.146188	−	0.422645i
$21$			3.19932i			0.698148i
$22$	−2.30676	+	0.387673i	−0.491804	+	0.0826523i
$23$	−0.716404	−	4.74202i	−0.149381	−	0.988780i
$23$	−0.716404	−	4.74202i	−0.149381	−	0.988780i
$24$	−1.86948	−	3.42604i	−0.381605	−	0.699337i
$25$	−1.00000			−0.200000
$26$	4.85717	−	0.816294i	0.952570	−	0.160088i
$27$			5.65189i			1.08771i
$28$	4.38233	−	1.51580i	0.828183	−	0.286459i
$29$	4.94862			0.918935			0.459468	−	0.888194i	$-0.348040\pi$
$29$	4.94862			0.918935			0.459468	+	0.888194i	$0.348040\pi$
$30$	−1.92446	+	0.323424i	−0.351357	+	0.0590489i
$31$			3.53020i			0.634042i	0.948419	+	0.317021i	$0.102683\pi$
$31$			3.53020i			0.634042i	−0.948419	+	0.317021i	$0.897317\pi$
$32$	−3.80715	+	4.18397i	−0.673016	+	0.739628i
$33$			2.28233i			0.397303i
$34$	1.30493	+	7.76468i	0.223793	+	1.33163i
$35$		−	2.31854i		−	0.391904i
$36$	2.07142	−	0.716481i	0.345237	−	0.119413i
$37$			9.38162i			1.54233i	0.636636	+	0.771164i	$0.280325\pi$
$37$			9.38162i			1.54233i	−0.636636	+	0.771164i	$0.719675\pi$
$38$	−9.24672	+	1.55400i	−1.50002	+	0.252092i
$39$		−	4.80573i		−	0.769533i
$40$	1.35481	+	2.48284i	0.214213	+	0.392572i
$41$	−6.37131			−0.995031			−0.497516	−	0.867455i	$-0.665754\pi$
$41$	−6.37131			−0.995031			−0.497516	+	0.867455i	$0.665754\pi$
$42$	−0.749872	−	4.46194i	−0.115708	−	0.688493i
$43$	12.8813			1.96438			0.982188	−	0.187900i	$-0.0601680\pi$
$43$	12.8813			1.96438			0.982188	+	0.187900i	$0.0601680\pi$
$44$	3.12628	−	1.08134i	0.471304	−	0.163018i
$45$		−	1.09592i		−	0.163370i
$46$	2.11060	+	6.44557i	0.311190	+	0.950348i
$47$			8.60850i			1.25568i	0.778343	+	0.627840i	$0.216061\pi$
$47$			8.60850i			1.25568i	−0.778343	+	0.627840i	$0.783939\pi$
$48$	3.41029	+	4.33996i	0.492232	+	0.626420i
$49$	−1.62438			−0.232055
$50$	1.39466	−	0.234385i	0.197234	−	0.0331470i
$51$	7.68244			1.07576
$52$	−6.58275	+	2.27690i	−0.912864	+	0.315749i
$53$			2.04707i			0.281187i	0.990067	+	0.140594i	$0.0449011\pi$
$53$			2.04707i			0.281187i	−0.990067	+	0.140594i	$0.955099\pi$
$54$	−1.32472	−	7.88245i	−0.180271	−	1.07267i
$55$		−	1.65400i		−	0.223026i
$56$	−5.75656	+	3.14117i	−0.769253	+	0.419756i
$57$			9.14879i			1.21179i
$58$	−6.90162	+	1.15988i	−0.906227	+	0.152300i
$59$		−	9.50571i		−	1.23754i	−0.785573	−	0.618769i	$-0.787632\pi$
$59$		−	9.50571i		−	1.23754i	0.785573	−	0.618769i	$-0.212368\pi$
$60$	2.60816	−	0.902131i	0.336712	−	0.116465i
$61$		−	3.86641i		−	0.495043i	−0.968882	−	0.247521i	$-0.920384\pi$
$61$		−	3.86641i		−	0.495043i	0.968882	−	0.247521i	$-0.0796161\pi$
$62$	−0.827425	−	4.92341i	−0.105083	−	0.625273i
$63$	2.54093			0.320127
$64$	4.32901	−	6.72753i	0.541126	−	0.840942i
$65$			3.48270i			0.431976i
$66$	−0.534945	−	3.18307i	−0.0658472	−	0.391809i
$67$	4.67720			0.571411			0.285705	−	0.958318i	$-0.407772\pi$
$67$	4.67720			0.571411			0.285705	+	0.958318i	$0.407772\pi$
$68$	−3.63985	−	10.5232i	−0.441396	−	1.27612i
$69$	6.54344	−	0.988556i	0.787738	−	0.119008i
$70$	0.543431	+	3.23356i	0.0649524	+	0.386484i
$71$			10.9401i			1.29835i	0.760639	+	0.649175i	$0.224886\pi$
$71$			10.9401i			1.29835i	−0.760639	+	0.649175i	$0.775114\pi$
$72$	−2.72099	+	1.48475i	−0.320672	+	0.174980i
$73$	6.51430			0.762441			0.381220	−	0.924484i	$-0.375504\pi$
$73$	6.51430			0.762441			0.381220	+	0.924484i	$0.375504\pi$
$74$	−2.19891	−	13.0841i	−0.255618	−	1.52100i
$75$		−	1.37989i		−	0.159335i
$76$	12.5318	−	4.33459i	1.43749	−	0.497211i
$77$	3.83487			0.437024
$78$	1.12639	+	6.70234i	0.127539	+	0.758891i
$79$	−4.23483			−0.476456			−0.238228	−	0.971209i	$-0.576566\pi$
$79$	−4.23483			−0.476456			−0.238228	+	0.971209i	$0.576566\pi$
$80$	−2.47143	−	3.14516i	−0.276314	−	0.351640i
$81$	−4.51121			−0.501246
$82$	8.88578	−	1.49334i	0.981270	−	0.164912i
$83$	−5.44089			−0.597215			−0.298608	−	0.954376i	$-0.596522\pi$
$83$	−5.44089			−0.597215			−0.298608	+	0.954376i	$0.596522\pi$
$84$	2.09163	+	6.04711i	0.228215	+	0.659794i
$85$	−5.56745			−0.603875
$86$	−17.9649	+	3.01918i	−1.93721	+	0.325566i
$87$			6.82852i			0.732095i
$88$	−4.10663	+	2.24085i	−0.437768	+	0.238876i
$89$		−	7.48765i		−	0.793689i	−0.917886	−	0.396845i	$-0.870105\pi$
$89$		−	7.48765i		−	0.793689i	0.917886	−	0.396845i	$-0.129895\pi$
$90$	0.256867	+	1.52843i	0.0270761	+	0.161110i
$91$	−8.07478			−0.846467
$92$	−4.45430	−	8.49466i	−0.464393	−	0.885629i
$93$	−4.87126			−0.505127
$94$	−2.01770	−	12.0059i	−0.208110	−	1.23831i
$95$		−	6.63011i		−	0.680235i
$96$	−5.77340	−	5.25343i	−0.589245	−	0.536176i
$97$		−	19.0123i		−	1.93040i	−0.261509	−	0.965201i	$-0.584220\pi$
$97$		−	19.0123i		−	1.93040i	0.261509	−	0.965201i	$-0.415780\pi$
$98$	2.26545	−	0.380731i	0.228845	−	0.0384596i
$99$	1.81265			0.182178
$100$	−1.89013	+	0.653773i	−0.189013	+	0.0653773i
$101$	4.06769			0.404750			0.202375	−	0.979308i	$-0.435134\pi$
$101$	4.06769			0.404750			0.202375	+	0.979308i	$0.435134\pi$
$102$	−10.7144	+	1.80065i	−1.06088	+	0.178291i
$103$	−15.5279			−1.53001			−0.765005	−	0.644025i	$-0.777263\pi$
$103$	−15.5279			−1.53001			−0.765005	+	0.644025i	$0.777263\pi$
$104$	8.64700	−	4.71839i	0.847908	−	0.462676i
$105$	3.19932			0.312221
$106$	−0.479803	−	2.85496i	−0.0466026	−	0.277298i
$107$	−16.9678			−1.64034			−0.820168	−	0.572123i	$-0.806120\pi$
$107$	−16.9678			−1.64034			−0.820168	+	0.572123i	$0.806120\pi$
$108$	3.69505	+	10.6828i	0.355557	+	1.02795i
$109$			4.30718i			0.412553i	0.978494	+	0.206276i	$0.0661346\pi$
$109$			4.30718i			0.412553i	−0.978494	+	0.206276i	$0.933865\pi$
$110$	0.387673	+	2.30676i	0.0369632	+	0.219941i
$111$	−12.9456			−1.22874
$112$	7.29218	−	5.73010i	0.689046	−	0.541443i
$113$		−	5.36983i		−	0.505151i	−0.967577	−	0.252575i	$-0.918722\pi$
$113$		−	5.36983i		−	0.505151i	0.967577	−	0.252575i	$-0.0812776\pi$
$114$	−2.14434	−	12.7594i	−0.200836	−	1.19503i
$115$	−4.74202	+	0.716404i	−0.442196	+	0.0668050i
$116$	9.35352	−	3.23527i	0.868452	−	0.300387i
$117$	−3.81676			−0.352859
$118$	2.22800	+	13.2572i	0.205104	+	1.22042i
$119$		−	12.9083i		−	1.18331i
$120$	−3.42604	+	1.86948i	−0.312753	+	0.170659i
$121$	−8.26427			−0.751298
$122$	0.906228	+	5.39231i	0.0820460	+	0.488196i
$123$		−	8.79167i		−	0.792718i
$124$	2.30795	+	6.67252i	0.207260	+	0.599210i
$125$			1.00000i			0.0894427i
$126$	−3.54372	+	0.595555i	−0.315699	+	0.0530562i
$127$		−	2.29388i		−	0.203549i	−0.994808	−	0.101774i	$-0.967548\pi$
$127$		−	2.29388i		−	0.203549i	0.994808	−	0.101774i	$-0.0324520\pi$
$128$	−4.46064	+	10.3972i	−0.394268	+	0.918995i
$129$			17.7747i			1.56497i
$130$	−0.816294	−	4.85717i	−0.0715937	−	0.426002i
$131$			13.9868i			1.22203i	0.791619	+	0.611015i	$0.209239\pi$
$131$			13.9868i			1.22203i	−0.791619	+	0.611015i	$0.790761\pi$
$132$	1.49213	+	4.31390i	0.129873	+	0.375477i
$133$	15.3722			1.33294
$134$	−6.52308	+	1.09627i	−0.563508	+	0.0947029i
$135$	5.65189			0.486438
$136$	7.54281	+	13.8231i	0.646791	+	1.18532i
$137$		−	12.2230i		−	1.04428i	−0.852860	−	0.522139i	$-0.825134\pi$
$137$		−	12.2230i		−	1.04428i	0.852860	−	0.522139i	$-0.174866\pi$
$138$	−8.89415	+	2.91238i	−0.757120	+	0.247918i
$139$		−	1.61414i		−	0.136910i	−0.997654	−	0.0684549i	$-0.978193\pi$
$139$		−	1.61414i		−	0.136910i	0.997654	−	0.0684549i	$-0.0218069\pi$
$140$	−1.51580	−	4.38233i	−0.128108	−	0.370375i
$141$	−11.8787			−1.00037
$142$	−2.56419	−	15.2577i	−0.215182	−	1.28039i
$143$	−5.76040			−0.481709
$144$	3.44684	−	2.70848i	0.287236	−	0.225707i
$145$		−	4.94862i		−	0.410960i
$146$	−9.08520	+	1.52685i	−0.751897	+	0.126363i
$147$		−	2.24146i		−	0.184873i
$148$	6.13344	+	17.7325i	0.504166	+	1.45760i
$149$		−	4.80668i		−	0.393779i	−0.980426	−	0.196889i	$-0.936916\pi$
$149$		−	4.80668i		−	0.393779i	0.980426	−	0.196889i	$-0.0630840\pi$
$150$	0.323424	+	1.92446i	0.0264075	+	0.157132i
$151$			9.37662i			0.763059i	0.924357	+	0.381529i	$0.124602\pi$
$151$			9.37662i			0.763059i	−0.924357	+	0.381529i	$0.875398\pi$
$152$	−16.4615	+	8.98251i	−1.33521	+	0.728578i
$153$		−	6.10147i		−	0.493274i
$154$	−5.34832	+	0.898836i	−0.430980	+	0.0724302i
$155$	3.53020			0.283552
$156$	−3.14186	−	9.08344i	−0.251550	−	0.727258i
$157$			14.5957i			1.16486i	0.812879	+	0.582432i	$0.197899\pi$
$157$			14.5957i			1.16486i	−0.812879	+	0.582432i	$0.802101\pi$
$158$	5.90613	−	0.992581i	0.469866	−	0.0789655i
$159$	−2.82472			−0.224015
$160$	4.18397	+	3.80715i	0.330772	+	0.300982i
$161$	−1.66101	−	10.9946i	−0.130906	−	0.866492i
$162$	6.29159	−	1.05736i	0.494314	−	0.0830741i
$163$		−	5.23715i		−	0.410205i	−0.978740	−	0.205103i	$-0.934247\pi$
$163$		−	5.23715i		−	0.410205i	0.978740	−	0.205103i	$-0.0657529\pi$
$164$	−12.0426	+	4.16539i	−0.940368	+	0.325262i
$165$	2.28233			0.177679
$166$	7.58817	−	1.27526i	0.588956	−	0.0989796i
$167$			2.65734i			0.205631i	0.994700	+	0.102816i	$0.0327852\pi$
$167$			2.65734i			0.205631i	−0.994700	+	0.102816i	$0.967215\pi$
$168$	−4.33445	−	7.94339i	−0.334410	−	0.612846i
$169$	−0.870770			−0.0669823
$170$	7.76468	−	1.30493i	0.595524	−	0.100083i
$171$	7.26606			0.555649
$172$	24.3473	−	8.42143i	1.85646	−	0.642128i
$173$	−8.91998			−0.678173			−0.339087	−	0.940755i	$-0.610118\pi$
$173$	−8.91998			−0.678173			−0.339087	+	0.940755i	$0.610118\pi$
$174$	−1.60050	−	9.52344i	−0.121334	−	0.721970i
$175$	−2.31854			−0.175265
$176$	5.20211	−	4.08775i	0.392124	−	0.308126i
$177$	13.1168			0.985918
$178$	1.75499	+	10.4427i	0.131542	+	0.782713i
$179$			1.37963i			0.103119i	0.998670	+	0.0515593i	$0.0164191\pi$
$179$			1.37963i			0.103119i	−0.998670	+	0.0515593i	$0.983581\pi$
$180$	−0.716481	−	2.07142i	−0.0534033	−	0.154395i
$181$		−	20.6166i		−	1.53242i	−0.642592	−	0.766208i	$-0.722141\pi$
$181$		−	20.6166i		−	1.53242i	0.642592	−	0.766208i	$-0.277859\pi$
$182$	11.2615	−	1.89261i	0.834761	−	0.140289i
$183$	5.33520			0.394389
$184$	8.20323	+	10.8031i	0.604750	+	0.796415i
$185$	9.38162			0.689750
$186$	6.79373	−	1.14175i	0.498141	−	0.0837173i
$187$		−	9.20858i		−	0.673398i
$188$	5.62800	+	16.2712i	0.410464	+	1.18670i
$189$			13.1041i			0.953185i
$190$	1.55400	+	9.24672i	0.112739	+	0.670828i
$191$	−7.65350			−0.553788			−0.276894	−	0.960901i	$-0.589305\pi$
$191$	−7.65350			−0.553788			−0.276894	+	0.960901i	$0.589305\pi$
$192$	9.28322	+	5.97353i	0.669959	+	0.431102i
$193$	−3.72049			−0.267807			−0.133904	−	0.990994i	$-0.542751\pi$
$193$	−3.72049			−0.267807			−0.133904	+	0.990994i	$0.542751\pi$
$194$	4.45619	+	26.5155i	0.319936	+	1.90371i
$195$	−4.80573			−0.344146
$196$	−3.07029	+	1.06198i	−0.219306	+	0.0758555i
$197$	2.90083			0.206675			0.103338	−	0.994646i	$-0.467048\pi$
$197$	2.90083			0.206675			0.103338	+	0.994646i	$0.467048\pi$
$198$	−2.52802	+	0.424858i	−0.179659	+	0.0301933i
$199$	−12.0631			−0.855130			−0.427565	−	0.903985i	$-0.640628\pi$
$199$	−12.0631			−0.855130			−0.427565	+	0.903985i	$0.640628\pi$
$200$	2.48284	−	1.35481i	0.175563	−	0.0957992i
$201$			6.45400i			0.455230i
$202$	−5.67303	+	0.953406i	−0.399153	+	0.0670814i
$203$	11.4736			0.805286
$204$	14.5208	−	5.02257i	1.01666	−	0.351650i
$205$			6.37131i			0.444991i
$206$	21.6561	−	3.63951i	1.50885	−	0.253576i
$207$	−0.785120	−	5.19686i	−0.0545696	−	0.361207i
$208$	−10.9537	+	8.60725i	−0.759500	+	0.596805i
$209$	10.9662			0.758550
$210$	−4.46194	+	0.749872i	−0.307903	+	0.0517461i
$211$			14.7717i			1.01692i	0.861084	+	0.508462i	$0.169786\pi$
$211$			14.7717i			1.01692i	−0.861084	+	0.508462i	$0.830214\pi$
$212$	1.33832	+	3.86923i	0.0919162	+	0.265740i
$213$	−15.0961			−1.03437
$214$	23.6642	−	3.97699i	1.61765	−	0.271862i
$215$		−	12.8813i		−	0.878496i
$216$	−7.65722	−	14.0328i	−0.521008	−	0.954808i
$217$			8.18489i			0.555627i
$218$	−1.00954	−	6.00703i	−0.0683746	−	0.406847i
$219$			8.98898i			0.607419i
$220$	−1.08134	−	3.12628i	−0.0729040	−	0.210773i
$221$			19.3898i			1.30430i
$222$	18.0546	−	3.03424i	1.21174	−	0.203645i
$223$		−	23.6624i		−	1.58455i	−0.610164	−	0.792275i	$-0.708896\pi$
$223$		−	23.6624i		−	1.58455i	0.610164	−	0.792275i	$-0.291104\pi$
$224$	−8.82703	+	9.70069i	−0.589781	+	0.648155i
$225$	−1.09592			−0.0730611
$226$	1.25861	+	7.48906i	0.0837213	+	0.498165i
$227$	26.1645			1.73660			0.868298	−	0.496042i	$-0.165214\pi$
$227$	26.1645			1.73660			0.868298	+	0.496042i	$0.165214\pi$
$228$	5.98123	+	17.2924i	0.396117	+	1.14522i
$229$		−	19.1863i		−	1.26787i	−0.773387	−	0.633934i	$-0.781439\pi$
$229$		−	19.1863i		−	1.26787i	0.773387	−	0.633934i	$-0.218561\pi$
$230$	6.44557	−	2.11060i	0.425008	−	0.139169i
$231$			5.29168i			0.348167i
$232$	−12.2866	+	6.70441i	−0.806657	+	0.440166i
$233$	27.4651			1.79930			0.899651	−	0.436611i	$-0.143821\pi$
$233$	27.4651			1.79930			0.899651	+	0.436611i	$0.143821\pi$
$234$	5.32306	−	0.894590i	0.347979	−	0.0584812i
$235$	8.60850			0.561557
$236$	−6.21458	−	17.9670i	−0.404534	−	1.16955i
$237$		−	5.84358i		−	0.379581i
$238$	3.02552	+	18.0027i	0.196116	+	1.16694i
$239$		−	0.599617i		−	0.0387860i	−0.999812	−	0.0193930i	$-0.993827\pi$
$239$		−	0.599617i		−	0.0387860i	0.999812	−	0.0193930i	$-0.00617337\pi$
$240$	4.33996	−	3.41029i	0.280143	−	0.220133i
$241$			14.3108i			0.921840i	0.887442	+	0.460920i	$0.152481\pi$
$241$			14.3108i			0.921840i	−0.887442	+	0.460920i	$0.847519\pi$
$242$	11.5258	−	1.93702i	0.740907	−	0.124517i
$243$			10.7307i			0.688377i
$244$	−2.52775	−	7.30800i	−0.161823	−	0.467847i
$245$			1.62438i			0.103778i
$246$	2.06064	+	12.2614i	0.131381	+	0.781755i
$247$	−23.0907			−1.46923
$248$	−4.78273	−	8.76492i	−0.303703	−	0.556573i
$249$		−	7.50780i		−	0.475788i
$250$	−0.234385	−	1.39466i	−0.0148238	−	0.0882058i
$251$	−18.5184			−1.16887			−0.584437	−	0.811439i	$-0.698685\pi$
$251$	−18.5184			−1.16887			−0.584437	+	0.811439i	$0.698685\pi$
$252$	4.80267	−	1.66119i	0.302540	−	0.104645i
$253$	−1.18493	−	7.84332i	−0.0744962	−	0.493105i
$254$	0.537650	+	3.19917i	0.0337352	+	0.200734i
$255$		−	7.68244i		−	0.481093i
$256$	3.78410	−	15.5461i	0.236506	−	0.971630i
$257$	−20.7306			−1.29314			−0.646569	−	0.762855i	$-0.723797\pi$
$257$	−20.7306			−1.29314			−0.646569	+	0.762855i	$0.723797\pi$
$258$	−4.16612	−	24.7896i	−0.259371	−	1.54333i
$259$			21.7516i			1.35158i
$260$	2.27690	+	6.58275i	0.141207	+	0.408245i
$261$	5.42328			0.335692
$262$	−3.27829	−	19.5067i	−0.202534	−	1.20513i
$263$	8.63352			0.532366			0.266183	−	0.963923i	$-0.414238\pi$
$263$	8.63352			0.532366			0.266183	+	0.963923i	$0.414238\pi$
$264$	−3.09212	−	5.66667i	−0.190307	−	0.348760i
$265$	2.04707			0.125751
$266$	−21.4389	+	3.60301i	−1.31450	+	0.220914i
$267$	10.3321			0.632314
$268$	8.84050	−	3.05782i	0.540019	−	0.186786i
$269$	−29.2749			−1.78492			−0.892461	−	0.451125i	$-0.851023\pi$
$269$	−29.2749			−1.78492			−0.892461	+	0.451125i	$0.851023\pi$
$270$	−7.88245	+	1.32472i	−0.479710	+	0.0806199i
$271$			7.04520i			0.427966i	0.976837	+	0.213983i	$0.0686437\pi$
$271$			7.04520i			0.427966i	−0.976837	+	0.213983i	$0.931356\pi$
$272$	−13.7596	−	17.5105i	−0.834295	−	1.06173i
$273$		−	11.1423i		−	0.674361i
$274$	2.86488	+	17.0468i	0.173074	+	1.02984i
$275$	−1.65400			−0.0997401
$276$	11.7217	−	6.14642i	0.705561	−	0.369971i
$277$	−17.7450			−1.06619			−0.533095	−	0.846055i	$-0.678971\pi$
$277$	−17.7450			−1.06619			−0.533095	+	0.846055i	$0.678971\pi$
$278$	0.378331	+	2.25117i	0.0226908	+	0.135016i
$279$			3.86880i			0.231619i
$280$	3.14117	+	5.75656i	0.187721	+	0.344020i
$281$			12.8863i			0.768735i	0.923180	+	0.384367i	$0.125580\pi$
$281$			12.8863i			0.768735i	−0.923180	+	0.384367i	$0.874420\pi$
$282$	16.5668	−	2.78420i	0.986536	−	0.165797i
$283$	−4.81508			−0.286227			−0.143113	−	0.989706i	$-0.545711\pi$
$283$	−4.81508			−0.286227			−0.143113	+	0.989706i	$0.545711\pi$
$284$	7.15233	+	20.6782i	0.424413	+	1.22702i
$285$	9.14879			0.541928
$286$	8.03378	−	1.35015i	0.475047	−	0.0798362i
$287$	−14.7721			−0.871971
$288$	−4.17232	+	4.58528i	−0.245857	+	0.270190i
$289$	−13.9965			−0.823325
$290$	1.15988	+	6.90162i	0.0681106	+	0.405277i
$291$	26.2347			1.53791
$292$	12.3129	−	4.25887i	0.720555	−	0.249232i
$293$			13.6754i			0.798926i	0.916749	+	0.399463i	$0.130803\pi$
$293$			13.6754i			0.798926i	−0.916749	+	0.399463i	$0.869197\pi$
$294$	0.525365	+	3.12607i	0.0306399	+	0.182316i
$295$	−9.50571			−0.553444
$296$	−12.7103	−	23.2931i	−0.738769	−	1.35388i
$297$			9.34825i			0.542440i
$298$	1.12661	+	6.70367i	0.0652630	+	0.388333i
$299$	2.49502	+	16.5151i	0.144291	+	0.955090i
$300$	−0.902131	−	2.60816i	−0.0520846	−	0.150582i
$301$	29.8657			1.72143
$302$	−2.19774	−	13.0772i	−0.126466	−	0.752506i
$303$			5.61294i			0.322455i
$304$	20.8528	−	16.3858i	1.19599	−	0.939793i
$305$	−3.86641			−0.221390
$306$	1.43009	+	8.50944i	0.0817529	+	0.486452i
$307$		−	8.25398i		−	0.471079i	−0.971865	−	0.235540i	$-0.924314\pi$
$307$		−	8.25398i		−	0.471079i	0.971865	−	0.235540i	$-0.0756858\pi$
$308$	7.24839	−	2.50713i	0.413015	−	0.142857i
$309$		−	21.4267i		−	1.21892i
$310$	−4.92341	+	0.827425i	−0.279631	+	0.0469946i
$311$			1.09686i			0.0621970i	0.999516	+	0.0310985i	$0.00990055\pi$
$311$			1.09686i			0.0621970i	−0.999516	+	0.0310985i	$0.990099\pi$
$312$	6.51083	+	11.9319i	0.368603	+	0.675509i
$313$			30.9986i			1.75214i	0.482180	+	0.876072i	$0.339845\pi$
$313$			30.9986i			1.75214i	−0.482180	+	0.876072i	$0.660155\pi$
$314$	−3.42101	−	20.3560i	−0.193059	−	1.14875i
$315$		−	2.54093i		−	0.143165i
$316$	−8.00437	+	2.76862i	−0.450281	+	0.155747i
$317$	−8.23636			−0.462600			−0.231300	−	0.972882i	$-0.574298\pi$
$317$	−8.23636			−0.462600			−0.231300	+	0.972882i	$0.574298\pi$
$318$	3.93952	−	0.662073i	0.220917	−	0.0371272i
$319$	8.18503			0.458274
$320$	−6.72753	−	4.32901i	−0.376081	−	0.241999i
$321$		−	23.4136i		−	1.30682i
$322$	4.89350	+	14.9443i	0.272704	+	0.832813i
$323$		−	36.9128i		−	2.05389i
$324$	−8.52677	+	2.94931i	−0.473709	+	0.163850i
$325$	3.48270			0.193186
$326$	1.22751	+	7.30402i	0.0679855	+	0.404532i
$327$	−5.94341			−0.328671
$328$	15.8190	−	8.63188i	0.873455	−	0.476616i
$329$			19.9591i			1.10038i
$330$	−3.18307	+	0.534945i	−0.175222	+	0.0294477i
$331$		−	8.65040i		−	0.475469i	−0.971330	−	0.237734i	$-0.923595\pi$
$331$		−	8.65040i		−	0.475469i	0.971330	−	0.237734i	$-0.0764048\pi$
$332$	−10.2840	+	3.55711i	−0.564407	+	0.195222i
$333$			10.2815i			0.563421i
$334$	−0.622841	−	3.70608i	−0.0340804	−	0.202787i
$335$		−	4.67720i		−	0.255543i
$336$	7.90688	+	10.0624i	0.431355	+	0.548947i
$337$			4.60244i			0.250711i	0.992112	+	0.125356i	$0.0400071\pi$
$337$			4.60244i			0.250711i	−0.992112	+	0.125356i	$0.959993\pi$
$338$	1.21442	−	0.204096i	0.0660560	−	0.0111013i
$339$	7.40974			0.402442
$340$	−10.5232	+	3.63985i	−0.570700	+	0.197398i
$341$			5.83895i			0.316197i
$342$	−10.1336	+	1.70305i	−0.547965	+	0.0920906i
$343$	−19.9960			−1.07968
$344$	−31.9822	+	17.4516i	−1.72436	+	0.940928i
$345$	−0.988556	−	6.54344i	−0.0532220	−	0.352287i
$346$	12.4403	−	2.09071i	0.668794	−	0.112397i
$347$			27.6570i			1.48471i	0.670008	+	0.742354i	$0.266291\pi$
$347$			27.6570i			1.48471i	−0.670008	+	0.742354i	$0.733709\pi$
$348$	4.46430	+	12.9068i	0.239312	+	0.691876i
$349$	0.443757			0.0237538			0.0118769	−	0.999929i	$-0.496219\pi$
$349$	0.443757			0.0237538			0.0118769	+	0.999929i	$0.496219\pi$
$350$	3.23356	−	0.543431i	0.172841	−	0.0290476i
$351$		−	19.6839i		−	1.05065i
$352$	−6.29704	+	6.92030i	−0.335633	+	0.368853i
$353$	−3.85949			−0.205420			−0.102710	−	0.994711i	$-0.532751\pi$
$353$	−3.85949			−0.205420			−0.102710	+	0.994711i	$0.532751\pi$
$354$	−18.2934	+	3.07438i	−0.972283	+	0.163401i
$355$	10.9401			0.580640
$356$	−4.89522	−	14.1526i	−0.259446	−	0.750087i
$357$	17.8120			0.942713
$358$	−0.323365	−	1.92411i	−0.0170904	−	0.101693i
$359$	−16.8300			−0.888253			−0.444127	−	0.895964i	$-0.646486\pi$
$359$	−16.8300			−0.888253			−0.444127	+	0.895964i	$0.646486\pi$
$360$	1.48475	+	2.72099i	0.0782534	+	0.143409i
$361$	24.9584			1.31360
$362$	4.83221	+	28.7530i	0.253975	+	1.51122i
$363$		−	11.4037i		−	0.598542i
$364$	−15.2624	+	5.27907i	−0.799965	+	0.276699i
$365$		−	6.51430i		−	0.340974i
$366$	−7.44076	+	1.25049i	−0.388935	+	0.0653642i
$367$	−2.40164			−0.125365			−0.0626824	−	0.998034i	$-0.519966\pi$
$367$	−2.40164			−0.125365			−0.0626824	+	0.998034i	$0.519966\pi$
$368$	−13.9728	−	13.1439i	−0.728381	−	0.685172i
$369$	−6.98243			−0.363491
$370$	−13.0841	+	2.19891i	−0.680211	+	0.114316i
$371$			4.74621i			0.246411i
$372$	−9.20731	+	3.18470i	−0.477377	+	0.165119i
$373$		−	0.740895i		−	0.0383621i	−0.999816	−	0.0191810i	$-0.993894\pi$
$373$		−	0.740895i		−	0.0383621i	0.999816	−	0.0191810i	$-0.00610589\pi$
$374$	2.15835	+	12.8428i	0.111606	+	0.664085i
$375$	−1.37989			−0.0712570
$376$	−11.6628	−	21.3736i	−0.601465	−	1.10226i
$377$	−17.2346			−0.887626
$378$	−3.07141	−	18.2757i	−0.157976	−	0.940003i
$379$	−13.8734			−0.712631			−0.356316	−	0.934366i	$-0.615967\pi$
$379$	−13.8734			−0.712631			−0.356316	+	0.934366i	$0.615967\pi$
$380$	−4.33459	−	12.5318i	−0.222360	−	0.642866i
$381$	3.16529			0.162163
$382$	10.6740	−	1.79387i	0.546129	−	0.0917821i
$383$	11.6143			0.593463			0.296732	−	0.954961i	$-0.404103\pi$
$383$	11.6143			0.593463			0.296732	+	0.954961i	$0.404103\pi$
$384$	−14.3470	−	6.15517i	−0.732142	−	0.314105i
$385$		−	3.83487i		−	0.195443i
$386$	5.18881	−	0.872028i	0.264103	−	0.0443851i
$387$	14.1168			0.717598
$388$	−12.4297	−	35.9356i	−0.631022	−	1.82435i
$389$		−	5.88082i		−	0.298170i	−0.988824	−	0.149085i	$-0.952367\pi$
$389$		−	5.88082i		−	0.298170i	0.988824	−	0.149085i	$-0.0476327\pi$
$390$	6.70234	−	1.12639i	0.339386	−	0.0570371i
$391$	−26.4010	+	3.98855i	−1.33515	+	0.201709i
$392$	4.03308	−	2.20072i	0.203702	−	0.111153i
$393$	−19.3002			−0.973564
$394$	−4.04566	+	0.679911i	−0.203817	+	0.0342534i
$395$			4.23483i			0.213077i
$396$	3.42614	−	1.18506i	0.172170	−	0.0595516i
$397$	25.6253			1.28610			0.643049	−	0.765825i	$-0.277669\pi$
$397$	25.6253			1.28610			0.643049	+	0.765825i	$0.277669\pi$
$398$	16.8239	−	2.82741i	0.843303	−	0.141725i
$399$			21.2118i			1.06192i
$400$	−3.14516	+	2.47143i	−0.157258	+	0.123571i
$401$		−	12.3949i		−	0.618972i	−0.950904	−	0.309486i	$-0.899843\pi$
$401$		−	12.3949i		−	0.618972i	0.950904	−	0.309486i	$-0.100157\pi$
$402$	−1.51272	−	9.00110i	−0.0754476	−	0.448934i
$403$		−	12.2946i		−	0.612439i
$404$	7.68845	−	2.65934i	0.382515	−	0.132307i
$405$			4.51121i			0.224164i
$406$	−16.0017	+	2.68923i	−0.794149	+	0.133464i
$407$			15.5172i			0.769160i
$408$	−19.0743	+	10.4082i	−0.944318	+	0.515283i
$409$	3.15508			0.156009			0.0780043	−	0.996953i	$-0.475145\pi$
$409$	3.15508			0.156009			0.0780043	+	0.996953i	$0.475145\pi$
$410$	−1.49334	−	8.88578i	−0.0737508	−	0.438837i
$411$	16.8663			0.831953
$412$	−29.3497	+	10.1517i	−1.44596	+	0.500139i
$413$		−	22.0394i		−	1.08449i
$414$	2.31304	+	7.06381i	0.113680	+	0.347167i
$415$			5.44089i			0.267083i
$416$	13.2592	−	14.5715i	0.650085	−	0.714428i
$417$	2.22733			0.109073
$418$	−15.2941	+	2.57032i	−0.748059	+	0.125718i
$419$	−0.845711			−0.0413157			−0.0206578	−	0.999787i	$-0.506576\pi$
$419$	−0.845711			−0.0413157			−0.0206578	+	0.999787i	$0.506576\pi$
$420$	6.04711	−	2.09163i	0.295069	−	0.102061i
$421$			26.0162i			1.26795i	0.773354	+	0.633975i	$0.218578\pi$
$421$			26.0162i			1.26795i	−0.773354	+	0.633975i	$0.781422\pi$
$422$	−3.46226	−	20.6014i	−0.168540	−	1.00286i
$423$			9.43421i			0.458707i
$424$	−2.77338	−	5.08256i	−0.134687	−	0.246831i
$425$			5.56745i			0.270061i
$426$	21.0538	−	3.53829i	1.02006	−	0.171431i
$427$		−	8.96441i		−	0.433818i
$428$	−32.0712	+	11.0931i	−1.55022	+	0.536204i
$429$		−	7.94869i		−	0.383767i
$430$	3.01918	+	17.9649i	0.145598	+	0.866347i
$431$	15.1645			0.730447			0.365224	−	0.930920i	$-0.380993\pi$
$431$	15.1645			0.730447			0.365224	+	0.930920i	$0.380993\pi$
$432$	13.9682	+	17.7761i	0.672048	+	0.855254i
$433$		−	4.87293i		−	0.234178i	−0.993121	−	0.117089i	$-0.962644\pi$
$433$		−	4.87293i		−	0.234178i	0.993121	−	0.117089i	$-0.0373563\pi$
$434$	−1.91842	−	11.4151i	−0.0920869	−	0.547943i
$435$	6.82852			0.327403
$436$	2.81592	+	8.14112i	0.134858	+	0.389889i
$437$	−4.74984	−	31.4401i	−0.227216	−	1.50399i
$438$	−2.10688	−	12.5365i	−0.100671	−	0.599019i
$439$		−	20.7315i		−	0.989460i	−0.869047	−	0.494730i	$-0.835267\pi$
$439$		−	20.7315i		−	0.989460i	0.869047	−	0.494730i	$-0.164733\pi$
$440$	2.24085	+	4.10663i	0.106828	+	0.195776i
$441$	−1.78019			−0.0847709
$442$	−4.54468	−	27.0421i	−0.216168	−	1.28626i
$443$		−	19.8054i		−	0.940984i	−0.882404	−	0.470492i	$-0.844076\pi$
$443$		−	19.8054i		−	0.940984i	0.882404	−	0.470492i	$-0.155924\pi$
$444$	−24.4687	+	8.46345i	−1.16124	+	0.401658i
$445$	−7.48765			−0.354949
$446$	5.54611	+	33.0009i	0.262616	+	1.56264i
$447$	6.63267			0.313715
$448$	10.0370	−	15.5980i	0.474202	−	0.736938i
$449$	7.22437			0.340939			0.170470	−	0.985363i	$-0.445472\pi$
$449$	7.22437			0.340939			0.170470	+	0.985363i	$0.445472\pi$
$450$	1.52843	−	0.256867i	0.0720507	−	0.0121088i
$451$	−10.5382			−0.496223
$452$	−3.51065	−	10.1497i	−0.165127	−	0.477400i
$453$	−12.9387			−0.607911
$454$	−36.4904	+	6.13256i	−1.71258	+	0.287815i
$455$			8.07478i			0.378552i
$456$	−12.3948	−	22.7150i	−0.580441	−	1.06373i
$457$		−	37.5343i		−	1.75578i	−0.478861	−	0.877891i	$-0.658950\pi$
$457$		−	37.5343i		−	1.75578i	0.478861	−	0.877891i	$-0.341050\pi$
$458$	4.49699	+	26.7583i	0.210131	+	1.25033i
$459$	31.4667			1.46874
$460$	−8.49466	+	4.45430i	−0.396065	+	0.207683i
$461$	12.1716			0.566889			0.283444	−	0.958989i	$-0.408523\pi$
$461$	12.1716			0.566889			0.283444	+	0.958989i	$0.408523\pi$
$462$	−1.24029	−	7.38007i	−0.0577035	−	0.343352i
$463$		−	2.25366i		−	0.104736i	−0.998628	−	0.0523681i	$-0.983323\pi$
$463$		−	2.25366i		−	0.104736i	0.998628	−	0.0523681i	$-0.0166769\pi$
$464$	15.5642	−	12.2302i	0.722550	−	0.567770i
$465$			4.87126i			0.225899i
$466$	−38.3044	+	6.43742i	−1.77442	+	0.298208i
$467$	4.35631			0.201586			0.100793	−	0.994907i	$-0.467862\pi$
$467$	4.35631			0.201586			0.100793	+	0.994907i	$0.467862\pi$
$468$	−7.21415	+	2.49529i	−0.333474	+	0.115345i
$469$	10.8443			0.500741
$470$	−12.0059	+	2.01770i	−0.553791	+	0.0930698i
$471$	−20.1404			−0.928020
$472$	12.8784	+	23.6012i	0.592776	+	1.08633i
$473$	21.3057			0.979636
$474$	1.36965	+	8.14978i	0.0629100	+	0.374332i
$475$	−6.63011			−0.304210
$476$	−8.43912	−	24.3984i	−0.386807	−	1.11830i
$477$			2.24342i			0.102719i
$478$	0.140541	+	0.836260i	0.00642821	+	0.0382496i
$479$	36.1090			1.64986			0.824932	−	0.565232i	$-0.191213\pi$
$479$	36.1090			1.64986			0.824932	+	0.565232i	$0.191213\pi$
$480$	−5.25343	+	5.77340i	−0.239785	+	0.263518i
$481$		−	32.6734i		−	1.48978i
$482$	−3.35424	−	19.9586i	−0.152781	−	0.909091i
$483$	15.1712	−	2.29200i	0.690315	−	0.104290i
$484$	−15.6205	+	5.40296i	−0.710024	+	0.245589i
$485$	−19.0123			−0.863302
$486$	−2.51512	−	14.9657i	−0.114088	−	0.678856i
$487$		−	18.1513i		−	0.822514i	−0.911519	−	0.411257i	$-0.865090\pi$
$487$		−	18.1513i		−	0.822514i	0.911519	−	0.411257i	$-0.134910\pi$
$488$	5.23823	+	9.59968i	0.237123	+	0.434557i
$489$	7.22667			0.326801
$490$	−0.380731	−	2.26545i	−0.0171997	−	0.102343i
$491$			22.6804i			1.02355i	0.859119	+	0.511776i	$0.171012\pi$
$491$			22.6804i			1.02355i	−0.859119	+	0.511776i	$0.828988\pi$
$492$	−5.74776	−	16.6174i	−0.259129	−	0.749169i
$493$		−	27.5512i		−	1.24084i
$494$	32.2036	−	5.41212i	1.44891	−	0.243503i
$495$		−	1.81265i		−	0.0814726i
$496$	8.72462	+	11.1030i	0.391747	+	0.498541i
$497$			25.3650i			1.13778i
$498$	1.75972	+	10.4708i	0.0788548	+	0.469208i
$499$			31.4754i			1.40903i	0.709688	+	0.704516i	$0.248836\pi$
$499$			31.4754i			1.40903i	−0.709688	+	0.704516i	$0.751164\pi$
$500$	0.653773	+	1.89013i	0.0292376	+	0.0845291i
$501$	−3.66683			−0.163822
$502$	25.8268	−	4.34045i	1.15271	−	0.193724i
$503$	−13.7449			−0.612853			−0.306426	−	0.951894i	$-0.599133\pi$
$503$	−13.7449			−0.612853			−0.306426	+	0.951894i	$0.599133\pi$
$504$	−6.30872	+	3.44246i	−0.281013	+	0.153339i
$505$		−	4.06769i		−	0.181010i
$506$	3.49093	+	10.6610i	0.155191	+	0.473939i
$507$		−	1.20156i		−	0.0533633i
$508$	−1.49967	−	4.33572i	−0.0665373	−	0.192366i
$509$	−14.8818			−0.659625			−0.329813	−	0.944046i	$-0.606986\pi$
$509$	−14.8818			−0.659625			−0.329813	+	0.944046i	$0.606986\pi$
$510$	1.80065	+	10.7144i	0.0797341	+	0.474440i
$511$	15.1036			0.668146
$512$	−1.63374	+	22.5684i	−0.0722018	+	0.997390i
$513$			37.4727i			1.65446i
$514$	28.9120	−	4.85894i	1.27525	−	0.214319i
$515$			15.5279i			0.684241i
$516$	11.6206	+	33.5964i	0.511568	+	1.47900i
$517$			14.2385i			0.626208i
$518$	−5.09826	−	30.3360i	−0.224005	−	1.33289i
$519$		−	12.3085i		−	0.540285i
$520$	−4.71839	−	8.64700i	−0.206915	−	0.379196i
$521$			14.8702i			0.651476i	0.945460	+	0.325738i	$0.105613\pi$
$521$			14.8702i			0.651476i	−0.945460	+	0.325738i	$0.894387\pi$
$522$	−7.56360	+	1.27113i	−0.331050	+	0.0556361i
$523$	2.95573			0.129245			0.0646226	−	0.997910i	$-0.479416\pi$
$523$	2.95573			0.129245			0.0646226	+	0.997910i	$0.479416\pi$
$524$	9.14418	+	26.4368i	0.399465	+	1.15490i
$525$		−	3.19932i		−	0.139630i
$526$	−12.0408	+	2.02357i	−0.525003	+	0.0882317i
$527$	19.6542			0.856150
$528$	5.64062	+	7.17831i	0.245477	+	0.312396i
$529$	−21.9735	+	6.79441i	−0.955371	+	0.295409i
$530$	−2.85496	+	0.479803i	−0.124012	+	0.0208413i
$531$		−	10.4175i		−	0.452080i
$532$	29.0554	−	10.0499i	1.25971	−	0.435719i
$533$	22.1894			0.961129
$534$	−14.4097	+	2.42169i	−0.623569	+	0.104797i
$535$			16.9678i			0.733581i
$536$	−11.6127	+	6.33669i	−0.501594	+	0.273703i
$537$	−1.90374			−0.0821523
$538$	40.8284	−	6.86160i	1.76024	−	0.295824i
$539$	−2.68673			−0.115726
$540$	10.6828	−	3.69505i	0.459715	−	0.159010i
$541$	−24.8102			−1.06667			−0.533337	−	0.845903i	$-0.679062\pi$
$541$	−24.8102			−1.06667			−0.533337	+	0.845903i	$0.679062\pi$
$542$	−1.65129	−	9.82563i	−0.0709290	−	0.422047i
$543$	28.4485			1.22084
$544$	23.2940	+	21.1961i	0.998724	+	0.908777i
$545$	4.30718			0.184499
$546$	2.61158	+	15.5396i	0.111765	+	0.665035i
$547$		−	14.3225i		−	0.612386i	−0.951969	−	0.306193i	$-0.900945\pi$
$547$		−	14.3225i		−	0.612386i	0.951969	−	0.306193i	$-0.0990553\pi$
$548$	−7.99104	−	23.1030i	−0.341360	−	0.986910i
$549$		−	4.23726i		−	0.180842i
$550$	2.30676	−	0.387673i	0.0983607	−	0.0165305i
$551$	32.8099			1.39775
$552$	−14.9070	+	11.3195i	−0.634486	+	0.481791i
$553$	−9.81861			−0.417530
$554$	24.7481	−	4.15915i	1.05145	−	0.176705i
$555$			12.9456i			0.549508i
$556$	−1.05528	−	3.05094i	−0.0447539	−	0.129388i
$557$			39.1149i			1.65735i	0.559730	+	0.828675i	$0.310905\pi$
$557$			39.1149i			1.65735i	−0.559730	+	0.828675i	$0.689095\pi$
$558$	−0.906789	−	5.39565i	−0.0383875	−	0.228416i
$559$	−44.8617			−1.89745
$560$	−5.73010	−	7.29218i	−0.242141	−	0.308151i
$561$	12.7068			0.536481
$562$	−3.02037	−	17.9720i	−0.127406	−	0.758104i
$563$	35.3742			1.49085			0.745423	−	0.666592i	$-0.232247\pi$
$563$	35.3742			1.49085			0.745423	+	0.666592i	$0.232247\pi$
$564$	−22.4523	+	7.76600i	−0.945414	+	0.327008i
$565$	−5.36983			−0.225910
$566$	6.71537	−	1.12858i	0.282268	−	0.0474378i
$567$	−10.4594			−0.439254
$568$	−14.8217	−	27.1625i	−0.621905	−	1.13971i
$569$			8.98709i			0.376758i	0.982096	+	0.188379i	$0.0603234\pi$
$569$			8.98709i			0.376758i	−0.982096	+	0.188379i	$0.939677\pi$
$570$	−12.7594	+	2.14434i	−0.534433	+	0.0898165i
$571$	16.6329			0.696067			0.348034	−	0.937482i	$-0.386849\pi$
$571$	16.6329			0.696067			0.348034	+	0.937482i	$0.386849\pi$
$572$	−10.8879	+	3.76599i	−0.455246	+	0.157464i
$573$		−	10.5609i		−	0.441190i
$574$	20.6020	−	3.46236i	0.859912	−	0.144516i
$575$	0.716404	+	4.74202i	0.0298761	+	0.197756i
$576$	4.74423	−	7.37282i	0.197676	−	0.307201i
$577$	−20.6514			−0.859729			−0.429865	−	0.902893i	$-0.641439\pi$
$577$	−20.6514			−0.859729			−0.429865	+	0.902893i	$0.641439\pi$
$578$	19.5203	−	3.28057i	0.811938	−	0.136454i
$579$		−	5.13385i		−	0.213356i
$580$	−3.23527	−	9.35352i	−0.134337	−	0.388384i
$581$	−12.6149			−0.523355
$582$	−36.5884	+	6.14903i	−1.51664	+	0.254885i
$583$			3.38586i			0.140228i
$584$	−16.1740	+	8.82560i	−0.669284	+	0.365206i
$585$			3.81676i			0.157803i
$586$	−3.20531	−	19.0725i	−0.132410	−	0.787877i
$587$			40.9822i			1.69152i	0.533566	+	0.845759i	$0.320852\pi$
$587$			40.9822i			1.69152i	−0.533566	+	0.845759i	$0.679148\pi$
$588$	−1.46541	−	4.23665i	−0.0604323	−	0.174716i
$589$			23.4056i			0.964411i
$590$	13.2572	−	2.22800i	0.545790	−	0.0917252i
$591$			4.00281i			0.164654i
$592$	23.1860	+	29.5067i	0.952938	+	1.21272i
$593$	26.5118			1.08871			0.544354	−	0.838855i	$-0.316775\pi$
$593$	26.5118			1.08871			0.544354	+	0.838855i	$0.316775\pi$
$594$	−2.19109	−	13.0376i	−0.0899015	−	0.534939i
$595$	−12.9083			−0.529191
$596$	−3.14248	−	9.08524i	−0.128721	−	0.372146i
$597$		−	16.6457i		−	0.681262i
$598$	−7.35058	−	22.4480i	−0.300588	−	0.917968i
$599$		−	1.77018i		−	0.0723276i	−0.999346	−	0.0361638i	$-0.988486\pi$
$599$		−	1.77018i		−	0.0723276i	0.999346	−	0.0361638i	$-0.0115138\pi$
$600$	1.86948	+	3.42604i	0.0763210	+	0.139867i
$601$	−46.2673			−1.88728			−0.943641	−	0.330970i	$-0.892624\pi$
$601$	−46.2673			−1.88728			−0.943641	+	0.330970i	$0.892624\pi$
$602$	−41.6524	+	7.00008i	−1.69763	+	0.285302i
$603$	5.12582			0.208740
$604$	6.13018	+	17.7230i	0.249433	+	0.721139i
$605$			8.26427i			0.335991i
$606$	−1.31559	−	7.82812i	−0.0534422	−	0.317996i
$607$		−	39.0068i		−	1.58324i	−0.611015	−	0.791619i	$-0.709239\pi$
$607$		−	39.0068i		−	1.58324i	0.611015	−	0.791619i	$-0.290761\pi$
$608$	−25.2419	+	27.7402i	−1.02369	+	1.12501i
$609$			15.8322i			0.641553i
$610$	5.39231	−	0.906228i	0.218328	−	0.0366921i
$611$		−	29.9809i		−	1.21290i
$612$	−3.98897	−	11.5325i	−0.161245	−	0.466176i
$613$			0.0667318i			0.00269527i	0.999999	+	0.00134764i	$0.000428966\pi$
$613$			0.0667318i			0.00269527i	−0.999999	+	0.00134764i	$0.999571\pi$
$614$	1.93461	+	11.5115i	0.0780744	+	0.464564i
$615$	−8.79167			−0.354514
$616$	−9.52137	+	5.19550i	−0.383627	+	0.209333i
$617$			13.1473i			0.529291i	0.964346	+	0.264645i	$0.0852549\pi$
$617$			13.1473i			0.529291i	−0.964346	+	0.264645i	$0.914745\pi$
$618$	5.02210	+	29.8829i	0.202019	+	1.20207i
$619$	−19.6605			−0.790220			−0.395110	−	0.918634i	$-0.629294\pi$
$619$	−19.6605			−0.790220			−0.395110	+	0.918634i	$0.629294\pi$
$620$	6.67252	−	2.30795i	0.267975	−	0.0926893i
$621$	26.8014	−	4.04904i	1.07550	−	0.162482i
$622$	−0.257087	−	1.52974i	−0.0103082	−	0.0613368i
$623$		−	17.3604i		−	0.695530i
$624$	−11.8770	−	15.1148i	−0.475461	−	0.605077i
$625$	1.00000			0.0400000
$626$	−7.26561	−	43.2324i	−0.290392	−	1.72791i
$627$			15.1321i			0.604319i
$628$	9.54227	+	27.5877i	0.380778	+	1.10087i
$629$	52.2317			2.08261
$630$	0.595555	+	3.54372i	0.0237275	+	0.141185i
$631$	3.93430			0.156622			0.0783111	−	0.996929i	$-0.475047\pi$
$631$	3.93430			0.156622			0.0783111	+	0.996929i	$0.475047\pi$
$632$	10.5144	−	5.73737i	0.418241	−	0.228220i
$633$	−20.3832			−0.810161
$634$	11.4869	−	1.93048i	0.456203	−	0.0766691i
$635$	−2.29388			−0.0910297
$636$	−5.33909	+	1.84673i	−0.211709	+	0.0732275i
$637$	5.65724			0.224148
$638$	−11.4153	+	1.91845i	−0.451936	+	0.0759521i
$639$			11.9894i			0.474295i
$640$	10.3972	+	4.46064i	0.410987	+	0.176322i
$641$			17.7243i			0.700067i	0.936737	+	0.350033i	$0.113830\pi$
$641$			17.7243i			0.700067i	−0.936737	+	0.350033i	$0.886170\pi$
$642$	5.48779	+	32.6539i	0.216586	+	1.28875i
$643$	−4.97285			−0.196110			−0.0980551	−	0.995181i	$-0.531262\pi$
$643$	−4.97285			−0.196110			−0.0980551	+	0.995181i	$0.531262\pi$
$644$	−10.3275	−	19.6952i	−0.406959	−	0.776099i
$645$	17.7747			0.699877
$646$	8.65182	+	51.4807i	0.340401	+	2.02548i
$647$			36.1791i			1.42235i	0.703016	+	0.711174i	$0.251836\pi$
$647$			36.1791i			1.42235i	−0.703016	+	0.711174i	$0.748164\pi$
$648$	11.2006	−	6.11182i	0.440002	−	0.240095i
$649$		−	15.7225i		−	0.617161i
$650$	−4.85717	+	0.816294i	−0.190514	+	0.0320177i
$651$	−11.2942			−0.442655
$652$	−3.42391	−	9.89889i	−0.134091	−	0.387670i
$653$	−20.9627			−0.820332			−0.410166	−	0.912011i	$-0.634529\pi$
$653$	−20.9627			−0.820332			−0.410166	+	0.912011i	$0.634529\pi$
$654$	8.28901	−	1.39305i	0.324126	−	0.0544724i
$655$	13.9868			0.546509
$656$	−20.0388	+	15.7462i	−0.782384	+	0.614787i
$657$	7.13913			0.278524
$658$	−4.67812	−	27.8361i	−0.182372	−	1.08517i
$659$	26.4259			1.02941			0.514703	−	0.857368i	$-0.327902\pi$
$659$	26.4259			1.02941			0.514703	+	0.857368i	$0.327902\pi$
$660$	4.31390	−	1.49213i	0.167918	−	0.0580810i
$661$		−	4.30861i		−	0.167586i	−0.996483	−	0.0837928i	$-0.973297\pi$
$661$		−	4.30861i		−	0.167586i	0.996483	−	0.0837928i	$-0.0267034\pi$
$662$	2.02752	+	12.0643i	0.0788020	+	0.468893i
$663$	−26.7557			−1.03910
$664$	13.5089	−	7.37135i	0.524246	−	0.286064i
$665$		−	15.3722i		−	0.596107i
$666$	−2.40982	−	14.3391i	−0.0933788	−	0.555629i
$667$	−3.54521	−	23.4665i	−0.137271	−	0.908625i
$668$	1.73730	+	5.02271i	0.0672181	+	0.194335i
$669$	32.6514			1.26238
$670$	1.09627	+	6.52308i	0.0423524	+	0.252009i
$671$		−	6.39505i		−	0.246878i
$672$	−13.3858	−	12.1803i	−0.516370	−	0.469865i
$673$	41.2693			1.59081			0.795407	−	0.606075i	$-0.207257\pi$
$673$	41.2693			1.59081			0.795407	+	0.606075i	$0.207257\pi$
$674$	−1.07874	−	6.41882i	−0.0415517	−	0.247244i
$675$		−	5.65189i		−	0.217542i
$676$	−1.64587	+	0.569286i	−0.0633026	+	0.0218956i
$677$		−	37.9054i		−	1.45682i	−0.685139	−	0.728412i	$-0.740259\pi$
$677$		−	37.9054i		−	1.45682i	0.685139	−	0.728412i	$-0.259741\pi$
$678$	−10.3340	+	1.73673i	−0.396876	+	0.0666988i
$679$		−	44.0806i		−	1.69166i
$680$	13.8231	−	7.54281i	0.530092	−	0.289254i
$681$			36.1040i			1.38351i
$682$	−1.36856	−	8.14333i	−0.0524050	−	0.311824i
$683$		−	30.0463i		−	1.14969i	−0.818262	−	0.574845i	$-0.805062\pi$
$683$		−	30.0463i		−	1.14969i	0.818262	−	0.574845i	$-0.194938\pi$
$684$	13.7338	−	4.75035i	0.525124	−	0.181634i
$685$	−12.2230			−0.467016
$686$	27.8875	−	4.68675i	1.06475	−	0.178941i
$687$	26.4749			1.01008
$688$	40.5137	−	31.8351i	1.54457	−	1.21370i
$689$		−	7.12935i		−	0.271607i
$690$	2.91238	+	8.89415i	0.110872	+	0.338594i
$691$			31.4123i			1.19498i	0.801876	+	0.597491i	$0.203835\pi$
$691$			31.4123i			1.19498i	−0.801876	+	0.597491i	$0.796165\pi$
$692$	−16.8599	+	5.83164i	−0.640917	+	0.221686i
$693$	4.20270			0.159647
$694$	−6.48239	−	38.5720i	−0.246068	−	1.46417i
$695$	−1.61414			−0.0612279
$696$	−9.25132	−	16.9541i	−0.350670	−	0.642645i
$697$			35.4720i			1.34360i
$698$	−0.618888	+	0.104010i	−0.0234253	+	0.00393684i
$699$			37.8987i			1.43346i
$700$	−4.38233	+	1.51580i	−0.165637	+	0.0572917i
$701$		−	27.3698i		−	1.03374i	−0.856063	−	0.516871i	$-0.827097\pi$
$701$		−	27.3698i		−	1.03374i	0.856063	−	0.516871i	$-0.172903\pi$
$702$	4.61361	+	27.4522i	0.174129	+	1.03612i
$703$			62.2012i			2.34596i
$704$	7.16019	−	11.1274i	0.269860	−	0.419378i
$705$			11.8787i			0.447379i
$706$	5.38266	−	0.904606i	0.202579	−	0.0340453i
$707$	9.43109			0.354693
$708$	24.7924	−	8.57540i	0.931756	−	0.322283i
$709$			46.7346i			1.75515i	0.479436	+	0.877577i	$0.340841\pi$
$709$			46.7346i			1.75515i	−0.479436	+	0.877577i	$0.659159\pi$
$710$	−15.2577	+	2.56419i	−0.572610	+	0.0962325i
$711$	−4.64102			−0.174052
$712$	10.1443	+	18.5906i	0.380174	+	0.696714i
$713$	16.7403	−	2.52905i	0.626928	−	0.0947136i
$714$	−24.8417	+	4.17487i	−0.929675	+	0.156241i
$715$			5.76040i			0.215427i
$716$	0.901967	+	2.60768i	0.0337081	+	0.0974537i
$717$	0.827403			0.0308999
$718$	23.4720	−	3.94470i	0.875969	−	0.147215i
$719$		−	23.8230i		−	0.888447i	−0.895916	−	0.444223i	$-0.853480\pi$
$719$		−	23.8230i		−	0.888447i	0.895916	−	0.444223i	$-0.146520\pi$
$720$	−2.70848	−	3.44684i	−0.100939	−	0.128456i
$721$	−36.0020			−1.34079
$722$	−34.8084	+	5.84988i	−1.29543	+	0.217710i
$723$	−19.7473			−0.734409
$724$	−13.4785	−	38.9679i	−0.500926	−	1.44823i
$725$	−4.94862			−0.183787
$726$	2.67287	+	15.9043i	0.0991994	+	0.590264i
$727$	−24.5081			−0.908956			−0.454478	−	0.890758i	$-0.650174\pi$
$727$	−24.5081			−0.908956			−0.454478	+	0.890758i	$0.650174\pi$
$728$	20.0484	−	10.9398i	0.743043	−	0.405454i
$729$	−28.3408			−1.04966
$730$	1.52685	+	9.08520i	0.0565114	+	0.336258i
$731$		−	71.7159i		−	2.65251i
$732$	10.0842	−	3.48801i	0.372723	−	0.128920i
$733$		−	14.8727i		−	0.549337i	−0.961539	−	0.274669i	$-0.911432\pi$
$733$		−	14.8727i		−	0.549337i	0.961539	−	0.274669i	$-0.0885681\pi$
$734$	3.34947	−	0.562910i	0.123631	−	0.0207774i
$735$	−2.24146			−0.0826775
$736$	22.5679	+	15.0562i	0.831865	+	0.554978i
$737$	7.73610			0.284963
$738$	9.73808	−	1.63658i	0.358464	−	0.0602432i
$739$			25.8160i			0.949658i	0.880078	+	0.474829i	$0.157490\pi$
$739$			25.8160i			0.949658i	−0.880078	+	0.474829i	$0.842510\pi$
$740$	17.7325	−	6.13344i	0.651858	−	0.225470i
$741$		−	31.8625i		−	1.17050i
$742$	−1.11244	−	6.61933i	−0.0408390	−	0.243003i
$743$	−26.3405			−0.966339			−0.483170	−	0.875527i	$-0.660515\pi$
$743$	−26.3405			−0.966339			−0.483170	+	0.875527i	$0.660515\pi$
$744$	12.0946	−	6.59961i	0.443409	−	0.241954i
$745$	−4.80668			−0.176103
$746$	0.173655	+	1.03329i	0.00635795	+	0.0378316i
$747$	−5.96277			−0.218166
$748$	−6.02032	−	17.4054i	−0.220125	−	0.636404i
$749$	−39.3404			−1.43747
$750$	1.92446	−	0.323424i	0.0702715	−	0.0118098i
$751$	−27.2225			−0.993364			−0.496682	−	0.867933i	$-0.665449\pi$
$751$	−27.2225			−0.993364			−0.496682	+	0.867933i	$0.665449\pi$
$752$	21.2753	+	27.0751i	0.775830	+	0.987329i
$753$		−	25.5533i		−	0.931215i
$754$	24.0363	−	4.03953i	0.875350	−	0.147111i
$755$	9.37662			0.341250
$756$	8.56712	+	24.7685i	0.311583	+	0.900821i
$757$		−	28.6707i		−	1.04205i	−0.853540	−	0.521027i	$-0.825549\pi$
$757$		−	28.6707i		−	1.04205i	0.853540	−	0.521027i	$-0.174451\pi$
$758$	19.3487	−	3.25173i	0.702776	−	0.118108i
$759$	10.8229	−	1.63507i	0.392845	−	0.0593494i
$760$	8.98251	+	16.4615i	0.325830	+	0.597122i
$761$	−23.3091			−0.844953			−0.422476	−	0.906374i	$-0.638839\pi$
$761$	−23.3091			−0.844953			−0.422476	+	0.906374i	$0.638839\pi$
$762$	−4.41448	+	0.741896i	−0.159920	+	0.0268761i
$763$			9.98636i			0.361530i
$764$	−14.4661	+	5.00365i	−0.523365	+	0.181026i
$765$	−6.10147			−0.220599
$766$	−16.1980	+	2.72222i	−0.585256	+	0.0983578i
$767$			33.1056i			1.19537i
$768$	21.4518	+	5.22162i	0.774075	+	0.188419i
$769$		−	48.0354i		−	1.73220i	−0.499871	−	0.866100i	$-0.666619\pi$
$769$		−	48.0354i		−	1.73220i	0.499871	−	0.866100i	$-0.333381\pi$
$770$	0.898836	+	5.34832i	0.0323918	+	0.192740i
$771$		−	28.6058i		−	1.03021i
$772$	−7.03221	+	2.43236i	−0.253095	+	0.0875425i
$773$			20.1340i			0.724170i	0.932145	+	0.362085i	$0.117935\pi$
$773$			20.1340i			0.724170i	−0.932145	+	0.362085i	$0.882065\pi$
$774$	−19.6881	+	3.30877i	−0.707674	+	0.118931i
$775$		−	3.53020i		−	0.126808i
$776$	25.7579	+	47.2044i	0.924655	+	1.69454i
$777$	−30.0148			−1.07677
$778$	1.37838	+	8.20172i	0.0494172	+	0.294046i
$779$	−42.2425			−1.51349
$780$	−9.08344	+	3.14186i	−0.325239	+	0.112496i
$781$			18.0949i			0.647488i
$782$	35.8854	−	11.7506i	1.28326	−	0.420202i
$783$			27.9691i			0.999533i
$784$	−5.10895	+	4.01454i	−0.182462	+	0.143377i
$785$	14.5957			0.520943
$786$	26.9171	−	4.52367i	0.960100	−	0.161354i
$787$	−7.68977			−0.274111			−0.137055	−	0.990563i	$-0.543764\pi$
$787$	−7.68977			−0.274111			−0.137055	+	0.990563i	$0.543764\pi$
$788$	5.48294	−	1.89648i	0.195321	−	0.0675594i
$789$			11.9133i			0.424123i
$790$	−0.992581	−	5.90613i	−0.0353144	−	0.210131i
$791$		−	12.4501i		−	0.442676i
$792$	−4.50052	+	2.45579i	−0.159919	+	0.0872626i
$793$			13.4656i			0.478176i
$794$	−35.7385	+	6.00619i	−1.26831	+	0.213152i
$795$			2.82472i			0.100183i
$796$	−22.8008	+	7.88652i	−0.808152	+	0.279530i
$797$			3.88875i			0.137747i	0.997625	+	0.0688734i	$0.0219404\pi$
$797$			3.88875i			0.137747i	−0.997625	+	0.0688734i	$0.978060\pi$
$798$	−4.97173	−	29.5832i	−0.175997	−	1.04723i
$799$	47.9274			1.69555
$800$	3.80715	−	4.18397i	0.134603	−	0.147926i
$801$		−	8.20584i		−	0.289939i
$802$	2.90518	+	17.2866i	0.102586	+	0.610412i
$803$	10.7747			0.380230
$804$	4.21945	+	12.1989i	0.148808	+	0.430221i
$805$	−10.9946	+	1.66101i	−0.387507	+	0.0585429i
$806$	2.88168	+	17.1468i	0.101503	+	0.603969i
$807$		−	40.3960i		−	1.42201i
$808$	−10.0994	+	5.51093i	−0.355297	+	0.193874i
$809$	−19.8128			−0.696581			−0.348290	−	0.937387i	$-0.613238\pi$
$809$	−19.8128			−0.696581			−0.348290	+	0.937387i	$0.613238\pi$
$810$	−1.05736	−	6.29159i	−0.0371519	−	0.221064i
$811$		−	44.4156i		−	1.55964i	−0.626003	−	0.779821i	$-0.715310\pi$
$811$		−	44.4156i		−	1.55964i	0.626003	−	0.779821i	$-0.284690\pi$
$812$	21.6865	−	7.50110i	0.761046	−	0.263237i
$813$	−9.72157			−0.340950
$814$	−3.63700	−	21.6412i	−0.127477	−	0.758523i
$815$	−5.23715			−0.183449
$816$	24.1625	−	18.9866i	0.845858	−	0.664664i
$817$	85.4043			2.98792
$818$	−4.40024	+	0.739503i	−0.153851	+	0.0258561i
$819$	−8.84929			−0.309219
$820$	4.16539	+	12.0426i	0.145462	+	0.420545i
$821$	36.9381			1.28915			0.644575	−	0.764541i	$-0.277034\pi$
$821$	36.9381			1.28915			0.644575	+	0.764541i	$0.277034\pi$
$822$	−23.5227	+	3.95321i	−0.820447	+	0.137884i
$823$			9.38371i			0.327096i	0.986535	+	0.163548i	$0.0522938\pi$
$823$			9.38371i			0.327096i	−0.986535	+	0.163548i	$0.947706\pi$
$824$	38.5533	−	21.0373i	1.34307	−	0.732868i
$825$		−	2.28233i		−	0.0794607i
$826$	5.16569	+	30.7373i	0.179738	+	1.06949i
$827$	−34.4624			−1.19837			−0.599187	−	0.800609i	$-0.704509\pi$
$827$	−34.4624			−1.19837			−0.599187	+	0.800609i	$0.704509\pi$
$828$	−4.88154	−	9.30944i	−0.169645	−	0.323525i
$829$	18.3378			0.636897			0.318449	−	0.947940i	$-0.396838\pi$
$829$	18.3378			0.636897			0.318449	+	0.947940i	$0.396838\pi$
$830$	−1.27526	−	7.58817i	−0.0442650	−	0.263389i
$831$		−	24.4860i		−	0.849410i
$832$	−15.0766	+	23.4300i	−0.522689	+	0.812289i
$833$			9.04367i			0.313345i
$834$	−3.10636	+	0.522053i	−0.107564	+	0.0180772i
$835$	2.65734			0.0919611
$836$	20.7276	−	7.16942i	0.716878	−	0.247960i
$837$	−19.9523			−0.689652
$838$	1.17948	−	0.198222i	0.0407443	−	0.00684746i
$839$	28.6022			0.987456			0.493728	−	0.869616i	$-0.335634\pi$
$839$	28.6022			0.987456			0.493728	+	0.869616i	$0.335634\pi$
$840$	−7.94339	+	4.33445i	−0.274073	+	0.149553i
$841$	−4.51118			−0.155558
$842$	−6.09780	−	36.2836i	−0.210144	−	1.25041i
$843$	−17.7817			−0.612433
$844$	9.65732	+	27.9204i	0.332419	+	0.961059i
$845$			0.870770i			0.0299554i
$846$	−2.21124	−	13.1575i	−0.0760239	−	0.452363i
$847$	−19.1610			−0.658381
$848$	5.05919	+	6.43838i	0.173733	+	0.221095i
$849$		−	6.64425i		−	0.228030i
$850$	−1.30493	−	7.76468i	−0.0447586	−	0.266326i
$851$	44.4878	−	6.72103i	1.52502	−	0.230394i
$852$	−28.5335	+	9.86940i	−0.977542	+	0.338120i
$853$	−15.5290			−0.531701			−0.265851	−	0.964014i	$-0.585653\pi$
$853$	−15.5290			−0.531701			−0.265851	+	0.964014i	$0.585653\pi$
$854$	2.10112	+	12.5023i	0.0718990	+	0.427819i
$855$		−	7.26606i		−	0.248494i
$856$	42.1283	−	22.9880i	1.43992	−	0.785714i
$857$	5.90572			0.201736			0.100868	−	0.994900i	$-0.467838\pi$
$857$	5.90572			0.201736			0.100868	+	0.994900i	$0.467838\pi$
$858$	1.86305	+	11.0857i	0.0636036	+	0.378459i
$859$		−	11.1944i		−	0.381947i	−0.981595	−	0.190973i	$-0.938836\pi$
$859$		−	11.1944i		−	0.381947i	0.981595	−	0.190973i	$-0.0611644\pi$
$860$	−8.42143	−	24.3473i	−0.287168	−	0.830235i
$861$		−	20.3838i		−	0.694679i
$862$	−21.1492	+	3.55433i	−0.720345	+	0.121061i
$863$			57.7691i			1.96648i	0.182310	+	0.983241i	$0.441643\pi$
$863$			57.7691i			1.96648i	−0.182310	+	0.983241i	$0.558357\pi$
$864$	−23.6473	−	21.5176i	−0.804499	−	0.732044i
$865$			8.91998i			0.303288i
$866$	1.14214	+	6.79606i	0.0388116	+	0.230939i
$867$		−	19.3136i		−	0.655924i
$868$	5.35106	+	15.4705i	0.181627	+	0.525103i
$869$	−7.00442			−0.237609
$870$	−9.52344	+	1.60050i	−0.322875	+	0.0542622i
$871$	−16.2893			−0.551942
$872$	−5.83539	−	10.6940i	−0.197611	−	0.362146i
$873$		−	20.8359i		−	0.705187i
$874$	13.9935	+	42.7349i	0.473337	+	1.44553i
$875$			2.31854i			0.0783809i
$876$	5.87675	+	16.9903i	0.198557	+	0.574050i
$877$	17.2151			0.581312			0.290656	−	0.956828i	$-0.406127\pi$
$877$	17.2151			0.581312			0.290656	+	0.956828i	$0.406127\pi$
$878$	4.85915	+	28.9133i	0.163988	+	0.975776i
$879$	−18.8705			−0.636486
$880$	−4.08775	−	5.20211i	−0.137798	−	0.175363i
$881$		−	1.23909i		−	0.0417461i	−0.999782	−	0.0208730i	$-0.993355\pi$
$881$		−	1.23909i		−	0.0417461i	0.999782	−	0.0208730i	$-0.00664457\pi$
$882$	2.48275	−	0.417250i	0.0835985	−	0.0140495i
$883$			57.4856i			1.93454i	0.253742	+	0.967272i	$0.418339\pi$
$883$			57.4856i			1.93454i	−0.253742	+	0.967272i	$0.581661\pi$
$884$	12.6765	+	36.6492i	0.426357	+	1.23264i
$885$		−	13.1168i		−	0.440916i
$886$	4.64210	+	27.6217i	0.155954	+	0.927971i
$887$			3.53645i			0.118742i	0.998236	+	0.0593712i	$0.0189096\pi$
$887$			3.53645i			0.118742i	−0.998236	+	0.0593712i	$0.981090\pi$
$888$	32.1418	−	17.5387i	1.07861	−	0.588560i
$889$		−	5.31844i		−	0.178375i
$890$	10.4427	−	1.75499i	0.350040	−	0.0588275i
$891$	−7.46156			−0.249972
$892$	−15.4698	−	44.7249i	−0.517968	−	1.49750i
$893$			57.0754i			1.90995i
$894$	−9.25029	+	1.55460i	−0.309376	+	0.0519936i
$895$	1.37963			0.0461161
$896$	−10.3422	+	24.1064i	−0.345507	+	0.805338i
$897$	−22.7889	+	3.44285i	−0.760899	+	0.114953i
$898$	−10.0755	+	1.69328i	−0.336224	+	0.0565056i
$899$			17.4696i			0.582643i
$900$	−2.07142	+	0.716481i	−0.0690474	+	0.0238827i
$901$	11.3970			0.379688
$902$	14.6971	−	2.46999i	0.489360	−	0.0822416i
$903$			41.2113i			1.37143i
$904$	7.27507	+	13.3324i	0.241965	+	0.443430i
$905$	−20.6166			−0.685318
$906$	18.0450	−	3.03263i	0.599504	−	0.100752i
$907$	47.5207			1.57790			0.788949	−	0.614458i	$-0.210625\pi$
$907$	47.5207			1.57790			0.788949	+	0.614458i	$0.210625\pi$
$908$	49.4542	−	17.1056i	1.64119	−	0.567670i
$909$	4.45785			0.147858
$910$	−1.89261	−	11.2615i	−0.0627393	−	0.373316i
$911$	−2.29768			−0.0761255			−0.0380628	−	0.999275i	$-0.512119\pi$
$911$	−2.29768			−0.0761255			−0.0380628	+	0.999275i	$0.512119\pi$
$912$	22.6106	+	28.7744i	0.748711	+	0.952817i
$913$	−8.99925			−0.297832
$914$	8.79748	+	52.3474i	0.290995	+	1.73150i
$915$		−	5.33520i		−	0.176376i
$916$	−12.5435	−	36.2646i	−0.414449	−	1.19822i
$917$			32.4289i			1.07090i
$918$	−43.8851	+	7.37531i	−1.44843	+	0.243422i
$919$	−11.6989			−0.385910			−0.192955	−	0.981208i	$-0.561807\pi$
$919$	−11.6989			−0.385910			−0.192955	+	0.981208i	$0.561807\pi$
$920$	10.8031	−	8.20323i	0.356168	−	0.270453i
$921$	11.3895			0.375298
$922$	−16.9752	+	2.85284i	−0.559049	+	0.0939534i
$923$		−	38.1011i		−	1.25411i
$924$	3.45955	+	10.0019i	0.113811	+	0.329040i
$925$		−	9.38162i		−	0.308466i
$926$	0.528223	+	3.14307i	0.0173585	+	0.103288i
$927$	−17.0173			−0.558921
$928$	−18.8401	+	20.7049i	−0.618458	+	0.679670i
$929$	22.6705			0.743796			0.371898	−	0.928274i	$-0.378707\pi$
$929$	22.6705			0.743796			0.371898	+	0.928274i	$0.378707\pi$
$930$	−1.14175	−	6.79373i	−0.0374395	−	0.222775i
$931$	−10.7698			−0.352967
$932$	51.9126	−	17.9560i	1.70045	−	0.588167i
$933$	−1.51353			−0.0495509
$934$	−6.07555	+	1.02105i	−0.198798	+	0.0334099i
$935$	−9.20858			−0.301153
$936$	9.47640	−	5.17096i	0.309746	−	0.169018i
$937$		−	21.3724i		−	0.698206i	−0.937084	−	0.349103i	$-0.886486\pi$
$937$		−	21.3724i		−	0.698206i	0.937084	−	0.349103i	$-0.113514\pi$
$938$	−15.1240	+	2.54173i	−0.493816	+	0.0829905i
$939$	−42.7745			−1.39589
$940$	16.2712	−	5.62800i	0.530707	−	0.183565i
$941$			19.2671i			0.628091i	0.949408	+	0.314045i	$0.101684\pi$
$941$			19.2671i			0.628091i	−0.949408	+	0.314045i	$0.898316\pi$
$942$	28.0889	−	4.72061i	0.915186	−	0.153806i
$943$	4.56443	+	30.2129i	0.148638	+	0.983867i
$944$	−23.4927	−	29.8970i	−0.764622	−	0.973065i
$945$	13.1041			0.426277
$946$	−29.7141	+	4.99373i	−0.966088	+	0.162360i
$947$			1.73836i			0.0564891i	0.999601	+	0.0282446i	$0.00899172\pi$
$947$			1.73836i			0.0564891i	−0.999601	+	0.0282446i	$0.991008\pi$
$948$	−3.82037	−	11.0451i	−0.124080	−	0.358728i
$949$	−22.6874			−0.736463
$950$	9.24672	−	1.55400i	0.300003	−	0.0504184i
$951$		−	11.3652i		−	0.368543i
$952$	17.4883	+	32.0494i	0.566799	+	1.03873i
$953$		−	49.8435i		−	1.61459i	−0.590149	−	0.807295i	$-0.700931\pi$
$953$		−	49.8435i		−	1.61459i	0.590149	−	0.807295i	$-0.299069\pi$
$954$	−0.525824	−	3.12880i	−0.0170242	−	0.101299i
$955$			7.65350i			0.247661i
$956$	−0.392013	−	1.13335i	−0.0126786	−	0.0366553i
$957$			11.2944i			0.365096i
$958$	−50.3597	+	8.46342i	−1.62705	+	0.273441i
$959$		−	28.3394i		−	0.915127i
$960$	5.97353	−	9.28322i	0.192795	−	0.299615i
$961$	18.5377			0.597991
$962$	7.65816	+	45.5681i	0.246909	+	1.46918i
$963$	−18.5953			−0.599224
$964$	9.35602	+	27.0493i	0.301337	+	0.871198i
$965$			3.72049i			0.119767i
$966$	−20.6214	+	6.75246i	−0.663483	+	0.217257i
$967$		−	48.8626i		−	1.57131i	−0.618662	−	0.785657i	$-0.712325\pi$
$967$		−	48.8626i		−	1.57131i	0.618662	−	0.785657i	$-0.287675\pi$
$968$	20.5189	−	11.1965i	0.659502	−	0.359869i
$969$	50.9355			1.63628
$970$	26.5155	−	4.45619i	0.851363	−	0.143080i
$971$	−48.9550			−1.57104			−0.785520	−	0.618837i	$-0.787604\pi$
$971$	−48.9550			−1.57104			−0.785520	+	0.618837i	$0.787604\pi$
$972$	7.01546	+	20.2824i	0.225021	+	0.650560i
$973$		−	3.74245i		−	0.119977i
$974$	4.25439	+	25.3148i	0.136320	+	0.811139i
$975$			4.80573i			0.153907i
$976$	−9.55555	−	12.1605i	−0.305866	−	0.389248i
$977$		−	28.3251i		−	0.906201i	−0.891459	−	0.453100i	$-0.850318\pi$
$977$		−	28.3251i		−	0.906201i	0.891459	−	0.453100i	$-0.149682\pi$
$978$	−10.0787	+	1.69382i	−0.322282	+	0.0541625i
$979$		−	12.3846i		−	0.395813i
$980$	1.06198	+	3.07029i	0.0339236	+	0.0980768i
$981$			4.72031i			0.150708i
$982$	−5.31594	−	31.6313i	−0.169639	−	1.00940i
$983$	−11.9527			−0.381233			−0.190617	−	0.981665i	$-0.561049\pi$
$983$	−11.9527			−0.381233			−0.190617	+	0.981665i	$0.561049\pi$
$984$	11.9110	+	21.8283i	0.379709	+	0.695862i
$985$		−	2.90083i		−	0.0924281i
$986$	6.45759	+	38.4244i	0.205651	+	1.22368i
$987$	−27.5413			−0.876650
$988$	−43.6444	+	15.0961i	−1.38851	+	0.480270i
$989$	−9.22820	−	61.0833i	−0.293440	−	1.94234i
$990$	0.424858	+	2.52802i	0.0135029	+	0.0803458i
$991$			42.6367i			1.35440i	0.735800	+	0.677199i	$0.236806\pi$
$991$			42.6367i			1.35440i	−0.735800	+	0.677199i	$0.763194\pi$
$992$	−14.7702	−	13.4400i	−0.468955	−	0.426720i
$993$	11.9366			0.378795
$994$	−5.94518	−	35.3755i	−0.188570	−	1.12204i
$995$			12.0631i			0.382426i
$996$	−4.90840	−	14.1907i	−0.155529	−	0.449650i
$997$	−4.21192			−0.133393			−0.0666964	−	0.997773i	$-0.521246\pi$
$997$	−4.21192			−0.133393			−0.0666964	+	0.997773i	$0.521246\pi$
$998$	−7.37736	−	43.8973i	−0.233526	−	1.38955i
$999$	−53.0239			−1.67760

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.b.91.3	yes	32
4.3	odd	2	inner	460.2.e.b.91.1	✓	32
23.22	odd	2	inner	460.2.e.b.91.4	yes	32
92.91	even	2	inner	460.2.e.b.91.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.b.91.1	✓	32	4.3	odd	2	inner
460.2.e.b.91.2	yes	32	92.91	even	2	inner
460.2.e.b.91.3	yes	32	1.1	even	1	trivial
460.2.e.b.91.4	yes	32	23.22	odd	2	inner

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	460.2.e.b.91.3

Level	$460$
Weight	$2$
Character	460.91
Analytic conductor	$3.673$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$