LMFDB - Embedded newform 900.2.r.f.551.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] 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("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,6,0,0,4,0,0,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.6
Character	$\chi$	$=$	900.551
Dual form			900.2.r.f.851.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08940 + 0.901786i) q^{2} +(-1.35535 - 1.07843i) q^{3} +(0.373566 - 1.96480i) q^{4} +(2.44903 - 0.0473955i) q^{6} +(3.33246 + 1.92400i) q^{7} +(1.36487 + 2.47732i) q^{8} +(0.673959 + 2.92332i) q^{9} +(-1.40956 + 2.44144i) q^{11} +(-2.62522 + 2.26013i) q^{12} +(-2.89540 - 5.01498i) q^{13} +(-5.36540 + 0.909171i) q^{14} +(-3.72090 - 1.46797i) q^{16} +2.42512i q^{17} +(-3.37041 - 2.57688i) q^{18} +4.07233i q^{19} +(-2.44175 - 6.20153i) q^{21} +(-0.666079 - 3.93081i) q^{22} +(2.17379 + 3.76512i) q^{23} +(0.821751 - 4.82957i) q^{24} +(7.67667 + 2.85227i) q^{26} +(2.23915 - 4.68894i) q^{27} +(5.02517 - 5.82889i) q^{28} +(-6.07280 - 3.50613i) q^{29} +(1.94857 - 1.12501i) q^{31} +(5.37732 - 1.75626i) q^{32} +(4.54338 - 1.78888i) q^{33} +(-2.18694 - 2.64192i) q^{34} +(5.99551 - 0.232146i) q^{36} -4.29414 q^{37} +(-3.67237 - 4.43638i) q^{38} +(-1.48404 + 9.91956i) q^{39} +(0.0948994 - 0.0547902i) q^{41} +(8.25249 + 4.55399i) q^{42} +(-0.178397 - 0.102997i) q^{43} +(4.27038 + 3.68155i) q^{44} +(-5.76345 - 2.14141i) q^{46} +(-5.38793 + 9.33217i) q^{47} +(3.46002 + 6.00235i) q^{48} +(3.90353 + 6.76112i) q^{49} +(2.61533 - 3.28689i) q^{51} +(-10.9351 + 3.81546i) q^{52} +7.55580i q^{53} +(1.78910 + 7.12735i) q^{54} +(-0.217988 + 10.8816i) q^{56} +(4.39174 - 5.51944i) q^{57} +(9.77747 - 1.65680i) q^{58} +(4.16744 + 7.21822i) q^{59} +(-3.06480 + 5.30839i) q^{61} +(-1.10825 + 2.98277i) q^{62} +(-3.37851 + 11.0385i) q^{63} +(-4.27426 + 6.76245i) q^{64} +(-3.33635 + 6.04596i) q^{66} +(-4.48967 + 2.59211i) q^{67} +(4.76488 + 0.905942i) q^{68} +(1.11418 - 7.44736i) q^{69} -5.46464 q^{71} +(-6.32213 + 5.65956i) q^{72} +12.9936 q^{73} +(4.67802 - 3.87240i) q^{74} +(8.00132 + 1.52128i) q^{76} +(-9.39464 + 5.42400i) q^{77} +(-7.32861 - 12.1446i) q^{78} +(4.32475 + 2.49689i) q^{79} +(-8.09156 + 3.94039i) q^{81} +(-0.0539740 + 0.145267i) q^{82} +(-3.85716 + 6.68080i) q^{83} +(-13.0969 + 2.48088i) q^{84} +(0.287226 - 0.0486706i) q^{86} +(4.44965 + 11.3012i) q^{87} +(-7.97210 - 0.159703i) q^{88} +0.134752i q^{89} -22.2830i q^{91} +(8.20978 - 2.86456i) q^{92} +(-3.85425 - 0.576624i) q^{93} +(-2.54603 - 15.0252i) q^{94} +(-9.18217 - 3.41874i) q^{96} +(-6.49834 + 11.2555i) q^{97} +(-10.3496 - 3.84538i) q^{98} +(-8.08708 - 2.47517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 4 q^{9} + 22 q^{12} - 30 q^{14} + 16 q^{18} - 4 q^{21} - 28 q^{24} - 12 q^{29} + 44 q^{33} - 6 q^{34} + 42 q^{36} - 60 q^{38} - 60 q^{41} + 18 q^{42} - 12 q^{46} + 12 q^{48} + 24 q^{49}+ \cdots + 12 q^{97}+O(q^{100}) $ 48 * q + 6 * q^6 + 4 * q^9 + 22 * q^12 - 30 * q^14 + 16 * q^18 - 4 * q^21 - 28 * q^24 - 12 * q^29 + 44 * q^33 - 6 * q^34 + 42 * q^36 - 60 * q^38 - 60 * q^41 + 18 * q^42 - 12 * q^46 + 12 * q^48 + 24 * q^49 + 18 * q^52 - 32 * q^54 - 42 * q^56 + 12 * q^57 + 18 * q^58 - 48 * q^64 + 16 * q^66 - 48 * q^68 + 36 * q^69 - 60 * q^72 + 24 * q^73 + 84 * q^74 + 6 * q^76 - 48 * q^77 - 38 * q^78 + 36 * q^82 + 50 * q^84 - 54 * q^86 - 60 * q^92 + 32 * q^93 + 18 * q^94 - 18 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−1.08940	+	0.901786i	−0.770319	+	0.637659i
$2$	−1.08940	+	0.901786i	−0.770319	+	0.637659i
$3$	−1.35535	−	1.07843i	−0.782513	−	0.622634i
$3$	−1.35535	−	1.07843i	−0.782513	−	0.622634i
$4$	0.373566	−	1.96480i	0.186783	−	0.982401i
$5$		0			0
$5$		0			0
$6$	2.44903	−	0.0473955i	0.999813	−	0.0193492i
$7$	3.33246	+	1.92400i	1.25955	+	0.727203i	0.972987	−	0.230858i	$-0.0741534\pi$
$7$	3.33246	+	1.92400i	1.25955	+	0.727203i	0.286565	+	0.958061i	$0.407487\pi$
$8$	1.36487	+	2.47732i	0.482554	+	0.875866i
$9$	0.673959	+	2.92332i	0.224653	+	0.974439i
$10$		0			0
$11$	−1.40956	+	2.44144i	−0.425000	+	0.736121i	−0.996420	−	0.0845363i	$-0.973059\pi$
$11$	−1.40956	+	2.44144i	−0.425000	+	0.736121i	0.571421	+	0.820657i	$0.306392\pi$
$12$	−2.62522	+	2.26013i	−0.757837	+	0.652444i
$13$	−2.89540	−	5.01498i	−0.803039	−	1.39091i	−0.917607	−	0.397490i	$-0.869881\pi$
$13$	−2.89540	−	5.01498i	−0.803039	−	1.39091i	0.114567	−	0.993415i	$-0.463452\pi$
$14$	−5.36540	+	0.909171i	−1.43396	+	0.242986i
$15$		0			0
$16$	−3.72090	−	1.46797i	−0.930224	−	0.366991i
$17$			2.42512i			0.588178i	0.955778	+	0.294089i	$0.0950162\pi$
$17$			2.42512i			0.588178i	−0.955778	+	0.294089i	$0.904984\pi$
$18$	−3.37041	−	2.57688i	−0.794414	−	0.607377i
$19$			4.07233i			0.934256i	0.884190	+	0.467128i	$0.154711\pi$
$19$			4.07233i			0.934256i	−0.884190	+	0.467128i	$0.845289\pi$
$20$		0			0
$21$	−2.44175	−	6.20153i	−0.532834	−	1.35329i
$22$	−0.666079	−	3.93081i	−0.142009	−	0.838053i
$23$	2.17379	+	3.76512i	0.453267	+	0.785082i	0.998587	−	0.0531462i	$-0.0169249\pi$
$23$	2.17379	+	3.76512i	0.453267	+	0.785082i	−0.545319	+	0.838228i	$0.683592\pi$
$24$	0.821751	−	4.82957i	0.167739	−	0.985831i
$25$		0			0
$26$	7.67667	+	2.85227i	1.50552	+	0.559376i
$27$	2.23915	−	4.68894i	0.430925	−	0.902388i
$28$	5.02517	−	5.82889i	0.949667	−	1.10156i
$29$	−6.07280	−	3.50613i	−1.12769	−	0.651073i	−0.184338	−	0.982863i	$-0.559014\pi$
$29$	−6.07280	−	3.50613i	−1.12769	−	0.651073i	−0.943353	+	0.331790i	$0.892347\pi$
$30$		0			0
$31$	1.94857	−	1.12501i	0.349974	−	0.202058i	−0.314700	−	0.949191i	$-0.601904\pi$
$31$	1.94857	−	1.12501i	0.349974	−	0.202058i	0.664674	+	0.747134i	$0.268571\pi$
$32$	5.37732	−	1.75626i	0.950585	−	0.310465i
$33$	4.54338	−	1.78888i	0.790902	−	0.311405i
$34$	−2.18694	−	2.64192i	−0.375057	−	0.453085i
$35$		0			0
$36$	5.99551	−	0.232146i	0.999251	−	0.0386911i
$37$	−4.29414			−0.705953			−0.352976	−	0.935632i	$-0.614830\pi$
$37$	−4.29414			−0.705953			−0.352976	+	0.935632i	$0.614830\pi$
$38$	−3.67237	−	4.43638i	−0.595737	−	0.719675i
$39$	−1.48404	+	9.91956i	−0.237636	+	1.58840i
$40$		0			0
$41$	0.0948994	−	0.0547902i	0.0148208	−	0.00855679i	−0.492571	−	0.870272i	$-0.663943\pi$
$41$	0.0948994	−	0.0547902i	0.0148208	−	0.00855679i	0.507392	+	0.861715i	$0.330610\pi$
$42$	8.25249	+	4.55399i	1.27339	+	0.702695i
$43$	−0.178397	−	0.102997i	−0.0272052	−	0.0157069i	0.486336	−	0.873772i	$-0.338333\pi$
$43$	−0.178397	−	0.102997i	−0.0272052	−	0.0157069i	−0.513541	+	0.858065i	$0.671667\pi$
$44$	4.27038	+	3.68155i	0.643783	+	0.555015i
$45$		0			0
$46$	−5.76345	−	2.14141i	−0.849775	−	0.315734i
$47$	−5.38793	+	9.33217i	−0.785910	+	1.36124i	0.142543	+	0.989789i	$0.454472\pi$
$47$	−5.38793	+	9.33217i	−0.785910	+	1.36124i	−0.928454	+	0.371448i	$0.878861\pi$
$48$	3.46002	+	6.00235i	0.499411	+	0.866365i
$49$	3.90353	+	6.76112i	0.557647	+	0.965874i
$50$		0			0
$51$	2.61533	−	3.28689i	0.366220	−	0.460257i
$52$	−10.9351	+	3.81546i	−1.51642	+	0.529110i
$53$			7.55580i			1.03787i	0.854814	+	0.518934i	$0.173671\pi$
$53$			7.55580i			1.03787i	−0.854814	+	0.518934i	$0.826329\pi$
$54$	1.78910	+	7.12735i	0.243466	+	0.969910i
$55$		0			0
$56$	−0.217988	+	10.8816i	−0.0291299	+	1.45411i
$57$	4.39174	−	5.51944i	0.581700	−	0.731068i
$58$	9.77747	−	1.65680i	1.28384	−	0.217548i
$59$	4.16744	+	7.21822i	0.542554	+	0.939732i	0.998756	+	0.0498554i	$0.0158761\pi$
$59$	4.16744	+	7.21822i	0.542554	+	0.939732i	−0.456202	+	0.889876i	$0.650791\pi$
$60$		0			0
$61$	−3.06480	+	5.30839i	−0.392407	+	0.679669i	−0.992767	−	0.120061i	$-0.961691\pi$
$61$	−3.06480	+	5.30839i	−0.392407	+	0.679669i	0.600359	+	0.799730i	$0.295024\pi$
$62$	−1.10825	+	2.98277i	−0.140748	+	0.378813i
$63$	−3.37851	+	11.0385i	−0.425652	+	1.39072i
$64$	−4.27426	+	6.76245i	−0.534283	+	0.845306i
$65$		0			0
$66$	−3.33635	+	6.04596i	−0.410677	+	0.744206i
$67$	−4.48967	+	2.59211i	−0.548500	+	0.316677i	−0.748517	−	0.663116i	$-0.769234\pi$
$67$	−4.48967	+	2.59211i	−0.548500	+	0.316677i	0.200017	+	0.979792i	$0.435900\pi$
$68$	4.76488	+	0.905942i	0.577827	+	0.109862i
$69$	1.11418	−	7.44736i	0.134131	−	0.896557i
$70$		0			0
$71$	−5.46464			−0.648533			−0.324267	−	0.945966i	$-0.605118\pi$
$71$	−5.46464			−0.648533			−0.324267	+	0.945966i	$0.605118\pi$
$72$	−6.32213	+	5.65956i	−0.745071	+	0.666986i
$73$	12.9936			1.52078			0.760390	−	0.649466i	$-0.225008\pi$
$73$	12.9936			1.52078			0.760390	+	0.649466i	$0.225008\pi$
$74$	4.67802	−	3.87240i	0.543809	−	0.450157i
$75$		0			0
$76$	8.00132	+	1.52128i	0.917814	+	0.174503i
$77$	−9.39464	+	5.42400i	−1.07062	+	0.618122i
$78$	−7.32861	−	12.1446i	−0.829802	−	1.37511i
$79$	4.32475	+	2.49689i	0.486572	+	0.280923i	0.723151	−	0.690690i	$-0.242693\pi$
$79$	4.32475	+	2.49689i	0.486572	+	0.280923i	−0.236579	+	0.971612i	$0.576026\pi$
$80$		0			0
$81$	−8.09156	+	3.94039i	−0.899062	+	0.437821i
$82$	−0.0539740	+	0.145267i	−0.00596043	+	0.0160421i
$83$	−3.85716	+	6.68080i	−0.423379	+	0.733314i	−0.996267	−	0.0863196i	$-0.972489\pi$
$83$	−3.85716	+	6.68080i	−0.423379	+	0.733314i	0.572889	+	0.819633i	$0.305823\pi$
$84$	−13.0969	+	2.48088i	−1.42899	+	0.270687i
$85$		0			0
$86$	0.287226	−	0.0486706i	0.0309724	−	0.00524829i
$87$	4.44965	+	11.3012i	0.477053	+	1.21161i
$88$	−7.97210	−	0.159703i	−0.849829	−	0.0170244i
$89$			0.134752i			0.0142837i	0.999974	+	0.00714184i	$0.00227334\pi$
$89$			0.134752i			0.0142837i	−0.999974	+	0.00714184i	$0.997727\pi$
$90$		0			0
$91$		−	22.2830i		−	2.33589i
$92$	8.20978	−	2.86456i	0.855928	−	0.298651i
$93$	−3.85425	−	0.576624i	−0.399667	−	0.0597931i
$94$	−2.54603	−	15.0252i	−0.262603	−	1.54973i
$95$		0			0
$96$	−9.18217	−	3.41874i	−0.937151	−	0.348924i
$97$	−6.49834	+	11.2555i	−0.659806	+	1.14282i	0.320859	+	0.947127i	$0.396028\pi$
$97$	−6.49834	+	11.2555i	−0.659806	+	1.14282i	−0.980666	+	0.195691i	$0.937305\pi$
$98$	−10.3496	−	3.84538i	−1.04546	−	0.388442i
$99$	−8.08708	−	2.47517i	−0.812782	−	0.248764i
$100$		0			0
$101$	2.90860	+	1.67928i	0.289417	+	0.167095i	0.637679	−	0.770302i	$-0.279895\pi$
$101$	2.90860	+	1.67928i	0.289417	+	0.167095i	−0.348262	+	0.937397i	$0.613228\pi$
$102$	0.114940	+	5.93920i	0.0113807	+	0.588068i
$103$	−3.32353	+	1.91884i	−0.327477	+	0.189069i	−0.654720	−	0.755871i	$-0.727214\pi$
$103$	−3.32353	+	1.91884i	−0.327477	+	0.189069i	0.327244	+	0.944940i	$0.393880\pi$
$104$	8.47188	−	14.0176i	0.830736	−	1.37454i
$105$		0			0
$106$	−6.81371	−	8.23125i	−0.661806	−	0.799490i
$107$	0.556704			0.0538186			0.0269093	−	0.999638i	$-0.491433\pi$
$107$	0.556704			0.0538186			0.0269093	+	0.999638i	$0.491433\pi$
$108$	−8.37638	−	6.15112i	−0.806017	−	0.591892i
$109$	15.5306			1.48756			0.743779	−	0.668425i	$-0.233031\pi$
$109$	15.5306			1.48756			0.743779	+	0.668425i	$0.233031\pi$
$110$		0			0
$111$	5.82008	+	4.63095i	0.552417	+	0.439551i
$112$	−9.57538	−	12.0509i	−0.904789	−	1.13871i
$113$	6.56932	−	3.79280i	0.617989	−	0.356796i	−0.158096	−	0.987424i	$-0.550536\pi$
$113$	6.56932	−	3.79280i	0.617989	−	0.356796i	0.776086	+	0.630627i	$0.217202\pi$
$114$	0.193010	+	9.97326i	0.0180771	+	0.934081i
$115$		0			0
$116$	−9.15745	+	10.6221i	−0.850248	+	0.986236i
$117$	12.7090	−	11.8441i	1.17495	−	1.09498i
$118$	−11.0493	−	4.10536i	−1.01717	−	0.377929i
$119$	−4.66593	+	8.08162i	−0.427725	+	0.740841i
$120$		0			0
$121$	1.52626	+	2.64356i	0.138751	+	0.240323i
$122$	−1.44825	−	8.54673i	−0.131118	−	0.773784i
$123$	−0.187710	−	0.0280827i	−0.0169252	−	0.00253213i
$124$	−1.48250	−	4.24883i	−0.133132	−	0.381556i
$125$		0			0
$126$	−6.27386	−	15.0720i	−0.558920	−	1.34272i
$127$		−	18.5602i		−	1.64695i	−0.567352	−	0.823476i	$-0.692032\pi$
$127$		−	18.5602i		−	1.64695i	0.567352	−	0.823476i	$-0.307968\pi$
$128$	−1.44192	−	11.2214i	−0.127449	−	0.991845i
$129$	0.130714	+	0.331987i	0.0115088	+	0.0292298i
$130$		0			0
$131$	4.75330	+	8.23296i	0.415298	+	0.719317i	0.995460	−	0.0951841i	$-0.0303440\pi$
$131$	4.75330	+	8.23296i	0.415298	+	0.719317i	−0.580162	+	0.814501i	$0.697011\pi$
$132$	−1.81755	−	9.59512i	−0.158198	−	0.835148i
$133$	−7.83515	+	13.5709i	−0.679394	+	1.17674i
$134$	2.55350	−	6.87255i	0.220588	−	0.593698i
$135$		0			0
$136$	−6.00781	+	3.30997i	−0.515165	+	0.283828i
$137$	−0.693556	−	0.400425i	−0.0592545	−	0.0342106i	0.470080	−	0.882624i	$-0.344225\pi$
$137$	−0.693556	−	0.400425i	−0.0592545	−	0.0342106i	−0.529335	+	0.848413i	$0.677558\pi$
$138$	5.50214	+	9.11787i	0.468373	+	0.776165i
$139$	6.32423	−	3.65130i	0.536415	−	0.309699i	−0.207210	−	0.978296i	$-0.566438\pi$
$139$	6.32423	−	3.65130i	0.536415	−	0.309699i	0.743625	+	0.668597i	$0.233105\pi$
$140$		0			0
$141$	17.3667	−	6.83785i	1.46254	−	0.575851i
$142$	5.95316	−	4.92793i	0.499578	−	0.413543i
$143$	16.3250			1.36517
$144$	1.78359	−	11.8667i	0.148633	−	0.988892i
$145$		0			0
$146$	−14.1551	+	11.7174i	−1.17149	+	0.969739i
$147$	2.00076	−	13.3734i	0.165020	−	1.10302i
$148$	−1.60414	+	8.43715i	−0.131860	+	0.693529i
$149$	0.0985697	−	0.0569092i	0.00807514	−	0.00466219i	−0.495957	−	0.868347i	$-0.665183\pi$
$149$	0.0985697	−	0.0569092i	0.00807514	−	0.00466219i	0.504032	+	0.863685i	$0.331849\pi$
$150$		0			0
$151$	−1.46894	−	0.848093i	−0.119541	−	0.0690169i	0.439037	−	0.898469i	$-0.355320\pi$
$151$	−1.46894	−	0.848093i	−0.119541	−	0.0690169i	−0.558578	+	0.829452i	$0.688653\pi$
$152$	−10.0885	+	5.55820i	−0.818283	+	0.450829i
$153$	−7.08940	+	1.63443i	−0.573144	+	0.132136i
$154$	5.34319	−	14.3808i	0.430567	−	1.15884i
$155$		0			0
$156$	18.9356	+	6.62145i	1.51606	+	0.530140i
$157$	11.2470	+	19.4804i	0.897612	+	1.55471i	0.830539	+	0.556961i	$0.188033\pi$
$157$	11.2470	+	19.4804i	0.897612	+	1.55471i	0.0670730	+	0.997748i	$0.478634\pi$
$158$	−6.96302	+	1.17989i	−0.553948	+	0.0938669i
$159$	8.14843	−	10.2408i	0.646213	−	0.812146i
$160$		0			0
$161$			16.7295i			1.31847i
$162$	5.26152	−	11.5895i	0.413384	−	0.910557i
$163$			1.64377i			0.128750i	0.997926	+	0.0643749i	$0.0205054\pi$
$163$			1.64377i			0.128750i	−0.997926	+	0.0643749i	$0.979495\pi$
$164$	−0.0722007	−	0.206926i	−0.00563793	−	0.0161582i
$165$		0			0
$166$	−1.82268	−	10.7564i	−0.141467	−	0.834857i
$167$	−1.21935	−	2.11198i	−0.0943561	−	0.163430i	0.814984	−	0.579484i	$-0.196746\pi$
$167$	−1.21935	−	2.11198i	−0.0943561	−	0.163430i	−0.909340	+	0.416054i	$0.863413\pi$
$168$	12.0305	−	14.5133i	0.928175	−	1.11973i
$169$	−10.2667	+	17.7824i	−0.789745	+	1.36788i
$170$		0			0
$171$	−11.9047	+	2.74458i	−0.910376	+	0.209884i
$172$	−0.269012	+	0.312038i	−0.0205120	+	0.0237927i
$173$	9.14392	+	5.27925i	0.695200	+	0.401374i	0.805557	−	0.592518i	$-0.201866\pi$
$173$	9.14392	+	5.27925i	0.695200	+	0.401374i	−0.110357	+	0.993892i	$0.535200\pi$
$174$	−15.0387	−	8.29881i	−1.14008	−	0.629131i
$175$		0			0
$176$	8.82879	−	7.01514i	0.665495	−	0.528786i
$177$	2.13602	−	14.2775i	0.160553	−	1.07317i
$178$	−0.121517	−	0.146798i	−0.00910812	−	0.0110030i
$179$	−3.01061			−0.225023			−0.112512	−	0.993650i	$-0.535890\pi$
$179$	−3.01061			−0.225023			−0.112512	+	0.993650i	$0.535890\pi$
$180$		0			0
$181$	−19.5270			−1.45143			−0.725715	−	0.687996i	$-0.758491\pi$
$181$	−19.5270			−1.45143			−0.725715	+	0.687996i	$0.758491\pi$
$182$	20.0945	+	24.2750i	1.48950	+	1.79938i
$183$	9.87863	−	3.88955i	0.730249	−	0.287524i
$184$	−6.36048	+	10.5241i	−0.468901	+	0.775846i
$185$		0			0
$186$	4.71879	−	2.84754i	0.345999	−	0.208791i
$187$	−5.92078	−	3.41836i	−0.432970	−	0.249975i
$188$	16.3231	+	14.0724i	1.19049	+	1.02633i
$189$	16.4834	−	11.3176i	1.19899	−	0.823234i
$190$		0			0
$191$	0.482086	−	0.834997i	0.0348825	−	0.0604183i	−0.848057	−	0.529905i	$-0.822228\pi$
$191$	0.482086	−	0.834997i	0.0348825	−	0.0604183i	0.882940	+	0.469487i	$0.155561\pi$
$192$	13.0860	−	4.55599i	0.944400	−	0.328800i
$193$	−7.99670	−	13.8507i	−0.575615	−	0.996995i	−0.995974	−	0.0896373i	$-0.971429\pi$
$193$	−7.99670	−	13.8507i	−0.575615	−	0.996995i	0.420359	−	0.907358i	$-0.361904\pi$
$194$	−3.07074	−	18.1217i	−0.220466	−	1.30107i
$195$		0			0
$196$	14.7425	−	5.14395i	1.05303	−	0.367425i
$197$		−	26.0766i		−	1.85788i	−0.370233	−	0.928939i	$-0.620722\pi$
$197$		−	26.0766i		−	1.85788i	0.370233	−	0.928939i	$-0.379278\pi$
$198$	11.0421	−	4.59637i	0.784728	−	0.326650i
$199$			16.6714i			1.18181i	0.806743	+	0.590903i	$0.201228\pi$
$199$			16.6714i			1.18181i	−0.806743	+	0.590903i	$0.798772\pi$
$200$		0			0
$201$	8.88050	+	1.32859i	0.626382	+	0.0937113i
$202$	−4.68297	+	0.793533i	−0.329493	+	0.0558328i
$203$	−13.4916	−	23.3681i	−0.946924	−	1.64012i
$204$	−5.48110	−	6.36648i	−0.383753	−	0.445743i
$205$		0			0
$206$	1.89025	−	5.08748i	0.131700	−	0.354462i
$207$	−9.54159	+	8.89223i	−0.663187	+	0.618052i
$208$	3.41167	+	22.9106i	0.236557	+	1.58856i
$209$	−9.94233	−	5.74021i	−0.687726	−	0.397059i
$210$		0			0
$211$	−18.9378	+	10.9337i	−1.30373	+	0.752709i	−0.981042	−	0.193796i	$-0.937920\pi$
$211$	−18.9378	+	10.9337i	−1.30373	+	0.752709i	−0.322689	+	0.946505i	$0.604587\pi$
$212$	14.8457	+	2.82259i	1.01960	+	0.193856i
$213$	7.40651	+	5.89326i	0.507486	+	0.403799i
$214$	−0.606471	+	0.502027i	−0.0414575	+	0.0343179i
$215$		0			0
$216$	14.6722	−	0.852694i	0.998316	−	0.0580185i
$217$	8.65806			0.587747
$218$	−16.9189	+	14.0052i	−1.14589	+	0.948555i
$219$	−17.6108	−	14.0127i	−1.19003	−	0.946890i
$220$		0			0
$221$	12.1619	−	7.02169i	0.818100	−	0.472330i
$222$	−10.5165	+	0.203523i	−0.705821	+	0.0136596i
$223$	2.13791	+	1.23432i	0.143165	+	0.0826563i	0.569871	−	0.821734i	$-0.306993\pi$
$223$	2.13791	+	1.23432i	0.143165	+	0.0826563i	−0.426707	+	0.904390i	$0.640326\pi$
$224$	21.2987	+	4.49329i	1.42308	+	0.300221i
$225$		0			0
$226$	−3.73630	+	10.0560i	−0.248535	+	0.668913i
$227$	−4.51256	+	7.81598i	−0.299509	+	0.518765i	−0.976024	−	0.217664i	$-0.930156\pi$
$227$	−4.51256	+	7.81598i	−0.299509	+	0.518765i	0.676515	+	0.736429i	$0.263490\pi$
$228$	−9.20401	−	10.6908i	−0.609550	−	0.708014i
$229$	−6.05048	−	10.4797i	−0.399827	−	0.692521i	0.593877	−	0.804556i	$-0.297597\pi$
$229$	−6.05048	−	10.4797i	−0.399827	−	0.692521i	−0.993704	+	0.112035i	$0.964263\pi$
$230$		0			0
$231$	18.5825	+	2.78007i	1.22264	+	0.182915i
$232$	0.397244	−	19.8297i	0.0260803	−	1.30188i
$233$		−	12.9280i		−	0.846943i	−0.905909	−	0.423471i	$-0.860811\pi$
$233$		−	12.9280i		−	0.846943i	0.905909	−	0.423471i	$-0.139189\pi$
$234$	−3.16431	+	24.3637i	−0.206858	+	1.59270i
$235$		0			0
$236$	15.7392	−	5.49172i	1.02453	−	0.357480i
$237$	−3.16882	−	8.04813i	−0.205837	−	0.522782i
$238$	−2.20485	−	13.0117i	−0.142919	−	0.843426i
$239$	−4.58101	−	7.93455i	−0.296321	−	0.513243i	0.678970	−	0.734166i	$-0.262427\pi$
$239$	−4.58101	−	7.93455i	−0.296321	−	0.513243i	−0.975291	+	0.220923i	$0.929093\pi$
$240$		0			0
$241$	5.29982	−	9.17956i	0.341391	−	0.591307i	−0.643300	−	0.765614i	$-0.722435\pi$
$241$	5.29982	−	9.17956i	0.341391	−	0.591307i	0.984691	+	0.174307i	$0.0557685\pi$
$242$	−4.04662	−	1.50352i	−0.260127	−	0.0966500i
$243$	15.2164	+	3.38559i	0.976130	+	0.217186i
$244$	9.28503	+	8.00476i	0.594413	+	0.512452i
$245$		0			0
$246$	0.229815	−	0.138681i	0.0146524	−	0.00884195i
$247$	20.4226	−	11.7910i	1.29946	−	0.750245i
$248$	5.44656	+	3.29175i	0.345857	+	0.209027i
$249$	12.4326	−	4.89515i	0.787886	−	0.310217i
$250$		0			0
$251$	10.2219			0.645198			0.322599	−	0.946536i	$-0.395443\pi$
$251$	10.2219			0.645198			0.322599	+	0.946536i	$0.395443\pi$
$252$	20.4264	+	10.7617i	1.28675	+	0.677925i
$253$	−12.2564			−0.770554
$254$	16.7373	+	20.2194i	1.05019	+	1.26868i
$255$		0			0
$256$	11.6902	+	10.9243i	0.730635	+	0.682769i
$257$	−5.58322	+	3.22348i	−0.348272	+	0.201075i	−0.663924	−	0.747800i	$-0.731110\pi$
$257$	−5.58322	+	3.22348i	−0.348272	+	0.201075i	0.315652	+	0.948875i	$0.397777\pi$
$258$	−0.441780	−	0.243788i	−0.0275040	−	0.0151776i
$259$	−14.3101	−	8.26192i	−0.889184	−	0.513371i
$260$		0			0
$261$	6.15672	−	20.1157i	0.381091	−	1.24513i
$262$	−12.6026	−	4.68249i	−0.778591	−	0.289285i
$263$	−9.06727	+	15.7050i	−0.559112	+	0.968410i	0.438459	+	0.898751i	$0.355524\pi$
$263$	−9.06727	+	15.7050i	−0.559112	+	0.968410i	−0.997571	+	0.0696586i	$0.977809\pi$
$264$	10.6328	+	8.81384i	0.654402	+	0.542454i
$265$		0			0
$266$	−3.70244	−	21.8497i	−0.227011	−	1.33969i
$267$	0.145321	−	0.182636i	0.00889351	−	0.0111772i
$268$	3.41580	+	9.78963i	0.208653	+	0.597997i
$269$		−	3.40907i		−	0.207854i	−0.994585	−	0.103927i	$-0.966859\pi$
$269$		−	3.40907i		−	0.207854i	0.994585	−	0.103927i	$-0.0331409\pi$
$270$		0			0
$271$			8.61740i			0.523470i	0.965140	+	0.261735i	$0.0842946\pi$
$271$			8.61740i			0.523470i	−0.965140	+	0.261735i	$0.915705\pi$
$272$	3.55999	−	9.02363i	0.215856	−	0.547138i
$273$	−24.0307	+	30.2013i	−1.45440	+	1.82786i
$274$	1.11665	−	0.189218i	0.0674596	−	0.0114311i
$275$		0			0
$276$	−14.2164	−	4.97122i	−0.855725	−	0.299232i
$277$	3.61042	−	6.25343i	0.216929	−	0.375732i	−0.736938	−	0.675960i	$-0.763729\pi$
$277$	3.61042	−	6.25343i	0.216929	−	0.375732i	0.953868	+	0.300228i	$0.0970626\pi$
$278$	−3.59691	+	9.68081i	−0.215728	+	0.580617i
$279$	4.60202	+	4.93808i	0.275515	+	0.295635i
$280$		0			0
$281$	−23.6911	−	13.6781i	−1.41329	−	0.815964i	−0.417595	−	0.908633i	$-0.637127\pi$
$281$	−23.6911	−	13.6781i	−1.41329	−	0.815964i	−0.995697	+	0.0926691i	$0.970460\pi$
$282$	−12.7529	+	23.1101i	−0.759424	+	1.37619i
$283$	−4.67010	+	2.69628i	−0.277609	+	0.160277i	−0.632340	−	0.774691i	$-0.717906\pi$
$283$	−4.67010	+	2.69628i	−0.277609	+	0.160277i	0.354732	+	0.934968i	$0.384572\pi$
$284$	−2.04140	+	10.7369i	−0.121135	+	0.637120i
$285$		0			0
$286$	−17.7844	+	14.7217i	−1.05161	+	0.870510i
$287$	0.421665			0.0248901
$288$	8.75819	+	14.5360i	0.516081	+	0.856540i
$289$	11.1188			0.654046
$290$		0			0
$291$	20.9458	−	8.24707i	1.22786	−	0.483452i
$292$	4.85395	−	25.5298i	0.284056	−	1.49402i
$293$	15.4734	−	8.93355i	0.903964	−	0.521904i	0.0254795	−	0.999675i	$-0.491889\pi$
$293$	15.4734	−	8.93355i	0.903964	−	0.521904i	0.878484	+	0.477772i	$0.158555\pi$
$294$	9.88032	+	16.3732i	0.576232	+	0.954903i
$295$		0			0
$296$	−5.86095	−	10.6380i	−0.340661	−	0.618320i
$297$	8.29153	+	12.0761i	0.481123	+	0.700727i
$298$	−0.0560615	+	0.150885i	−0.00324755	+	0.00874056i
$299$	12.5880	−	21.8031i	0.727983	−	1.26090i
$300$		0			0
$301$	−0.396333	−	0.686469i	−0.0228443	−	0.0395674i
$302$	2.36506	−	0.400760i	0.136094	−	0.0230612i
$303$	−2.13119	−	5.41276i	−0.122433	−	0.310955i
$304$	5.97804	−	15.1527i	0.342864	−	0.869068i
$305$		0			0
$306$	6.24925	−	8.17366i	0.357246	−	0.467257i
$307$			5.37209i			0.306601i	0.988180	+	0.153301i	$0.0489903\pi$
$307$			5.37209i			0.306601i	−0.988180	+	0.153301i	$0.951010\pi$
$308$	7.14757	+	20.4848i	0.407270	+	1.16723i
$309$	6.57389	+	0.983502i	0.373976	+	0.0559495i
$310$		0			0
$311$	−15.1587	−	26.2557i	−0.859572	−	1.48882i	−0.872338	−	0.488903i	$-0.837397\pi$
$311$	−15.1587	−	26.2557i	−0.859572	−	1.48882i	0.0127664	−	0.999919i	$-0.495936\pi$
$312$	−26.5995	+	9.86246i	−1.50590	+	0.558352i
$313$	12.3588	−	21.4061i	0.698561	−	1.20994i	−0.270404	−	0.962747i	$-0.587157\pi$
$313$	12.3588	−	21.4061i	0.698561	−	1.20994i	0.968965	−	0.247196i	$-0.0795092\pi$
$314$	−29.8197	−	11.0795i	−1.68282	−	0.625252i
$315$		0			0
$316$	6.52148	−	7.56452i	0.366862	−	0.425537i
$317$	−21.1308	−	12.1999i	−1.18683	−	0.685215i	−0.229243	−	0.973369i	$-0.573625\pi$
$317$	−21.1308	−	12.1999i	−1.18683	−	0.685215i	−0.957584	+	0.288155i	$0.906958\pi$
$318$	0.358111	+	18.5044i	0.0200819	+	1.03767i
$319$	17.1200	−	9.88424i	0.958537	−	0.553411i
$320$		0			0
$321$	−0.754530	−	0.600368i	−0.0421137	−	0.0335093i
$322$	−15.0864	−	18.2250i	−0.840733	−	1.01564i
$323$	−9.87589			−0.549509
$324$	4.71937	+	17.3703i	0.262187	+	0.965017i
$325$		0			0
$326$	−1.48233	−	1.79071i	−0.0820985	−	0.0991785i
$327$	−21.0494	−	16.7487i	−1.16403	−	0.926205i
$328$	0.265258	+	0.160315i	0.0146464	+	0.00885191i
$329$	−35.9101	+	20.7327i	−1.97979	+	1.14303i
$330$		0			0
$331$	24.4351	+	14.1076i	1.34308	+	0.775426i	0.987258	−	0.159129i	$-0.0508685\pi$
$331$	24.4351	+	14.1076i	1.34308	+	0.775426i	0.355819	+	0.934555i	$0.384202\pi$
$332$	11.6856	+	10.0743i	0.641328	+	0.552898i
$333$	−2.89408	−	12.5531i	−0.158595	−	0.687908i
$334$	3.23290	+	1.20119i	0.176897	+	0.0657259i
$335$		0			0
$336$	−0.0181210	+	26.6597i	−0.000988584	+	1.45440i
$337$	14.3208	+	24.8043i	0.780101	+	1.35118i	0.931882	+	0.362761i	$0.118166\pi$
$337$	14.3208	+	24.8043i	0.780101	+	1.35118i	−0.151781	+	0.988414i	$0.548501\pi$
$338$	−4.85145	−	28.6304i	−0.263884	−	1.55729i
$339$	−12.9940	−	1.94400i	−0.705738	−	0.105584i
$340$		0			0
$341$			6.34309i			0.343498i
$342$	10.4939	−	13.7254i	0.567446	−	0.742186i
$343$			3.10557i			0.167685i
$344$	0.0116696	−	0.582524i	0.000629180	−	0.0314076i
$345$		0			0
$346$	−14.7221	+	2.49467i	−0.791465	+	0.134114i
$347$	10.4485	+	18.0974i	0.560907	+	0.971520i	0.997418	+	0.0718207i	$0.0228809\pi$
$347$	10.4485	+	18.0974i	0.560907	+	0.971520i	−0.436510	+	0.899699i	$0.643786\pi$
$348$	23.8668	−	4.52096i	1.27939	−	0.242349i
$349$	−6.50620	+	11.2691i	−0.348269	+	0.603219i	−0.985942	−	0.167088i	$-0.946564\pi$
$349$	−6.50620	+	11.2691i	−0.348269	+	0.603219i	0.637673	+	0.770307i	$0.279897\pi$
$350$		0			0
$351$	−29.9982	+	2.34707i	−1.60119	+	0.125277i
$352$	−3.29189	+	15.6039i	−0.175458	+	0.831693i
$353$	−24.6426	−	14.2274i	−1.31159	−	0.757249i	−0.329234	−	0.944248i	$-0.606790\pi$
$353$	−24.6426	−	14.2274i	−1.31159	−	0.757249i	−0.982360	+	0.186999i	$0.940124\pi$
$354$	10.5483	+	17.4801i	0.560636	+	0.929058i
$355$		0			0
$356$	0.264761	+	0.0503387i	0.0140323	+	0.00266795i
$357$	15.0395	−	5.92155i	0.795973	−	0.313402i
$358$	3.27974	−	2.71492i	0.173340	−	0.143488i
$359$	5.90878			0.311854			0.155927	−	0.987769i	$-0.450164\pi$
$359$	5.90878			0.311854			0.155927	+	0.987769i	$0.450164\pi$
$360$		0			0
$361$	2.41614			0.127165
$362$	21.2726	−	17.6092i	1.11806	−	0.925517i
$363$	0.782284	−	5.22892i	0.0410593	−	0.274447i
$364$	−43.7816	−	8.32415i	−2.29478	−	0.436304i
$365$		0			0
$366$	−7.25419	+	13.1457i	−0.379183	+	0.687135i
$367$	20.9815	+	12.1136i	1.09522	+	0.632327i	0.934962	−	0.354747i	$-0.115433\pi$
$367$	20.9815	+	12.1136i	1.09522	+	0.632327i	0.160261	+	0.987075i	$0.448766\pi$
$368$	−2.56140	−	17.2007i	−0.133522	−	0.896648i
$369$	0.224127	+	0.240495i	0.0116676	+	0.0125196i
$370$		0			0
$371$	−14.5373	+	25.1794i	−0.754741	+	1.30725i
$372$	−2.57277	+	7.35743i	−0.133392	+	0.381465i
$373$	3.78990	+	6.56430i	0.196234	+	0.339887i	0.947304	−	0.320335i	$-0.103796\pi$
$373$	3.78990	+	6.56430i	0.196234	+	0.339887i	−0.751071	+	0.660222i	$0.770462\pi$
$374$	9.53270	−	1.61532i	0.492924	−	0.0835264i
$375$		0			0
$376$	−30.4726	−	0.610451i	−1.57151	−	0.0314816i
$377$			40.6066i			2.09135i
$378$	−7.75090	+	27.1938i	−0.398663	+	1.39870i
$379$		−	27.0962i		−	1.39184i	−0.718120	−	0.695919i	$-0.754997\pi$
$379$		−	27.0962i		−	1.39184i	0.718120	−	0.695919i	$-0.245003\pi$
$380$		0			0
$381$	−20.0160	+	25.1556i	−1.02545	+	1.28876i
$382$	0.227806	+	1.34438i	0.0116556	+	0.0687845i
$383$	−13.2134	−	22.8862i	−0.675171	−	1.16943i	−0.976419	−	0.215885i	$-0.930736\pi$
$383$	−13.2134	−	22.8862i	−0.675171	−	1.16943i	0.301247	−	0.953546i	$-0.402597\pi$
$384$	−10.1473	+	16.7640i	−0.517827	+	0.855486i
$385$		0			0
$386$	21.2019	+	7.87758i	1.07915	+	0.400958i
$387$	0.180862	−	0.590926i	0.00919372	−	0.0300384i
$388$	19.6872	+	16.9726i	0.999465	+	0.861653i
$389$	−17.7208	−	10.2311i	−0.898482	−	0.518739i	−0.0217745	−	0.999763i	$-0.506932\pi$
$389$	−17.7208	−	10.2311i	−0.898482	−	0.518739i	−0.876707	+	0.481024i	$0.840265\pi$
$390$		0			0
$391$	−9.13087	+	5.27171i	−0.461768	+	0.266602i
$392$	−11.4217	+	18.8984i	−0.576881	+	0.954511i
$393$	2.43631	−	16.2847i	0.122895	−	0.821454i
$394$	23.5155	+	28.4077i	1.18469	+	1.43116i
$395$		0			0
$396$	−7.88428	+	14.9649i	−0.396200	+	0.752013i
$397$	0.127520			0.00640003			0.00320001	−	0.999995i	$-0.498981\pi$
$397$	0.127520			0.00640003			0.00320001	+	0.999995i	$0.498981\pi$
$398$	−15.0340	−	18.1618i	−0.753588	−	0.910367i
$399$	25.2547	−	9.94362i	1.26432	−	0.497804i
$400$		0			0
$401$	12.8500	−	7.41894i	0.641698	−	0.370484i	−0.143571	−	0.989640i	$-0.545858\pi$
$401$	12.8500	−	7.41894i	0.641698	−	0.370484i	0.785268	+	0.619156i	$0.212525\pi$
$402$	−10.8725	+	6.56095i	−0.542270	+	0.327230i
$403$	−11.2838	−	6.51470i	−0.562086	−	0.324520i
$404$	4.38601	−	5.08751i	0.218212	−	0.253113i
$405$		0			0
$406$	35.7707	+	13.2906i	1.77527	+	0.659602i
$407$	6.05287	−	10.4839i	0.300030	−	0.519667i
$408$	11.7123	+	1.99285i	0.579844	+	0.0986605i
$409$	7.36570	+	12.7578i	0.364210	+	0.630831i	0.988649	−	0.150243i	$-0.0480056\pi$
$409$	7.36570	+	12.7578i	0.364210	+	0.630831i	−0.624439	+	0.781074i	$0.714672\pi$
$410$		0			0
$411$	0.508181	+	1.29067i	0.0250667	+	0.0636641i
$412$	2.52858	+	7.24688i	0.124574	+	0.357028i
$413$			32.0726i			1.57819i
$414$	2.37569	−	18.2916i	0.116759	−	0.898984i
$415$		0			0
$416$	−24.3771	−	21.8821i	−1.19518	−	1.07286i
$417$	−12.5093	−	1.87148i	−0.612581	−	0.0916465i
$418$	16.0076	−	2.71249i	0.782956	−	0.132672i
$419$	5.63765	+	9.76469i	0.275417	+	0.477037i	0.970240	−	0.242144i	$-0.0778507\pi$
$419$	5.63765	+	9.76469i	0.275417	+	0.477037i	−0.694823	+	0.719181i	$0.744517\pi$
$420$		0			0
$421$	0.0177583	−	0.0307583i	0.000865488	−	0.00149907i	−0.865592	−	0.500749i	$-0.833058\pi$
$421$	0.0177583	−	0.0307583i	0.000865488	−	0.00149907i	0.866458	+	0.499250i	$0.166391\pi$
$422$	10.7709	−	28.9890i	0.524317	−	1.41116i
$423$	−30.9121	−	9.46112i	−1.50300	−	0.460016i
$424$	−18.7182	+	10.3127i	−0.909034	+	0.500828i
$425$		0			0
$426$	−13.3831	+	0.259000i	−0.648412	+	0.0125486i
$427$	−20.4266	+	11.7933i	−0.988515	+	0.570719i
$428$	0.207965	−	1.09381i	0.0100524	−	0.0528715i
$429$	−22.1261	−	17.6054i	−1.06826	−	0.849999i
$430$		0			0
$431$	−17.3085			−0.833722			−0.416861	−	0.908970i	$-0.636870\pi$
$431$	−17.3085			−0.833722			−0.416861	+	0.908970i	$0.636870\pi$
$432$	−15.2149	+	14.1601i	−0.732025	+	0.681277i
$433$	−16.3482			−0.785642			−0.392821	−	0.919615i	$-0.628501\pi$
$433$	−16.3482			−0.785642			−0.392821	+	0.919615i	$0.628501\pi$
$434$	−9.43205	+	7.80771i	−0.452753	+	0.374782i
$435$		0			0
$436$	5.80169	−	30.5145i	0.277850	−	1.46138i
$437$	−15.3328	+	8.85240i	−0.733468	+	0.423468i
$438$	31.8216	−	0.615837i	1.52050	−	0.0294258i
$439$	−9.80512	−	5.66099i	−0.467973	−	0.270184i	0.247418	−	0.968909i	$-0.420418\pi$
$439$	−9.80512	−	5.66099i	−0.467973	−	0.270184i	−0.715391	+	0.698725i	$0.753751\pi$
$440$		0			0
$441$	−17.1341	+	15.9680i	−0.815907	+	0.760380i
$442$	−6.91709	+	18.6169i	−0.329013	+	0.885514i
$443$	18.0034	−	31.1828i	0.855368	−	1.48154i	−0.0209350	−	0.999781i	$-0.506664\pi$
$443$	18.0034	−	31.1828i	0.855368	−	1.48154i	0.876303	−	0.481760i	$-0.160002\pi$
$444$	11.2731	−	9.70534i	0.534997	−	0.460595i
$445$		0			0
$446$	−3.44212	+	0.583270i	−0.162989	+	0.0276186i
$447$	−0.194970	−	0.0291689i	−0.00922174	−	0.00137964i
$448$	−27.2547	+	14.3119i	−1.28767	+	0.676175i
$449$			0.577403i			0.0272493i	0.999907	+	0.0136247i	$0.00433700\pi$
$449$			0.577403i			0.0272493i	−0.999907	+	0.0136247i	$0.995663\pi$
$450$		0			0
$451$			0.308921i			0.0145465i
$452$	−4.99803	−	14.3243i	−0.235087	−	0.673757i
$453$	1.07632	+	2.73362i	0.0505699	+	0.128437i
$454$	−2.13238	−	12.5841i	−0.100077	−	0.590599i
$455$		0			0
$456$	19.6676	+	3.34644i	0.921019	+	0.156711i
$457$	−11.6355	+	20.1532i	−0.544283	+	0.942727i	0.454368	+	0.890814i	$0.349865\pi$
$457$	−11.6355	+	20.1532i	−0.544283	+	0.942727i	−0.998652	+	0.0519127i	$0.983468\pi$
$458$	16.0419	+	5.96035i	0.749587	+	0.278509i
$459$	11.3713	+	5.43021i	0.530765	+	0.253461i
$460$		0			0
$461$	6.87023	+	3.96653i	0.319979	+	0.184740i	0.651383	−	0.758749i	$-0.274189\pi$
$461$	6.87023	+	3.96653i	0.319979	+	0.184740i	−0.331404	+	0.943489i	$0.607522\pi$
$462$	−22.7507	+	13.7288i	−1.05846	+	0.638721i
$463$	26.9910	−	15.5833i	1.25438	−	0.724216i	0.282403	−	0.959296i	$-0.408868\pi$
$463$	26.9910	−	15.5833i	1.25438	−	0.724216i	0.971976	+	0.235079i	$0.0755350\pi$
$464$	17.4494	+	21.9606i	0.810068	+	1.01950i
$465$		0			0
$466$	11.6583	+	14.0837i	0.540060	+	0.652416i
$467$	−28.3340			−1.31114			−0.655571	−	0.755133i	$-0.727572\pi$
$467$	−28.3340			−1.31114			−0.655571	+	0.755133i	$0.727572\pi$
$468$	−18.5236	−	29.3952i	−0.856254	−	1.35879i
$469$	−19.9488			−0.921152
$470$		0			0
$471$	5.76468	−	38.5321i	0.265622	−	1.77546i
$472$	−12.1938	+	20.1760i	−0.561267	+	0.928676i
$473$	0.502923	−	0.290363i	0.0231244	−	0.0133509i
$474$	10.7098	+	5.91000i	0.491917	+	0.271455i
$475$		0			0
$476$	14.1358	+	12.1866i	0.647911	+	0.558574i
$477$	−22.0880	+	5.09230i	−1.01134	+	0.233160i
$478$	12.1458	+	4.51277i	0.555536	+	0.206409i
$479$	−12.2322	+	21.1868i	−0.558904	+	0.968049i	0.438685	+	0.898641i	$0.355444\pi$
$479$	−12.2322	+	21.1868i	−0.558904	+	0.968049i	−0.997588	+	0.0694084i	$0.977889\pi$
$480$		0			0
$481$	12.4333	+	21.5350i	0.566908	+	0.981914i
$482$	2.50439	+	14.7795i	0.114072	+	0.673186i
$483$	18.0417	−	22.6744i	0.820924	−	1.03172i
$484$	5.76422	−	2.01125i	0.262010	−	0.0914206i
$485$		0			0
$486$	−19.6297	+	10.0336i	−0.890422	+	0.455136i
$487$		−	4.05853i		−	0.183909i	−0.995763	−	0.0919547i	$-0.970688\pi$
$487$		−	4.05853i		−	0.183909i	0.995763	−	0.0919547i	$-0.0293115\pi$
$488$	−17.3336	−	0.347241i	−0.784657	−	0.0157188i
$489$	1.77270	−	2.22788i	0.0801641	−	0.100748i
$490$		0			0
$491$	8.28040	+	14.3421i	0.373689	+	0.647249i	0.990130	−	0.140153i	$-0.0447593\pi$
$491$	8.28040	+	14.3421i	0.373689	+	0.647249i	−0.616441	+	0.787401i	$0.711426\pi$
$492$	−0.125299	+	0.358322i	−0.00564891	+	0.0161544i
$493$	8.50280	−	14.7273i	0.382947	−	0.663283i
$494$	−11.6154	+	31.2619i	−0.522600	+	1.40654i
$495$		0			0
$496$	−8.90191	+	1.32561i	−0.399708	+	0.0595215i
$497$	−18.2107	−	10.5140i	−0.816862	−	0.471615i
$498$	−9.12968	+	16.5443i	−0.409111	+	0.741368i
$499$	17.4221	−	10.0586i	0.779919	−	0.450287i	−0.0564823	−	0.998404i	$-0.517988\pi$
$499$	17.4221	−	10.0586i	0.779919	−	0.450287i	0.836402	+	0.548117i	$0.184655\pi$
$500$		0			0
$501$	−0.624979	+	4.17746i	−0.0279220	+	0.186635i
$502$	−11.1357	+	9.21793i	−0.497009	+	0.411416i
$503$	21.9942			0.980674			0.490337	−	0.871533i	$-0.336874\pi$
$503$	21.9942			0.980674			0.490337	+	0.871533i	$0.336874\pi$
$504$	−31.9572	+	6.69650i	−1.42349	+	0.298286i
$505$		0			0
$506$	13.3521	−	11.0527i	0.593572	−	0.491350i
$507$	33.0921	−	13.0295i	1.46967	−	0.578660i
$508$	−36.4671	−	6.93345i	−1.61797	−	0.307622i
$509$	19.2701	−	11.1256i	0.854134	−	0.493134i	−0.00790954	−	0.999969i	$-0.502518\pi$
$509$	19.2701	−	11.1256i	0.854134	−	0.493134i	0.862044	+	0.506834i	$0.169184\pi$
$510$		0			0
$511$	43.3005	+	24.9996i	1.91550	+	1.10592i
$512$	−22.5866	−	1.35887i	−0.998195	−	0.0600541i
$513$	19.0949	+	9.11856i	0.843061	+	0.402594i
$514$	3.17546	−	8.54651i	0.140063	−	0.376970i
$515$		0			0
$516$	0.701118	−	0.132809i	0.0308650	−	0.00584660i
$517$	−15.1893	−	26.3086i	−0.668023	−	1.15705i
$518$	23.0398	−	3.90411i	1.01231	−	0.171537i
$519$	−6.69992	−	17.0164i	−0.294094	−	0.746935i
$520$		0			0
$521$		−	18.5073i		−	0.810820i	−0.914135	−	0.405410i	$-0.867129\pi$
$521$		−	18.5073i		−	0.810820i	0.914135	−	0.405410i	$-0.132871\pi$
$522$	11.4330	+	27.4660i	0.500407	+	1.20215i
$523$		−	0.982630i		−	0.0429674i	−0.999769	−	0.0214837i	$-0.993161\pi$
$523$		−	0.982630i		−	0.0429674i	0.999769	−	0.0214837i	$-0.00683900\pi$
$524$	17.9518	−	6.26375i	0.784229	−	0.273633i
$525$		0			0
$526$	−4.28467	−	25.2856i	−0.186821	−	1.10251i
$527$	2.72828	+	4.72552i	0.118846	+	0.205847i
$528$	−19.5315	−	0.0132759i	−0.849999	−	0.000577759i
$529$	2.04924	−	3.54939i	0.0890973	−	0.154321i
$530$		0			0
$531$	−18.2924	+	17.0475i	−0.793824	+	0.739800i
$532$	23.7371	+	20.4641i	1.02914	+	0.887233i
$533$	−0.549543	−	0.317279i	−0.0238034	−	0.0137429i
$534$	0.00638665	+	0.330012i	0.000276377	+	0.0142810i
$535$		0			0
$536$	−12.5493	−	7.58446i	−0.542047	−	0.327599i
$537$	4.08043	+	3.24674i	0.176084	+	0.140107i
$538$	3.07425	+	3.71382i	0.132540	+	0.160114i
$539$	−22.0091			−0.948000
$540$		0			0
$541$	27.5892			1.18615			0.593077	−	0.805146i	$-0.297913\pi$
$541$	27.5892			1.18615			0.593077	+	0.805146i	$0.297913\pi$
$542$	−7.77104	−	9.38776i	−0.333795	−	0.403239i
$543$	26.4659	+	21.0586i	1.13576	+	0.903710i
$544$	4.25913	+	13.0406i	0.182609	+	0.559113i
$545$		0			0
$546$	−1.05611	−	54.5717i	−0.0451975	−	2.33545i
$547$	40.0026	+	23.0955i	1.71039	+	0.987492i	0.934029	+	0.357198i	$0.116268\pi$
$547$	40.0026	+	23.0955i	1.71039	+	0.987492i	0.776357	+	0.630293i	$0.217065\pi$
$548$	−1.04584	+	1.21312i	−0.0446763	+	0.0518218i
$549$	−17.5836	−	5.38174i	−0.750452	−	0.229687i
$550$		0			0
$551$	14.2781	−	24.7305i	0.608269	−	1.05355i
$552$	19.9702	−	7.40449i	0.849989	−	0.315156i
$553$	9.60803	+	16.6416i	0.408575	+	0.707673i
$554$	1.70608	+	10.0683i	0.0724843	+	0.427760i
$555$		0			0
$556$	−4.81156	−	13.7899i	−0.204056	−	0.584821i
$557$		−	44.3389i		−	1.87870i	−0.342960	−	0.939350i	$-0.611429\pi$
$557$		−	44.3389i		−	1.87870i	0.342960	−	0.939350i	$-0.388571\pi$
$558$	−9.46651	−	1.22950i	−0.400749	−	0.0520487i
$559$			1.19287i			0.0504532i
$560$		0			0
$561$	4.33826	+	11.0183i	0.183162	+	0.465191i
$562$	38.1436	−	6.46347i	1.60899	−	0.272645i
$563$	14.1349	+	24.4824i	0.595717	+	1.03181i	0.993445	+	0.114309i	$0.0364653\pi$
$563$	14.1349	+	24.4824i	0.595717	+	1.03181i	−0.397728	+	0.917503i	$0.630201\pi$
$564$	−6.94743	−	36.6765i	−0.292539	−	1.54436i
$565$		0			0
$566$	2.65612	−	7.14875i	0.111645	−	0.300484i
$567$	−34.5461	−	2.43693i	−1.45080	−	0.102341i
$568$	−7.45852	−	13.5377i	−0.312953	−	0.568028i
$569$	22.8891	+	13.2150i	0.959561	+	0.554003i	0.896038	−	0.443978i	$-0.146433\pi$
$569$	22.8891	+	13.2150i	0.959561	+	0.554003i	0.0635229	+	0.997980i	$0.479766\pi$
$570$		0			0
$571$	−14.6651	+	8.46690i	−0.613715	+	0.354329i	−0.774418	−	0.632674i	$-0.781957\pi$
$571$	−14.6651	+	8.46690i	−0.613715	+	0.354329i	0.160703	+	0.987003i	$0.448624\pi$
$572$	6.09846	−	32.0754i	0.254989	−	1.34114i
$573$	−1.55389	+	0.611817i	−0.0649145	+	0.0255590i
$574$	−0.459360	+	0.380251i	−0.0191733	+	0.0158714i
$575$		0			0
$576$	−22.6495	−	7.93740i	−0.943727	−	0.330725i
$577$	−7.68326			−0.319858			−0.159929	−	0.987129i	$-0.551127\pi$
$577$	−7.68326			−0.319858			−0.159929	+	0.987129i	$0.551127\pi$
$578$	−12.1128	+	10.0268i	−0.503824	+	0.417058i
$579$	−4.09872	+	27.3965i	−0.170337	+	1.13856i
$580$		0			0
$581$	−25.7077	+	14.8423i	−1.06654	+	0.615764i
$582$	−15.3812	+	27.8729i	−0.637570	+	1.15537i
$583$	−18.4470	−	10.6504i	−0.763997	−	0.441094i
$584$	17.7345	+	32.1892i	0.733859	+	1.33200i
$585$		0			0
$586$	−8.80047	+	23.6858i	−0.363544	+	0.978452i
$587$	18.1954	−	31.5153i	0.751003	−	1.30078i	−0.196334	−	0.980537i	$-0.562904\pi$
$587$	18.1954	−	31.5153i	0.751003	−	1.30078i	0.947337	−	0.320239i	$-0.103763\pi$
$588$	−25.5287	−	8.92693i	−1.05278	−	0.368141i
$589$	4.58141	+	7.93523i	0.188774	+	0.326965i
$590$		0			0
$591$	−28.1219	+	35.3429i	−1.15678	+	1.45381i
$592$	15.9781	+	6.30366i	0.656695	+	0.259079i
$593$			21.9804i			0.902628i	0.892365	+	0.451314i	$0.149045\pi$
$593$			21.9804i			0.902628i	−0.892365	+	0.451314i	$0.850955\pi$
$594$	−19.9228	−	5.67848i	−0.817443	−	0.232991i
$595$		0			0
$596$	−0.0749932	−	0.214929i	−0.00307184	−	0.00880385i
$597$	17.9790	−	22.5956i	0.735833	−	0.924778i
$598$	5.94837	+	35.1038i	0.243247	+	1.43550i
$599$	−6.71878	−	11.6373i	−0.274522	−	0.475486i	0.695493	−	0.718533i	$-0.255186\pi$
$599$	−6.71878	−	11.6373i	−0.274522	−	0.475486i	−0.970014	+	0.243048i	$0.921853\pi$
$600$		0			0
$601$	18.6923	−	32.3760i	0.762475	−	1.32064i	−0.179097	−	0.983831i	$-0.557317\pi$
$601$	18.6923	−	32.3760i	0.762475	−	1.32064i	0.941571	−	0.336813i	$-0.109349\pi$
$602$	1.05081	+	0.390429i	0.0428279	+	0.0159127i
$603$	−10.6034	−	11.3777i	−0.431804	−	0.463337i
$604$	−2.21508	+	2.56936i	−0.0901304	+	0.104546i
$605$		0			0
$606$	7.20285	+	3.97476i	0.292596	+	0.161464i
$607$	−41.2660	+	23.8250i	−1.67494	+	0.967025i	−0.710128	+	0.704072i	$0.751363\pi$
$607$	−41.2660	+	23.8250i	−1.67494	+	0.967025i	−0.964809	+	0.262953i	$0.915304\pi$
$608$	7.15205	+	21.8982i	0.290054	+	0.888090i
$609$	−6.91512	+	46.2218i	−0.280215	+	1.87300i
$610$		0			0
$611$	62.4008			2.52447
$612$	0.562983	+	14.5398i	0.0227572	+	0.587738i
$613$	−23.4840			−0.948509			−0.474254	−	0.880388i	$-0.657282\pi$
$613$	−23.4840			−0.948509			−0.474254	+	0.880388i	$0.657282\pi$
$614$	−4.84447	−	5.85233i	−0.195507	−	0.236181i
$615$		0			0
$616$	−26.2594	−	15.8705i	−1.05802	−	0.639441i
$617$	−19.8603	+	11.4664i	−0.799547	+	0.461619i	−0.843313	−	0.537423i	$-0.819398\pi$
$617$	−19.8603	+	11.4664i	−0.799547	+	0.461619i	0.0437658	+	0.999042i	$0.486064\pi$
$618$	−8.04848	+	4.85682i	−0.323757	+	0.195370i
$619$	22.6185	+	13.0588i	0.909116	+	0.524878i	0.880147	−	0.474702i	$-0.157444\pi$
$619$	22.6185	+	13.0588i	0.909116	+	0.524878i	0.0289695	+	0.999580i	$0.490777\pi$
$620$		0			0
$621$	22.5219	−	1.76212i	0.903773	−	0.0707114i
$622$	40.1908	+	14.9329i	1.61150	+	0.598754i
$623$	−0.259263	+	0.449056i	−0.0103871	+	0.0179910i
$624$	20.0835	−	34.7312i	0.803985	−	1.39036i
$625$		0			0
$626$	5.84006	+	34.4647i	0.233416	+	1.37749i
$627$	7.28493	+	18.5022i	0.290932	+	0.738905i
$628$	42.4767	−	14.8210i	1.69501	−	0.591422i
$629$		−	10.4138i		−	0.415226i
$630$		0			0
$631$		−	16.5066i		−	0.657117i	−0.944484	−	0.328558i	$-0.893437\pi$
$631$		−	16.5066i		−	0.657117i	0.944484	−	0.328558i	$-0.106563\pi$
$632$	−0.282897	+	14.1217i	−0.0112530	+	0.561732i
$633$	37.4587	+	5.60409i	1.48885	+	0.222743i
$634$	34.0215	−	5.76497i	1.35117	−	0.228956i
$635$		0			0
$636$	−17.0771	−	19.8357i	−0.677152	−	0.786535i
$637$	22.6046	−	39.1523i	0.895626	−	1.55127i
$638$	−9.73700	+	26.2064i	−0.385491	+	1.03752i
$639$	−3.68295	−	15.9749i	−0.145695	−	0.631956i
$640$		0			0
$641$	−9.94563	−	5.74211i	−0.392829	−	0.226800i	0.290556	−	0.956858i	$-0.406160\pi$
$641$	−9.94563	−	5.74211i	−0.392829	−	0.226800i	−0.683385	+	0.730058i	$0.739493\pi$
$642$	1.36339	−	0.0263853i	0.0538085	−	0.00104134i
$643$	−34.0395	+	19.6527i	−1.34239	+	0.775027i	−0.987157	−	0.159752i	$-0.948930\pi$
$643$	−34.0395	+	19.6527i	−1.34239	+	0.775027i	−0.355229	+	0.934779i	$0.615597\pi$
$644$	32.8702	+	6.24956i	1.29527	+	0.246267i
$645$		0			0
$646$	10.7587	−	8.90593i	0.423297	−	0.350399i
$647$	25.1943			0.990489			0.495244	−	0.868754i	$-0.335079\pi$
$647$	25.1943			0.990489			0.495244	+	0.868754i	$0.335079\pi$
$648$	−20.8055	−	14.6673i	−0.817319	−	0.576185i
$649$	−23.4971			−0.922341
$650$		0			0
$651$	−11.7347	−	9.33715i	−0.459920	−	0.365952i
$652$	3.22968	+	0.614055i	0.126484	+	0.0240483i
$653$	11.9400	−	6.89358i	0.467249	−	0.269766i	−0.247838	−	0.968801i	$-0.579720\pi$
$653$	11.9400	−	6.89358i	0.467249	−	0.269766i	0.715087	+	0.699035i	$0.246387\pi$
$654$	38.0348	−	0.736080i	1.48728	−	0.0287830i
$655$		0			0
$656$	−0.433541	+	0.0645596i	−0.0169269	+	0.00252063i
$657$	8.75713	+	37.9843i	0.341648	+	1.48191i
$658$	20.4239	−	54.9694i	0.796205	−	2.14293i
$659$	−2.25898	+	3.91266i	−0.0879972	+	0.152416i	−0.906664	−	0.421853i	$-0.861380\pi$
$659$	−2.25898	+	3.91266i	−0.0879972	+	0.152416i	0.818667	+	0.574268i	$0.194713\pi$
$660$		0			0
$661$	8.35512	+	14.4715i	0.324977	+	0.562876i	0.981508	−	0.191423i	$-0.0613102\pi$
$661$	8.35512	+	14.4715i	0.324977	+	0.562876i	−0.656531	+	0.754299i	$0.727977\pi$
$662$	−39.3416	+	6.66646i	−1.52905	+	0.259099i
$663$	−24.0561	−	3.59897i	−0.934263	−	0.139773i
$664$	−21.8150	−	0.437015i	−0.846588	−	0.0169595i
$665$		0			0
$666$	14.4730	+	11.0655i	0.560819	+	0.428779i
$667$		−	30.4865i		−	1.18044i
$668$	−4.60512	+	1.60682i	−0.178178	+	0.0621697i
$669$	−1.56648	−	3.97853i	−0.0605637	−	0.153819i
$670$		0			0
$671$	−8.64006	−	14.9650i	−0.333546	−	0.577718i
$672$	−24.0216	−	29.0593i	−0.926652	−	1.12099i
$673$	−5.13420	+	8.89270i	−0.197909	+	0.342789i	−0.947850	−	0.318716i	$-0.896748\pi$
$673$	−5.13420	+	8.89270i	−0.197909	+	0.342789i	0.749941	+	0.661504i	$0.230082\pi$
$674$	−37.9691	−	14.1074i	−1.46252	−	0.543398i
$675$		0			0
$676$	31.1036	+	26.8149i	1.19629	+	1.03134i
$677$	36.6920	+	21.1841i	1.41019	+	0.814172i	0.995406	−	0.0957490i	$-0.0305246\pi$
$677$	36.6920	+	21.1841i	1.41019	+	0.814172i	0.414782	+	0.909921i	$0.363858\pi$
$678$	15.9087	−	9.60003i	0.610970	−	0.368687i
$679$	−43.3109	+	25.0056i	−1.66212	+	0.959626i
$680$		0			0
$681$	14.5451	−	5.72691i	0.557371	−	0.219456i
$682$	−5.72011	−	6.91013i	−0.219034	−	0.264603i
$683$	−7.70020			−0.294640			−0.147320	−	0.989089i	$-0.547065\pi$
$683$	−7.70020			−0.294640			−0.147320	+	0.989089i	$0.547065\pi$
$684$	0.945376	+	24.4157i	0.0361474	+	0.933557i
$685$		0			0
$686$	−2.80056	−	3.38320i	−0.106926	−	0.129171i
$687$	−3.10118	+	20.7288i	−0.118317	+	0.790853i
$688$	0.512599	+	0.645122i	0.0195426	+	0.0245951i
$689$	37.8922	−	21.8771i	1.44358	−	0.833450i
$690$		0			0
$691$	−35.8315	−	20.6873i	−1.36309	−	0.786983i	−0.373060	−	0.927807i	$-0.621691\pi$
$691$	−35.8315	−	20.6873i	−1.36309	−	0.786983i	−0.990035	+	0.140824i	$0.955025\pi$
$692$	13.7885	−	15.9939i	0.524161	−	0.607995i
$693$	−22.1877	−	23.8079i	−0.842839	−	0.904389i
$694$	−27.7026	−	10.2929i	−1.05158	−	0.390713i
$695$		0			0
$696$	−21.9234	+	26.4478i	−0.831006	+	1.00250i
$697$	0.132873	+	0.230142i	0.00503292	+	0.00871726i
$698$	−3.07446	−	18.1437i	−0.116370	−	0.686748i
$699$	−13.9420	+	17.5220i	−0.527336	+	0.662744i
$700$		0			0
$701$		−	12.5415i		−	0.473685i	−0.971548	−	0.236842i	$-0.923887\pi$
$701$		−	12.5415i		−	0.473685i	0.971548	−	0.236842i	$-0.0761125\pi$
$702$	30.5634	−	29.6088i	1.15354	−	1.11751i
$703$		−	17.4872i		−	0.659541i
$704$	−10.4852	−	19.9674i	−0.395177	−	0.752551i
$705$		0			0
$706$	39.6756	−	6.72306i	1.49321	−	0.253026i
$707$	6.46187	+	11.1923i	0.243024	+	0.420929i
$708$	−27.2546	−	9.53046i	−1.02429	−	0.358177i
$709$	−0.973370	+	1.68593i	−0.0365557	+	0.0633163i	−0.883724	−	0.468008i	$-0.844972\pi$
$709$	−0.973370	+	1.68593i	−0.0365557	+	0.0633163i	0.847169	+	0.531324i	$0.178305\pi$
$710$		0			0
$711$	−4.38451	+	14.3254i	−0.164432	+	0.537245i
$712$	−0.333824	+	0.183919i	−0.0125106	+	0.00689265i
$713$	8.47159	+	4.89108i	0.317264	+	0.183172i
$714$	−11.0440	+	20.0133i	−0.413310	+	0.748978i
$715$		0			0
$716$	−1.12466	+	5.91525i	−0.0420305	+	0.221063i
$717$	−2.34800	+	15.6944i	−0.0876877	+	0.586119i
$718$	−6.43700	+	5.32846i	−0.240227	+	0.198856i
$719$	25.7606			0.960708			0.480354	−	0.877075i	$-0.340508\pi$
$719$	25.7606			0.960708			0.480354	+	0.877075i	$0.340508\pi$
$720$		0			0
$721$	−14.7674			−0.549965
$722$	−2.63213	+	2.17884i	−0.0979578	+	0.0810880i
$723$	−17.0827	+	6.72603i	−0.635311	+	0.250144i
$724$	−7.29461	+	38.3667i	−0.271102	+	1.42589i
$725$		0			0
$726$	3.86315	+	6.40181i	0.143375	+	0.237594i
$727$	7.10360	+	4.10126i	0.263458	+	0.152107i	0.625911	−	0.779895i	$-0.284727\pi$
$727$	7.10360	+	4.10126i	0.263458	+	0.152107i	−0.362453	+	0.932002i	$0.618061\pi$
$728$	55.2021	−	30.4133i	2.04593	−	1.12719i
$729$	−16.9724	−	20.9985i	−0.628607	−	0.777723i
$730$		0			0
$731$	0.249781	−	0.432633i	0.00923848	−	0.0160015i
$732$	−3.95188	−	20.8626i	−0.146066	−	0.771102i
$733$	10.5724	+	18.3119i	0.390499	+	0.676364i	0.992515	−	0.122120i	$-0.0389692\pi$
$733$	10.5724	+	18.3119i	0.390499	+	0.676364i	−0.602017	+	0.798484i	$0.705636\pi$
$734$	−33.7810	+	5.72422i	−1.24688	+	0.211285i
$735$		0			0
$736$	18.3017	+	16.4285i	0.674610	+	0.605563i
$737$		−	14.6150i		−	0.538350i
$738$	−0.461038	−	0.0598789i	−0.0169710	−	0.00220417i
$739$			0.668371i			0.0245864i	0.999924	+	0.0122932i	$0.00391315\pi$
$739$			0.668371i			0.0245864i	−0.999924	+	0.0122932i	$0.996087\pi$
$740$		0			0
$741$	−40.3957	−	6.04349i	−1.48397	−	0.222013i
$742$	−6.86951	−	40.5399i	−0.252188	−	1.48827i
$743$	16.9416	+	29.3436i	0.621526	+	1.07651i	0.989202	+	0.146560i	$0.0468201\pi$
$743$	16.9416	+	29.3436i	0.621526	+	1.07651i	−0.367676	+	0.929954i	$0.619847\pi$
$744$	−3.83207	−	10.3352i	−0.140490	−	0.378908i
$745$		0			0
$746$	−10.0483	−	3.73344i	−0.367894	−	0.136691i
$747$	−22.1297	−	6.77312i	−0.809683	−	0.247816i
$748$	−8.92821	+	10.3562i	−0.326448	+	0.378659i
$749$	1.85519	+	1.07110i	0.0677873	+	0.0391370i
$750$		0			0
$751$	9.22222	−	5.32445i	0.336524	−	0.194292i	−0.322210	−	0.946668i	$-0.604426\pi$
$751$	9.22222	−	5.32445i	0.336524	−	0.194292i	0.658734	+	0.752376i	$0.271092\pi$
$752$	33.7472	−	26.8147i	1.23064	−	0.977833i
$753$	−13.8542	−	11.0236i	−0.504876	−	0.401723i
$754$	−36.6185	−	44.2367i	−1.33357	−	1.61101i
$755$		0			0
$756$	−16.0792	−	36.6145i	−0.584796	−	1.33166i
$757$	11.8276			0.429880			0.214940	−	0.976627i	$-0.431044\pi$
$757$	11.8276			0.429880			0.214940	+	0.976627i	$0.431044\pi$
$758$	24.4350	+	29.5185i	0.887518	+	1.07216i
$759$	16.6118	+	13.2177i	0.602968	+	0.479773i
$760$		0			0
$761$	0.0449006	−	0.0259234i	0.00162765	−	0.000939722i	−0.499186	−	0.866495i	$-0.666368\pi$
$761$	0.0449006	−	0.0259234i	0.00162765	−	0.000939722i	0.500814	+	0.865555i	$0.333034\pi$
$762$	−0.879671	−	45.4545i	−0.0318671	−	1.64664i
$763$	51.7550	+	29.8808i	1.87366	+	1.08176i
$764$	−1.46051	−	1.25913i	−0.0528395	−	0.0455537i
$765$		0			0
$766$	35.0330	+	13.0165i	1.26580	+	0.470306i
$767$	24.1328	−	41.7992i	0.871385	−	1.50928i
$768$	−4.06314	−	27.4133i	−0.146616	−	0.989193i
$769$	13.0480	+	22.5999i	0.470524	+	0.814972i	0.999432	−	0.0337073i	$-0.0107314\pi$
$769$	13.0480	+	22.5999i	0.470524	+	0.814972i	−0.528907	+	0.848680i	$0.677398\pi$
$770$		0			0
$771$	11.0435	+	1.65219i	0.397723	+	0.0595023i
$772$	−30.2012	+	10.5378i	−1.08696	+	0.379264i
$773$		−	11.4187i		−	0.410702i	−0.978688	−	0.205351i	$-0.934166\pi$
$773$		−	11.4187i		−	0.410702i	0.978688	−	0.205351i	$-0.0658336\pi$
$774$	0.335858	+	0.806850i	0.0120722	+	0.0290016i
$775$		0			0
$776$	−36.7528	−	0.736259i	−1.31935	−	0.0264302i
$777$	10.4852	+	26.6303i	0.376156	+	0.955356i
$778$	28.5313	−	4.83464i	1.02290	−	0.173330i
$779$	0.223124	+	0.386461i	0.00799423	+	0.0138464i
$780$		0			0
$781$	7.70276	−	13.3416i	0.275626	−	0.477399i
$782$	5.19318	−	13.9771i	0.185708	−	0.499819i
$783$	−30.0380	+	20.6243i	−1.07347	+	0.737051i
$784$	−4.59956	−	30.8877i	−0.164270	−	1.10313i
$785$		0			0
$786$	12.0312	+	19.9375i	0.429138	+	0.711147i
$787$	−26.6858	+	15.4071i	−0.951246	+	0.549202i	−0.893468	−	0.449127i	$-0.851735\pi$
$787$	−26.6858	+	15.4071i	−0.951246	+	0.549202i	−0.0577782	+	0.998329i	$0.518402\pi$
$788$	−51.2353	−	9.74131i	−1.82518	−	0.347020i
$789$	29.2261	−	11.5073i	1.04048	−	0.409671i
$790$		0			0
$791$	29.1893			1.03785
$792$	−4.90601	−	23.4126i	−0.174327	−	0.831931i
$793$	35.4953			1.26047
$794$	−0.138919	+	0.114995i	−0.00493006	+	0.00408103i
$795$		0			0
$796$	32.7560	+	6.22787i	1.16101	+	0.220741i
$797$	43.2814	−	24.9885i	1.53311	−	0.885139i	0.533890	−	0.845554i	$-0.320730\pi$
$797$	43.2814	−	24.9885i	1.53311	−	0.885139i	0.999216	−	0.0395849i	$-0.0126036\pi$
$798$	−18.5453	+	33.6069i	−0.656497	+	1.18967i
$799$	−22.6316	−	13.0664i	−0.800650	−	0.462255i
$800$		0			0
$801$	−0.393923	+	0.0908174i	−0.0139186	+	0.00320887i
$802$	−7.30842	+	19.6701i	−0.258069	+	0.694575i
$803$	−18.3153	+	31.7229i	−0.646331	+	1.11948i
$804$	5.92786	−	16.9521i	0.209060	−	0.597855i
$805$		0			0
$806$	18.1674	−	3.07848i	0.639919	−	0.108435i
$807$	−3.67645	+	4.62049i	−0.129417	+	0.162649i
$808$	−0.190262	+	9.49756i	−0.00669340	+	0.334123i
$809$			31.1937i			1.09671i	0.836245	+	0.548356i	$0.184746\pi$
$809$			31.1937i			1.09671i	−0.836245	+	0.548356i	$0.815254\pi$
$810$		0			0
$811$		−	47.9220i		−	1.68277i	−0.540436	−	0.841385i	$-0.681741\pi$
$811$		−	47.9220i		−	1.68277i	0.540436	−	0.841385i	$-0.318259\pi$
$812$	−50.9537	+	17.7788i	−1.78813	+	0.623913i
$813$	9.29330	−	11.6796i	0.325930	−	0.409622i
$814$	2.86024	+	16.8795i	0.100251	+	0.591626i
$815$		0			0
$816$	−14.5564	+	8.39097i	−0.509577	+	0.293743i
$817$	0.419439	−	0.726489i	0.0146743	−	0.0254166i
$818$	−19.5289	−	7.25597i	−0.682813	−	0.253699i
$819$	65.1402	−	15.0178i	2.27618	−	0.524765i
$820$		0			0
$821$	−31.0074	−	17.9021i	−1.08216	−	0.624788i	−0.150685	−	0.988582i	$-0.548148\pi$
$821$	−31.0074	−	17.9021i	−1.08216	−	0.624788i	−0.931480	+	0.363794i	$0.881481\pi$
$822$	−1.71752	−	0.947782i	−0.0599054	−	0.0330577i
$823$	21.7026	−	12.5300i	0.756504	−	0.436768i	−0.0715352	−	0.997438i	$-0.522790\pi$
$823$	21.7026	−	12.5300i	0.756504	−	0.436768i	0.828039	+	0.560670i	$0.189457\pi$
$824$	−9.28976	−	5.61448i	−0.323624	−	0.195590i
$825$		0			0
$826$	−28.9226	−	34.9397i	−1.00635	−	1.21571i
$827$	−0.111136			−0.00386458			−0.00193229	−	0.999998i	$-0.500615\pi$
$827$	−0.111136			−0.00386458			−0.00193229	+	0.999998i	$0.500615\pi$
$828$	13.9071	+	22.0692i	0.483304	+	0.766957i
$829$	35.8024			1.24347			0.621735	−	0.783228i	$-0.286428\pi$
$829$	35.8024			1.24347			0.621735	+	0.783228i	$0.286428\pi$
$830$		0			0
$831$	−11.6373	+	4.58200i	−0.403694	+	0.158948i
$832$	46.2892	+	1.85535i	1.60479	+	0.0643226i
$833$	−16.3965	+	9.46654i	−0.568106	+	0.327996i
$834$	15.3152	−	9.24188i	0.530322	−	0.320020i
$835$		0			0
$836$	−14.9925	+	17.3904i	−0.518526	+	0.601459i
$837$	−0.911954	−	11.6558i	−0.0315217	−	0.402884i
$838$	−14.9473	−	5.55366i	−0.516346	−	0.191848i
$839$	1.71872	−	2.97691i	0.0593367	−	0.102774i	−0.834831	−	0.550506i	$-0.814435\pi$
$839$	1.71872	−	2.97691i	0.0593367	−	0.102774i	0.894168	+	0.447732i	$0.147768\pi$
$840$		0			0
$841$	10.0860	+	17.4694i	0.347792	+	0.602393i
$842$	0.00839157	+	0.0495222i	0.000289193	+	0.00170665i
$843$	17.3589	+	44.0879i	0.597872	+	1.51847i
$844$	14.4081	+	41.2935i	0.495948	+	1.42138i
$845$		0			0
$846$	42.2074	−	17.5692i	1.45112	−	0.604042i
$847$			11.7461i			0.403600i
$848$	11.0917	−	28.1144i	0.380889	−	0.965451i
$849$	9.23740	+	1.38198i	0.317027	+	0.0474295i
$850$		0			0
$851$	−9.33459	−	16.1680i	−0.319985	−	0.554231i
$852$	14.3459	−	12.3508i	0.491482	−	0.423132i
$853$	6.56957	−	11.3788i	0.224938	−	0.389604i	−0.731363	−	0.681988i	$-0.761115\pi$
$853$	6.56957	−	11.3788i	0.224938	−	0.389604i	0.956301	+	0.292385i	$0.0944488\pi$
$854$	11.6176	−	31.2681i	0.397548	−	1.06997i
$855$		0			0
$856$	0.759828	+	1.37914i	0.0259704	+	0.0471379i
$857$	18.1576	+	10.4833i	0.620253	+	0.358103i	0.776967	−	0.629541i	$-0.216757\pi$
$857$	18.1576	+	10.4833i	0.620253	+	0.358103i	−0.156715	+	0.987644i	$0.550090\pi$
$858$	39.9804	−	0.773733i	1.36491	−	0.0264148i
$859$	22.1231	−	12.7728i	0.754829	−	0.435801i	−0.0726072	−	0.997361i	$-0.523132\pi$
$859$	22.1231	−	12.7728i	0.754829	−	0.435801i	0.827436	+	0.561560i	$0.189799\pi$
$860$		0			0
$861$	−0.571504	−	0.454737i	−0.0194768	−	0.0154974i
$862$	18.8558	−	15.6086i	0.642232	−	0.531630i
$863$	−12.4343			−0.423267			−0.211633	−	0.977349i	$-0.567878\pi$
$863$	−12.4343			−0.423267			−0.211633	+	0.977349i	$0.567878\pi$
$864$	3.80565	−	29.1465i	0.129471	−	0.991583i
$865$		0			0
$866$	17.8096	−	14.7425i	0.605195	−	0.500972i
$867$	−15.0699	−	11.9909i	−0.511800	−	0.407232i
$868$	3.23435	−	17.0114i	0.109781	−	0.577404i
$869$	−12.1920	+	7.03906i	−0.413586	+	0.238784i
$870$		0			0
$871$	25.9988	+	15.0104i	0.880934	+	0.508608i
$872$	21.1972	+	38.4742i	0.717828	+	1.30290i
$873$	−37.2829	−	11.4110i	−1.26183	−	0.386203i
$874$	8.72053	−	23.4707i	0.294976	−	0.793908i
$875$		0			0
$876$	−34.1110	+	29.3672i	−1.15250	+	0.992225i
$877$	−3.42115	−	5.92561i	−0.115524	−	0.200094i	0.802465	−	0.596699i	$-0.203521\pi$
$877$	−3.42115	−	5.92561i	−0.115524	−	0.200094i	−0.917989	+	0.396605i	$0.870188\pi$
$878$	15.7867	−	2.67506i	0.532774	−	0.0902789i
$879$	−30.6061	−	4.57890i	−1.03232	−	0.154442i
$880$		0			0
$881$		−	11.7126i		−	0.394606i	−0.980343	−	0.197303i	$-0.936782\pi$
$881$		−	11.7126i		−	0.394606i	0.980343	−	0.197303i	$-0.0632183\pi$
$882$	4.26608	−	32.8467i	0.143646	−	1.10601i
$883$		−	15.1968i		−	0.511413i	−0.966754	−	0.255707i	$-0.917692\pi$
$883$		−	15.1968i		−	0.511413i	0.966754	−	0.255707i	$-0.0823082\pi$
$884$	−9.25296	−	26.5189i	−0.311211	−	0.891926i
$885$		0			0
$886$	8.50738	+	50.2057i	0.285811	+	1.68669i
$887$	−16.8814	−	29.2394i	−0.566820	−	0.981762i	−0.996878	−	0.0789600i	$-0.974840\pi$
$887$	−16.8814	−	29.2394i	−0.566820	−	0.981762i	0.430057	−	0.902802i	$-0.358493\pi$
$888$	−3.52872	+	20.7389i	−0.118416	+	0.695951i
$889$	35.7098	−	61.8511i	1.19767	−	2.07442i
$890$		0			0
$891$	1.78535	−	25.3093i	0.0598115	−	0.847892i
$892$	3.22385	−	3.73947i	0.107942	−	0.125207i
$893$	−38.0037	−	21.9414i	−1.27174	−	0.734242i
$894$	0.238703	−	0.144044i	0.00798342	−	0.00481756i
$895$		0			0
$896$	16.7849	−	40.1693i	0.560744	−	1.34196i
$897$	−40.5744	+	15.9755i	−1.35474	+	0.533406i
$898$	−0.520693	−	0.629020i	−0.0173758	−	0.0209907i
$899$	−15.7777			−0.526217
$900$		0			0
$901$	−18.3237			−0.610452
$902$	−0.278581	−	0.336537i	−0.00927572	−	0.0112055i
$903$	−0.203141	+	1.35783i	−0.00676010	+	0.0451856i
$904$	18.3622	+	11.0976i	0.610719	+	0.369102i
$905$		0			0
$906$	−3.63768	−	2.00739i	−0.120854	−	0.0666909i
$907$	−29.6927	−	17.1431i	−0.985931	−	0.569228i	−0.0818757	−	0.996643i	$-0.526091\pi$
$907$	−29.6927	−	17.1431i	−0.985931	−	0.569228i	−0.904056	+	0.427415i	$0.859424\pi$
$908$	13.6711	+	11.7861i	0.453692	+	0.391135i
$909$	−2.94880	+	9.63454i	−0.0978054	+	0.319557i
$910$		0			0
$911$	3.24141	−	5.61428i	0.107393	−	0.186010i	−0.807321	−	0.590113i	$-0.799083\pi$
$911$	3.24141	−	5.61428i	0.107393	−	0.186010i	0.914713	+	0.404104i	$0.132416\pi$
$912$	−24.4436	+	14.0903i	−0.809407	+	0.466578i
$913$	−10.8738	−	18.8340i	−0.359872	−	0.623316i
$914$	−5.49825	−	32.4475i	−0.181866	−	1.07327i
$915$		0			0
$916$	−22.8509	+	7.97313i	−0.755015	+	0.263440i
$917$			36.5814i			1.20802i
$918$	−17.2847	+	4.33878i	−0.570480	+	0.143201i
$919$			18.1763i			0.599580i	0.954005	+	0.299790i	$0.0969166\pi$
$919$			18.1763i			0.599580i	−0.954005	+	0.299790i	$0.903083\pi$
$920$		0			0
$921$	5.79345	−	7.28107i	0.190901	−	0.239920i
$922$	−11.0614	+	1.87436i	−0.364287	+	0.0617286i
$923$	15.8223	+	27.4051i	0.520798	+	0.902048i
$924$	12.4041	−	35.4723i	0.408064	−	1.16695i
$925$		0			0
$926$	−15.3511	+	41.3165i	−0.504470	+	1.35774i
$927$	−7.84929	−	8.42250i	−0.257805	−	0.276631i
$928$	−38.8131	−	8.18821i	−1.27410	−	0.268791i
$929$	20.6179	+	11.9038i	0.676452	+	0.390550i	0.798517	−	0.601972i	$-0.205618\pi$
$929$	20.6179	+	11.9038i	0.676452	+	0.390550i	−0.122065	+	0.992522i	$0.538952\pi$
$930$		0			0
$931$	−27.5335	+	15.8965i	−0.902373	+	0.520986i
$932$	−25.4010	−	4.82946i	−0.832038	−	0.158194i
$933$	−7.76961	+	51.9333i	−0.254365	+	1.70022i
$934$	30.8670	−	25.5512i	1.01000	−	0.836062i
$935$		0			0
$936$	46.6877	+	15.3187i	1.52603	+	0.500707i
$937$	−16.4490			−0.537366			−0.268683	−	0.963229i	$-0.586588\pi$
$937$	−16.4490			−0.537366			−0.268683	+	0.963229i	$0.586588\pi$
$938$	21.7322	−	17.9896i	0.709581	−	0.587381i
$939$	−39.8356	+	15.6846i	−1.29999	+	0.511848i
$940$		0			0
$941$	6.86226	−	3.96193i	0.223703	−	0.129155i	−0.383961	−	0.923349i	$-0.625440\pi$
$941$	6.86226	−	3.96193i	0.223703	−	0.129155i	0.607664	+	0.794194i	$0.292107\pi$
$942$	28.4676	+	47.1752i	0.927526	+	1.53705i
$943$	0.412583	+	0.238205i	0.0134356	+	0.00775703i
$944$	−4.91052	−	32.9759i	−0.159824	−	1.07327i
$945$		0			0
$946$	−0.286037	+	0.769848i	−0.00929987	+	0.0250299i
$947$	−25.1402	+	43.5441i	−0.816947	+	1.41499i	0.0909742	+	0.995853i	$0.471002\pi$
$947$	−25.1402	+	43.5441i	−0.816947	+	1.41499i	−0.907921	+	0.419141i	$0.862331\pi$
$948$	−16.9967	+	3.21960i	−0.552028	+	0.104568i
$949$	−37.6215	−	65.1624i	−1.22125	−	2.11526i
$950$		0			0
$951$	15.4829	+	39.3234i	0.502069	+	1.27515i
$952$	−26.3892	−	0.528648i	−0.855278	−	0.0171336i
$953$		−	32.4601i		−	1.05149i	−0.850644	−	0.525743i	$-0.823787\pi$
$953$		−	32.4601i		−	1.05149i	0.850644	−	0.525743i	$-0.176213\pi$
$954$	19.4704	−	25.4662i	0.630377	−	0.824497i
$955$		0			0
$956$	−17.3011	+	6.03671i	−0.559558	+	0.195241i
$957$	−33.8632	−	5.06618i	−1.09464	−	0.163766i
$958$	−5.78024	−	34.1116i	−0.186751	−	1.10210i
$959$	−1.54083	−	2.66880i	−0.0497561	−	0.0861801i
$960$		0			0
$961$	−12.9687	+	22.4625i	−0.418345	+	0.724596i
$962$	−32.9647	−	12.2480i	−1.06283	−	0.394893i
$963$	0.375196	+	1.62742i	0.0120905	+	0.0524429i
$964$	−16.0562	−	13.8423i	−0.517135	−	0.445829i
$965$		0			0
$966$	0.792904	+	40.9711i	0.0255113	+	1.31822i
$967$	22.0669	−	12.7403i	0.709623	−	0.409701i	−0.101299	−	0.994856i	$-0.532300\pi$
$967$	22.0669	−	12.7403i	0.709623	−	0.409701i	0.810921	+	0.585155i	$0.198966\pi$
$968$	−4.46580	+	7.38914i	−0.143536	+	0.237496i
$969$	13.3853	+	10.6505i	0.429998	+	0.342143i
$970$		0			0
$971$	−40.6423			−1.30427			−0.652137	−	0.758101i	$-0.726127\pi$
$971$	−40.6423			−1.30427			−0.652137	+	0.758101i	$0.726127\pi$
$972$	12.3363	−	28.6324i	0.395688	−	0.918385i
$973$	28.1004			0.900856
$974$	3.65992	+	4.42134i	0.117271	+	0.141669i
$975$		0			0
$976$	19.1963	−	15.2529i	0.614460	−	0.488235i
$977$	49.0482	−	28.3180i	1.56919	−	0.905973i	0.572929	−	0.819605i	$-0.305807\pi$
$977$	49.0482	−	28.3180i	1.56919	−	0.905973i	0.996263	−	0.0863680i	$-0.0275261\pi$
$978$	0.0779073	+	4.02564i	0.00249120	+	0.128726i
$979$	−0.328989	−	0.189942i	−0.0105145	−	0.00607056i
$980$		0			0
$981$	10.4670	+	45.4008i	0.334185	+	1.44953i
$982$	−21.9541	−	8.15705i	−0.700584	−	0.260302i
$983$	−5.25634	+	9.10425i	−0.167651	+	0.290380i	−0.937594	−	0.347733i	$-0.886952\pi$
$983$	−5.25634	+	9.10425i	−0.167651	+	0.290380i	0.769942	+	0.638113i	$0.220285\pi$
$984$	−0.186629	−	0.503347i	−0.00594952	−	0.0160461i
$985$		0			0
$986$	4.01794	+	23.7115i	0.127957	+	0.755129i
$987$	71.0298	+	10.6266i	2.26090	+	0.338248i
$988$	−15.5378	−	44.5312i	−0.494324	−	1.41673i
$989$		−	0.895580i		−	0.0284778i
$990$		0			0
$991$			31.2300i			0.992053i	0.868307	+	0.496027i	$0.165208\pi$
$991$			31.2300i			0.992053i	−0.868307	+	0.496027i	$0.834792\pi$
$992$	8.50229	−	9.47173i	0.269948	−	0.300728i
$993$	−17.9041	−	45.4725i	−0.568168	−	1.44303i
$994$	29.3200	−	4.96829i	0.929974	−	0.157585i
$995$		0			0
$996$	−4.97359	−	26.2563i	−0.157594	−	0.831963i
$997$	26.9178	−	46.6230i	0.852495	−	1.47657i	−0.0264537	−	0.999650i	$-0.508421\pi$
$997$	26.9178	−	46.6230i	0.852495	−	1.47657i	0.878949	−	0.476915i	$-0.158245\pi$
$998$	−9.90880	+	26.6688i	−0.313658	+	0.844187i
$999$	−9.61524	+	20.1350i	−0.304213	+	0.637043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.f.551.6		48
4.3	odd	2	inner	900.2.r.f.551.14		48
5.2	odd	4		900.2.o.c.299.7		48
5.3	odd	4		900.2.o.b.299.18		48
5.4	even	2		180.2.q.a.11.19	yes	48
9.5	odd	6	inner	900.2.r.f.851.14		48
15.14	odd	2		540.2.q.a.251.6		48
20.3	even	4		900.2.o.b.299.1		48
20.7	even	4		900.2.o.c.299.24		48
20.19	odd	2		180.2.q.a.11.11	✓	48
36.23	even	6	inner	900.2.r.f.851.6		48
45.4	even	6		540.2.q.a.71.14		48
45.14	odd	6		180.2.q.a.131.11	yes	48
45.23	even	12		900.2.o.c.599.24		48
45.29	odd	6		1620.2.e.b.971.44		48
45.32	even	12		900.2.o.b.599.1		48
45.34	even	6		1620.2.e.b.971.5		48
60.59	even	2		540.2.q.a.251.14		48
180.23	odd	12		900.2.o.c.599.7		48
180.59	even	6		180.2.q.a.131.19	yes	48
180.79	odd	6		1620.2.e.b.971.43		48
180.119	even	6		1620.2.e.b.971.6		48
180.139	odd	6		540.2.q.a.71.6		48
180.167	odd	12		900.2.o.b.599.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.11	✓	48	20.19	odd	2
180.2.q.a.11.19	yes	48	5.4	even	2
180.2.q.a.131.11	yes	48	45.14	odd	6
180.2.q.a.131.19	yes	48	180.59	even	6
540.2.q.a.71.6		48	180.139	odd	6
540.2.q.a.71.14		48	45.4	even	6
540.2.q.a.251.6		48	15.14	odd	2
540.2.q.a.251.14		48	60.59	even	2
900.2.o.b.299.1		48	20.3	even	4
900.2.o.b.299.18		48	5.3	odd	4
900.2.o.b.599.1		48	45.32	even	12
900.2.o.b.599.18		48	180.167	odd	12
900.2.o.c.299.7		48	5.2	odd	4
900.2.o.c.299.24		48	20.7	even	4
900.2.o.c.599.7		48	180.23	odd	12
900.2.o.c.599.24		48	45.23	even	12
900.2.r.f.551.6		48	1.1	even	1	trivial
900.2.r.f.551.14		48	4.3	odd	2	inner
900.2.r.f.851.6		48	36.23	even	6	inner
900.2.r.f.851.14		48	9.5	odd	6	inner
1620.2.e.b.971.5		48	45.34	even	6
1620.2.e.b.971.6		48	180.119	even	6
1620.2.e.b.971.43		48	180.79	odd	6
1620.2.e.b.971.44		48	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08940 + 0.901786i) q^{2} +(-1.35535 - 1.07843i) q^{3} +(0.373566 - 1.96480i) q^{4} +(2.44903 - 0.0473955i) q^{6} +(3.33246 + 1.92400i) q^{7} +(1.36487 + 2.47732i) q^{8} +(0.673959 + 2.92332i) q^{9} +(-1.40956 + 2.44144i) q^{11} +(-2.62522 + 2.26013i) q^{12} +(-2.89540 - 5.01498i) q^{13} +(-5.36540 + 0.909171i) q^{14} +(-3.72090 - 1.46797i) q^{16} +2.42512i q^{17} +(-3.37041 - 2.57688i) q^{18} +4.07233i q^{19} +(-2.44175 - 6.20153i) q^{21} +(-0.666079 - 3.93081i) q^{22} +(2.17379 + 3.76512i) q^{23} +(0.821751 - 4.82957i) q^{24} +(7.67667 + 2.85227i) q^{26} +(2.23915 - 4.68894i) q^{27} +(5.02517 - 5.82889i) q^{28} +(-6.07280 - 3.50613i) q^{29} +(1.94857 - 1.12501i) q^{31} +(5.37732 - 1.75626i) q^{32} +(4.54338 - 1.78888i) q^{33} +(-2.18694 - 2.64192i) q^{34} +(5.99551 - 0.232146i) q^{36} -4.29414 q^{37} +(-3.67237 - 4.43638i) q^{38} +(-1.48404 + 9.91956i) q^{39} +(0.0948994 - 0.0547902i) q^{41} +(8.25249 + 4.55399i) q^{42} +(-0.178397 - 0.102997i) q^{43} +(4.27038 + 3.68155i) q^{44} +(-5.76345 - 2.14141i) q^{46} +(-5.38793 + 9.33217i) q^{47} +(3.46002 + 6.00235i) q^{48} +(3.90353 + 6.76112i) q^{49} +(2.61533 - 3.28689i) q^{51} +(-10.9351 + 3.81546i) q^{52} +7.55580i q^{53} +(1.78910 + 7.12735i) q^{54} +(-0.217988 + 10.8816i) q^{56} +(4.39174 - 5.51944i) q^{57} +(9.77747 - 1.65680i) q^{58} +(4.16744 + 7.21822i) q^{59} +(-3.06480 + 5.30839i) q^{61} +(-1.10825 + 2.98277i) q^{62} +(-3.37851 + 11.0385i) q^{63} +(-4.27426 + 6.76245i) q^{64} +(-3.33635 + 6.04596i) q^{66} +(-4.48967 + 2.59211i) q^{67} +(4.76488 + 0.905942i) q^{68} +(1.11418 - 7.44736i) q^{69} -5.46464 q^{71} +(-6.32213 + 5.65956i) q^{72} +12.9936 q^{73} +(4.67802 - 3.87240i) q^{74} +(8.00132 + 1.52128i) q^{76} +(-9.39464 + 5.42400i) q^{77} +(-7.32861 - 12.1446i) q^{78} +(4.32475 + 2.49689i) q^{79} +(-8.09156 + 3.94039i) q^{81} +(-0.0539740 + 0.145267i) q^{82} +(-3.85716 + 6.68080i) q^{83} +(-13.0969 + 2.48088i) q^{84} +(0.287226 - 0.0486706i) q^{86} +(4.44965 + 11.3012i) q^{87} +(-7.97210 - 0.159703i) q^{88} +0.134752i q^{89} -22.2830i q^{91} +(8.20978 - 2.86456i) q^{92} +(-3.85425 - 0.576624i) q^{93} +(-2.54603 - 15.0252i) q^{94} +(-9.18217 - 3.41874i) q^{96} +(-6.49834 + 11.2555i) q^{97} +(-10.3496 - 3.84538i) q^{98} +(-8.08708 - 2.47517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 4 q^{9} + 22 q^{12} - 30 q^{14} + 16 q^{18} - 4 q^{21} - 28 q^{24} - 12 q^{29} + 44 q^{33} - 6 q^{34} + 42 q^{36} - 60 q^{38} - 60 q^{41} + 18 q^{42} - 12 q^{46} + 12 q^{48} + 24 q^{49}+ \cdots + 12 q^{97}+O(q^{100}) \) 48 * q + 6 * q^6 + 4 * q^9 + 22 * q^12 - 30 * q^14 + 16 * q^18 - 4 * q^21 - 28 * q^24 - 12 * q^29 + 44 * q^33 - 6 * q^34 + 42 * q^36 - 60 * q^38 - 60 * q^41 + 18 * q^42 - 12 * q^46 + 12 * q^48 + 24 * q^49 + 18 * q^52 - 32 * q^54 - 42 * q^56 + 12 * q^57 + 18 * q^58 - 48 * q^64 + 16 * q^66 - 48 * q^68 + 36 * q^69 - 60 * q^72 + 24 * q^73 + 84 * q^74 + 6 * q^76 - 48 * q^77 - 38 * q^78 + 36 * q^82 + 50 * q^84 - 54 * q^86 - 60 * q^92 + 32 * q^93 + 18 * q^94 - 18 * q^96 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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