LMFDB - Embedded newform 483.2.r.a.34.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(34,483)] 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("483.34"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.1
Character	$\chi$	$=$	483.34
Dual form			483.2.r.a.412.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.18339 + 1.40318i) q^{2} +(-0.989821 - 0.142315i) q^{3} +(1.96744 - 4.30810i) q^{4} +(-1.99005 + 0.584333i) q^{5} +(2.36086 - 1.07817i) q^{6} +(1.49161 - 2.18520i) q^{7} +(1.01061 + 7.02895i) q^{8} +(0.959493 + 0.281733i) q^{9} +(3.52514 - 4.06822i) q^{10} +(-0.546146 + 0.849820i) q^{11} +(-2.56052 + 3.98425i) q^{12} +(2.07798 + 1.80058i) q^{13} +(-0.190534 + 6.86413i) q^{14} +(2.05296 - 0.295171i) q^{15} +(-5.86647 - 6.77027i) q^{16} +(-1.29960 - 2.84573i) q^{17} +(-2.49027 + 0.731208i) q^{18} +(-2.30797 + 5.05375i) q^{19} +(-1.39795 + 9.72299i) q^{20} +(-1.78741 + 1.95068i) q^{21} -2.62183i q^{22} +(1.55518 - 4.53667i) q^{23} -7.10123i q^{24} +(-0.587398 + 0.377498i) q^{25} +(-7.06356 - 1.01559i) q^{26} +(-0.909632 - 0.415415i) q^{27} +(-6.47940 - 10.7253i) q^{28} +(-0.204348 - 0.447459i) q^{29} +(-4.06822 + 3.52514i) q^{30} +(-6.70072 + 0.963419i) q^{31} +(8.68150 + 2.54912i) q^{32} +(0.661529 - 0.763445i) q^{33} +(6.83060 + 4.38976i) q^{34} +(-1.69150 + 5.22026i) q^{35} +(3.10148 - 3.57930i) q^{36} +(0.106468 - 0.362596i) q^{37} +(-2.05212 - 14.2728i) q^{38} +(-1.80058 - 2.07798i) q^{39} +(-6.11842 - 13.3975i) q^{40} +(1.45543 + 4.95673i) q^{41} +(1.16546 - 6.76715i) q^{42} +(-8.56131 - 1.23093i) q^{43} +(2.58660 + 4.02482i) q^{44} -2.07407 q^{45} +(2.97019 + 12.0875i) q^{46} -12.1543i q^{47} +(4.84325 + 7.53624i) q^{48} +(-2.55021 - 6.51893i) q^{49} +(0.752820 - 1.64845i) q^{50} +(0.881384 + 3.00172i) q^{51} +(11.8454 - 5.40960i) q^{52} +(-0.165449 + 0.143362i) q^{53} +(2.56898 - 0.369364i) q^{54} +(0.590283 - 2.01032i) q^{55} +(16.8671 + 8.27606i) q^{56} +(3.00370 - 4.67385i) q^{57} +(1.07404 + 0.690241i) q^{58} +(-3.18828 - 2.76266i) q^{59} +(2.76745 - 9.42507i) q^{60} +(-1.30317 - 9.06375i) q^{61} +(13.2784 - 11.5058i) q^{62} +(2.04683 - 1.67645i) q^{63} +(-5.34100 + 1.56826i) q^{64} +(-5.18742 - 2.36902i) q^{65} +(-0.373125 + 2.59514i) q^{66} +(5.08137 + 7.90677i) q^{67} -14.8166 q^{68} +(-2.18499 + 4.26917i) q^{69} +(-3.63176 - 13.7713i) q^{70} +(-8.80148 + 5.65636i) q^{71} +(-1.01061 + 7.02895i) q^{72} +(-10.4960 - 4.79338i) q^{73} +(0.276326 + 0.941081i) q^{74} +(0.635142 - 0.290060i) q^{75} +(17.2312 + 19.8859i) q^{76} +(1.04239 + 2.46104i) q^{77} +(6.84713 + 2.01050i) q^{78} +(-5.51326 - 4.77727i) q^{79} +(15.6307 + 10.0452i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-10.1329 - 8.78023i) q^{82} +(-4.57899 - 1.34451i) q^{83} +(4.88709 + 11.5382i) q^{84} +(4.24913 + 4.90376i) q^{85} +(20.4199 - 9.32544i) q^{86} +(0.138588 + 0.471987i) q^{87} +(-6.52529 - 2.98000i) q^{88} +(-2.41840 + 16.8203i) q^{89} +(4.52849 - 2.91029i) q^{90} +(7.03415 - 1.85504i) q^{91} +(-16.4847 - 15.6255i) q^{92} +6.76963 q^{93} +(17.0546 + 26.5375i) q^{94} +(1.63991 - 11.4058i) q^{95} +(-8.23036 - 3.75868i) q^{96} +(-0.968153 + 0.284275i) q^{97} +(14.7153 + 10.6550i) q^{98} +(-0.763445 + 0.661529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49}+ \cdots + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	−2.18339	+	1.40318i	−1.54389	+	0.992197i	−0.557051	+	0.830478i	$0.688067\pi$
$2$	−2.18339	+	1.40318i	−1.54389	+	0.992197i	−0.986837	+	0.161718i	$0.948296\pi$
$3$	−0.989821	−	0.142315i	−0.571474	−	0.0821655i
$3$	−0.989821	−	0.142315i	−0.571474	−	0.0821655i
$4$	1.96744	−	4.30810i	0.983721	−	2.15405i
$5$	−1.99005	+	0.584333i	−0.889979	+	0.261321i	−0.694591	−	0.719405i	$-0.744415\pi$
$5$	−1.99005	+	0.584333i	−0.889979	+	0.261321i	−0.195388	+	0.980726i	$0.562597\pi$
$6$	2.36086	−	1.07817i	0.963816	−	0.440160i
$7$	1.49161	−	2.18520i	0.563775	−	0.825928i
$7$	1.49161	−	2.18520i	0.563775	−	0.825928i
$8$	1.01061	+	7.02895i	0.357305	+	2.48511i
$9$	0.959493	+	0.281733i	0.319831	+	0.0939109i
$10$	3.52514	−	4.06822i	1.11475	−	1.28649i
$11$	−0.546146	+	0.849820i	−0.164669	+	0.256230i	−0.913776	−	0.406219i	$-0.866847\pi$
$11$	−0.546146	+	0.849820i	−0.164669	+	0.256230i	0.749106	+	0.662450i	$0.230483\pi$
$12$	−2.56052	+	3.98425i	−0.739159	+	1.15015i
$13$	2.07798	+	1.80058i	0.576327	+	0.499390i	0.893552	−	0.448960i	$-0.148205\pi$
$13$	2.07798	+	1.80058i	0.576327	+	0.499390i	−0.317225	+	0.948350i	$0.602751\pi$
$14$	−0.190534	+	6.86413i	−0.0509224	+	1.83452i
$15$	2.05296	−	0.295171i	0.530071	−	0.0762127i
$16$	−5.86647	−	6.77027i	−1.46662	−	1.69257i
$17$	−1.29960	−	2.84573i	−0.315200	−	0.690191i	0.684029	−	0.729455i	$-0.260226\pi$
$17$	−1.29960	−	2.84573i	−0.315200	−	0.690191i	−0.999229	+	0.0392637i	$0.987499\pi$
$18$	−2.49027	+	0.731208i	−0.586961	+	0.172347i
$19$	−2.30797	+	5.05375i	−0.529484	+	1.15941i	0.436238	+	0.899831i	$0.356311\pi$
$19$	−2.30797	+	5.05375i	−0.529484	+	1.15941i	−0.965722	+	0.259578i	$0.916417\pi$
$20$	−1.39795	+	9.72299i	−0.312592	+	2.17413i
$21$	−1.78741	+	1.95068i	−0.390045	+	0.425673i
$22$		−	2.62183i		−	0.558975i
$23$	1.55518	−	4.53667i	0.324278	−	0.945962i
$23$	1.55518	−	4.53667i	0.324278	−	0.945962i
$24$		−	7.10123i		−	1.44953i
$25$	−0.587398	+	0.377498i	−0.117480	+	0.0754995i
$26$	−7.06356	−	1.01559i	−1.38528	−	0.199173i
$27$	−0.909632	−	0.415415i	−0.175059	−	0.0799467i
$28$	−6.47940	−	10.7253i	−1.22449	−	2.02688i
$29$	−0.204348	−	0.447459i	−0.0379464	−	0.0830911i	0.889710	−	0.456527i	$-0.150907\pi$
$29$	−0.204348	−	0.447459i	−0.0379464	−	0.0830911i	−0.927656	+	0.373436i	$0.878180\pi$
$30$	−4.06822	+	3.52514i	−0.742753	+	0.643599i
$31$	−6.70072	+	0.963419i	−1.20349	+	0.173035i	−0.714739	−	0.699391i	$-0.753455\pi$
$31$	−6.70072	+	0.963419i	−1.20349	+	0.173035i	−0.488746	+	0.872426i	$0.662546\pi$
$32$	8.68150	+	2.54912i	1.53469	+	0.450625i
$33$	0.661529	−	0.763445i	0.115157	−	0.132899i
$34$	6.83060	+	4.38976i	1.17144	+	0.752837i
$35$	−1.69150	+	5.22026i	−0.285915	+	0.882386i
$36$	3.10148	−	3.57930i	0.516913	−	0.596549i
$37$	0.106468	−	0.362596i	0.0175032	−	0.0596104i	−0.950278	−	0.311402i	$-0.899202\pi$
$37$	0.106468	−	0.362596i	0.0175032	−	0.0596104i	0.967782	+	0.251791i	$0.0810197\pi$
$38$	−2.05212	−	14.2728i	−0.332897	−	2.31535i
$39$	−1.80058	−	2.07798i	−0.288323	−	0.332743i
$40$	−6.11842	−	13.3975i	−0.967407	−	2.11833i
$41$	1.45543	+	4.95673i	0.227299	+	0.774111i	0.991610	+	0.129263i	$0.0412611\pi$
$41$	1.45543	+	4.95673i	0.227299	+	0.774111i	−0.764311	+	0.644848i	$0.776921\pi$
$42$	1.16546	−	6.76715i	0.179835	−	1.04419i
$43$	−8.56131	−	1.23093i	−1.30559	−	0.187715i	−0.545816	−	0.837905i	$-0.683780\pi$
$43$	−8.56131	−	1.23093i	−1.30559	−	0.187715i	−0.759771	+	0.650190i	$0.774689\pi$
$44$	2.58660	+	4.02482i	0.389944	+	0.606765i
$45$	−2.07407			−0.309184
$46$	2.97019	+	12.0875i	0.437931	+	1.78221i
$47$		−	12.1543i		−	1.77289i	−0.462837	−	0.886443i	$-0.653169\pi$
$47$		−	12.1543i		−	1.77289i	0.462837	−	0.886443i	$-0.346831\pi$
$48$	4.84325	+	7.53624i	0.699063	+	1.08776i
$49$	−2.55021	−	6.51893i	−0.364315	−	0.931276i
$50$	0.752820	−	1.64845i	0.106465	−	0.233126i
$51$	0.881384	+	3.00172i	0.123418	+	0.420324i
$52$	11.8454	−	5.40960i	1.64266	−	0.750176i
$53$	−0.165449	+	0.143362i	−0.0227261	+	0.0196923i	−0.666150	−	0.745818i	$-0.732059\pi$
$53$	−0.165449	+	0.143362i	−0.0227261	+	0.0196923i	0.643424	+	0.765510i	$0.277513\pi$
$54$	2.56898	−	0.369364i	0.349594	−	0.0502640i
$55$	0.590283	−	2.01032i	0.0795937	−	0.271071i
$56$	16.8671	+	8.27606i	2.25396	+	1.10594i
$57$	3.00370	−	4.67385i	0.397850	−	0.619066i
$58$	1.07404	+	0.690241i	0.141028	+	0.0906331i
$59$	−3.18828	−	2.76266i	−0.415079	−	0.359668i	0.422145	−	0.906528i	$-0.361277\pi$
$59$	−3.18828	−	2.76266i	−0.415079	−	0.359668i	−0.837224	+	0.546860i	$0.815823\pi$
$60$	2.76745	−	9.42507i	0.357276	−	1.21677i
$61$	−1.30317	−	9.06375i	−0.166854	−	1.16049i	−0.885337	−	0.464950i	$-0.846072\pi$
$61$	−1.30317	−	9.06375i	−0.166854	−	1.16049i	0.718483	−	0.695545i	$-0.244837\pi$
$62$	13.2784	−	11.5058i	1.68636	−	1.46124i
$63$	2.04683	−	1.67645i	0.257876	−	0.211213i
$64$	−5.34100	+	1.56826i	−0.667625	+	0.196032i
$65$	−5.18742	−	2.36902i	−0.643421	−	0.293840i
$66$	−0.373125	+	2.59514i	−0.0459285	+	0.319440i
$67$	5.08137	+	7.90677i	0.620789	+	0.965966i	0.999187	+	0.0403230i	$0.0128387\pi$
$67$	5.08137	+	7.90677i	0.620789	+	0.965966i	−0.378398	+	0.925643i	$0.623525\pi$
$68$	−14.8166			−1.79677
$69$	−2.18499	+	4.26917i	−0.263042	+	0.513948i
$70$	−3.63176	−	13.7713i	−0.434079	−	1.64599i
$71$	−8.80148	+	5.65636i	−1.04454	+	0.671287i	−0.946106	−	0.323856i	$-0.895021\pi$
$71$	−8.80148	+	5.65636i	−1.04454	+	0.671287i	−0.0984367	+	0.995143i	$0.531384\pi$
$72$	−1.01061	+	7.02895i	−0.119102	+	0.828370i
$73$	−10.4960	−	4.79338i	−1.22847	−	0.561022i	−0.307830	−	0.951441i	$-0.599603\pi$
$73$	−10.4960	−	4.79338i	−1.22847	−	0.561022i	−0.920637	+	0.390419i	$0.872330\pi$
$74$	0.276326	+	0.941081i	0.0321223	+	0.109398i
$75$	0.635142	−	0.290060i	0.0733399	−	0.0334932i
$76$	17.2312	+	19.8859i	1.97656	+	2.28107i
$77$	1.04239	+	2.46104i	0.118791	+	0.280461i
$78$	6.84713	+	2.01050i	0.775285	+	0.227644i
$79$	−5.51326	−	4.77727i	−0.620291	−	0.537485i	0.287031	−	0.957921i	$-0.407332\pi$
$79$	−5.51326	−	4.77727i	−0.620291	−	0.537485i	−0.907322	+	0.420436i	$0.861877\pi$
$80$	15.6307	+	10.0452i	1.74756	+	1.12309i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−10.1329	−	8.78023i	−1.11899	−	0.969615i
$83$	−4.57899	−	1.34451i	−0.502610	−	0.147580i	0.0205926	−	0.999788i	$-0.493445\pi$
$83$	−4.57899	−	1.34451i	−0.502610	−	0.147580i	−0.523203	+	0.852208i	$0.675263\pi$
$84$	4.88709	+	11.5382i	0.533225	+	1.25892i
$85$	4.24913	+	4.90376i	0.460883	+	0.531887i
$86$	20.4199	−	9.32544i	2.20193	−	1.00559i
$87$	0.138588	+	0.471987i	0.0148582	+	0.0506023i
$88$	−6.52529	−	2.98000i	−0.695598	−	0.317669i
$89$	−2.41840	+	16.8203i	−0.256349	+	1.78295i	0.301964	+	0.953319i	$0.402358\pi$
$89$	−2.41840	+	16.8203i	−0.256349	+	1.78295i	−0.558313	+	0.829630i	$0.688551\pi$
$90$	4.52849	−	2.91029i	0.477345	−	0.306771i
$91$	7.03415	−	1.85504i	0.737380	−	0.194461i
$92$	−16.4847	−	15.6255i	−1.71865	−	1.62907i
$93$	6.76963			0.701978
$94$	17.0546	+	26.5375i	1.75905	+	2.73714i
$95$	1.63991	−	11.4058i	0.168252	−	1.17022i
$96$	−8.23036	−	3.75868i	−0.840008	−	0.383619i
$97$	−0.968153	+	0.284275i	−0.0983011	+	0.0288638i	−0.330513	−	0.943801i	$-0.607222\pi$
$97$	−0.968153	+	0.284275i	−0.0983011	+	0.0288638i	0.232212	+	0.972665i	$0.425404\pi$
$98$	14.7153	+	10.6550i	1.48647	+	1.07631i
$99$	−0.763445	+	0.661529i	−0.0767291	+	0.0664862i
$100$	0.470625	+	3.27327i	0.0470625	+	0.327327i
$101$	−4.17046	+	14.2033i	−0.414977	+	1.41328i	0.441577	+	0.897223i	$0.354419\pi$
$101$	−4.17046	+	14.2033i	−0.414977	+	1.41328i	−0.856554	+	0.516058i	$0.827399\pi$
$102$	−6.13634	−	5.31717i	−0.607589	−	0.526479i
$103$	−11.7082	−	7.52441i	−1.15364	−	0.741402i	−0.183282	−	0.983060i	$-0.558672\pi$
$103$	−11.7082	−	7.52441i	−1.15364	−	0.741402i	−0.970361	+	0.241659i	$0.922309\pi$
$104$	−10.5562	+	16.4257i	−1.03512	+	1.61067i
$105$	2.41720	−	4.92640i	0.235895	−	0.480768i
$106$	0.160076	−	0.545169i	0.0155480	−	0.0529515i
$107$	−15.2327	+	2.19013i	−1.47260	+	0.211728i	−0.831413	−	0.555654i	$-0.812468\pi$
$107$	−15.2327	+	2.19013i	−1.47260	+	0.211728i	−0.641189	+	0.767383i	$0.721559\pi$
$108$	−3.57930	+	3.10148i	−0.344418	+	0.298440i
$109$	−18.0655	+	8.25026i	−1.73037	+	0.790232i	−0.736913	+	0.675988i	$0.763717\pi$
$109$	−18.0655	+	8.25026i	−1.73037	+	0.790232i	−0.993453	+	0.114244i	$0.963555\pi$
$110$	1.53202	+	5.21758i	0.146072	+	0.497476i
$111$	−0.156987	+	0.343753i	−0.0149005	+	0.0326276i
$112$	−23.5449	+	2.72083i	−2.22478	+	0.257094i
$113$	−4.05541	−	6.31035i	−0.381501	−	0.593627i	0.596402	−	0.802686i	$-0.296596\pi$
$113$	−4.05541	−	6.31035i	−0.381501	−	0.593627i	−0.977903	+	0.209058i	$0.932960\pi$
$114$			14.4195i			1.35051i
$115$	−0.443975	+	9.93697i	−0.0414008	+	0.926627i
$116$	−2.32974			−0.216311
$117$	1.48652	+	2.31308i	0.137429	+	0.213844i
$118$	10.8378	+	1.55823i	0.997697	+	0.143447i
$119$	−8.15699	−	1.40483i	−0.747750	−	0.128780i
$120$	4.14948	+	14.1318i	0.378794	+	1.29005i
$121$	4.14565	+	9.07770i	0.376877	+	0.825245i
$122$	15.5634	+	17.9611i	1.40904	+	1.62612i
$123$	−0.735197	−	5.11340i	−0.0662904	−	0.461060i
$124$	−9.03278	+	30.7628i	−0.811168	+	2.76258i
$125$	7.73950	−	8.93186i	0.692242	−	0.798890i
$126$	−2.11667	+	6.53241i	−0.188568	+	0.581953i
$127$	11.1692	+	7.17799i	0.991104	+	0.636944i	0.932437	−	0.361334i	$-0.117678\pi$
$127$	11.1692	+	7.17799i	0.991104	+	0.636944i	0.0586676	+	0.998278i	$0.481315\pi$
$128$	−2.38945	+	2.75757i	−0.211199	+	0.243737i
$129$	8.29899	+	2.43680i	0.730685	+	0.214548i
$130$	14.6503	−	2.10640i	1.28492	−	0.184743i
$131$	12.8762	−	11.1573i	1.12500	−	0.974814i	0.125146	−	0.992138i	$-0.460060\pi$
$131$	12.8762	−	11.1573i	1.12500	−	0.974814i	0.999850	+	0.0173243i	$0.00551477\pi$
$132$	−1.98748	−	4.35197i	−0.172988	−	0.378790i
$133$	7.60086	+	12.5816i	0.659079	+	1.09096i
$134$	−22.1892	−	10.1335i	−1.91686	−	0.875399i
$135$	2.05296	+	0.295171i	0.176690	+	0.0254042i
$136$	18.6891	−	12.0108i	1.60258	−	1.02991i
$137$		−	4.27656i		−	0.365372i	−0.983171	−	0.182686i	$-0.941521\pi$
$137$		−	4.27656i		−	0.365372i	0.983171	−	0.182686i	$-0.0584791\pi$
$138$	−1.21972	−	12.3872i	−0.103830	−	1.05447i
$139$			1.66501i			0.141225i	0.997504	+	0.0706123i	$0.0224953\pi$
$139$			1.66501i			0.141225i	−0.997504	+	0.0706123i	$0.977505\pi$
$140$	19.1615	+	17.5577i	1.61944	+	1.48390i
$141$	−1.72974	+	12.0306i	−0.145670	+	1.01316i
$142$	11.2801	−	24.7001i	0.946609	−	2.07278i
$143$	−2.66505	+	0.782528i	−0.222862	+	0.0654383i
$144$	−3.72143	−	8.14880i	−0.310119	−	0.679067i
$145$	0.668128	+	0.771061i	0.0554850	+	0.0640332i
$146$	29.6429	−	4.26200i	2.45326	−	0.352726i
$147$	1.59651	+	6.81551i	0.131678	+	0.562134i
$148$	−1.35263	−	1.17206i	−0.111185	−	0.0963427i
$149$	−1.32442	+	2.06084i	−0.108501	+	0.168831i	−0.891258	−	0.453497i	$-0.850176\pi$
$149$	−1.32442	+	2.06084i	−0.108501	+	0.168831i	0.782757	+	0.622328i	$0.213813\pi$
$150$	−0.979756	+	1.52453i	−0.0799968	+	0.124477i
$151$	0.444442	−	0.512914i	0.0361682	−	0.0417403i	−0.737377	−	0.675481i	$-0.763936\pi$
$151$	0.444442	−	0.512914i	0.0361682	−	0.0417403i	0.773545	+	0.633741i	$0.218481\pi$
$152$	−37.8550	−	11.1152i	−3.07045	−	0.901565i
$153$	−0.445224	−	3.09660i	−0.0359942	−	0.250345i
$154$	−5.72922	−	3.91074i	−0.461673	−	0.315136i
$155$	12.7718	−	5.83271i	1.02586	−	0.468494i
$156$	−12.4947	+	3.66876i	−1.00037	+	0.293736i
$157$	−3.78997	+	8.29888i	−0.302473	+	0.662323i	−0.998445	−	0.0557456i	$-0.982246\pi$
$157$	−3.78997	+	8.29888i	−0.302473	+	0.662323i	0.695972	+	0.718069i	$0.254974\pi$
$158$	18.7410	+	2.69454i	1.49095	+	0.214366i
$159$	0.184167	−	0.118357i	0.0146054	−	0.00938633i
$160$	−18.7662			−1.48360
$161$	−7.59382	−	10.1653i	−0.598477	−	0.801140i
$162$	−2.59540			−0.203914
$163$	8.09016	−	5.19923i	0.633670	−	0.407235i	−0.183997	−	0.982927i	$-0.558904\pi$
$163$	8.09016	−	5.19923i	0.633670	−	0.407235i	0.817667	+	0.575692i	$0.195267\pi$
$164$	24.2175	+	3.48196i	1.89107	+	0.271895i
$165$	−0.870373	+	1.90585i	−0.0677584	+	0.148370i
$166$	11.8843	−	3.48955i	0.922401	−	0.270841i
$167$	6.72684	−	3.07204i	0.520538	−	0.237722i	−0.137778	−	0.990463i	$-0.543996\pi$
$167$	6.72684	−	3.07204i	0.520538	−	0.237722i	0.658316	+	0.752741i	$0.271269\pi$
$168$	−15.5176	−	10.5923i	−1.19721	−	0.817211i
$169$	−0.774183	−	5.38456i	−0.0595525	−	0.414197i
$170$	−16.1583	−	4.74452i	−1.23929	−	0.363888i
$171$	−3.63828	+	4.19880i	−0.278227	+	0.321091i
$172$	−22.1468	+	34.4612i	−1.68868	+	2.62764i
$173$	3.24569	−	5.05039i	0.246765	−	0.383974i	−0.695671	−	0.718361i	$-0.744893\pi$
$173$	3.24569	−	5.05039i	0.246765	−	0.383974i	0.942436	+	0.334386i	$0.108529\pi$
$174$	−0.964872	−	0.836066i	−0.0731468	−	0.0633820i
$175$	−0.0512595	+	1.84666i	−0.00387486	+	0.139594i
$176$	8.95746	−	1.28789i	0.675194	−	0.0970782i
$177$	2.76266	+	3.18828i	0.207654	+	0.239646i
$178$	−18.3216	−	40.1187i	−1.37326	−	3.00702i
$179$	−0.984461	+	0.289064i	−0.0735820	+	0.0216056i	−0.318316	−	0.947985i	$-0.603117\pi$
$179$	−0.984461	+	0.289064i	−0.0735820	+	0.0216056i	0.244734	+	0.969590i	$0.421299\pi$
$180$	−4.08061	+	8.93529i	−0.304151	+	0.665997i
$181$	1.24975	−	8.69219i	0.0928930	−	0.646085i	−0.889176	−	0.457565i	$-0.848722\pi$
$181$	1.24975	−	8.69219i	0.0928930	−	0.646085i	0.982069	−	0.188520i	$-0.0603691\pi$
$182$	−12.7553	+	13.9204i	−0.945488	+	1.03185i
$183$			9.15696i			0.676902i
$184$	33.4598	+	6.34651i	2.46669	+	0.467871i
$185$			0.783798i			0.0576260i
$186$	−14.7807	+	9.49899i	−1.08377	+	0.696500i
$187$	3.12813	+	0.449757i	0.228752	+	0.0328895i
$188$	−52.3619	−	23.9129i	−3.81888	−	1.74403i
$189$	−2.26458	+	1.36809i	−0.164724	+	0.0995141i
$190$	12.4239	+	27.2045i	0.901322	+	1.97362i
$191$	5.49422	−	4.76077i	0.397548	−	0.344477i	−0.433030	−	0.901379i	$-0.642556\pi$
$191$	5.49422	−	4.76077i	0.397548	−	0.344477i	0.830578	+	0.556902i	$0.188010\pi$
$192$	5.50982	−	0.792193i	0.397637	−	0.0571716i
$193$	−10.2382	−	3.00619i	−0.736958	−	0.216390i	−0.108350	−	0.994113i	$-0.534557\pi$
$193$	−10.2382	−	3.00619i	−0.736958	−	0.216390i	−0.628608	+	0.777722i	$0.716375\pi$
$194$	1.71496	−	1.97917i	0.123127	−	0.142096i
$195$	4.79748	+	3.08315i	0.343554	+	0.220789i
$196$	−33.1016	−	1.83908i	−2.36440	−	0.131363i
$197$	−3.58337	+	4.13543i	−0.255305	+	0.294637i	−0.868904	−	0.494980i	$-0.835175\pi$
$197$	−3.58337	+	4.13543i	−0.255305	+	0.294637i	0.613600	+	0.789617i	$0.289721\pi$
$198$	0.738654	−	2.51562i	0.0524938	−	0.178778i
$199$	−1.40482	−	9.77074i	−0.0995851	−	0.692629i	−0.977053	−	0.212995i	$-0.931678\pi$
$199$	−1.40482	−	9.77074i	−0.0995851	−	0.692629i	0.877468	−	0.479635i	$-0.159231\pi$
$200$	−3.24704	−	3.74729i	−0.229601	−	0.264973i
$201$	−3.90440	−	8.54945i	−0.275395	−	0.603031i
$202$	−10.8240	−	36.8632i	−0.761575	−	2.59369i
$203$	−1.28260	−	0.220893i	−0.0900206	−	0.0155037i
$204$	14.6658	+	2.10862i	1.02681	+	0.147633i
$205$	−5.79275	−	9.01370i	−0.404584	−	0.629544i
$206$	36.1216			2.51671
$207$	2.77032	−	3.91476i	0.192550	−	0.272095i
$208$		−	24.6315i		−	1.70789i
$209$	−3.03429	−	4.72144i	−0.209886	−	0.326589i
$210$	1.63493	+	14.1480i	0.112821	+	0.976305i
$211$	2.31217	−	5.06294i	0.159176	−	0.348547i	−0.813194	−	0.581993i	$-0.802273\pi$
$211$	2.31217	−	5.06294i	0.159176	−	0.348547i	0.972370	+	0.233446i	$0.0750002\pi$
$212$	0.292107	+	0.994826i	0.0200620	+	0.0683249i
$213$	9.51687	−	4.34621i	0.652085	−	0.297797i
$214$	30.1858	−	26.1561i	2.06346	−	1.78800i
$215$	17.7567	−	2.55303i	1.21100	−	0.174115i
$216$	2.00065	−	6.81358i	0.136127	−	0.463606i
$217$	−7.88959	+	16.0795i	−0.535581	+	1.09155i
$218$	27.8675	−	43.3627i	1.88743	−	2.93689i
$219$	9.70703	+	6.23833i	0.655940	+	0.421547i
$220$	−7.49930	−	6.49818i	−0.505603	−	0.438107i
$221$	2.42342	−	8.25340i	0.163017	−	0.555183i
$222$	−0.139584	−	0.970827i	−0.00936826	−	0.0651577i
$223$	20.4316	−	17.7041i	1.36820	−	1.18556i	0.405790	−	0.913966i	$-0.366996\pi$
$223$	20.4316	−	17.7041i	1.36820	−	1.18556i	0.962413	−	0.271589i	$-0.0875491\pi$
$224$	18.5197	−	15.1685i	1.23740	−	1.01349i
$225$	−0.669957	+	0.196717i	−0.0446638	+	0.0131145i
$226$	17.7091	+	8.08746i	1.17799	+	0.537970i
$227$	1.74273	−	12.1210i	0.115669	−	0.804496i	−0.846568	−	0.532281i	$-0.821335\pi$
$227$	1.74273	−	12.1210i	0.115669	−	0.804496i	0.962237	−	0.272215i	$-0.0877560\pi$
$228$	−14.2258	−	22.1358i	−0.942126	−	1.46598i
$229$	14.1871			0.937511			0.468755	−	0.883328i	$-0.344703\pi$
$229$	14.1871			0.937511			0.468755	+	0.883328i	$0.344703\pi$
$230$	−12.9740	−	22.3192i	−0.855478	−	1.47169i
$231$	−0.681539	−	2.58434i	−0.0448420	−	0.170037i
$232$	2.93866	−	1.88856i	0.192932	−	0.123990i
$233$	−4.07104	+	28.3147i	−0.266703	+	1.85496i	0.212377	+	0.977188i	$0.431879\pi$
$233$	−4.07104	+	28.3147i	−0.266703	+	1.85496i	−0.479080	+	0.877771i	$0.659030\pi$
$234$	−6.49131	−	2.96448i	−0.424350	−	0.193794i
$235$	7.10215	+	24.1877i	0.463293	+	1.57783i
$236$	−18.1746	+	8.30005i	−1.18306	+	0.540287i
$237$	4.77727	+	5.51326i	0.310317	+	0.358125i
$238$	19.7811	−	8.37843i	1.28222	−	0.543093i
$239$	−27.3504	−	8.03080i	−1.76915	−	0.519469i	−0.775436	−	0.631426i	$-0.782470\pi$
$239$	−27.3504	−	8.03080i	−1.76915	−	0.519469i	−0.993713	+	0.111957i	$0.964288\pi$
$240$	−14.0420	−	12.1675i	−0.906407	−	0.785406i
$241$	20.8894	+	13.4248i	1.34560	+	0.864766i	0.997358	−	0.0726373i	$-0.0231416\pi$
$241$	20.8894	+	13.4248i	1.34560	+	0.864766i	0.348244	+	0.937404i	$0.386778\pi$
$242$	−21.7892	−	14.0031i	−1.40066	−	0.900150i
$243$	−0.755750	−	0.654861i	−0.0484814	−	0.0420093i
$244$	−41.6114	−	12.2182i	−2.66390	−	0.782191i
$245$	8.88427	+	11.4829i	0.567595	+	0.733613i
$246$	8.78023	+	10.1329i	0.559807	+	0.646052i
$247$	−13.8956	+	6.34589i	−0.884154	+	0.403780i
$248$	−13.5436	−	46.1254i	−0.860023	−	2.92897i
$249$	4.34104	+	1.98249i	0.275102	+	0.125635i
$250$	−4.36534	+	30.3616i	−0.276088	+	1.92024i
$251$	1.75130	−	1.12549i	0.110541	−	0.0710405i	−0.484202	−	0.874956i	$-0.660890\pi$
$251$	1.75130	−	1.12549i	0.110541	−	0.0710405i	0.594743	+	0.803916i	$0.297254\pi$
$252$	−3.19529	−	12.1163i	−0.201284	−	0.763253i
$253$	3.00600	+	3.79931i	0.188985	+	0.238861i
$254$	−34.4586			−2.16213
$255$	−3.50800	−	5.45856i	−0.219680	−	0.341828i
$256$	2.93212	−	20.3933i	0.183257	−	1.27458i
$257$	7.63411	+	3.48638i	0.476203	+	0.217474i	0.639032	−	0.769180i	$-0.279335\pi$
$257$	7.63411	+	3.48638i	0.476203	+	0.217474i	−0.162830	+	0.986654i	$0.552062\pi$
$258$	−21.5392	+	6.32447i	−1.34097	+	0.393744i
$259$	−0.633537	−	0.773505i	−0.0393661	−	0.0480633i
$260$	−20.4119	+	17.6870i	−1.26589	+	1.09690i
$261$	−0.0700065	−	0.486906i	−0.00433329	−	0.0301387i
$262$	−12.4580	+	42.4282i	−0.769660	+	2.62122i
$263$	16.2655	+	14.0942i	1.00298	+	0.869084i	0.991402	−	0.130849i	$-0.0417703\pi$
$263$	16.2655	+	14.0942i	1.00298	+	0.869084i	0.0115742	+	0.999933i	$0.496316\pi$
$264$	6.03477	+	3.87831i	0.371414	+	0.238694i
$265$	0.245481	−	0.381975i	0.0150798	−	0.0234646i
$266$	−34.2498	−	16.8051i	−2.09999	−	1.03039i
$267$	4.78756	−	16.3049i	0.292994	−	0.997846i
$268$	44.0604	−	6.33494i	2.69142	−	0.386968i
$269$	−16.3033	+	14.1269i	−0.994031	+	0.861333i	−0.990340	−	0.138660i	$-0.955720\pi$
$269$	−16.3033	+	14.1269i	−0.994031	+	0.861333i	−0.00369140	+	0.999993i	$0.501175\pi$
$270$	−4.89658	+	2.23619i	−0.297996	+	0.136090i
$271$	3.61685	+	12.3179i	0.219708	+	0.748257i	0.993401	+	0.114696i	$0.0365894\pi$
$271$	3.61685	+	12.3179i	0.219708	+	0.748257i	−0.773692	+	0.633561i	$0.781592\pi$
$272$	−11.6423	+	25.4930i	−0.705917	+	1.54574i
$273$	−7.22656	+	0.835095i	−0.437371	+	0.0505422i
$274$	6.00078	+	9.33740i	0.362520	+	0.564093i
$275$		−	0.705351i		−	0.0425343i
$276$	14.0932	+	17.8125i	0.848308	+	1.07219i
$277$	7.49972			0.450615			0.225307	−	0.974288i	$-0.427661\pi$
$277$	7.49972			0.450615			0.225307	+	0.974288i	$0.427661\pi$
$278$	−2.33631	−	3.63537i	−0.140123	−	0.218035i
$279$	−6.70072	−	0.963419i	−0.401162	−	0.0576784i
$280$	−38.4024	−	6.61381i	−2.29498	−	0.395250i
$281$	−5.47619	−	18.6502i	−0.326682	−	1.11258i	−0.945115	−	0.326739i	$-0.894050\pi$
$281$	−5.47619	−	18.6502i	−0.326682	−	1.11258i	0.618433	−	0.785838i	$-0.287768\pi$
$282$	−13.1044	−	28.6946i	−0.780353	−	1.70874i
$283$	−10.3526	−	11.9476i	−0.615400	−	0.710210i	0.359427	−	0.933173i	$-0.382972\pi$
$283$	−10.3526	−	11.9476i	−0.615400	−	0.710210i	−0.974827	+	0.222964i	$0.928427\pi$
$284$	7.05178	+	49.0462i	0.418446	+	2.91036i
$285$	−3.24644	+	11.0564i	−0.192303	+	0.654923i
$286$	4.72080	−	5.44810i	0.279147	−	0.322153i
$287$	13.0024	+	4.21310i	0.767506	+	0.248691i
$288$	7.61167	+	4.89172i	0.448522	+	0.288248i
$289$	4.72342	−	5.45111i	0.277848	−	0.320654i
$290$	−2.54072	−	0.746022i	−0.149196	−	0.0438079i
$291$	0.998755	−	0.143599i	0.0585481	−	0.00841794i
$292$	−41.3007	+	35.7872i	−2.41694	+	2.09429i
$293$	12.6884	+	27.7838i	0.741265	+	1.62314i	0.781462	+	0.623952i	$0.214474\pi$
$293$	12.6884	+	27.7838i	0.741265	+	1.62314i	−0.0401972	+	0.999192i	$0.512799\pi$
$294$	−13.0492	−	12.6407i	−0.761043	−	0.737221i
$295$	7.95917	+	3.63483i	0.463401	+	0.211628i
$296$	2.65627	+	0.381914i	0.154392	+	0.0221983i
$297$	0.849820	−	0.546146i	0.0493116	−	0.0316906i
$298$		−	6.35803i		−	0.368311i
$299$	11.4003	−	6.62687i	0.659295	−	0.383242i
$300$		−	3.30693i		−	0.190926i
$301$	−15.4599	+	16.8721i	−0.891097	+	0.972492i
$302$	−0.250680	+	1.74352i	−0.0144250	+	0.100328i
$303$	6.14936	−	13.4652i	0.353271	−	0.773556i
$304$	47.7549	−	14.0221i	2.73893	−	0.804222i
$305$	7.88963	+	17.2759i	0.451759	+	0.989214i
$306$	5.31717	+	6.13634i	0.303963	+	0.350791i
$307$	30.6844	−	4.41175i	1.75125	−	0.251792i	0.809264	−	0.587445i	$-0.199866\pi$
$307$	30.6844	−	4.41175i	1.75125	−	0.251792i	0.941985	+	0.335654i	$0.108957\pi$
$308$	12.6532	+	0.351228i	0.720985	+	0.0200131i
$309$	10.5182	+	9.11407i	0.598359	+	0.518481i
$310$	−19.7016	+	30.6562i	−1.11897	+	1.74116i
$311$	0.645723	−	1.00476i	0.0366156	−	0.0569750i	−0.822463	−	0.568818i	$-0.807401\pi$
$311$	0.645723	−	1.00476i	0.0366156	−	0.0569750i	0.859079	+	0.511843i	$0.171037\pi$
$312$	12.7863	−	14.7562i	0.723883	−	0.835406i
$313$	−13.4674	−	3.95440i	−0.761224	−	0.223516i	−0.121994	−	0.992531i	$-0.538929\pi$
$313$	−13.4674	−	3.95440i	−0.761224	−	0.223516i	−0.639231	+	0.769015i	$0.720747\pi$
$314$	−3.36983	−	23.4377i	−0.190171	−	1.32267i
$315$	−3.09370	+	4.53226i	−0.174310	+	0.255364i
$316$	−31.4280	+	14.3527i	−1.76796	+	0.807401i
$317$	−12.9750	+	3.80980i	−0.728748	+	0.213980i	−0.625001	−	0.780624i	$-0.714901\pi$
$317$	−12.9750	+	3.80980i	−0.728748	+	0.213980i	−0.103747	+	0.994604i	$0.533083\pi$
$318$	−0.236032	+	0.516839i	−0.0132360	+	0.0289829i
$319$	0.491864	+	0.0707193i	0.0275391	+	0.00395952i
$320$	9.71249	−	6.24184i	0.542945	−	0.348930i
$321$	15.3894			0.858951
$322$	30.8440	+	11.5394i	1.71887	+	0.643065i
$323$	17.3810			0.967107
$324$	3.98425	−	2.56052i	0.221347	−	0.142251i
$325$	−1.90031	−	0.273224i	−0.105410	−	0.0151557i
$326$	−10.3685	+	22.7039i	−0.574259	+	1.25745i
$327$	19.0558	−	5.59529i	1.05379	−	0.309420i
$328$	−33.3697	+	15.2395i	−1.84254	+	0.841458i
$329$	−26.5596	−	18.1295i	−1.46428	−	0.999509i
$330$	−0.773886	−	5.38250i	−0.0426010	−	0.296297i
$331$	−11.8353	−	3.47516i	−0.650527	−	0.191012i	−0.0602126	−	0.998186i	$-0.519178\pi$
$331$	−11.8353	−	3.47516i	−0.650527	−	0.191012i	−0.590314	+	0.807174i	$0.700996\pi$
$332$	−14.8012	+	17.0815i	−0.812322	+	0.937469i
$333$	0.204310	−	0.317913i	0.0111961	−	0.0174215i
$334$	−10.3767	+	16.1464i	−0.567786	+	0.883492i
$335$	−14.7324	−	12.7657i	−0.804917	−	0.697464i
$336$	23.6924	+	0.657654i	1.29253	+	0.0358779i
$337$	−32.2360	+	4.63483i	−1.75600	+	0.252475i	−0.943710	−	0.330773i	$-0.892691\pi$
$337$	−32.2360	+	4.63483i	−1.75600	+	0.252475i	−0.812294	+	0.583248i	$0.801781\pi$
$338$	9.24583	+	10.6703i	0.502907	+	0.580386i
$339$	3.11608	+	6.82326i	0.169242	+	0.370589i
$340$	29.4858	−	8.65780i	1.59909	−	0.469535i
$341$	2.84084	−	6.22058i	0.153840	−	0.336863i
$342$	2.05212	−	14.2728i	0.110966	−	0.771783i
$343$	−18.0491	−	4.15098i	−0.974559	−	0.224132i
$344$		−	61.4210i		−	3.31160i
$345$	1.85363	−	9.77264i	0.0997963	−	0.526141i
$346$			15.5812i			0.837653i
$347$	20.0947	−	12.9141i	1.07874	−	0.693265i	0.124475	−	0.992223i	$-0.460275\pi$
$347$	20.0947	−	12.9141i	1.07874	−	0.693265i	0.954266	+	0.298957i	$0.0966389\pi$
$348$	2.30603	+	0.331557i	0.123616	+	0.0177733i
$349$	12.3410	+	5.63593i	0.660597	+	0.301685i	0.717360	−	0.696703i	$-0.245350\pi$
$349$	12.3410	+	5.63593i	0.660597	+	0.301685i	−0.0567624	+	0.998388i	$0.518078\pi$
$350$	−2.47927	−	4.10390i	−0.132523	−	0.219363i
$351$	−1.14221	−	2.50109i	−0.0609665	−	0.133498i
$352$	−6.90766	+	5.98552i	−0.368180	+	0.319029i
$353$	−25.5982	+	3.68047i	−1.36246	+	0.195892i	−0.784476	−	0.620159i	$-0.787068\pi$
$353$	−25.5982	+	3.68047i	−1.36246	+	0.195892i	−0.577980	+	0.816051i	$0.696159\pi$
$354$	−10.5057	−	3.08475i	−0.558371	−	0.163953i
$355$	14.2102	−	16.3995i	0.754200	−	0.870393i
$356$	67.7055	+	43.5117i	3.58838	+	2.30611i
$357$	7.87403	+	2.55139i	0.416738	+	0.135034i
$358$	1.74385	−	2.01251i	0.0921654	−	0.106365i
$359$	1.51344	−	5.15429i	0.0798761	−	0.272033i	−0.909865	−	0.414904i	$-0.863815\pi$
$359$	1.51344	−	5.15429i	0.0798761	−	0.272033i	0.989741	+	0.142871i	$0.0456334\pi$
$360$	−2.09608	−	14.5785i	−0.110473	−	0.768356i
$361$	−7.77128	−	8.96853i	−0.409015	−	0.472028i
$362$	9.46800	+	20.7320i	0.497627	+	1.08965i
$363$	−2.81156	−	9.57529i	−0.147569	−	0.502572i
$364$	5.84759	−	33.9535i	0.306497	−	1.77965i
$365$	23.6886	+	3.40591i	1.23992	+	0.178273i
$366$	−12.8488	−	19.9932i	−0.671620	−	1.04506i
$367$	11.6178			0.606446			0.303223	−	0.952920i	$-0.401937\pi$
$367$	11.6178			0.606446			0.303223	+	0.952920i	$0.401937\pi$
$368$	−39.8379	+	16.0852i	−2.07670	+	0.838502i
$369$			5.16599i			0.268931i
$370$	−1.09981	−	1.71133i	−0.0571763	−	0.0889681i
$371$	0.0664903	+	0.575379i	0.00345200	+	0.0298722i
$372$	13.3188	−	29.1642i	0.690550	−	1.51209i
$373$	−2.67715	−	9.11753i	−0.138618	−	0.472088i	0.860697	−	0.509118i	$-0.170028\pi$
$373$	−2.67715	−	9.11753i	−0.138618	−	0.472088i	−0.999314	+	0.0370302i	$0.988210\pi$
$374$	−7.46101	+	3.40733i	−0.385800	+	0.176189i
$375$	−8.93186	+	7.73950i	−0.461239	+	0.399666i
$376$	85.4320	−	12.2833i	4.40582	−	0.633461i
$377$	0.381055	−	1.29775i	0.0196253	−	0.0668378i
$378$	3.02478	−	6.16468i	0.155578	−	0.317077i
$379$	−14.4188	+	22.4361i	−0.740646	+	1.15247i	0.242590	+	0.970129i	$0.422003\pi$
$379$	−14.4188	+	22.4361i	−0.740646	+	1.15247i	−0.983236	+	0.182338i	$0.941633\pi$
$380$	−45.9111	−	29.5053i	−2.35519	−	1.51359i
$381$	−10.0340	−	8.69447i	−0.514055	−	0.445431i
$382$	−5.31580	+	18.1040i	−0.271980	+	0.926279i
$383$	−1.85296	−	12.8877i	−0.0946821	−	0.658528i	−0.980792	−	0.195054i	$-0.937512\pi$
$383$	−1.85296	−	12.8877i	−0.0946821	−	0.658528i	0.886110	−	0.463474i	$-0.153397\pi$
$384$	2.75757	−	2.38945i	0.140722	−	0.121936i
$385$	−3.51248	−	4.28850i	−0.179012	−	0.218562i
$386$	26.5721	−	7.80226i	1.35248	−	0.397125i
$387$	−7.86772	−	3.59307i	−0.399939	−	0.182646i
$388$	−0.680099	+	4.73019i	−0.0345268	+	0.240139i
$389$	6.99119	+	10.8785i	0.354467	+	0.551562i	0.971999	−	0.234984i	$-0.0755037\pi$
$389$	6.99119	+	10.8785i	0.354467	+	0.551562i	−0.617532	+	0.786546i	$0.711867\pi$
$390$	−14.8010			−0.749476
$391$	−14.9313	+	1.47023i	−0.755107	+	0.0743528i
$392$	43.2440	−	24.5134i	2.18415	−	1.23811i
$393$	−14.3329	+	9.21122i	−0.723001	+	0.464645i
$394$	2.02114	−	14.0573i	0.101824	−	0.708199i
$395$	13.7632	+	6.28545i	0.692502	+	0.316255i
$396$	1.34790	+	4.59052i	0.0677344	+	0.230682i
$397$	18.5180	−	8.45688i	0.929391	−	0.424439i	0.107579	−	0.994197i	$-0.465690\pi$
$397$	18.5180	−	8.45688i	0.929391	−	0.424439i	0.821813	+	0.569758i	$0.192963\pi$
$398$	16.7774	+	19.3621i	0.840973	+	0.970534i
$399$	−5.73295	−	13.5352i	−0.287007	−	0.677610i
$400$	6.00171	+	1.76226i	0.300086	+	0.0881131i
$401$	0.173162	+	0.150046i	0.00864729	+	0.00749292i	0.659174	−	0.751991i	$-0.270906\pi$
$401$	0.173162	+	0.150046i	0.00864729	+	0.00749292i	−0.650526	+	0.759484i	$0.725452\pi$
$402$	20.5212	+	13.1882i	1.02351	+	0.657767i
$403$	−15.6587	−	10.0632i	−0.780013	−	0.501284i
$404$	52.9840	+	45.9109i	2.63605	+	2.28415i
$405$	−1.99005	−	0.584333i	−0.0988866	−	0.0290357i
$406$	3.11036	−	1.31741i	0.154364	−	0.0653822i
$407$	0.249994	+	0.288509i	0.0123918	+	0.0143009i
$408$	−20.2082	+	9.22877i	−1.00045	+	0.456892i
$409$	−5.22976	−	17.8109i	−0.258595	−	0.880694i	−0.981777	−	0.190037i	$-0.939139\pi$
$409$	−5.22976	−	17.8109i	−0.258595	−	0.880694i	0.723182	−	0.690658i	$-0.242679\pi$
$410$	25.2957	+	11.5521i	1.24926	+	0.570519i
$411$	−0.608619	+	4.23303i	−0.0300209	+	0.208800i
$412$	−55.4511	+	35.6362i	−2.73188	+	1.75567i
$413$	−10.7926	+	2.84623i	−0.531071	+	0.140054i
$414$	−0.555570	+	12.4347i	−0.0273048	+	0.611131i
$415$	9.89809			0.485878
$416$	13.4501	+	20.9287i	0.659444	+	1.02612i
$417$	0.236956	−	1.64807i	0.0116038	−	0.0807062i
$418$	13.2500	+	6.05109i	0.648081	+	0.295969i
$419$	−9.30302	+	2.73161i	−0.454482	+	0.133448i	−0.500958	−	0.865471i	$-0.667019\pi$
$419$	−9.30302	+	2.73161i	−0.454482	+	0.133448i	0.0464761	+	0.998919i	$0.485201\pi$
$420$	−16.4677	−	20.1060i	−0.803542	−	0.981070i
$421$	3.80770	−	3.29939i	0.185576	−	0.160802i	−0.557118	−	0.830433i	$-0.688093\pi$
$421$	3.80770	−	3.29939i	0.185576	−	0.160802i	0.742694	+	0.669631i	$0.233548\pi$
$422$	2.05585	+	14.2987i	0.100077	+	0.696052i
$423$	3.42426	−	11.6620i	0.166493	−	0.567024i
$424$	−1.17489	−	1.01805i	−0.0570577	−	0.0494408i
$425$	1.83764	+	1.18098i	0.0891386	+	0.0572859i
$426$	−14.6805	+	22.8433i	−0.711273	+	1.10676i
$427$	−21.7499	−	10.6719i	−1.05255	−	0.516449i
$428$	−20.5342	+	69.9330i	−0.992557	+	3.38034i
$429$	2.74929	−	0.395288i	0.132737	−	0.0190847i
$430$	−35.1875	+	30.4901i	−1.69689	+	1.47036i
$431$	26.9270	−	12.2971i	1.29703	−	0.592333i	0.357215	−	0.934022i	$-0.383726\pi$
$431$	26.9270	−	12.2971i	1.29703	−	0.592333i	0.939813	+	0.341689i	$0.110999\pi$
$432$	2.52386	+	8.59547i	0.121429	+	0.413550i
$433$	−12.7693	+	27.9609i	−0.613655	+	1.34372i	0.306391	+	0.951906i	$0.400878\pi$
$433$	−12.7693	+	27.9609i	−0.613655	+	1.34372i	−0.920046	+	0.391811i	$0.871849\pi$
$434$	−5.33631	−	46.1782i	−0.256151	−	2.21663i
$435$	−0.551594	−	0.858298i	−0.0264469	−	0.0411522i
$436$			94.0600i			4.50466i
$437$	19.3379	+	18.3300i	0.925056	+	0.876843i
$438$	−29.9477			−1.43096
$439$	−20.0437	−	31.1886i	−0.956635	−	1.48855i	−0.870440	−	0.492274i	$-0.836166\pi$
$439$	−20.0437	−	31.1886i	−0.956635	−	1.48855i	−0.0861944	−	0.996278i	$-0.527471\pi$
$440$	14.7270	+	2.11742i	0.702081	+	0.100944i
$441$	−0.610310	−	6.97334i	−0.0290624	−	0.332064i
$442$	6.28973	+	21.4208i	0.299172	+	1.01889i
$443$	−7.05817	−	15.4552i	−0.335344	−	0.734301i	0.664573	−	0.747224i	$-0.268614\pi$
$443$	−7.05817	−	15.4552i	−0.335344	−	0.734301i	−0.999916	+	0.0129231i	$0.995886\pi$
$444$	1.17206	+	1.35263i	0.0556235	+	0.0641930i
$445$	−5.01592	−	34.8865i	−0.237777	−	1.65378i
$446$	−19.7682	+	67.3242i	−0.936049	+	3.18789i
$447$	1.60423	−	1.85138i	0.0758776	−	0.0875674i
$448$	−4.53972	+	14.0104i	−0.214482	+	0.661929i
$449$	5.61401	+	3.60791i	0.264942	+	0.170268i	0.666367	−	0.745624i	$-0.267849\pi$
$449$	5.61401	+	3.60791i	0.264942	+	0.170268i	−0.401425	+	0.915892i	$0.631485\pi$
$450$	1.18675	−	1.36958i	0.0559438	−	0.0645626i
$451$	−5.00720	−	1.47025i	−0.235780	−	0.0692312i
$452$	−35.1644	+	5.05587i	−1.65399	+	0.237808i
$453$	−0.512914	+	0.444442i	−0.0240988	+	0.0208817i
$454$	13.2028	+	28.9101i	0.619638	+	1.35682i
$455$	−12.9144	+	7.80192i	−0.605436	+	0.365759i
$456$	35.8878	+	16.3894i	1.68060	+	0.767505i
$457$	14.6726	+	2.10960i	0.686355	+	0.0986829i	0.476665	−	0.879085i	$-0.341846\pi$
$457$	14.6726	+	2.10960i	0.686355	+	0.0986829i	0.209690	+	0.977768i	$0.432755\pi$
$458$	−30.9760	+	19.9070i	−1.44741	+	0.930195i
$459$			3.12844i			0.146023i
$460$	41.9359	+	21.4631i	1.95527	+	1.00072i
$461$			19.3620i			0.901780i	0.892580	+	0.450890i	$0.148893\pi$
$461$			19.3620i			0.901780i	−0.892580	+	0.450890i	$0.851107\pi$
$462$	5.11435	+	4.68629i	0.237941	+	0.218026i
$463$	1.84806	−	12.8535i	0.0858865	−	0.597354i	−0.900740	−	0.434358i	$-0.856975\pi$
$463$	1.84806	−	12.8535i	0.0858865	−	0.597354i	0.986627	−	0.162996i	$-0.0521157\pi$
$464$	−1.83062	+	4.00850i	−0.0849844	+	0.186090i
$465$	−13.4719	+	3.95571i	−0.624746	+	0.183442i
$466$	−30.8419	−	67.5344i	−1.42872	−	3.12847i
$467$	−18.3242	−	21.1472i	−0.847942	−	0.978577i	0.152010	−	0.988379i	$-0.451425\pi$
$467$	−18.3242	−	21.1472i	−0.847942	−	0.978577i	−0.999952	+	0.00980155i	$0.996880\pi$
$468$	12.8896	−	1.85325i	0.595822	−	0.0856663i
$469$	24.8573	+	0.689988i	1.14780	+	0.0318607i
$470$	−49.4464	−	42.8455i	−2.28079	−	1.97632i
$471$	4.93245	−	7.67504i	0.227275	−	0.353647i
$472$	16.1965	−	25.2023i	0.745505	−	1.16003i
$473$	5.72179	−	6.60330i	0.263088	−	0.303620i
$474$	−18.1667	−	5.33423i	−0.834425	−	0.245009i
$475$	−0.552082	−	3.83981i	−0.0253312	−	0.176183i
$476$	−22.1005	+	32.3772i	−1.01298	+	1.48401i
$477$	−0.199137	+	0.0909426i	−0.00911784	+	0.00416398i
$478$	70.9851	−	20.8431i	3.24678	−	0.953342i
$479$	−3.88339	+	8.50345i	−0.177437	+	0.388532i	−0.977364	−	0.211565i	$-0.932144\pi$
$479$	−3.88339	+	8.50345i	−0.177437	+	0.388532i	0.799927	+	0.600097i	$0.204871\pi$
$480$	18.5752	+	2.67071i	0.847837	+	0.121901i
$481$	0.874120	−	0.561763i	0.0398564	−	0.0256142i
$482$	−64.4470			−2.93548
$483$	6.06984	+	11.1426i	0.276187	+	0.507005i
$484$	47.2639			2.14836
$485$	1.76057	−	1.13145i	0.0799432	−	0.0513764i
$486$	2.56898	+	0.369364i	0.116531	+	0.0167547i
$487$	−17.9230	+	39.2460i	−0.812170	+	1.77840i	−0.214384	+	0.976749i	$0.568774\pi$
$487$	−17.9230	+	39.2460i	−0.812170	+	1.77840i	−0.597786	+	0.801655i	$0.703953\pi$
$488$	62.3917	−	18.3199i	2.82434	−	0.829301i
$489$	−8.74774	+	3.99496i	−0.395587	+	0.180658i
$490$	−35.5103	−	12.6053i	−1.60419	−	0.569450i
$491$	4.22050	+	29.3542i	0.190468	+	1.32474i	0.830771	+	0.556614i	$0.187900\pi$
$491$	4.22050	+	29.3542i	0.190468	+	1.32474i	−0.640303	+	0.768123i	$0.721191\pi$
$492$	−23.4755	−	6.89303i	−1.05836	−	0.310762i
$493$	−1.00778	+	1.16304i	−0.0453880	+	0.0523806i
$494$	21.4350	−	33.3535i	0.964406	−	1.50064i
$495$	1.13274	−	1.76258i	0.0509131	−	0.0792223i
$496$	45.8322	+	39.7138i	2.05793	+	1.78320i
$497$	−0.768065	+	27.6701i	−0.0344524	+	1.24117i
$498$	−12.2600	+	1.76272i	−0.549382	+	0.0789892i
$499$	−5.33474	−	6.15662i	−0.238816	−	0.275608i	0.623672	−	0.781686i	$-0.285640\pi$
$499$	−5.33474	−	6.15662i	−0.238816	−	0.275608i	−0.862488	+	0.506078i	$0.831095\pi$
$500$	−23.2523	−	50.9154i	−1.03987	−	2.27701i
$501$	−7.09556	+	2.08345i	−0.317006	+	0.0930815i
$502$	−2.24450	+	4.91478i	−0.100177	+	0.219357i
$503$	−1.29185	+	8.98504i	−0.0576009	+	0.400623i	0.940540	+	0.339682i	$0.110319\pi$
$503$	−1.29185	+	8.98504i	−0.0576009	+	0.400623i	−0.998141	+	0.0609413i	$0.980590\pi$
$504$	13.8522	+	12.6928i	0.617028	+	0.565384i
$505$		−	30.7023i		−	1.36623i
$506$	−11.8944	−	4.07742i	−0.528769	−	0.181264i
$507$			5.43993i			0.241596i
$508$	52.8982	−	33.9956i	2.34698	−	1.50831i
$509$	16.1695	+	2.32482i	0.716701	+	0.103046i	0.491011	−	0.871153i	$-0.336627\pi$
$509$	16.1695	+	2.32482i	0.716701	+	0.103046i	0.225690	+	0.974199i	$0.427536\pi$
$510$	15.3187	+	6.99579i	0.678321	+	0.309779i
$511$	−26.1305	+	15.7861i	−1.15594	+	0.698336i
$512$	19.1820	+	42.0027i	0.847732	+	1.85627i
$513$	4.19880	−	3.63828i	0.185382	−	0.160634i
$514$	−21.5602	+	3.09989i	−0.950981	+	0.136730i
$515$	27.6967	+	8.13249i	1.22046	+	0.358360i
$516$	26.8258	−	30.9586i	1.18094	−	1.36287i
$517$	10.3290	+	6.63802i	0.454267	+	0.291940i
$518$	2.46862	+	0.799896i	0.108465	+	0.0351454i
$519$	−3.93140	+	4.53708i	−0.172569	+	0.199156i
$520$	11.4092	−	38.8563i	0.500328	−	1.70396i
$521$	−0.822922	−	5.72355i	−0.0360529	−	0.250753i	0.963822	−	0.266545i	$-0.0858822\pi$
$521$	−0.822922	−	5.72355i	−0.0360529	−	0.250753i	−0.999875	+	0.0157919i	$0.994973\pi$
$522$	0.836066	+	0.964872i	0.0365936	+	0.0422313i
$523$	0.508065	+	1.11251i	0.0222161	+	0.0486465i	0.920415	−	0.390943i	$-0.127851\pi$
$523$	0.508065	+	1.11251i	0.0222161	+	0.0486465i	−0.898199	+	0.439590i	$0.855124\pi$
$524$	−22.7334	−	77.4230i	−0.993115	−	3.38224i
$525$	0.313545	−	1.82057i	0.0136842	−	0.0794562i
$526$	−55.2906	−	7.94959i	−2.41079	−	0.346619i
$527$	11.4499	+	17.8164i	0.498765	+	0.776094i
$528$	−9.04957			−0.393832
$529$	−18.1628	−	14.1107i	−0.789687	−	0.613510i
$530$			1.17845i			0.0511887i
$531$	−2.28080	−	3.54900i	−0.0989784	−	0.154013i
$532$	69.1570	−	7.99172i	2.99833	−	0.346485i
$533$	−5.90063	+	12.9206i	−0.255585	+	0.559652i
$534$	12.4256	+	42.3178i	0.537709	+	1.83127i
$535$	29.0342	−	13.2595i	1.25526	−	0.573257i
$536$	−50.4410	+	43.7074i	−2.17872	+	1.88787i
$537$	1.01558	−	0.146018i	0.0438254	−	0.00630115i
$538$	15.7739	−	53.7210i	0.680061	−	2.31608i
$539$	6.93270	+	1.39307i	0.298613	+	0.0600039i
$540$	5.31070	−	8.26361i	0.228536	−	0.355609i
$541$	26.8117	+	17.2308i	1.15272	+	0.740810i	0.970180	−	0.242388i	$-0.0779305\pi$
$541$	26.8117	+	17.2308i	1.15272	+	0.740810i	0.182544	+	0.983198i	$0.441567\pi$
$542$	−25.1812	−	21.8196i	−1.08162	−	0.937232i
$543$	−2.47405	+	8.42585i	−0.106172	+	0.361588i
$544$	−4.02839	−	28.0180i	−0.172716	−	1.20126i
$545$	31.1305	−	26.9748i	1.33349	−	1.15547i
$546$	14.6066	−	11.9635i	0.625104	−	0.511990i
$547$	23.4102	−	6.87386i	1.00095	−	0.293905i	0.260104	−	0.965581i	$-0.416243\pi$
$547$	23.4102	−	6.87386i	1.00095	−	0.293905i	0.740845	+	0.671676i	$0.234425\pi$
$548$	−18.4239	−	8.41389i	−0.787028	−	0.359424i
$549$	1.30317	−	9.06375i	0.0556180	−	0.386832i
$550$	0.989733	+	1.54005i	0.0422024	+	0.0656681i
$551$	2.73298			0.116429
$552$	−32.2160	−	11.0437i	−1.37120	−	0.470052i
$553$	−18.6629	+	4.92177i	−0.793629	+	0.209295i
$554$	−16.3748	+	10.5234i	−0.695699	+	0.447098i
$555$	0.111546	−	0.775820i	0.00473487	−	0.0329317i
$556$	7.17304	+	3.27582i	0.304205	+	0.138926i
$557$	−3.63224	−	12.3703i	−0.153903	−	0.524145i	0.846057	−	0.533092i	$-0.178970\pi$
$557$	−3.63224	−	12.3703i	−0.153903	−	0.524145i	−0.999960	+	0.00894714i	$0.997152\pi$
$558$	15.9821	−	7.29879i	0.676577	−	0.308982i
$559$	−15.5738	−	17.9731i	−0.658702	−	0.760183i
$560$	45.2657	−	19.1726i	1.91283	−	0.810192i
$561$	−3.03228	−	0.890359i	−0.128023	−	0.0375910i
$562$	38.1262	+	33.0365i	1.60826	+	1.39356i
$563$	−33.1104	−	21.2787i	−1.39544	−	0.896792i	−0.395669	−	0.918393i	$-0.629487\pi$
$563$	−33.1104	−	21.2787i	−1.39544	−	0.896792i	−0.999767	+	0.0216015i	$0.993124\pi$
$564$	48.4258	+	31.1213i	2.03909	+	1.31045i
$565$	11.7578	+	10.1882i	0.494656	+	0.428622i
$566$	39.3684	+	11.5596i	1.65478	+	0.485886i
$567$	2.43623	−	1.03188i	0.102312	−	0.0433350i
$568$	−48.6532	−	56.1488i	−2.04144	−	2.35595i
$569$	23.1176	−	10.5575i	0.969141	−	0.442592i	0.133006	−	0.991115i	$-0.457537\pi$
$569$	23.1176	−	10.5575i	0.969141	−	0.442592i	0.836135	+	0.548523i	$0.184810\pi$
$570$	−8.42581	−	28.6957i	−0.352918	−	1.20193i
$571$	−29.0788	−	13.2799i	−1.21691	−	0.555745i	−0.299657	−	0.954047i	$-0.596872\pi$
$571$	−29.0788	−	13.2799i	−1.21691	−	0.555745i	−0.917254	+	0.398302i	$0.869600\pi$
$572$	−1.87212	+	13.0209i	−0.0782771	+	0.544429i
$573$	−6.11582	+	3.93040i	−0.255492	+	0.164195i
$574$	−34.3009	+	9.04581i	−1.43169	+	0.377565i
$575$	0.799072	+	3.25191i	0.0333236	+	0.135614i
$576$	−5.56648			−0.231937
$577$	−2.55491	−	3.97552i	−0.106362	−	0.165503i	0.783992	−	0.620770i	$-0.213180\pi$
$577$	−2.55491	−	3.97552i	−0.106362	−	0.165503i	−0.890355	+	0.455267i	$0.849544\pi$
$578$	−2.66417	+	18.5297i	−0.110815	+	0.770733i
$579$	9.70612	+	4.43263i	0.403372	+	0.184214i
$580$	4.63631	−	1.36134i	0.192512	−	0.0565267i
$581$	−9.76810	+	8.00053i	−0.405249	+	0.331918i
$582$	−1.97917	+	1.71496i	−0.0820394	+	0.0710876i
$583$	−0.0314728	−	0.218898i	−0.00130347	−	0.00906584i
$584$	23.0850	−	78.6204i	0.955265	−	3.25333i
$585$	−4.30987	−	3.73452i	−0.178191	−	0.154403i
$586$	−66.6893	−	42.8586i	−2.75491	−	1.77047i
$587$	8.23270	−	12.8103i	0.339800	−	0.528739i	−0.628734	−	0.777620i	$-0.716427\pi$
$587$	8.23270	−	12.8103i	0.339800	−	0.528739i	0.968534	+	0.248881i	$0.0800629\pi$
$588$	32.5029	+	6.53120i	1.34040	+	0.269342i
$589$	10.5962	−	36.0873i	0.436608	−	1.48695i
$590$	−22.4783	+	3.23189i	−0.925415	+	0.133055i
$591$	4.13543	−	3.58337i	0.170109	−	0.147400i
$592$	−3.07946	+	1.40634i	−0.126565	+	0.0578004i
$593$	1.49731	+	5.09936i	0.0614871	+	0.209406i	0.984507	−	0.175347i	$-0.0561048\pi$
$593$	1.49731	+	5.09936i	0.0614871	+	0.209406i	−0.923020	+	0.384753i	$0.874287\pi$
$594$	−1.08915	+	2.38490i	−0.0446882	+	0.0978535i
$595$	17.0537	−	1.97071i	0.699135	−	0.0807914i
$596$	6.27259	+	9.76034i	0.256935	+	0.399799i
$597$			9.87121i			0.404002i
$598$	−15.5925	+	30.4656i	−0.637626	+	1.24583i
$599$	−26.2794			−1.07375			−0.536874	−	0.843663i	$-0.680395\pi$
$599$	−26.2794			−1.07375			−0.536874	+	0.843663i	$0.680395\pi$
$600$	2.68070	+	4.17125i	0.109439	+	0.170291i
$601$	12.9958	+	1.86852i	0.530111	+	0.0762184i	0.402173	−	0.915564i	$-0.368255\pi$
$601$	12.9958	+	1.86852i	0.530111	+	0.0762184i	0.127938	+	0.991782i	$0.459164\pi$
$602$	10.0805	−	58.5314i	0.410850	−	2.38556i
$603$	2.64795	+	9.01808i	0.107833	+	0.367245i
$604$	−1.33527	−	2.92383i	−0.0543313	−	0.118969i
$605$	−13.5545	−	15.6427i	−0.551067	−	0.635965i
$606$	5.46766	+	38.0284i	0.222108	+	1.54480i
$607$	−3.06319	+	10.4323i	−0.124331	+	0.423433i	−0.998009	−	0.0630720i	$-0.979910\pi$
$607$	−3.06319	+	10.4323i	−0.124331	+	0.423433i	0.873678	+	0.486505i	$0.161728\pi$
$608$	−32.9192	+	37.9908i	−1.33505	+	1.54073i
$609$	1.23810	+	0.401177i	0.0501705	+	0.0162565i
$610$	−41.4672	−	26.6494i	−1.67896	−	1.07900i
$611$	21.8848	−	25.2564i	0.885363	−	1.02176i
$612$	−14.2164	−	4.17431i	−0.574664	−	0.168736i
$613$	4.19384	−	0.602984i	0.169388	−	0.0243543i	−0.0570990	−	0.998369i	$-0.518185\pi$
$613$	4.19384	−	0.602984i	0.169388	−	0.0243543i	0.226487	+	0.974014i	$0.427276\pi$
$614$	−60.8054	+	52.6882i	−2.45391	+	2.12632i
$615$	4.45101	+	9.74635i	0.179482	+	0.393011i
$616$	−16.2451	+	9.81407i	−0.654533	+	0.395420i
$617$	−11.9294	−	5.44798i	−0.480260	−	0.219327i	0.160549	−	0.987028i	$-0.448674\pi$
$617$	−11.9294	−	5.44798i	−0.480260	−	0.219327i	−0.640809	+	0.767700i	$0.721401\pi$
$618$	−35.7540	−	5.14064i	−1.43824	−	0.206787i
$619$	−26.1921	+	16.8326i	−1.05275	+	0.676560i	−0.948107	−	0.317950i	$-0.897006\pi$
$619$	−26.1921	+	16.8326i	−1.05275	+	0.676560i	−0.104641	+	0.994510i	$0.533369\pi$
$620$		−	66.4978i		−	2.67062i
$621$	−3.29925	+	3.48066i	−0.132394	+	0.139674i
$622$			3.09985i			0.124293i
$623$	33.1485	+	30.3740i	1.32806	+	1.21691i
$624$	−3.50543	+	24.3808i	−0.140329	+	0.976013i
$625$	−8.73254	+	19.1216i	−0.349302	+	0.764864i
$626$	34.9533	−	10.2632i	1.39702	−	0.410201i
$627$	2.33147	+	5.10521i	0.0931100	+	0.203882i
$628$	28.2958	+	32.6551i	1.12913	+	1.30308i
$629$	−1.17022	+	0.168252i	−0.0466596	+	0.00670863i
$630$	0.395181	−	14.2367i	0.0157444	−	0.567203i
$631$	15.8261	+	13.7134i	0.630029	+	0.545923i	0.910274	−	0.414005i	$-0.135871\pi$
$631$	15.8261	+	13.7134i	0.630029	+	0.545923i	−0.280246	+	0.959928i	$0.590416\pi$
$632$	28.0075	−	43.5804i	1.11408	−	1.73354i
$633$	−3.00917	+	4.68235i	−0.119604	+	0.186107i
$634$	22.9836	−	26.5245i	0.912795	−	1.05342i
$635$	−26.4216	−	7.75808i	−1.04851	−	0.307870i
$636$	−0.147555	−	1.02627i	−0.00585096	−	0.0406943i
$637$	6.43857	−	18.1380i	0.255105	−	0.718655i
$638$	−1.17316	+	0.535765i	−0.0464459	+	0.0212111i
$639$	−10.0385	+	2.94758i	−0.397118	+	0.116604i
$640$	3.14379	−	6.88395i	0.124269	−	0.272112i
$641$	8.85888	+	1.27372i	0.349905	+	0.0503087i	0.315027	−	0.949083i	$-0.397987\pi$
$641$	8.85888	+	1.27372i	0.349905	+	0.0503087i	0.0348783	+	0.999392i	$0.488896\pi$
$642$	−33.6009	+	21.5940i	−1.32612	+	0.852248i
$643$	−41.3988			−1.63261			−0.816304	−	0.577622i	$-0.803981\pi$
$643$	−41.3988			−1.63261			−0.816304	+	0.577622i	$0.803981\pi$
$644$	−58.7336	+	12.7152i	−2.31443	+	0.501049i
$645$	−17.9393			−0.706360
$646$	−37.9495	+	24.3887i	−1.49310	+	0.959560i
$647$	28.4763	+	4.09427i	1.11952	+	0.160962i	0.677132	−	0.735862i	$-0.263223\pi$
$647$	28.4763	+	4.09427i	1.11952	+	0.160962i	0.442387	+	0.896824i	$0.354132\pi$
$648$	−2.94996	+	6.45951i	−0.115885	+	0.253754i
$649$	4.08903	−	1.20065i	0.160509	−	0.0471296i
$650$	4.53250	−	2.06992i	0.177779	−	0.0811891i
$651$	10.0976	−	14.7930i	0.395758	−	0.579783i
$652$	−6.48187	−	45.0824i	−0.253850	−	1.76556i
$653$	−8.76888	−	2.57478i	−0.343153	−	0.100759i	0.105615	−	0.994407i	$-0.466319\pi$
$653$	−8.76888	−	2.57478i	−0.343153	−	0.100759i	−0.448768	+	0.893648i	$0.648137\pi$
$654$	−33.7550	+	38.9554i	−1.31993	+	1.52328i
$655$	−19.1047	+	29.7275i	−0.746483	+	1.16155i
$656$	25.0202	−	38.9321i	0.976873	−	1.52004i
$657$	−8.72042	−	7.55629i	−0.340216	−	0.294799i
$658$	83.4287	+	2.31581i	3.25239	+	0.0902797i
$659$	31.5462	−	4.53566i	1.22887	−	0.176684i	0.502857	−	0.864369i	$-0.332282\pi$
$659$	31.5462	−	4.53566i	1.22887	−	0.176684i	0.726009	+	0.687685i	$0.241373\pi$
$660$	6.49818	+	7.49930i	0.252941	+	0.291910i
$661$	−7.85300	−	17.1957i	−0.305446	−	0.668834i	0.693206	−	0.720740i	$-0.256198\pi$
$661$	−7.85300	−	17.1957i	−0.305446	−	0.668834i	−0.998652	+	0.0519056i	$0.983470\pi$
$662$	30.7173	−	9.01941i	1.19386	−	0.350549i
$663$	−3.57333	+	7.82450i	−0.138777	+	0.303878i
$664$	4.82295	−	33.5443i	0.187167	−	1.30177i
$665$	−22.4780	−	20.5966i	−0.871658	−	0.798702i
$666$			0.980810i			0.0380056i
$667$	−2.34778	+	0.231178i	−0.0909062	+	0.00895124i
$668$		−	35.0239i		−	1.35512i
$669$	−22.7432	+	14.6162i	−0.879304	+	0.565094i
$670$	50.0790	+	7.20028i	1.93472	+	0.278171i
$671$	8.41428	+	3.84267i	0.324830	+	0.148345i
$672$	−20.4899	+	12.3785i	−0.790417	+	0.477511i
$673$	3.15616	+	6.91103i	0.121661	+	0.266401i	0.960657	−	0.277737i	$-0.0895843\pi$
$673$	3.15616	+	6.91103i	0.121661	+	0.266401i	−0.838996	+	0.544137i	$0.816857\pi$
$674$	63.8801	−	55.3524i	2.46057	−	2.13209i
$675$	0.691134	−	0.0993701i	0.0266018	−	0.00382476i
$676$	−24.7204	−	7.25855i	−0.950783	−	0.279175i
$677$	19.4910	−	22.4938i	0.749099	−	0.864506i	−0.245382	−	0.969427i	$-0.578913\pi$
$677$	19.4910	−	22.4938i	0.749099	−	0.864506i	0.994481	+	0.104920i	$0.0334587\pi$
$678$	−16.3779	−	10.5254i	−0.628988	−	0.404226i
$679$	−0.822907	+	2.53964i	−0.0315803	+	0.0974623i
$680$	−30.1741	+	34.8227i	−1.15712	+	1.33539i
$681$	−3.44998	+	11.7496i	−0.132204	+	0.450244i
$682$	2.52592	+	17.5681i	0.0967223	+	0.672718i
$683$	1.49058	+	1.72022i	0.0570354	+	0.0658224i	0.783550	−	0.621328i	$-0.213407\pi$
$683$	1.49058	+	1.72022i	0.0570354	+	0.0658224i	−0.726515	+	0.687151i	$0.758861\pi$
$684$	10.9307	+	23.9350i	0.417947	+	0.915177i
$685$	2.49894	+	8.51059i	0.0954794	+	0.325173i
$686$	45.2327	−	16.2629i	1.72699	−	0.620919i
$687$	−14.0427	−	2.01904i	−0.535763	−	0.0770310i
$688$	41.8909	+	65.1836i	1.59708	+	2.48510i
$689$	−0.601933			−0.0229318
$690$	9.66555	+	23.9384i	0.367961	+	0.911321i
$691$			12.7125i			0.483608i	0.970325	+	0.241804i	$0.0777391\pi$
$691$			12.7125i			0.483608i	−0.970325	+	0.241804i	$0.922261\pi$
$692$	−15.3719	−	23.9191i	−0.584351	−	0.909268i
$693$	0.306812	+	2.65502i	0.0116548	+	0.100856i
$694$	−25.7538	+	56.3930i	−0.977601	+	2.14065i
$695$	−0.972922	−	3.31347i	−0.0369050	−	0.125687i
$696$	−3.17751	+	1.45112i	−0.120443	+	0.0550046i
$697$	12.2140	−	10.5835i	0.462640	−	0.400879i
$698$	−34.8533	+	5.01115i	−1.31922	+	0.189675i
$699$	8.05921	−	27.4471i	0.304827	−	1.03815i
$700$	7.85474	+	3.85403i	0.296881	+	0.145669i
$701$	−10.4228	+	16.2182i	−0.393663	+	0.612552i	−0.980351	−	0.197261i	$-0.936795\pi$
$701$	−10.4228	+	16.2182i	−0.393663	+	0.612552i	0.586688	+	0.809813i	$0.300432\pi$
$702$	6.00335	+	3.85812i	0.226582	+	0.145615i
$703$	1.58674	+	1.37492i	0.0598452	+	0.0518561i
$704$	1.58423	−	5.39539i	0.0597079	−	0.203346i
$705$	−3.58759	−	24.9523i	−0.135117	−	0.939756i
$706$	50.7265	−	43.9548i	1.90912	−	1.65426i
$707$	24.8164	+	30.2991i	0.933315	+	1.13951i
$708$	19.1708	−	5.62906i	0.720483	−	0.211553i
$709$	−4.93459	−	2.25355i	−0.185322	−	0.0846339i	0.320593	−	0.947217i	$-0.396118\pi$
$709$	−4.93459	−	2.25355i	−0.185322	−	0.0846339i	−0.505915	+	0.862583i	$0.668845\pi$
$710$	−8.01504	+	55.7458i	−0.300799	+	2.09210i
$711$	−3.94403	−	6.13702i	−0.147913	−	0.230156i
$712$	−120.673			−4.52242
$713$	−6.05014	+	31.8973i	−0.226580	+	1.19456i
$714$	−20.7721	+	5.47800i	−0.777377	+	0.205009i
$715$	4.84633	−	3.11455i	0.181242	−	0.116477i
$716$	−0.691555	+	4.80987i	−0.0258446	+	0.179753i
$717$	25.9291	+	11.8414i	0.968340	+	0.442226i
$718$	3.92797	+	13.3774i	0.146591	+	0.499241i
$719$	12.2401	−	5.58987i	0.456479	−	0.208467i	−0.173886	−	0.984766i	$-0.555632\pi$
$719$	12.2401	−	5.58987i	0.456479	−	0.208467i	0.630365	+	0.776299i	$0.282905\pi$
$720$	12.1675	+	14.0420i	0.453455	+	0.523314i
$721$	−33.9064	+	14.3613i	−1.26274	+	0.534843i
$722$	29.5522	+	8.67730i	1.09982	+	0.322936i
$723$	−18.7662	−	16.2610i	−0.697923	−	0.604753i
$724$	−34.9880	−	22.4854i	−1.30032	−	0.835663i
$725$	0.288948	+	0.185696i	0.0107313	+	0.00689657i
$726$	19.5746	+	16.9614i	0.726480	+	0.629498i
$727$	−21.7072	−	6.37380i	−0.805074	−	0.236391i	−0.146797	−	0.989167i	$-0.546896\pi$
$727$	−21.7072	−	6.37380i	−0.805074	−	0.236391i	−0.658277	+	0.752776i	$0.728715\pi$
$728$	20.1478	+	47.5680i	0.746727	+	1.76299i
$729$	0.654861	+	0.755750i	0.0242541	+	0.0279907i
$730$	−56.5005	+	25.8029i	−2.09118	+	0.955008i
$731$	7.62339	+	25.9629i	0.281961	+	0.960272i
$732$	39.4491	+	18.0158i	1.45808	+	0.665882i
$733$	−1.68799	+	11.7402i	−0.0623473	+	0.433635i	0.934609	+	0.355676i	$0.115749\pi$
$733$	−1.68799	+	11.7402i	−0.0623473	+	0.433635i	−0.996957	+	0.0779588i	$0.975160\pi$
$734$	−25.3662	+	16.3019i	−0.936285	+	0.601714i
$735$	−7.15966	−	12.6303i	−0.264088	−	0.465877i
$736$	25.0659	−	35.4208i	0.923940	−	1.30563i
$737$	−9.49450			−0.349735
$738$	−7.24880	−	11.2793i	−0.266832	−	0.415199i
$739$	−6.67249	+	46.4082i	−0.245451	+	1.70715i	0.378427	+	0.925631i	$0.376465\pi$
$739$	−6.67249	+	46.4082i	−0.245451	+	1.70715i	−0.623879	+	0.781521i	$0.714444\pi$
$740$	3.37668	+	1.54208i	0.124129	+	0.0566879i
$741$	14.6572	−	4.30376i	0.538447	−	0.158102i
$742$	−0.952533	−	1.16298i	−0.0349686	−	0.0426942i
$743$	2.74294	−	2.37677i	0.100629	−	0.0871952i	−0.603094	−	0.797670i	$-0.706065\pi$
$743$	2.74294	−	2.37677i	0.100629	−	0.0871952i	0.703722	+	0.710475i	$0.251520\pi$
$744$	6.84146	+	47.5834i	0.250820	+	1.74449i
$745$	1.43146	−	4.87510i	0.0524445	−	0.178610i
$746$	18.6388	+	16.1506i	0.682414	+	0.591315i
$747$	−4.01472	−	2.58010i	−0.146891	−	0.0944011i
$748$	8.09201	−	12.5914i	0.295873	−	0.460388i
$749$	−17.9354	+	36.5534i	−0.655344	+	1.33563i
$750$	8.64181	−	29.4313i	0.315554	−	1.07468i
$751$	10.4135	−	1.49723i	0.379993	−	0.0546347i	0.0503278	−	0.998733i	$-0.483973\pi$
$751$	10.4135	−	1.49723i	0.379993	−	0.0546347i	0.329665	+	0.944098i	$0.393064\pi$
$752$	−82.2879	+	71.3028i	−3.00073	+	2.60015i
$753$	−1.89365	+	0.864802i	−0.0690085	+	0.0315151i
$754$	0.988990	+	3.36819i	0.0360169	+	0.122662i
$755$	−0.584752	+	1.28043i	−0.0212813	+	0.0465995i
$756$	1.43844	+	12.4477i	0.0523156	+	0.452717i
$757$	−17.6822	−	27.5140i	−0.642669	−	1.00001i	−0.997871	−	0.0652231i	$-0.979224\pi$
$757$	−17.6822	−	27.5140i	−0.642669	−	1.00001i	0.355201	−	0.934790i	$-0.384412\pi$
$758$		−	69.2190i		−	2.51415i
$759$	−2.43470	−	4.18844i	−0.0883741	−	0.152031i
$760$	81.8285			2.96823
$761$	−13.6250	−	21.2010i	−0.493907	−	0.768535i	0.501408	−	0.865211i	$-0.332815\pi$
$761$	−13.6250	−	21.2010i	−0.493907	−	0.768535i	−0.995316	+	0.0966757i	$0.969179\pi$
$762$	34.1079	+	4.90398i	1.23560	+	0.177652i
$763$	−8.91826	+	51.7830i	−0.322863	+	1.87467i
$764$	−9.70029	−	33.0362i	−0.350944	−	1.19521i
$765$	2.69546	+	5.90224i	0.0974546	+	0.213396i
$766$	22.1294	+	25.5387i	0.799568	+	0.922751i
$767$	−1.65079	−	11.4815i	−0.0596066	−	0.414573i
$768$	−5.80454	+	19.7685i	−0.209453	+	0.713333i
$769$	−7.94297	+	9.16667i	−0.286431	+	0.330559i	−0.880671	−	0.473729i	$-0.842908\pi$
$769$	−7.94297	+	9.16667i	−0.286431	+	0.330559i	0.594240	+	0.804288i	$0.297453\pi$
$770$	13.6866	+	4.43481i	0.493232	+	0.159820i
$771$	−7.06024	−	4.53734i	−0.254268	−	0.163408i
$772$	−33.0939	+	38.1924i	−1.19108	+	1.37458i
$773$	−17.2032	−	5.05132i	−0.618756	−	0.181683i	−0.0426928	−	0.999088i	$-0.513594\pi$
$773$	−17.2032	−	5.05132i	−0.618756	−	0.181683i	−0.576063	+	0.817405i	$0.695412\pi$
$774$	22.2200	−	3.19475i	0.798681	−	0.114833i
$775$	3.57230	−	3.09542i	0.128321	−	0.111191i
$776$	−2.97659	−	6.51781i	−0.106853	−	0.233976i
$777$	0.517007	+	0.855793i	0.0185475	+	0.0307014i
$778$	−30.5290	−	13.9421i	−1.09452	−	0.499849i
$779$	−28.4091	−	4.08462i	−1.01786	−	0.146347i
$780$	22.7213	−	14.6021i	0.813552	−	0.522838i
$781$		−	10.5689i		−	0.378184i
$782$	30.5377	−	24.1613i	1.09203	−	0.864007i
$783$			0.491913i			0.0175795i
$784$	−29.1742	+	55.5087i	−1.04194	+	1.98245i
$785$	2.69294	−	18.7298i	0.0961153	−	0.668496i
$786$	18.3694	−	40.2233i	0.655214	−	1.43472i
$787$	39.3249	−	11.5468i	1.40178	−	0.411600i	0.508486	−	0.861070i	$-0.330205\pi$
$787$	39.3249	−	11.5468i	1.40178	−	0.411600i	0.893295	+	0.449470i	$0.148387\pi$
$788$	10.7658	+	23.5737i	0.383514	+	0.839779i
$789$	−14.0942	−	16.2655i	−0.501766	−	0.579069i
$790$	−38.8700	+	5.58866i	−1.38293	+	0.198836i
$791$	−19.8385	−	0.550675i	−0.705375	−	0.0195798i
$792$	−5.42140	−	4.69767i	−0.192641	−	0.166925i
$793$	13.6120	−	21.1807i	0.483377	−	0.752150i
$794$	−28.5654	+	44.4487i	−1.01375	+	1.57742i
$795$	−0.297343	+	0.343152i	−0.0105457	+	0.0121703i
$796$	−44.8572	−	13.1713i	−1.58992	−	0.466843i
$797$	3.24842	+	22.5932i	0.115065	+	0.800293i	0.962866	+	0.269979i	$0.0870168\pi$
$797$	3.24842	+	22.5932i	0.115065	+	0.800293i	−0.847801	+	0.530314i	$0.822074\pi$
$798$	31.5096	+	21.5083i	1.11543	+	0.761386i
$799$	−34.5878	+	15.7957i	−1.22363	+	0.558813i
$800$	−6.06178	+	1.77990i	−0.214316	+	0.0629290i
$801$	−7.05926	+	15.4576i	−0.249427	+	0.546168i
$802$	−0.588620	−	0.0846308i	−0.0207849	−	0.00298842i
$803$	9.80588	−	6.30185i	0.346042	−	0.222388i
$804$	−44.5135			−1.56987
$805$	21.0520	+	15.7922i	0.741987	+	0.556603i
$806$	48.3094			1.70163
$807$	18.1479	−	11.6629i	0.638835	−	0.410554i
$808$	−104.049	−	14.9600i	−3.66043	−	0.526291i
$809$	19.8180	−	43.3954i	0.696764	−	1.52570i	−0.147088	−	0.989123i	$-0.546990\pi$
$809$	19.8180	−	43.3954i	0.696764	−	1.52570i	0.843852	−	0.536576i	$-0.180283\pi$
$810$	5.16498	−	1.51658i	0.181479	−	0.0532870i
$811$	22.5396	−	10.2935i	0.791473	−	0.361454i	0.0216944	−	0.999765i	$-0.493094\pi$
$811$	22.5396	−	10.2935i	0.791473	−	0.361454i	0.769779	+	0.638311i	$0.220367\pi$
$812$	−3.47506	+	5.09095i	−0.121951	+	0.178657i
$813$	−1.82702	−	12.7072i	−0.0640765	−	0.445662i
$814$	−0.950664	−	0.279140i	−0.0333207	−	0.00978385i
$815$	−13.0618	+	15.0741i	−0.457534	+	0.528022i
$816$	15.1518	−	23.5767i	0.530420	−	0.825349i
$817$	25.9800	−	40.4257i	0.908926	−	1.41432i
$818$	36.4105	+	31.5499i	1.27306	+	1.10312i
$819$	7.27185	+	0.201852i	0.254099	+	0.00705326i
$820$	−50.2288	+	7.22181i	−1.75407	+	0.252197i
$821$	21.3374	+	24.6247i	0.744680	+	0.859406i	0.994041	−	0.109004i	$-0.0347662\pi$
$821$	21.3374	+	24.6247i	0.744680	+	0.859406i	−0.249361	+	0.968410i	$0.580221\pi$
$822$	−4.61085	−	10.0964i	−0.160822	−	0.352151i
$823$	−43.3994	+	12.7432i	−1.51281	+	0.444200i	−0.929738	−	0.368222i	$-0.879967\pi$
$823$	−43.3994	+	12.7432i	−1.51281	+	0.444200i	−0.583070	+	0.812422i	$0.698149\pi$
$824$	41.0563	−	89.9007i	1.43026	−	3.13184i
$825$	−0.100382	+	0.698172i	−0.00349485	+	0.0243072i
$826$	19.5708	−	21.3584i	0.680954	−	0.743154i
$827$			8.18535i			0.284633i	0.989821	+	0.142316i	$0.0454550\pi$
$827$			8.18535i			0.284633i	−0.989821	+	0.142316i	$0.954545\pi$
$828$	−11.4147	−	19.6369i	−0.396689	−	0.682428i
$829$			33.8674i			1.17626i	0.808765	+	0.588131i	$0.200136\pi$
$829$			33.8674i			1.17626i	−0.808765	+	0.588131i	$0.799864\pi$
$830$	−21.6114	+	13.8888i	−0.750141	+	0.482087i
$831$	−7.42339	−	1.06732i	−0.257514	−	0.0370250i
$832$	−13.9223	−	6.35808i	−0.482667	−	0.220427i
$833$	−15.2369	+	15.7292i	−0.527926	+	0.544985i
$834$	1.79516	+	3.93086i	0.0621614	+	0.136115i
$835$	−11.5917	+	10.0442i	−0.401146	+	0.347595i
$836$	−26.3102	+	3.78284i	−0.909958	+	0.130832i
$837$	6.49541	+	1.90722i	0.224514	+	0.0659233i
$838$	16.4792	−	19.0180i	0.569263	−	0.656965i
$839$	2.15079	+	1.38223i	0.0742534	+	0.0477197i	0.577241	−	0.816574i	$-0.304129\pi$
$839$	2.15079	+	1.38223i	0.0742534	+	0.0477197i	−0.502987	+	0.864294i	$0.667766\pi$
$840$	37.0703	+	12.0117i	1.27905	+	0.414444i
$841$	18.8325	−	21.7339i	0.649397	−	0.749444i
$842$	−3.68405	+	12.5467i	−0.126961	+	0.432388i
$843$	2.76625	+	19.2397i	0.0952747	+	0.662650i
$844$	−17.2626	−	19.9221i	−0.594203	−	0.685747i
$845$	4.68704	+	10.2632i	0.161239	+	0.353064i
$846$	8.88732	+	30.2674i	0.305552	+	1.04062i
$847$	26.0203	+	4.48131i	0.894067	+	0.153980i
$848$	1.94120	+	0.279102i	0.0666611	+	0.00958442i
$849$	8.54694	+	13.2993i	0.293330	+	0.456431i
$850$	−5.66940			−0.194459
$851$	−1.47940	−	1.04691i	−0.0507133	−	0.0358877i
$852$		−	49.5505i		−	1.69757i
$853$	17.2584	+	26.8546i	0.590916	+	0.919483i	0.999976	+	0.00697553i	$0.00222040\pi$
$853$	17.2584	+	26.8546i	0.590916	+	0.919483i	−0.409060	+	0.912508i	$0.634143\pi$
$854$	62.4631	−	7.21818i	2.13744	−	0.247001i
$855$	4.78688	−	10.4818i	0.163708	−	0.358471i
$856$	−30.7887	−	104.857i	−1.05234	−	3.58393i
$857$	31.5223	−	14.3958i	1.07678	−	0.491750i	0.203555	−	0.979063i	$-0.434750\pi$
$857$	31.5223	−	14.3958i	1.07678	−	0.491750i	0.873227	+	0.487313i	$0.162023\pi$
$858$	−5.44810	+	4.72080i	−0.185995	+	0.161166i
$859$	−14.3908	+	2.06909i	−0.491009	+	0.0705965i	−0.383373	−	0.923594i	$-0.625237\pi$
$859$	−14.3908	+	2.06909i	−0.491009	+	0.0705965i	−0.107637	+	0.994190i	$0.534328\pi$
$860$	23.9366	−	81.5207i	0.816232	−	2.77983i
$861$	−12.2704	−	6.02065i	−0.418176	−	0.205183i
$862$	−41.5370	+	64.6328i	−1.41476	+	2.20140i
$863$	−9.47920	−	6.09191i	−0.322676	−	0.207371i	0.369267	−	0.929323i	$-0.379609\pi$
$863$	−9.47920	−	6.09191i	−0.322676	−	0.207371i	−0.691943	+	0.721952i	$0.743245\pi$
$864$	−6.83803	−	5.92519i	−0.232635	−	0.201579i
$865$	−3.50799	+	11.9471i	−0.119275	+	0.406214i
$866$	−11.3538	−	78.9672i	−0.385817	−	2.68341i
$867$	−5.45111	+	4.72342i	−0.185130	+	0.160416i
$868$	53.7496	+	65.6246i	1.82438	+	2.22744i
$869$	7.07087	−	2.07619i	0.239863	−	0.0704301i
$870$	2.40869	+	1.10001i	0.0816622	+	0.0372939i
$871$	−3.67778	+	25.5795i	−0.124617	+	0.866728i
$872$	−76.2479	−	118.644i	−2.58208	−	4.01780i
$873$	−1.00903			−0.0341504
$874$	−67.9423	−	12.8870i	−2.29818	−	0.435910i
$875$	−7.97360	−	30.2352i	−0.269557	−	1.02214i
$876$	45.9733	−	29.5453i	1.55330	−	0.998242i
$877$	4.65874	−	32.4022i	0.157314	−	1.09415i	−0.746242	−	0.665675i	$-0.768144\pi$
$877$	4.65874	−	32.4022i	0.157314	−	1.09415i	0.903556	−	0.428470i	$-0.140947\pi$
$878$	87.5264	+	39.9720i	2.95387	+	1.34899i
$879$	−8.60523	−	29.3067i	−0.290247	−	0.988491i
$880$	−17.0733	+	7.79710i	−0.575540	+	0.262840i
$881$	−30.7484	−	35.4855i	−1.03594	−	1.19554i	−0.980387	−	0.197082i	$-0.936853\pi$
$881$	−30.7484	−	35.4855i	−1.03594	−	1.19554i	−0.0555526	−	0.998456i	$-0.517692\pi$
$882$	11.1174	+	14.3691i	0.374342	+	0.483834i
$883$	14.9672	+	4.39477i	0.503687	+	0.147896i	0.523698	−	0.851904i	$-0.324552\pi$
$883$	14.9672	+	4.39477i	0.503687	+	0.147896i	−0.0200111	+	0.999800i	$0.506370\pi$
$884$	−30.7885	−	26.6784i	−1.03553	−	0.897291i
$885$	−7.36086	−	4.73054i	−0.247433	−	0.159015i
$886$	37.0972	+	23.8409i	1.24630	+	0.800951i
$887$	−15.0036	−	13.0007i	−0.503770	−	0.436519i	0.365533	−	0.930798i	$-0.380887\pi$
$887$	−15.0036	−	13.0007i	−0.503770	−	0.436519i	−0.869303	+	0.494279i	$0.835432\pi$
$888$	−2.57488	−	0.756053i	−0.0864073	−	0.0253715i
$889$	32.3454	−	13.7001i	1.08483	−	0.459488i
$890$	59.9036	+	69.1325i	2.00797	+	2.31733i
$891$	−0.918895	+	0.419645i	−0.0307841	+	0.0140586i
$892$	−36.0730	−	122.853i	−1.20781	−	4.11343i
$893$	61.4247	+	28.0517i	2.05550	+	0.938716i
$894$	−0.904841	+	6.29331i	−0.0302624	+	0.210480i
$895$	1.79022	−	1.15050i	0.0598405	−	0.0384571i
$896$	2.46172	+	9.33464i	0.0822404	+	0.311848i
$897$	−12.2273	+	4.93699i	−0.408259	+	0.164841i
$898$	−17.3201			−0.577979
$899$	1.80037	+	2.80143i	0.0600457	+	0.0934329i
$900$	−0.470625	+	3.27327i	−0.0156875	+	0.109109i
$901$	0.622987	+	0.284509i	0.0207547	+	0.00947836i
$902$	12.9957	−	3.81588i	0.432709	−	0.127055i
$903$	17.7037	−	14.5002i	0.589144	−	0.482536i
$904$	40.2567	−	34.8826i	1.33892	−	1.16018i
$905$	2.59206	+	18.0282i	0.0861630	+	0.599277i
$906$	0.496258	−	1.69010i	0.0164871	−	0.0561498i
$907$	9.78799	+	8.48135i	0.325005	+	0.281618i	0.802046	−	0.597263i	$-0.203745\pi$
$907$	9.78799	+	8.48135i	0.325005	+	0.281618i	−0.477041	+	0.878881i	$0.658291\pi$
$908$	−48.7895	−	31.3551i	−1.61914	−	1.04056i
$909$	−8.00306	+	12.4530i	−0.265445	+	0.413040i
$910$	17.2496	−	35.1558i	0.571820	−	1.16540i
$911$	0.319247	−	1.08726i	0.0105771	−	0.0360224i	−0.954035	−	0.299694i	$-0.903115\pi$
$911$	0.319247	−	1.08726i	0.0105771	−	0.0360224i	0.964612	+	0.263672i	$0.0849336\pi$
$912$	−49.2643	+	7.08314i	−1.63131	+	0.234546i
$913$	3.64339	−	3.15702i	0.120579	−	0.104482i
$914$	−34.9961	+	15.9822i	−1.15757	+	0.528643i
$915$	−5.35071	−	18.2228i	−0.176889	−	0.602429i
$916$	27.9123	−	61.1194i	0.922249	−	2.01944i
$917$	−5.17465	−	44.7793i	−0.170882	−	1.47874i
$918$	−4.38976	−	6.83060i	−0.144884	−	0.225443i
$919$			1.08435i			0.0357695i	0.999840	+	0.0178848i	$0.00569320\pi$
$919$			1.08435i			0.0357695i	−0.999840	+	0.0178848i	$0.994307\pi$
$920$	−70.2952	+	6.92173i	−2.31756	+	0.228203i
$921$	−30.9999			−1.02148
$922$	−27.1684	−	42.2748i	−0.894743	−	1.39225i
$923$	−28.4740	−	4.09394i	−0.937233	−	0.134754i
$924$	−12.4745	−	2.14840i	−0.410379	−	0.0706770i
$925$	0.0743402	+	0.253179i	0.00244429	+	0.00832449i
$926$	14.0007	+	30.6574i	0.460093	+	1.00746i
$927$	−9.11407	−	10.5182i	−0.299345	−	0.345463i
$928$	−0.633419	−	4.40553i	−0.0207930	−	0.144619i
$929$	−5.83587	+	19.8751i	−0.191469	+	0.652082i	0.806665	+	0.591009i	$0.201270\pi$
$929$	−5.83587	+	19.8751i	−0.191469	+	0.652082i	−0.998133	+	0.0610728i	$0.980548\pi$
$930$	23.8639	−	27.5404i	0.782527	−	0.903084i
$931$	38.8308	+	2.15739i	1.27263	+	0.0707056i
$932$	113.973	+	73.2460i	3.73331	+	2.39925i
$933$	−0.782143	+	0.902641i	−0.0256062	+	0.0295512i
$934$	69.6821	+	20.4605i	2.28007	+	0.669489i
$935$	−6.48796	+	0.932827i	−0.212179	+	0.0305067i
$936$	−14.7562	+	12.7863i	−0.482322	+	0.417934i
$937$	12.4005	+	27.1533i	0.405106	+	0.887058i	0.996727	+	0.0808422i	$0.0257610\pi$
$937$	12.4005	+	27.1533i	0.405106	+	0.887058i	−0.591621	+	0.806216i	$0.701512\pi$
$938$	−55.2413	+	33.3727i	−1.80369	+	1.08966i
$939$	12.7676	+	5.83076i	0.416654	+	0.190280i
$940$	118.176	+	16.9912i	3.85448	+	0.554190i
$941$	27.8113	−	17.8732i	0.906621	−	0.582650i	−0.00212552	−	0.999998i	$-0.500677\pi$
$941$	27.8113	−	17.8732i	0.906621	−	0.582650i	0.908747	+	0.417348i	$0.137040\pi$
$942$			23.6787i			0.771494i
$943$	24.7505	+	1.10583i	0.805988	+	0.0360108i
$944$			37.7926i			1.23004i
$945$	3.70722	−	4.04584i	0.120596	−	0.131611i
$946$	−3.22728	+	22.4463i	−0.104928	+	0.729791i
$947$	−13.6006	+	29.7812i	−0.441961	+	0.967761i	0.549273	+	0.835643i	$0.314905\pi$
$947$	−13.6006	+	29.7812i	−0.441961	+	0.967761i	−0.991234	+	0.132117i	$0.957822\pi$
$948$	33.1507	−	9.73392i	1.07668	−	0.316143i
$949$	−13.1797	−	28.8595i	−0.427830	−	0.936818i
$950$	6.59335	+	7.60913i	0.213916	+	0.246873i
$951$	13.3851	−	1.92449i	0.434042	−	0.0624058i
$952$	1.63091	−	58.7548i	0.0528582	−	1.90425i
$953$	25.7824	+	22.3406i	0.835175	+	0.723684i	0.963402	−	0.268061i	$-0.0863830\pi$
$953$	25.7824	+	22.3406i	0.835175	+	0.723684i	−0.128226	+	0.991745i	$0.540928\pi$
$954$	0.307184	−	0.477987i	0.00994544	−	0.0154754i
$955$	−8.15192	+	12.6846i	−0.263790	+	0.410465i
$956$	−88.4077	+	102.028i	−2.85931	+	3.29982i
$957$	−0.476793	−	0.139999i	−0.0154125	−	0.00452553i
$958$	−3.45289	−	24.0154i	−0.111558	−	0.775903i
$959$	−9.34515	−	6.37896i	−0.301771	−	0.205987i
$960$	−10.5019	+	4.79608i	−0.338949	+	0.154793i
$961$	14.2272	−	4.17749i	0.458943	−	0.134758i
$962$	−1.12029	+	2.45309i	−0.0361196	+	0.0790908i
$963$	−15.2327	−	2.19013i	−0.490868	−	0.0705761i
$964$	98.9339	−	63.5810i	3.18645	−	2.04780i
$965$	22.1311			0.712425
$966$	−28.8878	−	15.8115i	−0.929451	−	0.508726i
$967$	28.9877			0.932182			0.466091	−	0.884737i	$-0.345662\pi$
$967$	28.9877			0.932182			0.466091	+	0.884737i	$0.345662\pi$
$968$	−59.6171	+	38.3136i	−1.91617	+	1.23145i
$969$	−17.2041	−	2.47358i	−0.552676	−	0.0794628i
$970$	−2.25638	+	4.94077i	−0.0724479	+	0.158639i
$971$	−47.5559	+	13.9637i	−1.52614	+	0.448116i	−0.933867	−	0.357620i	$-0.883588\pi$
$971$	−47.5559	+	13.9637i	−1.52614	+	0.448116i	−0.592275	+	0.805736i	$0.701770\pi$
$972$	−4.30810	+	1.96744i	−0.138182	+	0.0631057i
$973$	3.63839	+	2.48355i	0.116641	+	0.0796190i
$974$	−15.9362	−	110.838i	−0.510627	−	3.55149i
$975$	1.84209	+	0.540885i	0.0589940	+	0.0173222i
$976$	−53.7190	+	61.9951i	−1.71950	+	1.98441i
$977$	13.4748	−	20.9673i	0.431098	−	0.670802i	−0.555952	−	0.831215i	$-0.687646\pi$
$977$	13.4748	−	20.9673i	0.431098	−	0.670802i	0.987050	+	0.160412i	$0.0512824\pi$
$978$	13.4941	−	20.9972i	0.431493	−	0.671416i
$979$	−12.9734	−	11.2415i	−0.414633	−	0.359281i
$980$	66.9485	−	15.6825i	2.13859	−	0.500958i
$981$	−19.6581	+	2.82641i	−0.627636	+	0.0902404i
$982$	−50.4041	−	58.1695i	−1.60846	−	1.85626i
$983$	−2.29809	−	5.03212i	−0.0732977	−	0.160500i	0.869436	−	0.494045i	$-0.164482\pi$
$983$	−2.29809	−	5.03212i	−0.0732977	−	0.160500i	−0.942734	+	0.333545i	$0.891755\pi$
$984$	35.1989	−	10.3353i	1.12210	−	0.329478i
$985$	4.71463	−	10.3236i	0.150221	−	0.328937i
$986$	0.568421	−	3.95345i	0.0181022	−	0.125904i
$987$	23.7092	+	21.7247i	0.754671	+	0.691506i
$988$			72.3486i			2.30172i
$989$	−18.8987	+	36.9255i	−0.600945	+	1.17416i
$990$			5.43785i			0.172826i
$991$	46.5006	−	29.8841i	1.47714	−	0.949300i	0.479726	−	0.877418i	$-0.340736\pi$
$991$	46.5006	−	29.8841i	1.47714	−	0.949300i	0.997413	−	0.0718813i	$-0.0229003\pi$
$992$	−60.6282	−	8.71702i	−1.92495	−	0.276766i
$993$	11.2203	+	5.12412i	0.356064	+	0.162609i
$994$	−37.1491	−	61.4922i	−1.17830	−	1.95041i
$995$	8.50503	+	18.6234i	0.269628	+	0.590402i
$996$	17.0815	−	14.8012i	0.541248	−	0.468994i
$997$	9.96137	−	1.43223i	0.315480	−	0.0453591i	0.0172438	−	0.999851i	$-0.494511\pi$
$997$	9.96137	−	1.43223i	0.315480	−	0.0453591i	0.298236	+	0.954492i	$0.403602\pi$
$998$	20.2866	+	5.95670i	0.642163	+	0.188556i
$999$	−0.247474	+	0.285601i	−0.00782974	+	0.00903600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.34.1	✓	320
7.6	odd	2	inner	483.2.r.a.34.2	yes	320
23.21	odd	22	inner	483.2.r.a.412.2	yes	320
161.90	even	22	inner	483.2.r.a.412.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.1	✓	320	1.1	even	1	trivial
483.2.r.a.34.2	yes	320	7.6	odd	2	inner
483.2.r.a.412.1	yes	320	161.90	even	22	inner
483.2.r.a.412.2	yes	320	23.21	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18339 + 1.40318i) q^{2} +(-0.989821 - 0.142315i) q^{3} +(1.96744 - 4.30810i) q^{4} +(-1.99005 + 0.584333i) q^{5} +(2.36086 - 1.07817i) q^{6} +(1.49161 - 2.18520i) q^{7} +(1.01061 + 7.02895i) q^{8} +(0.959493 + 0.281733i) q^{9} +(3.52514 - 4.06822i) q^{10} +(-0.546146 + 0.849820i) q^{11} +(-2.56052 + 3.98425i) q^{12} +(2.07798 + 1.80058i) q^{13} +(-0.190534 + 6.86413i) q^{14} +(2.05296 - 0.295171i) q^{15} +(-5.86647 - 6.77027i) q^{16} +(-1.29960 - 2.84573i) q^{17} +(-2.49027 + 0.731208i) q^{18} +(-2.30797 + 5.05375i) q^{19} +(-1.39795 + 9.72299i) q^{20} +(-1.78741 + 1.95068i) q^{21} -2.62183i q^{22} +(1.55518 - 4.53667i) q^{23} -7.10123i q^{24} +(-0.587398 + 0.377498i) q^{25} +(-7.06356 - 1.01559i) q^{26} +(-0.909632 - 0.415415i) q^{27} +(-6.47940 - 10.7253i) q^{28} +(-0.204348 - 0.447459i) q^{29} +(-4.06822 + 3.52514i) q^{30} +(-6.70072 + 0.963419i) q^{31} +(8.68150 + 2.54912i) q^{32} +(0.661529 - 0.763445i) q^{33} +(6.83060 + 4.38976i) q^{34} +(-1.69150 + 5.22026i) q^{35} +(3.10148 - 3.57930i) q^{36} +(0.106468 - 0.362596i) q^{37} +(-2.05212 - 14.2728i) q^{38} +(-1.80058 - 2.07798i) q^{39} +(-6.11842 - 13.3975i) q^{40} +(1.45543 + 4.95673i) q^{41} +(1.16546 - 6.76715i) q^{42} +(-8.56131 - 1.23093i) q^{43} +(2.58660 + 4.02482i) q^{44} -2.07407 q^{45} +(2.97019 + 12.0875i) q^{46} -12.1543i q^{47} +(4.84325 + 7.53624i) q^{48} +(-2.55021 - 6.51893i) q^{49} +(0.752820 - 1.64845i) q^{50} +(0.881384 + 3.00172i) q^{51} +(11.8454 - 5.40960i) q^{52} +(-0.165449 + 0.143362i) q^{53} +(2.56898 - 0.369364i) q^{54} +(0.590283 - 2.01032i) q^{55} +(16.8671 + 8.27606i) q^{56} +(3.00370 - 4.67385i) q^{57} +(1.07404 + 0.690241i) q^{58} +(-3.18828 - 2.76266i) q^{59} +(2.76745 - 9.42507i) q^{60} +(-1.30317 - 9.06375i) q^{61} +(13.2784 - 11.5058i) q^{62} +(2.04683 - 1.67645i) q^{63} +(-5.34100 + 1.56826i) q^{64} +(-5.18742 - 2.36902i) q^{65} +(-0.373125 + 2.59514i) q^{66} +(5.08137 + 7.90677i) q^{67} -14.8166 q^{68} +(-2.18499 + 4.26917i) q^{69} +(-3.63176 - 13.7713i) q^{70} +(-8.80148 + 5.65636i) q^{71} +(-1.01061 + 7.02895i) q^{72} +(-10.4960 - 4.79338i) q^{73} +(0.276326 + 0.941081i) q^{74} +(0.635142 - 0.290060i) q^{75} +(17.2312 + 19.8859i) q^{76} +(1.04239 + 2.46104i) q^{77} +(6.84713 + 2.01050i) q^{78} +(-5.51326 - 4.77727i) q^{79} +(15.6307 + 10.0452i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-10.1329 - 8.78023i) q^{82} +(-4.57899 - 1.34451i) q^{83} +(4.88709 + 11.5382i) q^{84} +(4.24913 + 4.90376i) q^{85} +(20.4199 - 9.32544i) q^{86} +(0.138588 + 0.471987i) q^{87} +(-6.52529 - 2.98000i) q^{88} +(-2.41840 + 16.8203i) q^{89} +(4.52849 - 2.91029i) q^{90} +(7.03415 - 1.85504i) q^{91} +(-16.4847 - 15.6255i) q^{92} +6.76963 q^{93} +(17.0546 + 26.5375i) q^{94} +(1.63991 - 11.4058i) q^{95} +(-8.23036 - 3.75868i) q^{96} +(-0.968153 + 0.284275i) q^{97} +(14.7153 + 10.6550i) q^{98} +(-0.763445 + 0.661529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49}+ \cdots + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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