LMFDB - Embedded newform 798.2.bf.a.683.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(569,798)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("798.569");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			683.10
Character	$\chi$	$=$	798.683
Dual form			798.2.bf.a.569.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.819227 - 1.52606i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.45289 - 0.838824i) q^{5} +(-0.911995 + 1.47250i) q^{6} +(-2.58974 - 0.541515i) q^{7} +1.00000 q^{8} +(-1.65773 + 2.50038i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.819227 - 1.52606i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.45289 - 0.838824i) q^{5} +(-0.911995 + 1.47250i) q^{6} +(-2.58974 - 0.541515i) q^{7} +1.00000 q^{8} +(-1.65773 + 2.50038i) q^{9} +(-1.45289 - 0.838824i) q^{10} +(1.63083 + 0.941562i) q^{11} +(1.73122 + 0.0535596i) q^{12} -6.20177i q^{13} +(0.825905 + 2.51354i) q^{14} +(-2.47034 - 1.53001i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.02644 - 2.90202i) q^{17} +(2.99426 + 0.185447i) q^{18} +(0.991378 + 4.24466i) q^{19} +1.67765i q^{20} +(1.29520 + 4.39573i) q^{21} -1.88312i q^{22} +(-4.73869 + 2.73588i) q^{23} +(-0.819227 - 1.52606i) q^{24} +(-1.09275 + 1.89269i) q^{25} +(-5.37089 + 3.10089i) q^{26} +(5.17380 + 0.481422i) q^{27} +(1.76384 - 1.97202i) q^{28} -6.90040 q^{29} +(-0.0898542 + 2.90438i) q^{30} +(-6.28440 - 3.62830i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.100859 - 3.26011i) q^{33} +5.80403i q^{34} +(-4.21684 + 1.38558i) q^{35} +(-1.33653 - 2.68583i) q^{36} +(3.04066 - 1.75553i) q^{37} +(3.18030 - 2.98089i) q^{38} +(-9.46429 + 5.08066i) q^{39} +(1.45289 - 0.838824i) q^{40} +2.11947 q^{41} +(3.15921 - 3.31954i) q^{42} +7.03656 q^{43} +(-1.63083 + 0.941562i) q^{44} +(-0.311115 + 5.02332i) q^{45} +(4.73869 + 2.73588i) q^{46} +(3.23065 - 1.86522i) q^{47} +(-0.911995 + 1.47250i) q^{48} +(6.41352 + 2.80477i) q^{49} +2.18549 q^{50} +(-0.310862 + 10.0481i) q^{51} +(5.37089 + 3.10089i) q^{52} +(-5.47641 + 9.48541i) q^{53} +(-2.16998 - 4.72136i) q^{54} +3.15922 q^{55} +(-2.58974 - 0.541515i) q^{56} +(5.66546 - 4.99025i) q^{57} +(3.45020 + 5.97592i) q^{58} +(-6.63269 + 11.4882i) q^{59} +(2.56020 - 1.37438i) q^{60} +(-6.54347 - 11.3336i) q^{61} +7.25660i q^{62} +(5.64710 - 5.57766i) q^{63} +1.00000 q^{64} +(-5.20220 - 9.01047i) q^{65} +(-2.87376 + 1.54271i) q^{66} +(5.36441 + 3.09715i) q^{67} +(5.02644 - 2.90202i) q^{68} +(8.05719 + 4.99022i) q^{69} +(3.30836 + 2.95910i) q^{70} -2.69469 q^{71} +(-1.65773 + 2.50038i) q^{72} +(1.42570 - 2.46938i) q^{73} +(-3.04066 - 1.75553i) q^{74} +(3.78358 + 0.117054i) q^{75} +(-4.17168 - 1.26377i) q^{76} +(-3.71357 - 3.32152i) q^{77} +(9.13213 + 5.65599i) q^{78} +(-4.30342 + 2.48458i) q^{79} +(-1.45289 - 0.838824i) q^{80} +(-3.50384 - 8.28994i) q^{81} +(-1.05973 - 1.83551i) q^{82} +10.7064i q^{83} +(-4.45442 - 1.07619i) q^{84} -9.73713 q^{85} +(-3.51828 - 6.09384i) q^{86} +(5.65300 + 10.5304i) q^{87} +(1.63083 + 0.941562i) q^{88} +(-3.30170 - 5.71872i) q^{89} +(4.50588 - 2.24223i) q^{90} +(-3.35835 + 16.0610i) q^{91} -5.47177i q^{92} +(-0.388661 + 12.5628i) q^{93} +(-3.23065 - 1.86522i) q^{94} +(5.00089 + 5.33542i) q^{95} +(1.73122 + 0.0535596i) q^{96} -11.3610i q^{97} +(-0.777761 - 6.95666i) q^{98} +(-5.05775 + 2.51685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8}+O(q^{10}) $ 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8	$ 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8} + 4 q^{14} + 8 q^{15} - 26 q^{16} + 2 q^{19} + 2 q^{21} + 18 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} - 4 q^{30} - 26 q^{32} + 8 q^{33} + 2 q^{38} + q^{39} + 16 q^{41} + 11 q^{42} - 8 q^{43} + 14 q^{45} + 4 q^{49} - 36 q^{50} - 19 q^{51} - 24 q^{53} - 3 q^{54} + 32 q^{55} - 8 q^{56} - 4 q^{57} + 4 q^{58} + 32 q^{59} - 4 q^{60} - 20 q^{61} - 7 q^{63} + 52 q^{64} - 44 q^{65} + 8 q^{66} + 62 q^{69} - 24 q^{71} - 32 q^{73} + 16 q^{75} - 4 q^{76} - 2 q^{78} - 28 q^{81} - 8 q^{82} - 13 q^{84} + 32 q^{85} + 4 q^{86} + 34 q^{87} - 36 q^{89} - 28 q^{90} + 20 q^{93} + 30 q^{95} - 20 q^{98} - 116 q^{99}+O(q^{100}) $ 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8 + 4 * q^14 + 8 * q^15 - 26 * q^16 + 2 * q^19 + 2 * q^21 + 18 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 - 4 * q^30 - 26 * q^32 + 8 * q^33 + 2 * q^38 + q^39 + 16 * q^41 + 11 * q^42 - 8 * q^43 + 14 * q^45 + 4 * q^49 - 36 * q^50 - 19 * q^51 - 24 * q^53 - 3 * q^54 + 32 * q^55 - 8 * q^56 - 4 * q^57 + 4 * q^58 + 32 * q^59 - 4 * q^60 - 20 * q^61 - 7 * q^63 + 52 * q^64 - 44 * q^65 + 8 * q^66 + 62 * q^69 - 24 * q^71 - 32 * q^73 + 16 * q^75 - 4 * q^76 - 2 * q^78 - 28 * q^81 - 8 * q^82 - 13 * q^84 + 32 * q^85 + 4 * q^86 + 34 * q^87 - 36 * q^89 - 28 * q^90 + 20 * q^93 + 30 * q^95 - 20 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.819227	−	1.52606i	−0.472981	−	0.881073i
$3$	−0.819227	−	1.52606i	−0.472981	−	0.881073i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.45289	−	0.838824i	0.649751	−	0.375134i	−0.138610	−	0.990347i	$-0.544263\pi$
$5$	1.45289	−	0.838824i	0.649751	−	0.375134i	0.788361	+	0.615213i	$0.210930\pi$
$6$	−0.911995	+	1.47250i	−0.372320	+	0.601147i
$7$	−2.58974	−	0.541515i	−0.978830	−	0.204673i
$7$	−2.58974	−	0.541515i	−0.978830	−	0.204673i
$8$	1.00000			0.353553
$9$	−1.65773	+	2.50038i	−0.552578	+	0.833461i
$10$	−1.45289	−	0.838824i	−0.459443	−	0.265260i
$11$	1.63083	+	0.941562i	0.491715	+	0.283892i	0.725286	−	0.688448i	$-0.241708\pi$
$11$	1.63083	+	0.941562i	0.491715	+	0.283892i	−0.233571	+	0.972340i	$0.575041\pi$
$12$	1.73122	+	0.0535596i	0.499761	+	0.0154613i
$13$		−	6.20177i		−	1.72006i	−0.510242	−	0.860031i	$-0.670444\pi$
$13$		−	6.20177i		−	1.72006i	0.510242	−	0.860031i	$-0.329556\pi$
$14$	0.825905	+	2.51354i	0.220732	+	0.671772i
$15$	−2.47034	−	1.53001i	−0.637840	−	0.395046i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.02644	−	2.90202i	−1.21909	−	0.703842i	−0.254367	−	0.967108i	$-0.581867\pi$
$17$	−5.02644	−	2.90202i	−1.21909	−	0.703842i	−0.964723	+	0.263265i	$0.915201\pi$
$18$	2.99426	+	0.185447i	0.705754	+	0.0437103i
$19$	0.991378	+	4.24466i	0.227438	+	0.973793i
$19$	0.991378	+	4.24466i	0.227438	+	0.973793i
$20$			1.67765i			0.375134i
$21$	1.29520	+	4.39573i	0.282636	+	0.959227i
$22$		−	1.88312i		−	0.401483i
$23$	−4.73869	+	2.73588i	−0.988085	+	0.570471i	−0.904701	−	0.426046i	$-0.859906\pi$
$23$	−4.73869	+	2.73588i	−0.988085	+	0.570471i	−0.0833836	+	0.996518i	$0.526573\pi$
$24$	−0.819227	−	1.52606i	−0.167224	−	0.311506i
$25$	−1.09275	+	1.89269i	−0.218549	+	0.378539i
$26$	−5.37089	+	3.10089i	−1.05332	+	0.608134i
$27$	5.17380	+	0.481422i	0.995699	+	0.0926497i
$28$	1.76384	−	1.97202i	0.333334	−	0.372678i
$29$	−6.90040			−1.28137			−0.640686	−	0.767803i	$-0.721350\pi$
$29$	−6.90040			−1.28137			−0.640686	+	0.767803i	$0.721350\pi$
$30$	−0.0898542	+	2.90438i	−0.0164051	+	0.530265i
$31$	−6.28440	−	3.62830i	−1.12871	−	0.651662i	−0.185101	−	0.982720i	$-0.559261\pi$
$31$	−6.28440	−	3.62830i	−1.12871	−	0.651662i	−0.943611	+	0.331058i	$0.892595\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.100859	−	3.26011i	0.0175574	−	0.567512i
$34$			5.80403i			0.995383i
$35$	−4.21684	+	1.38558i	−0.712775	+	0.234206i
$36$	−1.33653	−	2.68583i	−0.222755	−	0.447639i
$37$	3.04066	−	1.75553i	0.499882	−	0.288607i	−0.228783	−	0.973477i	$-0.573475\pi$
$37$	3.04066	−	1.75553i	0.499882	−	0.288607i	0.728665	+	0.684871i	$0.240141\pi$
$38$	3.18030	−	2.98089i	0.515912	−	0.483564i
$39$	−9.46429	+	5.08066i	−1.51550	+	0.813557i
$40$	1.45289	−	0.838824i	0.229722	−	0.132630i
$41$	2.11947			0.331005			0.165503	−	0.986209i	$-0.447075\pi$
$41$	2.11947			0.331005			0.165503	+	0.986209i	$0.447075\pi$
$42$	3.15921	−	3.31954i	0.487477	−	0.512217i
$43$	7.03656			1.07306			0.536532	−	0.843880i	$-0.319734\pi$
$43$	7.03656			1.07306			0.536532	+	0.843880i	$0.319734\pi$
$44$	−1.63083	+	0.941562i	−0.245857	+	0.141946i
$45$	−0.311115	+	5.02332i	−0.0463783	+	0.748832i
$46$	4.73869	+	2.73588i	0.698681	+	0.403384i
$47$	3.23065	−	1.86522i	0.471238	−	0.272070i	−0.245520	−	0.969392i	$-0.578959\pi$
$47$	3.23065	−	1.86522i	0.471238	−	0.272070i	0.716758	+	0.697322i	$0.245625\pi$
$48$	−0.911995	+	1.47250i	−0.131635	+	0.212537i
$49$	6.41352	+	2.80477i	0.916218	+	0.400681i
$50$	2.18549			0.309076
$51$	−0.310862	+	10.0481i	−0.0435293	+	1.40701i
$52$	5.37089	+	3.10089i	0.744809	+	0.430016i
$53$	−5.47641	+	9.48541i	−0.752242	+	1.30292i	0.194492	+	0.980904i	$0.437694\pi$
$53$	−5.47641	+	9.48541i	−0.752242	+	1.30292i	−0.946734	+	0.322017i	$0.895639\pi$
$54$	−2.16998	−	4.72136i	−0.295297	−	0.642495i
$55$	3.15922			0.425989
$56$	−2.58974	−	0.541515i	−0.346069	−	0.0723630i
$57$	5.66546	−	4.99025i	0.750408	−	0.660975i
$58$	3.45020	+	5.97592i	0.453034	+	0.784677i
$59$	−6.63269	+	11.4882i	−0.863503	+	1.49563i	0.00502360	+	0.999987i	$0.498401\pi$
$59$	−6.63269	+	11.4882i	−0.863503	+	1.49563i	−0.868526	+	0.495643i	$0.834932\pi$
$60$	2.56020	−	1.37438i	0.330520	−	0.177431i
$61$	−6.54347	−	11.3336i	−0.837806	−	1.45112i	−0.891725	−	0.452577i	$-0.850505\pi$
$61$	−6.54347	−	11.3336i	−0.837806	−	1.45112i	0.0539192	−	0.998545i	$-0.482829\pi$
$62$			7.25660i			0.921589i
$63$	5.64710	−	5.57766i	0.711467	−	0.702719i
$64$	1.00000			0.125000
$65$	−5.20220	−	9.01047i	−0.645253	−	1.11761i
$66$	−2.87376	+	1.54271i	−0.353736	+	0.189894i
$67$	5.36441	+	3.09715i	0.655367	+	0.378377i	0.790510	−	0.612450i	$-0.209816\pi$
$67$	5.36441	+	3.09715i	0.655367	+	0.378377i	−0.135142	+	0.990826i	$0.543149\pi$
$68$	5.02644	−	2.90202i	0.609545	−	0.351921i
$69$	8.05719	+	4.99022i	0.969972	+	0.600752i
$70$	3.30836	+	2.95910i	0.395425	+	0.353680i
$71$	−2.69469			−0.319800			−0.159900	−	0.987133i	$-0.551117\pi$
$71$	−2.69469			−0.319800			−0.159900	+	0.987133i	$0.551117\pi$
$72$	−1.65773	+	2.50038i	−0.195366	+	0.294673i
$73$	1.42570	−	2.46938i	0.166865	−	0.289019i	−0.770451	−	0.637500i	$-0.779969\pi$
$73$	1.42570	−	2.46938i	0.166865	−	0.289019i	0.937316	+	0.348480i	$0.113302\pi$
$74$	−3.04066	−	1.75553i	−0.353470	−	0.204076i
$75$	3.78358	+	0.117054i	0.436890	+	0.0135163i
$76$	−4.17168	−	1.26377i	−0.478524	−	0.144965i
$77$	−3.71357	−	3.32152i	−0.423200	−	0.378523i
$78$	9.13213	+	5.65599i	1.03401	+	0.640414i
$79$	−4.30342	+	2.48458i	−0.484172	+	0.279537i	−0.722153	−	0.691733i	$-0.756848\pi$
$79$	−4.30342	+	2.48458i	−0.484172	+	0.279537i	0.237981	+	0.971270i	$0.423514\pi$
$80$	−1.45289	−	0.838824i	−0.162438	−	0.0937834i
$81$	−3.50384	−	8.28994i	−0.389316	−	0.921104i
$82$	−1.05973	−	1.83551i	−0.117028	−	0.202698i
$83$			10.7064i			1.17518i	0.809158	+	0.587591i	$0.199924\pi$
$83$			10.7064i			1.17518i	−0.809158	+	0.587591i	$0.800076\pi$
$84$	−4.45442	−	1.07619i	−0.486017	−	0.117422i
$85$	−9.73713			−1.05614
$86$	−3.51828	−	6.09384i	−0.379386	−	0.657115i
$87$	5.65300	+	10.5304i	0.606065	+	1.12898i
$88$	1.63083	+	0.941562i	0.173847	+	0.100371i
$89$	−3.30170	−	5.71872i	−0.349980	−	0.606183i	0.636266	−	0.771470i	$-0.280478\pi$
$89$	−3.30170	−	5.71872i	−0.349980	−	0.606183i	−0.986245	+	0.165287i	$0.947145\pi$
$90$	4.50588	−	2.24223i	0.474962	−	0.236351i
$91$	−3.35835	+	16.0610i	−0.352051	+	1.68365i
$92$		−	5.47177i		−	0.570471i
$93$	−0.388661	+	12.5628i	−0.0403022	+	1.30270i
$94$	−3.23065	−	1.86522i	−0.333216	−	0.192382i
$95$	5.00089	+	5.33542i	0.513080	+	0.547403i
$96$	1.73122	+	0.0535596i	0.176692	+	0.00546640i
$97$		−	11.3610i		−	1.15353i	−0.816909	−	0.576766i	$-0.804314\pi$
$97$		−	11.3610i		−	1.15353i	0.816909	−	0.576766i	$-0.195686\pi$
$98$	−0.777761	−	6.95666i	−0.0785658	−	0.702729i
$99$	−5.05775	+	2.51685i	−0.508323	+	0.252953i
$100$	−1.09275	−	1.89269i	−0.109275	−	0.189269i
$101$	−2.15201	−	1.24246i	−0.214133	−	0.123629i	0.389098	−	0.921196i	$-0.372787\pi$
$101$	−2.15201	−	1.24246i	−0.214133	−	0.123629i	−0.603230	+	0.797567i	$0.706120\pi$
$102$	8.85732	−	4.75482i	0.877005	−	0.470798i
$103$	−11.9593	+	6.90469i	−1.17838	+	0.680339i	−0.955640	−	0.294538i	$-0.904834\pi$
$103$	−11.9593	+	6.90469i	−1.17838	+	0.680339i	−0.222742	+	0.974877i	$0.571501\pi$
$104$		−	6.20177i		−	0.608134i
$105$	5.56903	+	5.30005i	0.543481	+	0.517232i
$106$	10.9528			1.06383
$107$	−3.37596	−	5.84734i	−0.326366	−	0.565283i	0.655421	−	0.755263i	$-0.272491\pi$
$107$	−3.37596	−	5.84734i	−0.326366	−	0.565283i	−0.981788	+	0.189980i	$0.939158\pi$
$108$	−3.00382	+	4.23993i	−0.289043	+	0.407988i
$109$	1.19227	+	0.688355i	0.114198	+	0.0659325i	0.556011	−	0.831175i	$-0.312331\pi$
$109$	1.19227	+	0.688355i	0.114198	+	0.0659325i	−0.441813	+	0.897107i	$0.645664\pi$
$110$	−1.57961	−	2.73597i	−0.150610	−	0.260864i
$111$	−5.17004	−	3.20207i	−0.490718	−	0.303927i
$112$	0.825905	+	2.51354i	0.0780407	+	0.237507i
$113$	11.0633			1.04075			0.520373	−	0.853939i	$-0.325793\pi$
$113$	11.0633			1.04075			0.520373	+	0.853939i	$0.325793\pi$
$114$	−7.15441	−	2.41131i	−0.670072	−	0.225840i
$115$	−4.58985	+	7.94985i	−0.428006	+	0.741328i
$116$	3.45020	−	5.97592i	0.320343	−	0.554851i
$117$	15.5068	+	10.2809i	1.43361	+	0.950468i
$118$	13.2654			1.22118
$119$	11.4457	+	10.2374i	1.04923	+	0.938458i
$120$	−2.47034	−	1.53001i	−0.225510	−	0.139670i
$121$	−3.72692	−	6.45522i	−0.338811	−	0.586838i
$122$	−6.54347	+	11.3336i	−0.592418	+	1.02610i
$123$	−1.73632	−	3.23444i	−0.156559	−	0.291639i
$124$	6.28440	−	3.62830i	0.564356	−	0.325831i
$125$			12.0547i			1.07821i
$126$	−7.65394	−	2.10170i	−0.681868	−	0.187234i
$127$		−	13.4785i		−	1.19602i	−0.801489	−	0.598010i	$-0.795958\pi$
$127$		−	13.4785i		−	1.19602i	0.801489	−	0.598010i	$-0.204042\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.76454	−	10.7382i	−0.507539	−	0.945448i
$130$	−5.20220	+	9.01047i	−0.456263	+	0.790271i
$131$	10.8979	−	6.29193i	0.952158	−	0.549728i	0.0584071	−	0.998293i	$-0.481398\pi$
$131$	10.8979	−	6.29193i	0.952158	−	0.549728i	0.893751	+	0.448564i	$0.148065\pi$
$132$	2.77291	+	1.71740i	0.241350	+	0.149480i
$133$	−0.268863	−	11.5294i	−0.0233134	−	0.999728i
$134$		−	6.19429i		−	0.535105i
$135$	7.92078	−	3.64046i	0.681712	−	0.313321i
$136$	−5.02644	−	2.90202i	−0.431014	−	0.248846i
$137$	−15.1944	−	8.77249i	−1.29815	−	0.749485i	−0.318062	−	0.948070i	$-0.603032\pi$
$137$	−15.1944	−	8.77249i	−1.29815	−	0.749485i	−0.980084	+	0.198585i	$0.936365\pi$
$138$	0.293066	−	9.47284i	0.0249474	−	0.806382i
$139$	13.6779			1.16015			0.580073	−	0.814564i	$-0.303024\pi$
$139$	13.6779			1.16015			0.580073	+	0.814564i	$0.303024\pi$
$140$	0.908472	−	4.34468i	0.0767799	−	0.367192i
$141$	−5.49307	−	3.40213i	−0.462600	−	0.286511i
$142$	1.34734	+	2.33367i	0.113067	+	0.195837i
$143$	5.83935	−	10.1141i	0.488311	−	0.845780i
$144$	2.99426	+	0.185447i	0.249522	+	0.0154539i
$145$	−10.0255	+	5.78822i	−0.832572	+	0.480686i
$146$	−2.85140			−0.235983
$147$	−0.973882	−	12.0852i	−0.0803244	−	0.996769i
$148$			3.51106i			0.288607i
$149$	3.17968	−	1.83579i	0.260490	−	0.150394i	−0.364068	−	0.931372i	$-0.618613\pi$
$149$	3.17968	−	1.83579i	0.260490	−	0.150394i	0.624558	+	0.780978i	$0.285279\pi$
$150$	−1.79042	−	3.33520i	−0.146187	−	0.272318i
$151$	−11.0293	−	6.36774i	−0.897548	−	0.518199i	−0.0211439	−	0.999776i	$-0.506731\pi$
$151$	−11.0293	−	6.36774i	−0.897548	−	0.518199i	−0.876404	+	0.481577i	$0.840064\pi$
$152$	0.991378	+	4.24466i	0.0804114	+	0.344288i
$153$	15.5887	−	7.75726i	1.26027	−	0.627137i
$154$	−1.01974	+	4.87680i	−0.0821730	+	0.392984i
$155$	−12.1740			−0.977841
$156$	0.332165	−	10.7366i	0.0265944	−	0.859620i
$157$	8.82182	−	15.2798i	0.704058	−	1.21946i	−0.262973	−	0.964803i	$-0.584703\pi$
$157$	8.82182	−	15.2798i	0.704058	−	1.21946i	0.967031	−	0.254660i	$-0.0819636\pi$
$158$	4.30342	+	2.48458i	0.342361	+	0.197662i
$159$	18.9618	+	0.586628i	1.50376	+	0.0465226i
$160$			1.67765i			0.132630i
$161$	13.7535	−	4.51916i	1.08393	−	0.356160i
$162$	−5.42738	+	7.17938i	−0.426415	+	0.564066i
$163$	−9.12550	−	15.8058i	−0.714764	−	1.23801i	−0.963050	−	0.269321i	$-0.913201\pi$
$163$	−9.12550	−	15.8058i	−0.714764	−	1.23801i	0.248286	−	0.968687i	$-0.420133\pi$
$164$	−1.05973	+	1.83551i	−0.0827513	+	0.143329i
$165$	−2.58812	−	4.82117i	−0.201485	−	0.375327i
$166$	9.27203	−	5.35321i	0.719649	−	0.415490i
$167$	−9.66632			−0.748002			−0.374001	−	0.927428i	$-0.622014\pi$
$167$	−9.66632			−0.748002			−0.374001	+	0.927428i	$0.622014\pi$
$168$	1.29520	+	4.39573i	0.0999269	+	0.339138i
$169$	−25.4620			−1.95861
$170$	4.86856	+	8.43260i	0.373402	+	0.646751i
$171$	−12.2567	−	4.55770i	−0.937296	−	0.348536i
$172$	−3.51828	+	6.09384i	−0.268266	+	0.464651i
$173$	−12.8259	−	22.2151i	−0.975134	−	1.68898i	−0.679493	−	0.733682i	$-0.737800\pi$
$173$	−12.8259	−	22.2151i	−0.975134	−	1.68898i	−0.295641	−	0.955299i	$-0.595533\pi$
$174$	6.29313	−	10.1609i	0.477081	−	0.770293i
$175$	3.85486	−	4.30985i	0.291400	−	0.325794i
$176$		−	1.88312i		−	0.141946i
$177$	22.9653	+	0.710489i	1.72618	+	0.0534036i
$178$	−3.30170	+	5.71872i	−0.247473	+	0.428636i
$179$	4.86204	−	8.42131i	0.363406	−	0.629438i	−0.625113	−	0.780534i	$-0.714947\pi$
$179$	4.86204	−	8.42131i	0.363406	−	0.629438i	0.988519	+	0.151096i	$0.0482804\pi$
$180$	−4.19477	−	2.78109i	−0.312659	−	0.207291i
$181$			1.01843i			0.0756996i	0.999283	+	0.0378498i	$0.0120508\pi$
$181$			1.01843i			0.0756996i	−0.999283	+	0.0378498i	$0.987949\pi$
$182$	15.5884	−	5.12208i	1.15549	−	0.379674i
$183$	−11.9352	+	19.2706i	−0.882278	+	1.42452i
$184$	−4.73869	+	2.73588i	−0.349341	+	0.201692i
$185$	2.94516	−	5.10116i	0.216532	−	0.375045i
$186$	11.0740	−	5.94480i	0.811987	−	0.435894i
$187$	−5.46486	−	9.46541i	−0.399630	−	0.692179i
$188$			3.73043i			0.272070i
$189$	−13.1381	−	4.04845i	−0.955657	−	0.294481i
$190$	2.12017	−	6.99861i	0.153813	−	0.507732i
$191$	−6.78720	+	3.91859i	−0.491105	+	0.283539i	−0.725033	−	0.688715i	$-0.758175\pi$
$191$	−6.78720	+	3.91859i	−0.491105	+	0.283539i	0.233928	+	0.972254i	$0.424842\pi$
$192$	−0.819227	−	1.52606i	−0.0591226	−	0.110134i
$193$	10.8570	+	6.26830i	0.781505	+	0.451202i	0.836963	−	0.547259i	$-0.184329\pi$
$193$	10.8570	+	6.26830i	0.781505	+	0.451202i	−0.0554587	+	0.998461i	$0.517662\pi$
$194$	−9.83890	+	5.68049i	−0.706392	+	0.407835i
$195$	−9.48876	+	15.3205i	−0.679504	+	1.09712i
$196$	−5.63576	+	4.15189i	−0.402554	+	0.296564i
$197$			1.84349i			0.131343i	0.997841	+	0.0656716i	$0.0209190\pi$
$197$			1.84349i			0.131343i	−0.997841	+	0.0656716i	$0.979081\pi$
$198$	4.70853	+	3.12172i	0.334621	+	0.221851i
$199$	−8.23827	+	14.2691i	−0.583996	+	1.01151i	0.411004	+	0.911633i	$0.365178\pi$
$199$	−8.23827	+	14.2691i	−0.583996	+	1.01151i	−0.995000	+	0.0998768i	$0.968155\pi$
$200$	−1.09275	+	1.89269i	−0.0772689	+	0.133834i
$201$	0.331764	−	10.7237i	0.0234008	−	0.756391i
$202$			2.48492i			0.174838i
$203$	17.8703	+	3.73667i	1.25425	+	0.262263i
$204$	−8.54645	−	5.29325i	−0.598372	−	0.370602i
$205$	3.07934	−	1.77786i	0.215071	−	0.124171i
$206$	11.9593	+	6.90469i	0.833242	+	0.481072i
$207$	1.01472	−	16.3839i	0.0705282	−	1.13876i
$208$	−5.37089	+	3.10089i	−0.372404	+	0.215008i
$209$	−2.37984	+	7.85578i	−0.164617	+	0.543396i
$210$	1.80547	−	7.47294i	0.124589	−	0.515682i
$211$		−	12.9088i		−	0.888677i	−0.895859	−	0.444338i	$-0.853439\pi$
$211$		−	12.9088i		−	0.888677i	0.895859	−	0.444338i	$-0.146561\pi$
$212$	−5.47641	−	9.48541i	−0.376121	−	0.651461i
$213$	2.20756	+	4.11226i	0.151260	+	0.281767i
$214$	−3.37596	+	5.84734i	−0.230776	+	0.399716i
$215$	10.2233	−	5.90243i	0.697224	−	0.402543i
$216$	5.17380	+	0.481422i	0.352033	+	0.0327566i
$217$	14.3102	+	12.7995i	0.971439	+	0.868884i
$218$		−	1.37671i		−	0.0932426i
$219$	−4.93640	−	0.152720i	−0.333571	−	0.0103198i
$220$	−1.57961	+	2.73597i	−0.106497	+	0.184459i
$221$	−17.9976	+	31.1728i	−1.21065	+	2.09691i
$222$	−0.188051	+	6.07842i	−0.0126211	+	0.407957i
$223$		−	15.0341i		−	1.00676i	−0.864065	−	0.503381i	$-0.832089\pi$
$223$		−	15.0341i		−	1.00676i	0.864065	−	0.503381i	$-0.167911\pi$
$224$	1.76384	−	1.97202i	0.117851	−	0.131761i
$225$	−2.92098	−	5.86987i	−0.194732	−	0.391325i
$226$	−5.53164	−	9.58108i	−0.367959	−	0.637324i
$227$	−4.44013	+	7.69054i	−0.294702	+	0.510439i	−0.974916	−	0.222575i	$-0.928554\pi$
$227$	−4.44013	+	7.69054i	−0.294702	+	0.510439i	0.680213	+	0.733014i	$0.261887\pi$
$228$	1.48895	+	7.40156i	0.0986083	+	0.490180i
$229$	1.73528	+	3.00559i	0.114671	+	0.198615i	0.917648	−	0.397394i	$-0.130085\pi$
$229$	1.73528	+	3.00559i	0.114671	+	0.198615i	−0.802977	+	0.596009i	$0.796752\pi$
$230$	9.17970			0.605292
$231$	−2.02660	+	8.38822i	−0.133340	+	0.551904i
$232$	−6.90040			−0.453034
$233$	0.752525	−	0.434470i	0.0492995	−	0.0284631i	−0.475148	−	0.879906i	$-0.657605\pi$
$233$	0.752525	−	0.434470i	0.0492995	−	0.0284631i	0.524447	+	0.851443i	$0.324272\pi$
$234$	1.15010	−	18.5697i	0.0751845	−	1.21394i
$235$	3.12918	−	5.41989i	0.204125	−	0.353555i
$236$	−6.63269	−	11.4882i	−0.431751	−	0.747815i
$237$	7.31710	+	4.53185i	0.475296	+	0.294375i
$238$	3.14297	−	15.0309i	0.203729	−	0.974311i
$239$			11.5353i			0.746155i	0.927800	+	0.373078i	$0.121697\pi$
$239$			11.5353i			0.746155i	−0.927800	+	0.373078i	$0.878303\pi$
$240$	−0.0898542	+	2.90438i	−0.00580006	+	0.187477i
$241$	−1.96067	−	1.13200i	−0.126298	−	0.0729182i	0.435520	−	0.900179i	$-0.356565\pi$
$241$	−1.96067	−	1.13200i	−0.126298	−	0.0729182i	−0.561818	+	0.827261i	$0.689898\pi$
$242$	−3.72692	+	6.45522i	−0.239576	+	0.414957i
$243$	−9.78052	+	12.1384i	−0.627421	+	0.778680i
$244$	13.0869			0.837806
$245$	11.6708	−	1.30481i	0.745622	−	0.0833613i
$246$	−1.93294	+	3.12092i	−0.123240	+	0.198983i
$247$	26.3244	−	6.14830i	1.67498	−	0.391207i
$248$	−6.28440	−	3.62830i	−0.399060	−	0.230397i
$249$	16.3387	−	8.77099i	1.03542	−	0.555839i
$250$	10.4397	−	6.02737i	0.660265	−	0.381204i
$251$		−	21.5897i		−	1.36273i	−0.731945	−	0.681364i	$-0.761387\pi$
$251$		−	21.5897i		−	1.36273i	0.731945	−	0.681364i	$-0.238613\pi$
$252$	2.00685	+	7.67936i	0.126420	+	0.483754i
$253$	−10.3040			−0.647808
$254$	−11.6727	+	6.73923i	−0.732409	+	0.422857i
$255$	7.97692	+	14.8595i	0.499534	+	0.930536i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.182046	−	0.315313i	−0.0113557	−	0.0196687i	0.860292	−	0.509802i	$-0.170281\pi$
$257$	−0.182046	−	0.315313i	−0.0113557	−	0.0196687i	−0.871647	+	0.490133i	$0.836948\pi$
$258$	−6.41731	+	10.3613i	−0.399524	+	0.645069i
$259$	−8.82518	+	2.89980i	−0.548370	+	0.180185i
$260$	10.4044			0.645253
$261$	11.4390	−	17.2537i	0.708058	−	1.06797i
$262$	−10.8979	−	6.29193i	−0.673277	−	0.388717i
$263$	−19.3153	−	11.1517i	−1.19103	−	0.687643i	−0.232491	−	0.972598i	$-0.574688\pi$
$263$	−19.3153	−	11.1517i	−1.19103	−	0.687643i	−0.958541	+	0.284956i	$0.908021\pi$
$264$	0.100859	−	3.26011i	0.00620747	−	0.200646i
$265$			18.3750i			1.12877i
$266$	−9.85035	+	5.99756i	−0.603963	+	0.367734i
$267$	−6.02227	+	9.72353i	−0.368557	+	0.595071i
$268$	−5.36441	+	3.09715i	−0.327684	+	0.189188i
$269$	7.98963	−	13.8384i	0.487136	−	0.843745i	−0.512754	−	0.858535i	$-0.671375\pi$
$269$	7.98963	−	13.8384i	0.487136	−	0.843745i	0.999891	+	0.0147907i	$0.00470819\pi$
$270$	−7.11312	−	5.03936i	−0.432891	−	0.306686i
$271$	8.33777	+	14.4414i	0.506483	+	0.877255i	0.999972	+	0.00750263i	$0.00238818\pi$
$271$	8.33777	+	14.4414i	0.506483	+	0.877255i	−0.493488	+	0.869752i	$0.664278\pi$
$272$			5.80403i			0.351921i
$273$	27.2613	−	8.03254i	1.64993	−	0.486152i
$274$			17.5450i			1.05993i
$275$	−3.56418	+	2.05778i	−0.214928	+	0.124089i
$276$	−8.35026	+	4.48262i	−0.502626	+	0.269822i
$277$	−0.482345	+	0.835445i	−0.0289813	+	0.0501970i	−0.880152	−	0.474691i	$-0.842560\pi$
$277$	−0.482345	+	0.835445i	−0.0289813	+	0.0501970i	0.851171	+	0.524888i	$0.175893\pi$
$278$	−6.83897	−	11.8454i	−0.410174	−	0.710442i
$279$	19.4900	−	9.69866i	1.16684	−	0.580644i
$280$	−4.21684	+	1.38558i	−0.252004	+	0.0828042i
$281$	11.5077			0.686493			0.343246	−	0.939245i	$-0.388473\pi$
$281$	11.5077			0.686493			0.343246	+	0.939245i	$0.388473\pi$
$282$	−0.199800	+	6.45820i	−0.0118979	+	0.384580i
$283$	13.0864	−	22.6663i	0.777905	−	1.34737i	−0.155242	−	0.987877i	$-0.549616\pi$
$283$	13.0864	−	22.6663i	0.777905	−	1.34737i	0.933147	−	0.359495i	$-0.117051\pi$
$284$	1.34734	−	2.33367i	0.0799501	−	0.138478i
$285$	4.04533	−	12.0026i	0.239624	−	0.710972i
$286$	−11.6787			−0.690576
$287$	−5.48887	−	1.14772i	−0.323998	−	0.0677479i
$288$	−1.33653	−	2.68583i	−0.0787557	−	0.158264i
$289$	8.34340	+	14.4512i	0.490788	+	0.850070i
$290$	10.0255	+	5.78822i	0.588718	+	0.339896i
$291$	−17.3376	+	9.30722i	−1.01635	+	0.545599i
$292$	1.42570	+	2.46938i	0.0834327	+	0.144510i
$293$	−9.71891			−0.567785			−0.283892	−	0.958856i	$-0.591626\pi$
$293$	−9.71891			−0.567785			−0.283892	+	0.958856i	$0.591626\pi$
$294$	−9.97913	+	6.88600i	−0.581995	+	0.401599i
$295$			22.2546i			1.29572i
$296$	3.04066	−	1.75553i	0.176735	−	0.102038i
$297$	7.98432	+	5.65657i	0.463297	+	0.328228i
$298$	−3.17968	−	1.83579i	−0.184194	−	0.106344i
$299$	16.9673	+	29.3883i	0.981246	+	1.69957i
$300$	−1.99316	+	3.21815i	−0.115075	+	0.185800i
$301$	−18.2229	−	3.81040i	−1.05035	−	0.219628i
$302$			12.7355i			0.732845i
$303$	−0.133091	+	4.30195i	−0.00764590	+	0.247141i
$304$	3.18030	−	2.98089i	0.182403	−	0.170966i
$305$	−19.0138	−	10.9777i	−1.08873	−	0.628578i
$306$	−14.5123	−	9.62154i	−0.829614	−	0.550027i
$307$			19.3583i			1.10484i	0.833567	+	0.552418i	$0.186295\pi$
$307$			19.3583i			1.10484i	−0.833567	+	0.552418i	$0.813705\pi$
$308$	4.73331	−	1.55528i	0.269705	−	0.0886204i
$309$	20.3343	+	12.5941i	1.15678	+	0.716452i
$310$	6.08701	+	10.5430i	0.345719	+	0.598803i
$311$	22.8171	+	13.1735i	1.29384	+	0.746999i	0.979333	−	0.202256i	$-0.0648273\pi$
$311$	22.8171	+	13.1735i	1.29384	+	0.746999i	0.314508	+	0.949255i	$0.398161\pi$
$312$	−9.46429	+	5.08066i	−0.535810	+	0.287636i
$313$	5.38324	+	9.32405i	0.304279	+	0.527026i	0.977100	−	0.212778i	$-0.0682512\pi$
$313$	5.38324	+	9.32405i	0.304279	+	0.527026i	−0.672822	+	0.739805i	$0.734918\pi$
$314$	−17.6436			−0.995688
$315$	3.52591	−	12.8406i	0.198663	−	0.723488i
$316$		−	4.96916i		−	0.279537i
$317$	0.403484	+	0.698855i	0.0226619	+	0.0392516i	0.877134	−	0.480246i	$-0.159453\pi$
$317$	0.403484	+	0.698855i	0.0226619	+	0.0392516i	−0.854472	+	0.519497i	$0.826119\pi$
$318$	−8.97284	−	16.7147i	−0.503172	−	0.937312i
$319$	−11.2534	−	6.49716i	−0.630070	−	0.363771i
$320$	1.45289	−	0.838824i	0.0812188	−	0.0468917i
$321$	−6.15772	+	9.94223i	−0.343690	+	0.554921i
$322$	−10.7905	−	9.65130i	−0.601329	−	0.537846i
$323$	7.33498	−	24.2125i	0.408129	−	1.34722i
$324$	8.93122	+	1.11056i	0.496179	+	0.0616975i
$325$	11.7381	+	6.77697i	0.651110	+	0.375919i
$326$	−9.12550	+	15.8058i	−0.505415	+	0.875404i
$327$	0.0737361	−	2.38339i	0.00407761	−	0.131802i
$328$	2.11947			0.117028
$329$	−9.37658	+	3.08098i	−0.516948	+	0.169860i
$330$	−2.88119	+	4.65196i	−0.158605	+	0.256082i
$331$	−9.13676	+	5.27511i	−0.502202	+	0.289946i	−0.729622	−	0.683850i	$-0.760304\pi$
$331$	−9.13676	+	5.27511i	−0.502202	+	0.289946i	0.227421	+	0.973797i	$0.426971\pi$
$332$	−9.27203	−	5.35321i	−0.508869	−	0.293796i
$333$	−0.651115	+	10.5130i	−0.0356809	+	0.576110i
$334$	4.83316	+	8.37128i	0.264459	+	0.458056i
$335$	10.3918			0.567767
$336$	3.15921	−	3.31954i	0.172349	−	0.181096i
$337$		−	3.52393i		−	0.191961i	−0.995383	−	0.0959804i	$-0.969401\pi$
$337$		−	3.52393i		−	0.191961i	0.995383	−	0.0959804i	$-0.0305986\pi$
$338$	12.7310	+	22.0507i	0.692475	+	1.19940i
$339$	−9.06334	−	16.8833i	−0.492253	−	0.916973i
$340$	4.86856	−	8.43260i	0.264035	−	0.457322i
$341$	−6.83254	−	11.8343i	−0.370003	−	0.640863i
$342$	2.18128	+	12.8935i	0.117950	+	0.697200i
$343$	−15.0905	−	10.7366i	−0.814813	−	0.579724i
$344$	7.03656			0.379386
$345$	15.8921	+	0.491661i	0.855602	+	0.0264701i
$346$	−12.8259	+	22.2151i	−0.689524	+	1.19429i
$347$	11.0411	+	6.37460i	0.592719	+	0.342207i	0.766172	−	0.642636i	$-0.222159\pi$
$347$	11.0411	+	6.37460i	0.592719	+	0.342207i	−0.173453	+	0.984842i	$0.555492\pi$
$348$	−11.9461	−	0.369583i	−0.640380	−	0.0198117i
$349$	23.6648			1.26675			0.633373	−	0.773847i	$-0.281670\pi$
$349$	23.6648			1.26675			0.633373	+	0.773847i	$0.281670\pi$
$350$	−5.65987	−	1.18348i	−0.302533	−	0.0632596i
$351$	2.98567	−	32.0867i	0.159363	−	1.71266i
$352$	−1.63083	+	0.941562i	−0.0869237	+	0.0501854i
$353$	−7.10645	−	4.10291i	−0.378238	−	0.218376i	0.298813	−	0.954312i	$-0.403409\pi$
$353$	−7.10645	−	4.10291i	−0.378238	−	0.218376i	−0.677051	+	0.735936i	$0.736743\pi$
$354$	−10.8674	−	20.2438i	−0.577594	−	1.07595i
$355$	−3.91507	+	2.26037i	−0.207790	+	0.119968i
$356$	6.60341			0.349980
$357$	6.24623	−	25.8536i	0.330586	−	1.36832i
$358$	−9.72409			−0.513934
$359$	4.39323	−	2.53643i	0.231866	−	0.133868i	−0.379567	−	0.925164i	$-0.623927\pi$
$359$	4.39323	−	2.53643i	0.231866	−	0.133868i	0.611433	+	0.791297i	$0.290594\pi$
$360$	−0.311115	+	5.02332i	−0.0163972	+	0.264752i
$361$	−17.0343	+	8.41613i	−0.896544	+	0.442954i
$362$	0.881990	−	0.509217i	0.0463563	−	0.0267638i
$363$	−6.79787	+	10.9758i	−0.356796	+	0.576080i
$364$	−12.2300	−	10.9389i	−0.641029	−	0.573355i
$365$		−	4.78364i		−	0.250387i
$366$	22.6564	+	0.700932i	1.18427	+	0.0366383i
$367$	12.6569	−	21.9224i	0.660685	−	1.14434i	−0.319751	−	0.947502i	$-0.603599\pi$
$367$	12.6569	−	21.9224i	0.660685	−	1.14434i	0.980436	−	0.196838i	$-0.0630674\pi$
$368$	4.73869	+	2.73588i	0.247021	+	0.142618i
$369$	−3.51351	+	5.29948i	−0.182906	+	0.275880i
$370$	−5.89032			−0.306223
$371$	19.3190	−	21.5992i	1.00299	−	1.12138i
$372$	−10.6854	−	6.61798i	−0.554010	−	0.343127i
$373$	4.95651	−	2.86164i	0.256639	−	0.148170i	−0.366162	−	0.930551i	$-0.619328\pi$
$373$	4.95651	−	2.86164i	0.256639	−	0.148170i	0.622800	+	0.782381i	$0.285995\pi$
$374$	−5.46486	+	9.46541i	−0.282581	+	0.489445i
$375$	18.3963	−	9.87557i	0.949980	−	0.509972i
$376$	3.23065	−	1.86522i	0.166608	−	0.0961911i
$377$			42.7947i			2.20404i
$378$	3.06300	+	13.4022i	0.157544	+	0.689333i
$379$		−	11.9156i		−	0.612062i	−0.952022	−	0.306031i	$-0.900999\pi$
$379$		−	11.9156i		−	0.612062i	0.952022	−	0.306031i	$-0.0990012\pi$
$380$	−7.12105	+	1.66318i	−0.365302	+	0.0853195i
$381$	−20.5690	+	11.0419i	−1.05378	+	0.565694i
$382$	6.78720	+	3.91859i	0.347263	+	0.200493i
$383$	2.20238	+	3.81464i	0.112536	+	0.194919i	0.916792	−	0.399364i	$-0.130769\pi$
$383$	2.20238	+	3.81464i	0.112536	+	0.194919i	−0.804256	+	0.594283i	$0.797436\pi$
$384$	−0.911995	+	1.47250i	−0.0465401	+	0.0751433i
$385$	−8.18156	−	1.71077i	−0.416971	−	0.0871887i
$386$		−	12.5366i		−	0.638096i
$387$	−11.6647	+	17.5941i	−0.592952	+	0.894358i
$388$	9.83890	+	5.68049i	0.499494	+	0.288383i
$389$	−22.3267	−	12.8903i	−1.13201	−	0.653565i	−0.187569	−	0.982251i	$-0.560061\pi$
$389$	−22.3267	−	12.8903i	−1.13201	−	0.653565i	−0.944439	+	0.328686i	$0.893394\pi$
$390$	18.0123	+	0.557255i	0.912090	+	0.0282177i
$391$	31.7583			1.60609
$392$	6.41352	+	2.80477i	0.323932	+	0.141662i
$393$	−18.5298	−	11.4764i	−0.934703	−	0.578909i
$394$	1.59651	−	0.921744i	0.0804309	−	0.0464368i
$395$	−4.16825	+	7.21962i	−0.209727	+	0.363258i
$396$	0.349220	−	5.63857i	0.0175490	−	0.283349i
$397$	−0.832842	−	1.44252i	−0.0417991	−	0.0723982i	0.844369	−	0.535762i	$-0.179976\pi$
$397$	−0.832842	−	1.44252i	−0.0417991	−	0.0723982i	−0.886168	+	0.463364i	$0.846642\pi$
$398$	16.4765			0.825895
$399$	−17.3744	+	9.85552i	−0.869806	+	0.493393i
$400$	2.18549			0.109275
$401$	7.42121	+	12.8539i	0.370597	+	0.641894i	0.989658	−	0.143450i	$-0.0458196\pi$
$401$	7.42121	+	12.8539i	0.370597	+	0.641894i	−0.619060	+	0.785344i	$0.712486\pi$
$402$	−9.45287	+	5.07453i	−0.471467	+	0.253095i
$403$	−22.5019	+	38.9744i	−1.12090	+	1.94145i
$404$	2.15201	−	1.24246i	0.107066	−	0.0618147i
$405$	−12.0445	−	9.10523i	−0.598495	−	0.452443i
$406$	−5.69908	−	17.3444i	−0.282840	−	0.860790i
$407$	6.61175			0.327732
$408$	−0.310862	+	10.0481i	−0.0153899	+	0.497454i
$409$	28.8596	+	16.6621i	1.42702	+	0.823888i	0.996884	−	0.0788776i	$-0.0251336\pi$
$409$	28.8596	+	16.6621i	1.42702	+	0.823888i	0.430132	+	0.902766i	$0.358467\pi$
$410$	−3.07934	−	1.77786i	−0.152078	−	0.0878022i
$411$	−0.939702	+	30.3743i	−0.0463521	+	1.49825i
$412$		−	13.8094i		−	0.680339i
$413$	23.3980	−	26.1597i	1.15134	−	1.28723i
$414$	−14.6962	+	7.31318i	−0.722281	+	0.359423i
$415$	8.98081	+	15.5552i	0.440850	+	0.763575i
$416$	5.37089	+	3.10089i	0.263330	+	0.152033i
$417$	−11.2053	−	20.8734i	−0.548728	−	1.02217i
$418$	7.99323	−	1.86689i	0.390962	−	0.0913124i
$419$			3.21593i			0.157109i	0.996910	+	0.0785543i	$0.0250304\pi$
$419$			3.21593i			0.157109i	−0.996910	+	0.0785543i	$0.974970\pi$
$420$	−7.37449	+	2.17289i	−0.359838	+	0.106026i
$421$			2.71489i			0.132316i	0.997809	+	0.0661579i	$0.0210741\pi$
$421$			2.71489i			0.132316i	−0.997809	+	0.0661579i	$0.978926\pi$
$422$	−11.1793	+	6.45439i	−0.544201	+	0.314195i
$423$	−0.691798	+	11.1699i	−0.0336364	+	0.543099i
$424$	−5.47641	+	9.48541i	−0.265958	+	0.460652i
$425$	10.9853	−	6.34234i	0.532863	−	0.307649i
$426$	2.45754	−	3.96793i	0.119068	−	0.192247i
$427$	10.8086	+	32.8946i	0.523064	+	1.59188i
$428$	6.75192			0.326366
$429$	−20.2184	−	0.625507i	−0.976156	−	0.0301998i
$430$	−10.2233	−	5.90243i	−0.493012	−	0.284641i
$431$	−0.353770	+	0.612748i	−0.0170405	+	0.0295150i	−0.874420	−	0.485170i	$-0.838758\pi$
$431$	−0.353770	+	0.612748i	−0.0170405	+	0.0295150i	0.857379	+	0.514685i	$0.172091\pi$
$432$	−2.16998	−	4.72136i	−0.104403	−	0.227156i
$433$			15.7336i			0.756109i	0.925783	+	0.378054i	$0.123407\pi$
$433$			15.7336i			0.756109i	−0.925783	+	0.378054i	$0.876593\pi$
$434$	3.92956	−	18.7927i	0.188625	−	0.902079i
$435$	17.0464	+	10.5577i	0.817310	+	0.506201i
$436$	−1.19227	+	0.688355i	−0.0570992	+	0.0329662i
$437$	−16.3107	−	17.4018i	−0.780248	−	0.832443i
$438$	2.33594	+	4.35141i	0.111616	+	0.207918i
$439$	−0.395316	+	0.228236i	−0.0188674	+	0.0108931i	−0.509404	−	0.860527i	$-0.670134\pi$
$439$	−0.395316	+	0.228236i	−0.0188674	+	0.0108931i	0.490537	+	0.871421i	$0.336801\pi$
$440$	3.15922			0.150610
$441$	−17.6449	+	11.3867i	−0.840234	+	0.542224i
$442$	35.9953			1.71212
$443$	−28.8295	+	16.6447i	−1.36973	+	0.790814i	−0.990893	−	0.134650i	$-0.957009\pi$
$443$	−28.8295	+	16.6447i	−1.36973	+	0.790814i	−0.378836	+	0.925464i	$0.623676\pi$
$444$	5.35809	−	2.87635i	0.254284	−	0.136506i
$445$	−9.59400	−	5.53910i	−0.454799	−	0.262578i
$446$	−13.0200	+	7.51707i	−0.616513	+	0.355944i
$447$	−5.40641	−	3.34846i	−0.255715	−	0.158377i
$448$	−2.58974	−	0.541515i	−0.122354	−	0.0255842i
$449$	24.7667			1.16881			0.584407	−	0.811461i	$-0.301327\pi$
$449$	24.7667			1.16881			0.584407	+	0.811461i	$0.301327\pi$
$450$	−3.62297	+	5.46458i	−0.170788	+	0.257603i
$451$	3.45650	+	1.99561i	0.162760	+	0.0939695i
$452$	−5.53164	+	9.58108i	−0.260187	+	0.450656i
$453$	−0.682107	+	22.0480i	−0.0320482	+	1.03590i
$454$	8.88027			0.416772
$455$	8.59304	+	26.1519i	0.402848	+	1.22602i
$456$	5.66546	−	4.99025i	0.265309	−	0.233690i
$457$	−15.4070	−	26.6857i	−0.720709	−	1.24830i	−0.960716	−	0.277533i	$-0.910483\pi$
$457$	−15.4070	−	26.6857i	−0.720709	−	1.24830i	0.240007	−	0.970771i	$-0.422850\pi$
$458$	1.73528	−	3.00559i	0.0810844	−	0.140442i
$459$	−24.6087	−	17.4343i	−1.14864	−	0.813763i
$460$	−4.58985	−	7.94985i	−0.214003	−	0.370664i
$461$			22.3737i			1.04205i	0.853542	+	0.521024i	$0.174450\pi$
$461$			22.3737i			1.04205i	−0.853542	+	0.521024i	$0.825550\pi$
$462$	8.27771	−	2.43902i	0.385114	−	0.113474i
$463$	6.23559			0.289792			0.144896	−	0.989447i	$-0.453715\pi$
$463$	6.23559			0.289792			0.144896	+	0.989447i	$0.453715\pi$
$464$	3.45020	+	5.97592i	0.160172	+	0.277425i
$465$	9.97329	+	18.5783i	0.462500	+	0.861549i
$466$	−0.752525	−	0.434470i	−0.0348600	−	0.0201265i
$467$	−20.4308	+	11.7957i	−0.945425	+	0.545842i	−0.891657	−	0.452712i	$-0.850457\pi$
$467$	−20.4308	+	11.7957i	−0.945425	+	0.545842i	−0.0537685	+	0.998553i	$0.517123\pi$
$468$	−16.6569	+	8.28885i	−0.769966	+	0.383152i
$469$	−12.2153	−	10.9257i	−0.564050	−	0.504503i
$470$	−6.25835			−0.288676
$471$	−30.5451	−	0.944986i	−1.40744	−	0.0435427i
$472$	−6.63269	+	11.4882i	−0.305294	+	0.528785i
$473$	11.4754	+	6.62535i	0.527642	+	0.304634i
$474$	0.266146	−	8.60271i	0.0122245	−	0.395136i
$475$	−9.11718	−	2.76197i	−0.418325	−	0.126728i
$476$	−14.5887	+	4.79358i	−0.668670	+	0.219713i
$477$	−14.6388	−	29.4174i	−0.670262	−	1.34693i
$478$	9.98985	−	5.76764i	0.456925	−	0.263806i
$479$	−16.7018	−	9.64280i	−0.763126	−	0.440591i	0.0672910	−	0.997733i	$-0.478564\pi$
$479$	−16.7018	−	9.64280i	−0.763126	−	0.440591i	−0.830417	+	0.557142i	$0.811898\pi$
$480$	2.56020	−	1.37438i	0.116856	−	0.0627314i
$481$	−10.8874	−	18.8575i	−0.496422	−	0.859828i
$482$			2.26399i			0.103122i
$483$	−18.1638	−	17.2865i	−0.826480	−	0.786562i
$484$	7.45384			0.338811
$485$	−9.52987	−	16.5062i	−0.432729	−	0.749509i
$486$	15.4024	+	2.40097i	0.698669	+	0.108910i
$487$	13.2005	+	7.62129i	0.598170	+	0.345354i	0.768321	−	0.640064i	$-0.221092\pi$
$487$	13.2005	+	7.62129i	0.598170	+	0.345354i	−0.170151	+	0.985418i	$0.554426\pi$
$488$	−6.54347	−	11.3336i	−0.296209	−	0.513049i
$489$	−16.6448	+	26.8746i	−0.752705	+	1.21531i
$490$	−6.96541	−	9.45483i	−0.314665	−	0.427126i
$491$		−	31.8405i		−	1.43694i	−0.695557	−	0.718471i	$-0.744842\pi$
$491$		−	31.8405i		−	1.43694i	0.695557	−	0.718471i	$-0.255158\pi$
$492$	3.66927	+	0.113518i	0.165423	+	0.00511778i
$493$	34.6845	+	20.0251i	1.56211	+	0.901884i
$494$	−18.4868	−	19.7235i	−0.831761	−	0.887402i
$495$	−5.23714	+	7.89926i	−0.235392	+	0.355046i
$496$			7.25660i			0.325831i
$497$	6.97854	+	1.45921i	0.313030	+	0.0654546i
$498$	−15.7652	−	9.76421i	−0.706457	−	0.437545i
$499$	−10.9039	−	18.8860i	−0.488124	−	0.845455i	0.511783	−	0.859115i	$-0.328985\pi$
$499$	−10.9039	−	18.8860i	−0.488124	−	0.845455i	−0.999907	+	0.0136598i	$0.995652\pi$
$500$	−10.4397	−	6.02737i	−0.466878	−	0.269552i
$501$	7.91891	+	14.7514i	0.353791	+	0.659044i
$502$	−18.6972	+	10.7948i	−0.834497	+	0.481797i
$503$		−	17.8945i		−	0.797875i	−0.916978	−	0.398938i	$-0.869379\pi$
$503$		−	17.8945i		−	0.797875i	0.916978	−	0.398938i	$-0.130621\pi$
$504$	5.64710	−	5.57766i	0.251542	−	0.248449i
$505$	−4.16883			−0.185510
$506$	5.15201	+	8.92354i	0.229035	+	0.396700i
$507$	20.8592	+	38.8566i	0.926388	+	1.72568i
$508$	11.6727	+	6.73923i	0.517891	+	0.299005i
$509$	16.5121	+	28.5998i	0.731887	+	1.26767i	0.956076	+	0.293120i	$0.0946935\pi$
$509$	16.5121	+	28.5998i	0.731887	+	1.26767i	−0.224189	+	0.974546i	$0.571973\pi$
$510$	8.88021	−	14.3379i	0.393223	−	0.634895i
$511$	−5.02940	+	5.62303i	−0.222488	+	0.248748i
$512$	1.00000			0.0441942
$513$	3.08572	+	22.4383i	0.136238	+	0.990676i
$514$	−0.182046	+	0.315313i	−0.00802971	+	0.0139079i
$515$	−11.5836	+	20.0634i	−0.510436	+	0.884101i
$516$	12.1818	+	0.376875i	0.536276	+	0.0165910i
$517$	7.02486			0.308953
$518$	6.92389	+	6.19293i	0.304218	+	0.272102i
$519$	−23.3943	+	37.7723i	−1.02690	+	1.65802i
$520$	−5.20220	−	9.01047i	−0.228131	−	0.395135i
$521$	5.23770	−	9.07197i	0.229468	−	0.397450i	−0.728183	−	0.685383i	$-0.759635\pi$
$521$	5.23770	−	9.07197i	0.229468	−	0.397450i	0.957651	+	0.287933i	$0.0929681\pi$
$522$	−20.6616	−	1.27966i	−0.904334	−	0.0560092i
$523$	−5.30741	+	3.06423i	−0.232077	+	0.133989i	−0.611530	−	0.791221i	$-0.709446\pi$
$523$	−5.30741	+	3.06423i	−0.232077	+	0.133989i	0.379453	+	0.925211i	$0.376112\pi$
$524$			12.5839i			0.549728i
$525$	−9.73510	−	2.35200i	−0.424875	−	0.102650i
$526$			22.3034i			0.972474i
$527$	21.0588	+	36.4749i	0.917335	+	1.58887i
$528$	−2.87376	+	1.54271i	−0.125065	+	0.0671377i
$529$	3.47011	−	6.01041i	0.150874	−	0.261322i
$530$	15.9132	−	9.18748i	0.691225	−	0.399079i
$531$	−17.7296	−	35.6286i	−0.769398	−	1.54615i
$532$	10.1192	+	5.53187i	0.438723	+	0.239837i
$533$		−	13.1444i		−	0.569349i
$534$	11.4320	+	0.353676i	0.494710	+	0.0153050i
$535$	−9.80978	−	5.66368i	−0.424114	−	0.244862i
$536$	5.36441	+	3.09715i	0.231707	+	0.133776i
$537$	−16.8346	−	0.520818i	−0.726465	−	0.0224750i
$538$	−15.9793			−0.688915
$539$	7.81852	+	10.6128i	0.336768	+	0.457127i
$540$	−0.807657	+	8.67982i	−0.0347560	+	0.373520i
$541$	−7.06541	−	12.2377i	−0.303766	−	0.526138i	0.673220	−	0.739442i	$-0.264911\pi$
$541$	−7.06541	−	12.2377i	−0.303766	−	0.526138i	−0.976986	+	0.213305i	$0.931577\pi$
$542$	8.33777	−	14.4414i	0.358138	−	0.620313i
$543$	1.55419	−	0.834329i	0.0666968	−	0.0358045i
$544$	5.02644	−	2.90202i	0.215507	−	0.124423i
$545$	2.30964			0.0989339
$546$	−20.5871	−	19.5927i	−0.881044	−	0.838491i
$547$			26.1503i			1.11811i	0.829132	+	0.559053i	$0.188835\pi$
$547$			26.1503i			1.11811i	−0.829132	+	0.559053i	$0.811165\pi$
$548$	15.1944	−	8.77249i	0.649073	−	0.374742i
$549$	39.1858	+	2.42694i	1.67241	+	0.103579i
$550$	3.56418	+	2.05778i	0.151977	+	0.0877440i
$551$	−6.84090	−	29.2899i	−0.291432	−	1.24779i
$552$	8.05719	+	4.99022i	0.342937	+	0.212398i
$553$	12.4902	−	4.10405i	0.531136	−	0.174522i
$554$	0.964689			0.0409857
$555$	−10.1974	−	0.315483i	−0.432858	−	0.0133915i
$556$	−6.83897	+	11.8454i	−0.290037	+	0.502358i
$557$	38.2625	+	22.0909i	1.62123	+	0.936020i	0.986590	+	0.163216i	$0.0521866\pi$
$557$	38.2625	+	22.0909i	1.62123	+	0.936020i	0.634644	+	0.772805i	$0.281147\pi$
$558$	−18.1443	−	12.0295i	−0.768109	−	0.509250i
$559$		−	43.6391i		−	1.84574i
$560$	3.30836	+	2.95910i	0.139804	+	0.125045i
$561$	−9.96785	+	16.0940i	−0.420843	+	0.679491i
$562$	−5.75386	−	9.96598i	−0.242712	−	0.420389i
$563$	14.6974	−	25.4567i	0.619423	−	1.07287i	−0.370169	−	0.928965i	$-0.620700\pi$
$563$	14.6974	−	25.4567i	0.619423	−	1.07287i	0.989591	−	0.143907i	$-0.0459665\pi$
$564$	5.69287	−	3.05607i	0.239713	−	0.128684i
$565$	16.0737	−	9.28015i	0.676225	−	0.390419i
$566$	−26.1728			−1.10012
$567$	4.58491	+	23.3662i	0.192548	+	0.981287i
$568$	−2.69469			−0.113067
$569$	−5.07313	−	8.78693i	−0.212677	−	0.368367i	0.739875	−	0.672745i	$-0.234885\pi$
$569$	−5.07313	−	8.78693i	−0.212677	−	0.368367i	−0.952551	+	0.304378i	$0.901551\pi$
$570$	−12.4172	+	2.49794i	−0.520100	+	0.104627i
$571$	−2.20025	+	3.81095i	−0.0920777	+	0.159483i	−0.908385	−	0.418134i	$-0.862684\pi$
$571$	−2.20025	+	3.81095i	−0.0920777	+	0.159483i	0.816308	+	0.577618i	$0.196017\pi$
$572$	5.83935	+	10.1141i	0.244156	+	0.422890i
$573$	11.5403	+	7.14747i	0.482102	+	0.298590i
$574$	1.75048	+	5.32736i	0.0730635	+	0.222360i
$575$		−	11.9585i		−	0.498705i
$576$	−1.65773	+	2.50038i	−0.0690722	+	0.104183i
$577$	−0.987047	+	1.70962i	−0.0410913	+	0.0711722i	−0.885840	−	0.463992i	$-0.846417\pi$
$577$	−0.987047	+	1.70962i	−0.0410913	+	0.0711722i	0.844748	+	0.535164i	$0.179750\pi$
$578$	8.34340	−	14.4512i	0.347040	−	0.601090i
$579$	0.671455	−	21.7036i	0.0279047	−	0.901972i
$580$		−	11.5764i		−	0.480686i
$581$	5.79769	−	27.7269i	0.240529	−	1.15030i
$582$	16.7291	+	10.3612i	0.693442	+	0.429484i
$583$	−17.8622	+	10.3128i	−0.739777	+	0.427110i
$584$	1.42570	−	2.46938i	0.0589958	−	0.102184i
$585$	31.1535	+	1.92947i	1.28804	+	0.0797736i
$586$	4.85946	+	8.41682i	0.200742	+	0.347696i
$587$			24.6473i			1.01730i	0.860972	+	0.508652i	$0.169856\pi$
$587$			24.6473i			1.01730i	−0.860972	+	0.508652i	$0.830144\pi$
$588$	10.9530	+	5.19918i	0.451695	+	0.214411i
$589$	9.17070	−	30.2722i	0.377872	−	1.24734i
$590$	19.2731	−	11.1273i	0.793461	−	0.458105i
$591$	2.81328	−	1.51024i	0.115723	−	0.0621228i
$592$	−3.04066	−	1.75553i	−0.124970	−	0.0721517i
$593$	0.825213	−	0.476437i	0.0338875	−	0.0195649i	−0.482961	−	0.875642i	$-0.660439\pi$
$593$	0.825213	−	0.476437i	0.0338875	−	0.0195649i	0.516848	+	0.856077i	$0.327105\pi$
$594$	0.906577	−	9.74291i	0.0371973	−	0.399756i
$595$	25.2166	+	5.27280i	1.03378	+	0.216164i
$596$			3.67158i			0.150394i
$597$	28.5246	+	0.882477i	1.16743	+	0.0361174i
$598$	16.9673	−	29.3883i	0.693846	−	1.20178i
$599$	−3.89609	+	6.74823i	−0.159190	+	0.275725i	−0.934577	−	0.355761i	$-0.884222\pi$
$599$	−3.89609	+	6.74823i	−0.159190	+	0.275725i	0.775387	+	0.631487i	$0.217555\pi$
$600$	3.78358	+	0.117054i	0.154464	+	0.00477872i
$601$		−	8.21500i		−	0.335097i	−0.985864	−	0.167548i	$-0.946415\pi$
$601$		−	8.21500i		−	0.335097i	0.985864	−	0.167548i	$-0.0535851\pi$
$602$	5.81153	+	17.6867i	0.236860	+	0.720855i
$603$	−16.6368	+	8.27885i	−0.677504	+	0.337141i
$604$	11.0293	−	6.36774i	0.448774	−	0.259100i
$605$	−10.8296	−	6.25247i	−0.440285	−	0.254199i
$606$	3.79215	−	2.03572i	0.154045	−	0.0826953i
$607$	−29.1674	+	16.8398i	−1.18387	+	0.683507i	−0.956907	−	0.290396i	$-0.906213\pi$
$607$	−29.1674	+	16.8398i	−1.18387	+	0.683507i	−0.226963	+	0.973903i	$0.572880\pi$
$608$	−4.17168	−	1.26377i	−0.169184	−	0.0512528i
$609$	−8.93741	−	30.3323i	−0.362162	−	1.22913i
$610$			21.9553i			0.888944i
$611$	−11.5676	−	20.0357i	−0.467977	−	0.810559i
$612$	−1.07634	+	17.3788i	−0.0435085	+	0.702496i
$613$	10.0732	−	17.4474i	0.406854	−	0.704693i	−0.587681	−	0.809093i	$-0.699959\pi$
$613$	10.0732	−	17.4474i	0.406854	−	0.704693i	0.994535	+	0.104400i	$0.0332923\pi$
$614$	16.7648	−	9.67915i	0.676572	−	0.390619i
$615$	−5.23581	−	3.24280i	−0.211128	−	0.130762i
$616$	−3.71357	−	3.32152i	−0.149624	−	0.133828i
$617$			7.95233i			0.320149i	0.987105	+	0.160074i	$0.0511734\pi$
$617$			7.95233i			0.320149i	−0.987105	+	0.160074i	$0.948827\pi$
$618$	0.739625	−	23.9071i	0.0297521	−	0.961684i
$619$	9.72833	−	16.8500i	0.391014	−	0.677257i	−0.601569	−	0.798821i	$-0.705458\pi$
$619$	9.72833	−	16.8500i	0.391014	−	0.677257i	0.992584	+	0.121564i	$0.0387909\pi$
$620$	6.08701	−	10.5430i	0.244460	−	0.423418i
$621$	−25.8342	+	11.8736i	−1.03669	+	0.476472i
$622$		−	26.3469i		−	1.05642i
$623$	5.45379	+	16.5979i	0.218501	+	0.664982i
$624$	9.13213	+	5.65599i	0.365578	+	0.226421i
$625$	4.64807	+	8.05069i	0.185923	+	0.322028i
$626$	5.38324	−	9.32405i	0.215158	−	0.372664i
$627$	13.9380	−	2.80388i	0.556632	−	0.111976i
$628$	8.82182	+	15.2798i	0.352029	+	0.609732i
$629$	−20.3783			−0.812535
$630$	−12.8833	+	3.36679i	−0.513282	+	0.134136i
$631$	12.3930			0.493359			0.246680	−	0.969097i	$-0.420660\pi$
$631$	12.3930			0.493359			0.246680	+	0.969097i	$0.420660\pi$
$632$	−4.30342	+	2.48458i	−0.171181	+	0.0988312i
$633$	−19.6996	+	10.5752i	−0.782989	+	0.420327i
$634$	0.403484	−	0.698855i	0.0160244	−	0.0277551i
$635$	−11.3061	−	19.5827i	−0.448667	−	0.777114i
$636$	−9.98891	+	16.1280i	−0.396086	+	0.639519i
$637$	17.3945	−	39.7752i	0.689197	−	1.57595i
$638$			12.9943i			0.514450i
$639$	4.46707	−	6.73775i	0.176715	−	0.266541i
$640$	−1.45289	−	0.838824i	−0.0574304	−	0.0331574i
$641$	−18.0642	+	31.2882i	−0.713495	+	1.23581i	0.250042	+	0.968235i	$0.419555\pi$
$641$	−18.0642	+	31.2882i	−0.713495	+	1.23581i	−0.963537	+	0.267574i	$0.913778\pi$
$642$	11.6891	+	0.361630i	0.461331	+	0.0142724i
$643$	20.5963			0.812237			0.406119	−	0.913820i	$-0.366882\pi$
$643$	20.5963			0.812237			0.406119	+	0.913820i	$0.366882\pi$
$644$	−2.96304	+	14.1705i	−0.116760	+	0.558394i
$645$	−17.3827	−	10.7660i	−0.684443	−	0.423910i
$646$	−24.6362	+	5.75399i	−0.969297	+	0.226388i
$647$	−25.6124	−	14.7873i	−1.00693	−	0.581350i	−0.0966369	−	0.995320i	$-0.530809\pi$
$647$	−25.6124	−	14.7873i	−1.00693	−	0.581350i	−0.910291	+	0.413970i	$0.864142\pi$
$648$	−3.50384	−	8.28994i	−0.137644	−	0.325660i
$649$	−21.6336	+	12.4902i	−0.849194	+	0.490282i
$650$		−	13.5539i		−	0.531629i
$651$	7.80947	−	32.3239i	0.306077	−	1.26687i
$652$	18.2510			0.714764
$653$	30.9910	−	17.8927i	1.21277	−	0.700195i	0.249411	−	0.968398i	$-0.419763\pi$
$653$	30.9910	−	17.8927i	1.21277	−	0.700195i	0.963362	+	0.268203i	$0.0864297\pi$
$654$	−2.10095	+	1.12784i	−0.0821535	+	0.0441020i
$655$	10.5556	−	18.2829i	0.412443	−	0.714373i
$656$	−1.05973	−	1.83551i	−0.0413756	−	0.0716647i
$657$	3.81098	+	7.65837i	0.148680	+	0.298782i
$658$	7.35650	+	6.57987i	0.286786	+	0.256510i
$659$	−7.97290			−0.310580			−0.155290	−	0.987869i	$-0.549631\pi$
$659$	−7.97290			−0.310580			−0.155290	+	0.987869i	$0.549631\pi$
$660$	5.46931	+	0.169207i	0.212893	+	0.00658636i
$661$	−36.4070	−	21.0196i	−1.41607	−	0.817566i	−0.420116	−	0.907470i	$-0.638011\pi$
$661$	−36.4070	−	21.0196i	−1.41607	−	0.817566i	−0.995950	+	0.0899038i	$0.971344\pi$
$662$	9.13676	+	5.27511i	0.355110	+	0.205023i
$663$	62.3159	+	1.92789i	2.42015	+	0.0748732i
$664$			10.7064i			0.415490i
$665$	−10.0618	−	16.5254i	−0.390180	−	0.640828i
$666$	9.43010	−	4.69263i	0.365409	−	0.181836i
$667$	32.6989	−	18.8787i	1.26610	−	0.730986i
$668$	4.83316	−	8.37128i	0.187001	−	0.323894i
$669$	−22.9431	+	12.3164i	−0.887030	+	0.476179i
$670$	−5.19592	−	8.99960i	−0.200736	−	0.347685i
$671$		−	24.6443i		−	0.951384i
$672$	−4.45442	−	1.07619i	−0.171833	−	0.0415149i
$673$			6.77033i			0.260977i	0.991450	+	0.130488i	$0.0416546\pi$
$673$			6.77033i			0.260977i	−0.991450	+	0.130488i	$0.958345\pi$
$674$	−3.05182	+	1.76197i	−0.117552	+	0.0678684i
$675$	−6.56484	+	9.26635i	−0.252681	+	0.356662i
$676$	12.7310	−	22.0507i	0.489654	−	0.848105i
$677$	−9.66590	−	16.7418i	−0.371491	−	0.643441i	0.618304	−	0.785939i	$-0.287820\pi$
$677$	−9.66590	−	16.7418i	−0.371491	−	0.643441i	−0.989795	+	0.142498i	$0.954487\pi$
$678$	−10.0897	+	16.2907i	−0.387491	+	0.625641i
$679$	−6.15214	+	29.4220i	−0.236098	+	1.12911i
$680$	−9.73713			−0.373402
$681$	15.3737	+	0.475624i	0.589122	+	0.0182259i
$682$	−6.83254	+	11.8343i	−0.261631	+	0.453159i
$683$	−4.84130	+	8.38537i	−0.185247	+	0.320857i	−0.943660	−	0.330917i	$-0.892642\pi$
$683$	−4.84130	+	8.38537i	−0.185247	+	0.320857i	0.758413	+	0.651775i	$0.225975\pi$
$684$	10.0754	−	8.33579i	0.385244	−	0.318727i
$685$	−29.4343			−1.12463
$686$	−1.75293	+	18.4371i	−0.0669273	+	0.703932i
$687$	3.16514	−	5.11041i	0.120757	−	0.194974i
$688$	−3.51828	−	6.09384i	−0.134133	−	0.232325i
$689$	58.8264	+	33.9634i	2.24111	+	1.29390i
$690$	−7.52026	−	14.0088i	−0.286291	−	0.533306i
$691$	−20.3764	−	35.2930i	−0.775157	−	1.34261i	−0.934706	−	0.355421i	$-0.884338\pi$
$691$	−20.3764	−	35.2930i	−0.775157	−	1.34261i	0.159550	−	0.987190i	$-0.448996\pi$
$692$	25.6518			0.975134
$693$	14.4612	−	3.77914i	0.549335	−	0.143558i
$694$		−	12.7492i		−	0.483953i
$695$	19.8725	−	11.4734i	0.753806	−	0.435210i
$696$	5.65300	+	10.5304i	0.214276	+	0.399155i
$697$	−10.6534	−	6.15073i	−0.403525	−	0.232975i
$698$	−11.8324	−	20.4943i	−0.447862	−	0.775720i
$699$	−1.27952	−	0.792470i	−0.0483958	−	0.0299740i
$700$	1.80501	+	5.49333i	0.0682230	+	0.207628i
$701$			35.1465i			1.32746i	0.747971	+	0.663732i	$0.231028\pi$
$701$			35.1465i			1.32746i	−0.747971	+	0.663732i	$0.768972\pi$
$702$	−29.2808	+	13.4577i	−1.10513	+	0.507928i
$703$	10.4661	+	11.1662i	0.394735	+	0.421141i
$704$	1.63083	+	0.941562i	0.0614643	+	0.0354865i
$705$	−10.8346	−	0.335195i	−0.408055	−	0.0126242i
$706$			8.20582i			0.308830i
$707$	4.90033	+	4.38300i	0.184296	+	0.164840i
$708$	−12.0980	+	19.5333i	−0.454669	+	0.734107i
$709$	19.4394	+	33.6700i	0.730061	+	1.26450i	0.956857	+	0.290561i	$0.0938418\pi$
$709$	19.4394	+	33.6700i	0.730061	+	1.26450i	−0.226795	+	0.973942i	$0.572825\pi$
$710$	3.91507	+	2.26037i	0.146930	+	0.0848301i
$711$	0.921516	−	14.8790i	0.0345595	−	0.558005i
$712$	−3.30170	−	5.71872i	−0.123737	−	0.214318i
$713$	39.7064			1.48702
$714$	−25.5130	+	7.51739i	−0.954799	+	0.281331i
$715$		−	19.5928i		−	0.732728i
$716$	4.86204	+	8.42131i	0.181703	+	0.314719i
$717$	17.6036	−	9.45002i	0.657417	−	0.352917i
$718$	−4.39323	−	2.53643i	−0.163954	−	0.0946588i
$719$	−32.0990	+	18.5323i	−1.19709	+	0.691140i	−0.959905	−	0.280325i	$-0.909558\pi$
$719$	−32.0990	+	18.5323i	−1.19709	+	0.691140i	−0.237184	+	0.971465i	$0.576225\pi$
$720$	4.50588	−	2.24223i	0.167924	−	0.0835629i
$721$	34.7104	−	11.4052i	1.29268	−	0.424753i
$722$	15.8058	+	10.5441i	0.588229	+	0.392411i
$723$	−0.121258	+	3.91947i	−0.00450965	+	0.145767i
$724$	−0.881990	−	0.509217i	−0.0327789	−	0.0189249i
$725$	7.54040	−	13.0603i	0.280043	−	0.485049i
$726$	12.9043	+	0.399225i	0.478922	+	0.0148166i
$727$	8.11741			0.301058			0.150529	−	0.988606i	$-0.451902\pi$
$727$	8.11741			0.301058			0.150529	+	0.988606i	$0.451902\pi$
$728$	−3.35835	+	16.0610i	−0.124469	+	0.595260i
$729$	26.5365	+	4.98156i	0.982832	+	0.184502i
$730$	−4.14276	+	2.39182i	−0.153330	+	0.0885253i
$731$	−35.3688	−	20.4202i	−1.30816	−	0.755268i
$732$	−10.7212	−	19.9715i	−0.396266	−	0.738168i
$733$	0.922882	+	1.59848i	0.0340874	+	0.0590412i	0.882566	−	0.470189i	$-0.155814\pi$
$733$	0.922882	+	1.59848i	0.0340874	+	0.0590412i	−0.848478	+	0.529230i	$0.822481\pi$
$734$	−25.3138			−0.934350
$735$	−11.5523	−	16.7415i	−0.426112	−	0.617519i
$736$		−	5.47177i		−	0.201692i
$737$	5.83231	+	10.1019i	0.214836	+	0.372107i
$738$	6.34624	+	0.393049i	0.233608	+	0.0144683i
$739$	−9.74739	+	16.8830i	−0.358563	+	0.621050i	−0.987721	−	0.156228i	$-0.950067\pi$
$739$	−9.74739	+	16.8830i	−0.358563	+	0.621050i	0.629158	+	0.777278i	$0.283400\pi$
$740$	2.94516	+	5.10116i	0.108266	+	0.187523i
$741$	−30.9484	−	35.1359i	−1.13692	−	1.29075i
$742$	−28.3650	−	5.93111i	−1.04131	−	0.217738i
$743$	23.9925			0.880200			0.440100	−	0.897949i	$-0.354943\pi$
$743$	23.9925			0.880200			0.440100	+	0.897949i	$0.354943\pi$
$744$	−0.388661	+	12.5628i	−0.0142490	+	0.460574i
$745$	3.07981	−	5.33439i	0.112836	−	0.195437i
$746$	−4.95651	−	2.86164i	−0.181471	−	0.104772i
$747$	−26.7702	−	17.7484i	−0.979469	−	0.649380i
$748$	10.9297			0.399630
$749$	5.57645	+	16.9712i	0.203759	+	0.620115i
$750$	−17.7506	−	10.9939i	−0.648161	−	0.401439i
$751$	−14.6805	+	8.47581i	−0.535700	+	0.309287i	−0.743335	−	0.668920i	$-0.766757\pi$
$751$	−14.6805	+	8.47581i	−0.535700	+	0.309287i	0.207634	+	0.978207i	$0.433424\pi$
$752$	−3.23065	−	1.86522i	−0.117810	−	0.0680174i
$753$	−32.9472	+	17.6868i	−1.20066	+	0.644544i
$754$	37.0613	−	21.3974i	1.34969	−	0.779246i
$755$	−21.3657			−0.777576
$756$	10.0751	−	9.35372i	0.366428	−	0.340191i
$757$	−34.7601			−1.26338			−0.631689	−	0.775222i	$-0.717638\pi$
$757$	−34.7601			−1.26338			−0.631689	+	0.775222i	$0.717638\pi$
$758$	−10.3192	+	5.95779i	−0.374810	+	0.216397i
$759$	8.44133	+	15.7246i	0.306401	+	0.570766i
$760$	5.00089	+	5.33542i	0.181401	+	0.193536i
$761$	13.4406	−	7.75991i	0.487220	−	0.281297i	−0.236200	−	0.971704i	$-0.575902\pi$
$761$	13.4406	−	7.75991i	0.487220	−	0.281297i	0.723420	+	0.690408i	$0.242569\pi$
$762$	19.8471	+	12.2923i	0.718983	+	0.445302i
$763$	−2.71491	−	2.42829i	−0.0982862	−	0.0879101i
$764$		−	7.83718i		−	0.283539i
$765$	16.1416	−	24.3466i	0.583599	−	0.880252i
$766$	2.20238	−	3.81464i	0.0795753	−	0.137828i
$767$	71.2469	+	41.1344i	2.57258	+	1.48528i
$768$	1.73122	+	0.0535596i	0.0624701	+	0.00193267i
$769$	−53.7765			−1.93923			−0.969615	−	0.244636i	$-0.921332\pi$
$769$	−53.7765			−1.93923			−0.969615	+	0.244636i	$0.921332\pi$
$770$	2.60922	+	7.94083i	0.0940296	+	0.286167i
$771$	−0.332050	+	0.536127i	−0.0119585	+	0.0193081i
$772$	−10.8570	+	6.26830i	−0.390752	+	0.225601i
$773$	5.30069	−	9.18107i	0.190653	−	0.330220i	−0.754814	−	0.655939i	$-0.772273\pi$
$773$	5.30069	−	9.18107i	0.190653	−	0.330220i	0.945467	+	0.325719i	$0.105606\pi$
$774$	21.0693	+	1.30491i	0.757320	+	0.0469040i
$775$	13.7345	−	7.92963i	0.493359	−	0.284841i
$776$		−	11.3610i		−	0.407835i
$777$	11.6551	+	11.0922i	0.418124	+	0.397930i
$778$			25.7806i			0.924281i
$779$	2.10119	+	8.99642i	0.0752830	+	0.322330i
$780$	−8.52357	−	15.8778i	−0.305193	−	0.568515i
$781$	−4.39458	−	2.53721i	−0.157251	−	0.0907886i
$782$	−15.8792	−	27.5035i	−0.567837	−	0.983523i
$783$	−35.7013	−	3.32200i	−1.27586	−	0.118719i
$784$	−0.777761	−	6.95666i	−0.0277772	−	0.248452i
$785$		−	29.5998i		−	1.05646i
$786$	−0.673987	+	21.7855i	−0.0240403	+	0.777062i
$787$	−26.4523	−	15.2722i	−0.942922	−	0.544397i	−0.0520472	−	0.998645i	$-0.516575\pi$
$787$	−26.4523	−	15.2722i	−0.942922	−	0.544397i	−0.890875	+	0.454248i	$0.849908\pi$
$788$	−1.59651	−	0.921744i	−0.0568732	−	0.0328358i
$789$	−1.19456	+	38.6121i	−0.0425275	+	1.37463i
$790$	8.33650			0.296599
$791$	−28.6510	−	5.99093i	−1.01871	−	0.213013i
$792$	−5.05775	+	2.51685i	−0.179719	+	0.0894324i
$793$	−70.2886	+	40.5811i	−2.49602	+	1.44108i
$794$	−0.832842	+	1.44252i	−0.0295565	+	0.0511933i
$795$	28.0414	−	15.0533i	0.994524	−	0.533885i
$796$	−8.23827	−	14.2691i	−0.291998	−	0.505755i
$797$	9.20729			0.326139			0.163069	−	0.986615i	$-0.447861\pi$
$797$	9.20729			0.326139			0.163069	+	0.986615i	$0.447861\pi$
$798$	17.2223	+	10.1189i	0.609663	+	0.358205i
$799$	−21.6515			−0.765976
$800$	−1.09275	−	1.89269i	−0.0386345	−	0.0669168i
$801$	19.7723	+	1.22458i	0.698621	+	0.0432685i
$802$	7.42121	−	12.8539i	0.262052	−	0.453887i
$803$	4.65015	−	2.68477i	0.164100	−	0.0947434i
$804$	9.12111	+	5.64916i	0.321677	+	0.199231i
$805$	16.1915	−	18.1026i	0.570675	−	0.638033i
$806$	45.0038			1.58519
$807$	−27.6636	−	0.855843i	−0.973806	−	0.0301271i
$808$	−2.15201	−	1.24246i	−0.0757073	−	0.0437096i
$809$	37.5452	+	21.6767i	1.32002	+	0.762113i	0.983731	−	0.179646i	$-0.0574952\pi$
$809$	37.5452	+	21.6767i	1.32002	+	0.762113i	0.336288	+	0.941759i	$0.390829\pi$
$810$	−1.86312	+	14.9834i	−0.0654634	+	0.526465i
$811$			2.37812i			0.0835070i	0.999128	+	0.0417535i	$0.0132944\pi$
$811$			2.37812i			0.0835070i	−0.999128	+	0.0417535i	$0.986706\pi$
$812$	−12.1712	+	13.6078i	−0.427125	+	0.477539i
$813$	15.2080	−	24.5548i	0.533368	−	0.861174i
$814$	−3.30588	−	5.72595i	−0.115871	−	0.200694i
$815$	−26.5166	−	15.3094i	−0.928837	−	0.536264i
$816$	8.85732	−	4.75482i	0.310068	−	0.166452i
$817$	6.97589	+	29.8678i	0.244055	+	1.04494i
$818$		−	33.3242i		−	1.16515i
$819$	−34.5914	−	35.0220i	−1.20872	−	1.22377i
$820$			3.55572i			0.124171i
$821$	45.5218	−	26.2820i	1.58872	−	0.917248i	0.595202	−	0.803576i	$-0.297072\pi$
$821$	45.5218	−	26.2820i	1.58872	−	0.917248i	0.993518	−	0.113672i	$-0.0362613\pi$
$822$	26.7747	−	14.3733i	0.933876	−	0.501327i
$823$	3.54044	−	6.13222i	0.123412	−	0.213756i	−0.797699	−	0.603056i	$-0.793950\pi$
$823$	3.54044	−	6.13222i	0.123412	−	0.213756i	0.921111	+	0.389300i	$0.127283\pi$
$824$	−11.9593	+	6.90469i	−0.416621	+	0.240536i
$825$	6.06017	+	3.75337i	0.210988	+	0.130676i
$826$	−34.3539	−	7.18340i	−1.19533	−	0.249943i
$827$	−3.77750			−0.131357			−0.0656784	−	0.997841i	$-0.520921\pi$
$827$	−3.77750			−0.131357			−0.0656784	+	0.997841i	$0.520921\pi$
$828$	13.6815	+	9.07073i	0.475466	+	0.315230i
$829$	−35.0687	−	20.2469i	−1.21799	−	0.703205i	−0.253499	−	0.967336i	$-0.581582\pi$
$829$	−35.0687	−	20.2469i	−1.21799	−	0.703205i	−0.964487	+	0.264131i	$0.914915\pi$
$830$	8.98081	−	15.5552i	0.311728	−	0.539929i
$831$	1.67009	+	0.0516684i	0.0579348	+	0.00179236i
$832$		−	6.20177i		−	0.215008i
$833$	−24.0977	−	32.7101i	−0.834936	−	1.13334i
$834$	−12.4742	+	20.1408i	−0.431946	+	0.697419i
$835$	−14.0441	+	8.10834i	−0.486015	+	0.280601i
$836$	−5.61339	−	5.98889i	−0.194143	−	0.207130i
$837$	−30.7675	−	21.7976i	−1.06348	−	0.753434i
$838$	2.78508	−	1.60797i	0.0962090	−	0.0555463i
$839$	−17.2654			−0.596069			−0.298034	−	0.954555i	$-0.596331\pi$
$839$	−17.2654			−0.596069			−0.298034	+	0.954555i	$0.596331\pi$
$840$	5.56903	+	5.30005i	0.192150	+	0.182869i
$841$	18.6155			0.641915
$842$	2.35117	−	1.35745i	0.0810265	−	0.0467807i
$843$	−9.42744	−	17.5615i	−0.324698	−	0.604850i
$844$	11.1793	+	6.45439i	0.384808	+	0.222169i
$845$	−36.9934	+	21.3581i	−1.27261	+	0.734742i
$846$	10.0193	−	4.98583i	0.344471	−	0.171416i
$847$	6.15617	+	18.7355i	0.211528	+	0.643760i
$848$	10.9528			0.376121
$849$	−45.3109	−	1.40180i	−1.55507	−	0.0481098i
$850$	−10.9853	−	6.34234i	−0.376791	−	0.217541i
$851$	−9.60584	+	16.6378i	−0.329284	+	0.570336i
$852$	−4.66510	−	0.144326i	−0.159824	−	0.00494454i
$853$	−28.6752			−0.981821			−0.490911	−	0.871210i	$-0.663336\pi$
$853$	−28.6752			−0.981821			−0.490911	+	0.871210i	$0.663336\pi$
$854$	23.0832	−	25.8078i	0.789892	−	0.883124i
$855$	−21.6307	+	3.65943i	−0.739756	+	0.125150i
$856$	−3.37596	−	5.84734i	−0.115388	−	0.199858i
$857$	5.27762	−	9.14110i	0.180280	−	0.312254i	−0.761696	−	0.647935i	$-0.775633\pi$
$857$	5.27762	−	9.14110i	0.180280	−	0.312254i	0.941976	+	0.335681i	$0.108966\pi$
$858$	9.56752	+	17.8224i	0.326630	+	0.608448i
$859$	10.6346	+	18.4196i	0.362847	+	0.628470i	0.988428	−	0.151689i	$-0.0484714\pi$
$859$	10.6346	+	18.4196i	0.362847	+	0.628470i	−0.625581	+	0.780159i	$0.715138\pi$
$860$			11.8049i			0.402543i
$861$	2.74514	+	9.31660i	0.0935540	+	0.317509i
$862$	0.707540			0.0240989
$863$	−16.6074	−	28.7649i	−0.565323	−	0.979167i	−0.997020	−	0.0771487i	$-0.975418\pi$
$863$	−16.6074	−	28.7649i	−0.565323	−	0.979167i	0.431697	−	0.902019i	$-0.357915\pi$
$864$	−3.00382	+	4.23993i	−0.102192	+	0.144245i
$865$	−37.2691	−	21.5173i	−1.26719	−	0.731611i
$866$	13.6257	−	7.86680i	0.463020	−	0.267325i
$867$	15.2183	−	24.5714i	0.516840	−	0.834487i
$868$	−18.2398	+	5.99326i	−0.619097	+	0.203425i
$869$	−9.35754			−0.317433
$870$	0.620030	−	20.0414i	0.0210210	−	0.679467i
$871$	19.2078	−	33.2689i	0.650831	−	1.12727i
$872$	1.19227	+	0.688355i	0.0403752	+	0.0233106i
$873$	28.4068	+	18.8335i	0.961425	+	0.637417i
$874$	−6.91507	+	22.8264i	−0.233906	+	0.772116i
$875$	6.52782	−	31.2187i	0.220681	−	1.05538i
$876$	2.60046	−	4.19869i	0.0878614	−	0.141861i
$877$	−4.44865	+	2.56843i	−0.150220	+	0.0867297i	−0.573226	−	0.819397i	$-0.694308\pi$
$877$	−4.44865	+	2.56843i	−0.150220	+	0.0867297i	0.423006	+	0.906127i	$0.360975\pi$
$878$	0.395316	+	0.228236i	0.0133413	+	0.00770258i
$879$	7.96200	+	14.8317i	0.268552	+	0.500260i
$880$	−1.57961	−	2.73597i	−0.0532486	−	0.0922294i
$881$		−	50.3341i		−	1.69580i	−0.530157	−	0.847900i	$-0.677867\pi$
$881$		−	50.3341i		−	1.69580i	0.530157	−	0.847900i	$-0.322133\pi$
$882$	18.6836	+	9.58758i	0.629111	+	0.322831i
$883$	0.790125			0.0265898			0.0132949	−	0.999912i	$-0.495768\pi$
$883$	0.790125			0.0265898			0.0132949	+	0.999912i	$0.495768\pi$
$884$	−17.9976	−	31.1728i	−0.605326	−	1.04846i
$885$	33.9620	−	18.2316i	1.14162	−	0.612849i
$886$	28.8295	+	16.6447i	0.968545	+	0.559190i
$887$	10.7878	+	18.6850i	0.362219	+	0.627382i	0.988326	−	0.152356i	$-0.0486859\pi$
$887$	10.7878	+	18.6850i	0.362219	+	0.627382i	−0.626107	+	0.779737i	$0.715353\pi$
$888$	−5.17004	−	3.20207i	−0.173495	−	0.107454i
$889$	−7.29878	+	34.9057i	−0.244793	+	1.17070i
$890$			11.0782i			0.371342i
$891$	2.09131	−	16.8186i	0.0700616	−	0.563444i
$892$	13.0200	+	7.51707i	0.435940	+	0.251690i
$893$	11.1200	+	11.8639i	0.372117	+	0.397010i
$894$	−0.196648	+	6.35632i	−0.00657691	+	0.212587i
$895$		−	16.3136i		−	0.545304i
$896$	0.825905	+	2.51354i	0.0275916	+	0.0839715i
$897$	30.9482	−	49.9689i	1.03333	−	1.66841i
$898$	−12.3834	−	21.4486i	−0.413238	−	0.715750i
$899$	43.3649	+	25.0367i	1.44630	+	0.835022i
$900$	6.54395	+	0.405294i	0.218132	+	0.0135098i
$901$	55.0536	−	31.7852i	1.83410	−	1.05892i
$902$		−	3.99122i		−	0.132893i
$903$	9.11376	+	30.9308i	0.303287	+	1.02931i
$904$	11.0633			0.367959
$905$	0.854287	+	1.47967i	0.0283975	+	0.0491859i
$906$	19.4351	−	10.4333i	0.645689	−	0.346622i
$907$	18.6722	+	10.7804i	0.619999	+	0.357957i	0.776869	−	0.629663i	$-0.216807\pi$
$907$	18.6722	+	10.7804i	0.619999	+	0.357957i	−0.156869	+	0.987619i	$0.550140\pi$
$908$	−4.44013	−	7.69054i	−0.147351	−	0.255219i
$909$	6.67408	−	3.32117i	0.221365	−	0.110156i
$910$	18.3517	−	20.5177i	0.608351	−	0.680156i
$911$	−1.77715			−0.0588797			−0.0294398	−	0.999567i	$-0.509372\pi$
$911$	−1.77715			−0.0588797			−0.0294398	+	0.999567i	$0.509372\pi$
$912$	−7.15441	−	2.41131i	−0.236906	−	0.0798463i
$913$	−10.0808	+	17.4604i	−0.333624	+	0.577854i
$914$	−15.4070	+	26.6857i	−0.509618	+	0.882685i
$915$	−1.17592	+	38.0095i	−0.0388746	+	1.25656i
$916$	−3.47056			−0.114671
$917$	−31.6300	+	10.3931i	−1.04452	+	0.343209i
$918$	−2.79419	+	30.0289i	−0.0922220	+	0.991102i
$919$	17.3122	+	29.9856i	0.571077	+	0.989134i	0.996456	+	0.0841185i	$0.0268074\pi$
$919$	17.3122	+	29.9856i	0.571077	+	0.989134i	−0.425379	+	0.905015i	$0.639859\pi$
$920$	−4.58985	+	7.94985i	−0.151323	+	0.262099i
$921$	29.5420	−	15.8588i	0.973441	−	0.522567i
$922$	19.3762	−	11.1869i	0.638122	−	0.368420i
$923$			16.7118i			0.550077i
$924$	−6.25111	−	5.94919i	−0.205646	−	0.195714i
$925$			7.67339i			0.252300i
$926$	−3.11779	−	5.40018i	−0.102457	−	0.177461i
$927$	2.56091	−	41.3489i	0.0841113	−	1.35808i
$928$	3.45020	−	5.97592i	0.113258	−	0.196169i
$929$	1.97501	−	1.14027i	0.0647980	−	0.0374112i	−0.467251	−	0.884125i	$-0.654756\pi$
$929$	1.97501	−	1.14027i	0.0647980	−	0.0374112i	0.532049	+	0.846714i	$0.321422\pi$
$930$	11.1027	−	17.9263i	0.364070	−	0.587826i
$931$	−5.54707	+	30.0038i	−0.181798	+	0.983336i
$932$			0.868941i			0.0284631i
$933$	1.41113	−	45.6124i	0.0461984	−	1.49328i
$934$	20.4308	+	11.7957i	0.668517	+	0.385968i
$935$	−15.8796	−	9.16811i	−0.519319	−	0.299829i
$936$	15.5068	+	10.2809i	0.506856	+	0.336041i
$937$	53.3235			1.74200			0.871001	−	0.491281i	$-0.163471\pi$
$937$	53.3235			1.74200			0.871001	+	0.491281i	$0.163471\pi$
$938$	−3.35430	+	16.0416i	−0.109522	+	0.523777i
$939$	9.81898	−	15.8537i	0.320430	−	0.517365i
$940$	3.12918	+	5.41989i	0.102062	+	0.176777i
$941$	−25.9239	+	44.9016i	−0.845096	+	1.46375i	0.0404409	+	0.999182i	$0.487124\pi$
$941$	−25.9239	+	44.9016i	−0.845096	+	1.46375i	−0.885537	+	0.464568i	$0.846210\pi$
$942$	14.4541	+	26.9253i	0.470941	+	0.877273i
$943$	−10.0435	+	5.79861i	−0.327061	+	0.188829i
$944$	13.2654			0.431751
$945$	−22.4841	+	5.13863i	−0.731409	+	0.167160i
$946$		−	13.2507i		−	0.430818i
$947$	10.0954	−	5.82859i	0.328057	−	0.189404i	−0.326921	−	0.945052i	$-0.606011\pi$
$947$	10.0954	−	5.82859i	0.328057	−	0.189404i	0.654978	+	0.755648i	$0.272678\pi$
$948$	−7.58324	+	4.07087i	−0.246292	+	0.132216i
$949$	−15.3146	−	8.84186i	−0.497131	−	0.287019i
$950$	2.16665	+	9.27669i	0.0702954	+	0.300976i
$951$	0.735951	−	1.18826i	0.0238648	−	0.0385321i
$952$	11.4457	+	10.2374i	0.370957	+	0.331795i
$953$	−10.3944			−0.336707			−0.168354	−	0.985727i	$-0.553845\pi$
$953$	−10.3944			−0.336707			−0.168354	+	0.985727i	$0.553845\pi$
$954$	−18.1568	+	27.3862i	−0.587849	+	0.886662i
$955$	−6.57402	+	11.3865i	−0.212730	+	0.368460i
$956$	−9.98985	−	5.76764i	−0.323095	−	0.186539i
$957$	−0.695970	+	22.4960i	−0.0224975	+	0.727194i
$958$			19.2856i			0.623090i
$959$	34.5991	+	30.9465i	1.11726	+	0.999314i
$960$	−2.47034	−	1.53001i	−0.0797300	−	0.0493808i
$961$	10.8291	+	18.7566i	0.349327	+	0.605051i
$962$	−10.8874	+	18.8575i	−0.351023	+	0.607990i
$963$	20.2170	+	1.25213i	0.651485	+	0.0403492i
$964$	1.96067	−	1.13200i	0.0631490	−	0.0364591i
$965$	21.0320			0.677044
$966$	−5.88865	+	24.3735i	−0.189464	+	0.784205i
$967$	15.5191			0.499060			0.249530	−	0.968367i	$-0.419724\pi$
$967$	15.5191			0.499060			0.249530	+	0.968367i	$0.419724\pi$
$968$	−3.72692	−	6.45522i	−0.119788	−	0.207479i
$969$	−42.9589	+	8.64193i	−1.38004	+	0.277619i
$970$	−9.52987	+	16.5062i	−0.305986	+	0.529983i
$971$	26.5466	+	45.9801i	0.851922	+	1.47557i	0.879471	+	0.475952i	$0.157896\pi$
$971$	26.5466	+	45.9801i	0.851922	+	1.47557i	−0.0275491	+	0.999620i	$0.508770\pi$
$972$	−5.62192	−	14.5394i	−0.180323	−	0.466351i
$973$	−35.4223	−	7.40680i	−1.13559	−	0.237451i
$974$		−	15.2426i		−	0.488404i
$975$	0.725944	−	23.4649i	0.0232488	−	0.751478i
$976$	−6.54347	+	11.3336i	−0.209452	+	0.362781i
$977$	−12.2250	+	21.1743i	−0.391112	+	0.677426i	−0.992596	−	0.121459i	$-0.961243\pi$
$977$	−12.2250	+	21.1743i	−0.391112	+	0.677426i	0.601484	+	0.798884i	$0.294576\pi$
$978$	31.5965	+	0.977516i	1.01035	+	0.0312575i
$979$		−	12.4350i		−	0.397425i
$980$	−4.70542	+	10.7596i	−0.150309	+	0.343704i
$981$	−3.69761	+	1.84001i	−0.118056	+	0.0587471i
$982$	−27.5747	+	15.9203i	−0.879944	+	0.508036i
$983$	25.1696	−	43.5949i	0.802784	−	1.39046i	−0.114993	−	0.993366i	$-0.536685\pi$
$983$	25.1696	−	43.5949i	0.802784	−	1.39046i	0.917777	−	0.397096i	$-0.129982\pi$
$984$	−1.73632	−	3.23444i	−0.0553520	−	0.103110i
$985$	1.54636	+	2.67838i	0.0492712	+	0.0853403i
$986$		−	40.0502i		−	1.27546i
$987$	12.3833	+	11.7852i	0.394165	+	0.375128i
$988$	−7.83764	+	25.8718i	−0.249348	+	0.823091i
$989$	−33.3440	+	19.2512i	−1.06028	+	0.612152i
$990$	9.45954	+	0.585869i	0.300644	+	0.0186201i
$991$	34.8170	+	20.1016i	1.10600	+	0.638549i	0.937790	−	0.347203i	$-0.112868\pi$
$991$	34.8170	+	20.1016i	1.10600	+	0.638549i	0.168208	+	0.985751i	$0.446202\pi$
$992$	6.28440	−	3.62830i	0.199530	−	0.115199i
$993$	15.5352	+	9.62175i	0.492996	+	0.305337i
$994$	−2.22555	−	6.77320i	−0.0705903	−	0.214833i
$995$			27.6419i			0.876306i
$996$	−0.573432	+	18.5352i	−0.0181699	+	0.587310i
$997$	−7.71246	+	13.3584i	−0.244256	+	0.423064i	−0.961922	−	0.273323i	$-0.911877\pi$
$997$	−7.71246	+	13.3584i	−0.244256	+	0.423064i	0.717666	+	0.696387i	$0.245210\pi$
$998$	−10.9039	+	18.8860i	−0.345155	+	0.597827i
$999$	16.5769	−	7.61891i	0.524471	−	0.241052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bf.a.683.10	yes	52
3.2	odd	2		798.2.bf.b.683.1	yes	52
7.2	even	3	inner	798.2.bf.a.569.26	yes	52
19.18	odd	2		798.2.bf.b.683.17	yes	52
21.2	odd	6		798.2.bf.b.569.17	yes	52
57.56	even	2	inner	798.2.bf.a.683.26	yes	52
133.37	odd	6		798.2.bf.b.569.1	yes	52
399.170	even	6	inner	798.2.bf.a.569.10	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bf.a.569.10	✓	52	399.170	even	6	inner
798.2.bf.a.569.26	yes	52	7.2	even	3	inner
798.2.bf.a.683.10	yes	52	1.1	even	1	trivial
798.2.bf.a.683.26	yes	52	57.56	even	2	inner
798.2.bf.b.569.1	yes	52	133.37	odd	6
798.2.bf.b.569.17	yes	52	21.2	odd	6
798.2.bf.b.683.1	yes	52	3.2	odd	2
798.2.bf.b.683.17	yes	52	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.819227 - 1.52606i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.45289 - 0.838824i) q^{5} +(-0.911995 + 1.47250i) q^{6} +(-2.58974 - 0.541515i) q^{7} +1.00000 q^{8} +(-1.65773 + 2.50038i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.819227 - 1.52606i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.45289 - 0.838824i) q^{5} +(-0.911995 + 1.47250i) q^{6} +(-2.58974 - 0.541515i) q^{7} +1.00000 q^{8} +(-1.65773 + 2.50038i) q^{9} +(-1.45289 - 0.838824i) q^{10} +(1.63083 + 0.941562i) q^{11} +(1.73122 + 0.0535596i) q^{12} -6.20177i q^{13} +(0.825905 + 2.51354i) q^{14} +(-2.47034 - 1.53001i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.02644 - 2.90202i) q^{17} +(2.99426 + 0.185447i) q^{18} +(0.991378 + 4.24466i) q^{19} +1.67765i q^{20} +(1.29520 + 4.39573i) q^{21} -1.88312i q^{22} +(-4.73869 + 2.73588i) q^{23} +(-0.819227 - 1.52606i) q^{24} +(-1.09275 + 1.89269i) q^{25} +(-5.37089 + 3.10089i) q^{26} +(5.17380 + 0.481422i) q^{27} +(1.76384 - 1.97202i) q^{28} -6.90040 q^{29} +(-0.0898542 + 2.90438i) q^{30} +(-6.28440 - 3.62830i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.100859 - 3.26011i) q^{33} +5.80403i q^{34} +(-4.21684 + 1.38558i) q^{35} +(-1.33653 - 2.68583i) q^{36} +(3.04066 - 1.75553i) q^{37} +(3.18030 - 2.98089i) q^{38} +(-9.46429 + 5.08066i) q^{39} +(1.45289 - 0.838824i) q^{40} +2.11947 q^{41} +(3.15921 - 3.31954i) q^{42} +7.03656 q^{43} +(-1.63083 + 0.941562i) q^{44} +(-0.311115 + 5.02332i) q^{45} +(4.73869 + 2.73588i) q^{46} +(3.23065 - 1.86522i) q^{47} +(-0.911995 + 1.47250i) q^{48} +(6.41352 + 2.80477i) q^{49} +2.18549 q^{50} +(-0.310862 + 10.0481i) q^{51} +(5.37089 + 3.10089i) q^{52} +(-5.47641 + 9.48541i) q^{53} +(-2.16998 - 4.72136i) q^{54} +3.15922 q^{55} +(-2.58974 - 0.541515i) q^{56} +(5.66546 - 4.99025i) q^{57} +(3.45020 + 5.97592i) q^{58} +(-6.63269 + 11.4882i) q^{59} +(2.56020 - 1.37438i) q^{60} +(-6.54347 - 11.3336i) q^{61} +7.25660i q^{62} +(5.64710 - 5.57766i) q^{63} +1.00000 q^{64} +(-5.20220 - 9.01047i) q^{65} +(-2.87376 + 1.54271i) q^{66} +(5.36441 + 3.09715i) q^{67} +(5.02644 - 2.90202i) q^{68} +(8.05719 + 4.99022i) q^{69} +(3.30836 + 2.95910i) q^{70} -2.69469 q^{71} +(-1.65773 + 2.50038i) q^{72} +(1.42570 - 2.46938i) q^{73} +(-3.04066 - 1.75553i) q^{74} +(3.78358 + 0.117054i) q^{75} +(-4.17168 - 1.26377i) q^{76} +(-3.71357 - 3.32152i) q^{77} +(9.13213 + 5.65599i) q^{78} +(-4.30342 + 2.48458i) q^{79} +(-1.45289 - 0.838824i) q^{80} +(-3.50384 - 8.28994i) q^{81} +(-1.05973 - 1.83551i) q^{82} +10.7064i q^{83} +(-4.45442 - 1.07619i) q^{84} -9.73713 q^{85} +(-3.51828 - 6.09384i) q^{86} +(5.65300 + 10.5304i) q^{87} +(1.63083 + 0.941562i) q^{88} +(-3.30170 - 5.71872i) q^{89} +(4.50588 - 2.24223i) q^{90} +(-3.35835 + 16.0610i) q^{91} -5.47177i q^{92} +(-0.388661 + 12.5628i) q^{93} +(-3.23065 - 1.86522i) q^{94} +(5.00089 + 5.33542i) q^{95} +(1.73122 + 0.0535596i) q^{96} -11.3610i q^{97} +(-0.777761 - 6.95666i) q^{98} +(-5.05775 + 2.51685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8}+O(q^{10}) \) 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8	\( 52 q - 26 q^{2} - 26 q^{4} - 8 q^{7} + 52 q^{8} + 4 q^{14} + 8 q^{15} - 26 q^{16} + 2 q^{19} + 2 q^{21} + 18 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} - 4 q^{30} - 26 q^{32} + 8 q^{33} + 2 q^{38} + q^{39} + 16 q^{41} + 11 q^{42} - 8 q^{43} + 14 q^{45} + 4 q^{49} - 36 q^{50} - 19 q^{51} - 24 q^{53} - 3 q^{54} + 32 q^{55} - 8 q^{56} - 4 q^{57} + 4 q^{58} + 32 q^{59} - 4 q^{60} - 20 q^{61} - 7 q^{63} + 52 q^{64} - 44 q^{65} + 8 q^{66} + 62 q^{69} - 24 q^{71} - 32 q^{73} + 16 q^{75} - 4 q^{76} - 2 q^{78} - 28 q^{81} - 8 q^{82} - 13 q^{84} + 32 q^{85} + 4 q^{86} + 34 q^{87} - 36 q^{89} - 28 q^{90} + 20 q^{93} + 30 q^{95} - 20 q^{98} - 116 q^{99}+O(q^{100}) \) 52 * q - 26 * q^2 - 26 * q^4 - 8 * q^7 + 52 * q^8 + 4 * q^14 + 8 * q^15 - 26 * q^16 + 2 * q^19 + 2 * q^21 + 18 * q^25 + 6 * q^27 + 4 * q^28 - 8 * q^29 - 4 * q^30 - 26 * q^32 + 8 * q^33 + 2 * q^38 + q^39 + 16 * q^41 + 11 * q^42 - 8 * q^43 + 14 * q^45 + 4 * q^49 - 36 * q^50 - 19 * q^51 - 24 * q^53 - 3 * q^54 + 32 * q^55 - 8 * q^56 - 4 * q^57 + 4 * q^58 + 32 * q^59 - 4 * q^60 - 20 * q^61 - 7 * q^63 + 52 * q^64 - 44 * q^65 + 8 * q^66 + 62 * q^69 - 24 * q^71 - 32 * q^73 + 16 * q^75 - 4 * q^76 - 2 * q^78 - 28 * q^81 - 8 * q^82 - 13 * q^84 + 32 * q^85 + 4 * q^86 + 34 * q^87 - 36 * q^89 - 28 * q^90 + 20 * q^93 + 30 * q^95 - 20 * q^98 - 116 * q^99

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