LMFDB - Embedded newform 637.2.bc.b.619.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(31,637)] 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("637.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			619.6
Character	$\chi$	$=$	637.619
Dual form			637.2.bc.b.460.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.423548 - 1.58070i) q^{2} +(1.71590 + 0.990678i) q^{3} +(-0.587174 - 0.339005i) q^{4} +(2.77274 + 0.742954i) q^{5} +(2.29273 - 2.29273i) q^{6} +(1.52975 - 1.52975i) q^{8} +(0.462886 + 0.801742i) q^{9} +(2.34878 - 4.06820i) q^{10} +(0.894725 + 3.33916i) q^{11} +(-0.671689 - 1.16340i) q^{12} +(-2.29273 - 2.78269i) q^{13} +(4.02173 + 4.02173i) q^{15} +(-2.44816 - 4.24034i) q^{16} +(-3.22444 + 5.58489i) q^{17} +(1.46337 - 0.392109i) q^{18} +(-2.93592 - 0.786677i) q^{19} +(-1.37622 - 1.37622i) q^{20} +5.65717 q^{22} +(-2.97203 + 1.71590i) q^{23} +(4.14038 - 1.10941i) q^{24} +(2.80599 + 1.62004i) q^{25} +(-5.36969 + 2.44553i) q^{26} -4.10978i q^{27} -4.40371 q^{29} +(8.06056 - 4.65376i) q^{30} +(-0.868206 - 3.24019i) q^{31} +(-3.56028 + 0.953974i) q^{32} +(-1.77277 + 6.61607i) q^{33} +(7.46233 + 7.46233i) q^{34} -0.627683i q^{36} +(3.75982 + 1.00744i) q^{37} +(-2.48700 + 4.30762i) q^{38} +(-1.17736 - 7.04619i) q^{39} +(5.37812 - 3.10506i) q^{40} +(3.03989 - 3.03989i) q^{41} +4.48958i q^{43} +(0.606632 - 2.26398i) q^{44} +(0.687806 + 2.56693i) q^{45} +(1.45353 + 5.42467i) q^{46} +(1.47790 - 5.51561i) q^{47} -9.70136i q^{48} +(3.74927 - 3.74927i) q^{50} +(-11.0656 + 6.38875i) q^{51} +(0.402887 + 2.41117i) q^{52} +(5.72526 - 9.91644i) q^{53} +(-6.49634 - 1.74069i) q^{54} +9.92337i q^{55} +(-4.25841 - 4.25841i) q^{57} +(-1.86518 + 6.96095i) q^{58} +(-2.86050 + 0.766469i) q^{59} +(-0.998069 - 3.72484i) q^{60} +(3.03504 - 1.75228i) q^{61} -5.48950 q^{62} -3.76085i q^{64} +(-4.28975 - 9.41908i) q^{65} +(9.70717 + 5.60444i) q^{66} +(-7.04645 + 1.88809i) q^{67} +(3.78661 - 2.18620i) q^{68} -6.79964 q^{69} +(8.31408 + 8.31408i) q^{71} +(1.93456 + 0.518364i) q^{72} +(-4.51174 + 1.20892i) q^{73} +(3.18492 - 5.51645i) q^{74} +(3.20988 + 5.55967i) q^{75} +(1.45721 + 1.45721i) q^{76} +(-11.6366 - 1.12334i) q^{78} +(-0.543920 - 0.942097i) q^{79} +(-3.63774 - 13.5762i) q^{80} +(5.46013 - 9.45722i) q^{81} +(-3.51762 - 6.09269i) q^{82} +(-2.01261 + 2.01261i) q^{83} +(-13.0898 + 13.0898i) q^{85} +(7.09668 + 1.90155i) q^{86} +(-7.55635 - 4.36266i) q^{87} +(6.47677 + 3.73937i) q^{88} +(-1.28423 + 4.79280i) q^{89} +4.34887 q^{90} +2.32680 q^{92} +(1.72023 - 6.41997i) q^{93} +(-8.09257 - 4.67225i) q^{94} +(-7.55608 - 4.36250i) q^{95} +(-7.05418 - 1.89016i) q^{96} +(3.20816 - 3.20816i) q^{97} +(-2.26299 + 2.26299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9} - 10 q^{11} - 44 q^{15} + 12 q^{16} - 4 q^{18} - 12 q^{19} - 8 q^{22} + 12 q^{24} - 24 q^{26} + 16 q^{29} - 24 q^{31} + 4 q^{32} - 48 q^{33} - 8 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9 - 10 * q^11 - 44 * q^15 + 12 * q^16 - 4 * q^18 - 12 * q^19 - 8 * q^22 + 12 * q^24 - 24 * q^26 + 16 * q^29 - 24 * q^31 + 4 * q^32 - 48 * q^33 - 8 * q^37 - 6 * q^39 + 132 * q^40 - 42 * q^44 + 24 * q^45 + 12 * q^46 - 30 * q^47 + 88 * q^50 - 36 * q^52 - 12 * q^53 - 78 * q^54 + 40 * q^57 + 26 * q^58 + 54 * q^59 + 16 * q^60 + 48 * q^61 - 8 * q^65 - 12 * q^66 + 16 * q^67 + 48 * q^68 - 36 * q^71 + 22 * q^72 - 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 - 138 * q^80 + 16 * q^81 - 84 * q^85 + 42 * q^86 + 24 * q^87 + 60 * q^89 + 48 * q^92 + 6 * q^93 + 72 * q^94 + 42 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.423548	−	1.58070i	0.299493	−	1.11772i	−0.638089	−	0.769962i	$-0.720275\pi$
$2$	0.423548	−	1.58070i	0.299493	−	1.11772i	0.937583	−	0.347762i	$-0.113058\pi$
$3$	1.71590	+	0.990678i	0.990678	+	0.571968i	0.905477	−	0.424395i	$-0.139513\pi$
$3$	1.71590	+	0.990678i	0.990678	+	0.571968i	0.0852012	+	0.996364i	$0.472847\pi$
$4$	−0.587174	−	0.339005i	−0.293587	−	0.169502i
$5$	2.77274	+	0.742954i	1.24001	+	0.332259i	0.818469	−	0.574551i	$-0.194823\pi$
$5$	2.77274	+	0.742954i	1.24001	+	0.332259i	0.421539	+	0.906810i	$0.361490\pi$
$6$	2.29273	−	2.29273i	0.936005	−	0.936005i
$7$		0			0
$7$		0			0
$8$	1.52975	−	1.52975i	0.540847	−	0.540847i
$9$	0.462886	+	0.801742i	0.154295	+	0.267247i
$10$	2.34878	−	4.06820i	0.742749	−	1.28648i
$11$	0.894725	+	3.33916i	0.269770	+	1.00679i	0.959266	+	0.282505i	$0.0911654\pi$
$11$	0.894725	+	3.33916i	0.269770	+	1.00679i	−0.689496	+	0.724290i	$0.742168\pi$
$12$	−0.671689	−	1.16340i	−0.193900	−	0.335845i
$13$	−2.29273	−	2.78269i	−0.635890	−	0.771780i
$13$	−2.29273	−	2.78269i	−0.635890	−	0.771780i
$14$		0			0
$15$	4.02173	+	4.02173i	1.03841	+	1.03841i
$16$	−2.44816	−	4.24034i	−0.612040	−	1.06008i
$17$	−3.22444	+	5.58489i	−0.782040	+	1.35453i	0.148711	+	0.988881i	$0.452488\pi$
$17$	−3.22444	+	5.58489i	−0.782040	+	1.35453i	−0.930751	+	0.365653i	$0.880846\pi$
$18$	1.46337	−	0.392109i	0.344920	−	0.0924209i
$19$	−2.93592	−	0.786677i	−0.673546	−	0.180476i	−0.0941943	−	0.995554i	$-0.530027\pi$
$19$	−2.93592	−	0.786677i	−0.673546	−	0.180476i	−0.579352	+	0.815078i	$0.696694\pi$
$20$	−1.37622	−	1.37622i	−0.307731	−	0.307731i
$21$		0			0
$22$	5.65717			1.20611
$23$	−2.97203	+	1.71590i	−0.619712	+	0.357791i	−0.776757	−	0.629801i	$-0.783137\pi$
$23$	−2.97203	+	1.71590i	−0.619712	+	0.357791i	0.157045	+	0.987591i	$0.449803\pi$
$24$	4.14038	−	1.10941i	0.845153	−	0.226458i
$25$	2.80599	+	1.62004i	0.561198	+	0.324008i
$26$	−5.36969	+	2.44553i	−1.05308	+	0.479607i
$27$		−	4.10978i		−	0.790928i
$28$		0			0
$29$	−4.40371			−0.817748			−0.408874	−	0.912591i	$-0.634079\pi$
$29$	−4.40371			−0.817748			−0.408874	+	0.912591i	$0.634079\pi$
$30$	8.06056	−	4.65376i	1.47165	−	0.849657i
$31$	−0.868206	−	3.24019i	−0.155934	−	0.581955i	−0.999024	−	0.0441812i	$-0.985932\pi$
$31$	−0.868206	−	3.24019i	−0.155934	−	0.581955i	0.843089	−	0.537774i	$-0.180735\pi$
$32$	−3.56028	+	0.953974i	−0.629374	+	0.168640i
$33$	−1.77277	+	6.61607i	−0.308600	+	1.15171i
$34$	7.46233	+	7.46233i	1.27978	+	1.27978i
$35$		0			0
$36$		−	0.627683i		−	0.104614i
$37$	3.75982	+	1.00744i	0.618110	+	0.165622i	0.554268	−	0.832338i	$-0.312998\pi$
$37$	3.75982	+	1.00744i	0.618110	+	0.165622i	0.0638414	+	0.997960i	$0.479665\pi$
$38$	−2.48700	+	4.30762i	−0.403445	+	0.698787i
$39$	−1.17736	−	7.04619i	−0.188529	−	1.12829i
$40$	5.37812	−	3.10506i	0.850356	−	0.490953i
$41$	3.03989	−	3.03989i	0.474751	−	0.474751i	−0.428697	−	0.903448i	$-0.641027\pi$
$41$	3.03989	−	3.03989i	0.474751	−	0.474751i	0.903448	+	0.428697i	$0.141027\pi$
$42$		0			0
$43$			4.48958i			0.684654i	0.939581	+	0.342327i	$0.111215\pi$
$43$			4.48958i			0.684654i	−0.939581	+	0.342327i	$0.888785\pi$
$44$	0.606632	−	2.26398i	0.0914533	−	0.341308i
$45$	0.687806	+	2.56693i	0.102532	+	0.382655i
$46$	1.45353	+	5.42467i	0.214312	+	0.799823i
$47$	1.47790	−	5.51561i	0.215574	−	0.804535i	−0.770389	−	0.637574i	$-0.779938\pi$
$47$	1.47790	−	5.51561i	0.215574	−	0.804535i	0.985964	−	0.166961i	$-0.0533953\pi$
$48$		−	9.70136i		−	1.40027i
$49$		0			0
$50$	3.74927	−	3.74927i	0.530227	−	0.530227i
$51$	−11.0656	+	6.38875i	−1.54950	+	0.894605i
$52$	0.402887	+	2.41117i	0.0558704	+	0.334369i
$53$	5.72526	−	9.91644i	0.786425	−	1.36213i	−0.141719	−	0.989907i	$-0.545263\pi$
$53$	5.72526	−	9.91644i	0.786425	−	1.36213i	0.928144	−	0.372221i	$-0.121404\pi$
$54$	−6.49634	−	1.74069i	−0.884040	−	0.236878i
$55$			9.92337i			1.33807i
$56$		0			0
$57$	−4.25841	−	4.25841i	−0.564041	−	0.564041i
$58$	−1.86518	+	6.96095i	−0.244910	+	0.914018i
$59$	−2.86050	+	0.766469i	−0.372405	+	0.0997857i	−0.440167	−	0.897916i	$-0.645081\pi$
$59$	−2.86050	+	0.766469i	−0.372405	+	0.0997857i	0.0677619	+	0.997702i	$0.478414\pi$
$60$	−0.998069	−	3.72484i	−0.128850	−	0.480875i
$61$	3.03504	−	1.75228i	0.388598	−	0.224357i	−0.292955	−	0.956126i	$-0.594639\pi$
$61$	3.03504	−	1.75228i	0.388598	−	0.224357i	0.681552	+	0.731769i	$0.261305\pi$
$62$	−5.48950			−0.697167
$63$		0			0
$64$		−	3.76085i		−	0.470107i
$65$	−4.28975	−	9.41908i	−0.532078	−	1.16829i
$66$	9.70717	+	5.60444i	1.19487	+	0.689859i
$67$	−7.04645	+	1.88809i	−0.860861	+	0.230667i	−0.662132	−	0.749387i	$-0.730348\pi$
$67$	−7.04645	+	1.88809i	−0.860861	+	0.230667i	−0.198729	+	0.980054i	$0.563681\pi$
$68$	3.78661	−	2.18620i	0.459193	−	0.265115i
$69$	−6.79964			−0.818580
$70$		0			0
$71$	8.31408	+	8.31408i	0.986700	+	0.986700i	0.999913	−	0.0132127i	$-0.00420586\pi$
$71$	8.31408	+	8.31408i	0.986700	+	0.986700i	−0.0132127	+	0.999913i	$0.504206\pi$
$72$	1.93456	+	0.518364i	0.227990	+	0.0610898i
$73$	−4.51174	+	1.20892i	−0.528059	+	0.141493i	−0.512992	−	0.858393i	$-0.671463\pi$
$73$	−4.51174	+	1.20892i	−0.528059	+	0.141493i	−0.0150673	+	0.999886i	$0.504796\pi$
$74$	3.18492	−	5.51645i	0.370240	−	0.641274i
$75$	3.20988	+	5.55967i	0.370645	+	0.641975i
$76$	1.45721	+	1.45721i	0.167153	+	0.167153i
$77$		0			0
$78$	−11.6366	−	1.12334i	−1.31759	−	0.127193i
$79$	−0.543920	−	0.942097i	−0.0611957	−	0.105994i	0.833804	−	0.552060i	$-0.186158\pi$
$79$	−0.543920	−	0.942097i	−0.0611957	−	0.105994i	−0.895000	+	0.446066i	$0.852825\pi$
$80$	−3.63774	−	13.5762i	−0.406712	−	1.51787i
$81$	5.46013	−	9.45722i	0.606681	−	1.05080i
$82$	−3.51762	−	6.09269i	−0.388456	−	0.672825i
$83$	−2.01261	+	2.01261i	−0.220913	+	0.220913i	−0.808883	−	0.587970i	$-0.799927\pi$
$83$	−2.01261	+	2.01261i	−0.220913	+	0.220913i	0.587970	+	0.808883i	$0.299927\pi$
$84$		0			0
$85$	−13.0898	+	13.0898i	−1.41979	+	1.41979i
$86$	7.09668	+	1.90155i	0.765255	+	0.205049i
$87$	−7.55635	−	4.36266i	−0.810125	−	0.467726i
$88$	6.47677	+	3.73937i	0.690426	+	0.398618i
$89$	−1.28423	+	4.79280i	−0.136128	+	0.508036i	0.863863	+	0.503727i	$0.168038\pi$
$89$	−1.28423	+	4.79280i	−0.136128	+	0.508036i	−0.999991	+	0.00430871i	$0.998628\pi$
$90$	4.34887			0.458411
$91$		0			0
$92$	2.32680			0.242586
$93$	1.72023	−	6.41997i	0.178379	−	0.665720i
$94$	−8.09257	−	4.67225i	−0.834685	−	0.481906i
$95$	−7.55608	−	4.36250i	−0.775237	−	0.447584i
$96$	−7.05418	−	1.89016i	−0.719964	−	0.192914i
$97$	3.20816	−	3.20816i	0.325739	−	0.325739i	−0.525225	−	0.850964i	$-0.676019\pi$
$97$	3.20816	−	3.20816i	0.325739	−	0.325739i	0.850964	+	0.525225i	$0.176019\pi$
$98$		0			0
$99$	−2.26299	+	2.26299i	−0.227439	+	0.227439i
$100$	−1.09840	−	1.90249i	−0.109840	−	0.190249i
$101$	4.57037	−	7.91611i	0.454769	−	0.787682i	−0.543906	−	0.839146i	$-0.683055\pi$
$101$	4.57037	−	7.91611i	0.454769	−	0.787682i	0.998675	+	0.0514637i	$0.0163887\pi$
$102$	5.41188	+	20.1974i	0.535856	+	1.99984i
$103$	2.56180	+	4.43716i	0.252421	+	0.437207i	0.964192	−	0.265205i	$-0.0854397\pi$
$103$	2.56180	+	4.43716i	0.252421	+	0.437207i	−0.711771	+	0.702412i	$0.752106\pi$
$104$	−7.76411	−	0.749511i	−0.761334	−	0.0734956i
$105$		0			0
$106$	−13.2500	−	13.2500i	−1.28696	−	1.28696i
$107$	6.27683	+	10.8718i	0.606804	+	1.05102i	0.991764	+	0.128082i	$0.0408821\pi$
$107$	6.27683	+	10.8718i	0.606804	+	1.05102i	−0.384960	+	0.922933i	$0.625785\pi$
$108$	−1.39324	+	2.41316i	−0.134064	+	0.232206i
$109$	−18.8614	+	5.05389i	−1.80659	+	0.484075i	−0.994976	−	0.100114i	$-0.968079\pi$
$109$	−18.8614	+	5.05389i	−1.80659	+	0.484075i	−0.811617	+	0.584190i	$0.801412\pi$
$110$	15.6859	+	4.20302i	1.49559	+	0.400742i
$111$	5.45344	+	5.45344i	0.517617	+	0.517617i
$112$		0			0
$113$	0.000230976	0		2.17284e−5	0		1.08642e−5	−	1.00000i	$-0.499997\pi$
$113$	0.000230976	0		2.17284e−5	0		1.08642e−5		1.00000i	$0.499997\pi$
$114$	−8.53492	+	4.92764i	−0.799368	+	0.461516i
$115$	−9.51552	+	2.54968i	−0.887327	+	0.237759i
$116$	2.58574	+	1.49288i	0.240080	+	0.138610i
$117$	1.16973	−	3.12625i	0.108141	−	0.289022i
$118$			4.84623i			0.446132i
$119$		0			0
$120$	12.3045			1.12324
$121$	−0.823180	+	0.475263i	−0.0748345	+	0.0432057i
$122$	−1.48435	−	5.53967i	−0.134387	−	0.501539i
$123$	8.22771	−	2.20461i	0.741867	−	0.198783i
$124$	−0.588652	+	2.19688i	−0.0528625	+	0.197286i
$125$	−3.57226	−	3.57226i	−0.319513	−	0.319513i
$126$		0			0
$127$		−	12.4887i		−	1.10820i	−0.832452	−	0.554098i	$-0.813063\pi$
$127$		−	12.4887i		−	1.10820i	0.832452	−	0.554098i	$-0.186937\pi$
$128$	−13.0653	−	3.50085i	−1.15482	−	0.309434i
$129$	−4.44773	+	7.70369i	−0.391600	+	0.678272i
$130$	−16.7057	+	2.79138i	−1.46518	+	0.244820i
$131$	11.7665	−	6.79340i	1.02805	−	0.593542i	0.111621	−	0.993751i	$-0.464396\pi$
$131$	11.7665	−	6.79340i	1.02805	−	0.593542i	0.916424	+	0.400209i	$0.131062\pi$
$132$	3.28380	−	3.28380i	0.285818	−	0.285818i
$133$		0			0
$134$			11.9380i			1.03129i
$135$	3.05338	−	11.3954i	0.262793	−	0.980757i
$136$	3.61089	+	13.4760i	0.309631	+	1.15556i
$137$	0.349865	+	1.30571i	0.0298910	+	0.111555i	0.979260	−	0.202610i	$-0.0649423\pi$
$137$	0.349865	+	1.30571i	0.0298910	+	0.111555i	−0.949369	+	0.314164i	$0.898276\pi$
$138$	−2.87997	+	10.7482i	−0.245159	+	0.914947i
$139$			18.8190i			1.59621i	0.602521	+	0.798103i	$0.294163\pi$
$139$			18.8190i			1.59621i	−0.602521	+	0.798103i	$0.705837\pi$
$140$		0			0
$141$	8.00014	−	8.00014i	0.673733	−	0.673733i
$142$	16.6635	−	9.62067i	1.39837	−	0.807349i
$143$	7.24049	−	10.1456i	0.605480	−	0.848414i
$144$	2.26644	−	3.92559i	0.188870	−	0.327132i
$145$	−12.2104	−	3.27175i	−1.01401	−	0.271704i
$146$			7.64375i			0.632601i
$147$		0			0
$148$	−1.86614	−	1.86614i	−0.153396	−	0.153396i
$149$	−5.52045	+	20.6026i	−0.452253	+	1.68783i	0.243787	+	0.969829i	$0.421610\pi$
$149$	−5.52045	+	20.6026i	−0.452253	+	1.68783i	−0.696040	+	0.718003i	$0.745056\pi$
$150$	10.1477	−	2.71907i	0.828557	−	0.222011i
$151$	4.36658	+	16.2963i	0.355348	+	1.32618i	0.880047	+	0.474887i	$0.157511\pi$
$151$	4.36658	+	16.2963i	0.355348	+	1.32618i	−0.524699	+	0.851288i	$0.675822\pi$
$152$	−5.69463	+	3.28779i	−0.461895	+	0.266675i
$153$	−5.97019			−0.482661
$154$		0			0
$155$		−	9.62925i		−	0.773440i
$156$	−1.69738	+	4.53647i	−0.135899	+	0.363208i
$157$	9.46297	+	5.46345i	0.755227	+	0.436031i	0.827580	−	0.561348i	$-0.189717\pi$
$157$	9.46297	+	5.46345i	0.755227	+	0.436031i	−0.0723522	+	0.997379i	$0.523051\pi$
$158$	−1.71955	+	0.460752i	−0.136800	+	0.0366554i
$159$	19.6480	−	11.3438i	1.55819	−	0.899620i
$160$	−10.5805			−0.836462
$161$		0			0
$162$	−12.6364	−	12.6364i	−0.992811	−	0.992811i
$163$	8.37856	+	2.24503i	0.656259	+	0.175844i	0.571557	−	0.820562i	$-0.306340\pi$
$163$	8.37856	+	2.24503i	0.656259	+	0.175844i	0.0847019	+	0.996406i	$0.473006\pi$
$164$	−2.81548	+	0.754405i	−0.219852	+	0.0589091i
$165$	−9.83087	+	17.0276i	−0.765332	+	1.32559i
$166$	2.32890	+	4.03377i	0.180758	+	0.313082i
$167$	8.00174	+	8.00174i	0.619193	+	0.619193i	0.945324	−	0.326131i	$-0.105745\pi$
$167$	8.00174	+	8.00174i	0.619193	+	0.619193i	−0.326131	+	0.945324i	$0.605745\pi$
$168$		0			0
$169$	−2.48674	+	12.7599i	−0.191288	+	0.981534i
$170$	15.1470	+	26.2353i	1.16172	+	2.01216i
$171$	−0.728284	−	2.71799i	−0.0556933	−	0.207850i
$172$	1.52199	−	2.63616i	0.116050	−	0.201005i
$173$	−1.63833	−	2.83768i	−0.124560	−	0.215745i	0.797001	−	0.603978i	$-0.206419\pi$
$173$	−1.63833	−	2.83768i	−0.124560	−	0.215745i	−0.921561	+	0.388234i	$0.873085\pi$
$174$	−10.0965	+	10.0965i	−0.765416	+	0.765416i
$175$		0			0
$176$	11.9687	−	11.9687i	0.902178	−	0.902178i
$177$	−5.66767	−	1.51865i	−0.426008	−	0.114149i
$178$	7.03205	+	4.05996i	0.527075	+	0.304307i
$179$	−1.94863	−	1.12504i	−0.145648	−	0.0840897i	0.425405	−	0.905003i	$-0.360132\pi$
$179$	−1.94863	−	1.12504i	−0.145648	−	0.0840897i	−0.571053	+	0.820913i	$0.693465\pi$
$180$	0.466339	−	1.74040i	0.0347589	−	0.129722i
$181$	15.5420			1.15523			0.577615	−	0.816310i	$-0.303984\pi$
$181$	15.5420			1.15523			0.577615	+	0.816310i	$0.303984\pi$
$182$		0			0
$183$	6.94380			0.513300
$184$	−1.92156	+	7.17136i	−0.141659	+	0.528679i
$185$	9.67652	+	5.58674i	0.711432	+	0.410745i
$186$	−9.41946	−	5.43833i	−0.690668	−	0.398757i
$187$	−21.5338	−	5.76997i	−1.57471	−	0.421942i
$188$	−2.73761	+	2.73761i	−0.199660	+	0.199660i
$189$		0			0
$190$	−10.0962	+	10.0962i	−0.732454	+	0.732454i
$191$	1.18897	+	2.05936i	0.0860308	+	0.149010i	0.905830	−	0.423641i	$-0.139248\pi$
$191$	1.18897	+	2.05936i	0.0860308	+	0.149010i	−0.819799	+	0.572651i	$0.805915\pi$
$192$	3.72579	−	6.45326i	0.268886	−	0.465724i
$193$	−2.02038	−	7.54017i	−0.145430	−	0.542753i	−0.999736	−	0.0229822i	$-0.992684\pi$
$193$	−2.02038	−	7.54017i	−0.145430	−	0.542753i	0.854306	−	0.519771i	$-0.173983\pi$
$194$	−3.71233	−	6.42995i	−0.266530	−	0.461643i
$195$	1.97048	−	20.4120i	0.141109	−	1.46173i
$196$		0			0
$197$	−10.9402	−	10.9402i	−0.779454	−	0.779454i	0.200284	−	0.979738i	$-0.435813\pi$
$197$	−10.9402	−	10.9402i	−0.779454	−	0.779454i	−0.979738	+	0.200284i	$0.935813\pi$
$198$	2.61863	+	4.53560i	0.186098	+	0.322331i
$199$	10.0868	−	17.4708i	0.715031	−	1.23847i	−0.247916	−	0.968781i	$-0.579746\pi$
$199$	10.0868	−	17.4708i	0.715031	−	1.23847i	0.962947	−	0.269689i	$-0.0869209\pi$
$200$	6.77070	−	1.81420i	0.478761	−	0.128284i
$201$	−13.9615	−	3.74098i	−0.984771	−	0.263868i
$202$	−10.5772	−	10.5772i	−0.744212	−	0.744212i
$203$		0			0
$204$	8.66327			0.606551
$205$	10.6873	−	6.17033i	0.746435	−	0.430954i
$206$	8.09887	−	2.17009i	0.564275	−	0.151197i
$207$	−2.75143	−	1.58854i	−0.191237	−	0.110411i
$208$	−6.18657	+	16.5344i	−0.428962	+	1.14646i
$209$		−	10.5074i		−	0.726809i
$210$		0			0
$211$	2.36943			0.163118			0.0815591	−	0.996669i	$-0.474010\pi$
$211$	2.36943			0.163118			0.0815591	+	0.996669i	$0.474010\pi$
$212$	−6.72344	+	3.88178i	−0.461768	+	0.266602i
$213$	6.02959	+	22.5028i	0.413141	+	1.54186i
$214$	19.8436	−	5.31707i	1.35648	−	0.363468i
$215$	−3.33555	+	12.4484i	−0.227483	+	0.848976i
$216$	−6.28693	−	6.28693i	−0.427771	−	0.427771i
$217$		0			0
$218$			31.9548i			2.16425i
$219$	−8.93936	−	2.39530i	−0.604066	−	0.161859i
$220$	3.36407	−	5.82674i	0.226806	−	0.392839i
$221$	22.9338	−	3.83205i	1.54269	−	0.257771i
$222$	10.9300	−	6.31046i	0.733577	−	0.423531i
$223$	−9.67825	+	9.67825i	−0.648103	+	0.648103i	−0.952534	−	0.304431i	$-0.901534\pi$
$223$	−9.67825	+	9.67825i	−0.648103	+	0.648103i	0.304431	+	0.952534i	$0.401534\pi$
$224$		0			0
$225$			2.99958i			0.199972i
$226$	9.78292e−5	0	0.000365104i	6.50750e−6	0	2.42863e-5i
$227$	3.37455	+	12.5940i	0.223977	+	0.835894i	0.982812	+	0.184611i	$0.0591024\pi$
$227$	3.37455	+	12.5940i	0.223977	+	0.835894i	−0.758835	+	0.651283i	$0.774231\pi$
$228$	1.05680	+	3.94405i	0.0699886	+	0.261201i
$229$	−3.93373	+	14.6809i	−0.259948	+	0.970139i	0.705322	+	0.708887i	$0.250802\pi$
$229$	−3.93373	+	14.6809i	−0.259948	+	0.970139i	−0.965270	+	0.261253i	$0.915864\pi$
$230$			16.1211i			1.06299i
$231$		0			0
$232$	−6.73656	+	6.73656i	−0.442277	+	0.442277i
$233$	−6.69859	+	3.86743i	−0.438839	+	0.253364i	−0.703105	−	0.711086i	$-0.748204\pi$
$233$	−6.69859	+	3.86743i	−0.438839	+	0.253364i	0.264266	+	0.964450i	$0.414870\pi$
$234$	−4.44624	−	3.17311i	−0.290659	−	0.207432i
$235$	8.19569	−	14.1954i	0.534628	−	0.926003i
$236$	1.93945	+	0.519673i	0.126247	+	0.0338278i
$237$		−	2.15540i		−	0.140008i
$238$		0			0
$239$	2.10971	+	2.10971i	0.136466	+	0.136466i	0.772040	−	0.635574i	$-0.219237\pi$
$239$	2.10971	+	2.10971i	0.136466	+	0.136466i	−0.635574	+	0.772040i	$0.719237\pi$
$240$	7.20766	−	26.8994i	0.465253	−	1.73635i
$241$	−25.5066	+	6.83448i	−1.64303	+	0.440247i	−0.957648	−	0.287941i	$-0.907029\pi$
$241$	−25.5066	+	6.83448i	−1.64303	+	0.440247i	−0.685377	+	0.728188i	$0.740363\pi$
$242$	0.402593	+	1.50250i	0.0258797	+	0.0965843i
$243$	8.06060	−	4.65379i	0.517088	−	0.298541i
$244$	−2.37613			−0.152116
$245$		0			0
$246$		−	13.9393i		−	0.888738i
$247$	4.54220	+	9.97340i	0.289013	+	0.634592i
$248$	−6.28480	−	3.62853i	−0.399085	−	0.230412i
$249$	−5.44730	+	1.45960i	−0.345209	+	0.0924984i
$250$	−7.15971	+	4.13366i	−0.452820	+	0.261436i
$251$	−7.06132			−0.445707			−0.222853	−	0.974852i	$-0.571537\pi$
$251$	−7.06132			−0.445707			−0.222853	+	0.974852i	$0.571537\pi$
$252$		0			0
$253$	−8.38884	−	8.38884i	−0.527402	−	0.527402i
$254$	−19.7409	−	5.28957i	−1.23866	−	0.331897i
$255$	−35.4287	+	9.49310i	−2.21863	+	0.594481i
$256$	−7.30674	+	12.6556i	−0.456671	+	0.790978i
$257$	−6.52671	−	11.3046i	−0.407125	−	0.705161i	0.587441	−	0.809267i	$-0.300135\pi$
$257$	−6.52671	−	11.3046i	−0.407125	−	0.705161i	−0.994566	+	0.104106i	$0.966802\pi$
$258$	10.2934	+	10.2934i	0.640839	+	0.640839i
$259$		0			0
$260$	−0.674288	+	6.98488i	−0.0418175	+	0.433184i
$261$	−2.03842	−	3.53064i	−0.126175	−	0.218541i
$262$	−5.75466	−	21.4767i	−0.355524	−	1.32683i
$263$	−11.1673	+	19.3423i	−0.688606	+	1.19270i	0.283684	+	0.958918i	$0.408443\pi$
$263$	−11.1673	+	19.3423i	−0.688606	+	1.19270i	−0.972289	+	0.233782i	$0.924890\pi$
$264$	7.40901	+	12.8328i	0.455993	+	0.789804i
$265$	23.2421	−	23.2421i	1.42775	−	1.42775i
$266$		0			0
$267$	−6.95173	+	6.95173i	−0.425439	+	0.425439i
$268$	4.77756	+	1.28014i	0.291836	+	0.0781972i
$269$	−2.71439	−	1.56715i	−0.165499	−	0.0955511i	0.414963	−	0.909838i	$-0.363795\pi$
$269$	−2.71439	−	1.56715i	−0.165499	−	0.0955511i	−0.580462	+	0.814287i	$0.697128\pi$
$270$	−16.7194	−	9.65297i	−1.01751	−	0.587461i
$271$	4.09187	−	15.2711i	0.248563	−	0.927651i	−0.722995	−	0.690853i	$-0.757235\pi$
$271$	4.09187	−	15.2711i	0.248563	−	0.927651i	0.971559	−	0.236798i	$-0.0760981\pi$
$272$	31.5757			1.91456
$273$		0			0
$274$	2.21213			0.133639
$275$	−2.89898	+	10.8191i	−0.174815	+	0.652419i
$276$	3.99257	+	2.30511i	0.240324	+	0.138751i
$277$	−25.5340	−	14.7421i	−1.53419	−	0.885765i	−0.999162	−	0.0409305i	$-0.986968\pi$
$277$	−25.5340	−	14.7421i	−1.53419	−	0.885765i	−0.535028	−	0.844834i	$-0.679699\pi$
$278$	29.7472	+	7.97074i	1.78412	+	0.478053i
$279$	2.19592	−	2.19592i	0.131466	−	0.131466i
$280$		0			0
$281$	16.8969	−	16.8969i	1.00798	−	1.00798i	0.00801615	−	0.999968i	$-0.497448\pi$
$281$	16.8969	−	16.8969i	1.00798	−	1.00798i	0.999968	−	0.00801615i	$-0.00255165\pi$
$282$	−9.25739	−	16.0343i	−0.551270	−	0.954827i
$283$	−4.66719	+	8.08381i	−0.277436	+	0.480533i	−0.970747	−	0.240106i	$-0.922818\pi$
$283$	−4.66719	+	8.08381i	−0.277436	+	0.480533i	0.693311	+	0.720638i	$0.256151\pi$
$284$	−2.06330	−	7.70032i	−0.122434	−	0.456930i
$285$	−8.64368	−	14.9713i	−0.512007	−	0.886822i
$286$	−12.9704	−	15.7422i	−0.766956	−	0.930854i
$287$		0			0
$288$	−2.41285	−	2.41285i	−0.142178	−	0.142178i
$289$	−12.2940	−	21.2938i	−0.723174	−	1.25257i
$290$	−10.3433	+	17.9152i	−0.607381	+	1.05202i
$291$	8.68315	−	2.32664i	0.509015	−	0.136390i
$292$	3.05900	+	0.819657i	0.179015	+	0.0479668i
$293$	−2.08232	−	2.08232i	−0.121650	−	0.121650i	0.643661	−	0.765311i	$-0.277415\pi$
$293$	−2.08232	−	2.08232i	−0.121650	−	0.121650i	−0.765311	+	0.643661i	$0.777415\pi$
$294$		0			0
$295$	−8.50088			−0.494940
$296$	7.29269	−	4.21044i	0.423879	−	0.244727i
$297$	13.7232	−	3.67713i	0.796302	−	0.213369i
$298$	30.2284	+	17.4524i	1.75108	+	1.01099i
$299$	11.5889	+	4.33614i	0.670204	+	0.250766i
$300$		−	4.35265i		−	0.251301i
$301$		0			0
$302$	27.6091			1.58872
$303$	15.6846	−	9.05553i	0.901058	−	0.520226i
$304$	3.85182	+	14.3752i	0.220917	+	0.824474i
$305$	9.71726	−	2.60373i	0.556409	−	0.149089i
$306$	−2.52866	+	9.43708i	−0.144554	+	0.539482i
$307$	3.85597	+	3.85597i	0.220072	+	0.220072i	0.808529	−	0.588457i	$-0.200264\pi$
$307$	3.85597	+	3.85597i	0.220072	+	0.220072i	−0.588457	+	0.808529i	$0.700264\pi$
$308$		0			0
$309$			10.1517i			0.577508i
$310$	−15.2210	−	4.07844i	−0.864493	−	0.231640i
$311$	7.03750	−	12.1893i	0.399060	−	0.691192i	−0.594550	−	0.804058i	$-0.702670\pi$
$311$	7.03750	−	12.1893i	0.399060	−	0.691192i	0.993610	+	0.112866i	$0.0360032\pi$
$312$	−12.5800	−	8.97783i	−0.712200	−	0.508269i
$313$	−4.07599	+	2.35327i	−0.230388	+	0.133015i	−0.610751	−	0.791823i	$-0.709132\pi$
$313$	−4.07599	+	2.35327i	−0.230388	+	0.133015i	0.380363	+	0.924837i	$0.375799\pi$
$314$	12.6441	−	12.6441i	0.713548	−	0.713548i
$315$		0			0
$316$			0.737566i			0.0414913i
$317$	7.57921	−	28.2860i	0.425691	−	1.58870i	−0.336720	−	0.941605i	$-0.609317\pi$
$317$	7.57921	−	28.2860i	0.425691	−	1.58870i	0.762410	−	0.647094i	$-0.224016\pi$
$318$	−9.60926	−	35.8623i	−0.538861	−	2.01106i
$319$	−3.94011	−	14.7047i	−0.220604	−	0.823305i
$320$	2.79414	−	10.4279i	0.156197	−	0.582936i
$321$			24.8733i			1.38829i
$322$		0			0
$323$	13.8602	−	13.8602i	0.771201	−	0.771201i
$324$	−6.41209	+	3.70202i	−0.356227	+	0.205668i
$325$	−1.92532	−	11.5225i	−0.106798	−	0.639155i
$326$	7.09744	−	12.2931i	0.393091	−	0.680853i
$327$	−37.3711	−	10.0136i	−2.06663	−	0.553751i
$328$		−	9.30051i		−	0.513535i
$329$		0			0
$330$	22.7516	+	22.7516i	1.25244	+	1.25244i
$331$	3.83537	−	14.3138i	0.210811	−	0.786757i	−0.776788	−	0.629762i	$-0.783152\pi$
$331$	3.83537	−	14.3138i	0.210811	−	0.786757i	0.987599	−	0.156996i	$-0.0501808\pi$
$332$	1.86404	−	0.499467i	0.102302	−	0.0274118i
$333$	0.932660	+	3.48073i	0.0511094	+	0.190743i
$334$	16.0375	−	9.25924i	0.877532	−	0.506643i
$335$	−20.9408			−1.14412
$336$		0			0
$337$			9.51919i			0.518543i	0.965804	+	0.259272i	$0.0834825\pi$
$337$			9.51919i			0.518543i	−0.965804	+	0.259272i	$0.916518\pi$
$338$	19.1164	+	9.33524i	1.03980	+	0.507770i
$339$	0.000396332	0	0.000228823i	2.15258e−5	0	1.24279e-5i
$340$	12.1235	−	3.24849i	0.657491	−	0.176174i
$341$	10.0427	−	5.79816i	0.543843	−	0.313988i
$342$	−4.60480			−0.248999
$343$		0			0
$344$	6.86791	+	6.86791i	0.370293	+	0.370293i
$345$	−18.8536	−	5.05182i	−1.01505	−	0.271981i
$346$	−5.17944	+	1.38783i	−0.278448	+	0.0746100i
$347$	17.5649	−	30.4233i	0.942933	−	1.63321i	0.183095	−	0.983095i	$-0.441388\pi$
$347$	17.5649	−	30.4233i	0.942933	−	1.63321i	0.759838	−	0.650112i	$-0.225278\pi$
$348$	2.95792	+	5.12328i	0.158561	+	0.274636i
$349$	6.64759	+	6.64759i	0.355837	+	0.355837i	0.862276	−	0.506439i	$-0.169038\pi$
$349$	6.64759	+	6.64759i	0.355837	+	0.355837i	−0.506439	+	0.862276i	$0.669038\pi$
$350$		0			0
$351$	−11.4363	+	9.42264i	−0.610422	+	0.502943i
$352$	−6.37094	−	11.0348i	−0.339572	−	0.588157i
$353$	−3.20243	−	11.9516i	−0.170448	−	0.636121i	−0.997282	−	0.0736752i	$-0.976527\pi$
$353$	−3.20243	−	11.9516i	−0.170448	−	0.636121i	0.826834	−	0.562446i	$-0.190139\pi$
$354$	−4.80106	+	8.31567i	−0.255173	+	0.441973i
$355$	16.8758	+	29.2298i	0.895676	+	1.55136i
$356$	2.37885	−	2.37885i	0.126079	−	0.126079i
$357$		0			0
$358$	−2.60370	+	2.60370i	−0.137610	+	0.137610i
$359$	4.14143	+	1.10969i	0.218576	+	0.0585673i	0.366445	−	0.930440i	$-0.380575\pi$
$359$	4.14143	+	1.10969i	0.218576	+	0.0585673i	−0.147869	+	0.989007i	$0.547241\pi$
$360$	4.97892	+	2.87458i	0.262412	+	0.151504i
$361$	−8.45373	−	4.88076i	−0.444933	−	0.256882i
$362$	6.58279	−	24.5673i	0.345984	−	1.29123i
$363$	−1.88333			−0.0988493
$364$		0			0
$365$	−13.4081			−0.701810
$366$	2.94103	−	10.9761i	0.153730	−	0.573728i
$367$	21.4207	+	12.3672i	1.11815	+	0.645565i	0.940928	−	0.338606i	$-0.109955\pi$
$367$	21.4207	+	12.3672i	1.11815	+	0.645565i	0.177223	+	0.984171i	$0.443289\pi$
$368$	14.5520	+	8.40162i	0.758577	+	0.437965i
$369$	3.84433	+	1.03008i	0.200128	+	0.0536241i
$370$	12.9294	−	12.9294i	0.672169	−	0.672169i
$371$		0			0
$372$	−3.18647	+	3.18647i	−0.165211	+	0.165211i
$373$	3.95677	+	6.85332i	0.204874	+	0.354852i	0.950092	−	0.311968i	$-0.100988\pi$
$373$	3.95677	+	6.85332i	0.204874	+	0.354852i	−0.745219	+	0.666820i	$0.767655\pi$
$374$	−18.2412	+	31.5947i	−0.943230	+	1.63372i
$375$	−2.59070	−	9.66863i	−0.133783	−	0.499286i
$376$	−6.17667	−	10.6983i	−0.318537	−	0.551723i
$377$	10.0965	+	12.2542i	0.519998	+	0.631122i
$378$		0			0
$379$	3.32389	+	3.32389i	0.170737	+	0.170737i	0.787303	−	0.616566i	$-0.211477\pi$
$379$	3.32389	+	3.32389i	0.170737	+	0.170737i	−0.616566	+	0.787303i	$0.711477\pi$
$380$	2.95782	+	5.12309i	0.151733	+	0.262809i
$381$	12.3723	−	21.4295i	0.633853	−	1.09786i
$382$	3.75881	−	1.00717i	0.192318	−	0.0515313i
$383$	8.74833	+	2.34411i	0.447019	+	0.119778i	0.475304	−	0.879822i	$-0.342338\pi$
$383$	8.74833	+	2.34411i	0.447019	+	0.119778i	−0.0282852	+	0.999600i	$0.509005\pi$
$384$	−18.9507	−	18.9507i	−0.967072	−	0.967072i
$385$		0			0
$386$	−12.7745			−0.650204
$387$	−3.59948	+	2.07816i	−0.182972	+	0.105639i
$388$	−2.97133	+	0.796165i	−0.150846	+	0.0404191i
$389$	18.5856	+	10.7304i	0.942328	+	0.544053i	0.890689	−	0.454612i	$-0.150222\pi$
$389$	18.5856	+	10.7304i	0.942328	+	0.544053i	0.0516387	+	0.998666i	$0.483556\pi$
$390$	−31.4307	−	11.7602i	−1.59156	−	0.595501i
$391$		−	22.1313i		−	1.11923i
$392$		0			0
$393$	26.9203			1.35795
$394$	−21.9268	+	12.6594i	−1.10466	+	0.637773i
$395$	−0.808215	−	3.01630i	−0.0406657	−	0.151766i
$396$	2.09593	−	0.561604i	0.105325	−	0.0282216i
$397$	3.38387	−	12.6288i	0.169831	−	0.633819i	−0.827543	−	0.561402i	$-0.810262\pi$
$397$	3.38387	−	12.6288i	0.169831	−	0.633819i	0.997374	−	0.0724172i	$-0.0230713\pi$
$398$	−23.3439	−	23.3439i	−1.17012	−	1.17012i
$399$		0			0
$400$		−	15.8645i		−	0.793224i
$401$	20.5002	+	5.49301i	1.02373	+	0.274308i	0.731356	−	0.681996i	$-0.238888\pi$
$401$	20.5002	+	5.49301i	1.02373	+	0.274308i	0.292375	+	0.956304i	$0.405555\pi$
$402$	−11.8267	+	20.4845i	−0.589865	+	1.02168i
$403$	−7.02588	+	9.84484i	−0.349984	+	0.490406i
$404$	−5.36720	+	3.09875i	−0.267028	+	0.154169i
$405$	22.1658	−	22.1658i	1.10143	−	1.10143i
$406$		0			0
$407$			13.4560i			0.666990i
$408$	−7.15446	+	26.7008i	−0.354199	+	1.32189i
$409$	2.20463	+	8.22781i	0.109012	+	0.406839i	0.998769	−	0.0495951i	$-0.0157931\pi$
$409$	2.20463	+	8.22781i	0.109012	+	0.406839i	−0.889757	+	0.456434i	$0.849126\pi$
$410$	−5.22686	−	19.5069i	−0.258136	−	0.963377i
$411$	−0.693207	+	2.58708i	−0.0341934	+	0.127611i
$412$		−	3.47385i		−	0.171144i
$413$		0			0
$414$	−3.67636	+	3.67636i	−0.180683	+	0.180683i
$415$	−7.07573	+	4.08517i	−0.347334	+	0.200533i
$416$	10.8174	+	7.71995i	0.530366	+	0.378502i
$417$	−18.6436	+	32.2916i	−0.912979	+	1.58133i
$418$	−16.6090	−	4.45037i	−0.812373	−	0.217675i
$419$		−	8.39090i		−	0.409922i	−0.978770	−	0.204961i	$-0.934293\pi$
$419$		−	8.39090i		−	0.409922i	0.978770	−	0.204961i	$-0.0657068\pi$
$420$		0			0
$421$	20.5414	+	20.5414i	1.00113	+	1.00113i	0.999999	+	0.00112764i	$0.000358939\pi$
$421$	20.5414	+	20.5414i	1.00113	+	1.00113i	0.00112764	+	0.999999i	$0.499641\pi$
$422$	1.00357	−	3.74536i	0.0488528	−	0.182321i
$423$	5.10620	−	1.36820i	0.248272	−	0.0665243i
$424$	−6.41144	−	23.9278i	−0.311367	−	1.16204i
$425$	−18.0955	+	10.4474i	−0.877760	+	0.506775i
$426$	38.1240			1.84711
$427$		0			0
$428$		−	8.51150i		−	0.411419i
$429$	22.4750	−	10.2358i	1.08510	−	0.494189i
$430$	18.2645	+	10.5450i	0.880792	+	0.508526i
$431$	−9.66314	+	2.58923i	−0.465457	+	0.124719i	−0.483923	−	0.875111i	$-0.660788\pi$
$431$	−9.66314	+	2.58923i	−0.465457	+	0.124719i	0.0184658	+	0.999829i	$0.494122\pi$
$432$	−17.4269	+	10.0614i	−0.838451	+	0.484080i
$433$	−41.3846			−1.98882			−0.994409	−	0.105595i	$-0.966325\pi$
$433$	−41.3846			−1.98882			−0.994409	+	0.105595i	$0.966325\pi$
$434$		0			0
$435$	−17.7105	−	17.7105i	−0.849156	−	0.849156i
$436$	12.7882	+	3.42659i	0.612444	+	0.164104i
$437$	10.0755	−	2.69973i	0.481977	−	0.129145i
$438$	−7.57249	+	13.1159i	−0.361828	+	0.626704i
$439$	0.0712884	+	0.123475i	0.00340241	+	0.00589314i	0.867722	−	0.497051i	$-0.165584\pi$
$439$	0.0712884	+	0.123475i	0.00340241	+	0.00589314i	−0.864319	+	0.502944i	$0.832250\pi$
$440$	15.1802	+	15.1802i	0.723689	+	0.723689i
$441$		0			0
$442$	3.65623	−	37.8745i	0.173909	−	1.80151i
$443$	−12.9368	−	22.4072i	−0.614647	−	1.06460i	−0.990446	−	0.137898i	$-0.955965\pi$
$443$	−12.9368	−	22.4072i	−0.614647	−	1.06460i	0.375800	−	0.926701i	$-0.377368\pi$
$444$	−1.35337	−	5.05085i	−0.0642282	−	0.239703i
$445$	−7.12166	+	12.3351i	−0.337599	+	0.584738i
$446$	11.1992	+	19.3976i	0.530298	+	0.918504i
$447$	−29.8831	+	29.8831i	−1.41342	+	1.41342i
$448$		0			0
$449$	1.26645	−	1.26645i	0.0597675	−	0.0597675i	−0.676591	−	0.736359i	$-0.736544\pi$
$449$	1.26645	−	1.26645i	0.0597675	−	0.0597675i	0.736359	+	0.676591i	$0.236544\pi$
$450$	4.74144	+	1.27046i	0.223513	+	0.0598902i
$451$	12.8705	+	7.43081i	0.606050	+	0.349903i
$452$	−0.000135623	0	7.83019e-5i	−6.37916e−6	0	3.68301e-6i
$453$	−8.65176	+	32.2888i	−0.406495	+	1.51706i
$454$	21.3367			1.00138
$455$		0			0
$456$	−13.0286			−0.610119
$457$	−1.20672	+	4.50353i	−0.0564479	+	0.210666i	−0.988389	−	0.151942i	$-0.951447\pi$
$457$	−1.20672	+	4.50353i	−0.0564479	+	0.210666i	0.931941	+	0.362609i	$0.118114\pi$
$458$	21.5400	+	12.4361i	1.00650	+	0.581101i
$459$	22.9527	+	13.2517i	1.07134	+	0.618538i
$460$	6.45162	+	1.72871i	0.300808	+	0.0806013i
$461$	−3.60896	+	3.60896i	−0.168086	+	0.168086i	−0.786137	−	0.618052i	$-0.787922\pi$
$461$	−3.60896	+	3.60896i	−0.168086	+	0.168086i	0.618052	+	0.786137i	$0.287922\pi$
$462$		0			0
$463$	−4.00230	+	4.00230i	−0.186003	+	0.186003i	−0.793965	−	0.607963i	$-0.791987\pi$
$463$	−4.00230	+	4.00230i	−0.186003	+	0.186003i	0.607963	+	0.793965i	$0.291987\pi$
$464$	10.7810	+	18.6732i	0.500495	+	0.866883i
$465$	9.53948	−	16.5229i	0.442383	−	0.766230i
$466$	3.27608	+	12.2265i	0.151762	+	0.566382i
$467$	20.0309	+	34.6946i	0.926921	+	1.60547i	0.788442	+	0.615109i	$0.210888\pi$
$467$	20.0309	+	34.6946i	0.926921	+	1.60547i	0.138479	+	0.990365i	$0.455779\pi$
$468$	−1.74665	+	1.43911i	−0.0807388	+	0.0665228i
$469$		0			0
$470$	−18.9674	−	18.9674i	−0.874899	−	0.874899i
$471$	10.8250	+	18.7495i	0.498791	+	0.863932i
$472$	−3.20334	+	5.54834i	−0.147446	+	0.255383i
$473$	−14.9914	+	4.01694i	−0.689306	+	0.184699i
$474$	−3.40704	−	0.912914i	−0.156491	−	0.0419315i
$475$	−6.96371	−	6.96371i	−0.319517	−	0.319517i
$476$		0			0
$477$	10.6006			0.485367
$478$	4.22838	−	2.44126i	0.193402	−	0.111661i
$479$	−11.3889	+	3.05163i	−0.520370	+	0.139433i	−0.509438	−	0.860508i	$-0.670147\pi$
$479$	−11.3889	+	3.05163i	−0.520370	+	0.139433i	−0.0109323	+	0.999940i	$0.503480\pi$
$480$	−18.1551	−	10.4819i	−0.828664	−	0.478430i
$481$	−5.81686	−	12.7722i	−0.265226	−	0.582362i
$482$			43.2131i			1.96830i
$483$		0			0
$484$	0.644466			0.0292939
$485$	11.2789	−	6.51188i	0.512149	−	0.295689i
$486$	−3.94220	−	14.7125i	−0.178822	−	0.667373i
$487$	−0.531550	+	0.142428i	−0.0240868	+	0.00645405i	−0.270842	−	0.962624i	$-0.587302\pi$
$487$	−0.531550	+	0.142428i	−0.0240868	+	0.00645405i	0.246756	+	0.969078i	$0.420636\pi$
$488$	1.96230	−	7.32340i	0.0888291	−	0.331515i
$489$	12.1527	+	12.1527i	0.549564	+	0.549564i
$490$		0			0
$491$		−	3.02403i		−	0.136472i	−0.997669	−	0.0682362i	$-0.978263\pi$
$491$		−	3.02403i		−	0.136472i	0.997669	−	0.0682362i	$-0.0217372\pi$
$492$	−5.57846	−	1.49474i	−0.251497	−	0.0673883i
$493$	14.1995	−	24.5942i	0.639512	−	1.10767i
$494$	17.6888	−	2.95565i	0.795857	−	0.132981i
$495$	−7.95599	+	4.59339i	−0.357595	+	0.206458i
$496$	−11.6140	+	11.6140i	−0.521484	+	0.521484i
$497$		0			0
$498$			9.22876i			0.413551i
$499$	−9.92557	+	37.0427i	−0.444330	+	1.65826i	0.273371	+	0.961909i	$0.411861\pi$
$499$	−9.92557	+	37.0427i	−0.444330	+	1.65826i	−0.717701	+	0.696352i	$0.754805\pi$
$500$	0.886524	+	3.30855i	0.0396466	+	0.147963i
$501$	5.80307	+	21.6574i	0.259262	+	0.967580i
$502$	−2.99081	+	11.1618i	−0.133486	+	0.498178i
$503$		−	27.2615i		−	1.21553i	−0.794117	−	0.607765i	$-0.792066\pi$
$503$		−	27.2615i		−	1.21553i	0.794117	−	0.607765i	$-0.207934\pi$
$504$		0			0
$505$	18.5538	−	18.5538i	0.825631	−	0.825631i
$506$	−16.8133	+	9.70717i	−0.747443	+	0.431536i
$507$	−16.9080	+	19.4313i	−0.750911	+	0.862974i
$508$	−4.23374	+	7.33305i	−0.187842	+	0.325351i
$509$	17.4575	+	4.67772i	0.773790	+	0.207336i	0.624045	−	0.781388i	$-0.285488\pi$
$509$	17.4575	+	4.67772i	0.773790	+	0.207336i	0.149745	+	0.988725i	$0.452155\pi$
$510$			60.0230i			2.65786i
$511$		0			0
$512$	−2.21895	−	2.21895i	−0.0980646	−	0.0980646i
$513$	−3.23307	+	12.0660i	−0.142744	+	0.532726i
$514$	−20.6336	+	5.52874i	−0.910107	+	0.243862i
$515$	3.80660	+	14.2064i	0.167739	+	0.626009i
$516$	5.22317	−	3.01560i	0.229937	−	0.132754i
$517$	19.7398			0.868157
$518$		0			0
$519$		−	6.49225i		−	0.284978i
$520$	−20.9710	−	7.84658i	−0.919640	−	0.344095i
$521$	−10.0266	−	5.78888i	−0.439275	−	0.253616i	0.264015	−	0.964519i	$-0.414953\pi$
$521$	−10.0266	−	5.78888i	−0.439275	−	0.253616i	−0.703290	+	0.710903i	$0.748286\pi$
$522$	−6.44426	+	1.72673i	−0.282057	+	0.0755771i
$523$	8.36503	−	4.82955i	0.365777	−	0.211182i	−0.305835	−	0.952085i	$-0.598935\pi$
$523$	8.36503	−	4.82955i	0.365777	−	0.211182i	0.671612	+	0.740903i	$0.265602\pi$
$524$	−9.21198			−0.402427
$525$		0			0
$526$	25.8446	+	25.8446i	1.12688	+	1.12688i
$527$	20.8956	+	5.59895i	0.910225	+	0.243894i
$528$	32.3944	−	8.68005i	1.40978	−	0.377751i
$529$	−5.61134	+	9.71913i	−0.243971	+	0.422571i
$530$	−26.8947	−	46.5830i	−1.16823	−	2.02344i
$531$	−1.93860	−	1.93860i	−0.0841279	−	0.0841279i
$532$		0			0
$533$	−15.4287	−	1.48942i	−0.668292	−	0.0645138i
$534$	8.04422	+	13.9330i	0.348107	+	0.602940i
$535$	9.32679	+	34.8081i	0.403232	+	1.50488i
$536$	−7.89098	+	13.6676i	−0.340839	+	0.590350i
$537$	−2.22911	−	3.86094i	−0.0961933	−	0.166612i
$538$	−3.62688	+	3.62688i	−0.156366	+	0.156366i
$539$		0			0
$540$	−5.65595	+	5.65595i	−0.243393	+	0.243393i
$541$	−29.4151	−	7.88175i	−1.26465	−	0.338863i	−0.436673	−	0.899620i	$-0.643843\pi$
$541$	−29.4151	−	7.88175i	−1.26465	−	0.338863i	−0.827980	+	0.560757i	$0.810510\pi$
$542$	−22.4059	−	12.9360i	−0.962415	−	0.555651i
$543$	26.6686	+	15.3971i	1.14446	+	0.660754i
$544$	6.15205	−	22.9598i	0.263767	−	0.984392i
$545$	−56.0526			−2.40103
$546$		0			0
$547$	41.0288			1.75427			0.877133	−	0.480247i	$-0.159453\pi$
$547$	41.0288			1.75427			0.877133	+	0.480247i	$0.159453\pi$
$548$	0.237212	−	0.885286i	0.0101332	−	0.0378176i
$549$	2.80976	+	1.62222i	0.119918	+	0.0692345i
$550$	15.8740	+	9.16485i	0.676869	+	0.390790i
$551$	12.9289	+	3.46430i	0.550791	+	0.147584i
$552$	−10.4017	+	10.4017i	−0.442727	+	0.442727i
$553$		0			0
$554$	−34.1177	+	34.1177i	−1.44952	+	1.44952i
$555$	11.0693	+	19.1726i	0.469867	+	0.813833i
$556$	6.37973	−	11.0500i	0.270561	−	0.468625i
$557$	1.02281	+	3.81720i	0.0433381	+	0.161740i	0.984204	−	0.177040i	$-0.0566523\pi$
$557$	1.02281	+	3.81720i	0.0433381	+	0.161740i	−0.940866	+	0.338780i	$0.889986\pi$
$558$	−2.54101	−	4.40116i	−0.107570	−	0.186316i
$559$	12.4931	−	10.2934i	0.528402	−	0.435365i
$560$		0			0
$561$	−31.2338	−	31.2338i	−1.31869	−	1.31869i
$562$	−19.5523	−	33.8656i	−0.824764	−	1.42853i
$563$	14.8777	−	25.7689i	0.627018	−	1.08603i	−0.361128	−	0.932516i	$-0.617608\pi$
$563$	14.8777	−	25.7689i	0.627018	−	1.08603i	0.988147	−	0.153512i	$-0.0490583\pi$
$564$	−7.40956	+	1.98538i	−0.311999	+	0.0835998i
$565$	0.000640436	0	0.000171604i	2.69433e−5	0	7.21945e-6i
$566$	10.8013	+	10.8013i	0.454013	+	0.454013i
$567$		0			0
$568$	25.4369			1.06731
$569$	−10.3301	+	5.96411i	−0.433062	+	0.250028i	−0.700650	−	0.713505i	$-0.747107\pi$
$569$	−10.3301	+	5.96411i	−0.433062	+	0.250028i	0.267588	+	0.963533i	$0.413773\pi$
$570$	−27.3261	+	7.32202i	−1.14457	+	0.306686i
$571$	−9.93851	−	5.73800i	−0.415914	−	0.240128i	0.277414	−	0.960751i	$-0.410523\pi$
$571$	−9.93851	−	5.73800i	−0.415914	−	0.240128i	−0.693328	+	0.720623i	$0.743856\pi$
$572$	−7.69081	+	3.50264i	−0.321569	+	0.146453i
$573$			4.71154i			0.196828i
$574$		0			0
$575$	−11.1193			−0.463708
$576$	3.01524	−	1.74085i	0.125635	−	0.0725353i
$577$	−0.995790	−	3.71634i	−0.0414553	−	0.154713i	0.942096	−	0.335344i	$-0.108853\pi$
$577$	−0.995790	−	3.71634i	−0.0414553	−	0.154713i	−0.983551	+	0.180631i	$0.942186\pi$
$578$	−38.8662	+	10.4142i	−1.61662	+	0.433172i
$579$	4.00310	−	14.9398i	0.166363	−	0.620875i
$580$	6.06046	+	6.06046i	0.251647	+	0.251647i
$581$		0			0
$582$		−	14.7109i		−	0.609787i
$583$	38.2351	+	10.2451i	1.58354	+	0.424308i
$584$	−5.05248	+	8.75115i	−0.209073	+	0.362125i
$585$	5.56601	−	7.79924i	0.230126	−	0.322459i
$586$	−4.17348	+	2.40956i	−0.172405	+	0.0995380i
$587$	26.9080	−	26.9080i	1.11061	−	1.11061i	0.117543	−	0.993068i	$-0.462498\pi$
$587$	26.9080	−	26.9080i	1.11061	−	1.11061i	0.993068	−	0.117543i	$-0.0375018\pi$
$588$		0			0
$589$			10.1959i			0.420116i
$590$	−3.60053	+	13.4374i	−0.148231	+	0.553207i
$591$	−7.93409	−	29.6104i	−0.326365	−	1.21801i
$592$	−4.93275	−	18.4093i	−0.202735	−	0.756616i
$593$	−2.64245	+	9.86174i	−0.108512	+	0.404973i	−0.998720	−	0.0505817i	$-0.983892\pi$
$593$	−2.64245	+	9.86174i	−0.108512	+	0.404973i	0.890208	+	0.455555i	$0.150559\pi$
$594$		−	23.2498i		−	0.953949i
$595$		0			0
$596$	10.2258	−	10.2258i	0.418867	−	0.418867i
$597$	34.6158	−	19.9855i	1.41673	−	0.817950i
$598$	11.7626	−	16.4821i	0.481009	−	0.674001i
$599$	11.3254	−	19.6162i	0.462745	−	0.801498i	−0.536352	−	0.843995i	$-0.680198\pi$
$599$	11.3254	−	19.6162i	0.462745	−	0.801498i	0.999097	+	0.0424970i	$0.0135313\pi$
$600$	13.4152	+	3.59459i	0.547672	+	0.146748i
$601$			8.02946i			0.327529i	0.986499	+	0.163764i	$0.0523637\pi$
$601$			8.02946i			0.327529i	−0.986499	+	0.163764i	$0.947636\pi$
$602$		0			0
$603$	−4.77547	−	4.77547i	−0.194472	−	0.194472i
$604$	2.96059	−	11.0491i	0.120465	−	0.449580i
$605$	−2.63556	+	0.706197i	−0.107151	+	0.0287110i
$606$	−7.67089	−	28.6282i	−0.311609	−	1.16294i
$607$	−2.91774	+	1.68456i	−0.118427	+	0.0683741i	−0.558044	−	0.829812i	$-0.688448\pi$
$607$	−2.91774	+	1.68456i	−0.118427	+	0.0683741i	0.439616	+	0.898186i	$0.355114\pi$
$608$	11.2032			0.454348
$609$		0			0
$610$		−	16.4629i		−	0.666563i
$611$	−18.7367	+	8.53328i	−0.758005	+	0.345220i
$612$	3.50554	+	2.02392i	0.141703	+	0.0818122i
$613$	31.4399	−	8.42429i	1.26984	−	0.340254i	0.439873	−	0.898060i	$-0.355023\pi$
$613$	31.4399	−	8.42429i	1.26984	−	0.340254i	0.829971	+	0.557806i	$0.188357\pi$
$614$	7.72832	−	4.46195i	0.311889	−	0.180069i
$615$	24.4512			0.985969
$616$		0			0
$617$	−24.9178	−	24.9178i	−1.00315	−	1.00315i	−0.999995	−	0.00315687i	$-0.998995\pi$
$617$	−24.9178	−	24.9178i	−1.00315	−	1.00315i	−0.00315687	−	0.999995i	$-0.501005\pi$
$618$	16.0468	+	4.29971i	0.645495	+	0.172960i
$619$	−15.3745	+	4.11957i	−0.617951	+	0.165580i	−0.554196	−	0.832386i	$-0.686974\pi$
$619$	−15.3745	+	4.11957i	−0.617951	+	0.165580i	−0.0637551	+	0.997966i	$0.520308\pi$
$620$	−3.26436	+	5.65404i	−0.131100	+	0.227072i
$621$	7.05200	+	12.2144i	0.282987	+	0.490148i
$622$	−16.2869	−	16.2869i	−0.653047	−	0.653047i
$623$		0			0
$624$	−26.9959	+	22.2426i	−1.08070	+	0.890418i
$625$	−15.3511	−	26.5890i	−0.614046	−	1.06356i
$626$	1.99345	+	7.43964i	0.0796741	+	0.297348i
$627$	10.4094	−	18.0296i	0.415712	−	0.720034i
$628$	−3.70427	−	6.41599i	−0.147817	−	0.256026i
$629$	−17.7497	+	17.7497i	−0.707727	+	0.707727i
$630$		0			0
$631$	−31.7103	+	31.7103i	−1.26237	+	1.26237i	−0.312427	+	0.949942i	$0.601142\pi$
$631$	−31.7103	+	31.7103i	−1.26237	+	1.26237i	−0.949942	+	0.312427i	$0.898858\pi$
$632$	−2.27323	−	0.609110i	−0.0904241	−	0.0242291i
$633$	4.06571	+	2.34734i	0.161598	+	0.0932984i
$634$	−41.5015	−	23.9609i	−1.64824	−	0.951610i
$635$	9.27855	−	34.6280i	0.368208	−	1.37417i
$636$	−15.3824			−0.609951
$637$		0			0
$638$	−24.9126			−0.986298
$639$	−2.81728	+	10.5142i	−0.111450	+	0.415936i
$640$	−33.6259	−	19.4139i	−1.32918	−	0.767402i
$641$	−3.56700	−	2.05941i	−0.140888	−	0.0813418i	0.427899	−	0.903827i	$-0.359254\pi$
$641$	−3.56700	−	2.05941i	−0.140888	−	0.0813418i	−0.568787	+	0.822485i	$0.692587\pi$
$642$	39.3172	+	10.5350i	1.55173	+	0.415784i
$643$	−6.89221	+	6.89221i	−0.271802	+	0.271802i	−0.829825	−	0.558023i	$-0.811560\pi$
$643$	−6.89221	+	6.89221i	−0.271802	+	0.271802i	0.558023	+	0.829825i	$0.311560\pi$
$644$		0			0
$645$	−18.0559	+	18.0559i	−0.710950	+	0.710950i
$646$	−16.0384	−	27.7793i	−0.631021	−	1.09296i
$647$	6.39418	−	11.0750i	0.251381	−	0.435405i	−0.712525	−	0.701646i	$-0.752449\pi$
$647$	6.39418	−	11.0750i	0.251381	−	0.435405i	0.963906	+	0.266242i	$0.0857820\pi$
$648$	−6.11454	−	22.8198i	−0.240202	−	0.896445i
$649$	−5.11872	−	8.86589i	−0.200927	−	0.348017i
$650$	−19.0291	−	1.83698i	−0.746384	−	0.0720524i
$651$		0			0
$652$	−4.15859	−	4.15859i	−0.162863	−	0.162863i
$653$	−7.12903	−	12.3479i	−0.278981	−	0.483209i	0.692151	−	0.721753i	$-0.256663\pi$
$653$	−7.12903	−	12.3479i	−0.278981	−	0.483209i	−0.971132	+	0.238544i	$0.923330\pi$
$654$	−31.6569	+	54.8314i	−1.23788	+	2.14408i
$655$	37.6727	−	10.0944i	1.47199	−	0.394420i
$656$	−20.3323	−	5.44802i	−0.793842	−	0.212709i
$657$	−3.05766	−	3.05766i	−0.119291	−	0.119291i
$658$		0			0
$659$	18.4714			0.719542			0.359771	−	0.933041i	$-0.382855\pi$
$659$	18.4714			0.719542			0.359771	+	0.933041i	$0.382855\pi$
$660$	11.5448	−	6.66542i	0.449383	−	0.259451i
$661$	31.6076	−	8.46923i	1.22939	−	0.329415i	0.415050	−	0.909799i	$-0.363764\pi$
$661$	31.6076	−	8.46923i	1.22939	−	0.329415i	0.814343	+	0.580384i	$0.197097\pi$
$662$	−21.0014	−	12.1251i	−0.816242	−	0.471257i
$663$	43.1485	+	16.1446i	1.67575	+	0.627003i
$664$			6.15757i			0.238960i
$665$		0			0
$666$	5.89703			0.228505
$667$	13.0880	−	7.55635i	0.506768	−	0.292583i
$668$	−1.98578	−	7.41104i	−0.0768322	−	0.286742i
$669$	−26.1950	+	7.01892i	−1.01276	+	0.271367i
$670$	−8.86941	+	33.1011i	−0.342655	+	1.27881i
$671$	8.56669	+	8.56669i	0.330713	+	0.330713i
$672$		0			0
$673$		−	35.6367i		−	1.37370i	−0.726801	−	0.686848i	$-0.758994\pi$
$673$		−	35.6367i		−	1.37370i	0.726801	−	0.686848i	$-0.241006\pi$
$674$	15.0470	+	4.03183i	0.579588	+	0.155300i
$675$	6.65801	−	11.5320i	0.256267	−	0.443868i
$676$	5.78583	−	6.64928i	0.222532	−	0.255742i
$677$	−23.9548	+	13.8303i	−0.920657	+	0.531542i	−0.883845	−	0.467781i	$-0.845054\pi$
$677$	−23.9548	+	13.8303i	−0.920657	+	0.531542i	−0.0368124	+	0.999322i	$0.511720\pi$
$678$	0.000529566	0	0.000529566i	2.03379e−5	0	2.03379e-5i
$679$		0			0
$680$			40.0483i			1.53578i
$681$	−6.68620	+	24.9532i	−0.256216	+	0.956210i
$682$	−4.91159	−	18.3303i	−0.188075	−	0.701904i
$683$	−0.418104	−	1.56039i	−0.0159983	−	0.0597065i	0.957465	−	0.288549i	$-0.0931727\pi$
$683$	−0.418104	−	1.56039i	−0.0159983	−	0.0597065i	−0.973464	+	0.228842i	$0.926506\pi$
$684$	−0.493783	+	1.84282i	−0.0188803	+	0.0704622i
$685$			3.88034i			0.148260i
$686$		0			0
$687$	−21.2939	+	21.2939i	−0.812414	+	0.812414i
$688$	19.0373	−	10.9912i	0.725791	−	0.419036i
$689$	−40.7209	+	6.80413i	−1.55134	+	0.259217i
$690$	−15.9708	+	27.6623i	−0.607999	+	1.05309i
$691$	25.7402	+	6.89707i	0.979204	+	0.262377i	0.712709	−	0.701460i	$-0.247468\pi$
$691$	25.7402	+	6.89707i	0.979204	+	0.262377i	0.266494	+	0.963836i	$0.414135\pi$
$692$			2.22161i			0.0844531i
$693$		0			0
$694$	−40.6506	−	40.6506i	−1.54307	−	1.54307i
$695$	−13.9816	+	52.1802i	−0.530354	+	1.97931i
$696$	−18.2331	+	4.88553i	−0.691122	+	0.185186i
$697$	7.17550	+	26.7793i	0.271792	+	1.01434i
$698$	13.3234	−	7.69228i	0.504299	−	0.291157i
$699$	−15.3255			−0.579665
$700$		0			0
$701$		−	5.72322i		−	0.216163i	−0.994142	−	0.108081i	$-0.965529\pi$
$701$		−	5.72322i		−	0.216163i	0.994142	−	0.108081i	$-0.0344707\pi$
$702$	10.0506	+	22.0682i	0.379335	+	0.832912i
$703$	−10.2460	−	5.91552i	−0.386434	−	0.223108i
$704$	12.5581	−	3.36493i	0.473301	−	0.126821i
$705$	28.1261	−	16.2386i	1.05929	−	0.611581i
$706$	−20.2483			−0.762056
$707$		0			0
$708$	2.81308	+	2.81308i	0.105722	+	0.105722i
$709$	11.5808	+	3.10307i	0.434927	+	0.116538i	0.469638	−	0.882859i	$-0.344384\pi$
$709$	11.5808	+	3.10307i	0.434927	+	0.116538i	−0.0347112	+	0.999397i	$0.511051\pi$
$710$	53.3513	−	14.2954i	2.00224	−	0.536498i
$711$	0.503546	−	0.872167i	0.0188844	−	0.0327088i
$712$	5.36722	+	9.29630i	0.201145	+	0.348394i
$713$	8.14019	+	8.14019i	0.304853	+	0.304853i
$714$		0			0
$715$	27.6137	−	22.7516i	1.03269	−	0.850863i
$716$	0.762791	+	1.32119i	0.0285068	+	0.0493753i
$717$	1.53002	+	5.71010i	0.0571396	+	0.213248i
$718$	3.50818	−	6.07635i	0.130924	−	0.226767i
$719$	7.61939	+	13.1972i	0.284155	+	0.492172i	0.972404	−	0.233303i	$-0.0749535\pi$
$719$	7.61939	+	13.1972i	0.284155	+	0.492172i	−0.688249	+	0.725475i	$0.741620\pi$
$720$	9.20079	−	9.20079i	0.342893	−	0.342893i
$721$		0			0
$722$	−11.2956	+	11.2956i	−0.420378	+	0.420378i
$723$	−50.5377	−	13.5415i	−1.87952	−	0.503615i
$724$	−9.12586	−	5.26882i	−0.339160	−	0.195814i
$725$	−12.3568	−	7.13419i	−0.458919	−	0.264957i
$726$	−0.797681	+	2.97698i	−0.0296047	+	0.110486i
$727$	19.4937			0.722981			0.361491	−	0.932376i	$-0.382268\pi$
$727$	19.4937			0.722981			0.361491	+	0.932376i	$0.382268\pi$
$728$		0			0
$729$	−14.3192			−0.530339
$730$	−5.67895	+	21.1941i	−0.210187	+	0.784430i
$731$	−25.0738	−	14.4763i	−0.927387	−	0.535427i
$732$	−4.07721	−	2.35398i	−0.150698	−	0.0870056i
$733$	−28.6716	−	7.68254i	−1.05901	−	0.283761i	−0.313040	−	0.949740i	$-0.601348\pi$
$733$	−28.6716	−	7.68254i	−1.05901	−	0.283761i	−0.745971	+	0.665979i	$0.768014\pi$
$734$	28.6216	−	28.6216i	1.05644	−	1.05644i
$735$		0			0
$736$	8.94434	−	8.94434i	0.329693	−	0.329693i
$737$	−12.6093	−	21.8399i	−0.464469	−	0.804484i
$738$	3.25651	−	5.64045i	0.119874	−	0.207628i
$739$	−0.217474	−	0.811625i	−0.00799992	−	0.0298561i	0.961811	−	0.273716i	$-0.0882529\pi$
$739$	−0.217474	−	0.811625i	−0.00799992	−	0.0298561i	−0.969810	+	0.243860i	$0.921586\pi$
$740$	−3.78786	−	6.56077i	−0.139245	−	0.241179i
$741$	−2.08644	+	21.6133i	−0.0766474	+	0.793983i
$742$		0			0
$743$	22.5891	+	22.5891i	0.828715	+	0.828715i	0.987339	−	0.158624i	$-0.0507056\pi$
$743$	22.5891	+	22.5891i	0.828715	+	0.828715i	−0.158624	+	0.987339i	$0.550706\pi$
$744$	−7.18941	−	12.4524i	−0.263577	−	0.456528i
$745$	−30.6136	+	53.0243i	−1.12160	+	1.94266i
$746$	12.5089	−	3.35176i	0.457985	−	0.122717i
$747$	−2.54521	−	0.681986i	−0.0931242	−	0.0249526i
$748$	10.6880	+	10.6880i	0.390793	+	0.390793i
$749$		0			0
$750$	−16.3805			−0.598131
$751$	−12.9789	+	7.49334i	−0.473605	+	0.273436i	−0.717748	−	0.696303i	$-0.754827\pi$
$751$	−12.9789	+	7.49334i	−0.473605	+	0.273436i	0.244143	+	0.969739i	$0.421494\pi$
$752$	−27.0062	+	7.23629i	−0.984815	+	0.263880i
$753$	−12.1166	−	6.99550i	−0.441552	−	0.254930i
$754$	23.6465	−	10.7694i	0.861156	−	0.392198i
$755$			48.4296i			1.76254i
$756$		0			0
$757$	−4.27355			−0.155325			−0.0776624	−	0.996980i	$-0.524746\pi$
$757$	−4.27355			−0.155325			−0.0776624	+	0.996980i	$0.524746\pi$
$758$	6.66191	−	3.84626i	0.241971	−	0.139702i
$759$	−6.08381	−	22.7051i	−0.220828	−	0.824142i
$760$	−18.2324	+	4.88536i	−0.661359	+	0.177211i
$761$	2.03075	−	7.57885i	0.0736145	−	0.274733i	−0.919301	−	0.393555i	$-0.871245\pi$
$761$	2.03075	−	7.57885i	0.0736145	−	0.274733i	0.992916	+	0.118822i	$0.0379118\pi$
$762$	−28.6333	−	28.6333i	−1.03728	−	1.03728i
$763$		0			0
$764$		−	1.61227i		−	0.0583297i
$765$	−16.5538	−	4.43557i	−0.598503	−	0.160369i
$766$	7.41067	−	12.8357i	0.267758	−	0.463771i
$767$	8.69121	+	6.20258i	0.313821	+	0.223962i
$768$	−25.0753	+	14.4773i	−0.904828	+	0.522403i
$769$	5.34450	−	5.34450i	0.192727	−	0.192727i	−0.604146	−	0.796874i	$-0.706486\pi$
$769$	5.34450	−	5.34450i	0.192727	−	0.192727i	0.796874	+	0.604146i	$0.206486\pi$
$770$		0			0
$771$		−	25.8635i		−	0.931450i
$772$	−1.36984	+	5.11231i	−0.0493016	+	0.183996i
$773$	7.88945	+	29.4438i	0.283764	+	1.05902i	0.949738	+	0.313046i	$0.101349\pi$
$773$	7.88945	+	29.4438i	0.283764	+	1.05902i	−0.665974	+	0.745975i	$0.731984\pi$
$774$	1.76040	+	6.56991i	0.0632764	+	0.236151i
$775$	2.81306	−	10.4985i	0.101048	−	0.377116i
$776$		−	9.81534i		−	0.352350i
$777$		0			0
$778$	24.8335	−	24.8335i	0.890323	−	0.890323i
$779$	−11.3163	+	6.53345i	−0.405447	+	0.234085i
$780$	−8.07678	+	11.3174i	−0.289195	+	0.405228i
$781$	−20.3232	+	35.2009i	−0.727222	+	1.25959i
$782$	−34.9830	−	9.37366i	−1.25099	−	0.335201i
$783$			18.0983i			0.646780i
$784$		0			0
$785$	22.1793	+	22.1793i	0.791613	+	0.791613i
$786$	11.4020	−	42.5529i	0.406697	−	1.51781i
$787$	52.3495	−	14.0270i	1.86606	−	0.500008i	0.866057	−	0.499946i	$-0.166647\pi$
$787$	52.3495	−	14.0270i	1.86606	−	0.500008i	1.00000		6.28799e-5i	$-2.00153e-5\pi$
$788$	2.71500	+	10.1325i	0.0967180	+	0.360957i
$789$	−38.3241	+	22.1264i	−1.36437	+	0.787721i
$790$	−5.11018			−0.181812
$791$		0			0
$792$			6.92360i			0.246020i
$793$	−11.8346	−	4.42807i	−0.420259	−	0.157245i
$794$	−18.5291	−	10.6978i	−0.657572	−	0.379650i
$795$	62.9068	−	16.8558i	2.23107	−	0.597814i
$796$	−11.8454	+	6.83892i	−0.419847	+	0.242399i
$797$	28.0843			0.994797			0.497399	−	0.867522i	$-0.334289\pi$
$797$	28.0843			0.994797			0.497399	+	0.867522i	$0.334289\pi$
$798$		0			0
$799$	26.0387	+	26.0387i	0.921181	+	0.921181i
$800$	−11.5356	−	3.09095i	−0.407845	−	0.109282i
$801$	−4.43704	+	1.18890i	−0.156775	+	0.0420078i
$802$	17.3656	−	30.0781i	0.613201	−	1.06210i
$803$	−8.07354	−	13.9838i	−0.284909	−	0.493477i
$804$	6.92963	+	6.92963i	0.244389	+	0.244389i
$805$		0			0
$806$	12.5860	+	15.2756i	0.443321	+	0.538059i
$807$	−3.10509	−	5.37818i	−0.109304	−	0.189321i
$808$	−5.11813	−	19.1011i	−0.180055	−	0.671976i
$809$	6.38747	−	11.0634i	0.224572	−	0.388969i	−0.731619	−	0.681714i	$-0.761235\pi$
$809$	6.38747	−	11.0634i	0.224572	−	0.388969i	0.956191	+	0.292744i	$0.0945684\pi$
$810$	−25.6493	−	44.4258i	−0.901223	−	1.56096i
$811$	−20.6613	+	20.6613i	−0.725515	+	0.725515i	−0.969723	−	0.244208i	$-0.921472\pi$
$811$	−20.6613	+	20.6613i	−0.725515	+	0.725515i	0.244208	+	0.969723i	$0.421472\pi$
$812$		0			0
$813$	22.1500	−	22.1500i	0.776833	−	0.776833i
$814$	21.2699	+	5.69926i	0.745511	+	0.199759i
$815$	21.5636	+	12.4498i	0.755341	+	0.436096i
$816$	54.1810	+	31.2814i	1.89671	+	1.09507i
$817$	3.53185	−	13.1810i	0.123564	−	0.461146i
$818$	13.9395			0.487382
$819$		0			0
$820$	−8.36708			−0.292191
$821$	0.330074	−	1.23185i	0.0115197	−	0.0429920i	−0.959927	−	0.280251i	$-0.909582\pi$
$821$	0.330074	−	1.23185i	0.0115197	−	0.0429920i	0.971446	+	0.237259i	$0.0762490\pi$
$822$	3.79580	+	2.19151i	0.132394	+	0.0764376i
$823$	19.1222	+	11.0402i	0.666559	+	0.384838i	0.794771	−	0.606909i	$-0.207591\pi$
$823$	19.1222	+	11.0402i	0.666559	+	0.384838i	−0.128213	+	0.991747i	$0.540924\pi$
$824$	10.7066	+	2.86883i	0.372983	+	0.0999406i
$825$	−15.6927	+	15.6927i	−0.546349	+	0.546349i
$826$		0			0
$827$	9.30639	−	9.30639i	0.323615	−	0.323615i	−0.526537	−	0.850152i	$-0.676510\pi$
$827$	9.30639	−	9.30639i	0.323615	−	0.323615i	0.850152	+	0.526537i	$0.176510\pi$
$828$	1.07704	+	1.86549i	0.0374299	+	0.0648304i
$829$	−15.4841	+	26.8192i	−0.537784	+	0.931469i	0.461239	+	0.887276i	$0.347405\pi$
$829$	−15.4841	+	26.8192i	−0.537784	+	0.931469i	−0.999023	+	0.0441933i	$0.985928\pi$
$830$	3.46053	+	12.9149i	0.120117	+	0.448282i
$831$	−29.2093	−	50.5920i	−1.01326	−	1.75502i
$832$	−10.4653	+	8.62263i	−0.362819	+	0.298936i
$833$		0			0
$834$	43.1470	+	43.1470i	1.49406	+	1.49406i
$835$	16.2418	+	28.1317i	0.562072	+	0.973537i
$836$	−3.56205	+	6.16965i	−0.123196	+	0.213382i
$837$	−13.3165	+	3.56814i	−0.460285	+	0.123333i
$838$	−13.2635	−	3.55395i	−0.458180	−	0.122769i
$839$	22.1620	+	22.1620i	0.765116	+	0.765116i	0.977242	−	0.212126i	$-0.0680389\pi$
$839$	22.1620	+	22.1620i	0.765116	+	0.765116i	−0.212126	+	0.977242i	$0.568039\pi$
$840$		0			0
$841$	−9.60734			−0.331288
$842$	41.1701	−	23.7696i	1.41882	−	0.819153i
$843$	45.7328	−	12.2541i	1.57512	−	0.422053i
$844$	−1.39127	−	0.803248i	−0.0478893	−	0.0276489i
$845$	−16.3751	+	33.5325i	−0.563322	+	1.15355i
$846$		−	8.65088i		−	0.297423i
$847$		0			0
$848$	−56.0654			−1.92530
$849$	−16.0169	+	9.24736i	−0.549699	+	0.317369i
$850$	8.84997	+	33.0285i	0.303551	+	1.13287i
$851$	−12.9030	+	3.45734i	−0.442308	+	0.118516i
$852$	4.08812	−	15.2571i	0.140057	−	0.522699i
$853$	−15.0740	−	15.0740i	−0.516125	−	0.516125i	0.400271	−	0.916397i	$-0.368916\pi$
$853$	−15.0740	−	15.0740i	−0.516125	−	0.516125i	−0.916397	+	0.400271i	$0.868916\pi$
$854$		0			0
$855$		−	8.07737i		−	0.276240i
$856$	26.2330	+	7.02912i	0.896627	+	0.240250i
$857$	18.8426	−	32.6363i	0.643650	−	1.11483i	−0.340961	−	0.940077i	$-0.610753\pi$
$857$	18.8426	−	32.6363i	0.643650	−	1.11483i	0.984612	−	0.174757i	$-0.0559141\pi$
$858$	−6.66054	−	39.8616i	−0.227387	−	1.36085i
$859$	−8.05583	+	4.65104i	−0.274861	+	0.158691i	−0.631095	−	0.775706i	$-0.717394\pi$
$859$	−8.05583	+	4.65104i	−0.274861	+	0.158691i	0.356233	+	0.934397i	$0.384061\pi$
$860$	6.17863	−	6.17863i	0.210689	−	0.210689i
$861$		0			0
$862$			16.3712i			0.557605i
$863$	5.95141	−	22.2110i	0.202588	−	0.756070i	−0.787583	−	0.616209i	$-0.788668\pi$
$863$	5.95141	−	22.2110i	0.202588	−	0.756070i	0.990171	−	0.139861i	$-0.0446656\pi$
$864$	3.92063	+	14.6320i	0.133382	+	0.497790i
$865$	−2.43441	−	9.08536i	−0.0827726	−	0.308911i
$866$	−17.5284	+	65.4167i	−0.595638	+	2.22295i
$867$		−	48.7174i		−	1.65453i
$868$		0			0
$869$	2.65915	−	2.65915i	0.0902056	−	0.0902056i
$870$	−35.4963	+	20.4938i	−1.20344	+	0.694806i
$871$	21.4096	+	15.2792i	0.725437	+	0.517716i
$872$	−21.1220	+	36.5843i	−0.715280	+	1.23890i
$873$	4.05713	+	1.08710i	0.137313	+	0.0367929i
$874$		−	17.0698i		−	0.577396i
$875$		0			0
$876$	4.43694	+	4.43694i	0.149910	+	0.149910i
$877$	−2.73667	+	10.2134i	−0.0924108	+	0.344882i	−0.996614	−	0.0822203i	$-0.973799\pi$
$877$	−2.73667	+	10.2134i	−0.0924108	+	0.344882i	0.904203	+	0.427102i	$0.140466\pi$
$878$	0.225371	−	0.0603880i	0.00760591	−	0.00203800i
$879$	−1.51015	−	5.63596i	−0.0509362	−	0.190096i
$880$	42.0785	−	24.2940i	1.41846	−	0.818951i
$881$	−19.0687			−0.642440			−0.321220	−	0.947005i	$-0.604093\pi$
$881$	−19.0687			−0.642440			−0.321220	+	0.947005i	$0.604093\pi$
$882$		0			0
$883$		−	4.27586i		−	0.143894i	−0.997408	−	0.0719471i	$-0.977079\pi$
$883$		−	4.27586i		−	0.143894i	0.997408	−	0.0719471i	$-0.0229213\pi$
$884$	−14.7652	−	5.52459i	−0.496607	−	0.185812i
$885$	−14.5867	−	8.42164i	−0.490327	−	0.283090i
$886$	−40.8985	+	10.9587i	−1.37401	+	0.368165i
$887$	−5.75705	+	3.32383i	−0.193303	+	0.111603i	−0.593528	−	0.804813i	$-0.702265\pi$
$887$	−5.75705	+	3.32383i	−0.193303	+	0.111603i	0.400225	+	0.916417i	$0.368932\pi$
$888$	16.6847			0.559903
$889$		0			0
$890$	16.4817	+	16.4817i	0.552468	+	0.552468i
$891$	36.4645	+	9.77064i	1.22161	+	0.327329i
$892$	8.96378	−	2.40184i	0.300130	−	0.0804195i
$893$	−8.67801	+	15.0308i	−0.290399	+	0.502985i
$894$	34.5794	+	59.8932i	1.15651	+	2.00313i
$895$	−4.56720	−	4.56720i	−0.152665	−	0.152665i
$896$		0			0
$897$	15.5898	+	18.9213i	0.520527	+	0.631764i
$898$	−1.46548	−	2.53828i	−0.0489036	−	0.0847036i
$899$	3.82333	+	14.2689i	0.127515	+	0.475893i
$900$	1.01687	−	1.76127i	0.0338957	−	0.0587091i
$901$	36.9215	+	63.9499i	1.23003	+	2.13048i
$902$	17.1972	−	17.1972i	0.572603	−	0.572603i
$903$		0			0
$904$	0.000353334	0	0.000353334i	1.17517e−5	0	1.17517e-5i
$905$	43.0940	+	11.5470i	1.43249	+	0.383835i
$906$	47.3745	+	27.3517i	1.57391	+	0.908699i
$907$	−12.7208	−	7.34433i	−0.422386	−	0.243865i	0.273712	−	0.961812i	$-0.411749\pi$
$907$	−12.7208	−	7.34433i	−0.422386	−	0.243865i	−0.696098	+	0.717947i	$0.745082\pi$
$908$	2.28798	−	8.53886i	0.0759293	−	0.283372i
$909$	8.46224			0.280675
$910$		0			0
$911$	17.7868			0.589301			0.294651	−	0.955605i	$-0.404797\pi$
$911$	17.7868			0.589301			0.294651	+	0.955605i	$0.404797\pi$
$912$	−7.63184	+	28.4824i	−0.252715	+	0.943146i
$913$	−8.52117	−	4.91970i	−0.282009	−	0.162818i
$914$	6.60764	+	3.81492i	0.218561	+	0.126186i
$915$	19.2534	+	5.15892i	0.636496	+	0.170549i
$916$	7.28667	−	7.28667i	0.240758	−	0.240758i
$917$		0			0
$918$	30.6686	−	30.6686i	1.01221	−	1.01221i
$919$	−11.1432	−	19.3006i	−0.367581	−	0.636670i	0.621605	−	0.783331i	$-0.286481\pi$
$919$	−11.1432	−	19.3006i	−0.367581	−	0.636670i	−0.989187	+	0.146661i	$0.953147\pi$
$920$	−10.6560	+	18.4567i	−0.351317	+	0.608499i
$921$	2.79645	+	10.4365i	0.0921461	+	0.343894i
$922$	4.17612	+	7.23325i	0.137533	+	0.238214i
$923$	4.07355	−	42.1975i	0.134082	−	1.38895i
$924$		0			0
$925$	8.91792	+	8.91792i	0.293219	+	0.293219i
$926$	4.63127	+	8.02160i	0.152193	+	0.263606i
$927$	−2.37164	+	4.10780i	−0.0778949	+	0.134918i
$928$	15.6784	−	4.20102i	0.514670	−	0.137905i
$929$	−41.4886	−	11.1168i	−1.36120	−	0.364731i	−0.496940	−	0.867785i	$-0.665543\pi$
$929$	−41.4886	−	11.1168i	−1.36120	−	0.364731i	−0.864255	+	0.503054i	$0.832210\pi$
$930$	−22.0773	−	22.0773i	−0.723943	−	0.723943i
$931$		0			0
$932$	5.24431			0.171783
$933$	24.1514	−	13.9438i	0.790680	−	0.456499i
$934$	63.3258	−	16.9681i	2.07208	−	0.555213i
$935$	−55.4209	−	31.9973i	−1.81246	−	1.04642i
$936$	−2.99299	−	6.57176i	−0.0978288	−	0.214805i
$937$		−	52.3733i		−	1.71096i	−0.517835	−	0.855481i	$-0.673262\pi$
$937$		−	52.3733i		−	1.71096i	0.517835	−	0.855481i	$-0.326738\pi$
$938$		0			0
$939$	−9.32534			−0.304321
$940$	−9.62459	+	5.55676i	−0.313919	+	0.181241i
$941$	−4.03247	−	15.0494i	−0.131455	−	0.490596i	0.868532	−	0.495632i	$-0.165064\pi$
$941$	−4.03247	−	15.0494i	−0.131455	−	0.490596i	−0.999987	+	0.00503603i	$0.998397\pi$
$942$	34.2223	−	9.16984i	1.11502	−	0.298770i
$943$	−3.81849	+	14.2508i	−0.124347	+	0.464070i
$944$	10.2531	+	10.2531i	0.333708	+	0.333708i
$945$		0			0
$946$			25.3983i			0.825771i
$947$	−41.1510	−	11.0264i	−1.33723	−	0.358309i	−0.481822	−	0.876269i	$-0.660025\pi$
$947$	−41.1510	−	11.0264i	−1.33723	−	0.358309i	−0.855405	+	0.517960i	$0.826692\pi$
$948$	−0.730690	+	1.26559i	−0.0237317	+	0.0411045i
$949$	13.7083	+	9.78306i	0.444989	+	0.317571i
$950$	−13.9570	+	8.05809i	−0.452825	+	0.261439i
$951$	41.0275	−	41.0275i	1.33041	−	1.33041i
$952$		0			0
$953$		−	35.9437i		−	1.16433i	−0.813070	−	0.582165i	$-0.802206\pi$
$953$		−	35.9437i		−	1.16433i	0.813070	−	0.582165i	$-0.197794\pi$
$954$	4.48985	−	16.7563i	0.145364	−	0.542507i
$955$	1.76670	+	6.59341i	0.0571690	+	0.213358i
$956$	−0.523564	−	1.95397i	−0.0169333	−	0.0631958i
$957$	7.80676	−	29.1352i	0.252357	−	0.941808i
$958$			19.2949i			0.623390i
$959$		0			0
$960$	15.1251	−	15.1251i	0.488162	−	0.488162i
$961$	17.1017	−	9.87370i	0.551669	−	0.318506i
$962$	−22.6527	+	3.78509i	−0.730354	+	0.122036i
$963$	−5.81092	+	10.0648i	−0.187254	+	0.324334i
$964$	17.2937	+	4.63384i	0.556993	+	0.149246i
$965$		−	22.4080i		−	0.721339i
$966$		0			0
$967$	−31.7209	−	31.7209i	−1.02008	−	1.02008i	−0.999794	−	0.0202813i	$-0.993544\pi$
$967$	−31.7209	−	31.7209i	−1.02008	−	1.02008i	−0.0202813	−	0.999794i	$-0.506456\pi$
$968$	−0.532224	+	1.98629i	−0.0171063	+	0.0638417i
$969$	37.5137	−	10.0518i	1.20511	−	0.322909i
$970$	−5.51618	−	20.5867i	−0.177114	−	0.660998i
$971$	−20.7204	+	11.9629i	−0.664950	+	0.383909i	−0.794161	−	0.607708i	$-0.792089\pi$
$971$	−20.7204	+	11.9629i	−0.664950	+	0.383909i	0.129210	+	0.991617i	$0.458756\pi$
$972$	−6.31063			−0.202414
$973$		0			0
$974$			0.900548i			0.0288554i
$975$	8.11145	−	21.6789i	0.259774	−	0.694282i
$976$	−14.8606	−	8.57975i	−0.475675	−	0.274631i
$977$	42.6772	−	11.4353i	1.36537	−	0.365849i	0.499582	−	0.866267i	$-0.333487\pi$
$977$	42.6772	−	11.4353i	1.36537	−	0.365849i	0.865784	+	0.500418i	$0.166820\pi$
$978$	24.3570	−	14.0625i	0.778852	−	0.449671i
$979$	−17.1530			−0.548211
$980$		0			0
$981$	−12.7826	−	12.7826i	−0.408117	−	0.408117i
$982$	−4.78009	−	1.28082i	−0.152539	−	0.0408726i
$983$	3.90158	−	1.04542i	0.124441	−	0.0333439i	−0.196061	−	0.980592i	$-0.562815\pi$
$983$	3.90158	−	1.04542i	0.124441	−	0.0333439i	0.320502	+	0.947248i	$0.396148\pi$
$984$	9.21381	−	15.9588i	0.293726	−	0.508748i
$985$	−22.2062	−	38.4623i	−0.707548	−	1.22551i
$986$	−32.8620	−	32.8620i	−1.04654	−	1.04654i
$987$		0			0
$988$	0.713969	−	7.39594i	0.0227144	−	0.235296i
$989$	−7.70369	−	13.3432i	−0.244963	−	0.424288i
$990$	3.89104	+	14.5216i	0.123665	+	0.461526i
$991$	15.4084	−	26.6881i	0.489463	−	0.847774i	−0.510464	−	0.859899i	$-0.670526\pi$
$991$	15.4084	−	26.6881i	0.489463	−	0.847774i	0.999926	+	0.0121250i	$0.00385960\pi$
$992$	6.18211	+	10.7077i	0.196282	+	0.339971i
$993$	20.7615	−	20.7615i	0.658846	−	0.658846i
$994$		0			0
$995$	40.9480	−	40.9480i	1.29814	−	1.29814i
$996$	3.69332	+	0.989622i	0.117027	+	0.0313574i
$997$	−34.9509	−	20.1789i	−1.10691	−	0.639072i	−0.168879	−	0.985637i	$-0.554015\pi$
$997$	−34.9509	−	20.1789i	−1.10691	−	0.639072i	−0.938026	+	0.346565i	$0.887348\pi$
$998$	54.3496	+	31.3787i	1.72040	+	0.993276i
$999$	4.14036	−	15.4520i	0.130995	−	0.488880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.b.619.6		32
7.2	even	3		91.2.bb.a.47.3	yes	32
7.3	odd	6		637.2.i.a.489.12		32
7.4	even	3		637.2.i.a.489.11		32
7.5	odd	6	inner	637.2.bc.b.411.3		32
7.6	odd	2		91.2.bb.a.73.6	yes	32
13.5	odd	4	inner	637.2.bc.b.31.3		32
21.2	odd	6		819.2.fn.e.775.6		32
21.20	even	2		819.2.fn.e.73.3		32
91.5	even	12	inner	637.2.bc.b.460.6		32
91.18	odd	12		637.2.i.a.538.11		32
91.31	even	12		637.2.i.a.538.12		32
91.44	odd	12		91.2.bb.a.5.6	✓	32
91.83	even	4		91.2.bb.a.31.3	yes	32
273.44	even	12		819.2.fn.e.460.3		32
273.83	odd	4		819.2.fn.e.577.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.6	✓	32	91.44	odd	12
91.2.bb.a.31.3	yes	32	91.83	even	4
91.2.bb.a.47.3	yes	32	7.2	even	3
91.2.bb.a.73.6	yes	32	7.6	odd	2
637.2.i.a.489.11		32	7.4	even	3
637.2.i.a.489.12		32	7.3	odd	6
637.2.i.a.538.11		32	91.18	odd	12
637.2.i.a.538.12		32	91.31	even	12
637.2.bc.b.31.3		32	13.5	odd	4	inner
637.2.bc.b.411.3		32	7.5	odd	6	inner
637.2.bc.b.460.6		32	91.5	even	12	inner
637.2.bc.b.619.6		32	1.1	even	1	trivial
819.2.fn.e.73.3		32	21.20	even	2
819.2.fn.e.460.3		32	273.44	even	12
819.2.fn.e.577.6		32	273.83	odd	4
819.2.fn.e.775.6		32	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.423548 - 1.58070i) q^{2} +(1.71590 + 0.990678i) q^{3} +(-0.587174 - 0.339005i) q^{4} +(2.77274 + 0.742954i) q^{5} +(2.29273 - 2.29273i) q^{6} +(1.52975 - 1.52975i) q^{8} +(0.462886 + 0.801742i) q^{9} +(2.34878 - 4.06820i) q^{10} +(0.894725 + 3.33916i) q^{11} +(-0.671689 - 1.16340i) q^{12} +(-2.29273 - 2.78269i) q^{13} +(4.02173 + 4.02173i) q^{15} +(-2.44816 - 4.24034i) q^{16} +(-3.22444 + 5.58489i) q^{17} +(1.46337 - 0.392109i) q^{18} +(-2.93592 - 0.786677i) q^{19} +(-1.37622 - 1.37622i) q^{20} +5.65717 q^{22} +(-2.97203 + 1.71590i) q^{23} +(4.14038 - 1.10941i) q^{24} +(2.80599 + 1.62004i) q^{25} +(-5.36969 + 2.44553i) q^{26} -4.10978i q^{27} -4.40371 q^{29} +(8.06056 - 4.65376i) q^{30} +(-0.868206 - 3.24019i) q^{31} +(-3.56028 + 0.953974i) q^{32} +(-1.77277 + 6.61607i) q^{33} +(7.46233 + 7.46233i) q^{34} -0.627683i q^{36} +(3.75982 + 1.00744i) q^{37} +(-2.48700 + 4.30762i) q^{38} +(-1.17736 - 7.04619i) q^{39} +(5.37812 - 3.10506i) q^{40} +(3.03989 - 3.03989i) q^{41} +4.48958i q^{43} +(0.606632 - 2.26398i) q^{44} +(0.687806 + 2.56693i) q^{45} +(1.45353 + 5.42467i) q^{46} +(1.47790 - 5.51561i) q^{47} -9.70136i q^{48} +(3.74927 - 3.74927i) q^{50} +(-11.0656 + 6.38875i) q^{51} +(0.402887 + 2.41117i) q^{52} +(5.72526 - 9.91644i) q^{53} +(-6.49634 - 1.74069i) q^{54} +9.92337i q^{55} +(-4.25841 - 4.25841i) q^{57} +(-1.86518 + 6.96095i) q^{58} +(-2.86050 + 0.766469i) q^{59} +(-0.998069 - 3.72484i) q^{60} +(3.03504 - 1.75228i) q^{61} -5.48950 q^{62} -3.76085i q^{64} +(-4.28975 - 9.41908i) q^{65} +(9.70717 + 5.60444i) q^{66} +(-7.04645 + 1.88809i) q^{67} +(3.78661 - 2.18620i) q^{68} -6.79964 q^{69} +(8.31408 + 8.31408i) q^{71} +(1.93456 + 0.518364i) q^{72} +(-4.51174 + 1.20892i) q^{73} +(3.18492 - 5.51645i) q^{74} +(3.20988 + 5.55967i) q^{75} +(1.45721 + 1.45721i) q^{76} +(-11.6366 - 1.12334i) q^{78} +(-0.543920 - 0.942097i) q^{79} +(-3.63774 - 13.5762i) q^{80} +(5.46013 - 9.45722i) q^{81} +(-3.51762 - 6.09269i) q^{82} +(-2.01261 + 2.01261i) q^{83} +(-13.0898 + 13.0898i) q^{85} +(7.09668 + 1.90155i) q^{86} +(-7.55635 - 4.36266i) q^{87} +(6.47677 + 3.73937i) q^{88} +(-1.28423 + 4.79280i) q^{89} +4.34887 q^{90} +2.32680 q^{92} +(1.72023 - 6.41997i) q^{93} +(-8.09257 - 4.67225i) q^{94} +(-7.55608 - 4.36250i) q^{95} +(-7.05418 - 1.89016i) q^{96} +(3.20816 - 3.20816i) q^{97} +(-2.26299 + 2.26299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9} - 10 q^{11} - 44 q^{15} + 12 q^{16} - 4 q^{18} - 12 q^{19} - 8 q^{22} + 12 q^{24} - 24 q^{26} + 16 q^{29} - 24 q^{31} + 4 q^{32} - 48 q^{33} - 8 q^{37}+ \cdots - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9 - 10 * q^11 - 44 * q^15 + 12 * q^16 - 4 * q^18 - 12 * q^19 - 8 * q^22 + 12 * q^24 - 24 * q^26 + 16 * q^29 - 24 * q^31 + 4 * q^32 - 48 * q^33 - 8 * q^37 - 6 * q^39 + 132 * q^40 - 42 * q^44 + 24 * q^45 + 12 * q^46 - 30 * q^47 + 88 * q^50 - 36 * q^52 - 12 * q^53 - 78 * q^54 + 40 * q^57 + 26 * q^58 + 54 * q^59 + 16 * q^60 + 48 * q^61 - 8 * q^65 - 12 * q^66 + 16 * q^67 + 48 * q^68 - 36 * q^71 + 22 * q^72 - 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 - 138 * q^80 + 16 * q^81 - 84 * q^85 + 42 * q^86 + 24 * q^87 + 60 * q^89 + 48 * q^92 + 6 * q^93 + 72 * q^94 + 42 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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