LMFDB - Embedded newform 403.2.s.a.160.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [403,2,Mod(160,403)] 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("403.160"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(403, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			160.8
Character	$\chi$	$=$	403.160
Dual form			403.2.s.a.335.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.77854 - 1.02684i) q^{2} +(1.56768 + 2.71530i) q^{3} +(1.10881 + 1.92051i) q^{4} +(0.188573 - 0.108873i) q^{5} -6.43902i q^{6} +0.507266i q^{7} -0.446916i q^{8} +(-3.41522 + 5.91533i) q^{9} -0.447180 q^{10} +0.767453i q^{11} +(-3.47651 + 6.02149i) q^{12} +(2.60377 + 2.49407i) q^{13} +(0.520882 - 0.902194i) q^{14} +(0.591243 + 0.341354i) q^{15} +(1.75870 - 3.04617i) q^{16} -1.71042 q^{17} +(12.1482 - 7.01378i) q^{18} -6.42155i q^{19} +(0.418183 + 0.241438i) q^{20} +(-1.37738 + 0.795229i) q^{21} +(0.788053 - 1.36495i) q^{22} +(-3.83089 + 6.63529i) q^{23} +(1.21351 - 0.700620i) q^{24} +(-2.47629 + 4.28907i) q^{25} +(-2.06990 - 7.10947i) q^{26} -12.0098 q^{27} +(-0.974211 + 0.562461i) q^{28} +(-0.564228 + 0.977272i) q^{29} +(-0.701034 - 1.21423i) q^{30} +(5.49748 - 0.881879i) q^{31} +(-7.02994 + 4.05874i) q^{32} +(-2.08386 + 1.20312i) q^{33} +(3.04205 + 1.75633i) q^{34} +(0.0552274 + 0.0956567i) q^{35} -15.1473 q^{36} +(-3.65242 + 2.10873i) q^{37} +(-6.59392 + 11.4210i) q^{38} +(-2.69027 + 10.9799i) q^{39} +(-0.0486570 - 0.0842764i) q^{40} -0.999173i q^{41} +3.26630 q^{42} +0.336841 q^{43} +(-1.47390 + 0.850958i) q^{44} +1.48730i q^{45} +(13.6268 - 7.86743i) q^{46} -5.20790i q^{47} +11.0283 q^{48} +6.74268 q^{49} +(8.80839 - 5.08552i) q^{50} +(-2.68138 - 4.64429i) q^{51} +(-1.90281 + 7.76602i) q^{52} +(-0.955041 - 1.65418i) q^{53} +(21.3599 + 12.3321i) q^{54} +(0.0835547 + 0.144721i) q^{55} +0.226705 q^{56} +(17.4364 - 10.0669i) q^{57} +(2.00701 - 1.15875i) q^{58} +8.54639i q^{59} +1.51399i q^{60} +(2.36475 + 4.09587i) q^{61} +(-10.6831 - 4.07658i) q^{62} +(-3.00065 - 1.73242i) q^{63} +9.63592 q^{64} +(0.762537 + 0.186835i) q^{65} +4.94165 q^{66} +11.7202i q^{67} +(-1.89653 - 3.28488i) q^{68} -24.0224 q^{69} -0.226839i q^{70} +(2.56006 + 1.47805i) q^{71} +(2.64366 + 1.52632i) q^{72} +(6.24102 - 3.60326i) q^{73} +8.66132 q^{74} -15.5281 q^{75} +(12.3327 - 7.12027i) q^{76} -0.389303 q^{77} +(16.0594 - 16.7657i) q^{78} +(1.60640 - 2.78236i) q^{79} -0.765900i q^{80} +(-8.58179 - 14.8641i) q^{81} +(-1.02599 + 1.77707i) q^{82} +(5.30623 - 3.06355i) q^{83} +(-3.05449 - 1.76351i) q^{84} +(-0.322539 + 0.186218i) q^{85} +(-0.599087 - 0.345883i) q^{86} -3.53811 q^{87} +0.342987 q^{88} +(-10.8125 - 6.24258i) q^{89} +(1.52722 - 2.64522i) q^{90} +(-1.26516 + 1.32080i) q^{91} -16.9909 q^{92} +(11.0128 + 13.5448i) q^{93} +(-5.34769 + 9.26246i) q^{94} +(-0.699132 - 1.21093i) q^{95} +(-22.0414 - 12.7256i) q^{96} +(11.4488 - 6.60997i) q^{97} +(-11.9921 - 6.92367i) q^{98} +(-4.53974 - 2.62102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9} + 2 q^{10} + 13 q^{12} + q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} - 12 q^{17} - 3 q^{20} - 9 q^{21} + 4 q^{22} + 10 q^{23} + 18 q^{24} + 19 q^{25} + 6 q^{26}+ \cdots + 93 q^{99}+O(q^{100}) $ 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9 + 2 * q^10 + 13 * q^12 + q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 - 12 * q^17 - 3 * q^20 - 9 * q^21 + 4 * q^22 + 10 * q^23 + 18 * q^24 + 19 * q^25 + 6 * q^26 + 34 * q^27 - 33 * q^28 - 18 * q^29 - 31 * q^30 - 2 * q^31 + 36 * q^32 - 12 * q^33 + 9 * q^34 - 12 * q^35 - 16 * q^36 - 18 * q^37 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 98 * q^42 - 38 * q^43 + 42 * q^44 - 6 * q^46 + 54 * q^48 - 18 * q^49 - 51 * q^50 - 7 * q^51 + 41 * q^52 - 22 * q^53 + 18 * q^54 - 15 * q^55 - 50 * q^56 + 15 * q^57 - 12 * q^58 - 13 * q^61 - 23 * q^62 - 6 * q^63 - 38 * q^64 - 12 * q^65 - 52 * q^66 - 44 * q^68 + 32 * q^69 + 27 * q^71 - 15 * q^72 - 9 * q^73 + 38 * q^74 - 50 * q^75 + 126 * q^76 + 34 * q^77 + 14 * q^78 + 6 * q^79 - 11 * q^81 + 39 * q^82 - 54 * q^83 + 15 * q^84 - 33 * q^85 - 24 * q^86 + 28 * q^87 - 32 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 14 * q^93 - 43 * q^94 + 25 * q^95 + 36 * q^96 - 75 * q^97 + 93 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.77854	−	1.02684i	−1.25762	−	0.726087i	−0.285008	−	0.958525i	$-0.591996\pi$
$2$	−1.77854	−	1.02684i	−1.25762	−	0.726087i	−0.972611	+	0.232438i	$0.925330\pi$
$3$	1.56768	+	2.71530i	0.905098	+	1.56768i	0.820785	+	0.571237i	$0.193536\pi$
$3$	1.56768	+	2.71530i	0.905098	+	1.56768i	0.0843136	+	0.996439i	$0.473130\pi$
$4$	1.10881	+	1.92051i	0.554404	+	0.960256i
$5$	0.188573	−	0.108873i	0.0843324	−	0.0486894i	−0.457241	−	0.889343i	$-0.651162\pi$
$5$	0.188573	−	0.108873i	0.0843324	−	0.0486894i	0.541573	+	0.840654i	$0.317829\pi$
$6$		−	6.43902i		−	2.62872i
$7$			0.507266i			0.191728i	0.995394	+	0.0958642i	$0.0305615\pi$
$7$			0.507266i			0.191728i	−0.995394	+	0.0958642i	$0.969439\pi$
$8$		−	0.446916i		−	0.158009i
$9$	−3.41522	+	5.91533i	−1.13841	+	1.97178i
$10$	−0.447180			−0.141411
$11$			0.767453i			0.231396i	0.993284	+	0.115698i	$0.0369104\pi$
$11$			0.767453i			0.231396i	−0.993284	+	0.115698i	$0.963090\pi$
$12$	−3.47651	+	6.02149i	−1.00358	+	1.73825i
$13$	2.60377	+	2.49407i	0.722155	+	0.691731i
$13$	2.60377	+	2.49407i	0.722155	+	0.691731i
$14$	0.520882	−	0.902194i	0.139212	−	0.241121i
$15$	0.591243	+	0.341354i	0.152658	+	0.0881373i
$16$	1.75870	−	3.04617i	0.439676	−	0.761541i
$17$	−1.71042			−0.414838			−0.207419	−	0.978252i	$-0.566506\pi$
$17$	−1.71042			−0.414838			−0.207419	+	0.978252i	$0.566506\pi$
$18$	12.1482	−	7.01378i	2.86336	−	1.65316i
$19$		−	6.42155i		−	1.47320i	−0.676326	−	0.736602i	$-0.736429\pi$
$19$		−	6.42155i		−	1.47320i	0.676326	−	0.736602i	$-0.263571\pi$
$20$	0.418183	+	0.241438i	0.0935085	+	0.0539872i
$21$	−1.37738	+	0.795229i	−0.300568	+	0.173533i
$22$	0.788053	−	1.36495i	0.168013	−	0.291008i
$23$	−3.83089	+	6.63529i	−0.798795	+	1.38355i	0.121605	+	0.992579i	$0.461196\pi$
$23$	−3.83089	+	6.63529i	−0.798795	+	1.38355i	−0.920401	+	0.390976i	$0.872138\pi$
$24$	1.21351	−	0.700620i	0.247707	−	0.143014i
$25$	−2.47629	+	4.28907i	−0.495259	+	0.857813i
$26$	−2.06990	−	7.10947i	−0.405940	−	1.39428i
$27$	−12.0098			−2.31128
$28$	−0.974211	+	0.562461i	−0.184108	+	0.106295i
$29$	−0.564228	+	0.977272i	−0.104775	+	0.181475i	−0.913646	−	0.406511i	$-0.866745\pi$
$29$	−0.564228	+	0.977272i	−0.104775	+	0.181475i	0.808872	+	0.587985i	$0.200079\pi$
$30$	−0.701034	−	1.21423i	−0.127991	−	0.221686i
$31$	5.49748	−	0.881879i	0.987377	−	0.158390i
$31$	5.49748	−	0.881879i	0.987377	−	0.158390i
$32$	−7.02994	+	4.05874i	−1.24273	+	0.717491i
$33$	−2.08386	+	1.20312i	−0.362754	+	0.209436i
$34$	3.04205	+	1.75633i	0.521708	+	0.301208i
$35$	0.0552274	+	0.0956567i	0.00933514	+	0.0161689i
$36$	−15.1473			−2.52455
$37$	−3.65242	+	2.10873i	−0.600455	+	0.346673i	−0.769221	−	0.638983i	$-0.779355\pi$
$37$	−3.65242	+	2.10873i	−0.600455	+	0.346673i	0.168766	+	0.985656i	$0.446022\pi$
$38$	−6.59392	+	11.4210i	−1.06967	+	1.85273i
$39$	−2.69027	+	10.9799i	−0.430788	+	1.75819i
$40$	−0.0486570	−	0.0842764i	−0.00769335	−	0.0133253i
$41$		−	0.999173i		−	0.156045i	−0.996952	−	0.0780223i	$-0.975139\pi$
$41$		−	0.999173i		−	0.156045i	0.996952	−	0.0780223i	$-0.0248605\pi$
$42$	3.26630			0.504001
$43$	0.336841			0.0513678			0.0256839	−	0.999670i	$-0.491824\pi$
$43$	0.336841			0.0513678			0.0256839	+	0.999670i	$0.491824\pi$
$44$	−1.47390	+	0.850958i	−0.222199	+	0.128287i
$45$			1.48730i			0.221713i
$46$	13.6268	−	7.86743i	2.00916	−	1.15999i
$47$		−	5.20790i		−	0.759650i	−0.925058	−	0.379825i	$-0.875984\pi$
$47$		−	5.20790i		−	0.759650i	0.925058	−	0.379825i	$-0.124016\pi$
$48$	11.0283			1.59180
$49$	6.74268			0.963240
$50$	8.80839	−	5.08552i	1.24569	−	0.719202i
$51$	−2.68138	−	4.64429i	−0.375469	−	0.650331i
$52$	−1.90281	+	7.76602i	−0.263873	+	1.07695i
$53$	−0.955041	−	1.65418i	−0.131185	−	0.227219i	0.792949	−	0.609289i	$-0.208545\pi$
$53$	−0.955041	−	1.65418i	−0.131185	−	0.227219i	−0.924134	+	0.382069i	$0.875212\pi$
$54$	21.3599	+	12.3321i	2.90671	+	1.67819i
$55$	0.0835547	+	0.144721i	0.0112665	+	0.0195142i
$56$	0.226705			0.0302948
$57$	17.4364	−	10.0669i	2.30951	−	1.33340i
$58$	2.00701	−	1.15875i	0.263533	−	0.152151i
$59$			8.54639i			1.11265i	0.830966	+	0.556323i	$0.187788\pi$
$59$			8.54639i			1.11265i	−0.830966	+	0.556323i	$0.812212\pi$
$60$			1.51399i			0.195455i
$61$	2.36475	+	4.09587i	0.302775	+	0.524422i	0.976763	−	0.214320i	$-0.0687536\pi$
$61$	2.36475	+	4.09587i	0.302775	+	0.524422i	−0.673988	+	0.738742i	$0.735420\pi$
$62$	−10.6831	−	4.07658i	−1.35675	−	0.517727i
$63$	−3.00065	−	1.73242i	−0.378046	−	0.218265i
$64$	9.63592			1.20449
$65$	0.762537	+	0.186835i	0.0945811	+	0.0231741i
$66$	4.94165			0.608275
$67$			11.7202i			1.43186i	0.698174	+	0.715928i	$0.253996\pi$
$67$			11.7202i			1.43186i	−0.698174	+	0.715928i	$0.746004\pi$
$68$	−1.89653	−	3.28488i	−0.229988	−	0.398351i
$69$	−24.0224			−2.89195
$70$		−	0.226839i		−	0.0271125i
$71$	2.56006	+	1.47805i	0.303823	+	0.175412i	0.644159	−	0.764891i	$-0.277207\pi$
$71$	2.56006	+	1.47805i	0.303823	+	0.175412i	−0.340336	+	0.940304i	$0.610541\pi$
$72$	2.64366	+	1.52632i	0.311558	+	0.179878i
$73$	6.24102	−	3.60326i	0.730457	−	0.421729i	−0.0881326	−	0.996109i	$-0.528090\pi$
$73$	6.24102	−	3.60326i	0.730457	−	0.421729i	0.818589	+	0.574379i	$0.194757\pi$
$74$	8.66132			1.00686
$75$	−15.5281			−1.79303
$76$	12.3327	−	7.12027i	1.41465	−	0.816751i
$77$	−0.389303			−0.0443652
$78$	16.0594	−	16.7657i	1.81837	−	1.89834i
$79$	1.60640	−	2.78236i	0.180734	−	0.313040i	−0.761397	−	0.648286i	$-0.775486\pi$
$79$	1.60640	−	2.78236i	0.180734	−	0.313040i	0.942131	+	0.335246i	$0.108819\pi$
$80$		−	0.765900i		−	0.0856302i
$81$	−8.58179	−	14.8641i	−0.953533	−	1.65157i
$82$	−1.02599	+	1.77707i	−0.113302	+	0.196245i
$83$	5.30623	−	3.06355i	0.582435	−	0.336269i	−0.179666	−	0.983728i	$-0.557502\pi$
$83$	5.30623	−	3.06355i	0.582435	−	0.336269i	0.762100	+	0.647459i	$0.224168\pi$
$84$	−3.05449	−	1.76351i	−0.333273	−	0.192415i
$85$	−0.322539	+	0.186218i	−0.0349843	+	0.0201982i
$86$	−0.599087	−	0.345883i	−0.0646012	−	0.0372975i
$87$	−3.53811			−0.379325
$88$	0.342987			0.0365626
$89$	−10.8125	−	6.24258i	−1.14612	−	0.661712i	−0.198180	−	0.980166i	$-0.563503\pi$
$89$	−10.8125	−	6.24258i	−1.14612	−	0.661712i	−0.947938	+	0.318454i	$0.896837\pi$
$90$	1.52722	−	2.64522i	0.160983	−	0.278831i
$91$	−1.26516	+	1.32080i	−0.132624	+	0.138458i
$92$	−16.9909			−1.77142
$93$	11.0128	+	13.5448i	1.14198	+	1.40453i
$94$	−5.34769	+	9.26246i	−0.551572	+	0.955350i
$95$	−0.699132	−	1.21093i	−0.0717294	−	0.124239i
$96$	−22.0414	−	12.7256i	−2.24959	−	1.29880i
$97$	11.4488	−	6.60997i	1.16245	−	0.671140i	0.210559	−	0.977581i	$-0.432471\pi$
$97$	11.4488	−	6.60997i	1.16245	−	0.671140i	0.951890	+	0.306441i	$0.0991382\pi$
$98$	−11.9921	−	6.92367i	−1.21139	−	0.699396i
$99$	−4.53974	−	2.62102i	−0.456261	−	0.263422i
$100$	−10.9829			−1.09829
$101$	6.00480	−	10.4006i	0.597500	−	1.03490i	−0.395689	−	0.918385i	$-0.629494\pi$
$101$	6.00480	−	10.4006i	0.597500	−	1.03490i	0.993189	−	0.116516i	$-0.0371725\pi$
$102$			11.0134i			1.09049i
$103$	−3.22765	−	5.59045i	−0.318029	−	0.550843i	0.662047	−	0.749462i	$-0.269688\pi$
$103$	−3.22765	−	5.59045i	−0.318029	−	0.550843i	−0.980077	+	0.198619i	$0.936354\pi$
$104$	1.11464	−	1.16367i	0.109300	−	0.114107i
$105$	−0.173157	+	0.299917i	−0.0168984	+	0.0292689i
$106$			3.92271i			0.381007i
$107$	6.52683	+	11.3048i	0.630973	+	1.09288i	0.987353	+	0.158536i	$0.0506773\pi$
$107$	6.52683	+	11.3048i	0.630973	+	1.09288i	−0.356381	+	0.934341i	$0.615989\pi$
$108$	−13.3165	−	23.0649i	−1.28139	−	2.21942i
$109$		−	11.1150i		−	1.06462i	−0.846549	−	0.532310i	$-0.821324\pi$
$109$		−	11.1150i		−	1.06462i	0.846549	−	0.532310i	$-0.178676\pi$
$110$		−	0.343190i		−	0.0327219i
$111$	−11.4516	−	6.61161i	−1.08694	−	0.627546i
$112$	1.54522	+	0.892131i	0.146009	+	0.0842984i
$113$	10.1117	−	17.5140i	0.951229	−	1.64758i	0.208458	−	0.978031i	$-0.433156\pi$
$113$	10.1117	−	17.5140i	0.951229	−	1.64758i	0.742771	−	0.669545i	$-0.233511\pi$
$114$	−41.3485			−3.87264
$115$			1.66832i			0.155571i
$116$	−2.50248			−0.232350
$117$	−23.6457	+	6.88436i	−2.18605	+	0.636459i
$118$	8.77579	−	15.2001i	0.807877	−	1.39928i
$119$		−	0.867638i		−	0.0795362i
$120$	0.152557	−	0.264236i	0.0139265	−	0.0241214i
$121$	10.4110			0.946456
$122$		−	9.71289i		−	0.879364i
$123$	2.71305	−	1.56638i	0.244627	−	0.141236i
$124$	7.78931	+	9.58015i	0.699501	+	0.860322i
$125$			2.16713i			0.193834i
$126$	3.55785	+	6.16238i	0.316959	+	0.548988i
$127$	8.46593	+	14.6634i	0.751229	+	1.30117i	0.947227	+	0.320563i	$0.103872\pi$
$127$	8.46593	+	14.6634i	0.751229	+	1.30117i	−0.195998	+	0.980604i	$0.562795\pi$
$128$	−3.07800	−	1.77708i	−0.272059	−	0.157073i
$129$	0.528058	+	0.914624i	0.0464929	+	0.0805281i
$130$	−1.16435	−	1.11530i	−0.102121	−	0.0978182i
$131$	2.64528	−	4.58176i	0.231119	−	0.400311i	−0.727018	−	0.686618i	$-0.759095\pi$
$131$	2.64528	−	4.58176i	0.231119	−	0.400311i	0.958138	+	0.286307i	$0.0924279\pi$
$132$	−4.62121	−	2.66805i	−0.402224	−	0.232224i
$133$	3.25743			0.282455
$134$	12.0348	−	20.8449i	1.03965	−	1.80073i
$135$	−2.26472	+	1.30754i	−0.194916	+	0.112535i
$136$			0.764415i			0.0655480i
$137$	−8.43578	−	4.87040i	−0.720718	−	0.416107i	0.0942991	−	0.995544i	$-0.469939\pi$
$137$	−8.43578	−	4.87040i	−0.720718	−	0.416107i	−0.815017	+	0.579437i	$0.803272\pi$
$138$	42.7248	+	24.6672i	3.63698	+	2.09981i
$139$	−6.60038	−	11.4322i	−0.559837	−	0.969665i	−0.997510	−	0.0705312i	$-0.977531\pi$
$139$	−6.60038	−	11.4322i	−0.559837	−	0.969665i	0.437673	−	0.899134i	$-0.355803\pi$
$140$	−0.122473	+	0.212130i	−0.0103509	+	0.0179282i
$141$	14.1410	−	8.16430i	1.19088	−	0.687558i
$142$	−3.03545	−	5.25756i	−0.254729	−	0.441204i
$143$	−1.91408	+	1.99827i	−0.160064	+	0.167104i
$144$	12.0127	+	20.8066i	1.00106	+	1.73389i
$145$			0.245716i			0.0204056i
$146$	−14.7999			−1.22485
$147$	10.5703	+	18.3084i	0.871827	+	1.51005i
$148$	−8.09968	−	4.67635i	−0.665790	−	0.384394i
$149$		−	15.1692i		−	1.24271i	−0.783530	−	0.621355i	$-0.786583\pi$
$149$		−	15.1692i		−	1.24271i	0.783530	−	0.621355i	$-0.213417\pi$
$150$	27.6174	+	15.9449i	2.25495	+	1.30190i
$151$		−	2.60316i		−	0.211842i	−0.994375	−	0.105921i	$-0.966221\pi$
$151$		−	2.60316i		−	0.211842i	0.994375	−	0.105921i	$-0.0337791\pi$
$152$	−2.86990			−0.232779
$153$	5.84146	−	10.1177i	0.472254	−	0.817968i
$154$	0.692391	+	0.399752i	0.0557945	+	0.0322130i
$155$	0.940664	−	0.764824i	0.0755560	−	0.0614322i
$156$	−24.0700	+	7.00790i	−1.92714	+	0.561081i
$157$	10.2482			0.817896			0.408948	−	0.912558i	$-0.365896\pi$
$157$	10.2482			0.817896			0.408948	+	0.912558i	$0.365896\pi$
$158$	−5.71409	+	3.29903i	−0.454589	+	0.262457i
$159$	2.99439	−	5.18644i	0.237471	−	0.411311i
$160$	−0.883772	+	1.53074i	−0.0698683	+	0.121015i
$161$	−3.36586	−	1.94328i	−0.265267	−	0.153152i
$162$			35.2486i			2.76939i
$163$	3.08507	−	1.78117i	0.241642	−	0.139512i	−0.374289	−	0.927312i	$-0.622113\pi$
$163$	3.08507	−	1.78117i	0.241642	−	0.139512i	0.615931	+	0.787800i	$0.288780\pi$
$164$	1.91892	−	1.10789i	0.149843	−	0.0865118i
$165$	−0.261973	+	0.453751i	−0.0203946	+	0.0353245i
$166$	−12.5831			−0.976641
$167$	−5.25705	+	3.03516i	−0.406803	+	0.234868i	−0.689415	−	0.724366i	$-0.742132\pi$
$167$	−5.25705	+	3.03516i	−0.406803	+	0.234868i	0.282612	+	0.959234i	$0.408799\pi$
$168$	0.355401	+	0.615572i	0.0274198	+	0.0474924i
$169$	0.559221	+	12.9880i	0.0430170	+	0.999074i
$170$	0.764866			0.0586625
$171$	37.9856	+	21.9310i	2.90483	+	1.67711i
$172$	0.373493	+	0.646908i	0.0284785	+	0.0493263i
$173$	−3.37314	+	5.84245i	−0.256455	+	0.444193i	−0.965290	−	0.261182i	$-0.915888\pi$
$173$	−3.37314	+	5.84245i	−0.256455	+	0.444193i	0.708835	+	0.705375i	$0.249221\pi$
$174$	6.29268	+	3.63308i	0.477047	+	0.275423i
$175$	−2.17570	−	1.25614i	−0.164467	−	0.0949552i
$176$	2.33779	+	1.34972i	0.176217	+	0.101739i
$177$	−23.2060	+	13.3980i	−1.74427	+	1.00705i
$178$	12.8203	+	22.2054i	0.960921	+	1.66436i
$179$	10.0247	+	17.3633i	0.749282	+	1.29779i	0.948167	+	0.317771i	$0.102934\pi$
$179$	10.0247	+	17.3633i	0.749282	+	1.29779i	−0.198886	+	0.980023i	$0.563732\pi$
$180$	−2.85637	+	1.64913i	−0.212901	+	0.122919i
$181$	−9.04888	−	15.6731i	−0.672598	−	1.16497i	−0.977165	−	0.212483i	$-0.931845\pi$
$181$	−9.04888	−	15.6731i	−0.672598	−	1.16497i	0.304567	−	0.952491i	$-0.401488\pi$
$182$	3.60639	−	1.04999i	0.267323	−	0.0778303i
$183$	−7.41432	+	12.8420i	−0.548083	+	0.949307i
$184$	2.96542	+	1.71209i	0.218614	+	0.126217i
$185$	−0.459166	+	0.795299i	−0.0337586	+	0.0584715i
$186$	−5.67844	−	35.3984i	−0.416363	−	2.59554i
$187$		−	1.31267i		−	0.0959917i
$188$	10.0018	−	5.77456i	0.729458	−	0.421153i
$189$		−	6.09215i		−	0.443139i
$190$			2.87159i			0.208327i
$191$	−7.03354	+	12.1825i	−0.508929	+	0.881491i	0.491017	+	0.871150i	$0.336625\pi$
$191$	−7.03354	+	12.1825i	−0.508929	+	0.881491i	−0.999947	+	0.0103415i	$0.996708\pi$
$192$	15.1060	+	26.1644i	1.09018	+	1.88825i
$193$	19.7988	−	11.4308i	1.42515	−	0.822808i	0.428413	−	0.903583i	$-0.359073\pi$
$193$	19.7988	−	11.4308i	1.42515	−	0.822808i	0.996732	+	0.0807749i	$0.0257395\pi$
$194$	−27.1496			−1.94922
$195$	0.688098	+	2.36341i	0.0492757	+	0.169247i
$196$	7.47634	+	12.9494i	0.534024	+	0.924957i
$197$			5.66210i			0.403408i	0.979447	+	0.201704i	$0.0646479\pi$
$197$			5.66210i			0.403408i	−0.979447	+	0.201704i	$0.935352\pi$
$198$	5.38275	+	9.32319i	0.382535	+	0.662570i
$199$	6.13552	−	10.6270i	0.434935	−	0.753330i	−0.562355	−	0.826896i	$-0.690105\pi$
$199$	6.13552	−	10.6270i	0.434935	−	0.753330i	0.997290	+	0.0735659i	$0.0234379\pi$
$200$	1.91685	+	1.10670i	0.135542	+	0.0782552i
$201$	−31.8239	+	18.3735i	−2.24469	+	1.29597i
$202$	−21.3596	+	12.3320i	−1.50286	+	0.867674i
$203$	−0.495737	−	0.286214i	−0.0347939	−	0.0200883i
$204$	5.94628	−	10.2993i	0.416323	−	0.721093i
$205$	−0.108783	−	0.188417i	−0.00759771	−	0.0131596i
$206$			13.2571i			0.923668i
$207$	−26.1667	−	45.3220i	−1.81871	−	3.15009i
$208$	12.1766	−	3.54518i	0.844296	−	0.245814i
$209$	4.92824			0.340893
$210$	0.615936	−	0.355611i	0.0425036	−	0.0245395i
$211$	6.60804	+	11.4455i	0.454916	+	0.787938i	0.998683	−	0.0512981i	$-0.0163359\pi$
$211$	6.60804	+	11.4455i	0.454916	+	0.787938i	−0.543767	+	0.839236i	$0.683003\pi$
$212$	2.11792	−	3.66834i	0.145459	−	0.251943i
$213$			9.26843i			0.635062i
$214$		−	26.8081i		−	1.83256i
$215$	0.0635192	−	0.0366728i	0.00433197	−	0.00250107i
$216$			5.36737i			0.365203i
$217$	0.447347	+	2.78868i	0.0303679	+	0.189308i
$218$	−11.4133	+	19.7684i	−0.773007	+	1.33889i
$219$	19.5678	+	11.2975i	1.32227	+	0.763413i
$220$	−0.185292	+	0.320936i	−0.0124924	+	0.0216375i
$221$	−4.45354	−	4.26591i	−0.299577	−	0.286956i
$222$	13.5782	+	23.5181i	0.911306	+	1.57843i
$223$	−19.2363	+	11.1061i	−1.28816	+	0.743717i	−0.978325	−	0.207074i	$-0.933606\pi$
$223$	−19.2363	+	11.1061i	−1.28816	+	0.743717i	−0.309831	+	0.950792i	$0.600272\pi$
$224$	−2.05886	−	3.56605i	−0.137563	−	0.238267i
$225$	−16.9142	−	29.2962i	−1.12761	−	1.95308i
$226$	−35.9682	+	20.7662i	−2.39257	+	1.38135i
$227$	15.4736	+	8.93369i	1.02702	+	0.592950i	0.916129	−	0.400883i	$-0.131296\pi$
$227$	15.4736	+	8.93369i	1.02702	+	0.592950i	0.110890	+	0.993833i	$0.464630\pi$
$228$	38.6673	+	22.3246i	2.56080	+	1.47848i
$229$	−20.8093	−	12.0143i	−1.37512	−	0.793926i	−0.383553	−	0.923519i	$-0.625299\pi$
$229$	−20.8093	−	12.0143i	−1.37512	−	0.793926i	−0.991567	+	0.129593i	$0.958633\pi$
$230$	1.71310	−	2.96717i	0.112958	−	0.195650i
$231$	−0.610301	−	1.05707i	−0.0401548	−	0.0695502i
$232$	0.436759	+	0.252163i	0.0286746	+	0.0165553i
$233$	23.4169			1.53409			0.767045	−	0.641593i	$-0.221726\pi$
$233$	23.4169			1.53409			0.767045	+	0.641593i	$0.221726\pi$
$234$	49.1240	+	12.0363i	3.21134	+	0.786836i
$235$	−0.566998	−	0.982069i	−0.0369868	−	0.0640631i
$236$	−16.4135	+	9.47631i	−1.06842	+	0.616855i
$237$	10.0733			0.654328
$238$	−0.890927	+	1.54313i	−0.0577502	+	0.100026i
$239$	0.814218	−	0.470089i	0.0526674	−	0.0304075i	−0.473435	−	0.880829i	$-0.656986\pi$
$239$	0.814218	−	0.470089i	0.0526674	−	0.0304075i	0.526102	+	0.850421i	$0.323653\pi$
$240$	2.07964	−	1.20068i	0.134240	−	0.0775037i
$241$			28.4059i			1.82978i	0.403699	+	0.914892i	$0.367724\pi$
$241$			28.4059i			1.82978i	−0.403699	+	0.914892i	$0.632276\pi$
$242$	−18.5164	−	10.6905i	−1.19028	−	0.687209i
$243$	8.89228	−	15.4019i	0.570440	−	0.988031i
$244$	−5.24411	+	9.08306i	−0.335720	+	0.581483i
$245$	1.27149	−	0.734094i	0.0812324	−	0.0468995i
$246$	−6.43370			−0.410197
$247$	16.0158	−	16.7202i	1.01906	−	1.06388i
$248$	−0.394126	−	2.45691i	−0.0250270	−	0.156014i
$249$	16.6369	+	9.60532i	1.05432	+	0.608713i
$250$	2.22530	−	3.85433i	0.140740	−	0.243769i
$251$	−4.38228			−0.276607			−0.138304	−	0.990390i	$-0.544165\pi$
$251$	−4.38228			−0.276607			−0.138304	+	0.990390i	$0.544165\pi$
$252$		−	7.68371i		−	0.484028i
$253$	−5.09228	−	2.94003i	−0.320149	−	0.184838i
$254$		−	34.7727i		−	2.18183i
$255$	−1.01127	−	0.583859i	−0.0633284	−	0.0365627i
$256$	−5.98635	−	10.3687i	−0.374147	−	0.648041i
$257$	31.1747			1.94462			0.972311	−	0.233691i	$-0.0750805\pi$
$257$	31.1747			1.94462			0.972311	+	0.233691i	$0.0750805\pi$
$258$		−	2.16893i		−	0.135032i
$259$	−1.06969	−	1.85275i	−0.0664671	−	0.115124i
$260$	0.486688	+	1.67163i	0.0301831	+	0.103670i
$261$	−3.85393	−	6.67520i	−0.238552	−	0.413184i
$262$	−9.40949	+	5.43257i	−0.581320	+	0.335626i
$263$	7.94366	−	13.7588i	0.489827	−	0.848406i	−0.510104	−	0.860113i	$-0.670393\pi$
$263$	7.94366	−	13.7588i	0.489827	−	0.848406i	0.999931	+	0.0117068i	$0.00372648\pi$
$264$	0.537693	+	0.931312i	0.0330927	+	0.0573183i
$265$	−0.360190	−	0.207956i	−0.0221263	−	0.0127746i
$266$	−5.79348	−	3.34487i	−0.355221	−	0.205087i
$267$		−	39.1454i		−	2.39566i
$268$	−22.5089	+	12.9955i	−1.37495	+	0.793827i
$269$	3.95948	−	6.85803i	0.241414	−	0.418141i	−0.719703	−	0.694282i	$-0.755722\pi$
$269$	3.95948	−	6.85803i	0.241414	−	0.418141i	0.961117	+	0.276140i	$0.0890555\pi$
$270$	5.37054			0.326840
$271$	−10.5337	−	6.08161i	−0.639874	−	0.369432i	0.144692	−	0.989477i	$-0.453781\pi$
$271$	−10.5337	−	6.08161i	−0.639874	−	0.369432i	−0.784566	+	0.620045i	$0.787114\pi$
$272$	−3.00812	+	5.21022i	−0.182394	+	0.315916i
$273$	−5.56973	−	1.36468i	−0.337095	−	0.0825944i
$274$	10.0023	+	17.3244i	0.604259	+	1.04661i
$275$	−3.29166	−	1.90044i	−0.198494	−	0.114601i
$276$	−26.6362	−	46.1353i	−1.60331	−	2.77702i
$277$	7.16713	+	12.4138i	0.430631	+	0.745875i	0.996928	−	0.0783266i	$-0.0249577\pi$
$277$	7.16713	+	12.4138i	0.430631	+	0.745875i	−0.566297	+	0.824201i	$0.691624\pi$
$278$			27.1102i			1.62596i
$279$	−13.5585	+	35.5312i	−0.811726	+	2.12720i
$280$	0.0427505	−	0.0246820i	0.00255483	−	0.00147503i
$281$			13.7650i			0.821149i	0.911827	+	0.410574i	$0.134672\pi$
$281$			13.7650i			0.821149i	−0.911827	+	0.410574i	$0.865328\pi$
$282$	−33.5338			−1.99691
$283$	−3.91821	+	6.78654i	−0.232914	+	0.403418i	−0.958664	−	0.284540i	$-0.908159\pi$
$283$	−3.91821	+	6.78654i	−0.232914	+	0.403418i	0.725751	+	0.687958i	$0.241493\pi$
$284$			6.55551i			0.388998i
$285$	2.19202	−	3.79670i	0.129844	−	0.224897i
$286$	5.45618	−	1.58855i	0.322631	−	0.0939328i
$287$	0.506846			0.0299182
$288$		−	55.4459i		−	3.26718i
$289$	−14.0745			−0.827910
$290$	0.252312	−	0.437017i	0.0148163	−	0.0256625i
$291$	35.8960	+	20.7246i	2.10426	+	1.21490i
$292$	13.8402	+	7.99064i	0.809936	+	0.467617i
$293$		−	13.4895i		−	0.788067i	−0.919096	−	0.394034i	$-0.871079\pi$
$293$		−	13.4895i		−	0.788067i	0.919096	−	0.394034i	$-0.128921\pi$
$294$		−	43.4163i		−	2.53209i
$295$	0.930469	+	1.61162i	0.0541740	+	0.0938321i
$296$	0.942425	+	1.63233i	0.0547774	+	0.0948772i
$297$		−	9.21694i		−	0.534821i
$298$	−15.5764	+	26.9791i	−0.902315	+	1.56285i
$299$	−26.5236	+	7.72226i	−1.53390	+	0.446590i
$300$	−17.2177	−	29.8219i	−0.994064	−	1.72177i
$301$			0.170868i			0.00984868i
$302$	−2.67303	+	4.62983i	−0.153816	+	0.266417i
$303$	37.6543			2.16319
$304$	−19.5611	−	11.2936i	−1.12191	−	0.647733i
$305$	0.891856	+	0.514913i	0.0510675	+	0.0294838i
$306$	−20.7786	+	11.9965i	−1.18783	+	0.685795i
$307$	−16.8023	−	9.70084i	−0.958961	−	0.553656i	−0.0631076	−	0.998007i	$-0.520101\pi$
$307$	−16.8023	−	9.70084i	−0.958961	−	0.553656i	−0.895853	+	0.444351i	$0.853434\pi$
$308$	−0.431662	−	0.747661i	−0.0245962	−	0.0426019i
$309$	10.1198	−	17.5280i	0.575696	−	0.997135i
$310$	−2.45836	+	0.394359i	−0.139626	+	0.0223981i
$311$	−4.68521			−0.265674			−0.132837	−	0.991138i	$-0.542409\pi$
$311$	−4.68521			−0.265674			−0.132837	+	0.991138i	$0.542409\pi$
$312$	4.90710	+	1.20233i	0.277810	+	0.0680684i
$313$	−8.13460	+	14.0895i	−0.459795	+	0.796388i	−0.998950	−	0.0458187i	$-0.985410\pi$
$313$	−8.13460	+	14.0895i	−0.459795	+	0.796388i	0.539155	+	0.842207i	$0.318744\pi$
$314$	−18.2269	−	10.5233i	−1.02860	−	0.593864i
$315$	−0.754455			−0.0425087
$316$	7.12475			0.400799
$317$	−14.3768	−	8.30045i	−0.807482	−	0.466200i	0.0385987	−	0.999255i	$-0.487711\pi$
$317$	−14.3768	−	8.30045i	−0.807482	−	0.466200i	−0.846081	+	0.533055i	$0.821044\pi$
$318$	−10.6513	+	6.14953i	−0.597296	+	0.344849i
$319$	−0.750010	−	0.433019i	−0.0419925	−	0.0242444i
$320$	1.81707	−	1.04909i	0.101578	−	0.0586458i
$321$	−20.4639	+	35.4446i	−1.14218	+	1.97832i
$322$	3.99088	+	6.91241i	0.222403	+	0.385213i
$323$			10.9835i			0.611141i
$324$	19.0311	−	32.9629i	1.05728	−	1.83127i
$325$	−17.1449	+	4.99168i	−0.951030	+	0.276889i
$326$	−7.31591			−0.405191
$327$	30.1804	−	17.4247i	1.66898	−	0.963586i
$328$	−0.446547			−0.0246564
$329$	2.64179			0.145646
$330$	0.931862	−	0.538011i	0.0512973	−	0.0296165i
$331$	6.54115	+	3.77654i	0.359534	+	0.207577i	0.668876	−	0.743374i	$-0.266776\pi$
$331$	6.54115	+	3.77654i	0.359534	+	0.207577i	−0.309342	+	0.950951i	$0.600109\pi$
$332$	11.7672	+	6.79379i	0.645808	+	0.372858i
$333$		−	28.8071i		−	1.57862i
$334$	12.4665			0.682138
$335$	1.27601	+	2.21012i	0.0697161	+	0.120752i
$336$			5.59429i			0.305194i
$337$	−22.3844			−1.21936			−0.609678	−	0.792649i	$-0.708701\pi$
$337$	−22.3844			−1.21936			−0.609678	+	0.792649i	$0.708701\pi$
$338$	12.3420	−	23.6739i	0.671316	−	1.28769i
$339$	63.4075			3.44382
$340$	−0.715268	−	0.412960i	−0.0387909	−	0.0223959i
$341$	0.676800	+	4.21906i	0.0366508	+	0.228475i
$342$	−45.0394	−	78.0105i	−2.43545	−	4.21832i
$343$			6.97119i			0.376409i
$344$		−	0.150540i		−	0.00811657i
$345$	−4.52997	+	2.61538i	−0.243886	+	0.140807i
$346$	11.9985	−	6.92736i	0.645045	−	0.372417i
$347$	15.7507			0.845542			0.422771	−	0.906236i	$-0.361057\pi$
$347$	15.7507			0.845542			0.422771	+	0.906236i	$0.361057\pi$
$348$	−3.92309	−	6.79498i	−0.210299	−	0.364249i
$349$	−7.95559	−	4.59316i	−0.425853	−	0.245866i	0.271725	−	0.962375i	$-0.412406\pi$
$349$	−7.95559	−	4.59316i	−0.425853	−	0.245866i	−0.697578	+	0.716508i	$0.745739\pi$
$350$	2.57971	+	4.46819i	0.137891	+	0.238835i
$351$	−31.2707	−	29.9532i	−1.66911	−	1.59879i
$352$	−3.11489	−	5.39515i	−0.166024	−	0.287562i
$353$	−18.6477	+	10.7663i	−0.992517	+	0.573030i	−0.906026	−	0.423223i	$-0.860899\pi$
$353$	−18.6477	+	10.7663i	−0.992517	+	0.573030i	−0.0864914	+	0.996253i	$0.527565\pi$
$354$	55.0304			2.92483
$355$	0.643678			0.0341629
$356$		−	27.6873i		−	1.46742i
$357$	2.35589	−	1.36018i	0.124687	−	0.0719881i
$358$		−	41.1752i		−	2.17617i
$359$	12.8323	−	7.40874i	0.677263	−	0.391018i	−0.121560	−	0.992584i	$-0.538790\pi$
$359$	12.8323	−	7.40874i	0.677263	−	0.391018i	0.798823	+	0.601566i	$0.205456\pi$
$360$	0.664697			0.0350326
$361$	−22.2363			−1.17033
$362$			37.1671i			1.95346i
$363$	16.3211	+	28.2690i	0.856636	+	1.48374i
$364$	−3.93944	−	0.965233i	−0.206483	−	0.0505919i
$365$	0.784593	−	1.35895i	0.0410675	−	0.0711309i
$366$	26.3734	−	15.2267i	1.37856	−	0.795911i
$367$	−33.5236			−1.74992			−0.874960	−	0.484195i	$-0.839113\pi$
$367$	−33.5236			−1.74992			−0.874960	+	0.484195i	$0.839113\pi$
$368$	13.4748	+	23.3390i	0.702423	+	1.21663i
$369$	5.91044	+	3.41239i	0.307685	+	0.177642i
$370$	1.63329	−	0.942982i	0.0849108	−	0.0490233i
$371$	0.839109	−	0.484460i	0.0435644	−	0.0251519i
$372$	−13.8018	+	36.1689i	−0.715590	+	1.87527i
$373$	2.82490	+	4.89287i	0.146268	+	0.253343i	0.929845	−	0.367951i	$-0.119941\pi$
$373$	2.82490	+	4.89287i	0.146268	+	0.253343i	−0.783577	+	0.621294i	$0.786607\pi$
$374$	−1.34790	+	2.33463i	−0.0696983	+	0.120721i
$375$	−5.88440	+	3.39736i	−0.303869	+	0.175439i
$376$	−2.32749			−0.120031
$377$	−3.90650	+	1.13736i	−0.201195	+	0.0585773i
$378$	−6.25568	+	10.8351i	−0.321757	+	0.557300i
$379$	−7.43294	+	4.29141i	−0.381805	+	0.220435i	−0.678603	−	0.734505i	$-0.737414\pi$
$379$	−7.43294	+	4.29141i	−0.381805	+	0.220435i	0.296799	+	0.954940i	$0.404081\pi$
$380$	1.55041	−	2.68538i	0.0795342	−	0.137757i
$381$	−26.5437	+	45.9750i	−1.35987	+	2.35537i
$382$	25.0189	−	14.4447i	1.28008	−	0.739054i
$383$	−8.69524	−	5.02020i	−0.444306	−	0.256520i	0.261116	−	0.965307i	$-0.415909\pi$
$383$	−8.69524	−	5.02020i	−0.444306	−	0.256520i	−0.705422	+	0.708787i	$0.749243\pi$
$384$		−	11.1436i		−	0.568668i
$385$	−0.0734120	+	0.0423844i	−0.00374142	+	0.00216011i
$386$	−46.9506			−2.38972
$387$	−1.15039	+	1.99253i	−0.0584775	+	0.101286i
$388$	25.3890	+	14.6584i	1.28893	+	0.744166i
$389$	−17.9280	+	31.0522i	−0.908987	+	1.57441i	−0.0935125	+	0.995618i	$0.529809\pi$
$389$	−17.9280	+	31.0522i	−0.908987	+	1.57441i	−0.815474	+	0.578793i	$0.803524\pi$
$390$	1.20304	−	4.90999i	0.0609181	−	0.248627i
$391$	6.55243	−	11.3491i	0.331370	−	0.573951i
$392$		−	3.01342i		−	0.152200i
$393$	16.5878			0.836743
$394$	5.81408	−	10.0703i	0.292909	−	0.507334i
$395$		−	0.699572i		−	0.0351993i
$396$		−	11.6248i		−	0.584170i
$397$		−	16.9077i		−	0.848573i	−0.905528	−	0.424287i	$-0.860525\pi$
$397$		−	16.9077i		−	0.848573i	0.905528	−	0.424287i	$-0.139475\pi$
$398$	−21.8246	+	12.6004i	−1.09397	+	0.631602i
$399$	5.10660	+	8.84490i	0.255650	+	0.442799i
$400$	8.71014	+	15.0864i	0.435507	+	0.754320i
$401$	13.7228	+	7.92289i	0.685286	+	0.395650i	0.801844	−	0.597534i	$-0.203853\pi$
$401$	13.7228	+	7.92289i	0.685286	+	0.395650i	−0.116557	+	0.993184i	$0.537186\pi$
$402$	75.4669			3.76395
$403$	16.5136	+	11.4149i	0.822603	+	0.568617i
$404$	26.6327			1.32503
$405$	−3.23659	−	1.86865i	−0.160827	−	0.0928538i
$406$	0.587792	+	1.01809i	0.0291716	+	0.0505268i
$407$	−1.61835	−	2.80306i	−0.0802186	−	0.138943i
$408$	−2.07561	+	1.19836i	−0.102758	+	0.0593274i
$409$		−	12.7545i		−	0.630670i	−0.948980	−	0.315335i	$-0.897883\pi$
$409$		−	12.7545i		−	0.630670i	0.948980	−	0.315335i	$-0.102117\pi$
$410$			0.446810i			0.0220664i
$411$		−	30.5409i		−	1.50647i
$412$	7.15768	−	12.3975i	0.352634	−	0.610780i
$413$	−4.33529			−0.213326
$414$			107.476i			5.28216i
$415$	0.667075	−	1.15541i	0.0327454	−	0.0567167i
$416$	−28.4271	−	6.96516i	−1.39375	−	0.341495i
$417$	20.6945	−	35.8439i	1.01341	−	1.75529i
$418$	−8.76508	−	5.06052i	−0.428714	−	0.247518i
$419$	2.16950	−	3.75769i	0.105987	−	0.183575i	−0.808154	−	0.588971i	$-0.799533\pi$
$419$	2.16950	−	3.75769i	0.105987	−	0.183575i	0.914141	+	0.405396i	$0.132866\pi$
$420$	−0.767994			−0.0374743
$421$	−13.3261	+	7.69382i	−0.649473	+	0.374974i	−0.788254	−	0.615349i	$-0.789015\pi$
$421$	−13.3261	+	7.69382i	−0.649473	+	0.374974i	0.138781	+	0.990323i	$0.455682\pi$
$422$		−	27.1416i		−	1.32123i
$423$	30.8064	+	17.7861i	1.49786	+	0.864790i
$424$	−0.739280	+	0.426824i	−0.0359026	+	0.0207284i
$425$	4.23550	−	7.33610i	0.205452	−	0.355853i
$426$	9.51721	−	16.4843i	0.461110	−	0.798667i
$427$	−2.07769	+	1.19956i	−0.100547	+	0.0580506i
$428$	−14.4740	+	25.0697i	−0.699628	+	1.21179i
$429$	−8.42655	−	2.06466i	−0.406838	−	0.0996826i
$430$	−0.150629			−0.00726397
$431$	−17.2796	+	9.97640i	−0.832330	+	0.480546i	−0.854650	−	0.519205i	$-0.826228\pi$
$431$	−17.2796	+	9.97640i	−0.832330	+	0.480546i	0.0223195	+	0.999751i	$0.492895\pi$
$432$	−21.1217	+	36.5838i	−1.01622	+	1.76014i
$433$	3.09917	+	5.36792i	0.148937	+	0.257966i	0.930835	−	0.365441i	$-0.119082\pi$
$433$	3.09917	+	5.36792i	0.148937	+	0.257966i	−0.781898	+	0.623406i	$0.785748\pi$
$434$	2.06791	−	5.41915i	0.0992630	−	0.260127i
$435$	−0.667192	+	0.385204i	−0.0319894	+	0.0184691i
$436$	21.3464	−	12.3244i	1.02231	−	0.590230i
$437$	42.6089	+	24.6002i	2.03826	+	1.17679i
$438$	−23.2015	−	40.1861i	−1.10861	−	1.92017i
$439$	37.0039			1.76610			0.883050	−	0.469280i	$-0.155486\pi$
$439$	37.0039			1.76610			0.883050	+	0.469280i	$0.155486\pi$
$440$	0.0646782	−	0.0373420i	0.00308341	−	0.00178021i
$441$	−23.0277	+	39.8852i	−1.09656	+	1.89930i
$442$	3.54039	+	12.1602i	0.168399	+	0.578401i
$443$	−19.3219	−	33.4665i	−0.918010	−	1.59004i	−0.802434	−	0.596741i	$-0.796462\pi$
$443$	−19.3219	−	33.4665i	−0.918010	−	1.59004i	−0.115576	−	0.993299i	$-0.536871\pi$
$444$		−	29.3240i		−	1.39166i
$445$	−2.71859			−0.128873
$446$	45.6167			2.16001
$447$	41.1889	−	23.7804i	1.94817	−	1.12477i
$448$			4.88797i			0.230935i
$449$	−0.0179258	+	0.0103495i	−0.000845970	+	0.000488421i	−0.500423	−	0.865781i	$-0.666822\pi$
$449$	−0.0179258	+	0.0103495i	−0.000845970	+	0.000488421i	0.499577	+	0.866270i	$0.333489\pi$
$450$			69.4727i			3.27498i
$451$	0.766818			0.0361080
$452$	44.8478			2.10946
$453$	7.06835	−	4.08091i	0.332100	−	0.191738i
$454$	−18.3470	−	31.7779i	−0.861067	−	1.49141i
$455$	−0.0947751	+	0.386809i	−0.00444313	+	0.0181339i
$456$	−4.49907	−	7.79262i	−0.210688	−	0.364923i
$457$	−22.9426	−	13.2459i	−1.07321	−	0.619617i	−0.144152	−	0.989556i	$-0.546045\pi$
$457$	−22.9426	−	13.2459i	−1.07321	−	0.619617i	−0.929056	+	0.369939i	$0.879379\pi$
$458$	24.6735	+	42.7358i	1.15292	+	1.99691i
$459$	20.5418			0.958808
$460$	−3.20402	+	1.84984i	−0.149388	+	0.0862494i
$461$	29.8277	−	17.2210i	1.38921	−	0.802063i	0.395987	−	0.918256i	$-0.370403\pi$
$461$	29.8277	−	17.2210i	1.38921	−	0.802063i	0.993227	+	0.116193i	$0.0370692\pi$
$462$			2.50673i			0.116624i
$463$			17.6493i			0.820231i	0.912034	+	0.410115i	$0.134512\pi$
$463$			17.6493i			0.820231i	−0.912034	+	0.410115i	$0.865488\pi$
$464$	1.98462	+	3.43746i	0.0921337	+	0.159580i
$465$	3.55138	+	1.35518i	0.164691	+	0.0628452i
$466$	−41.6479	−	24.0454i	−1.92930	−	1.11388i
$467$	30.4395			1.40857			0.704286	−	0.709917i	$-0.251267\pi$
$467$	30.4395			1.40857			0.704286	+	0.709917i	$0.251267\pi$
$468$	−39.4401	−	37.7784i	−1.82312	−	1.74631i
$469$	−5.94528			−0.274527
$470$			2.32887i			0.107423i
$471$	16.0659	+	27.8269i	0.740276	+	1.28220i
$472$	3.81952			0.175808
$473$			0.258510i			0.0118863i
$474$	−17.9157	−	10.3436i	−0.822896	−	0.475099i
$475$	27.5425	+	15.9016i	1.26373	+	0.729618i
$476$	1.66631	−	0.962044i	0.0763751	−	0.0440952i
$477$	13.0467			0.597368
$478$	−1.93083			−0.0883141
$479$	−26.0606	+	15.0461i	−1.19074	+	0.687473i	−0.958474	−	0.285180i	$-0.907947\pi$
$479$	−26.0606	+	15.0461i	−1.19074	+	0.687473i	−0.232264	+	0.972653i	$0.574613\pi$
$480$	−5.54187			−0.252951
$481$	−14.7694	−	3.61877i	−0.673426	−	0.165002i
$482$	29.1683	−	50.5211i	1.32858	−	2.30117i
$483$		−	12.1857i		−	0.554470i
$484$	11.5438	+	19.9945i	0.524719	+	0.908840i
$485$	1.43929	−	2.49292i	0.0653548	−	0.113198i
$486$	−31.6306	+	18.2619i	−1.43479	+	0.828378i
$487$	−26.3894	−	15.2359i	−1.19582	−	0.690406i	−0.236198	−	0.971705i	$-0.575901\pi$
$487$	−26.3894	−	15.2359i	−1.19582	−	0.690406i	−0.959620	+	0.281299i	$0.909235\pi$
$488$	1.83051	−	1.05685i	0.0828633	−	0.0478411i
$489$	9.67280	+	5.58459i	0.437419	+	0.252544i
$490$	−3.01519			−0.136213
$491$	−23.0689			−1.04108			−0.520541	−	0.853836i	$-0.674270\pi$
$491$	−23.0689			−1.04108			−0.520541	+	0.853836i	$0.674270\pi$
$492$	6.01650	+	3.47363i	0.271245	+	0.156603i
$493$	0.965067	−	1.67155i	0.0434644	−	0.0752826i
$494$	−45.6538	+	13.2919i	−2.05406	+	0.598033i
$495$	−1.14143			−0.0513035
$496$	6.98209	−	18.2972i	0.313505	−	0.821568i
$497$	−0.749765	+	1.29863i	−0.0336316	+	0.0582516i
$498$	−19.7263	−	34.1670i	−0.883957	−	1.53106i
$499$	2.00746	+	1.15900i	0.0898660	+	0.0518842i	0.544260	−	0.838917i	$-0.316811\pi$
$499$	2.00746	+	1.15900i	0.0898660	+	0.0518842i	−0.454394	+	0.890801i	$0.650144\pi$
$500$	−4.16200	+	2.40293i	−0.186130	+	0.107462i
$501$	−16.4827	−	9.51630i	−0.736394	−	0.425157i
$502$	7.79407	+	4.49991i	0.347866	+	0.200841i
$503$	−16.4008			−0.731276			−0.365638	−	0.930757i	$-0.619149\pi$
$503$	−16.4008			−0.731276			−0.365638	+	0.930757i	$0.619149\pi$
$504$	−0.774249	+	1.34104i	−0.0344878	+	0.0597346i
$505$		−	2.61504i		−	0.116368i
$506$	6.03788	+	10.4579i	0.268417	+	0.464911i
$507$	−34.3895	+	21.8794i	−1.52729	+	0.971697i
$508$	−18.7742	+	32.5178i	−0.832970	+	1.44275i
$509$		−	37.4386i		−	1.65944i	−0.558183	−	0.829718i	$-0.688501\pi$
$509$		−	37.4386i		−	1.65944i	0.558183	−	0.829718i	$-0.311499\pi$
$510$	1.19906	+	2.07684i	0.0530954	+	0.0919639i
$511$	1.82781	+	3.16586i	0.0808575	+	0.140049i
$512$			31.6965i			1.40080i
$513$			77.1214i			3.40499i
$514$	−55.4454	−	32.0114i	−2.44559	−	1.41196i
$515$	−1.21729	−	0.702805i	−0.0536404	−	0.0309693i
$516$	−1.17103	+	2.02829i	−0.0515518	+	0.0892903i
$517$	3.99681			0.175780
$518$			4.39359i			0.193043i
$519$	−21.1520			−0.928468
$520$	0.0834997	−	0.340790i	0.00366171	−	0.0149446i
$521$	16.8897	−	29.2539i	0.739952	−	1.28163i	−0.212564	−	0.977147i	$-0.568181\pi$
$521$	16.8897	−	29.2539i	0.739952	−	1.28163i	0.952516	−	0.304488i	$-0.0984852\pi$
$522$			15.8295i			0.692838i
$523$	16.9057	−	29.2815i	0.739234	−	1.28039i	−0.213607	−	0.976920i	$-0.568521\pi$
$523$	16.9057	−	29.2815i	0.739234	−	1.28039i	0.952841	−	0.303471i	$-0.0981454\pi$
$524$	11.7324			0.512534
$525$		−	7.87688i		−	0.343775i
$526$	−28.2563	+	16.3138i	−1.23203	+	0.711314i
$527$	−9.40300	+	1.50838i	−0.409601	+	0.0657062i
$528$			8.46372i			0.368336i
$529$	−17.8514	−	30.9196i	−0.776148	−	1.34433i
$530$	0.427076	+	0.739717i	0.0185510	+	0.0321312i
$531$	−50.5548	−	29.1878i	−2.19389	−	1.26664i
$532$	3.61187	+	6.25594i	0.156594	+	0.271230i
$533$	2.49201	−	2.60161i	0.107941	−	0.112688i
$534$	−40.1961	+	69.6217i	−1.73946	+	3.01283i
$535$	2.46157	+	1.42119i	0.106423	+	0.0614433i
$536$	5.23797			0.226246
$537$	−31.4310	+	54.4401i	−1.35635	+	2.34926i
$538$	−14.0842	+	8.13153i	−0.607214	+	0.350575i
$539$			5.17469i			0.222890i
$540$	−5.02228	−	2.89962i	−0.216125	−	0.124780i
$541$	34.5021	+	19.9198i	1.48336	+	0.856420i	0.999821	−	0.0189012i	$-0.00601681\pi$
$541$	34.5021	+	19.9198i	1.48336	+	0.856420i	0.483542	+	0.875321i	$0.339350\pi$
$542$	12.4897	+	21.6328i	0.536479	+	0.929209i
$543$	28.3714	−	49.1408i	1.21753	−	2.10883i
$544$	12.0242	−	6.94215i	0.515531	−	0.297642i
$545$	−1.21012	−	2.09598i	−0.0518357	−	0.0897820i
$546$	8.50468	+	8.14638i	0.363967	+	0.348633i
$547$	5.72867	+	9.92235i	0.244940	+	0.424249i	0.962115	−	0.272645i	$-0.0878983\pi$
$547$	5.72867	+	9.92235i	0.244940	+	0.424249i	−0.717175	+	0.696894i	$0.754565\pi$
$548$		−	21.6014i		−	0.922765i
$549$	−32.3046			−1.37872
$550$	3.90290	+	6.76002i	0.166420	+	0.288248i
$551$	6.27560	+	3.62322i	0.267350	+	0.154354i
$552$			10.7360i			0.456954i
$553$	1.41140	+	0.814871i	0.0600188	+	0.0346518i
$554$		−	29.4380i		−	1.25070i
$555$	−2.87929			−0.122219
$556$	14.6371	−	25.3522i	0.620752	−	1.07517i
$557$	−33.3522	−	19.2559i	−1.41318	−	0.815898i	−0.417490	−	0.908681i	$-0.637090\pi$
$557$	−33.3522	−	19.2559i	−1.41318	−	0.815898i	−0.995686	+	0.0927834i	$0.970424\pi$
$558$	60.5993	−	49.2714i	2.56537	−	2.08582i
$559$	0.877057	+	0.840106i	0.0370956	+	0.0355327i
$560$	0.388515			0.0164177
$561$	3.56428	−	2.05784i	0.150484	−	0.0868819i
$562$	14.1344	−	24.4816i	0.596225	−	1.03269i
$563$	10.7583	−	18.6339i	0.453408	−	0.785326i	−0.545187	−	0.838314i	$-0.683541\pi$
$563$	10.7583	−	18.6339i	0.453408	−	0.785326i	0.998595	+	0.0529887i	$0.0168747\pi$
$564$	31.3593	+	18.1053i	1.32046	+	0.762370i
$565$		−	4.40355i		−	0.185259i
$566$	13.9374	−	8.04677i	0.585833	−	0.338231i
$567$	7.54005	−	4.35325i	0.316652	−	0.182819i
$568$	0.660566	−	1.14413i	0.0277167	−	0.0480068i
$569$	−13.4121			−0.562266			−0.281133	−	0.959669i	$-0.590710\pi$
$569$	−13.4121			−0.562266			−0.281133	+	0.959669i	$0.590710\pi$
$570$	−7.79722	+	4.50173i	−0.326589	+	0.188557i
$571$	−9.15929	−	15.8643i	−0.383304	−	0.663902i	0.608228	−	0.793762i	$-0.291881\pi$
$571$	−9.15929	−	15.8643i	−0.383304	−	0.663902i	−0.991532	+	0.129860i	$0.958547\pi$
$572$	−5.96005	−	1.46032i	−0.249202	−	0.0610591i
$573$	−44.1053			−1.84252
$574$	−0.901447	−	0.520451i	−0.0376257	−	0.0217232i
$575$	−18.9728	−	32.8619i	−0.791221	−	1.37043i
$576$	−32.9088	+	56.9997i	−1.37120	+	2.37499i
$577$	23.6746	+	13.6685i	0.985587	+	0.569029i	0.903952	−	0.427634i	$-0.140653\pi$
$577$	23.6746	+	13.6685i	0.985587	+	0.569029i	0.0816345	+	0.996662i	$0.473986\pi$
$578$	25.0320	+	14.4522i	1.04120	+	0.601134i
$579$	62.0761	+	35.8396i	2.57979	+	1.48944i
$580$	−0.471901	+	0.272452i	−0.0195946	+	0.0113130i
$581$	1.55404	+	2.69167i	0.0644723	+	0.111669i
$582$	−42.5617	−	73.7191i	−1.76424	−	3.05575i
$583$	1.26951	−	0.732949i	0.0525775	−	0.0303557i
$584$	−1.61035	−	2.78922i	−0.0666370	−	0.115419i
$585$	−3.70942	+	3.87258i	−0.153366	+	0.160111i
$586$	−13.8516	+	23.9917i	−0.572205	+	0.991088i
$587$	28.8437	+	16.6529i	1.19051	+	0.687340i	0.958422	−	0.285355i	$-0.0921114\pi$
$587$	28.8437	+	16.6529i	1.19051	+	0.687340i	0.232087	+	0.972695i	$0.425445\pi$
$588$	−23.4410	+	40.6010i	−0.966689	+	1.67436i
$589$	−5.66303	−	35.3024i	−0.233341	−	1.45461i
$590$		−	3.82178i		−	0.157340i
$591$	−15.3743	+	8.87634i	−0.632413	+	0.365124i
$592$			14.8345i			0.609695i
$593$		−	21.0385i		−	0.863946i	−0.901887	−	0.431973i	$-0.857818\pi$
$593$		−	21.0385i		−	0.863946i	0.901887	−	0.431973i	$-0.142182\pi$
$594$	−9.46434	+	16.3927i	−0.388327	+	0.672601i
$595$	−0.0944620	−	0.163613i	−0.00387257	−	0.00670748i
$596$	29.1326	−	16.8197i	1.19332	−	0.688963i
$597$	38.4740			1.57464
$598$	55.1030	+	13.5012i	2.25333	+	0.552106i
$599$	9.13716	+	15.8260i	0.373334	+	0.646634i	0.990076	−	0.140532i	$-0.0448811\pi$
$599$	9.13716	+	15.8260i	0.373334	+	0.646634i	−0.616742	+	0.787165i	$0.711548\pi$
$600$			6.93977i			0.283315i
$601$	−19.0331	−	32.9663i	−0.776378	−	1.34473i	−0.934017	−	0.357229i	$-0.883722\pi$
$601$	−19.0331	−	32.9663i	−0.776378	−	1.34473i	0.157639	−	0.987497i	$-0.449612\pi$
$602$	0.175455	−	0.303896i	0.00715099	−	0.0123859i
$603$	−69.3291	−	40.0272i	−2.82330	−	1.63003i
$604$	4.99940	−	2.88640i	0.203423	−	0.117446i
$605$	1.96324	−	1.13348i	0.0798169	−	0.0460823i
$606$	−66.9698	−	38.6651i	−2.72046	−	1.57066i
$607$	−12.4040	+	21.4844i	−0.503463	+	0.872024i	0.496529	+	0.868020i	$0.334608\pi$
$607$	−12.4040	+	21.4844i	−0.503463	+	0.872024i	−0.999992	+	0.00400382i	$0.998726\pi$
$608$	26.0634	+	45.1431i	1.05701	+	1.83080i
$609$		−	1.79476i		−	0.0727274i
$610$	−1.05747	−	1.83159i	−0.0428157	−	0.0741589i
$611$	12.9889	−	13.5602i	0.525473	−	0.548585i
$612$	25.9082			1.04728
$613$	6.71831	−	3.87882i	0.271350	−	0.156664i	−0.358151	−	0.933664i	$-0.616593\pi$
$613$	6.71831	−	3.87882i	0.271350	−	0.156664i	0.629501	+	0.777000i	$0.283259\pi$
$614$	19.9225	+	34.5067i	0.804005	+	1.39258i
$615$	0.341072	−	0.590754i	0.0137533	−	0.0238215i
$616$			0.173986i			0.00701009i
$617$			7.06655i			0.284488i	0.989832	+	0.142244i	$0.0454318\pi$
$617$			7.06655i			0.284488i	−0.989832	+	0.142244i	$0.954568\pi$
$618$	−35.9970	+	20.7829i	−1.44801	+	0.836011i
$619$			4.20844i			0.169152i	0.996417	+	0.0845758i	$0.0269535\pi$
$619$			4.20844i			0.169152i	−0.996417	+	0.0845758i	$0.973046\pi$
$620$	2.51187	+	0.958514i	0.100879	+	0.0384948i
$621$	46.0081	−	79.6884i	1.84624	−	3.19779i
$622$	8.33285	+	4.81097i	0.334117	+	0.192903i
$623$	3.16665	−	5.48479i	0.126869	−	0.219744i
$624$	28.7152	+	27.5054i	1.14953	+	1.10110i
$625$	−12.1455	−	21.0367i	−0.485821	−	0.841467i
$626$	28.9355	−	16.7059i	1.15649	−	0.667702i
$627$	7.72588	+	13.3816i	0.308542	+	0.534411i
$628$	11.3633	+	19.6818i	0.453445	+	0.785390i
$629$	6.24718	−	3.60681i	0.249091	−	0.143813i
$630$	1.34183	+	0.774706i	0.0534598	+	0.0308650i
$631$	23.2561	+	13.4269i	0.925810	+	0.534517i	0.885484	−	0.464670i	$-0.153827\pi$
$631$	23.2561	+	13.4269i	0.925810	+	0.534517i	0.0403259	+	0.999187i	$0.487160\pi$
$632$	−1.24348	−	0.717926i	−0.0494631	−	0.0285576i
$633$	−20.7185	+	35.8856i	−0.823488	+	1.42632i
$634$	17.0465	+	29.5254i	0.677003	+	1.17260i
$635$	3.19289	+	1.84342i	0.126706	+	0.0731537i
$636$	13.2808			0.526619
$637$	17.5564	+	16.8167i	0.695609	+	0.666303i
$638$	0.889283	+	1.54028i	0.0352071	+	0.0609804i
$639$	−17.4863	+	10.0957i	−0.691749	+	0.399381i
$640$	−0.773904			−0.0305912
$641$	−13.5053	+	23.3918i	−0.533426	+	0.923921i	0.465812	+	0.884884i	$0.345762\pi$
$641$	−13.5053	+	23.3918i	−0.533426	+	0.923921i	−0.999238	+	0.0390370i	$0.987571\pi$
$642$	72.7919	−	42.0264i	2.87287	−	1.65865i
$643$	9.86275	−	5.69426i	0.388949	−	0.224560i	−0.292756	−	0.956187i	$-0.594572\pi$
$643$	9.86275	−	5.69426i	0.388949	−	0.224560i	0.681705	+	0.731627i	$0.261239\pi$
$644$		−	8.61890i		−	0.339632i
$645$	0.199155	+	0.114982i	0.00784173	+	0.00452742i
$646$	11.2784	−	19.5347i	0.443741	−	0.768583i
$647$	−4.63041	+	8.02011i	−0.182040	+	0.315303i	−0.942575	−	0.333994i	$-0.891603\pi$
$647$	−4.63041	+	8.02011i	−0.182040	+	0.315303i	0.760535	+	0.649297i	$0.224937\pi$
$648$	−6.64301	+	3.83534i	−0.260962	+	0.150667i
$649$	−6.55895			−0.257461
$650$	35.6187	+	8.72721i	1.39708	+	0.342309i
$651$	−6.87081	+	5.58643i	−0.269288	+	0.218950i
$652$	6.84151	+	3.94995i	0.267934	+	0.154692i
$653$	9.25775	−	16.0349i	0.362284	−	0.627494i	−0.626053	−	0.779781i	$-0.715330\pi$
$653$	9.25775	−	16.0349i	0.362284	−	0.627494i	0.988336	+	0.152287i	$0.0486638\pi$
$654$	−71.5695			−2.79859
$655$		−	1.15200i		−	0.0450122i
$656$	−3.04364	−	1.75725i	−0.118834	−	0.0686091i
$657$			49.2237i			1.92040i
$658$	−4.69853	−	2.71270i	−0.183168	−	0.105752i
$659$	−2.79465	−	4.84048i	−0.108864	−	0.188558i	0.806446	−	0.591308i	$-0.201388\pi$
$659$	−2.79465	−	4.84048i	−0.108864	−	0.188558i	−0.915310	+	0.402749i	$0.868055\pi$
$660$	−1.16191			−0.0452274
$661$		−	46.8365i		−	1.82173i	−0.412706	−	0.910864i	$-0.635416\pi$
$661$		−	46.8365i		−	1.82173i	0.412706	−	0.910864i	$-0.364584\pi$
$662$	−7.75581	−	13.4335i	−0.301438	−	0.522106i
$663$	4.60150	−	18.7802i	0.178707	−	0.729364i
$664$	−1.36915	−	2.37144i	−0.0531334	−	0.0920298i
$665$	0.614264	−	0.354646i	0.0238201	−	0.0137526i
$666$	−29.5803	+	51.2346i	−1.14621	+	1.98530i
$667$	−4.32299	−	7.48764i	−0.167387	−	0.289923i
$668$	−11.6581	−	6.73083i	−0.451067	−	0.260423i
$669$	−60.3125	−	34.8214i	−2.33182	−	1.34627i
$670$		−	5.24106i		−	0.202480i
$671$	−3.14338	+	1.81483i	−0.121349	+	0.0700609i
$672$	6.45525	−	11.1808i	0.249017	−	0.431310i
$673$	−20.0433			−0.772611			−0.386305	−	0.922371i	$-0.626249\pi$
$673$	−20.0433			−0.772611			−0.386305	+	0.922371i	$0.626249\pi$
$674$	39.8116	+	22.9852i	1.53349	+	0.885359i
$675$	29.7397	−	51.5107i	1.14468	−	1.98265i
$676$	−24.3235	+	15.4752i	−0.935519	+	0.595198i
$677$	−3.42152	−	5.92625i	−0.131500	−	0.227764i	0.792755	−	0.609540i	$-0.208646\pi$
$677$	−3.42152	−	5.92625i	−0.131500	−	0.227764i	−0.924255	+	0.381776i	$0.875313\pi$
$678$	−112.773	−	65.1095i	−4.33102	−	2.50051i
$679$	3.35301	+	5.80758i	0.128677	+	0.222875i
$680$	0.0832239	+	0.144148i	0.00319149	+	0.00552782i
$681$			56.0206i			2.14671i
$682$	3.12859	−	8.19874i	0.119800	−	0.313946i
$683$	−4.97926	+	2.87477i	−0.190526	+	0.110000i	−0.592229	−	0.805770i	$-0.701752\pi$
$683$	−4.97926	+	2.87477i	−0.190526	+	0.110000i	0.401703	+	0.915770i	$0.368418\pi$
$684$			97.2692i			3.71918i
$685$	−2.12102			−0.0810398
$686$	7.15831	−	12.3986i	0.273306	−	0.473379i
$687$		−	75.3380i		−	2.87432i
$688$	0.592404	−	1.02607i	0.0225852	−	0.0391187i
$689$	1.63894	−	6.68904i	0.0624385	−	0.254832i
$690$	10.7423			0.408954
$691$			41.1344i			1.56483i	0.622760	+	0.782413i	$0.286011\pi$
$691$			41.1344i			1.56483i	−0.622760	+	0.782413i	$0.713989\pi$
$692$	−14.9607			−0.568719
$693$	1.32955	−	2.30286i	0.0505056	−	0.0874782i
$694$	−28.0133	−	16.1735i	−1.06337	−	0.613937i
$695$	−2.48931	−	1.43720i	−0.0944248	−	0.0545162i
$696$			1.58124i			0.0599367i
$697$			1.70900i			0.0647332i
$698$	9.43290	+	16.3383i	0.357041	+	0.618413i
$699$	36.7101	+	63.5837i	1.38850	+	2.40496i
$700$		−	5.57127i		−	0.210574i
$701$	−21.2790	+	36.8564i	−0.803698	+	1.39205i	0.113468	+	0.993542i	$0.463804\pi$
$701$	−21.2790	+	36.8564i	−0.803698	+	1.39205i	−0.917166	+	0.398505i	$0.869529\pi$
$702$	24.8590	+	85.3832i	0.938242	+	3.22258i
$703$	13.5413	+	23.4542i	0.510720	+	0.884593i
$704$			7.39511i			0.278714i
$705$	1.77774	−	3.07913i	0.0669535	−	0.115967i
$706$	44.2210			1.66428
$707$	5.27588	+	3.04603i	0.198420	+	0.114558i
$708$	−51.4620	−	29.7116i	−1.93406	−	1.11663i
$709$	11.4035	−	6.58379i	0.428266	−	0.247259i	−0.270342	−	0.962764i	$-0.587137\pi$
$709$	11.4035	−	6.58379i	0.428266	−	0.247259i	0.698608	+	0.715505i	$0.253803\pi$
$710$	−1.14481	−	0.660956i	−0.0429639	−	0.0248052i
$711$	10.9724	+	19.0048i	0.411497	+	0.712734i
$712$	−2.78991	+	4.83227i	−0.104556	+	0.181097i
$713$	−15.2087	+	39.8558i	−0.569571	+	1.49261i
$714$	−5.58674			−0.209078
$715$	−0.143387	+	0.585211i	−0.00536238	+	0.0218857i
$716$	−22.2310	+	38.5052i	−0.830810	+	1.43901i
$717$	2.55286	+	1.47390i	0.0953384	+	0.0550436i
$718$	−30.4304			−1.13565
$719$	8.63003			0.321846			0.160923	−	0.986967i	$-0.448553\pi$
$719$	8.63003			0.321846			0.160923	+	0.986967i	$0.448553\pi$
$720$	4.53055	+	2.61572i	0.168844	+	0.0974820i
$721$	2.83584	−	1.63727i	0.105612	−	0.0609753i
$722$	39.5482	+	22.8332i	1.47183	+	0.849763i
$723$	−77.1304	+	44.5312i	−2.86851	+	1.65613i
$724$	20.0669	−	34.7570i	0.745782	−	1.29173i
$725$	−2.79439	−	4.84002i	−0.103781	−	0.179754i
$726$		−	67.0368i		−	2.48797i
$727$	2.78786	−	4.82872i	0.103396	−	0.179087i	−0.809686	−	0.586864i	$-0.800362\pi$
$727$	2.78786	−	4.82872i	0.103396	−	0.179087i	0.913082	+	0.407776i	$0.133696\pi$
$728$	0.590289	+	0.565419i	0.0218775	+	0.0209558i
$729$	4.27012			0.158153
$730$	−2.79086	+	1.61131i	−0.103294	+	0.0596371i
$731$	−0.576140			−0.0213093
$732$	−32.8843			−1.21544
$733$	−32.7742	+	18.9222i	−1.21054	+	0.698908i	−0.962878	−	0.269938i	$-0.912997\pi$
$733$	−32.7742	+	18.9222i	−1.21054	+	0.698908i	−0.247666	+	0.968845i	$0.579664\pi$
$734$	59.6232	+	34.4235i	2.20073	+	1.27059i
$735$	3.98656	+	2.30164i	0.147047	+	0.0848974i
$736$		−	62.1943i		−	2.29251i
$737$	−8.99473			−0.331325
$738$	−7.00798	−	12.1382i	−0.257967	−	0.446812i
$739$		−	8.33086i		−	0.306456i	−0.988191	−	0.153228i	$-0.951033\pi$
$739$		−	8.33086i		−	0.306456i	0.988191	−	0.153228i	$-0.0489668\pi$
$740$	−2.03651			−0.0748635
$741$	70.5080	+	17.2757i	2.59018	+	0.634640i
$742$	−1.98985			−0.0730499
$743$	−7.73060	−	4.46326i	−0.283608	−	0.163741i	0.351448	−	0.936208i	$-0.385690\pi$
$743$	−7.73060	−	4.46326i	−0.283608	−	0.163741i	−0.635056	+	0.772466i	$0.719023\pi$
$744$	6.05339	−	4.92182i	0.221928	−	0.180443i
$745$	−1.65151	−	2.86050i	−0.0605067	−	0.104801i
$746$		−	11.6029i		−	0.424812i
$747$			41.8508i			1.53124i
$748$	2.52099	−	1.45550i	0.0921766	−	0.0532182i
$749$	−5.73454	+	3.31084i	−0.209536	+	0.120975i
$750$	13.9542			0.509535
$751$	−13.3067	−	23.0479i	−0.485569	−	0.841031i	0.514293	−	0.857614i	$-0.328054\pi$
$751$	−13.3067	−	23.0479i	−0.485569	−	0.841031i	−0.999862	+	0.0165837i	$0.994721\pi$
$752$	−15.8641	−	9.15915i	−0.578505	−	0.334000i
$753$	−6.87000	−	11.8992i	−0.250357	−	0.433630i
$754$	8.11578	+	1.98851i	0.295559	+	0.0724173i
$755$	−0.283413	−	0.490886i	−0.0103145	−	0.0178652i
$756$	11.7001	−	6.75503i	0.425527	−	0.245678i
$757$	−32.4994			−1.18121			−0.590606	−	0.806960i	$-0.701111\pi$
$757$	−32.4994			−1.18121			−0.590606	+	0.806960i	$0.701111\pi$
$758$	17.6264			0.640220
$759$		−	18.4360i		−	0.669186i
$760$	−0.541185	+	0.312453i	−0.0196309	+	0.0113339i
$761$		−	24.3944i		−	0.884296i	−0.896942	−	0.442148i	$-0.854217\pi$
$761$		−	24.3944i		−	0.884296i	0.896942	−	0.442148i	$-0.145783\pi$
$762$	94.4181	−	54.5123i	3.42041	−	1.97477i
$763$	5.63824			0.204118
$764$	−31.1954			−1.12861
$765$		−	2.54390i		−	0.0919750i
$766$	10.3099	+	17.8573i	0.372512	+	0.645210i
$767$	−21.3153	+	22.2528i	−0.769651	+	0.803503i
$768$	18.7693	−	32.5094i	0.677279	−	1.17308i
$769$	10.7740	−	6.22037i	0.388520	−	0.224312i	−0.292999	−	0.956113i	$-0.594653\pi$
$769$	10.7740	−	6.22037i	0.388520	−	0.224312i	0.681519	+	0.731801i	$0.261320\pi$
$770$	0.174088			0.00627371
$771$	48.8718	+	84.6484i	1.76007	+	3.04854i
$772$	43.9061	+	25.3492i	1.58021	+	0.912337i
$773$	43.1127	−	24.8911i	1.55065	−	0.895271i	0.552566	−	0.833469i	$-0.313649\pi$
$773$	43.1127	−	24.8911i	1.55065	−	0.895271i	0.998088	−	0.0618017i	$-0.0196846\pi$
$774$	4.09203	−	2.36253i	0.147085	−	0.0849195i
$775$	−9.83094	+	25.7628i	−0.353138	+	0.925429i
$776$	−2.95410	−	5.11666i	−0.106046	−	0.183677i
$777$	3.35384	−	5.80903i	0.120318	−	0.208398i
$778$	63.7715	−	36.8185i	2.28632	−	1.32001i
$779$	−6.41624			−0.229886
$780$	−3.77599	+	3.94207i	−0.135202	+	0.141149i
$781$	−1.13434	+	1.96473i	−0.0405897	+	0.0703034i
$782$	−23.3075	+	13.4566i	−0.833476	+	0.481208i
$783$	6.77626	−	11.7368i	0.242164	−	0.419440i
$784$	11.8584	−	20.5393i	0.423514	−	0.733547i
$785$	1.93254	−	1.11575i	0.0689752	−	0.0398228i
$786$	−29.5021	−	17.0330i	−1.05230	−	0.607548i
$787$			24.1232i			0.859900i	0.902853	+	0.429950i	$0.141469\pi$
$787$			24.1232i			0.859900i	−0.902853	+	0.429950i	$0.858531\pi$
$788$	−10.8741	+	6.27818i	−0.387375	+	0.223651i
$789$	49.8124			1.77337
$790$	−0.718350	+	1.24422i	−0.0255577	+	0.0442673i
$791$	8.88424	+	5.12932i	0.315887	+	0.182378i
$792$	−1.17138	+	2.02888i	−0.0416231	+	0.0720933i
$793$	−4.05812	+	16.5625i	−0.144108	+	0.588153i
$794$	−17.3615	+	30.0711i	−0.616138	+	1.06718i
$795$		−	1.30403i		−	0.0462492i
$796$	27.2125			0.964520
$797$	10.5396	−	18.2551i	0.373331	−	0.646628i	−0.616745	−	0.787163i	$-0.711549\pi$
$797$	10.5396	−	18.2551i	0.373331	−	0.646628i	0.990076	+	0.140535i	$0.0448823\pi$
$798$		−	20.9747i		−	0.742496i
$799$			8.90769i			0.315131i
$800$		−	40.2025i		−	1.42137i
$801$	73.8539	−	42.6396i	2.60950	−	1.50659i
$802$	−16.2711	−	28.1824i	−0.574553	−	0.995155i
$803$	2.76533	+	4.78969i	0.0975864	+	0.169025i
$804$	−70.5733	−	40.7455i	−2.48893	−	1.43698i
$805$	−0.846280			−0.0298275
$806$	−17.6489	−	37.2588i	−0.621656	−	1.31238i
$807$	24.8288			0.874014
$808$	−4.64821	−	2.68364i	−0.163523	−	0.0944103i
$809$	−4.50588	−	7.80442i	−0.158418	−	0.274389i	0.775880	−	0.630880i	$-0.217306\pi$
$809$	−4.50588	−	7.80442i	−0.158418	−	0.274389i	−0.934298	+	0.356492i	$0.883973\pi$
$810$	3.83761	+	6.64693i	0.134840	+	0.233549i
$811$	−23.7190	+	13.6942i	−0.832886	+	0.480867i	−0.854840	−	0.518892i	$-0.826345\pi$
$811$	−23.7190	+	13.6942i	−0.832886	+	0.480867i	0.0219538	+	0.999759i	$0.493011\pi$
$812$		−	1.26942i		−	0.0445481i
$813$		−	38.1360i		−	1.33749i
$814$			6.64716i			0.232983i
$815$	0.387841	−	0.671761i	0.0135855	−	0.0235308i
$816$	−18.8631			−0.660339
$817$		−	2.16304i		−	0.0756753i
$818$	−13.0969	+	22.6844i	−0.457921	+	0.793143i
$819$	−3.49220	−	11.9947i	−0.122027	−	0.419127i
$820$	0.241238	−	0.417837i	0.00842440	−	0.0145915i
$821$	47.9978	+	27.7115i	1.67513	+	0.967139i	0.964691	+	0.263383i	$0.0848383\pi$
$821$	47.9978	+	27.7115i	1.67513	+	0.967139i	0.710442	+	0.703756i	$0.248495\pi$
$822$	−31.3606	+	54.3182i	−1.09383	+	1.89457i
$823$	7.75438			0.270301			0.135150	−	0.990825i	$-0.456848\pi$
$823$	7.75438			0.270301			0.135150	+	0.990825i	$0.456848\pi$
$824$	−2.49846	+	1.44249i	−0.0870381	+	0.0502515i
$825$		−	11.9171i		−	0.414900i
$826$	7.71050	+	4.45166i	0.268283	+	0.154893i
$827$	15.0751	−	8.70359i	0.524211	−	0.302654i	−0.214445	−	0.976736i	$-0.568794\pi$
$827$	15.0751	−	8.70359i	0.524211	−	0.302654i	0.738656	+	0.674083i	$0.235461\pi$
$828$	58.0276	−	100.507i	2.01660	−	3.49285i
$829$	0.683681	−	1.18417i	0.0237452	−	0.0411279i	−0.853909	−	0.520423i	$-0.825774\pi$
$829$	0.683681	−	1.18417i	0.0237452	−	0.0411279i	0.877654	+	0.479295i	$0.159108\pi$
$830$	−2.37284	+	1.36996i	−0.0823625	+	0.0475520i
$831$	−22.4715	+	38.9217i	−0.779527	+	1.35018i
$832$	25.0897	+	24.0327i	0.869829	+	0.833182i
$833$	−11.5328			−0.399588
$834$	−73.6121	+	42.5000i	−2.54898	+	1.47165i
$835$	−0.660892	+	1.14470i	−0.0228711	+	0.0396140i
$836$	5.46447	+	9.46474i	0.188993	+	0.327345i
$837$	−66.0235	+	10.5912i	−2.28211	+	0.366084i
$838$	−7.71710	+	4.45547i	−0.266583	+	0.153912i
$839$	−5.14371	+	2.96972i	−0.177581	+	0.102526i	−0.586156	−	0.810199i	$-0.699359\pi$
$839$	−5.14371	+	2.96972i	−0.177581	+	0.102526i	0.408575	+	0.912725i	$0.366026\pi$
$840$	0.134038	+	0.0773869i	0.00462475	+	0.00267010i
$841$	13.8633	+	24.0119i	0.478045	+	0.827998i
$842$	31.6013			1.08905
$843$	−37.3759	+	21.5790i	−1.28730	+	0.743220i
$844$	−14.6541	+	25.3816i	−0.504415	+	0.873672i
$845$	1.51949	+	2.38830i	0.0522720	+	0.0821599i
$846$	−36.5270	−	63.2667i	−1.25583	−	2.17515i
$847$			5.28115i			0.181463i
$848$	−6.71854			−0.230716
$849$	−24.5700			−0.843239
$850$	−15.0660	+	8.69838i	−0.516761	+	0.298352i
$851$		−	32.3132i		−	1.10768i
$852$	−17.8001	+	10.2769i	−0.609823	+	0.352081i
$853$			23.3531i			0.799593i	0.916604	+	0.399797i	$0.130919\pi$
$853$			23.3531i			0.799593i	−0.916604	+	0.399797i	$0.869081\pi$
$854$	4.92702			0.168599
$855$	9.55075			0.326629
$856$	5.05230	−	2.91695i	0.172684	−	0.0996992i
$857$	−24.4691	−	42.3818i	−0.835850	−	1.44773i	−0.893337	−	0.449388i	$-0.851642\pi$
$857$	−24.4691	−	42.3818i	−0.835850	−	1.44773i	0.0574873	−	0.998346i	$-0.481691\pi$
$858$	12.8669	+	12.3248i	0.439269	+	0.420762i
$859$	4.53891	+	7.86162i	0.154866	+	0.268235i	0.933010	−	0.359850i	$-0.117172\pi$
$859$	4.53891	+	7.86162i	0.154866	+	0.268235i	−0.778144	+	0.628085i	$0.783839\pi$
$860$	0.140861	+	0.0813263i	0.00480333	+	0.00277320i
$861$	0.794571	+	1.37624i	0.0270789	+	0.0469020i
$862$	40.9767			1.39567
$863$	−15.5437	+	8.97416i	−0.529114	+	0.305484i	−0.740656	−	0.671885i	$-0.765485\pi$
$863$	−15.5437	+	8.97416i	−0.529114	+	0.305484i	0.211542	+	0.977369i	$0.432152\pi$
$864$	84.4281	−	48.7446i	2.87230	−	1.65832i
$865$			1.46897i			0.0499465i
$866$		−	12.7294i		−	0.432563i
$867$	−22.0642	−	38.2163i	−0.749340	−	1.29789i
$868$	−4.85968	+	3.95125i	−0.164948	+	0.134114i
$869$	2.13533	+	1.23284i	0.0724362	+	0.0418211i
$870$	1.58217			0.0536407
$871$	−29.2311	+	30.5168i	−0.990458	+	1.03402i
$872$	−4.96746			−0.168219
$873$			90.2979i			3.05612i
$874$	−50.5211	−	87.5052i	−1.70890	−	2.95991i
$875$	−1.09931			−0.0371635
$876$			50.1070i			1.69296i
$877$	28.4170	+	16.4065i	0.959572	+	0.554009i	0.896041	−	0.443971i	$-0.146431\pi$
$877$	28.4170	+	16.4065i	0.959572	+	0.554009i	0.0635309	+	0.997980i	$0.479764\pi$
$878$	−65.8130	−	37.9971i	−2.22108	−	1.28234i
$879$	36.6281	−	21.1472i	1.23543	−	0.713278i
$880$	0.587792			0.0198145
$881$	24.7328			0.833270			0.416635	−	0.909074i	$-0.363209\pi$
$881$	24.7328			0.833270			0.416635	+	0.909074i	$0.363209\pi$
$882$	81.9116	−	47.2917i	2.75811	−	1.59239i
$883$	−17.3770			−0.584781			−0.292391	−	0.956299i	$-0.594451\pi$
$883$	−17.3770			−0.584781			−0.292391	+	0.956299i	$0.594451\pi$
$884$	3.25461	−	13.2831i	0.109464	−	0.446761i
$885$	−2.91735	+	5.05299i	−0.0980656	+	0.169855i
$886$			79.3620i			2.66622i
$887$	−22.1685	−	38.3970i	−0.744345	−	1.28924i	−0.950500	−	0.310724i	$-0.899428\pi$
$887$	−22.1685	−	38.3970i	−0.744345	−	1.28924i	0.206155	−	0.978519i	$-0.433905\pi$
$888$	−2.95484	+	5.11793i	−0.0991578	+	0.171746i
$889$	−7.43825	+	4.29447i	−0.249471	+	0.144032i
$890$	4.83512	+	2.79156i	0.162074	+	0.0935732i
$891$	11.4075	−	6.58612i	0.382166	−	0.220643i
$892$	−42.6587	−	24.6290i	−1.42832	−	0.824640i
$893$	−33.4428			−1.11912
$894$	−97.6748			−3.26673
$895$	3.78078	+	2.18283i	0.126378	+	0.0729641i
$896$	0.901454	−	1.56136i	0.0301155	−	0.0521615i
$897$	−62.5487	−	59.9135i	−2.08844	−	2.00045i
$898$	0.0425090			0.00141854
$899$	−2.24000	+	5.87011i	−0.0747081	+	0.195779i
$900$	37.5092	−	64.9678i	1.25031	−	2.16559i
$901$	1.63352	+	2.82934i	0.0544205	+	0.0942591i
$902$	−1.36382	−	0.787401i	−0.0454102	−	0.0262176i
$903$	−0.463958	+	0.267866i	−0.0154395	+	0.00891402i
$904$	−7.82729	−	4.51909i	−0.260332	−	0.150303i
$905$	−3.41275	−	1.97035i	−0.113444	−	0.0654967i
$906$	−16.7618			−0.556874
$907$	−6.21374	+	10.7625i	−0.206324	+	0.357363i	−0.950554	−	0.310560i	$-0.899483\pi$
$907$	−6.21374	+	10.7625i	−0.206324	+	0.357363i	0.744230	+	0.667924i	$0.232817\pi$
$908$			39.6230i			1.31494i
$909$	41.0154	+	71.0408i	1.36040	+	2.35627i
$910$	0.565753	−	0.590637i	0.0187545	−	0.0195794i
$911$	−5.72707	+	9.91957i	−0.189746	+	0.328650i	−0.945166	−	0.326592i	$-0.894100\pi$
$911$	−5.72707	+	9.91957i	−0.189746	+	0.328650i	0.755419	+	0.655242i	$0.227433\pi$
$912$		−	70.8189i		−	2.34505i
$913$	2.35113	+	4.07228i	0.0778112	+	0.134773i
$914$	27.2029	+	47.1168i	0.899791	+	1.55848i
$915$			3.22887i			0.106743i
$916$		−	53.2861i		−	1.76062i
$917$	2.32417	+	1.34186i	0.0767509	+	0.0443122i
$918$	−36.5344	−	21.0931i	−1.20581	−	0.696178i
$919$	−9.83721	+	17.0386i	−0.324500	+	0.562050i	−0.981411	−	0.191918i	$-0.938529\pi$
$919$	−9.83721	+	17.0386i	−0.324500	+	0.562050i	0.656911	+	0.753968i	$0.271863\pi$
$920$	0.745598			0.0245816
$921$		−	60.8311i		−	2.00445i
$922$	−70.7331			−2.32947
$923$	2.97944	+	10.2335i	0.0980695	+	0.336839i
$924$	1.35341	−	2.34418i	0.0445240	−	0.0771179i
$925$		−	20.8873i		−	0.686771i
$926$	18.1230	−	31.3900i	0.595559	−	1.03154i
$927$	44.0925			1.44819
$928$		−	9.16022i		−	0.300699i
$929$	−18.9104	+	10.9179i	−0.620430	+	0.358205i	−0.777036	−	0.629456i	$-0.783278\pi$
$929$	−18.9104	+	10.9179i	−0.620430	+	0.358205i	0.156606	+	0.987661i	$0.449945\pi$
$930$	−4.92472	−	6.05696i	−0.161488	−	0.198615i
$931$		−	43.2985i		−	1.41905i
$932$	25.9648	+	44.9724i	0.850506	+	1.47312i
$933$	−7.34490	−	12.7217i	−0.240461	−	0.416491i
$934$	−54.1379	−	31.2565i	−1.77145	−	1.02275i
$935$	−0.142914	−	0.247534i	−0.00467377	−	0.00809521i
$936$	3.07673	+	10.5677i	0.100566	+	0.345415i
$937$	15.3977	−	26.6696i	0.503021	−	0.871257i	−0.496973	−	0.867766i	$-0.665555\pi$
$937$	15.3977	−	26.6696i	0.503021	−	0.871257i	0.999994	−	0.00349140i	$-0.00111135\pi$
$938$	10.5739	+	6.10486i	0.345251	+	0.199331i
$939$	−51.0097			−1.66464
$940$	1.25738	−	2.17785i	0.0410113	−	0.0710337i
$941$	31.8368	−	18.3810i	1.03785	−	0.599203i	0.118627	−	0.992939i	$-0.462151\pi$
$941$	31.8368	−	18.3810i	1.03785	−	0.599203i	0.919224	+	0.393735i	$0.128817\pi$
$942$		−	65.9885i		−	2.15002i
$943$	6.62980	+	3.82772i	0.215896	+	0.124648i
$944$	26.0337	+	15.0306i	0.847325	+	0.489204i
$945$	−0.663269	−	1.14882i	−0.0215761	−	0.0373710i
$946$	0.265449	−	0.459771i	0.00863049	−	0.0149484i
$947$	−16.8697	+	9.73971i	−0.548191	+	0.316498i	−0.748392	−	0.663257i	$-0.769174\pi$
$947$	−16.8697	+	9.73971i	−0.548191	+	0.316498i	0.200201	+	0.979755i	$0.435840\pi$
$948$	11.1693	+	19.3458i	0.362762	+	0.628323i
$949$	25.2370	+	6.18351i	0.819226	+	0.200725i
$950$	−32.6570	−	56.5635i	−1.05953	−	1.83516i
$951$		−	52.0497i		−	1.68783i
$952$	−0.387761			−0.0125674
$953$	26.8369	+	46.4828i	0.869331	+	1.50573i	0.862681	+	0.505748i	$0.168783\pi$
$953$	26.8369	+	46.4828i	0.869331	+	1.50573i	0.00664978	+	0.999978i	$0.497883\pi$
$954$	−23.2041	−	13.3969i	−0.751261	−	0.433741i
$955$			3.06304i			0.0991177i
$956$	1.80562	+	1.04248i	0.0583981	+	0.0337161i
$957$		−	2.71533i		−	0.0877742i
$958$	61.7997			1.99666
$959$	2.47059	−	4.27918i	0.0797795	−	0.138182i
$960$	5.69717	+	3.28926i	0.183875	+	0.106160i
$961$	29.4446	−	9.69622i	0.949825	−	0.312781i
$962$	22.5521	+	21.6020i	0.727108	+	0.696475i
$963$	−89.1623			−2.87321
$964$	−54.5539	+	31.4967i	−1.75706	+	1.01444i
$965$	2.48901	−	4.31109i	0.0801240	−	0.138779i
$966$	−12.5128	+	21.6728i	−0.402593	+	0.697312i
$967$	−46.0010	−	26.5587i	−1.47929	−	0.854070i	−0.479567	−	0.877505i	$-0.659206\pi$
$967$	−46.0010	−	26.5587i	−1.47929	−	0.854070i	−0.999725	+	0.0234352i	$0.992540\pi$
$968$		−	4.65285i		−	0.149548i
$969$	−29.8236	+	17.2187i	−0.958071	+	0.553143i
$970$	−5.11967	+	2.95585i	−0.164383	+	0.0949065i
$971$	27.2590	−	47.2140i	0.874784	−	1.51517i	0.0177908	−	0.999842i	$-0.494337\pi$
$971$	27.2590	−	47.2140i	0.874784	−	1.51517i	0.856993	−	0.515328i	$-0.172330\pi$
$972$	39.4393			1.26502
$973$	5.79916	−	3.34815i	0.185912	−	0.107337i
$974$	31.2898	+	54.1955i	1.00259	+	1.73654i
$975$	−40.4316	−	38.7282i	−1.29485	−	1.24030i
$976$	16.6356			0.532492
$977$	−24.9939	−	14.4302i	−0.799626	−	0.461665i	0.0437141	−	0.999044i	$-0.486081\pi$
$977$	−24.9939	−	14.4302i	−0.799626	−	0.461665i	−0.843341	+	0.537380i	$0.819414\pi$
$978$	−11.4690	−	19.8649i	−0.366738	−	0.635208i
$979$	4.79089	−	8.29806i	0.153117	−	0.265207i
$980$	2.81967	+	1.62794i	0.0900712	+	0.0520026i
$981$	65.7487	+	37.9600i	2.09919	+	1.21197i
$982$	41.0289	+	23.6881i	1.30929	+	0.755917i
$983$	−17.7260	+	10.2341i	−0.565373	+	0.326418i	−0.755299	−	0.655380i	$-0.772508\pi$
$983$	−17.7260	+	10.2341i	−0.565373	+	0.326418i	0.189926	+	0.981798i	$0.439175\pi$
$984$	−0.700041	−	1.21251i	−0.0223165	−	0.0386533i
$985$	0.616448	+	1.06772i	0.0196417	+	0.0340204i
$986$	−3.43282	+	1.98194i	−0.109323	+	0.0631179i
$987$	4.14147	+	7.17323i	0.131824	+	0.228327i
$988$	49.8699	+	12.2190i	1.58657	+	0.388739i
$989$	−1.29040	+	2.23504i	−0.0410324	+	0.0710702i
$990$	2.03008	+	1.17207i	0.0645202	+	0.0372508i
$991$	3.10319	−	5.37488i	0.0985761	−	0.170739i	−0.812519	−	0.582934i	$-0.801905\pi$
$991$	3.10319	−	5.37488i	0.0985761	−	0.170739i	0.911095	+	0.412195i	$0.135238\pi$
$992$	−35.0677	+	28.5124i	−1.11340	+	0.905269i
$993$			23.6816i			0.751511i
$994$	2.66698	−	1.53978i	0.0845914	−	0.0488389i
$995$		−	2.67196i		−	0.0847069i
$996$			42.6019i			1.34989i
$997$	−8.85320	+	15.3342i	−0.280384	+	0.485639i	−0.971479	−	0.237124i	$-0.923795\pi$
$997$	−8.85320	+	15.3342i	−0.280384	+	0.485639i	0.691095	+	0.722763i	$0.257128\pi$
$998$	−2.38023	−	4.12268i	−0.0753448	−	0.130501i
$999$	43.8648	−	25.3254i	1.38782	−	0.801259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.s.a.160.8	✓	70
13.10	even	6		403.2.v.a.36.8	yes	70
31.25	even	3		403.2.v.a.56.8	yes	70
403.335	even	6	inner	403.2.s.a.335.8	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.s.a.160.8	✓	70	1.1	even	1	trivial
403.2.s.a.335.8	yes	70	403.335	even	6	inner
403.2.v.a.36.8	yes	70	13.10	even	6
403.2.v.a.56.8	yes	70	31.25	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.77854 - 1.02684i) q^{2} +(1.56768 + 2.71530i) q^{3} +(1.10881 + 1.92051i) q^{4} +(0.188573 - 0.108873i) q^{5} -6.43902i q^{6} +0.507266i q^{7} -0.446916i q^{8} +(-3.41522 + 5.91533i) q^{9} -0.447180 q^{10} +0.767453i q^{11} +(-3.47651 + 6.02149i) q^{12} +(2.60377 + 2.49407i) q^{13} +(0.520882 - 0.902194i) q^{14} +(0.591243 + 0.341354i) q^{15} +(1.75870 - 3.04617i) q^{16} -1.71042 q^{17} +(12.1482 - 7.01378i) q^{18} -6.42155i q^{19} +(0.418183 + 0.241438i) q^{20} +(-1.37738 + 0.795229i) q^{21} +(0.788053 - 1.36495i) q^{22} +(-3.83089 + 6.63529i) q^{23} +(1.21351 - 0.700620i) q^{24} +(-2.47629 + 4.28907i) q^{25} +(-2.06990 - 7.10947i) q^{26} -12.0098 q^{27} +(-0.974211 + 0.562461i) q^{28} +(-0.564228 + 0.977272i) q^{29} +(-0.701034 - 1.21423i) q^{30} +(5.49748 - 0.881879i) q^{31} +(-7.02994 + 4.05874i) q^{32} +(-2.08386 + 1.20312i) q^{33} +(3.04205 + 1.75633i) q^{34} +(0.0552274 + 0.0956567i) q^{35} -15.1473 q^{36} +(-3.65242 + 2.10873i) q^{37} +(-6.59392 + 11.4210i) q^{38} +(-2.69027 + 10.9799i) q^{39} +(-0.0486570 - 0.0842764i) q^{40} -0.999173i q^{41} +3.26630 q^{42} +0.336841 q^{43} +(-1.47390 + 0.850958i) q^{44} +1.48730i q^{45} +(13.6268 - 7.86743i) q^{46} -5.20790i q^{47} +11.0283 q^{48} +6.74268 q^{49} +(8.80839 - 5.08552i) q^{50} +(-2.68138 - 4.64429i) q^{51} +(-1.90281 + 7.76602i) q^{52} +(-0.955041 - 1.65418i) q^{53} +(21.3599 + 12.3321i) q^{54} +(0.0835547 + 0.144721i) q^{55} +0.226705 q^{56} +(17.4364 - 10.0669i) q^{57} +(2.00701 - 1.15875i) q^{58} +8.54639i q^{59} +1.51399i q^{60} +(2.36475 + 4.09587i) q^{61} +(-10.6831 - 4.07658i) q^{62} +(-3.00065 - 1.73242i) q^{63} +9.63592 q^{64} +(0.762537 + 0.186835i) q^{65} +4.94165 q^{66} +11.7202i q^{67} +(-1.89653 - 3.28488i) q^{68} -24.0224 q^{69} -0.226839i q^{70} +(2.56006 + 1.47805i) q^{71} +(2.64366 + 1.52632i) q^{72} +(6.24102 - 3.60326i) q^{73} +8.66132 q^{74} -15.5281 q^{75} +(12.3327 - 7.12027i) q^{76} -0.389303 q^{77} +(16.0594 - 16.7657i) q^{78} +(1.60640 - 2.78236i) q^{79} -0.765900i q^{80} +(-8.58179 - 14.8641i) q^{81} +(-1.02599 + 1.77707i) q^{82} +(5.30623 - 3.06355i) q^{83} +(-3.05449 - 1.76351i) q^{84} +(-0.322539 + 0.186218i) q^{85} +(-0.599087 - 0.345883i) q^{86} -3.53811 q^{87} +0.342987 q^{88} +(-10.8125 - 6.24258i) q^{89} +(1.52722 - 2.64522i) q^{90} +(-1.26516 + 1.32080i) q^{91} -16.9909 q^{92} +(11.0128 + 13.5448i) q^{93} +(-5.34769 + 9.26246i) q^{94} +(-0.699132 - 1.21093i) q^{95} +(-22.0414 - 12.7256i) q^{96} +(11.4488 - 6.60997i) q^{97} +(-11.9921 - 6.92367i) q^{98} +(-4.53974 - 2.62102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9} + 2 q^{10} + 13 q^{12} + q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} - 12 q^{17} - 3 q^{20} - 9 q^{21} + 4 q^{22} + 10 q^{23} + 18 q^{24} + 19 q^{25} + 6 q^{26}+ \cdots + 93 q^{99}+O(q^{100}) \) 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9 + 2 * q^10 + 13 * q^12 + q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 - 12 * q^17 - 3 * q^20 - 9 * q^21 + 4 * q^22 + 10 * q^23 + 18 * q^24 + 19 * q^25 + 6 * q^26 + 34 * q^27 - 33 * q^28 - 18 * q^29 - 31 * q^30 - 2 * q^31 + 36 * q^32 - 12 * q^33 + 9 * q^34 - 12 * q^35 - 16 * q^36 - 18 * q^37 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 98 * q^42 - 38 * q^43 + 42 * q^44 - 6 * q^46 + 54 * q^48 - 18 * q^49 - 51 * q^50 - 7 * q^51 + 41 * q^52 - 22 * q^53 + 18 * q^54 - 15 * q^55 - 50 * q^56 + 15 * q^57 - 12 * q^58 - 13 * q^61 - 23 * q^62 - 6 * q^63 - 38 * q^64 - 12 * q^65 - 52 * q^66 - 44 * q^68 + 32 * q^69 + 27 * q^71 - 15 * q^72 - 9 * q^73 + 38 * q^74 - 50 * q^75 + 126 * q^76 + 34 * q^77 + 14 * q^78 + 6 * q^79 - 11 * q^81 + 39 * q^82 - 54 * q^83 + 15 * q^84 - 33 * q^85 - 24 * q^86 + 28 * q^87 - 32 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 14 * q^93 - 43 * q^94 + 25 * q^95 + 36 * q^96 - 75 * q^97 + 93 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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