LMFDB - Embedded newform 847.2.n.d.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(9,847)] 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("847.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-1,4,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.1
Character	$\chi$	$=$	847.9
Dual form			847.2.n.d.753.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22735 - 1.36311i) q^{2} +(-2.00860 - 0.894288i) q^{3} +(-0.142624 + 1.35697i) q^{4} +(0.621664 + 0.132139i) q^{5} +(1.24625 + 3.83555i) q^{6} +(1.80096 - 1.93818i) q^{7} +(-0.943117 + 0.685215i) q^{8} +(1.22735 + 1.36311i) q^{9} +(-0.582878 - 1.00958i) q^{10} +(1.50000 - 2.59808i) q^{12} +(0.556635 - 1.71315i) q^{13} +(-4.85235 - 0.0760860i) q^{14} +(-1.13051 - 0.821361i) q^{15} +(4.76082 + 1.01194i) q^{16} +(1.89648 - 2.10625i) q^{17} +(0.351681 - 3.34602i) q^{18} +(-0.581506 - 5.53266i) q^{19} +(-0.267973 + 0.824735i) q^{20} +(-5.35071 + 2.28245i) q^{21} +(-1.08288 + 1.87560i) q^{23} +(2.50713 - 0.532907i) q^{24} +(-4.19872 - 1.86939i) q^{25} +(-3.01839 + 1.34387i) q^{26} +(0.792054 + 2.43769i) q^{27} +(2.37320 + 2.72029i) q^{28} +(-8.43830 - 6.13079i) q^{29} +(0.267921 + 2.54910i) q^{30} +(-6.28980 + 1.33694i) q^{31} +(-3.29804 - 5.71237i) q^{32} -5.19869 q^{34} +(1.37570 - 0.966918i) q^{35} +(-2.02475 + 1.47107i) q^{36} +(5.54145 - 2.46721i) q^{37} +(-6.82791 + 7.58316i) q^{38} +(-2.65011 + 2.94324i) q^{39} +(-0.676845 + 0.301351i) q^{40} +(6.09648 - 4.42935i) q^{41} +(9.67842 + 4.49223i) q^{42} +4.86718 q^{43} +(0.582878 + 1.00958i) q^{45} +(3.88572 - 0.825934i) q^{46} +(0.296259 + 2.81872i) q^{47} +(-8.65763 - 6.29014i) q^{48} +(-0.513073 - 6.98117i) q^{49} +(2.60511 + 8.01771i) q^{50} +(-5.69287 + 2.53463i) q^{51} +(2.24530 + 0.999674i) q^{52} +(-7.30656 + 1.55306i) q^{53} +(2.35071 - 4.07155i) q^{54} +(-0.370450 + 3.06197i) q^{56} +(-3.77978 + 11.6330i) q^{57} +(1.99981 + 19.0269i) q^{58} +(-1.23414 + 11.7421i) q^{59} +(1.27580 - 1.41692i) q^{60} +(-4.23686 - 0.900572i) q^{61} +(9.54217 + 6.93279i) q^{62} +(4.85235 + 0.0760860i) q^{63} +(-0.730655 + 2.24872i) q^{64} +(0.572413 - 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(2.58765 + 2.87387i) q^{68} +(3.85240 - 2.79893i) q^{69} +(-3.00648 - 0.688484i) q^{70} +(1.32631 + 4.08197i) q^{71} +(-2.09155 - 0.444574i) q^{72} +(-1.67177 + 15.9058i) q^{73} +(-10.1644 - 4.52547i) q^{74} +(6.76180 + 7.50974i) q^{75} +7.59061 q^{76} +7.26456 q^{78} +(-3.18629 - 3.53873i) q^{79} +(2.82591 + 1.25818i) q^{80} +(1.16427 - 11.0773i) q^{81} +(-13.5202 - 2.87381i) q^{82} +(2.85273 + 8.77980i) q^{83} +(-2.33409 - 7.58630i) q^{84} +(1.45729 - 1.05878i) q^{85} +(-5.97372 - 6.63449i) q^{86} +(11.4665 + 19.8606i) q^{87} +(-0.182224 + 0.315621i) q^{89} +(0.660765 - 2.03363i) q^{90} +(-2.31791 - 4.16417i) q^{91} +(-2.39070 - 1.73694i) q^{92} +(13.8293 + 2.93951i) q^{93} +(3.47860 - 3.86338i) q^{94} +(0.369578 - 3.51630i) q^{95} +(1.51595 + 14.4233i) q^{96} +(-0.802231 + 2.46901i) q^{97} +(-8.88637 + 9.26770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8} - 36 q^{10} + 36 q^{12} - 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} - 28 q^{20} - 40 q^{21} - 48 q^{23}+ \cdots + 96 q^{98}+O(q^{100}) $ 24 * q - q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8 - 36 * q^10 + 36 * q^12 - 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 - 28 * q^20 - 40 * q^21 - 48 * q^23 - 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 + 13 * q^28 - 18 * q^29 - 2 * q^30 - 3 * q^31 - 12 * q^32 - 80 * q^34 + 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 - 10 * q^41 + 2 * q^42 - 16 * q^43 + 36 * q^45 + 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 - 6 * q^50 - 2 * q^51 + 7 * q^52 + 17 * q^53 - 32 * q^54 + 12 * q^56 + 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 + 24 * q^61 + 26 * q^62 + 12 * q^63 + 14 * q^64 + 60 * q^65 + 64 * q^67 - 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 + 25 * q^75 + 312 * q^76 - 48 * q^78 - 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 - 22 * q^83 + 12 * q^84 + 22 * q^85 - 21 * q^86 + 120 * q^87 - 4 * q^89 + 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 - 18 * q^97 + 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.22735	−	1.36311i	−0.867866	−	0.963863i	0.131758	−	0.991282i	$-0.457938\pi$
$2$	−1.22735	−	1.36311i	−0.867866	−	0.963863i	−0.999624	+	0.0274188i	$0.991271\pi$
$3$	−2.00860	−	0.894288i	−1.15967	−	0.516318i	−0.265527	−	0.964103i	$-0.585546\pi$
$3$	−2.00860	−	0.894288i	−1.15967	−	0.516318i	−0.894141	+	0.447786i	$0.852213\pi$
$4$	−0.142624	+	1.35697i	−0.0713118	+	0.678487i
$5$	0.621664	+	0.132139i	0.278016	+	0.0590942i	0.344810	−	0.938673i	$-0.387943\pi$
$5$	0.621664	+	0.132139i	0.278016	+	0.0590942i	−0.0667932	+	0.997767i	$0.521277\pi$
$6$	1.24625	+	3.83555i	0.508778	+	1.56586i
$7$	1.80096	−	1.93818i	0.680700	−	0.732563i
$7$	1.80096	−	1.93818i	0.680700	−	0.732563i
$8$	−0.943117	+	0.685215i	−0.333442	+	0.242260i
$9$	1.22735	+	1.36311i	0.409116	+	0.454369i
$10$	−0.582878	−	1.00958i	−0.184322	−	0.319256i
$11$		0			0
$11$		0			0
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	0.556635	−	1.71315i	0.154383	−	0.475141i	−0.843715	−	0.536791i	$-0.819636\pi$
$13$	0.556635	−	1.71315i	0.154383	−	0.475141i	0.998098	+	0.0616500i	$0.0196362\pi$
$14$	−4.85235	−	0.0760860i	−1.29685	−	0.0203348i
$15$	−1.13051	−	0.821361i	−0.291895	−	0.212074i
$16$	4.76082	+	1.01194i	1.19020	+	0.252986i
$17$	1.89648	−	2.10625i	0.459964	−	0.510841i	−0.467890	−	0.883787i	$-0.654986\pi$
$17$	1.89648	−	2.10625i	0.459964	−	0.510841i	0.927853	+	0.372946i	$0.121652\pi$
$18$	0.351681	−	3.34602i	0.0828919	−	0.788664i
$19$	−0.581506	−	5.53266i	−0.133407	−	1.26928i	−0.832409	−	0.554161i	$-0.813039\pi$
$19$	−0.581506	−	5.53266i	−0.133407	−	1.26928i	0.699003	−	0.715119i	$-0.253628\pi$
$20$	−0.267973	+	0.824735i	−0.0599205	+	0.184416i
$21$	−5.35071	+	2.28245i	−1.16762	+	0.498073i
$22$		0			0
$23$	−1.08288	+	1.87560i	−0.225796	+	0.391090i	−0.956558	−	0.291542i	$-0.905832\pi$
$23$	−1.08288	+	1.87560i	−0.225796	+	0.391090i	0.730762	+	0.682632i	$0.239165\pi$
$24$	2.50713	−	0.532907i	0.511765	−	0.108779i
$25$	−4.19872	−	1.86939i	−0.839744	−	0.373878i
$26$	−3.01839	+	1.34387i	−0.591955	+	0.263555i
$27$	0.792054	+	2.43769i	0.152431	+	0.469134i
$28$	2.37320	+	2.72029i	0.448492	+	0.514086i
$29$	−8.43830	−	6.13079i	−1.56695	−	1.13846i	−0.930002	−	0.367555i	$-0.880195\pi$
$29$	−8.43830	−	6.13079i	−1.56695	−	1.13846i	−0.636952	−	0.770904i	$-0.719805\pi$
$30$	0.267921	+	2.54910i	0.0489155	+	0.465400i
$31$	−6.28980	+	1.33694i	−1.12968	+	0.240121i	−0.734584	−	0.678518i	$-0.762623\pi$
$31$	−6.28980	+	1.33694i	−1.12968	+	0.240121i	−0.395098	+	0.918639i	$0.629289\pi$
$32$	−3.29804	−	5.71237i	−0.583016	−	1.00981i
$33$		0			0
$34$	−5.19869			−0.891568
$35$	1.37570	−	0.966918i	0.232536	−	0.163439i
$36$	−2.02475	+	1.47107i	−0.337458	+	0.245178i
$37$	5.54145	−	2.46721i	0.911008	−	0.405607i	0.102934	−	0.994688i	$-0.467177\pi$
$37$	5.54145	−	2.46721i	0.911008	−	0.405607i	0.808074	+	0.589081i	$0.200510\pi$
$38$	−6.82791	+	7.58316i	−1.10763	+	1.23015i
$39$	−2.65011	+	2.94324i	−0.424357	+	0.471296i
$40$	−0.676845	+	0.301351i	−0.107019	+	0.0476477i
$41$	6.09648	−	4.42935i	0.952110	−	0.691749i	0.000805217	−	1.00000i	$-0.499744\pi$
$41$	6.09648	−	4.42935i	0.952110	−	0.691749i	0.951305	+	0.308251i	$0.0997437\pi$
$42$	9.67842	+	4.49223i	1.49341	+	0.693166i
$43$	4.86718			0.742238			0.371119	−	0.928585i	$-0.378974\pi$
$43$	4.86718			0.742238			0.371119	+	0.928585i	$0.378974\pi$
$44$		0			0
$45$	0.582878	+	1.00958i	0.0868904	+	0.150499i
$46$	3.88572	−	0.825934i	0.572917	−	0.121777i
$47$	0.296259	+	2.81872i	0.0432138	+	0.411152i	0.994650	+	0.103305i	$0.0329418\pi$
$47$	0.296259	+	2.81872i	0.0432138	+	0.411152i	−0.951436	+	0.307847i	$0.900392\pi$
$48$	−8.65763	−	6.29014i	−1.24962	−	0.907903i
$49$	−0.513073	−	6.98117i	−0.0732961	−	0.997310i
$50$	2.60511	+	8.01771i	0.368418	+	1.13388i
$51$	−5.69287	+	2.53463i	−0.797162	+	0.354919i
$52$	2.24530	+	0.999674i	0.311368	+	0.138630i
$53$	−7.30656	+	1.55306i	−1.00363	+	0.213329i	−0.680282	−	0.732950i	$-0.738143\pi$
$53$	−7.30656	+	1.55306i	−1.00363	+	0.213329i	−0.323351	+	0.946279i	$0.604810\pi$
$54$	2.35071	−	4.07155i	0.319891	−	0.554068i
$55$		0			0
$56$	−0.370450	+	3.06197i	−0.0495034	+	0.409174i
$57$	−3.77978	+	11.6330i	−0.500644	+	1.54082i
$58$	1.99981	+	19.0269i	0.262588	+	2.49836i
$59$	−1.23414	+	11.7421i	−0.160672	+	1.52869i	0.555943	+	0.831220i	$0.312357\pi$
$59$	−1.23414	+	11.7421i	−0.160672	+	1.52869i	−0.716615	+	0.697469i	$0.754309\pi$
$60$	1.27580	−	1.41692i	0.164705	−	0.182924i
$61$	−4.23686	−	0.900572i	−0.542474	−	0.115306i	−0.0714789	−	0.997442i	$-0.522772\pi$
$61$	−4.23686	−	0.900572i	−0.542474	−	0.115306i	−0.470995	+	0.882136i	$0.656105\pi$
$62$	9.54217	+	6.93279i	1.21186	+	0.880465i
$63$	4.85235	+	0.0760860i	0.611339	+	0.00958594i
$64$	−0.730655	+	2.24872i	−0.0913318	+	0.281090i
$65$	0.572413	−	0.991448i	0.0709990	−	0.122974i
$66$		0			0
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	0.910813	−	0.412818i	$-0.135456\pi$
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	−0.812918	+	0.582378i	$0.802122\pi$
$68$	2.58765	+	2.87387i	0.313798	+	0.348508i
$69$	3.85240	−	2.79893i	0.463775	−	0.336952i
$70$	−3.00648	−	0.688484i	−0.359343	−	0.0822895i
$71$	1.32631	+	4.08197i	0.157404	+	0.484441i	0.998397	−	0.0566066i	$-0.0180281\pi$
$71$	1.32631	+	4.08197i	0.157404	+	0.484441i	−0.840992	+	0.541047i	$0.818028\pi$
$72$	−2.09155	−	0.444574i	−0.246492	−	0.0523935i
$73$	−1.67177	+	15.9058i	−0.195666	+	1.86164i	0.252381	+	0.967628i	$0.418786\pi$
$73$	−1.67177	+	15.9058i	−0.195666	+	1.86164i	−0.448047	+	0.894010i	$0.647880\pi$
$74$	−10.1644	−	4.52547i	−1.18158	−	0.526075i
$75$	6.76180	+	7.50974i	0.780785	+	0.867150i
$76$	7.59061			0.870703
$77$		0			0
$78$	7.26456			0.822549
$79$	−3.18629	−	3.53873i	−0.358485	−	0.398138i	0.536743	−	0.843746i	$-0.319654\pi$
$79$	−3.18629	−	3.53873i	−0.358485	−	0.398138i	−0.895228	+	0.445607i	$0.852988\pi$
$80$	2.82591	+	1.25818i	0.315946	+	0.140668i
$81$	1.16427	−	11.0773i	0.129363	−	1.23081i
$82$	−13.5202	−	2.87381i	−1.49306	−	0.317359i
$83$	2.85273	+	8.77980i	0.313128	+	0.963708i	0.976518	+	0.215435i	$0.0691168\pi$
$83$	2.85273	+	8.77980i	0.313128	+	0.963708i	−0.663391	+	0.748273i	$0.730883\pi$
$84$	−2.33409	−	7.58630i	−0.254670	−	0.827734i
$85$	1.45729	−	1.05878i	0.158065	−	0.114841i
$86$	−5.97372	−	6.63449i	−0.644163	−	0.715415i
$87$	11.4665	+	19.8606i	1.22934	+	2.12928i
$88$		0			0
$89$	−0.182224	+	0.315621i	−0.0193157	+	0.0334558i	−0.875522	−	0.483179i	$-0.839482\pi$
$89$	−0.182224	+	0.315621i	−0.0193157	+	0.0334558i	0.856206	+	0.516635i	$0.172815\pi$
$90$	0.660765	−	2.03363i	0.0696508	−	0.214363i
$91$	−2.31791	−	4.16417i	−0.242982	−	0.436524i
$92$	−2.39070	−	1.73694i	−0.249247	−	0.181089i
$93$	13.8293	+	2.93951i	1.43403	+	0.304813i
$94$	3.47860	−	3.86338i	0.358791	−	0.398477i
$95$	0.369578	−	3.51630i	0.0379179	−	0.360764i
$96$	1.51595	+	14.4233i	0.154721	+	1.47207i
$97$	−0.802231	+	2.46901i	−0.0814542	+	0.250690i	−0.983487	−	0.180976i	$-0.942074\pi$
$97$	−0.802231	+	2.46901i	−0.0814542	+	0.250690i	0.902033	+	0.431667i	$0.142074\pi$
$98$	−8.88637	+	9.26770i	−0.897659	+	0.936179i
$99$		0			0
$100$	3.13555	−	5.43094i	0.313555	−	0.543094i
$101$	−9.68377	+	2.05835i	−0.963571	+	0.204813i	−0.662728	−	0.748860i	$-0.730601\pi$
$101$	−9.68377	+	2.05835i	−0.963571	+	0.204813i	−0.300843	+	0.953674i	$0.597268\pi$
$102$	10.4421	+	4.64913i	1.03392	+	0.460332i
$103$	5.69287	−	2.53463i	0.560935	−	0.249745i	−0.106626	−	0.994299i	$-0.534005\pi$
$103$	5.69287	−	2.53463i	0.560935	−	0.249745i	0.667562	+	0.744555i	$0.267338\pi$
$104$	0.648901	+	1.99711i	0.0636300	+	0.195833i
$105$	−3.62794	+	0.711883i	−0.354051	+	0.0694727i
$106$	11.0847	+	8.05349i	1.07664	+	0.782224i
$107$	1.16014	+	11.0380i	0.112155	+	1.06708i	0.895367	+	0.445329i	$0.146913\pi$
$107$	1.16014	+	11.0380i	0.112155	+	1.06708i	−0.783212	+	0.621755i	$0.786420\pi$
$108$	−3.42085	+	0.727123i	−0.329171	+	0.0699675i
$109$	−7.15202	−	12.3877i	−0.685039	−	1.18652i	−0.973424	−	0.229008i	$-0.926452\pi$
$109$	−7.15202	−	12.3877i	−0.685039	−	1.18652i	0.288385	−	0.957514i	$-0.406882\pi$
$110$		0			0
$111$	−13.3370			−1.26589
$112$	10.5354	−	7.40484i	0.995500	−	0.699692i
$113$	7.02989	−	5.10751i	0.661316	−	0.480474i	−0.205791	−	0.978596i	$-0.565977\pi$
$113$	7.02989	−	5.10751i	0.661316	−	0.480474i	0.867107	+	0.498122i	$0.165977\pi$
$114$	20.4961	−	9.12545i	1.91964	−	0.854677i
$115$	−0.921025	+	1.02290i	−0.0858861	+	0.0953861i
$116$	9.52282	−	10.5762i	0.884171	−	0.981972i
$117$	3.01839	−	1.34387i	0.279050	−	0.124241i
$118$	17.5205	−	12.7294i	1.61289	−	1.17183i
$119$	−0.666809	−	7.46900i	−0.0611262	−	0.684682i
$120$	1.62901			0.148707
$121$		0			0
$122$	3.97252	+	6.88061i	0.359655	+	0.622942i
$123$	−16.2065	+	3.44481i	−1.46129	+	0.310608i
$124$	−0.917115	−	8.72577i	−0.0823594	−	0.783597i
$125$	−4.93404	−	3.58479i	−0.441314	−	0.320633i
$126$	−5.85182	−	6.70767i	−0.521321	−	0.597567i
$127$	−6.48902	−	19.9712i	−0.575808	−	1.77215i	−0.633413	−	0.773814i	$-0.718346\pi$
$127$	−6.48902	−	19.9712i	−0.575808	−	1.77215i	0.0576053	−	0.998339i	$-0.481654\pi$
$128$	−8.08960	+	3.60172i	−0.715027	+	0.318350i
$129$	−9.77623	−	4.35266i	−0.860749	−	0.383230i
$130$	−2.05400	+	0.436591i	−0.180148	+	0.0382916i
$131$	−6.85071	+	11.8658i	−0.598549	+	1.03672i	0.394486	+	0.918902i	$0.370923\pi$
$131$	−6.85071	+	11.8658i	−0.598549	+	1.03672i	−0.993035	+	0.117816i	$0.962411\pi$
$132$		0			0
$133$	−11.7706	−	8.83705i	−1.02064	−	0.766270i
$134$	0.908383	−	2.79572i	0.0784724	−	0.241513i
$135$	0.170278	+	1.62008i	0.0146552	+	0.139435i
$136$	−0.345366	+	3.28594i	−0.0296149	+	0.281767i
$137$	4.86094	−	5.39862i	0.415298	−	0.461235i	−0.498807	−	0.866713i	$-0.666228\pi$
$137$	4.86094	−	5.39862i	0.415298	−	0.461235i	0.914105	+	0.405478i	$0.132895\pi$
$138$	−8.54349	−	1.81597i	−0.727270	−	0.154586i
$139$	−2.10556	−	1.52978i	−0.178591	−	0.129754i	0.494898	−	0.868951i	$-0.335205\pi$
$139$	−2.10556	−	1.52978i	−0.178591	−	0.129754i	−0.673490	+	0.739197i	$0.735205\pi$
$140$	1.11588	+	2.00469i	0.0943087	+	0.169428i
$141$	1.92568	−	5.92663i	0.162171	−	0.499112i
$142$	3.93632	−	6.81790i	0.330328	−	0.572146i
$143$		0			0
$144$	4.46379	+	7.73152i	0.371983	+	0.644293i
$145$	−4.43567	−	4.92631i	−0.368363	−	0.409108i
$146$	23.7332	−	17.2432i	1.96418	−	1.42706i
$147$	−5.21262	+	14.4812i	−0.429930	+	1.19439i
$148$	2.55760	+	7.87148i	0.210233	+	0.647032i
$149$	−0.978148	−	0.207912i	−0.0801330	−	0.0170328i	0.167671	−	0.985843i	$-0.446375\pi$
$149$	−0.978148	−	0.207912i	−0.0801330	−	0.0170328i	−0.247804	+	0.968810i	$0.579709\pi$
$150$	1.93750	−	18.4341i	0.158197	−	1.50514i
$151$	−1.58540	−	0.705867i	−0.129018	−	0.0574426i	0.341212	−	0.939986i	$-0.389163\pi$
$151$	−1.58540	−	0.705867i	−0.129018	−	0.0574426i	−0.470230	+	0.882544i	$0.655829\pi$
$152$	4.33949	+	4.81949i	0.351979	+	0.390913i
$153$	5.19869			0.420289
$154$		0			0
$155$	−4.08680			−0.328260
$156$	−3.61593	−	4.01590i	−0.289506	−	0.321529i
$157$	−7.25318	−	3.22932i	−0.578867	−	0.257728i	0.0963501	−	0.995348i	$-0.469283\pi$
$157$	−7.25318	−	3.22932i	−0.578867	−	0.257728i	−0.675217	+	0.737620i	$0.735950\pi$
$158$	−0.912989	+	8.68651i	−0.0726335	+	0.691061i
$159$	16.0649	+	3.41469i	1.27403	+	0.270803i
$160$	−1.29544	−	3.98697i	−0.102414	−	0.315198i
$161$	1.68503	+	5.47670i	0.132799	+	0.431624i
$162$	−16.5285	+	12.0086i	−1.29860	+	0.943488i
$163$	−10.7097	−	11.8944i	−0.838852	−	0.931639i	0.159605	−	0.987181i	$-0.448978\pi$
$163$	−10.7097	−	11.8944i	−0.838852	−	0.931639i	−0.998456	+	0.0555417i	$0.982311\pi$
$164$	5.14101	+	8.90449i	0.401446	+	0.695324i
$165$		0			0
$166$	8.46652	−	14.6644i	0.657130	−	1.13818i
$167$	−0.358217	+	1.10248i	−0.0277196	+	0.0853122i	−0.963959	−	0.266050i	$-0.914281\pi$
$167$	−0.358217	+	1.10248i	−0.0277196	+	0.0853122i	0.936240	+	0.351362i	$0.114281\pi$
$168$	3.48237	−	5.81901i	0.268671	−	0.448946i
$169$	7.89219	+	5.73401i	0.607092	+	0.441078i
$170$	−3.23184	−	0.686948i	−0.247871	−	0.0526865i
$171$	6.82791	−	7.58316i	0.522143	−	0.579899i
$172$	−0.694175	+	6.60463i	−0.0529303	+	0.503598i
$173$	−0.103844	−	0.988014i	−0.00789515	−	0.0751173i	0.989865	−	0.142013i	$-0.0453573\pi$
$173$	−0.103844	−	0.988014i	−0.00789515	−	0.0751173i	−0.997760	+	0.0668952i	$0.978691\pi$
$174$	12.9987	−	40.0060i	0.985431	−	3.03285i
$175$	−11.1850	+	4.77117i	−0.845503	+	0.360667i
$176$		0			0
$177$	12.9797	−	22.4815i	0.975615	−	1.68982i
$178$	0.653878	−	0.138986i	0.0490103	−	0.0104175i
$179$	−17.9621	−	7.99723i	−1.34255	−	0.597741i	−0.395392	−	0.918512i	$-0.629391\pi$
$179$	−17.9621	−	7.99723i	−1.34255	−	0.597741i	−0.947157	+	0.320771i	$0.896058\pi$
$180$	−1.45310	+	0.646961i	−0.108308	+	0.0482216i
$181$	−7.37705	−	22.7042i	−0.548332	−	1.68759i	−0.712933	−	0.701232i	$-0.752634\pi$
$181$	−7.37705	−	22.7042i	−0.548332	−	1.68759i	0.164602	−	0.986360i	$-0.447366\pi$
$182$	−2.83134	+	8.27044i	−0.209873	+	0.613046i
$183$	7.70480	+	5.59787i	0.569555	+	0.413806i
$184$	−0.263908	−	2.51091i	−0.0194555	−	0.185107i
$185$	3.77093	−	0.801536i	0.277244	−	0.0589301i
$186$	−12.9665	−	22.4587i	−0.950752	−	1.64675i
$187$		0			0
$188$	−3.86718			−0.282043
$189$	6.15114	+	2.85505i	0.447429	+	0.207674i
$190$	−5.24669	+	3.81194i	−0.380635	+	0.276548i
$191$	−10.1693	+	4.52769i	−0.735828	+	0.327612i	−0.740207	−	0.672379i	$-0.765273\pi$
$191$	−10.1693	+	4.52769i	−0.735828	+	0.327612i	0.00437921	+	0.999990i	$0.498606\pi$
$192$	3.47860	−	3.86338i	0.251047	−	0.278815i
$193$	−2.41865	+	2.68619i	−0.174098	+	0.193356i	−0.823879	−	0.566766i	$-0.808194\pi$
$193$	−2.41865	+	2.68619i	−0.174098	+	0.193356i	0.649780	+	0.760122i	$0.274861\pi$
$194$	4.35015	−	1.93681i	0.312322	−	0.139055i
$195$	−2.03639	+	1.47952i	−0.145829	+	0.105951i
$196$	9.54644	+	0.299454i	0.681889	+	0.0213896i
$197$	−2.41831			−0.172298			−0.0861489	−	0.996282i	$-0.527456\pi$
$197$	−2.41831			−0.172298			−0.0861489	+	0.996282i	$0.527456\pi$
$198$		0			0
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	0.981748	+	0.190186i	$0.0609091\pi$
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	−0.326168	+	0.945312i	$0.605758\pi$
$200$	5.24082	−	1.11397i	0.370582	−	0.0787696i
$201$	−0.368323	−	3.50436i	−0.0259795	−	0.247178i
$202$	14.6911	+	10.6737i	1.03366	+	0.751000i
$203$	−27.0796	+	5.31363i	−1.90062	+	0.372943i
$204$	−2.62749	−	8.08658i	−0.183961	−	0.566174i
$205$	4.37525	−	1.94799i	0.305581	−	0.136053i
$206$	−10.4421	−	4.64913i	−0.727537	−	0.323920i
$207$	−3.88572	+	0.825934i	−0.270076	+	0.0574064i
$208$	4.38364	−	7.59270i	0.303951	−	0.526459i
$209$		0			0
$210$	5.42312	+	4.07155i	0.374231	+	0.280964i
$211$	2.42738	−	7.47072i	0.167108	−	0.514305i	−0.832078	−	0.554659i	$-0.812849\pi$
$211$	2.42738	−	7.47072i	0.167108	−	0.514305i	0.999185	+	0.0403541i	$0.0128486\pi$
$212$	−1.06537	−	10.1363i	−0.0731699	−	0.696165i
$213$	0.986421	−	9.38516i	0.0675884	−	0.643061i
$214$	13.6221	−	15.1289i	0.931187	−	1.03419i
$215$	3.02575	+	0.643142i	0.206354	+	0.0438619i
$216$	−2.41734	−	1.75630i	−0.164479	−	0.119501i
$217$	−8.73646	+	14.5985i	−0.593070	+	0.991013i
$218$	−8.10771	+	24.9530i	−0.549123	+	1.69003i
$219$	17.5823	−	30.4535i	1.18810	−	2.05786i
$220$		0			0
$221$	−2.55267	−	4.42136i	−0.171711	−	0.297413i
$222$	16.3691	+	18.1797i	1.09862	+	1.22014i
$223$	−16.4530	+	11.9538i	−1.10177	+	0.800484i	−0.981348	−	0.192239i	$-0.938425\pi$
$223$	−16.4530	+	11.9538i	−1.10177	+	0.800484i	−0.120423	+	0.992723i	$0.538425\pi$
$224$	−17.0112	−	3.89557i	−1.13661	−	0.260284i
$225$	−2.60511	−	8.01771i	−0.173674	−	0.534514i
$226$	−15.5902	−	3.31380i	−1.03705	−	0.220431i
$227$	0.754656	−	7.18007i	0.0500883	−	0.476558i	−0.940511	−	0.339763i	$-0.889653\pi$
$227$	0.754656	−	7.18007i	0.0500883	−	0.476558i	0.990599	−	0.136795i	$-0.0436802\pi$
$228$	−15.2465	−	6.78820i	−1.00973	−	0.449559i
$229$	8.07729	+	8.97074i	0.533763	+	0.592804i	0.948358	−	0.317202i	$-0.102743\pi$
$229$	8.07729	+	8.97074i	0.533763	+	0.592804i	−0.414595	+	0.910006i	$0.636077\pi$
$230$	2.52475			0.166477
$231$		0			0
$232$	12.1592			0.798291
$233$	5.04672	+	5.60495i	0.330622	+	0.367193i	0.885420	−	0.464793i	$-0.153871\pi$
$233$	5.04672	+	5.60495i	0.330622	+	0.367193i	−0.554798	+	0.831985i	$0.687204\pi$
$234$	−5.53646	−	2.46499i	−0.361930	−	0.161141i
$235$	−0.188288	+	1.79144i	−0.0122826	+	0.116861i
$236$	−15.7577	−	3.34940i	−1.02574	−	0.218027i
$237$	3.23534	+	9.95737i	0.210158	+	0.646800i
$238$	−9.36264	+	10.0760i	−0.606890	+	0.653130i
$239$	−7.96578	+	5.78748i	−0.515264	+	0.374361i	−0.814817	−	0.579719i	$-0.803162\pi$
$239$	−7.96578	+	5.78748i	−0.515264	+	0.374361i	0.299553	+	0.954080i	$0.403162\pi$
$240$	−4.55096	−	5.05436i	−0.293763	−	0.326257i
$241$	−0.837515	−	1.45062i	−0.0539491	−	0.0934426i	0.837790	−	0.545993i	$-0.183848\pi$
$241$	−0.837515	−	1.45062i	−0.0539491	−	0.0934426i	−0.891739	+	0.452551i	$0.850514\pi$
$242$		0			0
$243$	−8.40011	+	14.5494i	−0.538867	+	0.933346i
$244$	1.82633	−	5.62086i	0.116919	−	0.359839i
$245$	0.603524	−	4.40774i	0.0385577	−	0.281600i
$246$	24.5867	+	17.8633i	1.56759	+	1.13892i
$247$	−9.80195	−	2.08347i	−0.623683	−	0.132568i
$248$	5.01593	−	5.57075i	0.318512	−	0.353743i
$249$	2.12167	−	20.1863i	0.134455	−	1.27925i
$250$	1.16933	+	11.1254i	0.0739548	+	0.703632i
$251$	6.11045	−	18.8060i	0.385688	−	1.18703i	−0.550292	−	0.834973i	$-0.685483\pi$
$251$	6.11045	−	18.8060i	0.385688	−	1.18703i	0.935980	−	0.352054i	$-0.114517\pi$
$252$	−0.795307	+	6.57367i	−0.0500997	+	0.414102i
$253$		0			0
$254$	−19.2586	+	33.3568i	−1.20839	+	2.09299i
$255$	−3.87397	+	0.823439i	−0.242598	+	0.0515657i
$256$	19.1584	+	8.52985i	1.19740	+	0.533116i
$257$	2.48481	−	1.10631i	0.154998	−	0.0690097i	−0.327771	−	0.944757i	$-0.606298\pi$
$257$	2.48481	−	1.10631i	0.154998	−	0.0690097i	0.482770	+	0.875747i	$0.339631\pi$
$258$	6.06570	+	18.6683i	0.377634	+	1.16224i
$259$	5.19804	−	15.1837i	0.322990	−	0.943467i
$260$	1.26373	+	0.918153i	0.0783731	+	0.0569414i
$261$	−1.99981	−	19.0269i	−0.123785	−	1.17774i
$262$	24.5825	−	5.22518i	1.51871	−	0.322813i
$263$	6.34744	+	10.9941i	0.391400	+	0.677924i	0.992634	−	0.121148i	$-0.0386576\pi$
$263$	6.34744	+	10.9941i	0.391400	+	0.677924i	−0.601235	+	0.799073i	$0.705324\pi$
$264$		0			0
$265$	−4.74744			−0.291633
$266$	2.40072	+	26.8907i	0.147197	+	1.64877i
$267$	0.648272	−	0.470997i	0.0396736	−	0.0288246i
$268$	−1.99764	+	0.889406i	−0.122025	+	0.0543291i
$269$	−4.74637	+	5.27138i	−0.289392	+	0.321402i	−0.870257	−	0.492598i	$-0.836047\pi$
$269$	−4.74637	+	5.27138i	−0.289392	+	0.321402i	0.580866	+	0.813999i	$0.302714\pi$
$270$	1.99936	−	2.22051i	0.121677	−	0.135136i
$271$	16.6413	−	7.40918i	1.01089	−	0.450075i	0.166632	−	0.986019i	$-0.446711\pi$
$271$	16.6413	−	7.40918i	1.01089	−	0.450075i	0.844254	+	0.535944i	$0.180044\pi$
$272$	11.1602	−	8.10836i	0.676686	−	0.491642i
$273$	0.931787	+	10.4370i	0.0563943	+	0.631679i
$274$	−13.3250			−0.804991
$275$		0			0
$276$	3.24864	+	5.62680i	0.195545	+	0.338694i
$277$	13.5460	−	2.87929i	0.813901	−	0.173000i	0.217887	−	0.975974i	$-0.430084\pi$
$277$	13.5460	−	2.87929i	0.813901	−	0.173000i	0.596014	+	0.802974i	$0.296750\pi$
$278$	0.499001	+	4.74768i	0.0299281	+	0.284747i
$279$	−9.54217	−	6.93279i	−0.571274	−	0.415055i
$280$	−0.634900	+	1.85457i	−0.0379425	+	0.110832i
$281$	−6.49953	−	20.0035i	−0.387730	−	1.19331i	−0.934481	−	0.356014i	$-0.884136\pi$
$281$	−6.49953	−	20.0035i	−0.387730	−	1.19331i	0.546751	−	0.837295i	$-0.315864\pi$
$282$	−10.4421	+	4.64913i	−0.621819	+	0.276852i
$283$	−0.321975	−	0.143352i	−0.0191394	−	0.00852141i	0.397145	−	0.917756i	$-0.370001\pi$
$283$	−0.321975	−	0.143352i	−0.0191394	−	0.00852141i	−0.416284	+	0.909235i	$0.636668\pi$
$284$	−5.72829	+	1.21758i	−0.339911	+	0.0722504i
$285$	−3.88692	+	6.73234i	−0.230241	+	0.398789i
$286$		0			0
$287$	2.39465	−	19.7932i	0.141352	−	1.16835i
$288$	3.73874	−	11.5066i	0.220307	−	0.678036i
$289$	0.937314	+	8.91794i	0.0551361	+	0.524585i
$290$	−1.27098	+	12.0926i	−0.0746347	+	0.710102i
$291$	3.81937	−	4.24184i	0.223896	−	0.248661i
$292$	−21.3454	−	4.53710i	−1.24914	−	0.265514i
$293$	−2.80183	−	2.03565i	−0.163685	−	0.118924i	0.502928	−	0.864329i	$-0.332256\pi$
$293$	−2.80183	−	2.03565i	−0.163685	−	0.118924i	−0.666612	+	0.745405i	$0.732256\pi$
$294$	26.1372	−	10.6682i	1.52435	−	0.622180i
$295$	−2.31881	+	7.13655i	−0.135006	+	0.415506i
$296$	−3.53566	+	6.12395i	−0.205506	+	0.355947i
$297$		0			0
$298$	0.917122	+	1.58850i	0.0531274	+	0.0920194i
$299$	2.61041	+	2.89915i	0.150964	+	0.167662i
$300$	−11.1549	+	8.10451i	−0.644029	+	0.467914i
$301$	8.76560	−	9.43346i	0.505241	−	0.543736i
$302$	0.983669	+	3.02742i	0.0566038	+	0.174209i
$303$	21.2916	+	4.52567i	1.22317	+	0.259993i
$304$	2.83029	−	26.9285i	0.162329	−	1.54445i
$305$	−2.51490	−	1.11971i	−0.144003	−	0.0641142i
$306$	−6.38060	−	7.08638i	−0.364755	−	0.405101i
$307$	6.51473			0.371815			0.185908	−	0.982567i	$-0.440477\pi$
$307$	6.51473			0.371815			0.185908	+	0.982567i	$0.440477\pi$
$308$		0			0
$309$	−13.7014			−0.779447
$310$	5.01593	+	5.57075i	0.284886	+	0.316397i
$311$	10.6246	+	4.73038i	0.602467	+	0.268236i	0.685222	−	0.728334i	$-0.259705\pi$
$311$	10.6246	+	4.73038i	0.602467	+	0.268236i	−0.0827550	+	0.996570i	$0.526372\pi$
$312$	0.482608	−	4.59171i	0.0273223	−	0.259955i
$313$	26.5056	+	5.63393i	1.49818	+	0.318449i	0.882789	−	0.469770i	$-0.155663\pi$
$313$	26.5056	+	5.63393i	1.49818	+	0.318449i	0.615395	+	0.788219i	$0.288997\pi$
$314$	4.50026	+	13.8504i	0.253964	+	0.781622i
$315$	3.00648	+	0.688484i	0.169396	+	0.0387917i
$316$	5.25640	−	3.81900i	0.295696	−	0.214836i
$317$	2.58399	+	2.86982i	0.145132	+	0.161185i	0.811328	−	0.584592i	$-0.198745\pi$
$317$	2.58399	+	2.86982i	0.145132	+	0.161185i	−0.666196	+	0.745777i	$0.732079\pi$
$318$	−15.0626	−	26.0892i	−0.844668	−	1.46301i
$319$		0			0
$320$	−0.751365	+	1.30140i	−0.0420026	+	0.0727506i
$321$	7.54089	−	23.2085i	0.420892	−	1.29537i
$322$	5.39722	−	9.01869i	0.300775	−	0.502592i
$323$	−12.7560	−	9.26778i	−0.709763	−	0.515673i
$324$	14.8655	+	3.15976i	0.825861	+	0.175542i
$325$	−5.53970	+	6.15246i	−0.307287	+	0.341277i
$326$	−3.06874	+	29.1971i	−0.169962	+	1.61708i
$327$	3.28744	+	31.2779i	0.181796	+	1.72967i
$328$	−2.71464	+	8.35480i	−0.149891	+	0.461316i
$329$	5.99673	+	4.50220i	0.330610	+	0.248214i
$330$		0			0
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	−0.938077	−	0.346426i	$-0.887395\pi$
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	0.769052	+	0.639186i	$0.220729\pi$
$332$	−12.3208	+	2.61887i	−0.676193	+	0.143729i
$333$	10.1644	+	4.52547i	0.557004	+	0.247994i
$334$	1.94245	−	0.864835i	0.106286	−	0.0473217i
$335$	0.314748	+	0.968695i	0.0171965	+	0.0529255i
$336$	−27.7835	+	5.45174i	−1.51571	+	0.297417i
$337$	−9.51464	−	6.91279i	−0.518296	−	0.376564i	0.297666	−	0.954670i	$-0.403792\pi$
$337$	−9.51464	−	6.91279i	−0.518296	−	0.376564i	−0.815961	+	0.578106i	$0.803792\pi$
$338$	−1.87039	−	17.7955i	−0.101736	−	0.967950i
$339$	−18.6878	+	3.97223i	−1.01498	+	0.215742i
$340$	1.22890	+	2.12851i	0.0666462	+	0.115435i
$341$		0			0
$342$	−18.7169			−1.01209
$343$	−14.4548	−	11.5784i	−0.780485	−	0.625175i
$344$	−4.59032	+	3.33506i	−0.247493	+	0.179814i
$345$	2.76475	−	1.23094i	0.148849	−	0.0662718i
$346$	−1.21932	+	1.35419i	−0.0655509	+	0.0728016i
$347$	0.562596	−	0.624826i	0.0302018	−	0.0335424i	−0.727855	−	0.685731i	$-0.759482\pi$
$347$	0.562596	−	0.624826i	0.0302018	−	0.0335424i	0.758056	+	0.652189i	$0.226149\pi$
$348$	−28.5857	+	12.7272i	−1.53235	+	0.682248i
$349$	7.38773	−	5.36750i	0.395456	−	0.287316i	−0.372231	−	0.928140i	$-0.621407\pi$
$349$	7.38773	−	5.36750i	0.395456	−	0.287316i	0.767688	+	0.640824i	$0.221407\pi$
$350$	20.2315	+	9.39042i	1.08142	+	0.501939i
$351$	4.61701			0.246438
$352$		0			0
$353$	−11.3639	−	19.6829i	−0.604840	−	1.04761i	−0.992077	−	0.125633i	$-0.959904\pi$
$353$	−11.3639	−	19.6829i	−0.604840	−	1.04761i	0.387237	−	0.921980i	$-0.373429\pi$
$354$	−46.5754	+	9.89991i	−2.47545	+	0.526174i
$355$	0.285134	+	2.71287i	0.0151333	+	0.143984i
$356$	−0.402300	−	0.292288i	−0.0213219	−	0.0154912i
$357$	−5.34008	+	15.5986i	−0.282627	+	0.825564i
$358$	11.1446	+	34.2996i	0.589012	+	1.81279i
$359$	23.9518	−	10.6640i	1.26413	−	0.562827i	0.338396	−	0.941004i	$-0.390116\pi$
$359$	23.9518	−	10.6640i	1.26413	−	0.562827i	0.925733	+	0.378177i	$0.123449\pi$
$360$	−1.24150	−	0.552751i	−0.0654327	−	0.0291325i
$361$	−11.6874	+	2.48424i	−0.615127	+	0.130749i
$362$	−21.8941	+	37.9217i	−1.15073	+	1.99312i
$363$		0			0
$364$	5.98126	−	2.55143i	0.313503	−	0.133731i
$365$	−3.14106	+	9.66718i	−0.164410	+	0.506003i
$366$	−1.82598	−	17.3730i	−0.0954454	−	0.908102i
$367$	0.399533	−	3.80130i	0.0208554	−	0.198426i	−0.979133	−	0.203220i	$-0.934859\pi$
$367$	0.399533	−	3.80130i	0.0208554	−	0.198426i	0.999989	+	0.00479386i	$0.00152594\pi$
$368$	−7.05339	+	7.83358i	−0.367683	+	0.408354i
$369$	13.5202	+	2.87381i	0.703833	+	0.149604i
$370$	−5.72082	−	4.15642i	−0.297412	−	0.216082i
$371$	−10.1487	+	16.9584i	−0.526896	+	0.880437i
$372$	−5.96123	+	18.3468i	−0.309075	+	0.951236i
$373$	7.55387	−	13.0837i	0.391124	−	0.677447i	−0.601474	−	0.798893i	$-0.705420\pi$
$373$	7.55387	−	13.0837i	0.391124	−	0.677447i	0.992598	+	0.121445i	$0.0387529\pi$
$374$		0			0
$375$	6.70469	+	11.6129i	0.346229	+	0.599686i
$376$	−2.21083	−	2.45538i	−0.114015	−	0.126627i
$377$	−15.2000	+	11.0434i	−0.782839	+	0.568766i
$378$	−3.65785	−	11.8888i	−0.188140	−	0.611494i
$379$	−3.51552	−	10.8196i	−0.180580	−	0.555768i	0.819264	−	0.573416i	$-0.194382\pi$
$379$	−3.51552	−	10.8196i	−0.180580	−	0.555768i	−0.999844	+	0.0176481i	$0.994382\pi$
$380$	4.71881	+	1.00301i	0.242070	+	0.0514535i
$381$	−4.82609	+	45.9172i	−0.247248	+	2.35241i
$382$	18.6531	+	8.30488i	0.954373	+	0.424914i
$383$	5.94571	+	6.60338i	0.303812	+	0.337417i	0.875647	−	0.482951i	$-0.160435\pi$
$383$	5.94571	+	6.60338i	0.303812	+	0.337417i	−0.571836	+	0.820368i	$0.693769\pi$
$384$	19.4698			0.993564
$385$		0			0
$386$	6.63009			0.337463
$387$	5.97372	+	6.63449i	0.303661	+	0.337250i
$388$	−3.23597	−	1.44075i	−0.164281	−	0.0731428i
$389$	2.08001	−	19.7900i	0.105461	−	1.00339i	−0.805974	−	0.591950i	$-0.798358\pi$
$389$	2.08001	−	19.7900i	0.105461	−	1.00339i	0.911435	−	0.411443i	$-0.134975\pi$
$390$	4.51611	+	0.959929i	0.228682	+	0.0486079i
$391$	1.89683	+	5.83785i	0.0959270	+	0.295233i
$392$	5.26749	+	6.23250i	0.266048	+	0.314789i
$393$	24.3718	−	17.7071i	1.22939	−	0.893207i
$394$	2.96811	+	3.29642i	0.149531	+	0.166071i
$395$	−1.51320	−	2.62093i	−0.0761371	−	0.131873i
$396$		0			0
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.0178296	−	0.999841i	$-0.494324\pi$
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.856973	−	0.515361i	$-0.172342\pi$
$398$	10.4839	−	32.2660i	0.525509	−	1.61735i
$399$	15.7395	+	28.2764i	0.787962	+	1.41559i
$400$	−18.0976	−	13.1487i	−0.904882	−	0.657435i
$401$	−11.1473	−	2.36942i	−0.556668	−	0.118323i	−0.0790171	−	0.996873i	$-0.525178\pi$
$401$	−11.1473	−	2.36942i	−0.556668	−	0.118323i	−0.477651	+	0.878550i	$0.658511\pi$
$402$	−4.32476	+	4.80313i	−0.215699	+	0.239558i
$403$	−1.21075	+	11.5195i	−0.0603118	+	0.573829i
$404$	−1.41199	−	13.4342i	−0.0702491	−	0.668376i
$405$	2.18752	−	6.73249i	0.108699	−	0.334540i
$406$	40.4792	+	30.3908i	2.00895	+	1.50827i
$407$		0			0
$408$	3.63228	−	6.29129i	0.179825	−	0.311465i
$409$	−3.99855	+	0.849919i	−0.197716	+	0.0420258i	−0.305705	−	0.952126i	$-0.598892\pi$
$409$	−3.99855	+	0.849919i	−0.197716	+	0.0420258i	0.107989	+	0.994152i	$0.465559\pi$
$410$	−8.02527	−	3.57308i	−0.396340	−	0.176462i
$411$	−14.5916	+	6.49661i	−0.719752	+	0.320454i
$412$	2.62749	+	8.08658i	0.129447	+	0.398397i
$413$	20.5356	+	23.5390i	1.01049	+	1.15828i
$414$	5.89496	+	4.28294i	0.289722	+	0.210495i
$415$	0.613287	+	5.83504i	0.0301051	+	0.286431i
$416$	−11.6219	+	2.47032i	−0.569812	+	0.121117i
$417$	2.86118	+	4.95570i	0.140112	+	0.242682i
$418$		0			0
$419$	32.8002			1.60240			0.801198	−	0.598399i	$-0.204196\pi$
$419$	32.8002			1.60240			0.801198	+	0.598399i	$0.204196\pi$
$420$	−0.448576	−	5.02455i	−0.0218883	−	0.245173i
$421$	6.89386	−	5.00868i	0.335986	−	0.244108i	−0.406980	−	0.913437i	$-0.633418\pi$
$421$	6.89386	−	5.00868i	0.335986	−	0.244108i	0.742966	+	0.669329i	$0.233418\pi$
$422$	−13.1626	+	5.86038i	−0.640747	+	0.285279i
$423$	−3.47860	+	3.86338i	−0.169135	+	0.187844i
$424$	5.82677	−	6.47128i	0.282973	−	0.314273i
$425$	−11.9002	+	5.29831i	−0.577244	+	0.257006i
$426$	−14.0037	+	10.1743i	−0.678480	+	0.492945i
$427$	−9.37589	+	6.58989i	−0.453731	+	0.318907i
$428$	−15.1437			−0.732000
$429$		0			0
$430$	−2.83697	−	4.91378i	−0.136811	−	0.236964i
$431$	−16.3687	+	3.47927i	−0.788451	+	0.167590i	−0.584503	−	0.811391i	$-0.698711\pi$
$431$	−16.3687	+	3.47927i	−0.788451	+	0.167590i	−0.203948	+	0.978982i	$0.565377\pi$
$432$	1.30402	+	12.4069i	0.0627397	+	0.596928i
$433$	20.9261	+	15.2037i	1.00564	+	0.730644i	0.963291	−	0.268459i	$-0.0865144\pi$
$433$	20.9261	+	15.2037i	1.00564	+	0.730644i	0.0423535	+	0.999103i	$0.486514\pi$
$434$	30.6221	−	6.00873i	1.46991	−	0.288428i
$435$	4.50397	+	13.8618i	0.215949	+	0.664622i
$436$	17.8298	−	7.93833i	0.853891	−	0.380177i
$437$	11.0068	+	4.90053i	0.526525	+	0.234424i
$438$	−63.0911	+	13.4104i	−3.01461	+	0.640775i
$439$	−4.78430	+	8.28665i	−0.228342	+	0.395500i	−0.957317	−	0.289040i	$-0.906664\pi$
$439$	−4.78430	+	8.28665i	−0.228342	+	0.395500i	0.728975	+	0.684541i	$0.239997\pi$
$440$		0			0
$441$	8.88637	−	9.26770i	0.423161	−	0.441319i
$442$	−2.89377	+	8.90612i	−0.137643	+	0.423621i
$443$	−1.98948	−	18.9287i	−0.0945232	−	0.899328i	−0.934322	−	0.356430i	$-0.883994\pi$
$443$	−1.98948	−	18.9287i	−0.0945232	−	0.899328i	0.839799	−	0.542898i	$-0.182673\pi$
$444$	1.90217	−	18.0979i	0.0902729	−	0.858889i
$445$	−0.154988	+	0.172131i	−0.00734713	+	0.00815981i
$446$	36.4878	+	7.75572i	1.72775	+	0.367244i
$447$	1.77878	+	1.29236i	0.0841333	+	0.0611264i
$448$	3.04255	+	5.46600i	0.143747	+	0.258244i
$449$	10.3034	−	31.7105i	0.486246	−	1.49651i	−0.343921	−	0.938999i	$-0.611755\pi$
$449$	10.3034	−	31.7105i	0.486246	−	1.49651i	0.830167	−	0.557514i	$-0.188245\pi$
$450$	−7.73163	+	13.3916i	−0.364472	+	0.631285i
$451$		0			0
$452$	5.92813	+	10.2678i	0.278836	+	0.482958i
$453$	2.55320	+	2.83562i	0.119960	+	0.133229i
$454$	−10.7134	+	7.78377i	−0.502807	+	0.365311i
$455$	−0.890710	−	2.89500i	−0.0417571	−	0.135720i
$456$	−4.40630	−	13.5612i	−0.206344	−	0.635062i
$457$	11.6992	+	2.48673i	0.547263	+	0.116324i	0.473242	−	0.880932i	$-0.343083\pi$
$457$	11.6992	+	2.48673i	0.547263	+	0.116324i	0.0740210	+	0.997257i	$0.476417\pi$
$458$	2.31444	−	22.0205i	0.108147	−	1.02895i
$459$	6.63651	+	2.95476i	0.309766	+	0.137917i
$460$	−1.25669	−	1.39570i	−0.0585935	−	0.0650747i
$461$	−12.4896			−0.581701			−0.290850	−	0.956769i	$-0.593938\pi$
$461$	−12.4896			−0.581701			−0.290850	+	0.956769i	$0.593938\pi$
$462$		0			0
$463$	12.3095			0.572071			0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095			0.572071			0.286035	+	0.958219i	$0.407662\pi$
$464$	−33.9692	−	37.7266i	−1.57698	−	1.75142i
$465$	8.20877	+	3.65478i	0.380672	+	0.169486i
$466$	1.44607	−	13.7585i	0.0669880	−	0.637348i
$467$	−32.0448	−	6.81134i	−1.48286	−	0.315191i	−0.605816	−	0.795605i	$-0.707153\pi$
$467$	−32.0448	−	6.81134i	−1.48286	−	0.315191i	−0.877042	+	0.480413i	$0.840487\pi$
$468$	1.39311	+	4.28754i	0.0643964	+	0.198192i
$469$	4.13314	+	0.946489i	0.190851	+	0.0437048i
$470$	2.67302	−	1.94206i	0.123297	−	0.0895808i
$471$	11.6808	+	12.9729i	0.538224	+	0.597758i
$472$	−6.88191	−	11.9198i	−0.316766	−	0.548654i
$473$		0			0
$474$	9.60208	−	16.6313i	0.441038	−	0.763900i
$475$	−7.90113	+	24.3172i	−0.362529	+	1.11575i
$476$	10.2303	+	0.160414i	0.468907	+	0.00735256i
$477$	−11.0847	−	8.05349i	−0.507533	−	0.368744i
$478$	17.6657	+	3.75497i	0.808012	+	0.171748i
$479$	−17.3827	+	19.3054i	−0.794234	+	0.882086i	−0.995235	−	0.0975046i	$-0.968914\pi$
$479$	−17.3827	+	19.3054i	−0.794234	+	0.882086i	0.201001	+	0.979591i	$0.435581\pi$
$480$	−0.963464	+	9.16674i	−0.0439759	+	0.418403i
$481$	−1.14213	−	10.8666i	−0.0520767	−	0.495476i
$482$	−0.949428	+	2.92204i	−0.0432452	+	0.133095i
$483$	1.51320	−	12.5074i	0.0688528	−	0.569107i
$484$		0			0
$485$	−0.824970	+	1.42889i	−0.0374600	+	0.0648825i
$486$	30.1423	−	6.40694i	1.36728	−	0.290625i
$487$	13.2790	+	5.91219i	0.601728	+	0.267907i	0.684910	−	0.728628i	$-0.259841\pi$
$487$	13.2790	+	5.91219i	0.601728	+	0.267907i	−0.0831816	+	0.996534i	$0.526508\pi$
$488$	4.61294	−	2.05381i	0.208818	−	0.0929718i
$489$	10.8746	+	33.4687i	0.491768	+	1.51351i
$490$	−6.74896	+	4.58716i	−0.304887	+	0.207227i
$491$	−31.8714	−	23.1559i	−1.43834	−	1.04501i	−0.988387	−	0.151958i	$-0.951442\pi$
$491$	−31.8714	−	23.1559i	−1.43834	−	1.04501i	−0.449949	−	0.893054i	$-0.648558\pi$
$492$	−2.36307	−	22.4831i	−0.106536	−	1.01362i
$493$	−28.9161	+	6.14630i	−1.30231	+	0.276815i
$494$	9.19041	+	15.9183i	0.413496	+	0.716196i
$495$		0			0
$496$	−31.2975			−1.40530
$497$	10.3002	+	4.78084i	0.462028	+	0.214450i
$498$	−30.1201	+	21.8836i	−1.34972	+	0.980626i
$499$	−23.9628	+	10.6689i	−1.07272	+	0.477607i	−0.865614	−	0.500712i	$-0.833072\pi$
$499$	−23.9628	+	10.6689i	−1.07272	+	0.477607i	−0.207108	+	0.978318i	$0.566405\pi$
$500$	5.56817	−	6.18408i	0.249016	−	0.276560i
$501$	1.70545	−	1.89409i	0.0761938	−	0.0846218i
$502$	−33.1343	+	14.7523i	−1.47886	+	0.658429i
$503$	3.19249	−	2.31948i	0.142346	−	0.103420i	−0.514333	−	0.857590i	$-0.671961\pi$
$503$	3.19249	−	2.31948i	0.142346	−	0.103420i	0.656679	+	0.754170i	$0.271961\pi$
$504$	−4.62847	+	3.25315i	−0.206169	+	0.144907i
$505$	−6.29204			−0.279992
$506$		0			0
$507$	−10.7244	−	18.5753i	−0.476289	−	0.824956i
$508$	28.0258	−	5.95707i	1.24344	−	0.264302i
$509$	−1.76711	−	16.8130i	−0.0783259	−	0.745221i	−0.961245	−	0.275696i	$-0.911092\pi$
$509$	−1.76711	−	16.8130i	−0.0783259	−	0.745221i	0.882919	−	0.469525i	$-0.155575\pi$
$510$	5.87715	+	4.27000i	0.260245	+	0.189079i
$511$	27.8176	+	31.8860i	1.23058	+	1.41055i
$512$	−6.41407	−	19.7405i	−0.283465	−	0.872414i
$513$	13.0263	−	5.79970i	0.575127	−	0.256063i
$514$	−4.55775	−	2.02924i	−0.201034	−	0.0895060i
$515$	3.87397	−	0.823439i	0.170708	−	0.0362850i
$516$	7.30077	−	12.6453i	0.321398	−	0.556678i
$517$		0			0
$518$	−27.0768	+	11.5502i	−1.18969	+	0.507485i
$519$	−0.674987	+	2.07740i	−0.0296286	+	0.0911876i
$520$	0.139502	+	1.32728i	0.00611759	+	0.0582049i
$521$	−0.162822	+	1.54915i	−0.00713336	+	0.0678694i	−0.997509	−	0.0705329i	$-0.977530\pi$
$521$	−0.162822	+	1.54915i	−0.00713336	+	0.0678694i	0.990376	+	0.138402i	$0.0441967\pi$
$522$	−23.4813	+	26.0786i	−1.02775	+	1.14143i
$523$	−12.2295	−	2.59946i	−0.534759	−	0.113667i	−0.0673866	−	0.997727i	$-0.521466\pi$
$523$	−12.2295	−	2.59946i	−0.534759	−	0.113667i	−0.467373	+	0.884060i	$0.654799\pi$
$524$	−15.1245	−	10.9886i	−0.660716	−	0.480038i
$525$	26.7329	+	0.419179i	1.16672	+	0.0182945i
$526$	7.19561	−	22.1458i	0.313744	−	0.965604i
$527$	−9.11254	+	15.7834i	−0.396949	+	0.687535i
$528$		0			0
$529$	9.15475	+	15.8565i	0.398033	+	0.689413i
$530$	5.82677	+	6.47128i	0.253099	+	0.281094i
$531$	−17.5205	+	12.7294i	−0.760323	+	0.552407i
$532$	13.6704	−	14.7120i	0.592687	−	0.637845i
$533$	−4.19461	−	12.9097i	−0.181689	−	0.559181i
$534$	−1.43768	−	0.305588i	−0.0622144	−	0.0132241i
$535$	−0.737330	+	7.01522i	−0.0318775	+	0.303295i
$536$	−1.70674	−	0.759891i	−0.0737200	−	0.0328223i
$537$	28.9269	+	32.1266i	1.24829	+	1.38636i
$538$	13.0109			0.560941
$539$		0			0
$540$	−2.22270			−0.0956497
$541$	11.0822	+	12.3080i	0.476460	+	0.529162i	0.932680	−	0.360704i	$-0.117464\pi$
$541$	11.0822	+	12.3080i	0.476460	+	0.529162i	−0.456220	+	0.889867i	$0.650797\pi$
$542$	−30.5242	−	13.5902i	−1.31113	−	0.583750i
$543$	−5.48655	+	52.2010i	−0.235450	+	2.24016i
$544$	−18.2863	−	3.88688i	−0.784021	−	0.166649i
$545$	−2.80926	−	8.64602i	−0.120336	−	0.370355i
$546$	13.0832	−	14.0800i	0.559909	−	0.602569i
$547$	−5.37550	+	3.90553i	−0.229840	+	0.166988i	−0.696745	−	0.717319i	$-0.745369\pi$
$547$	−5.37550	+	3.90553i	−0.229840	+	0.166988i	0.466905	+	0.884307i	$0.345369\pi$
$548$	6.63250	+	7.36614i	0.283326	+	0.314666i
$549$	−3.97252	−	6.88061i	−0.169543	−	0.293657i
$550$		0			0
$551$	−29.0127	+	50.2514i	−1.23598	+	2.14078i
$552$	−1.71540	+	5.27944i	−0.0730121	+	0.224708i
$553$	−12.5971	−	0.197525i	−0.535682	−	0.00839961i
$554$	−20.5505	−	14.9308i	−0.873105	−	0.634348i
$555$	−8.29111	−	1.76233i	−0.351938	−	0.0748067i
$556$	2.37617	−	2.63901i	0.100772	−	0.111919i
$557$	1.37057	−	13.0401i	0.0580727	−	0.552525i	−0.926345	−	0.376677i	$-0.877067\pi$
$557$	1.37057	−	13.0401i	0.0580727	−	0.552525i	0.984417	−	0.175848i	$-0.0562667\pi$
$558$	2.26142	+	21.5160i	0.0957334	+	0.910843i
$559$	2.70924	−	8.33819i	0.114589	−	0.352668i
$560$	7.52793	−	3.21119i	0.318113	−	0.135698i
$561$		0			0
$562$	−19.2898	+	33.4108i	−0.813689	+	1.40935i
$563$	29.8223	−	6.33893i	1.25686	−	0.267154i	0.469105	−	0.883142i	$-0.344577\pi$
$563$	29.8223	−	6.33893i	1.25686	−	0.267154i	0.787755	+	0.615988i	$0.211243\pi$
$564$	7.76763	+	3.45837i	0.327076	+	0.145624i
$565$	5.04512	−	2.24623i	0.212250	−	0.0944998i
$566$	0.199770	+	0.614830i	0.00839697	+	0.0258432i
$567$	−19.3729	−	22.2063i	−0.813586	−	0.932577i
$568$	−4.04789	−	2.94097i	−0.169846	−	0.123400i
$569$	−3.69591	−	35.1642i	−0.154940	−	1.47416i	−0.745143	−	0.666905i	$-0.767619\pi$
$569$	−3.69591	−	35.1642i	−0.154940	−	1.47416i	0.590202	−	0.807255i	$-0.299048\pi$
$570$	13.9475	−	2.96463i	0.584197	−	0.124175i
$571$	−20.6422	−	35.7533i	−0.863849	−	1.49623i	−0.868185	−	0.496240i	$-0.834713\pi$
$571$	−20.6422	−	35.7533i	−0.863849	−	1.49623i	0.00433587	−	0.999991i	$-0.498620\pi$
$572$		0			0
$573$	24.4753			1.02247
$574$	−29.9193	+	21.0289i	−1.24881	+	0.877731i
$575$	8.05294	−	5.85080i	0.335831	−	0.243995i
$576$	−3.96202	+	1.76401i	−0.165084	+	0.0735002i
$577$	5.82311	−	6.46722i	0.242419	−	0.269234i	−0.609641	−	0.792678i	$-0.708686\pi$
$577$	5.82311	−	6.46722i	0.242419	−	0.269234i	0.852060	+	0.523444i	$0.175353\pi$
$578$	11.0057	−	12.2231i	0.457777	−	0.508413i
$579$	7.26034	−	3.23251i	0.301730	−	0.134339i
$580$	7.31751	−	5.31648i	0.303843	−	0.220755i
$581$	22.1545	+	10.2830i	0.919122	+	0.426610i
$582$	−10.4698			−0.433987
$583$		0			0
$584$	−9.32224	−	16.1466i	−0.385757	−	0.668151i
$585$	2.05400	−	0.436591i	0.0849225	−	0.0180508i
$586$	0.664011	+	6.31765i	0.0274301	+	0.260980i
$587$	18.6510	+	13.5507i	0.769808	+	0.559298i	0.901903	−	0.431939i	$-0.142170\pi$
$587$	18.6510	+	13.5507i	0.769808	+	0.559298i	−0.132095	+	0.991237i	$0.542170\pi$
$588$	−18.9072	−	9.13876i	−0.779721	−	0.376876i
$589$	11.0544	+	34.0219i	0.455488	+	1.40185i
$590$	12.5739	−	5.59825i	0.517658	−	0.230476i
$591$	4.85744	+	2.16267i	0.199808	+	0.0889604i
$592$	28.8785	−	6.13831i	1.18690	−	0.252283i
$593$	15.0494	−	26.0663i	0.618005	−	1.07042i	−0.371844	−	0.928295i	$-0.621275\pi$
$593$	15.0494	−	26.0663i	0.618005	−	1.07042i	0.989849	−	0.142121i	$-0.0453921\pi$
$594$		0			0
$595$	0.572413	−	4.73131i	0.0234666	−	0.193965i
$596$	0.421638	−	1.29767i	0.0172710	−	0.0531545i
$597$	−4.25090	−	40.4446i	−0.173978	−	1.65529i
$598$	0.747979	−	7.11654i	0.0305871	−	0.291017i
$599$	19.5731	−	21.7381i	0.799733	−	0.888194i	−0.195987	−	0.980606i	$-0.562791\pi$
$599$	19.5731	−	21.7381i	0.799733	−	0.888194i	0.995721	+	0.0924125i	$0.0294578\pi$
$600$	−11.5229	−	2.44928i	−0.470422	−	0.0999914i
$601$	−21.6996	−	15.7657i	−0.885147	−	0.643097i	0.0494611	−	0.998776i	$-0.484250\pi$
$601$	−21.6996	−	15.7657i	−0.885147	−	0.643097i	−0.934608	+	0.355679i	$0.884250\pi$
$602$	−23.6173	−	0.370324i	−0.962568	−	0.0150933i
$603$	−0.908383	+	2.79572i	−0.0369922	+	0.113850i
$604$	1.18396	−	2.05068i	0.0481746	−	0.0834409i
$605$		0			0
$606$	−19.9633	−	34.5774i	−0.810952	−	1.40461i
$607$	−21.5524	−	23.9364i	−0.874786	−	0.971549i	0.125001	−	0.992157i	$-0.460107\pi$
$607$	−21.5524	−	23.9364i	−0.874786	−	0.971549i	−0.999788	+	0.0206079i	$0.993440\pi$
$608$	−29.6868	+	21.5687i	−1.20396	+	0.874727i
$609$	59.1442	+	13.5440i	2.39664	+	0.548831i
$610$	1.56038	+	4.80235i	0.0631779	+	0.194442i
$611$	4.99378	+	1.06146i	0.202027	+	0.0429421i
$612$	−0.741456	+	7.05449i	−0.0299716	+	0.285161i
$613$	−40.7395	−	18.1384i	−1.64545	−	0.732604i	−0.645929	−	0.763397i	$-0.723530\pi$
$613$	−40.7395	−	18.1384i	−1.64545	−	0.732604i	−0.999526	+	0.0307936i	$0.990197\pi$
$614$	−7.99585	−	8.88029i	−0.322686	−	0.358379i
$615$	−10.5302			−0.424619
$616$		0			0
$617$	−0.531290			−0.0213889			−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290			−0.0213889			−0.0106945	+	0.999943i	$0.503404\pi$
$618$	16.8164	+	18.6765i	0.676455	+	0.751280i
$619$	38.1362	+	16.9793i	1.53282	+	0.682457i	0.987766	−	0.155942i	$-0.0498412\pi$
$619$	38.1362	+	16.9793i	1.53282	+	0.682457i	0.545057	+	0.838399i	$0.316508\pi$
$620$	0.582874	−	5.54568i	0.0234088	−	0.222720i
$621$	−5.42983	−	1.15415i	−0.217892	−	0.0463143i
$622$	−6.59208	−	20.2883i	−0.264318	−	0.813488i
$623$	0.283552	+	0.921605i	0.0113603	+	0.0369233i
$624$	−15.5951	+	11.3305i	−0.624302	+	0.453582i
$625$	12.7832	+	14.1972i	0.511330	+	0.567889i
$626$	−24.8519	−	43.0448i	−0.993282	−	1.72041i
$627$		0			0
$628$	5.41658	−	9.38179i	0.216145	−	0.374374i
$629$	5.31267	−	16.3507i	0.211830	−	0.651945i
$630$	−2.75152	−	4.94317i	−0.109623	−	0.196940i
$631$	0.175749	+	0.127689i	0.00699646	+	0.00508323i	0.591278	−	0.806468i	$-0.298624\pi$
$631$	0.175749	+	0.127689i	0.00699646	+	0.00508323i	−0.584282	+	0.811551i	$0.698624\pi$
$632$	5.42983	+	1.15415i	0.215987	+	0.0459095i
$633$	−11.5566	+	12.8349i	−0.459335	+	0.510143i
$634$	0.740410	−	7.04453i	0.0294054	−	0.279774i
$635$	−1.39503	−	13.2728i	−0.0553599	−	0.526715i
$636$	−6.92488	+	21.3126i	−0.274589	+	0.845099i
$637$	−12.2454	−	3.00700i	−0.485179	−	0.119142i
$638$		0			0
$639$	−3.93632	+	6.81790i	−0.155718	+	0.269712i
$640$	−5.50494	+	1.17011i	−0.217602	+	0.0462527i
$641$	−8.85271	−	3.94148i	−0.349661	−	0.155679i	0.224388	−	0.974500i	$-0.427962\pi$
$641$	−8.85271	−	3.94148i	−0.349661	−	0.155679i	−0.574049	+	0.818821i	$0.694628\pi$
$642$	−40.8910	+	18.2058i	−1.61384	+	0.718527i
$643$	5.08742	+	15.6575i	0.200628	+	0.617471i	0.999865	+	0.0164538i	$0.00523763\pi$
$643$	5.08742	+	15.6575i	0.200628	+	0.617471i	−0.799236	+	0.601017i	$0.794762\pi$
$644$	−7.67206	+	1.50543i	−0.302321	+	0.0593222i
$645$	−5.50237	−	3.99771i	−0.216656	−	0.157410i
$646$	3.02307	+	28.7626i	0.118941	+	1.13165i
$647$	−0.854628	+	0.181657i	−0.0335989	+	0.00714167i	−0.224680	−	0.974432i	$-0.572134\pi$
$647$	−0.854628	+	0.181657i	−0.0335989	+	0.00714167i	0.191082	+	0.981574i	$0.438801\pi$
$648$	6.49226	+	11.2449i	0.255040	+	0.441743i
$649$		0			0
$650$	15.1856			0.595628
$651$	30.6034	−	21.5098i	1.19944	−	0.843034i
$652$	17.6678	−	12.8364i	0.691925	−	0.502713i
$653$	−36.4807	+	16.2422i	−1.42760	+	0.635608i	−0.967640	−	0.252333i	$-0.918802\pi$
$653$	−36.4807	+	16.2422i	−1.42760	+	0.635608i	−0.459958	+	0.887941i	$0.652135\pi$
$654$	38.6003	−	42.8700i	1.50939	−	1.67635i
$655$	−5.82677	+	6.47128i	−0.227671	+	0.252854i
$656$	33.5065	−	14.9180i	1.30821	−	0.582452i
$657$	−23.7332	+	17.2432i	−0.925922	+	0.672721i
$658$	−1.22309	−	13.7000i	−0.0476810	−	0.534080i
$659$	6.89465			0.268578			0.134289	−	0.990942i	$-0.457125\pi$
$659$	6.89465			0.268578			0.134289	+	0.990942i	$0.457125\pi$
$660$		0			0
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	0.932984	+	0.359917i	$0.117195\pi$
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	−0.154795	+	0.987947i	$0.549472\pi$
$662$	11.0346	−	2.34548i	0.428872	−	0.0911595i
$663$	1.17334	+	11.1636i	0.0455688	+	0.433558i
$664$	−8.70650	−	6.32565i	−0.337878	−	0.245483i
$665$	−6.14961	−	7.04902i	−0.238472	−	0.273349i
$666$	−6.30651	−	19.4094i	−0.244372	−	0.752101i
$667$	20.6366	−	9.18799i	0.799051	−	0.355760i
$668$	−1.44494	−	0.643330i	−0.0559065	−	0.0248912i
$669$	43.7376	−	9.29671i	1.69099	−	0.359432i
$670$	0.934131	−	1.61796i	0.0360886	−	0.0625073i
$671$		0			0
$672$	30.6851	+	23.0376i	1.18370	+	0.888695i
$673$	−9.69659	+	29.8430i	−0.373776	+	1.15036i	0.570524	+	0.821281i	$0.306740\pi$
$673$	−9.69659	+	29.8430i	−0.373776	+	1.15036i	−0.944301	+	0.329084i	$0.893260\pi$
$674$	2.25490	+	21.4539i	0.0868553	+	0.826373i
$675$	1.23138	−	11.7158i	0.0473960	−	0.450943i
$676$	−8.90652	+	9.89169i	−0.342558	+	0.380450i
$677$	−35.7332	−	7.59533i	−1.37334	−	0.291912i	−0.538601	−	0.842561i	$-0.681047\pi$
$677$	−35.7332	−	7.59533i	−1.37334	−	0.291912i	−0.834737	+	0.550649i	$0.814380\pi$
$678$	28.3511	+	20.5983i	1.08882	+	0.791071i
$679$	3.34060	+	6.00146i	0.128200	+	0.230315i
$680$	−0.648901	+	1.99711i	−0.0248842	+	0.0765858i
$681$	−7.93686	+	13.7470i	−0.304141	+	0.526788i
$682$		0			0
$683$	7.63501	+	13.2242i	0.292146	+	0.506011i	0.974317	−	0.225181i	$-0.0722975\pi$
$683$	7.63501	+	13.2242i	0.292146	+	0.506011i	−0.682171	+	0.731192i	$0.738964\pi$
$684$	9.31633	+	10.3468i	0.356219	+	0.395621i
$685$	3.73524	−	2.71381i	0.142716	−	0.103689i
$686$	1.95844	+	33.9142i	0.0747736	+	1.29485i
$687$	−8.20166	−	25.2421i	−0.312913	−	0.963046i
$688$	23.1717	+	4.92531i	0.883415	+	0.187776i
$689$	−1.40647	+	13.3817i	−0.0535824	+	0.509802i
$690$	−5.07122	−	2.25785i	−0.193058	−	0.0859549i
$691$	−25.6841	−	28.5251i	−0.977069	−	1.08515i	−0.996353	−	0.0853315i	$-0.972805\pi$
$691$	−25.6841	−	28.5251i	−0.977069	−	1.08515i	0.0192832	−	0.999814i	$-0.493862\pi$
$692$	1.35552			0.0515291
$693$		0			0
$694$	−1.54221			−0.0585414
$695$	−1.10681	−	1.22923i	−0.0419836	−	0.0466275i
$696$	−24.4230	−	10.8738i	−0.925753	−	0.412172i
$697$	2.23251	−	21.2409i	0.0845623	−	0.804557i
$698$	−16.3838	−	3.48248i	−0.620136	−	0.131814i
$699$	−5.12442	−	15.7714i	−0.193824	−	0.596528i
$700$	−4.87911	−	15.8582i	−0.184413	−	0.599382i
$701$	14.4859	−	10.5246i	0.547125	−	0.397510i	−0.279599	−	0.960117i	$-0.590202\pi$
$701$	14.4859	−	10.5246i	0.547125	−	0.397510i	0.826724	+	0.562607i	$0.190202\pi$
$702$	−5.66667	−	6.29348i	−0.213875	−	0.237532i
$703$	−16.8726	−	29.2243i	−0.636364	−	1.10221i
$704$		0			0
$705$	1.98026	−	3.42991i	0.0745809	−	0.129178i
$706$	−12.8824	+	39.6480i	−0.484836	+	1.49217i
$707$	−13.4507	+	22.4759i	−0.505864	+	0.845293i
$708$	28.6556	+	20.8195i	1.07694	+	0.782446i
$709$	−33.6477	−	7.15203i	−1.26366	−	0.268600i	−0.473116	−	0.881000i	$-0.656871\pi$
$709$	−33.6477	−	7.15203i	−1.26366	−	0.268600i	−0.790548	+	0.612400i	$0.790204\pi$
$710$	3.34797	−	3.71830i	0.125647	−	0.139545i
$711$	0.912989	−	8.68651i	0.0342398	−	0.325769i
$712$	−0.0444097	−	0.422530i	−0.00166433	−	0.0158350i
$713$	4.30353	−	13.2449i	0.161168	−	0.496025i
$714$	27.8167	−	11.8658i	1.04101	−	0.444066i
$715$		0			0
$716$	13.4138	−	23.2335i	0.501299	−	0.868276i
$717$	21.1758	−	4.50105i	0.790824	−	0.168095i
$718$	−43.9335	−	19.5604i	−1.63958	−	0.729989i
$719$	45.1449	−	20.0998i	1.68362	−	0.749596i	0.683819	−	0.729652i	$-0.260318\pi$
$719$	45.1449	−	20.0998i	1.68362	−	0.749596i	0.999801	−	0.0199443i	$-0.00634890\pi$
$720$	1.75335	+	5.39624i	0.0653433	+	0.201106i
$721$	5.34008	−	15.5986i	0.198875	−	0.580921i
$722$	17.7308	+	12.8822i	0.659873	+	0.479425i
$723$	0.384965	+	3.66270i	0.0143170	+	0.136217i
$724$	31.8612	−	6.77230i	1.18411	−	0.251691i
$725$	23.9693	+	41.5160i	0.890196	+	1.54186i
$726$		0			0
$727$	−19.8201			−0.735086			−0.367543	−	0.930007i	$-0.619801\pi$
$727$	−19.8201			−0.735086			−0.367543	+	0.930007i	$0.619801\pi$
$728$	5.03941	+	2.33904i	0.186773	+	0.0866905i
$729$	2.85070	−	2.07116i	0.105582	−	0.0767095i
$730$	17.0326	−	7.58339i	0.630404	−	0.280674i
$731$	9.23050	−	10.2515i	0.341402	−	0.379166i
$732$	−8.69505	+	9.65683i	−0.321378	+	0.356927i
$733$	27.9979	−	12.4655i	1.03413	−	0.460423i	0.181747	−	0.983345i	$-0.441825\pi$
$733$	27.9979	−	12.4655i	1.03413	−	0.460423i	0.852380	+	0.522922i	$0.175158\pi$
$734$	−5.67195	+	4.12091i	−0.209356	+	0.152106i
$735$	−5.15403	+	8.31368i	−0.190109	+	0.306655i
$736$	14.2855			0.526570
$737$		0			0
$738$	−12.6767	−	21.9566i	−0.466635	−	0.808235i
$739$	16.7282	−	3.55568i	0.615355	−	0.130798i	0.110319	−	0.993896i	$-0.464813\pi$
$739$	16.7282	−	3.55568i	0.615355	−	0.130798i	0.505036	+	0.863098i	$0.331479\pi$
$740$	0.549839	+	5.23137i	0.0202125	+	0.192309i
$741$	17.8250	+	12.9506i	0.654818	+	0.475753i
$742$	35.5722	−	6.98006i	1.30590	−	0.256246i
$743$	2.15463	+	6.63127i	0.0790457	+	0.243278i	0.982769	−	0.184840i	$-0.0591768\pi$
$743$	2.15463	+	6.63127i	0.0790457	+	0.243278i	−0.903723	+	0.428118i	$0.859177\pi$
$744$	−15.0569	+	6.70375i	−0.552012	+	0.245771i
$745$	−0.580606	−	0.258502i	−0.0212717	−	0.00947079i
$746$	−27.1057	+	5.76149i	−0.992410	+	0.210943i
$747$	−8.46652	+	14.6644i	−0.309774	+	0.536544i
$748$		0			0
$749$	23.4830	+	17.6305i	0.858050	+	0.644203i
$750$	7.60060	−	23.3923i	0.277535	−	0.854164i
$751$	−1.59225	−	15.1493i	−0.0581021	−	0.552804i	−0.984392	−	0.175992i	$-0.943687\pi$
$751$	−1.59225	−	15.1493i	−0.0581021	−	0.552804i	0.926290	−	0.376813i	$-0.122980\pi$
$752$	−1.44195	+	13.7192i	−0.0525823	+	0.500288i
$753$	−29.0915	+	32.3094i	−1.06015	+	1.17742i
$754$	33.7091	+	7.16509i	1.22761	+	0.260937i
$755$	−0.892315	−	0.648305i	−0.0324747	−	0.0235942i
$756$	−4.75152	+	7.93973i	−0.172811	+	0.288765i
$757$	−4.49082	+	13.8213i	−0.163222	+	0.502344i	−0.998901	−	0.0468735i	$-0.985074\pi$
$757$	−4.49082	+	13.8213i	−0.163222	+	0.502344i	0.835679	+	0.549218i	$0.185074\pi$
$758$	−10.4336	+	18.0715i	−0.378965	+	0.656387i
$759$		0			0
$760$	2.06086	+	3.56952i	0.0747553	+	0.129480i
$761$	1.14650	+	1.27332i	0.0415607	+	0.0461579i	0.763567	−	0.645729i	$-0.223446\pi$
$761$	1.14650	+	1.27332i	0.0415607	+	0.0461579i	−0.722006	+	0.691887i	$0.756780\pi$
$762$	68.5134	−	49.7779i	2.48198	−	1.80326i
$763$	−36.8900	−	8.44781i	−1.33551	−	0.305831i
$764$	−4.69356	−	14.4453i	−0.169807	−	0.522612i
$765$	3.23184	+	0.686948i	0.116847	+	0.0248367i
$766$	1.70367	−	16.2093i	0.0615559	−	0.585666i
$767$	19.4290	+	8.65033i	0.701539	+	0.312345i
$768$	−30.8534	−	34.2662i	−1.11333	−	1.23648i
$769$	36.5874			1.31937			0.659687	−	0.751540i	$-0.270689\pi$
$769$	36.5874			1.31937			0.659687	+	0.751540i	$0.270689\pi$
$770$		0			0
$771$	−5.98037			−0.215378
$772$	−3.30013	−	3.66516i	−0.118774	−	0.131912i
$773$	24.5023	+	10.9091i	0.881288	+	0.392375i	0.796938	−	0.604061i	$-0.206452\pi$
$773$	24.5023	+	10.9091i	0.881288	+	0.392375i	0.0843503	+	0.996436i	$0.473119\pi$
$774$	1.71169	−	16.2857i	0.0615255	−	0.585376i
$775$	28.9084	+	6.14467i	1.03842	+	0.220723i
$776$	−0.935206	−	2.87827i	−0.0335719	−	0.103324i
$777$	−24.0194	+	25.8494i	−0.861690	+	0.927343i
$778$	−29.5288	+	21.4540i	−1.05866	+	0.769162i
$779$	−28.0513	−	31.1541i	−1.00504	−	1.11621i
$780$	−1.71724	−	2.97434i	−0.0614870	−	0.106499i
$781$		0			0
$782$	5.62955	−	9.75067i	0.201312	−	0.348683i
$783$	8.26137	−	25.4259i	0.295237	−	0.908647i
$784$	4.62190	−	33.7553i	0.165068	−	1.20555i
$785$	−4.08232	−	2.96598i	−0.145704	−	0.105860i
$786$	−54.0494	−	11.4886i	−1.92788	−	0.409783i
$787$	−3.31326	+	3.67975i	−0.118105	+	0.131169i	−0.799298	−	0.600935i	$-0.794795\pi$
$787$	−3.31326	+	3.67975i	−0.118105	+	0.131169i	0.681193	+	0.732104i	$0.261462\pi$
$788$	0.344909	−	3.28159i	0.0122869	−	0.116902i
$789$	−2.91761	−	27.7592i	−0.103870	−	0.988254i
$790$	−1.71540	+	5.27944i	−0.0610310	+	0.187834i
$791$	2.76129	−	22.8236i	0.0981801	−	0.811514i
$792$		0			0
$793$	−3.90120	+	6.75707i	−0.138536	+	0.239951i
$794$	−62.5456	+	13.2945i	−2.21966	+	0.471803i
$795$	9.53573	+	4.24558i	0.338198	+	0.150575i
$796$	−23.0552	+	10.2648i	−0.817171	+	0.363828i
$797$	−8.24513	−	25.3759i	−0.292057	−	0.898860i	−0.984194	−	0.177094i	$-0.943330\pi$
$797$	−8.24513	−	25.3759i	−0.292057	−	0.898860i	0.692137	−	0.721766i	$-0.256670\pi$
$798$	19.2259	−	56.1597i	0.680591	−	1.98803i
$799$	6.49878	+	4.72164i	0.229910	+	0.167040i
$800$	3.16889	+	30.1500i	0.112037	+	1.06596i
$801$	−0.653878	+	0.138986i	−0.0231037	+	0.00491083i
$802$	10.4518	+	18.1030i	0.369066	+	0.639240i
$803$		0			0
$804$	4.80785			0.169560
$805$	0.323836	+	3.62732i	0.0114137	+	0.127846i
$806$	17.1884	−	12.4881i	0.605435	−	0.439874i
$807$	14.2477	−	6.34349i	0.501544	−	0.223302i
$808$	7.72252	−	8.57673i	0.271677	−	0.301728i
$809$	26.4574	−	29.3840i	0.930194	−	1.03309i	−0.0691759	−	0.997604i	$-0.522037\pi$
$809$	26.4574	−	29.3840i	0.930194	−	1.03309i	0.999370	−	0.0354811i	$-0.0112963\pi$
$810$	−11.8620	+	5.28128i	−0.416787	+	0.185565i
$811$	−27.0651	+	19.6640i	−0.950385	+	0.690495i	−0.950898	−	0.309505i	$-0.899837\pi$
$811$	−27.0651	+	19.6640i	−0.950385	+	0.690495i	0.000513088		1.00000i	$0.499837\pi$
$812$	−3.34826	−	37.5042i	−0.117501	−	1.31614i
$813$	−40.0517			−1.40467
$814$		0			0
$815$	−5.08615	−	8.80947i	−0.178160	−	0.308582i
$816$	−29.6676	+	6.30605i	−1.03858	+	0.220756i
$817$	−2.83029	−	26.9285i	−0.0990195	−	0.942107i
$818$	6.06615	+	4.40732i	0.212098	+	0.154098i
$819$	2.83134	−	8.27044i	0.0989349	−	0.288993i
$820$	2.01935	+	6.21493i	0.0705188	+	0.217035i
$821$	−51.9460	+	23.1278i	−1.81293	+	0.807167i	−0.855915	+	0.517116i	$0.827006\pi$
$821$	−51.9460	+	23.1278i	−1.81293	+	0.807167i	−0.957011	+	0.290051i	$0.906328\pi$
$822$	26.7646	+	11.9164i	0.933522	+	0.415631i
$823$	39.2977	−	8.35297i	1.36983	−	0.291166i	0.536481	−	0.843913i	$-0.319753\pi$
$823$	39.2977	−	8.35297i	1.36983	−	0.291166i	0.833350	+	0.552746i	$0.186420\pi$
$824$	−3.63228	+	6.29129i	−0.126536	+	0.219168i
$825$		0			0
$826$	6.88191	−	56.8829i	0.239452	−	1.97921i
$827$	1.77235	−	5.45473i	0.0616306	−	0.189679i	−0.915501	−	0.402316i	$-0.868205\pi$
$827$	1.77235	−	5.45473i	0.0616306	−	0.189679i	0.977131	+	0.212637i	$0.0682052\pi$
$828$	−0.566576	−	5.39061i	−0.0196899	−	0.187337i
$829$	3.72080	−	35.4011i	0.129229	−	1.22953i	−0.717139	−	0.696931i	$-0.754549\pi$
$829$	3.72080	−	35.4011i	0.129229	−	1.22953i	0.846367	−	0.532600i	$-0.178785\pi$
$830$	7.20107	−	7.99760i	0.249953	−	0.277601i
$831$	−29.7835	−	6.33067i	−1.03318	−	0.219609i
$832$	3.44569	+	2.50344i	0.119458	+	0.0867911i
$833$	−15.6771	−	12.1590i	−0.543181	−	0.421284i
$834$	3.24350	−	9.98247i	0.112313	−	0.345665i
$835$	−0.368370	+	0.638036i	−0.0127480	+	0.0220801i
$836$		0			0
$837$	−8.24090	−	14.2737i	−0.284847	−	0.493370i
$838$	−40.2573	−	44.7103i	−1.39067	−	1.54449i
$839$	33.7949	−	24.5534i	1.16673	−	0.847678i	0.176115	−	0.984370i	$-0.443647\pi$
$839$	33.7949	−	24.5534i	1.16673	−	0.847678i	0.990614	+	0.136692i	$0.0436471\pi$
$840$	2.93378	−	3.15731i	0.101225	−	0.108938i
$841$	24.6569	+	75.8862i	0.850239	+	2.61677i
$842$	−15.2885	−	3.24968i	−0.526878	−	0.111991i
$843$	−4.83391	+	45.9916i	−0.166489	+	1.58403i
$844$	9.79136	+	4.35939i	0.337033	+	0.150057i
$845$	4.14860	+	4.60749i	0.142716	+	0.158503i
$846$	9.53566			0.327843
$847$		0			0
$848$	−36.3568			−1.24850
$849$	0.518521	+	0.575876i	0.0177956	+	0.0197640i
$850$	21.8279	+	9.71839i	0.748689	+	0.333338i
$851$	−1.37321	+	13.0652i	−0.0470731	+	0.447870i
$852$	12.5947	+	2.67709i	0.431488	+	0.0917157i
$853$	−15.3851	−	47.3504i	−0.526775	−	1.62125i	−0.760779	−	0.649011i	$-0.775183\pi$
$853$	−15.3851	−	47.3504i	−0.526775	−	1.62125i	0.234005	−	0.972236i	$-0.424817\pi$
$854$	20.4902	+	4.69226i	0.701161	+	0.160566i
$855$	5.24669	−	3.81194i	0.179433	−	0.130366i
$856$	−8.65755	−	9.61518i	−0.295909	−	0.328640i
$857$	12.7394	+	22.0652i	0.435168	+	0.753734i	0.997309	−	0.0733077i	$-0.0233555\pi$
$857$	12.7394	+	22.0652i	0.435168	+	0.753734i	−0.562141	+	0.827041i	$0.690022\pi$
$858$		0			0
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	−0.970315	−	0.241845i	$-0.922247\pi$
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	0.694602	+	0.719395i	$0.255581\pi$
$860$	−1.30427	+	4.01413i	−0.0444752	+	0.136881i
$861$	−22.5107	+	37.6151i	−0.767163	+	1.28192i
$862$	24.8327	+	18.0420i	0.845804	+	0.614513i
$863$	−2.83568	−	0.602742i	−0.0965276	−	0.0205176i	0.159395	−	0.987215i	$-0.449046\pi$
$863$	−2.83568	−	0.602742i	−0.0965276	−	0.0205176i	−0.255922	+	0.966697i	$0.582379\pi$
$864$	11.3128	−	12.5641i	0.384868	−	0.427439i
$865$	0.0659985	−	0.627934i	0.00224402	−	0.0213504i
$866$	−4.95932	−	47.1848i	−0.168525	−	1.60340i
$867$	6.09252	−	18.7508i	0.206913	−	0.636812i
$868$	−18.5638	−	13.9372i	−0.630096	−	0.473061i
$869$		0			0
$870$	13.3672	−	23.1526i	0.453190	−	0.784948i
$871$	2.82373	−	0.600201i	0.0956783	−	0.0203370i
$872$	15.2334	+	6.78235i	0.515868	+	0.229679i
$873$	−4.35015	+	1.93681i	−0.147230	+	0.0655511i
$874$	−6.82919	−	21.0181i	−0.231001	−	0.710947i
$875$	−15.8340	+	3.10698i	−0.535286	+	0.105035i
$876$	38.8169	+	28.2022i	1.31150	+	0.952862i
$877$	−0.879591	−	8.36875i	−0.0297017	−	0.282593i	−0.999284	−	0.0378281i	$-0.987956\pi$
$877$	−0.879591	−	8.36875i	−0.0297017	−	0.282593i	0.969583	−	0.244764i	$-0.0787106\pi$
$878$	17.1676	−	3.64909i	0.579379	−	0.123151i
$879$	3.80731	+	6.59445i	0.128417	+	0.222425i
$880$		0			0
$881$	41.5335			1.39930			0.699649	−	0.714486i	$-0.253340\pi$
$881$	41.5335			1.39930			0.699649	+	0.714486i	$0.253340\pi$
$882$	−23.5396	−	0.738393i	−0.792618	−	0.0248630i
$883$	45.6894	−	33.1953i	1.53757	−	1.11711i	0.585737	−	0.810501i	$-0.300805\pi$
$883$	45.6894	−	33.1953i	1.53757	−	1.11711i	0.951835	−	0.306610i	$-0.0991948\pi$
$884$	6.36374	−	2.83332i	0.214036	−	0.0952949i
$885$	11.0397	−	12.2608i	0.371095	−	0.412143i
$886$	−23.3600	+	25.9440i	−0.784796	+	0.871604i
$887$	31.5900	−	14.0648i	1.06069	−	0.472248i	0.199164	−	0.979966i	$-0.436177\pi$
$887$	31.5900	−	14.0648i	1.06069	−	0.472248i	0.861523	+	0.507718i	$0.169511\pi$
$888$	12.5783	−	9.13869i	0.422101	−	0.306674i
$889$	−50.3941	−	23.3904i	−1.69017	−	0.784489i
$890$	0.424858			0.0142413
$891$		0			0
$892$	−13.8744	−	24.0311i	−0.464548	−	0.804621i
$893$	15.4227	−	3.27820i	0.516102	−	0.109701i
$894$	−0.421556	−	4.01084i	−0.0140990	−	0.134143i
$895$	−10.1096	−	7.34507i	−0.337928	−	0.245519i
$896$	−7.58829	+	22.1657i	−0.253507	+	0.740503i
$897$	−2.65060	−	8.15771i	−0.0885010	−	0.272378i
$898$	−55.8707	+	24.8753i	−1.86443	+	0.830098i
$899$	61.2717	+	27.2799i	2.04353	+	0.909836i
$900$	11.2514	−	2.39155i	0.375046	−	0.0797184i
$901$	−10.5856	+	18.3348i	−0.352658	+	0.610821i
$902$		0			0
$903$	−26.0429	+	11.1091i	−0.866652	+	0.369688i
$904$	−3.13026	+	9.63396i	−0.104111	+	0.320421i
$905$	−1.58594	−	15.0892i	−0.0527183	−	0.501581i
$906$	0.731586	−	6.96057i	0.0243053	−	0.231250i
$907$	5.62260	−	6.24453i	0.186695	−	0.207346i	−0.642530	−	0.766260i	$-0.722115\pi$
$907$	5.62260	−	6.24453i	0.186695	−	0.207346i	0.829225	+	0.558914i	$0.188782\pi$
$908$	9.63554	+	2.04810i	0.319767	+	0.0679685i
$909$	−14.6911	−	10.6737i	−0.487273	−	0.354025i
$910$	−2.85298	+	4.76730i	−0.0945755	+	0.158035i
$911$	−0.183460	+	0.564632i	−0.00607830	+	0.0187071i	−0.954050	−	0.299649i	$-0.903131\pi$
$911$	−0.183460	+	0.564632i	−0.00607830	+	0.0187071i	0.947971	+	0.318356i	$0.103131\pi$
$912$	−29.7667	+	51.5575i	−0.985675	+	1.70724i
$913$		0			0
$914$	−10.9693	−	18.9993i	−0.362831	−	0.628441i
$915$	4.05010	+	4.49809i	0.133892	+	0.148702i
$916$	−13.3251	+	9.68123i	−0.440273	+	0.319877i
$917$	10.6601	+	34.6477i	0.352028	+	1.14417i
$918$	−4.11764	−	12.6728i	−0.135902	−	0.418265i
$919$	−15.9800	−	3.39665i	−0.527131	−	0.112045i	−0.0633436	−	0.997992i	$-0.520176\pi$
$919$	−15.9800	−	3.39665i	−0.527131	−	0.112045i	−0.463787	+	0.885947i	$0.653510\pi$
$920$	0.167727	−	1.59582i	0.00552980	−	0.0526125i
$921$	−13.0855	−	5.82605i	−0.431183	−	0.191975i
$922$	15.3291	+	17.0247i	0.504838	+	0.560680i
$923$	7.73128			0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$	−15.1080	−	16.7792i	−0.496481	−	0.551398i
$927$	10.4421	+	4.64913i	0.342964	+	0.152697i
$928$	−7.19147	+	68.4223i	−0.236072	+	2.24607i
$929$	−8.70668	−	1.85066i	−0.285657	−	0.0607183i	0.0628547	−	0.998023i	$-0.479980\pi$
$929$	−8.70668	−	1.85066i	−0.285657	−	0.0607183i	−0.348512	+	0.937304i	$0.613313\pi$
$930$	−5.09316	−	15.6751i	−0.167011	−	0.514007i
$931$	−38.3261	+	6.89825i	−1.25609	+	0.226081i
$932$	−8.32555	+	6.04887i	−0.272713	+	0.198137i
$933$	−17.1103	−	19.0029i	−0.560167	−	0.622128i
$934$	30.0456	+	52.0405i	0.983122	+	1.70282i
$935$		0			0
$936$	−1.92585	+	3.33567i	−0.0629485	+	0.109030i
$937$	−13.9787	+	43.0220i	−0.456664	+	1.40547i	0.412506	+	0.910955i	$0.364653\pi$
$937$	−13.9787	+	43.0220i	−0.456664	+	1.40547i	−0.869170	+	0.494513i	$0.835347\pi$
$938$	−3.78263	−	6.79559i	−0.123507	−	0.221884i
$939$	−48.2008	−	35.0200i	−1.57298	−	1.14283i
$940$	−2.40408	−	0.511004i	−0.0784126	−	0.0166671i
$941$	4.63911	−	5.15226i	0.151231	−	0.167959i	−0.662769	−	0.748824i	$-0.730619\pi$
$941$	4.63911	−	5.15226i	0.151231	−	0.167959i	0.814000	+	0.580865i	$0.197286\pi$
$942$	3.34699	−	31.8444i	0.109051	−	1.03755i
$943$	1.70595	+	16.2310i	0.0555533	+	0.528554i
$944$	−17.7579	+	54.6531i	−0.577969	+	1.77881i
$945$	3.44668	+	2.58768i	0.112120	+	0.0841773i
$946$		0			0
$947$	−10.3716	+	17.9642i	−0.337033	+	0.583758i	−0.983873	−	0.178867i	$-0.942757\pi$
$947$	−10.3716	+	17.9642i	−0.337033	+	0.583758i	0.646840	+	0.762626i	$0.276090\pi$
$948$	−13.9733	+	2.97012i	−0.453832	+	0.0964650i
$949$	26.3185	+	11.7177i	0.854334	+	0.380374i
$950$	42.8444	−	19.0756i	1.39006	−	0.618893i
$951$	−2.62378	−	8.07516i	−0.0850819	−	0.261855i
$952$	5.74674	+	6.58723i	0.186253	+	0.213493i
$953$	16.3483	+	11.8777i	0.529574	+	0.384758i	0.820198	−	0.572079i	$-0.193863\pi$
$953$	16.3483	+	11.8777i	0.529574	+	0.384758i	−0.290625	+	0.956837i	$0.593863\pi$
$954$	2.62698	+	24.9941i	0.0850517	+	0.809213i
$955$	−6.92020	+	1.47093i	−0.223932	+	0.0475983i
$956$	−6.71735	−	11.6348i	−0.217254	−	0.376296i
$957$		0			0
$958$	47.6499			1.53950
$959$	−1.70912	−	19.1441i	−0.0551905	−	0.618195i
$960$	2.67302	−	1.94206i	0.0862715	−	0.0626799i
$961$	9.45426	−	4.20931i	0.304976	−	0.135784i
$962$	−13.4106	+	14.8940i	−0.432376	+	0.480202i
$963$	−13.6221	+	15.1289i	−0.438966	+	0.487521i
$964$	2.08790	−	0.929593i	0.0672467	−	0.0299402i
$965$	−1.85854	+	1.35031i	−0.0598284	+	0.0434679i
$966$	−18.9062	+	13.2883i	−0.608296	+	0.427544i
$967$	7.98254			0.256701			0.128351	−	0.991729i	$-0.459032\pi$
$967$	7.98254			0.256701			0.128351	+	0.991729i	$0.459032\pi$
$968$		0			0
$969$	17.3337	+	30.0229i	0.556839	+	0.964473i
$970$	2.96026	−	0.629222i	0.0950481	−	0.0202031i
$971$	1.44033	+	13.7038i	0.0462223	+	0.439776i	0.993020	+	0.117947i	$0.0376311\pi$
$971$	1.44033	+	13.7038i	0.0462223	+	0.439776i	−0.946798	+	0.321830i	$0.895702\pi$
$972$	−18.5451	−	13.4738i	−0.594835	−	0.432173i
$973$	−6.75702	+	1.32588i	−0.216620	+	0.0425057i
$974$	−8.23899	−	25.3570i	−0.263994	−	0.812491i
$975$	16.6291	−	7.40377i	0.532558	−	0.237110i
$976$	−19.2596	−	8.57492i	−0.616484	−	0.274477i
$977$	−11.7582	+	2.49929i	−0.376180	+	0.0799594i	−0.392121	−	0.919913i	$-0.628259\pi$
$977$	−11.7582	+	2.49929i	−0.376180	+	0.0799594i	0.0159418	+	0.999873i	$0.494925\pi$
$978$	32.2745	−	55.9010i	1.03202	−	1.78752i
$979$		0			0
$980$	5.89511	+	1.44761i	0.188312	+	0.0462423i
$981$	8.10771	−	24.9530i	0.258859	−	0.796686i
$982$	7.55327	+	71.8646i	0.241034	+	2.29329i
$983$	4.66765	−	44.4097i	0.148875	−	1.41645i	−0.623769	−	0.781609i	$-0.714399\pi$
$983$	4.66765	−	44.4097i	0.148875	−	1.41645i	0.772643	−	0.634840i	$-0.218934\pi$
$984$	12.9242	−	14.3538i	0.412009	−	0.457583i
$985$	−1.50338	−	0.319553i	−0.0479016	−	0.0101818i
$986$	43.8681	+	31.8721i	1.39705	+	1.01501i
$987$	−8.01879	−	14.4059i	−0.255241	−	0.458546i
$988$	4.22520	−	13.0038i	0.134422	−	0.413707i
$989$	−5.27056	+	9.12888i	−0.167594	+	0.290282i
$990$		0			0
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	0.988739	−	0.149650i	$-0.0478146\pi$
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	−0.623970	+	0.781448i	$0.714481\pi$
$992$	28.3811	+	31.5204i	0.901100	+	1.00077i
$993$	10.9400	−	7.94837i	0.347170	−	0.252234i
$994$	−6.12516	−	19.9081i	−0.194278	−	0.631446i
$995$	3.63258	+	11.1799i	0.115161	+	0.354428i
$996$	27.0897	+	5.75809i	0.858369	+	0.182452i
$997$	0.141006	−	1.34159i	0.00446572	−	0.0424884i	−0.992062	−	0.125749i	$-0.959867\pi$
$997$	0.141006	−	1.34159i	0.00446572	−	0.0424884i	0.996528	+	0.0832604i	$0.0265333\pi$
$998$	43.9536	+	19.5694i	1.39133	+	0.619458i
$999$	10.4034	+	11.5542i	0.329150	+	0.365558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.d.9.1		24
7.4	even	3	inner	847.2.n.d.130.3		24
11.2	odd	10		847.2.n.e.366.1		24
11.3	even	5	inner	847.2.n.d.807.1		24
11.4	even	5		847.2.e.d.485.3		6
11.5	even	5	inner	847.2.n.d.632.3		24
11.6	odd	10		847.2.n.e.632.1		24
11.7	odd	10		77.2.e.b.23.1	✓	6
11.8	odd	10		847.2.n.e.807.3		24
11.9	even	5	inner	847.2.n.d.366.3		24
11.10	odd	2		847.2.n.e.9.3		24
33.29	even	10		693.2.i.g.100.3		6
44.7	even	10		1232.2.q.k.177.1		6
77.4	even	15		847.2.e.d.606.3		6
77.18	odd	30		77.2.e.b.67.1	yes	6
77.25	even	15	inner	847.2.n.d.81.3		24
77.26	odd	30		5929.2.a.w.1.1		3
77.32	odd	6		847.2.n.e.130.1		24
77.37	even	15		5929.2.a.v.1.1		3
77.39	odd	30		847.2.n.e.753.3		24
77.40	even	30		539.2.a.i.1.3		3
77.46	odd	30		847.2.n.e.487.3		24
77.51	odd	30		539.2.a.h.1.3		3
77.53	even	15	inner	847.2.n.d.487.1		24
77.60	even	15	inner	847.2.n.d.753.1		24
77.62	even	10		539.2.e.l.177.1		6
77.73	even	30		539.2.e.l.67.1		6
77.74	odd	30		847.2.n.e.81.1		24
231.95	even	30		693.2.i.g.298.3		6
231.128	even	30		4851.2.a.bo.1.1		3
231.194	odd	30		4851.2.a.bn.1.1		3
308.51	even	30		8624.2.a.cl.1.3		3
308.95	even	30		1232.2.q.k.529.1		6
308.271	odd	30		8624.2.a.ck.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	11.7	odd	10
77.2.e.b.67.1	yes	6	77.18	odd	30
539.2.a.h.1.3		3	77.51	odd	30
539.2.a.i.1.3		3	77.40	even	30
539.2.e.l.67.1		6	77.73	even	30
539.2.e.l.177.1		6	77.62	even	10
693.2.i.g.100.3		6	33.29	even	10
693.2.i.g.298.3		6	231.95	even	30
847.2.e.d.485.3		6	11.4	even	5
847.2.e.d.606.3		6	77.4	even	15
847.2.n.d.9.1		24	1.1	even	1	trivial
847.2.n.d.81.3		24	77.25	even	15	inner
847.2.n.d.130.3		24	7.4	even	3	inner
847.2.n.d.366.3		24	11.9	even	5	inner
847.2.n.d.487.1		24	77.53	even	15	inner
847.2.n.d.632.3		24	11.5	even	5	inner
847.2.n.d.753.1		24	77.60	even	15	inner
847.2.n.d.807.1		24	11.3	even	5	inner
847.2.n.e.9.3		24	11.10	odd	2
847.2.n.e.81.1		24	77.74	odd	30
847.2.n.e.130.1		24	77.32	odd	6
847.2.n.e.366.1		24	11.2	odd	10
847.2.n.e.487.3		24	77.46	odd	30
847.2.n.e.632.1		24	11.6	odd	10
847.2.n.e.753.3		24	77.39	odd	30
847.2.n.e.807.3		24	11.8	odd	10
1232.2.q.k.177.1		6	44.7	even	10
1232.2.q.k.529.1		6	308.95	even	30
4851.2.a.bn.1.1		3	231.194	odd	30
4851.2.a.bo.1.1		3	231.128	even	30
5929.2.a.v.1.1		3	77.37	even	15
5929.2.a.w.1.1		3	77.26	odd	30
8624.2.a.ck.1.1		3	308.271	odd	30
8624.2.a.cl.1.3		3	308.51	even	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22735 - 1.36311i) q^{2} +(-2.00860 - 0.894288i) q^{3} +(-0.142624 + 1.35697i) q^{4} +(0.621664 + 0.132139i) q^{5} +(1.24625 + 3.83555i) q^{6} +(1.80096 - 1.93818i) q^{7} +(-0.943117 + 0.685215i) q^{8} +(1.22735 + 1.36311i) q^{9} +(-0.582878 - 1.00958i) q^{10} +(1.50000 - 2.59808i) q^{12} +(0.556635 - 1.71315i) q^{13} +(-4.85235 - 0.0760860i) q^{14} +(-1.13051 - 0.821361i) q^{15} +(4.76082 + 1.01194i) q^{16} +(1.89648 - 2.10625i) q^{17} +(0.351681 - 3.34602i) q^{18} +(-0.581506 - 5.53266i) q^{19} +(-0.267973 + 0.824735i) q^{20} +(-5.35071 + 2.28245i) q^{21} +(-1.08288 + 1.87560i) q^{23} +(2.50713 - 0.532907i) q^{24} +(-4.19872 - 1.86939i) q^{25} +(-3.01839 + 1.34387i) q^{26} +(0.792054 + 2.43769i) q^{27} +(2.37320 + 2.72029i) q^{28} +(-8.43830 - 6.13079i) q^{29} +(0.267921 + 2.54910i) q^{30} +(-6.28980 + 1.33694i) q^{31} +(-3.29804 - 5.71237i) q^{32} -5.19869 q^{34} +(1.37570 - 0.966918i) q^{35} +(-2.02475 + 1.47107i) q^{36} +(5.54145 - 2.46721i) q^{37} +(-6.82791 + 7.58316i) q^{38} +(-2.65011 + 2.94324i) q^{39} +(-0.676845 + 0.301351i) q^{40} +(6.09648 - 4.42935i) q^{41} +(9.67842 + 4.49223i) q^{42} +4.86718 q^{43} +(0.582878 + 1.00958i) q^{45} +(3.88572 - 0.825934i) q^{46} +(0.296259 + 2.81872i) q^{47} +(-8.65763 - 6.29014i) q^{48} +(-0.513073 - 6.98117i) q^{49} +(2.60511 + 8.01771i) q^{50} +(-5.69287 + 2.53463i) q^{51} +(2.24530 + 0.999674i) q^{52} +(-7.30656 + 1.55306i) q^{53} +(2.35071 - 4.07155i) q^{54} +(-0.370450 + 3.06197i) q^{56} +(-3.77978 + 11.6330i) q^{57} +(1.99981 + 19.0269i) q^{58} +(-1.23414 + 11.7421i) q^{59} +(1.27580 - 1.41692i) q^{60} +(-4.23686 - 0.900572i) q^{61} +(9.54217 + 6.93279i) q^{62} +(4.85235 + 0.0760860i) q^{63} +(-0.730655 + 2.24872i) q^{64} +(0.572413 - 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(2.58765 + 2.87387i) q^{68} +(3.85240 - 2.79893i) q^{69} +(-3.00648 - 0.688484i) q^{70} +(1.32631 + 4.08197i) q^{71} +(-2.09155 - 0.444574i) q^{72} +(-1.67177 + 15.9058i) q^{73} +(-10.1644 - 4.52547i) q^{74} +(6.76180 + 7.50974i) q^{75} +7.59061 q^{76} +7.26456 q^{78} +(-3.18629 - 3.53873i) q^{79} +(2.82591 + 1.25818i) q^{80} +(1.16427 - 11.0773i) q^{81} +(-13.5202 - 2.87381i) q^{82} +(2.85273 + 8.77980i) q^{83} +(-2.33409 - 7.58630i) q^{84} +(1.45729 - 1.05878i) q^{85} +(-5.97372 - 6.63449i) q^{86} +(11.4665 + 19.8606i) q^{87} +(-0.182224 + 0.315621i) q^{89} +(0.660765 - 2.03363i) q^{90} +(-2.31791 - 4.16417i) q^{91} +(-2.39070 - 1.73694i) q^{92} +(13.8293 + 2.93951i) q^{93} +(3.47860 - 3.86338i) q^{94} +(0.369578 - 3.51630i) q^{95} +(1.51595 + 14.4233i) q^{96} +(-0.802231 + 2.46901i) q^{97} +(-8.88637 + 9.26770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 18 q^{8} - 36 q^{10} + 36 q^{12} - 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} - 28 q^{20} - 40 q^{21} - 48 q^{23}+ \cdots + 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 18 * q^8 - 36 * q^10 + 36 * q^12 - 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 - 28 * q^20 - 40 * q^21 - 48 * q^23 - 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 + 13 * q^28 - 18 * q^29 - 2 * q^30 - 3 * q^31 - 12 * q^32 - 80 * q^34 + 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 - 10 * q^41 + 2 * q^42 - 16 * q^43 + 36 * q^45 + 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 - 6 * q^50 - 2 * q^51 + 7 * q^52 + 17 * q^53 - 32 * q^54 + 12 * q^56 + 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 + 24 * q^61 + 26 * q^62 + 12 * q^63 + 14 * q^64 + 60 * q^65 + 64 * q^67 - 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 + 25 * q^75 + 312 * q^76 - 48 * q^78 - 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 - 22 * q^83 + 12 * q^84 + 22 * q^85 - 21 * q^86 + 120 * q^87 - 4 * q^89 + 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 - 18 * q^97 + 96 * q^98

Introduction

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