LMFDB - Embedded newform 605.2.m.e.403.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] 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("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,10,-4,0,-2,20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			403.3
Character	$\chi$	$=$	605.403
Dual form			605.2.m.e.602.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0763931 + 0.482327i) q^{2} +(-1.01518 + 0.517260i) q^{3} +(1.67531 - 0.544341i) q^{4} +(1.47656 - 1.67922i) q^{5} +(-0.327041 - 0.450133i) q^{6} +(1.32402 - 2.59854i) q^{7} +(0.833936 + 1.63669i) q^{8} +(-1.00032 + 1.37683i) q^{9} +(0.922733 + 0.583903i) q^{10} +(-1.41917 + 1.41917i) q^{12} +(2.89049 - 0.457808i) q^{13} +(1.35449 + 0.440102i) q^{14} +(-0.630376 + 2.46847i) q^{15} +(2.12449 - 1.54353i) q^{16} +(-5.20325 - 0.824113i) q^{17} +(-0.740500 - 0.377304i) q^{18} +(1.26677 - 3.89873i) q^{19} +(1.55962 - 3.61696i) q^{20} +3.32285i q^{21} +(-2.12046 - 2.12046i) q^{23} +(-1.69319 - 1.23017i) q^{24} +(-0.639563 - 4.95893i) q^{25} +(0.441627 + 1.35919i) q^{26} +(0.838037 - 5.29116i) q^{27} +(0.803656 - 5.07408i) q^{28} +(0.817241 + 2.51521i) q^{29} +(-1.23877 - 0.115473i) q^{30} +(5.45328 + 3.96204i) q^{31} +(3.50456 + 3.50456i) q^{32} -2.57262i q^{34} +(-2.40853 - 6.06022i) q^{35} +(-0.926389 + 2.85113i) q^{36} +(1.03649 + 0.528116i) q^{37} +(1.97724 + 0.313163i) q^{38} +(-2.69755 + 1.95989i) q^{39} +(3.97972 + 1.01630i) q^{40} +(3.38136 + 1.09867i) q^{41} +(-1.60270 + 0.253843i) q^{42} +(-5.07292 + 5.07292i) q^{43} +(0.834964 + 3.71273i) q^{45} +(0.860769 - 1.18475i) q^{46} +(1.67145 + 3.28041i) q^{47} +(-1.35833 + 2.66588i) q^{48} +(-0.884888 - 1.21794i) q^{49} +(2.34297 - 0.687307i) q^{50} +(5.70851 - 1.85481i) q^{51} +(4.59325 - 2.34038i) q^{52} +(-0.231169 - 1.45955i) q^{53} +2.61609 q^{54} +5.35716 q^{56} +(0.730652 + 4.61316i) q^{57} +(-1.15072 + 0.586323i) q^{58} +(1.52672 - 0.496061i) q^{59} +(0.287615 + 4.47859i) q^{60} +(4.07810 + 5.61302i) q^{61} +(-1.49441 + 2.93294i) q^{62} +(2.25330 + 4.42234i) q^{63} +(1.66445 - 2.29092i) q^{64} +(3.49920 - 5.52974i) q^{65} +(1.31471 - 1.31471i) q^{67} +(-9.16564 + 1.45170i) q^{68} +(3.24948 + 1.05582i) q^{69} +(2.73902 - 1.62466i) q^{70} +(-2.32441 + 1.68878i) q^{71} +(-3.08765 - 0.489036i) q^{72} +(-13.1886 - 6.71992i) q^{73} +(-0.175544 + 0.540270i) q^{74} +(3.21432 + 4.70338i) q^{75} -7.22113i q^{76} +(-1.15138 - 1.15138i) q^{78} +(12.3342 + 8.96129i) q^{79} +(0.544999 - 5.84661i) q^{80} +(0.308439 + 0.949277i) q^{81} +(-0.271606 + 1.71486i) q^{82} +(1.04540 - 6.60041i) q^{83} +(1.80876 + 5.56680i) q^{84} +(-9.06675 + 7.52055i) q^{85} +(-2.83434 - 2.05927i) q^{86} +(-2.13066 - 2.13066i) q^{87} +11.1726i q^{89} +(-1.72697 + 0.686353i) q^{90} +(2.63744 - 8.11720i) q^{91} +(-4.70669 - 2.39818i) q^{92} +(-7.58545 - 1.20142i) q^{93} +(-1.45454 + 1.05679i) q^{94} +(-4.67636 - 7.88388i) q^{95} +(-5.37052 - 1.74499i) q^{96} +(-9.94447 + 1.57505i) q^{97} +(0.519848 - 0.519848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8} + 12 q^{12} + 10 q^{13} + 14 q^{15} - 8 q^{16} + 10 q^{18} + 16 q^{20} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} - 50 q^{28} - 30 q^{30} - 28 q^{31}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 - 4 * q^3 - 2 * q^5 + 20 * q^6 + 10 * q^8 + 12 * q^12 + 10 * q^13 + 14 * q^15 - 8 * q^16 + 10 * q^18 + 16 * q^20 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 - 50 * q^28 - 30 * q^30 - 28 * q^31 + 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 40 * q^41 - 10 * q^42 - 28 * q^45 - 60 * q^46 - 28 * q^47 - 54 * q^48 + 50 * q^50 - 20 * q^51 + 50 * q^52 - 24 * q^53 - 80 * q^56 - 30 * q^57 - 50 * q^58 + 34 * q^60 + 60 * q^61 - 100 * q^62 + 30 * q^63 - 8 * q^67 + 30 * q^68 + 30 * q^70 + 24 * q^71 - 80 * q^72 - 50 * q^73 + 34 * q^75 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 - 90 * q^83 - 30 * q^85 + 100 * q^86 + 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.0763931	+	0.482327i	0.0540181	+	0.341057i	0.999865	+	0.0164432i	$0.00523428\pi$
$2$	0.0763931	+	0.482327i	0.0540181	+	0.341057i	−0.945847	+	0.324614i	$0.894766\pi$
$3$	−1.01518	+	0.517260i	−0.586114	+	0.298640i	−0.721789	−	0.692114i	$-0.756680\pi$
$3$	−1.01518	+	0.517260i	−0.586114	+	0.298640i	0.135675	+	0.990753i	$0.456680\pi$
$4$	1.67531	−	0.544341i	0.837655	−	0.272170i
$5$	1.47656	−	1.67922i	0.660336	−	0.750970i
$5$	1.47656	−	1.67922i	0.660336	−	0.750970i
$6$	−0.327041	−	0.450133i	−0.133514	−	0.183766i
$7$	1.32402	−	2.59854i	0.500434	−	0.982157i	−0.493244	−	0.869891i	$-0.664189\pi$
$7$	1.32402	−	2.59854i	0.500434	−	0.982157i	0.993678	−	0.112266i	$-0.0358109\pi$
$8$	0.833936	+	1.63669i	0.294841	+	0.578658i
$9$	−1.00032	+	1.37683i	−0.333442	+	0.458943i
$10$	0.922733	+	0.583903i	0.291794	+	0.184646i
$11$		0			0
$11$		0			0
$12$	−1.41917	+	1.41917i	−0.409680	+	0.409680i
$13$	2.89049	−	0.457808i	0.801677	−	0.126973i	0.257866	−	0.966181i	$-0.416981\pi$
$13$	2.89049	−	0.457808i	0.801677	−	0.126973i	0.543811	+	0.839208i	$0.316981\pi$
$14$	1.35449	+	0.440102i	0.362004	+	0.117622i
$15$	−0.630376	+	2.46847i	−0.162762	+	0.637357i
$16$	2.12449	−	1.54353i	0.531123	−	0.385884i
$17$	−5.20325	−	0.824113i	−1.26197	−	0.199877i	−0.510636	−	0.859797i	$-0.670590\pi$
$17$	−5.20325	−	0.824113i	−1.26197	−	0.199877i	−0.751336	+	0.659920i	$0.770590\pi$
$18$	−0.740500	−	0.377304i	−0.174538	−	0.0889313i
$19$	1.26677	−	3.89873i	0.290618	−	0.894429i	−0.694041	−	0.719936i	$-0.744171\pi$
$19$	1.26677	−	3.89873i	0.290618	−	0.894429i	0.984658	−	0.174494i	$-0.0558288\pi$
$20$	1.55962	−	3.61696i	0.348742	−	0.808778i
$21$			3.32285i			0.725105i
$22$		0			0
$23$	−2.12046	−	2.12046i	−0.442147	−	0.442147i	0.450586	−	0.892733i	$-0.351215\pi$
$23$	−2.12046	−	2.12046i	−0.442147	−	0.442147i	−0.892733	+	0.450586i	$0.851215\pi$
$24$	−1.69319	−	1.23017i	−0.345621	−	0.251108i
$25$	−0.639563	−	4.95893i	−0.127913	−	0.991785i
$26$	0.441627	+	1.35919i	0.0866101	+	0.266558i
$27$	0.838037	−	5.29116i	0.161280	−	1.01828i
$28$	0.803656	−	5.07408i	0.151877	−	0.958912i
$29$	0.817241	+	2.51521i	0.151758	+	0.467063i	0.997818	−	0.0660248i	$-0.0210316\pi$
$29$	0.817241	+	2.51521i	0.151758	+	0.467063i	−0.846060	+	0.533088i	$0.821032\pi$
$30$	−1.23877	−	0.115473i	−0.226167	−	0.0210824i
$31$	5.45328	+	3.96204i	0.979438	+	0.711603i	0.957583	−	0.288158i	$-0.0930429\pi$
$31$	5.45328	+	3.96204i	0.979438	+	0.711603i	0.0218548	+	0.999761i	$0.493043\pi$
$32$	3.50456	+	3.50456i	0.619524	+	0.619524i
$33$		0			0
$34$		−	2.57262i		−	0.441201i
$35$	−2.40853	−	6.06022i	−0.407116	−	1.02436i
$36$	−0.926389	+	2.85113i	−0.154398	+	0.475189i
$37$	1.03649	+	0.528116i	0.170397	+	0.0868218i	0.537109	−	0.843513i	$-0.319516\pi$
$37$	1.03649	+	0.528116i	0.170397	+	0.0868218i	−0.366712	+	0.930335i	$0.619516\pi$
$38$	1.97724	+	0.313163i	0.320750	+	0.0508018i
$39$	−2.69755	+	1.95989i	−0.431954	+	0.313833i
$40$	3.97972	+	1.01630i	0.629249	+	0.160692i
$41$	3.38136	+	1.09867i	0.528080	+	0.171584i	0.560909	−	0.827877i	$-0.310452\pi$
$41$	3.38136	+	1.09867i	0.528080	+	0.171584i	−0.0328289	+	0.999461i	$0.510452\pi$
$42$	−1.60270	+	0.253843i	−0.247302	+	0.0391688i
$43$	−5.07292	+	5.07292i	−0.773613	+	0.773613i	−0.978736	−	0.205123i	$-0.934241\pi$
$43$	−5.07292	+	5.07292i	−0.773613	+	0.773613i	0.205123	+	0.978736i	$0.434241\pi$
$44$		0			0
$45$	0.834964	+	3.71273i	0.124469	+	0.553461i
$46$	0.860769	−	1.18475i	0.126913	−	0.174681i
$47$	1.67145	+	3.28041i	0.243806	+	0.478497i	0.980188	−	0.198070i	$-0.0634672\pi$
$47$	1.67145	+	3.28041i	0.243806	+	0.478497i	−0.736382	+	0.676566i	$0.763467\pi$
$48$	−1.35833	+	2.66588i	−0.196058	+	0.384786i
$49$	−0.884888	−	1.21794i	−0.126413	−	0.173992i
$50$	2.34297	−	0.687307i	0.331346	−	0.0971998i
$51$	5.70851	−	1.85481i	0.799351	−	0.259725i
$52$	4.59325	−	2.34038i	0.636970	−	0.324552i
$53$	−0.231169	−	1.45955i	−0.0317536	−	0.200484i	0.966712	−	0.255869i	$-0.0823615\pi$
$53$	−0.231169	−	1.45955i	−0.0317536	−	0.200484i	−0.998465	+	0.0553847i	$0.982361\pi$
$54$	2.61609			0.356005
$55$		0			0
$56$	5.35716			0.715881
$57$	0.730652	+	4.61316i	0.0967773	+	0.611028i
$58$	−1.15072	+	0.586323i	−0.151097	+	0.0769879i
$59$	1.52672	−	0.496061i	0.198762	−	0.0645817i	−0.207944	−	0.978141i	$-0.566677\pi$
$59$	1.52672	−	0.496061i	0.198762	−	0.0645817i	0.406706	+	0.913559i	$0.366677\pi$
$60$	0.287615	+	4.47859i	0.0371310	+	0.578184i
$61$	4.07810	+	5.61302i	0.522147	+	0.718674i	0.985908	−	0.167286i	$-0.0535004\pi$
$61$	4.07810	+	5.61302i	0.522147	+	0.718674i	−0.463761	+	0.885960i	$0.653500\pi$
$62$	−1.49441	+	2.93294i	−0.189790	+	0.372483i
$63$	2.25330	+	4.42234i	0.283889	+	0.557163i
$64$	1.66445	−	2.29092i	0.208056	−	0.286365i
$65$	3.49920	−	5.52974i	0.434023	−	0.685880i
$66$		0			0
$67$	1.31471	−	1.31471i	0.160617	−	0.160617i	−0.622223	−	0.782840i	$-0.713770\pi$
$67$	1.31471	−	1.31471i	0.160617	−	0.160617i	0.782840	+	0.622223i	$0.213770\pi$
$68$	−9.16564	+	1.45170i	−1.11150	+	0.176044i
$69$	3.24948	+	1.05582i	0.391192	+	0.127106i
$70$	2.73902	−	1.62466i	0.327375	−	0.194184i
$71$	−2.32441	+	1.68878i	−0.275857	+	0.200422i	−0.717108	−	0.696962i	$-0.754535\pi$
$71$	−2.32441	+	1.68878i	−0.275857	+	0.200422i	0.441251	+	0.897384i	$0.354535\pi$
$72$	−3.08765	−	0.489036i	−0.363883	−	0.0576334i
$73$	−13.1886	−	6.71992i	−1.54361	−	0.786507i	−0.544957	−	0.838464i	$-0.683454\pi$
$73$	−13.1886	−	6.71992i	−1.54361	−	0.786507i	−0.998649	+	0.0519568i	$0.983454\pi$
$74$	−0.175544	+	0.540270i	−0.0204066	+	0.0628051i
$75$	3.21432	+	4.70338i	0.371158	+	0.543099i
$76$		−	7.22113i		−	0.828321i
$77$		0			0
$78$	−1.15138	−	1.15138i	−0.130368	−	0.130368i
$79$	12.3342	+	8.96129i	1.38770	+	1.00822i	0.996113	+	0.0880839i	$0.0280744\pi$
$79$	12.3342	+	8.96129i	1.38770	+	1.00822i	0.391589	+	0.920140i	$0.371926\pi$
$80$	0.544999	−	5.84661i	0.0609327	−	0.653671i
$81$	0.308439	+	0.949277i	0.0342710	+	0.105475i
$82$	−0.271606	+	1.71486i	−0.0299939	+	0.189374i
$83$	1.04540	−	6.60041i	0.114748	−	0.724489i	−0.861488	−	0.507778i	$-0.830467\pi$
$83$	1.04540	−	6.60041i	0.114748	−	0.724489i	0.976236	−	0.216711i	$-0.0695329\pi$
$84$	1.80876	+	5.56680i	0.197352	+	0.607388i
$85$	−9.06675	+	7.52055i	−0.983427	+	0.815718i
$86$	−2.83434	−	2.05927i	−0.305635	−	0.222057i
$87$	−2.13066	−	2.13066i	−0.228431	−	0.228431i
$88$		0			0
$89$			11.1726i			1.18429i	0.805830	+	0.592147i	$0.201719\pi$
$89$			11.1726i			1.18429i	−0.805830	+	0.592147i	$0.798281\pi$
$90$	−1.72697	+	0.686353i	−0.182038	+	0.0723480i
$91$	2.63744	−	8.11720i	0.276479	−	0.850914i
$92$	−4.70669	−	2.39818i	−0.490706	−	0.250027i
$93$	−7.58545	−	1.20142i	−0.786575	−	0.124581i
$94$	−1.45454	+	1.05679i	−0.150025	+	0.108999i
$95$	−4.67636	−	7.88388i	−0.479784	−	0.808869i
$96$	−5.37052	−	1.74499i	−0.548126	−	0.178097i
$97$	−9.94447	+	1.57505i	−1.00971	+	0.159922i	−0.639308	−	0.768951i	$-0.720779\pi$
$97$	−9.94447	+	1.57505i	−1.00971	+	0.159922i	−0.370400	+	0.928873i	$0.620779\pi$
$98$	0.519848	−	0.519848i	0.0525126	−	0.0525126i
$99$		0			0
$100$	−3.77081	−	7.95960i	−0.377081	−	0.795960i
$101$	1.12216	−	1.54452i	0.111659	−	0.153686i	−0.749530	−	0.661971i	$-0.769720\pi$
$101$	1.12216	−	1.54452i	0.111659	−	0.153686i	0.861189	+	0.508285i	$0.169720\pi$
$102$	1.33071	+	2.61167i	0.131760	+	0.258594i
$103$	2.80172	−	5.49869i	0.276062	−	0.541802i	−0.710795	−	0.703399i	$-0.751665\pi$
$103$	2.80172	−	5.49869i	0.276062	−	0.541802i	0.986857	+	0.161597i	$0.0516646\pi$
$104$	3.15977	+	4.34905i	0.309841	+	0.426459i
$105$	5.57980	+	4.90637i	0.544532	+	0.478813i
$106$	0.686319	−	0.222999i	0.0666612	−	0.0216595i
$107$	−0.388059	+	0.197726i	−0.0375151	+	0.0191149i	−0.472647	−	0.881252i	$-0.656702\pi$
$107$	−0.388059	+	0.197726i	−0.0375151	+	0.0191149i	0.435132	+	0.900367i	$0.356702\pi$
$108$	−1.47622	−	9.32051i	−0.142050	−	0.896866i
$109$	−9.46672			−0.906748			−0.453374	−	0.891320i	$-0.649780\pi$
$109$	−9.46672			−0.906748			−0.453374	+	0.891320i	$0.649780\pi$
$110$		0			0
$111$	−1.32539			−0.125801
$112$	−1.19806	−	7.56426i	−0.113206	−	0.714755i
$113$	−18.0576	+	9.20080i	−1.69871	+	0.865538i	−0.712178	+	0.701999i	$0.752291\pi$
$113$	−18.0576	+	9.20080i	−1.69871	+	0.865538i	−0.986537	+	0.163539i	$0.947709\pi$
$114$	−2.16923	+	0.704827i	−0.203167	+	0.0660131i
$115$	−6.69171	+	0.429742i	−0.624006	+	0.0400737i
$116$	2.73826	+	3.76890i	0.254241	+	0.349933i
$117$	−2.26110	+	4.43766i	−0.209039	+	0.410262i
$118$	0.355895	+	0.698483i	0.0327628	+	0.0643005i
$119$	−9.03071	+	12.4297i	−0.827844	+	1.13943i
$120$	−4.56582	+	1.02682i	−0.416800	+	0.0937351i
$121$		0			0
$122$	−2.39578	+	2.39578i	−0.216903	+	0.216903i
$123$	−4.00099	+	0.633694i	−0.360757	+	0.0571383i
$124$	11.2926	+	3.66920i	1.01411	+	0.329504i
$125$	−9.27148	−	6.24817i	−0.829267	−	0.558853i
$126$	−1.96088	+	1.42466i	−0.174689	+	0.126919i
$127$	9.31359	+	1.47513i	0.826447	+	0.130896i	0.555309	−	0.831644i	$-0.312600\pi$
$127$	9.31359	+	1.47513i	0.826447	+	0.130896i	0.271138	+	0.962540i	$0.412600\pi$
$128$	10.0641	+	5.12793i	0.889551	+	0.453249i
$129$	2.52591	−	7.77394i	0.222394	−	0.684457i
$130$	2.93446	+	1.26533i	0.257369	+	0.110977i
$131$		−	7.51676i		−	0.656743i	−0.944549	−	0.328371i	$-0.893500\pi$
$131$		−	7.51676i		−	0.656743i	0.944549	−	0.328371i	$-0.106500\pi$
$132$		0			0
$133$	−8.45377	−	8.45377i	−0.733035	−	0.733035i
$134$	0.734554	+	0.533685i	0.0634558	+	0.0461034i
$135$	−7.64761	−	9.21994i	−0.658202	−	0.793526i
$136$	−2.99035	−	9.20336i	−0.256421	−	0.789182i
$137$	−2.40429	+	15.1801i	−0.205413	+	1.29692i	0.642294	+	0.766458i	$0.277983\pi$
$137$	−2.40429	+	15.1801i	−0.205413	+	1.29692i	−0.847706	+	0.530466i	$0.822017\pi$
$138$	−0.261013	+	1.64797i	−0.0222189	+	0.140285i
$139$	1.28625	+	3.95867i	0.109098	+	0.335770i	0.990670	−	0.136279i	$-0.0435145\pi$
$139$	1.28625	+	3.95867i	0.109098	+	0.335770i	−0.881572	+	0.472049i	$0.843514\pi$
$140$	−7.33386	−	8.84168i	−0.619824	−	0.747259i
$141$	−3.39364	−	2.46563i	−0.285796	−	0.207643i
$142$	−0.992116	−	0.992116i	−0.0832565	−	0.0832565i
$143$		0			0
$144$			4.46910i			0.372425i
$145$	5.43029	+	2.34152i	0.450961	+	0.194453i
$146$	2.23368	−	6.87457i	0.184861	−	0.568943i
$147$	1.52831	+	0.778714i	0.126053	+	0.0642273i
$148$	2.02391	+	0.320556i	0.166364	+	0.0263495i
$149$	−14.5440	+	10.5669i	−1.19149	+	0.865672i	−0.993421	−	0.114516i	$-0.963468\pi$
$149$	−14.5440	+	10.5669i	−1.19149	+	0.865672i	−0.198073	+	0.980187i	$0.563468\pi$
$150$	−2.02302	+	1.90966i	−0.165179	+	0.155923i
$151$	−16.9214	−	5.49808i	−1.37704	−	0.447427i	−0.475345	−	0.879800i	$-0.657677\pi$
$151$	−16.9214	−	5.49808i	−1.37704	−	0.447427i	−0.901695	+	0.432372i	$0.857677\pi$
$152$	7.43742	−	1.17797i	0.603254	−	0.0955461i
$153$	6.33960	−	6.33960i	0.512526	−	0.512526i
$154$		0			0
$155$	14.7052	−	3.30708i	1.18115	−	0.265631i
$156$	−3.45239	+	4.75181i	−0.276413	+	0.380449i
$157$	9.74483	+	19.1253i	0.777722	+	1.52636i	0.848693	+	0.528887i	$0.177390\pi$
$157$	9.74483	+	19.1253i	0.777722	+	1.52636i	−0.0709708	+	0.997478i	$0.522610\pi$
$158$	−3.38003	+	6.63368i	−0.268901	+	0.527748i
$159$	0.989642	+	1.36213i	0.0784837	+	0.108024i
$160$	11.0596	−	0.710248i	0.874338	−	0.0561500i
$161$	−8.31766	+	2.70257i	−0.655524	+	0.212993i
$162$	−0.434300	+	0.221287i	−0.0341218	+	0.0173859i
$163$	−1.63083	−	10.2967i	−0.127737	−	0.806497i	−0.965488	−	0.260446i	$-0.916130\pi$
$163$	−1.63083	−	10.2967i	−0.127737	−	0.806497i	0.837752	−	0.546051i	$-0.183870\pi$
$164$	6.26288			0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	1.76660	+	11.1538i	0.136703	+	0.863110i	0.956771	+	0.290843i	$0.0939359\pi$
$167$	1.76660	+	11.1538i	0.136703	+	0.863110i	−0.820067	+	0.572267i	$0.806064\pi$
$168$	−5.43848	+	2.77104i	−0.419588	+	0.213791i
$169$	−4.21842	+	1.37065i	−0.324493	+	0.105434i
$170$	−4.32000	−	3.79862i	−0.331329	−	0.291341i
$171$	4.10070	+	5.64412i	0.313588	+	0.431617i
$172$	−5.73731	+	11.2601i	−0.437466	+	0.858575i
$173$	5.99367	+	11.7632i	0.455691	+	0.894343i	0.998514	+	0.0544963i	$0.0173553\pi$
$173$	5.99367	+	11.7632i	0.455691	+	0.894343i	−0.542823	+	0.839847i	$0.682645\pi$
$174$	0.864909	−	1.19044i	0.0655686	−	0.0902474i
$175$	−13.7328	−	4.90381i	−1.03810	−	0.370693i
$176$		0			0
$177$	−1.29330	+	1.29330i	−0.0972104	+	0.0972104i
$178$	−5.38885	+	0.853510i	−0.403912	+	0.0639733i
$179$	−2.11776	−	0.688100i	−0.158288	−	0.0514310i	0.228801	−	0.973473i	$-0.426520\pi$
$179$	−2.11776	−	0.688100i	−0.158288	−	0.0514310i	−0.387089	+	0.922042i	$0.626520\pi$
$180$	3.41981	+	5.76547i	0.254898	+	0.429733i
$181$	−3.50687	+	2.54789i	−0.260664	+	0.189383i	−0.710440	−	0.703758i	$-0.751504\pi$
$181$	−3.50687	+	2.54789i	−0.260664	+	0.189383i	0.449776	+	0.893141i	$0.351504\pi$
$182$	4.11663	+	0.652010i	0.305145	+	0.0483302i
$183$	−7.04339	−	3.58879i	−0.520663	−	0.265291i
$184$	1.70221	−	5.23888i	0.125489	−	0.386215i
$185$	2.41725	−	0.960696i	0.177720	−	0.0706318i
$186$		−	3.75045i		−	0.274996i
$187$		0			0
$188$	4.58586	+	4.58586i	0.334458	+	0.334458i
$189$	−12.6397	−	9.18329i	−0.919404	−	0.667986i
$190$	3.44537	−	2.85781i	0.249953	−	0.207327i
$191$	−1.26010	−	3.87820i	−0.0911779	−	0.280617i	0.895061	−	0.445944i	$-0.147132\pi$
$191$	−1.26010	−	3.87820i	−0.0911779	−	0.280617i	−0.986239	+	0.165327i	$0.947132\pi$
$192$	−0.504715	+	3.18664i	−0.0364247	+	0.229976i
$193$	3.26960	−	20.6434i	0.235351	−	1.48595i	−0.533108	−	0.846047i	$-0.678976\pi$
$193$	3.26960	−	20.6434i	0.235351	−	1.48595i	0.768459	−	0.639899i	$-0.221024\pi$
$194$	−1.51938	−	4.67617i	−0.109085	−	0.335729i
$195$	−0.692007	+	7.42367i	−0.0495557	+	0.531620i
$196$	−2.14544	−	1.55875i	−0.153246	−	0.111339i
$197$	−0.213782	−	0.213782i	−0.0152313	−	0.0152313i	0.699450	−	0.714681i	$-0.253428\pi$
$197$	−0.213782	−	0.213782i	−0.0152313	−	0.0152313i	−0.714681	+	0.699450i	$0.753428\pi$
$198$		0			0
$199$		−	11.0815i		−	0.785549i	−0.919635	−	0.392775i	$-0.871515\pi$
$199$		−	11.0815i		−	0.785549i	0.919635	−	0.392775i	$-0.128485\pi$
$200$	7.58288	−	5.18219i	0.536190	−	0.366436i
$201$	−0.654619	+	2.01471i	−0.0461733	+	0.142107i
$202$	0.830691	+	0.423258i	0.0584472	+	0.0297803i
$203$	7.61793	+	1.20656i	0.534674	+	0.0846840i
$204$	8.55387	−	6.21475i	0.598890	−	0.435119i
$205$	6.83769	−	4.05581i	0.477565	−	0.283270i
$206$	2.86620	+	0.931285i	0.199698	+	0.0648857i
$207$	5.04067	−	0.798364i	0.350351	−	0.0554901i
$208$	5.43417	−	5.43417i	0.376792	−	0.376792i
$209$		0			0
$210$	−1.94022	+	3.06610i	−0.133888	+	0.211581i
$211$	5.20512	−	7.16423i	0.358335	−	0.493206i	−0.591349	−	0.806416i	$-0.701404\pi$
$211$	5.20512	−	7.16423i	0.358335	−	0.493206i	0.949684	+	0.313210i	$0.101404\pi$
$212$	−1.18177	−	2.31936i	−0.0811644	−	0.159294i
$213$	1.48615	−	2.91674i	0.101830	−	0.199852i
$214$	−0.125014	−	0.172067i	−0.00854576	−	0.0117622i
$215$	1.02810	+	16.0090i	0.0701158	+	1.09181i
$216$	9.35886	−	3.04088i	0.636790	−	0.206906i
$217$	17.5158	−	8.92474i	1.18905	−	0.605851i
$218$	−0.723193	−	4.56606i	−0.0489808	−	0.309253i
$219$	16.8647			1.13961
$220$		0			0
$221$	−15.4172			−1.03707
$222$	−0.101251	−	0.639273i	−0.00679551	−	0.0429052i
$223$	5.50839	−	2.80667i	0.368869	−	0.187948i	−0.259723	−	0.965683i	$-0.583631\pi$
$223$	5.50839	−	2.80667i	0.368869	−	0.187948i	0.628593	+	0.777735i	$0.283631\pi$
$224$	13.7469	−	4.46662i	0.918500	−	0.298439i
$225$	7.46737	+	4.07997i	0.497824	+	0.271998i
$226$	−5.81727	−	8.00679i	−0.386959	−	0.532604i
$227$	1.50576	−	2.95522i	0.0999406	−	0.196145i	−0.835622	−	0.549304i	$-0.814893\pi$
$227$	1.50576	−	2.95522i	0.0999406	−	0.196145i	0.935563	+	0.353160i	$0.114893\pi$
$228$	3.73520	+	7.33074i	0.247370	+	0.485490i
$229$	−3.13876	+	4.32013i	−0.207415	+	0.285482i	−0.900032	−	0.435823i	$-0.856457\pi$
$229$	−3.13876	+	4.32013i	−0.207415	+	0.285482i	0.692618	+	0.721305i	$0.256457\pi$
$230$	−0.718477	−	3.19477i	−0.0473750	−	0.210657i
$231$		0			0
$232$	−3.43509	+	3.43509i	−0.225525	+	0.225525i
$233$	−4.36386	+	0.691167i	−0.285886	+	0.0452799i	−0.297730	−	0.954650i	$-0.596230\pi$
$233$	−4.36386	+	0.691167i	−0.285886	+	0.0452799i	0.0118446	+	0.999930i	$0.496230\pi$
$234$	−2.31314	−	0.751584i	−0.151215	−	0.0491326i
$235$	7.97652	+	2.03697i	0.520331	+	0.132877i
$236$	2.28770	−	1.66211i	0.148917	−	0.108194i
$237$	−17.1567	−	2.71735i	−1.11445	−	0.176511i
$238$	−6.68507	−	3.40621i	−0.433329	−	0.220792i
$239$	−3.23012	+	9.94128i	−0.208939	+	0.643048i	0.790590	+	0.612346i	$0.209774\pi$
$239$	−3.23012	+	9.94128i	−0.208939	+	0.643048i	−0.999529	+	0.0307017i	$0.990226\pi$
$240$	2.47094	+	6.21726i	0.159499	+	0.401322i
$241$			27.8579i			1.79449i	0.441536	+	0.897243i	$0.354434\pi$
$241$			27.8579i			1.79449i	−0.441536	+	0.897243i	$0.645566\pi$
$242$		0			0
$243$	10.5600	+	10.5600i	0.677425	+	0.677425i
$244$	9.88748	+	7.18367i	0.632981	+	0.459888i
$245$	−3.35178	−	0.312441i	−0.214138	−	0.0199611i
$246$	−0.611296	−	1.88138i	−0.0389748	−	0.119952i
$247$	1.87672	−	11.8492i	0.119413	−	0.753944i
$248$	−1.93695	+	12.2294i	−0.122996	+	0.776569i
$249$	2.35285	+	7.24134i	0.149106	+	0.458901i
$250$	2.30538	−	4.94921i	0.145805	−	0.313015i
$251$	8.04670	+	5.84627i	0.507903	+	0.369013i	0.812028	−	0.583619i	$-0.198364\pi$
$251$	8.04670	+	5.84627i	0.507903	+	0.369013i	−0.304124	+	0.952632i	$0.598364\pi$
$252$	6.18223	+	6.18223i	0.389444	+	0.389444i
$253$		0			0
$254$			4.60489i			0.288936i
$255$	5.31430	−	12.3246i	0.332795	−	0.771794i
$256$	0.0455968	−	0.140332i	0.00284980	−	0.00877078i
$257$	3.77828	+	1.92513i	0.235683	+	0.120086i	0.567844	−	0.823136i	$-0.307778\pi$
$257$	3.77828	+	1.92513i	0.235683	+	0.120086i	−0.332161	+	0.943223i	$0.607778\pi$
$258$	3.94254	+	0.624438i	0.245452	+	0.0388758i
$259$	2.74467	−	1.99412i	0.170545	−	0.123908i
$260$	2.85218	−	11.1688i	0.176885	−	0.692659i
$261$	−4.28052	−	1.39083i	−0.264958	−	0.0860899i
$262$	3.62554	−	0.574229i	0.223987	−	0.0354760i
$263$	−16.1830	+	16.1830i	−0.997884	+	0.997884i	−0.999998	−	0.00211364i	$-0.999327\pi$
$263$	−16.1830	+	16.1830i	−0.997884	+	0.997884i	0.00211364	+	0.999998i	$0.499327\pi$
$264$		0			0
$265$	−2.79223	−	1.76692i	−0.171526	−	0.108541i
$266$	3.43167	−	4.72330i	0.210409	−	0.289604i
$267$	−5.77914	−	11.3422i	−0.353677	−	0.694131i
$268$	1.48689	−	2.91819i	0.0908265	−	0.178257i
$269$	−13.4435	−	18.5034i	−0.819666	−	1.12817i	−0.989759	−	0.142745i	$-0.954407\pi$
$269$	−13.4435	−	18.5034i	−0.819666	−	1.12817i	0.170094	−	0.985428i	$-0.445593\pi$
$270$	3.86281	−	4.39299i	0.235083	−	0.267349i
$271$	1.32229	−	0.429640i	0.0803237	−	0.0260987i	−0.268580	−	0.963258i	$-0.586554\pi$
$271$	1.32229	−	0.429640i	0.0803237	−	0.0260987i	0.348903	+	0.937159i	$0.386554\pi$
$272$	−12.3263	+	6.28057i	−0.747392	+	0.380815i
$273$	1.52123	+	9.60465i	0.0920688	+	0.581300i
$274$	−7.50545			−0.453421
$275$		0			0
$276$	6.01861			0.362278
$277$	2.23010	+	14.0803i	0.133994	+	0.846002i	0.959520	+	0.281639i	$0.0908781\pi$
$277$	2.23010	+	14.0803i	0.133994	+	0.846002i	−0.825527	+	0.564363i	$0.809122\pi$
$278$	−1.81111	+	0.922808i	−0.108623	+	0.0553464i
$279$	−10.9101	+	3.54491i	−0.653171	+	0.212228i
$280$	7.91015	−	8.99586i	0.472722	−	0.537605i
$281$	−14.9161	−	20.5302i	−0.889818	−	1.22473i	−0.973604	−	0.228246i	$-0.926701\pi$
$281$	−14.9161	−	20.5302i	−0.889818	−	1.22473i	0.0837853	−	0.996484i	$-0.473299\pi$
$282$	0.929988	−	1.82520i	0.0553800	−	0.108689i
$283$	−3.36440	−	6.60300i	−0.199993	−	0.392508i	0.769128	−	0.639095i	$-0.220691\pi$
$283$	−3.36440	−	6.60300i	−0.199993	−	0.392508i	−0.969121	+	0.246587i	$0.920691\pi$
$284$	−2.97484	+	4.09451i	−0.176524	+	0.242964i
$285$	8.82536	+	5.58466i	0.522769	+	0.330807i
$286$		0			0
$287$	7.33195	−	7.33195i	0.432791	−	0.432791i
$288$	−8.33087	+	1.31948i	−0.490901	+	0.0777511i
$289$	10.2266	+	3.32284i	0.601567	+	0.195461i
$290$	−0.714542	+	2.79806i	−0.0419594	+	0.164307i
$291$	9.28071	−	6.74283i	0.544045	−	0.395272i
$292$	−25.7529	−	4.07886i	−1.50707	−	0.238697i
$293$	13.0777	+	6.66340i	0.764005	+	0.389280i	0.792152	−	0.610324i	$-0.208961\pi$
$293$	13.0777	+	6.66340i	0.764005	+	0.389280i	−0.0281472	+	0.999604i	$0.508961\pi$
$294$	−0.258843	+	0.796636i	−0.0150960	+	0.0464607i
$295$	1.42129	−	3.29616i	0.0827507	−	0.191910i
$296$			2.13682i			0.124200i
$297$		0			0
$298$	−6.20775	−	6.20775i	−0.359606	−	0.359606i
$299$	−7.09994	−	5.15841i	−0.410600	−	0.298318i
$300$	7.94523	+	6.12993i	0.458718	+	0.353911i
$301$	6.46553	+	19.8989i	0.372667	+	1.14695i
$302$	1.35920	−	8.58165i	0.0782131	−	0.493818i
$303$	−0.340276	+	2.14842i	−0.0195483	+	0.123423i
$304$	−3.32657	−	10.2381i	−0.190792	−	0.587197i
$305$	15.4471	+	1.43992i	0.884496	+	0.0824494i
$306$	3.54206	+	2.57346i	0.202486	+	0.147115i
$307$	0.874954	+	0.874954i	0.0499363	+	0.0499363i	0.731634	−	0.681698i	$-0.238758\pi$
$307$	0.874954	+	0.874954i	0.0499363	+	0.0499363i	−0.681698	+	0.731634i	$0.738758\pi$
$308$		0			0
$309$			7.03137i			0.400001i
$310$	2.71847	+	6.84008i	0.154399	+	0.388491i
$311$	4.37162	−	13.4545i	0.247892	−	0.762933i	−0.747256	−	0.664537i	$-0.768629\pi$
$311$	4.37162	−	13.4545i	0.247892	−	0.762933i	0.995147	−	0.0983958i	$-0.0313711\pi$
$312$	−5.45732	−	2.78064i	−0.308960	−	0.157423i
$313$	0.730542	+	0.115706i	0.0412927	+	0.00654011i	0.177047	−	0.984202i	$-0.443346\pi$
$313$	0.730542	+	0.115706i	0.0412927	+	0.00654011i	−0.135754	+	0.990743i	$0.543346\pi$
$314$	−8.48022	+	6.16124i	−0.478566	+	0.347699i
$315$	10.7532	+	2.74606i	0.605874	+	0.154723i
$316$	25.5415	+	8.29895i	1.43682	+	0.466852i
$317$	−16.8560	+	2.66972i	−0.946726	+	0.149947i	−0.610661	−	0.791892i	$-0.709096\pi$
$317$	−16.8560	+	2.66972i	−0.946726	+	0.149947i	−0.336065	+	0.941839i	$0.609096\pi$
$318$	−0.581389	+	0.581389i	−0.0326027	+	0.0326027i
$319$		0			0
$320$	−1.38930	−	6.17765i	−0.0776644	−	0.345341i
$321$	0.291674	−	0.401454i	0.0162796	−	0.0224070i
$322$	−1.93894	−	3.80538i	−0.108053	−	0.212065i
$323$	−9.80433	+	19.2421i	−0.545527	+	1.07066i
$324$	1.03346	+	1.42244i	0.0574145	+	0.0790243i
$325$	−4.11888	−	14.0409i	−0.228475	−	0.778850i
$326$	4.84178	−	1.57319i	0.268161	−	0.0871309i
$327$	9.61042	−	4.89675i	0.531457	−	0.270791i
$328$	1.02165	+	6.45047i	0.0564114	+	0.356168i
$329$	10.7373			0.591967
$330$		0			0
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	−1.84150	−	11.6268i	−0.101065	−	0.638102i
$333$	−1.76395	+	0.898777i	−0.0966638	+	0.0492527i
$334$	−5.24485	+	1.70415i	−0.286985	+	0.0932472i
$335$	−0.266444	−	4.14893i	−0.0145574	−	0.226680i
$336$	5.12893	+	7.05937i	0.279806	+	0.385120i
$337$	4.28455	−	8.40891i	0.233394	−	0.458062i	−0.744370	−	0.667767i	$-0.767250\pi$
$337$	4.28455	−	8.40891i	0.233394	−	0.458062i	0.977765	+	0.209705i	$0.0672503\pi$
$338$	−0.983358	−	1.92995i	−0.0534876	−	0.104975i
$339$	13.5725	−	18.6809i	0.737156	−	1.01461i
$340$	−11.0959	+	17.5346i	−0.601758	+	0.950950i
$341$		0			0
$342$	−2.40905	+	2.40905i	−0.130267	+	0.130267i
$343$	15.8271	−	2.50676i	0.854581	−	0.135352i
$344$	−12.5333	−	4.07231i	−0.675750	−	0.219564i
$345$	6.57100	−	3.89762i	0.353771	−	0.209841i
$346$	−5.21586	+	3.78954i	−0.280406	+	0.203727i
$347$	19.0026	+	3.00971i	1.02011	+	0.161570i	0.644016	−	0.765012i	$-0.277267\pi$
$347$	19.0026	+	3.00971i	1.02011	+	0.161570i	0.376094	+	0.926581i	$0.377267\pi$
$348$	−4.72933	−	2.40971i	−0.253518	−	0.129174i
$349$	4.59599	−	14.1450i	0.246018	−	0.757164i	−0.749450	−	0.662061i	$-0.769682\pi$
$349$	4.59599	−	14.1450i	0.246018	−	0.757164i	0.995467	−	0.0951031i	$-0.0303181\pi$
$350$	1.31615	−	6.99831i	0.0703511	−	0.374075i
$351$		−	15.6777i		−	0.836813i
$352$		0			0
$353$	1.78406	+	1.78406i	0.0949560	+	0.0949560i	0.752989	−	0.658033i	$-0.228611\pi$
$353$	1.78406	+	1.78406i	0.0949560	+	0.0949560i	−0.658033	+	0.752989i	$0.728611\pi$
$354$	−0.722594	−	0.524995i	−0.0384054	−	0.0279032i
$355$	−0.596284	+	6.39679i	−0.0316475	+	0.339506i
$356$	6.08171	+	18.7176i	0.322330	+	0.992029i
$357$	2.73840	−	17.2896i	0.144932	−	0.915063i
$358$	0.170108	−	1.07402i	0.00899047	−	0.0567636i
$359$	−2.62416	−	8.07635i	−0.138498	−	0.426253i	0.857620	−	0.514285i	$-0.171942\pi$
$359$	−2.62416	−	8.07635i	−0.138498	−	0.426253i	−0.996118	+	0.0880312i	$0.971942\pi$
$360$	−5.38029	+	4.46276i	−0.283566	+	0.235208i
$361$	1.77596	+	1.29031i	0.0934717	+	0.0679111i
$362$	−1.49682	−	1.49682i	−0.0786711	−	0.0786711i
$363$		0			0
$364$		−	15.0345i		−	0.788021i
$365$	−30.7579	+	12.2242i	−1.60994	+	0.639844i
$366$	1.19290	−	3.67138i	0.0623541	−	0.191906i
$367$	18.9156	+	9.63799i	0.987387	+	0.503099i	0.871622	−	0.490178i	$-0.163068\pi$
$367$	18.9156	+	9.63799i	0.987387	+	0.503099i	0.115765	+	0.993277i	$0.463068\pi$
$368$	−7.77792	−	1.23190i	−0.405452	−	0.0642173i
$369$	−4.89515	+	3.55653i	−0.254831	+	0.185146i
$370$	0.648032	+	1.09252i	0.0336896	+	0.0567973i
$371$	−4.09877	−	1.33177i	−0.212797	−	0.0691420i
$372$	−13.3620	+	2.11633i	−0.692786	+	0.109726i
$373$	−2.57445	+	2.57445i	−0.133300	+	0.133300i	−0.770609	−	0.637309i	$-0.780048\pi$
$373$	−2.57445	+	2.57445i	−0.133300	+	0.133300i	0.637309	+	0.770609i	$0.280048\pi$
$374$		0			0
$375$	12.6441	+	1.54725i	0.652940	+	0.0798995i
$376$	−3.97513	+	5.47130i	−0.205002	+	0.282161i
$377$	3.51371	+	6.89604i	0.180965	+	0.355164i
$378$	3.46377	−	6.79802i	0.178157	−	0.349653i
$379$	9.74713	+	13.4158i	0.500677	+	0.689122i	0.982312	−	0.187249i	$-0.0599572\pi$
$379$	9.74713	+	13.4158i	0.500677	+	0.689122i	−0.481636	+	0.876371i	$0.659957\pi$
$380$	−12.1259	−	10.6624i	−0.622044	−	0.546970i
$381$	−10.2180	+	3.32002i	−0.523483	+	0.170090i
$382$	1.77430	−	0.904051i	0.0907810	−	0.0462553i
$383$	1.77402	+	11.2007i	0.0906481	+	0.572330i	0.990648	+	0.136440i	$0.0435662\pi$
$383$	1.77402	+	11.2007i	0.0906481	+	0.572330i	−0.900000	+	0.435890i	$0.856434\pi$
$384$	−12.8694			−0.656736
$385$		0			0
$386$	10.2067			0.519505
$387$	−1.90998	−	12.0591i	−0.0970895	−	0.612999i
$388$	−15.8027	+	8.05188i	−0.802260	+	0.408772i
$389$	−0.777554	+	0.252643i	−0.0394236	+	0.0128095i	−0.328662	−	0.944447i	$-0.606598\pi$
$389$	−0.777554	+	0.252643i	−0.0394236	+	0.0128095i	0.289239	+	0.957257i	$0.406598\pi$
$390$	−3.63351	+	0.233344i	−0.183990	+	0.0118158i
$391$	9.28580	+	12.7808i	0.469603	+	0.646353i
$392$	1.25546	−	2.46398i	0.0634102	−	0.124450i
$393$	3.88812	+	7.63086i	0.196130	+	0.384926i
$394$	0.0867814	−	0.119444i	0.00437198	−	0.00601752i
$395$	33.2601	−	7.47992i	1.67350	−	0.376356i
$396$		0			0
$397$	11.8504	−	11.8504i	0.594752	−	0.594752i	−0.344159	−	0.938911i	$-0.611836\pi$
$397$	11.8504	−	11.8504i	0.594752	−	0.594752i	0.938911	+	0.344159i	$0.111836\pi$
$398$	5.34493	−	0.846553i	0.267917	−	0.0424339i
$399$	12.9549	+	4.20930i	0.648555	+	0.210728i
$400$	−9.01302	−	9.54802i	−0.450651	−	0.477401i
$401$	23.0228	−	16.7270i	1.14970	−	0.835308i	0.161262	−	0.986912i	$-0.448444\pi$
$401$	23.0228	−	16.7270i	1.14970	−	0.835308i	0.988441	+	0.151603i	$0.0484436\pi$
$402$	−1.02176	−	0.161831i	−0.0509607	−	0.00807137i
$403$	17.5765	+	8.95566i	0.875547	+	0.446113i
$404$	1.03922	−	3.19839i	0.0517032	−	0.159126i
$405$	2.04947	+	0.883724i	0.101839	+	0.0439126i
$406$			3.76651i			0.186929i
$407$		0			0
$408$	7.79627	+	7.79627i	0.385973	+	0.385973i
$409$	1.95998	+	1.42401i	0.0969146	+	0.0704126i	0.635187	−	0.772358i	$-0.280923\pi$
$409$	1.95998	+	1.42401i	0.0969146	+	0.0704126i	−0.538273	+	0.842771i	$0.680923\pi$
$410$	2.47858	+	2.98817i	0.122408	+	0.147575i
$411$	−5.41127	−	16.6542i	−0.266918	−	0.821490i
$412$	1.70059	−	10.7371i	0.0837820	−	0.528979i
$413$	0.732376	−	4.62404i	0.0360379	−	0.227534i
$414$	0.770145	+	2.37026i	0.0378506	+	0.116492i
$415$	−9.53994	−	11.5013i	−0.468297	−	0.564578i
$416$	11.7343	+	8.52546i	0.575321	+	0.417995i
$417$	−3.35343	−	3.35343i	−0.164218	−	0.164218i
$418$		0			0
$419$			16.4371i			0.803006i	0.915858	+	0.401503i	$0.131512\pi$
$419$			16.4371i			0.803006i	−0.915858	+	0.401503i	$0.868488\pi$
$420$	12.0186	+	5.18238i	0.586449	+	0.252874i
$421$	−3.85294	+	11.8581i	−0.187781	+	0.577930i	−0.999985	−	0.00544310i	$-0.998267\pi$
$421$	−3.85294	+	11.8581i	−0.187781	+	0.577930i	0.812204	+	0.583373i	$0.198267\pi$
$422$	3.85314	+	1.96327i	0.187568	+	0.0955707i
$423$	−6.18855	−	0.980171i	−0.300898	−	0.0476575i
$424$	2.19605	−	1.59552i	0.106649	−	0.0774853i
$425$	−0.758915	+	26.3296i	−0.0368128	+	1.27717i
$426$	1.52036	+	0.493994i	0.0736615	+	0.0239341i
$427$	19.9852	−	3.16534i	0.967151	−	0.153182i
$428$	−0.542488	+	0.542488i	−0.0262222	+	0.0262222i
$429$		0			0
$430$	−7.64304	+	1.71886i	−0.368580	+	0.0828907i
$431$	11.6588	−	16.0470i	0.561586	−	0.772957i	−0.429941	−	0.902857i	$-0.641466\pi$
$431$	11.6588	−	16.0470i	0.561586	−	0.772957i	0.991527	+	0.129900i	$0.0414655\pi$
$432$	−6.38668	−	12.5346i	−0.307279	−	0.603070i
$433$	12.9956	−	25.5054i	0.624531	−	1.22571i	−0.334496	−	0.942397i	$-0.608566\pi$
$433$	12.9956	−	25.5054i	0.624531	−	1.22571i	0.959027	−	0.283314i	$-0.0914339\pi$
$434$	5.64273	+	7.76656i	0.270860	+	0.372807i
$435$	−6.72389	+	0.431809i	−0.322386	+	0.0207036i
$436$	−15.8597	+	5.15313i	−0.759541	+	0.246790i
$437$	−10.9533	+	5.58097i	−0.523966	+	0.266974i
$438$	1.28835	+	8.13431i	0.0615597	+	0.388672i
$439$	3.12279			0.149043			0.0745214	−	0.997219i	$-0.476257\pi$
$439$	3.12279			0.149043			0.0745214	+	0.997219i	$0.476257\pi$
$440$		0			0
$441$	2.56208			0.122004
$442$	−1.17777	−	7.43613i	−0.0560207	−	0.353701i
$443$	28.2787	−	14.4087i	1.34356	−	0.684579i	0.373545	−	0.927612i	$-0.378142\pi$
$443$	28.2787	−	14.4087i	1.34356	−	0.684579i	0.970018	+	0.243033i	$0.0781422\pi$
$444$	−2.22044	+	0.721465i	−0.105378	+	0.0342392i
$445$	18.7613	+	16.4970i	0.889369	+	0.782032i
$446$	1.77454	+	2.44244i	0.0840267	+	0.115653i
$447$	9.29900	−	18.2503i	0.439827	−	0.863210i
$448$	−3.74928	−	7.35837i	−0.177137	−	0.347650i
$449$	20.5693	−	28.3112i	0.970726	−	1.33609i	0.0290462	−	0.999578i	$-0.490753\pi$
$449$	20.5693	−	28.3112i	0.970726	−	1.33609i	0.941679	−	0.336511i	$-0.109247\pi$
$450$	−1.39743	+	3.91340i	−0.0658753	+	0.184479i
$451$		0			0
$452$	−25.2437	+	25.2437i	−1.18736	+	1.18736i
$453$	20.0221	−	3.17119i	0.940722	−	0.148996i
$454$	1.54041	+	0.500510i	0.0722951	+	0.0234901i
$455$	−9.73624	−	16.4143i	−0.456442	−	0.769516i
$456$	−6.94099	+	5.04293i	−0.325042	+	0.236157i
$457$	5.03728	+	0.797826i	0.235634	+	0.0373207i	0.273134	−	0.961976i	$-0.411940\pi$
$457$	5.03728	+	0.797826i	0.235634	+	0.0373207i	−0.0375006	+	0.999297i	$0.511940\pi$
$458$	−2.32350	−	1.18388i	−0.108570	−	0.0553191i
$459$	−8.72103	+	26.8406i	−0.407063	+	1.25281i
$460$	−10.9768	+	4.36253i	−0.511794	+	0.203404i
$461$			12.4703i			0.580801i	0.956905	+	0.290400i	$0.0937885\pi$
$461$			12.4703i			0.580801i	−0.956905	+	0.290400i	$0.906211\pi$
$462$		0			0
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	0.0993669	−	0.995051i	$-0.468318\pi$
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	−0.995051	+	0.0993669i	$0.968318\pi$
$464$	5.61854	+	4.08211i	0.260834	+	0.189507i
$465$	−13.2178	+	10.9637i	−0.612961	+	0.508429i
$466$	−0.666738	−	2.05201i	−0.0308860	−	0.0950574i
$467$	−6.20937	+	39.2044i	−0.287335	+	1.81416i	0.247141	+	0.968980i	$0.420509\pi$
$467$	−6.20937	+	39.2044i	−0.287335	+	1.81416i	−0.534476	+	0.845184i	$0.679491\pi$
$468$	−1.37244	+	8.66527i	−0.0634412	+	0.400552i
$469$	−1.67562	−	5.15703i	−0.0773730	−	0.238130i
$470$	−0.373136	+	4.00290i	−0.0172115	+	0.184640i
$471$	−19.7855	−	14.3750i	−0.911667	−	0.662365i
$472$	2.08508	+	2.08508i	0.0959738	+	0.0959738i
$473$		0			0
$474$		−	8.48273i		−	0.389625i
$475$	−20.1437	−	3.78836i	−0.924256	−	0.173822i
$476$	−8.36324	+	25.7394i	−0.383328	+	1.17976i
$477$	2.24079	+	1.14174i	0.102599	+	0.0522767i
$478$	−5.04171	−	0.798528i	−0.230602	−	0.0365238i
$479$	30.9491	−	22.4858i	1.41410	−	1.02740i	0.421388	−	0.906880i	$-0.361543\pi$
$479$	30.9491	−	22.4858i	1.41410	−	1.02740i	0.992711	−	0.120523i	$-0.0384570\pi$
$480$	−10.8601	+	6.44171i	−0.495693	+	0.294022i
$481$	3.23773	+	1.05200i	0.147628	+	0.0479671i
$482$	−13.4366	+	2.12815i	−0.612022	+	0.0969348i
$483$	7.04599	−	7.04599i	0.320603	−	0.320603i
$484$		0			0
$485$	−12.0387	+	19.0246i	−0.546650	+	0.863863i
$486$	−4.28667	+	5.90009i	−0.194447	+	0.267634i
$487$	−12.3391	−	24.2169i	−0.559139	−	1.09737i	−0.981593	−	0.190987i	$-0.938831\pi$
$487$	−12.3391	−	24.2169i	−0.559139	−	1.09737i	0.422454	−	0.906384i	$-0.361169\pi$
$488$	−5.78591	+	11.3555i	−0.261916	+	0.514039i
$489$	6.98164	+	9.60940i	0.315720	+	0.434552i
$490$	−0.105355	−	1.64053i	−0.00475944	−	0.0741114i
$491$	−3.77748	+	1.22738i	−0.170475	+	0.0553907i	−0.393011	−	0.919534i	$-0.628567\pi$
$491$	−3.77748	+	1.22738i	−0.170475	+	0.0553907i	0.222536	+	0.974925i	$0.428567\pi$
$492$	−6.35795	+	3.23954i	−0.286638	+	0.146050i
$493$	−2.17949	−	13.7608i	−0.0981593	−	0.619753i
$494$	5.85854			0.263588
$495$		0			0
$496$	17.7010			0.794798
$497$	1.31080	+	8.27608i	0.0587975	+	0.371233i
$498$	−3.31295	+	1.68803i	−0.148457	+	0.0756426i
$499$	6.11060	−	1.98546i	0.273548	−	0.0888812i	−0.169031	−	0.985611i	$-0.554064\pi$
$499$	6.11060	−	1.98546i	0.273548	−	0.0888812i	0.442579	+	0.896730i	$0.354064\pi$
$500$	−18.9337	−	5.42077i	−0.846742	−	0.242424i
$501$	−7.56284	−	10.4094i	−0.337883	−	0.465056i
$502$	−2.20510	+	4.32776i	−0.0984186	+	0.193157i
$503$	−18.4896	−	36.2878i	−0.824409	−	1.61799i	−0.785590	−	0.618747i	$-0.787640\pi$
$503$	−18.4896	−	36.2878i	−0.824409	−	1.61799i	−0.0388190	−	0.999246i	$-0.512360\pi$
$504$	−5.35890	+	7.37590i	−0.238704	+	0.328549i
$505$	−0.936660	−	4.16493i	−0.0416808	−	0.185337i
$506$		0			0
$507$	3.57347	−	3.57347i	0.158703	−	0.158703i
$508$	16.4061	−	2.59847i	0.727904	−	0.115289i
$509$	−8.83124	−	2.86944i	−0.391438	−	0.127186i	0.106684	−	0.994293i	$-0.465977\pi$
$509$	−8.83124	−	2.86944i	−0.391438	−	0.127186i	−0.498122	+	0.867107i	$0.665977\pi$
$510$	6.35045	+	1.62172i	0.281203	+	0.0718110i
$511$	−34.9240	+	25.3738i	−1.54495	+	1.12247i
$512$	22.3835	+	3.54520i	0.989220	+	0.156677i
$513$	−19.5672	−	9.96998i	−0.863912	−	0.440185i
$514$	−0.639909	+	1.96944i	−0.0282252	+	0.0868681i
$515$	−5.09661	−	12.8238i	−0.224584	−	0.565086i
$516$		−	14.3987i		−	0.633868i
$517$		0			0
$518$	1.17149	+	1.17149i	0.0514723	+	0.0514723i
$519$	−12.1693	−	8.84152i	−0.534173	−	0.388099i
$520$	11.9686	+	1.11567i	0.524857	+	0.0489252i
$521$	−4.57564	−	14.0824i	−0.200462	−	0.616960i	−0.999869	−	0.0161698i	$-0.994853\pi$
$521$	−4.57564	−	14.0824i	−0.200462	−	0.616960i	0.799407	−	0.600790i	$-0.205147\pi$
$522$	0.343831	−	2.17086i	0.0150491	−	0.0950160i
$523$	−6.07643	+	38.3651i	−0.265704	+	1.67759i	0.388640	+	0.921390i	$0.372945\pi$
$523$	−6.07643	+	38.3651i	−0.265704	+	1.67759i	−0.654344	+	0.756197i	$0.727055\pi$
$524$	−4.09168	−	12.5929i	−0.178746	−	0.550124i
$525$	16.4778	−	2.12517i	0.719149	−	0.0927501i
$526$	−9.04175	−	6.56922i	−0.394239	−	0.286431i
$527$	−25.1096	−	25.1096i	−1.09379	−	1.09379i
$528$		0			0
$529$		−	14.0073i		−	0.609011i
$530$	0.638925	−	1.48175i	0.0277531	−	0.0643632i
$531$	−0.844224	+	2.59825i	−0.0366362	+	0.112755i
$532$	−18.7644	−	9.56095i	−0.813541	−	0.414520i
$533$	10.2768	+	1.62768i	0.445136	+	0.0705027i
$534$	5.02916	−	3.65390i	0.217633	−	0.158120i
$535$	−0.240966	+	0.943590i	−0.0104178	+	0.0407950i
$536$	3.24815	+	1.05539i	0.140299	+	0.0455859i
$537$	2.50583	−	0.396884i	0.108134	−	0.0171268i
$538$	7.89771	−	7.89771i	0.340495	−	0.340495i
$539$		0			0
$540$	−17.8309	−	11.2833i	−0.767320	−	0.485558i
$541$	−10.2392	+	14.0930i	−0.440217	+	0.605907i	−0.970260	−	0.242064i	$-0.922176\pi$
$541$	−10.2392	+	14.0930i	−0.440217	+	0.605907i	0.530043	+	0.847971i	$0.322176\pi$
$542$	0.308241	+	0.604957i	0.0132401	+	0.0259851i
$543$	2.24218	−	4.40053i	0.0962213	−	0.188845i
$544$	−15.3469	−	21.1232i	−0.657994	−	0.905650i
$545$	−13.9781	+	15.8967i	−0.598758	+	0.680940i
$546$	−4.51637	+	1.46746i	−0.193283	+	0.0628014i
$547$	−34.9333	+	17.7994i	−1.49364	+	0.761048i	−0.994427	−	0.105430i	$-0.966378\pi$
$547$	−34.9333	+	17.7994i	−1.49364	+	0.761048i	−0.499215	+	0.866478i	$0.666378\pi$
$548$	4.23522	+	26.7401i	0.180920	+	1.14228i
$549$	−11.8076			−0.503936
$550$		0			0
$551$	10.8414			0.461858
$552$	0.981807	+	6.19888i	0.0417885	+	0.263842i
$553$	39.6170	−	20.1859i	1.68469	−	0.858391i
$554$	−6.62094	+	2.15127i	−0.281297	+	0.0913989i
$555$	−1.95702	+	2.22563i	−0.0830707	+	0.0944726i
$556$	4.30973	+	5.93184i	0.182773	+	0.251566i
$557$	−16.6620	+	32.7010i	−0.705991	+	1.38558i	0.207301	+	0.978277i	$0.433532\pi$
$557$	−16.6620	+	32.7010i	−0.705991	+	1.38558i	−0.913291	+	0.407307i	$0.866468\pi$
$558$	−2.54326	−	4.99143i	−0.107665	−	0.211304i
$559$	−12.3408	+	16.9856i	−0.521959	+	0.718416i
$560$	−14.4711	−	9.15725i	−0.611514	−	0.386964i
$561$		0			0
$562$	8.76280	−	8.76280i	0.369636	−	0.369636i
$563$	−16.6732	+	2.64077i	−0.702690	+	0.111295i	−0.497547	−	0.867437i	$-0.665766\pi$
$563$	−16.6732	+	2.64077i	−0.702690	+	0.111295i	−0.205143	+	0.978732i	$0.565766\pi$
$564$	−7.02754	−	2.28339i	−0.295913	−	0.0961480i
$565$	−11.2129	+	43.9082i	−0.471729	+	1.84723i
$566$	2.92779	−	2.12716i	0.123064	−	0.0894114i
$567$	2.87512	+	0.455374i	0.120744	+	0.0191239i
$568$	−4.70243	−	2.39601i	−0.197310	−	0.100534i
$569$	0.818531	−	2.51918i	0.0343146	−	0.105609i	−0.932432	−	0.361345i	$-0.882318\pi$
$569$	0.818531	−	2.51918i	0.0343146	−	0.105609i	0.966747	+	0.255736i	$0.0823176\pi$
$570$	−2.01944	+	4.68334i	−0.0845849	+	0.196164i
$571$		−	29.8675i		−	1.24992i	−0.780658	−	0.624959i	$-0.785116\pi$
$571$		−	29.8675i		−	1.24992i	0.780658	−	0.624959i	$-0.214884\pi$
$572$		0			0
$573$	3.28527	+	3.28527i	0.137244	+	0.137244i
$574$	4.09651	+	2.97629i	0.170985	+	0.124228i
$575$	−9.15906	+	11.8714i	−0.381959	+	0.495072i
$576$	1.48921	+	4.58332i	0.0620505	+	0.190972i
$577$	−0.0561437	+	0.354477i	−0.00233729	+	0.0147571i	−0.988829	−	0.149052i	$-0.952378\pi$
$577$	−0.0561437	+	0.354477i	−0.00233729	+	0.0147571i	0.986492	+	0.163809i	$0.0523780\pi$
$578$	−0.821450	+	5.18643i	−0.0341678	+	0.215727i
$579$	7.35878	+	22.6480i	0.305821	+	0.941219i
$580$	10.3720	+	0.966840i	0.430674	+	0.0401458i
$581$	−15.7673	−	11.4556i	−0.654138	−	0.475259i
$582$	3.96123	+	3.96123i	0.164198	+	0.164198i
$583$		0			0
$584$		−	27.1896i		−	1.12511i
$585$	4.11317	+	10.3493i	0.170059	+	0.427893i
$586$	−2.21490	+	6.81675i	−0.0914965	+	0.281597i
$587$	−23.0298	−	11.7343i	−0.950543	−	0.484326i	−0.0912603	−	0.995827i	$-0.529090\pi$
$587$	−23.0298	−	11.7343i	−0.950543	−	0.484326i	−0.859282	+	0.511501i	$0.829090\pi$
$588$	2.98428	+	0.472664i	0.123070	+	0.0194923i
$589$	22.3550	−	16.2418i	0.921121	−	0.669233i
$590$	1.69840	+	0.433723i	0.0699222	+	0.0178561i
$591$	0.327608	+	0.106446i	0.0134760	+	0.00437861i
$592$	3.01717	−	0.477873i	0.124005	−	0.0196405i
$593$	9.56872	−	9.56872i	0.392940	−	0.392940i	−0.482794	−	0.875734i	$-0.660378\pi$
$593$	9.56872	−	9.56872i	0.392940	−	0.392940i	0.875734	+	0.482794i	$0.160378\pi$
$594$		0			0
$595$	7.53787	+	33.5177i	0.309022	+	1.37409i
$596$	−18.6138	+	25.6197i	−0.762451	+	1.04942i
$597$	5.73203	+	11.2497i	0.234596	+	0.460421i
$598$	1.94565	−	3.81856i	0.0795637	−	0.156153i
$599$	−6.65542	−	9.16040i	−0.271933	−	0.374284i	0.651108	−	0.758985i	$-0.274304\pi$
$599$	−6.65542	−	9.16040i	−0.271933	−	0.374284i	−0.923041	+	0.384701i	$0.874304\pi$
$600$	−5.01744	+	9.18317i	−0.204836	+	0.374901i
$601$	15.6822	−	5.09545i	0.639689	−	0.207848i	0.0288267	−	0.999584i	$-0.490823\pi$
$601$	15.6822	−	5.09545i	0.639689	−	0.207848i	0.610862	+	0.791737i	$0.290823\pi$
$602$	−9.10384	+	4.63864i	−0.371045	+	0.189057i
$603$	0.494993	+	3.12526i	0.0201577	+	0.127271i
$604$	−31.3413			−1.27526
$605$		0			0
$606$	−1.06223			−0.0431503
$607$	0.779724	+	4.92298i	0.0316480	+	0.199818i	0.998446	−	0.0557232i	$-0.0177465\pi$
$607$	0.779724	+	4.92298i	0.0316480	+	0.199818i	−0.966798	+	0.255541i	$0.917746\pi$
$608$	18.1028	−	9.22383i	0.734165	−	0.374076i
$609$	−8.35766	+	2.71557i	−0.338670	+	0.110040i
$610$	0.485538	+	7.56053i	0.0196589	+	0.306117i
$611$	6.33310	+	8.71677i	0.256210	+	0.352643i
$612$	7.16989	−	14.0717i	0.289825	−	0.568814i
$613$	−8.29879	−	16.2873i	−0.335185	−	0.657837i	0.660481	−	0.750843i	$-0.270352\pi$
$613$	−8.29879	−	16.2873i	−0.335185	−	0.657837i	−0.995666	+	0.0930058i	$0.970352\pi$
$614$	−0.355174	+	0.488855i	−0.0143337	+	0.0197286i
$615$	−4.84357	+	7.65423i	−0.195312	+	0.308648i
$616$		0			0
$617$	15.4942	−	15.4942i	0.623773	−	0.623773i	−0.322721	−	0.946494i	$-0.604598\pi$
$617$	15.4942	−	15.4942i	0.623773	−	0.623773i	0.946494	+	0.322721i	$0.104598\pi$
$618$	−3.39142	+	0.537149i	−0.136423	+	0.0216073i
$619$	−46.8070	−	15.2085i	−1.88133	−	0.611282i	−0.986219	−	0.165445i	$-0.947094\pi$
$619$	−46.8070	−	15.2085i	−1.88133	−	0.611282i	−0.895114	−	0.445837i	$-0.852906\pi$
$620$	22.8356	−	13.5450i	0.917099	−	0.543982i
$621$	−12.9967	+	9.44269i	−0.521541	+	0.378922i
$622$	6.82342	+	1.08072i	0.273594	+	0.0433330i
$623$	29.0325	+	14.7928i	1.16316	+	0.592661i
$624$	−2.70578	+	8.32754i	−0.108318	+	0.333368i
$625$	−24.1819	+	6.34309i	−0.967277	+	0.253724i
$626$			0.361199i			0.0144364i
$627$		0			0
$628$	26.7363	+	26.7363i	1.06689	+	1.06689i
$629$	−4.95787	−	3.60210i	−0.197683	−	0.143625i
$630$	−0.503027	+	5.39634i	−0.0200411	+	0.214995i
$631$	−2.79731	−	8.60924i	−0.111359	−	0.342729i	0.879811	−	0.475324i	$-0.157669\pi$
$631$	−2.79731	−	8.60924i	−0.111359	−	0.342729i	−0.991170	+	0.132595i	$0.957669\pi$
$632$	−4.38097	+	27.6604i	−0.174266	+	1.10027i
$633$	−1.57836	+	9.96538i	−0.0627342	+	0.396088i
$634$	−2.57536	−	7.92615i	−0.102281	−	0.314788i
$635$	16.2291	−	13.4615i	0.644032	−	0.534202i
$636$	2.39942	+	1.74328i	0.0951431	+	0.0691255i
$637$	−3.11534	−	3.11534i	−0.123434	−	0.123434i
$638$		0			0
$639$		−	4.88965i		−	0.193432i
$640$	23.4712	−	9.32821i	0.927779	−	0.368730i
$641$	−8.63030	+	26.5613i	−0.340876	+	1.04911i	0.622878	+	0.782319i	$0.285963\pi$
$641$	−8.63030	+	26.5613i	−0.340876	+	1.04911i	−0.963755	+	0.266791i	$0.914037\pi$
$642$	0.215914	+	0.110014i	0.00852146	+	0.00434190i
$643$	−9.51085	−	1.50637i	−0.375071	−	0.0594055i	−0.0339470	−	0.999424i	$-0.510808\pi$
$643$	−9.51085	−	1.50637i	−0.375071	−	0.0594055i	−0.341124	+	0.940018i	$0.610808\pi$
$644$	−12.4635	+	9.05529i	−0.491132	+	0.356828i
$645$	−9.32451	−	15.7202i	−0.367152	−	0.618983i
$646$	−10.0300	−	3.25893i	−0.394624	−	0.128221i
$647$	30.5702	−	4.84185i	1.20184	−	0.190353i	0.476770	−	0.879028i	$-0.341807\pi$
$647$	30.5702	−	4.84185i	1.20184	−	0.190353i	0.725070	+	0.688675i	$0.241807\pi$
$648$	−1.29645	+	1.29645i	−0.0509296	+	0.0509296i
$649$		0			0
$650$	6.45766	−	3.05928i	0.253290	−	0.119995i
$651$	−13.1653	+	18.1204i	−0.515987	+	0.710195i
$652$	−8.33705	−	16.3624i	−0.326504	−	0.640800i
$653$	2.77406	−	5.44440i	0.108557	−	0.213056i	−0.830337	−	0.557262i	$-0.811852\pi$
$653$	2.77406	−	5.44440i	0.108557	−	0.213056i	0.938894	+	0.344206i	$0.111852\pi$
$654$	3.09601	+	4.26129i	0.121063	+	0.166630i
$655$	−12.6223	−	11.0989i	−0.493194	−	0.433671i
$656$	8.87952	−	2.88513i	0.346687	−	0.112645i
$657$	22.4450	−	11.4363i	0.875665	−	0.446173i
$658$	0.820257	+	5.17890i	0.0319770	+	0.201895i
$659$	−12.0647			−0.469975			−0.234988	−	0.971998i	$-0.575505\pi$
$659$	−12.0647			−0.469975			−0.234988	+	0.971998i	$0.575505\pi$
$660$		0			0
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	−1.13970	−	7.19579i	−0.0442957	−	0.279672i
$663$	15.6512	−	7.97469i	0.607843	−	0.309711i
$664$	11.6746	−	3.79331i	0.453063	−	0.147209i
$665$	−26.6782	+	1.71328i	−1.03454	+	0.0664380i
$666$	−0.568258	−	0.782140i	−0.0220196	−	0.0303073i
$667$	3.60048	−	7.06635i	0.139411	−	0.273610i
$668$	9.03109	+	17.7245i	0.349423	+	0.685782i
$669$	−4.14023	+	5.69854i	−0.160071	+	0.220318i
$670$	1.98079	−	0.445463i	0.0765244	−	0.0172097i
$671$		0			0
$672$	−11.6451	+	11.6451i	−0.449220	+	0.449220i
$673$	4.97380	−	0.787773i	0.191726	−	0.0303664i	−0.0598329	−	0.998208i	$-0.519057\pi$
$673$	4.97380	−	0.787773i	0.191726	−	0.0303664i	0.251559	+	0.967842i	$0.419057\pi$
$674$	4.38316	+	1.42417i	0.168833	+	0.0548571i
$675$	−26.7744	−	0.771738i	−1.03055	−	0.0297042i
$676$	−6.32105	+	4.59251i	−0.243117	+	0.176635i
$677$	35.9579	+	5.69516i	1.38197	+	0.218883i	0.802764	−	0.596297i	$-0.203362\pi$
$677$	35.9579	+	5.69516i	1.38197	+	0.218883i	0.579208	+	0.815180i	$0.303362\pi$
$678$	10.0472	+	5.11928i	0.385859	+	0.196605i
$679$	−9.07388	+	27.9265i	−0.348223	+	1.07172i
$680$	−19.8699	−	8.56782i	−0.761976	−	0.328561i
$681$			3.77894i			0.144809i
$682$		0			0
$683$	−8.07353	−	8.07353i	−0.308925	−	0.308925i	0.535567	−	0.844492i	$-0.320098\pi$
$683$	−8.07353	−	8.07353i	−0.308925	−	0.308925i	−0.844492	+	0.535567i	$0.820098\pi$
$684$	9.94226	+	7.22348i	0.380152	+	0.276197i
$685$	21.9407	+	26.4516i	0.838310	+	1.01066i
$686$	2.41816	+	7.44232i	0.0923257	+	0.284149i
$687$	0.951773	−	6.00926i	0.0363124	−	0.229267i
$688$	−2.94716	+	18.6076i	−0.112359	+	0.709408i
$689$	−1.33638	−	4.11297i	−0.0509122	−	0.156692i
$690$	2.38191	+	2.87162i	0.0906776	+	0.109321i
$691$	9.61076	+	6.98263i	0.365611	+	0.265632i	0.755388	−	0.655277i	$-0.227448\pi$
$691$	9.61076	+	6.98263i	0.365611	+	0.265632i	−0.389778	+	0.920909i	$0.627448\pi$
$692$	16.4445	+	16.4445i	0.625125	+	0.625125i
$693$		0			0
$694$			9.39538i			0.356644i
$695$	8.54670	+	3.68530i	0.324195	+	0.139791i
$696$	1.71040	−	5.26407i	0.0648326	−	0.199534i
$697$	−16.6886	−	8.50329i	−0.632127	−	0.322085i
$698$	7.17362	+	1.13619i	0.271526	+	0.0430054i
$699$	4.07258	−	2.95891i	0.154039	−	0.111916i
$700$	−25.6760	−	0.740076i	−0.970461	−	0.0279722i
$701$	25.2475	+	8.20342i	0.953586	+	0.309839i	0.744172	−	0.667988i	$-0.232844\pi$
$701$	25.2475	+	8.20342i	0.953586	+	0.309839i	0.209414	+	0.977827i	$0.432844\pi$
$702$	7.56177	−	1.19767i	0.285401	−	0.0452030i
$703$	3.37197	−	3.37197i	0.127176	−	0.127176i
$704$		0			0
$705$	−9.15124	+	2.05804i	−0.344655	+	0.0775102i
$706$	−0.724212	+	0.996792i	−0.0272561	+	0.0375148i
$707$	−2.52774	−	4.96097i	−0.0950654	−	0.186576i
$708$	−1.46268	+	2.87068i	−0.0549710	+	0.107887i
$709$	10.4984	+	14.4498i	0.394275	+	0.542673i	0.959296	−	0.282404i	$-0.0911318\pi$
$709$	10.4984	+	14.4498i	0.394275	+	0.542673i	−0.565021	+	0.825077i	$0.691132\pi$
$710$	−3.13090	+	0.201066i	−0.117500	+	0.00754589i
$711$	−24.6763	+	8.01783i	−0.925435	+	0.300692i
$712$	−18.2861	+	9.31723i	−0.685301	+	0.349178i
$713$	−3.16212	−	19.9648i	−0.118422	−	0.747689i
$714$	8.54844			0.319917
$715$		0			0
$716$	−3.92246			−0.146589
$717$	−1.86307	−	11.7630i	−0.0695778	−	0.439297i
$718$	3.69497	−	1.88268i	0.137895	−	0.0702611i
$719$	31.1609	−	10.1248i	1.16211	−	0.377592i	0.336416	−	0.941714i	$-0.390785\pi$
$719$	31.1609	−	10.1248i	1.16211	−	0.377592i	0.825691	+	0.564122i	$0.190785\pi$
$720$	7.50460	+	6.59888i	0.279680	+	0.245926i
$721$	−10.5790	−	14.5608i	−0.393984	−	0.542272i
$722$	−0.486681	+	0.955166i	−0.0181124	+	0.0355476i
$723$	−14.4098	−	28.2808i	−0.535905	−	1.05177i
$724$	−4.48818	+	6.17744i	−0.166802	+	0.229583i
$725$	11.9501	−	5.66127i	0.443814	−	0.210254i
$726$		0			0
$727$	0.964903	−	0.964903i	0.0357863	−	0.0357863i	−0.688987	−	0.724773i	$-0.741944\pi$
$727$	0.964903	−	0.964903i	0.0357863	−	0.0357863i	0.724773	+	0.688987i	$0.241944\pi$
$728$	15.4848	−	2.45255i	0.573905	−	0.0908976i
$729$	−19.0304	−	6.18335i	−0.704830	−	0.229013i
$730$	−8.24576	−	13.9015i	−0.305189	−	0.514519i
$731$	30.5763	−	22.2150i	1.13091	−	0.821651i
$732$	−13.7534	−	2.17832i	−0.508340	−	0.0805131i
$733$	10.5079	+	5.35405i	0.388119	+	0.197756i	0.637151	−	0.770739i	$-0.280113\pi$
$733$	10.5079	+	5.35405i	0.388119	+	0.197756i	−0.249033	+	0.968495i	$0.580113\pi$
$734$	−3.20364	+	9.85979i	−0.118249	+	0.363932i
$735$	3.56427	−	1.41656i	0.131470	−	0.0522506i
$736$		−	14.8626i		−	0.547842i
$737$		0			0
$738$	−2.08937	−	2.08937i	−0.0769107	−	0.0769107i
$739$	−34.8645	−	25.3305i	−1.28251	−	0.931798i	−0.282884	−	0.959154i	$-0.591291\pi$
$739$	−34.8645	−	25.3305i	−1.28251	−	0.931798i	−0.999626	+	0.0273561i	$0.991291\pi$
$740$	3.52670	−	2.92527i	0.129644	−	0.107535i
$741$	4.22388	+	12.9998i	0.155168	+	0.477558i
$742$	0.329231	−	2.07868i	0.0120865	−	0.0763109i
$743$	5.93105	−	37.4472i	0.217589	−	1.37380i	−0.600920	−	0.799309i	$-0.705199\pi$
$743$	5.93105	−	37.4472i	0.217589	−	1.37380i	0.818509	−	0.574494i	$-0.194801\pi$
$744$	−4.35943	−	13.4170i	−0.159825	−	0.491889i
$745$	−3.73100	+	40.0252i	−0.136693	+	1.46641i
$746$	−1.43840	−	1.04506i	−0.0526636	−	0.0382623i
$747$	8.04189	+	8.04189i	0.294237	+	0.294237i
$748$		0			0
$749$			1.27018i			0.0464114i
$750$	0.219646	+	6.21681i	0.00802034	+	0.227006i
$751$	10.7881	−	33.2025i	0.393665	−	1.21158i	−0.536331	−	0.844008i	$-0.680190\pi$
$751$	10.7881	−	33.2025i	0.393665	−	1.21158i	0.929996	−	0.367569i	$-0.119810\pi$
$752$	8.61441	+	4.38926i	0.314135	+	0.160060i
$753$	−11.1929	−	1.77278i	−0.407891	−	0.0646036i
$754$	−3.05772	+	2.22157i	−0.111356	+	0.0809047i
$755$	−34.2178	+	20.2965i	−1.24531	+	0.738664i
$756$	−26.1743	−	8.50454i	−0.951950	−	0.309307i
$757$	34.0513	−	5.39320i	1.23762	−	0.196019i	0.496883	−	0.867818i	$-0.334478\pi$
$757$	34.0513	−	5.39320i	1.23762	−	0.196019i	0.740734	+	0.671798i	$0.234478\pi$
$758$	−5.72618	+	5.72618i	−0.207984	+	0.207984i
$759$		0			0
$760$	9.00370	−	14.2284i	0.326598	−	0.516119i
$761$	8.17878	−	11.2571i	0.296481	−	0.408071i	−0.634625	−	0.772820i	$-0.718845\pi$
$761$	8.17878	−	11.2571i	0.296481	−	0.408071i	0.931106	+	0.364750i	$0.118845\pi$
$762$	−2.38192	−	4.67478i	−0.0862879	−	0.169350i
$763$	−12.5342	+	24.5997i	−0.453767	+	0.890568i
$764$	−4.22213	−	5.81126i	−0.152751	−	0.210244i
$765$	−1.28481	−	20.0064i	−0.0464524	−	0.723331i
$766$	−5.26689	+	1.71132i	−0.190300	+	0.0618323i
$767$	4.18586	−	2.13280i	0.151143	−	0.0770110i
$768$	0.0262994	+	0.166048i	0.000948998	+	0.00599174i
$769$	13.3273			0.480596			0.240298	−	0.970699i	$-0.422755\pi$
$769$	13.3273			0.480596			0.240298	+	0.970699i	$0.422755\pi$
$770$		0			0
$771$	−4.83143			−0.174000
$772$	−5.75948	−	36.3639i	−0.207288	−	1.30877i
$773$	11.1372	−	5.67471i	0.400579	−	0.204105i	−0.242082	−	0.970256i	$-0.577830\pi$
$773$	11.1372	−	5.67471i	0.400579	−	0.204105i	0.642661	+	0.766151i	$0.277830\pi$
$774$	5.67053	−	1.84247i	0.203823	−	0.0662261i
$775$	16.1597	−	29.5764i	0.580475	−	1.06241i
$776$	−10.8709	−	14.9625i	−0.390243	−	0.537124i
$777$	−1.75485	+	3.44409i	−0.0629549	+	0.123556i
$778$	−0.181256	−	0.355735i	−0.00649835	−	0.0127537i
$779$	8.56685	−	11.7913i	0.306939	−	0.422465i
$780$	2.88168	+	12.8136i	0.103181	+	0.458802i
$781$		0			0
$782$	−5.45516	+	5.45516i	−0.195076	+	0.195076i
$783$	13.9933	−	2.21631i	0.500078	−	0.0792046i
$784$	−3.75988	−	1.22166i	−0.134281	−	0.0436306i
$785$	46.5044	+	11.8759i	1.65981	+	0.423868i
$786$	−3.38355	+	2.45829i	−0.120687	+	0.0876843i
$787$	6.21530	+	0.984406i	0.221551	+	0.0350903i	0.266223	−	0.963911i	$-0.414224\pi$
$787$	6.21530	+	0.984406i	0.221551	+	0.0350903i	−0.0446718	+	0.999002i	$0.514224\pi$
$788$	−0.474521	−	0.241781i	−0.0169041	−	0.00861308i
$789$	8.05781	−	24.7994i	0.286866	−	0.882882i
$790$	6.14861	+	15.4708i	0.218758	+	0.550427i
$791$			59.1055i			2.10155i
$792$		0			0
$793$	14.3574	+	14.3574i	0.509846	+	0.509846i
$794$	6.62104	+	4.81046i	0.234972	+	0.170717i
$795$	3.74857	+	0.349428i	0.132948	+	0.0123929i
$796$	−6.03213	−	18.5650i	−0.213803	−	0.658019i
$797$	−0.276667	+	1.74680i	−0.00980003	+	0.0618750i	−0.992104	−	0.125420i	$-0.959972\pi$
$797$	−0.276667	+	1.74680i	−0.00980003	+	0.0618750i	0.982304	+	0.187295i	$0.0599721\pi$
$798$	−1.04059	+	6.57006i	−0.0368367	+	0.232577i
$799$	−5.99354	−	18.4462i	−0.212036	−	0.652581i
$800$	15.1375	−	19.6202i	0.535190	−	0.693680i
$801$	−15.3828	−	11.1762i	−0.543523	−	0.394893i
$802$	9.82669	+	9.82669i	0.346992	+	0.346992i
$803$		0			0
$804$			3.73160i			0.131603i
$805$	−7.74328	+	17.9577i	−0.272915	+	0.632925i
$806$	−2.97684	+	9.16176i	−0.104855	+	0.322709i
$807$	23.2186	+	11.8305i	0.817335	+	0.416453i
$808$	3.46372	+	0.548599i	0.121853	+	0.0192996i
$809$	−14.9294	+	10.8468i	−0.524889	+	0.381354i	−0.818443	−	0.574588i	$-0.805162\pi$
$809$	−14.9294	+	10.8468i	−0.524889	+	0.381354i	0.293553	+	0.955943i	$0.405162\pi$
$810$	−0.269679	+	1.05603i	−0.00947554	+	0.0371050i
$811$	12.4057	+	4.03086i	0.435624	+	0.141543i	0.518616	−	0.855007i	$-0.326448\pi$
$811$	12.4057	+	4.03086i	0.435624	+	0.141543i	−0.0829918	+	0.996550i	$0.526448\pi$
$812$	13.4192	−	2.12539i	0.470920	−	0.0745865i
$813$	−1.12013	+	1.12013i	−0.0392847	+	0.0392847i
$814$		0			0
$815$	−19.6984	−	12.4651i	−0.690004	−	0.436633i
$816$	9.26472	−	12.7518i	0.324330	−	0.446402i
$817$	13.3517	+	26.2042i	0.467117	+	0.916768i
$818$	−0.537108	+	1.05413i	−0.0187796	+	0.0368569i
$819$	8.53770	+	11.7511i	0.298331	+	0.410618i
$820$	9.24750	−	10.5168i	0.322937	−	0.367261i
$821$	24.7703	−	8.04835i	0.864489	−	0.280889i	0.156987	−	0.987601i	$-0.449822\pi$
$821$	24.7703	−	8.04835i	0.864489	−	0.280889i	0.707502	+	0.706711i	$0.249822\pi$
$822$	7.61938	−	3.88227i	0.265756	−	0.135410i
$823$	0.785962	+	4.96237i	0.0273969	+	0.172977i	0.997593	−	0.0693449i	$-0.0220909\pi$
$823$	0.785962	+	4.96237i	0.0273969	+	0.172977i	−0.970196	+	0.242322i	$0.922091\pi$
$824$	11.3361			0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−1.90393	−	12.0210i	−0.0662062	−	0.418010i	−0.998424	−	0.0561130i	$-0.982129\pi$
$827$	−1.90393	−	12.0210i	−0.0662062	−	0.418010i	0.932218	−	0.361897i	$-0.117871\pi$
$828$	8.01010	−	4.08135i	0.278370	−	0.141837i
$829$	−10.4727	+	3.40277i	−0.363730	+	0.118183i	−0.485180	−	0.874415i	$-0.661246\pi$
$829$	−10.4727	+	3.40277i	−0.363730	+	0.118183i	0.121449	+	0.992598i	$0.461246\pi$
$830$	4.81862	−	5.48000i	0.167257	−	0.190213i
$831$	−9.54711	−	13.1405i	−0.331185	−	0.455838i
$832$	3.76227	−	7.38386i	0.130433	−	0.255989i
$833$	3.60057	+	7.06651i	0.124752	+	0.244840i
$834$	1.36127	−	1.87363i	0.0471370	−	0.0648785i
$835$	21.3382	+	13.5028i	0.738440	+	0.467283i
$836$		0			0
$837$	25.5338	−	25.5338i	0.882578	−	0.882578i
$838$	−7.92807	+	1.25568i	−0.273871	+	0.0433769i
$839$	8.83685	+	2.87127i	0.305082	+	0.0991272i	0.457557	−	0.889180i	$-0.348724\pi$
$839$	8.83685	+	2.87127i	0.305082	+	0.0991272i	−0.152475	+	0.988307i	$0.548724\pi$
$840$	−3.37703	+	13.2240i	−0.116519	+	0.456271i
$841$	17.8031	−	12.9347i	0.613900	−	0.446024i
$842$	−6.01384	−	0.952498i	−0.207251	−	0.0328253i
$843$	25.7619	+	13.1264i	0.887288	+	0.452096i
$844$	4.82040	−	14.8357i	0.165925	−	0.510665i
$845$	−3.92711	+	9.10749i	−0.135097	+	0.313307i
$846$		−	3.05979i		−	0.105198i
$847$		0			0
$848$	−2.74398	−	2.74398i	−0.0942286	−	0.0942286i
$849$	6.83093	+	4.96296i	0.234437	+	0.170328i
$850$	−12.7575	+	1.64535i	−0.437577	+	0.0564352i
$851$	−1.07798	−	3.31768i	−0.0369527	−	0.113729i
$852$	0.902066	−	5.69542i	0.0309043	−	0.195122i
$853$	−4.23097	+	26.7133i	−0.144866	+	0.914645i	0.803001	+	0.595978i	$0.203235\pi$
$853$	−4.23097	+	26.7133i	−0.144866	+	0.914645i	−0.947867	+	0.318667i	$0.896765\pi$
$854$	3.05346	+	9.39759i	0.104487	+	0.321579i
$855$	15.5326	+	1.44789i	0.531205	+	0.0495169i
$856$	−0.647232	−	0.470242i	−0.0221220	−	0.0160725i
$857$	−33.1497	−	33.1497i	−1.13237	−	1.13237i	−0.989782	−	0.142591i	$-0.954457\pi$
$857$	−33.1497	−	33.1497i	−1.13237	−	1.13237i	−0.142591	−	0.989782i	$-0.545543\pi$
$858$		0			0
$859$			47.2517i			1.61221i	0.591775	+	0.806103i	$0.298427\pi$
$859$			47.2517i			1.61221i	−0.591775	+	0.806103i	$0.701573\pi$
$860$	10.4367	+	26.2604i	0.355890	+	0.895472i
$861$	−3.65072	+	11.2358i	−0.124416	+	0.382914i
$862$	8.63057	+	4.39749i	0.293958	+	0.149779i
$863$	15.3690	+	2.43422i	0.523168	+	0.0828617i	0.412432	−	0.910988i	$-0.364679\pi$
$863$	15.3690	+	2.43422i	0.523168	+	0.0828617i	0.110736	+	0.993850i	$0.464679\pi$
$864$	21.4801	−	15.6062i	0.730768	−	0.530934i
$865$	28.6031	+	7.30440i	0.972534	+	0.248357i
$866$	13.2947	+	4.31972i	0.451773	+	0.146790i
$867$	−12.1006	+	1.91655i	−0.410959	+	0.0650896i
$868$	24.4863	−	24.4863i	0.831118	−	0.831118i
$869$		0			0
$870$	−0.721933	−	3.21013i	−0.0244758	−	0.108834i
$871$	3.19826	−	4.40203i	0.108369	−	0.149157i
$872$	−7.89464	−	15.4941i	−0.267346	−	0.524696i
$873$	7.77913	−	15.2674i	0.263284	−	0.516723i
$874$	−3.52861	−	4.85671i	−0.119357	−	0.164281i
$875$	−28.5118	+	15.8196i	−0.963875	+	0.534801i
$876$	28.2536	−	9.18015i	0.954601	−	0.310169i
$877$	25.9562	−	13.2254i	0.876480	−	0.446589i	0.0429592	−	0.999077i	$-0.486321\pi$
$877$	25.9562	−	13.2254i	0.876480	−	0.446589i	0.833521	+	0.552488i	$0.186321\pi$
$878$	0.238560	+	1.50621i	0.00805101	+	0.0508321i
$879$	−16.7229			−0.564048
$880$		0			0
$881$	4.18815			0.141102			0.0705512	−	0.997508i	$-0.477524\pi$
$881$	4.18815			0.141102			0.0705512	+	0.997508i	$0.477524\pi$
$882$	0.195725	+	1.23576i	0.00659041	+	0.0416102i
$883$	−40.7349	+	20.7555i	−1.37084	+	0.698477i	−0.975488	−	0.220053i	$-0.929377\pi$
$883$	−40.7349	+	20.7555i	−1.37084	+	0.698477i	−0.395351	+	0.918530i	$0.629377\pi$
$884$	−25.8286	+	8.39221i	−0.868709	+	0.282261i
$885$	0.262106	+	4.08137i	0.00881059	+	0.137194i
$886$	9.11003	+	12.5389i	0.306057	+	0.421252i
$887$	15.6438	−	30.7027i	0.525267	−	1.03090i	−0.464144	−	0.885760i	$-0.653638\pi$
$887$	15.6438	−	30.7027i	0.525267	−	1.03090i	0.989412	−	0.145136i	$-0.0463619\pi$
$888$	−1.10529	−	2.16926i	−0.0370912	−	0.0727955i
$889$	16.1646	−	22.2487i	0.542143	−	0.746196i
$890$	−6.52371	+	10.3093i	−0.218675	+	0.345569i
$891$		0			0
$892$	7.70048	−	7.70048i	0.257831	−	0.257831i
$893$	14.9068	−	2.36100i	0.498836	−	0.0790078i
$894$	9.51300	+	3.09096i	0.318162	+	0.103377i
$895$	−4.28246	+	2.54016i	−0.143147	+	0.0849081i
$896$	26.6503	−	19.3626i	0.890323	−	0.646857i
$897$	9.87594	+	1.56420i	0.329748	+	0.0522270i
$898$	15.2266	+	7.75836i	0.508119	+	0.258900i
$899$	−5.50871	+	16.9541i	−0.183726	+	0.565450i
$900$	14.7310	+	2.77042i	0.491035	+	0.0923473i
$901$			7.78489i			0.259352i
$902$		0			0
$903$	−16.8566	−	16.8566i	−0.560951	−	0.560951i
$904$	−30.1177	−	21.8818i	−1.00170	−	0.727778i
$905$	−0.899623	+	9.65092i	−0.0299045	+	0.320807i
$906$	3.05911	+	9.41497i	0.101632	+	0.312791i
$907$	6.02474	−	38.0387i	0.200048	−	1.26306i	−0.659384	−	0.751806i	$-0.729183\pi$
$907$	6.02474	−	38.0387i	0.200048	−	1.26306i	0.859433	−	0.511249i	$-0.170817\pi$
$908$	0.913965	−	5.77055i	0.0303310	−	0.191502i
$909$	1.00402	+	3.09005i	0.0333012	+	0.102490i
$910$	7.17330	−	5.95000i	0.237793	−	0.197241i
$911$	29.8280	+	21.6713i	0.988244	+	0.718002i	0.959536	−	0.281586i	$-0.0908605\pi$
$911$	29.8280	+	21.6713i	0.988244	+	0.718002i	0.0287085	+	0.999588i	$0.490861\pi$
$912$	8.67283	+	8.67283i	0.287186	+	0.287186i
$913$		0			0
$914$			2.49056i			0.0823805i
$915$	−16.4263	+	6.52836i	−0.543038	+	0.215821i
$916$	−2.90677	+	8.94611i	−0.0960423	+	0.295588i
$917$	−19.5326	−	9.95237i	−0.645024	−	0.328656i
$918$	−13.6122	−	2.15595i	−0.449268	−	0.0711571i
$919$	−24.5973	+	17.8710i	−0.811392	+	0.589510i	−0.914234	−	0.405187i	$-0.867206\pi$
$919$	−24.5973	+	17.8710i	−0.811392	+	0.589510i	0.102842	+	0.994698i	$0.467206\pi$
$920$	−6.28381	−	10.5939i	−0.207171	−	0.349270i
$921$	−1.34081	−	0.435657i	−0.0441813	−	0.0143554i
$922$	−6.01478	+	0.952647i	−0.198086	+	0.0313738i
$923$	−5.94554	+	5.94554i	−0.195700	+	0.195700i
$924$		0			0
$925$	1.95599	−	5.47762i	0.0643126	−	0.180103i
$926$	7.82350	−	10.7681i	0.257096	−	0.353862i
$927$	4.76812	+	9.35797i	0.156606	+	0.307356i
$928$	−5.95063	+	11.6788i	−0.195339	+	0.383374i
$929$	−13.6936	−	18.8477i	−0.449273	−	0.618372i	0.522968	−	0.852352i	$-0.324825\pi$
$929$	−13.6936	−	18.8477i	−0.449273	−	0.618372i	−0.972241	+	0.233981i	$0.924825\pi$
$930$	−6.29784	−	5.53775i	−0.206514	−	0.181590i
$931$	−5.86938	+	1.90708i	−0.192361	+	0.0625020i
$932$	−6.93458	+	3.53335i	−0.227150	+	0.115739i
$933$	2.52147	+	15.9199i	0.0825493	+	0.521196i
$934$	−19.3837			−0.634254
$935$		0			0
$936$	−9.14869			−0.299034
$937$	−1.25828	−	7.94449i	−0.0411063	−	0.259535i	0.958573	−	0.284846i	$-0.0919425\pi$
$937$	−1.25828	−	7.94449i	−0.0411063	−	0.259535i	−0.999680	+	0.0253108i	$0.991942\pi$
$938$	2.35937	−	1.20216i	0.0770362	−	0.0392519i
$939$	−0.801481	+	0.260417i	−0.0261553	+	0.00849838i
$940$	14.4719	−	0.929389i	0.472023	−	0.0303133i
$941$	−28.1490	−	38.7438i	−0.917631	−	1.26301i	−0.964493	−	0.264110i	$-0.914922\pi$
$941$	−28.1490	−	38.7438i	−0.917631	−	1.26301i	0.0468615	−	0.998901i	$-0.485078\pi$
$942$	5.42198	−	10.6412i	0.176658	−	0.346710i
$943$	−4.84037	−	9.49976i	−0.157624	−	0.309355i
$944$	2.47782	−	3.41042i	0.0806460	−	0.111000i
$945$	−34.0840	+	7.66523i	−1.10875	+	0.249350i
$946$		0			0
$947$	9.38618	−	9.38618i	0.305010	−	0.305010i	−0.537960	−	0.842970i	$-0.680805\pi$
$947$	9.38618	−	9.38618i	0.305010	−	0.305010i	0.842970	+	0.537960i	$0.180805\pi$
$948$	−30.2219	+	4.78668i	−0.981563	+	0.155464i
$949$	−41.1978	−	13.3860i	−1.33734	−	0.434528i
$950$	0.288388	−	10.0053i	0.00935654	−	0.324613i
$951$	15.7309	−	11.4292i	0.510109	−	0.370616i
$952$	−27.8746	−	4.41491i	−0.903422	−	0.143088i
$953$	−47.4428	−	24.1733i	−1.53682	−	0.783051i	−0.538597	−	0.842564i	$-0.681045\pi$
$953$	−47.4428	−	24.1733i	−1.53682	−	0.783051i	−0.998228	+	0.0595128i	$0.981045\pi$
$954$	−0.379511	+	1.16802i	−0.0122871	+	0.0378159i
$955$	−8.37297	−	3.61039i	−0.270943	−	0.116829i
$956$			18.4130i			0.595519i
$957$		0			0
$958$	13.2098	+	13.2098i	0.426790	+	0.426790i
$959$	36.2628	+	26.3465i	1.17099	+	0.850772i
$960$	4.60584	+	5.55279i	0.148653	+	0.179215i
$961$	4.46097	+	13.7294i	0.143902	+	0.442885i
$962$	−0.260069	+	1.64201i	−0.00838495	+	0.0529405i
$963$	0.115950	−	0.732081i	0.00373644	−	0.0235910i
$964$	15.1642	+	46.6706i	0.488406	+	1.50316i
$965$	−29.8371	−	35.9716i	−0.960491	−	1.15797i
$966$	3.93674	+	2.86021i	0.126662	+	0.0920256i
$967$	38.6475	+	38.6475i	1.24282	+	1.24282i	0.958826	+	0.283994i	$0.0916596\pi$
$967$	38.6475	+	38.6475i	1.24282	+	1.24282i	0.283994	+	0.958826i	$0.408340\pi$
$968$		0			0
$969$		−	24.6055i		−	0.790443i
$970$	−10.0958	−	4.35325i	−0.324155	−	0.139774i
$971$	2.55556	−	7.86521i	0.0820119	−	0.252407i	−0.901640	−	0.432487i	$-0.857636\pi$
$971$	2.55556	−	7.86521i	0.0820119	−	0.252407i	0.983652	+	0.180081i	$0.0576360\pi$
$972$	23.4395	+	11.9430i	0.751823	+	0.383073i
$973$	11.9898	+	1.89900i	0.384375	+	0.0608790i
$974$	10.7378	−	7.80149i	0.344062	−	0.249976i
$975$	11.4442	+	12.1235i	0.366508	+	0.388263i
$976$	17.3278	+	5.63014i	0.554649	+	0.180216i
$977$	−54.0805	+	8.56551i	−1.73019	+	0.274035i	−0.940579	−	0.339575i	$-0.889717\pi$
$977$	−54.0805	+	8.56551i	−1.73019	+	0.274035i	−0.789610	+	0.613610i	$0.789717\pi$
$978$	−4.10153	+	4.10153i	−0.131152	+	0.131152i
$979$		0			0
$980$	−5.78535	+	1.30108i	−0.184806	+	0.0415614i
$981$	9.46980	−	13.0341i	0.302347	−	0.416145i
$982$	−0.880571	−	1.72822i	−0.0281001	−	0.0551496i
$983$	−6.19202	+	12.1525i	−0.197495	+	0.387606i	−0.968422	−	0.249318i	$-0.919793\pi$
$983$	−6.19202	+	12.1525i	−0.197495	+	0.387606i	0.770927	+	0.636924i	$0.219793\pi$
$984$	−4.37373	−	6.01992i	−0.139429	−	0.191908i
$985$	−0.674648	+	0.0433259i	−0.0214961	+	0.00138048i
$986$	6.47069	−	2.10245i	0.206069	−	0.0669558i
$987$	−10.9003	+	5.55398i	−0.346960	+	0.176785i
$988$	−3.30589	−	20.8726i	−0.105174	−	0.664045i
$989$	21.5139			0.684102
$990$		0			0
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	5.22613	+	32.9965i	0.165930	+	1.04764i
$993$	15.1453	−	7.71694i	0.480623	−	0.244890i
$994$	−3.89164	+	1.26447i	−0.123435	+	0.0401066i
$995$	−18.6083	−	16.3625i	−0.589924	−	0.518726i
$996$	7.88351	+	10.8507i	0.249799	+	0.343818i
$997$	9.65934	−	18.9575i	0.305914	−	0.600391i	−0.685956	−	0.727643i	$-0.740616\pi$
$997$	9.65934	−	18.9575i	0.305914	−	0.600391i	0.991870	+	0.127252i	$0.0406158\pi$
$998$	1.42445	+	2.79564i	0.0450901	+	0.0884943i
$999$	3.66296	−	5.04163i	0.115891	−	0.159510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.e.403.3		32
5.2	odd	4	inner	605.2.m.e.282.2		32
11.2	odd	10		605.2.m.d.578.2		32
11.3	even	5		55.2.l.a.8.3	yes	32
11.4	even	5		605.2.m.d.233.2		32
11.5	even	5		605.2.e.b.483.8		32
11.6	odd	10		605.2.e.b.483.9		32
11.7	odd	10		605.2.m.c.233.3		32
11.8	odd	10	inner	605.2.m.e.118.2		32
11.9	even	5		605.2.m.c.578.3		32
11.10	odd	2		55.2.l.a.18.2	yes	32
33.14	odd	10		495.2.bj.a.118.2		32
33.32	even	2		495.2.bj.a.73.3		32
44.3	odd	10		880.2.cm.a.833.2		32
44.43	even	2		880.2.cm.a.513.3		32
55.2	even	20		605.2.m.d.457.2		32
55.3	odd	20		275.2.bm.b.107.3		32
55.7	even	20		605.2.m.c.112.3		32
55.14	even	10		275.2.bm.b.118.2		32
55.17	even	20		605.2.e.b.362.8		32
55.27	odd	20		605.2.e.b.362.9		32
55.32	even	4		55.2.l.a.7.3	✓	32
55.37	odd	20		605.2.m.d.112.2		32
55.42	odd	20		605.2.m.c.457.3		32
55.43	even	4		275.2.bm.b.7.2		32
55.47	odd	20		55.2.l.a.52.2	yes	32
55.52	even	20	inner	605.2.m.e.602.3		32
55.54	odd	2		275.2.bm.b.18.3		32
165.32	odd	4		495.2.bj.a.172.2		32
165.47	even	20		495.2.bj.a.217.3		32
220.47	even	20		880.2.cm.a.657.3		32
220.87	odd	4		880.2.cm.a.337.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	55.32	even	4
55.2.l.a.8.3	yes	32	11.3	even	5
55.2.l.a.18.2	yes	32	11.10	odd	2
55.2.l.a.52.2	yes	32	55.47	odd	20
275.2.bm.b.7.2		32	55.43	even	4
275.2.bm.b.18.3		32	55.54	odd	2
275.2.bm.b.107.3		32	55.3	odd	20
275.2.bm.b.118.2		32	55.14	even	10
495.2.bj.a.73.3		32	33.32	even	2
495.2.bj.a.118.2		32	33.14	odd	10
495.2.bj.a.172.2		32	165.32	odd	4
495.2.bj.a.217.3		32	165.47	even	20
605.2.e.b.362.8		32	55.17	even	20
605.2.e.b.362.9		32	55.27	odd	20
605.2.e.b.483.8		32	11.5	even	5
605.2.e.b.483.9		32	11.6	odd	10
605.2.m.c.112.3		32	55.7	even	20
605.2.m.c.233.3		32	11.7	odd	10
605.2.m.c.457.3		32	55.42	odd	20
605.2.m.c.578.3		32	11.9	even	5
605.2.m.d.112.2		32	55.37	odd	20
605.2.m.d.233.2		32	11.4	even	5
605.2.m.d.457.2		32	55.2	even	20
605.2.m.d.578.2		32	11.2	odd	10
605.2.m.e.118.2		32	11.8	odd	10	inner
605.2.m.e.282.2		32	5.2	odd	4	inner
605.2.m.e.403.3		32	1.1	even	1	trivial
605.2.m.e.602.3		32	55.52	even	20	inner
880.2.cm.a.337.2		32	220.87	odd	4
880.2.cm.a.513.3		32	44.43	even	2
880.2.cm.a.657.3		32	220.47	even	20
880.2.cm.a.833.2		32	44.3	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0763931 + 0.482327i) q^{2} +(-1.01518 + 0.517260i) q^{3} +(1.67531 - 0.544341i) q^{4} +(1.47656 - 1.67922i) q^{5} +(-0.327041 - 0.450133i) q^{6} +(1.32402 - 2.59854i) q^{7} +(0.833936 + 1.63669i) q^{8} +(-1.00032 + 1.37683i) q^{9} +(0.922733 + 0.583903i) q^{10} +(-1.41917 + 1.41917i) q^{12} +(2.89049 - 0.457808i) q^{13} +(1.35449 + 0.440102i) q^{14} +(-0.630376 + 2.46847i) q^{15} +(2.12449 - 1.54353i) q^{16} +(-5.20325 - 0.824113i) q^{17} +(-0.740500 - 0.377304i) q^{18} +(1.26677 - 3.89873i) q^{19} +(1.55962 - 3.61696i) q^{20} +3.32285i q^{21} +(-2.12046 - 2.12046i) q^{23} +(-1.69319 - 1.23017i) q^{24} +(-0.639563 - 4.95893i) q^{25} +(0.441627 + 1.35919i) q^{26} +(0.838037 - 5.29116i) q^{27} +(0.803656 - 5.07408i) q^{28} +(0.817241 + 2.51521i) q^{29} +(-1.23877 - 0.115473i) q^{30} +(5.45328 + 3.96204i) q^{31} +(3.50456 + 3.50456i) q^{32} -2.57262i q^{34} +(-2.40853 - 6.06022i) q^{35} +(-0.926389 + 2.85113i) q^{36} +(1.03649 + 0.528116i) q^{37} +(1.97724 + 0.313163i) q^{38} +(-2.69755 + 1.95989i) q^{39} +(3.97972 + 1.01630i) q^{40} +(3.38136 + 1.09867i) q^{41} +(-1.60270 + 0.253843i) q^{42} +(-5.07292 + 5.07292i) q^{43} +(0.834964 + 3.71273i) q^{45} +(0.860769 - 1.18475i) q^{46} +(1.67145 + 3.28041i) q^{47} +(-1.35833 + 2.66588i) q^{48} +(-0.884888 - 1.21794i) q^{49} +(2.34297 - 0.687307i) q^{50} +(5.70851 - 1.85481i) q^{51} +(4.59325 - 2.34038i) q^{52} +(-0.231169 - 1.45955i) q^{53} +2.61609 q^{54} +5.35716 q^{56} +(0.730652 + 4.61316i) q^{57} +(-1.15072 + 0.586323i) q^{58} +(1.52672 - 0.496061i) q^{59} +(0.287615 + 4.47859i) q^{60} +(4.07810 + 5.61302i) q^{61} +(-1.49441 + 2.93294i) q^{62} +(2.25330 + 4.42234i) q^{63} +(1.66445 - 2.29092i) q^{64} +(3.49920 - 5.52974i) q^{65} +(1.31471 - 1.31471i) q^{67} +(-9.16564 + 1.45170i) q^{68} +(3.24948 + 1.05582i) q^{69} +(2.73902 - 1.62466i) q^{70} +(-2.32441 + 1.68878i) q^{71} +(-3.08765 - 0.489036i) q^{72} +(-13.1886 - 6.71992i) q^{73} +(-0.175544 + 0.540270i) q^{74} +(3.21432 + 4.70338i) q^{75} -7.22113i q^{76} +(-1.15138 - 1.15138i) q^{78} +(12.3342 + 8.96129i) q^{79} +(0.544999 - 5.84661i) q^{80} +(0.308439 + 0.949277i) q^{81} +(-0.271606 + 1.71486i) q^{82} +(1.04540 - 6.60041i) q^{83} +(1.80876 + 5.56680i) q^{84} +(-9.06675 + 7.52055i) q^{85} +(-2.83434 - 2.05927i) q^{86} +(-2.13066 - 2.13066i) q^{87} +11.1726i q^{89} +(-1.72697 + 0.686353i) q^{90} +(2.63744 - 8.11720i) q^{91} +(-4.70669 - 2.39818i) q^{92} +(-7.58545 - 1.20142i) q^{93} +(-1.45454 + 1.05679i) q^{94} +(-4.67636 - 7.88388i) q^{95} +(-5.37052 - 1.74499i) q^{96} +(-9.94447 + 1.57505i) q^{97} +(0.519848 - 0.519848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8} + 12 q^{12} + 10 q^{13} + 14 q^{15} - 8 q^{16} + 10 q^{18} + 16 q^{20} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} - 50 q^{28} - 30 q^{30} - 28 q^{31}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 - 4 * q^3 - 2 * q^5 + 20 * q^6 + 10 * q^8 + 12 * q^12 + 10 * q^13 + 14 * q^15 - 8 * q^16 + 10 * q^18 + 16 * q^20 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 - 50 * q^28 - 30 * q^30 - 28 * q^31 + 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 + 50 * q^40 - 40 * q^41 - 10 * q^42 - 28 * q^45 - 60 * q^46 - 28 * q^47 - 54 * q^48 + 50 * q^50 - 20 * q^51 + 50 * q^52 - 24 * q^53 - 80 * q^56 - 30 * q^57 - 50 * q^58 + 34 * q^60 + 60 * q^61 - 100 * q^62 + 30 * q^63 - 8 * q^67 + 30 * q^68 + 30 * q^70 + 24 * q^71 - 80 * q^72 - 50 * q^73 + 34 * q^75 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 - 90 * q^83 - 30 * q^85 + 100 * q^86 + 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 + 40 * q^95 - 8 * q^97

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