LMFDB - Embedded newform 845.2.n.h.484.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(484,845)] 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("845.484"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,16,0,-16] 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.3
Character	$\chi$	$=$	845.484
Dual form			845.2.n.h.529.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86013 + 1.07395i) q^{2} +(2.05625 - 1.18717i) q^{3} +(1.30673 - 2.26333i) q^{4} +(1.11435 + 1.93861i) q^{5} +(-2.54993 + 4.41661i) q^{6} +(3.07334 + 1.77439i) q^{7} +1.31766i q^{8} +(1.31877 - 2.28417i) q^{9} +(-4.15482 - 2.40932i) q^{10} +(-1.04426 - 1.80871i) q^{11} -6.20528i q^{12} -7.62244 q^{14} +(4.59285 + 2.66334i) q^{15} +(1.19836 + 2.07562i) q^{16} +(5.19678 + 3.00036i) q^{17} +5.66516i q^{18} +(-2.52362 + 4.37104i) q^{19} +(5.84388 + 0.0111067i) q^{20} +8.42607 q^{21} +(3.88493 + 2.24297i) q^{22} +(1.84180 - 1.06337i) q^{23} +(1.56430 + 2.70944i) q^{24} +(-2.51644 + 4.32059i) q^{25} +0.860615i q^{27} +(8.03208 - 4.63732i) q^{28} +(-5.07154 - 8.78417i) q^{29} +(-11.4036 - 0.0216733i) q^{30} +3.10862 q^{31} +(-6.74049 - 3.89162i) q^{32} +(-4.29452 - 2.47944i) q^{33} -12.8889 q^{34} +(-0.0150816 + 7.93532i) q^{35} +(-3.44656 - 5.96961i) q^{36} +(0.0865149 - 0.0499494i) q^{37} -10.8410i q^{38} +(-2.55444 + 1.46834i) q^{40} +(-1.89809 - 3.28758i) q^{41} +(-15.6736 + 9.04917i) q^{42} +(1.83303 + 1.05830i) q^{43} -5.45829 q^{44} +(5.89770 + 0.0112090i) q^{45} +(-2.28400 + 3.95601i) q^{46} -5.00374i q^{47} +(4.92826 + 2.84533i) q^{48} +(2.79695 + 4.84446i) q^{49} +(0.0408221 - 10.7394i) q^{50} +14.2478 q^{51} +5.29557i q^{53} +(-0.924257 - 1.60086i) q^{54} +(2.34272 - 4.03996i) q^{55} +(-2.33806 + 4.04963i) q^{56} +11.9839i q^{57} +(18.8675 + 10.8932i) q^{58} +(-1.50179 + 2.60118i) q^{59} +(12.0296 - 6.91487i) q^{60} +(2.38336 - 4.12811i) q^{61} +(-5.78245 + 3.33850i) q^{62} +(8.10605 - 4.68003i) q^{63} +11.9242 q^{64} +10.6512 q^{66} +(-5.86866 + 3.38827i) q^{67} +(13.5816 - 7.84135i) q^{68} +(2.52480 - 4.37309i) q^{69} +(-8.49408 - 14.7770i) q^{70} +(2.44796 - 4.24000i) q^{71} +(3.00977 + 1.73769i) q^{72} +4.02118i q^{73} +(-0.107286 + 0.185825i) q^{74} +(-0.0451260 + 11.8717i) q^{75} +(6.59541 + 11.4236i) q^{76} -7.41173i q^{77} +4.71456 q^{79} +(-2.68844 + 4.63614i) q^{80} +(4.97801 + 8.62216i) q^{81} +(7.06139 + 4.07690i) q^{82} -11.2703i q^{83} +(11.0106 - 19.0710i) q^{84} +(-0.0255018 + 13.4180i) q^{85} -4.54625 q^{86} +(-20.8567 - 12.0416i) q^{87} +(2.38328 - 1.37599i) q^{88} +(0.952337 + 1.64950i) q^{89} +(-10.9826 + 6.31298i) q^{90} -5.55814i q^{92} +(6.39209 - 3.69047i) q^{93} +(5.37376 + 9.30762i) q^{94} +(-11.2860 - 0.0214497i) q^{95} -18.4802 q^{96} +(-4.65004 - 2.68470i) q^{97} +(-10.4054 - 6.00757i) q^{98} -5.50856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 16 q^{4} - 16 q^{6} + 18 q^{9} - 13 q^{10} - 22 q^{11} - 8 q^{14} - 8 q^{15} + 12 q^{16} + 28 q^{19} + 10 q^{20} + 52 q^{21} + 34 q^{24} - 16 q^{25} - 20 q^{29} - 31 q^{30} + 64 q^{31} - 36 q^{34}+ \cdots - 152 q^{99}+O(q^{100}) $ 36 * q + 16 * q^4 - 16 * q^6 + 18 * q^9 - 13 * q^10 - 22 * q^11 - 8 * q^14 - 8 * q^15 + 12 * q^16 + 28 * q^19 + 10 * q^20 + 52 * q^21 + 34 * q^24 - 16 * q^25 - 20 * q^29 - 31 * q^30 + 64 * q^31 - 36 * q^34 - 10 * q^35 - 32 * q^36 + 6 * q^40 - 52 * q^41 - 100 * q^44 - 5 * q^45 - 30 * q^46 + 44 * q^49 - 29 * q^50 - 80 * q^51 + 90 * q^54 + 20 * q^55 + 20 * q^56 + 76 * q^59 + 86 * q^60 - 8 * q^61 + 136 * q^64 + 16 * q^66 + 30 * q^69 + 92 * q^70 - 72 * q^71 + 30 * q^74 - 13 * q^75 - 4 * q^76 - 32 * q^79 - 73 * q^80 + 30 * q^81 + 78 * q^84 - 29 * q^85 - 60 * q^86 + 94 * q^89 - 140 * q^90 - 128 * q^94 - 41 * q^95 - 36 * q^96 - 152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.86013	+	1.07395i	−1.31531	+	0.759397i	−0.982971	−	0.183762i	$-0.941172\pi$
$2$	−1.86013	+	1.07395i	−1.31531	+	0.759397i	−0.332343	+	0.943159i	$0.607839\pi$
$3$	2.05625	−	1.18717i	1.18717	−	0.685416i	0.229511	−	0.973306i	$-0.426287\pi$
$3$	2.05625	−	1.18717i	1.18717	−	0.685416i	0.957663	+	0.287890i	$0.0929538\pi$
$4$	1.30673	−	2.26333i	0.653367	−	1.13166i
$5$	1.11435	+	1.93861i	0.498353	+	0.866974i
$5$	1.11435	+	1.93861i	0.498353	+	0.866974i
$6$	−2.54993	+	4.41661i	−1.04100	+	1.80307i
$7$	3.07334	+	1.77439i	1.16161	+	0.670658i	0.951690	−	0.307060i	$-0.0993451\pi$
$7$	3.07334	+	1.77439i	1.16161	+	0.670658i	0.209924	+	0.977718i	$0.432678\pi$
$8$			1.31766i			0.465865i
$9$	1.31877	−	2.28417i	0.439589	−	0.761391i
$10$	−4.15482	−	2.40932i	−1.31387	−	0.761895i
$11$	−1.04426	−	1.80871i	−0.314857	−	0.545348i	0.664550	−	0.747243i	$-0.268623\pi$
$11$	−1.04426	−	1.80871i	−0.314857	−	0.545348i	−0.979407	+	0.201896i	$0.935290\pi$
$12$		−	6.20528i		−	1.79131i
$13$		0			0
$13$		0			0
$14$	−7.62244			−2.03718
$15$	4.59285	+	2.66334i	1.18587	+	0.687671i
$16$	1.19836	+	2.07562i	0.299591	+	0.518906i
$17$	5.19678	+	3.00036i	1.26040	+	0.727695i	0.973153	−	0.230161i	$-0.0739252\pi$
$17$	5.19678	+	3.00036i	1.26040	+	0.727695i	0.287251	+	0.957855i	$0.407259\pi$
$18$			5.66516i			1.33529i
$19$	−2.52362	+	4.37104i	−0.578959	+	1.00279i	0.416640	+	0.909071i	$0.363208\pi$
$19$	−2.52362	+	4.37104i	−0.578959	+	1.00279i	−0.995599	+	0.0937148i	$0.970126\pi$
$20$	5.84388	+	0.0111067i	1.30673	+	0.00248353i
$21$	8.42607			1.83872
$22$	3.88493	+	2.24297i	0.828271	+	0.478202i
$23$	1.84180	−	1.06337i	0.384043	−	0.221727i	−0.295533	−	0.955333i	$-0.595497\pi$
$23$	1.84180	−	1.06337i	0.384043	−	0.221727i	0.679576	+	0.733605i	$0.262164\pi$
$24$	1.56430	+	2.70944i	0.319311	+	0.553063i
$25$	−2.51644	+	4.32059i	−0.503288	+	0.864119i
$26$		0			0
$27$			0.860615i			0.165625i
$28$	8.03208	−	4.63732i	1.51792	−	0.876371i
$29$	−5.07154	−	8.78417i	−0.941762	−	1.63118i	−0.762109	−	0.647449i	$-0.775836\pi$
$29$	−5.07154	−	8.78417i	−0.941762	−	1.63118i	−0.179653	−	0.983730i	$-0.557498\pi$
$30$	−11.4036	−	0.0216733i	−2.08201	−	0.00395699i
$31$	3.10862			0.558324			0.279162	−	0.960244i	$-0.409943\pi$
$31$	3.10862			0.558324			0.279162	+	0.960244i	$0.409943\pi$
$32$	−6.74049	−	3.89162i	−1.19156	−	0.687949i
$33$	−4.29452	−	2.47944i	−0.747580	−	0.431615i
$34$	−12.8889			−2.21044
$35$	−0.0150816	+	7.93532i	−0.00254926	+	1.34131i
$36$	−3.44656	−	5.96961i	−0.574426	−	0.994935i
$37$	0.0865149	−	0.0499494i	0.0142230	−	0.00821163i	−0.492872	−	0.870102i	$-0.664053\pi$
$37$	0.0865149	−	0.0499494i	0.0142230	−	0.00821163i	0.507095	+	0.861890i	$0.330719\pi$
$38$		−	10.8410i		−	1.75864i
$39$		0			0
$40$	−2.55444	+	1.46834i	−0.403893	+	0.232165i
$41$	−1.89809	−	3.28758i	−0.296431	−	0.513434i	0.678886	−	0.734244i	$-0.262463\pi$
$41$	−1.89809	−	3.28758i	−0.296431	−	0.513434i	−0.975317	+	0.220810i	$0.929130\pi$
$42$	−15.6736	+	9.04917i	−2.41849	+	1.39632i
$43$	1.83303	+	1.05830i	0.279535	+	0.161390i	0.633213	−	0.773978i	$-0.281736\pi$
$43$	1.83303	+	1.05830i	0.279535	+	0.161390i	−0.353678	+	0.935367i	$0.615069\pi$
$44$	−5.45829			−0.822868
$45$	5.89770	+	0.0112090i	0.879177	+	0.00167094i
$46$	−2.28400	+	3.95601i	−0.336758	+	0.583282i
$47$		−	5.00374i		−	0.729870i	−0.931033	−	0.364935i	$-0.881091\pi$
$47$		−	5.00374i		−	0.729870i	0.931033	−	0.364935i	$-0.118909\pi$
$48$	4.92826	+	2.84533i	0.711333	+	0.410688i
$49$	2.79695	+	4.84446i	0.399565	+	0.692066i
$50$	0.0408221	−	10.7394i	0.00577312	−	1.51878i
$51$	14.2478			1.99509
$52$		0			0
$53$			5.29557i			0.727402i	0.931516	+	0.363701i	$0.118487\pi$
$53$			5.29557i			0.727402i	−0.931516	+	0.363701i	$0.881513\pi$
$54$	−0.924257	−	1.60086i	−0.125775	−	0.217849i
$55$	2.34272	−	4.03996i	0.315893	−	0.544748i
$56$	−2.33806	+	4.04963i	−0.312436	+	0.541155i
$57$			11.9839i			1.58731i
$58$	18.8675	+	10.8932i	2.47742	+	1.43034i
$59$	−1.50179	+	2.60118i	−0.195517	+	0.338645i	−0.947070	−	0.321028i	$-0.895972\pi$
$59$	−1.50179	+	2.60118i	−0.195517	+	0.338645i	0.751553	+	0.659672i	$0.229305\pi$
$60$	12.0296	−	6.91487i	1.55302	−	0.892706i
$61$	2.38336	−	4.12811i	0.305158	−	0.528550i	−0.672138	−	0.740426i	$-0.734624\pi$
$61$	2.38336	−	4.12811i	0.305158	−	0.528550i	0.977297	+	0.211876i	$0.0679572\pi$
$62$	−5.78245	+	3.33850i	−0.734371	+	0.423990i
$63$	8.10605	−	4.68003i	1.02127	−	0.589628i
$64$	11.9242			1.49052
$65$		0			0
$66$	10.6512			1.31107
$67$	−5.86866	+	3.38827i	−0.716971	+	0.413944i	−0.813637	−	0.581373i	$-0.802516\pi$
$67$	−5.86866	+	3.38827i	−0.716971	+	0.413944i	0.0966656	+	0.995317i	$0.469182\pi$
$68$	13.5816	−	7.84135i	1.64701	−	0.950903i
$69$	2.52480	−	4.37309i	0.303951	−	0.526458i
$70$	−8.49408	−	14.7770i	−1.01524	−	1.76618i
$71$	2.44796	−	4.24000i	0.290520	−	0.503195i	−0.683413	−	0.730032i	$-0.739505\pi$
$71$	2.44796	−	4.24000i	0.290520	−	0.503195i	0.973933	+	0.226837i	$0.0728385\pi$
$72$	3.00977	+	1.73769i	0.354705	+	0.204789i
$73$			4.02118i			0.470643i	0.971918	+	0.235321i	$0.0756143\pi$
$73$			4.02118i			0.470643i	−0.971918	+	0.235321i	$0.924386\pi$
$74$	−0.107286	+	0.185825i	−0.0124718	+	0.0216018i
$75$	−0.0451260	+	11.8717i	−0.00521070	+	1.37082i
$76$	6.59541	+	11.4236i	0.756545	+	1.31037i
$77$		−	7.41173i		−	0.844645i
$78$		0			0
$79$	4.71456			0.530429			0.265215	−	0.964189i	$-0.414557\pi$
$79$	4.71456			0.530429			0.265215	+	0.964189i	$0.414557\pi$
$80$	−2.68844	+	4.63614i	−0.300576	+	0.518336i
$81$	4.97801	+	8.62216i	0.553112	+	0.958018i
$82$	7.06139	+	4.07690i	0.779800	+	0.450218i
$83$		−	11.2703i		−	1.23707i	−0.785757	−	0.618536i	$-0.787726\pi$
$83$		−	11.2703i		−	1.23707i	0.785757	−	0.618536i	$-0.212274\pi$
$84$	11.0106	−	19.0710i	1.20136	−	2.08081i
$85$	−0.0255018	+	13.4180i	−0.00276606	+	1.45539i
$86$	−4.54625			−0.490235
$87$	−20.8567	−	12.0416i	−2.23607	−	1.29100i
$88$	2.38328	−	1.37599i	0.254058	−	0.146681i
$89$	0.952337	+	1.64950i	0.100948	+	0.174846i	0.912075	−	0.410023i	$-0.134479\pi$
$89$	0.952337	+	1.64950i	0.100948	+	0.174846i	−0.811128	+	0.584869i	$0.801146\pi$
$90$	−10.9826	+	6.31298i	−1.15766	+	0.665446i
$91$		0			0
$92$		−	5.55814i		−	0.579477i
$93$	6.39209	−	3.69047i	0.662828	−	0.382684i
$94$	5.37376	+	9.30762i	0.554261	+	0.960008i
$95$	−11.2860	−	0.0214497i	−1.15792	−	0.00220070i
$96$	−18.4802			−1.88612
$97$	−4.65004	−	2.68470i	−0.472140	−	0.272590i	0.244995	−	0.969524i	$-0.421214\pi$
$97$	−4.65004	−	2.68470i	−0.472140	−	0.272590i	−0.717135	+	0.696934i	$0.754547\pi$
$98$	−10.4054	−	6.00757i	−1.05111	−	0.606856i
$99$	−5.50856			−0.553631
$100$	6.49060	+	11.3414i	0.649060	+	1.13414i
$101$	5.60547	+	9.70896i	0.557765	+	0.966078i	0.997683	+	0.0680393i	$0.0216743\pi$
$101$	5.60547	+	9.70896i	0.557765	+	0.966078i	−0.439918	+	0.898038i	$0.644992\pi$
$102$	−26.5029	+	15.3014i	−2.62417	+	1.51507i
$103$			11.8123i			1.16390i	0.813224	+	0.581951i	$0.197710\pi$
$103$			11.8123i			1.16390i	−0.813224	+	0.581951i	$0.802290\pi$
$104$		0			0
$105$	9.38960	+	16.3349i	0.916331	+	1.59412i
$106$	−5.68717	−	9.85047i	−0.552387	−	0.956762i
$107$	4.77561	−	2.75720i	0.461675	−	0.266548i	−0.251073	−	0.967968i	$-0.580783\pi$
$107$	4.77561	−	2.75720i	0.461675	−	0.266548i	0.712748	+	0.701420i	$0.247450\pi$
$108$	1.94786	+	1.12459i	0.187432	+	0.108214i
$109$	12.0982			1.15880			0.579401	−	0.815043i	$-0.303287\pi$
$109$	12.0982			1.15880			0.579401	+	0.815043i	$0.303287\pi$
$110$	−0.0190643	+	10.0308i	−0.00181771	+	0.956403i
$111$	0.118597	−	0.205417i	0.0112568	−	0.0194973i
$112$			8.50547i			0.803691i
$113$	−5.16509	−	2.98207i	−0.485891	−	0.280529i	0.236977	−	0.971515i	$-0.423843\pi$
$113$	−5.16509	−	2.98207i	−0.485891	−	0.280529i	−0.722868	+	0.690986i	$0.757177\pi$
$114$	−12.8701	−	22.2917i	−1.20540	−	2.08781i
$115$	4.11387	+	2.38558i	0.383621	+	0.222457i
$116$	−26.5086			−2.46126
$117$		0			0
$118$		−	6.45139i		−	0.593898i
$119$	10.6476	+	18.4423i	0.976068	+	1.69060i
$120$	−3.50939	+	6.05184i	−0.320362	+	0.552455i
$121$	3.31904	−	5.74874i	0.301731	−	0.522613i
$122$			10.2384i			0.926945i
$123$	−7.80587	−	4.50672i	−0.703831	−	0.406357i
$124$	4.06213	−	7.03582i	0.364790	−	0.631836i
$125$	−11.1802	−	0.0637465i	−0.999984	−	0.00570166i
$126$	−10.0522	+	17.4110i	−0.895524	+	1.55109i
$127$	−10.3837	+	5.99503i	−0.921405	+	0.531973i	−0.884083	−	0.467330i	$-0.845216\pi$
$127$	−10.3837	+	5.99503i	−0.921405	+	0.531973i	−0.0373216	+	0.999303i	$0.511883\pi$
$128$	−8.69959	+	5.02271i	−0.768943	+	0.443949i
$129$	5.02556			0.442476
$130$		0			0
$131$	−19.5464			−1.70777			−0.853886	−	0.520459i	$-0.825761\pi$
$131$	−19.5464			−1.70777			−0.853886	+	0.520459i	$0.825761\pi$
$132$	−11.2236	+	6.47994i	−0.976888	+	0.564006i
$133$	−15.5119	+	8.95581i	−1.34505	+	0.776567i
$134$	7.27767	−	12.6053i	0.628695	−	1.08893i
$135$	−1.66840	+	0.959028i	−0.143593	+	0.0825400i
$136$	−3.95347	+	6.84761i	−0.339007	+	0.587178i
$137$	11.1190	+	6.41957i	0.949962	+	0.548461i	0.893069	−	0.449919i	$-0.148547\pi$
$137$	11.1190	+	6.41957i	0.949962	+	0.548461i	0.0568932	+	0.998380i	$0.481881\pi$
$138$			10.8460i			0.923276i
$139$	2.69126	−	4.66141i	0.228270	−	0.395375i	−0.729025	−	0.684487i	$-0.760026\pi$
$139$	2.69126	−	4.66141i	0.228270	−	0.395375i	0.957296	+	0.289111i	$0.0933597\pi$
$140$	17.9405	+	10.4035i	1.51625	+	0.879255i
$141$	−5.94031	−	10.2889i	−0.500264	−	0.866483i
$142$			10.5160i			0.882479i
$143$		0			0
$144$	6.32145			0.526787
$145$	11.3776	−	19.6204i	0.944860	−	1.62939i
$146$	−4.31854	−	7.47993i	−0.357405	−	0.619043i
$147$	11.5024	+	6.64094i	0.948706	+	0.547736i
$148$		−	0.261082i		−	0.0214608i
$149$	7.77574	−	13.4680i	0.637013	−	1.10334i	−0.349072	−	0.937096i	$-0.613503\pi$
$149$	7.77574	−	13.4680i	0.637013	−	1.10334i	0.986085	−	0.166243i	$-0.0531637\pi$
$150$	−12.6656	−	22.1314i	−1.03414	−	1.80702i
$151$	11.6494			0.948012			0.474006	−	0.880522i	$-0.342808\pi$
$151$	11.6494			0.948012			0.474006	+	0.880522i	$0.342808\pi$
$152$	−5.75957	−	3.32529i	−0.467163	−	0.269717i
$153$	13.7067	−	7.91356i	1.10812	−	0.639774i
$154$	7.95982	+	13.7868i	0.641420	+	1.11097i
$155$	3.46409	+	6.02641i	0.278243	+	0.484053i
$156$		0			0
$157$		−	2.02732i		−	0.161798i	−0.996722	−	0.0808989i	$-0.974221\pi$
$157$		−	2.02732i		−	0.161798i	0.996722	−	0.0808989i	$-0.0257791\pi$
$158$	−8.76971	+	5.06320i	−0.697681	+	0.402806i
$159$	6.28676	+	10.8890i	0.498573	+	0.863553i
$160$	0.0330772	−	17.4038i	0.00261498	−	1.37589i
$161$	7.54732			0.594812
$162$	−18.5195	−	10.6922i	−1.45503	−	0.840062i
$163$	−7.34711	−	4.24185i	−0.575470	−	0.332248i	0.183861	−	0.982952i	$-0.441140\pi$
$163$	−7.34711	−	4.24185i	−0.575470	−	0.332248i	−0.759331	+	0.650705i	$0.774474\pi$
$164$	−9.92117			−0.774713
$165$	0.0210742	−	11.0884i	0.00164063	−	0.863229i
$166$	12.1037	+	20.9642i	0.939428	+	1.62714i
$167$	3.92266	−	2.26475i	0.303545	−	0.175252i	−0.340490	−	0.940248i	$-0.610593\pi$
$167$	3.92266	−	2.26475i	0.303545	−	0.175252i	0.644034	+	0.764997i	$0.277259\pi$
$168$			11.1027i			0.856594i
$169$		0			0
$170$	−14.3628	−	24.9867i	−1.10158	−	1.91639i
$171$	6.65615	+	11.5288i	0.509008	+	0.881628i
$172$	4.79057	−	2.76584i	0.365278	−	0.210893i
$173$	−0.893052	−	0.515604i	−0.0678975	−	0.0392006i	0.465667	−	0.884960i	$-0.345814\pi$
$173$	−0.893052	−	0.515604i	−0.0678975	−	0.0392006i	−0.533564	+	0.845759i	$0.679148\pi$
$174$	51.7283			3.92151
$175$	−15.4003	+	8.81350i	−1.16415	+	0.666238i
$176$	2.50281	−	4.33499i	0.188656	−	0.326762i
$177$			7.13155i			0.536040i
$178$	−3.54295	−	2.04552i	−0.265555	−	0.153318i
$179$	−8.70157	−	15.0716i	−0.650386	−	1.12650i	−0.983029	−	0.183449i	$-0.941274\pi$
$179$	−8.70157	−	15.0716i	−0.650386	−	1.12650i	0.332643	−	0.943053i	$-0.392060\pi$
$180$	7.73209	−	13.3338i	0.576316	−	0.993842i
$181$	−22.2540			−1.65412			−0.827062	−	0.562111i	$-0.809989\pi$
$181$	−22.2540			−1.65412			−0.827062	+	0.562111i	$0.809989\pi$
$182$		0			0
$183$		−	11.3179i		−	0.836642i
$184$	1.40116	+	2.42688i	0.103295	+	0.178912i
$185$	0.193241	+	0.112058i	0.0142073	+	0.00823865i
$186$	−7.92676	+	13.7295i	−0.581218	+	1.00670i
$187$		−	12.5326i		−	0.916478i
$188$	−11.3251	−	6.53855i	−0.825968	−	0.476873i
$189$	−1.52707	+	2.64496i	−0.111078	+	0.192393i
$190$	21.0165	−	12.0807i	1.52469	−	0.876423i
$191$	3.52968	−	6.11359i	0.255399	−	0.442364i	−0.709605	−	0.704600i	$-0.751127\pi$
$191$	3.52968	−	6.11359i	0.255399	−	0.442364i	0.965004	+	0.262236i	$0.0844598\pi$
$192$	24.5191	−	14.1561i	1.76951	−	1.02163i
$193$	18.8681	−	10.8935i	1.35815	−	0.784130i	0.368779	−	0.929517i	$-0.379776\pi$
$193$	18.8681	−	10.8935i	1.35815	−	0.784130i	0.989375	+	0.145387i	$0.0464427\pi$
$194$	11.5329			0.828016
$195$		0			0
$196$	14.6195			1.04425
$197$	−19.4369	+	11.2219i	−1.38482	+	0.799526i	−0.992726	−	0.120398i	$-0.961583\pi$
$197$	−19.4369	+	11.2219i	−1.38482	+	0.799526i	−0.392095	+	0.919925i	$0.628249\pi$
$198$	10.2467	−	5.91591i	0.728198	−	0.420425i
$199$	−6.10483	+	10.5739i	−0.432760	+	0.749562i	−0.997110	−	0.0759734i	$-0.975794\pi$
$199$	−6.10483	+	10.5739i	−0.432760	+	0.749562i	0.564350	+	0.825536i	$0.309127\pi$
$200$	−5.69309	−	3.31583i	−0.402562	−	0.234464i
$201$	−8.04495	+	13.9343i	−0.567447	+	0.982847i
$202$	−20.8539	−	12.0400i	−1.46727	−	0.847130i
$203$		−	35.9957i		−	2.52640i
$204$	18.6181	−	32.2475i	1.30353	−	2.25778i
$205$	4.25821	−	7.34318i	0.297406	−	0.512870i
$206$	−12.6858	−	21.9725i	−0.883863	−	1.53090i
$207$		−	5.60933i		−	0.389876i
$208$		0			0
$209$	10.5413			0.729156
$210$	−35.0088	−	20.3011i	−2.41583	−	1.40091i
$211$	−8.65902	−	14.9979i	−0.596111	−	1.03250i	−0.993389	−	0.114797i	$-0.963378\pi$
$211$	−8.65902	−	14.9979i	−0.596111	−	1.03250i	0.397278	−	0.917699i	$-0.369955\pi$
$212$	11.9856	+	6.91989i	0.823175	+	0.475260i
$213$		−	11.6246i		−	0.796507i
$214$	−5.92218	+	10.2575i	−0.404832	+	0.701189i
$215$	−0.00899513	+	4.73286i	−0.000613463	+	0.322779i
$216$	−1.13400			−0.0771591
$217$	9.55384	+	5.51591i	0.648557	+	0.374445i
$218$	−22.5044	+	12.9929i	−1.52419	+	0.879990i
$219$	4.77384	+	8.26853i	0.322586	+	0.558735i
$220$	−6.08245	−	10.5815i	−0.410079	−	0.713405i
$221$		0			0
$222$			0.509470i			0.0341934i
$223$	−4.57552	+	2.64168i	−0.306399	+	0.176900i	−0.645314	−	0.763917i	$-0.723274\pi$
$223$	−4.57552	+	2.64168i	−0.306399	+	0.176900i	0.338915	+	0.940817i	$0.389940\pi$
$224$	−13.8106	−	23.9206i	−0.922757	−	1.59826i
$225$	6.55038	+	11.4458i	0.436692	+	0.763057i
$226$	12.8103			0.852131
$227$	2.55428	+	1.47471i	0.169533	+	0.0978802i	0.582366	−	0.812927i	$-0.302127\pi$
$227$	2.55428	+	1.47471i	0.169533	+	0.0978802i	−0.412832	+	0.910807i	$0.635460\pi$
$228$	27.1236	+	15.6598i	1.79630	+	1.03710i
$229$	3.09371			0.204438			0.102219	−	0.994762i	$-0.467406\pi$
$229$	3.09371			0.204438			0.102219	+	0.994762i	$0.467406\pi$
$230$	−10.2143	−	0.0194131i	−0.673514	−	0.00128006i
$231$	−8.79902	−	15.2403i	−0.578933	−	1.00274i
$232$	11.5746	−	6.68259i	0.759909	−	0.438734i
$233$		−	6.38449i		−	0.418262i	−0.977888	−	0.209131i	$-0.932937\pi$
$233$		−	6.38449i		−	0.418262i	0.977888	−	0.209131i	$-0.0670635\pi$
$234$		0			0
$235$	9.70031	−	5.57592i	0.632778	−	0.363733i
$236$	3.92488	+	6.79809i	0.255488	+	0.442518i
$237$	9.69430	−	5.59701i	0.629712	−	0.363565i
$238$	−39.6121	−	22.8701i	−2.56767	−	1.48245i
$239$	−23.8468			−1.54252			−0.771260	−	0.636521i	$-0.780373\pi$
$239$	−23.8468			−1.54252			−0.771260	+	0.636521i	$0.780373\pi$
$240$	−0.0241841	+	12.7247i	−0.00156108	+	0.821375i
$241$	13.7660	−	23.8433i	0.886744	−	1.53589i	0.0430417	−	0.999073i	$-0.486295\pi$
$241$	13.7660	−	23.8433i	0.886744	−	1.53589i	0.843702	−	0.536812i	$-0.180371\pi$
$242$			14.2579i			0.916533i
$243$	18.2361	+	10.5286i	1.16984	+	0.675410i
$244$	−6.22884	−	10.7887i	−0.398761	−	0.690674i
$245$	−6.27475	+	10.8206i	−0.400879	+	0.691305i
$246$	19.3600			1.23435
$247$		0			0
$248$			4.09611i			0.260104i
$249$	−13.3798	−	23.1744i	−0.847908	−	1.46862i
$250$	20.8651	−	11.8883i	1.31962	−	0.751885i
$251$	−0.115410	+	0.199896i	−0.00728462	+	0.0126173i	−0.869645	−	0.493678i	$-0.835652\pi$
$251$	−0.115410	+	0.199896i	−0.00728462	+	0.0126173i	0.862360	+	0.506295i	$0.168985\pi$
$252$		−	24.4622i		−	1.54097i
$253$	−3.84665	−	2.22086i	−0.241837	−	0.139625i
$254$	12.8767	−	22.3031i	0.807957	−	1.39942i
$255$	15.8771	+	27.6210i	0.994261	+	1.72969i
$256$	−1.13590	+	1.96744i	−0.0709940	+	0.122965i
$257$	11.2076	−	6.47068i	0.699108	−	0.403630i	−0.107907	−	0.994161i	$-0.534415\pi$
$257$	11.2076	−	6.47068i	0.699108	−	0.403630i	0.807015	+	0.590531i	$0.201082\pi$
$258$	−9.34822	+	5.39720i	−0.581995	+	0.336015i
$259$	0.354520			0.0220288
$260$		0			0
$261$	−26.7528			−1.65595
$262$	36.3588	−	20.9918i	2.24626	−	1.29688i
$263$	−8.57099	+	4.94847i	−0.528510	+	0.305135i	−0.740410	−	0.672156i	$-0.765368\pi$
$263$	−8.57099	+	4.94847i	−0.528510	+	0.305135i	0.211899	+	0.977291i	$0.432035\pi$
$264$	3.26707	−	5.65874i	0.201074	−	0.348271i
$265$	−10.2661	+	5.90112i	−0.630639	+	0.362503i
$266$	19.2362	−	33.3180i	1.17944	−	2.04286i
$267$	3.91648	+	2.26118i	0.239685	+	0.138382i
$268$			17.7103i			1.08183i
$269$	6.31999	−	10.9465i	0.385337	−	0.667423i	−0.606479	−	0.795099i	$-0.707419\pi$
$269$	6.31999	−	10.9465i	0.385337	−	0.667423i	0.991816	+	0.127677i	$0.0407519\pi$
$270$	2.07350	−	3.57570i	0.126189	−	0.217610i
$271$	−9.73877	−	16.8680i	−0.591588	−	1.02466i	−0.994019	−	0.109210i	$-0.965168\pi$
$271$	−9.73877	−	16.8680i	−0.591588	−	1.02466i	0.402430	−	0.915451i	$-0.368166\pi$
$272$			14.3821i			0.872042i
$273$		0			0
$274$	−27.5772			−1.66600
$275$	10.4425	+	0.0396936i	0.629709	+	0.00239362i
$276$	−6.59849	−	11.4289i	−0.397182	−	0.687940i
$277$	−24.1284	−	13.9305i	−1.44973	−	0.837004i	−0.451268	−	0.892388i	$-0.649028\pi$
$277$	−24.1284	−	13.9305i	−1.44973	−	0.837004i	−0.998465	+	0.0553842i	$0.982362\pi$
$278$			11.5611i			0.693390i
$279$	4.09955	−	7.10062i	0.245433	−	0.425103i
$280$	−10.4561	−	0.0198725i	−0.624871	−	0.00118761i
$281$	−22.0533			−1.31559			−0.657796	−	0.753197i	$-0.728511\pi$
$281$	−22.0533			−1.31559			−0.657796	+	0.753197i	$0.728511\pi$
$282$	22.0996	+	12.7592i	1.31601	+	0.759798i
$283$	21.7682	−	12.5679i	1.29399	−	0.747083i	0.314628	−	0.949215i	$-0.398120\pi$
$283$	21.7682	−	12.5679i	1.29399	−	0.747083i	0.979358	+	0.202132i	$0.0647869\pi$
$284$	−6.39767	−	11.0811i	−0.379632	−	0.657542i
$285$	−23.2322	+	13.3543i	−1.37616	+	0.791041i
$286$		0			0
$287$		−	13.4718i		−	0.795216i
$288$	−17.7783	+	10.2643i	−1.04760	+	0.604830i
$289$	9.50434	+	16.4620i	0.559079	+	0.968353i
$290$	−0.0925873	+	48.7156i	−0.00543691	+	2.86068i
$291$	−12.7488			−0.747350
$292$	9.10124	+	5.25460i	0.532610	+	0.307502i
$293$	6.27336	+	3.62192i	0.366493	+	0.211595i	0.671925	−	0.740619i	$-0.265468\pi$
$293$	6.27336	+	3.62192i	0.366493	+	0.211595i	−0.305432	+	0.952214i	$0.598801\pi$
$294$	−28.5281			−1.66379
$295$	−6.71620	−	0.0127646i	−0.391032	−	0.000743183i
$296$	0.0658166	+	0.113998i	0.00382551	+	0.00662598i
$297$	1.55661	−	0.898707i	0.0903235	−	0.0521483i
$298$			33.4030i			1.93498i
$299$		0			0
$300$	26.8105	+	15.6152i	1.54791	+	0.901546i
$301$	3.75569	+	6.50505i	0.216475	+	0.374945i
$302$	−21.6694	+	12.5108i	−1.24693	+	0.719917i
$303$	23.0525	+	13.3093i	1.32433	+	0.764602i
$304$	−12.0969			−0.693802
$305$	10.6587	+	0.0202576i	0.610316	+	0.00115995i
$306$	−16.9975	+	29.4406i	−0.971684	+	1.68301i
$307$		−	29.4770i		−	1.68234i	−0.540770	−	0.841170i	$-0.681867\pi$
$307$		−	29.4770i		−	1.68234i	0.540770	−	0.841170i	$-0.318133\pi$
$308$	−16.7752	−	9.68515i	−0.955854	−	0.551863i
$309$	14.0233	+	24.2890i	0.797757	+	1.38176i
$310$	−12.9157	−	7.48967i	−0.733564	−	0.425384i
$311$	−16.3474			−0.926978			−0.463489	−	0.886103i	$-0.653403\pi$
$311$	−16.3474			−0.926978			−0.463489	+	0.886103i	$0.653403\pi$
$312$		0			0
$313$			29.4517i			1.66471i	0.554244	+	0.832355i	$0.313008\pi$
$313$			29.4517i			1.66471i	−0.554244	+	0.832355i	$0.686992\pi$
$314$	2.17724	+	3.77109i	0.122869	+	0.212815i
$315$	18.1058	+	10.4993i	1.02014	+	0.591568i
$316$	6.16067	−	10.6706i	0.346565	−	0.600268i
$317$			16.8218i			0.944804i	0.881383	+	0.472402i	$0.156613\pi$
$317$			16.8218i			0.944804i	−0.881383	+	0.472402i	$0.843387\pi$
$318$	−23.3885	−	13.5033i	−1.31156	−	0.757229i
$319$	−10.5920	+	18.3459i	−0.593040	+	1.02718i
$320$	13.2877	+	23.1164i	0.742807	+	1.29224i
$321$	6.54655	−	11.3390i	0.365393	−	0.632879i
$322$	−14.0390	+	8.10544i	−0.782365	+	0.451699i
$323$	−26.2294	+	15.1436i	−1.45944	+	0.842610i
$324$	26.0197			1.44554
$325$		0			0
$326$	18.2221			1.00923
$327$	24.8770	−	14.3627i	1.37570	−	0.794261i
$328$	4.33193	−	2.50104i	0.239191	−	0.138097i
$329$	8.87860	−	15.3782i	0.489493	−	0.847827i
$330$	11.8692	+	20.6485i	0.653376	+	1.13666i
$331$	−1.07525	+	1.86238i	−0.0591009	+	0.102366i	−0.894062	−	0.447943i	$-0.852157\pi$
$331$	−1.07525	+	1.86238i	−0.0591009	+	0.102366i	0.834961	+	0.550309i	$0.185490\pi$
$332$	−25.5083	−	14.7272i	−1.39995	−	0.808261i
$333$		−	0.263487i		−	0.0144390i
$334$	−4.86445	+	8.42547i	−0.266171	+	0.461021i
$335$	−13.1083	−	7.60134i	−0.716183	−	0.415306i
$336$	10.0975	+	17.4893i	0.550863	+	0.954122i
$337$		−	2.37962i		−	0.129626i	−0.997897	−	0.0648131i	$-0.979355\pi$
$337$		−	2.37962i		−	0.129626i	0.997897	−	0.0648131i	$-0.0206451\pi$
$338$		0			0
$339$	−14.1609			−0.769116
$340$	30.3360	+	17.5915i	1.64520	+	0.954031i
$341$	−3.24621	−	5.62260i	−0.175792	−	0.304481i
$342$	−24.7627	−	14.2967i	−1.33901	−	0.773079i
$343$		−	4.98994i		−	0.269431i
$344$	−1.39449	+	2.41532i	−0.0751858	+	0.130226i
$345$	11.2912	+	0.0214598i	0.607900	+	0.00115535i
$346$	2.21493			0.119075
$347$	−22.5960	−	13.0458i	−1.21302	−	0.700336i	−0.249602	−	0.968348i	$-0.580300\pi$
$347$	−22.5960	−	13.0458i	−1.21302	−	0.700336i	−0.963416	+	0.268012i	$0.913633\pi$
$348$	−54.5083	+	31.4704i	−2.92195	+	1.68699i
$349$	8.17947	+	14.1673i	0.437837	+	0.758356i	0.997522	−	0.0703492i	$-0.0224113\pi$
$349$	8.17947	+	14.1673i	0.437837	+	0.758356i	−0.559685	+	0.828705i	$0.689078\pi$
$350$	19.1814	−	32.9335i	1.02529	−	1.76037i
$351$		0			0
$352$			16.2555i			0.866421i
$353$	2.39871	−	1.38489i	0.127670	−	0.0737105i	−0.434805	−	0.900525i	$-0.643183\pi$
$353$	2.39871	−	1.38489i	0.127670	−	0.0737105i	0.562475	+	0.826814i	$0.309849\pi$
$354$	−7.65893	−	13.2656i	−0.407067	−	0.705061i
$355$	10.9476	+	0.0208067i	0.581038	+	0.00110430i
$356$	4.97780			0.263823
$357$	43.7884	+	25.2812i	2.31753	+	1.33803i
$358$	32.3722	+	18.6901i	1.71092	+	0.987802i
$359$	−17.9581			−0.947791			−0.473896	−	0.880581i	$-0.657153\pi$
$359$	−17.9581			−0.947791			−0.473896	+	0.880581i	$0.657153\pi$
$360$	−0.0147697	+	7.77119i	−0.000778430	+	0.409578i
$361$	−3.23735	−	5.60725i	−0.170387	−	0.295119i
$362$	41.3954	−	23.8996i	2.17569	−	1.25614i
$363$		−	15.7611i		−	0.827243i
$364$		0			0
$365$	−7.79550	+	4.48100i	−0.408035	+	0.234546i
$366$	12.1548	+	21.0528i	0.635343	+	1.10045i
$367$	23.4260	−	13.5250i	1.22283	−	0.706001i	0.257309	−	0.966329i	$-0.417164\pi$
$367$	23.4260	−	13.5250i	1.22283	−	0.706001i	0.965520	+	0.260328i	$0.0838307\pi$
$368$	4.41430	+	2.54860i	0.230111	+	0.132855i
$369$	−10.0125			−0.521232
$370$	−0.479798		0.000911888i	−0.0249435		4.74068e-5i
$371$	−9.39642	+	16.2751i	−0.487838	+	0.844960i
$372$		−	19.2899i		−	1.00013i
$373$	0.570084	+	0.329138i	0.0295178	+	0.0170421i	0.514686	−	0.857379i	$-0.327908\pi$
$373$	0.570084	+	0.329138i	0.0295178	+	0.0170421i	−0.485168	+	0.874421i	$0.661242\pi$
$374$	13.4594	+	23.3124i	0.695970	+	1.20546i
$375$	−23.0648	+	13.1417i	−1.19106	+	0.678636i
$376$	6.59325			0.340021
$377$		0			0
$378$		−	6.55999i		−	0.337409i
$379$	−8.98576	−	15.5638i	−0.461568	−	0.799459i	0.537472	−	0.843282i	$-0.319380\pi$
$379$	−8.98576	−	15.5638i	−0.461568	−	0.799459i	−0.999039	+	0.0438232i	$0.986046\pi$
$380$	−14.7963	+	25.5158i	−0.759034	+	1.30893i
$381$	−14.2343	+	24.6545i	−0.729246	+	1.26309i
$382$			15.1628i			0.775797i
$383$	−1.19483	−	0.689834i	−0.0610529	−	0.0352489i	0.469163	−	0.883112i	$-0.344556\pi$
$383$	−1.19483	−	0.689834i	−0.0610529	−	0.0352489i	−0.530216	+	0.847863i	$0.677889\pi$
$384$	−11.9257	+	20.6559i	−0.608580	+	1.05409i
$385$	14.3685	−	8.25927i	0.732285	−	0.420931i
$386$	−23.3981	+	40.5267i	−1.19093	+	2.06275i
$387$	4.83469	−	2.79131i	0.245761	−	0.141890i
$388$	−12.1527	+	7.01637i	−0.616961	+	0.356202i
$389$	−6.64124			−0.336724			−0.168362	−	0.985725i	$-0.553848\pi$
$389$	−6.64124			−0.336724			−0.168362	+	0.985725i	$0.553848\pi$
$390$		0			0
$391$	12.7619			0.645399
$392$	−6.38338	+	3.68544i	−0.322409	+	0.186143i
$393$	−40.1921	+	23.2049i	−2.02743	+	1.17053i
$394$	24.1035	−	41.7484i	1.21432	−	2.10326i
$395$	5.25368	+	9.13971i	0.264341	+	0.459868i
$396$	−7.19821	+	12.4677i	−0.361724	+	0.626524i
$397$	−15.0829	−	8.70813i	−0.756990	−	0.437048i	0.0712239	−	0.997460i	$-0.477310\pi$
$397$	−15.0829	−	8.70813i	−0.756990	−	0.437048i	−0.828214	+	0.560412i	$0.810643\pi$
$398$		−	26.2251i		−	1.31455i
$399$	−21.2642	+	36.8307i	−1.06454	+	1.84384i
$400$	−11.9835	−	0.0455512i	−0.599177	−	0.00227756i
$401$	13.5781	+	23.5179i	0.678058	+	1.17443i	0.975565	+	0.219711i	$0.0705113\pi$
$401$	13.5781	+	23.5179i	0.678058	+	1.17443i	−0.297508	+	0.954719i	$0.596155\pi$
$402$		−	34.5595i		−	1.72367i
$403$		0			0
$404$	29.2994			1.45770
$405$	−11.1678	+	19.2585i	−0.554931	+	0.956965i
$406$	38.6575	+	66.9568i	1.91854	+	3.32301i
$407$	−0.180688	−	0.104321i	−0.00895639	−	0.00517098i
$408$			18.7738i			0.929444i
$409$	−1.56077	+	2.70333i	−0.0771751	+	0.133671i	−0.902030	−	0.431673i	$-0.857923\pi$
$409$	−1.56077	+	2.70333i	−0.0771751	+	0.133671i	0.824855	+	0.565344i	$0.191257\pi$
$410$	−0.0346519	+	18.2324i	−0.00171134	+	0.900434i
$411$	30.4846			1.50370
$412$	26.7352	+	15.4355i	1.31715	+	0.760455i
$413$	−9.23103	+	5.32954i	−0.454229	+	0.262249i
$414$	6.02414	+	10.4341i	0.296070	+	0.512809i
$415$	21.8487	−	12.5590i	1.07251	−	0.616498i
$416$		0			0
$417$		−	12.7800i		−	0.625840i
$418$	−19.6082	+	11.3208i	−0.959069	+	0.553719i
$419$	−1.67932	−	2.90867i	−0.0820402	−	0.142098i	0.822086	−	0.569363i	$-0.192810\pi$
$419$	−1.67932	−	2.90867i	−0.0820402	−	0.142098i	−0.904126	+	0.427266i	$0.859477\pi$
$420$	49.2409	+	0.0935857i	2.40271	+	0.00456651i
$421$	−9.50793			−0.463388			−0.231694	−	0.972789i	$-0.574427\pi$
$421$	−9.50793			−0.463388			−0.231694	+	0.972789i	$0.574427\pi$
$422$	32.2139	+	18.5987i	1.56815	+	0.905370i
$423$	−11.4294	−	6.59877i	−0.555717	−	0.320843i
$424$	−6.97778			−0.338871
$425$	−26.0407	+	14.9029i	−1.26316	+	0.722898i
$426$	12.4843	+	21.6234i	0.604865	+	1.04766i
$427$	14.6498	−	8.45806i	0.708953	−	0.409314i
$428$		−	14.4117i		−	0.696615i
$429$		0			0
$430$	−5.06612	−	8.81343i	−0.244310	−	0.425021i
$431$	−18.8515	−	32.6517i	−0.908043	−	1.57278i	−0.816780	−	0.576949i	$-0.804243\pi$
$431$	−18.8515	−	32.6517i	−0.908043	−	1.57278i	−0.0912624	−	0.995827i	$-0.529090\pi$
$432$	−1.78631	+	1.03133i	−0.0859441	+	0.0496198i
$433$	−18.1546	−	10.4816i	−0.872456	−	0.503712i	−0.00429212	−	0.999991i	$-0.501366\pi$
$433$	−18.1546	−	10.4816i	−0.872456	−	0.503712i	−0.868163	+	0.496278i	$0.834700\pi$
$434$	−23.6952			−1.13741
$435$	0.102349	−	53.8516i	0.00490724	−	2.58199i
$436$	15.8092	−	27.3823i	0.757123	−	1.31137i
$437$			10.7341i			0.513484i
$438$	−17.7600	−	10.2537i	−0.848604	−	0.489942i
$439$	−5.23003	−	9.05868i	−0.249616	−	0.432347i	0.713803	−	0.700346i	$-0.246971\pi$
$439$	−5.23003	−	9.05868i	−0.249616	−	0.432347i	−0.963419	+	0.267999i	$0.913638\pi$
$440$	5.32332	+	3.08692i	0.253779	+	0.147163i
$441$	14.7541			0.702577
$442$		0			0
$443$		−	19.6909i		−	0.935543i	−0.883849	−	0.467772i	$-0.845057\pi$
$443$		−	19.6909i		−	0.935543i	0.883849	−	0.467772i	$-0.154943\pi$
$444$	−0.309950	−	0.536850i	−0.0147096	−	0.0254778i
$445$	−2.13650	+	3.68433i	−0.101280	+	0.174654i
$446$	5.67405	−	9.82775i	0.268674	−	0.465357i
$447$		−	36.9246i		−	1.74648i
$448$	36.6471	+	21.1582i	1.73141	+	0.999631i
$449$	3.96933	−	6.87507i	0.187324	−	0.324455i	−0.757033	−	0.653376i	$-0.773352\pi$
$449$	3.96933	−	6.87507i	0.187324	−	0.324455i	0.944357	+	0.328922i	$0.106685\pi$
$450$	−24.4768	−	14.2560i	−1.15385	−	0.672036i
$451$	−3.96420	+	6.86619i	−0.186667	+	0.323316i
$452$	−13.4988	+	7.79353i	−0.634930	+	0.366577i
$453$	23.9540	−	13.8298i	1.12546	−	0.649782i
$454$	−6.33507			−0.297319
$455$		0			0
$456$	−15.7908			−0.739472
$457$	−6.15395	+	3.55299i	−0.287870	+	0.166202i	−0.636981	−	0.770880i	$-0.719817\pi$
$457$	−6.15395	+	3.55299i	−0.287870	+	0.166202i	0.349111	+	0.937081i	$0.386484\pi$
$458$	−5.75472	+	3.32249i	−0.268901	+	0.155250i
$459$	−2.58216	+	4.47243i	−0.120525	+	0.208755i
$460$	10.7751	−	6.19373i	0.502391	−	0.288784i
$461$	−7.67119	+	13.2869i	−0.357283	+	0.618832i	−0.987506	−	0.157582i	$-0.949630\pi$
$461$	−7.67119	+	13.2869i	−0.357283	+	0.618832i	0.630223	+	0.776414i	$0.282963\pi$
$462$	32.7347	+	18.8994i	1.52296	+	0.879279i
$463$			10.1047i			0.469606i	0.972043	+	0.234803i	$0.0754446\pi$
$463$			10.1047i			0.469606i	−0.972043	+	0.234803i	$0.924555\pi$
$464$	12.1551	−	21.0532i	0.564286	−	0.977372i
$465$	14.2774	+	8.27930i	0.662100	+	0.383943i
$466$	6.85662	+	11.8760i	0.317627	+	0.550146i
$467$			14.2884i			0.661190i	0.943773	+	0.330595i	$0.107249\pi$
$467$			14.2884i			0.661190i	−0.943773	+	0.330595i	$0.892751\pi$
$468$		0			0
$469$	−24.0485			−1.11046
$470$	−12.0556	+	20.7896i	−0.556084	+	0.958953i
$471$	−2.40678	−	4.16867i	−0.110899	−	0.192082i
$472$	−3.42748	−	1.97886i	−0.157763	−	0.0910843i
$473$		−	4.42058i		−	0.203258i
$474$	−12.0218	+	20.8224i	−0.552180	+	0.956403i
$475$	−12.5350	−	21.9030i	−0.575143	−	1.00498i
$476$	55.6546			2.55092
$477$	12.0960	+	6.98363i	0.553837	+	0.319758i
$478$	44.3582	−	25.6102i	2.02890	−	1.17138i
$479$	16.9338	+	29.3303i	0.773727	+	1.34013i	0.935507	+	0.353307i	$0.114943\pi$
$479$	16.9338	+	29.3303i	0.773727	+	1.34013i	−0.161780	+	0.986827i	$0.551724\pi$
$480$	−20.5934	−	35.8259i	−0.939955	−	1.63522i
$481$		0			0
$482$			59.1358i			2.69356i
$483$	15.5192	−	8.95999i	0.706146	−	0.407694i
$484$	−8.67419	−	15.0241i	−0.394281	−	0.682915i
$485$	0.0228188	−	12.0063i	0.00103615	−	0.545179i
$486$	−45.2287			−2.05162
$487$	−11.3081	−	6.52871i	−0.512417	−	0.295844i	0.221409	−	0.975181i	$-0.428934\pi$
$487$	−11.3081	−	6.52871i	−0.512417	−	0.295844i	−0.733827	+	0.679337i	$0.762268\pi$
$488$	5.43946	+	3.14047i	0.246233	+	0.142163i
$489$	−20.1433			−0.910911
$490$	0.0510618	−	26.8666i	0.00230674	−	1.21371i
$491$	−20.4102	−	35.3515i	−0.921101	−	1.59539i	−0.797715	−	0.603034i	$-0.793958\pi$
$491$	−20.4102	−	35.3515i	−0.921101	−	1.59539i	−0.123385	−	0.992359i	$-0.539375\pi$
$492$	−20.4004	+	11.7782i	−0.919720	+	0.531001i
$493$		−	60.8658i		−	2.74126i
$494$		0			0
$495$	−6.13847	−	10.6790i	−0.275904	−	0.479983i
$496$	3.72525	+	6.45232i	0.167269	+	0.289718i
$497$	15.0469	−	8.68730i	0.674944	−	0.389679i
$498$	49.7763	+	28.7384i	2.23053	+	1.28780i
$499$	34.5723			1.54767			0.773833	−	0.633389i	$-0.218337\pi$
$499$	34.5723			1.54767			0.773833	+	0.633389i	$0.218337\pi$
$500$	−14.7538	+	25.2211i	−0.659808	+	1.12792i
$501$	5.37730	−	9.31377i	0.240240	−	0.416108i
$502$		−	0.495779i		−	0.0221277i
$503$	38.1624	+	22.0331i	1.70158	+	0.982407i	0.944166	+	0.329470i	$0.106870\pi$
$503$	38.1624	+	22.0331i	1.70158	+	0.982407i	0.757412	+	0.652937i	$0.226463\pi$
$504$	6.16671	+	10.6811i	0.274687	+	0.475772i
$505$	−12.5755	+	21.6860i	−0.559600	+	0.965016i
$506$	9.54038			0.424122
$507$		0			0
$508$			31.3356i			1.39029i
$509$	21.0886	+	36.5265i	0.934735	+	1.61901i	0.775105	+	0.631832i	$0.217697\pi$
$509$	21.0886	+	36.5265i	0.934735	+	1.61901i	0.159630	+	0.987177i	$0.448970\pi$
$510$	−59.1970	−	34.3276i	−2.62129	−	1.52005i
$511$	−7.13515	+	12.3584i	−0.315641	+	0.546705i
$512$		−	24.9705i		−	1.10355i
$513$	−3.76179	−	2.17187i	−0.166087	−	0.0958904i
$514$	−13.8984	+	24.0727i	−0.613031	+	1.06180i
$515$	−22.8995	+	13.1631i	−1.00907	+	0.580034i
$516$	6.56707	−	11.3745i	0.289099	−	0.500734i
$517$	−9.05033	+	5.22521i	−0.398033	+	0.229804i
$518$	−0.659455	+	0.380736i	−0.0289748	+	0.0167286i
$519$	−2.44845			−0.107475
$520$		0			0
$521$	28.6488			1.25513			0.627564	−	0.778565i	$-0.284052\pi$
$521$	28.6488			1.25513			0.627564	+	0.778565i	$0.284052\pi$
$522$	49.7637	−	28.7311i	2.17810	−	1.25753i
$523$	−17.9133	+	10.3423i	−0.783295	+	0.452235i	−0.837597	−	0.546289i	$-0.816040\pi$
$523$	−17.9133	+	10.3423i	−0.783295	+	0.452235i	0.0543019	+	0.998525i	$0.482707\pi$
$524$	−25.5419	+	44.2398i	−1.11580	+	1.93263i
$525$	−21.2037	+	36.4056i	−0.925405	+	1.58887i
$526$	10.6288	−	18.4096i	0.463438	−	0.802698i
$527$	16.1548	+	9.32698i	0.703714	+	0.406289i
$528$		−	11.8851i		−	0.517232i
$529$	−9.23851	+	16.0016i	−0.401674	+	0.695720i
$530$	12.7587	−	22.0021i	0.554204	−	0.955710i
$531$	3.96103	+	6.86070i	0.171894	+	0.297729i
$532$			46.8114i			2.02953i
$533$		0			0
$534$	−9.71357			−0.420347
$535$	10.6668	+	6.18556i	0.461168	+	0.267425i
$536$	−4.46461	−	7.73293i	−0.192842	−	0.334012i
$537$	−35.7852	−	20.6606i	−1.54424	−	0.891570i
$538$			27.1494i			1.17049i
$539$	5.84150	−	10.1178i	0.251611	−	0.435803i
$540$	−0.00955858	+	5.02933i	−0.000411336	+	0.216428i
$541$	−25.8647			−1.11201			−0.556005	−	0.831179i	$-0.687666\pi$
$541$	−25.8647			−1.11201			−0.556005	+	0.831179i	$0.687666\pi$
$542$	36.2308	+	20.9179i	1.55625	+	0.898500i
$543$	−45.7596	+	26.4193i	−1.96373	+	1.13376i
$544$	−23.3526	−	40.4478i	−1.00123	−	1.73419i
$545$	13.4817	+	23.4538i	0.577493	+	1.00465i
$546$		0			0
$547$			29.5937i			1.26533i	0.774424	+	0.632667i	$0.218040\pi$
$547$			29.5937i			1.26533i	−0.774424	+	0.632667i	$0.781960\pi$
$548$	29.0592	−	16.7773i	1.24135	−	0.716692i
$549$	−6.28621	−	10.8880i	−0.268289	−	0.464690i
$550$	−19.4672	+	11.1409i	−0.830082	+	0.475050i
$551$	51.1947			2.18097
$552$	5.76226	+	3.32684i	0.245258	+	0.141600i
$553$	14.4894	+	8.36549i	0.616154	+	0.355737i
$554$	59.8427			2.54247
$555$	0.530383	+	0.00100803i	0.0225135	+	4.27884e-5i
$556$	−7.03353	−	12.1824i	−0.298288	−	0.516650i
$557$	−24.5536	+	14.1760i	−1.04037	+	0.600657i	−0.919938	−	0.392065i	$-0.871761\pi$
$557$	−24.5536	+	14.1760i	−1.04037	+	0.600657i	−0.120431	+	0.992722i	$0.538428\pi$
$558$			17.6108i			0.745525i
$559$		0			0
$560$	−16.4888	+	9.47808i	−0.696780	+	0.400522i
$561$	−14.8784	−	25.7702i	−0.628168	−	1.08802i
$562$	41.0222	−	23.6841i	1.73041	−	0.999056i
$563$	11.4377	+	6.60357i	0.482043	+	0.278307i	0.721267	−	0.692657i	$-0.243560\pi$
$563$	11.4377	+	6.60357i	0.482043	+	0.278307i	−0.239225	+	0.970964i	$0.576893\pi$
$564$	−31.0496			−1.30742
$565$	0.0253463	−	13.3362i	0.00106633	−	0.561057i
$566$	−26.9945	+	46.7559i	−1.13467	+	1.96530i
$567$			35.3318i			1.48380i
$568$	5.58689	+	3.22559i	0.234421	+	0.135343i
$569$	−5.42968	−	9.40447i	−0.227624	−	0.394256i	0.729480	−	0.684003i	$-0.239762\pi$
$569$	−5.42968	−	9.40447i	−0.227624	−	0.394256i	−0.957103	+	0.289747i	$0.906429\pi$
$570$	28.8732	−	49.7910i	1.20936	−	2.08552i
$571$	3.37601			0.141282			0.0706409	−	0.997502i	$-0.477496\pi$
$571$	3.37601			0.141282			0.0706409	+	0.997502i	$0.477496\pi$
$572$		0			0
$573$		−	16.7614i		−	0.700218i
$574$	14.4680	+	25.0594i	0.603884	+	1.04596i
$575$	−0.0404198	+	10.6336i	−0.00168562	+	0.443451i
$576$	15.7252	−	27.2369i	0.655218	−	1.13487i
$577$		−	0.958534i		−	0.0399043i	−0.999801	−	0.0199521i	$-0.993649\pi$
$577$		−	0.958534i		−	0.0399043i	0.999801	−	0.0199521i	$-0.00635139\pi$
$578$	−35.3587	−	20.4144i	−1.47073	−	0.849125i
$579$	25.8649	−	44.7994i	1.07491	−	1.86180i
$580$	−29.5399	−	51.3900i	−1.22658	−	2.13385i
$581$	19.9979	−	34.6373i	0.829652	−	1.43700i
$582$	23.7145	−	13.6916i	0.982999	−	0.567535i
$583$	9.57817	−	5.52996i	0.396687	−	0.229027i
$584$	−5.29856			−0.219256
$585$		0			0
$586$	−15.5590			−0.642738
$587$	18.7776	−	10.8413i	0.775035	−	0.447467i	−0.0596325	−	0.998220i	$-0.518993\pi$
$587$	18.7776	−	10.8413i	0.775035	−	0.447467i	0.834668	+	0.550753i	$0.185660\pi$
$588$	30.0613	−	17.3559i	1.23971	−	0.715744i
$589$	−7.84498	+	13.5879i	−0.323247	+	0.559880i
$590$	12.5067	−	7.18911i	0.514895	−	0.295971i
$591$	−26.6447	+	46.1500i	−1.09602	+	1.89836i
$592$	0.207352	+	0.119715i	0.00852213	+	0.00492026i
$593$			37.9527i			1.55853i	0.626695	+	0.779264i	$0.284407\pi$
$593$			37.9527i			1.55853i	−0.626695	+	0.779264i	$0.715593\pi$
$594$	−1.93033	+	3.34343i	−0.0792025	+	0.137183i
$595$	−23.8872	+	41.1928i	−0.979280	+	1.68874i
$596$	−20.3216	−	35.1981i	−0.832406	−	1.44177i
$597$			28.9900i			1.18648i
$598$		0			0
$599$	4.17043			0.170399			0.0851995	−	0.996364i	$-0.472847\pi$
$599$	4.17043			0.170399			0.0851995	+	0.996364i	$0.472847\pi$
$600$	−15.6429	−	0.0594609i	−0.638618	−	0.00242748i
$601$	−21.1117	−	36.5666i	−0.861165	−	1.49158i	−0.870806	−	0.491627i	$-0.836402\pi$
$601$	−21.1117	−	36.5666i	−0.861165	−	1.49158i	0.00964108	−	0.999954i	$-0.496931\pi$
$602$	−13.9722	−	8.06685i	−0.569464	−	0.328780i
$603$			17.8734i			0.727861i
$604$	15.2226	−	26.3663i	0.619399	−	1.07283i
$605$	14.8432	+	0.0282104i	0.603460	+	0.00114692i
$606$	−57.1742			−2.32254
$607$	7.47812	+	4.31749i	0.303527	+	0.175242i	0.644026	−	0.765003i	$-0.277263\pi$
$607$	7.47812	+	4.31749i	0.303527	+	0.175242i	−0.340499	+	0.940245i	$0.610596\pi$
$608$	34.0209	−	19.6420i	1.37973	−	0.796588i
$609$	−42.7332	−	74.0160i	−1.73163	−	2.99928i
$610$	−19.8484	+	11.4092i	−0.803638	+	0.461946i
$611$		0			0
$612$		−	41.3637i		−	1.67203i
$613$	−30.9707	+	17.8809i	−1.25090	+	0.722205i	−0.971287	−	0.237910i	$-0.923538\pi$
$613$	−30.9707	+	17.8809i	−1.25090	+	0.722205i	−0.279608	+	0.960114i	$0.590204\pi$
$614$	31.6568	+	54.8312i	1.27756	+	2.21281i
$615$	0.0383052	−	20.1546i	0.00154462	−	0.812713i
$616$	9.76617			0.393490
$617$	0.983506	+	0.567827i	0.0395944	+	0.0228599i	0.519667	−	0.854369i	$-0.326056\pi$
$617$	0.983506	+	0.567827i	0.0395944	+	0.0228599i	−0.480072	+	0.877229i	$0.659390\pi$
$618$	−52.1704	−	30.1206i	−2.09860	−	1.21163i
$619$	47.6316			1.91447			0.957237	−	0.289305i	$-0.0934241\pi$
$619$	47.6316			1.91447			0.957237	+	0.289305i	$0.0934241\pi$
$620$	18.1664	+	0.0345264i	0.729580	+	0.00138662i
$621$	0.915149	+	1.58508i	0.0367237	+	0.0636073i
$622$	30.4084	−	17.5563i	1.21927	−	0.703944i
$623$			6.75929i			0.270805i
$624$		0			0
$625$	−12.3350	−	21.7450i	−0.493402	−	0.869801i
$626$	−31.6296	−	54.7841i	−1.26417	−	2.18961i
$627$	21.6755	−	12.5144i	0.865636	−	0.499775i
$628$	−4.58849	−	2.64917i	−0.183101	−	0.105713i
$629$	0.599465			0.0239022
$630$	−44.9549	−	0.0854397i	−1.79104	−	0.00340400i
$631$	3.83621	−	6.64450i	0.152717	−	0.264513i	−0.779508	−	0.626392i	$-0.784531\pi$
$631$	3.83621	−	6.64450i	0.152717	−	0.264513i	0.932225	+	0.361878i	$0.117864\pi$
$632$			6.21221i			0.247108i
$633$	−35.6102	−	20.5595i	−1.41538	−	0.817168i
$634$	−18.0657	−	31.2907i	−0.717481	−	1.24271i
$635$	−23.1931	−	13.4494i	−0.920392	−	0.533723i
$636$	32.8605			1.30300
$637$		0			0
$638$		−	45.5012i		−	1.80141i
$639$	−6.45659	−	11.1831i	−0.255419	−	0.442398i
$640$	−19.4315	−	11.2681i	−0.768098	−	0.445410i
$641$	7.92722	−	13.7303i	0.313106	−	0.542316i	−0.665927	−	0.746017i	$-0.731964\pi$
$641$	7.92722	−	13.7303i	0.313106	−	0.542316i	0.979033	+	0.203701i	$0.0652970\pi$
$642$			28.1226i			1.10991i
$643$	17.6914	+	10.2141i	0.697680	+	0.402806i	0.806483	−	0.591258i	$-0.201368\pi$
$643$	17.6914	+	10.2141i	0.697680	+	0.402806i	−0.108803	+	0.994063i	$0.534702\pi$
$644$	9.86234	−	17.0821i	0.388631	−	0.673128i
$645$	5.60024	+	9.74262i	0.220509	+	0.383615i
$646$	32.5268	−	56.3381i	1.27975	−	2.21659i
$647$	−20.6202	+	11.9051i	−0.810663	+	0.468036i	−0.847186	−	0.531296i	$-0.821705\pi$
$647$	−20.6202	+	11.9051i	−0.810663	+	0.468036i	0.0365231	+	0.999333i	$0.488372\pi$
$648$	−11.3611	+	6.55934i	−0.446307	+	0.257675i
$649$	6.27305			0.246239
$650$		0			0
$651$	26.1934			1.02660
$652$	−19.2014	+	11.0859i	−0.751986	+	0.434159i
$653$	26.9921	−	15.5839i	1.05628	−	0.609844i	0.131880	−	0.991266i	$-0.457899\pi$
$653$	26.9921	−	15.5839i	1.05628	−	0.609844i	0.924401	+	0.381421i	$0.124565\pi$
$654$	−30.8497	+	53.4332i	−1.20632	+	2.08940i
$655$	−21.7815	−	37.8928i	−0.851074	−	1.48059i
$656$	4.54919	−	7.87943i	0.177616	−	0.307640i
$657$	9.18506	+	5.30300i	0.358343	+	0.206890i
$658$			38.1407i			1.48688i
$659$	17.5459	−	30.3904i	0.683492	−	1.18384i	−0.290416	−	0.956900i	$-0.593794\pi$
$659$	17.5459	−	30.3904i	0.683492	−	1.18384i	0.973908	−	0.226942i	$-0.0728729\pi$
$660$	−25.0691	−	14.5373i	−0.975814	−	0.565862i
$661$	8.18204	+	14.1717i	0.318244	+	0.551215i	0.980122	−	0.198397i	$-0.0635734\pi$
$661$	8.18204	+	14.1717i	0.318244	+	0.551215i	−0.661877	+	0.749612i	$0.730240\pi$
$662$		−	4.61904i		−	0.179524i
$663$		0			0
$664$	14.8504			0.576308
$665$	−34.6476	−	20.0917i	−1.34358	−	0.779122i
$666$	0.282971	+	0.490121i	0.0109649	+	0.0189918i
$667$	−18.6816	−	10.7858i	−0.723353	−	0.417628i
$668$		−	11.8377i		−	0.458014i
$669$	−6.27227	+	10.8639i	−0.242500	+	0.420022i
$670$	32.5467	+	0.0618571i	1.25739	+	0.00238975i
$671$	−9.95542			−0.384325
$672$	−56.7958	−	32.7911i	−2.19095	−	1.26494i
$673$	40.8495	−	23.5844i	1.57463	−	0.909114i	0.579042	−	0.815298i	$-0.303427\pi$
$673$	40.8495	−	23.5844i	1.57463	−	0.909114i	0.995590	−	0.0938157i	$-0.0299064\pi$
$674$	2.55559	+	4.42641i	0.0984377	+	0.170499i
$675$	−3.71837	−	2.16569i	−0.143120	−	0.0833574i
$676$		0			0
$677$		−	6.68421i		−	0.256895i	−0.991716	−	0.128448i	$-0.959001\pi$
$677$		−	6.68421i		−	0.256895i	0.991716	−	0.128448i	$-0.0409994\pi$
$678$	26.3412	−	15.2081i	1.01163	−	0.584064i
$679$	−9.52743	−	16.5020i	−0.365629	−	0.633288i
$680$	−17.6804	−	0.0336028i	−0.678013	−	0.00128861i
$681$	7.00297			0.268354
$682$	12.0768	+	6.97253i	0.462443	+	0.266992i
$683$	−18.5826	−	10.7287i	−0.711044	−	0.410522i	0.100403	−	0.994947i	$-0.467987\pi$
$683$	−18.5826	−	10.7287i	−0.711044	−	0.410522i	−0.811448	+	0.584425i	$0.801320\pi$
$684$	34.7912			1.33028
$685$	−0.0545637	+	28.7091i	−0.00208477	+	1.09692i
$686$	5.35894	+	9.28196i	0.204605	+	0.354387i
$687$	6.36144	−	3.67278i	0.242704	−	0.140125i
$688$			5.07292i			0.193403i
$689$		0			0
$690$	−21.0263	+	12.0863i	−0.800457	+	0.460118i
$691$	18.3937	+	31.8588i	0.699728	+	1.21196i	0.968561	+	0.248778i	$0.0800289\pi$
$691$	18.3937	+	31.8588i	0.699728	+	1.21196i	−0.268832	+	0.963187i	$0.586638\pi$
$692$	−2.33396	+	1.34751i	−0.0887239	+	0.0512248i
$693$	−16.9297	−	9.77435i	−0.643105	−	0.371297i
$694$	56.0422			2.12733
$695$	12.0357	+	0.0228746i	0.456539	+	0.000867684i
$696$	15.8668	−	27.4821i	0.601430	−	1.04171i
$697$		−	22.7798i		−	0.862846i
$698$	−30.4298	−	17.5687i	−1.15179	−	0.664984i
$699$	−7.57951	−	13.1281i	−0.286683	−	0.496550i
$700$	−0.176270	+	46.3729i	−0.00666239	+	1.75273i
$701$	26.7626			1.01081			0.505404	−	0.862883i	$-0.331344\pi$
$701$	26.7626			1.01081			0.505404	+	0.862883i	$0.331344\pi$
$702$		0			0
$703$			0.504214i			0.0190168i
$704$	−12.4520	−	21.5674i	−0.469301	−	0.812853i
$705$	13.3266	−	22.9814i	0.501910	−	0.865531i
$706$	−2.97461	+	5.15218i	−0.111951	+	0.193905i
$707$			39.7853i			1.49628i
$708$	16.1411	+	9.31904i	0.606618	+	0.350231i
$709$	−11.7424	+	20.3384i	−0.440994	+	0.763824i	−0.997764	−	0.0668430i	$-0.978707\pi$
$709$	−11.7424	+	20.3384i	−0.440994	+	0.763824i	0.556770	+	0.830667i	$0.312041\pi$
$710$	−20.3864	+	11.7185i	−0.765086	+	0.439786i
$711$	6.21741	−	10.7689i	0.233171	−	0.403864i
$712$	−2.17348	+	1.25486i	−0.0814547	+	0.0470279i
$713$	5.72546	−	3.30560i	0.214420	−	0.123796i
$714$	−108.603			−4.06437
$715$		0			0
$716$	−45.4825			−1.69976
$717$	−49.0349	+	28.3103i	−1.83124	+	1.05727i
$718$	33.4044	−	19.2861i	1.24664	−	0.719750i
$719$	−8.66421	+	15.0069i	−0.323121	+	0.559661i	−0.981130	−	0.193348i	$-0.938065\pi$
$719$	−8.66421	+	15.0069i	−0.323121	+	0.559661i	0.658010	+	0.753009i	$0.271399\pi$
$720$	7.04431	+	12.2548i	0.262526	+	0.456711i
$721$	−20.9597	+	36.3033i	−0.780580	+	1.35200i
$722$	12.0438	+	6.95350i	0.448224	+	0.258782i
$723$		−	65.3704i		−	2.43115i
$724$	−29.0800	+	50.3680i	−1.08075	+	1.87191i
$725$	50.7151	+	0.192775i	1.88351	+	0.00715950i
$726$	16.9266	+	29.3178i	0.628206	+	1.08808i
$727$			2.13255i			0.0790919i	0.999218	+	0.0395460i	$0.0125912\pi$
$727$			2.13255i			0.0790919i	−0.999218	+	0.0395460i	$0.987409\pi$
$728$		0			0
$729$	20.1291			0.745524
$730$	9.68831	−	16.7072i	0.358581	−	0.618363i
$731$	6.35058	+	10.9995i	0.234885	+	0.406832i
$732$	−25.6161	−	14.7895i	−0.946798	−	0.546634i
$733$		−	4.01857i		−	0.148429i	−0.997242	−	0.0742147i	$-0.976355\pi$
$733$		−	4.01857i		−	0.148429i	0.997242	−	0.0742147i	$-0.0236450\pi$
$734$	−29.0504	+	50.3168i	−1.07227	+	1.85723i
$735$	−0.0564452	+	29.6991i	−0.00208201	+	1.09547i
$736$	−16.5529			−0.610147
$737$	12.2568	+	7.07649i	0.451486	+	0.260666i
$738$	18.6247	−	10.7530i	0.685584	−	0.395822i
$739$	1.00246	+	1.73631i	0.0368759	+	0.0638710i	0.883874	−	0.467724i	$-0.154926\pi$
$739$	1.00246	+	1.73631i	0.0368759	+	0.0638710i	−0.846998	+	0.531595i	$0.821593\pi$
$740$	0.506138	−	0.290937i	0.0186060	−	0.0106951i
$741$		0			0
$742$		−	40.3651i		−	1.48185i
$743$	5.62049	−	3.24499i	0.206196	−	0.119047i	−0.393346	−	0.919390i	$-0.628683\pi$
$743$	5.62049	−	3.24499i	0.206196	−	0.119047i	0.599542	+	0.800343i	$0.295349\pi$
$744$	4.86280	+	8.42262i	0.178279	+	0.308788i
$745$	34.7741	+	0.0660905i	1.27402	+	0.00242137i
$746$	−1.41391			−0.0517669
$747$	−25.7432	−	14.8629i	−0.941895	−	0.543803i
$748$	−28.3655	−	16.3768i	−1.03715	−	0.598796i
$749$	19.5694			0.715051
$750$	28.7902	−	49.2158i	1.05127	−	1.79711i
$751$	14.3696	+	24.8889i	0.524355	+	0.908210i	0.999598	+	0.0283552i	$0.00902695\pi$
$751$	14.3696	+	24.8889i	0.524355	+	0.908210i	−0.475243	+	0.879855i	$0.657640\pi$
$752$	10.3859	−	5.99629i	0.378734	−	0.218662i
$753$			0.548048i			0.0199720i
$754$		0			0
$755$	12.9815	+	22.5836i	0.472445	+	0.821902i
$756$	3.99095	+	6.91253i	0.145149	+	0.251406i
$757$	−37.3868	+	21.5853i	−1.35885	+	0.784530i	−0.989468	−	0.144750i	$-0.953762\pi$
$757$	−37.3868	+	21.5853i	−1.35885	+	0.784530i	−0.369377	+	0.929280i	$0.620429\pi$
$758$	33.4295	+	19.3005i	1.21421	+	0.701026i
$759$	−10.5462			−0.382803
$760$	0.0282636	−	14.8711i	0.00102523	−	0.539432i
$761$	−2.50567	+	4.33994i	−0.0908303	+	0.157323i	−0.907861	−	0.419272i	$-0.862285\pi$
$761$	−2.50567	+	4.33994i	−0.0908303	+	0.157323i	0.817030	+	0.576595i	$0.195619\pi$
$762$		−	61.1477i		−	2.21515i
$763$	37.1820	+	21.4671i	1.34608	+	0.777160i
$764$	−9.22471	−	15.9777i	−0.333738	−	0.578052i
$765$	30.6154	+	17.7535i	1.10690	+	0.641879i
$766$	2.96339			0.107072
$767$		0			0
$768$			5.39406i			0.194642i
$769$	−0.0585443	−	0.101402i	−0.00211116	−	0.00365664i	0.864968	−	0.501827i	$-0.167339\pi$
$769$	−0.0585443	−	0.101402i	−0.00211116	−	0.00365664i	−0.867079	+	0.498171i	$0.834005\pi$
$770$	−17.8573	+	30.7944i	−0.643531	+	1.10975i
$771$	15.3637	−	26.6106i	0.553309	−	0.958359i
$772$		−	56.9395i		−	2.04930i
$773$	−18.9136	−	10.9197i	−0.680273	−	0.392756i	0.119685	−	0.992812i	$-0.461812\pi$
$773$	−18.9136	−	10.9197i	−0.680273	−	0.392756i	−0.799958	+	0.600056i	$0.795145\pi$
$774$	−5.99545	+	10.3844i	−0.215502	+	0.373261i
$775$	−7.82265	+	13.4311i	−0.280998	+	0.482458i
$776$	3.53753	−	6.12719i	0.126990	−	0.219953i
$777$	0.728981	−	0.420877i	0.0261520	−	0.0150989i
$778$	12.3536	−	7.13235i	0.442898	−	0.255707i
$779$	19.1602			0.686486
$780$		0			0
$781$	−10.2253			−0.365888
$782$	−23.7389	+	13.7057i	−0.848902	+	0.490114i
$783$	7.55979	−	4.36465i	0.270165	−	0.155980i
$784$	−6.70352	+	11.6108i	−0.239412	+	0.414673i
$785$	3.93019	−	2.25915i	0.140274	−	0.0806324i
$786$	49.8419	−	86.3286i	1.77780	−	3.07924i
$787$	−24.0427	−	13.8811i	−0.857030	−	0.494807i	0.00598642	−	0.999982i	$-0.498094\pi$
$787$	−24.0427	−	13.8811i	−0.857030	−	0.494807i	−0.863017	+	0.505175i	$0.831428\pi$
$788$			58.6561i			2.08954i
$789$	−11.7494	+	20.3505i	−0.418289	+	0.724498i
$790$	−19.5881	−	11.3589i	−0.696914	−	0.404132i
$791$	−10.5827	−	18.3298i	−0.376278	−	0.651733i
$792$		−	7.25843i		−	0.257917i
$793$		0			0
$794$	37.4084			1.32757
$795$	−14.1039	+	24.3218i	−0.500213	+	0.862604i
$796$	15.9548	+	27.6345i	0.565502	+	0.979478i
$797$	36.3354	+	20.9783i	1.28707	+	0.743088i	0.978130	−	0.207995i	$-0.0666937\pi$
$797$	36.3354	+	20.9783i	1.28707	+	0.743088i	0.308936	+	0.951083i	$0.400027\pi$
$798$		−	91.3468i		−	3.23364i
$799$	15.0130	−	26.0033i	0.531122	−	0.919931i
$800$	33.7762	−	19.3299i	1.19417	−	0.683414i
$801$	5.02365			0.177502
$802$	−50.5142	−	29.1644i	−1.78372	−	1.02983i
$803$	7.27316	−	4.19916i	0.256664	−	0.148185i
$804$	21.0252	+	36.4167i	0.741502	+	1.28432i
$805$	8.41037	+	14.6313i	0.296427	+	0.515687i
$806$		0			0
$807$		−	30.0117i		−	1.05646i
$808$	−12.7932	+	7.38613i	−0.450062	+	0.259843i
$809$	4.03354	+	6.98629i	0.141812	+	0.245625i	0.928179	−	0.372134i	$-0.121374\pi$
$809$	4.03354	+	6.98629i	0.141812	+	0.245625i	−0.786367	+	0.617759i	$0.788041\pi$
$810$	0.0908796	−	47.8171i	0.00319318	−	1.68012i
$811$	16.0953			0.565181			0.282591	−	0.959241i	$-0.408806\pi$
$811$	16.0953			0.565181			0.282591	+	0.959241i	$0.408806\pi$
$812$	−81.4700	−	47.0367i	−2.85904	−	1.65067i
$813$	−40.0506	−	23.1232i	−1.40464	−	0.810968i
$814$	0.448140			0.0157073
$815$	0.0360540	−	18.9701i	0.00126292	−	0.664494i
$816$	17.0740	+	29.5731i	0.597711	+	1.03527i
$817$	−9.25178	+	5.34151i	−0.323679	+	0.186876i
$818$		−	6.70475i		−	0.234426i
$819$		0			0
$820$	−11.0557	−	19.2333i	−0.386081	−	0.671656i
$821$	8.28883	+	14.3567i	0.289282	+	0.501051i	0.973639	−	0.228096i	$-0.0732501\pi$
$821$	8.28883	+	14.3567i	0.289282	+	0.501051i	−0.684356	+	0.729148i	$0.739917\pi$
$822$	−56.7055	+	32.7389i	−1.97783	+	1.14190i
$823$	21.6415	+	12.4948i	0.754377	+	0.435540i	0.827273	−	0.561800i	$-0.189891\pi$
$823$	21.6415	+	12.4948i	0.754377	+	0.435540i	−0.0728963	+	0.997340i	$0.523224\pi$
$824$	−15.5647			−0.542221
$825$	21.5196	−	12.3155i	0.749215	−	0.428771i
$826$	11.4473	−	19.8273i	0.398303	−	0.689881i
$827$			9.28575i			0.322897i	0.986881	+	0.161449i	$0.0516166\pi$
$827$			9.28575i			0.322897i	−0.986881	+	0.161449i	$0.948383\pi$
$828$	−12.6958	−	7.32990i	−0.441208	−	0.254732i
$829$	24.1845	+	41.8887i	0.839961	+	1.45486i	0.889926	+	0.456105i	$0.150756\pi$
$829$	24.1845	+	41.8887i	0.839961	+	1.45486i	−0.0499648	+	0.998751i	$0.515911\pi$
$830$	−27.1537	+	46.8258i	−0.942519	+	1.62535i
$831$	−66.1519			−2.29478
$832$		0			0
$833$			33.5675i			1.16304i
$834$	13.7251	+	23.7725i	0.475261	+	0.823176i
$835$	8.76169	+	5.08079i	0.303211	+	0.175828i
$836$	13.7747	−	23.8584i	0.476406	−	0.825160i
$837$			2.67532i			0.0924727i
$838$	6.24753	+	3.60701i	0.215817	+	0.124602i
$839$	13.7886	−	23.8825i	0.476034	−	0.824515i	−0.523589	−	0.851971i	$-0.675407\pi$
$839$	13.7886	−	23.8825i	0.476034	−	0.824515i	0.999623	+	0.0274561i	$0.00874065\pi$
$840$	−21.5239	+	12.3723i	−0.742645	+	0.426886i
$841$	−36.9411	+	63.9838i	−1.27383	+	2.20634i
$842$	17.6860	−	10.2110i	0.609501	−	0.351895i
$843$	−45.3471	+	26.1812i	−1.56184	+	0.901727i
$844$	−45.2601			−1.55792
$845$		0			0
$846$	28.3470			0.974589
$847$	20.4011	−	11.7786i	0.700989	−	0.404716i
$848$	−10.9916	+	6.34601i	−0.377453	+	0.217923i
$849$	29.8406	−	51.6854i	1.02413	−	1.77384i
$850$	32.4343	−	55.6879i	1.11249	−	1.91008i
$851$	0.106229	−	0.183994i	0.00364148	−	0.00630724i
$852$	−26.3104	−	15.1903i	−0.901379	−	0.520411i
$853$			36.3384i			1.24420i	0.782937	+	0.622101i	$0.213721\pi$
$853$			36.3384i			1.24420i	−0.782937	+	0.622101i	$0.786279\pi$
$854$	−18.1670	+	31.4662i	−0.621663	+	1.07675i
$855$	−14.9326	+	25.7508i	−0.510683	+	0.880659i
$856$	3.63306	+	6.29265i	0.124175	+	0.215078i
$857$			18.4246i			0.629373i	0.949196	+	0.314687i	$0.101899\pi$
$857$			18.4246i			0.629373i	−0.949196	+	0.314687i	$0.898101\pi$
$858$		0			0
$859$	36.8252			1.25646			0.628229	−	0.778028i	$-0.283780\pi$
$859$	36.8252			1.25646			0.628229	+	0.778028i	$0.283780\pi$
$860$	10.7003	+	6.20495i	0.364876	+	0.211587i
$861$	−15.9934	−	27.7014i	−0.545054	−	0.944060i
$862$	70.1325	+	40.4910i	2.38872	+	1.37913i
$863$			12.0557i			0.410380i	0.978722	+	0.205190i	$0.0657812\pi$
$863$			12.0557i			0.410380i	−0.978722	+	0.205190i	$0.934219\pi$
$864$	3.34919	−	5.80097i	0.113942	−	0.197353i
$865$	0.00438242	−	2.30585i	0.000149007	−	0.0784011i
$866$	45.0267			1.53007
$867$	39.0865	+	22.5666i	1.32745	+	0.766403i
$868$	24.9687	−	14.4157i	0.847491	−	0.489299i
$869$	−4.92323	−	8.52729i	−0.167009	−	0.289268i
$870$	57.6435	+	100.281i	1.95430	+	3.39985i
$871$		0			0
$872$			15.9414i			0.539845i
$873$	−12.2646	+	7.08099i	−0.415095	+	0.239655i
$874$	−11.5279	−	19.9669i	−0.389938	−	0.675392i
$875$	−34.2473	−	20.0339i	−1.15777	−	0.677270i
$876$	24.9525			0.843068
$877$	15.9725	+	9.22175i	0.539354	+	0.311396i	0.744817	−	0.667269i	$-0.232537\pi$
$877$	15.9725	+	9.22175i	0.539354	+	0.311396i	−0.205463	+	0.978665i	$0.565870\pi$
$878$	19.4571	+	11.2336i	0.656646	+	0.379115i
$879$	17.1994			0.580122
$880$	11.1929	+	0.0212728i	0.377312	+	0.000717106i
$881$	−21.7185	−	37.6176i	−0.731716	−	1.26737i	−0.956149	−	0.292880i	$-0.905386\pi$
$881$	−21.7185	−	37.6176i	−0.731716	−	1.26737i	0.224433	−	0.974489i	$-0.427947\pi$
$882$	−27.4447	+	15.8452i	−0.924110	+	0.533535i
$883$			26.7242i			0.899341i	0.893195	+	0.449670i	$0.148459\pi$
$883$			26.7242i			0.899341i	−0.893195	+	0.449670i	$0.851541\pi$
$884$		0			0
$885$	−13.8253	+	7.94706i	−0.464733	+	0.267137i
$886$	21.1470	+	36.6277i	0.710449	+	1.23053i
$887$	−36.6973	+	21.1872i	−1.23217	+	0.711396i	−0.967483	−	0.252937i	$-0.918604\pi$
$887$	−36.6973	+	21.1872i	−1.23217	+	0.711396i	−0.264692	+	0.964333i	$0.585270\pi$
$888$	0.270670	+	0.156272i	0.00908310	+	0.00524413i
$889$	−42.5502			−1.42709
$890$	0.0173861	−	9.14784i	0.000582783	−	0.306636i
$891$	10.3967	−	18.0076i	0.348302	−	0.603276i
$892$			13.8079i			0.462322i
$893$	21.8716	+	12.6275i	0.731904	+	0.422565i
$894$	39.6552	+	68.6848i	1.32627	+	2.29716i
$895$	19.5213	−	33.6640i	0.652526	−	1.12526i
$896$	−35.6491			−1.19095
$897$		0			0
$898$			17.0514i			0.569013i
$899$	−15.7655	−	27.3066i	−0.525808	−	0.910727i
$900$	34.4653	+	0.131008i	1.14884	+	0.00436693i
$901$	−15.8886	+	27.5199i	−0.529326	+	0.916820i
$902$		−	17.0294i		−	0.567016i
$903$	15.4453	+	8.91733i	0.513986	+	0.296750i
$904$	3.92936	−	6.80585i	0.130689	−	0.226359i
$905$	−24.7987	−	43.1418i	−0.824338	−	1.43408i
$906$	−29.7051	+	51.4507i	−0.986885	+	1.70933i
$907$	−17.6921	+	10.2145i	−0.587457	+	0.339168i	−0.764091	−	0.645108i	$-0.776812\pi$
$907$	−17.6921	+	10.2145i	−0.587457	+	0.339168i	0.176634	+	0.984277i	$0.443479\pi$
$908$	6.67552	−	3.85411i	0.221535	−	0.127903i
$909$	29.5693			0.980751
$910$		0			0
$911$	23.7626			0.787290			0.393645	−	0.919263i	$-0.371214\pi$
$911$	23.7626			0.787290			0.393645	+	0.919263i	$0.371214\pi$
$912$	−24.8741	+	14.3611i	−0.823665	+	0.475543i
$913$	−20.3847	+	11.7691i	−0.674634	+	0.389500i
$914$	7.63145	−	13.2181i	0.252426	−	0.437215i
$915$	21.9410	−	12.6121i	0.725347	−	0.416943i
$916$	4.04266	−	7.00209i	0.133573	−	0.231356i
$917$	−60.0726	−	34.6829i	−1.98377	−	1.14533i
$918$		−	11.0924i		−	0.366104i
$919$	−3.23809	+	5.60854i	−0.106815	+	0.185009i	−0.914478	−	0.404635i	$-0.867399\pi$
$919$	−3.23809	+	5.60854i	−0.106815	+	0.185009i	0.807663	+	0.589644i	$0.200732\pi$
$920$	−3.14340	+	5.42070i	−0.103635	+	0.178715i
$921$	−34.9943	−	60.6120i	−1.15310	−	1.99723i
$922$		−	32.9539i		−	1.08528i
$923$		0			0
$924$	−45.9919			−1.51302
$925$	−0.00189864	+	0.499491i	−6.24268e−5	+	0.0164232i
$926$	−10.8520	−	18.7962i	−0.356618	−	0.617680i
$927$	26.9814	+	15.5777i	0.886185	+	0.511639i
$928$			78.9462i			2.59153i
$929$	−10.4103	+	18.0312i	−0.341551	+	0.591583i	−0.984721	−	0.174140i	$-0.944285\pi$
$929$	−10.4103	+	18.0312i	−0.341551	+	0.591583i	0.643170	+	0.765723i	$0.277619\pi$
$930$	−35.4495	−	0.0673741i	−1.16243	−	0.00220928i
$931$	−28.2338			−0.925326
$932$	−14.4502	−	8.34283i	−0.473332	−	0.273278i
$933$	−33.6144	+	19.4073i	−1.10049	+	0.635365i
$934$	−15.3451	−	26.5784i	−0.502106	−	0.869673i
$935$	24.2960	−	13.9658i	0.794563	−	0.456730i
$936$		0			0
$937$			18.1838i			0.594039i	0.954871	+	0.297019i	$0.0959926\pi$
$937$			18.1838i			0.594039i	−0.954871	+	0.297019i	$0.904007\pi$
$938$	44.7335	−	25.8269i	1.46060	−	0.843279i
$939$	34.9643	+	60.5600i	1.14102	+	1.97630i
$940$	0.0555749	−	29.2412i	0.00181265	−	0.953744i
$941$	−4.73191			−0.154256			−0.0771279	−	0.997021i	$-0.524575\pi$
$941$	−4.73191			−0.154256			−0.0771279	+	0.997021i	$0.524575\pi$
$942$	8.95388	+	5.16953i	0.291733	+	0.168432i
$943$	−6.99180	−	4.03672i	−0.227684	−	0.131454i
$944$	−7.19876			−0.234300
$945$	−6.82926	−	0.0129795i	−0.222156	−	0.000422222i
$946$	4.74748	+	8.22287i	0.154354	+	0.267349i
$947$	−25.6304	+	14.7977i	−0.832875	+	0.480861i	−0.854836	−	0.518898i	$-0.826342\pi$
$947$	−25.6304	+	14.7977i	−0.832875	+	0.480861i	0.0219609	+	0.999759i	$0.493009\pi$
$948$		−	29.2552i		−	0.950164i
$949$		0			0
$950$	46.8394	+	27.2807i	1.51967	+	0.885102i
$951$	19.9704	+	34.5897i	0.647584	+	1.12165i
$952$	−24.3007	+	14.0300i	−0.787591	+	0.454716i
$953$	−1.29331	−	0.746693i	−0.0418944	−	0.0241877i	0.478907	−	0.877866i	$-0.341033\pi$
$953$	−1.29331	−	0.746693i	−0.0418944	−	0.0241877i	−0.520801	+	0.853678i	$0.674367\pi$
$954$	−30.0002			−0.971293
$955$	15.7852	+	0.0300008i	0.510797	+	0.000970804i
$956$	−31.1614	+	53.9731i	−1.00783	+	1.74561i
$957$			50.2984i			1.62592i
$958$	−62.9984	−	36.3722i	−2.03539	−	1.17513i
$959$	22.7817	+	39.4591i	0.735660	+	1.27420i
$960$	54.7660	+	31.7581i	1.76757	+	1.02499i
$961$	−21.3365			−0.688274
$962$		0			0
$963$		−	14.5444i		−	0.468687i
$964$	−35.9769	−	62.3138i	−1.15874	−	2.00699i
$965$	42.1439	+	24.4387i	1.35666	+	0.786710i
$966$	−19.2452	+	33.3336i	−0.619203	+	1.07249i
$967$		−	10.0656i		−	0.323687i	−0.986816	−	0.161844i	$-0.948256\pi$
$967$		−	10.0656i		−	0.323687i	0.986816	−	0.161844i	$-0.0517440\pi$
$968$	7.57491	+	4.37338i	0.243467	+	0.140566i
$969$	−35.9561	+	62.2778i	−1.15508	+	2.00065i
$970$	12.8517	+	22.3579i	0.412644	+	0.717868i
$971$	6.15928	−	10.6682i	0.197661	−	0.342359i	−0.750109	−	0.661315i	$-0.769999\pi$
$971$	6.15928	−	10.6682i	0.197661	−	0.342359i	0.947770	+	0.318956i	$0.103332\pi$
$972$	47.6594	−	27.5162i	1.52868	−	0.882581i
$973$	16.5424	−	9.55073i	0.530323	−	0.306182i
$974$	28.0460			0.898653
$975$		0			0
$976$	11.4245			0.365690
$977$	−12.8698	+	7.43038i	−0.411741	+	0.237719i	−0.691538	−	0.722340i	$-0.743066\pi$
$977$	−12.8698	+	7.43038i	−0.411741	+	0.237719i	0.279796	+	0.960059i	$0.409733\pi$
$978$	37.4692	−	21.6329i	1.19813	−	0.691743i
$979$	1.98898	−	3.44501i	0.0635680	−	0.110103i
$980$	16.2912	+	28.3415i	0.520405	+	0.905337i
$981$	15.9548	−	27.6345i	0.509397	−	0.882302i
$982$	75.9315	+	43.8391i	2.42307	+	1.39896i
$983$		−	51.5408i		−	1.64390i	−0.569562	−	0.821948i	$-0.692887\pi$
$983$		−	51.5408i		−	1.64390i	0.569562	−	0.821948i	$-0.307113\pi$
$984$	5.93835	−	10.2855i	0.189308	−	0.327890i
$985$	−43.4144	−	25.1755i	−1.38330	−	0.802157i
$986$	65.3668	+	113.219i	2.08170	+	3.60562i
$987$		−	42.1618i		−	1.34203i
$988$		0			0
$989$	4.50145			0.143138
$990$	22.8870	+	13.2719i	0.727398	+	0.421809i
$991$	2.78760	+	4.82827i	0.0885511	+	0.153375i	0.906899	−	0.421348i	$-0.138443\pi$
$991$	2.78760	+	4.82827i	0.0885511	+	0.153375i	−0.818348	+	0.574723i	$0.805110\pi$
$992$	−20.9536	−	12.0976i	−0.665278	−	0.384098i
$993$			5.10602i			0.162035i
$994$	−18.6594	+	32.3191i	−0.591842	+	1.02510i
$995$	−27.3016	−	0.0518885i	−0.865519	−	0.00164498i
$996$	−69.9351			−2.21598
$997$	−22.2577	−	12.8505i	−0.704909	−	0.406979i	0.104264	−	0.994550i	$-0.466751\pi$
$997$	−22.2577	−	12.8505i	−0.704909	−	0.406979i	−0.809173	+	0.587570i	$0.800085\pi$
$998$	−64.3090	+	37.1288i	−2.03567	+	1.17529i
$999$	0.0429872	+	0.0744561i	0.00136006	+	0.00235569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.h.484.3		36
5.4	even	2	inner	845.2.n.h.484.16		36
13.2	odd	12		845.2.d.e.844.6		36
13.3	even	3		845.2.b.h.339.3	yes	18
13.4	even	6		845.2.n.i.529.3		36
13.5	odd	4		845.2.l.g.699.32		72
13.6	odd	12		845.2.l.g.654.31		72
13.7	odd	12		845.2.l.g.654.5		72
13.8	odd	4		845.2.l.g.699.6		72
13.9	even	3	inner	845.2.n.h.529.16		36
13.10	even	6		845.2.b.g.339.16	yes	18
13.11	odd	12		845.2.d.e.844.32		36
13.12	even	2		845.2.n.i.484.16		36
65.3	odd	12		4225.2.a.cb.1.3		18
65.4	even	6		845.2.n.i.529.16		36
65.9	even	6	inner	845.2.n.h.529.3		36
65.19	odd	12		845.2.l.g.654.6		72
65.23	odd	12		4225.2.a.ca.1.16		18
65.24	odd	12		845.2.d.e.844.5		36
65.29	even	6		845.2.b.h.339.16	yes	18
65.34	odd	4		845.2.l.g.699.31		72
65.42	odd	12		4225.2.a.cb.1.16		18
65.44	odd	4		845.2.l.g.699.5		72
65.49	even	6		845.2.b.g.339.3	✓	18
65.54	odd	12		845.2.d.e.844.31		36
65.59	odd	12		845.2.l.g.654.32		72
65.62	odd	12		4225.2.a.ca.1.3		18
65.64	even	2		845.2.n.i.484.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.b.g.339.3	✓	18	65.49	even	6
845.2.b.g.339.16	yes	18	13.10	even	6
845.2.b.h.339.3	yes	18	13.3	even	3
845.2.b.h.339.16	yes	18	65.29	even	6
845.2.d.e.844.5		36	65.24	odd	12
845.2.d.e.844.6		36	13.2	odd	12
845.2.d.e.844.31		36	65.54	odd	12
845.2.d.e.844.32		36	13.11	odd	12
845.2.l.g.654.5		72	13.7	odd	12
845.2.l.g.654.6		72	65.19	odd	12
845.2.l.g.654.31		72	13.6	odd	12
845.2.l.g.654.32		72	65.59	odd	12
845.2.l.g.699.5		72	65.44	odd	4
845.2.l.g.699.6		72	13.8	odd	4
845.2.l.g.699.31		72	65.34	odd	4
845.2.l.g.699.32		72	13.5	odd	4
845.2.n.h.484.3		36	1.1	even	1	trivial
845.2.n.h.484.16		36	5.4	even	2	inner
845.2.n.h.529.3		36	65.9	even	6	inner
845.2.n.h.529.16		36	13.9	even	3	inner
845.2.n.i.484.3		36	65.64	even	2
845.2.n.i.484.16		36	13.12	even	2
845.2.n.i.529.3		36	13.4	even	6
845.2.n.i.529.16		36	65.4	even	6
4225.2.a.ca.1.3		18	65.62	odd	12
4225.2.a.ca.1.16		18	65.23	odd	12
4225.2.a.cb.1.3		18	65.3	odd	12
4225.2.a.cb.1.16		18	65.42	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86013 + 1.07395i) q^{2} +(2.05625 - 1.18717i) q^{3} +(1.30673 - 2.26333i) q^{4} +(1.11435 + 1.93861i) q^{5} +(-2.54993 + 4.41661i) q^{6} +(3.07334 + 1.77439i) q^{7} +1.31766i q^{8} +(1.31877 - 2.28417i) q^{9} +(-4.15482 - 2.40932i) q^{10} +(-1.04426 - 1.80871i) q^{11} -6.20528i q^{12} -7.62244 q^{14} +(4.59285 + 2.66334i) q^{15} +(1.19836 + 2.07562i) q^{16} +(5.19678 + 3.00036i) q^{17} +5.66516i q^{18} +(-2.52362 + 4.37104i) q^{19} +(5.84388 + 0.0111067i) q^{20} +8.42607 q^{21} +(3.88493 + 2.24297i) q^{22} +(1.84180 - 1.06337i) q^{23} +(1.56430 + 2.70944i) q^{24} +(-2.51644 + 4.32059i) q^{25} +0.860615i q^{27} +(8.03208 - 4.63732i) q^{28} +(-5.07154 - 8.78417i) q^{29} +(-11.4036 - 0.0216733i) q^{30} +3.10862 q^{31} +(-6.74049 - 3.89162i) q^{32} +(-4.29452 - 2.47944i) q^{33} -12.8889 q^{34} +(-0.0150816 + 7.93532i) q^{35} +(-3.44656 - 5.96961i) q^{36} +(0.0865149 - 0.0499494i) q^{37} -10.8410i q^{38} +(-2.55444 + 1.46834i) q^{40} +(-1.89809 - 3.28758i) q^{41} +(-15.6736 + 9.04917i) q^{42} +(1.83303 + 1.05830i) q^{43} -5.45829 q^{44} +(5.89770 + 0.0112090i) q^{45} +(-2.28400 + 3.95601i) q^{46} -5.00374i q^{47} +(4.92826 + 2.84533i) q^{48} +(2.79695 + 4.84446i) q^{49} +(0.0408221 - 10.7394i) q^{50} +14.2478 q^{51} +5.29557i q^{53} +(-0.924257 - 1.60086i) q^{54} +(2.34272 - 4.03996i) q^{55} +(-2.33806 + 4.04963i) q^{56} +11.9839i q^{57} +(18.8675 + 10.8932i) q^{58} +(-1.50179 + 2.60118i) q^{59} +(12.0296 - 6.91487i) q^{60} +(2.38336 - 4.12811i) q^{61} +(-5.78245 + 3.33850i) q^{62} +(8.10605 - 4.68003i) q^{63} +11.9242 q^{64} +10.6512 q^{66} +(-5.86866 + 3.38827i) q^{67} +(13.5816 - 7.84135i) q^{68} +(2.52480 - 4.37309i) q^{69} +(-8.49408 - 14.7770i) q^{70} +(2.44796 - 4.24000i) q^{71} +(3.00977 + 1.73769i) q^{72} +4.02118i q^{73} +(-0.107286 + 0.185825i) q^{74} +(-0.0451260 + 11.8717i) q^{75} +(6.59541 + 11.4236i) q^{76} -7.41173i q^{77} +4.71456 q^{79} +(-2.68844 + 4.63614i) q^{80} +(4.97801 + 8.62216i) q^{81} +(7.06139 + 4.07690i) q^{82} -11.2703i q^{83} +(11.0106 - 19.0710i) q^{84} +(-0.0255018 + 13.4180i) q^{85} -4.54625 q^{86} +(-20.8567 - 12.0416i) q^{87} +(2.38328 - 1.37599i) q^{88} +(0.952337 + 1.64950i) q^{89} +(-10.9826 + 6.31298i) q^{90} -5.55814i q^{92} +(6.39209 - 3.69047i) q^{93} +(5.37376 + 9.30762i) q^{94} +(-11.2860 - 0.0214497i) q^{95} -18.4802 q^{96} +(-4.65004 - 2.68470i) q^{97} +(-10.4054 - 6.00757i) q^{98} -5.50856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 16 q^{4} - 16 q^{6} + 18 q^{9} - 13 q^{10} - 22 q^{11} - 8 q^{14} - 8 q^{15} + 12 q^{16} + 28 q^{19} + 10 q^{20} + 52 q^{21} + 34 q^{24} - 16 q^{25} - 20 q^{29} - 31 q^{30} + 64 q^{31} - 36 q^{34}+ \cdots - 152 q^{99}+O(q^{100}) \) 36 * q + 16 * q^4 - 16 * q^6 + 18 * q^9 - 13 * q^10 - 22 * q^11 - 8 * q^14 - 8 * q^15 + 12 * q^16 + 28 * q^19 + 10 * q^20 + 52 * q^21 + 34 * q^24 - 16 * q^25 - 20 * q^29 - 31 * q^30 + 64 * q^31 - 36 * q^34 - 10 * q^35 - 32 * q^36 + 6 * q^40 - 52 * q^41 - 100 * q^44 - 5 * q^45 - 30 * q^46 + 44 * q^49 - 29 * q^50 - 80 * q^51 + 90 * q^54 + 20 * q^55 + 20 * q^56 + 76 * q^59 + 86 * q^60 - 8 * q^61 + 136 * q^64 + 16 * q^66 + 30 * q^69 + 92 * q^70 - 72 * q^71 + 30 * q^74 - 13 * q^75 - 4 * q^76 - 32 * q^79 - 73 * q^80 + 30 * q^81 + 78 * q^84 - 29 * q^85 - 60 * q^86 + 94 * q^89 - 140 * q^90 - 128 * q^94 - 41 * q^95 - 36 * q^96 - 152 * q^99

Introduction

L-functions

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