LMFDB - Embedded newform 675.2.u.e.49.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03778 - 1.23677i) q^{2} +(-1.23848 - 1.21085i) q^{3} +(-0.105334 + 0.597379i) q^{4} +(-0.212279 + 2.78832i) q^{6} +(-1.71440 + 0.302296i) q^{7} +(-1.94825 + 1.12482i) q^{8} +(0.0676836 + 2.99924i) q^{9} +(2.93339 + 1.06767i) q^{11} +(0.853791 - 0.612300i) q^{12} +(-1.21663 + 1.44992i) q^{13} +(2.15304 + 1.80662i) q^{14} +(4.55303 + 1.65717i) q^{16} +(5.56291 + 3.21175i) q^{17} +(3.63914 - 3.19625i) q^{18} +(-2.43505 - 4.21762i) q^{19} +(2.48930 + 1.70150i) q^{21} +(-1.72374 - 4.73595i) q^{22} +(2.73355 + 0.481999i) q^{23} +(3.77487 + 0.965965i) q^{24} +3.05582 q^{26} +(3.54780 - 3.79646i) q^{27} -1.05599i q^{28} +(-5.94510 + 4.98853i) q^{29} +(-0.687222 + 3.89743i) q^{31} +(-1.13664 - 3.12289i) q^{32} +(-2.34017 - 4.87419i) q^{33} +(-1.80085 - 10.2132i) q^{34} +(-1.79881 - 0.275489i) q^{36} +(0.704120 + 0.406524i) q^{37} +(-2.68922 + 7.38856i) q^{38} +(3.26242 - 0.322550i) q^{39} +(5.80103 + 4.86764i) q^{41} +(-0.478965 - 4.84447i) q^{42} +(0.901745 - 2.47752i) q^{43} +(-0.946788 + 1.63988i) q^{44} +(-2.24069 - 3.88100i) q^{46} +(7.03326 - 1.24015i) q^{47} +(-3.63227 - 7.56541i) q^{48} +(-3.73005 + 1.35763i) q^{49} +(-3.00063 - 10.7136i) q^{51} +(-0.738001 - 0.879516i) q^{52} -1.86813i q^{53} +(-8.37719 - 0.447951i) q^{54} +(3.00006 - 2.51735i) q^{56} +(-2.09115 + 8.17194i) q^{57} +(12.3394 + 2.17576i) q^{58} +(-0.971077 + 0.353443i) q^{59} +(-1.78476 - 10.1219i) q^{61} +(5.53342 - 3.19472i) q^{62} +(-1.02269 - 5.12144i) q^{63} +(2.16250 - 3.74556i) q^{64} +(-3.59969 + 7.95259i) q^{66} +(-8.76411 + 10.4447i) q^{67} +(-2.50460 + 2.98486i) q^{68} +(-2.80183 - 3.90687i) q^{69} +(4.06389 - 7.03886i) q^{71} +(-3.50548 - 5.76713i) q^{72} +(8.53538 - 4.92790i) q^{73} +(-0.227941 - 1.29272i) q^{74} +(2.77601 - 1.01039i) q^{76} +(-5.35177 - 0.943662i) q^{77} +(-3.78459 - 3.70014i) q^{78} +(11.3969 - 9.56310i) q^{79} +(-8.99084 + 0.405998i) q^{81} -12.2261i q^{82} +(5.92935 + 7.06632i) q^{83} +(-1.27865 + 1.30783i) q^{84} +(-3.99995 + 1.45586i) q^{86} +(13.4033 + 1.02041i) q^{87} +(-6.91592 + 1.21946i) q^{88} +(6.28136 + 10.8796i) q^{89} +(1.64749 - 2.85354i) q^{91} +(-0.575872 + 1.58220i) q^{92} +(5.57031 - 3.99478i) q^{93} +(-8.83274 - 7.41155i) q^{94} +(-2.37364 + 5.24395i) q^{96} +(-5.39248 + 14.8157i) q^{97} +(5.55004 + 3.20432i) q^{98} +(-3.00365 + 8.87020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−1.03778	−	1.23677i	−0.733819	−	0.874532i	0.262076	−	0.965047i	$-0.415593\pi$
$2$	−1.03778	−	1.23677i	−0.733819	−	0.874532i	−0.995895	+	0.0905154i	$0.971149\pi$
$3$	−1.23848	−	1.21085i	−0.715039	−	0.699085i
$3$	−1.23848	−	1.21085i	−0.715039	−	0.699085i
$4$	−0.105334	+	0.597379i	−0.0526670	+	0.298689i
$5$		0			0
$5$		0			0
$6$	−0.212279	+	2.78832i	−0.0866625	+	1.13833i
$7$	−1.71440	+	0.302296i	−0.647984	+	0.114257i	−0.487974	−	0.872858i	$-0.662264\pi$
$7$	−1.71440	+	0.302296i	−0.647984	+	0.114257i	−0.160010	+	0.987115i	$0.551153\pi$
$8$	−1.94825	+	1.12482i	−0.688811	+	0.397685i
$9$	0.0676836	+	2.99924i	0.0225612	+	0.999745i
$10$		0			0
$11$	2.93339	+	1.06767i	0.884451	+	0.321914i	0.744005	−	0.668174i	$-0.232924\pi$
$11$	2.93339	+	1.06767i	0.884451	+	0.321914i	0.140447	+	0.990088i	$0.455146\pi$
$12$	0.853791	−	0.612300i	0.246468	−	0.176756i
$13$	−1.21663	+	1.44992i	−0.337433	+	0.402137i	−0.907902	−	0.419182i	$-0.862317\pi$
$13$	−1.21663	+	1.44992i	−0.337433	+	0.402137i	0.570469	+	0.821319i	$0.306761\pi$
$14$	2.15304	+	1.80662i	0.575424	+	0.482838i
$15$		0			0
$16$	4.55303	+	1.65717i	1.13826	+	0.414292i
$17$	5.56291	+	3.21175i	1.34921	+	0.778964i	0.988137	−	0.153576i	$-0.0490789\pi$
$17$	5.56291	+	3.21175i	1.34921	+	0.778964i	0.361068	+	0.932539i	$0.382412\pi$
$18$	3.63914	−	3.19625i	0.857754	−	0.753363i
$19$	−2.43505	−	4.21762i	−0.558638	−	0.967590i	−0.997611	−	0.0690890i	$-0.977991\pi$
$19$	−2.43505	−	4.21762i	−0.558638	−	0.967590i	0.438972	−	0.898501i	$-0.355343\pi$
$20$		0			0
$21$	2.48930	+	1.70150i	0.543209	+	0.371297i
$22$	−1.72374	−	4.73595i	−0.367504	−	1.00971i
$23$	2.73355	+	0.481999i	0.569985	+	0.100504i	0.451211	−	0.892418i	$-0.350992\pi$
$23$	2.73355	+	0.481999i	0.569985	+	0.100504i	0.118774	+	0.992921i	$0.462103\pi$
$24$	3.77487	+	0.965965i	0.770542	+	0.197177i
$25$		0			0
$26$	3.05582			0.599296
$27$	3.54780	−	3.79646i	0.682775	−	0.730629i
$28$		−	1.05599i		−	0.199563i
$29$	−5.94510	+	4.98853i	−1.10398	+	0.926346i	−0.997686	−	0.0679886i	$-0.978342\pi$
$29$	−5.94510	+	4.98853i	−1.10398	+	0.926346i	−0.106291	+	0.994335i	$0.533897\pi$
$30$		0			0
$31$	−0.687222	+	3.89743i	−0.123429	+	0.699999i	0.858800	+	0.512311i	$0.171210\pi$
$31$	−0.687222	+	3.89743i	−0.123429	+	0.699999i	−0.982229	+	0.187688i	$0.939901\pi$
$32$	−1.13664	−	3.12289i	−0.200931	−	0.552054i
$33$	−2.34017	−	4.87419i	−0.407372	−	0.848487i
$34$	−1.80085	−	10.2132i	−0.308844	−	1.75154i
$35$		0			0
$36$	−1.79881	−	0.275489i	−0.299802	−	0.0459148i
$37$	0.704120	+	0.406524i	0.115757	+	0.0668321i	0.556760	−	0.830673i	$-0.312044\pi$
$37$	0.704120	+	0.406524i	0.115757	+	0.0668321i	−0.441004	+	0.897505i	$0.645377\pi$
$38$	−2.68922	+	7.38856i	−0.436248	+	1.19858i
$39$	3.26242	−	0.322550i	0.522405	−	0.0516493i
$40$		0			0
$41$	5.80103	+	4.86764i	0.905969	+	0.760198i	0.971348	−	0.237662i	$-0.0763811\pi$
$41$	5.80103	+	4.86764i	0.905969	+	0.760198i	−0.0653788	+	0.997861i	$0.520826\pi$
$42$	−0.478965	−	4.84447i	−0.0739059	−	0.747519i
$43$	0.901745	−	2.47752i	0.137515	−	0.377819i	−0.851751	−	0.523947i	$-0.824459\pi$
$43$	0.901745	−	2.47752i	0.137515	−	0.377819i	0.989266	+	0.146128i	$0.0466812\pi$
$44$	−0.946788	+	1.63988i	−0.142734	+	0.247222i
$45$		0			0
$46$	−2.24069	−	3.88100i	−0.330372	−	0.572222i
$47$	7.03326	−	1.24015i	1.02591	−	0.180895i	0.364720	−	0.931117i	$-0.381165\pi$
$47$	7.03326	−	1.24015i	1.02591	−	0.180895i	0.661186	+	0.750222i	$0.270054\pi$
$48$	−3.63227	−	7.56541i	−0.524273	−	1.09197i
$49$	−3.73005	+	1.35763i	−0.532864	+	0.193947i
$50$		0			0
$51$	−3.00063	−	10.7136i	−0.420172	−	1.50020i
$52$	−0.738001	−	0.879516i	−0.102342	−	0.121967i
$53$		−	1.86813i		−	0.256608i	−0.991735	−	0.128304i	$-0.959047\pi$
$53$		−	1.86813i		−	0.256608i	0.991735	−	0.128304i	$-0.0409533\pi$
$54$	−8.37719	−	0.447951i	−1.13999	−	0.0609584i
$55$		0			0
$56$	3.00006	−	2.51735i	0.400900	−	0.336395i
$57$	−2.09115	+	8.17194i	−0.276979	+	1.08240i
$58$	12.3394	+	2.17576i	1.62024	+	0.285692i
$59$	−0.971077	+	0.353443i	−0.126423	+	0.0460144i	−0.404457	−	0.914557i	$-0.632540\pi$
$59$	−0.971077	+	0.353443i	−0.126423	+	0.0460144i	0.278034	+	0.960571i	$0.410317\pi$
$60$		0			0
$61$	−1.78476	−	10.1219i	−0.228515	−	1.29597i	−0.855850	−	0.517224i	$-0.826966\pi$
$61$	−1.78476	−	10.1219i	−0.228515	−	1.29597i	0.627335	−	0.778749i	$-0.284146\pi$
$62$	5.53342	−	3.19472i	0.702746	−	0.405730i
$63$	−1.02269	−	5.12144i	−0.128847	−	0.645241i
$64$	2.16250	−	3.74556i	0.270312	−	0.468195i
$65$		0			0
$66$	−3.59969	+	7.95259i	−0.443092	+	0.978896i
$67$	−8.76411	+	10.4447i	−1.07071	+	1.27602i	−0.111363	+	0.993780i	$0.535521\pi$
$67$	−8.76411	+	10.4447i	−1.07071	+	1.27602i	−0.959344	+	0.282239i	$0.908923\pi$
$68$	−2.50460	+	2.98486i	−0.303727	+	0.361967i
$69$	−2.80183	−	3.90687i	−0.337301	−	0.470332i
$70$		0			0
$71$	4.06389	−	7.03886i	0.482294	−	0.835359i	−0.517499	−	0.855684i	$-0.673137\pi$
$71$	4.06389	−	7.03886i	0.482294	−	0.835359i	0.999793	+	0.0203253i	$0.00647020\pi$
$72$	−3.50548	−	5.76713i	−0.413124	−	0.679663i
$73$	8.53538	−	4.92790i	0.998991	−	0.576768i	0.0910412	−	0.995847i	$-0.470980\pi$
$73$	8.53538	−	4.92790i	0.998991	−	0.576768i	0.907950	+	0.419080i	$0.137647\pi$
$74$	−0.227941	−	1.29272i	−0.0264976	−	0.150276i
$75$		0			0
$76$	2.77601	−	1.01039i	0.318430	−	0.115899i
$77$	−5.35177	−	0.943662i	−0.609891	−	0.107540i
$78$	−3.78459	−	3.70014i	−0.428520	−	0.418959i
$79$	11.3969	−	9.56310i	1.28225	−	1.07593i	0.289317	−	0.957233i	$-0.406572\pi$
$79$	11.3969	−	9.56310i	1.28225	−	1.07593i	0.992930	−	0.118700i	$-0.0378726\pi$
$80$		0			0
$81$	−8.99084	+	0.405998i	−0.998982	+	0.0451109i
$82$		−	12.2261i		−	1.35015i
$83$	5.92935	+	7.06632i	0.650830	+	0.775630i	0.986039	−	0.166514i	$-0.0532512\pi$
$83$	5.92935	+	7.06632i	0.650830	+	0.775630i	−0.335209	+	0.942144i	$0.608807\pi$
$84$	−1.27865	+	1.30783i	−0.139512	+	0.142696i
$85$		0			0
$86$	−3.99995	+	1.45586i	−0.431326	+	0.156990i
$87$	13.4033	+	1.02041i	1.43698	+	0.109399i
$88$	−6.91592	+	1.21946i	−0.737240	+	0.129995i
$89$	6.28136	+	10.8796i	0.665823	+	1.15324i	0.979061	+	0.203565i	$0.0652529\pi$
$89$	6.28136	+	10.8796i	0.665823	+	1.15324i	−0.313238	+	0.949675i	$0.601414\pi$
$90$		0			0
$91$	1.64749	−	2.85354i	0.172704	−	0.299132i
$92$	−0.575872	+	1.58220i	−0.0600388	+	0.164955i
$93$	5.57031	−	3.99478i	0.577615	−	0.414239i
$94$	−8.83274	−	7.41155i	−0.911028	−	0.764443i
$95$		0			0
$96$	−2.37364	+	5.24395i	−0.242259	+	0.535208i
$97$	−5.39248	+	14.8157i	−0.547523	+	1.50431i	0.289521	+	0.957172i	$0.406504\pi$
$97$	−5.39248	+	14.8157i	−0.547523	+	1.50431i	−0.837044	+	0.547136i	$0.815718\pi$
$98$	5.55004	+	3.20432i	0.560639	+	0.323685i
$99$	−3.00365	+	8.87020i	−0.301878	+	0.891489i
$100$		0			0
$101$	1.11330	+	6.31385i	0.110778	+	0.628251i	0.988754	+	0.149548i	$0.0477818\pi$
$101$	1.11330	+	6.31385i	0.110778	+	0.628251i	−0.877977	+	0.478703i	$0.841107\pi$
$102$	−10.1363	+	14.8294i	−1.00364	+	1.46833i
$103$	2.47454	+	6.79875i	0.243824	+	0.669901i	0.999881	+	0.0153956i	$0.00490077\pi$
$103$	2.47454	+	6.79875i	0.243824	+	0.669901i	−0.756058	+	0.654505i	$0.772877\pi$
$104$	0.739394	−	4.19331i	0.0725035	−	0.411188i
$105$		0			0
$106$	−2.31046	+	1.93871i	−0.224412	+	0.188304i
$107$			4.53705i			0.438613i	0.975656	+	0.219307i	$0.0703795\pi$
$107$			4.53705i			0.438613i	−0.975656	+	0.219307i	$0.929620\pi$
$108$	1.89422	+	2.51928i	0.182271	+	0.242418i
$109$	7.64924			0.732665			0.366332	−	0.930484i	$-0.380613\pi$
$109$	7.64924			0.732665			0.366332	+	0.930484i	$0.380613\pi$
$110$		0			0
$111$	−0.379802	−	1.35606i	−0.0360492	−	0.128711i
$112$	−8.30668	−	1.46469i	−0.784908	−	0.138400i
$113$	1.15121	+	3.16293i	0.108297	+	0.297544i	0.981990	−	0.188935i	$-0.0605034\pi$
$113$	1.15121	+	3.16293i	0.108297	+	0.297544i	−0.873693	+	0.486478i	$0.838281\pi$
$114$	12.2770	−	5.89437i	1.14985	−	0.552059i
$115$		0			0
$116$	−2.35382	−	4.07694i	−0.218547	−	0.378534i
$117$	−4.43101	−	3.55083i	−0.409647	−	0.328274i
$118$	1.44489	+	0.834208i	0.133013	+	0.0767951i
$119$	−10.5080	−	3.82459i	−0.963265	−	0.350600i
$120$		0			0
$121$	−0.961609	−	0.806886i	−0.0874190	−	0.0733532i
$122$	−10.6663	+	12.7116i	−0.965681	+	1.15085i
$123$	−1.29050	−	13.0527i	−0.116360	−	1.17692i
$124$	−2.25585	−	0.821063i	−0.202582	−	0.0737336i
$125$		0			0
$126$	−5.27274	+	6.57976i	−0.469733	+	0.586171i
$127$	15.4617	−	8.92679i	1.37200	−	0.792125i	0.380820	−	0.924649i	$-0.375642\pi$
$127$	15.4617	−	8.92679i	1.37200	−	0.792125i	0.991180	+	0.132524i	$0.0423083\pi$
$128$	−13.4222	+	2.36670i	−1.18637	+	0.209189i
$129$	−4.11671	+	1.97649i	−0.362456	+	0.174021i
$130$		0			0
$131$	−2.37367	+	13.4617i	−0.207388	+	1.17616i	0.686249	+	0.727367i	$0.259256\pi$
$131$	−2.37367	+	13.4617i	−0.207388	+	1.17616i	−0.893637	+	0.448790i	$0.851855\pi$
$132$	3.15824	−	0.884552i	0.274889	−	0.0769904i
$133$	5.44962	+	6.49461i	0.472542	+	0.563154i
$134$	22.0129			1.90162
$135$		0			0
$136$	−14.4506			−1.23913
$137$	−8.95490	−	10.6720i	−0.765069	−	0.911773i	0.233089	−	0.972456i	$-0.425117\pi$
$137$	−8.95490	−	10.6720i	−0.765069	−	0.911773i	−0.998157	+	0.0606822i	$0.980672\pi$
$138$	−1.92424	+	7.51970i	−0.163802	+	0.640119i
$139$	−3.10046	+	17.5836i	−0.262977	+	1.49142i	0.511756	+	0.859131i	$0.328995\pi$
$139$	−3.10046	+	17.5836i	−0.262977	+	1.49142i	−0.774734	+	0.632288i	$0.782116\pi$
$140$		0			0
$141$	−10.2122	−	6.98031i	−0.860023	−	0.587848i
$142$	−12.9229	+	2.27865i	−1.08446	+	0.191220i
$143$	−5.11689	+	2.95424i	−0.427896	+	0.247046i
$144$	−4.66207	+	13.7678i	−0.388506	+	1.14731i
$145$		0			0
$146$	−14.9525	−	5.44228i	−1.23748	−	0.450406i
$147$	6.26349	+	2.83513i	0.516604	+	0.233838i
$148$	−0.317017	+	0.377806i	−0.0260586	+	0.0310554i
$149$	13.7598	+	11.5458i	1.12725	+	0.945872i	0.998948	−	0.0458641i	$-0.0146041\pi$
$149$	13.7598	+	11.5458i	1.12725	+	0.945872i	0.128298	+	0.991736i	$0.459049\pi$
$150$		0			0
$151$	18.3678	+	6.68534i	1.49475	+	0.544045i	0.954696	−	0.297583i	$-0.0961806\pi$
$151$	18.3678	+	6.68534i	1.49475	+	0.544045i	0.540057	+	0.841629i	$0.318403\pi$
$152$	9.48817	+	5.47800i	0.769592	+	0.444324i
$153$	−9.25628	+	16.9019i	−0.748326	+	1.36644i
$154$	4.38685	+	7.59825i	0.353502	+	0.612284i
$155$		0			0
$156$	−0.150959	+	1.98287i	−0.0120864	+	0.158757i
$157$	2.75155	+	7.55982i	0.219598	+	0.603339i	0.999753	−	0.0222470i	$-0.00708202\pi$
$157$	2.75155	+	7.55982i	0.219598	+	0.603339i	−0.780155	+	0.625586i	$0.784860\pi$
$158$	−23.6548	−	4.17098i	−1.88188	−	0.331825i
$159$	−2.26203	+	2.31365i	−0.179391	+	0.183485i
$160$		0			0
$161$	−4.83212			−0.380824
$162$	9.83262	+	10.6983i	0.772523	+	0.840538i
$163$			5.27505i			0.413174i	0.978428	+	0.206587i	$0.0662356\pi$
$163$			5.27505i			0.413174i	−0.978428	+	0.206587i	$0.933764\pi$
$164$	−3.51887	+	2.95269i	−0.274778	+	0.230566i
$165$		0			0
$166$	2.58611	−	14.6665i	0.200721	−	1.13834i
$167$	−5.65972	−	15.5499i	−0.437962	−	1.20329i	−0.940816	−	0.338919i	$-0.889939\pi$
$167$	−5.65972	−	15.5499i	−0.437962	−	1.20329i	0.502854	−	0.864372i	$-0.332284\pi$
$168$	−6.76366	−	0.514927i	−0.521828	−	0.0397275i
$169$	1.63534	+	9.27446i	0.125795	+	0.713420i
$170$		0			0
$171$	12.4848	−	7.58875i	0.954740	−	0.580326i
$172$	1.38504	+	0.799651i	0.105608	+	0.0609728i
$173$	−6.69046	+	18.3819i	−0.508666	+	1.39755i	0.373948	+	0.927450i	$0.378004\pi$
$173$	−6.69046	+	18.3819i	−0.508666	+	1.39755i	−0.882614	+	0.470099i	$0.844218\pi$
$174$	−12.6476	−	17.6358i	−0.958811	−	1.33697i
$175$		0			0
$176$	11.5865	+	9.72224i	0.873367	+	0.732842i
$177$	1.63063	+	0.738095i	0.122566	+	0.0554786i
$178$	6.93701	−	19.0593i	0.519951	−	1.42855i
$179$	0.604142	−	1.04640i	0.0451557	−	0.0782119i	−0.842564	−	0.538596i	$-0.818955\pi$
$179$	0.604142	−	1.04640i	0.0451557	−	0.0782119i	0.887720	+	0.460384i	$0.152288\pi$
$180$		0			0
$181$	−10.2446	−	17.7442i	−0.761474	−	1.31891i	−0.942090	−	0.335359i	$-0.891142\pi$
$181$	−10.2446	−	17.7442i	−0.761474	−	1.31891i	0.180616	−	0.983554i	$-0.442191\pi$
$182$	−5.23891	+	0.923761i	−0.388334	+	0.0684738i
$183$	−10.0457	+	14.6969i	−0.742598	+	1.08642i
$184$	−5.86781	+	2.13571i	−0.432581	+	0.157447i
$185$		0			0
$186$	−10.7214	−	2.74353i	−0.786130	−	0.201166i
$187$	12.8891	+	15.3607i	0.942547	+	1.12328i
$188$			4.33215i			0.315954i
$189$	−4.93471	+	7.58115i	−0.358947	+	0.551447i
$190$		0			0
$191$	−1.41048	+	1.18353i	−0.102059	+	0.0856373i	−0.692389	−	0.721524i	$-0.743442\pi$
$191$	−1.41048	+	1.18353i	−0.102059	+	0.0856373i	0.590331	+	0.807162i	$0.298997\pi$
$192$	−7.21353	+	2.02035i	−0.520592	+	0.145806i
$193$	13.0401	+	2.29931i	0.938643	+	0.165508i	0.621983	−	0.783031i	$-0.286327\pi$
$193$	13.0401	+	2.29931i	0.938643	+	0.165508i	0.316660	+	0.948539i	$0.397438\pi$
$194$	23.9199	−	8.70613i	1.71735	−	0.625064i
$195$		0			0
$196$	−0.418117	−	2.37126i	−0.0298655	−	0.169376i
$197$	16.2191	−	9.36409i	1.15556	−	0.667164i	0.205325	−	0.978694i	$-0.434175\pi$
$197$	16.2191	−	9.36409i	1.15556	−	0.667164i	0.950236	+	0.311530i	$0.100841\pi$
$198$	14.0876	−	5.49046i	1.00116	−	0.390190i
$199$	3.20552	−	5.55213i	0.227233	−	0.393580i	−0.729754	−	0.683710i	$-0.760365\pi$
$199$	3.20552	−	5.55213i	0.227233	−	0.393580i	0.956987	+	0.290130i	$0.0936987\pi$
$200$		0			0
$201$	23.5011	−	2.32352i	1.65764	−	0.163888i
$202$	6.65345	−	7.92927i	0.468135	−	0.557901i
$203$	8.68429	−	10.3495i	0.609517	−	0.726394i
$204$	6.71612	−	0.664011i	0.470222	−	0.0464901i
$205$		0			0
$206$	5.84050	−	10.1160i	0.406927	−	0.704818i
$207$	−1.26061	+	8.23119i	−0.0876186	+	0.572107i
$208$	−7.94212	+	4.58539i	−0.550687	+	0.317939i
$209$	−2.63993	−	14.9718i	−0.182608	−	1.03562i
$210$		0			0
$211$	−15.3119	+	5.57306i	−1.05411	+	0.383665i	−0.810213	−	0.586135i	$-0.800649\pi$
$211$	−15.3119	+	5.57306i	−1.05411	+	0.383665i	−0.243899	+	0.969801i	$0.578426\pi$
$212$	1.11598	+	0.196778i	0.0766461	+	0.0135148i
$213$	−13.5561	+	3.79675i	−0.928846	+	0.260149i
$214$	5.61131	−	4.70845i	0.383581	−	0.321863i
$215$		0			0
$216$	−2.64166	+	11.3871i	−0.179742	+	0.774794i
$217$		−	6.88951i		−	0.467690i
$218$	−7.93821	−	9.46039i	−0.537643	−	0.640739i
$219$	−16.5379	−	4.23194i	−1.11753	−	0.285968i
$220$		0			0
$221$	−11.4248	+	4.15829i	−0.768516	+	0.279717i
$222$	−1.28299	+	1.87701i	−0.0861085	+	0.125977i
$223$	−18.4332	+	3.25026i	−1.23438	+	0.217654i	−0.752504	−	0.658588i	$-0.771154\pi$
$223$	−18.4332	+	3.25026i	−1.23438	+	0.217654i	−0.481872	+	0.876242i	$0.660043\pi$
$224$	2.89269	+	5.01029i	0.193276	+	0.334764i
$225$		0			0
$226$	2.71713	−	4.70621i	0.180741	−	0.313053i
$227$	6.00696	−	16.5040i	0.398696	−	1.09541i	−0.564224	−	0.825622i	$-0.690825\pi$
$227$	6.00696	−	16.5040i	0.398696	−	1.09541i	0.962920	−	0.269787i	$-0.0869532\pi$
$228$	−4.66147	−	2.10999i	−0.308714	−	0.139737i
$229$	5.79494	+	4.86253i	0.382940	+	0.321325i	0.813855	−	0.581067i	$-0.197365\pi$
$229$	5.79494	+	4.86253i	0.382940	+	0.321325i	−0.430915	+	0.902392i	$0.641809\pi$
$230$		0			0
$231$	5.48545	+	7.64890i	0.360916	+	0.503261i
$232$	5.97133	−	16.4061i	0.392037	−	1.07711i
$233$	−6.01595	−	3.47331i	−0.394118	−	0.227544i	0.289825	−	0.957080i	$-0.406403\pi$
$233$	−6.01595	−	3.47331i	−0.394118	−	0.227544i	−0.683943	+	0.729536i	$0.739736\pi$
$234$	0.206829	+	9.16513i	0.0135208	+	0.599143i
$235$		0			0
$236$	−0.108852	−	0.617330i	−0.00708566	−	0.0401848i
$237$	−25.6943	−	1.95615i	−1.66902	−	0.127065i
$238$	6.17478	+	16.9651i	0.400252	+	1.09968i
$239$	3.56006	−	20.1901i	0.230281	−	1.30599i	−0.622046	−	0.782981i	$-0.713698\pi$
$239$	3.56006	−	20.1901i	0.230281	−	1.30599i	0.852327	−	0.523009i	$-0.175191\pi$
$240$		0			0
$241$	−17.8973	+	15.0176i	−1.15287	+	0.967369i	−0.999783	−	0.0208438i	$-0.993365\pi$
$241$	−17.8973	+	15.0176i	−1.15287	+	0.967369i	−0.153083	+	0.988213i	$0.548920\pi$
$242$			2.02666i			0.130279i
$243$	11.6266	+	10.3837i	0.745847	+	0.666117i
$244$	6.23459			0.399129
$245$		0			0
$246$	−14.8040	+	15.1418i	−0.943867	+	0.965408i
$247$	9.07779	+	1.60066i	0.577606	+	0.101847i
$248$	−3.04504	−	8.36617i	−0.193360	−	0.531252i
$249$	1.21286	−	15.9311i	0.0768616	−	1.00959i
$250$		0			0
$251$	4.60669	+	7.97903i	0.290772	+	0.503632i	0.973992	−	0.226580i	$-0.0727546\pi$
$251$	4.60669	+	7.97903i	0.290772	+	0.503632i	−0.683221	+	0.730212i	$0.739421\pi$
$252$	3.16716	−	0.0714732i	0.199513	−	0.00450239i
$253$	7.50397	+	4.33242i	0.471770	+	0.272377i
$254$	−27.0862	−	9.85857i	−1.69954	−	0.618581i
$255$		0			0
$256$	10.2301	+	8.58408i	0.639381	+	0.536505i
$257$	−16.5773	+	19.7561i	−1.03406	+	1.23235i	−0.0618912	+	0.998083i	$0.519713\pi$
$257$	−16.5773	+	19.7561i	−1.03406	+	1.23235i	−0.972172	+	0.234266i	$0.924731\pi$
$258$	6.71670	+	3.04028i	0.418164	+	0.189279i
$259$	−1.33004	−	0.484094i	−0.0826445	−	0.0300801i
$260$		0			0
$261$	−15.3642	−	17.4931i	−0.951018	−	1.08280i
$262$	19.1125	−	11.0346i	1.18077	−	0.681719i
$263$	22.5375	−	3.97396i	1.38972	−	0.245045i	0.571807	−	0.820388i	$-0.306242\pi$
$263$	22.5375	−	3.97396i	1.38972	−	0.245045i	0.817912	+	0.575343i	$0.195131\pi$
$264$	10.0418	+	6.86386i	0.618033	+	0.422441i
$265$		0			0
$266$	2.37687	−	13.4799i	0.145735	−	0.826507i
$267$	5.39425	−	21.0801i	0.330123	−	1.29008i
$268$	−5.31626	−	6.33567i	−0.324742	−	0.387013i
$269$	−18.4780			−1.12662			−0.563311	−	0.826245i	$-0.690473\pi$
$269$	−18.4780			−1.12662			−0.563311	+	0.826245i	$0.690473\pi$
$270$		0			0
$271$	4.64576			0.282210			0.141105	−	0.989995i	$-0.454935\pi$
$271$	4.64576			0.282210			0.141105	+	0.989995i	$0.454935\pi$
$272$	20.0057	+	23.8419i	1.21302	+	1.44563i
$273$	−5.49560	+	1.53920i	−0.332609	+	0.0931563i
$274$	−3.90571	+	22.1504i	−0.235953	+	1.33815i
$275$		0			0
$276$	2.62901	−	1.26223i	0.158248	−	0.0759772i
$277$	−25.4825	+	4.49325i	−1.53109	+	0.269973i	−0.874782	−	0.484517i	$-0.838995\pi$
$277$	−25.4825	+	4.49325i	−1.53109	+	0.269973i	−0.656311	+	0.754490i	$0.727884\pi$
$278$	24.9645	−	14.4133i	1.49727	−	0.864450i
$279$	−11.7358	−	1.79735i	−0.702605	−	0.107604i
$280$		0			0
$281$	10.1177	+	3.68254i	0.603572	+	0.219682i	0.625688	−	0.780073i	$-0.284818\pi$
$281$	10.1177	+	3.68254i	0.603572	+	0.219682i	−0.0221165	+	0.999755i	$0.507040\pi$
$282$	1.96493	+	19.8742i	0.117010	+	1.18349i
$283$	10.1924	−	12.1469i	0.605877	−	0.722056i	−0.372697	−	0.927953i	$-0.621567\pi$
$283$	10.1924	−	12.1469i	0.605877	−	0.722056i	0.978574	+	0.205897i	$0.0660113\pi$
$284$	3.77680	+	3.16911i	0.224112	+	0.188052i
$285$		0			0
$286$	8.96393	+	3.26260i	0.530048	+	0.192922i
$287$	−11.4168	−	6.59148i	−0.673911	−	0.389083i
$288$	9.28935	−	3.62042i	0.547380	−	0.213335i
$289$	12.1307	+	21.0110i	0.713569	+	1.23594i
$290$		0			0
$291$	24.6181	−	11.8195i	1.44314	−	0.692873i
$292$	2.04476	+	5.61793i	0.119661	+	0.328765i
$293$	−3.27620	−	0.577683i	−0.191398	−	0.0337486i	0.0771274	−	0.997021i	$-0.475425\pi$
$293$	−3.27620	−	0.577683i	−0.191398	−	0.0337486i	−0.268525	+	0.963273i	$0.586536\pi$
$294$	−2.99369	−	10.6888i	−0.174595	−	0.623382i
$295$		0			0
$296$	−1.82907			−0.106313
$297$	14.4605	−	7.34864i	0.839081	−	0.426411i
$298$		−	28.9998i		−	1.67991i
$299$	−4.02459	+	3.37703i	−0.232748	+	0.195299i
$300$		0			0
$301$	−0.797010	+	4.52007i	−0.0459389	+	0.260532i
$302$	−10.7935	−	29.6548i	−0.621093	−	1.70644i
$303$	6.26632	−	9.16764i	0.359990	−	0.526667i
$304$	−4.09753	−	23.2382i	−0.235009	−	1.33280i
$305$		0			0
$306$	30.5098	−	6.09245i	1.74413	−	0.348282i
$307$	−3.80928	−	2.19929i	−0.217407	−	0.125520i	0.387342	−	0.921936i	$-0.373393\pi$
$307$	−3.80928	−	2.19929i	−0.217407	−	0.125520i	−0.604749	+	0.796416i	$0.706727\pi$
$308$	1.12745	−	3.09763i	0.0642422	−	0.176504i
$309$	5.16759	−	11.4164i	0.293974	−	0.649459i
$310$		0			0
$311$	−11.8600	−	9.95173i	−0.672519	−	0.564311i	0.241290	−	0.970453i	$-0.422429\pi$
$311$	−11.8600	−	9.95173i	−0.672519	−	0.564311i	−0.913810	+	0.406142i	$0.866874\pi$
$312$	−5.99320	+	4.29805i	−0.339298	+	0.243329i
$313$	−3.70561	+	10.1811i	−0.209454	+	0.575469i	−0.999283	−	0.0378572i	$-0.987947\pi$
$313$	−3.70561	+	10.1811i	−0.209454	+	0.575469i	0.789829	+	0.613327i	$0.210169\pi$
$314$	6.49430	−	11.2485i	0.366495	−	0.634787i
$315$		0			0
$316$	4.51232	+	7.81556i	0.253838	+	0.439660i
$317$	−10.4118	+	1.83589i	−0.584787	+	0.103114i	−0.458212	−	0.888843i	$-0.651510\pi$
$317$	−10.4118	+	1.83589i	−0.584787	+	0.103114i	−0.126576	+	0.991957i	$0.540399\pi$
$318$	5.20895	+	0.396565i	0.292104	+	0.0222383i
$319$	−22.7654	+	8.28593i	−1.27462	+	0.463923i
$320$		0			0
$321$	5.49369	−	5.61906i	0.306628	−	0.313626i
$322$	5.01466	+	5.97624i	0.279456	+	0.333043i
$323$		−	31.2831i		−	1.74064i
$324$	0.704506	−	5.41370i	0.0391392	−	0.300761i
$325$		0			0
$326$	6.52405	−	5.47433i	0.361334	−	0.303195i
$327$	−9.47346	−	9.26209i	−0.523884	−	0.512195i
$328$	−16.7771	−	2.95826i	−0.926361	−	0.163342i
$329$	−11.6829	+	4.25225i	−0.644102	+	0.234434i
$330$		0			0
$331$	−1.83100	−	10.3841i	−0.100641	−	0.570762i	−0.992872	−	0.119184i	$-0.961972\pi$
$331$	−1.83100	−	10.3841i	−0.100641	−	0.570762i	0.892231	−	0.451578i	$-0.149139\pi$
$332$	−4.84583	+	2.79774i	−0.265950	+	0.153546i
$333$	−1.17160	+	2.13934i	−0.0642035	+	0.117235i
$334$	−13.3583	+	23.1372i	−0.730931	+	1.26601i
$335$		0			0
$336$	8.51417	+	11.8721i	0.464486	+	0.647679i
$337$	0.783347	−	0.933557i	0.0426717	−	0.0508541i	−0.744287	−	0.667860i	$-0.767210\pi$
$337$	0.783347	−	0.933557i	0.0426717	−	0.0508541i	0.786958	+	0.617006i	$0.211655\pi$
$338$	9.77330	−	11.6474i	0.531597	−	0.633533i
$339$	2.40408	−	5.31119i	0.130572	−	0.288464i
$340$		0			0
$341$	−6.17705	+	10.6990i	−0.334506	+	0.579381i
$342$	−22.3421	−	7.56551i	−1.20812	−	0.409096i
$343$	16.5378	−	9.54808i	0.892955	−	0.515548i
$344$	1.02995	+	5.84114i	0.0555312	+	0.314933i
$345$		0			0
$346$	29.6775	−	10.8017i	1.59547	−	0.580703i
$347$	1.00408	+	0.177046i	0.0539016	+	0.00950431i	0.200534	−	0.979687i	$-0.435732\pi$
$347$	1.00408	+	0.177046i	0.0539016	+	0.00950431i	−0.146632	+	0.989191i	$0.546843\pi$
$348$	−2.02139	+	7.89934i	−0.108358	+	0.423449i
$349$	19.3802	−	16.2620i	1.03740	−	0.870483i	0.0456879	−	0.998956i	$-0.485452\pi$
$349$	19.3802	−	16.2620i	1.03740	−	0.870483i	0.991713	+	0.128473i	$0.0410076\pi$
$350$		0			0
$351$	1.18821	+	9.76293i	0.0634222	+	0.521107i
$352$		−	10.3742i		−	0.552947i
$353$	9.43633	+	11.2458i	0.502245	+	0.598552i	0.956288	−	0.292428i	$-0.0944631\pi$
$353$	9.43633	+	11.2458i	0.502245	+	0.598552i	−0.454043	+	0.890980i	$0.650019\pi$
$354$	−0.779373	−	2.78270i	−0.0414232	−	0.147899i
$355$		0			0
$356$	−7.16091	+	2.60636i	−0.379527	+	0.138137i
$357$	8.38295	+	17.4603i	0.443673	+	0.924096i
$358$	−1.92113	+	0.338747i	−0.101535	+	0.0179033i
$359$	11.7675	+	20.3820i	0.621067	+	1.07572i	0.989287	+	0.145981i	$0.0466337\pi$
$359$	11.7675	+	20.3820i	0.621067	+	1.07572i	−0.368221	+	0.929738i	$0.620033\pi$
$360$		0			0
$361$	−2.35891	+	4.08575i	−0.124153	+	0.215039i
$362$	−11.3139	+	31.0847i	−0.594646	+	1.63378i
$363$	0.213919	+	2.16368i	0.0112278	+	0.113564i
$364$	1.53111	+	1.28475i	0.0802517	+	0.0673392i
$365$		0			0
$366$	28.6019	−	2.82782i	1.49504	−	0.147812i
$367$	8.52841	−	23.4316i	0.445180	−	1.22312i	−0.490864	−	0.871236i	$-0.663319\pi$
$367$	8.52841	−	23.4316i	0.445180	−	1.22312i	0.936043	−	0.351884i	$-0.114459\pi$
$368$	11.6472	+	6.72451i	0.607152	+	0.350539i
$369$	−14.2066	+	17.7281i	−0.739565	+	0.922890i
$370$		0			0
$371$	0.564729	+	3.20274i	0.0293193	+	0.166278i
$372$	1.79965	+	3.74837i	0.0933076	+	0.194344i
$373$	−4.39750	−	12.0820i	−0.227694	−	0.625584i	0.772259	−	0.635308i	$-0.219127\pi$
$373$	−4.39750	−	12.0820i	−0.227694	−	0.625584i	−0.999953	+	0.00972404i	$0.996905\pi$
$374$	5.62164	−	31.8819i	0.290688	−	1.64857i
$375$		0			0
$376$	−12.3076	+	10.3273i	−0.634716	+	0.532590i
$377$		−	14.6891i		−	0.756529i
$378$	14.4973	−	1.76442i	0.745661	−	0.0907520i
$379$	−3.07162			−0.157779			−0.0788894	−	0.996883i	$-0.525137\pi$
$379$	−3.07162			−0.157779			−0.0788894	+	0.996883i	$0.525137\pi$
$380$		0			0
$381$	−29.9580	−	7.66606i	−1.53480	−	0.392744i
$382$	2.92752	+	0.516201i	0.149785	+	0.0264112i
$383$	−2.47718	−	6.80599i	−0.126578	−	0.347770i	0.860175	−	0.509998i	$-0.170354\pi$
$383$	−2.47718	−	6.80599i	−0.126578	−	0.347770i	−0.986753	+	0.162229i	$0.948132\pi$
$384$	19.4890	+	13.3212i	0.994542	+	0.679795i
$385$		0			0
$386$	−10.6889	−	18.5138i	−0.544053	−	0.942327i
$387$	7.49171	+	2.53686i	0.380825	+	0.128956i
$388$	−8.28258	−	4.78195i	−0.420484	−	0.242767i
$389$	6.63847	+	2.41621i	0.336584	+	0.122507i	0.504782	−	0.863247i	$-0.331573\pi$
$389$	6.63847	+	2.41621i	0.336584	+	0.122507i	−0.168198	+	0.985753i	$0.553795\pi$
$390$		0			0
$391$	13.6585	+	11.4608i	0.690738	+	0.579598i
$392$	5.73999	−	6.84065i	0.289913	−	0.345505i
$393$	19.2399	−	13.7980i	0.970524	−	0.696016i
$394$	−28.4131	−	10.3415i	−1.43143	−	0.520998i
$395$		0			0
$396$	−4.98248	−	2.72865i	−0.250379	−	0.137120i
$397$	−22.4696	+	12.9728i	−1.12772	+	0.651088i	−0.943360	−	0.331771i	$-0.892354\pi$
$397$	−22.4696	+	12.9728i	−1.12772	+	0.651088i	−0.184358	+	0.982859i	$0.559021\pi$
$398$	−10.1933	+	1.79736i	−0.510946	+	0.0900936i
$399$	1.11473	−	14.6421i	0.0558062	−	0.733024i
$400$		0			0
$401$	2.29238	−	13.0007i	0.114476	−	0.649226i	−0.872532	−	0.488557i	$-0.837524\pi$
$401$	2.29238	−	13.0007i	0.114476	−	0.649226i	0.987008	−	0.160670i	$-0.0513654\pi$
$402$	−27.2626	−	26.6543i	−1.35974	−	1.32940i
$403$	−4.81488	−	5.73815i	−0.239846	−	0.285838i
$404$	−3.88903			−0.193486
$405$		0			0
$406$	−21.8124			−1.08253
$407$	1.63143	+	1.94426i	0.0808669	+	0.0963734i
$408$	17.8968	+	17.4975i	0.886026	+	0.866256i
$409$	2.60351	−	14.7653i	0.128735	−	0.730095i	−0.850283	−	0.526325i	$-0.823570\pi$
$409$	2.60351	−	14.7653i	0.128735	−	0.730095i	0.979019	−	0.203770i	$-0.0653194\pi$
$410$		0			0
$411$	−1.83174	+	24.0602i	−0.0903529	+	1.18680i
$412$	−4.32208	+	0.762100i	−0.212934	+	0.0375460i
$413$	1.55797	−	0.899496i	0.0766628	−	0.0442613i
$414$	11.4884	−	6.98305i	0.564623	−	0.343198i
$415$		0			0
$416$	5.91082	+	2.15136i	0.289802	+	0.105479i
$417$	25.1309	−	18.0228i	1.23067	−	0.882579i
$418$	−15.7771	+	18.8024i	−0.771681	+	0.919654i
$419$	−21.5326	−	18.0680i	−1.05194	−	0.882681i	−0.0586424	−	0.998279i	$-0.518677\pi$
$419$	−21.5326	−	18.0680i	−1.05194	−	0.882681i	−0.993296	+	0.115598i	$0.963122\pi$
$420$		0			0
$421$	26.6729	+	9.70814i	1.29996	+	0.473146i	0.896983	−	0.442066i	$-0.145754\pi$
$421$	26.6729	+	9.70814i	1.29996	+	0.473146i	0.402974	+	0.915211i	$0.367976\pi$
$422$	22.7829	+	13.1537i	1.10906	+	0.640313i
$423$	4.19555	+	21.0105i	0.203995	+	1.02156i
$424$	2.10132	+	3.63959i	0.102049	+	0.176754i
$425$		0			0
$426$	18.7639	+	12.8256i	0.909114	+	0.621403i
$427$	6.11960	+	16.8135i	0.296148	+	0.813660i
$428$	−2.71034	−	0.477906i	−0.131009	−	0.0231004i
$429$	9.91433	+	2.53701i	0.478668	+	0.122488i
$430$		0			0
$431$	8.66843			0.417543			0.208772	−	0.977964i	$-0.433053\pi$
$431$	8.66843			0.417543			0.208772	+	0.977964i	$0.433053\pi$
$432$	22.4446	−	11.4061i	1.07987	−	0.548776i
$433$		−	8.61185i		−	0.413859i	−0.978356	−	0.206929i	$-0.933653\pi$
$433$		−	8.61185i		−	0.413859i	0.978356	−	0.206929i	$-0.0663471\pi$
$434$	−8.52077	+	7.14978i	−0.409010	+	0.343200i
$435$		0			0
$436$	−0.805725	+	4.56949i	−0.0385872	+	0.218839i
$437$	−4.62344	−	12.7028i	−0.221169	−	0.607657i
$438$	11.9287	+	24.8455i	0.569975	+	1.18716i
$439$	2.79044	+	15.8254i	0.133181	+	0.755305i	0.976109	+	0.217280i	$0.0697183\pi$
$439$	2.79044	+	15.8254i	0.133181	+	0.755305i	−0.842929	+	0.538025i	$0.819171\pi$
$440$		0			0
$441$	−4.32431	−	11.0954i	−0.205919	−	0.528353i
$442$	16.9993	+	9.81454i	0.808573	+	0.466830i
$443$	3.16082	−	8.68429i	0.150175	−	0.412603i	−0.841679	−	0.539977i	$-0.818433\pi$
$443$	3.16082	−	8.68429i	0.150175	−	0.412603i	0.991855	+	0.127374i	$0.0406550\pi$
$444$	0.850086	−	0.0840465i	0.0403433	−	0.00398867i
$445$		0			0
$446$	23.1494	+	19.4246i	1.09615	+	0.919782i
$447$	−3.06100	−	30.9604i	−0.144780	−	1.46438i
$448$	−2.57513	+	7.07511i	−0.121663	+	0.334268i
$449$	−18.5220	+	32.0810i	−0.874106	+	1.51400i	−0.0163930	+	0.999866i	$0.505218\pi$
$449$	−18.5220	+	32.0810i	−0.874106	+	1.51400i	−0.857713	+	0.514130i	$0.828115\pi$
$450$		0			0
$451$	11.8197	+	20.4723i	0.556567	+	0.964002i
$452$	−2.01073	+	0.354546i	−0.0945768	+	0.0166764i
$453$	−14.6533	−	30.5204i	−0.688472	−	1.43397i
$454$	−26.6456	+	9.69821i	−1.25054	+	0.455160i
$455$		0			0
$456$	−5.11791	−	18.2732i	−0.239668	−	0.855719i
$457$	−0.875976	−	1.04395i	−0.0409764	−	0.0488338i	0.745167	−	0.666878i	$-0.232370\pi$
$457$	−0.875976	−	1.04395i	−0.0409764	−	0.0488338i	−0.786143	+	0.618044i	$0.787925\pi$
$458$		−	12.2133i		−	0.570688i
$459$	31.9294	−	9.72473i	1.49034	−	0.453912i
$460$		0			0
$461$	−6.41944	+	5.38655i	−0.298983	+	0.250876i	−0.779921	−	0.625878i	$-0.784741\pi$
$461$	−6.41944	+	5.38655i	−0.298983	+	0.250876i	0.480938	+	0.876755i	$0.340296\pi$
$462$	3.76730	−	14.7221i	0.175271	−	0.684935i
$463$	−28.1832	−	4.96946i	−1.30978	−	0.230950i	−0.525203	−	0.850977i	$-0.676011\pi$
$463$	−28.1832	−	4.96946i	−1.30978	−	0.230950i	−0.784581	+	0.620027i	$0.787122\pi$
$464$	−35.3350	+	12.8609i	−1.64039	+	0.597052i
$465$		0			0
$466$	1.94751	+	11.0449i	0.0902168	+	0.511645i
$467$	1.99894	−	1.15409i	0.0925000	−	0.0534049i	−0.453036	−	0.891492i	$-0.649659\pi$
$467$	1.99894	−	1.15409i	0.0925000	−	0.0534049i	0.545536	+	0.838087i	$0.316326\pi$
$468$	2.58792	−	2.27297i	0.119627	−	0.105068i
$469$	11.8679	−	20.5557i	0.548006	−	0.949175i
$470$		0			0
$471$	5.74606	−	12.6944i	0.264765	−	0.584928i
$472$	1.49434	−	1.78089i	0.0687826	−	0.0819719i
$473$	5.29034	−	6.30479i	0.243250	−	0.289894i
$474$	24.2457	+	33.8081i	1.11364	+	1.55286i
$475$		0			0
$476$	3.39158	−	5.87438i	0.155453	−	0.269252i
$477$	5.60298	−	0.126442i	0.256543	−	0.00578938i
$478$	−28.6652	+	16.5498i	−1.31111	+	0.756972i
$479$	0.150408	+	0.853009i	0.00687234	+	0.0389750i	0.988051	−	0.154127i	$-0.0492564\pi$
$479$	0.150408	+	0.853009i	0.00687234	+	0.0389750i	−0.981179	+	0.193102i	$0.938145\pi$
$480$		0			0
$481$	−1.44608	+	0.526331i	−0.0659357	+	0.0239986i
$482$	37.1468	+	6.54999i	1.69199	+	0.298344i
$483$	5.98450	+	5.85097i	0.272304	+	0.266228i
$484$	0.583306	−	0.489452i	0.0265139	−	0.0222478i
$485$		0			0
$486$	0.776512	−	25.1555i	0.0352233	−	1.14108i
$487$			20.4700i			0.927584i	0.885944	+	0.463792i	$0.153512\pi$
$487$			20.4700i			0.927584i	−0.885944	+	0.463792i	$0.846488\pi$
$488$	14.8625	+	17.7124i	0.672793	+	0.801803i
$489$	6.38730	−	6.53307i	0.288844	−	0.295435i
$490$		0			0
$491$	−40.3022	+	14.6688i	−1.81881	+	0.661993i	−0.823272	+	0.567647i	$0.807854\pi$
$491$	−40.3022	+	14.6688i	−1.81881	+	0.661993i	−0.995539	+	0.0943459i	$0.969924\pi$
$492$	7.93333	+	0.603976i	0.357662	+	0.0272293i
$493$	−49.0940	+	8.65659i	−2.21108	+	0.389873i
$494$	−7.44107	−	12.8883i	−0.334790	−	0.579872i
$495$		0			0
$496$	−9.58763	+	16.6063i	−0.430497	+	0.745643i
$497$	−4.83932	+	13.2959i	−0.217073	+	0.596404i
$498$	−20.9618	+	15.0329i	−0.939322	+	0.673639i
$499$	−4.70186	−	3.94533i	−0.210484	−	0.176617i	0.531451	−	0.847089i	$-0.321647\pi$
$499$	−4.70186	−	3.94533i	−0.210484	−	0.176617i	−0.741935	+	0.670472i	$0.766092\pi$
$500$		0			0
$501$	−11.8192	+	26.1114i	−0.528042	+	1.16657i
$502$	5.08754	−	13.9779i	0.227068	−	0.623864i
$503$	5.95329	+	3.43713i	0.265444	+	0.153254i	0.626815	−	0.779168i	$-0.284358\pi$
$503$	5.95329	+	3.43713i	0.265444	+	0.153254i	−0.361371	+	0.932422i	$0.617691\pi$
$504$	7.75318	+	8.82751i	0.345354	+	0.393208i
$505$		0			0
$506$	−2.42922	−	13.7768i	−0.107992	−	0.612454i
$507$	9.20464	−	13.4664i	0.408792	−	0.598064i
$508$	3.70404	+	10.1768i	0.164340	+	0.451521i
$509$	2.31722	−	13.1416i	0.102709	−	0.582493i	−0.889401	−	0.457127i	$-0.848878\pi$
$509$	2.31722	−	13.1416i	0.102709	−	0.582493i	0.992111	−	0.125366i	$-0.0400104\pi$
$510$		0			0
$511$	−13.1434	+	11.0286i	−0.581430	+	0.487878i
$512$			5.69791i			0.251815i
$513$	−24.6511	−	5.71874i	−1.08837	−	0.252488i
$514$	41.6373			1.83654
$515$		0			0
$516$	−0.747087	−	2.66743i	−0.0328887	−	0.117427i
$517$	21.9554	+	3.87133i	0.965596	+	0.170261i
$518$	0.781567	+	2.14734i	0.0343401	+	0.0943486i
$519$	30.5437	−	14.6645i	1.34072	−	0.643701i
$520$		0			0
$521$	−12.2664	−	21.2461i	−0.537401	−	0.930807i	−0.999043	−	0.0437400i	$-0.986073\pi$
$521$	−12.2664	−	21.2461i	−0.537401	−	0.930807i	0.461642	−	0.887067i	$-0.347261\pi$
$522$	−5.69046	+	37.1560i	−0.249065	+	1.62627i
$523$	−34.2687	−	19.7850i	−1.49847	−	0.865140i	−0.498468	−	0.866908i	$-0.666104\pi$
$523$	−34.2687	−	19.7850i	−1.49847	−	0.865140i	−0.999998	+	0.00176851i	$0.999437\pi$
$524$	−7.79172	−	2.83595i	−0.340383	−	0.123889i
$525$		0			0
$526$	−28.3038	−	23.7497i	−1.23410	−	1.03554i
$527$	−16.3405	+	19.4739i	−0.711804	+	0.848295i
$528$	−2.57753	−	26.0704i	−0.112173	−	1.13457i
$529$	−14.3729	−	5.23132i	−0.624911	−	0.227449i
$530$		0			0
$531$	−1.12578	−	2.88857i	−0.0488549	−	0.125353i
$532$	−4.45377	+	2.57139i	−0.193095	+	0.111484i
$533$	−14.1154	+	2.48893i	−0.611407	+	0.107808i
$534$	−31.6693	+	15.2049i	−1.37047	+	0.657982i
$535$		0			0
$536$	5.32629	−	30.2069i	0.230061	−	1.30474i
$537$	−2.01526	+	0.564429i	−0.0869648	+	0.0243569i
$538$	19.1760	+	22.8531i	0.826737	+	0.985267i
$539$	−12.3912			−0.533727
$540$		0			0
$541$	32.1065			1.38036			0.690182	−	0.723635i	$-0.257530\pi$
$541$	32.1065			1.38036			0.690182	+	0.723635i	$0.257530\pi$
$542$	−4.82126	−	5.74576i	−0.207091	−	0.246801i
$543$	−8.79775	+	34.3805i	−0.377548	+	1.47541i
$544$	3.70692	−	21.0230i	0.158933	−	0.901352i
$545$		0			0
$546$	7.60684	+	5.19947i	0.325543	+	0.222517i
$547$	−21.6885	+	3.82427i	−0.927333	+	0.163514i	−0.616864	−	0.787070i	$-0.711597\pi$
$547$	−21.6885	+	3.82427i	−0.927333	+	0.163514i	−0.310469	+	0.950583i	$0.600486\pi$
$548$	7.31850	−	4.22534i	0.312631	−	0.180497i
$549$	30.2371	−	6.03800i	1.29049	−	0.257696i
$550$		0			0
$551$	35.5163	+	12.9269i	1.51305	+	0.550704i
$552$	9.85321	+	4.46000i	0.419380	+	0.189830i
$553$	−16.6479	+	19.8402i	−0.707942	+	0.843693i
$554$	32.0023	+	26.8531i	1.35965	+	1.14088i
$555$		0			0
$556$	−10.1775	−	3.70429i	−0.431621	−	0.157097i
$557$	−19.2621	−	11.1210i	−0.816163	−	0.471212i	0.0329284	−	0.999458i	$-0.489517\pi$
$557$	−19.2621	−	11.1210i	−0.816163	−	0.471212i	−0.849092	+	0.528246i	$0.822850\pi$
$558$	9.95625	+	16.3798i	0.421482	+	0.693413i
$559$	2.49513	+	4.32169i	0.105533	+	0.182788i
$560$		0			0
$561$	2.63649	−	34.6307i	0.111313	−	1.46211i
$562$	−5.94545	−	16.3350i	−0.250794	−	0.689050i
$563$	13.9452	+	2.45892i	0.587721	+	0.103631i	0.459598	−	0.888127i	$-0.347994\pi$
$563$	13.9452	+	2.45892i	0.587721	+	0.103631i	0.128123	+	0.991758i	$0.459105\pi$
$564$	5.24558	−	5.36529i	0.220879	−	0.225920i
$565$		0			0
$566$	−25.6004			−1.07607
$567$	15.2912	−	3.41394i	0.642170	−	0.143372i
$568$			18.2846i			0.767205i
$569$	4.81198	−	4.03773i	0.201729	−	0.169270i	−0.536327	−	0.844010i	$-0.680189\pi$
$569$	4.81198	−	4.03773i	0.201729	−	0.169270i	0.738056	+	0.674740i	$0.235744\pi$
$570$		0			0
$571$	−5.42129	+	30.7457i	−0.226874	+	1.28667i	0.632196	+	0.774809i	$0.282154\pi$
$571$	−5.42129	+	30.7457i	−0.226874	+	1.28667i	−0.859070	+	0.511858i	$0.828957\pi$
$572$	−1.22582	−	3.36790i	−0.0512540	−	0.140819i
$573$	3.17993	+	0.242093i	0.132844	+	0.0101136i
$574$	3.69590	+	20.9605i	0.154264	+	0.874873i
$575$		0			0
$576$	11.3802	+	6.23233i	0.474174	+	0.259680i
$577$	−15.8293	−	9.13906i	−0.658983	−	0.380464i	0.132906	−	0.991129i	$-0.457569\pi$
$577$	−15.8293	−	9.13906i	−0.658983	−	0.380464i	−0.791889	+	0.610664i	$0.790902\pi$
$578$	13.3969	−	36.8076i	0.557237	−	1.53100i
$579$	−13.3658	−	18.6372i	−0.555462	−	0.774536i
$580$		0			0
$581$	−12.3014	−	10.3221i	−0.510349	−	0.428233i
$582$	−40.1662	−	18.1810i	−1.66494	−	0.753627i
$583$	1.99455	−	5.47997i	0.0826057	−	0.226957i
$584$	−11.0860	+	19.2016i	−0.458744	+	0.794568i
$585$		0			0
$586$	2.68551	+	4.65143i	0.110937	+	0.192149i
$587$	−8.10900	+	1.42984i	−0.334694	+	0.0590156i	−0.338470	−	0.940977i	$-0.609909\pi$
$587$	−8.10900	+	1.42984i	−0.334694	+	0.0590156i	0.00377558	+	0.999993i	$0.498798\pi$
$588$	−2.35341	+	3.44304i	−0.0970529	+	0.141989i
$589$	18.1113	−	6.59198i	0.746263	−	0.271618i
$590$		0			0
$591$	−31.4256	−	8.04160i	−1.29268	−	0.330787i
$592$	2.53220	+	3.01776i	0.104073	+	0.124029i
$593$			38.8812i			1.59666i	0.602222	+	0.798329i	$0.294282\pi$
$593$			38.8812i			1.59666i	−0.602222	+	0.798329i	$0.705718\pi$
$594$	−24.0953	−	10.2581i	−0.988644	−	0.420894i
$595$		0			0
$596$	−8.34661	+	7.00364i	−0.341890	+	0.286880i
$597$	−10.6928	+	2.99481i	−0.437626	+	0.122569i
$598$	8.35325	+	1.47290i	0.341590	+	0.0602315i
$599$	−0.729650	+	0.265571i	−0.0298127	+	0.0108509i	−0.356883	−	0.934149i	$-0.616161\pi$
$599$	−0.729650	+	0.265571i	−0.0298127	+	0.0108509i	0.327071	+	0.945000i	$0.393938\pi$
$600$		0			0
$601$	−4.46708	−	25.3341i	−0.182216	−	1.03340i	−0.929481	−	0.368871i	$-0.879744\pi$
$601$	−4.46708	−	25.3341i	−0.182216	−	1.03340i	0.747265	−	0.664527i	$-0.231367\pi$
$602$	6.41743	−	3.70510i	0.261555	−	0.151009i
$603$	−31.9192	−	25.5787i	−1.29985	−	1.04165i
$604$	−5.92844	+	10.2684i	−0.241225	+	0.417813i
$605$		0			0
$606$	−17.8413	+	1.76394i	−0.724755	+	0.0716553i
$607$	−4.27987	+	5.10054i	−0.173714	+	0.207025i	−0.845876	−	0.533380i	$-0.820922\pi$
$607$	−4.27987	+	5.10054i	−0.173714	+	0.207025i	0.672161	+	0.740405i	$0.265366\pi$
$608$	−10.4034	+	12.3983i	−0.421914	+	0.502817i
$609$	−23.2871	+	2.30235i	−0.943640	+	0.0932961i
$610$		0			0
$611$	−6.75875	+	11.7065i	−0.273430	+	0.473594i
$612$	−9.12182	−	7.30985i	−0.368728	−	0.295483i
$613$	28.5617	−	16.4901i	1.15360	−	0.666030i	0.203837	−	0.979005i	$-0.434659\pi$
$613$	28.5617	−	16.4901i	1.15360	−	0.666030i	0.949761	+	0.312975i	$0.101326\pi$
$614$	1.23316	+	6.99359i	0.0497662	+	0.282238i
$615$		0			0
$616$	11.4880	−	4.18131i	0.462867	−	0.168470i
$617$	36.0737	+	6.36077i	1.45227	+	0.256075i	0.843440	−	0.537223i	$-0.180527\pi$
$617$	36.0737	+	6.36077i	1.45227	+	0.256075i	0.608834	+	0.793298i	$0.291638\pi$
$618$	−19.4824	+	5.45658i	−0.783696	+	0.219496i
$619$	−10.7534	+	9.02320i	−0.432217	+	0.362673i	−0.832787	−	0.553593i	$-0.813256\pi$
$619$	−10.7534	+	9.02320i	−0.432217	+	0.362673i	0.400571	+	0.916266i	$0.368812\pi$
$620$		0			0
$621$	11.5280	−	8.66779i	0.462602	−	0.347826i
$622$			24.9958i			1.00224i
$623$	−14.0577	−	16.7533i	−0.563208	−	0.671206i
$624$	15.3884	+	3.93779i	0.616029	+	0.157638i
$625$		0			0
$626$	16.4373	−	5.98270i	0.656967	−	0.239117i
$627$	−14.8591	+	21.7389i	−0.593414	+	0.868166i
$628$	−4.80591	+	0.847411i	−0.191777	+	0.0338154i
$629$	2.61131	+	4.52292i	0.104120	+	0.180340i
$630$		0			0
$631$	1.61405	−	2.79562i	0.0642543	−	0.111292i	−0.832109	−	0.554613i	$-0.812866\pi$
$631$	1.61405	−	2.79562i	0.0642543	−	0.111292i	0.896363	+	0.443321i	$0.146200\pi$
$632$	−11.4471	+	31.4508i	−0.455343	+	1.25104i
$633$	25.7116	+	11.6382i	1.02195	+	0.462578i
$634$	13.0758	+	10.9719i	0.519305	+	0.435748i
$635$		0			0
$636$	−1.14386	−	1.59500i	−0.0453569	−	0.0632457i
$637$	2.56964	−	7.06002i	0.101813	−	0.279728i
$638$	33.8732	+	19.5567i	1.34105	+	0.774258i
$639$	21.3863	+	11.7121i	0.846027	+	0.463325i
$640$		0			0
$641$	−1.01704	−	5.76795i	−0.0401709	−	0.227820i	0.958112	−	0.286393i	$-0.0924562\pi$
$641$	−1.01704	−	5.76795i	−0.0401709	−	0.227820i	−0.998283	+	0.0585725i	$0.981345\pi$
$642$	−12.6507	−	0.963120i	−0.499285	−	0.0380113i
$643$	−5.68345	−	15.6152i	−0.224134	−	0.615802i	0.775750	−	0.631040i	$-0.217372\pi$
$643$	−5.68345	−	15.6152i	−0.224134	−	0.615802i	−0.999884	+	0.0152381i	$0.995149\pi$
$644$	0.508986	−	2.88660i	0.0200569	−	0.113748i
$645$		0			0
$646$	−38.6901	+	32.4648i	−1.52224	+	1.27731i
$647$			5.31018i			0.208765i	0.994537	+	0.104382i	$0.0332865\pi$
$647$			5.31018i			0.208765i	−0.994537	+	0.104382i	$0.966713\pi$
$648$	17.0597	−	10.9041i	0.670170	−	0.428353i
$649$	−3.22591			−0.126628
$650$		0			0
$651$	−8.34216	+	8.53254i	−0.326955	+	0.334417i
$652$	−3.15120	−	0.555642i	−0.123411	−	0.0217606i
$653$	8.60359	+	23.6382i	0.336685	+	0.925034i	0.986328	+	0.164794i	$0.0526960\pi$
$653$	8.60359	+	23.6382i	0.336685	+	0.925034i	−0.649643	+	0.760239i	$0.725082\pi$
$654$	−1.62377	+	21.3285i	−0.0634945	+	0.834011i
$655$		0			0
$656$	18.3458	+	31.7758i	0.716282	+	1.24064i
$657$	15.3577	+	25.2661i	0.599159	+	0.985724i
$658$	17.3834	+	10.0363i	0.677674	+	0.391255i
$659$	−0.253053	−	0.0921038i	−0.00985755	−	0.00358786i	0.337087	−	0.941474i	$-0.390558\pi$
$659$	−0.253053	−	0.0921038i	−0.00985755	−	0.00358786i	−0.346944	+	0.937886i	$0.612781\pi$
$660$		0			0
$661$	−17.1827	−	14.4180i	−0.668329	−	0.560795i	0.244241	−	0.969714i	$-0.421461\pi$
$661$	−17.1827	−	14.4180i	−0.668329	−	0.560795i	−0.912570	+	0.408920i	$0.865906\pi$
$662$	−10.9426	+	13.0409i	−0.425298	+	0.506850i
$663$	19.1845	+	8.68376i	0.745064	+	0.337249i
$664$	−19.5002	−	7.09750i	−0.756755	−	0.275436i
$665$		0			0
$666$	3.86174	−	0.771146i	0.149640	−	0.0298813i
$667$	−18.6557	+	10.7709i	−0.722352	+	0.417050i
$668$	9.88537	−	1.74306i	0.382476	−	0.0674409i
$669$	26.7647	+	18.2944i	1.03478	+	0.707302i
$670$		0			0
$671$	5.57140	−	31.5970i	0.215081	−	1.21979i
$672$	2.48416	−	9.70778i	0.0958285	−	0.374486i
$673$	10.7270	+	12.7839i	0.413494	+	0.492784i	0.932085	−	0.362239i	$-0.117988\pi$
$673$	10.7270	+	12.7839i	0.413494	+	0.492784i	−0.518591	+	0.855023i	$0.673543\pi$
$674$	−1.96754			−0.0757868
$675$		0			0
$676$	−5.71262			−0.219716
$677$	19.0984	+	22.7606i	0.734012	+	0.874762i	0.995912	−	0.0903336i	$-0.0287933\pi$
$677$	19.0984	+	22.7606i	0.734012	+	0.874762i	−0.261899	+	0.965095i	$0.584349\pi$
$678$	−9.06364	+	2.53853i	−0.348087	+	0.0974915i
$679$	4.76616	−	27.0302i	0.182908	−	1.03733i
$680$		0			0
$681$	−27.4234	+	13.1664i	−1.05087	+	0.504537i
$682$	19.6426	−	3.46352i	0.752154	−	0.132625i
$683$	10.8573	−	6.26849i	0.415445	−	0.239857i	−0.277682	−	0.960673i	$-0.589566\pi$
$683$	10.8573	−	6.26849i	0.415445	−	0.239857i	0.693126	+	0.720816i	$0.256233\pi$
$684$	3.21828	+	8.25753i	0.123054	+	0.315735i
$685$		0			0
$686$	−28.9713	−	10.5447i	−1.10613	−	0.402599i
$687$	−1.28914	−	13.0390i	−0.0491838	−	0.497467i
$688$	8.21134	−	9.78590i	0.313054	−	0.373084i
$689$	2.70865	+	2.27283i	0.103191	+	0.0865879i
$690$		0			0
$691$	−6.85438	−	2.49479i	−0.260753	−	0.0949064i	0.208336	−	0.978057i	$-0.433195\pi$
$691$	−6.85438	−	2.49479i	−0.260753	−	0.0949064i	−0.469089	+	0.883151i	$0.655418\pi$
$692$	−10.2762	−	5.93297i	−0.390643	−	0.225538i
$693$	2.46804	−	16.1151i	0.0937530	−	0.612162i
$694$	−0.823042	−	1.42555i	−0.0312422	−	0.0541131i
$695$		0			0
$696$	−27.2607	+	13.0883i	−1.03331	+	0.496110i
$697$	16.6370	+	45.7098i	0.630171	+	1.73138i
$698$	−40.2248	−	7.09271i	−1.52253	−	0.268463i
$699$	3.24500	+	11.5860i	0.122737	+	0.438225i
$700$		0			0
$701$	−10.1934			−0.384998			−0.192499	−	0.981297i	$-0.561659\pi$
$701$	−10.1934			−0.384998			−0.192499	+	0.981297i	$0.561659\pi$
$702$	10.8414	−	11.6013i	0.409184	−	0.437863i
$703$		−	3.95962i		−	0.149340i
$704$	10.3425	−	8.67836i	0.389796	−	0.327078i
$705$		0			0
$706$	4.11569	−	23.3412i	0.154896	−	0.878459i
$707$	−3.81730	−	10.4879i	−0.143564	−	0.394439i
$708$	−0.612683	+	0.896357i	−0.0230260	+	0.0336871i
$709$	−3.06522	−	17.3837i	−0.115117	−	0.652860i	−0.986692	−	0.162599i	$-0.948012\pi$
$709$	−3.06522	−	17.3837i	−0.115117	−	0.652860i	0.871575	−	0.490261i	$-0.163099\pi$
$710$		0			0
$711$	29.4534	+	33.5346i	1.10459	+	1.25765i
$712$	−24.4754	−	14.1309i	−0.917253	−	0.529576i
$713$	−3.75711	+	10.3226i	−0.140705	+	0.386584i
$714$	12.8948	−	28.4877i	0.482576	−	1.06613i
$715$		0			0
$716$	0.561463	+	0.471123i	0.0209828	+	0.0176067i
$717$	−28.8563	+	20.6944i	−1.07766	+	0.772847i
$718$	12.9958	−	35.7057i	0.485000	−	1.33253i
$719$	−1.57416	+	2.72652i	−0.0587062	+	0.101682i	−0.893885	−	0.448297i	$-0.852031\pi$
$719$	−1.57416	+	2.72652i	−0.0587062	+	0.101682i	0.835179	+	0.549979i	$0.185364\pi$
$720$		0			0
$721$	−6.29760	−	10.9078i	−0.234535	−	0.406226i
$722$	7.50117	−	1.32266i	0.279165	−	0.0492242i
$723$	40.3496	+	3.07187i	1.50062	+	0.114244i
$724$	11.6791	−	4.25084i	0.434050	−	0.157981i
$725$		0			0
$726$	2.45398	−	2.50999i	0.0910759	−	0.0931544i
$727$	−21.1284	−	25.1799i	−0.783609	−	0.933869i	0.215481	−	0.976508i	$-0.430868\pi$
$727$	−21.1284	−	25.1799i	−0.783609	−	0.933869i	−0.999091	+	0.0426388i	$0.986424\pi$
$728$			7.41254i			0.274727i
$729$	−1.82622	−	26.9382i	−0.0676377	−	0.997710i
$730$		0			0
$731$	12.9735	−	10.8861i	0.479843	−	0.402636i
$732$	−7.72143	−	7.54915i	−0.285392	−	0.279025i
$733$	6.85262	+	1.20830i	0.253107	+	0.0446297i	0.298762	−	0.954328i	$-0.403426\pi$
$733$	6.85262	+	1.20830i	0.253107	+	0.0446297i	−0.0456547	+	0.998957i	$0.514537\pi$
$734$	−37.8302	+	13.7691i	−1.39634	+	0.508226i
$735$		0			0
$736$	−1.60183	−	9.08444i	−0.0590443	−	0.334857i
$737$	−36.8600	+	21.2811i	−1.35776	+	0.783901i
$738$	36.6690	−	0.827507i	1.34980	−	0.0304609i
$739$	−3.80631	+	6.59273i	−0.140017	+	0.242517i	−0.927503	−	0.373816i	$-0.878049\pi$
$739$	−3.80631	+	6.59273i	−0.140017	+	0.242517i	0.787485	+	0.616333i	$0.211383\pi$
$740$		0			0
$741$	−9.30453	−	12.9742i	−0.341811	−	0.476620i
$742$	3.37500	−	4.02217i	0.123900	−	0.147658i
$743$	2.02092	−	2.40844i	0.0741404	−	0.0883571i	−0.727699	−	0.685896i	$-0.759410\pi$
$743$	2.02092	−	2.40844i	0.0741404	−	0.0883571i	0.801840	+	0.597539i	$0.203855\pi$
$744$	−6.35895	+	14.0485i	−0.233130	+	0.515041i
$745$		0			0
$746$	−10.3791	+	17.9772i	−0.380007	+	0.658191i
$747$	−20.7922	+	18.2618i	−0.760749	+	0.668164i
$748$	−10.5338	+	6.08169i	−0.385154	+	0.222369i
$749$	−1.37153	−	7.77834i	−0.0501146	−	0.284214i
$750$		0			0
$751$	4.55689	−	1.65857i	0.166283	−	0.0605222i	−0.257537	−	0.966268i	$-0.582911\pi$
$751$	4.55689	−	1.65857i	0.166283	−	0.0605222i	0.423821	+	0.905746i	$0.360689\pi$
$752$	34.0778	+	6.00883i	1.24269	+	0.219119i
$753$	3.95609	−	15.4599i	0.144168	−	0.563390i
$754$	−18.1672	+	15.2441i	−0.661609	+	0.555156i
$755$		0			0
$756$	−4.00902	−	3.74644i	−0.145807	−	0.136257i
$757$		−	16.2063i		−	0.589028i	−0.955647	−	0.294514i	$-0.904842\pi$
$757$		−	16.2063i		−	0.589028i	0.955647	−	0.294514i	$-0.0951578\pi$
$758$	3.18766	+	3.79891i	0.115781	+	0.137983i
$759$	−4.04763	−	14.4518i	−0.146920	−	0.524567i
$760$		0			0
$761$	−37.9046	+	13.7961i	−1.37404	+	0.500110i	−0.920366	−	0.391058i	$-0.872109\pi$
$761$	−37.9046	+	13.7961i	−1.37404	+	0.500110i	−0.453674	+	0.891168i	$0.649887\pi$
$762$	21.6086	+	45.0070i	0.782795	+	1.63043i
$763$	−13.1139	+	2.31233i	−0.474755	+	0.0837121i
$764$	−0.558445	−	0.967255i	−0.0202038	−	0.0349941i
$765$		0			0
$766$	−5.84672	+	10.1268i	−0.211250	+	0.365896i
$767$	0.668976	−	1.83800i	0.0241553	−	0.0663662i
$768$	−2.27579	−	23.0184i	−0.0821204	−	0.830604i
$769$	−8.23144	−	6.90700i	−0.296833	−	0.249073i	0.482191	−	0.876066i	$-0.339841\pi$
$769$	−8.23144	−	6.90700i	−0.296833	−	0.249073i	−0.779025	+	0.626993i	$0.784285\pi$
$770$		0			0
$771$	44.4523	−	4.39493i	1.60091	−	0.158279i
$772$	−2.74712	+	7.54765i	−0.0988711	+	0.271646i
$773$	−47.2189	−	27.2618i	−1.69835	−	0.980540i	−0.947332	−	0.320254i	$-0.896232\pi$
$773$	−47.2189	−	27.2618i	−1.69835	−	0.980540i	−0.751014	−	0.660286i	$-0.770435\pi$
$774$	−4.63721	−	11.8983i	−0.166681	−	0.427674i
$775$		0			0
$776$	−6.15916	−	34.9303i	−0.221101	−	1.25393i
$777$	1.06106	+	2.21002i	0.0380654	+	0.0792839i
$778$	−3.90095	−	10.7178i	−0.139856	−	0.384251i
$779$	6.40411	−	36.3195i	0.229451	−	1.30128i
$780$		0			0
$781$	19.4361	−	16.3089i	0.695479	−	0.583577i
$782$		−	28.7862i		−	1.02939i
$783$	−2.15327	+	40.2686i	−0.0769516	+	1.43908i
$784$	−19.2328			−0.686887
$785$		0			0
$786$	−37.0317	−	9.47617i	−1.32088	−	0.338004i
$787$	19.5354	+	3.44462i	0.696363	+	0.122788i	0.510614	−	0.859810i	$-0.329418\pi$
$787$	19.5354	+	3.44462i	0.696363	+	0.122788i	0.185748	+	0.982597i	$0.440529\pi$
$788$	3.88549	+	10.6753i	0.138415	+	0.380291i
$789$	−32.7242	−	22.3678i	−1.16501	−	0.796315i
$790$		0			0
$791$	−2.92979	−	5.07454i	−0.104171	−	0.180430i
$792$	−4.12556	−	20.6600i	−0.146595	−	0.734119i
$793$	16.8473	+	9.72682i	0.598267	+	0.345409i
$794$	39.3630	+	14.3269i	1.39694	+	0.508444i
$795$		0			0
$796$	2.97907	+	2.49974i	0.105590	+	0.0886008i
$797$	7.38501	−	8.80112i	0.261591	−	0.311752i	−0.619223	−	0.785216i	$-0.712552\pi$
$797$	7.38501	−	8.80112i	0.261591	−	0.311752i	0.880813	+	0.473464i	$0.156997\pi$
$798$	−19.2659	+	13.8166i	−0.682005	+	0.489103i
$799$	43.1085	+	15.6902i	1.52507	+	0.555079i
$800$		0			0
$801$	−32.2055	+	19.5757i	−1.13792	+	0.691672i
$802$	−18.4580	+	10.6567i	−0.651774	+	0.376302i
$803$	30.2990	−	5.34253i	1.06923	−	0.188534i
$804$	−1.08745	+	14.2838i	−0.0383513	+	0.503752i
$805$		0			0
$806$	−2.10003	+	11.9098i	−0.0739703	+	0.419506i
$807$	22.8847	+	22.3741i	0.805579	+	0.787604i
$808$	−9.27095	−	11.0487i	−0.326151	−	0.388692i
$809$	37.5291			1.31945			0.659727	−	0.751506i	$-0.270672\pi$
$809$	37.5291			1.31945			0.659727	+	0.751506i	$0.270672\pi$
$810$		0			0
$811$	31.9363			1.12143			0.560717	−	0.828008i	$-0.310526\pi$
$811$	31.9363			1.12143			0.560717	+	0.828008i	$0.310526\pi$
$812$	5.26784	+	6.27796i	0.184865	+	0.220313i
$813$	−5.75369	−	5.62532i	−0.201791	−	0.197288i
$814$	0.711553	−	4.03542i	0.0249399	−	0.141441i
$815$		0			0
$816$	4.09219	−	53.7517i	0.143255	−	1.88169i
$817$	−12.6451	+	2.22966i	−0.442395	+	0.0780061i
$818$	−20.9632	+	12.1031i	−0.732960	+	0.423174i
$819$	8.66994	+	4.74808i	0.302952	+	0.165911i
$820$		0			0
$821$	34.2903	+	12.4806i	1.19674	+	0.435577i	0.862085	−	0.506764i	$-0.169158\pi$
$821$	34.2903	+	12.4806i	1.19674	+	0.435577i	0.334654	+	0.942341i	$0.391381\pi$
$822$	31.6580	−	22.7037i	1.10420	−	0.791881i
$823$	20.8016	−	24.7904i	0.725100	−	0.864140i	−0.270016	−	0.962856i	$-0.587029\pi$
$823$	20.8016	−	24.7904i	0.725100	−	0.864140i	0.995116	+	0.0987156i	$0.0314734\pi$
$824$	−12.4684	−	10.4622i	−0.434358	−	0.364470i
$825$		0			0
$826$	−2.72930	−	0.993385i	−0.0949646	−	0.0345643i
$827$	−44.7028	−	25.8092i	−1.55447	−	0.897473i	−0.997769	−	0.0667595i	$-0.978734\pi$
$827$	−44.7028	−	25.8092i	−1.55447	−	0.897473i	−0.556700	−	0.830714i	$-0.687933\pi$
$828$	−4.78435	−	1.62009i	−0.166268	−	0.0563019i
$829$	0.662012	+	1.14664i	0.0229926	+	0.0398244i	0.877293	−	0.479956i	$-0.159347\pi$
$829$	0.662012	+	1.14664i	0.0229926	+	0.0398244i	−0.854300	+	0.519780i	$0.826014\pi$
$830$		0			0
$831$	37.0003	+	25.2906i	1.28352	+	0.877322i
$832$	2.79981	+	7.69242i	0.0970660	+	0.266687i
$833$	−25.1103	−	4.42763i	−0.870021	−	0.153408i
$834$	−48.3704	−	12.3777i	−1.67493	−	0.428604i
$835$		0			0
$836$	9.22189			0.318946
$837$	12.3583	+	16.4363i	0.427165	+	0.568122i
$838$			45.3816i			1.56768i
$839$	−6.77496	+	5.68487i	−0.233898	+	0.196263i	−0.752202	−	0.658933i	$-0.771008\pi$
$839$	−6.77496	+	5.68487i	−0.233898	+	0.196263i	0.518304	+	0.855196i	$0.326564\pi$
$840$		0			0
$841$	5.42296	−	30.7551i	0.186999	−	1.06052i
$842$	−15.6737	−	43.0632i	−0.540153	−	1.48406i
$843$	−8.07160	−	16.8118i	−0.278001	−	0.579029i
$844$	−1.71637	−	9.73401i	−0.0590799	−	0.335059i
$845$		0			0
$846$	21.6312	−	26.9931i	0.743695	−	0.928043i
$847$	1.89250	+	1.09264i	0.0650272	+	0.0375435i
$848$	3.09581	−	8.50567i	0.106311	−	0.292086i
$849$	−27.3312	+	2.70219i	−0.938004	+	0.0927388i
$850$		0			0
$851$	1.72881	+	1.45064i	0.0592627	+	0.0497273i
$852$	−0.840185	−	8.49803i	−0.0287843	−	0.291138i
$853$	−7.74759	+	21.2863i	−0.265272	+	0.728830i	0.733518	+	0.679670i	$0.237877\pi$
$853$	−7.74759	+	21.2863i	−0.265272	+	0.728830i	−0.998791	+	0.0491605i	$0.984345\pi$
$854$	14.4437	−	25.0172i	0.494252	−	0.856070i
$855$		0			0
$856$	−5.10338	−	8.83931i	−0.174430	−	0.302122i
$857$	−7.37341	+	1.30013i	−0.251871	+	0.0444116i	−0.298158	−	0.954517i	$-0.596372\pi$
$857$	−7.37341	+	1.30013i	−0.251871	+	0.0444116i	0.0462871	+	0.998928i	$0.485261\pi$
$858$	−7.15115	−	14.8947i	−0.244136	−	0.508495i
$859$	38.2228	−	13.9119i	1.30414	−	0.474669i	0.405800	−	0.913962i	$-0.366993\pi$
$859$	38.2228	−	13.9119i	1.30414	−	0.474669i	0.898344	+	0.439293i	$0.144771\pi$
$860$		0			0
$861$	6.15820	+	21.9875i	0.209871	+	0.749330i
$862$	−8.99590	−	10.7209i	−0.306401	−	0.365155i
$863$			8.68298i			0.295572i	0.989019	+	0.147786i	$0.0472147\pi$
$863$			8.68298i			0.295572i	−0.989019	+	0.147786i	$0.952785\pi$
$864$	−15.8885	−	6.76419i	−0.540538	−	0.230122i
$865$		0			0
$866$	−10.6509	+	8.93718i	−0.361933	+	0.303698i
$867$	10.4175	−	40.7102i	0.353796	−	1.38259i
$868$	4.11565	+	0.725699i	0.139694	+	0.0246318i
$869$	43.6417	−	15.8843i	1.48044	−	0.538837i
$870$		0			0
$871$	−4.48128	−	25.4146i	−0.151842	−	0.861141i
$872$	−14.9026	+	8.60405i	−0.504667	+	0.291370i
$873$	−44.8008	−	15.1705i	−1.51628	−	0.513445i
$874$	−10.9124	+	18.9008i	−0.369117	+	0.639330i
$875$		0			0
$876$	4.27007	−	9.43361i	0.144272	−	0.318732i
$877$	18.8985	−	22.5224i	0.638157	−	0.760526i	−0.345920	−	0.938264i	$-0.612433\pi$
$877$	18.8985	−	22.5224i	0.638157	−	0.760526i	0.984078	+	0.177737i	$0.0568778\pi$
$878$	16.6766	−	19.8744i	0.562808	−	0.670728i
$879$	3.35804	+	4.68244i	0.113264	+	0.157935i
$880$		0			0
$881$	12.3020	−	21.3077i	0.414466	−	0.717876i	−0.580906	−	0.813970i	$-0.697302\pi$
$881$	12.3020	−	21.3077i	0.414466	−	0.717876i	0.995372	+	0.0960945i	$0.0306351\pi$
$882$	−9.23486	+	16.8628i	−0.310954	+	0.567799i
$883$	40.6122	−	23.4475i	1.36671	−	0.789070i	0.376203	−	0.926537i	$-0.377230\pi$
$883$	40.6122	−	23.4475i	1.36671	−	0.789070i	0.990506	+	0.137468i	$0.0438963\pi$
$884$	−1.28065	−	7.26295i	−0.0430730	−	0.244279i
$885$		0			0
$886$	−14.0207	+	5.10313i	−0.471036	+	0.171443i
$887$	46.3007	+	8.16406i	1.55462	+	0.274122i	0.883933	−	0.467614i	$-0.154886\pi$
$887$	46.3007	+	8.16406i	1.55462	+	0.274122i	0.670692	+	0.741736i	$0.265997\pi$
$888$	2.26527	+	2.21473i	0.0760176	+	0.0743215i
$889$	−23.8090	+	19.9781i	−0.798528	+	0.670044i
$890$		0			0
$891$	−26.8071	−	8.40827i	−0.898073	−	0.281688i
$892$		−	11.3539i		−	0.380158i
$893$	−22.3568	−	26.6438i	−0.748142	−	0.891601i
$894$	−35.1144	+	35.9157i	−1.17440	+	1.20120i
$895$		0			0
$896$	22.2957	−	8.11497i	0.744847	−	0.271102i
$897$	9.07346	+	0.690776i	0.302954	+	0.0230643i
$898$	58.8986	−	10.3854i	1.96547	−	0.346566i
$899$	−15.3568	−	26.5988i	−0.512179	−	0.887120i
$900$		0			0
$901$	5.99998	−	10.3923i	0.199888	−	0.346217i
$902$	13.0534	−	35.8640i	0.434631	−	1.19414i
$903$	6.46021	−	4.63297i	0.214982	−	0.154176i
$904$	−5.80060	−	4.86728i	−0.192925	−	0.161883i
$905$		0			0
$906$	−22.5400	+	49.7962i	−0.748840	+	1.65437i
$907$	12.9206	−	35.4991i	0.429022	−	1.17873i	−0.517386	−	0.855752i	$-0.673095\pi$
$907$	12.9206	−	35.4991i	0.429022	−	1.17873i	0.946408	−	0.322975i	$-0.104683\pi$
$908$	9.22640	+	5.32686i	0.306189	+	0.176778i
$909$	−18.8614	+	3.76640i	−0.625592	+	0.124924i
$910$		0			0
$911$	3.66733	+	20.7985i	0.121504	+	0.689084i	0.983323	+	0.181868i	$0.0582142\pi$
$911$	3.66733	+	20.7985i	0.121504	+	0.689084i	−0.861819	+	0.507216i	$0.830675\pi$
$912$	−23.0633	+	33.7417i	−0.763703	+	1.11730i
$913$	9.84862	+	27.0589i	0.325942	+	0.895518i
$914$	−0.382060	+	2.16677i	−0.0126374	+	0.0716704i
$915$		0			0
$916$	−3.51517	+	2.94958i	−0.116145	+	0.0974569i
$917$		−	23.7964i		−	0.785826i
$918$	−45.1629	−	29.3974i	−1.49060	−	0.970258i
$919$	−46.4789			−1.53320			−0.766599	−	0.642126i	$-0.778053\pi$
$919$	−46.4789			−1.53320			−0.766599	+	0.642126i	$0.778053\pi$
$920$		0			0
$921$	2.05472	+	7.33624i	0.0677053	+	0.241737i
$922$	13.3239	+	2.34936i	0.438799	+	0.0773721i
$923$	5.26156	+	14.4560i	0.173186	+	0.475825i
$924$	−5.14710	+	2.47120i	−0.169327	+	0.0812965i
$925$		0			0
$926$	23.1018	+	40.0135i	0.759171	+	1.31492i
$927$	−20.2236	+	7.88190i	−0.664229	+	0.258876i
$928$	22.3361	+	12.8957i	0.733217	+	0.423323i
$929$	39.5960	+	14.4118i	1.29910	+	0.472834i	0.896704	−	0.442630i	$-0.145955\pi$
$929$	39.5960	+	14.4118i	1.29910	+	0.472834i	0.402398	+	0.915465i	$0.368177\pi$
$930$		0			0
$931$	14.8088	+	12.4261i	0.485339	+	0.407248i
$932$	2.70856	−	3.22794i	0.0887220	−	0.105735i
$933$	2.63837	+	26.6857i	0.0863765	+	0.873652i
$934$	−3.50181	−	1.27455i	−0.114583	−	0.0417047i
$935$		0			0
$936$	12.6268	+	1.93380i	0.412719	+	0.0632082i
$937$	35.5924	−	20.5493i	1.16275	−	0.671316i	0.210791	−	0.977531i	$-0.432396\pi$
$937$	35.5924	−	20.5493i	1.16275	−	0.671316i	0.951962	+	0.306215i	$0.0990626\pi$
$938$	−37.7390	+	6.65440i	−1.23222	+	0.217274i
$939$	16.9171	−	8.12217i	0.552069	−	0.265057i
$940$		0			0
$941$	−0.695320	+	3.94336i	−0.0226668	+	0.128550i	−0.994041	−	0.109003i	$-0.965234\pi$
$941$	−0.695320	+	3.94336i	−0.0226668	+	0.128550i	0.971375	+	0.237553i	$0.0763453\pi$
$942$	−21.6633	+	6.06741i	−0.705828	+	0.197687i
$943$	13.5112	+	16.1021i	0.439986	+	0.524355i
$944$	−5.00705			−0.162966
$945$		0			0
$946$	−13.2878			−0.432024
$947$	−11.1686	−	13.3102i	−0.362931	−	0.432524i	0.553419	−	0.832903i	$-0.313323\pi$
$947$	−11.1686	−	13.3102i	−0.362931	−	0.432524i	−0.916350	+	0.400379i	$0.868879\pi$
$948$	3.87504	−	15.1432i	0.125856	−	0.491828i
$949$	−3.23932	+	18.3711i	−0.105153	+	0.596351i
$950$		0			0
$951$	15.1179	+	10.3335i	0.490231	+	0.335086i
$952$	24.7742	−	4.36836i	0.802936	−	0.141579i
$953$	−41.4931	+	23.9561i	−1.34409	+	0.776013i	−0.987405	−	0.158211i	$-0.949427\pi$
$953$	−41.4931	+	23.9561i	−1.34409	+	0.776013i	−0.356688	+	0.934223i	$0.616094\pi$
$954$	−5.97102	−	6.79840i	−0.193319	−	0.220106i
$955$		0			0
$956$	11.6861	+	4.25341i	0.377957	+	0.137565i
$957$	38.2276	+	17.3035i	1.23572	+	0.559343i
$958$	0.898889	−	1.07125i	0.0290418	−	0.0346107i
$959$	18.5784	+	15.5891i	0.599928	+	0.503400i
$960$		0			0
$961$	14.4128	+	5.24583i	0.464929	+	0.169220i
$962$	2.15167	+	1.24226i	0.0693725	+	0.0400522i
$963$	−13.6077	+	0.307084i	−0.438502	+	0.00989564i
$964$	−7.08601	−	12.2733i	−0.228225	−	0.395297i
$965$		0			0
$966$	1.02576	−	13.4735i	0.0330032	−	0.433502i
$967$	−13.1922	−	36.2453i	−0.424233	−	1.16557i	−0.949262	−	0.314486i	$-0.898168\pi$
$967$	−13.1922	−	36.2453i	−0.424233	−	1.16557i	0.525029	−	0.851084i	$-0.324054\pi$
$968$	2.78106	+	0.490376i	0.0893866	+	0.0157613i
$969$	−37.8791	+	38.7435i	−1.21685	+	1.24462i
$970$		0			0
$971$	−14.6886			−0.471379			−0.235689	−	0.971828i	$-0.575735\pi$
$971$	−14.6886			−0.471379			−0.235689	+	0.971828i	$0.575735\pi$
$972$	−7.42770	+	5.85173i	−0.238244	+	0.187694i
$973$		−	31.0826i		−	0.996462i
$974$	25.3168	−	21.2433i	0.811202	−	0.680679i
$975$		0			0
$976$	8.64757	−	49.0428i	0.276802	−	1.56982i
$977$	1.90462	+	5.23291i	0.0609343	+	0.167416i	0.966424	−	0.256953i	$-0.0827184\pi$
$977$	1.90462	+	5.23291i	0.0609343	+	0.167416i	−0.905490	+	0.424368i	$0.860496\pi$
$978$	−14.7085	−	1.11978i	−0.470327	−	0.0358067i
$979$	6.80987	+	38.6207i	0.217644	+	1.23432i
$980$		0			0
$981$	0.517728	+	22.9419i	0.0165298	+	0.732478i
$982$	59.9667	+	34.6218i	1.91361	+	1.10483i
$983$	−10.2816	+	28.2485i	−0.327932	+	0.900987i	0.660702	+	0.750648i	$0.270259\pi$
$983$	−10.2816	+	28.2485i	−0.327932	+	0.900987i	−0.988635	+	0.150339i	$0.951964\pi$
$984$	17.1962	+	23.9783i	0.548194	+	0.764401i
$985$		0			0
$986$	61.6549	+	51.7346i	1.96349	+	1.64756i
$987$	19.6180	+	8.87996i	0.624447	+	0.282652i
$988$	−1.91240	+	5.25427i	−0.0608415	+	0.167161i
$989$	3.65913	−	6.33780i	0.116354	−	0.201530i
$990$		0			0
$991$	28.1316	+	48.7254i	0.893631	+	1.54781i	0.835490	+	0.549506i	$0.185184\pi$
$991$	28.1316	+	48.7254i	0.893631	+	1.54781i	0.0581407	+	0.998308i	$0.481483\pi$
$992$	12.9524	−	2.28385i	0.411238	−	0.0725123i
$993$	−10.3059	+	15.0776i	−0.327049	+	0.478474i
$994$	21.4662	−	7.81307i	0.680867	−	0.247815i
$995$		0			0
$996$	9.38913	+	2.40262i	0.297506	+	0.0761299i
$997$	1.23074	+	1.46674i	0.0389779	+	0.0464520i	0.785181	−	0.619266i	$-0.212570\pi$
$997$	1.23074	+	1.46674i	0.0389779	+	0.0464520i	−0.746203	+	0.665718i	$0.768125\pi$
$998$			9.90951i			0.313680i
$999$	4.04143	−	1.23090i	0.127865	−	0.0389439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.5		132
5.2	odd	4		675.2.l.g.76.9	yes	66
5.3	odd	4		675.2.l.f.76.3	✓	66
5.4	even	2	inner	675.2.u.e.49.18		132
27.16	even	9	inner	675.2.u.e.124.18		132
135.43	odd	36		675.2.l.f.151.3	yes	66
135.97	odd	36		675.2.l.g.151.9	yes	66
135.124	even	18	inner	675.2.u.e.124.5		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.3	✓	66	5.3	odd	4
675.2.l.f.151.3	yes	66	135.43	odd	36
675.2.l.g.76.9	yes	66	5.2	odd	4
675.2.l.g.151.9	yes	66	135.97	odd	36
675.2.u.e.49.5		132	1.1	even	1	trivial
675.2.u.e.49.18		132	5.4	even	2	inner
675.2.u.e.124.5		132	135.124	even	18	inner
675.2.u.e.124.18		132	27.16	even	9	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03778 - 1.23677i) q^{2} +(-1.23848 - 1.21085i) q^{3} +(-0.105334 + 0.597379i) q^{4} +(-0.212279 + 2.78832i) q^{6} +(-1.71440 + 0.302296i) q^{7} +(-1.94825 + 1.12482i) q^{8} +(0.0676836 + 2.99924i) q^{9} +(2.93339 + 1.06767i) q^{11} +(0.853791 - 0.612300i) q^{12} +(-1.21663 + 1.44992i) q^{13} +(2.15304 + 1.80662i) q^{14} +(4.55303 + 1.65717i) q^{16} +(5.56291 + 3.21175i) q^{17} +(3.63914 - 3.19625i) q^{18} +(-2.43505 - 4.21762i) q^{19} +(2.48930 + 1.70150i) q^{21} +(-1.72374 - 4.73595i) q^{22} +(2.73355 + 0.481999i) q^{23} +(3.77487 + 0.965965i) q^{24} +3.05582 q^{26} +(3.54780 - 3.79646i) q^{27} -1.05599i q^{28} +(-5.94510 + 4.98853i) q^{29} +(-0.687222 + 3.89743i) q^{31} +(-1.13664 - 3.12289i) q^{32} +(-2.34017 - 4.87419i) q^{33} +(-1.80085 - 10.2132i) q^{34} +(-1.79881 - 0.275489i) q^{36} +(0.704120 + 0.406524i) q^{37} +(-2.68922 + 7.38856i) q^{38} +(3.26242 - 0.322550i) q^{39} +(5.80103 + 4.86764i) q^{41} +(-0.478965 - 4.84447i) q^{42} +(0.901745 - 2.47752i) q^{43} +(-0.946788 + 1.63988i) q^{44} +(-2.24069 - 3.88100i) q^{46} +(7.03326 - 1.24015i) q^{47} +(-3.63227 - 7.56541i) q^{48} +(-3.73005 + 1.35763i) q^{49} +(-3.00063 - 10.7136i) q^{51} +(-0.738001 - 0.879516i) q^{52} -1.86813i q^{53} +(-8.37719 - 0.447951i) q^{54} +(3.00006 - 2.51735i) q^{56} +(-2.09115 + 8.17194i) q^{57} +(12.3394 + 2.17576i) q^{58} +(-0.971077 + 0.353443i) q^{59} +(-1.78476 - 10.1219i) q^{61} +(5.53342 - 3.19472i) q^{62} +(-1.02269 - 5.12144i) q^{63} +(2.16250 - 3.74556i) q^{64} +(-3.59969 + 7.95259i) q^{66} +(-8.76411 + 10.4447i) q^{67} +(-2.50460 + 2.98486i) q^{68} +(-2.80183 - 3.90687i) q^{69} +(4.06389 - 7.03886i) q^{71} +(-3.50548 - 5.76713i) q^{72} +(8.53538 - 4.92790i) q^{73} +(-0.227941 - 1.29272i) q^{74} +(2.77601 - 1.01039i) q^{76} +(-5.35177 - 0.943662i) q^{77} +(-3.78459 - 3.70014i) q^{78} +(11.3969 - 9.56310i) q^{79} +(-8.99084 + 0.405998i) q^{81} -12.2261i q^{82} +(5.92935 + 7.06632i) q^{83} +(-1.27865 + 1.30783i) q^{84} +(-3.99995 + 1.45586i) q^{86} +(13.4033 + 1.02041i) q^{87} +(-6.91592 + 1.21946i) q^{88} +(6.28136 + 10.8796i) q^{89} +(1.64749 - 2.85354i) q^{91} +(-0.575872 + 1.58220i) q^{92} +(5.57031 - 3.99478i) q^{93} +(-8.83274 - 7.41155i) q^{94} +(-2.37364 + 5.24395i) q^{96} +(-5.39248 + 14.8157i) q^{97} +(5.55004 + 3.20432i) q^{98} +(-3.00365 + 8.87020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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