LMFDB - Embedded newform 675.2.u.e.49.18

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			49.18
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.18

$q$-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	0.995895	−	0.0905154i	$-0.0288514\pi$
$2$	1.03778	+	1.23677i	0.733819	+	0.874532i	−0.262076	+	0.965047i	$0.584407\pi$
$3$	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	0.160010	−	0.987115i	$-0.448847\pi$
$7$	1.71440	−	0.302296i	0.647984	−	0.114257i	0.487974	+	0.872858i	$0.337736\pi$
$8$	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	−0.570469	−	0.821319i	$-0.693239\pi$
$13$	1.21663	−	1.44992i	0.337433	−	0.402137i	0.907902	+	0.419182i	$0.137683\pi$
$14$	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	−0.361068	−	0.932539i	$-0.617588\pi$
$17$	−5.56291	−	3.21175i	−1.34921	−	0.778964i	−0.988137	+	0.153576i	$0.950921\pi$
$18$	−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	−0.118774	−	0.992921i	$-0.537897\pi$
$23$	−2.73355	−	0.481999i	−0.569985	−	0.100504i	−0.451211	+	0.892418i	$0.649008\pi$
$24$	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	0.441004	−	0.897505i	$-0.354623\pi$
$37$	−0.704120	−	0.406524i	−0.115757	−	0.0668321i	−0.556760	+	0.830673i	$0.687956\pi$
$38$	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	−0.989266	−	0.146128i	$-0.953319\pi$
$43$	−0.901745	+	2.47752i	−0.137515	+	0.377819i	0.851751	+	0.523947i	$0.175541\pi$
$44$	−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	−0.661186	−	0.750222i	$-0.729946\pi$
$47$	−7.03326	+	1.24015i	−1.02591	+	0.180895i	−0.364720	+	0.931117i	$0.618835\pi$
$48$	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	$0.0409533\pi$
$53$			1.86813i			0.256608i	−0.991735	+	0.128304i	$0.959047\pi$
$54$	−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	$-0.464479\pi$
$67$	8.76411	−	10.4447i	1.07071	−	1.27602i	0.959344	−	0.282239i	$-0.0910770\pi$
$68$	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	−0.907950	−	0.419080i	$-0.862353\pi$
$73$	−8.53538	+	4.92790i	−0.998991	+	0.576768i	−0.0910412	+	0.995847i	$0.529020\pi$
$74$	−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	0.335209	−	0.942144i	$-0.391193\pi$
$83$	−5.92935	−	7.06632i	−0.650830	−	0.775630i	−0.986039	+	0.166514i	$0.946749\pi$
$84$	−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	$-0.593496\pi$
$97$	5.39248	−	14.8157i	0.547523	−	1.50431i	0.837044	−	0.547136i	$-0.184282\pi$
$98$	−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	$-0.995099\pi$
$103$	−2.47454	−	6.79875i	−0.243824	−	0.669901i	0.756058	−	0.654505i	$-0.227123\pi$
$104$	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	$-0.929620\pi$
$107$		−	4.53705i		−	0.438613i	0.975656	−	0.219307i	$-0.0703795\pi$
$108$	−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	0.873693	−	0.486478i	$-0.161719\pi$
$113$	−1.15121	−	3.16293i	−0.108297	−	0.297544i	−0.981990	+	0.188935i	$0.939497\pi$
$114$	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	−0.991180	−	0.132524i	$-0.957692\pi$
$127$	−15.4617	+	8.92679i	−1.37200	+	0.792125i	−0.380820	+	0.924649i	$0.624358\pi$
$128$	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	0.998157	−	0.0606822i	$-0.0193276\pi$
$137$	8.95490	+	10.6720i	0.765069	+	0.911773i	−0.233089	+	0.972456i	$0.574883\pi$
$138$	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	0.780155	−	0.625586i	$-0.215140\pi$
$157$	−2.75155	−	7.55982i	−0.219598	−	0.603339i	−0.999753	+	0.0222470i	$0.992918\pi$
$158$	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	$-0.933764\pi$
$163$		−	5.27505i		−	0.413174i	0.978428	−	0.206587i	$-0.0662356\pi$
$164$	−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	$0.110061\pi$
$167$	5.65972	+	15.5499i	0.437962	+	1.20329i	−0.502854	+	0.864372i	$0.667716\pi$
$168$	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	$-0.621996\pi$
$173$	6.69046	−	18.3819i	0.508666	−	1.39755i	0.882614	−	0.470099i	$-0.155782\pi$
$174$	−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	−0.316660	−	0.948539i	$-0.602562\pi$
$193$	−13.0401	−	2.29931i	−0.938643	−	0.165508i	−0.621983	+	0.783031i	$0.713673\pi$
$194$	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	−0.950236	−	0.311530i	$-0.899159\pi$
$197$	−16.2191	+	9.36409i	−1.15556	+	0.667164i	−0.205325	+	0.978694i	$0.565825\pi$
$198$	−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	0.481872	−	0.876242i	$-0.339957\pi$
$223$	18.4332	−	3.25026i	1.23438	−	0.217654i	0.752504	+	0.658588i	$0.228846\pi$
$224$	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	$0.309175\pi$
$227$	−6.00696	+	16.5040i	−0.398696	+	1.09541i	−0.962920	+	0.269787i	$0.913047\pi$
$228$	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	0.683943	−	0.729536i	$-0.260264\pi$
$233$	6.01595	+	3.47331i	0.394118	+	0.227544i	−0.289825	+	0.957080i	$0.593597\pi$
$234$	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	$-0.480287\pi$
$257$	16.5773	−	19.7561i	1.03406	−	1.23235i	0.972172	−	0.234266i	$-0.0752687\pi$
$258$	−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	−0.817912	−	0.575343i	$-0.804869\pi$
$263$	−22.5375	+	3.97396i	−1.38972	+	0.245045i	−0.571807	+	0.820388i	$0.693758\pi$
$264$	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	0.656311	−	0.754490i	$-0.272116\pi$
$277$	25.4825	−	4.49325i	1.53109	−	0.269973i	0.874782	+	0.484517i	$0.161005\pi$
$278$	−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	−0.978574	−	0.205897i	$-0.933989\pi$
$283$	−10.1924	+	12.1469i	−0.605877	+	0.722056i	0.372697	+	0.927953i	$0.378433\pi$
$284$	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	0.268525	−	0.963273i	$-0.413464\pi$
$293$	3.27620	+	0.577683i	0.191398	+	0.0337486i	−0.0771274	+	0.997021i	$0.524575\pi$
$294$	−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	0.604749	−	0.796416i	$-0.293273\pi$
$307$	3.80928	+	2.19929i	0.217407	+	0.125520i	−0.387342	+	0.921936i	$0.626607\pi$
$308$	−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	−0.789829	−	0.613327i	$-0.789831\pi$
$313$	3.70561	−	10.1811i	0.209454	−	0.575469i	0.999283	+	0.0378572i	$0.0120532\pi$
$314$	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	0.126576	−	0.991957i	$-0.459601\pi$
$317$	10.4118	−	1.83589i	0.584787	−	0.103114i	0.458212	+	0.888843i	$0.348490\pi$
$318$	−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	−0.786958	−	0.617006i	$-0.788345\pi$
$337$	−0.783347	+	0.933557i	−0.0426717	+	0.0508541i	0.744287	+	0.667860i	$0.232790\pi$
$338$	−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	0.146632	−	0.989191i	$-0.453157\pi$
$347$	−1.00408	−	0.177046i	−0.0539016	−	0.00950431i	−0.200534	+	0.979687i	$0.564268\pi$
$348$	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	0.454043	−	0.890980i	$-0.349981\pi$
$353$	−9.43633	−	11.2458i	−0.502245	−	0.598552i	−0.956288	+	0.292428i	$0.905537\pi$
$354$	−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	$0.336681\pi$
$367$	−8.52841	+	23.4316i	−0.445180	+	1.22312i	−0.936043	+	0.351884i	$0.885541\pi$
$368$	−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	0.999953	−	0.00972404i	$-0.00309531\pi$
$373$	4.39750	+	12.0820i	0.227694	+	0.625584i	−0.772259	+	0.635308i	$0.780873\pi$
$374$	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	0.986753	−	0.162229i	$-0.0518682\pi$
$383$	2.47718	+	6.80599i	0.126578	+	0.347770i	−0.860175	+	0.509998i	$0.829646\pi$
$384$	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	0.184358	−	0.982859i	$-0.440979\pi$
$397$	22.4696	−	12.9728i	1.12772	−	0.651088i	0.943360	+	0.331771i	$0.107646\pi$
$398$	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	$0.0663471\pi$
$433$			8.61185i			0.413859i	−0.978356	+	0.206929i	$0.933653\pi$
$434$	−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	−0.991855	−	0.127374i	$-0.959345\pi$
$443$	−3.16082	+	8.68429i	−0.150175	+	0.412603i	0.841679	+	0.539977i	$0.181567\pi$
$444$	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	0.786143	−	0.618044i	$-0.212075\pi$
$457$	0.875976	+	1.04395i	0.0409764	+	0.0488338i	−0.745167	+	0.666878i	$0.767630\pi$
$458$			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	0.784581	−	0.620027i	$-0.212878\pi$
$463$	28.1832	+	4.96946i	1.30978	+	0.230950i	0.525203	+	0.850977i	$0.323989\pi$
$464$	−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	−0.545536	−	0.838087i	$-0.683674\pi$
$467$	−1.99894	+	1.15409i	−0.0925000	+	0.0534049i	0.453036	+	0.891492i	$0.350341\pi$
$468$	−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	$-0.846488\pi$
$487$		−	20.4700i		−	0.927584i	0.885944	−	0.463792i	$-0.153512\pi$
$488$	−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	0.361371	−	0.932422i	$-0.382309\pi$
$503$	−5.95329	−	3.43713i	−0.265444	−	0.153254i	−0.626815	+	0.779168i	$0.715642\pi$
$504$	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	0.999998	−	0.00176851i	$-0.000562935\pi$
$523$	34.2687	+	19.7850i	1.49847	+	0.865140i	0.498468	+	0.866908i	$0.333896\pi$
$524$	−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	0.310469	−	0.950583i	$-0.399514\pi$
$547$	21.6885	−	3.82427i	0.927333	−	0.163514i	0.616864	+	0.787070i	$0.288403\pi$
$548$	−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	0.849092	−	0.528246i	$-0.177150\pi$
$557$	19.2621	+	11.1210i	0.816163	+	0.471212i	−0.0329284	+	0.999458i	$0.510483\pi$
$558$	−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	−0.128123	−	0.991758i	$-0.540895\pi$
$563$	−13.9452	−	2.45892i	−0.587721	−	0.103631i	−0.459598	+	0.888127i	$0.652006\pi$
$564$	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	0.791889	−	0.610664i	$-0.209098\pi$
$577$	15.8293	+	9.13906i	0.658983	+	0.380464i	−0.132906	+	0.991129i	$0.542431\pi$
$578$	−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	−0.00377558	−	0.999993i	$-0.501202\pi$
$587$	8.10900	−	1.42984i	0.334694	−	0.0590156i	0.338470	+	0.940977i	$0.390091\pi$
$588$	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	$-0.705718\pi$
$593$		−	38.8812i		−	1.59666i	0.602222	−	0.798329i	$-0.294282\pi$
$594$	−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	−0.672161	−	0.740405i	$-0.734634\pi$
$607$	4.27987	−	5.10054i	0.173714	−	0.207025i	0.845876	+	0.533380i	$0.179078\pi$
$608$	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	−0.949761	−	0.312975i	$-0.898674\pi$
$613$	−28.5617	+	16.4901i	−1.15360	+	0.666030i	−0.203837	+	0.979005i	$0.565341\pi$
$614$	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	−0.608834	−	0.793298i	$-0.708362\pi$
$617$	−36.0737	−	6.36077i	−1.45227	−	0.256075i	−0.843440	+	0.537223i	$0.819473\pi$
$618$	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	0.999884	−	0.0152381i	$-0.00485063\pi$
$643$	5.68345	+	15.6152i	0.224134	+	0.615802i	−0.775750	+	0.631040i	$0.782628\pi$
$644$	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	$-0.966713\pi$
$647$		−	5.31018i		−	0.208765i	0.994537	−	0.104382i	$-0.0332865\pi$
$648$	−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	$-0.947304\pi$
$653$	−8.60359	−	23.6382i	−0.336685	−	0.925034i	0.649643	−	0.760239i	$-0.274918\pi$
$654$	−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	0.518591	−	0.855023i	$-0.326457\pi$
$673$	−10.7270	−	12.7839i	−0.413494	−	0.492784i	−0.932085	+	0.362239i	$0.882012\pi$
$674$	−1.96754			−0.0757868
$675$		0			0
$676$	−5.71262			−0.219716
$677$	−19.0984	−	22.7606i	−0.734012	−	0.874762i	0.261899	−	0.965095i	$-0.415651\pi$
$677$	−19.0984	−	22.7606i	−0.734012	−	0.874762i	−0.995912	+	0.0903336i	$0.971207\pi$
$678$	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	−0.693126	−	0.720816i	$-0.743767\pi$
$683$	−10.8573	+	6.26849i	−0.415445	+	0.239857i	0.277682	+	0.960673i	$0.410434\pi$
$684$	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	0.999091	−	0.0426388i	$-0.0135765\pi$
$727$	21.1284	+	25.1799i	0.783609	+	0.933869i	−0.215481	+	0.976508i	$0.569132\pi$
$728$		−	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	0.0456547	−	0.998957i	$-0.485463\pi$
$733$	−6.85262	−	1.20830i	−0.253107	−	0.0446297i	−0.298762	+	0.954328i	$0.596574\pi$
$734$	−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	−0.801840	−	0.597539i	$-0.796145\pi$
$743$	−2.02092	+	2.40844i	−0.0741404	+	0.0883571i	0.727699	+	0.685896i	$0.240590\pi$
$744$	−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	$0.0951578\pi$
$757$			16.2063i			0.589028i	−0.955647	+	0.294514i	$0.904842\pi$
$758$	−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	$0.103768\pi$
$773$	47.2189	+	27.2618i	1.69835	+	0.980540i	0.751014	+	0.660286i	$0.229565\pi$
$774$	−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	−0.185748	−	0.982597i	$-0.559471\pi$
$787$	−19.5354	−	3.44462i	−0.696363	−	0.122788i	−0.510614	+	0.859810i	$0.670582\pi$
$788$	−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	−0.880813	−	0.473464i	$-0.843003\pi$
$797$	−7.38501	+	8.80112i	−0.261591	+	0.311752i	0.619223	+	0.785216i	$0.287448\pi$
$798$	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	−0.995116	−	0.0987156i	$-0.968527\pi$
$823$	−20.8016	+	24.7904i	−0.725100	+	0.864140i	0.270016	+	0.962856i	$0.412971\pi$
$824$	−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	$0.0212660\pi$
$827$	44.7028	+	25.8092i	1.55447	+	0.897473i	0.556700	+	0.830714i	$0.312067\pi$
$828$	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	$-0.762123\pi$
$853$	7.74759	−	21.2863i	0.265272	−	0.728830i	0.998791	−	0.0491605i	$-0.0156546\pi$
$854$	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	−0.0462871	−	0.998928i	$-0.514739\pi$
$857$	7.37341	−	1.30013i	0.251871	−	0.0444116i	0.298158	+	0.954517i	$0.403628\pi$
$858$	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	$-0.952785\pi$
$863$		−	8.68298i		−	0.295572i	0.989019	−	0.147786i	$-0.0472147\pi$
$864$	−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	−0.984078	−	0.177737i	$-0.943122\pi$
$877$	−18.8985	+	22.5224i	−0.638157	+	0.760526i	0.345920	+	0.938264i	$0.387567\pi$
$878$	−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	−0.990506	−	0.137468i	$-0.956104\pi$
$883$	−40.6122	+	23.4475i	−1.36671	+	0.789070i	−0.376203	+	0.926537i	$0.622770\pi$
$884$	−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	−0.670692	−	0.741736i	$-0.734003\pi$
$887$	−46.3007	−	8.16406i	−1.55462	−	0.274122i	−0.883933	+	0.467614i	$0.845114\pi$
$888$	−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	$0.326905\pi$
$907$	−12.9206	+	35.4991i	−0.429022	+	1.17873i	−0.946408	+	0.322975i	$0.895317\pi$
$908$	−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	−0.951962	−	0.306215i	$-0.900937\pi$
$937$	−35.5924	+	20.5493i	−1.16275	+	0.671316i	−0.210791	+	0.977531i	$0.567604\pi$
$938$	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	0.916350	−	0.400379i	$-0.131121\pi$
$947$	11.1686	+	13.3102i	0.362931	+	0.432524i	−0.553419	+	0.832903i	$0.686677\pi$
$948$	−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	0.356688	−	0.934223i	$-0.383906\pi$
$953$	41.4931	−	23.9561i	1.34409	−	0.776013i	0.987405	+	0.158211i	$0.0505725\pi$
$954$	−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	$0.101832\pi$
$967$	13.1922	+	36.2453i	0.424233	+	1.16557i	−0.525029	+	0.851084i	$0.675946\pi$
$968$	−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	0.905490	−	0.424368i	$-0.139504\pi$
$977$	−1.90462	−	5.23291i	−0.0609343	−	0.167416i	−0.966424	+	0.256953i	$0.917282\pi$
$978$	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	$-0.729741\pi$
$983$	10.2816	−	28.2485i	0.327932	−	0.900987i	0.988635	−	0.150339i	$-0.0480364\pi$
$984$	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	0.746203	−	0.665718i	$-0.231875\pi$
$997$	−1.23074	−	1.46674i	−0.0389779	−	0.0464520i	−0.785181	+	0.619266i	$0.787430\pi$
$998$		−	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.49.18		132
5.2	odd	4		675.2.l.f.76.3	✓	66
5.3	odd	4		675.2.l.g.76.9	yes	66
5.4	even	2	inner	675.2.u.e.49.5		132
27.16	even	9	inner	675.2.u.e.124.5		132
135.43	odd	36		675.2.l.g.151.9	yes	66
135.97	odd	36		675.2.l.f.151.3	yes	66
135.124	even	18	inner	675.2.u.e.124.18		132

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

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