LMFDB - Embedded newform 675.2.l.f.151.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] 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("675.76"); 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, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.3
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23677 - 1.03778i) q^{2} +(1.21085 + 1.23848i) q^{3} +(0.105334 + 0.597379i) q^{4} +(-0.212279 - 2.78832i) q^{6} +(0.302296 - 1.71440i) q^{7} +(-1.12482 + 1.94825i) q^{8} +(-0.0676836 + 2.99924i) q^{9} +(2.93339 - 1.06767i) q^{11} +(-0.612300 + 0.853791i) q^{12} +(-1.44992 + 1.21663i) q^{13} +(-2.15304 + 1.80662i) q^{14} +(4.55303 - 1.65717i) q^{16} +(3.21175 + 5.56291i) q^{17} +(3.19625 - 3.63914i) q^{18} +(2.43505 - 4.21762i) q^{19} +(2.48930 - 1.70150i) q^{21} +(-4.73595 - 1.72374i) q^{22} +(-0.481999 - 2.73355i) q^{23} +(-3.77487 + 0.965965i) q^{24} +3.05582 q^{26} +(-3.79646 + 3.54780i) q^{27} +1.05599 q^{28} +(5.94510 + 4.98853i) q^{29} +(-0.687222 - 3.89743i) q^{31} +(-3.12289 - 1.13664i) q^{32} +(4.87419 + 2.34017i) q^{33} +(1.80085 - 10.2132i) q^{34} +(-1.79881 + 0.275489i) q^{36} +(0.406524 + 0.704120i) q^{37} +(-7.38856 + 2.68922i) q^{38} +(-3.26242 - 0.322550i) q^{39} +(5.80103 - 4.86764i) q^{41} +(-4.84447 - 0.478965i) q^{42} +(2.47752 - 0.901745i) q^{43} +(0.946788 + 1.63988i) q^{44} +(-2.24069 + 3.88100i) q^{46} +(-1.24015 + 7.03326i) q^{47} +(7.56541 + 3.63227i) q^{48} +(3.73005 + 1.35763i) q^{49} +(-3.00063 + 10.7136i) q^{51} +(-0.879516 - 0.738001i) q^{52} +1.86813 q^{53} +(8.37719 - 0.447951i) q^{54} +(3.00006 + 2.51735i) q^{56} +(8.17194 - 2.09115i) q^{57} +(-2.17576 - 12.3394i) q^{58} +(0.971077 + 0.353443i) q^{59} +(-1.78476 + 10.1219i) q^{61} +(-3.19472 + 5.53342i) q^{62} +(5.12144 + 1.02269i) q^{63} +(-2.16250 - 3.74556i) q^{64} +(-3.59969 - 7.95259i) q^{66} +(10.4447 - 8.76411i) q^{67} +(-2.98486 + 2.50460i) q^{68} +(2.80183 - 3.90687i) q^{69} +(4.06389 + 7.03886i) q^{71} +(-5.76713 - 3.50548i) q^{72} +(4.92790 - 8.53538i) q^{73} +(0.227941 - 1.29272i) q^{74} +(2.77601 + 1.01039i) q^{76} +(-0.943662 - 5.35177i) q^{77} +(3.70014 + 3.78459i) q^{78} +(-11.3969 - 9.56310i) q^{79} +(-8.99084 - 0.405998i) q^{81} -12.2261 q^{82} +(-7.06632 - 5.92935i) q^{83} +(1.27865 + 1.30783i) q^{84} +(-3.99995 - 1.45586i) q^{86} +(1.02041 + 13.4033i) q^{87} +(-1.21946 + 6.91592i) q^{88} +(-6.28136 + 10.8796i) q^{89} +(1.64749 + 2.85354i) q^{91} +(1.58220 - 0.575872i) q^{92} +(3.99478 - 5.57031i) q^{93} +(8.83274 - 7.41155i) q^{94} +(-2.37364 - 5.24395i) q^{96} +(14.8157 - 5.39248i) q^{97} +(-3.20432 - 5.55004i) q^{98} +(3.00365 + 8.87020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−1.23677	−	1.03778i	−0.874532	−	0.733819i	0.0905154	−	0.995895i	$-0.471149\pi$
$2$	−1.23677	−	1.03778i	−0.874532	−	0.733819i	−0.965047	+	0.262076i	$0.915593\pi$
$3$	1.21085	+	1.23848i	0.699085	+	0.715039i
$3$	1.21085	+	1.23848i	0.699085	+	0.715039i
$4$	0.105334	+	0.597379i	0.0526670	+	0.298689i
$5$		0			0
$5$		0			0
$6$	−0.212279	−	2.78832i	−0.0866625	−	1.13833i
$7$	0.302296	−	1.71440i	0.114257	−	0.647984i	−0.872858	−	0.487974i	$-0.837736\pi$
$7$	0.302296	−	1.71440i	0.114257	−	0.647984i	0.987115	−	0.160010i	$-0.0511527\pi$
$8$	−1.12482	+	1.94825i	−0.397685	+	0.688811i
$9$	−0.0676836	+	2.99924i	−0.0225612	+	0.999745i
$10$		0			0
$11$	2.93339	−	1.06767i	0.884451	−	0.321914i	0.140447	−	0.990088i	$-0.455146\pi$
$11$	2.93339	−	1.06767i	0.884451	−	0.321914i	0.744005	+	0.668174i	$0.232924\pi$
$12$	−0.612300	+	0.853791i	−0.176756	+	0.246468i
$13$	−1.44992	+	1.21663i	−0.402137	+	0.337433i	−0.821319	−	0.570469i	$-0.806761\pi$
$13$	−1.44992	+	1.21663i	−0.402137	+	0.337433i	0.419182	+	0.907902i	$0.362317\pi$
$14$	−2.15304	+	1.80662i	−0.575424	+	0.482838i
$15$		0			0
$16$	4.55303	−	1.65717i	1.13826	−	0.414292i
$17$	3.21175	+	5.56291i	0.778964	+	1.34921i	0.932539	+	0.361068i	$0.117588\pi$
$17$	3.21175	+	5.56291i	0.778964	+	1.34921i	−0.153576	+	0.988137i	$0.549079\pi$
$18$	3.19625	−	3.63914i	0.753363	−	0.857754i
$19$	2.43505	−	4.21762i	0.558638	−	0.967590i	−0.438972	−	0.898501i	$-0.644657\pi$
$19$	2.43505	−	4.21762i	0.558638	−	0.967590i	0.997611	−	0.0690890i	$-0.0220092\pi$
$20$		0			0
$21$	2.48930	−	1.70150i	0.543209	−	0.371297i
$22$	−4.73595	−	1.72374i	−1.00971	−	0.367504i
$23$	−0.481999	−	2.73355i	−0.100504	−	0.569985i	−0.992921	−	0.118774i	$-0.962103\pi$
$23$	−0.481999	−	2.73355i	−0.100504	−	0.569985i	0.892418	−	0.451211i	$-0.149008\pi$
$24$	−3.77487	+	0.965965i	−0.770542	+	0.197177i
$25$		0			0
$26$	3.05582			0.599296
$27$	−3.79646	+	3.54780i	−0.730629	+	0.682775i
$28$	1.05599			0.199563
$29$	5.94510	+	4.98853i	1.10398	+	0.926346i	0.997686	−	0.0679886i	$-0.0216582\pi$
$29$	5.94510	+	4.98853i	1.10398	+	0.926346i	0.106291	+	0.994335i	$0.466103\pi$
$30$		0			0
$31$	−0.687222	−	3.89743i	−0.123429	−	0.699999i	−0.982229	−	0.187688i	$-0.939901\pi$
$31$	−0.687222	−	3.89743i	−0.123429	−	0.699999i	0.858800	−	0.512311i	$-0.171210\pi$
$32$	−3.12289	−	1.13664i	−0.552054	−	0.200931i
$33$	4.87419	+	2.34017i	0.848487	+	0.407372i
$34$	1.80085	−	10.2132i	0.308844	−	1.75154i
$35$		0			0
$36$	−1.79881	+	0.275489i	−0.299802	+	0.0459148i
$37$	0.406524	+	0.704120i	0.0668321	+	0.115757i	0.897505	−	0.441004i	$-0.145377\pi$
$37$	0.406524	+	0.704120i	0.0668321	+	0.115757i	−0.830673	+	0.556760i	$0.812044\pi$
$38$	−7.38856	+	2.68922i	−1.19858	+	0.436248i
$39$	−3.26242	−	0.322550i	−0.522405	−	0.0516493i
$40$		0			0
$41$	5.80103	−	4.86764i	0.905969	−	0.760198i	−0.0653788	−	0.997861i	$-0.520826\pi$
$41$	5.80103	−	4.86764i	0.905969	−	0.760198i	0.971348	+	0.237662i	$0.0763811\pi$
$42$	−4.84447	−	0.478965i	−0.747519	−	0.0739059i
$43$	2.47752	−	0.901745i	0.377819	−	0.137515i	−0.146128	−	0.989266i	$-0.546681\pi$
$43$	2.47752	−	0.901745i	0.377819	−	0.137515i	0.523947	+	0.851751i	$0.324459\pi$
$44$	0.946788	+	1.63988i	0.142734	+	0.247222i
$45$		0			0
$46$	−2.24069	+	3.88100i	−0.330372	+	0.572222i
$47$	−1.24015	+	7.03326i	−0.180895	+	1.02591i	0.750222	+	0.661186i	$0.229946\pi$
$47$	−1.24015	+	7.03326i	−0.180895	+	1.02591i	−0.931117	+	0.364720i	$0.881165\pi$
$48$	7.56541	+	3.63227i	1.09197	+	0.524273i
$49$	3.73005	+	1.35763i	0.532864	+	0.193947i
$50$		0			0
$51$	−3.00063	+	10.7136i	−0.420172	+	1.50020i
$52$	−0.879516	−	0.738001i	−0.121967	−	0.102342i
$53$	1.86813			0.256608			0.128304	−	0.991735i	$-0.459047\pi$
$53$	1.86813			0.256608			0.128304	+	0.991735i	$0.459047\pi$
$54$	8.37719	−	0.447951i	1.13999	−	0.0609584i
$55$		0			0
$56$	3.00006	+	2.51735i	0.400900	+	0.336395i
$57$	8.17194	−	2.09115i	1.08240	−	0.276979i
$58$	−2.17576	−	12.3394i	−0.285692	−	1.62024i
$59$	0.971077	+	0.353443i	0.126423	+	0.0460144i	0.404457	−	0.914557i	$-0.367460\pi$
$59$	0.971077	+	0.353443i	0.126423	+	0.0460144i	−0.278034	+	0.960571i	$0.589683\pi$
$60$		0			0
$61$	−1.78476	+	10.1219i	−0.228515	+	1.29597i	0.627335	+	0.778749i	$0.284146\pi$
$61$	−1.78476	+	10.1219i	−0.228515	+	1.29597i	−0.855850	+	0.517224i	$0.826966\pi$
$62$	−3.19472	+	5.53342i	−0.405730	+	0.702746i
$63$	5.12144	+	1.02269i	0.645241	+	0.128847i
$64$	−2.16250	−	3.74556i	−0.270312	−	0.468195i
$65$		0			0
$66$	−3.59969	−	7.95259i	−0.443092	−	0.978896i
$67$	10.4447	−	8.76411i	1.27602	−	1.07071i	0.282239	−	0.959344i	$-0.408923\pi$
$67$	10.4447	−	8.76411i	1.27602	−	1.07071i	0.993780	−	0.111363i	$-0.0355215\pi$
$68$	−2.98486	+	2.50460i	−0.361967	+	0.303727i
$69$	2.80183	−	3.90687i	0.337301	−	0.470332i
$70$		0			0
$71$	4.06389	+	7.03886i	0.482294	+	0.835359i	0.999793	−	0.0203253i	$-0.00647020\pi$
$71$	4.06389	+	7.03886i	0.482294	+	0.835359i	−0.517499	+	0.855684i	$0.673137\pi$
$72$	−5.76713	−	3.50548i	−0.679663	−	0.413124i
$73$	4.92790	−	8.53538i	0.576768	−	0.998991i	−0.419080	−	0.907950i	$-0.637647\pi$
$73$	4.92790	−	8.53538i	0.576768	−	0.998991i	0.995847	−	0.0910412i	$-0.0290195\pi$
$74$	0.227941	−	1.29272i	0.0264976	−	0.150276i
$75$		0			0
$76$	2.77601	+	1.01039i	0.318430	+	0.115899i
$77$	−0.943662	−	5.35177i	−0.107540	−	0.609891i
$78$	3.70014	+	3.78459i	0.418959	+	0.428520i
$79$	−11.3969	−	9.56310i	−1.28225	−	1.07593i	−0.992930	−	0.118700i	$-0.962127\pi$
$79$	−11.3969	−	9.56310i	−1.28225	−	1.07593i	−0.289317	−	0.957233i	$-0.593428\pi$
$80$		0			0
$81$	−8.99084	−	0.405998i	−0.998982	−	0.0451109i
$82$	−12.2261			−1.35015
$83$	−7.06632	−	5.92935i	−0.775630	−	0.650830i	0.166514	−	0.986039i	$-0.446749\pi$
$83$	−7.06632	−	5.92935i	−0.775630	−	0.650830i	−0.942144	+	0.335209i	$0.891193\pi$
$84$	1.27865	+	1.30783i	0.139512	+	0.142696i
$85$		0			0
$86$	−3.99995	−	1.45586i	−0.431326	−	0.156990i
$87$	1.02041	+	13.4033i	0.109399	+	1.43698i
$88$	−1.21946	+	6.91592i	−0.129995	+	0.737240i
$89$	−6.28136	+	10.8796i	−0.665823	+	1.15324i	0.313238	+	0.949675i	$0.398586\pi$
$89$	−6.28136	+	10.8796i	−0.665823	+	1.15324i	−0.979061	+	0.203565i	$0.934747\pi$
$90$		0			0
$91$	1.64749	+	2.85354i	0.172704	+	0.299132i
$92$	1.58220	−	0.575872i	0.164955	−	0.0600388i
$93$	3.99478	−	5.57031i	0.414239	−	0.577615i
$94$	8.83274	−	7.41155i	0.911028	−	0.764443i
$95$		0			0
$96$	−2.37364	−	5.24395i	−0.242259	−	0.535208i
$97$	14.8157	−	5.39248i	1.50431	−	0.547523i	0.547136	−	0.837044i	$-0.315718\pi$
$97$	14.8157	−	5.39248i	1.50431	−	0.547523i	0.957172	+	0.289521i	$0.0934959\pi$
$98$	−3.20432	−	5.55004i	−0.323685	−	0.560639i
$99$	3.00365	+	8.87020i	0.301878	+	0.891489i
$100$		0			0
$101$	1.11330	−	6.31385i	0.110778	−	0.628251i	−0.877977	−	0.478703i	$-0.841107\pi$
$101$	1.11330	−	6.31385i	0.110778	−	0.628251i	0.988754	−	0.149548i	$-0.0477818\pi$
$102$	14.8294	−	10.1363i	1.46833	−	1.00364i
$103$	−6.79875	−	2.47454i	−0.669901	−	0.243824i	−0.0153956	−	0.999881i	$-0.504901\pi$
$103$	−6.79875	−	2.47454i	−0.669901	−	0.243824i	−0.654505	+	0.756058i	$0.727123\pi$
$104$	−0.739394	−	4.19331i	−0.0725035	−	0.411188i
$105$		0			0
$106$	−2.31046	−	1.93871i	−0.224412	−	0.188304i
$107$	4.53705			0.438613			0.219307	−	0.975656i	$-0.429620\pi$
$107$	4.53705			0.438613			0.219307	+	0.975656i	$0.429620\pi$
$108$	−2.51928	−	1.89422i	−0.242418	−	0.182271i
$109$	−7.64924			−0.732665			−0.366332	−	0.930484i	$-0.619387\pi$
$109$	−7.64924			−0.732665			−0.366332	+	0.930484i	$0.619387\pi$
$110$		0			0
$111$	−0.379802	+	1.35606i	−0.0360492	+	0.128711i
$112$	−1.46469	−	8.30668i	−0.138400	−	0.784908i
$113$	−3.16293	−	1.15121i	−0.297544	−	0.108297i	0.188935	−	0.981990i	$-0.439497\pi$
$113$	−3.16293	−	1.15121i	−0.297544	−	0.108297i	−0.486478	+	0.873693i	$0.661719\pi$
$114$	−12.2770	−	5.89437i	−1.14985	−	0.552059i
$115$		0			0
$116$	−2.35382	+	4.07694i	−0.218547	+	0.378534i
$117$	−3.55083	−	4.43101i	−0.328274	−	0.409647i
$118$	−0.834208	−	1.44489i	−0.0767951	−	0.133013i
$119$	10.5080	−	3.82459i	0.963265	−	0.350600i
$120$		0			0
$121$	−0.961609	+	0.806886i	−0.0874190	+	0.0733532i
$122$	12.7116	−	10.6663i	1.15085	−	0.965681i
$123$	13.0527	+	1.29050i	1.17692	+	0.116360i
$124$	2.25585	−	0.821063i	0.202582	−	0.0737336i
$125$		0			0
$126$	−5.27274	−	6.57976i	−0.469733	−	0.586171i
$127$	−8.92679	+	15.4617i	−0.792125	+	1.37200i	0.132524	+	0.991180i	$0.457692\pi$
$127$	−8.92679	+	15.4617i	−0.792125	+	1.37200i	−0.924649	+	0.380820i	$0.875642\pi$
$128$	−2.36670	+	13.4222i	−0.209189	+	1.18637i
$129$	4.11671	+	1.97649i	0.362456	+	0.174021i
$130$		0			0
$131$	−2.37367	−	13.4617i	−0.207388	−	1.17616i	−0.893637	−	0.448790i	$-0.851855\pi$
$131$	−2.37367	−	13.4617i	−0.207388	−	1.17616i	0.686249	−	0.727367i	$-0.259256\pi$
$132$	−0.884552	+	3.15824i	−0.0769904	+	0.274889i
$133$	−6.49461	−	5.44962i	−0.563154	−	0.472542i
$134$	−22.0129			−1.90162
$135$		0			0
$136$	−14.4506			−1.23913
$137$	−10.6720	−	8.95490i	−0.911773	−	0.765069i	0.0606822	−	0.998157i	$-0.480672\pi$
$137$	−10.6720	−	8.95490i	−0.911773	−	0.765069i	−0.972456	+	0.233089i	$0.925117\pi$
$138$	−7.51970	+	1.92424i	−0.640119	+	0.163802i
$139$	3.10046	+	17.5836i	0.262977	+	1.49142i	0.774734	+	0.632288i	$0.217884\pi$
$139$	3.10046	+	17.5836i	0.262977	+	1.49142i	−0.511756	+	0.859131i	$0.671005\pi$
$140$		0			0
$141$	−10.2122	+	6.98031i	−0.860023	+	0.587848i
$142$	2.27865	−	12.9229i	0.191220	−	1.08446i
$143$	−2.95424	+	5.11689i	−0.247046	+	0.427896i
$144$	4.66207	+	13.7678i	0.388506	+	1.14731i
$145$		0			0
$146$	−14.9525	+	5.44228i	−1.23748	+	0.450406i
$147$	2.83513	+	6.26349i	0.233838	+	0.516604i
$148$	−0.377806	+	0.317017i	−0.0310554	+	0.0260586i
$149$	−13.7598	+	11.5458i	−1.12725	+	0.945872i	−0.998948	−	0.0458641i	$-0.985396\pi$
$149$	−13.7598	+	11.5458i	−1.12725	+	0.945872i	−0.128298	+	0.991736i	$0.540951\pi$
$150$		0			0
$151$	18.3678	−	6.68534i	1.49475	−	0.544045i	0.540057	−	0.841629i	$-0.318403\pi$
$151$	18.3678	−	6.68534i	1.49475	−	0.544045i	0.954696	+	0.297583i	$0.0961806\pi$
$152$	5.47800	+	9.48817i	0.444324	+	0.769592i
$153$	−16.9019	+	9.25628i	−1.36644	+	0.748326i
$154$	−4.38685	+	7.59825i	−0.353502	+	0.612284i
$155$		0			0
$156$	−0.150959	−	1.98287i	−0.0120864	−	0.158757i
$157$	7.55982	+	2.75155i	0.603339	+	0.219598i	0.625586	−	0.780155i	$-0.284860\pi$
$157$	7.55982	+	2.75155i	0.603339	+	0.219598i	−0.0222470	+	0.999753i	$0.507082\pi$
$158$	4.17098	+	23.6548i	0.331825	+	1.88188i
$159$	2.26203	+	2.31365i	0.179391	+	0.183485i
$160$		0			0
$161$	−4.83212			−0.380824
$162$	10.6983	+	9.83262i	0.840538	+	0.772523i
$163$	−5.27505			−0.413174			−0.206587	−	0.978428i	$-0.566236\pi$
$163$	−5.27505			−0.413174			−0.206587	+	0.978428i	$0.566236\pi$
$164$	3.51887	+	2.95269i	0.274778	+	0.230566i
$165$		0			0
$166$	2.58611	+	14.6665i	0.200721	+	1.13834i
$167$	−15.5499	−	5.65972i	−1.20329	−	0.437962i	−0.338919	−	0.940816i	$-0.610061\pi$
$167$	−15.5499	−	5.65972i	−1.20329	−	0.437962i	−0.864372	+	0.502854i	$0.832284\pi$
$168$	0.514927	+	6.76366i	0.0397275	+	0.521828i
$169$	−1.63534	+	9.27446i	−0.125795	+	0.713420i
$170$		0			0
$171$	12.4848	+	7.58875i	0.954740	+	0.580326i
$172$	0.799651	+	1.38504i	0.0609728	+	0.105608i
$173$	−18.3819	+	6.69046i	−1.39755	+	0.508666i	−0.927450	−	0.373948i	$-0.878004\pi$
$173$	−18.3819	+	6.69046i	−1.39755	+	0.508666i	−0.470099	+	0.882614i	$0.655782\pi$
$174$	12.6476	−	17.6358i	0.958811	−	1.33697i
$175$		0			0
$176$	11.5865	−	9.72224i	0.873367	−	0.732842i
$177$	0.738095	+	1.63063i	0.0554786	+	0.122566i
$178$	19.0593	−	6.93701i	1.42855	−	0.519951i
$179$	−0.604142	−	1.04640i	−0.0451557	−	0.0782119i	0.842564	−	0.538596i	$-0.181045\pi$
$179$	−0.604142	−	1.04640i	−0.0451557	−	0.0782119i	−0.887720	+	0.460384i	$0.847712\pi$
$180$		0			0
$181$	−10.2446	+	17.7442i	−0.761474	+	1.31891i	0.180616	+	0.983554i	$0.442191\pi$
$181$	−10.2446	+	17.7442i	−0.761474	+	1.31891i	−0.942090	+	0.335359i	$0.891142\pi$
$182$	0.923761	−	5.23891i	0.0684738	−	0.388334i
$183$	−14.6969	+	10.0457i	−1.08642	+	0.742598i
$184$	5.86781	+	2.13571i	0.432581	+	0.157447i
$185$		0			0
$186$	−10.7214	+	2.74353i	−0.786130	+	0.201166i
$187$	15.3607	+	12.8891i	1.12328	+	0.942547i
$188$	−4.33215			−0.315954
$189$	4.93471	+	7.58115i	0.358947	+	0.551447i
$190$		0			0
$191$	−1.41048	−	1.18353i	−0.102059	−	0.0856373i	0.590331	−	0.807162i	$-0.298997\pi$
$191$	−1.41048	−	1.18353i	−0.102059	−	0.0856373i	−0.692389	+	0.721524i	$0.743442\pi$
$192$	2.02035	−	7.21353i	0.145806	−	0.520592i
$193$	−2.29931	−	13.0401i	−0.165508	−	0.938643i	−0.948539	−	0.316660i	$-0.897438\pi$
$193$	−2.29931	−	13.0401i	−0.165508	−	0.938643i	0.783031	−	0.621983i	$-0.213673\pi$
$194$	−23.9199	−	8.70613i	−1.71735	−	0.625064i
$195$		0			0
$196$	−0.418117	+	2.37126i	−0.0298655	+	0.169376i
$197$	−9.36409	+	16.2191i	−0.667164	+	1.15556i	0.311530	+	0.950236i	$0.399159\pi$
$197$	−9.36409	+	16.2191i	−0.667164	+	1.15556i	−0.978694	+	0.205325i	$0.934175\pi$
$198$	5.49046	−	14.0876i	0.390190	−	1.00116i
$199$	−3.20552	−	5.55213i	−0.227233	−	0.393580i	0.729754	−	0.683710i	$-0.239635\pi$
$199$	−3.20552	−	5.55213i	−0.227233	−	0.393580i	−0.956987	+	0.290130i	$0.906301\pi$
$200$		0			0
$201$	23.5011	+	2.32352i	1.65764	+	0.163888i
$202$	−7.92927	+	6.65345i	−0.557901	+	0.468135i
$203$	10.3495	−	8.68429i	0.726394	−	0.609517i
$204$	−6.71612	−	0.664011i	−0.470222	−	0.0464901i
$205$		0			0
$206$	5.84050	+	10.1160i	0.406927	+	0.704818i
$207$	8.23119	−	1.26061i	0.572107	−	0.0876186i
$208$	−4.58539	+	7.94212i	−0.317939	+	0.550687i
$209$	2.63993	−	14.9718i	0.182608	−	1.03562i
$210$		0			0
$211$	−15.3119	−	5.57306i	−1.05411	−	0.383665i	−0.243899	−	0.969801i	$-0.578426\pi$
$211$	−15.3119	−	5.57306i	−1.05411	−	0.383665i	−0.810213	+	0.586135i	$0.800649\pi$
$212$	0.196778	+	1.11598i	0.0135148	+	0.0766461i
$213$	−3.79675	+	13.5561i	−0.260149	+	0.928846i
$214$	−5.61131	−	4.70845i	−0.383581	−	0.321863i
$215$		0			0
$216$	−2.64166	−	11.3871i	−0.179742	−	0.774794i
$217$	−6.88951			−0.467690
$218$	9.46039	+	7.93821i	0.640739	+	0.537643i
$219$	16.5379	−	4.23194i	1.11753	−	0.285968i
$220$		0			0
$221$	−11.4248	−	4.15829i	−0.768516	−	0.279717i
$222$	1.87701	−	1.28299i	0.125977	−	0.0861085i
$223$	−3.25026	+	18.4332i	−0.217654	+	1.23438i	0.658588	+	0.752504i	$0.271154\pi$
$223$	−3.25026	+	18.4332i	−0.217654	+	1.23438i	−0.876242	+	0.481872i	$0.839957\pi$
$224$	−2.89269	+	5.01029i	−0.193276	+	0.334764i
$225$		0			0
$226$	2.71713	+	4.70621i	0.180741	+	0.313053i
$227$	−16.5040	+	6.00696i	−1.09541	+	0.398696i	−0.825622	−	0.564224i	$-0.809175\pi$
$227$	−16.5040	+	6.00696i	−1.09541	+	0.398696i	−0.269787	+	0.962920i	$0.586953\pi$
$228$	2.10999	+	4.66147i	0.139737	+	0.308714i
$229$	−5.79494	+	4.86253i	−0.382940	+	0.321325i	−0.813855	−	0.581067i	$-0.802635\pi$
$229$	−5.79494	+	4.86253i	−0.382940	+	0.321325i	0.430915	+	0.902392i	$0.358191\pi$
$230$		0			0
$231$	5.48545	−	7.64890i	0.360916	−	0.503261i
$232$	−16.4061	+	5.97133i	−1.07711	+	0.392037i
$233$	3.47331	+	6.01595i	0.227544	+	0.394118i	0.957080	−	0.289825i	$-0.0935971\pi$
$233$	3.47331	+	6.01595i	0.227544	+	0.394118i	−0.729536	+	0.683943i	$0.760264\pi$
$234$	−0.206829	+	9.16513i	−0.0135208	+	0.599143i
$235$		0			0
$236$	−0.108852	+	0.617330i	−0.00708566	+	0.0401848i
$237$	−1.95615	−	25.6943i	−0.127065	−	1.66902i
$238$	−16.9651	−	6.17478i	−1.09968	−	0.400252i
$239$	−3.56006	−	20.1901i	−0.230281	−	1.30599i	−0.852327	−	0.523009i	$-0.824809\pi$
$239$	−3.56006	−	20.1901i	−0.230281	−	1.30599i	0.622046	−	0.782981i	$-0.286302\pi$
$240$		0			0
$241$	−17.8973	−	15.0176i	−1.15287	−	0.967369i	−0.153083	−	0.988213i	$-0.548920\pi$
$241$	−17.8973	−	15.0176i	−1.15287	−	0.967369i	−0.999783	+	0.0208438i	$0.993365\pi$
$242$	2.02666			0.130279
$243$	−10.3837	−	11.6266i	−0.666117	−	0.745847i
$244$	−6.23459			−0.399129
$245$		0			0
$246$	−14.8040	−	15.1418i	−0.943867	−	0.965408i
$247$	1.60066	+	9.07779i	0.101847	+	0.577606i
$248$	8.36617	+	3.04504i	0.531252	+	0.193360i
$249$	−1.21286	−	15.9311i	−0.0768616	−	1.00959i
$250$		0			0
$251$	4.60669	−	7.97903i	0.290772	−	0.503632i	−0.683221	−	0.730212i	$-0.739421\pi$
$251$	4.60669	−	7.97903i	0.290772	−	0.503632i	0.973992	+	0.226580i	$0.0727546\pi$
$252$	−0.0714732	+	3.16716i	−0.00450239	+	0.199513i
$253$	−4.33242	−	7.50397i	−0.272377	−	0.471770i
$254$	27.0862	−	9.85857i	1.69954	−	0.618581i
$255$		0			0
$256$	10.2301	−	8.58408i	0.639381	−	0.536505i
$257$	19.7561	−	16.5773i	1.23235	−	1.03406i	0.234266	−	0.972172i	$-0.424731\pi$
$257$	19.7561	−	16.5773i	1.23235	−	1.03406i	0.998083	−	0.0618912i	$-0.0197132\pi$
$258$	−3.04028	−	6.71670i	−0.189279	−	0.418164i
$259$	1.33004	−	0.484094i	0.0826445	−	0.0300801i
$260$		0			0
$261$	−15.3642	+	17.4931i	−0.951018	+	1.08280i
$262$	−11.0346	+	19.1125i	−0.681719	+	1.18077i
$263$	3.97396	−	22.5375i	0.245045	−	1.38972i	−0.575343	−	0.817912i	$-0.695131\pi$
$263$	3.97396	−	22.5375i	0.245045	−	1.38972i	0.820388	−	0.571807i	$-0.193758\pi$
$264$	−10.0418	+	6.86386i	−0.618033	+	0.422441i
$265$		0			0
$266$	2.37687	+	13.4799i	0.145735	+	0.826507i
$267$	−21.0801	+	5.39425i	−1.29008	+	0.330123i
$268$	6.33567	+	5.31626i	0.387013	+	0.324742i
$269$	18.4780			1.12662			0.563311	−	0.826245i	$-0.309527\pi$
$269$	18.4780			1.12662			0.563311	+	0.826245i	$0.309527\pi$
$270$		0			0
$271$	4.64576			0.282210			0.141105	−	0.989995i	$-0.454935\pi$
$271$	4.64576			0.282210			0.141105	+	0.989995i	$0.454935\pi$
$272$	23.8419	+	20.0057i	1.44563	+	1.21302i
$273$	−1.53920	+	5.49560i	−0.0931563	+	0.332609i
$274$	3.90571	+	22.1504i	0.235953	+	1.33815i
$275$		0			0
$276$	2.62901	+	1.26223i	0.158248	+	0.0759772i
$277$	4.49325	−	25.4825i	0.269973	−	1.53109i	−0.484517	−	0.874782i	$-0.661005\pi$
$277$	4.49325	−	25.4825i	0.269973	−	1.53109i	0.754490	−	0.656311i	$-0.227884\pi$
$278$	14.4133	−	24.9645i	0.864450	−	1.49727i
$279$	11.7358	−	1.79735i	0.702605	−	0.107604i
$280$		0			0
$281$	10.1177	−	3.68254i	0.603572	−	0.219682i	−0.0221165	−	0.999755i	$-0.507040\pi$
$281$	10.1177	−	3.68254i	0.603572	−	0.219682i	0.625688	+	0.780073i	$0.284818\pi$
$282$	19.8742	+	1.96493i	1.18349	+	0.117010i
$283$	12.1469	−	10.1924i	0.722056	−	0.605877i	−0.205897	−	0.978574i	$-0.566011\pi$
$283$	12.1469	−	10.1924i	0.722056	−	0.605877i	0.927953	+	0.372697i	$0.121567\pi$
$284$	−3.77680	+	3.16911i	−0.224112	+	0.188052i
$285$		0			0
$286$	8.96393	−	3.26260i	0.530048	−	0.192922i
$287$	−6.59148	−	11.4168i	−0.389083	−	0.673911i
$288$	3.62042	−	9.28935i	0.213335	−	0.547380i
$289$	−12.1307	+	21.0110i	−0.713569	+	1.23594i
$290$		0			0
$291$	24.6181	+	11.8195i	1.44314	+	0.692873i
$292$	5.61793	+	2.04476i	0.328765	+	0.119661i
$293$	0.577683	+	3.27620i	0.0337486	+	0.191398i	0.997021	−	0.0771274i	$-0.0245748\pi$
$293$	0.577683	+	3.27620i	0.0337486	+	0.191398i	−0.963273	+	0.268525i	$0.913464\pi$
$294$	2.99369	−	10.6888i	0.174595	−	0.623382i
$295$		0			0
$296$	−1.82907			−0.106313
$297$	−7.34864	+	14.4605i	−0.426411	+	0.839081i
$298$	28.9998			1.67991
$299$	4.02459	+	3.37703i	0.232748	+	0.195299i
$300$		0			0
$301$	−0.797010	−	4.52007i	−0.0459389	−	0.260532i
$302$	−29.6548	−	10.7935i	−1.70644	−	0.621093i
$303$	9.16764	−	6.26632i	0.526667	−	0.359990i
$304$	4.09753	−	23.2382i	0.235009	−	1.33280i
$305$		0			0
$306$	30.5098	+	6.09245i	1.74413	+	0.348282i
$307$	−2.19929	−	3.80928i	−0.125520	−	0.217407i	0.796416	−	0.604749i	$-0.206727\pi$
$307$	−2.19929	−	3.80928i	−0.125520	−	0.217407i	−0.921936	+	0.387342i	$0.873393\pi$
$308$	3.09763	−	1.12745i	0.176504	−	0.0642422i
$309$	−5.16759	−	11.4164i	−0.293974	−	0.649459i
$310$		0			0
$311$	−11.8600	+	9.95173i	−0.672519	+	0.564311i	−0.913810	−	0.406142i	$-0.866874\pi$
$311$	−11.8600	+	9.95173i	−0.672519	+	0.564311i	0.241290	+	0.970453i	$0.422429\pi$
$312$	4.29805	−	5.99320i	0.243329	−	0.339298i
$313$	−10.1811	+	3.70561i	−0.575469	+	0.209454i	−0.613327	−	0.789829i	$-0.710169\pi$
$313$	−10.1811	+	3.70561i	−0.575469	+	0.209454i	0.0378572	+	0.999283i	$0.487947\pi$
$314$	−6.49430	−	11.2485i	−0.366495	−	0.634787i
$315$		0			0
$316$	4.51232	−	7.81556i	0.253838	−	0.439660i
$317$	1.83589	−	10.4118i	0.103114	−	0.584787i	−0.888843	−	0.458212i	$-0.848490\pi$
$317$	1.83589	−	10.4118i	0.103114	−	0.584787i	0.991957	−	0.126576i	$-0.0403987\pi$
$318$	−0.396565	−	5.20895i	−0.0222383	−	0.292104i
$319$	22.7654	+	8.28593i	1.27462	+	0.463923i
$320$		0			0
$321$	5.49369	+	5.61906i	0.306628	+	0.313626i
$322$	5.97624	+	5.01466i	0.333043	+	0.279456i
$323$	31.2831			1.74064
$324$	−0.704506	−	5.41370i	−0.0391392	−	0.300761i
$325$		0			0
$326$	6.52405	+	5.47433i	0.361334	+	0.303195i
$327$	−9.26209	−	9.47346i	−0.512195	−	0.523884i
$328$	2.95826	+	16.7771i	0.163342	+	0.926361i
$329$	11.6829	+	4.25225i	0.644102	+	0.234434i
$330$		0			0
$331$	−1.83100	+	10.3841i	−0.100641	+	0.570762i	0.892231	+	0.451578i	$0.149139\pi$
$331$	−1.83100	+	10.3841i	−0.100641	+	0.570762i	−0.992872	+	0.119184i	$0.961972\pi$
$332$	2.79774	−	4.84583i	0.153546	−	0.265950i
$333$	−2.13934	+	1.17160i	−0.117235	+	0.0642035i
$334$	13.3583	+	23.1372i	0.730931	+	1.26601i
$335$		0			0
$336$	8.51417	−	11.8721i	0.464486	−	0.647679i
$337$	−0.933557	+	0.783347i	−0.0508541	+	0.0426717i	−0.667860	−	0.744287i	$-0.732790\pi$
$337$	−0.933557	+	0.783347i	−0.0508541	+	0.0426717i	0.617006	+	0.786958i	$0.288345\pi$
$338$	11.6474	−	9.77330i	0.633533	−	0.531597i
$339$	−2.40408	−	5.31119i	−0.130572	−	0.288464i
$340$		0			0
$341$	−6.17705	−	10.6990i	−0.334506	−	0.579381i
$342$	−7.56551	−	22.3421i	−0.409096	−	1.20812i
$343$	9.54808	−	16.5378i	0.515548	−	0.892955i
$344$	−1.02995	+	5.84114i	−0.0555312	+	0.314933i
$345$		0			0
$346$	29.6775	+	10.8017i	1.59547	+	0.580703i
$347$	0.177046	+	1.00408i	0.00950431	+	0.0539016i	0.989191	−	0.146632i	$-0.0468434\pi$
$347$	0.177046	+	1.00408i	0.00950431	+	0.0539016i	−0.979687	+	0.200534i	$0.935732\pi$
$348$	−7.89934	+	2.02139i	−0.423449	+	0.108358i
$349$	−19.3802	−	16.2620i	−1.03740	−	0.870483i	−0.0456879	−	0.998956i	$-0.514548\pi$
$349$	−19.3802	−	16.2620i	−1.03740	−	0.870483i	−0.991713	+	0.128473i	$0.958992\pi$
$350$		0			0
$351$	1.18821	−	9.76293i	0.0634222	−	0.521107i
$352$	−10.3742			−0.552947
$353$	−11.2458	−	9.43633i	−0.598552	−	0.502245i	0.292428	−	0.956288i	$-0.405537\pi$
$353$	−11.2458	−	9.43633i	−0.598552	−	0.502245i	−0.890980	+	0.454043i	$0.849981\pi$
$354$	0.779373	−	2.78270i	0.0414232	−	0.147899i
$355$		0			0
$356$	−7.16091	−	2.60636i	−0.379527	−	0.138137i
$357$	17.4603	+	8.38295i	0.924096	+	0.443673i
$358$	−0.338747	+	1.92113i	−0.0179033	+	0.101535i
$359$	−11.7675	+	20.3820i	−0.621067	+	1.07572i	0.368221	+	0.929738i	$0.379967\pi$
$359$	−11.7675	+	20.3820i	−0.621067	+	1.07572i	−0.989287	+	0.145981i	$0.953366\pi$
$360$		0			0
$361$	−2.35891	−	4.08575i	−0.124153	−	0.215039i
$362$	31.0847	−	11.3139i	1.63378	−	0.594646i
$363$	−2.16368	−	0.213919i	−0.113564	−	0.0112278i
$364$	−1.53111	+	1.28475i	−0.0802517	+	0.0673392i
$365$		0			0
$366$	28.6019	+	2.82782i	1.49504	+	0.147812i
$367$	−23.4316	+	8.52841i	−1.22312	+	0.445180i	−0.871236	−	0.490864i	$-0.836681\pi$
$367$	−23.4316	+	8.52841i	−1.22312	+	0.445180i	−0.351884	+	0.936043i	$0.614459\pi$
$368$	−6.72451	−	11.6472i	−0.350539	−	0.607152i
$369$	14.2066	+	17.7281i	0.739565	+	0.922890i
$370$		0			0
$371$	0.564729	−	3.20274i	0.0293193	−	0.166278i
$372$	3.74837	+	1.79965i	0.194344	+	0.0933076i
$373$	12.0820	+	4.39750i	0.625584	+	0.227694i	0.635308	−	0.772259i	$-0.280873\pi$
$373$	12.0820	+	4.39750i	0.625584	+	0.227694i	−0.00972404	+	0.999953i	$0.503095\pi$
$374$	−5.62164	−	31.8819i	−0.290688	−	1.64857i
$375$		0			0
$376$	−12.3076	−	10.3273i	−0.634716	−	0.532590i
$377$	−14.6891			−0.756529
$378$	1.76442	−	14.4973i	0.0907520	−	0.745661i
$379$	3.07162			0.157779			0.0788894	−	0.996883i	$-0.474863\pi$
$379$	3.07162			0.157779			0.0788894	+	0.996883i	$0.474863\pi$
$380$		0			0
$381$	−29.9580	+	7.66606i	−1.53480	+	0.392744i
$382$	0.516201	+	2.92752i	0.0264112	+	0.149785i
$383$	6.80599	+	2.47718i	0.347770	+	0.126578i	0.509998	−	0.860175i	$-0.329646\pi$
$383$	6.80599	+	2.47718i	0.347770	+	0.126578i	−0.162229	+	0.986753i	$0.551868\pi$
$384$	−19.4890	+	13.3212i	−0.994542	+	0.679795i
$385$		0			0
$386$	−10.6889	+	18.5138i	−0.544053	+	0.942327i
$387$	2.53686	+	7.49171i	0.128956	+	0.380825i
$388$	4.78195	+	8.28258i	0.242767	+	0.420484i
$389$	−6.63847	+	2.41621i	−0.336584	+	0.122507i	−0.504782	−	0.863247i	$-0.668427\pi$
$389$	−6.63847	+	2.41621i	−0.336584	+	0.122507i	0.168198	+	0.985753i	$0.446205\pi$
$390$		0			0
$391$	13.6585	−	11.4608i	0.690738	−	0.579598i
$392$	−6.84065	+	5.73999i	−0.345505	+	0.289913i
$393$	13.7980	−	19.2399i	0.696016	−	0.970524i
$394$	28.4131	−	10.3415i	1.43143	−	0.520998i
$395$		0			0
$396$	−4.98248	+	2.72865i	−0.250379	+	0.137120i
$397$	12.9728	−	22.4696i	0.651088	−	1.12772i	−0.331771	−	0.943360i	$-0.607646\pi$
$397$	12.9728	−	22.4696i	0.651088	−	1.12772i	0.982859	−	0.184358i	$-0.0590206\pi$
$398$	−1.79736	+	10.1933i	−0.0900936	+	0.510946i
$399$	−1.11473	−	14.6421i	−0.0558062	−	0.733024i
$400$		0			0
$401$	2.29238	+	13.0007i	0.114476	+	0.649226i	0.987008	+	0.160670i	$0.0513654\pi$
$401$	2.29238	+	13.0007i	0.114476	+	0.649226i	−0.872532	+	0.488557i	$0.837524\pi$
$402$	−26.6543	−	27.2626i	−1.32940	−	1.35974i
$403$	5.73815	+	4.81488i	0.285838	+	0.239846i
$404$	3.88903			0.193486
$405$		0			0
$406$	−21.8124			−1.08253
$407$	1.94426	+	1.63143i	0.0963734	+	0.0808669i
$408$	−17.4975	−	17.8968i	−0.866256	−	0.886026i
$409$	−2.60351	−	14.7653i	−0.128735	−	0.730095i	−0.979019	−	0.203770i	$-0.934681\pi$
$409$	−2.60351	−	14.7653i	−0.128735	−	0.730095i	0.850283	−	0.526325i	$-0.176430\pi$
$410$		0			0
$411$	−1.83174	−	24.0602i	−0.0903529	−	1.18680i
$412$	0.762100	−	4.32208i	0.0375460	−	0.212934i
$413$	0.899496	−	1.55797i	0.0442613	−	0.0766628i
$414$	−11.4884	−	6.98305i	−0.564623	−	0.343198i
$415$		0			0
$416$	5.91082	−	2.15136i	0.289802	−	0.105479i
$417$	−18.0228	+	25.1309i	−0.882579	+	1.23067i
$418$	−18.8024	+	15.7771i	−0.919654	+	0.771681i
$419$	21.5326	−	18.0680i	1.05194	−	0.882681i	0.0586424	−	0.998279i	$-0.481323\pi$
$419$	21.5326	−	18.0680i	1.05194	−	0.882681i	0.993296	+	0.115598i	$0.0368784\pi$
$420$		0			0
$421$	26.6729	−	9.70814i	1.29996	−	0.473146i	0.402974	−	0.915211i	$-0.367976\pi$
$421$	26.6729	−	9.70814i	1.29996	−	0.473146i	0.896983	+	0.442066i	$0.145754\pi$
$422$	13.1537	+	22.7829i	0.640313	+	1.10906i
$423$	−21.0105	−	4.19555i	−1.02156	−	0.203995i
$424$	−2.10132	+	3.63959i	−0.102049	+	0.176754i
$425$		0			0
$426$	18.7639	−	12.8256i	0.909114	−	0.621403i
$427$	16.8135	+	6.11960i	0.813660	+	0.296148i
$428$	0.477906	+	2.71034i	0.0231004	+	0.131009i
$429$	−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	$0.433053\pi$
$432$	−11.4061	+	22.4446i	−0.548776	+	1.07987i
$433$	8.61185			0.413859			0.206929	−	0.978356i	$-0.433653\pi$
$433$	8.61185			0.413859			0.206929	+	0.978356i	$0.433653\pi$
$434$	8.52077	+	7.14978i	0.409010	+	0.343200i
$435$		0			0
$436$	−0.805725	−	4.56949i	−0.0385872	−	0.218839i
$437$	−12.7028	−	4.62344i	−0.607657	−	0.221169i
$438$	−24.8455	−	11.9287i	−1.18716	−	0.569975i
$439$	−2.79044	+	15.8254i	−0.133181	+	0.755305i	0.842929	+	0.538025i	$0.180829\pi$
$439$	−2.79044	+	15.8254i	−0.133181	+	0.755305i	−0.976109	+	0.217280i	$0.930282\pi$
$440$		0			0
$441$	−4.32431	+	11.0954i	−0.205919	+	0.528353i
$442$	9.81454	+	16.9993i	0.466830	+	0.808573i
$443$	8.68429	−	3.16082i	0.412603	−	0.150175i	−0.127374	−	0.991855i	$-0.540655\pi$
$443$	8.68429	−	3.16082i	0.412603	−	0.150175i	0.539977	+	0.841679i	$0.318433\pi$
$444$	−0.850086	−	0.0840465i	−0.0403433	−	0.00398867i
$445$		0			0
$446$	23.1494	−	19.4246i	1.09615	−	0.919782i
$447$	−30.9604	−	3.06100i	−1.46438	−	0.144780i
$448$	−7.07511	+	2.57513i	−0.334268	+	0.121663i
$449$	18.5220	+	32.0810i	0.874106	+	1.51400i	0.857713	+	0.514130i	$0.171885\pi$
$449$	18.5220	+	32.0810i	0.874106	+	1.51400i	0.0163930	+	0.999866i	$0.494782\pi$
$450$		0			0
$451$	11.8197	−	20.4723i	0.556567	−	0.964002i
$452$	0.354546	−	2.01073i	0.0166764	−	0.0945768i
$453$	30.5204	+	14.6533i	1.43397	+	0.688472i
$454$	26.6456	+	9.69821i	1.25054	+	0.455160i
$455$		0			0
$456$	−5.11791	+	18.2732i	−0.239668	+	0.855719i
$457$	−1.04395	−	0.875976i	−0.0488338	−	0.0409764i	0.618044	−	0.786143i	$-0.287925\pi$
$457$	−1.04395	−	0.875976i	−0.0488338	−	0.0409764i	−0.666878	+	0.745167i	$0.732370\pi$
$458$	12.2133			0.570688
$459$	−31.9294	−	9.72473i	−1.49034	−	0.453912i
$460$		0			0
$461$	−6.41944	−	5.38655i	−0.298983	−	0.250876i	0.480938	−	0.876755i	$-0.340296\pi$
$461$	−6.41944	−	5.38655i	−0.298983	−	0.250876i	−0.779921	+	0.625878i	$0.784741\pi$
$462$	−14.7221	+	3.76730i	−0.684935	+	0.175271i
$463$	4.96946	+	28.1832i	0.230950	+	1.30978i	0.850977	+	0.525203i	$0.176011\pi$
$463$	4.96946	+	28.1832i	0.230950	+	1.30978i	−0.620027	+	0.784581i	$0.712878\pi$
$464$	35.3350	+	12.8609i	1.64039	+	0.597052i
$465$		0			0
$466$	1.94751	−	11.0449i	0.0902168	−	0.511645i
$467$	−1.15409	+	1.99894i	−0.0534049	+	0.0925000i	−0.891492	−	0.453036i	$-0.850341\pi$
$467$	−1.15409	+	1.99894i	−0.0534049	+	0.0925000i	0.838087	+	0.545536i	$0.183674\pi$
$468$	2.27297	−	2.58792i	0.105068	−	0.119627i
$469$	−11.8679	−	20.5557i	−0.548006	−	0.949175i
$470$		0			0
$471$	5.74606	+	12.6944i	0.264765	+	0.584928i
$472$	−1.78089	+	1.49434i	−0.0819719	+	0.0687826i
$473$	6.30479	−	5.29034i	0.289894	−	0.243250i
$474$	−24.2457	+	33.8081i	−1.11364	+	1.55286i
$475$		0			0
$476$	3.39158	+	5.87438i	0.155453	+	0.269252i
$477$	−0.126442	+	5.60298i	−0.00578938	+	0.256543i
$478$	−16.5498	+	28.6652i	−0.756972	+	1.31111i
$479$	−0.150408	+	0.853009i	−0.00687234	+	0.0389750i	−0.988051	−	0.154127i	$-0.950744\pi$
$479$	−0.150408	+	0.853009i	−0.00687234	+	0.0389750i	0.981179	+	0.193102i	$0.0618547\pi$
$480$		0			0
$481$	−1.44608	−	0.526331i	−0.0659357	−	0.0239986i
$482$	6.54999	+	37.1468i	0.298344	+	1.69199i
$483$	−5.85097	−	5.98450i	−0.266228	−	0.272304i
$484$	−0.583306	−	0.489452i	−0.0265139	−	0.0222478i
$485$		0			0
$486$	0.776512	+	25.1555i	0.0352233	+	1.14108i
$487$	20.4700			0.927584			0.463792	−	0.885944i	$-0.346488\pi$
$487$	20.4700			0.927584			0.463792	+	0.885944i	$0.346488\pi$
$488$	−17.7124	−	14.8625i	−0.801803	−	0.672793i
$489$	−6.38730	−	6.53307i	−0.288844	−	0.295435i
$490$		0			0
$491$	−40.3022	−	14.6688i	−1.81881	−	0.661993i	−0.995539	−	0.0943459i	$-0.969924\pi$
$491$	−40.3022	−	14.6688i	−1.81881	−	0.661993i	−0.823272	−	0.567647i	$-0.807854\pi$
$492$	0.603976	+	7.93333i	0.0272293	+	0.357662i
$493$	−8.65659	+	49.0940i	−0.389873	+	2.21108i
$494$	7.44107	−	12.8883i	0.334790	−	0.579872i
$495$		0			0
$496$	−9.58763	−	16.6063i	−0.430497	−	0.745643i
$497$	13.2959	−	4.83932i	0.596404	−	0.217073i
$498$	−15.0329	+	20.9618i	−0.673639	+	0.939322i
$499$	4.70186	−	3.94533i	0.210484	−	0.176617i	−0.531451	−	0.847089i	$-0.678353\pi$
$499$	4.70186	−	3.94533i	0.210484	−	0.176617i	0.741935	+	0.670472i	$0.233908\pi$
$500$		0			0
$501$	−11.8192	−	26.1114i	−0.528042	−	1.16657i
$502$	−13.9779	+	5.08754i	−0.623864	+	0.227068i
$503$	−3.43713	−	5.95329i	−0.153254	−	0.265444i	0.779168	−	0.626815i	$-0.215642\pi$
$503$	−3.43713	−	5.95329i	−0.153254	−	0.265444i	−0.932422	+	0.361371i	$0.882309\pi$
$504$	−7.75318	+	8.82751i	−0.345354	+	0.393208i
$505$		0			0
$506$	−2.42922	+	13.7768i	−0.107992	+	0.612454i
$507$	−13.4664	+	9.20464i	−0.598064	+	0.408792i
$508$	−10.1768	−	3.70404i	−0.451521	−	0.164340i
$509$	−2.31722	−	13.1416i	−0.102709	−	0.582493i	−0.992111	−	0.125366i	$-0.959990\pi$
$509$	−2.31722	−	13.1416i	−0.102709	−	0.582493i	0.889401	−	0.457127i	$-0.151122\pi$
$510$		0			0
$511$	−13.1434	−	11.0286i	−0.581430	−	0.487878i
$512$	5.69791			0.251815
$513$	5.71874	+	24.6511i	0.252488	+	1.08837i
$514$	−41.6373			−1.83654
$515$		0			0
$516$	−0.747087	+	2.66743i	−0.0328887	+	0.117427i
$517$	3.87133	+	21.9554i	0.170261	+	0.965596i
$518$	−2.14734	−	0.781567i	−0.0943486	−	0.0343401i
$519$	−30.5437	−	14.6645i	−1.34072	−	0.643701i
$520$		0			0
$521$	−12.2664	+	21.2461i	−0.537401	+	0.930807i	0.461642	+	0.887067i	$0.347261\pi$
$521$	−12.2664	+	21.2461i	−0.537401	+	0.930807i	−0.999043	+	0.0437400i	$0.986073\pi$
$522$	37.1560	−	5.69046i	1.62627	−	0.249065i
$523$	19.7850	+	34.2687i	0.865140	+	1.49847i	0.866908	+	0.498468i	$0.166104\pi$
$523$	19.7850	+	34.2687i	0.865140	+	1.49847i	−0.00176851	+	0.999998i	$0.500563\pi$
$524$	7.79172	−	2.83595i	0.340383	−	0.123889i
$525$		0			0
$526$	−28.3038	+	23.7497i	−1.23410	+	1.03554i
$527$	19.4739	−	16.3405i	0.848295	−	0.711804i
$528$	26.0704	+	2.57753i	1.13457	+	0.112173i
$529$	14.3729	−	5.23132i	0.624911	−	0.227449i
$530$		0			0
$531$	−1.12578	+	2.88857i	−0.0488549	+	0.125353i
$532$	2.57139	−	4.45377i	0.111484	−	0.193095i
$533$	−2.48893	+	14.1154i	−0.107808	+	0.611407i
$534$	31.6693	+	15.2049i	1.37047	+	0.657982i
$535$		0			0
$536$	5.32629	+	30.2069i	0.230061	+	1.30474i
$537$	0.564429	−	2.01526i	0.0243569	−	0.0869648i
$538$	−22.8531	−	19.1760i	−0.985267	−	0.826737i
$539$	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	$0.257530\pi$
$542$	−5.74576	−	4.82126i	−0.246801	−	0.207091i
$543$	−34.3805	+	8.79775i	−1.47541	+	0.377548i
$544$	−3.70692	−	21.0230i	−0.158933	−	0.901352i
$545$		0			0
$546$	7.60684	−	5.19947i	0.325543	−	0.222517i
$547$	3.82427	−	21.6885i	0.163514	−	0.927333i	−0.787070	−	0.616864i	$-0.788403\pi$
$547$	3.82427	−	21.6885i	0.163514	−	0.927333i	0.950583	−	0.310469i	$-0.100486\pi$
$548$	4.22534	−	7.31850i	0.180497	−	0.312631i
$549$	−30.2371	−	6.03800i	−1.29049	−	0.257696i
$550$		0			0
$551$	35.5163	−	12.9269i	1.51305	−	0.550704i
$552$	4.46000	+	9.85321i	0.189830	+	0.419380i
$553$	−19.8402	+	16.6479i	−0.843693	+	0.707942i
$554$	−32.0023	+	26.8531i	−1.35965	+	1.14088i
$555$		0			0
$556$	−10.1775	+	3.70429i	−0.431621	+	0.157097i
$557$	−11.1210	−	19.2621i	−0.471212	−	0.816163i	0.528246	−	0.849092i	$-0.322850\pi$
$557$	−11.1210	−	19.2621i	−0.471212	−	0.816163i	−0.999458	+	0.0329284i	$0.989517\pi$
$558$	−16.3798	−	9.95625i	−0.693413	−	0.421482i
$559$	−2.49513	+	4.32169i	−0.105533	+	0.182788i
$560$		0			0
$561$	2.63649	+	34.6307i	0.111313	+	1.46211i
$562$	−16.3350	−	5.94545i	−0.689050	−	0.250794i
$563$	−2.45892	−	13.9452i	−0.103631	−	0.587721i	−0.991758	−	0.128123i	$-0.959105\pi$
$563$	−2.45892	−	13.9452i	−0.103631	−	0.587721i	0.888127	−	0.459598i	$-0.152006\pi$
$564$	−5.24558	−	5.36529i	−0.220879	−	0.225920i
$565$		0			0
$566$	−25.6004			−1.07607
$567$	−3.41394	+	15.2912i	−0.143372	+	0.642170i
$568$	−18.2846			−0.767205
$569$	−4.81198	−	4.03773i	−0.201729	−	0.169270i	0.536327	−	0.844010i	$-0.319811\pi$
$569$	−4.81198	−	4.03773i	−0.201729	−	0.169270i	−0.738056	+	0.674740i	$0.764256\pi$
$570$		0			0
$571$	−5.42129	−	30.7457i	−0.226874	−	1.28667i	−0.859070	−	0.511858i	$-0.828957\pi$
$571$	−5.42129	−	30.7457i	−0.226874	−	1.28667i	0.632196	−	0.774809i	$-0.282154\pi$
$572$	−3.36790	−	1.22582i	−0.140819	−	0.0512540i
$573$	−0.242093	−	3.17993i	−0.0101136	−	0.132844i
$574$	−3.69590	+	20.9605i	−0.154264	+	0.874873i
$575$		0			0
$576$	11.3802	−	6.23233i	0.474174	−	0.259680i
$577$	−9.13906	−	15.8293i	−0.380464	−	0.658983i	0.610664	−	0.791889i	$-0.290902\pi$
$577$	−9.13906	−	15.8293i	−0.380464	−	0.658983i	−0.991129	+	0.132906i	$0.957569\pi$
$578$	36.8076	−	13.3969i	1.53100	−	0.557237i
$579$	13.3658	−	18.6372i	0.555462	−	0.774536i
$580$		0			0
$581$	−12.3014	+	10.3221i	−0.510349	+	0.428233i
$582$	−18.1810	−	40.1662i	−0.753627	−	1.66494i
$583$	5.47997	−	1.99455i	0.226957	−	0.0826057i
$584$	11.0860	+	19.2016i	0.458744	+	0.794568i
$585$		0			0
$586$	2.68551	−	4.65143i	0.110937	−	0.192149i
$587$	1.42984	−	8.10900i	0.0590156	−	0.334694i	−0.940977	−	0.338470i	$-0.890091\pi$
$587$	1.42984	−	8.10900i	0.0590156	−	0.334694i	0.999993	+	0.00377558i	$0.00120181\pi$
$588$	−3.44304	+	2.35341i	−0.141989	+	0.0970529i
$589$	−18.1113	−	6.59198i	−0.746263	−	0.271618i
$590$		0			0
$591$	−31.4256	+	8.04160i	−1.29268	+	0.330787i
$592$	3.01776	+	2.53220i	0.124029	+	0.104073i
$593$	−38.8812			−1.59666			−0.798329	−	0.602222i	$-0.794282\pi$
$593$	−38.8812			−1.59666			−0.798329	+	0.602222i	$0.794282\pi$
$594$	24.0953	−	10.2581i	0.988644	−	0.420894i
$595$		0			0
$596$	−8.34661	−	7.00364i	−0.341890	−	0.286880i
$597$	2.99481	−	10.6928i	0.122569	−	0.437626i
$598$	−1.47290	−	8.35325i	−0.0602315	−	0.341590i
$599$	0.729650	+	0.265571i	0.0298127	+	0.0108509i	0.356883	−	0.934149i	$-0.383839\pi$
$599$	0.729650	+	0.265571i	0.0298127	+	0.0108509i	−0.327071	+	0.945000i	$0.606062\pi$
$600$		0			0
$601$	−4.46708	+	25.3341i	−0.182216	+	1.03340i	0.747265	+	0.664527i	$0.231367\pi$
$601$	−4.46708	+	25.3341i	−0.182216	+	1.03340i	−0.929481	+	0.368871i	$0.879744\pi$
$602$	−3.70510	+	6.41743i	−0.151009	+	0.261555i
$603$	25.5787	+	31.9192i	1.04165	+	1.29985i
$604$	5.92844	+	10.2684i	0.241225	+	0.417813i
$605$		0			0
$606$	−17.8413	−	1.76394i	−0.724755	−	0.0716553i
$607$	5.10054	−	4.27987i	0.207025	−	0.173714i	−0.533380	−	0.845876i	$-0.679078\pi$
$607$	5.10054	−	4.27987i	0.207025	−	0.173714i	0.740405	+	0.672161i	$0.234634\pi$
$608$	−12.3983	+	10.4034i	−0.502817	+	0.421914i
$609$	23.2871	+	2.30235i	0.943640	+	0.0932961i
$610$		0			0
$611$	−6.75875	−	11.7065i	−0.273430	−	0.473594i
$612$	−7.30985	−	9.12182i	−0.295483	−	0.368728i
$613$	16.4901	−	28.5617i	0.666030	−	1.15360i	−0.312975	−	0.949761i	$-0.601326\pi$
$613$	16.4901	−	28.5617i	0.666030	−	1.15360i	0.979005	−	0.203837i	$-0.0653412\pi$
$614$	−1.23316	+	6.99359i	−0.0497662	+	0.282238i
$615$		0			0
$616$	11.4880	+	4.18131i	0.462867	+	0.168470i
$617$	6.36077	+	36.0737i	0.256075	+	1.45227i	0.793298	+	0.608834i	$0.208362\pi$
$617$	6.36077	+	36.0737i	0.256075	+	1.45227i	−0.537223	+	0.843440i	$0.680527\pi$
$618$	−5.45658	+	19.4824i	−0.219496	+	0.783696i
$619$	10.7534	+	9.02320i	0.432217	+	0.362673i	0.832787	−	0.553593i	$-0.186744\pi$
$619$	10.7534	+	9.02320i	0.432217	+	0.362673i	−0.400571	+	0.916266i	$0.631188\pi$
$620$		0			0
$621$	11.5280	+	8.66779i	0.462602	+	0.347826i
$622$	24.9958			1.00224
$623$	16.7533	+	14.0577i	0.671206	+	0.563208i
$624$	−15.3884	+	3.93779i	−0.616029	+	0.157638i
$625$		0			0
$626$	16.4373	+	5.98270i	0.656967	+	0.239117i
$627$	21.7389	−	14.8591i	0.868166	−	0.593414i
$628$	−0.847411	+	4.80591i	−0.0338154	+	0.191777i
$629$	−2.61131	+	4.52292i	−0.104120	+	0.180340i
$630$		0			0
$631$	1.61405	+	2.79562i	0.0642543	+	0.111292i	0.896363	−	0.443321i	$-0.146200\pi$
$631$	1.61405	+	2.79562i	0.0642543	+	0.111292i	−0.832109	+	0.554613i	$0.812866\pi$
$632$	31.4508	−	11.4471i	1.25104	−	0.455343i
$633$	−11.6382	−	25.7116i	−0.462578	−	1.02195i
$634$	−13.0758	+	10.9719i	−0.519305	+	0.435748i
$635$		0			0
$636$	−1.14386	+	1.59500i	−0.0453569	+	0.0632457i
$637$	−7.06002	+	2.56964i	−0.279728	+	0.101813i
$638$	−19.5567	−	33.8732i	−0.774258	−	1.34105i
$639$	−21.3863	+	11.7121i	−0.846027	+	0.463325i
$640$		0			0
$641$	−1.01704	+	5.76795i	−0.0401709	+	0.227820i	−0.998283	−	0.0585725i	$-0.981345\pi$
$641$	−1.01704	+	5.76795i	−0.0401709	+	0.227820i	0.958112	+	0.286393i	$0.0924562\pi$
$642$	−0.963120	−	12.6507i	−0.0380113	−	0.499285i
$643$	15.6152	+	5.68345i	0.615802	+	0.224134i	0.631040	−	0.775750i	$-0.282628\pi$
$643$	15.6152	+	5.68345i	0.615802	+	0.224134i	−0.0152381	+	0.999884i	$0.504851\pi$
$644$	−0.508986	−	2.88660i	−0.0200569	−	0.113748i
$645$		0			0
$646$	−38.6901	−	32.4648i	−1.52224	−	1.27731i
$647$	5.31018			0.208765			0.104382	−	0.994537i	$-0.466713\pi$
$647$	5.31018			0.208765			0.104382	+	0.994537i	$0.466713\pi$
$648$	10.9041	−	17.0597i	0.428353	−	0.670170i
$649$	3.22591			0.126628
$650$		0			0
$651$	−8.34216	−	8.53254i	−0.326955	−	0.334417i
$652$	−0.555642	−	3.15120i	−0.0217606	−	0.123411i
$653$	−23.6382	−	8.60359i	−0.925034	−	0.336685i	−0.164794	−	0.986328i	$-0.552696\pi$
$653$	−23.6382	−	8.60359i	−0.925034	−	0.336685i	−0.760239	+	0.649643i	$0.774918\pi$
$654$	1.62377	+	21.3285i	0.0634945	+	0.834011i
$655$		0			0
$656$	18.3458	−	31.7758i	0.716282	−	1.24064i
$657$	25.2661	+	15.3577i	0.985724	+	0.599159i
$658$	−10.0363	−	17.3834i	−0.391255	−	0.677674i
$659$	0.253053	−	0.0921038i	0.00985755	−	0.00358786i	−0.337087	−	0.941474i	$-0.609442\pi$
$659$	0.253053	−	0.0921038i	0.00985755	−	0.00358786i	0.346944	+	0.937886i	$0.387219\pi$
$660$		0			0
$661$	−17.1827	+	14.4180i	−0.668329	+	0.560795i	−0.912570	−	0.408920i	$-0.865906\pi$
$661$	−17.1827	+	14.4180i	−0.668329	+	0.560795i	0.244241	+	0.969714i	$0.421461\pi$
$662$	13.0409	−	10.9426i	0.506850	−	0.425298i
$663$	−8.68376	−	19.1845i	−0.337249	−	0.745064i
$664$	19.5002	−	7.09750i	0.756755	−	0.275436i
$665$		0			0
$666$	3.86174	+	0.771146i	0.149640	+	0.0298813i
$667$	10.7709	−	18.6557i	0.417050	−	0.722352i
$668$	1.74306	−	9.88537i	0.0674409	−	0.382476i
$669$	−26.7647	+	18.2944i	−1.03478	+	0.707302i
$670$		0			0
$671$	5.57140	+	31.5970i	0.215081	+	1.21979i
$672$	−9.70778	+	2.48416i	−0.374486	+	0.0958285i
$673$	−12.7839	−	10.7270i	−0.492784	−	0.413494i	0.362239	−	0.932085i	$-0.382012\pi$
$673$	−12.7839	−	10.7270i	−0.492784	−	0.413494i	−0.855023	+	0.518591i	$0.826457\pi$
$674$	1.96754			0.0757868
$675$		0			0
$676$	−5.71262			−0.219716
$677$	22.7606	+	19.0984i	0.874762	+	0.734012i	0.965095	−	0.261899i	$-0.0843489\pi$
$677$	22.7606	+	19.0984i	0.874762	+	0.734012i	−0.0903336	+	0.995912i	$0.528793\pi$
$678$	−2.53853	+	9.06364i	−0.0974915	+	0.348087i
$679$	−4.76616	−	27.0302i	−0.182908	−	1.03733i
$680$		0			0
$681$	−27.4234	−	13.1664i	−1.05087	−	0.504537i
$682$	−3.46352	+	19.6426i	−0.132625	+	0.752154i
$683$	6.26849	−	10.8573i	0.239857	−	0.415445i	−0.720816	−	0.693126i	$-0.756233\pi$
$683$	6.26849	−	10.8573i	0.239857	−	0.415445i	0.960673	+	0.277682i	$0.0895661\pi$
$684$	−3.21828	+	8.25753i	−0.123054	+	0.315735i
$685$		0			0
$686$	−28.9713	+	10.5447i	−1.10613	+	0.402599i
$687$	−13.0390	−	1.28914i	−0.497467	−	0.0491838i
$688$	9.78590	−	8.21134i	0.373084	−	0.313054i
$689$	−2.70865	+	2.27283i	−0.103191	+	0.0865879i
$690$		0			0
$691$	−6.85438	+	2.49479i	−0.260753	+	0.0949064i	−0.469089	−	0.883151i	$-0.655418\pi$
$691$	−6.85438	+	2.49479i	−0.260753	+	0.0949064i	0.208336	+	0.978057i	$0.433195\pi$
$692$	−5.93297	−	10.2762i	−0.225538	−	0.390643i
$693$	16.1151	−	2.46804i	0.612162	−	0.0937530i
$694$	0.823042	−	1.42555i	0.0312422	−	0.0541131i
$695$		0			0
$696$	−27.2607	−	13.0883i	−1.03331	−	0.496110i
$697$	45.7098	+	16.6370i	1.73138	+	0.630171i
$698$	7.09271	+	40.2248i	0.268463	+	1.52253i
$699$	−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	$0.561659\pi$
$702$	−11.6013	+	10.8414i	−0.437863	+	0.409184i
$703$	3.95962			0.149340
$704$	−10.3425	−	8.67836i	−0.389796	−	0.327078i
$705$		0			0
$706$	4.11569	+	23.3412i	0.154896	+	0.878459i
$707$	−10.4879	−	3.81730i	−0.394439	−	0.143564i
$708$	−0.896357	+	0.612683i	−0.0336871	+	0.0230260i
$709$	3.06522	−	17.3837i	0.115117	−	0.652860i	−0.871575	−	0.490261i	$-0.836901\pi$
$709$	3.06522	−	17.3837i	0.115117	−	0.652860i	0.986692	−	0.162599i	$-0.0519876\pi$
$710$		0			0
$711$	29.4534	−	33.5346i	1.10459	−	1.25765i
$712$	−14.1309	−	24.4754i	−0.529576	−	0.917253i
$713$	−10.3226	+	3.75711i	−0.386584	+	0.140705i
$714$	−12.8948	−	28.4877i	−0.482576	−	1.06613i
$715$		0			0
$716$	0.561463	−	0.471123i	0.0209828	−	0.0176067i
$717$	20.6944	−	28.8563i	0.772847	−	1.07766i
$718$	35.7057	−	12.9958i	1.33253	−	0.485000i
$719$	1.57416	+	2.72652i	0.0587062	+	0.101682i	0.893885	−	0.448297i	$-0.147969\pi$
$719$	1.57416	+	2.72652i	0.0587062	+	0.101682i	−0.835179	+	0.549979i	$0.814636\pi$
$720$		0			0
$721$	−6.29760	+	10.9078i	−0.234535	+	0.406226i
$722$	−1.32266	+	7.50117i	−0.0492242	+	0.279165i
$723$	−3.07187	−	40.3496i	−0.114244	−	1.50062i
$724$	−11.6791	−	4.25084i	−0.434050	−	0.157981i
$725$		0			0
$726$	2.45398	+	2.50999i	0.0910759	+	0.0931544i
$727$	−25.1799	−	21.1284i	−0.933869	−	0.783609i	0.0426388	−	0.999091i	$-0.486424\pi$
$727$	−25.1799	−	21.1284i	−0.933869	−	0.783609i	−0.976508	+	0.215481i	$0.930868\pi$
$728$	−7.41254			−0.274727
$729$	1.82622	−	26.9382i	0.0676377	−	0.997710i
$730$		0			0
$731$	12.9735	+	10.8861i	0.479843	+	0.402636i
$732$	−7.54915	−	7.72143i	−0.279025	−	0.285392i
$733$	−1.20830	−	6.85262i	−0.0446297	−	0.253107i	0.954328	−	0.298762i	$-0.0965737\pi$
$733$	−1.20830	−	6.85262i	−0.0446297	−	0.253107i	−0.998957	+	0.0456547i	$0.985463\pi$
$734$	37.8302	+	13.7691i	1.39634	+	0.508226i
$735$		0			0
$736$	−1.60183	+	9.08444i	−0.0590443	+	0.334857i
$737$	21.2811	−	36.8600i	0.783901	−	1.35776i
$738$	0.827507	−	36.6690i	0.0304609	−	1.34980i
$739$	3.80631	+	6.59273i	0.140017	+	0.242517i	0.927503	−	0.373816i	$-0.121951\pi$
$739$	3.80631	+	6.59273i	0.140017	+	0.242517i	−0.787485	+	0.616333i	$0.788617\pi$
$740$		0			0
$741$	−9.30453	+	12.9742i	−0.341811	+	0.476620i
$742$	−4.02217	+	3.37500i	−0.147658	+	0.123900i
$743$	2.40844	−	2.02092i	0.0883571	−	0.0741404i	−0.597539	−	0.801840i	$-0.703855\pi$
$743$	2.40844	−	2.02092i	0.0883571	−	0.0741404i	0.685896	+	0.727699i	$0.259410\pi$
$744$	6.35895	+	14.0485i	0.233130	+	0.515041i
$745$		0			0
$746$	−10.3791	−	17.9772i	−0.380007	−	0.658191i
$747$	18.2618	−	20.7922i	0.668164	−	0.760749i
$748$	−6.08169	+	10.5338i	−0.222369	+	0.385154i
$749$	1.37153	−	7.77834i	0.0501146	−	0.284214i
$750$		0			0
$751$	4.55689	+	1.65857i	0.166283	+	0.0605222i	0.423821	−	0.905746i	$-0.360689\pi$
$751$	4.55689	+	1.65857i	0.166283	+	0.0605222i	−0.257537	+	0.966268i	$0.582911\pi$
$752$	6.00883	+	34.0778i	0.219119	+	1.24269i
$753$	15.4599	−	3.95609i	0.563390	−	0.144168i
$754$	18.1672	+	15.2441i	0.661609	+	0.555156i
$755$		0			0
$756$	−4.00902	+	3.74644i	−0.145807	+	0.136257i
$757$	−16.2063			−0.589028			−0.294514	−	0.955647i	$-0.595158\pi$
$757$	−16.2063			−0.589028			−0.294514	+	0.955647i	$0.595158\pi$
$758$	−3.79891	−	3.18766i	−0.137983	−	0.115781i
$759$	4.04763	−	14.4518i	0.146920	−	0.524567i
$760$		0			0
$761$	−37.9046	−	13.7961i	−1.37404	−	0.500110i	−0.453674	−	0.891168i	$-0.649887\pi$
$761$	−37.9046	−	13.7961i	−1.37404	−	0.500110i	−0.920366	+	0.391058i	$0.872109\pi$
$762$	45.0070	+	21.6086i	1.63043	+	0.782795i
$763$	−2.31233	+	13.1139i	−0.0837121	+	0.474755i
$764$	0.558445	−	0.967255i	0.0202038	−	0.0349941i
$765$		0			0
$766$	−5.84672	−	10.1268i	−0.211250	−	0.365896i
$767$	−1.83800	+	0.668976i	−0.0663662	+	0.0241553i
$768$	23.0184	+	2.27579i	0.830604	+	0.0821204i
$769$	8.23144	−	6.90700i	0.296833	−	0.249073i	−0.482191	−	0.876066i	$-0.660159\pi$
$769$	8.23144	−	6.90700i	0.296833	−	0.249073i	0.779025	+	0.626993i	$0.215715\pi$
$770$		0			0
$771$	44.4523	+	4.39493i	1.60091	+	0.158279i
$772$	7.54765	−	2.74712i	0.271646	−	0.0988711i
$773$	27.2618	+	47.2189i	0.980540	+	1.69835i	0.660286	+	0.751014i	$0.270435\pi$
$773$	27.2618	+	47.2189i	0.980540	+	1.69835i	0.320254	+	0.947332i	$0.396232\pi$
$774$	4.63721	−	11.8983i	0.166681	−	0.427674i
$775$		0			0
$776$	−6.15916	+	34.9303i	−0.221101	+	1.25393i
$777$	2.21002	+	1.06106i	0.0792839	+	0.0380654i
$778$	10.7178	+	3.90095i	0.384251	+	0.139856i
$779$	−6.40411	−	36.3195i	−0.229451	−	1.30128i
$780$		0			0
$781$	19.4361	+	16.3089i	0.695479	+	0.583577i
$782$	−28.7862			−1.02939
$783$	−40.2686	+	2.15327i	−1.43908	+	0.0769516i
$784$	19.2328			0.686887
$785$		0			0
$786$	−37.0317	+	9.47617i	−1.32088	+	0.338004i
$787$	3.44462	+	19.5354i	0.122788	+	0.696363i	0.982597	+	0.185748i	$0.0594709\pi$
$787$	3.44462	+	19.5354i	0.122788	+	0.696363i	−0.859810	+	0.510614i	$0.829418\pi$
$788$	−10.6753	−	3.88549i	−0.380291	−	0.138415i
$789$	32.7242	−	22.3678i	1.16501	−	0.796315i
$790$		0			0
$791$	−2.92979	+	5.07454i	−0.104171	+	0.180430i
$792$	−20.6600	−	4.12556i	−0.734119	−	0.146595i
$793$	−9.72682	−	16.8473i	−0.345409	−	0.598267i
$794$	−39.3630	+	14.3269i	−1.39694	+	0.508444i
$795$		0			0
$796$	2.97907	−	2.49974i	0.105590	−	0.0886008i
$797$	−8.80112	+	7.38501i	−0.311752	+	0.261591i	−0.785216	−	0.619223i	$-0.787448\pi$
$797$	−8.80112	+	7.38501i	−0.311752	+	0.261591i	0.473464	+	0.880813i	$0.343003\pi$
$798$	−13.8166	+	19.2659i	−0.489103	+	0.682005i
$799$	−43.1085	+	15.6902i	−1.52507	+	0.555079i
$800$		0			0
$801$	−32.2055	−	19.5757i	−1.13792	−	0.691672i
$802$	10.6567	−	18.4580i	0.376302	−	0.651774i
$803$	5.34253	−	30.2990i	0.188534	−	1.06923i
$804$	1.08745	+	14.2838i	0.0383513	+	0.503752i
$805$		0			0
$806$	−2.10003	−	11.9098i	−0.0739703	−	0.419506i
$807$	22.3741	+	22.8847i	0.787604	+	0.805579i
$808$	11.0487	+	9.27095i	0.388692	+	0.326151i
$809$	−37.5291			−1.31945			−0.659727	−	0.751506i	$-0.729328\pi$
$809$	−37.5291			−1.31945			−0.659727	+	0.751506i	$0.729328\pi$
$810$		0			0
$811$	31.9363			1.12143			0.560717	−	0.828008i	$-0.310526\pi$
$811$	31.9363			1.12143			0.560717	+	0.828008i	$0.310526\pi$
$812$	6.27796	+	5.26784i	0.220313	+	0.184865i
$813$	5.62532	+	5.75369i	0.197288	+	0.201791i
$814$	−0.711553	−	4.03542i	−0.0249399	−	0.141441i
$815$		0			0
$816$	4.09219	+	53.7517i	0.143255	+	1.88169i
$817$	2.22966	−	12.6451i	0.0780061	−	0.442395i
$818$	−12.1031	+	20.9632i	−0.423174	+	0.732960i
$819$	−8.66994	+	4.74808i	−0.302952	+	0.165911i
$820$		0			0
$821$	34.2903	−	12.4806i	1.19674	−	0.435577i	0.334654	−	0.942341i	$-0.391381\pi$
$821$	34.2903	−	12.4806i	1.19674	−	0.435577i	0.862085	+	0.506764i	$0.169158\pi$
$822$	−22.7037	+	31.6580i	−0.791881	+	1.10420i
$823$	24.7904	−	20.8016i	0.864140	−	0.725100i	−0.0987156	−	0.995116i	$-0.531473\pi$
$823$	24.7904	−	20.8016i	0.864140	−	0.725100i	0.962856	+	0.270016i	$0.0870290\pi$
$824$	12.4684	−	10.4622i	0.434358	−	0.364470i
$825$		0			0
$826$	−2.72930	+	0.993385i	−0.0949646	+	0.0345643i
$827$	−25.8092	−	44.7028i	−0.897473	−	1.55447i	−0.830714	−	0.556700i	$-0.812067\pi$
$827$	−25.8092	−	44.7028i	−0.897473	−	1.55447i	−0.0667595	−	0.997769i	$-0.521266\pi$
$828$	1.62009	+	4.78435i	0.0563019	+	0.166268i
$829$	−0.662012	+	1.14664i	−0.0229926	+	0.0398244i	−0.877293	−	0.479956i	$-0.840653\pi$
$829$	−0.662012	+	1.14664i	−0.0229926	+	0.0398244i	0.854300	+	0.519780i	$0.173986\pi$
$830$		0			0
$831$	37.0003	−	25.2906i	1.28352	−	0.877322i
$832$	7.69242	+	2.79981i	0.266687	+	0.0970660i
$833$	4.42763	+	25.1103i	0.153408	+	0.870021i
$834$	48.3704	−	12.3777i	1.67493	−	0.428604i
$835$		0			0
$836$	9.22189			0.318946
$837$	16.4363	+	12.3583i	0.568122	+	0.427165i
$838$	−45.3816			−1.56768
$839$	6.77496	+	5.68487i	0.233898	+	0.196263i	0.752202	−	0.658933i	$-0.228992\pi$
$839$	6.77496	+	5.68487i	0.233898	+	0.196263i	−0.518304	+	0.855196i	$0.673436\pi$
$840$		0			0
$841$	5.42296	+	30.7551i	0.186999	+	1.06052i
$842$	−43.0632	−	15.6737i	−1.48406	−	0.540153i
$843$	16.8118	+	8.07160i	0.579029	+	0.278001i
$844$	1.71637	−	9.73401i	0.0590799	−	0.335059i
$845$		0			0
$846$	21.6312	+	26.9931i	0.743695	+	0.928043i
$847$	1.09264	+	1.89250i	0.0375435	+	0.0650272i
$848$	8.50567	−	3.09581i	0.292086	−	0.106311i
$849$	27.3312	+	2.70219i	0.938004	+	0.0927388i
$850$		0			0
$851$	1.72881	−	1.45064i	0.0592627	−	0.0497273i
$852$	−8.49803	−	0.840185i	−0.291138	−	0.0287843i
$853$	−21.2863	+	7.74759i	−0.728830	+	0.265272i	−0.679670	−	0.733518i	$-0.737877\pi$
$853$	−21.2863	+	7.74759i	−0.728830	+	0.265272i	−0.0491605	+	0.998791i	$0.515655\pi$
$854$	−14.4437	−	25.0172i	−0.494252	−	0.856070i
$855$		0			0
$856$	−5.10338	+	8.83931i	−0.174430	+	0.302122i
$857$	1.30013	−	7.37341i	0.0444116	−	0.251871i	−0.954517	−	0.298158i	$-0.903628\pi$
$857$	1.30013	−	7.37341i	0.0444116	−	0.251871i	0.998928	+	0.0462871i	$0.0147389\pi$
$858$	14.8947	+	7.15115i	0.508495	+	0.244136i
$859$	−38.2228	−	13.9119i	−1.30414	−	0.474669i	−0.405800	−	0.913962i	$-0.633007\pi$
$859$	−38.2228	−	13.9119i	−1.30414	−	0.474669i	−0.898344	+	0.439293i	$0.855229\pi$
$860$		0			0
$861$	6.15820	−	21.9875i	0.209871	−	0.749330i
$862$	−10.7209	−	8.99590i	−0.365155	−	0.306401i
$863$	−8.68298			−0.295572			−0.147786	−	0.989019i	$-0.547215\pi$
$863$	−8.68298			−0.295572			−0.147786	+	0.989019i	$0.547215\pi$
$864$	15.8885	−	6.76419i	0.540538	−	0.230122i
$865$		0			0
$866$	−10.6509	−	8.93718i	−0.361933	−	0.303698i
$867$	−40.7102	+	10.4175i	−1.38259	+	0.353796i
$868$	−0.725699	−	4.11565i	−0.0246318	−	0.139694i
$869$	−43.6417	−	15.8843i	−1.48044	−	0.538837i
$870$		0			0
$871$	−4.48128	+	25.4146i	−0.151842	+	0.861141i
$872$	8.60405	−	14.9026i	0.291370	−	0.504667i
$873$	15.1705	+	44.8008i	0.513445	+	1.51628i
$874$	10.9124	+	18.9008i	0.369117	+	0.639330i
$875$		0			0
$876$	4.27007	+	9.43361i	0.144272	+	0.318732i
$877$	−22.5224	+	18.8985i	−0.760526	+	0.638157i	−0.938264	−	0.345920i	$-0.887567\pi$
$877$	−22.5224	+	18.8985i	−0.760526	+	0.638157i	0.177737	+	0.984078i	$0.443122\pi$
$878$	19.8744	−	16.6766i	0.670728	−	0.562808i
$879$	−3.35804	+	4.68244i	−0.113264	+	0.157935i
$880$		0			0
$881$	12.3020	+	21.3077i	0.414466	+	0.717876i	0.995372	−	0.0960945i	$-0.0306351\pi$
$881$	12.3020	+	21.3077i	0.414466	+	0.717876i	−0.580906	+	0.813970i	$0.697302\pi$
$882$	16.8628	−	9.23486i	0.567799	−	0.310954i
$883$	23.4475	−	40.6122i	0.789070	−	1.36671i	−0.137468	−	0.990506i	$-0.543896\pi$
$883$	23.4475	−	40.6122i	0.789070	−	1.36671i	0.926537	−	0.376203i	$-0.122770\pi$
$884$	1.28065	−	7.26295i	0.0430730	−	0.244279i
$885$		0			0
$886$	−14.0207	−	5.10313i	−0.471036	−	0.171443i
$887$	8.16406	+	46.3007i	0.274122	+	1.55462i	0.741736	+	0.670692i	$0.234003\pi$
$887$	8.16406	+	46.3007i	0.274122	+	1.55462i	−0.467614	+	0.883933i	$0.654886\pi$
$888$	−2.21473	−	2.26527i	−0.0743215	−	0.0760176i
$889$	23.8090	+	19.9781i	0.798528	+	0.670044i
$890$		0			0
$891$	−26.8071	+	8.40827i	−0.898073	+	0.281688i
$892$	−11.3539			−0.380158
$893$	26.6438	+	22.3568i	0.891601	+	0.748142i
$894$	35.1144	+	35.9157i	1.17440	+	1.20120i
$895$		0			0
$896$	22.2957	+	8.11497i	0.744847	+	0.271102i
$897$	0.690776	+	9.07346i	0.0230643	+	0.302954i
$898$	10.3854	−	58.8986i	0.346566	−	1.96547i
$899$	15.3568	−	26.5988i	0.512179	−	0.887120i
$900$		0			0
$901$	5.99998	+	10.3923i	0.199888	+	0.346217i
$902$	−35.8640	+	13.0534i	−1.19414	+	0.434631i
$903$	4.63297	−	6.46021i	0.154176	−	0.214982i
$904$	5.80060	−	4.86728i	0.192925	−	0.161883i
$905$		0			0
$906$	−22.5400	−	49.7962i	−0.748840	−	1.65437i
$907$	−35.4991	+	12.9206i	−1.17873	+	0.429022i	−0.855752	−	0.517386i	$-0.826905\pi$
$907$	−35.4991	+	12.9206i	−1.17873	+	0.429022i	−0.322975	+	0.946408i	$0.604683\pi$
$908$	−5.32686	−	9.22640i	−0.176778	−	0.306189i
$909$	18.8614	+	3.76640i	0.625592	+	0.124924i
$910$		0			0
$911$	3.66733	−	20.7985i	0.121504	−	0.689084i	−0.861819	−	0.507216i	$-0.830675\pi$
$911$	3.66733	−	20.7985i	0.121504	−	0.689084i	0.983323	−	0.181868i	$-0.0582142\pi$
$912$	33.7417	−	23.0633i	1.11730	−	0.763703i
$913$	−27.0589	−	9.84862i	−0.895518	−	0.325942i
$914$	0.382060	+	2.16677i	0.0126374	+	0.0716704i
$915$		0			0
$916$	−3.51517	−	2.94958i	−0.116145	−	0.0974569i
$917$	−23.7964			−0.785826
$918$	29.3974	+	45.1629i	0.970258	+	1.49060i
$919$	46.4789			1.53320			0.766599	−	0.642126i	$-0.221947\pi$
$919$	46.4789			1.53320			0.766599	+	0.642126i	$0.221947\pi$
$920$		0			0
$921$	2.05472	−	7.33624i	0.0677053	−	0.241737i
$922$	2.34936	+	13.3239i	0.0773721	+	0.438799i
$923$	−14.4560	−	5.26156i	−0.475825	−	0.173186i
$924$	5.14710	+	2.47120i	0.169327	+	0.0812965i
$925$		0			0
$926$	23.1018	−	40.0135i	0.759171	−	1.31492i
$927$	7.88190	−	20.2236i	0.258876	−	0.664229i
$928$	−12.8957	−	22.3361i	−0.423323	−	0.733217i
$929$	−39.5960	+	14.4118i	−1.29910	+	0.472834i	−0.896704	−	0.442630i	$-0.854045\pi$
$929$	−39.5960	+	14.4118i	−1.29910	+	0.472834i	−0.402398	+	0.915465i	$0.631823\pi$
$930$		0			0
$931$	14.8088	−	12.4261i	0.485339	−	0.407248i
$932$	−3.22794	+	2.70856i	−0.105735	+	0.0887220i
$933$	−26.6857	−	2.63837i	−0.873652	−	0.0863765i
$934$	3.50181	−	1.27455i	0.114583	−	0.0417047i
$935$		0			0
$936$	12.6268	−	1.93380i	0.412719	−	0.0632082i
$937$	−20.5493	+	35.5924i	−0.671316	+	1.16275i	0.306215	+	0.951962i	$0.400937\pi$
$937$	−20.5493	+	35.5924i	−0.671316	+	1.16275i	−0.977531	+	0.210791i	$0.932396\pi$
$938$	−6.65440	+	37.7390i	−0.217274	+	1.23222i
$939$	−16.9171	−	8.12217i	−0.552069	−	0.265057i
$940$		0			0
$941$	−0.695320	−	3.94336i	−0.0226668	−	0.128550i	0.971375	−	0.237553i	$-0.0763453\pi$
$941$	−0.695320	−	3.94336i	−0.0226668	−	0.128550i	−0.994041	+	0.109003i	$0.965234\pi$
$942$	6.06741	−	21.6633i	0.197687	−	0.705828i
$943$	−16.1021	−	13.5112i	−0.524355	−	0.439986i
$944$	5.00705			0.162966
$945$		0			0
$946$	−13.2878			−0.432024
$947$	−13.3102	−	11.1686i	−0.432524	−	0.362931i	0.400379	−	0.916350i	$-0.368879\pi$
$947$	−13.3102	−	11.1686i	−0.432524	−	0.362931i	−0.832903	+	0.553419i	$0.813323\pi$
$948$	15.1432	−	3.87504i	0.491828	−	0.125856i
$949$	3.23932	+	18.3711i	0.105153	+	0.596351i
$950$		0			0
$951$	15.1179	−	10.3335i	0.490231	−	0.335086i
$952$	−4.36836	+	24.7742i	−0.141579	+	0.802936i
$953$	−23.9561	+	41.4931i	−0.776013	+	1.34409i	0.158211	+	0.987405i	$0.449427\pi$
$953$	−23.9561	+	41.4931i	−0.776013	+	1.34409i	−0.934223	+	0.356688i	$0.883906\pi$
$954$	5.97102	−	6.79840i	0.193319	−	0.220106i
$955$		0			0
$956$	11.6861	−	4.25341i	0.377957	−	0.137565i
$957$	17.3035	+	38.2276i	0.559343	+	1.23572i
$958$	1.07125	−	0.898889i	0.0346107	−	0.0290418i
$959$	−18.5784	+	15.5891i	−0.599928	+	0.503400i
$960$		0			0
$961$	14.4128	−	5.24583i	0.464929	−	0.169220i
$962$	1.24226	+	2.15167i	0.0400522	+	0.0693725i
$963$	−0.307084	+	13.6077i	−0.00989564	+	0.438502i
$964$	7.08601	−	12.2733i	0.228225	−	0.395297i
$965$		0			0
$966$	1.02576	+	13.4735i	0.0330032	+	0.433502i
$967$	−36.2453	−	13.1922i	−1.16557	−	0.424233i	−0.314486	−	0.949262i	$-0.601832\pi$
$967$	−36.2453	−	13.1922i	−1.16557	−	0.424233i	−0.851084	+	0.525029i	$0.824054\pi$
$968$	−0.490376	−	2.78106i	−0.0157613	−	0.0893866i
$969$	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	$0.575735\pi$
$972$	5.85173	−	7.42770i	0.187694	−	0.238244i
$973$	31.0826			0.996462
$974$	−25.3168	−	21.2433i	−0.811202	−	0.680679i
$975$		0			0
$976$	8.64757	+	49.0428i	0.276802	+	1.56982i
$977$	5.23291	+	1.90462i	0.167416	+	0.0609343i	0.424368	−	0.905490i	$-0.360496\pi$
$977$	5.23291	+	1.90462i	0.167416	+	0.0609343i	−0.256953	+	0.966424i	$0.582718\pi$
$978$	1.11978	+	14.7085i	0.0358067	+	0.470327i
$979$	−6.80987	+	38.6207i	−0.217644	+	1.23432i
$980$		0			0
$981$	0.517728	−	22.9419i	0.0165298	−	0.732478i
$982$	34.6218	+	59.9667i	1.10483	+	1.91361i
$983$	−28.2485	+	10.2816i	−0.900987	+	0.327932i	−0.750648	−	0.660702i	$-0.770259\pi$
$983$	−28.2485	+	10.2816i	−0.900987	+	0.327932i	−0.150339	+	0.988635i	$0.548036\pi$
$984$	−17.1962	+	23.9783i	−0.548194	+	0.764401i
$985$		0			0
$986$	61.6549	−	51.7346i	1.96349	−	1.64756i
$987$	8.87996	+	19.6180i	0.282652	+	0.624447i
$988$	−5.25427	+	1.91240i	−0.167161	+	0.0608415i
$989$	−3.65913	−	6.33780i	−0.116354	−	0.201530i
$990$		0			0
$991$	28.1316	−	48.7254i	0.893631	−	1.54781i	0.0581407	−	0.998308i	$-0.481483\pi$
$991$	28.1316	−	48.7254i	0.893631	−	1.54781i	0.835490	−	0.549506i	$-0.185184\pi$
$992$	−2.28385	+	12.9524i	−0.0725123	+	0.411238i
$993$	−15.0776	+	10.3059i	−0.478474	+	0.327049i
$994$	−21.4662	−	7.81307i	−0.680867	−	0.247815i
$995$		0			0
$996$	9.38913	−	2.40262i	0.297506	−	0.0761299i
$997$	1.46674	+	1.23074i	0.0464520	+	0.0389779i	0.665718	−	0.746203i	$-0.268125\pi$
$997$	1.46674	+	1.23074i	0.0464520	+	0.0389779i	−0.619266	+	0.785181i	$0.712570\pi$
$998$	−9.90951			−0.313680
$999$	−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.l.f.151.3	yes	66
5.2	odd	4		675.2.u.e.124.18		132
5.3	odd	4		675.2.u.e.124.5		132
5.4	even	2		675.2.l.g.151.9	yes	66
27.22	even	9	inner	675.2.l.f.76.3	✓	66
135.22	odd	36		675.2.u.e.49.5		132
135.49	even	18		675.2.l.g.76.9	yes	66
135.103	odd	36		675.2.u.e.49.18		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.3	✓	66	27.22	even	9	inner
675.2.l.f.151.3	yes	66	1.1	even	1	trivial
675.2.l.g.76.9	yes	66	135.49	even	18
675.2.l.g.151.9	yes	66	5.4	even	2
675.2.u.e.49.5		132	135.22	odd	36
675.2.u.e.49.18		132	135.103	odd	36
675.2.u.e.124.5		132	5.3	odd	4
675.2.u.e.124.18		132	5.2	odd	4

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23677 - 1.03778i) q^{2} +(1.21085 + 1.23848i) q^{3} +(0.105334 + 0.597379i) q^{4} +(-0.212279 - 2.78832i) q^{6} +(0.302296 - 1.71440i) q^{7} +(-1.12482 + 1.94825i) q^{8} +(-0.0676836 + 2.99924i) q^{9} +(2.93339 - 1.06767i) q^{11} +(-0.612300 + 0.853791i) q^{12} +(-1.44992 + 1.21663i) q^{13} +(-2.15304 + 1.80662i) q^{14} +(4.55303 - 1.65717i) q^{16} +(3.21175 + 5.56291i) q^{17} +(3.19625 - 3.63914i) q^{18} +(2.43505 - 4.21762i) q^{19} +(2.48930 - 1.70150i) q^{21} +(-4.73595 - 1.72374i) q^{22} +(-0.481999 - 2.73355i) q^{23} +(-3.77487 + 0.965965i) q^{24} +3.05582 q^{26} +(-3.79646 + 3.54780i) q^{27} +1.05599 q^{28} +(5.94510 + 4.98853i) q^{29} +(-0.687222 - 3.89743i) q^{31} +(-3.12289 - 1.13664i) q^{32} +(4.87419 + 2.34017i) q^{33} +(1.80085 - 10.2132i) q^{34} +(-1.79881 + 0.275489i) q^{36} +(0.406524 + 0.704120i) q^{37} +(-7.38856 + 2.68922i) q^{38} +(-3.26242 - 0.322550i) q^{39} +(5.80103 - 4.86764i) q^{41} +(-4.84447 - 0.478965i) q^{42} +(2.47752 - 0.901745i) q^{43} +(0.946788 + 1.63988i) q^{44} +(-2.24069 + 3.88100i) q^{46} +(-1.24015 + 7.03326i) q^{47} +(7.56541 + 3.63227i) q^{48} +(3.73005 + 1.35763i) q^{49} +(-3.00063 + 10.7136i) q^{51} +(-0.879516 - 0.738001i) q^{52} +1.86813 q^{53} +(8.37719 - 0.447951i) q^{54} +(3.00006 + 2.51735i) q^{56} +(8.17194 - 2.09115i) q^{57} +(-2.17576 - 12.3394i) q^{58} +(0.971077 + 0.353443i) q^{59} +(-1.78476 + 10.1219i) q^{61} +(-3.19472 + 5.53342i) q^{62} +(5.12144 + 1.02269i) q^{63} +(-2.16250 - 3.74556i) q^{64} +(-3.59969 - 7.95259i) q^{66} +(10.4447 - 8.76411i) q^{67} +(-2.98486 + 2.50460i) q^{68} +(2.80183 - 3.90687i) q^{69} +(4.06389 + 7.03886i) q^{71} +(-5.76713 - 3.50548i) q^{72} +(4.92790 - 8.53538i) q^{73} +(0.227941 - 1.29272i) q^{74} +(2.77601 + 1.01039i) q^{76} +(-0.943662 - 5.35177i) q^{77} +(3.70014 + 3.78459i) q^{78} +(-11.3969 - 9.56310i) q^{79} +(-8.99084 - 0.405998i) q^{81} -12.2261 q^{82} +(-7.06632 - 5.92935i) q^{83} +(1.27865 + 1.30783i) q^{84} +(-3.99995 - 1.45586i) q^{86} +(1.02041 + 13.4033i) q^{87} +(-1.21946 + 6.91592i) q^{88} +(-6.28136 + 10.8796i) q^{89} +(1.64749 + 2.85354i) q^{91} +(1.58220 - 0.575872i) q^{92} +(3.99478 - 5.57031i) q^{93} +(8.83274 - 7.41155i) q^{94} +(-2.37364 - 5.24395i) q^{96} +(14.8157 - 5.39248i) q^{97} +(-3.20432 - 5.55004i) q^{98} +(3.00365 + 8.87020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Introduction

L-functions

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