LMFDB - Embedded newform 585.2.cm.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(11,585)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("585.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.cm (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	585.11
Dual form			585.2.cm.a.266.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46697 + 1.46697i) q^{2} +(-0.594527 - 1.62682i) q^{3} -2.30401i q^{4} +(-0.965926 - 0.258819i) q^{5} +(3.25865 + 1.51434i) q^{6} +(2.58328 + 0.692188i) q^{7} +(0.445979 + 0.445979i) q^{8} +(-2.29307 + 1.93438i) q^{9} +(1.79667 - 1.03731i) q^{10} +(-0.763900 - 0.763900i) q^{11} +(-3.74821 + 1.36980i) q^{12} +(2.66510 + 2.42842i) q^{13} +(-4.80502 + 2.77418i) q^{14} +(0.153218 + 1.72526i) q^{15} +3.29955 q^{16} +(1.63379 - 2.82981i) q^{17} +(0.526200 - 6.20155i) q^{18} +(-5.93362 + 1.58991i) q^{19} +(-0.596323 + 2.22551i) q^{20} +(-0.409767 - 4.61405i) q^{21} +2.24124 q^{22} +(-0.571291 + 0.989505i) q^{23} +(0.460380 - 0.990674i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-7.47206 + 0.347209i) q^{26} +(4.51017 + 2.58037i) q^{27} +(1.59481 - 5.95191i) q^{28} -9.51041i q^{29} +(-2.75568 - 2.30614i) q^{30} +(2.46382 - 9.19510i) q^{31} +(-5.73230 + 5.73230i) q^{32} +(-0.788566 + 1.69688i) q^{33} +(1.75453 + 6.54799i) q^{34} +(-2.31611 - 1.33720i) q^{35} +(4.45683 + 5.28327i) q^{36} +(4.07168 + 1.09100i) q^{37} +(6.37211 - 11.0368i) q^{38} +(2.36612 - 5.77940i) q^{39} +(-0.315355 - 0.546211i) q^{40} +(-0.202241 - 0.754775i) q^{41} +(7.36980 + 6.16757i) q^{42} +(8.14484 - 4.70243i) q^{43} +(-1.76003 + 1.76003i) q^{44} +(2.71559 - 1.27497i) q^{45} +(-0.613508 - 2.28964i) q^{46} +(10.4956 - 2.81229i) q^{47} +(-1.96167 - 5.36777i) q^{48} +(0.132033 + 0.0762291i) q^{49} +(-2.00392 + 0.536949i) q^{50} +(-5.57493 - 0.975484i) q^{51} +(5.59511 - 6.14043i) q^{52} -6.57880i q^{53} +(-10.4016 + 2.83096i) q^{54} +(0.540159 + 0.935582i) q^{55} +(0.843388 + 1.46079i) q^{56} +(6.11420 + 8.70768i) q^{57} +(13.9515 + 13.9515i) q^{58} +(4.39838 + 4.39838i) q^{59} +(3.97502 - 0.353016i) q^{60} +(-4.13589 - 7.16357i) q^{61} +(9.87460 + 17.1033i) q^{62} +(-7.26260 + 3.40980i) q^{63} -10.2192i q^{64} +(-1.94577 - 3.03545i) q^{65} +(-1.33248 - 3.64609i) q^{66} +(-10.2656 + 2.75065i) q^{67} +(-6.51993 - 3.76428i) q^{68} +(1.94939 + 0.341098i) q^{69} +(5.35930 - 1.43602i) q^{70} +(1.99342 + 7.43953i) q^{71} +(-1.88536 - 0.159972i) q^{72} +(3.79653 - 3.79653i) q^{73} +(-7.57352 + 4.37257i) q^{74} +(0.298533 - 1.70613i) q^{75} +(3.66317 + 13.6711i) q^{76} +(-1.44460 - 2.50213i) q^{77} +(5.00719 + 11.9493i) q^{78} +(6.30268 - 10.9166i) q^{79} +(-3.18712 - 0.853986i) q^{80} +(1.51638 - 8.87134i) q^{81} +(1.40392 + 0.810551i) q^{82} +(1.13855 + 4.24911i) q^{83} +(-10.6308 + 0.944109i) q^{84} +(-2.31053 + 2.31053i) q^{85} +(-5.04993 + 18.8466i) q^{86} +(-15.4717 + 5.65420i) q^{87} -0.681367i q^{88} +(-3.13094 + 11.6848i) q^{89} +(-2.11335 + 5.85405i) q^{90} +(5.20379 + 8.11804i) q^{91} +(2.27983 + 1.31626i) q^{92} +(-16.4236 + 1.45855i) q^{93} +(-11.2712 + 19.5223i) q^{94} +6.14294 q^{95} +(12.7334 + 5.91740i) q^{96} +(3.46224 - 12.9212i) q^{97} +(-0.305514 + 0.0818622i) q^{98} +(3.22935 + 0.274009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 24 q^{6} + 4 q^{7} - 36 q^{8} + 8 q^{15} - 224 q^{16} - 4 q^{18} - 8 q^{19} - 24 q^{21} - 8 q^{24} + 48 q^{26} + 24 q^{27} - 16 q^{28} - 48 q^{30} + 32 q^{31} - 72 q^{32} + 4 q^{33} - 12 q^{36}+ \cdots + 8 q^{99}+O(q^{100}) $ 224 * q + 24 * q^6 + 4 * q^7 - 36 * q^8 + 8 * q^15 - 224 * q^16 - 4 * q^18 - 8 * q^19 - 24 * q^21 - 8 * q^24 + 48 * q^26 + 24 * q^27 - 16 * q^28 - 48 * q^30 + 32 * q^31 - 72 * q^32 + 4 * q^33 - 12 * q^36 - 4 * q^37 + 8 * q^39 - 24 * q^41 + 64 * q^42 + 48 * q^43 + 8 * q^45 - 8 * q^48 - 52 * q^52 + 32 * q^54 - 72 * q^58 - 16 * q^60 - 36 * q^62 + 88 * q^63 - 108 * q^66 - 56 * q^67 - 72 * q^69 + 48 * q^71 + 12 * q^72 + 28 * q^73 - 120 * q^74 + 16 * q^76 - 144 * q^77 + 48 * q^78 - 12 * q^79 + 48 * q^80 - 84 * q^81 + 20 * q^84 - 12 * q^85 + 96 * q^86 + 8 * q^87 - 60 * q^89 + 16 * q^91 - 120 * q^92 - 132 * q^93 - 176 * q^96 - 4 * q^97 - 96 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	−1.46697	+	1.46697i	−1.03731	+	1.03731i	−0.0380292	+	0.999277i	$0.512108\pi$
$2$	−1.46697	+	1.46697i	−1.03731	+	1.03731i	−0.999277	+	0.0380292i	$0.987892\pi$
$3$	−0.594527	−	1.62682i	−0.343251	−	0.939244i
$3$	−0.594527	−	1.62682i	−0.343251	−	0.939244i
$4$		−	2.30401i		−	1.15201i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	3.25865	+	1.51434i	1.33034	+	0.618227i
$7$	2.58328	+	0.692188i	0.976388	+	0.261622i	0.711523	−	0.702663i	$-0.248006\pi$
$7$	2.58328	+	0.692188i	0.976388	+	0.261622i	0.264865	+	0.964285i	$0.414673\pi$
$8$	0.445979	+	0.445979i	0.157678	+	0.157678i
$9$	−2.29307	+	1.93438i	−0.764358	+	0.644792i
$10$	1.79667	−	1.03731i	0.568156	−	0.328025i
$11$	−0.763900	−	0.763900i	−0.230324	−	0.230324i	0.582504	−	0.812828i	$-0.302073\pi$
$11$	−0.763900	−	0.763900i	−0.230324	−	0.230324i	−0.812828	+	0.582504i	$0.802073\pi$
$12$	−3.74821	+	1.36980i	−1.08202	+	0.395427i
$13$	2.66510	+	2.42842i	0.739167	+	0.673522i
$13$	2.66510	+	2.42842i	0.739167	+	0.673522i
$14$	−4.80502	+	2.77418i	−1.28420	+	0.741431i
$15$	0.153218	+	1.72526i	0.0395607	+	0.445460i
$16$	3.29955			0.824887
$17$	1.63379	−	2.82981i	0.396253	−	0.686331i	−0.597007	−	0.802236i	$-0.703644\pi$
$17$	1.63379	−	2.82981i	0.396253	−	0.686331i	0.993260	+	0.115905i	$0.0369769\pi$
$18$	0.526200	−	6.20155i	0.124027	−	1.46172i
$19$	−5.93362	+	1.58991i	−1.36127	+	0.364750i	−0.864281	−	0.503009i	$-0.832226\pi$
$19$	−5.93362	+	1.58991i	−1.36127	+	0.364750i	−0.496985	+	0.867759i	$0.665560\pi$
$20$	−0.596323	+	2.22551i	−0.133342	+	0.497638i
$21$	−0.409767	−	4.61405i	−0.0894186	−	1.00687i
$22$	2.24124			0.477834
$23$	−0.571291	+	0.989505i	−0.119122	+	0.206326i	−0.919420	−	0.393277i	$-0.871341\pi$
$23$	−0.571291	+	0.989505i	−0.119122	+	0.206326i	0.800298	+	0.599603i	$0.204675\pi$
$24$	0.460380	−	0.990674i	0.0939747	−	0.202221i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−7.47206	+	0.347209i	−1.46539	+	0.0680932i
$27$	4.51017	+	2.58037i	0.867983	+	0.496593i
$28$	1.59481	−	5.95191i	0.301391	−	1.12481i
$29$		−	9.51041i		−	1.76604i	−0.469336	−	0.883020i	$-0.655507\pi$
$29$		−	9.51041i		−	1.76604i	0.469336	−	0.883020i	$-0.344493\pi$
$30$	−2.75568	−	2.30614i	−0.503115	−	0.421042i
$31$	2.46382	−	9.19510i	0.442515	−	1.65149i	−0.279900	−	0.960029i	$-0.590301\pi$
$31$	2.46382	−	9.19510i	0.442515	−	1.65149i	0.722415	−	0.691459i	$-0.243032\pi$
$32$	−5.73230	+	5.73230i	−1.01334	+	1.01334i
$33$	−0.788566	+	1.69688i	−0.137272	+	0.295390i
$34$	1.75453	+	6.54799i	0.300899	+	1.12297i
$35$	−2.31611	−	1.33720i	−0.391493	−	0.226029i
$36$	4.45683	+	5.28327i	0.742805	+	0.880546i
$37$	4.07168	+	1.09100i	0.669381	+	0.179360i	0.577476	−	0.816408i	$-0.304038\pi$
$37$	4.07168	+	1.09100i	0.669381	+	0.179360i	0.0919048	+	0.995768i	$0.470704\pi$
$38$	6.37211	−	11.0368i	1.03369	−	1.79041i
$39$	2.36612	−	5.77940i	0.378882	−	0.925445i
$40$	−0.315355	−	0.546211i	−0.0498620	−	0.0863635i
$41$	−0.202241	−	0.754775i	−0.0315848	−	0.117876i	0.948334	−	0.317275i	$-0.102768\pi$
$41$	−0.202241	−	0.754775i	−0.0315848	−	0.117876i	−0.979918	+	0.199399i	$0.936101\pi$
$42$	7.36980	+	6.16757i	1.13718	+	0.951676i
$43$	8.14484	−	4.70243i	1.24208	−	0.717113i	0.272560	−	0.962139i	$-0.412130\pi$
$43$	8.14484	−	4.70243i	1.24208	−	0.717113i	0.969517	+	0.245026i	$0.0787964\pi$
$44$	−1.76003	+	1.76003i	−0.265335	+	0.265335i
$45$	2.71559	−	1.27497i	0.404817	−	0.190062i
$46$	−0.613508	−	2.28964i	−0.0904568	−	0.337589i
$47$	10.4956	−	2.81229i	1.53094	−	0.410215i	0.607616	−	0.794231i	$-0.292126\pi$
$47$	10.4956	−	2.81229i	1.53094	−	0.410215i	0.923326	+	0.384016i	$0.125459\pi$
$48$	−1.96167	−	5.36777i	−0.283143	−	0.774770i
$49$	0.132033	+	0.0762291i	0.0188618	+	0.0108899i
$50$	−2.00392	+	0.536949i	−0.283397	+	0.0759361i
$51$	−5.57493	−	0.975484i	−0.780646	−	0.136595i
$52$	5.59511	−	6.14043i	0.775902	−	0.851525i
$53$		−	6.57880i		−	0.903667i	−0.892102	−	0.451834i	$-0.850770\pi$
$53$		−	6.57880i		−	0.903667i	0.892102	−	0.451834i	$-0.149230\pi$
$54$	−10.4016	+	2.83096i	−1.41548	+	0.385245i
$55$	0.540159	+	0.935582i	0.0728350	+	0.126154i
$56$	0.843388	+	1.46079i	0.112702	+	0.195206i
$57$	6.11420	+	8.70768i	0.809845	+	1.15336i
$58$	13.9515	+	13.9515i	1.83192	+	1.83192i
$59$	4.39838	+	4.39838i	0.572620	+	0.572620i	0.932860	−	0.360240i	$-0.117305\pi$
$59$	4.39838	+	4.39838i	0.572620	+	0.572620i	−0.360240	+	0.932860i	$0.617305\pi$
$60$	3.97502	−	0.353016i	0.513173	−	0.0455742i
$61$	−4.13589	−	7.16357i	−0.529546	−	0.917201i	−0.999406	−	0.0344600i	$-0.989029\pi$
$61$	−4.13589	−	7.16357i	−0.529546	−	0.917201i	0.469860	−	0.882741i	$-0.344304\pi$
$62$	9.87460	+	17.1033i	1.25408	+	2.17212i
$63$	−7.26260	+	3.40980i	−0.915002	+	0.429594i
$64$		−	10.2192i		−	1.27740i
$65$	−1.94577	−	3.03545i	−0.241343	−	0.376502i
$66$	−1.33248	−	3.64609i	−0.164017	−	0.448802i
$67$	−10.2656	+	2.75065i	−1.25414	+	0.336046i	−0.823935	−	0.566685i	$-0.808226\pi$
$67$	−10.2656	+	2.75065i	−1.25414	+	0.336046i	−0.430206	+	0.902731i	$0.641559\pi$
$68$	−6.51993	−	3.76428i	−0.790658	−	0.456487i
$69$	1.94939	+	0.341098i	0.234679	+	0.0410634i
$70$	5.35930	−	1.43602i	0.640559	−	0.171637i
$71$	1.99342	+	7.43953i	0.236575	+	0.882909i	0.977433	+	0.211247i	$0.0677526\pi$
$71$	1.99342	+	7.43953i	0.236575	+	0.882909i	−0.740858	+	0.671662i	$0.765581\pi$
$72$	−1.88536	−	0.159972i	−0.222191	−	0.0188529i
$73$	3.79653	−	3.79653i	0.444350	−	0.444350i	−0.449121	−	0.893471i	$-0.648263\pi$
$73$	3.79653	−	3.79653i	0.444350	−	0.444350i	0.893471	+	0.449121i	$0.148263\pi$
$74$	−7.57352	+	4.37257i	−0.880403	+	0.508301i
$75$	0.298533	−	1.70613i	0.0344716	−	0.197007i
$76$	3.66317	+	13.6711i	0.420195	+	1.56819i
$77$	−1.44460	−	2.50213i	−0.164628	−	0.285144i
$78$	5.00719	+	11.9493i	0.566952	+	1.35299i
$79$	6.30268	−	10.9166i	0.709107	−	1.22821i	−0.256082	−	0.966655i	$-0.582432\pi$
$79$	6.30268	−	10.9166i	0.709107	−	1.22821i	0.965189	−	0.261554i	$-0.0842351\pi$
$80$	−3.18712	−	0.853986i	−0.356331	−	0.0954785i
$81$	1.51638	−	8.87134i	0.168486	−	0.985704i
$82$	1.40392	+	0.810551i	0.155037	+	0.0895104i
$83$	1.13855	+	4.24911i	0.124972	+	0.466401i	0.999839	−	0.0179625i	$-0.00571794\pi$
$83$	1.13855	+	4.24911i	0.124972	+	0.466401i	−0.874867	+	0.484363i	$0.839051\pi$
$84$	−10.6308	+	0.944109i	−1.15992	+	0.103011i
$85$	−2.31053	+	2.31053i	−0.250613	+	0.250613i
$86$	−5.04993	+	18.8466i	−0.544548	+	2.03228i
$87$	−15.4717	+	5.65420i	−1.65874	+	0.606194i
$88$		−	0.681367i		−	0.0726340i
$89$	−3.13094	+	11.6848i	−0.331879	+	1.23859i	0.575334	+	0.817919i	$0.304872\pi$
$89$	−3.13094	+	11.6848i	−0.331879	+	1.23859i	−0.907213	+	0.420672i	$0.861794\pi$
$90$	−2.11335	+	5.85405i	−0.222767	+	0.617071i
$91$	5.20379	+	8.11804i	0.545505	+	0.851002i
$92$	2.27983	+	1.31626i	0.237689	+	0.137230i
$93$	−16.4236	+	1.45855i	−1.70304	+	0.151245i
$94$	−11.2712	+	19.5223i	−1.16254	+	2.01357i
$95$	6.14294			0.630252
$96$	12.7334	+	5.91740i	1.29960	+	0.603942i
$97$	3.46224	−	12.9212i	0.351537	−	1.31195i	−0.533250	−	0.845958i	$-0.679029\pi$
$97$	3.46224	−	12.9212i	0.351537	−	1.31195i	0.884787	−	0.465996i	$-0.154304\pi$
$98$	−0.305514	+	0.0818622i	−0.0308616	+	0.00826933i
$99$	3.22935	+	0.274009i	0.324562	+	0.0275390i
$100$	1.15201	−	1.99533i	0.115201	−	0.199533i
$101$	2.72782			0.271428			0.135714	−	0.990748i	$-0.456667\pi$
$101$	2.72782			0.271428			0.135714	+	0.990748i	$0.456667\pi$
$102$	9.60927	−	6.74726i	0.951460	−	0.668078i
$103$	2.49159	−	1.43852i	0.245504	−	0.141742i	−0.372200	−	0.928153i	$-0.621396\pi$
$103$	2.49159	−	1.43852i	0.245504	−	0.141742i	0.617704	+	0.786411i	$0.288063\pi$
$104$	0.105556	+	2.27161i	0.0103506	+	0.222749i
$105$	−0.798399	+	4.56289i	−0.0779158	+	0.445292i
$106$	9.65091	+	9.65091i	0.937379	+	0.937379i
$107$	1.55742	−	0.899175i	0.150561	−	0.0869265i	−0.422827	−	0.906211i	$-0.638962\pi$
$107$	1.55742	−	0.899175i	0.150561	−	0.0869265i	0.573388	+	0.819284i	$0.305629\pi$
$108$	5.94522	−	10.3915i	0.572079	−	0.999923i
$109$	−7.67306	−	7.67306i	−0.734946	−	0.734946i	0.236649	−	0.971595i	$-0.423951\pi$
$109$	−7.67306	−	7.67306i	−0.734946	−	0.734946i	−0.971595	+	0.236649i	$0.923951\pi$
$110$	−2.16487	−	0.580075i	−0.206412	−	0.0553080i
$111$	−0.645862	−	7.27252i	−0.0613025	−	0.690277i
$112$	8.52366	+	2.28391i	0.805410	+	0.215809i
$113$			3.10902i			0.292472i	0.989250	+	0.146236i	$0.0467159\pi$
$113$			3.10902i			0.292472i	−0.989250	+	0.146236i	$0.953284\pi$
$114$	−21.7433	−	3.80457i	−2.03644	−	0.356331i
$115$	0.807927	−	0.807927i	0.0753396	−	0.0753396i
$116$	−21.9121			−2.03449
$117$	−10.8088	−	0.413234i	−0.999270	−	0.0382035i
$118$	−12.9046			−1.18796
$119$	6.17931	−	6.17931i	0.566457	−	0.566457i
$120$	−0.701099	+	0.837763i	−0.0640013	+	0.0764769i
$121$		−	9.83291i		−	0.893901i
$122$	16.5760	+	4.44152i	1.50072	+	0.402117i
$123$	−1.10764	+	0.777744i	−0.0998728	+	0.0701268i
$124$	−21.1856	−	5.67667i	−1.90253	−	0.509780i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	5.65196	−	15.6561i	0.503517	−	1.39476i
$127$	−1.31108	+	0.756950i	−0.116339	+	0.0671684i	−0.557040	−	0.830485i	$-0.688063\pi$
$127$	−1.31108	+	0.756950i	−0.116339	+	0.0671684i	0.440701	+	0.897654i	$0.354730\pi$
$128$	3.52662	+	3.52662i	0.311712	+	0.311712i
$129$	−12.4923	−	10.4545i	−1.09989	−	0.920463i
$130$	7.30732	+	1.59853i	0.640894	+	0.140201i
$131$	−3.41120	+	1.96946i	−0.298038	+	0.172072i	−0.641561	−	0.767072i	$-0.721713\pi$
$131$	−3.41120	+	1.96946i	−0.298038	+	0.172072i	0.343523	+	0.939144i	$0.388380\pi$
$132$	3.90965	+	1.81687i	0.340291	+	0.158138i
$133$	−16.4287			−1.42455
$134$	11.0242	−	19.0945i	0.952345	−	1.64951i
$135$	−3.68864	−	3.65977i	−0.317468	−	0.314983i
$136$	1.99068	−	0.533400i	0.170699	−	0.0457387i
$137$	4.29876	−	16.0432i	0.367267	−	1.37066i	−0.497053	−	0.867720i	$-0.665585\pi$
$137$	4.29876	−	16.0432i	0.367267	−	1.37066i	0.864321	−	0.502941i	$-0.167749\pi$
$138$	−3.36009	+	2.35932i	−0.286029	+	0.200839i
$139$	−7.57542			−0.642538			−0.321269	−	0.946988i	$-0.604109\pi$
$139$	−7.57542			−0.642538			−0.321269	+	0.946988i	$0.604109\pi$
$140$	−3.08094	+	5.33634i	−0.260387	+	0.451003i
$141$	−10.8150	−	15.4025i	−0.910788	−	1.29712i
$142$	−13.8379	−	7.98929i	−1.16125	−	0.670447i
$143$	−0.180803	−	3.89094i	−0.0151195	−	0.325377i
$144$	−7.56611	+	6.38257i	−0.630509	+	0.531881i
$145$	−2.46148	+	9.18635i	−0.204414	+	0.762885i
$146$			11.1388i			0.921854i
$147$	0.0455138	−	0.260113i	0.00375391	−	0.0214538i
$148$	2.51369	−	9.38121i	0.206624	−	0.771131i
$149$	7.38365	−	7.38365i	0.604892	−	0.604892i	−0.336715	−	0.941607i	$-0.609316\pi$
$149$	7.38365	−	7.38365i	0.604892	−	0.604892i	0.941607	+	0.336715i	$0.109316\pi$
$150$	2.06490	+	2.94078i	0.168599	+	0.240114i
$151$	5.82311	+	21.7321i	0.473878	+	1.76854i	0.625632	+	0.780119i	$0.284841\pi$
$151$	5.82311	+	21.7321i	0.473878	+	1.76854i	−0.151754	+	0.988418i	$0.548492\pi$
$152$	−3.35534	−	1.93721i	−0.272154	−	0.157128i
$153$	1.72751	+	9.64935i	0.139661	+	0.780104i
$154$	5.78975	+	1.55136i	0.466551	+	0.125012i
$155$	−4.75973	+	8.24410i	−0.382311	+	0.662182i
$156$	−13.3158	−	5.45157i	−1.06612	−	0.436475i
$157$	−2.99321	−	5.18439i	−0.238884	−	0.413759i	0.721510	−	0.692404i	$-0.243448\pi$
$157$	−2.99321	−	5.18439i	−0.238884	−	0.413759i	−0.960394	+	0.278644i	$0.910115\pi$
$158$	6.76844	+	25.2602i	0.538468	+	2.00959i
$159$	−10.7025	+	3.91128i	−0.848764	+	0.310184i
$160$	7.02061	−	4.05335i	0.555028	−	0.320446i
$161$	−2.16073	+	2.16073i	−0.170289	+	0.170289i
$162$	10.7895	+	15.2385i	0.847705	+	1.19725i
$163$	0.241750	+	0.902222i	0.0189353	+	0.0706675i	0.974747	−	0.223312i	$-0.0716869\pi$
$163$	0.241750	+	0.902222i	0.0189353	+	0.0706675i	−0.955812	+	0.293980i	$0.905020\pi$
$164$	−1.73901	+	0.465967i	−0.135794	+	0.0363859i
$165$	1.20088	−	1.43497i	0.0934886	−	0.111712i
$166$	−7.90355	−	4.56312i	−0.613434	−	0.354166i
$167$	−17.7562	+	4.75777i	−1.37402	+	0.368167i	−0.868945	−	0.494908i	$-0.835202\pi$
$167$	−17.7562	+	4.75777i	−1.37402	+	0.368167i	−0.505075	+	0.863076i	$0.668535\pi$
$168$	1.87502	−	2.24052i	0.144661	−	0.172860i
$169$	1.20555	+	12.9440i	0.0927350	+	0.995691i
$170$		−	6.77898i		−	0.519924i
$171$	10.5308	−	15.1236i	0.805307	−	1.15653i
$172$	−10.8345	−	18.7658i	−0.826119	−	1.43088i
$173$	10.3501	+	17.9269i	0.786902	+	1.36295i	0.927856	+	0.372939i	$0.121650\pi$
$173$	10.3501	+	17.9269i	0.786902	+	1.36295i	−0.140954	+	0.990016i	$0.545017\pi$
$174$	14.4020	−	30.9911i	1.09181	−	2.34943i
$175$	1.89109	+	1.89109i	0.142953	+	0.142953i
$176$	−2.52052	−	2.52052i	−0.189992	−	0.189992i
$177$	4.54040	−	9.77031i	0.341278	−	0.734382i
$178$	−12.5483	−	21.7343i	−0.940537	−	1.62906i
$179$	−4.02579	−	6.97288i	−0.300902	−	0.521177i	0.675439	−	0.737416i	$-0.263954\pi$
$179$	−4.02579	−	6.97288i	−0.300902	−	0.521177i	−0.976340	+	0.216239i	$0.930621\pi$
$180$	−2.93755	−	6.25676i	−0.218952	−	0.466352i
$181$			8.78244i			0.652794i	0.945233	+	0.326397i	$0.105835\pi$
$181$			8.78244i			0.652794i	−0.945233	+	0.326397i	$0.894165\pi$
$182$	−19.5427	−	4.27513i	−1.44860	−	0.316894i
$183$	−9.19492	+	10.9873i	−0.679708	+	0.812203i
$184$	−0.696083	+	0.186515i	−0.0513159	+	0.0137501i
$185$	−3.65057	−	2.10766i	−0.268395	−	0.154958i
$186$	21.9532	−	26.2326i	1.60969	−	1.92346i
$187$	−3.40975	+	0.913640i	−0.249346	+	0.0668119i
$188$	−6.47955	−	24.1820i	−0.472570	−	1.76366i
$189$	9.86494	+	9.78772i	0.717569	+	0.711952i
$190$	−9.01152	+	9.01152i	−0.653764	+	0.653764i
$191$	−17.1535	+	9.90359i	−1.24119	+	0.716599i	−0.969336	−	0.245741i	$-0.920969\pi$
$191$	−17.1535	+	9.90359i	−1.24119	+	0.716599i	−0.271850	+	0.962340i	$0.587636\pi$
$192$	−16.6247	+	6.07557i	−1.19979	+	0.438467i
$193$	6.30062	+	23.5142i	0.453529	+	1.69259i	0.692377	+	0.721536i	$0.256563\pi$
$193$	6.30062	+	23.5142i	0.453529	+	1.69259i	−0.238849	+	0.971057i	$0.576770\pi$
$194$	13.8761	+	24.0341i	0.996246	+	1.72555i
$195$	−3.78132	+	4.97008i	−0.270786	+	0.355915i
$196$	0.175633	−	0.304205i	0.0125452	−	0.0217289i
$197$	4.82402	+	1.29259i	0.343697	+	0.0920934i	0.426539	−	0.904469i	$-0.359733\pi$
$197$	4.82402	+	1.29259i	0.343697	+	0.0920934i	−0.0828413	+	0.996563i	$0.526399\pi$
$198$	−5.13933	+	4.33540i	−0.365236	+	0.308103i
$199$	−1.37927	−	0.796323i	−0.0977740	−	0.0564499i	0.450316	−	0.892869i	$-0.351311\pi$
$199$	−1.37927	−	0.796323i	−0.0977740	−	0.0564499i	−0.548090	+	0.836420i	$0.684645\pi$
$200$	0.163240	+	0.609219i	0.0115428	+	0.0430783i
$201$	10.5780	+	15.0649i	0.746114	+	1.06260i
$202$	−4.00163	+	4.00163i	−0.281554	+	0.281554i
$203$	6.58299	−	24.5681i	0.462035	−	1.72434i
$204$	−2.24753	+	12.8447i	−0.157358	+	0.899310i
$205$			0.781400i			0.0545754i
$206$	−1.54482	+	5.76536i	−0.107633	+	0.401692i
$207$	−0.604062	−	3.37410i	−0.0419852	−	0.234516i
$208$	8.79364	+	8.01269i	0.609729	+	0.555580i
$209$	5.74722	+	3.31816i	0.397544	+	0.229522i
$210$	−5.52240	−	7.86486i	−0.381082	−	0.542727i
$211$	−6.79885	+	11.7760i	−0.468052	+	0.810690i	−0.999333	−	0.0365054i	$-0.988377\pi$
$211$	−6.79885	+	11.7760i	−0.468052	+	0.810690i	0.531281	+	0.847195i	$0.321711\pi$
$212$	−15.1576			−1.04103
$213$	10.9176	−	7.66593i	0.748063	−	0.525261i
$214$	−0.965622	+	3.60375i	−0.0660086	+	0.246347i
$215$	−9.08439	+	2.43415i	−0.619550	+	0.166008i
$216$	0.860651	+	3.16224i	0.0585599	+	0.215163i
$217$	12.7295	−	22.0481i	0.864133	−	1.49672i
$218$	22.5123			1.52473
$219$	−8.43340	−	3.91912i	−0.569877	−	0.264830i
$220$	2.15559	−	1.24453i	0.145330	−	0.0839064i
$221$	11.2262	−	3.57421i	0.755157	−	0.240427i
$222$	11.6160	+	9.72112i	0.779618	+	0.652439i
$223$	−0.0463874	−	0.0463874i	−0.00310633	−	0.00310633i	0.705552	−	0.708658i	$-0.250699\pi$
$223$	−0.0463874	−	0.0463874i	−0.00310633	−	0.00310633i	−0.708658	+	0.705552i	$0.750699\pi$
$224$	−18.7760	+	10.8403i	−1.25452	+	0.724299i
$225$	−2.95305	+	0.528682i	−0.196870	+	0.0352455i
$226$	−4.56084	−	4.56084i	−0.303383	−	0.303383i
$227$	−14.4302	−	3.86656i	−0.957765	−	0.256632i	−0.254111	−	0.967175i	$-0.581783\pi$
$227$	−14.4302	−	3.86656i	−0.957765	−	0.256632i	−0.703654	+	0.710543i	$0.748449\pi$
$228$	20.0626	−	14.0872i	1.32868	−	0.932947i
$229$	−11.0054	−	2.94888i	−0.727256	−	0.194868i	−0.123849	−	0.992301i	$-0.539524\pi$
$229$	−11.0054	−	2.94888i	−0.727256	−	0.194868i	−0.603407	+	0.797434i	$0.706190\pi$
$230$			2.37041i			0.156300i
$231$	−3.21165	+	3.83769i	−0.211311	+	0.252502i
$232$	4.24145	−	4.24145i	0.278465	−	0.278465i
$233$	19.6737			1.28887			0.644434	−	0.764660i	$-0.277093\pi$
$233$	19.6737			1.28887			0.644434	+	0.764660i	$0.277093\pi$
$234$	16.4623	−	15.2499i	1.07618	−	0.996920i
$235$	−10.8659			−0.708810
$236$	10.1339	−	10.1339i	0.659662	−	0.659662i
$237$	−21.5064	−	3.76312i	−1.39699	−	0.244441i
$238$			18.1298i			1.17518i
$239$	18.0063	+	4.82476i	1.16473	+	0.312088i	0.788853	−	0.614582i	$-0.210675\pi$
$239$	18.0063	+	4.82476i	1.16473	+	0.312088i	0.375875	+	0.926670i	$0.377342\pi$
$240$	0.505550	+	5.69258i	0.0326331	+	0.367455i
$241$	23.1037	+	6.19063i	1.48824	+	0.398773i	0.909143	−	0.416484i	$-0.136738\pi$
$241$	23.1037	+	6.19063i	1.48824	+	0.398773i	0.579099	+	0.815257i	$0.303404\pi$
$242$	14.4246	+	14.4246i	0.927249	+	0.927249i
$243$	−15.3336	+	2.80738i	−0.983649	+	0.180094i
$244$	−16.5050	+	9.52914i	−1.05662	+	0.610041i
$245$	−0.107804	−	0.107804i	−0.00688736	−	0.00688736i
$246$	0.483953	−	2.76581i	0.0308557	−	0.176342i
$247$	−19.6747	−	10.1721i	−1.25187	−	0.647232i
$248$	5.19964	−	3.00201i	0.330177	−	0.190628i
$249$	6.23564	−	4.37842i	0.395168	−	0.277471i
$250$	2.07461			0.131210
$251$	4.94622	−	8.56711i	0.312203	−	0.540751i	−0.666636	−	0.745383i	$-0.732266\pi$
$251$	4.94622	−	8.56711i	0.312203	−	0.540751i	0.978839	+	0.204632i	$0.0655998\pi$
$252$	7.85622	+	16.7331i	0.494895	+	1.05409i
$253$	1.19229	−	0.319473i	0.0749587	−	0.0200851i
$254$	0.812887	−	3.03373i	0.0510050	−	0.190353i
$255$	5.13250	+	2.38514i	0.321409	+	0.149363i
$256$	10.0914			0.630714
$257$	7.14898	−	12.3824i	0.445941	−	0.772393i	−0.552176	−	0.833727i	$-0.686202\pi$
$257$	7.14898	−	12.3824i	0.445941	−	0.772393i	0.998117	+	0.0613348i	$0.0195357\pi$
$258$	33.6623	−	2.98950i	2.09572	−	0.186118i
$259$	9.76312	+	5.63674i	0.606650	+	0.350250i
$260$	−6.99372	+	4.48308i	−0.433732	+	0.278029i
$261$	18.3967	+	21.8081i	1.13873	+	1.34989i
$262$	2.11500	−	7.89327i	0.130665	−	0.487648i
$263$			14.8791i			0.917482i	0.888570	+	0.458741i	$0.151699\pi$
$263$			14.8791i			0.917482i	−0.888570	+	0.458741i	$0.848301\pi$
$264$	−1.10846	+	0.405091i	−0.0682210	+	0.0249316i
$265$	−1.70272	+	6.35463i	−0.104597	+	0.390362i
$266$	24.1005	−	24.1005i	1.47770	−	1.47770i
$267$	20.8705	−	1.85348i	1.27726	−	0.113431i
$268$	6.33755	+	23.6520i	0.387127	+	1.44478i
$269$	−5.18816	−	2.99539i	−0.316328	−	0.182632i	0.333427	−	0.942776i	$-0.391795\pi$
$269$	−5.18816	−	2.99539i	−0.316328	−	0.182632i	−0.649755	+	0.760144i	$0.725128\pi$
$270$	10.7799	−	0.0423571i	0.656045	−	0.00257777i
$271$	−5.30526	−	1.42154i	−0.322272	−	0.0863524i	0.0940564	−	0.995567i	$-0.470017\pi$
$271$	−5.30526	−	1.42154i	−0.322272	−	0.0863524i	−0.416328	+	0.909214i	$0.636683\pi$
$272$	5.39078	−	9.33711i	0.326864	−	0.566146i
$273$	10.1128	−	13.2920i	0.612053	−	0.804469i
$274$	17.2287	+	29.8410i	1.04083	+	1.80276i
$275$	−0.279607	−	1.04351i	−0.0168609	−	0.0629258i
$276$	0.785895	−	4.49143i	0.0473053	−	0.270352i
$277$	−6.36746	+	3.67625i	−0.382584	+	0.220885i	−0.678942	−	0.734192i	$-0.737561\pi$
$277$	−6.36746	+	3.67625i	−0.382584	+	0.220885i	0.296358	+	0.955077i	$0.404228\pi$
$278$	11.1129	−	11.1129i	0.666509	−	0.666509i
$279$	12.1371	+	25.8510i	0.726627	+	1.54766i
$280$	−0.436570	−	1.62930i	−0.0260900	−	0.0973693i
$281$	22.3846	−	5.99793i	1.33535	−	0.357807i	0.480645	−	0.876916i	$-0.340403\pi$
$281$	22.3846	−	5.99793i	1.33535	−	0.357807i	0.854708	+	0.519109i	$0.173736\pi$
$282$	38.4603	+	6.72966i	2.29028	+	0.400746i
$283$	9.43487	+	5.44722i	0.560845	+	0.323804i	0.753484	−	0.657466i	$-0.228372\pi$
$283$	9.43487	+	5.44722i	0.560845	+	0.323804i	−0.192640	+	0.981270i	$0.561705\pi$
$284$	17.1408	−	4.59286i	1.01712	−	0.272536i
$285$	−3.65215	−	9.99344i	−0.216334	−	0.591960i
$286$	5.97313	+	5.44267i	0.353199	+	0.321832i
$287$		−	2.08978i		−	0.123356i
$288$	2.05617	−	24.2330i	0.121161	−	1.42795i
$289$	3.16143	+	5.47576i	0.185967	+	0.322104i
$290$	−9.86521	−	17.0870i	−0.579305	−	1.00339i
$291$	−23.0789	+	2.04961i	−1.35291	+	0.120150i
$292$	−8.74725	−	8.74725i	−0.511894	−	0.511894i
$293$	0.872414	+	0.872414i	0.0509670	+	0.0509670i	0.732131	−	0.681164i	$-0.238526\pi$
$293$	0.872414	+	0.872414i	0.0509670	+	0.0509670i	−0.681164	+	0.732131i	$0.738526\pi$
$294$	0.314811	+	0.448346i	0.0183602	+	0.0261481i
$295$	−3.11012	−	5.38689i	−0.181078	−	0.313637i
$296$	1.32932	+	2.30245i	0.0772652	+	0.133827i
$297$	−1.47417	−	5.41647i	−0.0855402	−	0.314295i
$298$			21.6632i			1.25492i
$299$	−3.92548	+	1.24980i	−0.227016	+	0.0722777i
$300$	−3.93095	−	0.687824i	−0.226953	−	0.0397116i
$301$	24.2954	−	6.50992i	1.40036	−	0.375226i
$302$	−40.4228	−	23.3381i	−2.32607	−	1.34296i
$303$	−1.62176	−	4.43766i	−0.0931678	−	0.254937i
$304$	−19.5783	+	5.24598i	−1.12289	+	0.300878i
$305$	2.14089	+	7.98992i	0.122587	+	0.457502i
$306$	−16.6895	−	11.6211i	−0.954077	−	0.664335i
$307$	−3.99158	+	3.99158i	−0.227812	+	0.227812i	−0.811778	−	0.583966i	$-0.801500\pi$
$307$	−3.99158	+	3.99158i	−0.227812	+	0.227812i	0.583966	+	0.811778i	$0.301500\pi$
$308$	−5.76494	+	3.32839i	−0.328488	+	0.189653i
$309$	−3.82153	−	3.19812i	−0.217399	−	0.181935i
$310$	−5.11147	−	19.0763i	−0.290312	−	1.08346i
$311$	−8.57819	−	14.8579i	−0.486424	−	0.842512i	0.513454	−	0.858117i	$-0.328366\pi$
$311$	−8.57819	−	14.8579i	−0.486424	−	0.842512i	−0.999878	+	0.0156054i	$0.995032\pi$
$312$	3.63273	−	1.52225i	0.205663	−	0.0861806i
$313$	1.34824	−	2.33521i	0.0762068	−	0.131994i	−0.825404	−	0.564543i	$-0.809052\pi$
$313$	1.34824	−	2.33521i	0.0762068	−	0.131994i	0.901610	+	0.432549i	$0.142386\pi$
$314$	11.9963	+	3.21440i	0.676991	+	0.181399i
$315$	7.89766	−	1.41391i	0.444983	−	0.0796649i
$316$	−25.1519	−	14.5215i	−1.41491	−	0.816896i
$317$	1.57927	+	5.89392i	0.0887007	+	0.331035i	0.995989	−	0.0894732i	$-0.0285183\pi$
$317$	1.57927	+	5.89392i	0.0887007	+	0.331035i	−0.907289	+	0.420509i	$0.861852\pi$
$318$	9.96254	−	21.4380i	0.558672	−	1.20218i
$319$	−7.26500	+	7.26500i	−0.406762	+	0.406762i
$320$	−2.64491	+	9.87095i	−0.147855	+	0.551803i
$321$	−2.38872	−	1.99905i	−0.133325	−	0.111576i
$322$		−	6.33945i		−	0.353284i
$323$	−5.19517	+	19.3886i	−0.289067	+	1.07881i
$324$	−20.4397	−	3.49376i	−1.13554	−	0.194098i
$325$	1.09384	+	3.43563i	0.0606752	+	0.190574i
$326$	−1.67818	−	0.968895i	−0.0929455	−	0.0536621i
$327$	−7.92083	+	17.0445i	−0.438023	+	0.942564i
$328$	0.246418	−	0.426809i	0.0136062	−	0.0235666i
$329$	29.0597			1.60211
$330$	0.343398	+	3.86672i	0.0189034	+	0.212856i
$331$	−4.11958	+	15.3745i	−0.226433	+	0.845058i	0.755393	+	0.655272i	$0.227446\pi$
$331$	−4.11958	+	15.3745i	−0.226433	+	0.845058i	−0.981825	+	0.189786i	$0.939221\pi$
$332$	9.79002	−	2.62323i	0.537297	−	0.143968i
$333$	−11.4471	+	5.37441i	−0.627296	+	0.294516i
$334$	19.0684	−	33.0274i	1.04338	−	1.80718i
$335$	10.6277			0.580654
$336$	−1.35205	−	15.2243i	−0.0737602	−	0.830553i
$337$	3.52653	−	2.03604i	0.192102	−	0.110910i	−0.400864	−	0.916138i	$-0.631290\pi$
$337$	3.52653	−	2.03604i	0.192102	−	0.110910i	0.592966	+	0.805227i	$0.297957\pi$
$338$	−20.7570	−	17.2199i	−1.12903	−	0.936641i
$339$	5.05781	−	1.84840i	0.274702	−	0.100391i
$340$	5.32350	+	5.32350i	0.288707	+	0.288707i
$341$	−8.90624	+	5.14202i	−0.482300	+	0.278456i
$342$	6.73763	+	37.6343i	0.364329	+	2.03503i
$343$	−12.9493	−	12.9493i	−0.699198	−	0.699198i
$344$	5.72962	+	1.53525i	0.308920	+	0.0827749i
$345$	−1.79469	−	0.834016i	−0.0966226	−	0.0449019i
$346$	−41.4815	−	11.1149i	−2.23006	−	0.597543i
$347$			20.8078i			1.11702i	0.829498	+	0.558510i	$0.188627\pi$
$347$			20.8078i			1.11702i	−0.829498	+	0.558510i	$0.811373\pi$
$348$	13.0274	+	35.6470i	0.698340	+	1.91088i
$349$	2.15366	−	2.15366i	0.115283	−	0.115283i	−0.647112	−	0.762395i	$-0.724023\pi$
$349$	2.15366	−	2.15366i	0.115283	−	0.115283i	0.762395	+	0.647112i	$0.224023\pi$
$350$	−5.54836			−0.296572
$351$	5.75385	+	17.8296i	0.307118	+	0.951672i
$352$	8.75781			0.466793
$353$	−13.9940	+	13.9940i	−0.744823	+	0.744823i	−0.973502	−	0.228679i	$-0.926559\pi$
$353$	−13.9940	+	13.9940i	−0.744823	+	0.744823i	0.228679	+	0.973502i	$0.426559\pi$
$354$	7.67213	+	20.9934i	0.407769	+	1.11579i
$355$		−	7.70197i		−	0.408778i
$356$	26.9220	+	7.21374i	1.42686	+	0.382327i
$357$	−13.7264	−	6.37884i	−0.726477	−	0.337604i
$358$	16.1347	+	4.32329i	0.852748	+	0.228493i
$359$	6.01973	+	6.01973i	0.317709	+	0.317709i	0.847887	−	0.530177i	$-0.177875\pi$
$359$	6.01973	+	6.01973i	0.317709	+	0.317709i	−0.530177	+	0.847887i	$0.677875\pi$
$360$	1.77971	+	0.642487i	0.0937989	+	0.0338620i
$361$	16.2256	−	9.36785i	0.853978	−	0.493044i
$362$	−12.8836	−	12.8836i	−0.677147	−	0.677147i
$363$	−15.9964	+	5.84594i	−0.839591	+	0.306832i
$364$	18.7041	−	11.9896i	0.980360	−	0.628425i
$365$	−4.64978	+	2.68455i	−0.243381	+	0.140516i
$366$	−2.62933	−	29.6067i	−0.137437	−	1.54757i
$367$	21.5161			1.12313			0.561565	−	0.827433i	$-0.310200\pi$
$367$	21.5161			1.12313			0.561565	+	0.827433i	$0.310200\pi$
$368$	−1.88500	+	3.26492i	−0.0982625	+	0.170196i
$369$	1.92377	+	1.33954i	0.100148	+	0.0697338i
$370$	8.44716	−	2.26341i	0.439147	−	0.117669i
$371$	4.55376	−	16.9949i	0.236420	−	0.882330i
$372$	3.36053	+	37.8401i	0.174235	+	1.96192i
$373$	−10.4384			−0.540479			−0.270240	−	0.962793i	$-0.587103\pi$
$373$	−10.4384			−0.540479			−0.270240	+	0.962793i	$0.587103\pi$
$374$	3.66172	−	6.34229i	0.189343	−	0.327952i
$375$	−0.729940	+	1.57073i	−0.0376939	+	0.0811121i
$376$	5.93505	+	3.42660i	0.306077	+	0.176714i
$377$	23.0953	−	25.3462i	1.18947	−	1.30540i
$378$	−28.8299	+	0.113280i	−1.48285	+	0.00582650i
$379$	−7.03906	+	26.2701i	−0.361572	+	1.34941i	0.510437	+	0.859915i	$0.329484\pi$
$379$	−7.03906	+	26.2701i	−0.361572	+	1.34941i	−0.872009	+	0.489490i	$0.837183\pi$
$380$		−	14.1534i		−	0.726055i
$381$	2.01089	+	1.68285i	0.103021	+	0.0862152i
$382$	10.6355	−	39.6920i	0.544157	−	2.03082i
$383$	0.244869	−	0.244869i	0.0125122	−	0.0125122i	−0.700823	−	0.713335i	$-0.747184\pi$
$383$	0.244869	−	0.244869i	0.0125122	−	0.0125122i	0.713335	+	0.700823i	$0.247184\pi$
$384$	3.64049	−	7.83383i	0.185778	−	0.399769i
$385$	0.747782	+	2.79076i	0.0381105	+	0.142230i
$386$	−43.7376	−	25.2519i	−2.22618	−	1.28529i
$387$	−9.58046	+	26.5382i	−0.487002	+	1.34901i
$388$	−29.7707	−	7.97704i	−1.51138	−	0.404973i
$389$	13.3578	−	23.1363i	0.677266	−	1.17306i	−0.298535	−	0.954399i	$-0.596498\pi$
$389$	13.3578	−	23.1363i	0.677266	−	1.17306i	0.975801	−	0.218660i	$-0.0701686\pi$
$390$	−1.74388	−	12.8380i	−0.0883047	−	0.650080i
$391$	1.86674	+	3.23329i	0.0944053	+	0.163515i
$392$	0.0248872	+	0.0928804i	0.00125699	+	0.00469117i
$393$	5.23200	+	4.37850i	0.263919	+	0.220866i
$394$	−8.97290	+	5.18051i	−0.452048	+	0.260990i
$395$	−8.91334	+	8.91334i	−0.448479	+	0.448479i
$396$	0.631321	−	7.44046i	0.0317251	−	0.373897i
$397$	−4.94591	−	18.4584i	−0.248228	−	0.926399i	−0.971733	−	0.236081i	$-0.924137\pi$
$397$	−4.94591	−	18.4584i	−0.248228	−	0.926399i	0.723505	−	0.690319i	$-0.242530\pi$
$398$	3.19154	−	0.855170i	0.159977	−	0.0428658i
$399$	9.76733	+	26.7265i	0.488978	+	1.33800i
$400$	2.85749	+	1.64977i	0.142875	+	0.0824887i
$401$	−3.19381	+	0.855779i	−0.159491	+	0.0427356i	−0.337681	−	0.941261i	$-0.609643\pi$
$401$	−3.19381	+	0.855779i	−0.159491	+	0.0427356i	0.178190	+	0.983996i	$0.442976\pi$
$402$	−37.6174	−	6.58217i	−1.87618	−	0.328289i
$403$	28.8959	−	18.5227i	1.43941	−	0.922682i
$404$		−	6.28493i		−	0.312687i
$405$	−3.76078	+	8.17658i	−0.186875	+	0.406298i
$406$	26.3836	+	45.6977i	1.30940	+	2.26794i
$407$	−2.27694	−	3.94377i	−0.112864	−	0.195486i
$408$	−2.05126	−	2.92135i	−0.101552	−	0.144628i
$409$	−19.1585	−	19.1585i	−0.947328	−	0.947328i	0.0513527	−	0.998681i	$-0.483647\pi$
$409$	−19.1585	−	19.1585i	−0.947328	−	0.947328i	−0.998681	+	0.0513527i	$0.983647\pi$
$410$	−1.14629	−	1.14629i	−0.0566113	−	0.0566113i
$411$	−28.6551	+	2.54482i	−1.41345	+	0.125526i
$412$	−3.31437	−	5.74066i	−0.163287	−	0.282822i
$413$	8.31773	+	14.4067i	0.409289	+	0.708909i
$414$	5.83585	+	4.06357i	0.286816	+	0.199713i
$415$		−	4.39901i		−	0.215939i
$416$	−29.1976	+	1.35674i	−1.43153	+	0.0665199i
$417$	4.50379	+	12.3238i	0.220552	+	0.603500i
$418$	−13.2987	+	3.56337i	−0.650459	+	0.174290i
$419$	−20.5289	−	11.8524i	−1.00290	−	0.579027i	−0.0937973	−	0.995591i	$-0.529901\pi$
$419$	−20.5289	−	11.8524i	−1.00290	−	0.579027i	−0.909106	+	0.416565i	$0.863234\pi$
$420$	10.5130	+	1.83952i	0.512980	+	0.0897595i
$421$	11.2245	−	3.00759i	0.547048	−	0.146581i	0.0252989	−	0.999680i	$-0.491946\pi$
$421$	11.2245	−	3.00759i	0.547048	−	0.146581i	0.521749	+	0.853099i	$0.325280\pi$
$422$	−7.30127	−	27.2487i	−0.355420	−	1.32645i
$423$	−18.6272	+	26.7512i	−0.905685	+	1.30069i
$424$	2.93401	−	2.93401i	0.142488	−	0.142488i
$425$	2.82981	−	1.63379i	0.137266	−	0.0792507i
$426$	−4.77014	+	27.2615i	−0.231114	+	1.32083i
$427$	−5.72562	−	21.3683i	−0.277082	−	1.03409i
$428$	−2.07171	−	3.58831i	−0.100140	−	0.173447i
$429$	−6.22236	+	2.60740i	−0.300418	+	0.125887i
$430$	9.75571	−	16.8974i	0.470462	−	0.814864i
$431$	30.7674	+	8.24410i	1.48201	+	0.397104i	0.907032	−	0.421062i	$-0.138343\pi$
$431$	30.7674	+	8.24410i	1.48201	+	0.397104i	0.574981	+	0.818167i	$0.305009\pi$
$432$	14.8815	+	8.51407i	0.715988	+	0.409633i
$433$	−10.7719	−	6.21917i	−0.517665	−	0.298874i	0.218314	−	0.975879i	$-0.429944\pi$
$433$	−10.7719	−	6.21917i	−0.517665	−	0.298874i	−0.735979	+	0.677005i	$0.763278\pi$
$434$	13.6702	+	51.0177i	0.656188	+	2.44893i
$435$	16.4079	−	1.45717i	0.786701	−	0.0698658i
$436$	−17.6788	+	17.6788i	−0.846663	+	0.846663i
$437$	1.81660	−	6.77965i	0.0868998	−	0.324315i
$438$	18.1208	−	6.62232i	0.865846	−	0.316427i
$439$		−	14.4266i		−	0.688545i	−0.938870	−	0.344272i	$-0.888126\pi$
$439$		−	14.4266i		−	0.688545i	0.938870	−	0.344272i	$-0.111874\pi$
$440$	−0.176351	+	0.658150i	−0.00840719	+	0.0313761i
$441$	−0.450216	+	0.0806018i	−0.0214389	+	0.00383818i
$442$	−11.2253	+	21.7118i	−0.533932	+	1.03273i
$443$	−16.2814	−	9.40006i	−0.773552	−	0.446610i	0.0605886	−	0.998163i	$-0.480702\pi$
$443$	−16.2814	−	9.40006i	−0.773552	−	0.446610i	−0.834140	+	0.551553i	$0.814036\pi$
$444$	−16.7560	+	1.48808i	−0.795204	+	0.0706209i
$445$	6.04852	−	10.4763i	0.286727	−	0.496626i
$446$	0.136098			0.00644443
$447$	−16.4016	−	7.62207i	−0.775771	−	0.360512i
$448$	7.07358	−	26.3990i	0.334195	−	1.24723i
$449$	−14.4762	+	3.87888i	−0.683172	+	0.183055i	−0.583681	−	0.811983i	$-0.698388\pi$
$449$	−14.4762	+	3.87888i	−0.683172	+	0.183055i	−0.0994911	+	0.995038i	$0.531721\pi$
$450$	3.55648	−	5.10760i	0.167654	−	0.240775i
$451$	−0.422080	+	0.731064i	−0.0198750	+	0.0344245i
$452$	7.16322			0.336930
$453$	31.8922	−	22.3935i	1.49843	−	1.05214i
$454$	26.8408	−	15.4965i	1.25970	−	0.727289i
$455$	−2.92537	−	9.18826i	−0.137143	−	0.430752i
$456$	−1.15664	+	6.61025i	−0.0541647	+	0.309553i
$457$	13.9229	+	13.9229i	0.651288	+	0.651288i	0.953303	−	0.302016i	$-0.0976594\pi$
$457$	13.9229	+	13.9229i	0.651288	+	0.651288i	−0.302016	+	0.953303i	$0.597659\pi$
$458$	20.4705	−	11.8187i	0.956524	−	0.552249i
$459$	14.6707	−	8.54716i	0.684769	−	0.398947i
$460$	−1.86148	−	1.86148i	−0.0867917	−	0.0867917i
$461$	−25.7243	−	6.89282i	−1.19810	−	0.321031i	−0.396019	−	0.918242i	$-0.629609\pi$
$461$	−25.7243	−	6.89282i	−1.19810	−	0.321031i	−0.802084	+	0.597212i	$0.796275\pi$
$462$	−0.918386	−	10.3412i	−0.0427272	−	0.481116i
$463$	−33.3055	−	8.92419i	−1.54784	−	0.414742i	−0.619050	−	0.785351i	$-0.712482\pi$
$463$	−33.3055	−	8.92419i	−1.54784	−	0.414742i	−0.928789	+	0.370609i	$0.879149\pi$
$464$		−	31.3801i		−	1.45678i
$465$	16.2414	+	2.84188i	0.753179	+	0.131789i
$466$	−28.8608	+	28.8608i	−1.33695	+	1.33695i
$467$	−0.782062			−0.0361895			−0.0180947	−	0.999836i	$-0.505760\pi$
$467$	−0.782062			−0.0361895			−0.0180947	+	0.999836i	$0.505760\pi$
$468$	−0.952096	+	24.9035i	−0.0440106	+	1.15117i
$469$	−28.4228			−1.31244
$470$	15.9399	−	15.9399i	0.735253	−	0.735253i
$471$	−6.65451	+	7.95167i	−0.306624	+	0.366394i
$472$			3.92317i			0.180579i
$473$	−9.81402	−	2.62966i	−0.451249	−	0.120912i
$474$	37.0697	−	26.0289i	1.70267	−	1.19555i
$475$	−5.93362	−	1.58991i	−0.272253	−	0.0729500i
$476$	−14.2372	−	14.2372i	−0.652562	−	0.652562i
$477$	12.7259	+	15.0857i	0.582677	+	0.690725i
$478$	−33.4925	+	19.3369i	−1.53191	+	0.884449i
$479$	5.40659	+	5.40659i	0.247033	+	0.247033i	0.819752	−	0.572719i	$-0.194111\pi$
$479$	5.40659	+	5.40659i	0.247033	+	0.247033i	−0.572719	+	0.819752i	$0.694111\pi$
$480$	−10.7680	−	9.01143i	−0.491490	−	0.411313i
$481$	8.20204	+	12.7954i	0.373981	+	0.583420i
$482$	−42.9740	+	24.8111i	−1.95741	+	1.13011i
$483$	4.79972	+	2.23050i	0.218395	+	0.101491i
$484$	−22.6552			−1.02978
$485$	−6.68853	+	11.5849i	−0.303710	+	0.526042i
$486$	18.3756	−	26.6123i	0.833533	−	1.20716i
$487$	1.26402	−	0.338692i	0.0572780	−	0.0153476i	−0.230066	−	0.973175i	$-0.573894\pi$
$487$	1.26402	−	0.338692i	0.0572780	−	0.0153476i	0.287344	+	0.957827i	$0.407228\pi$
$488$	1.35028	−	5.03932i	0.0611244	−	0.228120i
$489$	1.32402	−	0.929679i	0.0598745	−	0.0420415i
$490$	0.316291			0.0142886
$491$	−0.136112	+	0.235752i	−0.00614263	+	0.0106394i	−0.869080	−	0.494671i	$-0.835289\pi$
$491$	−0.136112	+	0.235752i	−0.00614263	+	0.0106394i	0.862938	+	0.505310i	$0.168622\pi$
$492$	1.79193	+	2.55202i	0.0807866	+	0.115054i
$493$	−26.9127	−	15.5381i	−1.21209	−	0.699799i
$494$	43.7843	−	13.9401i	1.96995	−	0.627195i
$495$	−3.04839	−	1.10049i	−0.137015	−	0.0494633i
$496$	8.12949	−	30.3397i	0.365025	−	1.36229i
$497$			20.5982i			0.923955i
$498$	−2.72448	+	15.5705i	−0.122087	+	0.697732i
$499$	0.159115	−	0.593827i	0.00712298	−	0.0265833i	−0.962273	−	0.272086i	$-0.912286\pi$
$499$	0.159115	−	0.593827i	0.00712298	−	0.0265833i	0.969396	+	0.245503i	$0.0789531\pi$
$500$	−1.62918	+	1.62918i	−0.0728593	+	0.0728593i
$501$	18.2966	+	26.0576i	0.817432	+	1.16417i
$502$	5.31174	+	19.8237i	0.237074	+	0.884774i
$503$	34.4363	+	19.8818i	1.53544	+	0.886486i	0.999097	+	0.0424855i	$0.0135276\pi$
$503$	34.4363	+	19.8818i	1.53544	+	0.886486i	0.536342	+	0.844001i	$0.319806\pi$
$504$	−4.75967	−	1.71827i	−0.212013	−	0.0765379i
$505$	−2.63487	−	0.706011i	−0.117250	−	0.0314171i
$506$	−1.28040	+	2.21772i	−0.0569207	+	0.0985895i
$507$	20.3408	−	9.65677i	0.903365	−	0.428872i
$508$	1.74402	+	3.02073i	0.0773785	+	0.134023i
$509$	−8.90329	−	33.2275i	−0.394631	−	1.47278i	−0.822407	−	0.568899i	$-0.807369\pi$
$509$	−8.90329	−	33.2275i	−0.394631	−	1.47278i	0.427776	−	0.903885i	$-0.359297\pi$
$510$	−11.0282	+	4.03029i	−0.488335	+	0.178464i
$511$	12.4354	−	7.17959i	0.550110	−	0.317606i
$512$	−21.8571	+	21.8571i	−0.965955	+	0.965955i
$513$	−30.8642	−	8.14020i	−1.36269	−	0.359399i
$514$	7.67728	+	28.6520i	0.338630	+	1.26378i
$515$	−2.77901	+	0.744633i	−0.122458	+	0.0328124i
$516$	−24.0872	+	28.7825i	−1.06038	+	1.26708i
$517$	−10.1659	−	5.86928i	−0.447096	−	0.258131i
$518$	−22.5912	+	6.05328i	−0.992598	+	0.265966i
$519$	23.0103	−	27.4957i	1.01004	−	1.20693i
$520$	0.485976	−	2.22152i	0.0213114	−	0.0974202i
$521$		−	17.0580i		−	0.747324i	−0.927565	−	0.373662i	$-0.878102\pi$
$521$		−	17.0580i		−	0.747324i	0.927565	−	0.373662i	$-0.121898\pi$
$522$	−58.9793	−	5.00438i	−2.58145	−	0.219036i
$523$	−20.8653	−	36.1397i	−0.912375	−	1.58028i	−0.810700	−	0.585462i	$-0.800913\pi$
$523$	−20.8653	−	36.1397i	−0.912375	−	1.58028i	−0.101675	−	0.994818i	$-0.532420\pi$
$524$	4.53765	+	7.85945i	0.198228	+	0.343342i
$525$	1.95216	−	4.20077i	0.0851991	−	0.183337i
$526$	−21.8272	−	21.8272i	−0.951709	−	0.951709i
$527$	−21.9951	−	21.9951i	−0.958120	−	0.958120i
$528$	−2.60191	+	5.59895i	−0.113234	+	0.243663i
$529$	10.8473	+	18.7880i	0.471620	+	0.816869i
$530$	−6.82422	−	11.8199i	−0.296425	−	0.513424i
$531$	−18.5939	−	1.57769i	−0.806907	−	0.0684659i
$532$			37.8520i			1.64109i
$533$	1.29392	−	2.50268i	0.0560457	−	0.108403i
$534$	−27.8975	+	33.3355i	−1.20724	+	1.44257i
$535$	−1.73707	+	0.465447i	−0.0751002	+	0.0201230i
$536$	−5.80497	−	3.35150i	−0.250737	−	0.144763i
$537$	−8.95016	+	10.6948i	−0.386228	+	0.461515i
$538$	12.0050	−	3.21674i	0.517574	−	0.138684i
$539$	−0.0426283	−	0.159091i	−0.00183613	−	0.00685253i
$540$	−8.43216	+	8.49868i	−0.362862	+	0.365725i
$541$	25.0643	−	25.0643i	1.07760	−	1.07760i	0.0808753	−	0.996724i	$-0.474228\pi$
$541$	25.0643	−	25.0643i	1.07760	−	1.07760i	0.996724	−	0.0808753i	$-0.0257716\pi$
$542$	9.86803	−	5.69731i	0.423868	−	0.244720i
$543$	14.2874	−	5.22140i	0.613133	−	0.224072i
$544$	6.85595	+	25.5868i	0.293947	+	1.09702i
$545$	5.42567	+	9.39754i	0.232410	+	0.402546i
$546$	4.66384	+	34.3342i	0.199594	+	1.46937i
$547$	18.4241	−	31.9115i	0.787759	−	1.36444i	−0.139578	−	0.990211i	$-0.544575\pi$
$547$	18.4241	−	31.9115i	0.787759	−	1.36444i	0.927337	−	0.374227i	$-0.122092\pi$
$548$	−36.9637	−	9.90439i	−1.57901	−	0.423095i
$549$	23.3409	+	8.42623i	0.996167	+	0.359623i
$550$	1.94097	+	1.12062i	0.0827632	+	0.0477834i
$551$	15.1207	+	56.4312i	0.644163	+	2.40405i
$552$	0.717266	+	1.02151i	0.0305289	+	0.0434784i
$553$	23.8379	−	23.8379i	1.01369	−	1.01369i
$554$	3.94792	−	14.7338i	0.167731	−	0.625981i
$555$	−1.25841	+	7.19188i	−0.0534166	+	0.305278i
$556$			17.4539i			0.740209i
$557$	2.10961	−	7.87316i	0.0893869	−	0.333596i	−0.906722	−	0.421729i	$-0.861423\pi$
$557$	2.10961	−	7.87316i	0.0893869	−	0.333596i	0.996109	+	0.0881328i	$0.0280900\pi$
$558$	−55.7274	−	20.1180i	−2.35913	−	0.851661i
$559$	33.1263	+	7.24664i	1.40109	+	0.306500i
$560$	−7.64210	−	4.41217i	−0.322938	−	0.186448i
$561$	3.51351	+	5.00386i	0.148341	+	0.211263i
$562$	−24.0388	+	41.6364i	−1.01401	+	1.75632i
$563$	−10.2561			−0.432243			−0.216121	−	0.976367i	$-0.569341\pi$
$563$	−10.2561			−0.432243			−0.216121	+	0.976367i	$0.569341\pi$
$564$	−35.4875	+	24.9179i	−1.49429	+	1.04923i
$565$	0.804673	−	3.00308i	0.0338529	−	0.126341i
$566$	−21.8316	+	5.84976i	−0.917651	+	0.245884i
$567$	10.0579	−	21.8675i	0.422390	−	0.918350i
$568$	−2.42885	+	4.20690i	−0.101912	+	0.176518i
$569$	−37.2588			−1.56197			−0.780986	−	0.624549i	$-0.785283\pi$
$569$	−37.2588			−1.56197			−0.780986	+	0.624549i	$0.785283\pi$
$570$	20.0177	+	9.30251i	0.838449	+	0.389639i
$571$	−13.7037	+	7.91184i	−0.573483	+	0.331100i	−0.758539	−	0.651628i	$-0.774087\pi$
$571$	−13.7037	+	7.91184i	−0.573483	+	0.331100i	0.185056	+	0.982728i	$0.440753\pi$
$572$	−8.96478	+	0.416572i	−0.374836	+	0.0174177i
$573$	26.3096	+	22.0177i	1.09910	+	0.919803i
$574$	3.06565	+	3.06565i	0.127958	+	0.127958i
$575$	−0.989505	+	0.571291i	−0.0412652	+	0.0238245i
$576$	19.7677	+	23.4333i	0.823654	+	0.976387i
$577$	−16.3724	−	16.3724i	−0.681591	−	0.681591i	0.278767	−	0.960359i	$-0.410074\pi$
$577$	−16.3724	−	16.3724i	−0.681591	−	0.681591i	−0.960359	+	0.278767i	$0.910074\pi$
$578$	−12.6705	−	3.39506i	−0.527024	−	0.141216i
$579$	34.5075	−	24.2298i	1.43408	−	1.00696i
$580$	21.1655	+	5.67127i	0.878849	+	0.235487i
$581$			11.7647i			0.488084i
$582$	30.8494	−	36.8628i	1.27875	−	1.52801i
$583$	−5.02554	+	5.02554i	−0.208137	+	0.208137i
$584$	3.38635			0.140128
$585$	10.3335	+	3.19667i	0.427238	+	0.132166i
$586$	−2.55961			−0.105737
$587$	−29.0086	+	29.0086i	−1.19731	+	1.19731i	−0.222345	+	0.974968i	$0.571371\pi$
$587$	−29.0086	+	29.0086i	−1.19731	+	1.19731i	−0.974968	+	0.222345i	$0.928629\pi$
$588$	−0.599305	−	0.104864i	−0.0247149	−	0.00432454i
$589$			58.4775i			2.40952i
$590$	12.4649	+	3.33995i	0.513171	+	0.137504i
$591$	−0.765200	−	8.61629i	−0.0314761	−	0.354427i
$592$	13.4347	+	3.59982i	0.552163	+	0.147952i
$593$	2.85864	+	2.85864i	0.117390	+	0.117390i	0.763362	−	0.645971i	$-0.223547\pi$
$593$	2.85864	+	2.85864i	0.117390	+	0.117390i	−0.645971	+	0.763362i	$0.723547\pi$
$594$	10.1084	+	5.78323i	0.414752	+	0.237289i
$595$	−7.56808	+	4.36943i	−0.310261	+	0.179129i
$596$	−17.0120	−	17.0120i	−0.696840	−	0.696840i
$597$	−0.475458	+	2.71726i	−0.0194592	+	0.111210i
$598$	3.92515	−	7.59199i	0.160511	−	0.310460i
$599$	4.47306	−	2.58252i	0.182764	−	0.105519i	−0.405827	−	0.913950i	$-0.633016\pi$
$599$	4.47306	−	2.58252i	0.182764	−	0.105519i	0.588591	+	0.808431i	$0.299683\pi$
$600$	0.894038	−	0.627759i	0.0364990	−	0.0256282i
$601$	−14.4915			−0.591122			−0.295561	−	0.955324i	$-0.595507\pi$
$601$	−14.4915			−0.591122			−0.295561	+	0.955324i	$0.595507\pi$
$602$	−26.0907	+	45.1905i	−1.06338	+	1.84183i
$603$	18.2189	−	26.1650i	0.741933	−	1.06552i
$604$	50.0712	−	13.4165i	2.03737	−	0.545911i
$605$	−2.54495	+	9.49787i	−0.103467	+	0.386143i
$606$	8.88901	+	4.13085i	0.361091	+	0.167804i
$607$	12.9064			0.523854			0.261927	−	0.965088i	$-0.415642\pi$
$607$	12.9064			0.523854			0.261927	+	0.965088i	$0.415642\pi$
$608$	24.8995	−	43.1272i	1.00981	−	1.74904i
$609$	−43.8815	+	3.89706i	−1.77817	+	0.157917i
$610$	−14.8616	−	8.58036i	−0.601730	−	0.347409i
$611$	34.8013	+	17.9927i	1.40791	+	0.727907i
$612$	22.2322	−	3.98022i	0.898685	−	0.160891i
$613$	−10.6753	+	39.8409i	−0.431173	+	1.60916i	0.318891	+	0.947792i	$0.396690\pi$
$613$	−10.6753	+	39.8409i	−0.431173	+	1.60916i	−0.750063	+	0.661366i	$0.769977\pi$
$614$		−	11.7111i		−	0.472620i
$615$	1.27120	−	0.464564i	0.0512596	−	0.0187330i
$616$	0.471634	−	1.76016i	0.0190027	−	0.0709189i
$617$	21.9136	−	21.9136i	0.882209	−	0.882209i	−0.111550	−	0.993759i	$-0.535581\pi$
$617$	21.9136	−	21.9136i	0.882209	−	0.882209i	0.993759	+	0.111550i	$0.0355814\pi$
$618$	10.2976	−	0.914518i	0.414232	−	0.0367873i
$619$	0.0992889	+	0.370551i	0.00399076	+	0.0148937i	0.967892	−	0.251364i	$-0.0808793\pi$
$619$	0.0992889	+	0.370551i	0.00399076	+	0.0148937i	−0.963902	+	0.266258i	$0.914213\pi$
$620$	18.9945	+	10.9665i	0.762838	+	0.440425i
$621$	−5.12991	+	2.98869i	−0.205856	+	0.119932i
$622$	34.3800	+	9.21210i	1.37851	+	0.369372i
$623$	−16.1762	+	28.0180i	−0.648086	+	1.12252i
$624$	7.80713	−	19.0694i	0.312535	−	0.763388i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	1.44787	+	5.40352i	0.0578685	+	0.215968i
$627$	1.98116	−	11.3224i	0.0791200	−	0.452174i
$628$	−11.9449	+	6.89639i	−0.476654	+	0.275196i
$629$	9.73963	−	9.73963i	0.388345	−	0.388345i
$630$	−9.51147	+	13.6598i	−0.378946	+	0.544220i
$631$	−0.974058	−	3.63524i	−0.0387766	−	0.144716i	0.943823	−	0.330450i	$-0.107201\pi$
$631$	−0.974058	−	3.63524i	−0.0387766	−	0.144716i	−0.982600	+	0.185734i	$0.940534\pi$
$632$	7.67943	−	2.05770i	0.305471	−	0.0818508i
$633$	23.1994	+	4.05936i	0.922095	+	0.161345i
$634$	−10.9630	−	6.32947i	−0.435395	−	0.251375i
$635$	1.46231	−	0.391826i	0.0580302	−	0.0155491i
$636$	9.01163	+	24.6587i	0.357334	+	0.977782i
$637$	0.166764	+	0.523789i	0.00660745	+	0.0207533i
$638$		−	21.3151i		−	0.843873i
$639$	−18.9619	−	13.2034i	−0.750121	−	0.522317i
$640$	−2.49369	−	4.31920i	−0.0985719	−	0.170732i
$641$	−14.1013	−	24.4241i	−0.556966	−	0.964694i	−0.997748	−	0.0670796i	$-0.978632\pi$
$641$	−14.1013	−	24.4241i	−0.556966	−	0.964694i	0.440781	−	0.897615i	$-0.354701\pi$
$642$	6.43674	−	0.571637i	0.254038	−	0.0225607i
$643$	32.7375	+	32.7375i	1.29104	+	1.29104i	0.934143	+	0.356900i	$0.116166\pi$
$643$	32.7375	+	32.7375i	1.29104	+	1.29104i	0.356900	+	0.934143i	$0.383834\pi$
$644$	4.97834	+	4.97834i	0.196174	+	0.196174i
$645$	9.36085	+	13.3315i	0.368583	+	0.524926i
$646$	−20.8214	−	36.0638i	−0.819208	−	1.41891i
$647$	−3.30585	−	5.72590i	−0.129966	−	0.225109i	0.793697	−	0.608313i	$-0.208154\pi$
$647$	−3.30585	−	5.72590i	−0.129966	−	0.225109i	−0.923663	+	0.383205i	$0.874820\pi$
$648$	4.63271	−	3.28016i	0.181990	−	0.128857i
$649$		−	6.71983i		−	0.263777i
$650$	−6.64459	−	3.43534i	−0.260622	−	0.134745i
$651$	−43.4362	−	7.60034i	−1.70240	−	0.297881i
$652$	2.07873	−	0.556995i	0.0814094	−	0.0218136i
$653$	30.4325	+	17.5702i	1.19092	+	0.687576i	0.958514	−	0.285044i	$-0.0920083\pi$
$653$	30.4325	+	17.5702i	1.19092	+	0.687576i	0.232402	+	0.972620i	$0.425342\pi$
$654$	−13.3842	−	36.6235i	−0.523364	−	1.43209i
$655$	3.80470	−	1.01947i	0.148662	−	0.0398338i
$656$	−0.667305	−	2.49042i	−0.0260539	−	0.0972344i
$657$	−1.36181	+	16.0496i	−0.0531292	+	0.626156i
$658$	−42.6298	+	42.6298i	−1.66188	+	1.66188i
$659$	5.11437	−	2.95278i	0.199227	−	0.115024i	−0.397068	−	0.917789i	$-0.629972\pi$
$659$	5.11437	−	2.95278i	0.199227	−	0.115024i	0.596295	+	0.802765i	$0.296639\pi$
$660$	−3.30619	−	2.76685i	−0.128693	−	0.107699i
$661$	3.39510	+	12.6707i	0.132054	+	0.492832i	0.999993	−	0.00383925i	$-0.00122207\pi$
$661$	3.39510	+	12.6707i	0.132054	+	0.492832i	−0.867939	+	0.496671i	$0.834555\pi$
$662$	−16.5106	−	28.5973i	−0.641704	−	1.11146i
$663$	−12.4889	−	16.1380i	−0.485028	−	0.626749i
$664$	−1.38725	+	2.40279i	−0.0538357	+	0.0932462i
$665$	15.8689	+	4.25207i	0.615371	+	0.164888i
$666$	8.90844	−	24.6767i	0.345195	−	0.956201i
$667$	9.41060	+	5.43321i	0.364380	+	0.210375i
$668$	10.9620	+	40.9106i	0.424131	+	1.58288i
$669$	−0.0478853	+	0.103042i	−0.00185135	+	0.00398385i
$670$	−15.5906	+	15.5906i	−0.602316	+	0.602316i
$671$	−2.31284	+	8.63165i	−0.0892863	+	0.333221i
$672$	28.7981	+	24.1002i	1.11091	+	0.929687i
$673$			1.22014i			0.0470331i	0.999723	+	0.0235165i	$0.00748624\pi$
$673$			1.22014i			0.0470331i	−0.999723	+	0.0235165i	$0.992514\pi$
$674$	−2.18650	+	8.16014i	−0.0842209	+	0.314317i
$675$	2.61574	+	4.48976i	0.100680	+	0.172811i
$676$	29.8231	−	2.77761i	1.14704	−	0.106831i
$677$	12.0421	+	6.95250i	0.462815	+	0.267206i	0.713227	−	0.700933i	$-0.247233\pi$
$677$	12.0421	+	6.95250i	0.462815	+	0.267206i	−0.250412	+	0.968139i	$0.580566\pi$
$678$	−4.70812	+	10.1312i	−0.180814	+	0.389087i
$679$	17.8879	−	30.9827i	0.686473	−	1.18901i
$680$	−2.06090			−0.0790320
$681$	2.28896	+	25.7741i	0.0877130	+	0.987664i
$682$	5.52201	−	20.6084i	0.211449	−	0.789137i
$683$	−33.9016	+	9.08391i	−1.29721	+	0.347586i	−0.840394	−	0.541976i	$-0.817676\pi$
$683$	−33.9016	+	9.08391i	−1.29721	+	0.347586i	−0.456815	+	0.889562i	$0.651010\pi$
$684$	−34.8451	−	24.2630i	−1.33233	−	0.927719i
$685$	−8.30456	+	14.3839i	−0.317301	+	0.549581i
$686$	37.9926			1.45056
$687$	1.74570	+	19.6569i	0.0666028	+	0.749959i
$688$	26.8743	−	15.5159i	1.02457	−	0.591538i
$689$	15.9761	−	17.5332i	0.608640	−	0.667961i
$690$	3.85623	−	1.40928i	0.146804	−	0.0536502i
$691$	18.0478	+	18.0478i	0.686570	+	0.686570i	0.961472	−	0.274902i	$-0.0886456\pi$
$691$	18.0478	+	18.0478i	0.686570	+	0.686570i	−0.274902	+	0.961472i	$0.588646\pi$
$692$	41.3038	−	23.8467i	1.57013	−	0.906517i
$693$	8.15264	+	2.94316i	0.309693	+	0.111801i
$694$	−30.5244	−	30.5244i	−1.15869	−	1.15869i
$695$	7.31729	+	1.96066i	0.277561	+	0.0743721i
$696$	−9.42172	−	4.37841i	−0.357129	−	0.165963i
$697$	−2.46629	−	0.660841i	−0.0934175	−	0.0250311i
$698$			6.31871i			0.239167i
$699$	−11.6966	−	32.0055i	−0.442404	−	1.21056i
$700$	4.35710	−	4.35710i	0.164683	−	0.164683i
$701$	−30.8403			−1.16482			−0.582410	−	0.812895i	$-0.697890\pi$
$701$	−30.8403			−1.16482			−0.582410	+	0.812895i	$0.697890\pi$
$702$	−34.5962	−	17.7147i	−1.30575	−	0.668600i
$703$	−25.8944			−0.976627
$704$	−7.80641	+	7.80641i	−0.294215	+	0.294215i
$705$	6.46005	+	17.6768i	0.243300	+	0.665746i
$706$		−	41.0575i		−	1.54522i
$707$	7.04672	+	1.88816i	0.265019	+	0.0710116i
$708$	−22.5109	−	10.4611i	−0.846013	−	0.393154i
$709$	−39.2458	−	10.5159i	−1.47391	−	0.394932i	−0.569637	−	0.821896i	$-0.692916\pi$
$709$	−39.2458	−	10.5159i	−1.47391	−	0.394932i	−0.904268	+	0.426965i	$0.859583\pi$
$710$	11.2986	+	11.2986i	0.424028	+	0.424028i
$711$	6.66423	+	37.2243i	0.249928	+	1.39602i
$712$	−6.60753	+	3.81486i	−0.247628	+	0.142968i
$713$	7.69104	+	7.69104i	0.288032	+	0.288032i
$714$	29.4938	−	10.7786i	1.10378	−	0.403380i
$715$	−0.832407	+	3.80515i	−0.0311303	+	0.142305i
$716$	−16.0656	+	9.27548i	−0.600400	+	0.346641i
$717$	−2.85621	−	32.1614i	−0.106667	−	1.20109i
$718$	−17.6616			−0.659124
$719$	1.05350	−	1.82472i	0.0392890	−	0.0680505i	−0.845712	−	0.533639i	$-0.820824\pi$
$719$	1.05350	−	1.82472i	0.0392890	−	0.0680505i	0.885001	+	0.465589i	$0.154157\pi$
$720$	8.96023	−	4.20683i	0.333928	−	0.156779i
$721$	7.43220	−	1.99145i	0.276790	−	0.0741656i
$722$	−10.0601	+	37.5448i	−0.374399	+	1.39727i
$723$	−3.66478	−	41.2661i	−0.136295	−	1.53470i
$724$	20.2349			0.752023
$725$	4.75521	−	8.23626i	0.176604	−	0.305887i
$726$	14.8904	−	32.0420i	0.552634	−	1.18919i
$727$	24.7343	+	14.2804i	0.917345	+	0.529630i	0.882787	−	0.469773i	$-0.155664\pi$
$727$	24.7343	+	14.2804i	0.917345	+	0.529630i	0.0345581	+	0.999403i	$0.488998\pi$
$728$	−1.29970	+	5.94126i	−0.0481700	+	0.220198i
$729$	13.6833	+	23.2759i	0.506790	+	0.862069i
$730$	2.88293	−	10.7593i	0.106702	−	0.398218i
$731$		−	30.7312i		−	1.13663i
$732$	25.3148	+	21.1852i	0.935663	+	0.783029i
$733$	7.99030	−	29.8202i	0.295128	−	1.10143i	−0.645987	−	0.763348i	$-0.723554\pi$
$733$	7.99030	−	29.8202i	0.295128	−	1.10143i	0.941115	−	0.338086i	$-0.109779\pi$
$734$	−31.5635	+	31.5635i	−1.16503	+	1.16503i
$735$	−0.111285	+	0.239470i	−0.00410482	+	0.00883299i
$736$	−2.39733	−	8.94695i	−0.0883667	−	0.329789i
$737$	9.94310	+	5.74065i	0.366259	+	0.211460i
$738$	−4.78719	+	0.857047i	−0.176219	+	0.0315483i
$739$	−38.7183	−	10.3745i	−1.42428	−	0.381633i	−0.537277	−	0.843406i	$-0.680547\pi$
$739$	−38.7183	−	10.3745i	−1.42428	−	0.381633i	−0.886998	+	0.461773i	$0.847214\pi$
$740$	−4.85607	+	8.41096i	−0.178513	+	0.309193i
$741$	−4.85094	+	38.0547i	−0.178204	+	1.39797i
$742$	18.2508	+	31.6112i	0.670007	+	1.16049i
$743$	5.41980	+	20.2270i	0.198833	+	0.742055i	0.991241	+	0.132064i	$0.0421605\pi$
$743$	5.41980	+	20.2270i	0.198833	+	0.742055i	−0.792408	+	0.609991i	$0.791173\pi$
$744$	−7.97505	−	6.67409i	−0.292380	−	0.244684i
$745$	−9.04309	+	5.22103i	−0.331313	+	0.191284i
$746$	15.3128	−	15.3128i	0.560642	−	0.560642i
$747$	−10.8302	−	7.54116i	−0.396255	−	0.275916i
$748$	2.10504	+	7.85611i	0.0769678	+	0.287248i
$749$	4.64564	−	1.24480i	0.169748	−	0.0454838i
$750$	−1.23341	−	3.37502i	−0.0450379	−	0.123238i
$751$	18.9743	+	10.9548i	0.692382	+	0.399747i	0.804504	−	0.593948i	$-0.202431\pi$
$751$	18.9743	+	10.9548i	0.692382	+	0.399747i	−0.112122	+	0.993694i	$0.535765\pi$
$752$	34.6308	−	9.27929i	1.26285	−	0.338381i
$753$	−16.8778	−	2.95322i	−0.615061	−	0.107621i
$754$	3.30210	+	71.0623i	0.120255	+	2.58794i
$755$		−	22.4988i		−	0.818814i
$756$	22.5510	−	22.7289i	0.820173	−	0.826644i
$757$	24.5657	+	42.5491i	0.892856	+	1.54647i	0.836435	+	0.548066i	$0.184636\pi$
$757$	24.5657	+	42.5491i	0.892856	+	1.54647i	0.0564212	+	0.998407i	$0.482031\pi$
$758$	−28.2114	−	48.8636i	−1.02469	−	1.77481i
$759$	−1.22857	−	1.74970i	−0.0445944	−	0.0635103i
$760$	2.73962	+	2.73962i	0.0993766	+	0.0993766i
$761$	27.9337	+	27.9337i	1.01259	+	1.01259i	0.999920	+	0.0126745i	$0.00403453\pi$
$761$	27.9337	+	27.9337i	1.01259	+	1.01259i	0.0126745	+	0.999920i	$0.495965\pi$
$762$	−5.41862	+	0.481220i	−0.196296	+	0.0174328i
$763$	−14.5105	−	25.1329i	−0.525314	−	0.909871i
$764$	22.8180	+	39.5220i	0.825527	+	1.42985i
$765$	0.828784	−	9.76767i	0.0299647	−	0.353151i
$766$			0.718433i			0.0259581i
$767$	1.04102	+	22.4032i	0.0375892	+	0.808934i
$768$	−5.99963	−	16.4169i	−0.216493	−	0.592395i
$769$	1.72451	−	0.462082i	0.0621875	−	0.0166631i	−0.227591	−	0.973757i	$-0.573085\pi$
$769$	1.72451	−	0.462082i	0.0621875	−	0.0166631i	0.289779	+	0.957094i	$0.406418\pi$
$770$	−5.19094	−	2.99699i	−0.187069	−	0.108004i
$771$	−24.3942	−	4.26841i	−0.878535	−	0.153723i
$772$	54.1771	−	14.5167i	1.94988	−	0.522468i
$773$	−1.45507	−	5.43041i	−0.0523353	−	0.195318i	0.934809	−	0.355152i	$-0.115571\pi$
$773$	−1.45507	−	5.43041i	−0.0523353	−	0.195318i	−0.987144	+	0.159834i	$0.948904\pi$
$774$	−24.8765	−	52.9851i	−0.894168	−	1.90451i
$775$	6.73128	−	6.73128i	0.241795	−	0.241795i
$776$	7.30670	−	4.21852i	0.262295	−	0.151436i
$777$	3.36551	−	19.2340i	0.120737	−	0.690016i
$778$	14.3449	+	53.5358i	0.514289	+	1.91935i
$779$	2.40005	+	4.15700i	0.0859906	+	0.148940i
$780$	11.4511	+	8.71220i	0.410016	+	0.311947i
$781$	4.16028	−	7.20582i	0.148867	−	0.257845i
$782$	−7.48161	−	2.00469i	−0.267542	−	0.0716876i
$783$	24.5404	−	42.8936i	0.877003	−	1.53289i
$784$	0.435648	+	0.251521i	0.0155589	+	0.00898291i
$785$	1.54940	+	5.78244i	0.0553004	+	0.206384i
$786$	−14.0983	+	1.25205i	−0.502871	+	0.0446593i
$787$	−3.03585	+	3.03585i	−0.108216	+	0.108216i	−0.759142	−	0.650925i	$-0.774381\pi$
$787$	−3.03585	+	3.03585i	−0.108216	+	0.108216i	0.650925	+	0.759142i	$0.274381\pi$
$788$	2.97815	−	11.1146i	0.106092	−	0.395942i
$789$	24.2055	−	8.84601i	0.861739	−	0.314926i
$790$		−	26.1512i		−	0.930419i
$791$	−2.15202	+	8.03147i	−0.0765172	+	0.285566i
$792$	1.31802	+	1.56242i	0.0468338	+	0.0555183i
$793$	6.37358	−	29.1353i	0.226332	−	1.03463i
$794$	34.3334	+	19.8224i	1.21845	+	0.703471i
$795$	11.3501	−	1.00799i	0.402548	−	0.0357497i
$796$	−1.83474	+	3.17786i	−0.0650306	+	0.112636i
$797$	14.9687			0.530219			0.265110	−	0.964218i	$-0.414592\pi$
$797$	14.9687			0.530219			0.265110	+	0.964218i	$0.414592\pi$
$798$	−53.5355	−	24.8787i	−1.89514	−	0.880696i
$799$	9.18941	−	34.2953i	0.325098	−	1.21328i
$800$	−7.83047	+	2.09817i	−0.276849	+	0.0741815i
$801$	−15.4234	−	32.8506i	−0.544959	−	1.16072i
$802$	3.42983	−	5.94064i	0.121111	−	0.209771i
$803$	−5.80033			−0.204689
$804$	34.7097	−	24.3718i	1.22412	−	0.859528i
$805$	2.64634	−	1.52786i	0.0932712	−	0.0538502i
$806$	−15.2172	+	69.5618i	−0.536002	+	2.45021i
$807$	−1.78844	+	10.2210i	−0.0629562	+	0.359798i
$808$	1.21655	+	1.21655i	0.0427981	+	0.0427981i
$809$	18.9132	−	10.9196i	0.664954	−	0.383912i	−0.129208	−	0.991618i	$-0.541243\pi$
$809$	18.9132	−	10.9196i	0.664954	−	0.383912i	0.794162	+	0.607706i	$0.207910\pi$
$810$	−6.47786	−	17.5118i	−0.227609	−	0.615301i
$811$	−20.1801	−	20.1801i	−0.708620	−	0.708620i	0.257625	−	0.966245i	$-0.417060\pi$
$811$	−20.1801	−	20.1801i	−0.708620	−	0.708620i	−0.966245	+	0.257625i	$0.917060\pi$
$812$	−56.6051	−	15.1673i	−1.98645	−	0.532268i
$813$	0.841536	+	9.47584i	0.0295140	+	0.332332i
$814$	9.12561	+	2.44520i	0.319853	+	0.0857042i
$815$		−	0.934049i		−	0.0327183i
$816$	−18.3948	−	3.21866i	−0.643945	−	0.112675i
$817$	−40.8520	+	40.8520i	−1.42923	+	1.42923i
$818$	56.2100			1.96534
$819$	−27.6360	−	8.54919i	−0.965680	−	0.298733i
$820$	1.80036			0.0628712
$821$	22.8017	−	22.8017i	0.795784	−	0.795784i	−0.186644	−	0.982428i	$-0.559761\pi$
$821$	22.8017	−	22.8017i	0.795784	−	0.795784i	0.982428	+	0.186644i	$0.0597610\pi$
$822$	38.3030	−	45.7693i	1.33597	−	1.59639i
$823$			51.7610i			1.80428i	0.431449	+	0.902138i	$0.358003\pi$
$823$			51.7610i			1.80428i	−0.431449	+	0.902138i	$0.641997\pi$
$824$	1.75275	+	0.469647i	0.0610599	+	0.0163609i
$825$	−1.53136	+	1.07526i	−0.0533151	+	0.0374358i
$826$	−33.3362	−	8.93240i	−1.15991	−	0.310798i
$827$	12.8185	+	12.8185i	0.445742	+	0.445742i	0.893936	−	0.448194i	$-0.147933\pi$
$827$	12.8185	+	12.8185i	0.445742	+	0.445742i	−0.448194	+	0.893936i	$0.647933\pi$
$828$	−7.77397	+	1.39177i	−0.270164	+	0.0483673i
$829$	−31.5438	+	18.2118i	−1.09556	+	0.632523i	−0.935052	−	0.354512i	$-0.884647\pi$
$829$	−31.5438	+	18.2118i	−1.09556	+	0.632523i	−0.160510	+	0.987034i	$0.551314\pi$
$830$	6.45322	+	6.45322i	0.223995	+	0.223995i
$831$	9.76623	+	8.17306i	0.338787	+	0.283520i
$832$	24.8164	−	27.2351i	0.860354	−	0.944208i
$833$	0.431428	−	0.249085i	0.0149481	−	0.00863029i
$834$	−24.6856	−	11.4718i	−0.854794	−	0.397235i
$835$	18.3826			0.636157
$836$	7.64509	−	13.2417i	0.264411	−	0.457973i
$837$	34.8391	−	35.1139i	1.20421	−	1.21371i
$838$	47.5025	−	12.7282i	1.64095	−	0.439690i
$839$	−4.88038	+	18.2138i	−0.168489	+	0.628811i	0.829080	+	0.559130i	$0.188865\pi$
$839$	−4.88038	+	18.2138i	−0.168489	+	0.628811i	−0.997569	+	0.0696809i	$0.977802\pi$
$840$	−2.39102	+	1.67888i	−0.0824981	+	0.0579270i
$841$	−61.4480			−2.11889
$842$	−12.0540	+	20.8781i	−0.415407	+	0.719506i
$843$	−23.0658	−	32.8497i	−0.794428	−	1.13140i
$844$	27.1320	+	15.6646i	0.933920	+	0.539199i
$845$	2.18567	−	12.8149i	0.0751894	−	0.440848i
$846$	−11.9178	−	66.5689i	−0.409741	−	2.28869i
$847$	6.80622	−	25.4012i	0.233865	−	0.872795i
$848$		−	21.7071i		−	0.745424i
$849$	3.25235	−	18.5873i	0.111620	−	0.637916i
$850$	−1.75453	+	6.54799i	−0.0601798	+	0.224594i
$851$	−3.40567	+	3.40567i	−0.116745	+	0.116745i
$852$	−17.6624	−	25.1543i	−0.605104	−	0.861773i
$853$	−6.26038	−	23.3640i	−0.214351	−	0.799969i	−0.986394	−	0.164399i	$-0.947432\pi$
$853$	−6.26038	−	23.3640i	−0.214351	−	0.799969i	0.772043	−	0.635571i	$-0.219235\pi$
$854$	39.7460	+	22.9474i	1.36008	+	0.785244i
$855$	−14.0862	+	11.8828i	−0.481738	+	0.406382i
$856$	1.09559	+	0.293562i	0.0374465	+	0.0100337i
$857$	−3.31541	+	5.74247i	−0.113252	+	0.196159i	−0.917080	−	0.398704i	$-0.869460\pi$
$857$	−3.31541	+	5.74247i	−0.113252	+	0.196159i	0.803827	+	0.594863i	$0.202794\pi$
$858$	5.30304	−	12.9530i	0.181043	−	0.442209i
$859$	8.43503	+	14.6099i	0.287800	+	0.498484i	0.973284	−	0.229604i	$-0.0737430\pi$
$859$	8.43503	+	14.6099i	0.287800	+	0.498484i	−0.685485	+	0.728087i	$0.740410\pi$
$860$	5.60833	+	20.9306i	0.191242	+	0.713726i
$861$	−3.39970	+	1.24243i	−0.115861	+	0.0423420i
$862$	−57.2288	+	33.0410i	−1.94922	+	1.12538i
$863$	−35.2400	+	35.2400i	−1.19958	+	1.19958i	−0.225294	+	0.974291i	$0.572334\pi$
$863$	−35.2400	+	35.2400i	−1.19958	+	1.19958i	−0.974291	+	0.225294i	$0.927666\pi$
$864$	−40.6452	+	11.0622i	−1.38278	+	0.376344i
$865$	−5.35760	−	19.9948i	−0.182164	−	0.679844i
$866$	24.9254	−	6.67875i	0.847001	−	0.226953i
$867$	7.02851	−	8.39856i	0.238701	−	0.285230i
$868$	−50.7991	−	29.3289i	−1.72423	−	0.995487i
$869$	−13.1538	+	3.52454i	−0.446211	+	0.119562i
$870$	−21.9324	+	26.2076i	−0.743577	+	0.888521i
$871$	−34.0386	−	17.5984i	−1.15335	−	0.596298i
$872$		−	6.84405i		−	0.231769i
$873$	17.0554	+	36.3266i	0.577237	+	1.22947i
$874$	7.28065	+	12.6105i	0.246272	+	0.426555i
$875$	−1.33720	−	2.31611i	−0.0452057	−	0.0782986i
$876$	−9.02971	+	19.4307i	−0.305086	+	0.656502i
$877$	−27.6264	−	27.6264i	−0.932876	−	0.932876i	0.0650086	−	0.997885i	$-0.479293\pi$
$877$	−27.6264	−	27.6264i	−0.932876	−	0.932876i	−0.997885	+	0.0650086i	$0.979293\pi$
$878$	21.1634	+	21.1634i	0.714232	+	0.714232i
$879$	0.900585	−	1.93793i	0.0303760	−	0.0653649i
$880$	1.78228	+	3.08700i	0.0600806	+	0.104063i
$881$	7.91421	+	13.7078i	0.266637	+	0.461828i	0.967991	−	0.250985i	$-0.0807543\pi$
$881$	7.91421	+	13.7078i	0.266637	+	0.461828i	−0.701355	+	0.712813i	$0.747421\pi$
$882$	0.542214	−	0.778695i	0.0182573	−	0.0262200i
$883$		−	25.7550i		−	0.866726i	−0.901219	−	0.433363i	$-0.857327\pi$
$883$		−	25.7550i		−	0.866726i	0.901219	−	0.433363i	$-0.142673\pi$
$884$	−8.23503	−	25.8653i	−0.276974	−	0.869946i
$885$	−6.91443	+	8.26226i	−0.232426	+	0.277733i
$886$	37.6739	−	10.0947i	1.26568	−	0.339138i
$887$	−4.73067	−	2.73125i	−0.158840	−	0.0917065i	0.418473	−	0.908229i	$-0.362566\pi$
$887$	−4.73067	−	2.73125i	−0.158840	−	0.0917065i	−0.577313	+	0.816523i	$0.695899\pi$
$888$	2.95535	−	3.53143i	0.0991751	−	0.118507i
$889$	−3.91083	+	1.04790i	−0.131165	+	0.0351455i
$890$	6.49549	+	24.2415i	0.217729	+	0.812577i
$891$	−7.93517	+	5.61845i	−0.265838	+	0.188225i
$892$	−0.106877	+	0.106877i	−0.00357851	+	0.00357851i
$893$	−57.8057	+	33.3741i	−1.93439	+	1.11682i
$894$	35.2421	−	12.8794i	1.17867	−	0.430751i
$895$	2.08390	+	7.77723i	0.0696572	+	0.259964i
$896$	6.66915	+	11.5513i	0.222801	+	0.385902i
$897$	4.36700	+	5.64301i	0.145810	+	0.188414i
$898$	15.5459	−	26.9263i	0.518774	−	0.898543i
$899$	−87.4492	−	23.4319i	−2.91659	−	0.781499i
$900$	1.21809	+	6.80386i	0.0406030	+	0.226795i
$901$	−18.6168	−	10.7484i	−0.620215	−	0.358081i
$902$	−0.453271	−	1.69163i	−0.0150923	−	0.0563251i
$903$	−25.0347	−	35.6538i	−0.833103	−	1.18648i
$904$	−1.38656	+	1.38656i	−0.0461162	+	0.0461162i
$905$	2.27306	−	8.48319i	0.0755592	−	0.281991i
$906$	−13.9344	+	79.6357i	−0.462939	+	2.64572i
$907$		−	6.10681i		−	0.202773i	−0.994847	−	0.101387i	$-0.967672\pi$
$907$		−	6.10681i		−	0.202773i	0.994847	−	0.101387i	$-0.0323279\pi$
$908$	−8.90860	+	33.2473i	−0.295642	+	1.10335i
$909$	−6.25509	+	5.27663i	−0.207468	+	0.175015i
$910$	17.7704	+	9.18749i	0.589082	+	0.304562i
$911$	4.83489	+	2.79143i	0.160187	+	0.0924841i	0.577951	−	0.816072i	$-0.303853\pi$
$911$	4.83489	+	2.79143i	0.160187	+	0.0924841i	−0.417763	+	0.908556i	$0.637186\pi$
$912$	20.1741	+	28.7314i	0.668031	+	0.951392i
$913$	2.37616	−	4.11563i	0.0786395	−	0.136208i
$914$	−40.8491			−1.35117
$915$	11.7253	−	8.23307i	0.387627	−	0.272177i
$916$	−6.79426	+	25.3565i	−0.224489	+	0.837803i
$917$	−10.1753	+	2.72647i	−0.336018	+	0.0900359i
$918$	−8.98304	+	34.0599i	−0.296484	+	1.12414i
$919$	0.687472	−	1.19074i	0.0226776	−	0.0392788i	−0.854464	−	0.519511i	$-0.826114\pi$
$919$	0.687472	−	1.19074i	0.0226776	−	0.0392788i	0.877141	+	0.480232i	$0.159448\pi$
$920$	0.720638			0.0237587
$921$	8.86668	+	4.12047i	0.292167	+	0.135774i
$922$	47.8485	−	27.6253i	1.57581	−	0.909792i
$923$	−12.7536	+	24.6680i	−0.419791	+	0.811956i
$924$	8.84210	+	7.39969i	0.290884	+	0.243432i
$925$	2.98068	+	2.98068i	0.0980041	+	0.0980041i
$926$	61.9498	−	35.7667i	2.03580	−	1.17537i
$927$	−2.93076	+	8.11831i	−0.0962588	+	0.266640i
$928$	54.5166	+	54.5166i	1.78959	+	1.78959i
$929$	−28.8296	−	7.72487i	−0.945869	−	0.253445i	−0.247260	−	0.968949i	$-0.579530\pi$
$929$	−28.8296	−	7.72487i	−0.945869	−	0.253445i	−0.698608	+	0.715504i	$0.746197\pi$
$930$	−27.9947	+	19.6568i	−0.917982	+	0.644572i
$931$	−0.904629	−	0.242395i	−0.0296480	−	0.00794416i
$932$		−	45.3285i		−	1.48478i
$933$	−19.0711	+	22.7886i	−0.624359	+	0.746064i
$934$	1.14726	−	1.14726i	0.0375396	−	0.0375396i
$935$	3.53003			0.115444
$936$	−4.63619	−	5.00478i	−0.151539	−	0.163586i
$937$	42.2013			1.37866			0.689328	−	0.724449i	$-0.257906\pi$
$937$	42.2013			1.37866			0.689328	+	0.724449i	$0.257906\pi$
$938$	41.6955	−	41.6955i	1.36141	−	1.36141i
$939$	−4.60053	−	0.804987i	−0.150133	−	0.0262697i
$940$			25.0351i			0.816554i
$941$	−27.4076	−	7.34384i	−0.893462	−	0.239402i	−0.217255	−	0.976115i	$-0.569710\pi$
$941$	−27.4076	−	7.34384i	−0.893462	−	0.239402i	−0.676206	+	0.736712i	$0.736377\pi$
$942$	−1.90289	−	21.4269i	−0.0619995	−	0.698125i
$943$	0.862392	+	0.231077i	0.0280833	+	0.00752491i
$944$	14.5127	+	14.5127i	0.472347	+	0.472347i
$945$	−6.99555	−	12.0074i	−0.227565	−	0.390602i
$946$	18.2545	−	10.5393i	0.593506	−	0.342661i
$947$	−27.8155	−	27.8155i	−0.903881	−	0.903881i	0.0918881	−	0.995769i	$-0.470710\pi$
$947$	−27.8155	−	27.8155i	−0.903881	−	0.903881i	−0.995769	+	0.0918881i	$0.970710\pi$
$948$	−8.67028	+	49.5510i	−0.281597	+	1.60934i
$949$	19.3377	−	0.898577i	0.627729	−	0.0291691i
$950$	11.0368	−	6.37211i	0.358081	−	0.206738i
$951$	8.64941	−	6.07328i	0.280476	−	0.196940i
$952$	5.51169			0.178635
$953$	−5.10301	+	8.83867i	−0.165303	+	0.286312i	−0.936763	−	0.349965i	$-0.886193\pi$
$953$	−5.10301	+	8.83867i	−0.165303	+	0.286312i	0.771460	+	0.636278i	$0.219527\pi$
$954$	−40.7987	−	3.46176i	−1.32091	−	0.112079i
$955$	19.1323	−	5.12648i	0.619106	−	0.165889i
$956$	11.1163	−	41.4867i	0.359527	−	1.34177i
$957$	16.1381	+	7.49959i	0.521670	+	0.242427i
$958$	−15.8626			−0.512498
$959$	22.2098	−	38.4685i	0.717191	−	1.24221i
$960$	17.6307	−	1.56576i	0.569029	−	0.0505347i
$961$	−51.6327	−	29.8101i	−1.66557	−	0.961617i
$962$	−30.8026	−	6.73832i	−0.993117	−	0.217252i
$963$	−1.83193	+	5.07450i	−0.0590331	+	0.163524i
$964$	14.2633	−	53.2313i	0.459390	−	1.71447i
$965$		−	24.3437i		−	0.783653i
$966$	−10.3131	+	3.76898i	−0.331820	+	0.121265i
$967$	3.95568	−	14.7628i	0.127206	−	0.474740i	−0.872703	−	0.488252i	$-0.837635\pi$
$967$	3.95568	−	14.7628i	0.127206	−	0.474740i	0.999909	+	0.0135124i	$0.00430126\pi$
$968$	4.38528	−	4.38528i	0.140948	−	0.140948i
$969$	34.6305	−	3.07548i	1.11249	−	0.0987987i
$970$	−7.18280	−	26.8066i	−0.230626	−	0.860707i
$971$	11.1799	+	6.45471i	0.358780	+	0.207141i	0.668545	−	0.743671i	$-0.266917\pi$
$971$	11.1799	+	6.45471i	0.358780	+	0.207141i	−0.309766	+	0.950813i	$0.600251\pi$
$972$	6.46825	+	35.3288i	0.207469	+	1.13317i
$973$	−19.5694	−	5.24361i	−0.627367	−	0.168102i
$974$	−1.35742	+	2.35113i	−0.0434947	+	0.0753350i
$975$	4.93882	−	3.82205i	0.158169	−	0.122404i
$976$	−13.6466	−	23.6365i	−0.436816	−	0.756587i
$977$	7.50653	+	28.0148i	0.240155	+	0.896272i	0.975757	+	0.218857i	$0.0702329\pi$
$977$	7.50653	+	28.0148i	0.240155	+	0.896272i	−0.735602	+	0.677414i	$0.763100\pi$
$978$	−0.578494	+	3.30612i	−0.0184982	+	0.105718i
$979$	11.3178	−	6.53432i	0.361717	−	0.208838i
$980$	−0.248382	+	0.248382i	−0.00793428	+	0.00793428i
$981$	32.4375	+	2.75231i	1.03565	+	0.0878745i
$982$	−0.146170	−	0.545514i	−0.00466447	−	0.0174080i
$983$	37.6972	−	10.1009i	1.20235	−	0.322170i	0.398596	−	0.917127i	$-0.369498\pi$
$983$	37.6972	−	10.1009i	1.20235	−	0.322170i	0.803757	+	0.594957i	$0.202831\pi$
$984$	−0.840844	−	0.147128i	−0.0268051	−	0.00469027i
$985$	−4.32510	−	2.49710i	−0.137809	−	0.0795642i
$986$	62.2741	−	16.6863i	1.98321	−	0.531400i
$987$	−17.2768	−	47.2749i	−0.549927	−	1.50478i
$988$	−23.4365	+	45.3307i	−0.745616	+	1.44216i
$989$			10.7458i			0.341697i
$990$	6.08629	−	2.85752i	0.193435	−	0.0908179i
$991$	−10.5963	−	18.3533i	−0.336602	−	0.583012i	0.647189	−	0.762329i	$-0.275944\pi$
$991$	−10.5963	−	18.3533i	−0.336602	−	0.583012i	−0.983791	+	0.179318i	$0.942611\pi$
$992$	38.5857	+	66.8325i	1.22510	+	2.12193i
$993$	27.4607	−	2.43875i	0.871439	−	0.0773913i
$994$	−30.2170	−	30.2170i	−0.958424	−	0.958424i
$995$	1.12617	+	1.12617i	0.0357020	+	0.0357020i
$996$	−10.0879	−	14.3670i	−0.319649	−	0.455236i
$997$	2.27387	+	3.93845i	0.0720141	+	0.124732i	0.899784	−	0.436336i	$-0.143724\pi$
$997$	2.27387	+	3.93845i	0.0720141	+	0.124732i	−0.827770	+	0.561068i	$0.810391\pi$
$998$	0.637709	+	1.10454i	0.0201863	+	0.0349638i
$999$	15.5488	+	15.4271i	0.491942	+	0.488091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.cm.a.11.9	✓	224
9.5	odd	6		585.2.dd.a.401.48	yes	224
13.6	odd	12		585.2.dd.a.461.48	yes	224
117.32	even	12	inner	585.2.cm.a.266.9	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.cm.a.11.9	✓	224	1.1	even	1	trivial
585.2.cm.a.266.9	yes	224	117.32	even	12	inner
585.2.dd.a.401.48	yes	224	9.5	odd	6
585.2.dd.a.461.48	yes	224	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.cm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46697 + 1.46697i) q^{2} +(-0.594527 - 1.62682i) q^{3} -2.30401i q^{4} +(-0.965926 - 0.258819i) q^{5} +(3.25865 + 1.51434i) q^{6} +(2.58328 + 0.692188i) q^{7} +(0.445979 + 0.445979i) q^{8} +(-2.29307 + 1.93438i) q^{9} +(1.79667 - 1.03731i) q^{10} +(-0.763900 - 0.763900i) q^{11} +(-3.74821 + 1.36980i) q^{12} +(2.66510 + 2.42842i) q^{13} +(-4.80502 + 2.77418i) q^{14} +(0.153218 + 1.72526i) q^{15} +3.29955 q^{16} +(1.63379 - 2.82981i) q^{17} +(0.526200 - 6.20155i) q^{18} +(-5.93362 + 1.58991i) q^{19} +(-0.596323 + 2.22551i) q^{20} +(-0.409767 - 4.61405i) q^{21} +2.24124 q^{22} +(-0.571291 + 0.989505i) q^{23} +(0.460380 - 0.990674i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-7.47206 + 0.347209i) q^{26} +(4.51017 + 2.58037i) q^{27} +(1.59481 - 5.95191i) q^{28} -9.51041i q^{29} +(-2.75568 - 2.30614i) q^{30} +(2.46382 - 9.19510i) q^{31} +(-5.73230 + 5.73230i) q^{32} +(-0.788566 + 1.69688i) q^{33} +(1.75453 + 6.54799i) q^{34} +(-2.31611 - 1.33720i) q^{35} +(4.45683 + 5.28327i) q^{36} +(4.07168 + 1.09100i) q^{37} +(6.37211 - 11.0368i) q^{38} +(2.36612 - 5.77940i) q^{39} +(-0.315355 - 0.546211i) q^{40} +(-0.202241 - 0.754775i) q^{41} +(7.36980 + 6.16757i) q^{42} +(8.14484 - 4.70243i) q^{43} +(-1.76003 + 1.76003i) q^{44} +(2.71559 - 1.27497i) q^{45} +(-0.613508 - 2.28964i) q^{46} +(10.4956 - 2.81229i) q^{47} +(-1.96167 - 5.36777i) q^{48} +(0.132033 + 0.0762291i) q^{49} +(-2.00392 + 0.536949i) q^{50} +(-5.57493 - 0.975484i) q^{51} +(5.59511 - 6.14043i) q^{52} -6.57880i q^{53} +(-10.4016 + 2.83096i) q^{54} +(0.540159 + 0.935582i) q^{55} +(0.843388 + 1.46079i) q^{56} +(6.11420 + 8.70768i) q^{57} +(13.9515 + 13.9515i) q^{58} +(4.39838 + 4.39838i) q^{59} +(3.97502 - 0.353016i) q^{60} +(-4.13589 - 7.16357i) q^{61} +(9.87460 + 17.1033i) q^{62} +(-7.26260 + 3.40980i) q^{63} -10.2192i q^{64} +(-1.94577 - 3.03545i) q^{65} +(-1.33248 - 3.64609i) q^{66} +(-10.2656 + 2.75065i) q^{67} +(-6.51993 - 3.76428i) q^{68} +(1.94939 + 0.341098i) q^{69} +(5.35930 - 1.43602i) q^{70} +(1.99342 + 7.43953i) q^{71} +(-1.88536 - 0.159972i) q^{72} +(3.79653 - 3.79653i) q^{73} +(-7.57352 + 4.37257i) q^{74} +(0.298533 - 1.70613i) q^{75} +(3.66317 + 13.6711i) q^{76} +(-1.44460 - 2.50213i) q^{77} +(5.00719 + 11.9493i) q^{78} +(6.30268 - 10.9166i) q^{79} +(-3.18712 - 0.853986i) q^{80} +(1.51638 - 8.87134i) q^{81} +(1.40392 + 0.810551i) q^{82} +(1.13855 + 4.24911i) q^{83} +(-10.6308 + 0.944109i) q^{84} +(-2.31053 + 2.31053i) q^{85} +(-5.04993 + 18.8466i) q^{86} +(-15.4717 + 5.65420i) q^{87} -0.681367i q^{88} +(-3.13094 + 11.6848i) q^{89} +(-2.11335 + 5.85405i) q^{90} +(5.20379 + 8.11804i) q^{91} +(2.27983 + 1.31626i) q^{92} +(-16.4236 + 1.45855i) q^{93} +(-11.2712 + 19.5223i) q^{94} +6.14294 q^{95} +(12.7334 + 5.91740i) q^{96} +(3.46224 - 12.9212i) q^{97} +(-0.305514 + 0.0818622i) q^{98} +(3.22935 + 0.274009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 24 q^{6} + 4 q^{7} - 36 q^{8} + 8 q^{15} - 224 q^{16} - 4 q^{18} - 8 q^{19} - 24 q^{21} - 8 q^{24} + 48 q^{26} + 24 q^{27} - 16 q^{28} - 48 q^{30} + 32 q^{31} - 72 q^{32} + 4 q^{33} - 12 q^{36}+ \cdots + 8 q^{99}+O(q^{100}) \) 224 * q + 24 * q^6 + 4 * q^7 - 36 * q^8 + 8 * q^15 - 224 * q^16 - 4 * q^18 - 8 * q^19 - 24 * q^21 - 8 * q^24 + 48 * q^26 + 24 * q^27 - 16 * q^28 - 48 * q^30 + 32 * q^31 - 72 * q^32 + 4 * q^33 - 12 * q^36 - 4 * q^37 + 8 * q^39 - 24 * q^41 + 64 * q^42 + 48 * q^43 + 8 * q^45 - 8 * q^48 - 52 * q^52 + 32 * q^54 - 72 * q^58 - 16 * q^60 - 36 * q^62 + 88 * q^63 - 108 * q^66 - 56 * q^67 - 72 * q^69 + 48 * q^71 + 12 * q^72 + 28 * q^73 - 120 * q^74 + 16 * q^76 - 144 * q^77 + 48 * q^78 - 12 * q^79 + 48 * q^80 - 84 * q^81 + 20 * q^84 - 12 * q^85 + 96 * q^86 + 8 * q^87 - 60 * q^89 + 16 * q^91 - 120 * q^92 - 132 * q^93 - 176 * q^96 - 4 * q^97 - 96 * q^98 + 8 * q^99

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