LMFDB - Embedded newform 552.2.bb.a.469.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(13,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.3
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37435 + 0.333417i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.77767 - 0.916463i) q^{4} +(1.90545 - 0.273963i) q^{5} +(-0.820321 + 1.15199i) q^{6} +(1.21206 - 2.65404i) q^{7} +(-2.13757 + 1.85224i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.52741 + 1.01183i) q^{10} +(0.357105 - 1.21619i) q^{11} +(0.743314 - 1.85674i) q^{12} +(1.67723 - 0.765966i) q^{13} +(-0.780888 + 4.05169i) q^{14} +(1.26064 - 1.45486i) q^{15} +(2.32019 - 3.25833i) q^{16} +(1.80523 + 1.16015i) q^{17} +(0.134434 + 1.40781i) q^{18} +(-2.43448 - 3.78813i) q^{19} +(3.13618 - 2.23329i) q^{20} +(-0.822012 - 2.79952i) q^{21} +(-0.0852884 + 1.79053i) q^{22} +(-2.90893 + 3.81289i) q^{23} +(-0.402503 + 2.79964i) q^{24} +(-1.24176 + 0.364614i) q^{25} +(-2.04971 + 1.61192i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(-0.277694 - 5.82880i) q^{28} +(-0.814044 + 1.26668i) q^{29} +(-1.24748 + 2.41980i) q^{30} +(-2.29505 + 2.64863i) q^{31} +(-2.10236 + 5.25167i) q^{32} +(-0.526552 - 1.15299i) q^{33} +(-2.86783 - 0.992557i) q^{34} +(1.58241 - 5.38921i) q^{35} +(-0.654147 - 1.89000i) q^{36} +(-0.0379154 - 0.00545141i) q^{37} +(4.60886 + 4.39451i) q^{38} +(0.765966 - 1.67723i) q^{39} +(-3.56559 + 4.11498i) q^{40} +(0.229399 + 1.59551i) q^{41} +(2.06314 + 3.57344i) q^{42} +(9.53369 - 8.26099i) q^{43} +(-0.479779 - 2.48925i) q^{44} -1.92505i q^{45} +(2.72659 - 6.21013i) q^{46} -3.76249 q^{47} +(-0.380271 - 3.98188i) q^{48} +(-0.990805 - 1.14345i) q^{49} +(1.58504 - 0.915132i) q^{50} +(2.12404 - 0.305391i) q^{51} +(2.27958 - 2.89875i) q^{52} +(2.76904 + 1.26458i) q^{53} +(1.02352 + 0.975916i) q^{54} +(0.347257 - 2.41523i) q^{55} +(2.32507 + 7.91821i) q^{56} +(-4.32056 - 1.26863i) q^{57} +(0.696447 - 2.01227i) q^{58} +(6.29482 - 2.87475i) q^{59} +(0.907673 - 3.74158i) q^{60} +(3.68678 + 3.19461i) q^{61} +(2.27110 - 4.40535i) q^{62} +(-2.45453 - 1.57743i) q^{63} +(1.13838 - 7.91859i) q^{64} +(2.98604 - 1.91901i) q^{65} +(1.10809 + 1.40905i) q^{66} +(-3.58132 - 12.1969i) q^{67} +(4.27234 + 0.407933i) q^{68} +(0.298495 + 4.78653i) q^{69} +(-0.377932 + 7.93425i) q^{70} +(-2.13046 + 0.625560i) q^{71} +(1.52918 + 2.37941i) q^{72} +(1.10391 - 0.709440i) q^{73} +(0.0539266 - 0.00514952i) q^{74} +(-0.699690 + 1.08874i) q^{75} +(-7.79938 - 4.50291i) q^{76} +(-2.79498 - 2.42186i) q^{77} +(-0.493485 + 2.56049i) q^{78} +(6.01487 + 13.1707i) q^{79} +(3.52835 - 6.84425i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.847244 - 2.11630i) q^{82} +(9.71731 + 1.39714i) q^{83} +(-4.02692 - 4.22326i) q^{84} +(3.75763 + 1.71605i) q^{85} +(-10.3482 + 14.5322i) q^{86} +(0.214284 + 1.49038i) q^{87} +(1.48934 + 3.26113i) q^{88} +(6.34166 + 7.31866i) q^{89} +(0.641845 + 2.64569i) q^{90} -5.37983i q^{91} +(-1.67672 + 9.44397i) q^{92} +3.50464i q^{93} +(5.17097 - 1.25448i) q^{94} +(-5.67661 - 6.55115i) q^{95} +(1.85025 + 5.34570i) q^{96} +(-0.798747 - 5.55541i) q^{97} +(1.74296 + 1.24115i) q^{98} +(-1.15299 - 0.526552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.37435	+	0.333417i	−0.971811	+	0.235762i
$2$	−1.37435	+	0.333417i	−0.971811	+	0.235762i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$4$	1.77767	−	0.916463i	0.888833	−	0.458232i
$5$	1.90545	−	0.273963i	0.852145	−	0.122520i	0.297618	−	0.954685i	$-0.403808\pi$
$5$	1.90545	−	0.273963i	0.852145	−	0.122520i	0.554528	+	0.832165i	$0.312899\pi$
$6$	−0.820321	+	1.15199i	−0.334895	+	0.470297i
$7$	1.21206	−	2.65404i	0.458115	−	1.00313i	−0.529798	−	0.848124i	$-0.677732\pi$
$7$	1.21206	−	2.65404i	0.458115	−	1.00313i	0.987913	−	0.155008i	$-0.0495404\pi$
$8$	−2.13757	+	1.85224i	−0.755744	+	0.654867i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−2.52741	+	1.01183i	−0.799239	+	0.319970i
$11$	0.357105	−	1.21619i	0.107671	−	0.366695i	−0.887977	−	0.459889i	$-0.847889\pi$
$11$	0.357105	−	1.21619i	0.107671	−	0.366695i	0.995648	+	0.0931936i	$0.0297075\pi$
$12$	0.743314	−	1.85674i	0.214576	−	0.535995i
$13$	1.67723	−	0.765966i	0.465180	−	0.212441i	−0.169015	−	0.985613i	$-0.554059\pi$
$13$	1.67723	−	0.765966i	0.465180	−	0.212441i	0.634195	+	0.773173i	$0.281331\pi$
$14$	−0.780888	+	4.05169i	−0.208701	+	1.08286i
$15$	1.26064	−	1.45486i	0.325496	−	0.375642i
$16$	2.32019	−	3.25833i	0.580047	−	0.814583i
$17$	1.80523	+	1.16015i	0.437833	+	0.281378i	0.740931	−	0.671581i	$-0.234385\pi$
$17$	1.80523	+	1.16015i	0.437833	+	0.281378i	−0.303098	+	0.952959i	$0.598021\pi$
$18$	0.134434	+	1.40781i	0.0316863	+	0.331824i
$19$	−2.43448	−	3.78813i	−0.558509	−	0.869057i	0.441087	−	0.897464i	$-0.354593\pi$
$19$	−2.43448	−	3.78813i	−0.558509	−	0.869057i	−0.999596	+	0.0284072i	$0.990956\pi$
$20$	3.13618	−	2.23329i	0.701272	−	0.499380i
$21$	−0.822012	−	2.79952i	−0.179378	−	0.610905i
$22$	−0.0852884	+	1.79053i	−0.0181835	+	0.381743i
$23$	−2.90893	+	3.81289i	−0.606553	+	0.795043i
$23$	−2.90893	+	3.81289i	−0.606553	+	0.795043i
$24$	−0.402503	+	2.79964i	−0.0821605	+	0.571474i
$25$	−1.24176	+	0.364614i	−0.248352	+	0.0729228i
$26$	−2.04971	+	1.61192i	−0.401982	+	0.316124i
$27$	−0.540641	−	0.841254i	−0.104046	−	0.161899i
$28$	−0.277694	−	5.82880i	−0.0524792	−	1.10154i
$29$	−0.814044	+	1.26668i	−0.151164	+	0.235216i	−0.908574	−	0.417724i	$-0.862828\pi$
$29$	−0.814044	+	1.26668i	−0.151164	+	0.235216i	0.757410	+	0.652940i	$0.226464\pi$
$30$	−1.24748	+	2.41980i	−0.227758	+	0.441792i
$31$	−2.29505	+	2.64863i	−0.412203	+	0.475708i	−0.923446	−	0.383728i	$-0.874640\pi$
$31$	−2.29505	+	2.64863i	−0.412203	+	0.475708i	0.511243	+	0.859436i	$0.329185\pi$
$32$	−2.10236	+	5.25167i	−0.371649	+	0.928373i
$33$	−0.526552	−	1.15299i	−0.0916610	−	0.200710i
$34$	−2.86783	−	0.992557i	−0.491829	−	0.170222i
$35$	1.58241	−	5.38921i	0.267477	−	0.910943i
$36$	−0.654147	−	1.89000i	−0.109024	−	0.315000i
$37$	−0.0379154	−	0.00545141i	−0.00623325	−	0.000896207i	0.139198	−	0.990265i	$-0.455548\pi$
$37$	−0.0379154	−	0.00545141i	−0.00623325	−	0.000896207i	−0.145431	+	0.989368i	$0.546457\pi$
$38$	4.60886	+	4.39451i	0.747655	+	0.712884i
$39$	0.765966	−	1.67723i	0.122653	−	0.268572i
$40$	−3.56559	+	4.11498i	−0.563769	+	0.650636i
$41$	0.229399	+	1.59551i	0.0358261	+	0.249176i	0.999862	−	0.0165949i	$-0.00528255\pi$
$41$	0.229399	+	1.59551i	0.0358261	+	0.249176i	−0.964036	+	0.265771i	$0.914373\pi$
$42$	2.06314	+	3.57344i	0.318349	+	0.551393i
$43$	9.53369	−	8.26099i	1.45387	−	1.25979i	0.547840	−	0.836583i	$-0.315450\pi$
$43$	9.53369	−	8.26099i	1.45387	−	1.25979i	0.906034	−	0.423206i	$-0.139095\pi$
$44$	−0.479779	−	2.48925i	−0.0723294	−	0.375269i
$45$		−	1.92505i		−	0.286969i
$46$	2.72659	−	6.21013i	0.402014	−	0.915634i
$47$	−3.76249			−0.548816			−0.274408	−	0.961613i	$-0.588482\pi$
$47$	−3.76249			−0.548816			−0.274408	+	0.961613i	$0.588482\pi$
$48$	−0.380271	−	3.98188i	−0.0548873	−	0.574735i
$49$	−0.990805	−	1.14345i	−0.141544	−	0.163350i
$50$	1.58504	−	0.915132i	0.224159	−	0.129419i
$51$	2.12404	−	0.305391i	0.297425	−	0.0427633i
$52$	2.27958	−	2.89875i	0.316120	−	0.401985i
$53$	2.76904	+	1.26458i	0.380357	+	0.173703i	0.596413	−	0.802678i	$-0.296592\pi$
$53$	2.76904	+	1.26458i	0.380357	+	0.173703i	−0.216056	+	0.976381i	$0.569319\pi$
$54$	1.02352	+	0.975916i	0.139283	+	0.132805i
$55$	0.347257	−	2.41523i	0.0468242	−	0.325669i
$56$	2.32507	+	7.91821i	0.310701	+	1.05812i
$57$	−4.32056	−	1.26863i	−0.572272	−	0.168034i
$58$	0.696447	−	2.01227i	0.0914480	−	0.264224i
$59$	6.29482	−	2.87475i	0.819516	−	0.374260i	0.0388781	−	0.999244i	$-0.487622\pi$
$59$	6.29482	−	2.87475i	0.819516	−	0.374260i	0.780638	+	0.624984i	$0.214894\pi$
$60$	0.907673	−	3.74158i	0.117180	−	0.483035i
$61$	3.68678	+	3.19461i	0.472043	+	0.409028i	0.858128	−	0.513435i	$-0.171627\pi$
$61$	3.68678	+	3.19461i	0.472043	+	0.409028i	−0.386085	+	0.922463i	$0.626173\pi$
$62$	2.27110	−	4.40535i	0.288430	−	0.559480i
$63$	−2.45453	−	1.57743i	−0.309242	−	0.198738i
$64$	1.13838	−	7.91859i	0.142297	−	0.989824i
$65$	2.98604	−	1.91901i	0.370373	−	0.238024i
$66$	1.10809	+	1.40905i	0.136397	+	0.173442i
$67$	−3.58132	−	12.1969i	−0.437528	−	1.49008i	−0.823362	−	0.567516i	$-0.807904\pi$
$67$	−3.58132	−	12.1969i	−0.437528	−	1.49008i	0.385834	−	0.922568i	$-0.373914\pi$
$68$	4.27234	+	0.407933i	0.518097	+	0.0494692i
$69$	0.298495	+	4.78653i	0.0359345	+	0.576231i
$70$	−0.377932	+	7.93425i	−0.0451715	+	0.948325i
$71$	−2.13046	+	0.625560i	−0.252839	+	0.0742404i	−0.405696	−	0.914008i	$-0.632971\pi$
$71$	−2.13046	+	0.625560i	−0.252839	+	0.0742404i	0.152857	+	0.988248i	$0.451153\pi$
$72$	1.52918	+	2.37941i	0.180216	+	0.280416i
$73$	1.10391	−	0.709440i	0.129203	−	0.0830337i	−0.474443	−	0.880286i	$-0.657350\pi$
$73$	1.10391	−	0.709440i	0.129203	−	0.0830337i	0.603646	+	0.797253i	$0.293714\pi$
$74$	0.0539266	−	0.00514952i	0.00626883	−	0.000598620i
$75$	−0.699690	+	1.08874i	−0.0807932	+	0.125717i
$76$	−7.79938	−	4.50291i	−0.894650	−	0.516520i
$77$	−2.79498	−	2.42186i	−0.318518	−	0.275997i
$78$	−0.493485	+	2.56049i	−0.0558762	+	0.289918i
$79$	6.01487	+	13.1707i	0.676726	+	1.48182i	0.866076	+	0.499913i	$0.166635\pi$
$79$	6.01487	+	13.1707i	0.676726	+	1.48182i	−0.189350	+	0.981910i	$0.560638\pi$
$80$	3.52835	−	6.84425i	0.394482	−	0.765210i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−0.847244	−	2.11630i	−0.0935625	−	0.233706i
$83$	9.71731	+	1.39714i	1.06661	+	0.153356i	0.653199	−	0.757187i	$-0.273427\pi$
$83$	9.71731	+	1.39714i	1.06661	+	0.153356i	0.413415	+	0.910543i	$0.364336\pi$
$84$	−4.02692	−	4.22326i	−0.439373	−	0.460796i
$85$	3.75763	+	1.71605i	0.407572	+	0.186132i
$86$	−10.3482	+	14.5322i	−1.11588	+	1.56704i
$87$	0.214284	+	1.49038i	0.0229736	+	0.159785i
$88$	1.48934	+	3.26113i	0.158765	+	0.347638i
$89$	6.34166	+	7.31866i	0.672214	+	0.775777i	0.984721	−	0.174139i	$-0.0557141\pi$
$89$	6.34166	+	7.31866i	0.672214	+	0.775777i	−0.312507	+	0.949916i	$0.601169\pi$
$90$	0.641845	+	2.64569i	0.0676564	+	0.278880i
$91$		−	5.37983i		−	0.563959i
$92$	−1.67672	+	9.44397i	−0.174810	+	0.984602i
$93$			3.50464i			0.363414i
$94$	5.17097	−	1.25448i	0.533345	−	0.129390i
$95$	−5.67661	−	6.55115i	−0.582408	−	0.672134i
$96$	1.85025	+	5.34570i	0.188841	+	0.545594i
$97$	−0.798747	−	5.55541i	−0.0811005	−	0.564066i	−0.989341	−	0.145618i	$-0.953483\pi$
$97$	−0.798747	−	5.55541i	−0.0811005	−	0.564066i	0.908240	−	0.418449i	$-0.137426\pi$
$98$	1.74296	+	1.24115i	0.176065	+	0.125375i
$99$	−1.15299	−	0.526552i	−0.115880	−	0.0529205i
$100$	−1.87328	+	1.78619i	−0.187328	+	0.178619i
$101$	−0.452990	−	0.0651301i	−0.0450742	−	0.00648069i	0.119741	−	0.992805i	$-0.461794\pi$
$101$	−0.452990	−	0.0651301i	−0.0450742	−	0.00648069i	−0.164815	+	0.986324i	$0.552703\pi$
$102$	−2.81735	+	1.12791i	−0.278959	+	0.111679i
$103$	−7.38609	−	2.16875i	−0.727773	−	0.213693i	−0.103201	−	0.994661i	$-0.532908\pi$
$103$	−7.38609	−	2.16875i	−0.727773	−	0.213693i	−0.624572	+	0.780967i	$0.714727\pi$
$104$	−2.16644	+	4.74394i	−0.212437	+	0.465182i
$105$	−2.33327	−	5.10915i	−0.227704	−	0.498602i
$106$	−4.22726	−	0.814724i	−0.410588	−	0.0791330i
$107$	−2.58665	−	2.24135i	−0.250061	−	0.216679i	0.520806	−	0.853675i	$-0.325631\pi$
$107$	−2.58665	−	2.24135i	−0.250061	−	0.216679i	−0.770867	+	0.636996i	$0.780177\pi$
$108$	−1.73206	−	0.999990i	−0.166667	−	0.0962241i
$109$	−9.56625	+	14.8854i	−0.916281	+	1.42576i	−0.0114757	+	0.999934i	$0.503653\pi$
$109$	−9.56625	+	14.8854i	−0.916281	+	1.42576i	−0.904805	+	0.425826i	$0.859983\pi$
$110$	0.328027	+	3.43515i	0.0312761	+	0.327528i
$111$	−0.0322245	+	0.0207094i	−0.00305861	+	0.00196565i
$112$	−5.83553	−	10.1072i	−0.551406	−	0.955037i
$113$	−7.42283	+	2.17954i	−0.698281	+	0.205034i	−0.611559	−	0.791199i	$-0.709457\pi$
$113$	−7.42283	+	2.17954i	−0.698281	+	0.205034i	−0.0867219	+	0.996233i	$0.527639\pi$
$114$	6.36094	+	0.302990i	0.595756	+	0.0283776i
$115$	−4.49823	+	8.06223i	−0.419463	+	0.751807i
$116$	−0.286235	+	2.99777i	−0.0265762	+	0.278336i
$117$	−0.519474	−	1.76917i	−0.0480254	−	0.163560i
$118$	−7.69278	+	6.04971i	−0.708178	+	0.556921i
$119$	5.26713	−	3.38498i	0.482837	−	0.310301i
$120$	4.77283e−5		5.44486i	4.35698e−6		0.497046i
$121$	7.90220	+	5.07843i	0.718381	+	0.461676i
$122$	−6.13205	−	3.16127i	−0.555170	−	0.286208i
$123$	1.21820	+	1.05558i	0.109842	+	0.0951783i
$124$	−1.65246	+	6.81171i	−0.148395	+	0.611710i
$125$	−11.0217	+	5.03342i	−0.985807	+	0.450203i
$126$	3.89932	+	1.34956i	0.347379	+	0.120228i
$127$	18.0534	+	5.30095i	1.60198	+	0.470383i	0.956096	−	0.293054i	$-0.0946716\pi$
$127$	18.0534	+	5.30095i	1.60198	+	0.470383i	0.645882	+	0.763437i	$0.276490\pi$
$128$	1.07567	+	11.2625i	0.0950764	+	0.995470i
$129$	1.79528	−	12.4865i	0.158066	−	1.09937i
$130$	−3.46403	+	3.63299i	−0.303815	+	0.318634i
$131$	−17.8324	−	8.14380i	−1.55803	−	0.711527i	−0.564533	−	0.825410i	$-0.690944\pi$
$131$	−17.8324	−	8.14380i	−1.55803	−	0.711527i	−0.993494	+	0.113883i	$0.963671\pi$
$132$	−1.99271	−	1.56706i	−0.173443	−	0.136395i
$133$	−13.0046	+	1.86978i	−1.12764	+	0.162130i
$134$	8.98863	+	15.5687i	0.776500	+	1.34493i
$135$	−1.26064	−	1.45486i	−0.108499	−	0.125214i
$136$	−6.00769	+	0.863829i	−0.515155	+	0.0740727i
$137$	−2.86586			−0.244847			−0.122423	−	0.992478i	$-0.539067\pi$
$137$	−2.86586			−0.244847			−0.122423	+	0.992478i	$0.539067\pi$
$138$	−2.00615	−	6.47884i	−0.170775	−	0.551515i
$139$			10.8820i			0.922998i	0.887141	+	0.461499i	$0.152688\pi$
$139$			10.8820i			0.922998i	−0.887141	+	0.461499i	$0.847312\pi$
$140$	−2.12601	−	11.0304i	−0.179681	−	0.932242i
$141$	−2.84350	+	2.46391i	−0.239466	+	0.207498i
$142$	2.71942	−	1.57007i	0.228209	−	0.131757i
$143$	−0.332611	−	2.31336i	−0.0278143	−	0.193453i
$144$	−2.89497	−	2.76028i	−0.241247	−	0.230024i
$145$	−1.20410	+	2.63661i	−0.0999952	+	0.218959i
$146$	−1.28062	+	1.34308i	−0.105985	+	0.111154i
$147$	−1.49760	−	0.215323i	−0.123520	−	0.0177595i
$148$	−0.0723969	+	0.0250573i	−0.00595099	+	0.00205970i
$149$	−2.61860	+	8.91814i	−0.214524	+	0.730603i	0.779971	+	0.625816i	$0.215234\pi$
$149$	−2.61860	+	8.91814i	−0.214524	+	0.730603i	−0.994495	+	0.104786i	$0.966584\pi$
$150$	0.598613	−	1.72959i	0.0488765	−	0.141221i
$151$	3.62771	+	7.94358i	0.295219	+	0.646439i	0.997880	−	0.0650858i	$-0.0207321\pi$
$151$	3.62771	+	7.94358i	0.295219	+	0.646439i	−0.702661	+	0.711525i	$0.748005\pi$
$152$	12.2204	+	3.58812i	0.991207	+	0.291035i
$153$	1.40525	−	1.62175i	0.113608	−	0.131111i
$154$	4.64877	+	2.39659i	0.374608	+	0.193123i
$155$	−3.64749	+	5.67560i	−0.292973	+	0.455876i
$156$	−0.175490	−	3.68354i	−0.0140504	−	0.294919i
$157$	7.53882	+	11.7306i	0.601664	+	0.936207i	0.999822	+	0.0188901i	$0.00601326\pi$
$157$	7.53882	+	11.7306i	0.601664	+	0.936207i	−0.398158	+	0.917317i	$0.630350\pi$
$158$	−12.6579	−	16.0957i	−1.00701	−	1.28050i
$159$	2.92082	−	0.857631i	0.231636	−	0.0680146i
$160$	−2.56719	+	10.5828i	−0.202955	+	0.836643i
$161$	6.59377	+	12.3418i	0.519662	+	0.972674i
$162$	1.41261	+	0.0672869i	0.110985	+	0.00528656i
$163$	−1.95551	−	6.65987i	−0.153168	−	0.521641i	0.846779	−	0.531944i	$-0.178538\pi$
$163$	−1.95551	−	6.65987i	−0.153168	−	0.521641i	−0.999947	+	0.0103032i	$0.996720\pi$
$164$	1.87002	+	2.62604i	0.146024	+	0.205059i
$165$	−1.31920	−	2.05271i	−0.102699	−	0.159803i
$166$	−13.8208	+	1.31977i	−1.07270	+	0.102434i
$167$	−13.4297	−	8.63076i	−1.03922	−	0.667869i	−0.0944291	−	0.995532i	$-0.530103\pi$
$167$	−13.4297	−	8.63076i	−1.03922	−	0.667869i	−0.944795	+	0.327663i	$0.893739\pi$
$168$	6.94250	+	4.46159i	0.535625	+	0.344219i
$169$	−6.28679	+	7.25534i	−0.483599	+	0.558103i
$170$	−5.73645	−	1.10559i	−0.439966	−	0.0847951i
$171$	−4.09604	+	1.87060i	−0.313232	+	0.143048i
$172$	9.37681	−	23.4225i	0.714975	−	1.78595i
$173$	−2.77874	+	9.46350i	−0.211263	+	0.719497i	0.783867	+	0.620929i	$0.213244\pi$
$173$	−2.77874	+	9.46350i	−0.211263	+	0.719497i	−0.995130	+	0.0985680i	$0.968574\pi$
$174$	−0.791418	−	1.97685i	−0.0599972	−	0.149865i
$175$	−0.537388	+	3.73762i	−0.0406227	+	0.282537i
$176$	−3.13420	−	3.98536i	−0.236249	−	0.300408i
$177$	2.87475	−	6.29482i	0.216079	−	0.473148i
$178$	−11.1558	−	7.94397i	−0.836164	−	0.595426i
$179$	−16.8980	+	2.42957i	−1.26302	+	0.181595i	−0.741096	−	0.671399i	$-0.765694\pi$
$179$	−16.8980	+	2.42957i	−1.26302	+	0.181595i	−0.521922	+	0.852993i	$0.674785\pi$
$180$	−1.76424	−	3.42209i	−0.131498	−	0.255068i
$181$	3.07099	−	2.66102i	0.228265	−	0.197792i	−0.533218	−	0.845978i	$-0.679017\pi$
$181$	3.07099	−	2.66102i	0.228265	−	0.197792i	0.761482	+	0.648186i	$0.224472\pi$
$182$	1.79373	+	7.39376i	0.132960	+	0.548062i
$183$	4.87831			0.360615
$184$	−0.844389	−	13.5384i	−0.0622492	−	0.998061i
$185$	−0.0737396			−0.00542144
$186$	−1.16851	−	4.81660i	−0.0856792	−	0.353170i
$187$	2.05562	−	1.78121i	0.150322	−	0.130255i
$188$	−6.68845	+	3.44818i	−0.487805	+	0.251485i
$189$	−2.88801	+	0.415233i	−0.210072	+	0.0302037i
$190$	9.98590	+	7.11089i	0.724454	+	0.515878i
$191$	6.55225	−	14.3474i	0.474104	−	1.03814i	−0.509938	−	0.860211i	$-0.670332\pi$
$191$	6.55225	−	14.3474i	0.474104	−	1.03814i	0.984043	−	0.177933i	$-0.0569410\pi$
$192$	−4.32524	−	6.72995i	−0.312148	−	0.485692i
$193$	−1.84486	+	12.8313i	−0.132796	+	0.923614i	0.809091	+	0.587684i	$0.199960\pi$
$193$	−1.84486	+	12.8313i	−0.132796	+	0.923614i	−0.941887	+	0.335931i	$0.890949\pi$
$194$	2.95003	+	7.36875i	0.211800	+	0.529046i
$195$	1.00001	−	3.40573i	0.0716125	−	0.243890i
$196$	−2.80925	−	1.12464i	−0.200661	−	0.0803311i
$197$	21.3134	−	9.73352i	1.51852	−	0.693485i	0.530482	−	0.847696i	$-0.322011\pi$
$197$	21.3134	−	9.73352i	1.51852	−	0.693485i	0.988038	+	0.154211i	$0.0492836\pi$
$198$	1.76017	+	0.339240i	0.125090	+	0.0241087i
$199$	−4.17996	+	4.82393i	−0.296310	+	0.341960i	−0.884309	−	0.466902i	$-0.845370\pi$
$199$	−4.17996	+	4.82393i	−0.296310	+	0.341960i	0.588000	+	0.808861i	$0.299916\pi$
$200$	1.97899	−	3.07943i	0.139936	−	0.217749i
$201$	−10.6938	−	6.87251i	−0.754285	−	0.484749i
$202$	0.644281	−	0.0615233i	0.0453315	−	0.00432876i
$203$	2.37514	+	3.69579i	0.166702	+	0.259394i
$204$	3.49596	−	2.48949i	0.244766	−	0.174299i
$205$	0.874220	+	2.97732i	0.0610581	+	0.207945i
$206$	10.8742	+	0.517968i	0.757638	+	0.0360885i
$207$	3.36010	+	3.42195i	0.233543	+	0.237842i
$208$	1.39572	−	7.24216i	0.0967760	−	0.502153i
$209$	−5.47645	+	1.60803i	−0.378814	+	0.111230i
$210$	4.91021	+	6.24380i	0.338837	+	0.430863i
$211$	10.2546	+	15.9564i	0.705953	+	1.09848i	0.990190	+	0.139731i	$0.0446236\pi$
$211$	10.2546	+	15.9564i	0.705953	+	1.09848i	−0.284236	+	0.958754i	$0.591740\pi$
$212$	6.08137	−	0.289727i	0.417670	−	0.0198985i
$213$	−1.20044	+	1.86792i	−0.0822529	+	0.127988i
$214$	4.30227	+	2.21796i	0.294097	+	0.151616i
$215$	15.9028	−	18.3528i	1.08456	−	1.25165i
$216$	2.71386	+	0.796836i	0.184655	+	0.0542178i
$217$	4.24783	+	9.30145i	0.288361	+	0.631423i
$218$	8.18431	−	23.6472i	0.554312	−	1.60159i
$219$	0.369695	−	1.25907i	0.0249817	−	0.0850799i
$220$	−1.59616	−	4.61172i	−0.107613	−	0.310922i
$221$	3.91643	+	0.563097i	0.263447	+	0.0378780i
$222$	0.0373828	−	0.0392061i	0.00250897	−	0.00263134i
$223$	−7.52172	+	16.4703i	−0.503692	+	1.10293i	0.471560	+	0.881834i	$0.343691\pi$
$223$	−7.52172	+	16.4703i	−0.503692	+	1.10293i	−0.975252	+	0.221097i	$0.929036\pi$
$224$	11.3899	+	11.9451i	0.761023	+	0.798115i
$225$	0.184182	+	1.28101i	0.0122788	+	0.0854008i
$226$	9.47485	−	5.47035i	0.630258	−	0.363882i
$227$	18.7213	−	16.2221i	1.24258	−	1.07670i	0.248429	−	0.968650i	$-0.420086\pi$
$227$	18.7213	−	16.2221i	1.24258	−	1.07670i	0.994146	−	0.108047i	$-0.0344598\pi$
$228$	−8.84316	+	1.70443i	−0.585653	+	0.112879i
$229$		−	1.99483i		−	0.131822i	−0.997825	−	0.0659112i	$-0.979005\pi$
$229$		−	1.99483i		−	0.131822i	0.997825	−	0.0659112i	$-0.0209954\pi$
$230$	3.49405	−	12.5801i	0.230391	−	0.829508i
$231$	−3.69829			−0.243330
$232$	−0.606123	−	4.21541i	−0.0397939	−	0.276756i
$233$	6.46351	+	7.45928i	0.423438	+	0.488674i	0.926881	−	0.375355i	$-0.122479\pi$
$233$	6.46351	+	7.45928i	0.423438	+	0.488674i	−0.503443	+	0.864028i	$0.667934\pi$
$234$	1.30381	+	2.25825i	0.0852327	+	0.147626i
$235$	−7.16926	+	1.03078i	−0.467671	+	0.0672409i
$236$	8.55549	−	10.8793i	0.556915	−	0.708183i
$237$	13.1707	+	6.01487i	0.855530	+	0.390708i
$238$	−6.11026	+	6.40830i	−0.396070	+	0.415388i
$239$	1.90638	−	13.2591i	0.123313	−	0.857662i	−0.830448	−	0.557096i	$-0.811915\pi$
$239$	1.90638	−	13.2591i	0.123313	−	0.857662i	0.953761	−	0.300566i	$-0.0971754\pi$
$240$	−1.81548	−	7.48312i	−0.117189	−	0.483033i
$241$	−17.1037	−	5.02209i	−1.10174	−	0.323501i	−0.320199	−	0.947350i	$-0.603750\pi$
$241$	−17.1037	−	5.02209i	−1.10174	−	0.323501i	−0.781545	+	0.623849i	$0.785568\pi$
$242$	−12.5536	−	4.34480i	−0.806976	−	0.279295i
$243$	−0.909632	+	0.415415i	−0.0583529	+	0.0266489i
$244$	9.48160	+	2.30015i	0.606997	+	0.147252i
$245$	−2.20120	−	1.90735i	−0.140629	−	0.121856i
$246$	−2.02618	−	1.04456i	−0.129185	−	0.0665989i
$247$	−6.98477	−	4.48884i	−0.444430	−	0.285618i
$248$	−8.68916e−5	−	9.91262i	−5.51762e−6	−	0.629452i
$249$	8.25879	−	5.30760i	0.523379	−	0.336355i
$250$	13.4694	−	10.5925i	0.851878	−	0.669928i
$251$	2.88109	+	9.81210i	0.181853	+	0.619334i	0.999075	+	0.0430107i	$0.0136950\pi$
$251$	2.88109	+	9.81210i	0.181853	+	0.619334i	−0.817222	+	0.576323i	$0.804487\pi$
$252$	−5.80899	−	0.554657i	−0.365932	−	0.0349401i
$253$	3.59841	+	4.89941i	0.226230	+	0.308023i
$254$	−26.5791	−	1.26604i	−1.66772	−	0.0794383i
$255$	3.96360	−	1.16382i	0.248210	−	0.0728811i
$256$	−5.23344	−	15.1199i	−0.327090	−	0.944993i
$257$	0.974695	−	0.626399i	0.0607998	−	0.0390737i	−0.509888	−	0.860241i	$-0.670313\pi$
$257$	0.974695	−	0.626399i	0.0607998	−	0.0390737i	0.570688	+	0.821167i	$0.306677\pi$
$258$	1.69586	+	17.7593i	0.105580	+	1.10565i
$259$	−0.0604239	+	0.0940215i	−0.00375456	+	0.00584221i
$260$	3.54948	−	6.14796i	0.220129	−	0.381280i
$261$	1.13793	+	0.986025i	0.0704363	+	0.0610334i
$262$	27.2233	+	5.24677i	1.68186	+	0.324147i
$263$	−5.91617	−	12.9546i	−0.364807	−	0.798815i	−0.999657	−	0.0261804i	$-0.991666\pi$
$263$	−5.91617	−	12.9546i	−0.364807	−	0.798815i	0.634850	−	0.772635i	$-0.281062\pi$
$264$	3.26116	+	1.48929i	0.200710	+	0.0916593i
$265$	5.62273	+	1.65098i	0.345402	+	0.101419i
$266$	17.2494	−	6.90568i	1.05763	−	0.423414i
$267$	9.58541	+	1.37817i	0.586618	+	0.0843429i
$268$	−17.5444	−	18.3998i	−1.07169	−	1.12395i
$269$	6.51213	+	2.97399i	0.397051	+	0.181327i	0.603926	−	0.797040i	$-0.293602\pi$
$269$	6.51213	+	2.97399i	0.397051	+	0.181327i	−0.206875	+	0.978367i	$0.566329\pi$
$270$	2.21763	+	1.57916i	0.134961	+	0.0961045i
$271$	3.92761	+	27.3171i	0.238585	+	1.65940i	0.659059	+	0.752091i	$0.270955\pi$
$271$	3.92761	+	27.3171i	0.238585	+	1.65940i	−0.420474	+	0.907304i	$0.638136\pi$
$272$	7.96864	−	3.19027i	0.483170	−	0.193439i
$273$	−3.52304	−	4.06580i	−0.213224	−	0.246074i
$274$	3.93868	−	0.955526i	0.237945	−	0.0577255i
$275$			1.64042i			0.0989213i
$276$	4.91731	+	8.23530i	0.295987	+	0.495707i
$277$		−	21.7858i		−	1.30898i	−0.756069	−	0.654492i	$-0.772882\pi$
$277$		−	21.7858i		−	1.30898i	0.756069	−	0.654492i	$-0.227118\pi$
$278$	−3.62824	−	14.9556i	−0.217608	−	0.896979i
$279$	2.29505	+	2.64863i	0.137401	+	0.158569i
$280$	6.59962	+	14.4508i	0.394403	+	0.863601i
$281$	1.11977	+	7.78814i	0.0667996	+	0.464601i	0.995576	+	0.0939607i	$0.0299528\pi$
$281$	1.11977	+	7.78814i	0.0667996	+	0.464601i	−0.928776	+	0.370641i	$0.879138\pi$
$282$	3.08645	−	4.33434i	0.183795	−	0.258106i
$283$	18.6883	+	8.53467i	1.11090	+	0.507333i	0.884425	−	0.466683i	$-0.154551\pi$
$283$	18.6883	+	8.53467i	1.11090	+	0.507333i	0.226480	+	0.974016i	$0.427278\pi$
$284$	−3.21395	+	3.06453i	−0.190713	+	0.181846i
$285$	−8.58019	−	1.23364i	−0.508246	−	0.0730748i
$286$	1.22844	+	3.06847i	0.0726391	+	0.181442i
$287$	4.51258	+	1.32501i	0.266369	+	0.0782130i
$288$	4.89902	+	2.82836i	0.288678	+	0.166662i
$289$	−5.14915	−	11.2751i	−0.302891	−	0.663239i
$290$	0.775761	−	4.02509i	0.0455543	−	0.236362i
$291$	−4.24167	−	3.67543i	−0.248651	−	0.215458i
$292$	1.31221	−	2.27284i	0.0767912	−	0.133008i
$293$	−8.74456	+	13.6068i	−0.510863	+	0.794918i	−0.996872	−	0.0790359i	$-0.974816\pi$
$293$	−8.74456	+	13.6068i	−0.510863	+	0.794918i	0.486009	+	0.873954i	$0.338452\pi$
$294$	2.13002	−	0.203398i	0.124225	−	0.0118624i
$295$	11.2069	−	7.20225i	0.652492	−	0.419331i
$296$	0.0911440	−	0.0585758i	0.00529764	−	0.00340465i
$297$	−1.21619	+	0.357105i	−0.0705705	+	0.0207214i
$298$	0.625407	−	13.1297i	0.0362289	−	0.760584i
$299$	−1.95839	+	8.62324i	−0.113257	+	0.498695i
$300$	−0.246025	+	2.57665i	−0.0142043	+	0.148763i
$301$	−10.3696	−	35.3156i	−0.597693	−	2.03556i
$302$	−7.63427	−	9.70770i	−0.439303	−	0.558615i
$303$	−0.384998	+	0.247423i	−0.0221175	+	0.0142141i
$304$	−17.9914	−	0.856828i	−1.03188	−	0.0491424i
$305$	7.90019	+	5.07715i	0.452364	+	0.290717i
$306$	−1.39059	+	2.69739i	−0.0794947	+	0.154199i
$307$	−3.39203	−	2.93921i	−0.193594	−	0.167750i	0.552670	−	0.833400i	$-0.313609\pi$
$307$	−3.39203	−	2.93921i	−0.193594	−	0.167750i	−0.746264	+	0.665650i	$0.768154\pi$
$308$	−7.18809	−	1.74377i	−0.409579	−	0.0993604i
$309$	−7.00226	+	3.19783i	−0.398345	+	0.181918i
$310$	3.12057	−	9.01639i	0.177237	−	0.512097i
$311$	−23.1719	−	6.80389i	−1.31396	−	0.385813i	−0.451650	−	0.892195i	$-0.649164\pi$
$311$	−23.1719	−	6.80389i	−1.31396	−	0.385813i	−0.862309	+	0.506382i	$0.830983\pi$
$312$	1.46934	+	5.00395i	0.0831850	+	0.283293i
$313$	−0.0472598	+	0.328699i	−0.00267128	+	0.0185792i	−0.991113	−	0.133019i	$-0.957533\pi$
$313$	−0.0472598	+	0.328699i	−0.00267128	+	0.0185792i	0.988442	+	0.151598i	$0.0484420\pi$
$314$	−14.2722	−	13.6084i	−0.805425	−	0.767967i
$315$	−5.10915	−	2.33327i	−0.287868	−	0.131465i
$316$	22.7629	+	17.9007i	1.28051	+	1.00700i
$317$	−24.6881	+	3.54962i	−1.38662	+	0.199366i	−0.794884	−	0.606762i	$-0.792468\pi$
$317$	−24.6881	+	3.54962i	−1.38662	+	0.199366i	−0.591741	+	0.806128i	$0.701559\pi$
$318$	−3.72828	+	2.15254i	−0.209072	+	0.120708i
$319$	1.24982	+	1.44237i	0.0699765	+	0.0807572i
$320$	−0.000269992	−	15.4004i	−1.50930e−5	−	0.860908i
$321$	−3.42263			−0.191033
$322$	−13.1771	−	14.7635i	−0.734333	−	0.822738i
$323$		−	9.66283i		−	0.537654i
$324$	−1.96386	+	0.378514i	−0.109103	+	0.0210286i
$325$	−1.80344	+	1.56269i	−0.100037	+	0.0866824i
$326$	4.90807	+	8.50098i	0.271833	+	0.470826i
$327$	2.51816	+	17.5142i	0.139254	+	0.968536i
$328$	−3.44562	−	2.98560i	−0.190253	−	0.164852i
$329$	−4.56036	+	9.98579i	−0.251421	+	0.550534i
$330$	2.49745	+	2.38130i	0.137480	+	0.131086i
$331$	−6.22593	−	0.895153i	−0.342208	−	0.0492021i	−0.0309315	−	0.999522i	$-0.509847\pi$
$331$	−6.22593	−	0.895153i	−0.342208	−	0.0492021i	−0.311276	+	0.950319i	$0.600756\pi$
$332$	18.5546	−	6.42192i	1.01831	−	0.352448i
$333$	−0.0107918	+	0.0367537i	−0.000591390	+	0.00201409i
$334$	21.3348	+	7.38397i	1.16739	+	0.404033i
$335$	−10.1655	−	22.2594i	−0.555403	−	1.21616i
$336$	−11.0290	−	3.81702i	−0.601680	−	0.208236i
$337$	20.2139	−	23.3281i	1.10112	−	1.27076i	0.141359	−	0.989958i	$-0.454853\pi$
$337$	20.2139	−	23.3281i	1.10112	−	1.27076i	0.959764	−	0.280806i	$-0.0906018\pi$
$338$	6.22118	−	12.0675i	0.338388	−	0.656385i
$339$	−4.18251	+	6.50811i	−0.227163	+	0.353472i
$340$	8.25250	−	0.393164i	0.447555	−	0.0213223i
$341$	2.40166	+	3.73706i	0.130057	+	0.202373i
$342$	5.00569	−	3.93654i	0.270677	−	0.212864i
$343$	15.3609	−	4.51038i	0.829413	−	0.243538i
$344$	−5.07752	+	35.3171i	−0.273762	+	1.90417i
$345$	1.88010	+	9.03875i	0.101221	+	0.486630i
$346$	0.663652	−	13.9326i	0.0356782	−	0.749023i
$347$	2.96282	+	10.0904i	0.159052	+	0.541683i	1.00000		0.000565890i	$0.000180128\pi$
$347$	2.96282	+	10.0904i	0.159052	+	0.541683i	−0.840947	+	0.541117i	$0.818002\pi$
$348$	1.74680	+	2.45301i	0.0936383	+	0.131495i
$349$	1.74773	+	2.71953i	0.0935540	+	0.145573i	0.884876	−	0.465827i	$-0.154243\pi$
$349$	1.74773	+	2.71953i	0.0935540	+	0.145573i	−0.791322	+	0.611400i	$0.790607\pi$
$350$	−0.507628	−	5.31596i	−0.0271339	−	0.284150i
$351$	−1.55115	−	0.996864i	−0.0827943	−	0.0532087i
$352$	5.63626	+	4.43227i	0.300414	+	0.236241i
$353$	23.9259	−	27.6120i	1.27345	−	1.46964i	0.460093	−	0.887871i	$-0.347816\pi$
$353$	23.9259	−	27.6120i	1.27345	−	1.46964i	0.813355	−	0.581767i	$-0.197639\pi$
$354$	−1.85210	+	9.60977i	−0.0984381	+	0.510753i
$355$	−3.88812	+	1.77565i	−0.206360	+	0.0942415i
$356$	17.9806	+	7.19824i	0.952972	+	0.381506i
$357$	1.76394	−	6.00744i	0.0933578	−	0.317947i
$358$	22.4137	−	8.97318i	1.18460	−	0.474247i
$359$	−1.57592	+	10.9607i	−0.0831738	+	0.578486i	0.905031	+	0.425346i	$0.139848\pi$
$359$	−1.57592	+	10.9607i	−0.0831738	+	0.578486i	−0.988204	+	0.153140i	$0.951061\pi$
$360$	3.56566	+	4.11492i	0.187927	+	0.216875i
$361$	−0.530339	+	1.16128i	−0.0279126	+	0.0611201i
$362$	−3.33337	+	4.68109i	−0.175198	+	0.246033i
$363$	9.29775	−	1.33681i	0.488005	−	0.0701646i
$364$	−4.93042	−	9.56354i	−0.258424	−	0.501266i
$365$	1.90909	−	1.65424i	0.0999264	−	0.0865868i
$366$	−6.70449	+	1.62651i	−0.350449	+	0.0850192i
$367$	−14.9479			−0.780276			−0.390138	−	0.920756i	$-0.627573\pi$
$367$	−14.9479			−0.780276			−0.390138	+	0.920756i	$0.627573\pi$
$368$	5.67441	+	18.3249i	0.295799	+	0.955250i
$369$	1.61191			0.0839129
$370$	0.101344	−	0.0245861i	0.00526862	−	0.00127817i
$371$	6.71248	−	5.81639i	0.348494	−	0.301972i
$372$	3.21187	+	6.23008i	0.166528	+	0.323014i
$373$	−9.71969	+	1.39748i	−0.503267	+	0.0723588i	−0.389273	−	0.921123i	$-0.627274\pi$
$373$	−9.71969	+	1.39748i	−0.503267	+	0.0723588i	−0.113994	+	0.993481i	$0.536364\pi$
$374$	−2.23126	+	3.13338i	−0.115376	+	0.162023i
$375$	−5.03342	+	11.0217i	−0.259925	+	0.569156i
$376$	8.04257	−	6.96905i	0.414764	−	0.359401i
$377$	−0.395108	+	2.74804i	−0.0203491	+	0.141531i
$378$	3.83068	−	1.53359i	0.197029	−	0.0788792i
$379$	−8.37305	+	28.5160i	−0.430095	+	1.46477i	0.404824	+	0.914395i	$0.367333\pi$
$379$	−8.37305	+	28.5160i	−0.430095	+	1.46477i	−0.834919	+	0.550373i	$0.814485\pi$
$380$	−16.0950	−	6.44336i	−0.825656	−	0.330537i
$381$	17.1152	−	7.81626i	0.876839	−	0.400439i
$382$	−4.22139	+	21.9030i	−0.215985	+	1.12066i
$383$	−15.3905	+	17.7616i	−0.786417	+	0.907573i	−0.997555	−	0.0698830i	$-0.977737\pi$
$383$	−15.3905	+	17.7616i	−0.786417	+	0.907573i	0.211139	+	0.977456i	$0.432283\pi$
$384$	8.18828	+	7.80719i	0.417856	+	0.398409i
$385$	−5.98921	−	3.84903i	−0.305238	−	0.196165i
$386$	−1.74269	−	18.2497i	−0.0887007	−	0.928887i
$387$	−6.82012	−	10.6123i	−0.346686	−	0.539454i
$388$	−6.51124	−	9.14364i	−0.330558	−	0.464198i
$389$	0.109100	+	0.371559i	0.00553157	+	0.0188388i	0.962213	−	0.272300i	$-0.0877842\pi$
$389$	0.109100	+	0.371559i	0.00553157	+	0.0188388i	−0.956681	+	0.291138i	$0.905966\pi$
$390$	−0.238836	+	5.01409i	−0.0120939	+	0.253898i
$391$	−9.67482	+	3.50836i	−0.489277	+	0.177425i
$392$	4.23586	+	0.608987i	0.213943	+	0.0307585i
$393$	−18.8099	+	5.52309i	−0.948835	+	0.278603i
$394$	−26.0468	+	20.4835i	−1.31222	+	1.03195i
$395$	15.0694	+	23.4484i	0.758221	+	1.17982i
$396$	−2.53219	+	0.120638i	−0.127248	+	0.00606229i
$397$	13.1207	−	20.4162i	0.658509	−	1.02466i	−0.337997	−	0.941147i	$-0.609749\pi$
$397$	13.1207	−	20.4162i	0.658509	−	1.02466i	0.996507	−	0.0835135i	$-0.0266142\pi$
$398$	4.13634	−	8.02344i	0.207336	−	0.402179i
$399$	−8.60376	+	9.92927i	−0.430727	+	0.497085i
$400$	−1.69309	+	4.89205i	−0.0846545	+	0.244602i
$401$	−8.01973	−	17.5608i	−0.400486	−	0.876942i	−0.997221	−	0.0745035i	$-0.976263\pi$
$401$	−8.01973	−	17.5608i	−0.400486	−	0.876942i	0.596735	−	0.802439i	$-0.296464\pi$
$402$	16.9885	+	5.87971i	0.847307	+	0.293253i
$403$	−1.82057	+	6.20029i	−0.0906891	+	0.308859i
$404$	−0.864953	+	0.299369i	−0.0430330	+	0.0148942i
$405$	−1.90545	−	0.273963i	−0.0946828	−	0.0136133i
$406$	−4.49651	−	4.28739i	−0.223158	−	0.212780i
$407$	−0.0201697	+	0.0441656i	−0.000999777	+	0.00218921i
$408$	−3.97462	+	4.58704i	−0.196773	+	0.227092i
$409$	−1.20774	−	8.39999i	−0.0597187	−	0.415353i	−0.997649	−	0.0685292i	$-0.978169\pi$
$409$	−1.20774	−	8.39999i	−0.0597187	−	0.415353i	0.937930	−	0.346824i	$-0.112740\pi$
$410$	−2.19417	−	3.80039i	−0.108362	−	0.187688i
$411$	−2.16587	+	1.87674i	−0.106834	+	0.0925726i
$412$	−15.1176	+	2.91377i	−0.744789	+	0.143551i
$413$		−	20.1911i		−	0.993537i
$414$	−5.75888	−	3.58263i	−0.283034	−	0.176077i
$415$	18.8987			0.927699
$416$	0.496452	+	10.4186i	0.0243406	+	0.510814i
$417$	7.12619	+	8.22406i	0.348971	+	0.402734i
$418$	6.99041	−	4.03594i	0.341912	−	0.197404i
$419$	−39.4906	+	5.67789i	−1.92924	+	0.277383i	−0.996529	−	0.0832410i	$-0.973473\pi$
$419$	−39.4906	+	5.67789i	−1.92924	+	0.277383i	−0.932711	+	0.360624i	$0.882564\pi$
$420$	−8.83013	−	6.94401i	−0.430866	−	0.338833i
$421$	19.5494	+	8.92791i	0.952779	+	0.435120i	0.830278	−	0.557349i	$-0.188181\pi$
$421$	19.5494	+	8.92791i	0.952779	+	0.435120i	0.122501	+	0.992468i	$0.460909\pi$
$422$	−19.4135	−	18.5106i	−0.945034	−	0.901083i
$423$	−0.535458	+	3.72419i	−0.0260349	+	0.181076i
$424$	−8.26132	+	2.42582i	−0.401205	+	0.117808i
$425$	−2.66468	−	0.782420i	−0.129256	−	0.0379529i
$426$	1.02703	−	2.96743i	0.0497596	−	0.143772i
$427$	12.9472	−	5.91279i	0.626559	−	0.286140i
$428$	−6.65232	−	1.61379i	−0.321552	−	0.0780056i
$429$	−1.76630	−	1.53051i	−0.0852778	−	0.0738936i
$430$	−15.7368	+	30.5254i	−0.758898	+	1.47207i
$431$	1.78825	+	1.14924i	0.0861369	+	0.0553568i	0.583000	−	0.812472i	$-0.301879\pi$
$431$	1.78825	+	1.14924i	0.0861369	+	0.0553568i	−0.496863	+	0.867829i	$0.665515\pi$
$432$	−3.99547	−	0.190281i	−0.192232	−	0.00915490i
$433$	−17.0325	+	10.9461i	−0.818531	+	0.526038i	−0.881615	−	0.471970i	$-0.843543\pi$
$433$	−17.0325	+	10.9461i	−0.818531	+	0.526038i	0.0630833	+	0.998008i	$0.479907\pi$
$434$	−8.93926	−	11.3671i	−0.429098	−	0.545639i
$435$	0.816616	+	2.78114i	0.0391537	+	0.133345i
$436$	−3.36369	+	35.2283i	−0.161092	+	1.68713i
$437$	21.5255	+	1.73696i	1.02970	+	0.0830903i
$438$	−0.0882953	+	1.85366i	−0.00421891	+	0.0885713i
$439$	−17.5464	+	5.15209i	−0.837444	+	0.245896i	−0.672212	−	0.740359i	$-0.734655\pi$
$439$	−17.5464	+	5.15209i	−0.837444	+	0.245896i	−0.165232	+	0.986255i	$0.552837\pi$
$440$	3.73131	+	5.80592i	0.177883	+	0.276786i
$441$	−1.27282	+	0.817990i	−0.0606104	+	0.0389519i
$442$	−5.57028	+	0.531914i	−0.264951	+	0.0253006i
$443$	−13.8536	+	21.5566i	−0.658204	+	1.02419i	0.338332	+	0.941027i	$0.390137\pi$
$443$	−13.8536	+	21.5566i	−0.658204	+	1.02419i	−0.996536	+	0.0831586i	$0.973499\pi$
$444$	−0.0383049	+	0.0663469i	−0.00181787	+	0.00314869i
$445$	14.0888	+	12.2080i	0.667873	+	0.578715i
$446$	4.84599	−	25.1438i	0.229464	−	1.19059i
$447$	3.86113	+	8.45470i	0.182625	+	0.399894i
$448$	−19.6365	−	12.6191i	−0.927735	−	0.596196i
$449$	28.1582	+	8.26800i	1.32887	+	0.390191i	0.867686	−	0.497114i	$-0.165607\pi$
$449$	28.1582	+	8.26800i	1.32887	+	0.390191i	0.461184	+	0.887305i	$0.347425\pi$
$450$	−0.680242	−	1.69915i	−0.0320669	−	0.0800986i
$451$	2.02236	+	0.290771i	0.0952291	+	0.0136919i
$452$	−11.1978	+	10.6772i	−0.526702	+	0.502215i
$453$	7.94358	+	3.62771i	0.373222	+	0.170445i
$454$	−20.3208	+	28.5368i	−0.953704	+	1.33930i
$455$	−1.47387	−	10.2510i	−0.0690963	−	0.480575i
$456$	11.5853	−	5.29095i	0.542531	−	0.247771i
$457$	−6.59049	−	7.60583i	−0.308290	−	0.355786i	0.580369	−	0.814353i	$-0.302908\pi$
$457$	−6.59049	−	7.60583i	−0.308290	−	0.355786i	−0.888660	+	0.458568i	$0.848363\pi$
$458$	0.665113	+	2.74160i	0.0310787	+	0.128106i
$459$		−	2.14588i		−	0.100161i
$460$	−0.607614	+	18.4544i	−0.0283302	+	0.860442i
$461$		−	42.9230i		−	1.99912i	−0.0296309	−	0.999561i	$-0.509433\pi$
$461$		−	42.9230i		−	1.99912i	0.0296309	−	0.999561i	$-0.490567\pi$
$462$	5.08274	−	1.23307i	0.236470	−	0.0573678i
$463$	−1.76976	−	2.04242i	−0.0822479	−	0.0949191i	0.713134	−	0.701028i	$-0.247275\pi$
$463$	−1.76976	−	2.04242i	−0.0822479	−	0.0949191i	−0.795382	+	0.606109i	$0.792730\pi$
$464$	2.23852	+	5.59135i	0.103921	+	0.259572i
$465$	0.960142	+	6.67793i	0.0445255	+	0.309682i
$466$	−11.3702	−	8.09661i	−0.526713	−	0.375068i
$467$	−5.81597	−	2.65607i	−0.269131	−	0.122908i	0.276279	−	0.961078i	$-0.410899\pi$
$467$	−5.81597	−	2.65607i	−0.269131	−	0.122908i	−0.545410	+	0.838169i	$0.683626\pi$
$468$	−2.54483	−	2.66891i	−0.117635	−	0.123370i
$469$	−36.7117	−	5.27835i	−1.69519	−	0.243731i
$470$	9.50937	−	3.80701i	0.438635	−	0.175604i
$471$	13.3794	+	3.92855i	0.616490	+	0.181018i
$472$	−8.13086	+	17.8045i	−0.374253	+	0.819519i
$473$	−6.64239	−	14.5448i	−0.305418	−	0.668771i
$474$	−20.1066	−	3.87517i	−0.923528	−	0.177993i
$475$	4.40426	+	3.81631i	0.202081	+	0.175104i
$476$	6.26099	−	10.8445i	0.286972	−	0.497057i
$477$	1.64578	−	2.56089i	0.0753552	−	0.117255i
$478$	1.80080	+	18.8583i	0.0823668	+	0.862558i
$479$	−16.5779	+	10.6540i	−0.757462	+	0.486792i	−0.861485	−	0.507783i	$-0.830465\pi$
$479$	−16.5779	+	10.6540i	−0.757462	+	0.486792i	0.104022	+	0.994575i	$0.466829\pi$
$480$	4.99010	+	9.67910i	0.227766	+	0.441788i
$481$	−0.0677685	+	0.0198986i	−0.00308998	+	0.000907299i
$482$	25.1808	+	1.19944i	1.14696	+	0.0546328i
$483$	13.0654	+	5.00934i	0.594498	+	0.227933i
$484$	18.7017	+	1.78568i	0.850075	+	0.0811674i
$485$	−3.04395	−	10.3668i	−0.138219	−	0.470730i
$486$	1.11164	−	0.874212i	0.0504252	−	0.0396551i
$487$	28.9859	−	18.6281i	1.31348	−	0.844120i	0.318865	−	0.947800i	$-0.396698\pi$
$487$	28.9859	−	18.6281i	1.31348	−	0.844120i	0.994611	+	0.103680i	$0.0330619\pi$
$488$	−13.7979		0.000120949i	−0.624603		5.47512e-6i
$489$	−5.83917	−	3.75260i	−0.264056	−	0.169699i
$490$	3.66116	+	1.88744i	0.165394	+	0.0852660i
$491$	16.6299	+	14.4099i	0.750499	+	0.650311i	0.943683	−	0.330852i	$-0.107336\pi$
$491$	16.6299	+	14.4099i	0.750499	+	0.650311i	−0.193184	+	0.981163i	$0.561881\pi$
$492$	3.13296	+	0.760028i	0.141245	+	0.0342647i
$493$	−2.93908	+	1.34223i	−0.132369	+	0.0604511i
$494$	11.0962	+	3.84038i	0.499240	+	0.172787i
$495$	−2.34122	−	0.687446i	−0.105230	−	0.0308984i
$496$	3.30516	+	13.6234i	0.148406	+	0.611707i
$497$	−0.921985	+	6.41254i	−0.0413567	+	0.287642i
$498$	−9.58080	+	10.0481i	−0.429326	+	0.450267i
$499$	−35.6763	−	16.2928i	−1.59709	−	0.729367i	−0.599609	−	0.800293i	$-0.704677\pi$
$499$	−35.6763	−	16.2928i	−1.59709	−	0.729367i	−0.997482	+	0.0709268i	$0.977404\pi$
$500$	−14.9799	+	19.0487i	−0.669921	+	0.851884i
$501$	−15.8015	+	2.27191i	−0.705957	+	0.101501i
$502$	−7.23115	−	12.5246i	−0.322742	−	0.559002i
$503$	18.7017	+	21.5829i	0.833868	+	0.962335i	0.999716	−	0.0238164i	$-0.00758172\pi$
$503$	18.7017	+	21.5829i	0.833868	+	0.962335i	−0.165848	+	0.986151i	$0.553036\pi$
$504$	8.16851	−	1.17453i	0.363854	−	0.0523176i
$505$	−0.880995			−0.0392037
$506$	−6.57901	−	5.53372i	−0.292473	−	0.246004i
$507$			9.60019i			0.426360i
$508$	36.9510	−	7.12194i	1.63944	−	0.315985i
$509$	10.0072	−	8.67127i	0.443561	−	0.384347i	−0.404248	−	0.914649i	$-0.632467\pi$
$509$	10.0072	−	8.67127i	0.443561	−	0.384347i	0.847809	+	0.530302i	$0.177921\pi$
$510$	−5.05933	+	2.92102i	−0.224031	+	0.129345i
$511$	−0.544877	−	3.78970i	−0.0241039	−	0.167647i
$512$	12.2338	+	19.0351i	0.540663	+	0.841239i
$513$	−1.87060	+	4.09604i	−0.0825889	+	0.180844i
$514$	−1.13072	+	1.18587i	−0.0498738	+	0.0523065i
$515$	−14.6680	−	2.10894i	−0.646350	−	0.0929311i
$516$	−8.25198	−	23.8421i	−0.363273	−	1.04959i
$517$	−1.34361	+	4.57590i	−0.0590917	+	0.201248i
$518$	0.0516951	−	0.149365i	0.00227135	−	0.00656271i
$519$	4.09725	+	8.97172i	0.179849	+	0.393815i
$520$	−2.82838	+	9.63290i	−0.124033	+	0.422430i
$521$	9.17493	−	10.5884i	0.401961	−	0.463887i	−0.518297	−	0.855201i	$-0.673434\pi$
$521$	9.17493	−	10.5884i	0.401961	−	0.463887i	0.920257	+	0.391313i	$0.127979\pi$
$522$	−1.89267	−	0.975735i	−0.0828401	−	0.0427067i
$523$	−7.29025	+	11.3439i	−0.318781	+	0.496032i	−0.963253	−	0.268595i	$-0.913441\pi$
$523$	−7.29025	+	11.3439i	−0.318781	+	0.496032i	0.644473	+	0.764627i	$0.277077\pi$
$524$	−39.1636	+	1.86582i	−1.71087	+	0.0815088i
$525$	2.04149	+	3.17662i	0.0890978	+	0.138639i
$526$	12.4502	+	15.8316i	0.542853	+	0.690290i
$527$	−7.21591	+	2.11878i	−0.314330	+	0.0922957i
$528$	−4.97852	−	0.959471i	−0.216662	−	0.0417556i
$529$	−6.07630	−	22.1828i	−0.264187	−	0.964471i
$530$	−8.27805	−	0.394308i	−0.359576	−	0.0171276i
$531$	−1.94964	−	6.63987i	−0.0846072	−	0.288146i
$532$	−21.4042	+	15.2421i	−0.927990	+	0.660827i
$533$	1.60686	+	2.50032i	0.0696008	+	0.108301i
$534$	−13.6332	+	1.30185i	−0.589966	+	0.0563367i
$535$	−5.54280	−	3.56214i	−0.239636	−	0.154005i
$536$	30.2469	+	19.4381i	1.30647	+	0.839599i
$537$	−11.1797	+	12.9020i	−0.482438	+	0.556763i
$538$	−9.94151	−	1.91604i	−0.428609	−	0.0826063i
$539$	−1.74447	+	0.796675i	−0.0751398	+	0.0343152i
$540$	−3.57432	−	1.43092i	−0.153814	−	0.0615768i
$541$	12.2319	−	41.6581i	0.525891	−	1.79102i	−0.0815646	−	0.996668i	$-0.525992\pi$
$541$	12.2319	−	41.6581i	0.525891	−	1.79102i	0.607456	−	0.794353i	$-0.292190\pi$
$542$	−14.5059	−	36.2337i	−0.623081	−	1.55637i
$543$	0.578296	−	4.02214i	0.0248171	−	0.172606i
$544$	−9.88799	+	7.04143i	−0.423944	+	0.301899i
$545$	−14.1500	+	30.9842i	−0.606120	+	1.32722i
$546$	6.19749	+	4.41319i	0.265228	+	0.188867i
$547$	−0.623370	+	0.0896271i	−0.0266534	+	0.00383218i	−0.155629	−	0.987816i	$-0.549740\pi$
$547$	−0.623370	+	0.0896271i	−0.0266534	+	0.00383218i	0.128975	+	0.991648i	$0.458831\pi$
$548$	−5.09453	+	2.62645i	−0.217628	+	0.112196i
$549$	3.68678	−	3.19461i	0.157348	−	0.136343i
$550$	−0.546946	−	2.25451i	−0.0233219	−	0.0961328i
$551$	6.78012			0.288843
$552$	−9.50388	−	9.67865i	−0.404512	−	0.411951i
$553$	42.2460			1.79648
$554$	7.26378	+	29.9413i	0.308608	+	1.27209i
$555$	−0.0557287	+	0.0482892i	−0.00236555	+	0.00204976i
$556$	9.97294	+	19.3445i	0.422947	+	0.820391i
$557$	4.93990	−	0.710250i	0.209310	−	0.0300943i	−0.0368620	−	0.999320i	$-0.511736\pi$
$557$	4.93990	−	0.710250i	0.209310	−	0.0300943i	0.246172	+	0.969226i	$0.420827\pi$
$558$	−4.03730	−	2.87493i	−0.170912	−	0.121705i
$559$	9.66256	−	21.1581i	0.408683	−	0.894891i
$560$	−13.8883	−	17.6600i	−0.586889	−	0.746272i
$561$	0.387093	−	2.69229i	0.0163431	−	0.113669i
$562$	−4.13565	−	10.3303i	−0.174452	−	0.435756i
$563$	3.39292	−	11.5552i	0.142995	−	0.486995i	−0.856584	−	0.516007i	$-0.827418\pi$
$563$	3.39292	−	11.5552i	0.142995	−	0.486995i	0.999579	+	0.0290119i	$0.00923608\pi$
$564$	−2.79671	+	6.98597i	−0.117763	+	0.294162i
$565$	−13.5468	+	6.18659i	−0.569916	+	0.260272i
$566$	−28.5299	−	5.49859i	−1.19920	−	0.231123i
$567$	−1.91069	+	2.20505i	−0.0802415	+	0.0926036i
$568$	3.39531	−	5.28331i	0.142464	−	0.221683i
$569$	33.1170	+	21.2830i	1.38834	+	0.892230i	0.999576	−	0.0291095i	$-0.00926715\pi$
$569$	33.1170	+	21.2830i	1.38834	+	0.892230i	0.388760	+	0.921339i	$0.372904\pi$
$570$	12.2035	−	1.16533i	0.511148	−	0.0488102i
$571$	8.11085	+	12.6207i	0.339429	+	0.528161i	0.968444	−	0.249232i	$-0.0801781\pi$
$571$	8.11085	+	12.6207i	0.339429	+	0.528161i	−0.629015	+	0.777393i	$0.716542\pi$
$572$	−2.71138	−	3.80756i	−0.113369	−	0.159202i
$573$	−4.44371	−	15.1339i	−0.185639	−	0.632227i
$574$	−6.64364	−	0.316456i	−0.277300	−	0.0132086i
$575$	2.22196	−	5.79534i	0.0926621	−	0.241682i
$576$	−7.67598	−	2.25373i	−0.319833	−	0.0939052i
$577$	12.5101	−	3.67330i	0.520803	−	0.152922i	−0.0107571	−	0.999942i	$-0.503424\pi$
$577$	12.5101	−	3.67330i	0.520803	−	0.152922i	0.531560	+	0.847021i	$0.321606\pi$
$578$	10.8360	+	13.7790i	0.450719	+	0.573132i
$579$	7.00844	+	10.9053i	0.291261	+	0.453211i
$580$	0.275871	+	5.79053i	0.0114549	+	0.240439i
$581$	15.4860	−	24.0967i	0.642468	−	0.999700i
$582$	7.05499	+	3.63707i	0.292439	+	0.150762i
$583$	2.52681	−	2.91609i	0.104650	−	0.120772i
$584$	−1.04563	+	3.56119i	−0.0432683	+	0.147363i
$585$	−1.47452	−	3.22875i	−0.0609640	−	0.133492i
$586$	7.48132	−	21.6161i	0.309051	−	0.892952i
$587$	8.88101	−	30.2459i	0.366559	−	1.24838i	−0.545426	−	0.838159i	$-0.683632\pi$
$587$	8.88101	−	30.2459i	0.366559	−	1.24838i	0.911984	−	0.410225i	$-0.134550\pi$
$588$	−2.85957	+	0.989725i	−0.117927	+	0.0408156i
$589$	15.6206	+	2.24591i	0.643637	+	0.0925410i
$590$	−13.0009	+	13.6350i	−0.535237	+	0.561344i
$591$	9.73352	−	21.3134i	0.400384	−	0.876718i
$592$	−0.105733	+	0.110893i	−0.00434562	+	0.00455766i
$593$	−1.48201	−	10.3076i	−0.0608589	−	0.423283i	−0.997360	−	0.0726180i	$-0.976865\pi$
$593$	−1.48201	−	10.3076i	−0.0608589	−	0.423283i	0.936501	−	0.350665i	$-0.114044\pi$
$594$	1.55240	−	0.896286i	0.0636958	−	0.0367751i
$595$	9.10893	−	7.89293i	0.373430	−	0.323579i
$596$	3.51815	+	18.2533i	0.144109	+	0.747685i
$597$			6.38298i			0.261238i
$598$	−0.183623	−	12.5043i	−0.00750889	−	0.511339i
$599$	−17.3680			−0.709638			−0.354819	−	0.934935i	$-0.615458\pi$
$599$	−17.3680			−0.709638			−0.354819	+	0.934935i	$0.615458\pi$
$600$	−0.520977	−	3.62325i	−0.0212688	−	0.147918i
$601$	−19.6309	−	22.6553i	−0.800762	−	0.924129i	0.197661	−	0.980270i	$-0.436666\pi$
$601$	−19.6309	−	22.6553i	−0.800762	−	0.924129i	−0.998423	+	0.0561418i	$0.982120\pi$
$602$	26.0262	+	45.0785i	1.06075	+	1.83726i
$603$	−12.5824	+	1.80908i	−0.512395	+	0.0736712i
$604$	13.7289	+	10.7964i	0.558619	+	0.439298i
$605$	16.4486	+	7.51182i	0.668730	+	0.305399i
$606$	0.446626	−	0.468411i	0.0181429	−	0.0190279i
$607$	5.15520	−	35.8552i	0.209243	−	1.45532i	−0.566392	−	0.824136i	$-0.691661\pi$
$607$	5.15520	−	35.8552i	0.209243	−	1.45532i	0.775635	−	0.631182i	$-0.217430\pi$
$608$	25.0122	−	4.82108i	1.01438	−	0.195521i
$609$	4.21524	+	1.23771i	0.170810	+	0.0501544i
$610$	−12.5504	−	4.34370i	−0.508152	−	0.175871i
$611$	−6.31056	+	2.88194i	−0.255298	+	0.116591i
$612$	1.01180	−	4.17079i	0.0408995	−	0.168594i
$613$	11.8534	+	10.2710i	0.478754	+	0.414843i	0.860520	−	0.509416i	$-0.170139\pi$
$613$	11.8534	+	10.2710i	0.478754	+	0.414843i	−0.381766	+	0.924259i	$0.624684\pi$
$614$	5.64182	+	2.90854i	0.227685	+	0.117379i
$615$	2.61042	+	1.67762i	0.105262	+	0.0676480i
$616$	10.4603		9.16928e-5i	0.421459		3.69441e-6i
$617$	−29.8192	+	19.1636i	−1.20048	+	0.771499i	−0.979039	−	0.203675i	$-0.934711\pi$
$617$	−29.8192	+	19.1636i	−1.20048	+	0.771499i	−0.221438	+	0.975174i	$0.571075\pi$
$618$	8.55734	−	6.72960i	0.344227	−	0.270704i
$619$	7.87860	+	26.8321i	0.316668	+	1.07847i	0.951966	+	0.306204i	$0.0990591\pi$
$619$	7.87860	+	26.8321i	0.316668	+	1.07847i	−0.635298	+	0.772267i	$0.719123\pi$
$620$	−1.28253	+	13.4321i	−0.0515077	+	0.539447i
$621$	4.78029	+	0.385738i	0.191827	+	0.0154791i
$622$	34.1148	+	1.62499i	1.36788	+	0.0651561i
$623$	27.1105	−	7.96035i	1.08616	−	0.318925i
$624$	−3.68779	−	6.38726i	−0.147630	−	0.255695i
$625$	−14.1786	+	9.11204i	−0.567145	+	0.364482i
$626$	−0.0446426	−	0.467504i	−0.00178428	−	0.0186852i
$627$	−3.08579	+	4.80158i	−0.123235	+	0.191757i
$628$	24.1522	+	13.9441i	0.963778	+	0.556430i
$629$	−0.0621216	−	0.0538287i	−0.00247695	−	0.00214629i
$630$	7.79971	+	1.50325i	0.310748	+	0.0598908i
$631$	9.70082	+	21.2418i	0.386183	+	0.845624i	0.998486	+	0.0550004i	$0.0175160\pi$
$631$	9.70082	+	21.2418i	0.386183	+	0.845624i	−0.612303	+	0.790623i	$0.709757\pi$
$632$	−37.2526	−	17.0123i	−1.48183	−	0.676713i
$633$	18.1991	+	5.34374i	0.723350	+	0.212395i
$634$	32.7466	−	13.1099i	1.30053	−	0.520659i
$635$	35.8522	+	5.15476i	1.42275	+	0.204560i
$636$	4.40626	−	4.20141i	0.174720	−	0.166597i
$637$	−2.53765	−	1.15891i	−0.100545	−	0.0459176i
$638$	−2.19860	−	1.56561i	−0.0870433	−	0.0619829i
$639$	0.315997	+	2.19780i	0.0125006	+	0.0869438i
$640$	5.13513	+	21.1654i	0.202984	+	0.836636i
$641$	19.7821	+	22.8298i	0.781348	+	0.901723i	0.997206	−	0.0747013i	$-0.0238003\pi$
$641$	19.7821	+	22.8298i	0.781348	+	0.901723i	−0.215858	+	0.976425i	$0.569255\pi$
$642$	4.70389	−	1.14117i	0.185648	−	0.0450382i
$643$		−	40.8097i		−	1.60938i	−0.593698	−	0.804688i	$-0.702332\pi$
$643$		−	40.8097i		−	1.60938i	0.593698	−	0.804688i	$-0.297668\pi$
$644$	23.0324	+	15.8967i	0.907603	+	0.626419i
$645$		−	24.2843i		−	0.956192i
$646$	3.22176	+	13.2801i	0.126758	+	0.522498i
$647$	−10.9613	−	12.6501i	−0.430935	−	0.497325i	0.498202	−	0.867061i	$-0.333994\pi$
$647$	−10.9613	−	12.6501i	−0.430935	−	0.497325i	−0.929137	+	0.369736i	$0.879448\pi$
$648$	2.57282	−	1.17499i	0.101070	−	0.0461581i
$649$	−1.24832	−	8.68228i	−0.0490010	−	0.340809i
$650$	1.95753	−	2.74898i	0.0767805	−	0.107824i
$651$	9.30145	+	4.24783i	0.364552	+	0.166486i
$652$	−9.57978	−	10.0469i	−0.375173	−	0.393466i
$653$	−48.1339	−	6.92062i	−1.88363	−	0.270825i	−0.898030	−	0.439935i	$-0.855002\pi$
$653$	−48.1339	−	6.92062i	−1.88363	−	0.270825i	−0.985597	+	0.169110i	$0.945911\pi$
$654$	−9.30036	−	23.2310i	−0.363673	−	0.908403i
$655$	−36.2100	−	10.6322i	−1.41484	−	0.415435i
$656$	5.73094	+	2.95442i	0.223756	+	0.115351i
$657$	−0.545116	−	1.19364i	−0.0212670	−	0.0465683i
$658$	2.93808	−	15.2445i	0.114538	−	0.594291i
$659$	13.2663	+	11.4954i	0.516783	+	0.447795i	0.873788	−	0.486307i	$-0.161656\pi$
$659$	13.2663	+	11.4954i	0.516783	+	0.447795i	−0.357004	+	0.934103i	$0.616202\pi$
$660$	−4.22633	−	2.44004i	−0.164510	−	0.0949784i
$661$	12.9823	−	20.2008i	0.504952	−	0.785720i	−0.491411	−	0.870928i	$-0.663519\pi$
$661$	12.9823	−	20.2008i	0.504952	−	0.785720i	0.996363	+	0.0852071i	$0.0271552\pi$
$662$	8.85505	−	0.845581i	0.344161	−	0.0328644i
$663$	3.32859	−	2.13915i	0.129272	−	0.0830779i
$664$	−23.3592	+	15.0124i	−0.906515	+	0.582593i
$665$	−24.2674	+	7.12555i	−0.941049	+	0.276317i
$666$	0.00257744	−	0.0541105i	9.98739e−5	−	0.00209674i
$667$	−2.46171	−	6.78853i	−0.0953178	−	0.262853i
$668$	−31.7833	−	3.03475i	−1.22973	−	0.117418i
$669$	5.10120	+	17.3731i	0.197224	+	0.671682i
$670$	21.3927	+	27.2028i	0.826471	+	1.05094i
$671$	5.20182	−	3.34301i	0.200814	−	0.129055i
$672$	16.4303	+	1.56866i	0.633813	+	0.0605125i
$673$	−18.4719	−	11.8712i	−0.712040	−	0.457600i	0.133820	−	0.991006i	$-0.457276\pi$
$673$	−18.4719	−	11.8712i	−0.712040	−	0.457600i	−0.845860	+	0.533405i	$0.820912\pi$
$674$	−20.0030	+	38.8007i	−0.770486	+	1.49455i
$675$	0.978080	+	0.847511i	0.0376463	+	0.0326207i
$676$	−4.52655	+	18.6592i	−0.174098	+	0.717661i
$677$	−22.1626	+	10.1213i	−0.851776	+	0.388993i	−0.792958	−	0.609276i	$-0.791460\pi$
$677$	−22.1626	+	10.1213i	−0.851776	+	0.388993i	−0.0588176	+	0.998269i	$0.518733\pi$
$678$	3.57830	−	10.3389i	0.137424	−	0.397064i
$679$	−15.7124	−	4.61358i	−0.602986	−	0.177053i
$680$	−11.2107	+	3.29187i	−0.429912	+	0.126238i
$681$	3.52540	−	24.5197i	0.135093	−	0.939596i
$682$	−4.54672	−	4.33526i	−0.174103	−	0.166006i
$683$	−26.6852	−	12.1867i	−1.02108	−	0.466312i	−0.166727	−	0.986003i	$-0.553320\pi$
$683$	−26.6852	−	12.1867i	−1.02108	−	0.466312i	−0.854355	+	0.519691i	$0.826047\pi$
$684$	−5.56705	+	7.07916i	−0.212861	+	0.270679i
$685$	−5.46076	+	0.785139i	−0.208645	+	0.0299986i
$686$	−19.6074	+	11.3204i	−0.748616	+	0.432216i
$687$	−1.30634	−	1.50760i	−0.0498399	−	0.0575183i
$688$	−4.79707	−	50.2310i	−0.182887	−	1.91504i
$689$	5.61294			0.213836
$690$	−5.59759	−	11.7955i	−0.213097	−	0.449048i
$691$		−	35.2072i		−	1.33934i	−0.742657	−	0.669672i	$-0.766435\pi$
$691$		−	35.2072i		−	1.33934i	0.742657	−	0.669672i	$-0.233565\pi$
$692$	3.73329	+	19.3696i	0.141918	+	0.736320i
$693$	−2.79498	+	2.42186i	−0.106173	+	0.0919990i
$694$	−7.43627	−	12.8799i	−0.282277	−	0.488915i
$695$	2.98126	+	20.7351i	0.113086	+	0.786528i
$696$	−3.21859	−	2.78887i	−0.122000	−	0.105712i
$697$	−1.43691	+	3.14640i	−0.0544269	+	0.119178i
$698$	−3.30873	−	3.15485i	−0.125237	−	0.119413i
$699$	9.76959	+	1.40465i	0.369520	+	0.0531289i
$700$	2.47009	+	7.13673i	0.0933607	+	0.269743i
$701$	12.1454	−	41.3634i	0.458725	−	1.56227i	−0.327820	−	0.944740i	$-0.606314\pi$
$701$	12.1454	−	41.3634i	0.458725	−	1.56227i	0.786545	−	0.617533i	$-0.211868\pi$
$702$	2.46419	+	0.852858i	0.0930050	+	0.0321890i
$703$	0.0716538	+	0.156900i	0.00270247	+	0.00591759i
$704$	−9.22399	−	4.21226i	−0.347642	−	0.158755i
$705$	−4.74314	+	5.47388i	−0.178637	+	0.206158i
$706$	−23.6762	+	45.9258i	−0.891067	+	1.72844i
$707$	−0.721908	+	1.12331i	−0.0271501	+	0.0422464i
$708$	−0.658632	−	13.8247i	−0.0247529	−	0.519564i
$709$	8.58532	+	13.3590i	0.322428	+	0.501708i	0.964196	−	0.265191i	$-0.0854350\pi$
$709$	8.58532	+	13.3590i	0.322428	+	0.501708i	−0.641768	+	0.766899i	$0.721799\pi$
$710$	4.75160	−	3.73672i	0.178324	−	0.140237i
$711$	13.8927	−	4.07926i	0.521016	−	0.152984i
$712$	−27.1117	−	3.89783i	−1.01605	−	0.146077i
$713$	−3.42281	−	16.4555i	−0.128185	−	0.616262i
$714$	−0.421287	+	8.84444i	−0.0157663	+	0.330995i
$715$	−1.26755	−	4.31688i	−0.0474037	−	0.161442i
$716$	−27.8124	+	19.8054i	−1.03940	+	0.740162i
$717$	−7.24214	−	11.2690i	−0.270463	−	0.420848i
$718$	−1.48865	−	15.5893i	−0.0555558	−	0.581788i
$719$	11.1166	+	7.14418i	0.414578	+	0.266433i	0.731260	−	0.682099i	$-0.238933\pi$
$719$	11.1166	+	7.14418i	0.414578	+	0.266433i	−0.316682	+	0.948532i	$0.602569\pi$
$720$	−6.27245	−	4.46648i	−0.233760	−	0.166456i
$721$	−14.7083	+	16.9743i	−0.547766	+	0.632156i
$722$	0.341679	−	1.77283i	0.0127160	−	0.0659779i
$723$	−16.2148	+	7.40507i	−0.603037	+	0.275398i
$724$	3.02045	−	7.54486i	0.112254	−	0.280402i
$725$	0.549000	−	1.86972i	0.0203894	−	0.0694398i
$726$	−12.3326	+	4.93728i	−0.457707	+	0.183240i
$727$	1.89646	−	13.1902i	0.0703360	−	0.489198i	−0.923956	−	0.382500i	$-0.875063\pi$
$727$	1.89646	−	13.1902i	0.0703360	−	0.489198i	0.994292	−	0.106698i	$-0.0340277\pi$
$728$	9.96476	+	11.4997i	0.369319	+	0.426209i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−2.07221	+	2.91002i	−0.0766958	+	0.107705i
$731$	26.7945	−	3.85247i	0.991031	−	0.142489i
$732$	8.67200	−	4.47079i	0.320526	−	0.165245i
$733$	−17.5796	+	15.2328i	−0.649316	+	0.562636i	−0.916015	−	0.401144i	$-0.868613\pi$
$733$	−17.5796	+	15.2328i	−0.649316	+	0.562636i	0.266699	+	0.963780i	$0.414067\pi$
$734$	20.5437	−	4.98391i	0.758281	−	0.183959i
$735$	−2.91260			−0.107433
$736$	−13.9084	−	23.2928i	−0.512672	−	0.858584i
$737$	−16.1126			−0.593516
$738$	−2.21533	+	0.537440i	−0.0815474	+	0.0197834i
$739$	29.2641	−	25.3575i	1.07650	−	0.932790i	0.0785553	−	0.996910i	$-0.474969\pi$
$739$	29.2641	−	25.3575i	1.07650	−	0.932790i	0.997942	+	0.0641194i	$0.0204238\pi$
$740$	−0.131084	+	0.0675796i	−0.00481875	+	0.00248428i
$741$	−8.21830	+	1.18161i	−0.301907	+	0.0434077i
$742$	−7.28599	+	10.2318i	−0.267477	+	0.375622i
$743$	−1.24831	+	2.73342i	−0.0457961	+	0.100279i	−0.931147	−	0.364644i	$-0.881191\pi$
$743$	−1.24831	+	2.73342i	−0.0457961	+	0.100279i	0.885351	+	0.464923i	$0.153918\pi$
$744$	−6.49145	−	7.49140i	−0.237988	−	0.274648i
$745$	−2.54639	+	17.7105i	−0.0932924	+	0.648863i
$746$	12.8923	−	5.16134i	0.472021	−	0.188970i
$747$	2.76584	−	9.41957i	0.101197	−	0.344644i
$748$	2.02180	−	5.05030i	0.0739243	−	0.184657i
$749$	−9.08379	+	4.14843i	−0.331915	+	0.151580i
$750$	3.24286	−	16.8258i	0.118413	−	0.614393i
$751$	−5.65312	+	6.52405i	−0.206285	+	0.238066i	−0.849459	−	0.527654i	$-0.823072\pi$
$751$	−5.65312	+	6.52405i	−0.206285	+	0.238066i	0.643174	+	0.765720i	$0.277617\pi$
$752$	−8.72969	+	12.2594i	−0.318339	+	0.447056i
$753$	8.60294	+	5.52877i	0.313509	+	0.201480i
$754$	−0.373228	−	3.90850i	−0.0135922	−	0.142339i
$755$	9.08869	+	14.1423i	0.330771	+	0.514690i
$756$	−4.75336	+	3.38490i	−0.172878	+	0.123108i
$757$	−0.788800	−	2.68641i	−0.0286694	−	0.0976391i	0.943915	−	0.330187i	$-0.107112\pi$
$757$	−0.788800	−	2.68641i	−0.0286694	−	0.0976391i	−0.972585	+	0.232548i	$0.925294\pi$
$758$	1.99976	−	41.9826i	0.0726344	−	1.52488i
$759$	5.92793	+	1.34627i	0.215170	+	0.0488665i
$760$	24.2685	+	3.48906i	0.880310	+	0.126562i
$761$	−42.9278	+	12.6047i	−1.55613	+	0.456922i	−0.942926	−	0.333001i	$-0.891939\pi$
$761$	−42.9278	+	12.6047i	−1.55613	+	0.456922i	−0.613206	+	0.789923i	$0.710121\pi$
$762$	−20.9162	+	16.4488i	−0.757713	+	0.595876i
$763$	27.9115	+	43.4311i	1.01046	+	1.57231i
$764$	−1.50118	−	31.5098i	−0.0543109	−	1.13999i
$765$	2.23335	−	3.47516i	0.0807469	−	0.125645i
$766$	15.2299	−	29.5420i	0.550277	−	1.06740i
$767$	8.35591	−	9.64324i	0.301714	−	0.348197i
$768$	−13.8566	−	7.99968i	−0.500007	−	0.288663i
$769$	−4.65003	−	10.1821i	−0.167684	−	0.367178i	0.807071	−	0.590455i	$-0.201052\pi$
$769$	−4.65003	−	10.1821i	−0.167684	−	0.367178i	−0.974755	+	0.223277i	$0.928324\pi$
$770$	9.51459	+	3.29300i	0.342882	+	0.118672i
$771$	0.326422	−	1.11169i	0.0117558	−	0.0400365i
$772$	8.47984	+	24.5004i	0.305196	+	0.881790i
$773$	44.3473	+	6.37618i	1.59506	+	0.229335i	0.881821	−	0.471584i	$-0.156318\pi$
$773$	44.3473	+	6.37618i	1.59506	+	0.229335i	0.713240	+	0.700920i	$0.247227\pi$
$774$	12.9115	+	12.3111i	0.464096	+	0.442512i
$775$	1.88418	−	4.12578i	0.0676817	−	0.148202i
$776$	11.9974	+	10.3956i	0.430680	+	0.373180i
$777$	0.0159056	+	0.110626i	0.000570611	+	0.00396868i
$778$	−0.273825	−	0.474276i	−0.00981710	−	0.0170036i
$779$	5.48552	−	4.75323i	0.196539	−	0.170302i
$780$	−1.34354	−	6.97073i	−0.0481065	−	0.249592i
$781$			2.81444i			0.100708i
$782$	12.1268	−	8.04746i	0.433654	−	0.287777i
$783$	1.50570			0.0538094
$784$	−6.02460	+	0.575350i	−0.215164	+	0.0205482i
$785$	17.5787	+	20.2868i	0.627409	+	0.724069i
$786$	24.0099	−	13.8622i	0.856404	−	0.494448i
$787$	−18.9557	+	2.72542i	−0.675697	+	0.0971506i	−0.471617	−	0.881804i	$-0.656329\pi$
$787$	−18.9557	+	2.72542i	−0.675697	+	0.0971506i	−0.204080	+	0.978954i	$0.565420\pi$
$788$	28.9678	−	36.8359i	1.03193	−	1.31223i
$789$	−12.9546	−	5.91617i	−0.461196	−	0.210621i
$790$	−28.5286	−	27.2018i	−1.01500	−	0.967798i
$791$	−3.21232	+	22.3422i	−0.114217	+	0.794397i
$792$	3.43989	−	1.01008i	0.122231	−	0.0358915i
$793$	8.63054	+	2.53416i	0.306479	+	0.0899905i
$794$	−11.2253	+	32.4337i	−0.398371	+	1.15103i
$795$	5.33054	−	2.43438i	0.189055	−	0.0863384i
$796$	−3.00962	+	12.4061i	−0.106673	+	0.439723i
$797$	21.9093	+	18.9846i	0.776069	+	0.672468i	0.949986	−	0.312293i	$-0.101097\pi$
$797$	21.9093	+	18.9846i	0.776069	+	0.672468i	−0.173917	+	0.984760i	$0.555642\pi$
$798$	8.51397	−	16.5149i	0.301391	−	0.584622i
$799$	−6.79217	−	4.36506i	−0.240290	−	0.154425i
$800$	0.695801	−	7.28788i	0.0246003	−	0.257665i
$801$	8.14668	−	5.23555i	0.287849	−	0.184989i
$802$	16.8770	+	21.4607i	0.595946	+	0.757803i
$803$	−0.468601	−	1.59591i	−0.0165366	−	0.0563184i
$804$	−25.3085	−	2.41652i	−0.892560	−	0.0852239i
$805$	15.9453	+	21.7104i	0.562000	+	0.765190i
$806$	0.434811	−	9.12837i	0.0153156	−	0.321533i
$807$	6.86909	−	2.01695i	0.241803	−	0.0709998i
$808$	1.08893	−	0.699828i	0.0383085	−	0.0246199i
$809$	−0.818217	+	0.525836i	−0.0287670	+	0.0184874i	−0.554945	−	0.831887i	$-0.687261\pi$
$809$	−0.818217	+	0.525836i	−0.0287670	+	0.0184874i	0.526178	+	0.850374i	$0.323624\pi$
$810$	2.71010	−	0.258791i	0.0952233	−	0.00909300i
$811$	−8.99614	+	13.9983i	−0.315897	+	0.491546i	−0.962500	−	0.271281i	$-0.912553\pi$
$811$	−8.99614	+	13.9983i	−0.315897	+	0.491546i	0.646603	+	0.762827i	$0.276189\pi$
$812$	7.60926	+	4.39315i	0.267033	+	0.154169i
$813$	20.8572	+	18.0728i	0.731493	+	0.633842i
$814$	0.0129947	−	0.0674238i	0.000455463	−	0.00236320i
$815$	−5.55070	−	12.1543i	−0.194433	−	0.425748i
$816$	3.93311	−	7.62940i	0.137687	−	0.267082i
$817$	−54.5033	−	16.0036i	−1.90683	−	0.559896i
$818$	4.46055	+	11.1418i	0.155960	+	0.389565i
$819$	−5.32507	−	0.765630i	−0.186073	−	0.0267533i
$820$	4.28267	+	4.49149i	0.149557	+	0.156850i
$821$	−35.8364	−	16.3659i	−1.25070	−	0.571175i	−0.323671	−	0.946170i	$-0.604917\pi$
$821$	−35.8364	−	16.3659i	−1.25070	−	0.571175i	−0.927027	+	0.374995i	$0.877644\pi$
$822$	2.35092	−	3.30143i	0.0819978	−	0.115151i
$823$	3.63957	+	25.3137i	0.126867	+	0.882382i	0.949491	+	0.313795i	$0.101600\pi$
$823$	3.63957	+	25.3137i	0.126867	+	0.882382i	−0.822623	+	0.568587i	$0.807490\pi$
$824$	19.8053	−	9.04499i	0.689951	−	0.315097i
$825$	1.07425	+	1.23975i	0.0374005	+	0.0431625i
$826$	6.73205	+	27.7495i	0.234238	+	0.965530i
$827$		−	33.8581i		−	1.17736i	−0.808365	−	0.588681i	$-0.799647\pi$
$827$		−	33.8581i		−	1.17736i	0.808365	−	0.588681i	$-0.200353\pi$
$828$	9.10922	+	3.00367i	0.316567	+	0.104385i
$829$			7.69420i			0.267231i	0.991033	+	0.133615i	$0.0426587\pi$
$829$			7.69420i			0.267231i	−0.991033	+	0.133615i	$0.957341\pi$
$830$	−25.9733	+	6.30115i	−0.901548	+	0.218716i
$831$	−14.2667	−	16.4646i	−0.494906	−	0.571152i
$832$	−4.15604	−	14.1533i	−0.144085	−	0.490676i
$833$	−0.462057	−	3.21368i	−0.0160093	−	0.111347i
$834$	−12.5359	−	8.92672i	−0.434083	−	0.309107i
$835$	−27.9543	−	12.7663i	−0.967397	−	0.441795i
$836$	−8.26160	+	7.87751i	−0.285733	+	0.272449i
$837$	3.46897	+	0.498762i	0.119905	+	0.0172397i
$838$	52.3807	−	20.9702i	1.80946	−	0.724405i
$839$	43.1612	+	12.6733i	1.49009	+	0.437530i	0.922570	−	0.385831i	$-0.126085\pi$
$839$	43.1612	+	12.6733i	1.49009	+	0.437530i	0.567519	+	0.823360i	$0.307903\pi$
$840$	14.4509	+	6.59936i	0.498604	+	0.227700i
$841$	11.1052	+	24.3171i	0.382939	+	0.838520i
$842$	−29.8444	−	5.75194i	−1.02851	−	0.198225i
$843$	5.94641	+	5.15259i	0.204805	+	0.177465i
$844$	32.8527	+	18.9672i	1.13084	+	0.652879i
$845$	−9.99150	+	15.5471i	−0.343718	+	0.534836i
$846$	−0.505805	−	5.29687i	−0.0173899	−	0.182110i
$847$	23.0563	−	14.8174i	0.792223	−	0.509131i
$848$	10.5451	−	6.08839i	0.362121	−	0.209076i
$849$	19.7127	−	5.78817i	0.676538	−	0.198650i
$850$	3.92307	+	0.186867i	0.134560	+	0.00640949i
$851$	0.131079	−	0.128710i	0.00449332	−	0.00441211i
$852$	−0.422100	+	4.42070i	−0.0144609	+	0.151451i
$853$	−6.52712	−	22.2293i	−0.223485	−	0.761118i	−0.992538	−	0.121934i	$-0.961090\pi$
$853$	−6.52712	−	22.2293i	−0.223485	−	0.761118i	0.769054	−	0.639184i	$-0.220728\pi$
$854$	−15.8225	+	12.4431i	−0.541436	+	0.425793i
$855$	−7.29234	+	4.68650i	−0.249393	+	0.160275i
$856$	9.68067		8.48584e-5i	0.330878		2.90040e-6i
$857$	26.4013	+	16.9671i	0.901850	+	0.579584i	0.907338	−	0.420401i	$-0.138111\pi$
$857$	26.4013	+	16.9671i	0.901850	+	0.579584i	−0.00548808	+	0.999985i	$0.501747\pi$
$858$	2.93781	+	1.51454i	0.100295	+	0.0517054i
$859$	3.42977	+	2.97191i	0.117022	+	0.101400i	0.711406	−	0.702781i	$-0.248059\pi$
$859$	3.42977	+	2.97191i	0.117022	+	0.101400i	−0.594384	+	0.804181i	$0.702604\pi$
$860$	11.4502	−	47.1995i	0.390448	−	1.60949i
$861$	4.27808	−	1.95373i	0.145797	−	0.0665830i
$862$	−2.84085	−	0.983219i	−0.0967598	−	0.0334886i
$863$	−20.7136	−	6.08205i	−0.705098	−	0.207036i	−0.0905238	−	0.995894i	$-0.528854\pi$
$863$	−20.7136	−	6.08205i	−0.705098	−	0.207036i	−0.614575	+	0.788859i	$0.710672\pi$
$864$	5.55461	−	1.07065i	0.188972	−	0.0364242i
$865$	−2.70210	+	18.7935i	−0.0918743	+	0.639000i
$866$	19.7590	−	20.7228i	0.671438	−	0.704188i
$867$	−11.2751	−	5.14915i	−0.382921	−	0.174874i
$868$	16.0757	+	12.6419i	0.545643	+	0.429093i
$869$	18.1660	−	2.61188i	0.616241	−	0.0886020i
$870$	−2.04959	−	3.54998i	−0.0694878	−	0.120356i
$871$	−15.3491	−	17.7138i	−0.520084	−	0.600209i
$872$	−7.12286	−	49.5375i	−0.241211	−	1.67755i
$873$	−5.61254			−0.189956
$874$	−30.1626	+	4.78978i	−1.02027	+	0.162017i
$875$			35.3527i			1.19514i
$876$	−0.496694	−	2.57701i	−0.0167817	−	0.0870692i
$877$	−6.77340	+	5.86919i	−0.228722	+	0.198188i	−0.761681	−	0.647953i	$-0.775625\pi$
$877$	−6.77340	+	5.86919i	−0.228722	+	0.198188i	0.532959	+	0.846141i	$0.321080\pi$
$878$	22.3971	−	12.9310i	0.755864	−	0.436401i
$879$	2.30186	+	16.0098i	0.0776399	+	0.539997i
$880$	−7.06391	−	6.73527i	−0.238124	−	0.227046i
$881$	8.52519	−	18.6676i	0.287221	−	0.628926i	−0.709937	−	0.704265i	$-0.751277\pi$
$881$	8.52519	−	18.6676i	0.287221	−	0.628926i	0.997158	+	0.0753391i	$0.0240039\pi$
$882$	1.47656	−	1.54858i	0.0497184	−	0.0521435i
$883$	−38.5495	−	5.54258i	−1.29729	−	0.186523i	−0.541149	−	0.840927i	$-0.682011\pi$
$883$	−38.5495	−	5.54258i	−1.29729	−	0.186523i	−0.756145	+	0.654404i	$0.772920\pi$
$884$	7.47816	−	2.58826i	0.251518	−	0.0870528i
$885$	3.75316	−	12.7821i	0.126161	−	0.429665i
$886$	11.8523	−	34.2453i	0.398186	−	1.15049i
$887$	7.88087	+	17.2567i	0.264614	+	0.579423i	0.994570	−	0.104071i	$-0.0331869\pi$
$887$	7.88087	+	17.2567i	0.264614	+	0.579423i	−0.729956	+	0.683494i	$0.760460\pi$
$888$	0.0305230	−	0.103955i	0.00102429	−	0.00348851i
$889$	35.9507	−	41.4893i	1.20575	−	1.39151i
$890$	−23.4333	−	12.0806i	−0.785485	−	0.404943i
$891$	−0.685280	+	1.06632i	−0.0229578	+	0.0357230i
$892$	1.72330	+	36.1720i	0.0577003	+	1.21113i
$893$	9.15972	+	14.2528i	0.306518	+	0.476952i
$894$	−8.12549	−	10.3323i	−0.271757	−	0.345565i
$895$	−31.5328	+	9.25887i	−1.05403	+	0.309490i
$896$	31.1948	+	10.7959i	1.04214	+	0.360666i
$897$	4.16696	+	7.79949i	0.139131	+	0.260417i
$898$	−41.4559	−	1.97467i	−1.38340	−	0.0658955i
$899$	−1.48669	−	5.06319i	−0.0495838	−	0.168867i
$900$	1.50141	+	2.10842i	0.0500472	+	0.0702805i
$901$	3.53166	+	5.49537i	0.117657	+	0.183077i
$902$	−2.87637	+	0.274669i	−0.0957727	+	0.00914547i
$903$	−30.9636	−	19.8991i	−1.03040	−	0.662200i
$904$	11.8297	−	18.4078i	0.393452	−	0.612234i
$905$	5.12260	−	5.91180i	0.170281	−	0.196515i
$906$	−12.1268	−	2.33721i	−0.402885	−	0.0776486i
$907$	−10.2239	+	4.66912i	−0.339480	+	0.155036i	−0.577859	−	0.816137i	$-0.696111\pi$
$907$	−10.2239	+	4.66912i	−0.339480	+	0.155036i	0.238378	+	0.971172i	$0.423384\pi$
$908$	18.4132	−	45.9948i	0.611065	−	1.52639i
$909$	−0.128934	+	0.439110i	−0.00427648	+	0.0145644i
$910$	5.44349	+	13.5971i	0.180450	+	0.450738i
$911$	−4.12879	+	28.7164i	−0.136793	+	0.951416i	0.799618	+	0.600509i	$0.205036\pi$
$911$	−4.12879	+	28.7164i	−0.136793	+	0.951416i	−0.936411	+	0.350906i	$0.885874\pi$
$912$	−14.1581	+	11.1343i	−0.468823	+	0.368695i
$913$	5.16929	−	11.3192i	0.171079	−	0.374610i
$914$	11.5935	+	8.25568i	0.383480	+	0.273073i
$915$	9.29539	−	1.33648i	0.307296	−	0.0441825i
$916$	−1.82819	−	3.54615i	−0.0604052	−	0.117168i
$917$	−43.2279	+	37.4572i	−1.42751	+	1.23695i
$918$	0.715475	+	2.94919i	0.0236142	+	0.0973378i
$919$	−16.9126			−0.557897			−0.278948	−	0.960306i	$-0.589986\pi$
$919$	−16.9126			−0.557897			−0.278948	+	0.960306i	$0.589986\pi$
$920$	−5.31795	−	25.5654i	−0.175328	−	0.842866i
$921$	−4.48830			−0.147895
$922$	14.3113	+	58.9911i	0.471317	+	1.94277i
$923$	−3.09412	+	2.68107i	−0.101844	+	0.0882485i
$924$	−6.57432	+	3.38935i	−0.216279	+	0.111501i
$925$	0.0490696	−	0.00705514i	0.00161340	−	0.000231972i
$926$	3.11325	+	2.21692i	0.102308	+	0.0728525i
$927$	−3.19783	+	7.00226i	−0.105030	+	0.229984i
$928$	−4.94076	−	6.93811i	−0.162188	−	0.227755i
$929$	−3.72028	+	25.8751i	−0.122059	+	0.848936i	0.833159	+	0.553033i	$0.186530\pi$
$929$	−3.72028	+	25.8751i	−0.122059	+	0.848936i	−0.955218	+	0.295903i	$0.904379\pi$
$930$	−3.54611	−	8.85768i	−0.116281	−	0.290455i
$931$	−1.91944	+	6.53701i	−0.0629071	+	0.214242i
$932$	18.3261	+	7.33655i	0.600292	+	0.240317i
$933$	−21.9678	+	10.0323i	−0.719193	+	0.328444i
$934$	8.87875	+	1.71121i	0.290522	+	0.0559926i
$935$	3.42891	−	3.95718i	0.112137	−	0.129413i
$936$	4.38734	+	2.81952i	0.143405	+	0.0921589i
$937$	−1.90283	−	1.22288i	−0.0621628	−	0.0399496i	0.509190	−	0.860654i	$-0.329945\pi$
$937$	−1.90283	−	1.22288i	−0.0621628	−	0.0399496i	−0.571353	+	0.820704i	$0.693581\pi$
$938$	52.2146	−	4.98604i	1.70487	−	0.162800i
$939$	0.179535	+	0.279363i	0.00585892	+	0.00911666i
$940$	−11.7999	+	8.40275i	−0.384869	+	0.274067i
$941$	−4.24807	−	14.4676i	−0.138483	−	0.471631i	0.860822	−	0.508907i	$-0.169950\pi$
$941$	−4.24807	−	14.4676i	−0.138483	−	0.471631i	−0.999305	+	0.0372759i	$0.988132\pi$
$942$	−19.6978	−	0.938264i	−0.641789	−	0.0305703i
$943$	−6.75080	−	3.76653i	−0.219836	−	0.122655i
$944$	5.23830	−	27.1806i	0.170492	−	0.884652i
$945$	−5.38921	+	1.58241i	−0.175311	+	0.0514759i
$946$	13.9785	+	17.7749i	0.454479	+	0.577913i
$947$	−28.8409	−	44.8774i	−0.937204	−	1.45832i	−0.888167	−	0.459521i	$-0.848021\pi$
$947$	−28.8409	−	44.8774i	−0.937204	−	1.45832i	−0.0490375	−	0.998797i	$-0.515615\pi$
$948$	28.9255	−	1.37806i	0.939458	−	0.0447574i
$949$	1.30811	−	2.03545i	0.0424629	−	0.0660736i
$950$	−7.32541	−	3.77648i	−0.237668	−	0.122525i
$951$	−16.3335	+	18.8499i	−0.529652	+	0.611250i
$952$	−4.98904	+	16.9916i	−0.161696	+	0.550702i
$953$	−11.0796	−	24.2609i	−0.358902	−	0.785886i	−0.999833	−	0.0182873i	$-0.994179\pi$
$953$	−11.0796	−	24.2609i	−0.358902	−	0.785886i	0.640931	−	0.767599i	$-0.278549\pi$
$954$	−1.40803	+	4.06828i	−0.0455868	+	0.131716i
$955$	8.55436	−	29.1335i	0.276813	−	0.942737i
$956$	−8.76261	−	25.3174i	−0.283403	−	0.818824i
$957$	1.88910	+	0.271612i	0.0610660	+	0.00877996i
$958$	19.2316	−	20.1696i	0.621343	−	0.651650i
$959$	−3.47358	+	7.60609i	−0.112168	+	0.245613i
$960$	−10.0853	−	11.6387i	−0.325502	−	0.375636i
$961$	2.66378	+	18.5270i	0.0859283	+	0.597645i
$962$	0.0865029	−	0.0499428i	0.00278897	−	0.00161022i
$963$	−2.58665	+	2.24135i	−0.0833537	+	0.0722264i
$964$	−35.0071	+	6.74728i	−1.12750	+	0.217315i
$965$			24.9548i			0.803324i
$966$	−19.6267	−	2.52834i	−0.631477	−	0.0813479i
$967$	2.21364			0.0711860			0.0355930	−	0.999366i	$-0.488668\pi$
$967$	2.21364			0.0711860			0.0355930	+	0.999366i	$0.488668\pi$
$968$	−26.2980	+	3.78131i	−0.845249	+	0.121536i
$969$	−6.32781	−	7.30268i	−0.203278	−	0.234596i
$970$	7.63991	+	13.2326i	0.245303	+	0.424874i
$971$	−31.9537	+	4.59424i	−1.02544	+	0.147436i	−0.634455	−	0.772960i	$-0.718775\pi$
$971$	−31.9537	+	4.59424i	−1.02544	+	0.147436i	−0.390987	+	0.920396i	$0.627866\pi$
$972$	−1.23631	+	1.57211i	−0.0396546	+	0.0504256i
$973$	28.8812	+	13.1896i	0.925889	+	0.422839i
$974$	−33.6258	+	35.2659i	−1.07744	+	1.12999i
$975$	−0.339605	+	2.36200i	−0.0108761	+	0.0756447i
$976$	18.9631	−	4.60064i	0.606995	−	0.147263i
$977$	3.65300	+	1.07262i	0.116870	+	0.0343160i	0.339644	−	0.940554i	$-0.389693\pi$
$977$	3.65300	+	1.07262i	0.116870	+	0.0343160i	−0.222775	+	0.974870i	$0.571511\pi$
$978$	9.27623	+	3.21050i	0.296621	+	0.102661i
$979$	11.1655	−	5.09912i	0.356852	−	0.162969i
$980$	−5.66101	−	1.37331i	−0.180834	−	0.0438688i
$981$	13.3724	+	11.5873i	0.426949	+	0.369954i
$982$	−27.6598	−	14.2595i	−0.882661	−	0.455040i
$983$	37.8129	+	24.3009i	1.20605	+	0.775078i	0.979992	−	0.199037i	$-0.0637813\pi$
$983$	37.8129	+	24.3009i	1.20605	+	0.775078i	0.226053	+	0.974115i	$0.427418\pi$
$984$	−4.55918		3.99647e-5i	−0.145341		1.27403e-6i
$985$	37.9452	−	24.3859i	1.20903	−	0.776999i
$986$	3.59179	−	2.82463i	0.114386	−	0.0899546i
$987$	3.09281	+	10.5332i	0.0984453	+	0.335274i
$988$	−16.5304	−	1.57837i	−0.525903	−	0.0502146i
$989$	3.76547	+	60.3815i	0.119735	+	1.92002i
$990$	3.44686	+	0.164184i	0.109549	+	0.00521812i
$991$	29.8194	−	8.75576i	0.947244	−	0.278136i	0.228605	−	0.973519i	$-0.426584\pi$
$991$	29.8194	−	8.75576i	0.947244	−	0.278136i	0.718639	+	0.695383i	$0.244765\pi$
$992$	−9.08471	−	17.6212i	−0.288440	−	0.559475i
$993$	−5.29144	+	3.40060i	−0.167919	+	0.107915i
$994$	−0.870927	−	9.12047i	−0.0276241	−	0.289284i
$995$	−6.64315	+	10.3369i	−0.210602	+	0.327703i
$996$	9.81714	−	17.0040i	0.311068	−	0.538793i
$997$	15.0145	+	13.0101i	0.475513	+	0.412034i	0.859367	−	0.511359i	$-0.170858\pi$
$997$	15.0145	+	13.0101i	0.475513	+	0.412034i	−0.383854	+	0.923394i	$0.625403\pi$
$998$	54.4640	+	10.4969i	1.72403	+	0.332274i
$999$	0.0159126	+	0.0348437i	0.000503452	+	0.00110241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.3	yes	480
8.5	even	2	inner	552.2.bb.a.469.6	yes	480
23.18	even	11	inner	552.2.bb.a.133.6	yes	480
184.133	even	22	inner	552.2.bb.a.133.3	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.3	✓	480	184.133	even	22	inner
552.2.bb.a.133.6	yes	480	23.18	even	11	inner
552.2.bb.a.469.3	yes	480	1.1	even	1	trivial
552.2.bb.a.469.6	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37435 + 0.333417i) q^{2} +(0.755750 - 0.654861i) q^{3} +(1.77767 - 0.916463i) q^{4} +(1.90545 - 0.273963i) q^{5} +(-0.820321 + 1.15199i) q^{6} +(1.21206 - 2.65404i) q^{7} +(-2.13757 + 1.85224i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.52741 + 1.01183i) q^{10} +(0.357105 - 1.21619i) q^{11} +(0.743314 - 1.85674i) q^{12} +(1.67723 - 0.765966i) q^{13} +(-0.780888 + 4.05169i) q^{14} +(1.26064 - 1.45486i) q^{15} +(2.32019 - 3.25833i) q^{16} +(1.80523 + 1.16015i) q^{17} +(0.134434 + 1.40781i) q^{18} +(-2.43448 - 3.78813i) q^{19} +(3.13618 - 2.23329i) q^{20} +(-0.822012 - 2.79952i) q^{21} +(-0.0852884 + 1.79053i) q^{22} +(-2.90893 + 3.81289i) q^{23} +(-0.402503 + 2.79964i) q^{24} +(-1.24176 + 0.364614i) q^{25} +(-2.04971 + 1.61192i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(-0.277694 - 5.82880i) q^{28} +(-0.814044 + 1.26668i) q^{29} +(-1.24748 + 2.41980i) q^{30} +(-2.29505 + 2.64863i) q^{31} +(-2.10236 + 5.25167i) q^{32} +(-0.526552 - 1.15299i) q^{33} +(-2.86783 - 0.992557i) q^{34} +(1.58241 - 5.38921i) q^{35} +(-0.654147 - 1.89000i) q^{36} +(-0.0379154 - 0.00545141i) q^{37} +(4.60886 + 4.39451i) q^{38} +(0.765966 - 1.67723i) q^{39} +(-3.56559 + 4.11498i) q^{40} +(0.229399 + 1.59551i) q^{41} +(2.06314 + 3.57344i) q^{42} +(9.53369 - 8.26099i) q^{43} +(-0.479779 - 2.48925i) q^{44} -1.92505i q^{45} +(2.72659 - 6.21013i) q^{46} -3.76249 q^{47} +(-0.380271 - 3.98188i) q^{48} +(-0.990805 - 1.14345i) q^{49} +(1.58504 - 0.915132i) q^{50} +(2.12404 - 0.305391i) q^{51} +(2.27958 - 2.89875i) q^{52} +(2.76904 + 1.26458i) q^{53} +(1.02352 + 0.975916i) q^{54} +(0.347257 - 2.41523i) q^{55} +(2.32507 + 7.91821i) q^{56} +(-4.32056 - 1.26863i) q^{57} +(0.696447 - 2.01227i) q^{58} +(6.29482 - 2.87475i) q^{59} +(0.907673 - 3.74158i) q^{60} +(3.68678 + 3.19461i) q^{61} +(2.27110 - 4.40535i) q^{62} +(-2.45453 - 1.57743i) q^{63} +(1.13838 - 7.91859i) q^{64} +(2.98604 - 1.91901i) q^{65} +(1.10809 + 1.40905i) q^{66} +(-3.58132 - 12.1969i) q^{67} +(4.27234 + 0.407933i) q^{68} +(0.298495 + 4.78653i) q^{69} +(-0.377932 + 7.93425i) q^{70} +(-2.13046 + 0.625560i) q^{71} +(1.52918 + 2.37941i) q^{72} +(1.10391 - 0.709440i) q^{73} +(0.0539266 - 0.00514952i) q^{74} +(-0.699690 + 1.08874i) q^{75} +(-7.79938 - 4.50291i) q^{76} +(-2.79498 - 2.42186i) q^{77} +(-0.493485 + 2.56049i) q^{78} +(6.01487 + 13.1707i) q^{79} +(3.52835 - 6.84425i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.847244 - 2.11630i) q^{82} +(9.71731 + 1.39714i) q^{83} +(-4.02692 - 4.22326i) q^{84} +(3.75763 + 1.71605i) q^{85} +(-10.3482 + 14.5322i) q^{86} +(0.214284 + 1.49038i) q^{87} +(1.48934 + 3.26113i) q^{88} +(6.34166 + 7.31866i) q^{89} +(0.641845 + 2.64569i) q^{90} -5.37983i q^{91} +(-1.67672 + 9.44397i) q^{92} +3.50464i q^{93} +(5.17097 - 1.25448i) q^{94} +(-5.67661 - 6.55115i) q^{95} +(1.85025 + 5.34570i) q^{96} +(-0.798747 - 5.55541i) q^{97} +(1.74296 + 1.24115i) q^{98} +(-1.15299 - 0.526552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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