LMFDB - Embedded newform 252.2.bj.b.103.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(103,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.103"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.34
Character	$\chi$	$=$	252.103
Dual form			252.2.bj.b.115.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06666 + 0.928568i) q^{2} +(0.187499 - 1.72187i) q^{3} +(0.275522 + 1.98093i) q^{4} +(2.33177 - 1.34625i) q^{5} +(1.79887 - 1.66254i) q^{6} +(-1.11915 - 2.39740i) q^{7} +(-1.54554 + 2.36882i) q^{8} +(-2.92969 - 0.645699i) q^{9} +(3.73728 + 0.729218i) q^{10} +(1.22399 + 0.706672i) q^{11} +(3.46257 - 0.102991i) q^{12} +(2.46297 + 1.42199i) q^{13} +(1.03240 - 3.59641i) q^{14} +(-1.88086 - 4.26742i) q^{15} +(-3.84817 + 1.09158i) q^{16} +(-1.23338 + 0.712090i) q^{17} +(-2.52540 - 3.40916i) q^{18} +(-1.48153 + 2.56609i) q^{19} +(3.30927 + 4.24815i) q^{20} +(-4.33785 + 1.47752i) q^{21} +(0.649389 + 1.89034i) q^{22} +(-1.67612 + 0.967709i) q^{23} +(3.78902 + 3.10538i) q^{24} +(1.12475 - 1.94813i) q^{25} +(1.30673 + 3.80381i) q^{26} +(-1.66113 + 4.92348i) q^{27} +(4.44073 - 2.87749i) q^{28} +(0.423772 + 0.733994i) q^{29} +(1.95636 - 6.29839i) q^{30} +9.87356 q^{31} +(-5.11830 - 2.40895i) q^{32} +(1.44630 - 1.97506i) q^{33} +(-1.97682 - 0.385717i) q^{34} +(-5.83707 - 4.08352i) q^{35} +(0.471891 - 5.98141i) q^{36} +(-5.49245 + 9.51321i) q^{37} +(-3.96307 + 1.36144i) q^{38} +(2.91030 - 3.97429i) q^{39} +(-0.414828 + 7.60421i) q^{40} +(-5.99620 - 3.46191i) q^{41} +(-5.99898 - 2.45198i) q^{42} +(5.96812 - 3.44570i) q^{43} +(-1.06263 + 2.61935i) q^{44} +(-7.70061 + 2.43846i) q^{45} +(-2.68643 - 0.524177i) q^{46} -10.6848 q^{47} +(1.15803 + 6.83074i) q^{48} +(-4.49502 + 5.36608i) q^{49} +(3.00870 - 1.03358i) q^{50} +(0.994872 + 2.25723i) q^{51} +(-2.13827 + 5.27076i) q^{52} +(-6.58617 - 11.4076i) q^{53} +(-6.34364 + 3.70921i) q^{54} +3.80542 q^{55} +(7.40869 + 1.05422i) q^{56} +(4.14069 + 3.03214i) q^{57} +(-0.229544 + 1.17642i) q^{58} -1.42192 q^{59} +(7.93525 - 4.90162i) q^{60} -2.03270i q^{61} +(10.5317 + 9.16828i) q^{62} +(1.73075 + 7.74626i) q^{63} +(-3.22261 - 7.32221i) q^{64} +7.65741 q^{65} +(3.37668 - 0.763728i) q^{66} -8.74356i q^{67} +(-1.75042 - 2.24704i) q^{68} +(1.35200 + 3.06751i) q^{69} +(-2.43434 - 9.77584i) q^{70} +1.95293i q^{71} +(6.05750 - 5.94195i) q^{72} +(7.16234 - 4.13518i) q^{73} +(-14.6922 + 5.04723i) q^{74} +(-3.14354 - 2.30195i) q^{75} +(-5.49143 - 2.22779i) q^{76} +(0.324347 - 3.72526i) q^{77} +(6.79469 - 1.53680i) q^{78} +11.8351i q^{79} +(-7.50350 + 7.72590i) q^{80} +(8.16615 + 3.78339i) q^{81} +(-3.18128 - 9.26055i) q^{82} +(-2.85384 - 4.94299i) q^{83} +(-4.12204 - 8.18589i) q^{84} +(-1.91730 + 3.32085i) q^{85} +(9.56552 + 1.86643i) q^{86} +(1.34330 - 0.592057i) q^{87} +(-3.56571 + 1.80722i) q^{88} +(5.75795 + 3.32435i) q^{89} +(-10.4782 - 4.54954i) q^{90} +(0.652664 - 7.49613i) q^{91} +(-2.37877 - 3.05365i) q^{92} +(1.85128 - 17.0010i) q^{93} +(-11.3970 - 9.92156i) q^{94} +7.97801i q^{95} +(-5.10758 + 8.36138i) q^{96} +(13.1164 - 7.57275i) q^{97} +(-9.77742 + 1.54984i) q^{98} +(-3.12962 - 2.86066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26}+ \cdots + 21 q^{98}+O(q^{100}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.06666	+	0.928568i	0.754242	+	0.656597i
$2$	1.06666	+	0.928568i	0.754242	+	0.656597i
$3$	0.187499	−	1.72187i	0.108253	−	0.994123i
$3$	0.187499	−	1.72187i	0.108253	−	0.994123i
$4$	0.275522	+	1.98093i	0.137761	+	0.990465i
$5$	2.33177	−	1.34625i	1.04280	−	0.602059i	0.122173	−	0.992509i	$-0.461014\pi$
$5$	2.33177	−	1.34625i	1.04280	−	0.602059i	0.920624	+	0.390450i	$0.127680\pi$
$6$	1.79887	−	1.66254i	0.734387	−	0.678731i
$7$	−1.11915	−	2.39740i	−0.422998	−	0.906131i
$7$	−1.11915	−	2.39740i	−0.422998	−	0.906131i
$8$	−1.54554	+	2.36882i	−0.546431	+	0.837504i
$9$	−2.92969	−	0.645699i	−0.976563	−	0.215233i
$10$	3.73728	+	0.729218i	1.18183	+	0.230599i
$11$	1.22399	+	0.706672i	0.369048	+	0.213070i	0.673042	−	0.739604i	$-0.264987\pi$
$11$	1.22399	+	0.706672i	0.369048	+	0.213070i	−0.303995	+	0.952674i	$0.598321\pi$
$12$	3.46257	−	0.102991i	0.999558	−	0.0297311i
$13$	2.46297	+	1.42199i	0.683104	+	0.394390i	0.801024	−	0.598633i	$-0.204289\pi$
$13$	2.46297	+	1.42199i	0.683104	+	0.394390i	−0.117920	+	0.993023i	$0.537622\pi$
$14$	1.03240	−	3.59641i	0.275920	−	0.961181i
$15$	−1.88086	−	4.26742i	−0.485636	−	1.10184i
$16$	−3.84817	+	1.09158i	−0.962044	+	0.272895i
$17$	−1.23338	+	0.712090i	−0.299138	+	0.172707i	−0.642055	−	0.766658i	$-0.721918\pi$
$17$	−1.23338	+	0.712090i	−0.299138	+	0.172707i	0.342918	+	0.939365i	$0.388585\pi$
$18$	−2.52540	−	3.40916i	−0.595243	−	0.803546i
$19$	−1.48153	+	2.56609i	−0.339886	+	0.588700i	−0.984411	−	0.175883i	$-0.943722\pi$
$19$	−1.48153	+	2.56609i	−0.339886	+	0.588700i	0.644525	+	0.764583i	$0.277055\pi$
$20$	3.30927	+	4.24815i	0.739976	+	0.949914i
$21$	−4.33785	+	1.47752i	−0.946596	+	0.322421i
$22$	0.649389	+	1.89034i	0.138450	+	0.403021i
$23$	−1.67612	+	0.967709i	−0.349495	+	0.201781i	−0.664463	−	0.747321i	$-0.731340\pi$
$23$	−1.67612	+	0.967709i	−0.349495	+	0.201781i	0.314968	+	0.949102i	$0.398006\pi$
$24$	3.78902	+	3.10538i	0.773430	+	0.633882i
$25$	1.12475	−	1.94813i	0.224950	−	0.389626i
$26$	1.30673	+	3.80381i	0.256270	+	0.745989i
$27$	−1.66113	+	4.92348i	−0.319684	+	0.947524i
$28$	4.44073	−	2.87749i	0.839219	−	0.543794i
$29$	0.423772	+	0.733994i	0.0786924	+	0.136299i	0.902686	−	0.430300i	$-0.141592\pi$
$29$	0.423772	+	0.733994i	0.0786924	+	0.136299i	−0.823994	+	0.566599i	$0.808259\pi$
$30$	1.95636	−	6.29839i	0.357180	−	1.14992i
$31$	9.87356			1.77334			0.886672	−	0.462398i	$-0.153011\pi$
$31$	9.87356			1.77334			0.886672	+	0.462398i	$0.153011\pi$
$32$	−5.11830	−	2.40895i	−0.904796	−	0.425846i
$33$	1.44630	−	1.97506i	0.251768	−	0.343813i
$34$	−1.97682	−	0.385717i	−0.339021	−	0.0661499i
$35$	−5.83707	−	4.08352i	−0.986645	−	0.690241i
$36$	0.471891	−	5.98141i	0.0786484	−	0.996902i
$37$	−5.49245	+	9.51321i	−0.902953	+	1.56396i	−0.0793124	+	0.996850i	$0.525272\pi$
$37$	−5.49245	+	9.51321i	−0.902953	+	1.56396i	−0.823641	+	0.567111i	$0.808061\pi$
$38$	−3.96307	+	1.36144i	−0.642895	+	0.220854i
$39$	2.91030	−	3.97429i	0.466020	−	0.636396i
$40$	−0.414828	+	7.60421i	−0.0655900	+	1.20233i
$41$	−5.99620	−	3.46191i	−0.936449	−	0.540659i	−0.0476034	−	0.998866i	$-0.515158\pi$
$41$	−5.99620	−	3.46191i	−0.936449	−	0.540659i	−0.888845	+	0.458207i	$0.848492\pi$
$42$	−5.99898	−	2.45198i	−0.925663	−	0.378349i
$43$	5.96812	−	3.44570i	0.910131	−	0.525464i	0.0296574	−	0.999560i	$-0.490558\pi$
$43$	5.96812	−	3.44570i	0.910131	−	0.525464i	0.880473	+	0.474096i	$0.157225\pi$
$44$	−1.06263	+	2.61935i	−0.160198	+	0.394882i
$45$	−7.70061	+	2.43846i	−1.14794	+	0.363504i
$46$	−2.68643	−	0.524177i	−0.396093	−	0.0772857i
$47$	−10.6848			−1.55854			−0.779269	−	0.626690i	$-0.784409\pi$
$47$	−10.6848			−1.55854			−0.779269	+	0.626690i	$0.784409\pi$
$48$	1.15803	+	6.83074i	0.167148	+	0.985932i
$49$	−4.49502	+	5.36608i	−0.642146	+	0.766582i
$50$	3.00870	−	1.03358i	0.425494	−	0.146170i
$51$	0.994872	+	2.25723i	0.139310	+	0.316076i
$52$	−2.13827	+	5.27076i	−0.296525	+	0.730923i
$53$	−6.58617	−	11.4076i	−0.904681	−	1.56695i	−0.821345	−	0.570431i	$-0.806776\pi$
$53$	−6.58617	−	11.4076i	−0.904681	−	1.56695i	−0.0833354	−	0.996522i	$-0.526557\pi$
$54$	−6.34364	+	3.70921i	−0.863260	+	0.504759i
$55$	3.80542			0.513122
$56$	7.40869	+	1.05422i	0.990027	+	0.140876i
$57$	4.14069	+	3.03214i	0.548447	+	0.401617i
$58$	−0.229544	+	1.17642i	−0.0301406	+	0.154472i
$59$	−1.42192			−0.185118			−0.0925589	−	0.995707i	$-0.529505\pi$
$59$	−1.42192			−0.185118			−0.0925589	+	0.995707i	$0.529505\pi$
$60$	7.93525	−	4.90162i	1.02444	−	0.632796i
$61$		−	2.03270i		−	0.260260i	−0.991497	−	0.130130i	$-0.958461\pi$
$61$		−	2.03270i		−	0.260260i	0.991497	−	0.130130i	$-0.0415395\pi$
$62$	10.5317	+	9.16828i	1.33753	+	1.16437i
$63$	1.73075	+	7.74626i	0.218055	+	0.975937i
$64$	−3.22261	−	7.32221i	−0.402826	−	0.915277i
$65$	7.65741			0.949785
$66$	3.37668	−	0.763728i	0.415641	−	0.0940084i
$67$		−	8.74356i		−	1.06820i	−0.845423	−	0.534098i	$-0.820651\pi$
$67$		−	8.74356i		−	1.06820i	0.845423	−	0.534098i	$-0.179349\pi$
$68$	−1.75042	−	2.24704i	−0.212270	−	0.272493i
$69$	1.35200	+	3.06751i	0.162762	+	0.369285i
$70$	−2.43434	−	9.77584i	−0.290959	−	1.16844i
$71$			1.95293i			0.231770i	0.993263	+	0.115885i	$0.0369704\pi$
$71$			1.95293i			0.231770i	−0.993263	+	0.115885i	$0.963030\pi$
$72$	6.05750	−	5.94195i	0.713883	−	0.700265i
$73$	7.16234	−	4.13518i	0.838289	−	0.483986i	−0.0183933	−	0.999831i	$-0.505855\pi$
$73$	7.16234	−	4.13518i	0.838289	−	0.483986i	0.856682	+	0.515844i	$0.172522\pi$
$74$	−14.6922	+	5.04723i	−1.70794	+	0.586728i
$75$	−3.14354	−	2.30195i	−0.362984	−	0.265806i
$76$	−5.49143	−	2.22779i	−0.629910	−	0.255546i
$77$	0.324347	−	3.72526i	0.0369627	−	0.424533i
$78$	6.79469	−	1.53680i	0.769348	−	0.174009i
$79$			11.8351i			1.33155i	0.746151	+	0.665776i	$0.231899\pi$
$79$			11.8351i			1.33155i	−0.746151	+	0.665776i	$0.768101\pi$
$80$	−7.50350	+	7.72590i	−0.838917	+	0.863782i
$81$	8.16615	+	3.78339i	0.907350	+	0.420377i
$82$	−3.18128	−	9.26055i	−0.351314	−	1.02266i
$83$	−2.85384	−	4.94299i	−0.313249	−	0.542563i	0.665815	−	0.746117i	$-0.268084\pi$
$83$	−2.85384	−	4.94299i	−0.313249	−	0.542563i	−0.979064	+	0.203554i	$0.934751\pi$
$84$	−4.12204	−	8.18589i	−0.449751	−	0.893154i
$85$	−1.91730	+	3.32085i	−0.207960	+	0.360197i
$86$	9.56552	+	1.86643i	1.03148	+	0.201262i
$87$	1.34330	−	0.592057i	0.144017	−	0.0634752i
$88$	−3.56571	+	1.80722i	−0.380106	+	0.192651i
$89$	5.75795	+	3.32435i	0.610341	+	0.352381i	0.773099	−	0.634285i	$-0.218706\pi$
$89$	5.75795	+	3.32435i	0.610341	+	0.352381i	−0.162758	+	0.986666i	$0.552039\pi$
$90$	−10.4782	−	4.54954i	−1.10450	−	0.479564i
$91$	0.652664	−	7.49613i	0.0684177	−	0.785808i
$92$	−2.37877	−	3.05365i	−0.248004	−	0.318365i
$93$	1.85128	−	17.0010i	0.191969	−	1.76292i
$94$	−11.3970	−	9.92156i	−1.17551	−	1.02333i
$95$			7.97801i			0.818527i
$96$	−5.10758	+	8.36138i	−0.521290	+	0.853380i
$97$	13.1164	−	7.57275i	1.33177	−	0.768896i	0.346197	−	0.938162i	$-0.387473\pi$
$97$	13.1164	−	7.57275i	1.33177	−	0.768896i	0.985570	+	0.169266i	$0.0541396\pi$
$98$	−9.77742	+	1.54984i	−0.987669	+	0.156558i
$99$	−3.12962	−	2.86066i	−0.314538	−	0.287507i
$100$	4.16900	+	1.69130i	0.416900	+	0.169130i
$101$	14.5192	+	8.38265i	1.44471	+	0.834105i	0.998159	−	0.0606528i	$-0.0193182\pi$
$101$	14.5192	+	8.38265i	1.44471	+	0.834105i	0.446553	+	0.894757i	$0.352652\pi$
$102$	−1.03481	+	3.33150i	−0.102461	+	0.329868i
$103$	−1.31815	−	2.28310i	−0.129881	−	0.224960i	0.793749	−	0.608245i	$-0.208126\pi$
$103$	−1.31815	−	2.28310i	−0.129881	−	0.224960i	−0.923630	+	0.383285i	$0.874793\pi$
$104$	−7.17506	+	3.63657i	−0.703573	+	0.356595i
$105$	−8.12574	+	9.28503i	−0.792992	+	0.906127i
$106$	3.56752	−	18.2837i	0.346508	−	1.77587i
$107$	−0.702055	−	0.405332i	−0.0678702	−	0.0391849i	0.465681	−	0.884953i	$-0.345809\pi$
$107$	−0.702055	−	0.405332i	−0.0678702	−	0.0391849i	−0.533551	+	0.845768i	$0.679143\pi$
$108$	−10.2108	−	1.93405i	−0.982530	−	0.186104i
$109$	5.19986	+	9.00642i	0.498056	+	0.862659i	0.999997	−	0.00224278i	$-0.000713901\pi$
$109$	5.19986	+	9.00642i	0.498056	+	0.862659i	−0.501941	+	0.864902i	$0.667381\pi$
$110$	4.05908	+	3.53359i	0.387018	+	0.336914i
$111$	15.3507	+	11.2410i	1.45702	+	1.06695i
$112$	6.92363	+	8.00396i	0.654221	+	0.756303i
$113$	4.37629	−	7.57996i	0.411687	−	0.713063i	−0.583387	−	0.812194i	$-0.698273\pi$
$113$	4.37629	−	7.57996i	0.411687	−	0.713063i	0.995074	+	0.0991313i	$0.0316064\pi$
$114$	1.60115	+	7.07917i	0.149961	+	0.663025i
$115$	−2.60555	+	4.51294i	−0.242968	+	0.420834i
$116$	−1.33723	+	1.04169i	−0.124159	+	0.0967189i
$117$	−6.29754	−	5.75633i	−0.582208	−	0.532173i
$118$	−1.51670	−	1.32035i	−0.139624	−	0.121548i
$119$	3.08749	+	2.15996i	0.283030	+	0.198003i
$120$	13.0157	+	2.14006i	1.18816	+	0.195360i
$121$	−4.50123	−	7.79636i	−0.409203	−	0.708760i
$122$	1.88750	−	2.16819i	0.170886	−	0.196299i
$123$	−7.08524	+	9.67558i	−0.638855	+	0.872418i
$124$	2.72039	+	19.5588i	0.244298	+	1.75644i
$125$			7.40568i			0.662384i
$126$	−5.34680	+	9.86974i	−0.476331	+	0.879266i
$127$			15.2544i			1.35361i	0.736164	+	0.676803i	$0.236635\pi$
$127$			15.2544i			1.35361i	−0.736164	+	0.676803i	$0.763365\pi$
$128$	3.36175	−	10.8027i	0.297140	−	0.954834i
$129$	−4.81403	−	10.9224i	−0.423852	−	0.961665i
$130$	8.16785	+	7.11043i	0.716368	+	0.623626i
$131$	0.0339597	+	0.0588199i	0.00296707	+	0.00513912i	0.867505	−	0.497428i	$-0.165722\pi$
$131$	0.0339597	+	0.0588199i	0.00296707	+	0.00513912i	−0.864538	+	0.502567i	$0.832389\pi$
$132$	4.31094	+	2.32084i	0.375219	+	0.202003i
$133$	7.80997	+	0.679989i	0.677211	+	0.0589625i
$134$	8.11899	−	9.32639i	0.701374	−	0.805678i
$135$	2.75486	+	13.7167i	0.237101	+	1.18054i
$136$	0.219421	−	4.02221i	0.0188152	−	0.344902i
$137$	−2.59483	+	4.49438i	−0.221691	+	0.383981i	−0.955322	−	0.295568i	$-0.904491\pi$
$137$	−2.59483	+	4.49438i	−0.221691	+	0.383981i	0.733630	+	0.679549i	$0.237824\pi$
$138$	−1.40627	+	4.52741i	−0.119710	+	0.385399i
$139$	5.27411	−	9.13502i	0.447344	−	0.774823i	−0.550868	−	0.834592i	$-0.685703\pi$
$139$	5.27411	−	9.13502i	0.447344	−	0.774823i	0.998212	+	0.0597697i	$0.0190366\pi$
$140$	6.48093	−	12.6879i	0.547738	−	1.07233i
$141$	−2.00339	+	18.3979i	−0.168716	+	1.54938i
$142$	−1.81343	+	2.08311i	−0.152179	+	0.174810i
$143$	2.00977	+	3.48102i	0.168065	+	0.291097i
$144$	11.9788	−	0.713230i	0.998232	−	0.0594359i
$145$	1.97627	+	1.14100i	0.164120	+	0.0947550i
$146$	11.4796	+	2.23990i	0.950056	+	0.185375i
$147$	8.39689	+	8.74599i	0.692564	+	0.721357i
$148$	−20.3583	−	8.25907i	−1.67344	−	0.678891i
$149$	−9.18336	−	15.9060i	−0.752330	−	1.30307i	−0.946691	−	0.322143i	$-0.895597\pi$
$149$	−9.18336	−	15.9060i	−0.752330	−	1.30307i	0.194361	−	0.980930i	$-0.437737\pi$
$150$	−1.21556	−	5.37439i	−0.0992503	−	0.438817i
$151$	−4.40011	−	2.54041i	−0.358076	−	0.206735i	0.310160	−	0.950684i	$-0.399617\pi$
$151$	−4.40011	−	2.54041i	−0.358076	−	0.206735i	−0.668236	+	0.743949i	$0.732951\pi$
$152$	−3.78883	−	7.47547i	−0.307314	−	0.606340i
$153$	4.07321	−	1.28981i	0.329299	−	0.104275i
$154$	3.80513	−	3.67241i	0.306626	−	0.295931i
$155$	23.0228	−	13.2922i	1.84924	−	1.06766i
$156$	8.67465	+	4.67009i	0.694528	+	0.373906i
$157$			2.41701i			0.192898i	0.995338	+	0.0964492i	$0.0307485\pi$
$157$			2.41701i			0.192898i	−0.995338	+	0.0964492i	$0.969251\pi$
$158$	−10.9897	+	12.6240i	−0.874293	+	1.00431i
$159$	−20.8773	+	9.20164i	−1.65568	+	0.729737i
$160$	−15.1777	+	1.27338i	−1.19990	+	0.100670i
$161$	4.19581	+	2.93532i	0.330676	+	0.231335i
$162$	5.19735	+	11.6184i	0.408343	+	0.912829i
$163$	−13.8321	−	7.98598i	−1.08342	−	0.625510i	−0.151600	−	0.988442i	$-0.548442\pi$
$163$	−13.8321	−	7.98598i	−1.08342	−	0.625510i	−0.931816	+	0.362932i	$0.881776\pi$
$164$	5.20571	−	12.8319i	0.406498	−	1.00200i
$165$	0.713512	−	6.55244i	0.0555468	−	0.510107i
$166$	1.54583	−	7.92246i	0.119980	−	0.614902i
$167$	6.99445	−	12.1147i	0.541247	−	0.937467i	−0.457586	−	0.889165i	$-0.651286\pi$
$167$	6.99445	−	12.1147i	0.541247	−	0.937467i	0.998833	−	0.0483016i	$-0.0153809\pi$
$168$	3.20435	−	12.5591i	0.247221	−	0.968959i
$169$	−2.45586	−	4.25368i	−0.188913	−	0.327206i
$170$	−5.12874	+	1.76188i	−0.393357	+	0.135130i
$171$	5.99734	−	6.56121i	0.458628	−	0.501748i
$172$	8.47004	+	10.8731i	0.645835	+	0.829064i
$173$		−	24.9568i		−	1.89743i	−0.316131	−	0.948716i	$-0.602384\pi$
$173$		−	24.9568i		−	1.89743i	0.316131	−	0.948716i	$-0.397616\pi$
$174$	1.98261	+	0.615823i	0.150301	+	0.0466854i
$175$	−5.92920	−	0.516236i	−0.448205	−	0.0390238i
$176$	−5.48153	−	1.38331i	−0.413186	−	0.104271i
$177$	−0.266608	+	2.44836i	−0.0200395	+	0.184030i
$178$	3.05488	+	8.89259i	0.228973	+	0.666528i
$179$	−0.618502	+	0.357092i	−0.0462290	+	0.0266903i	−0.522936	−	0.852372i	$-0.675163\pi$
$179$	−0.618502	+	0.357092i	−0.0462290	+	0.0266903i	0.476707	+	0.879062i	$0.341830\pi$
$180$	−6.95211	−	14.5825i	−0.518180	−	1.08692i
$181$			13.5134i			1.00445i	0.864738	+	0.502223i	$0.167484\pi$
$181$			13.5134i			1.00445i	−0.864738	+	0.502223i	$0.832516\pi$
$182$	7.65683	−	7.38977i	0.567562	−	0.547766i
$183$	−3.50004	−	0.381129i	−0.258731	−	0.0281738i
$184$	0.298187	−	5.46606i	0.0219826	−	0.402963i
$185$			29.5767i			2.17453i
$186$	17.7613	−	16.4152i	1.30232	−	1.20362i
$187$	−2.01286			−0.147195
$188$	−2.94390	−	21.1658i	−0.214706	−	1.54368i
$189$	13.6626	−	1.52772i	0.993806	−	0.111125i
$190$	−7.40813	+	8.50982i	−0.537442	+	0.617367i
$191$			15.2620i			1.10432i	0.833738	+	0.552161i	$0.186197\pi$
$191$			15.2620i			1.10432i	−0.833738	+	0.552161i	$0.813803\pi$
$192$	−13.2122	+	4.17601i	−0.953505	+	0.301377i
$193$	8.93048			0.642830			0.321415	−	0.946938i	$-0.395842\pi$
$193$	8.93048			0.642830			0.321415	+	0.946938i	$0.395842\pi$
$194$	21.0225	+	4.10192i	1.50933	+	0.294501i
$195$	1.43576	−	13.1851i	0.102817	−	0.944204i
$196$	−11.8683	−	7.42585i	−0.847736	−	0.530418i
$197$	−3.57570			−0.254758			−0.127379	−	0.991854i	$-0.540656\pi$
$197$	−3.57570			−0.254758			−0.127379	+	0.991854i	$0.540656\pi$
$198$	−0.681917	−	5.95741i	−0.0484617	−	0.423375i
$199$	−7.27270	−	12.5967i	−0.515548	−	0.892955i	−0.999837	−	0.0180470i	$-0.994255\pi$
$199$	−7.27270	−	12.5967i	−0.515548	−	0.892955i	0.484289	−	0.874908i	$-0.339078\pi$
$200$	2.87641	+	5.67525i	0.203393	+	0.401300i
$201$	−15.0553	−	1.63941i	−1.06192	−	0.115635i
$202$	7.70314	+	22.4235i	0.541991	+	1.57771i
$203$	1.28541	−	1.83740i	0.0902182	−	0.128960i
$204$	−4.19731	+	2.59269i	−0.293871	+	0.181525i
$205$	−18.6423			−1.30203
$206$	0.713998	−	3.65927i	0.0497466	−	0.254954i
$207$	5.53536	−	1.75282i	0.384734	−	0.121829i
$208$	−11.0301	−	2.78355i	−0.764803	−	0.193005i
$209$	−3.62676	+	2.09391i	−0.250868	+	0.144839i
$210$	−17.2892	+	2.35866i	−1.19307	+	0.162763i
$211$	−11.3933	−	6.57792i	−0.784347	−	0.452843i	0.0536217	−	0.998561i	$-0.482923\pi$
$211$	−11.3933	−	6.57792i	−0.784347	−	0.452843i	−0.837969	+	0.545718i	$0.816257\pi$
$212$	20.7830	−	16.1898i	1.42738	−	1.11192i
$213$	3.36269	+	0.366172i	0.230408	+	0.0250897i
$214$	−0.372475	−	1.08426i	−0.0254619	−	0.0741183i
$215$	9.27751	−	16.0691i	0.632721	−	1.09590i
$216$	−9.09550	−	11.5443i	−0.618870	−	0.785493i
$217$	−11.0500	−	23.6709i	−0.750121	−	1.60688i
$218$	−2.81660	+	14.4352i	−0.190764	+	0.977676i
$219$	−5.77732	−	13.1080i	−0.390395	−	0.885756i
$220$	1.04848	+	7.53827i	0.0706883	+	0.508230i
$221$	−4.05035			−0.272456
$222$	5.93590	+	26.2445i	0.398392	+	1.76142i
$223$	7.88047	+	13.6494i	0.527715	+	0.914030i	0.999478	+	0.0323043i	$0.0102846\pi$
$223$	7.88047	+	13.6494i	0.527715	+	0.914030i	−0.471763	+	0.881726i	$0.656382\pi$
$224$	−0.0470774	+	14.9666i	−0.00314549	+	0.999995i
$225$	−4.55308	+	4.98116i	−0.303538	+	0.332077i
$226$	11.7065	−	4.02155i	0.778706	−	0.267509i
$227$	0.947912	−	1.64183i	0.0629152	−	0.108972i	−0.832852	−	0.553496i	$-0.813294\pi$
$227$	0.947912	−	1.64183i	0.0629152	−	0.108972i	0.895767	+	0.444523i	$0.146627\pi$
$228$	−4.86562	+	9.03784i	−0.322233	+	0.598545i
$229$	7.39322	−	4.26848i	0.488558	−	0.282069i	−0.235418	−	0.971894i	$-0.575646\pi$
$229$	7.39322	−	4.26848i	0.488558	−	0.282069i	0.723976	+	0.689825i	$0.242313\pi$
$230$	−6.96980	+	2.39434i	−0.459575	+	0.157878i
$231$	−6.35362	−	1.25697i	−0.418037	−	0.0827024i
$232$	−2.39366	−	0.130580i	−0.157151	−	0.00857298i
$233$	−8.18028	+	14.1687i	−0.535908	+	0.928220i	0.463211	+	0.886248i	$0.346697\pi$
$233$	−8.18028	+	14.1687i	−0.535908	+	0.928220i	−0.999119	+	0.0419719i	$0.986636\pi$
$234$	−1.37218	−	11.9877i	−0.0897023	−	0.783663i
$235$	−24.9144	+	14.3844i	−1.62524	+	0.938332i
$236$	−0.391770	−	2.81672i	−0.0255020	−	0.183353i
$237$	20.3785	+	2.21907i	1.32373	+	0.144144i
$238$	1.28763	+	5.17089i	0.0834648	+	0.335179i
$239$	5.95333	+	3.43716i	0.385089	+	0.222331i	0.680030	−	0.733184i	$-0.261967\pi$
$239$	5.95333	+	3.43716i	0.385089	+	0.222331i	−0.294941	+	0.955515i	$0.595300\pi$
$240$	11.8961	+	14.3687i	0.767891	+	0.927494i
$241$	8.63910	+	4.98779i	0.556493	+	0.321292i	0.751737	−	0.659463i	$-0.229216\pi$
$241$	8.63910	+	4.98779i	0.556493	+	0.321292i	−0.195244	+	0.980755i	$0.562550\pi$
$242$	2.43817	−	12.4958i	0.156732	−	0.803257i
$243$	8.04566	−	13.3517i	0.516130	−	0.856510i
$244$	4.02663	−	0.560053i	0.257779	−	0.0358537i
$245$	−3.25728	+	18.5638i	−0.208100	+	1.18600i
$246$	−16.5420	+	3.74142i	−1.05468	+	0.238544i
$247$	−7.29792	+	4.21345i	−0.464355	+	0.268096i
$248$	−15.2600	+	23.3887i	−0.969011	+	1.48518i
$249$	−9.04629	+	3.98713i	−0.573285	+	0.252674i
$250$	−6.87668	+	7.89934i	−0.434920	+	0.499598i
$251$	−16.6175			−1.04889			−0.524444	−	0.851445i	$-0.675727\pi$
$251$	−16.6175			−1.04889			−0.524444	+	0.851445i	$0.675727\pi$
$252$	−14.8679	+	5.56277i	−0.936592	+	0.350422i
$253$	−2.73541			−0.171974
$254$	−14.1647	+	16.2712i	−0.888773	+	1.02095i
$255$	5.35860	+	3.92400i	0.335568	+	0.245730i
$256$	13.6169	−	8.40119i	0.851056	−	0.525074i
$257$	6.63756	−	3.83220i	0.414040	−	0.239046i	−0.278484	−	0.960441i	$-0.589832\pi$
$257$	6.63756	−	3.83220i	0.414040	−	0.239046i	0.692524	+	0.721395i	$0.256499\pi$
$258$	5.00727	−	16.1206i	0.311739	−	1.00363i
$259$	28.9538	+	2.52091i	1.79910	+	0.156642i
$260$	2.10979	+	15.1688i	0.130843	+	0.940729i
$261$	−0.767580	−	2.42400i	−0.0475120	−	0.150042i
$262$	−0.0183949	+	0.0942747i	−0.00113644	+	0.00582431i
$263$	9.88765	+	5.70864i	0.609699	+	0.352010i	0.772848	−	0.634592i	$-0.218832\pi$
$263$	9.88765	+	5.70864i	0.609699	+	0.352010i	−0.163149	+	0.986601i	$0.552165\pi$
$264$	2.44324	+	6.47855i	0.150371	+	0.398727i
$265$	−30.7148	−	17.7332i	−1.88680	−	1.08934i
$266$	7.69916	+	7.97741i	0.472066	+	0.489126i
$267$	6.80372	−	9.29113i	0.416381	−	0.568608i
$268$	17.3204	−	2.40905i	1.05801	−	0.147156i
$269$	−4.88573	+	2.82078i	−0.297888	+	0.171986i	−0.641494	−	0.767128i	$-0.721685\pi$
$269$	−4.88573	+	2.82078i	−0.297888	+	0.171986i	0.343606	+	0.939114i	$0.388352\pi$
$270$	−9.79838	+	17.1891i	−0.596310	+	1.04610i
$271$	3.13192	−	5.42464i	0.190251	−	0.329524i	−0.755083	−	0.655630i	$-0.772403\pi$
$271$	3.13192	−	5.42464i	0.190251	−	0.329524i	0.945333	+	0.326106i	$0.105737\pi$
$272$	3.96894	−	4.08658i	0.240653	−	0.247785i
$273$	−12.7850	−	2.52932i	−0.773783	−	0.153081i
$274$	−6.94114	+	2.38449i	−0.419330	+	0.144052i
$275$	2.75338	−	1.58966i	0.166035	−	0.0958602i
$276$	−5.70402	+	3.52339i	−0.343342	+	0.212083i
$277$	−10.0179	+	17.3515i	−0.601917	+	1.04255i	0.390614	+	0.920555i	$0.372263\pi$
$277$	−10.0179	+	17.3515i	−0.601917	+	1.04255i	−0.992531	+	0.121996i	$0.961070\pi$
$278$	14.1082	−	4.84658i	0.846152	−	0.290679i
$279$	−28.9265	−	6.37535i	−1.73178	−	0.381682i
$280$	18.6946	−	7.51572i	1.11721	−	0.449150i
$281$	−9.81283	−	16.9963i	−0.585384	−	1.01392i	−0.994827	−	0.101580i	$-0.967610\pi$
$281$	−9.81283	−	16.9963i	−0.585384	−	1.01392i	0.409443	−	0.912336i	$-0.365723\pi$
$282$	−19.2206	+	17.7640i	−1.14457	+	1.05783i
$283$	1.67820			0.0997585			0.0498792	−	0.998755i	$-0.484116\pi$
$283$	1.67820			0.0997585			0.0498792	+	0.998755i	$0.484116\pi$
$284$	−3.86861	+	0.538075i	−0.229560	+	0.0319289i
$285$	13.7371	+	1.49587i	0.813716	+	0.0886077i
$286$	−1.08863	+	5.57927i	−0.0643719	+	0.329909i
$287$	−1.58894	+	18.2496i	−0.0937920	+	1.07724i
$288$	13.4396	+	10.3623i	0.791934	+	0.610607i
$289$	−7.48585	+	12.9659i	−0.440344	+	0.762699i
$290$	1.04851	+	3.05216i	0.0615707	+	0.179229i
$291$	−10.5800	−	24.0046i	−0.620210	−	1.40718i
$292$	10.1649	+	13.0488i	0.594855	+	0.763622i
$293$	−9.06774	−	5.23526i	−0.529743	−	0.305847i	0.211169	−	0.977450i	$-0.432273\pi$
$293$	−9.06774	−	5.23526i	−0.529743	−	0.305847i	−0.740912	+	0.671602i	$0.765606\pi$
$294$	0.835369	+	17.1261i	0.0487197	+	0.998812i
$295$	−3.31558	+	1.91425i	−0.193040	+	0.111452i
$296$	−14.0462	−	27.7137i	−0.816422	−	1.61082i
$297$	−5.51249	+	4.85243i	−0.319867	+	0.281567i
$298$	4.97433	−	25.4937i	0.288155	−	1.47681i
$299$	−5.50430			−0.318322
$300$	3.69389	−	6.86137i	0.213267	−	0.396141i
$301$	−14.9399	−	10.4517i	−0.861122	−	0.602427i
$302$	−2.33448	−	6.79555i	−0.134334	−	0.391040i
$303$	17.1562	−	23.4284i	0.985597	−	1.34593i
$304$	2.90010	−	11.4920i	0.166332	−	0.659109i
$305$	−2.73651	−	4.73977i	−0.156692	−	0.271398i
$306$	5.54240	+	2.40646i	0.316838	+	0.137568i
$307$	−0.644576			−0.0367879			−0.0183939	−	0.999831i	$-0.505855\pi$
$307$	−0.644576			−0.0367879			−0.0183939	+	0.999831i	$0.505855\pi$
$308$	7.46886	−	0.383885i	0.425578	−	0.0218739i
$309$	−4.17835	+	1.84160i	−0.237698	+	0.104765i
$310$	36.9003	+	7.19999i	2.09579	+	0.408932i
$311$	−18.0913			−1.02586			−0.512931	−	0.858430i	$-0.671440\pi$
$311$	−18.0913			−1.02586			−0.512931	+	0.858430i	$0.671440\pi$
$312$	4.91639	+	13.0364i	0.278336	+	0.738041i
$313$		−	0.0623583i		−	0.00352470i	−0.999998	−	0.00176235i	$-0.999439\pi$
$313$		−	0.0623583i		−	0.00352470i	0.999998	−	0.00176235i	$-0.000560974\pi$
$314$	−2.24436	+	2.57812i	−0.126656	+	0.145492i
$315$	14.4641	+	15.7324i	0.814958	+	0.886422i
$316$	−23.4445	+	3.26083i	−1.31886	+	0.183436i
$317$	−8.44530			−0.474335			−0.237168	−	0.971469i	$-0.576219\pi$
$317$	−8.44530			−0.474335			−0.237168	+	0.971469i	$0.576219\pi$
$318$	−30.8133	−	9.57100i	−1.72793	−	0.536715i
$319$			1.19787i			0.0670679i
$320$	−17.3719	−	12.7353i	−0.971116	−	0.711923i
$321$	−0.829564	+	1.13285i	−0.0463018	+	0.0632295i
$322$	1.74985	+	7.02707i	0.0975154	+	0.391604i
$323$		−	4.21993i		−	0.234803i
$324$	−5.24469	+	17.2190i	−0.291371	+	0.956610i
$325$	5.54045	−	3.19878i	0.307329	−	0.177437i
$326$	−7.33863	−	21.3624i	−0.406449	−	1.18315i
$327$	16.4829	−	7.26480i	0.911505	−	0.401744i
$328$	17.4680	−	8.85339i	0.964509	−	0.488847i
$329$	11.9579	+	25.6157i	0.659258	+	1.41224i
$330$	6.84546	−	6.32667i	0.376830	−	0.348272i
$331$		−	15.4700i		−	0.850306i	−0.905122	−	0.425153i	$-0.860220\pi$
$331$		−	15.4700i		−	0.850306i	0.905122	−	0.425153i	$-0.139780\pi$
$332$	9.00542	−	7.01515i	0.494237	−	0.385007i
$333$	22.2338	−	24.3243i	1.21841	−	1.33296i
$334$	18.7101	−	6.42747i	1.02377	−	0.351696i
$335$	−11.7710	−	20.3879i	−0.643117	−	1.11391i
$336$	15.0800	−	10.4209i	0.822680	−	0.568505i
$337$	1.49961	−	2.59739i	0.0816887	−	0.141489i	−0.822287	−	0.569073i	$-0.807302\pi$
$337$	1.49961	−	2.59739i	0.0816887	−	0.141489i	0.903975	+	0.427584i	$0.140635\pi$
$338$	1.33026	−	6.81767i	0.0723568	−	0.370832i
$339$	−12.2312	−	8.95665i	−0.664306	−	0.486459i
$340$	−7.10664	−	2.88306i	−0.385412	−	0.156356i
$341$	12.0852	+	6.97737i	0.654448	+	0.377846i
$342$	12.4896	−	1.42963i	0.675363	−	0.0773056i
$343$	17.8952	+	4.77092i	0.966250	+	0.257605i
$344$	−1.06175	+	19.4629i	−0.0572456	+	1.04937i
$345$	7.28217	+	5.33259i	0.392059	+	0.287097i
$346$	23.1741	−	26.6204i	1.24585	−	1.43112i
$347$		−	30.0283i		−	1.61200i	−0.591915	−	0.806001i	$-0.701628\pi$
$347$		−	30.0283i		−	1.61200i	0.591915	−	0.806001i	$-0.298372\pi$
$348$	1.54293	+	2.49786i	0.0827100	+	0.133899i
$349$	16.0196	−	9.24890i	0.857507	−	0.495082i	−0.00566949	−	0.999984i	$-0.501805\pi$
$349$	16.0196	−	9.24890i	0.857507	−	0.495082i	0.863177	+	0.504902i	$0.168471\pi$
$350$	−5.84507	−	6.05631i	−0.312432	−	0.323724i
$351$	−11.0925	+	9.76426i	−0.592072	+	0.521177i
$352$	−4.56242	−	6.56549i	−0.243178	−	0.349942i
$353$	−6.81136	−	3.93254i	−0.362532	−	0.209308i	0.307659	−	0.951497i	$-0.400454\pi$
$353$	−6.81136	−	3.93254i	−0.362532	−	0.209308i	−0.670191	+	0.742189i	$0.733788\pi$
$354$	−2.55785	+	2.36400i	−0.135948	+	0.125645i
$355$	2.62912	+	4.55377i	0.139539	+	0.241689i
$356$	−4.99887	+	12.3220i	−0.264939	+	0.653066i
$357$	4.29808	−	4.91128i	0.227478	−	0.259932i
$358$	−0.991314	−	0.193425i	−0.0523926	−	0.0102229i
$359$	15.0238	+	8.67397i	0.792924	+	0.457795i	0.840991	−	0.541049i	$-0.181973\pi$
$359$	15.0238	+	8.67397i	0.792924	+	0.457795i	−0.0480670	+	0.998844i	$0.515306\pi$
$360$	6.12534	−	22.0101i	0.322834	−	1.16003i
$361$	5.11014	+	8.85102i	0.268955	+	0.465843i
$362$	−12.5482	+	14.4142i	−0.659516	+	0.757595i
$363$	−14.2683	+	6.28873i	−0.748892	+	0.330073i
$364$	15.0291	−	0.772469i	0.787741	−	0.0404884i
$365$	11.1339	−	19.2845i	0.582777	−	1.00940i
$366$	−3.37945	−	3.65656i	−0.176647	−	0.191132i
$367$	−0.510070	+	0.883467i	−0.0266254	+	0.0461166i	−0.879031	−	0.476764i	$-0.841809\pi$
$367$	−0.510070	+	0.883467i	−0.0266254	+	0.0461166i	0.852406	+	0.522881i	$0.175143\pi$
$368$	5.39367	−	5.55353i	0.281165	−	0.289498i
$369$	15.3316	+	14.0140i	0.798133	+	0.729542i
$370$	−27.4640	+	31.5483i	−1.42779	+	1.64012i
$371$	−19.9776	+	28.5564i	−1.03719	+	1.48258i
$372$	34.1879	−	1.01689i	1.77256	−	0.0527234i
$373$	0.0376831	+	0.0652691i	0.00195116	+	0.00337951i	0.866999	−	0.498309i	$-0.166046\pi$
$373$	0.0376831	+	0.0652691i	0.00195116	+	0.00337951i	−0.865048	+	0.501689i	$0.832712\pi$
$374$	−2.14703	−	1.86908i	−0.111020	−	0.0966476i
$375$	12.7516	+	1.38856i	0.658492	+	0.0717049i
$376$	16.5138	−	25.3104i	0.851634	−	1.30528i
$377$			2.41040i			0.124142i
$378$	15.9919	+	11.0571i	0.822535	+	0.568715i
$379$			29.5406i			1.51740i	0.651442	+	0.758699i	$0.274165\pi$
$379$			29.5406i			1.51740i	−0.651442	+	0.758699i	$0.725835\pi$
$380$	−15.8039	+	2.19812i	−0.810722	+	0.112761i
$381$	26.2661	+	2.86018i	1.34565	+	0.146531i
$382$	−14.1718	+	16.2794i	−0.725094	+	0.832925i
$383$	14.2357	+	24.6569i	0.727410	+	1.25991i	0.957974	+	0.286854i	$0.0926095\pi$
$383$	14.2357	+	24.6569i	0.727410	+	1.25991i	−0.230564	+	0.973057i	$0.574057\pi$
$384$	−17.9706	−	7.81401i	−0.917057	−	0.398757i
$385$	−4.25882	−	9.12309i	−0.217050	−	0.464956i
$386$	9.52577	+	8.29256i	0.484849	+	0.422080i
$387$	−19.7096	+	6.24121i	−1.00190	+	0.317259i
$388$	18.6149	+	23.8962i	0.945031	+	1.21315i
$389$	−10.8878	+	18.8582i	−0.552032	+	0.956148i	0.446095	+	0.894985i	$0.352814\pi$
$389$	−10.8878	+	18.8582i	−0.552032	+	0.956148i	−0.998128	+	0.0611628i	$0.980519\pi$
$390$	13.7747	−	12.7308i	0.697510	−	0.644649i
$391$	1.37819	−	2.38710i	0.0696982	−	0.120721i
$392$	−5.76402	−	18.9414i	−0.291127	−	0.956684i
$393$	0.107648	−	0.0474456i	0.00543011	−	0.00239331i
$394$	−3.81405	−	3.32028i	−0.192149	−	0.167273i
$395$	15.9329	+	27.5967i	0.801673	+	1.38854i
$396$	4.80449	−	6.98773i	0.241435	−	0.351147i
$397$	−1.28100	−	0.739586i	−0.0642915	−	0.0371187i	0.467510	−	0.883988i	$-0.345151\pi$
$397$	−1.28100	−	0.739586i	−0.0642915	−	0.0371187i	−0.531801	+	0.846869i	$0.678485\pi$
$398$	3.93939	−	20.1896i	0.197464	−	1.01201i
$399$	2.63522	−	13.3203i	0.131926	−	0.666848i
$400$	−2.20170	+	8.72450i	−0.110085	+	0.436225i
$401$	12.4003	+	21.4780i	0.619242	+	1.07256i	0.989624	+	0.143679i	$0.0458934\pi$
$401$	12.4003	+	21.4780i	0.619242	+	1.07256i	−0.370382	+	0.928879i	$0.620773\pi$
$402$	−14.5366	−	15.7286i	−0.725018	−	0.784469i
$403$	24.3183	+	14.0402i	1.21138	+	0.699390i
$404$	−12.6051	+	31.0711i	−0.627127	+	1.54584i
$405$	24.1349	−	2.17165i	1.19927	−	0.107910i
$406$	3.07724	−	0.766282i	0.152721	−	0.0380299i
$407$	−13.4454	+	7.76273i	−0.666465	+	0.384784i
$408$	−6.88459	−	1.13198i	−0.340838	−	0.0560412i
$409$		−	9.36239i		−	0.462941i	−0.972842	−	0.231470i	$-0.925646\pi$
$409$		−	9.36239i		−	0.462941i	0.972842	−	0.231470i	$-0.0743536\pi$
$410$	−19.8850	−	17.3106i	−0.982049	−	0.854912i
$411$	7.25222	+	5.31066i	0.357726	+	0.261956i
$412$	4.15948	−	3.24020i	0.204923	−	0.159633i
$413$	1.59133	+	3.40890i	0.0783044	+	0.167741i
$414$	7.53195	+	3.27030i	0.370175	+	0.160727i
$415$	−13.3089	−	7.68392i	−0.653311	−	0.377189i
$416$	−9.18068	−	13.2113i	−0.450120	−	0.647740i
$417$	−14.7405	−	10.7941i	−0.721843	−	0.528592i
$418$	−5.81286	−	1.13421i	−0.284316	−	0.0554758i
$419$	−5.21230	+	9.02797i	−0.254637	+	0.441045i	−0.964797	−	0.262996i	$-0.915289\pi$
$419$	−5.21230	+	9.02797i	−0.254637	+	0.441045i	0.710160	+	0.704041i	$0.248623\pi$
$420$	−20.6318	−	13.5383i	−1.00673	−	0.660602i
$421$	−3.45213	−	5.97927i	−0.168247	−	0.291412i	0.769557	−	0.638578i	$-0.220477\pi$
$421$	−3.45213	−	5.97927i	−0.168247	−	0.291412i	−0.937803	+	0.347167i	$0.887144\pi$
$422$	−6.04471	−	17.5959i	−0.294252	−	0.856553i
$423$	31.3031	+	6.89916i	1.52201	+	0.335449i
$424$	37.2017	+	2.02944i	1.80668	+	0.0985585i
$425$			3.20370i			0.155402i
$426$	3.24683	+	3.51307i	0.157309	+	0.170209i
$427$	−4.87318	+	2.27488i	−0.235830	+	0.110089i
$428$	0.609502	−	1.50240i	0.0294614	−	0.0726213i
$429$	6.37070	−	2.80788i	0.307580	−	0.135565i
$430$	24.8172	−	8.52547i	1.19679	−	0.411135i
$431$	12.4348	−	7.17921i	0.598961	−	0.345810i	−0.169672	−	0.985501i	$-0.554271\pi$
$431$	12.4348	−	7.17921i	0.598961	−	0.345810i	0.768633	+	0.639690i	$0.220937\pi$
$432$	1.01792	−	20.7597i	0.0489747	−	0.998800i
$433$		−	25.8458i		−	1.24207i	−0.783783	−	0.621035i	$-0.786712\pi$
$433$		−	25.8458i		−	1.24207i	0.783783	−	0.621035i	$-0.213288\pi$
$434$	10.1935	−	35.5094i	0.489301	−	1.70450i
$435$	2.33521	−	3.18895i	0.111965	−	0.152899i
$436$	−16.4084	+	12.7820i	−0.785821	+	0.612149i
$437$		−	5.73476i		−	0.274331i
$438$	6.00923	−	19.3464i	0.287132	−	0.924406i
$439$	−14.5869			−0.696195			−0.348097	−	0.937458i	$-0.613172\pi$
$439$	−14.5869			−0.696195			−0.348097	+	0.937458i	$0.613172\pi$
$440$	−5.88143	+	9.01434i	−0.280386	+	0.429742i
$441$	16.6339	−	12.8185i	0.792090	−	0.610405i
$442$	−4.32035	−	3.76103i	−0.205498	−	0.178894i
$443$			35.3820i			1.68105i	0.541775	+	0.840524i	$0.317753\pi$
$443$			35.3820i			1.68105i	−0.541775	+	0.840524i	$0.682247\pi$
$444$	−18.0382	+	33.5058i	−0.856056	+	1.59012i
$445$	17.9016			0.848616
$446$	−4.26860	+	21.8768i	−0.202124	+	1.03590i
$447$	−29.1100	+	12.8302i	−1.37686	+	0.606848i
$448$	−13.9477	+	15.9205i	−0.658966	+	0.752173i
$449$	−0.329740			−0.0155614			−0.00778070	−	0.999970i	$-0.502477\pi$
$449$	−0.329740			−0.0155614			−0.00778070	+	0.999970i	$0.502477\pi$
$450$	−9.48192	+	1.08535i	−0.446982	+	0.0511640i
$451$	−4.89287	−	8.47469i	−0.230396	−	0.399058i
$452$	16.2211	+	6.58069i	0.762979	+	0.309529i
$453$	−5.19927	+	7.10011i	−0.244283	+	0.333592i
$454$	2.53565	−	0.871074i	0.119004	−	0.0408815i
$455$	−8.56977	−	18.3579i	−0.401757	−	0.860629i
$456$	−13.5822	+	5.12223i	−0.636045	+	0.239870i
$457$	25.8843			1.21081			0.605407	−	0.795916i	$-0.293010\pi$
$457$	25.8843			1.21081			0.605407	+	0.795916i	$0.293010\pi$
$458$	11.8496	+	2.31210i	0.553696	+	0.108037i
$459$	−1.45717	−	7.25538i	−0.0680149	−	0.338652i
$460$	−9.65770	−	3.91799i	−0.450293	−	0.182677i
$461$	−24.3535	+	14.0605i	−1.13426	+	0.654863i	−0.945002	−	0.327065i	$-0.893940\pi$
$461$	−24.3535	+	14.0605i	−1.13426	+	0.654863i	−0.189254	+	0.981928i	$0.560607\pi$
$462$	−5.60996	−	7.24052i	−0.260999	−	0.336859i
$463$	17.0012	+	9.81564i	0.790112	+	0.456171i	0.840002	−	0.542583i	$-0.182554\pi$
$463$	17.0012	+	9.81564i	0.790112	+	0.456171i	−0.0498901	+	0.998755i	$0.515887\pi$
$464$	−2.43196	−	2.36196i	−0.112901	−	0.109651i
$465$	−18.5708	−	42.1347i	−0.861199	−	1.95395i
$466$	−21.8821	+	7.51718i	−1.01367	+	0.348227i
$467$	10.9101	−	18.8969i	0.504861	−	0.874446i	−0.495123	−	0.868823i	$-0.664877\pi$
$467$	10.9101	−	18.8969i	0.504861	−	0.874446i	0.999984	−	0.00562261i	$-0.00178974\pi$
$468$	9.66779	−	14.0610i	0.446894	−	0.649970i
$469$	−20.9618	+	9.78532i	−0.967925	+	0.451844i
$470$	−39.9321	−	7.79155i	−1.84193	−	0.359398i
$471$	4.16178	+	0.453187i	0.191765	+	0.0208818i
$472$	2.19763	−	3.36826i	0.101154	−	0.155037i
$473$	9.73992			0.447842
$474$	19.6764	+	21.2898i	0.903766	+	0.977875i
$475$	3.33271	+	5.77242i	0.152915	+	0.264857i
$476$	−3.42806	+	6.71123i	−0.157125	+	0.307609i
$477$	11.9296	+	37.6734i	0.546217	+	1.72494i
$478$	3.15854	+	9.19435i	0.144468	+	0.420540i
$479$	14.7030	−	25.4664i	0.671799	−	1.16359i	−0.305594	−	0.952162i	$-0.598855\pi$
$479$	14.7030	−	25.4664i	0.671799	−	1.16359i	0.977393	−	0.211429i	$-0.0678116\pi$
$480$	−0.653202	+	26.3728i	−0.0298145	+	1.20375i
$481$	−27.0554	+	15.6205i	−1.23362	+	0.712232i
$482$	4.58347	+	13.3423i	0.208771	+	0.607723i
$483$	5.84095	−	6.67427i	0.265773	−	0.303690i
$484$	14.2039	−	11.0647i	0.645630	−	0.502941i
$485$	20.3896	−	35.3157i	0.925842	−	1.60361i
$486$	20.9799	−	6.77074i	0.951669	−	0.307127i
$487$	−3.83992	+	2.21698i	−0.174003	+	0.100461i	−0.584472	−	0.811414i	$-0.698698\pi$
$487$	−3.83992	+	2.21698i	−0.174003	+	0.100461i	0.410469	+	0.911875i	$0.365365\pi$
$488$	4.81509	+	3.14161i	0.217969	+	0.142214i
$489$	−16.3443	+	22.3198i	−0.739117	+	1.00934i
$490$	−20.7122	+	16.7767i	−0.935681	+	0.757893i
$491$	0.492024	+	0.284070i	0.0222047	+	0.0128199i	0.511061	−	0.859544i	$-0.329253\pi$
$491$	0.492024	+	0.284070i	0.0222047	+	0.0128199i	−0.488857	+	0.872364i	$0.662586\pi$
$492$	−21.1188	−	11.3695i	−0.952109	−	0.512578i
$493$	−1.04534	−	0.603527i	−0.0470798	−	0.0271815i
$494$	−11.6969	−	2.28230i	−0.526267	−	0.102685i
$495$	−11.1487	−	2.45715i	−0.501096	−	0.110441i
$496$	−37.9952	+	10.7778i	−1.70604	+	0.483937i
$497$	4.68194	−	2.18561i	0.210014	−	0.0980381i
$498$	−13.3516	−	4.14718i	−0.598301	−	0.185840i
$499$	7.10975	−	4.10482i	0.318276	−	0.183757i	−0.332348	−	0.943157i	$-0.607841\pi$
$499$	7.10975	−	4.10482i	0.318276	−	0.183757i	0.650624	+	0.759400i	$0.274507\pi$
$500$	−14.6701	+	2.04043i	−0.656069	+	0.0912508i
$501$	−19.5486	−	14.3151i	−0.873366	−	0.639549i
$502$	−17.7252	−	15.4305i	−0.791116	−	0.688697i
$503$	23.6082			1.05264			0.526319	−	0.850287i	$-0.323572\pi$
$503$	23.6082			1.05264			0.526319	+	0.850287i	$0.323572\pi$
$504$	−21.0244	−	7.87231i	−0.936503	−	0.350661i
$505$	45.1404			2.00872
$506$	−2.91775	−	2.54002i	−0.129710	−	0.112917i
$507$	−7.78477	+	3.43112i	−0.345734	+	0.152382i
$508$	−30.2178	+	4.20292i	−1.34070	+	0.186474i
$509$	−27.4898	+	15.8713i	−1.21847	+	0.703482i	−0.964590	−	0.263755i	$-0.915039\pi$
$509$	−27.4898	+	15.8713i	−1.21847	+	0.703482i	−0.253876	+	0.967237i	$0.581706\pi$
$510$	2.07210	+	9.16139i	0.0917540	+	0.405673i
$511$	−17.9294	−	12.5431i	−0.793149	−	0.554874i
$512$	22.3257	+	3.68301i	0.986664	+	0.162768i
$513$	−10.1731	−	11.5569i	−0.449152	−	0.510248i
$514$	10.6385	+	2.07578i	0.469243	+	0.0915587i
$515$	−6.14722	−	3.54910i	−0.270879	−	0.156392i
$516$	20.3102	−	12.5456i	0.894106	−	0.552291i
$517$	−13.0781	−	7.55065i	−0.575175	−	0.332077i
$518$	28.5430	+	29.5745i	1.25411	+	1.29943i
$519$	−42.9724	−	4.67938i	−1.88628	−	0.205402i
$520$	−11.8348	+	18.1390i	−0.518992	+	0.795449i
$521$	−2.09032	+	1.20685i	−0.0915786	+	0.0528730i	−0.545090	−	0.838378i	$-0.683505\pi$
$521$	−2.09032	+	1.20685i	−0.0915786	+	0.0528730i	0.453511	+	0.891251i	$0.350171\pi$
$522$	1.43211	−	3.29833i	0.0626816	−	0.144364i
$523$	4.85017	−	8.40075i	0.212083	−	0.367339i	−0.740283	−	0.672295i	$-0.765309\pi$
$523$	4.85017	−	8.40075i	0.212083	−	0.367339i	0.952366	+	0.304956i	$0.0986419\pi$
$524$	−0.107162	+	0.0834780i	−0.00468137	+	0.00364675i
$525$	−2.00061	+	10.1125i	−0.0873139	+	0.441347i
$526$	5.24589	+	15.2705i	0.228732	+	0.665827i
$527$	−12.1778	+	7.03087i	−0.530474	+	0.306270i
$528$	−3.40967	+	9.17912i	−0.148387	+	0.399470i
$529$	−9.62708	+	16.6746i	−0.418569	+	0.724982i
$530$	−16.2957	−	47.4361i	−0.707842	−	2.06049i
$531$	4.16577	+	0.918130i	0.180779	+	0.0398435i
$532$	0.804810	+	15.6584i	0.0348930	+	0.678876i
$533$	−9.84562	−	17.0531i	−0.426461	−	0.738653i
$534$	15.8847	−	3.59275i	0.687398	−	0.155474i
$535$	−2.18270			−0.0943665
$536$	20.7119	+	13.5135i	0.894618	+	0.583696i
$537$	0.498898	+	1.13194i	0.0215291	+	0.0488466i
$538$	−7.83070	−	1.52793i	−0.337605	−	0.0658736i
$539$	−9.29393	+	3.39153i	−0.400318	+	0.146084i
$540$	−26.4128	+	9.23644i	−1.13662	+	0.397473i
$541$	−2.43786	+	4.22250i	−0.104812	+	0.181539i	−0.913661	−	0.406476i	$-0.866757\pi$
$541$	−2.43786	+	4.22250i	−0.104812	+	0.181539i	0.808850	+	0.588016i	$0.200091\pi$
$542$	8.37784	−	2.87804i	0.359859	−	0.123623i
$543$	23.2684	+	2.53376i	0.998544	+	0.108734i
$544$	8.02818	−	0.673550i	0.344205	−	0.0288782i
$545$	24.2497	+	14.0006i	1.03874	+	0.599719i
$546$	−11.2886	−	14.5697i	−0.483107	−	0.623524i
$547$	−22.7649	+	13.1433i	−0.973356	+	0.561967i	−0.900258	−	0.435357i	$-0.856622\pi$
$547$	−22.7649	+	13.1433i	−0.973356	+	0.561967i	−0.0730983	+	0.997325i	$0.523289\pi$
$548$	−9.61799	−	3.90188i	−0.410860	−	0.166680i
$549$	−1.31251	+	5.95516i	−0.0560165	+	0.254160i
$550$	4.41302	+	0.861070i	0.188172	+	0.0367161i
$551$	−2.51132			−0.106986
$552$	−9.35595	−	1.53832i	−0.398215	−	0.0654753i
$553$	28.3734	−	13.2452i	1.20656	−	0.563244i
$554$	−26.7977	+	9.20584i	−1.13853	+	0.391119i
$555$	50.9274	+	5.54561i	2.16175	+	0.235398i
$556$	19.5490	+	7.93074i	0.829062	+	0.336338i
$557$	−0.740402	−	1.28241i	−0.0313719	−	0.0543377i	0.849913	−	0.526923i	$-0.176654\pi$
$557$	−0.740402	−	1.28241i	−0.0313719	−	0.0543377i	−0.881285	+	0.472585i	$0.843321\pi$
$558$	−24.9347	−	33.6605i	−1.05557	−	1.42496i
$559$	19.5991			0.828952
$560$	26.9196	+	9.34246i	1.13756	+	0.394791i
$561$	−0.377409	+	3.46588i	−0.0159342	+	0.146330i
$562$	5.31530	−	27.2412i	0.224212	−	1.14910i
$563$	0.200896			0.00846677			0.00423339	−	0.999991i	$-0.498652\pi$
$563$	0.200896			0.00846677			0.00423339	+	0.999991i	$0.498652\pi$
$564$	−36.9969	+	1.10044i	−1.55785	+	0.0463370i
$565$		−	23.5663i		−	0.991440i
$566$	1.79006	+	1.55832i	0.0752420	+	0.0655011i
$567$	−0.0688211	−	23.8117i	−0.00289021	−	0.999996i
$568$	−4.62613	−	3.01833i	−0.194108	−	0.126646i
$569$	43.8164			1.83688			0.918441	−	0.395559i	$-0.129449\pi$
$569$	43.8164			1.83688			0.918441	+	0.395559i	$0.129449\pi$
$570$	13.2638	+	14.3514i	0.555559	+	0.601115i
$571$			13.2983i			0.556516i	0.960506	+	0.278258i	$0.0897570\pi$
$571$			13.2983i			0.556516i	−0.960506	+	0.278258i	$0.910243\pi$
$572$	−6.34192	+	4.94031i	−0.265169	+	0.206565i
$573$	26.2793	+	2.86162i	1.09783	+	0.119546i
$574$	−18.6409	+	17.9907i	−0.778056	+	0.750918i
$575$			4.35373i			0.181563i
$576$	4.71328	+	23.5326i	0.196387	+	0.980527i
$577$	7.21473	−	4.16543i	0.300353	−	0.173409i	−0.342248	−	0.939610i	$-0.611188\pi$
$577$	7.21473	−	4.16543i	0.300353	−	0.173409i	0.642602	+	0.766201i	$0.277855\pi$
$578$	−20.0246	+	6.87905i	−0.832912	+	0.286131i
$579$	1.67446	−	15.3771i	0.0695880	−	0.639052i
$580$	−1.71574	+	4.22923i	−0.0712421	+	0.175609i
$581$	−8.65644	+	12.3737i	−0.359130	+	0.513348i
$582$	11.0047	−	35.4290i	0.456159	−	1.46858i
$583$		−	18.6171i		−	0.771040i
$584$	−1.27420	+	23.3574i	−0.0527269	+	0.966536i
$585$	−22.4338	−	4.94438i	−0.927525	−	0.204425i
$586$	−4.81089	−	14.0043i	−0.198736	−	0.578511i
$587$	−4.37925	−	7.58509i	−0.180751	−	0.313070i	0.761385	−	0.648299i	$-0.224520\pi$
$587$	−4.37925	−	7.58509i	−0.180751	−	0.313070i	−0.942137	+	0.335229i	$0.891186\pi$
$588$	−15.0117	+	19.0434i	−0.619071	+	0.785335i
$589$	−14.6280	+	25.3364i	−0.602736	+	1.04397i
$590$	−5.31410	−	1.03689i	−0.218778	−	0.0426880i
$591$	−0.670440	+	6.15689i	−0.0275782	+	0.253261i
$592$	10.7515	−	42.6039i	0.441883	−	1.75101i
$593$	−10.4931	−	6.05820i	−0.430900	−	0.248780i	0.268830	−	0.963188i	$-0.413363\pi$
$593$	−10.4931	−	6.05820i	−0.430900	−	0.248780i	−0.699730	+	0.714407i	$0.746696\pi$
$594$	−10.3858	+	0.0571649i	−0.426133	+	0.00234551i
$595$	10.1071	+	0.879996i	0.414352	+	0.0360763i
$596$	28.9785	−	22.5741i	1.18701	−	0.924670i
$597$	−23.0535	+	10.1608i	−0.943517	+	0.415853i
$598$	−5.87121	−	5.11112i	−0.240092	−	0.209009i
$599$			39.4741i			1.61287i	0.591323	+	0.806434i	$0.298606\pi$
$599$			39.4741i			1.61287i	−0.591323	+	0.806434i	$0.701394\pi$
$600$	10.3114	−	3.88871i	0.420960	−	0.158756i
$601$	−3.43670	+	1.98418i	−0.140186	+	0.0809363i	−0.568453	−	0.822716i	$-0.692458\pi$
$601$	−3.43670	+	1.98418i	−0.140186	+	0.0809363i	0.428267	+	0.903652i	$0.359124\pi$
$602$	−6.23066	−	25.0211i	−0.253943	−	1.01979i
$603$	−5.64571	+	25.6159i	−0.229911	+	1.04316i
$604$	3.82004	−	9.41626i	0.155435	−	0.383142i
$605$	−20.9916	−	12.1195i	−0.853431	−	0.492728i
$606$	40.0547	−	9.05945i	1.62711	−	0.368015i
$607$	14.3423	+	24.8416i	0.582136	+	1.00829i	0.995226	+	0.0975993i	$0.0311163\pi$
$607$	14.3423	+	24.8416i	0.582136	+	1.00829i	−0.413089	+	0.910690i	$0.635550\pi$
$608$	13.7645	−	9.56506i	0.558223	−	0.387914i
$609$	−2.92275	−	2.55783i	−0.118436	−	0.103648i
$610$	1.48228	−	7.59675i	0.0600157	−	0.307583i
$611$	−26.3163	−	15.1937i	−1.06464	−	0.614672i
$612$	3.67729	+	7.71337i	0.148646	+	0.311794i
$613$	−1.55941	−	2.70099i	−0.0629842	−	0.109092i	0.832814	−	0.553553i	$-0.186728\pi$
$613$	−1.55941	−	2.70099i	−0.0629842	−	0.109092i	−0.895798	+	0.444461i	$0.853395\pi$
$614$	−0.687542	−	0.598532i	−0.0277469	−	0.0241548i
$615$	−3.49541	+	32.0997i	−0.140949	+	1.29438i
$616$	8.32319	+	6.52587i	0.335351	+	0.262935i
$617$	1.30847	−	2.26634i	0.0526770	−	0.0912393i	−0.838485	−	0.544925i	$-0.816558\pi$
$617$	1.30847	−	2.26634i	0.0526770	−	0.0912393i	0.891162	+	0.453686i	$0.149891\pi$
$618$	−6.16693	−	1.91552i	−0.248070	−	0.0770537i
$619$	−12.3184	+	21.3361i	−0.495119	+	0.857571i	−0.999984	−	0.00562710i	$-0.998209\pi$
$619$	−12.3184	+	21.3361i	−0.495119	+	0.857571i	0.504865	+	0.863198i	$0.331542\pi$
$620$	32.6743	+	41.9443i	1.31223	+	1.68453i
$621$	−1.98025	−	9.85983i	−0.0794647	−	0.395661i
$622$	−19.2972	−	16.7990i	−0.773748	−	0.673578i
$623$	1.52580	−	17.5245i	0.0611300	−	0.702105i
$624$	−6.86107	+	18.4706i	−0.274663	+	0.739415i
$625$	15.5936	+	27.0090i	0.623745	+	1.08036i
$626$	0.0579040	−	0.0665151i	0.00231431	−	0.00265848i
$627$	2.92543	+	6.63743i	0.116831	+	0.265073i
$628$	−4.78793	+	0.665940i	−0.191059	+	0.0265739i
$629$		−	15.6445i		−	0.623787i
$630$	0.819598	+	30.2120i	0.0326536	+	1.20368i
$631$		−	8.86244i		−	0.352808i	−0.984318	−	0.176404i	$-0.943553\pi$
$631$		−	8.86244i		−	0.352808i	0.984318	−	0.176404i	$-0.0564466\pi$
$632$	−28.0352	−	18.2916i	−1.11518	−	0.727602i
$633$	−13.4626	+	18.3844i	−0.535089	+	0.730716i
$634$	−9.00826	−	7.84204i	−0.357764	−	0.311447i
$635$	20.5361	+	35.5696i	0.814951	+	1.41154i
$636$	−23.9800	−	38.8213i	−0.950868	−	1.53936i
$637$	−18.7016	+	6.82457i	−0.740985	+	0.270399i
$638$	−1.11230	+	1.27772i	−0.0440366	+	0.0505854i
$639$	1.26100	−	5.72147i	0.0498845	−	0.226338i
$640$	−6.70428	−	29.7151i	−0.265010	−	1.17459i
$641$	18.3397	−	31.7654i	0.724376	−	1.25466i	−0.234854	−	0.972031i	$-0.575461\pi$
$641$	18.3397	−	31.7654i	0.724376	−	1.25466i	0.959230	−	0.282626i	$-0.0912055\pi$
$642$	−1.93679	+	0.438058i	−0.0764390	+	0.0172888i
$643$	10.9509	−	18.9675i	0.431860	−	0.748004i	−0.565173	−	0.824972i	$-0.691191\pi$
$643$	10.9509	−	18.9675i	0.431860	−	0.748004i	0.997034	+	0.0769685i	$0.0245241\pi$
$644$	−4.65862	+	9.12035i	−0.183575	+	0.359392i
$645$	−25.9294	−	18.9876i	−1.02097	−	0.747637i
$646$	3.91850	−	4.50123i	0.154171	−	0.177098i
$647$	−15.1436	−	26.2296i	−0.595358	−	1.03119i	−0.993496	−	0.113865i	$-0.963677\pi$
$647$	−15.1436	−	26.2296i	−0.595358	−	1.03119i	0.398138	−	0.917326i	$-0.369657\pi$
$648$	−21.5833	+	13.4967i	−0.847872	+	0.530202i
$649$	−1.74042	−	1.00483i	−0.0683173	−	0.0394430i
$650$	8.88006	+	1.73268i	0.348305	+	0.0679613i
$651$	−42.8300	+	14.5884i	−1.67864	+	0.571763i
$652$	12.0086	−	29.6008i	0.470294	−	1.15926i
$653$	−4.36506	−	7.56050i	−0.170818	−	0.295865i	0.767888	−	0.640584i	$-0.221308\pi$
$653$	−4.36506	−	7.56050i	−0.170818	−	0.295865i	−0.938706	+	0.344719i	$0.887974\pi$
$654$	24.3275	+	7.55642i	0.951280	+	0.295479i
$655$	0.158372	+	0.0914362i	0.00618811	+	0.00357271i
$656$	26.8534	+	6.77668i	1.04845	+	0.264585i
$657$	−23.6535	+	7.49007i	−0.922812	+	0.292216i
$658$	−11.0310	+	38.4269i	−0.430032	+	1.49804i
$659$	38.1510	−	22.0265i	1.48615	−	0.858030i	0.486276	−	0.873806i	$-0.338355\pi$
$659$	38.1510	−	22.0265i	1.48615	−	0.858030i	0.999876	+	0.0157758i	$0.00502180\pi$
$660$	13.1765	−	0.391925i	0.512895	−	0.0152557i
$661$			38.9747i			1.51594i	0.652289	+	0.757971i	$0.273809\pi$
$661$			38.9747i			1.51594i	−0.652289	+	0.757971i	$0.726191\pi$
$662$	14.3649	−	16.5012i	0.558308	−	0.641336i
$663$	−0.759438	+	6.97419i	−0.0294941	+	0.270855i
$664$	16.1198	+	0.879372i	0.625568	+	0.0341263i
$665$	19.1265	−	8.92856i	0.741692	−	0.346235i
$666$	46.3026	−	5.30005i	1.79419	−	0.205373i
$667$	−1.42058	−	0.820175i	−0.0550053	−	0.0317573i
$668$	25.9256	+	10.5176i	1.00309	+	0.406940i
$669$	24.9801	−	11.0099i	0.965785	−	0.425668i
$670$	6.37596	−	32.6771i	0.246325	−	1.26243i
$671$	1.43645	−	2.48800i	0.0554535	−	0.0960483i
$672$	25.7617	+	2.88728i	0.993778	+	0.111379i
$673$	6.18407	+	10.7111i	0.238379	+	0.412884i	0.960249	−	0.279144i	$-0.0900508\pi$
$673$	6.18407	+	10.7111i	0.238379	+	0.412884i	−0.721871	+	0.692028i	$0.756717\pi$
$674$	4.01142	−	1.37805i	0.154514	−	0.0530804i
$675$	7.72322	+	8.77378i	0.297267	+	0.337703i
$676$	7.74961	−	6.03688i	0.298062	−	0.232188i
$677$			13.4525i			0.517022i	0.966008	+	0.258511i	$0.0832317\pi$
$677$			13.4525i			0.517022i	−0.966008	+	0.258511i	$0.916768\pi$
$678$	−4.72963	−	20.9112i	−0.181640	−	0.803089i
$679$	−32.8340	−	22.9702i	−1.26005	−	0.881514i
$680$	−4.90324	−	9.67425i	−0.188031	−	0.370990i
$681$	−2.64929	−	1.94003i	−0.101521	−	0.0743420i
$682$	6.41178	+	18.6644i	0.245520	+	0.714696i
$683$	−13.0760	+	7.54945i	−0.500340	+	0.288872i	−0.728854	−	0.684669i	$-0.759947\pi$
$683$	−13.0760	+	7.54945i	−0.500340	+	0.288872i	0.228514	+	0.973541i	$0.426613\pi$
$684$	14.6497	+	10.0726i	0.560145	+	0.385134i
$685$			13.9731i			0.533886i
$686$	14.6580	+	21.7059i	0.559643	+	0.828734i
$687$	−5.96355	−	13.5305i	−0.227524	−	0.516221i
$688$	−19.2051	+	19.7743i	−0.732189	+	0.753890i
$689$		−	37.4620i		−	1.42719i
$690$	2.81591	+	12.4500i	0.107200	+	0.473965i
$691$	−26.4012			−1.00435			−0.502175	−	0.864766i	$-0.667467\pi$
$691$	−26.4012			−1.00435			−0.502175	+	0.864766i	$0.667467\pi$
$692$	49.4377	−	6.87616i	1.87934	−	0.261392i
$693$	−3.35563	+	10.7044i	−0.127470	+	0.406628i
$694$	27.8833	−	32.0299i	1.05843	−	1.21584i
$695$		−	28.4010i		−	1.07731i
$696$	−0.673650	+	4.09709i	−0.0255346	+	0.155300i
$697$	9.86076			0.373503
$698$	25.6756	+	5.00983i	0.971837	+	0.189625i
$699$	22.8628	+	16.7420i	0.864752	+	0.633241i
$700$	−0.610998	−	11.8876i	−0.0230936	−	0.449308i
$701$	−9.14551			−0.345421			−0.172711	−	0.984973i	$-0.555253\pi$
$701$	−9.14551			−0.345421			−0.172711	+	0.984973i	$0.555253\pi$
$702$	−20.8986	+	0.115030i	−0.788769	+	0.00434151i
$703$	−16.2745	−	28.1882i	−0.613803	−	1.06314i
$704$	1.22996	−	11.2397i	0.0463559	−	0.423611i
$705$	20.0966	+	45.5965i	0.756882	+	1.71726i
$706$	−3.61376	−	10.5195i	−0.136006	−	0.395906i
$707$	3.84745	−	44.1896i	0.144698	−	1.66192i
$708$	−4.92349	+	0.146445i	−0.185036	+	0.00550375i
$709$	−19.1952			−0.720890			−0.360445	−	0.932781i	$-0.617375\pi$
$709$	−19.1952			−0.720890			−0.360445	+	0.932781i	$0.617375\pi$
$710$	−1.42411	+	7.29863i	−0.0534459	+	0.273913i
$711$	7.64191	−	34.6731i	0.286594	−	1.30034i
$712$	−16.7739	+	8.50161i	−0.628630	+	0.318611i
$713$	−16.5493	+	9.55473i	−0.619776	+	0.357828i
$714$	9.14504	−	1.24760i	0.342244	−	0.0466903i
$715$	9.37261	+	5.41128i	0.350516	+	0.202370i
$716$	−0.877786	−	1.12682i	−0.0328044	−	0.0421113i
$717$	7.03459	−	9.60642i	0.262712	−	0.358758i
$718$	7.97085	+	23.2028i	0.297470	+	0.865919i
$719$	−2.31150	+	4.00364i	−0.0862046	+	0.149311i	−0.905904	−	0.423483i	$-0.860807\pi$
$719$	−2.31150	+	4.00364i	−0.0862046	+	0.149311i	0.819699	+	0.572794i	$0.194141\pi$
$720$	26.9715	−	17.7895i	1.00517	−	0.662974i
$721$	−3.99829	+	5.71524i	−0.148904	+	0.212847i
$722$	−2.76800	+	14.1861i	−0.103014	+	0.527953i
$723$	10.2082	−	13.9402i	0.379645	−	0.518442i
$724$	−26.7692	+	3.72326i	−0.994870	+	0.138374i
$725$	1.90655			0.0708076
$726$	−21.0589	−	6.54116i	−0.781570	−	0.242765i
$727$	−4.10913	−	7.11723i	−0.152399	−	0.263963i	0.779710	−	0.626141i	$-0.215367\pi$
$727$	−4.10913	−	7.11723i	−0.152399	−	0.263963i	−0.932109	+	0.362178i	$0.882033\pi$
$728$	16.7482	+	13.1316i	0.620731	+	0.486690i
$729$	−21.4813	−	16.3570i	−0.795605	−	0.605816i
$730$	29.7831	−	10.2314i	1.10232	−	0.378681i
$731$	−4.90730	+	8.49969i	−0.181503	+	0.314372i
$732$	−0.209350	−	7.03835i	−0.00773781	−	0.260145i
$733$	18.9227	−	10.9250i	0.698927	−	0.403526i	−0.108021	−	0.994149i	$-0.534451\pi$
$733$	18.9227	−	10.9250i	0.698927	−	0.403526i	0.806948	+	0.590623i	$0.201118\pi$
$734$	−1.36443	+	0.468723i	−0.0503620	+	0.0173009i
$735$	31.3538	+	9.08932i	1.15650	+	0.335265i
$736$	10.9100	−	0.915334i	0.402150	−	0.0337396i
$737$	6.17883	−	10.7020i	0.227600	−	0.394215i
$738$	3.34063	+	29.1847i	0.122970	+	1.07430i
$739$	16.9483	−	9.78511i	0.623454	−	0.359951i	−0.154759	−	0.987952i	$-0.549460\pi$
$739$	16.9483	−	9.78511i	0.623454	−	0.359951i	0.778212	+	0.628001i	$0.216127\pi$
$740$	−58.5895	+	8.14905i	−2.15379	+	0.299565i
$741$	5.88668	+	13.3561i	0.216252	+	0.490649i
$742$	−47.8259	+	11.9094i	−1.75574	+	0.437208i
$743$	7.26557	+	4.19478i	0.266548	+	0.153892i	0.627318	−	0.778763i	$-0.284153\pi$
$743$	7.26557	+	4.19478i	0.266548	+	0.153892i	−0.360770	+	0.932655i	$0.617486\pi$
$744$	37.4111	+	30.6611i	1.37156	+	1.12409i
$745$	−42.8269	−	24.7261i	−1.56905	−	0.905894i
$746$	−0.0204118	+	0.104611i	−0.000747328	+	0.00383009i
$747$	5.16917	+	16.3241i	0.189130	+	0.597269i
$748$	−0.554587	−	3.98733i	−0.0202777	−	0.145791i
$749$	−0.186038	+	2.13673i	−0.00679769	+	0.0780744i
$750$	12.3123	+	13.3219i	0.449581	+	0.486446i
$751$	−11.8250	+	6.82717i	−0.431501	+	0.249127i	−0.699986	−	0.714157i	$-0.746810\pi$
$751$	−11.8250	+	6.82717i	−0.431501	+	0.249127i	0.268485	+	0.963284i	$0.413477\pi$
$752$	41.1170	−	11.6633i	1.49938	−	0.425318i
$753$	−3.11577	+	28.6132i	−0.113545	+	1.04272i
$754$	−2.23822	+	2.57108i	−0.0815113	+	0.0936331i
$755$	−13.6800			−0.497868
$756$	6.79066	+	26.6437i	0.246974	+	0.969022i
$757$	22.0851			0.802697			0.401348	−	0.915925i	$-0.368542\pi$
$757$	22.0851			0.802697			0.401348	+	0.915925i	$0.368542\pi$
$758$	−27.4304	+	31.5097i	−0.996318	+	1.14448i
$759$	−0.512887	+	4.71003i	−0.0186166	+	0.170963i
$760$	−18.8985	−	12.3303i	−0.685519	−	0.447269i
$761$	−22.6153	+	13.0569i	−0.819804	+	0.473314i	−0.850349	−	0.526220i	$-0.823609\pi$
$761$	−22.6153	+	13.0569i	−0.819804	+	0.473314i	0.0305452	+	0.999533i	$0.490276\pi$
$762$	25.3611	+	27.4407i	0.918734	+	0.994070i
$763$	15.7726	−	22.5456i	0.571005	−	0.816207i
$764$	−30.2330	+	4.20503i	−1.09379	+	0.152133i
$765$	7.76135	−	8.49107i	0.280612	−	0.306995i
$766$	−7.71103	+	39.5194i	−0.278611	+	1.42789i
$767$	−3.50213	−	2.02196i	−0.126455	−	0.0730087i
$768$	−11.9126	−	25.0218i	−0.429860	−	0.902896i
$769$	14.6518	+	8.45923i	0.528358	+	0.305048i	0.740348	−	0.672224i	$-0.234661\pi$
$769$	14.6518	+	8.45923i	0.528358	+	0.305048i	−0.211989	+	0.977272i	$0.567994\pi$
$770$	3.92871	−	13.6858i	0.141581	−	0.493203i
$771$	−5.35402	−	12.1476i	−0.192820	−	0.437484i
$772$	2.46055	+	17.6907i	0.0885570	+	0.636701i
$773$	18.8030	−	10.8559i	0.676298	−	0.390461i	−0.122161	−	0.992510i	$-0.538982\pi$
$773$	18.8030	−	10.8559i	0.676298	−	0.390461i	0.798459	+	0.602049i	$0.205649\pi$
$774$	−26.8188	−	11.6445i	−0.963983	−	0.418553i
$775$	11.1053	−	19.2350i	0.398915	−	0.690940i
$776$	−2.33344	+	42.7743i	−0.0837657	+	1.53551i
$777$	9.76950	−	49.3821i	0.350479	−	1.77157i
$778$	−29.1247	+	10.0052i	−1.04417	+	0.358704i
$779$	17.7671	−	10.2578i	0.636572	−	0.367525i
$780$	26.5143	−	0.788648i	0.949365	−	0.0282381i
$781$	−1.38008	+	2.39037i	−0.0493831	+	0.0855341i
$782$	3.68664	−	1.26647i	0.131834	−	0.0452890i
$783$	−4.31774	+	0.867176i	−0.154304	+	0.0309903i
$784$	11.4401	−	25.5563i	0.408576	−	0.912724i
$785$	3.25389	+	5.63590i	0.116136	+	0.201154i
$786$	0.158880	+	0.0493501i	0.00566706	+	0.00176026i
$787$	−19.5188			−0.695769			−0.347884	−	0.937537i	$-0.613100\pi$
$787$	−19.5188			−0.695769			−0.347884	+	0.937537i	$0.613100\pi$
$788$	−0.985184	−	7.08321i	−0.0350957	−	0.252329i
$789$	11.6835	−	15.9549i	0.415943	−	0.568010i
$790$	−8.63037	+	44.2311i	−0.307055	+	1.57367i
$791$	−23.0699	−	2.00862i	−0.820271	−	0.0714183i
$792$	11.6133	−	2.99223i	0.412662	−	0.106324i
$793$	2.89048	−	5.00646i	0.102644	−	0.177785i
$794$	−0.679634	−	1.97838i	−0.0241193	−	0.0702101i
$795$	−36.2933	+	49.5620i	−1.28719	+	1.75778i
$796$	22.9494	−	17.8774i	0.813419	−	0.633647i
$797$	−23.1795	−	13.3827i	−0.821059	−	0.474039i	0.0297223	−	0.999558i	$-0.490538\pi$
$797$	−23.1795	−	13.3827i	−0.821059	−	0.474039i	−0.850782	+	0.525519i	$0.823871\pi$
$798$	15.1797	−	11.7612i	0.537354	−	0.416343i
$799$	13.1784	−	7.60854i	0.466218	−	0.269171i
$800$	−10.4498	+	7.26163i	−0.369455	+	0.256737i
$801$	−14.7225	−	13.4572i	−0.520192	−	0.475487i
$802$	−6.71686	+	34.4242i	−0.237181	+	1.21556i
$803$	11.6889			0.412491
$804$	−0.900512	−	30.2752i	−0.0317586	−	1.06772i
$805$	13.7353	+	1.19589i	0.484105	+	0.0421495i
$806$	12.9020	+	37.5572i	0.454455	+	1.32290i
$807$	3.94095	+	8.94150i	0.138728	+	0.314756i
$808$	−42.2969	+	21.4376i	−1.48800	+	0.754171i
$809$	13.9813	+	24.2164i	0.491557	+	0.851402i	0.999953	−	0.00972146i	$-0.00309448\pi$
$809$	13.9813	+	24.2164i	0.491557	+	0.851402i	−0.508395	+	0.861124i	$0.669761\pi$
$810$	27.7602	+	20.0945i	0.975395	+	0.706049i
$811$	44.1723			1.55110			0.775550	−	0.631286i	$-0.217473\pi$
$811$	44.1723			1.55110			0.775550	+	0.631286i	$0.217473\pi$
$812$	3.99391	+	2.04007i	0.140159	+	0.0715924i
$813$	−8.75331	−	6.40988i	−0.306992	−	0.224804i
$814$	−21.5499	−	4.20482i	−0.755324	−	0.147379i
$815$	−43.0043			−1.50638
$816$	−6.29239	−	7.60025i	−0.220278	−	0.266062i
$817$			20.4196i			0.714392i
$818$	8.69362	−	9.98648i	0.303965	−	0.349169i
$819$	−6.75234	+	21.5399i	−0.235946	+	0.752665i
$820$	−5.13637	−	36.9291i	−0.179370	−	1.28962i
$821$	−10.5891			−0.369562			−0.184781	−	0.982780i	$-0.559158\pi$
$821$	−10.5891			−0.369562			−0.184781	+	0.982780i	$0.559158\pi$
$822$	2.80433	+	12.3988i	0.0978124	+	0.432459i
$823$		−	1.56546i		−	0.0545685i	−0.999628	−	0.0272843i	$-0.991314\pi$
$823$		−	1.56546i		−	0.0545685i	0.999628	−	0.0272843i	$-0.00868593\pi$
$824$	7.44549	+	0.406170i	0.259376	+	0.0141496i
$825$	−2.22094	−	5.03902i	−0.0773232	−	0.175436i
$826$	−1.46798	+	5.11379i	−0.0510777	+	0.177932i
$827$		−	1.44507i		−	0.0502499i	−0.999684	−	0.0251249i	$-0.992002\pi$
$827$		−	1.44507i		−	0.0502499i	0.999684	−	0.0251249i	$-0.00799836\pi$
$828$	4.99732	+	10.4822i	0.173669	+	0.364282i
$829$	−33.2429	+	19.1928i	−1.15457	+	0.666594i	−0.949998	−	0.312257i	$-0.898915\pi$
$829$	−33.2429	+	19.1928i	−1.15457	+	0.666594i	−0.204577	+	0.978851i	$0.565582\pi$
$830$	−7.06106	−	20.5544i	−0.245093	−	0.713453i
$831$	27.9987	+	20.5029i	0.971265	+	0.711239i
$832$	2.47498	−	22.6169i	0.0858044	−	0.784100i
$833$	1.72292	−	9.81926i	0.0596957	−	0.340217i
$834$	−5.69993	−	25.2012i	−0.197372	−	0.872646i
$835$		−	37.6650i		−	1.30345i
$836$	−5.14715	−	6.60745i	−0.178018	−	0.228523i
$837$	−16.4012	+	48.6123i	−0.566909	+	1.68029i
$838$	−13.9428	+	4.78979i	−0.481647	+	0.165460i
$839$	−8.96149	−	15.5217i	−0.309385	−	0.535870i	0.668843	−	0.743404i	$-0.266790\pi$
$839$	−8.96149	−	15.5217i	−0.309385	−	0.535870i	−0.978228	+	0.207533i	$0.933456\pi$
$840$	−9.43589	−	33.5988i	−0.325569	−	1.15927i
$841$	14.1408	−	24.4926i	0.487615	−	0.844574i
$842$	1.86991	−	9.58338i	0.0644414	−	0.330265i
$843$	−31.1054	+	13.7096i	−1.07133	+	0.472185i
$844$	9.89130	−	24.3817i	0.340473	−	0.839253i
$845$	−11.4530	−	6.61239i	−0.393995	−	0.227473i
$846$	26.9834	+	36.4261i	0.927709	+	1.25236i
$847$	−13.6534	+	19.5165i	−0.469137	+	0.670595i
$848$	37.7971	+	36.7091i	1.29796	+	1.26059i
$849$	0.314660	−	2.88964i	0.0107991	−	0.0991722i
$850$	−2.97485	+	3.41726i	−0.102037	+	0.117211i
$851$		−	21.2604i		−	0.728796i
$852$	0.201135	+	6.76215i	0.00689077	+	0.231667i
$853$	13.3860	−	7.72843i	0.458329	−	0.264616i	−0.253013	−	0.967463i	$-0.581421\pi$
$853$	13.3860	−	7.72843i	0.458329	−	0.264616i	0.711341	+	0.702847i	$0.248088\pi$
$854$	−7.31040	−	2.09855i	−0.250157	−	0.0718110i
$855$	5.15139	−	23.3731i	0.176174	−	0.799343i
$856$	2.04521	−	1.03658i	0.0699039	−	0.0354297i
$857$	19.7121	+	11.3808i	0.673352	+	0.388760i	0.797346	−	0.603523i	$-0.206237\pi$
$857$	19.7121	+	11.3808i	0.673352	+	0.388760i	−0.123993	+	0.992283i	$0.539570\pi$
$858$	9.40267	+	2.92059i	0.321002	+	0.0997071i
$859$	0.444083	+	0.769174i	0.0151519	+	0.0262439i	0.873502	−	0.486821i	$-0.161843\pi$
$859$	0.444083	+	0.769174i	0.0151519	+	0.0262439i	−0.858350	+	0.513065i	$0.828510\pi$
$860$	34.3880	+	13.9507i	1.17262	+	0.475715i
$861$	31.1256	+	6.15774i	1.06076	+	0.209855i
$862$	19.9300	+	3.88875i	0.678819	+	0.132451i
$863$	−39.6368	−	22.8843i	−1.34925	−	0.778992i	−0.361110	−	0.932523i	$-0.617602\pi$
$863$	−39.6368	−	22.8843i	−1.34925	−	0.778992i	−0.988144	+	0.153531i	$0.950935\pi$
$864$	20.3625	−	21.1983i	0.692748	−	0.721180i
$865$	−33.5980	−	58.1934i	−1.14237	−	1.97864i
$866$	23.9996	−	27.5687i	0.815539	−	0.936821i
$867$	20.9220	+	15.3208i	0.710548	+	0.520321i
$868$	43.8458	−	28.4111i	1.48822	−	0.964335i
$869$	−8.36353	+	14.4861i	−0.283713	+	0.491406i
$870$	5.45203	−	1.23312i	0.184841	−	0.0418068i
$871$	12.4333	−	21.5351i	0.421286	−	0.729689i
$872$	−29.3712	−	1.60227i	−0.994634	−	0.0542597i
$873$	−43.3166	+	13.7166i	−1.46605	+	0.464235i
$874$	5.32511	−	6.11703i	0.180125	−	0.206912i
$875$	17.7544	−	8.28805i	0.600207	−	0.280187i
$876$	24.3742	−	15.0560i	0.823529	−	0.508696i
$877$	15.7434	+	27.2683i	0.531616	+	0.920786i	0.999319	+	0.0369000i	$0.0117483\pi$
$877$	15.7434	+	27.2683i	0.531616	+	0.920786i	−0.467703	+	0.883886i	$0.654918\pi$
$878$	−15.5592	−	13.5449i	−0.525099	−	0.457119i
$879$	−10.7146	+	14.6319i	−0.361396	+	0.493521i
$880$	−14.6439	+	4.15392i	−0.493646	+	0.140029i
$881$			12.0700i			0.406649i	0.979111	+	0.203324i	$0.0651746\pi$
$881$			12.0700i			0.406649i	−0.979111	+	0.203324i	$0.934825\pi$
$882$	29.6455	+	1.77272i	0.998217	+	0.0596907i
$883$		−	26.0164i		−	0.875522i	−0.899091	−	0.437761i	$-0.855772\pi$
$883$		−	26.0164i		−	0.875522i	0.899091	−	0.437761i	$-0.144228\pi$
$884$	−1.11596	−	8.02347i	−0.0375339	−	0.269859i
$885$	2.67442	+	6.06792i	0.0898998	+	0.203971i
$886$	−32.8546	+	37.7405i	−1.10377	+	1.26792i
$887$	−12.7190	−	22.0300i	−0.427063	−	0.739694i	0.569548	−	0.821958i	$-0.307118\pi$
$887$	−12.7190	−	22.0300i	−0.427063	−	0.739694i	−0.996611	+	0.0822640i	$0.973785\pi$
$888$	−50.3531	+	18.9896i	−1.68974	+	0.637248i
$889$	36.5707	−	17.0719i	1.22654	−	0.572572i
$890$	19.0949	+	16.6228i	0.640061	+	0.557198i
$891$	7.32168	+	10.4016i	0.245285	+	0.348468i
$892$	−24.8672	+	19.3714i	−0.832616	+	0.648602i
$893$	15.8299	−	27.4181i	0.529726	−	0.917512i
$894$	−42.9642	−	13.3452i	−1.43694	−	0.446331i
$895$	−0.961467	+	1.66531i	−0.0321383	+	0.0556652i
$896$	−29.6607	+	4.03036i	−0.990894	+	0.134645i
$897$	−1.03205	+	9.47771i	−0.0344592	+	0.316451i
$898$	−0.351720	−	0.306186i	−0.0117371	−	0.0102176i
$899$	4.18414	+	7.24714i	0.139549	+	0.241706i
$900$	−11.1218	−	7.64691i	−0.370727	−	0.254897i
$901$	16.2465	+	9.37990i	0.541248	+	0.312490i
$902$	2.65031	−	13.5830i	0.0882457	−	0.452263i
$903$	−20.7977	+	23.7649i	−0.692106	+	0.790848i
$904$	11.1918	+	22.0818i	0.372234	+	0.734429i
$905$	18.1924	+	31.5102i	0.604736	+	1.04743i
$906$	−12.1388	+	2.74551i	−0.403284	+	0.0912136i
$907$	−25.3966	−	14.6627i	−0.843281	−	0.486868i	0.0150974	−	0.999886i	$-0.495194\pi$
$907$	−25.3966	−	14.6627i	−0.843281	−	0.486868i	−0.858378	+	0.513018i	$0.828528\pi$
$908$	3.51353	+	1.42539i	0.116601	+	0.0473031i
$909$	−37.1240	−	33.9336i	−1.23132	−	1.12551i
$910$	7.90550	−	27.5392i	0.262065	−	0.912915i
$911$	12.1668	−	7.02448i	0.403103	−	0.232731i	−0.284719	−	0.958611i	$-0.591900\pi$
$911$	12.1668	−	7.02448i	0.403103	−	0.232731i	0.687822	+	0.725880i	$0.258567\pi$
$912$	−19.2439	−	7.14833i	−0.637230	−	0.236705i
$913$		−	8.06690i		−	0.266976i
$914$	27.6097	+	24.0353i	0.913247	+	0.795017i
$915$	−8.67437	+	3.82321i	−0.286766	+	0.126391i
$916$	10.4926	+	13.4694i	0.346684	+	0.445041i
$917$	0.103009	−	0.147243i	0.00340165	−	0.00486239i
$918$	5.18281	−	9.09210i	0.171058	−	0.300084i
$919$	43.1553	+	24.9157i	1.42356	+	0.821894i	0.996601	−	0.0823755i	$-0.0262507\pi$
$919$	43.1553	+	24.9157i	1.42356	+	0.821894i	0.426961	+	0.904270i	$0.359584\pi$
$920$	−6.66335	−	13.1470i	−0.219684	−	0.433444i
$921$	−0.120857	+	1.10988i	−0.00398238	+	0.0365717i
$922$	−39.0330	−	7.61613i	−1.28548	−	0.250824i
$923$	−2.77705	+	4.80999i	−0.0914078	+	0.158323i
$924$	0.739403	−	12.9324i	0.0243246	−	0.425445i
$925$	12.3553	+	21.4000i	0.406240	+	0.703628i
$926$	9.01997	+	26.2567i	0.296415	+	0.862848i
$927$	2.38757	+	7.53989i	0.0784179	+	0.247642i
$928$	−0.400836	−	4.77764i	−0.0131581	−	0.156834i
$929$			27.6268i			0.906406i	0.891407	+	0.453203i	$0.149719\pi$
$929$			27.6268i			0.906406i	−0.891407	+	0.453203i	$0.850281\pi$
$930$	19.3162	−	62.1875i	0.633404	−	2.03921i
$931$	−7.11030	−	19.4846i	−0.233031	−	0.638582i
$932$	−30.3210	−	12.3008i	−0.993197	−	0.402926i
$933$	−3.39210	+	31.1509i	−0.111052	+	1.01983i
$934$	29.1845	−	10.0258i	0.954946	−	0.328053i
$935$	−4.69351	+	2.70980i	−0.153494	+	0.0886199i
$936$	23.3688	−	6.02109i	0.763834	−	0.196805i
$937$		−	5.47306i		−	0.178797i	−0.995996	−	0.0893986i	$-0.971505\pi$
$937$		−	5.47306i		−	0.178797i	0.995996	−	0.0893986i	$-0.0284945\pi$
$938$	−31.4454	−	9.02684i	−1.02673	−	0.294737i
$939$	−0.107373	−	0.0116921i	−0.00350399	−	0.000381558i
$940$	−35.3589	−	45.3906i	−1.15328	−	1.48048i
$941$		−	14.4602i		−	0.471388i	−0.971827	−	0.235694i	$-0.924264\pi$
$941$		−	14.4602i		−	0.471388i	0.971827	−	0.235694i	$-0.0757363\pi$
$942$	4.01839	+	4.34789i	0.130926	+	0.141662i
$943$	13.4005			0.436379
$944$	5.47178	−	1.55214i	0.178091	−	0.0505178i
$945$	29.8012	−	21.9555i	0.969434	−	0.714211i
$946$	10.3892	+	9.04418i	0.337781	+	0.294052i
$947$			42.3981i			1.37775i	0.724879	+	0.688877i	$0.241896\pi$
$947$			42.3981i			1.37775i	−0.724879	+	0.688877i	$0.758104\pi$
$948$	1.21891	+	40.9799i	0.0395885	+	1.33096i
$949$	23.5208			0.763518
$950$	−1.80522	+	9.25185i	−0.0585692	+	0.300170i
$951$	−1.58349	+	14.5417i	−0.0513481	+	0.471548i
$952$	−9.88840	+	3.97540i	−0.320485	+	0.128844i
$953$	−11.7969			−0.382138			−0.191069	−	0.981577i	$-0.561196\pi$
$953$	−11.7969			−0.382138			−0.191069	+	0.981577i	$0.561196\pi$
$954$	−22.2575	+	51.2620i	−0.720613	+	1.65967i
$955$	20.5464	+	35.5875i	0.664867	+	1.15158i
$956$	−5.16850	+	12.7402i	−0.167161	+	0.412046i
$957$	2.06258	+	0.224600i	0.0666737	+	0.00726028i
$958$	39.3304	−	13.5112i	1.27071	−	0.436527i
$959$	13.6788	+	1.19097i	0.441712	+	0.0384584i
$960$	−25.1857	+	27.5243i	−0.812865	+	0.888342i
$961$	66.4873			2.14475
$962$	−43.3636	−	8.46111i	−1.39810	−	0.272797i
$963$	1.79508	+	1.64081i	0.0578457	+	0.0528744i
$964$	−7.50020	+	18.4877i	−0.241565	+	0.595449i
$965$	20.8238	−	12.0226i	0.670341	−	0.387022i
$966$	12.4278	−	1.69545i	0.399859	−	0.0545502i
$967$	9.83637	+	5.67903i	0.316316	+	0.182625i	0.649749	−	0.760148i	$-0.274874\pi$
$967$	9.83637	+	5.67903i	0.316316	+	0.182625i	−0.333433	+	0.942774i	$0.608207\pi$
$968$	25.4250	+	1.38699i	0.817190	+	0.0445797i
$969$	−7.26619	−	0.791234i	−0.233424	−	0.0254181i
$970$	54.5418	−	18.7368i	1.75123	−	0.601601i
$971$	−9.77591	+	16.9324i	−0.313724	+	0.543386i	−0.979165	−	0.203064i	$-0.934910\pi$
$971$	−9.77591	+	16.9324i	−0.313724	+	0.543386i	0.665442	+	0.746450i	$0.268243\pi$
$972$	28.6655	+	12.2592i	0.919447	+	0.393215i
$973$	−27.8028	−	2.42070i	−0.891316	−	0.0776040i
$974$	−6.15449	−	1.20087i	−0.197203	−	0.0384782i
$975$	−4.46906	−	10.1397i	−0.143125	−	0.324731i
$976$	2.21885	+	7.82217i	0.0710237	+	0.250381i
$977$	−4.26325			−0.136393			−0.0681967	−	0.997672i	$-0.521725\pi$
$977$	−4.26325			−0.136393			−0.0681967	+	0.997672i	$0.521725\pi$
$978$	−38.1593	+	8.63075i	−1.22020	+	0.275981i
$979$	4.69845	+	8.13796i	0.150163	+	0.260090i
$980$	−37.6711	−	1.33769i	−1.20336	−	0.0427310i
$981$	−9.41853	−	29.7436i	−0.300711	−	0.949639i
$982$	0.261043	+	0.759884i	0.00833022	+	0.0242489i
$983$	−17.8283	+	30.8795i	−0.568633	+	0.984902i	0.428068	+	0.903746i	$0.359194\pi$
$983$	−17.8283	+	30.8795i	−0.568633	+	0.984902i	−0.996701	+	0.0811554i	$0.974139\pi$
$984$	−11.9692	−	31.7377i	−0.381563	−	1.01176i
$985$	−8.33768	+	4.81376i	−0.265661	+	0.153379i
$986$	−0.554605	−	1.61443i	−0.0176622	−	0.0514138i
$987$	46.3491	−	15.7870i	1.47531	−	0.502505i
$988$	−10.3573	−	13.2958i	−0.329510	−	0.422995i
$989$	−6.66886	+	11.5508i	−0.212058	+	0.367294i
$990$	−9.61021	−	12.9733i	−0.305432	−	0.412317i
$991$	−21.9593	+	12.6782i	−0.697561	+	0.402737i	−0.806438	−	0.591318i	$-0.798608\pi$
$991$	−21.9593	+	12.6782i	−0.697561	+	0.402737i	0.108877	+	0.994055i	$0.465274\pi$
$992$	−50.5358	−	23.7849i	−1.60451	−	0.755171i
$993$	−26.6373	−	2.90060i	−0.845309	−	0.0920479i
$994$	7.02352	+	2.01620i	0.222773	+	0.0639500i
$995$	−33.9164	−	19.5817i	−1.07522	−	0.620780i
$996$	−10.3907	−	16.8215i	−0.329242	−	0.533010i
$997$	−23.4164	−	13.5195i	−0.741606	−	0.428166i	0.0810469	−	0.996710i	$-0.474174\pi$
$997$	−23.4164	−	13.5195i	−0.741606	−	0.428166i	−0.822653	+	0.568544i	$0.807507\pi$
$998$	11.3953	+	2.22345i	0.360711	+	0.0703821i
$999$	−37.7144	−	42.8446i	−1.19323	−	1.35554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.b.103.34	yes	84
3.2	odd	2		756.2.bj.b.523.9		84
4.3	odd	2	inner	252.2.bj.b.103.33	yes	84
7.3	odd	6		252.2.n.b.31.5	✓	84
9.2	odd	6		756.2.n.b.19.19		84
9.7	even	3		252.2.n.b.187.24	yes	84
12.11	even	2		756.2.bj.b.523.10		84
21.17	even	6		756.2.n.b.199.38		84
28.3	even	6		252.2.n.b.31.24	yes	84
36.7	odd	6		252.2.n.b.187.5	yes	84
36.11	even	6		756.2.n.b.19.38		84
63.38	even	6		756.2.bj.b.451.9		84
63.52	odd	6	inner	252.2.bj.b.115.34	yes	84
84.59	odd	6		756.2.n.b.199.19		84
252.115	even	6	inner	252.2.bj.b.115.33	yes	84
252.227	odd	6		756.2.bj.b.451.10		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.5	✓	84	7.3	odd	6
252.2.n.b.31.24	yes	84	28.3	even	6
252.2.n.b.187.5	yes	84	36.7	odd	6
252.2.n.b.187.24	yes	84	9.7	even	3
252.2.bj.b.103.33	yes	84	4.3	odd	2	inner
252.2.bj.b.103.34	yes	84	1.1	even	1	trivial
252.2.bj.b.115.33	yes	84	252.115	even	6	inner
252.2.bj.b.115.34	yes	84	63.52	odd	6	inner
756.2.n.b.19.19		84	9.2	odd	6
756.2.n.b.19.38		84	36.11	even	6
756.2.n.b.199.19		84	84.59	odd	6
756.2.n.b.199.38		84	21.17	even	6
756.2.bj.b.451.9		84	63.38	even	6
756.2.bj.b.451.10		84	252.227	odd	6
756.2.bj.b.523.9		84	3.2	odd	2
756.2.bj.b.523.10		84	12.11	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06666 + 0.928568i) q^{2} +(0.187499 - 1.72187i) q^{3} +(0.275522 + 1.98093i) q^{4} +(2.33177 - 1.34625i) q^{5} +(1.79887 - 1.66254i) q^{6} +(-1.11915 - 2.39740i) q^{7} +(-1.54554 + 2.36882i) q^{8} +(-2.92969 - 0.645699i) q^{9} +(3.73728 + 0.729218i) q^{10} +(1.22399 + 0.706672i) q^{11} +(3.46257 - 0.102991i) q^{12} +(2.46297 + 1.42199i) q^{13} +(1.03240 - 3.59641i) q^{14} +(-1.88086 - 4.26742i) q^{15} +(-3.84817 + 1.09158i) q^{16} +(-1.23338 + 0.712090i) q^{17} +(-2.52540 - 3.40916i) q^{18} +(-1.48153 + 2.56609i) q^{19} +(3.30927 + 4.24815i) q^{20} +(-4.33785 + 1.47752i) q^{21} +(0.649389 + 1.89034i) q^{22} +(-1.67612 + 0.967709i) q^{23} +(3.78902 + 3.10538i) q^{24} +(1.12475 - 1.94813i) q^{25} +(1.30673 + 3.80381i) q^{26} +(-1.66113 + 4.92348i) q^{27} +(4.44073 - 2.87749i) q^{28} +(0.423772 + 0.733994i) q^{29} +(1.95636 - 6.29839i) q^{30} +9.87356 q^{31} +(-5.11830 - 2.40895i) q^{32} +(1.44630 - 1.97506i) q^{33} +(-1.97682 - 0.385717i) q^{34} +(-5.83707 - 4.08352i) q^{35} +(0.471891 - 5.98141i) q^{36} +(-5.49245 + 9.51321i) q^{37} +(-3.96307 + 1.36144i) q^{38} +(2.91030 - 3.97429i) q^{39} +(-0.414828 + 7.60421i) q^{40} +(-5.99620 - 3.46191i) q^{41} +(-5.99898 - 2.45198i) q^{42} +(5.96812 - 3.44570i) q^{43} +(-1.06263 + 2.61935i) q^{44} +(-7.70061 + 2.43846i) q^{45} +(-2.68643 - 0.524177i) q^{46} -10.6848 q^{47} +(1.15803 + 6.83074i) q^{48} +(-4.49502 + 5.36608i) q^{49} +(3.00870 - 1.03358i) q^{50} +(0.994872 + 2.25723i) q^{51} +(-2.13827 + 5.27076i) q^{52} +(-6.58617 - 11.4076i) q^{53} +(-6.34364 + 3.70921i) q^{54} +3.80542 q^{55} +(7.40869 + 1.05422i) q^{56} +(4.14069 + 3.03214i) q^{57} +(-0.229544 + 1.17642i) q^{58} -1.42192 q^{59} +(7.93525 - 4.90162i) q^{60} -2.03270i q^{61} +(10.5317 + 9.16828i) q^{62} +(1.73075 + 7.74626i) q^{63} +(-3.22261 - 7.32221i) q^{64} +7.65741 q^{65} +(3.37668 - 0.763728i) q^{66} -8.74356i q^{67} +(-1.75042 - 2.24704i) q^{68} +(1.35200 + 3.06751i) q^{69} +(-2.43434 - 9.77584i) q^{70} +1.95293i q^{71} +(6.05750 - 5.94195i) q^{72} +(7.16234 - 4.13518i) q^{73} +(-14.6922 + 5.04723i) q^{74} +(-3.14354 - 2.30195i) q^{75} +(-5.49143 - 2.22779i) q^{76} +(0.324347 - 3.72526i) q^{77} +(6.79469 - 1.53680i) q^{78} +11.8351i q^{79} +(-7.50350 + 7.72590i) q^{80} +(8.16615 + 3.78339i) q^{81} +(-3.18128 - 9.26055i) q^{82} +(-2.85384 - 4.94299i) q^{83} +(-4.12204 - 8.18589i) q^{84} +(-1.91730 + 3.32085i) q^{85} +(9.56552 + 1.86643i) q^{86} +(1.34330 - 0.592057i) q^{87} +(-3.56571 + 1.80722i) q^{88} +(5.75795 + 3.32435i) q^{89} +(-10.4782 - 4.54954i) q^{90} +(0.652664 - 7.49613i) q^{91} +(-2.37877 - 3.05365i) q^{92} +(1.85128 - 17.0010i) q^{93} +(-11.3970 - 9.92156i) q^{94} +7.97801i q^{95} +(-5.10758 + 8.36138i) q^{96} +(13.1164 - 7.57275i) q^{97} +(-9.77742 + 1.54984i) q^{98} +(-3.12962 - 2.86066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26}+ \cdots + 21 q^{98}+O(q^{100}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

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