LMFDB - Embedded newform 552.2.j.c.323.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.19
Character	$\chi$	$=$	552.323
Dual form			552.2.j.c.323.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.484105 - 1.32877i) q^{2} +(-1.59465 - 0.676097i) q^{3} +(-1.53128 + 1.28653i) q^{4} +1.67234 q^{5} +(-0.126404 + 2.44623i) q^{6} -2.28745i q^{7} +(2.45082 + 1.41191i) q^{8} +(2.08579 + 2.15627i) q^{9} +O(q^{10})$	\(q+(-0.484105 - 1.32877i) q^{2} +(-1.59465 - 0.676097i) q^{3} +(-1.53128 + 1.28653i) q^{4} +1.67234 q^{5} +(-0.126404 + 2.44623i) q^{6} -2.28745i q^{7} +(2.45082 + 1.41191i) q^{8} +(2.08579 + 2.15627i) q^{9} +(-0.809588 - 2.22216i) q^{10} +2.91064i q^{11} +(3.31168 - 1.01627i) q^{12} +4.63743i q^{13} +(-3.03950 + 1.10737i) q^{14} +(-2.66679 - 1.13066i) q^{15} +(0.689663 - 3.94010i) q^{16} +3.10443i q^{17} +(1.85546 - 3.81540i) q^{18} +7.70658 q^{19} +(-2.56083 + 2.15152i) q^{20} +(-1.54654 + 3.64767i) q^{21} +(3.86758 - 1.40905i) q^{22} -1.00000 q^{23} +(-2.95359 - 3.90849i) q^{24} -2.20328 q^{25} +(6.16210 - 2.24500i) q^{26} +(-1.86824 - 4.84868i) q^{27} +(2.94288 + 3.50273i) q^{28} +8.53054 q^{29} +(-0.211391 + 4.09092i) q^{30} -7.88372i q^{31} +(-5.56937 + 0.991014i) q^{32} +(1.96787 - 4.64143i) q^{33} +(4.12508 - 1.50287i) q^{34} -3.82539i q^{35} +(-5.96804 - 0.618427i) q^{36} -3.97637i q^{37} +(-3.73079 - 10.2403i) q^{38} +(3.13535 - 7.39505i) q^{39} +(4.09860 + 2.36120i) q^{40} +5.01274i q^{41} +(5.59561 + 0.289143i) q^{42} +7.62705 q^{43} +(-3.74463 - 4.45701i) q^{44} +(3.48814 + 3.60601i) q^{45} +(0.484105 + 1.32877i) q^{46} -4.61765 q^{47} +(-3.76366 + 5.81678i) q^{48} +1.76758 q^{49} +(1.06662 + 2.92766i) q^{50} +(2.09889 - 4.95046i) q^{51} +(-5.96621 - 7.10122i) q^{52} +0.427900 q^{53} +(-5.53837 + 4.82974i) q^{54} +4.86757i q^{55} +(3.22968 - 5.60611i) q^{56} +(-12.2893 - 5.21039i) q^{57} +(-4.12968 - 11.3352i) q^{58} +9.10118i q^{59} +(5.53825 - 1.69955i) q^{60} -9.06577i q^{61} +(-10.4757 + 3.81655i) q^{62} +(4.93235 - 4.77113i) q^{63} +(4.01300 + 6.92068i) q^{64} +7.75536i q^{65} +(-7.12008 - 0.367917i) q^{66} -8.29515 q^{67} +(-3.99395 - 4.75376i) q^{68} +(1.59465 + 0.676097i) q^{69} +(-5.08308 + 1.85189i) q^{70} +4.33432 q^{71} +(2.06741 + 8.22957i) q^{72} +6.91010 q^{73} +(-5.28370 + 1.92498i) q^{74} +(3.51345 + 1.48963i) q^{75} +(-11.8010 + 9.91477i) q^{76} +6.65793 q^{77} +(-11.3442 - 0.586191i) q^{78} -6.46025i q^{79} +(1.15335 - 6.58918i) q^{80} +(-0.298990 + 8.99503i) q^{81} +(6.66080 - 2.42669i) q^{82} +12.7870i q^{83} +(-2.32466 - 7.57529i) q^{84} +5.19165i q^{85} +(-3.69230 - 10.1346i) q^{86} +(-13.6032 - 5.76747i) q^{87} +(-4.10957 + 7.13344i) q^{88} -4.52095i q^{89} +(3.10295 - 6.38065i) q^{90} +10.6079 q^{91} +(1.53128 - 1.28653i) q^{92} +(-5.33016 + 12.5717i) q^{93} +(2.23543 + 6.13582i) q^{94} +12.8880 q^{95} +(9.55119 + 2.18512i) q^{96} -8.58440 q^{97} +(-0.855696 - 2.34872i) q^{98} +(-6.27612 + 6.07097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−0.484105	−	1.32877i	−0.342314	−	0.939586i
$2$	−0.484105	−	1.32877i	−0.342314	−	0.939586i
$3$	−1.59465	−	0.676097i	−0.920669	−	0.390345i
$3$	−1.59465	−	0.676097i	−0.920669	−	0.390345i
$4$	−1.53128	+	1.28653i	−0.765642	+	0.643267i
$5$	1.67234			0.747893			0.373947	−	0.927450i	$-0.378004\pi$
$5$	1.67234			0.747893			0.373947	+	0.927450i	$0.378004\pi$
$6$	−0.126404	+	2.44623i	−0.0516043	+	0.998668i
$7$		−	2.28745i		−	0.864574i	−0.901736	−	0.432287i	$-0.857707\pi$
$7$		−	2.28745i		−	0.864574i	0.901736	−	0.432287i	$-0.142293\pi$
$8$	2.45082	+	1.41191i	0.866494	+	0.499187i
$9$	2.08579	+	2.15627i	0.695262	+	0.718756i
$10$	−0.809588	−	2.22216i	−0.256014	−	0.702710i
$11$			2.91064i			0.877590i	0.898587	+	0.438795i	$0.144595\pi$
$11$			2.91064i			0.877590i	−0.898587	+	0.438795i	$0.855405\pi$
$12$	3.31168	−	1.01627i	0.955999	−	0.293371i
$13$			4.63743i			1.28619i	0.765786	+	0.643096i	$0.222350\pi$
$13$			4.63743i			1.28619i	−0.765786	+	0.643096i	$0.777650\pi$
$14$	−3.03950	+	1.10737i	−0.812341	+	0.295956i
$15$	−2.66679	−	1.13066i	−0.688562	−	0.291936i
$16$	0.689663	−	3.94010i	0.172416	−	0.985024i
$17$			3.10443i			0.752934i	0.926430	+	0.376467i	$0.122861\pi$
$17$			3.10443i			0.752934i	−0.926430	+	0.376467i	$0.877139\pi$
$18$	1.85546	−	3.81540i	0.437335	−	0.899299i
$19$	7.70658			1.76801			0.884005	−	0.467477i	$-0.154837\pi$
$19$	7.70658			1.76801			0.884005	+	0.467477i	$0.154837\pi$
$20$	−2.56083	+	2.15152i	−0.572618	+	0.481095i
$21$	−1.54654	+	3.64767i	−0.337482	+	0.795986i
$22$	3.86758	−	1.40905i	0.824571	−	0.300411i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−2.95359	−	3.90849i	−0.602899	−	0.797817i
$25$	−2.20328			−0.440656
$26$	6.16210	−	2.24500i	1.20849	−	0.440281i
$27$	−1.86824	−	4.84868i	−0.359544	−	0.933128i
$28$	2.94288	+	3.50273i	0.556152	+	0.661954i
$29$	8.53054			1.58408			0.792041	−	0.610468i	$-0.209018\pi$
$29$	8.53054			1.58408			0.792041	+	0.610468i	$0.209018\pi$
$30$	−0.211391	+	4.09092i	−0.0385945	+	0.746897i
$31$		−	7.88372i		−	1.41596i	−0.706234	−	0.707979i	$-0.749607\pi$
$31$		−	7.88372i		−	1.41596i	0.706234	−	0.707979i	$-0.250393\pi$
$32$	−5.56937	+	0.991014i	−0.984535	+	0.175188i
$33$	1.96787	−	4.64143i	0.342563	−	0.807970i
$34$	4.12508	−	1.50287i	0.707446	−	0.257740i
$35$		−	3.82539i		−	0.646609i
$36$	−5.96804	−	0.618427i	−0.994674	−	0.103071i
$37$		−	3.97637i		−	0.653711i	−0.945074	−	0.326856i	$-0.894011\pi$
$37$		−	3.97637i		−	0.653711i	0.945074	−	0.326856i	$-0.105989\pi$
$38$	−3.73079	−	10.2403i	−0.605215	−	1.66120i
$39$	3.13535	−	7.39505i	0.502058	−	1.18416i
$40$	4.09860	+	2.36120i	0.648045	+	0.373339i
$41$			5.01274i			0.782859i	0.920208	+	0.391429i	$0.128019\pi$
$41$			5.01274i			0.782859i	−0.920208	+	0.391429i	$0.871981\pi$
$42$	5.59561	+	0.289143i	0.863422	+	0.0446158i
$43$	7.62705			1.16311			0.581557	−	0.813505i	$-0.302444\pi$
$43$	7.62705			1.16311			0.581557	+	0.813505i	$0.302444\pi$
$44$	−3.74463	−	4.45701i	−0.564525	−	0.671920i
$45$	3.48814	+	3.60601i	0.519982	+	0.537553i
$46$	0.484105	+	1.32877i	0.0713774	+	0.195917i
$47$	−4.61765			−0.673554			−0.336777	−	0.941584i	$-0.609337\pi$
$47$	−4.61765			−0.673554			−0.336777	+	0.941584i	$0.609337\pi$
$48$	−3.76366	+	5.81678i	−0.543237	+	0.839579i
$49$	1.76758			0.252512
$50$	1.06662	+	2.92766i	0.150843	+	0.414034i
$51$	2.09889	−	4.95046i	0.293904	−	0.693203i
$52$	−5.96621	−	7.10122i	−0.827364	−	0.984762i
$53$	0.427900			0.0587766			0.0293883	−	0.999568i	$-0.490644\pi$
$53$	0.427900			0.0587766			0.0293883	+	0.999568i	$0.490644\pi$
$54$	−5.53837	+	4.82974i	−0.753677	+	0.657245i
$55$			4.86757i			0.656344i
$56$	3.22968	−	5.60611i	0.431584	−	0.749148i
$57$	−12.2893	−	5.21039i	−1.62775	−	0.690133i
$58$	−4.12968	−	11.3352i	−0.542254	−	1.48838i
$59$			9.10118i			1.18487i	0.805617	+	0.592436i	$0.201834\pi$
$59$			9.10118i			1.18487i	−0.805617	+	0.592436i	$0.798166\pi$
$60$	5.53825	−	1.69955i	0.714985	−	0.219410i
$61$		−	9.06577i		−	1.16075i	−0.814348	−	0.580376i	$-0.802905\pi$
$61$		−	9.06577i		−	1.16075i	0.814348	−	0.580376i	$-0.197095\pi$
$62$	−10.4757	+	3.81655i	−1.33041	+	0.484702i
$63$	4.93235	−	4.77113i	0.621418	−	0.601106i
$64$	4.01300	+	6.92068i	0.501624	+	0.865085i
$65$			7.75536i			0.961933i
$66$	−7.12008	−	0.367917i	−0.876421	−	0.0452874i
$67$	−8.29515			−1.01341			−0.506707	−	0.862118i	$-0.669137\pi$
$67$	−8.29515			−1.01341			−0.506707	+	0.862118i	$0.669137\pi$
$68$	−3.99395	−	4.75376i	−0.484337	−	0.576478i
$69$	1.59465	+	0.676097i	0.191973	+	0.0813925i
$70$	−5.08308	+	1.85189i	−0.607544	+	0.221343i
$71$	4.33432			0.514390			0.257195	−	0.966360i	$-0.417202\pi$
$71$	4.33432			0.514390			0.257195	+	0.966360i	$0.417202\pi$
$72$	2.06741	+	8.22957i	0.243647	+	0.969864i
$73$	6.91010			0.808766			0.404383	−	0.914590i	$-0.367486\pi$
$73$	6.91010			0.808766			0.404383	+	0.914590i	$0.367486\pi$
$74$	−5.28370	+	1.92498i	−0.614218	+	0.223775i
$75$	3.51345	+	1.48963i	0.405698	+	0.172008i
$76$	−11.8010	+	9.91477i	−1.35366	+	1.13730i
$77$	6.65793			0.758742
$78$	−11.3442	−	0.586191i	−1.28448	−	0.0663730i
$79$		−	6.46025i		−	0.726835i	−0.931626	−	0.363418i	$-0.881610\pi$
$79$		−	6.46025i		−	0.726835i	0.931626	−	0.363418i	$-0.118390\pi$
$80$	1.15335	−	6.58918i	0.128949	−	0.736693i
$81$	−0.298990	+	8.99503i	−0.0332212	+	0.999448i
$82$	6.66080	−	2.42669i	0.735563	−	0.267983i
$83$			12.7870i			1.40355i	0.712396	+	0.701777i	$0.247610\pi$
$83$			12.7870i			1.40355i	−0.712396	+	0.701777i	$0.752390\pi$
$84$	−2.32466	−	7.57529i	−0.253641	−	0.826532i
$85$			5.19165i			0.563114i
$86$	−3.69230	−	10.1346i	−0.398150	−	1.09285i
$87$	−13.6032	−	5.76747i	−1.45842	−	0.618338i
$88$	−4.10957	+	7.13344i	−0.438082	+	0.760427i
$89$		−	4.52095i		−	0.479220i	−0.970869	−	0.239610i	$-0.922980\pi$
$89$		−	4.52095i		−	0.479220i	0.970869	−	0.239610i	$-0.0770195\pi$
$90$	3.10295	−	6.38065i	0.327080	−	0.672579i
$91$	10.6079			1.11201
$92$	1.53128	−	1.28653i	0.159647	−	0.134130i
$93$	−5.33016	+	12.5717i	−0.552712	+	1.30363i
$94$	2.23543	+	6.13582i	0.230567	+	0.632861i
$95$	12.8880			1.32228
$96$	9.55119	+	2.18512i	0.974814	+	0.223018i
$97$	−8.58440			−0.871613			−0.435807	−	0.900040i	$-0.643537\pi$
$97$	−8.58440			−0.871613			−0.435807	+	0.900040i	$0.643537\pi$
$98$	−0.855696	−	2.34872i	−0.0864383	−	0.237256i
$99$	−6.27612	+	6.07097i	−0.630774	+	0.610155i
$100$	3.37385	−	2.83459i	0.337385	−	0.283459i
$101$	19.6859			1.95882			0.979412	−	0.201874i	$-0.0647030\pi$
$101$	19.6859			1.95882			0.979412	+	0.201874i	$0.0647030\pi$
$102$	−7.59413	−	0.392413i	−0.751931	−	0.0388546i
$103$		−	2.89731i		−	0.285481i	−0.989760	−	0.142740i	$-0.954409\pi$
$103$		−	2.89731i		−	0.285481i	0.989760	−	0.142740i	$-0.0455914\pi$
$104$	−6.54765	+	11.3655i	−0.642050	+	1.11448i
$105$	−2.58633	+	6.10014i	−0.252400	+	0.595313i
$106$	−0.207149	−	0.568583i	−0.0201201	−	0.0552257i
$107$			2.73473i			0.264376i	0.991225	+	0.132188i	$0.0422003\pi$
$107$			2.73473i			0.264376i	−0.991225	+	0.132188i	$0.957800\pi$
$108$	9.09880	+	5.02115i	0.875532	+	0.483160i
$109$			18.5012i			1.77210i	0.463592	+	0.886049i	$0.346560\pi$
$109$			18.5012i			1.77210i	−0.463592	+	0.886049i	$0.653440\pi$
$110$	6.46791	−	2.35642i	0.616691	−	0.224676i
$111$	−2.68841	+	6.34090i	−0.255173	+	0.601852i
$112$	−9.01277	−	1.57757i	−0.851626	−	0.149066i
$113$			3.69006i			0.347131i	0.984822	+	0.173566i	$0.0555289\pi$
$113$			3.69006i			0.347131i	−0.984822	+	0.173566i	$0.944471\pi$
$114$	−0.974144	+	18.8520i	−0.0912370	+	1.76565i
$115$	−1.67234			−0.155946
$116$	−13.0627	+	10.9748i	−1.21284	+	1.01899i
$117$	−9.99954	+	9.67269i	−0.924458	+	0.894240i
$118$	12.0934	−	4.40593i	1.11329	−	0.405599i
$119$	7.10121			0.650967
$120$	−4.93941	−	6.53632i	−0.450904	−	0.596682i
$121$	2.52819			0.229835
$122$	−12.0464	+	4.38879i	−1.09063	+	0.397342i
$123$	3.38910	−	7.99354i	0.305585	−	0.720753i
$124$	10.1427	+	12.0722i	0.910839	+	1.08412i
$125$	−12.0463			−1.07746
$126$	−8.72753	−	4.24426i	−0.777510	−	0.378109i
$127$			3.49738i			0.310342i	0.987888	+	0.155171i	$0.0495929\pi$
$127$			3.49738i			0.310342i	−0.987888	+	0.155171i	$0.950407\pi$
$128$	7.25332	−	8.68271i	0.641109	−	0.767450i
$129$	−12.1624	−	5.15663i	−1.07084	−	0.454016i
$130$	10.3051	−	3.75441i	0.903819	−	0.329283i
$131$		−	2.59666i		−	0.226871i	−0.993545	−	0.113436i	$-0.963814\pi$
$131$		−	2.59666i		−	0.226871i	0.993545	−	0.113436i	$-0.0361856\pi$
$132$	2.95799	+	9.63909i	0.257460	+	0.838975i
$133$		−	17.6284i		−	1.52858i
$134$	4.01573	+	11.0224i	0.346906	+	0.952189i
$135$	−3.12434	−	8.10863i	−0.268900	−	0.697880i
$136$	−4.38318	+	7.60838i	−0.375855	+	0.652413i
$137$		−	18.1669i		−	1.55210i	−0.630668	−	0.776052i	$-0.717219\pi$
$137$		−	18.1669i		−	1.55210i	0.630668	−	0.776052i	$-0.282781\pi$
$138$	0.126404	−	2.44623i	0.0107602	−	0.208237i
$139$	−4.65828			−0.395110			−0.197555	−	0.980292i	$-0.563300\pi$
$139$	−4.65828			−0.395110			−0.197555	+	0.980292i	$0.563300\pi$
$140$	4.92149	+	5.85776i	0.415942	+	0.495071i
$141$	7.36352	+	3.12198i	0.620120	+	0.262918i
$142$	−2.09827	−	5.75934i	−0.176083	−	0.483313i
$143$	−13.4979			−1.12875
$144$	9.93440	−	6.73110i	0.827867	−	0.560925i
$145$	14.2660			1.18472
$146$	−3.34521	−	9.18196i	−0.276852	−	0.759905i
$147$	−2.81867	−	1.19506i	−0.232480	−	0.0985666i
$148$	5.11573	+	6.08896i	0.420511	+	0.500509i
$149$	14.7435			1.20784			0.603919	−	0.797045i	$-0.293605\pi$
$149$	14.7435			1.20784			0.603919	+	0.797045i	$0.293605\pi$
$150$	0.278504	−	5.38972i	0.0227398	−	0.440069i
$151$			8.88943i			0.723412i	0.932292	+	0.361706i	$0.117806\pi$
$151$			8.88943i			0.723412i	−0.932292	+	0.361706i	$0.882194\pi$
$152$	18.8874	+	10.8810i	1.53197	+	0.882568i
$153$	−6.69398	+	6.47517i	−0.541176	+	0.523486i
$154$	−3.22314	−	8.84689i	−0.259728	−	0.712903i
$155$		−	13.1843i		−	1.05899i
$156$	4.71287	+	15.3577i	0.377332	+	1.22960i
$157$			8.04774i			0.642279i	0.947032	+	0.321140i	$0.104066\pi$
$157$			8.04774i			0.642279i	−0.947032	+	0.321140i	$0.895934\pi$
$158$	−8.58422	+	3.12744i	−0.682924	+	0.248806i
$159$	−0.682349	−	0.289302i	−0.0541138	−	0.0229431i
$160$	−9.31388	+	1.65731i	−0.736327	+	0.131022i
$161$			2.28745i			0.180276i
$162$	12.0971	−	3.95725i	0.950439	−	0.310911i
$163$	−8.22815			−0.644479			−0.322239	−	0.946658i	$-0.604436\pi$
$163$	−8.22815			−0.644479			−0.322239	+	0.946658i	$0.604436\pi$
$164$	−6.44906	−	7.67593i	−0.503587	−	0.599389i
$165$	3.29095	−	7.76205i	0.256200	−	0.604275i
$166$	16.9910	−	6.19025i	1.31876	−	0.480457i
$167$	17.1392			1.32627			0.663134	−	0.748501i	$-0.269226\pi$
$167$	17.1392			1.32627			0.663134	+	0.748501i	$0.269226\pi$
$168$	−8.94047	+	6.75618i	−0.689772	+	0.521251i
$169$	−8.50574			−0.654288
$170$	6.89854	−	2.51331i	0.529094	−	0.192762i
$171$	16.0743	+	16.6175i	1.22923	+	1.27077i
$172$	−11.6792	+	9.81246i	−0.890530	+	0.748193i
$173$	−20.0458			−1.52405			−0.762027	−	0.647546i	$-0.775796\pi$
$173$	−20.0458			−1.52405			−0.762027	+	0.647546i	$0.775796\pi$
$174$	−1.07830	+	20.8676i	−0.0817455	+	1.58197i
$175$			5.03989i			0.380980i
$176$	11.4682	+	2.00736i	0.864448	+	0.151310i
$177$	6.15328	−	14.5131i	0.462509	−	1.09088i
$178$	−6.00732	+	2.18861i	−0.450268	+	0.164044i
$179$			13.0220i			0.973309i	0.873594	+	0.486655i	$0.161783\pi$
$179$			13.0220i			0.973309i	−0.873594	+	0.486655i	$0.838217\pi$
$180$	−9.98060	−	1.03422i	−0.743910	−	0.0770862i
$181$		−	21.4856i		−	1.59701i	−0.601987	−	0.798506i	$-0.705624\pi$
$181$		−	21.4856i		−	1.59701i	0.601987	−	0.798506i	$-0.294376\pi$
$182$	−5.13533	−	14.0955i	−0.380656	−	1.04483i
$183$	−6.12934	+	14.4567i	−0.453094	+	1.06867i
$184$	−2.45082	−	1.41191i	−0.180677	−	0.104088i
$185$		−	6.64984i		−	0.488906i
$186$	19.2854	+	0.996536i	1.41407	+	0.0730695i
$187$	−9.03586			−0.660767
$188$	7.07094	−	5.94076i	0.515701	−	0.433275i
$189$	−11.0911	+	4.27351i	−0.806759	+	0.310852i
$190$	−6.23916	−	17.1253i	−0.452636	−	1.24240i
$191$	−22.2870			−1.61263			−0.806314	−	0.591488i	$-0.798541\pi$
$191$	−22.2870			−1.61263			−0.806314	+	0.591488i	$0.798541\pi$
$192$	−1.72025	−	13.7492i	−0.124149	−	0.992264i
$193$	5.72840			0.412339			0.206170	−	0.978516i	$-0.433900\pi$
$193$	5.72840			0.412339			0.206170	+	0.978516i	$0.433900\pi$
$194$	4.15575	+	11.4067i	0.298366	+	0.818955i
$195$	5.24337	−	12.3670i	0.375486	−	0.885622i
$196$	−2.70667	+	2.27405i	−0.193334	+	0.162432i
$197$	−12.4216			−0.884999			−0.442499	−	0.896769i	$-0.645908\pi$
$197$	−12.4216			−0.884999			−0.442499	+	0.896769i	$0.645908\pi$
$198$	11.1053	+	5.40056i	0.789216	+	0.383801i
$199$		−	14.2662i		−	1.01130i	−0.862738	−	0.505650i	$-0.831253\pi$
$199$		−	14.2662i		−	1.01130i	0.862738	−	0.505650i	$-0.168747\pi$
$200$	−5.39983	−	3.11084i	−0.381826	−	0.219970i
$201$	13.2278	+	5.60832i	0.933019	+	0.395581i
$202$	−9.53006	−	26.1582i	−0.670533	−	1.84048i
$203$		−	19.5132i		−	1.36956i
$204$	3.15493	+	10.2809i	0.220889	+	0.719804i
$205$			8.38300i			0.585494i
$206$	−3.84988	+	1.40260i	−0.268234	+	0.0977241i
$207$	−2.08579	−	2.15627i	−0.144972	−	0.149871i
$208$	18.2719	+	3.19826i	1.26693	+	0.221760i
$209$			22.4311i			1.55159i
$210$	9.35777	+	0.483546i	0.645747	+	0.0333678i
$211$	−25.3506			−1.74521			−0.872604	−	0.488428i	$-0.837571\pi$
$211$	−25.3506			−1.74521			−0.872604	+	0.488428i	$0.837571\pi$
$212$	−0.655237	+	0.550508i	−0.0450019	+	0.0378090i
$213$	−6.91171	−	2.93042i	−0.473582	−	0.200789i
$214$	3.63384	−	1.32390i	0.248404	−	0.0904996i
$215$	12.7550			0.869885
$216$	2.26720	−	14.5210i	0.154263	−	0.988030i
$217$	−18.0336			−1.22420
$218$	24.5840	−	8.95655i	1.66504	−	0.606614i
$219$	−11.0192	−	4.67189i	−0.744605	−	0.315697i
$220$	−6.26230	−	7.45364i	−0.422204	−	0.502524i
$221$	−14.3966			−0.968417
$222$	9.72710	+	0.502630i	0.652840	+	0.0337343i
$223$		−	4.13720i		−	0.277048i	−0.990359	−	0.138524i	$-0.955764\pi$
$223$		−	4.13720i		−	0.277048i	0.990359	−	0.138524i	$-0.0442358\pi$
$224$	2.26689	+	12.7396i	0.151463	+	0.851203i
$225$	−4.59557	−	4.75086i	−0.306371	−	0.316724i
$226$	4.90325	−	1.78638i	0.326160	−	0.118828i
$227$		−	11.1121i		−	0.737536i	−0.929522	−	0.368768i	$-0.879780\pi$
$227$		−	11.1121i		−	0.737536i	0.929522	−	0.368768i	$-0.120220\pi$
$228$	25.5217	−	7.83195i	1.69022	−	0.518684i
$229$			8.33587i			0.550850i	0.961323	+	0.275425i	$0.0888185\pi$
$229$			8.33587i			0.550850i	−0.961323	+	0.275425i	$0.911182\pi$
$230$	0.809588	+	2.22216i	0.0533827	+	0.146525i
$231$	−10.6170	−	4.50141i	−0.698550	−	0.296171i
$232$	20.9068	+	12.0444i	1.37260	+	0.790753i
$233$		−	1.94318i		−	0.127302i	−0.997972	−	0.0636510i	$-0.979726\pi$
$233$		−	1.94318i		−	0.127302i	0.997972	−	0.0636510i	$-0.0202744\pi$
$234$	17.6936	+	8.60454i	1.15667	+	0.562496i
$235$	−7.72228			−0.503746
$236$	−11.7090	−	13.9365i	−0.762189	−	0.907188i
$237$	−4.36776	+	10.3018i	−0.283716	+	0.669175i
$238$	−3.43773	−	9.43591i	−0.222835	−	0.611639i
$239$	−16.9988			−1.09956			−0.549781	−	0.835309i	$-0.685289\pi$
$239$	−16.9988			−1.09956			−0.549781	+	0.835309i	$0.685289\pi$
$240$	−6.29411	+	9.72763i	−0.406283	+	0.627916i
$241$	4.17570			0.268981			0.134490	−	0.990915i	$-0.457060\pi$
$241$	4.17570			0.268981			0.134490	+	0.990915i	$0.457060\pi$
$242$	−1.22391	−	3.35939i	−0.0786758	−	0.215950i
$243$	6.55830	−	14.1417i	0.420715	−	0.907193i
$244$	11.6634	+	13.8823i	0.746674	+	0.888721i
$245$	2.95600			0.188852
$246$	−12.2623	−	0.633632i	−0.781815	−	0.0403989i
$247$			35.7387i			2.27400i
$248$	11.1311	−	19.3215i	0.706828	−	1.22692i
$249$	8.64524	−	20.3907i	0.547870	−	1.29221i
$250$	5.83169	+	16.0069i	0.368829	+	1.01236i
$251$		−	2.42594i		−	0.153124i	−0.997065	−	0.0765619i	$-0.975606\pi$
$251$		−	2.42594i		−	0.153124i	0.997065	−	0.0765619i	$-0.0243943\pi$
$252$	−1.41462	+	13.6516i	−0.0891126	+	0.859969i
$253$		−	2.91064i		−	0.182990i
$254$	4.64723	−	1.69310i	0.291593	−	0.106235i
$255$	3.51006	−	8.27885i	0.219809	−	0.518442i
$256$	−15.0487	−	5.43468i	−0.940546	−	0.339668i
$257$			6.11395i			0.381378i	0.981651	+	0.190689i	$0.0610722\pi$
$257$			6.11395i			0.381378i	−0.981651	+	0.190689i	$0.938928\pi$
$258$	−0.964092	+	18.6575i	−0.0600217	+	1.16156i
$259$	−9.09574			−0.565182
$260$	−9.97752	−	11.8757i	−0.618780	−	0.736497i
$261$	17.7929	+	18.3941i	1.10135	+	1.13857i
$262$	−3.45038	+	1.25706i	−0.213165	+	0.0776613i
$263$	6.15397			0.379470			0.189735	−	0.981835i	$-0.439237\pi$
$263$	6.15397			0.379470			0.189735	+	0.981835i	$0.439237\pi$
$264$	11.3762	−	8.59683i	0.700157	−	0.529098i
$265$	0.715594			0.0439586
$266$	−23.4242	+	8.53400i	−1.43623	+	0.523253i
$267$	−3.05660	+	7.20931i	−0.187061	+	0.441203i
$268$	12.7022	−	10.6720i	0.775913	−	0.651896i
$269$	−20.4694			−1.24804			−0.624021	−	0.781407i	$-0.714502\pi$
$269$	−20.4694			−1.24804			−0.624021	+	0.781407i	$0.714502\pi$
$270$	−9.26204	+	8.07697i	−0.563670	+	0.491549i
$271$			5.78075i			0.351156i	0.984466	+	0.175578i	$0.0561794\pi$
$271$			5.78075i			0.351156i	−0.984466	+	0.175578i	$0.943821\pi$
$272$	12.2317	+	2.14101i	0.741658	+	0.129818i
$273$	−16.9158	−	7.17195i	−1.02379	−	0.434066i
$274$	−24.1397	+	8.79470i	−1.45834	+	0.531307i
$275$		−	6.41295i		−	0.386715i
$276$	−3.31168	+	1.01627i	−0.199339	+	0.0611721i
$277$		−	6.92990i		−	0.416377i	−0.978089	−	0.208189i	$-0.933243\pi$
$277$		−	6.92990i		−	0.416377i	0.978089	−	0.208189i	$-0.0667568\pi$
$278$	2.25510	+	6.18981i	0.135252	+	0.371240i
$279$	16.9994	−	16.4438i	1.01773	−	0.984462i
$280$	5.40112	−	9.37533i	0.322779	−	0.560283i
$281$		−	6.80878i		−	0.406178i	−0.979160	−	0.203089i	$-0.934902\pi$
$281$		−	6.80878i		−	0.406178i	0.979160	−	0.203089i	$-0.0650980\pi$
$282$	0.583691	−	11.2958i	0.0347583	−	0.672656i
$283$	23.2198			1.38027			0.690136	−	0.723679i	$-0.257551\pi$
$283$	23.2198			1.38027			0.690136	+	0.723679i	$0.257551\pi$
$284$	−6.63708	+	5.57625i	−0.393838	+	0.330890i
$285$	−20.5518	−	8.71355i	−1.21738	−	0.516146i
$286$	6.53439	+	17.9356i	0.386387	+	1.06056i
$287$	11.4664			0.676839
$288$	−13.7534	−	9.94202i	−0.810427	−	0.585839i
$289$	7.36254			0.433091
$290$	−6.90623	−	18.9563i	−0.405548	−	1.11315i
$291$	13.6891	+	5.80388i	0.802467	+	0.340230i
$292$	−10.5813	+	8.89007i	−0.619225	+	0.520252i
$293$	4.43092			0.258857			0.129429	−	0.991589i	$-0.458686\pi$
$293$	4.43092			0.258857			0.129429	+	0.991589i	$0.458686\pi$
$294$	−0.223430	+	4.32391i	−0.0130307	+	0.252175i
$295$			15.2203i			0.886158i
$296$	5.61430	−	9.74535i	0.326324	−	0.566437i
$297$	14.1127	−	5.43778i	0.818904	−	0.315532i
$298$	−7.13743	−	19.5909i	−0.413460	−	1.13487i
$299$		−	4.63743i		−	0.268189i
$300$	−7.29655	+	2.23912i	−0.421267	+	0.129276i
$301$		−	17.4465i		−	1.00560i
$302$	11.8121	−	4.30342i	0.679707	−	0.247634i
$303$	−31.3921	−	13.3096i	−1.80343	−	0.764616i
$304$	5.31495	−	30.3647i	0.304833	−	1.74153i
$305$		−	15.1610i		−	0.868119i
$306$	11.8446	+	5.76012i	0.677112	+	0.329284i
$307$	24.5271			1.39983			0.699917	−	0.714224i	$-0.253220\pi$
$307$	24.5271			1.39983			0.699917	+	0.714224i	$0.253220\pi$
$308$	−10.1952	+	8.56565i	−0.580925	+	0.488073i
$309$	−1.95886	+	4.62019i	−0.111436	+	0.262833i
$310$	−17.5189	+	6.38257i	−0.995007	+	0.362505i
$311$	6.45799			0.366199			0.183100	−	0.983094i	$-0.441387\pi$
$311$	6.45799			0.366199			0.183100	+	0.983094i	$0.441387\pi$
$312$	18.1253	−	13.6971i	1.02615	−	0.775444i
$313$	−1.06905			−0.0604265			−0.0302132	−	0.999543i	$-0.509619\pi$
$313$	−1.06905			−0.0604265			−0.0302132	+	0.999543i	$0.509619\pi$
$314$	10.6936	−	3.89595i	0.603476	−	0.219861i
$315$	8.24857	−	7.97895i	0.464754	−	0.449563i
$316$	8.31133	+	9.89248i	0.467549	+	0.556496i
$317$	5.60014			0.314535			0.157268	−	0.987556i	$-0.449732\pi$
$317$	5.60014			0.314535			0.157268	+	0.987556i	$0.449732\pi$
$318$	−0.0540884	+	1.04674i	−0.00303313	+	0.0586983i
$319$			24.8293i			1.39018i
$320$	6.71109	+	11.5737i	0.375161	+	0.646991i
$321$	1.84894	−	4.36092i	0.103198	−	0.243403i
$322$	3.03950	−	1.10737i	0.169385	−	0.0617111i
$323$			23.9245i			1.33120i
$324$	−11.1146	−	14.1586i	−0.617476	−	0.786590i
$325$		−	10.2176i		−	0.566768i
$326$	3.98329	+	10.9334i	0.220614	+	0.605543i
$327$	12.5086	−	29.5029i	0.691729	−	1.63151i
$328$	−7.07756	+	12.2853i	−0.390793	+	0.678342i
$329$			10.5626i			0.582337i
$330$	−11.9072	−	0.615282i	−0.655469	−	0.0338702i
$331$	−3.95776			−0.217538			−0.108769	−	0.994067i	$-0.534691\pi$
$331$	−3.95776			−0.217538			−0.108769	+	0.994067i	$0.534691\pi$
$332$	−16.4509	−	19.5805i	−0.902860	−	1.07462i
$333$	8.57413	−	8.29386i	0.469859	−	0.454501i
$334$	−8.29715	−	22.7741i	−0.454000	−	1.24614i
$335$	−13.8723			−0.757925
$336$	13.3056	+	8.60916i	0.725879	+	0.469668i
$337$	−15.1916			−0.827540			−0.413770	−	0.910381i	$-0.635788\pi$
$337$	−15.1916			−0.827540			−0.413770	+	0.910381i	$0.635788\pi$
$338$	4.11767	+	11.3022i	0.223972	+	0.614759i
$339$	2.49483	−	5.88433i	0.135501	−	0.319593i
$340$	−6.67924	−	7.94990i	−0.362232	−	0.431144i
$341$	22.9467			1.24263
$342$	14.2992	−	29.4037i	0.773213	−	1.58997i
$343$		−	20.0554i		−	1.08289i
$344$	18.6925	+	10.7687i	1.00783	+	0.580612i
$345$	2.66679	+	1.13066i	0.143575	+	0.0608729i
$346$	9.70427	+	26.6363i	0.521705	+	1.43198i
$347$		−	17.8879i		−	0.960272i	−0.877194	−	0.480136i	$-0.840587\pi$
$347$		−	17.8879i		−	0.960272i	0.877194	−	0.480136i	$-0.159413\pi$
$348$	28.2504	−	8.66932i	1.51438	−	0.464724i
$349$		−	6.58198i		−	0.352325i	−0.984361	−	0.176163i	$-0.943632\pi$
$349$		−	6.58198i		−	0.352325i	0.984361	−	0.176163i	$-0.0563685\pi$
$350$	6.69688	−	2.43984i	0.357963	−	0.130415i
$351$	22.4854	−	8.66384i	1.20018	−	0.462442i
$352$	−2.88448	−	16.2104i	−0.153743	−	0.864018i
$353$		−	19.9404i		−	1.06132i	−0.847584	−	0.530661i	$-0.821944\pi$
$353$		−	19.9404i		−	1.06132i	0.847584	−	0.530661i	$-0.178056\pi$
$354$	−22.2635	−	1.15043i	−1.18329	−	0.0611445i
$355$	7.24846			0.384708
$356$	5.81635	+	6.92286i	0.308266	+	0.366911i
$357$	−11.3239	−	4.80111i	−0.599325	−	0.254102i
$358$	17.3033	−	6.30401i	0.914507	−	0.333177i
$359$	−20.8705			−1.10150			−0.550752	−	0.834669i	$-0.685659\pi$
$359$	−20.8705			−1.10150			−0.550752	+	0.834669i	$0.685659\pi$
$360$	3.45741	+	13.7626i	0.182222	+	0.725355i
$361$	40.3914			2.12586
$362$	−28.5495	+	10.4013i	−1.50053	+	0.546680i
$363$	−4.03156	−	1.70930i	−0.211602	−	0.0897150i
$364$	−16.2437	+	13.6474i	−0.851400	+	0.715317i
$365$	11.5560			0.604870
$366$	22.1769	+	1.14595i	1.15921	+	0.0598999i
$367$			28.7454i			1.50050i	0.661155	+	0.750249i	$0.270066\pi$
$367$			28.7454i			1.50050i	−0.661155	+	0.750249i	$0.729934\pi$
$368$	−0.689663	+	3.94010i	−0.0359512	+	0.205392i
$369$	−10.8088	+	10.4555i	−0.562684	+	0.544292i
$370$	−8.83614	+	3.21922i	−0.459369	+	0.167359i
$371$		−	0.978799i		−	0.0508167i
$372$	−8.01197	−	26.1083i	−0.415401	−	1.35365i
$373$			2.12022i			0.109781i	0.998492	+	0.0548903i	$0.0174809\pi$
$373$			2.12022i			0.109781i	−0.998492	+	0.0548903i	$0.982519\pi$
$374$	4.37431	+	12.0066i	0.226190	+	0.620848i
$375$	19.2096	+	8.14449i	0.991981	+	0.420579i
$376$	−11.3170	−	6.51973i	−0.583630	−	0.336229i
$377$			39.5598i			2.03743i
$378$	11.0478	+	12.6687i	0.568237	+	0.651610i
$379$	−17.5425			−0.901099			−0.450550	−	0.892751i	$-0.648772\pi$
$379$	−17.5425			−0.901099			−0.450550	+	0.892751i	$0.648772\pi$
$380$	−19.7352	+	16.5809i	−1.01240	+	0.850580i
$381$	2.36457	−	5.57708i	0.121141	−	0.285723i
$382$	10.7892	+	29.6143i	0.552025	+	1.51520i
$383$	−13.6105			−0.695464			−0.347732	−	0.937594i	$-0.613048\pi$
$383$	−13.6105			−0.695464			−0.347732	+	0.937594i	$0.613048\pi$
$384$	−17.4368	+	8.94189i	−0.889819	+	0.456314i
$385$	11.1343			0.567458
$386$	−2.77315	−	7.61175i	−0.141150	−	0.387428i
$387$	15.9084	+	16.4460i	0.808670	+	0.835996i
$388$	13.1452	−	11.0441i	0.667344	−	0.560680i
$389$	9.47011			0.480154			0.240077	−	0.970754i	$-0.422827\pi$
$389$	9.47011			0.480154			0.240077	+	0.970754i	$0.422827\pi$
$390$	−18.9714	−	0.980310i	−0.960652	−	0.0496399i
$391$		−	3.10443i		−	0.156998i
$392$	4.33202	+	2.49567i	0.218800	+	0.126051i
$393$	−1.75559	+	4.14075i	−0.0885580	+	0.208873i
$394$	6.01334	+	16.5054i	0.302948	+	0.831532i
$395$		−	10.8037i		−	0.543595i
$396$	1.80002	−	17.3708i	0.0904542	−	0.872916i
$397$		−	22.0808i		−	1.10821i	−0.832448	−	0.554103i	$-0.813061\pi$
$397$		−	22.0808i		−	1.10821i	0.832448	−	0.554103i	$-0.186939\pi$
$398$	−18.9565	+	6.90632i	−0.950204	+	0.346183i
$399$	−11.9185	+	28.1110i	−0.596671	+	1.40731i
$400$	−1.51952	+	8.68114i	−0.0759761	+	0.434057i
$401$			15.5379i			0.775927i	0.921675	+	0.387963i	$0.126821\pi$
$401$			15.5379i			0.775927i	−0.921675	+	0.387963i	$0.873179\pi$
$402$	1.04854	−	20.2918i	0.0522965	−	1.01206i
$403$	36.5602			1.82119
$404$	−30.1448	+	25.3266i	−1.49976	+	1.26005i
$405$	−0.500013	+	15.0427i	−0.0248459	+	0.747480i
$406$	−25.9286	+	9.44643i	−1.28682	+	0.468818i
$407$	11.5738			0.573691
$408$	12.1336	−	9.16920i	0.600704	−	0.453943i
$409$	−27.3129			−1.35054			−0.675268	−	0.737572i	$-0.735972\pi$
$409$	−27.3129			−1.35054			−0.675268	+	0.737572i	$0.735972\pi$
$410$	11.1391	−	4.05826i	0.550122	−	0.200423i
$411$	−12.2826	+	28.9698i	−0.605856	+	1.42897i
$412$	3.72749	+	4.43661i	0.183640	+	0.218576i
$413$	20.8185			1.02441
$414$	−1.85546	+	3.81540i	−0.0911907	+	0.187517i
$415$			21.3842i			1.04971i
$416$	−4.59576	−	25.8276i	−0.225326	−	1.26630i
$417$	7.42831	+	3.14945i	0.363766	+	0.154229i
$418$	29.8058	−	10.8590i	1.45785	−	0.531131i
$419$			26.1832i			1.27913i	0.768736	+	0.639566i	$0.220886\pi$
$419$			26.1832i			1.27913i	−0.768736	+	0.639566i	$0.779114\pi$
$420$	−3.88762	−	12.6685i	−0.189696	−	0.618157i
$421$		−	13.1612i		−	0.641436i	−0.947175	−	0.320718i	$-0.896076\pi$
$421$		−	13.1612i		−	0.641436i	0.947175	−	0.320718i	$-0.103924\pi$
$422$	12.2724	+	33.6853i	0.597409	+	1.63977i
$423$	−9.63144	−	9.95690i	−0.468296	−	0.484121i
$424$	1.04870	+	0.604158i	0.0509296	+	0.0293405i
$425$		−	6.83992i		−	0.331785i
$426$	−0.547877	+	10.6027i	−0.0265447	+	0.513704i
$427$	−20.7375			−1.00356
$428$	−3.51832	−	4.18765i	−0.170064	−	0.202417i
$429$	21.5243	+	9.12587i	1.03920	+	0.440601i
$430$	−6.17477	−	16.9486i	−0.297774	−	0.817332i
$431$	−9.94800			−0.479178			−0.239589	−	0.970874i	$-0.577013\pi$
$431$	−9.94800			−0.479178			−0.239589	+	0.970874i	$0.577013\pi$
$432$	−20.3927	+	4.01710i	−0.981145	+	0.193273i
$433$	−2.05253			−0.0986383			−0.0493192	−	0.998783i	$-0.515705\pi$
$433$	−2.05253			−0.0986383			−0.0493192	+	0.998783i	$0.515705\pi$
$434$	8.73016	+	23.9626i	0.419061	+	1.15024i
$435$	−22.7492	−	9.64517i	−1.09074	−	0.462451i
$436$	−23.8025	−	28.3307i	−1.13993	−	1.35679i
$437$	−7.70658			−0.368656
$438$	−0.873466	+	16.9037i	−0.0417358	+	0.807688i
$439$		−	32.5669i		−	1.55433i	−0.629296	−	0.777166i	$-0.716657\pi$
$439$		−	32.5669i		−	1.55433i	0.629296	−	0.777166i	$-0.283343\pi$
$440$	−6.87260	+	11.9295i	−0.327638	+	0.568718i
$441$	3.68680	+	3.81138i	0.175562	+	0.181494i
$442$	6.96945	+	19.1298i	0.331503	+	0.909911i
$443$		−	16.4142i		−	0.779861i	−0.920844	−	0.389931i	$-0.872499\pi$
$443$		−	16.4142i		−	0.779861i	0.920844	−	0.389931i	$-0.127501\pi$
$444$	−4.04106	−	13.1685i	−0.191780	−	0.624947i
$445$		−	7.56056i		−	0.358405i
$446$	−5.49741	+	2.00284i	−0.260310	+	0.0948373i
$447$	−23.5107	−	9.96807i	−1.11202	−	0.471473i
$448$	15.8307	−	9.17952i	0.747930	−	0.433691i
$449$		−	30.6773i		−	1.44775i	−0.689929	−	0.723877i	$-0.742358\pi$
$449$		−	30.6773i		−	1.44775i	0.689929	−	0.723877i	$-0.257642\pi$
$450$	−4.08809	+	8.40640i	−0.192714	+	0.396281i
$451$	−14.5903			−0.687029
$452$	−4.74738	−	5.65052i	−0.223298	−	0.265778i
$453$	6.01012	−	14.1755i	0.282380	−	0.666023i
$454$	−14.7655	+	5.37942i	−0.692978	+	0.252469i
$455$	17.7400			0.831663
$456$	−22.7621	−	30.1211i	−1.06593	−	1.41055i
$457$	−21.4345			−1.00266			−0.501331	−	0.865255i	$-0.667156\pi$
$457$	−21.4345			−1.00266			−0.501331	+	0.865255i	$0.667156\pi$
$458$	11.0765	−	4.03544i	0.517570	−	0.188564i
$459$	15.0524	−	5.79982i	0.702584	−	0.270712i
$460$	2.56083	−	2.15152i	0.119399	−	0.100315i
$461$	9.57418			0.445914			0.222957	−	0.974828i	$-0.428429\pi$
$461$	9.57418			0.445914			0.222957	+	0.974828i	$0.428429\pi$
$462$	−0.841591	+	16.2868i	−0.0391544	+	0.757731i
$463$			23.0254i			1.07008i	0.844826	+	0.535042i	$0.179704\pi$
$463$			23.0254i			1.07008i	−0.844826	+	0.535042i	$0.820296\pi$
$464$	5.88320	−	33.6112i	0.273121	−	1.56036i
$465$	−8.91383	+	21.0242i	−0.413369	+	0.974975i
$466$	−2.58205	+	0.940704i	−0.119611	+	0.0435773i
$467$			31.8460i			1.47366i	0.676080	+	0.736828i	$0.263677\pi$
$467$			31.8460i			1.47366i	−0.676080	+	0.736828i	$0.736323\pi$
$468$	2.86791	−	27.6764i	0.132569	−	1.27934i
$469$			18.9747i			0.876171i
$470$	3.73840	+	10.2612i	0.172439	+	0.473313i
$471$	5.44105	−	12.8333i	0.250710	−	0.591326i
$472$	−12.8501	+	22.3053i	−0.591473	+	1.02669i
$473$			22.1996i			1.02074i
$474$	15.8032	+	0.816603i	0.725867	+	0.0375078i
$475$	−16.9798			−0.779084
$476$	−10.8740	+	9.13595i	−0.498408	+	0.418745i
$477$	0.892508	+	0.922668i	0.0408652	+	0.0422461i
$478$	8.22921	+	22.5876i	0.376395	+	1.03313i
$479$	8.50882			0.388778			0.194389	−	0.980925i	$-0.437728\pi$
$479$	8.50882			0.388778			0.194389	+	0.980925i	$0.437728\pi$
$480$	15.9728	+	3.65426i	0.729057	+	0.166793i
$481$	18.4401			0.840798
$482$	−2.02148	−	5.54857i	−0.0920759	−	0.252730i
$483$	1.54654	−	3.64767i	0.0703698	−	0.165975i
$484$	−3.87137	+	3.25260i	−0.175972	+	0.147845i
$485$	−14.3560			−0.651874
$486$	−21.9661	−	1.86841i	−0.996402	−	0.0847527i
$487$			10.2419i			0.464104i	0.972703	+	0.232052i	$0.0745440\pi$
$487$			10.2419i			0.464104i	−0.972703	+	0.232052i	$0.925456\pi$
$488$	12.8001	−	22.2185i	0.579433	−	1.00579i
$489$	13.1210	+	5.56303i	0.593351	+	0.251569i
$490$	−1.43101	−	3.92786i	−0.0646466	−	0.177442i
$491$			32.3151i			1.45836i	0.684321	+	0.729181i	$0.260099\pi$
$491$			32.3151i			1.45836i	−0.684321	+	0.729181i	$0.739901\pi$
$492$	5.09429	+	16.6006i	0.229668	+	0.748412i
$493$			26.4824i			1.19271i
$494$	47.4887	−	17.3013i	2.13662	−	0.778422i
$495$	−10.4958	+	10.1527i	−0.471751	+	0.456331i
$496$	−31.0626	−	5.43711i	−1.39475	−	0.244134i
$497$		−	9.91454i		−	0.444728i
$498$	−31.2799	−	1.61633i	−1.40168	−	0.0724295i
$499$	−42.5250			−1.90368			−0.951841	−	0.306593i	$-0.900811\pi$
$499$	−42.5250			−1.90368			−0.951841	+	0.306593i	$0.900811\pi$
$500$	18.4464	−	15.4980i	0.824946	−	0.693092i
$501$	−27.3309	−	11.5877i	−1.22105	−	0.517702i
$502$	−3.22352	+	1.17441i	−0.143873	+	0.0524164i
$503$	−6.73586			−0.300337			−0.150168	−	0.988660i	$-0.547982\pi$
$503$	−6.73586			−0.300337			−0.150168	+	0.988660i	$0.547982\pi$
$504$	18.8247	−	4.72910i	0.838519	−	0.210651i
$505$	32.9216			1.46499
$506$	−3.86758	+	1.40905i	−0.171935	+	0.0626401i
$507$	13.5636	+	5.75070i	0.602382	+	0.255398i
$508$	−4.49950	−	5.35549i	−0.199633	−	0.237611i
$509$	−41.3469			−1.83267			−0.916334	−	0.400416i	$-0.868866\pi$
$509$	−41.3469			−1.83267			−0.916334	+	0.400416i	$0.868866\pi$
$510$	−12.7000	−	0.656247i	−0.562364	−	0.0290591i
$511$		−	15.8065i		−	0.699238i
$512$	0.0637002	+	22.6273i	0.00281518	+	0.999996i
$513$	−14.3978	−	37.3667i	−0.635677	−	1.64978i
$514$	8.12407	−	2.95980i	0.358337	−	0.130551i
$515$		−	4.84529i		−	0.213509i
$516$	25.2583	−	7.75113i	1.11194	−	0.341224i
$517$		−	13.4403i		−	0.591104i
$518$	4.40330	+	12.0862i	0.193470	+	0.531037i
$519$	31.9659	+	13.5529i	1.40315	+	0.594906i
$520$	−10.9499	+	19.0069i	−0.480185	+	0.833510i
$521$		−	24.8813i		−	1.09007i	−0.838413	−	0.545035i	$-0.816516\pi$
$521$		−	24.8813i		−	1.09007i	0.838413	−	0.545035i	$-0.183484\pi$
$522$	15.8280	−	32.5474i	0.692775	−	1.42456i
$523$	−6.99915			−0.306052			−0.153026	−	0.988222i	$-0.548902\pi$
$523$	−6.99915			−0.306052			−0.153026	+	0.988222i	$0.548902\pi$
$524$	3.34069	+	3.97623i	0.145939	+	0.173702i
$525$	3.40745	−	8.03683i	0.148713	−	0.350756i
$526$	−2.97917	−	8.17724i	−0.129898	−	0.356545i
$527$	24.4744			1.06612
$528$	−16.9305	−	10.9546i	−0.736807	−	0.476739i
$529$	1.00000			0.0434783
$530$	−0.346423	−	0.950864i	−0.0150477	−	0.0413029i
$531$	−19.6246	+	18.9831i	−0.851635	+	0.823797i
$532$	22.6795	+	26.9941i	0.983282	+	1.17034i
$533$	−23.2462			−1.00691
$534$	11.0593	+	0.571467i	0.478581	+	0.0247298i
$535$			4.57339i			0.197725i
$536$	−20.3299	−	11.7120i	−0.878117	−	0.505883i
$537$	8.80412	−	20.7655i	0.379926	−	0.896095i
$538$	9.90936	+	27.1993i	0.427223	+	1.17264i
$539$			5.14479i			0.221602i
$540$	15.2163	+	8.39706i	0.654804	+	0.361352i
$541$			0.299027i			0.0128562i	0.999979	+	0.00642808i	$0.00204614\pi$
$541$			0.299027i			0.0128562i	−0.999979	+	0.00642808i	$0.997954\pi$
$542$	7.68132	−	2.79849i	0.329941	−	0.120205i
$543$	−14.5263	+	34.2619i	−0.623385	+	1.47032i
$544$	−3.07653	−	17.2897i	−0.131905	−	0.741290i
$545$			30.9404i			1.32534i
$546$	−1.34088	+	25.9493i	−0.0573844	+	1.11053i
$547$	−22.3488			−0.955564			−0.477782	−	0.878478i	$-0.658559\pi$
$547$	−22.3488			−0.955564			−0.477782	+	0.878478i	$0.658559\pi$
$548$	23.3724	+	27.8187i	0.998417	+	1.18836i
$549$	19.5482	−	18.9093i	0.834298	−	0.807028i
$550$	−8.52137	+	3.10454i	−0.363352	+	0.132378i
$551$	65.7413			2.80067
$552$	2.95359	+	3.90849i	0.125713	+	0.166356i
$553$	−14.7775			−0.628403
$554$	−9.20827	+	3.35480i	−0.391222	+	0.142532i
$555$	−4.49594	+	10.6041i	−0.190842	+	0.450121i
$556$	7.13316	−	5.99304i	0.302513	−	0.254161i
$557$	−16.6755			−0.706562			−0.353281	−	0.935517i	$-0.614934\pi$
$557$	−16.6755			−0.706562			−0.353281	+	0.935517i	$0.614934\pi$
$558$	−30.0796	−	14.6279i	−1.27337	−	0.619248i
$559$			35.3699i			1.49599i
$560$	−15.0724	−	2.63823i	−0.636925	−	0.111486i
$561$	14.4090	+	6.10912i	0.608348	+	0.257927i
$562$	−9.04733	+	3.29617i	−0.381639	+	0.139040i
$563$		−	12.6843i		−	0.534578i	−0.963616	−	0.267289i	$-0.913872\pi$
$563$		−	12.6843i		−	0.534578i	0.963616	−	0.267289i	$-0.0861279\pi$
$564$	−15.2922	+	4.69277i	−0.643916	+	0.197601i
$565$			6.17103i			0.259617i
$566$	−11.2408	−	30.8539i	−0.472487	−	1.29688i
$567$	20.5757	+	0.683925i	0.864097	+	0.0287221i
$568$	10.6226	+	6.11969i	0.445716	+	0.256777i
$569$			23.7045i			0.993743i	0.867824	+	0.496872i	$0.165518\pi$
$569$			23.7045i			0.993743i	−0.867824	+	0.496872i	$0.834482\pi$
$570$	−1.62910	+	31.5270i	−0.0682355	+	1.32052i
$571$	−14.6959			−0.615004			−0.307502	−	0.951548i	$-0.599493\pi$
$571$	−14.6959			−0.615004			−0.307502	+	0.951548i	$0.599493\pi$
$572$	20.6691	−	17.3655i	0.864218	−	0.726087i
$573$	35.5398	+	15.0681i	1.48470	+	0.629481i
$574$	−5.55094	−	15.2362i	−0.231692	−	0.635948i
$575$	2.20328			0.0918831
$576$	−6.55260	+	23.0882i	−0.273025	+	0.962007i
$577$	10.0148			0.416920			0.208460	−	0.978031i	$-0.433155\pi$
$577$	10.0148			0.416920			0.208460	+	0.978031i	$0.433155\pi$
$578$	−3.56424	−	9.78316i	−0.148253	−	0.406926i
$579$	−9.13476	−	3.87295i	−0.379628	−	0.160954i
$580$	−21.8453	+	18.3536i	−0.907075	+	0.762094i
$581$	29.2496			1.21348
$582$	1.08510	−	20.9994i	0.0449790	−	0.870452i
$583$			1.24546i			0.0515818i
$584$	16.9354	+	9.75647i	0.700791	+	0.403725i
$585$	−16.7226	+	16.1760i	−0.691396	+	0.668796i
$586$	−2.14503	−	5.88770i	−0.0886105	−	0.243219i
$587$			31.6906i			1.30801i	0.756489	+	0.654006i	$0.226913\pi$
$587$			31.6906i			1.30801i	−0.756489	+	0.654006i	$0.773087\pi$
$588$	5.85366	−	1.79634i	0.241401	−	0.0740797i
$589$		−	60.7565i		−	2.50343i
$590$	20.2243	−	7.36821i	0.832621	−	0.303344i
$591$	19.8080	+	8.39817i	0.814791	+	0.345455i
$592$	−15.6673	−	2.74236i	−0.643922	−	0.112710i
$593$		−	23.0186i		−	0.945262i	−0.881261	−	0.472631i	$-0.843304\pi$
$593$		−	23.0186i		−	0.945262i	0.881261	−	0.472631i	$-0.156696\pi$
$594$	−14.0576	−	16.1202i	−0.576792	−	0.661420i
$595$	11.8756			0.486854
$596$	−22.5766	+	18.9681i	−0.924772	+	0.776962i
$597$	−9.64530	+	22.7495i	−0.394756	+	0.931073i
$598$	−6.16210	+	2.24500i	−0.251987	+	0.0918050i
$599$	−11.4463			−0.467681			−0.233841	−	0.972275i	$-0.575129\pi$
$599$	−11.4463			−0.467681			−0.233841	+	0.972275i	$0.575129\pi$
$600$	6.50759	+	8.61150i	0.265671	+	0.351563i
$601$	−31.9168			−1.30191			−0.650957	−	0.759114i	$-0.725632\pi$
$601$	−31.9168			−1.30191			−0.650957	+	0.759114i	$0.725632\pi$
$602$	−23.1824	+	8.44593i	−0.944846	+	0.344231i
$603$	−17.3019	−	17.8866i	−0.704588	−	0.728398i
$604$	−11.4366	−	13.6123i	−0.465347	−	0.553875i
$605$	4.22799			0.171892
$606$	−2.48839	+	48.1562i	−0.101084	+	1.95621i
$607$			8.79097i			0.356815i	0.983957	+	0.178407i	$0.0570945\pi$
$607$			8.79097i			0.356815i	−0.983957	+	0.178407i	$0.942906\pi$
$608$	−42.9208	+	7.63733i	−1.74067	+	0.309735i
$609$	−13.1928	+	31.1166i	−0.534599	+	1.26091i
$610$	−20.1456	+	7.33954i	−0.815672	+	0.297169i
$611$		−	21.4140i		−	0.866319i
$612$	1.91986	−	18.5274i	0.0776057	−	0.748924i
$613$		−	23.9647i		−	0.967925i	−0.875089	−	0.483963i	$-0.839197\pi$
$613$		−	23.9647i		−	0.967925i	0.875089	−	0.483963i	$-0.160803\pi$
$614$	−11.8737	−	32.5910i	−0.479183	−	1.31526i
$615$	5.66772	−	13.3679i	0.228545	−	0.539046i
$616$	16.3174	+	9.40043i	0.657445	+	0.378754i
$617$		−	20.0313i		−	0.806431i	−0.915105	−	0.403215i	$-0.867893\pi$
$617$		−	20.0313i		−	0.806431i	0.915105	−	0.403215i	$-0.132107\pi$
$618$	7.08749	+	0.366233i	0.285100	+	0.0147320i
$619$	36.0899			1.45057			0.725287	−	0.688446i	$-0.241707\pi$
$619$	36.0899			1.45057			0.725287	+	0.688446i	$0.241707\pi$
$620$	16.9620	+	20.1888i	0.681210	+	0.810804i
$621$	1.86824	+	4.84868i	0.0749700	+	0.194571i
$622$	−3.12635	−	8.58122i	−0.125355	−	0.344075i
$623$	−10.3414			−0.414321
$624$	−26.9749	−	17.4537i	−1.07986	−	0.698706i
$625$	−9.12916			−0.365166
$626$	0.517534	+	1.42053i	0.0206848	+	0.0567758i
$627$	15.1656	−	35.7696i	0.605654	−	1.42850i
$628$	−10.3537	−	12.3234i	−0.413157	−	0.491756i
$629$	12.3444			0.492202
$630$	−14.5954	−	7.09784i	−0.581494	−	0.282785i
$631$			23.6810i			0.942725i	0.881940	+	0.471362i	$0.156238\pi$
$631$			23.6810i			0.942725i	−0.881940	+	0.471362i	$0.843762\pi$
$632$	9.12132	−	15.8329i	0.362827	−	0.629799i
$633$	40.4252	+	17.1395i	1.60676	+	0.681233i
$634$	−2.71106	−	7.44132i	−0.107670	−	0.295533i
$635$			5.84881i			0.232103i
$636$	1.41707	−	0.434861i	0.0561904	−	0.0172434i
$637$			8.19704i			0.324778i
$638$	32.9926	−	12.0200i	1.30619	−	0.475877i
$639$	9.04047	+	9.34597i	0.357636	+	0.369721i
$640$	12.1300	−	14.5204i	0.479481	−	0.573971i
$641$		−	20.8766i		−	0.824577i	−0.911053	−	0.412288i	$-0.864730\pi$
$641$		−	20.8766i		−	0.824577i	0.911053	−	0.412288i	$-0.135270\pi$
$642$	−6.68976	−	0.345681i	−0.264024	−	0.0136429i
$643$	33.5342			1.32246			0.661230	−	0.750183i	$-0.270035\pi$
$643$	33.5342			1.32246			0.661230	+	0.750183i	$0.270035\pi$
$644$	−2.94288	−	3.50273i	−0.115966	−	0.138027i
$645$	−20.3397	−	8.62363i	−0.800876	−	0.339555i
$646$	31.7903	−	11.5820i	1.25077	−	0.455687i
$647$	−18.4765			−0.726385			−0.363193	−	0.931714i	$-0.618313\pi$
$647$	−18.4765			−0.726385			−0.363193	+	0.931714i	$0.618313\pi$
$648$	−13.4330	+	21.6230i	−0.527698	+	0.849432i
$649$	−26.4902			−1.03983
$650$	−13.5768	+	4.94637i	−0.532527	+	0.194013i
$651$	28.7572	+	12.1925i	1.12708	+	0.477860i
$652$	12.5996	−	10.5858i	0.493440	−	0.414572i
$653$	−23.6502			−0.925504			−0.462752	−	0.886488i	$-0.653138\pi$
$653$	−23.6502			−0.925504			−0.462752	+	0.886488i	$0.653138\pi$
$654$	−45.2582	−	2.33864i	−1.76974	−	0.0914479i
$655$		−	4.34250i		−	0.169676i
$656$	19.7507	+	3.45710i	0.771135	+	0.134977i
$657$	14.4130	+	14.9000i	0.562304	+	0.581305i
$658$	14.0354	−	5.11343i	0.547156	−	0.199342i
$659$		−	22.5920i		−	0.880059i	−0.897983	−	0.440029i	$-0.854968\pi$
$659$		−	22.5920i		−	0.880059i	0.897983	−	0.440029i	$-0.145032\pi$
$660$	4.94676	+	16.1198i	0.192552	+	0.627464i
$661$		−	40.2172i		−	1.56427i	−0.623110	−	0.782135i	$-0.714131\pi$
$661$		−	40.2172i		−	1.56427i	0.623110	−	0.782135i	$-0.285869\pi$
$662$	1.91597	+	5.25897i	0.0744663	+	0.204396i
$663$	22.9574	+	9.73346i	0.891591	+	0.378016i
$664$	−18.0541	+	31.3386i	−0.700636	+	1.21617i
$665$		−	29.4807i		−	1.14321i
$666$	−15.1715	−	7.37798i	−0.587882	−	0.285891i
$667$	−8.53054			−0.330304
$668$	−26.2449	+	22.0501i	−1.01545	+	0.853144i
$669$	−2.79715	+	6.59737i	−0.108144	+	0.255069i
$670$	6.71566	+	18.4332i	0.259448	+	0.712136i
$671$	26.3872			1.01867
$672$	4.99834	−	21.8479i	0.192815	−	0.842799i
$673$	9.31167			0.358939			0.179469	−	0.983764i	$-0.442562\pi$
$673$	9.31167			0.358939			0.179469	+	0.983764i	$0.442562\pi$
$674$	7.35434	+	20.1862i	0.283279	+	0.777545i
$675$	4.11626	+	10.6830i	0.158435	+	0.411189i
$676$	13.0247	−	10.9429i	0.500950	−	0.420882i
$677$	−15.7282			−0.604482			−0.302241	−	0.953231i	$-0.597735\pi$
$677$	−15.7282			−0.604482			−0.302241	+	0.953231i	$0.597735\pi$
$678$	−9.02671	−	0.466439i	−0.346669	−	0.0179135i
$679$			19.6364i			0.753574i
$680$	−7.33017	+	12.7238i	−0.281099	+	0.487935i
$681$	−7.51285	+	17.7199i	−0.287893	+	0.679026i
$682$	−11.1086	−	30.4909i	−0.425370	−	1.16756i
$683$		−	29.9693i		−	1.14674i	−0.819295	−	0.573372i	$-0.805635\pi$
$683$		−	29.9693i		−	1.14674i	0.819295	−	0.573372i	$-0.194365\pi$
$684$	−45.9932	−	4.76595i	−1.75859	−	0.182231i
$685$		−	30.3813i		−	1.16081i
$686$	−26.6491	+	9.70892i	−1.01747	+	0.370688i
$687$	5.63585	−	13.2927i	0.215021	−	0.507150i
$688$	5.26010	−	30.0513i	0.200539	−	1.14570i
$689$			1.98436i			0.0755980i
$690$	0.211391	−	4.09092i	0.00804751	−	0.155739i
$691$	10.7673			0.409606			0.204803	−	0.978803i	$-0.434345\pi$
$691$	10.7673			0.409606			0.204803	+	0.978803i	$0.434345\pi$
$692$	30.6958	−	25.7896i	1.16688	−	0.980373i
$693$	13.8870	+	14.3563i	0.527524	+	0.545350i
$694$	−23.7690	+	8.65962i	−0.902257	+	0.328714i
$695$	−7.79023			−0.295500
$696$	−25.1957	−	33.3416i	−0.955042	−	1.26381i
$697$	−15.5617			−0.589441
$698$	−8.74597	+	3.18637i	−0.331040	+	0.120606i
$699$	−1.31378	+	3.09868i	−0.0496916	+	0.117203i
$700$	−6.48398	−	7.71750i	−0.245072	−	0.291694i
$701$	−39.5604			−1.49417			−0.747087	−	0.664726i	$-0.768548\pi$
$701$	−39.5604			−1.49417			−0.747087	+	0.664726i	$0.768548\pi$
$702$	−22.3976	−	25.6838i	−0.845343	−	0.969373i
$703$		−	30.6442i		−	1.15577i
$704$	−20.1436	+	11.6804i	−0.759191	+	0.440221i
$705$	12.3143	+	5.22101i	0.463783	+	0.196635i
$706$	−26.4963	+	9.65326i	−0.997203	+	0.363305i
$707$		−	45.0305i		−	1.69355i
$708$	9.24924	+	30.1402i	0.347608	+	1.13274i
$709$			31.7211i			1.19131i	0.803240	+	0.595655i	$0.203108\pi$
$709$			31.7211i			1.19131i	−0.803240	+	0.595655i	$0.796892\pi$
$710$	−3.50902	−	9.63157i	−0.131691	−	0.361466i
$711$	13.9300	−	13.4747i	0.522417	−	0.505341i
$712$	6.38319	−	11.0800i	0.239220	−	0.415241i
$713$			7.88372i			0.295248i
$714$	−0.897623	+	17.3712i	−0.0335927	+	0.650100i
$715$	−22.5730			−0.844183
$716$	−16.7532	−	19.9404i	−0.626097	−	0.745207i
$717$	27.1071	+	11.4928i	1.01233	+	0.429208i
$718$	10.1035	+	27.7322i	0.377061	+	1.03496i
$719$	−16.6643			−0.621475			−0.310737	−	0.950496i	$-0.600576\pi$
$719$	−16.6643			−0.621475			−0.310737	+	0.950496i	$0.600576\pi$
$720$	16.6137	−	11.2567i	0.619156	−	0.419512i
$721$	−6.62746			−0.246819
$722$	−19.5537	−	53.6710i	−0.727712	−	1.99743i
$723$	−6.65876	−	2.82318i	−0.247642	−	0.104995i
$724$	27.6419	+	32.9006i	1.02730	+	1.22274i
$725$	−18.7952			−0.698035
$726$	−0.319574	+	6.18452i	−0.0118605	+	0.229529i
$727$		−	28.4645i		−	1.05569i	−0.849341	−	0.527845i	$-0.823000\pi$
$727$		−	28.4645i		−	1.05569i	0.849341	−	0.527845i	$-0.177000\pi$
$728$	25.9979	+	14.9774i	0.963548	+	0.555100i
$729$	−20.0193	+	18.1170i	−0.741457	+	0.671000i
$730$	−5.59433	−	15.3554i	−0.207056	−	0.568327i
$731$			23.6776i			0.875748i
$732$	−9.21325	−	30.0229i	−0.340532	−	1.10968i
$733$			19.2342i			0.710431i	0.934785	+	0.355215i	$0.115592\pi$
$733$			19.2342i			0.710431i	−0.934785	+	0.355215i	$0.884408\pi$
$734$	38.1962	−	13.9158i	1.40985	−	0.513642i
$735$	−4.71377	−	1.99854i	−0.173870	−	0.0737173i
$736$	5.56937	−	0.991014i	0.205290	−	0.0365293i
$737$		−	24.1442i		−	0.889362i
$738$	19.1256	+	9.30092i	0.704024	+	0.342371i
$739$	−21.7895			−0.801538			−0.400769	−	0.916179i	$-0.631257\pi$
$739$	−21.7895			−0.801538			−0.400769	+	0.916179i	$0.631257\pi$
$740$	8.55525	+	10.1828i	0.314497	+	0.374327i
$741$	24.1628	−	56.9906i	0.887644	−	2.09360i
$742$	−1.30060	+	0.473842i	−0.0477467	+	0.0173953i
$743$	−24.4226			−0.895980			−0.447990	−	0.894039i	$-0.647860\pi$
$743$	−24.4226			−0.895980			−0.447990	+	0.894039i	$0.647860\pi$
$744$	−30.8134	+	23.2853i	−1.12968	+	0.853680i
$745$	24.6562			0.903334
$746$	2.81729	−	1.02641i	0.103148	−	0.0375794i
$747$	−27.5722	+	26.6709i	−1.00881	+	0.975838i
$748$	13.8365	−	11.6249i	0.505911	−	0.425050i
$749$	6.25555			0.228573
$750$	1.52271	−	29.4680i	0.0556014	−	1.07602i
$751$			13.8921i			0.506931i	0.967344	+	0.253465i	$0.0815704\pi$
$751$			13.8921i			0.506931i	−0.967344	+	0.253465i	$0.918430\pi$
$752$	−3.18463	+	18.1940i	−0.116131	+	0.663467i
$753$	−1.64017	+	3.86851i	−0.0597710	+	0.140976i
$754$	52.5660	−	19.1511i	1.91434	−	0.697442i
$755$			14.8662i			0.541035i
$756$	11.4856	−	20.8130i	0.417728	−	0.756962i
$757$		−	8.05974i		−	0.292936i	−0.989215	−	0.146468i	$-0.953209\pi$
$757$		−	8.05974i		−	0.292936i	0.989215	−	0.146468i	$-0.0467906\pi$
$758$	8.49243	+	23.3101i	0.308459	+	0.846660i
$759$	−1.96787	+	4.64143i	−0.0714293	+	0.168473i
$760$	31.5862	+	18.1968i	1.14575	+	0.660066i
$761$			18.9559i			0.687151i	0.939125	+	0.343576i	$0.111638\pi$
$761$			18.9559i			0.687151i	−0.939125	+	0.343576i	$0.888362\pi$
$762$	−8.55539	−	0.442084i	−0.309929	−	0.0160150i
$763$	42.3206			1.53211
$764$	34.1277	−	28.6729i	1.23470	−	1.03735i
$765$	−11.1946	+	10.8287i	−0.404742	+	0.391512i
$766$	6.58892	+	18.0853i	0.238067	+	0.653448i
$767$	−42.2061			−1.52397
$768$	20.3230	+	18.8408i	0.733344	+	0.679858i
$769$	33.9584			1.22457			0.612286	−	0.790636i	$-0.290250\pi$
$769$	33.9584			1.22457			0.612286	+	0.790636i	$0.290250\pi$
$770$	−5.39018	−	14.7950i	−0.194249	−	0.533175i
$771$	4.13362	−	9.74959i	0.148869	−	0.351123i
$772$	−8.77181	+	7.36978i	−0.315704	+	0.265244i
$773$	2.59044			0.0931716			0.0465858	−	0.998914i	$-0.485166\pi$
$773$	2.59044			0.0931716			0.0465858	+	0.998914i	$0.485166\pi$
$774$	14.1517	−	29.1003i	0.508671	−	1.04599i
$775$			17.3700i			0.623950i
$776$	−21.0388	−	12.1204i	−0.755248	−	0.435098i
$777$	14.5045	+	6.14960i	0.520345	+	0.220616i
$778$	−4.58453	−	12.5836i	−0.164363	−	0.451145i
$779$			38.6311i			1.38410i
$780$	7.88152	+	25.6832i	0.282204	+	0.919607i
$781$			12.6156i			0.451423i
$782$	−4.12508	+	1.50287i	−0.147513	+	0.0537425i
$783$	−15.9371	−	41.3619i	−0.569546	−	1.47815i
$784$	1.21904	−	6.96445i	0.0435370	−	0.248730i
$785$			13.4585i			0.480356i
$786$	6.35202	+	0.328229i	0.226569	+	0.0117075i
$787$	22.7336			0.810365			0.405182	−	0.914236i	$-0.367208\pi$
$787$	22.7336			0.810365			0.405182	+	0.914236i	$0.367208\pi$
$788$	19.0209	−	15.9807i	0.677592	−	0.569290i
$789$	−9.81340	−	4.16068i	−0.349366	−	0.148124i
$790$	−14.3557	+	5.23015i	−0.510754	+	0.186080i
$791$	8.44081			0.300121
$792$	−23.9533	+	6.01749i	−0.851143	+	0.213822i
$793$	42.0419			1.49295
$794$	−29.3405	+	10.6895i	−1.04125	+	0.379355i
$795$	−1.14112	−	0.483811i	−0.0404713	−	0.0171590i
$796$	18.3539	+	21.8455i	0.650536	+	0.774295i
$797$	44.9272			1.59140			0.795702	−	0.605689i	$-0.207102\pi$
$797$	44.9272			1.59140			0.795702	+	0.605689i	$0.207102\pi$
$798$	43.1230	+	2.22830i	1.52654	+	0.0788811i
$799$		−	14.3352i		−	0.507141i
$800$	12.2709	−	2.18348i	0.433841	−	0.0771977i
$801$	9.74838	−	9.42973i	0.344442	−	0.333183i
$802$	20.6464	−	7.52199i	0.729050	−	0.265611i
$803$			20.1128i			0.709765i
$804$	−27.4709	+	8.43010i	−0.968822	+	0.297307i
$805$			3.82539i			0.134827i
$806$	−17.6990	−	48.5803i	−0.623420	−	1.71117i
$807$	32.6415	+	13.8393i	1.14903	+	0.487167i
$808$	48.2466	+	27.7948i	1.69731	+	0.977819i
$809$			37.6032i			1.32206i	0.750361	+	0.661028i	$0.229880\pi$
$809$			37.6032i			1.32206i	−0.750361	+	0.661028i	$0.770120\pi$
$810$	20.2305	−	6.61787i	0.710827	−	0.232528i
$811$	9.33068			0.327644			0.163822	−	0.986490i	$-0.447618\pi$
$811$	9.33068			0.327644			0.163822	+	0.986490i	$0.447618\pi$
$812$	25.1044	+	29.8802i	0.880990	+	1.04859i
$813$	3.90835	−	9.21825i	0.137072	−	0.323298i
$814$	−5.60293	−	15.3789i	−0.196382	−	0.539032i
$815$	−13.7603			−0.482001
$816$	−18.0578	−	11.6840i	−0.632148	−	0.409021i
$817$	58.7785			2.05640
$818$	13.2223	+	36.2927i	0.462308	+	1.26894i
$819$	22.1258	+	22.8734i	0.773137	+	0.799262i
$820$	−10.7850	−	12.8368i	−0.376629	−	0.448279i
$821$	32.4718			1.13327			0.566636	−	0.823968i	$-0.308244\pi$
$821$	32.4718			1.13327			0.566636	+	0.823968i	$0.308244\pi$
$822$	44.4404	+	2.29638i	1.55004	+	0.0800953i
$823$		−	32.3017i		−	1.12597i	−0.826468	−	0.562983i	$-0.809653\pi$
$823$		−	32.3017i		−	1.12597i	0.826468	−	0.562983i	$-0.190347\pi$
$824$	4.09076	−	7.10078i	0.142508	−	0.247368i
$825$	−4.33577	+	10.2264i	−0.150952	+	0.356037i
$826$	−10.0783	−	27.6631i	−0.350670	−	0.962521i
$827$		−	47.3767i		−	1.64745i	−0.566989	−	0.823725i	$-0.691892\pi$
$827$		−	47.3767i		−	1.64745i	0.566989	−	0.823725i	$-0.308108\pi$
$828$	5.96804	+	0.618427i	0.207404	+	0.0214918i
$829$			10.6496i			0.369875i	0.982750	+	0.184937i	$0.0592082\pi$
$829$			10.6496i			0.369875i	−0.982750	+	0.184937i	$0.940792\pi$
$830$	28.4148	−	10.3522i	0.986291	−	0.359330i
$831$	−4.68528	+	11.0507i	−0.162531	+	0.383346i
$832$	−32.0942	+	18.6100i	−1.11267	+	0.645185i
$833$			5.48733i			0.190125i
$834$	0.588827	−	11.3952i	0.0203894	−	0.394584i
$835$	28.6625			0.991906
$836$	−28.8583	−	34.3483i	−0.998085	−	1.18796i
$837$	−38.2256	+	14.7287i	−1.32127	+	0.509098i
$838$	34.7915	−	12.6754i	1.20185	−	0.437865i
$839$	48.9856			1.69117			0.845585	−	0.533841i	$-0.179252\pi$
$839$	48.9856			1.69117			0.845585	+	0.533841i	$0.179252\pi$
$840$	−14.9515	+	11.2986i	−0.515876	+	0.389840i
$841$	43.7702			1.50932
$842$	−17.4882	+	6.37139i	−0.602684	+	0.219573i
$843$	−4.60339	+	10.8576i	−0.158549	+	0.373955i
$844$	38.8190	−	32.6144i	1.33621	−	1.12263i
$845$	−14.2245			−0.489337
$846$	−8.56785	+	17.6182i	−0.294569	+	0.605726i
$847$		−	5.78310i		−	0.198710i
$848$	0.295107	−	1.68597i	0.0101340	−	0.0578964i
$849$	−37.0273	−	15.6988i	−1.27077	−	0.538782i
$850$	−9.08871	+	3.31124i	−0.311740	+	0.113575i
$851$			3.97637i			0.136308i
$852$	14.3539	−	4.40483i	0.491756	−	0.150907i
$853$		−	7.48762i		−	0.256371i	−0.991750	−	0.128186i	$-0.959085\pi$
$853$		−	7.48762i		−	0.256371i	0.991750	−	0.128186i	$-0.0409153\pi$
$854$	10.0391	+	27.5554i	0.343532	+	0.942928i
$855$	26.8817	+	27.7900i	0.919333	+	0.950399i
$856$	−3.86120	+	6.70231i	−0.131973	+	0.229080i
$857$		−	21.3312i		−	0.728659i	−0.931270	−	0.364330i	$-0.881298\pi$
$857$		−	21.3312i		−	0.728659i	0.931270	−	0.364330i	$-0.118702\pi$
$858$	1.70619	−	33.0189i	0.0582483	−	1.12724i
$859$	35.6085			1.21495			0.607474	−	0.794340i	$-0.292183\pi$
$859$	35.6085			1.21495			0.607474	+	0.794340i	$0.292183\pi$
$860$	−19.5316	+	16.4098i	−0.666021	+	0.559568i
$861$	−18.2848	−	7.75238i	−0.623145	−	0.264201i
$862$	4.81588	+	13.2187i	0.164030	+	0.450229i
$863$	−16.0883			−0.547653			−0.273827	−	0.961779i	$-0.588289\pi$
$863$	−16.0883			−0.547653			−0.273827	+	0.961779i	$0.588289\pi$
$864$	15.2100	+	25.1526i	0.517456	+	0.855710i
$865$	−33.5234			−1.13983
$866$	0.993641	+	2.72735i	0.0337653	+	0.0926792i
$867$	−11.7406	−	4.97779i	−0.398733	−	0.169055i
$868$	27.6146	−	23.2008i	0.937299	−	0.787487i
$869$	18.8035			0.637864
$870$	−1.80328	+	34.8978i	−0.0611369	+	1.18315i
$871$		−	38.4682i		−	1.30344i
$872$	−26.1222	+	45.3431i	−0.884608	+	1.53551i
$873$	−17.9052	−	18.5103i	−0.606000	−	0.626478i
$874$	3.73079	+	10.2403i	0.126196	+	0.346384i
$875$			27.5554i			0.931541i
$876$	22.8840	−	7.02251i	0.773179	−	0.237269i
$877$		−	30.9575i		−	1.04536i	−0.852529	−	0.522680i	$-0.824932\pi$
$877$		−	30.9575i		−	1.04536i	0.852529	−	0.522680i	$-0.175068\pi$
$878$	−43.2740	+	15.7658i	−1.46043	+	0.532070i
$879$	−7.06575	−	2.99573i	−0.238322	−	0.101044i
$880$	19.1787	+	3.35699i	0.646514	+	0.113164i
$881$		−	35.0906i		−	1.18223i	−0.806586	−	0.591116i	$-0.798687\pi$
$881$		−	35.0906i		−	1.18223i	0.806586	−	0.591116i	$-0.201313\pi$
$882$	3.27967	−	6.74404i	0.110432	−	0.227083i
$883$	−30.4343			−1.02420			−0.512098	−	0.858927i	$-0.671131\pi$
$883$	−30.4343			−1.02420			−0.512098	+	0.858927i	$0.671131\pi$
$884$	22.0452	−	18.5216i	0.741461	−	0.622950i
$885$	10.2904	−	24.2709i	0.345907	−	0.815858i
$886$	−21.8107	+	7.94619i	−0.732746	+	0.266957i
$887$	−35.1003			−1.17855			−0.589277	−	0.807931i	$-0.700587\pi$
$887$	−35.1003			−1.17855			−0.589277	+	0.807931i	$0.700587\pi$
$888$	−15.5416	+	11.7446i	−0.521542	+	0.394122i
$889$	8.00008			0.268314
$890$	−10.0463	+	3.66011i	−0.336752	+	0.122687i
$891$	−26.1813	−	0.870253i	−0.877106	−	0.0291546i
$892$	5.32265	+	6.33524i	0.178216	+	0.212119i
$893$	−35.5863			−1.19085
$894$	−1.86365	+	36.0661i	−0.0623297	+	1.20623i
$895$			21.7772i			0.727931i
$896$	−19.8612	−	16.5916i	−0.663517	−	0.554286i
$897$	−3.13535	+	7.39505i	−0.104686	+	0.246914i
$898$	−40.7633	+	14.8511i	−1.36029	+	0.495586i
$899$		−	67.2524i		−	2.24299i
$900$	13.1493	+	1.36257i	0.438309	+	0.0454189i
$901$			1.32838i			0.0442549i
$902$	7.06323	+	19.3872i	0.235180	+	0.645523i
$903$	−11.7955	+	27.8210i	−0.392530	+	0.925823i
$904$	−5.21004	+	9.04365i	−0.173283	+	0.300787i
$905$		−	35.9312i		−	1.19439i
$906$	−21.7456	−	1.12366i	−0.722448	−	0.0373312i
$907$	−6.22500			−0.206698			−0.103349	−	0.994645i	$-0.532956\pi$
$907$	−6.22500			−0.206698			−0.103349	+	0.994645i	$0.532956\pi$
$908$	14.2961	+	17.0158i	0.474432	+	0.564689i
$909$	41.0606	+	42.4482i	1.36190	+	1.40792i
$910$	−8.58801	−	23.5724i	−0.284690	−	0.781418i
$911$	−12.2456			−0.405714			−0.202857	−	0.979208i	$-0.565023\pi$
$911$	−12.2456			−0.405714			−0.202857	+	0.979208i	$0.565023\pi$
$912$	−29.0049	+	44.8275i	−0.960448	+	1.48439i
$913$	−37.2183			−1.23175
$914$	10.3765	+	28.4816i	0.343226	+	0.942088i
$915$	−10.2503	+	24.1765i	−0.338866	+	0.799250i
$916$	−10.7244	−	12.7646i	−0.354343	−	0.421754i
$917$	−5.93973			−0.196147
$918$	−14.9936	−	17.1935i	−0.494862	−	0.567469i
$919$		−	23.4762i		−	0.774407i	−0.921994	−	0.387203i	$-0.873441\pi$
$919$		−	23.4762i		−	0.774407i	0.921994	−	0.387203i	$-0.126559\pi$
$920$	−4.09860	−	2.36120i	−0.135127	−	0.0778465i
$921$	−39.1120	−	16.5827i	−1.28878	−	0.546418i
$922$	−4.63491	−	12.7219i	−0.152643	−	0.418974i
$923$			20.1001i			0.661603i
$924$	22.0489	−	6.76624i	0.725356	−	0.222593i
$925$			8.76106i			0.288062i
$926$	30.5956	−	11.1467i	1.00543	−	0.366305i
$927$	6.24739	−	6.04318i	0.205191	−	0.198484i
$928$	−47.5098	+	8.45389i	−1.55958	+	0.277513i
$929$		−	8.59904i		−	0.282126i	−0.990001	−	0.141063i	$-0.954948\pi$
$929$		−	8.59904i		−	0.282126i	0.990001	−	0.141063i	$-0.0450519\pi$
$930$	32.2517	+	1.66655i	1.05757	+	0.0546482i
$931$	13.6220			0.446443
$932$	2.49997	+	2.97556i	0.0818891	+	0.0974678i
$933$	−10.2982	−	4.36623i	−0.337148	−	0.142944i
$934$	42.3161	−	15.4168i	1.38463	−	0.504453i
$935$	−15.1110			−0.494183
$936$	−38.1640	+	9.58747i	−1.24743	+	0.313376i
$937$	40.6559			1.32817			0.664085	−	0.747657i	$-0.268821\pi$
$937$	40.6559			1.32817			0.664085	+	0.747657i	$0.268821\pi$
$938$	25.2131	−	9.18576i	0.823238	−	0.299926i
$939$	1.70476	+	0.722784i	0.0556328	+	0.0235872i
$940$	11.8250	−	9.93498i	0.385689	−	0.324043i
$941$	11.6231			0.378901			0.189450	−	0.981890i	$-0.439329\pi$
$941$	11.6231			0.378901			0.189450	+	0.981890i	$0.439329\pi$
$942$	−19.6866	−	1.01727i	−0.641424	−	0.0331444i
$943$		−	5.01274i		−	0.163237i
$944$	35.8595	+	6.27675i	1.16713	+	0.204291i
$945$	−18.5481	+	7.14676i	−0.603369	+	0.232484i
$946$	29.4982	−	10.7469i	0.959071	−	0.349413i
$947$			30.2719i			0.983705i	0.870678	+	0.491853i	$0.163680\pi$
$947$			30.2719i			0.983705i	−0.870678	+	0.491853i	$0.836320\pi$
$948$	−6.56535	−	21.3943i	−0.213233	−	0.694853i
$949$			32.0451i			1.04023i
$950$	8.21999	+	22.5623i	0.266692	+	0.732017i
$951$	−8.93023	−	3.78623i	−0.289583	−	0.122777i
$952$	17.4038	+	10.0263i	0.564059	+	0.324954i
$953$			2.66840i			0.0864379i	0.999066	+	0.0432189i	$0.0137613\pi$
$953$			2.66840i			0.0864379i	−0.999066	+	0.0432189i	$0.986239\pi$
$954$	0.793950	−	1.63261i	0.0257051	−	0.0528577i
$955$	−37.2714			−1.20607
$956$	26.0300	−	21.8695i	0.841871	−	0.707311i
$957$	16.7870	−	39.5940i	0.542647	−	1.27989i
$958$	−4.11916	−	11.3063i	−0.133084	−	0.365290i
$959$	−41.5559			−1.34191
$960$	−2.87685	−	22.9933i	−0.0928498	−	0.742107i
$961$	−31.1530			−1.00494
$962$	−8.92697	−	24.5028i	−0.287817	−	0.790002i
$963$	−5.89681	+	5.70406i	−0.190022	+	0.183811i
$964$	−6.39419	+	5.37218i	−0.205943	+	0.173026i
$965$	9.57983			0.308386
$966$	−5.59561	−	0.289143i	−0.180036	−	0.00930303i
$967$		−	41.6296i		−	1.33872i	−0.742939	−	0.669359i	$-0.766569\pi$
$967$		−	41.6296i		−	1.33872i	0.742939	−	0.669359i	$-0.233431\pi$
$968$	6.19612	+	3.56959i	0.199151	+	0.114731i
$969$	16.1753	−	38.1511i	0.519625	−	1.22559i
$970$	6.94983	+	19.0759i	0.223145	+	0.612491i
$971$		−	31.1228i		−	0.998778i	−0.866378	−	0.499389i	$-0.833558\pi$
$971$		−	31.1228i		−	0.998778i	0.866378	−	0.499389i	$-0.166442\pi$
$972$	8.15120	+	30.0925i	0.261450	+	0.965217i
$973$			10.6556i			0.341602i
$974$	13.6092	−	4.95815i	0.436066	−	0.158869i
$975$	−6.90805	+	16.2934i	−0.221235	+	0.521806i
$976$	−35.7200	−	6.25233i	−1.14337	−	0.200132i
$977$		−	20.3893i		−	0.652312i	−0.945316	−	0.326156i	$-0.894247\pi$
$977$		−	20.3893i		−	0.652312i	0.945316	−	0.326156i	$-0.105753\pi$
$978$	1.04007	−	20.1279i	0.0332579	−	0.643620i
$979$	13.1588			0.420558
$980$	−4.52647	+	3.80299i	−0.144593	+	0.121482i
$981$	−39.8937	+	38.5896i	−1.27371	+	1.23207i
$982$	42.9395	−	15.6439i	1.37026	−	0.499218i
$983$	54.2769			1.73116			0.865582	−	0.500766i	$-0.166948\pi$
$983$	54.2769			1.73116			0.865582	+	0.500766i	$0.166948\pi$
$984$	19.5923	−	14.8056i	0.624578	−	0.471985i
$985$	−20.7731			−0.661884
$986$	35.1892	−	12.8203i	1.12065	−	0.408281i
$987$	7.14137	−	16.8437i	0.227312	−	0.536140i
$988$	−45.9790	−	54.7261i	−1.46279	−	1.74107i
$989$	−7.62705			−0.242526
$990$	18.5718	+	9.03157i	0.590249	+	0.287042i
$991$		−	50.6391i		−	1.60861i	−0.594220	−	0.804303i	$-0.702539\pi$
$991$		−	50.6391i		−	1.60861i	0.594220	−	0.804303i	$-0.297461\pi$
$992$	7.81288	+	43.9074i	0.248059	+	1.39406i
$993$	6.31122	+	2.67583i	0.200281	+	0.0849148i
$994$	−13.1742	+	4.79968i	−0.417860	+	0.152237i
$995$		−	23.8579i		−	0.756345i
$996$	12.9950	+	42.3464i	0.411763	+	1.34180i
$997$			42.5149i			1.34646i	0.739433	+	0.673230i	$0.235094\pi$
$997$			42.5149i			1.34646i	−0.739433	+	0.673230i	$0.764906\pi$
$998$	20.5866	+	56.5062i	0.651657	+	1.78867i
$999$	−19.2801	+	7.42883i	−0.609997	+	0.235038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.c.323.19	✓	42
3.2	odd	2		552.2.j.d.323.24	yes	42
4.3	odd	2		2208.2.j.c.47.38		42
8.3	odd	2		552.2.j.d.323.23	yes	42
8.5	even	2		2208.2.j.d.47.38		42
12.11	even	2		2208.2.j.d.47.37		42
24.5	odd	2		2208.2.j.c.47.37		42
24.11	even	2	inner	552.2.j.c.323.20	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.19	✓	42	1.1	even	1	trivial
552.2.j.c.323.20	yes	42	24.11	even	2	inner
552.2.j.d.323.23	yes	42	8.3	odd	2
552.2.j.d.323.24	yes	42	3.2	odd	2
2208.2.j.c.47.37		42	24.5	odd	2
2208.2.j.c.47.38		42	4.3	odd	2
2208.2.j.d.47.37		42	12.11	even	2
2208.2.j.d.47.38		42	8.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.484105 - 1.32877i) q^{2} +(-1.59465 - 0.676097i) q^{3} +(-1.53128 + 1.28653i) q^{4} +1.67234 q^{5} +(-0.126404 + 2.44623i) q^{6} -2.28745i q^{7} +(2.45082 + 1.41191i) q^{8} +(2.08579 + 2.15627i) q^{9} +O(q^{10})\)	\(q+(-0.484105 - 1.32877i) q^{2} +(-1.59465 - 0.676097i) q^{3} +(-1.53128 + 1.28653i) q^{4} +1.67234 q^{5} +(-0.126404 + 2.44623i) q^{6} -2.28745i q^{7} +(2.45082 + 1.41191i) q^{8} +(2.08579 + 2.15627i) q^{9} +(-0.809588 - 2.22216i) q^{10} +2.91064i q^{11} +(3.31168 - 1.01627i) q^{12} +4.63743i q^{13} +(-3.03950 + 1.10737i) q^{14} +(-2.66679 - 1.13066i) q^{15} +(0.689663 - 3.94010i) q^{16} +3.10443i q^{17} +(1.85546 - 3.81540i) q^{18} +7.70658 q^{19} +(-2.56083 + 2.15152i) q^{20} +(-1.54654 + 3.64767i) q^{21} +(3.86758 - 1.40905i) q^{22} -1.00000 q^{23} +(-2.95359 - 3.90849i) q^{24} -2.20328 q^{25} +(6.16210 - 2.24500i) q^{26} +(-1.86824 - 4.84868i) q^{27} +(2.94288 + 3.50273i) q^{28} +8.53054 q^{29} +(-0.211391 + 4.09092i) q^{30} -7.88372i q^{31} +(-5.56937 + 0.991014i) q^{32} +(1.96787 - 4.64143i) q^{33} +(4.12508 - 1.50287i) q^{34} -3.82539i q^{35} +(-5.96804 - 0.618427i) q^{36} -3.97637i q^{37} +(-3.73079 - 10.2403i) q^{38} +(3.13535 - 7.39505i) q^{39} +(4.09860 + 2.36120i) q^{40} +5.01274i q^{41} +(5.59561 + 0.289143i) q^{42} +7.62705 q^{43} +(-3.74463 - 4.45701i) q^{44} +(3.48814 + 3.60601i) q^{45} +(0.484105 + 1.32877i) q^{46} -4.61765 q^{47} +(-3.76366 + 5.81678i) q^{48} +1.76758 q^{49} +(1.06662 + 2.92766i) q^{50} +(2.09889 - 4.95046i) q^{51} +(-5.96621 - 7.10122i) q^{52} +0.427900 q^{53} +(-5.53837 + 4.82974i) q^{54} +4.86757i q^{55} +(3.22968 - 5.60611i) q^{56} +(-12.2893 - 5.21039i) q^{57} +(-4.12968 - 11.3352i) q^{58} +9.10118i q^{59} +(5.53825 - 1.69955i) q^{60} -9.06577i q^{61} +(-10.4757 + 3.81655i) q^{62} +(4.93235 - 4.77113i) q^{63} +(4.01300 + 6.92068i) q^{64} +7.75536i q^{65} +(-7.12008 - 0.367917i) q^{66} -8.29515 q^{67} +(-3.99395 - 4.75376i) q^{68} +(1.59465 + 0.676097i) q^{69} +(-5.08308 + 1.85189i) q^{70} +4.33432 q^{71} +(2.06741 + 8.22957i) q^{72} +6.91010 q^{73} +(-5.28370 + 1.92498i) q^{74} +(3.51345 + 1.48963i) q^{75} +(-11.8010 + 9.91477i) q^{76} +6.65793 q^{77} +(-11.3442 - 0.586191i) q^{78} -6.46025i q^{79} +(1.15335 - 6.58918i) q^{80} +(-0.298990 + 8.99503i) q^{81} +(6.66080 - 2.42669i) q^{82} +12.7870i q^{83} +(-2.32466 - 7.57529i) q^{84} +5.19165i q^{85} +(-3.69230 - 10.1346i) q^{86} +(-13.6032 - 5.76747i) q^{87} +(-4.10957 + 7.13344i) q^{88} -4.52095i q^{89} +(3.10295 - 6.38065i) q^{90} +10.6079 q^{91} +(1.53128 - 1.28653i) q^{92} +(-5.33016 + 12.5717i) q^{93} +(2.23543 + 6.13582i) q^{94} +12.8880 q^{95} +(9.55119 + 2.18512i) q^{96} -8.58440 q^{97} +(-0.855696 - 2.34872i) q^{98} +(-6.27612 + 6.07097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} - 8 q^{5} + q^{6} + 9 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{14} + 8 q^{15} - 12 q^{16} + 16 q^{18} + 4 q^{19} + 2 q^{20} - 8 q^{21} + 18 q^{22} - 42 q^{23} - 24 q^{24} + 22 q^{25} - 11 q^{26} - 16 q^{27} + 6 q^{28} - 24 q^{30} + 20 q^{32} + 12 q^{33} + 14 q^{34} + 15 q^{36} + 22 q^{38} - 8 q^{39} + 4 q^{40} + 36 q^{42} + 28 q^{43} - 56 q^{44} + 8 q^{45} - 9 q^{48} - 50 q^{49} - 20 q^{50} + 28 q^{51} - q^{52} - 24 q^{53} - 24 q^{54} + 34 q^{56} - 8 q^{57} - 21 q^{58} + 18 q^{60} + 79 q^{62} + 16 q^{63} + 7 q^{64} + 16 q^{66} - 4 q^{67} - 20 q^{68} - 2 q^{69} - 8 q^{70} - 62 q^{72} + 4 q^{73} - 36 q^{74} - 6 q^{75} + 14 q^{76} - 32 q^{77} - 62 q^{78} + 52 q^{80} + 18 q^{81} + 11 q^{82} + 66 q^{84} + 28 q^{86} + 48 q^{87} - 38 q^{88} - 8 q^{91} - 4 q^{92} + 22 q^{93} + q^{94} + 16 q^{95} - 54 q^{96} + 20 q^{97} - 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 - 8 * q^5 + q^6 + 9 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^14 + 8 * q^15 - 12 * q^16 + 16 * q^18 + 4 * q^19 + 2 * q^20 - 8 * q^21 + 18 * q^22 - 42 * q^23 - 24 * q^24 + 22 * q^25 - 11 * q^26 - 16 * q^27 + 6 * q^28 - 24 * q^30 + 20 * q^32 + 12 * q^33 + 14 * q^34 + 15 * q^36 + 22 * q^38 - 8 * q^39 + 4 * q^40 + 36 * q^42 + 28 * q^43 - 56 * q^44 + 8 * q^45 - 9 * q^48 - 50 * q^49 - 20 * q^50 + 28 * q^51 - q^52 - 24 * q^53 - 24 * q^54 + 34 * q^56 - 8 * q^57 - 21 * q^58 + 18 * q^60 + 79 * q^62 + 16 * q^63 + 7 * q^64 + 16 * q^66 - 4 * q^67 - 20 * q^68 - 2 * q^69 - 8 * q^70 - 62 * q^72 + 4 * q^73 - 36 * q^74 - 6 * q^75 + 14 * q^76 - 32 * q^77 - 62 * q^78 + 52 * q^80 + 18 * q^81 + 11 * q^82 + 66 * q^84 + 28 * q^86 + 48 * q^87 - 38 * q^88 - 8 * q^91 - 4 * q^92 + 22 * q^93 + q^94 + 16 * q^95 - 54 * q^96 + 20 * q^97 - 64 * q^98

Introduction

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