LMFDB - Embedded newform 168.2.ba.c.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41416 - 0.0117470i) q^{2} +(1.70617 - 0.298296i) q^{3} +(1.99972 + 0.0332243i) q^{4} +(0.337879 + 0.195075i) q^{5} +(-2.41631 + 0.401798i) q^{6} +(1.39526 + 2.24795i) q^{7} +(-2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +(-0.475526 - 0.279837i) q^{10} +(-0.748582 - 1.29658i) q^{11} +(3.42178 - 0.539824i) q^{12} -3.28768 q^{13} +(-1.94672 - 3.19536i) q^{14} +(0.634670 + 0.232043i) q^{15} +(3.99779 + 0.132879i) q^{16} +(1.68169 + 2.91278i) q^{17} +(-4.00278 + 1.40631i) q^{18} +(2.56203 - 4.43756i) q^{19} +(0.669184 + 0.401321i) q^{20} +(3.05110 + 3.41918i) q^{21} +(1.04339 + 1.84237i) q^{22} +(4.72764 + 2.72950i) q^{23} +(-4.84530 + 0.723204i) q^{24} +(-2.42389 - 4.19830i) q^{25} +(4.64932 + 0.0386203i) q^{26} +(4.51125 - 2.57850i) q^{27} +(2.71544 + 4.54163i) q^{28} -4.13801 q^{29} +(-0.894802 - 0.335602i) q^{30} +(-3.60237 + 2.07983i) q^{31} +(-5.65198 - 0.234875i) q^{32} +(-1.66397 - 1.98889i) q^{33} +(-2.34398 - 4.13891i) q^{34} +(0.0329110 + 1.03171i) q^{35} +(5.67712 - 1.94174i) q^{36} +(-7.46581 - 4.31038i) q^{37} +(-3.67525 + 6.24534i) q^{38} +(-5.60934 + 0.980702i) q^{39} +(-0.941622 - 0.575396i) q^{40} -11.1607 q^{41} +(-4.27459 - 4.87112i) q^{42} +4.79323i q^{43} +(-1.45388 - 2.61768i) q^{44} +(1.15207 + 0.206585i) q^{45} +(-6.65359 - 3.91550i) q^{46} +(2.51067 - 4.34861i) q^{47} +(6.86055 - 0.965812i) q^{48} +(-3.10652 + 6.27292i) q^{49} +(3.37846 + 5.96557i) q^{50} +(3.73813 + 4.46806i) q^{51} +(-6.57445 - 0.109231i) q^{52} +(-0.499243 - 0.864715i) q^{53} +(-6.40994 + 3.59342i) q^{54} -0.584118i q^{55} +(-3.78673 - 6.45451i) q^{56} +(3.04755 - 8.33548i) q^{57} +(5.85183 + 0.0486091i) q^{58} +(1.36034 - 0.785391i) q^{59} +(1.26146 + 0.485108i) q^{60} +(-3.40889 + 5.90437i) q^{61} +(5.11878 - 2.89891i) q^{62} +(6.22563 + 4.92357i) q^{63} +(7.99007 + 0.398545i) q^{64} +(-1.11084 - 0.641343i) q^{65} +(2.32977 + 2.83217i) q^{66} +(-3.05467 + 1.76361i) q^{67} +(3.26615 + 5.88063i) q^{68} +(8.88036 + 3.24676i) q^{69} +(-0.0344221 - 1.45940i) q^{70} -14.3360i q^{71} +(-8.05119 + 2.67925i) q^{72} +(2.76107 - 1.59410i) q^{73} +(10.5072 + 6.18329i) q^{74} +(-5.38791 - 6.43999i) q^{75} +(5.27078 - 8.78877i) q^{76} +(1.87018 - 3.49184i) q^{77} +(7.94406 - 1.32098i) q^{78} +(-0.239413 + 0.414676i) q^{79} +(1.32485 + 0.824765i) q^{80} +(6.92781 - 5.74504i) q^{81} +(15.7831 + 0.131105i) q^{82} +17.4548i q^{83} +(5.98776 + 6.93879i) q^{84} +1.31222i q^{85} +(0.0563059 - 6.77842i) q^{86} +(-7.06016 + 1.23435i) q^{87} +(2.02527 + 3.71891i) q^{88} +(-2.54840 + 4.41396i) q^{89} +(-1.62679 - 0.305678i) q^{90} +(-4.58716 - 7.39053i) q^{91} +(9.36328 + 5.61532i) q^{92} +(-5.52586 + 4.62312i) q^{93} +(-3.60159 + 6.12016i) q^{94} +(1.73131 - 0.999573i) q^{95} +(-9.71330 + 1.28523i) q^{96} +9.00074i q^{97} +(4.46682 - 8.83445i) q^{98} +(-3.43230 - 2.89703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41416	−	0.0117470i	−0.999966	−	0.00830636i
$2$	−1.41416	−	0.0117470i	−0.999966	−	0.00830636i
$3$	1.70617	−	0.298296i	0.985058	−	0.172221i
$3$	1.70617	−	0.298296i	0.985058	−	0.172221i
$4$	1.99972	+	0.0332243i	0.999862	+	0.0166122i
$5$	0.337879	+	0.195075i	0.151104	+	0.0872401i	0.573646	−	0.819103i	$-0.305529\pi$
$5$	0.337879	+	0.195075i	0.151104	+	0.0872401i	−0.422542	+	0.906344i	$0.638862\pi$
$6$	−2.41631	+	0.401798i	−0.986455	+	0.164033i
$7$	1.39526	+	2.24795i	0.527357	+	0.849644i
$7$	1.39526	+	2.24795i	0.527357	+	0.849644i
$8$	−2.82755	−	0.0704754i	−0.999690	−	0.0249168i
$9$	2.82204	−	1.01789i	0.940680	−	0.339296i
$10$	−0.475526	−	0.279837i	−0.150374	−	0.0884922i
$11$	−0.748582	−	1.29658i	−0.225706	−	0.390934i	0.730825	−	0.682565i	$-0.239136\pi$
$11$	−0.748582	−	1.29658i	−0.225706	−	0.390934i	−0.956531	+	0.291631i	$0.905802\pi$
$12$	3.42178	−	0.539824i	0.987783	−	0.155834i
$13$	−3.28768			−0.911838			−0.455919	−	0.890021i	$-0.650689\pi$
$13$	−3.28768			−0.911838			−0.455919	+	0.890021i	$0.650689\pi$
$14$	−1.94672	−	3.19536i	−0.520282	−	0.853995i
$15$	0.634670	+	0.232043i	0.163871	+	0.0599132i
$16$	3.99779	+	0.132879i	0.999448	+	0.0332197i
$17$	1.68169	+	2.91278i	0.407871	+	0.706453i	0.994651	−	0.103293i	$-0.0329381\pi$
$17$	1.68169	+	2.91278i	0.407871	+	0.706453i	−0.586780	+	0.809746i	$0.699605\pi$
$18$	−4.00278	+	1.40631i	−0.943465	+	0.331471i
$19$	2.56203	−	4.43756i	0.587769	−	1.01805i	−0.406755	−	0.913537i	$-0.633340\pi$
$19$	2.56203	−	4.43756i	0.587769	−	1.01805i	0.994524	−	0.104509i	$-0.0333270\pi$
$20$	0.669184	+	0.401321i	0.149634	+	0.0897382i
$21$	3.05110	+	3.41918i	0.665805	+	0.746126i
$22$	1.04339	+	1.84237i	0.222451	+	0.392795i
$23$	4.72764	+	2.72950i	0.985780	+	0.569141i	0.904010	−	0.427511i	$-0.140609\pi$
$23$	4.72764	+	2.72950i	0.985780	+	0.569141i	0.0817700	+	0.996651i	$0.473943\pi$
$24$	−4.84530	+	0.723204i	−0.989044	+	0.147623i
$25$	−2.42389	−	4.19830i	−0.484778	−	0.839661i
$26$	4.64932	+	0.0386203i	0.911807	+	0.00757406i
$27$	4.51125	−	2.57850i	0.868190	−	0.496232i
$28$	2.71544	+	4.54163i	0.513170	+	0.858287i
$29$	−4.13801			−0.768410			−0.384205	−	0.923248i	$-0.625524\pi$
$29$	−4.13801			−0.768410			−0.384205	+	0.923248i	$0.625524\pi$
$30$	−0.894802	−	0.335602i	−0.163368	−	0.0612723i
$31$	−3.60237	+	2.07983i	−0.647005	+	0.373549i	−0.787308	−	0.616560i	$-0.788526\pi$
$31$	−3.60237	+	2.07983i	−0.647005	+	0.373549i	0.140303	+	0.990109i	$0.455192\pi$
$32$	−5.65198	−	0.234875i	−0.999138	−	0.0415204i
$33$	−1.66397	−	1.98889i	−0.289661	−	0.346222i
$34$	−2.34398	−	4.13891i	−0.401989	−	0.709816i
$35$	0.0329110	+	1.03171i	0.00556298	+	0.174391i
$36$	5.67712	−	1.94174i	0.946186	−	0.323623i
$37$	−7.46581	−	4.31038i	−1.22737	−	0.708623i	−0.260892	−	0.965368i	$-0.584017\pi$
$37$	−7.46581	−	4.31038i	−1.22737	−	0.708623i	−0.966479	+	0.256745i	$0.917350\pi$
$38$	−3.67525	+	6.24534i	−0.596205	+	1.01313i
$39$	−5.60934	+	0.980702i	−0.898214	+	0.157038i
$40$	−0.941622	−	0.575396i	−0.148884	−	0.0909780i
$41$	−11.1607			−1.74301			−0.871505	−	0.490387i	$-0.836855\pi$
$41$	−11.1607			−1.74301			−0.871505	+	0.490387i	$0.836855\pi$
$42$	−4.27459	−	4.87112i	−0.659584	−	0.751631i
$43$			4.79323i			0.730961i	0.930819	+	0.365480i	$0.119095\pi$
$43$			4.79323i			0.730961i	−0.930819	+	0.365480i	$0.880905\pi$
$44$	−1.45388	−	2.61768i	−0.219181	−	0.394630i
$45$	1.15207	+	0.206585i	0.171741	+	0.0307959i
$46$	−6.65359	−	3.91550i	−0.981019	−	0.577309i
$47$	2.51067	−	4.34861i	0.366219	−	0.634310i	−0.622752	−	0.782419i	$-0.713985\pi$
$47$	2.51067	−	4.34861i	0.366219	−	0.634310i	0.988971	+	0.148109i	$0.0473187\pi$
$48$	6.86055	−	0.965812i	0.990236	−	0.139403i
$49$	−3.10652	+	6.27292i	−0.443788	+	0.896132i
$50$	3.37846	+	5.96557i	0.477787	+	0.843658i
$51$	3.73813	+	4.46806i	0.523443	+	0.625653i
$52$	−6.57445	−	0.109231i	−0.911712	−	0.0151476i
$53$	−0.499243	−	0.864715i	−0.0685763	−	0.118778i	0.829699	−	0.558212i	$-0.188512\pi$
$53$	−0.499243	−	0.864715i	−0.0685763	−	0.118778i	−0.898275	+	0.439434i	$0.855179\pi$
$54$	−6.40994	+	3.59342i	−0.872282	+	0.489003i
$55$		−	0.584118i		−	0.0787624i
$56$	−3.78673	−	6.45451i	−0.506023	−	0.862520i
$57$	3.04755	−	8.33548i	0.403657	−	1.10406i
$58$	5.85183	+	0.0486091i	0.768383	+	0.00638269i
$59$	1.36034	−	0.785391i	0.177101	−	0.102249i	−0.408829	−	0.912611i	$-0.634063\pi$
$59$	1.36034	−	0.785391i	0.177101	−	0.102249i	0.585930	+	0.810362i	$0.300729\pi$
$60$	1.26146	+	0.485108i	0.162853	+	0.0626272i
$61$	−3.40889	+	5.90437i	−0.436464	+	0.755977i	−0.997414	−	0.0718723i	$-0.977103\pi$
$61$	−3.40889	+	5.90437i	−0.436464	+	0.755977i	0.560950	+	0.827850i	$0.310436\pi$
$62$	5.11878	−	2.89891i	0.650085	−	0.368161i
$63$	6.22563	+	4.92357i	0.784355	+	0.620312i
$64$	7.99007	+	0.398545i	0.998758	+	0.0498181i
$65$	−1.11084	−	0.641343i	−0.137783	−	0.0795488i
$66$	2.32977	+	2.83217i	0.286775	+	0.348616i
$67$	−3.05467	+	1.76361i	−0.373187	+	0.215460i	−0.674850	−	0.737955i	$-0.735792\pi$
$67$	−3.05467	+	1.76361i	−0.373187	+	0.215460i	0.301663	+	0.953415i	$0.402458\pi$
$68$	3.26615	+	5.88063i	0.396079	+	0.713131i
$69$	8.88036	+	3.24676i	1.06907	+	0.390864i
$70$	−0.0344221	−	1.45940i	−0.00411423	−	0.174432i
$71$		−	14.3360i		−	1.70137i	−0.525677	−	0.850684i	$-0.676188\pi$
$71$		−	14.3360i		−	1.70137i	0.525677	−	0.850684i	$-0.323812\pi$
$72$	−8.05119	+	2.67925i	−0.948842	+	0.315752i
$73$	2.76107	−	1.59410i	0.323159	−	0.186576i	−0.329641	−	0.944106i	$-0.606928\pi$
$73$	2.76107	−	1.59410i	0.323159	−	0.186576i	0.652800	+	0.757531i	$0.273594\pi$
$74$	10.5072	+	6.18329i	1.22144	+	0.718793i
$75$	−5.38791	−	6.43999i	−0.622142	−	0.743626i
$76$	5.27078	−	8.78877i	0.604600	−	1.00814i
$77$	1.87018	−	3.49184i	0.213127	−	0.397932i
$78$	7.94406	−	1.32098i	0.899487	−	0.149572i
$79$	−0.239413	+	0.414676i	−0.0269361	+	0.0466547i	−0.879179	−	0.476491i	$-0.841908\pi$
$79$	−0.239413	+	0.414676i	−0.0269361	+	0.0466547i	0.852243	+	0.523146i	$0.175242\pi$
$80$	1.32485	+	0.824765i	0.148123	+	0.0922116i
$81$	6.92781	−	5.74504i	0.769756	−	0.638338i
$82$	15.7831	+	0.131105i	1.74295	+	0.0144781i
$83$			17.4548i			1.91591i	0.286911	+	0.957957i	$0.407372\pi$
$83$			17.4548i			1.91591i	−0.286911	+	0.957957i	$0.592628\pi$
$84$	5.98776	+	6.93879i	0.653318	+	0.757084i
$85$			1.31222i			0.142331i
$86$	0.0563059	−	6.77842i	0.00607163	−	0.730935i
$87$	−7.06016	+	1.23435i	−0.756928	+	0.132337i
$88$	2.02527	+	3.71891i	0.215895	+	0.396437i
$89$	−2.54840	+	4.41396i	−0.270130	+	0.467879i	−0.968895	−	0.247473i	$-0.920400\pi$
$89$	−2.54840	+	4.41396i	−0.270130	+	0.467879i	0.698765	+	0.715351i	$0.253733\pi$
$90$	−1.62679	−	0.305678i	−0.171479	−	0.0322213i
$91$	−4.58716	−	7.39053i	−0.480865	−	0.774738i
$92$	9.36328	+	5.61532i	0.976190	+	0.585438i
$93$	−5.52586	+	4.62312i	−0.573005	+	0.479395i
$94$	−3.60159	+	6.12016i	−0.371475	+	0.631246i
$95$	1.73131	−	0.999573i	0.177629	−	0.102554i
$96$	−9.71330	+	1.28523i	−0.991360	+	0.131173i
$97$			9.00074i			0.913887i	0.889496	+	0.456943i	$0.151056\pi$
$97$			9.00074i			0.913887i	−0.889496	+	0.456943i	$0.848944\pi$
$98$	4.46682	−	8.83445i	0.451217	−	0.892414i
$99$	−3.43230	−	2.89703i	−0.344959	−	0.291163i
$100$	−4.70763	−	8.47598i	−0.470763	−	0.847598i
$101$	−4.63907	+	2.67837i	−0.461605	+	0.266508i	−0.712719	−	0.701450i	$-0.752536\pi$
$101$	−4.63907	+	2.67837i	−0.461605	+	0.266508i	0.251114	+	0.967958i	$0.419203\pi$
$102$	−5.23384	−	6.36248i	−0.518228	−	0.629980i
$103$	7.70831	+	4.45039i	0.759522	+	0.438510i	0.829124	−	0.559065i	$-0.188840\pi$
$103$	7.70831	+	4.45039i	0.759522	+	0.438510i	−0.0696021	+	0.997575i	$0.522173\pi$
$104$	9.29608	+	0.231700i	0.911555	+	0.0227201i
$105$	0.363908	+	1.75046i	0.0355138	+	0.170828i
$106$	0.695854	+	1.22871i	0.0675874	+	0.119343i
$107$	7.85256	−	13.6010i	0.759135	−	1.31486i	−0.184157	−	0.982897i	$-0.558955\pi$
$107$	7.85256	−	13.6010i	0.759135	−	1.31486i	0.943292	−	0.331964i	$-0.107711\pi$
$108$	9.10692	−	5.00640i	0.876314	−	0.481741i
$109$	15.1582	−	8.75159i	1.45189	−	0.838250i	0.453303	−	0.891357i	$-0.350246\pi$
$109$	15.1582	−	8.75159i	1.45189	−	0.838250i	0.998589	+	0.0531069i	$0.0169124\pi$
$110$	−0.00686161	+	0.826039i	−0.000654229	+	0.0787597i
$111$	−14.0237	−	5.12723i	−1.33107	−	0.486655i
$112$	5.27924	+	9.17222i	0.498841	+	0.866693i
$113$		−	0.0726142i		−	0.00683097i	−0.999994	−	0.00341549i	$-0.998913\pi$
$113$		−	0.0726142i		−	0.00683097i	0.999994	−	0.00341549i	$-0.00108718\pi$
$114$	−4.40765	+	11.7519i	−0.412814	+	1.10067i
$115$	1.06491	+	1.84448i	0.0993037	+	0.171999i
$116$	−8.27488	−	0.137483i	−0.768304	−	0.0127649i
$117$	−9.27796	+	3.34649i	−0.857748	+	0.309383i
$118$	−1.93297	+	1.09469i	−0.177944	+	0.100775i
$119$	−4.20138	+	7.84443i	−0.385139	+	0.719098i
$120$	−1.77821	−	0.700841i	−0.162327	−	0.0639777i
$121$	4.37925	−	7.58508i	0.398114	−	0.689553i
$122$	4.89009	−	8.30971i	0.442728	−	0.752326i
$123$	−19.0421	+	3.32920i	−1.71697	+	0.300183i
$124$	−7.27285	+	4.03940i	−0.653121	+	0.362749i
$125$		−	3.84211i		−	0.343649i
$126$	−8.74622	−	7.03588i	−0.779176	−	0.626806i
$127$	−8.81577			−0.782273			−0.391137	−	0.920333i	$-0.627918\pi$
$127$	−8.81577			−0.782273			−0.391137	+	0.920333i	$0.627918\pi$
$128$	−11.2946	−	0.657467i	−0.998310	−	0.0581125i
$129$	1.42980	+	8.17807i	0.125887	+	0.720039i
$130$	1.56338	+	0.920014i	0.137117	+	0.0806906i
$131$	4.36183	+	2.51830i	0.381095	+	0.220025i	0.678294	−	0.734790i	$-0.262719\pi$
$131$	4.36183	+	2.51830i	0.381095	+	0.220025i	−0.297200	+	0.954815i	$0.596053\pi$
$132$	−3.26141	−	4.03252i	−0.283869	−	0.350986i
$133$	13.5501	−	0.432239i	1.17494	−	0.0374799i
$134$	4.34052	−	2.45816i	0.374964	−	0.212352i
$135$	2.02726	+	0.00881014i	0.174478	+	0.000758256i
$136$	−4.54979	−	8.35455i	−0.390142	−	0.716396i
$137$	6.34787	−	3.66494i	0.542335	−	0.313117i	−0.203690	−	0.979035i	$-0.565293\pi$
$137$	6.34787	−	3.66494i	0.542335	−	0.313117i	0.746025	+	0.665918i	$0.231960\pi$
$138$	−12.5201	−	4.69577i	−1.06579	−	0.399731i
$139$	−15.7497			−1.33587			−0.667935	−	0.744220i	$-0.732822\pi$
$139$	−15.7497			−1.33587			−0.667935	+	0.744220i	$0.732822\pi$
$140$	0.0315350	+	2.06424i	0.00266519	+	0.174460i
$141$	2.98646	−	8.16840i	0.251505	−	0.687903i
$142$	−0.168404	+	20.2735i	−0.0141322	+	1.70131i
$143$	2.46110	+	4.26275i	0.205807	+	0.356469i
$144$	11.4172	−	3.69432i	0.951432	−	0.307860i
$145$	−1.39815	−	0.807222i	−0.116110	−	0.0670361i
$146$	−3.92333	+	2.22189i	−0.324697	+	0.183885i
$147$	−3.42906	+	11.6293i	−0.282824	+	0.959172i
$148$	−14.7863	−	8.86763i	−1.21543	−	0.728914i
$149$	8.98969	−	15.5706i	0.736464	−	1.27559i	−0.217613	−	0.976035i	$-0.569827\pi$
$149$	8.98969	−	15.5706i	0.736464	−	1.27559i	0.954078	−	0.299559i	$-0.0968395\pi$
$150$	7.54374	+	9.17049i	0.615944	+	0.748768i
$151$	−7.89149	−	13.6685i	−0.642201	−	1.11232i	−0.984940	−	0.172894i	$-0.944688\pi$
$151$	−7.89149	−	13.6685i	−0.642201	−	1.11232i	0.342740	−	0.939430i	$-0.388645\pi$
$152$	−7.55699	+	12.3669i	−0.612953	+	1.00308i
$153$	7.71069	+	6.50820i	0.623373	+	0.526157i
$154$	−2.68576	+	4.91606i	−0.216425	+	0.396148i
$155$	−1.62289			−0.130354
$156$	−11.2497	+	1.77477i	−0.900699	+	0.142095i
$157$	2.53274	+	4.38683i	0.202134	+	0.350107i	0.949216	−	0.314625i	$-0.101879\pi$
$157$	2.53274	+	4.38683i	0.202134	+	0.350107i	−0.747082	+	0.664732i	$0.768546\pi$
$158$	0.343441	−	0.583608i	0.0273227	−	0.0464294i
$159$	−1.10974	−	1.32643i	−0.0880077	−	0.105193i
$160$	−1.86387	−	1.18192i	−0.147352	−	0.0934387i
$161$	0.460494	+	14.4358i	0.0362920	+	1.13770i
$162$	−9.86455	+	8.04306i	−0.775032	+	0.631922i
$163$	10.8745	+	6.27840i	0.851757	+	0.491762i	0.861243	−	0.508193i	$-0.169686\pi$
$163$	10.8745	+	6.27840i	0.851757	+	0.491762i	−0.00948597	+	0.999955i	$0.503020\pi$
$164$	−22.3183	−	0.370807i	−1.74277	−	0.0289551i
$165$	−0.174240	−	0.996605i	−0.0135646	−	0.0775856i
$166$	0.205041	−	24.6840i	0.0159143	−	1.91585i
$167$	7.43145			0.575063			0.287531	−	0.957771i	$-0.407165\pi$
$167$	7.43145			0.575063			0.287531	+	0.957771i	$0.407165\pi$
$168$	−8.38617	−	9.88293i	−0.647007	−	0.762484i
$169$	−2.19116			−0.168551
$170$	0.0154147	−	1.85570i	0.00118225	−	0.142326i
$171$	2.71320	−	15.1308i	0.207483	−	1.15708i
$172$	−0.159252	+	9.58514i	−0.0121428	+	0.730860i
$173$	15.2445	+	8.80144i	1.15902	+	0.669161i	0.951069	−	0.308978i	$-0.0999870\pi$
$173$	15.2445	+	8.80144i	1.15902	+	0.669161i	0.207952	+	0.978139i	$0.433320\pi$
$174$	9.99873	−	1.66264i	0.758002	−	0.126045i
$175$	6.05561	−	11.3065i	0.457761	−	0.854690i
$176$	−2.82039	−	5.28294i	−0.212595	−	0.398216i
$177$	2.08669	−	1.74579i	0.156845	−	0.131222i
$178$	3.65571	−	6.21213i	0.274007	−	0.465619i
$179$	8.11784	+	14.0605i	0.606756	+	1.05093i	0.991771	+	0.128022i	$0.0408627\pi$
$179$	8.11784	+	14.0605i	0.606756	+	1.05093i	−0.385016	+	0.922910i	$0.625804\pi$
$180$	2.29696	+	0.451390i	0.171206	+	0.0336446i
$181$	6.19340			0.460351			0.230176	−	0.973149i	$-0.426070\pi$
$181$	6.19340			0.460351			0.230176	+	0.973149i	$0.426070\pi$
$182$	6.40018	+	10.5053i	0.474413	+	0.778705i
$183$	−4.05490	+	11.0907i	−0.299747	+	0.819850i
$184$	−13.1753	−	8.05098i	−0.971293	−	0.593526i
$185$	−1.68169	−	2.91278i	−0.123641	−	0.214152i
$186$	7.86878	−	6.47294i	0.576967	−	0.474619i
$187$	2.51777	−	4.36091i	0.184118	−	0.318901i
$188$	5.16513	−	8.61261i	0.376706	−	0.628139i
$189$	12.0907	+	6.54338i	0.879467	+	0.475961i
$190$	−2.46010	+	1.39322i	−0.178475	+	0.101075i
$191$	7.28788	+	4.20766i	0.527333	+	0.304456i	0.739930	−	0.672684i	$-0.234859\pi$
$191$	7.28788	+	4.20766i	0.527333	+	0.304456i	−0.212597	+	0.977140i	$0.568192\pi$
$192$	13.7513	−	1.70342i	0.992415	−	0.122934i
$193$	6.57333	+	11.3853i	0.473158	+	0.819534i	0.999528	−	0.0307215i	$-0.00978048\pi$
$193$	6.57333	+	11.3853i	0.473158	+	0.819534i	−0.526370	+	0.850256i	$0.676447\pi$
$194$	0.105731	−	12.7285i	0.00759108	−	0.913855i
$195$	−2.08659	−	0.762882i	−0.149424	−	0.0546311i
$196$	−6.42059	+	12.4409i	−0.458614	+	0.888636i
$197$	−17.6119			−1.25480			−0.627398	−	0.778699i	$-0.715880\pi$
$197$	−17.6119			−1.25480			−0.627398	+	0.778699i	$0.715880\pi$
$198$	4.81981	+	4.13720i	0.342529	+	0.294018i
$199$	17.2688	−	9.97017i	1.22416	−	0.706767i	0.258354	−	0.966050i	$-0.416820\pi$
$199$	17.2688	−	9.97017i	1.22416	−	0.706767i	0.965801	+	0.259284i	$0.0834864\pi$
$200$	6.55780	+	12.0417i	0.463706	+	0.851479i
$201$	−4.68570	+	3.92022i	−0.330504	+	0.276511i
$202$	6.59187	−	3.73316i	0.463803	−	0.262664i
$203$	−5.77359	−	9.30203i	−0.405227	−	0.652874i
$204$	7.32678	+	9.05908i	0.512977	+	0.634262i
$205$	−3.77097	−	2.17717i	−0.263376	−	0.152060i
$206$	−10.8485	−	6.38414i	−0.755853	−	0.444804i
$207$	16.1199	+	2.89055i	1.12041	+	0.200907i
$208$	−13.1435	−	0.436863i	−0.911335	−	0.0302910i
$209$	−7.67154			−0.530652
$210$	−0.494063	−	2.47972i	−0.0340936	−	0.171117i
$211$			14.5159i			0.999314i	0.866223	+	0.499657i	$0.166541\pi$
$211$			14.5159i			0.999314i	−0.866223	+	0.499657i	$0.833459\pi$
$212$	−0.969619	−	1.74578i	−0.0665937	−	0.119901i
$213$	−4.27637	−	24.4596i	−0.293012	−	1.67595i
$214$	−11.2646	+	19.1419i	−0.770031	+	1.30851i
$215$	−0.935038	+	1.61953i	−0.0637691	+	0.110451i
$216$	−12.9375	+	6.97289i	−0.880285	+	0.474445i
$217$	−9.70158	−	5.19604i	−0.658586	−	0.352730i
$218$	−21.5390	+	12.1981i	−1.45880	+	0.826161i
$219$	4.23534	−	3.54343i	0.286198	−	0.239443i
$220$	0.0194069	−	1.16807i	0.00130841	−	0.0787515i
$221$	−5.52887	−	9.57629i	−0.371912	−	0.644171i
$222$	19.7716	+	7.41549i	1.32698	+	0.497695i
$223$			2.77897i			0.186093i	0.995662	+	0.0930467i	$0.0296606\pi$
$223$			2.77897i			0.186093i	−0.995662	+	0.0930467i	$0.970339\pi$
$224$	−7.35797	−	13.0330i	−0.491625	−	0.870807i
$225$	−11.1137	−	9.38052i	−0.740915	−	0.625368i
$226$	−0.000852997		0.102688i	−5.67405e−5		0.00683074i
$227$	−14.0438	+	8.10819i	−0.932119	+	0.538159i	−0.887481	−	0.460844i	$-0.847547\pi$
$227$	−14.0438	+	8.10819i	−0.932119	+	0.538159i	−0.0446379	+	0.999003i	$0.514213\pi$
$228$	6.37119	−	16.5674i	0.421943	−	1.09720i
$229$	−10.3150	+	17.8661i	−0.681633	+	1.18062i	0.292849	+	0.956159i	$0.405397\pi$
$229$	−10.3150	+	17.8661i	−0.681633	+	1.18062i	−0.974482	+	0.224464i	$0.927937\pi$
$230$	−1.48430	−	2.62091i	−0.0978716	−	0.172818i
$231$	2.14925	−	6.51554i	0.141410	−	0.428691i
$232$	11.7004	+	0.291628i	0.768171	+	0.0191463i
$233$	1.80462	+	1.04190i	0.118225	+	0.0682572i	0.557946	−	0.829877i	$-0.311589\pi$
$233$	1.80462	+	1.04190i	0.118225	+	0.0682572i	−0.439721	+	0.898134i	$0.644923\pi$
$234$	13.1599	−	4.62350i	0.860288	−	0.302248i
$235$	1.69661	−	0.979538i	0.110675	−	0.0638980i
$236$	2.74639	−	1.52537i	0.178775	−	0.0992931i
$237$	−0.284784	+	0.778925i	−0.0184987	+	0.0505966i
$238$	6.03359	−	11.0440i	0.391099	−	0.715874i
$239$			0.851762i			0.0550959i	0.999620	+	0.0275480i	$0.00876990\pi$
$239$			0.851762i			0.0550959i	−0.999620	+	0.0275480i	$0.991230\pi$
$240$	2.50645	+	1.01199i	0.161790	+	0.0653239i
$241$	13.0417	−	7.52961i	0.840087	−	0.485025i	−0.0172066	−	0.999852i	$-0.505477\pi$
$241$	13.0417	−	7.52961i	0.840087	−	0.485025i	0.857294	+	0.514827i	$0.172144\pi$
$242$	−6.28208	+	10.6751i	−0.403828	+	0.686222i
$243$	10.1063	−	11.8686i	0.648319	−	0.761369i
$244$	−7.01301	+	11.6939i	−0.448962	+	0.748622i
$245$	−2.27332	+	1.51349i	−0.145237	+	0.0966932i
$246$	26.9677	−	4.48434i	1.71940	−	0.285911i
$247$	−8.42312	+	14.5893i	−0.535950	+	0.928293i
$248$	10.3325	−	5.62694i	0.656112	−	0.357311i
$249$	5.20670	+	29.7809i	0.329961	+	1.88729i
$250$	−0.0451331	+	5.43337i	−0.00285447	+	0.343637i
$251$		−	11.8022i		−	0.744948i	−0.928043	−	0.372474i	$-0.878510\pi$
$251$		−	11.8022i		−	0.744948i	0.928043	−	0.372474i	$-0.121490\pi$
$252$	12.2860	+	10.0526i	0.773942	+	0.633256i
$253$		−	8.17302i		−	0.513834i
$254$	12.4670	+	0.103559i	0.782246	+	0.00649785i
$255$	0.391432	+	2.23888i	0.0245124	+	0.140204i
$256$	15.9647	+	1.06244i	0.997793	+	0.0664028i
$257$	8.86901	−	15.3616i	0.553233	−	0.958228i	−0.444805	−	0.895627i	$-0.646727\pi$
$257$	8.86901	−	15.3616i	0.553233	−	0.958228i	0.998039	−	0.0626011i	$-0.0199396\pi$
$258$	−1.92591	−	11.5819i	−0.119902	−	0.721060i
$259$	−0.727204	−	22.7968i	−0.0451863	−	1.41653i
$260$	−2.20006	−	1.31942i	−0.136442	−	0.0818267i
$261$	−11.6776	+	4.21204i	−0.722827	+	0.260719i
$262$	−6.13876	−	3.61253i	−0.379254	−	0.223183i
$263$	−6.27815	+	3.62469i	−0.387128	+	0.223508i	−0.680915	−	0.732363i	$-0.738418\pi$
$263$	−6.27815	+	3.62469i	−0.387128	+	0.223508i	0.293787	+	0.955871i	$0.405084\pi$
$264$	4.56480	+	5.74096i	0.280944	+	0.353331i
$265$		−	0.389559i		−	0.0239304i
$266$	−19.1671	+	0.452085i	−1.17521	+	0.0277191i
$267$	−3.03134	+	8.29114i	−0.185515	+	0.507410i
$268$	−6.16709	+	3.42525i	−0.376715	+	0.209230i
$269$	−2.95817	+	1.70790i	−0.180363	+	0.104132i	−0.587463	−	0.809251i	$-0.699873\pi$
$269$	−2.95817	+	1.70790i	−0.180363	+	0.104132i	0.407100	+	0.913383i	$0.366540\pi$
$270$	−2.86677	−	0.0362731i	−0.174466	−	0.00220751i
$271$	3.96989	+	2.29201i	0.241153	+	0.139230i	0.615707	−	0.787975i	$-0.288871\pi$
$271$	3.96989	+	2.29201i	0.241153	+	0.139230i	−0.374553	+	0.927205i	$0.622204\pi$
$272$	6.33602	+	11.8682i	0.384177	+	0.719612i
$273$	−10.0310	−	11.2412i	−0.607106	−	0.680346i
$274$	−9.01998	+	5.10826i	−0.544917	+	0.308601i
$275$	−3.62896	+	6.28555i	−0.218835	+	0.379033i
$276$	17.6504	+	6.78767i	1.06243	+	0.408570i
$277$	10.6940	−	6.17421i	0.642543	−	0.370972i	−0.143050	−	0.989715i	$-0.545691\pi$
$277$	10.6940	−	6.17421i	0.642543	−	0.370972i	0.785593	+	0.618743i	$0.212358\pi$
$278$	22.2726	+	0.185011i	1.33582	+	0.0110962i
$279$	−8.04900	+	9.53617i	−0.481881	+	0.570916i
$280$	−0.0203471	−	2.91954i	−0.00121597	−	0.174476i
$281$			7.91565i			0.472208i	0.971728	+	0.236104i	$0.0758706\pi$
$281$			7.91565i			0.472208i	−0.971728	+	0.236104i	$0.924129\pi$
$282$	−4.31930	+	11.5164i	−0.257211	+	0.685791i
$283$	11.3552	+	19.6678i	0.674999	+	1.16913i	0.976469	+	0.215656i	$0.0691891\pi$
$283$	11.3552	+	19.6678i	0.674999	+	1.16913i	−0.301471	+	0.953475i	$0.597478\pi$
$284$	0.476303	−	28.6680i	0.0282634	−	1.70113i
$285$	2.65574	−	2.22189i	0.157313	−	0.131613i
$286$	−3.43032	−	6.05714i	−0.202839	−	0.358166i
$287$	−15.5720	−	25.0887i	−0.919189	−	1.48094i
$288$	−16.1892	+	5.09026i	−0.953956	+	0.299946i
$289$	2.84381	−	4.92562i	0.167283	−	0.289742i
$290$	1.96773	+	1.15797i	0.115549	+	0.0679983i
$291$	2.68489	+	15.3568i	0.157391	+	0.900232i
$292$	5.57434	−	3.09603i	0.326214	−	0.181182i
$293$			12.8246i			0.749220i	0.927183	+	0.374610i	$0.122223\pi$
$293$			12.8246i			0.749220i	−0.927183	+	0.374610i	$0.877777\pi$
$294$	4.98587	−	16.4055i	0.290782	−	0.956789i
$295$	0.612840			0.0356809
$296$	20.8062	+	12.7140i	1.20933	+	0.738985i
$297$	−6.72027	−	3.91899i	−0.389950	−	0.227403i
$298$	−12.8958	+	21.9138i	−0.747035	+	1.26943i
$299$	−15.5430	−	8.97373i	−0.898872	−	0.518964i
$300$	−10.5604	−	13.0572i	−0.609703	−	0.753858i
$301$	−10.7749	+	6.68778i	−0.621056	+	0.385477i
$302$	10.9993	+	19.4222i	0.632939	+	1.11762i
$303$	−7.11610	+	5.95357i	−0.408809	+	0.342024i
$304$	10.8321	−	17.4000i	0.621264	−	0.997958i
$305$	−2.30359	+	1.32998i	−0.131903	+	0.0761542i
$306$	−10.8277	−	9.29425i	−0.618981	−	0.531317i
$307$	12.3622			0.705549			0.352774	−	0.935708i	$-0.385238\pi$
$307$	12.3622			0.705549			0.352774	+	0.935708i	$0.385238\pi$
$308$	3.85586	−	6.92057i	0.219708	−	0.394336i
$309$	14.4792	+	5.29377i	0.823694	+	0.301152i
$310$	2.29503	+	0.0190640i	0.130349	+	0.00108276i
$311$	−0.720819	−	1.24850i	−0.0408739	−	0.0707957i	0.844865	−	0.534980i	$-0.179681\pi$
$311$	−0.720819	−	1.24850i	−0.0408739	−	0.0707957i	−0.885739	+	0.464184i	$0.846348\pi$
$312$	15.9298	−	2.37766i	0.901848	−	0.134609i
$313$	−20.8822	−	12.0564i	−1.18033	−	0.681466i	−0.224242	−	0.974533i	$-0.571991\pi$
$313$	−20.8822	−	12.0564i	−1.18033	−	0.681466i	−0.956092	+	0.293067i	$0.905324\pi$
$314$	−3.53017	−	6.23345i	−0.199219	−	0.351774i
$315$	1.14305	+	2.87804i	0.0644033	+	0.162159i
$316$	−0.492538	+	0.821284i	−0.0277074	+	0.0462008i
$317$	−13.4686	+	23.3283i	−0.756472	+	1.31025i	0.188167	+	0.982137i	$0.439745\pi$
$317$	−13.4686	+	23.3283i	−0.756472	+	1.31025i	−0.944639	+	0.328111i	$0.893588\pi$
$318$	1.55377	+	1.88882i	0.0871309	+	0.105920i
$319$	3.09764	+	5.36527i	0.173435	+	0.300398i
$320$	2.62193	+	1.69332i	0.146570	+	0.0946595i
$321$	9.34067	−	25.5481i	0.521345	−	1.42595i
$322$	−0.481637	−	20.4200i	−0.0268406	−	1.13796i
$323$	17.2342			0.958935
$324$	14.0446	−	11.2583i	0.780254	−	0.625463i
$325$	7.96898	+	13.8027i	0.442039	+	0.765635i
$326$	−15.3046	−	9.00644i	−0.847643	−	0.498820i
$327$	23.2519	−	19.4533i	1.28583	−	1.07577i
$328$	31.5574	+	0.786555i	1.74247	+	0.0434302i
$329$	13.2785	−	0.423575i	0.732066	−	0.0233524i
$330$	0.234697	+	1.41141i	0.0129196	+	0.0776956i
$331$	15.2782	+	8.82087i	0.839766	+	0.484839i	0.857185	−	0.515009i	$-0.172212\pi$
$331$	15.2782	+	8.82087i	0.839766	+	0.484839i	−0.0174189	+	0.999848i	$0.505545\pi$
$332$	−0.579924	+	34.9048i	−0.0318275	+	1.91565i
$333$	−25.4563	−	4.56471i	−1.39500	−	0.250145i
$334$	−10.5093	−	0.0872970i	−0.575043	−	0.00477668i
$335$	−1.37615			−0.0751868
$336$	11.7433	+	14.0746i	0.640651	+	0.767832i
$337$	11.0396			0.601365			0.300682	−	0.953724i	$-0.402786\pi$
$337$	11.0396			0.601365			0.300682	+	0.953724i	$0.402786\pi$
$338$	3.09866	+	0.0257395i	0.168545	+	0.00140005i
$339$	−0.0216605	−	0.123892i	−0.00117644	−	0.00672890i
$340$	−0.0435978	+	2.62409i	−0.00236442	+	0.142311i
$341$	5.39334	+	3.11385i	0.292066	+	0.168624i
$342$	−4.01465	+	21.3656i	−0.217087	+	1.15532i
$343$	−18.4356	+	1.76905i	−0.995428	+	0.0955198i
$344$	0.337805	−	13.5531i	0.0182132	−	0.730734i
$345$	2.36713	+	2.82935i	0.127442	+	0.152327i
$346$	−21.4549	−	12.6258i	−1.15342	−	0.678765i
$347$	−10.8299	−	18.7579i	−0.581377	−	1.00697i	−0.995316	−	0.0966701i	$-0.969181\pi$
$347$	−10.8299	−	18.7579i	−0.581377	−	1.00697i	0.413940	−	0.910304i	$-0.364152\pi$
$348$	−14.1594	+	2.23380i	−0.759022	+	0.119744i
$349$	−6.46130			−0.345865			−0.172933	−	0.984934i	$-0.555324\pi$
$349$	−6.46130			−0.345865			−0.172933	+	0.984934i	$0.555324\pi$
$350$	−8.69644	+	15.9181i	−0.464844	+	0.850858i
$351$	−14.8315	+	8.47727i	−0.791649	+	0.452483i
$352$	3.92643	+	7.50407i	0.209280	+	0.399968i
$353$	−14.9846	−	25.9541i	−0.797549	−	1.38140i	−0.921208	−	0.389071i	$-0.872796\pi$
$353$	−14.9846	−	25.9541i	−0.797549	−	1.38140i	0.123659	−	0.992325i	$-0.460537\pi$
$354$	−2.97143	+	2.44433i	−0.157930	+	0.129915i
$355$	2.79659	−	4.84383i	0.148428	−	0.257084i
$356$	−5.24275	+	8.74203i	−0.277865	+	0.463327i
$357$	−4.82830	+	14.6372i	−0.255541	+	0.774683i
$358$	−11.3148	−	19.9792i	−0.598005	−	1.05594i
$359$	−9.44412	−	5.45257i	−0.498442	−	0.287775i	0.229628	−	0.973278i	$-0.426249\pi$
$359$	−9.44412	−	5.45257i	−0.498442	−	0.287775i	−0.728070	+	0.685503i	$0.759582\pi$
$360$	−3.24298	−	0.665322i	−0.170920	−	0.0350655i
$361$	−3.62795	−	6.28380i	−0.190945	−	0.330726i
$362$	−8.75848	−	0.0727537i	−0.460336	−	0.00382385i
$363$	5.20915	−	14.2478i	0.273409	−	0.747814i
$364$	−8.92750	−	14.9314i	−0.467928	−	0.782619i
$365$	1.24388			0.0651075
$366$	5.86458	−	15.6365i	0.306546	−	0.817332i
$367$	−2.43552	+	1.40615i	−0.127133	+	0.0734002i	−0.562218	−	0.826989i	$-0.690052\pi$
$367$	−2.43552	+	1.40615i	−0.127133	+	0.0734002i	0.435085	+	0.900389i	$0.356718\pi$
$368$	18.5374	+	11.5402i	0.966330	+	0.601574i
$369$	−31.4959	+	11.3604i	−1.63961	+	0.591396i
$370$	2.34398	+	4.13891i	0.121858	+	0.215171i
$371$	1.24726	−	2.32877i	0.0647545	−	0.120904i
$372$	−11.2038	+	9.06137i	−0.580889	+	0.469810i
$373$	−26.9266	−	15.5461i	−1.39421	−	0.804947i	−0.400431	−	0.916327i	$-0.631140\pi$
$373$	−26.9266	−	15.5461i	−1.39421	−	0.804947i	−0.993778	+	0.111380i	$0.964473\pi$
$374$	−3.61177	+	6.13747i	−0.186760	+	0.317361i
$375$	−1.14609	−	6.55529i	−0.0591836	−	0.338514i
$376$	−7.40552	+	12.1190i	−0.381911	+	0.624988i
$377$	13.6045			0.700665
$378$	−17.0213	−	9.39544i	−0.875483	−	0.483249i
$379$		−	17.6950i		−	0.908931i	−0.890764	−	0.454465i	$-0.849830\pi$
$379$		−	17.6950i		−	0.908931i	0.890764	−	0.454465i	$-0.150170\pi$
$380$	3.49535	−	1.94135i	0.179308	−	0.0995891i
$381$	−15.0412	+	2.62971i	−0.770585	+	0.134724i
$382$	−10.2568	−	6.03594i	−0.524786	−	0.308825i
$383$	−17.4953	+	30.3028i	−0.893968	+	1.54840i	−0.0588917	+	0.998264i	$0.518757\pi$
$383$	−17.4953	+	30.3028i	−0.893968	+	1.54840i	−0.835076	+	0.550134i	$0.814577\pi$
$384$	−19.4666	+	2.24738i	−0.993402	+	0.114686i
$385$	1.31306	−	0.814994i	0.0669200	−	0.0415359i
$386$	−9.16202	−	16.1780i	−0.466335	−	0.823436i
$387$	4.87897	+	13.5267i	0.248012	+	0.687600i
$388$	−0.299044	+	17.9990i	−0.0151816	+	0.913761i
$389$	10.4422	+	18.0864i	0.529439	+	0.917015i	0.999410	+	0.0343338i	$0.0109309\pi$
$389$	10.4422	+	18.0864i	0.529439	+	0.917015i	−0.469971	+	0.882682i	$0.655736\pi$
$390$	2.94182	+	1.10335i	0.148965	+	0.0558704i
$391$			18.3608i			0.928543i
$392$	9.22592	−	17.5181i	0.465979	−	0.884796i
$393$	8.19322	+	2.99554i	0.413293	+	0.151105i
$394$	24.9061	+	0.206886i	1.25475	+	0.0104228i
$395$	−0.161786	+	0.0934070i	−0.00814032	+	0.00469982i
$396$	−6.76741	−	5.90730i	−0.340075	−	0.296853i
$397$	−2.44443	+	4.23387i	−0.122682	+	0.212492i	−0.920825	−	0.389977i	$-0.872483\pi$
$397$	−2.44443	+	4.23387i	−0.122682	+	0.212492i	0.798142	+	0.602469i	$0.205816\pi$
$398$	−24.5381	+	13.8966i	−1.22998	+	0.696574i
$399$	22.9898	−	4.77941i	1.15093	−	0.239270i
$400$	−9.13235	−	17.1060i	−0.456617	−	0.855301i
$401$	−6.62355	−	3.82411i	−0.330764	−	0.190967i	0.325416	−	0.945571i	$-0.394496\pi$
$401$	−6.62355	−	3.82411i	−0.330764	−	0.190967i	−0.656180	+	0.754604i	$0.727829\pi$
$402$	6.67241	−	5.48879i	0.332790	−	0.273756i
$403$	11.8434	−	6.83782i	0.589964	−	0.340616i
$404$	−9.36585	+	5.20187i	−0.465968	+	0.258803i
$405$	3.46148	−	0.589691i	0.172002	−	0.0293020i
$406$	8.05554	+	13.2224i	0.399790	+	0.656218i
$407$			12.9067i			0.639762i
$408$	−10.2549	−	12.8971i	−0.507691	−	0.638501i
$409$	−6.66584	+	3.84852i	−0.329604	+	0.190297i	−0.655666	−	0.755051i	$-0.727612\pi$
$409$	−6.66584	+	3.84852i	−0.329604	+	0.190297i	0.326061	+	0.945349i	$0.394279\pi$
$410$	5.30720	+	3.12318i	0.262104	+	0.154243i
$411$	9.73731	−	8.14656i	0.480306	−	0.401840i
$412$	15.2666	+	9.15566i	0.752133	+	0.451067i
$413$	3.66354	+	1.96214i	0.180271	+	0.0965507i
$414$	−22.7622	−	4.27708i	−1.11870	−	0.210207i
$415$	−3.40499	+	5.89762i	−0.167145	+	0.289503i
$416$	18.5819	+	0.772193i	0.911052	+	0.0378599i
$417$	−26.8716	+	4.69807i	−1.31591	+	0.230065i
$418$	10.8488	+	0.0901174i	0.530634	+	0.00440779i
$419$			4.38235i			0.214092i	0.994254	+	0.107046i	$0.0341392\pi$
$419$			4.38235i			0.214092i	−0.994254	+	0.107046i	$0.965861\pi$
$420$	0.669558	+	3.51253i	0.0326711	+	0.171394i
$421$		−	11.9400i		−	0.581921i	−0.956735	−	0.290961i	$-0.906025\pi$
$421$		−	11.9400i		−	0.581921i	0.956735	−	0.290961i	$-0.0939749\pi$
$422$	0.170518	−	20.5278i	0.00830067	−	0.999280i
$423$	2.65881	−	14.8275i	0.129276	−	0.720940i
$424$	1.35069	+	2.48021i	0.0655955	+	0.120450i
$425$	8.15249	−	14.1205i	0.395454	−	0.684946i
$426$	5.76017	+	34.6402i	0.279081	+	1.67832i
$427$	−18.0290	+	0.575113i	−0.872484	+	0.0278317i
$428$	16.1548	−	26.9374i	0.780873	−	1.30207i
$429$	5.47061	+	6.53884i	0.264124	+	0.315698i
$430$	1.34132	−	2.27930i	0.0646843	−	0.109918i
$431$	0.588922	−	0.340014i	0.0283674	−	0.0163779i	−0.485749	−	0.874098i	$-0.661453\pi$
$431$	0.588922	−	0.340014i	0.0283674	−	0.0163779i	0.514117	+	0.857720i	$0.328120\pi$
$432$	18.3777	−	9.70884i	0.884196	−	0.467117i
$433$			0.238499i			0.0114615i	0.999984	+	0.00573077i	$0.00182417\pi$
$433$			0.238499i			0.0114615i	−0.999984	+	0.00573077i	$0.998176\pi$
$434$	13.6586	+	7.46202i	0.655633	+	0.358188i
$435$	−2.62627	−	0.960196i	−0.125920	−	0.0460379i
$436$	30.6030	−	16.9971i	1.46562	−	0.814015i
$437$	24.2247	−	13.9861i	1.15882	−	0.669046i
$438$	−6.03110	+	4.96124i	−0.288177	+	0.237057i
$439$	3.29894	+	1.90465i	0.157450	+	0.0909038i	0.576655	−	0.816988i	$-0.304358\pi$
$439$	3.29894	+	1.90465i	0.157450	+	0.0909038i	−0.419205	+	0.907892i	$0.637691\pi$
$440$	−0.0411659	+	1.65162i	−0.00196251	+	0.0787380i
$441$	−2.38158	+	20.8645i	−0.113409	+	0.993548i
$442$	7.70624	+	13.6074i	0.366549	+	0.647238i
$443$	3.02001	−	5.23080i	0.143485	−	0.248523i	−0.785322	−	0.619088i	$-0.787503\pi$
$443$	3.02001	−	5.23080i	0.143485	−	0.248523i	0.928807	+	0.370565i	$0.120836\pi$
$444$	−27.8732	−	10.7190i	−1.32280	−	0.508700i
$445$	−1.72210	+	0.994257i	−0.0816355	+	0.0471323i
$446$	0.0326445	−	3.92992i	0.00154576	−	0.186087i
$447$	10.6933	−	29.2477i	0.505776	−	1.38337i
$448$	10.2523	+	18.5173i	0.484375	+	0.874861i
$449$			28.1482i			1.32839i	0.747558	+	0.664197i	$0.231226\pi$
$449$			28.1482i			1.32839i	−0.747558	+	0.664197i	$0.768774\pi$
$450$	15.6064	+	13.3962i	0.735695	+	0.631501i
$451$	8.35470	+	14.4708i	0.393408	+	0.681402i
$452$	0.00241256	−	0.145208i	0.000113477	−	0.00683003i
$453$	−17.5415	−	20.9667i	−0.824171	−	0.985103i
$454$	19.9555	−	11.3013i	0.936557	−	0.530398i
$455$	−0.108201	−	3.39194i	−0.00507254	−	0.159017i
$456$	−9.20453	+	23.3542i	−0.431042	+	1.09366i
$457$	−6.23304	+	10.7959i	−0.291569	+	0.505013i	−0.974181	−	0.225768i	$-0.927511\pi$
$457$	−6.23304	+	10.7959i	−0.291569	+	0.505013i	0.682612	+	0.730781i	$0.260844\pi$
$458$	14.7970	−	25.1444i	0.691416	−	1.17492i
$459$	15.0971	+	8.80403i	0.704674	+	0.410937i
$460$	2.06825	+	3.72384i	0.0964327	+	0.173625i
$461$		−	31.6209i		−	1.47273i	−0.676583	−	0.736367i	$-0.736540\pi$
$461$		−	31.6209i		−	1.47273i	0.676583	−	0.736367i	$-0.263460\pi$
$462$	−3.11593	+	9.18880i	−0.144966	+	0.427501i
$463$	23.5095			1.09258			0.546290	−	0.837596i	$-0.316040\pi$
$463$	23.5095			1.09258			0.546290	+	0.837596i	$0.316040\pi$
$464$	−16.5429	−	0.549855i	−0.767986	−	0.0255264i
$465$	−2.76893	+	0.484102i	−0.128406	+	0.0224497i
$466$	−2.53980	−	1.49462i	−0.117654	−	0.0692368i
$467$	−12.7642	−	7.36942i	−0.590657	−	0.341016i	0.174700	−	0.984622i	$-0.444104\pi$
$467$	−12.7642	−	7.36942i	−0.590657	−	0.341016i	−0.765357	+	0.643606i	$0.777438\pi$
$468$	−18.6645	+	6.38381i	−0.862769	+	0.295092i
$469$	−8.22655	−	4.40603i	−0.379867	−	0.203452i
$470$	−2.41079	+	1.36530i	−0.111201	+	0.0629765i
$471$	5.62985	+	6.72917i	0.259410	+	0.310064i
$472$	−3.90177	+	2.12486i	−0.179594	+	0.0978047i
$473$	6.21481	−	3.58812i	0.285757	−	0.164982i
$474$	0.411881	−	1.09818i	0.0189183	−	0.0504412i
$475$	−24.8403			−1.13975
$476$	−8.66222	+	15.5471i	−0.397032	+	0.712601i
$477$	−2.28907	−	1.93208i	−0.104809	−	0.0884641i
$478$	0.0100056	−	1.20453i	0.000457647	−	0.0550940i
$479$	17.3034	+	29.9703i	0.790611	+	1.36938i	0.925589	+	0.378529i	$0.123570\pi$
$479$	17.3034	+	29.9703i	0.790611	+	1.36938i	−0.134979	+	0.990848i	$0.543097\pi$
$480$	−3.53264	−	1.46057i	−0.161242	−	0.0666655i
$481$	24.5452	+	14.1712i	1.11916	+	0.646150i
$482$	−18.5315	+	10.4949i	−0.844087	+	0.478030i
$483$	5.09183	+	24.4926i	0.231686	+	1.11445i
$484$	9.00930	−	15.0226i	0.409514	−	0.682844i
$485$	−1.75582	+	3.04117i	−0.0797276	+	0.138092i
$486$	−14.4314	+	16.6654i	−0.654621	+	0.755957i
$487$	−12.0284	−	20.8338i	−0.545058	−	0.944068i	−0.998603	−	0.0528351i	$-0.983174\pi$
$487$	−12.0284	−	20.8338i	−0.545058	−	0.944068i	0.453545	−	0.891233i	$-0.350159\pi$
$488$	10.0549	−	16.4547i	0.455165	−	0.744867i
$489$	20.4266	+	7.46820i	0.923723	+	0.337724i
$490$	3.23262	−	2.11362i	0.146035	−	0.0954834i
$491$	15.3708			0.693675			0.346837	−	0.937925i	$-0.387256\pi$
$491$	15.3708			0.693675			0.346837	+	0.937925i	$0.387256\pi$
$492$	−38.1895	+	6.02481i	−1.72172	+	0.271620i
$493$	−6.95887	−	12.0531i	−0.313412	−	0.542845i
$494$	12.0831	−	20.5327i	0.543643	−	0.923809i
$495$	−0.594567	−	1.64840i	−0.0267238	−	0.0740902i
$496$	−14.6779	+	7.83605i	−0.659057	+	0.351849i
$497$	32.2265	−	20.0024i	1.44556	−	0.897229i
$498$	−7.01330	−	42.1763i	−0.314274	−	1.88996i
$499$	−22.8684	−	13.2031i	−1.02373	−	0.591051i	−0.108548	−	0.994091i	$-0.534620\pi$
$499$	−22.8684	−	13.2031i	−1.02373	−	0.591051i	−0.915182	+	0.403040i	$0.867953\pi$
$500$	0.127651	−	7.68315i	0.00570874	−	0.343601i
$501$	12.6793	−	2.21677i	0.566470	−	0.0990381i
$502$	−0.138640	+	16.6902i	−0.00618781	+	0.744922i
$503$	28.3616			1.26458			0.632291	−	0.774731i	$-0.282115\pi$
$503$	28.3616			1.26458			0.632291	+	0.774731i	$0.282115\pi$
$504$	−17.2563	−	14.3604i	−0.768655	−	0.639663i
$505$	−2.08993			−0.0930006
$506$	−0.0960083	+	11.5580i	−0.00426809	+	0.513816i
$507$	−3.73850	+	0.653615i	−0.166032	+	0.0290281i
$508$	−17.6291	−	0.292898i	−0.782165	−	0.0129952i
$509$	18.3731	+	10.6077i	0.814373	+	0.470179i	0.848472	−	0.529240i	$-0.177523\pi$
$509$	18.3731	+	10.6077i	0.814373	+	0.470179i	−0.0340991	+	0.999418i	$0.510856\pi$
$510$	−0.527249	−	3.17074i	−0.0233470	−	0.140403i
$511$	7.43586	+	3.98255i	0.328943	+	0.176178i
$512$	−22.5642	−	1.69001i	−0.997207	−	0.0746885i
$513$	0.115709	−	26.6251i	0.00510866	−	1.17553i
$514$	−12.7227	+	21.6196i	−0.561174	+	0.953600i
$515$	1.73632	+	3.00739i	0.0765113	+	0.132522i
$516$	2.58750	+	16.4014i	0.113908	+	0.722031i
$517$	−7.51778			−0.330631
$518$	0.760593	+	32.2470i	0.0334185	+	1.41685i
$519$	28.6352	+	10.4694i	1.25695	+	0.459554i
$520$	3.09575	+	1.89172i	0.135758	+	0.0829572i
$521$	5.91179	+	10.2395i	0.259000	+	0.448601i	0.965974	−	0.258638i	$-0.0832737\pi$
$521$	5.91179	+	10.2395i	0.259000	+	0.448601i	−0.706974	+	0.707239i	$0.749940\pi$
$522$	16.5636	−	5.81934i	0.724968	−	0.254705i
$523$	−3.37960	+	5.85364i	−0.147780	+	0.255962i	−0.930407	−	0.366529i	$-0.880546\pi$
$523$	−3.37960	+	5.85364i	−0.147780	+	0.255962i	0.782627	+	0.622491i	$0.213879\pi$
$524$	8.63878	+	5.18083i	0.377387	+	0.226326i
$525$	6.95922	−	21.0972i	0.303725	−	0.920756i
$526$	8.92092	−	5.05217i	0.388971	−	0.220285i
$527$	−12.1162	−	6.99528i	−0.527789	−	0.304719i
$528$	−6.38794	−	8.17228i	−0.277999	−	0.355653i
$529$	3.40036	+	5.88960i	0.147842	+	0.256070i
$530$	−0.00457614	+	0.550901i	−0.000198775	+	0.0239296i
$531$	3.03948	−	3.60108i	0.131902	−	0.156273i
$532$	27.1108	−	0.414166i	1.17540	−	0.0179564i
$533$	36.6928			1.58934
$534$	4.38421	−	11.6894i	0.189723	−	0.505851i
$535$	5.30643	−	3.06367i	0.229417	−	0.132454i
$536$	8.76151	−	4.77142i	0.378440	−	0.206094i
$537$	18.0446	+	21.5681i	0.778683	+	0.930733i
$538$	4.20340	−	2.38050i	0.181221	−	0.102631i
$539$	10.4588	−	0.667940i	0.450494	−	0.0287702i
$540$	4.05366	+	0.0849721i	0.174442	+	0.00365662i
$541$	15.3128	+	8.84087i	0.658351	+	0.380099i	0.791648	−	0.610977i	$-0.209223\pi$
$541$	15.3128	+	8.84087i	0.658351	+	0.380099i	−0.133298	+	0.991076i	$0.542557\pi$
$542$	−5.58715	−	3.28792i	−0.239989	−	0.141228i
$543$	10.5670	−	1.84747i	0.453473	−	0.0792824i
$544$	−8.82076	−	16.8580i	−0.378187	−	0.722779i
$545$	6.82885			0.292516
$546$	14.0535	+	16.0147i	0.601434	+	0.685366i
$547$		−	1.49834i		−	0.0640644i	−0.999487	−	0.0320322i	$-0.989802\pi$
$547$		−	1.49834i		−	0.0640644i	0.999487	−	0.0320322i	$-0.0101979\pi$
$548$	12.8157	−	7.11797i	0.547461	−	0.304065i
$549$	−3.61003	+	20.1322i	−0.154072	+	0.859223i
$550$	5.20579	−	8.84617i	0.221976	−	0.377202i
$551$	−10.6017	+	18.3627i	−0.451647	+	0.782276i
$552$	−24.8808	−	9.80622i	−1.05900	−	0.417381i
$553$	−1.26621	+	0.0403914i	−0.0538448	+	0.00171762i
$554$	−15.1957	+	8.60573i	−0.645602	+	0.365622i
$555$	−3.73813	−	4.46806i	−0.158675	−	0.189658i
$556$	−31.4950	−	0.523272i	−1.33569	−	0.0221917i
$557$	−1.46808	−	2.54278i	−0.0622044	−	0.107741i	0.833246	−	0.552902i	$-0.186480\pi$
$557$	−1.46808	−	2.54278i	−0.0622044	−	0.107741i	−0.895450	+	0.445161i	$0.853146\pi$
$558$	11.4946	−	13.3912i	0.486606	−	0.566893i
$559$		−	15.7586i		−	0.666518i
$560$	−0.00552159	+	4.12895i	−0.000233330	+	0.174480i
$561$	2.99491	−	8.19150i	0.126445	−	0.345845i
$562$	0.0929850	−	11.1940i	0.00392233	−	0.472192i
$563$	14.3950	−	8.31096i	0.606677	−	0.350265i	−0.164987	−	0.986296i	$-0.552758\pi$
$563$	14.3950	−	8.31096i	0.606677	−	0.350265i	0.771664	+	0.636031i	$0.219425\pi$
$564$	6.24349	−	16.2353i	0.262898	−	0.683630i
$565$	0.0141652	−	0.0245348i	0.000595934	−	0.00103219i
$566$	−15.8271	−	27.9470i	−0.665264	−	1.17470i
$567$	22.5806	+	7.55752i	0.948296	+	0.317386i
$568$	−1.01033	+	40.5357i	−0.0423927	+	1.70084i
$569$	−19.2204	−	11.0969i	−0.805763	−	0.465207i	0.0397194	−	0.999211i	$-0.487354\pi$
$569$	−19.2204	−	11.0969i	−0.805763	−	0.465207i	−0.845482	+	0.534003i	$0.820687\pi$
$570$	−3.78176	+	3.11092i	−0.158401	+	0.130302i
$571$	−5.22532	+	3.01684i	−0.218673	+	0.126251i	−0.605336	−	0.795970i	$-0.706961\pi$
$571$	−5.22532	+	3.01684i	−0.218673	+	0.126251i	0.386663	+	0.922221i	$0.373628\pi$
$572$	4.77989	+	8.60608i	0.199857	+	0.359838i
$573$	13.6895	+	5.00504i	0.571887	+	0.209089i
$574$	21.7267	+	35.6624i	0.906856	+	1.48852i
$575$		−	26.4641i		−	1.10363i
$576$	22.9540	−	7.00829i	0.956415	−	0.292012i
$577$	−17.4549	+	10.0776i	−0.726659	+	0.419537i	−0.817199	−	0.576356i	$-0.804474\pi$
$577$	−17.4549	+	10.0776i	−0.726659	+	0.419537i	0.0905396	+	0.995893i	$0.471141\pi$
$578$	−4.07947	+	6.93223i	−0.169684	+	0.288343i
$579$	14.6114	+	17.4645i	0.607230	+	0.725801i
$580$	−2.76909	−	1.66067i	−0.114980	−	0.0689557i
$581$	−39.2375	+	24.3539i	−1.62784	+	1.01037i
$582$	−3.61648	−	21.7486i	−0.149908	−	0.901508i
$583$	−0.747449	+	1.29462i	−0.0309562	+	0.0536177i
$584$	−7.91941	+	4.31282i	−0.327707	+	0.178466i
$585$	−3.78765	−	0.679185i	−0.156600	−	0.0280808i
$586$	0.150650	−	18.1361i	0.00622329	−	0.749194i
$587$			0.369829i			0.0152645i	0.999971	+	0.00763224i	$0.00242944\pi$
$587$			0.369829i			0.0152645i	−0.999971	+	0.00763224i	$0.997571\pi$
$588$	−7.24355	+	23.1415i	−0.298719	+	0.954341i
$589$			21.3143i			0.878241i
$590$	−0.866656	−	0.00719901i	−0.0356797	−	0.000296379i
$591$	−30.0489	+	5.25356i	−1.23605	+	0.216103i
$592$	−29.2740	−	18.2241i	−1.20315	−	0.749005i
$593$	−4.89233	+	8.47376i	−0.200904	+	0.347976i	−0.948820	−	0.315818i	$-0.897721\pi$
$593$	−4.89233	+	8.47376i	−0.200904	+	0.347976i	0.747916	+	0.663793i	$0.231055\pi$
$594$	9.45753	+	5.62104i	0.388047	+	0.230634i
$595$	−2.94981	+	1.83089i	−0.120930	+	0.0750592i
$596$	18.4942	−	30.8382i	0.757553	−	1.26318i
$597$	26.4895	−	22.1620i	1.08414	−	0.907032i
$598$	21.8749	+	12.8729i	0.894531	+	0.526413i
$599$	−31.2524	+	18.0436i	−1.27694	+	0.737240i	−0.976284	−	0.216494i	$-0.930538\pi$
$599$	−31.2524	+	18.0436i	−1.27694	+	0.737240i	−0.300653	+	0.953734i	$0.597205\pi$
$600$	14.7807	+	18.5891i	0.603421	+	0.758896i
$601$		−	9.75944i		−	0.398096i	−0.979990	−	0.199048i	$-0.936215\pi$
$601$		−	9.75944i		−	0.398096i	0.979990	−	0.199048i	$-0.0637849\pi$
$602$	15.3161	−	9.33106i	0.624236	−	0.380305i
$603$	−6.82523	+	8.08629i	−0.277945	+	0.329299i
$604$	−15.3267	−	27.5954i	−0.623634	−	1.12284i
$605$	2.95932	−	1.70856i	0.120313	−	0.0694629i
$606$	10.1333	−	8.33574i	0.411636	−	0.338616i
$607$	−7.33740	−	4.23625i	−0.297816	−	0.171944i	0.343645	−	0.939099i	$-0.388338\pi$
$607$	−7.33740	−	4.23625i	−0.297816	−	0.171944i	−0.641461	+	0.767155i	$0.721672\pi$
$608$	−15.5228	+	24.4792i	−0.629532	+	0.992764i
$609$	−12.6255	−	14.1486i	−0.511611	−	0.573331i
$610$	3.27328	−	1.85375i	0.132531	−	0.0750560i
$611$	−8.25429	+	14.2968i	−0.333933	+	0.578388i
$612$	15.2030	+	13.2708i	0.614546	+	0.536440i
$613$	10.1968	−	5.88712i	0.411844	−	0.237779i	−0.279737	−	0.960077i	$-0.590247\pi$
$613$	10.1968	−	5.88712i	0.411844	−	0.237779i	0.691582	+	0.722298i	$0.256914\pi$
$614$	−17.4822	−	0.145219i	−0.705525	−	0.00586055i
$615$	−7.08336	−	2.58976i	−0.285629	−	0.104429i
$616$	−5.53412	+	9.74153i	−0.222976	+	0.392498i
$617$			17.5244i			0.705506i	0.935717	+	0.352753i	$0.114754\pi$
$617$			17.5244i			0.705506i	−0.935717	+	0.352753i	$0.885246\pi$
$618$	−20.4138	−	7.65635i	−0.821164	−	0.307984i
$619$	−12.8081	−	22.1843i	−0.514801	−	0.891661i	−0.999852	−	0.0171755i	$-0.994533\pi$
$619$	−12.8081	−	22.1843i	−0.514801	−	0.891661i	0.485052	−	0.874485i	$-0.338801\pi$
$620$	−3.24533	−	0.0539194i	−0.130336	−	0.00216545i
$621$	28.3655	+	0.123272i	1.13827	+	0.00494674i
$622$	1.00469	+	1.77405i	0.0402844	+	0.0711328i
$623$	−13.4780	+	0.429940i	−0.539985	+	0.0172252i
$624$	−22.5553	+	3.17528i	−0.902935	+	0.127113i
$625$	−11.3700	+	19.6933i	−0.454798	+	0.787734i
$626$	29.3893	+	17.2950i	1.17463	+	0.691247i
$627$	−13.0890	+	2.28839i	−0.522723	+	0.0913896i
$628$	4.91902	+	8.85659i	0.196290	+	0.353416i
$629$		−	28.9950i		−	1.15611i
$630$	−1.58265	−	4.08344i	−0.0630542	−	0.162688i
$631$	−7.24555			−0.288441			−0.144220	−	0.989546i	$-0.546067\pi$
$631$	−7.24555			−0.288441			−0.144220	+	0.989546i	$0.546067\pi$
$632$	0.706178	−	1.15564i	0.0280902	−	0.0459691i
$633$	4.33003	+	24.7666i	0.172103	+	0.984383i
$634$	19.3209	−	32.8319i	0.767330	−	1.30392i
$635$	−2.97867	−	1.71973i	−0.118205	−	0.0682456i
$636$	−2.17509	−	2.68936i	−0.0862481	−	0.106640i
$637$	10.2132	−	20.6234i	0.404663	−	0.817127i
$638$	−4.31755	−	7.62377i	−0.170933	−	0.301828i
$639$	−14.5924	−	40.4567i	−0.577268	−	1.60044i
$640$	−3.68795	−	2.42543i	−0.145779	−	0.0958737i
$641$	11.9401	−	6.89362i	0.471606	−	0.272282i	−0.245306	−	0.969446i	$-0.578888\pi$
$641$	11.9401	−	6.89362i	0.471606	−	0.272282i	0.716912	+	0.697164i	$0.245555\pi$
$642$	−13.5094	+	36.0195i	−0.533172	+	1.42157i
$643$	−20.7470			−0.818184			−0.409092	−	0.912493i	$-0.634154\pi$
$643$	−20.7470			−0.818184			−0.409092	+	0.912493i	$0.634154\pi$
$644$	0.441240	+	28.8830i	0.0173873	+	1.13815i
$645$	−1.11223	+	3.04212i	−0.0437942	+	0.119783i
$646$	−24.3720	−	0.202449i	−0.958902	−	0.00796527i
$647$	−16.1242	−	27.9279i	−0.633907	−	1.09796i	−0.986746	−	0.162275i	$-0.948117\pi$
$647$	−16.1242	−	27.9279i	−0.633907	−	1.09796i	0.352838	−	0.935684i	$-0.385217\pi$
$648$	−19.9936	+	15.7561i	−0.785423	+	0.618960i
$649$	−2.03665	−	1.17586i	−0.0799454	−	0.0461565i
$650$	−11.1073	−	19.6129i	−0.435665	−	0.769280i
$651$	−18.1025	−	5.97139i	−0.709493	−	0.234037i
$652$	21.5374	+	12.9164i	0.843471	+	0.505844i
$653$	−9.95455	+	17.2418i	−0.389552	+	0.674723i	−0.992389	−	0.123141i	$-0.960703\pi$
$653$	−9.95455	+	17.2418i	−0.389552	+	0.674723i	0.602838	+	0.797864i	$0.294037\pi$
$654$	−33.1105	+	27.2371i	−1.29472	+	1.06505i
$655$	0.982514	+	1.70176i	0.0383900	+	0.0664934i
$656$	−44.6182	−	1.48302i	−1.74205	−	0.0579023i
$657$	6.16923	−	7.30909i	0.240684	−	0.285155i
$658$	−18.7829	+	0.443023i	−0.732235	+	0.0172708i
$659$	−11.4275			−0.445153			−0.222576	−	0.974915i	$-0.571447\pi$
$659$	−11.4275			−0.445153			−0.222576	+	0.974915i	$0.571447\pi$
$660$	−0.315321	−	1.99872i	−0.0122738	−	0.0778002i
$661$	2.31268	+	4.00568i	0.0899529	+	0.155803i	0.907491	−	0.420071i	$-0.137995\pi$
$661$	2.31268	+	4.00568i	0.0899529	+	0.155803i	−0.817538	+	0.575875i	$0.804662\pi$
$662$	−21.5023	−	12.6536i	−0.835709	−	0.491798i
$663$	−12.2898	−	14.6895i	−0.477295	−	0.570495i
$664$	1.23013	−	49.3543i	0.0477385	−	1.91532i
$665$	4.66261	+	2.49723i	0.180808	+	0.0968385i
$666$	35.9458	+	6.75429i	1.39287	+	0.261724i
$667$	−19.5630	−	11.2947i	−0.757483	−	0.437333i
$668$	14.8608	+	0.246905i	0.574983	+	0.00955303i
$669$	0.828955	+	4.74139i	0.0320493	+	0.183313i
$670$	1.94610	+	0.0161655i	0.0751842	+	0.000624529i
$671$	10.2073			0.394050
$672$	−16.4417	−	20.0417i	−0.634251	−	0.773127i
$673$	19.2606			0.742441			0.371220	−	0.928545i	$-0.378939\pi$
$673$	19.2606			0.742441			0.371220	+	0.928545i	$0.378939\pi$
$674$	−15.6118	−	0.129682i	−0.601344	−	0.00499516i
$675$	−21.7601	−	12.6896i	−0.837546	−	0.488423i
$676$	−4.38172	−	0.0727998i	−0.168528	−	0.00279999i
$677$	−36.2236	−	20.9137i	−1.39219	−	0.803780i	−0.398630	−	0.917112i	$-0.630514\pi$
$677$	−36.2236	−	20.9137i	−1.39219	−	0.803780i	−0.993557	+	0.113332i	$0.963848\pi$
$678$	0.0291762	+	0.175459i	0.00112051	+	0.00673844i
$679$	−20.2332	+	12.5583i	−0.776478	+	0.481945i
$680$	0.0924795	−	3.71038i	0.00354643	−	0.142287i
$681$	−21.5425	+	18.0232i	−0.825509	+	0.690649i
$682$	−7.59049	−	4.46685i	−0.290655	−	0.171044i
$683$	6.73357	+	11.6629i	0.257653	+	0.446268i	0.965613	−	0.259985i	$-0.0837176\pi$
$683$	6.73357	+	11.6629i	0.257653	+	0.446268i	−0.707960	+	0.706253i	$0.750384\pi$
$684$	5.92835	−	30.1673i	0.226676	−	1.15348i
$685$	2.85975			0.109265
$686$	26.0917	−	2.28517i	0.996187	−	0.0872481i
$687$	−12.2697	+	33.5595i	−0.468120	+	1.28037i
$688$	−0.636919	+	19.1623i	−0.0242823	+	0.730557i
$689$	1.64135	+	2.84291i	0.0625305	+	0.108306i
$690$	−3.31427	−	4.02897i	−0.126172	−	0.153380i
$691$	−15.2232	+	26.3674i	−0.579118	+	1.00306i	0.416463	+	0.909153i	$0.363270\pi$
$691$	−15.2232	+	26.3674i	−0.579118	+	1.00306i	−0.995581	+	0.0939090i	$0.970064\pi$
$692$	30.1925	+	18.1069i	1.14774	+	0.688323i
$693$	1.72342	−	11.7577i	0.0654675	−	0.446639i
$694$	15.0948	+	26.6539i	0.572993	+	1.01177i
$695$	−5.32149	−	3.07236i	−0.201856	−	0.116541i
$696$	20.0499	−	2.99263i	0.759991	−	0.113435i
$697$	−18.7689	−	32.5087i	−0.710923	−	1.23135i
$698$	9.13734	+	0.0759007i	0.345853	+	0.00287288i
$699$	3.38979	+	1.23935i	0.128214	+	0.0468764i
$700$	12.4852	−	22.4087i	0.471896	−	0.846968i
$701$	−37.2839			−1.40819			−0.704096	−	0.710105i	$-0.748647\pi$
$701$	−37.2839			−1.40819			−0.704096	+	0.710105i	$0.748647\pi$
$702$	21.0738	−	11.8140i	0.795380	−	0.445892i
$703$	−38.2552	+	22.0866i	−1.44282	+	0.833013i
$704$	−5.46447	−	10.6581i	−0.205950	−	0.401693i
$705$	2.60251	−	2.17735i	0.0980163	−	0.0820038i
$706$	20.8858	+	36.8793i	0.786047	+	1.38797i
$707$	−12.4935	−	6.69137i	−0.469867	−	0.251655i
$708$	4.23080	−	3.42178i	0.159003	−	0.128598i
$709$	39.5076	+	22.8097i	1.48374	+	0.856637i	0.999829	−	0.0184810i	$-0.00588302\pi$
$709$	39.5076	+	22.8097i	1.48374	+	0.856637i	0.483910	+	0.875118i	$0.339216\pi$
$710$	−4.01174	+	6.81713i	−0.150558	+	0.255842i
$711$	−0.253540	+	1.41393i	−0.00950848	+	0.0530265i
$712$	7.51680	−	12.3011i	0.281704	−	0.461003i
$713$	−22.7076			−0.850406
$714$	6.99996	−	20.6427i	0.261967	−	0.772533i
$715$			1.92039i			0.0718186i
$716$	15.7663	+	28.3868i	0.589214	+	1.06087i
$717$	0.254077	+	1.45325i	0.00948869	+	0.0542727i
$718$	13.2915	+	7.82177i	0.496034	+	0.291906i
$719$	8.37315	−	14.5027i	0.312266	−	0.540860i	−0.666587	−	0.745428i	$-0.732245\pi$
$719$	8.37315	−	14.5027i	0.312266	−	0.540860i	0.978853	+	0.204567i	$0.0655787\pi$
$720$	4.57830	+	0.978970i	0.170623	+	0.0364840i
$721$	0.750825	+	23.5373i	0.0279622	+	0.876575i
$722$	5.05671	+	8.92895i	0.188191	+	0.332301i
$723$	20.0053	−	16.7371i	0.744003	−	0.622458i
$724$	12.3851	+	0.205771i	0.460288	+	0.00764743i
$725$	10.0301	+	17.3726i	0.372508	+	0.645204i
$726$	−7.53396	+	20.0875i	−0.279612	+	0.745517i
$727$		−	14.7144i		−	0.545726i	−0.962053	−	0.272863i	$-0.912029\pi$
$727$		−	14.7144i		−	0.545726i	0.962053	−	0.272863i	$-0.0879705\pi$
$728$	12.4496	+	21.2204i	0.461411	+	0.786479i
$729$	13.7027	−	23.2645i	0.507508	−	0.861647i
$730$	−1.75905	−	0.0146118i	−0.0651053	−	0.000540807i
$731$	−13.9616	+	8.06075i	−0.516389	+	0.298137i
$732$	−8.47716	+	22.0437i	−0.313325	+	0.814757i
$733$	17.1186	−	29.6503i	0.632290	−	1.09516i	−0.354793	−	0.934945i	$-0.615449\pi$
$733$	17.1186	−	29.6503i	0.632290	−	1.09516i	0.987082	−	0.160213i	$-0.0512181\pi$
$734$	3.46074	−	1.95991i	0.127738	−	0.0723417i
$735$	−3.42720	+	3.26039i	−0.126414	+	0.120261i
$736$	−26.0794	−	16.5375i	−0.961299	−	0.609580i
$737$	4.57334	+	2.64042i	0.168461	+	0.0972610i
$738$	44.6739	−	15.6954i	1.64447	−	0.577757i
$739$	−1.92964	+	1.11408i	−0.0709829	+	0.0409820i	−0.535071	−	0.844807i	$-0.679715\pi$
$739$	−1.92964	+	1.11408i	−0.0709829	+	0.0409820i	0.464089	+	0.885789i	$0.346382\pi$
$740$	−3.26615	−	5.88063i	−0.120066	−	0.216176i
$741$	−10.0194	+	27.4044i	−0.368070	+	1.00673i
$742$	−1.79119	+	3.27861i	−0.0657565	+	0.120362i
$743$		−	14.7964i		−	0.542829i	−0.962463	−	0.271414i	$-0.912509\pi$
$743$		−	14.7964i		−	0.542829i	0.962463	−	0.271414i	$-0.0874914\pi$
$744$	15.9504	−	12.6827i	0.584772	−	0.464969i
$745$	6.07486	−	3.50732i	0.222566	−	0.128498i
$746$	37.8961	+	22.3011i	1.38747	+	0.816500i
$747$	17.7671	+	49.2582i	0.650063	+	1.80226i
$748$	5.17974	−	8.63696i	0.189390	−	0.315799i
$749$	41.5307	−	1.32480i	1.51750	−	0.0484073i
$750$	1.54375	+	9.28373i	0.0563698	+	0.338994i
$751$	18.2439	−	31.5994i	0.665729	−	1.15308i	−0.313358	−	0.949635i	$-0.601454\pi$
$751$	18.2439	−	31.5994i	0.665729	−	1.15308i	0.979087	−	0.203442i	$-0.0652128\pi$
$752$	10.6150	−	17.0512i	0.387089	−	0.621795i
$753$	−3.52055	−	20.1366i	−0.128296	−	0.733817i
$754$	−19.2390	−	0.159811i	−0.700641	−	0.00581998i
$755$		−	6.15772i		−	0.224103i
$756$	23.9606	+	13.4867i	0.871438	+	0.490505i
$757$		−	19.9557i		−	0.725302i	−0.931925	−	0.362651i	$-0.881872\pi$
$757$		−	19.9557i		−	0.725302i	0.931925	−	0.362651i	$-0.118128\pi$
$758$	−0.207863	+	25.0236i	−0.00754991	+	0.908899i
$759$	−2.43798	−	13.9446i	−0.0884931	−	0.506156i
$760$	−4.96581	+	2.70433i	−0.180129	+	0.0980962i
$761$	18.2013	−	31.5257i	0.659798	−	1.14280i	−0.320869	−	0.947124i	$-0.603975\pi$
$761$	18.2013	−	31.5257i	0.659798	−	1.14280i	0.980668	−	0.195681i	$-0.0626917\pi$
$762$	21.3016	−	3.54216i	0.771677	−	0.128319i
$763$	40.8227	+	21.8641i	1.47788	+	0.791533i
$764$	14.4340	+	8.65630i	0.522202	+	0.313174i
$765$	1.33570	+	3.70315i	0.0482923	+	0.133888i
$766$	25.0972	−	42.6476i	0.906799	−	1.54092i
$767$	−4.47235	+	2.58211i	−0.161487	+	0.0932347i
$768$	27.5554	−	2.94949i	0.994320	−	0.106431i
$769$			33.7570i			1.21731i	0.793436	+	0.608654i	$0.208290\pi$
$769$			33.7570i			1.21731i	−0.793436	+	0.608654i	$0.791710\pi$
$770$	−1.86646	+	1.13711i	−0.0672627	+	0.0409786i
$771$	10.5497	−	28.8551i	0.379940	−	1.03919i
$772$	12.7666	+	22.9859i	0.459479	+	0.827282i
$773$	−35.3297	+	20.3976i	−1.27072	+	0.733651i	−0.975124	−	0.221662i	$-0.928852\pi$
$773$	−35.3297	+	20.3976i	−1.27072	+	0.733651i	−0.295597	+	0.955313i	$0.595519\pi$
$774$	−6.74078	−	19.1863i	−0.242292	−	0.689636i
$775$	17.4635	+	10.0826i	0.627308	+	0.362176i
$776$	0.634331	−	25.4500i	0.0227711	−	0.913603i
$777$	−8.04094	−	38.6783i	−0.288467	−	1.38758i
$778$	−14.5545	−	25.6998i	−0.521804	−	0.921382i
$779$	−28.5940	+	49.5263i	−1.02449	+	1.77446i
$780$	−4.14726	−	1.59488i	−0.148496	−	0.0571058i
$781$	−18.5878	+	10.7317i	−0.665123	+	0.384009i
$782$	0.215683	−	25.9651i	0.00771282	−	0.928511i
$783$	−18.6676	+	10.6698i	−0.667126	+	0.381309i
$784$	−13.2528	+	24.6650i	−0.473313	+	0.880895i
$785$			1.97629i			0.0705368i
$786$	−11.5514	−	4.33243i	−0.412024	−	0.154533i
$787$	−5.80545	−	10.0553i	−0.206942	−	0.358434i	0.743808	−	0.668394i	$-0.233018\pi$
$787$	−5.80545	−	10.0553i	−0.206942	−	0.358434i	−0.950750	+	0.309960i	$0.899684\pi$
$788$	−35.2189	−	0.585143i	−1.25462	−	0.0208449i
$789$	−9.63037	+	8.05710i	−0.342850	+	0.286840i
$790$	0.229889	−	0.130192i	0.00817908	−	0.00463204i
$791$	0.163233	−	0.101315i	0.00580389	−	0.00360236i
$792$	9.50084	+	8.43339i	0.337597	+	0.299667i
$793$	11.2073	−	19.4117i	0.397984	−	0.689329i
$794$	3.50656	−	5.95868i	0.124443	−	0.211466i
$795$	−0.116204	−	0.664654i	−0.00412133	−	0.0235729i
$796$	34.8642	−	19.3638i	1.23573	−	0.686333i
$797$			9.90792i			0.350956i	0.984483	+	0.175478i	$0.0561472\pi$
$797$			9.90792i			0.350956i	−0.984483	+	0.175478i	$0.943853\pi$
$798$	−32.5675	+	6.48881i	−1.15288	+	0.229701i
$799$	16.8887			0.597481
$800$	12.7137	+	24.2980i	0.449497	+	0.859065i
$801$	−2.69877	+	15.0503i	−0.0953562	+	0.531778i
$802$	9.32187	+	5.48573i	0.329167	+	0.193708i
$803$	−4.13377	−	2.38664i	−0.145878	−	0.0842225i
$804$	−9.50036	+	7.68368i	−0.335052	+	0.270982i
$805$	−2.66047	+	4.96740i	−0.0937694	+	0.175078i
$806$	−16.8289	+	9.53067i	−0.592773	+	0.335704i
$807$	−4.53768	+	3.79638i	−0.159734	+	0.133639i
$808$	13.3060	−	7.24628i	0.468102	−	0.254923i
$809$	−14.3590	+	8.29016i	−0.504835	+	0.291466i	−0.730708	−	0.682690i	$-0.760810\pi$
$809$	−14.3590	+	8.29016i	−0.504835	+	0.291466i	0.225873	+	0.974157i	$0.427477\pi$
$810$	−4.90202	+	0.793259i	−0.172240	+	0.0278723i
$811$	49.5706			1.74066			0.870330	−	0.492470i	$-0.163906\pi$
$811$	49.5706			1.74066			0.870330	+	0.492470i	$0.163906\pi$
$812$	−11.2365	−	18.7933i	−0.394325	−	0.659516i
$813$	7.45700	+	2.72637i	0.261528	+	0.0956179i
$814$	0.151615	−	18.2522i	0.00531409	−	0.639739i
$815$	2.44952	+	4.24268i	0.0858028	+	0.148615i
$816$	14.3506	+	18.3591i	0.502370	+	0.642697i
$817$	21.2702	+	12.2804i	0.744151	+	0.429636i
$818$	9.47180	−	5.36414i	0.331174	−	0.187553i
$819$	−20.4679	−	16.1871i	−0.715205	−	0.565624i
$820$	−7.46857	−	4.47903i	−0.260814	−	0.156415i
$821$	26.4055	−	45.7357i	0.921559	−	1.59619i	0.124554	−	0.992213i	$-0.460250\pi$
$821$	26.4055	−	45.7357i	0.921559	−	1.59619i	0.797004	−	0.603973i	$-0.206417\pi$
$822$	−13.8659	+	11.4062i	−0.483627	+	0.397837i
$823$	12.3351	+	21.3650i	0.429975	+	0.744739i	0.996871	−	0.0790510i	$-0.0251890\pi$
$823$	12.3351	+	21.3650i	0.429975	+	0.744739i	−0.566896	+	0.823790i	$0.691856\pi$
$824$	−21.4820	−	13.1269i	−0.748360	−	0.457299i
$825$	−4.31668	+	11.8067i	−0.150287	+	0.411057i
$826$	−5.15779	−	2.81783i	−0.179463	−	0.0980447i
$827$	23.0662			0.802091			0.401045	−	0.916058i	$-0.368647\pi$
$827$	23.0662			0.802091			0.401045	+	0.916058i	$0.368647\pi$
$828$	32.1393	+	6.31588i	1.11692	+	0.219492i
$829$	12.2068	+	21.1429i	0.423961	+	0.734322i	0.996323	−	0.0856795i	$-0.0273061\pi$
$829$	12.2068	+	21.1429i	0.423961	+	0.734322i	−0.572362	+	0.820001i	$0.693973\pi$
$830$	4.88450	−	8.30021i	0.169543	−	0.288104i
$831$	16.4041	−	13.7243i	0.569053	−	0.476089i
$832$	−26.2688	−	1.31029i	−0.910706	−	0.0454261i
$833$	−23.4959	+	1.50053i	−0.814083	+	0.0519904i
$834$	38.0561	−	6.32818i	1.31778	−	0.219127i
$835$	2.51093	+	1.44969i	0.0868944	+	0.0501685i
$836$	−15.3410	−	0.254882i	−0.530579	−	0.00881527i
$837$	−10.8884	+	18.6713i	−0.376357	+	0.645376i
$838$	0.0514793	−	6.19736i	0.00177832	−	0.214084i
$839$	48.3464			1.66910			0.834551	−	0.550931i	$-0.185727\pi$
$839$	48.3464			1.66910			0.834551	+	0.550931i	$0.185727\pi$
$840$	−0.905603	−	4.97517i	−0.0312463	−	0.171660i
$841$	−11.8768			−0.409546
$842$	−0.140259	+	16.8852i	−0.00483365	+	0.581901i
$843$	2.36121	+	13.5055i	0.0813244	+	0.465153i
$844$	−0.482280	+	29.0278i	−0.0166008	+	0.999176i
$845$	−0.740348	−	0.427440i	−0.0254688	−	0.0147044i
$846$	−3.93418	+	20.9373i	−0.135260	+	0.719841i
$847$	23.1610	−	0.738822i	0.795823	−	0.0253862i
$848$	−1.88097	−	3.52329i	−0.0645927	−	0.120990i
$849$	25.2408	+	30.1695i	0.866262	+	1.03541i
$850$	−11.6948	+	19.8730i	−0.401130	+	0.681638i
$851$	−23.5304	−	40.7559i	−0.806612	−	1.39709i
$852$	−7.73891	−	49.0546i	−0.265131	−	1.68058i
$853$	−34.6867			−1.18765			−0.593825	−	0.804595i	$-0.702383\pi$
$853$	−34.6867			−1.18765			−0.593825	+	0.804595i	$0.702383\pi$
$854$	25.5027	−	0.601519i	0.872685	−	0.0205835i
$855$	3.86837	−	4.58312i	0.132296	−	0.156739i
$856$	−23.1620	+	37.9042i	−0.791662	+	1.29554i
$857$	−10.7545	−	18.6273i	−0.367366	−	0.636297i	0.621786	−	0.783187i	$-0.286407\pi$
$857$	−10.7545	−	18.6273i	−0.367366	−	0.636297i	−0.989153	+	0.146889i	$0.953074\pi$
$858$	−7.65954	−	9.31126i	−0.261492	−	0.317881i
$859$	0.332259	−	0.575490i	0.0113365	−	0.0196355i	−0.860301	−	0.509786i	$-0.829725\pi$
$859$	0.332259	−	0.575490i	0.0113365	−	0.0196355i	0.871638	+	0.490150i	$0.163058\pi$
$860$	−1.92363	+	3.20755i	−0.0655951	+	0.109377i
$861$	−34.0524	−	38.1605i	−1.16050	−	1.30050i
$862$	−0.836827	+	0.473918i	−0.0285025	+	0.0161417i
$863$	14.2150	+	8.20702i	0.483883	+	0.279370i	0.722033	−	0.691858i	$-0.243208\pi$
$863$	14.2150	+	8.20702i	0.483883	+	0.279370i	−0.238150	+	0.971228i	$0.576541\pi$
$864$	−26.1031	+	13.5140i	−0.888045	+	0.459756i
$865$	3.43388	+	5.94765i	0.116755	+	0.202226i
$866$	0.00280165	−	0.337277i	9.52038e−5	−	0.0114612i
$867$	3.38273	−	9.25225i	0.114884	−	0.314223i
$868$	−19.2278	−	10.7130i	−0.652635	−	0.363622i
$869$	0.716882			0.0243186
$870$	3.70270	+	1.38873i	0.125533	+	0.0470822i
$871$	10.0428	−	5.79819i	0.340286	−	0.196464i
$872$	−43.4773	+	23.6773i	−1.47233	+	0.801813i
$873$	9.16175	+	25.4004i	0.310078	+	0.859675i
$874$	−34.4219	+	19.4941i	−1.16434	+	0.659398i
$875$	8.63685	−	5.36073i	0.291979	−	0.181226i
$876$	8.58724	−	6.94517i	0.290136	−	0.234655i
$877$	11.1473	+	6.43591i	0.376419	+	0.217325i	0.676259	−	0.736664i	$-0.263600\pi$
$877$	11.1473	+	6.43591i	0.376419	+	0.217325i	−0.299840	+	0.953989i	$0.596933\pi$
$878$	−4.64288	−	2.73224i	−0.156690	−	0.0922085i
$879$	3.82552	+	21.8809i	0.129032	+	0.738025i
$880$	0.0776169	−	2.33518i	0.00261647	−	0.0787189i
$881$	−42.1373			−1.41964			−0.709821	−	0.704382i	$-0.751224\pi$
$881$	−42.1373			−1.41964			−0.709821	+	0.704382i	$0.751224\pi$
$882$	3.61304	−	29.4779i	0.121657	−	0.992572i
$883$		−	14.3108i		−	0.481596i	−0.970575	−	0.240798i	$-0.922591\pi$
$883$		−	14.3108i		−	0.481596i	0.970575	−	0.240798i	$-0.0774091\pi$
$884$	−10.7381	−	19.3336i	−0.361160	−	0.650260i
$885$	1.04561	−	0.182808i	0.0351478	−	0.00614502i
$886$	−4.33223	+	7.36174i	−0.145544	+	0.247323i
$887$	3.93855	−	6.82176i	0.132243	−	0.229052i	−0.792298	−	0.610135i	$-0.791115\pi$
$887$	3.93855	−	6.82176i	0.132243	−	0.229052i	0.924541	+	0.381082i	$0.124449\pi$
$888$	39.2914	+	15.4858i	1.31853	+	0.519670i
$889$	−12.3003	−	19.8174i	−0.412538	−	0.664653i
$890$	2.44702	−	1.38581i	0.0820242	−	0.0464526i
$891$	−12.6349	−	4.68183i	−0.423287	−	0.156847i
$892$	−0.0923293	+	5.55717i	−0.00309141	+	0.186068i
$893$	−12.8648	−	22.2825i	−0.430505	−	0.745656i
$894$	−15.4657	+	41.2355i	−0.517249	+	1.37912i
$895$			6.33434i			0.211734i
$896$	−14.2809	−	26.3070i	−0.477091	−	0.878854i
$897$	−29.1958	−	10.6743i	−0.974818	−	0.356405i
$898$	0.330656	−	39.8061i	0.0110341	−	1.32835i
$899$	14.9067	−	8.60636i	0.497165	−	0.287038i
$900$	−21.9127	−	19.1277i	−0.730424	−	0.637590i
$901$	1.67915	−	2.90837i	0.0559406	−	0.0968919i
$902$	−11.6449	−	20.5622i	−0.387734	−	0.684646i
$903$	−16.3889	+	14.6246i	−0.545389	+	0.486677i
$904$	−0.00511751	+	0.205320i	−0.000170206	+	0.00682885i
$905$	2.09262	+	1.20818i	0.0695611	+	0.0401611i
$906$	24.5603	+	29.8565i	0.815960	+	0.991915i
$907$	24.8886	−	14.3694i	0.826413	−	0.477130i	−0.0262101	−	0.999656i	$-0.508344\pi$
$907$	24.8886	−	14.3694i	0.826413	−	0.477130i	0.852623	+	0.522527i	$0.175011\pi$
$908$	−28.3531	+	15.7475i	−0.940930	+	0.522600i
$909$	−10.3654	+	12.2805i	−0.343797	+	0.407319i
$910$	0.113169	+	4.79804i	0.00375151	+	0.159053i
$911$			4.32207i			0.143197i	0.997434	+	0.0715983i	$0.0228100\pi$
$911$			4.32207i			0.143197i	−0.997434	+	0.0715983i	$0.977190\pi$
$912$	13.2911	−	32.9186i	0.440111	−	1.09004i
$913$	22.6316	−	13.0664i	0.748996	−	0.432433i
$914$	8.94137	−	15.1940i	0.295754	−	0.502574i
$915$	−3.53359	+	2.95632i	−0.116817	+	0.0977329i
$916$	−21.2207	+	35.3845i	−0.701152	+	1.16914i
$917$	0.424862	+	13.3188i	0.0140302	+	0.439826i
$918$	−21.2464	−	12.6277i	−0.701236	−	0.416776i
$919$	18.1008	−	31.3515i	0.597089	−	1.03419i	−0.396159	−	0.918182i	$-0.629657\pi$
$919$	18.1008	−	31.3515i	0.597089	−	1.03419i	0.993248	−	0.116007i	$-0.0370095\pi$
$920$	−2.88111	−	5.29042i	−0.0949872	−	0.174420i
$921$	21.0921	−	3.68760i	0.695007	−	0.121511i
$922$	−0.371450	+	44.7172i	−0.0122331	+	1.47268i
$923$			47.1321i			1.55137i
$924$	4.51438	−	12.9579i	0.148512	−	0.426283i
$925$			41.7916i			1.37410i
$926$	−33.2463	−	0.276166i	−1.09254	−	0.00907537i
$927$	26.2831	+	4.71298i	0.863252	+	0.154795i
$928$	23.3880	+	0.971914i	0.767747	+	0.0319047i
$929$	0.370626	−	0.641943i	0.0121598	−	0.0210615i	−0.859881	−	0.510494i	$-0.829463\pi$
$929$	0.370626	−	0.641943i	0.0121598	−	0.0210615i	0.872041	+	0.489432i	$0.162796\pi$
$930$	3.92140	−	0.652073i	0.128588	−	0.0213823i
$931$	19.8775	+	29.8567i	0.651458	+	0.978515i
$932$	3.57413	+	2.14347i	0.117075	+	0.0702117i
$933$	−1.60226	−	1.91513i	−0.0524557	−	0.0626985i
$934$	17.9641	+	10.5715i	0.587804	+	0.345910i
$935$	1.70141	−	0.982307i	0.0556419	−	0.0321249i
$936$	26.4697	−	8.80850i	0.865190	−	0.287915i
$937$		−	49.0746i		−	1.60320i	−0.597863	−	0.801598i	$-0.703983\pi$
$937$		−	49.0746i		−	1.60320i	0.597863	−	0.801598i	$-0.296017\pi$
$938$	11.5819	+	6.32749i	0.378164	+	0.206600i
$939$	−39.2250	−	14.3411i	−1.28006	−	0.468005i
$940$	3.42529	−	1.90244i	0.111721	−	0.0620506i
$941$	26.9660	−	15.5688i	0.879065	−	0.507529i	0.00871528	−	0.999962i	$-0.497226\pi$
$941$	26.9660	−	15.5688i	0.879065	−	0.507529i	0.870350	+	0.492433i	$0.163892\pi$
$942$	−7.88249	−	9.58229i	−0.256826	−	0.312208i
$943$	−52.7638	−	30.4632i	−1.71822	−	0.992017i
$944$	5.54271	−	2.95907i	0.180400	−	0.0963095i
$945$	2.80874	+	4.56946i	0.0913683	+	0.148644i
$946$	−8.83092	+	5.00119i	−0.287118	+	0.162603i
$947$	11.6780	−	20.2270i	0.379485	−	0.657288i	−0.611502	−	0.791243i	$-0.709434\pi$
$947$	11.6780	−	20.2270i	0.379485	−	0.657288i	0.990987	+	0.133955i	$0.0427678\pi$
$948$	−0.595368	+	1.54817i	−0.0193367	+	0.0502823i
$949$	−9.07751	+	5.24090i	−0.294669	+	0.170127i
$950$	35.1283	+	0.291798i	1.13971	+	0.00946719i
$951$	−16.0210	+	43.8197i	−0.519517	+	1.42095i
$952$	12.4324	−	21.8844i	0.402938	−	0.709278i
$953$			37.3593i			1.21019i	0.796155	+	0.605093i	$0.206864\pi$
$953$			37.3593i			1.21019i	−0.796155	+	0.605093i	$0.793136\pi$
$954$	3.21442	+	2.75918i	0.104071	+	0.0893316i
$955$	1.64162	+	2.84336i	0.0531215	+	0.0920091i
$956$	−0.0282992	+	1.70329i	−0.000915262	+	0.0550883i
$957$	6.88555	+	8.23006i	0.222578	+	0.266040i
$958$	−24.1177	−	42.5862i	−0.779209	−	1.37590i
$959$	17.0955	+	9.15612i	0.552042	+	0.295667i
$960$	4.97858	+	2.10698i	0.160683	+	0.0680025i
$961$	−6.84861	+	11.8621i	−0.220923	+	0.382650i
$962$	−34.5445	−	20.3287i	−1.11376	−	0.655423i
$963$	8.31589	−	46.3757i	0.267976	−	1.49443i
$964$	26.3299	−	14.6238i	0.848029	−	0.471002i
$965$			5.12916i			0.165114i
$966$	−6.91298	−	34.6964i	−0.222421	−	1.11634i
$967$	−32.9761			−1.06044			−0.530220	−	0.847860i	$-0.677891\pi$
$967$	−32.9761			−1.06044			−0.530220	+	0.847860i	$0.677891\pi$
$968$	−12.9171	+	21.1386i	−0.415172	+	0.679419i
$969$	29.4045	−	5.14089i	0.944607	−	0.165149i
$970$	2.51874	−	4.28008i	0.0808719	−	0.137425i
$971$	14.3859	+	8.30570i	0.461665	+	0.266543i	0.712744	−	0.701424i	$-0.247452\pi$
$971$	14.3859	+	8.30570i	0.461665	+	0.266543i	−0.251079	+	0.967967i	$0.580785\pi$
$972$	20.6041	−	23.3981i	0.660878	−	0.750494i
$973$	−21.9748	−	35.4044i	−0.704481	−	1.13501i
$974$	16.7654	+	29.6037i	0.537198	+	0.948563i
$975$	17.7137	+	21.1726i	0.567293	+	0.678066i
$976$	−14.4126	+	23.1515i	−0.461336	+	0.741061i
$977$	0.641595	−	0.370425i	0.0205264	−	0.0118509i	−0.489702	−	0.871890i	$-0.662894\pi$
$977$	0.641595	−	0.370425i	0.0205264	−	0.0118509i	0.510228	+	0.860039i	$0.329561\pi$
$978$	−28.7988	−	10.8012i	−0.920886	−	0.345385i
$979$	7.63074			0.243880
$980$	−4.59629	+	2.95103i	−0.146823	+	0.0942671i
$981$	33.8689	−	40.1267i	1.08135	−	1.28115i
$982$	−21.7369	−	0.180560i	−0.693651	−	0.00576192i
$983$	5.11340	+	8.85666i	0.163092	+	0.282484i	0.935976	−	0.352064i	$-0.114520\pi$
$983$	5.11340	+	8.85666i	0.163092	+	0.282484i	−0.772884	+	0.634547i	$0.781187\pi$
$984$	54.0770	−	8.07147i	1.72391	−	0.257309i
$985$	−5.95069	−	3.43563i	−0.189605	−	0.109468i
$986$	9.69941	+	17.1268i	0.308892	+	0.545430i
$987$	22.5290	−	4.68361i	0.717106	−	0.149081i
$988$	−17.3286	+	28.8947i	−0.551297	+	0.919262i
$989$	−13.0831	+	22.6606i	−0.416019	+	0.720567i
$990$	0.821452	+	2.33810i	0.0261074	+	0.0743096i
$991$	22.7297	+	39.3690i	0.722032	+	1.25060i	0.960184	+	0.279369i	$0.0901252\pi$
$991$	22.7297	+	39.3690i	0.722032	+	1.25060i	−0.238152	+	0.971228i	$0.576541\pi$
$992$	20.8490	−	10.9090i	0.661957	−	0.346362i
$993$	28.6984	+	10.4925i	0.910718	+	0.332969i
$994$	−45.8086	+	27.9081i	−1.45296	+	0.885191i
$995$	7.77971			0.246633
$996$	9.42252	+	59.7266i	0.298564	+	1.89251i
$997$	−13.6051	−	23.5647i	−0.430877	−	0.746300i	0.566072	−	0.824356i	$-0.308462\pi$
$997$	−13.6051	−	23.5647i	−0.430877	−	0.746300i	−0.996949	+	0.0780552i	$0.975129\pi$
$998$	32.1846	+	18.9400i	1.01879	+	0.599534i
$999$	−44.7944	−	0.194670i	−1.41723	−	0.00615907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.1	✓	48
3.2	odd	2	inner	168.2.ba.c.5.24	yes	48
4.3	odd	2		672.2.bi.c.593.2		48
7.3	odd	6	inner	168.2.ba.c.101.16	yes	48
8.3	odd	2		672.2.bi.c.593.23		48
8.5	even	2	inner	168.2.ba.c.5.9	yes	48
12.11	even	2		672.2.bi.c.593.19		48
21.17	even	6	inner	168.2.ba.c.101.9	yes	48
24.5	odd	2	inner	168.2.ba.c.5.16	yes	48
24.11	even	2		672.2.bi.c.593.6		48
28.3	even	6		672.2.bi.c.17.6		48
56.3	even	6		672.2.bi.c.17.19		48
56.45	odd	6	inner	168.2.ba.c.101.24	yes	48
84.59	odd	6		672.2.bi.c.17.23		48
168.59	odd	6		672.2.bi.c.17.2		48
168.101	even	6	inner	168.2.ba.c.101.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.1	✓	48	1.1	even	1	trivial
168.2.ba.c.5.9	yes	48	8.5	even	2	inner
168.2.ba.c.5.16	yes	48	24.5	odd	2	inner
168.2.ba.c.5.24	yes	48	3.2	odd	2	inner
168.2.ba.c.101.1	yes	48	168.101	even	6	inner
168.2.ba.c.101.9	yes	48	21.17	even	6	inner
168.2.ba.c.101.16	yes	48	7.3	odd	6	inner
168.2.ba.c.101.24	yes	48	56.45	odd	6	inner
672.2.bi.c.17.2		48	168.59	odd	6
672.2.bi.c.17.6		48	28.3	even	6
672.2.bi.c.17.19		48	56.3	even	6
672.2.bi.c.17.23		48	84.59	odd	6
672.2.bi.c.593.2		48	4.3	odd	2
672.2.bi.c.593.6		48	24.11	even	2
672.2.bi.c.593.19		48	12.11	even	2
672.2.bi.c.593.23		48	8.3	odd	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41416 - 0.0117470i) q^{2} +(1.70617 - 0.298296i) q^{3} +(1.99972 + 0.0332243i) q^{4} +(0.337879 + 0.195075i) q^{5} +(-2.41631 + 0.401798i) q^{6} +(1.39526 + 2.24795i) q^{7} +(-2.82755 - 0.0704754i) q^{8} +(2.82204 - 1.01789i) q^{9} +(-0.475526 - 0.279837i) q^{10} +(-0.748582 - 1.29658i) q^{11} +(3.42178 - 0.539824i) q^{12} -3.28768 q^{13} +(-1.94672 - 3.19536i) q^{14} +(0.634670 + 0.232043i) q^{15} +(3.99779 + 0.132879i) q^{16} +(1.68169 + 2.91278i) q^{17} +(-4.00278 + 1.40631i) q^{18} +(2.56203 - 4.43756i) q^{19} +(0.669184 + 0.401321i) q^{20} +(3.05110 + 3.41918i) q^{21} +(1.04339 + 1.84237i) q^{22} +(4.72764 + 2.72950i) q^{23} +(-4.84530 + 0.723204i) q^{24} +(-2.42389 - 4.19830i) q^{25} +(4.64932 + 0.0386203i) q^{26} +(4.51125 - 2.57850i) q^{27} +(2.71544 + 4.54163i) q^{28} -4.13801 q^{29} +(-0.894802 - 0.335602i) q^{30} +(-3.60237 + 2.07983i) q^{31} +(-5.65198 - 0.234875i) q^{32} +(-1.66397 - 1.98889i) q^{33} +(-2.34398 - 4.13891i) q^{34} +(0.0329110 + 1.03171i) q^{35} +(5.67712 - 1.94174i) q^{36} +(-7.46581 - 4.31038i) q^{37} +(-3.67525 + 6.24534i) q^{38} +(-5.60934 + 0.980702i) q^{39} +(-0.941622 - 0.575396i) q^{40} -11.1607 q^{41} +(-4.27459 - 4.87112i) q^{42} +4.79323i q^{43} +(-1.45388 - 2.61768i) q^{44} +(1.15207 + 0.206585i) q^{45} +(-6.65359 - 3.91550i) q^{46} +(2.51067 - 4.34861i) q^{47} +(6.86055 - 0.965812i) q^{48} +(-3.10652 + 6.27292i) q^{49} +(3.37846 + 5.96557i) q^{50} +(3.73813 + 4.46806i) q^{51} +(-6.57445 - 0.109231i) q^{52} +(-0.499243 - 0.864715i) q^{53} +(-6.40994 + 3.59342i) q^{54} -0.584118i q^{55} +(-3.78673 - 6.45451i) q^{56} +(3.04755 - 8.33548i) q^{57} +(5.85183 + 0.0486091i) q^{58} +(1.36034 - 0.785391i) q^{59} +(1.26146 + 0.485108i) q^{60} +(-3.40889 + 5.90437i) q^{61} +(5.11878 - 2.89891i) q^{62} +(6.22563 + 4.92357i) q^{63} +(7.99007 + 0.398545i) q^{64} +(-1.11084 - 0.641343i) q^{65} +(2.32977 + 2.83217i) q^{66} +(-3.05467 + 1.76361i) q^{67} +(3.26615 + 5.88063i) q^{68} +(8.88036 + 3.24676i) q^{69} +(-0.0344221 - 1.45940i) q^{70} -14.3360i q^{71} +(-8.05119 + 2.67925i) q^{72} +(2.76107 - 1.59410i) q^{73} +(10.5072 + 6.18329i) q^{74} +(-5.38791 - 6.43999i) q^{75} +(5.27078 - 8.78877i) q^{76} +(1.87018 - 3.49184i) q^{77} +(7.94406 - 1.32098i) q^{78} +(-0.239413 + 0.414676i) q^{79} +(1.32485 + 0.824765i) q^{80} +(6.92781 - 5.74504i) q^{81} +(15.7831 + 0.131105i) q^{82} +17.4548i q^{83} +(5.98776 + 6.93879i) q^{84} +1.31222i q^{85} +(0.0563059 - 6.77842i) q^{86} +(-7.06016 + 1.23435i) q^{87} +(2.02527 + 3.71891i) q^{88} +(-2.54840 + 4.41396i) q^{89} +(-1.62679 - 0.305678i) q^{90} +(-4.58716 - 7.39053i) q^{91} +(9.36328 + 5.61532i) q^{92} +(-5.52586 + 4.62312i) q^{93} +(-3.60159 + 6.12016i) q^{94} +(1.73131 - 0.999573i) q^{95} +(-9.71330 + 1.28523i) q^{96} +9.00074i q^{97} +(4.46682 - 8.83445i) q^{98} +(-3.43230 - 2.89703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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