LMFDB - Embedded newform 539.2.r.b.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(23,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([38, 0]))

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

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

chi := DirichletCharacter("539.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.r (of order $21$, degree $12$, 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$276$
Relative dimension:	$23$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	539.23
Dual form			539.2.r.b.375.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.185221 + 2.47160i) q^{2} +(0.579946 - 0.178890i) q^{3} +(-4.09683 - 0.617498i) q^{4} +(-0.257511 - 0.238935i) q^{5} +(0.334725 + 1.46653i) q^{6} +(-1.95317 - 1.78470i) q^{7} +(1.18198 - 5.17858i) q^{8} +(-2.17438 + 1.48247i) q^{9} +O(q^{10})$	\(q+(-0.185221 + 2.47160i) q^{2} +(0.579946 - 0.178890i) q^{3} +(-4.09683 - 0.617498i) q^{4} +(-0.257511 - 0.238935i) q^{5} +(0.334725 + 1.46653i) q^{6} +(-1.95317 - 1.78470i) q^{7} +(1.18198 - 5.17858i) q^{8} +(-2.17438 + 1.48247i) q^{9} +(0.638248 - 0.592207i) q^{10} +(0.826239 + 0.563320i) q^{11} +(-2.48641 + 0.374765i) q^{12} +(-5.80120 + 2.79371i) q^{13} +(4.77282 - 4.49688i) q^{14} +(-0.192085 - 0.0925034i) q^{15} +(4.66236 + 1.43815i) q^{16} +(2.78668 - 7.10034i) q^{17} +(-3.26132 - 5.64878i) q^{18} +(-0.128838 + 0.223154i) q^{19} +(0.907436 + 1.13789i) q^{20} +(-1.45199 - 0.685626i) q^{21} +(-1.54534 + 1.93779i) q^{22} +(-1.42396 - 3.62818i) q^{23} +(-0.240911 - 3.21474i) q^{24} +(-0.364429 - 4.86296i) q^{25} +(-5.83043 - 14.8557i) q^{26} +(-2.13103 + 2.67223i) q^{27} +(6.89975 + 8.51768i) q^{28} +(1.42959 + 1.79265i) q^{29} +(0.264209 - 0.457624i) q^{30} +(0.0233099 + 0.0403739i) q^{31} +(-0.536884 + 1.36796i) q^{32} +(0.579946 + 0.178890i) q^{33} +(17.0330 + 8.20268i) q^{34} +(0.0765347 + 0.926258i) q^{35} +(9.82349 - 4.73074i) q^{36} +(-4.85075 + 0.731132i) q^{37} +(-0.527683 - 0.359768i) q^{38} +(-2.86462 + 2.65798i) q^{39} +(-1.54171 + 1.05112i) q^{40} +(-1.69619 + 7.43148i) q^{41} +(1.96353 - 3.46176i) q^{42} +(-2.66692 - 11.6845i) q^{43} +(-3.03711 - 2.81803i) q^{44} +(0.914139 + 0.137784i) q^{45} +(9.23115 - 2.84743i) q^{46} +(-0.682047 + 9.10128i) q^{47} +2.96119 q^{48} +(0.629717 + 6.97162i) q^{49} +12.0868 q^{50} +(0.345946 - 4.61632i) q^{51} +(25.4917 - 7.86313i) q^{52} +(-11.3907 - 1.71688i) q^{53} +(-6.20996 - 5.76200i) q^{54} +(-0.0781684 - 0.342478i) q^{55} +(-11.5508 + 8.00515i) q^{56} +(-0.0347991 + 0.152465i) q^{57} +(-4.69550 + 3.20134i) q^{58} +(-7.85195 + 7.28555i) q^{59} +(0.729820 + 0.497583i) q^{60} +(-3.21825 + 0.485072i) q^{61} +(-0.104106 + 0.0501346i) q^{62} +(6.89268 + 0.985104i) q^{63} +(5.51028 + 2.65361i) q^{64} +(2.16139 + 0.666699i) q^{65} +(-0.549562 + 1.40026i) q^{66} +(6.48311 + 11.2291i) q^{67} +(-15.8010 + 27.3681i) q^{68} +(-1.47486 - 1.84942i) q^{69} +(-2.30351 + 0.0176009i) q^{70} +(-2.54955 + 3.19704i) q^{71} +(5.10701 + 13.0124i) q^{72} +(0.136786 + 1.82528i) q^{73} +(-0.908607 - 12.1245i) q^{74} +(-1.08128 - 2.75506i) q^{75} +(0.665624 - 0.834666i) q^{76} +(-0.608426 - 2.57484i) q^{77} +(-6.03886 - 7.57250i) q^{78} +(-0.640490 + 1.10936i) q^{79} +(-0.856983 - 1.48434i) q^{80} +(2.12651 - 5.41827i) q^{81} +(-18.0535 - 5.56875i) q^{82} +(-7.58560 - 3.65303i) q^{83} +(5.52521 + 3.70550i) q^{84} +(-2.41412 + 1.16258i) q^{85} +(29.3734 - 4.42733i) q^{86} +(1.14977 + 0.783901i) q^{87} +(3.89379 - 3.61291i) q^{88} +(-0.999932 + 0.681742i) q^{89} +(-0.509865 + 2.23386i) q^{90} +(16.3166 + 4.89680i) q^{91} +(3.59331 + 15.7433i) q^{92} +(0.0207409 + 0.0192448i) q^{93} +(-22.3684 - 3.37149i) q^{94} +(0.0864963 - 0.0266806i) q^{95} +(-0.0666501 + 0.889384i) q^{96} +12.8843 q^{97} +(-17.3477 + 0.265119i) q^{98} -2.63166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 23 q^{11} - 32 q^{12} - 27 q^{13} - 23 q^{14} + 6 q^{15} + 70 q^{16} - 3 q^{17} - 20 q^{18} - 61 q^{19} - 12 q^{20} - 23 q^{21} - 6 q^{23} + 6 q^{24} - 11 q^{25} + 9 q^{26} - 12 q^{27} - 3 q^{28} - 24 q^{29} - 26 q^{30} - 75 q^{31} + 137 q^{32} + 3 q^{33} - 58 q^{34} + 15 q^{35} - 36 q^{36} - 29 q^{37} - 6 q^{39} - 53 q^{40} - 25 q^{41} + 4 q^{42} + 20 q^{43} + 6 q^{44} + 3 q^{45} + 52 q^{46} + 25 q^{47} + 288 q^{48} + 84 q^{49} - 218 q^{50} - 160 q^{51} + 65 q^{52} + 5 q^{53} + 66 q^{54} - 12 q^{55} - 178 q^{56} + 23 q^{57} + 5 q^{58} + 28 q^{59} - 54 q^{60} - 65 q^{61} - 92 q^{62} + 85 q^{63} - 50 q^{64} + 201 q^{65} - 38 q^{66} - 16 q^{67} - 91 q^{68} - 42 q^{69} - 255 q^{70} - 63 q^{71} - 165 q^{72} + 6 q^{73} - 166 q^{74} - 117 q^{75} - 87 q^{76} + 33 q^{78} + 2 q^{79} - 48 q^{80} + 5 q^{81} + 53 q^{82} + 37 q^{83} - 84 q^{84} + 26 q^{85} + 67 q^{86} - 59 q^{87} - 3 q^{88} - 155 q^{89} + 9 q^{90} + 47 q^{91} - 19 q^{92} + 81 q^{93} + 126 q^{94} - 37 q^{95} + 395 q^{96} + 302 q^{97} + 90 q^{98} + 268 q^{99}+O(q^{100}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 23 * q^11 - 32 * q^12 - 27 * q^13 - 23 * q^14 + 6 * q^15 + 70 * q^16 - 3 * q^17 - 20 * q^18 - 61 * q^19 - 12 * q^20 - 23 * q^21 - 6 * q^23 + 6 * q^24 - 11 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 - 24 * q^29 - 26 * q^30 - 75 * q^31 + 137 * q^32 + 3 * q^33 - 58 * q^34 + 15 * q^35 - 36 * q^36 - 29 * q^37 - 6 * q^39 - 53 * q^40 - 25 * q^41 + 4 * q^42 + 20 * q^43 + 6 * q^44 + 3 * q^45 + 52 * q^46 + 25 * q^47 + 288 * q^48 + 84 * q^49 - 218 * q^50 - 160 * q^51 + 65 * q^52 + 5 * q^53 + 66 * q^54 - 12 * q^55 - 178 * q^56 + 23 * q^57 + 5 * q^58 + 28 * q^59 - 54 * q^60 - 65 * q^61 - 92 * q^62 + 85 * q^63 - 50 * q^64 + 201 * q^65 - 38 * q^66 - 16 * q^67 - 91 * q^68 - 42 * q^69 - 255 * q^70 - 63 * q^71 - 165 * q^72 + 6 * q^73 - 166 * q^74 - 117 * q^75 - 87 * q^76 + 33 * q^78 + 2 * q^79 - 48 * q^80 + 5 * q^81 + 53 * q^82 + 37 * q^83 - 84 * q^84 + 26 * q^85 + 67 * q^86 - 59 * q^87 - 3 * q^88 - 155 * q^89 + 9 * q^90 + 47 * q^91 - 19 * q^92 + 81 * q^93 + 126 * q^94 - 37 * q^95 + 395 * q^96 + 302 * q^97 + 90 * q^98 + 268 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{19}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.185221	+	2.47160i	−0.130971	+	1.74768i	0.414947	+	0.909846i	$0.363800\pi$
$2$	−0.185221	+	2.47160i	−0.130971	+	1.74768i	−0.545918	+	0.837839i	$0.683819\pi$
$3$	0.579946	−	0.178890i	0.334832	−	0.103282i	−0.122780	−	0.992434i	$-0.539181\pi$
$3$	0.579946	−	0.178890i	0.334832	−	0.103282i	0.457612	+	0.889152i	$0.348705\pi$
$4$	−4.09683	−	0.617498i	−2.04842	−	0.308749i
$5$	−0.257511	−	0.238935i	−0.115162	−	0.106855i	0.620490	−	0.784214i	$-0.286934\pi$
$5$	−0.257511	−	0.238935i	−0.115162	−	0.106855i	−0.735652	+	0.677359i	$0.763124\pi$
$6$	0.334725	+	1.46653i	0.136651	+	0.598708i
$7$	−1.95317	−	1.78470i	−0.738227	−	0.674552i
$7$	−1.95317	−	1.78470i	−0.738227	−	0.674552i
$8$	1.18198	−	5.17858i	0.417892	−	1.83090i
$9$	−2.17438	+	1.48247i	−0.724793	+	0.494156i
$10$	0.638248	−	0.592207i	0.201832	−	0.187272i
$11$	0.826239	+	0.563320i	0.249120	+	0.169847i
$11$	0.826239	+	0.563320i	0.249120	+	0.169847i
$12$	−2.48641	+	0.374765i	−0.717764	+	0.108185i
$13$	−5.80120	+	2.79371i	−1.60896	+	0.774836i	−0.999834	−	0.0182346i	$-0.994195\pi$
$13$	−5.80120	+	2.79371i	−1.60896	+	0.774836i	−0.609130	+	0.793071i	$0.708481\pi$
$14$	4.77282	−	4.49688i	1.27559	−	1.20184i
$15$	−0.192085	−	0.0925034i	−0.0495962	−	0.0238843i
$16$	4.66236	+	1.43815i	1.16559	+	0.359537i
$17$	2.78668	−	7.10034i	0.675869	−	1.72209i	−0.0158040	−	0.999875i	$-0.505031\pi$
$17$	2.78668	−	7.10034i	0.675869	−	1.72209i	0.691673	−	0.722211i	$-0.256874\pi$
$18$	−3.26132	−	5.64878i	−0.768702	−	1.33143i
$19$	−0.128838	+	0.223154i	−0.0295574	+	0.0511950i	−0.880426	−	0.474184i	$-0.842743\pi$
$19$	−0.128838	+	0.223154i	−0.0295574	+	0.0511950i	0.850868	+	0.525379i	$0.176076\pi$
$20$	0.907436	+	1.13789i	0.202909	+	0.254440i
$21$	−1.45199	−	0.685626i	−0.316851	−	0.149616i
$22$	−1.54534	+	1.93779i	−0.329467	+	0.413139i
$23$	−1.42396	−	3.62818i	−0.296915	−	0.756528i	−0.999012	−	0.0444461i	$-0.985848\pi$
$23$	−1.42396	−	3.62818i	−0.296915	−	0.756528i	0.702096	−	0.712082i	$-0.252248\pi$
$24$	−0.240911	−	3.21474i	−0.0491758	−	0.656206i
$25$	−0.364429	−	4.86296i	−0.0728857	−	0.972592i
$26$	−5.83043	−	14.8557i	−1.14344	−	2.91344i
$27$	−2.13103	+	2.67223i	−0.410117	+	0.514270i
$28$	6.89975	+	8.51768i	1.30393	+	1.60969i
$29$	1.42959	+	1.79265i	0.265468	+	0.332887i	0.896643	−	0.442754i	$-0.145998\pi$
$29$	1.42959	+	1.79265i	0.265468	+	0.332887i	−0.631175	+	0.775640i	$0.717427\pi$
$30$	0.264209	−	0.457624i	0.0482378	−	0.0835504i
$31$	0.0233099	+	0.0403739i	0.00418658	+	0.00725136i	0.868111	−	0.496370i	$-0.165334\pi$
$31$	0.0233099	+	0.0403739i	0.00418658	+	0.00725136i	−0.863925	+	0.503621i	$0.832001\pi$
$32$	−0.536884	+	1.36796i	−0.0949085	+	0.241823i
$33$	0.579946	+	0.178890i	0.100956	+	0.0311407i
$34$	17.0330	+	8.20268i	2.92114	+	1.40675i
$35$	0.0765347	+	0.926258i	0.0129367	+	0.156566i
$36$	9.82349	−	4.73074i	1.63725	−	0.788457i
$37$	−4.85075	+	0.731132i	−0.797458	+	0.120197i	−0.535117	−	0.844778i	$-0.679732\pi$
$37$	−4.85075	+	0.731132i	−0.797458	+	0.120197i	−0.262341	+	0.964975i	$0.584494\pi$
$38$	−0.527683	−	0.359768i	−0.0856015	−	0.0583621i
$39$	−2.86462	+	2.65798i	−0.458706	+	0.425617i
$40$	−1.54171	+	1.05112i	−0.243766	+	0.166197i
$41$	−1.69619	+	7.43148i	−0.264900	+	1.16060i	0.650963	+	0.759110i	$0.274365\pi$
$41$	−1.69619	+	7.43148i	−0.264900	+	1.16060i	−0.915863	+	0.401492i	$0.868492\pi$
$42$	1.96353	−	3.46176i	0.302980	−	0.534161i
$43$	−2.66692	−	11.6845i	−0.406701	−	1.78187i	−0.599225	−	0.800581i	$-0.704525\pi$
$43$	−2.66692	−	11.6845i	−0.406701	−	1.78187i	0.192524	−	0.981292i	$-0.438333\pi$
$44$	−3.03711	−	2.81803i	−0.457862	−	0.424834i
$45$	0.914139	+	0.137784i	0.136272	+	0.0205397i
$46$	9.23115	−	2.84743i	1.36106	−	0.419831i
$47$	−0.682047	+	9.10128i	−0.0994868	+	1.32756i	0.694442	+	0.719548i	$0.255651\pi$
$47$	−0.682047	+	9.10128i	−0.0994868	+	1.32756i	−0.793929	+	0.608010i	$0.791968\pi$
$48$	2.96119			0.427410
$49$	0.629717	+	6.97162i	0.0899595	+	0.995945i
$50$	12.0868			1.70933
$51$	0.345946	−	4.61632i	0.0484421	−	0.646415i
$52$	25.4917	−	7.86313i	3.53506	−	1.09042i
$53$	−11.3907	−	1.71688i	−1.56464	−	0.235831i	−0.691162	−	0.722699i	$-0.742901\pi$
$53$	−11.3907	−	1.71688i	−1.56464	−	0.235831i	−0.873475	+	0.486868i	$0.838139\pi$
$54$	−6.20996	−	5.76200i	−0.845069	−	0.784110i
$55$	−0.0781684	−	0.342478i	−0.0105402	−	0.0461797i
$56$	−11.5508	+	8.00515i	−1.54354	+	1.06973i
$57$	−0.0347991	+	0.152465i	−0.00460926	+	0.0201945i
$58$	−4.69550	+	3.20134i	−0.616549	+	0.420356i
$59$	−7.85195	+	7.28555i	−1.02224	+	0.948497i	−0.998687	−	0.0512253i	$-0.983687\pi$
$59$	−7.85195	+	7.28555i	−1.02224	+	0.948497i	−0.0235499	+	0.999723i	$0.507497\pi$
$60$	0.729820	+	0.497583i	0.0942194	+	0.0642377i
$61$	−3.21825	+	0.485072i	−0.412054	+	0.0621072i	−0.351798	−	0.936076i	$-0.614430\pi$
$61$	−3.21825	+	0.485072i	−0.412054	+	0.0621072i	−0.0602558	+	0.998183i	$0.519192\pi$
$62$	−0.104106	+	0.0501346i	−0.0132214	+	0.00636710i
$63$	6.89268	+	0.985104i	0.868396	+	0.124111i
$64$	5.51028	+	2.65361i	0.688785	+	0.331701i
$65$	2.16139	+	0.666699i	0.268087	+	0.0826939i
$66$	−0.549562	+	1.40026i	−0.0676463	+	0.172360i
$67$	6.48311	+	11.2291i	0.792038	+	1.37185i	0.924703	+	0.380690i	$0.124313\pi$
$67$	6.48311	+	11.2291i	0.792038	+	1.37185i	−0.132664	+	0.991161i	$0.542353\pi$
$68$	−15.8010	+	27.3681i	−1.91615	+	3.31887i
$69$	−1.47486	−	1.84942i	−0.177552	−	0.222644i
$70$	−2.30351	+	0.0176009i	−0.275323	+	0.00210371i
$71$	−2.54955	+	3.19704i	−0.302576	+	0.379419i	−0.909754	−	0.415147i	$-0.863730\pi$
$71$	−2.54955	+	3.19704i	−0.302576	+	0.379419i	0.607178	+	0.794566i	$0.292302\pi$
$72$	5.10701	+	13.0124i	0.601866	+	1.53353i
$73$	0.136786	+	1.82528i	0.0160096	+	0.213633i	0.999471	+	0.0325163i	$0.0103521\pi$
$73$	0.136786	+	1.82528i	0.0160096	+	0.213633i	−0.983462	+	0.181117i	$0.942029\pi$
$74$	−0.908607	−	12.1245i	−0.105623	−	1.40945i
$75$	−1.08128	−	2.75506i	−0.124856	−	0.318127i
$76$	0.665624	−	0.834666i	0.0763523	−	0.0957428i
$77$	−0.608426	−	2.57484i	−0.0693366	−	0.293431i
$78$	−6.03886	−	7.57250i	−0.683767	−	0.857416i
$79$	−0.640490	+	1.10936i	−0.0720608	+	0.124813i	−0.899804	−	0.436294i	$-0.856291\pi$
$79$	−0.640490	+	1.10936i	−0.0720608	+	0.124813i	0.827744	+	0.561107i	$0.189624\pi$
$80$	−0.856983	−	1.48434i	−0.0958136	−	0.165954i
$81$	2.12651	−	5.41827i	0.236279	−	0.602029i
$82$	−18.0535	−	5.56875i	−1.99367	−	0.614966i
$83$	−7.58560	−	3.65303i	−0.832628	−	0.400972i	−0.0315278	−	0.999503i	$-0.510037\pi$
$83$	−7.58560	−	3.65303i	−0.832628	−	0.400972i	−0.801100	+	0.598530i	$0.795752\pi$
$84$	5.52521	+	3.70550i	0.602849	+	0.404303i
$85$	−2.41412	+	1.16258i	−0.261848	+	0.126099i
$86$	29.3734	−	4.42733i	3.16742	−	0.477411i
$87$	1.14977	+	0.783901i	0.123268	+	0.0840430i
$88$	3.89379	−	3.61291i	0.415080	−	0.385138i
$89$	−0.999932	+	0.681742i	−0.105993	+	0.0722645i	−0.615156	−	0.788405i	$-0.710907\pi$
$89$	−0.999932	+	0.681742i	−0.105993	+	0.0722645i	0.509164	+	0.860670i	$0.329955\pi$
$90$	−0.509865	+	2.23386i	−0.0537445	+	0.235470i
$91$	16.3166	+	4.89680i	1.71045	+	0.513324i
$92$	3.59331	+	15.7433i	0.374629	+	1.64136i
$93$	0.0207409	+	0.0192448i	0.00215074	+	0.00199559i
$94$	−22.3684	−	3.37149i	−2.30712	−	0.347743i
$95$	0.0864963	−	0.0266806i	0.00887434	−	0.00273737i
$96$	−0.0666501	+	0.889384i	−0.00680245	+	0.0907724i
$97$	12.8843			1.30820			0.654101	−	0.756407i	$-0.273047\pi$
$97$	12.8843			1.30820			0.654101	+	0.756407i	$0.273047\pi$
$98$	−17.3477	+	0.265119i	−1.75238	+	0.0267811i
$99$	−2.63166			−0.264492
$100$	−1.50987	+	20.1478i	−0.150987	+	2.01478i
$101$	0.524451	−	0.161772i	0.0521848	−	0.0160969i	−0.268553	−	0.963265i	$-0.586545\pi$
$101$	0.524451	−	0.161772i	0.0521848	−	0.0160969i	0.320738	+	0.947168i	$0.396069\pi$
$102$	11.3456	+	1.71008i	1.12338	+	0.169323i
$103$	7.37174	+	6.83997i	0.726359	+	0.673963i	0.954008	−	0.299781i	$-0.0969135\pi$
$103$	7.37174	+	6.83997i	0.726359	+	0.673963i	−0.227649	+	0.973743i	$0.573104\pi$
$104$	7.61057	+	33.3441i	0.746277	+	3.26965i
$105$	0.210084	+	0.523488i	0.0205021	+	0.0510872i
$106$	6.35323	−	27.8353i	0.617080	−	2.70361i
$107$	11.3671	−	7.74993i	1.09890	−	0.749214i	0.128735	−	0.991679i	$-0.458908\pi$
$107$	11.3671	−	7.74993i	1.09890	−	0.749214i	0.970160	+	0.242465i	$0.0779560\pi$
$108$	10.3806	−	9.63176i	0.998871	−	0.926817i
$109$	−7.57828	−	5.16678i	−0.725867	−	0.494888i	0.143130	−	0.989704i	$-0.454283\pi$
$109$	−7.57828	−	5.16678i	−0.725867	−	0.494888i	−0.868998	+	0.494816i	$0.835236\pi$
$110$	0.860947	−	0.129767i	0.0820881	−	0.0123728i
$111$	−2.68238	+	1.29177i	−0.254600	+	0.122609i
$112$	−6.53970	−	11.1298i	−0.617944	−	1.05167i
$113$	−5.91966	−	2.85076i	−0.556875	−	0.268177i	0.134207	−	0.990953i	$-0.457151\pi$
$113$	−5.91966	−	2.85076i	−0.556875	−	0.268177i	−0.691082	+	0.722776i	$0.742866\pi$
$114$	−0.370387	−	0.114249i	−0.0346899	−	0.0107004i
$115$	−0.500215	+	1.27453i	−0.0466453	+	0.118850i
$116$	−4.74983	−	8.22695i	−0.441011	−	0.763853i
$117$	8.47243	−	14.6747i	0.783277	−	1.35667i
$118$	−16.5526	−	20.7563i	−1.52379	−	1.91077i
$119$	−18.1148	+	8.89477i	−1.66058	+	0.815382i
$120$	−0.706076	+	0.885391i	−0.0644556	+	0.0808248i
$121$	0.365341	+	0.930874i	0.0332128	+	0.0846249i
$122$	−0.602819	−	8.04406i	−0.0545766	−	0.728275i
$123$	0.345718	+	4.61329i	0.0311723	+	0.415966i
$124$	−0.0705658	−	0.179799i	−0.00633700	−	0.0161464i
$125$	−2.16320	+	2.71257i	−0.193483	+	0.242620i
$126$	−3.71145	+	16.8535i	−0.330642	+	1.50143i
$127$	11.6100	+	14.5585i	1.03022	+	1.29186i	0.955607	+	0.294645i	$0.0952014\pi$
$127$	11.6100	+	14.5585i	1.03022	+	1.29186i	0.0746151	+	0.997212i	$0.476227\pi$
$128$	−9.04882	+	15.6730i	−0.799810	+	1.38531i
$129$	−3.63691	−	6.29931i	−0.320212	−	0.554623i
$130$	−2.04815	+	5.21859i	−0.179634	+	0.457701i
$131$	−21.1394	−	6.52064i	−1.84696	−	0.569711i	−0.999228	−	0.0392820i	$-0.987493\pi$
$131$	−21.1394	−	6.52064i	−1.84696	−	0.569711i	−0.847729	−	0.530429i	$-0.822031\pi$
$132$	−2.26548	−	1.09100i	−0.197185	−	0.0949591i
$133$	0.649903	−	0.205920i	0.0563538	−	0.0178555i
$134$	−28.9546	+	13.9438i	−2.50130	+	1.20456i
$135$	1.18725	−	0.178949i	0.102182	−	0.0154015i
$136$	−33.4759	−	22.8235i	−2.87053	−	1.95710i
$137$	8.43652	−	7.82795i	0.720780	−	0.668787i	−0.231907	−	0.972738i	$-0.574497\pi$
$137$	8.43652	−	7.82795i	0.720780	−	0.668787i	0.952688	+	0.303951i	$0.0983061\pi$
$138$	4.84419	−	3.30272i	0.412365	−	0.281146i
$139$	2.43955	−	10.6884i	0.206920	−	0.906577i	−0.759682	−	0.650295i	$-0.774645\pi$
$139$	2.43955	−	10.6884i	0.206920	−	0.906577i	0.966602	−	0.256282i	$-0.0824975\pi$
$140$	0.258413	−	3.84198i	0.0218399	−	0.324707i
$141$	1.23258	+	5.40026i	0.103802	+	0.454784i
$142$	−7.42957	−	6.89363i	−0.623475	−	0.578501i
$143$	−6.36693	−	0.959660i	−0.532429	−	0.0802508i
$144$	−12.2697	+	3.78471i	−1.02248	+	0.315393i
$145$	0.0601919	−	0.803205i	0.00499867	−	0.0667026i
$146$	−4.53669			−0.375460
$147$	1.61235	+	3.93051i	0.132985	+	0.324183i
$148$	20.3242			1.67064
$149$	0.953910	−	12.7290i	0.0781473	−	1.04280i	−0.810959	−	0.585103i	$-0.801054\pi$
$149$	0.953910	−	12.7290i	0.0781473	−	1.04280i	0.889106	−	0.457701i	$-0.151327\pi$
$150$	7.00969	−	2.16220i	0.572339	−	0.176543i
$151$	−5.37449	−	0.810073i	−0.437369	−	0.0659228i	−0.0733329	−	0.997308i	$-0.523364\pi$
$151$	−5.37449	−	0.810073i	−0.437369	−	0.0659228i	−0.364036	+	0.931385i	$0.618602\pi$
$152$	1.00334	+	0.930959i	0.0813813	+	0.0755108i
$153$	4.46673	+	19.5700i	0.361113	+	1.58214i
$154$	6.47667	−	1.02687i	0.521905	−	0.0827477i
$155$	0.00364419	−	0.0159662i	0.000292709	−	0.00128244i
$156$	13.3772	−	9.12039i	1.07103	−	0.730215i
$157$	−11.4375	+	10.6125i	−0.912814	+	0.846967i	−0.988663	−	0.150152i	$-0.952024\pi$
$157$	−11.4375	+	10.6125i	−0.912814	+	0.846967i	0.0758491	+	0.997119i	$0.475833\pi$
$158$	−2.62326	−	1.78851i	−0.208696	−	0.142286i
$159$	−6.91314	+	1.04199i	−0.548248	+	0.0826351i
$160$	0.465106	−	0.223983i	0.0367699	−	0.0177074i
$161$	−3.69398	+	9.62777i	−0.291126	+	0.758774i
$162$	12.9979	+	6.25946i	1.02121	+	0.491790i
$163$	−14.8060	−	4.56705i	−1.15970	−	0.357719i	−0.345562	−	0.938396i	$-0.612312\pi$
$163$	−14.8060	−	4.56705i	−1.15970	−	0.357719i	−0.814134	+	0.580677i	$0.802788\pi$
$164$	11.5379	−	29.3981i	0.900959	−	2.29561i
$165$	−0.106599	−	0.184635i	−0.00829874	−	0.0143738i
$166$	10.4338	−	18.0719i	0.809823	−	1.40265i
$167$	−4.01225	−	5.03120i	−0.310477	−	0.389326i	0.601971	−	0.798518i	$-0.294382\pi$
$167$	−4.01225	−	5.03120i	−0.310477	−	0.389326i	−0.912448	+	0.409192i	$0.865811\pi$
$168$	−5.26679	+	6.70887i	−0.406342	+	0.517601i
$169$	17.7437	−	22.2499i	1.36490	−	1.71153i
$170$	−2.42628	−	6.18207i	−0.186087	−	0.474143i
$171$	−0.0506756	−	0.676219i	−0.00387526	−	0.0517118i
$172$	3.71074	+	49.5163i	0.282941	+	3.77559i
$173$	−5.34424	−	13.6169i	−0.406315	−	1.03527i	−0.976836	−	0.213991i	$-0.931354\pi$
$173$	−5.34424	−	13.6169i	−0.406315	−	1.03527i	0.570520	−	0.821283i	$-0.306742\pi$
$174$	−2.15045	+	2.69658i	−0.163025	+	0.204427i
$175$	−7.96712	+	10.1486i	−0.602258	+	0.767160i
$176$	3.04208	+	3.81465i	0.229306	+	0.287540i
$177$	−3.25040	+	5.62986i	−0.244315	+	0.423166i
$178$	−1.49978	−	2.59770i	−0.112414	−	0.194706i
$179$	−4.24491	+	10.8159i	−0.317280	+	0.808416i	0.679896	+	0.733309i	$0.262025\pi$
$179$	−4.24491	+	10.8159i	−0.317280	+	0.808416i	−0.997175	+	0.0751069i	$0.976070\pi$
$180$	−3.65999	−	1.12896i	−0.272800	−	0.0841476i
$181$	1.32729	+	0.639187i	0.0986564	+	0.0475104i	0.482561	−	0.875862i	$-0.339707\pi$
$181$	1.32729	+	0.639187i	0.0986564	+	0.0475104i	−0.383905	+	0.923373i	$0.625421\pi$
$182$	−15.1251	+	39.4212i	−1.12115	+	2.92209i
$183$	−1.77963	+	0.857027i	−0.131554	+	0.0633532i
$184$	−20.4719	+	3.08564i	−1.50921	+	0.227477i
$185$	1.42381	+	0.970738i	0.104681	+	0.0713701i
$186$	−0.0514070	+	0.0476988i	−0.00376935	+	0.00349744i
$187$	6.30223	−	4.29679i	0.460865	−	0.314212i
$188$	8.41426	−	36.8653i	0.613673	−	2.68868i
$189$	8.93137	−	1.41606i	0.649662	−	0.103003i
$190$	0.0499228	+	0.218726i	0.00362178	+	0.0158681i
$191$	1.40523	+	1.30386i	0.101679	+	0.0943442i	0.729374	−	0.684115i	$-0.239811\pi$
$191$	1.40523	+	1.30386i	0.101679	+	0.0943442i	−0.627696	+	0.778459i	$0.716002\pi$
$192$	3.67037	+	0.553219i	0.264886	+	0.0399251i
$193$	15.9893	−	4.93206i	1.15094	−	0.355017i	0.340158	−	0.940368i	$-0.389520\pi$
$193$	15.9893	−	4.93206i	1.15094	−	0.355017i	0.810780	+	0.585351i	$0.199043\pi$
$194$	−2.38644	+	31.8448i	−0.171336	+	2.28632i
$195$	1.37275			0.0983049
$196$	1.72512	−	28.9504i	0.123223	−	2.06789i
$197$	15.1875			1.08207			0.541033	−	0.841001i	$-0.318033\pi$
$197$	15.1875			1.08207			0.541033	+	0.841001i	$0.318033\pi$
$198$	0.487438	−	6.50441i	0.0346407	−	0.462248i
$199$	−8.67886	+	2.67707i	−0.615228	+	0.189773i	−0.586679	−	0.809820i	$-0.699565\pi$
$199$	−8.67886	+	2.67707i	−0.615228	+	0.189773i	−0.0285490	+	0.999592i	$0.509089\pi$
$200$	−25.6140	−	3.86069i	−1.81118	−	0.272992i
$201$	5.76862	+	5.35250i	0.406887	+	0.377536i
$202$	0.302695	+	1.32620i	0.0212976	+	0.0933108i
$203$	0.407108	−	6.05273i	0.0285734	−	0.424818i
$204$	−4.26785	+	18.6987i	−0.298809	+	1.30917i
$205$	2.21242	−	1.50841i	0.154522	−	0.105352i
$206$	−18.2711	+	16.9531i	−1.27301	+	1.18118i
$207$	8.47488	+	5.77808i	0.589045	+	0.401604i
$208$	−31.0650	+	4.68230i	−2.15397	+	0.324659i
$209$	−0.232158	+	0.111801i	−0.0160587	+	0.00773346i
$210$	−1.33277	+	0.422282i	−0.0919695	+	0.0291403i
$211$	−5.42684	−	2.61343i	−0.373599	−	0.179916i	0.237656	−	0.971349i	$-0.423621\pi$
$211$	−5.42684	−	2.61343i	−0.373599	−	0.179916i	−0.611255	+	0.791433i	$0.709335\pi$
$212$	45.6058	+	14.0675i	3.13222	+	0.966161i
$213$	−0.906686	+	2.31020i	−0.0621251	+	0.158292i
$214$	17.0493	+	29.5303i	1.16547	+	2.01865i
$215$	−2.10508	+	3.64611i	−0.143565	+	0.248662i
$216$	11.3195	+	14.1942i	0.770195	+	0.965794i
$217$	0.0265271	−	0.120458i	0.00180078	−	0.00817722i
$218$	14.1739	−	17.7735i	0.959975	−	1.20377i
$219$	0.405852	+	1.03409i	0.0274249	+	0.0698776i
$220$	0.108763	+	1.45134i	0.00733282	+	0.0978496i
$221$	3.67022	+	48.9757i	0.246886	+	3.29446i
$222$	−2.69589	−	6.86903i	−0.180937	−	0.461019i
$223$	1.40396	−	1.76051i	0.0940161	−	0.117893i	−0.732598	−	0.680661i	$-0.761692\pi$
$223$	1.40396	−	1.76051i	0.0940161	−	0.117893i	0.826614	+	0.562769i	$0.190264\pi$
$224$	3.49001	−	1.71367i	0.233186	−	0.114500i
$225$	8.00159	+	10.0337i	0.533439	+	0.668912i
$226$	8.14238	−	14.1030i	0.541623	−	0.938119i
$227$	−3.35471	−	5.81053i	−0.222660	−	0.385658i	0.732955	−	0.680277i	$-0.238141\pi$
$227$	−3.35471	−	5.81053i	−0.222660	−	0.385658i	−0.955615	+	0.294619i	$0.904807\pi$
$228$	0.236713	−	0.603135i	0.0156767	−	0.0399436i
$229$	26.3989	+	8.14297i	1.74449	+	0.538103i	0.992626	−	0.121219i	$-0.0386803\pi$
$229$	26.3989	+	8.14297i	1.74449	+	0.538103i	0.751861	+	0.659322i	$0.229156\pi$
$230$	−3.05747	−	1.47240i	−0.201604	−	0.0970872i
$231$	−0.813467	−	1.38443i	−0.0535222	−	0.0910887i
$232$	10.9731	−	5.28437i	0.720420	−	0.346936i
$233$	12.3597	−	1.86292i	0.809708	−	0.122044i	0.268877	−	0.963175i	$-0.413348\pi$
$233$	12.3597	−	1.86292i	0.809708	−	0.122044i	0.540832	+	0.841131i	$0.318110\pi$
$234$	34.7007	+	23.6585i	2.26845	+	1.54660i
$235$	2.35025	−	2.18071i	0.153313	−	0.142254i
$236$	36.6669	−	24.9991i	2.38681	−	1.62730i
$237$	−0.172996	+	0.757947i	−0.0112373	+	0.0492339i
$238$	−18.6291	−	46.4200i	−1.20754	−	3.00896i
$239$	1.59268	+	6.97799i	0.103022	+	0.451369i	0.999958	+	0.00920770i	$0.00293094\pi$
$239$	1.59268	+	6.97799i	0.103022	+	0.451369i	−0.896936	+	0.442161i	$0.854212\pi$
$240$	−0.762537	−	0.707531i	−0.0492215	−	0.0456709i
$241$	−17.2516	−	2.60027i	−1.11128	−	0.167498i	−0.432351	−	0.901706i	$-0.642316\pi$
$241$	−17.2516	−	2.60027i	−1.11128	−	0.167498i	−0.678925	+	0.734208i	$0.737554\pi$
$242$	−2.36842	+	0.730559i	−0.152247	+	0.0469621i
$243$	1.03025	−	13.7478i	0.0660907	−	0.881919i
$244$	13.4841			0.863234
$245$	1.50360	−	1.94573i	0.0960617	−	0.124308i
$246$	−11.4662			−0.731060
$247$	0.123987	−	1.65450i	0.00788912	−	0.105273i
$248$	0.236631	−	0.0729910i	0.0150261	−	0.00463493i
$249$	−5.05273	−	0.761576i	−0.320204	−	0.0482629i
$250$	−6.30371	−	5.84899i	−0.398682	−	0.369923i
$251$	0.991162	+	4.34256i	0.0625616	+	0.274100i	0.996528	−	0.0832612i	$-0.0265336\pi$
$251$	0.991162	+	4.34256i	0.0625616	+	0.274100i	−0.933966	+	0.357361i	$0.883676\pi$
$252$	−27.6299	−	8.29202i	−1.74052	−	0.522348i
$253$	0.867299	−	3.79989i	0.0545266	−	0.238897i
$254$	−38.1332	+	25.9988i	−2.39269	+	1.63131i
$255$	−1.19209	+	1.10609i	−0.0746513	+	0.0692663i
$256$	−26.9549	−	18.3775i	−1.68468	−	1.14860i
$257$	12.7287	−	1.91854i	0.793994	−	0.119675i	0.260494	−	0.965475i	$-0.416115\pi$
$257$	12.7287	−	1.91854i	0.793994	−	0.119675i	0.533500	+	0.845800i	$0.320876\pi$
$258$	16.2430	−	7.82221i	1.01124	−	0.486990i
$259$	10.7792	+	7.22909i	0.669785	+	0.449194i
$260$	−8.44315	−	4.06601i	−0.523622	−	0.252163i
$261$	−5.76602	−	1.77858i	−0.356907	−	0.110091i
$262$	20.0319	−	51.0403i	1.23757	−	3.15328i
$263$	3.41607	+	5.91680i	0.210644	+	0.364845i	0.951916	−	0.306359i	$-0.0991107\pi$
$263$	3.41607	+	5.91680i	0.210644	+	0.364845i	−0.741273	+	0.671204i	$0.765777\pi$
$264$	1.61188	−	2.79185i	0.0992041	−	0.171827i
$265$	2.52301	+	3.16376i	0.154987	+	0.194348i
$266$	0.388576	+	1.64444i	0.0238251	+	0.100827i
$267$	−0.457950	+	0.574251i	−0.0280261	+	0.0351436i
$268$	−19.6263	−	50.0070i	−1.19887	−	3.05466i
$269$	−1.99847	−	26.6678i	−0.121849	−	1.62596i	−0.638399	−	0.769706i	$-0.720403\pi$
$269$	−1.99847	−	26.6678i	−0.121849	−	1.62596i	0.516550	−	0.856257i	$-0.327216\pi$
$270$	0.222387	+	2.96755i	0.0135341	+	0.180600i
$271$	3.84674	+	9.80133i	0.233673	+	0.595388i	0.998825	−	0.0484609i	$-0.0154316\pi$
$271$	3.84674	+	9.80133i	0.233673	+	0.595388i	−0.765152	+	0.643849i	$0.777336\pi$
$272$	23.2038	−	29.0967i	1.40694	−	1.76425i
$273$	10.3388	−	0.0789974i	0.625730	−	0.00478114i
$274$	17.7849	+	22.3016i	1.07443	+	1.34729i
$275$	2.43830	−	4.22326i	0.147035	−	0.254672i
$276$	4.90025	+	8.48748i	0.294960	+	0.510886i
$277$	6.44513	−	16.4219i	0.387251	−	0.986698i	−0.595762	−	0.803161i	$-0.703150\pi$
$277$	6.44513	−	16.4219i	0.387251	−	0.986698i	0.983013	−	0.183537i	$-0.0587548\pi$
$278$	25.9655	+	8.00931i	1.55731	+	0.480366i
$279$	−0.110538	−	0.0532321i	−0.00661771	−	0.00318692i
$280$	4.88716	+	0.698474i	0.292064	+	0.0417418i
$281$	7.83495	−	3.77311i	0.467394	−	0.225085i	−0.185337	−	0.982675i	$-0.559338\pi$
$281$	7.83495	−	3.77311i	0.467394	−	0.225085i	0.652731	+	0.757590i	$0.273623\pi$
$282$	−13.5756	+	2.04619i	−0.808414	+	0.121849i
$283$	3.76375	+	2.56608i	0.223732	+	0.152538i	0.669999	−	0.742362i	$-0.266295\pi$
$283$	3.76375	+	2.56608i	0.223732	+	0.152538i	−0.446267	+	0.894900i	$0.647247\pi$
$284$	12.4193	−	11.5234i	0.736947	−	0.683787i
$285$	0.0453903	−	0.0309466i	0.00268869	−	0.00183312i
$286$	3.55118	−	15.5587i	0.209986	−	0.920008i
$287$	16.5759	−	11.4877i	0.978442	−	0.678099i
$288$	−0.860563	−	3.77037i	−0.0507091	−	0.222171i
$289$	−30.1874	−	28.0098i	−1.77573	−	1.64764i
$290$	1.97405	+	0.297540i	0.115920	+	0.0174722i
$291$	7.47220	−	2.30487i	0.438028	−	0.135114i
$292$	0.566718	−	7.56233i	0.0331647	−	0.442552i
$293$	−8.18958			−0.478441			−0.239220	−	0.970965i	$-0.576892\pi$
$293$	−8.18958			−0.478441			−0.239220	+	0.970965i	$0.576892\pi$
$294$	−10.0133	+	3.25708i	−0.583987	+	0.189956i
$295$	3.76273			0.219075
$296$	−1.94724	+	25.9841i	−0.113181	+	1.51030i
$297$	−3.26606	+	1.00745i	−0.189516	+	0.0584579i
$298$	31.2844	+	4.71536i	1.81226	+	0.273154i
$299$	18.3967	+	17.0697i	1.06391	+	0.987165i
$300$	2.72859	+	11.9547i	0.157535	+	0.690206i
$301$	−15.6444	+	27.5815i	−0.901728	+	1.58977i
$302$	2.99764	−	13.1335i	0.172495	−	0.755750i
$303$	0.275214	−	0.187638i	0.0158106	−	0.0107795i
$304$	−0.921616	+	0.855135i	−0.0528583	+	0.0490453i
$305$	0.944633	+	0.644040i	0.0540895	+	0.0368776i
$306$	−49.1965	+	7.41518i	−2.81238	+	0.423898i
$307$	−1.74982	+	0.842669i	−0.0998675	+	0.0480936i	−0.483151	−	0.875537i	$-0.660508\pi$
$307$	−1.74982	+	0.842669i	−0.0998675	+	0.0480936i	0.383283	+	0.923631i	$0.374793\pi$
$308$	0.902660	+	10.9244i	0.0514338	+	0.622476i
$309$	5.49881	+	2.64809i	0.312816	+	0.150644i
$310$	0.0387872	+	0.0119643i	0.00220296	+	0.000679524i
$311$	−5.27244	+	13.4340i	−0.298973	+	0.761770i	0.699897	+	0.714244i	$0.253229\pi$
$311$	−5.27244	+	13.4340i	−0.298973	+	0.761770i	−0.998870	+	0.0475266i	$0.984866\pi$
$312$	10.3786	+	17.9763i	0.587574	+	1.01771i
$313$	4.57078	−	7.91683i	0.258356	−	0.447486i	−0.707446	−	0.706768i	$-0.750153\pi$
$313$	4.57078	−	7.91683i	0.258356	−	0.447486i	0.965802	+	0.259282i	$0.0834859\pi$
$314$	−24.1113	−	30.2346i	−1.36068	−	1.70624i
$315$	−1.53956	−	1.90058i	−0.0867445	−	0.107085i
$316$	3.30901	−	4.14937i	0.186146	−	0.233420i
$317$	3.15209	+	8.03140i	0.177039	+	0.451088i	0.991656	−	0.128911i	$-0.0411481\pi$
$317$	3.15209	+	8.03140i	0.177039	+	0.451088i	−0.814617	+	0.579999i	$0.803053\pi$
$318$	−1.29492	−	17.2795i	−0.0726155	−	0.968987i
$319$	0.171347	+	2.28647i	0.00959362	+	0.128018i
$320$	−0.784915	−	1.99993i	−0.0438781	−	0.111799i
$321$	5.20590	−	6.52799i	0.290565	−	0.364357i
$322$	−23.1118	−	10.9133i	−1.28797	−	0.608174i
$323$	1.22544	+	1.53665i	0.0681852	+	0.0855015i
$324$	−12.0577	+	20.8846i	−0.669874	+	1.16026i
$325$	15.6998	+	27.1929i	0.870870	+	1.50839i
$326$	14.0303	−	35.7486i	0.777066	−	1.97993i
$327$	−5.31928	−	1.64078i	−0.294157	−	0.0907353i
$328$	36.4796	+	17.5677i	2.01425	+	0.970012i
$329$	17.5752	−	16.5591i	0.968951	−	0.912931i
$330$	0.476089	−	0.229272i	0.0262078	−	0.0126210i
$331$	−20.4755	+	3.08619i	−1.12544	+	0.169632i	−0.685273	−	0.728286i	$-0.740317\pi$
$331$	−20.4755	+	3.08619i	−1.12544	+	0.169632i	−0.440162	+	0.897918i	$0.645079\pi$
$332$	28.8212	+	19.6500i	1.58177	+	1.07843i
$333$	9.46349	−	8.78083i	0.518596	−	0.481187i
$334$	13.1783	−	8.98479i	0.721083	−	0.491626i
$335$	1.01355	−	4.44065i	0.0553761	−	0.242619i
$336$	−5.78369	−	5.28482i	−0.315526	−	0.288310i
$337$	−4.91947	−	21.5536i	−0.267981	−	1.17410i	−0.912358	−	0.409392i	$-0.865741\pi$
$337$	−4.91947	−	21.5536i	−0.267981	−	1.17410i	0.644378	−	0.764707i	$-0.277116\pi$
$338$	51.7064	+	47.9766i	2.81246	+	2.60958i
$339$	−3.94306	−	0.594320i	−0.214158	−	0.0322790i
$340$	10.6081	−	3.27217i	0.575307	−	0.177459i
$341$	−0.00348390	+	0.0464894i	−0.000188664	+	0.00251754i
$342$	1.68073			0.0908834
$343$	11.2123	−	14.7406i	0.605406	−	0.795917i
$344$	−63.6614			−3.43239
$345$	−0.0620980	+	0.828641i	−0.00334325	+	0.0446125i
$346$	34.6454	−	10.6867i	1.86255	−	0.574520i
$347$	−28.0836	−	4.23293i	−1.50761	−	0.227235i	−0.657344	−	0.753591i	$-0.728320\pi$
$347$	−28.0836	−	4.23293i	−1.50761	−	0.227235i	−0.850265	+	0.526355i	$0.823558\pi$
$348$	−4.22636	−	3.92149i	−0.226557	−	0.210214i
$349$	3.20182	+	14.0281i	0.171390	+	0.750907i	0.985428	+	0.170096i	$0.0544077\pi$
$349$	3.20182	+	14.0281i	0.171390	+	0.750907i	−0.814038	+	0.580812i	$0.802735\pi$
$350$	−23.6075	−	21.5713i	−1.26187	−	1.15303i
$351$	4.89710	−	21.4556i	0.261388	−	1.14522i
$352$	−1.21419	+	0.827822i	−0.0647166	+	0.0441231i
$353$	−10.4535	+	9.69947i	−0.556386	+	0.516251i	−0.907483	−	0.420088i	$-0.861999\pi$
$353$	−10.4535	+	9.69947i	−0.556386	+	0.516251i	0.351097	+	0.936339i	$0.385809\pi$
$354$	−13.3127	−	9.07645i	−0.707562	−	0.482408i
$355$	1.42042	−	0.214094i	0.0753881	−	0.0113629i
$356$	4.51753	−	2.17553i	0.239428	−	0.115303i
$357$	−8.91443	+	8.39904i	−0.471801	+	0.444524i
$358$	−25.9462	−	12.4950i	−1.37130	−	0.660384i
$359$	−21.3702	−	6.59184i	−1.12788	−	0.347904i	−0.325986	−	0.945375i	$-0.605696\pi$
$359$	−21.3702	−	6.59184i	−1.12788	−	0.347904i	−0.801891	+	0.597471i	$0.796172\pi$
$360$	1.79402	−	4.57108i	0.0945530	−	0.240917i
$361$	9.46680	+	16.3970i	0.498253	+	0.862999i
$362$	−1.82566	+	3.16213i	−0.0959543	+	0.166198i
$363$	0.378402	+	0.474501i	0.0198609	+	0.0249048i
$364$	−63.8227	−	30.1369i	−3.34522	−	1.57960i
$365$	0.400899	−	0.502712i	0.0209840	−	0.0263131i
$366$	−1.78860	−	4.55728i	−0.0934917	−	0.238213i
$367$	1.16162	+	15.5007i	0.0606358	+	0.809129i	0.941769	+	0.336261i	$0.109162\pi$
$367$	1.16162	+	15.5007i	0.0606358	+	0.809129i	−0.881133	+	0.472868i	$0.843219\pi$
$368$	−1.42114	−	18.9637i	−0.0740818	−	0.988553i
$369$	−7.32877	−	18.6734i	−0.381520	−	0.972098i
$370$	−2.66299	+	3.33929i	−0.138442	+	0.173601i
$371$	19.1839	+	23.6824i	0.995978	+	1.22953i
$372$	−0.0730885	−	0.0916501i	−0.00378946	−	0.00475184i
$373$	−6.07377	+	10.5201i	−0.314488	+	0.544709i	−0.979328	−	0.202276i	$-0.935166\pi$
$373$	−6.07377	+	10.5201i	−0.314488	+	0.544709i	0.664841	+	0.746985i	$0.268499\pi$
$374$	9.45263	+	16.3724i	0.488784	+	0.846598i
$375$	−0.769290	+	1.96012i	−0.0397260	+	0.101220i
$376$	46.3255	+	14.2895i	2.38906	+	0.736926i
$377$	−13.3015	−	6.40566i	−0.685061	−	0.329908i
$378$	1.84566	+	22.3371i	0.0949307	+	1.14889i
$379$	9.78901	−	4.71414i	0.502828	−	0.242149i	−0.165235	−	0.986254i	$-0.552838\pi$
$379$	9.78901	−	4.71414i	0.502828	−	0.242149i	0.668062	+	0.744105i	$0.267124\pi$
$380$	−0.370836	+	0.0558946i	−0.0190235	+	0.00286733i
$381$	9.33754	+	6.36623i	0.478377	+	0.326152i
$382$	−3.48290	+	3.23166i	−0.178201	+	0.165346i
$383$	−12.0845	+	8.23911i	−0.617492	+	0.420999i	−0.831259	−	0.555886i	$-0.812379\pi$
$383$	−12.0845	+	8.23911i	−0.617492	+	0.420999i	0.213767	+	0.976885i	$0.431427\pi$
$384$	−2.44409	+	10.7082i	−0.124724	+	0.546453i
$385$	−0.458544	+	0.808424i	−0.0233696	+	0.0412011i
$386$	9.22851	+	40.4327i	0.469719	+	2.05797i
$387$	23.1208	+	21.4530i	1.17530	+	1.09052i
$388$	−52.7848	−	7.95603i	−2.67974	−	0.403906i
$389$	7.76378	−	2.39481i	0.393639	−	0.121422i	−0.0916155	−	0.995794i	$-0.529203\pi$
$389$	7.76378	−	2.39481i	0.393639	−	0.121422i	0.485255	+	0.874373i	$0.338727\pi$
$390$	−0.254262	+	3.39289i	−0.0128751	+	0.171806i
$391$	−29.7294			−1.50348
$392$	36.8474	+	4.97925i	1.86107	+	0.251490i
$393$	−13.4262			−0.677261
$394$	−2.81304	+	37.5375i	−0.141719	+	1.89111i
$395$	0.429998	−	0.132637i	0.0216356	−	0.00667368i
$396$	10.7815	+	1.62505i	0.541789	+	0.0816616i
$397$	−3.66903	−	3.40436i	−0.184143	−	0.170860i	0.582715	−	0.812677i	$-0.301990\pi$
$397$	−3.66903	−	3.40436i	−0.184143	−	0.170860i	−0.766858	+	0.641817i	$0.778181\pi$
$398$	−5.00915	−	21.9465i	−0.251086	−	1.10008i
$399$	0.340072	−	0.235683i	0.0170249	−	0.0117989i
$400$	5.29456	−	23.1970i	0.264728	−	1.15985i
$401$	−8.39175	+	5.72140i	−0.419064	+	0.285713i	−0.754437	−	0.656372i	$-0.772090\pi$
$401$	−8.39175	+	5.72140i	−0.419064	+	0.285713i	0.335373	+	0.942085i	$0.391138\pi$
$402$	−14.2977	+	13.2663i	−0.713105	+	0.661664i
$403$	−0.248018	−	0.169096i	−0.0123547	−	0.00842327i
$404$	−2.24848	+	0.338904i	−0.111866	+	0.0168611i
$405$	−1.84221	+	0.887163i	−0.0915403	+	0.0440835i
$406$	14.8845	+	2.12730i	0.738706	+	0.105576i
$407$	−4.41974	−	2.12843i	−0.219078	−	0.105502i
$408$	−23.4971	−	7.24789i	−1.16328	−	0.358824i
$409$	−11.0646	+	28.1922i	−0.547111	+	1.39402i	0.343459	+	0.939168i	$0.388401\pi$
$409$	−11.0646	+	28.1922i	−0.547111	+	1.39402i	−0.890569	+	0.454847i	$0.849694\pi$
$410$	3.31839	+	5.74761i	0.163883	+	0.283854i
$411$	3.49239	−	6.04899i	0.172267	−	0.298375i
$412$	−25.9771	−	32.5743i	−1.27980	−	1.60482i
$413$	28.3387	−	0.216533i	1.39445	−	0.0106549i
$414$	−15.8508	+	19.8763i	−0.779025	+	0.976866i
$415$	1.08054	+	2.75316i	0.0530414	+	0.135147i
$416$	−0.707107	−	9.43569i	−0.0346688	−	0.462623i
$417$	−0.497232	−	6.63510i	−0.0243495	−	0.324922i
$418$	−0.233328	−	0.594509i	−0.0114124	−	0.0290784i
$419$	1.17936	−	1.47887i	0.0576155	−	0.0722476i	−0.752189	−	0.658948i	$-0.771002\pi$
$419$	1.17936	−	1.47887i	0.0576155	−	0.0722476i	0.809804	+	0.586700i	$0.199573\pi$
$420$	−0.537426	−	2.27437i	−0.0262237	−	0.110978i
$421$	−5.74094	−	7.19891i	−0.279796	−	0.350854i	0.621998	−	0.783019i	$-0.286321\pi$
$421$	−5.74094	−	7.19891i	−0.279796	−	0.350854i	−0.901794	+	0.432165i	$0.857750\pi$
$422$	7.46451	−	12.9289i	0.363367	−	0.629370i
$423$	−12.0093	−	20.8008i	−0.583913	−	1.01137i
$424$	−22.3546	+	56.9585i	−1.08563	+	2.76615i
$425$	−35.5442	−	10.9639i	−1.72415	−	0.531830i
$426$	−5.54195	−	2.66886i	−0.268508	−	0.129307i
$427$	7.15148	+	4.79616i	0.346084	+	0.232103i
$428$	−51.3545	+	24.7310i	−2.48231	+	1.19542i
$429$	−3.86415	+	0.582427i	−0.186563	+	0.0281198i
$430$	−8.62181	−	5.87825i	−0.415781	−	0.283474i
$431$	17.2222	−	15.9799i	0.829566	−	0.769725i	−0.146034	−	0.989280i	$-0.546651\pi$
$431$	17.2222	−	15.9799i	0.829566	−	0.769725i	0.975600	+	0.219555i	$0.0704604\pi$
$432$	−13.7787	+	9.39415i	−0.662927	+	0.451976i
$433$	3.52769	−	15.4558i	0.169530	−	0.742759i	−0.816657	−	0.577123i	$-0.804175\pi$
$433$	3.52769	−	15.4558i	0.169530	−	0.742759i	0.986187	−	0.165636i	$-0.0529676\pi$
$434$	0.292810	+	0.0878756i	0.0140553	+	0.00421816i
$435$	−0.108777	−	0.476583i	−0.00521546	−	0.0228504i
$436$	27.8565	+	25.8470i	1.33408	+	1.23785i
$437$	0.993101	+	0.149686i	0.0475065	+	0.00716045i
$438$	−2.63104	+	0.811568i	−0.125716	+	0.0387782i
$439$	0.739305	−	9.86534i	0.0352851	−	0.470847i	−0.951373	−	0.308041i	$-0.900327\pi$
$439$	0.739305	−	9.86534i	0.0352851	−	0.470847i	0.986658	−	0.162806i	$-0.0520544\pi$
$440$	−1.86594			−0.0889553
$441$	−11.7044	−	14.2254i	−0.557354	−	0.677401i
$442$	−121.728			−5.79001
$443$	1.32478	−	17.6780i	0.0629424	−	0.839908i	−0.872992	−	0.487734i	$-0.837823\pi$
$443$	1.32478	−	17.6780i	0.0629424	−	0.839908i	0.935935	−	0.352174i	$-0.114557\pi$
$444$	11.7869	−	3.63578i	0.559382	−	0.172547i
$445$	0.420385	+	0.0633628i	0.0199282	+	0.00300369i
$446$	4.09123	+	3.79611i	0.193725	+	0.179751i
$447$	−1.72388	−	7.55280i	−0.0815366	−	0.357235i
$448$	−6.02660	−	15.0171i	−0.284730	−	0.709492i
$449$	4.94040	−	21.6453i	0.233152	−	1.02151i	−0.713855	−	0.700293i	$-0.753053\pi$
$449$	4.94040	−	21.6453i	0.233152	−	1.02151i	0.947007	−	0.321212i	$-0.104090\pi$
$450$	−26.2813	+	17.9183i	−1.23891	+	0.844676i
$451$	−5.58775	+	5.18468i	−0.263117	+	0.244137i
$452$	22.4915	+	15.3345i	1.05791	+	0.721273i
$453$	−3.26183	+	0.491641i	−0.153254	+	0.0230993i
$454$	14.9826	−	7.21526i	0.703171	−	0.338629i
$455$	−3.03169	−	5.15959i	−0.142128	−	0.241885i
$456$	0.748419	+	0.360420i	0.0350480	+	0.0168782i
$457$	−0.0608322	−	0.0187642i	−0.00284561	−	0.000877754i	0.293332	−	0.956011i	$-0.405236\pi$
$457$	−0.0608322	−	0.0187642i	−0.00284561	−	0.000877754i	−0.296178	+	0.955133i	$0.595712\pi$
$458$	−25.0158	+	63.7392i	−1.16891	+	2.97834i
$459$	13.0352	+	22.5777i	0.608433	+	1.05384i
$460$	2.83632	−	4.91264i	0.132244	−	0.229053i
$461$	−7.49883	−	9.40323i	−0.349255	−	0.437952i	0.575912	−	0.817512i	$-0.304647\pi$
$461$	−7.49883	−	9.40323i	−0.349255	−	0.437952i	−0.925167	+	0.379559i	$0.876076\pi$
$462$	3.57242	−	1.75414i	0.166204	−	0.0816100i
$463$	11.7570	−	14.7429i	0.546396	−	0.685159i	−0.429582	−	0.903028i	$-0.641339\pi$
$463$	11.7570	−	14.7429i	0.546396	−	0.685159i	0.975978	+	0.217869i	$0.0699105\pi$
$464$	4.08717	+	10.4139i	0.189742	+	0.483455i
$465$	−0.000742762	−	0.00991147i	−3.44448e−5	−	0.000459633i
$466$	2.31512	+	30.8932i	0.107246	+	1.43110i
$467$	−4.77833	−	12.1750i	−0.221115	−	0.563391i	0.776671	−	0.629907i	$-0.216907\pi$
$467$	−4.77833	−	12.1750i	−0.221115	−	0.563391i	−0.997785	+	0.0665156i	$0.978812\pi$
$468$	−43.7717	+	54.8880i	−2.02335	+	2.53720i
$469$	7.37791	−	33.5027i	0.340680	−	1.54701i
$470$	4.95453	+	6.21278i	0.228535	+	0.286574i
$471$	−4.73469	+	8.20072i	−0.218163	+	0.377869i
$472$	28.4479	+	49.2733i	1.30942	+	2.26799i
$473$	4.37862	−	11.1565i	0.201329	−	0.512978i
$474$	−1.84130	−	0.567965i	−0.0845736	−	0.0260875i
$475$	1.13214	+	0.545210i	0.0519462	+	0.0250160i
$476$	79.7058	−	25.2545i	3.65331	−	1.15754i
$477$	27.3130	−	13.1533i	1.25058	−	0.602246i
$478$	−17.5418	+	2.64400i	−0.802343	+	0.120934i
$479$	−11.6398	−	7.93589i	−0.531837	−	0.362600i	0.267429	−	0.963577i	$-0.413826\pi$
$479$	−11.6398	−	7.93589i	−0.531837	−	0.362600i	−0.799266	+	0.600977i	$0.794778\pi$
$480$	0.229668	−	0.213101i	0.0104829	−	0.00972668i
$481$	26.0976	−	17.7930i	1.18995	−	0.811292i
$482$	9.62217	−	42.1575i	0.438278	−	1.92022i
$483$	−0.420000	+	6.24440i	−0.0191107	+	0.284130i
$484$	−0.921928	−	4.03923i	−0.0419058	−	0.183601i
$485$	−3.31784	−	3.07851i	−0.150656	−	0.139788i
$486$	33.7881	+	5.09274i	1.53266	+	0.231011i
$487$	−32.0698	+	9.89223i	−1.45322	+	0.448260i	−0.918044	−	0.396479i	$-0.870232\pi$
$487$	−32.0698	+	9.89223i	−1.45322	+	0.448260i	−0.535179	+	0.844739i	$0.679756\pi$
$488$	−1.29191	+	17.2393i	−0.0584818	+	0.780385i
$489$	−9.40368			−0.425249
$490$	4.53056	+	4.07670i	0.204670	+	0.184166i
$491$	−6.27274			−0.283085			−0.141542	−	0.989932i	$-0.545206\pi$
$491$	−6.27274			−0.283085			−0.141542	+	0.989932i	$0.545206\pi$
$492$	1.43235	−	19.1133i	0.0645752	−	0.861696i
$493$	16.7122	−	5.15504i	0.752681	−	0.232171i
$494$	4.06628	+	0.612894i	0.182951	+	0.0275754i
$495$	0.677681	+	0.628796i	0.0304595	+	0.0282623i
$496$	0.0506154	+	0.221761i	0.00227270	+	0.00995734i
$497$	10.6854	−	1.69417i	0.479308	−	0.0759939i
$498$	2.81818	−	12.3473i	0.126286	−	0.553294i
$499$	0.0128680	−	0.00877323i	0.000576049	−	0.000392744i	−0.563032	−	0.826435i	$-0.690365\pi$
$499$	0.0128680	−	0.00877323i	0.000576049	−	0.000392744i	0.563608	+	0.826042i	$0.309413\pi$
$500$	10.5373	−	9.77717i	0.471242	−	0.437248i
$501$	−3.22692	−	2.20008i	−0.144168	−	0.0982922i
$502$	−10.9167	+	1.64542i	−0.487234	+	0.0734388i
$503$	−2.00155	+	0.963895i	−0.0892446	+	0.0429780i	−0.477974	−	0.878374i	$-0.658629\pi$
$503$	−2.00155	+	0.963895i	−0.0892446	+	0.0429780i	0.388729	+	0.921352i	$0.372914\pi$
$504$	13.2484	−	34.5299i	0.590132	−	1.53808i
$505$	−0.173704	−	0.0836517i	−0.00772975	−	0.00372245i
$506$	9.23115	+	2.84743i	0.410375	+	0.126584i
$507$	6.31013	−	16.0779i	0.280243	−	0.714046i
$508$	−38.5744	−	66.8129i	−1.71146	−	2.96434i
$509$	−12.1866	+	21.1079i	−0.540164	+	0.935591i	0.458731	+	0.888575i	$0.348304\pi$
$509$	−12.1866	+	21.1079i	−0.540164	+	0.935591i	−0.998894	+	0.0470154i	$0.985029\pi$
$510$	−2.51302	−	3.15123i	−0.111278	−	0.139539i
$511$	2.99041	−	3.80920i	0.132288	−	0.168509i
$512$	27.8471	−	34.9192i	1.23068	−	1.54323i
$513$	−0.321760	−	0.819832i	−0.0142061	−	0.0361964i
$514$	2.38425	+	31.8156i	0.105165	+	1.40332i
$515$	−0.263992	−	3.52273i	−0.0116329	−	0.155230i
$516$	11.0100	+	28.0530i	0.484688	+	1.23496i
$517$	−5.69047	+	7.13562i	−0.250267	+	0.313824i
$518$	−19.8639	+	25.3028i	−0.872771	+	1.11174i
$519$	−5.53530	−	6.94104i	−0.242973	−	0.304678i
$520$	6.00726	−	10.4049i	0.263436	−	0.456284i
$521$	−2.25507	−	3.90590i	−0.0987964	−	0.171120i	0.812390	−	0.583114i	$-0.198166\pi$
$521$	−2.25507	−	3.90590i	−0.0987964	−	0.171120i	−0.911187	+	0.411994i	$0.864833\pi$
$522$	5.46392	−	13.9218i	0.239149	−	0.609343i
$523$	19.0669	+	5.88136i	0.833738	+	0.257174i	0.682097	−	0.731262i	$-0.261068\pi$
$523$	19.0669	+	5.88136i	0.833738	+	0.257174i	0.151641	+	0.988436i	$0.451544\pi$
$524$	82.5781	+	39.7675i	3.60744	+	1.73725i
$525$	−2.80503	+	7.31086i	−0.122421	+	0.319072i
$526$	−15.2567	+	7.34723i	−0.665223	+	0.320354i
$527$	0.351626	−	0.0529990i	0.0153170	−	0.00230867i
$528$	2.44665	+	1.66810i	0.106477	+	0.0725945i
$529$	5.72415	−	5.31124i	0.248876	−	0.230923i
$530$	−8.28686	+	5.64988i	−0.359958	+	0.245415i
$531$	6.27254	−	27.4818i	0.272205	−	1.19261i
$532$	−2.78970	+	0.442305i	−0.120949	+	0.0191764i
$533$	−10.9215	−	47.8501i	−0.473062	−	2.07262i
$534$	−1.33450	−	1.23823i	−0.0577493	−	0.0535835i
$535$	−4.77887	−	0.720298i	−0.206608	−	0.0311412i
$536$	65.8136	−	20.3008i	2.84271	−	0.876861i
$537$	−0.526975	+	7.03199i	−0.0227406	+	0.303453i
$538$	66.2822			2.85763
$539$	−3.40696	+	6.11495i	−0.146748	+	0.263390i
$540$	−4.97447			−0.214067
$541$	1.45399	−	19.4021i	0.0625117	−	0.834161i	−0.874536	−	0.484960i	$-0.838834\pi$
$541$	1.45399	−	19.4021i	0.0625117	−	0.834161i	0.937048	−	0.349201i	$-0.113547\pi$
$542$	−24.9375	+	7.69219i	−1.07116	+	0.330408i
$543$	0.884099	+	0.133256i	0.0379403	+	0.00571858i
$544$	8.21684	+	7.62412i	0.352294	+	0.326881i
$545$	0.716962	+	3.14122i	0.0307113	+	0.134555i
$546$	−1.71970	+	25.5679i	−0.0735964	+	1.09420i
$547$	−3.65405	+	16.0095i	−0.156236	+	0.684515i	0.834759	+	0.550616i	$0.185607\pi$
$547$	−3.65405	+	16.0095i	−0.156236	+	0.684515i	−0.990995	+	0.133899i	$0.957250\pi$
$548$	−39.3967	+	26.8602i	−1.68295	+	1.14741i
$549$	6.27859	−	5.82568i	0.267964	−	0.248634i
$550$	9.98658	+	6.80873i	0.425829	+	0.290325i
$551$	−0.584222	+	0.0880572i	−0.0248887	+	0.00375136i
$552$	−11.3206	+	5.45172i	−0.481837	+	0.232040i
$553$	3.23086	−	1.02369i	0.137390	−	0.0435316i
$554$	39.3947	+	18.9715i	1.67372	+	0.806020i
$555$	0.999389	+	0.308271i	0.0424217	+	0.0130854i
$556$	−16.5945	+	42.2821i	−0.703763	+	1.79316i
$557$	−13.4031	−	23.2148i	−0.567906	−	0.983642i	−0.996773	−	0.0802744i	$-0.974420\pi$
$557$	−13.4031	−	23.2148i	−0.567906	−	0.983642i	0.428867	−	0.903368i	$-0.358913\pi$
$558$	0.152042	−	0.263345i	0.00643646	−	0.0111483i
$559$	48.1145	+	60.3337i	2.03503	+	2.55184i
$560$	−0.975263	+	4.42861i	−0.0412124	+	0.187143i
$561$	2.88630	−	3.61931i	0.121860	−	0.152807i
$562$	7.87443	+	20.0637i	0.332163	+	0.846337i
$563$	0.443000	+	5.91143i	0.0186702	+	0.249137i	0.998728	+	0.0504238i	$0.0160572\pi$
$563$	0.443000	+	5.91143i	0.0186702	+	0.249137i	−0.980058	+	0.198713i	$0.936324\pi$
$564$	−1.71500	−	22.8851i	−0.0722145	−	0.963636i
$565$	0.843230	+	2.14852i	0.0354750	+	0.0903887i
$566$	−7.03945	+	8.82719i	−0.295890	+	0.371034i
$567$	−13.8234	+	6.78759i	−0.580528	+	0.285052i
$568$	13.5426	+	16.9819i	0.568235	+	0.712544i
$569$	15.1794	−	26.2915i	0.636353	−	1.10220i	−0.349873	−	0.936797i	$-0.613775\pi$
$569$	15.1794	−	26.2915i	0.636353	−	1.10220i	0.986227	−	0.165399i	$-0.0528913\pi$
$570$	0.0680804	+	0.117919i	0.00285157	+	0.00493907i
$571$	−17.0488	+	43.4395i	−0.713469	+	1.81789i	−0.155870	+	0.987778i	$0.549818\pi$
$571$	−17.0488	+	43.4395i	−0.713469	+	1.81789i	−0.557599	+	0.830110i	$0.688277\pi$
$572$	25.4917	+	7.86313i	1.06586	+	0.328774i
$573$	1.04820	+	0.504789i	0.0437894	+	0.0210879i
$574$	25.3229	+	43.0966i	1.05696	+	1.79882i
$575$	−17.1248	+	8.24686i	−0.714152	+	0.343918i
$576$	−15.9153	+	2.39885i	−0.663139	+	0.0999521i
$577$	12.2851	+	8.37585i	0.511436	+	0.348691i	0.791379	−	0.611325i	$-0.209363\pi$
$577$	12.2851	+	8.37585i	0.511436	+	0.348691i	−0.279943	+	0.960017i	$0.590316\pi$
$578$	74.8204	−	69.4231i	3.11212	−	2.88762i
$579$	8.39066	−	5.72065i	0.348704	−	0.237742i
$580$	−0.742574	+	3.25343i	−0.0308337	+	0.135091i
$581$	8.29638	+	20.6730i	0.344192	+	0.857660i
$582$	4.31270	+	18.8952i	0.178767	+	0.783231i
$583$	−8.44432	−	7.83518i	−0.349728	−	0.324500i
$584$	9.61403	+	1.44908i	0.397831	+	0.0599634i
$585$	−5.68803	+	1.75453i	−0.235171	+	0.0725407i
$586$	1.51688	−	20.2414i	0.0626618	−	0.836163i
$587$	−28.9269			−1.19394			−0.596971	−	0.802263i	$-0.703629\pi$
$587$	−28.9269			−1.19394			−0.596971	+	0.802263i	$0.703629\pi$
$588$	−4.17845	−	17.0983i	−0.172316	−	0.705121i
$589$	−0.0120128			−0.000494978
$590$	−0.696936	+	9.29996i	−0.0286924	+	0.382873i
$591$	8.80795	−	2.71689i	0.362310	−	0.111758i
$592$	−23.6674	−	3.56728i	−0.972723	−	0.146614i
$593$	−5.74554	−	5.33109i	−0.235941	−	0.218921i	0.553337	−	0.832958i	$-0.313354\pi$
$593$	−5.74554	−	5.33109i	−0.235941	−	0.218921i	−0.789278	+	0.614036i	$0.789545\pi$
$594$	−1.88506	−	8.25899i	−0.0773450	−	0.338870i
$595$	6.79003	+	2.03776i	0.278364	+	0.0835400i
$596$	−11.7682	+	51.5597i	−0.482043	+	2.11197i
$597$	−4.55437	+	3.10512i	−0.186398	+	0.127084i
$598$	−45.5969	+	42.3077i	−1.86459	+	1.73009i
$599$	−9.12136	−	6.21884i	−0.372689	−	0.254095i	0.362462	−	0.931999i	$-0.381936\pi$
$599$	−9.12136	−	6.21884i	−0.372689	−	0.254095i	−0.735151	+	0.677904i	$0.762889\pi$
$600$	−15.5454	+	2.34309i	−0.634637	+	0.0956561i
$601$	15.7839	−	7.60111i	0.643837	−	0.310056i	−0.0833238	−	0.996523i	$-0.526554\pi$
$601$	15.7839	−	7.60111i	0.643837	−	0.310056i	0.727161	+	0.686467i	$0.240839\pi$
$602$	−65.2726	−	43.7753i	−2.66031	−	1.78415i
$603$	−30.7435	−	14.8053i	−1.25197	−	0.602918i
$604$	21.5181	+	6.63747i	0.875561	+	0.270075i
$605$	0.128339	−	0.327003i	0.00521772	−	0.0132945i
$606$	0.412790	+	0.714973i	0.0167684	+	0.0290438i
$607$	−14.0210	+	24.2850i	−0.569093	+	0.985699i	0.427563	+	0.903986i	$0.359372\pi$
$607$	−14.0210	+	24.2850i	−0.569093	+	0.985699i	−0.996656	+	0.0817128i	$0.973961\pi$
$608$	−0.236094	−	0.296052i	−0.00957487	−	0.0120065i
$609$	−0.846670	−	3.58308i	−0.0343088	−	0.145194i
$610$	−1.76677	+	2.21546i	−0.0715346	+	0.0897015i
$611$	−21.4697	−	54.7038i	−0.868570	−	2.21308i
$612$	−6.21499	−	82.9332i	−0.251226	−	3.35238i
$613$	1.36330	+	18.1920i	0.0550632	+	0.734768i	0.954594	+	0.297910i	$0.0962896\pi$
$613$	1.36330	+	18.1920i	0.0550632	+	0.734768i	−0.899531	+	0.436858i	$0.856091\pi$
$614$	−1.75864	−	4.48093i	−0.0709728	−	0.180836i
$615$	1.01325	−	1.27057i	0.0408581	−	0.0512345i
$616$	−14.0532	+	0.107379i	−0.566218	+	0.00432642i
$617$	−6.77149	−	8.49118i	−0.272610	−	0.341842i	0.626615	−	0.779329i	$-0.284440\pi$
$617$	−6.77149	−	8.49118i	−0.272610	−	0.341842i	−0.899225	+	0.437487i	$0.855869\pi$
$618$	−7.56350	+	13.1004i	−0.304249	+	0.526974i
$619$	16.0387	+	27.7798i	0.644650	+	1.11657i	0.984382	+	0.176044i	$0.0563301\pi$
$619$	16.0387	+	27.7798i	0.644650	+	1.11657i	−0.339733	+	0.940522i	$0.610337\pi$
$620$	−0.0247888	+	0.0631608i	−0.000995541	+	0.00253660i
$621$	12.7298	+	3.92663i	0.510830	+	0.157570i
$622$	−32.2268	−	15.5196i	−1.29218	−	0.622280i
$623$	3.16973	+	0.453019i	0.126993	+	0.0181498i
$624$	−17.1784	+	8.27270i	−0.687688	+	0.331173i
$625$	−22.9055	+	3.45245i	−0.916219	+	0.138098i
$626$	18.7206	+	12.7635i	0.748226	+	0.510132i
$627$	−0.114639	+	0.106369i	−0.00457824	+	0.00424798i
$628$	53.4108	−	36.4149i	2.13132	−	1.45311i
$629$	−8.32618	+	36.4794i	−0.331987	+	1.45453i
$630$	4.98262	−	3.45316i	0.198512	−	0.137577i
$631$	7.50659	+	32.8885i	0.298833	+	1.30927i	0.871868	+	0.489741i	$0.162909\pi$
$631$	7.50659	+	32.8885i	0.298833	+	1.30927i	−0.573035	+	0.819531i	$0.694234\pi$
$632$	4.98787	+	4.62807i	0.198407	+	0.184095i
$633$	−3.61479	−	0.544842i	−0.143675	−	0.0216555i
$634$	−20.4342	+	6.30312i	−0.811547	+	0.250329i
$635$	0.488832	−	6.52300i	0.0193987	−	0.258857i
$636$	28.9654			1.14855
$637$	−23.1298	−	38.6845i	−0.916436	−	1.53274i
$638$	−5.68298			−0.224991
$639$	0.804193	−	10.7312i	0.0318134	−	0.424520i
$640$	6.07500	−	1.87389i	0.240135	−	0.0740719i
$641$	−14.0620	−	2.11950i	−0.555414	−	0.0837152i	−0.134663	−	0.990891i	$-0.542995\pi$
$641$	−14.0620	−	2.11950i	−0.555414	−	0.0837152i	−0.420751	+	0.907176i	$0.638233\pi$
$642$	15.1703	+	14.0760i	0.598725	+	0.555536i
$643$	1.09748	+	4.80839i	0.0432806	+	0.189625i	0.991947	−	0.126654i	$-0.0404238\pi$
$643$	1.09748	+	4.80839i	0.0432806	+	0.189625i	−0.948666	+	0.316278i	$0.897567\pi$
$644$	21.0787	−	37.1623i	0.830619	−	1.46440i
$645$	−0.568583	+	2.49112i	−0.0223879	+	0.0980879i
$646$	−4.02496	+	2.74417i	−0.158360	+	0.107968i
$647$	−8.28244	+	7.68498i	−0.325616	+	0.302128i	−0.825993	−	0.563680i	$-0.809385\pi$
$647$	−8.28244	+	7.68498i	−0.325616	+	0.302128i	0.500377	+	0.865808i	$0.333195\pi$
$648$	−25.5454	−	17.4166i	−1.00352	−	0.684187i
$649$	−10.5917	+	1.59644i	−0.415760	+	0.0626657i
$650$	−70.1179	+	33.7670i	−2.75025	+	1.32445i
$651$	−0.00616441	−	0.0746045i	−0.000241602	−	0.00292398i
$652$	57.8376	+	27.8531i	2.26509	+	1.09081i
$653$	20.3187	+	6.26748i	0.795131	+	0.245266i	0.665599	−	0.746310i	$-0.268176\pi$
$653$	20.3187	+	6.26748i	0.795131	+	0.245266i	0.129532	+	0.991575i	$0.458652\pi$
$654$	5.04059	−	12.8432i	0.197103	−	0.502209i
$655$	3.88561	+	6.73007i	0.151823	+	0.262966i
$656$	−18.5958	+	32.2088i	−0.726043	+	1.25754i
$657$	−3.00334	−	3.76607i	−0.117172	−	0.146928i
$658$	37.6721	+	46.5059i	1.46861	+	1.81299i
$659$	−5.88152	+	7.37519i	−0.229111	+	0.287297i	−0.883077	−	0.469227i	$-0.844533\pi$
$659$	−5.88152	+	7.37519i	−0.229111	+	0.287297i	0.653966	+	0.756524i	$0.273104\pi$
$660$	0.322707	+	0.822245i	0.0125614	+	0.0320058i
$661$	−0.880740	−	11.7527i	−0.0342568	−	0.457125i	−0.987785	−	0.155822i	$-0.950197\pi$
$661$	−0.880740	−	11.7527i	−0.0342568	−	0.457125i	0.953528	−	0.301303i	$-0.0974217\pi$
$662$	−3.83532	−	51.1788i	−0.149064	−	1.98912i
$663$	10.8898	+	27.7467i	0.422924	+	1.07759i
$664$	−27.8835	+	34.9648i	−1.08209	+	1.35690i
$665$	−0.216558	−	0.102258i	−0.00839778	−	0.00396540i
$666$	19.9499	+	25.0163i	0.773041	+	0.969363i
$667$	4.46838	−	7.73946i	0.173016	−	0.299673i
$668$	13.3308	+	23.0896i	0.515783	+	0.893362i
$669$	0.499284	−	1.27216i	0.0193034	−	0.0491844i
$670$	10.7878	+	3.32759i	0.416768	+	0.128556i
$671$	−2.93229	−	1.41212i	−0.113200	−	0.0545142i
$672$	1.71746	−	1.61817i	0.0662525	−	0.0624221i
$673$	8.73896	−	4.20846i	0.336862	−	0.162224i	−0.257804	−	0.966197i	$-0.582999\pi$
$673$	8.73896	−	4.20846i	0.336862	−	0.162224i	0.594666	+	0.803973i	$0.297284\pi$
$674$	54.1831	−	8.16678i	2.08705	−	0.314573i
$675$	13.7716	+	9.38929i	0.530067	+	0.361394i
$676$	−86.4324	+	80.1976i	−3.32432	+	3.08452i
$677$	−4.71132	+	3.21212i	−0.181071	+	0.123452i	−0.650463	−	0.759538i	$-0.725425\pi$
$677$	−4.71132	+	3.21212i	−0.181071	+	0.123452i	0.469393	+	0.882990i	$0.344473\pi$
$678$	2.19926	−	9.63558i	0.0844620	−	0.370052i
$679$	−25.1652	−	22.9946i	−0.965751	−	0.882450i
$680$	3.16707	+	13.8758i	0.121452	+	0.532114i
$681$	−2.98499	−	2.76967i	−0.114385	−	0.106134i
$682$	−0.114258	−	0.0172216i	−0.00437516	−	0.000659449i
$683$	−12.3269	+	3.80234i	−0.471676	+	0.145493i	−0.521475	−	0.853267i	$-0.674618\pi$
$683$	−12.3269	+	3.80234i	−0.471676	+	0.145493i	0.0497994	+	0.998759i	$0.484142\pi$
$684$	−0.209954	+	2.80165i	−0.00802781	+	0.107124i
$685$	−4.04286			−0.154470
$686$	34.3561	+	30.4425i	1.31172	+	1.16230i
$687$	16.7666			0.639686
$688$	4.36994	−	58.3128i	0.166603	−	2.22316i
$689$	70.8764	−	21.8625i	2.70018	−	0.832894i
$690$	−2.03657	−	0.306963i	−0.0775307	−	0.0116859i
$691$	−26.0607	−	24.1808i	−0.991395	−	0.919880i	0.00539166	−	0.999985i	$-0.498284\pi$
$691$	−26.0607	−	24.1808i	−0.991395	−	0.919880i	−0.996786	+	0.0801056i	$0.974474\pi$
$692$	13.4861	+	59.0863i	0.512663	+	2.24612i
$693$	5.14007	+	4.69672i	0.195255	+	0.178413i
$694$	15.6638	−	68.6275i	0.594589	−	2.60506i
$695$	−3.18204	+	2.16948i	−0.120702	+	0.0822930i
$696$	5.41849	−	5.02763i	0.205387	−	0.190572i
$697$	48.0393	+	32.7526i	1.81962	+	1.24059i
$698$	−35.2649	+	5.31533i	−1.33480	+	0.201188i
$699$	6.83468	−	3.29141i	0.258511	−	0.124493i
$700$	38.9067	−	36.6573i	1.47053	−	1.38552i
$701$	−11.5264	−	5.55081i	−0.435345	−	0.209651i	0.203358	−	0.979104i	$-0.434814\pi$
$701$	−11.5264	−	5.55081i	−0.435345	−	0.209651i	−0.638703	+	0.769453i	$0.720529\pi$
$702$	52.1226	+	16.0777i	1.96724	+	0.606814i
$703$	0.461805	−	1.17666i	0.0174173	−	0.0443786i
$704$	3.05797	+	5.29656i	0.115252	+	0.199622i
$705$	0.972911	−	1.68513i	0.0366419	−	0.0634657i
$706$	−22.0370	−	27.6335i	−0.829373	−	1.04000i
$707$	−1.31305	−	0.620018i	−0.0493824	−	0.0233182i
$708$	16.7928	−	21.0575i	0.631111	−	0.791388i
$709$	0.253802	+	0.646676i	0.00953172	+	0.0242864i	0.935560	−	0.353167i	$-0.114895\pi$
$709$	0.253802	+	0.646676i	0.00953172	+	0.0242864i	−0.926029	+	0.377453i	$0.876800\pi$
$710$	0.266063	+	3.55037i	0.00998517	+	0.133243i
$711$	−0.251923	−	3.36168i	−0.00944785	−	0.126073i
$712$	2.34856	+	5.98403i	0.0880159	+	0.224261i
$713$	0.113292	−	0.142063i	0.00424280	−	0.00532030i
$714$	−19.1079	−	23.5886i	−0.715096	−	0.882780i
$715$	1.41026	+	1.76840i	0.0527406	+	0.0661346i
$716$	24.0695	−	41.6896i	0.899519	−	1.55801i
$717$	2.17196	+	3.76195i	0.0811133	+	0.140492i
$718$	20.2506	−	51.5977i	0.755745	−	1.92561i
$719$	−14.5141	−	4.47701i	−0.541285	−	0.166964i	0.0120432	−	0.999927i	$-0.496166\pi$
$719$	−14.5141	−	4.47701i	−0.541285	−	0.166964i	−0.553329	+	0.832963i	$0.686643\pi$
$720$	4.06389	+	1.95707i	0.151452	+	0.0729355i
$721$	−2.19095	−	26.5159i	−0.0815954	−	0.987504i
$722$	−42.2802	+	20.3611i	−1.57351	+	0.757761i
$723$	−10.4702	+	1.57813i	−0.389390	+	0.0586911i
$724$	−5.04297	−	3.43824i	−0.187421	−	0.127781i
$725$	8.19660	−	7.60534i	0.304414	−	0.282455i
$726$	−1.24286	+	0.847370i	−0.0461270	+	0.0314489i
$727$	−4.48810	+	19.6636i	−0.166454	+	0.729284i	0.820941	+	0.571012i	$0.193449\pi$
$727$	−4.48810	+	19.6636i	−0.166454	+	0.729284i	−0.987396	+	0.158271i	$0.949408\pi$
$728$	44.6443	−	78.7090i	1.65463	−	2.91715i
$729$	2.02379	+	8.86680i	0.0749552	+	0.328400i
$730$	1.16825	+	1.08397i	0.0432388	+	0.0401197i
$731$	−90.3959	−	13.6250i	−3.34341	−	0.503939i
$732$	7.82008	−	2.41217i	0.289038	−	0.0891565i
$733$	1.41786	−	18.9200i	0.0523699	−	0.698828i	−0.907799	−	0.419406i	$-0.862238\pi$
$733$	1.41786	−	18.9200i	0.0523699	−	0.698828i	0.960169	−	0.279422i	$-0.0901427\pi$
$734$	−38.5266			−1.42204
$735$	0.523939	−	1.39740i	0.0193258	−	0.0515437i
$736$	5.72769			0.211126
$737$	−0.968967	+	12.9300i	−0.0356924	+	0.476282i
$738$	47.5106	−	14.6551i	1.74889	−	0.539461i
$739$	−7.63608	−	1.15095i	−0.280898	−	0.0423385i	0.00708234	−	0.999975i	$-0.497746\pi$
$739$	−7.63608	−	1.15095i	−0.280898	−	0.0423385i	−0.287980	+	0.957636i	$0.592984\pi$
$740$	−5.23369	−	4.85615i	−0.192394	−	0.178516i
$741$	−0.224066	−	0.981698i	−0.00823128	−	0.0360636i
$742$	−62.0865	+	43.0284i	−2.27927	+	1.57962i
$743$	0.991534	−	4.34420i	0.0363759	−	0.159373i	−0.953478	−	0.301463i	$-0.902525\pi$
$743$	0.991534	−	4.34420i	0.0363759	−	0.159373i	0.989854	+	0.142090i	$0.0453822\pi$
$744$	0.124176	−	0.0846617i	0.00455251	−	0.00310385i
$745$	−3.28705	+	3.04994i	−0.120428	+	0.111741i
$746$	−24.8764	−	16.9605i	−0.910790	−	0.620966i
$747$	21.9095	−	3.30232i	0.801626	−	0.120826i
$748$	−28.4724	+	13.7116i	−1.04105	+	0.501346i
$749$	−36.0330	−	5.14985i	−1.31662	−	0.188171i
$750$	−4.70214	−	2.26443i	−0.171698	−	0.0826853i
$751$	29.3192	+	9.04377i	1.06987	+	0.330012i	0.779177	−	0.626804i	$-0.215637\pi$
$751$	29.3192	+	9.04377i	1.06987	+	0.330012i	0.290695	+	0.956816i	$0.406114\pi$
$752$	−16.2689	+	41.4525i	−0.593267	+	1.51162i
$753$	1.35166	+	2.34114i	0.0492572	+	0.0853160i
$754$	18.2959	−	31.6895i	0.666298	−	1.15406i
$755$	1.19043	+	1.49275i	0.0433243	+	0.0543269i
$756$	−37.4648	+	0.286264i	−1.36258	+	0.0104113i
$757$	12.9800	−	16.2765i	0.471767	−	0.591578i	−0.487835	−	0.872936i	$-0.662213\pi$
$757$	12.9800	−	16.2765i	0.471767	−	0.591578i	0.959603	+	0.281358i	$0.0907848\pi$
$758$	9.83833	+	25.0677i	0.357344	+	0.910499i
$759$	−0.176774	−	2.35888i	−0.00641648	−	0.0856219i
$760$	−0.0359308	−	0.479464i	−0.00130335	−	0.0173920i
$761$	17.9346	+	45.6967i	0.650130	+	1.65650i	0.749947	+	0.661497i	$0.230079\pi$
$761$	17.9346	+	45.6967i	0.650130	+	1.65650i	−0.0998179	+	0.995006i	$0.531826\pi$
$762$	−17.4643	+	21.8995i	−0.632664	+	0.793335i
$763$	5.58050	+	23.6165i	0.202028	+	0.854975i
$764$	−4.95186	−	6.20943i	−0.179152	−	0.224649i
$765$	3.52573	−	6.10674i	0.127473	−	0.220790i
$766$	−18.1255	−	31.3942i	−0.654899	−	1.13432i
$767$	25.1970	−	64.2010i	0.909812	−	2.31816i
$768$	−18.9199	−	5.83603i	−0.682714	−	0.210590i
$769$	8.59337	+	4.13835i	0.309885	+	0.149233i	0.582362	−	0.812930i	$-0.302129\pi$
$769$	8.59337	+	4.13835i	0.309885	+	0.149233i	−0.272477	+	0.962162i	$0.587843\pi$
$770$	−1.91317	−	1.28307i	−0.0689458	−	0.0462387i
$771$	7.03875	−	3.38968i	0.253494	−	0.122076i
$772$	−68.5511	+	10.3324i	−2.46721	+	0.371872i
$773$	−18.1519	−	12.3758i	−0.652880	−	0.445126i	0.191050	−	0.981580i	$-0.438811\pi$
$773$	−18.1519	−	12.3758i	−0.652880	−	0.445126i	−0.843929	+	0.536455i	$0.819763\pi$
$774$	−57.3056	+	53.1718i	−2.05981	+	1.91122i
$775$	0.187842	−	0.128068i	0.00674748	−	0.00460035i
$776$	15.2289	−	66.7223i	0.546687	−	2.39519i
$777$	7.54454	+	2.26420i	0.270659	+	0.0812277i
$778$	4.48099	+	19.6325i	0.160651	+	0.703860i
$779$	−1.43983	−	1.33597i	−0.0515872	−	0.0478659i
$780$	−5.62394	−	0.847672i	−0.201369	−	0.0303515i
$781$	−3.90750	+	1.20530i	−0.139821	+	0.0431291i
$782$	5.50651	−	73.4792i	0.196912	−	2.62761i
$783$	−7.83687			−0.280067
$784$	−7.09024	+	33.4098i	−0.253223	+	1.19321i
$785$	5.48097			0.195624
$786$	2.48681	−	33.1841i	0.0887015	−	1.18364i
$787$	−9.05531	+	2.79319i	−0.322787	+	0.0995666i	−0.451914	−	0.892061i	$-0.649259\pi$
$787$	−9.05531	+	2.79319i	−0.322787	+	0.0995666i	0.129127	+	0.991628i	$0.458782\pi$
$788$	−62.2207	−	9.37827i	−2.21652	−	0.334087i
$789$	3.03959	+	2.82033i	0.108212	+	0.100406i
$790$	0.248181	+	1.08735i	0.00882987	+	0.0386862i
$791$	6.47435	+	16.1328i	0.230201	+	0.573617i
$792$	−3.11056	+	13.6283i	−0.110529	+	0.484259i
$793$	17.3145	−	11.8049i	0.614857	−	0.419203i
$794$	9.09379	−	8.43780i	0.322726	−	0.299446i
$795$	2.02918	+	1.38347i	0.0719674	+	0.0490666i
$796$	37.2089	−	5.60834i	1.31883	−	0.198782i
$797$	35.6759	−	17.1806i	1.26371	−	0.608569i	0.322553	−	0.946551i	$-0.395459\pi$
$797$	35.6759	−	17.1806i	1.26371	−	0.608569i	0.941152	+	0.337983i	$0.109745\pi$
$798$	0.519526	+	0.884175i	0.0183910	+	0.0312995i
$799$	62.7216	+	30.2051i	2.21893	+	1.06858i
$800$	6.84798	+	2.11232i	0.242113	+	0.0746819i
$801$	1.16357	−	2.96473i	0.0411128	−	0.104754i
$802$	−12.5867	−	21.8008i	−0.444451	−	0.769812i
$803$	−0.915199	+	1.58517i	−0.0322967	+	0.0559395i
$804$	−20.3279	−	25.4904i	−0.716911	−	0.898977i
$805$	3.25165	−	1.59663i	0.114606	−	0.0562739i
$806$	0.463875	−	0.581681i	0.0163393	−	0.0204889i
$807$	−5.92960	−	15.1084i	−0.208732	−	0.531840i
$808$	−0.217858	−	2.90712i	−0.00766423	−	0.102272i
$809$	3.22382	+	43.0189i	0.113344	+	1.51247i	0.706693	+	0.707520i	$0.250186\pi$
$809$	3.22382	+	43.0189i	0.113344	+	1.51247i	−0.593349	+	0.804945i	$0.702195\pi$
$810$	−1.85149	−	4.71753i	−0.0650549	−	0.165757i
$811$	21.1727	−	26.5497i	0.743473	−	0.932286i	−0.255934	−	0.966694i	$-0.582383\pi$
$811$	21.1727	−	26.5497i	0.743473	−	0.932286i	0.999408	+	0.0344080i	$0.0109546\pi$
$812$	−5.40540	+	24.5456i	−0.189692	+	0.861382i
$813$	3.98426	+	4.99610i	0.139734	+	0.175221i
$814$	6.07926	−	10.5296i	0.213078	−	0.369062i
$815$	2.72148	+	4.71374i	0.0953292	+	0.165115i
$816$	8.25187	−	21.0254i	0.288873	−	0.736037i
$817$	2.95104	+	0.910277i	0.103244	+	0.0318466i
$818$	−67.6304	−	32.5691i	−2.36464	−	1.13875i
$819$	−42.7379	+	13.5414i	−1.49338	+	0.473174i
$820$	−9.99537	+	4.81352i	−0.349053	+	0.168095i
$821$	−9.81612	+	1.47954i	−0.342585	+	0.0516364i	−0.318081	−	0.948063i	$-0.603039\pi$
$821$	−9.81612	+	1.47954i	−0.342585	+	0.0516364i	−0.0245034	+	0.999700i	$0.507800\pi$
$822$	14.3038	+	9.75218i	0.498903	+	0.340146i
$823$	−0.870596	+	0.807795i	−0.0303471	+	0.0281580i	−0.695201	−	0.718816i	$-0.744684\pi$
$823$	−0.870596	+	0.807795i	−0.0303471	+	0.0281580i	0.664853	+	0.746974i	$0.268494\pi$
$824$	44.1345	−	30.0904i	1.53750	−	1.04825i
$825$	0.658585	−	2.88545i	0.0229290	−	0.100458i
$826$	−4.71372	+	70.0819i	−0.164011	+	2.43846i
$827$	2.81048	+	12.3135i	0.0977298	+	0.428182i	0.999996	−	0.00299816i	$-0.000954345\pi$
$827$	2.81048	+	12.3135i	0.0977298	+	0.428182i	−0.902266	+	0.431181i	$0.858097\pi$
$828$	−31.1522	−	28.9050i	−1.08261	−	1.00452i
$829$	−27.5772	−	4.15659i	−0.957795	−	0.144364i	−0.348501	−	0.937309i	$-0.613309\pi$
$829$	−27.5772	−	4.15659i	−0.957795	−	0.144364i	−0.609294	+	0.792944i	$0.708547\pi$
$830$	−7.00484	+	2.16071i	−0.243142	+	0.0749993i
$831$	0.800116	−	10.6768i	0.0277557	−	0.370374i
$832$	−39.3796			−1.36524
$833$	51.2557	+	14.9565i	1.77590	+	0.518210i
$834$	16.4914			0.571050
$835$	−0.168933	+	2.25426i	−0.00584617	+	0.0780117i
$836$	1.02015	−	0.314674i	0.0352826	−	0.0108832i
$837$	−0.157562	−	0.0237487i	−0.00544615	−	0.000820875i
$838$	3.43674	+	3.18882i	0.118720	+	0.110156i
$839$	3.96682	+	17.3798i	0.136950	+	0.600016i	0.996095	+	0.0882846i	$0.0281385\pi$
$839$	3.96682	+	17.3798i	0.136950	+	0.600016i	−0.859146	+	0.511731i	$0.829004\pi$
$840$	2.95924	−	0.469185i	0.102103	−	0.0161884i
$841$	5.28324	−	23.1474i	0.182181	−	0.798186i
$842$	18.8562	−	12.8559i	0.649827	−	0.443044i
$843$	3.86888	−	3.58979i	0.133251	−	0.123639i
$844$	20.6191	+	14.0578i	0.709738	+	0.483891i
$845$	−9.88549	+	1.49000i	−0.340071	+	0.0512575i
$846$	53.6355	−	25.8295i	1.84403	−	0.888037i
$847$	0.947755	−	2.47017i	0.0325653	−	0.0848762i
$848$	−50.6386	−	24.3862i	−1.73894	−	0.837427i
$849$	2.64182	+	0.814893i	0.0906669	+	0.0279670i
$850$	33.6820	−	85.8204i	1.15528	−	2.94361i
$851$	9.55993	+	16.5583i	0.327710	+	0.567610i
$852$	5.14109	−	8.90462i	0.176131	−	0.305067i
$853$	−9.51423	−	11.9305i	−0.325761	−	0.408491i	0.591801	−	0.806084i	$-0.298417\pi$
$853$	−9.51423	−	11.9305i	−0.325761	−	0.408491i	−0.917562	+	0.397593i	$0.869846\pi$
$854$	−13.1788	+	16.7872i	−0.450969	+	0.574447i
$855$	−0.148523	+	0.186242i	−0.00507937	+	0.00636933i
$856$	−26.6980	−	68.0254i	−0.912519	−	2.32506i
$857$	−0.355724	−	4.74681i	−0.0121513	−	0.162148i	−0.999978	−	0.00659118i	$-0.997902\pi$
$857$	−0.355724	−	4.74681i	−0.0121513	−	0.162148i	0.987827	−	0.155557i	$-0.0497171\pi$
$858$	−0.723805	−	9.65850i	−0.0247103	−	0.329736i
$859$	13.3489	+	34.0124i	0.455458	+	1.16049i	0.955632	+	0.294563i	$0.0951742\pi$
$859$	13.3489	+	34.0124i	0.455458	+	1.16049i	−0.500174	+	0.865925i	$0.666731\pi$
$860$	10.8756	−	13.6376i	0.370856	−	0.465039i
$861$	7.55807	−	9.62751i	0.257578	−	0.328105i
$862$	36.3060	+	45.5263i	1.23659	+	1.55063i
$863$	6.80176	−	11.7810i	0.231534	−	0.401029i	−0.726725	−	0.686928i	$-0.758959\pi$
$863$	6.80176	−	11.7810i	0.231534	−	0.401029i	0.958260	+	0.285899i	$0.0922921\pi$
$864$	−2.51138	−	4.34983i	−0.0854388	−	0.147984i
$865$	−1.87736	+	4.78342i	−0.0638320	+	0.162641i
$866$	37.5472	+	11.5818i	1.27590	+	0.393564i
$867$	−22.5177	−	10.8440i	−0.764742	−	0.368280i
$868$	−0.183060	+	0.477116i	−0.00621345	+	0.0161944i
$869$	−1.15412	+	0.555796i	−0.0391509	+	0.0188541i
$870$	1.19807	−	0.180580i	0.0406184	−	0.00612224i
$871$	−68.9807	−	47.0302i	−2.33732	−	1.59356i
$872$	−35.7139	+	33.1377i	−1.20943	+	1.12218i
$873$	−28.0154	+	19.1006i	−0.948177	+	0.646456i
$874$	−0.553907	+	2.42682i	−0.0187362	+	0.0820885i
$875$	9.06621	−	1.43744i	0.306494	−	0.0485944i
$876$	−1.02416	−	4.48712i	−0.0346030	−	0.151606i
$877$	−15.1796	−	14.0846i	−0.512578	−	0.475603i	0.380959	−	0.924592i	$-0.375594\pi$
$877$	−15.1796	−	14.0846i	−0.512578	−	0.475603i	−0.893537	+	0.448989i	$0.851784\pi$
$878$	24.2462	+	3.65453i	0.818271	+	0.123334i
$879$	−4.74952	+	1.46503i	−0.160197	+	0.0494143i
$880$	0.128085	−	1.70917i	0.00431774	−	0.0576162i
$881$	18.5977			0.626571			0.313286	−	0.949659i	$-0.398570\pi$
$881$	18.5977			0.626571			0.313286	+	0.949659i	$0.398570\pi$
$882$	37.3274	−	26.2938i	1.25688	−	0.885360i
$883$	−27.3496			−0.920386			−0.460193	−	0.887819i	$-0.652220\pi$
$883$	−27.3496			−0.920386			−0.460193	+	0.887819i	$0.652220\pi$
$884$	15.2061	−	202.912i	0.511437	−	6.82465i
$885$	2.18218	−	0.673114i	0.0733532	−	0.0226265i
$886$	43.4476	+	6.54867i	1.45965	+	0.220007i
$887$	12.3794	+	11.4864i	0.415658	+	0.385674i	0.860093	−	0.510137i	$-0.170405\pi$
$887$	12.3794	+	11.4864i	0.415658	+	0.385674i	−0.444435	+	0.895811i	$0.646596\pi$
$888$	3.51900	+	15.4177i	0.118090	+	0.517386i
$889$	3.30621	−	49.1555i	0.110887	−	1.64862i
$890$	−0.234471	+	1.02729i	−0.00785950	+	0.0344347i
$891$	4.80922	−	3.27887i	0.161115	−	0.109846i
$892$	−6.83890	+	6.34557i	−0.228983	+	0.212466i
$893$	−1.94311	−	1.32479i	−0.0650238	−	0.0443324i
$894$	18.9868	−	2.86180i	0.635013	−	0.0957129i
$895$	3.67740	−	1.77094i	0.122922	−	0.0591961i
$896$	45.6454	−	14.4626i	1.52491	−	0.483162i
$897$	13.7227	+	6.60851i	0.458188	+	0.220652i
$898$	52.5835	+	16.2199i	1.75473	+	0.541264i
$899$	−0.0390527	+	0.0995045i	−0.00130248	+	0.00331866i
$900$	−26.5854	−	46.0473i	−0.886180	−	1.53491i
$901$	−43.9327	+	76.0937i	−1.46361	+	2.53505i
$902$	−11.7795	−	14.7710i	−0.392214	−	0.491820i
$903$	−4.13887	+	18.7944i	−0.137733	+	0.625438i
$904$	−21.7598	+	27.2859i	−0.723720	+	0.907516i
$905$	−0.189066	−	0.481733i	−0.00628477	−	0.0160133i
$906$	−0.610982	−	8.15299i	−0.0202985	−	0.270865i
$907$	−1.40763	−	18.7836i	−0.0467397	−	0.623698i	−0.970558	−	0.240867i	$-0.922568\pi$
$907$	−1.40763	−	18.7836i	−0.0467397	−	0.623698i	0.923818	−	0.382831i	$-0.125051\pi$
$908$	10.1557	+	25.8763i	0.337028	+	0.858734i
$909$	−0.900534	+	1.12923i	−0.0298688	+	0.0374543i
$910$	13.3140	−	6.53746i	0.441354	−	0.216715i
$911$	30.8323	+	38.6625i	1.02152	+	1.28095i	0.959151	+	0.282893i	$0.0912942\pi$
$911$	30.8323	+	38.6625i	1.02152	+	1.28095i	0.0623692	+	0.998053i	$0.480134\pi$
$912$	−0.381513	+	0.660800i	−0.0126332	+	0.0218813i
$913$	−4.20969	−	7.29140i	−0.139320	−	0.241310i
$914$	0.0576450	−	0.146877i	0.00190673	−	0.00485826i
$915$	0.663048	+	0.204523i	0.0219197	+	0.00676133i
$916$	−103.123	−	49.6617i	−3.40730	−	1.64087i
$917$	29.6514	+	50.4633i	0.979175	+	1.66644i
$918$	−58.2174	+	28.0360i	−1.92146	+	0.925326i
$919$	−16.1921	+	2.44057i	−0.534129	+	0.0805069i	−0.410568	−	0.911830i	$-0.634669\pi$
$919$	−16.1921	+	2.44057i	−0.534129	+	0.0805069i	−0.123561	+	0.992337i	$0.539431\pi$
$920$	6.00900	+	4.09686i	0.198111	+	0.135070i
$921$	−0.864056	+	0.801727i	−0.0284716	+	0.0264178i
$922$	24.6299	−	16.7924i	0.811144	−	0.553029i
$923$	5.85887	−	25.6694i	0.192847	−	0.844918i
$924$	2.47776	+	6.17409i	0.0815122	+	0.203113i
$925$	5.32322	+	23.3225i	0.175026	+	0.766841i
$926$	34.2608	+	31.7894i	1.12588	+	1.04466i
$927$	−26.1690	−	3.94434i	−0.859503	−	0.129549i
$928$	−3.21979	+	0.993174i	−0.105695	+	0.0326025i
$929$	0.362613	−	4.83874i	0.0118970	−	0.158754i	−0.988091	−	0.153870i	$-0.950826\pi$
$929$	0.362613	−	4.83874i	0.0118970	−	0.158754i	0.999988	−	0.00488396i	$-0.00155462\pi$
$930$	0.0246348			0.000807805
$931$	−1.63687	−	0.757685i	−0.0536464	−	0.0248321i
$932$	−51.7858			−1.69630
$933$	−0.654535	+	8.73416i	−0.0214285	+	0.285944i
$934$	30.9767	−	9.55506i	1.01359	−	0.312651i
$935$	−2.64954	−	0.399354i	−0.0866493	−	0.0130603i
$936$	−65.9798	−	61.2203i	−2.15662	−	2.00105i
$937$	−3.54157	−	15.5166i	−0.115698	−	0.506906i	−0.999255	−	0.0385831i	$-0.987716\pi$
$937$	−3.54157	−	15.5166i	−0.115698	−	0.506906i	0.883557	−	0.468323i	$-0.155142\pi$
$938$	81.4386	+	24.4406i	2.65906	+	0.798014i
$939$	1.23457	−	5.40900i	0.0402886	−	0.176516i
$940$	−10.9752	+	7.48274i	−0.357970	+	0.244060i
$941$	−15.0852	+	13.9971i	−0.491765	+	0.456291i	−0.886651	−	0.462439i	$-0.846974\pi$
$941$	−15.0852	+	13.9971i	−0.491765	+	0.456291i	0.394886	+	0.918730i	$0.370784\pi$
$942$	−19.3919	−	13.2212i	−0.631823	−	0.430770i
$943$	29.3780	−	4.42803i	0.956680	−	0.144196i
$944$	−47.0863	+	22.6756i	−1.53253	+	0.738027i
$945$	−2.63827	−	1.76937i	−0.0858229	−	0.0575575i
$946$	26.7635	+	12.8886i	0.870155	+	0.419045i
$947$	52.7594	+	16.2741i	1.71445	+	0.528838i	0.987468	−	0.157820i	$-0.0504465\pi$
$947$	52.7594	+	16.2741i	1.71445	+	0.528838i	0.726981	+	0.686657i	$0.240923\pi$
$948$	1.17677	−	2.99836i	0.0382196	−	0.0973821i
$949$	−5.89283	−	10.2067i	−0.191289	−	0.331323i
$950$	−1.55724	+	2.69721i	−0.0505234	+	0.0875091i
$951$	3.26478	+	4.09390i	0.105868	+	0.132754i
$952$	24.6510	+	104.322i	0.798943	+	3.38111i
$953$	3.83895	−	4.81389i	0.124356	−	0.155937i	−0.715756	−	0.698350i	$-0.753918\pi$
$953$	3.83895	−	4.81389i	0.124356	−	0.155937i	0.840112	+	0.542413i	$0.182489\pi$
$954$	27.4506	+	69.9430i	0.888747	+	2.26449i
$955$	−0.0503232	−	0.671517i	−0.00162842	−	0.0217298i
$956$	−2.21605	−	29.5711i	−0.0716722	−	0.956399i
$957$	0.508399	+	1.29538i	0.0164342	+	0.0418736i
$958$	21.7703	−	27.2991i	0.703366	−	0.881993i
$959$	−30.4484	+	0.232653i	−0.983231	+	0.00751277i
$960$	−0.812975	−	1.01944i	−0.0262387	−	0.0329022i
$961$	15.4989	−	26.8449i	0.499965	−	0.865965i
$962$	39.1434	+	67.7984i	1.26203	+	2.18591i
$963$	−13.2273	+	33.7026i	−0.426244	+	1.08605i
$964$	69.0714	+	21.3057i	2.22464	+	0.686210i
$965$	−5.29586	−	2.55035i	−0.170480	−	0.0820988i
$966$	−15.3559	−	2.19466i	−0.494067	−	0.0706121i
$967$	−4.10178	+	1.97531i	−0.131904	+	0.0635217i	−0.498672	−	0.866791i	$-0.666179\pi$
$967$	−4.10178	+	1.97531i	−0.131904	+	0.0635217i	0.366768	+	0.930313i	$0.380464\pi$
$968$	5.25243	−	0.791676i	0.168819	−	0.0254454i
$969$	0.985579	+	0.671956i	0.0316614	+	0.0215863i
$970$	8.22337	−	7.63018i	0.264037	−	0.244990i
$971$	12.8018	−	8.72810i	0.410829	−	0.280098i	−0.340219	−	0.940346i	$-0.610501\pi$
$971$	12.8018	−	8.72810i	0.410829	−	0.280098i	0.751048	+	0.660248i	$0.229549\pi$
$972$	−12.7100	+	55.6861i	−0.407673	+	1.78613i
$973$	−23.8404	+	16.5223i	−0.764287	+	0.529681i
$974$	−18.5096	−	81.0960i	−0.593087	−	2.59848i
$975$	13.9696	+	12.9619i	0.447385	+	0.415113i
$976$	−15.7022	−	2.36673i	−0.502616	−	0.0757571i
$977$	−53.2580	+	16.4279i	−1.70388	+	0.525576i	−0.985441	−	0.170018i	$-0.945617\pi$
$977$	−53.2580	+	16.4279i	−1.70388	+	0.525576i	−0.718435	+	0.695594i	$0.755141\pi$
$978$	1.74176	−	23.2421i	0.0556952	−	0.743201i
$979$	−1.21022			−0.0386788
$980$	−7.36150	+	7.04284i	−0.235154	+	0.224975i
$981$	24.1376			0.770656
$982$	1.16184	−	15.5037i	0.0370758	−	0.494743i
$983$	−35.4814	+	10.9446i	−1.13168	+	0.349077i	−0.803363	−	0.595490i	$-0.796958\pi$
$983$	−35.4814	+	10.9446i	−1.13168	+	0.349077i	−0.328318	+	0.944567i	$0.606482\pi$
$984$	24.2989	+	3.66247i	0.774620	+	0.116755i
$985$	−3.91095	−	3.62883i	−0.124613	−	0.115624i
$986$	9.64574	+	42.2607i	0.307183	+	1.34586i
$987$	7.23041	−	12.7474i	0.230146	−	0.405754i
$988$	−1.52960	+	6.70163i	−0.0486631	+	0.213207i
$989$	−38.5960	+	26.3143i	−1.22728	+	0.836746i
$990$	−1.67965	+	1.55849i	−0.0533828	+	0.0495320i
$991$	−28.6986	−	19.5664i	−0.911642	−	0.621547i	0.0140190	−	0.999902i	$-0.495537\pi$
$991$	−28.6986	−	19.5664i	−0.911642	−	0.621547i	−0.925661	+	0.378355i	$0.876490\pi$
$992$	−0.0677444	+	0.0102108i	−0.00215089	+	0.000324194i
$993$	−11.3226	+	5.45268i	−0.359312	+	0.173035i
$994$	2.20814	+	26.7239i	0.0700380	+	0.847632i
$995$	2.87454	+	1.38431i	0.0911292	+	0.0438855i
$996$	20.2299	+	6.24010i	0.641009	+	0.197725i
$997$	−4.04337	+	10.3023i	−0.128055	+	0.326278i	−0.980494	−	0.196548i	$-0.937027\pi$
$997$	−4.04337	+	10.3023i	−0.128055	+	0.326278i	0.852440	+	0.522826i	$0.175122\pi$
$998$	0.0193005	+	0.0334294i	0.000610946	+	0.00105819i
$999$	8.38334	−	14.5204i	0.265237	−	0.459404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.r.b.23.3	✓	276
49.32	even	21	inner	539.2.r.b.375.3	yes	276

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.r.b.23.3	✓	276	1.1	even	1	trivial
539.2.r.b.375.3	yes	276	49.32	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.r (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.185221 + 2.47160i) q^{2} +(0.579946 - 0.178890i) q^{3} +(-4.09683 - 0.617498i) q^{4} +(-0.257511 - 0.238935i) q^{5} +(0.334725 + 1.46653i) q^{6} +(-1.95317 - 1.78470i) q^{7} +(1.18198 - 5.17858i) q^{8} +(-2.17438 + 1.48247i) q^{9} +O(q^{10})\)	\(q+(-0.185221 + 2.47160i) q^{2} +(0.579946 - 0.178890i) q^{3} +(-4.09683 - 0.617498i) q^{4} +(-0.257511 - 0.238935i) q^{5} +(0.334725 + 1.46653i) q^{6} +(-1.95317 - 1.78470i) q^{7} +(1.18198 - 5.17858i) q^{8} +(-2.17438 + 1.48247i) q^{9} +(0.638248 - 0.592207i) q^{10} +(0.826239 + 0.563320i) q^{11} +(-2.48641 + 0.374765i) q^{12} +(-5.80120 + 2.79371i) q^{13} +(4.77282 - 4.49688i) q^{14} +(-0.192085 - 0.0925034i) q^{15} +(4.66236 + 1.43815i) q^{16} +(2.78668 - 7.10034i) q^{17} +(-3.26132 - 5.64878i) q^{18} +(-0.128838 + 0.223154i) q^{19} +(0.907436 + 1.13789i) q^{20} +(-1.45199 - 0.685626i) q^{21} +(-1.54534 + 1.93779i) q^{22} +(-1.42396 - 3.62818i) q^{23} +(-0.240911 - 3.21474i) q^{24} +(-0.364429 - 4.86296i) q^{25} +(-5.83043 - 14.8557i) q^{26} +(-2.13103 + 2.67223i) q^{27} +(6.89975 + 8.51768i) q^{28} +(1.42959 + 1.79265i) q^{29} +(0.264209 - 0.457624i) q^{30} +(0.0233099 + 0.0403739i) q^{31} +(-0.536884 + 1.36796i) q^{32} +(0.579946 + 0.178890i) q^{33} +(17.0330 + 8.20268i) q^{34} +(0.0765347 + 0.926258i) q^{35} +(9.82349 - 4.73074i) q^{36} +(-4.85075 + 0.731132i) q^{37} +(-0.527683 - 0.359768i) q^{38} +(-2.86462 + 2.65798i) q^{39} +(-1.54171 + 1.05112i) q^{40} +(-1.69619 + 7.43148i) q^{41} +(1.96353 - 3.46176i) q^{42} +(-2.66692 - 11.6845i) q^{43} +(-3.03711 - 2.81803i) q^{44} +(0.914139 + 0.137784i) q^{45} +(9.23115 - 2.84743i) q^{46} +(-0.682047 + 9.10128i) q^{47} +2.96119 q^{48} +(0.629717 + 6.97162i) q^{49} +12.0868 q^{50} +(0.345946 - 4.61632i) q^{51} +(25.4917 - 7.86313i) q^{52} +(-11.3907 - 1.71688i) q^{53} +(-6.20996 - 5.76200i) q^{54} +(-0.0781684 - 0.342478i) q^{55} +(-11.5508 + 8.00515i) q^{56} +(-0.0347991 + 0.152465i) q^{57} +(-4.69550 + 3.20134i) q^{58} +(-7.85195 + 7.28555i) q^{59} +(0.729820 + 0.497583i) q^{60} +(-3.21825 + 0.485072i) q^{61} +(-0.104106 + 0.0501346i) q^{62} +(6.89268 + 0.985104i) q^{63} +(5.51028 + 2.65361i) q^{64} +(2.16139 + 0.666699i) q^{65} +(-0.549562 + 1.40026i) q^{66} +(6.48311 + 11.2291i) q^{67} +(-15.8010 + 27.3681i) q^{68} +(-1.47486 - 1.84942i) q^{69} +(-2.30351 + 0.0176009i) q^{70} +(-2.54955 + 3.19704i) q^{71} +(5.10701 + 13.0124i) q^{72} +(0.136786 + 1.82528i) q^{73} +(-0.908607 - 12.1245i) q^{74} +(-1.08128 - 2.75506i) q^{75} +(0.665624 - 0.834666i) q^{76} +(-0.608426 - 2.57484i) q^{77} +(-6.03886 - 7.57250i) q^{78} +(-0.640490 + 1.10936i) q^{79} +(-0.856983 - 1.48434i) q^{80} +(2.12651 - 5.41827i) q^{81} +(-18.0535 - 5.56875i) q^{82} +(-7.58560 - 3.65303i) q^{83} +(5.52521 + 3.70550i) q^{84} +(-2.41412 + 1.16258i) q^{85} +(29.3734 - 4.42733i) q^{86} +(1.14977 + 0.783901i) q^{87} +(3.89379 - 3.61291i) q^{88} +(-0.999932 + 0.681742i) q^{89} +(-0.509865 + 2.23386i) q^{90} +(16.3166 + 4.89680i) q^{91} +(3.59331 + 15.7433i) q^{92} +(0.0207409 + 0.0192448i) q^{93} +(-22.3684 - 3.37149i) q^{94} +(0.0864963 - 0.0266806i) q^{95} +(-0.0666501 + 0.889384i) q^{96} +12.8843 q^{97} +(-17.3477 + 0.265119i) q^{98} -2.63166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 23 q^{11} - 32 q^{12} - 27 q^{13} - 23 q^{14} + 6 q^{15} + 70 q^{16} - 3 q^{17} - 20 q^{18} - 61 q^{19} - 12 q^{20} - 23 q^{21} - 6 q^{23} + 6 q^{24} - 11 q^{25} + 9 q^{26} - 12 q^{27} - 3 q^{28} - 24 q^{29} - 26 q^{30} - 75 q^{31} + 137 q^{32} + 3 q^{33} - 58 q^{34} + 15 q^{35} - 36 q^{36} - 29 q^{37} - 6 q^{39} - 53 q^{40} - 25 q^{41} + 4 q^{42} + 20 q^{43} + 6 q^{44} + 3 q^{45} + 52 q^{46} + 25 q^{47} + 288 q^{48} + 84 q^{49} - 218 q^{50} - 160 q^{51} + 65 q^{52} + 5 q^{53} + 66 q^{54} - 12 q^{55} - 178 q^{56} + 23 q^{57} + 5 q^{58} + 28 q^{59} - 54 q^{60} - 65 q^{61} - 92 q^{62} + 85 q^{63} - 50 q^{64} + 201 q^{65} - 38 q^{66} - 16 q^{67} - 91 q^{68} - 42 q^{69} - 255 q^{70} - 63 q^{71} - 165 q^{72} + 6 q^{73} - 166 q^{74} - 117 q^{75} - 87 q^{76} + 33 q^{78} + 2 q^{79} - 48 q^{80} + 5 q^{81} + 53 q^{82} + 37 q^{83} - 84 q^{84} + 26 q^{85} + 67 q^{86} - 59 q^{87} - 3 q^{88} - 155 q^{89} + 9 q^{90} + 47 q^{91} - 19 q^{92} + 81 q^{93} + 126 q^{94} - 37 q^{95} + 395 q^{96} + 302 q^{97} + 90 q^{98} + 268 q^{99}+O(q^{100}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 23 * q^11 - 32 * q^12 - 27 * q^13 - 23 * q^14 + 6 * q^15 + 70 * q^16 - 3 * q^17 - 20 * q^18 - 61 * q^19 - 12 * q^20 - 23 * q^21 - 6 * q^23 + 6 * q^24 - 11 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 - 24 * q^29 - 26 * q^30 - 75 * q^31 + 137 * q^32 + 3 * q^33 - 58 * q^34 + 15 * q^35 - 36 * q^36 - 29 * q^37 - 6 * q^39 - 53 * q^40 - 25 * q^41 + 4 * q^42 + 20 * q^43 + 6 * q^44 + 3 * q^45 + 52 * q^46 + 25 * q^47 + 288 * q^48 + 84 * q^49 - 218 * q^50 - 160 * q^51 + 65 * q^52 + 5 * q^53 + 66 * q^54 - 12 * q^55 - 178 * q^56 + 23 * q^57 + 5 * q^58 + 28 * q^59 - 54 * q^60 - 65 * q^61 - 92 * q^62 + 85 * q^63 - 50 * q^64 + 201 * q^65 - 38 * q^66 - 16 * q^67 - 91 * q^68 - 42 * q^69 - 255 * q^70 - 63 * q^71 - 165 * q^72 + 6 * q^73 - 166 * q^74 - 117 * q^75 - 87 * q^76 + 33 * q^78 + 2 * q^79 - 48 * q^80 + 5 * q^81 + 53 * q^82 + 37 * q^83 - 84 * q^84 + 26 * q^85 + 67 * q^86 - 59 * q^87 - 3 * q^88 - 155 * q^89 + 9 * q^90 + 47 * q^91 - 19 * q^92 + 81 * q^93 + 126 * q^94 - 37 * q^95 + 395 * q^96 + 302 * q^97 + 90 * q^98 + 268 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more