LMFDB - Embedded newform 507.2.q.b.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39808 - 0.112865i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.0322011 - 0.00523319i) q^{4} +(-2.59137 - 2.29575i) q^{5} +(1.12132 + 0.842620i) q^{6} +(2.75817 - 2.87156i) q^{7} +(2.76818 + 0.682294i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-1.39808 - 0.112865i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.0322011 - 0.00523319i) q^{4} +(-2.59137 - 2.29575i) q^{5} +(1.12132 + 0.842620i) q^{6} +(2.75817 - 2.87156i) q^{7} +(2.76818 + 0.682294i) q^{8} +(0.428693 + 0.903450i) q^{9} +(3.36384 + 3.50213i) q^{10} +(2.44192 - 5.14624i) q^{11} +(0.0244191 + 0.0216334i) q^{12} +(2.61590 + 2.48134i) q^{13} +(-4.18025 + 3.70337i) q^{14} +(0.963199 + 3.32535i) q^{15} +(-3.73125 - 1.24567i) q^{16} +(0.177198 - 0.184482i) q^{17} +(-0.497380 - 1.31148i) q^{18} +(0.635441 - 1.10062i) q^{19} +(0.0714309 + 0.0874870i) q^{20} +(-3.86592 + 0.952864i) q^{21} +(-3.99484 + 6.91927i) q^{22} +(-3.36244 - 5.82392i) q^{23} +(-1.97497 - 2.05616i) q^{24} +(0.842032 + 6.93476i) q^{25} +(-3.37719 - 3.76437i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.103843 + 0.0780333i) q^{28} +(-5.33671 - 0.430824i) q^{29} +(-0.971317 - 4.75783i) q^{30} +(0.887429 - 7.30864i) q^{31} +(-0.169762 - 0.0723289i) q^{32} +(-4.81438 + 3.04443i) q^{33} +(-0.268559 + 0.237922i) q^{34} +(-13.7398 + 1.10919i) q^{35} +(-0.00907645 - 0.0313355i) q^{36} +(-3.83618 + 1.63444i) q^{37} +(-1.01262 + 1.46703i) q^{38} +(-0.884744 - 3.49532i) q^{39} +(-5.60699 - 8.12313i) q^{40} +(8.76874 + 5.54502i) q^{41} +(5.51243 - 0.895857i) q^{42} +(8.62210 + 3.67353i) q^{43} +(-0.105564 + 0.152936i) q^{44} +(0.963199 - 3.32535i) q^{45} +(4.04366 + 8.52183i) q^{46} +(0.362160 - 0.954939i) q^{47} +(2.48784 + 3.04705i) q^{48} +(-0.356487 - 8.84613i) q^{49} +(-0.394540 - 9.79041i) q^{50} +(-0.248365 + 0.0612165i) q^{51} +(-0.0712497 - 0.0935915i) q^{52} +(-1.75331 - 0.432153i) q^{53} +(-0.280562 + 1.37429i) q^{54} +(-18.1424 + 7.72977i) q^{55} +(9.59434 - 6.06709i) q^{56} +(-1.12531 + 0.590608i) q^{57} +(7.41254 + 1.20466i) q^{58} +(-4.92586 + 1.64449i) q^{59} +(-0.0136139 - 0.112121i) q^{60} +(-0.672589 + 2.32205i) q^{61} +(-2.06559 + 10.1179i) q^{62} +(3.77671 + 1.26085i) q^{63} +(7.19539 + 3.77643i) q^{64} +(-1.08223 - 12.4355i) q^{65} +(7.07452 - 3.71299i) q^{66} +(-6.74720 + 1.09653i) q^{67} +(-0.00667140 + 0.00501323i) q^{68} +(-0.270784 + 6.71943i) q^{69} +19.3346 q^{70} +(-0.408278 + 10.1313i) q^{71} +(0.570278 + 2.79341i) q^{72} +(-2.63605 - 3.81898i) q^{73} +(5.54777 - 1.85212i) q^{74} +(2.99471 - 6.31123i) q^{75} +(-0.0262216 + 0.0321157i) q^{76} +(-8.04249 - 21.2063i) q^{77} +(0.842447 + 4.98660i) q^{78} +(-3.45188 + 9.10187i) q^{79} +(6.80928 + 11.7940i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-11.6336 - 8.74208i) q^{82} +(-12.7104 - 6.67093i) q^{83} +(0.129474 - 0.0104522i) q^{84} +(-0.882711 + 0.0712598i) q^{85} +(-11.6398 - 6.10904i) q^{86} +(4.28027 + 3.21642i) q^{87} +(10.2709 - 12.5796i) q^{88} +(6.94124 + 12.0226i) q^{89} +(-1.72195 + 4.54040i) q^{90} +(14.3404 - 0.667760i) q^{91} +(0.0777967 + 0.205133i) q^{92} +(-4.65626 + 5.70289i) q^{93} +(-0.614110 + 1.29421i) q^{94} +(-4.17341 + 1.39329i) q^{95} +(0.104824 + 0.151864i) q^{96} +(-1.18680 - 5.81335i) q^{97} +(-0.500020 + 12.4079i) q^{98} +5.69621 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	−1.39808	−	0.112865i	−0.988594	−	0.0798076i	−0.424422	−	0.905465i	$-0.639523\pi$
$2$	−1.39808	−	0.112865i	−0.988594	−	0.0798076i	−0.564173	+	0.825657i	$0.690805\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	−0.0322011	−	0.00523319i	−0.0161006	−	0.00261660i
$5$	−2.59137	−	2.29575i	−1.15890	−	1.02669i	−0.999219	−	0.0395233i	$-0.987416\pi$
$5$	−2.59137	−	2.29575i	−1.15890	−	1.02669i	−0.159678	−	0.987169i	$-0.551045\pi$
$6$	1.12132	+	0.842620i	0.457779	+	0.343998i
$7$	2.75817	−	2.87156i	1.04249	−	1.08535i	0.0462296	−	0.998931i	$-0.485279\pi$
$7$	2.75817	−	2.87156i	1.04249	−	1.08535i	0.996259	−	0.0864150i	$-0.0275411\pi$
$8$	2.76818	+	0.682294i	0.978698	+	0.241228i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	3.36384	+	3.50213i	1.06374	+	1.10747i
$11$	2.44192	−	5.14624i	0.736268	−	1.55165i	−0.0948105	−	0.995495i	$-0.530225\pi$
$11$	2.44192	−	5.14624i	0.736268	−	1.55165i	0.831078	−	0.556156i	$-0.187724\pi$
$12$	0.0244191	+	0.0216334i	0.00704919	+	0.00624504i
$13$	2.61590	+	2.48134i	0.725521	+	0.688200i
$13$	2.61590	+	2.48134i	0.725521	+	0.688200i
$14$	−4.18025	+	3.70337i	−1.11722	+	0.989768i
$15$	0.963199	+	3.32535i	0.248697	+	0.858601i
$16$	−3.73125	−	1.24567i	−0.932812	−	0.311418i
$17$	0.177198	−	0.184482i	0.0429768	−	0.0447435i	−0.699367	−	0.714763i	$-0.746535\pi$
$17$	0.177198	−	0.184482i	0.0429768	−	0.0447435i	0.742344	+	0.670019i	$0.233714\pi$
$18$	−0.497380	−	1.31148i	−0.117234	−	0.309120i
$19$	0.635441	−	1.10062i	0.145780	−	0.252499i	−0.783884	−	0.620908i	$-0.786764\pi$
$19$	0.635441	−	1.10062i	0.145780	−	0.252499i	0.929664	+	0.368409i	$0.120097\pi$
$20$	0.0714309	+	0.0874870i	0.0159724	+	0.0195627i
$21$	−3.86592	+	0.952864i	−0.843614	+	0.207932i
$22$	−3.99484	+	6.91927i	−0.851704	+	1.47519i
$23$	−3.36244	−	5.82392i	−0.701117	−	1.21437i	−0.968075	−	0.250663i	$-0.919352\pi$
$23$	−3.36244	−	5.82392i	−0.701117	−	1.21437i	0.266957	−	0.963708i	$-0.413982\pi$
$24$	−1.97497	−	2.05616i	−0.403140	−	0.419713i
$25$	0.842032	+	6.93476i	0.168406	+	1.38695i
$26$	−3.37719	−	3.76437i	−0.662322	−	0.738253i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−0.103843	+	0.0780333i	−0.0196246	+	0.0147469i
$29$	−5.33671	−	0.430824i	−0.991002	−	0.0800020i	−0.425682	−	0.904873i	$-0.639966\pi$
$29$	−5.33671	−	0.430824i	−0.991002	−	0.0800020i	−0.565321	+	0.824871i	$0.691248\pi$
$30$	−0.971317	−	4.75783i	−0.177337	−	0.868656i
$31$	0.887429	−	7.30864i	0.159387	−	1.31267i	−0.665085	−	0.746768i	$-0.731605\pi$
$31$	0.887429	−	7.30864i	0.159387	−	1.31267i	0.824472	−	0.565903i	$-0.191472\pi$
$32$	−0.169762	−	0.0723289i	−0.0300100	−	0.0127861i
$33$	−4.81438	+	3.04443i	−0.838076	+	0.529967i
$34$	−0.268559	+	0.237922i	−0.0460575	+	0.0408033i
$35$	−13.7398	+	1.10919i	−2.32245	+	0.187488i
$36$	−0.00907645	−	0.0313355i	−0.00151274	−	0.00522259i
$37$	−3.83618	+	1.63444i	−0.630664	+	0.268701i	−0.683555	−	0.729899i	$-0.739567\pi$
$37$	−3.83618	+	1.63444i	−0.630664	+	0.268701i	0.0528904	+	0.998600i	$0.483157\pi$
$38$	−1.01262	+	1.46703i	−0.164269	+	0.237984i
$39$	−0.884744	−	3.49532i	−0.141672	−	0.559698i
$40$	−5.60699	−	8.12313i	−0.886544	−	1.28438i
$41$	8.76874	+	5.54502i	1.36945	+	0.865986i	0.998046	−	0.0624862i	$-0.0199029\pi$
$41$	8.76874	+	5.54502i	1.36945	+	0.865986i	0.371402	+	0.928472i	$0.378877\pi$
$42$	5.51243	−	0.895857i	0.850586	−	0.138234i
$43$	8.62210	+	3.67353i	1.31486	+	0.560209i	0.931618	−	0.363440i	$-0.118398\pi$
$43$	8.62210	+	3.67353i	1.31486	+	0.560209i	0.383240	+	0.923649i	$0.374808\pi$
$44$	−0.105564	+	0.152936i	−0.0159144	+	0.0230559i
$45$	0.963199	−	3.32535i	0.143585	−	0.495714i
$46$	4.04366	+	8.52183i	0.596205	+	1.25647i
$47$	0.362160	−	0.954939i	0.0528265	−	0.139292i	−0.906006	−	0.423266i	$-0.860884\pi$
$47$	0.362160	−	0.954939i	0.0528265	−	0.139292i	0.958832	+	0.283974i	$0.0916529\pi$
$48$	2.48784	+	3.04705i	0.359089	+	0.439804i
$49$	−0.356487	−	8.84613i	−0.0509267	−	1.26373i
$50$	−0.394540	−	9.79041i	−0.0557964	−	1.38457i
$51$	−0.248365	+	0.0612165i	−0.0347781	+	0.00857203i
$52$	−0.0712497	−	0.0935915i	−0.00988055	−	0.0129788i
$53$	−1.75331	−	0.432153i	−0.240836	−	0.0593608i	0.117050	−	0.993126i	$-0.462656\pi$
$53$	−1.75331	−	0.432153i	−0.240836	−	0.0593608i	−0.357886	+	0.933765i	$0.616502\pi$
$54$	−0.280562	+	1.37429i	−0.0381797	+	0.187017i
$55$	−18.1424	+	7.72977i	−2.44633	+	1.04228i
$56$	9.59434	−	6.06709i	1.28210	−	0.810749i
$57$	−1.12531	+	0.590608i	−0.149051	+	0.0782280i
$58$	7.41254	+	1.20466i	0.973315	+	0.158179i
$59$	−4.92586	+	1.64449i	−0.641292	+	0.214095i	−0.618672	−	0.785649i	$-0.712329\pi$
$59$	−4.92586	+	1.64449i	−0.641292	+	0.214095i	−0.0226201	+	0.999744i	$0.507201\pi$
$60$	−0.0136139	−	0.112121i	−0.00175755	−	0.0144747i
$61$	−0.672589	+	2.32205i	−0.0861162	+	0.297308i	−0.992003	−	0.126211i	$-0.959718\pi$
$61$	−0.672589	+	2.32205i	−0.0861162	+	0.297308i	0.905887	+	0.423519i	$0.139205\pi$
$62$	−2.06559	+	10.1179i	−0.262330	+	1.28498i
$63$	3.77671	+	1.26085i	0.475821	+	0.158852i
$64$	7.19539	+	3.77643i	0.899424	+	0.472054i
$65$	−1.08223	−	12.4355i	−0.134234	−	1.54244i
$66$	7.07452	−	3.71299i	0.870813	−	0.457038i
$67$	−6.74720	+	1.09653i	−0.824302	+	0.133962i	−0.557909	−	0.829902i	$-0.688396\pi$
$67$	−6.74720	+	1.09653i	−0.824302	+	0.133962i	−0.266393	+	0.963864i	$0.585832\pi$
$68$	−0.00667140	+	0.00501323i	−0.000809026	+	0.000607943i
$69$	−0.270784	+	6.71943i	−0.0325985	+	0.808924i
$70$	19.3346			2.31093
$71$	−0.408278	+	10.1313i	−0.0484537	+	1.20237i	0.773869	+	0.633346i	$0.218319\pi$
$71$	−0.408278	+	10.1313i	−0.0484537	+	1.20237i	−0.822323	+	0.569021i	$0.807322\pi$
$72$	0.570278	+	2.79341i	0.0672079	+	0.329206i
$73$	−2.63605	−	3.81898i	−0.308526	−	0.446977i	0.637794	−	0.770207i	$-0.279847\pi$
$73$	−2.63605	−	3.81898i	−0.308526	−	0.446977i	−0.946321	+	0.323229i	$0.895232\pi$
$74$	5.54777	−	1.85212i	0.644915	−	0.215304i
$75$	2.99471	−	6.31123i	0.345800	−	0.728758i
$76$	−0.0262216	+	0.0321157i	−0.00300783	+	0.00368392i
$77$	−8.04249	−	21.2063i	−0.916527	−	2.41668i
$78$	0.842447	+	4.98660i	0.0953883	+	0.564621i
$79$	−3.45188	+	9.10187i	−0.388367	+	1.02404i	0.588179	+	0.808731i	$0.299845\pi$
$79$	−3.45188	+	9.10187i	−0.388367	+	1.02404i	−0.976546	+	0.215309i	$0.930924\pi$
$80$	6.80928	+	11.7940i	0.761301	+	1.31861i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−11.6336	−	8.74208i	−1.28472	−	0.965401i
$83$	−12.7104	−	6.67093i	−1.39515	−	0.732230i	−0.411343	−	0.911480i	$-0.634940\pi$
$83$	−12.7104	−	6.67093i	−1.39515	−	0.732230i	−0.983803	+	0.179251i	$0.942633\pi$
$84$	0.129474	−	0.0104522i	0.0141267	−	0.00114043i
$85$	−0.882711	+	0.0712598i	−0.0957435	+	0.00772921i
$86$	−11.6398	−	6.10904i	−1.25515	−	0.658755i
$87$	4.28027	+	3.21642i	0.458894	+	0.344836i
$88$	10.2709	−	12.5796i	1.09488	−	1.34099i
$89$	6.94124	+	12.0226i	0.735770	+	1.27439i	0.954384	+	0.298580i	$0.0965131\pi$
$89$	6.94124	+	12.0226i	0.735770	+	1.27439i	−0.218614	+	0.975811i	$0.570154\pi$
$90$	−1.72195	+	4.54040i	−0.181509	+	0.478601i
$91$	14.3404	−	0.667760i	1.50328	−	0.0700003i
$92$	0.0777967	+	0.205133i	0.00811086	+	0.0213866i
$93$	−4.65626	+	5.70289i	−0.482832	+	0.591362i
$94$	−0.614110	+	1.29421i	−0.0633406	+	0.133487i
$95$	−4.17341	+	1.39329i	−0.428182	+	0.142948i
$96$	0.104824	+	0.151864i	0.0106986	+	0.0154995i
$97$	−1.18680	−	5.81335i	−0.120502	−	0.590256i	−0.994536	−	0.104392i	$-0.966710\pi$
$97$	−1.18680	−	5.81335i	−0.120502	−	0.590256i	0.874035	−	0.485864i	$-0.161495\pi$
$98$	−0.500020	+	12.4079i	−0.0505096	+	1.25338i
$99$	5.69621			0.572491
$100$	0.00917654	−	0.227713i	0.000917654	−	0.0227713i
$101$	−5.46953	+	4.11008i	−0.544238	+	0.408968i	−0.836989	−	0.547220i	$-0.815686\pi$
$101$	−5.46953	+	4.11008i	−0.544238	+	0.408968i	0.292750	+	0.956189i	$0.405430\pi$
$102$	0.354145	−	0.0575541i	0.0350655	−	0.00569871i
$103$	3.73437	−	1.95995i	0.367958	−	0.193119i	−0.270602	−	0.962691i	$-0.587223\pi$
$103$	3.73437	−	1.95995i	0.367958	−	0.193119i	0.638560	+	0.769572i	$0.279530\pi$
$104$	5.54828	+	8.65361i	0.544053	+	0.848556i
$105$	12.2056	+	6.40598i	1.19114	+	0.625160i
$106$	2.40250	+	0.802074i	0.233352	+	0.0779043i
$107$	1.65828	−	8.12279i	0.160312	−	0.785260i	−0.817525	−	0.575893i	$-0.804654\pi$
$107$	1.65828	−	8.12279i	0.160312	−	0.785260i	0.977837	−	0.209367i	$-0.0671404\pi$
$108$	−0.00907645	+	0.0313355i	−0.000873382	+	0.00301526i
$109$	0.422229	+	3.47737i	0.0404422	+	0.333072i	0.998861	+	0.0477074i	$0.0151915\pi$
$109$	0.422229	+	3.47737i	0.0404422	+	0.333072i	−0.958419	+	0.285364i	$0.907885\pi$
$110$	26.2371	−	8.75922i	2.50161	−	0.835159i
$111$	4.11586	+	0.668892i	0.390660	+	0.0634884i
$112$	−13.8684	+	7.27871i	−1.31044	+	0.687773i
$113$	4.12625	−	2.60928i	0.388165	−	0.245461i	−0.326101	−	0.945335i	$-0.605735\pi$
$113$	4.12625	−	2.60928i	0.388165	−	0.245461i	0.714266	+	0.699874i	$0.246761\pi$
$114$	1.63994	−	0.698712i	0.153594	−	0.0654403i
$115$	−4.65695	+	22.8113i	−0.434263	+	2.12716i
$116$	0.169593	+	0.0418010i	0.0157464	+	0.00388113i
$117$	−1.12035	+	3.42707i	−0.103576	+	0.316833i
$118$	7.07237	−	1.74318i	0.651064	−	0.160473i
$119$	−0.0410105	−	1.01767i	−0.00375943	−	0.0932893i
$120$	0.397439	+	9.86234i	0.0362810	+	0.900304i
$121$	−13.5639	−	16.6128i	−1.23309	−	1.51026i
$122$	1.20241	−	3.17051i	0.108861	−	0.287044i
$123$	−4.44763	−	9.37319i	−0.401029	−	0.845152i
$124$	−0.0668237	+	0.230702i	−0.00600095	+	0.0207177i
$125$	3.90518	−	5.65763i	0.349290	−	0.506034i
$126$	−5.13786	−	2.18904i	−0.457717	−	0.195015i
$127$	14.2781	−	2.32042i	1.26698	−	0.205904i	0.510474	−	0.859893i	$-0.329470\pi$
$127$	14.2781	−	2.32042i	1.26698	−	0.205904i	0.756504	+	0.653989i	$0.226906\pi$
$128$	−9.32161	−	5.89463i	−0.823922	−	0.521017i
$129$	−5.32393	−	7.71305i	−0.468746	−	0.679096i
$130$	0.109506	+	17.5081i	0.00960430	+	1.53556i
$131$	11.3495	−	16.4426i	0.991610	−	1.43659i	0.0941192	−	0.995561i	$-0.469997\pi$
$131$	11.3495	−	16.4426i	0.991610	−	1.43659i	0.897491	−	0.441034i	$-0.145388\pi$
$132$	0.170961	−	0.0728395i	0.0148802	−	0.00633986i
$133$	−1.40783	−	4.86038i	−0.122074	−	0.421449i
$134$	9.55691	−	0.771514i	0.825592	−	0.0666486i
$135$	−2.59137	+	2.29575i	−0.223030	+	0.197587i
$136$	0.616386	−	0.389779i	0.0528547	−	0.0334233i
$137$	14.6828	+	6.25577i	1.25444	+	0.534467i	0.913967	−	0.405788i	$-0.133003\pi$
$137$	14.6828	+	6.25577i	1.25444	+	0.534467i	0.340472	+	0.940254i	$0.389413\pi$
$138$	1.13697	−	9.36376i	0.0967850	−	0.797096i
$139$	−0.852307	−	4.17488i	−0.0722918	−	0.354109i	0.927515	−	0.373787i	$-0.121941\pi$
$139$	−0.852307	−	4.17488i	−0.0722918	−	0.354109i	−0.999806	+	0.0196784i	$0.993736\pi$
$140$	0.448242	+	0.0361858i	0.0378834	+	0.00305826i
$141$	−0.816477	+	0.613542i	−0.0687597	+	0.0516696i
$142$	1.71428	−	14.1184i	0.143859	−	1.18479i
$143$	19.1574	−	7.40283i	1.60202	−	0.619056i
$144$	−0.474154	−	3.90501i	−0.0395128	−	0.325417i
$145$	12.8403	+	13.3682i	1.06633	+	1.11017i
$146$	3.25439	+	5.63677i	0.269335	+	0.466502i
$147$	−4.42666	+	7.66719i	−0.365104	+	0.632379i
$148$	0.132083	−	0.0325554i	0.0108571	−	0.00267604i
$149$	8.28506	+	10.1474i	0.678739	+	0.831304i	0.993010	−	0.118029i	$-0.0376576\pi$
$149$	8.28506	+	10.1474i	0.678739	+	0.831304i	−0.314271	+	0.949333i	$0.601760\pi$
$150$	−4.89918	+	8.48562i	−0.400016	+	0.692848i
$151$	−6.33910	−	16.7148i	−0.515869	−	1.36023i	−0.899570	−	0.436777i	$-0.856120\pi$
$151$	−6.33910	−	16.7148i	−0.515869	−	1.36023i	0.383701	−	0.923457i	$-0.374649\pi$
$152$	2.50996	−	2.61314i	0.203584	−	0.211954i
$153$	0.242634	+	0.0810031i	0.0196158	+	0.00654872i
$154$	8.85063	+	30.5559i	0.713204	+	2.46227i
$155$	−19.0785	+	16.9021i	−1.53242	+	1.35761i
$156$	0.0101981	+	0.117183i	0.000816500	+	0.00938216i
$157$	−8.19450	−	7.25970i	−0.653993	−	0.579387i	0.269501	−	0.963000i	$-0.413141\pi$
$157$	−8.19450	−	7.25970i	−0.653993	−	0.579387i	−0.923494	+	0.383613i	$0.874680\pi$
$158$	5.85330	−	12.3356i	0.465664	−	0.981366i
$159$	1.25091	+	1.30234i	0.0992038	+	0.103282i
$160$	0.273868	+	0.577164i	0.0216511	+	0.0456288i
$161$	−25.9979	−	6.40790i	−2.04892	−	0.505013i
$162$	0.971637	−	1.01158i	0.0763390	−	0.0794774i
$163$	11.0960	+	8.33813i	0.869108	+	0.653092i	0.938795	−	0.344477i	$-0.111944\pi$
$163$	11.0960	+	8.33813i	0.869108	+	0.653092i	−0.0696868	+	0.997569i	$0.522200\pi$
$164$	−0.253345	−	0.224444i	−0.0197829	−	0.0175261i
$165$	19.4651	+	3.16339i	1.51536	+	0.246269i
$166$	17.0173	+	10.7611i	1.32080	+	0.835221i
$167$	14.4415	+	1.16584i	1.11752	+	0.0902152i	0.625392	−	0.780310i	$-0.284939\pi$
$167$	14.4415	+	1.16584i	1.11752	+	0.0902152i	0.492123	+	0.870526i	$0.336221\pi$
$168$	−11.3517			−0.875802
$169$	0.685897	+	12.9819i	0.0527613	+	0.998607i
$170$	1.24215			0.0952683
$171$	1.26676	+	0.102263i	0.0968716	+	0.00782028i
$172$	−0.258417	−	0.163413i	−0.0197041	−	0.0124601i
$173$	−7.27837	−	1.18285i	−0.553364	−	0.0899304i	−0.122702	−	0.992444i	$-0.539156\pi$
$173$	−7.27837	−	1.18285i	−0.553364	−	0.0899304i	−0.430662	+	0.902513i	$0.641720\pi$
$174$	−5.62116	−	4.97991i	−0.426139	−	0.377526i
$175$	22.2360	+	16.7093i	1.68088	+	1.26310i
$176$	−15.5220	+	16.1601i	−1.17001	+	1.21811i
$177$	5.04221	+	1.24279i	0.378996	+	0.0934141i
$178$	−8.34751	−	17.5920i	−0.625672	−	1.31858i
$179$	4.04798	+	4.21440i	0.302561	+	0.314999i	0.855075	−	0.518504i	$-0.173511\pi$
$179$	4.04798	+	4.21440i	0.302561	+	0.314999i	−0.552514	+	0.833503i	$0.686332\pi$
$180$	−0.0484183	+	0.102039i	−0.00360888	+	0.00760556i
$181$	−16.8013	−	14.8847i	−1.24883	−	1.10637i	−0.990091	−	0.140424i	$-0.955153\pi$
$181$	−16.8013	−	14.8847i	−1.24883	−	1.10637i	−0.258742	−	0.965946i	$-0.583308\pi$
$182$	−20.1244	−	0.684945i	−1.49172	−	0.0507715i
$183$	1.80952	−	1.60310i	0.133764	−	0.118504i
$184$	−5.33421	−	18.4158i	−0.393243	−	1.35763i
$185$	13.6932	+	4.57148i	1.00675	+	0.336102i
$186$	7.15350	−	7.44759i	0.524520	−	0.546083i
$187$	−0.516688	−	1.36239i	−0.0377840	−	0.0996282i
$188$	−0.0166593	+	0.0288548i	−0.00121501	+	0.00210446i
$189$	−2.51816	−	3.08418i	−0.183169	−	0.224341i
$190$	5.99202	−	1.47690i	0.434707	−	0.107146i
$191$	−10.9769	+	19.0125i	−0.794258	+	1.37569i	0.129052	+	0.991638i	$0.458807\pi$
$191$	−10.9769	+	19.0125i	−0.794258	+	1.37569i	−0.923309	+	0.384057i	$0.874527\pi$
$192$	−4.06310	−	7.03750i	−0.293229	−	0.507888i
$193$	−6.41358	−	6.67724i	−0.461660	−	0.480638i	0.449155	−	0.893454i	$-0.351725\pi$
$193$	−6.41358	−	6.67724i	−0.461660	−	0.480638i	−0.910815	+	0.412815i	$0.864546\pi$
$194$	1.00313	+	8.26150i	0.0720204	+	0.593141i
$195$	−5.73169	+	11.0888i	−0.410455	+	0.794086i
$196$	−0.0348142	+	0.286721i	−0.00248673	+	0.0204801i
$197$	−7.90821	+	5.94263i	−0.563436	+	0.423395i	−0.843924	−	0.536463i	$-0.819760\pi$
$197$	−7.90821	+	5.94263i	−0.563436	+	0.423395i	0.280488	+	0.959858i	$0.409504\pi$
$198$	−7.96378	−	0.642903i	−0.565961	−	0.0456891i
$199$	0.823215	+	4.03237i	0.0583562	+	0.285847i	0.998488	−	0.0549624i	$-0.0175039\pi$
$199$	0.823215	+	4.03237i	0.0583562	+	0.285847i	−0.940132	+	0.340810i	$0.889299\pi$
$200$	−2.40065	+	19.7712i	−0.169752	+	1.39803i
$201$	6.28872	+	2.67938i	0.443572	+	0.188989i
$202$	8.11074	−	5.12892i	0.570670	−	0.360870i
$203$	−15.9567	+	14.1364i	−1.11994	+	0.992179i
$204$	0.00831800		0.000671498i	0.000582376		4.70143e-5i
$205$	−9.99307	−	34.5001i	−0.697946	−	2.40959i
$206$	−5.44217	+	2.31869i	−0.379174	+	0.161551i
$207$	3.82017	−	5.53447i	0.265520	−	0.384672i
$208$	−6.66964	−	12.5171i	−0.462456	−	0.867902i
$209$	−4.11234	−	5.95775i	−0.284457	−	0.412106i
$210$	−16.3414	−	10.3337i	−1.12766	−	0.713092i
$211$	−2.79763	+	0.454660i	−0.192597	+	0.0313001i	−0.255945	−	0.966691i	$-0.582386\pi$
$211$	−2.79763	+	0.454660i	−0.192597	+	0.0313001i	0.0633475	+	0.997992i	$0.479822\pi$
$212$	0.0541971	+	0.0230912i	0.00372227	+	0.00158591i
$213$	5.75992	−	8.34468i	0.394663	−	0.571768i
$214$	−3.23519	+	11.1692i	−0.221153	+	0.763510i
$215$	−13.9095	−	29.3137i	−0.948622	−	1.99918i
$216$	1.01099	−	2.66575i	0.0687889	−	0.181381i
$217$	−18.5395	−	22.7067i	−1.25854	−	1.54143i
$218$	−0.197838	−	4.90931i	−0.0133993	−	0.332500i
$219$	0.186850	+	4.63664i	0.0126262	+	0.313315i
$220$	0.624658	−	0.153964i	0.0421144	−	0.0103803i
$221$	0.921296	−	0.0429001i	0.0619730	−	0.00288577i
$222$	−5.67882	−	1.39970i	−0.381137	−	0.0939419i
$223$	3.75508	−	18.3936i	0.251459	−	1.23173i	−0.636309	−	0.771434i	$-0.719540\pi$
$223$	3.75508	−	18.3936i	0.251459	−	1.23173i	0.887768	−	0.460292i	$-0.152255\pi$
$224$	−0.675929	+	0.287987i	−0.0451624	+	0.0192419i
$225$	−5.90424	+	3.73361i	−0.393616	+	0.248908i
$226$	−6.06334	+	3.18229i	−0.403328	+	0.211683i
$227$	−4.23925	−	0.688945i	−0.281369	−	0.0457269i	0.0180892	−	0.999836i	$-0.494242\pi$
$227$	−4.23925	−	0.688945i	−0.281369	−	0.0457269i	−0.299458	+	0.954110i	$0.596806\pi$
$228$	0.0393270	−	0.0131293i	0.00260449	−	0.000869508i
$229$	−0.278244	−	2.29154i	−0.0183869	−	0.151429i	0.980624	−	0.195900i	$-0.0627629\pi$
$229$	−0.278244	−	2.29154i	−0.0183869	−	0.151429i	−0.999011	+	0.0444709i	$0.985840\pi$
$230$	9.08541	−	31.3665i	0.599074	−	2.06824i
$231$	−4.53661	+	22.2218i	−0.298487	+	1.46209i
$232$	−14.4790	−	4.83381i	−0.950594	−	0.317355i
$233$	−2.71121	−	1.42296i	−0.177618	−	0.0932209i	0.373571	−	0.927602i	$-0.378133\pi$
$233$	−2.71121	−	1.42296i	−0.177618	−	0.0932209i	−0.551189	+	0.834381i	$0.685826\pi$
$234$	1.95314	−	4.66488i	0.127681	−	0.304953i
$235$	−3.13080	+	1.64317i	−0.204231	+	0.107189i
$236$	0.167224	−	0.0271766i	0.0108854	−	0.00176904i
$237$	7.78213	−	5.84789i	0.505504	−	0.379862i
$238$	−0.0575227	+	1.42741i	−0.00372864	+	0.0925253i
$239$	−2.79520			−0.180806			−0.0904031	−	0.995905i	$-0.528816\pi$
$239$	−2.79520			−0.180806			−0.0904031	+	0.995905i	$0.528816\pi$
$240$	0.548365	−	13.6075i	0.0353968	−	0.878362i
$241$	−0.918931	−	4.50122i	−0.0591936	−	0.289949i	0.939409	−	0.342799i	$-0.111375\pi$
$241$	−0.918931	−	4.50122i	−0.0591936	−	0.289949i	−0.998603	+	0.0528493i	$0.983170\pi$
$242$	17.0885	+	24.7570i	1.09849	+	1.59144i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	0.0338098	−	0.0712527i	0.00216445	−	0.00456149i
$245$	−19.3848	+	23.7420i	−1.23845	+	1.51682i
$246$	5.16026	+	13.6065i	0.329006	+	0.867517i
$247$	4.39325	−	1.30236i	0.279536	−	0.0828671i
$248$	7.44320	−	19.6261i	0.472644	−	1.24626i
$249$	7.17731	+	12.4315i	0.454844	+	0.787813i
$250$	−6.09831	+	7.46908i	−0.385691	+	0.472386i
$251$	18.4872	+	13.8922i	1.16690	+	0.876870i	0.994141	−	0.108093i	$-0.0344745\pi$
$251$	18.4872	+	13.8922i	1.16690	+	0.876870i	0.172762	+	0.984964i	$0.444731\pi$
$252$	−0.115016	−	0.0603651i	−0.00724533	−	0.00380264i
$253$	−38.1821	+	3.08238i	−2.40049	+	0.193788i
$254$	−20.2239	+	1.63264i	−1.26896	+	0.102441i
$255$	0.784145	+	0.411551i	0.0491050	+	0.0257723i
$256$	−0.625769	−	0.470235i	−0.0391106	−	0.0293897i
$257$	14.0735	−	17.2369i	0.877881	−	1.07521i	−0.118728	−	0.992927i	$-0.537882\pi$
$257$	14.0735	−	17.2369i	0.877881	−	1.07521i	0.996609	−	0.0822825i	$-0.0262210\pi$
$258$	6.57277	+	11.3844i	0.409203	+	0.708760i
$259$	−5.88743	+	15.5239i	−0.365827	+	0.964606i
$260$	−0.0302287	+	0.406102i	−0.00187470	+	0.0251854i
$261$	−1.89858	−	5.00615i	−0.117519	−	0.309873i
$262$	−17.7233	+	21.7071i	−1.09495	+	1.34107i
$263$	−8.48586	+	17.8836i	−0.523261	+	1.10275i	0.454058	+	0.890972i	$0.349976\pi$
$263$	−8.48586	+	17.8836i	−0.523261	+	1.10275i	−0.977318	+	0.211776i	$0.932075\pi$
$264$	−15.4043	+	5.14270i	−0.948067	+	0.316511i
$265$	3.55137	+	5.14505i	0.218159	+	0.316058i
$266$	1.41969	+	6.95412i	0.0870470	+	0.426384i
$267$	0.558991	−	13.8712i	0.0342097	−	0.848906i
$268$	0.223006			0.0136222
$269$	−0.287374	+	7.13111i	−0.0175215	+	0.434792i	0.966492	+	0.256697i	$0.0826343\pi$
$269$	−0.287374	+	7.13111i	−0.0175215	+	0.434792i	−0.984013	+	0.178094i	$0.943007\pi$
$270$	3.88206	−	2.91718i	0.236255	−	0.177534i
$271$	25.7894	−	4.19119i	1.56660	−	0.254597i	0.685692	−	0.727892i	$-0.259500\pi$
$271$	25.7894	−	4.19119i	1.56660	−	0.254597i	0.880904	+	0.473296i	$0.156936\pi$
$272$	−0.890973	+	0.467619i	−0.0540232	+	0.0283536i
$273$	−12.4773	−	7.10007i	−0.755158	−	0.429716i
$274$	−19.8218	−	10.4033i	−1.19748	−	0.628485i
$275$	37.7441	+	12.6008i	2.27606	+	0.759859i
$276$	0.0438836	−	0.214956i	0.00264148	−	0.0129388i
$277$	3.50097	−	12.0868i	0.210353	−	0.726223i	−0.784062	−	0.620683i	$-0.786856\pi$
$277$	3.50097	−	12.0868i	0.210353	−	0.726223i	0.994415	−	0.105541i	$-0.0336573\pi$
$278$	0.720400	+	5.93302i	0.0432067	+	0.355839i
$279$	6.98343	−	2.33141i	0.418087	−	0.139578i
$280$	−38.7910	−	6.30416i	−2.31821	−	0.376746i
$281$	2.83906	−	1.49005i	0.169364	−	0.0888891i	−0.377911	−	0.925842i	$-0.623357\pi$
$281$	2.83906	−	1.49005i	0.169364	−	0.0888891i	0.547275	+	0.836953i	$0.315665\pi$
$282$	1.21075	−	0.765632i	0.0720991	−	0.0455927i
$283$	−23.5524	+	10.0347i	−1.40005	+	0.596504i	−0.954353	−	0.298682i	$-0.903453\pi$
$283$	−23.5524	+	10.0347i	−1.40005	+	0.596504i	−0.445693	+	0.895186i	$0.647043\pi$
$284$	0.0661662	−	0.324103i	0.00392624	−	0.0192320i
$285$	4.27199	+	1.05295i	0.253051	+	0.0623714i
$286$	−27.6192	+	8.18758i	−1.63316	+	0.484142i
$287$	40.1085	−	9.88585i	2.36753	−	0.583543i
$288$	−0.00743021	−	0.184379i	−0.000437829	−	0.0108646i
$289$	0.681886	+	16.9208i	0.0401110	+	0.995343i
$290$	−16.4431	−	20.1391i	−0.965570	−	1.18261i
$291$	−2.10396	+	5.54769i	−0.123336	+	0.325211i
$292$	0.0648983	+	0.136770i	0.00379789	+	0.00800387i
$293$	1.68747	−	5.82581i	0.0985828	−	0.340347i	−0.896032	−	0.443990i	$-0.853563\pi$
$293$	1.68747	−	5.82581i	0.0985828	−	0.340347i	0.994615	+	0.103643i	$0.0330498\pi$
$294$	7.05419	−	10.2198i	0.411409	−	0.596029i
$295$	16.5401	+	7.04707i	0.963001	+	0.410296i
$296$	−11.7344	+	1.90703i	−0.682048	+	0.110844i
$297$	−4.81438	−	3.04443i	−0.279359	−	0.176656i
$298$	−10.4379	−	15.1220i	−0.604653	−	0.875991i
$299$	5.65531	−	23.5782i	0.327055	−	1.36356i
$300$	−0.129461	+	0.187557i	−0.00747443	+	0.0108286i
$301$	34.3299	−	14.6266i	1.97874	−	0.843064i
$302$	6.97607	+	24.0842i	0.401428	+	1.38589i
$303$	6.81949	−	0.550526i	0.391769	−	0.0316269i
$304$	−3.74199	+	3.31512i	−0.214618	+	0.190135i
$305$	7.07378	−	4.47319i	0.405043	−	0.256134i
$306$	−0.330080	−	0.140634i	−0.0188694	−	0.00803951i
$307$	1.16677	−	9.60918i	0.0665909	−	0.548425i	−0.920790	−	0.390059i	$-0.872454\pi$
$307$	1.16677	−	9.60918i	0.0665909	−	0.548425i	0.987381	−	0.158366i	$-0.0506225\pi$
$308$	0.148001	+	0.724955i	0.00843312	+	0.0413081i
$309$	−4.20378	−	0.339364i	−0.239144	−	0.0193057i
$310$	28.5810	−	21.4772i	1.62329	−	1.21982i
$311$	−2.79616	+	23.0284i	−0.158556	+	1.30582i	0.668504	+	0.743709i	$0.266935\pi$
$311$	−2.79616	+	23.0284i	−0.158556	+	1.30582i	−0.827059	+	0.562114i	$0.809988\pi$
$312$	−0.0642929	−	10.2793i	−0.00363987	−	0.581951i
$313$	−1.19186	−	9.81583i	−0.0673678	−	0.554824i	−0.986844	−	0.161677i	$-0.948310\pi$
$313$	−1.19186	−	9.81583i	−0.0673678	−	0.554824i	0.919476	−	0.393146i	$-0.128613\pi$
$314$	10.6372	+	11.0745i	0.600294	+	0.624972i
$315$	−6.89226	−	11.9377i	−0.388335	−	0.672616i
$316$	0.158786	−	0.275026i	0.00893243	−	0.0154714i
$317$	28.3235	−	6.98113i	1.59081	−	0.392099i	0.658158	−	0.752880i	$-0.271336\pi$
$317$	28.3235	−	6.98113i	1.59081	−	0.392099i	0.932651	+	0.360781i	$0.117490\pi$
$318$	−1.60189	−	1.96196i	−0.0898296	−	0.110021i
$319$	−15.2490	+	26.4120i	−0.853778	+	1.47879i
$320$	−9.97617	−	26.3050i	−0.557685	−	1.47049i
$321$	−5.74292	+	5.97901i	−0.320538	+	0.333716i
$322$	35.6240	+	11.8930i	1.98525	+	0.662773i
$323$	−0.0904455	−	0.312254i	−0.00503252	−	0.0173743i
$324$	0.0244191	−	0.0216334i	0.00135662	−	0.00120186i
$325$	−15.0048	+	20.2300i	−0.832318	+	1.12216i
$326$	−14.5721	−	12.9097i	−0.807074	−	0.715005i
$327$	1.50167	−	3.16471i	0.0830426	−	0.175009i
$328$	20.4901	+	21.3325i	1.13138	+	1.17789i
$329$	−1.74326	−	3.67384i	−0.0961091	−	0.202546i
$330$	−26.8568	−	6.61961i	−1.47842	−	0.364398i
$331$	2.27045	−	2.36379i	0.124795	−	0.129926i	−0.655873	−	0.754871i	$-0.727699\pi$
$331$	2.27045	−	2.36379i	0.124795	−	0.129926i	0.780668	+	0.624946i	$0.214879\pi$
$332$	0.374379	+	0.281327i	0.0205467	+	0.0154398i
$333$	−3.12118	−	2.76512i	−0.171040	−	0.151528i
$334$	−20.0588	−	3.25988i	−1.09757	−	0.178372i
$335$	20.0019	+	12.6484i	1.09282	+	0.691056i
$336$	15.6117	+	1.26030i	0.851686	+	0.0687552i
$337$	3.54607			0.193167			0.0965833	−	0.995325i	$-0.469209\pi$
$337$	3.54607			0.193167			0.0965833	+	0.995325i	$0.469209\pi$
$338$	0.506259	−	18.2272i	0.0275369	−	0.991428i
$339$	−4.88204			−0.265156
$340$	0.0287972	+	0.00232475i	0.00156175	+	0.000126077i
$341$	−35.4450	−	22.4141i	−1.91945	−	1.21379i
$342$	−1.75950	−	0.285946i	−0.0951426	−	0.0154622i
$343$	−5.52340	−	4.89330i	−0.298235	−	0.264214i
$344$	21.3611	+	16.0518i	1.15171	+	0.865455i
$345$	16.1279	−	16.7909i	0.868295	−	0.903990i
$346$	10.0423	+	2.47520i	0.539876	+	0.133067i
$347$	−2.99169	−	6.30485i	−0.160602	−	0.338462i	0.807158	−	0.590336i	$-0.201005\pi$
$347$	−2.99169	−	6.30485i	−0.160602	−	0.338462i	−0.967760	+	0.251873i	$0.918953\pi$
$348$	−0.120998	−	0.125972i	−0.00648615	−	0.00675279i
$349$	−0.931478	+	1.96305i	−0.0498609	+	0.105080i	−0.926852	−	0.375427i	$-0.877496\pi$
$349$	−0.931478	+	1.96305i	−0.0498609	+	0.105080i	0.876991	+	0.480507i	$0.159547\pi$
$350$	−29.2019	−	25.8706i	−1.56091	−	1.38284i
$351$	2.77856	−	2.29774i	0.148309	−	0.122644i
$352$	−0.786769	+	0.697016i	−0.0419349	+	0.0371511i
$353$	−2.49783	−	8.62351i	−0.132946	−	0.458983i	0.866227	−	0.499651i	$-0.166539\pi$
$353$	−2.49783	−	8.62351i	−0.132946	−	0.458983i	−0.999173	+	0.0406681i	$0.987051\pi$
$354$	−6.90917	−	2.30662i	−0.367218	−	0.122595i
$355$	24.3170	−	25.3167i	1.29061	−	1.34367i
$356$	−0.160599	−	0.423466i	−0.00851175	−	0.0224436i
$357$	−0.509246	+	0.882040i	−0.0269522	+	0.0466825i
$358$	−5.18376	−	6.34896i	−0.273970	−	0.335553i
$359$	1.81073	−	0.446305i	0.0955667	−	0.0235551i	−0.191242	−	0.981543i	$-0.561252\pi$
$359$	1.81073	−	0.446305i	0.0955667	−	0.0235551i	0.286809	+	0.957988i	$0.407405\pi$
$360$	4.93517	−	8.54797i	0.260106	−	0.450517i
$361$	8.69243	+	15.0557i	0.457496	+	0.792407i
$362$	21.8097	+	22.7063i	1.14629	+	1.19342i
$363$	2.58513	+	21.2904i	0.135684	+	1.11746i
$364$	−0.465271	−	0.0535434i	−0.0243869	−	0.00280644i
$365$	−1.93645	+	15.9481i	−0.101358	+	0.834762i
$366$	−2.71080	+	2.03703i	−0.141696	+	0.106477i
$367$	−28.2336	−	2.27925i	−1.47378	−	0.118976i	−0.682705	−	0.730694i	$-0.739197\pi$
$367$	−28.2336	−	2.27925i	−1.47378	−	0.118976i	−0.791076	+	0.611718i	$0.790479\pi$
$368$	5.29140	+	25.9190i	0.275833	+	1.35112i
$369$	−1.25055	+	10.2992i	−0.0651012	+	0.536157i
$370$	−18.6283	−	7.93680i	−0.968442	−	0.412614i
$371$	−6.07688	+	3.84279i	−0.315496	+	0.199508i
$372$	0.179781	−	0.159272i	0.00932122	−	0.00825788i
$373$	−10.3654	+	0.836786i	−0.536703	+	0.0433271i	−0.345847	−	0.938291i	$-0.612408\pi$
$373$	−10.3654	+	0.836786i	−0.536703	+	0.0433271i	−0.190856	+	0.981618i	$0.561126\pi$
$374$	0.568607	+	1.96306i	0.0294019	+	0.101507i
$375$	−6.32443	+	2.69459i	−0.326592	+	0.139148i
$376$	1.65407	−	2.39634i	0.0853023	−	0.123582i
$377$	−12.8913	−	14.3692i	−0.663936	−	0.740051i
$378$	3.17250	+	4.59616i	0.163176	+	0.236401i
$379$	19.5372	+	12.3546i	1.00356	+	0.634611i	0.931861	−	0.362816i	$-0.118185\pi$
$379$	19.5372	+	12.3546i	1.00356	+	0.634611i	0.0716959	+	0.997427i	$0.477159\pi$
$380$	0.141680	−	0.0230252i	0.00726801	−	0.00118117i
$381$	−13.3079	−	5.66997i	−0.681785	−	0.290481i
$382$	17.4924	−	25.3421i	0.894990	−	1.29662i
$383$	−1.17667	+	4.06235i	−0.0601252	+	0.207576i	−0.984957	−	0.172800i	$-0.944718\pi$
$383$	−1.17667	+	4.06235i	−0.0601252	+	0.207576i	0.924832	+	0.380377i	$0.124206\pi$
$384$	4.72806	+	9.96417i	0.241278	+	0.508482i
$385$	−27.8434	+	73.4170i	−1.41903	+	3.74168i
$386$	8.21309	+	10.0592i	0.418035	+	0.512000i
$387$	0.377375	+	9.36446i	0.0191830	+	0.476022i
$388$	0.00779404	+	0.193407i	0.000395682	+	0.00981876i
$389$	−23.1847	+	5.71450i	−1.17551	+	0.289737i	−0.778241	−	0.627966i	$-0.783888\pi$
$389$	−23.1847	+	5.71450i	−1.17551	+	0.289737i	−0.397268	+	0.917703i	$0.630042\pi$
$390$	9.26492	−	14.8562i	0.469147	−	0.752272i
$391$	−1.67023	−	0.411674i	−0.0844670	−	0.0208192i
$392$	5.04885	−	24.7309i	0.255005	−	1.24910i
$393$	−18.3805	+	7.83119i	−0.927172	+	0.395031i
$394$	11.7270	−	7.41574i	0.590800	−	0.373599i
$395$	29.8408	−	15.6616i	1.50145	−	0.788022i
$396$	−0.183424	−	0.0298094i	−0.00921742	−	0.00149798i
$397$	−2.39581	+	0.799840i	−0.120242	+	0.0401428i	−0.376152	−	0.926558i	$-0.622753\pi$
$397$	−2.39581	+	0.799840i	−0.120242	+	0.0401428i	0.255910	+	0.966701i	$0.417625\pi$
$398$	−0.695810	−	5.73051i	−0.0348778	−	0.287244i
$399$	−1.40783	+	4.86038i	−0.0704795	+	0.243324i
$400$	5.49661	−	26.9242i	0.274831	−	1.34621i
$401$	9.09658	+	3.03688i	0.454261	+	0.151655i	0.534586	−	0.845114i	$-0.320468\pi$
$401$	9.09658	+	3.03688i	0.454261	+	0.151655i	−0.0803247	+	0.996769i	$0.525596\pi$
$402$	−8.48976	−	4.45577i	−0.423431	−	0.222233i
$403$	20.4566	−	16.9167i	1.01902	−	0.842680i
$404$	0.197634	−	0.103726i	0.00983264	−	0.00516057i
$405$	3.41720	−	0.555350i	0.169802	−	0.0275955i
$406$	23.9043	−	17.9629i	1.18635	−	0.891483i
$407$	−0.956412	+	23.7331i	−0.0474076	+	1.17641i
$408$	−0.729287			−0.0361051
$409$	−0.389311	+	9.66064i	−0.0192502	+	0.477688i	0.960598	+	0.277943i	$0.0896525\pi$
$409$	−0.389311	+	9.66064i	−0.0192502	+	0.477688i	−0.979848	+	0.199745i	$0.935988\pi$
$410$	10.0773	+	49.3619i	0.497682	+	2.43781i
$411$	−9.06630	−	13.1348i	−0.447207	−	0.647892i
$412$	−0.130508	+	0.0435698i	−0.00642965	+	0.00214653i
$413$	−8.86408	+	18.6807i	−0.436173	+	0.919215i
$414$	−5.96556	+	7.30649i	−0.293191	+	0.359094i
$415$	17.6225	+	46.4668i	0.865056	+	2.28096i
$416$	−0.264609	−	0.610444i	−0.0129735	−	0.0299295i
$417$	−1.51097	+	3.98409i	−0.0739924	+	0.195102i
$418$	5.07697	+	8.79358i	0.248323	+	0.430108i
$419$	4.38548	−	5.37124i	0.214245	−	0.262402i	−0.656290	−	0.754508i	$-0.727875\pi$
$419$	4.38548	−	5.37124i	0.214245	−	0.262402i	0.870535	+	0.492106i	$0.163773\pi$
$420$	−0.359510	−	0.270154i	−0.0175423	−	0.0131822i
$421$	4.59271	+	2.41044i	0.223835	+	0.117478i	0.572913	−	0.819616i	$-0.305813\pi$
$421$	4.59271	+	2.41044i	0.223835	+	0.117478i	−0.349079	+	0.937093i	$0.613505\pi$
$422$	3.96264	−	0.319897i	0.192898	−	0.0155724i
$423$	1.01800	−	0.0821811i	0.0494966	−	0.00399578i
$424$	−4.55863	−	2.39255i	−0.221387	−	0.116193i
$425$	1.42855	+	1.07348i	0.0692947	+	0.0520716i
$426$	−8.99467	+	11.0165i	−0.435793	+	0.533750i
$427$	4.81278	+	8.33597i	0.232907	+	0.403406i
$428$	−0.0959066	+	0.252885i	−0.00463582	+	0.0122237i
$429$	−20.1482	−	3.98219i	−0.972765	−	0.192262i
$430$	16.1382	+	42.5529i	0.778253	+	2.05208i
$431$	1.39169	−	1.70451i	0.0670351	−	0.0821031i	−0.739999	−	0.672608i	$-0.765174\pi$
$431$	1.39169	−	1.70451i	0.0670351	−	0.0821031i	0.807034	+	0.590505i	$0.201071\pi$
$432$	−1.68634	+	3.55389i	−0.0811342	+	0.170987i
$433$	3.27945	−	1.09484i	0.157600	−	0.0526147i	−0.236773	−	0.971565i	$-0.576090\pi$
$433$	3.27945	−	1.09484i	0.157600	−	0.0526147i	0.394373	+	0.918950i	$0.370962\pi$
$434$	23.3569	+	33.8384i	1.12117	+	1.62429i
$435$	−3.70767	−	18.1614i	−0.177769	−	0.870772i
$436$	0.00460149	−	0.114185i	0.000220371	−	0.00546846i
$437$	−8.54653			−0.408836
$438$	0.262082	−	6.50350i	0.0125228	−	0.310749i
$439$	24.9350	−	18.7374i	1.19008	−	0.894288i	0.193851	−	0.981031i	$-0.437902\pi$
$439$	24.9350	−	18.7374i	1.19008	−	0.894288i	0.996231	+	0.0867429i	$0.0276459\pi$
$440$	−55.4955	+	9.01889i	−2.64564	+	0.429959i
$441$	7.83922	−	4.11434i	0.373296	−	0.195921i
$442$	−1.29289	−	0.0440041i	−0.0614965	−	0.00209306i
$443$	−6.19890	−	3.25343i	−0.294518	−	0.154575i	0.310992	−	0.950412i	$-0.399339\pi$
$443$	−6.19890	−	3.25343i	−0.294518	−	0.154575i	−0.605511	+	0.795837i	$0.707031\pi$
$444$	−0.129035	−	0.0430781i	−0.00612372	−	0.00204440i
$445$	9.61357	−	47.0904i	0.455727	−	2.23230i
$446$	−7.32591	+	25.2920i	−0.346892	+	1.19761i
$447$	−1.57904	−	13.0045i	−0.0746859	−	0.615093i
$448$	30.6903	−	10.2459i	1.44998	−	0.484075i
$449$	24.9647	+	4.05715i	1.17815	+	0.191469i	0.717789	−	0.696260i	$-0.245154\pi$
$449$	24.9647	+	4.05715i	1.17815	+	0.191469i	0.460366	+	0.887729i	$0.347718\pi$
$450$	8.67601	−	4.55352i	0.408991	−	0.214655i
$451$	49.9486	−	31.5856i	2.35199	−	1.48731i
$452$	−0.146525	+	0.0624284i	−0.00689195	+	0.00293638i
$453$	−3.57576	+	17.5152i	−0.168004	+	0.822938i
$454$	5.84906	+	1.44166i	0.274510	+	0.0676607i
$455$	−38.6943	−	31.1916i	−1.81402	−	1.46229i
$456$	−3.51803	+	0.867115i	−0.164747	+	0.0406064i
$457$	0.465079	+	11.5408i	0.0217555	+	0.539856i	0.972916	+	0.231159i	$0.0742518\pi$
$457$	0.465079	+	11.5408i	0.0217555	+	0.539856i	−0.951160	+	0.308697i	$0.900107\pi$
$458$	0.130373	+	3.23517i	0.00609193	+	0.151170i
$459$	−0.161778	−	0.198143i	−0.00755117	−	0.00924851i
$460$	0.269335	−	0.710178i	0.0125578	−	0.0331122i
$461$	−4.27652	−	9.01257i	−0.199177	−	0.419757i	0.779146	−	0.626843i	$-0.215653\pi$
$461$	−4.27652	−	9.01257i	−0.199177	−	0.419757i	−0.978323	+	0.207086i	$0.933602\pi$
$462$	8.85063	−	30.5559i	0.411769	−	1.42159i
$463$	12.4789	−	18.0787i	0.579941	−	0.840190i	−0.417717	−	0.908577i	$-0.637170\pi$
$463$	12.4789	−	18.0787i	0.579941	−	0.840190i	0.997659	+	0.0683868i	$0.0217852\pi$
$464$	19.3759	+	8.25531i	0.899505	+	0.383243i
$465$	25.1585	−	4.08866i	1.16670	−	0.189607i
$466$	3.62990	+	2.29541i	0.168152	+	0.106333i
$467$	−18.9944	−	27.5181i	−0.878954	−	1.27338i	−0.960942	−	0.276752i	$-0.910742\pi$
$467$	−18.9944	−	27.5181i	−0.878954	−	1.27338i	0.0819874	−	0.996633i	$-0.473873\pi$
$468$	0.0540110	−	0.104493i	0.00249666	−	0.00483017i
$469$	−15.4612	+	22.3994i	−0.713930	+	1.03431i
$470$	4.56257	−	1.94393i	0.210456	−	0.0896668i
$471$	3.04585	+	10.5155i	0.140346	+	0.484529i
$472$	−14.7577	+	1.19136i	−0.679277	+	0.0548369i
$473$	39.9594	−	35.4009i	1.83734	−	1.62774i
$474$	−11.5401	+	7.29751i	−0.530054	+	0.335186i
$475$	8.16756	+	3.47987i	0.374754	+	0.159668i
$476$	−0.00400506	+	0.0329846i	−0.000183571	+	0.00151185i
$477$	−0.361204	−	1.76929i	−0.0165384	−	0.0810104i
$478$	3.90792	+	0.315480i	0.178744	+	0.0144297i
$479$	−7.78865	+	5.85279i	−0.355872	+	0.267421i	−0.763609	−	0.645679i	$-0.776575\pi$
$479$	−7.78865	+	5.85279i	−0.355872	+	0.267421i	0.407737	+	0.913100i	$0.366318\pi$
$480$	0.0770041	−	0.634186i	0.00351474	−	0.0289465i
$481$	−14.0907	−	5.24332i	−0.642480	−	0.239075i
$482$	0.776712	+	6.39680i	0.0353783	+	0.291366i
$483$	18.5483	+	19.3109i	0.843979	+	0.878675i
$484$	0.349836	+	0.605934i	0.0159016	+	0.0275424i
$485$	−10.2706	+	17.7892i	−0.466363	+	0.807764i
$486$	−1.36187	+	0.335672i	−0.0617759	+	0.0152264i
$487$	18.3179	+	22.4353i	0.830063	+	1.01664i	0.999516	+	0.0311043i	$0.00990242\pi$
$487$	18.3179	+	22.4353i	0.830063	+	1.01664i	−0.169453	+	0.985538i	$0.554200\pi$
$488$	−3.44617	+	5.96894i	−0.156001	+	0.270201i
$489$	−4.92181	−	12.9777i	−0.222572	−	0.586874i
$490$	29.7811	−	31.0055i	1.34538	−	1.40068i
$491$	−18.2651	−	6.09779i	−0.824292	−	0.275189i	−0.126933	−	0.991911i	$-0.540513\pi$
$491$	−18.2651	−	6.09779i	−0.824292	−	0.275189i	−0.697359	+	0.716722i	$0.745642\pi$
$492$	0.0941670	+	0.325102i	0.00424538	+	0.0146567i
$493$	−1.02513	+	0.908188i	−0.0461696	+	0.0409027i
$494$	−6.28913	+	1.32496i	−0.282961	+	0.0596129i
$495$	−14.7610	−	13.0771i	−0.663457	−	0.587772i
$496$	−12.4154	+	26.1649i	−0.557468	+	1.17484i
$497$	27.9666	+	29.1163i	1.25447	+	1.30604i
$498$	−8.63141	−	18.1903i	−0.386783	−	0.815127i
$499$	23.8312	+	5.87388i	1.06683	+	0.262951i	0.733382	−	0.679817i	$-0.237941\pi$
$499$	23.8312	+	5.87388i	1.06683	+	0.262951i	0.333451	+	0.942767i	$0.391787\pi$
$500$	−0.155359	+	0.161745i	−0.00694785	+	0.00723347i
$501$	−11.5827	−	8.70383i	−0.517477	−	0.388859i
$502$	−24.2787	−	21.5091i	−1.08361	−	0.959997i
$503$	26.4013	+	4.29063i	1.17718	+	0.191310i	0.717359	−	0.696704i	$-0.245351\pi$
$503$	26.4013	+	4.29063i	1.17718	+	0.191310i	0.459818	+	0.888013i	$0.347915\pi$
$504$	9.59434	+	6.06709i	0.427366	+	0.270250i
$505$	23.6093	+	1.90594i	1.05060	+	0.0848132i
$506$	53.7297			2.38858
$507$	6.35866	−	11.3388i	0.282398	−	0.503572i
$508$	−0.471914			−0.0209378
$509$	−0.752296	−	0.0607316i	−0.0333449	−	0.00269188i	0.0637828	−	0.997964i	$-0.479683\pi$
$509$	−0.752296	−	0.0607316i	−0.0333449	−	0.00269188i	−0.0971278	+	0.995272i	$0.530966\pi$
$510$	−1.04985	−	0.663885i	−0.0464881	−	0.0293973i
$511$	−18.2371	−	2.96381i	−0.806760	−	0.131111i
$512$	17.3325	+	15.3552i	0.765994	+	0.678612i
$513$	−1.01600	−	0.763472i	−0.0448574	−	0.0337081i
$514$	−21.6214	+	22.5102i	−0.953678	+	0.992884i
$515$	−14.1767	−	3.49424i	−0.624700	−	0.153975i
$516$	0.131073	+	0.276230i	0.00577016	+	0.0121603i
$517$	−4.02998	−	4.19565i	−0.177238	−	0.184525i
$518$	9.98322	−	21.0392i	0.438637	−	0.924409i
$519$	5.51941	+	4.88977i	0.242275	+	0.214637i
$520$	5.48891	−	35.1622i	0.240705	−	1.54196i
$521$	17.9729	−	15.9226i	0.787409	−	0.697584i	−0.170278	−	0.985396i	$-0.554466\pi$
$521$	17.9729	−	15.9226i	0.787409	−	0.697584i	0.957687	+	0.287813i	$0.0929280\pi$
$522$	2.08936	+	7.21329i	0.0914486	+	0.315717i
$523$	−32.6184	−	10.8896i	−1.42630	−	0.476170i	−0.504360	−	0.863493i	$-0.668272\pi$
$523$	−32.6184	−	10.8896i	−1.42630	−	0.476170i	−0.921944	+	0.387323i	$0.873400\pi$
$524$	−0.451513	+	0.470075i	−0.0197245	+	0.0205353i
$525$	−9.86311	−	26.0069i	−0.430462	−	1.13503i
$526$	13.8824	−	24.0450i	0.605300	−	1.04841i
$527$	−1.19106	−	1.45879i	−0.0518836	−	0.0635458i
$528$	21.7560	−	5.36237i	0.946809	−	0.233367i
$529$	−11.1120	+	19.2466i	−0.483131	+	0.836808i
$530$	−4.38442	−	7.59403i	−0.190447	−	0.329864i
$531$	−3.59740	−	3.74529i	−0.156114	−	0.162532i
$532$	0.0198983	+	0.163877i	0.000862701	+	0.00710498i
$533$	9.17910	+	36.2635i	0.397591	+	1.57074i
$534$	−2.34709	+	19.3300i	−0.101569	+	0.836493i
$535$	−22.9452	+	17.2422i	−0.992006	+	0.745444i
$536$	−19.4256	−	1.56820i	−0.839058	−	0.0677358i
$537$	−1.16886	−	5.72548i	−0.0504402	−	0.247073i
$538$	1.20663	−	9.93746i	0.0520213	−	0.428434i
$539$	−46.3949	−	19.7670i	−1.99837	−	0.851425i
$540$	0.0954592	−	0.0603647i	0.00410791	−	0.00259768i
$541$	6.36634	−	5.64009i	0.273710	−	0.242486i	−0.515089	−	0.857136i	$-0.672241\pi$
$541$	6.36634	−	5.64009i	0.273710	−	0.242486i	0.788800	+	0.614650i	$0.210703\pi$
$542$	−36.5288	+	2.94891i	−1.56905	+	0.126667i
$543$	6.24497	+	21.5601i	0.267997	+	0.925234i
$544$	−0.0434249	+	0.0185016i	−0.00186183	+	0.000793250i
$545$	6.88903	−	9.98049i	0.295094	−	0.427517i
$546$	16.6429	+	11.3347i	0.712251	+	0.485082i
$547$	14.4836	+	20.9832i	0.619275	+	0.897175i	0.999617	−	0.0276709i	$-0.00880905\pi$
$547$	14.4836	+	20.9832i	0.619275	+	0.897175i	−0.380342	+	0.924846i	$0.624194\pi$
$548$	−0.440066	−	0.278281i	−0.0187987	−	0.0118876i
$549$	−2.38619	+	0.387793i	−0.101840	+	0.0165506i
$550$	−51.3473	−	21.8770i	−2.18945	−	0.932839i
$551$	−3.86534	+	5.59991i	−0.164669	+	0.238564i
$552$	−5.33421	+	18.4158i	−0.227039	+	0.783829i
$553$	16.6156	+	35.0167i	0.706569	+	1.48906i
$554$	−6.25883	+	16.5032i	−0.265912	+	0.701153i
$555$	−9.13010	−	11.1823i	−0.387551	−	0.474664i
$556$	0.00559732	+	0.138896i	0.000237379	+	0.00589050i
$557$	−1.31047	−	32.5191i	−0.0555266	−	1.37788i	−0.751463	−	0.659775i	$-0.770652\pi$
$557$	−1.31047	−	32.5191i	−0.0555266	−	1.37788i	0.695937	−	0.718103i	$-0.254989\pi$
$558$	−10.0265	+	2.47132i	−0.424458	+	0.104619i
$559$	13.4393	+	31.0040i	0.568421	+	1.31133i
$560$	52.6483	+	12.9767i	2.22480	+	0.548364i
$561$	−0.291454	+	1.42763i	−0.0123052	+	0.0602748i
$562$	−4.13741	+	1.76279i	−0.174526	+	0.0743587i
$563$	27.0546	−	17.1083i	1.14022	−	0.721030i	0.175542	−	0.984472i	$-0.443832\pi$
$563$	27.0546	−	17.1083i	1.14022	−	0.721030i	0.964675	+	0.263442i	$0.0848578\pi$
$564$	0.0295022	−	0.0154840i	0.00124227	−	0.000651993i
$565$	−16.6829	−	2.71124i	−0.701856	−	0.114063i
$566$	34.0608	−	11.3712i	1.43168	−	0.477966i
$567$	0.479931	+	3.95259i	0.0201552	+	0.165993i
$568$	−8.04273	+	27.7667i	−0.337466	+	1.16507i
$569$	4.44226	−	21.7596i	0.186229	−	0.912211i	−0.774040	−	0.633137i	$-0.781767\pi$
$569$	4.44226	−	21.7596i	0.186229	−	0.912211i	0.960269	−	0.279075i	$-0.0900277\pi$
$570$	−5.85375	−	1.95427i	−0.245187	−	0.0818554i
$571$	19.8935	+	10.4409i	0.832518	+	0.436939i	0.826428	−	0.563042i	$-0.190369\pi$
$571$	19.8935	+	10.4409i	0.832518	+	0.436939i	0.00608997	+	0.999981i	$0.498061\pi$
$572$	−0.655631	+	0.138125i	−0.0274133	+	0.00577530i
$573$	19.4391	−	10.2024i	0.812078	−	0.426212i
$574$	−57.1908	+	9.29440i	−2.38710	+	0.387941i
$575$	37.5562	−	28.2216i	1.56620	−	1.17692i
$576$	−0.327209	+	8.11961i	−0.0136337	+	0.338317i
$577$	18.5398			0.771823			0.385912	−	0.922536i	$-0.373887\pi$
$577$	18.5398			0.771823			0.385912	+	0.922536i	$0.373887\pi$
$578$	0.956435	−	23.7337i	0.0397825	−	0.987192i
$579$	1.85194	+	9.07138i	0.0769638	+	0.376994i
$580$	−0.343515	−	0.497667i	−0.0142637	−	0.0206645i
$581$	−54.2133	+	18.0991i	−2.24915	+	0.750876i
$582$	3.56766	−	7.51867i	0.147884	−	0.311659i
$583$	−6.50542	+	7.96770i	−0.269427	+	0.329988i
$584$	−4.69139	−	12.3702i	−0.194131	−	0.511881i
$585$	10.7710	−	6.30876i	0.445324	−	0.260835i
$586$	−3.01675	+	7.95451i	−0.124621	+	0.328598i
$587$	−18.3775	−	31.8307i	−0.758520	−	1.31379i	−0.943605	−	0.331073i	$-0.892590\pi$
$587$	−18.3775	−	31.8307i	−0.758520	−	1.31379i	0.185085	−	0.982722i	$-0.440744\pi$
$588$	0.182667	−	0.223727i	0.00753307	−	0.00922633i
$589$	−7.48009	−	5.62093i	−0.308212	−	0.231606i
$590$	−22.3290	−	11.7192i	−0.919272	−	0.482471i
$591$	9.86007	−	0.795987i	0.405589	−	0.0327425i
$592$	16.3497	−	1.31989i	0.671969	−	0.0542470i
$593$	−5.29771	−	2.78045i	−0.217551	−	0.114179i	0.352428	−	0.935839i	$-0.385356\pi$
$593$	−5.29771	−	2.78045i	−0.217551	−	0.114179i	−0.569979	+	0.821660i	$0.693049\pi$
$594$	6.38730	+	4.79974i	0.262074	+	0.196936i
$595$	−2.23004	+	2.73130i	−0.0914226	+	0.111972i
$596$	−0.213685	−	0.370114i	−0.00875289	−	0.0151604i
$597$	1.45939	−	3.84810i	0.0597290	−	0.157492i
$598$	−10.5677	+	32.3260i	−0.432147	+	1.32191i
$599$	−8.98561	−	23.6931i	−0.367142	−	0.968074i	−0.983548	−	0.180646i	$-0.942181\pi$
$599$	−8.98561	−	23.6931i	−0.367142	−	0.968074i	0.616406	−	0.787429i	$-0.288588\pi$
$600$	12.5960	−	15.4273i	0.514230	−	0.629817i
$601$	8.11469	−	17.1014i	0.331005	−	0.697579i	−0.667905	−	0.744246i	$-0.732809\pi$
$601$	8.11469	−	17.1014i	0.331005	−	0.697579i	0.998910	+	0.0466676i	$0.0148602\pi$
$602$	−49.6470	+	16.5746i	−2.02346	+	0.675530i
$603$	−3.88313	−	5.62569i	−0.158133	−	0.229096i
$604$	0.116654	+	0.571410i	0.00474659	+	0.0232503i
$605$	−2.98973	+	74.1894i	−0.121550	+	3.01623i
$606$	−9.59635			−0.389825
$607$	1.05570	−	26.1969i	0.0428496	−	1.06330i	−0.824581	−	0.565743i	$-0.808589\pi$
$607$	1.05570	−	26.1969i	0.0428496	−	1.06330i	0.867431	−	0.497557i	$-0.165770\pi$
$608$	−0.187480	+	0.140882i	−0.00760333	+	0.00571353i
$609$	21.0418	−	3.41963i	0.852658	−	0.138570i
$610$	−10.3946	+	5.45551i	−0.420865	+	0.220887i
$611$	3.31690	−	1.59938i	0.134188	−	0.0647041i
$612$	−0.00738918	−	0.00387814i	−0.000298690	−	0.000156765i
$613$	−29.7719	−	9.93932i	−1.20248	−	0.401445i	−0.356311	−	0.934367i	$-0.615966\pi$
$613$	−29.7719	−	9.93932i	−1.20248	−	0.401445i	−0.846164	+	0.532922i	$0.821094\pi$
$614$	−2.71578	+	13.3028i	−0.109600	+	0.536856i
$615$	−9.99307	+	34.5001i	−0.402959	+	1.39118i
$616$	−7.79410	−	64.1902i	−0.314033	−	2.58630i
$617$	−39.5453	+	13.2022i	−1.59203	+	0.531499i	−0.968225	−	0.250079i	$-0.919543\pi$
$617$	−39.5453	+	13.2022i	−1.59203	+	0.531499i	−0.623808	+	0.781578i	$0.714415\pi$
$618$	5.83893	+	0.948918i	0.234876	+	0.0381711i
$619$	−30.9988	+	16.2694i	−1.24595	+	0.653924i	−0.953222	−	0.302272i	$-0.902255\pi$
$619$	−30.9988	+	16.2694i	−1.24595	+	0.653924i	−0.292727	+	0.956196i	$0.594563\pi$
$620$	0.702801	−	0.444424i	0.0282252	−	0.0178485i
$621$	−6.18675	+	2.63593i	−0.248266	+	0.105776i
$622$	6.50837	−	31.8801i	0.260962	−	1.27828i
$623$	53.6686	+	13.2281i	2.15019	+	0.529974i
$624$	−1.05282	+	14.1440i	−0.0421467	+	0.566213i
$625$	10.8052	−	2.66324i	0.432208	−	0.106530i
$626$	0.558453	+	13.8579i	0.0223203	+	0.553872i
$627$	0.291494	+	7.23334i	0.0116411	+	0.288872i
$628$	0.225881	+	0.276654i	0.00901363	+	0.0110397i
$629$	−0.378236	+	0.997327i	−0.0150813	+	0.0397660i
$630$	8.28860	+	17.4679i	0.330226	+	0.695936i
$631$	2.22289	−	7.67430i	0.0884917	−	0.305509i	−0.904048	−	0.427431i	$-0.859419\pi$
$631$	2.22289	−	7.67430i	0.0884917	−	0.305509i	0.992540	+	0.121922i	$0.0389058\pi$
$632$	−15.7656	+	22.8404i	−0.627121	+	0.908542i
$633$	2.60753	+	1.11097i	0.103640	+	0.0441569i
$634$	−40.3866	+	6.56346i	−1.60396	+	0.260668i
$635$	−42.3270	−	26.7660i	−1.67970	−	1.06218i
$636$	−0.0334654	−	0.0484830i	−0.00132699	−	0.00192248i
$637$	21.0177	−	24.0252i	0.832753	−	0.951913i
$638$	24.3003	−	35.2051i	0.962059	−	1.39378i
$639$	−9.32817	+	3.97436i	−0.369017	+	0.157223i
$640$	10.6231	+	36.6753i	0.419916	+	1.44972i
$641$	45.6692	−	3.68680i	1.80383	−	0.145620i	0.867656	−	0.497165i	$-0.165626\pi$
$641$	45.6692	−	3.68680i	1.80383	−	0.145620i	0.936171	+	0.351546i	$0.114344\pi$
$642$	8.70390	−	7.71098i	0.343516	−	0.304328i
$643$	26.3578	−	16.6677i	1.03945	−	0.657309i	0.0982524	−	0.995162i	$-0.468675\pi$
$643$	26.3578	−	16.6677i	1.03945	−	0.657309i	0.941199	+	0.337852i	$0.109700\pi$
$644$	0.803627	+	0.342393i	0.0316673	+	0.0134922i
$645$	−3.91098	+	32.2098i	−0.153995	+	1.26826i
$646$	0.0912079	+	0.446766i	0.00358853	+	0.0175778i
$647$	−43.8873	−	3.54295i	−1.72539	−	0.139288i	−0.822388	−	0.568927i	$-0.807359\pi$
$647$	−43.8873	−	3.54295i	−1.72539	−	0.139288i	−0.903001	+	0.429639i	$0.858641\pi$
$648$	−2.27923	+	1.71273i	−0.0895366	+	0.0672824i
$649$	−3.56560	+	29.3654i	−0.139962	+	1.15269i
$650$	23.2613	−	26.5897i	0.912381	−	1.04294i
$651$	3.53341	+	29.1002i	0.138485	+	1.14053i
$652$	−0.313670	−	0.326565i	−0.0122842	−	0.0127893i
$653$	19.0484	+	32.9927i	0.745420	+	1.29110i	0.949998	+	0.312255i	$0.101084\pi$
$653$	19.0484	+	32.9927i	0.745420	+	1.29110i	−0.204579	+	0.978850i	$0.565582\pi$
$654$	−2.45665	+	4.25504i	−0.0960625	+	0.166385i
$655$	−67.1589	+	16.5532i	−2.62411	+	0.646786i
$656$	−25.8111	−	31.6128i	−1.00775	−	1.23427i
$657$	2.32020	−	4.01871i	0.0905197	−	0.156785i
$658$	2.02258	+	5.33309i	0.0788482	+	0.207906i
$659$	−9.15694	+	9.53338i	−0.356704	+	0.371368i	−0.875241	−	0.483687i	$-0.839297\pi$
$659$	−9.15694	+	9.53338i	−0.356704	+	0.371368i	0.518537	+	0.855055i	$0.326477\pi$
$660$	−0.610244	−	0.203729i	−0.0237537	−	0.00793015i
$661$	−3.73599	−	12.8981i	−0.145313	−	0.501679i	0.854530	−	0.519402i	$-0.173845\pi$
$661$	−3.73599	−	12.8981i	−0.145313	−	0.501679i	−0.999843	+	0.0177231i	$0.994358\pi$
$662$	−3.44107	+	3.04852i	−0.133741	+	0.118484i
$663$	−0.801599	−	0.456142i	−0.0311315	−	0.0177151i
$664$	−30.6331	−	27.1385i	−1.18879	−	1.05318i
$665$	−7.51005	+	15.8271i	−0.291227	+	0.613748i
$666$	4.05159	+	4.21815i	0.156996	+	0.163450i
$667$	15.4353	+	32.5292i	0.597657	+	1.25954i
$668$	−0.458931	−	0.113116i	−0.0177566	−	0.00437660i
$669$	−13.0045	+	13.5391i	−0.502783	+	0.523453i
$670$	−26.5367	−	19.9410i	−1.02520	−	0.770390i
$671$	10.3074	+	9.13157i	0.397913	+	0.352520i
$672$	0.725208	+	0.117858i	0.0279755	+	0.00454646i
$673$	0.168220	+	0.106376i	0.00648440	+	0.00410049i	0.537704	−	0.843134i	$-0.319292\pi$
$673$	0.168220	+	0.106376i	0.00648440	+	0.00410049i	−0.531220	+	0.847234i	$0.678266\pi$
$674$	−4.95770	−	0.400227i	−0.190964	−	0.0154162i
$675$	6.98569			0.268879
$676$	0.0458501	−	0.421621i	0.00176346	−	0.0162162i
$677$	18.8906			0.726025			0.363013	−	0.931784i	$-0.381748\pi$
$677$	18.8906			0.726025			0.363013	+	0.931784i	$0.381748\pi$
$678$	6.82550	+	0.551011i	0.262132	+	0.0211615i
$679$	−19.9668	−	12.6262i	−0.766254	−	0.484550i
$680$	−2.49212	−	0.405009i	−0.0955685	−	0.0155314i
$681$	3.21475	+	2.84802i	0.123190	+	0.109136i
$682$	47.0253	+	35.3372i	1.80069	+	1.35313i
$683$	25.7703	−	26.8297i	0.986073	−	1.02661i	−0.0135708	−	0.999908i	$-0.504320\pi$
$683$	25.7703	−	26.8297i	0.986073	−	1.02661i	0.999643	−	0.0267024i	$-0.00850065\pi$
$684$	−0.0402559	−	0.00992220i	−0.00153922	−	0.000379385i
$685$	−23.6870	−	49.9192i	−0.905033	−	1.90732i
$686$	7.16989	+	7.46465i	0.273748	+	0.285002i
$687$	−0.989582	+	2.08550i	−0.0377549	+	0.0795668i
$688$	−27.5952	−	24.4472i	−1.05206	−	0.932040i
$689$	−3.51418	−	5.48104i	−0.133880	−	0.208811i
$690$	−24.4432	+	21.6548i	−0.930537	+	0.824383i
$691$	0.0601623	+	0.207704i	0.00228868	+	0.00790145i	0.961654	−	0.274264i	$-0.0884343\pi$
$691$	0.0601623	+	0.207704i	0.00228868	+	0.00790145i	−0.959366	+	0.282166i	$0.908947\pi$
$692$	0.228182	+	0.0761782i	0.00867416	+	0.00289586i
$693$	15.7111	−	16.3570i	0.596815	−	0.621350i
$694$	3.47104	+	9.15237i	0.131759	+	0.347419i
$695$	−7.37585	+	12.7753i	−0.279782	+	0.484596i
$696$	9.65402	+	11.8240i	0.365935	+	0.448188i
$697$	2.57676	−	0.635114i	0.0976017	−	0.0240567i
$698$	1.52384	−	2.63937i	0.0576783	−	0.0999018i
$699$	1.53097	+	2.65172i	0.0579066	+	0.100297i
$700$	−0.628581	−	0.654422i	−0.0237581	−	0.0247348i
$701$	−5.97828	−	49.2355i	−0.225796	−	1.85960i	−0.460666	−	0.887574i	$-0.652389\pi$
$701$	−5.97828	−	49.2355i	−0.225796	−	1.85960i	0.234869	−	0.972027i	$-0.424534\pi$
$702$	−4.14400	+	2.89883i	−0.156405	+	0.109409i
$703$	−0.638771	+	5.26075i	−0.0240917	+	0.198413i
$704$	37.0051	−	27.8075i	1.39468	−	1.04803i
$705$	3.52434	+	0.284514i	0.132734	+	0.0107154i
$706$	2.51888	+	12.3383i	0.0947995	+	0.464358i
$707$	−3.28353	+	27.0423i	−0.123490	+	1.01703i
$708$	−0.155861	−	0.0664062i	−0.00585762	−	0.00249570i
$709$	17.8035	−	11.2583i	0.668625	−	0.422813i	−0.156565	−	0.987668i	$-0.550042\pi$
$709$	17.8035	−	11.2583i	0.668625	−	0.422813i	0.825191	+	0.564855i	$0.191068\pi$
$710$	−36.8546	+	32.6503i	−1.38313	+	1.22535i
$711$	−9.70288	+	0.783298i	−0.363886	+	0.0293760i
$712$	11.0117	+	38.0166i	0.412679	+	1.42473i
$713$	−45.5488	+	19.4065i	−1.70582	+	0.726781i
$714$	0.811520	−	1.17569i	0.0303704	−	0.0439991i
$715$	−66.6391	−	24.7972i	−2.49216	−	0.927364i
$716$	−0.108295	−	0.156892i	−0.00404717	−	0.00586334i
$717$	2.36247	+	1.49394i	0.0882282	+	0.0557921i
$718$	−2.58192	+	0.419604i	−0.0963566	+	0.0156595i
$719$	−1.05821	−	0.450863i	−0.0394647	−	0.0168143i	0.372144	−	0.928175i	$-0.378623\pi$
$719$	−1.05821	−	0.450863i	−0.0394647	−	0.0168143i	−0.411609	+	0.911361i	$0.635033\pi$
$720$	−7.73623	+	11.2079i	−0.288312	+	0.417692i
$721$	4.67191	−	16.1293i	0.173991	−	0.600687i
$722$	−10.4535	−	22.0302i	−0.389038	−	0.819881i
$723$	−1.62908	+	4.29553i	−0.0605861	+	0.159752i
$724$	0.463128	+	0.567228i	0.0172120	+	0.0210809i
$725$	−1.50602	−	37.3716i	−0.0559323	−	1.38795i
$726$	−1.21128	−	30.0576i	−0.0449548	−	1.11554i
$727$	16.9405	−	4.17547i	0.628289	−	0.154859i	0.0877013	−	0.996147i	$-0.472048\pi$
$727$	16.9405	−	4.17547i	0.628289	−	0.154859i	0.540588	+	0.841287i	$0.318202\pi$
$728$	40.1524	+	7.93590i	1.48815	+	0.294124i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	4.50730	−	22.0782i	0.166823	−	0.817152i
$731$	2.20552	−	0.939683i	0.0815740	−	0.0347554i
$732$	−0.0666579	+	0.0421519i	−0.00246375	+	0.00155798i
$733$	28.8151	−	15.1233i	1.06431	−	0.558594i	0.160725	−	0.986999i	$-0.448617\pi$
$733$	28.8151	−	15.1233i	1.06431	−	0.558594i	0.903586	+	0.428406i	$0.140925\pi$
$734$	39.2157	+	6.37317i	1.44748	+	0.235238i
$735$	29.0731	−	9.70603i	1.07238	−	0.358012i
$736$	0.149578	+	1.23188i	0.00551351	+	0.0454078i
$737$	−10.8332	+	37.4004i	−0.399044	+	1.37766i
$738$	2.91080	−	14.2580i	0.107148	−	0.524846i
$739$	13.1115	+	4.37725i	0.482313	+	0.161020i	0.547419	−	0.836859i	$-0.315610\pi$
$739$	13.1115	+	4.37725i	0.482313	+	0.161020i	−0.0651062	+	0.997878i	$0.520739\pi$
$740$	−0.417014	−	0.218866i	−0.0153298	−	0.00804568i
$741$	−4.40920	−	1.24730i	−0.161976	−	0.0458208i
$742$	8.92971	−	4.68667i	0.327820	−	0.172053i
$743$	−36.2255	+	5.88721i	−1.32898	+	0.215981i	−0.783108	−	0.621886i	$-0.786367\pi$
$743$	−36.2255	+	5.88721i	−1.32898	+	0.215981i	−0.545875	+	0.837866i	$0.683803\pi$
$744$	−16.7804	+	12.6097i	−0.615200	+	0.462293i
$745$	1.82617	−	45.3160i	0.0669059	−	1.66025i
$746$	14.5862			0.534039
$747$	0.578003	−	14.3430i	0.0211480	−	0.524782i
$748$	0.00950826	+	0.0465746i	0.000347657	+	0.00170293i
$749$	−18.7512	−	27.1659i	−0.685155	−	0.992619i
$750$	9.14620	−	3.05345i	0.333972	−	0.111496i
$751$	−13.8438	+	29.1753i	−0.505169	+	1.06462i	0.477393	+	0.878690i	$0.341582\pi$
$751$	−13.8438	+	29.1753i	−0.505169	+	1.06462i	−0.982563	+	0.185932i	$0.940470\pi$
$752$	−2.54085	+	3.11198i	−0.0926553	+	0.113482i
$753$	−8.20028	−	21.6224i	−0.298835	−	0.787963i
$754$	16.4013	+	21.5443i	0.597301	+	0.784597i
$755$	−21.9462	+	57.8674i	−0.798704	+	2.10601i
$756$	0.0649474	+	0.112492i	0.00236211	+	0.00409130i
$757$	18.9219	−	23.1751i	0.687727	−	0.842313i	−0.306244	−	0.951953i	$-0.599072\pi$
$757$	18.9219	−	23.1751i	0.687727	−	0.842313i	0.993971	+	0.109640i	$0.0349699\pi$
$758$	−25.9202	−	19.4778i	−0.941464	−	0.707464i
$759$	33.9186	+	17.8018i	1.23117	+	0.646166i
$760$	−12.5034	+	1.00938i	−0.453545	+	0.0366139i
$761$	−7.64490	+	0.617160i	−0.277127	+	0.0223720i	−0.218249	−	0.975893i	$-0.570034\pi$
$761$	−7.64490	+	0.617160i	−0.277127	+	0.0223720i	−0.0588785	+	0.998265i	$0.518752\pi$
$762$	17.9656	+	9.42909i	0.650826	+	0.341580i
$763$	11.1500	+	8.37871i	0.403659	+	0.303330i
$764$	0.452963	−	0.554779i	0.0163876	−	0.0200712i
$765$	−0.442791	−	0.766937i	−0.0160092	−	0.0277287i
$766$	2.10359	−	5.54670i	0.0760056	−	0.200410i
$767$	−16.9661	−	7.92090i	−0.612611	−	0.286007i
$768$	0.277569	+	0.731890i	0.0100159	+	0.0264098i
$769$	24.6460	−	30.1859i	0.888758	−	1.08853i	−0.106791	−	0.994281i	$-0.534058\pi$
$769$	24.6460	−	30.1859i	0.888758	−	1.08853i	0.995549	−	0.0942489i	$-0.0300450\pi$
$770$	47.2136	−	99.5006i	1.70146	−	3.58575i
$771$	−21.1073	+	7.04666i	−0.760162	+	0.253779i
$772$	0.171581	+	0.248578i	0.00617534	+	0.00894652i
$773$	10.2607	+	50.2602i	0.369051	+	1.80773i	0.562700	+	0.826661i	$0.309763\pi$
$773$	10.2607	+	50.2602i	0.369051	+	1.80773i	−0.193649	+	0.981071i	$0.562032\pi$
$774$	0.529318	−	13.1349i	0.0190259	−	0.472124i
$775$	51.4309			1.84745
$776$	0.681133	−	16.9021i	0.0244512	−	0.606751i
$777$	13.2730	−	9.97399i	0.476165	−	0.357815i
$778$	33.0590	−	5.37262i	1.18522	−	0.192618i
$779$	11.6749	−	6.12749i	0.418298	−	0.219540i
$780$	0.242597	−	0.327077i	0.00868635	−	0.0117112i
$781$	51.1413	+	26.8410i	1.82998	+	0.960447i
$782$	2.28865	+	0.764065i	0.0818421	+	0.0273229i
$783$	−1.07095	+	5.24587i	−0.0382727	+	0.187472i
$784$	−9.68925	+	33.4512i	−0.346045	+	1.19468i
$785$	4.56852	+	37.6251i	0.163057	+	1.34290i
$786$	26.5813	−	8.87414i	0.948124	−	0.316530i
$787$	5.26142	+	0.855064i	0.187549	+	0.0304797i	0.253460	−	0.967346i	$-0.418431\pi$
$787$	5.26142	+	0.855064i	0.187549	+	0.0304797i	−0.0659110	+	0.997826i	$0.520995\pi$
$788$	0.285752	−	0.149974i	0.0101795	−	0.00534261i
$789$	16.7303	−	10.5796i	0.595615	−	0.376644i
$790$	−43.4875	+	18.5283i	−1.54722	+	0.659207i
$791$	3.88819	−	19.0456i	0.138248	−	0.677184i
$792$	15.7681	+	3.88649i	0.560296	+	0.138101i
$793$	−7.52122	+	4.40533i	−0.267086	+	0.156438i
$794$	3.43982	−	0.847840i	0.122075	−	0.0300887i
$795$	−0.251730	−	6.24663i	−0.00892796	−	0.221545i
$796$	−0.00540626	−	0.134155i	−0.000191620	−	0.00475500i
$797$	−30.1379	−	36.9123i	−1.06754	−	1.30750i	−0.949250	−	0.314521i	$-0.898156\pi$
$797$	−30.1379	−	36.9123i	−1.06754	−	1.30750i	−0.118290	−	0.992979i	$-0.537741\pi$
$798$	2.51683	−	6.63633i	0.0890947	−	0.234924i
$799$	−0.111995	−	0.236025i	−0.00396211	−	0.00834997i
$800$	0.358638	−	1.23816i	0.0126798	−	0.0437757i
$801$	−7.88615	+	11.4251i	−0.278644	+	0.403685i
$802$	−12.3750	−	5.27250i	−0.436977	−	0.186179i
$803$	−26.0904	+	4.24011i	−0.920711	+	0.149630i
$804$	−0.188482	−	0.119189i	−0.00664726	−	0.00420347i
$805$	52.6592	+	76.2900i	1.85599	+	2.68887i
$806$	−30.5094	+	21.3421i	−1.07465	+	0.751743i
$807$	4.05422	−	5.87355i	0.142715	−	0.206759i
$808$	−17.9449	+	7.64561i	−0.631300	+	0.268972i
$809$	6.52096	+	22.5130i	0.229265	+	0.791513i	0.989830	+	0.142252i	$0.0454345\pi$
$809$	6.52096	+	22.5130i	0.229265	+	0.791513i	−0.760566	+	0.649261i	$0.775078\pi$
$810$	−4.84022	+	0.390743i	−0.170068	+	0.0137293i
$811$	−32.5139	+	28.8048i	−1.14172	+	1.01147i	−0.141951	+	0.989874i	$0.545338\pi$
$811$	−32.5139	+	28.8048i	−1.14172	+	1.01147i	−0.999767	+	0.0216003i	$0.993124\pi$
$812$	0.587801	−	0.371703i	0.0206278	−	0.0130442i
$813$	−24.0370	−	10.2412i	−0.843015	−	0.359175i
$814$	4.01578	−	33.0729i	0.140753	−	1.15921i
$815$	−9.61164	−	47.0809i	−0.336681	−	1.64917i
$816$	1.00297	+	0.0809679i	0.0351109	+	0.00283444i
$817$	9.52198	−	7.15531i	0.333132	−	0.250332i
$818$	1.63464	−	13.4624i	0.0571538	−	0.470703i
$819$	6.75091	+	12.6696i	0.235896	+	0.442711i
$820$	0.141242	+	1.16324i	0.00493240	+	0.0406220i
$821$	−5.87611	−	6.11768i	−0.205078	−	0.213508i	0.610719	−	0.791848i	$-0.290881\pi$
$821$	−5.87611	−	6.11768i	−0.205078	−	0.213508i	−0.815796	+	0.578339i	$0.803701\pi$
$822$	11.1930	+	19.3868i	0.390400	+	0.676193i
$823$	−4.90779	+	8.50054i	−0.171075	+	0.296310i	−0.938796	−	0.344474i	$-0.888057\pi$
$823$	−4.90779	+	8.50054i	−0.171075	+	0.296310i	0.767721	+	0.640784i	$0.221391\pi$
$824$	11.6747	−	2.87754i	0.406706	−	0.100244i
$825$	−25.1662	−	30.8231i	−0.876176	−	1.07312i
$826$	14.5011	−	25.1167i	0.504559	−	0.873921i
$827$	4.29187	+	11.3167i	0.149243	+	0.393522i	0.988701	−	0.149904i	$-0.0478963\pi$
$827$	4.29187	+	11.3167i	0.149243	+	0.393522i	−0.839458	+	0.543425i	$0.817127\pi$
$828$	−0.151977	+	0.158224i	−0.00528155	+	0.00549868i
$829$	10.0282	+	3.34792i	0.348295	+	0.116278i	0.485433	−	0.874274i	$-0.338662\pi$
$829$	10.0282	+	3.34792i	0.348295	+	0.116278i	−0.137137	+	0.990552i	$0.543790\pi$
$830$	−19.3933	−	66.9534i	−0.673151	−	2.32399i
$831$	−9.41895	+	8.34446i	−0.326740	+	0.289466i
$832$	9.45183	+	27.7330i	0.327683	+	0.961469i
$833$	−1.69512	−	1.50175i	−0.0587326	−	0.0520325i
$834$	2.56212	−	5.39956i	0.0887191	−	0.186972i
$835$	−34.7468	−	36.1752i	−1.20246	−	1.25189i
$836$	0.101244	+	0.213367i	0.00350159	+	0.00737945i
$837$	−7.14838	−	1.76192i	−0.247084	−	0.0609008i
$838$	−6.73750	+	7.01448i	−0.232743	+	0.242311i
$839$	0.476051	+	0.357729i	0.0164351	+	0.0123502i	0.608928	−	0.793225i	$-0.291600\pi$
$839$	0.476051	+	0.357729i	0.0164351	+	0.0123502i	−0.592493	+	0.805576i	$0.701856\pi$
$840$	29.4164	+	26.0607i	1.01496	+	0.899180i
$841$	−0.329577	−	0.0535616i	−0.0113647	−	0.00184695i
$842$	−6.14893	−	3.88835i	−0.211906	−	0.134001i
$843$	−3.19593	−	0.258002i	−0.110074	−	0.00888605i
$844$	0.0924662			0.00318282
$845$	28.0258	−	35.2156i	0.964118	−	1.21145i
$846$	−1.43252			−0.0492510
$847$	−85.1162	−	6.87129i	−2.92463	−	0.236100i
$848$	6.00373	+	3.79653i	0.206169	+	0.130373i
$849$	25.2695	+	4.10669i	0.867247	+	0.140941i
$850$	−1.87607	−	1.66205i	−0.0643486	−	0.0570079i
$851$	22.4178	+	16.8459i	0.768472	+	0.577469i
$852$	−0.229145	+	0.238565i	−0.00785038	+	0.00817311i
$853$	−3.73093	−	0.919592i	−0.127745	−	0.0314862i	0.174925	−	0.984582i	$-0.444032\pi$
$853$	−3.73093	−	0.919592i	−0.127745	−	0.0314862i	−0.302670	+	0.953096i	$0.597878\pi$
$854$	−5.78782	−	12.1976i	−0.198055	−	0.417393i
$855$	−3.04787	−	3.17317i	−0.104235	−	0.108520i
$856$	10.1326	−	21.3539i	0.346323	−	0.729861i
$857$	−11.6546	−	10.3250i	−0.398112	−	0.352697i	0.440188	−	0.897906i	$-0.354912\pi$
$857$	−11.6546	−	10.3250i	−0.398112	−	0.352697i	−0.838300	+	0.545209i	$0.816450\pi$
$858$	27.7195	+	7.84146i	0.946326	+	0.267703i
$859$	−23.3191	+	20.6589i	−0.795636	+	0.704872i	−0.959530	−	0.281606i	$-0.909133\pi$
$859$	−23.3191	+	20.6589i	−0.795636	+	0.704872i	0.163894	+	0.986478i	$0.447595\pi$
$860$	0.294498	+	1.01673i	0.0100423	+	0.0346700i
$861$	−39.1829	−	13.0812i	−1.33535	−	0.445806i
$862$	−2.13807	+	2.22597i	−0.0728230	+	0.0758168i
$863$	−14.1745	−	37.3750i	−0.482505	−	1.27226i	−0.926522	−	0.376242i	$-0.877216\pi$
$863$	−14.1745	−	37.3750i	−0.482505	−	1.27226i	0.444017	−	0.896018i	$-0.353553\pi$
$864$	−0.0922642	+	0.159806i	−0.00313889	+	0.00543672i
$865$	16.1454	+	19.7746i	0.548961	+	0.672355i
$866$	−4.70851	+	1.16054i	−0.160002	+	0.0394369i
$867$	8.46728	−	14.6658i	0.287564	−	0.498076i
$868$	0.478163	+	0.828203i	0.0162299	+	0.0281110i
$869$	38.4112	+	39.9903i	1.30301	+	1.35658i
$870$	3.13385	+	25.8096i	0.106248	+	0.875028i
$871$	−20.3709	−	13.8737i	−0.690241	−	0.470092i
$872$	−1.20378	+	9.91406i	−0.0407653	+	0.335732i
$873$	4.74330	−	3.56436i	0.160536	−	0.120635i
$874$	11.9488	+	0.964604i	0.404173	+	0.0326282i
$875$	−5.47506	−	26.8186i	−0.185091	−	0.906635i
$876$	0.0182476	−	0.150283i	0.000616530	−	0.00507759i
$877$	−4.75035	−	2.02393i	−0.160408	−	0.0683434i	0.310270	−	0.950648i	$-0.399580\pi$
$877$	−4.75035	−	2.02393i	−0.160408	−	0.0683434i	−0.470678	+	0.882305i	$0.655991\pi$
$878$	−36.9760	+	23.3822i	−1.24788	+	0.789111i
$879$	−4.53992	+	4.02202i	−0.153128	+	0.135659i
$880$	77.3227	−	6.24213i	2.60655	−	0.210422i
$881$	−2.91449	−	10.0620i	−0.0981916	−	0.338997i	0.896349	−	0.443350i	$-0.146210\pi$
$881$	−2.91449	−	10.0620i	−0.0981916	−	0.338997i	−0.994540	+	0.104353i	$0.966723\pi$
$882$	−11.4242	+	4.86742i	−0.384674	+	0.163894i
$883$	−21.4277	+	31.0434i	−0.721099	+	1.04469i	0.275420	+	0.961324i	$0.411183\pi$
$883$	−21.4277	+	31.0434i	−0.721099	+	1.04469i	−0.996519	+	0.0833683i	$0.973432\pi$
$884$	−0.0298913	−	0.00343988i	−0.00100535	−	0.000115696i
$885$	−10.2131	−	14.7962i	−0.343309	−	0.497369i
$886$	8.29938	+	5.24821i	0.278823	+	0.176317i
$887$	29.0655	−	4.72360i	0.975923	−	0.158603i	0.348523	−	0.937300i	$-0.386683\pi$
$887$	29.0655	−	4.72360i	0.975923	−	0.158603i	0.627400	+	0.778697i	$0.284119\pi$
$888$	10.9370	+	4.65984i	0.367023	+	0.156374i
$889$	32.7182	−	47.4005i	1.09733	−	1.58976i
$890$	−18.7554	+	64.7512i	−0.628683	+	2.17047i
$891$	2.44192	+	5.14624i	0.0818075	+	0.172406i
$892$	−0.217175	+	0.572643i	−0.00727155	+	0.0191735i
$893$	−0.820889	−	1.00541i	−0.0274700	−	0.0336446i
$894$	0.739868	+	18.3596i	0.0247449	+	0.614038i
$895$	−0.814606	−	20.2142i	−0.0272293	−	0.675688i
$896$	−42.6373	+	10.5092i	−1.42441	+	0.351086i
$897$	−17.3815	+	16.9055i	−0.580353	+	0.564457i
$898$	−34.4448	−	8.48987i	−1.14944	−	0.283311i
$899$	−7.88469	+	38.6218i	−0.262969	+	1.28811i
$900$	0.209662	−	0.0893285i	0.00698872	−	0.00297762i
$901$	−0.390408	+	0.246879i	−0.0130064	+	0.00822473i
$902$	−73.3972	+	38.5218i	−2.44386	+	1.28264i
$903$	−36.8327	−	5.98590i	−1.22572	−	0.199198i
$904$	13.2025	−	4.40764i	0.439109	−	0.146596i
$905$	9.36692	+	77.1435i	0.311367	+	2.56434i
$906$	6.97607	−	24.0842i	0.231765	−	0.800144i
$907$	2.78715	−	13.6524i	0.0925458	−	0.453319i	−0.906940	−	0.421259i	$-0.861588\pi$
$907$	2.78715	−	13.6524i	0.0925458	−	0.453319i	0.999486	−	0.0320598i	$-0.0102067\pi$
$908$	0.132903	+	0.0443696i	0.00441054	+	0.00147246i
$909$	−6.05800	−	3.17948i	−0.200931	−	0.105457i
$910$	50.5774	+	47.9757i	1.67663	+	1.59038i
$911$	−15.7766	+	8.28019i	−0.522702	+	0.274335i	−0.705370	−	0.708840i	$-0.749219\pi$
$911$	−15.7766	+	8.28019i	−0.522702	+	0.274335i	0.182668	+	0.983175i	$0.441527\pi$
$912$	4.93451	−	0.801936i	0.163398	−	0.0265548i
$913$	−65.3680	+	49.1209i	−2.16337	+	1.62566i
$914$	0.652334	−	16.1875i	0.0215773	−	0.535435i
$915$	−8.36945			−0.276686
$916$	−0.00303232	+	0.0752463i	−0.000100191	+	0.00248621i
$917$	−15.9120	−	77.9421i	−0.525460	−	2.57387i
$918$	0.203816	+	0.295279i	0.00672694	+	0.00974566i
$919$	−55.1882	+	18.4245i	−1.82049	+	0.607769i	−0.821179	+	0.570671i	$0.806683\pi$
$919$	−55.1882	+	18.4245i	−1.82049	+	0.607769i	−0.999312	+	0.0370977i	$0.988189\pi$
$920$	−28.4553	+	59.9682i	−0.938143	+	1.97709i
$921$	−6.12192	+	7.49799i	−0.201724	+	0.247067i
$922$	4.96172	+	13.0830i	0.163406	+	0.430865i
$923$	−26.2073	+	25.4895i	−0.862623	+	0.838996i
$924$	0.262375	−	0.691826i	0.00863150	−	0.0227594i
$925$	−14.5647	−	25.2267i	−0.478883	−	0.829450i
$926$	−19.4869	+	23.8672i	−0.640380	+	0.784324i
$927$	3.37161	+	2.53360i	0.110738	+	0.0832144i
$928$	0.874811	+	0.459136i	0.0287171	+	0.0150719i
$929$	−29.2587	+	2.36201i	−0.959946	+	0.0774949i	−0.550496	−	0.834838i	$-0.685561\pi$
$929$	−29.2587	+	2.36201i	−0.959946	+	0.0774949i	−0.409450	+	0.912333i	$0.634279\pi$
$930$	−35.6352	+	2.87677i	−1.16852	+	0.0943330i
$931$	−9.96272	−	5.22884i	−0.326515	−	0.171368i
$932$	0.0798576	+	0.0600091i	0.00261582	+	0.00196566i
$933$	14.6712	−	17.9690i	0.480314	−	0.588277i
$934$	23.4499	+	40.6164i	0.767303	+	1.32901i
$935$	−1.78879	+	4.71666i	−0.0584998	+	0.154251i
$936$	−5.43960	+	8.72233i	−0.177799	+	0.285098i
$937$	12.2381	+	32.2693i	0.399802	+	1.05419i	0.972187	+	0.234206i	$0.0752490\pi$
$937$	12.2381	+	32.2693i	0.399802	+	1.05419i	−0.572385	+	0.819985i	$0.693982\pi$
$938$	24.1441	−	29.5712i	0.788333	−	0.965533i
$939$	−4.23888	+	8.93325i	−0.138331	+	0.291526i
$940$	0.109414	−	0.0365278i	0.00356870	−	0.00119141i
$941$	19.0611	+	27.6147i	0.621373	+	0.900214i	0.999676	−	0.0254680i	$-0.00810759\pi$
$941$	19.0611	+	27.6147i	0.621373	+	0.900214i	−0.378303	+	0.925682i	$0.623492\pi$
$942$	−3.07153	−	15.0453i	−0.100076	−	0.490203i
$943$	2.80935	−	69.7132i	0.0914849	−	2.27018i
$944$	20.4281			0.664878
$945$	−0.555046	+	13.7733i	−0.0180557	+	0.448047i
$946$	−59.8621	+	44.9835i	−1.94629	+	1.46254i
$947$	32.1724	−	5.22853i	1.04546	−	0.169904i	0.386662	−	0.922222i	$-0.373628\pi$
$947$	32.1724	−	5.22853i	1.04546	−	0.169904i	0.658801	+	0.752317i	$0.271064\pi$
$948$	−0.281197	+	0.147583i	−0.00913284	+	0.00479328i
$949$	2.58053	−	16.5310i	0.0837676	−	0.536619i
$950$	−11.0262	−	5.78699i	−0.357737	−	0.187755i
$951$	−27.6700	−	9.23759i	−0.897260	−	0.299549i
$952$	0.580823	−	2.84506i	0.0188246	−	0.0922090i
$953$	−2.41041	+	8.32169i	−0.0780808	+	0.269566i	−0.990055	−	0.140682i	$-0.955071\pi$
$953$	−2.41041	+	8.32169i	−0.0780808	+	0.269566i	0.911974	+	0.410248i	$0.134558\pi$
$954$	0.305302	+	2.51439i	0.00988451	+	0.0814063i
$955$	72.0931	−	24.0682i	2.33288	−	0.778829i
$956$	0.0900085	+	0.0146278i	0.00291108	+	0.000473097i
$957$	27.0046	−	14.1731i	0.872934	−	0.458151i
$958$	11.5498	−	7.30362i	0.373156	−	0.235969i
$959$	58.4615	−	24.9081i	1.88782	−	0.804325i
$960$	−5.62736	+	27.5646i	−0.181622	+	0.889645i
$961$	−22.5295	−	5.55301i	−0.726757	−	0.179129i
$962$	19.1082	+	8.92095i	0.616072	+	0.287623i
$963$	8.04943	−	1.98401i	0.259389	−	0.0639337i
$964$	0.00603485	+	0.149753i	0.000194370	+	0.00482323i
$965$	1.29065	+	32.0272i	0.0415476	+	1.03099i
$966$	−23.7526	−	29.0917i	−0.764228	−	0.936009i
$967$	−14.2170	+	37.4871i	−0.457188	+	1.20550i	0.486211	+	0.873842i	$0.338379\pi$
$967$	−14.2170	+	37.4871i	−0.457188	+	1.20550i	−0.943398	+	0.331663i	$0.892390\pi$
$968$	−26.2126	−	55.2418i	−0.842504	−	1.77554i
$969$	−0.0904455	+	0.312254i	−0.00290553	+	0.0100311i
$970$	16.3669	−	23.7115i	0.525509	−	0.761332i
$971$	30.9061	+	13.1679i	0.991825	+	0.422577i	0.826056	−	0.563587i	$-0.190579\pi$
$971$	30.9061	+	13.1679i	0.991825	+	0.422577i	0.165769	+	0.986165i	$0.446989\pi$
$972$	−0.0322011	+	0.00523319i	−0.00103285	+	0.000167855i
$973$	−14.3392	−	9.06756i	−0.459694	−	0.290693i
$974$	−23.0778	−	33.4339i	−0.739460	−	1.07129i
$975$	23.4942	−	9.07865i	0.752416	−	0.290749i
$976$	5.40211	−	7.82631i	0.172917	−	0.250514i
$977$	38.1287	−	16.2451i	1.21985	−	0.519728i	0.316480	−	0.948599i	$-0.397499\pi$
$977$	38.1287	−	16.2451i	1.21985	−	0.519728i	0.903366	+	0.428871i	$0.141089\pi$
$978$	5.41637	+	18.6995i	0.173196	+	0.597943i
$979$	78.8212	−	6.36310i	2.51914	−	0.203366i
$980$	0.748457	−	0.663075i	0.0239086	−	0.0211812i
$981$	−2.96062	+	1.87219i	−0.0945255	+	0.0597743i
$982$	24.8479	+	10.5867i	0.792929	+	0.337835i
$983$	2.69074	−	22.1602i	0.0858213	−	0.706802i	−0.884763	−	0.466041i	$-0.845680\pi$
$983$	2.69074	−	22.1602i	0.0858213	−	0.706802i	0.970584	−	0.240761i	$-0.0773970\pi$
$984$	−5.91656	−	28.9812i	−0.188613	−	0.923888i
$985$	34.1359	+	2.75574i	1.08766	+	0.0878051i
$986$	1.53572	−	1.15402i	0.0489074	−	0.0367515i
$987$	−0.490157	+	4.03681i	−0.0156019	+	0.128493i
$988$	−0.148283	+	0.0189467i	−0.00471752	+	0.000602774i
$989$	−7.59694	−	62.5664i	−0.241569	−	1.98950i
$990$	19.1612	+	19.9489i	0.608982	+	0.634017i
$991$	−14.6034	−	25.2938i	−0.463891	−	0.803483i	0.535260	−	0.844688i	$-0.320214\pi$
$991$	−14.6034	−	25.2938i	−0.463891	−	0.803483i	−0.999151	+	0.0412047i	$0.986880\pi$
$992$	−0.679278	+	1.17654i	−0.0215671	+	0.0373553i
$993$	−3.18233	+	0.784373i	−0.100988	+	0.0248913i
$994$	−35.8134	−	43.8634i	−1.13593	−	1.39126i
$995$	7.12408	−	12.3393i	0.225849	−	0.391181i
$996$	−0.166061	−	0.437868i	−0.00526185	−	0.0138744i
$997$	21.4066	−	22.2867i	0.677955	−	0.705826i	−0.289978	−	0.957033i	$-0.593648\pi$
$997$	21.4066	−	22.2867i	0.677955	−	0.705826i	0.967933	+	0.251207i	$0.0808276\pi$
$998$	−32.6551	−	10.9019i	−1.03368	−	0.345093i
$999$	1.16013	+	4.00522i	0.0367048	+	0.126720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.16.6	✓	384
169.74	even	39	inner	507.2.q.b.412.6	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.16.6	✓	384	1.1	even	1	trivial
507.2.q.b.412.6	yes	384	169.74	even	39	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39808 - 0.112865i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.0322011 - 0.00523319i) q^{4} +(-2.59137 - 2.29575i) q^{5} +(1.12132 + 0.842620i) q^{6} +(2.75817 - 2.87156i) q^{7} +(2.76818 + 0.682294i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-1.39808 - 0.112865i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.0322011 - 0.00523319i) q^{4} +(-2.59137 - 2.29575i) q^{5} +(1.12132 + 0.842620i) q^{6} +(2.75817 - 2.87156i) q^{7} +(2.76818 + 0.682294i) q^{8} +(0.428693 + 0.903450i) q^{9} +(3.36384 + 3.50213i) q^{10} +(2.44192 - 5.14624i) q^{11} +(0.0244191 + 0.0216334i) q^{12} +(2.61590 + 2.48134i) q^{13} +(-4.18025 + 3.70337i) q^{14} +(0.963199 + 3.32535i) q^{15} +(-3.73125 - 1.24567i) q^{16} +(0.177198 - 0.184482i) q^{17} +(-0.497380 - 1.31148i) q^{18} +(0.635441 - 1.10062i) q^{19} +(0.0714309 + 0.0874870i) q^{20} +(-3.86592 + 0.952864i) q^{21} +(-3.99484 + 6.91927i) q^{22} +(-3.36244 - 5.82392i) q^{23} +(-1.97497 - 2.05616i) q^{24} +(0.842032 + 6.93476i) q^{25} +(-3.37719 - 3.76437i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.103843 + 0.0780333i) q^{28} +(-5.33671 - 0.430824i) q^{29} +(-0.971317 - 4.75783i) q^{30} +(0.887429 - 7.30864i) q^{31} +(-0.169762 - 0.0723289i) q^{32} +(-4.81438 + 3.04443i) q^{33} +(-0.268559 + 0.237922i) q^{34} +(-13.7398 + 1.10919i) q^{35} +(-0.00907645 - 0.0313355i) q^{36} +(-3.83618 + 1.63444i) q^{37} +(-1.01262 + 1.46703i) q^{38} +(-0.884744 - 3.49532i) q^{39} +(-5.60699 - 8.12313i) q^{40} +(8.76874 + 5.54502i) q^{41} +(5.51243 - 0.895857i) q^{42} +(8.62210 + 3.67353i) q^{43} +(-0.105564 + 0.152936i) q^{44} +(0.963199 - 3.32535i) q^{45} +(4.04366 + 8.52183i) q^{46} +(0.362160 - 0.954939i) q^{47} +(2.48784 + 3.04705i) q^{48} +(-0.356487 - 8.84613i) q^{49} +(-0.394540 - 9.79041i) q^{50} +(-0.248365 + 0.0612165i) q^{51} +(-0.0712497 - 0.0935915i) q^{52} +(-1.75331 - 0.432153i) q^{53} +(-0.280562 + 1.37429i) q^{54} +(-18.1424 + 7.72977i) q^{55} +(9.59434 - 6.06709i) q^{56} +(-1.12531 + 0.590608i) q^{57} +(7.41254 + 1.20466i) q^{58} +(-4.92586 + 1.64449i) q^{59} +(-0.0136139 - 0.112121i) q^{60} +(-0.672589 + 2.32205i) q^{61} +(-2.06559 + 10.1179i) q^{62} +(3.77671 + 1.26085i) q^{63} +(7.19539 + 3.77643i) q^{64} +(-1.08223 - 12.4355i) q^{65} +(7.07452 - 3.71299i) q^{66} +(-6.74720 + 1.09653i) q^{67} +(-0.00667140 + 0.00501323i) q^{68} +(-0.270784 + 6.71943i) q^{69} +19.3346 q^{70} +(-0.408278 + 10.1313i) q^{71} +(0.570278 + 2.79341i) q^{72} +(-2.63605 - 3.81898i) q^{73} +(5.54777 - 1.85212i) q^{74} +(2.99471 - 6.31123i) q^{75} +(-0.0262216 + 0.0321157i) q^{76} +(-8.04249 - 21.2063i) q^{77} +(0.842447 + 4.98660i) q^{78} +(-3.45188 + 9.10187i) q^{79} +(6.80928 + 11.7940i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-11.6336 - 8.74208i) q^{82} +(-12.7104 - 6.67093i) q^{83} +(0.129474 - 0.0104522i) q^{84} +(-0.882711 + 0.0712598i) q^{85} +(-11.6398 - 6.10904i) q^{86} +(4.28027 + 3.21642i) q^{87} +(10.2709 - 12.5796i) q^{88} +(6.94124 + 12.0226i) q^{89} +(-1.72195 + 4.54040i) q^{90} +(14.3404 - 0.667760i) q^{91} +(0.0777967 + 0.205133i) q^{92} +(-4.65626 + 5.70289i) q^{93} +(-0.614110 + 1.29421i) q^{94} +(-4.17341 + 1.39329i) q^{95} +(0.104824 + 0.151864i) q^{96} +(-1.18680 - 5.81335i) q^{97} +(-0.500020 + 12.4079i) q^{98} +5.69621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

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