LMFDB - Embedded newform 81.2.g.a.40.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

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

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			40.4
Character	$\chi$	$=$	81.40
Dual form			81.2.g.a.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00720285 - 0.123668i) q^{2} +(1.39452 - 1.02729i) q^{3} +(1.97123 - 0.230404i) q^{4} +(-3.27944 - 0.777242i) q^{5} +(-0.137087 - 0.165058i) q^{6} +(-2.23379 + 3.00051i) q^{7} +(-0.0857144 - 0.486111i) q^{8} +(0.889352 - 2.86514i) q^{9} +O(q^{10})$	\(q+(-0.00720285 - 0.123668i) q^{2} +(1.39452 - 1.02729i) q^{3} +(1.97123 - 0.230404i) q^{4} +(-3.27944 - 0.777242i) q^{5} +(-0.137087 - 0.165058i) q^{6} +(-2.23379 + 3.00051i) q^{7} +(-0.0857144 - 0.486111i) q^{8} +(0.889352 - 2.86514i) q^{9} +(-0.0724987 + 0.411161i) q^{10} +(3.13353 + 3.32135i) q^{11} +(2.51223 - 2.34633i) q^{12} +(-1.13603 + 0.570535i) q^{13} +(0.387157 + 0.254637i) q^{14} +(-5.37169 + 2.28506i) q^{15} +(3.80282 - 0.901284i) q^{16} +(-1.54764 + 0.563296i) q^{17} +(-0.360733 - 0.0893473i) q^{18} +(-4.14528 - 1.50876i) q^{19} +(-6.64363 - 0.776529i) q^{20} +(-0.0326736 + 6.47901i) q^{21} +(0.388175 - 0.411441i) q^{22} +(-0.637677 - 0.856549i) q^{23} +(-0.618907 - 0.589836i) q^{24} +(5.68246 + 2.85384i) q^{25} +(0.0787396 + 0.136381i) q^{26} +(-1.70312 - 4.90911i) q^{27} +(-3.71200 + 6.42938i) q^{28} +(-1.50657 + 0.990889i) q^{29} +(0.321280 + 0.647847i) q^{30} +(2.68833 - 6.23225i) q^{31} +(-0.421989 - 1.40954i) q^{32} +(7.78175 + 1.41263i) q^{33} +(0.0808092 + 0.187337i) q^{34} +(9.65772 - 8.10379i) q^{35} +(1.09298 - 5.85278i) q^{36} +(-2.46619 - 2.06938i) q^{37} +(-0.156728 + 0.523507i) q^{38} +(-0.998105 + 1.96265i) q^{39} +(-0.0967301 + 1.66079i) q^{40} +(0.0586186 - 1.00644i) q^{41} +(0.801482 - 0.0426266i) q^{42} +(0.660457 - 2.20608i) q^{43} +(6.94218 + 5.82518i) q^{44} +(-5.14349 + 8.70483i) q^{45} +(-0.101335 + 0.0850299i) q^{46} +(3.77360 + 8.74819i) q^{47} +(4.37721 - 5.16345i) q^{48} +(-2.00558 - 6.69911i) q^{49} +(0.311999 - 0.723295i) q^{50} +(-1.57955 + 2.37540i) q^{51} +(-2.10792 + 1.38640i) q^{52} +(1.43978 - 2.49378i) q^{53} +(-0.594833 + 0.245981i) q^{54} +(-7.69474 - 13.3277i) q^{55} +(1.65005 + 0.828685i) q^{56} +(-7.33060 + 2.15442i) q^{57} +(0.133393 + 0.179178i) q^{58} +(7.30814 - 7.74618i) q^{59} +(-10.0624 + 5.74205i) q^{60} +(-5.27275 - 0.616296i) q^{61} +(-0.790095 - 0.287571i) q^{62} +(6.61026 + 9.06865i) q^{63} +(7.17367 - 2.61100i) q^{64} +(4.16898 - 0.988066i) q^{65} +(0.118647 - 0.972529i) q^{66} +(2.54074 + 1.67107i) q^{67} +(-2.92098 + 1.46697i) q^{68} +(-1.76917 - 0.539392i) q^{69} +(-1.07174 - 1.13598i) q^{70} +(-0.346694 + 1.96620i) q^{71} +(-1.46901 - 0.186739i) q^{72} +(2.80114 + 15.8860i) q^{73} +(-0.238153 + 0.319894i) q^{74} +(10.8560 - 1.85781i) q^{75} +(-8.51895 - 2.01903i) q^{76} +(-16.9654 + 1.98297i) q^{77} +(0.249906 + 0.109297i) q^{78} +(0.326714 + 5.60945i) q^{79} -13.1716 q^{80} +(-7.41811 - 5.09624i) q^{81} -0.124887 q^{82} +(-0.701083 - 12.0371i) q^{83} +(1.42838 + 12.7792i) q^{84} +(5.51322 - 0.644403i) q^{85} +(-0.277579 - 0.0657875i) q^{86} +(-1.08301 + 2.92950i) q^{87} +(1.34595 - 1.80793i) q^{88} +(1.69819 + 9.63089i) q^{89} +(1.11356 + 0.573386i) q^{90} +(0.825760 - 4.68312i) q^{91} +(-1.45436 - 1.54153i) q^{92} +(-2.65341 - 11.4527i) q^{93} +(1.05469 - 0.529686i) q^{94} +(12.4215 + 8.16978i) q^{95} +(-2.03648 - 1.53212i) q^{96} +(-9.14226 + 2.16676i) q^{97} +(-0.814020 + 0.296279i) q^{98} +(12.3030 - 6.02417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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 $

$2$	−0.00720285	−	0.123668i	−0.00509318	−	0.0874466i	0.994804	−	0.101812i	$-0.0324641\pi$
$2$	−0.00720285	−	0.123668i	−0.00509318	−	0.0874466i	−0.999897	+	0.0143658i	$0.995427\pi$
$3$	1.39452	−	1.02729i	0.805124	−	0.593106i
$3$	1.39452	−	1.02729i	0.805124	−	0.593106i
$4$	1.97123	−	0.230404i	0.985617	−	0.115202i
$5$	−3.27944	−	0.777242i	−1.46661	−	0.347593i	−0.581719	−	0.813390i	$-0.697620\pi$
$5$	−3.27944	−	0.777242i	−1.46661	−	0.347593i	−0.884892	+	0.465797i	$0.845768\pi$
$6$	−0.137087	−	0.165058i	−0.0559657	−	0.0673846i
$7$	−2.23379	+	3.00051i	−0.844295	+	1.13409i	0.145183	+	0.989405i	$0.453623\pi$
$7$	−2.23379	+	3.00051i	−0.844295	+	1.13409i	−0.989478	+	0.144680i	$0.953785\pi$
$8$	−0.0857144	−	0.486111i	−0.0303046	−	0.171866i
$9$	0.889352	−	2.86514i	0.296451	−	0.955048i
$10$	−0.0724987	+	0.411161i	−0.0229261	+	0.130020i
$11$	3.13353	+	3.32135i	0.944795	+	1.00142i	0.999996	+	0.00294930i	$0.000938793\pi$
$11$	3.13353	+	3.32135i	0.944795	+	1.00142i	−0.0552003	+	0.998475i	$0.517580\pi$
$12$	2.51223	−	2.34633i	0.725218	−	0.677328i
$13$	−1.13603	+	0.570535i	−0.315077	+	0.158238i	−0.599309	−	0.800518i	$-0.704558\pi$
$13$	−1.13603	+	0.570535i	−0.315077	+	0.158238i	0.284232	+	0.958756i	$0.408262\pi$
$14$	0.387157	+	0.254637i	0.103472	+	0.0680546i
$15$	−5.37169	+	2.28506i	−1.38696	+	0.590000i
$16$	3.80282	−	0.901284i	0.950704	−	0.225321i
$17$	−1.54764	+	0.563296i	−0.375359	+	0.136619i	−0.522808	−	0.852450i	$-0.675116\pi$
$17$	−1.54764	+	0.563296i	−0.375359	+	0.136619i	0.147450	+	0.989070i	$0.452893\pi$
$18$	−0.360733	−	0.0893473i	−0.0850255	−	0.0210594i
$19$	−4.14528	−	1.50876i	−0.950993	−	0.346133i	−0.180495	−	0.983576i	$-0.557770\pi$
$19$	−4.14528	−	1.50876i	−0.950993	−	0.346133i	−0.770498	+	0.637443i	$0.779992\pi$
$20$	−6.64363	−	0.776529i	−1.48556	−	0.173637i
$21$	−0.0326736	+	6.47901i	−0.00712997	+	1.41384i
$22$	0.388175	−	0.411441i	0.0827591	−	0.0877195i
$23$	−0.637677	−	0.856549i	−0.132965	−	0.178603i	0.730654	−	0.682748i	$-0.239215\pi$
$23$	−0.637677	−	0.856549i	−0.132965	−	0.178603i	−0.863619	+	0.504145i	$0.831808\pi$
$24$	−0.618907	−	0.589836i	−0.126334	−	0.120400i
$25$	5.68246	+	2.85384i	1.13649	+	0.570768i
$26$	0.0787396	+	0.136381i	0.0154421	+	0.0267465i
$27$	−1.70312	−	4.90911i	−0.327765	−	0.944759i
$28$	−3.71200	+	6.42938i	−0.701503	+	1.21504i
$29$	−1.50657	+	0.990889i	−0.279764	+	0.184003i	−0.681634	−	0.731693i	$-0.738731\pi$
$29$	−1.50657	+	0.990889i	−0.279764	+	0.184003i	0.401871	+	0.915696i	$0.368360\pi$
$30$	0.321280	+	0.647847i	0.0586575	+	0.118280i
$31$	2.68833	−	6.23225i	0.482839	−	1.11935i	−0.486514	−	0.873673i	$-0.661732\pi$
$31$	2.68833	−	6.23225i	0.482839	−	1.11935i	0.969353	−	0.245673i	$-0.0790090\pi$
$32$	−0.421989	−	1.40954i	−0.0745978	−	0.249174i
$33$	7.78175	+	1.41263i	1.35463	+	0.245908i
$34$	0.0808092	+	0.187337i	0.0138587	+	0.0321280i
$35$	9.65772	−	8.10379i	1.63245	−	1.36979i
$36$	1.09298	−	5.85278i	0.182163	−	0.975464i
$37$	−2.46619	−	2.06938i	−0.405439	−	0.340204i	0.417152	−	0.908837i	$-0.363028\pi$
$37$	−2.46619	−	2.06938i	−0.405439	−	0.340204i	−0.822592	+	0.568633i	$0.807473\pi$
$38$	−0.156728	+	0.523507i	−0.0254246	+	0.0849240i
$39$	−0.998105	+	1.96265i	−0.159825	+	0.314275i
$40$	−0.0967301	+	1.66079i	−0.0152944	+	0.262594i
$41$	0.0586186	−	1.00644i	0.00915468	−	0.157180i	−0.990633	−	0.136554i	$-0.956397\pi$
$41$	0.0586186	−	1.00644i	0.00915468	−	0.157180i	0.999787	−	0.0206256i	$-0.00656578\pi$
$42$	0.801482	−	0.0426266i	0.123671	−	0.00657743i
$43$	0.660457	−	2.20608i	0.100719	−	0.336424i	−0.892746	−	0.450559i	$-0.851225\pi$
$43$	0.660457	−	2.20608i	0.100719	−	0.336424i	0.993465	+	0.114135i	$0.0364097\pi$
$44$	6.94218	+	5.82518i	1.04657	+	0.878179i
$45$	−5.14349	+	8.70483i	−0.766746	+	1.29764i
$46$	−0.101335	+	0.0850299i	−0.0149410	+	0.0125370i
$47$	3.77360	+	8.74819i	0.550436	+	1.27605i	0.935553	+	0.353187i	$0.114902\pi$
$47$	3.77360	+	8.74819i	0.550436	+	1.27605i	−0.385116	+	0.922868i	$0.625839\pi$
$48$	4.37721	−	5.16345i	0.631796	−	0.745280i
$49$	−2.00558	−	6.69911i	−0.286512	−	0.957015i
$50$	0.311999	−	0.723295i	0.0441233	−	0.102289i
$51$	−1.57955	+	2.37540i	−0.221181	+	0.332623i
$52$	−2.10792	+	1.38640i	−0.292316	+	0.192260i
$53$	1.43978	−	2.49378i	0.197769	−	0.342547i	−0.750035	−	0.661398i	$-0.769964\pi$
$53$	1.43978	−	2.49378i	0.197769	−	0.342547i	0.947805	+	0.318851i	$0.103297\pi$
$54$	−0.594833	+	0.245981i	−0.0809466	+	0.0334738i
$55$	−7.69474	−	13.3277i	−1.03756	−	1.79710i
$56$	1.65005	+	0.828685i	0.220497	+	0.110738i
$57$	−7.33060	+	2.15442i	−0.970962	+	0.285359i
$58$	0.133393	+	0.179178i	0.0175154	+	0.0235272i
$59$	7.30814	−	7.74618i	0.951439	−	1.00847i	−0.0485142	−	0.998822i	$-0.515449\pi$
$59$	7.30814	−	7.74618i	0.951439	−	1.00847i	0.999953	−	0.00964429i	$-0.00306992\pi$
$60$	−10.0624	+	5.74205i	−1.29905	+	0.741295i
$61$	−5.27275	−	0.616296i	−0.675107	−	0.0789086i	−0.228370	−	0.973574i	$-0.573340\pi$
$61$	−5.27275	−	0.616296i	−0.675107	−	0.0789086i	−0.446736	+	0.894666i	$0.647414\pi$
$62$	−0.790095	−	0.287571i	−0.100342	−	0.0365215i
$63$	6.61026	+	9.06865i	0.832814	+	1.14254i
$64$	7.17367	−	2.61100i	0.896708	−	0.326375i
$65$	4.16898	−	0.988066i	0.517098	−	0.122555i
$66$	0.118647	−	0.972529i	0.0146044	−	0.119710i
$67$	2.54074	+	1.67107i	0.310400	+	0.204154i	0.695145	−	0.718869i	$-0.255340\pi$
$67$	2.54074	+	1.67107i	0.310400	+	0.204154i	−0.384745	+	0.923023i	$0.625710\pi$
$68$	−2.92098	+	1.46697i	−0.354221	+	0.177897i
$69$	−1.76917	−	0.539392i	−0.212984	−	0.0649352i
$70$	−1.07174	−	1.13598i	−0.128098	−	0.135776i
$71$	−0.346694	+	1.96620i	−0.0411451	+	0.233345i	−0.998445	−	0.0557526i	$-0.982244\pi$
$71$	−0.346694	+	1.96620i	−0.0411451	+	0.233345i	0.957300	+	0.289098i	$0.0933553\pi$
$72$	−1.46901	−	0.186739i	−0.173124	−	0.0220074i
$73$	2.80114	+	15.8860i	0.327848	+	1.85932i	0.488854	+	0.872366i	$0.337415\pi$
$73$	2.80114	+	15.8860i	0.327848	+	1.85932i	−0.161006	+	0.986953i	$0.551474\pi$
$74$	−0.238153	+	0.319894i	−0.0276847	+	0.0371870i
$75$	10.8560	−	1.85781i	1.25354	−	0.214521i
$76$	−8.51895	−	2.01903i	−0.977191	−	0.231598i
$77$	−16.9654	+	1.98297i	−1.93339	+	0.225981i
$78$	0.249906	+	0.109297i	0.0282963	+	0.0123755i
$79$	0.326714	+	5.60945i	0.0367581	+	0.631113i	0.965503	+	0.260393i	$0.0838521\pi$
$79$	0.326714	+	5.60945i	0.0367581	+	0.631113i	−0.928745	+	0.370720i	$0.879111\pi$
$80$	−13.1716			−1.47263
$81$	−7.41811	−	5.09624i	−0.824234	−	0.566249i
$82$	−0.124887			−0.0137915
$83$	−0.701083	−	12.0371i	−0.0769538	−	1.32125i	−0.786940	−	0.617030i	$-0.788336\pi$
$83$	−0.701083	−	12.0371i	−0.0769538	−	1.32125i	0.709986	−	0.704216i	$-0.248701\pi$
$84$	1.42838	+	12.7792i	0.155850	+	1.39432i
$85$	5.51322	−	0.644403i	0.597993	−	0.0698953i
$86$	−0.277579	−	0.0657875i	−0.0299321	−	0.00709404i
$87$	−1.08301	+	2.92950i	−0.116111	+	0.314075i
$88$	1.34595	−	1.80793i	0.143479	−	0.192726i
$89$	1.69819	+	9.63089i	0.180007	+	1.02087i	0.932204	+	0.361934i	$0.117883\pi$
$89$	1.69819	+	9.63089i	0.180007	+	1.02087i	−0.752197	+	0.658939i	$0.771006\pi$
$90$	1.11356	+	0.573386i	0.117379	+	0.0604402i
$91$	0.825760	−	4.68312i	0.0865631	−	0.490924i
$92$	−1.45436	−	1.54153i	−0.151628	−	0.160716i
$93$	−2.65341	−	11.4527i	−0.275145	−	1.18759i
$94$	1.05469	−	0.529686i	0.108783	−	0.0546329i
$95$	12.4215	+	8.16978i	1.27442	+	0.838201i
$96$	−2.03648	−	1.53212i	−0.207847	−	0.156372i
$97$	−9.14226	+	2.16676i	−0.928256	+	0.220001i	−0.666819	−	0.745220i	$-0.732345\pi$
$97$	−9.14226	+	2.16676i	−0.928256	+	0.220001i	−0.261437	+	0.965220i	$0.584196\pi$
$98$	−0.814020	+	0.296279i	−0.0822284	+	0.0299287i
$99$	12.3030	−	6.02417i	1.23649	−	0.605452i
$100$	11.8590	+	4.31632i	1.18590	+	0.431632i
$101$	5.43839	+	0.635656i	0.541140	+	0.0632502i	0.382272	−	0.924050i	$-0.375142\pi$
$101$	5.43839	+	0.635656i	0.541140	+	0.0632502i	0.158868	+	0.987300i	$0.449216\pi$
$102$	0.305139	+	0.178230i	0.0302132	+	0.0176474i
$103$	1.60904	−	1.70548i	0.158543	−	0.168046i	−0.643233	−	0.765671i	$-0.722407\pi$
$103$	1.60904	−	1.70548i	0.158543	−	0.168046i	0.801776	+	0.597625i	$0.203889\pi$
$104$	0.374717	+	0.503332i	0.0367440	+	0.0493558i
$105$	5.14291	−	21.2221i	0.501896	−	2.07107i
$106$	−0.318771	−	0.160093i	−0.0309618	−	0.0155496i
$107$	−5.88377	−	10.1910i	−0.568805	−	0.985200i	−0.996684	−	0.0813640i	$-0.974072\pi$
$107$	−5.88377	−	10.1910i	−0.568805	−	0.985200i	0.427879	−	0.903836i	$-0.359261\pi$
$108$	−4.48832	−	9.28461i	−0.431889	−	0.893412i
$109$	−0.211790	+	0.366831i	−0.0202858	+	0.0351361i	−0.875990	−	0.482329i	$-0.839791\pi$
$109$	−0.211790	+	0.366831i	−0.0202858	+	0.0351361i	0.855704	+	0.517465i	$0.173124\pi$
$110$	−1.59278	+	1.04759i	−0.151866	+	0.0998839i
$111$	−5.56499	−	0.352292i	−0.528206	−	0.0334381i
$112$	−5.79040	+	13.4237i	−0.547142	+	1.26842i
$113$	3.93747	+	13.1521i	0.370406	+	1.23724i	0.916675	+	0.399633i	$0.130863\pi$
$113$	3.93747	+	13.1521i	0.370406	+	1.23724i	−0.546269	+	0.837610i	$0.683952\pi$
$114$	0.319234	+	0.891043i	0.0298990	+	0.0834539i
$115$	1.42548	+	3.30463i	0.132926	+	0.308158i
$116$	−2.74151	+	2.30040i	−0.254542	+	0.213586i
$117$	0.624335	+	3.76229i	0.0577198	+	0.347824i
$118$	−1.01059	−	0.847990i	−0.0930328	−	0.0780638i
$119$	1.76694	−	5.90200i	0.161975	−	0.541036i
$120$	1.57122	+	2.41537i	0.143432	+	0.220492i
$121$	−0.572749	+	9.83372i	−0.0520681	+	0.893975i
$122$	−0.0382374	+	0.656510i	−0.00346185	+	0.0594376i
$123$	−0.952163	−	1.46372i	−0.0858536	−	0.131979i
$124$	3.86340	−	12.9046i	0.346943	−	1.15887i
$125$	−3.50823	−	2.94375i	−0.313785	−	0.263297i
$126$	1.07389	−	0.882798i	0.0956698	−	0.0786459i
$127$	2.77429	−	2.32790i	0.246178	−	0.206568i	−0.511346	−	0.859375i	$-0.670853\pi$
$127$	2.77429	−	2.32790i	0.246178	−	0.206568i	0.757524	+	0.652807i	$0.226409\pi$
$128$	−1.54011	−	3.57039i	−0.136128	−	0.315581i
$129$	−1.34527	−	3.75490i	−0.118444	−	0.330600i
$130$	−0.152221	−	0.508453i	−0.0133506	−	0.0445943i
$131$	−2.47542	+	5.73866i	−0.216278	+	0.501389i	−0.991470	−	0.130337i	$-0.958394\pi$
$131$	−2.47542	+	5.73866i	−0.216278	+	0.501389i	0.775192	+	0.631726i	$0.217653\pi$
$132$	15.6651	+	0.991680i	1.36347	+	0.0863147i
$133$	13.7868	−	9.06769i	1.19546	−	0.786269i
$134$	0.188357	−	0.326245i	0.0162716	−	0.0281832i
$135$	1.76970	+	17.4229i	0.152312	+	1.49952i
$136$	0.406480	+	0.704043i	0.0348553	+	0.0603712i
$137$	−14.6344	−	7.34965i	−1.25030	−	0.627923i	−0.304448	−	0.952529i	$-0.598472\pi$
$137$	−14.6344	−	7.34965i	−1.25030	−	0.627923i	−0.945849	+	0.324606i	$0.894768\pi$
$138$	−0.0539625	+	0.222676i	−0.00459360	+	0.0189554i
$139$	11.6699	+	15.6754i	0.989827	+	1.32957i	0.943760	+	0.330630i	$0.107261\pi$
$139$	11.6699	+	15.6754i	0.989827	+	1.32957i	0.0460666	+	0.998938i	$0.485331\pi$
$140$	17.1705	−	18.1996i	1.45117	−	1.53815i
$141$	14.2493	+	8.32292i	1.20001	+	0.700916i
$142$	0.245654	+	0.0287128i	0.0206148	+	0.00240952i
$143$	−5.45472	−	1.98536i	−0.456147	−	0.166024i
$144$	0.799733	−	11.6972i	0.0666444	−	0.974765i
$145$	5.71088	−	2.07859i	0.474263	−	0.172617i
$146$	1.94442	−	0.460836i	0.160921	−	0.0381390i
$147$	−9.67874	−	7.28170i	−0.798289	−	0.600585i
$148$	−5.33823	−	3.51101i	−0.438800	−	0.288603i
$149$	−3.65975	+	1.83800i	−0.299819	+	0.150575i	−0.592349	−	0.805682i	$-0.701799\pi$
$149$	−3.65975	+	1.83800i	−0.299819	+	0.150575i	0.292530	+	0.956256i	$0.405503\pi$
$150$	−0.307946	−	1.32916i	−0.0251437	−	0.108525i
$151$	−6.08551	−	6.45026i	−0.495232	−	0.524915i	0.430756	−	0.902468i	$-0.358247\pi$
$151$	−6.08551	−	6.45026i	−0.495232	−	0.524915i	−0.925988	+	0.377553i	$0.876765\pi$
$152$	−0.378114	+	2.14439i	−0.0306691	+	0.173933i
$153$	0.237525	+	4.93519i	0.0192028	+	0.398986i
$154$	0.367429	+	2.08380i	0.0296083	+	0.167917i
$155$	−13.6602	+	18.3488i	−1.09721	+	1.47381i
$156$	−1.51530	+	4.09881i	−0.121321	+	0.328167i
$157$	5.15953	+	1.22283i	0.411776	+	0.0975926i	0.431282	−	0.902217i	$-0.358061\pi$
$157$	5.15953	+	1.22283i	0.411776	+	0.0975926i	−0.0195065	+	0.999810i	$0.506210\pi$
$158$	0.691357	−	0.0808081i	0.0550014	−	0.00642875i
$159$	−0.554031	−	4.95669i	−0.0439375	−	0.393091i
$160$	0.288333	+	4.95049i	0.0227948	+	0.391371i
$161$	3.99452			0.314812
$162$	−0.576811	+	0.954091i	−0.0453186	+	0.0749604i
$163$	−4.86655			−0.381178			−0.190589	−	0.981670i	$-0.561040\pi$
$163$	−4.86655			−0.381178			−0.190589	+	0.981670i	$0.561040\pi$
$164$	−0.116338	−	1.99744i	−0.00908444	−	0.155974i
$165$	−24.4218	−	10.6809i	−1.90124	−	0.831510i
$166$	−1.48356	+	0.173403i	−0.115146	+	0.0134587i
$167$	−21.7466	−	5.15404i	−1.68280	−	0.398831i	−0.725569	−	0.688150i	$-0.758423\pi$
$167$	−21.7466	−	5.15404i	−1.68280	−	0.398831i	−0.957233	+	0.289318i	$0.906571\pi$
$168$	3.15232	−	0.539462i	0.243207	−	0.0416204i
$169$	−6.79801	+	9.13132i	−0.522924	+	0.702409i
$170$	−0.119403	−	0.677168i	−0.00915779	−	0.0519364i
$171$	−8.00943	+	10.5350i	−0.612497	+	0.805633i
$172$	0.793626	−	4.50088i	0.0605134	−	0.343189i
$173$	2.39525	+	2.53882i	0.182108	+	0.193023i	0.811996	−	0.583663i	$-0.198381\pi$
$173$	2.39525	+	2.53882i	0.182108	+	0.193023i	−0.629889	+	0.776686i	$0.716899\pi$
$174$	0.370086	+	0.112833i	0.0280562	+	0.00855387i
$175$	−21.2564	+	10.6754i	−1.60683	+	0.806983i
$176$	14.9097	+	9.80628i	1.12386	+	0.739176i
$177$	2.23376	−	18.3098i	0.167899	−	1.37625i
$178$	1.17880	−	0.279381i	0.0883550	−	0.0209405i
$179$	−14.1428	+	5.14757i	−1.05709	+	0.384748i	−0.811332	−	0.584585i	$-0.801257\pi$
$179$	−14.1428	+	5.14757i	−1.05709	+	0.384748i	−0.245753	+	0.969333i	$0.579035\pi$
$180$	−8.13339	+	18.3443i	−0.606227	+	1.36731i
$181$	−2.01428	−	0.733137i	−0.149720	−	0.0544936i	0.266073	−	0.963953i	$-0.414274\pi$
$181$	−2.01428	−	0.733137i	−0.149720	−	0.0544936i	−0.415793	+	0.909459i	$0.636496\pi$
$182$	−0.585100	−	0.0683884i	−0.0433705	−	0.00506928i
$183$	−7.98605	+	4.55721i	−0.590346	+	0.336878i
$184$	−0.361719	+	0.383400i	−0.0266663	+	0.0282646i
$185$	6.47932	+	8.70323i	0.476369	+	0.639874i
$186$	−1.39722	+	0.410634i	−0.102449	+	0.0301091i
$187$	−6.72049	−	3.37516i	−0.491451	−	0.246816i
$188$	9.45428	+	16.3753i	0.689524	+	1.19429i
$189$	18.5342	+	5.85574i	1.34817	+	0.425942i
$190$	0.920870	−	1.59499i	0.0668069	−	0.115713i
$191$	17.3988	−	11.4434i	1.25893	−	0.828014i	0.268139	−	0.963380i	$-0.413591\pi$
$191$	17.3988	−	11.4434i	1.25893	−	0.828014i	0.990796	+	0.135366i	$0.0432210\pi$
$192$	7.32154	−	11.0105i	0.528387	−	0.794615i
$193$	5.58282	−	12.9424i	0.401860	−	0.931617i	−0.590362	−	0.807139i	$-0.701015\pi$
$193$	5.58282	−	12.9424i	0.401860	−	0.931617i	0.992222	−	0.124478i	$-0.0397257\pi$
$194$	0.333809	+	1.11500i	0.0239661	+	0.0800523i
$195$	4.79868	−	5.66062i	0.343641	−	0.405366i
$196$	−5.49697	−	12.7434i	−0.392641	−	0.910244i
$197$	1.46772	−	1.23157i	0.104571	−	0.0877455i	−0.589003	−	0.808131i	$-0.700479\pi$
$197$	1.46772	−	1.23157i	0.104571	−	0.0877455i	0.693574	+	0.720385i	$0.256035\pi$
$198$	−0.833614	−	1.47809i	−0.0592424	−	0.105043i
$199$	12.3341	+	10.3495i	0.874339	+	0.733658i	0.965007	−	0.262223i	$-0.0844557\pi$
$199$	12.3341	+	10.3495i	0.874339	+	0.733658i	−0.0906679	+	0.995881i	$0.528900\pi$
$200$	0.900213	−	3.00692i	0.0636547	−	0.212621i
$201$	5.25977	−	0.279740i	0.370996	−	0.0197313i
$202$	0.0394385	−	0.677134i	0.00277489	−	0.0476430i
$203$	0.392207	−	6.73393i	0.0275275	−	0.472629i
$204$	−2.56635	+	5.04641i	−0.179681	+	0.353319i
$205$	−0.974485	+	3.25501i	−0.0680610	+	0.227340i
$206$	−0.222503	−	0.186703i	−0.0155025	−	0.0130082i
$207$	−3.02125	+	1.06526i	−0.209992	+	0.0740409i
$208$	−3.80589	+	3.19352i	−0.263891	+	0.221431i
$209$	−7.97826	−	18.4957i	−0.551868	−	1.27937i
$210$	−2.66154	−	0.483154i	−0.183664	−	0.0333408i
$211$	−1.10667	−	3.69652i	−0.0761860	−	0.254479i	0.911409	−	0.411502i	$-0.134996\pi$
$211$	−1.10667	−	3.69652i	−0.0761860	−	0.254479i	−0.987595	+	0.157023i	$0.949810\pi$
$212$	2.26357	−	5.24756i	0.155463	−	0.360404i
$213$	1.53639	+	3.09806i	0.105272	+	0.212275i
$214$	−1.21792	+	0.801039i	−0.0832553	+	0.0547579i
$215$	−3.88059	+	6.72138i	−0.264654	+	0.458394i
$216$	−2.24039	+	1.24869i	−0.152439	+	0.0849623i
$217$	12.6947	+	21.9879i	0.861775	+	1.49264i
$218$	0.0468908	+	0.0235495i	0.00317585	+	0.00159497i
$219$	20.2258	+	19.2758i	1.36673	+	1.30253i
$220$	−18.2389	−	24.4991i	−1.22967	−	1.65173i
$221$	1.43679	−	1.52290i	0.0966486	−	0.102442i
$222$	−0.00348345	+	0.690750i	−0.000233794	+	0.0463601i
$223$	−2.97171	−	0.347344i	−0.199001	−	0.0232598i	0.0160086	−	0.999872i	$-0.494904\pi$
$223$	−2.97171	−	0.347344i	−0.199001	−	0.0232598i	−0.215009	+	0.976612i	$0.568978\pi$
$224$	5.17198	+	1.88245i	0.345567	+	0.125776i
$225$	13.2304	−	13.7430i	0.882025	−	0.916201i
$226$	1.59813	−	0.581672i	0.106306	−	0.0386923i
$227$	23.3853	−	5.54241i	1.55214	−	0.367863i	0.636953	−	0.770902i	$-0.280194\pi$
$227$	23.3853	−	5.54241i	1.55214	−	0.367863i	0.915183	+	0.403039i	$0.132046\pi$
$228$	−13.9539	+	5.93586i	−0.924123	+	0.393112i
$229$	3.95450	+	2.60092i	0.261321	+	0.171873i	0.673408	−	0.739271i	$-0.264830\pi$
$229$	3.95450	+	2.60092i	0.261321	+	0.171873i	−0.412087	+	0.911144i	$0.635200\pi$
$230$	0.398410	−	0.200089i	0.0262704	−	0.0131935i
$231$	−21.6214	+	20.1937i	−1.42259	+	1.32865i
$232$	0.610817	+	0.647428i	0.0401021	+	0.0425057i
$233$	−1.81475	+	10.2920i	−0.118888	+	0.674250i	0.865863	+	0.500282i	$0.166770\pi$
$233$	−1.81475	+	10.2920i	−0.118888	+	0.674250i	−0.984751	+	0.173968i	$0.944341\pi$
$234$	0.460778	−	0.104310i	0.0301220	−	0.00681893i
$235$	−5.57584	−	31.6222i	−0.363728	−	2.06280i
$236$	12.6213	−	16.9534i	0.821578	−	1.10357i
$237$	6.21814	+	7.48685i	0.403912	+	0.486323i
$238$	−0.742616	−	0.176003i	−0.0481367	−	0.0114086i
$239$	15.7205	−	1.83746i	1.01687	−	0.118855i	0.408707	−	0.912666i	$-0.365980\pi$
$239$	15.7205	−	1.83746i	1.01687	−	0.118855i	0.608165	+	0.793810i	$0.291906\pi$
$240$	−18.3680	+	13.5311i	−1.18565	+	0.873427i
$241$	−1.02572	−	17.6110i	−0.0660726	−	1.13442i	−0.854554	−	0.519363i	$-0.826169\pi$
$241$	−1.02572	−	17.6110i	−0.0660726	−	1.13442i	0.788481	−	0.615059i	$-0.210868\pi$
$242$	1.22024			0.0784402
$243$	−15.5800	+	0.513747i	−0.999457	+	0.0329569i
$244$	−10.5358			−0.674487
$245$	1.37036	+	23.5281i	0.0875490	+	1.50316i
$246$	−0.174157	+	0.128295i	−0.0111038	+	0.00817980i
$247$	5.56996	−	0.651035i	0.354408	−	0.0414243i
$248$	−3.25999	−	0.772633i	−0.207010	−	0.0490622i
$249$	−13.3433	−	16.0658i	−0.845596	−	1.01813i
$250$	−0.338779	+	0.455059i	−0.0214263	+	0.0287805i
$251$	−3.58499	−	20.3315i	−0.226282	−	1.28331i	−0.860218	−	0.509926i	$-0.829673\pi$
$251$	−3.58499	−	20.3315i	−0.226282	−	1.28331i	0.633936	−	0.773386i	$-0.281438\pi$
$252$	15.1198	+	16.3534i	0.952459	+	1.03017i
$253$	0.846717	−	4.80197i	0.0532326	−	0.301897i
$254$	−0.307870	−	0.326323i	−0.0193175	−	0.0204753i
$255$	7.02629	−	6.56230i	0.440003	−	0.410947i
$256$	13.2136	−	6.63614i	0.825852	−	0.414758i
$257$	−6.08872	−	4.00462i	−0.379804	−	0.249801i	0.345224	−	0.938520i	$-0.387803\pi$
$257$	−6.08872	−	4.00462i	−0.379804	−	0.249801i	−0.725028	+	0.688719i	$0.758173\pi$
$258$	−0.454671	+	0.193412i	−0.0283066	+	0.0120413i
$259$	11.7181	−	2.77725i	0.728130	−	0.172570i
$260$	7.99038	−	2.90826i	0.495542	−	0.180363i
$261$	1.49917	+	5.19780i	0.0927961	+	0.321736i
$262$	0.727519	+	0.264795i	0.0449463	+	0.0163591i
$263$	10.3713	+	1.21223i	0.639521	+	0.0747493i	0.429673	−	0.902985i	$-0.358629\pi$
$263$	10.3713	+	1.21223i	0.639521	+	0.0747493i	0.209848	+	0.977734i	$0.432703\pi$
$264$	0.0196872	−	3.90387i	0.00121166	−	0.240267i
$265$	−6.65995	+	7.05914i	−0.409118	+	0.433639i
$266$	−1.22069	−	1.63967i	−0.0748452	−	0.100535i
$267$	12.2619	+	11.6859i	0.750414	+	0.715166i
$268$	5.39341	+	2.70867i	0.329455	+	0.165459i
$269$	−11.1578	−	19.3259i	−0.680304	−	1.17832i	−0.974888	−	0.222695i	$-0.928515\pi$
$269$	−11.1578	−	19.3259i	−0.680304	−	1.17832i	0.294585	−	0.955625i	$-0.404819\pi$
$270$	2.14191	−	0.344350i	0.130352	−	0.0209565i
$271$	11.6312	−	20.1458i	0.706544	−	1.22377i	−0.259588	−	0.965720i	$-0.583587\pi$
$271$	11.6312	−	20.1458i	0.706544	−	1.22377i	0.966132	−	0.258050i	$-0.0830800\pi$
$272$	−5.37771	+	3.53698i	−0.326072	+	0.214461i
$273$	−3.65938	−	7.37898i	−0.221476	−	0.446596i
$274$	−0.803509	+	1.86274i	−0.0485417	+	0.112532i
$275$	8.32758	+	27.8160i	0.502172	+	1.67737i
$276$	−3.61174	−	0.655643i	−0.217401	−	0.0394651i
$277$	3.50985	+	8.13675i	0.210886	+	0.488890i	0.990524	−	0.137342i	$-0.0438558\pi$
$277$	3.50985	+	8.13675i	0.210886	+	0.488890i	−0.779637	+	0.626231i	$0.784597\pi$
$278$	1.85449	−	1.55610i	0.111225	−	0.0933287i
$279$	−15.4654	−	13.2451i	−0.925891	−	0.792965i
$280$	−4.76714	−	4.00011i	−0.284891	−	0.239052i
$281$	−6.16156	+	20.5810i	−0.367568	+	1.22776i	0.551671	+	0.834062i	$0.313990\pi$
$281$	−6.16156	+	20.5810i	−0.367568	+	1.22776i	−0.919239	+	0.393700i	$0.871195\pi$
$282$	0.926644	−	1.82213i	0.0551808	−	0.108506i
$283$	0.0355631	−	0.610594i	0.00211401	−	0.0362961i	−0.997086	−	0.0762833i	$-0.975695\pi$
$283$	0.0355631	−	0.610594i	0.00211401	−	0.0362961i	0.999200	+	0.0399872i	$0.0127317\pi$
$284$	−0.230395	+	3.95573i	−0.0136714	+	0.234729i
$285$	25.7148	−	1.36763i	1.52321	−	0.0810116i
$286$	−0.206236	+	0.688875i	−0.0121950	+	0.0407341i
$287$	2.88890	+	2.42407i	0.170526	+	0.143088i
$288$	−4.41384	−	0.0445190i	−0.260088	−	0.00262331i
$289$	−10.9449	+	9.18383i	−0.643815	+	0.540225i
$290$	−0.298190	−	0.691282i	−0.0175103	−	0.0405935i
$291$	−10.5232	+	12.4133i	−0.616878	+	0.727682i
$292$	9.18191	+	30.6697i	0.537330	+	1.79481i
$293$	12.2618	−	28.4261i	0.716344	−	1.66067i	−0.0338263	−	0.999428i	$-0.510769\pi$
$293$	12.2618	−	28.4261i	0.716344	−	1.66067i	0.750170	−	0.661245i	$-0.229971\pi$
$294$	−0.830800	+	1.24940i	−0.0484532	+	0.0728665i
$295$	−29.9873	+	19.7229i	−1.74593	+	1.14831i
$296$	−0.794559	+	1.37622i	−0.0461828	+	0.0799910i
$297$	10.9681	−	21.0395i	0.636434	−	1.22084i
$298$	0.253662	+	0.439356i	0.0146943	+	0.0254512i
$299$	1.21311	+	0.609246i	0.0701559	+	0.0352336i
$300$	20.9717	−	6.16345i	1.21080	−	0.355847i
$301$	5.14404	+	6.90964i	0.296497	+	0.398265i
$302$	−0.753859	+	0.799044i	−0.0433797	+	0.0459798i
$303$	8.23692	−	4.70037i	0.473199	−	0.270029i
$304$	−17.1236	−	2.00146i	−0.982104	−	0.114792i
$305$	16.8127	+	6.11931i	0.962690	+	0.350391i
$306$	0.608615	−	0.0649217i	0.0347922	−	0.00371133i
$307$	−21.3773	+	7.78069i	−1.22007	+	0.444068i	−0.870184	−	0.492726i	$-0.836000\pi$
$307$	−21.3773	+	7.78069i	−1.22007	+	0.444068i	−0.349882	+	0.936794i	$0.613778\pi$
$308$	−32.9859	+	7.81780i	−1.87955	+	0.445461i
$309$	0.491808	−	4.03127i	0.0279780	−	0.229331i
$310$	2.36756	+	1.55717i	0.134468	+	0.0884411i
$311$	−27.3750	+	13.7482i	−1.55229	+	0.779591i	−0.998588	−	0.0531218i	$-0.983083\pi$
$311$	−27.3750	+	13.7482i	−1.55229	+	0.779591i	−0.553705	+	0.832713i	$0.686787\pi$
$312$	1.03962	+	0.316962i	0.0588567	+	0.0179444i
$313$	15.6532	+	16.5914i	0.884770	+	0.937802i	0.998447	−	0.0557161i	$-0.0177442\pi$
$313$	15.6532	+	16.5914i	0.884770	+	0.937802i	−0.113676	+	0.993518i	$0.536263\pi$
$314$	0.114062	−	0.646878i	0.00643689	−	0.0365054i
$315$	−14.6294	−	34.8779i	−0.824274	−	1.96515i
$316$	1.93647	+	10.9823i	0.108935	+	0.617801i
$317$	−4.79052	+	6.43479i	−0.269062	+	0.361414i	−0.916034	−	0.401100i	$-0.868628\pi$
$317$	−4.79052	+	6.43479i	−0.269062	+	0.361414i	0.646972	+	0.762514i	$0.276035\pi$
$318$	−0.608994	+	0.104218i	−0.0341507	+	0.00584427i
$319$	−8.01199	−	1.89888i	−0.448585	−	0.106317i
$320$	−25.5550	+	2.98695i	−1.42857	+	0.166976i
$321$	−18.6741	−	8.16716i	−1.04229	−	0.455847i
$322$	−0.0287719	−	0.493995i	−0.00160340	−	0.0275292i
$323$	7.26530			0.404252
$324$	−15.7970	−	8.33673i	−0.877613	−	0.463152i
$325$	−8.08365			−0.448400
$326$	0.0350530	+	0.601837i	0.00194141	+	0.0333327i
$327$	0.0814971	+	0.729122i	0.00450680	+	0.0403205i
$328$	−0.494267	+	0.0577715i	−0.0272913	+	0.00318990i
$329$	−34.6785	−	8.21895i	−1.91189	−	0.453125i
$330$	−1.14499	+	3.09713i	−0.0630294	+	0.170492i
$331$	10.9874	−	14.7586i	0.603919	−	0.811205i	−0.390058	−	0.920790i	$-0.627545\pi$
$331$	10.9874	−	14.7586i	0.603919	−	0.811205i	0.993977	+	0.109586i	$0.0349524\pi$
$332$	−4.15540	−	23.5665i	−0.228057	−	1.29338i
$333$	−8.12238	+	5.22558i	−0.445104	+	0.286360i
$334$	−0.480753	+	2.72648i	−0.0263056	+	0.149187i
$335$	−7.03337	−	7.45494i	−0.384274	−	0.407307i
$336$	5.71518	+	24.6679i	0.311788	+	1.34575i
$337$	23.8437	−	11.9748i	1.29885	−	0.652307i	0.341131	−	0.940016i	$-0.389190\pi$
$337$	23.8437	−	11.9748i	1.29885	−	0.652307i	0.957718	+	0.287709i	$0.0928936\pi$
$338$	1.17822	+	0.774926i	0.0640866	+	0.0421504i
$339$	19.0019	+	14.2959i	1.03204	+	0.776445i
$340$	10.7194	−	2.54054i	0.581340	−	0.137780i
$341$	29.1235	−	10.6001i	1.57712	−	0.574026i
$342$	1.36054	+	0.914629i	0.0735694	+	0.0494575i
$343$	−0.0250188	−	0.00910611i	−0.00135089	−	0.000491683i
$344$	−1.12901	−	0.131962i	−0.0608722	−	0.00711494i
$345$	5.38266	+	3.14398i	0.289793	+	0.169266i
$346$	0.296719	−	0.314503i	0.0159517	−	0.0169078i
$347$	14.6527	+	19.6820i	0.786599	+	1.05659i	0.996879	+	0.0789443i	$0.0251549\pi$
$347$	14.6527	+	19.6820i	0.786599	+	1.05659i	−0.210280	+	0.977641i	$0.567438\pi$
$348$	−1.45990	+	6.02426i	−0.0782589	+	0.322934i
$349$	14.9935	+	7.53000i	0.802582	+	0.403072i	0.802295	−	0.596928i	$-0.203612\pi$
$349$	14.9935	+	7.53000i	0.802582	+	0.403072i	0.000287376		1.00000i	$0.499909\pi$
$350$	1.47331	+	2.55185i	0.0787517	+	0.136402i
$351$	4.73561	+	4.60520i	0.252768	+	0.245807i
$352$	3.35926	−	5.81841i	0.179049	−	0.310123i
$353$	−16.4381	+	10.8115i	−0.874913	+	0.575440i	−0.905621	−	0.424089i	$-0.860594\pi$
$353$	−16.4381	+	10.8115i	−0.874913	+	0.575440i	0.0307072	+	0.999528i	$0.490224\pi$
$354$	−2.28042	−	0.144362i	−0.121203	−	0.00767276i
$355$	2.66518	−	6.17858i	0.141453	−	0.327925i
$356$	5.56652	+	18.5935i	0.295025	+	0.985452i
$357$	−3.59903	−	10.0456i	−0.190481	−	0.531670i
$358$	0.738459	+	1.71194i	0.0390288	+	0.0904789i
$359$	−27.1083	+	22.7466i	−1.43072	+	1.20052i	−0.485436	+	0.874272i	$0.661339\pi$
$359$	−27.1083	+	22.7466i	−1.43072	+	1.20052i	−0.945285	+	0.326245i	$0.894216\pi$
$360$	4.67238	+	1.75417i	0.246256	+	0.0924531i
$361$	0.352176	+	0.295511i	0.0185356	+	0.0155532i
$362$	−0.0761571	+	0.254382i	−0.00400273	+	0.0133700i
$363$	9.30337	+	14.3017i	0.488300	+	0.750643i
$364$	0.548756	−	9.42178i	0.0287626	−	0.493835i
$365$	3.16113	−	54.2745i	0.165461	−	2.84085i
$366$	0.621103	+	0.954795i	0.0324656	+	0.0499079i
$367$	−5.62009	+	18.7724i	−0.293366	+	0.979912i	0.676534	+	0.736411i	$0.263481\pi$
$367$	−5.62009	+	18.7724i	−0.293366	+	0.979912i	−0.969901	+	0.243501i	$0.921704\pi$
$368$	−3.19696	−	2.68257i	−0.166653	−	0.139839i
$369$	−2.83147	−	1.06303i	−0.147400	−	0.0553392i
$370$	1.02964	−	0.863973i	0.0535286	−	0.0449158i
$371$	4.26642	+	9.89067i	0.221501	+	0.513498i
$372$	−7.86923	−	21.9646i	−0.408001	−	1.13881i
$373$	−9.29538	−	31.0487i	−0.481297	−	1.60764i	−0.761815	−	0.647794i	$-0.775692\pi$
$373$	−9.29538	−	31.0487i	−0.481297	−	1.60764i	0.280518	−	0.959849i	$-0.409494\pi$
$374$	−0.368993	+	0.855421i	−0.0190802	+	0.0442328i
$375$	−7.91636	−	0.501145i	−0.408799	−	0.0258790i
$376$	3.92914	−	2.58423i	0.202630	−	0.133272i
$377$	1.14617	−	1.98523i	0.0590309	−	0.102245i
$378$	0.590668	−	2.33427i	0.0303807	−	0.120062i
$379$	7.22233	+	12.5094i	0.370986	+	0.642567i	0.989718	−	0.143036i	$-0.0456863\pi$
$379$	7.22233	+	12.5094i	0.370986	+	0.642567i	−0.618731	+	0.785603i	$0.712353\pi$
$380$	26.3681	+	13.2426i	1.35266	+	0.679329i
$381$	1.47736	−	6.09629i	0.0756873	−	0.312323i
$382$	−1.54050	−	2.06925i	−0.0788190	−	0.105872i
$383$	15.0027	−	15.9020i	0.766604	−	0.812553i	−0.220032	−	0.975493i	$-0.570616\pi$
$383$	15.0027	−	15.9020i	0.766604	−	0.812553i	0.986636	+	0.162940i	$0.0520975\pi$
$384$	−5.81554	−	3.39682i	−0.296773	−	0.173343i
$385$	57.1783	+	6.68318i	2.91407	+	0.340606i
$386$	−1.64078	−	0.597194i	−0.0835134	−	0.0303964i
$387$	−5.73336	−	3.85429i	−0.291443	−	0.195925i
$388$	−17.5223	+	6.37760i	−0.889561	+	0.323774i
$389$	−18.2511	+	4.32559i	−0.925367	+	0.219316i	−0.665560	−	0.746344i	$-0.731807\pi$
$389$	−18.2511	+	4.32559i	−0.925367	+	0.219316i	−0.259807	+	0.965660i	$0.583659\pi$
$390$	−0.734603	−	0.552671i	−0.0371980	−	0.0279856i
$391$	1.46939	+	0.966431i	0.0743101	+	0.0488745i
$392$	−3.08460	+	1.54914i	−0.155796	+	0.0782436i
$393$	2.44326	+	10.5456i	0.123246	+	0.531956i
$394$	−0.162877	−	0.172640i	−0.00820564	−	0.00869747i
$395$	3.28846	−	18.6498i	0.165461	−	0.938374i
$396$	22.8640	−	14.7097i	1.14896	−	0.739191i
$397$	−3.33925	−	18.9379i	−0.167592	−	0.950463i	−0.946351	−	0.323140i	$-0.895262\pi$
$397$	−3.33925	−	18.9379i	−0.167592	−	0.950463i	0.778759	−	0.627323i	$-0.215850\pi$
$398$	1.19106	−	1.59988i	0.0597027	−	0.0801946i
$399$	9.91071	−	26.8080i	0.496156	−	1.34208i
$400$	24.1815	+	5.73112i	1.20907	+	0.286556i
$401$	4.48498	−	0.524219i	0.223969	−	0.0261783i	−0.00336797	−	0.999994i	$-0.501072\pi$
$401$	4.48498	−	0.524219i	0.223969	−	0.0261783i	0.227337	+	0.973816i	$0.426998\pi$
$402$	−0.0724802	−	0.648451i	−0.00361498	−	0.0323418i
$403$	0.501697	+	8.61380i	0.0249913	+	0.429084i
$404$	10.8668			0.540643
$405$	20.3662	+	22.4785i	1.01201	+	1.11697i
$406$	−0.835597			−0.0414700
$407$	−0.854753	−	14.6755i	−0.0423685	−	0.727440i
$408$	1.29010	+	0.564228i	0.0638694	+	0.0279334i
$409$	−35.5723	+	4.15781i	−1.75894	+	0.205590i	−0.933420	−	0.358787i	$-0.883191\pi$
$409$	−35.5723	+	4.15781i	−1.75894	+	0.205590i	−0.825517	+	0.564377i	$0.809117\pi$
$410$	0.409560	+	0.0970674i	0.0202267	+	0.00479382i
$411$	−27.9581	+	4.78452i	−1.37907	+	0.236003i
$412$	2.77884	−	3.73264i	0.136904	−	0.183894i
$413$	6.91757	+	39.2315i	0.340392	+	1.93046i
$414$	0.153501	+	0.365960i	0.00754415	+	0.0179859i
$415$	−7.05659	+	40.0199i	−0.346395	+	1.96450i
$416$	1.28358	+	1.36052i	0.0629328	+	0.0667049i
$417$	32.3770	+	9.87122i	1.58551	+	0.483396i
$418$	−2.22986	+	1.11988i	−0.109066	+	0.0547750i
$419$	−20.8326	−	13.7018i	−1.01774	−	0.669376i	−0.0730427	−	0.997329i	$-0.523271\pi$
$419$	−20.8326	−	13.7018i	−1.01774	−	0.669376i	−0.944694	+	0.327953i	$0.893641\pi$
$420$	5.24821	−	43.0188i	0.256086	−	2.09910i
$421$	−35.1178	+	8.32306i	−1.71154	+	0.405641i	−0.965529	−	0.260297i	$-0.916179\pi$
$421$	−35.1178	+	8.32306i	−1.71154	+	0.405641i	−0.746007	+	0.665938i	$0.768031\pi$
$422$	−0.449170	+	0.163485i	−0.0218653	+	0.00795831i
$423$	28.4209	−	3.03169i	1.38187	−	0.147406i
$424$	−1.33566	−	0.486141i	−0.0648655	−	0.0236091i
$425$	−10.4020	−	1.21582i	−0.504570	−	0.0589758i
$426$	0.372064	−	0.212317i	0.0180266	−	0.0102868i
$427$	13.6274	−	14.4442i	0.659478	−	0.699006i
$428$	−13.9463	−	18.7332i	−0.674122	−	0.905503i
$429$	−9.64624	+	2.83497i	−0.465725	+	0.136874i
$430$	0.859171	+	0.431492i	0.0414329	+	0.0208084i
$431$	12.8170	+	22.1998i	0.617375	+	1.06933i	0.989963	+	0.141329i	$0.0451374\pi$
$431$	12.8170	+	22.1998i	0.617375	+	1.06933i	−0.372587	+	0.927997i	$0.621529\pi$
$432$	−10.9011	−	17.1335i	−0.524482	−	0.824334i
$433$	−2.49590	+	4.32302i	−0.119945	+	0.207751i	−0.919746	−	0.392515i	$-0.871605\pi$
$433$	−2.49590	+	4.32302i	−0.119945	+	0.207751i	0.799801	+	0.600266i	$0.204939\pi$
$434$	2.62777	−	1.72831i	0.126137	−	0.0829615i
$435$	5.82860	−	8.76535i	0.279460	−	0.420267i
$436$	−0.332969	+	0.771908i	−0.0159463	+	0.0369677i
$437$	1.35103	+	4.51274i	0.0646283	+	0.215874i
$438$	2.23811	−	2.64012i	0.106941	−	0.126150i
$439$	1.33282	+	3.08983i	0.0636120	+	0.147469i	0.947057	−	0.321066i	$-0.104041\pi$
$439$	1.33282	+	3.08983i	0.0636120	+	0.147469i	−0.883445	+	0.468535i	$0.844782\pi$
$440$	−5.81918	+	4.88287i	−0.277418	+	0.232782i
$441$	−20.9776	−	0.211585i	−0.998932	−	0.0100755i
$442$	−0.198684	−	0.166715i	−0.00945041	−	0.00792984i
$443$	3.83903	−	12.8232i	0.182398	−	0.609251i	−0.817067	−	0.576542i	$-0.804402\pi$
$443$	3.83903	−	12.8232i	0.182398	−	0.609251i	0.999465	−	0.0327082i	$-0.0104132\pi$
$444$	−11.0511	+	0.587749i	−0.524461	+	0.0278933i
$445$	1.91643	−	32.9038i	0.0908475	−	1.55979i
$446$	−0.0215505	+	0.370008i	−0.00102045	+	0.0175204i
$447$	−3.21543	+	6.32274i	−0.152085	+	0.299055i
$448$	−8.19017	+	27.3571i	−0.386949	+	1.29250i
$449$	−25.1690	−	21.1193i	−1.18780	−	0.996683i	−0.999895	−	0.0144961i	$-0.995386\pi$
$449$	−25.1690	−	21.1193i	−1.18780	−	0.996683i	−0.187906	−	0.982187i	$-0.560170\pi$
$450$	−1.79487	−	1.53719i	−0.0846109	−	0.0724637i
$451$	3.52643	−	2.95903i	0.166053	−	0.139335i
$452$	10.7920	+	25.0186i	0.507612	+	1.17678i
$453$	−15.1126	−	2.74342i	−0.710053	−	0.128897i
$454$	−0.853861	−	2.85209i	−0.0400737	−	0.133855i
$455$	−6.34794	+	14.7162i	−0.297596	+	0.689905i
$456$	1.67562	+	3.37882i	0.0784682	+	0.158228i
$457$	17.7088	−	11.6472i	0.828380	−	0.544834i	−0.0630403	−	0.998011i	$-0.520080\pi$
$457$	17.7088	−	11.6472i	0.828380	−	0.544834i	0.891421	+	0.453177i	$0.149709\pi$
$458$	0.293167	−	0.507780i	0.0136988	−	0.0237270i
$459$	5.40110	+	6.63820i	0.252102	+	0.309844i
$460$	3.57135	+	6.18576i	0.166515	+	0.288413i
$461$	14.8202	+	7.44297i	0.690245	+	0.346654i	0.759101	−	0.650973i	$-0.225639\pi$
$461$	14.8202	+	7.44297i	0.690245	+	0.346654i	−0.0688566	+	0.997627i	$0.521935\pi$
$462$	2.65305	+	2.52843i	0.123431	+	0.117633i
$463$	2.04248	+	2.74353i	0.0949220	+	0.127502i	0.847047	−	0.531518i	$-0.178378\pi$
$463$	2.04248	+	2.74353i	0.0949220	+	0.127502i	−0.752125	+	0.659021i	$0.770971\pi$
$464$	−4.83615	+	5.12602i	−0.224513	+	0.237970i
$465$	−0.199807	+	39.6207i	−0.00926583	+	1.83737i
$466$	1.28586	+	0.150296i	0.0595664	+	0.00696231i
$467$	8.87582	+	3.23054i	0.410724	+	0.149491i	0.539115	−	0.842232i	$-0.318759\pi$
$467$	8.87582	+	3.23054i	0.410724	+	0.149491i	−0.128391	+	0.991724i	$0.540981\pi$
$468$	2.09756	+	7.27251i	0.0969597	+	0.336172i
$469$	−10.6895	+	3.89067i	−0.493597	+	0.179655i
$470$	−3.87049	+	0.917324i	−0.178533	+	0.0423130i
$471$	8.45126	−	3.59508i	0.389413	−	0.165652i
$472$	−4.39191	−	2.88861i	−0.202154	−	0.132959i
$473$	9.39673	−	4.71922i	0.432062	−	0.216990i
$474$	0.881096	−	0.822912i	0.0404701	−	0.0377976i
$475$	−19.2497	−	20.4034i	−0.883235	−	0.936174i
$476$	2.12321	−	12.0413i	0.0973173	−	0.551914i
$477$	−5.86456	−	6.34304i	−0.268520	−	0.290428i
$478$	−0.340467	−	1.93089i	−0.0155726	−	0.0883166i
$479$	10.9101	−	14.6547i	0.498493	−	0.669592i	−0.479666	−	0.877451i	$-0.659242\pi$
$479$	10.9101	−	14.6547i	0.498493	−	0.669592i	0.978159	+	0.207859i	$0.0666495\pi$
$480$	5.48768	+	6.60734i	0.250477	+	0.301583i
$481$	3.98231	+	0.943825i	0.181578	+	0.0430347i
$482$	−2.17053	+	0.253698i	−0.0988648	+	0.0115556i
$483$	5.57042	−	4.10353i	0.253463	−	0.186717i
$484$	1.13671	+	19.5165i	0.0516686	+	0.887115i
$485$	31.6656			1.43786
$486$	0.175754	+	1.92305i	0.00797238	+	0.0872312i
$487$	31.2157			1.41452			0.707260	−	0.706954i	$-0.249931\pi$
$487$	31.2157			1.41452			0.707260	+	0.706954i	$0.249931\pi$
$488$	0.152363	+	2.61597i	0.00689713	+	0.118419i
$489$	−6.78649	+	4.99936i	−0.306896	+	0.226079i
$490$	2.89981	−	0.338939i	0.131000	−	0.0153117i
$491$	2.12757	+	0.504243i	0.0960159	+	0.0227562i	0.278343	−	0.960482i	$-0.410215\pi$
$491$	2.12757	+	0.504243i	0.0960159	+	0.0227562i	−0.182327	+	0.983238i	$0.558363\pi$
$492$	−2.21418	−	2.66595i	−0.0998231	−	0.120190i
$493$	1.77347	−	2.38219i	0.0798733	−	0.107288i
$494$	−0.120632	−	0.684137i	−0.00542748	−	0.0307808i
$495$	−45.0291	+	10.1935i	−2.02391	+	0.458166i
$496$	4.60620	−	26.1231i	0.206825	−	1.17296i
$497$	−5.12516	−	5.43235i	−0.229895	−	0.243674i
$498$	−1.89071	+	1.76586i	−0.0847248	+	0.0791300i
$499$	0.562307	−	0.282401i	0.0251723	−	0.0126420i	−0.436169	−	0.899865i	$-0.643665\pi$
$499$	0.562307	−	0.282401i	0.0251723	−	0.0126420i	0.461341	+	0.887223i	$0.347369\pi$
$500$	−7.59379	−	4.99451i	−0.339605	−	0.223361i
$501$	−35.6207	+	15.1527i	−1.59141	+	0.676971i
$502$	−2.48853	+	0.589793i	−0.111069	+	0.0263238i
$503$	5.84089	−	2.12591i	0.260432	−	0.0947897i	−0.208504	−	0.978021i	$-0.566859\pi$
$503$	5.84089	−	2.12591i	0.260432	−	0.0947897i	0.468937	+	0.883232i	$0.344637\pi$
$504$	3.84177	−	3.99063i	0.171126	−	0.177757i
$505$	−17.3408	−	6.31154i	−0.771656	−	0.280860i
$506$	−0.599949	−	0.0701240i	−0.0266710	−	0.00311739i
$507$	−0.0994342	+	19.7173i	−0.00441603	+	0.875676i
$508$	4.93241	−	5.22805i	0.218840	−	0.231957i
$509$	11.1759	+	15.0119i	0.495365	+	0.665390i	0.977556	−	0.210676i	$-0.0675665\pi$
$509$	11.1759	+	15.0119i	0.495365	+	0.665390i	−0.482191	+	0.876066i	$0.660159\pi$
$510$	−0.862157	−	0.821660i	−0.0381770	−	0.0363837i
$511$	−53.9233	−	27.0813i	−2.38543	−	1.19801i
$512$	−4.80425	−	8.32121i	−0.212320	−	0.367749i
$513$	−0.346769	+	22.9193i	−0.0153102	+	1.01191i
$514$	−0.451387	+	0.781825i	−0.0199098	+	0.0344848i
$515$	−6.60232	+	4.34242i	−0.290933	+	0.191350i
$516$	−3.51698	−	7.09183i	−0.154826	−	0.312200i
$517$	−17.2311	+	39.9462i	−0.757823	+	1.75683i
$518$	−0.427862	−	1.42916i	−0.0187992	−	0.0627936i
$519$	5.94833	+	1.07981i	0.261103	+	0.0473983i
$520$	−0.837651	−	1.94189i	−0.0367334	−	0.0851577i
$521$	−10.7516	+	9.02171i	−0.471038	+	0.395248i	−0.847173	−	0.531317i	$-0.821697\pi$
$521$	−10.7516	+	9.02171i	−0.471038	+	0.395248i	0.376135	+	0.926565i	$0.377253\pi$
$522$	0.632004	−	0.222838i	0.0276621	−	0.00975335i
$523$	−15.7777	−	13.2390i	−0.689910	−	0.578903i	0.228973	−	0.973433i	$-0.426463\pi$
$523$	−15.7777	−	13.2390i	−0.689910	−	0.578903i	−0.918883	+	0.394530i	$0.870908\pi$
$524$	−3.55741	+	11.8826i	−0.155406	+	0.519093i
$525$	−18.6757	+	36.7235i	−0.815075	+	1.60274i
$526$	0.0752113	−	1.29133i	0.00327937	−	0.0563046i
$527$	−0.649974	+	11.1596i	−0.0283133	+	0.486121i
$528$	30.8657	−	1.64159i	1.34326	−	0.0714409i
$529$	6.26943	−	20.9414i	0.272584	−	0.910494i
$530$	0.920961	+	0.772778i	0.0400040	+	0.0335673i
$531$	−15.6944	−	27.8280i	−0.681080	−	1.20763i
$532$	25.0877	−	21.0511i	1.08769	−	0.912680i
$533$	0.507618	+	1.17679i	0.0219874	+	0.0509724i
$534$	1.35685	−	1.60057i	0.0587168	−	0.0692636i
$535$	11.3746	+	37.9939i	0.491767	+	1.64262i
$536$	0.594547	−	1.37831i	0.0256805	−	0.0595341i
$537$	−14.4344	+	21.7072i	−0.622889	+	0.936733i
$538$	−2.30963	+	1.51907i	−0.0995751	+	0.0654916i
$539$	15.9655	−	27.6531i	0.687684	−	1.19110i
$540$	7.50281	+	33.9368i	0.322870	+	1.46041i
$541$	−19.2442	−	33.3319i	−0.827372	−	1.43305i	−0.900093	−	0.435698i	$-0.856502\pi$
$541$	−19.2442	−	33.3319i	−0.827372	−	1.43305i	0.0727213	−	0.997352i	$-0.476832\pi$
$542$	−2.57517	−	1.29330i	−0.110613	−	0.0555519i
$543$	−3.56209	+	1.04687i	−0.152864	+	0.0449257i
$544$	1.44708	+	1.94376i	0.0620429	+	0.0833381i
$545$	0.979670	−	1.03839i	0.0419644	−	0.0444797i
$546$	−0.886186	+	0.505698i	−0.0379253	+	0.0216419i
$547$	−18.3380	−	2.14340i	−0.784075	−	0.0916453i	−0.285371	−	0.958417i	$-0.592117\pi$
$547$	−18.3380	−	2.14340i	−0.784075	−	0.0916453i	−0.498705	+	0.866772i	$0.666191\pi$
$548$	−30.5412	−	11.1161i	−1.30465	−	0.474855i
$549$	−6.45511	+	14.5591i	−0.275497	+	0.621367i
$550$	3.37997	−	1.23021i	0.144123	−	0.0524563i
$551$	7.74019	−	1.83446i	0.329743	−	0.0781506i
$552$	−0.110561	+	0.906248i	−0.00470577	+	0.0385725i
$553$	−17.5610	−	11.5501i	−0.746770	−	0.491159i
$554$	0.980975	−	0.492664i	0.0416776	−	0.0209313i
$555$	17.9763	+	5.48067i	0.763049	+	0.232641i
$556$	26.6158	+	28.2111i	1.12876	+	1.19642i
$557$	1.24763	−	7.07568i	0.0528639	−	0.299806i	−0.946900	−	0.321528i	$-0.895804\pi$
$557$	1.24763	−	7.07568i	0.0528639	−	0.299806i	0.999764	+	0.0217217i	$0.00691477\pi$
$558$	−1.52660	+	2.00798i	−0.0646263	+	0.0850047i
$559$	0.508348	+	2.88298i	0.0215008	+	0.121937i
$560$	29.4227	−	39.5216i	1.24334	−	1.67009i
$561$	−12.8391	+	2.19718i	−0.542067	+	0.0927649i
$562$	2.58960	+	0.613746i	0.109236	+	0.0258893i
$563$	30.5750	−	3.57370i	1.28858	−	0.150613i	0.555936	−	0.831225i	$-0.312360\pi$
$563$	30.5750	−	3.57370i	1.28858	−	0.150613i	0.732645	+	0.680611i	$0.238286\pi$
$564$	30.0063	+	13.1233i	1.26349	+	0.552592i
$565$	−2.69037	−	46.1918i	−0.113185	−	1.94330i
$566$	−0.0757672			−0.00318473
$567$	31.8618	−	10.8741i	1.33807	−	0.456670i
$568$	0.985508			0.0413510
$569$	1.75691	+	30.1649i	0.0736534	+	1.26458i	0.809374	+	0.587294i	$0.199807\pi$
$569$	1.75691	+	30.1649i	0.0736534	+	1.26458i	−0.735720	+	0.677285i	$0.763156\pi$
$570$	−0.354352	−	3.17025i	−0.0148422	−	0.132787i
$571$	7.84368	−	0.916795i	0.328248	−	0.0383667i	0.0496269	−	0.998768i	$-0.484197\pi$
$571$	7.84368	−	0.916795i	0.328248	−	0.0383667i	0.278621	+	0.960401i	$0.410123\pi$
$572$	−11.2100	−	2.65681i	−0.468713	−	0.111087i
$573$	12.5073	−	33.8316i	0.522499	−	1.41334i
$574$	0.278972	−	0.374724i	0.0116441	−	0.0156407i
$575$	−1.17912	−	6.68713i	−0.0491728	−	0.278873i
$576$	−1.10098	−	22.8757i	−0.0458742	−	0.953154i
$577$	−1.81528	+	10.2950i	−0.0755710	+	0.428585i	0.923425	+	0.383780i	$0.125378\pi$
$577$	−1.81528	+	10.2950i	−0.0755710	+	0.428585i	−0.998996	+	0.0448050i	$0.985733\pi$
$578$	1.21458	+	1.28738i	0.0505199	+	0.0535480i
$579$	−5.51029	−	23.7836i	−0.229000	−	0.988413i
$580$	10.7786	−	5.41320i	0.447556	−	0.224771i
$581$	37.6835	+	24.7849i	1.56338	+	1.02825i
$582$	1.61093	+	1.21197i	0.0667752	+	0.0502376i
$583$	12.7943	−	3.03231i	0.529887	−	0.125585i
$584$	7.48227	−	2.72332i	0.309619	−	0.112692i
$585$	0.876737	−	12.8235i	0.0362486	−	0.530185i
$586$	−3.60373	−	1.31165i	−0.148869	−	0.0541837i
$587$	14.9536	+	1.74783i	0.617201	+	0.0721405i	0.418948	−	0.908010i	$-0.362399\pi$
$587$	14.9536	+	1.74783i	0.617201	+	0.0721405i	0.198253	+	0.980151i	$0.436473\pi$
$588$	−20.7568	−	12.1239i	−0.855996	−	0.499982i
$589$	−20.5469	+	21.7784i	−0.846619	+	0.897364i
$590$	2.65509	+	3.56641i	0.109308	+	0.146827i
$591$	0.781590	−	3.22522i	0.0321503	−	0.132668i
$592$	−11.2436	−	5.64673i	−0.462108	−	0.232079i
$593$	9.50914	+	16.4703i	0.390494	+	0.676355i	0.992515	−	0.122125i	$-0.0389710\pi$
$593$	9.50914	+	16.4703i	0.390494	+	0.676355i	−0.602021	+	0.798480i	$0.705638\pi$
$594$	−2.68092	−	1.20486i	−0.109999	−	0.0494360i
$595$	−10.3819	+	17.9819i	−0.425615	+	0.737187i
$596$	−6.79075	+	4.46635i	−0.278160	+	0.182949i
$597$	27.8320	+	1.76190i	1.13909	+	0.0721100i
$598$	0.0666065	−	0.154411i	0.00272374	−	0.00631434i
$599$	11.4208	+	38.1481i	0.466641	+	1.55869i	0.790424	+	0.612560i	$0.209860\pi$
$599$	11.4208	+	38.1481i	0.466641	+	1.55869i	−0.323783	+	0.946131i	$0.604955\pi$
$600$	−1.83362	−	5.11798i	−0.0748571	−	0.208941i
$601$	2.21155	+	5.12695i	0.0902111	+	0.209133i	0.957348	−	0.288937i	$-0.0933017\pi$
$601$	2.21155	+	5.12695i	0.0902111	+	0.209133i	−0.867137	+	0.498069i	$0.834042\pi$
$602$	0.817450	−	0.685922i	0.0333168	−	0.0279561i
$603$	7.04746	−	5.79341i	0.286995	−	0.235926i
$604$	−13.4821	−	11.3129i	−0.548580	−	0.460314i
$605$	9.52147	−	31.8039i	0.387103	−	1.29301i
$606$	−0.640615	−	0.984789i	−0.0260232	−	0.0400043i
$607$	−0.818590	+	14.0546i	−0.0332255	+	0.570460i	0.940081	+	0.340951i	$0.110749\pi$
$607$	−0.818590	+	14.0546i	−0.0332255	+	0.570460i	−0.973307	+	0.229509i	$0.926288\pi$
$608$	−0.377395	+	6.47963i	−0.0153054	+	0.262784i
$609$	−6.37076	−	9.79348i	−0.258156	−	0.396852i
$610$	0.635664	−	2.12327i	0.0257373	−	0.0859685i
$611$	−9.27806	−	7.78522i	−0.375350	−	0.314956i
$612$	1.60531	+	9.67369i	0.0648907	+	0.391036i
$613$	−13.7550	+	11.5418i	−0.555561	+	0.466171i	−0.876819	−	0.480821i	$-0.840339\pi$
$613$	−13.7550	+	11.5418i	−0.555561	+	0.466171i	0.321258	+	0.946992i	$0.395894\pi$
$614$	1.11620	+	2.58764i	0.0450462	+	0.104429i
$615$	1.98490	+	5.54024i	0.0800389	+	0.223404i
$616$	2.41812	+	8.07709i	0.0974290	+	0.325435i
$617$	13.5528	−	31.4190i	0.545617	−	1.26488i	−0.392879	−	0.919590i	$-0.628521\pi$
$617$	13.5528	−	31.4190i	0.545617	−	1.26488i	0.938496	−	0.345291i	$-0.112220\pi$
$618$	−0.502082	−	0.0317843i	−0.0201967	−	0.00127855i
$619$	28.9445	−	19.0371i	1.16338	−	0.765165i	0.187239	−	0.982314i	$-0.440046\pi$
$619$	28.9445	−	19.0371i	1.16338	−	0.765165i	0.976138	+	0.217149i	$0.0696759\pi$
$620$	−22.6998	+	39.3172i	−0.911646	+	1.57902i
$621$	−3.11886	+	4.58923i	−0.125155	+	0.184159i
$622$	1.89740	+	3.28639i	0.0760787	+	0.131772i
$623$	−32.6910	−	16.4180i	−1.30974	−	0.657774i
$624$	−2.02671	+	8.36317i	−0.0811332	+	0.334795i
$625$	−9.76915	−	13.1222i	−0.390766	−	0.524890i
$626$	1.93908	−	2.05531i	0.0775012	−	0.0821465i
$627$	−30.1262	−	17.5966i	−1.20313	−	0.702739i
$628$	10.4524	+	1.22171i	0.417096	+	0.0487515i
$629$	4.98245	+	1.81347i	0.198663	+	0.0723076i
$630$	−4.20791	+	2.06041i	−0.167647	+	0.0820887i
$631$	40.5340	−	14.7532i	1.61363	−	0.587314i	0.631478	−	0.775394i	$-0.282449\pi$
$631$	40.5340	−	14.7532i	1.61363	−	0.587314i	0.982154	+	0.188080i	$0.0602263\pi$
$632$	2.69881	−	0.639630i	0.107353	−	0.0254431i
$633$	−5.34066	−	4.01799i	−0.212272	−	0.159701i
$634$	0.830283	+	0.546086i	0.0329748	+	0.0216878i
$635$	−10.9074	+	5.47793i	−0.432849	+	0.217385i
$636$	−2.23417	−	9.64315i	−0.0885905	−	0.382376i
$637$	6.10047	+	6.46612i	0.241709	+	0.256197i
$638$	−0.177121	+	1.00450i	−0.00701230	+	0.0397687i
$639$	5.32512	+	2.74198i	0.210658	+	0.108471i
$640$	2.27566	+	12.9059i	0.0899534	+	0.510151i
$641$	2.87030	−	3.85549i	0.113370	−	0.152283i	−0.741816	−	0.670603i	$-0.766035\pi$
$641$	2.87030	−	3.85549i	0.113370	−	0.152283i	0.855186	+	0.518321i	$0.173443\pi$
$642$	−0.875511	+	2.36822i	−0.0345537	+	0.0934661i
$643$	8.07150	+	1.91298i	0.318309	+	0.0754405i	0.386664	−	0.922220i	$-0.373627\pi$
$643$	8.07150	+	1.91298i	0.318309	+	0.0754405i	−0.0683558	+	0.997661i	$0.521775\pi$
$644$	7.87414	−	0.920354i	0.310284	−	0.0362670i
$645$	1.49326	+	13.3596i	0.0587969	+	0.526032i
$646$	−0.0523308	−	0.898486i	−0.00205893	−	0.0353504i
$647$	−24.6332			−0.968431			−0.484215	−	0.874949i	$-0.660895\pi$
$647$	−24.6332			−0.968431			−0.484215	+	0.874949i	$0.660895\pi$
$648$	−1.84150	+	4.04284i	−0.0723410	+	0.158818i
$649$	48.6281			1.90882
$650$	0.0582253	+	0.999689i	0.00228378	+	0.0392110i
$651$	40.2910	+	17.6214i	1.57913	+	0.690636i
$652$	−9.59312	+	1.12127i	−0.375695	+	0.0439125i
$653$	10.4367	+	2.47355i	0.408420	+	0.0967974i	0.429690	−	0.902976i	$-0.358623\pi$
$653$	10.4367	+	2.47355i	0.408420	+	0.0967974i	−0.0212699	+	0.999774i	$0.506771\pi$
$654$	0.0895821	−	0.0153304i	0.00350294	−	0.000599464i
$655$	12.5783	−	16.8956i	0.491475	−	0.660166i
$656$	−0.684175	−	3.88015i	−0.0267125	−	0.151494i
$657$	48.0070	+	6.10261i	1.87293	+	0.238086i
$658$	−0.766638	+	4.34782i	−0.0298867	+	0.169496i
$659$	−11.6727	−	12.3723i	−0.454704	−	0.481958i	0.458944	−	0.888465i	$-0.348228\pi$
$659$	−11.6727	−	12.3723i	−0.454704	−	0.481958i	−0.913647	+	0.406507i	$0.866747\pi$
$660$	−50.6021	−	15.4278i	−1.96968	−	0.600524i
$661$	−27.9077	+	14.0158i	−1.08549	+	0.545151i	−0.899286	−	0.437361i	$-0.855913\pi$
$661$	−27.9077	+	14.0158i	−1.08549	+	0.545151i	−0.186199	+	0.982512i	$0.559617\pi$
$662$	−1.90431	−	1.25248i	−0.0740129	−	0.0486791i
$663$	0.439158	−	3.59971i	0.0170555	−	0.139801i
$664$	−5.79128	+	1.37256i	−0.224745	+	0.0532656i
$665$	−52.2606	+	19.0213i	−2.02658	+	0.737615i
$666$	0.704742	+	0.966840i	0.0273082	+	0.0374643i
$667$	1.80945	+	0.658587i	0.0700622	+	0.0255006i
$668$	−44.0552	−	5.14931i	−1.70454	−	0.199233i
$669$	−4.50093	+	2.56843i	−0.174016	+	0.0993014i
$670$	−0.871278	+	0.923501i	−0.0336604	+	0.0356779i
$671$	−14.4754	−	19.4438i	−0.558816	−	0.750621i
$672$	9.14622	−	2.68802i	0.352823	−	0.103692i
$673$	−7.29455	−	3.66346i	−0.281184	−	0.141216i	0.302618	−	0.953112i	$-0.402139\pi$
$673$	−7.29455	−	3.66346i	−0.281184	−	0.141216i	−0.583802	+	0.811896i	$0.698436\pi$
$674$	−1.65264	−	2.86245i	−0.0636572	−	0.110258i
$675$	4.33192	−	32.7563i	0.166736	−	1.26079i
$676$	−11.2966	+	19.5663i	−0.434484	+	0.752548i
$677$	4.55342	−	2.99483i	0.175002	−	0.115101i	−0.458986	−	0.888444i	$-0.651787\pi$
$677$	4.55342	−	2.99483i	0.175002	−	0.115101i	0.633988	+	0.773343i	$0.281417\pi$
$678$	1.63107	−	2.45289i	0.0626410	−	0.0942029i
$679$	13.9206	−	32.2715i	0.534223	−	1.23847i
$680$	−0.785814	−	2.62480i	−0.0301346	−	0.100657i
$681$	26.9175	−	31.7525i	1.03148	−	1.21676i
$682$	−1.52066	−	3.52529i	−0.0582292	−	0.134990i
$683$	−2.37757	+	1.99502i	−0.0909753	+	0.0763374i	−0.687141	−	0.726524i	$-0.741135\pi$
$683$	−2.37757	+	1.99502i	−0.0909753	+	0.0763374i	0.596166	+	0.802861i	$0.296690\pi$
$684$	−13.3612	+	22.6124i	−0.510877	+	0.864607i
$685$	42.2801	+	35.4772i	1.61544	+	1.35551i
$686$	−0.000945928		0.00315962i	−3.61157e−5		0.000120635i
$687$	8.18651	−	0.435398i	0.312335	−	0.0166115i
$688$	0.523292	−	8.98458i	0.0199503	−	0.342534i
$689$	−0.212847	+	3.65445i	−0.00810884	+	0.139223i
$690$	0.350040	−	0.688309i	0.0133258	−	0.0262035i
$691$	−7.28011	+	24.3173i	−0.276948	+	0.925072i	0.700456	+	0.713695i	$0.252980\pi$
$691$	−7.28011	+	24.3173i	−0.276948	+	0.925072i	−0.977405	+	0.211377i	$0.932205\pi$
$692$	5.30656	+	4.45274i	0.201725	+	0.169268i
$693$	−9.40671	+	50.3719i	−0.357332	+	1.91347i
$694$	2.32850	−	1.95384i	0.0883885	−	0.0741667i
$695$	−26.0871	−	60.4768i	−0.989542	−	2.29402i
$696$	1.51689	+	0.275363i	0.0574976	+	0.0104376i
$697$	0.476204	+	1.59063i	0.0180375	+	0.0602495i
$698$	0.823226	−	1.90845i	0.0311596	−	0.0722360i
$699$	8.04214	+	16.2166i	0.304182	+	0.613369i
$700$	−39.4417	+	25.9412i	−1.49076	+	0.980487i
$701$	0.473675	−	0.820430i	0.0178905	−	0.0309872i	−0.856942	−	0.515414i	$-0.827638\pi$
$701$	0.473675	−	0.820430i	0.0178905	−	0.0309872i	0.874832	+	0.484426i	$0.160972\pi$
$702$	0.535407	−	0.618814i	0.0202076	−	0.0233556i
$703$	7.10086	+	12.2991i	0.267814	+	0.463868i
$704$	31.1510	+	15.6446i	1.17405	+	0.589628i
$705$	−40.2607	−	38.3696i	−1.51631	−	1.44508i
$706$	1.45544	+	1.95500i	0.0547763	+	0.0735773i
$707$	−14.0555	+	14.8980i	−0.528613	+	0.560297i
$708$	0.184611	−	36.6075i	0.00693812	−	1.37579i
$709$	−32.0392	−	3.74485i	−1.20326	−	0.140641i	−0.509257	−	0.860615i	$-0.670080\pi$
$709$	−32.0392	−	3.74485i	−1.20326	−	0.140641i	−0.694001	+	0.719974i	$0.744154\pi$
$710$	−0.783290	−	0.285094i	−0.0293963	−	0.0106994i
$711$	16.3625	+	4.05270i	0.613640	+	0.151988i
$712$	4.53612	−	1.65101i	0.169998	−	0.0618743i
$713$	−7.05251	+	1.67148i	−0.264119	+	0.0625973i
$714$	−1.21640	+	0.517443i	−0.0455225	+	0.0193648i
$715$	16.3453	+	10.7505i	0.611281	+	0.402046i
$716$	−26.6928	+	13.4056i	−0.997558	+	0.500992i
$717$	20.0348	−	18.7118i	0.748215	−	0.698806i
$718$	3.00828	+	3.18859i	0.112268	+	0.118997i
$719$	−4.35548	+	24.7012i	−0.162432	+	0.921198i	0.789241	+	0.614084i	$0.210474\pi$
$719$	−4.35548	+	24.7012i	−0.162432	+	0.921198i	−0.951673	+	0.307114i	$0.900637\pi$
$720$	−11.7142	+	37.7386i	−0.436563	+	1.40644i
$721$	1.52305	+	8.63763i	0.0567213	+	0.321682i
$722$	0.0340086	−	0.0456815i	0.00126567	−	0.00170009i
$723$	−19.5220	−	23.5051i	−0.726029	−	0.874163i
$724$	−4.13953	−	0.981087i	−0.153844	−	0.0364618i
$725$	−11.3889	+	1.33117i	−0.422973	+	0.0494384i
$726$	1.70165	−	1.25354i	0.0631541	−	0.0465233i
$727$	0.505316	+	8.67595i	0.0187411	+	0.321773i	0.994629	+	0.103502i	$0.0330047\pi$
$727$	0.505316	+	8.67595i	0.0187411	+	0.321773i	−0.975888	+	0.218271i	$0.929958\pi$
$728$	−2.34729			−0.0869964
$729$	−21.1988	+	16.7216i	−0.785140	+	0.619318i
$730$	−6.73479			−0.249266
$731$	0.220524	+	3.78626i	0.00815639	+	0.140040i
$732$	−14.6924	+	10.8233i	−0.543046	+	0.400042i
$733$	−8.61465	+	1.00691i	−0.318189	+	0.0371910i	−0.273689	−	0.961818i	$-0.588244\pi$
$733$	−8.61465	+	1.00691i	−0.318189	+	0.0371910i	−0.0445007	+	0.999009i	$0.514170\pi$
$734$	2.36203	+	0.559811i	0.0871841	+	0.0206630i
$735$	26.0812	+	31.4026i	0.962020	+	1.15830i
$736$	−0.938248	+	1.26029i	−0.0345843	+	0.0464547i
$737$	2.41128	+	13.6750i	0.0888205	+	0.503726i
$738$	−0.111069	+	0.357819i	−0.00408849	+	0.0131715i
$739$	−0.311908	+	1.76892i	−0.0114737	+	0.0650707i	−0.990007	−	0.141018i	$-0.954962\pi$
$739$	−0.311908	+	1.76892i	−0.0114737	+	0.0650707i	0.978533	+	0.206089i	$0.0660736\pi$
$740$	14.7775	+	15.6633i	0.543232	+	0.575793i
$741$	7.09859	−	6.62984i	0.260773	−	0.243553i
$742$	1.19243	−	0.598861i	0.0437755	−	0.0219849i
$743$	−19.4949	−	12.8220i	−0.715198	−	0.470393i	0.139032	−	0.990288i	$-0.455601\pi$
$743$	−19.4949	−	12.8220i	−0.715198	−	0.470393i	−0.854230	+	0.519895i	$0.825971\pi$
$744$	−5.33983	+	2.27151i	−0.195768	+	0.0832776i
$745$	13.4305	−	3.18309i	0.492056	−	0.116619i
$746$	−3.77279	+	1.37318i	−0.138132	+	0.0502758i
$747$	−35.1116	−	8.69654i	−1.28467	−	0.318190i
$748$	−14.0253	−	5.10480i	−0.512816	−	0.186650i
$749$	43.7213	+	5.11028i	1.59754	+	0.186726i
$750$	−0.00495530	+	0.982611i	−0.000180942	+	0.0358799i
$751$	−13.3169	+	14.1151i	−0.485942	+	0.515069i	−0.923227	−	0.384254i	$-0.874459\pi$
$751$	−13.3169	+	14.1151i	−0.485942	+	0.515069i	0.437285	+	0.899323i	$0.355940\pi$
$752$	22.2349	+	29.8667i	0.810824	+	1.08913i
$753$	−25.8856	−	24.6698i	−0.943325	−	0.899016i
$754$	−0.253765	−	0.127446i	−0.00924159	−	0.00464130i
$755$	14.9437	+	25.8832i	0.543855	+	0.941985i
$756$	37.8845	+	7.27266i	1.37785	+	0.264504i
$757$	−8.52025	+	14.7575i	−0.309674	+	0.536371i	−0.978291	−	0.207236i	$-0.933553\pi$
$757$	−8.52025	+	14.7575i	−0.309674	+	0.536371i	0.668617	+	0.743607i	$0.266886\pi$
$758$	1.49500	−	0.983276i	0.0543008	−	0.0357142i
$759$	−3.75225	−	7.56625i	−0.136198	−	0.274637i
$760$	2.90671	−	6.73851i	0.105437	−	0.244432i
$761$	−12.2986	−	41.0803i	−0.445826	−	1.48916i	−0.825693	−	0.564120i	$-0.809215\pi$
$761$	−12.2986	−	41.0803i	−0.445826	−	1.48916i	0.379867	−	0.925041i	$-0.375970\pi$
$762$	−0.764558	−	0.138791i	−0.0276970	−	0.00502788i
$763$	−0.627584	−	1.45490i	−0.0227201	−	0.0526710i
$764$	31.6606	−	26.5664i	1.14544	−	0.961137i
$765$	3.05689	−	16.3693i	0.110522	−	0.591832i
$766$	−2.07463	−	1.74082i	−0.0749594	−	0.0628984i
$767$	−3.88279	+	12.9694i	−0.140199	+

Overview	Random
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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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00720285 - 0.123668i) q^{2} +(1.39452 - 1.02729i) q^{3} +(1.97123 - 0.230404i) q^{4} +(-3.27944 - 0.777242i) q^{5} +(-0.137087 - 0.165058i) q^{6} +(-2.23379 + 3.00051i) q^{7} +(-0.0857144 - 0.486111i) q^{8} +(0.889352 - 2.86514i) q^{9} +O(q^{10})\)	\(q+(-0.00720285 - 0.123668i) q^{2} +(1.39452 - 1.02729i) q^{3} +(1.97123 - 0.230404i) q^{4} +(-3.27944 - 0.777242i) q^{5} +(-0.137087 - 0.165058i) q^{6} +(-2.23379 + 3.00051i) q^{7} +(-0.0857144 - 0.486111i) q^{8} +(0.889352 - 2.86514i) q^{9} +(-0.0724987 + 0.411161i) q^{10} +(3.13353 + 3.32135i) q^{11} +(2.51223 - 2.34633i) q^{12} +(-1.13603 + 0.570535i) q^{13} +(0.387157 + 0.254637i) q^{14} +(-5.37169 + 2.28506i) q^{15} +(3.80282 - 0.901284i) q^{16} +(-1.54764 + 0.563296i) q^{17} +(-0.360733 - 0.0893473i) q^{18} +(-4.14528 - 1.50876i) q^{19} +(-6.64363 - 0.776529i) q^{20} +(-0.0326736 + 6.47901i) q^{21} +(0.388175 - 0.411441i) q^{22} +(-0.637677 - 0.856549i) q^{23} +(-0.618907 - 0.589836i) q^{24} +(5.68246 + 2.85384i) q^{25} +(0.0787396 + 0.136381i) q^{26} +(-1.70312 - 4.90911i) q^{27} +(-3.71200 + 6.42938i) q^{28} +(-1.50657 + 0.990889i) q^{29} +(0.321280 + 0.647847i) q^{30} +(2.68833 - 6.23225i) q^{31} +(-0.421989 - 1.40954i) q^{32} +(7.78175 + 1.41263i) q^{33} +(0.0808092 + 0.187337i) q^{34} +(9.65772 - 8.10379i) q^{35} +(1.09298 - 5.85278i) q^{36} +(-2.46619 - 2.06938i) q^{37} +(-0.156728 + 0.523507i) q^{38} +(-0.998105 + 1.96265i) q^{39} +(-0.0967301 + 1.66079i) q^{40} +(0.0586186 - 1.00644i) q^{41} +(0.801482 - 0.0426266i) q^{42} +(0.660457 - 2.20608i) q^{43} +(6.94218 + 5.82518i) q^{44} +(-5.14349 + 8.70483i) q^{45} +(-0.101335 + 0.0850299i) q^{46} +(3.77360 + 8.74819i) q^{47} +(4.37721 - 5.16345i) q^{48} +(-2.00558 - 6.69911i) q^{49} +(0.311999 - 0.723295i) q^{50} +(-1.57955 + 2.37540i) q^{51} +(-2.10792 + 1.38640i) q^{52} +(1.43978 - 2.49378i) q^{53} +(-0.594833 + 0.245981i) q^{54} +(-7.69474 - 13.3277i) q^{55} +(1.65005 + 0.828685i) q^{56} +(-7.33060 + 2.15442i) q^{57} +(0.133393 + 0.179178i) q^{58} +(7.30814 - 7.74618i) q^{59} +(-10.0624 + 5.74205i) q^{60} +(-5.27275 - 0.616296i) q^{61} +(-0.790095 - 0.287571i) q^{62} +(6.61026 + 9.06865i) q^{63} +(7.17367 - 2.61100i) q^{64} +(4.16898 - 0.988066i) q^{65} +(0.118647 - 0.972529i) q^{66} +(2.54074 + 1.67107i) q^{67} +(-2.92098 + 1.46697i) q^{68} +(-1.76917 - 0.539392i) q^{69} +(-1.07174 - 1.13598i) q^{70} +(-0.346694 + 1.96620i) q^{71} +(-1.46901 - 0.186739i) q^{72} +(2.80114 + 15.8860i) q^{73} +(-0.238153 + 0.319894i) q^{74} +(10.8560 - 1.85781i) q^{75} +(-8.51895 - 2.01903i) q^{76} +(-16.9654 + 1.98297i) q^{77} +(0.249906 + 0.109297i) q^{78} +(0.326714 + 5.60945i) q^{79} -13.1716 q^{80} +(-7.41811 - 5.09624i) q^{81} -0.124887 q^{82} +(-0.701083 - 12.0371i) q^{83} +(1.42838 + 12.7792i) q^{84} +(5.51322 - 0.644403i) q^{85} +(-0.277579 - 0.0657875i) q^{86} +(-1.08301 + 2.92950i) q^{87} +(1.34595 - 1.80793i) q^{88} +(1.69819 + 9.63089i) q^{89} +(1.11356 + 0.573386i) q^{90} +(0.825760 - 4.68312i) q^{91} +(-1.45436 - 1.54153i) q^{92} +(-2.65341 - 11.4527i) q^{93} +(1.05469 - 0.529686i) q^{94} +(12.4215 + 8.16978i) q^{95} +(-2.03648 - 1.53212i) q^{96} +(-9.14226 + 2.16676i) q^{97} +(-0.814020 + 0.296279i) q^{98} +(12.3030 - 6.02417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

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