LMFDB - Embedded newform 81.2.g.a.79.4

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			79.4
Character	$\chi$	$=$	81.79
Dual form			81.2.g.a.40.4

$q$-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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{14}{27}\right)$

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	−0.999897	−	0.0143658i	$-0.995427\pi$
$2$	−0.00720285	+	0.123668i	−0.00509318	+	0.0874466i	0.994804	+	0.101812i	$0.0324641\pi$
$3$	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	−0.884892	−	0.465797i	$-0.845768\pi$
$5$	−3.27944	+	0.777242i	−1.46661	+	0.347593i	−0.581719	+	0.813390i	$0.697620\pi$
$6$	−0.137087	+	0.165058i	−0.0559657	+	0.0673846i
$7$	−2.23379	−	3.00051i	−0.844295	−	1.13409i	−0.989478	−	0.144680i	$-0.953785\pi$
$7$	−2.23379	−	3.00051i	−0.844295	−	1.13409i	0.145183	−	0.989405i	$-0.453623\pi$
$8$	−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	−0.0552003	−	0.998475i	$-0.517580\pi$
$11$	3.13353	−	3.32135i	0.944795	−	1.00142i	0.999996	−	0.00294930i	$-0.000938793\pi$
$12$	2.51223	+	2.34633i	0.725218	+	0.677328i
$13$	−1.13603	−	0.570535i	−0.315077	−	0.158238i	0.284232	−	0.958756i	$-0.408262\pi$
$13$	−1.13603	−	0.570535i	−0.315077	−	0.158238i	−0.599309	+	0.800518i	$0.704558\pi$
$14$	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	0.147450	−	0.989070i	$-0.452893\pi$
$17$	−1.54764	−	0.563296i	−0.375359	−	0.136619i	−0.522808	+	0.852450i	$0.675116\pi$
$18$	−0.360733	+	0.0893473i	−0.0850255	+	0.0210594i
$19$	−4.14528	+	1.50876i	−0.950993	+	0.346133i	−0.770498	−	0.637443i	$-0.779992\pi$
$19$	−4.14528	+	1.50876i	−0.950993	+	0.346133i	−0.180495	+	0.983576i	$0.557770\pi$
$20$	−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	−0.863619	−	0.504145i	$-0.831808\pi$
$23$	−0.637677	+	0.856549i	−0.132965	+	0.178603i	0.730654	+	0.682748i	$0.239215\pi$
$24$	−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	0.401871	−	0.915696i	$-0.368360\pi$
$29$	−1.50657	−	0.990889i	−0.279764	−	0.184003i	−0.681634	+	0.731693i	$0.738731\pi$
$30$	0.321280	−	0.647847i	0.0586575	−	0.118280i
$31$	2.68833	+	6.23225i	0.482839	+	1.11935i	0.969353	+	0.245673i	$0.0790090\pi$
$31$	2.68833	+	6.23225i	0.482839	+	1.11935i	−0.486514	+	0.873673i	$0.661732\pi$
$32$	−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	−0.822592	−	0.568633i	$-0.807473\pi$
$37$	−2.46619	+	2.06938i	−0.405439	+	0.340204i	0.417152	+	0.908837i	$0.363028\pi$
$38$	−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	0.999787	+	0.0206256i	$0.00656578\pi$
$41$	0.0586186	+	1.00644i	0.00915468	+	0.157180i	−0.990633	+	0.136554i	$0.956397\pi$
$42$	0.801482	+	0.0426266i	0.123671	+	0.00657743i
$43$	0.660457	+	2.20608i	0.100719	+	0.336424i	0.993465	−	0.114135i	$-0.0364097\pi$
$43$	0.660457	+	2.20608i	0.100719	+	0.336424i	−0.892746	+	0.450559i	$0.851225\pi$
$44$	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	−0.385116	−	0.922868i	$-0.625839\pi$
$47$	3.77360	−	8.74819i	0.550436	−	1.27605i	0.935553	−	0.353187i	$-0.114902\pi$
$48$	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	0.947805	−	0.318851i	$-0.103297\pi$
$53$	1.43978	+	2.49378i	0.197769	+	0.342547i	−0.750035	+	0.661398i	$0.769964\pi$
$54$	−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	0.999953	+	0.00964429i	$0.00306992\pi$
$59$	7.30814	+	7.74618i	0.951439	+	1.00847i	−0.0485142	+	0.998822i	$0.515449\pi$
$60$	−10.0624	−	5.74205i	−1.29905	−	0.741295i
$61$	−5.27275	+	0.616296i	−0.675107	+	0.0789086i	−0.446736	−	0.894666i	$-0.647414\pi$
$61$	−5.27275	+	0.616296i	−0.675107	+	0.0789086i	−0.228370	+	0.973574i	$0.573340\pi$
$62$	−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	−0.384745	−	0.923023i	$-0.625710\pi$
$67$	2.54074	−	1.67107i	0.310400	−	0.204154i	0.695145	+	0.718869i	$0.255340\pi$
$68$	−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	0.957300	−	0.289098i	$-0.0933553\pi$
$71$	−0.346694	−	1.96620i	−0.0411451	−	0.233345i	−0.998445	+	0.0557526i	$0.982244\pi$
$72$	−1.46901	+	0.186739i	−0.173124	+	0.0220074i
$73$	2.80114	−	15.8860i	0.327848	−	1.85932i	−0.161006	−	0.986953i	$-0.551474\pi$
$73$	2.80114	−	15.8860i	0.327848	−	1.85932i	0.488854	−	0.872366i	$-0.337415\pi$
$74$	−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	−0.928745	−	0.370720i	$-0.879111\pi$
$79$	0.326714	−	5.60945i	0.0367581	−	0.631113i	0.965503	−	0.260393i	$-0.0838521\pi$
$80$	−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	0.709986	+	0.704216i	$0.248701\pi$
$83$	−0.701083	+	12.0371i	−0.0769538	+	1.32125i	−0.786940	+	0.617030i	$0.788336\pi$
$84$	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	−0.752197	−	0.658939i	$-0.771006\pi$
$89$	1.69819	−	9.63089i	0.180007	−	1.02087i	0.932204	−	0.361934i	$-0.117883\pi$
$90$	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	−0.261437	−	0.965220i	$-0.584196\pi$
$97$	−9.14226	−	2.16676i	−0.928256	−	0.220001i	−0.666819	+	0.745220i	$0.732345\pi$
$98$	−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	0.158868	−	0.987300i	$-0.449216\pi$
$101$	5.43839	−	0.635656i	0.541140	−	0.0632502i	0.382272	+	0.924050i	$0.375142\pi$
$102$	0.305139	−	0.178230i	0.0302132	−	0.0176474i
$103$	1.60904	+	1.70548i	0.158543	+	0.168046i	0.801776	−	0.597625i	$-0.203889\pi$
$103$	1.60904	+	1.70548i	0.158543	+	0.168046i	−0.643233	+	0.765671i	$0.722407\pi$
$104$	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	0.427879	+	0.903836i	$0.359261\pi$
$107$	−5.88377	+	10.1910i	−0.568805	+	0.985200i	−0.996684	+	0.0813640i	$0.974072\pi$
$108$	−4.48832	+	9.28461i	−0.431889	+	0.893412i
$109$	−0.211790	−	0.366831i	−0.0202858	−	0.0351361i	0.855704	−	0.517465i	$-0.173124\pi$
$109$	−0.211790	−	0.366831i	−0.0202858	−	0.0351361i	−0.875990	+	0.482329i	$0.839791\pi$
$110$	−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	−0.546269	−	0.837610i	$-0.683952\pi$
$113$	3.93747	−	13.1521i	0.370406	−	1.23724i	0.916675	−	0.399633i	$-0.130863\pi$
$114$	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	0.757524	−	0.652807i	$-0.226409\pi$
$127$	2.77429	+	2.32790i	0.246178	+	0.206568i	−0.511346	+	0.859375i	$0.670853\pi$
$128$	−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	0.775192	−	0.631726i	$-0.217653\pi$
$131$	−2.47542	−	5.73866i	−0.216278	−	0.501389i	−0.991470	+	0.130337i	$0.958394\pi$
$132$	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	−0.945849	−	0.324606i	$-0.894768\pi$
$137$	−14.6344	+	7.34965i	−1.25030	+	0.627923i	−0.304448	+	0.952529i	$0.598472\pi$
$138$	−0.0539625	−	0.222676i	−0.00459360	−	0.0189554i
$139$	11.6699	−	15.6754i	0.989827	−	1.32957i	0.0460666	−	0.998938i	$-0.485331\pi$
$139$	11.6699	−	15.6754i	0.989827	−	1.32957i	0.943760	−	0.330630i	$-0.107261\pi$
$140$	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	0.292530	−	0.956256i	$-0.405503\pi$
$149$	−3.65975	−	1.83800i	−0.299819	−	0.150575i	−0.592349	+	0.805682i	$0.701799\pi$
$150$	−0.307946	+	1.32916i	−0.0251437	+	0.108525i
$151$	−6.08551	+	6.45026i	−0.495232	+	0.524915i	−0.925988	−	0.377553i	$-0.876765\pi$
$151$	−6.08551	+	6.45026i	−0.495232	+	0.524915i	0.430756	+	0.902468i	$0.358247\pi$
$152$	−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	−0.0195065	−	0.999810i	$-0.506210\pi$
$157$	5.15953	−	1.22283i	0.411776	−	0.0975926i	0.431282	+	0.902217i	$0.358061\pi$
$158$	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	−0.957233	−	0.289318i	$-0.906571\pi$
$167$	−21.7466	+	5.15404i	−1.68280	+	0.398831i	−0.725569	+	0.688150i	$0.758423\pi$
$168$	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	−0.629889	−	0.776686i	$-0.716899\pi$
$173$	2.39525	−	2.53882i	0.182108	−	0.193023i	0.811996	+	0.583663i	$0.198381\pi$
$174$	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	−0.245753	−	0.969333i	$-0.579035\pi$
$179$	−14.1428	−	5.14757i	−1.05709	−	0.384748i	−0.811332	+	0.584585i	$0.801257\pi$
$180$	−8.13339	−	18.3443i	−0.606227	−	1.36731i
$181$	−2.01428	+	0.733137i	−0.149720	+	0.0544936i	−0.415793	−	0.909459i	$-0.636496\pi$
$181$	−2.01428	+	0.733137i	−0.149720	+	0.0544936i	0.266073	+	0.963953i	$0.414274\pi$
$182$	−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	0.990796	−	0.135366i	$-0.0432210\pi$
$191$	17.3988	+	11.4434i	1.25893	+	0.828014i	0.268139	+	0.963380i	$0.413591\pi$
$192$	7.32154	+	11.0105i	0.528387	+	0.794615i
$193$	5.58282	+	12.9424i	0.401860	+	0.931617i	0.992222	+	0.124478i	$0.0397257\pi$
$193$	5.58282	+	12.9424i	0.401860	+	0.931617i	−0.590362	+	0.807139i	$0.701015\pi$
$194$	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	0.693574	−	0.720385i	$-0.256035\pi$
$197$	1.46772	+	1.23157i	0.104571	+	0.0877455i	−0.589003	+	0.808131i	$0.700479\pi$
$198$	−0.833614	+	1.47809i	−0.0592424	+	0.105043i
$199$	12.3341	−	10.3495i	0.874339	−	0.733658i	−0.0906679	−	0.995881i	$-0.528900\pi$
$199$	12.3341	−	10.3495i	0.874339	−	0.733658i	0.965007	+	0.262223i	$0.0844557\pi$
$200$	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	−0.987595	−	0.157023i	$-0.949810\pi$
$211$	−1.10667	+	3.69652i	−0.0761860	+	0.254479i	0.911409	+	0.411502i	$0.134996\pi$
$212$	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	−0.215009	−	0.976612i	$-0.568978\pi$
$223$	−2.97171	+	0.347344i	−0.199001	+	0.0232598i	0.0160086	+	0.999872i	$0.494904\pi$
$224$	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	0.915183	−	0.403039i	$-0.132046\pi$
$227$	23.3853	+	5.54241i	1.55214	+	0.367863i	0.636953	+	0.770902i	$0.280194\pi$
$228$	−13.9539	−	5.93586i	−0.924123	−	0.393112i
$229$	3.95450	−	2.60092i	0.261321	−	0.171873i	−0.412087	−	0.911144i	$-0.635200\pi$
$229$	3.95450	−	2.60092i	0.261321	−	0.171873i	0.673408	+	0.739271i	$0.264830\pi$
$230$	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	−0.984751	−	0.173968i	$-0.944341\pi$
$233$	−1.81475	−	10.2920i	−0.118888	−	0.674250i	0.865863	−	0.500282i	$-0.166770\pi$
$234$	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	0.608165	−	0.793810i	$-0.291906\pi$
$239$	15.7205	+	1.83746i	1.01687	+	0.118855i	0.408707	+	0.912666i	$0.365980\pi$
$240$	−18.3680	−	13.5311i	−1.18565	−	0.873427i
$241$	−1.02572	+	17.6110i	−0.0660726	+	1.13442i	0.788481	+	0.615059i	$0.210868\pi$
$241$	−1.02572	+	17.6110i	−0.0660726	+	1.13442i	−0.854554	+	0.519363i	$0.826169\pi$
$242$	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	0.633936	+	0.773386i	$0.281438\pi$
$251$	−3.58499	+	20.3315i	−0.226282	+	1.28331i	−0.860218	+	0.509926i	$0.829673\pi$
$252$	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	−0.725028	−	0.688719i	$-0.758173\pi$
$257$	−6.08872	+	4.00462i	−0.379804	+	0.249801i	0.345224	+	0.938520i	$0.387803\pi$
$258$	−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	0.209848	−	0.977734i	$-0.432703\pi$
$263$	10.3713	−	1.21223i	0.639521	−	0.0747493i	0.429673	+	0.902985i	$0.358629\pi$
$264$	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	0.294585	+	0.955625i	$0.404819\pi$
$269$	−11.1578	+	19.3259i	−0.680304	+	1.17832i	−0.974888	+	0.222695i	$0.928515\pi$
$270$	2.14191	+	0.344350i	0.130352	+	0.0209565i
$271$	11.6312	+	20.1458i	0.706544	+	1.22377i	0.966132	+	0.258050i	$0.0830800\pi$
$271$	11.6312	+	20.1458i	0.706544	+	1.22377i	−0.259588	+	0.965720i	$0.583587\pi$
$272$	−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	−0.779637	−	0.626231i	$-0.784597\pi$
$277$	3.50985	−	8.13675i	0.210886	−	0.488890i	0.990524	+	0.137342i	$0.0438558\pi$
$278$	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	−0.919239	−	0.393700i	$-0.871195\pi$
$281$	−6.16156	−	20.5810i	−0.367568	−	1.22776i	0.551671	−	0.834062i	$-0.313990\pi$
$282$	0.926644	+	1.82213i	0.0551808	+	0.108506i
$283$	0.0355631	+	0.610594i	0.00211401	+	0.0362961i	0.999200	−	0.0399872i	$-0.0127317\pi$
$283$	0.0355631	+	0.610594i	0.00211401	+	0.0362961i	−0.997086	+	0.0762833i	$0.975695\pi$
$284$	−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	0.750170	+	0.661245i	$0.229971\pi$
$293$	12.2618	+	28.4261i	0.716344	+	1.66067i	−0.0338263	+	0.999428i	$0.510769\pi$
$294$	−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	−0.349882	−	0.936794i	$-0.613778\pi$
$307$	−21.3773	−	7.78069i	−1.22007	−	0.444068i	−0.870184	+	0.492726i	$0.836000\pi$
$308$	−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	−0.553705	−	0.832713i	$-0.686787\pi$
$311$	−27.3750	−	13.7482i	−1.55229	−	0.779591i	−0.998588	+	0.0531218i	$0.983083\pi$
$312$	1.03962	−	0.316962i	0.0588567	−	0.0179444i
$313$	15.6532	−	16.5914i	0.884770	−	0.937802i	−0.113676	−	0.993518i	$-0.536263\pi$
$313$	15.6532	−	16.5914i	0.884770	−	0.937802i	0.998447	+	0.0557161i	$0.0177442\pi$
$314$	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	0.646972	−	0.762514i	$-0.276035\pi$
$317$	−4.79052	−	6.43479i	−0.269062	−	0.361414i	−0.916034	+	0.401100i	$0.868628\pi$
$318$	−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	0.993977	−	0.109586i	$-0.0349524\pi$
$331$	10.9874	+	14.7586i	0.603919	+	0.811205i	−0.390058	+	0.920790i	$0.627545\pi$
$332$	−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	0.957718	−	0.287709i	$-0.0928936\pi$
$337$	23.8437	+	11.9748i	1.29885	+	0.652307i	0.341131	+	0.940016i	$0.389190\pi$
$338$	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	−0.210280	−	0.977641i	$-0.567438\pi$
$347$	14.6527	−	19.6820i	0.786599	−	1.05659i	0.996879	−	0.0789443i	$-0.0251549\pi$
$348$	−1.45990	−	6.02426i	−0.0782589	−	0.322934i
$349$	14.9935	−	7.53000i	0.802582	−	0.403072i	0.000287376	−	1.00000i	$-0.499909\pi$
$349$	14.9935	−	7.53000i	0.802582	−	0.403072i	0.802295	+	0.596928i	$0.203612\pi$
$350$	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	0.0307072	−	0.999528i	$-0.490224\pi$
$353$	−16.4381	−	10.8115i	−0.874913	−	0.575440i	−0.905621	+	0.424089i	$0.860594\pi$
$354$	−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	−0.945285	−	0.326245i	$-0.894216\pi$
$359$	−27.1083	−	22.7466i	−1.43072	−	1.20052i	−0.485436	−	0.874272i	$-0.661339\pi$
$360$	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	−0.969901	−	0.243501i	$-0.921704\pi$
$367$	−5.62009	−	18.7724i	−0.293366	−	0.979912i	0.676534	−	0.736411i	$-0.263481\pi$
$368$	−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	0.280518	+	0.959849i	$0.409494\pi$
$373$	−9.29538	+	31.0487i	−0.481297	+	1.60764i	−0.761815	+	0.647794i	$0.775692\pi$
$374$	−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	−0.618731	−	0.785603i	$-0.712353\pi$
$379$	7.22233	−	12.5094i	0.370986	−	0.642567i	0.989718	+	0.143036i	$0.0456863\pi$
$380$	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	0.986636	−	0.162940i	$-0.0520975\pi$
$383$	15.0027	+	15.9020i	0.766604	+	0.812553i	−0.220032	+	0.975493i	$0.570616\pi$
$384$	−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	−0.259807	−	0.965660i	$-0.583659\pi$
$389$	−18.2511	−	4.32559i	−0.925367	−	0.219316i	−0.665560	+	0.746344i	$0.731807\pi$
$390$	−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	0.778759	+	0.627323i	$0.215850\pi$
$397$	−3.33925	+	18.9379i	−0.167592	+	0.950463i	−0.946351	+	0.323140i	$0.895262\pi$
$398$	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	0.227337	−	0.973816i	$-0.426998\pi$
$401$	4.48498	+	0.524219i	0.223969	+	0.0261783i	−0.00336797	+	0.999994i	$0.501072\pi$
$402$	−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	−0.825517	−	0.564377i	$-0.809117\pi$
$409$	−35.5723	−	4.15781i	−1.75894	−	0.205590i	−0.933420	+	0.358787i	$0.883191\pi$
$410$	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	−0.944694	−	0.327953i	$-0.893641\pi$
$419$	−20.8326	+	13.7018i	−1.01774	+	0.669376i	−0.0730427	+	0.997329i	$0.523271\pi$
$420$	5.24821	+	43.0188i	0.256086	+	2.09910i
$421$	−35.1178	−	8.32306i	−1.71154	−	0.405641i	−0.746007	−	0.665938i	$-0.768031\pi$
$421$	−35.1178	−	8.32306i	−1.71154	−	0.405641i	−0.965529	+	0.260297i	$0.916179\pi$
$422$	−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	−0.372587	−	0.927997i	$-0.621529\pi$
$431$	12.8170	−	22.1998i	0.617375	−	1.06933i	0.989963	−	0.141329i	$-0.0451374\pi$
$432$	−10.9011	+	17.1335i	−0.524482	+	0.824334i
$433$	−2.49590	−	4.32302i	−0.119945	−	0.207751i	0.799801	−	0.600266i	$-0.204939\pi$
$433$	−2.49590	−	4.32302i	−0.119945	−	0.207751i	−0.919746	+	0.392515i	$0.871605\pi$
$434$	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	−0.883445	−	0.468535i	$-0.844782\pi$
$439$	1.33282	−	3.08983i	0.0636120	−	0.147469i	0.947057	+	0.321066i	$0.104041\pi$
$440$	−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	0.999465	+	0.0327082i	$0.0104132\pi$
$443$	3.83903	+	12.8232i	0.182398	+	0.609251i	−0.817067	+	0.576542i	$0.804402\pi$
$444$	−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	−0.187906	+	0.982187i	$0.560170\pi$
$449$	−25.1690	+	21.1193i	−1.18780	+	0.996683i	−0.999895	+	0.0144961i	$0.995386\pi$
$450$	−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	0.891421	−	0.453177i	$-0.149709\pi$
$457$	17.7088	+	11.6472i	0.828380	+	0.544834i	−0.0630403	+	0.998011i	$0.520080\pi$
$458$	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	−0.0688566	−	0.997627i	$-0.521935\pi$
$461$	14.8202	−	7.44297i	0.690245	−	0.346654i	0.759101	+	0.650973i	$0.225639\pi$
$462$	2.65305	−	2.52843i	0.123431	−	0.117633i
$463$	2.04248	−	2.74353i	0.0949220	−	0.127502i	−0.752125	−	0.659021i	$-0.770971\pi$
$463$	2.04248	−	2.74353i	0.0949220	−	0.127502i	0.847047	+	0.531518i	$0.178378\pi$
$464$	−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	−0.128391	−	0.991724i	$-0.540981\pi$
$467$	8.87582	−	3.23054i	0.410724	−	0.149491i	0.539115	+	0.842232i	$0.318759\pi$
$468$	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	0.978159	−	0.207859i	$-0.0666495\pi$
$479$	10.9101	+	14.6547i	0.498493	+	0.669592i	−0.479666	+	0.877451i	$0.659242\pi$
$480$	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	−0.182327	−	0.983238i	$-0.558363\pi$
$491$	2.12757	−	0.504243i	0.0960159	−	0.0227562i	0.278343	+	0.960482i	$0.410215\pi$
$492$	−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	0.461341	−	0.887223i	$-0.347369\pi$
$499$	0.562307	+	0.282401i	0.0251723	+	0.0126420i	−0.436169	+	0.899865i	$0.643665\pi$
$500$	−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	0.468937	−	0.883232i	$-0.344637\pi$
$503$	5.84089	+	2.12591i	0.260432	+	0.0947897i	−0.208504	+	0.978021i	$0.566859\pi$
$504$	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	−0.482191	−	0.876066i	$-0.660159\pi$
$509$	11.1759	−	15.0119i	0.495365	−	0.665390i	0.977556	+	0.210676i	$0.0675665\pi$
$510$	−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	0.376135	−	0.926565i	$-0.377253\pi$
$521$	−10.7516	−	9.02171i	−0.471038	−	0.395248i	−0.847173	+	0.531317i	$0.821697\pi$
$522$	0.632004	+	0.222838i	0.0276621	+	0.00975335i
$523$	−15.7777	+	13.2390i	−0.689910	+	0.578903i	−0.918883	−	0.394530i	$-0.870908\pi$
$523$	−15.7777	+	13.2390i	−0.689910	+	0.578903i	0.228973	+	0.973433i	$0.426463\pi$
$524$	−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	0.0727213	+	0.997352i	$0.476832\pi$
$541$	−19.2442	+	33.3319i	−0.827372	+	1.43305i	−0.900093	+	0.435698i	$0.856502\pi$
$542$	−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	−0.498705	−	0.866772i	$-0.666191\pi$
$547$	−18.3380	+	2.14340i	−0.784075	+	0.0916453i	−0.285371	+	0.958417i	$0.592117\pi$
$548$	−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	0.999764	−	0.0217217i	$-0.00691477\pi$
$557$	1.24763	+	7.07568i	0.0528639	+	0.299806i	−0.946900	+	0.321528i	$0.895804\pi$
$558$	−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	0.732645	−	0.680611i	$-0.238286\pi$
$563$	30.5750	+	3.57370i	1.28858	+	0.150613i	0.555936	+	0.831225i	$0.312360\pi$
$564$	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	−0.735720	−	0.677285i	$-0.763156\pi$
$569$	1.75691	−	30.1649i	0.0736534	−	1.26458i	0.809374	−	0.587294i	$-0.199807\pi$
$570$	−0.354352	+	3.17025i	−0.0148422	+	0.132787i
$571$	7.84368	+	0.916795i	0.328248	+	0.0383667i	0.278621	−	0.960401i	$-0.410123\pi$
$571$	7.84368	+	0.916795i	0.328248	+	0.0383667i	0.0496269	+	0.998768i	$0.484197\pi$
$572$	−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	−0.998996	−	0.0448050i	$-0.985733\pi$
$577$	−1.81528	−	10.2950i	−0.0755710	−	0.428585i	0.923425	−	0.383780i	$-0.125378\pi$
$578$	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	0.198253	−	0.980151i	$-0.436473\pi$
$587$	14.9536	−	1.74783i	0.617201	−	0.0721405i	0.418948	+	0.908010i	$0.362399\pi$
$588$	−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	−0.602021	−	0.798480i	$-0.705638\pi$
$593$	9.50914	−	16.4703i	0.390494	−	0.676355i	0.992515	+	0.122125i	$0.0389710\pi$
$594$	−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	−0.323783	−	0.946131i	$-0.604955\pi$
$599$	11.4208	−	38.1481i	0.466641	−	1.55869i	0.790424	−	0.612560i	$-0.209860\pi$
$600$	−1.83362	+	5.11798i	−0.0748571	+	0.208941i
$601$	2.21155	−	5.12695i	0.0902111	−	0.209133i	−0.867137	−	0.498069i	$-0.834042\pi$
$601$	2.21155	−	5.12695i	0.0902111	−	0.209133i	0.957348	+	0.288937i	$0.0933017\pi$
$602$	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	−0.973307	−	0.229509i	$-0.926288\pi$
$607$	−0.818590	−	14.0546i	−0.0332255	−	0.570460i	0.940081	−	0.340951i	$-0.110749\pi$
$608$	−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	0.321258	−	0.946992i	$-0.395894\pi$
$613$	−13.7550	−	11.5418i	−0.555561	−	0.466171i	−0.876819	+	0.480821i	$0.840339\pi$
$614$	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	0.938496	+	0.345291i	$0.112220\pi$
$617$	13.5528	+	31.4190i	0.545617	+	1.26488i	−0.392879	+	0.919590i	$0.628521\pi$
$618$	−0.502082	+	0.0317843i	−0.0201967	+	0.00127855i
$619$	28.9445	+	19.0371i	1.16338	+	0.765165i	0.976138	−	0.217149i	$-0.0696759\pi$
$619$	28.9445	+	19.0371i	1.16338	+	0.765165i	0.187239	+	0.982314i	$0.440046\pi$
$620$	−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	0.982154	−	0.188080i	$-0.0602263\pi$
$631$	40.5340	+	14.7532i	1.61363	+	0.587314i	0.631478	+	0.775394i	$0.282449\pi$
$632$	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	0.855186	−	0.518321i	$-0.173443\pi$
$641$	2.87030	+	3.85549i	0.113370	+	0.152283i	−0.741816	+	0.670603i	$0.766035\pi$
$642$	−0.875511	−	2.36822i	−0.0345537	−	0.0934661i
$643$	8.07150	−	1.91298i	0.318309	−	0.0754405i	−0.0683558	−	0.997661i	$-0.521775\pi$
$643$	8.07150	−	1.91298i	0.318309	−	0.0754405i	0.386664	+	0.922220i	$0.373627\pi$
$644$	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	−0.0212699	−	0.999774i	$-0.506771\pi$
$653$	10.4367	−	2.47355i	0.408420	−	0.0967974i	0.429690	+	0.902976i	$0.358623\pi$
$654$	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	−0.913647	−	0.406507i	$-0.866747\pi$
$659$	−11.6727	+	12.3723i	−0.454704	+	0.481958i	0.458944	+	0.888465i	$0.348228\pi$
$660$	−50.6021	+	15.4278i	−1.96968	+	0.600524i
$661$	−27.9077	−	14.0158i	−1.08549	−	0.545151i	−0.186199	−	0.982512i	$-0.559617\pi$
$661$	−27.9077	−	14.0158i	−1.08549	−	0.545151i	−0.899286	+	0.437361i	$0.855913\pi$
$662$	−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	−0.583802	−	0.811896i	$-0.698436\pi$
$673$	−7.29455	+	3.66346i	−0.281184	+	0.141216i	0.302618	+	0.953112i	$0.402139\pi$
$674$	−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	0.633988	−	0.773343i	$-0.281417\pi$
$677$	4.55342	+	2.99483i	0.175002	+	0.115101i	−0.458986	+	0.888444i	$0.651787\pi$
$678$	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	0.596166	−	0.802861i	$-0.296690\pi$
$683$	−2.37757	−	1.99502i	−0.0909753	−	0.0763374i	−0.687141	+	0.726524i	$0.741135\pi$
$684$	−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	−0.977405	−	0.211377i	$-0.932205\pi$
$691$	−7.28011	−	24.3173i	−0.276948	−	0.925072i	0.700456	−	0.713695i	$-0.252980\pi$
$692$	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	0.874832	−	0.484426i	$-0.160972\pi$
$701$	0.473675	+	0.820430i	0.0178905	+	0.0309872i	−0.856942	+	0.515414i	$0.827638\pi$
$702$	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	−0.694001	−	0.719974i	$-0.744154\pi$
$709$	−32.0392	+	3.74485i	−1.20326	+	0.140641i	−0.509257	+	0.860615i	$0.670080\pi$
$710$	−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	−0.951673	−	0.307114i	$-0.900637\pi$
$719$	−4.35548	−	24.7012i	−0.162432	−	0.921198i	0.789241	−	0.614084i	$-0.210474\pi$
$720$	−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	−0.975888	−	0.218271i	$-0.929958\pi$
$727$	0.505316	−	8.67595i	0.0187411	−	0.321773i	0.994629	−	0.103502i	$-0.0330047\pi$
$728$	−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	−0.0445007	−	0.999009i	$-0.514170\pi$
$733$	−8.61465	−	1.00691i	−0.318189	−	0.0371910i	−0.273689	+	0.961818i	$0.588244\pi$
$734$	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	0.978533	−	0.206089i	$-0.0660736\pi$
$739$	−0.311908	−	1.76892i	−0.0114737	−	0.0650707i	−0.990007	+	0.141018i	$0.954962\pi$
$740$	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	−0.854230	−	0.519895i	$-0.825971\pi$
$743$	−19.4949	+	12.8220i	−0.715198	+	0.470393i	0.139032	+	0.990288i	$0.455601\pi$
$744$	−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	0.437285	−	0.899323i	$-0.355940\pi$
$751$	−13.3169	−	14.1151i	−0.485942	−	0.515069i	−0.923227	+	0.384254i	$0.874459\pi$
$752$	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	0.668617	−	0.743607i	$-0.266886\pi$
$757$	−8.52025	−	14.7575i	−0.309674	−	0.536371i	−0.978291	+	0.207236i	$0.933553\pi$
$758$	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	0.379867	+	0.925041i	$0.375970\pi$
$761$	−12.2986	+	41.0803i	−0.445826	+	1.48916i	−0.825693	+	0.564120i	$0.809215\pi$
$762$	−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	−	0.468299i
$768$	11.6094	+	22.8284i	0.418918	+	0.823750i
$769$	−1.65895	−	28.4831i	−0.0598232	−	1.02713i	−0.885991	−	0.463702i	$-0.846521\pi$
$769$	−1.65895	−	28.4831i	−0.0598232	−	1.02713i	0.826168	−	0.563424i	$-0.190516\pi$
$770$	0.414650	+	7.11927i	0.0149429	+	0.256561i
$771$	−12.6047	−	0.670379i	−0.453948	−	0.0241431i
$772$	8.02306	+	26.7989i	0.288756	+	0.964513i
$773$	31.5157	−	26.4448i	1.13354	−	0.951155i	0.134334	−	0.990936i	$-0.457111\pi$
$773$	31.5157	−	26.4448i	1.13354	−	0.951155i	0.999208	+	0.0397813i	$0.0126661\pi$
$774$	−0.435356	−	0.736796i	−0.0156486	−	0.0264836i
$775$	33.0622	+	27.7425i	1.18763	+	0.996539i
$776$	1.83691	−	4.25843i	0.0659411	−	0.152869i
$777$	13.4881	+	15.9109i	0.483883	+	0.570799i
$778$	0.666397	−	2.22592i	0.0238915	−	0.0798032i
$779$	−1.76147	−	4.08355i	−0.0631112	−	0.146308i
$780$	8.15509	+	12.2641i	0.291999	+	0.439123i
$781$	−7.61682	−	5.00966i	−0.272551	−	0.179260i
$782$	0.108933	+	0.188677i	0.00389543	+	0.00674709i
$783$	7.43026	−	5.70834i	0.265536	−	0.203999i
$784$	−13.6647	+	23.6679i	−0.488023	+	0.845281i
$785$	−15.9699	+	8.02041i	−0.569992	+	0.286261i
$786$	1.28656	+	0.378112i	0.0458900	+	0.0134868i
$787$	−12.4606	+	16.7375i	−0.444172	+	0.596626i	−0.966674	−	0.256012i	$-0.917591\pi$
$787$	−12.4606	+	16.7375i	−0.444172	+	0.596626i	0.522502	+	0.852638i	$0.324999\pi$
$788$	2.60947	+	2.76588i	0.0929585	+	0.0985303i
$789$	15.7082	+	8.96384i	0.559228	+	0.319121i
$790$	−2.33007	+	0.272346i	−0.0829003	+	0.00968965i
$791$	−48.2584	+	17.5646i	−1.71587	+	0.624526i
$792$	−3.98296	+	5.46424i	−0.141528	+	0.194163i
$793$	6.34161	+	2.30816i	0.225197	+	0.0819650i
$794$	−2.31796	−	0.549366i	−0.0822612	−	0.0194963i
$795$	−2.03563	−	16.6858i	−0.0721965	−	0.591784i
$796$	26.6979	−	17.5595i	0.946283	−	0.622380i
$797$	35.8557	+	18.0074i	1.27007	+	0.637855i	0.950799	−	0.309807i	$-0.100264\pi$
$797$	35.8557	+	18.0074i	1.27007	+	0.637855i	0.319275	+	0.947662i	$0.396561\pi$
$798$	−3.38668	+	1.03254i	−0.119887	+	0.0365517i
$799$	−10.7680	+	11.4134i	−0.380945	+	0.403778i
$800$	1.62467	+	9.21395i	0.0574407	+	0.325762i
$801$	29.1042	−	3.69970i	1.02835	−	0.130723i
$802$	−0.0971339	+	0.550874i	−0.00342992	+	0.0194520i
$803$	−43.9856	−	59.0829i	−1.55222	−	2.08499i
$804$	10.3038	+	1.76331i	0.363387	+	0.0621870i
$805$	−13.0998	+	3.10471i	−0.461707	+	0.109427i
$806$	1.06164	+	0.124088i	0.0373946	+	0.00437080i
$807$	−35.4130	+	15.4880i	−1.24660	+	0.545202i
$808$	−0.157149	+	2.69814i	−0.00552848	+	0.0949203i
$809$	−25.7049			−0.903736			−0.451868	−	0.892085i	$-0.649242\pi$
$809$	−25.7049			−0.903736			−0.451868	+	0.892085i	$0.649242\pi$
$810$	2.63318	+	2.68056i	0.0925204	+	0.0941853i
$811$	37.0961			1.30262			0.651310	−	0.758812i	$-0.274220\pi$
$811$	37.0961			1.30262			0.651310	+	0.758812i	$0.274220\pi$
$812$	−0.778395	+	13.3645i	−0.0273163	+	0.469003i
$813$	−4.47569	+	40.0422i	−0.156969	+	1.40434i
$814$	−1.80874	−	0.211411i	−0.0633963	−	0.00740997i
$815$	15.9596	−	3.78249i	0.559039	−	0.132495i
$816$	−3.86581	−	10.4568i	−0.135330	−	0.366063i
$817$	−6.06623	−	8.14836i	−0.212231	−	0.285075i
$818$	0.770410	−	4.36921i	0.0269367	−	0.152766i
$819$	−12.6834	+	6.53086i	−0.443194	+	0.228207i
$820$	−1.17097	−	6.64091i	−0.0408921	−	0.231911i
$821$	−16.3369	+	17.3161i	−0.570161	+	0.604335i	−0.946720	−	0.322057i	$-0.895626\pi$
$821$	−16.3369	+	17.3161i	−0.570161	+	0.604335i	0.376559	+	0.926392i	$0.377107\pi$
$822$	0.793070	−	3.42306i	0.0276615	−	0.119393i
$823$	10.0579	+	5.05129i	0.350598	+	0.176077i	0.615378	−	0.788232i	$-0.289003\pi$
$823$	10.0579	+	5.05129i	0.350598	+	0.176077i	−0.264781	+	0.964309i	$0.585300\pi$
$824$	−0.966971	+	0.635987i	−0.0336860	+	0.0221557i
$825$	40.1881	−	30.2351i	1.39917	−	1.05265i
$826$	4.80186	+	1.13806i	0.167078	+	0.0395982i
$827$	−20.1174	−	7.32212i	−0.699549	−	0.254615i	−0.0323307	−	0.999477i	$-0.510293\pi$
$827$	−20.1174	−	7.32212i	−0.699549	−	0.254615i	−0.667218	+	0.744862i	$0.732515\pi$
$828$	−5.71016	−	2.79599i	−0.198442	−	0.0971675i
$829$	−0.656956	+	0.239112i	−0.0228170	+	0.00830471i	−0.353403	−	0.935471i	$-0.614976\pi$
$829$	−0.656956	+	0.239112i	−0.0228170	+	0.00830471i	0.330586	+	0.943776i	$0.392753\pi$
$830$	5.00002	−	0.584418i	0.173553	−	0.0202855i
$831$	13.2533	−	7.74119i	0.459753	−	0.268539i
$832$	−6.65982	−	7.05899i	−0.230888	−	0.244727i
$833$	6.87750	−	9.23809i	0.238291	−	0.320081i
$834$	0.987548	+	4.07510i	0.0341960	+	0.141109i
$835$	67.3107	−	33.8047i	2.32938	−	1.16986i
$836$	−19.9885	+	34.6211i	−0.691317	+	1.19740i
$837$	−35.1734	+	2.58307i	−1.21577	+	0.0892838i
$838$	−1.54442	−	2.67501i	−0.0533511	−	0.0924068i
$839$	30.9593	+	20.3622i	1.06883	+	0.702982i	0.956807	−	0.290723i	$-0.0938959\pi$
$839$	30.9593	+	20.3622i	1.06883	+	0.702982i	0.112025	+	0.993705i	$0.464266\pi$
$840$	−10.7571	+	0.680980i	−0.371156	+	0.0234960i
$841$	−10.1984	−	23.6426i	−0.351669	−	0.815261i
$842$	1.28225	−	4.28300i	0.0441891	−	0.147602i
$843$	12.5503	−	35.0303i	0.432255	−	1.20651i
$844$	−3.03319	+	7.03173i	−0.104407	+	0.242042i
$845$	29.3909	+	24.6619i	1.01108	+	0.848395i
$846$	−0.579635	+	3.49292i	−0.0199283	+	0.120089i
$847$	−28.2267	+	23.6850i	−0.969882	+	0.813828i
$848$	3.22763	+	10.7810i	0.110837	+	0.370222i
$849$	−0.577664	+	0.888017i	−0.0198254	+	0.0304767i
$850$	−0.0754339	−	1.29515i	−0.00258736	−	0.0444233i
$851$	−0.199892	−	3.43201i	−0.00685220	−	0.117648i
$852$	3.74239	−	5.75301i	0.128212	−	0.197095i
$853$	4.34824	+	14.5241i	0.148881	+	0.497297i	0.999599	−	0.0283256i	$-0.00901751\pi$
$853$	4.34824	+	14.5241i	0.148881	+	0.497297i	−0.850718	+	0.525623i	$0.823832\pi$
$854$	−1.88445	+	1.58124i	−0.0644845	+	0.0541089i
$855$	34.4547	+	28.3237i	1.17833	+	0.968650i
$856$	−4.44962	−	3.73368i	−0.152085	−	0.127614i
$857$	−2.42316	+	5.61751i	−0.0827734	+	0.191890i	−0.954576	−	0.297966i	$-0.903692\pi$
$857$	−2.42316	+	5.61751i	−0.0827734	+	0.191890i	0.871803	+	0.489857i	$0.162951\pi$
$858$	0.420075	−	1.17251i	0.0143411	−	0.0400289i
$859$	1.68413	−	5.62537i	0.0574616	−	0.191935i	−0.924440	−	0.381328i	$-0.875467\pi$
$859$	1.68413	−	5.62537i	0.0574616	−	0.191935i	0.981901	+	0.189393i	$0.0606520\pi$
$860$	−6.10092	−	14.1435i	−0.208040	−	0.482290i
$861$	6.51883	−	0.412675i	0.222161	−	0.0140639i
$862$	2.65309	+	1.74496i	0.0903644	+	0.0594336i
$863$	−0.872485	−	1.51119i	−0.0296997	−	0.0514414i	0.850794	−	0.525500i	$-0.176122\pi$
$863$	−0.872485	−	1.51119i	−0.0296997	−	0.0514414i	−0.880493	+	0.474059i	$0.842788\pi$
$864$	−6.20090	−	4.47221i	−0.210959	−	0.152148i
$865$	−5.88182	+	10.1876i	−0.199988	+	0.346389i
$866$	0.552597	−	0.277525i	0.0187780	−	0.00943068i
$867$	−5.82834	−	24.0505i	−0.197941	−	0.816799i
$868$	30.0904	−	40.4185i	1.02134	−	1.37189i
$869$	−17.6072	−	18.6625i	−0.597283	−	0.633083i
$870$	−1.12598	+	0.657676i	−0.0381742	+	0.0222973i
$871$	−3.83975	+	0.448802i	−0.130105	+	0.0152071i
$872$	0.196474	−	0.0715107i	0.00665345	−	0.00242166i
$873$	−1.92262	−	28.1209i	−0.0650709	−	0.951749i
$874$	0.548351	+	0.199583i	0.0185482	+	0.00675100i
$875$	16.6694	+	3.95072i	0.563529	+	0.133559i
$876$	44.3110	−	33.3369i	1.49713	−	1.12635i
$877$	−39.4245	+	25.9299i	−1.33127	+	0.875591i	−0.997743	−	0.0671485i	$-0.978610\pi$
$877$	−39.4245	+	25.9299i	−1.33127	+	0.875591i	−0.333529	+	0.942740i	$0.608240\pi$
$878$	0.372513	+	0.187083i	0.0125717	+	0.00631374i
$879$	−12.1025	+	52.2372i	−0.408208	+	1.76192i
$880$	−41.2737	+	43.7476i	−1.39134	+	1.47473i
$881$	3.06509	+	17.3830i	0.103266	+	0.585648i	0.991899	+	0.127030i	$0.0405443\pi$
$881$	3.06509	+	17.3830i	0.103266	+	0.585648i	−0.888633	+	0.458618i	$0.848345\pi$
$882$	0.124932	−	2.59578i	0.00420668	−	0.0874045i
$883$	1.28101	−	7.26495i	0.0431093	−	0.244485i	−0.955637	−	0.294548i	$-0.904831\pi$
$883$	1.28101	−	7.26495i	0.0431093	−	0.244485i	0.998746	+	0.0500627i	$0.0159421\pi$
$884$	2.48136	+	3.33304i	0.0834571	+	0.112102i
$885$	−21.5566	−	58.3096i	−0.724616	−	1.96006i
$886$	−1.61348	+	0.382401i	−0.0542058	+	0.0128470i
$887$	2.92907	+	0.342359i	0.0983484	+	0.0114953i	0.165125	−	0.986273i	$-0.447197\pi$
$887$	2.92907	+	0.342359i	0.0983484	+	0.0114953i	−0.0667763	+	0.997768i	$0.521271\pi$
$888$	0.305748	−	2.73540i	0.0102602	−	0.0917940i
$889$	0.787702	−	13.5243i	0.0264187	−	0.453591i
$890$	−4.08296			−0.136861
$891$	−6.31846	+	40.6074i	−0.211676	+	1.36040i
$892$	−5.93798			−0.198818
$893$	−2.44373	+	41.9572i	−0.0817763	+	1.40404i
$894$	0.805082	−	0.352104i	0.0269260	−	0.0117761i
$895$	50.3815	+	5.88875i	1.68407	+	0.196839i
$896$	14.1533	−	3.35439i	0.472828	−	0.112062i
$897$	2.31757	+	0.396610i	0.0773815	+	0.0132424i
$898$	−2.43050	−	3.26473i	−0.0811068	−	0.108945i
$899$	2.12530	−	12.0532i	0.0708828	−	0.401996i
$900$	22.9137	+	30.1390i	0.763791	+	1.00463i
$901$	−0.823536	−	4.67050i	−0.0274360	−	0.155597i
$902$	−0.391337	+	0.414793i	−0.0130301	+	0.0138111i
$903$	14.2716	−	4.35119i	0.474931	−	0.144799i
$904$	6.05587	+	3.04137i	0.201415	+	0.101154i
$905$	6.03588	−	3.96986i	0.200639	−	0.131963i
$906$	−0.230419	−	1.88871i	−0.00765516	−	0.0627482i
$907$	7.01551	+	1.66271i	0.232946	+	0.0552093i	0.345431	−	0.938444i	$-0.387733\pi$
$907$	7.01551	+	1.66271i	0.232946	+	0.0552093i	−0.112485	+	0.993653i	$0.535881\pi$
$908$	44.8209	+	16.3135i	1.48743	+	0.541382i
$909$	6.65789	+	15.0164i	0.220828	+	0.498064i
$910$	1.86565	−	0.679040i	0.0618456	−	0.0225099i
$911$	14.2433	−	1.66481i	0.471902	−	0.0551575i	0.123182	−	0.992384i	$-0.460690\pi$
$911$	14.2433	−	1.66481i	0.471902	−	0.0551575i	0.348721	+	0.937227i	$0.386616\pi$
$912$	−25.9352	−	14.7998i	−0.858800	−	0.490070i
$913$	37.7826	+	40.0472i	1.25042	+	1.32537i
$914$	−1.56794	+	2.10611i	−0.0518630	+	0.0696641i
$915$	29.7318	+	8.73800i	0.982904	+	0.288869i
$916$	8.39452	−	4.21588i	0.277363	−	0.139297i
$917$	−11.6893	+	20.2465i	−0.386015	+	0.668598i
$918$	0.782030	+	0.715758i	0.0258108	+	0.0236235i
$919$	23.7632	+	41.1591i	0.783875	+	1.35771i	0.929669	+	0.368397i	$0.120093\pi$
$919$	23.7632	+	41.1591i	0.783875	+	1.35771i	−0.145793	+	0.989315i	$0.546573\pi$
$920$	1.48423	+	0.976194i	0.0489337	+	0.0321842i
$921$	−21.8179	−	32.8110i	−0.718926	−	1.08116i
$922$	0.813711	+	1.88639i	0.0267981	+	0.0621251i
$923$	−0.727932	+	2.43146i	−0.0239602	+	0.0800325i
$924$	−37.9682	−	44.7881i	−1.24906	−	1.47342i
$925$	−8.10836	+	18.7973i	−0.266601	+	0.618051i
$926$	0.324575	+	0.272351i	0.0106662	+	0.00895000i
$927$	−3.45545	+	6.12691i	−0.113492	+	0.201234i
$928$	2.03246	−	1.70543i	0.0667186	−	0.0559836i
$929$	−14.6368	−	48.8903i	−0.480217	−	1.60404i	−0.764046	−	0.645162i	$-0.776790\pi$
$929$	−14.6368	−	48.8903i	−0.480217	−	1.60404i	0.283829	−	0.958875i	$-0.408395\pi$
$930$	4.90126	+	0.260672i	0.160719	+	0.00854778i
$931$	−1.79364	−	30.7956i	−0.0587842	−	1.00929i
$932$	−1.20599	−	20.7060i	−0.0395035	−	0.678249i
$933$	−24.0515	−	47.2942i	−0.787409	−	1.54834i
$934$	0.335583	+	1.12093i	0.0109806	+	0.0366778i
$935$	19.4161	−	16.2921i	0.634976	−	0.532808i
$936$	1.77537	+	0.625979i	0.0580299	+	0.0204608i
$937$	−22.5978	−	18.9618i	−0.738237	−	0.619454i	0.194127	−	0.980976i	$-0.437813\pi$
$937$	−22.5978	−	18.9618i	−0.738237	−	0.619454i	−0.932364	+	0.361522i	$0.882257\pi$
$938$	0.558147	−	1.29393i	0.0182242	−	0.0422484i
$939$	38.8728	−	7.05663i	1.26857	−	0.230285i
$940$	−18.2772	+	61.0500i	−0.596136	+	1.99123i
$941$	−23.2693	−	53.9442i	−0.758557	−	1.75853i	−0.643876	−	0.765129i	$-0.722675\pi$
$941$	−23.2693	−	53.9442i	−0.758557	−	1.75853i	−0.114680	−	0.993402i	$-0.536584\pi$
$942$	−0.505469	+	1.01926i	−0.0164691	+	0.0332092i
$943$	−0.899446	−	0.591575i	−0.0292900	−	0.0192643i
$944$	20.8100	+	36.0440i	0.677309	+	1.17313i
$945$	−56.2306	+	33.6091i	−1.82918	+	1.09330i
$946$	−0.651300	+	1.12808i	−0.0211756	+	0.0366772i
$947$	−10.5308	+	5.28878i	−0.342206	+	0.171862i	−0.611599	−	0.791168i	$-0.709473\pi$
$947$	−10.5308	+	5.28878i	−0.342206	+	0.171862i	0.269393	+	0.963030i	$0.413177\pi$
$948$	13.9824	−	13.3256i	0.454128	−	0.432797i
$949$	−12.2457	+	16.4488i	−0.397512	+	0.533951i
$950$	−2.38460	−	2.52753i	−0.0773667	−	0.0820040i
$951$	−0.0700707	−	13.8947i	−0.00227220	−	0.450565i
$952$	−3.02048	+	0.353043i	−0.0978943	+	0.0114422i
$953$	33.2006	−	12.0840i	1.07547	−	0.391441i	0.257253	−	0.966344i	$-0.417183\pi$
$953$	33.2006	−	12.0840i	1.07547	−	0.391441i	0.818221	+	0.574904i	$0.194960\pi$
$954$	−0.742190	−	0.770947i	−0.0240293	−	0.0249603i
$955$	−65.9527	−	24.0048i	−2.13418	−	0.776778i
$956$	30.5654	+	7.24413i	0.988555	+	0.234292i
$957$	−13.1235	−	5.58262i	−0.424224	−	0.180460i
$958$	−1.89091	+	1.24367i	−0.0610924	+	0.0401811i
$959$	54.7428	+	27.4929i	1.76774	+	0.887792i
$960$	−32.5684	−	30.4177i	−1.05114	−	0.981728i
$961$	−10.3404	+	10.9602i	−0.333560	+	0.353553i
$962$	0.0880371	+	0.499283i	0.00283843	+	0.0160975i
$963$	−34.4314	−	7.79447i	−1.10954	−	0.251173i
$964$	−6.07958	+	34.4790i	−0.195810	+	1.11049i
$965$	−28.3679	−	38.1047i	−0.913196	−	1.22663i
$966$	−0.547598	+	0.659326i	−0.0176187	+	0.0212135i
$967$	−55.7139	+	13.2044i	−1.79164	+	0.424626i	−0.985857	−	0.167587i	$-0.946403\pi$
$967$	−55.7139	+	13.2044i	−1.79164	+	0.424626i	−0.805782	+	0.592213i	$0.798254\pi$
$968$	4.82937	+	0.564472i	0.155222	+	0.0181428i
$969$	10.1316	+	7.46356i	0.325473	+	0.239764i
$970$	−0.228082	+	3.91602i	−0.00732329	+	0.125736i
$971$	−25.0907			−0.805200			−0.402600	−	0.915376i	$-0.631893\pi$
$971$	−25.0907			−0.805200			−0.402600	+	0.915376i	$0.631893\pi$
$972$	−30.5934	−	4.60241i	−0.981285	−	0.147622i
$973$	−73.1022			−2.34355
$974$	−0.224842	+	3.86039i	−0.00720441	+	0.123695i
$975$	−11.2728	−	8.30425i	−0.361018	−	0.265949i
$976$	−20.6068	−	2.40858i	−0.659606	−	0.0770969i
$977$	28.7634	−	6.81706i	0.920224	−	0.218097i	0.256907	−	0.966436i	$-0.417297\pi$
$977$	28.7634	−	6.81706i	0.920224	−	0.218097i	0.663316	+	0.748339i	$0.269148\pi$
$978$	0.667143	−	0.803262i	0.0213329	−	0.0256855i
$979$	−26.6662	−	35.8190i	−0.852257	−	1.14478i
$980$	8.12229	−	46.0638i	0.259457	−	1.47145i
$981$	0.862669	−	0.933051i	0.0275429	−	0.0297900i
$982$	0.0470343	+	0.266745i	0.00150092	+	0.00851216i
$983$	33.3876	−	35.3888i	1.06490	−	1.12873i	0.0735760	−	0.997290i	$-0.476559\pi$
$983$	33.3876	−	35.3888i	1.06490	−	1.12873i	0.991324	−	0.131439i	$-0.0419597\pi$
$984$	−0.629915	−	0.588318i	−0.0200810	−	0.0187549i
$985$	−5.77054	−	2.89807i	−0.183865	−	0.0923403i
$986$	−0.307375	+	0.202164i	−0.00978881	+	0.00643820i
$987$	−56.8029	−	24.1634i	−1.80806	−	0.769129i
$988$	10.8297	+	2.56668i	0.344538	+	0.0816571i
$989$	−2.31077	−	0.841053i	−0.0734783	−	0.0267439i
$990$	1.58495	−	5.49524i	0.0503731	−	0.174650i
$991$	20.7603	−	7.55612i	0.659472	−	0.240028i	0.00946345	−	0.999955i	$-0.496988\pi$
$991$	20.7603	−	7.55612i	0.659472	−	0.240028i	0.650008	+	0.759927i	$0.274765\pi$
$992$	−9.91906	+	1.15937i	−0.314931	+	0.0368101i
$993$	0.160711	+	31.8683i	0.00510002	+	1.01131i
$994$	−0.634893	−	0.672947i	−0.0201376	−	0.0213446i
$995$	−32.4048	+	43.5272i	−1.02730	+	1.37990i
$996$	−30.0044	+	28.5950i	−0.950725	+	0.906068i
$997$	5.82285	−	2.92435i	0.184412	−	0.0926150i	−0.354198	−	0.935170i	$-0.615246\pi$
$997$	5.82285	−	2.92435i	0.184412	−	0.0926150i	0.538610	+	0.842555i	$0.318950\pi$
$998$	−0.0389742	+	0.0675054i	−0.00123371	+	0.00213684i
$999$	−5.95861	−	15.6312i	−0.188522	−	0.494549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.79.4	yes	144
3.2	odd	2		243.2.g.a.235.5		144
9.2	odd	6		729.2.g.b.460.4		144
9.4	even	3		729.2.g.d.703.4		144
9.5	odd	6		729.2.g.a.703.5		144
9.7	even	3		729.2.g.c.460.5		144
81.11	odd	54		6561.2.a.d.1.36		72
81.13	even	27		729.2.g.d.28.4		144
81.14	odd	54		729.2.g.b.271.4		144
81.40	even	27	inner	81.2.g.a.40.4	✓	144
81.41	odd	54		243.2.g.a.91.5		144
81.67	even	27		729.2.g.c.271.5		144
81.68	odd	54		729.2.g.a.28.5		144
81.70	even	27		6561.2.a.c.1.37		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.4	✓	144	81.40	even	27	inner
81.2.g.a.79.4	yes	144	1.1	even	1	trivial
243.2.g.a.91.5		144	81.41	odd	54
243.2.g.a.235.5		144	3.2	odd	2
729.2.g.a.28.5		144	81.68	odd	54
729.2.g.a.703.5		144	9.5	odd	6
729.2.g.b.271.4		144	81.14	odd	54
729.2.g.b.460.4		144	9.2	odd	6
729.2.g.c.271.5		144	81.67	even	27
729.2.g.c.460.5		144	9.7	even	3
729.2.g.d.28.4		144	81.13	even	27
729.2.g.d.703.4		144	9.4	even	3
6561.2.a.c.1.37		72	81.70	even	27
6561.2.a.d.1.36		72	81.11	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
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

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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