LMFDB - Embedded newform 169.2.g.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.479816 + 0.695133i) q^{2} +(-2.71090 + 1.42279i) q^{3} +(0.456223 + 1.20296i) q^{4} +(-1.82534 - 1.61711i) q^{5} +(0.311704 - 2.56712i) q^{6} +(-0.220084 - 0.0542458i) q^{7} +(-2.69533 - 0.664340i) q^{8} +(3.62047 - 5.24515i) q^{9} +O(q^{10})$	\(q+(-0.479816 + 0.695133i) q^{2} +(-2.71090 + 1.42279i) q^{3} +(0.456223 + 1.20296i) q^{4} +(-1.82534 - 1.61711i) q^{5} +(0.311704 - 2.56712i) q^{6} +(-0.220084 - 0.0542458i) q^{7} +(-2.69533 - 0.664340i) q^{8} +(3.62047 - 5.24515i) q^{9} +(1.99993 - 0.492940i) q^{10} +(0.946194 + 1.37080i) q^{11} +(-2.94834 - 2.61200i) q^{12} +(1.80673 - 3.12021i) q^{13} +(0.143308 - 0.126960i) q^{14} +(7.24913 + 1.78675i) q^{15} +(-0.170950 + 0.151448i) q^{16} +(-6.94760 - 1.71243i) q^{17} +(1.90892 + 5.03341i) q^{18} -2.98564 q^{19} +(1.11256 - 2.93358i) q^{20} +(0.673806 - 0.166078i) q^{21} -1.40689 q^{22} -3.28291 q^{23} +(8.25200 - 2.03394i) q^{24} +(0.114138 + 0.940009i) q^{25} +(1.30206 + 2.75305i) q^{26} +(-1.24487 + 10.2525i) q^{27} +(-0.0351517 - 0.289500i) q^{28} +(-5.74770 + 8.32698i) q^{29} +(-4.72028 + 4.18180i) q^{30} +(-0.249708 + 2.05653i) q^{31} +(-0.692472 - 5.70302i) q^{32} +(-4.51540 - 2.36987i) q^{33} +(4.52394 - 4.00786i) q^{34} +(0.314006 + 0.454917i) q^{35} +(7.96145 + 1.96232i) q^{36} +(-0.411599 + 3.38982i) q^{37} +(1.43256 - 2.07542i) q^{38} +(-0.458474 + 11.0292i) q^{39} +(3.84559 + 5.57130i) q^{40} +(8.41285 - 4.41540i) q^{41} +(-0.207856 + 0.548072i) q^{42} +(0.371090 + 3.05620i) q^{43} +(-1.21734 + 1.76362i) q^{44} +(-15.0906 + 3.71949i) q^{45} +(1.57519 - 2.28206i) q^{46} +(1.34366 - 3.54295i) q^{47} +(0.247949 - 0.653788i) q^{48} +(-6.15270 - 3.22918i) q^{49} +(-0.708197 - 0.371690i) q^{50} +(21.2707 - 5.24276i) q^{51} +(4.57776 + 0.749920i) q^{52} +(-6.17579 - 1.52220i) q^{53} +(-6.52951 - 5.78464i) q^{54} +(0.489607 - 4.03228i) q^{55} +(0.557162 + 0.292421i) q^{56} +(8.09377 - 4.24794i) q^{57} +(-3.03052 - 7.99083i) q^{58} +(-5.19351 - 4.60105i) q^{59} +(1.15783 + 9.53558i) q^{60} +(-6.24190 + 1.53849i) q^{61} +(-1.30975 - 1.16034i) q^{62} +(-1.08133 + 0.957978i) q^{63} +(3.89216 + 2.04276i) q^{64} +(-8.34363 + 2.77376i) q^{65} +(3.81393 - 2.00171i) q^{66} +(-4.48794 + 11.8337i) q^{67} +(-1.10967 - 9.13894i) q^{68} +(8.89964 - 4.67089i) q^{69} -0.466893 q^{70} +(6.44186 - 3.38095i) q^{71} +(-13.2429 + 11.7322i) q^{72} +(4.02863 + 5.83648i) q^{73} +(-2.15888 - 1.91260i) q^{74} +(-1.64685 - 2.38588i) q^{75} +(-1.36212 - 3.59160i) q^{76} +(-0.133882 - 0.353018i) q^{77} +(-7.44678 - 5.61068i) q^{78} +(-1.21302 + 3.19846i) q^{79} +0.556951 q^{80} +(-4.43234 - 11.6871i) q^{81} +(-0.967324 + 7.96663i) q^{82} +(-0.599062 - 0.314412i) q^{83} +(0.507192 + 0.734794i) q^{84} +(9.91255 + 14.3608i) q^{85} +(-2.30252 - 1.20846i) q^{86} +(3.73390 - 30.7514i) q^{87} +(-1.63963 - 4.32335i) q^{88} -1.22376 q^{89} +(4.65515 - 12.2746i) q^{90} +(-0.566891 + 0.588700i) q^{91} +(-1.49774 - 3.94921i) q^{92} +(-2.24908 - 5.93033i) q^{93} +(1.81811 + 2.63399i) q^{94} +(5.44981 + 4.82811i) q^{95} +(9.99143 + 14.4751i) q^{96} +(8.86437 - 7.85315i) q^{97} +(5.19688 - 2.72753i) q^{98} +10.6157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

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 $

$2$	−0.479816	+	0.695133i	−0.339281	+	0.491533i	−0.955071	−	0.296377i	$-0.904222\pi$
$2$	−0.479816	+	0.695133i	−0.339281	+	0.491533i	0.615790	+	0.787910i	$0.288837\pi$
$3$	−2.71090	+	1.42279i	−1.56514	+	0.821449i	−0.999994	−	0.00354112i	$-0.998873\pi$
$3$	−2.71090	+	1.42279i	−1.56514	+	0.821449i	−0.565147	+	0.824990i	$0.691181\pi$
$4$	0.456223	+	1.20296i	0.228111	+	0.601480i
$5$	−1.82534	−	1.61711i	−0.816317	−	0.723194i	0.147701	−	0.989032i	$-0.452813\pi$
$5$	−1.82534	−	1.61711i	−0.816317	−	0.723194i	−0.964018	+	0.265838i	$0.914351\pi$
$6$	0.311704	−	2.56712i	0.127253	−	1.04802i
$7$	−0.220084	−	0.0542458i	−0.0831839	−	0.0205030i	0.197504	−	0.980302i	$-0.436716\pi$
$7$	−0.220084	−	0.0542458i	−0.0831839	−	0.0205030i	−0.280688	+	0.959799i	$0.590563\pi$
$8$	−2.69533	−	0.664340i	−0.952944	−	0.234880i
$9$	3.62047	−	5.24515i	1.20682	−	1.74838i
$10$	1.99993	−	0.492940i	0.632435	−	0.155881i
$11$	0.946194	+	1.37080i	0.285288	+	0.413312i	0.939259	−	0.343208i	$-0.111514\pi$
$11$	0.946194	+	1.37080i	0.285288	+	0.413312i	−0.653971	+	0.756520i	$0.726898\pi$
$12$	−2.94834	−	2.61200i	−0.851112	−	0.754019i
$13$	1.80673	−	3.12021i	0.501098	−	0.865391i
$13$	1.80673	−	3.12021i	0.501098	−	0.865391i
$14$	0.143308	−	0.126960i	0.0383006	−	0.0339314i
$15$	7.24913	+	1.78675i	1.87172	+	0.461337i
$16$	−0.170950	+	0.151448i	−0.0427375	+	0.0378621i
$17$	−6.94760	−	1.71243i	−1.68504	−	0.415325i	−0.723574	−	0.690247i	$-0.757502\pi$
$17$	−6.94760	−	1.71243i	−1.68504	−	0.415325i	−0.961467	+	0.274922i	$0.911348\pi$
$18$	1.90892	+	5.03341i	0.449937	+	1.18639i
$19$	−2.98564			−0.684952			−0.342476	−	0.939527i	$-0.611266\pi$
$19$	−2.98564			−0.684952			−0.342476	+	0.939527i	$0.611266\pi$
$20$	1.11256	−	2.93358i	0.248776	−	0.655967i
$21$	0.673806	−	0.166078i	0.147037	−	0.0362413i
$22$	−1.40689			−0.299949
$23$	−3.28291			−0.684533			−0.342267	−	0.939603i	$-0.611195\pi$
$23$	−3.28291			−0.684533			−0.342267	+	0.939603i	$0.611195\pi$
$24$	8.25200	−	2.03394i	1.68443	−	0.415175i
$25$	0.114138	+	0.940009i	0.0228275	+	0.188002i
$26$	1.30206	+	2.75305i	0.255355	+	0.539917i
$27$	−1.24487	+	10.2525i	−0.239576	+	1.97309i
$28$	−0.0351517	−	0.289500i	−0.00664305	−	0.0547104i
$29$	−5.74770	+	8.32698i	−1.06732	+	1.54628i	−0.251604	+	0.967830i	$0.580958\pi$
$29$	−5.74770	+	8.32698i	−1.06732	+	1.54628i	−0.815717	+	0.578451i	$0.803657\pi$
$30$	−4.72028	+	4.18180i	−0.861801	+	0.763489i
$31$	−0.249708	+	2.05653i	−0.0448488	+	0.369364i	0.952954	+	0.303114i	$0.0980264\pi$
$31$	−0.249708	+	2.05653i	−0.0448488	+	0.369364i	−0.997803	+	0.0662493i	$0.978897\pi$
$32$	−0.692472	−	5.70302i	−0.122413	−	1.00816i
$33$	−4.51540	−	2.36987i	−0.786031	−	0.412541i
$34$	4.52394	−	4.00786i	0.775849	−	0.687342i
$35$	0.314006	+	0.454917i	0.0530768	+	0.0768950i
$36$	7.96145	+	1.96232i	1.32691	+	0.327053i
$37$	−0.411599	+	3.38982i	−0.0676664	+	0.557283i	0.918968	+	0.394332i	$0.129024\pi$
$37$	−0.411599	+	3.38982i	−0.0676664	+	0.557283i	−0.986634	+	0.162950i	$0.947899\pi$
$38$	1.43256	−	2.07542i	0.232391	−	0.336677i
$39$	−0.458474	+	11.0292i	−0.0734146	+	1.76608i
$40$	3.84559	+	5.57130i	0.608041	+	0.880899i
$41$	8.41285	−	4.41540i	1.31387	−	0.689570i	0.345339	−	0.938478i	$-0.387764\pi$
$41$	8.41285	−	4.41540i	1.31387	−	0.689570i	0.968527	+	0.248908i	$0.0800716\pi$
$42$	−0.207856	+	0.548072i	−0.0320729	+	0.0845694i
$43$	0.371090	+	3.05620i	0.0565907	+	0.466067i	0.993265	+	0.115865i	$0.0369639\pi$
$43$	0.371090	+	3.05620i	0.0565907	+	0.466067i	−0.936674	+	0.350202i	$0.886113\pi$
$44$	−1.21734	+	1.76362i	−0.183521	+	0.265876i
$45$	−15.0906	+	3.71949i	−2.24957	+	0.554469i
$46$	1.57519	−	2.28206i	0.232249	−	0.336471i
$47$	1.34366	−	3.54295i	0.195993	−	0.516792i	−0.800606	−	0.599191i	$-0.795489\pi$
$47$	1.34366	−	3.54295i	0.195993	−	0.516792i	0.996599	+	0.0823991i	$0.0262582\pi$
$48$	0.247949	−	0.653788i	0.0357884	−	0.0943662i
$49$	−6.15270	−	3.22918i	−0.878957	−	0.461312i
$50$	−0.708197	−	0.371690i	−0.100154	−	0.0525649i
$51$	21.2707	−	5.24276i	2.97849	−	0.734133i
$52$	4.57776	+	0.749920i	0.634822	+	0.103995i
$53$	−6.17579	−	1.52220i	−0.848311	−	0.209090i	−0.208883	−	0.977941i	$-0.566983\pi$
$53$	−6.17579	−	1.52220i	−0.848311	−	0.209090i	−0.639428	+	0.768851i	$0.720829\pi$
$54$	−6.52951	−	5.78464i	−0.888554	−	0.787190i
$55$	0.489607	−	4.03228i	0.0660186	−	0.543712i
$56$	0.557162	+	0.292421i	0.0744538	+	0.0390764i
$57$	8.09377	−	4.24794i	1.07205	−	0.562654i
$58$	−3.03052	−	7.99083i	−0.397927	−	1.04925i
$59$	−5.19351	−	4.60105i	−0.676137	−	0.599005i	0.253565	−	0.967318i	$-0.418397\pi$
$59$	−5.19351	−	4.60105i	−0.676137	−	0.599005i	−0.929702	+	0.368313i	$0.879935\pi$
$60$	1.15783	+	9.53558i	0.149475	+	1.23104i
$61$	−6.24190	+	1.53849i	−0.799194	+	0.196984i	−0.617706	−	0.786409i	$-0.711938\pi$
$61$	−6.24190	+	1.53849i	−0.799194	+	0.196984i	−0.181488	+	0.983393i	$0.558091\pi$
$62$	−1.30975	−	1.16034i	−0.166338	−	0.147363i
$63$	−1.08133	+	0.957978i	−0.136235	+	0.120694i
$64$	3.89216	+	2.04276i	0.486520	+	0.255346i
$65$	−8.34363	+	2.77376i	−1.03490	+	0.344042i
$66$	3.81393	−	2.00171i	0.469463	−	0.246393i
$67$	−4.48794	+	11.8337i	−0.548289	+	1.44572i	0.318924	+	0.947780i	$0.396679\pi$
$67$	−4.48794	+	11.8337i	−0.548289	+	1.44572i	−0.867213	+	0.497938i	$0.834091\pi$
$68$	−1.10967	−	9.13894i	−0.134567	−	1.10826i
$69$	8.89964	−	4.67089i	1.07139	−	0.562309i
$70$	−0.466893			−0.0558044
$71$	6.44186	−	3.38095i	0.764508	−	0.401245i	−0.0369335	−	0.999318i	$-0.511759\pi$
$71$	6.44186	−	3.38095i	0.764508	−	0.401245i	0.801442	+	0.598073i	$0.204067\pi$
$72$	−13.2429	+	11.7322i	−1.56069	+	1.38265i
$73$	4.02863	+	5.83648i	0.471515	+	0.683108i	0.984519	−	0.175279i	$-0.0560826\pi$
$73$	4.02863	+	5.83648i	0.471515	+	0.683108i	−0.513004	+	0.858386i	$0.671467\pi$
$74$	−2.15888	−	1.91260i	−0.250965	−	0.222336i
$75$	−1.64685	−	2.38588i	−0.190162	−	0.275498i
$76$	−1.36212	−	3.59160i	−0.156245	−	0.411985i
$77$	−0.133882	−	0.353018i	−0.0152573	−	0.0402301i
$78$	−7.44678	−	5.61068i	−0.843181	−	0.635285i
$79$	−1.21302	+	3.19846i	−0.136475	+	0.359855i	−0.985779	−	0.168050i	$-0.946253\pi$
$79$	−1.21302	+	3.19846i	−0.136475	+	0.359855i	0.849303	+	0.527905i	$0.177022\pi$
$80$	0.556951			0.0622690
$81$	−4.43234	−	11.6871i	−0.492482	−	1.29857i
$82$	−0.967324	+	7.96663i	−0.106823	+	0.879767i
$83$	−0.599062	−	0.314412i	−0.0657556	−	0.0345112i	0.431525	−	0.902101i	$-0.357976\pi$
$83$	−0.599062	−	0.314412i	−0.0657556	−	0.0345112i	−0.497281	+	0.867590i	$0.665668\pi$
$84$	0.507192	+	0.734794i	0.0553391	+	0.0801726i
$85$	9.91255	+	14.3608i	1.07517	+	1.55765i
$86$	−2.30252	−	1.20846i	−0.248287	−	0.130311i
$87$	3.73390	−	30.7514i	0.400316	−	3.29690i
$88$	−1.63963	−	4.32335i	−0.174785	−	0.460871i
$89$	−1.22376			−0.129718			−0.0648592	−	0.997894i	$-0.520660\pi$
$89$	−1.22376			−0.129718			−0.0648592	+	0.997894i	$0.520660\pi$
$90$	4.65515	−	12.2746i	0.490696	−	1.29386i
$91$	−0.566891	+	0.588700i	−0.0594264	+	0.0617125i
$92$	−1.49774	−	3.94921i	−0.156150	−	0.411733i
$93$	−2.24908	−	5.93033i	−0.233219	−	0.614947i
$94$	1.81811	+	2.63399i	0.187524	+	0.271675i
$95$	5.44981	+	4.82811i	0.559138	+	0.495353i
$96$	9.99143	+	14.4751i	1.01975	+	1.47736i
$97$	8.86437	−	7.85315i	0.900040	−	0.797366i	−0.0798699	−	0.996805i	$-0.525450\pi$
$97$	8.86437	−	7.85315i	0.900040	−	0.797366i	0.979910	+	0.199439i	$0.0639120\pi$
$98$	5.19688	−	2.72753i	0.524964	−	0.275522i
$99$	10.6157			1.06692
$100$	−1.07872	+	0.566157i	−0.107872	+	0.0566157i
$101$	1.39091	+	11.4552i	0.138401	+	1.13983i	0.882014	+	0.471224i	$0.156187\pi$
$101$	1.39091	+	11.4552i	0.138401	+	1.13983i	−0.743613	+	0.668610i	$0.766889\pi$
$102$	−6.56160	+	17.3015i	−0.649696	+	1.71311i
$103$	−9.93322	+	5.21336i	−0.978750	+	0.513687i	−0.876672	−	0.481089i	$-0.840241\pi$
$103$	−9.93322	+	5.21336i	−0.978750	+	0.513687i	−0.102078	+	0.994776i	$0.532549\pi$
$104$	−6.94263	+	7.20972i	−0.680781	+	0.706971i
$105$	−1.49849	−	0.786470i	−0.146238	−	0.0767516i
$106$	4.02137	−	3.56263i	0.390590	−	0.346033i
$107$	10.2014	+	9.03765i	0.986206	+	0.873703i	0.991995	−	0.126281i	$-0.0403040\pi$
$107$	10.2014	+	9.03765i	0.986206	+	0.873703i	−0.00578814	+	0.999983i	$0.501842\pi$
$108$	−12.9012	+	3.17987i	−1.24142	+	0.305983i
$109$	−2.13622	−	17.5933i	−0.204613	−	1.68514i	−0.627235	−	0.778830i	$-0.715813\pi$
$109$	−2.13622	−	17.5933i	−0.204613	−	1.68514i	0.422622	−	0.906306i	$-0.361110\pi$
$110$	2.56805	+	2.27509i	0.244854	+	0.216922i
$111$	−3.70720	−	9.77509i	−0.351872	−	0.927811i
$112$	0.0458388	−	0.0240580i	0.00433136	−	0.00227327i
$113$	−1.04779	−	0.549925i	−0.0985682	−	0.0517326i	0.414719	−	0.909950i	$-0.363880\pi$
$113$	−1.04779	−	0.549925i	−0.0985682	−	0.0517326i	−0.513287	+	0.858217i	$0.671572\pi$
$114$	−0.930636	+	7.66448i	−0.0871621	+	0.717844i
$115$	5.99242	+	5.30882i	0.558796	+	0.495050i
$116$	−12.6393	−	3.11530i	−1.17353	−	0.289248i
$117$	−9.82475	−	20.7732i	−0.908298	−	1.92048i
$118$	5.69027	−	1.40253i	0.523832	−	0.129113i
$119$	1.43616	+	0.753756i	0.131653	+	0.0690967i
$120$	−18.3518	−	9.63177i	−1.67528	−	0.879257i
$121$	2.91685	−	7.69109i	0.265168	−	0.699190i
$122$	1.92551	−	5.07715i	0.174327	−	0.459663i
$123$	−16.5242	+	23.9395i	−1.48994	+	2.15855i
$124$	−2.58785	+	0.637847i	−0.232395	+	0.0572803i
$125$	−5.61474	+	8.13435i	−0.502198	+	0.727559i
$126$	−0.147081	−	1.21132i	−0.0131030	−	0.107913i
$127$	5.58872	−	14.7362i	0.495919	−	1.30763i	−0.420458	−	0.907312i	$-0.638131\pi$
$127$	5.58872	−	14.7362i	0.495919	−	1.30763i	0.916376	−	0.400318i	$-0.131100\pi$
$128$	6.88620	−	3.61416i	0.608660	−	0.319450i
$129$	−5.35433	−	7.75709i	−0.471422	−	0.682973i
$130$	2.07528	−	7.13083i	0.182014	−	0.625415i
$131$	−2.17315	+	3.14836i	−0.189869	+	0.275073i	−0.906345	−	0.422539i	$-0.861139\pi$
$131$	−2.17315	+	3.14836i	−0.189869	+	0.275073i	0.716475	+	0.697612i	$0.245754\pi$
$132$	0.790826	−	6.51304i	0.0688326	−	0.566887i
$133$	0.657091	+	0.161958i	0.0569770	+	0.0140436i
$134$	−6.07263	−	8.79772i	−0.524595	−	0.760007i
$135$	18.8517	−	16.7011i	1.62249	−	1.43740i
$136$	17.5885	+	9.23114i	1.50820	+	0.791563i
$137$	2.18620	+	18.0050i	0.186779	+	1.53827i	0.721008	+	0.692927i	$0.243679\pi$
$137$	2.18620	+	18.0050i	0.186779	+	1.53827i	−0.534229	+	0.845340i	$0.679398\pi$
$138$	−1.02330	+	8.42760i	−0.0871088	+	0.717405i
$139$	−11.8913	+	10.5347i	−1.00860	+	0.893546i	−0.994328	−	0.106352i	$-0.966083\pi$
$139$	−11.8913	+	10.5347i	−1.00860	+	0.893546i	−0.0142760	+	0.999898i	$0.504544\pi$
$140$	−0.403990	+	0.585281i	−0.0341434	+	0.0494653i
$141$	1.39834	+	11.5163i	0.117761	+	0.969851i
$142$	−0.740696	+	6.10018i	−0.0621579	+	0.511916i
$143$	5.98670	−	0.475654i	0.500633	−	0.0397762i
$144$	0.175451	+	1.44497i	0.0146209	+	0.120414i
$145$	23.9572	−	5.90491i	1.98953	−	0.490376i
$146$	−5.99013			−0.495747
$147$	21.2738			1.75464
$148$	−4.26560	+	1.05138i	−0.350630	+	0.0864226i
$149$	2.81725	−	7.42847i	0.230798	−	0.608564i	−0.768721	−	0.639584i	$-0.779106\pi$
$149$	2.81725	−	7.42847i	0.230798	−	0.608564i	0.999519	+	0.0310203i	$0.00987566\pi$
$150$	2.44869			0.199935
$151$	0.0402609	+	0.106159i	0.00327638	+	0.00863912i	0.936644	−	0.350282i	$-0.113914\pi$
$151$	0.0402609	+	0.106159i	0.00327638	+	0.00863912i	−0.933368	+	0.358921i	$0.883145\pi$
$152$	8.04729	+	1.98348i	0.652721	+	0.160881i
$153$	−34.1355	+	30.2414i	−2.75969	+	2.44487i
$154$	0.309633	+	0.0763177i	0.0249510	+	0.00614986i
$155$	3.78144	−	3.35006i	0.303732	−	0.269083i
$156$	−13.4769	+	4.48024i	−1.07901	+	0.358707i
$157$	−2.86478	−	2.53797i	−0.228634	−	0.202552i	0.541026	−	0.841006i	$-0.318036\pi$
$157$	−2.86478	−	2.53797i	−0.228634	−	0.202552i	−0.769660	+	0.638454i	$0.779574\pi$
$158$	−1.64133	−	2.37788i	−0.130577	−	0.189174i
$159$	18.9077	−	4.66034i	1.49948	−	0.369589i
$160$	−7.95841	+	11.5297i	−0.629168	+	0.911507i
$161$	0.722515	+	0.178084i	0.0569421	+	0.0140350i
$162$	10.2508	+	2.52660i	0.805379	+	0.198508i
$163$	−1.78058	+	14.6644i	−0.139466	+	1.14860i	0.739989	+	0.672619i	$0.234831\pi$
$163$	−1.78058	+	14.6644i	−0.139466	+	1.14860i	−0.879454	+	0.475983i	$0.842092\pi$
$164$	9.14969	+	8.10592i	0.714471	+	0.632966i
$165$	4.40981	+	11.6277i	0.343303	+	0.905217i
$166$	0.505998	−	0.265568i	0.0392730	−	0.0206121i
$167$	−12.8423	+	18.6052i	−0.993765	+	1.43972i	−0.0980017	+	0.995186i	$0.531245\pi$
$167$	−12.8423	+	18.6052i	−0.993765	+	1.43972i	−0.895763	+	0.444531i	$0.853370\pi$
$168$	−1.92647			−0.148630
$169$	−6.47142	−	11.2748i	−0.497801	−	0.867291i
$170$	−14.7389			−1.13042
$171$	−10.8094	+	15.6601i	−0.826615	+	1.19756i
$172$	−3.50719	+	1.84072i	−0.267421	+	0.140353i
$173$	3.52787	+	9.30222i	0.268219	+	0.707235i	0.999679	+	0.0253504i	$0.00807016\pi$
$173$	3.52787	+	9.30222i	0.268219	+	0.707235i	−0.731460	+	0.681885i	$0.761161\pi$
$174$	19.5847	+	17.3506i	1.48472	+	1.31534i
$175$	0.0258717	−	0.213072i	0.00195571	−	0.0161068i
$176$	−0.369357	−	0.0910384i	−0.0278414	−	0.00686228i
$177$	20.6254	+	5.08371i	1.55030	+	0.382115i
$178$	0.587180	−	0.850677i	0.0440110	−	0.0637610i
$179$	4.05954	−	1.00059i	0.303425	−	0.0747875i	−0.0846639	−	0.996410i	$-0.526982\pi$
$179$	4.05954	−	1.00059i	0.303425	−	0.0747875i	0.388088	+	0.921622i	$0.373135\pi$
$180$	−11.3591	−	16.4564i	−0.846654	−	1.22659i
$181$	−6.21244	−	5.50375i	−0.461767	−	0.409090i	0.399904	−	0.916557i	$-0.369044\pi$
$181$	−6.21244	−	5.50375i	−0.461767	−	0.409090i	−0.861671	+	0.507467i	$0.830582\pi$
$182$	−0.137221	−	0.676533i	−0.0101715	−	0.0501479i
$183$	14.7322	−	13.0516i	1.08904	−	0.964804i
$184$	8.84853	+	2.18097i	0.652322	+	0.160783i
$185$	6.23302	−	5.52197i	0.458261	−	0.405984i
$186$	5.20151	+	1.28206i	0.381394	+	0.0940051i
$187$	−4.22638	−	11.1441i	−0.309064	−	0.814934i
$188$	4.87504			0.355548
$189$	0.830129	−	2.18887i	0.0603830	−	0.159217i
$190$	−5.97108	+	1.47174i	−0.433188	+	0.106771i
$191$	−1.97291			−0.142755			−0.0713775	−	0.997449i	$-0.522739\pi$
$191$	−1.97291			−0.142755			−0.0713775	+	0.997449i	$0.522739\pi$
$192$	−13.4577			−0.971226
$193$	3.92637	−	0.967764i	0.282627	−	0.0696612i	−0.0954542	−	0.995434i	$-0.530430\pi$
$193$	3.92637	−	0.967764i	0.282627	−	0.0696612i	0.378081	+	0.925773i	$0.376584\pi$
$194$	1.20572	+	9.92998i	0.0865655	+	0.712931i
$195$	18.6723	−	19.3906i	1.33715	−	1.38859i
$196$	1.07758	−	8.87468i	0.0769701	−	0.633906i
$197$	−1.54318	−	12.7092i	−0.109947	−	0.905494i	−0.938427	−	0.345476i	$-0.887717\pi$
$197$	−1.54318	−	12.7092i	−0.109947	−	0.905494i	0.828481	−	0.560018i	$-0.189206\pi$
$198$	−5.09359	+	7.37933i	−0.361985	+	0.524426i
$199$	−1.15087	+	1.01958i	−0.0815827	+	0.0722760i	−0.702929	−	0.711260i	$-0.748125\pi$
$199$	−1.15087	+	1.01958i	−0.0815827	+	0.0722760i	0.621346	+	0.783536i	$0.286586\pi$
$200$	0.316846	−	2.60946i	0.0224044	−	0.184517i
$201$	−4.67055	−	38.4655i	−0.329435	−	2.71314i
$202$	−8.63026	−	4.52951i	−0.607223	−	0.318695i
$203$	1.71668	−	1.52085i	0.120487	−	0.106742i
$204$	16.0110	+	23.1960i	1.12099	+	1.62404i
$205$	−22.4965	−	5.54489i	−1.57122	−	0.387272i
$206$	1.14214	−	9.40637i	0.0795766	−	0.655373i
$207$	−11.8856	+	17.2193i	−0.826110	+	1.19683i
$208$	0.163690	+	0.807027i	0.0113498	+	0.0559572i
$209$	−2.82499	−	4.09271i	−0.195409	−	0.283099i
$210$	1.26570	−	0.664292i	0.0873417	−	0.0458405i
$211$	3.99840	−	10.5429i	0.275261	−	0.725805i	−0.724087	−	0.689709i	$-0.757739\pi$
$211$	3.99840	−	10.5429i	0.275261	−	0.725805i	0.999348	−	0.0360961i	$-0.0114922\pi$
$212$	−0.986396	−	8.12370i	−0.0677459	−	0.557938i
$213$	−12.6529	+	18.3309i	−0.866961	+	1.25601i
$214$	−11.1772	+	2.75492i	−0.764055	+	0.188323i
$215$	4.26485	−	6.17870i	0.290860	−	0.421384i
$216$	10.1665	−	26.8068i	0.691740	−	1.82397i
$217$	0.166515	−	0.439063i	0.0113038	−	0.0298056i
$218$	13.2547	+	6.95661i	0.897722	+	0.471161i
$219$	−19.2253	−	10.0902i	−1.29913	−	0.681834i
$220$	5.07404	−	1.25064i	0.342092	−	0.0843180i
$221$	−17.8956	+	18.5841i	−1.20379	+	1.25010i
$222$	8.57376	+	2.11324i	0.575433	+	0.141832i
$223$	−14.6965	−	13.0200i	−0.984150	−	0.871881i	0.00761246	−	0.999971i	$-0.497577\pi$
$223$	−14.6965	−	13.0200i	−0.984150	−	0.871881i	−0.991763	+	0.128090i	$0.959115\pi$
$224$	−0.156963	+	1.29271i	−0.0104875	+	0.0863725i
$225$	5.34372	+	2.80460i	0.356248	+	0.186973i
$226$	0.885020	−	0.464494i	0.0588706	−	0.0308977i
$227$	−5.30068	−	13.9767i	−0.351818	−	0.927669i	−0.987767	−	0.155937i	$-0.950160\pi$
$227$	−5.30068	−	13.9767i	−0.351818	−	0.927669i	0.635949	−	0.771731i	$-0.280609\pi$
$228$	8.80267	+	7.79849i	0.582971	+	0.516467i
$229$	0.691141	+	5.69206i	0.0456719	+	0.376142i	0.997567	+	0.0697171i	$0.0222096\pi$
$229$	0.691141	+	5.69206i	0.0456719	+	0.376142i	−0.951895	+	0.306425i	$0.900867\pi$
$230$	−6.56560	+	1.61827i	−0.432923	+	0.106706i
$231$	0.865212	+	0.766511i	0.0569268	+	0.0504327i
$232$	21.0239	−	18.6256i	1.38029	−	1.22283i
$233$	14.1855	+	7.44512i	0.929322	+	0.487746i	0.860254	−	0.509866i	$-0.170305\pi$
$233$	14.1855	+	7.44512i	0.929322	+	0.487746i	0.0690683	+	0.997612i	$0.477997\pi$
$234$	19.1542	+	3.13780i	1.25215	+	0.205125i
$235$	−8.18198	+	4.29423i	−0.533733	+	0.280125i
$236$	3.16548	−	8.34669i	0.206055	−	0.543323i
$237$	−1.26238	−	10.3966i	−0.0820001	−	0.675331i
$238$	−1.21305	+	0.636660i	−0.0786306	+	0.0412685i
$239$	−28.7050			−1.85677			−0.928385	−	0.371619i	$-0.878803\pi$
$239$	−28.7050			−1.85677			−0.928385	+	0.371619i	$0.878803\pi$
$240$	−1.50984	+	0.792425i	−0.0974597	+	0.0511508i
$241$	0.840097	−	0.744261i	0.0541154	−	0.0479421i	−0.635632	−	0.771993i	$-0.719260\pi$
$241$	0.840097	−	0.744261i	0.0541154	−	0.0479421i	0.689747	+	0.724050i	$0.257722\pi$
$242$	3.94679	+	5.71791i	0.253709	+	0.367561i
$243$	5.45264	+	4.83062i	0.349787	+	0.309884i
$244$	−4.69844	−	6.80687i	−0.300787	−	0.435765i
$245$	6.00882	+	15.8440i	0.383889	+	1.01223i
$246$	−8.71254	−	22.9731i	−0.555491	−	1.46471i
$247$	−5.39426	+	9.31582i	−0.343228	+	0.592751i
$248$	2.03928	−	5.37714i	0.129494	−	0.341449i
$249$	2.07134			0.131266
$250$	−2.96042	−	7.80598i	−0.187233	−	0.493694i
$251$	1.81986	−	14.9879i	0.114869	−	0.946028i	−0.815336	−	0.578988i	$-0.803448\pi$
$251$	1.81986	−	14.9879i	0.114869	−	0.946028i	0.930205	−	0.367041i	$-0.119629\pi$
$252$	−1.64574	−	0.863750i	−0.103672	−	0.0544111i
$253$	−3.10627	−	4.50021i	−0.195289	−	0.282926i
$254$	7.56209	+	10.9556i	0.474488	+	0.687414i
$255$	−47.3044	−	24.8273i	−2.96232	−	1.55474i
$256$	−1.85146	+	15.2482i	−0.115716	+	0.953011i
$257$	−1.74711	−	4.60676i	−0.108982	−	0.287362i	0.869420	−	0.494074i	$-0.164493\pi$
$257$	−1.74711	−	4.60676i	−0.108982	−	0.287362i	−0.978402	+	0.206712i	$0.933724\pi$
$258$	7.96130			0.495649
$259$	0.274470	−	0.723717i	0.0170547	−	0.0449696i
$260$	−7.14327	−	8.77161i	−0.443007	−	0.543992i
$261$	22.8669	+	60.2951i	1.41543	+	3.73217i
$262$	−1.14581	−	3.02126i	−0.0707886	−	0.186654i
$263$	−3.35040	−	4.85390i	−0.206595	−	0.299304i	0.705966	−	0.708246i	$-0.250513\pi$
$263$	−3.35040	−	4.85390i	−0.206595	−	0.299304i	−0.912560	+	0.408942i	$0.865898\pi$
$264$	10.5961	+	9.38734i	0.652146	+	0.577751i
$265$	8.81137	+	12.7655i	0.541278	+	0.784176i
$266$	−0.427865	+	0.379055i	−0.0262341	+	0.0232414i
$267$	3.31750	−	1.74116i	0.203028	−	0.106557i
$268$	−16.2830			−0.994642
$269$	19.0362	−	9.99098i	1.16066	−	0.609161i	0.229333	−	0.973348i	$-0.426345\pi$
$269$	19.0362	−	9.99098i	1.16066	−	0.609161i	0.931326	+	0.364187i	$0.118653\pi$
$270$	2.56418	+	21.1179i	0.156051	+	1.28519i
$271$	7.91131	−	20.8604i	0.480578	−	1.26718i	−0.447330	−	0.894369i	$-0.647625\pi$
$271$	7.91131	−	20.8604i	0.480578	−	1.26718i	0.927908	−	0.372810i	$-0.121606\pi$
$272$	1.44704	−	0.759463i	0.0877395	−	0.0460492i
$273$	0.699190	−	2.40248i	0.0423169	−	0.145405i
$274$	−13.5648	−	7.11936i	−0.819480	−	0.430096i
$275$	−1.18057	+	1.04589i	−0.0711909	+	0.0630696i
$276$	9.67912	+	8.57495i	0.582615	+	0.516151i
$277$	−2.36419	+	0.582720i	−0.142050	+	0.0350123i	−0.309700	−	0.950834i	$-0.600229\pi$
$277$	−2.36419	+	0.582720i	−0.142050	+	0.0350123i	0.167649	+	0.985847i	$0.446382\pi$
$278$	−1.61743	−	13.3208i	−0.0970072	−	0.798926i
$279$	9.88274	+	8.75535i	0.591664	+	0.524169i
$280$	−0.544132	−	1.43476i	−0.0325181	−	0.0857433i
$281$	17.1904	−	9.02220i	1.02549	−	0.538219i	0.133869	−	0.990999i	$-0.457260\pi$
$281$	17.1904	−	9.02220i	1.02549	−	0.538219i	0.891622	+	0.452780i	$0.149568\pi$
$282$	−8.67633	−	4.55369i	−0.516668	−	0.271168i
$283$	1.37256	−	11.3041i	0.0815904	−	0.671958i	−0.893330	−	0.449402i	$-0.851637\pi$
$283$	1.37256	−	11.3041i	0.0815904	−	0.671958i	0.974920	−	0.222556i	$-0.0714399\pi$
$284$	7.00607	+	6.20684i	0.415734	+	0.368308i
$285$	−21.6433	−	5.33459i	−1.28204	−	0.315994i
$286$	−2.54187	+	4.38978i	−0.150304	+	0.259573i
$287$	−2.09105	+	0.515397i	−0.123431	+	0.0304229i
$288$	−32.4202	−	17.0155i	−1.91038	−	1.00265i
$289$	30.2840	+	15.8943i	1.78141	+	0.934957i
$290$	−7.39032	+	19.4867i	−0.433975	+	1.14430i
$291$	−12.8571	+	33.9013i	−0.753694	+	1.98733i
$292$	−5.18310	+	7.50902i	−0.303318	+	0.439432i
$293$	7.14148	−	1.76022i	0.417210	−	0.102833i	−0.0251223	−	0.999684i	$-0.507998\pi$
$293$	7.14148	−	1.76022i	0.417210	−	0.102833i	0.442332	+	0.896851i	$0.354151\pi$
$294$	−10.2075	+	14.7881i	−0.595315	+	0.862462i
$295$	2.03952	+	16.7970i	0.118745	+	0.977956i
$296$	3.36139	−	8.86325i	0.195377	−	0.515166i
$297$	−15.2320	+	7.99435i	−0.883848	+	0.463879i
$298$	3.81202	+	5.52266i	0.220824	+	0.319919i
$299$	−5.93134	+	10.2434i	−0.343018	+	0.592389i
$300$	2.11879	−	3.06959i	0.122328	−	0.177223i
$301$	0.0841152	−	0.692751i	0.00484832	−	0.0399295i
$302$	−0.0931126	−	0.0229502i	−0.00535803	−	0.00132064i
$303$	−20.0690	−	29.0749i	−1.15293	−	1.67031i
$304$	0.510395	−	0.452170i	0.0292731	−	0.0259337i
$305$	13.8815	+	7.28558i	0.794853	+	0.417171i
$306$	−4.64306	−	38.2390i	−0.265426	−	2.18598i
$307$	1.87111	−	15.4100i	0.106790	−	0.879494i	−0.836601	−	0.547812i	$-0.815461\pi$
$307$	1.87111	−	15.4100i	0.106790	−	0.879494i	0.943391	−	0.331682i	$-0.107616\pi$
$308$	0.363587	−	0.322110i	0.0207173	−	0.0183539i
$309$	19.5105	−	28.2658i	1.10991	−	1.60799i
$310$	0.514345	+	4.23601i	0.0292128	+	0.240589i
$311$	−1.84119	+	15.1635i	−0.104404	+	0.859846i	0.842581	+	0.538569i	$0.181035\pi$
$311$	−1.84119	+	15.1635i	−0.104404	+	0.859846i	−0.946985	+	0.321277i	$0.895888\pi$
$312$	8.56287	−	29.4228i	0.484777	−	1.66574i
$313$	0.819129	+	6.74613i	0.0462999	+	0.381314i	0.997378	+	0.0723642i	$0.0230544\pi$
$313$	0.819129	+	6.74613i	0.0462999	+	0.381314i	−0.951078	+	0.308950i	$0.900023\pi$
$314$	3.13879	−	0.773643i	0.177132	−	0.0436592i
$315$	3.52296			0.198496
$316$	−4.40103			−0.247577
$317$	11.7885	−	2.90561i	0.662108	−	0.163195i	0.106079	−	0.994358i	$-0.466170\pi$
$317$	11.7885	−	2.90561i	0.662108	−	0.163195i	0.556029	+	0.831163i	$0.312324\pi$
$318$	−5.83268	+	15.3795i	−0.327080	+	0.862440i
$319$	−16.8531			−0.943590
$320$	−3.80114	−	10.0228i	−0.212490	−	0.560291i
$321$	−40.5137	−	9.98573i	−2.26125	−	0.557349i
$322$	−0.470466	+	0.416797i	−0.0262180	+	0.0232272i
$323$	20.7430	+	5.11269i	1.15417	+	0.284478i
$324$	12.0370	−	10.6638i	0.668722	−	0.592436i
$325$	3.13924	+	1.34221i	0.174134	+	0.0744526i
$326$	−9.33935	−	8.27394i	−0.517259	−	0.458251i
$327$	30.8227	+	44.6544i	1.70450	+	2.46940i
$328$	−25.6088	+	6.31199i	−1.41401	+	0.348521i
$329$	−0.487908	+	0.706857i	−0.0268993	+	0.0389703i
$330$	−10.1987	−	2.51376i	−0.561421	−	0.138378i
$331$	29.5340	+	7.27947i	1.62333	+	0.400116i	0.943001	−	0.332789i	$-0.107990\pi$
$331$	29.5340	+	7.27947i	1.62333	+	0.400116i	0.680332	+	0.732904i	$0.261836\pi$
$332$	0.104920	−	0.864090i	0.00575821	−	0.0474231i
$333$	16.2899	+	14.4316i	0.892683	+	0.790848i
$334$	−6.77120	−	17.8542i	−0.370504	−	0.976938i
$335$	27.3284	−	14.3431i	1.49311	−	0.783646i
$336$	−0.0900349	+	0.130438i	−0.00491180	+	0.00711598i
$337$	11.5446			0.628877			0.314439	−	0.949278i	$-0.398184\pi$
$337$	11.5446			0.628877			0.314439	+	0.949278i	$0.398184\pi$
$338$	10.9426	+	0.911321i	0.595197	+	0.0495693i
$339$	3.62290			0.196769
$340$	−12.7532	+	18.4761i	−0.691637	+	1.00201i
$341$	−3.05536	+	1.60358i	−0.165457	+	0.0868386i
$342$	−5.69935	−	15.0279i	−0.308185	−	0.812618i
$343$	2.36660	+	2.09662i	0.127784	+	0.113207i
$344$	1.03015	−	8.48401i	0.0555417	−	0.457427i
$345$	−23.7982	−	5.86574i	−1.28125	−	0.315801i
$346$	−8.15901	−	2.01102i	−0.438631	−	0.108113i
$347$	6.76598	−	9.80221i	0.363217	−	0.526210i	−0.598185	−	0.801358i	$-0.704111\pi$
$347$	6.76598	−	9.80221i	0.363217	−	0.526210i	0.961402	+	0.275148i	$0.0887267\pi$
$348$	38.6962	−	9.53776i	2.07434	−	0.511278i
$349$	−7.65838	−	11.0951i	−0.409944	−	0.593906i	0.562570	−	0.826749i	$-0.309813\pi$
$349$	−7.65838	−	11.0951i	−0.409944	−	0.593906i	−0.972514	+	0.232843i	$0.925197\pi$
$350$	0.135700	+	0.120220i	0.00725347	+	0.00642601i
$351$	29.7407	+	22.4077i	1.58744	+	1.19604i
$352$	7.16248	−	6.34540i	0.381761	−	0.338211i
$353$	−16.5391	−	4.07652i	−0.880288	−	0.216971i	−0.226830	−	0.973934i	$-0.572836\pi$
$353$	−16.5391	−	4.07652i	−0.880288	−	0.216971i	−0.653458	+	0.756963i	$0.726682\pi$
$354$	−13.4303	+	11.8982i	−0.713811	+	0.632381i
$355$	−17.2260	−	4.24582i	−0.914259	−	0.225345i
$356$	−0.558308	−	1.47214i	−0.0295903	−	0.0780231i
$357$	−4.96574			−0.262815
$358$	−1.25229	+	3.30202i	−0.0661857	+	0.174517i
$359$	−20.3741	+	5.02177i	−1.07530	+	0.265039i	−0.736927	−	0.675972i	$-0.763724\pi$
$359$	−20.3741	+	5.02177i	−1.07530	+	0.265039i	−0.338377	+	0.941011i	$0.609878\pi$
$360$	43.1451			2.27395
$361$	−10.0860			−0.530840
$362$	6.80667	−	1.67769i	0.357750	−	0.0881776i
$363$	3.03553	+	24.9999i	0.159324	+	1.31215i
$364$	−0.966812	−	0.413370i	−0.0506747	−	0.0216665i
$365$	2.08461	−	17.1683i	0.109113	−	0.898630i
$366$	2.00386	+	16.5032i	0.104743	+	0.862639i
$367$	−12.0144	+	17.4058i	−0.627146	+	0.908577i	−0.999812	−	0.0193881i	$-0.993828\pi$
$367$	−12.0144	+	17.4058i	−0.627146	+	0.908577i	0.372666	+	0.927965i	$0.378444\pi$
$368$	0.561213	−	0.497191i	0.0292552	−	0.0259179i
$369$	7.29898	−	60.1125i	0.379969	−	3.12933i
$370$	0.847806	+	6.98231i	0.0440753	+	0.362993i
$371$	1.27662	+	0.670022i	0.0662788	+	0.0347858i
$372$	6.10788	−	5.41111i	0.316679	−	0.280553i
$373$	−10.5276	−	15.2519i	−0.545100	−	0.789713i	0.449524	−	0.893268i	$-0.351594\pi$
$373$	−10.5276	−	15.2519i	−0.545100	−	0.789713i	−0.994624	+	0.103555i	$0.966978\pi$
$374$	9.77449	+	2.40920i	0.505427	+	0.124577i
$375$	3.64752	−	30.0400i	0.188357	−	1.55126i
$376$	−5.97534	+	8.65677i	−0.308155	+	0.446439i
$377$	15.5974	+	32.9787i	0.803305	+	1.69849i
$378$	1.12325	+	1.62731i	0.0577736	+	0.0836996i
$379$	−31.6963	+	16.6355i	−1.62813	+	0.854507i	−0.631246	+	0.775582i	$0.717456\pi$
$379$	−31.6963	+	16.6355i	−1.62813	+	0.854507i	−0.996881	+	0.0789246i	$0.974851\pi$
$380$	−3.32170	+	8.75859i	−0.170399	+	0.449306i
$381$	5.81612	+	47.9001i	0.297969	+	2.45400i
$382$	0.946635	−	1.37144i	0.0484341	−	0.0701688i
$383$	3.74401	−	0.922815i	0.191310	−	0.0471537i	−0.142496	−	0.989795i	$-0.545513\pi$
$383$	3.74401	−	0.922815i	0.191310	−	0.0471537i	0.333806	+	0.942642i	$0.391667\pi$
$384$	−13.5256	+	19.5953i	−0.690227	+	0.999967i
$385$	−0.326489	+	0.860880i	−0.0166394	+	0.0438745i
$386$	−1.21121	+	3.19370i	−0.0616490	+	0.162555i
$387$	17.3738	+	9.11845i	0.883158	+	0.463517i
$388$	13.4912	+	7.08070i	0.684909	+	0.359468i
$389$	−0.323511	+	0.0797384i	−0.0164027	+	0.00404290i	−0.247508	−	0.968886i	$-0.579612\pi$
$389$	−0.323511	+	0.0797384i	−0.0164027	+	0.00404290i	0.231106	+	0.972929i	$0.425766\pi$
$390$	4.51981	+	22.2837i	0.228869	+	1.12838i
$391$	22.8083	+	5.62175i	1.15347	+	0.284304i
$392$	14.4383	+	12.7912i	0.729244	+	0.646054i
$393$	1.41175	−	11.6268i	0.0712135	−	0.586496i
$394$	9.57504	+	5.02537i	0.482384	+	0.253174i
$395$	7.38644	−	3.87670i	0.371652	−	0.195058i
$396$	4.84313	+	12.7703i	0.243376	+	0.641731i
$397$	4.77641	+	4.23153i	0.239721	+	0.212375i	0.774426	−	0.632664i	$-0.218039\pi$
$397$	4.77641	+	4.23153i	0.239721	+	0.212375i	−0.534705	+	0.845039i	$0.679577\pi$
$398$	−0.156539	−	1.28921i	−0.00784659	−	0.0646225i
$399$	−2.01174	+	0.495850i	−0.100713	+	0.0248235i
$400$	−0.161875	−	0.143408i	−0.00809374	−	0.00717042i
$401$	−7.05112	+	6.24675i	−0.352116	+	0.311948i	−0.820576	−	0.571537i	$-0.806347\pi$
$401$	−7.05112	+	6.24675i	−0.352116	+	0.311948i	0.468460	+	0.883485i	$0.344809\pi$
$402$	28.9796	+	15.2097i	1.44537	+	0.758590i
$403$	5.96565	+	4.49474i	0.297170	+	0.223899i
$404$	−13.1456	+	6.89933i	−0.654017	+	0.343255i
$405$	−10.8088	+	28.5005i	−0.537095	+	1.41620i
$406$	0.233500	+	1.92305i	0.0115884	+	0.0954392i
$407$	−5.03621	+	2.64321i	−0.249636	+	0.131019i
$408$	−60.8146			−3.01077
$409$	−18.1553	+	9.52862i	−0.897720	+	0.471160i	−0.849447	−	0.527674i	$-0.823064\pi$
$409$	−18.1553	+	9.52862i	−0.897720	+	0.471160i	−0.0482735	+	0.998834i	$0.515372\pi$
$410$	14.6486	−	12.9775i	0.723444	−	0.640915i
$411$	−31.5439	−	45.6992i	−1.55594	−	2.25417i
$412$	−10.8032	−	9.57082i	−0.532237	−	0.471521i
$413$	0.893420	+	1.29434i	0.0439623	+	0.0636904i
$414$	−6.26681	−	16.5242i	−0.307997	−	0.812121i
$415$	0.585053	+	1.54266i	0.0287191	+	0.0757261i
$416$	−19.0457	−	8.14318i	−0.933793	−	0.399252i
$417$	17.2473	−	45.4775i	0.844606	−	2.22704i
$418$	4.20046			0.205451
$419$	5.25125	+	13.8464i	0.256540	+	0.676441i	0.999971	+	0.00762795i	$0.00242808\pi$
$419$	5.25125	+	13.8464i	0.256540	+	0.676441i	−0.743431	+	0.668813i	$0.766803\pi$
$420$	0.262446	−	2.16143i	0.0128060	−	0.105467i
$421$	−7.03272	−	3.69105i	−0.342754	−	0.179891i	0.284559	−	0.958659i	$-0.408153\pi$
$421$	−7.03272	−	3.69105i	−0.342754	−	0.179891i	−0.627313	+	0.778768i	$0.715845\pi$
$422$	5.41024	+	7.83809i	0.263366	+	0.381552i
$423$	−13.7186	−	19.8748i	−0.667021	−	0.966347i
$424$	15.6346	+	8.20565i	0.759282	+	0.398502i
$425$	0.816716	−	6.72626i	0.0396165	−	0.326272i
$426$	−6.67134	−	17.5909i	−0.323227	−	0.852280i
$427$	1.45720			0.0705188
$428$	−6.21783	+	16.3951i	−0.300550	+	0.792485i
$429$	−15.5526	+	9.80729i	−0.750887	+	0.473500i
$430$	2.24868	+	5.92928i	0.108441	+	0.285935i
$431$	−1.95863	−	5.16448i	−0.0943439	−	0.248764i	0.879534	−	0.475836i	$-0.157854\pi$
$431$	−1.95863	−	5.16448i	−0.0943439	−	0.248764i	−0.973878	+	0.227071i	$0.927085\pi$
$432$	−1.33991	−	1.94119i	−0.0644663	−	0.0933956i
$433$	−5.64330	−	4.99953i	−0.271200	−	0.240262i	0.516550	−	0.856257i	$-0.327216\pi$
$433$	−5.64330	−	4.99953i	−0.271200	−	0.240262i	−0.787750	+	0.615995i	$0.788754\pi$
$434$	0.225311	+	0.326419i	0.0108153	+	0.0156686i
$435$	−56.5441	+	50.0937i	−2.71108	+	2.40181i
$436$	20.1895	−	10.5963i	0.966902	−	0.507469i
$437$	9.80157			0.468873
$438$	16.2387	−	8.52271i	0.775913	−	0.407231i
$439$	2.27829	+	18.7634i	0.108737	+	0.895529i	0.940358	+	0.340186i	$0.110490\pi$
$439$	2.27829	+	18.7634i	0.108737	+	0.895529i	−0.831621	+	0.555343i	$0.812587\pi$
$440$	−3.99846	+	10.5431i	−0.190619	+	0.502621i
$441$	−39.2132	+	20.5807i	−1.86729	+	0.980032i
$442$	−4.33180	−	21.3568i	−0.206043	−	1.01584i
$443$	−9.17713	−	4.81653i	−0.436019	−	0.228840i	0.232408	−	0.972618i	$-0.425340\pi$
$443$	−9.17713	−	4.81653i	−0.436019	−	0.228840i	−0.668427	+	0.743778i	$0.733032\pi$
$444$	10.0677	−	8.91924i	0.477794	−	0.423288i
$445$	2.23378	+	1.97896i	0.105891	+	0.0938116i
$446$	16.1022	−	3.96884i	0.762462	−	0.187930i
$447$	2.93188	+	24.1462i	0.138673	+	1.14208i
$448$	−0.745791	−	0.660713i	−0.0352353	−	0.0312157i
$449$	−0.0892520	−	0.235338i	−0.00421206	−	0.0111063i	0.932894	−	0.360152i	$-0.117275\pi$
$449$	−0.0892520	−	0.235338i	−0.00421206	−	0.0111063i	−0.937106	+	0.349045i	$0.886506\pi$
$450$	−4.51357	+	2.36891i	−0.212772	+	0.111671i
$451$	14.0128	+	7.35450i	0.659838	+	0.346310i
$452$	0.183510	−	1.51134i	0.00863160	−	0.0710876i
$453$	−0.260186	−	0.230505i	−0.0122246	−	0.0108300i
$454$	12.2590	+	3.02158i	0.575346	+	0.141810i
$455$	1.98676	−	0.157852i	0.0931409	−	0.00740021i
$456$	−24.6375	+	6.07260i	−1.15376	+	0.284375i
$457$	24.1443	+	12.6719i	1.12942	+	0.592768i	0.922657	−	0.385622i	$-0.126013\pi$
$457$	24.1443	+	12.6719i	1.12942	+	0.592768i	0.206768	+	0.978390i	$0.433705\pi$
$458$	−4.28836	−	2.25070i	−0.200382	−	0.105168i
$459$	26.2055	−	69.0982i	1.22317	−	3.22523i
$460$	−3.65243	+	9.63065i	−0.170295	+	0.449032i
$461$	7.79623	−	11.2948i	0.363107	−	0.526051i	−0.598267	−	0.801297i	$-0.704144\pi$
$461$	7.79623	−	11.2948i	0.363107	−	0.526051i	0.961374	+	0.275246i	$0.0887593\pi$
$462$	−0.947970	+	0.233654i	−0.0441035	+	0.0108705i
$463$	−22.8504	+	33.1045i	−1.06195	+	1.53850i	−0.238470	+	0.971150i	$0.576646\pi$
$463$	−22.8504	+	33.1045i	−1.06195	+	1.53850i	−0.823478	+	0.567348i	$0.807970\pi$
$464$	−0.278539	−	2.29398i	−0.0129309	−	0.106495i
$465$	−5.48467	+	14.4619i	−0.254345	+	0.670654i
$466$	−11.9818	+	6.28852i	−0.555045	+	0.291310i
$467$	21.1098	+	30.5828i	0.976845	+	1.41520i	0.908663	+	0.417531i	$0.137105\pi$
$467$	21.1098	+	30.5828i	0.976845	+	1.41520i	0.0681822	+	0.997673i	$0.478280\pi$
$468$	20.5071	−	21.2960i	0.947940	−	0.984408i
$469$	1.62965	−	2.36096i	0.0752503	−	0.109019i
$470$	0.940778	−	7.74801i	0.0433949	−	0.357389i
$471$	11.3771	+	2.80421i	0.524231	+	0.129211i
$472$	10.9416	+	15.8516i	0.503627	+	0.729629i
$473$	−3.83832	+	3.40045i	−0.176486	+	0.156353i
$474$	7.83273	+	4.11093i	0.359769	+	0.188821i
$475$	−0.340774	−	2.80653i	−0.0156358	−	0.128772i
$476$	−0.251529	+	2.07153i	−0.0115288	+	0.0949483i
$477$	−30.3434	+	26.8819i	−1.38933	+	1.23084i
$478$	13.7731	−	19.9538i	0.629967	−	0.912665i
$479$	−2.25484	−	18.5703i	−0.103026	−	0.848498i	−0.949001	−	0.315274i	$-0.897903\pi$
$479$	−2.25484	−	18.5703i	−0.103026	−	0.848498i	0.845974	−	0.533224i	$-0.179020\pi$
$480$	5.17005	−	42.5792i	0.235979	−	1.94347i
$481$	9.83330	+	7.40878i	0.448360	+	0.337811i
$482$	0.114269	+	0.941088i	0.00520480	+	0.0428654i
$483$	−2.21204	+	0.545220i	−0.100651	+	0.0248084i
$484$	10.5828			0.481037
$485$	−28.8799			−1.31137
$486$	−5.97418	+	1.47250i	−0.270994	+	0.0667941i
$487$	14.9848	−	39.5118i	0.679028	−	1.79045i	0.0696475	−	0.997572i	$-0.477813\pi$
$487$	14.9848	−	39.5118i	0.679028	−	1.79045i	0.609380	−	0.792878i	$-0.291418\pi$
$488$	17.8461			0.807854
$489$	−16.0374	−	42.2871i	−0.725236	−	1.91229i
$490$	−13.8968	−	3.42525i	−0.627793	−	0.154737i
$491$	−17.7231	+	15.7013i	−0.799831	+	0.708589i	−0.960458	−	0.278427i	$-0.910187\pi$
$491$	−17.7231	+	15.7013i	−0.799831	+	0.708589i	0.160626	+	0.987015i	$0.448649\pi$
$492$	−36.3370	−	8.95626i	−1.63820	−	0.403779i
$493$	54.1921	−	48.0100i	2.44069	−	2.16226i
$494$	−3.88748	−	8.21960i	−0.174906	−	0.369817i
$495$	−19.3773	−	17.1668i	−0.870944	−	0.771589i
$496$	−0.268771	−	0.389381i	−0.0120682	−	0.0174837i
$497$	−1.60115	+	0.394648i	−0.0718215	+	0.0177024i
$498$	−0.993863	+	1.43986i	−0.0445361	+	0.0645216i
$499$	−32.3278	−	7.96809i	−1.44719	−	0.356701i	−0.564024	−	0.825758i	$-0.690748\pi$
$499$	−32.3278	−	7.96809i	−1.44719	−	0.356701i	−0.883168	+	0.469057i	$0.844594\pi$
$500$	−12.3469	−	3.04323i	−0.552169	−	0.136097i
$501$	8.34277	−	68.7089i	0.372728	−	3.06969i
$502$	9.54539	+	8.45648i	0.426032	+	0.377431i
$503$	9.32256	+	24.5816i	0.415672	+	1.09604i	0.965418	+	0.260706i	$0.0839552\pi$
$503$	9.32256	+	24.5816i	0.415672	+	1.09604i	−0.549746	+	0.835332i	$0.685276\pi$
$504$	3.55098	−	1.86370i	0.158173	−	0.0830156i
$505$	15.9854	−	23.1589i	0.711342	−	1.03056i
$506$	4.61868			0.205325
$507$	33.5851	+	21.3574i	1.49156	+	0.948514i
$508$	20.2768			0.899638
$509$	9.87609	−	14.3080i	0.437750	−	0.634191i	−0.540567	−	0.841301i	$-0.681790\pi$
$509$	9.87609	−	14.3080i	0.437750	−	0.634191i	0.978318	+	0.207110i	$0.0664058\pi$
$510$	39.9556	−	20.9703i	1.76927	−	0.928582i
$511$	−0.570032	−	1.50305i	−0.0252167	−	0.0664910i
$512$	1.93120	+	1.71090i	0.0853480	+	0.0756117i
$513$	3.71674	−	30.6101i	0.164098	−	1.35147i
$514$	4.04060	+	0.995919i	0.178223	+	0.0439281i
$515$	26.5621	+	6.54697i	1.17047	+	0.288494i
$516$	6.88870	−	9.98001i	0.303258	−	0.439345i
$517$	6.12804	−	1.51043i	0.269511	−	0.0664284i
$518$	0.371385	+	0.538044i	0.0163177	+	0.0236403i
$519$	−22.7988	−	20.1980i	−1.00076	−	0.886594i
$520$	24.3316	−	1.93319i	1.06701	−	0.0847759i
$521$	−16.7478	+	14.8372i	−0.733733	+	0.650030i	−0.944877	−	0.327424i	$-0.893819\pi$
$521$	−16.7478	+	14.8372i	−0.733733	+	0.650030i	0.211145	+	0.977455i	$0.432281\pi$
$522$	−52.8850	−	13.0350i	−2.31471	−	0.570526i
$523$	1.78122	−	1.57802i	0.0778872	−	0.0690020i	−0.623281	−	0.781998i	$-0.714201\pi$
$523$	1.78122	−	1.57802i	0.0778872	−	0.0690020i	0.701168	+	0.712996i	$0.252662\pi$
$524$	−4.77879	−	1.17787i	−0.208762	−	0.0514553i
$525$	0.233022	+	0.614428i	0.0101699	+	0.0268158i
$526$	4.98168			0.217212
$527$	5.25653	−	13.8603i	0.228978	−	0.603766i
$528$	1.13082	−	0.278722i	0.0492126	−	0.0121298i
$529$	−12.2225			−0.531414
$530$	−13.1015			−0.569094
$531$	−42.9361	+	10.5828i	−1.86327	+	0.459254i
$532$	0.104950	+	0.864343i	0.00455017	+	0.0374740i
$533$	1.42280	−	34.2273i	0.0616284	−	1.48255i
$534$	−0.381452	+	3.14154i	−0.0165070	+	0.135948i
$535$	−4.00615	−	32.9936i	−0.173201	−	1.42644i
$536$	19.9581	−	28.9143i	0.862058	−	1.24891i
$537$	−9.58140	+	8.48838i	−0.413468	+	0.366301i
$538$	−2.18882	+	18.0265i	−0.0943667	+	0.777180i
$539$	−1.39508	−	11.4896i	−0.0600905	−	0.494890i
$540$	28.6914	+	15.0584i	1.23468	+	0.648010i
$541$	−2.45114	+	2.17152i	−0.105383	+	0.0933608i	−0.714169	−	0.699973i	$-0.753195\pi$
$541$	−2.45114	+	2.17152i	−0.105383	+	0.0933608i	0.608786	+	0.793334i	$0.291657\pi$
$542$	10.7048	+	15.5086i	0.459810	+	0.666150i
$543$	24.6720	+	6.08111i	1.05878	+	0.260965i
$544$	−4.95500	+	40.8081i	−0.212444	+	1.74963i
$545$	−24.5510	+	35.5683i	−1.05165	+	1.52358i
$546$	1.33456	+	1.63878i	0.0571139	+	0.0701332i
$547$	−9.89411	−	14.3341i	−0.423041	−	0.612881i	0.552283	−	0.833657i	$-0.313757\pi$
$547$	−9.89411	−	14.3341i	−0.423041	−	0.612881i	−0.975325	+	0.220775i	$0.929141\pi$
$548$	−20.6619	+	10.8442i	−0.882631	+	0.463240i
$549$	−14.5290	+	38.3098i	−0.620082	+	1.63502i
$550$	−0.160579	−	1.32249i	−0.00684711	−	0.0563910i
$551$	17.1605	−	24.8613i	0.731064	−	1.05913i
$552$	−27.0906	+	6.67722i	−1.15305	+	0.284201i
$553$	0.440469	−	0.638129i	0.0187306	−	0.0271360i
$554$	0.729307	−	1.92302i	0.0309853	−	0.0817015i
$555$	−9.04049	+	23.8378i	−0.383748	+	1.01186i
$556$	−18.0980	−	9.49854i	−0.767524	−	0.402828i
$557$	3.82954	+	2.00990i	0.162263	+	0.0851621i	0.543900	−	0.839150i	$-0.316947\pi$
$557$	3.82954	+	2.00990i	0.162263	+	0.0851621i	−0.381637	+	0.924312i	$0.624640\pi$
$558$	−10.8280	+	2.66887i	−0.458387	+	0.112982i
$559$	10.2065	+	4.36387i	0.431687	+	0.184572i
$560$	−0.122576	−	0.0302122i	−0.00517977	−	0.00127670i
$561$	27.3130	+	24.1972i	1.15316	+	1.02161i
$562$	−1.97658	+	16.2786i	−0.0833769	+	0.686671i
$563$	−15.6973	−	8.23856i	−0.661561	−	0.347214i	0.100298	−	0.994957i	$-0.468020\pi$
$563$	−15.6973	−	8.23856i	−0.661561	−	0.347214i	−0.761858	+	0.647744i	$0.775713\pi$
$564$	−13.2157	+	6.93616i	−0.556483	+	0.292065i
$565$	1.02329	+	2.69820i	0.0430502	+	0.113514i
$566$	7.19926	+	6.37799i	0.302608	+	0.268087i
$567$	0.341509	+	2.81258i	0.0143420	+	0.118117i
$568$	−19.6091	+	4.83320i	−0.822778	+	0.202797i
$569$	31.9246	+	28.2827i	1.33835	+	1.18567i	0.966288	+	0.257465i	$0.0828871\pi$
$569$	31.9246	+	28.2827i	1.33835	+	1.18567i	0.372061	+	0.928208i	$0.378651\pi$
$570$	14.0930	−	12.4853i	0.590292	−	0.522954i
$571$	−37.7625	−	19.8193i	−1.58031	−	0.829412i	−0.999886	−	0.0150991i	$-0.995194\pi$
$571$	−37.7625	−	19.8193i	−1.58031	−	0.829412i	−0.580426	−	0.814313i	$-0.697114\pi$
$572$	3.30346	+	6.98477i	0.138125	+	0.292048i
$573$	5.34838	−	2.80704i	0.223432	−	0.117266i
$574$	0.645049	−	1.70085i	0.0269238	−	0.0709923i
$575$	−0.374704	−	3.08596i	−0.0156262	−	0.128693i
$576$	24.8060	−	13.0192i	1.03358	−	0.542467i
$577$	−9.32244			−0.388098			−0.194049	−	0.980992i	$-0.562162\pi$
$577$	−9.32244			−0.388098			−0.194049	+	0.980992i	$0.562162\pi$
$578$	−25.5794	+	13.4251i	−1.06396	+	0.558410i
$579$	−9.26709	+	8.20993i	−0.385127	+	0.341193i
$580$	18.0332	+	26.1256i	0.748787	+	1.08480i
$581$	0.114788	+	0.101694i	0.00476222	+	0.00421896i
$582$	−17.3969	−	25.2037i	−0.721124	−	1.04473i
$583$	−3.75688	−	9.90607i	−0.155594	−	0.410267i
$584$	−6.98109	−	18.4076i	−0.288880	−	0.761713i
$585$	−15.6591	+	53.8059i	−0.647422	+	2.22460i
$586$	−2.20301	+	5.80886i	−0.0910055	+	0.239962i
$587$	−27.8180			−1.14817			−0.574085	−	0.818796i	$-0.694642\pi$
$587$	−27.8180			−1.14817			−0.574085	+	0.818796i	$0.694642\pi$
$588$	9.70560	+	25.5916i	0.400252	+	1.05538i
$589$	0.745537	−	6.14005i	0.0307193	−	0.252996i
$590$	−12.6547	−	6.64171i	−0.520986	−	0.273435i
$591$	22.2660	+	32.2578i	0.915900	+	1.32691i
$592$	−0.443020	−	0.641825i	−0.0182080	−	0.0263789i
$593$	12.1212	+	6.36169i	0.497757	+	0.261243i	0.694867	−	0.719138i	$-0.255463\pi$
$593$	12.1212	+	6.36169i	0.497757	+	0.261243i	−0.197110	+	0.980381i	$0.563155\pi$
$594$	1.75140	−	14.4241i	0.0718607	−	0.591826i
$595$	−1.40258	−	3.69829i	−0.0575001	−	0.151615i
$596$	10.2215			0.418687
$597$	1.66924	−	4.40142i	0.0683174	−	0.180138i
$598$	−4.27455	−	9.03800i	−0.174799	−	0.369591i
$599$	−3.35429	−	8.84452i	−0.137052	−	0.361377i	0.848865	−	0.528609i	$-0.177286\pi$
$599$	−3.35429	−	8.84452i	−0.137052	−	0.361377i	−0.985918	+	0.167232i	$0.946517\pi$
$600$	2.85378	+	7.52481i	0.116505	+	0.307199i
$601$	19.2035	+	27.8210i	0.783326	+	1.13484i	0.987763	+	0.155963i	$0.0498482\pi$
$601$	19.2035	+	27.8210i	0.783326	+	1.13484i	−0.204437	+	0.978880i	$0.565536\pi$
$602$	0.441194	+	0.390864i	0.0179817	+	0.0159304i
$603$	45.8212	+	66.3835i	1.86598	+	2.70334i
$604$	−0.109337	+	0.0968645i	−0.00444888	+	0.00394136i
$605$	−17.7616	+	9.32200i	−0.722111	+	0.378993i
$606$	29.8404			1.21218
$607$	−12.0446	+	6.32151i	−0.488877	+	0.256582i	−0.691103	−	0.722757i	$-0.742875\pi$
$607$	−12.0446	+	6.32151i	−0.488877	+	0.256582i	0.202226	+	0.979339i	$0.435182\pi$
$608$	2.06747	+	17.0271i	0.0838469	+	0.690542i
$609$	−2.48991	+	6.56534i	−0.100896	+	0.266041i
$610$	−11.7250	+	6.15376i	−0.474732	+	0.249159i
$611$	−8.62710	−	10.5937i	−0.349015	−	0.428574i
$612$	−51.9526	−	27.2668i	−2.10006	−	1.10220i
$613$	15.0012	−	13.2899i	0.605893	−	0.536775i	−0.303436	−	0.952852i	$-0.598134\pi$
$613$	15.0012	−	13.2899i	0.605893	−	0.536775i	0.909329	+	0.416077i	$0.136595\pi$
$614$	9.81420	+	8.69462i	0.396069	+	0.350886i
$615$	68.8751	−	16.9762i	2.77731	−	0.684546i
$616$	0.126333	+	1.04044i	0.00509009	+	0.0419207i
$617$	−13.4674	−	11.9311i	−0.542178	−	0.480327i	0.347016	−	0.937859i	$-0.387195\pi$
$617$	−13.4674	−	11.9311i	−0.542178	−	0.480327i	−0.889193	+	0.457532i	$0.848734\pi$
$618$	10.2871	+	27.1248i	0.413807	+	1.09112i
$619$	−17.7313	+	9.30611i	−0.712682	+	0.374044i	−0.781770	−	0.623566i	$-0.785683\pi$
$619$	−17.7313	+	9.30611i	−0.712682	+	0.374044i	0.0690889	+	0.997611i	$0.477991\pi$
$620$	5.75517	+	3.02055i	0.231133	+	0.121308i
$621$	4.08680	−	33.6579i	0.163998	−	1.35064i
$622$	−9.65726	−	8.55558i	−0.387221	−	0.343048i
$623$	0.269330	+	0.0663839i	0.0107905	+	0.00265962i
$624$	−1.59198	−	1.95488i	−0.0637301	−	0.0782576i
$625$	27.9999	−	6.90137i	1.12000	−	0.276055i
$626$	−5.08249	−	2.66750i	−0.203137	−	0.106615i
$627$	13.4814	+	7.07556i	0.538394	+	0.282571i
$628$	1.74610	−	4.60410i	0.0696771	−	0.183723i
$629$	8.66445	−	22.8463i	0.345474	−	0.910941i
$630$	−1.69037	+	2.44892i	−0.0673460	+	0.0975675i
$631$	26.9566	−	6.64421i	1.07313	−	0.264502i	0.337110	−	0.941465i	$-0.390551\pi$
$631$	26.9566	−	6.64421i	1.07313	−	0.264502i	0.736017	+	0.676963i	$0.236704\pi$
$632$	5.39435	−	7.81507i	0.214576	−	0.310867i
$633$	4.16110	+	34.2697i	0.165389	+	1.36210i
$634$	−3.63653	+	9.58874i	−0.144425	+	0.380817i
$635$	−34.0314	+	17.8611i	−1.35050	+	0.708795i
$636$	14.2324	+	20.6191i	0.564349	+	0.817601i
$637$	−21.1920	+	13.3634i	−0.839659	+	0.529478i
$638$	8.08636	−	11.7151i	0.320142	−	0.463806i
$639$	5.58895	−	46.0291i	0.221095	−	1.82088i
$640$	−18.4142	−	4.53868i	−0.727884	−	0.179407i
$641$	10.8180	+	15.6726i	0.427286	+	0.619031i	0.976206	−	0.216844i	$-0.0695763\pi$
$641$	10.8180	+	15.6726i	0.427286	+	0.619031i	−0.548920	+	0.835875i	$0.684961\pi$
$642$	26.3805	−	23.3711i	1.04116	−	0.922384i
$643$	12.5689	+	6.59669i	0.495671	+	0.260148i	0.693984	−	0.719991i	$-0.255854\pi$
$643$	12.5689	+	6.59669i	0.495671	+	0.260148i	−0.198313	+	0.980139i	$0.563546\pi$
$644$	0.115400	+	0.950403i	0.00454739	+	0.0374511i
$645$	−2.77059	+	22.8179i	−0.109092	+	0.898453i
$646$	−13.5068	+	11.9660i	−0.531419	+	0.470796i
$647$	−7.56329	+	10.9573i	−0.297343	+	0.430776i	−0.942970	−	0.332877i	$-0.891981\pi$
$647$	−7.56329	+	10.9573i	−0.297343	+	0.430776i	0.645627	+	0.763653i	$0.276596\pi$
$648$	4.18241	+	34.4452i	0.164300	+	1.35314i
$649$	1.39304	−	11.4727i	0.0546817	−	0.450345i
$650$	−2.43927	+	1.53818i	−0.0956762	+	0.0603322i
$651$	0.173290	+	1.42717i	0.00679178	+	0.0559353i
$652$	−18.4530	+	4.54826i	−0.722676	+	0.178124i
$653$	−16.2237			−0.634882			−0.317441	−	0.948278i	$-0.602824\pi$
$653$	−16.2237			−0.634882			−0.317441	+	0.948278i	$0.602824\pi$
$654$	−45.8300			−1.79210
$655$	9.05799	−	2.23259i	0.353925	−	0.0872346i
$656$	−0.769470	+	2.02893i	−0.0300428	+	0.0792163i
$657$	45.1987			1.76337
$658$	−0.257254	−	0.678323i	−0.0100288	−	0.0264438i
$659$	24.6829	+	6.08380i	0.961511	+	0.236991i	0.688676	−	0.725070i	$-0.258192\pi$
$659$	24.6829	+	6.08380i	0.961511	+	0.236991i	0.272835	+	0.962061i	$0.412039\pi$
$660$	−11.9758	+	10.6097i	−0.466159	+	0.412980i
$661$	−28.0712	−	6.91892i	−1.09184	−	0.269115i	−0.348016	−	0.937488i	$-0.613145\pi$
$661$	−28.0712	−	6.91892i	−1.09184	−	0.269115i	−0.743826	+	0.668374i	$0.766991\pi$
$662$	−19.2311	+	17.0372i	−0.747436	+	0.662171i
$663$	22.0720	−	75.8413i	0.857206	−	2.94543i
$664$	1.40580	+	1.24543i	0.0545554	+	0.0483319i
$665$	−0.937510	−	1.35822i	−0.0363551	−	0.0526694i
$666$	−17.8481	+	4.39915i	−0.691598	+	0.170464i
$667$	18.8692	−	27.3367i	0.730617	−	1.05848i
$668$	−28.2403	−	6.96061i	−1.09265	−	0.269314i
$669$	58.3655	+	14.3858i	2.25654	+	0.556187i
$670$	−3.14227	+	25.8789i	−0.121397	+	0.999790i
$671$	−8.01502	−	7.10069i	−0.309416	−	0.274119i
$672$	−1.41374	−	3.72772i	−0.0545362	−	0.143800i
$673$	12.6435	−	6.63582i	0.487371	−	0.255792i	−0.203092	−	0.979160i	$-0.565099\pi$
$673$	12.6435	−	6.63582i	0.487371	−	0.255792i	0.690463	+	0.723367i	$0.257407\pi$
$674$	−5.53930	+	8.02507i	−0.213366	+	0.309114i
$675$	−9.77949			−0.376413
$676$	10.6107	−	12.9287i	0.408104	−	0.497257i
$677$	−25.8817			−0.994714			−0.497357	−	0.867546i	$-0.665696\pi$
$677$	−25.8817			−0.994714			−0.497357	+	0.867546i	$0.665696\pi$
$678$	−1.73832	+	2.51840i	−0.0667599	+	0.0967185i
$679$	−2.37690	+	1.24750i	−0.0912172	+	0.0478745i
$680$	−17.1772	−	45.2924i	−0.658714	−	1.73689i
$681$	34.2556	+	30.3478i	1.31268	+	1.16293i
$682$	0.351311	−	2.89330i	0.0134524	−	0.110790i
$683$	20.6230	+	5.08312i	0.789119	+	0.194500i	0.613224	−	0.789909i	$-0.289872\pi$
$683$	20.6230	+	5.08312i	0.789119	+	0.194500i	0.175894	+	0.984409i	$0.443718\pi$
$684$	−23.7700	−	5.85878i	−0.908869	−	0.224016i
$685$	25.1254	−	36.4005i	0.959994	−	1.39079i
$686$	−2.59296	+	0.639108i	−0.0989998	+	0.0244012i
$687$	−9.97223	−	14.4473i	−0.380464	−	0.551197i
$688$	−0.526295	−	0.466257i	−0.0200648	−	0.0177759i
$689$	−15.9076	+	16.5196i	−0.606031	+	0.629345i
$690$	15.4962	−	13.7285i	0.589931	−	0.522634i
$691$	16.4604	+	4.05712i	0.626183	+	0.154340i	0.539623	−	0.841907i	$-0.318567\pi$
$691$	16.4604	+	4.05712i	0.626183	+	0.154340i	0.0865593	+	0.996247i	$0.472413\pi$
$692$	−9.58072	+	8.48777i	−0.364204	+	0.322657i
$693$	−2.33635	−	0.575858i	−0.0887505	−	0.0218750i
$694$	3.56742	+	9.40651i	0.135417	+	0.357066i
$695$	38.7415			1.46955
$696$	−30.4935	+	80.4047i	−1.15585	+	3.04773i
$697$	−66.0102	+	16.2701i	−2.50031	+	0.616272i
$698$	11.3872			0.431011
$699$	−49.0483			−1.85518
$700$	0.268121	−	0.0660858i	0.0101340	−	0.00249781i
$701$	−1.04215	−	8.58284i	−0.0393613	−	0.324169i	−0.999068	−	0.0431655i	$-0.986256\pi$
$701$	−1.04215	−	8.58284i	−0.0393613	−	0.324169i	0.959707	−	0.281004i	$-0.0906673\pi$
$702$	−29.8464	+	9.92213i	−1.12648	+	0.374487i
$703$	1.22888	−	10.1208i	0.0463482	−	0.381712i
$704$	0.882522	+	7.26823i	0.0332613	+	0.273932i
$705$	16.0707	−	23.2825i	0.605259	−	0.876870i
$706$	10.7695	−	9.54090i	0.405314	−	0.359077i
$707$	0.315279	−	2.59655i	0.0118573	−	0.0976534i
$708$	3.29429	+	27.1309i	0.123807	+	1.01964i
$709$	5.66849	+	2.97505i	0.212885	+	0.111730i	0.567795	−	0.823170i	$-0.307796\pi$
$709$	5.66849	+	2.97505i	0.212885	+	0.111730i	−0.354911	+	0.934900i	$0.615489\pi$
$710$	11.2167	−	9.93712i	0.420955	−	0.372934i
$711$	12.3847	+	17.9424i	0.464464	+	0.672892i
$712$	3.29844	+	0.812993i	0.123614	+	0.0304682i
$713$	0.819767	−	6.75139i	0.0307005	−	0.252842i
$714$	2.38264	−	3.45185i	0.0891680	−	0.129182i
$715$	−11.6970	−	8.81293i	−0.437441	−	0.329585i
$716$	3.05572	+	4.42698i	0.114198	+	0.165444i
$717$	77.8164	−	40.8412i	2.90611	−	1.52524i
$718$	6.28502	−	16.5722i	0.234555	−	0.618471i
$719$	1.03865	+	8.55404i	0.0387350	+	0.319012i	0.999178	+	0.0405353i	$0.0129063\pi$
$719$	1.03865	+	8.55404i	0.0387350	+	0.319012i	−0.960443	+	0.278476i	$0.910171\pi$
$720$	2.01642	−	2.92129i	0.0751476	−	0.108870i
$721$	2.46894	−	0.608540i	0.0919483	−	0.0226632i
$722$	4.83941	−	7.01109i	0.180104	−	0.260926i
$723$	−1.21849	+	3.21290i	−0.0453163	+	0.119489i
$724$	3.78653	−	9.98426i	0.140725	−	0.371062i
$725$	−8.48347	−	4.45247i	−0.315068	−	0.165360i
$726$	−18.8347	−	9.88523i	−0.699023	−	0.366875i
$727$	−39.9715	+	9.85209i	−1.48246	+	0.365394i	−0.895807	−	0.444443i	$-0.853401\pi$
$727$	−39.9715	+	9.85209i	−1.48246	+	0.365394i	−0.586654	+	0.809837i	$0.699555\pi$
$728$	1.91906	−	1.21013i	0.0711250	−	0.0448505i
$729$	14.7539	+	3.63652i	0.546442	+	0.134686i
$730$	10.9340	+	9.68670i	0.404686	+	0.358521i
$731$	2.65535	−	21.8687i	0.0982115	−	0.808845i
$732$	22.4218	+	11.7679i	0.828733	+	0.434953i
$733$	12.2398	−	6.42393i	0.452086	−	0.237273i	−0.223282	−	0.974754i	$-0.571677\pi$
$733$	12.2398	−	6.42393i	0.452086	−	0.237273i	0.675368	+	0.737481i	$0.263985\pi$
$734$	−6.33468	−	16.7032i	−0.233817	−	0.616526i
$735$	−38.8320	−	34.4021i	−1.43234	−	1.26894i
$736$	2.27332	+	18.7225i	0.0837957	+	0.690119i
$737$	−20.4681	+	5.04494i	−0.753953	+	0.185833i
$738$	38.2840	+	33.9167i	1.40925	+	1.24849i
$739$	−1.44961	+	1.28424i	−0.0533247	+	0.0472416i	−0.689364	−	0.724415i	$-0.742110\pi$
$739$	−1.44961	+	1.28424i	−0.0533247	+	0.0472416i	0.636039	+	0.771657i	$0.280572\pi$
$740$	9.48636	+	4.97883i	0.348726	+	0.183025i
$741$	1.36884	−	32.9292i	0.0502855	−	1.20968i
$742$	−1.07830	+	0.565934i	−0.0395855	+	0.0207761i
$743$	4.92916	−	12.9971i	0.180833	−	0.476818i	−0.813694	−	0.581293i	$-0.802547\pi$
$743$	4.92916	−	12.9971i	0.180833	−	0.476818i	0.994528	+	0.104475i	$0.0333162\pi$
$744$	2.12226	+	17.4784i	0.0778058	+	0.640788i
$745$	−17.1551	+	9.00369i	−0.628514	+	0.329870i
$746$	15.6534			0.573112
$747$	−3.81802	+	2.00385i	−0.139694	+	0.0733171i
$748$	11.4777	−	10.1683i	0.419666	−	0.371792i
$749$	−1.75491	−	2.54242i	−0.0641230	−	0.0928981i
$750$	19.1317	+	16.9492i	0.698591	+	0.618897i
$751$	2.56137	+	3.71079i	0.0934659	+	0.135409i	0.866927	−	0.498435i	$-0.166092\pi$
$751$	2.56137	+	3.71079i	0.0934659	+	0.135409i	−0.773461	+	0.633844i	$0.781476\pi$
$752$	0.306875	+	0.809162i	0.0111906	+	0.0295071i
$753$	16.3912	+	43.2200i	0.597329	+	1.57503i
$754$	−30.4084	−	4.98145i	−1.10741	−	0.181414i
$755$	0.0981814	−	0.258883i	0.00357319	−	0.00942172i
$756$	3.01185			0.109540
$757$	−1.94117	−	5.11845i	−0.0705531	−	0.186033i	0.895102	−	0.445862i	$-0.147103\pi$
$757$	−1.94117	−	5.11845i	−0.0705531	−	0.186033i	−0.965655	+	0.259829i	$0.916334\pi$
$758$	3.64449	−	30.0151i	0.132374	−	1.09020i
$759$	14.8236	+	7.78005i	0.538064	+	0.282398i
$760$	−11.4815	−	16.6339i	−0.416479	−	0.603374i
$761$	−6.00880	−	8.70525i	−0.217819	−	0.315565i	0.698808	−	0.715309i	$-0.253714\pi$
$761$	−6.00880	−	8.70525i	−0.217819	−	0.315565i	−0.916627	+	0.399744i	$0.869099\pi$
$762$	−36.0876	−	18.9402i	−1.30732	−	0.686133i
$763$	−0.484218	+	3.98789i	−0.0175299	+	0.144371i
$764$	−0.900088	−	2.37334i	−0.0325640	−	0.0858643i
$765$	111.213			4.02090
$766$	−1.15496	+	3.04537i	−0.0417302	+	0.110034i
$767$	−23.7395	+	7.89196i	−0.857185	+	0.284962i
$768$

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.479816 + 0.695133i) q^{2} +(-2.71090 + 1.42279i) q^{3} +(0.456223 + 1.20296i) q^{4} +(-1.82534 - 1.61711i) q^{5} +(0.311704 - 2.56712i) q^{6} +(-0.220084 - 0.0542458i) q^{7} +(-2.69533 - 0.664340i) q^{8} +(3.62047 - 5.24515i) q^{9} +O(q^{10})\)	\(q+(-0.479816 + 0.695133i) q^{2} +(-2.71090 + 1.42279i) q^{3} +(0.456223 + 1.20296i) q^{4} +(-1.82534 - 1.61711i) q^{5} +(0.311704 - 2.56712i) q^{6} +(-0.220084 - 0.0542458i) q^{7} +(-2.69533 - 0.664340i) q^{8} +(3.62047 - 5.24515i) q^{9} +(1.99993 - 0.492940i) q^{10} +(0.946194 + 1.37080i) q^{11} +(-2.94834 - 2.61200i) q^{12} +(1.80673 - 3.12021i) q^{13} +(0.143308 - 0.126960i) q^{14} +(7.24913 + 1.78675i) q^{15} +(-0.170950 + 0.151448i) q^{16} +(-6.94760 - 1.71243i) q^{17} +(1.90892 + 5.03341i) q^{18} -2.98564 q^{19} +(1.11256 - 2.93358i) q^{20} +(0.673806 - 0.166078i) q^{21} -1.40689 q^{22} -3.28291 q^{23} +(8.25200 - 2.03394i) q^{24} +(0.114138 + 0.940009i) q^{25} +(1.30206 + 2.75305i) q^{26} +(-1.24487 + 10.2525i) q^{27} +(-0.0351517 - 0.289500i) q^{28} +(-5.74770 + 8.32698i) q^{29} +(-4.72028 + 4.18180i) q^{30} +(-0.249708 + 2.05653i) q^{31} +(-0.692472 - 5.70302i) q^{32} +(-4.51540 - 2.36987i) q^{33} +(4.52394 - 4.00786i) q^{34} +(0.314006 + 0.454917i) q^{35} +(7.96145 + 1.96232i) q^{36} +(-0.411599 + 3.38982i) q^{37} +(1.43256 - 2.07542i) q^{38} +(-0.458474 + 11.0292i) q^{39} +(3.84559 + 5.57130i) q^{40} +(8.41285 - 4.41540i) q^{41} +(-0.207856 + 0.548072i) q^{42} +(0.371090 + 3.05620i) q^{43} +(-1.21734 + 1.76362i) q^{44} +(-15.0906 + 3.71949i) q^{45} +(1.57519 - 2.28206i) q^{46} +(1.34366 - 3.54295i) q^{47} +(0.247949 - 0.653788i) q^{48} +(-6.15270 - 3.22918i) q^{49} +(-0.708197 - 0.371690i) q^{50} +(21.2707 - 5.24276i) q^{51} +(4.57776 + 0.749920i) q^{52} +(-6.17579 - 1.52220i) q^{53} +(-6.52951 - 5.78464i) q^{54} +(0.489607 - 4.03228i) q^{55} +(0.557162 + 0.292421i) q^{56} +(8.09377 - 4.24794i) q^{57} +(-3.03052 - 7.99083i) q^{58} +(-5.19351 - 4.60105i) q^{59} +(1.15783 + 9.53558i) q^{60} +(-6.24190 + 1.53849i) q^{61} +(-1.30975 - 1.16034i) q^{62} +(-1.08133 + 0.957978i) q^{63} +(3.89216 + 2.04276i) q^{64} +(-8.34363 + 2.77376i) q^{65} +(3.81393 - 2.00171i) q^{66} +(-4.48794 + 11.8337i) q^{67} +(-1.10967 - 9.13894i) q^{68} +(8.89964 - 4.67089i) q^{69} -0.466893 q^{70} +(6.44186 - 3.38095i) q^{71} +(-13.2429 + 11.7322i) q^{72} +(4.02863 + 5.83648i) q^{73} +(-2.15888 - 1.91260i) q^{74} +(-1.64685 - 2.38588i) q^{75} +(-1.36212 - 3.59160i) q^{76} +(-0.133882 - 0.353018i) q^{77} +(-7.44678 - 5.61068i) q^{78} +(-1.21302 + 3.19846i) q^{79} +0.556951 q^{80} +(-4.43234 - 11.6871i) q^{81} +(-0.967324 + 7.96663i) q^{82} +(-0.599062 - 0.314412i) q^{83} +(0.507192 + 0.734794i) q^{84} +(9.91255 + 14.3608i) q^{85} +(-2.30252 - 1.20846i) q^{86} +(3.73390 - 30.7514i) q^{87} +(-1.63963 - 4.32335i) q^{88} -1.22376 q^{89} +(4.65515 - 12.2746i) q^{90} +(-0.566891 + 0.588700i) q^{91} +(-1.49774 - 3.94921i) q^{92} +(-2.24908 - 5.93033i) q^{93} +(1.81811 + 2.63399i) q^{94} +(5.44981 + 4.82811i) q^{95} +(9.99143 + 14.4751i) q^{96} +(8.86437 - 7.85315i) q^{97} +(5.19688 - 2.72753i) q^{98} +10.6157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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