LMFDB - Embedded newform 81.2.g.a.58.6

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			58.6
Character	$\chi$	$=$	81.58
Dual form			81.2.g.a.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.470263 - 0.631673i) q^{2} +(-1.10956 + 1.32999i) q^{3} +(0.395743 + 1.32187i) q^{4} +(2.32750 + 1.53082i) q^{5} +(0.318331 + 1.32633i) q^{6} +(-3.41908 - 3.62402i) q^{7} +(2.50111 + 0.910331i) q^{8} +(-0.537739 - 2.95141i) q^{9} +O(q^{10})$	\(q+(0.470263 - 0.631673i) q^{2} +(-1.10956 + 1.32999i) q^{3} +(0.395743 + 1.32187i) q^{4} +(2.32750 + 1.53082i) q^{5} +(0.318331 + 1.32633i) q^{6} +(-3.41908 - 3.62402i) q^{7} +(2.50111 + 0.910331i) q^{8} +(-0.537739 - 2.95141i) q^{9} +(2.06152 - 0.750330i) q^{10} +(1.55231 + 0.779598i) q^{11} +(-2.19718 - 0.940369i) q^{12} +(0.859891 - 1.99345i) q^{13} +(-3.89706 + 0.455501i) q^{14} +(-4.61848 + 1.39701i) q^{15} +(-0.554469 + 0.364680i) q^{16} +(-3.39468 - 2.84848i) q^{17} +(-2.11721 - 1.04827i) q^{18} +(-1.63306 + 1.37030i) q^{19} +(-1.10246 + 3.68247i) q^{20} +(8.61359 - 0.526266i) q^{21} +(1.22244 - 0.613935i) q^{22} +(0.465342 - 0.493234i) q^{23} +(-3.98587 + 2.31638i) q^{24} +(1.09345 + 2.53489i) q^{25} +(-0.854835 - 1.48062i) q^{26} +(4.52200 + 2.55959i) q^{27} +(3.43741 - 5.95378i) q^{28} +(5.71522 + 0.668013i) q^{29} +(-1.28945 + 3.57433i) q^{30} +(-5.72212 - 1.35617i) q^{31} +(-0.339908 + 5.83599i) q^{32} +(-2.75924 + 1.19954i) q^{33} +(-3.39570 + 0.804795i) q^{34} +(-2.41020 - 13.6689i) q^{35} +(3.68859 - 1.87882i) q^{36} +(0.131814 - 0.747552i) q^{37} +(0.0976137 + 1.67596i) q^{38} +(1.69716 + 3.35551i) q^{39} +(4.42779 + 5.94755i) q^{40} +(0.0737288 + 0.0990350i) q^{41} +(3.71823 - 5.68845i) q^{42} +(-0.148059 - 2.54207i) q^{43} +(-0.416216 + 2.36048i) q^{44} +(3.26650 - 7.69260i) q^{45} +(-0.0927292 - 0.525894i) q^{46} +(1.65271 - 0.391699i) q^{47} +(0.130198 - 1.14207i) q^{48} +(-1.03635 + 17.7935i) q^{49} +(2.11543 + 0.501366i) q^{50} +(7.55505 - 1.35432i) q^{51} +(2.97539 + 0.347773i) q^{52} +(-5.02192 + 8.69822i) q^{53} +(3.74336 - 1.65274i) q^{54} +(2.41957 + 4.19082i) q^{55} +(-5.25246 - 12.1766i) q^{56} +(-0.0104999 - 3.69239i) q^{57} +(3.10962 - 3.29601i) q^{58} +(-10.3931 + 5.21959i) q^{59} +(-3.67440 - 5.55220i) q^{60} +(-2.27150 + 7.58734i) q^{61} +(-3.54755 + 2.97675i) q^{62} +(-8.85739 + 12.0399i) q^{63} +(2.50983 + 2.10599i) q^{64} +(5.05301 - 3.32342i) q^{65} +(-0.539853 + 2.30704i) q^{66} +(0.462282 - 0.0540330i) q^{67} +(2.42190 - 5.61460i) q^{68} +(0.139669 + 1.16617i) q^{69} +(-9.76770 - 4.90552i) q^{70} +(11.4588 - 4.17067i) q^{71} +(1.34182 - 7.87134i) q^{72} +(-2.01159 - 0.732160i) q^{73} +(-0.410222 - 0.434809i) q^{74} +(-4.58462 - 1.35835i) q^{75} +(-2.45764 - 1.61641i) q^{76} +(-2.48219 - 8.29110i) q^{77} +(2.91770 + 0.505918i) q^{78} +(4.18797 - 5.62542i) q^{79} -1.84879 q^{80} +(-8.42167 + 3.17418i) q^{81} +0.0972297 q^{82} +(-1.97654 + 2.65495i) q^{83} +(4.10442 + 11.1778i) q^{84} +(-3.54061 - 11.8265i) q^{85} +(-1.67538 - 1.10192i) q^{86} +(-7.22985 + 6.85997i) q^{87} +(3.17281 + 3.36298i) q^{88} +(-4.72182 - 1.71860i) q^{89} +(-3.32309 - 5.68090i) q^{90} +(-10.1643 + 3.69952i) q^{91} +(0.836149 + 0.419930i) q^{92} +(8.15274 - 6.10560i) q^{93} +(0.529782 - 1.22817i) q^{94} +(-5.89863 + 0.689452i) q^{95} +(-7.38465 - 6.92748i) q^{96} +(6.27220 - 4.12529i) q^{97} +(10.7523 + 9.02224i) q^{98} +(1.46618 - 5.00072i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{27}\right)$

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 $

$2$	0.470263	−	0.631673i	0.332526	−	0.446660i	−0.604143	−	0.796876i	$-0.706484\pi$
$2$	0.470263	−	0.631673i	0.332526	−	0.446660i	0.936669	+	0.350216i	$0.113892\pi$
$3$	−1.10956	+	1.32999i	−0.640607	+	0.767869i
$3$	−1.10956	+	1.32999i	−0.640607	+	0.767869i
$4$	0.395743	+	1.32187i	0.197872	+	0.660937i
$5$	2.32750	+	1.53082i	1.04089	+	0.684604i	0.950316	−	0.311286i	$-0.100760\pi$
$5$	2.32750	+	1.53082i	1.04089	+	0.684604i	0.0905734	+	0.995890i	$0.471130\pi$
$6$	0.318331	+	1.32633i	0.129958	+	0.541470i
$7$	−3.41908	−	3.62402i	−1.29229	−	1.36975i	−0.891134	−	0.453740i	$-0.850089\pi$
$7$	−3.41908	−	3.62402i	−1.29229	−	1.36975i	−0.401158	−	0.916009i	$-0.631392\pi$
$8$	2.50111	+	0.910331i	0.884277	+	0.321851i
$9$	−0.537739	−	2.95141i	−0.179246	−	0.983804i
$10$	2.06152	−	0.750330i	0.651909	−	0.237275i
$11$	1.55231	+	0.779598i	0.468038	+	0.235058i	0.667156	−	0.744918i	$-0.267511\pi$
$11$	1.55231	+	0.779598i	0.468038	+	0.235058i	−0.199118	+	0.979976i	$0.563808\pi$
$12$	−2.19718	−	0.940369i	−0.634271	−	0.271461i
$13$	0.859891	−	1.99345i	0.238491	−	0.552884i	−0.756369	−	0.654145i	$-0.773029\pi$
$13$	0.859891	−	1.99345i	0.238491	−	0.552884i	0.994860	+	0.101261i	$0.0322878\pi$
$14$	−3.89706	+	0.455501i	−1.04153	+	0.121738i
$15$	−4.61848	+	1.39701i	−1.19249	+	0.360705i
$16$	−0.554469	+	0.364680i	−0.138617	+	0.0911700i
$17$	−3.39468	−	2.84848i	−0.823331	−	0.690857i	0.130419	−	0.991459i	$-0.458368\pi$
$17$	−3.39468	−	2.84848i	−0.823331	−	0.690857i	−0.953750	+	0.300602i	$0.902812\pi$
$18$	−2.11721	−	1.04827i	−0.499030	−	0.247079i
$19$	−1.63306	+	1.37030i	−0.374650	+	0.314369i	−0.810598	−	0.585603i	$-0.800858\pi$
$19$	−1.63306	+	1.37030i	−0.374650	+	0.314369i	0.435948	+	0.899972i	$0.356413\pi$
$20$	−1.10246	+	3.68247i	−0.246518	+	0.823426i
$21$	8.61359	−	0.526266i	1.87964	−	0.114841i
$22$	1.22244	−	0.613935i	0.260626	−	0.130891i
$23$	0.465342	−	0.493234i	0.0970305	−	0.102846i	−0.677038	−	0.735948i	$-0.736737\pi$
$23$	0.465342	−	0.493234i	0.0970305	−	0.102846i	0.774069	+	0.633101i	$0.218218\pi$
$24$	−3.98587	+	2.31638i	−0.813613	+	0.472830i
$25$	1.09345	+	2.53489i	0.218689	+	0.506978i
$26$	−0.854835	−	1.48062i	−0.167647	−	0.290373i
$27$	4.52200	+	2.55959i	0.870259	+	0.492594i
$28$	3.43741	−	5.95378i	0.649610	−	1.12516i
$29$	5.71522	+	0.668013i	1.06129	+	0.124047i	0.628781	−	0.777583i	$-0.283554\pi$
$29$	5.71522	+	0.668013i	1.06129	+	0.124047i	0.432509	+	0.901630i	$0.357628\pi$
$30$	−1.28945	+	3.57433i	−0.235421	+	0.652581i
$31$	−5.72212	−	1.35617i	−1.02772	−	0.243575i	−0.318026	−	0.948082i	$-0.603020\pi$
$31$	−5.72212	−	1.35617i	−1.02772	−	0.243575i	−0.709697	+	0.704507i	$0.751168\pi$
$32$	−0.339908	+	5.83599i	−0.0600878	+	1.03167i
$33$	−2.75924	+	1.19954i	−0.480322	+	0.208813i
$34$	−3.39570	+	0.804795i	−0.582357	+	0.138021i
$35$	−2.41020	−	13.6689i	−0.407397	−	2.31047i
$36$	3.68859	−	1.87882i	0.614765	−	0.313137i
$37$	0.131814	−	0.747552i	0.0216700	−	0.122897i	−0.972054	−	0.234758i	$-0.924570\pi$
$37$	0.131814	−	0.747552i	0.0216700	−	0.122897i	0.993724	+	0.111861i	$0.0356813\pi$
$38$	0.0976137	+	1.67596i	0.0158350	+	0.271877i
$39$	1.69716	+	3.35551i	0.271764	+	0.537311i
$40$	4.42779	+	5.94755i	0.700095	+	0.940391i
$41$	0.0737288	+	0.0990350i	0.0115145	+	0.0154667i	0.807843	−	0.589398i	$-0.200635\pi$
$41$	0.0737288	+	0.0990350i	0.0115145	+	0.0154667i	−0.796329	+	0.604864i	$0.793227\pi$
$42$	3.71823	−	5.68845i	0.573735	−	0.877748i
$43$	−0.148059	−	2.54207i	−0.0225787	−	0.387662i	−0.990600	−	0.136792i	$-0.956321\pi$
$43$	−0.148059	−	2.54207i	−0.0225787	−	0.387662i	0.968021	−	0.250869i	$-0.0807164\pi$
$44$	−0.416216	+	2.36048i	−0.0627469	+	0.355855i
$45$	3.26650	−	7.69260i	0.486941	−	1.14674i
$46$	−0.0927292	−	0.525894i	−0.0136722	−	0.0775388i
$47$	1.65271	−	0.391699i	0.241072	−	0.0571351i	−0.108304	−	0.994118i	$-0.534542\pi$
$47$	1.65271	−	0.391699i	0.241072	−	0.0571351i	0.349376	+	0.936983i	$0.386394\pi$
$48$	0.130198	−	1.14207i	0.0187925	−	0.164844i
$49$	−1.03635	+	17.7935i	−0.148050	+	2.54192i
$50$	2.11543	+	0.501366i	0.299167	+	0.0709039i
$51$	7.55505	−	1.35432i	1.05792	−	0.189643i
$52$	2.97539	+	0.347773i	0.412612	+	0.0482274i
$53$	−5.02192	+	8.69822i	−0.689814	+	1.19479i	0.282084	+	0.959390i	$0.408974\pi$
$53$	−5.02192	+	8.69822i	−0.689814	+	1.19479i	−0.971898	+	0.235403i	$0.924359\pi$
$54$	3.74336	−	1.65274i	0.509406	−	0.224910i
$55$	2.41957	+	4.19082i	0.326255	+	0.565090i
$56$	−5.25246	−	12.1766i	−0.701890	−	1.62716i
$57$	−0.0104999	−	3.69239i	−0.00139074	−	0.489069i
$58$	3.10962	−	3.29601i	0.408314	−	0.432787i
$59$	−10.3931	+	5.21959i	−1.35306	+	0.679533i	−0.969753	−	0.244087i	$-0.921512\pi$
$59$	−10.3931	+	5.21959i	−1.35306	+	0.679533i	−0.383309	+	0.923620i	$0.625215\pi$
$60$	−3.67440	−	5.55220i	−0.474363	−	0.716786i
$61$	−2.27150	+	7.58734i	−0.290836	+	0.971460i	0.680300	+	0.732934i	$0.261849\pi$
$61$	−2.27150	+	7.58734i	−0.290836	+	0.971460i	−0.971136	+	0.238526i	$0.923336\pi$
$62$	−3.54755	+	2.97675i	−0.450540	+	0.378048i
$63$	−8.85739	+	12.0399i	−1.11593	+	1.51688i
$64$	2.50983	+	2.10599i	0.313728	+	0.263249i
$65$	5.05301	−	3.32342i	0.626749	−	0.412220i
$66$	−0.539853	+	2.30704i	−0.0664514	+	0.283977i
$67$	0.462282	−	0.0540330i	0.0564767	−	0.00660118i	−0.0878076	−	0.996137i	$-0.527986\pi$
$67$	0.462282	−	0.0540330i	0.0564767	−	0.00660118i	0.144284	+	0.989536i	$0.453912\pi$
$68$	2.42190	−	5.61460i	0.293699	−	0.680871i
$69$	0.139669	+	1.16617i	0.0168141	+	0.140391i
$70$	−9.76770	−	4.90552i	−1.16746	−	0.586322i
$71$	11.4588	−	4.17067i	1.35991	−	0.494968i	0.443885	−	0.896084i	$-0.353600\pi$
$71$	11.4588	−	4.17067i	1.35991	−	0.494968i	0.916027	+	0.401116i	$0.131378\pi$
$72$	1.34182	−	7.87134i	0.158135	−	0.927646i
$73$	−2.01159	−	0.732160i	−0.235439	−	0.0856928i	0.221606	−	0.975136i	$-0.428870\pi$
$73$	−2.01159	−	0.732160i	−0.235439	−	0.0856928i	−0.457045	+	0.889443i	$0.651092\pi$
$74$	−0.410222	−	0.434809i	−0.0476873	−	0.0505456i
$75$	−4.58462	−	1.35835i	−0.529387	−	0.156849i
$76$	−2.45764	−	1.61641i	−0.281910	−	0.185415i
$77$	−2.48219	−	8.29110i	−0.282872	−	0.944858i
$78$	2.91770	+	0.505918i	0.330364	+	0.0572839i
$79$	4.18797	−	5.62542i	0.471184	−	0.632910i	−0.501469	−	0.865176i	$-0.667207\pi$
$79$	4.18797	−	5.62542i	0.471184	−	0.632910i	0.972652	+	0.232266i	$0.0746141\pi$
$80$	−1.84879			−0.206701
$81$	−8.42167	+	3.17418i	−0.935742	+	0.352686i
$82$	0.0972297			0.0107372
$83$	−1.97654	+	2.65495i	−0.216953	+	0.291419i	−0.897254	−	0.441514i	$-0.854442\pi$
$83$	−1.97654	+	2.65495i	−0.216953	+	0.291419i	0.680301	+	0.732933i	$0.261849\pi$
$84$	4.10442	+	11.1778i	0.447829	+	1.21960i
$85$	−3.54061	−	11.8265i	−0.384034	−	1.28276i
$86$	−1.67538	−	1.10192i	−0.180661	−	0.118823i
$87$	−7.22985	+	6.85997i	−0.775121	+	0.735466i
$88$	3.17281	+	3.36298i	0.338222	+	0.358495i
$89$	−4.72182	−	1.71860i	−0.500512	−	0.182171i	0.0794124	−	0.996842i	$-0.474696\pi$
$89$	−4.72182	−	1.71860i	−0.500512	−	0.182171i	−0.579924	+	0.814670i	$0.696918\pi$
$90$	−3.32309	−	5.68090i	−0.350285	−	0.598820i
$91$	−10.1643	+	3.69952i	−1.06551	+	0.387815i
$92$	0.836149	+	0.419930i	0.0871745	+	0.0437807i
$93$	8.15274	−	6.10560i	0.845399	−	0.633121i
$94$	0.529782	−	1.22817i	0.0546428	−	0.126676i
$95$	−5.89863	+	0.689452i	−0.605187	+	0.0707362i
$96$	−7.38465	−	6.92748i	−0.753693	−	0.707033i
$97$	6.27220	−	4.12529i	0.636846	−	0.418860i	−0.189612	−	0.981859i	$-0.560723\pi$
$97$	6.27220	−	4.12529i	0.636846	−	0.418860i	0.826457	+	0.562999i	$0.190353\pi$
$98$	10.7523	+	9.02224i	1.08615	+	0.911384i
$99$	1.46618	−	5.00072i	0.147357	−	0.502591i
$100$	−2.91808	+	2.44856i	−0.291808	+	0.244856i
$101$	−0.648115	+	2.16486i	−0.0644899	+	0.215411i	−0.984161	−	0.177279i	$-0.943270\pi$
$101$	−0.648115	+	2.16486i	−0.0644899	+	0.215411i	0.919671	+	0.392690i	$0.128456\pi$
$102$	2.69737	−	5.40921i	0.267080	−	0.535592i
$103$	−0.239343	+	0.120203i	−0.0235832	+	0.0118439i	−0.460552	−	0.887633i	$-0.652348\pi$
$103$	−0.239343	+	0.120203i	−0.0235832	+	0.0118439i	0.436969	+	0.899477i	$0.356052\pi$
$104$	3.96539	−	4.20306i	0.388838	−	0.412144i
$105$	20.8537	+	11.9610i	2.03512	+	1.16727i
$106$	3.13281	+	7.26267i	0.304285	+	0.705412i
$107$	4.97987	+	8.62539i	0.481423	+	0.833848i	0.999773	−	0.0213201i	$-0.00678691\pi$
$107$	4.97987	+	8.62539i	0.481423	+	0.833848i	−0.518350	+	0.855169i	$0.673454\pi$
$108$	−1.59391	+	6.99046i	−0.153374	+	0.672657i
$109$	6.70725	−	11.6173i	0.642438	−	1.11273i	−0.342449	−	0.939536i	$-0.611256\pi$
$109$	6.70725	−	11.6173i	0.642438	−	1.11273i	0.984887	−	0.173198i	$-0.0554102\pi$
$110$	3.78506	+	0.442411i	0.360892	+	0.0421822i
$111$	0.847980	+	1.00477i	0.0804867	+	0.0953683i
$112$	3.21738	+	0.762533i	0.304014	+	0.0720526i
$113$	−0.0233225	+	0.400431i	−0.00219399	+	0.0376694i	−0.999227	−	0.0392998i	$-0.987487\pi$
$113$	−0.0233225	+	0.400431i	−0.00219399	+	0.0376694i	0.997033	+	0.0769692i	$0.0245243\pi$
$114$	−2.33732	−	1.72976i	−0.218910	−	0.162007i
$115$	1.83814	−	0.435646i	0.171407	−	0.0406242i
$116$	1.37873	+	7.81916i	0.128012	+	0.725991i
$117$	−6.34590	−	1.46594i	−0.586678	−	0.135526i
$118$	−1.59040	+	9.01960i	−0.146408	+	0.830322i
$119$	1.28377	+	22.0415i	0.117683	+	2.02055i
$120$	−12.8231	−	0.710278i	−1.17058	−	0.0648392i
$121$	−4.76686	−	6.40300i	−0.433351	−	0.582091i
$122$	3.72452	+	5.00289i	0.337202	+	0.452941i
$123$	−0.213522	−	0.0118271i	−0.0192527	−	0.00106641i
$124$	−0.471807	−	8.10061i	−0.0423695	−	0.727456i
$125$	1.08327	−	6.14355i	0.0968909	−	0.549495i
$126$	3.43997	+	11.2569i	0.306457	+	1.00284i
$127$	−1.81470	−	10.2917i	−0.161029	−	0.913239i	−0.953065	−	0.302765i	$-0.902090\pi$
$127$	−1.81470	−	10.2917i	−0.161029	−	0.913239i	0.792037	−	0.610474i	$-0.209021\pi$
$128$	−8.86603	+	2.10129i	−0.783654	+	0.185729i
$129$	3.54520	+	2.62367i	0.312137	+	0.231001i
$130$	0.276932	−	4.75474i	0.0242885	−	0.417018i
$131$	13.0882	+	3.10197i	1.14353	+	0.271021i	0.758366	−	0.651829i	$-0.225998\pi$
$131$	13.0882	+	3.10197i	1.14353	+	0.271021i	0.385160	+	0.922850i	$0.374146\pi$
$132$	−2.67759	−	3.17266i	−0.233054	−	0.276145i
$133$	10.5496	+	1.23307i	0.914763	+	0.106920i
$134$	0.183263	−	0.317421i	0.0158315	−	0.0274210i
$135$	6.60668	+	12.8798i	0.568612	+	1.10852i
$136$	−5.89743	−	10.2146i	−0.505700	−	0.875898i
$137$	−5.66340	−	13.1292i	−0.483857	−	1.12171i	−0.968953	−	0.247246i	$-0.920475\pi$
$137$	−5.66340	−	13.1292i	−0.483857	−	1.12171i	0.485096	−	0.874461i	$-0.338785\pi$
$138$	0.802321	+	0.460183i	0.0682981	+	0.0391734i
$139$	0.222217	−	0.235537i	0.0188482	−	0.0199780i	−0.717881	−	0.696166i	$-0.754888\pi$
$139$	0.222217	−	0.235537i	0.0188482	−	0.0199780i	0.736729	+	0.676188i	$0.236369\pi$
$140$	17.1147	−	8.59535i	1.44646	−	0.726439i
$141$	−1.31283	+	2.63270i	−0.110560	+	0.221713i
$142$	2.75416	−	9.19954i	0.231124	−	0.772009i
$143$	2.88891	−	2.42408i	0.241583	−	0.202712i
$144$	1.37448	+	1.44036i	0.114540	+	0.120030i
$145$	12.2796	+	10.3038i	1.01976	+	0.855682i
$146$	−1.40846	+	0.926361i	−0.116565	+	0.0766662i
$147$	−22.5152	−	21.1213i	−1.85702	−	1.74206i
$148$	1.04033	−	0.121598i	0.0855149	−	0.00999526i
$149$	−1.21912	+	2.82624i	−0.0998744	+	0.231535i	−0.960826	−	0.277152i	$-0.910610\pi$
$149$	−1.21912	+	2.82624i	−0.0998744	+	0.231535i	0.860952	+	0.508687i	$0.169869\pi$
$150$	−3.01401	+	2.25720i	−0.246093	+	0.184300i
$151$	11.1937	+	5.62167i	0.910928	+	0.457485i	0.841596	−	0.540108i	$-0.181617\pi$
$151$	11.1937	+	5.62167i	0.910928	+	0.457485i	0.0693326	+	0.997594i	$0.477913\pi$
$152$	−5.33190	+	1.94065i	−0.432474	+	0.157408i
$153$	−6.58157	+	11.5508i	−0.532089	+	0.933830i
$154$	−6.40455	−	2.33106i	−0.516093	−	0.187843i
$155$	−11.2422	−	11.9160i	−0.902993	−	0.957117i
$156$	−3.76392	+	3.57136i	−0.301354	+	0.285937i
$157$	−4.86355	−	3.19881i	−0.388153	−	0.255292i	0.340401	−	0.940280i	$-0.389437\pi$
$157$	−4.86355	−	3.19881i	−0.388153	−	0.255292i	−0.728554	+	0.684988i	$0.759807\pi$
$158$	−1.58398	−	5.29086i	−0.126015	−	0.420918i
$159$	−5.99640	−	16.3303i	−0.475545	−	1.29508i
$160$	−9.72499	+	13.0629i	−0.768828	+	1.03272i
$161$	−3.37853			−0.266265
$162$	−1.95536	+	6.81244i	−0.153628	+	0.535236i
$163$	−6.75084			−0.528767			−0.264383	−	0.964418i	$-0.585168\pi$
$163$	−6.75084			−0.528767			−0.264383	+	0.964418i	$0.585168\pi$
$164$	−0.101734	+	0.136653i	−0.00794410	+	0.0106708i
$165$	−8.25841	−	1.43198i	−0.642916	−	0.111479i
$166$	0.747568	+	2.49705i	0.0580226	+	0.193809i
$167$	14.5276	+	9.55498i	1.12418	+	0.739387i	0.968646	−	0.248444i	$-0.0799191\pi$
$167$	14.5276	+	9.55498i	1.12418	+	0.739387i	0.155536	+	0.987830i	$0.450289\pi$
$168$	22.0226	+	6.52497i	1.69908	+	0.503412i
$169$	5.68670	+	6.02755i	0.437439	+	0.463658i
$170$	−9.13549	−	3.32504i	−0.700660	−	0.255019i
$171$	4.92248	+	4.08297i	0.376432	+	0.312233i
$172$	3.30170	−	1.20172i	0.251752	−	0.0916303i
$173$	−12.2830	−	6.16877i	−0.933862	−	0.469003i	−0.0842696	−	0.996443i	$-0.526856\pi$
$173$	−12.2830	−	6.16877i	−0.933862	−	0.469003i	−0.849592	+	0.527440i	$0.823152\pi$
$174$	0.933329	+	7.79289i	0.0707555	+	0.590778i
$175$	5.44791	−	12.6297i	0.411823	−	0.954713i
$176$	−1.14501	+	0.133832i	−0.0863084	+	0.0100880i
$177$	4.58976	−	19.6141i	0.344988	−	1.47429i
$178$	−3.30609	+	2.17445i	−0.247802	+	0.162982i
$179$	1.66053	+	1.39335i	0.124114	+	0.104144i	0.702732	−	0.711455i	$-0.251963\pi$
$179$	1.66053	+	1.39335i	0.124114	+	0.104144i	−0.578618	+	0.815599i	$0.696408\pi$
$180$	11.4613	+	1.27361i	0.854277	+	0.0949290i
$181$	−17.7173	+	14.8665i	−1.31691	+	1.10502i	−0.329963	+	0.943994i	$0.607036\pi$
$181$	−17.7173	+	14.8665i	−1.31691	+	1.10502i	−0.986950	+	0.161028i	$0.948519\pi$
$182$	−2.44303	+	8.16029i	−0.181089	+	0.604881i
$183$	−7.57070	−	11.4397i	−0.559643	−	0.845647i
$184$	1.61288	−	0.810018i	0.118903	−	0.0597153i
$185$	1.45116	−	1.53814i	0.106692	−	0.113087i
$186$	−0.0228092	−	8.02110i	−0.00167245	−	0.588136i
$187$	−3.04892	−	7.06820i	−0.222959	−	0.516878i
$188$	1.17182	+	2.02966i	0.0854640	+	0.148028i
$189$	−6.18509	−	25.1393i	−0.449899	−	1.82861i
$190$	−2.33840	+	4.05023i	−0.169646	+	0.293835i
$191$	21.7391	+	2.54094i	1.57299	+	0.183856i	0.857395	−	0.514660i	$-0.172082\pi$
$191$	21.7391	+	2.54094i	1.57299	+	0.183856i	0.715595	+	0.698516i	$0.246156\pi$
$192$	−5.58576	+	1.00131i	−0.403118	+	0.0722631i
$193$	−7.02015	−	1.66381i	−0.505322	−	0.119763i	−0.0299550	−	0.999551i	$-0.509536\pi$
$193$	−7.02015	−	1.66381i	−0.505322	−	0.119763i	−0.475367	+	0.879788i	$0.657685\pi$
$194$	0.343750	−	5.90195i	0.0246798	−	0.423736i
$195$	−1.18653	+	10.4080i	−0.0849691	+	0.745332i
$196$	−23.9308	+	5.67171i	−1.70935	+	0.405122i
$197$	2.84835	+	16.1538i	0.202936	+	1.15091i	0.900654	+	0.434537i	$0.143088\pi$
$197$	2.84835	+	16.1538i	0.202936	+	1.15091i	−0.697718	+	0.716373i	$0.745801\pi$
$198$	−2.46933	−	3.27780i	−0.175488	−	0.232943i
$199$	−1.40107	+	7.94587i	−0.0993193	+	0.563268i	0.894019	+	0.448030i	$0.147874\pi$
$199$	−1.40107	+	7.94587i	−0.0993193	+	0.563268i	−0.993338	+	0.115238i	$0.963237\pi$
$200$	0.427241	+	7.33545i	0.0302105	+	0.518695i
$201$	−0.441067	+	0.674782i	−0.0311105	+	0.0475955i
$202$	1.06270	+	1.42745i	0.0747710	+	0.100435i
$203$	−17.1199	−	22.9960i	−1.20158	−	1.61401i
$204$	4.78010	+	9.45086i	0.334674	+	0.661693i
$205$	0.0199990	+	0.343370i	0.00139679	+	0.0239820i
$206$	−0.0366255	+	0.207713i	−0.00255182	+	0.0144721i
$207$	−1.70597	−	1.10819i	−0.118573	−	0.0770242i
$208$	0.250189	+	1.41889i	0.0173475	+	0.0983824i
$209$	−3.60330	+	0.853997i	−0.249245	+	0.0590722i
$210$	17.3622	−	7.54794i	1.19810	−	0.520857i
$211$	1.39097	−	23.8821i	0.0957585	−	1.64411i	−0.518553	−	0.855046i	$-0.673529\pi$
$211$	1.39097	−	23.8821i	0.0957585	−	1.64411i	0.614311	−	0.789064i	$-0.289434\pi$
$212$	−13.4853	−	3.19609i	−0.926177	−	0.219508i
$213$	−7.16735	+	19.8677i	−0.491098	+	1.36131i
$214$	7.79028	+	0.910553i	0.532533	+	0.0622441i
$215$	3.54684	−	6.14331i	0.241893	−	0.418970i
$216$	8.97996	+	10.5183i	0.611009	+	0.715683i
$217$	14.6496	+	25.3739i	0.994481	+	1.72249i
$218$	−4.18416	−	9.69997i	−0.283387	−	0.656965i
$219$	3.20575	−	1.86302i	0.216625	−	0.125891i
$220$	−4.58221	+	4.85686i	−0.308932	+	0.327449i
$221$	−8.59735	+	4.31775i	−0.578321	+	0.290444i
$222$	1.03346	−	0.0631413i	0.0693612	−	0.00423777i
$223$	−3.43182	+	11.4631i	−0.229812	+	0.767624i	0.762837	+	0.646591i	$0.223806\pi$
$223$	−3.43182	+	11.4631i	−0.229812	+	0.767624i	−0.992648	+	0.121033i	$0.961379\pi$
$224$	22.3119	−	18.7219i	1.49078	−	1.25091i
$225$	6.89352	−	4.59032i	0.459568	−	0.306021i
$226$	0.241974	+	0.203040i	0.0160959	+	0.0135060i
$227$	20.9815	−	13.7997i	1.39259	−	0.915921i	0.392598	−	0.919710i	$-0.371577\pi$
$227$	20.9815	−	13.7997i	1.39259	−	0.915921i	0.999993	+	0.00378925i	$0.00120616\pi$
$228$	4.87672	−	1.47512i	0.322968	−	0.0976920i
$229$	25.5994	−	2.99214i	1.69166	−	0.197726i	0.784971	−	0.619533i	$-0.212678\pi$
$229$	25.5994	−	2.99214i	1.69166	−	0.197726i	0.906686	+	0.421806i	$0.138604\pi$
$230$	0.589222	−	1.36597i	0.0388521	−	0.0900694i
$231$	13.7812	+	5.89821i	0.906737	+	0.388074i
$232$	13.6863	+	6.87352i	0.898550	+	0.451269i
$233$	−8.58260	+	3.12381i	−0.562265	+	0.204648i	−0.607488	−	0.794329i	$-0.707823\pi$
$233$	−8.58260	+	3.12381i	−0.562265	+	0.204648i	0.0452226	+	0.998977i	$0.485600\pi$
$234$	−3.91023	+	3.31915i	−0.255620	+	0.216980i
$235$	4.44630	+	1.61832i	0.290044	+	0.105568i
$236$	−11.0126	−	11.6727i	−0.716861	−	0.759828i
$237$	2.83493	+	11.8117i	0.184148	+	0.767254i
$238$	14.5268	+	9.55440i	0.941630	+	0.619320i
$239$	6.24071	+	20.8454i	0.403678	+	1.34838i	0.882437	+	0.470431i	$0.155902\pi$
$239$	6.24071	+	20.8454i	0.403678	+	1.34838i	−0.478759	+	0.877946i	$0.658913\pi$
$240$	2.05134	−	2.45886i	0.132414	−	0.158719i
$241$	8.27944	−	11.1212i	0.533326	−	0.716381i	−0.451043	−	0.892502i	$-0.648948\pi$
$241$	8.27944	−	11.1212i	0.533326	−	0.716381i	0.984368	+	0.176122i	$0.0563552\pi$
$242$	−6.28628			−0.404097
$243$	5.12276	−	14.7227i	0.328625	−	0.944460i
$244$	−10.9284			−0.699622
$245$	−29.6507	+	39.8278i	−1.89431	+	2.54451i
$246$	−0.107883	+	0.129314i	−0.00687834	+	0.00824478i
$247$	1.32737	+	4.43374i	0.0844588	+	0.282112i
$248$	−13.0771	−	8.60095i	−0.830397	−	0.546161i
$249$	−1.33796	−	5.57461i	−0.0847898	−	0.353277i
$250$	−3.37129	−	3.57336i	−0.213219	−	0.225999i
$251$	−10.0143	−	3.64492i	−0.632099	−	0.230065i	0.00604584	−	0.999982i	$-0.498076\pi$
$251$	−10.0143	−	3.64492i	−0.632099	−	0.230065i	−0.638144	+	0.769917i	$0.720298\pi$
$252$	−19.4205	−	6.94365i	−1.22338	−	0.437409i
$253$	1.10688	−	0.402871i	0.0695888	−	0.0253283i
$254$	−7.35436	−	3.69350i	−0.461454	−	0.231751i
$255$	19.6576	+	8.41325i	1.23101	+	0.526858i
$256$	−5.43743	+	12.6054i	−0.339839	+	0.787836i
$257$	1.16759	−	0.136472i	0.0728323	−	0.00851287i	−0.0795987	−	0.996827i	$-0.525364\pi$
$257$	1.16759	−	0.136472i	0.0728323	−	0.00851287i	0.152431	+	0.988314i	$0.451290\pi$
$258$	3.32448	−	1.00559i	0.206973	−	0.0626055i
$259$	−3.15982	+	2.07825i	−0.196342	+	0.129136i
$260$	6.39284	+	5.36423i	0.396467	+	0.332675i
$261$	−1.10171	−	17.2272i	−0.0681942	−	1.06634i
$262$	8.11435	−	6.80875i	0.501306	−	0.420646i
$263$	−2.67668	+	8.94073i	−0.165051	+	0.551309i	0.834948	+	0.550328i	$0.185497\pi$
$263$	−2.67668	+	8.94073i	−0.165051	+	0.551309i	−1.00000		0.000980948i	$0.999688\pi$
$264$	−7.99315	+	0.488359i	−0.491944	+	0.0300564i
$265$	−25.0039	+	12.5575i	−1.53598	+	0.771398i
$266$	5.73996	−	6.08401i	0.351940	−	0.373034i
$267$	7.52488	−	4.37307i	0.460515	−	0.267627i
$268$	0.254369	+	0.589695i	0.0155381	+	0.0360213i
$269$	−1.25116	−	2.16707i	−0.0762845	−	0.132129i	0.825360	−	0.564607i	$-0.190972\pi$
$269$	−1.25116	−	2.16707i	−0.0762845	−	0.132129i	−0.901644	+	0.432479i	$0.857639\pi$
$270$	11.2427	+	1.88365i	0.684210	+	0.114635i
$271$	−2.76243	+	4.78467i	−0.167806	+	0.290648i	−0.937648	−	0.347586i	$-0.887002\pi$
$271$	−2.76243	+	4.78467i	−0.167806	+	0.290648i	0.769842	+	0.638234i	$0.220335\pi$
$272$	2.92103	+	0.341419i	0.177113	+	0.0207016i
$273$	6.35766	−	17.6233i	0.384783	−	1.06661i
$274$	−10.9567	−	2.59678i	−0.661917	−	0.156877i
$275$	−0.278833	+	4.78738i	−0.0168143	+	0.288690i
$276$	−1.48626	+	0.646130i	−0.0894624	+	0.0388924i
$277$	25.9932	−	6.16051i	1.56178	−	0.370149i	0.643301	−	0.765613i	$-0.277564\pi$
$277$	25.9932	−	6.16051i	1.56178	−	0.370149i	0.918482	+	0.395464i	$0.129416\pi$
$278$	−0.0442815	−	0.251133i	−0.00265583	−	0.0150620i
$279$	−0.925604	+	17.6176i	−0.0554144	+	1.05474i
$280$	6.41505	−	36.3816i	0.383373	−	2.17421i
$281$	−1.83046	−	31.4278i	−0.109196	−	1.87482i	−0.397930	−	0.917416i	$-0.630271\pi$
$281$	−1.83046	−	31.4278i	−0.109196	−	1.87482i	0.288734	−	0.957409i	$-0.406766\pi$
$282$	1.04563	+	2.06734i	0.0622663	+	0.123108i
$283$	3.99576	+	5.36724i	0.237523	+	0.319049i	0.904862	−	0.425705i	$-0.139974\pi$
$283$	3.99576	+	5.36724i	0.237523	+	0.319049i	−0.667338	+	0.744755i	$0.732567\pi$
$284$	10.0479	+	13.4966i	0.596230	+	0.800876i
$285$	5.62795	−	8.61011i	0.333371	−	0.510019i
$286$	−0.172680	−	2.96480i	−0.0102108	−	0.175312i
$287$	0.106819	−	0.605803i	0.00630535	−	0.0357594i
$288$	17.4072	−	2.13503i	1.02573	−	0.125808i
$289$	0.458026	+	2.59759i	0.0269427	+	0.152800i
$290$	12.2832	−	2.91118i	0.721297	−	0.170951i
$291$	−1.47281	+	12.9192i	−0.0863379	+	0.757339i
$292$	0.171749	−	2.94882i	0.0100509	−	0.172567i
$293$	3.65264	+	0.865692i	0.213390	+	0.0505743i	0.335920	−	0.941890i	$-0.390953\pi$
$293$	3.65264	+	0.865692i	0.213390	+	0.0505743i	−0.122530	+	0.992465i	$0.539101\pi$
$294$	−23.9298	+	4.28967i	−1.39562	+	0.250179i
$295$	−32.1801	−	3.76132i	−1.87360	−	0.218992i
$296$	1.01020	−	1.74972i	0.0587167	−	0.101700i
$297$	5.02408	+	7.49862i	0.291527	+	0.435114i
$298$	1.21195	+	2.09916i	0.0702066	+	0.121601i
$299$	−0.583094	−	1.35176i	−0.0337212	−	0.0781745i
$300$	−0.0187620	−	6.59785i	−0.00108323	−	0.380927i
$301$	−8.70627	+	9.22810i	−0.501821	+	0.531899i
$302$	8.81503	−	4.42708i	0.507248	−	0.254750i
$303$	−2.16011	−	3.26403i	−0.124095	−	0.187514i
$304$	0.405760	−	1.35533i	0.0232719	−	0.0777337i
$305$	−16.9018	+	14.1823i	−0.967793	+	0.812075i
$306$	4.20128	+	9.58934i	0.240171	+	0.548186i
$307$	−22.9491	−	19.2566i	−1.30977	−	1.09903i	−0.988367	−	0.152088i	$-0.951400\pi$
$307$	−22.9491	−	19.2566i	−1.30977	−	1.09903i	−0.321406	−	0.946942i	$-0.604155\pi$
$308$	9.97748	−	6.56229i	0.568520	−	0.373921i
$309$	0.105698	−	0.451696i	0.00601296	−	0.0256961i
$310$	−12.8138	+	1.49772i	−0.727775	+	0.0850647i
$311$	1.76187	−	4.08446i	0.0999062	−	0.231609i	−0.860931	−	0.508721i	$-0.830118\pi$
$311$	1.76187	−	4.08446i	0.0999062	−	0.231609i	0.960837	+	0.277113i	$0.0893776\pi$
$312$	1.19018	+	9.93748i	0.0673807	+	0.562599i
$313$	−27.9019	−	14.0129i	−1.57711	−	0.792054i	−0.577406	−	0.816457i	$-0.695935\pi$
$313$	−27.9019	−	14.0129i	−1.57711	−	0.792054i	−0.999702	+	0.0244032i	$0.992231\pi$
$314$	−4.30775	+	1.56789i	−0.243100	+	0.0884812i
$315$	−39.0465	+	14.4638i	−2.20002	+	0.814942i
$316$	9.09346	+	3.30975i	0.511547	+	0.186188i
$317$	19.0975	+	20.2421i	1.07262	+	1.13691i	0.990106	+	0.140321i	$0.0448135\pi$
$317$	19.0975	+	20.2421i	1.07262	+	1.13691i	0.0825140	+	0.996590i	$0.473705\pi$
$318$	−13.1353	−	3.89179i	−0.736592	−	0.218241i
$319$	8.35100	+	5.49254i	0.467566	+	0.307523i
$320$	2.61772	+	8.74380i	0.146335	+	0.488793i
$321$	−16.9972	−	2.94725i	−0.948689	−	0.164499i
$322$	−1.58880	+	2.13413i	−0.0885402	+	0.118930i
$323$	9.44699			0.525644
$324$	−7.52868	−	9.87623i	−0.418260	−	0.548680i
$325$	5.99343			0.332456
$326$	−3.17467	+	4.26433i	−0.175829	+	0.236179i
$327$	8.00875	+	21.8107i	0.442885	+	1.20613i
$328$	0.0942496	+	0.314815i	0.00520406	+	0.0173828i
$329$	−7.07027	−	4.65019i	−0.389796	−	0.256373i
$330$	−4.78817	+	4.54321i	−0.263580	+	0.250095i
$331$	−0.135248	−	0.143354i	−0.00743388	−	0.00787946i	0.723646	−	0.690171i	$-0.242465\pi$
$331$	−0.135248	−	0.143354i	−0.00743388	−	0.00787946i	−0.731080	+	0.682292i	$0.760983\pi$
$332$	−4.29171	−	1.56206i	−0.235538	−	0.0857289i
$333$	−2.27722	+	0.0129513i	−0.124791	+	0.000709729i
$334$	12.8674	−	4.68336i	0.704075	−	0.256262i
$335$	1.15868	+	0.581909i	0.0633052	+	0.0317931i
$336$	−4.58405	+	3.43300i	−0.250080	+	0.187285i
$337$	−7.09164	+	16.4403i	−0.386306	+	0.895559i	0.608479	+	0.793570i	$0.291780\pi$
$337$	−7.09164	+	16.4403i	−0.386306	+	0.895559i	−0.994786	+	0.101989i	$0.967479\pi$
$338$	6.48169	−	0.757601i	0.352557	−	0.0412081i
$339$	−0.506691	−	0.475322i	−0.0275197	−	0.0258160i
$340$	14.2319	−	9.36049i	0.771835	−	0.507644i
$341$	−7.82522	−	6.56614i	−0.423759	−	0.355576i
$342$	4.89397	−	1.18933i	0.264635	−	0.0643115i
$343$	41.3103	−	34.6635i	2.23055	−	1.87165i
$344$	1.94381	−	6.49278i	0.104803	−	0.350067i
$345$	−1.46012	+	2.92808i	−0.0786104	+	0.157642i
$346$	−9.67291	+	4.85792i	−0.520019	+	0.261163i
$347$	−15.4622	+	16.3889i	−0.830052	+	0.879804i	−0.994300	−	0.106615i	$-0.965999\pi$
$347$	−15.4622	+	16.3889i	−0.830052	+	0.879804i	0.164248	+	0.986419i	$0.447480\pi$
$348$	−11.9292	−	6.84216i	−0.639471	−	0.366778i
$349$	−4.69595	−	10.8864i	−0.251368	−	0.582737i	0.745077	−	0.666978i	$-0.232413\pi$
$349$	−4.69595	−	10.8864i	−0.251368	−	0.582737i	−0.996445	+	0.0842411i	$0.973153\pi$
$350$	−5.41587	−	9.38056i	−0.289490	−	0.501412i
$351$	8.99085	−	6.81342i	0.479896	−	0.363673i
$352$	−5.07737	+	8.79426i	−0.270625	+	0.468736i
$353$	18.6770	+	2.18302i	0.994074	+	0.116191i	0.597548	−	0.801833i	$-0.296142\pi$
$353$	18.6770	+	2.18302i	0.994074	+	0.116191i	0.396526	+	0.918024i	$0.370216\pi$
$354$	−10.2313	−	12.1230i	−0.543788	−	0.644332i
$355$	33.0550	+	7.83417i	1.75438	+	0.415795i
$356$	0.403147	−	6.92177i	0.0213668	−	0.366853i
$357$	−30.7394	−	22.7491i	−1.62690	−	1.20401i
$358$	1.66103	−	0.393671i	0.0877880	−	0.0208061i
$359$	−1.61227	−	9.14366i	−0.0850926	−	0.482584i	−0.997337	−	0.0729368i	$-0.976763\pi$
$359$	−1.61227	−	9.14366i	−0.0850926	−	0.482584i	0.912244	−	0.409647i	$-0.134348\pi$
$360$	15.1727	−	16.2665i	0.799671	−	0.857318i
$361$	−2.51015	+	14.2358i	−0.132113	+	0.749251i
$362$	1.05902	+	18.1827i	0.0556609	+	0.955661i
$363$	13.8050	+	0.764669i	0.724577	+	0.0401347i
$364$	−8.91276	−	11.9719i	−0.467156	−	0.627499i
$365$	−3.56118	−	4.78349i	−0.186401	−	0.250379i
$366$	−10.7864	−	0.597463i	−0.563813	−	0.0312299i
$367$	1.69898	+	29.1704i	0.0886861	+	1.52268i	0.690083	+	0.723731i	$0.257574\pi$
$367$	1.69898	+	29.1704i	0.0886861	+	1.52268i	−0.601396	+	0.798951i	$0.705389\pi$
$368$	−0.0781452	+	0.443183i	−0.00407360	+	0.0231025i
$369$	0.252646	−	0.270859i	0.0131522	−	0.0141004i
$370$	−0.289175	−	1.63999i	−0.0150335	−	0.0852593i
$371$	48.6929	−	11.5404i	2.52801	−	0.599149i
$372$	11.2972	+	8.36064i	0.585733	+	0.433479i
$373$	−0.323556	+	5.55523i	−0.0167531	+	0.287639i	0.979518	+	0.201358i	$0.0645354\pi$
$373$	−0.323556	+	5.55523i	−0.0167531	+	0.287639i	−0.996271	+	0.0862813i	$0.972502\pi$
$374$	−5.89859	−	1.39799i	−0.305009	−	0.0722884i
$375$	6.96889	+	8.25739i	0.359872	+	0.426410i
$376$	4.49018	+	0.524827i	0.231564	+	0.0270659i
$377$	6.24612	−	10.8186i	0.321692	−	0.557186i
$378$	−18.7884	−	7.91511i	−0.966372	−	0.407110i
$379$	−14.7919	−	25.6203i	−0.759808	−	1.31603i	−0.942948	−	0.332940i	$-0.891959\pi$
$379$	−14.7919	−	25.6203i	−0.759808	−	1.31603i	0.183140	−	0.983087i	$-0.441374\pi$
$380$	−3.24571	−	7.52441i	−0.166501	−	0.385994i
$381$	15.7013	+	9.00574i	0.804404	+	0.461378i
$382$	11.8282	−	12.5371i	0.605181	−	0.641455i
$383$	−11.0692	+	5.55918i	−0.565612	+	0.284061i	−0.708538	−	0.705672i	$-0.750645\pi$
$383$	−11.0692	+	5.55918i	−0.565612	+	0.284061i	0.142926	+	0.989733i	$0.454349\pi$
$384$	7.04273	−	14.1232i	0.359398	−	0.720723i
$385$	6.91489	−	23.0973i	0.352415	−	1.17715i
$386$	−4.35230	+	3.65201i	−0.221526	+	0.185883i
$387$	−7.42307	+	1.80395i	−0.377336	+	0.0916999i
$388$	7.93530	+	6.65850i	0.402854	+	0.338034i
$389$	−15.5223	+	10.2092i	−0.787012	+	0.517626i	−0.878249	−	0.478203i	$-0.841288\pi$
$389$	−15.5223	+	10.2092i	−0.787012	+	0.517626i	0.0912370	+	0.995829i	$0.470918\pi$
$390$	6.01647	+	5.64400i	0.304656	+	0.285795i
$391$	−2.98465	+	0.348856i	−0.150940	+	0.0176424i
$392$	−18.7900	+	43.5600i	−0.949037	+	2.20011i
$393$	−18.6478	+	13.9654i	−0.940658	+	0.704460i
$394$	11.5434	+	5.79730i	0.581547	+	0.292064i
$395$	18.3590	−	6.68214i	0.923743	−	0.336215i
$396$	7.19055	−	0.0408952i	0.361339	−	0.00205506i
$397$	9.59694	+	3.49300i	0.481657	+	0.175309i	0.571426	−	0.820654i	$-0.306391\pi$
$397$	9.59694	+	3.49300i	0.481657	+	0.175309i	−0.0897688	+	0.995963i	$0.528613\pi$
$398$	4.36032	+	4.62167i	0.218563	+	0.231663i
$399$	−13.3454	+	12.6626i	−0.668104	+	0.633924i
$400$	−1.53071	−	1.00676i	−0.0765353	−	0.0503380i
$401$	−0.579017	−	1.93405i	−0.0289148	−	0.0965820i	0.942314	−	0.334730i	$-0.108645\pi$
$401$	−0.579017	−	1.93405i	−0.0289148	−	0.0965820i	−0.971229	+	0.238148i	$0.923460\pi$
$402$	0.218824	+	0.595936i	0.0109139	+	0.0297226i
$403$	−7.62385	+	10.2406i	−0.379771	+	0.510121i
$404$	−3.11815			−0.155134
$405$	−24.4605	−	5.50418i	−1.21545	−	0.273505i
$406$	−22.5768			−1.12047
$407$	0.787406	−	1.05767i	0.0390303	−	0.0524267i
$408$	20.1289	+	3.49028i	0.996530	+	0.172795i
$409$	0.249431	+	0.833158i	0.0123336	+	0.0411970i	0.963935	−	0.266138i	$-0.0857478\pi$
$409$	0.249431	+	0.833158i	0.0123336	+	0.0411970i	−0.951601	+	0.307335i	$0.900563\pi$
$410$	0.226302	+	0.148841i	0.0111763	+	0.00735075i
$411$	23.7456	+	7.03546i	1.17129	+	0.347034i
$412$	−0.253611	−	0.268812i	−0.0124945	−	0.0132434i
$413$	54.4506	+	19.8184i	2.67934	+	0.975200i
$414$	−1.50226	+	0.556476i	−0.0738323	+	0.0273493i
$415$	−8.66465	+	3.15367i	−0.425331	+	0.154808i
$416$	11.3415	+	5.69591i	0.556062	+	0.279265i
$417$	0.0666968	+	0.556889i	0.00326616	+	0.0272710i
$418$	−1.15505	+	2.67771i	−0.0564954	+	0.130971i
$419$	25.0738	−	2.93070i	1.22493	−	0.143174i	0.521072	−	0.853512i	$-0.325532\pi$
$419$	25.0738	−	2.93070i	1.22493	−	0.143174i	0.703860	+	0.710338i	$0.251458\pi$
$420$	−7.55818	+	32.2995i	−0.368801	+	1.57605i
$421$	−13.9967	+	9.20577i	−0.682157	+	0.448662i	−0.842712	−	0.538365i	$-0.819042\pi$
$421$	−13.9967	+	9.20577i	−0.682157	+	0.448662i	0.160554	+	0.987027i	$0.448672\pi$
$422$	−14.4315	−	12.1095i	−0.702516	−	0.589481i
$423$	−2.04479	−	4.66719i	−0.0994211	−	0.226927i
$424$	−20.4787	+	17.1836i	−0.994532	+	0.834511i
$425$	3.50868	−	11.7198i	0.170196	−	0.568494i
$426$	9.17937	+	13.8705i	0.444742	+	0.672027i
$427$	35.2631	−	17.7098i	1.70650	−	0.857037i
$428$	−9.43093	+	9.99621i	−0.455861	+	0.483185i
$429$	0.0185744	+	6.53189i	0.000896782	+	0.315362i
$430$	−2.21262	−	5.12942i	−0.106702	−	0.247363i
$431$	−13.1811	−	22.8303i	−0.634911	−	1.09970i	−0.986534	−	0.163556i	$-0.947703\pi$
$431$	−13.1811	−	22.8303i	−0.634911	−	1.09970i	0.351623	−	0.936142i	$-0.385630\pi$
$432$	−3.44074	+	0.229868i	−0.165543	+	0.0110595i
$433$	6.29345	−	10.9006i	0.302444	−	0.523848i	−0.674245	−	0.738508i	$-0.735531\pi$
$433$	6.29345	−	10.9006i	0.302444	−	0.523848i	0.976689	+	0.214660i	$0.0688642\pi$
$434$	22.9172	+	2.67863i	1.10006	+	0.128579i
$435$	−27.3289	+	4.89899i	−1.31032	+	0.234888i
$436$	18.0109	+	4.26867i	0.862568	+	0.204432i
$437$	−0.0840533	+	1.44314i	−0.00402081	+	0.0690347i
$438$	0.330730	−	2.90110i	0.0158029	−	0.138620i
$439$	8.56156	−	2.02913i	0.408621	−	0.0968449i	−0.0211645	−	0.999776i	$-0.506737\pi$
$439$	8.56156	−	2.02913i	0.408621	−	0.0968449i	0.429785	+	0.902931i	$0.358589\pi$
$440$	2.23659	+	12.6843i	0.106625	+	0.604702i
$441$	53.0731	−	6.50953i	2.52729	−	0.309978i
$442$	−1.31561	+	7.46120i	−0.0625772	+	0.354893i
$443$	0.885106	+	15.1967i	0.0420527	+	0.722017i	0.951775	+	0.306798i	$0.0992577\pi$
$443$	0.885106	+	15.1967i	0.0420527	+	0.722017i	−0.909722	+	0.415218i	$0.863705\pi$
$444$	−0.992593	+	1.51855i	−0.0471064	+	0.0720673i
$445$	−8.35916	−	11.2283i	−0.396262	−	0.532273i
$446$	5.62705	+	7.55845i	0.266449	+	0.357903i
$447$	−2.40618	−	4.75731i	−0.113808	−	0.225013i
$448$	−0.949147	−	16.2962i	−0.0448430	−	0.769924i
$449$	−0.214786	+	1.21811i	−0.0101364	+	0.0574862i	−0.989456	−	0.144831i	$-0.953736\pi$
$449$	−0.214786	+	1.21811i	−0.0101364	+	0.0574862i	0.979320	+	0.202317i	$0.0648472\pi$
$450$	0.342190	−	6.51311i	0.0161310	−	0.307031i
$451$	0.0372423	+	0.211212i	0.00175367	+	0.00994557i
$452$	−0.538549	+	0.127639i	−0.0253312	+	0.00600361i
$453$	−19.8968	+	8.64985i	−0.934836	+	0.406406i
$454$	1.14990	−	19.7430i	0.0539673	−	0.926583i
$455$	−29.3208	−	6.94916i	−1.37458	−	0.325782i
$456$	3.33503	−	9.24464i	0.156177	−	0.432920i
$457$	−30.7759	−	3.59718i	−1.43963	−	0.168269i	−0.639824	−	0.768522i	$-0.720993\pi$
$457$	−30.7759	−	3.59718i	−1.43963	−	0.168269i	−0.799810	+	0.600253i	$0.795067\pi$
$458$	10.1484	−	17.5776i	0.474204	−	0.821345i
$459$	−8.05981	−	21.5698i	−0.376200	−	1.00679i
$460$	1.30330	+	2.25738i	0.0607666	+	0.105251i
$461$	−6.71020	−	15.5560i	−0.312525	−	0.724514i	0.687474	−	0.726209i	$-0.258720\pi$
$461$	−6.71020	−	15.5560i	−0.312525	−	0.724514i	−0.999999	+	0.00169503i	$0.999460\pi$
$462$	10.2065	−	5.93151i	0.474851	−	0.275959i
$463$	−24.4901	+	25.9580i	−1.13815	+	1.20637i	−0.162578	+	0.986696i	$0.551981\pi$
$463$	−24.4901	+	25.9580i	−1.13815	+	1.20637i	−0.975573	+	0.219674i	$0.929501\pi$
$464$	−3.41252	+	1.71383i	−0.158422	+	0.0795627i
$465$	28.3221	−	1.73040i	1.31340	−	0.0802453i
$466$	−2.06285	+	6.89041i	−0.0955599	+	0.319192i
$467$	−32.1894	+	27.0101i	−1.48955	+	1.24988i	−0.594353	+	0.804204i	$0.702592\pi$
$467$	−32.1894	+	27.0101i	−1.48955	+	1.24988i	−0.895195	+	0.445675i	$0.852964\pi$
$468$	−0.573560	−	8.96861i	−0.0265128	−	0.414574i
$469$	−1.77640	−	1.49057i	−0.0820263	−	0.0688282i
$470$	3.11318	−	2.04757i	0.143600	−	0.0944474i
$471$	9.65079	−	2.91918i	0.444685	−	0.134509i
$472$	−30.7458	+	3.59367i	−1.41519	+	0.165412i
$473$	1.75196	−	4.06150i	0.0805552	−	0.186748i
$474$	8.79431	+	3.76387i	0.403936	+	0.172880i
$475$	−5.25923	−	2.64128i	−0.241310	−	0.121190i
$476$	−28.6281	+	10.4198i	−1.31217	+	0.477590i
$477$	28.3725	+	10.1444i	1.29909	+	0.464480i
$478$	16.1023	+	5.86074i	0.736500	+	0.268064i
$479$	−24.7671	−	26.2516i	−1.13164	−	1.19947i	−0.977392	−	0.211435i	$-0.932186\pi$
$479$	−24.7671	−	26.2516i	−1.13164	−	1.19947i	−0.154247	−	0.988032i	$-0.549295\pi$
$480$	−6.58306	−	27.4283i	−0.300474	−	1.25192i
$481$	−1.37686	−	0.905578i	−0.0627796	−	0.0412908i
$482$	−3.13146	−	10.4598i	−0.142634	−	0.476431i
$483$	3.74869	−	4.49340i	0.170571	−	0.204457i
$484$	6.57751	−	8.83513i	0.298978	−	0.401597i
$485$	20.9136			0.949639
$486$	−6.89087	−	10.1594i	−0.312576	−	0.460842i
$487$	27.8890			1.26377			0.631885	−	0.775062i	$-0.282282\pi$
$487$	27.8890			1.26377			0.631885	+	0.775062i	$0.282282\pi$
$488$	−12.5883	+	16.9090i	−0.569844	+	0.765434i
$489$	7.49049	−	8.97855i	0.338732	−	0.406024i
$490$	11.2145	+	37.4591i	0.506620	+	1.69223i
$491$	−18.1734	−	11.9528i	−0.820155	−	0.539424i	0.0686871	−	0.997638i	$-0.478119\pi$
$491$	−18.1734	−	11.9528i	−0.820155	−	0.539424i	−0.888842	+	0.458214i	$0.848489\pi$
$492$	−0.0688660	−	0.286930i	−0.00310472	−	0.0129358i
$493$	−17.4985	−	18.5474i	−0.788094	−	0.835331i
$494$	3.42489	+	1.24656i	0.154093	+	0.0560853i
$495$	11.0677	−	9.39472i	0.497458	−	0.422261i
$496$	3.66730	−	1.33479i	0.164667	−	0.0599338i
$497$	−54.2932	−	27.2671i	−2.43538	−	1.22310i
$498$	−4.15052	−	1.77638i	−0.185989	−	0.0796015i
$499$	−1.18204	+	2.74029i	−0.0529156	+	0.122672i	−0.942623	−	0.333859i	$-0.891649\pi$
$499$	−1.18204	+	2.74029i	−0.0529156	+	0.122672i	0.889707	+	0.456531i	$0.150908\pi$
$500$	8.54969	−	0.999316i	0.382354	−	0.0446908i
$501$	−28.8274	+	8.71974i	−1.28791	+	0.389569i
$502$	−7.01176	+	4.61171i	−0.312950	+	0.205831i
$503$	−30.5223	−	25.6113i	−1.36092	−	1.14195i	−0.975696	−	0.219128i	$-0.929679\pi$
$503$	−30.5223	−	25.6113i	−1.36092	−	1.14195i	−0.385227	−	0.922822i	$-0.625877\pi$
$504$	−33.1136	+	22.0500i	−1.47500	+	0.982185i
$505$	−4.82249	+	4.04655i	−0.214598	+	0.180069i
$506$	0.266041	−	0.888640i	0.0118270	−	0.0395049i
$507$	−14.3263	+	0.875298i	−0.636255	+	0.0388734i
$508$	12.8861	−	6.47167i	0.571730	−	0.287134i
$509$	13.6753	−	14.4950i	0.606147	−	0.642479i	−0.349519	−	0.936929i	$-0.613655\pi$
$509$	13.6753	−	14.4950i	0.606147	−	0.642479i	0.955667	+	0.294451i	$0.0951366\pi$
$510$	14.5587	−	8.46074i	0.644669	−	0.374648i
$511$	4.22444	+	9.79336i	0.186878	+	0.433233i
$512$	−3.70618	−	6.41930i	−0.163792	−	0.283695i
$513$	−10.8921	+	2.01653i	−0.480899	+	0.0890319i
$514$	0.462869	−	0.801713i	0.0204163	−	0.0353620i
$515$	−0.741079	−	0.0866197i	−0.0326559	−	0.00381692i
$516$	−2.06517	+	5.72461i	−0.0909140	+	0.252012i
$517$	2.87088	+	0.680411i	0.126261	+	0.0299244i
$518$	−0.173175	+	2.97330i	−0.00760887	+	0.130639i
$519$	21.8332	−	9.49165i	0.958371	−	0.416637i
$520$	15.6636	−	3.71234i	0.686893	−	0.162797i
$521$	−6.17183	−	35.0022i	−0.270393	−	1.53347i	−0.753226	−	0.657762i	$-0.771503\pi$
$521$	−6.17183	−	35.0022i	−0.270393	−	1.53347i	0.482833	−	0.875713i	$-0.339608\pi$
$522$	−11.4000	−	7.40539i	−0.498966	−	0.324125i
$523$	4.17875	−	23.6989i	0.182724	−	1.03628i	−0.746121	−	0.665810i	$-0.768086\pi$
$523$	4.17875	−	23.6989i	0.182724	−	1.03628i	0.928845	−	0.370469i	$-0.120803\pi$
$524$	1.07917	+	18.5286i	0.0471437	+	0.809425i
$525$	10.7525	+	21.2591i	0.469278	+	0.927822i
$526$	4.38888	+	5.89528i	0.191364	+	0.257047i
$527$	15.5617	+	20.9031i	0.677880	+	0.910551i
$528$	1.09247	−	1.67135i	0.0475435	−	0.0727360i
$529$	1.31059	+	22.5020i	0.0569824	+	0.978350i
$530$	−3.82623	+	21.6996i	−0.166201	+	0.942571i
$531$	20.9939	+	27.8675i	0.911059	+	1.20934i
$532$	2.54496	+	14.4332i	0.110338	+	0.625757i
$533$	0.260820	−	0.0618155i	0.0112974	−	0.00267753i
$534$	0.776324	−	6.80975i	0.0335948	−	0.294687i
$535$	−1.61328	+	27.6989i	−0.0697481	+	1.19753i
$536$	1.20541	+	0.285687i	0.0520656	+	0.0123398i
$537$	−3.69560	+	0.662475i	−0.159477	+	0.0285879i
$538$	−1.95726	−	0.228770i	−0.0843833	−	0.00986299i
$539$	−15.4805	+	26.8130i	−0.666792	+	1.15492i
$540$	−14.4110	+	13.8303i	−0.620149	+	0.595161i
$541$	5.32644	+	9.22567i	0.229002	+	0.396642i	0.957512	−	0.288392i	$-0.0931206\pi$
$541$	5.32644	+	9.22567i	0.229002	+	0.396642i	−0.728511	+	0.685034i	$0.759787\pi$
$542$	1.72328	+	3.99501i	0.0740212	+	0.171600i
$543$	−0.113914	−	40.0591i	−0.00488853	−	1.71910i
$544$	17.7776	−	18.8431i	0.762206	−	0.807892i
$545$	33.3951	−	16.7717i	1.43049	−	0.718419i
$546$	−8.14239	−	12.3036i	−0.348462	−	0.526544i
$547$	−3.90060	+	13.0289i	−0.166777	+	0.557076i	0.833214	+	0.552951i	$0.186498\pi$
$547$	−3.90060	+	13.0289i	−0.166777	+	0.557076i	−0.999991	+	0.00412495i	$0.998687\pi$
$548$	15.1139	−	12.6821i	0.645636	−	0.541753i
$549$	23.6149	+	2.62413i	1.00786	+	0.111995i
$550$	2.89293	+	2.42746i	0.123355	+	0.103507i
$551$	−10.2487	+	6.74066i	−0.436609	+	0.287162i
$552$	−0.712276	+	3.04388i	−0.0303165	+	0.129556i
$553$	−34.7056	+	4.05651i	−1.47583	+	0.172500i
$554$	8.33224	−	19.3163i	0.354003	−	0.820671i
$555$	0.435556	+	3.63670i	0.0184883	+	0.154369i
$556$	0.399291	+	0.200531i	0.0169337	+	0.00850443i
$557$	4.31357	−	1.57001i	0.182772	−	0.0665235i	−0.249013	−	0.968500i	$-0.580106\pi$
$557$	4.31357	−	1.57001i	0.182772	−	0.0665235i	0.431785	+	0.901977i	$0.357884\pi$
$558$	10.6933	+	8.86958i	0.452683	+	0.375479i
$559$	−5.19480	−	1.89075i	−0.219717	−	0.0799704i
$560$	6.32115	+	6.70003i	0.267117	+	0.283128i
$561$	12.7836	+	3.78758i	0.539724	+	0.159912i
$562$	−20.7129	−	13.6231i	−0.873720	−	0.574655i
$563$	−0.284251	−	0.949463i	−0.0119797	−	0.0400151i	0.951791	−	0.306748i	$-0.0992410\pi$
$563$	−0.284251	−	0.949463i	−0.0119797	−	0.0400151i	−0.963770	+	0.266733i	$0.914056\pi$
$564$	−3.99964	−	0.693522i	−0.168415	−	0.0292026i
$565$	−0.667271	+	0.896301i	−0.0280723	+	0.0377077i
$566$	5.26940			0.221489
$567$	40.2977	+	19.6675i	1.69234	+	0.825958i
$568$	32.4565			1.36185
$569$	−4.63945	+	6.23186i	−0.194496	+	0.261253i	−0.888663	−	0.458560i	$-0.848365\pi$
$569$	−4.63945	+	6.23186i	−0.194496	+	0.261253i	0.694167	+	0.719814i	$0.255773\pi$
$570$	−2.79216	−	7.60404i	−0.116951	−	0.318498i
$571$	−6.13681	−	20.4984i	−0.256818	−	0.857830i	−0.985016	−	0.172464i	$-0.944827\pi$
$571$	−6.13681	−	20.4984i	−0.256818	−	0.857830i	0.728198	−	0.685367i	$-0.240358\pi$
$572$	4.34760	+	2.85946i	0.181782	+	0.119560i
$573$	−27.5004	+	26.0935i	−1.14884	+	1.09007i
$574$	−0.332436	−	0.352362i	−0.0138756	−	0.0147073i
$575$	1.75912	+	0.640267i	0.0733604	+	0.0267010i
$576$	4.86603	−	8.54001i	0.202751	−	0.355834i
$577$	−8.13925	+	2.96244i	−0.338841	+	0.123328i	−0.505836	−	0.862630i	$-0.668816\pi$
$577$	−8.13925	+	2.96244i	−0.338841	+	0.123328i	0.166995	+	0.985958i	$0.446594\pi$
$578$	1.85622	+	0.932230i	0.0772087	+	0.0387757i
$579$	10.0021	−	7.49062i	0.415675	−	0.311300i
$580$	−8.76075	+	20.3097i	−0.363770	+	0.843314i
$581$	16.3795	−	1.91449i	0.679538	−	0.0794266i
$582$	7.46812	+	7.00577i	0.309563	+	0.290399i
$583$	−14.5767	+	9.58724i	−0.603705	+	0.397063i
$584$	−4.36471	−	3.66243i	−0.180613	−	0.151552i
$585$	−12.5260	−	13.1264i	−0.517886	−	0.542710i
$586$	2.26454	−	1.90017i	0.0935472	−	0.0784954i
$587$	−3.01536	+	10.0720i	−0.124457	+	0.415716i	−0.997396	−	0.0721128i	$-0.977026\pi$
$587$	−3.01536	+	10.0720i	−0.124457	+	0.415716i	0.872939	+	0.487829i	$0.162211\pi$
$588$	19.0095	−	38.1209i	0.783937	−	1.57208i
$589$	11.2029	−	5.62632i	0.461608	−	0.231828i
$590$	−17.5091	+	18.5585i	−0.720836	+	0.764042i
$591$	−24.6448	−	14.1354i	−1.01375	−	0.581452i
$592$	0.199531	+	0.462564i	0.00820066	+	0.0190113i
$593$	14.0175	+	24.2790i	0.575630	+	0.997020i	0.995973	+	0.0896551i	$0.0285765\pi$
$593$	14.0175	+	24.2790i	0.575630	+	0.997020i	−0.420343	+	0.907365i	$0.638090\pi$
$594$	7.09932	+	0.352748i	0.291288	+	0.0144734i
$595$	−30.7537	+	53.2669i	−1.26078	+	2.18373i
$596$	−4.21840	−	0.493060i	−0.172792	−	0.0201965i
$597$	−9.01334	−	10.6799i	−0.368891	−	0.437097i
$598$	−1.12808	−	0.267360i	−0.0461306	−	0.0109332i
$599$	1.35310	−	23.2319i	0.0552863	−	0.949229i	−0.850628	−	0.525768i	$-0.823778\pi$
$599$	1.35310	−	23.2319i	0.0552863	−	0.949229i	0.905914	−	0.423461i	$-0.139185\pi$
$600$	−10.2301	−	7.57092i	−0.417643	−	0.309082i
$601$	20.9118	−	4.95618i	0.853009	−	0.202167i	0.219222	−	0.975675i	$-0.429648\pi$
$601$	20.9118	−	4.95618i	0.853009	−	0.202167i	0.633786	+	0.773508i	$0.281500\pi$
$602$	1.73491	+	9.83915i	0.0707096	+	0.401014i
$603$	−0.408060	−	1.33533i	−0.0166175	−	0.0543788i
$604$	−3.00133	+	17.0214i	−0.122122	+	0.692589i
$605$	−1.29301	−	22.2002i	−0.0525685	−	0.902566i
$606$	−3.07762	−	0.170471i	−0.125020	−	0.00692491i
$607$	2.89262	+	3.88547i	0.117408	+	0.157706i	0.856942	−	0.515413i	$-0.172361\pi$
$607$	2.89262	+	3.88547i	0.117408	+	0.157706i	−0.739534	+	0.673119i	$0.764954\pi$
$608$	−7.44197	−	9.99631i	−0.301812	−	0.405404i
$609$	49.5801	+	2.74627i	2.00909	+	0.111284i
$610$	1.01028	+	17.3458i	0.0409050	+	0.702311i
$611$	0.640316	−	3.63141i	0.0259044	−	0.146911i
$612$	−17.8734	−	4.12885i	−0.722488	−	0.166899i
$613$	2.42381	+	13.7461i	0.0978969	+	0.555201i	0.993821	+	0.110994i	$0.0354034\pi$
$613$	2.42381	+	13.7461i	0.0978969	+	0.555201i	−0.895924	+	0.444207i	$0.853485\pi$
$614$	−22.9559	+	5.44066i	−0.926427	+	0.219567i
$615$	−0.478868	−	0.354392i	−0.0193098	−	0.0142905i
$616$	1.33940	−	22.9966i	0.0539659	−	0.926559i
$617$	19.6655	+	4.66081i	0.791704	+	0.187637i	0.606522	−	0.795067i	$-0.292564\pi$
$617$	19.6655	+	4.66081i	0.791704	+	0.187637i	0.185182	+	0.982704i	$0.440712\pi$
$618$	−0.235618	−	0.279182i	−0.00947795	−	0.0112304i
$619$	28.6674	+	3.35073i	1.15224	+	0.134677i	0.670687	−	0.741740i	$-0.265999\pi$
$619$	28.6674	+	3.35073i	1.15224	+	0.134677i	0.481552	+	0.876418i	$0.340073\pi$
$620$	11.3025	−	19.5764i	0.453917	−	0.786208i
$621$	3.36675	−	1.03932i	0.135103	−	0.0417063i
$622$	−1.75151	−	3.03370i	−0.0702290	−	0.121640i
$623$	9.91605	+	22.9880i	0.397278	+	0.920994i
$624$	−2.16471	−	1.24160i	−0.0866578	−	0.0497038i
$625$	21.3984	−	22.6810i	0.855937	−	0.907240i
$626$	−21.9728	+	11.0351i	−0.878209	+	0.441053i
$627$	2.86228	−	5.73991i	0.114308	−	0.229230i
$628$	2.30370	−	7.69490i	0.0919277	−	0.307060i
$629$	−2.57685	+	2.16223i	−0.102746	+	0.0862139i
$630$	−9.22576	+	31.4664i	−0.367563	+	1.25365i
$631$	−35.3851	−	29.6916i	−1.40866	−	1.18200i	−0.957099	−	0.289762i	$-0.906424\pi$
$631$	−35.3851	−	29.6916i	−1.40866	−	1.18200i	−0.451558	−	0.892242i	$-0.649132\pi$
$632$	15.5956	−	10.2574i	0.620359	−	0.408017i
$633$	30.2195	+	28.3486i	1.20112	+	1.12676i
$634$	21.7672	−	2.54422i	0.864487	−	0.101044i
$635$	11.5310	−	26.7319i	0.457594	−	1.06082i
$636$	19.2136	−	14.3891i	0.761869	−	0.570565i
$637$	34.5793	+	17.3664i	1.37008	+	0.688080i
$638$	7.39666	−	2.69216i	0.292836	−	0.106584i
$639$	−18.4712	−	31.5770i	−0.730710	−	1.24917i
$640$	−23.8524	−	8.68156i	−0.942848	−	0.343169i
$641$	17.0820	+	18.1058i	0.674698	+	0.715138i	0.970766	−	0.240029i	$-0.0771570\pi$
$641$	17.0820	+	18.1058i	0.674698	+	0.715138i	−0.296068	+	0.955167i	$0.595675\pi$
$642$	−9.85483	+	9.35067i	−0.388939	+	0.369041i
$643$	−1.84993	−	1.21672i	−0.0729540	−	0.0479826i	0.512508	−	0.858682i	$-0.328716\pi$
$643$	−1.84993	−	1.21672i	−0.0729540	−	0.0479826i	−0.585462	+	0.810700i	$0.699087\pi$
$644$	−1.33703	−	4.46599i	−0.0526863	−	0.175985i
$645$	4.23509	+	11.5337i	0.166756	+	0.454137i
$646$	4.44257	−	5.96741i	0.174791	−	0.234784i
$647$	26.5378			1.04331			0.521654	−	0.853157i	$-0.325315\pi$
$647$	26.5378			1.04331			0.521654	+	0.853157i	$0.325315\pi$
$648$	−23.9531	+	0.272469i	−0.940967	+	0.0107036i
$649$	−20.2024			−0.793015
$650$	2.81849	−	3.78589i	0.110550	−	0.148495i
$651$	−50.0017	−	8.67011i	−1.95972	−	0.339808i
$652$	−2.67160	−	8.92377i	−0.104628	−	0.349482i
$653$	−0.177323	−	0.116627i	−0.00693920	−	0.00456398i	0.546035	−	0.837763i	$-0.316137\pi$
$653$	−0.177323	−	0.116627i	−0.00693920	−	0.00456398i	−0.552974	+	0.833199i	$0.686507\pi$
$654$	17.5434	+	5.19785i	0.686003	+	0.203252i
$655$	25.7143	+	27.2556i	1.00474	+	1.06496i
$656$	−0.0769964	−	0.0280244i	−0.00300620	−	0.00109417i
$657$	−1.07919	+	6.33075i	−0.0421034	+	0.246986i
$658$	−6.26228	+	2.27928i	−0.244129	+	0.0888558i
$659$	−24.1950	−	12.1512i	−0.942505	−	0.473344i	−0.0899295	−	0.995948i	$-0.528664\pi$
$659$	−24.1950	−	12.1512i	−0.942505	−	0.473344i	−0.852575	+	0.522604i	$0.824960\pi$
$660$	−1.37531	−	11.4833i	−0.0535340	−	0.446986i
$661$	14.1708	−	32.8515i	0.551179	−	1.27778i	−0.383912	−	0.923370i	$-0.625423\pi$
$661$	14.1708	−	32.8515i	0.551179	−	1.27778i	0.935091	−	0.354407i	$-0.115317\pi$
$662$	−0.154155	+	0.0180181i	−0.00599140	+	0.000700294i
$663$	3.79675	−	16.2252i	0.147453	−	0.630135i
$664$	−7.36043	+	4.84103i	−0.285640	+	0.187868i
$665$	22.6665	+	19.0195i	0.878969	+	0.737543i
$666$	−1.06271	+	1.44455i	−0.0411792	+	0.0559751i
$667$	2.98902	−	2.50808i	0.115735	−	0.0971134i
$668$	−6.88127	+	22.9850i	−0.266244	+	0.889317i
$669$	−11.4379	−	17.2833i	−0.442216	−	0.668210i
$670$	0.912458	−	0.458254i	0.0352513	−	0.0177039i
$671$	−9.44115	+	10.0070i	−0.364471	+	0.386317i
$672$	0.143456	+	50.4477i	0.00553393	+	1.94606i
$673$	−11.3090	−	26.2172i	−0.435930	−	1.01060i	−0.984642	−	0.174588i	$-0.944141\pi$
$673$	−11.3090	−	26.2172i	−0.435930	−	1.01060i	0.548711	−	0.836012i	$-0.315119\pi$
$674$	7.04994	+	12.2109i	0.271554	+	0.470345i
$675$	−1.54373	+	14.2616i	−0.0594182	+	0.548928i
$676$	−5.71719	+	9.90247i	−0.219892	+	0.380864i
$677$	−14.6253	−	1.70945i	−0.562097	−	0.0656997i	−0.169700	−	0.985496i	$-0.554280\pi$
$677$	−14.6253	−	1.70945i	−0.562097	−	0.0656997i	−0.392397	+	0.919796i	$0.628354\pi$
$678$	−0.538526	+	0.0965365i	−0.0206820	+	0.00370746i
$679$	−36.3953	−	8.62584i	−1.39672	−	0.331030i
$680$	1.91053	−	32.8025i	0.0732654	−	1.25792i
$681$	−4.92679	+	43.2168i	−0.188795	+	1.65607i
$682$	−7.82757	+	1.85517i	−0.299733	+	0.0710380i
$683$	0.764140	+	4.33365i	0.0292390	+	0.165823i	0.995931	−	0.0901204i	$-0.0287252\pi$
$683$	0.764140	+	4.33365i	0.0292390	+	0.165823i	−0.966692	+	0.255943i	$0.917614\pi$
$684$	−3.44914	+	8.12271i	−0.131881	+	0.310580i
$685$	6.91695	−	39.2280i	0.264283	−	1.49882i
$686$	−2.46926	−	42.3956i	−0.0942769	−	1.61867i
$687$	−24.4247	+	37.3669i	−0.931859	+	1.42564i
$688$	1.00913	+	1.35550i	0.0384729	+	0.0516781i
$689$	13.0212	+	17.4905i	0.496068	+	0.666334i
$690$	1.16294	+	2.29929i	0.0442726	+	0.0875324i
$691$	−0.176090	−	3.02335i	−0.00669878	−	0.115014i	0.993301	−	0.115555i	$-0.0368647\pi$
$691$	−0.176090	−	3.02335i	−0.00669878	−	0.115014i	−1.00000		0.000541509i	$0.999828\pi$
$692$	3.29341	−	18.6779i	0.125197	−	0.710026i
$693$	−23.1357	+	11.7844i	−0.878852	+	0.447653i
$694$	3.08116	+	17.4741i	0.116959	+	0.663309i
$695$	0.877776	−	0.208037i	0.0332959	−	0.00789128i
$696$	−24.3275	+	10.5760i	−0.922132	+	0.400883i
$697$	0.0318129	−	0.546207i	0.00120500	−	0.0206891i
$698$	−9.08500	−	2.15318i	−0.343872	−	0.0814992i
$699$	5.36831	−	14.8808i	0.203048	−	0.562845i
$700$	18.8508	+	2.20334i	0.712493	+	0.0832785i
$701$	−21.6147	+	37.4378i	−0.816377	+	1.41401i	0.0919585	+	0.995763i	$0.470687\pi$
$701$	−21.6147	+	37.4378i	−0.816377	+	1.41401i	−0.908335	+	0.418243i	$0.862646\pi$
$702$	−0.0757854	−	8.88338i	−0.00286034	−	0.335282i
$703$	0.809112	+	1.40142i	0.0305162	+	0.0528557i
$704$	2.25419	+	5.22581i	0.0849581	+	0.196955i
$705$	−7.08580	+	4.11790i	−0.266867	+	0.155089i
$706$	10.1620	−	10.7711i	0.382453	−	0.405377i
$707$	10.0614	−	5.05304i	0.378399	−	0.190039i
$708$	27.7438	−	1.69507i	1.04267	−	0.0637045i
$709$	9.22829	−	30.8246i	0.346576	−	1.15764i	−0.590066	−	0.807355i	$-0.700898\pi$
$709$	9.22829	−	30.8246i	0.346576	−	1.15764i	0.936642	−	0.350289i	$-0.113917\pi$
$710$	20.4932	−	17.1958i	0.769095	−	0.645347i
$711$	−18.8550	−	9.33543i	−0.707117	−	0.350106i
$712$	−10.2453	−	8.59684i	−0.383959	−	0.322180i
$713$	−3.33165	+	2.19126i	−0.124771	+	0.0820633i
$714$	−28.8256	+	8.71921i	−1.07877	+	0.326308i
$715$	10.4348	−	1.21965i	0.390238	−	0.0456123i
$716$	−1.18469	+	2.74642i	−0.0442739	+	0.102638i
$717$	−34.6486	−	14.8292i	−1.29398	−	0.553808i
$718$	−6.53400	−	3.28150i	−0.243847	−	0.122464i
$719$	−9.54600	+	3.47446i	−0.356006	+	0.129576i	−0.513831	−	0.857892i	$-0.671774\pi$
$719$	−9.54600	+	3.47446i	−0.356006	+	0.129576i	0.157825	+	0.987467i	$0.449552\pi$
$720$	0.994164	+	5.45653i	0.0370503	+	0.203353i
$721$	1.25395	+	0.456400i	0.0466995	+	0.0169972i
$722$	7.81193	+	8.28016i	0.290730	+	0.308156i
$723$	5.60453	+	23.3513i	0.208435	+	0.868443i
$724$	−26.6632	−	17.5366i	−0.990929	−	0.651744i
$725$	4.55594	+	15.2179i	0.169203	+	0.565179i
$726$	6.97503	−	8.36068i	0.258868	−	0.310294i
$727$	8.41672	−	11.3056i	0.312159	−	0.419302i	−0.618161	−	0.786052i	$-0.712122\pi$
$727$	8.41672	−	11.3056i	0.312159	−	0.419302i	0.930320	+	0.366749i	$0.119529\pi$
$728$	−28.7900			−1.06703
$729$	13.8970	+	23.1490i	0.514703	+	0.857369i
$730$	−4.69629			−0.173818
$731$	−6.73840	+	9.05125i	−0.249229	+	0.334772i
$732$	12.1258	−	14.5347i	0.448182	−	0.537218i
$733$	4.50233	+	15.0388i	0.166297	+	0.555471i	0.999995	+	0.00324994i	$0.00103449\pi$
$733$	4.50233	+	15.0388i	0.166297	+	0.555471i	−0.833698	+	0.552221i	$0.813780\pi$
$734$	19.2251	+	12.6446i	0.709612	+	0.466719i
$735$	−20.0712	−	83.6266i	−0.740337	−	3.08461i
$736$	2.72033	+	2.88339i	0.100273	+	0.106283i
$737$	0.759727	+	0.276518i	0.0279849	+	0.0101857i
$738$	−0.0522842	−	0.286965i	−0.00192461	−	0.0105633i
$739$	−3.42025	+	1.24487i	−0.125816	+	0.0457933i	−0.404161	−	0.914688i	$-0.632436\pi$
$739$	−3.42025	+	1.24487i	−0.125816	+	0.0457933i	0.278345	+	0.960481i	$0.410214\pi$
$740$	2.60752	+	1.30955i	0.0958544	+	0.0481399i
$741$	−7.36963	−	3.15412i	−0.270730	−	0.115870i
$742$	15.6087	−	36.1850i	0.573013	−	1.32839i
$743$	−23.1239	+	2.70280i	−0.848334	+	0.0991560i	−0.529141	−	0.848534i	$-0.677486\pi$
$743$	−23.1239	+	2.70280i	−0.848334	+	0.0991560i	−0.319193	+	0.947690i	$0.603412\pi$
$744$	25.9490	−	7.84910i	0.951338	−	0.287762i
$745$	−7.16398	+	4.71182i	−0.262468	+	0.172628i
$746$	3.35694	+	2.81680i	0.122906	+	0.103130i
$747$	8.89872	+	4.40591i	0.325587	+	0.161204i
$748$	8.13668	−	6.82748i	0.297506	−	0.249637i
$749$	14.2320	−	47.5381i	0.520025	−	1.73700i
$750$	8.49318	−	0.518909i	0.310127	−	0.0189479i
$751$	7.05894	−	3.54513i	0.257584	−	0.129364i	−0.315322	−	0.948985i	$-0.602112\pi$
$751$	7.05894	−	3.54513i	0.257584	−	0.129364i	0.572906	+	0.819621i	$0.305816\pi$
$752$	−0.773530	+	0.819894i	−0.0282077	+	0.0298985i
$753$	15.9592	−	9.27467i	0.581586	−	0.337988i
$754$	−3.89650	−	9.03309i	−0.141902	−	0.328966i
$755$	17.4475	+	30.2200i	0.634980	+	1.09982i
$756$	30.7832	−	18.1246i	1.11958	−	0.659185i
$757$	−2.12074	+	3.67323i	−0.0770795	+	0.133506i	−0.901989	−	0.431760i	$-0.857893\pi$
$757$	−2.12074	+	3.67323i	−0.0770795	+	0.133506i	0.824909	+	0.565265i	$0.191226\pi$
$758$	−23.1397	−	2.70465i	−0.840473	−	0.0982372i
$759$	−0.692338	+	1.91915i	−0.0251303	+	0.0696606i
$760$	−15.3808	−	3.64531i	−0.557920	−	0.132229i
$761$	−2.37743	+	40.8189i	−0.0861818	+	1.47968i	0.627173	+	0.778880i	$0.284212\pi$
$761$	−2.37743	+	40.8189i	−0.0861818	+	1.47968i	−0.713354	+	0.700803i	$0.752825\pi$
$762$	13.0724	−	5.68305i	0.473565	−	0.205875i
$763$	−65.0339	+	15.4133i	−2.35438	+	0.557999i
$764$	5.24431	+	29.7420i	0.189733	+	1.07603i
$765$	−33.0009	+	16.8094i	−1.19315	+	0.607744i
$766$	−1.69387	+	9.60642i	−0.0612020

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)

\(f(q)\)	\(=\)	\(q+(0.470263 - 0.631673i) q^{2} +(-1.10956 + 1.32999i) q^{3} +(0.395743 + 1.32187i) q^{4} +(2.32750 + 1.53082i) q^{5} +(0.318331 + 1.32633i) q^{6} +(-3.41908 - 3.62402i) q^{7} +(2.50111 + 0.910331i) q^{8} +(-0.537739 - 2.95141i) q^{9} +O(q^{10})\)	\(q+(0.470263 - 0.631673i) q^{2} +(-1.10956 + 1.32999i) q^{3} +(0.395743 + 1.32187i) q^{4} +(2.32750 + 1.53082i) q^{5} +(0.318331 + 1.32633i) q^{6} +(-3.41908 - 3.62402i) q^{7} +(2.50111 + 0.910331i) q^{8} +(-0.537739 - 2.95141i) q^{9} +(2.06152 - 0.750330i) q^{10} +(1.55231 + 0.779598i) q^{11} +(-2.19718 - 0.940369i) q^{12} +(0.859891 - 1.99345i) q^{13} +(-3.89706 + 0.455501i) q^{14} +(-4.61848 + 1.39701i) q^{15} +(-0.554469 + 0.364680i) q^{16} +(-3.39468 - 2.84848i) q^{17} +(-2.11721 - 1.04827i) q^{18} +(-1.63306 + 1.37030i) q^{19} +(-1.10246 + 3.68247i) q^{20} +(8.61359 - 0.526266i) q^{21} +(1.22244 - 0.613935i) q^{22} +(0.465342 - 0.493234i) q^{23} +(-3.98587 + 2.31638i) q^{24} +(1.09345 + 2.53489i) q^{25} +(-0.854835 - 1.48062i) q^{26} +(4.52200 + 2.55959i) q^{27} +(3.43741 - 5.95378i) q^{28} +(5.71522 + 0.668013i) q^{29} +(-1.28945 + 3.57433i) q^{30} +(-5.72212 - 1.35617i) q^{31} +(-0.339908 + 5.83599i) q^{32} +(-2.75924 + 1.19954i) q^{33} +(-3.39570 + 0.804795i) q^{34} +(-2.41020 - 13.6689i) q^{35} +(3.68859 - 1.87882i) q^{36} +(0.131814 - 0.747552i) q^{37} +(0.0976137 + 1.67596i) q^{38} +(1.69716 + 3.35551i) q^{39} +(4.42779 + 5.94755i) q^{40} +(0.0737288 + 0.0990350i) q^{41} +(3.71823 - 5.68845i) q^{42} +(-0.148059 - 2.54207i) q^{43} +(-0.416216 + 2.36048i) q^{44} +(3.26650 - 7.69260i) q^{45} +(-0.0927292 - 0.525894i) q^{46} +(1.65271 - 0.391699i) q^{47} +(0.130198 - 1.14207i) q^{48} +(-1.03635 + 17.7935i) q^{49} +(2.11543 + 0.501366i) q^{50} +(7.55505 - 1.35432i) q^{51} +(2.97539 + 0.347773i) q^{52} +(-5.02192 + 8.69822i) q^{53} +(3.74336 - 1.65274i) q^{54} +(2.41957 + 4.19082i) q^{55} +(-5.25246 - 12.1766i) q^{56} +(-0.0104999 - 3.69239i) q^{57} +(3.10962 - 3.29601i) q^{58} +(-10.3931 + 5.21959i) q^{59} +(-3.67440 - 5.55220i) q^{60} +(-2.27150 + 7.58734i) q^{61} +(-3.54755 + 2.97675i) q^{62} +(-8.85739 + 12.0399i) q^{63} +(2.50983 + 2.10599i) q^{64} +(5.05301 - 3.32342i) q^{65} +(-0.539853 + 2.30704i) q^{66} +(0.462282 - 0.0540330i) q^{67} +(2.42190 - 5.61460i) q^{68} +(0.139669 + 1.16617i) q^{69} +(-9.76770 - 4.90552i) q^{70} +(11.4588 - 4.17067i) q^{71} +(1.34182 - 7.87134i) q^{72} +(-2.01159 - 0.732160i) q^{73} +(-0.410222 - 0.434809i) q^{74} +(-4.58462 - 1.35835i) q^{75} +(-2.45764 - 1.61641i) q^{76} +(-2.48219 - 8.29110i) q^{77} +(2.91770 + 0.505918i) q^{78} +(4.18797 - 5.62542i) q^{79} -1.84879 q^{80} +(-8.42167 + 3.17418i) q^{81} +0.0972297 q^{82} +(-1.97654 + 2.65495i) q^{83} +(4.10442 + 11.1778i) q^{84} +(-3.54061 - 11.8265i) q^{85} +(-1.67538 - 1.10192i) q^{86} +(-7.22985 + 6.85997i) q^{87} +(3.17281 + 3.36298i) q^{88} +(-4.72182 - 1.71860i) q^{89} +(-3.32309 - 5.68090i) q^{90} +(-10.1643 + 3.69952i) q^{91} +(0.836149 + 0.419930i) q^{92} +(8.15274 - 6.10560i) q^{93} +(0.529782 - 1.22817i) q^{94} +(-5.89863 + 0.689452i) q^{95} +(-7.38465 - 6.92748i) q^{96} +(6.27220 - 4.12529i) q^{97} +(10.7523 + 9.02224i) q^{98} +(1.46618 - 5.00072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

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