LMFDB - Embedded newform 162.2.g.a.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			103.2
Character	$\chi$	$=$	162.103
Dual form			162.2.g.a.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.686242 + 0.727374i) q^{2} +(-0.301962 + 1.70553i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(1.83788 - 0.214818i) q^{5} +(-1.44777 + 0.950764i) q^{6} +(-0.0854199 - 0.0428995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-2.81764 - 1.03001i) q^{9} +O(q^{10})$	\(q+(0.686242 + 0.727374i) q^{2} +(-0.301962 + 1.70553i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(1.83788 - 0.214818i) q^{5} +(-1.44777 + 0.950764i) q^{6} +(-0.0854199 - 0.0428995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-2.81764 - 1.03001i) q^{9} +(1.41748 + 1.18941i) q^{10} +(0.254448 + 0.589876i) q^{11} +(-1.68508 - 0.400618i) q^{12} +(-1.34720 - 0.319292i) q^{13} +(-0.0274147 - 0.0915716i) q^{14} +(-0.188593 + 3.19942i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(0.845419 - 4.79461i) q^{17} +(-1.18438 - 2.75631i) q^{18} +(0.680482 + 3.85921i) q^{19} +(0.107591 + 1.84726i) q^{20} +(0.0989597 - 0.132732i) q^{21} +(-0.254448 + 0.589876i) q^{22} +(6.15084 - 3.08907i) q^{23} +(-0.864975 - 1.50061i) q^{24} +(-1.53356 + 0.363461i) q^{25} +(-0.692260 - 1.19903i) q^{26} +(2.60752 - 4.49453i) q^{27} +(0.0477936 - 0.0827810i) q^{28} +(1.82044 - 6.08068i) q^{29} +(-2.45660 + 2.05840i) q^{30} +(0.00237360 + 0.00156114i) q^{31} +(-0.597159 - 0.802123i) q^{32} +(-1.08288 + 0.255847i) q^{33} +(4.06763 - 2.67532i) q^{34} +(-0.166207 - 0.0604945i) q^{35} +(1.19210 - 2.75298i) q^{36} +(4.08936 - 1.48841i) q^{37} +(-2.34011 + 3.14331i) q^{38} +(0.951365 - 2.20127i) q^{39} +(-1.26982 + 1.34593i) q^{40} +(5.48346 - 5.81212i) q^{41} +(0.164456 - 0.0191054i) q^{42} +(-6.66233 + 8.94907i) q^{43} +(-0.603673 + 0.219719i) q^{44} +(-5.39975 - 1.28775i) q^{45} +(6.46787 + 2.35411i) q^{46} +(-7.83630 + 5.15401i) q^{47} +(0.497919 - 1.65894i) q^{48} +(-4.17465 - 5.60753i) q^{49} +(-1.31677 - 0.866050i) q^{50} +(7.92205 + 2.88967i) q^{51} +(0.397085 - 1.32636i) q^{52} +(-5.22121 + 9.04341i) q^{53} +(5.05860 - 1.18769i) q^{54} +(0.594361 + 1.02946i) q^{55} +(0.0930107 - 0.0220439i) q^{56} +(-6.78746 - 0.00475209i) q^{57} +(5.67219 - 2.84868i) q^{58} +(1.22224 - 2.83346i) q^{59} +(-3.18304 - 0.374304i) q^{60} +(0.152155 + 2.61240i) q^{61} +(0.000493330 + 0.00279781i) q^{62} +(0.196496 + 0.208858i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-2.54459 - 0.297419i) q^{65} +(-0.929216 - 0.612088i) q^{66} +(-2.24149 - 7.48709i) q^{67} +(4.73734 + 1.12277i) q^{68} +(3.41117 + 11.4232i) q^{69} +(-0.0700562 - 0.162409i) q^{70} +(-6.01585 - 5.04790i) q^{71} +(2.82051 - 1.02211i) q^{72} +(-5.97101 + 5.01027i) q^{73} +(3.88892 + 1.95309i) q^{74} +(-0.156815 - 2.72528i) q^{75} +(-3.89224 + 0.454938i) q^{76} +(0.00357048 - 0.0613028i) q^{77} +(2.25401 - 0.818607i) q^{78} +(7.38094 + 7.82334i) q^{79} -1.85039 q^{80} +(6.87817 + 5.80437i) q^{81} +7.99056 q^{82} +(-1.46065 - 1.54820i) q^{83} +(0.126753 + 0.106510i) q^{84} +(0.523814 - 8.99354i) q^{85} +(-11.0813 + 1.29522i) q^{86} +(9.82106 + 4.94094i) q^{87} +(-0.574084 - 0.288316i) q^{88} +(-3.99341 + 3.35087i) q^{89} +(-2.76886 - 4.81135i) q^{90} +(0.101380 + 0.0850681i) q^{91} +(2.72620 + 6.32005i) q^{92} +(-0.00337930 + 0.00357683i) q^{93} +(-9.12649 - 2.16302i) q^{94} +(2.07967 + 6.94659i) q^{95} +(1.54836 - 0.776259i) q^{96} +(-16.4189 - 1.91909i) q^{97} +(1.21395 - 6.88466i) q^{98} +(-0.109365 - 1.92414i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	0.686242	+	0.727374i	0.485246	+	0.514331i
$2$	0.686242	+	0.727374i	0.485246	+	0.514331i
$3$	−0.301962	+	1.70553i	−0.174338	+	0.984686i
$3$	−0.301962	+	1.70553i	−0.174338	+	0.984686i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	1.83788	−	0.214818i	0.821926	−	0.0960693i	0.305274	−	0.952265i	$-0.401252\pi$
$5$	1.83788	−	0.214818i	0.821926	−	0.0960693i	0.516652	+	0.856195i	$0.327178\pi$
$6$	−1.44777	+	0.950764i	−0.591051	+	0.388148i
$7$	−0.0854199	−	0.0428995i	−0.0322857	−	0.0162145i	0.432583	−	0.901594i	$-0.357602\pi$
$7$	−0.0854199	−	0.0428995i	−0.0322857	−	0.0162145i	−0.464869	+	0.885380i	$0.653899\pi$
$8$	−0.766044	+	0.642788i	−0.270838	+	0.227260i
$9$	−2.81764	−	1.03001i	−0.939213	−	0.343336i
$10$	1.41748	+	1.18941i	0.448248	+	0.376124i
$11$	0.254448	+	0.589876i	0.0767189	+	0.177854i	0.952259	−	0.305291i	$-0.0987536\pi$
$11$	0.254448	+	0.589876i	0.0767189	+	0.177854i	−0.875540	+	0.483145i	$0.839494\pi$
$12$	−1.68508	−	0.400618i	−0.486442	−	0.115649i
$13$	−1.34720	−	0.319292i	−0.373646	−	0.0885558i	0.0395022	−	0.999219i	$-0.487423\pi$
$13$	−1.34720	−	0.319292i	−0.373646	−	0.0885558i	−0.413148	+	0.910664i	$0.635571\pi$
$14$	−0.0274147	−	0.0915716i	−0.00732689	−	0.0244735i
$15$	−0.188593	+	3.19942i	−0.0486945	+	0.826087i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	0.845419	−	4.79461i	0.205044	−	1.16286i	−0.692326	−	0.721585i	$-0.743414\pi$
$17$	0.845419	−	4.79461i	0.205044	−	1.16286i	0.897370	−	0.441279i	$-0.145475\pi$
$18$	−1.18438	−	2.75631i	−0.279161	−	0.649668i
$19$	0.680482	+	3.85921i	0.156113	+	0.885363i	0.957761	+	0.287566i	$0.0928460\pi$
$19$	0.680482	+	3.85921i	0.156113	+	0.885363i	−0.801648	+	0.597797i	$0.796043\pi$
$20$	0.107591	+	1.84726i	0.0240580	+	0.413061i
$21$	0.0989597	−	0.132732i	0.0215948	−	0.0289645i
$22$	−0.254448	+	0.589876i	−0.0542485	+	0.125762i
$23$	6.15084	−	3.08907i	1.28254	−	0.644116i	0.328701	−	0.944434i	$-0.393389\pi$
$23$	6.15084	−	3.08907i	1.28254	−	0.644116i	0.953839	+	0.300319i	$0.0970930\pi$
$24$	−0.864975	−	1.50061i	−0.176562	−	0.306310i
$25$	−1.53356	+	0.363461i	−0.306712	+	0.0726921i
$26$	−0.692260	−	1.19903i	−0.135763	−	0.235149i
$27$	2.60752	−	4.49453i	0.501818	−	0.864973i
$28$	0.0477936	−	0.0827810i	0.00903214	−	0.0156441i
$29$	1.82044	−	6.08068i	0.338047	−	1.12915i	−0.604925	−	0.796282i	$-0.706797\pi$
$29$	1.82044	−	6.08068i	0.338047	−	1.12915i	0.942972	−	0.332872i	$-0.108018\pi$
$30$	−2.45660	+	2.05840i	−0.448511	+	0.375811i
$31$	0.00237360	+	0.00156114i	0.000426311	+	0.000280389i	0.549722	−	0.835348i	$-0.314734\pi$
$31$	0.00237360	+	0.00156114i	0.000426311	+	0.000280389i	−0.549296	+	0.835628i	$0.685104\pi$
$32$	−0.597159	−	0.802123i	−0.105564	−	0.141797i
$33$	−1.08288	+	0.255847i	−0.188506	+	0.0445373i
$34$	4.06763	−	2.67532i	0.697593	−	0.458814i
$35$	−0.166207	−	0.0604945i	−0.0280941	−	0.0102254i
$36$	1.19210	−	2.75298i	0.198683	−	0.458830i
$37$	4.08936	−	1.48841i	0.672287	−	0.244693i	0.0167549	−	0.999860i	$-0.494667\pi$
$37$	4.08936	−	1.48841i	0.672287	−	0.244693i	0.655532	+	0.755167i	$0.272444\pi$
$38$	−2.34011	+	3.14331i	−0.379616	+	0.509913i
$39$	0.951365	−	2.20127i	0.152340	−	0.352486i
$40$	−1.26982	+	1.34593i	−0.200776	+	0.212810i
$41$	5.48346	−	5.81212i	0.856372	−	0.907701i	−0.140226	−	0.990120i	$-0.544783\pi$
$41$	5.48346	−	5.81212i	0.856372	−	0.907701i	0.996598	+	0.0824182i	$0.0262643\pi$
$42$	0.164456	−	0.0191054i	0.0253761	−	0.00294803i
$43$	−6.66233	+	8.94907i	−1.01600	+	1.36472i	−0.0863506	+	0.996265i	$0.527521\pi$
$43$	−6.66233	+	8.94907i	−1.01600	+	1.36472i	−0.929646	+	0.368455i	$0.879887\pi$
$44$	−0.603673	+	0.219719i	−0.0910072	+	0.0331239i
$45$	−5.39975	−	1.28775i	−0.804947	−	0.191967i
$46$	6.46787	+	2.35411i	0.953636	+	0.347095i
$47$	−7.83630	+	5.15401i	−1.14304	+	0.751790i	−0.972349	−	0.233534i	$-0.924971\pi$
$47$	−7.83630	+	5.15401i	−1.14304	+	0.751790i	−0.170693	+	0.985324i	$0.554601\pi$
$48$	0.497919	−	1.65894i	0.0718685	−	0.239447i
$49$	−4.17465	−	5.60753i	−0.596379	−	0.801076i
$50$	−1.31677	−	0.866050i	−0.186219	−	0.122478i
$51$	7.92205	+	2.88967i	1.10931	+	0.404635i
$52$	0.397085	−	1.32636i	0.0550658	−	0.183933i
$53$	−5.22121	+	9.04341i	−0.717189	+	1.24221i	0.244920	+	0.969543i	$0.421238\pi$
$53$	−5.22121	+	9.04341i	−0.717189	+	1.24221i	−0.962109	+	0.272664i	$0.912095\pi$
$54$	5.05860	−	1.18769i	0.688388	−	0.161625i
$55$	0.594361	+	1.02946i	0.0801436	+	0.138813i
$56$	0.0930107	−	0.0220439i	0.0124291	−	0.00294574i
$57$	−6.78746	−	0.00475209i	−0.899021	−	0.000629430i
$58$	5.67219	−	2.84868i	0.744795	−	0.374050i
$59$	1.22224	−	2.83346i	0.159121	−	0.368885i	−0.819940	−	0.572449i	$-0.805993\pi$
$59$	1.22224	−	2.83346i	0.159121	−	0.368885i	0.979062	+	0.203564i	$0.0652526\pi$
$60$	−3.18304	−	0.374304i	−0.410929	−	0.0483224i
$61$	0.152155	+	2.61240i	0.0194815	+	0.334484i	0.993941	+	0.109919i	$0.0350591\pi$
$61$	0.152155	+	2.61240i	0.0194815	+	0.334484i	−0.974459	+	0.224565i	$0.927904\pi$
$62$	0.000493330		0.00279781i	6.26529e−5		0.000355323i
$63$	0.196496	+	0.208858i	0.0247561	+	0.0263137i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	−2.54459	−	0.297419i	−0.315617	−	0.0368903i
$66$	−0.929216	−	0.612088i	−0.114379	−	0.0753428i
$67$	−2.24149	−	7.48709i	−0.273841	−	0.914693i	−0.978691	−	0.205337i	$-0.934171\pi$
$67$	−2.24149	−	7.48709i	−0.273841	−	0.914693i	0.704850	−	0.709356i	$-0.251014\pi$
$68$	4.73734	+	1.12277i	0.574487	+	0.136156i
$69$	3.41117	+	11.4232i	0.410657	+	1.37519i
$70$	−0.0700562	−	0.162409i	−0.00837332	−	0.0194115i
$71$	−6.01585	−	5.04790i	−0.713951	−	0.599076i	0.211754	−	0.977323i	$-0.432082\pi$
$71$	−6.01585	−	5.04790i	−0.713951	−	0.599076i	−0.925705	+	0.378247i	$0.876527\pi$
$72$	2.82051	−	1.02211i	0.332401	−	0.120457i
$73$	−5.97101	+	5.01027i	−0.698854	+	0.586408i	−0.921447	−	0.388504i	$-0.872992\pi$
$73$	−5.97101	+	5.01027i	−0.698854	+	0.586408i	0.222594	+	0.974911i	$0.428548\pi$
$74$	3.88892	+	1.95309i	0.452078	+	0.227042i
$75$	−0.156815	−	2.72528i	−0.0181074	−	0.314688i
$76$	−3.89224	+	0.454938i	−0.446471	+	0.0521850i
$77$	0.00357048	−	0.0613028i	0.000406894	−	0.00698611i
$78$	2.25401	−	0.818607i	0.255217	−	0.0926890i
$79$	7.38094	+	7.82334i	0.830421	+	0.880195i	0.994336	−	0.106280i	$-0.0338938\pi$
$79$	7.38094	+	7.82334i	0.830421	+	0.880195i	−0.163915	+	0.986474i	$0.552412\pi$
$80$	−1.85039			−0.206880
$81$	6.87817	+	5.80437i	0.764241	+	0.644930i
$82$	7.99056			0.882410
$83$	−1.46065	−	1.54820i	−0.160327	−	0.169937i	0.642230	−	0.766512i	$-0.278009\pi$
$83$	−1.46065	−	1.54820i	−0.160327	−	0.169937i	−0.802557	+	0.596575i	$0.796528\pi$
$84$	0.126753	+	0.106510i	0.0138299	+	0.0116212i
$85$	0.523814	−	8.99354i	0.0568156	−	0.975486i
$86$	−11.0813	+	1.29522i	−1.19493	+	0.139667i
$87$	9.82106	+	4.94094i	1.05293	+	0.529724i
$88$	−0.574084	−	0.288316i	−0.0611975	−	0.0307346i
$89$	−3.99341	+	3.35087i	−0.423300	+	0.355191i	−0.829417	−	0.558630i	$-0.811327\pi$
$89$	−3.99341	+	3.35087i	−0.423300	+	0.355191i	0.406117	+	0.913821i	$0.366883\pi$
$90$	−2.76886	−	4.81135i	−0.291863	−	0.507160i
$91$	0.101380	+	0.0850681i	0.0106275	+	0.00891756i
$92$	2.72620	+	6.32005i	0.284226	+	0.658911i
$93$	−0.00337930	+	0.00357683i	−0.000350417	+	0.000370900i
$94$	−9.12649	−	2.16302i	−0.941325	−	0.223098i
$95$	2.07967	+	6.94659i	0.213370	+	0.712705i
$96$	1.54836	−	0.776259i	0.158029	−	0.0792266i
$97$	−16.4189	−	1.91909i	−1.66709	−	0.194855i	−0.770413	−	0.637546i	$-0.779950\pi$
$97$	−16.4189	−	1.91909i	−1.66709	−	0.194855i	−0.896674	+	0.442691i	$0.854024\pi$
$98$	1.21395	−	6.88466i	0.122628	−	0.695455i
$99$	−0.109365	−	1.92414i	−0.0109916	−	0.193384i
$100$	−0.273677	−	1.55210i	−0.0273677	−	0.155210i
$101$	0.753338	+	12.9343i	0.0749600	+	1.28701i	0.800709	+	0.599053i	$0.204456\pi$
$101$	0.753338	+	12.9343i	0.0749600	+	1.28701i	−0.725749	+	0.687959i	$0.758507\pi$
$102$	3.33457	+	7.74530i	0.330171	+	0.766899i
$103$	−3.93939	+	9.13253i	−0.388159	+	0.899855i	0.606349	+	0.795199i	$0.292633\pi$
$103$	−3.93939	+	9.13253i	−0.388159	+	0.899855i	−0.994508	+	0.104656i	$0.966626\pi$
$104$	1.23725	−	0.621372i	0.121323	−	0.0609305i
$105$	0.153363	−	0.265204i	0.0149667	−	0.0258812i
$106$	−10.1610	+	2.40819i	−0.986919	+	0.233904i
$107$	2.34543	+	4.06240i	0.226741	+	0.392727i	0.956840	−	0.290614i	$-0.0938595\pi$
$107$	2.34543	+	4.06240i	0.226741	+	0.392727i	−0.730099	+	0.683341i	$0.760526\pi$
$108$	4.33532	+	2.86444i	0.417166	+	0.275631i
$109$	6.87792	−	11.9129i	0.658785	−	1.14105i	−0.322145	−	0.946690i	$-0.604404\pi$
$109$	6.87792	−	11.9129i	0.658785	−	1.14105i	0.980930	−	0.194360i	$-0.0622629\pi$
$110$	−0.340929	+	1.13878i	−0.0325063	+	0.108579i
$111$	1.30369	+	7.42396i	0.123740	+	0.704651i
$112$	0.0798620	+	0.0525260i	0.00754625	+	0.00496324i
$113$	3.48372	+	4.67944i	0.327721	+	0.440205i	0.935194	−	0.354135i	$-0.115225\pi$
$113$	3.48372	+	4.67944i	0.327721	+	0.440205i	−0.607474	+	0.794340i	$0.707817\pi$
$114$	−4.65438	−	4.94028i	−0.435923	−	0.462699i
$115$	10.6409	−	6.99865i	0.992273	−	0.652628i
$116$	5.96455	+	2.17092i	0.553794	+	0.201565i
$117$	3.46705	+	2.28728i	0.320529	+	0.211459i
$118$	2.89973	−	1.05542i	0.266942	−	0.0971589i
$119$	−0.277902	+	0.373287i	−0.0254752	+	0.0342191i
$120$	−1.91208	−	2.57212i	−0.174548	−	0.234802i
$121$	7.26545	−	7.70092i	0.660495	−	0.700084i
$122$	−1.79578	+	1.90341i	−0.162582	+	0.172327i
$123$	8.25694	+	11.1072i	0.744503	+	1.00150i
$124$	−0.00169651	+	0.00227881i	−0.000152351	+	0.000204643i
$125$	−11.4344	+	4.16179i	−1.02273	+	0.372242i
$126$	−0.0170746	+	0.286253i	−0.00152112	+	0.0255014i
$127$	−20.5123	−	7.46588i	−1.82018	−	0.662490i	−0.995262	−	0.0972332i	$-0.969001\pi$
$127$	−20.5123	−	7.46588i	−1.82018	−	0.662490i	−0.824915	−	0.565257i	$-0.808777\pi$
$128$	0.835488	−	0.549509i	0.0738474	−	0.0485702i
$129$	−13.2511	−	14.0651i	−1.16669	−	1.23836i
$130$	−1.52987	−	2.05497i	−0.134178	−	0.180232i
$131$	−3.99260	−	2.62598i	−0.348835	−	0.229433i	0.362984	−	0.931795i	$-0.381758\pi$
$131$	−3.99260	−	2.62598i	−0.348835	−	0.229433i	−0.711819	+	0.702363i	$0.752128\pi$
$132$	−0.192451	−	1.09593i	−0.0167507	−	0.0953882i
$133$	0.107431	−	0.358845i	0.00931547	−	0.0311158i
$134$	3.90771	−	6.76835i	0.337575	−	0.584696i
$135$	3.82681	−	8.82056i	0.329360	−	0.759153i
$136$	2.43429	+	4.21631i	0.208738	+	0.361545i
$137$	14.3557	−	3.40236i	1.22649	−	0.290683i	0.434192	−	0.900820i	$-0.357034\pi$
$137$	14.3557	−	3.40236i	1.22649	−	0.290683i	0.792296	+	0.610137i	$0.208886\pi$
$138$	−5.96805	+	10.3203i	−0.508034	+	0.878520i
$139$	14.8523	−	7.45913i	1.25976	−	0.632675i	0.311522	−	0.950239i	$-0.399161\pi$
$139$	14.8523	−	7.45913i	1.25976	−	0.632675i	0.948237	+	0.317564i	$0.102865\pi$
$140$	0.0700562	−	0.162409i	0.00592083	−	0.0137260i
$141$	−6.42404	−	14.9213i	−0.541002	−	1.25660i
$142$	−0.456620	−	7.83985i	−0.0383187	−	0.657906i
$143$	−0.154449	−	0.875925i	−0.0129157	−	0.0732486i
$144$	2.67901	+	1.35015i	0.223251	+	0.112513i
$145$	2.03951	−	11.5666i	0.169372	−	0.960557i
$146$	−7.74189	−	0.904897i	−0.640724	−	0.0748898i
$147$	10.8244	−	5.42672i	0.892780	−	0.447588i
$148$	1.24811	+	4.16899i	0.102594	+	0.342689i
$149$	9.15970	+	2.17089i	0.750392	+	0.177846i	0.587978	−	0.808877i	$-0.299924\pi$
$149$	9.15970	+	2.17089i	0.750392	+	0.177846i	0.162413	+	0.986723i	$0.448072\pi$
$150$	1.87468	−	1.98426i	0.153067	−	0.162014i
$151$	3.34444	+	7.75329i	0.272167	+	0.630954i	0.998403	−	0.0564913i	$-0.0179913\pi$
$151$	3.34444	+	7.75329i	0.272167	+	0.630954i	−0.726236	+	0.687445i	$0.758732\pi$
$152$	−3.00193	−	2.51892i	−0.243489	−	0.204311i
$153$	−7.32056	+	12.6387i	−0.591833	+	1.02178i
$154$	0.0470403	−	0.0394715i	0.00379061	−	0.00318070i
$155$	0.00469775	+	0.00235930i	0.000377333	+	0.000189504i
$156$	2.14223	+	1.07775i	0.171516	+	0.0862889i
$157$	4.74920	−	0.555101i	0.379027	−	0.0443019i	0.0755535	−	0.997142i	$-0.475928\pi$
$157$	4.74920	−	0.555101i	0.379027	−	0.0443019i	0.303474	+	0.952840i	$0.401854\pi$
$158$	−0.625383	+	10.7374i	−0.0497528	+	0.854222i
$159$	−13.8472	−	11.6357i	−1.09815	−	0.922769i
$160$	−1.26982	−	1.34593i	−0.100388	−	0.106405i
$161$	−0.657924			−0.0518516
$162$	0.498139	+	8.98620i	0.0391375	+	0.706023i
$163$	8.48436			0.664547			0.332273	−	0.943183i	$-0.392184\pi$
$163$	8.48436			0.664547			0.332273	+	0.943183i	$0.392184\pi$
$164$	5.48346	+	5.81212i	0.428186	+	0.453851i
$165$	−1.93525	+	0.702840i	−0.150659	+	0.0547160i
$166$	0.123760	−	2.12488i	0.00960564	−	0.164922i
$167$	−19.0481	+	2.22641i	−1.47399	+	0.172285i	−0.814822	−	0.579711i	$-0.803165\pi$
$167$	−19.0481	+	2.22641i	−1.47399	+	0.172285i	−0.659168	+	0.751996i	$0.729091\pi$
$168$	0.00951085	+	0.165289i	0.000733778	+	0.0127523i
$169$	−9.90422	−	4.97409i	−0.761863	−	0.382622i
$170$	6.90112	−	5.79073i	0.529292	−	0.444129i
$171$	2.05766	−	11.5747i	0.157353	−	0.885143i
$172$	−8.54655	−	7.17140i	−0.651668	−	0.546814i
$173$	−1.82326	−	4.22678i	−0.138620	−	0.321356i	0.834738	−	0.550647i	$-0.185619\pi$
$173$	−1.82326	−	4.22678i	−0.138620	−	0.321356i	−0.973358	+	0.229290i	$0.926360\pi$
$174$	3.14572	+	10.5343i	0.238476	+	0.798600i
$175$	0.146589	+	0.0347422i	0.0110811	+	0.00262626i
$176$	−0.184247	−	0.615428i	−0.0138881	−	0.0463896i
$177$	4.46347	+	2.94015i	0.335495	+	0.220995i
$178$	−5.17777	−	0.605195i	−0.388091	−	0.0453613i
$179$	4.23157	−	23.9984i	0.316282	−	1.79373i	−0.248654	−	0.968592i	$-0.579988\pi$
$179$	4.23157	−	23.9984i	0.316282	−	1.79373i	0.564937	−	0.825134i	$-0.308901\pi$
$180$	1.59954	−	5.31574i	0.119223	−	0.396212i
$181$	1.52052	+	8.62329i	0.113019	+	0.640964i	0.987712	+	0.156286i	$0.0499522\pi$
$181$	1.52052	+	8.62329i	0.113019	+	0.640964i	−0.874693	+	0.484678i	$0.838937\pi$
$182$	0.00769503	+	0.132119i	0.000570394	+	0.00979328i
$183$	−4.50147	−	0.529341i	−0.332758	−	0.0391300i
$184$	−2.72620	+	6.32005i	−0.200978	+	0.465920i
$185$	7.19603	−	3.61398i	0.529063	−	0.265705i
$186$	−0.00492071		3.44513e-6i	−0.000360804		2.52609e-7i
$187$	3.04334	−	0.721285i	0.222551	−	0.0527456i
$188$	−4.68965	−	8.12272i	−0.342028	−	0.592410i
$189$	−0.415547	+	0.272061i	−0.0302266	+	0.0197895i
$190$	−3.62561	+	6.27973i	−0.263029	+	0.455580i
$191$	1.28389	−	4.28848i	0.0928988	−	0.310304i	−0.898893	−	0.438169i	$-0.855627\pi$
$191$	1.28389	−	4.28848i	0.0928988	−	0.310304i	0.991792	+	0.127865i	$0.0408125\pi$
$192$	1.62718	+	0.593536i	0.117432	+	0.0428347i
$193$	3.74426	+	2.46264i	0.269518	+	0.177264i	0.677073	−	0.735916i	$-0.263248\pi$
$193$	3.74426	+	2.46264i	0.269518	+	0.177264i	−0.407555	+	0.913181i	$0.633619\pi$
$194$	−9.87143	−	13.2596i	−0.708728	−	0.951987i
$195$	1.27562	−	4.25005i	0.0913493	−	0.304352i
$196$	5.84078	−	3.84154i	0.417199	−	0.274396i
$197$	9.23931	+	3.36283i	0.658274	+	0.239592i	0.649491	−	0.760369i	$-0.274982\pi$
$197$	9.23931	+	3.36283i	0.658274	+	0.239592i	0.00878277	+	0.999961i	$0.497204\pi$
$198$	1.32452	−	1.39998i	0.0941295	−	0.0994919i
$199$	−7.93930	+	2.88967i	−0.562802	+	0.204843i	−0.607725	−	0.794147i	$-0.707918\pi$
$199$	−7.93930	+	2.88967i	−0.562802	+	0.204843i	0.0449233	+	0.998990i	$0.485696\pi$
$200$	0.941148	−	1.26418i	0.0665492	−	0.0893911i
$201$	13.4463	−	1.56210i	0.948427	−	0.110182i
$202$	−8.89111	+	9.42403i	−0.625576	+	0.663072i
$203$	−0.416360	+	0.441315i	−0.0292227	+	0.0309743i
$204$	−3.34541	+	7.74062i	−0.234225	+	0.541952i
$205$	8.82940	−	11.8599i	0.616672	−	0.828334i
$206$	−9.34613	+	3.40171i	−0.651176	+	0.237009i
$207$	−20.5126	+	2.36847i	−1.42573	+	0.164620i
$208$	1.30102	+	0.473534i	0.0902098	+	0.0328337i
$209$	−2.10331	+	1.38337i	−0.145489	+	0.0956895i
$210$	0.298146	−	0.0704415i	0.0205740	−	0.00486093i
$211$	12.6849	+	17.0387i	0.873262	+	1.17300i	0.983826	+	0.179126i	$0.0573270\pi$
$211$	12.6849	+	17.0387i	0.873262	+	1.17300i	−0.110564	+	0.993869i	$0.535266\pi$
$212$	−8.72452	−	5.73821i	−0.599203	−	0.394102i
$213$	10.4259	−	8.73592i	0.714370	−	0.598576i
$214$	−1.34535	+	4.49379i	−0.0919665	+	0.307189i
$215$	−10.3222	+	17.8785i	−0.703966	+	1.21930i
$216$	0.891552	+	5.11910i	0.0606625	+	0.348310i
$217$	−0.000135780	0	0.000235179i	−9.21737e−6	0	1.59650e-5i
$218$	13.3851	−	3.17232i	0.906550	−	0.214856i
$219$	−6.74213	−	11.6966i	−0.455591	−	0.790384i
$220$	−1.06228	+	0.533497i	−0.0716190	+	0.0359684i
$221$	−2.66983	+	6.18937i	−0.179592	+	0.416342i
$222$	−4.50535	+	6.04290i	−0.302379	+	0.405573i
$223$	1.64105	+	28.1757i	0.109893	+	1.88679i	0.381485	+	0.924375i	$0.375413\pi$
$223$	1.64105	+	28.1757i	0.109893	+	1.88679i	−0.271592	+	0.962412i	$0.587550\pi$
$224$	0.0165985	+	0.0941350i	0.00110904	+	0.00628966i
$225$	4.69539	+	0.555478i	0.313026	+	0.0370318i
$226$	−1.01303	+	5.74519i	−0.0673859	+	0.382165i
$227$	−6.40577	−	0.748727i	−0.425166	−	0.0496948i	−0.0991802	−	0.995069i	$-0.531622\pi$
$227$	−6.40577	−	0.748727i	−0.425166	−	0.0496948i	−0.325986	+	0.945375i	$0.605696\pi$
$228$	0.399400	−	6.77570i	0.0264509	−	0.448732i
$229$	3.59448	+	12.0064i	0.237530	+	0.793405i	0.990758	+	0.135645i	$0.0433106\pi$
$229$	3.59448	+	12.0064i	0.237530	+	0.793405i	−0.753228	+	0.657760i	$0.771504\pi$
$230$	12.3929	+	2.93717i	0.817163	+	0.193671i
$231$	0.103475	+	0.0246007i	0.00680818	+	0.00161860i
$232$	2.51405	+	5.82823i	0.165056	+	0.382642i
$233$	12.4844	+	10.4756i	0.817878	+	0.686281i	0.952474	−	0.304620i	$-0.0985293\pi$
$233$	12.4844	+	10.4756i	0.817878	+	0.686281i	−0.134596	+	0.990901i	$0.542974\pi$
$234$	0.715530	+	4.09147i	0.0467757	+	0.267468i
$235$	−13.2950	+	11.1558i	−0.867271	+	0.727727i
$236$	2.75760	+	1.38492i	0.179504	+	0.0901505i
$237$	−15.5717	+	10.2260i	−1.01149	+	0.664253i
$238$	−0.462227	+	0.0540266i	−0.0299617	+	0.00350202i
$239$	0.995746	−	17.0963i	0.0644095	−	1.10587i	−0.798989	−	0.601345i	$-0.794632\pi$
$239$	0.995746	−	17.0963i	0.0644095	−	1.10587i	0.863399	−	0.504522i	$-0.168331\pi$
$240$	0.558748	−	3.15589i	0.0360670	−	0.203712i
$241$	18.0715	+	19.1546i	1.16409	+	1.23386i	0.967361	+	0.253401i	$0.0815491\pi$
$241$	18.0715	+	19.1546i	1.16409	+	1.23386i	0.196725	+	0.980459i	$0.436969\pi$
$242$	10.5873			0.680578
$243$	−11.9765	+	9.97820i	−0.768290	+	0.640102i
$244$	−2.61683			−0.167525
$245$	−8.87712	−	9.40920i	−0.567138	−	0.601131i
$246$	−2.41284	+	13.6281i	−0.153837	+	0.868897i
$247$	0.315469	−	5.41640i	0.0200728	−	0.344637i
$248$	−0.00282176		0.000329817i	−0.000179182		2.09434e-5i
$249$	3.08155	−	2.02368i	0.195286	−	0.128246i
$250$	−10.8740	−	5.46111i	−0.687730	−	0.345391i
$251$	3.95236	−	3.31643i	0.249471	−	0.209331i	−0.509474	−	0.860486i	$-0.670160\pi$
$251$	3.95236	−	3.31643i	0.249471	−	0.209331i	0.758944	+	0.651155i	$0.225715\pi$
$252$	−0.219930	+	0.184019i	−0.0138543	+	0.0115921i
$253$	3.38724	+	2.84223i	0.212954	+	0.178690i
$254$	−8.64594	−	20.0435i	−0.542495	−	1.25764i
$255$	15.1805	+	3.60908i	0.950642	+	0.226009i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	8.49061	+	28.3606i	0.529630	+	1.76909i	0.632684	+	0.774410i	$0.281953\pi$
$257$	8.49061	+	28.3606i	0.529630	+	1.76909i	−0.103055	+	0.994676i	$0.532862\pi$
$258$	1.13710	−	19.2905i	0.0707926	−	1.20098i
$259$	−0.413165	−	0.0482920i	−0.0256728	−	0.00300072i
$260$	0.444871	−	2.52299i	0.0275897	−	0.156469i
$261$	−11.3925	+	15.2581i	−0.705177	+	0.944453i
$262$	−0.829824	−	4.70617i	−0.0512667	−	0.290748i
$263$	−0.0529456	−	0.909040i	−0.00326476	−	0.0560538i	0.996282	−	0.0861488i	$-0.0274561\pi$
$263$	−0.0529456	−	0.909040i	−0.00326476	−	0.0560538i	−0.999547	+	0.0300950i	$0.990419\pi$
$264$	0.665081	−	0.892054i	0.0409329	−	0.0549022i
$265$	−7.65329	+	17.7423i	−0.470138	+	1.08990i
$266$	0.334738	−	0.168112i	0.0205241	−	0.0103076i
$267$	−4.50914	−	7.82269i	−0.275955	−	0.478741i
$268$	7.60475	−	1.80236i	0.464534	−	0.110097i
$269$	3.31673	+	5.74474i	0.202224	+	0.350263i	0.949245	−	0.314538i	$-0.101850\pi$
$269$	3.31673	+	5.74474i	0.202224	+	0.350263i	−0.747020	+	0.664801i	$0.768516\pi$
$270$	9.04196	−	3.26951i	0.550276	−	0.198976i
$271$	−4.24842	+	7.35848i	−0.258073	+	0.446996i	−0.965726	−	0.259565i	$-0.916421\pi$
$271$	−4.24842	+	7.35848i	−0.258073	+	0.446996i	0.707653	+	0.706561i	$0.249754\pi$
$272$	−1.39632	+	4.66404i	−0.0846645	+	0.282799i
$273$	−0.175699	+	0.147219i	−0.0106338	+	0.00891012i
$274$	12.3262	+	8.10710i	0.744656	+	0.489768i
$275$	−0.604608	−	0.812130i	−0.0364592	−	0.0489733i
$276$	−11.6022	+	2.74120i	−0.698372	+	0.165001i
$277$	20.7636	−	13.6564i	1.24756	−	0.820535i	0.258213	−	0.966088i	$-0.416866\pi$
$277$	20.7636	−	13.6564i	1.24756	−	0.820535i	0.989351	+	0.145553i	$0.0464960\pi$
$278$	15.6179	+	5.68444i	0.936697	+	0.340930i
$279$	−0.00507996	−	0.00684355i	−0.000304129	−	0.000409713i
$280$	0.166207	−	0.0604945i	0.00993278	−	0.00361524i
$281$	8.51787	−	11.4415i	0.508134	−	0.682542i	−0.471836	−	0.881686i	$-0.656409\pi$
$281$	8.51787	−	11.4415i	0.508134	−	0.682542i	0.979970	+	0.199144i	$0.0638161\pi$
$282$	6.44493	−	14.9123i	0.383790	−	0.888015i
$283$	2.78315	−	2.94997i	0.165441	−	0.175357i	−0.639349	−	0.768917i	$-0.720796\pi$
$283$	2.78315	−	2.94997i	0.165441	−	0.175357i	0.804790	+	0.593559i	$0.202278\pi$
$284$	5.38915	−	5.71217i	0.319787	−	0.338955i
$285$	−12.4756	+	1.44933i	−0.738989	+	0.0858510i
$286$	0.531136	−	0.713439i	0.0314067	−	0.0421865i
$287$	−0.717733	+	0.261234i	−0.0423665	+	0.0154201i
$288$	0.856385	+	2.87517i	0.0504629	+	0.169421i
$289$	−6.29876	−	2.29256i	−0.370516	−	0.134857i
$290$	9.81287	−	6.45402i	0.576231	−	0.378993i
$291$	8.23094	−	27.4234i	0.482506	−	1.60759i
$292$	−4.65461	−	6.25223i	−0.272390	−	0.365884i
$293$	0.871473	+	0.573177i	0.0509120	+	0.0334853i	0.574710	−	0.818357i	$-0.305115\pi$
$293$	0.871473	+	0.573177i	0.0509120	+	0.0334853i	−0.523798	+	0.851843i	$0.675485\pi$
$294$	11.3754	+	4.14933i	0.663426	+	0.241994i
$295$	1.63765	−	5.47012i	0.0953475	−	0.318483i
$296$	−2.17591	+	3.76878i	−0.126472	+	0.219056i
$297$	3.31470	+	0.394492i	0.192338	+	0.0228907i
$298$	4.70672	+	8.15228i	0.272653	+	0.472249i
$299$	−9.27274	+	2.19768i	−0.536256	+	0.127095i
$300$	2.72979	+	0.00191120i	0.157604	+	0.000110343i
$301$	0.953006	−	0.478617i	0.0549303	−	0.0275871i
$302$	−3.34444	+	7.75329i	−0.192451	+	0.446152i
$303$	−22.2873	−	2.62083i	−1.28037	−	0.150563i
$304$	−0.227855	−	3.91211i	−0.0130684	−	0.224375i
$305$	0.840834	+	4.76860i	0.0481460	+	0.273049i
$306$	−14.2167	+	3.34841i	−0.812716	+	0.191416i
$307$	1.21262	−	6.87713i	0.0692081	−	0.392499i	−0.930452	−	0.366415i	$-0.880585\pi$
$307$	1.21262	−	6.87713i	0.0692081	−	0.392499i	0.999660	−	0.0260839i	$-0.00830371\pi$
$308$	0.0609915	+	0.00712889i	0.00347531	+	0.000406206i
$309$	−14.3862	−	9.47640i	−0.818403	−	0.539094i
$310$	0.00150770	+	0.00503607i	8.56317e−5	+	0.000286030i
$311$	−26.8911	−	6.37331i	−1.52486	−	0.361397i	−0.619139	−	0.785282i	$-0.712518\pi$
$311$	−26.8911	−	6.37331i	−1.52486	−	0.361397i	−0.905716	+	0.423884i	$0.860666\pi$
$312$	0.686163	+	2.29780i	0.0388463	+	0.130087i
$313$	−8.14092	−	18.8728i	−0.460152	−	1.06675i	−0.977492	−	0.210972i	$-0.932337\pi$
$313$	−8.14092	−	18.8728i	−0.460152	−	1.06675i	0.517340	−	0.855780i	$-0.326922\pi$
$314$	3.66286	+	3.07351i	0.206707	+	0.173448i
$315$	0.406002	+	0.341646i	0.0228756	+	0.0192496i
$316$	−8.23927	+	6.91357i	−0.463495	+	0.388919i
$317$	−6.91037	−	3.47052i	−0.388125	−	0.194924i	0.244026	−	0.969769i	$-0.421532\pi$
$317$	−6.91037	−	3.47052i	−0.388125	−	0.194924i	−0.632151	+	0.774845i	$0.717828\pi$
$318$	−1.03901	−	18.0569i	−0.0582650	−	1.01258i
$319$	4.05006	−	0.473384i	0.226760	−	0.0265044i
$320$	0.107591	−	1.84726i	0.00601451	−	0.103265i
$321$	−7.63676	+	2.77350i	−0.426243	+	0.154802i
$322$	−0.451495	−	0.478556i	−0.0251608	−	0.0266689i
$323$	19.0787			1.06157
$324$	−6.19448	+	6.52904i	−0.344138	+	0.362724i
$325$	2.18206			0.121039
$326$	5.82232	+	6.17130i	0.322469	+	0.341797i
$327$	18.2409	+	15.3277i	1.00872	+	0.847625i
$328$	−0.464610	+	7.97704i	−0.0256538	+	0.440459i
$329$	0.890480	−	0.104082i	0.0490937	−	0.00573824i
$330$	−1.83928	−	0.925333i	−0.101249	−	0.0509379i
$331$	−16.6330	−	8.35342i	−0.914234	−	0.459146i	−0.0714787	−	0.997442i	$-0.522772\pi$
$331$	−16.6330	−	8.35342i	−0.914234	−	0.459146i	−0.842756	+	0.538296i	$0.819068\pi$
$332$	1.63051	−	1.36816i	0.0894858	−	0.0750875i
$333$	−13.0554	−	0.0182810i	−0.715432	−	0.00100179i
$334$	−14.6911	−	12.3273i	−0.803859	−	0.674518i
$335$	−5.72795	−	13.2789i	−0.312951	−	0.725502i
$336$	−0.113700	+	0.120346i	−0.00620283	+	0.00656540i
$337$	−20.7662	−	4.92168i	−1.13121	−	0.268101i	−0.377949	−	0.925826i	$-0.623370\pi$
$337$	−20.7662	−	4.92168i	−1.13121	−	0.268101i	−0.753258	+	0.657726i	$0.771519\pi$
$338$	−3.17867	−	10.6175i	−0.172897	−	0.577516i
$339$	−9.03286	+	4.52856i	−0.490598	+	0.245957i
$340$	8.94786	+	1.04586i	0.485266	+	0.0567195i
$341$	−0.000316923		0.00179736i	−1.71623e−5		9.73324e-5i
$342$	9.83122	−	6.44639i	0.531611	−	0.348581i
$343$	0.232228	+	1.31703i	0.0125391	+	0.0711130i
$344$	−0.648706	−	11.1378i	−0.0349759	−	0.600512i
$345$	8.72323	+	20.2617i	0.469643	+	1.09085i
$346$	1.82326	−	4.22678i	0.0980189	−	0.227233i
$347$	3.44661	−	1.73095i	0.185024	−	0.0929225i	−0.353876	−	0.935292i	$-0.615136\pi$
$347$	3.44661	−	1.73095i	0.185024	−	0.0929225i	0.538900	+	0.842370i	$0.318840\pi$
$348$	−5.50362	+	9.51716i	−0.295025	+	0.510173i
$349$	3.81710	−	0.904669i	0.204325	−	0.0484258i	−0.127179	−	0.991880i	$-0.540592\pi$
$349$	3.81710	−	0.904669i	0.204325	−	0.0484258i	0.331504	+	0.943454i	$0.392444\pi$
$350$	0.0753248	+	0.130466i	0.00402628	+	0.00697372i
$351$	−4.94793	+	5.22248i	−0.264101	+	0.278755i
$352$	0.321208	−	0.556348i	0.0171204	−	0.0296535i
$353$	8.33521	−	27.8415i	0.443638	−	1.48186i	−0.385445	−	0.922731i	$-0.625952\pi$
$353$	8.33521	−	27.8415i	0.443638	−	1.48186i	0.829084	−	0.559125i	$-0.188863\pi$
$354$	0.924432	+	5.26426i	0.0491330	+	0.279793i
$355$	−12.1408	−	7.98514i	−0.644367	−	0.423807i
$356$	−3.11300	−	4.18149i	−0.164989	−	0.221618i
$357$	−0.552735	−	0.586687i	−0.0292538	−	0.0310508i
$358$	20.3597	−	13.3908i	1.07604	−	0.707725i
$359$	6.34158	+	2.30815i	0.334696	+	0.121819i	0.503901	−	0.863762i	$-0.331898\pi$
$359$	6.34158	+	2.30815i	0.334696	+	0.121819i	−0.169205	+	0.985581i	$0.554120\pi$
$360$	4.96420	−	2.48442i	0.261636	−	0.130940i
$361$	3.42374	−	1.24614i	0.180197	−	0.0655863i
$362$	−5.22891	+	7.02365i	−0.274826	+	0.369155i
$363$	10.9402	+	14.7168i	0.574214	+	0.772431i
$364$	−0.0908189	+	0.0962625i	−0.00476021	+	0.00504552i
$365$	−9.89771	+	10.4910i	−0.518070	+	0.549122i
$366$	−2.70407	−	3.63750i	−0.141344	−	0.190135i
$367$	6.81775	−	9.15782i	0.355884	−	0.478035i	−0.587742	−	0.809048i	$-0.699983\pi$
$367$	6.81775	−	9.15782i	0.355884	−	0.478035i	0.943626	+	0.331014i	$0.107391\pi$
$368$	−6.46787	+	2.35411i	−0.337161	+	0.122717i
$369$	−21.4369	+	10.7285i	−1.11596	+	0.558502i
$370$	7.56693	+	2.75414i	0.393386	+	0.143181i
$371$	0.833953	−	0.548499i	0.0432967	−	0.0284767i
$372$	−0.00337429	−	0.00358156i	−0.000174949	−	0.000185695i
$373$	13.0936	+	17.5877i	0.677960	+	0.910658i	0.999341	−	0.0362917i	$-0.0115545\pi$
$373$	13.0936	+	17.5877i	0.677960	+	0.910658i	−0.321381	+	0.946950i	$0.604147\pi$
$374$	2.61311	+	1.71867i	0.135121	+	0.0888703i
$375$	−3.64529	−	20.7584i	−0.188242	−	1.07196i
$376$	2.69002	−	8.98528i	0.138727	−	0.463380i
$377$	−4.39401	+	7.61065i	−0.226303	+	0.391968i
$378$	−0.483056	−	0.115558i	−0.0248457	−	0.00594369i
$379$	−0.853488	−	1.47829i	−0.0438408	−	0.0759344i	0.843272	−	0.537486i	$-0.180626\pi$
$379$	−0.853488	−	1.47829i	−0.0438408	−	0.0759344i	−0.887113	+	0.461552i	$0.847293\pi$
$380$	−7.05576	+	1.67224i	−0.361953	+	0.0857844i
$381$	18.9272	−	32.7299i	0.969670	−	1.67681i
$382$	4.00038	−	2.00907i	0.204677	−	0.102793i
$383$	−7.89013	+	18.2914i	−0.403167	+	0.934646i	0.588815	+	0.808268i	$0.299595\pi$
$383$	−7.89013	+	18.2914i	−0.403167	+	0.934646i	−0.991982	+	0.126378i	$0.959665\pi$
$384$	0.684917	+	1.59088i	0.0349520	+	0.0811841i
$385$	−0.00660680	−	0.113434i	−0.000336714	−	0.00578115i
$386$	0.778208	+	4.41344i	0.0396098	+	0.224638i
$387$	27.9896	−	18.3530i	1.42279	−	0.932935i
$388$	2.87052	−	16.2795i	0.145729	−	0.826468i
$389$	7.38106	+	0.862722i	0.374235	+	0.0437418i	0.301131	−	0.953583i	$-0.402636\pi$
$389$	7.38106	+	0.862722i	0.374235	+	0.0437418i	0.0731032	+	0.997324i	$0.476710\pi$
$390$	3.96676	−	1.98870i	0.200865	−	0.100702i
$391$	−9.61084	−	32.1024i	−0.486041	−	1.62349i
$392$	6.80242	+	1.61220i	0.343574	+	0.0814286i
$393$	5.68428	−	6.01654i	0.286734	−	0.303494i
$394$	3.89436	+	9.02815i	0.196195	+	0.454831i
$395$	15.2459	+	12.7928i	0.767104	+	0.643677i
$396$	1.92725	+	0.00269864i	0.0968477	+	0.000135612i
$397$	7.09210	−	5.95098i	0.355942	−	0.298671i	−0.447229	−	0.894420i	$-0.647589\pi$
$397$	7.09210	−	5.95098i	0.355942	−	0.298671i	0.803171	+	0.595749i	$0.203145\pi$
$398$	−7.55015	−	3.79183i	−0.378455	−	0.190067i
$399$	0.579580	+	0.291584i	0.0290153	+	0.0145975i
$400$	1.56539	−	0.182967i	0.0782693	−	0.00914837i
$401$	1.79505	−	30.8199i	0.0896407	−	1.53907i	−0.591130	−	0.806576i	$-0.701318\pi$
$401$	1.79505	−	30.8199i	0.0896407	−	1.53907i	0.680771	−	0.732496i	$-0.261645\pi$
$402$	10.3636	+	8.70848i	0.516890	+	0.434340i
$403$	−0.00269925	−	0.00286104i	−0.000134459	−	0.000142519i
$404$	−12.9562			−0.644597
$405$	13.8881	+	9.19020i	0.690108	+	0.456665i
$406$	−0.606724			−0.0301112
$407$	1.91851	+	2.03350i	0.0950968	+	0.100797i
$408$	−7.92608	+	2.87858i	−0.392400	+	0.142511i
$409$	−1.96913	+	33.8086i	−0.0973670	+	1.67173i	0.497166	+	0.867656i	$0.334374\pi$
$409$	−1.96913	+	33.8086i	−0.0973670	+	1.67173i	−0.594533	+	0.804071i	$0.702663\pi$
$410$	14.6857	−	1.71651i	0.725276	−	0.0847726i
$411$	1.46795	+	25.5114i	0.0724085	+	1.25838i
$412$	−8.88802	−	4.46373i	−0.437881	−	0.219912i
$413$	−0.225957	+	0.189600i	−0.0111186	+	0.00932963i
$414$	−15.7994	−	13.2950i	−0.776497	−	0.653413i
$415$	−3.01708	−	2.53163i	−0.148103	−	0.124273i
$416$	0.548381	+	1.27129i	0.0268866	+	0.0623301i
$417$	8.23690	+	27.5834i	0.403363	+	1.35077i
$418$	−2.44960	−	0.580566i	−0.119814	−	0.0283964i
$419$	−2.43636	−	8.13801i	−0.119024	−	0.397568i	0.877627	−	0.479345i	$-0.159126\pi$
$419$	−2.43636	−	8.13801i	−0.119024	−	0.397568i	−0.996651	+	0.0817769i	$0.973941\pi$
$420$	0.255838	+	0.168524i	0.0124836	+	0.00822312i
$421$	−29.0779	−	3.39872i	−1.41717	−	0.165644i	−0.627234	−	0.778831i	$-0.715813\pi$
$421$	−29.0779	−	3.39872i	−1.41717	−	0.165644i	−0.789937	+	0.613188i	$0.789887\pi$
$422$	−3.68864	+	20.9193i	−0.179560	+	1.01834i
$423$	27.3885	−	6.45071i	1.33168	−	0.313644i
$424$	−1.81331	−	10.2838i	−0.0880621	−	0.499425i
$425$	0.446150	+	7.66010i	0.0216415	+	0.371569i
$426$	13.5090	+	1.58856i	0.654511	+	0.0769659i
$427$	0.0990737	−	0.229679i	0.00479451	−	0.0111149i
$428$	−4.19190	+	2.10525i	−0.202623	+	0.101761i
$429$	1.54055	+	0.00107858i	0.0743785	+	5.20745e-5i
$430$	−20.0879	+	4.76091i	−0.968722	+	0.229591i
$431$	5.10804	+	8.84738i	0.246045	+	0.426163i	0.962425	−	0.271548i	$-0.0875354\pi$
$431$	5.10804	+	8.84738i	0.246045	+	0.426163i	−0.716380	+	0.697711i	$0.754202\pi$
$432$	−3.11167	+	4.16143i	−0.149711	+	0.200217i
$433$	6.10277	−	10.5703i	0.293280	−	0.507976i	−0.681303	−	0.732001i	$-0.738586\pi$
$433$	6.10277	−	10.5703i	0.293280	−	0.507976i	0.974583	+	0.224025i	$0.0719197\pi$
$434$	7.78845e−5	0	0.000260152i	3.73858e−6	0	1.24877e-5i
$435$	19.1114	+	6.97112i	0.916319	+	0.334240i
$436$	11.4928	+	7.55896i	0.550407	+	0.362009i
$437$	16.1069	+	21.6353i	0.770497	+	1.03496i
$438$	3.88108	−	12.9308i	0.185445	−	0.617855i
$439$	18.7061	−	12.3032i	0.892793	−	0.587199i	−0.0181027	−	0.999836i	$-0.505763\pi$
$439$	18.7061	−	12.3032i	0.892793	−	0.587199i	0.910896	+	0.412637i	$0.135392\pi$
$440$	−1.11703	−	0.406567i	−0.0532525	−	0.0193823i
$441$	5.98687	+	20.0999i	0.285089	+	0.957139i
$442$	−6.33413	+	2.30544i	−0.301284	+	0.109658i
$443$	−13.1848	+	17.7103i	−0.626431	+	0.841443i	−0.996147	−	0.0877021i	$-0.972048\pi$
$443$	−13.1848	+	17.7103i	−0.626431	+	0.841443i	0.369716	+	0.929145i	$0.379455\pi$
$444$	−7.48720	+	0.869815i	−0.355327	+	0.0412796i
$445$	−6.61959	+	7.01635i	−0.313799	+	0.332607i
$446$	−19.3681	+	20.5290i	−0.917108	+	0.972078i
$447$	−6.46838	+	14.9666i	−0.305944	+	0.707895i
$448$	−0.0570807	+	0.0766727i	−0.00269681	+	0.00362245i
$449$	13.6831	−	4.98026i	0.645747	−	0.235033i	0.00167637	−	0.999999i	$-0.499466\pi$
$449$	13.6831	−	4.98026i	0.645747	−	0.235033i	0.644071	+	0.764966i	$0.277244\pi$
$450$	2.81813	+	3.79649i	0.132848	+	0.178968i
$451$	4.82369	+	1.75568i	0.227139	+	0.0826717i
$452$	−4.87409	+	3.20574i	−0.229258	+	0.150785i
$453$	−14.2333	+	3.36284i	−0.668741	+	0.158000i
$454$	−3.85130	−	5.17319i	−0.180750	−	0.242790i
$455$	0.204599	+	0.134567i	0.00959175	+	0.00630859i
$456$	5.20255	−	4.35925i	0.243632	−	0.204141i
$457$	6.87963	−	22.9796i	0.321815	−	1.07494i	−0.632106	−	0.774882i	$-0.717809\pi$
$457$	6.87963	−	22.9796i	0.321815	−	1.07494i	0.953921	−	0.300057i	$-0.0970056\pi$
$458$	−6.26645	+	10.8538i	−0.292812	+	0.507165i
$459$	−19.3451	−	16.3018i	−0.902951	−	0.760903i
$460$	6.36810	+	11.0299i	0.296914	+	0.514270i
$461$	−5.26464	+	1.24774i	−0.245199	+	0.0581132i	−0.351377	−	0.936234i	$-0.614287\pi$
$461$	−5.26464	+	1.24774i	−0.245199	+	0.0581132i	0.106179	+	0.994347i	$0.466138\pi$
$462$	0.0531153	+	0.0921473i	0.00247115	+	0.00428708i
$463$	−25.1069	+	12.6091i	−1.16681	+	0.585996i	−0.923367	−	0.383918i	$-0.874575\pi$
$463$	−25.1069	+	12.6091i	−1.16681	+	0.585996i	−0.243447	+	0.969914i	$0.578278\pi$
$464$	−2.51405	+	5.82823i	−0.116712	+	0.270569i
$465$	−0.00544239	+	0.00729972i	−0.000252385	+	0.000338517i
$466$	0.947597	+	16.2696i	0.0438966	+	0.753675i
$467$	−4.25830	−	24.1500i	−0.197051	−	1.11753i	−0.909468	−	0.415774i	$-0.863511\pi$
$467$	−4.25830	−	24.1500i	−0.197051	−	1.11753i	0.712418	−	0.701756i	$-0.247600\pi$
$468$	−2.48500	+	3.32819i	−0.114869	+	0.153846i
$469$	−0.129725	+	0.735705i	−0.00599013	+	0.0339717i
$470$	−17.2381	−	2.01484i	−0.795132	−	0.0929376i
$471$	−0.487335	+	8.26750i	−0.0224552	+	0.380946i
$472$	0.885026	+	2.95619i	0.0407366	+	0.136070i
$473$	−6.97406	−	1.65288i	−0.320668	−	0.0759996i
$474$	−18.1241	−	4.30889i	−0.832467	−	0.197914i
$475$	−2.44623	−	5.67100i	−0.112241	−	0.260203i
$476$	−0.356497	−	0.299136i	−0.0163400	−	0.0137109i
$477$	24.0263	−	20.1032i	1.10009	−	0.920461i
$478$	13.1187	−	11.0079i	0.600036	−	0.503490i
$479$	29.6240	+	14.8777i	1.35355	+	0.679780i	0.969856	−	0.243678i	$-0.0783541\pi$
$479$	29.6240	+	14.8777i	1.35355	+	0.679780i	0.383698	+	0.923459i	$0.374650\pi$
$480$	2.67895	−	1.75929i	0.122277	−	0.0803001i
$481$	−5.98443	+	0.699480i	−0.272867	+	0.0318935i
$482$	−1.53119	+	26.2894i	−0.0697436	+	1.19745i
$483$	0.198668	−	1.12211i	0.00903969	−	0.0510576i
$484$	7.26545	+	7.70092i	0.330248	+	0.350042i
$485$	−30.5883			−1.38894
$486$	−15.4766	−	1.86390i	−0.702034	−	0.0845482i
$487$	−23.7318			−1.07539			−0.537695	−	0.843140i	$-0.680705\pi$
$487$	−23.7318			−1.07539			−0.537695	+	0.843140i	$0.680705\pi$
$488$	−1.79578	−	1.90341i	−0.0812911	−	0.0861635i
$489$	−2.56195	+	14.4703i	−0.115855	+	0.654370i
$490$	0.752153	−	12.9140i	0.0339788	−	0.583393i
$491$	−2.11340	+	0.247021i	−0.0953765	+	0.0111479i	−0.163647	−	0.986519i	$-0.552326\pi$
$491$	−2.11340	+	0.247021i	−0.0953765	+	0.0111479i	0.0682708	+	0.997667i	$0.478252\pi$
$492$	−11.5685	+	7.59714i	−0.521549	+	0.342506i
$493$	−27.6155	−	13.8690i	−1.24374	−	0.624629i
$494$	4.15623	−	3.48749i	0.186998	−	0.156910i
$495$	−0.614340	−	3.51285i	−0.0276125	−	0.157891i
$496$	−0.00217631	−	0.00182614i	−9.77193e−5	−	8.19962e-5i
$497$	0.297321	+	0.689268i	0.0133367	+	0.0309179i
$498$	3.58666	+	0.852707i	0.160722	+	0.0382107i
$499$	14.6923	+	3.48213i	0.657717	+	0.155882i	0.545904	−	0.837848i	$-0.316186\pi$
$499$	14.6923	+	3.48213i	0.657717	+	0.155882i	0.111813	+	0.993729i	$0.464334\pi$
$500$	−3.48990	−	11.6571i	−0.156073	−	0.521320i
$501$	1.95461	−	33.1594i	0.0873256	−	1.48145i
$502$	5.12456	+	0.598975i	0.228720	+	0.0267336i
$503$	2.86626	−	16.2554i	0.127800	−	0.724791i	−0.851805	−	0.523859i	$-0.824492\pi$
$503$	2.86626	−	16.2554i	0.127800	−	0.724791i	0.979605	−	0.200932i	$-0.0643971\pi$
$504$	−0.284776	−	0.0336898i	−0.0126849	−	0.00150066i
$505$	4.16307	+	23.6099i	0.185254	+	1.05063i
$506$	0.257100	+	4.41424i	0.0114295	+	0.196237i
$507$	11.4741	−	15.3899i	0.509584	−	0.683491i
$508$	8.64594	−	20.0435i	0.383602	−	0.889288i
$509$	−29.7920	+	14.9621i	−1.32051	+	0.663183i	−0.962689	−	0.270610i	$-0.912775\pi$
$509$	−29.7920	+	14.9621i	−1.32051	+	0.663183i	−0.357816	+	0.933792i	$0.616478\pi$
$510$	7.79237	+	13.5186i	0.345052	+	0.598615i
$511$	0.724981	−	0.171824i	0.0320713	−	0.00760103i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	19.1197	+	7.00452i	0.844156	+	0.309257i
$514$	−14.8021	+	25.6381i	−0.652895	+	1.13085i
$515$	−5.27830	+	17.6308i	−0.232590	+	0.776904i
$516$	14.8117	−	12.4109i	0.652051	−	0.546358i
$517$	−5.03416	−	3.31102i	−0.221402	−	0.145618i
$518$	−0.248405	−	0.333665i	−0.0109143	−	0.0146604i
$519$	7.75944	−	1.83329i	0.340602	−	0.0804723i
$520$	2.14044	−	1.40779i	0.0938647	−	0.0617358i
$521$	−14.5717	−	5.30368i	−0.638399	−	0.232358i	0.00248380	−	0.999997i	$-0.499209\pi$
$521$	−14.5717	−	5.30368i	−0.638399	−	0.232358i	−0.640883	+	0.767639i	$0.721432\pi$
$522$	−18.9163	+	2.18416i	−0.827946	+	0.0955980i
$523$	−3.81870	+	1.38989i	−0.166980	+	0.0607758i	−0.424158	−	0.905588i	$-0.639430\pi$
$523$	−3.81870	+	1.38989i	−0.166980	+	0.0607758i	0.257177	+	0.966364i	$0.417208\pi$
$524$	2.85368	−	3.83316i	0.124664	−	0.167452i
$525$	−0.103518	+	0.239520i	−0.00451789	+	0.0104535i
$526$	0.624878	−	0.662332i	0.0272460	−	0.0288791i
$527$	0.00949174	−	0.0100607i	0.000413467	−	0.000438249i
$528$	1.10526	−	0.128402i	0.0481004	−	0.00558800i
$529$	14.5559	−	19.5519i	0.632864	−	0.850084i
$530$	−18.1573	+	6.60872i	−0.788703	+	0.287064i
$531$	−6.36230	+	6.72475i	−0.276100	+	0.291829i
$532$	0.351992	+	0.128114i	0.0152608	+	0.00555447i
$533$	−9.24309	+	6.07927i	−0.400362	+	0.263323i
$534$	2.59567	−	8.64808i	0.112325	−	0.374239i
$535$	5.18330	+	6.96238i	0.224093	+	0.301010i
$536$	6.52969	+	4.29464i	0.282040	+	0.185500i
$537$	39.6522	+	14.4637i	1.71112	+	0.624153i
$538$	−1.90250	+	6.35478i	−0.0820224	+	0.273974i
$539$	2.24552	−	3.88935i	0.0967214	−	0.167526i
$540$	8.58313	+	4.33321i	0.369359	+	0.186472i
$541$	−5.89817	−	10.2159i	−0.253582	−	0.439217i	0.710927	−	0.703265i	$-0.248275\pi$
$541$	−5.89817	−	10.2159i	−0.253582	−	0.439217i	−0.964509	+	0.264048i	$0.914942\pi$
$542$	−8.26781	+	1.95951i	−0.355133	+	0.0841680i
$543$	−15.1664	−	0.0106184i	−0.650852	−	0.000455680i
$544$	−4.35072	+	2.18501i	−0.186535	+	0.0936816i
$545$	10.0817	−	23.3720i	0.431853	−	1.00115i
$546$	−0.227655	−	0.0267707i	−0.00974275	−	0.00114568i
$547$	1.77358	+	30.4511i	0.0758326	+	1.30200i	0.794766	+	0.606916i	$0.207594\pi$
$547$	1.77358	+	30.4511i	0.0758326	+	1.30200i	−0.718933	+	0.695079i	$0.755369\pi$
$548$	2.56189	+	14.5292i	0.109439	+	0.620657i
$549$	2.26208	−	7.51753i	0.0965430	−	0.320840i
$550$	0.175814	−	0.997093i	0.00749675	−	0.0425162i
$551$	24.7054	+	2.88765i	1.05248	+	0.123018i
$552$	−9.95580	−	6.55802i	−0.423747	−	0.279128i
$553$	−0.294862	−	0.984908i	−0.0125388	−	0.0418825i
$554$	24.1822	+	5.73128i	1.02740	+	0.243499i
$555$	3.99082	+	13.3643i	0.169401	+	0.567283i
$556$	6.58292	+	15.2609i	0.279178	+	0.647207i
$557$	8.21928	+	6.89680i	0.348262	+	0.292227i	0.800092	−	0.599878i	$-0.204784\pi$
$557$	8.21928	+	6.89680i	0.348262	+	0.292227i	−0.451830	+	0.892104i	$0.649229\pi$
$558$	0.00149174	−	0.00839136i	6.31504e−5	−	0.000355234i
$559$	11.8329	−	9.92896i	0.500477	−	0.419950i
$560$	0.158060	+	0.0793809i	0.00667927	+	0.00335446i
$561$	0.311198	+	5.40830i	0.0131388	+	0.228339i
$562$	14.1676	−	1.65595i	0.597622	−	0.0698520i
$563$	1.78771	−	30.6939i	0.0753432	−	1.29359i	−0.722772	−	0.691087i	$-0.757132\pi$
$563$	1.78771	−	30.6939i	0.0753432	−	1.29359i	0.798115	−	0.602505i	$-0.205831\pi$
$564$	15.2696	−	5.54558i	0.642966	−	0.233511i
$565$	7.40789	+	7.85190i	0.311652	+	0.330332i
$566$	4.05565			0.170471
$567$	−0.338528	−	0.790879i	−0.0142168	−	0.0332138i
$568$	7.85314			0.329510
$569$	−15.4655	−	16.3925i	−0.648347	−	0.687208i	0.316926	−	0.948450i	$-0.397349\pi$
$569$	−15.4655	−	16.3925i	−0.648347	−	0.687208i	−0.965273	+	0.261242i	$0.915868\pi$
$570$	−9.61546	−	8.07981i	−0.402747	−	0.338426i
$571$	1.00671	−	17.2845i	0.0421294	−	0.723334i	−0.909428	−	0.415862i	$-0.863480\pi$
$571$	1.00671	−	17.2845i	0.0421294	−	0.723334i	0.951557	−	0.307472i	$-0.0994831\pi$
$572$	0.883424	−	0.103257i	0.0369378	−	0.00431741i
$573$	6.92643	+	3.48466i	0.289356	+	0.145574i
$574$	−0.682553	−	0.342791i	−0.0284892	−	0.0143078i
$575$	−8.30994	+	6.97287i	−0.346548	+	0.290789i
$576$	−1.50364	+	2.59597i	−0.0626515	+	0.108166i
$577$	−5.34742	−	4.48702i	−0.222616	−	0.186797i	0.524658	−	0.851313i	$-0.324193\pi$
$577$	−5.34742	−	4.48702i	−0.222616	−	0.186797i	−0.747274	+	0.664516i	$0.768638\pi$
$578$	−2.65492	−	6.15481i	−0.110430	−	0.256006i
$579$	−5.33071	+	5.64231i	−0.221537	+	0.234486i
$580$	11.4285	+	2.70860i	0.474542	+	0.112469i
$581$	0.0583517	+	0.194908i	0.00242083	+	0.00808615i
$582$	25.5955	−	12.8321i	1.06097	−	0.531907i
$583$	−6.66302	−	0.778795i	−0.275954	−	0.0322544i
$584$	1.35352	−	7.67618i	0.0560090	−	0.317643i
$585$	6.86338	+	3.45896i	0.283766	+	0.143010i
$586$	0.181127	+	1.02722i	0.00748230	+	0.0424342i
$587$	0.582916	+	10.0083i	0.0240595	+	0.413086i	0.988738	+	0.149656i	$0.0478167\pi$
$587$	0.582916	+	10.0083i	0.0240595	+	0.413086i	−0.964679	+	0.263430i	$0.915146\pi$
$588$	4.78816	+	11.1216i	0.197460	+	0.458647i
$589$	−0.00440957	+	0.0102225i	−0.000181693	+	0.000421212i
$590$	5.10264	−	2.56264i	0.210073	−	0.105502i
$591$	−8.52532	+	14.7424i	−0.350685	+	0.606423i
$592$	−4.23451	+	1.00360i	−0.174037	+	0.0412476i
$593$	−22.8981	−	39.6606i	−0.940311	−	1.62867i	−0.764878	−	0.644176i	$-0.777201\pi$
$593$	−22.8981	−	39.6606i	−0.940311	−	1.62867i	−0.175434	−	0.984491i	$-0.556133\pi$
$594$	1.98774	+	2.68174i	0.0815580	+	0.110033i
$595$	−0.430562	+	0.745755i	−0.0176513	+	0.0305730i
$596$	−2.69980	+	9.01797i	−0.110588	+	0.369391i
$597$	−2.53104	−	14.4133i	−0.103589	−	0.589895i
$598$	−7.96187	−	5.23661i	−0.325585	−	0.214141i
$599$	0.572891	+	0.769526i	0.0234077	+	0.0314420i	0.813673	−	0.581323i	$-0.197465\pi$
$599$	0.572891	+	0.769526i	0.0234077	+	0.0314420i	−0.790265	+	0.612765i	$0.790057\pi$
$600$	1.87190	+	1.98689i	0.0764201	+	0.0811143i
$601$	−15.2900	+	10.0564i	−0.623693	+	0.410210i	−0.821643	−	0.570003i	$-0.806942\pi$
$601$	−15.2900	+	10.0564i	−0.623693	+	0.410210i	0.197949	+	0.980212i	$0.436572\pi$
$602$	1.00213	+	0.364744i	0.0408436	+	0.0148659i
$603$	−1.39605	+	23.4047i	−0.0568516	+	0.953111i
$604$	−7.93464	+	2.88797i	−0.322856	+	0.117510i
$605$	11.6987	−	15.7141i	0.475621	−	0.638870i
$606$	−13.3881	−	18.0097i	−0.543856	−	0.731595i
$607$	14.5943	−	15.4691i	0.592366	−	0.627871i	−0.359955	−	0.932970i	$-0.617208\pi$
$607$	14.5943	−	15.4691i	0.592366	−	0.627871i	0.952321	+	0.305098i	$0.0986894\pi$
$608$	2.68920	−	2.85039i	0.109062	−	0.115599i
$609$	−0.626950	−	0.843372i	−0.0254053	−	0.0341752i
$610$	−2.89154	+	3.88401i	−0.117075	+	0.157259i
$611$	12.2027	−	4.44142i	0.493669	−	0.179681i
$612$	−12.1917	−	8.04305i	−0.492818	−	0.325121i
$613$	26.0835	+	9.49362i	1.05350	+	0.383444i	0.809984	−	0.586452i	$-0.199476\pi$
$613$	26.0835	+	9.49362i	1.05350	+	0.383444i	0.243519	+	0.969896i	$0.421698\pi$
$614$	5.83440	−	3.83734i	0.235457	−	0.154863i
$615$	17.5613	+	18.6400i	0.708140	+	0.751638i
$616$	0.0366696	+	0.0492558i	0.00147746	+	0.00198457i
$617$	18.7062	+	12.3033i	0.753085	+	0.495311i	0.867079	−	0.498170i	$-0.165994\pi$
$617$	18.7062	+	12.3033i	0.753085	+	0.495311i	−0.113995	+	0.993481i	$0.536365\pi$
$618$	−2.97954	−	16.9673i	−0.119855	−	0.682523i
$619$	3.91251	−	13.0687i	0.157257	−	0.525275i	−0.842656	−	0.538452i	$-0.819009\pi$
$619$	3.91251	−	13.0687i	0.157257	−	0.525275i	0.999913	+	0.0131772i	$0.00419457\pi$
$620$	−0.00262846	+	0.00455263i	−0.000105561	+	0.000182838i
$621$	2.15453	−	35.7000i	0.0864585	−	1.43259i
$622$	−13.8180	−	23.9335i	−0.554052	−	0.959647i
$623$	0.484867	−	0.114916i	0.0194258	−	0.00460399i
$624$	−1.20048	+	2.07594i	−0.0480578	+	0.0831042i
$625$	−13.0791	+	6.56857i	−0.523164	+	0.262743i
$626$	8.14092	−	18.8728i	0.325377	−	0.754308i
$627$	−1.72425	−	4.00497i	−0.0688599	−	0.159943i
$628$	0.278021	+	4.77344i	0.0110942	+	0.190481i
$629$	−3.67910	−	20.8652i	−0.146695	−	0.831951i
$630$	0.0301111	+	0.529767i	0.00119966	+	0.0211064i
$631$	−7.39656	+	41.9480i	−0.294453	+	1.66992i	0.374966	+	0.927038i	$0.377654\pi$
$631$	−7.39656	+	41.9480i	−0.294453	+	1.66992i	−0.669419	+	0.742885i	$0.733457\pi$
$632$	−10.6829	−	1.24865i	−0.424942	−	0.0496686i
$633$	−32.8904	+	16.4893i	−1.30727	+	0.655392i
$634$	−2.21782	−	7.40803i	−0.0880809	−	0.294211i
$635$	−39.3031	−	9.31500i	−1.55970	−	0.369655i
$636$	12.4211	−	13.1472i	0.492530	−	0.521320i
$637$	3.83365	+	8.88741i	0.151895	+	0.352132i
$638$	3.12365	+	2.62105i	0.123666	+	0.103768i
$639$	11.7511	+	20.4195i	0.464867	+	0.807784i
$640$	1.41748	−	1.18941i	0.0560310	−	0.0470156i
$641$	−13.9867	−	7.02436i	−0.552440	−	0.277446i	0.150602	−	0.988595i	$-0.451879\pi$
$641$	−13.9867	−	7.02436i	−0.552440	−	0.277446i	−0.703042	+	0.711149i	$0.748175\pi$
$642$	−7.25804	−	3.65149i	−0.286452	−	0.144113i
$643$	−6.41606	+	0.749930i	−0.253025	+	0.0295743i	−0.241660	−	0.970361i	$-0.577692\pi$
$643$	−6.41606	+	0.749930i	−0.253025	+	0.0295743i	−0.0113650	+	0.999935i	$0.503618\pi$
$644$	0.0382549	−	0.656811i	0.00150745	−	0.0258820i
$645$	−27.3754	−	23.0033i	−1.07790	−	0.905756i
$646$	13.0926	+	13.8773i	0.515121	+	0.545996i
$647$	12.8813			0.506417			0.253209	−	0.967412i	$-0.418514\pi$
$647$	12.8813			0.506417			0.253209	+	0.967412i	$0.418514\pi$
$648$	−8.99996	−	0.0252046i	−0.353552	−	0.000990130i
$649$	1.98239			0.0778155
$650$	1.49742	+	1.58718i	0.0587338	+	0.0622542i
$651$	0.000442104	0	0.000160562i	1.73274e−5	0	6.29292e-6i
$652$	−0.493322	+	8.47001i	−0.0193200	+	0.331711i
$653$	42.1106	−	4.92202i	1.64791	−	0.192614i	0.759130	−	0.650939i	$-0.225625\pi$
$653$	42.1106	−	4.92202i	1.64791	−	0.192614i	0.888784	+	0.458326i	$0.151551\pi$
$654$	1.36870	+	23.7865i	0.0535202	+	0.930125i
$655$	−7.90204	−	3.96855i	−0.308758	−	0.155064i
$656$	−6.12113	+	5.13623i	−0.238990	+	0.200536i
$657$	21.9848	−	7.96695i	0.857707	−	0.310820i
$658$	0.686791	+	0.576286i	0.0267739	+	0.0224660i
$659$	14.2014	+	32.9225i	0.553208	+	1.28248i	0.933819	+	0.357745i	$0.116454\pi$
$659$	14.2014	+	32.9225i	0.553208	+	1.28248i	−0.380611	+	0.924735i	$0.624286\pi$
$660$	−0.589126	−	1.97284i	−0.0229317	−	0.0767928i
$661$	17.4665	+	4.13964i	0.679369	+	0.161013i	0.555792	−	0.831322i	$-0.312415\pi$
$661$	17.4665	+	4.13964i	0.679369	+	0.161013i	0.123577	+	0.992335i	$0.460563\pi$
$662$	−5.33822	−	17.8309i	−0.207476	−	0.693018i
$663$	−9.74994	−	6.42242i	−0.378656	−	0.249426i
$664$	2.11409	+	0.247101i	0.0820425	+	0.00958939i
$665$	0.120360	−	0.682593i	0.00466735	−	0.0264698i
$666$	−8.94587	−	9.50871i	−0.346646	−	0.368455i
$667$	−7.58643	−	43.0248i	−0.293748	−	1.66593i
$668$	−1.11509	−	19.1454i	−0.0431442	−	0.740757i
$669$	−48.5500	−	5.70914i	−1.87705	−	0.220728i
$670$	5.72795	−	13.2789i	0.221290	−	0.513008i
$671$	−1.50228	+	0.754473i	−0.0579949	+	0.0291261i
$672$	−0.165562		0.000115915i	−0.00638669		4.47151e-6i
$673$	−42.4250	+	10.0549i	−1.63537	+	0.387589i	−0.942692	−	0.333663i	$-0.891715\pi$
$673$	−42.4250	+	10.0549i	−1.63537	+	0.387589i	−0.692673	+	0.721252i	$0.743567\pi$
$674$	−10.6707	−	18.4822i	−0.411021	−	0.711909i
$675$	−2.36521	+	7.84037i	−0.0910369	+	0.301776i
$676$	5.54155	−	9.59825i	0.213137	−	0.369163i
$677$	−9.25729	+	30.9215i	−0.355787	+	1.18841i	0.573548	+	0.819172i	$0.305567\pi$
$677$	−9.25729	+	30.9215i	−0.355787	+	1.18841i	−0.929335	+	0.369238i	$0.879619\pi$
$678$	−9.49268	−	3.46258i	−0.364564	−	0.132980i
$679$	1.32017	+	0.868291i	0.0506636	+	0.0333219i
$680$	5.37967	+	7.22615i	0.206301	+	0.277110i
$681$	3.21127	−	10.6991i	0.123056	−	0.409991i
$682$	−0.00152484	+	0.00100290i	−5.83890e−5	+	3.84031e-5i
$683$	−7.75469	−	2.82248i	−0.296725	−	0.107999i	0.189368	−	0.981906i	$-0.439356\pi$
$683$	−7.75469	−	2.82248i	−0.296725	−	0.107999i	−0.486093	+	0.873907i	$0.661578\pi$
$684$	11.4355	+	2.72719i	0.437248	+	0.104277i
$685$	25.6532	−	9.33698i	0.980157	−	0.356748i
$686$	−0.798609	+	1.07272i	−0.0304910	+	0.0409566i
$687$	−21.5626	+	2.50501i	−0.822665	+	0.0955719i
$688$	7.65621	−	8.11511i	0.291890	−	0.309386i
$689$	9.92152	−	10.5162i	0.377980	−	0.400635i
$690$	−8.75160	+	20.2495i	−0.333168	+	0.770885i
$691$	−5.62712	+	7.55853i	−0.214066	+	0.287540i	−0.896166	−	0.443718i	$-0.853659\pi$
$691$	−5.62712	+	7.55853i	−0.214066	+	0.287540i	0.682101	+	0.731258i	$0.261067\pi$
$692$	4.32565	−	1.57441i	0.164436	−	0.0598499i
$693$	−0.0732027	+	0.169052i	−0.00278074	+	0.00642174i
$694$	3.62426	+	1.31912i	0.137575	+	0.0500732i
$695$	25.6945	−	16.8995i	0.974648	−	0.641036i
$696$	−10.6993	+	2.52788i	−0.405558	+	0.0958191i
$697$	−23.2310	−	31.2047i	−0.879939	−	1.18196i
$698$	3.27748	+	2.15563i	0.124055	+	0.0815920i
$699$	−21.6362	+	18.1292i	−0.818358	+	0.685708i
$700$	−0.0432068	+	0.144321i	−0.00163306	+	0.00545481i
$701$	8.79871	−	15.2398i	0.332323	−	0.575600i	−0.650644	−	0.759383i	$-0.725501\pi$
$701$	8.79871	−	15.2398i	0.332323	−	0.575600i	0.982967	+	0.183783i	$0.0588344\pi$
$702$	−7.19417	−	0.0151105i	−0.271526	−	0.000570311i
$703$	8.52681	+	14.7689i	0.321595	+	0.557018i
$704$	0.625099	−	0.148151i	0.0235593	−	0.00558366i
$705$	−15.0120	−	26.0436i	−0.565384	−	0.980860i
$706$	25.9712	−	13.0432i	0.977438	−	0.490888i
$707$	0.490525	−	1.13717i	0.0184481	−	0.0427675i
$708$	−3.19470	+	4.28497i	−0.120064	+	0.161039i
$709$	2.54446	+	43.6868i	0.0955594	+	1.64069i	0.616684	+	0.787211i	$0.288476\pi$
$709$	2.54446	+	43.6868i	0.0955594	+	1.64069i	−0.521125	+	0.853480i	$0.674487\pi$
$710$	−2.52335	−	14.3106i	−0.0946997	−	0.537069i
$711$	−12.7387	−	29.6458i	−0.477740	−	1.11180i
$712$	0.905232	−	5.13383i	0.0339250	−	0.192398i
$713$	0.0194221	+	0.00227012i	0.000727363	+	8.50166e-5i
$714$	0.0474310	−	0.804654i	0.00177506	−	0.0301134i
$715$	−0.472024	−	1.57667i	−0.0176527	−	0.0589641i
$716$	23.7118	+	5.61980i	0.886151	+	0.210022i
$717$	28.8575	+	6.86070i	1.07770	+	0.256217i
$718$	2.67297	+	6.19665i	0.0997544	+	0.231257i
$719$	−0.280642	−	0.235486i	−0.0104662	−	0.00878215i	0.637540	−	0.770418i	$-0.279952\pi$
$719$	−0.280642	−	0.235486i	−0.0104662	−	0.00878215i	−0.648006	+	0.761635i	$0.724397\pi$
$720$	5.21374	+	1.90592i	0.194305	+	0.0710294i
$721$	0.728283	−	0.611102i	0.0271227	−	0.0227586i
$722$	3.25592	+	1.63519i	0.121173	+	0.0608553i
$723$	−38.1256	+	25.0374i	−1.41791	+	0.931151i
$724$	−8.69711	+	1.01655i	−0.323226	+	0.0377797i
$725$	−0.581662	+	9.98676i	−0.0216024	+	0.370899i
$726$	−3.19696	+	18.0569i	−0.118650	+	0.670155i
$727$	16.2157	+	17.1877i	0.601408	+	0.637455i	0.954527	−	0.298123i	$-0.0963606\pi$
$727$	16.2157	+	17.1877i	0.601408	+	0.637455i	−0.353120	+	0.935578i	$0.614879\pi$
$728$	−0.132343			−0.00490494
$729$	−13.4017	−	23.4392i	−0.496358	−	0.868118i
$730$	−14.4231			−0.533822
$731$	37.2748	+	39.5090i	1.37866	+	1.46129i
$732$	0.790183	−	4.46307i	0.0292060	−	0.164960i
$733$	−0.563137	+	9.66869i	−0.0207999	+	0.357121i	0.971809	+	0.235768i	$0.0757605\pi$
$733$	−0.563137	+	9.66869i	−0.0207999	+	0.357121i	−0.992609	+	0.121353i	$0.961277\pi$
$734$	11.3398	−	1.32543i	0.418559	−	0.0489225i
$735$	18.7282	−	12.2989i	0.690799	−	0.453653i
$736$	−6.15084	−	3.08907i	−0.226723	−	0.113865i
$737$	3.84612	−	3.22727i	0.141673	−	0.118878i
$738$	−22.5145	−	8.23033i	−0.828771	−	0.302963i
$739$	30.9774	+	25.9931i	1.13952	+	0.956172i	0.999423	−	0.0339660i	$-0.0108138\pi$
$739$	30.9774	+	25.9931i	1.13952	+	0.956172i	0.140098	+	0.990138i	$0.455258\pi$
$740$	3.18946	+	7.39399i	0.117247	+	0.271809i
$741$	9.14255	+	2.17359i	0.335860	+	0.0798487i
$742$	0.971257	+	0.230192i	0.0356560	+	0.00845062i
$743$	−0.0999801	−	0.333957i	−0.00366792	−	0.0122517i	0.956136	−	0.292923i	$-0.0946280\pi$
$743$	−0.0999801	−	0.333957i	−0.00366792	−	0.0122517i	−0.959804	+	0.280672i	$0.909443\pi$
$744$	0.000289553	−	0.00491218i	1.06155e−5	−	0.000180089i
$745$	17.3008	+	2.02217i	0.633852	+	0.0740866i
$746$	−3.80749	+	21.5934i	−0.139402	+	0.790589i
$747$	2.52093	+	5.86675i	0.0922360	+	0.214653i
$748$	0.543110	+	3.08013i	0.0198581	+	0.112621i
$749$	−0.0260713	−	0.447628i	−0.000952626	−	0.0163560i
$750$	12.5976	−	16.8968i	0.459999	−	0.616983i
$751$	17.8544	−	41.3912i	0.651518	−	1.51039i	−0.196547	−	0.980494i	$-0.562973\pi$
$751$	17.8544	−	41.3912i	0.651518	−	1.51039i	0.848064	−	0.529893i	$-0.177768\pi$
$752$	8.38166	−	4.20943i	0.305648	−	0.153502i
$753$	4.46279	+	7.74229i	0.162633	+	0.282145i
$754$	−8.55114	+	2.02666i	−0.311414	+	0.0738065i
$755$	7.81224	+	13.5312i	0.284316	+	0.492451i
$756$	−0.247439	−	0.430663i	−0.00899927	−	0.0156631i
$757$	−1.07067	+	1.85445i	−0.0389141	+	0.0674011i	−0.884826	−	0.465921i	$-0.845723\pi$
$757$	−1.07067	+	1.85445i	−0.0389141	+	0.0674011i	0.845912	+	0.533322i	$0.179057\pi$
$758$	0.489566	−	1.63527i	0.0177819	−	0.0593955i
$759$	−5.87031	+	4.91878i	−0.213079	+	0.178540i
$760$	−6.05830	−	3.98461i	−0.219758	−	0.144537i
$761$	−10.4708	−	14.0647i	−0.379565	−	0.509844i	0.570755	−	0.821121i	$-0.306651\pi$
$761$	−10.4708	−	14.0647i	−0.379565	−	0.509844i	−0.950319	+	0.311277i	$0.899243\pi$
$762$	36.7955	−	8.69350i	1.33296	−	0.314932i
$763$	−1.09857	+	0.722540i	−0.0397709	+	0.0261577i
$764$	4.20657	+	1.53107i	0.152188	+	0.0553921i
$765$	−10.7393	+	24.8010i	−0.388281	+	0.896682i
$766$	−18.7192	+	6.81323i	−0.676352	+	0.246172i
$767$	−2.55130

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.686242 + 0.727374i) q^{2} +(-0.301962 + 1.70553i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(1.83788 - 0.214818i) q^{5} +(-1.44777 + 0.950764i) q^{6} +(-0.0854199 - 0.0428995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-2.81764 - 1.03001i) q^{9} +O(q^{10})\)	\(q+(0.686242 + 0.727374i) q^{2} +(-0.301962 + 1.70553i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(1.83788 - 0.214818i) q^{5} +(-1.44777 + 0.950764i) q^{6} +(-0.0854199 - 0.0428995i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-2.81764 - 1.03001i) q^{9} +(1.41748 + 1.18941i) q^{10} +(0.254448 + 0.589876i) q^{11} +(-1.68508 - 0.400618i) q^{12} +(-1.34720 - 0.319292i) q^{13} +(-0.0274147 - 0.0915716i) q^{14} +(-0.188593 + 3.19942i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(0.845419 - 4.79461i) q^{17} +(-1.18438 - 2.75631i) q^{18} +(0.680482 + 3.85921i) q^{19} +(0.107591 + 1.84726i) q^{20} +(0.0989597 - 0.132732i) q^{21} +(-0.254448 + 0.589876i) q^{22} +(6.15084 - 3.08907i) q^{23} +(-0.864975 - 1.50061i) q^{24} +(-1.53356 + 0.363461i) q^{25} +(-0.692260 - 1.19903i) q^{26} +(2.60752 - 4.49453i) q^{27} +(0.0477936 - 0.0827810i) q^{28} +(1.82044 - 6.08068i) q^{29} +(-2.45660 + 2.05840i) q^{30} +(0.00237360 + 0.00156114i) q^{31} +(-0.597159 - 0.802123i) q^{32} +(-1.08288 + 0.255847i) q^{33} +(4.06763 - 2.67532i) q^{34} +(-0.166207 - 0.0604945i) q^{35} +(1.19210 - 2.75298i) q^{36} +(4.08936 - 1.48841i) q^{37} +(-2.34011 + 3.14331i) q^{38} +(0.951365 - 2.20127i) q^{39} +(-1.26982 + 1.34593i) q^{40} +(5.48346 - 5.81212i) q^{41} +(0.164456 - 0.0191054i) q^{42} +(-6.66233 + 8.94907i) q^{43} +(-0.603673 + 0.219719i) q^{44} +(-5.39975 - 1.28775i) q^{45} +(6.46787 + 2.35411i) q^{46} +(-7.83630 + 5.15401i) q^{47} +(0.497919 - 1.65894i) q^{48} +(-4.17465 - 5.60753i) q^{49} +(-1.31677 - 0.866050i) q^{50} +(7.92205 + 2.88967i) q^{51} +(0.397085 - 1.32636i) q^{52} +(-5.22121 + 9.04341i) q^{53} +(5.05860 - 1.18769i) q^{54} +(0.594361 + 1.02946i) q^{55} +(0.0930107 - 0.0220439i) q^{56} +(-6.78746 - 0.00475209i) q^{57} +(5.67219 - 2.84868i) q^{58} +(1.22224 - 2.83346i) q^{59} +(-3.18304 - 0.374304i) q^{60} +(0.152155 + 2.61240i) q^{61} +(0.000493330 + 0.00279781i) q^{62} +(0.196496 + 0.208858i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-2.54459 - 0.297419i) q^{65} +(-0.929216 - 0.612088i) q^{66} +(-2.24149 - 7.48709i) q^{67} +(4.73734 + 1.12277i) q^{68} +(3.41117 + 11.4232i) q^{69} +(-0.0700562 - 0.162409i) q^{70} +(-6.01585 - 5.04790i) q^{71} +(2.82051 - 1.02211i) q^{72} +(-5.97101 + 5.01027i) q^{73} +(3.88892 + 1.95309i) q^{74} +(-0.156815 - 2.72528i) q^{75} +(-3.89224 + 0.454938i) q^{76} +(0.00357048 - 0.0613028i) q^{77} +(2.25401 - 0.818607i) q^{78} +(7.38094 + 7.82334i) q^{79} -1.85039 q^{80} +(6.87817 + 5.80437i) q^{81} +7.99056 q^{82} +(-1.46065 - 1.54820i) q^{83} +(0.126753 + 0.106510i) q^{84} +(0.523814 - 8.99354i) q^{85} +(-11.0813 + 1.29522i) q^{86} +(9.82106 + 4.94094i) q^{87} +(-0.574084 - 0.288316i) q^{88} +(-3.99341 + 3.35087i) q^{89} +(-2.76886 - 4.81135i) q^{90} +(0.101380 + 0.0850681i) q^{91} +(2.72620 + 6.32005i) q^{92} +(-0.00337930 + 0.00357683i) q^{93} +(-9.12649 - 2.16302i) q^{94} +(2.07967 + 6.94659i) q^{95} +(1.54836 - 0.776259i) q^{96} +(-16.4189 - 1.91909i) q^{97} +(1.21395 - 6.88466i) q^{98} +(-0.109365 - 1.92414i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

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