LMFDB - Embedded newform 162.2.g.b.7.4

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:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	162.7
Dual form			162.2.g.b.139.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597159 + 0.802123i) q^{2} +(0.497048 + 1.65920i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-3.09160 + 2.03338i) q^{5} +(-1.03407 + 1.38950i) q^{6} +(2.90797 - 3.08226i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.50589 + 1.64940i) q^{9} +O(q^{10})$	\(q+(0.597159 + 0.802123i) q^{2} +(0.497048 + 1.65920i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-3.09160 + 2.03338i) q^{5} +(-1.03407 + 1.38950i) q^{6} +(2.90797 - 3.08226i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.50589 + 1.64940i) q^{9} +(-3.47720 - 1.26560i) q^{10} +(0.759128 - 0.381249i) q^{11} +(-1.73205 + 0.000303164i) q^{12} +(0.965987 + 2.23941i) q^{13} +(4.20887 + 0.491947i) q^{14} +(-4.91046 - 4.11890i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(4.11923 - 3.45644i) q^{17} +(-2.81944 - 1.02507i) q^{18} +(3.07959 + 2.58408i) q^{19} +(-1.06127 - 3.54490i) q^{20} +(6.55949 + 3.29286i) q^{21} +(0.759128 + 0.381249i) q^{22} +(3.04612 + 3.22870i) q^{23} +(-1.03455 - 1.38914i) q^{24} +(3.44298 - 7.98172i) q^{25} +(-1.21944 + 2.11212i) q^{26} +(-3.98224 - 3.33793i) q^{27} +(2.11876 + 3.66980i) q^{28} +(-4.35310 + 0.508805i) q^{29} +(0.371542 - 6.39843i) q^{30} +(-4.10084 + 0.971917i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(1.00989 + 1.07005i) q^{33} +(5.23232 + 1.24008i) q^{34} +(-2.72287 + 15.4421i) q^{35} +(-0.861416 - 2.87367i) q^{36} +(-0.683139 - 3.87428i) q^{37} +(-0.233749 + 4.01332i) q^{38} +(-3.23549 + 2.71586i) q^{39} +(2.20970 - 2.96814i) q^{40} +(6.04398 - 8.11847i) q^{41} +(1.27577 + 7.22788i) q^{42} +(0.482068 - 8.27679i) q^{43} +(0.147512 + 0.836580i) q^{44} +(4.39334 - 10.1947i) q^{45} +(-0.770798 + 4.37141i) q^{46} +(-4.05284 - 0.960540i) q^{47} +(0.496467 - 1.65937i) q^{48} +(-0.637071 - 10.9381i) q^{49} +(8.45833 - 2.00466i) q^{50} +(7.78238 + 5.11660i) q^{51} +(-2.42238 + 0.283136i) q^{52} +(-2.33116 - 4.03769i) q^{53} +(0.299405 - 5.18752i) q^{54} +(-1.57170 + 2.72226i) q^{55} +(-1.67840 + 3.89096i) q^{56} +(-2.75680 + 6.39407i) q^{57} +(-3.00762 - 3.18789i) q^{58} +(2.34412 + 1.17726i) q^{59} +(5.35420 - 3.52285i) q^{60} +(2.78615 + 9.30637i) q^{61} +(-3.22845 - 2.70899i) q^{62} +(-2.20313 + 12.5202i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-7.54002 - 4.95915i) q^{65} +(-0.255244 + 1.44904i) q^{66} +(-5.95198 - 0.695686i) q^{67} +(2.12983 + 4.93749i) q^{68} +(-3.84299 + 6.65895i) q^{69} +(-14.0125 + 7.03733i) q^{70} +(-8.10000 - 2.94816i) q^{71} +(1.79063 - 2.40700i) q^{72} +(-11.0832 + 4.03394i) q^{73} +(2.69970 - 2.86152i) q^{74} +(14.9546 + 1.74529i) q^{75} +(-3.35876 + 2.20909i) q^{76} +(1.03241 - 3.44849i) q^{77} +(-4.11055 - 0.973459i) q^{78} +(-3.24979 - 4.36523i) q^{79} +3.70036 q^{80} +(3.55893 - 8.26644i) q^{81} +10.1212 q^{82} +(5.59485 + 7.51519i) q^{83} +(-5.03581 + 5.33952i) q^{84} +(-5.70675 + 19.0619i) q^{85} +(6.92687 - 4.55588i) q^{86} +(-3.00791 - 6.96977i) q^{87} +(-0.582953 + 0.617894i) q^{88} +(2.76651 - 1.00693i) q^{89} +(10.8009 - 2.56386i) q^{90} +(9.71151 + 3.53470i) q^{91} +(-3.96670 + 1.99215i) q^{92} +(-3.65092 - 6.32102i) q^{93} +(-1.64971 - 3.82447i) q^{94} +(-14.7753 - 1.72698i) q^{95} +(1.62749 - 0.592681i) q^{96} +(12.7982 + 8.41752i) q^{97} +(8.39326 - 7.04278i) q^{98} +(-1.27346 + 2.20747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$2$	0.597159	+	0.802123i	0.422255	+	0.567187i
$3$	0.497048	+	1.65920i	0.286971	+	0.957939i
$3$	0.497048	+	1.65920i	0.286971	+	0.957939i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	−3.09160	+	2.03338i	−1.38261	+	0.909355i	−0.999895	−	0.0145128i	$-0.995380\pi$
$5$	−3.09160	+	2.03338i	−1.38261	+	0.909355i	−0.382712	+	0.923868i	$0.625010\pi$
$6$	−1.03407	+	1.38950i	−0.422156	+	0.567261i
$7$	2.90797	−	3.08226i	1.09911	−	1.16499i	0.113923	−	0.993490i	$-0.463658\pi$
$7$	2.90797	−	3.08226i	1.09911	−	1.16499i	0.985185	−	0.171497i	$-0.0548604\pi$
$8$	−0.939693	+	0.342020i	−0.332232	+	0.120922i
$9$	−2.50589	+	1.64940i	−0.835295	+	0.549801i
$10$	−3.47720	−	1.26560i	−1.09959	−	0.400217i
$11$	0.759128	−	0.381249i	0.228886	−	0.114951i	−0.330661	−	0.943750i	$-0.607272\pi$
$11$	0.759128	−	0.381249i	0.228886	−	0.114951i	0.559547	+	0.828799i	$0.310975\pi$
$12$	−1.73205		0.000303164i	−0.500000		8.75158e-5i
$13$	0.965987	+	2.23941i	0.267917	+	0.621101i	0.998064	−	0.0621886i	$-0.0198080\pi$
$13$	0.965987	+	2.23941i	0.267917	+	0.621101i	−0.730148	+	0.683289i	$0.760549\pi$
$14$	4.20887	+	0.491947i	1.12487	+	0.131478i
$15$	−4.91046	−	4.11890i	−1.26787	−	1.06350i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	4.11923	−	3.45644i	0.999059	−	0.838310i	0.0122051	−	0.999926i	$-0.496115\pi$
$17$	4.11923	−	3.45644i	0.999059	−	0.838310i	0.986854	+	0.161616i	$0.0516705\pi$
$18$	−2.81944	−	1.02507i	−0.664548	−	0.241612i
$19$	3.07959	+	2.58408i	0.706506	+	0.592829i	0.923616	−	0.383318i	$-0.125219\pi$
$19$	3.07959	+	2.58408i	0.706506	+	0.592829i	−0.217110	+	0.976147i	$0.569663\pi$
$20$	−1.06127	−	3.54490i	−0.237308	−	0.792664i
$21$	6.55949	+	3.29286i	1.43140	+	0.718562i
$22$	0.759128	+	0.381249i	0.161847	+	0.0812825i
$23$	3.04612	+	3.22870i	0.635161	+	0.673231i	0.962377	−	0.271718i	$-0.0875920\pi$
$23$	3.04612	+	3.22870i	0.635161	+	0.673231i	−0.327216	+	0.944950i	$0.606110\pi$
$24$	−1.03455	−	1.38914i	−0.211177	−	0.283556i
$25$	3.44298	−	7.98172i	0.688596	−	1.59634i
$26$	−1.21944	+	2.11212i	−0.239151	+	0.414222i
$27$	−3.98224	−	3.33793i	−0.766382	−	0.642385i
$28$	2.11876	+	3.66980i	0.400409	+	0.693528i
$29$	−4.35310	+	0.508805i	−0.808351	+	0.0944827i	−0.510222	−	0.860043i	$-0.670437\pi$
$29$	−4.35310	+	0.508805i	−0.808351	+	0.0944827i	−0.298129	+	0.954525i	$0.596363\pi$
$30$	0.371542	−	6.39843i	0.0678340	−	1.16819i
$31$	−4.10084	+	0.971917i	−0.736532	+	0.174561i	−0.581728	−	0.813384i	$-0.697623\pi$
$31$	−4.10084	+	0.971917i	−0.736532	+	0.174561i	−0.154805	+	0.987945i	$0.549475\pi$
$32$	−0.0581448	−	0.998308i	−0.0102787	−	0.176478i
$33$	1.00989	+	1.07005i	0.175799	+	0.186271i
$34$	5.23232	+	1.24008i	0.897336	+	0.212672i
$35$	−2.72287	+	15.4421i	−0.460248	+	2.61020i
$36$	−0.861416	−	2.87367i	−0.143569	−	0.478945i
$37$	−0.683139	−	3.87428i	−0.112307	−	0.636927i	−0.988048	−	0.154145i	$-0.950738\pi$
$37$	−0.683139	−	3.87428i	−0.112307	−	0.636927i	0.875741	−	0.482782i	$-0.160374\pi$
$38$	−0.233749	+	4.01332i	−0.0379191	+	0.651046i
$39$	−3.23549	+	2.71586i	−0.518093	+	0.434886i
$40$	2.20970	−	2.96814i	0.349384	−	0.469304i
$41$	6.04398	−	8.11847i	0.943911	−	1.26789i	−0.0194854	−	0.999810i	$-0.506203\pi$
$41$	6.04398	−	8.11847i	0.943911	−	1.26789i	0.963396	−	0.268082i	$-0.0863898\pi$
$42$	1.27577	+	7.22788i	0.196856	+	1.11529i
$43$	0.482068	−	8.27679i	0.0735147	−	1.26220i	−0.736763	−	0.676151i	$-0.763646\pi$
$43$	0.482068	−	8.27679i	0.0735147	−	1.26220i	0.810277	−	0.586047i	$-0.199316\pi$
$44$	0.147512	+	0.836580i	0.0222382	+	0.126119i
$45$	4.39334	−	10.1947i	0.654921	−	1.51974i
$46$	−0.770798	+	4.37141i	−0.113648	+	0.644530i
$47$	−4.05284	−	0.960540i	−0.591167	−	0.140109i	−0.0758654	−	0.997118i	$-0.524172\pi$
$47$	−4.05284	−	0.960540i	−0.591167	−	0.140109i	−0.515302	+	0.857009i	$0.672320\pi$
$48$	0.496467	−	1.65937i	0.0716589	−	0.239510i
$49$	−0.637071	−	10.9381i	−0.0910101	−	1.56258i
$50$	8.45833	−	2.00466i	1.19619	−	0.283502i
$51$	7.78238	+	5.11660i	1.08975	+	0.716467i
$52$	−2.42238	+	0.283136i	−0.335924	+	0.0392638i
$53$	−2.33116	−	4.03769i	−0.320210	−	0.554620i	0.660321	−	0.750983i	$-0.270420\pi$
$53$	−2.33116	−	4.03769i	−0.320210	−	0.554620i	−0.980531	+	0.196363i	$0.937087\pi$
$54$	0.299405	−	5.18752i	0.0407439	−	0.705932i
$55$	−1.57170	+	2.72226i	−0.211928	+	0.367070i
$56$	−1.67840	+	3.89096i	−0.224285	+	0.519952i
$57$	−2.75680	+	6.39407i	−0.365148	+	0.846915i
$58$	−3.00762	−	3.18789i	−0.394920	−	0.418590i
$59$	2.34412	+	1.17726i	0.305179	+	0.153266i	0.594797	−	0.803876i	$-0.297232\pi$
$59$	2.34412	+	1.17726i	0.305179	+	0.153266i	−0.289619	+	0.957142i	$0.593529\pi$
$60$	5.35420	−	3.52285i	0.691224	−	0.454798i
$61$	2.78615	+	9.30637i	0.356729	+	1.19156i	0.928558	+	0.371186i	$0.121049\pi$
$61$	2.78615	+	9.30637i	0.356729	+	1.19156i	−0.571829	+	0.820373i	$0.693766\pi$
$62$	−3.22845	−	2.70899i	−0.410013	−	0.344042i
$63$	−2.20313	+	12.5202i	−0.277569	+	1.57740i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	−7.54002	−	4.95915i	−0.935224	−	0.615107i
$66$	−0.255244	+	1.44904i	−0.0314184	+	0.178365i
$67$	−5.95198	−	0.695686i	−0.727150	−	0.0849916i	−0.255539	−	0.966799i	$-0.582253\pi$
$67$	−5.95198	−	0.695686i	−0.727150	−	0.0849916i	−0.471610	+	0.881807i	$0.656327\pi$
$68$	2.12983	+	4.93749i	0.258279	+	0.598759i
$69$	−3.84299	+	6.65895i	−0.462642	+	0.801643i
$70$	−14.0125	+	7.03733i	−1.67481	+	0.841122i
$71$	−8.10000	−	2.94816i	−0.961293	−	0.349882i	−0.186753	−	0.982407i	$-0.559796\pi$
$71$	−8.10000	−	2.94816i	−0.961293	−	0.349882i	−0.774540	+	0.632525i	$0.782019\pi$
$72$	1.79063	−	2.40700i	0.211028	−	0.283667i
$73$	−11.0832	+	4.03394i	−1.29719	+	0.472137i	−0.896079	−	0.443894i	$-0.853597\pi$
$73$	−11.0832	+	4.03394i	−1.29719	+	0.472137i	−0.401107	+	0.916031i	$0.631374\pi$
$74$	2.69970	−	2.86152i	0.313834	−	0.332645i
$75$	14.9546	+	1.74529i	1.72681	+	0.201529i
$76$	−3.35876	+	2.20909i	−0.385276	+	0.253400i
$77$	1.03241	−	3.44849i	0.117654	−	0.392992i
$78$	−4.11055	−	0.973459i	−0.465429	−	0.110223i
$79$	−3.24979	−	4.36523i	−0.365630	−	0.491126i	0.580795	−	0.814050i	$-0.302742\pi$
$79$	−3.24979	−	4.36523i	−0.365630	−	0.491126i	−0.946425	+	0.322923i	$0.895334\pi$
$80$	3.70036			0.413712
$81$	3.55893	−	8.26644i	0.395437	−	0.918493i
$82$	10.1212			1.11770
$83$	5.59485	+	7.51519i	0.614115	+	0.824900i	0.995016	−	0.0997163i	$-0.0317935\pi$
$83$	5.59485	+	7.51519i	0.614115	+	0.824900i	−0.380901	+	0.924616i	$0.624386\pi$
$84$	−5.03581	+	5.33952i	−0.549452	+	0.582589i
$85$	−5.70675	+	19.0619i	−0.618984	+	2.06755i
$86$	6.92687	−	4.55588i	0.746944	−	0.491273i
$87$	−3.00791	−	6.96977i	−0.322482	−	0.747238i
$88$	−0.582953	+	0.617894i	−0.0621430	+	0.0658677i
$89$	2.76651	−	1.00693i	0.293249	−	0.106734i	−0.191206	−	0.981550i	$-0.561240\pi$
$89$	2.76651	−	1.00693i	0.293249	−	0.106734i	0.484456	+	0.874816i	$0.339018\pi$
$90$	10.8009	−	2.56386i	1.13852	−	0.270255i
$91$	9.71151	+	3.53470i	1.01804	+	0.370537i
$92$	−3.96670	+	1.99215i	−0.413557	+	0.207696i
$93$	−3.65092	−	6.32102i	−0.378583	−	0.655459i
$94$	−1.64971	−	3.82447i	−0.170155	−	0.394464i
$95$	−14.7753	−	1.72698i	−1.51591	−	0.177185i
$96$	1.62749	−	0.592681i	0.166105	−	0.0604903i
$97$	12.7982	+	8.41752i	1.29946	+	0.854670i	0.995195	−	0.0979163i	$-0.0312177\pi$
$97$	12.7982	+	8.41752i	1.29946	+	0.854670i	0.304268	+	0.952586i	$0.401588\pi$
$98$	8.39326	−	7.04278i	0.847847	−	0.711428i
$99$	−1.27346	+	2.20747i	−0.127987	+	0.221860i
$100$	6.65895	+	5.58752i	0.665895	+	0.558752i
$101$	−1.95419	−	6.52745i	−0.194449	−	0.649506i	−0.998490	−	0.0549317i	$-0.982506\pi$
$101$	−1.95419	−	6.52745i	−0.194449	−	0.649506i	0.804041	−	0.594574i	$-0.202679\pi$
$102$	0.543171	+	9.29785i	0.0537819	+	0.920624i
$103$	9.10920	+	4.57481i	0.897556	+	0.450770i	0.836879	−	0.547388i	$-0.184378\pi$
$103$	9.10920	+	4.57481i	0.897556	+	0.450770i	0.0606772	+	0.998157i	$0.480674\pi$
$104$	−1.67365	−	1.77397i	−0.164115	−	0.173952i
$105$	−26.9750	+	3.15771i	−2.63249	+	0.308161i
$106$	1.84665	−	4.28102i	0.179363	−	0.415810i
$107$	−7.46197	+	12.9245i	−0.721376	+	1.24946i	0.239072	+	0.971002i	$0.423157\pi$
$107$	−7.46197	+	12.9245i	−0.721376	+	1.24946i	−0.960448	+	0.278458i	$0.910177\pi$
$108$	4.33982	−	2.85761i	0.417600	−	0.274974i
$109$	−4.54355	−	7.86965i	−0.435193	−	0.753776i	0.562119	−	0.827057i	$-0.309986\pi$
$109$	−4.54355	−	7.86965i	−0.435193	−	0.753776i	−0.997311	+	0.0732806i	$0.976653\pi$
$110$	−3.12215	+	0.364927i	−0.297685	+	0.0347944i
$111$	6.08864	−	3.05917i	0.577909	−	0.290363i
$112$	−4.12330	+	0.977241i	−0.389615	+	0.0923406i
$113$	0.0979757	+	1.68218i	0.00921678	+	0.158246i	0.999776	+	0.0211611i	$0.00673628\pi$
$113$	0.0979757	+	1.68218i	0.00921678	+	0.158246i	−0.990559	+	0.137085i	$0.956227\pi$
$114$	−6.77508	+	1.60698i	−0.634544	+	0.150507i
$115$	−15.9826	−	3.78794i	−1.49038	−	0.353227i
$116$	0.761055	−	4.31616i	0.0706622	−	0.400745i
$117$	−6.11435	−	4.01840i	−0.565272	−	0.371502i
$118$	0.455503	+	2.58329i	0.0419325	+	0.237811i
$119$	1.32491	−	22.7478i	0.121454	−	2.08528i
$120$	6.02307	+	2.19102i	0.549828	+	0.200012i
$121$	−6.13782	+	8.24452i	−0.557984	+	0.749502i
$122$	−5.80109	+	7.79221i	−0.525206	+	0.705474i
$123$	16.4743	+	5.99289i	1.48544	+	0.540361i
$124$	0.245048	−	4.20731i	0.0220059	−	0.377828i
$125$	2.37274	+	13.4565i	0.212225	+	1.20359i
$126$	−11.3584	+	5.70937i	−1.01188	+	0.508631i
$127$	−1.62342	+	9.20689i	−0.144056	+	0.816979i	0.824065	+	0.566495i	$0.191701\pi$
$127$	−1.62342	+	9.20689i	−0.144056	+	0.816979i	−0.968121	+	0.250484i	$0.919410\pi$
$128$	0.973045	+	0.230616i	0.0860058	+	0.0203838i
$129$	13.9725	−	3.31411i	1.23021	−	0.291792i
$130$	−0.524739	−	9.00942i	−0.0460227	−	0.790179i
$131$	9.10031	−	2.15681i	0.795098	−	0.188442i	0.187059	−	0.982349i	$-0.440105\pi$
$131$	9.10031	−	2.15681i	0.795098	−	0.188442i	0.608039	+	0.793907i	$0.291956\pi$
$132$	−1.31473	+	0.660572i	−0.114433	+	0.0574954i
$133$	16.9202	−	1.97768i	1.46716	−	0.171487i
$134$	−2.99625	−	5.18965i	−0.258836	−	0.448318i
$135$	19.0988	+	2.22216i	1.64376	+	0.191253i
$136$	−2.68863	+	4.65685i	−0.230548	+	0.399322i
$137$	1.93523	−	4.48637i	0.165338	−	0.383296i	−0.815324	−	0.579005i	$-0.803441\pi$
$137$	1.93523	−	4.48637i	0.165338	−	0.383296i	0.980662	+	0.195708i	$0.0627006\pi$
$138$	−7.63617	+	0.893895i	−0.650034	+	0.0760934i
$139$	3.51680	+	3.72759i	0.298291	+	0.316170i	0.859132	−	0.511753i	$-0.171004\pi$
$139$	3.51680	+	3.72759i	0.298291	+	0.316170i	−0.560842	+	0.827923i	$0.689522\pi$
$140$	−14.0125	−	7.03733i	−1.18427	−	0.594763i
$141$	−0.420728	−	7.20190i	−0.0354317	−	0.606509i
$142$	−2.47220	−	8.25771i	−0.207462	−	0.692972i
$143$	1.58708	+	1.33172i	0.132718	+	0.111364i
$144$	3.00000	−	0.00105019i	0.250000	−	8.75158e-5i
$145$	12.4235	−	10.4245i	1.03171	−	0.865711i
$146$	−9.85412	−	6.48116i	−0.815533	−	0.536384i
$147$	17.8318	−	6.49378i	1.47074	−	0.535598i
$148$	3.90744	+	0.456715i	0.321190	+	0.0375417i
$149$	−7.82714	−	18.1453i	−0.641224	−	1.48652i	−0.859761	−	0.510696i	$-0.829388\pi$
$149$	−7.82714	−	18.1453i	−0.641224	−	1.48652i	0.218537	−	0.975829i	$-0.429871\pi$
$150$	7.53033	+	13.0376i	0.614849	+	1.06452i
$151$	−2.82524	+	1.41889i	−0.229915	+	0.115468i	−0.560028	−	0.828474i	$-0.689209\pi$
$151$	−2.82524	+	1.41889i	−0.229915	+	0.115468i	0.330113	+	0.943941i	$0.392913\pi$
$152$	−3.77768	−	1.37496i	−0.306410	−	0.111524i
$153$	−4.62124	+	15.4557i	−0.373605	+	1.24952i
$154$	3.38263	−	1.23118i	0.272580	−	0.0992110i
$155$	10.7019	−	11.3433i	0.859596	−	0.911119i
$156$	−1.67382	−	3.87848i	−0.134013	−	0.310527i
$157$	−4.37176	+	2.87535i	−0.348904	+	0.229478i	−0.711849	−	0.702333i	$-0.752142\pi$
$157$	−4.37176	+	2.87535i	−0.348904	+	0.229478i	0.362945	+	0.931811i	$0.381771\pi$
$158$	1.56081	−	5.21347i	0.124171	−	0.414761i
$159$	5.54064	−	5.87479i	0.439401	−	0.465901i
$160$	2.20970	+	2.96814i	0.174692	+	0.234652i
$161$	18.8097			1.48242
$162$	8.75595	−	2.08167i	0.687932	−	0.163552i
$163$	−21.8143			−1.70863			−0.854313	−	0.519758i	$-0.826022\pi$
$163$	−21.8143			−1.70863			−0.854313	+	0.519758i	$0.826022\pi$
$164$	6.04398	+	8.11847i	0.471955	+	0.633946i
$165$	−5.29799	−	1.25467i	−0.412448	−	0.0976757i
$166$	−2.68710	+	8.97552i	−0.208559	+	0.696636i
$167$	−9.73624	+	6.40363i	−0.753413	+	0.495528i	−0.867189	−	0.497979i	$-0.834076\pi$
$167$	−9.73624	+	6.40363i	−0.753413	+	0.495528i	0.113776	+	0.993506i	$0.463705\pi$
$168$	−7.29013	−	0.850801i	−0.562446	−	0.0656407i
$169$	4.83931	−	5.12937i	0.372255	−	0.394567i
$170$	−18.6978	+	6.80545i	−1.43406	+	0.521954i
$171$	−11.9793	−	1.39593i	−0.916080	−	0.106749i
$172$	7.79082	+	2.83563i	0.594044	+	0.216214i
$173$	6.75404	−	3.39201i	0.513500	−	0.257889i	−0.173127	−	0.984900i	$-0.555387\pi$
$173$	6.75404	−	3.39201i	0.513500	−	0.257889i	0.686627	+	0.727010i	$0.259091\pi$
$174$	3.79441	−	6.57477i	0.287654	−	0.498432i
$175$	−14.5897	−	33.8227i	−1.10288	−	2.55676i
$176$	−0.843742	−	0.0986193i	−0.0635994	−	0.00743371i
$177$	−0.788171	+	4.47452i	−0.0592426	+	0.336326i
$178$	2.45972	+	1.61779i	0.184364	+	0.121258i
$179$	12.7702	−	10.7154i	0.954487	−	0.800910i	−0.0255605	−	0.999673i	$-0.508137\pi$
$179$	12.7702	−	10.7154i	0.954487	−	0.800910i	0.980047	+	0.198764i	$0.0636926\pi$
$180$	8.50641	+	7.13265i	0.634030	+	0.531637i
$181$	−1.90857	−	1.60148i	−0.141863	−	0.119037i	0.569095	−	0.822272i	$-0.307294\pi$
$181$	−1.90857	−	1.60148i	−0.141863	−	0.119037i	−0.710958	+	0.703235i	$0.751738\pi$
$182$	2.96405	+	9.90061i	0.219710	+	0.733882i
$183$	−14.0563	+	9.24849i	−1.03907	+	0.683668i
$184$	−3.96670	−	1.99215i	−0.292429	−	0.146863i
$185$	9.98987	+	10.5886i	0.734470	+	0.778492i
$186$	2.89006	−	6.70314i	0.211909	−	0.491498i
$187$	1.80926	−	4.19433i	0.132306	−	0.306720i
$188$	2.08255	−	3.60709i	0.151886	−	0.263074i
$189$	−21.8686	+	2.56771i	−1.59071	+	0.186774i
$190$	−7.43794	−	12.8829i	−0.539605	−	0.934622i
$191$	−0.00194585		0.000227437i	−0.000140796		1.64567e-5i	−0.116163	−	0.993230i	$-0.537060\pi$
$191$	−0.00194585		0.000227437i	−0.000140796		1.64567e-5i	0.116023	+	0.993247i	$0.462986\pi$
$192$	1.44727	+	0.951524i	0.104448	+	0.0686703i
$193$	25.5240	−	6.04931i	1.83726	−	0.435439i	0.842590	−	0.538555i	$-0.181030\pi$
$193$	25.5240	−	6.04931i	1.83726	−	0.435439i	0.994669	+	0.103116i	$0.0328814\pi$
$194$	0.890678	+	15.2923i	0.0639469	+	1.09793i
$195$	4.48046	−	14.9753i	0.320853	−	1.07241i
$196$	10.6613	+	2.52677i	0.761520	+	0.180484i
$197$	1.10535	−	6.26875i	0.0787529	−	0.446630i	−0.919778	−	0.392440i	$-0.871631\pi$
$197$	1.10535	−	6.26875i	0.0787529	−	0.446630i	0.998531	−	0.0541902i	$-0.0172577\pi$
$198$	−2.53112	+	0.296744i	−0.179879	+	0.0210887i
$199$	−2.41889	−	13.7182i	−0.171470	−	0.972456i	−0.942140	−	0.335221i	$-0.891189\pi$
$199$	−2.41889	−	13.7182i	−0.171470	−	0.972456i	0.770669	−	0.637235i	$-0.219922\pi$
$200$	−0.505432	+	8.67793i	−0.0357394	+	0.613622i
$201$	−1.80414	−	10.2213i	−0.127254	−	0.720955i
$202$	4.06886	−	5.46543i	0.286284	−	0.384546i
$203$	−11.0904	+	14.8970i	−0.778394	+	1.04557i
$204$	−7.13366	+	5.98798i	−0.499456	+	0.419242i
$205$	−2.17765	+	37.3888i	−0.152094	+	2.61135i
$206$	1.77007	+	10.0386i	0.123327	+	0.699422i
$207$	−12.9587	−	3.06647i	−0.900690	−	0.213135i
$208$	0.423506	−	2.40182i	0.0293648	−	0.166536i
$209$	3.32298	+	0.787561i	0.229855	+	0.0544767i
$210$	−18.6412	−	19.7516i	−1.28637	−	1.36299i
$211$	0.944677	+	16.2195i	0.0650342	+	1.11659i	0.860118	+	0.510095i	$0.170390\pi$
$211$	0.944677	+	16.2195i	0.0650342	+	1.11659i	−0.795084	+	0.606500i	$0.792573\pi$
$212$	4.53665	−	1.07521i	0.311579	−	0.0738455i
$213$	0.865493	−	14.9049i	0.0593026	−	1.02127i
$214$	−14.8230	+	1.73256i	−1.01328	+	0.118436i
$215$	15.3395	+	26.5688i	1.04614	+	1.81197i
$216$	4.88372	+	1.77462i	0.332295	+	0.120748i
$217$	−8.92940	+	15.4662i	−0.606167	+	1.04991i
$218$	3.59921	−	8.34392i	0.243770	−	0.565121i
$219$	−12.2020	−	16.3841i	−0.824533	−	1.10714i
$220$	−2.15713	−	2.28643i	−0.145434	−	0.154151i
$221$	11.7195	+	5.88576i	0.788339	+	0.395919i
$222$	6.08972	+	3.05704i	0.408715	+	0.205175i
$223$	3.55470	+	11.8735i	0.238040	+	0.795110i	0.990624	+	0.136614i	$0.0436220\pi$
$223$	3.55470	+	11.8735i	0.238040	+	0.795110i	−0.752584	+	0.658496i	$0.771193\pi$
$224$	−3.24613	−	2.72383i	−0.216891	−	0.181993i
$225$	4.53737	+	25.6801i	0.302492	+	1.71201i
$226$	−1.29081	+	1.08312i	−0.0858632	+	0.0720478i
$227$	−11.0359	−	7.25846i	−0.732482	−	0.481761i	0.127659	−	0.991818i	$-0.459254\pi$
$227$	−11.0359	−	7.25846i	−0.732482	−	0.481761i	−0.860140	+	0.510057i	$0.829624\pi$
$228$	−5.33479	−	4.47483i	−0.353305	−	0.296353i
$229$	−4.62420	−	0.540492i	−0.305576	−	0.0357167i	−0.0380769	−	0.999275i	$-0.512123\pi$
$229$	−4.62420	−	0.540492i	−0.305576	−	0.0357167i	−0.267499	+	0.963558i	$0.586197\pi$
$230$	−6.50574	−	15.0820i	−0.428976	−	0.994478i
$231$	6.23489	−	0.00109130i	0.410226	−	7.18025e-5i
$232$	3.91656	−	1.96697i	0.257135	−	0.129138i
$233$	−10.6174	−	3.86441i	−0.695568	−	0.253166i	−0.0300503	−	0.999548i	$-0.509567\pi$
$233$	−10.6174	−	3.86441i	−0.695568	−	0.253166i	−0.665517	+	0.746383i	$0.731789\pi$
$234$	−0.427980	−	7.30409i	−0.0279779	−	0.477483i
$235$	14.4829	−	5.27135i	0.944760	−	0.343865i
$236$	−1.80011	+	1.90800i	−0.117177	+	0.124200i
$237$	5.62748	−	7.56178i	0.365544	−	0.491190i
$238$	19.0377	−	12.5213i	1.23403	−	0.811634i
$239$	−4.38992	+	14.6634i	−0.283960	+	0.948493i	0.690386	+	0.723441i	$0.257441\pi$
$239$	−4.38992	+	14.6634i	−0.283960	+	0.948493i	−0.974347	+	0.225053i	$0.927745\pi$
$240$	1.83926	+	6.13963i	0.118723	+	0.396311i
$241$	−13.5565	−	18.2095i	−0.873250	−	1.17298i	−0.983829	−	0.179111i	$-0.942678\pi$
$241$	−13.5565	−	18.2095i	−0.873250	−	1.17298i	0.110579	−	0.993867i	$-0.464729\pi$
$242$	−10.2784			−0.660719
$243$	15.4846	+	1.79616i	0.993340	+	0.115224i
$244$	−9.71448			−0.621906
$245$	24.2108	+	32.5208i	1.54677	+	2.07768i
$246$	5.03074	+	16.7931i	0.320748	+	1.07069i
$247$	−2.81198	+	9.39266i	−0.178922	+	0.597640i
$248$	3.52111	−	2.31587i	0.223591	−	0.147058i
$249$	−9.68829	+	13.0184i	−0.613971	+	0.825007i
$250$	−9.37686	+	9.93889i	−0.593045	+	0.628591i
$251$	3.27400	−	1.19164i	0.206653	−	0.0752155i	−0.236620	−	0.971602i	$-0.576040\pi$
$251$	3.27400	−	1.19164i	0.206653	−	0.0752155i	0.443273	+	0.896387i	$0.353817\pi$
$252$	−11.3624	−	5.70142i	−0.715762	−	0.359156i
$253$	3.54334	+	1.28967i	0.222768	+	0.0810808i
$254$	−8.35450	+	4.19579i	−0.524208	+	0.263267i
$255$	−34.4640	+	0.00603229i	−2.15822	+	0.000377757i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	−11.8364	−	1.38348i	−0.738335	−	0.0862990i	−0.261392	−	0.965233i	$-0.584181\pi$
$257$	−11.8364	−	1.38348i	−0.738335	−	0.0862990i	−0.476944	+	0.878934i	$0.658255\pi$
$258$	11.0021	+	9.22858i	0.684961	+	0.574546i
$259$	−13.9281	−	9.16065i	−0.865450	−	0.569215i
$260$	6.91332	−	5.80096i	0.428746	−	0.359760i
$261$	10.0692	−	8.45504i	0.623265	−	0.523354i
$262$	7.16436	+	6.01161i	0.442616	+	0.371399i
$263$	6.56549	+	21.9303i	0.404846	+	1.35228i	0.881083	+	0.472962i	$0.156815\pi$
$263$	6.56549	+	21.9303i	0.404846	+	1.35228i	−0.476238	+	0.879317i	$0.658000\pi$
$264$	−1.31496	−	0.660112i	−0.0809305	−	0.0406271i
$265$	15.4172	+	7.74280i	0.947070	+	0.475637i
$266$	11.6904	+	12.3911i	0.716783	+	0.759745i
$267$	3.04578	+	4.08970i	0.186399	+	0.250285i
$268$	2.37351	−	5.50241i	0.144985	−	0.336113i
$269$	−2.38522	+	4.13132i	−0.145429	+	0.251891i	−0.929533	−	0.368739i	$-0.879790\pi$
$269$	−2.38522	+	4.13132i	−0.145429	+	0.251891i	0.784104	+	0.620630i	$0.213123\pi$
$270$	9.62255	+	16.6466i	0.585610	+	1.01308i
$271$	1.70961	+	2.96113i	0.103851	+	0.179876i	0.913268	−	0.407359i	$-0.133550\pi$
$271$	1.70961	+	2.96113i	0.103851	+	0.179876i	−0.809417	+	0.587234i	$0.800217\pi$
$272$	−5.34091	+	0.624263i	−0.323840	+	0.0378515i
$273$	−1.03769	+	17.8703i	−0.0628036	+	1.08156i
$274$	4.75426	−	1.12678i	0.287215	−	0.0680713i
$275$	−0.429357	−	7.37178i	−0.0258912	−	0.444535i
$276$	−5.27702	−	5.59135i	−0.317639	−	0.336560i
$277$	8.67401	+	2.05578i	0.521171	+	0.123520i	0.482778	−	0.875743i	$-0.339628\pi$
$277$	8.67401	+	2.05578i	0.521171	+	0.123520i	0.0383932	+	0.999263i	$0.487776\pi$
$278$	−0.889899	+	5.04687i	−0.0533726	+	0.302691i
$279$	8.67315	−	9.19945i	0.519248	−	0.550757i
$280$	−2.72287	−	15.4421i	−0.162722	−	0.922844i
$281$	−1.53913	+	26.4258i	−0.0918167	+	1.57643i	0.566737	+	0.823899i	$0.308205\pi$
$281$	−1.53913	+	26.4258i	−0.0918167	+	1.57643i	−0.658554	+	0.752533i	$0.728832\pi$
$282$	5.52557	−	4.63815i	0.329043	−	0.276198i
$283$	2.73371	−	3.67201i	0.162502	−	0.218278i	−0.713413	−	0.700744i	$-0.752851\pi$
$283$	2.73371	−	3.67201i	0.162502	−	0.218278i	0.875915	+	0.482466i	$0.160259\pi$
$284$	5.14741	−	6.91417i	0.305443	−	0.410281i
$285$	−4.47862	−	25.3735i	−0.265291	−	1.50300i
$286$	−0.120464	+	2.06828i	−0.00712317	+	0.122300i
$287$	−7.44759	−	42.2374i	−0.439617	−	2.49319i
$288$	1.79232	+	2.40574i	0.105613	+	0.141760i
$289$	2.06902	−	11.7340i	0.121707	−	0.690234i
$290$	15.7805	+	3.74006i	0.926666	+	0.219624i
$291$	−7.60502	+	25.4187i	−0.445814	+	1.49007i
$292$	−0.685786	−	11.7745i	−0.0401326	−	0.689050i
$293$	−7.55876	+	1.79146i	−0.441588	+	0.104658i	−0.445394	−	0.895335i	$-0.646936\pi$
$293$	−7.55876	+	1.79146i	−0.441588	+	0.104658i	0.00380664	+	0.999993i	$0.498788\pi$
$294$	15.8572	+	10.4255i	0.924813	+	0.608027i
$295$	−9.64091	+	1.12686i	−0.561316	+	0.0656084i
$296$	1.96702	+	3.40698i	0.114331	+	0.198027i
$297$	−4.29561	−	1.01570i	−0.249257	−	0.0589367i
$298$	9.88076	−	17.1140i	0.572377	−	0.991386i
$299$	−4.28787	+	9.94041i	−0.247974	+	0.574869i
$300$	−5.96099	+	13.8258i	−0.344158	+	0.798232i
$301$	−24.1094	−	25.5545i	−1.38964	−	1.47294i
$302$	−2.82524	−	1.41889i	−0.162574	−	0.0816479i
$303$	9.85902	−	6.48685i	0.566386	−	0.372660i
$304$	−1.15298	−	3.85123i	−0.0661281	−	0.220883i
$305$	−27.5370	−	23.1063i	−1.57677	−	1.32306i
$306$	−15.1570	+	5.52271i	−0.866468	+	0.315712i
$307$	11.1475	−	9.35388i	0.636223	−	0.533854i	−0.266633	−	0.963798i	$-0.585911\pi$
$307$	11.1475	−	9.35388i	0.636223	−	0.533854i	0.902856	+	0.429944i	$0.141467\pi$
$308$	3.00752	+	1.97808i	0.171369	+	0.112711i
$309$	−3.06282	+	17.3879i	−0.174237	+	0.989162i
$310$	15.4895	+	1.81046i	0.879743	+	0.102827i
$311$	4.29539	+	9.95783i	0.243569	+	0.564657i	0.995519	−	0.0945637i	$-0.0301456\pi$
$311$	4.29539	+	9.95783i	0.243569	+	0.564657i	−0.751950	+	0.659221i	$0.770886\pi$
$312$	2.11148	−	3.65868i	0.119539	−	0.207132i
$313$	−12.4847	+	6.27004i	−0.705675	+	0.354403i	−0.765173	−	0.643825i	$-0.777346\pi$
$313$	−12.4847	+	6.27004i	−0.705675	+	0.354403i	0.0594976	+	0.998228i	$0.481050\pi$
$314$	−4.91702	−	1.78965i	−0.277483	−	0.100996i
$315$	−18.6471	−	43.1873i	−1.05065	−	2.43333i
$316$	5.11389	−	1.86130i	0.287679	−	0.104707i
$317$	−6.46671	+	6.85431i	−0.363207	+	0.384977i	−0.883045	−	0.469288i	$-0.844511\pi$
$317$	−6.46671	+	6.85431i	−0.363207	+	0.384977i	0.519838	+	0.854265i	$0.325992\pi$
$318$	8.02095	+	0.936091i	0.449792	+	0.0524934i
$319$	−3.11058	+	2.04586i	−0.174159	+	0.114546i
$320$	−1.06127	+	3.54490i	−0.0593270	+	0.198166i
$321$	−25.1533	−	5.95679i	−1.40392	−	0.332476i
$322$	11.2324	+	15.0877i	0.625957	+	0.840806i
$323$	21.6172			1.20282
$324$	6.89845	+	5.78026i	0.383247	+	0.321126i
$325$	21.2002			1.17598
$326$	−13.0266	−	17.4977i	−0.721476	−	0.969111i
$327$	10.7990	−	11.4502i	0.597184	−	0.633200i
$328$	−2.90280	+	9.69603i	−0.160280	+	0.535374i
$329$	−14.7462	+	9.69870i	−0.812982	+	0.534706i
$330$	−2.15734	−	4.99888i	−0.118758	−	0.275179i
$331$	5.00602	−	5.30607i	0.275156	−	0.291648i	−0.575029	−	0.818133i	$-0.695009\pi$
$331$	5.00602	−	5.30607i	0.275156	−	0.291648i	0.850184	+	0.526486i	$0.176491\pi$
$332$	−8.80410	+	3.20443i	−0.483188	+	0.175866i
$333$	8.10212	+	8.58172i	0.443993	+	0.470276i
$334$	−10.9506	−	3.98569i	−0.599189	−	0.218087i
$335$	19.8157	−	9.95184i	1.08265	−	0.543727i
$336$	−3.67092	−	6.35565i	−0.200265	−	0.346729i
$337$	5.87211	+	13.6131i	0.319874	+	0.741552i	0.999965	+	0.00842332i	$0.00268126\pi$
$337$	5.87211	+	13.6131i	0.319874	+	0.741552i	−0.680090	+	0.733128i	$0.738059\pi$
$338$	7.00423	+	0.818677i	0.380980	+	0.0445301i
$339$	−2.74237	+	0.998685i	−0.148945	+	0.0542411i
$340$	−16.6244	−	10.9340i	−0.901583	−	0.592981i
$341$	−2.74252	+	2.30125i	−0.148516	+	0.124620i
$342$	−6.03383	−	10.4425i	−0.326272	−	0.564664i
$343$	−12.8437	−	10.7772i	−0.693496	−	0.581912i
$344$	2.37783	+	7.94251i	0.128204	+	0.428232i
$345$	−1.65916	−	28.4011i	−0.0893263	−	1.52906i
$346$	6.75404	+	3.39201i	0.363099	+	0.182355i
$347$	−18.5194	−	19.6294i	−0.994174	−	1.05376i	−0.998553	−	0.0537726i	$-0.982875\pi$
$347$	−18.5194	−	19.6294i	−0.994174	−	1.05376i	0.00437908	−	0.999990i	$-0.498606\pi$
$348$	7.53964	−	0.882596i	0.404167	−	0.0473121i
$349$	2.71137	−	6.28567i	0.145136	−	0.336464i	−0.830105	−	0.557607i	$-0.811720\pi$
$349$	2.71137	−	6.28567i	0.145136	−	0.336464i	0.975241	+	0.221143i	$0.0709788\pi$
$350$	18.4176	−	31.9003i	0.984464	−	1.70514i
$351$	3.62821	−	12.1423i	0.193659	−	0.648106i
$352$	−0.424743	−	0.735676i	−0.0226389	−	0.0392117i
$353$	2.78941	−	0.326035i	0.148465	−	0.0173531i	−0.0415355	−	0.999137i	$-0.513225\pi$
$353$	2.78941	−	0.326035i	0.148465	−	0.0173531i	0.190001	+	0.981784i	$0.439151\pi$
$354$	−4.05978	+	2.03979i	−0.215775	+	0.108414i
$355$	31.0367	−	7.35583i	1.64726	−	0.390407i
$356$	0.171182	+	2.93908i	0.00907261	+	0.155771i
$357$	38.4016	−	9.10845i	2.03243	−	0.482070i
$358$	16.2209	+	3.84443i	0.857302	+	0.203184i
$359$	0.772968	−	4.38372i	0.0407957	−	0.231364i	−0.957592	−	0.288128i	$-0.906967\pi$
$359$	0.772968	−	4.38372i	0.0407957	−	0.231364i	0.998388	+	0.0567640i	$0.0180783\pi$
$360$	−0.641590	+	11.0825i	−0.0338148	+	0.584100i
$361$	−0.492926	−	2.79552i	−0.0259435	−	0.147133i
$362$	0.144865	−	2.48724i	0.00761396	−	0.130727i
$363$	−16.7301	−	6.08594i	−0.878102	−	0.319429i
$364$	−6.17150	+	8.28977i	−0.323475	+	0.434502i
$365$	26.0622	−	35.0076i	1.36416	−	1.83238i
$366$	−15.8123	−	5.75206i	−0.826520	−	0.300665i
$367$	−0.147416	+	2.53104i	−0.00769508	+	0.132119i	0.992273	+	0.124077i	$0.0395970\pi$
$367$	−0.147416	+	2.53104i	−0.00769508	+	0.132119i	−0.999968	+	0.00804230i	$0.997440\pi$
$368$	−0.770798	−	4.37141i	−0.0401806	−	0.227876i
$369$	−1.75488	+	30.3129i	−0.0913554	+	1.57803i
$370$	−2.52786	+	14.3362i	−0.131417	+	0.745304i
$371$	−19.2242	−	4.55621i	−0.998070	−	0.236547i
$372$	7.10257	−	1.68465i	0.368251	−	0.0873451i
$373$	1.44475	+	24.8054i	0.0748063	+	1.28437i	0.801742	+	0.597670i	$0.203907\pi$
$373$	1.44475	+	24.8054i	0.0748063	+	1.28437i	−0.726936	+	0.686705i	$0.759056\pi$
$374$	4.44478	−	1.05343i	0.229834	−	0.0544717i
$375$	−21.1476	+	10.6254i	−1.09206	+	0.548692i
$376$	4.13694	−	0.483539i	0.213347	−	0.0249366i
$377$	−5.34447	−	9.25689i	−0.275254	−	0.476754i
$378$	−15.1186	−	16.0080i	−0.777619	−	0.823362i
$379$	−9.73928	+	16.8689i	−0.500273	+	0.866498i	0.499727	+	0.866183i	$0.333434\pi$
$379$	−9.73928	+	16.8689i	−0.500273	+	0.866498i	−1.00000		0.000315369i	$0.999900\pi$
$380$	5.89203	−	13.6593i	0.302255	−	0.700705i
$381$	−16.0830	+	1.88269i	−0.823956	+	0.0964529i
$382$	−0.00134441	−	0.00142499i	−6.87860e−5	−	7.29090e-5i
$383$	−4.01037	−	2.01408i	−0.204920	−	0.102915i	0.343379	−	0.939197i	$-0.388428\pi$
$383$	−4.01037	−	2.01408i	−0.204920	−	0.102915i	−0.548300	+	0.836282i	$0.684725\pi$
$384$	0.101012	+	1.72910i	0.00515477	+	0.0882379i
$385$	3.82029	+	12.7607i	0.194700	+	0.650343i
$386$	20.0942	+	16.8610i	1.02277	+	0.858203i
$387$	12.4438	+	21.5358i	0.632552	+	1.09473i
$388$	−11.7345	+	9.84639i	−0.595728	+	0.499875i
$389$	9.37133	+	6.16362i	0.475145	+	0.312508i	0.764398	−	0.644745i	$-0.223036\pi$
$389$	9.37133	+	6.16362i	0.475145	+	0.312508i	−0.289253	+	0.957253i	$0.593407\pi$
$390$	14.6876	−	5.34876i	0.743736	−	0.270845i
$391$	23.7075	+	2.77101i	1.19894	+	0.140136i
$392$	4.33970	+	10.0605i	0.219188	+	0.508134i
$393$	8.10188	+	14.0272i	0.408686	+	0.707578i
$394$	5.68838	−	2.85681i	0.286576	−	0.143924i
$395$	18.9232	+	6.88749i	0.952131	+	0.346547i
$396$	−1.74951	−	1.85307i	−0.0879160	−	0.0931202i
$397$	−18.0705	+	6.57714i	−0.906934	+	0.330097i	−0.753028	−	0.657988i	$-0.771408\pi$
$397$	−18.0705	+	6.57714i	−0.906934	+	0.330097i	−0.153906	+	0.988085i	$0.549185\pi$
$398$	9.55921	−	10.1322i	0.479160	−	0.507880i
$399$	11.6915	+	27.0909i	0.585308	+	1.35624i
$400$	−7.26259	+	4.77668i	−0.363130	+	0.238834i
$401$	2.97116	−	9.92436i	0.148373	−	0.495599i	−0.851200	−	0.524842i	$-0.824124\pi$
$401$	2.97116	−	9.92436i	0.148373	−	0.495599i	0.999572	+	0.0292429i	$0.00930962\pi$
$402$	7.12139	−	7.55088i	0.355183	−	0.376604i
$403$	−6.13788	−	8.24460i	−0.305750	−	0.410693i
$404$	6.81370			0.338994
$405$	5.80600	+	32.7932i	0.288503	+	1.62951i
$406$	−18.5720			−0.921711
$407$	−1.99565	−	2.68063i	−0.0989208	−	0.132874i
$408$	−9.06302	−	2.14630i	−0.448686	−	0.106258i
$409$	−4.80893	+	16.0630i	−0.237786	+	0.794262i	0.752904	+	0.658130i	$0.228652\pi$
$409$	−4.80893	+	16.0630i	−0.237786	+	0.794262i	−0.990691	+	0.136132i	$0.956533\pi$
$410$	−31.2908	+	20.5803i	−1.54534	+	1.01639i
$411$	8.40569	+	0.980992i	0.414622	+	0.0483888i
$412$	−6.99517	+	7.41445i	−0.344627	+	0.365284i
$413$	10.4453	−	3.80176i	0.513978	−	0.187073i
$414$	−5.27870	−	12.2256i	−0.259434	−	0.600857i
$415$	−32.5783	−	11.8575i	−1.59921	−	0.582063i
$416$	2.17945	−	1.09456i	0.106857	−	0.0536654i
$417$	−4.43680	+	7.68786i	−0.217271	+	0.376476i
$418$	1.35263	+	3.13574i	0.0661591	+	0.153374i
$419$	15.4042	+	1.80049i	0.752544	+	0.0879597i	0.483712	−	0.875227i	$-0.339288\pi$
$419$	15.4042	+	1.80049i	0.752544	+	0.0879597i	0.268832	+	0.963187i	$0.413362\pi$
$420$	4.71146	−	26.7474i	0.229896	−	1.30514i
$421$	−24.9374	−	16.4016i	−1.21537	−	0.799364i	−0.230573	−	0.973055i	$-0.574060\pi$
$421$	−24.9374	−	16.4016i	−1.21537	−	0.799364i	−0.984800	+	0.173691i	$0.944430\pi$
$422$	−12.4459	+	10.4433i	−0.605857	+	0.508374i
$423$	11.7403	−	4.27776i	0.570831	−	0.207992i
$424$	3.57155	+	2.99689i	0.173450	+	0.145542i
$425$	−13.4059	−	44.7790i	−0.650284	−	2.17210i
$426$	12.4724	−	8.20635i	0.604289	−	0.397599i
$427$	36.7867	+	18.4750i	1.78023	+	0.894067i
$428$	−10.2414	−	10.8553i	−0.495038	−	0.524710i
$429$	−1.42073	+	3.29521i	−0.0685936	+	0.159094i
$430$	−12.1513	+	28.1699i	−0.585989	+	1.35847i
$431$	−3.60948	+	6.25181i	−0.173863	+	0.301139i	−0.939767	−	0.341816i	$-0.888958\pi$
$431$	−3.60948	+	6.25181i	−0.173863	+	0.301139i	0.765904	+	0.642954i	$0.222292\pi$
$432$	1.49289	+	4.97708i	0.0718266	+	0.239460i
$433$	−14.5409	−	25.1855i	−0.698790	−	1.21034i	−0.968886	−	0.247507i	$-0.920389\pi$
$433$	−14.5409	−	25.1855i	−0.698790	−	1.21034i	0.270096	−	0.962833i	$-0.412945\pi$
$434$	−17.7380	+	2.07328i	−0.851453	+	0.0995206i
$435$	23.4715	+	15.4315i	1.12537	+	0.739885i
$436$	8.84215	−	2.09563i	0.423462	−	0.100362i
$437$	1.03758	+	17.8145i	0.0496340	+	0.852184i
$438$	5.85556	−	19.5714i	0.279789	−	0.935158i
$439$	24.5752	+	5.82442i	1.17291	+	0.277985i	0.770478	−	0.637466i	$-0.220017\pi$
$439$	24.5752	+	5.82442i	1.17291	+	0.277985i	0.402430	+	0.915451i	$0.368166\pi$
$440$	0.545846	−	3.09565i	0.0260222	−	0.147579i
$441$	19.6378	+	26.3588i	0.935131	+	1.25518i
$442$	2.27730	+	12.9152i	0.108320	+	0.614314i
$443$	−1.64807	+	28.2963i	−0.0783024	+	1.34440i	0.698932	+	0.715188i	$0.253659\pi$
$443$	−1.64807	+	28.2963i	−0.0783024	+	1.34440i	−0.777234	+	0.629211i	$0.783378\pi$
$444$	1.18441	+	6.71024i	0.0562095	+	0.318454i
$445$	−6.50548	+	8.73838i	−0.308389	+	0.414239i
$446$	−7.40131	+	9.94169i	−0.350462	+	0.470753i
$447$	26.2163	−	22.0059i	1.23999	−	1.04084i
$448$	0.246390	−	4.23036i	0.0116408	−	0.199866i
$449$	−6.31732	−	35.8273i	−0.298133	−	1.69080i	−0.654189	−	0.756331i	$-0.726990\pi$
$449$	−6.31732	−	35.8273i	−0.298133	−	1.69080i	0.356056	−	0.934465i	$-0.384121\pi$
$450$	−17.8891	+	18.9747i	−0.843301	+	0.894474i
$451$	1.49300	−	8.46722i	0.0703026	−	0.398706i
$452$	−1.63961	−	0.388594i	−0.0771207	−	0.0182779i
$453$	−3.75850	−	3.98238i	−0.176590	−	0.187109i
$454$	−0.768034	−	13.1866i	−0.0360456	−	0.618880i
$455$	−37.2115	+	8.81930i	−1.74450	+	0.413455i
$456$	0.403649	−	6.95134i	0.0189026	−	0.325526i
$457$	20.0513	−	2.34366i	0.937959	−	0.109632i	0.366643	−	0.930362i	$-0.380507\pi$
$457$	20.0513	−	2.34366i	0.937959	−	0.109632i	0.571316	+	0.820730i	$0.306433\pi$
$458$	−2.32784	−	4.03194i	−0.108773	−	0.188400i
$459$	−27.9411	+	0.0146717i	−1.30418	+	0.000684818i
$460$	8.21266	−	14.2248i	0.382917	−	0.663233i
$461$	0.566853	−	1.31411i	0.0264010	−	0.0612044i	−0.904506	−	0.426462i	$-0.859760\pi$
$461$	0.566853	−	1.31411i	0.0264010	−	0.0612044i	0.930907	+	0.365258i	$0.119019\pi$
$462$	3.72410	+	5.00050i	0.173261	+	0.232644i
$463$	−23.2466	−	24.6400i	−1.08036	−	1.14512i	−0.988789	−	0.149318i	$-0.952292\pi$
$463$	−23.2466	−	24.6400i	−1.08036	−	1.14512i	−0.0915720	−	0.995798i	$-0.529189\pi$
$464$	3.91656	+	1.96697i	0.181822	+	0.0913143i
$465$	24.1402	+	12.1184i	1.11948	+	0.561977i
$466$	−3.24053	−	10.8241i	−0.150114	−	0.501417i
$467$	11.7951	+	9.89728i	0.545813	+	0.457992i	0.873520	−	0.486788i	$-0.161832\pi$
$467$	11.7951	+	9.89728i	0.545813	+	0.457992i	−0.327707	+	0.944779i	$0.606276\pi$
$468$	5.60320	−	4.70499i	0.259008	−	0.217488i
$469$	−19.4524	+	16.3225i	−0.898230	+	0.753705i
$470$	12.8769	+	8.46924i	0.593965	+	0.390657i
$471$	−6.94375	−	5.82443i	−0.319951	−	0.268375i
$472$	−2.60540	−	0.304528i	−0.119923	−	0.0140170i
$473$	−2.78956	−	6.46693i	−0.128264	−	0.297350i
$474$	9.42598	−	0.00164984i	0.432949	−	7.57799e-5i
$475$	31.2284	−	15.6835i	1.43286	−	0.719608i
$476$	21.4121	+	7.79338i	0.981423	+	0.357209i
$477$	12.5014	+	6.27297i	0.572401	+	0.287219i
$478$	−14.3833	+	5.23509i	−0.657877	+	0.239447i
$479$	21.9298	−	23.2442i	1.00200	−	1.06206i	0.00392602	−	0.999992i	$-0.498750\pi$
$479$	21.9298	−	23.2442i	1.00200	−	1.06206i	0.998072	−	0.0620638i	$-0.0197682\pi$
$480$	−3.82641	+	5.14164i	−0.174651	+	0.234683i
$481$	8.01619	−	5.27233i	0.365507	−	0.240398i
$482$	6.51091	−	21.7479i	0.296564	−	0.990592i
$483$	9.34935	+	31.2091i	0.425410	+	1.42006i
$484$	−6.13782	−	8.24452i	−0.278992	−	0.374751i
$485$	−56.6830			−2.57384
$486$	7.80604	+	13.4932i	0.354089	+	0.612063i
$487$	−19.3766			−0.878039			−0.439019	−	0.898478i	$-0.644674\pi$
$487$	−19.3766			−0.878039			−0.439019	+	0.898478i	$0.644674\pi$
$488$	−5.80109	−	7.79221i	−0.262603	−	0.352737i
$489$	−10.8428	−	36.1943i	−0.490326	−	1.63676i
$490$	−11.6280	+	38.8402i	−0.525299	+	1.75462i
$491$	17.4495	−	11.4767i	0.787483	−	0.517936i	−0.0909188	−	0.995858i	$-0.528980\pi$
$491$	17.4495	−	11.4767i	0.787483	−	0.517936i	0.878402	+	0.477922i	$0.158610\pi$
$492$	−10.4660	+	14.0634i	−0.471844	+	0.634029i
$493$	−16.1728	+	17.1421i	−0.728385	+	0.772043i
$494$	−9.21326	+	3.35335i	−0.414524	+	0.150875i
$495$	−0.551613	−	9.41405i	−0.0247932	−	0.423130i
$496$	3.96028	+	1.44142i	0.177822	+	0.0647218i
$497$	−32.6415	+	16.3932i	−1.46417	+	0.735335i
$498$	−16.2278	+	0.00284038i	−0.727185	+	0.000127280i
$499$	−7.20158	−	16.6951i	−0.322387	−	0.747377i	−0.999929	−	0.0118930i	$-0.996214\pi$
$499$	−7.20158	−	16.6951i	−0.322387	−	0.747377i	0.677542	−	0.735484i	$-0.263045\pi$
$500$	−13.5717	−	1.58630i	−0.606944	−	0.0709416i
$501$	−15.4643	−	12.9715i	−0.690893	−	0.579522i
$502$	2.91094	+	1.91455i	0.129921	+	0.0854507i
$503$	−33.4921	+	28.1032i	−1.49334	+	1.25306i	−0.603016	+	0.797729i	$0.706034\pi$
$503$	−33.4921	+	28.1032i	−1.49334	+	1.25306i	−0.890323	+	0.455330i	$0.849521\pi$
$504$	−2.21190	−	12.5187i	−0.0985258	−	0.557626i
$505$	19.3144	+	16.2067i	0.859478	+	0.721188i
$506$	1.08146	+	3.61233i	0.0480768	+	0.160588i
$507$	10.9160	+	5.47984i	0.484798	+	0.243368i
$508$	−8.35450	−	4.19579i	−0.370671	−	0.186158i
$509$	7.43124	+	7.87666i	0.329384	+	0.349127i	0.870808	−	0.491623i	$-0.163596\pi$
$509$	7.43124	+	7.87666i	0.329384	+	0.349127i	−0.541424	+	0.840750i	$0.682115\pi$
$510$	−20.5853	−	27.6408i	−0.911533	−	1.22395i
$511$	−19.7958	+	45.8918i	−0.875714	+	2.03013i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−3.63816	−	20.5699i	−0.160629	−	0.908183i
$514$	−5.95850	−	10.3204i	−0.262818	−	0.455214i
$515$	−37.4644	+	4.37896i	−1.65088	+	0.192960i
$516$	−0.832457	+	14.3360i	−0.0366469	+	0.631105i
$517$	−3.44283	+	0.815965i	−0.151415	+	0.0358861i
$518$	−0.969310	−	16.6424i	−0.0425890	−	0.731225i
$519$	8.98510	+	9.52031i	0.394402	+	0.417895i
$520$	8.78143	+	2.08124i	0.385091	+	0.0912683i
$521$	−0.342723	+	1.94368i	−0.0150150	+	0.0851542i	−0.991394	−	0.130909i	$-0.958211\pi$
$521$	−0.342723	+	1.94368i	−0.0150150	+	0.0851542i	0.976379	+	0.216063i	$0.0693216\pi$
$522$	12.7949	+	3.02771i	0.560016	+	0.132519i
$523$	5.38019	+	30.5126i	0.235259	+	1.33422i	0.842067	+	0.539374i	$0.181339\pi$
$523$	5.38019	+	30.5126i	0.235259	+	1.33422i	−0.606807	+	0.794849i	$0.707550\pi$
$524$	−0.543794	+	9.33658i	−0.0237558	+	0.407871i
$525$	48.8669	−	41.0188i	2.13273	−	1.79021i
$526$	−13.6701	+	18.3622i	−0.596046	+	0.800629i
$527$	−13.5329	+	18.1778i	−0.589503	+	0.791839i
$528$	−0.255751	−	1.44895i	−0.0111301	−	0.0630577i
$529$	0.191681	−	3.29103i	0.00833394	−	0.143088i
$530$	2.99582	+	16.9902i	0.130130	+	0.738006i
$531$	−7.81588	+	0.916319i	−0.339180	+	0.0397649i
$532$	−2.95816	+	16.7765i	−0.128252	+	0.727356i
$533$	24.0190	+	5.69261i	1.04038	+	0.246574i
$534$	−1.46163	+	4.88529i	−0.0632508	+	0.211407i
$535$	−3.21099	−	55.1305i	−0.138823	−	2.38350i
$536$	5.83097	−	1.38196i	0.251859	−	0.0596918i
$537$	24.1264	+	15.8622i	1.04113	+	0.684503i
$538$	−4.73818	+	0.553814i	−0.204278	+	0.0238766i
$539$	−4.65375	−	8.06053i	−0.200451	−	0.347192i
$540$	−7.60640	+	17.6591i	−0.327327	+	0.759927i
$541$	18.8444	−	32.6395i	0.810185	−	1.40328i	−0.102550	−	0.994728i	$-0.532700\pi$
$541$	18.8444	−	32.6395i	0.810185	−	1.40328i	0.912734	−	0.408553i	$-0.133967\pi$
$542$	−1.35428	+	3.13958i	−0.0581714	+	0.134856i
$543$	1.70852	−	3.96271i	0.0733197	−	0.170056i
$544$	−3.69010	−	3.91128i	−0.158212	−	0.167695i
$545$	30.0488	+	15.0911i	1.28715	+	0.646431i
$546$	−14.9538	+	9.83903i	−0.639964	+	0.421071i
$547$	−1.78950	−	5.97736i	−0.0765136	−	0.255573i	0.911172	−	0.412027i	$-0.135179\pi$
$547$	−1.78950	−	5.97736i	−0.0765136	−	0.255573i	−0.987685	+	0.156454i	$0.949994\pi$
$548$	3.74286	+	3.14064i	0.159887	+	0.134161i
$549$	−22.3317	−	18.7252i	−0.953095	−	0.799173i
$550$	5.65668	−	4.74652i	0.241202	−	0.202392i
$551$	−14.7206	−	9.68187i	−0.627117	−	0.412462i
$552$	1.33374	−	7.57175i	0.0567676	−	0.322275i
$553$	−22.9051	−	2.67722i	−0.974023	−	0.113847i
$554$	3.53077	+	8.18525i	0.150008	+	0.347758i
$555$	−12.6032	+	21.8383i	−0.534977	+	0.926982i
$556$	−4.57962	+	2.29997i	−0.194219	+	0.0975405i
$557$	20.4801	+	7.45413i	0.867768	+	0.315842i	0.737263	−	0.675606i	$-0.236118\pi$
$557$	20.4801	+	7.45413i	0.867768	+	0.315842i	0.130505	+	0.991448i	$0.458340\pi$
$558$	12.5583	+	1.46340i	0.531637	+	0.0619508i
$559$	19.0008	−	6.91572i	0.803648	−	0.292504i
$560$	10.7605	−	11.4055i	0.454715	−	0.481969i
$561$	7.85852	+	0.917135i	0.331787	+	0.0387215i
$562$	−22.1159	+	14.5458i	−0.932901	+	0.613579i
$563$	3.43155	−	11.4622i	0.144623	−	0.483073i	−0.854729	−	0.519074i	$-0.826277\pi$
$563$	3.43155	−	11.4622i	0.144623	−	0.483073i	0.999352	+	0.0360012i	$0.0114620\pi$
$564$	7.02001	+	1.66248i	0.295596	+	0.0700028i
$565$	−3.72341	−	5.00140i	−0.156645	−	0.210411i
$566$	4.57786			0.192422
$567$	−15.1301	−	35.0081i	−0.635404	−	1.47020i
$568$	8.61984			0.361680
$569$	9.89673	+	13.2936i	0.414893	+	0.557298i	0.959614	−	0.281319i	$-0.0907721\pi$
$569$	9.89673	+	13.2936i	0.414893	+	0.557298i	−0.544722	+	0.838617i	$0.683365\pi$
$570$	17.6783	−	18.7444i	0.740461	−	0.785118i
$571$	0.105574	−	0.352641i	0.00441813	−	0.0147576i	−0.955752	−	0.294174i	$-0.904956\pi$
$571$	0.105574	−	0.352641i	0.00441813	−	0.0147576i	0.960170	+	0.279416i	$0.0901408\pi$
$572$	−1.73095	+	1.13847i	−0.0723748	+	0.0476016i
$573$	−0.00134454	−	0.00311550i	−5.61691e−5	−	0.000130152i
$574$	29.4322	−	31.1963i	1.22848	−	1.30211i
$575$	36.2583	−	13.1970i	1.51208	−	0.550351i
$576$	−0.859404	+	2.87427i	−0.0358085	+	0.119761i
$577$	39.7657	+	14.4735i	1.65547	+	0.602540i	0.989641	−	0.143567i	$-0.0458572\pi$
$577$	39.7657	+	14.4735i	1.65547	+	0.602540i	0.665826	+	0.746107i	$0.268079\pi$
$578$	10.6476	−	5.34744i	0.442883	−	0.222424i
$579$	22.7237	+	39.3427i	0.944364	+	1.63503i
$580$	6.42350	+	14.8914i	0.266721	+	0.618330i
$581$	39.4335	+	4.60911i	1.63598	+	0.191218i
$582$	−24.9303	+	9.07885i	−1.03340	+	0.376330i
$583$	−3.30902	−	2.17637i	−0.137045	−	0.0901362i
$584$	9.03507	−	7.58133i	0.373874	−	0.313718i
$585$	27.0741	−	0.00947764i	1.11938	−	0.000391852i
$586$	−5.95075	−	4.99327i	−0.245823	−	0.206270i
$587$	4.22512	+	14.1129i	0.174390	+	0.582502i	0.999838	+	0.0180235i	$0.00573736\pi$
$587$	4.22512	+	14.1129i	0.174390	+	0.582502i	−0.825448	+	0.564478i	$0.809077\pi$
$588$	1.10676	+	18.9451i	0.0456418	+	0.781284i
$589$	−15.1404	−	7.60380i	−0.623850	−	0.313309i
$590$	−6.66103	−	7.06028i	−0.274230	−	0.290667i
$591$	10.9505	−	1.28188i	0.450444	−	0.0527293i
$592$	−1.55820	+	3.61230i	−0.0640414	+	0.148465i
$593$	−0.654941	+	1.13439i	−0.0268952	+	0.0465838i	−0.879160	−	0.476527i	$-0.841895\pi$
$593$	−0.654941	+	1.13439i	−0.0268952	+	0.0465838i	0.852265	+	0.523111i	$0.175229\pi$
$594$	−1.75045	−	4.05214i	−0.0718217	−	0.166261i
$595$	42.1587	+	73.0211i	1.72834	+	2.99357i
$596$	19.6279	−	2.29417i	0.803990	−	0.0939729i
$597$	21.5589	−	10.8320i	0.882347	−	0.443325i
$598$	−10.5340	+	2.49660i	−0.430766	+	0.102093i
$599$	0.980298	+	16.8311i	0.0400539	+	0.687699i	0.957250	+	0.289262i	$0.0934100\pi$
$599$	0.980298	+	16.8311i	0.0400539	+	0.687699i	−0.917196	+	0.398436i	$0.869553\pi$
$600$	−14.6496	+	3.47474i	−0.598069	+	0.141856i
$601$	−21.4900	−	5.09322i	−0.876596	−	0.207757i	−0.232402	−	0.972620i	$-0.574659\pi$
$601$	−21.4900	−	5.09322i	−0.876596	−	0.207757i	−0.644193	+	0.764863i	$0.722807\pi$
$602$	6.10070	−	34.5988i	0.248646	−	1.41014i
$603$	16.0624	−	8.07390i	0.654113	−	0.328795i
$604$	−0.548993	−	3.11349i	−0.0223382	−	0.126686i
$605$	2.21146	−	37.9693i	0.0899086	−	1.54367i
$606$	11.0907	+	4.03447i	0.450527	+	0.163889i
$607$	−3.38873	+	4.55185i	−0.137544	+	0.184754i	−0.865558	−	0.500808i	$-0.833036\pi$
$607$	−3.38873	+	4.55185i	−0.137544	+	0.184754i	0.728014	+	0.685562i	$0.240444\pi$
$608$	2.40065	−	3.22463i	0.0973591	−	0.130776i
$609$	−30.2296	−	10.9967i	−1.22496	−	0.445608i
$610$	2.09014	−	35.8862i	0.0846271	−	1.45299i
$611$	−1.76395	−	10.0038i	−0.0713616	−	0.404712i
$612$	−13.4810	−	8.85985i	−0.544938	−	0.358138i
$613$	3.65539	−	20.7308i	0.147640	−	0.837307i	−0.817570	−	0.575830i	$-0.804679\pi$
$613$	3.65539	−	20.7308i	0.147640	−	0.837307i	0.965210	−	0.261478i	$-0.0842098\pi$
$614$	14.1598	+	3.35593i	0.571443	+	0.135434i
$615$	−63.1178	+	14.9709i	−2.54516	+	0.603684i
$616$	0.209305	+	3.59363i	0.00843314	+	0.144791i
$617$	−2.70887	+	0.642014i	−0.109055	+	0.0258465i	−0.284781	−	0.958593i	$-0.591921\pi$
$617$	−2.70887	+	0.642014i	−0.109055	+	0.0258465i	0.175726	+	0.984439i	$0.443773\pi$
$618$	−15.7762	+	7.92657i	−0.634612	+	0.318853i
$619$	−40.0240	+	4.67814i	−1.60870	+	0.188030i	−0.872459	−	0.488687i	$-0.837476\pi$
$619$	−40.0240	+	4.67814i	−1.60870	+	0.188030i	−0.736243	+	0.676718i	$0.763402\pi$
$620$	7.79746	+	13.5056i	0.313154	+	0.542398i
$621$	−1.35320	−	23.0252i	−0.0543020	−	0.923970i
$622$	−5.42238	+	9.39184i	−0.217418	+	0.376578i
$623$	4.94130	−	11.4552i	0.197969	−	0.458944i
$624$	4.19560	−	0.491140i	0.167958	−	0.0196613i
$625$	−4.87147	−	5.16346i	−0.194859	−	0.206538i
$626$	−12.4847	−	6.27004i	−0.498988	−	0.250601i
$627$	0.344961	+	5.90494i	0.0137764	+	0.235821i
$628$	−1.50072	−	5.01276i	−0.0598853	−	0.200031i
$629$	−16.2052	−	13.5978i	−0.646144	−	0.542179i
$630$	23.5063	−	40.7470i	0.936512	−	1.62340i
$631$	16.2491	−	13.6346i	0.646866	−	0.542785i	−0.259252	−	0.965810i	$-0.583476\pi$
$631$	16.2491	−	13.6346i	0.646866	−	0.542785i	0.906118	+	0.423024i	$0.139032\pi$
$632$	4.54680	+	2.99048i	0.180862	+	0.118955i
$633$	−26.4418	+	9.62927i	−1.05097	+	0.382729i
$634$	−9.35966	−	1.09399i	−0.371720	−	0.0434478i
$635$	−13.7021	−	31.7651i	−0.543752	−	1.26056i
$636$	4.03892	+	6.99278i	0.160153	+	0.277282i
$637$	23.8795	−	11.9927i	0.946139	−	0.475169i
$638$	−3.49855	−	1.27337i	−0.138509	−	0.0504131i
$639$	25.1604	−	5.97242i	0.995329	−	0.236265i
$640$	−3.47720	+	1.26560i	−0.137448	+	0.0500271i
$641$	−30.8679	+	32.7181i	−1.21921	+	1.29229i	−0.275583	+	0.961277i	$0.588871\pi$
$641$	−30.8679	+	32.7181i	−1.21921	+	1.29229i	−0.943627	+	0.331010i	$0.892611\pi$
$642$	−10.2424	−	23.7332i	−0.404237	−	0.936675i
$643$	−24.9099	+	16.3835i	−0.982349	+	0.646101i	−0.935695	−	0.352810i	$-0.885226\pi$
$643$	−24.9099	+	16.3835i	−0.982349	+	0.646101i	−0.0466543	+	0.998911i	$0.514856\pi$
$644$	−5.39469	+	18.0195i	−0.212581	+	0.710069i
$645$	−36.4584	+	38.6572i	−1.43555	+	1.52213i
$646$	12.9089	+	17.3397i	0.507895	+	0.682221i
$647$	−10.0398			−0.394707			−0.197354	−	0.980332i	$-0.563235\pi$
$647$	−10.0398			−0.394707			−0.197354	+	0.980332i	$0.563235\pi$
$648$	−0.517013	+	8.98514i	−0.0203102	+	0.352970i
$649$	2.22832			0.0874691
$650$	12.6599	+	17.0052i	0.496562	+	0.666998i
$651$	−30.0998	−	7.12822i	−1.17970	−	0.279377i
$652$	6.25641	−	20.8979i	0.245020	−	0.818423i
$653$	29.9563	−	19.7025i	1.17228	−	0.771020i	0.194550	−	0.980893i	$-0.437675\pi$
$653$	29.9563	−	19.7025i	1.17228	−	0.771020i	0.977729	+	0.209873i	$0.0673050\pi$
$654$	15.6332	+	1.82449i	0.611307	+	0.0713430i
$655$	−23.7489	+	25.1724i	−0.927947	+	0.983567i
$656$	−9.51084	+	3.46166i	−0.371336	+	0.135155i
$657$	21.1195	−	28.3892i	0.823952	−	1.10757i
$658$	−16.5853	−	6.03657i	−0.646564	−	0.235330i
$659$	13.6400	−	6.85028i	0.531340	−	0.266849i	−0.162837	−	0.986653i	$-0.552065\pi$
$659$	13.6400	−	6.85028i	0.531340	−	0.266849i	0.694177	+	0.719804i	$0.255768\pi$
$660$	2.72144	−	4.71558i	0.105932	−	0.183554i
$661$	−6.68590	−	15.4997i	−0.260051	−	0.602867i	0.737303	−	0.675562i	$-0.236099\pi$
$661$	−6.68590	−	15.4997i	−0.260051	−	0.602867i	−0.997354	+	0.0726957i	$0.976840\pi$
$662$	7.24550	+	0.846878i	0.281605	+	0.0329148i
$663$	−3.94049	+	22.3705i	−0.153036	+	0.868799i
$664$	−7.82779	−	5.14842i	−0.303777	−	0.199797i
$665$	−48.2891	+	40.5193i	−1.87257	+	1.57127i
$666$	−2.04535	+	11.6235i	−0.0792557	+	0.450403i
$667$	−14.9029	−	12.5050i	−0.577042	−	0.484195i
$668$	−3.34222	−	11.1638i	−0.129314	−	0.431940i
$669$	−17.9337	+	11.7997i	−0.693357	+	0.456202i
$670$	19.8157	+	9.95184i	0.765549	+	0.384473i
$671$	5.66308	+	6.00252i	0.218621	+	0.231725i
$672$	2.90589	−	6.73986i	0.112097	−	0.259996i
$673$	15.4754	−	35.8761i	0.596535	−	1.38292i	−0.305887	−	0.952068i	$-0.598953\pi$
$673$	15.4754	−	35.8761i	0.596535	−	1.38292i	0.902421	−	0.430855i	$-0.141788\pi$
$674$	−7.41279	+	12.8393i	−0.285530	+	0.494552i
$675$	−40.3532	+	20.2927i	−1.55320	+	0.781066i
$676$	3.52595	+	6.10713i	0.135614	+	0.234890i
$677$	4.50420	−	0.526465i	0.173110	−	0.0202337i	−0.0290960	−	0.999577i	$-0.509263\pi$
$677$	4.50420	−	0.526465i	0.173110	−	0.0202337i	0.202206	+	0.979343i	$0.435189\pi$
$678$	−2.43870	−	1.60335i	−0.0936576	−	0.0615761i
$679$	63.1618	−	14.9696i	2.42393	−	0.574482i
$680$	−1.15695	−	19.8641i	−0.0443672	−	0.761755i
$681$	6.55783	−	21.9186i	0.251297	−	0.839924i
$682$	−3.48360	−	0.825629i	−0.133394	−	0.0316150i
$683$	−1.80163	+	10.2175i	−0.0689373	+	0.390963i	0.930743	+	0.365674i	$0.119162\pi$
$683$	−1.80163	+	10.2175i	−0.0689373	+	0.390963i	−0.999680	+	0.0252887i	$0.991950\pi$
$684$	4.77299	−	11.0757i	0.182500	−	0.423489i
$685$	3.13953	+	17.8051i	0.119955	+	0.680299i
$686$	0.974873	−	16.7379i	0.0372208	−	0.639057i
$687$	−1.40167	−	7.94113i	−0.0534770	−	0.302973i
$688$	−4.95093	+	6.65025i	−0.188752	+	0.253539i
$689$	6.79018	−	9.12079i	0.258685	−	0.347474i
$690$	21.7904	−	18.2908i	0.829546	−	0.696319i
$691$	−0.472513	+	8.11274i	−0.0179753	+	0.308623i	0.977322	+	0.211758i	$0.0679188\pi$
$691$	−0.472513	+	8.11274i	−0.0179753	+	0.308623i	−0.995297	+	0.0968656i	$0.969118\pi$
$692$	1.31243	+	7.44314i	0.0498909	+	0.282946i
$693$	3.10085	+	10.3444i	0.117792	+	0.392951i
$694$	4.68620	−	26.5767i	0.177886	−	1.00884i
$695$	−18.4521	−	4.37324i	−0.699930	−	0.165886i
$696$	5.21031	+	5.52067i	0.197496	+	0.209261i
$697$	−3.16451	−	54.3325i	−0.119864	−	2.05799i
$698$	6.66100	−	1.57869i	0.252122	−	0.0597541i
$699$	1.13448	−	19.5371i	0.0429099	−	0.738963i
$700$	36.5862	−	4.27631i	1.38283	−	0.161630i
$701$	5.56488	+	9.63865i	0.210183	+	0.364047i	0.951772	−	0.306808i	$-0.0992608\pi$
$701$	5.56488	+	9.63865i	0.210183	+	0.364047i	−0.741589	+	0.670854i	$0.765928\pi$
$702$	11.9062	−	4.34059i	0.449371	−	0.163825i
$703$	7.90766	−	13.6965i	0.298243	−	0.516572i
$704$	0.336464	−	0.780012i	0.0126810	−	0.0293978i
$705$	15.9449	+	21.4099i	0.600520	+	0.806344i
$706$	1.92724	+	2.04276i	0.0725327	+	0.0768802i
$707$	−25.8021	−	12.9583i	−0.970386	−	0.487346i
$708$	−4.06049	−	2.03837i	−0.152603	−	0.0766065i
$709$	−7.16813	−	23.9432i	−0.269205	−	0.899207i	−0.980534	−	0.196348i	$-0.937092\pi$
$709$	−7.16813	−	23.9432i	−0.269205	−	0.899207i	0.711329	−	0.702859i	$-0.248093\pi$
$710$	24.4341	+	20.5027i	0.916996	+	0.769451i
$711$	15.3436	+	5.57854i	0.575431	+	0.209212i
$712$	−2.25528	+	1.89240i	−0.0845201	+	0.0709208i
$713$	−15.6297	−	10.2798i	−0.585337	−	0.384982i
$714$	30.2379	+	25.3636i	1.13163	+	0.949210i
$715$	−7.61451	−	0.890009i	−0.284767	−	0.0332844i
$716$	6.60275	+	15.3069i	0.246757	+	0.572046i
$717$	−26.5114	+	0.00464034i	−0.990087	+	0.000173297i
$718$	3.97787	−	1.99776i	0.148453	−	0.0745558i
$719$	27.9057	+	10.1568i	1.04071	+	0.378786i	0.805148	−	0.593074i	$-0.202086\pi$
$719$	27.9057	+	10.1568i	1.04071	+	0.378786i	0.235559	+	0.971860i	$0.424308\pi$
$720$	−9.27267	+	6.10338i	−0.345572	+	0.227460i
$721$	40.5900	−	14.7736i	1.51165	−	0.550196i
$722$	1.94800	−	2.06476i	0.0724971	−	0.0768424i
$723$	23.4750	−	31.5439i	0.873045	−	1.17313i
$724$	2.08158	−	1.36908i	0.0773615	−	0.0508814i
$725$	−10.9265	+	36.4971i	−0.405800	+	1.35547i
$726$	−5.10885	−	17.0539i	−0.189607	−	0.632929i
$727$	14.8483	+	19.9447i	0.550691	+	0.739707i	0.987111	−	0.160036i	$-0.0511611\pi$
$727$	14.8483	+	19.9447i	0.550691	+	0.739707i	−0.436420	+	0.899743i	$0.643754\pi$
$728$	−10.3348			−0.383032
$729$	4.71642	+	26.5849i	0.174682	+	0.984625i
$730$	43.6437			1.61532
$731$	−26.6225	−	35.7602i	−0.984668	−	1.32264i
$732$	−4.82857	−	16.1183i	−0.178469	−	0.595748i
$733$	10.3778	−	34.6641i	0.383311	−	1.28035i	−0.521030	−	0.853538i	$-0.674452\pi$
$733$	10.3778	−	34.6641i	0.383311	−	1.28035i	0.904341	−	0.426810i	$-0.140363\pi$
$734$	−2.11824	+	1.39319i	−0.0781856	+	0.0514235i
$735$	−41.9246	+	56.3350i	−1.54641	+	2.07795i
$736$	3.04612	−	3.22870i	0.112282	−	0.119012i
$737$	−4.78354	+	1.74107i	−0.176204	+	0.0641330i
$738$	−25.3626	+	16.6940i	−0.933612	+	0.614514i
$739$	36.4709	+	13.2743i	1.34160	+	0.488304i	0.910317	−	0.413911i	$-0.135837\pi$
$739$	36.4709	+	13.2743i	1.34160	+	0.488304i	0.431287	+	0.902215i	$0.358060\pi$
$740$	−13.0089	+	6.53333i	−0.478218	+	0.240170i
$741$	−16.9820	+	0.00297238i	−0.623849	+	0.000109193i
$742$	−7.82524	−	18.1409i	−0.287274	−	0.665975i
$743$	−19.5715	−	2.28758i	−0.718008	−	0.0839231i	−0.250760	−	0.968049i	$-0.580680\pi$
$743$	−19.5715	−	2.28758i	−0.718008	−	0.0839231i	−0.467248	+	0.884126i	$0.654755\pi$
$744$	5.59266	+	4.69113i	0.205037	+	0.171985i
$745$	61.0948	+	40.1827i	2.23834	+	1.47218i
$746$	−19.0342	+	15.9716i	−0.696893	+	0.584763i
$747$	−26.4157	−	9.60404i	−0.966498	−	0.351394i
$748$	3.49922	+	2.93620i	0.127944	+	0.107358i
$749$	18.1376	+	60.5838i	0.662734	+	2.21369i
$750$	−21.1514	−	10.6180i	−0.772338	−	0.387714i
$751$	1.38764	+	0.696900i	0.0506357	+	0.0254302i	0.473937	−	0.880559i	$-0.342832\pi$
$751$	1.38764	+	0.696900i	0.0506357	+	0.0254302i	−0.423301	+	0.905989i	$0.639129\pi$
$752$	2.85827	+	3.02959i	0.104230	+	0.110478i
$753$	3.60450	+	4.83991i	0.131355	+	0.176376i
$754$	4.23367	−	9.81475i	0.154181	−	0.357432i
$755$	5.84938	−	10.1314i	0.212881	−	0.368720i
$756$	3.81214	−	21.6863i	0.138646	−	0.788724i
$757$	−15.9246	−	27.5822i	−0.578790	−	1.00249i	−0.995618	−	0.0935085i	$-0.970192\pi$
$757$	−15.9246	−	27.5822i	−0.578790	−	1.00249i	0.416828	−	0.908985i	$-0.363142\pi$
$758$	−19.3468	+	2.26132i	−0.702709	+	0.0821349i
$759$	−0.378609	+	6.52013i	−0.0137426	+	0.236666i
$760$	14.4749	−	3.43061i	0.525059	−	0.124441i
$761$	0.836994	+	14.3706i	0.0303410	+	0.520935i	0.978901	+	0.204336i	$0.0655037\pi$
$761$	0.836994	+	14.3706i	0.0303410	+	0.520935i	−0.948560	+	0.316598i	$0.897459\pi$
$762$	−11.1142	−	11.7763i	−0.402626	−	0.426609i
$763$	−37.4688	−	8.88028i	−1.35646	−	0.321488i
$764$	0.000340193	−	0.00192933i	1.23077e−5	−	6.98007e-5i
$765$	−17.1403	−	57.1797i	−0.619708	−	2.06734i
$766$	−0.779283	−	4.41953i	−0.0281566	−	0.159684i
$767$	−0.371981	+	6.38667i	−0.0134315	+	0.230609i

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)

\(f(q)\)	\(=\)	\(q+(0.597159 + 0.802123i) q^{2} +(0.497048 + 1.65920i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-3.09160 + 2.03338i) q^{5} +(-1.03407 + 1.38950i) q^{6} +(2.90797 - 3.08226i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.50589 + 1.64940i) q^{9} +O(q^{10})\)	\(q+(0.597159 + 0.802123i) q^{2} +(0.497048 + 1.65920i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-3.09160 + 2.03338i) q^{5} +(-1.03407 + 1.38950i) q^{6} +(2.90797 - 3.08226i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-2.50589 + 1.64940i) q^{9} +(-3.47720 - 1.26560i) q^{10} +(0.759128 - 0.381249i) q^{11} +(-1.73205 + 0.000303164i) q^{12} +(0.965987 + 2.23941i) q^{13} +(4.20887 + 0.491947i) q^{14} +(-4.91046 - 4.11890i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(4.11923 - 3.45644i) q^{17} +(-2.81944 - 1.02507i) q^{18} +(3.07959 + 2.58408i) q^{19} +(-1.06127 - 3.54490i) q^{20} +(6.55949 + 3.29286i) q^{21} +(0.759128 + 0.381249i) q^{22} +(3.04612 + 3.22870i) q^{23} +(-1.03455 - 1.38914i) q^{24} +(3.44298 - 7.98172i) q^{25} +(-1.21944 + 2.11212i) q^{26} +(-3.98224 - 3.33793i) q^{27} +(2.11876 + 3.66980i) q^{28} +(-4.35310 + 0.508805i) q^{29} +(0.371542 - 6.39843i) q^{30} +(-4.10084 + 0.971917i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(1.00989 + 1.07005i) q^{33} +(5.23232 + 1.24008i) q^{34} +(-2.72287 + 15.4421i) q^{35} +(-0.861416 - 2.87367i) q^{36} +(-0.683139 - 3.87428i) q^{37} +(-0.233749 + 4.01332i) q^{38} +(-3.23549 + 2.71586i) q^{39} +(2.20970 - 2.96814i) q^{40} +(6.04398 - 8.11847i) q^{41} +(1.27577 + 7.22788i) q^{42} +(0.482068 - 8.27679i) q^{43} +(0.147512 + 0.836580i) q^{44} +(4.39334 - 10.1947i) q^{45} +(-0.770798 + 4.37141i) q^{46} +(-4.05284 - 0.960540i) q^{47} +(0.496467 - 1.65937i) q^{48} +(-0.637071 - 10.9381i) q^{49} +(8.45833 - 2.00466i) q^{50} +(7.78238 + 5.11660i) q^{51} +(-2.42238 + 0.283136i) q^{52} +(-2.33116 - 4.03769i) q^{53} +(0.299405 - 5.18752i) q^{54} +(-1.57170 + 2.72226i) q^{55} +(-1.67840 + 3.89096i) q^{56} +(-2.75680 + 6.39407i) q^{57} +(-3.00762 - 3.18789i) q^{58} +(2.34412 + 1.17726i) q^{59} +(5.35420 - 3.52285i) q^{60} +(2.78615 + 9.30637i) q^{61} +(-3.22845 - 2.70899i) q^{62} +(-2.20313 + 12.5202i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-7.54002 - 4.95915i) q^{65} +(-0.255244 + 1.44904i) q^{66} +(-5.95198 - 0.695686i) q^{67} +(2.12983 + 4.93749i) q^{68} +(-3.84299 + 6.65895i) q^{69} +(-14.0125 + 7.03733i) q^{70} +(-8.10000 - 2.94816i) q^{71} +(1.79063 - 2.40700i) q^{72} +(-11.0832 + 4.03394i) q^{73} +(2.69970 - 2.86152i) q^{74} +(14.9546 + 1.74529i) q^{75} +(-3.35876 + 2.20909i) q^{76} +(1.03241 - 3.44849i) q^{77} +(-4.11055 - 0.973459i) q^{78} +(-3.24979 - 4.36523i) q^{79} +3.70036 q^{80} +(3.55893 - 8.26644i) q^{81} +10.1212 q^{82} +(5.59485 + 7.51519i) q^{83} +(-5.03581 + 5.33952i) q^{84} +(-5.70675 + 19.0619i) q^{85} +(6.92687 - 4.55588i) q^{86} +(-3.00791 - 6.96977i) q^{87} +(-0.582953 + 0.617894i) q^{88} +(2.76651 - 1.00693i) q^{89} +(10.8009 - 2.56386i) q^{90} +(9.71151 + 3.53470i) q^{91} +(-3.96670 + 1.99215i) q^{92} +(-3.65092 - 6.32102i) q^{93} +(-1.64971 - 3.82447i) q^{94} +(-14.7753 - 1.72698i) q^{95} +(1.62749 - 0.592681i) q^{96} +(12.7982 + 8.41752i) q^{97} +(8.39326 - 7.04278i) q^{98} +(-1.27346 + 2.20747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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