LMFDB - Embedded newform 162.2.g.b.7.1

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			7.1
Character	$\chi$	$=$	162.7
Dual form			162.2.g.b.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.597159 + 0.802123i) q^{2} +(-1.58049 + 0.708545i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.763144 + 0.501928i) q^{5} +(-1.51215 - 0.844638i) q^{6} +(-2.48772 + 2.63683i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(1.99593 - 2.23970i) q^{9} +O(q^{10})$	\(q+(0.597159 + 0.802123i) q^{2} +(-1.58049 + 0.708545i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.763144 + 0.501928i) q^{5} +(-1.51215 - 0.844638i) q^{6} +(-2.48772 + 2.63683i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(1.99593 - 2.23970i) q^{9} +(-0.858326 - 0.312405i) q^{10} +(-1.62549 + 0.816349i) q^{11} +(-0.225488 - 1.71731i) q^{12} +(1.14262 + 2.64888i) q^{13} +(-3.60062 - 0.420852i) q^{14} +(0.850507 - 1.33402i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(1.97937 - 1.66088i) q^{17} +(2.98840 + 0.263522i) q^{18} +(4.50167 + 3.77735i) q^{19} +(-0.261969 - 0.875039i) q^{20} +(2.06351 - 5.93015i) q^{21} +(-1.62549 - 0.816349i) q^{22} +(-3.04911 - 3.23187i) q^{23} +(1.24284 - 1.20638i) q^{24} +(-1.64994 + 3.82499i) q^{25} +(-1.44241 + 2.49832i) q^{26} +(-1.56762 + 4.95404i) q^{27} +(-1.81257 - 3.13946i) q^{28} +(6.36671 - 0.744162i) q^{29} +(1.57793 - 0.114408i) q^{30} +(9.98756 - 2.36710i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(1.99065 - 2.44197i) q^{33} +(2.51423 + 0.595883i) q^{34} +(0.574991 - 3.26093i) q^{35} +(1.57317 + 2.55443i) q^{36} +(-0.884718 - 5.01748i) q^{37} +(-0.341689 + 5.86657i) q^{38} +(-3.68275 - 3.37695i) q^{39} +(0.545452 - 0.732669i) q^{40} +(-1.92249 + 2.58235i) q^{41} +(5.98896 - 1.88605i) q^{42} +(-0.617386 + 10.6001i) q^{43} +(-0.315860 - 1.79133i) q^{44} +(-0.399012 + 2.71103i) q^{45} +(0.771554 - 4.37570i) q^{46} +(-4.74694 - 1.12505i) q^{47} +(1.70984 + 0.276515i) q^{48} +(-0.357102 - 6.13120i) q^{49} +(-4.05339 + 0.960672i) q^{50} +(-1.95157 + 4.02749i) q^{51} +(-2.86531 + 0.334906i) q^{52} +(-0.666030 - 1.15360i) q^{53} +(-4.90987 + 1.70092i) q^{54} +(0.830731 - 1.43887i) q^{55} +(1.43584 - 3.32866i) q^{56} +(-9.79129 - 2.78045i) q^{57} +(4.39885 + 4.66251i) q^{58} +(-1.58253 - 0.794775i) q^{59} +(1.03405 + 1.19738i) q^{60} +(-0.231163 - 0.772139i) q^{61} +(7.86286 + 6.59772i) q^{62} +(0.940404 + 10.8347i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-2.20153 - 1.44797i) q^{65} +(3.14749 + 0.138507i) q^{66} +(-1.82355 - 0.213142i) q^{67} +(1.02342 + 2.37256i) q^{68} +(7.10903 + 2.94752i) q^{69} +(2.95903 - 1.48608i) q^{70} +(-10.4580 - 3.80641i) q^{71} +(-1.10954 + 2.78728i) q^{72} +(1.36325 - 0.496181i) q^{73} +(3.49632 - 3.70589i) q^{74} +(-0.102456 - 7.21444i) q^{75} +(-4.90976 + 3.22920i) q^{76} +(1.89118 - 6.31697i) q^{77} +(0.509543 - 4.97059i) q^{78} +(-8.29167 - 11.1376i) q^{79} +0.913412 q^{80} +(-1.03254 - 8.94057i) q^{81} -3.21940 q^{82} +(10.1964 + 13.6962i) q^{83} +(5.08920 + 3.67761i) q^{84} +(-0.676897 + 2.26099i) q^{85} +(-8.87127 + 5.83473i) q^{86} +(-9.53529 + 5.68725i) q^{87} +(1.24825 - 1.32307i) q^{88} +(11.0639 - 4.02694i) q^{89} +(-2.41285 + 1.29886i) q^{90} +(-9.82714 - 3.57679i) q^{91} +(3.97059 - 1.99411i) q^{92} +(-14.1081 + 10.8178i) q^{93} +(-1.93225 - 4.47946i) q^{94} +(-5.33138 - 0.623149i) q^{95} +(0.799244 + 1.53662i) q^{96} +(-3.03948 - 1.99910i) q^{97} +(4.70473 - 3.94774i) q^{98} +(-1.41597 + 5.26998i) 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
$3$	−1.58049	+	0.708545i	−0.912499	+	0.409079i
$3$	−1.58049	+	0.708545i	−0.912499	+	0.409079i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	−0.763144	+	0.501928i	−0.341289	+	0.224469i	−0.708569	−	0.705641i	$-0.750659\pi$
$5$	−0.763144	+	0.501928i	−0.341289	+	0.224469i	0.367281	+	0.930110i	$0.380289\pi$
$6$	−1.51215	−	0.844638i	−0.617331	−	0.344822i
$7$	−2.48772	+	2.63683i	−0.940269	+	0.996627i	−0.999999	−	0.00158777i	$-0.999495\pi$
$7$	−2.48772	+	2.63683i	−0.940269	+	0.996627i	0.0597298	+	0.998215i	$0.480976\pi$
$8$	−0.939693	+	0.342020i	−0.332232	+	0.120922i
$9$	1.99593	−	2.23970i	0.665309	−	0.746568i
$10$	−0.858326	−	0.312405i	−0.271427	−	0.0987912i
$11$	−1.62549	+	0.816349i	−0.490102	+	0.246139i	−0.676647	−	0.736308i	$-0.736567\pi$
$11$	−1.62549	+	0.816349i	−0.490102	+	0.246139i	0.186544	+	0.982447i	$0.440271\pi$
$12$	−0.225488	−	1.71731i	−0.0650927	−	0.495745i
$13$	1.14262	+	2.64888i	0.316905	+	0.734667i	0.999991	+	0.00432944i	$0.00137811\pi$
$13$	1.14262	+	2.64888i	0.316905	+	0.734667i	−0.683086	+	0.730338i	$0.739363\pi$
$14$	−3.60062	−	0.420852i	−0.962307	−	0.112478i
$15$	0.850507	−	1.33402i	0.219600	−	0.344442i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	1.97937	−	1.66088i	0.480067	−	0.402824i	−0.370384	−	0.928879i	$-0.620774\pi$
$17$	1.97937	−	1.66088i	0.480067	−	0.402824i	0.850451	+	0.526055i	$0.176329\pi$
$18$	2.98840	+	0.263522i	0.704373	+	0.0621128i
$19$	4.50167	+	3.77735i	1.03275	+	0.866584i	0.991176	−	0.132551i	$-0.0423170\pi$
$19$	4.50167	+	3.77735i	1.03275	+	0.866584i	0.0415782	+	0.999135i	$0.486761\pi$
$20$	−0.261969	−	0.875039i	−0.0585781	−	0.195665i
$21$	2.06351	−	5.93015i	0.450296	−	1.29407i
$22$	−1.62549	−	0.816349i	−0.346555	−	0.174046i
$23$	−3.04911	−	3.23187i	−0.635784	−	0.673891i	0.326732	−	0.945117i	$-0.394053\pi$
$23$	−3.04911	−	3.23187i	−0.635784	−	0.673891i	−0.962516	+	0.271226i	$0.912571\pi$
$24$	1.24284	−	1.20638i	0.253694	−	0.246250i
$25$	−1.64994	+	3.82499i	−0.329988	+	0.764999i
$26$	−1.44241	+	2.49832i	−0.282879	+	0.489961i
$27$	−1.56762	+	4.95404i	−0.301689	+	0.953406i
$28$	−1.81257	−	3.13946i	−0.342543	−	0.593302i
$29$	6.36671	−	0.744162i	1.18227	−	0.138187i	0.497841	−	0.867268i	$-0.334126\pi$
$29$	6.36671	−	0.744162i	1.18227	−	0.138187i	0.684428	+	0.729081i	$0.260052\pi$
$30$	1.57793	−	0.114408i	0.288090	−	0.0208879i
$31$	9.98756	−	2.36710i	1.79382	−	0.425143i	0.807483	−	0.589891i	$-0.200829\pi$
$31$	9.98756	−	2.36710i	1.79382	−	0.425143i	0.986336	+	0.164748i	$0.0526811\pi$
$32$	−0.0581448	−	0.998308i	−0.0102787	−	0.176478i
$33$	1.99065	−	2.44197i	0.346528	−	0.425092i
$34$	2.51423	+	0.595883i	0.431187	+	0.102193i
$35$	0.574991	−	3.26093i	0.0971912	−	0.551199i
$36$	1.57317	+	2.55443i	0.262196	+	0.425739i
$37$	−0.884718	−	5.01748i	−0.145447	−	0.824869i	−0.967007	−	0.254748i	$-0.918007\pi$
$37$	−0.884718	−	5.01748i	−0.145447	−	0.824869i	0.821561	−	0.570121i	$-0.193104\pi$
$38$	−0.341689	+	5.86657i	−0.0554293	+	0.951684i
$39$	−3.68275	−	3.37695i	−0.589712	−	0.540744i
$40$	0.545452	−	0.732669i	0.0862435	−	0.115845i
$41$	−1.92249	+	2.58235i	−0.300243	+	0.403296i	−0.926484	−	0.376333i	$-0.877185\pi$
$41$	−1.92249	+	2.58235i	−0.300243	+	0.403296i	0.626242	+	0.779629i	$0.284592\pi$
$42$	5.98896	−	1.88605i	0.924116	−	0.291023i
$43$	−0.617386	+	10.6001i	−0.0941505	+	1.61650i	0.538885	+	0.842379i	$0.318846\pi$
$43$	−0.617386	+	10.6001i	−0.0941505	+	1.61650i	−0.633036	+	0.774123i	$0.718191\pi$
$44$	−0.315860	−	1.79133i	−0.0476176	−	0.270053i
$45$	−0.399012	+	2.71103i	−0.0594811	+	0.404136i
$46$	0.771554	−	4.37570i	0.113759	−	0.645162i
$47$	−4.74694	−	1.12505i	−0.692413	−	0.164105i	−0.130681	−	0.991424i	$-0.541716\pi$
$47$	−4.74694	−	1.12505i	−0.692413	−	0.164105i	−0.561732	+	0.827320i	$0.689865\pi$
$48$	1.70984	+	0.276515i	0.246794	+	0.0399116i
$49$	−0.357102	−	6.13120i	−0.0510146	−	0.875886i
$50$	−4.05339	+	0.960672i	−0.573236	+	0.135859i
$51$	−1.95157	+	4.02749i	−0.273274	+	0.563961i
$52$	−2.86531	+	0.334906i	−0.397346	+	0.0464431i
$53$	−0.666030	−	1.15360i	−0.0914863	−	0.158459i	0.816650	−	0.577133i	$-0.195828\pi$
$53$	−0.666030	−	1.15360i	−0.0914863	−	0.158459i	−0.908137	+	0.418674i	$0.862495\pi$
$54$	−4.90987	+	1.70092i	−0.668149	+	0.231466i
$55$	0.830731	−	1.43887i	0.112016	−	0.194017i
$56$	1.43584	−	3.32866i	0.191872	−	0.444810i
$57$	−9.79129	−	2.78045i	−1.29689	−	0.368279i
$58$	4.39885	+	4.66251i	0.577597	+	0.612217i
$59$	−1.58253	−	0.794775i	−0.206028	−	0.103471i	0.342793	−	0.939411i	$-0.388627\pi$
$59$	−1.58253	−	0.794775i	−0.206028	−	0.103471i	−0.548821	+	0.835940i	$0.684923\pi$
$60$	1.03405	+	1.19738i	0.133495	+	0.154581i
$61$	−0.231163	−	0.772139i	−0.0295974	−	0.0988623i	0.941915	−	0.335852i	$-0.109024\pi$
$61$	−0.231163	−	0.772139i	−0.0295974	−	0.0988623i	−0.971512	+	0.236990i	$0.923839\pi$
$62$	7.86286	+	6.59772i	0.998584	+	0.837912i
$63$	0.940404	+	10.8347i	0.118480	+	1.36504i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	−2.20153	−	1.44797i	−0.273066	−	0.179598i
$66$	3.14749	+	0.138507i	0.387429	+	0.0170490i
$67$	−1.82355	−	0.213142i	−0.222782	−	0.0260394i	0.00396976	−	0.999992i	$-0.498736\pi$
$67$	−1.82355	−	0.213142i	−0.222782	−	0.0260394i	−0.226751	+	0.973953i	$0.572810\pi$
$68$	1.02342	+	2.37256i	0.124108	+	0.287715i
$69$	7.10903	+	2.94752i	0.855827	+	0.354840i
$70$	2.95903	−	1.48608i	0.353672	−	0.177621i
$71$	−10.4580	−	3.80641i	−1.24114	−	0.451738i	−0.363742	−	0.931500i	$-0.618501\pi$
$71$	−10.4580	−	3.80641i	−1.24114	−	0.451738i	−0.877399	+	0.479761i	$0.840723\pi$
$72$	−1.10954	+	2.78728i	−0.130760	+	0.328484i
$73$	1.36325	−	0.496181i	0.159556	−	0.0580736i	−0.261007	−	0.965337i	$-0.584055\pi$
$73$	1.36325	−	0.496181i	0.159556	−	0.0580736i	0.420563	+	0.907263i	$0.361832\pi$
$74$	3.49632	−	3.70589i	0.406439	−	0.430801i
$75$	−0.102456	−	7.21444i	−0.0118306	−	0.833052i
$76$	−4.90976	+	3.22920i	−0.563188	+	0.370414i
$77$	1.89118	−	6.31697i	0.215520	−	0.719885i
$78$	0.509543	−	4.97059i	0.0576944	−	0.562809i
$79$	−8.29167	−	11.1376i	−0.932885	−	1.25308i	−0.967290	−	0.253675i	$-0.918361\pi$
$79$	−8.29167	−	11.1376i	−0.932885	−	1.25308i	0.0344042	−	0.999408i	$-0.489047\pi$
$80$	0.913412			0.102123
$81$	−1.03254	−	8.94057i	−0.114727	−	0.993397i
$82$	−3.21940			−0.355523
$83$	10.1964	+	13.6962i	1.11921	+	1.50335i	0.839573	+	0.543247i	$0.182805\pi$
$83$	10.1964	+	13.6962i	1.11921	+	1.50335i	0.279633	+	0.960107i	$0.409787\pi$
$84$	5.08920	+	3.67761i	0.555277	+	0.401260i
$85$	−0.676897	+	2.26099i	−0.0734198	+	0.245239i
$86$	−8.87127	+	5.83473i	−0.956614	+	0.629175i
$87$	−9.53529	+	5.68725i	−1.02229	+	0.609737i
$88$	1.24825	−	1.32307i	0.133064	−	0.141039i
$89$	11.0639	−	4.02694i	1.17277	−	0.426855i	0.319130	−	0.947711i	$-0.396609\pi$
$89$	11.0639	−	4.02694i	1.17277	−	0.426855i	0.853645	+	0.520856i	$0.174387\pi$
$90$	−2.41285	+	1.29886i	−0.254337	+	0.136912i
$91$	−9.82714	−	3.57679i	−1.03016	−	0.374949i
$92$	3.97059	−	1.99411i	0.413963	−	0.207900i
$93$	−14.1081	+	10.8178i	−1.46294	+	1.12176i
$94$	−1.93225	−	4.47946i	−0.199297	−	0.462021i
$95$	−5.33138	−	0.623149i	−0.546988	−	0.0639338i
$96$	0.799244	+	1.53662i	0.0815725	+	0.156831i
$97$	−3.03948	−	1.99910i	−0.308613	−	0.202978i	0.385749	−	0.922604i	$-0.373943\pi$
$97$	−3.03948	−	1.99910i	−0.308613	−	0.202978i	−0.694362	+	0.719626i	$0.744313\pi$
$98$	4.70473	−	3.94774i	0.475250	−	0.398782i
$99$	−1.41597	+	5.26998i	−0.142310	+	0.529653i
$100$	−3.19110	−	2.67765i	−0.319110	−	0.267765i
$101$	3.45933	+	11.5550i	0.344217	+	1.14976i	0.938434	+	0.345459i	$0.112277\pi$
$101$	3.45933	+	11.5550i	0.344217	+	1.14976i	−0.594217	+	0.804305i	$0.702538\pi$
$102$	−4.39594	+	0.839654i	−0.435263	+	0.0831381i
$103$	5.04294	+	2.53266i	0.496895	+	0.249550i	0.679553	−	0.733626i	$-0.262174\pi$
$103$	5.04294	+	2.53266i	0.496895	+	0.249550i	−0.182658	+	0.983177i	$0.558470\pi$
$104$	−1.97968	−	2.09834i	−0.194123	−	0.205759i
$105$	1.40175	+	5.56130i	0.136797	+	0.542727i
$106$	0.527602	−	1.22312i	0.0512453	−	0.118800i
$107$	7.59333	−	13.1520i	0.734075	−	1.27146i	−0.221053	−	0.975262i	$-0.570949\pi$
$107$	7.59333	−	13.1520i	0.734075	−	1.27146i	0.955128	−	0.296194i	$-0.0957174\pi$
$108$	−4.29632	−	2.92260i	−0.413414	−	0.281228i
$109$	0.697000	+	1.20724i	0.0667605	+	0.115633i	0.897474	−	0.441068i	$-0.145400\pi$
$109$	0.697000	+	1.20724i	0.0667605	+	0.115633i	−0.830713	+	0.556701i	$0.812067\pi$
$110$	1.65023	−	0.192884i	0.157343	−	0.0183908i
$111$	4.95341	+	7.30325i	0.470156	+	0.693193i
$112$	3.52742	−	0.836013i	0.333310	−	0.0789958i
$113$	0.942909	+	16.1891i	0.0887014	+	1.52294i	0.689935	+	0.723871i	$0.257639\pi$
$113$	0.942909	+	16.1891i	0.0887014	+	1.52294i	−0.601234	+	0.799073i	$0.705324\pi$
$114$	−3.61669	−	9.51419i	−0.338734	−	0.891086i
$115$	3.94908	+	0.935949i	0.368253	+	0.0872776i
$116$	−1.11309	+	6.31267i	−0.103348	+	0.586117i
$117$	8.21329	+	2.72786i	0.759318	+	0.252190i
$118$	−0.307512	−	1.74399i	−0.0283088	−	0.160547i
$119$	−0.544637	+	9.35106i	−0.0499268	+	0.857210i
$120$	−0.342955	+	1.54446i	−0.0313073	+	0.140989i
$121$	−4.59297	+	6.16943i	−0.417543	+	0.560857i
$122$	0.481310	−	0.646511i	0.0435757	−	0.0585324i
$123$	1.20877	−	5.44357i	0.108991	−	0.490830i
$124$	−0.596812	+	10.2469i	−0.0535953	+	0.920196i
$125$	−1.45379	−	8.24485i	−0.130031	−	0.737442i
$126$	−8.12917	+	7.22433i	−0.724204	+	0.643595i
$127$	0.311069	−	1.76416i	0.0276029	−	0.156544i	−0.967891	−	0.251371i	$-0.919119\pi$
$127$	0.311069	−	1.76416i	0.0276029	−	0.156544i	0.995494	+	0.0948268i	$0.0302297\pi$
$128$	0.973045	+	0.230616i	0.0860058	+	0.0203838i
$129$	−6.53488	−	17.1909i	−0.575364	−	1.51357i
$130$	−0.153213	−	2.63056i	−0.0134377	−	0.230716i
$131$	18.7905	−	4.45344i	1.64174	−	0.389098i	0.697036	−	0.717036i	$-0.254502\pi$
$131$	18.7905	−	4.45344i	1.64174	−	0.389098i	0.944699	+	0.327937i	$0.106354\pi$
$132$	1.76845	+	2.60739i	0.153924	+	0.226944i
$133$	−21.1591	+	2.47315i	−1.83473	+	0.214449i
$134$	−0.917980	−	1.58999i	−0.0793014	−	0.137354i
$135$	−1.29025	−	4.56749i	−0.111047	−	0.393107i
$136$	−1.29194	+	2.23770i	−0.110783	+	0.191882i
$137$	6.79776	−	15.7590i	0.580772	−	1.34638i	−0.334063	−	0.942551i	$-0.608420\pi$
$137$	6.79776	−	15.7590i	0.580772	−	1.34638i	0.914834	−	0.403829i	$-0.132321\pi$
$138$	1.88094	+	7.46245i	0.160117	+	0.635246i
$139$	−0.228493	−	0.242188i	−0.0193805	−	0.0205421i	0.717611	−	0.696444i	$-0.245236\pi$
$139$	−0.228493	−	0.242188i	−0.0193805	−	0.0205421i	−0.736991	+	0.675902i	$0.763754\pi$
$140$	2.95903	+	1.48608i	0.250084	+	0.125597i
$141$	8.29967	−	1.58529i	0.698958	−	0.133506i
$142$	−3.19189	−	10.6617i	−0.267858	−	0.894707i
$143$	−4.01972	−	3.37294i	−0.336146	−	0.282060i
$144$	−2.89831	+	0.774464i	−0.241526	+	0.0645387i
$145$	−4.48521	+	3.76353i	−0.372476	+	0.312545i
$146$	1.21207	+	0.797193i	0.100312	+	0.0659761i
$147$	4.90863	+	9.43731i	0.404857	+	0.778376i
$148$	5.06044	+	0.591480i	0.415965	+	0.0486194i
$149$	0.482969	+	1.11965i	0.0395664	+	0.0917252i	0.936853	−	0.349723i	$-0.113724\pi$
$149$	0.482969	+	1.11965i	0.0395664	+	0.0917252i	−0.897287	+	0.441448i	$0.854465\pi$
$150$	5.72569	−	4.39035i	0.467500	−	0.358470i
$151$	13.7265	−	6.89370i	1.11704	−	0.561001i	0.208180	−	0.978091i	$-0.433246\pi$
$151$	13.7265	−	6.89370i	1.11704	−	0.561001i	0.908865	+	0.417090i	$0.136950\pi$
$152$	−5.52212	−	2.00989i	−0.447903	−	0.163023i
$153$	0.230782	−	7.74820i	0.0186576	−	0.626405i
$154$	6.19632	−	2.25528i	0.499314	−	0.181735i
$155$	−6.43384	+	6.81947i	−0.516778	+	0.547753i
$156$	4.29130	−	2.55952i	0.343579	−	0.204925i
$157$	5.57611	−	3.66747i	0.445022	−	0.292696i	−0.307151	−	0.951661i	$-0.599376\pi$
$157$	5.57611	−	3.66747i	0.445022	−	0.292696i	0.752174	+	0.658965i	$0.229005\pi$
$158$	3.98232	−	13.3019i	0.316816	−	1.05824i
$159$	1.87003	+	1.35134i	0.148303	+	0.107169i
$160$	0.545452	+	0.732669i	0.0431217	+	0.0579225i
$161$	16.1072			1.26943
$162$	6.55485	−	6.16717i	0.514998	−	0.484538i
$163$	15.5984			1.22176			0.610881	−	0.791723i	$-0.290815\pi$
$163$	15.5984			1.22176			0.610881	+	0.791723i	$0.290815\pi$
$164$	−1.92249	−	2.58235i	−0.150121	−	0.201648i
$165$	−0.293463	+	2.86274i	−0.0228461	+	0.222864i
$166$	−4.89715	+	16.3576i	−0.380092	+	1.26960i
$167$	17.6277	−	11.5939i	1.36407	−	0.897164i	0.364649	−	0.931145i	$-0.381189\pi$
$167$	17.6277	−	11.5939i	1.36407	−	0.897164i	0.999422	+	0.0339814i	$0.0108187\pi$
$168$	0.0891615	+	6.27828i	0.00687896	+	0.484380i
$169$	3.21014	−	3.40255i	0.246934	−	0.261735i
$170$	−2.21781	+	0.807217i	−0.170098	+	0.0619107i
$171$	17.4452	−	2.54309i	1.33406	−	0.194475i
$172$	−9.97773	−	3.63160i	−0.760795	−	0.276907i
$173$	−13.7739	+	6.91749i	−1.04721	+	0.525927i	−0.887294	−	0.461204i	$-0.847418\pi$
$173$	−13.7739	+	6.91749i	−1.04721	+	0.525927i	−0.159913	+	0.987131i	$0.551121\pi$
$174$	−10.2560	−	4.25229i	−0.777502	−	0.322365i
$175$	−5.98126	−	13.8661i	−0.452141	−	1.04818i
$176$	1.80666	+	0.211169i	0.136182	+	0.0159174i
$177$	3.06431	+	0.134846i	0.230328	+	0.0101357i
$178$	9.83703	+	6.46991i	0.737316	+	0.484941i
$179$	−12.0338	+	10.0976i	−0.899452	+	0.754730i	−0.970083	−	0.242773i	$-0.921943\pi$
$179$	−12.0338	+	10.0976i	−0.899452	+	0.754730i	0.0706312	+	0.997502i	$0.477499\pi$
$180$	−2.48270	−	1.15978i	−0.185049	−	0.0864450i
$181$	4.16827	+	3.49760i	0.309825	+	0.259974i	0.784420	−	0.620230i	$-0.212961\pi$
$181$	4.16827	+	3.49760i	0.309825	+	0.259974i	−0.474594	+	0.880205i	$0.657405\pi$
$182$	−2.99934	−	10.0185i	−0.222326	−	0.742620i
$183$	0.912448	+	1.05657i	0.0674501	+	0.0781041i
$184$	3.97059	+	1.99411i	0.292716	+	0.147007i
$185$	3.19358	+	3.38500i	0.234797	+	0.248870i
$186$	−17.1020	−	4.85648i	−1.25398	−	0.356094i
$187$	−1.86157	+	4.31560i	−0.136131	+	0.315588i
$188$	2.43922	−	4.22485i	0.177898	−	0.308129i
$189$	−9.16315	−	16.4578i	−0.666521	−	1.19713i
$190$	−2.68384	−	4.64855i	−0.194706	−	0.337241i
$191$	−13.2127	+	1.54434i	−0.956035	+	0.111744i	−0.579781	−	0.814772i	$-0.696862\pi$
$191$	−13.2127	+	1.54434i	−0.956035	+	0.111744i	−0.376253	+	0.926517i	$0.622788\pi$
$192$	−0.755285	+	1.55870i	−0.0545080	+	0.112489i
$193$	17.1642	−	4.06798i	1.23550	−	0.292820i	0.439573	−	0.898207i	$-0.355130\pi$
$193$	17.1642	−	4.06798i	1.23550	−	0.292820i	0.795931	+	0.605387i	$0.206982\pi$
$194$	−0.211529	−	3.63182i	−0.0151869	−	0.260749i
$195$	4.50545	+	0.728624i	0.322642	+	0.0521778i
$196$	5.97605	+	1.41635i	0.426860	+	0.101168i
$197$	−4.53564	+	25.7229i	−0.323151	+	1.83268i	0.199214	+	0.979956i	$0.436161\pi$
$197$	−4.53564	+	25.7229i	−0.323151	+	1.83268i	−0.522364	+	0.852722i	$0.674950\pi$
$198$	−5.07273	+	2.01123i	−0.360503	+	0.142932i
$199$	−3.56722	−	20.2307i	−0.252874	−	1.43412i	−0.801472	−	0.598032i	$-0.795950\pi$
$199$	−3.56722	−	20.2307i	−0.252874	−	1.43412i	0.548599	−	0.836086i	$-0.315162\pi$
$200$	0.242213	−	4.15863i	0.0171270	−	0.294060i
$201$	3.03313	−	0.955194i	0.213940	−	0.0673742i
$202$	−7.20275	+	9.67497i	−0.506784	+	0.680728i
$203$	−13.8764	+	18.6392i	−0.973930	+	1.30821i
$204$	−3.29858	−	3.02468i	−0.230947	−	0.211770i
$205$	0.170983	−	2.93566i	0.0119419	−	0.205035i
$206$	0.979930	+	5.55746i	0.0682749	+	0.387206i
$207$	−13.3242	+	0.378526i	−0.926098	+	0.0263094i
$208$	0.500942	−	2.84098i	0.0347341	−	0.196987i
$209$	−10.4010	−	2.46509i	−0.719455	−	0.170514i
$210$	−3.62378	+	4.44535i	−0.250064	+	0.306758i
$211$	−0.930015	−	15.9677i	−0.0640249	−	1.09927i	−0.865393	−	0.501094i	$-0.832931\pi$
$211$	−0.930015	−	15.9677i	−0.0640249	−	1.09927i	0.801368	−	0.598171i	$-0.204106\pi$
$212$	1.29615	−	0.307194i	0.0890203	−	0.0210982i
$213$	19.2259	−	1.39397i	1.31734	−	0.0955134i
$214$	15.0840	−	1.76306i	1.03112	−	0.120521i
$215$	−4.84934	−	8.39930i	−0.330722	−	0.572827i
$216$	−0.221299	−	5.19144i	−0.0150575	−	0.353233i
$217$	−18.6046	+	32.2241i	−1.26296	+	2.18752i
$218$	−0.552135	+	1.27999i	−0.0373953	+	0.0866921i
$219$	−1.80304	+	1.75013i	−0.121838	+	0.118263i
$220$	1.14016	+	1.20850i	0.0768699	+	0.0814773i
$221$	6.66114	+	3.34535i	0.448077	+	0.225033i
$222$	−2.90013	+	8.33444i	−0.194644	+	0.559371i
$223$	2.02932	+	6.77839i	0.135893	+	0.453914i	0.998664	−	0.0516812i	$-0.0164580\pi$
$223$	2.02932	+	6.77839i	0.135893	+	0.453914i	−0.862771	+	0.505596i	$0.831273\pi$
$224$	2.77701	+	2.33019i	0.185547	+	0.155692i
$225$	5.27369	+	11.3298i	0.351579	+	0.755319i
$226$	−12.4226	+	10.4238i	−0.826339	+	0.693381i
$227$	−16.2835	−	10.7098i	−1.08077	−	0.710836i	−0.121295	−	0.992617i	$-0.538705\pi$
$227$	−16.2835	−	10.7098i	−1.08077	−	0.710836i	−0.959479	+	0.281781i	$0.909075\pi$
$228$	5.47181	−	8.58251i	0.362380	−	0.568391i
$229$	−4.72356	−	0.552105i	−0.312142	−	0.0364841i	−0.0414200	−	0.999142i	$-0.513188\pi$
$229$	−4.72356	−	0.552105i	−0.312142	−	0.0364841i	−0.270722	+	0.962658i	$0.587262\pi$
$230$	1.60748	+	3.72656i	0.105994	+	0.245722i
$231$	1.48686	+	11.3239i	0.0978283	+	0.745059i
$232$	−5.72824	+	2.87683i	−0.376077	+	0.188873i
$233$	−11.1130	−	4.04481i	−0.728038	−	0.264984i	−0.0487037	−	0.998813i	$-0.515509\pi$
$233$	−11.1130	−	4.04481i	−0.728038	−	0.264984i	−0.679334	+	0.733829i	$0.737731\pi$
$234$	2.71656	+	8.21703i	0.177587	+	0.537164i
$235$	4.18729	−	1.52405i	0.273149	−	0.0994181i
$236$	1.21526	−	1.28810i	0.0791067	−	0.0838482i
$237$	20.9965	+	11.7280i	1.36387	+	0.761813i
$238$	−7.82593	+	5.14720i	−0.507280	+	0.333643i
$239$	−0.631771	+	2.11026i	−0.0408659	+	0.136502i	−0.975988	−	0.217824i	$-0.930104\pi$
$239$	−0.631771	+	2.11026i	−0.0408659	+	0.136502i	0.935122	+	0.354325i	$0.115289\pi$
$240$	−1.44364	+	0.647193i	−0.0931867	+	0.0417761i
$241$	−8.59016	−	11.5386i	−0.553341	−	0.743265i	0.434168	−	0.900832i	$-0.357043\pi$
$241$	−8.59016	−	11.5386i	−0.553341	−	0.743265i	−0.987508	+	0.157567i	$0.949635\pi$
$242$	−7.69137			−0.494420
$243$	7.96673	+	13.3989i	0.511066	+	0.859542i
$244$	0.806000			0.0515989
$245$	3.34994	+	4.49975i	0.214020	+	0.287479i
$246$	5.08824	−	2.28109i	0.324414	−	0.145437i
$247$	−4.86207	+	16.2405i	−0.309366	+	1.03336i
$248$	−8.57564	+	5.64029i	−0.544554	+	0.358159i
$249$	−25.8198	−	14.4221i	−1.63626	−	0.913966i
$250$	5.74524	−	6.08960i	0.363361	−	0.385140i
$251$	−8.59039	+	3.12664i	−0.542220	+	0.197352i	−0.598587	−	0.801058i	$-0.704271\pi$
$251$	−8.59039	+	3.12664i	−0.542220	+	0.197352i	0.0563663	+	0.998410i	$0.482049\pi$
$252$	−10.6492	−	2.20652i	−0.670837	−	0.138998i
$253$	7.59462	+	2.76422i	0.477470	+	0.173785i
$254$	1.60083	−	0.803968i	0.100445	−	0.0504455i
$255$	−0.532183	−	4.05310i	−0.0333266	−	0.253815i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	−6.89126	−	0.805473i	−0.429865	−	0.0502440i	−0.101590	−	0.994826i	$-0.532393\pi$
$257$	−6.89126	−	0.805473i	−0.429865	−	0.0502440i	−0.328275	+	0.944582i	$0.606467\pi$
$258$	9.88684	−	15.5075i	0.615527	−	0.965452i
$259$	15.4312	+	10.1492i	0.958846	+	0.630643i
$260$	2.01854	−	1.69376i	0.125185	−	0.105042i
$261$	11.0408	−	15.7448i	0.683408	−	0.974581i
$262$	14.7931	+	12.4129i	0.913922	+	0.766872i
$263$	−6.25296	−	20.8863i	−0.385574	−	1.28791i	−0.902060	−	0.431611i	$-0.857945\pi$
$263$	−6.25296	−	20.8863i	−0.385574	−	1.28791i	0.516486	−	0.856296i	$-0.327240\pi$
$264$	−1.03540	+	2.97554i	−0.0637244	+	0.183132i
$265$	1.08730	+	0.546063i	0.0667923	+	0.0335444i
$266$	−14.6191	−	15.4954i	−0.896355	−	0.950081i
$267$	−14.6332	+	14.2039i	−0.895539	+	0.869262i
$268$	0.727186	−	1.68581i	0.0444200	−	0.102977i
$269$	−12.1002	+	20.9582i	−0.737764	+	1.27784i	0.215736	+	0.976452i	$0.430785\pi$
$269$	−12.1002	+	20.9582i	−0.737764	+	1.27784i	−0.953500	+	0.301393i	$0.902548\pi$
$270$	2.89320	−	3.76245i	0.176075	−	0.228976i
$271$	10.8050	+	18.7148i	0.656357	+	1.13684i	0.981552	+	0.191196i	$0.0612366\pi$
$271$	10.8050	+	18.7148i	0.656357	+	1.13684i	−0.325195	+	0.945647i	$0.605430\pi$
$272$	−2.56641	+	0.299970i	−0.155611	+	0.0181883i
$273$	18.0661	−	1.30988i	1.09341	−	0.0792774i
$274$	16.7000	−	3.95797i	1.00888	−	0.239110i
$275$	−0.440576	−	7.56440i	−0.0265677	−	0.456150i
$276$	−4.86259	+	5.96502i	−0.292693	+	0.359052i
$277$	−6.95302	−	1.64790i	−0.417767	−	0.0990125i	0.0163561	−	0.999866i	$-0.494793\pi$
$277$	−6.95302	−	1.64790i	−0.417767	−	0.0990125i	−0.434123	+	0.900854i	$0.642942\pi$
$278$	0.0578183	−	0.327904i	0.00346771	−	0.0196664i
$279$	14.6329	−	27.0937i	0.876046	−	1.62206i
$280$	0.574991	+	3.26093i	0.0343623	+	0.194878i
$281$	−0.831592	+	14.2779i	−0.0496086	+	0.851748i	0.878108	+	0.478462i	$0.158806\pi$
$281$	−0.831592	+	14.2779i	−0.0496086	+	0.851748i	−0.927717	+	0.373285i	$0.878231\pi$
$282$	6.22782	+	5.71068i	0.370861	+	0.340066i
$283$	−13.9323	+	18.7143i	−0.828190	+	1.11245i	0.163845	+	0.986486i	$0.447610\pi$
$283$	−13.9323	+	18.7143i	−0.828190	+	1.11245i	−0.992035	+	0.125966i	$0.959797\pi$
$284$	6.64590	−	8.92700i	0.394362	−	0.529720i
$285$	8.86775	−	2.79264i	0.525280	−	0.165422i
$286$	0.305107	−	5.23849i	0.0180414	−	0.309758i
$287$	−2.02660	−	11.4934i	−0.119627	−	0.678436i
$288$	−2.35197	−	1.86232i	−0.138591	−	0.109739i
$289$	−1.79267	+	10.1667i	−0.105451	+	0.598043i
$290$	−5.69720	−	1.35026i	−0.334551	−	0.0792900i
$291$	6.22034	+	1.00596i	0.364643	+	0.0589702i
$292$	0.0843528	+	1.44828i	0.00493637	+	0.0847543i
$293$	−14.3638	+	3.40429i	−0.839145	+	0.198881i	−0.627648	−	0.778498i	$-0.715982\pi$
$293$	−14.3638	+	3.40429i	−0.839145	+	0.198881i	−0.211497	+	0.977379i	$0.567834\pi$
$294$	−4.63866	+	9.57290i	−0.270532	+	0.558303i
$295$	1.60662	−	0.187787i	0.0935409	−	0.0109334i
$296$	2.54744	+	4.41230i	0.148067	+	0.256460i
$297$	−1.49608	−	9.33245i	−0.0868115	−	0.541524i
$298$	−0.609687	+	1.05601i	−0.0353182	+	0.0611729i
$299$	5.07687	−	11.7695i	0.293603	−	0.680649i
$300$	6.94074	+	1.97097i	0.400724	+	0.113794i
$301$	−26.4148	−	27.9980i	−1.52252	−	1.61378i
$302$	13.7265	+	6.89370i	0.789870	+	0.396688i
$303$	−13.6547	−	15.8115i	−0.784441	−	0.908347i
$304$	−1.68540	−	5.62964i	−0.0966645	−	0.322882i
$305$	0.563969	+	0.473226i	0.0322928	+	0.0270969i
$306$	6.35282	−	4.44179i	0.363167	−	0.253920i
$307$	13.1475	−	11.0321i	0.750368	−	0.629633i	−0.185233	−	0.982695i	$-0.559304\pi$
$307$	13.1475	−	11.0321i	0.750368	−	0.629633i	0.935600	+	0.353062i	$0.114859\pi$
$308$	5.50919	+	3.62345i	0.313916	+	0.206465i
$309$	−9.76484	−	0.429706i	−0.555502	−	0.0244451i
$310$	−9.31208	−	1.08843i	−0.528890	−	0.0618184i
$311$	−3.20825	−	7.43755i	−0.181923	−	0.421745i	0.802713	−	0.596366i	$-0.203389\pi$
$311$	−3.20825	−	7.43755i	−0.181923	−	0.421745i	−0.984636	+	0.174621i	$0.944130\pi$
$312$	4.61564	+	1.91372i	0.261309	+	0.108343i
$313$	−2.75103	+	1.38162i	−0.155497	+	0.0780937i	−0.524846	−	0.851197i	$-0.675877\pi$
$313$	−2.75103	+	1.38162i	−0.155497	+	0.0780937i	0.369349	+	0.929291i	$0.379581\pi$
$314$	6.27159	+	2.28267i	0.353926	+	0.128819i
$315$	−6.15589	−	7.79640i	−0.346845	−	0.439277i
$316$	13.0478	−	4.74902i	0.733997	−	0.267153i
$317$	15.6150	−	16.5509i	0.877025	−	0.929592i	−0.120985	−	0.992654i	$-0.538605\pi$
$317$	15.6150	−	16.5509i	0.877025	−	0.929592i	0.998010	+	0.0630627i	$0.0200868\pi$
$318$	0.0327625	+	2.30696i	0.00183723	+	0.129368i
$319$	−9.74150	+	6.40709i	−0.545419	+	0.358728i
$320$	−0.261969	+	0.875039i	−0.0146445	+	0.0489162i
$321$	−2.68241	+	26.1670i	−0.149718	+	1.46050i
$322$	9.61856	+	12.9200i	0.536021	+	0.720001i
$323$	15.1842			0.844871
$324$	8.86111	+	1.57502i	0.492284	+	0.0875012i
$325$	−12.0172			−0.666594
$326$	9.31472	+	12.5118i	0.515895	+	0.692967i
$327$	−1.95699	−	1.41418i	−0.108222	−	0.0782043i
$328$	0.923333	−	3.08415i	0.0509826	−	0.170294i
$329$	14.7756	−	9.71807i	0.814606	−	0.535774i
$330$	−2.47151	+	1.47411i	−0.136052	+	0.0811473i
$331$	14.6606	−	15.5393i	0.805820	−	0.854119i	−0.185896	−	0.982569i	$-0.559519\pi$
$331$	14.6606	−	15.5393i	0.805820	−	0.854119i	0.991716	+	0.128450i	$0.0410002\pi$
$332$	−16.0452	+	5.83997i	−0.880595	+	0.320510i
$333$	−13.0035	−	8.03303i	−0.712588	−	0.440207i
$334$	19.8263	+	7.21617i	1.08485	+	0.394851i
$335$	1.49861	−	0.752630i	0.0818778	−	0.0411206i
$336$	−4.98271	+	3.82065i	−0.271829	+	0.208433i
$337$	6.60652	+	15.3156i	0.359880	+	0.834296i	0.997931	+	0.0643014i	$0.0204819\pi$
$337$	6.60652	+	15.3156i	0.359880	+	0.834296i	−0.638050	+	0.769995i	$0.720259\pi$
$338$	4.64623	+	0.543067i	0.252722	+	0.0295389i
$339$	−12.9610	−	24.9187i	−0.703944	−	1.35340i
$340$	−1.97187	−	1.29692i	−0.106940	−	0.0703354i
$341$	−14.3023	+	12.0010i	−0.774510	+	0.649891i
$342$	12.4574	+	12.4745i	0.673619	+	0.674546i
$343$	−2.38380	−	2.00025i	−0.128713	−	0.108003i
$344$	−3.04530	−	10.1720i	−0.164192	−	0.548438i
$345$	−6.90466	+	1.31884i	−0.371734	+	0.0710038i
$346$	−13.7739	−	6.91749i	−0.740487	−	0.371887i
$347$	6.55347	+	6.94628i	0.351809	+	0.372896i	0.878976	−	0.476866i	$-0.158227\pi$
$347$	6.55347	+	6.94628i	0.351809	+	0.372896i	−0.527167	+	0.849762i	$0.676746\pi$
$348$	−2.71357	−	10.7658i	−0.145463	−	0.577109i
$349$	2.87774	−	6.67136i	0.154042	−	0.357110i	−0.823667	−	0.567074i	$-0.808075\pi$
$349$	2.87774	−	6.67136i	0.154042	−	0.357110i	0.977709	+	0.209964i	$0.0673347\pi$
$350$	7.55057	−	13.0780i	0.403595	−	0.699047i
$351$	−14.9139	+	1.50812i	−0.796043	+	0.0804975i
$352$	0.909482	+	1.57527i	0.0484755	+	0.0839621i
$353$	15.6180	−	1.82548i	0.831261	−	0.0971604i	0.310191	−	0.950674i	$-0.399607\pi$
$353$	15.6180	−	1.82548i	0.831261	−	0.0971604i	0.521070	+	0.853514i	$0.325533\pi$
$354$	1.72172	+	2.53848i	0.0915082	+	0.134919i
$355$	9.89154	−	2.34434i	0.524988	−	0.124425i
$356$	0.684597	+	11.7541i	0.0362836	+	0.622965i
$357$	−5.76485	−	15.1652i	−0.305108	−	0.802627i
$358$	−15.2856	−	3.62276i	−0.807871	−	0.191469i
$359$	0.639302	−	3.62566i	0.0337411	−	0.191355i	−0.963278	−	0.268504i	$-0.913471\pi$
$359$	0.639302	−	3.62566i	0.0337411	−	0.191355i	0.997020	+	0.0771492i	$0.0245818\pi$
$360$	−0.552278	−	2.68400i	−0.0291076	−	0.141459i
$361$	2.69735	+	15.2974i	0.141966	+	0.805129i
$362$	−0.316383	+	5.43209i	−0.0166287	+	0.285504i
$363$	2.88785	−	13.0051i	0.151573	−	0.682589i
$364$	6.24498	−	8.38847i	0.327326	−	0.439675i
$365$	−0.791306	+	1.06291i	−0.0414189	+	0.0556352i
$366$	−0.302625	+	1.36284i	−0.0158185	+	0.0712366i
$367$	1.43152	−	24.5783i	0.0747249	−	1.28298i	−0.727563	−	0.686041i	$-0.759347\pi$
$367$	1.43152	−	24.5783i	0.0747249	−	1.28298i	0.802288	−	0.596937i	$-0.203616\pi$
$368$	0.771554	+	4.37570i	0.0402200	+	0.228099i
$369$	1.94655	+	9.46000i	0.101333	+	0.492468i
$370$	−0.808112	+	4.58303i	−0.0420117	+	0.238260i
$371$	4.69873	+	1.11362i	0.243946	+	0.0578163i
$372$	−6.31711	−	16.6180i	−0.327527	−	0.861603i
$373$	−1.87049	−	32.1151i	−0.0968505	−	1.66286i	−0.601005	−	0.799246i	$-0.705233\pi$
$373$	−1.87049	−	32.1151i	−0.0968505	−	1.66286i	0.504154	−	0.863614i	$-0.331804\pi$
$374$	−4.57329	+	1.08389i	−0.236479	+	0.0560466i
$375$	8.13955	+	12.0009i	0.420325	+	0.619722i
$376$	4.84546	−	0.566353i	0.249885	−	0.0292074i
$377$	9.24590	+	16.0144i	0.476188	+	0.824782i
$378$	7.72934	−	17.1779i	0.397554	−	0.883536i
$379$	5.50063	−	9.52737i	0.282548	−	0.489388i	−0.689463	−	0.724321i	$-0.742154\pi$
$379$	5.50063	−	9.52737i	0.282548	−	0.489388i	0.972012	+	0.234933i	$0.0754869\pi$
$380$	2.12603	−	4.92869i	0.109063	−	0.252836i
$381$	0.758344	+	3.00865i	0.0388512	+	0.154138i
$382$	−9.12880	−	9.67597i	−0.467070	−	0.495065i
$383$	14.8322	+	7.44901i	0.757890	+	0.380627i	0.785395	−	0.618995i	$-0.212460\pi$
$383$	14.8322	+	7.44901i	0.757890	+	0.380627i	−0.0275050	+	0.999622i	$0.508756\pi$
$384$	−1.70129	+	0.324959i	−0.0868188	+	0.0165830i
$385$	1.72742	+	5.76999i	0.0880376	+	0.294066i
$386$	13.5128	+	11.3386i	0.687781	+	0.577117i
$387$	22.5088	+	22.5398i	1.14419	+	1.14576i
$388$	2.78685	−	2.33844i	0.141481	−	0.118717i
$389$	−12.9544	−	8.52024i	−0.656814	−	0.431993i	0.176871	−	0.984234i	$-0.443403\pi$
$389$	−12.9544	−	8.52024i	−0.656814	−	0.431993i	−0.833685	+	0.552241i	$0.813773\pi$
$390$	2.10602	+	4.04903i	0.106643	+	0.205031i
$391$	−11.4031	−	1.33283i	−0.576678	−	0.0674040i
$392$	2.43256	+	5.63931i	0.122863	+	0.284828i
$393$	−26.5429	+	20.3526i	−1.33891	+	1.02665i
$394$	−23.3414	+	11.7225i	−1.17592	+	0.590571i
$395$	11.9180	+	4.33781i	0.599661	+	0.218259i
$396$	−4.64248	−	2.86793i	−0.233293	−	0.144119i
$397$	0.773497	−	0.281530i	0.0388207	−	0.0141296i	−0.322537	−	0.946557i	$-0.604536\pi$
$397$	0.773497	−	0.281530i	0.0388207	−	0.0141296i	0.361358	+	0.932427i	$0.382313\pi$
$398$	14.0973	−	14.9423i	0.706636	−	0.748990i
$399$	31.6895	−	18.9010i	1.58646	−	0.946232i
$400$	3.48037	−	2.28908i	0.174019	−	0.114454i
$401$	0.189823	−	0.634052i	0.00947929	−	0.0316630i	−0.953119	−	0.302596i	$-0.902147\pi$
$401$	0.189823	−	0.634052i	0.00947929	−	0.0316630i	0.962598	+	0.270933i	$0.0873320\pi$
$402$	2.57744	+	1.86254i	0.128551	+	0.0928949i
$403$	17.6821	+	23.7512i	0.880808	+	1.18313i
$404$	−12.0617			−0.600092
$405$	5.27550	+	6.30469i	0.262142	+	0.313282i
$406$	−23.2373			−1.15325
$407$	5.53412	+	7.43361i	0.274316	+	0.368470i
$408$	0.456389	−	4.45208i	0.0225946	−	0.220411i
$409$	−7.32433	+	24.4650i	−0.362165	+	1.20971i	0.561812	+	0.827265i	$0.310105\pi$
$409$	−7.32433	+	24.4650i	−0.362165	+	1.20971i	−0.923976	+	0.382450i	$0.875081\pi$
$410$	2.45686	−	1.61590i	0.121336	−	0.0798039i
$411$	0.422120	+	29.7235i	0.0208217	+	1.46615i
$412$	−3.87259	+	4.10471i	−0.190789	+	0.202224i
$413$	6.03257	−	2.19568i	0.296843	−	0.108042i
$414$	−8.26031	−	10.4616i	−0.405972	−	0.514161i
$415$	−14.6559	−	5.33430i	−0.719428	−	0.261851i
$416$	2.57796	−	1.29470i	0.126395	−	0.0634779i
$417$	0.532732	+	0.220880i	0.0260880	+	0.0108165i
$418$	−4.23376	−	9.81496i	−0.207080	−	0.480066i
$419$	10.3106	+	1.20513i	0.503704	+	0.0588745i	0.364151	−	0.931340i	$-0.381359\pi$
$419$	10.3106	+	1.20513i	0.503704	+	0.0588745i	0.139553	+	0.990215i	$0.455433\pi$
$420$	−5.72969	−	0.252137i	−0.279580	−	0.0123030i
$421$	7.04001	+	4.63029i	0.343109	+	0.225666i	0.709355	−	0.704852i	$-0.248987\pi$
$421$	7.04001	+	4.63029i	0.343109	+	0.225666i	−0.366245	+	0.930518i	$0.619357\pi$
$422$	12.2527	−	10.2813i	0.596454	−	0.500484i
$423$	−11.9943	+	8.38623i	−0.583184	+	0.407753i
$424$	1.02042	+	0.856232i	0.0495559	+	0.0415823i
$425$	3.08704	+	10.3114i	0.149743	+	0.500177i
$426$	12.5990	+	14.5891i	0.610426	+	0.706845i
$427$	2.61107	+	1.31133i	0.126358	+	0.0634596i
$428$	10.4217	+	11.0464i	0.503753	+	0.533947i
$429$	8.74302	+	2.48277i	0.422117	+	0.119869i
$430$	3.84145	−	8.90548i	0.185251	−	0.429460i
$431$	1.09556	−	1.89756i	0.0527711	−	0.0914023i	−0.838433	−	0.545004i	$-0.816528\pi$
$431$	1.09556	−	1.89756i	0.0527711	−	0.0914023i	0.891204	+	0.453602i	$0.149861\pi$
$432$	4.03202	−	3.27762i	0.193991	−	0.157695i
$433$	5.99721	+	10.3875i	0.288208	+	0.499190i	0.973382	−	0.229189i	$-0.0736074\pi$
$433$	5.99721	+	10.3875i	0.288208	+	0.499190i	−0.685174	+	0.728379i	$0.740274\pi$
$434$	−36.9576	+	4.31973i	−1.77402	+	0.207354i
$435$	4.42221	−	9.12622i	0.212029	−	0.437569i
$436$	−1.35642	+	0.321478i	−0.0649609	+	0.0153960i
$437$	−1.51819	−	26.0664i	−0.0726250	−	1.24692i
$438$	−2.48052	−	0.401151i	−0.118524	−	0.0191677i
$439$	17.6661	+	4.18694i	0.843157	+	0.199832i	0.629426	−	0.777061i	$-0.283290\pi$
$439$	17.6661	+	4.18694i	0.843157	+	0.199832i	0.213731	+	0.976893i	$0.431438\pi$
$440$	−0.288510	+	1.63622i	−0.0137542	+	0.0780038i
$441$	−14.4448	−	11.4376i	−0.687849	−	0.544649i
$442$	1.29437	+	7.34076i	0.0615671	+	0.349164i
$443$	0.685175	−	11.7640i	0.0325537	−	0.558925i	−0.942118	−	0.335283i	$-0.891168\pi$
$443$	0.685175	−	11.7640i	0.0325537	−	0.558925i	0.974671	−	0.223642i	$-0.0717948\pi$
$444$	−8.41709	+	2.65072i	−0.399457	+	0.125797i
$445$	−6.42214	+	8.62644i	−0.304439	+	0.408932i
$446$	−4.22528	+	5.67553i	−0.200073	+	0.268744i
$447$	−1.55665	−	1.42739i	−0.0736271	−	0.0675134i
$448$	−0.210783	+	3.61900i	−0.00995855	+	0.170982i
$449$	5.48097	+	31.0841i	0.258663	+	1.46695i	0.786493	+	0.617599i	$0.211895\pi$
$449$	5.48097	+	31.0841i	0.258663	+	1.46695i	−0.527830	+	0.849350i	$0.676994\pi$
$450$	−5.93866	+	10.9958i	−0.279951	+	0.518348i
$451$	1.01688	−	5.76700i	0.0478829	−	0.271557i
$452$	−15.7794	−	3.73979i	−0.742202	−	0.175905i
$453$	−16.8101	+	20.6213i	−0.789809	+	0.968872i
$454$	−1.13323	−	19.4568i	−0.0531852	−	0.913154i
$455$	9.29482	−	2.20291i	0.435748	−	0.103274i
$456$	10.1518	−	0.736053i	0.475400	−	0.0344689i
$457$	−16.2916	+	1.90421i	−0.762089	+	0.0890754i	−0.488254	−	0.872701i	$-0.662366\pi$
$457$	−16.2916	+	1.90421i	−0.762089	+	0.0890754i	−0.273835	+	0.961777i	$0.588292\pi$
$458$	−2.37786	−	4.11857i	−0.111110	−	0.192448i
$459$	5.12520	+	12.4095i	0.239224	+	0.579226i
$460$	−2.02924	+	3.51474i	−0.0946137	+	0.163876i
$461$	11.5408	−	26.7547i	0.537511	−	1.24609i	−0.405734	−	0.913991i	$-0.632984\pi$
$461$	11.5408	−	26.7547i	0.537511	−	1.24609i	0.943245	−	0.332098i	$-0.107757\pi$
$462$	−8.19529	+	7.95482i	−0.381279	+	0.370092i
$463$	−20.6101	−	21.8455i	−0.957834	−	1.01524i	−0.999870	−	0.0161284i	$-0.994866\pi$
$463$	−20.6101	−	21.8455i	−0.957834	−	1.01524i	0.0420362	−	0.999116i	$-0.486616\pi$
$464$	−5.72824	−	2.87683i	−0.265927	−	0.133553i
$465$	5.33675	−	15.3368i	0.247486	−	0.711227i
$466$	−3.39180	−	11.3294i	−0.157122	−	0.524824i
$467$	−17.5939	−	14.7630i	−0.814148	−	0.683151i	0.137446	−	0.990509i	$-0.456111\pi$
$467$	−17.5939	−	14.7630i	−0.814148	−	0.683151i	−0.951594	+	0.307358i	$0.900555\pi$
$468$	−4.96885	+	7.08588i	−0.229685	+	0.327545i
$469$	5.09848	−	4.27814i	0.235426	−	0.197546i
$470$	3.72296	+	2.44863i	0.171727	+	0.112947i
$471$	−6.21445	+	9.74734i	−0.286347	+	0.449134i
$472$	1.75892	+	0.205588i	0.0809608	+	0.00946296i
$473$	−7.64984	−	17.7343i	−0.351740	−	0.815425i
$474$	3.13094	+	23.8452i	0.143809	+	1.09525i
$475$	−21.8758	+	10.9865i	−1.00373	+	0.504093i
$476$	−8.80201	−	3.20367i	−0.403439	−	0.146840i
$477$	−3.91307	−	0.810789i	−0.179167	−	0.0371235i
$478$	−2.06996	+	0.753403i	−0.0946777	+	0.0344599i
$479$	−17.1741	+	18.2034i	−0.784702	+	0.831736i	−0.989114	−	0.147149i	$-0.952990\pi$
$479$	−17.1741	+	18.2034i	−0.784702	+	0.831736i	0.204412	+	0.978885i	$0.434472\pi$
$480$	−1.38121	−	0.771502i	−0.0630434	−	0.0352141i
$481$	12.2798	−	8.07657i	0.559912	−	0.368260i
$482$	4.12568	−	13.7807i	0.187920	−	0.627695i
$483$	−25.4574	+	11.4127i	−1.15835	+	0.519295i
$484$	−4.59297	−	6.16943i	−0.208771	−	0.280429i
$485$	3.32297			0.150888
$486$	−5.99019	+	14.3916i	−0.271721	+	0.652815i
$487$	7.06465			0.320130			0.160065	−	0.987106i	$-0.448830\pi$
$487$	7.06465			0.320130			0.160065	+	0.987106i	$0.448830\pi$
$488$	0.481310	+	0.646511i	0.0217879	+	0.0292662i
$489$	−24.6532	+	11.0522i	−1.11486	+	0.499797i
$490$	−1.60891	+	5.37413i	−0.0726831	+	0.242779i
$491$	−3.69238	+	2.42852i	−0.166635	+	0.109598i	−0.630087	−	0.776524i	$-0.716981\pi$
$491$	−3.69238	+	2.42852i	−0.166635	+	0.109598i	0.463452	+	0.886122i	$0.346611\pi$
$492$	4.86820	+	2.71922i	0.219475	+	0.122592i
$493$	11.3661	−	12.0473i	0.511903	−	0.542585i
$494$	−15.9303	+	5.79814i	−0.716737	+	0.260871i
$495$	−1.56456	−	4.73247i	−0.0703217	−	0.212709i
$496$	−9.64522	−	3.51057i	−0.433083	−	0.157629i
$497$	36.0535	−	18.1067i	1.61722	−	0.812199i
$498$	−3.85019	−	29.3230i	−0.172531	−	1.31399i
$499$	−4.27301	−	9.90595i	−0.191286	−	0.443451i	0.795400	−	0.606084i	$-0.207261\pi$
$499$	−4.27301	−	9.90595i	−0.191286	−	0.443451i	−0.986687	+	0.162633i	$0.948001\pi$
$500$	8.31543	+	0.971934i	0.371877	+	0.0434662i
$501$	−19.6457	+	30.8141i	−0.877703	+	1.37667i
$502$	−7.63778	−	5.02344i	−0.340891	−	0.224207i
$503$	−15.1319	+	12.6972i	−0.674700	+	0.566140i	−0.914452	−	0.404694i	$-0.867378\pi$
$503$	−15.1319	+	12.6972i	−0.674700	+	0.566140i	0.239753	+	0.970834i	$0.422934\pi$
$504$	−4.58936	−	9.85962i	−0.204427	−	0.439182i
$505$	−8.43974	−	7.08178i	−0.375563	−	0.315135i
$506$	2.31795	+	7.74249i	0.103045	+	0.344196i
$507$	−2.66275	+	7.65225i	−0.118257	+	0.339848i
$508$	1.60083	+	0.803968i	0.0710255	+	0.0356703i
$509$	4.87909	+	5.17153i	0.216262	+	0.229224i	0.826418	−	0.563057i	$-0.190375\pi$
$509$	4.87909	+	5.17153i	0.216262	+	0.229224i	−0.610156	+	0.792281i	$0.708893\pi$
$510$	2.93329	−	2.84722i	0.129888	−	0.126077i
$511$	−2.08303	+	4.82900i	−0.0921477	+	0.213622i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−25.7701	+	16.3800i	−1.13778	+	0.723195i
$514$	−3.46909	−	6.00863i	−0.153015	−	0.265029i
$515$	−5.11970	+	0.598407i	−0.225601	+	0.0263690i
$516$	18.3429	−	1.32995i	0.807501	−	0.0585478i
$517$	8.63452	−	2.04642i	0.379746	−	0.0900014i
$518$	1.07391	+	18.4384i	0.0471851	+	0.810137i
$519$	16.8682	−	20.6925i	0.740430	−	0.908298i
$520$	2.56399	+	0.607678i	0.112439	+	0.0266484i
$521$	1.53744	−	8.71925i	0.0673565	−	0.381997i	−0.932430	−	0.361350i	$-0.882316\pi$
$521$	1.53744	−	8.71925i	0.0673565	−	0.381997i	0.999787	−	0.0206477i	$-0.00657284\pi$
$522$	19.2224	−	0.546087i	0.841342	−	0.0239016i
$523$	−1.45069	−	8.22726i	−0.0634341	−	0.359753i	−0.999958	−	0.00914935i	$-0.997088\pi$
$523$	−1.45069	−	8.22726i	−0.0634341	−	0.359753i	0.936524	−	0.350603i	$-0.114023\pi$
$524$	−1.12284	+	19.2784i	−0.0490514	+	0.842180i
$525$	19.2781	+	17.6773i	0.841366	+	0.771502i
$526$	13.0194	−	17.4881i	0.567673	−	0.762517i
$527$	15.8376	−	21.2735i	0.689895	−	0.926690i
$528$	−3.00505	+	0.946352i	−0.130778	+	0.0411847i
$529$	0.189433	−	3.25243i	0.00823620	−	0.141410i
$530$	0.211281	+	1.19824i	0.00917747	+	0.0520480i
$531$	−4.93867	+	1.95808i	−0.214320	+	0.0849734i
$532$	3.69925	−	20.9795i	0.160383	−	0.909577i
$533$	−9.03701	−	2.14181i	−0.391436	−	0.0927721i
$534$	−20.1316	−	3.25569i	−0.871179	−	0.140888i
$535$	0.806566	+	13.8482i	0.0348709	+	0.598710i
$536$	1.78647	−	0.423401i	0.0771638	−	0.0182882i
$537$	11.8648	−	24.4857i	0.512005	−	1.05664i
$538$	−24.0368	+	2.80950i	−1.03630	+	0.121126i
$539$	5.58567	+	9.67466i	0.240592	+	0.416717i
$540$	4.74565	+	0.0739233i	0.204220	+	0.00318115i
$541$	8.33973	−	14.4448i	0.358553	−	0.621032i	−0.629166	−	0.777271i	$-0.716604\pi$
$541$	8.33973	−	14.4448i	0.358553	−	0.621032i	0.987719	+	0.156238i	$0.0499368\pi$
$542$	−8.55928	+	19.8426i	−0.367652	+	0.852314i
$543$	−9.06614	−	2.57452i	−0.389065	−	0.110483i
$544$	−1.77316	−	1.87944i	−0.0760238	−	0.0805805i
$545$	−1.13786	−	0.571454i	−0.0487405	−	0.0244784i
$546$	11.8390	+	13.7090i	0.506662	+	0.586691i
$547$	−0.0804591	−	0.268752i	−0.00344018	−	0.0114910i	0.956252	−	0.292544i	$-0.0945017\pi$
$547$	−0.0804591	−	0.268752i	−0.00344018	−	0.0114910i	−0.959692	+	0.281053i	$0.909316\pi$
$548$	13.1473	+	11.0319i	0.561625	+	0.471260i
$549$	−2.19075	−	1.02340i	−0.0934989	−	0.0436775i
$550$	5.80449	−	4.87054i	0.247504	−	0.207681i
$551$	31.4718	+	20.6993i	1.34074	+	0.881822i
$552$	−7.68841	−	0.338332i	−0.327241	−	0.0144004i
$553$	49.9954	+	5.84362i	2.12602	+	0.248496i
$554$	−2.83024	−	6.56124i	−0.120245	−	0.278760i
$555$	−7.44587	−	3.08718i	−0.316059	−	0.131043i
$556$	0.297546	−	0.149433i	0.0126188	−	0.00633738i
$557$	25.8852	+	9.42145i	1.09679	+	0.399200i	0.826133	−	0.563476i	$-0.190536\pi$
$557$	25.8852	+	9.42145i	1.09679	+	0.399200i	0.270659	+	0.962675i	$0.412758\pi$
$558$	30.4706	−	4.44189i	1.28993	−	0.188040i
$559$	−28.7839	+	10.4765i	−1.21743	+	0.443108i
$560$	−2.27231	+	2.40851i	−0.0960226	+	0.101778i
$561$	−0.115598	−	8.13978i	−0.00488054	−	0.343662i
$562$	−11.9492	+	7.85913i	−0.504047	+	0.331517i
$563$	−6.26457	+	20.9251i	−0.264020	+	0.881889i	0.718467	+	0.695561i	$0.244844\pi$
$563$	−6.26457	+	20.9251i	−0.264020	+	0.881889i	−0.982488	+	0.186328i	$0.940341\pi$
$564$	−0.861677	+	8.40566i	−0.0362831	+	0.353942i
$565$	−8.84534	−	11.8814i	−0.372126	−	0.499853i
$566$	−23.3310			−0.980675
$567$	26.1434	+	19.5190i	1.09792	+	0.819720i
$568$	11.1292			0.466971
$569$	−11.0801	−	14.8831i	−0.464500	−	0.623932i	0.506722	−	0.862110i	$-0.330857\pi$
$569$	−11.0801	−	14.8831i	−0.464500	−	0.623932i	−0.971222	+	0.238178i	$0.923450\pi$
$570$	7.53550	+	5.44538i	0.315627	+	0.228082i
$571$	−5.07772	+	16.9608i	−0.212496	+	0.709786i	0.783581	+	0.621290i	$0.213391\pi$
$571$	−5.07772	+	16.9608i	−0.212496	+	0.709786i	−0.996077	+	0.0884956i	$0.971794\pi$
$572$	4.38411	−	2.88348i	0.183309	−	0.120564i
$573$	19.7883	−	11.8026i	0.826668	−	0.493060i
$574$	8.00895	−	8.48899i	0.334287	−	0.354324i
$575$	17.3927	−	6.33044i	0.725327	−	0.263997i
$576$	0.0893161	−	2.99867i	0.00372150	−	0.124945i
$577$	12.4265	+	4.52287i	0.517321	+	0.188289i	0.587468	−	0.809247i	$-0.300125\pi$
$577$	12.4265	+	4.52287i	0.517321	+	0.188289i	−0.0701474	+	0.997537i	$0.522347\pi$
$578$	−9.22548	+	4.63321i	−0.383730	+	0.192716i
$579$	−24.2455	+	18.5910i	−1.00761	+	0.772616i
$580$	−2.31906	−	5.37617i	−0.0962935	−	0.223233i
$581$	−61.4804	−	7.18603i	−2.55064	−	0.298127i
$582$	2.90763	+	5.59019i	0.120525	+	0.231721i
$583$	2.02436	+	1.33144i	0.0838405	+	0.0551428i
$584$	−1.11133	+	0.932515i	−0.0459871	+	0.0385878i
$585$	−7.63711	+	2.04073i	−0.315756	+	0.0843738i
$586$	−11.3082	−	9.48867i	−0.467136	−	0.391973i
$587$	−3.78089	−	12.6291i	−0.156054	−	0.521257i	0.843828	−	0.536614i	$-0.180297\pi$
$587$	−3.78089	−	12.6291i	−0.156054	−	0.521257i	−0.999882	+	0.0153567i	$0.995112\pi$
$588$	−10.4487	+	1.99577i	−0.430895	+	0.0823040i
$589$	53.9021	+	27.0706i	2.22100	+	1.11543i
$590$	1.11003	+	1.17657i	0.0456994	+	0.0484385i
$591$	−11.0573	−	43.8686i	−0.454835	−	1.80451i
$592$	−2.01798	+	4.67821i	−0.0829385	+	0.192273i
$593$	22.1023	−	38.2823i	0.907631	−	1.57206i	0.0902859	−	0.995916i	$-0.471222\pi$
$593$	22.1023	−	38.2823i	0.907631	−	1.57206i	0.817346	−	0.576148i	$-0.195445\pi$
$594$	6.59238	−	6.77300i	0.270489	−	0.277899i
$595$	−4.27792	−	7.40957i	−0.175378	−	0.303763i
$596$	−1.21113	+	0.141561i	−0.0496098	+	0.00579855i
$597$	19.9724	+	29.4470i	0.817414	+	1.20519i
$598$	12.4723	−	2.95599i	0.510030	−	0.120879i
$599$	0.894517	+	15.3583i	0.0365490	+	0.627521i	0.965995	+	0.258562i	$0.0832487\pi$
$599$	0.894517	+	15.3583i	0.0365490	+	0.627521i	−0.929446	+	0.368959i	$0.879714\pi$
$600$	2.56376	+	6.74431i	0.104665	+	0.275335i
$601$	−7.05651	−	1.67242i	−0.287841	−	0.0682196i	0.0841588	−	0.996452i	$-0.473180\pi$
$601$	−7.05651	−	1.67242i	−0.287841	−	0.0682196i	−0.372000	+	0.928233i	$0.621328\pi$
$602$	6.68406	−	37.9072i	0.272422	−	1.54498i
$603$	−4.11704	+	3.65879i	−0.167659	+	0.148997i
$604$	2.66729	+	15.1270i	0.108531	+	0.615507i
$605$	0.408490	−	7.01350i	0.0166075	−	0.285139i
$606$	4.52875	−	20.3947i	0.183968	−	0.828478i
$607$	−26.3079	+	35.3377i	−1.06781	+	1.43431i	−0.174615	+	0.984637i	$0.555868\pi$
$607$	−26.3079	+	35.3377i	−1.06781	+	1.43431i	−0.893192	+	0.449676i	$0.851539\pi$
$608$	3.50921	−	4.71369i	0.142317	−	0.191165i
$609$	8.72481	−	39.2912i	0.353547	−	1.59216i
$610$	−0.0428068	+	0.734964i	−0.00173320	+	0.0297578i
$611$	−2.44382	−	13.8596i	−0.0988663	−	0.560699i
$612$	7.35650	+	2.44329i	0.297369	+	0.0987643i
$613$	3.68543	−	20.9011i	0.148853	−	0.844189i	−0.815339	−	0.578984i	$-0.803449\pi$
$613$	3.68543	−	20.9011i	0.148853	−	0.844189i	0.964192	−	0.265205i	$-0.0854396\pi$
$614$	16.7002	+	3.95802i	0.673966	+	0.159733i
$615$	1.80981	+	4.76094i	0.0729786	+	0.191980i
$616$	0.383406	+	6.58283i	0.0154479	+	0.265230i
$617$	−8.50799	+	2.01643i	−0.342519	+	0.0811784i	−0.398275	−	0.917266i	$-0.630391\pi$
$617$	−8.50799	+	2.01643i	−0.342519	+	0.0811784i	0.0557565	+	0.998444i	$0.482243\pi$
$618$	−5.48648	−	8.08921i	−0.220699	−	0.325396i
$619$	28.0493	−	3.27850i	1.12740	−	0.131774i	0.468114	−	0.883668i	$-0.344934\pi$
$619$	28.0493	−	3.27850i	1.12740	−	0.131774i	0.659284	+	0.751894i	$0.270860\pi$
$620$	−4.68774	−	8.11940i	−0.188264	−	0.326083i
$621$	20.7907	−	10.0391i	0.834301	−	0.402854i
$622$	4.05000	−	7.01481i	0.162390	−	0.281268i
$623$	−16.9056	+	39.1916i	−0.677308	+	1.57018i
$624$	1.22123	+	4.84510i	0.0488883	+	0.193959i
$625$	−9.04554	−	9.58771i	−0.361822	−	0.383509i
$626$	−2.75103	−	1.38162i	−0.109953	−	0.0552206i
$627$	18.1854	−	3.47354i	0.726256	−	0.138720i
$628$	1.91415	+	6.39370i	0.0763828	+	0.255136i
$629$	−10.0846	−	8.46202i	−0.402101	−	0.337403i
$630$	2.57763	−	9.59347i	0.102695	−	0.382213i
$631$	−2.46706	+	2.07011i	−0.0982123	+	0.0824099i	−0.690572	−	0.723264i	$-0.742641\pi$
$631$	−2.46706	+	2.07011i	−0.0982123	+	0.0824099i	0.592359	+	0.805674i	$0.298197\pi$
$632$	11.6009	+	7.63004i	0.461460	+	0.303507i
$633$	12.7838	+	24.5780i	0.508108	+	0.976887i
$634$	22.6005	+	2.64162i	0.897580	+	0.104912i
$635$	0.648091	+	1.50244i	0.0257187	+	0.0596227i
$636$	−1.83091	+	1.40390i	−0.0726001	+	0.0556684i
$637$	15.8328	−	7.95153i	0.627318	−	0.315051i
$638$	−10.9565	−	3.98784i	−0.433772	−	0.157880i
$639$	−29.3987	+	15.8256i	−1.16300	+	0.626050i
$640$	−0.858326	+	0.312405i	−0.0339283	+	0.0123489i
$641$	12.7537	−	13.5182i	0.503742	−	0.533935i	−0.424739	−	0.905316i	$-0.639634\pi$
$641$	12.7537	−	13.5182i	0.503742	−	0.533935i	0.928481	+	0.371381i	$0.121116\pi$
$642$	−22.5909	+	13.4742i	−0.891593	+	0.531784i
$643$	−35.4750	+	23.3323i	−1.39900	+	0.920136i	−0.399004	+	0.916949i	$0.630644\pi$
$643$	−35.4750	+	23.3323i	−1.39900	+	0.920136i	−0.999995	+	0.00318711i	$0.998986\pi$
$644$	−4.61960	+	15.4305i	−0.182038	+	0.608048i
$645$	13.6156	+	9.83908i	0.536115	+	0.387413i
$646$	9.06737	+	12.1796i	0.356751	+	0.479200i
$647$	7.70757			0.303016			0.151508	−	0.988456i	$-0.451587\pi$
$647$	7.70757			0.303016			0.151508	+	0.988456i	$0.451587\pi$
$648$	4.02813	+	8.04824i	0.158240	+	0.316165i
$649$	3.22119			0.126443
$650$	−7.17617	−	9.63927i	−0.281473	−	0.378083i
$651$	6.57225	−	64.1123i	0.257587	−	2.51276i
$652$	−4.47367	+	14.9431i	−0.175203	+	0.585217i
$653$	−35.1862	+	23.1424i	−1.37694	+	0.905630i	−0.999789	−	0.0205200i	$-0.993468\pi$
$653$	−35.1862	+	23.1424i	−1.37694	+	0.905630i	−0.377155	+	0.926150i	$0.623097\pi$
$654$	−0.0342859	−	2.41424i	−0.00134069	−	0.0944041i
$655$	−12.1046	+	12.8301i	−0.472965	+	0.501314i
$656$	3.02524	−	1.10110i	0.118116	−	0.0429907i
$657$	1.60964	−	4.04361i	0.0627981	−	0.157756i
$658$	16.6185	+	6.04863i	0.647855	+	0.235800i
$659$	3.58038	−	1.79814i	0.139472	−	0.0700455i	−0.377695	−	0.925930i	$-0.623283\pi$
$659$	3.58038	−	1.79814i	0.139472	−	0.0700455i	0.517167	+	0.855885i	$0.326987\pi$
$660$	−2.65830	−	1.10218i	−0.103474	−	0.0429022i
$661$	−3.49984	−	8.11353i	−0.136128	−	0.315580i	0.836493	−	0.547978i	$-0.184602\pi$
$661$	−3.49984	−	8.11353i	−0.136128	−	0.315580i	−0.972621	+	0.232398i	$0.925343\pi$
$662$	21.2192	+	2.48017i	0.824707	+	0.0963944i
$663$	−12.8982	−	0.567592i	−0.500926	−	0.0220434i
$664$	−14.2659	−	9.38283i	−0.553624	−	0.364125i
$665$	14.9061	−	12.5077i	0.578034	−	0.485028i
$666$	−1.32168	−	15.2274i	−0.0512139	−	0.590050i
$667$	−21.8179	−	18.3074i	−0.844791	−	0.708863i
$668$	6.05117	+	20.2123i	0.234127	+	0.782038i
$669$	−8.01012	−	9.27535i	−0.309689	−	0.358606i
$670$	1.49861	+	0.752630i	0.0578964	+	0.0290766i
$671$	1.00609	+	1.06639i	0.0388396	+	0.0411676i
$672$	−6.04010	−	1.71522i	−0.233002	−	0.0661659i
$673$	4.08051	−	9.45967i	0.157292	−	0.364644i	−0.821287	−	0.570515i	$-0.806744\pi$
$673$	4.08051	−	9.45967i	0.157292	−	0.364644i	0.978579	+	0.205871i	$0.0660029\pi$
$674$	−8.33989	+	14.4451i	−0.321241	+	0.556405i
$675$	−16.3627	−	14.1700i	−0.629801	−	0.545405i
$676$	2.33893	+	4.05115i	0.0899589	+	0.155813i
$677$	−2.79823	+	0.327067i	−0.107545	+	0.0125702i	−0.169695	−	0.985497i	$-0.554278\pi$
$677$	−2.79823	+	0.327067i	−0.107545	+	0.0125702i	0.0621502	+	0.998067i	$0.480204\pi$
$678$	12.2481	−	25.2767i	0.470386	−	0.970747i
$679$	12.8327	−	3.04139i	0.492472	−	0.116718i
$680$	−0.137230	−	2.35615i	−0.00526254	−	0.0903543i
$681$	33.3244	+	5.38923i	1.27699	+	0.206516i
$682$	−18.1670	−	4.30566i	−0.695651	−	0.164872i
$683$	−1.39262	+	7.89793i	−0.0532870	+	0.302206i	−0.999790	−	0.0204891i	$-0.993478\pi$
$683$	−1.39262	+	7.89793i	−0.0532870	+	0.302206i	0.946503	+	0.322695i	$0.104589\pi$
$684$	−2.56708	+	17.4416i	−0.0981546	+	0.666898i
$685$	2.72220	+	15.4384i	0.104010	+	0.589869i
$686$	0.180937	−	3.10657i	0.00690821	−	0.118609i
$687$	7.85675	−	2.47425i	0.299754	−	0.0943987i
$688$	6.34068	−	8.51701i	0.241736	−	0.324708i
$689$	2.29473	−	3.08235i	0.0874222	−	0.117428i
$690$	−5.18105	−	4.75083i	−0.197239	−	0.180861i
$691$	−1.22996	+	21.1176i	−0.0467898	+	0.803350i	0.890540	+	0.454906i	$0.150327\pi$
$691$	−1.22996	+	21.1176i	−0.0467898	+	0.803350i	−0.937329	+	0.348444i	$0.886710\pi$
$692$	−2.67650	−	15.1792i	−0.101745	−	0.577026i
$693$	−10.3735	−	16.8439i	−0.394056	−	0.639846i
$694$	−1.65831	+	9.40472i	−0.0629484	+	0.356998i
$695$	0.295934	+	0.0701376i	0.0112254	+	0.00266047i
$696$	7.01508	−	8.60552i	0.265906	−	0.326192i
$697$	0.483679	+	8.30445i	0.0183207	+	0.314554i
$698$	7.06972	−	1.67555i	0.267593	−	0.0634207i
$699$	20.4300	−	1.48127i	0.772733	−	0.0560269i
$700$	14.9990	−	1.75314i	0.566910	−	0.0662623i
$701$	−11.0590	−	19.1548i	−0.417694	−	0.723466i	0.578013	−	0.816027i	$-0.303828\pi$
$701$	−11.0590	−	19.1548i	−0.417694	−	0.723466i	−0.995707	+	0.0925608i	$0.970495\pi$
$702$	−10.1156	−	11.0622i	−0.381790	−	0.417515i
$703$	14.9701	−	25.9290i	0.564608	−	0.977929i
$704$	−0.720455	+	1.67020i	−0.0271532	+	0.0629481i
$705$	−5.53814	+	5.37564i	−0.208578	+	0.202458i
$706$	10.7907	+	11.4374i	0.406112	+	0.430454i
$707$	−39.0743	−	19.6239i	−1.46954	−	0.738031i
$708$	−1.00804	+	2.89690i	−0.0378843	+	0.108872i
$709$	5.05732	+	16.8926i	0.189932	+	0.634416i	0.998914	+	0.0465836i	$0.0148334\pi$
$709$	5.05732	+	16.8926i	0.189932	+	0.634416i	−0.808983	+	0.587832i	$0.799981\pi$
$710$	7.78726	+	6.53429i	0.292251	+	0.245228i
$711$	−41.4946	−	3.65906i	−1.55617	−	0.137225i
$712$	−9.01940	+	7.56818i	−0.338016	+	0.283629i
$713$	−38.1033	−	25.0609i	−1.42698	−	0.938540i
$714$	8.72183	−	13.6801i	0.326406	−	0.511967i
$715$	4.76060	+	0.556434i	0.178036	+	0.0208095i
$716$	−6.22205	−	14.4243i	−0.232529	−	0.539062i
$717$	−0.496705	−	3.78290i	−0.0185498	−	0.141275i
$718$	3.28999	−	1.65230i	0.122781	−	0.0616631i
$719$	10.3768	+	3.77684i	0.386989	+	0.140852i	0.528185	−	0.849129i	$-0.322873\pi$
$719$	10.3768	+	3.77684i	0.386989	+	0.140852i	−0.141196	+	0.989982i	$0.545095\pi$
$720$	1.82310	−	2.04577i	0.0679431	−	0.0762414i
$721$	−19.2236	+	6.99681i	−0.715924	+	0.260575i
$722$	−10.6597	+	11.2986i	−0.396712	+	0.420491i
$723$	21.7523	+	12.1502i	0.808977	+	0.451869i
$724$	−4.54614	+	2.99004i	−0.168956	+	0.111124i
$725$	−7.65829	+	25.5805i	−0.284422	+	0.950035i
$726$	12.1562	−	5.44968i	0.451158	−	0.202257i
$727$	0.779029	+	1.04642i	0.0288926	+	0.0388095i	0.816335	−	0.577579i	$-0.196002\pi$
$727$	0.779029	+	1.04642i	0.0288926	+	0.0388095i	−0.787442	+	0.616389i	$0.788595\pi$
$728$	10.4578			0.387593
$729$	−22.0851	−	15.5322i	−0.817967	−	0.575265i
$730$	−1.32512			−0.0490449
$731$	16.3835	+	22.0069i	0.605967	+	0.813955i
$732$	−1.27388	+	0.571087i	−0.0470839	+	0.0211080i
$733$	−1.27311	+	4.25249i	−0.0470234	+	0.157069i	−0.978277	−	0.207303i	$-0.933531\pi$
$733$	−1.27311	+	4.25249i	−0.0470234	+	0.157069i	0.931253	+	0.364372i	$0.118716\pi$
$734$	20.5697	−	13.5289i	0.759241	−	0.499361i
$735$	−8.48285	−	4.73825i	−0.312894	−	0.174773i
$736$	−3.04911	+	3.23187i	−0.112392	+	0.119128i
$737$	3.13814	−	1.14219i	0.115595	−	0.0420732i
$738$	−6.42568	+	7.21049i	−0.236533	+	0.265422i
$739$	−3.14169	−	1.14348i	−0.115569	−	0.0420637i	0.283588	−	0.958946i	$-0.408475\pi$
$739$	−3.14169	−	1.14348i	−0.115569	−	0.0420637i	−0.399157	+	0.916882i	$0.630697\pi$
$740$	−4.15872	+	2.08859i	−0.152878	+	0.0767781i
$741$	−3.82261	−	29.1129i	−0.140427	−	1.06949i
$742$	1.91263	+	4.43397i	0.0702148	+	0.162776i
$743$	40.6701	+	4.75365i	1.49204	+	0.174394i	0.822663	−	0.568529i	$-0.192487\pi$
$743$	40.6701	+	4.75365i	1.49204	+	0.174394i	0.669377	+	0.742923i	$0.266561\pi$
$744$	9.55736	−	14.9907i	0.350390	−	0.549585i
$745$	−0.930558	−	0.612038i	−0.0340930	−	0.0224233i
$746$	24.6433	−	20.6782i	0.902256	−	0.757083i
$747$	51.0268	+	4.49962i	1.86697	+	0.164633i
$748$	−3.60039	−	3.02109i	−0.131643	−	0.110462i
$749$	15.7896	+	52.7409i	0.576939	+	1.92711i
$750$	−4.76557	+	13.6953i	−0.174014	+	0.500083i
$751$	47.3644	+	23.7873i	1.72835	+	0.868011i	0.978456	+	0.206454i	$0.0661925\pi$
$751$	47.3644	+	23.7873i	1.72835	+	0.868011i	0.749895	+	0.661556i	$0.230104\pi$
$752$	3.34779	+	3.54845i	0.122081	+	0.129399i
$753$	11.3617	−	11.0283i	0.414043	−	0.401894i
$754$	−7.32423	+	16.9795i	−0.266733	+	0.618356i
$755$	−7.01515	+	12.1506i	−0.255307	+	0.442205i
$756$	18.3944	−	4.05805i	0.668999	−	0.147590i
$757$	−18.2910	−	31.6809i	−0.664797	−	1.15146i	−0.979340	−	0.202220i	$-0.935184\pi$
$757$	−18.2910	−	31.6809i	−0.664797	−	1.15146i	0.314543	−	0.949243i	$-0.398149\pi$
$758$	10.9269	−	1.27717i	0.396882	−	0.0463888i
$759$	−13.9618	+	1.01230i	−0.506782	+	0.0367442i
$760$	5.22299	−	1.23787i	0.189458	−	0.0449023i
$761$	−1.31575	−	22.5905i	−0.0476958	−	0.818904i	−0.934325	−	0.356423i	$-0.883996\pi$
$761$	−1.31575	−	22.5905i	−0.0476958	−	0.818904i	0.886629	−	0.462481i	$-0.153041\pi$
$762$	−1.96046	+	2.40493i	−0.0710200	+	0.0871214i
$763$	−4.91722	−	1.16540i	−0.178015	−	0.0421904i
$764$	2.30997	−	13.1005i	0.0835719	−	0.473960i
$765$	3.71292	+	6.02883i	0.134241	+	0.217973i
$766$	2.88215	+	16.3455i	0.104136	+	0.590587i
$767$	0.297044	−	5.10005i	0.0107256	−	0.184152i

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)

\(f(q)\)	\(=\)	\(q+(0.597159 + 0.802123i) q^{2} +(-1.58049 + 0.708545i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.763144 + 0.501928i) q^{5} +(-1.51215 - 0.844638i) q^{6} +(-2.48772 + 2.63683i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(1.99593 - 2.23970i) q^{9} +O(q^{10})\)	\(q+(0.597159 + 0.802123i) q^{2} +(-1.58049 + 0.708545i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-0.763144 + 0.501928i) q^{5} +(-1.51215 - 0.844638i) q^{6} +(-2.48772 + 2.63683i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(1.99593 - 2.23970i) q^{9} +(-0.858326 - 0.312405i) q^{10} +(-1.62549 + 0.816349i) q^{11} +(-0.225488 - 1.71731i) q^{12} +(1.14262 + 2.64888i) q^{13} +(-3.60062 - 0.420852i) q^{14} +(0.850507 - 1.33402i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(1.97937 - 1.66088i) q^{17} +(2.98840 + 0.263522i) q^{18} +(4.50167 + 3.77735i) q^{19} +(-0.261969 - 0.875039i) q^{20} +(2.06351 - 5.93015i) q^{21} +(-1.62549 - 0.816349i) q^{22} +(-3.04911 - 3.23187i) q^{23} +(1.24284 - 1.20638i) q^{24} +(-1.64994 + 3.82499i) q^{25} +(-1.44241 + 2.49832i) q^{26} +(-1.56762 + 4.95404i) q^{27} +(-1.81257 - 3.13946i) q^{28} +(6.36671 - 0.744162i) q^{29} +(1.57793 - 0.114408i) q^{30} +(9.98756 - 2.36710i) q^{31} +(-0.0581448 - 0.998308i) q^{32} +(1.99065 - 2.44197i) q^{33} +(2.51423 + 0.595883i) q^{34} +(0.574991 - 3.26093i) q^{35} +(1.57317 + 2.55443i) q^{36} +(-0.884718 - 5.01748i) q^{37} +(-0.341689 + 5.86657i) q^{38} +(-3.68275 - 3.37695i) q^{39} +(0.545452 - 0.732669i) q^{40} +(-1.92249 + 2.58235i) q^{41} +(5.98896 - 1.88605i) q^{42} +(-0.617386 + 10.6001i) q^{43} +(-0.315860 - 1.79133i) q^{44} +(-0.399012 + 2.71103i) q^{45} +(0.771554 - 4.37570i) q^{46} +(-4.74694 - 1.12505i) q^{47} +(1.70984 + 0.276515i) q^{48} +(-0.357102 - 6.13120i) q^{49} +(-4.05339 + 0.960672i) q^{50} +(-1.95157 + 4.02749i) q^{51} +(-2.86531 + 0.334906i) q^{52} +(-0.666030 - 1.15360i) q^{53} +(-4.90987 + 1.70092i) q^{54} +(0.830731 - 1.43887i) q^{55} +(1.43584 - 3.32866i) q^{56} +(-9.79129 - 2.78045i) q^{57} +(4.39885 + 4.66251i) q^{58} +(-1.58253 - 0.794775i) q^{59} +(1.03405 + 1.19738i) q^{60} +(-0.231163 - 0.772139i) q^{61} +(7.86286 + 6.59772i) q^{62} +(0.940404 + 10.8347i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-2.20153 - 1.44797i) q^{65} +(3.14749 + 0.138507i) q^{66} +(-1.82355 - 0.213142i) q^{67} +(1.02342 + 2.37256i) q^{68} +(7.10903 + 2.94752i) q^{69} +(2.95903 - 1.48608i) q^{70} +(-10.4580 - 3.80641i) q^{71} +(-1.10954 + 2.78728i) q^{72} +(1.36325 - 0.496181i) q^{73} +(3.49632 - 3.70589i) q^{74} +(-0.102456 - 7.21444i) q^{75} +(-4.90976 + 3.22920i) q^{76} +(1.89118 - 6.31697i) q^{77} +(0.509543 - 4.97059i) q^{78} +(-8.29167 - 11.1376i) q^{79} +0.913412 q^{80} +(-1.03254 - 8.94057i) q^{81} -3.21940 q^{82} +(10.1964 + 13.6962i) q^{83} +(5.08920 + 3.67761i) q^{84} +(-0.676897 + 2.26099i) q^{85} +(-8.87127 + 5.83473i) q^{86} +(-9.53529 + 5.68725i) q^{87} +(1.24825 - 1.32307i) q^{88} +(11.0639 - 4.02694i) q^{89} +(-2.41285 + 1.29886i) q^{90} +(-9.82714 - 3.57679i) q^{91} +(3.97059 - 1.99411i) q^{92} +(-14.1081 + 10.8178i) q^{93} +(-1.93225 - 4.47946i) q^{94} +(-5.33138 - 0.623149i) q^{95} +(0.799244 + 1.53662i) q^{96} +(-3.03948 - 1.99910i) q^{97} +(4.70473 - 3.94774i) q^{98} +(-1.41597 + 5.26998i) 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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