LMFDB - Embedded newform 648.2.t.a.37.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			37.18
Character	$\chi$	$=$	648.37
Dual form			648.2.t.a.613.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.301188 + 1.38177i) q^{2} +(-1.81857 + 0.832346i) q^{4} +(1.34230 + 3.68793i) q^{5} +(-0.499959 - 2.83541i) q^{7} +(-1.69784 - 2.26215i) q^{8} +(-4.69159 + 2.96551i) q^{10} +(-0.996019 + 2.73654i) q^{11} +(-2.55767 + 3.04812i) q^{13} +(3.76729 - 1.54482i) q^{14} +(2.61440 - 3.02736i) q^{16} +(-2.48745 + 4.30839i) q^{17} +(1.78004 - 1.02771i) q^{19} +(-5.51070 - 5.58951i) q^{20} +(-4.08125 - 0.552054i) q^{22} +(-0.165146 + 0.936587i) q^{23} +(-7.96887 + 6.68667i) q^{25} +(-4.98214 - 2.61606i) q^{26} +(3.26925 + 4.74025i) q^{28} +(-5.18495 - 6.17919i) q^{29} +(0.331534 - 1.88022i) q^{31} +(4.97054 + 2.70069i) q^{32} +(-6.70240 - 2.13945i) q^{34} +(9.78570 - 5.64977i) q^{35} +(8.31066 + 4.79816i) q^{37} +(1.95618 + 2.15007i) q^{38} +(6.06366 - 9.29801i) q^{40} +(-0.581151 - 0.487644i) q^{41} +(-2.14125 + 5.88303i) q^{43} +(-0.466416 - 5.80562i) q^{44} +(-1.34389 + 0.0538962i) q^{46} +(-0.932102 - 5.28621i) q^{47} +(-1.21172 + 0.441031i) q^{49} +(-11.6396 - 8.99718i) q^{50} +(2.11423 - 7.67209i) q^{52} -3.54207i q^{53} -11.4291 q^{55} +(-5.56527 + 5.94505i) q^{56} +(6.97656 - 9.02551i) q^{58} +(2.13303 + 5.86045i) q^{59} +(-3.22446 + 0.568559i) q^{61} +(2.69789 - 0.108198i) q^{62} +(-2.23467 + 7.68155i) q^{64} +(-14.6744 - 5.34105i) q^{65} +(4.40861 - 5.25398i) q^{67} +(0.937536 - 9.90554i) q^{68} +(10.7540 + 11.8199i) q^{70} +(-3.83709 + 6.64603i) q^{71} +(3.46824 + 6.00718i) q^{73} +(-4.12688 + 12.9286i) q^{74} +(-2.38172 + 3.35057i) q^{76} +(8.25717 + 1.45596i) q^{77} +(0.205269 - 0.172241i) q^{79} +(14.6740 + 5.57812i) q^{80} +(0.498775 - 0.949889i) q^{82} +(7.91149 + 9.42855i) q^{83} +(-19.2280 - 3.39041i) q^{85} +(-8.77391 - 1.18681i) q^{86} +(7.88155 - 2.39307i) q^{88} +(4.11349 + 7.12477i) q^{89} +(9.92138 + 5.72811i) q^{91} +(-0.479235 - 1.84071i) q^{92} +(7.02358 - 2.88009i) q^{94} +(6.17946 + 5.18518i) q^{95} +(5.06123 + 1.84214i) q^{97} +(-0.974360 - 1.54149i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.301188	+	1.38177i	0.212972	+	0.977058i
$2$	0.301188	+	1.38177i	0.212972	+	0.977058i
$3$		0			0
$3$		0			0
$4$	−1.81857	+	0.832346i	−0.909286	+	0.416173i
$5$	1.34230	+	3.68793i	0.600294	+	1.64929i	0.750679	+	0.660667i	$0.229726\pi$
$5$	1.34230	+	3.68793i	0.600294	+	1.64929i	−0.150386	+	0.988627i	$0.548052\pi$
$6$		0			0
$7$	−0.499959	−	2.83541i	−0.188967	−	1.07168i	−0.920752	−	0.390148i	$-0.872424\pi$
$7$	−0.499959	−	2.83541i	−0.188967	−	1.07168i	0.731786	−	0.681535i	$-0.238687\pi$
$8$	−1.69784	−	2.26215i	−0.600278	−	0.799792i
$9$		0			0
$10$	−4.69159	+	2.96551i	−1.48361	+	0.937776i
$11$	−0.996019	+	2.73654i	−0.300311	+	0.825098i	0.694135	+	0.719845i	$0.255787\pi$
$11$	−0.996019	+	2.73654i	−0.300311	+	0.825098i	−0.994446	+	0.105252i	$0.966435\pi$
$12$		0			0
$13$	−2.55767	+	3.04812i	−0.709371	+	0.845396i	−0.993552	−	0.113375i	$-0.963834\pi$
$13$	−2.55767	+	3.04812i	−0.709371	+	0.845396i	0.284181	+	0.958771i	$0.408278\pi$
$14$	3.76729	−	1.54482i	1.00685	−	0.412870i
$15$		0			0
$16$	2.61440	−	3.02736i	0.653600	−	0.756840i
$17$	−2.48745	+	4.30839i	−0.603296	+	1.04494i	0.389022	+	0.921228i	$0.372813\pi$
$17$	−2.48745	+	4.30839i	−0.603296	+	1.04494i	−0.992318	+	0.123711i	$0.960520\pi$
$18$		0			0
$19$	1.78004	−	1.02771i	0.408369	−	0.235772i	−0.281720	−	0.959497i	$-0.590905\pi$
$19$	1.78004	−	1.02771i	0.408369	−	0.235772i	0.690089	+	0.723725i	$0.257571\pi$
$20$	−5.51070	−	5.58951i	−1.23223	−	1.24985i
$21$		0			0
$22$	−4.08125	−	0.552054i	−0.870126	−	0.117698i
$23$	−0.165146	+	0.936587i	−0.0344352	+	0.195292i	−0.997173	−	0.0751465i	$-0.976058\pi$
$23$	−0.165146	+	0.936587i	−0.0344352	+	0.195292i	0.962737	+	0.270438i	$0.0871687\pi$
$24$		0			0
$25$	−7.96887	+	6.68667i	−1.59377	+	1.33733i
$26$	−4.98214	−	2.61606i	−0.977077	−	0.513051i
$27$		0			0
$28$	3.26925	+	4.74025i	0.617830	+	0.895823i
$29$	−5.18495	−	6.17919i	−0.962821	−	1.14745i	−0.989019	−	0.147789i	$-0.952784\pi$
$29$	−5.18495	−	6.17919i	−0.962821	−	1.14745i	0.0261974	−	0.999657i	$-0.491660\pi$
$30$		0			0
$31$	0.331534	−	1.88022i	0.0595453	−	0.337698i	−0.940452	−	0.339926i	$-0.889598\pi$
$31$	0.331534	−	1.88022i	0.0595453	−	0.337698i	0.999998	+	0.00222778i	$0.000709125\pi$
$32$	4.97054	+	2.70069i	0.878675	+	0.477420i
$33$		0			0
$34$	−6.70240	−	2.13945i	−1.14945	−	0.366912i
$35$	9.78570	−	5.64977i	1.65408	−	0.954986i
$36$		0			0
$37$	8.31066	+	4.79816i	1.36626	+	0.788813i	0.990449	−	0.137881i	$-0.0440293\pi$
$37$	8.31066	+	4.79816i	1.36626	+	0.788813i	0.375816	+	0.926694i	$0.377363\pi$
$38$	1.95618	+	2.15007i	0.317334	+	0.348788i
$39$		0			0
$40$	6.06366	−	9.29801i	0.958748	−	1.47014i
$41$	−0.581151	−	0.487644i	−0.0907605	−	0.0761571i	0.596278	−	0.802778i	$-0.296645\pi$
$41$	−0.581151	−	0.487644i	−0.0907605	−	0.0761571i	−0.687039	+	0.726621i	$0.741090\pi$
$42$		0			0
$43$	−2.14125	+	5.88303i	−0.326537	+	0.897154i	0.662444	+	0.749112i	$0.269519\pi$
$43$	−2.14125	+	5.88303i	−0.326537	+	0.897154i	−0.988981	+	0.148042i	$0.952703\pi$
$44$	−0.466416	−	5.80562i	−0.0703148	−	0.875231i
$45$		0			0
$46$	−1.34389	+	0.0538962i	−0.198145	+	0.00794656i
$47$	−0.932102	−	5.28621i	−0.135961	−	0.771073i	−0.974186	−	0.225748i	$-0.927517\pi$
$47$	−0.932102	−	5.28621i	−0.135961	−	0.771073i	0.838225	−	0.545325i	$-0.183594\pi$
$48$		0			0
$49$	−1.21172	+	0.441031i	−0.173103	+	0.0630044i
$50$	−11.6396	−	8.99718i	−1.64608	−	1.27239i
$51$		0			0
$52$	2.11423	−	7.67209i	0.293190	−	1.06393i
$53$		−	3.54207i		−	0.486541i	−0.969959	−	0.243270i	$-0.921780\pi$
$53$		−	3.54207i		−	0.486541i	0.969959	−	0.243270i	$-0.0782202\pi$
$54$		0			0
$55$	−11.4291			−1.54110
$56$	−5.56527	+	5.94505i	−0.743691	+	0.794441i
$57$		0			0
$58$	6.97656	−	9.02551i	0.916067	−	1.18511i
$59$	2.13303	+	5.86045i	0.277697	+	0.762966i	0.997623	+	0.0689146i	$0.0219536\pi$
$59$	2.13303	+	5.86045i	0.277697	+	0.762966i	−0.719926	+	0.694051i	$0.755824\pi$
$60$		0			0
$61$	−3.22446	+	0.568559i	−0.412849	+	0.0727965i	−0.376215	−	0.926532i	$-0.622775\pi$
$61$	−3.22446	+	0.568559i	−0.412849	+	0.0727965i	−0.0366341	+	0.999329i	$0.511664\pi$
$62$	2.69789	−	0.108198i	0.342632	−	0.0137412i
$63$		0			0
$64$	−2.23467	+	7.68155i	−0.279333	+	0.960194i
$65$	−14.6744	−	5.34105i	−1.82014	−	0.662476i
$66$		0			0
$67$	4.40861	−	5.25398i	0.538598	−	0.641876i	−0.426275	−	0.904594i	$-0.640174\pi$
$67$	4.40861	−	5.25398i	0.538598	−	0.641876i	0.964873	+	0.262718i	$0.0846188\pi$
$68$	0.937536	−	9.90554i	0.113693	−	1.20122i
$69$		0			0
$70$	10.7540	+	11.8199i	1.28535	+	1.41275i
$71$	−3.83709	+	6.64603i	−0.455378	+	0.788738i	−0.998710	−	0.0507798i	$-0.983829\pi$
$71$	−3.83709	+	6.64603i	−0.455378	+	0.788738i	0.543332	+	0.839518i	$0.317163\pi$
$72$		0			0
$73$	3.46824	+	6.00718i	0.405927	+	0.703087i	0.994429	−	0.105409i	$-0.0336153\pi$
$73$	3.46824	+	6.00718i	0.405927	+	0.703087i	−0.588502	+	0.808496i	$0.700282\pi$
$74$	−4.12688	+	12.9286i	−0.479740	+	1.50292i
$75$		0			0
$76$	−2.38172	+	3.35057i	−0.273202	+	0.384336i
$77$	8.25717	+	1.45596i	0.940992	+	0.165922i
$78$		0			0
$79$	0.205269	−	0.172241i	0.0230945	−	0.0193786i	−0.631167	−	0.775647i	$-0.717424\pi$
$79$	0.205269	−	0.172241i	0.0230945	−	0.0193786i	0.654262	+	0.756268i	$0.272979\pi$
$80$	14.6740	+	5.57812i	1.64060	+	0.623653i
$81$		0			0
$82$	0.498775	−	0.949889i	0.0550805	−	0.104898i
$83$	7.91149	+	9.42855i	0.868399	+	1.03492i	0.999054	+	0.0434896i	$0.0138475\pi$
$83$	7.91149	+	9.42855i	0.868399	+	1.03492i	−0.130655	+	0.991428i	$0.541708\pi$
$84$		0			0
$85$	−19.2280	−	3.39041i	−2.08557	−	0.367742i
$86$	−8.77391	−	1.18681i	−0.946115	−	0.127977i
$87$		0			0
$88$	7.88155	−	2.39307i	0.840176	−	0.255102i
$89$	4.11349	+	7.12477i	0.436029	+	0.755224i	0.997379	−	0.0723541i	$-0.0230512\pi$
$89$	4.11349	+	7.12477i	0.436029	+	0.755224i	−0.561350	+	0.827578i	$0.689718\pi$
$90$		0			0
$91$	9.92138	+	5.72811i	1.04004	+	0.600469i
$92$	−0.479235	−	1.84071i	−0.0499637	−	0.191907i
$93$		0			0
$94$	7.02358	−	2.88009i	0.724427	−	0.297059i
$95$	6.17946	+	5.18518i	0.633999	+	0.531988i
$96$		0			0
$97$	5.06123	+	1.84214i	0.513891	+	0.187041i	0.585931	−	0.810361i	$-0.300729\pi$
$97$	5.06123	+	1.84214i	0.513891	+	0.187041i	−0.0720406	+	0.997402i	$0.522951\pi$
$98$	−0.974360	−	1.54149i	−0.0984252	−	0.155714i
$99$		0			0
$100$	8.92633	−	18.7930i	0.892633	−	1.87930i
$101$	3.98336	−	0.702375i	0.396360	−	0.0698889i	0.0280840	−	0.999606i	$-0.491059\pi$
$101$	3.98336	−	0.702375i	0.396360	−	0.0698889i	0.368276	+	0.929717i	$0.379948\pi$
$102$		0			0
$103$	1.07241	−	0.390325i	0.105668	−	0.0384599i	−0.288645	−	0.957436i	$-0.593205\pi$
$103$	1.07241	−	0.390325i	0.105668	−	0.0384599i	0.394313	+	0.918976i	$0.370983\pi$
$104$	11.2378	+	0.610627i	1.10196	+	0.0598769i
$105$		0			0
$106$	4.89432	−	1.06683i	0.475379	−	0.103620i
$107$			4.87553i			0.471335i	0.971834	+	0.235667i	$0.0757276\pi$
$107$			4.87553i			0.471335i	−0.971834	+	0.235667i	$0.924272\pi$
$108$		0			0
$109$		−	2.52010i		−	0.241382i	−0.992690	−	0.120691i	$-0.961489\pi$
$109$		−	2.52010i		−	0.241382i	0.992690	−	0.120691i	$-0.0385111\pi$
$110$	−3.44232	−	15.7924i	−0.328212	−	1.50575i
$111$		0			0
$112$	−9.89089	−	5.89934i	−0.934601	−	0.557435i
$113$	6.79620	−	2.47361i	0.639332	−	0.232698i	−0.00195583	−	0.999998i	$-0.500623\pi$
$113$	6.79620	−	2.47361i	0.639332	−	0.232698i	0.641288	+	0.767300i	$0.278400\pi$
$114$		0			0
$115$	−3.67575	+	0.648133i	−0.342765	+	0.0604387i
$116$	14.5724	+	6.92162i	1.35302	+	0.642656i
$117$		0			0
$118$	−7.45535	+	4.71245i	−0.686320	+	0.433817i
$119$	13.4597	+	4.89892i	1.23385	+	0.449083i
$120$		0			0
$121$	1.92989	+	1.61937i	0.175445	+	0.147216i
$122$	−1.75679	−	4.28421i	−0.159052	−	0.387874i
$123$		0			0
$124$	0.962077	+	3.69527i	0.0863971	+	0.331845i
$125$	−18.3625	−	10.6016i	−1.64239	−	0.948236i
$126$		0			0
$127$	−2.38507	−	4.13106i	−0.211641	−	0.366573i	0.740587	−	0.671960i	$-0.234547\pi$
$127$	−2.38507	−	4.13106i	−0.211641	−	0.366573i	−0.952228	+	0.305387i	$0.901214\pi$
$128$	−11.2872	−	0.774196i	−0.997656	−	0.0684299i
$129$		0			0
$130$	2.96033	−	21.8853i	0.259638	−	1.91947i
$131$	3.45051	+	0.608417i	0.301472	+	0.0531577i	0.322338	−	0.946625i	$-0.395531\pi$
$131$	3.45051	+	0.608417i	0.301472	+	0.0531577i	−0.0208660	+	0.999782i	$0.506642\pi$
$132$		0			0
$133$	−3.80391	−	4.53333i	−0.329841	−	0.393089i
$134$	8.58761	+	4.50925i	0.741857	+	0.389540i
$135$		0			0
$136$	13.9695	−	1.68798i	1.19788	−	0.144743i
$137$	12.6574	−	10.6208i	1.08140	−	0.907400i	0.0853611	−	0.996350i	$-0.472796\pi$
$137$	12.6574	−	10.6208i	1.08140	−	0.907400i	0.996036	+	0.0889501i	$0.0283512\pi$
$138$		0			0
$139$	19.5648	+	3.44981i	1.65947	+	0.292609i	0.923268	−	0.384157i	$-0.125508\pi$
$139$	19.5648	+	3.44981i	1.65947	+	0.292609i	0.736199	+	0.676765i	$0.236619\pi$
$140$	−13.0934	+	18.4196i	−1.10660	+	1.55674i
$141$		0			0
$142$	−10.3390	−	3.30026i	−0.867626	−	0.276952i
$143$	−5.79380	−	10.0352i	−0.484502	−	0.839182i
$144$		0			0
$145$	15.8287	−	27.4161i	1.31450	−	2.27678i
$146$	−7.25593	+	6.60160i	−0.600505	+	0.546353i
$147$		0			0
$148$	−19.1073	−	1.80846i	−1.57061	−	0.148654i
$149$	−7.39950	+	8.81838i	−0.606190	+	0.722429i	−0.978630	−	0.205627i	$-0.934077\pi$
$149$	−7.39950	+	8.81838i	−0.606190	+	0.722429i	0.372440	+	0.928056i	$0.378521\pi$
$150$		0			0
$151$	−3.42462	−	1.24646i	−0.278692	−	0.101436i	0.198893	−	0.980021i	$-0.436265\pi$
$151$	−3.42462	−	1.24646i	−0.278692	−	0.101436i	−0.477585	+	0.878586i	$0.658488\pi$
$152$	−5.34706	−	2.28184i	−0.433704	−	0.185082i
$153$		0			0
$154$	0.475161	+	11.8480i	0.0382896	+	0.954741i
$155$	7.37916	−	1.30114i	0.592708	−	0.104510i
$156$		0			0
$157$	5.00630	+	13.7547i	0.399546	+	1.09774i	0.962506	+	0.271259i	$0.0874402\pi$
$157$	5.00630	+	13.7547i	0.399546	+	1.09774i	−0.562960	+	0.826484i	$0.690338\pi$
$158$	0.299821	+	0.231757i	0.0238525	+	0.0184376i
$159$		0			0
$160$	−3.28803	+	21.9562i	−0.259942	+	1.73579i
$161$	2.73817			0.215798
$162$		0			0
$163$			5.93891i			0.465171i	0.972576	+	0.232586i	$0.0747186\pi$
$163$			5.93891i			0.465171i	−0.972576	+	0.232586i	$0.925281\pi$
$164$	1.46275	+	0.403096i	0.114222	+	0.0314765i
$165$		0			0
$166$	−10.6452	+	13.7716i	−0.826230	+	1.06889i
$167$	18.7096	−	6.80974i	1.44779	−	0.526953i	0.505818	−	0.862640i	$-0.331191\pi$
$167$	18.7096	−	6.80974i	1.44779	−	0.526953i	0.941974	+	0.335687i	$0.108968\pi$
$168$		0			0
$169$	−0.491897	−	2.78968i	−0.0378382	−	0.214591i
$170$	−1.10648	−	27.5898i	−0.0848631	−	2.11604i
$171$		0			0
$172$	−1.00270	−	12.4810i	−0.0764555	−	0.951665i
$173$	−3.76876	+	10.3546i	−0.286534	+	0.787245i	0.710011	+	0.704190i	$0.248690\pi$
$173$	−3.76876	+	10.3546i	−0.286534	+	0.787245i	−0.996545	+	0.0830547i	$0.973532\pi$
$174$		0			0
$175$	22.9435	+	19.2519i	1.73437	+	1.45531i
$176$	5.68050	+	10.1697i	0.428183	+	0.766571i
$177$		0			0
$178$	−8.60585	+	7.82979i	−0.645036	+	0.586868i
$179$	−3.66363	−	2.11520i	−0.273832	−	0.158097i	0.356796	−	0.934182i	$-0.383869\pi$
$179$	−3.66363	−	2.11520i	−0.273832	−	0.158097i	−0.630628	+	0.776085i	$0.717203\pi$
$180$		0			0
$181$	−16.4676	+	9.50759i	−1.22403	+	0.706694i	−0.965775	−	0.259383i	$-0.916481\pi$
$181$	−16.4676	+	9.50759i	−1.22403	+	0.706694i	−0.258255	+	0.966077i	$0.583147\pi$
$182$	−4.92672	+	15.4343i	−0.365193	+	1.14407i
$183$		0			0
$184$	2.39909	−	1.21659i	0.176864	−	0.0896884i
$185$	−6.53992	+	37.0897i	−0.480825	+	2.72689i
$186$		0			0
$187$	−9.31254	−	11.0983i	−0.681000	−	0.811585i
$188$	6.09505	+	8.83752i	0.444527	+	0.644542i
$189$		0			0
$190$	−5.30354	+	10.1003i	−0.384759	+	0.732753i
$191$	−6.22796	+	5.22588i	−0.450639	+	0.378131i	−0.839673	−	0.543092i	$-0.817253\pi$
$191$	−6.22796	+	5.22588i	−0.450639	+	0.378131i	0.389034	+	0.921224i	$0.372809\pi$
$192$		0			0
$193$	−2.29037	+	12.9893i	−0.164864	+	0.934993i	0.784340	+	0.620332i	$0.213002\pi$
$193$	−2.29037	+	12.9893i	−0.164864	+	0.934993i	−0.949204	+	0.314661i	$0.898109\pi$
$194$	−1.02102	+	7.54829i	−0.0733053	+	0.541936i
$195$		0			0
$196$	1.83651	−	1.81062i	0.131180	−	0.129330i
$197$	5.35211	−	3.09004i	0.381322	−	0.220156i	−0.297071	−	0.954855i	$-0.596010\pi$
$197$	5.35211	−	3.09004i	0.381322	−	0.220156i	0.678393	+	0.734699i	$0.262677\pi$
$198$		0			0
$199$	4.43708	−	7.68525i	0.314537	−	0.544793i	−0.664802	−	0.747019i	$-0.731484\pi$
$199$	4.43708	−	7.68525i	0.314537	−	0.544793i	0.979339	+	0.202226i	$0.0648176\pi$
$200$	28.6561	+	6.67388i	2.02630	+	0.471914i
$201$		0			0
$202$	2.17026	+	5.29254i	0.152699	+	0.372382i
$203$	−14.9282	+	17.7908i	−1.04776	+	1.24867i
$204$		0			0
$205$	1.01832	−	2.79781i	0.0711225	−	0.195407i
$206$	0.862336	+	1.36426i	0.0600818	+	0.0950526i
$207$		0			0
$208$	2.54096	+	15.7120i	0.176184	+	1.08943i
$209$	1.03941	+	5.89477i	0.0718972	+	0.407750i
$210$		0			0
$211$	−6.04444	−	16.6070i	−0.416116	−	1.14327i	−0.953884	−	0.300177i	$-0.902954\pi$
$211$	−6.04444	−	16.6070i	−0.416116	−	1.14327i	0.537767	−	0.843093i	$-0.319268\pi$
$212$	2.94823	+	6.44151i	0.202485	+	0.442405i
$213$		0			0
$214$	−6.73685	+	1.46845i	−0.460522	+	0.100381i
$215$	−24.5704			−1.67569
$216$		0			0
$217$	−5.49695			−0.373157
$218$	3.48220	−	0.759026i	0.235844	−	0.0514077i
$219$		0			0
$220$	20.7847	−	9.51299i	1.40130	−	0.641365i
$221$	−6.77040	−	18.6015i	−0.455426	−	1.25127i
$222$		0			0
$223$	−4.05080	−	22.9732i	−0.271262	−	1.53840i	−0.750592	−	0.660767i	$-0.770231\pi$
$223$	−4.05080	−	22.9732i	−0.271262	−	1.53840i	0.479330	−	0.877635i	$-0.340880\pi$
$224$	5.17250	−	15.4437i	0.345602	−	1.03188i
$225$		0			0
$226$	5.46490	+	8.64575i	0.363520	+	0.575107i
$227$	8.48739	−	23.3189i	0.563328	−	1.54773i	−0.251398	−	0.967884i	$-0.580890\pi$
$227$	8.48739	−	23.3189i	0.563328	−	1.54773i	0.814726	−	0.579846i	$-0.196887\pi$
$228$		0			0
$229$	3.58229	−	4.26921i	0.236724	−	0.282117i	−0.634583	−	0.772855i	$-0.718828\pi$
$229$	3.58229	−	4.26921i	0.236724	−	0.282117i	0.871307	+	0.490738i	$0.163273\pi$
$230$	−2.00266	−	4.88382i	−0.132052	−	0.322030i
$231$		0			0
$232$	−5.17503	+	22.2204i	−0.339757	+	1.45884i
$233$	3.32571	−	5.76031i	0.217875	−	0.377370i	−0.736283	−	0.676673i	$-0.763421\pi$
$233$	3.32571	−	5.76031i	0.217875	−	0.377370i	0.954158	+	0.299303i	$0.0967542\pi$
$234$		0			0
$235$	18.2440	−	10.5332i	1.19011	−	0.687110i
$236$	−8.75699	−	8.88223i	−0.570031	−	0.578184i
$237$		0			0
$238$	−2.71528	+	20.0737i	−0.176005	+	1.30118i
$239$	4.54329	−	25.7663i	0.293881	−	1.66668i	−0.377836	−	0.925872i	$-0.623332\pi$
$239$	4.54329	−	25.7663i	0.293881	−	1.66668i	0.671717	−	0.740808i	$-0.265557\pi$
$240$		0			0
$241$	−19.2391	+	16.1435i	−1.23930	+	1.03989i	−0.241718	+	0.970347i	$0.577711\pi$
$241$	−19.2391	+	16.1435i	−1.23930	+	1.03989i	−0.997579	+	0.0695464i	$0.977845\pi$
$242$	−1.65634	+	3.15440i	−0.106473	+	0.202773i
$243$		0			0
$244$	5.39067	−	3.71783i	0.345102	−	0.238010i
$245$	−3.25299	−	3.87676i	−0.207826	−	0.247677i
$246$		0			0
$247$	−1.42019	+	8.05431i	−0.0903647	+	0.512484i
$248$	−4.81624	+	2.44234i	−0.305832	+	0.155089i
$249$		0			0
$250$	9.11839	−	28.5658i	0.576697	−	1.80666i
$251$	−25.2441	+	14.5747i	−1.59339	+	0.919945i	−0.600672	+	0.799495i	$0.705100\pi$
$251$	−25.2441	+	14.5747i	−1.59339	+	0.919945i	−0.992719	+	0.120450i	$0.961566\pi$
$252$		0			0
$253$	−2.39852	−	1.38479i	−0.150794	−	0.0870608i
$254$	4.98982	−	4.53985i	0.313089	−	0.284855i
$255$		0			0
$256$	−2.32981	−	15.8295i	−0.145613	−	0.989342i
$257$	5.42626	+	4.55318i	0.338481	+	0.284019i	0.796145	−	0.605106i	$-0.206869\pi$
$257$	5.42626	+	4.55318i	0.338481	+	0.284019i	−0.457664	+	0.889125i	$0.651314\pi$
$258$		0			0
$259$	9.44975	−	25.9630i	0.587179	−	1.61326i
$260$	31.1321	−	2.50111i	1.93073	−	0.155112i
$261$		0			0
$262$	0.198560	+	4.95105i	0.0122671	+	0.305877i
$263$	−1.99223	−	11.2985i	−0.122846	−	0.696695i	−0.982564	−	0.185926i	$-0.940472\pi$
$263$	−1.99223	−	11.2985i	−0.122846	−	0.696695i	0.859718	−	0.510770i	$-0.170639\pi$
$264$		0			0
$265$	13.0629	−	4.75451i	0.802449	−	0.292067i
$266$	5.11832	−	6.62151i	0.313824	−	0.405991i
$267$		0			0
$268$	−3.64425	+	13.2242i	−0.222608	+	0.807798i
$269$		−	15.1820i		−	0.925661i	−0.886447	−	0.462831i	$-0.846834\pi$
$269$		−	15.1820i		−	0.925661i	0.886447	−	0.462831i	$-0.153166\pi$
$270$		0			0
$271$	13.2808			0.806753			0.403376	−	0.915034i	$-0.367837\pi$
$271$	13.2808			0.806753			0.403376	+	0.915034i	$0.367837\pi$
$272$	6.53986	+	18.7943i	0.396537	+	1.13957i
$273$		0			0
$274$	18.4878	+	14.2908i	1.11689	+	0.863337i
$275$	−10.3612	−	28.4672i	−0.624804	−	1.71664i
$276$		0			0
$277$	2.53413	−	0.446836i	0.152261	−	0.0268478i	−0.0969979	−	0.995285i	$-0.530924\pi$
$277$	2.53413	−	0.446836i	0.152261	−	0.0268478i	0.249259	+	0.968437i	$0.419813\pi$
$278$	1.12586	+	28.0731i	0.0675248	+	1.68371i
$279$		0			0
$280$	−29.3952	−	12.5443i	−1.75670	−	0.749666i
$281$	−25.4277	−	9.25491i	−1.51689	−	0.552102i	−0.556518	−	0.830835i	$-0.687863\pi$
$281$	−25.4277	−	9.25491i	−1.51689	−	0.552102i	−0.960368	+	0.278734i	$0.910085\pi$
$282$		0			0
$283$	−17.1845	+	20.4797i	−1.02151	+	1.21739i	−0.0456626	+	0.998957i	$0.514540\pi$
$283$	−17.1845	+	20.4797i	−1.02151	+	1.21739i	−0.975851	+	0.218436i	$0.929905\pi$
$284$	1.44622	−	15.2801i	0.0858174	−	0.906705i
$285$		0			0
$286$	12.1212	−	11.0282i	0.716744	−	0.652109i
$287$	−1.09212	+	1.89160i	−0.0644656	+	0.111658i
$288$		0			0
$289$	−3.87484	−	6.71142i	−0.227932	−	0.394789i
$290$	42.6501	+	13.6142i	2.50450	+	0.799452i
$291$		0			0
$292$	−11.3073	−	8.03770i	−0.661709	−	0.470371i
$293$	17.3330	+	3.05628i	1.01261	+	0.178550i	0.655245	−	0.755416i	$-0.272565\pi$
$293$	17.3330	+	3.05628i	1.01261	+	0.178550i	0.357361	+	0.933966i	$0.383677\pi$
$294$		0			0
$295$	−18.7498	+	15.7329i	−1.09166	+	0.916007i
$296$	−3.25602	−	26.9465i	−0.189252	−	1.56623i
$297$		0			0
$298$	−14.4136	−	7.56840i	−0.834957	−	0.438426i
$299$	−2.43244	−	2.89887i	−0.140672	−	0.167646i
$300$		0			0
$301$	17.7513	+	3.13004i	1.02317	+	0.180412i
$302$	0.690864	−	5.10746i	0.0397547	−	0.293901i
$303$		0			0
$304$	1.54250	−	8.07566i	0.0884686	−	0.463171i
$305$	−6.42499	−	11.1284i	−0.367894	−	0.637211i
$306$		0			0
$307$	−10.1962	−	5.88676i	−0.581926	−	0.335975i	0.179972	−	0.983672i	$-0.442399\pi$
$307$	−10.1962	−	5.88676i	−0.581926	−	0.335975i	−0.761898	+	0.647696i	$0.775732\pi$
$308$	−16.2281	+	4.22505i	−0.924683	+	0.240745i
$309$		0			0
$310$	4.02040	+	9.80440i	0.228343	+	0.556852i
$311$	−26.0496	−	21.8582i	−1.47714	−	1.23947i	−0.909175	−	0.416414i	$-0.863287\pi$
$311$	−26.0496	−	21.8582i	−1.47714	−	1.23947i	−0.567965	−	0.823053i	$-0.692269\pi$
$312$		0			0
$313$	6.64081	+	2.41706i	0.375361	+	0.136620i	0.522809	−	0.852450i	$-0.324884\pi$
$313$	6.64081	+	2.41706i	0.375361	+	0.136620i	−0.147449	+	0.989070i	$0.547106\pi$
$314$	−17.4980	+	11.0603i	−0.987467	+	0.624169i
$315$		0			0
$316$	−0.229932	+	0.484086i	−0.0129347	+	0.0272320i
$317$	−5.34112	+	0.941783i	−0.299987	+	0.0528958i	−0.321616	−	0.946870i	$-0.604226\pi$
$317$	−5.34112	+	0.941783i	−0.299987	+	0.0528958i	0.0216287	+	0.999766i	$0.493115\pi$
$318$		0			0
$319$	22.0739	−	8.03424i	1.23590	−	0.449831i
$320$	−31.3286	+	2.06964i	−1.75132	+	0.115696i
$321$		0			0
$322$	0.824706	+	3.78352i	0.0459590	+	0.210847i
$323$			10.2255i			0.568961i
$324$		0			0
$325$		−	41.3924i		−	2.29604i
$326$	−8.20620	+	1.78873i	−0.454499	+	0.0990686i
$327$		0			0
$328$	−0.116421	+	2.14259i	−0.00642830	+	0.118305i
$329$	−14.5225	+	5.28577i	−0.800654	+	0.291414i
$330$		0			0
$331$	5.34260	−	0.942044i	0.293656	−	0.0517794i	−0.0248795	−	0.999690i	$-0.507920\pi$
$331$	5.34260	−	0.942044i	0.293656	−	0.0517794i	0.318535	+	0.947911i	$0.396809\pi$
$332$	−22.2354	−	10.5614i	−1.22033	−	0.579632i
$333$		0			0
$334$	15.0446	+	23.8013i	0.823204	+	1.30235i
$335$	25.2940	+	9.20627i	1.38196	+	0.502992i
$336$		0			0
$337$	−22.3325	−	18.7392i	−1.21653	−	1.02079i	−0.998999	−	0.0447328i	$-0.985756\pi$
$337$	−22.3325	−	18.7392i	−1.21653	−	1.02079i	−0.217528	−	0.976054i	$-0.569799\pi$
$338$	3.70654	−	1.51991i	0.201609	−	0.0826721i
$339$		0			0
$340$	37.7894	−	9.83862i	2.04942	−	0.533574i
$341$	4.81509	+	2.77999i	0.260752	+	0.150545i
$342$		0			0
$343$	−8.22070	−	14.2387i	−0.443876	−	0.768816i
$344$	16.9438	−	5.14463i	0.913550	−	0.277380i
$345$		0			0
$346$	−15.4428	−	2.08888i	−0.830208	−	0.112299i
$347$	17.1238	+	3.01939i	0.919255	+	0.162089i	0.613203	−	0.789925i	$-0.289881\pi$
$347$	17.1238	+	3.01939i	0.919255	+	0.162089i	0.306052	+	0.952015i	$0.400992\pi$
$348$		0			0
$349$	3.38478	+	4.03383i	0.181183	+	0.215926i	0.848990	−	0.528409i	$-0.177211\pi$
$349$	3.38478	+	4.03383i	0.181183	+	0.215926i	−0.667807	+	0.744335i	$0.732767\pi$
$350$	−19.6914	+	37.5011i	−1.05255	+	2.00452i
$351$		0			0
$352$	−12.3413	+	10.9121i	−0.657794	+	0.581619i
$353$	7.22029	−	6.05854i	0.384297	−	0.322463i	−0.430090	−	0.902786i	$-0.641518\pi$
$353$	7.22029	−	6.05854i	0.384297	−	0.322463i	0.814387	+	0.580323i	$0.197074\pi$
$354$		0			0
$355$	−29.6606	−	5.22997i	−1.57422	−	0.277578i
$356$	−13.4109	−	9.53306i	−0.710779	−	0.505251i
$357$		0			0
$358$	1.81927	−	5.69936i	0.0961515	−	0.301221i
$359$	8.12377	+	14.0708i	0.428756	+	0.742628i	0.996763	−	0.0803962i	$-0.0256186\pi$
$359$	8.12377	+	14.0708i	0.428756	+	0.742628i	−0.568007	+	0.823024i	$0.692285\pi$
$360$		0			0
$361$	−7.38764	+	12.7958i	−0.388823	+	0.673461i
$362$	−18.0972	−	19.8909i	−0.951165	−	1.04544i
$363$		0			0
$364$	−22.8105	−	2.15896i	−1.19560	−	0.113160i
$365$	−17.4986	+	20.8541i	−0.915921	+	1.09155i
$366$		0			0
$367$	12.0315	+	4.37912i	0.628042	+	0.228588i	0.636379	−	0.771377i	$-0.280432\pi$
$367$	12.0315	+	4.37912i	0.628042	+	0.228588i	−0.00833711	+	0.999965i	$0.502654\pi$
$368$	2.40363	+	2.94857i	0.125298	+	0.153705i
$369$		0			0
$370$	−53.2192	+	2.13434i	−2.76673	+	0.110959i
$371$	−10.0432	+	1.77089i	−0.521417	+	0.0919400i
$372$		0			0
$373$	−2.16442	−	5.94669i	−0.112069	−	0.307908i	0.870961	−	0.491353i	$-0.163497\pi$
$373$	−2.16442	−	5.94669i	−0.112069	−	0.307908i	−0.983030	+	0.183445i	$0.941275\pi$
$374$	12.5304	−	16.2104i	0.647931	−	0.838222i
$375$		0			0
$376$	−10.3757	+	11.0837i	−0.535083	+	0.571598i
$377$	32.0963			1.65304
$378$		0			0
$379$			28.5066i			1.46428i	0.681152	+	0.732142i	$0.261479\pi$
$379$			28.5066i			1.46428i	−0.681152	+	0.732142i	$0.738521\pi$
$380$	−15.5536	−	4.28618i	−0.797885	−	0.219876i
$381$		0			0
$382$	−9.09675	−	7.03163i	−0.465430	−	0.359769i
$383$	29.5410	−	10.7521i	1.50948	−	0.549405i	0.550983	−	0.834517i	$-0.314253\pi$
$383$	29.5410	−	10.7521i	1.50948	−	0.549405i	0.958494	+	0.285112i	$0.0920308\pi$
$384$		0			0
$385$	5.71409	+	32.4062i	0.291217	+	1.65157i
$386$	−18.6381	+	0.747475i	−0.948654	+	0.0380455i
$387$		0			0
$388$	−10.7375	+	0.862636i	−0.545115	+	0.0437937i
$389$	−1.34416	+	3.69306i	−0.0681518	+	0.187246i	−0.969093	−	0.246696i	$-0.920655\pi$
$389$	−1.34416	+	3.69306i	−0.0681518	+	0.187246i	0.900941	+	0.433941i	$0.142877\pi$
$390$		0			0
$391$	−3.62440	−	3.04123i	−0.183294	−	0.153802i
$392$	3.05499	+	1.99230i	0.154300	+	0.100626i
$393$		0			0
$394$	5.88171	+	6.46469i	0.296316	+	0.325686i
$395$	0.910744	+	0.525818i	0.0458245	+	0.0264568i
$396$		0			0
$397$	17.9961	−	10.3901i	0.903200	−	0.521463i	0.0249629	−	0.999688i	$-0.492053\pi$
$397$	17.9961	−	10.3901i	0.903200	−	0.521463i	0.878237	+	0.478226i	$0.158720\pi$
$398$	11.9556	+	3.81631i	0.599282	+	0.191295i
$399$		0			0
$400$	−0.590854	+	41.6063i	−0.0295427	+	2.08031i
$401$	4.02373	−	22.8197i	0.200935	−	1.13956i	−0.702774	−	0.711413i	$-0.748055\pi$
$401$	4.02373	−	22.8197i	0.200935	−	1.13956i	0.903709	−	0.428147i	$-0.140834\pi$
$402$		0			0
$403$	4.88319	+	5.81955i	0.243249	+	0.289893i
$404$	−6.65941	+	4.59285i	−0.331318	+	0.228503i
$405$		0			0
$406$	−29.0790	−	15.2690i	−1.44316	−	0.757788i
$407$	−21.4079	+	17.9634i	−1.06115	+	0.890412i
$408$		0			0
$409$	5.07096	−	28.7589i	0.250743	−	1.42203i	−0.556025	−	0.831165i	$-0.687674\pi$
$409$	5.07096	−	28.7589i	0.250743	−	1.42203i	0.806768	−	0.590868i	$-0.201215\pi$
$410$	4.17263	+	0.564414i	0.206072	+	0.0278744i
$411$		0			0
$412$	−1.62537	+	1.60245i	−0.0800761	+	0.0789470i
$413$	15.5503	−	8.97799i	0.765182	−	0.441778i
$414$		0			0
$415$	−24.1523	+	41.8330i	−1.18559	+	2.05350i
$416$	−20.9451	+	8.24329i	−1.02692	+	0.404161i
$417$		0			0
$418$	−7.83215	+	3.21165i	−0.383083	+	0.157087i
$419$	−8.33906	+	9.93810i	−0.407390	+	0.485508i	−0.930258	−	0.366905i	$-0.880417\pi$
$419$	−8.33906	+	9.93810i	−0.407390	+	0.485508i	0.522869	+	0.852413i	$0.324862\pi$
$420$		0			0
$421$	−1.49536	+	4.10848i	−0.0728795	+	0.200235i	−0.970784	−	0.239956i	$-0.922867\pi$
$421$	−1.49536	+	4.10848i	−0.0728795	+	0.200235i	0.897904	+	0.440191i	$0.145089\pi$
$422$	21.1265	−	13.3538i	1.02842	−	0.650055i
$423$		0			0
$424$	−8.01270	+	6.01388i	−0.389131	+	0.292060i
$425$	−8.98665	−	50.9658i	−0.435916	−	2.47220i
$426$		0			0
$427$	3.22419	+	8.85839i	0.156030	+	0.428688i
$428$	−4.05812	−	8.86649i	−0.196157	−	0.428578i
$429$		0			0
$430$	−7.40033	−	33.9507i	−0.356876	−	1.63725i
$431$	−1.15854			−0.0558051			−0.0279025	−	0.999611i	$-0.508883\pi$
$431$	−1.15854			−0.0558051			−0.0279025	+	0.999611i	$0.508883\pi$
$432$		0			0
$433$	37.7498			1.81414			0.907069	−	0.420982i	$-0.138314\pi$
$433$	37.7498			1.81414			0.907069	+	0.420982i	$0.138314\pi$
$434$	−1.65562	−	7.59552i	−0.0794722	−	0.364596i
$435$		0			0
$436$	2.09760	+	4.58299i	0.100457	+	0.219485i
$437$	0.668571	+	1.83688i	0.0319821	+	0.0878701i
$438$		0			0
$439$	−4.69964	−	26.6530i	−0.224301	−	1.27208i	−0.864016	−	0.503464i	$-0.832059\pi$
$439$	−4.69964	−	26.6530i	−0.224301	−	1.27208i	0.639715	−	0.768612i	$-0.279052\pi$
$440$	19.4049	+	25.8544i	0.925090	+	1.23256i
$441$		0			0
$442$	23.6638	−	14.9577i	1.12557	−	0.711465i
$443$	10.3614	−	28.4677i	0.492285	−	1.35254i	−0.406299	−	0.913740i	$-0.633181\pi$
$443$	10.3614	−	28.4677i	0.492285	−	1.35254i	0.898584	−	0.438802i	$-0.144597\pi$
$444$		0			0
$445$	−20.7542	+	24.7338i	−0.983841	+	1.17250i
$446$	30.5236	−	12.5165i	1.44534	−	0.592675i
$447$		0			0
$448$	22.8976	+	2.49573i	1.08181	+	0.117912i
$449$	1.70434	−	2.95201i	0.0804330	−	0.139314i	−0.823003	−	0.568037i	$-0.807703\pi$
$449$	1.70434	−	2.95201i	0.0804330	−	0.139314i	0.903436	+	0.428723i	$0.141036\pi$
$450$		0			0
$451$	1.91329	−	1.10464i	0.0900934	−	0.0520155i
$452$	−10.3005	+	10.1552i	−0.484493	+	0.477662i
$453$		0			0
$454$	34.7776	+	4.70422i	1.63220	+	0.220780i
$455$	−7.80745	+	44.2782i	−0.366019	+	2.07580i
$456$		0			0
$457$	7.27754	−	6.10658i	0.340429	−	0.285654i	−0.456504	−	0.889721i	$-0.650899\pi$
$457$	7.27754	−	6.10658i	0.340429	−	0.285654i	0.796933	+	0.604068i	$0.206454\pi$
$458$	6.97800	+	3.66406i	0.326060	+	0.171210i
$459$		0			0
$460$	6.14514	−	4.23817i	0.286518	−	0.197606i
$461$	19.8885	+	23.7021i	0.926298	+	1.10392i	0.994341	+	0.106236i	$0.0338799\pi$
$461$	19.8885	+	23.7021i	0.926298	+	1.10392i	−0.0680433	+	0.997682i	$0.521676\pi$
$462$		0			0
$463$	−4.27095	+	24.2217i	−0.198488	+	1.12568i	0.708876	+	0.705333i	$0.249203\pi$
$463$	−4.27095	+	24.2217i	−0.198488	+	1.12568i	−0.907364	+	0.420347i	$0.861908\pi$
$464$	−32.2622	−	0.458157i	−1.49773	−	0.0212694i
$465$		0			0
$466$	8.96108	+	2.86043i	0.415114	+	0.132507i
$467$	0.849394	−	0.490398i	0.0393052	−	0.0226929i	−0.480219	−	0.877149i	$-0.659443\pi$
$467$	0.849394	−	0.490398i	0.0393052	−	0.0226929i	0.519524	+	0.854456i	$0.326109\pi$
$468$		0			0
$469$	−17.1013	−	9.87344i	−0.789665	−	0.455913i
$470$	20.0493	+	22.0366i	0.924807	+	1.01647i
$471$		0			0
$472$	9.63568	−	14.7754i	0.443518	−	0.680091i
$473$	−13.9664	−	11.7192i	−0.642177	−	0.538851i
$474$		0			0
$475$	−7.31297	+	20.0922i	−0.335542	+	0.921894i
$476$	−28.5550	+	2.29407i	−1.30881	+	0.105148i
$477$		0			0
$478$	36.9714	−	1.48273i	1.69103	−	0.0678183i
$479$	1.26087	+	7.15074i	0.0576105	+	0.326726i	0.999969	−	0.00787960i	$-0.00250818\pi$
$479$	1.26087	+	7.15074i	0.0576105	+	0.326726i	−0.942358	+	0.334605i	$0.891397\pi$
$480$		0			0
$481$	−35.8813	+	13.0597i	−1.63605	+	0.595473i
$482$	−28.1011	−	21.7217i	−1.27997	−	0.989396i
$483$		0			0
$484$	−4.85753	−	1.33861i	−0.220797	−	0.0608458i
$485$			21.1382i			0.959836i
$486$		0			0
$487$	0.153837			0.00697103			0.00348552	−	0.999994i	$-0.498891\pi$
$487$	0.153837			0.00697103			0.00348552	+	0.999994i	$0.498891\pi$
$488$	6.76079	+	6.32889i	0.306046	+	0.286495i
$489$		0			0
$490$	4.37702	−	5.66251i	0.197734	−	0.255806i
$491$	−7.10851	−	19.5305i	−0.320802	−	0.881398i	−0.990345	−	0.138624i	$-0.955732\pi$
$491$	−7.10851	−	19.5305i	−0.320802	−	0.881398i	0.669543	−	0.742774i	$-0.266490\pi$
$492$		0			0
$493$	39.5197	−	6.96839i	1.77988	−	0.313840i
$494$	−11.5569	+	0.463488i	−0.519971	+	0.0208533i
$495$		0			0
$496$	−4.82535	−	5.91933i	−0.216665	−	0.265786i
$497$	20.7626	+	7.55696i	0.931329	+	0.338976i
$498$		0			0
$499$	12.0312	−	14.3382i	0.538588	−	0.641865i	−0.426282	−	0.904590i	$-0.640177\pi$
$499$	12.0312	−	14.3382i	0.538588	−	0.641865i	0.964871	+	0.262726i	$0.0846214\pi$
$500$	42.2177	+	3.99581i	1.88803	+	0.178698i
$501$		0			0
$502$	−27.7421	−	30.4918i	−1.23819	−	1.36091i
$503$	−15.2553	+	26.4230i	−0.680200	+	1.17814i	0.294719	+	0.955584i	$0.404774\pi$
$503$	−15.2553	+	26.4230i	−0.680200	+	1.17814i	−0.974919	+	0.222558i	$0.928559\pi$
$504$		0			0
$505$	7.93717	+	13.7476i	0.353200	+	0.611760i
$506$	1.19105	−	3.73128i	0.0529485	−	0.165876i
$507$		0			0
$508$	7.77589	+	5.52743i	0.344999	+	0.245240i
$509$	−25.1247	−	4.43017i	−1.11363	−	0.196364i	−0.413590	−	0.910463i	$-0.635725\pi$
$509$	−25.1247	−	4.43017i	−1.11363	−	0.196364i	−0.700044	+	0.714099i	$0.746836\pi$
$510$		0			0
$511$	15.2988	−	12.8372i	0.676779	−	0.567885i
$512$	21.1710	−	7.98691i	0.935633	−	0.352975i
$513$		0			0
$514$	−4.65711	+	8.86921i	−0.205416	+	0.391204i
$515$	2.87899	+	3.43104i	0.126863	+	0.151190i
$516$		0			0
$517$	15.3943	+	2.71443i	0.677041	+	0.119381i
$518$	38.7210	+	5.23763i	1.70130	+	0.230128i
$519$		0			0
$520$	12.8326	+	42.2640i	0.562745	+	1.85340i
$521$	8.58140	+	14.8634i	0.375958	+	0.651178i	0.990470	−	0.137729i	$-0.0439803\pi$
$521$	8.58140	+	14.8634i	0.375958	+	0.651178i	−0.614512	+	0.788908i	$0.710647\pi$
$522$		0			0
$523$	−35.9656	−	20.7647i	−1.57266	−	0.907978i	−0.995841	−	0.0911099i	$-0.970959\pi$
$523$	−35.9656	−	20.7647i	−1.57266	−	0.907978i	−0.576824	−	0.816869i	$-0.695708\pi$
$524$	−6.78140	+	1.76556i	−0.296247	+	0.0771290i
$525$		0			0
$526$	15.0119	−	6.15578i	0.654549	−	0.268405i
$527$	7.27607	+	6.10535i	0.316950	+	0.265953i
$528$		0			0
$529$	20.7630	+	7.55712i	0.902739	+	0.328570i
$530$	10.5040	+	16.6179i	0.456266	+	0.721837i
$531$		0			0
$532$	10.6910	+	5.07801i	0.463513	+	0.220160i
$533$	2.97279	−	0.524183i	0.128766	−	0.0227049i
$534$		0			0
$535$	−17.9806	+	6.54441i	−0.777370	+	0.282939i
$536$	−19.3704	−	1.05253i	−0.836675	−	0.0454622i
$537$		0			0
$538$	20.9780	−	4.57263i	0.904425	−	0.197140i
$539$		−	3.75520i		−	0.161748i
$540$		0			0
$541$		−	11.2309i		−	0.482852i	−0.970419	−	0.241426i	$-0.922385\pi$
$541$		−	11.2309i		−	0.482852i	0.970419	−	0.241426i	$-0.0776152\pi$
$542$	4.00003	+	18.3510i	0.171816	+	0.788244i
$543$		0			0
$544$	−23.9996	+	14.6972i	−1.02898	+	0.630137i
$545$	9.29398	−	3.38273i	0.398110	−	0.144900i
$546$		0			0
$547$	−19.8704	+	3.50369i	−0.849599	+	0.149807i	−0.581462	−	0.813574i	$-0.697519\pi$
$547$	−19.8704	+	3.50369i	−0.849599	+	0.149807i	−0.268137	+	0.963381i	$0.586408\pi$
$548$	−14.1782	+	29.8501i	−0.605664	+	1.27513i
$549$		0			0
$550$	36.2144	−	22.8908i	1.54419	−	0.976066i
$551$	−15.5798	−	5.67059i	−0.663722	−	0.241575i
$552$		0			0
$553$	−0.590998	−	0.495906i	−0.0251318	−	0.0210881i
$554$	1.38068	+	3.36700i	0.0586593	+	0.143050i
$555$		0			0
$556$	−38.4515	+	10.0110i	−1.63070	+	0.424560i
$557$	26.7781	+	15.4604i	1.13463	+	0.655076i	0.945094	−	0.326798i	$-0.105970\pi$
$557$	26.7781	+	15.4604i	1.13463	+	0.655076i	0.189532	+	0.981875i	$0.439303\pi$
$558$		0			0
$559$	−12.4556	−	21.5737i	−0.526814	−	0.912469i
$560$	8.47984	−	44.3956i	0.358339	−	1.87606i
$561$		0			0
$562$	5.12963	−	37.9226i	0.216380	−	1.59967i
$563$	−20.3052	−	3.58035i	−0.855761	−	0.150894i	−0.271479	−	0.962444i	$-0.587513\pi$
$563$	−20.3052	−	3.58035i	−0.855761	−	0.150894i	−0.584282	+	0.811551i	$0.698624\pi$
$564$		0			0
$565$	18.2450	+	21.7436i	0.767575	+	0.914760i
$566$	−33.4740	−	17.5768i	−1.40702	−	0.738808i
$567$		0			0
$568$	21.5491	−	2.60383i	0.904180	−	0.109254i
$569$	3.82688	−	3.21114i	0.160431	−	0.134618i	−0.559038	−	0.829142i	$-0.688829\pi$
$569$	3.82688	−	3.21114i	0.160431	−	0.134618i	0.719469	+	0.694524i	$0.244385\pi$
$570$		0			0
$571$	−7.54047	−	1.32959i	−0.315559	−	0.0556415i	0.0136257	−	0.999907i	$-0.495663\pi$
$571$	−7.54047	−	1.32959i	−0.315559	−	0.0556415i	−0.329184	+	0.944266i	$0.606774\pi$
$572$	18.8892	+	13.4272i	0.789796	+	0.561420i
$573$		0			0
$574$	−2.94269	−	0.939324i	−0.122825	−	0.0392066i
$575$	−4.94663	−	8.56781i	−0.206289	−	0.357303i
$576$		0			0
$577$	6.53703	−	11.3225i	0.272140	−	0.471361i	−0.697269	−	0.716809i	$-0.745602\pi$
$577$	6.53703	−	11.3225i	0.272140	−	0.471361i	0.969410	+	0.245449i	$0.0789352\pi$
$578$	8.10657	−	7.37553i	0.337189	−	0.306782i
$579$		0			0
$580$	−5.96592	+	63.0330i	−0.247722	+	2.61730i
$581$	22.7783	−	27.1462i	0.945005	−	1.12621i
$582$		0			0
$583$	9.69302	+	3.52797i	0.401444	+	0.146114i
$584$	7.70061	−	18.0449i	0.318654	−	0.746705i
$585$		0			0
$586$	0.997434	+	24.8708i	0.0412036	+	1.02740i
$587$	20.2706	−	3.57425i	0.836657	−	0.147525i	0.261126	−	0.965305i	$-0.415906\pi$
$587$	20.2706	−	3.57425i	0.836657	−	0.147525i	0.575532	+	0.817780i	$0.304795\pi$
$588$		0			0
$589$	−1.34217	−	3.68759i	−0.0553033	−	0.151945i
$590$	−27.3865	−	21.1693i	−1.12748	−	0.871526i
$591$		0			0
$592$	36.2532	−	12.6150i	1.49000	−	0.518475i
$593$	−35.4674			−1.45647			−0.728237	−	0.685326i	$-0.759660\pi$
$593$	−35.4674			−1.45647			−0.728237	+	0.685326i	$0.759660\pi$
$594$		0			0
$595$			56.2142i			2.30456i
$596$	6.11657	−	22.1958i	0.250545	−	0.909175i
$597$		0			0
$598$	3.27294	−	4.23418i	0.133841	−	0.173148i
$599$	−4.95171	+	1.80227i	−0.202321	+	0.0736389i	−0.441193	−	0.897412i	$-0.645445\pi$
$599$	−4.95171	+	1.80227i	−0.202321	+	0.0736389i	0.238872	+	0.971051i	$0.423222\pi$
$600$		0			0
$601$	−6.16086	−	34.9400i	−0.251307	−	1.42523i	−0.805378	−	0.592762i	$-0.798038\pi$
$601$	−6.16086	−	34.9400i	−0.251307	−	1.42523i	0.554071	−	0.832469i	$-0.313074\pi$
$602$	1.02151	+	25.4710i	0.0416334	+	1.03812i
$603$		0			0
$604$	7.26540	−	0.583692i	0.295625	−	0.0237501i
$605$	−3.38165	+	9.29100i	−0.137484	+	0.377733i
$606$		0			0
$607$	−6.68660	−	5.61072i	−0.271401	−	0.227732i	0.496922	−	0.867795i	$-0.334464\pi$
$607$	−6.68660	−	5.61072i	−0.271401	−	0.227732i	−0.768322	+	0.640063i	$0.778908\pi$
$608$	11.6233	−	0.300914i	0.471386	−	0.0122037i
$609$		0			0
$610$	13.4418	−	12.2296i	0.544241	−	0.495162i
$611$	18.4970	+	10.6793i	0.748309	+	0.432036i
$612$		0			0
$613$	−28.4795	+	16.4426i	−1.15028	+	0.664112i	−0.948954	−	0.315414i	$-0.897857\pi$
$613$	−28.4795	+	16.4426i	−1.15028	+	0.664112i	−0.201321	+	0.979525i	$0.564523\pi$
$614$	5.06318	−	15.8618i	0.204333	−	0.640129i
$615$		0			0
$616$	−10.7258	−	21.1510i	−0.432153	−	0.852197i
$617$	−5.77150	+	32.7318i	−0.232352	+	1.31773i	0.615767	+	0.787928i	$0.288846\pi$
$617$	−5.77150	+	32.7318i	−0.232352	+	1.31773i	−0.848119	+	0.529805i	$0.822265\pi$
$618$		0			0
$619$	−22.6481	−	26.9910i	−0.910305	−	1.08486i	−0.996072	−	0.0885446i	$-0.971778\pi$
$619$	−22.6481	−	26.9910i	−0.910305	−	1.08486i	0.0857667	−	0.996315i	$-0.472666\pi$
$620$	−12.3365	+	8.50823i	−0.495446	+	0.341699i
$621$		0			0
$622$	22.3572	−	42.5780i	0.896442	−	1.70722i
$623$	18.1451	−	15.2255i	0.726966	−	0.609997i
$624$		0			0
$625$	5.41806	−	30.7273i	0.216722	−	1.22909i
$626$	−1.33968	+	9.90405i	−0.0535444	+	0.395846i
$627$		0			0
$628$	−20.5530	−	20.8469i	−0.820152	−	0.831882i
$629$	−41.3448	+	23.8704i	−1.64852	+	0.951775i
$630$		0			0
$631$	−20.3613	+	35.2667i	−0.810569	+	1.40395i	0.101898	+	0.994795i	$0.467509\pi$
$631$	−20.3613	+	35.2667i	−0.810569	+	1.40395i	−0.912466	+	0.409152i	$0.865825\pi$
$632$	−0.738148	−	0.171911i	−0.0293620	−	0.00683826i
$633$		0			0
$634$	−2.91001	−	7.09654i	−0.115571	−	0.281840i
$635$	12.0336	−	14.3411i	0.477539	−	0.569109i
$636$		0			0
$637$	1.75488	−	4.82149i	0.0695308	−	0.191034i
$638$	17.7499	+	28.0812i	0.702724	+	1.11175i
$639$		0			0
$640$	−12.2956	−	42.6656i	−0.486026	−	1.68651i
$641$	8.76821	+	49.7270i	0.346323	+	1.96410i	0.246823	+	0.969061i	$0.420613\pi$
$641$	8.76821	+	49.7270i	0.346323	+	1.96410i	0.0995006	+	0.995038i	$0.468275\pi$
$642$		0			0
$643$	15.1261	+	41.5587i	0.596517	+	1.63892i	0.758162	+	0.652067i	$0.226098\pi$
$643$	15.1261	+	41.5587i	0.596517	+	1.63892i	−0.161645	+	0.986849i	$0.551680\pi$
$644$	−4.97956	+	2.27911i	−0.196222	+	0.0898093i
$645$		0			0
$646$	−14.1293	+	3.07980i	−0.555908	+	0.121173i
$647$	−2.96214			−0.116454			−0.0582268	−	0.998303i	$-0.518545\pi$
$647$	−2.96214			−0.116454			−0.0582268	+	0.998303i	$0.518545\pi$
$648$		0			0
$649$	−18.1619			−0.712917
$650$	57.1947	−	12.4669i	2.24336	−	0.488992i
$651$		0			0
$652$	−4.94322	−	10.8003i	−0.193592	−	0.422973i
$653$	0.829258	+	2.27837i	0.0324514	+	0.0891594i	0.954860	−	0.297055i	$-0.0960046\pi$
$653$	0.829258	+	2.27837i	0.0324514	+	0.0891594i	−0.922409	+	0.386215i	$0.873782\pi$
$654$		0			0
$655$	2.38780	+	13.5419i	0.0932992	+	0.529126i
$656$	−2.99563	+	0.484457i	−0.116960	+	0.0189149i
$657$		0			0
$658$	−11.6777	−	18.4748i	−0.455246	−	0.720222i
$659$	−14.7728	+	40.5879i	−0.575466	+	1.58108i	0.220272	+	0.975438i	$0.429305\pi$
$659$	−14.7728	+	40.5879i	−0.575466	+	1.58108i	−0.795738	+	0.605641i	$0.792917\pi$
$660$		0			0
$661$	11.3612	−	13.5398i	0.441901	−	0.526637i	−0.498415	−	0.866938i	$-0.666085\pi$
$661$	11.3612	−	13.5398i	0.441901	−	0.526637i	0.940317	+	0.340301i	$0.110529\pi$
$662$	2.91082	+	7.09850i	0.113132	+	0.275891i
$663$		0			0
$664$	7.89635	−	33.9052i	0.306438	−	1.31578i
$665$	11.6126	−	20.1137i	0.450318	−	0.779974i
$666$		0			0
$667$	6.64362	−	3.83570i	0.257242	−	0.148519i
$668$	−28.3567	+	27.9568i	−1.09715	+	1.08168i
$669$		0			0
$670$	−5.10267	+	37.7233i	−0.197133	+	1.45738i
$671$	1.65574	−	9.39015i	0.0639190	−	0.362503i
$672$		0			0
$673$	1.22568	−	1.02847i	0.0472465	−	0.0396445i	−0.618859	−	0.785502i	$-0.712405\pi$
$673$	1.22568	−	1.02847i	0.0472465	−	0.0396445i	0.666105	+	0.745858i	$0.267960\pi$
$674$	19.1669	−	36.5023i	0.738282	−	1.40602i
$675$		0			0
$676$	3.21653	+	4.66381i	0.123713	+	0.179377i
$677$	−4.41092	−	5.25673i	−0.169526	−	0.202033i	0.674592	−	0.738191i	$-0.264320\pi$
$677$	−4.41092	−	5.25673i	−0.169526	−	0.202033i	−0.844118	+	0.536158i	$0.819875\pi$
$678$		0			0
$679$	2.69280	−	15.2717i	0.103340	−	0.586072i
$680$	24.9764	+	49.2530i	0.957803	+	1.88877i
$681$		0			0
$682$	−2.39106	+	7.49065i	−0.0915584	+	0.286832i
$683$	4.11971	−	2.37852i	0.157636	−	0.0910113i	−0.419107	−	0.907937i	$-0.637657\pi$
$683$	4.11971	−	2.37852i	0.157636	−	0.0910113i	0.576743	+	0.816926i	$0.304323\pi$
$684$		0			0
$685$	56.1590	+	32.4234i	2.14573	+	1.23884i
$686$	17.1986	−	15.6476i	0.656645	−	0.597429i
$687$		0			0
$688$	12.2120	+	21.8629i	0.465577	+	0.833517i
$689$	10.7966	+	9.05946i	0.411320	+	0.345138i
$690$		0			0
$691$	−4.35017	+	11.9520i	−0.165488	+	0.454675i	−0.994523	−	0.104523i	$-0.966669\pi$
$691$	−4.35017	+	11.9520i	−0.165488	+	0.454675i	0.829034	+	0.559198i	$0.188891\pi$
$692$	−1.76484	−	21.9675i	−0.0670890	−	0.835078i
$693$		0			0
$694$	0.985395	+	24.5706i	0.0374051	+	0.932686i
$695$	13.5392	+	76.7844i	0.513570	+	2.91260i
$696$		0			0
$697$	3.54655	−	1.29084i	0.134335	−	0.0488939i
$698$	−4.55436	+	5.89193i	−0.172385	+	0.223013i
$699$		0			0
$700$	−57.7487	−	15.9140i	−2.18270	−	0.601493i
$701$		−	12.2688i		−	0.463386i	−0.972789	−	0.231693i	$-0.925573\pi$
$701$		−	12.2688i		−	0.463386i	0.972789	−	0.231693i	$-0.0744265\pi$
$702$		0			0
$703$	19.7244			0.743921
$704$	−18.7951	−	13.7662i	−0.708367	−	0.518834i
$705$		0			0
$706$	10.5462	+	8.15200i	0.396910	+	0.306805i
$707$	−3.98304	−	10.9433i	−0.149797	−	0.411565i
$708$		0			0
$709$	25.9792	−	4.58083i	0.975668	−	0.172037i	0.336988	−	0.941509i	$-0.390592\pi$
$709$	25.9792	−	4.58083i	0.975668	−	0.172037i	0.638680	+	0.769473i	$0.279481\pi$
$710$	−1.70683	−	42.5593i	−0.0640561	−	1.59722i
$711$		0			0
$712$	9.13326	−	21.4021i	0.342284	−	0.802077i
$713$	1.70624	+	0.621021i	0.0638993	+	0.0232574i
$714$		0			0
$715$	29.2320	−	34.8373i	1.09321	−	1.30284i
$716$	8.42314	+	0.797231i	0.314788	+	0.0297939i
$717$		0			0
$718$	−16.9958	+	15.4631i	−0.634277	+	0.577079i
$719$	15.9411	−	27.6108i	0.594502	−	1.02971i	−0.399115	−	0.916901i	$-0.630683\pi$
$719$	15.9411	−	27.6108i	0.594502	−	1.02971i	0.993617	−	0.112807i	$-0.0359841\pi$
$720$		0			0
$721$	−1.64289	−	2.84557i	−0.0611845	−	0.105975i
$722$	−19.9059	−	6.35407i	−0.740819	−	0.236474i
$723$		0			0
$724$	22.0340	−	30.9970i	0.818886	−	1.15199i
$725$	82.6364	+	14.5710i	3.06904	+	0.541154i
$726$		0			0
$727$	30.8679	−	25.9013i	1.14483	−	0.960625i	0.145243	−	0.989396i	$-0.453604\pi$
$727$	30.8679	−	25.9013i	1.14483	−	0.960625i	0.999586	+	0.0287706i	$0.00915924\pi$
$728$	−3.88708	−	32.1691i	−0.144065	−	1.19227i
$729$		0			0
$730$	−34.0859	−	17.8981i	−1.26158	−	0.662438i
$731$	−20.0202	−	23.8591i	−0.740473	−	0.882461i
$732$		0			0
$733$	0.103428	+	0.0182371i	0.00382018	+	0.000673601i	0.175558	−	0.984469i	$-0.443827\pi$
$733$	0.103428	+	0.0182371i	0.00382018	+	0.000673601i	−0.171738	+	0.985143i	$0.554938\pi$
$734$	−2.42718	+	17.9438i	−0.0895887	+	0.662316i
$735$		0			0
$736$	−3.35030	+	4.20934i	−0.123494	+	0.155158i
$737$	9.98667	+	17.2974i	0.367864	+	0.637158i
$738$		0			0
$739$	−26.3545	−	15.2158i	−0.969466	−	0.559722i	−0.0703928	−	0.997519i	$-0.522425\pi$
$739$	−26.3545	−	15.2158i	−0.969466	−	0.559722i	−0.899074	+	0.437798i	$0.855759\pi$
$740$	−18.9782	−	72.8938i	−0.697651	−	2.67963i
$741$		0			0
$742$	−5.47186	−	13.3440i	−0.200878	−	0.489875i
$743$	−12.9183	−	10.8397i	−0.473926	−	0.397671i	0.374298	−	0.927308i	$-0.377884\pi$
$743$	−12.9183	−	10.8397i	−0.473926	−	0.397671i	−0.848224	+	0.529637i	$0.822328\pi$
$744$		0			0
$745$	−42.4539	−	15.4520i	−1.55539	−	0.566116i
$746$	7.56506	−	4.78180i	0.276976	−	0.175074i
$747$		0			0
$748$	26.1731	+	12.4317i	0.956983	+	0.454548i
$749$	13.8241	−	2.43756i	0.505122	−	0.0890666i
$750$		0			0
$751$	14.6848	−	5.34482i	0.535855	−	0.195035i	−0.0598958	−	0.998205i	$-0.519077\pi$
$751$	14.6848	−	5.34482i	0.535855	−	0.195035i	0.595751	+	0.803169i	$0.296855\pi$
$752$	−18.4401	−	10.9985i	−0.672443	−	0.401073i
$753$		0			0
$754$	9.66704	+	44.3497i	0.352053	+	1.61512i
$755$		−	14.3029i		−	0.520536i
$756$		0			0
$757$			27.3201i			0.992967i	0.868046	+	0.496484i	$0.165376\pi$
$757$			27.3201i			0.992967i	−0.868046	+	0.496484i	$0.834624\pi$
$758$	−39.3895	+	8.58585i	−1.43069	+	0.311852i
$759$		0			0
$760$	1.23793	−	22.7825i	0.0449043	−	0.826408i
$761$	14.1817	−	5.16172i	0.514086	−	0.187112i	−0.0719327	−	0.997409i	$-0.522917\pi$
$761$	14.1817	−	5.16172i	0.514086	−	0.187112i	0.586019	+	0.810297i	$0.300694\pi$
$762$		0			0
$763$	−7.14552	+	1.25995i	−0.258685	+	0.0456132i
$764$	6.97625	−	14.6874i	0.252392	−	0.531373i
$765$		0			0
$766$	23.7543	+	37.5805i	0.858277	+	1.35784i
$767$	−23.3189	−	8.48740i	−0.841998	−	0.306462i
$768$		0			0
$769$	−11.4199	−	9.58242i	−0.411811	−	0.345551i	0.413226	−	0.910628i	$-0.364402\pi$
$769$	−11.4199	−	9.58242i	−0.411811	−	0.345551i	−0.825038	+	0.565077i	$0.808846\pi$
$770$	−43.0569	+	17.6559i	−1.55166	+	0.636276i
$771$		0			0
$772$	−6.64642	−	25.5284i	−0.239210	−	0.918788i
$773$	27.9615	+	16.1436i	1.00571	+	0.580644i	0.909931	−	0.414759i	$-0.136134\pi$
$773$	27.9615	+	16.1436i	1.00571	+	0.580644i	0.0957742	+	0.995403i	$0.469467\pi$
$774$		0			0
$775$	9.93049	+	17.2001i	0.356714	+	0.617846i
$776$	−4.42598	−	14.5769i	−0.158883	−	0.523282i
$777$		0			0
$778$	−5.50780	−	0.745017i	−0.197464	−	0.0267102i
$779$	−1.53563	−	0.270772i	−0.0550195	−	0.00970143i
$780$		0			0
$781$	−14.3653	−	17.1199i	−0.514031	−	0.612598i
$782$	3.11065	−	5.92406i	0.111237	−	0.211844i
$783$		0			0
$784$	−1.83277	+	4.82135i	−0.0654561	+	0.172191i
$785$	−44.0064	+	36.9258i	−1.57066	+	1.31794i
$786$		0			0
$787$	39.6718	+	6.99522i	1.41415	+	0.249353i	0.827944	−	0.560811i	$-0.189510\pi$
$787$	39.6718	+	6.99522i	1.41415	+	0.249353i	0.586204	+	0.810163i	$0.300622\pi$
$788$	−7.16120	+	10.0743i	−0.255107	+	0.358881i
$789$		0			0
$790$	−0.452254	+	1.41681i	−0.0160905	+	0.0504078i
$791$	−10.4115	−	18.0333i	−0.370191	−	0.641189i
$792$		0			0
$793$	6.51408	−	11.2827i	0.231322	−	0.400661i
$794$	19.7769	+	21.7371i	0.701856	+	0.771422i
$795$		0			0
$796$	−1.67236	+	17.6694i	−0.0592754	+	0.626274i
$797$	−2.35451	+	2.80599i	−0.0834009	+	0.0993934i	−0.806131	−	0.591737i	$-0.798442\pi$
$797$	−2.35451	+	2.80599i	−0.0834009	+	0.0993934i	0.722730	+	0.691130i	$0.242887\pi$
$798$		0			0
$799$	25.0936	+	9.13334i	0.887749	+	0.323114i
$800$	−57.6682	+	11.7149i	−2.03888	+	0.414184i
$801$		0			0
$802$	32.7434	−	1.31316i	1.15621	−	0.0463695i
$803$	−19.8933	+	3.50773i	−0.702020	+	0.123785i
$804$		0			0
$805$	3.67544	+	10.0982i	0.129542	+	0.355915i
$806$	−6.57052	+	8.50022i	−0.231437	+	0.299407i
$807$		0			0
$808$	−8.35200	−	7.81846i	−0.293822	−	0.275052i
$809$	41.2691			1.45094			0.725472	−	0.688252i	$-0.241622\pi$
$809$	41.2691			1.45094			0.725472	+	0.688252i	$0.241622\pi$
$810$		0			0
$811$		−	25.6578i		−	0.900966i	−0.892785	−	0.450483i	$-0.851252\pi$
$811$		−	25.6578i		−	0.900966i	0.892785	−	0.450483i	$-0.148748\pi$
$812$	12.3400	−	44.7793i	0.433049	−	1.57144i
$813$		0			0
$814$	−31.2691	−	24.1705i	−1.09598	−	0.847174i
$815$	−21.9023	+	7.97178i	−0.767204	+	0.279239i
$816$		0			0
$817$	2.23452	+	12.6726i	0.0781761	+	0.443359i
$818$	41.2654	−	1.65494i	1.44281	−	0.0578635i
$819$		0			0
$820$	0.476858	+	5.93561i	0.0166526	+	0.207280i
$821$	8.61194	−	23.6611i	0.300559	−	0.825778i	−0.693844	−	0.720125i	$-0.744084\pi$
$821$	8.61194	−	23.6611i	0.300559	−	0.825778i	0.994403	−	0.105653i	$-0.0336933\pi$
$822$		0			0
$823$	10.3916	+	8.71956i	0.362227	+	0.303945i	0.805678	−	0.592354i	$-0.201801\pi$
$823$	10.3916	+	8.71956i	0.362227	+	0.303945i	−0.443450	+	0.896299i	$0.646246\pi$
$824$	−2.70376	−	1.76324i	−0.0941898	−	0.0614255i
$825$		0			0
$826$	17.0891	+	18.7829i	0.594605	+	0.653541i
$827$	−9.62668	−	5.55796i	−0.334752	−	0.193269i	0.323197	−	0.946332i	$-0.395242\pi$
$827$	−9.62668	−	5.55796i	−0.334752	−	0.193269i	−0.657949	+	0.753062i	$0.728576\pi$
$828$		0			0
$829$	−26.4493	+	15.2705i	−0.918621	+	0.530366i	−0.883195	−	0.469006i	$-0.844612\pi$
$829$	−26.4493	+	15.2705i	−0.918621	+	0.530366i	−0.0354262	+	0.999372i	$0.511279\pi$
$830$	−65.0779	−	20.7733i	−2.25889	−	0.721050i
$831$		0			0
$832$	−17.6987	−	26.4584i	−0.613593	−	0.917281i
$833$	1.11397	−	6.31762i	0.0385967	−	0.218893i
$834$		0			0
$835$	50.2277	+	59.8590i	1.73820	+	2.07151i
$836$	−6.79672	−	9.85491i	−0.235069	−	0.340839i
$837$		0			0
$838$	−16.2438	−	8.52941i	−0.561132	−	0.294644i
$839$	3.67221	−	3.08135i	0.126779	−	0.106380i	−0.577194	−	0.816607i	$-0.695852\pi$
$839$	3.67221	−	3.08135i	0.126779	−	0.106380i	0.703972	+	0.710227i	$0.251408\pi$
$840$		0			0
$841$	−6.26281	+	35.5181i	−0.215959	+	1.22476i
$842$	−6.12735	−	0.828821i	−0.211162	−	0.0285631i
$843$		0			0
$844$	24.8150	+	25.1699i	0.854167	+	0.866383i
$845$	9.62790	−	5.55867i	0.331210	−	0.191224i
$846$		0			0
$847$	3.62672	−	6.28165i	0.124615	−	0.215840i
$848$	−10.7231	−	9.26039i	−0.368233	−	0.318003i
$849$		0			0
$850$	67.7163	−	27.7678i	2.32265	−	0.952427i
$851$	−5.86637	+	6.99127i	−0.201097	+	0.239657i
$852$		0			0
$853$	7.52367	−	20.6711i	0.257605	−	0.707765i	−0.741708	−	0.670723i	$-0.765984\pi$
$853$	7.52367	−	20.6711i	0.257605	−	0.707765i	0.999314	−	0.0370424i	$-0.0117937\pi$
$854$	−11.2692	+	7.12313i	−0.385623	+	0.243749i
$855$		0			0
$856$	11.0292	−	8.27787i	0.376970	−	0.282932i
$857$	1.54554	+	8.76520i	0.0527947	+	0.299414i	0.999760	−	0.0219232i	$-0.00697894\pi$
$857$	1.54554	+	8.76520i	0.0527947	+	0.299414i	−0.946965	+	0.321337i	$0.895868\pi$
$858$		0			0
$859$	−7.12897	−	19.5867i	−0.243237	−	0.668289i	−0.999895	−	0.0144780i	$-0.995391\pi$
$859$	−7.12897	−	19.5867i	−0.243237	−	0.668289i	0.756658	−	0.653811i	$-0.226831\pi$
$860$	44.6831	−	20.4511i	1.52368	−	0.697377i
$861$		0			0
$862$	−0.348940	−	1.60084i	−0.0118849	−	0.0545248i
$863$	21.4666			0.730731			0.365365	−	0.930864i	$-0.380944\pi$
$863$	21.4666			0.730731			0.365365	+	0.930864i	$0.380944\pi$
$864$		0			0
$865$	−43.2459			−1.47040
$866$	11.3698	+	52.1615i	0.386361	+	1.77252i
$867$		0			0
$868$	9.99660	−	4.57536i	0.339307	−	0.155298i
$869$	0.266892	+	0.733280i	0.00905370	+	0.0248748i
$870$		0			0
$871$	4.73896	+	26.8760i	0.160573	+	0.910657i
$872$	−5.70086	+	4.27874i	−0.193055	+	0.144896i
$873$		0			0
$874$	−2.33678	+	1.47706i	−0.0790429	+	0.0499623i
$875$	−20.8794	+	57.3655i	−0.705851	+	1.93931i
$876$		0			0
$877$	0.176559	−	0.210415i	0.00596198	−	0.00710521i	−0.763055	−	0.646333i	$-0.776302\pi$
$877$	0.176559	−	0.210415i	0.00596198	−	0.00710521i	0.769017	+	0.639228i	$0.220746\pi$
$878$	35.4128	−	14.5214i	1.19512	−	0.490073i
$879$		0			0
$880$	−29.8803	+	34.6001i	−1.00727	+	1.16637i
$881$	11.9250	−	20.6547i	0.401763	−	0.695873i	−0.592176	−	0.805809i	$-0.701731\pi$
$881$	11.9250	−	20.6547i	0.401763	−	0.695873i	0.993939	+	0.109935i	$0.0350643\pi$
$882$		0			0
$883$	4.93626	−	2.84995i	0.166118	−	0.0959085i	−0.414636	−	0.909987i	$-0.636091\pi$
$883$	4.93626	−	2.84995i	0.166118	−	0.0959085i	0.580754	+	0.814079i	$0.302758\pi$
$884$	27.7953	+	28.1929i	0.934859	+	0.948229i
$885$		0			0
$886$	42.4566	+	5.74292i	1.42636	+	0.192937i
$887$	2.98032	−	16.9022i	0.100069	−	0.567521i	−0.893006	−	0.450044i	$-0.851408\pi$
$887$	2.98032	−	16.9022i	0.100069	−	0.567521i	0.993076	−	0.117477i	$-0.0374806\pi$
$888$		0			0
$889$	−10.5208	+	8.82801i	−0.352857	+	0.296082i
$890$	−40.4274	−	21.2279i	−1.35513	−	0.711561i
$891$		0			0
$892$	26.4883	+	38.4068i	0.886895	+	1.28595i
$893$	−7.09185	−	8.45174i	−0.237320	−	0.282827i
$894$		0			0
$895$	2.88302	−	16.3504i	0.0963689	−	0.546535i
$896$	3.44797	+	32.3908i	0.115188	+	1.08210i
$897$		0			0
$898$	4.59232	+	1.46590i	0.153248	+	0.0489177i
$899$	−13.3372	+	7.70026i	−0.444822	+	0.256818i
$900$		0			0
$901$	15.2606	+	8.81073i	0.508405	+	0.293528i
$902$	2.10262	+	2.31102i	0.0700096	+	0.0769487i
$903$		0			0
$904$	−17.1346	−	11.1742i	−0.569887	−	0.371649i
$905$	−57.1678	−	47.9695i	−1.90032	−	1.59456i
$906$		0			0
$907$	−14.9621	+	41.1081i	−0.496809	+	1.36497i	0.397533	+	0.917588i	$0.369866\pi$
$907$	−14.9621	+	41.1081i	−0.496809	+	1.36497i	−0.894342	+	0.447383i	$0.852356\pi$
$908$	3.97447	+	49.4715i	0.131897	+	1.64177i
$909$		0			0
$910$	−63.5338	+	2.54800i	−2.10613	+	0.0844655i
$911$	−0.448255	−	2.54218i	−0.0148514	−	0.0842262i	0.976481	−	0.215602i	$-0.0691715\pi$
$911$	−0.448255	−	2.54218i	−0.0148514	−	0.0842262i	−0.991333	+	0.131376i	$0.958060\pi$
$912$		0			0
$913$	−33.6816	+	12.2591i	−1.11470	+	0.405717i
$914$	10.6298	+	8.21664i	0.351602	+	0.271782i
$915$		0			0
$916$	−2.96119	+	10.7456i	−0.0978405	+	0.355043i
$917$		−	10.0878i		−	0.333127i
$918$		0			0
$919$	−59.9068			−1.97614			−0.988071	−	0.153998i	$-0.950785\pi$
$919$	−59.9068			−1.97614			−0.988071	+	0.153998i	$0.950785\pi$
$920$	7.70701	+	7.21467i	0.254093	+	0.237861i
$921$		0			0
$922$	−26.7607	+	34.6201i	−0.881317	+	1.14015i
$923$	−10.4439	−	28.6943i	−0.343764	−	0.944483i
$924$		0			0
$925$	−98.3103	+	17.3348i	−3.23242	+	0.569963i
$926$	−34.7552	+	1.39385i	−1.14213	+	0.0458047i
$927$		0			0
$928$	−9.08392	−	44.7168i	−0.298194	−	1.46790i
$929$	30.1626	+	10.9783i	0.989604	+	0.360186i	0.785567	−	0.618777i	$-0.212371\pi$
$929$	30.1626	+	10.9783i	0.989604	+	0.360186i	0.204037	+	0.978963i	$0.434594\pi$
$930$		0			0
$931$	−1.70366	+	2.03035i	−0.0558354	+	0.0665420i
$932$	−1.25348	+	13.2437i	−0.0410592	+	0.433811i
$933$		0			0
$934$	0.933444	+	1.02596i	0.0305432	+	0.0335706i
$935$	28.4294	−	49.2412i	0.929741	−	1.61036i
$936$		0			0
$937$	8.40875	+	14.5644i	0.274702	+	0.475797i	0.970060	−	0.242866i	$-0.0780875\pi$
$937$	8.40875	+	14.5644i	0.274702	+	0.475797i	−0.695358	+	0.718663i	$0.744754\pi$
$938$	8.49210	−	26.6038i	0.277277	−	0.868645i
$939$		0			0
$940$	−24.4108	+	34.3407i	−0.796193	+	1.12007i
$941$	20.4427	+	3.60459i	0.666412	+	0.117506i	0.496613	−	0.867972i	$-0.334577\pi$
$941$	20.4427	+	3.60459i	0.666412	+	0.117506i	0.169799	+	0.985479i	$0.445688\pi$
$942$		0			0
$943$	0.552695	−	0.463766i	0.0179982	−	0.0151023i
$944$	23.3183	+	8.86412i	0.758946	+	0.288503i
$945$		0			0
$946$	11.9867	−	22.8281i	0.389722	−	0.742205i
$947$	11.7887	+	14.0493i	0.383082	+	0.456540i	0.922785	−	0.385316i	$-0.125908\pi$
$947$	11.7887	+	14.0493i	0.383082	+	0.456540i	−0.539702	+	0.841856i	$0.681463\pi$
$948$		0			0
$949$	−27.1812	−	4.79278i	−0.882340	−	0.155580i
$950$	−29.9654	−	4.05329i	−0.972205	−	0.131506i
$951$		0			0
$952$	−11.7703	−	38.7654i	−0.381477	−	1.25639i
$953$	−1.73534	−	3.00570i	−0.0562133	−	0.0973643i	0.836549	−	0.547892i	$-0.184569\pi$
$953$	−1.73534	−	3.00570i	−0.0562133	−	0.0973643i	−0.892763	+	0.450527i	$0.851236\pi$
$954$		0			0
$955$	−27.6325	−	15.9536i	−0.894166	−	0.516247i
$956$	13.1841	+	50.6393i	0.426406	+	1.63779i
$957$		0			0
$958$	−9.50091	+	3.89595i	−0.306960	+	0.125872i
$959$	−36.4426	−	30.5790i	−1.17679	−	0.987447i
$960$		0			0
$961$	25.7051	+	9.35591i	0.829198	+	0.301803i
$962$	−28.8526	−	45.6463i	−0.930245	−	1.47169i
$963$		0			0
$964$	21.5506	−	45.3716i	0.694099	−	1.46132i
$965$	−50.9782	+	8.98883i	−1.64105	+	0.289361i
$966$		0			0
$967$	−29.0536	+	10.5747i	−0.934301	+	0.340058i	−0.763913	−	0.645319i	$-0.776724\pi$
$967$	−29.0536	+	10.5747i	−0.934301	+	0.340058i	−0.170388	+	0.985377i	$0.554502\pi$
$968$	0.386614	−	7.11516i	0.0124262	−	0.228690i
$969$		0			0
$970$	−29.2081	+	6.36658i	−0.937816	+	0.204419i
$971$			0.278968i			0.00895249i	0.999990	+	0.00447625i	$0.00142484\pi$
$971$			0.278968i			0.00895249i	−0.999990	+	0.00447625i	$0.998575\pi$
$972$		0			0
$973$		−	57.1990i		−	1.83372i
$974$	0.0463340	+	0.212568i	0.00148464	+	0.00681110i
$975$		0			0
$976$	−6.70879	+	11.2480i	−0.214743	+	0.360041i
$977$	−20.1241	+	7.32457i	−0.643827	+	0.234334i	−0.643238	−	0.765666i	$-0.722409\pi$
$977$	−20.1241	+	7.32457i	−0.643827	+	0.234334i	−0.000588326		1.00000i	$0.500187\pi$
$978$		0			0
$979$	−23.5943	+	4.16032i	−0.754078	+	0.132964i
$980$	9.14259	+	4.34255i	0.292049	+	0.138718i
$981$		0			0
$982$	24.8456	−	15.7047i	0.792855	−	0.501156i
$983$	5.52983	+	2.01269i	0.176374	+	0.0641950i	0.428698	−	0.903448i	$-0.358973\pi$
$983$	5.52983	+	2.01269i	0.176374	+	0.0641950i	−0.252324	+	0.967643i	$0.581195\pi$
$984$		0			0
$985$	18.5800	+	15.5905i	0.592008	+	0.496753i
$986$	21.5316	+	52.5083i	0.685705	+	1.67220i
$987$		0			0
$988$	−4.12125	−	15.8294i	−0.131114	−	0.503601i
$989$	−5.15636	−	2.97702i	−0.163963	−	0.0946639i
$990$		0			0
$991$	17.5543	+	30.4049i	0.557631	+	0.965845i	0.997694	+	0.0678778i	$0.0216228\pi$
$991$	17.5543	+	30.4049i	0.557631	+	0.965845i	−0.440063	+	0.897967i	$0.645044\pi$
$992$	6.72581	−	8.45035i	0.213545	−	0.268299i
$993$		0			0
$994$	−4.18853	+	30.9652i	−0.132852	+	0.982155i
$995$	34.2986	+	6.04777i	1.08734	+	0.191727i
$996$		0			0
$997$	16.1819	+	19.2848i	0.512485	+	0.610756i	0.958787	−	0.284127i	$-0.0917036\pi$
$997$	16.1819	+	19.2848i	0.512485	+	0.610756i	−0.446302	+	0.894883i	$0.647259\pi$
$998$	23.4357	+	12.3058i	0.741844	+	0.389533i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.37.18		204
3.2	odd	2		216.2.t.a.157.17	✓	204
8.5	even	2	inner	648.2.t.a.37.4		204
12.11	even	2		864.2.bf.a.49.7		204
24.5	odd	2		216.2.t.a.157.31	yes	204
24.11	even	2		864.2.bf.a.49.28		204
27.11	odd	18		216.2.t.a.205.31	yes	204
27.16	even	9	inner	648.2.t.a.613.4		204
108.11	even	18		864.2.bf.a.529.28		204
216.11	even	18		864.2.bf.a.529.7		204
216.173	odd	18		216.2.t.a.205.17	yes	204
216.205	even	18	inner	648.2.t.a.613.18		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.17	✓	204	3.2	odd	2
216.2.t.a.157.31	yes	204	24.5	odd	2
216.2.t.a.205.17	yes	204	216.173	odd	18
216.2.t.a.205.31	yes	204	27.11	odd	18
648.2.t.a.37.4		204	8.5	even	2	inner
648.2.t.a.37.18		204	1.1	even	1	trivial
648.2.t.a.613.4		204	27.16	even	9	inner
648.2.t.a.613.18		204	216.205	even	18	inner
864.2.bf.a.49.7		204	12.11	even	2
864.2.bf.a.49.28		204	24.11	even	2
864.2.bf.a.529.7		204	216.11	even	18
864.2.bf.a.529.28		204	108.11	even	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.301188 + 1.38177i) q^{2} +(-1.81857 + 0.832346i) q^{4} +(1.34230 + 3.68793i) q^{5} +(-0.499959 - 2.83541i) q^{7} +(-1.69784 - 2.26215i) q^{8} +(-4.69159 + 2.96551i) q^{10} +(-0.996019 + 2.73654i) q^{11} +(-2.55767 + 3.04812i) q^{13} +(3.76729 - 1.54482i) q^{14} +(2.61440 - 3.02736i) q^{16} +(-2.48745 + 4.30839i) q^{17} +(1.78004 - 1.02771i) q^{19} +(-5.51070 - 5.58951i) q^{20} +(-4.08125 - 0.552054i) q^{22} +(-0.165146 + 0.936587i) q^{23} +(-7.96887 + 6.68667i) q^{25} +(-4.98214 - 2.61606i) q^{26} +(3.26925 + 4.74025i) q^{28} +(-5.18495 - 6.17919i) q^{29} +(0.331534 - 1.88022i) q^{31} +(4.97054 + 2.70069i) q^{32} +(-6.70240 - 2.13945i) q^{34} +(9.78570 - 5.64977i) q^{35} +(8.31066 + 4.79816i) q^{37} +(1.95618 + 2.15007i) q^{38} +(6.06366 - 9.29801i) q^{40} +(-0.581151 - 0.487644i) q^{41} +(-2.14125 + 5.88303i) q^{43} +(-0.466416 - 5.80562i) q^{44} +(-1.34389 + 0.0538962i) q^{46} +(-0.932102 - 5.28621i) q^{47} +(-1.21172 + 0.441031i) q^{49} +(-11.6396 - 8.99718i) q^{50} +(2.11423 - 7.67209i) q^{52} -3.54207i q^{53} -11.4291 q^{55} +(-5.56527 + 5.94505i) q^{56} +(6.97656 - 9.02551i) q^{58} +(2.13303 + 5.86045i) q^{59} +(-3.22446 + 0.568559i) q^{61} +(2.69789 - 0.108198i) q^{62} +(-2.23467 + 7.68155i) q^{64} +(-14.6744 - 5.34105i) q^{65} +(4.40861 - 5.25398i) q^{67} +(0.937536 - 9.90554i) q^{68} +(10.7540 + 11.8199i) q^{70} +(-3.83709 + 6.64603i) q^{71} +(3.46824 + 6.00718i) q^{73} +(-4.12688 + 12.9286i) q^{74} +(-2.38172 + 3.35057i) q^{76} +(8.25717 + 1.45596i) q^{77} +(0.205269 - 0.172241i) q^{79} +(14.6740 + 5.57812i) q^{80} +(0.498775 - 0.949889i) q^{82} +(7.91149 + 9.42855i) q^{83} +(-19.2280 - 3.39041i) q^{85} +(-8.77391 - 1.18681i) q^{86} +(7.88155 - 2.39307i) q^{88} +(4.11349 + 7.12477i) q^{89} +(9.92138 + 5.72811i) q^{91} +(-0.479235 - 1.84071i) q^{92} +(7.02358 - 2.88009i) q^{94} +(6.17946 + 5.18518i) q^{95} +(5.06123 + 1.84214i) q^{97} +(-0.974360 - 1.54149i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

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