LMFDB - Embedded newform 648.2.v.b.35.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(35,648)] 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("648.35"); 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([9, 9, 13])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.9
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.860856 + 1.12202i) q^{2} +(-0.517853 - 1.93179i) q^{4} +(-3.00936 - 1.09532i) q^{5} +(-4.58614 - 0.808660i) q^{7} +(2.61331 + 1.08196i) q^{8} +(3.81960 - 2.43365i) q^{10} +(0.303411 + 0.833616i) q^{11} +(1.22056 + 1.45461i) q^{13} +(4.85534 - 4.44959i) q^{14} +(-3.46366 + 2.00077i) q^{16} +(4.03247 - 2.32815i) q^{17} +(-0.171350 + 0.296787i) q^{19} +(-0.557523 + 6.38069i) q^{20} +(-1.19653 - 0.377190i) q^{22} +(1.00156 + 5.68012i) q^{23} +(4.02633 + 3.37849i) q^{25} +(-2.68283 + 0.117284i) q^{26} +(0.812780 + 9.27824i) q^{28} +(4.16935 + 3.49850i) q^{29} +(7.80815 - 1.37679i) q^{31} +(0.736809 - 5.60866i) q^{32} +(-0.859151 + 6.52870i) q^{34} +(12.9156 + 7.45683i) q^{35} +(-2.31812 + 1.33837i) q^{37} +(-0.185493 - 0.447749i) q^{38} +(-6.67930 - 6.11841i) q^{40} +(-0.0346849 - 0.0413359i) q^{41} +(-2.85915 + 1.04064i) q^{43} +(1.45325 - 1.01782i) q^{44} +(-7.23540 - 3.76600i) q^{46} +(1.90179 - 10.7856i) q^{47} +(13.8009 + 5.02311i) q^{49} +(-7.25682 + 1.60922i) q^{50} +(2.17793 - 3.11115i) q^{52} -1.27415 q^{53} -2.84099i q^{55} +(-11.1100 - 7.07528i) q^{56} +(-7.51460 + 1.66638i) q^{58} +(-2.43399 + 6.68734i) q^{59} +(8.19039 + 1.44419i) q^{61} +(-5.17691 + 9.94610i) q^{62} +(5.65874 + 5.65497i) q^{64} +(-2.07985 - 5.71435i) q^{65} +(-6.31205 + 5.29644i) q^{67} +(-6.58572 - 6.58426i) q^{68} +(-19.4852 + 8.07230i) q^{70} +(0.186788 + 0.323526i) q^{71} +(6.29550 - 10.9041i) q^{73} +(0.493895 - 3.75312i) q^{74} +(0.662065 + 0.177321i) q^{76} +(-0.717374 - 4.06843i) q^{77} +(-2.54509 + 3.03312i) q^{79} +(12.6149 - 2.22724i) q^{80} +(0.0762384 - 0.00333288i) q^{82} +(-8.90996 + 10.6185i) q^{83} +(-14.6852 + 2.58940i) q^{85} +(1.29369 - 4.10386i) q^{86} +(-0.109029 + 2.50677i) q^{88} +(6.35012 + 3.66624i) q^{89} +(-4.42138 - 7.65805i) q^{91} +(10.4542 - 4.87627i) q^{92} +(10.4645 + 11.4187i) q^{94} +(0.840731 - 0.705457i) q^{95} +(-0.833364 + 0.303320i) q^{97} +(-17.5166 + 11.1607i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Character values

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

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.860856	+	1.12202i	−0.608717	+	0.793387i
$2$	−0.860856	+	1.12202i	−0.608717	+	0.793387i
$3$		0			0
$3$		0			0
$4$	−0.517853	−	1.93179i	−0.258926	−	0.965897i
$5$	−3.00936	−	1.09532i	−1.34583	−	0.489842i	−0.434185	−	0.900824i	$-0.642964\pi$
$5$	−3.00936	−	1.09532i	−1.34583	−	0.489842i	−0.911643	+	0.410982i	$0.865186\pi$
$6$		0			0
$7$	−4.58614	−	0.808660i	−1.73340	−	0.305645i	−0.784242	−	0.620455i	$-0.786948\pi$
$7$	−4.58614	−	0.808660i	−1.73340	−	0.305645i	−0.949155	+	0.314810i	$0.898059\pi$
$8$	2.61331	+	1.08196i	0.923943	+	0.382529i
$9$		0			0
$10$	3.81960	−	2.43365i	1.20786	−	0.769588i
$11$	0.303411	+	0.833616i	0.0914819	+	0.251345i	0.976992	−	0.213275i	$-0.0684132\pi$
$11$	0.303411	+	0.833616i	0.0914819	+	0.251345i	−0.885510	+	0.464620i	$0.846191\pi$
$12$		0			0
$13$	1.22056	+	1.45461i	0.338523	+	0.403436i	0.908270	−	0.418384i	$-0.137403\pi$
$13$	1.22056	+	1.45461i	0.338523	+	0.403436i	−0.569747	+	0.821820i	$0.692959\pi$
$14$	4.85534	−	4.44959i	1.29764	−	1.18920i
$15$		0			0
$16$	−3.46366	+	2.00077i	−0.865914	+	0.500192i
$17$	4.03247	−	2.32815i	0.978017	−	0.564658i	0.0763460	−	0.997081i	$-0.475675\pi$
$17$	4.03247	−	2.32815i	0.978017	−	0.564658i	0.901671	+	0.432423i	$0.142341\pi$
$18$		0			0
$19$	−0.171350	+	0.296787i	−0.0393104	+	0.0680876i	−0.885011	−	0.465570i	$-0.845849\pi$
$19$	−0.171350	+	0.296787i	−0.0393104	+	0.0680876i	0.845701	+	0.533657i	$0.179183\pi$
$20$	−0.557523	+	6.38069i	−0.124666	+	1.42676i
$21$		0			0
$22$	−1.19653	−	0.377190i	−0.255100	−	0.0804172i
$23$	1.00156	+	5.68012i	0.208839	+	1.18439i	0.891282	+	0.453449i	$0.149806\pi$
$23$	1.00156	+	5.68012i	0.208839	+	1.18439i	−0.682443	+	0.730939i	$0.739082\pi$
$24$		0			0
$25$	4.02633	+	3.37849i	0.805265	+	0.675698i
$26$	−2.68283	+	0.117284i	−0.526146	+	0.0230013i
$27$		0			0
$28$	0.812780	+	9.27824i	0.153601	+	1.75342i
$29$	4.16935	+	3.49850i	0.774229	+	0.649655i	0.941788	−	0.336207i	$-0.109144\pi$
$29$	4.16935	+	3.49850i	0.774229	+	0.649655i	−0.167559	+	0.985862i	$0.553589\pi$
$30$		0			0
$31$	7.80815	−	1.37679i	1.40238	−	0.247278i	0.579262	−	0.815142i	$-0.303341\pi$
$31$	7.80815	−	1.37679i	1.40238	−	0.247278i	0.823123	+	0.567864i	$0.192230\pi$
$32$	0.736809	−	5.60866i	0.130251	−	0.991481i
$33$		0			0
$34$	−0.859151	+	6.52870i	−0.147343	+	1.11966i
$35$	12.9156	+	7.45683i	2.18314	+	1.26044i
$36$		0			0
$37$	−2.31812	+	1.33837i	−0.381097	+	0.220026i	−0.678295	−	0.734789i	$-0.737281\pi$
$37$	−2.31812	+	1.33837i	−0.381097	+	0.220026i	0.297199	+	0.954816i	$0.403948\pi$
$38$	−0.185493	−	0.447749i	−0.0300909	−	0.0726344i
$39$		0			0
$40$	−6.67930	−	6.11841i	−1.05609	−	0.967405i
$41$	−0.0346849	−	0.0413359i	−0.00541687	−	0.00645558i	0.763329	−	0.646010i	$-0.223563\pi$
$41$	−0.0346849	−	0.0413359i	−0.00541687	−	0.00645558i	−0.768746	+	0.639554i	$0.779119\pi$
$42$		0			0
$43$	−2.85915	+	1.04064i	−0.436016	+	0.158697i	−0.550696	−	0.834706i	$-0.685638\pi$
$43$	−2.85915	+	1.04064i	−0.436016	+	0.158697i	0.114681	+	0.993402i	$0.463416\pi$
$44$	1.45325	−	1.01782i	0.219086	−	0.153442i
$45$		0			0
$46$	−7.23540	−	3.76600i	−1.06680	−	0.555267i
$47$	1.90179	−	10.7856i	0.277404	−	1.57324i	−0.453814	−	0.891096i	$-0.649937\pi$
$47$	1.90179	−	10.7856i	0.277404	−	1.57324i	0.731219	−	0.682143i	$-0.238952\pi$
$48$		0			0
$49$	13.8009	+	5.02311i	1.97155	+	0.717587i
$50$	−7.25682	+	1.60922i	−1.02627	+	0.227578i
$51$		0			0
$52$	2.17793	−	3.11115i	0.302025	−	0.431438i
$53$	−1.27415			−0.175018			−0.0875092	−	0.996164i	$-0.527891\pi$
$53$	−1.27415			−0.175018			−0.0875092	+	0.996164i	$0.527891\pi$
$54$		0			0
$55$		−	2.84099i		−	0.383078i
$56$	−11.1100	−	7.07528i	−1.48464	−	0.945474i
$57$		0			0
$58$	−7.51460	+	1.66638i	−0.986715	+	0.218807i
$59$	−2.43399	+	6.68734i	−0.316879	+	0.870618i	0.674344	+	0.738417i	$0.264427\pi$
$59$	−2.43399	+	6.68734i	−0.316879	+	0.870618i	−0.991223	+	0.132201i	$0.957796\pi$
$60$		0			0
$61$	8.19039	+	1.44419i	1.04867	+	0.184909i	0.671326	−	0.741163i	$-0.265725\pi$
$61$	8.19039	+	1.44419i	1.04867	+	0.184909i	0.377347	+	0.926072i	$0.376836\pi$
$62$	−5.17691	+	9.94610i	−0.657468	+	1.26316i
$63$		0			0
$64$	5.65874	+	5.65497i	0.707343	+	0.706871i
$65$	−2.07985	−	5.71435i	−0.257974	−	0.708778i
$66$		0			0
$67$	−6.31205	+	5.29644i	−0.771139	+	0.647063i	−0.941000	−	0.338405i	$-0.890113\pi$
$67$	−6.31205	+	5.29644i	−0.771139	+	0.647063i	0.169861	+	0.985468i	$0.445668\pi$
$68$	−6.58572	−	6.58426i	−0.798636	−	0.798459i
$69$		0			0
$70$	−19.4852	+	8.07230i	−2.32893	+	0.964825i
$71$	0.186788	+	0.323526i	0.0221676	+	0.0383955i	0.876896	−	0.480679i	$-0.159610\pi$
$71$	0.186788	+	0.323526i	0.0221676	+	0.0383955i	−0.854729	+	0.519075i	$0.826277\pi$
$72$		0			0
$73$	6.29550	−	10.9041i	0.736832	−	1.27623i	−0.217083	−	0.976153i	$-0.569654\pi$
$73$	6.29550	−	10.9041i	0.736832	−	1.27623i	0.953915	−	0.300077i	$-0.0970125\pi$
$74$	0.493895	−	3.75312i	0.0574141	−	0.436291i
$75$		0			0
$76$	0.662065	+	0.177321i	0.0759441	+	0.0203401i
$77$	−0.717374	−	4.06843i	−0.0817524	−	0.463641i
$78$		0			0
$79$	−2.54509	+	3.03312i	−0.286345	+	0.341252i	−0.889973	−	0.456014i	$-0.849277\pi$
$79$	−2.54509	+	3.03312i	−0.286345	+	0.341252i	0.603628	+	0.797266i	$0.293721\pi$
$80$	12.6149	−	2.22724i	1.41039	−	0.249013i
$81$		0			0
$82$	0.0762384	−	0.00333288i	0.00841912	−	0.000368055i
$83$	−8.90996	+	10.6185i	−0.977996	+	1.16553i	0.00820363	+	0.999966i	$0.497389\pi$
$83$	−8.90996	+	10.6185i	−0.977996	+	1.16553i	−0.986199	+	0.165563i	$0.947056\pi$
$84$		0			0
$85$	−14.6852	+	2.58940i	−1.59284	+	0.280860i
$86$	1.29369	−	4.10386i	0.139502	−	0.442531i
$87$		0			0
$88$	−0.109029	+	2.50677i	−0.0116226	+	0.267223i
$89$	6.35012	+	3.66624i	0.673111	+	0.388621i	0.797254	−	0.603644i	$-0.206285\pi$
$89$	6.35012	+	3.66624i	0.673111	+	0.388621i	−0.124143	+	0.992264i	$0.539618\pi$
$90$		0			0
$91$	−4.42138	−	7.65805i	−0.463487	−	0.802782i
$92$	10.4542	−	4.87627i	1.08992	−	0.508387i
$93$		0			0
$94$	10.4645	+	11.4187i	1.07933	+	1.17775i
$95$	0.840731	−	0.705457i	0.0862572	−	0.0723783i
$96$		0			0
$97$	−0.833364	+	0.303320i	−0.0846153	+	0.0307975i	−0.383981	−	0.923341i	$-0.625447\pi$
$97$	−0.833364	+	0.303320i	−0.0846153	+	0.0307975i	0.299366	+	0.954138i	$0.403225\pi$
$98$	−17.5166	+	11.1607i	−1.76944	+	1.12740i
$99$		0			0
$100$	4.44150	−	9.52759i	0.444150	−	0.952759i
$101$	−1.09507	+	6.21046i	−0.108964	+	0.617964i	0.880599	+	0.473862i	$0.157140\pi$
$101$	−1.09507	+	6.21046i	−0.108964	+	0.617964i	−0.989563	+	0.144102i	$0.953971\pi$
$102$		0			0
$103$	−2.99018	+	8.21544i	−0.294631	+	0.809492i	0.700743	+	0.713414i	$0.252852\pi$
$103$	−2.99018	+	8.21544i	−0.294631	+	0.809492i	−0.995374	+	0.0960778i	$0.969370\pi$
$104$	1.61588	+	5.12193i	0.158450	+	0.502247i
$105$		0			0
$106$	1.09686	−	1.42962i	0.106537	−	0.138857i
$107$			3.23101i			0.312354i	0.987729	+	0.156177i	$0.0499170\pi$
$107$			3.23101i			0.312354i	−0.987729	+	0.156177i	$0.950083\pi$
$108$		0			0
$109$		−	10.8688i		−	1.04104i	−0.853849	−	0.520521i	$-0.825738\pi$
$109$		−	10.8688i		−	1.04104i	0.853849	−	0.520521i	$-0.174262\pi$
$110$	3.18764	+	2.44568i	0.303929	+	0.233186i
$111$		0			0
$112$	17.5027	−	6.37489i	1.65385	−	0.602370i
$113$	−3.71933	+	10.2188i	−0.349885	+	0.961301i	0.632521	+	0.774543i	$0.282020\pi$
$113$	−3.71933	+	10.2188i	−0.349885	+	0.961301i	−0.982406	+	0.186758i	$0.940202\pi$
$114$		0			0
$115$	3.20749	−	18.1906i	0.299100	−	1.69628i
$116$	4.59927	−	9.86604i	0.427032	−	0.916038i
$117$		0			0
$118$	−5.40801	−	8.48783i	−0.497847	−	0.781368i
$119$	−20.3761	+	7.41630i	−1.86788	+	0.679851i
$120$		0			0
$121$	7.82363	−	6.56481i	0.711239	−	0.596801i
$122$	−8.67116	+	7.94654i	−0.785050	+	0.719446i
$123$		0			0
$124$	−6.70314	−	14.3708i	−0.601960	−	1.29053i
$125$	−0.409913	−	0.709991i	−0.0366638	−	0.0635035i
$126$		0			0
$127$	12.2372	+	7.06513i	1.08587	+	0.626929i	0.932475	−	0.361235i	$-0.117645\pi$
$127$	12.2372	+	7.06513i	1.08587	+	0.626929i	0.153399	+	0.988164i	$0.450978\pi$
$128$	−11.2163	+	1.48110i	−0.991394	+	0.130912i
$129$		0			0
$130$	8.20207	+	2.58560i	0.719369	+	0.226772i
$131$	3.55599	−	0.627016i	0.310688	−	0.0547827i	−0.0161302	−	0.999870i	$-0.505135\pi$
$131$	3.55599	−	0.627016i	0.310688	−	0.0547827i	0.326818	+	0.945087i	$0.394024\pi$
$132$		0			0
$133$	1.02583	−	1.22254i	0.0889511	−	0.106008i
$134$	−0.508936	−	11.6417i	−0.0439654	−	1.00569i
$135$		0			0
$136$	13.0570	−	1.72120i	1.11963	−	0.147592i
$137$	8.46244	−	10.0851i	0.722995	−	0.861632i	−0.271923	−	0.962319i	$-0.587660\pi$
$137$	8.46244	−	10.0851i	0.722995	−	0.861632i	0.994918	+	0.100687i	$0.0321041\pi$
$138$		0			0
$139$	2.08259	+	11.8109i	0.176643	+	1.00179i	0.936230	+	0.351387i	$0.114290\pi$
$139$	2.08259	+	11.8109i	0.176643	+	1.00179i	−0.759588	+	0.650405i	$0.774599\pi$
$140$	7.71668	−	28.8119i	0.652179	−	2.43505i
$141$		0			0
$142$	−0.523800	−	0.0689300i	−0.0439563	−	0.00578447i
$143$	−0.842252	+	1.45882i	−0.0704327	+	0.121993i
$144$		0			0
$145$	−8.71512	−	15.0950i	−0.723751	−	1.25357i
$146$	6.81511	+	16.4505i	0.564022	+	1.36146i
$147$		0			0
$148$	3.78590	+	3.78505i	0.311199	+	0.311129i
$149$	6.78333	−	5.69189i	0.555712	−	0.466298i	−0.321158	−	0.947026i	$-0.604072\pi$
$149$	6.78333	−	5.69189i	0.555712	−	0.466298i	0.876870	+	0.480728i	$0.159628\pi$
$150$		0			0
$151$	−1.00187	−	2.75261i	−0.0815308	−	0.224004i	0.892229	−	0.451584i	$-0.149141\pi$
$151$	−1.00187	−	2.75261i	−0.0815308	−	0.224004i	−0.973759	+	0.227580i	$0.926919\pi$
$152$	−0.768900	+	0.590202i	−0.0623661	+	0.0478717i
$153$		0			0
$154$	5.18241	+	2.69743i	0.417611	+	0.217365i
$155$	−25.0056	−	4.40916i	−2.00850	−	0.354152i
$156$		0			0
$157$	3.73399	−	10.2591i	0.298005	−	0.818762i	−0.696828	−	0.717238i	$-0.745406\pi$
$157$	3.73399	−	10.2591i	0.298005	−	0.818762i	0.994833	−	0.101524i	$-0.0323717\pi$
$158$	−1.21226	−	5.46671i	−0.0964422	−	0.434908i
$159$		0			0
$160$	−8.36060	+	16.0715i	−0.660964	+	1.27056i
$161$		−	26.8597i		−	2.11684i
$162$		0			0
$163$	−0.983434			−0.0770285			−0.0385143	−	0.999258i	$-0.512263\pi$
$163$	−0.983434			−0.0770285			−0.0385143	+	0.999258i	$0.512263\pi$
$164$	−0.0618907	+	0.0884100i	−0.00483285	+	0.00690366i
$165$		0			0
$166$	−4.24394	−	19.1381i	−0.329393	−	1.48541i
$167$	1.50427	+	0.547510i	0.116404	+	0.0423676i	0.399565	−	0.916705i	$-0.369161\pi$
$167$	1.50427	+	0.547510i	0.116404	+	0.0423676i	−0.283161	+	0.959072i	$0.591383\pi$
$168$		0			0
$169$	1.63131	−	9.25162i	0.125485	−	0.711663i
$170$	9.73651	−	18.7062i	0.746756	−	1.43470i
$171$		0			0
$172$	3.49093	+	4.98438i	0.266181	+	0.380056i
$173$	13.3229	−	4.84914i	1.01292	−	0.368673i	0.218367	−	0.975867i	$-0.429927\pi$
$173$	13.3229	−	4.84914i	1.01292	−	0.368673i	0.794554	+	0.607193i	$0.207705\pi$
$174$		0			0
$175$	−15.7332	−	18.7501i	−1.18932	−	1.41738i
$176$	−2.71879	−	2.28030i	−0.204936	−	0.171884i
$177$		0			0
$178$	−9.58013	+	3.96884i	−0.718061	+	0.297477i
$179$	5.27151	−	3.04351i	0.394011	−	0.227483i	−0.289885	−	0.957061i	$-0.593617\pi$
$179$	5.27151	−	3.04351i	0.394011	−	0.227483i	0.683897	+	0.729579i	$0.260284\pi$
$180$		0			0
$181$	11.4059	+	6.58520i	0.847795	+	0.489474i	0.859906	−	0.510452i	$-0.170522\pi$
$181$	11.4059	+	6.58520i	0.847795	+	0.489474i	−0.0121116	+	0.999927i	$0.503855\pi$
$182$	12.3987	+	1.63161i	0.919049	+	0.120943i
$183$		0			0
$184$	−3.52827	+	15.9275i	−0.260107	+	1.17419i
$185$	8.44201	−	1.48855i	0.620669	−	0.109441i
$186$		0			0
$187$	3.16427	+	2.65514i	0.231395	+	0.194163i
$188$	−21.8204	+	1.91148i	−1.59141	+	0.139409i
$189$		0			0
$190$	0.0677875	+	1.55061i	0.00491783	+	0.112493i
$191$	16.3786	+	13.7433i	1.18512	+	0.994431i	0.999931	+	0.0117270i	$0.00373289\pi$
$191$	16.3786	+	13.7433i	1.18512	+	0.994431i	0.185185	+	0.982704i	$0.440712\pi$
$192$		0			0
$193$	3.64547	+	20.6745i	0.262407	+	1.48818i	0.776319	+	0.630341i	$0.217085\pi$
$193$	3.64547	+	20.6745i	0.262407	+	1.48818i	−0.513912	+	0.857843i	$0.671804\pi$
$194$	0.377076	−	1.19616i	0.0270725	−	0.0858796i
$195$		0			0
$196$	2.55679	−	29.2617i	0.182628	−	2.09012i
$197$	−5.23281	+	9.06349i	−0.372822	+	0.645747i	−0.989999	−	0.141078i	$-0.954943\pi$
$197$	−5.23281	+	9.06349i	−0.372822	+	0.645747i	0.617176	+	0.786825i	$0.288277\pi$
$198$		0			0
$199$	−14.3685	+	8.29565i	−1.01855	+	0.588063i	−0.913685	−	0.406423i	$-0.866776\pi$
$199$	−14.3685	+	8.29565i	−1.01855	+	0.588063i	−0.104870	+	0.994486i	$0.533443\pi$
$200$	6.86665	+	13.1853i	0.485545	+	0.932344i
$201$		0			0
$202$	−6.02556	−	6.57501i	−0.423957	−	0.462616i
$203$	−16.2921	−	19.4162i	−1.14348	−	1.36275i
$204$		0			0
$205$	0.0591036	+	0.162386i	0.00412797	+	0.0113415i
$206$	−6.64377	−	10.4273i	−0.462893	−	0.726508i
$207$		0			0
$208$	−7.13794	−	2.59620i	−0.494927	−	0.180014i
$209$	−0.299396	−	0.0527915i	−0.0207096	−	0.00365167i
$210$		0			0
$211$	−8.76523	−	3.19028i	−0.603423	−	0.219628i	0.0222000	−	0.999754i	$-0.492933\pi$
$211$	−8.76523	−	3.19028i	−0.603423	−	0.219628i	−0.625623	+	0.780126i	$0.715155\pi$
$212$	0.659824	+	2.46140i	0.0453169	+	0.169050i
$213$		0			0
$214$	−3.62526	−	2.78144i	−0.247817	−	0.190135i
$215$	9.74405			0.664539
$216$		0			0
$217$	−36.9226			−2.50647
$218$	12.1950	+	9.35647i	0.825949	+	0.633700i
$219$		0			0
$220$	−5.48820	+	1.47121i	−0.370014	+	0.0991891i
$221$	8.30841	+	3.02402i	0.558884	+	0.203417i
$222$		0			0
$223$	18.4672	+	3.25626i	1.23665	+	0.218055i	0.753481	−	0.657470i	$-0.228373\pi$
$223$	18.4672	+	3.25626i	1.23665	+	0.218055i	0.483172	+	0.875525i	$0.339485\pi$
$224$	−7.91461	+	25.1263i	−0.528817	+	1.67882i
$225$		0			0
$226$	−8.26384	−	12.9700i	−0.549703	−	0.862755i
$227$	−1.73323	−	4.76200i	−0.115038	−	0.316065i	0.868790	−	0.495181i	$-0.164898\pi$
$227$	−1.73323	−	4.76200i	−0.115038	−	0.316065i	−0.983828	+	0.179116i	$0.942676\pi$
$228$		0			0
$229$	14.4905	+	17.2691i	0.957559	+	1.14117i	0.989910	+	0.141698i	$0.0452562\pi$
$229$	14.4905	+	17.2691i	0.957559	+	1.14117i	−0.0323508	+	0.999477i	$0.510299\pi$
$230$	17.6490	+	19.2583i	1.16374	+	1.26986i
$231$		0			0
$232$	7.11056	+	13.6537i	0.466831	+	0.896410i
$233$	−4.93700	+	2.85038i	−0.323434	+	0.186735i	−0.652922	−	0.757425i	$-0.726457\pi$
$233$	−4.93700	+	2.85038i	−0.323434	+	0.186735i	0.329488	+	0.944160i	$0.393124\pi$
$234$		0			0
$235$	−17.5368	+	30.3747i	−1.14398	+	1.98143i
$236$	14.1790	+	1.23892i	0.922976	+	0.0806466i
$237$		0			0
$238$	9.21968	−	29.2468i	0.597623	−	1.89579i
$239$	−3.99952	−	22.6824i	−0.258707	−	1.46720i	−0.786374	−	0.617750i	$-0.788044\pi$
$239$	−3.99952	−	22.6824i	−0.258707	−	1.46720i	0.527667	−	0.849451i	$-0.323067\pi$
$240$		0			0
$241$	16.6164	+	13.9428i	1.07036	+	0.898137i	0.995085	−	0.0990259i	$-0.0315727\pi$
$241$	16.6164	+	13.9428i	1.07036	+	0.898137i	0.0752732	+	0.997163i	$0.476017\pi$
$242$	0.630814	+	14.4296i	0.0405503	+	0.927571i
$243$		0			0
$244$	−1.45155	−	16.5700i	−0.0929257	−	1.06079i
$245$	−36.0300	−	30.2327i	−2.30187	−	1.93150i
$246$		0			0
$247$	−0.640852	+	0.112999i	−0.0407764	+	0.00718999i
$248$	21.8947	+	4.85011i	1.39031	+	0.307982i
$249$		0			0
$250$	1.14950	+	0.151269i	0.0727007	+	0.00956712i
$251$	6.86745	+	3.96493i	0.433470	+	0.250264i	0.700824	−	0.713334i	$-0.252816\pi$
$251$	6.86745	+	3.96493i	0.433470	+	0.250264i	−0.267354	+	0.963598i	$0.586149\pi$
$252$		0			0
$253$	−4.43115	+	2.55833i	−0.278584	+	0.160841i
$254$	−18.4617	+	7.64827i	−1.15839	+	0.479895i
$255$		0			0
$256$	7.99384	−	13.8600i	0.499615	−	0.866248i
$257$	−0.0798480	−	0.0951592i	−0.00498078	−	0.00593587i	0.763548	−	0.645751i	$-0.223455\pi$
$257$	−0.0798480	−	0.0951592i	−0.00498078	−	0.00593587i	−0.768529	+	0.639815i	$0.779011\pi$
$258$		0			0
$259$	11.7135	−	4.26337i	0.727842	−	0.264913i
$260$	−9.96189	+	6.97704i	−0.617810	+	0.432698i
$261$		0			0
$262$	−2.35767	+	4.52965i	−0.145657	+	0.279843i
$263$	0.961362	−	5.45215i	0.0592801	−	0.336194i	−0.940715	−	0.339197i	$-0.889845\pi$
$263$	0.961362	−	5.45215i	0.0592801	−	0.336194i	0.999995	+	0.00300271i	$0.000955794\pi$
$264$		0			0
$265$	3.83439	+	1.39560i	0.235545	+	0.0857313i
$266$	0.488619	+	2.20344i	0.0299591	+	0.135101i
$267$		0			0
$268$	13.5003	+	9.45080i	0.824664	+	0.577300i
$269$	5.59805			0.341319			0.170659	−	0.985330i	$-0.445410\pi$
$269$	5.59805			0.341319			0.170659	+	0.985330i	$0.445410\pi$
$270$		0			0
$271$		−	1.56554i		−	0.0951000i	−0.998869	−	0.0475500i	$-0.984859\pi$
$271$		−	1.56554i		−	0.0951000i	0.998869	−	0.0475500i	$-0.0151413\pi$
$272$	−9.30900	+	16.1319i	−0.564441	+	0.978142i
$273$		0			0
$274$	4.03078	+	18.1769i	0.243508	+	1.09811i
$275$	−1.59473	+	4.38148i	−0.0961657	+	0.264213i
$276$		0			0
$277$	−27.6100	−	4.86839i	−1.65893	−	0.292513i	−0.735854	−	0.677140i	$-0.763219\pi$
$277$	−27.6100	−	4.86839i	−1.65893	−	0.292513i	−0.923072	+	0.384627i	$0.874330\pi$
$278$	−15.0449	−	7.83083i	−0.902334	−	0.469662i
$279$		0			0
$280$	25.6845	+	33.4611i	1.53494	+	1.99968i
$281$	−3.07719	−	8.45452i	−0.183570	−	0.504354i	0.813438	−	0.581651i	$-0.197593\pi$
$281$	−3.07719	−	8.45452i	−0.183570	−	0.504354i	−0.997008	+	0.0772972i	$0.975371\pi$
$282$		0			0
$283$	−22.1256	+	18.5656i	−1.31523	+	1.10361i	−0.327936	+	0.944700i	$0.606353\pi$
$283$	−22.1256	+	18.5656i	−1.31523	+	1.10361i	−0.987293	+	0.158909i	$0.949202\pi$
$284$	0.528257	−	0.528375i	0.0313463	−	0.0313533i
$285$		0			0
$286$	−0.911770	−	2.20086i	−0.0539141	−	0.130140i
$287$	0.125643	+	0.217620i	0.00741648	+	0.0128457i
$288$		0			0
$289$	2.34052	−	4.05391i	0.137678	−	0.238465i
$290$	24.4394	+	3.21612i	1.43513	+	0.188857i
$291$		0			0
$292$	−24.3247	−	6.51487i	−1.42349	−	0.381254i
$293$	3.10437	+	17.6058i	0.181359	+	1.02854i	0.930545	+	0.366179i	$0.119334\pi$
$293$	3.10437	+	17.6058i	0.181359	+	1.02854i	−0.749185	+	0.662360i	$0.769555\pi$
$294$		0			0
$295$	14.6495	−	17.4587i	0.852930	−	1.01648i
$296$	−7.50601	+	0.989458i	−0.436278	+	0.0575111i
$297$		0			0
$298$	0.546935	+	12.5109i	0.0316831	+	0.724738i
$299$	−7.03989	+	8.38981i	−0.407127	+	0.485196i
$300$		0			0
$301$	13.9540	−	2.46046i	0.804293	−	0.141819i
$302$	3.95094	+	1.24549i	0.227351	+	0.0716697i
$303$		0			0
$304$	−0.000304701	−	1.37080i	−1.74758e−5	−	0.0786208i
$305$	−23.0660	−	13.3172i	−1.32076	−	0.762540i
$306$		0			0
$307$	2.66885	+	4.62258i	0.152319	+	0.263825i	0.932080	−	0.362253i	$-0.117992\pi$
$307$	2.66885	+	4.62258i	0.152319	+	0.263825i	−0.779760	+	0.626078i	$0.784659\pi$
$308$	−7.48788	+	3.49267i	−0.426662	+	0.199013i
$309$		0			0
$310$	26.4734	−	24.2611i	1.50359	−	1.37794i
$311$	−7.48203	+	6.27817i	−0.424267	+	0.356002i	−0.829783	−	0.558086i	$-0.811536\pi$
$311$	−7.48203	+	6.27817i	−0.424267	+	0.356002i	0.405517	+	0.914088i	$0.367092\pi$
$312$		0			0
$313$	−20.9377	+	7.62069i	−1.18347	+	0.430747i	−0.857425	−	0.514608i	$-0.827937\pi$
$313$	−20.9377	+	7.62069i	−1.18347	+	0.430747i	−0.326042	+	0.945355i	$0.605715\pi$
$314$	8.29642	+	13.0212i	0.468194	+	0.734828i
$315$		0			0
$316$	7.17733	+	3.34587i	0.403757	+	0.188220i
$317$	−2.75422	+	15.6200i	−0.154692	+	0.877304i	0.804374	+	0.594123i	$0.202501\pi$
$317$	−2.75422	+	15.6200i	−0.154692	+	0.877304i	−0.959067	+	0.283181i	$0.908610\pi$
$318$		0			0
$319$	−1.65138	+	4.53712i	−0.0924593	+	0.254030i
$320$	−10.8352	−	23.2160i	−0.605707	−	1.29781i
$321$		0			0
$322$	30.1371	+	23.1224i	1.67948	+	1.28856i
$323$			1.59571i			0.0887877i
$324$		0			0
$325$			9.98038i			0.553612i
$326$	0.846596	−	1.10343i	0.0468886	−	0.0611134i
$327$		0			0
$328$	−0.0459187	−	0.145551i	−0.00253544	−	0.00803670i
$329$	−17.4437	+	47.9263i	−0.961704	+	2.64226i
$330$		0			0
$331$	4.91331	−	27.8648i	0.270060	−	1.53159i	−0.484169	−	0.874974i	$-0.660878\pi$
$331$	4.91331	−	27.8648i	0.270060	−	1.53159i	0.754229	−	0.656611i	$-0.228011\pi$
$332$	25.1268	+	11.7134i	1.37901	+	0.642857i
$333$		0			0
$334$	−1.90928	+	1.21649i	−0.104471	+	0.0665636i
$335$	24.7965	−	9.02520i	1.35478	−	0.493099i
$336$		0			0
$337$	−2.65131	+	2.22472i	−0.144426	+	0.121188i	−0.712138	−	0.702039i	$-0.752273\pi$
$337$	−2.65131	+	2.22472i	−0.144426	+	0.121188i	0.567712	+	0.823227i	$0.307829\pi$
$338$	8.97617	+	9.79468i	0.488239	+	0.532760i
$339$		0			0
$340$	12.6070	+	27.0279i	0.683709	+	1.46579i
$341$	3.51679	+	6.09126i	0.190445	+	0.329860i
$342$		0			0
$343$	−30.9999	−	17.8978i	−1.67383	−	0.966389i
$344$	−8.59776	−	0.373950i	−0.463560	−	0.0201620i
$345$		0			0
$346$	−6.02828	+	19.1230i	−0.324082	+	1.02806i
$347$	21.3082	−	3.75721i	1.14388	−	0.201698i	0.430581	−	0.902552i	$-0.358309\pi$
$347$	21.3082	−	3.75721i	1.14388	−	0.201698i	0.713304	+	0.700854i	$0.247198\pi$
$348$		0			0
$349$	−13.6098	+	16.2195i	−0.728514	+	0.868209i	−0.995428	−	0.0955113i	$-0.969551\pi$
$349$	−13.6098	+	16.2195i	−0.728514	+	0.868209i	0.266915	+	0.963720i	$0.413996\pi$
$350$	34.5821	−	1.51181i	1.84849	−	0.0808097i
$351$		0			0
$352$	4.89903	−	1.08752i	0.261119	−	0.0579648i
$353$	10.0326	−	11.9564i	0.533980	−	0.636373i	−0.429847	−	0.902902i	$-0.641432\pi$
$353$	10.0326	−	11.9564i	0.533980	−	0.636373i	0.963827	+	0.266529i	$0.0858768\pi$
$354$		0			0
$355$	−0.207748	−	1.17820i	−0.0110261	−	0.0625324i
$356$	3.79400	−	14.1657i	0.201081	−	0.750780i
$357$		0			0
$358$	−1.12314	+	8.53476i	−0.0593598	+	0.451076i
$359$	2.44114	−	4.22817i	0.128838	−	0.223154i	−0.794389	−	0.607410i	$-0.792209\pi$
$359$	2.44114	−	4.22817i	0.128838	−	0.223154i	0.923227	+	0.384256i	$0.125542\pi$
$360$		0			0
$361$	9.44128	+	16.3528i	0.496909	+	0.860672i
$362$	−17.2076	+	7.12873i	−0.904410	+	0.374678i
$363$		0			0
$364$	−12.5042	+	12.5069i	−0.655396	+	0.655542i
$365$	−30.8889	+	25.9189i	−1.61680	+	1.35666i
$366$		0			0
$367$	3.44230	+	9.45764i	0.179687	+	0.493685i	0.996536	−	0.0831666i	$-0.0265033\pi$
$367$	3.44230	+	9.45764i	0.179687	+	0.493685i	−0.816849	+	0.576852i	$0.804281\pi$
$368$	−14.8337	−	17.6701i	−0.773259	−	0.921118i
$369$		0			0
$370$	−5.59717	+	10.7535i	−0.290983	+	0.559049i
$371$	5.84344	+	1.03036i	0.303376	+	0.0534935i
$372$		0			0
$373$	0.511543	−	1.40545i	0.0264867	−	0.0727717i	−0.925745	−	0.378149i	$-0.876561\pi$
$373$	0.511543	−	1.40545i	0.0264867	−	0.0727717i	0.952231	+	0.305378i	$0.0987828\pi$
$374$	−5.70310	+	1.26468i	−0.294901	+	0.0653951i
$375$		0			0
$376$	16.6395	−	26.1284i	0.858116	−	1.34747i
$377$			10.3349i			0.532275i
$378$		0			0
$379$	26.4034			1.35625			0.678126	−	0.734945i	$-0.262792\pi$
$379$	26.4034			1.35625			0.678126	+	0.734945i	$0.262792\pi$
$380$	−1.79817	−	1.25880i	−0.0922443	−	0.0645749i
$381$		0			0
$382$	−29.5199	+	6.54612i	−1.51037	+	0.334929i
$383$	−14.7665	−	5.37456i	−0.754532	−	0.274627i	−0.0640204	−	0.997949i	$-0.520392\pi$
$383$	−14.7665	−	5.37456i	−0.754532	−	0.274627i	−0.690511	+	0.723321i	$0.742614\pi$
$384$		0			0
$385$	−2.29739	+	13.0291i	−0.117086	+	0.664027i
$386$	−26.3354	−	13.7075i	−1.34044	−	0.697693i
$387$		0			0
$388$	1.01751	+	1.45281i	0.0516563	+	0.0737554i
$389$	19.0208	−	6.92300i	0.964393	−	0.351010i	0.188639	−	0.982046i	$-0.439592\pi$
$389$	19.0208	−	6.92300i	0.964393	−	0.351010i	0.775753	+	0.631036i	$0.217370\pi$
$390$		0			0
$391$	17.2629	+	20.5731i	0.873023	+	1.04043i
$392$	30.6311	+	28.0589i	1.54711	+	1.41719i
$393$		0			0
$394$	−5.66471	−	13.6737i	−0.285384	−	0.688870i
$395$	10.9813	−	6.34007i	0.552530	−	0.319003i
$396$		0			0
$397$	−23.8679	−	13.7801i	−1.19789	−	0.691604i	−0.237808	−	0.971312i	$-0.576429\pi$
$397$	−23.8679	−	13.7801i	−1.19789	−	0.691604i	−0.960085	+	0.279708i	$0.909762\pi$
$398$	3.06133	−	23.2631i	0.153450	−	1.16607i
$399$		0			0
$400$	−20.7054	−	3.64617i	−1.03527	−	0.182309i
$401$	6.68368	−	1.17851i	0.333767	−	0.0588521i	−0.00425323	−	0.999991i	$-0.501354\pi$
$401$	6.68368	−	1.17851i	0.333767	−	0.0588521i	0.338020	+	0.941139i	$0.390243\pi$
$402$		0			0
$403$	11.5330	+	9.67734i	0.574500	+	0.482063i
$404$	12.5644	−	1.10065i	0.625103	−	0.0547595i
$405$		0			0
$406$	35.8105	−	1.56551i	1.77725	−	0.0776952i
$407$	−1.81903	−	1.52635i	−0.0901659	−	0.0756581i
$408$		0			0
$409$	−2.97274	−	16.8592i	−0.146992	−	0.833636i	−0.965746	−	0.259490i	$-0.916445\pi$
$409$	−2.97274	−	16.8592i	−0.146992	−	0.833636i	0.818753	−	0.574145i	$-0.194666\pi$
$410$	−0.233080	−	0.0734755i	−0.0115110	−	0.00362869i
$411$		0			0
$412$	17.4190	+	1.52202i	0.858173	+	0.0749843i
$413$	16.5704	−	28.7008i	0.815377	−	1.41227i
$414$		0			0
$415$	38.4439	−	22.1956i	1.88714	−	1.08954i
$416$	9.05773	−	5.77395i	0.444092	−	0.283091i
$417$		0			0
$418$	0.316970	−	0.290482i	0.0155035	−	0.0142079i
$419$	−0.999049	−	1.19062i	−0.0488067	−	0.0581656i	0.741089	−	0.671407i	$-0.234310\pi$
$419$	−0.999049	−	1.19062i	−0.0488067	−	0.0581656i	−0.789896	+	0.613241i	$0.789865\pi$
$420$		0			0
$421$	−4.61578	−	12.6818i	−0.224959	−	0.618071i	0.774943	−	0.632031i	$-0.217778\pi$
$421$	−4.61578	−	12.6818i	−0.224959	−	0.618071i	−0.999903	+	0.0139601i	$0.995556\pi$
$422$	11.1252	−	7.08837i	0.541564	−	0.345057i
$423$		0			0
$424$	−3.32975	−	1.37858i	−0.161707	−	0.0669497i
$425$	24.1016	+	4.24977i	1.16910	+	0.206144i
$426$		0			0
$427$	−36.3944	−	13.2465i	−1.76125	−	0.641042i
$428$	6.24165	−	1.67319i	0.301702	−	0.0808766i
$429$		0			0
$430$	−8.38823	+	10.9330i	−0.404516	+	0.527237i
$431$	−32.6219			−1.57134			−0.785671	−	0.618644i	$-0.787682\pi$
$431$	−32.6219			−1.57134			−0.785671	+	0.618644i	$0.787682\pi$
$432$		0			0
$433$	−20.4173			−0.981192			−0.490596	−	0.871387i	$-0.663221\pi$
$433$	−20.4173			−0.981192			−0.490596	+	0.871387i	$0.663221\pi$
$434$	31.7850	−	41.4278i	1.52573	−	1.98860i
$435$		0			0
$436$	−20.9963	+	5.62843i	−1.00554	+	0.269553i
$437$	−1.85740	−	0.676039i	−0.0888516	−	0.0323393i
$438$		0			0
$439$	−5.01912	−	0.885007i	−0.239550	−	0.0422391i	0.0525843	−	0.998616i	$-0.483254\pi$
$439$	−5.01912	−	0.885007i	−0.239550	−	0.0422391i	−0.292134	+	0.956377i	$0.594365\pi$
$440$	3.07382	−	7.42436i	0.146539	−	0.353943i
$441$		0			0
$442$	−10.5454	+	6.71896i	−0.501591	+	0.319588i
$443$	−6.33577	−	17.4074i	−0.301022	−	0.827050i	−0.994323	−	0.106403i	$-0.966067\pi$
$443$	−6.33577	−	17.4074i	−0.301022	−	0.827050i	0.693301	−	0.720648i	$-0.256155\pi$
$444$		0			0
$445$	−15.0941	−	17.9885i	−0.715529	−	0.852735i
$446$	−19.5512	+	17.9173i	−0.925774	+	0.848410i
$447$		0			0
$448$	−21.3788	−	30.5105i	−1.01005	−	1.44148i
$449$	−16.4019	+	9.46962i	−0.774052	+	0.446899i	−0.834318	−	0.551283i	$-0.814138\pi$
$449$	−16.4019	+	9.46962i	−0.774052	+	0.446899i	0.0602665	+	0.998182i	$0.480805\pi$
$450$		0			0
$451$	0.0239344	−	0.0414557i	0.00112703	−	0.00195207i
$452$	21.6666	+	1.89316i	1.01911	+	0.0890466i
$453$		0			0
$454$	6.83512	+	2.15469i	0.320788	+	0.101124i
$455$	4.91753	+	27.8887i	0.230537	+	1.30744i
$456$		0			0
$457$	−8.02025	−	6.72979i	−0.375172	−	0.314806i	0.435632	−	0.900125i	$-0.356525\pi$
$457$	−8.02025	−	6.72979i	−0.375172	−	0.314806i	−0.810803	+	0.585319i	$0.800969\pi$
$458$	−31.8505	+	1.39240i	−1.48828	+	0.0650624i
$459$		0			0
$460$	−36.8015	+	3.22383i	−1.71588	+	0.150312i
$461$	18.6832	+	15.6771i	0.870163	+	0.730153i	0.964132	−	0.265422i	$-0.0855113\pi$
$461$	18.6832	+	15.6771i	0.870163	+	0.730153i	−0.0939698	+	0.995575i	$0.529956\pi$
$462$		0			0
$463$	−15.5149	+	2.73570i	−0.721039	+	0.127139i	−0.522113	−	0.852876i	$-0.674856\pi$
$463$	−15.5149	+	2.73570i	−0.721039	+	0.127139i	−0.198925	+	0.980015i	$0.563745\pi$
$464$	−21.4409	−	3.77569i	−0.995369	−	0.175282i
$465$		0			0
$466$	1.05187	−	7.99318i	0.0487269	−	0.370277i
$467$	6.64718	+	3.83775i	0.307595	+	0.177590i	0.645850	−	0.763465i	$-0.276503\pi$
$467$	6.64718	+	3.83775i	0.307595	+	0.177590i	−0.338255	+	0.941055i	$0.609837\pi$
$468$		0			0
$469$	33.2309	−	19.1859i	1.53446	−	0.885922i
$470$	−18.9843	−	45.8249i	−0.875679	−	2.11374i
$471$		0			0
$472$	−13.5962	+	14.8426i	−0.625815	+	0.683186i
$473$	−1.73499	−	2.06769i	−0.0797751	−	0.0950723i
$474$		0			0
$475$	−1.69260	+	0.616057i	−0.0776619	+	0.0282666i
$476$	24.8786	+	35.5219i	1.14031	+	1.62814i
$477$		0			0
$478$	28.8931	+	15.0387i	1.32154	+	0.687856i
$479$	−5.41592	+	30.7152i	−0.247460	+	1.40341i	0.567250	+	0.823545i	$0.308007\pi$
$479$	−5.41592	+	30.7152i	−0.247460	+	1.40341i	−0.814710	+	0.579869i	$0.803104\pi$
$480$		0			0
$481$	−4.77621	−	1.73840i	−0.217776	−	0.0792641i
$482$	−29.9485	+	6.64116i	−1.36412	+	0.302497i
$483$		0			0
$484$	−16.7333	−	11.7140i	−0.760607	−	0.532457i
$485$	2.84013			0.128964
$486$		0			0
$487$			14.2176i			0.644263i	0.946695	+	0.322131i	$0.104399\pi$
$487$			14.2176i			0.644263i	−0.946695	+	0.322131i	$0.895601\pi$
$488$	19.8415	+	12.6358i	0.898181	+	0.571994i
$489$		0			0
$490$	64.9383	−	14.4003i	2.93361	−	0.650537i
$491$	−0.483056	+	1.32718i	−0.0218000	+	0.0598950i	−0.950115	−	0.311899i	$-0.899035\pi$
$491$	−0.483056	+	1.32718i	−0.0218000	+	0.0598950i	0.928315	+	0.371794i	$0.121257\pi$
$492$		0			0
$493$	24.9578	+	4.40073i	1.12404	+	0.198199i
$494$	0.424894	−	0.816324i	0.0191169	−	0.0367282i
$495$		0			0
$496$	−24.2901	+	20.3910i	−1.09066	+	0.915584i
$497$	−0.595012	−	1.63478i	−0.0266899	−	0.0733300i
$498$		0			0
$499$	22.9472	−	19.2550i	1.02726	−	0.861971i	0.0367345	−	0.999325i	$-0.488304\pi$
$499$	22.9472	−	19.2550i	1.02726	−	0.861971i	0.990522	+	0.137355i	$0.0438600\pi$
$500$	−1.15928	+	1.15954i	−0.0518446	+	0.0518561i
$501$		0			0
$502$	−10.3606	+	4.29218i	−0.462417	+	0.191569i
$503$	−4.40212	−	7.62469i	−0.196281	−	0.339968i	0.751039	−	0.660258i	$-0.229553\pi$
$503$	−4.40212	−	7.62469i	−0.196281	−	0.339968i	−0.947320	+	0.320290i	$0.896220\pi$
$504$		0			0
$505$	10.0979	−	17.4901i	0.449351	−	0.778299i
$506$	0.944095	−	7.17419i	0.0419701	−	0.318932i
$507$		0			0
$508$	7.31133	−	27.2984i	0.324388	−	1.21117i
$509$	−3.62638	−	20.5662i	−0.160737	−	0.911582i	−0.953352	−	0.301860i	$-0.902392\pi$
$509$	−3.62638	−	20.5662i	−0.160737	−	0.911582i	0.792616	−	0.609722i	$-0.208719\pi$
$510$		0			0
$511$	−37.6897	+	44.9169i	−1.66730	+	1.98701i
$512$	8.66959	+	20.9007i	0.383145	+	0.923688i
$513$		0			0
$514$	0.175508	−	0.00767262i	0.00774133	−	0.000338425i
$515$	17.9971	−	21.4481i	0.793045	−	0.945114i
$516$		0			0
$517$	9.56806	−	1.68711i	0.420803	−	0.0741988i
$518$	−5.30006	+	16.8129i	−0.232871	+	0.738717i
$519$		0			0
$520$	0.747385	−	17.1837i	0.0327750	−	0.753553i
$521$	−18.8404	−	10.8775i	−0.825413	−	0.476552i	0.0268665	−	0.999639i	$-0.491447\pi$
$521$	−18.8404	−	10.8775i	−0.825413	−	0.476552i	−0.852280	+	0.523087i	$0.824780\pi$
$522$		0			0
$523$	2.21522	+	3.83687i	0.0968647	+	0.167775i	0.910385	−	0.413761i	$-0.135785\pi$
$523$	2.21522	+	3.83687i	0.0968647	+	0.167775i	−0.813521	+	0.581536i	$0.802452\pi$
$524$	−3.05274	−	6.54473i	−0.133360	−	0.285908i
$525$		0			0
$526$	5.28983	+	5.77219i	0.230647	+	0.251679i
$527$	28.2807	−	23.7303i	1.23193	−	1.03371i
$528$		0			0
$529$	−9.64774	+	3.51149i	−0.419467	+	0.152673i
$530$	−4.86676	+	3.10085i	−0.211398	+	0.134692i
$531$		0			0
$532$	−2.89293	−	1.34860i	−0.125424	−	0.0584694i
$533$	0.0177924	−	0.100906i	0.000770676	−	0.00437072i
$534$		0			0
$535$	3.53899	−	9.72329i	0.153004	−	0.420375i
$536$	−22.2258	+	7.01185i	−0.960009	+	0.302866i
$537$		0			0
$538$	−4.81911	+	6.28112i	−0.207767	+	0.270798i
$539$			13.0287i			0.561186i
$540$		0			0
$541$			37.3027i			1.60377i	0.597479	+	0.801884i	$0.296169\pi$
$541$			37.3027i			1.60377i	−0.597479	+	0.801884i	$0.703831\pi$
$542$	1.75657	+	1.34771i	0.0754511	+	0.0578890i
$543$		0			0
$544$	−10.0866	−	24.3321i	−0.432461	−	1.04323i
$545$	−11.9048	+	32.7082i	−0.509945	+	1.40106i
$546$		0			0
$547$	3.56925	−	20.2422i	0.152610	−	0.865496i	−0.808328	−	0.588733i	$-0.799627\pi$
$547$	3.56925	−	20.2422i	0.152610	−	0.865496i	0.960938	−	0.276763i	$-0.0892618\pi$
$548$	−23.8647	−	11.1251i	−1.01945	−	0.475239i
$549$		0			0
$550$	−3.54327	−	5.56114i	−0.151086	−	0.237128i
$551$	−1.75273	+	0.637941i	−0.0746687	+	0.0271772i
$552$		0			0
$553$	14.1249	−	11.8522i	0.600651	−	0.504006i
$554$	29.2307	−	26.7880i	1.24189	−	1.13811i
$555$		0			0
$556$	21.7378	−	10.1395i	0.921890	−	0.430009i
$557$	−13.7564	−	23.8268i	−0.582877	−	1.00957i	−0.995136	−	0.0985064i	$-0.968593\pi$
$557$	−13.7564	−	23.8268i	−0.582877	−	1.00957i	0.412259	−	0.911067i	$-0.364740\pi$
$558$		0			0
$559$	−5.00349	−	2.88877i	−0.211625	−	0.122182i
$560$	−59.6547	+	0.0132600i	−2.52087	+	0.000560338i
$561$		0			0
$562$	12.1351	+	3.82546i	0.511890	+	0.161367i
$563$	28.2129	−	4.97470i	1.18903	−	0.209658i	0.456080	−	0.889939i	$-0.349253\pi$
$563$	28.2129	−	4.97470i	1.18903	−	0.209658i	0.732952	+	0.680280i	$0.238142\pi$
$564$		0			0
$565$	22.3856	−	26.6781i	0.941770	−	1.12236i
$566$	−1.78397	−	40.8076i	−0.0749859	−	1.71527i
$567$		0			0
$568$	0.138093	+	1.04757i	0.00579424	+	0.0439550i
$569$	4.16772	−	4.96689i	0.174720	−	0.208223i	−0.671577	−	0.740935i	$-0.734383\pi$
$569$	4.16772	−	4.96689i	0.174720	−	0.208223i	0.846297	+	0.532712i	$0.178827\pi$
$570$		0			0
$571$	−4.13866	−	23.4715i	−0.173197	−	0.982252i	−0.940204	−	0.340612i	$-0.889366\pi$
$571$	−4.13866	−	23.4715i	−0.173197	−	0.982252i	0.767006	−	0.641639i	$-0.221745\pi$
$572$	3.25431	+	0.871602i	0.136070	+	0.0364435i
$573$		0			0
$574$	−0.352335	−	0.0463658i	−0.0147062	−	0.00193527i
$575$	−15.1576	+	26.2538i	−0.632117	+	1.09486i
$576$		0			0
$577$	9.82303	+	17.0140i	0.408938	+	0.708302i	0.994771	−	0.102130i	$-0.0325658\pi$
$577$	9.82303	+	17.0140i	0.408938	+	0.708302i	−0.585833	+	0.810432i	$0.699232\pi$
$578$	2.53371	+	6.11595i	0.105388	+	0.254390i
$579$		0			0
$580$	−24.6473	+	24.6528i	−1.02343	+	1.02365i
$581$	49.4491	−	41.4927i	2.05149	−	1.72141i
$582$		0			0
$583$	−0.386593	−	1.06215i	−0.0160110	−	0.0439899i
$584$	28.2498	−	21.6843i	1.16899	−	0.897305i
$585$		0			0
$586$	−22.4264	−	11.6729i	−0.926426	−	0.482202i
$587$	0.851961	+	0.150224i	0.0351642	+	0.00620040i	0.191203	−	0.981551i	$-0.438761\pi$
$587$	0.851961	+	0.150224i	0.0351642	+	0.00620040i	−0.156038	+	0.987751i	$0.549872\pi$
$588$		0			0
$589$	−0.929313	+	2.55327i	−0.0382917	+	0.105206i
$590$	6.97778	+	31.4665i	0.287271	+	1.29545i
$591$		0			0
$592$	5.35141	−	9.27367i	0.219942	−	0.381145i
$593$			14.5405i			0.597108i	0.954393	+	0.298554i	$0.0965044\pi$
$593$			14.5405i			0.597108i	−0.954393	+	0.298554i	$0.903496\pi$
$594$		0			0
$595$	69.4424			2.84686
$596$	−14.5083	−	10.1564i	−0.594284	−	0.416024i
$597$		0			0
$598$	−3.35320	−	15.1213i	−0.137122	−	0.618357i
$599$	19.6014	+	7.13433i	0.800892	+	0.291501i	0.709856	−	0.704347i	$-0.248760\pi$
$599$	19.6014	+	7.13433i	0.800892	+	0.291501i	0.0910360	+	0.995848i	$0.470982\pi$
$600$		0			0
$601$	−3.10434	+	17.6056i	−0.126629	+	0.718147i	0.853699	+	0.520768i	$0.174354\pi$
$601$	−3.10434	+	17.6056i	−0.126629	+	0.718147i	−0.980327	+	0.197379i	$0.936757\pi$
$602$	−9.25168	+	17.7747i	−0.377070	+	0.724443i
$603$		0			0
$604$	−4.79865	+	3.36085i	−0.195254	+	0.136751i
$605$	−30.7347	+	11.1865i	−1.24954	+	0.454797i
$606$		0			0
$607$	11.4075	+	13.5950i	0.463017	+	0.551803i	0.946143	−	0.323748i	$-0.104943\pi$
$607$	11.4075	+	13.5950i	0.463017	+	0.551803i	−0.483126	+	0.875551i	$0.660499\pi$
$608$	1.53833	+	1.17972i	0.0623873	+	0.0478440i
$609$		0			0
$610$	34.7987	−	14.4163i	1.40896	−	0.583701i
$611$	18.0101	−	10.3981i	0.728609	−	0.420662i
$612$		0			0
$613$	6.61359	+	3.81836i	0.267120	+	0.154222i	0.627578	−	0.778554i	$-0.284046\pi$
$613$	6.61359	+	3.81836i	0.267120	+	0.154222i	−0.360458	+	0.932775i	$0.617380\pi$
$614$	−7.48412	−	0.984880i	−0.302035	−	0.0397465i
$615$		0			0
$616$	2.52715	−	11.4082i	0.101822	−	0.459651i
$617$	−1.20638	+	0.212717i	−0.0485669	+	0.00856365i	−0.197879	−	0.980226i	$-0.563405\pi$
$617$	−1.20638	+	0.212717i	−0.0485669	+	0.00856365i	0.149312	+	0.988790i	$0.452294\pi$
$618$		0			0
$619$	−4.70712	−	3.94975i	−0.189195	−	0.158754i	0.543270	−	0.839558i	$-0.317186\pi$
$619$	−4.70712	−	3.94975i	−0.189195	−	0.158754i	−0.732465	+	0.680804i	$0.761630\pi$
$620$	4.43162	+	50.5889i	0.177978	+	2.03170i
$621$		0			0
$622$	−0.603271	−	13.7996i	−0.0241890	−	0.553313i
$623$	−26.1578	−	21.9490i	−1.04799	−	0.879367i
$624$		0			0
$625$	−4.10756	−	23.2951i	−0.164302	−	0.931805i
$626$	9.47377	−	30.0528i	0.378648	−	1.20115i
$627$		0			0
$628$	−21.7520	−	1.90062i	−0.868001	−	0.0758430i
$629$	−6.23183	+	10.7938i	−0.248479	+	0.430379i
$630$		0			0
$631$	−4.14675	+	2.39413i	−0.165080	+	0.0953088i	−0.580264	−	0.814429i	$-0.697051\pi$
$631$	−4.14675	+	2.39413i	−0.165080	+	0.0953088i	0.415184	+	0.909737i	$0.363717\pi$
$632$	−9.93279	+	5.17279i	−0.395105	+	0.205762i
$633$		0			0
$634$	−15.1549	−	16.5368i	−0.601878	−	0.656761i
$635$	−29.0875	−	34.6652i	−1.15430	−	1.37565i
$636$		0			0
$637$	9.53816	+	26.2059i	0.377916	+	1.03832i
$638$	−3.66914	−	5.75868i	−0.145263	−	0.227989i
$639$		0			0
$640$	35.3763	+	7.82831i	1.39837	+	0.309441i
$641$	−7.66053	−	1.35076i	−0.302573	−	0.0533517i	0.0203006	−	0.999794i	$-0.493538\pi$
$641$	−7.66053	−	1.35076i	−0.302573	−	0.0533517i	−0.322873	+	0.946442i	$0.604649\pi$
$642$		0			0
$643$	22.0412	+	8.02234i	0.869220	+	0.316370i	0.737851	−	0.674964i	$-0.235841\pi$
$643$	22.0412	+	8.02234i	0.869220	+	0.316370i	0.131369	+	0.991334i	$0.458063\pi$
$644$	−51.8875	+	13.9094i	−2.04465	+	0.548107i
$645$		0			0
$646$	−1.79042	−	1.37368i	−0.0704430	−	0.0540466i
$647$	11.2669			0.442948			0.221474	−	0.975166i	$-0.428913\pi$
$647$	11.2669			0.442948			0.221474	+	0.975166i	$0.428913\pi$
$648$		0			0
$649$	−6.31318			−0.247814
$650$	−11.1982	−	8.59168i	−0.439229	−	0.336993i
$651$		0			0
$652$	0.509274	+	1.89979i	0.0199447	+	0.0744016i
$653$	−36.3675	−	13.2367i	−1.42317	−	0.517991i	−0.488203	−	0.872730i	$-0.662347\pi$
$653$	−36.3675	−	13.2367i	−1.42317	−	0.517991i	−0.934965	+	0.354739i	$0.884570\pi$
$654$		0			0
$655$	−11.3880	−	2.00802i	−0.444968	−	0.0784598i
$656$	0.202840	+	0.0737768i	0.00791958	+	0.00288050i
$657$		0			0
$658$	−38.7576	−	60.8298i	−1.51093	−	2.37139i
$659$	11.6740	+	32.0740i	0.454753	+	1.24942i	0.929343	+	0.369217i	$0.120374\pi$
$659$	11.6740	+	32.0740i	0.454753	+	1.24942i	−0.474590	+	0.880207i	$0.657404\pi$
$660$		0			0
$661$	−32.5831	−	38.8310i	−1.26734	−	1.51035i	−0.762252	−	0.647281i	$-0.775906\pi$
$661$	−32.5831	−	38.8310i	−1.26734	−	1.51035i	−0.505083	−	0.863071i	$-0.668538\pi$
$662$	27.0351	+	29.5004i	1.05075	+	1.14656i
$663$		0			0
$664$	−34.7732	+	18.1091i	−1.34946	+	0.702771i
$665$	−4.42618	+	2.55546i	−0.171640	+	0.0990964i
$666$		0			0
$667$	−15.6961	+	27.1864i	−0.607754	+	1.05266i
$668$	0.278686	−	3.18947i	0.0107827	−	0.123404i
$669$		0			0
$670$	−11.2198	+	35.5916i	−0.433459	+	1.37502i
$671$	1.28116	+	7.26582i	0.0494587	+	0.280494i
$672$		0			0
$673$	17.6716	+	14.8283i	0.681191	+	0.571587i	0.916354	−	0.400369i	$-0.131118\pi$
$673$	17.6716	+	14.8283i	0.681191	+	0.571587i	−0.235163	+	0.971956i	$0.575562\pi$
$674$	−0.213774	−	4.88999i	−0.00823426	−	0.188355i
$675$		0			0
$676$	−18.7170	+	1.63962i	−0.719885	+	0.0630624i
$677$	32.2459	+	27.0575i	1.23931	+	1.03991i	0.997578	+	0.0695623i	$0.0221603\pi$
$677$	32.2459	+	27.0575i	1.23931	+	1.03991i	0.241733	+	0.970343i	$0.422284\pi$
$678$		0			0
$679$	4.06720	−	0.717158i	0.156085	−	0.0275220i
$680$	−41.1786	−	9.12187i	−1.57913	−	0.349808i
$681$		0			0
$682$	−9.86196	−	1.29779i	−0.377634	−	0.0496951i
$683$	−34.0757	−	19.6736i	−1.30387	−	0.752789i	−0.322804	−	0.946466i	$-0.604625\pi$
$683$	−34.0757	−	19.6736i	−1.30387	−	0.752789i	−0.981065	+	0.193676i	$0.937959\pi$
$684$		0			0
$685$	−36.5130	+	21.0808i	−1.39509	+	0.805456i
$686$	46.7681	−	19.3750i	1.78561	−	0.739741i
$687$		0			0
$688$	7.82101	−	9.32493i	0.298173	−	0.355510i
$689$	−1.55518	−	1.85340i	−0.0592478	−	0.0706087i
$690$		0			0
$691$	34.6497	−	12.6115i	1.31814	−	0.479762i	0.415276	−	0.909696i	$-0.363685\pi$
$691$	34.6497	−	12.6115i	1.31814	−	0.479762i	0.902861	+	0.429933i	$0.141463\pi$
$692$	−16.2668	−	23.2260i	−0.618372	−	0.882919i
$693$		0			0
$694$	−14.1276	+	27.1426i	−0.536278	+	1.03032i
$695$	6.66949	−	37.8245i	0.252988	−	1.43477i
$696$		0			0
$697$	−0.236102	−	0.0859340i	−0.00894299	−	0.00325498i
$698$	−6.48252	−	29.2331i	−0.245367	−	1.10649i
$699$		0			0
$700$	−28.0739	+	40.1032i	−1.06109	+	1.51576i
$701$	−6.58502			−0.248713			−0.124356	−	0.992238i	$-0.539687\pi$
$701$	−6.58502			−0.248713			−0.124356	+	0.992238i	$0.539687\pi$
$702$		0			0
$703$		−	0.917317i		−	0.0345973i
$704$	−2.99714	+	6.43300i	−0.112959	+	0.242453i
$705$		0			0
$706$	4.77866	+	21.5495i	0.179847	+	0.811024i
$707$	10.0443	−	27.5965i	0.377755	−	1.03787i
$708$		0			0
$709$	11.2866	+	1.99013i	0.423876	+	0.0747408i	0.381517	−	0.924362i	$-0.375402\pi$
$709$	11.2866	+	1.99013i	0.423876	+	0.0747408i	0.0423588	+	0.999102i	$0.486513\pi$
$710$	1.50080	+	0.781163i	0.0563242	+	0.0293165i
$711$		0			0
$712$	12.6281	+	16.4516i	0.473257	+	0.616548i
$713$	15.6406	+	42.9723i	0.585746	+	1.60932i
$714$		0			0
$715$	4.13252	−	3.46760i	0.154548	−	0.129681i
$716$	−8.60930	−	8.60739i	−0.321745	−	0.321673i
$717$		0			0
$718$	2.64262	+	6.37885i	0.0986217	+	0.238057i
$719$	14.6250	+	25.3313i	0.545421	+	0.944697i	0.998580	+	0.0532673i	$0.0169635\pi$
$719$	14.6250	+	25.3313i	0.545421	+	0.944697i	−0.453159	+	0.891430i	$0.649703\pi$
$720$		0			0
$721$	20.3569	−	35.2591i	0.758129	−	1.31312i
$722$	−26.4757	−	3.48410i	−0.985324	−	0.129665i
$723$		0			0
$724$	6.81468	−	25.4440i	0.253266	−	0.945620i
$725$	4.96752	+	28.1722i	0.184489	+	1.04629i
$726$		0			0
$727$	32.7533	−	39.0339i	1.21475	−	1.44769i	0.356628	−	0.934246i	$-0.383926\pi$
$727$	32.7533	−	39.0339i	1.21475	−	1.44769i	0.858125	−	0.513440i	$-0.171629\pi$
$728$	−3.26874	−	24.7966i	−0.121147	−	0.919022i
$729$		0			0
$730$	−2.49055	−	56.9704i	−0.0921795	−	2.10857i
$731$	−9.10664	+	10.8529i	−0.336821	+	0.401408i
$732$		0			0
$733$	−2.54100	+	0.448046i	−0.0938538	+	0.0165490i	−0.220378	−	0.975415i	$-0.570729\pi$
$733$	−2.54100	+	0.448046i	−0.0938538	+	0.0165490i	0.126524	+	0.991964i	$0.459618\pi$
$734$	−13.5750	−	4.27935i	−0.501062	−	0.157954i
$735$		0			0
$736$	32.5959	−	1.43224i	1.20150	−	0.0527931i
$737$	−6.33034	−	3.65482i	−0.233181	−	0.134627i
$738$		0			0
$739$	3.86165	+	6.68857i	0.142053	+	0.246043i	0.928270	−	0.371908i	$-0.121296\pi$
$739$	3.86165	+	6.68857i	0.142053	+	0.246043i	−0.786217	+	0.617951i	$0.787963\pi$
$740$	−7.24730	−	15.5374i	−0.266416	−	0.571165i
$741$		0			0
$742$	−6.18645	+	5.66947i	−0.227112	+	0.208133i
$743$	−9.80501	+	8.22738i	−0.359711	+	0.301833i	−0.804676	−	0.593715i	$-0.797661\pi$
$743$	−9.80501	+	8.22738i	−0.359711	+	0.301833i	0.444965	+	0.895548i	$0.353216\pi$
$744$		0			0
$745$	−26.6479	+	9.69906i	−0.976305	+	0.355346i
$746$	1.13658	+	1.78386i	0.0416132	+	0.0653116i
$747$		0			0
$748$	3.49056	−	7.48770i	0.127627	−	0.273777i
$749$	2.61279	−	14.8179i	0.0954693	−	0.541433i
$750$		0			0
$751$	15.0834	−	41.4413i	0.550401	−	1.51221i	−0.282763	−	0.959190i	$-0.591251\pi$
$751$	15.0834	−	41.4413i	0.550401	−	1.51221i	0.833165	−	0.553025i	$-0.186527\pi$
$752$	14.9923	+	41.1626i	0.546714	+	1.50105i
$753$		0			0
$754$	−11.5960	−	8.89687i	−0.422300	−	0.324005i
$755$			9.38096i			0.341408i
$756$		0			0
$757$		−	27.9094i		−	1.01438i	−0.861833	−	0.507192i	$-0.830684\pi$
$757$		−	27.9094i		−	1.01438i	0.861833	−	0.507192i	$-0.169316\pi$
$758$	−22.7295	+	29.6251i	−0.825574	+	1.07603i
$759$		0			0
$760$	2.96036	−	0.933941i	0.107384	−	0.0338776i
$761$	7.20399	−	19.7928i	0.261145	−	0.717489i	−0.737946	−	0.674859i	$-0.764204\pi$
$761$	7.20399	−	19.7928i	0.261145	−	0.717489i	0.999091	−	0.0426294i	$-0.0135735\pi$
$762$		0			0
$763$	−8.78916	+	49.8458i	−0.318189	+	1.80454i
$764$	18.0675	−	38.7572i	0.653660	−	1.40218i
$765$		0			0
$766$	18.7422	−	11.9415i	0.677182	−	0.431466i
$767$	−12.6983	+	4.62181i	−0.458509	+	0.166884i
$768$		0			0
$769$	−9.76794	+	8.19627i	−0.352241	+	0.295565i	−0.801689	−	0.597741i	$-0.796065\pi$
$769$	−9.76794	+	8.19627i	−0.352241	+	0.295565i	0.449448	+	0.893306i	$0.351621\pi$
$770$	−12.6412	−	13.7939i	−0.455558	−	0.497099i
$771$		0			0
$772$	38.0511	−	17.7487i	1.36949	−	0.638788i
$773$	24.3894	+	42.2437i	0.877226	+	1.51940i	0.854372	+	0.519661i	$0.173942\pi$
$773$	24.3894	+	42.2437i	0.877226	+	1.51940i	0.0228536	+	0.999739i	$0.492725\pi$
$774$		0			0
$775$	36.0896	+	20.8363i	1.29638	+	0.748463i
$776$	−2.50601	−	0.108996i	−0.0899607	−	0.00391274i
$777$		0			0
$778$	−8.60643	+	27.3014i	−0.308556	+	0.978803i
$779$	0.0182112	−	0.00321113i	0.000652484	−	0.000115051i
$780$		0			0
$781$	−0.213023	+	0.253871i	−0.00762256	+	0.00908421i
$782$	−37.9443	+	1.65880i	−1.35689	+	0.0593185i
$783$		0			0
$784$	−57.8516	+	10.2141i	−2.06613	+	0.364788i
$785$	−22.4739	+	26.7833i	−0.802127	+	0.955938i
$786$		0			0
$787$	−4.56672	−	25.8991i	−0.162786	−	0.923205i	−0.951318	−	0.308211i	$-0.900270\pi$
$787$	−4.56672	−	25.8991i	−0.162786	−	0.923205i	0.788532	−	0.614994i	$-0.210841\pi$
$788$	20.2186	+	5.41516i	0.720259	+	0.192907i
$789$		0			0
$790$	−2.33966	+	17.7791i	−0.0832414	+	0.632553i
$791$	25.3209	−	43.8570i	0.900306	−	1.55938i
$792$		0			0
$793$	7.89615	+	13.6765i	0.280401	+	0.485668i
$794$	36.0084	−	14.9175i	1.27789	−	0.529402i
$795$		0			0
$796$	23.4662	+	23.4610i	0.831739	+	0.831554i
$797$	−27.3124	+	22.9179i	−0.967456	+	0.811792i	−0.982150	−	0.188100i	$-0.939767\pi$
$797$	−27.3124	+	22.9179i	−0.967456	+	0.811792i	0.0146935	+	0.999892i	$0.495323\pi$
$798$		0			0
$799$	−17.4415	−	47.9201i	−0.617036	−	1.69529i
$800$	21.9154	−	20.0930i	0.774828	−	0.710395i
$801$		0			0
$802$	−4.43137	+	8.51375i	−0.156477	+	0.300631i
$803$	11.0000	+	1.93959i	0.388180	+	0.0684467i
$804$		0			0
$805$	−29.4200	+	80.8307i	−1.03692	+	2.84891i
$806$	−20.7864	+	4.60945i	−0.732171	+	0.162361i
$807$		0			0
$808$	−9.58121	+	15.0450i	−0.337066	+	0.529282i
$809$			41.4917i			1.45877i	0.684103	+	0.729385i	$0.260194\pi$
$809$			41.4917i			1.45877i	−0.684103	+	0.729385i	$0.739806\pi$
$810$		0			0
$811$	29.0442			1.01988			0.509940	−	0.860210i	$-0.329667\pi$
$811$	29.0442			1.01988			0.509940	+	0.860210i	$0.329667\pi$
$812$	−29.0712	+	41.5277i	−1.02020	+	1.45734i
$813$		0			0
$814$	3.27851	−	0.727019i	0.114912	−	0.0254820i
$815$	2.95951	+	1.07717i	0.103667	+	0.0377318i
$816$		0			0
$817$	0.181065	−	1.02687i	0.00633467	−	0.0359257i
$818$	21.4755	+	11.1779i	0.750873	+	0.390827i
$819$		0			0
$820$	0.283089	−	0.198268i	0.00988589	−	0.00692381i
$821$	−47.7187	+	17.3682i	−1.66539	+	0.606153i	−0.991197	−	0.132399i	$-0.957732\pi$
$821$	−47.7187	+	17.3682i	−1.66539	+	0.606153i	−0.674196	+	0.738552i	$0.735510\pi$
$822$		0			0
$823$	10.2372	+	12.2002i	0.356847	+	0.425274i	0.914365	−	0.404891i	$-0.132691\pi$
$823$	10.2372	+	12.2002i	0.356847	+	0.425274i	−0.557518	+	0.830165i	$0.688246\pi$
$824$	−16.7030	+	18.2342i	−0.581877	+	0.635219i
$825$		0			0
$826$	17.9381	+	43.2996i	0.624146	+	1.50659i
$827$	−26.8166	+	15.4826i	−0.932504	+	0.538381i	−0.887603	−	0.460610i	$-0.847631\pi$
$827$	−26.8166	+	15.4826i	−0.932504	+	0.538381i	−0.0449012	+	0.998991i	$0.514297\pi$
$828$		0			0
$829$	5.02207	+	2.89949i	0.174424	+	0.100704i	0.584670	−	0.811271i	$-0.301224\pi$
$829$	5.02207	+	2.89949i	0.174424	+	0.100704i	−0.410246	+	0.911975i	$0.634557\pi$
$830$	−8.19081	+	62.2421i	−0.284307	+	2.16045i
$831$		0			0
$832$	−1.31892	+	15.1335i	−0.0457255	+	0.524659i
$833$	67.3461	−	11.8749i	2.33340	−	0.411442i
$834$		0			0
$835$	−3.92720	−	3.29531i	−0.135906	−	0.114039i
$836$	0.0530605	+	0.605709i	0.00183514	+	0.0209489i
$837$		0			0
$838$	2.19594	−	0.0959989i	0.0758573	−	0.00331623i
$839$	−11.9037	−	9.98841i	−0.410962	−	0.344838i	0.413750	−	0.910390i	$-0.364219\pi$
$839$	−11.9037	−	9.98841i	−0.410962	−	0.344838i	−0.824712	+	0.565552i	$0.808663\pi$
$840$		0			0
$841$	0.108181	+	0.613526i	0.00373038	+	0.0211561i
$842$	18.2027	+	5.73817i	0.627306	+	0.197751i
$843$		0			0
$844$	−1.62387	+	18.5847i	−0.0558959	+	0.639712i
$845$	−15.0427	+	26.0547i	−0.517484	+	0.896309i
$846$		0			0
$847$	−41.1889	+	23.7804i	−1.41527	+	0.817106i
$848$	4.41323	−	2.54929i	0.151551	−	0.0875429i
$849$		0			0
$850$	−25.5164	+	23.3841i	−0.875204	+	0.802067i
$851$	−9.92382	−	11.8268i	−0.340184	−	0.405416i
$852$		0			0
$853$	−5.27000	−	14.4792i	−0.180441	−	0.495758i	0.816189	−	0.577785i	$-0.196083\pi$
$853$	−5.27000	−	14.4792i	−0.180441	−	0.495758i	−0.996630	+	0.0820269i	$0.973861\pi$
$854$	46.1932	−	29.4319i	1.58070	−	1.00714i
$855$		0			0
$856$	−3.49582	+	8.44363i	−0.119485	+	0.288597i
$857$	43.4090	+	7.65418i	1.48282	+	0.261462i	0.855706	−	0.517463i	$-0.173123\pi$
$857$	43.4090	+	7.65418i	1.48282	+	0.261462i	0.627118	+	0.778924i	$0.284234\pi$
$858$		0			0
$859$	49.6251	+	18.0621i	1.69319	+	0.616270i	0.995021	−	0.0996665i	$-0.0317776\pi$
$859$	49.6251	+	18.0621i	1.69319	+	0.616270i	0.698166	+	0.715936i	$0.254000\pi$
$860$	−5.04598	−	18.8235i	−0.172067	−	0.641876i
$861$		0			0
$862$	28.0828	−	36.6024i	0.956504	−	1.24668i
$863$	51.1622			1.74158			0.870791	−	0.491653i	$-0.163607\pi$
$863$	51.1622			1.74158			0.870791	+	0.491653i	$0.163607\pi$
$864$		0			0
$865$	−45.4048			−1.54381
$866$	17.5764	−	22.9086i	0.597269	−	0.778465i
$867$		0			0
$868$	19.1205	+	71.3268i	0.648991	+	2.42099i
$869$	−3.30066	−	1.20134i	−0.111967	−	0.0407527i
$870$		0			0
$871$	−15.4085	−	2.71693i	−0.522097	−	0.0920597i
$872$	11.7596	−	28.4035i	0.398229	−	0.961863i
$873$		0			0
$874$	2.35749	−	1.50207i	0.0797431	−	0.0508082i
$875$	1.30578	+	3.58759i	0.0441433	+	0.121283i
$876$		0			0
$877$	21.3535	+	25.4481i	0.721055	+	0.859320i	0.994733	−	0.102501i	$-0.0326845\pi$
$877$	21.3535	+	25.4481i	0.721055	+	0.859320i	−0.273678	+	0.961822i	$0.588240\pi$
$878$	5.31374	−	4.86969i	0.179330	−	0.164344i
$879$		0			0
$880$	5.68416	+	9.84020i	0.191613	+	0.331713i
$881$	24.0135	−	13.8642i	0.809034	−	0.467096i	−0.0375862	−	0.999293i	$-0.511967\pi$
$881$	24.0135	−	13.8642i	0.809034	−	0.467096i	0.846620	+	0.532197i	$0.178634\pi$
$882$		0			0
$883$	7.38127	−	12.7847i	0.248400	−	0.430241i	−0.714682	−	0.699449i	$-0.753429\pi$
$883$	7.38127	−	12.7847i	0.248400	−	0.430241i	0.963082	+	0.269208i	$0.0867621\pi$
$884$	1.53924	−	17.6161i	0.0517702	−	0.592495i
$885$		0			0
$886$	24.9856	+	7.87641i	0.839408	+	0.264613i
$887$	−3.08832	−	17.5147i	−0.103695	−	0.588086i	−0.991733	−	0.128316i	$-0.959043\pi$
$887$	−3.08832	−	17.5147i	−0.103695	−	0.588086i	0.888038	−	0.459770i	$-0.152068\pi$
$888$		0			0
$889$	−50.4081	−	42.2974i	−1.69063	−	1.41861i
$890$	33.1772	−	1.45040i	1.11210	−	0.0486174i
$891$		0			0
$892$	−3.27285	−	37.3610i	−0.109583	−	1.25094i
$893$	2.87515	+	2.41254i	0.0962132	+	0.0807324i
$894$		0			0
$895$	−19.1975	+	3.38504i	−0.641702	+	0.113149i
$896$	52.6374	+	2.27768i	1.75849	+	0.0760921i
$897$		0			0
$898$	3.49455	−	26.5552i	0.116615	−	0.886158i
$899$	37.3716	+	21.5765i	1.24641	+	0.719616i
$900$		0			0
$901$	−5.13798	+	2.96642i	−0.171171	+	0.0988256i
$902$	0.0259099	+	0.0625423i	0.000862706	+	0.00208243i
$903$		0			0
$904$	−20.7760	+	22.6806i	−0.691000	+	0.754346i
$905$	−27.1116	−	32.3104i	−0.901221	−	1.07403i
$906$		0			0
$907$	−33.8368	+	12.3156i	−1.12353	+	0.408932i	−0.835940	−	0.548821i	$-0.815077\pi$
$907$	−33.8368	+	12.3156i	−1.12353	+	0.408932i	−0.287591	+	0.957753i	$0.592854\pi$
$908$	−8.30165	+	5.81426i	−0.275500	+	0.192953i
$909$		0			0
$910$	−35.5249	−	18.4906i	−1.17764	−	0.612957i
$911$	0.0484884	−	0.274992i	0.00160649	−	0.00911088i	−0.983994	−	0.178202i	$-0.942972\pi$
$911$	0.0484884	−	0.274992i	0.00160649	−	0.00911088i	0.985600	+	0.169091i	$0.0540831\pi$
$912$		0			0
$913$	−11.5551	−	4.20572i	−0.382418	−	0.139189i
$914$	14.4552	−	3.20549i	0.478137	−	0.106028i
$915$		0			0
$916$	25.8564	−	36.9355i	0.854320	−	1.22038i
$917$	−16.8153			−0.555290
$918$		0			0
$919$			19.5234i			0.644017i	0.946737	+	0.322008i	$0.104358\pi$
$919$			19.5234i			0.644017i	−0.946737	+	0.322008i	$0.895642\pi$
$920$	28.0636	−	44.0672i	0.925229	−	1.45285i
$921$		0			0
$922$	−33.6735	+	7.46719i	−1.10898	+	0.245919i
$923$	−0.242618	+	0.666587i	−0.00798586	+	0.0219410i
$924$		0			0
$925$	−13.8552	−	2.44304i	−0.455555	−	0.0803267i
$926$	10.2866	−	19.7631i	0.338039	−	0.649454i
$927$		0			0
$928$	22.6939	−	20.8068i	0.744965	−	0.683015i
$929$	12.7507	+	35.0323i	0.418338	+	1.14937i	0.952645	+	0.304083i	$0.0983502\pi$
$929$	12.7507	+	35.0323i	0.418338	+	1.14937i	−0.534308	+	0.845290i	$0.679428\pi$
$930$		0			0
$931$	−3.85557	+	3.23521i	−0.126361	+	0.106030i
$932$	8.06299	+	8.06120i	0.264112	+	0.264053i
$933$		0			0
$934$	−10.0283	+	4.15451i	−0.328136	+	0.135940i
$935$	−6.61423	−	11.4562i	−0.216308	−	0.374657i
$936$		0			0
$937$	−1.65449	+	2.86566i	−0.0540499	+	0.0936171i	−0.891784	−	0.452461i	$-0.850546\pi$
$937$	−1.65449	+	2.86566i	−0.0540499	+	0.0936171i	0.837735	+	0.546078i	$0.183880\pi$
$938$	−7.08013	+	53.8020i	−0.231174	+	1.75670i
$939$		0			0
$940$	67.7591	+	18.1479i	2.21006	+	0.591920i
$941$	−8.25196	−	46.7992i	−0.269006	−	1.52561i	−0.757379	−	0.652975i	$-0.773521\pi$
$941$	−8.25196	−	46.7992i	−0.269006	−	1.52561i	0.488373	−	0.872635i	$-0.337591\pi$
$942$		0			0
$943$	0.200054	−	0.238415i	0.00651465	−	0.00776386i
$944$	−4.94932	−	28.0325i	−0.161087	−	0.912381i
$945$		0			0
$946$	3.81356	−	0.166716i	0.123990	−	0.00542041i
$947$	−15.7887	+	18.8162i	−0.513063	+	0.611444i	−0.958926	−	0.283657i	$-0.908452\pi$
$947$	−15.7887	+	18.8162i	−0.513063	+	0.611444i	0.445863	+	0.895101i	$0.352897\pi$
$948$		0			0
$949$	23.5453	−	4.15167i	0.764312	−	0.134769i
$950$	0.765860	−	2.42947i	0.0248478	−	0.0788224i
$951$		0			0
$952$	−61.2732	−	2.66501i	−1.98587	−	0.0863735i
$953$	5.53399	+	3.19505i	0.179264	+	0.103498i	0.586947	−	0.809626i	$-0.300330\pi$
$953$	5.53399	+	3.19505i	0.179264	+	0.103498i	−0.407683	+	0.913124i	$0.633663\pi$
$954$		0			0
$955$	−34.2360	−	59.2984i	−1.10785	−	1.91885i
$956$	−41.7465	+	19.4724i	−1.35018	+	0.629782i
$957$		0			0
$958$	−29.8007	−	32.5182i	−0.962818	−	1.05061i
$959$	−46.9654	+	39.4086i	−1.51659	+	1.27257i
$960$		0			0
$961$	29.9411	−	10.8977i	0.965843	−	0.351538i
$962$	6.06214	−	3.86249i	0.195451	−	0.124532i
$963$		0			0
$964$	18.3298	−	39.3199i	0.590364	−	1.26641i
$965$	11.6746	−	66.2101i	0.375819	−	2.13138i
$966$		0			0
$967$	7.29798	−	20.0510i	0.234687	−	0.644798i	−0.765312	−	0.643659i	$-0.777415\pi$
$967$	7.29798	−	20.0510i	0.234687	−	0.644798i	0.999999	−	0.00113855i	$-0.000362411\pi$
$968$	27.5484	−	8.69102i	0.885439	−	0.279340i
$969$		0			0
$970$	−2.44494	+	3.18668i	−0.0785024	+	0.102318i
$971$		−	18.8858i		−	0.606074i	−0.952979	−	0.303037i	$-0.901999\pi$
$971$		−	18.8858i		−	0.606074i	0.952979	−	0.303037i	$-0.0980006\pi$
$972$		0			0
$973$		−	55.8507i		−	1.79049i
$974$	−15.9525	−	12.2393i	−0.511150	−	0.392174i
$975$		0			0
$976$	−31.2582	+	11.3849i	−1.00055	+	0.364423i
$977$	12.8528	−	35.3129i	0.411199	−	1.12976i	−0.545355	−	0.838205i	$-0.683605\pi$
$977$	12.8528	−	35.3129i	0.411199	−	1.12976i	0.956554	−	0.291555i	$-0.0941726\pi$
$978$		0			0
$979$	−1.12954	+	6.40593i	−0.0361002	+	0.204735i
$980$	−39.7452	+	85.2586i	−1.26961	+	2.72348i
$981$		0			0
$982$	−1.07328	−	1.68451i	−0.0342499	−	0.0537549i
$983$	−0.0615360	+	0.0223973i	−0.00196269	+	0.000714362i	−0.343001	−	0.939335i	$-0.611444\pi$
$983$	−0.0615360	+	0.0223973i	−0.00196269	+	0.000714362i	0.341039	+	0.940049i	$0.389221\pi$
$984$		0			0
$985$	25.6749	−	21.5438i	0.818069	−	0.686441i
$986$	−26.4228	+	24.2147i	−0.841472	+	0.771153i
$987$		0			0
$988$	0.550159	+	1.17948i	0.0175029	+	0.0375242i
$989$	−8.77459	−	15.1980i	−0.279016	−	0.483269i
$990$		0			0
$991$	−2.32285	−	1.34110i	−0.0737876	−	0.0426013i	0.462652	−	0.886540i	$-0.346898\pi$
$991$	−2.32285	−	1.34110i	−0.0737876	−	0.0426013i	−0.536440	+	0.843939i	$0.680231\pi$
$992$	−1.96882	−	44.8077i	−0.0625101	−	1.42265i
$993$		0			0
$994$	2.34648	+	0.739698i	0.0744257	+	0.0234618i
$995$	52.3264	−	9.22655i	1.65886	−	0.292501i
$996$		0			0
$997$	−6.81445	+	8.12114i	−0.215816	+	0.257199i	−0.863081	−	0.505066i	$-0.831468\pi$
$997$	−6.81445	+	8.12114i	−0.215816	+	0.257199i	0.647265	+	0.762265i	$0.275913\pi$
$998$	1.85021	+	42.3229i	0.0585675	+	1.33971i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.9		192
3.2	odd	2		216.2.v.b.11.24	✓	192
8.3	odd	2	inner	648.2.v.b.35.8		192
12.11	even	2		864.2.bh.b.335.4		192
24.5	odd	2		864.2.bh.b.335.3		192
24.11	even	2		216.2.v.b.11.25	yes	192
27.5	odd	18	inner	648.2.v.b.611.8		192
27.22	even	9		216.2.v.b.59.25	yes	192
108.103	odd	18		864.2.bh.b.815.3		192
216.59	even	18	inner	648.2.v.b.611.9		192
216.157	even	18		864.2.bh.b.815.4		192
216.211	odd	18		216.2.v.b.59.24	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.24	✓	192	3.2	odd	2
216.2.v.b.11.25	yes	192	24.11	even	2
216.2.v.b.59.24	yes	192	216.211	odd	18
216.2.v.b.59.25	yes	192	27.22	even	9
648.2.v.b.35.8		192	8.3	odd	2	inner
648.2.v.b.35.9		192	1.1	even	1	trivial
648.2.v.b.611.8		192	27.5	odd	18	inner
648.2.v.b.611.9		192	216.59	even	18	inner
864.2.bh.b.335.3		192	24.5	odd	2
864.2.bh.b.335.4		192	12.11	even	2
864.2.bh.b.815.3		192	108.103	odd	18
864.2.bh.b.815.4		192	216.157	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.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.860856 + 1.12202i) q^{2} +(-0.517853 - 1.93179i) q^{4} +(-3.00936 - 1.09532i) q^{5} +(-4.58614 - 0.808660i) q^{7} +(2.61331 + 1.08196i) q^{8} +(3.81960 - 2.43365i) q^{10} +(0.303411 + 0.833616i) q^{11} +(1.22056 + 1.45461i) q^{13} +(4.85534 - 4.44959i) q^{14} +(-3.46366 + 2.00077i) q^{16} +(4.03247 - 2.32815i) q^{17} +(-0.171350 + 0.296787i) q^{19} +(-0.557523 + 6.38069i) q^{20} +(-1.19653 - 0.377190i) q^{22} +(1.00156 + 5.68012i) q^{23} +(4.02633 + 3.37849i) q^{25} +(-2.68283 + 0.117284i) q^{26} +(0.812780 + 9.27824i) q^{28} +(4.16935 + 3.49850i) q^{29} +(7.80815 - 1.37679i) q^{31} +(0.736809 - 5.60866i) q^{32} +(-0.859151 + 6.52870i) q^{34} +(12.9156 + 7.45683i) q^{35} +(-2.31812 + 1.33837i) q^{37} +(-0.185493 - 0.447749i) q^{38} +(-6.67930 - 6.11841i) q^{40} +(-0.0346849 - 0.0413359i) q^{41} +(-2.85915 + 1.04064i) q^{43} +(1.45325 - 1.01782i) q^{44} +(-7.23540 - 3.76600i) q^{46} +(1.90179 - 10.7856i) q^{47} +(13.8009 + 5.02311i) q^{49} +(-7.25682 + 1.60922i) q^{50} +(2.17793 - 3.11115i) q^{52} -1.27415 q^{53} -2.84099i q^{55} +(-11.1100 - 7.07528i) q^{56} +(-7.51460 + 1.66638i) q^{58} +(-2.43399 + 6.68734i) q^{59} +(8.19039 + 1.44419i) q^{61} +(-5.17691 + 9.94610i) q^{62} +(5.65874 + 5.65497i) q^{64} +(-2.07985 - 5.71435i) q^{65} +(-6.31205 + 5.29644i) q^{67} +(-6.58572 - 6.58426i) q^{68} +(-19.4852 + 8.07230i) q^{70} +(0.186788 + 0.323526i) q^{71} +(6.29550 - 10.9041i) q^{73} +(0.493895 - 3.75312i) q^{74} +(0.662065 + 0.177321i) q^{76} +(-0.717374 - 4.06843i) q^{77} +(-2.54509 + 3.03312i) q^{79} +(12.6149 - 2.22724i) q^{80} +(0.0762384 - 0.00333288i) q^{82} +(-8.90996 + 10.6185i) q^{83} +(-14.6852 + 2.58940i) q^{85} +(1.29369 - 4.10386i) q^{86} +(-0.109029 + 2.50677i) q^{88} +(6.35012 + 3.66624i) q^{89} +(-4.42138 - 7.65805i) q^{91} +(10.4542 - 4.87627i) q^{92} +(10.4645 + 11.4187i) q^{94} +(0.840731 - 0.705457i) q^{95} +(-0.833364 + 0.303320i) q^{97} +(-17.5166 + 11.1607i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

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