LMFDB - Embedded newform 648.2.v.b.611.8

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			611.8
Character	$\chi$	$=$	648.611
Dual form			648.2.v.b.35.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.955487 - 1.04261i) q^{2} +(-0.174090 + 1.99241i) q^{4} +(3.00936 - 1.09532i) q^{5} +(4.58614 - 0.808660i) q^{7} +(2.24366 - 1.72221i) q^{8} +(-4.01740 - 2.09104i) q^{10} +(0.303411 - 0.833616i) q^{11} +(-1.22056 + 1.45461i) q^{13} +(-5.22511 - 4.00891i) q^{14} +(-3.93939 - 0.693717i) q^{16} +(4.03247 + 2.32815i) q^{17} +(-0.171350 - 0.296787i) q^{19} +(1.65842 + 6.18657i) q^{20} +(-1.15905 + 0.480168i) q^{22} +(-1.00156 + 5.68012i) q^{23} +(4.02633 - 3.37849i) q^{25} +(2.68283 - 0.117284i) q^{26} +(0.812780 + 9.27824i) q^{28} +(-4.16935 + 3.49850i) q^{29} +(-7.80815 - 1.37679i) q^{31} +(3.04075 + 4.77010i) q^{32} +(-1.42561 - 6.42882i) q^{34} +(12.9156 - 7.45683i) q^{35} +(2.31812 + 1.33837i) q^{37} +(-0.145712 + 0.462228i) q^{38} +(4.86560 - 7.64028i) q^{40} +(-0.0346849 + 0.0413359i) q^{41} +(-2.85915 - 1.04064i) q^{43} +(1.60808 + 0.749643i) q^{44} +(6.87915 - 4.38304i) q^{46} +(-1.90179 - 10.7856i) q^{47} +(13.8009 - 5.02311i) q^{49} +(-7.36956 - 0.969805i) q^{50} +(-2.68569 - 2.68509i) q^{52} +1.27415 q^{53} -2.84099i q^{55} +(8.89703 - 9.71265i) q^{56} +(7.63135 + 1.00425i) q^{58} +(-2.43399 - 6.68734i) q^{59} +(-8.19039 + 1.44419i) q^{61} +(6.02512 + 9.45639i) q^{62} +(2.06798 - 7.72810i) q^{64} +(-2.07985 + 5.71435i) q^{65} +(-6.31205 - 5.29644i) q^{67} +(-5.34063 + 7.62901i) q^{68} +(-20.1153 - 6.34110i) q^{70} +(-0.186788 + 0.323526i) q^{71} +(6.29550 + 10.9041i) q^{73} +(-0.819532 - 3.69570i) q^{74} +(0.621151 - 0.289732i) q^{76} +(0.717374 - 4.06843i) q^{77} +(2.54509 + 3.03312i) q^{79} +(-12.6149 + 2.22724i) q^{80} +(0.0762384 - 0.00333288i) q^{82} +(-8.90996 - 10.6185i) q^{83} +(14.6852 + 2.58940i) q^{85} +(1.64689 + 3.97531i) q^{86} +(-0.754912 - 2.39288i) q^{88} +(6.35012 - 3.66624i) q^{89} +(-4.42138 + 7.65805i) q^{91} +(-11.1428 - 2.98437i) q^{92} +(-9.42807 + 12.2883i) q^{94} +(-0.840731 - 0.705457i) q^{95} +(-0.833364 - 0.303320i) q^{97} +(-18.4237 - 9.58948i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.955487	−	1.04261i	−0.675631	−	0.737240i
$2$	−0.955487	−	1.04261i	−0.675631	−	0.737240i
$3$		0			0
$3$		0			0
$4$	−0.174090	+	1.99241i	−0.0870450	+	0.996204i
$5$	3.00936	−	1.09532i	1.34583	−	0.489842i	0.434185	−	0.900824i	$-0.357036\pi$
$5$	3.00936	−	1.09532i	1.34583	−	0.489842i	0.911643	+	0.410982i	$0.134814\pi$
$6$		0			0
$7$	4.58614	−	0.808660i	1.73340	−	0.305645i	0.784242	−	0.620455i	$-0.213052\pi$
$7$	4.58614	−	0.808660i	1.73340	−	0.305645i	0.949155	+	0.314810i	$0.101941\pi$
$8$	2.24366	−	1.72221i	0.793252	−	0.608894i
$9$		0			0
$10$	−4.01740	−	2.09104i	−1.27041	−	0.661246i
$11$	0.303411	−	0.833616i	0.0914819	−	0.251345i	−0.885510	−	0.464620i	$-0.846191\pi$
$11$	0.303411	−	0.833616i	0.0914819	−	0.251345i	0.976992	+	0.213275i	$0.0684132\pi$
$12$		0			0
$13$	−1.22056	+	1.45461i	−0.338523	+	0.403436i	−0.908270	−	0.418384i	$-0.862597\pi$
$13$	−1.22056	+	1.45461i	−0.338523	+	0.403436i	0.569747	+	0.821820i	$0.307041\pi$
$14$	−5.22511	−	4.00891i	−1.39647	−	1.07143i
$15$		0			0
$16$	−3.93939	−	0.693717i	−0.984846	−	0.173429i
$17$	4.03247	+	2.32815i	0.978017	+	0.564658i	0.901671	−	0.432423i	$-0.142341\pi$
$17$	4.03247	+	2.32815i	0.978017	+	0.564658i	0.0763460	+	0.997081i	$0.475675\pi$
$18$		0			0
$19$	−0.171350	−	0.296787i	−0.0393104	−	0.0680876i	0.845701	−	0.533657i	$-0.179183\pi$
$19$	−0.171350	−	0.296787i	−0.0393104	−	0.0680876i	−0.885011	+	0.465570i	$0.845849\pi$
$20$	1.65842	+	6.18657i	0.370835	+	1.38336i
$21$		0			0
$22$	−1.15905	+	0.480168i	−0.247109	+	0.102372i
$23$	−1.00156	+	5.68012i	−0.208839	+	1.18439i	0.682443	+	0.730939i	$0.260918\pi$
$23$	−1.00156	+	5.68012i	−0.208839	+	1.18439i	−0.891282	+	0.453449i	$0.850194\pi$
$24$		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	$-0.890856\pi$
$29$	−4.16935	+	3.49850i	−0.774229	+	0.649655i	0.167559	+	0.985862i	$0.446411\pi$
$30$		0			0
$31$	−7.80815	−	1.37679i	−1.40238	−	0.247278i	−0.579262	−	0.815142i	$-0.696659\pi$
$31$	−7.80815	−	1.37679i	−1.40238	−	0.247278i	−0.823123	+	0.567864i	$0.807770\pi$
$32$	3.04075	+	4.77010i	0.537534	+	0.843242i
$33$		0			0
$34$	−1.42561	−	6.42882i	−0.244490	−	1.10253i
$35$	12.9156	−	7.45683i	2.18314	−	1.26044i
$36$		0			0
$37$	2.31812	+	1.33837i	0.381097	+	0.220026i	0.678295	−	0.734789i	$-0.262719\pi$
$37$	2.31812	+	1.33837i	0.381097	+	0.220026i	−0.297199	+	0.954816i	$0.596052\pi$
$38$	−0.145712	+	0.462228i	−0.0236376	+	0.0749833i
$39$		0			0
$40$	4.86560	−	7.64028i	0.769320	−	1.20803i
$41$	−0.0346849	+	0.0413359i	−0.00541687	+	0.00645558i	−0.768746	−	0.639554i	$-0.779119\pi$
$41$	−0.0346849	+	0.0413359i	−0.00541687	+	0.00645558i	0.763329	+	0.646010i	$0.223563\pi$
$42$		0			0
$43$	−2.85915	−	1.04064i	−0.436016	−	0.158697i	0.114681	−	0.993402i	$-0.463416\pi$
$43$	−2.85915	−	1.04064i	−0.436016	−	0.158697i	−0.550696	+	0.834706i	$0.685638\pi$
$44$	1.60808	+	0.749643i	0.242428	+	0.113013i
$45$		0			0
$46$	6.87915	−	4.38304i	1.01428	−	0.646244i
$47$	−1.90179	−	10.7856i	−0.277404	−	1.57324i	−0.731219	−	0.682143i	$-0.761048\pi$
$47$	−1.90179	−	10.7856i	−0.277404	−	1.57324i	0.453814	−	0.891096i	$-0.350063\pi$
$48$		0			0
$49$	13.8009	−	5.02311i	1.97155	−	0.717587i
$50$	−7.36956	−	0.969805i	−1.04221	−	0.137151i
$51$		0			0
$52$	−2.68569	−	2.68509i	−0.372438	−	0.372355i
$53$	1.27415			0.175018			0.0875092	−	0.996164i	$-0.472109\pi$
$53$	1.27415			0.175018			0.0875092	+	0.996164i	$0.472109\pi$
$54$		0			0
$55$		−	2.84099i		−	0.383078i
$56$	8.89703	−	9.71265i	1.18892	−	1.29791i
$57$		0			0
$58$	7.63135	+	1.00425i	1.00204	+	0.131865i
$59$	−2.43399	−	6.68734i	−0.316879	−	0.870618i	−0.991223	−	0.132201i	$-0.957796\pi$
$59$	−2.43399	−	6.68734i	−0.316879	−	0.870618i	0.674344	−	0.738417i	$-0.264427\pi$
$60$		0			0
$61$	−8.19039	+	1.44419i	−1.04867	+	0.184909i	−0.671326	−	0.741163i	$-0.734275\pi$
$61$	−8.19039	+	1.44419i	−1.04867	+	0.184909i	−0.377347	+	0.926072i	$0.623164\pi$
$62$	6.02512	+	9.45639i	0.765191	+	1.20096i
$63$		0			0
$64$	2.06798	−	7.72810i	0.258497	−	0.966012i
$65$	−2.07985	+	5.71435i	−0.257974	+	0.708778i
$66$		0			0
$67$	−6.31205	−	5.29644i	−0.771139	−	0.647063i	0.169861	−	0.985468i	$-0.445668\pi$
$67$	−6.31205	−	5.29644i	−0.771139	−	0.647063i	−0.941000	+	0.338405i	$0.890113\pi$
$68$	−5.34063	+	7.62901i	−0.647647	+	0.925154i
$69$		0			0
$70$	−20.1153	−	6.34110i	−2.40424	−	0.757907i
$71$	−0.186788	+	0.323526i	−0.0221676	+	0.0383955i	−0.876896	−	0.480679i	$-0.840390\pi$
$71$	−0.186788	+	0.323526i	−0.0221676	+	0.0383955i	0.854729	+	0.519075i	$0.173723\pi$
$72$		0			0
$73$	6.29550	+	10.9041i	0.736832	+	1.27623i	0.953915	+	0.300077i	$0.0970125\pi$
$73$	6.29550	+	10.9041i	0.736832	+	1.27623i	−0.217083	+	0.976153i	$0.569654\pi$
$74$	−0.819532	−	3.69570i	−0.0952687	−	0.429616i
$75$		0			0
$76$	0.621151	−	0.289732i	0.0712509	−	0.0332345i
$77$	0.717374	−	4.06843i	0.0817524	−	0.463641i
$78$		0			0
$79$	2.54509	+	3.03312i	0.286345	+	0.341252i	0.889973	−	0.456014i	$-0.150723\pi$
$79$	2.54509	+	3.03312i	0.286345	+	0.341252i	−0.603628	+	0.797266i	$0.706279\pi$
$80$	−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	−0.986199	−	0.165563i	$-0.947056\pi$
$83$	−8.90996	−	10.6185i	−0.977996	−	1.16553i	0.00820363	−	0.999966i	$-0.497389\pi$
$84$		0			0
$85$	14.6852	+	2.58940i	1.59284	+	0.280860i
$86$	1.64689	+	3.97531i	0.177588	+	0.428669i
$87$		0			0
$88$	−0.754912	−	2.39288i	−0.0804739	−	0.255082i
$89$	6.35012	−	3.66624i	0.673111	−	0.388621i	−0.124143	−	0.992264i	$-0.539618\pi$
$89$	6.35012	−	3.66624i	0.673111	−	0.388621i	0.797254	+	0.603644i	$0.206285\pi$
$90$		0			0
$91$	−4.42138	+	7.65805i	−0.463487	+	0.802782i
$92$	−11.1428	−	2.98437i	−1.16171	−	0.311142i
$93$		0			0
$94$	−9.42807	+	12.2883i	−0.972431	+	1.26744i
$95$	−0.840731	−	0.705457i	−0.0862572	−	0.0723783i
$96$		0			0
$97$	−0.833364	−	0.303320i	−0.0846153	−	0.0307975i	0.299366	−	0.954138i	$-0.403225\pi$
$97$	−0.833364	−	0.303320i	−0.0846153	−	0.0307975i	−0.383981	+	0.923341i	$0.625447\pi$
$98$	−18.4237	−	9.58948i	−1.86108	−	0.968684i
$99$		0			0
$100$	6.03039	+	8.61025i	0.603039	+	0.861025i
$101$	1.09507	+	6.21046i	0.108964	+	0.617964i	0.989563	+	0.144102i	$0.0460294\pi$
$101$	1.09507	+	6.21046i	0.108964	+	0.617964i	−0.880599	+	0.473862i	$0.842860\pi$
$102$		0			0
$103$	2.99018	+	8.21544i	0.294631	+	0.809492i	0.995374	+	0.0960778i	$0.0306297\pi$
$103$	2.99018	+	8.21544i	0.294631	+	0.809492i	−0.700743	+	0.713414i	$0.747148\pi$
$104$	−0.233376	+	5.36571i	−0.0228844	+	0.526151i
$105$		0			0
$106$	−1.21744	−	1.32845i	−0.118248	−	0.129031i
$107$		−	3.23101i		−	0.312354i	−0.987729	−	0.156177i	$-0.950083\pi$
$107$		−	3.23101i		−	0.312354i	0.987729	−	0.156177i	$-0.0499170\pi$
$108$		0			0
$109$		−	10.8688i		−	1.04104i	−0.853849	−	0.520521i	$-0.825738\pi$
$109$		−	10.8688i		−	1.04104i	0.853849	−	0.520521i	$-0.174262\pi$
$110$	−2.96205	+	2.71452i	−0.282421	+	0.258820i
$111$		0			0
$112$	−18.6275	+	0.00414052i	−1.76014	+	0.000391242i
$113$	−3.71933	−	10.2188i	−0.349885	−	0.961301i	−0.982406	−	0.186758i	$-0.940202\pi$
$113$	−3.71933	−	10.2188i	−0.349885	−	0.961301i	0.632521	−	0.774543i	$-0.282020\pi$
$114$		0			0
$115$	3.20749	+	18.1906i	0.299100	+	1.69628i
$116$	−6.24460	−	8.91610i	−0.579797	−	0.827840i
$117$		0			0
$118$	−4.64667	+	8.92739i	−0.427761	+	0.821833i
$119$	20.3761	+	7.41630i	1.86788	+	0.679851i
$120$		0			0
$121$	7.82363	+	6.56481i	0.711239	+	0.596801i
$122$	9.33154	+	7.15952i	0.844838	+	0.648193i
$123$		0			0
$124$	4.10244	−	15.3173i	0.368410	−	1.37554i
$125$	0.409913	−	0.709991i	0.0366638	−	0.0635035i
$126$		0			0
$127$	−12.2372	+	7.06513i	−1.08587	+	0.626929i	−0.932475	−	0.361235i	$-0.882355\pi$
$127$	−12.2372	+	7.06513i	−1.08587	+	0.626929i	−0.153399	+	0.988164i	$0.549022\pi$
$128$	−10.0333	+	5.22799i	−0.886831	+	0.462094i
$129$		0			0
$130$	7.94514	−	3.29150i	0.696835	−	0.288684i
$131$	3.55599	+	0.627016i	0.310688	+	0.0547827i	0.326818	−	0.945087i	$-0.394024\pi$
$131$	3.55599	+	0.627016i	0.310688	+	0.0547827i	−0.0161302	+	0.999870i	$0.505135\pi$
$132$		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	0.994918	−	0.100687i	$-0.0321041\pi$
$137$	8.46244	+	10.0851i	0.722995	+	0.861632i	−0.271923	+	0.962319i	$0.587660\pi$
$138$		0			0
$139$	2.08259	−	11.8109i	0.176643	−	1.00179i	−0.759588	−	0.650405i	$-0.774599\pi$
$139$	2.08259	−	11.8109i	0.176643	−	1.00179i	0.936230	−	0.351387i	$-0.114290\pi$
$140$	12.6086	+	27.0313i	1.06562	+	2.28457i
$141$		0			0
$142$	0.515786	−	0.114377i	0.0432838	−	0.00959832i
$143$	0.842252	+	1.45882i	0.0704327	+	0.121993i
$144$		0			0
$145$	−8.71512	+	15.0950i	−0.723751	+	1.25357i
$146$	5.35353	−	16.9825i	0.443061	−	1.40548i
$147$		0			0
$148$	−3.07014	+	4.38565i	−0.252364	+	0.360498i
$149$	−6.78333	−	5.69189i	−0.555712	−	0.466298i	0.321158	−	0.947026i	$-0.395928\pi$
$149$	−6.78333	−	5.69189i	−0.555712	−	0.466298i	−0.876870	+	0.480728i	$0.840372\pi$
$150$		0			0
$151$	1.00187	−	2.75261i	0.0815308	−	0.224004i	−0.892229	−	0.451584i	$-0.850859\pi$
$151$	1.00187	−	2.75261i	0.0815308	−	0.224004i	0.973759	+	0.227580i	$0.0730813\pi$
$152$	−0.895580	−	0.370786i	−0.0726411	−	0.0300748i
$153$		0			0
$154$	−4.92725	+	3.13939i	−0.397049	+	0.252979i
$155$	−25.0056	+	4.40916i	−2.00850	+	0.354152i
$156$		0			0
$157$	−3.73399	−	10.2591i	−0.298005	−	0.818762i	−0.994833	−	0.101524i	$-0.967628\pi$
$157$	−3.73399	−	10.2591i	−0.298005	−	0.818762i	0.696828	−	0.717238i	$-0.254594\pi$
$158$	0.730574	−	5.55164i	0.0581214	−	0.441665i
$159$		0			0
$160$	14.3755	+	11.0244i	1.13648	+	0.871553i
$161$			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	$0.512263\pi$
$164$	−0.0763197	−	0.0763027i	−0.00595956	−	0.00595824i
$165$		0			0
$166$	−2.55763	+	19.4355i	−0.198511	+	1.50849i
$167$	−1.50427	+	0.547510i	−0.116404	+	0.0423676i	−0.399565	−	0.916705i	$-0.630839\pi$
$167$	−1.50427	+	0.547510i	−0.116404	+	0.0423676i	0.283161	+	0.959072i	$0.408617\pi$
$168$		0			0
$169$	1.63131	+	9.25162i	0.125485	+	0.711663i
$170$	−11.3318	−	17.7852i	−0.869109	−	1.36406i
$171$		0			0
$172$	2.57114	−	5.51542i	0.196047	−	0.420547i
$173$	−13.3229	−	4.84914i	−1.01292	−	0.368673i	−0.218367	−	0.975867i	$-0.570073\pi$
$173$	−13.3229	−	4.84914i	−1.01292	−	0.368673i	−0.794554	+	0.607193i	$0.792295\pi$
$174$		0			0
$175$	15.7332	−	18.7501i	1.18932	−	1.41738i
$176$	−1.77355	+	3.07345i	−0.133686	+	0.231670i
$177$		0			0
$178$	−9.88993	−	3.11768i	−0.741281	−	0.233680i
$179$	5.27151	+	3.04351i	0.394011	+	0.227483i	0.683897	−	0.729579i	$-0.260284\pi$
$179$	5.27151	+	3.04351i	0.394011	+	0.227483i	−0.289885	+	0.957061i	$0.593617\pi$
$180$		0			0
$181$	−11.4059	+	6.58520i	−0.847795	+	0.489474i	−0.859906	−	0.510452i	$-0.829478\pi$
$181$	−11.4059	+	6.58520i	−0.847795	+	0.489474i	0.0121116	+	0.999927i	$0.496145\pi$
$182$	12.2090	−	2.70737i	0.904989	−	0.200684i
$183$		0			0
$184$	7.53522	+	14.4691i	0.555504	+	1.06668i
$185$	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	−0.185185	+	0.982704i	$0.559288\pi$
$191$	−16.3786	+	13.7433i	−1.18512	+	0.994431i	−0.999931	+	0.0117270i	$0.996267\pi$
$192$		0			0
$193$	3.64547	−	20.6745i	0.262407	−	1.48818i	−0.513912	−	0.857843i	$-0.671804\pi$
$193$	3.64547	−	20.6745i	0.262407	−	1.48818i	0.776319	−	0.630341i	$-0.217085\pi$
$194$	0.480023	+	1.15870i	0.0344636	+	0.0831895i
$195$		0			0
$196$	7.60549	+	28.3715i	0.543249	+	2.02653i
$197$	5.23281	+	9.06349i	0.372822	+	0.645747i	0.989999	−	0.141078i	$-0.0450568\pi$
$197$	5.23281	+	9.06349i	0.372822	+	0.645747i	−0.617176	+	0.786825i	$0.711723\pi$
$198$		0			0
$199$	14.3685	+	8.29565i	1.01855	+	0.588063i	0.913685	−	0.406423i	$-0.133224\pi$
$199$	14.3685	+	8.29565i	1.01855	+	0.588063i	0.104870	+	0.994486i	$0.466557\pi$
$200$	3.21522	−	14.5143i	0.227350	−	1.02632i
$201$		0			0
$202$	5.42879	−	7.07575i	0.381968	−	0.497848i
$203$	−16.2921	+	19.4162i	−1.14348	+	1.36275i
$204$		0			0
$205$	−0.0591036	+	0.162386i	−0.00412797	+	0.0113415i
$206$	5.70847	−	10.9673i	0.397728	−	0.764131i
$207$		0			0
$208$	5.81735	−	4.88354i	0.403361	−	0.338613i
$209$	−0.299396	+	0.0527915i	−0.0207096	+	0.00365167i
$210$		0			0
$211$	−8.76523	+	3.19028i	−0.603423	+	0.219628i	−0.625623	−	0.780126i	$-0.715155\pi$
$211$	−8.76523	+	3.19028i	−0.603423	+	0.219628i	0.0222000	+	0.999754i	$0.492933\pi$
$212$	−0.221817	+	2.53864i	−0.0152345	+	0.174354i
$213$		0			0
$214$	−3.36870	+	3.08719i	−0.230280	+	0.211036i
$215$	−9.74405			−0.664539
$216$		0			0
$217$	−36.9226			−2.50647
$218$	−11.3320	+	10.3850i	−0.767497	+	0.703360i
$219$		0			0
$220$	5.66040	+	0.494587i	0.381624	+	0.0333451i
$221$	−8.30841	+	3.02402i	−0.558884	+	0.203417i
$222$		0			0
$223$	−18.4672	+	3.25626i	−1.23665	+	0.218055i	−0.753481	−	0.657470i	$-0.771627\pi$
$223$	−18.4672	+	3.25626i	−1.23665	+	0.218055i	−0.483172	+	0.875525i	$0.660515\pi$
$224$	17.8027	+	19.4174i	1.18949	+	1.29738i
$225$		0			0
$226$	−7.10047	+	13.6417i	−0.472316	+	0.907434i
$227$	−1.73323	+	4.76200i	−0.115038	+	0.316065i	−0.983828	−	0.179116i	$-0.942676\pi$
$227$	−1.73323	+	4.76200i	−0.115038	+	0.316065i	0.868790	+	0.495181i	$0.164898\pi$
$228$		0			0
$229$	−14.4905	+	17.2691i	−0.957559	+	1.14117i	0.0323508	+	0.999477i	$0.489701\pi$
$229$	−14.4905	+	17.2691i	−0.957559	+	1.14117i	−0.989910	+	0.141698i	$0.954744\pi$
$230$	15.9010	−	20.7250i	1.04848	−	1.36657i
$231$		0			0
$232$	−3.32943	+	15.0299i	−0.218588	+	0.986763i
$233$	−4.93700	−	2.85038i	−0.323434	−	0.186735i	0.329488	−	0.944160i	$-0.393124\pi$
$233$	−4.93700	−	2.85038i	−0.323434	−	0.186735i	−0.652922	+	0.757425i	$0.726457\pi$
$234$		0			0
$235$	−17.5368	−	30.3747i	−1.14398	−	1.98143i
$236$	13.7477	−	3.68531i	0.894896	−	0.239893i
$237$		0			0
$238$	−11.7368	−	28.3306i	−0.760782	−	1.83640i
$239$	3.99952	−	22.6824i	0.258707	−	1.46720i	−0.527667	−	0.849451i	$-0.676933\pi$
$239$	3.99952	−	22.6824i	0.258707	−	1.46720i	0.786374	−	0.617750i	$-0.211956\pi$
$240$		0			0
$241$	16.6164	−	13.9428i	1.07036	−	0.898137i	0.0752732	−	0.997163i	$-0.476017\pi$
$241$	16.6164	−	13.9428i	1.07036	−	0.898137i	0.995085	+	0.0990259i	$0.0315727\pi$
$242$	−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
$248$	−19.8899	+	10.3582i	−1.26301	+	0.657749i
$249$		0			0
$250$	−1.13191	+	0.251005i	−0.0715885	+	0.0158750i
$251$	6.86745	−	3.96493i	0.433470	−	0.250264i	−0.267354	−	0.963598i	$-0.586149\pi$
$251$	6.86745	−	3.96493i	0.433470	−	0.250264i	0.700824	+	0.713334i	$0.252816\pi$
$252$		0			0
$253$	4.43115	+	2.55833i	0.278584	+	0.160841i
$254$	19.0587	+	6.00801i	1.19585	+	0.376976i
$255$		0			0
$256$	15.0375	+	5.46564i	0.939845	+	0.341602i
$257$	−0.0798480	+	0.0951592i	−0.00498078	+	0.00593587i	−0.768529	−	0.639815i	$-0.779011\pi$
$257$	−0.0798480	+	0.0951592i	−0.00498078	+	0.00593587i	0.763548	+	0.645751i	$0.223455\pi$
$258$		0			0
$259$	11.7135	+	4.26337i	0.727842	+	0.264913i
$260$	−11.0232	−	5.13873i	−0.683632	−	0.318691i
$261$		0			0
$262$	−2.74396	−	4.30663i	−0.169523	−	0.266064i
$263$	−0.961362	−	5.45215i	−0.0592801	−	0.336194i	0.940715	−	0.339197i	$-0.110155\pi$
$263$	−0.961362	−	5.45215i	−0.0592801	−	0.336194i	−0.999995	+	0.00300271i	$0.999044\pi$
$264$		0			0
$265$	3.83439	−	1.39560i	0.235545	−	0.0857313i
$266$	−0.294469	+	2.23767i	−0.0180550	+	0.137200i
$267$		0			0
$268$	11.6515	−	11.6541i	0.711731	−	0.711889i
$269$	−5.59805			−0.341319			−0.170659	−	0.985330i	$-0.554590\pi$
$269$	−5.59805			−0.341319			−0.170659	+	0.985330i	$0.554590\pi$
$270$		0			0
$271$		−	1.56554i		−	0.0951000i	−0.998869	−	0.0475500i	$-0.984859\pi$
$271$		−	1.56554i		−	0.0951000i	0.998869	−	0.0475500i	$-0.0151413\pi$
$272$	−14.2704	−	11.9689i	−0.865268	−	0.725718i
$273$		0			0
$274$	2.42917	−	18.4593i	0.146751	−	1.11517i
$275$	−1.59473	−	4.38148i	−0.0961657	−	0.264213i
$276$		0			0
$277$	27.6100	−	4.86839i	1.65893	−	0.292513i	0.735854	−	0.677140i	$-0.236781\pi$
$277$	27.6100	−	4.86839i	1.65893	−	0.292513i	0.923072	+	0.384627i	$0.125670\pi$
$278$	−14.3042	+	9.11387i	−0.857906	+	0.546613i
$279$		0			0
$280$	16.1359	−	38.9740i	0.964307	−	2.32914i
$281$	−3.07719	+	8.45452i	−0.183570	+	0.504354i	−0.997008	−	0.0772972i	$-0.975371\pi$
$281$	−3.07719	+	8.45452i	−0.183570	+	0.504354i	0.813438	+	0.581651i	$0.197593\pi$
$282$		0			0
$283$	−22.1256	−	18.5656i	−1.31523	−	1.10361i	−0.987293	−	0.158909i	$-0.949202\pi$
$283$	−22.1256	−	18.5656i	−1.31523	−	1.10361i	−0.327936	−	0.944700i	$-0.606353\pi$
$284$	−0.612078	−	0.428480i	−0.0363202	−	0.0254256i
$285$		0			0
$286$	0.716230	−	2.27203i	0.0423516	−	0.134348i
$287$	−0.125643	+	0.217620i	−0.00741648	+	0.0128457i
$288$		0			0
$289$	2.34052	+	4.05391i	0.137678	+	0.238465i
$290$	24.0655	−	5.33659i	1.41317	−	0.313375i
$291$		0			0
$292$	−22.8214	+	10.6449i	−1.33552	+	0.622946i
$293$	−3.10437	+	17.6058i	−0.181359	+	1.02854i	0.749185	+	0.662360i	$0.230445\pi$
$293$	−3.10437	+	17.6058i	−0.181359	+	1.02854i	−0.930545	+	0.366179i	$0.880666\pi$
$294$		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
$302$	−3.82718	+	1.58552i	−0.220229	+	0.0912364i
$303$		0			0
$304$	0.469127	+	1.28803i	0.0269063	+	0.0738734i
$305$	−23.0660	+	13.3172i	−1.32076	+	0.762540i
$306$		0			0
$307$	2.66885	−	4.62258i	0.152319	−	0.263825i	−0.779760	−	0.626078i	$-0.784659\pi$
$307$	2.66885	−	4.62258i	0.152319	−	0.263825i	0.932080	+	0.362253i	$0.117992\pi$
$308$	7.98109	+	2.13758i	0.454765	+	0.121800i
$309$		0			0
$310$	28.4895	+	21.8583i	1.61810	+	1.24147i
$311$	7.48203	+	6.27817i	0.424267	+	0.356002i	0.829783	−	0.558086i	$-0.188464\pi$
$311$	7.48203	+	6.27817i	0.424267	+	0.356002i	−0.405517	+	0.914088i	$0.632908\pi$
$312$		0			0
$313$	−20.9377	−	7.62069i	−1.18347	−	0.430747i	−0.326042	−	0.945355i	$-0.605715\pi$
$313$	−20.9377	−	7.62069i	−1.18347	−	0.430747i	−0.857425	+	0.514608i	$0.827937\pi$
$314$	−7.12846	+	13.6955i	−0.402282	+	0.772882i
$315$		0			0
$316$	−6.48628	+	4.54282i	−0.364882	+	0.255553i
$317$	2.75422	+	15.6200i	0.154692	+	0.877304i	0.959067	+	0.283181i	$0.0913897\pi$
$317$	2.75422	+	15.6200i	0.154692	+	0.877304i	−0.804374	+	0.594123i	$0.797499\pi$
$318$		0			0
$319$	1.65138	+	4.53712i	0.0924593	+	0.254030i
$320$	−2.24144	−	25.5217i	−0.125300	−	1.42671i
$321$		0			0
$322$	28.0044	−	25.6641i	1.56062	−	1.43021i
$323$		−	1.59571i		−	0.0887877i
$324$		0			0
$325$			9.98038i			0.553612i
$326$	0.939658	+	1.02534i	0.0520429	+	0.0567885i
$327$		0			0
$328$	−0.00663187	+	0.152478i	−0.000366184	+	0.00841920i
$329$	−17.4437	−	47.9263i	−0.961704	−	2.64226i
$330$		0			0
$331$	4.91331	+	27.8648i	0.270060	+	1.53159i	0.754229	+	0.656611i	$0.228011\pi$
$331$	4.91331	+	27.8648i	0.270060	+	1.53159i	−0.484169	+	0.874974i	$0.660878\pi$
$332$	22.7075	−	15.9037i	1.24624	−	0.872830i
$333$		0			0
$334$	2.00815	+	1.04524i	0.109881	+	0.0571928i
$335$	−24.7965	−	9.02520i	−1.35478	−	0.493099i
$336$		0			0
$337$	−2.65131	−	2.22472i	−0.144426	−	0.121188i	0.567712	−	0.823227i	$-0.307829\pi$
$337$	−2.65131	−	2.22472i	−0.144426	−	0.121188i	−0.712138	+	0.702039i	$0.752273\pi$
$338$	8.08718	−	10.5406i	0.439885	−	0.573335i
$339$		0			0
$340$	−7.71570	+	28.8082i	−0.418442	+	1.56234i
$341$	−3.51679	+	6.09126i	−0.190445	+	0.329860i
$342$		0			0
$343$	30.9999	−	17.8978i	1.67383	−	0.966389i
$344$	−8.20715	+	2.58921i	−0.442500	+	0.139601i
$345$		0			0
$346$	7.67407	+	18.5239i	0.412561	+	0.995853i
$347$	21.3082	+	3.75721i	1.14388	+	0.201698i	0.713304	−	0.700854i	$-0.247198\pi$
$347$	21.3082	+	3.75721i	1.14388	+	0.201698i	0.430581	+	0.902552i	$0.358309\pi$
$348$		0			0
$349$	13.6098	+	16.2195i	0.728514	+	0.868209i	0.995428	−	0.0955113i	$-0.0304486\pi$
$349$	13.6098	+	16.2195i	0.728514	+	0.868209i	−0.266915	+	0.963720i	$0.586004\pi$
$350$	−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	0.963827	−	0.266529i	$-0.0858768\pi$
$353$	10.0326	+	11.9564i	0.533980	+	0.636373i	−0.429847	+	0.902902i	$0.641432\pi$
$354$		0			0
$355$	−0.207748	+	1.17820i	−0.0110261	+	0.0625324i
$356$	6.19916	+	13.2903i	0.328555	+	0.704384i
$357$		0			0
$358$	−1.86365	−	8.40419i	−0.0984971	−	0.444175i
$359$	−2.44114	−	4.22817i	−0.128838	−	0.223154i	0.794389	−	0.607410i	$-0.207791\pi$
$359$	−2.44114	−	4.22817i	−0.128838	−	0.223154i	−0.923227	+	0.384256i	$0.874458\pi$
$360$		0			0
$361$	9.44128	−	16.3528i	0.496909	−	0.860672i
$362$	17.7640	+	5.59989i	0.933656	+	0.294324i
$363$		0			0
$364$	−14.4883	−	10.1424i	−0.759391	−	0.531605i
$365$	30.8889	+	25.9189i	1.61680	+	1.35666i
$366$		0			0
$367$	−3.44230	+	9.45764i	−0.179687	+	0.493685i	−0.996536	−	0.0831666i	$-0.973497\pi$
$367$	−3.44230	+	9.45764i	−0.179687	+	0.493685i	0.816849	+	0.576852i	$0.195719\pi$
$368$	7.88592	−	21.6814i	0.411082	−	1.13022i
$369$		0			0
$370$	−6.51424	−	10.2241i	−0.338659	−	0.531523i
$371$	5.84344	−	1.03036i	0.303376	−	0.0534935i
$372$		0			0
$373$	−0.511543	−	1.40545i	−0.0264867	−	0.0727717i	0.925745	−	0.378149i	$-0.123439\pi$
$373$	−0.511543	−	1.40545i	−0.0264867	−	0.0727717i	−0.952231	+	0.305378i	$0.901217\pi$
$374$	−5.79171	−	0.762166i	−0.299482	−	0.0394107i
$375$		0			0
$376$	−22.8420	−	20.9238i	−1.17799	−	1.07906i
$377$		−	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	$0.262792\pi$
$380$	1.55192	−	1.55227i	0.0796119	−	0.0796296i
$381$		0			0
$382$	29.9785	+	3.94505i	1.53384	+	0.201847i
$383$	14.7665	−	5.37456i	0.754532	−	0.274627i	0.0640204	−	0.997949i	$-0.479608\pi$
$383$	14.7665	−	5.37456i	0.754532	−	0.274627i	0.690511	+	0.723321i	$0.257386\pi$
$384$		0			0
$385$	−2.29739	−	13.0291i	−0.117086	−	0.664027i
$386$	−25.0387	+	15.9534i	−1.27444	+	0.812006i
$387$		0			0
$388$	0.749417	−	1.60760i	0.0380459	−	0.0816134i
$389$	−19.0208	−	6.92300i	−0.964393	−	0.351010i	−0.188639	−	0.982046i	$-0.560408\pi$
$389$	−19.0208	−	6.92300i	−0.964393	−	0.351010i	−0.775753	+	0.631036i	$0.782630\pi$
$390$		0			0
$391$	−17.2629	+	20.5731i	−0.873023	+	1.04043i
$392$	22.3136	−	35.0381i	1.12700	−	1.76969i
$393$		0			0
$394$	4.44985	−	14.1159i	0.224180	−	0.711146i
$395$	10.9813	+	6.34007i	0.552530	+	0.319003i
$396$		0			0
$397$	23.8679	−	13.7801i	1.19789	−	0.691604i	0.237808	−	0.971312i	$-0.423571\pi$
$397$	23.8679	−	13.7801i	1.19789	−	0.691604i	0.960085	+	0.279708i	$0.0902376\pi$
$398$	−5.07973	−	22.9072i	−0.254624	−	1.14823i
$399$		0			0
$400$	−18.2050	+	10.5160i	−0.910248	+	0.525802i
$401$	6.68368	+	1.17851i	0.333767	+	0.0588521i	0.338020	−	0.941139i	$-0.390243\pi$
$401$	6.68368	+	1.17851i	0.333767	+	0.0588521i	−0.00425323	+	0.999991i	$0.501354\pi$
$402$		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	0.818753	+	0.574145i	$0.194666\pi$
$409$	−2.97274	+	16.8592i	−0.146992	+	0.833636i	−0.965746	+	0.259490i	$0.916445\pi$
$410$	0.225778	−	0.0935352i	0.0111504	−	0.00461937i
$411$		0			0
$412$	−16.8891	+	4.52743i	−0.832065	+	0.223050i
$413$	−16.5704	−	28.7008i	−0.815377	−	1.41227i
$414$		0			0
$415$	−38.4439	−	22.1956i	−1.88714	−	1.08954i
$416$	−10.6500	−	1.39910i	−0.522162	−	0.0685963i
$417$		0			0
$418$	0.341110	+	0.261713i	0.0166842	+	0.0128008i
$419$	−0.999049	+	1.19062i	−0.0488067	+	0.0581656i	−0.789896	−	0.613241i	$-0.789865\pi$
$419$	−0.999049	+	1.19062i	−0.0488067	+	0.0581656i	0.741089	+	0.671407i	$0.234310\pi$
$420$		0			0
$421$	4.61578	−	12.6818i	0.224959	−	0.618071i	−0.774943	−	0.632031i	$-0.782222\pi$
$421$	4.61578	−	12.6818i	0.224959	−	0.618071i	0.999903	+	0.0139601i	$0.00444380\pi$
$422$	11.7013	+	6.09048i	0.569610	+	0.296480i
$423$		0			0
$424$	2.85876	−	2.19436i	0.138834	−	0.106568i
$425$	24.1016	−	4.24977i	1.16910	−	0.206144i
$426$		0			0
$427$	−36.3944	+	13.2465i	−1.76125	+	0.641042i
$428$	6.43750	+	0.562487i	0.311168	+	0.0271888i
$429$		0			0
$430$	9.31031	+	10.1593i	0.448983	+	0.489924i
$431$	32.6219			1.57134			0.785671	−	0.618644i	$-0.212318\pi$
$431$	32.6219			1.57134			0.785671	+	0.618644i	$0.212318\pi$
$432$		0			0
$433$	−20.4173			−0.981192			−0.490596	−	0.871387i	$-0.663221\pi$
$433$	−20.4173			−0.981192			−0.490596	+	0.871387i	$0.663221\pi$
$434$	35.2790	+	38.4960i	1.69345	+	1.84787i
$435$		0			0
$436$	21.6551	+	1.89215i	1.03709	+	0.0906175i
$437$	1.85740	−	0.676039i	0.0888516	−	0.0323393i
$438$		0			0
$439$	5.01912	−	0.885007i	0.239550	−	0.0422391i	−0.0525843	−	0.998616i	$-0.516746\pi$
$439$	5.01912	−	0.885007i	0.239550	−	0.0422391i	0.292134	+	0.956377i	$0.405635\pi$
$440$	−4.89278	−	6.37419i	−0.233254	−	0.303878i
$441$		0			0
$442$	11.0915	+	5.77307i	0.527567	+	0.274597i
$443$	−6.33577	+	17.4074i	−0.301022	+	0.827050i	0.693301	+	0.720648i	$0.256155\pi$
$443$	−6.33577	+	17.4074i	−0.301022	+	0.827050i	−0.994323	+	0.106403i	$0.966067\pi$
$444$		0			0
$445$	15.0941	−	17.9885i	0.715529	−	0.852735i
$446$	21.0402	+	16.1428i	0.996280	+	0.764385i
$447$		0			0
$448$	3.23462	−	37.1144i	0.152821	−	1.75349i
$449$	−16.4019	−	9.46962i	−0.774052	−	0.446899i	0.0602665	−	0.998182i	$-0.480805\pi$
$449$	−16.4019	−	9.46962i	−0.774052	−	0.446899i	−0.834318	+	0.551283i	$0.814138\pi$
$450$		0			0
$451$	0.0239344	+	0.0414557i	0.00112703	+	0.00195207i
$452$	21.0075	−	5.63143i	0.988108	−	0.264880i
$453$		0			0
$454$	6.62101	−	2.74294i	0.310739	−	0.128733i
$455$	−4.91753	+	27.8887i	−0.230537	+	1.30744i
$456$		0			0
$457$	−8.02025	+	6.72979i	−0.375172	+	0.314806i	−0.810803	−	0.585319i	$-0.800969\pi$
$457$	−8.02025	+	6.72979i	−0.375172	+	0.314806i	0.435632	+	0.900125i	$0.356525\pi$
$458$	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	$-0.914489\pi$
$461$	−18.6832	+	15.6771i	−0.870163	+	0.730153i	0.0939698	+	0.995575i	$0.470044\pi$
$462$		0			0
$463$	15.5149	+	2.73570i	0.721039	+	0.127139i	0.522113	−	0.852876i	$-0.325144\pi$
$463$	15.5149	+	2.73570i	0.721039	+	0.127139i	0.198925	+	0.980015i	$0.436255\pi$
$464$	18.8516	−	10.8896i	0.875166	−	0.505537i
$465$		0			0
$466$	1.74539	+	7.87089i	0.0808538	+	0.364612i
$467$	6.64718	−	3.83775i	0.307595	−	0.177590i	−0.338255	−	0.941055i	$-0.609837\pi$
$467$	6.64718	−	3.83775i	0.307595	−	0.177590i	0.645850	+	0.763465i	$0.276503\pi$
$468$		0			0
$469$	−33.2309	−	19.1859i	−1.53446	−	0.885922i
$470$	−14.9129	+	47.3068i	−0.687880	+	2.18210i
$471$		0			0
$472$	−16.9781	−	10.8122i	−0.781479	−	0.497674i
$473$	−1.73499	+	2.06769i	−0.0797751	+	0.0950723i
$474$		0			0
$475$	−1.69260	−	0.616057i	−0.0776619	−	0.0282666i
$476$	−18.3236	+	39.3065i	−0.839860	+	1.80161i
$477$		0			0
$478$	−27.4705	+	17.5028i	−1.25647	+	0.800558i
$479$	5.41592	+	30.7152i	0.247460	+	1.40341i	0.814710	+	0.579869i	$0.196896\pi$
$479$	5.41592	+	30.7152i	0.247460	+	1.40341i	−0.567250	+	0.823545i	$0.691993\pi$
$480$		0			0
$481$	−4.77621	+	1.73840i	−0.217776	+	0.0792641i
$482$	−30.4138	−	4.00233i	−1.38531	−	0.182301i
$483$		0			0
$484$	−14.4418	+	14.4450i	−0.656445	+	0.656591i
$485$	−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	$0.895601\pi$
$488$	−15.8892	+	17.3459i	−0.719271	+	0.785210i
$489$		0			0
$490$	−65.9472	−	8.67839i	−2.97919	−	0.392050i
$491$	−0.483056	−	1.32718i	−0.0218000	−	0.0598950i	0.928315	−	0.371794i	$-0.121257\pi$
$491$	−0.483056	−	1.32718i	−0.0218000	−	0.0598950i	−0.950115	+	0.311899i	$0.899035\pi$
$492$		0			0
$493$	−24.9578	+	4.40073i	−1.12404	+	0.198199i
$494$	−0.494511	−	0.776131i	−0.0222491	−	0.0349198i
$495$		0			0
$496$	29.8042	+	10.8403i	1.33825	+	0.486745i
$497$	−0.595012	+	1.63478i	−0.0266899	+	0.0733300i
$498$		0			0
$499$	22.9472	+	19.2550i	1.02726	+	0.861971i	0.990522	−	0.137355i	$-0.0438600\pi$
$499$	22.9472	+	19.2550i	1.02726	+	0.861971i	0.0367345	+	0.999325i	$0.488304\pi$
$500$	1.34323	+	0.940317i	0.0600711	+	0.0420523i
$501$		0			0
$502$	−10.6957	−	3.37167i	−0.477370	−	0.150485i
$503$	4.40212	−	7.62469i	0.196281	−	0.339968i	−0.751039	−	0.660258i	$-0.770447\pi$
$503$	4.40212	−	7.62469i	0.196281	−	0.339968i	0.947320	+	0.320290i	$0.103780\pi$
$504$		0			0
$505$	10.0979	+	17.4901i	0.449351	+	0.778299i
$506$	−1.56656	−	7.06443i	−0.0696421	−	0.314052i
$507$		0			0
$508$	−11.9463	−	25.6114i	−0.530030	−	1.13632i
$509$	3.62638	−	20.5662i	0.160737	−	0.911582i	−0.792616	−	0.609722i	$-0.791281\pi$
$509$	3.62638	−	20.5662i	0.160737	−	0.911582i	0.953352	−	0.301860i	$-0.0976077\pi$
$510$		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
$518$	−6.74705	−	16.2863i	−0.296448	−	0.715577i
$519$		0			0
$520$	5.17485	+	16.4030i	0.226932	+	0.719318i
$521$	−18.8404	+	10.8775i	−0.825413	+	0.476552i	−0.852280	−	0.523087i	$-0.824780\pi$
$521$	−18.8404	+	10.8775i	−0.825413	+	0.476552i	0.0268665	+	0.999639i	$0.491447\pi$
$522$		0			0
$523$	2.21522	−	3.83687i	0.0968647	−	0.167775i	−0.813521	−	0.581536i	$-0.802452\pi$
$523$	2.21522	−	3.83687i	0.0968647	−	0.167775i	0.910385	+	0.413761i	$0.135785\pi$
$524$	−1.86833	+	6.97582i	−0.0816186	+	0.304740i
$525$		0			0
$526$	−4.76593	+	6.21179i	−0.207804	+	0.270847i
$527$	−28.2807	−	23.7303i	−1.23193	−	1.03371i
$528$		0			0
$529$	−9.64774	−	3.51149i	−0.419467	−	0.152673i
$530$	−5.11879	−	2.66431i	−0.222346	−	0.115730i
$531$		0			0
$532$	2.61439	−	1.83105i	0.113348	−	0.0793860i
$533$	−0.0177924	−	0.100906i	−0.000770676	−	0.00437072i
$534$		0			0
$535$	−3.53899	−	9.72329i	−0.153004	−	0.420375i
$536$	−23.2836	−	1.01270i	−1.00570	−	0.0437418i
$537$		0			0
$538$	5.34886	+	5.83661i	0.230606	+	0.251634i
$539$		−	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	$0.703831\pi$
$542$	−1.63226	+	1.49586i	−0.0701115	+	0.0642525i
$543$		0			0
$544$	1.15624	+	26.3146i	0.0495736	+	1.12823i
$545$	−11.9048	−	32.7082i	−0.509945	−	1.40106i
$546$		0			0
$547$	3.56925	+	20.2422i	0.152610	+	0.865496i	0.960938	+	0.276763i	$0.0892618\pi$
$547$	3.56925	+	20.2422i	0.152610	+	0.865496i	−0.808328	+	0.588733i	$0.799627\pi$
$548$	−21.5670	+	15.1049i	−0.921294	+	0.645250i
$549$		0			0
$550$	−3.04445	+	5.84913i	−0.129816	+	0.249408i
$551$	1.75273	+	0.637941i	0.0746687	+	0.0271772i
$552$		0			0
$553$	14.1249	+	11.8522i	0.600651	+	0.504006i
$554$	−31.4569	−	24.1349i	−1.33647	−	1.02540i
$555$		0			0
$556$	23.1697	+	6.20554i	0.982613	+	0.263173i
$557$	13.7564	−	23.8268i	0.582877	−	1.00957i	−0.412259	−	0.911067i	$-0.635260\pi$
$557$	13.7564	−	23.8268i	0.582877	−	1.00957i	0.995136	−	0.0985064i	$-0.0314065\pi$
$558$		0			0
$559$	5.00349	−	2.88877i	0.211625	−	0.122182i
$560$	−56.0525	+	20.4156i	−2.36865	+	0.862715i
$561$		0			0
$562$	11.7550	−	4.86985i	0.495856	−	0.205422i
$563$	28.2129	+	4.97470i	1.18903	+	0.209658i	0.732952	−	0.680280i	$-0.238142\pi$
$563$	28.2129	+	4.97470i	1.18903	+	0.209658i	0.456080	+	0.889939i	$0.349253\pi$
$564$		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	0.846297	−	0.532712i	$-0.178827\pi$
$569$	4.16772	+	4.96689i	0.174720	+	0.208223i	−0.671577	+	0.740935i	$0.734383\pi$
$570$		0			0
$571$	−4.13866	+	23.4715i	−0.173197	+	0.982252i	0.767006	+	0.641639i	$0.221745\pi$
$571$	−4.13866	+	23.4715i	−0.173197	+	0.982252i	−0.940204	+	0.340612i	$0.889366\pi$
$572$	−3.05320	+	1.42414i	−0.127661	+	0.0595465i
$573$		0			0
$574$	0.346944	−	0.0769360i	0.0144812	−	0.00321124i
$575$	15.1576	+	26.2538i	0.632117	+	1.09486i
$576$		0			0
$577$	9.82303	−	17.0140i	0.408938	−	0.708302i	−0.585833	−	0.810432i	$-0.699232\pi$
$577$	9.82303	−	17.0140i	0.408938	−	0.708302i	0.994771	+	0.102130i	$0.0325658\pi$
$578$	1.99032	−	6.31372i	0.0827865	−	0.262616i
$579$		0			0
$580$	−28.5583	−	19.9920i	−1.18582	−	0.830122i
$581$	−49.4491	−	41.4927i	−2.05149	−	1.72141i
$582$		0			0
$583$	0.386593	−	1.06215i	0.0160110	−	0.0439899i
$584$	32.9041	+	13.6229i	1.36158	+	0.563720i
$585$		0			0
$586$	21.3222	−	13.5854i	0.880812	−	0.561208i
$587$	0.851961	−	0.150224i	0.0351642	−	0.00620040i	−0.156038	−	0.987751i	$-0.549872\pi$
$587$	0.851961	−	0.150224i	0.0351642	−	0.00620040i	0.191203	+	0.981551i	$0.438761\pi$
$588$		0			0
$589$	0.929313	+	2.55327i	0.0382917	+	0.105206i
$590$	−4.20519	+	31.9553i	−0.173125	+	1.31558i
$591$		0			0
$592$	−8.20352	−	6.88046i	−0.337163	−	0.282785i
$593$		−	14.5405i		−	0.597108i	−0.954393	−	0.298554i	$-0.903496\pi$
$593$		−	14.5405i		−	0.597108i	0.954393	−	0.298554i	$-0.0965044\pi$
$594$		0			0
$595$	69.4424			2.84686
$596$	12.5215	−	12.5243i	0.512900	−	0.513014i
$597$		0			0
$598$	−2.02082	+	15.3562i	−0.0826375	+	0.627964i
$599$	−19.6014	+	7.13433i	−0.800892	+	0.291501i	−0.709856	−	0.704347i	$-0.751240\pi$
$599$	−19.6014	+	7.13433i	−0.800892	+	0.291501i	−0.0910360	+	0.995848i	$0.529018\pi$
$600$		0			0
$601$	−3.10434	−	17.6056i	−0.126629	−	0.718147i	−0.980327	−	0.197379i	$-0.936757\pi$
$601$	−3.10434	−	17.6056i	−0.126629	−	0.718147i	0.853699	−	0.520768i	$-0.174354\pi$
$602$	10.7675	+	16.8995i	0.438851	+	0.688774i
$603$		0			0
$604$	5.30991	+	2.47533i	0.216057	+	0.100720i
$605$	30.7347	+	11.1865i	1.24954	+	0.454797i
$606$		0			0
$607$	−11.4075	+	13.5950i	−0.463017	+	0.551803i	−0.946143	−	0.323748i	$-0.895057\pi$
$607$	−11.4075	+	13.5950i	−0.463017	+	0.551803i	0.483126	+	0.875551i	$0.339501\pi$
$608$	0.894670	−	1.71981i	0.0362837	−	0.0697476i
$609$		0			0
$610$	35.9240	+	11.3246i	1.45452	+	0.458519i
$611$	18.0101	+	10.3981i	0.728609	+	0.420662i
$612$		0			0
$613$	−6.61359	+	3.81836i	−0.267120	+	0.154222i	−0.627578	−	0.778554i	$-0.715954\pi$
$613$	−6.61359	+	3.81836i	−0.267120	+	0.154222i	0.360458	+	0.932775i	$0.382620\pi$
$614$	−7.36962	+	1.63424i	−0.297414	+	0.0659524i
$615$		0			0
$616$	−5.39716	−	10.3636i	−0.217458	−	0.417562i
$617$	−1.20638	−	0.212717i	−0.0485669	−	0.00856365i	0.149312	−	0.988790i	$-0.452294\pi$
$617$	−1.20638	−	0.212717i	−0.0485669	−	0.00856365i	−0.197879	+	0.980226i	$0.563405\pi$
$618$		0			0
$619$	−4.70712	+	3.94975i	−0.189195	+	0.158754i	−0.732465	−	0.680804i	$-0.761630\pi$
$619$	−4.70712	+	3.94975i	−0.189195	+	0.158754i	0.543270	+	0.839558i	$0.317186\pi$
$620$	−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
$626$	12.0602	+	29.1114i	0.482024	+	1.16353i
$627$		0			0
$628$	21.0903	−	5.65364i	0.841594	−	0.225605i
$629$	6.23183	+	10.7938i	0.248479	+	0.430379i
$630$		0			0
$631$	4.14675	+	2.39413i	0.165080	+	0.0953088i	0.580264	−	0.814429i	$-0.302949\pi$
$631$	4.14675	+	2.39413i	0.165080	+	0.0953088i	−0.415184	+	0.909737i	$0.636283\pi$
$632$	10.9340	+	2.42209i	0.434930	+	0.0963455i
$633$		0			0
$634$	13.6540	−	17.7962i	0.542268	−	0.706779i
$635$	−29.0875	+	34.6652i	−1.15430	+	1.37565i
$636$		0			0
$637$	−9.53816	+	26.2059i	−0.377916	+	1.03832i
$638$	3.15260	−	6.05691i	0.124813	−	0.239795i
$639$		0			0
$640$	−24.4677	+	26.7227i	−0.967170	+	1.05631i
$641$	−7.66053	+	1.35076i	−0.302573	+	0.0533517i	−0.322873	−	0.946442i	$-0.604649\pi$
$641$	−7.66053	+	1.35076i	−0.302573	+	0.0533517i	0.0203006	+	0.999794i	$0.493538\pi$
$642$		0			0
$643$	22.0412	−	8.02234i	0.869220	−	0.316370i	0.131369	−	0.991334i	$-0.458063\pi$
$643$	22.0412	−	8.02234i	0.869220	−	0.316370i	0.737851	+	0.674964i	$0.235841\pi$
$644$	−53.5156	−	4.67601i	−2.10881	−	0.184261i
$645$		0			0
$646$	−1.66371	+	1.52468i	−0.0654578	+	0.0599878i
$647$	−11.2669			−0.442948			−0.221474	−	0.975166i	$-0.571087\pi$
$647$	−11.2669			−0.442948			−0.221474	+	0.975166i	$0.571087\pi$
$648$		0			0
$649$	−6.31318			−0.247814
$650$	10.4057	−	9.53612i	0.408145	−	0.374038i
$651$		0			0
$652$	0.171206	−	1.95940i	0.00670495	−	0.0767361i
$653$	36.3675	−	13.2367i	1.42317	−	0.517991i	0.488203	−	0.872730i	$-0.337653\pi$
$653$	36.3675	−	13.2367i	1.42317	−	0.517991i	0.934965	+	0.354739i	$0.115430\pi$
$654$		0			0
$655$	11.3880	−	2.00802i	0.444968	−	0.0784598i
$656$	0.165313	−	0.138776i	0.00645438	−	0.00541831i
$657$		0			0
$658$	−33.3014	+	63.9800i	−1.29822	+	2.49420i
$659$	11.6740	−	32.0740i	0.454753	−	1.24942i	−0.474590	−	0.880207i	$-0.657404\pi$
$659$	11.6740	−	32.0740i	0.454753	−	1.24942i	0.929343	−	0.369217i	$-0.120374\pi$
$660$		0			0
$661$	32.5831	−	38.8310i	1.26734	−	1.51035i	0.505083	−	0.863071i	$-0.331462\pi$
$661$	32.5831	−	38.8310i	1.26734	−	1.51035i	0.762252	−	0.647281i	$-0.224094\pi$
$662$	24.3576	−	31.7471i	0.946685	−	1.23389i
$663$		0			0
$664$	−38.2782	−	8.47937i	−1.48548	−	0.329063i
$665$	−4.42618	−	2.55546i	−0.171640	−	0.0990964i
$666$		0			0
$667$	−15.6961	−	27.1864i	−0.607754	−	1.05266i
$668$	−0.828985	−	3.09244i	−0.0320744	−	0.119650i
$669$		0			0
$670$	14.2830	+	34.4767i	0.551799	+	1.33195i
$671$	−1.28116	+	7.26582i	−0.0494587	+	0.280494i
$672$		0			0
$673$	17.6716	−	14.8283i	0.681191	−	0.571587i	−0.235163	−	0.971956i	$-0.575562\pi$
$673$	17.6716	−	14.8283i	0.681191	−	0.571587i	0.916354	+	0.400369i	$0.131118\pi$
$674$	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	−0.241733	+	0.970343i	$0.577716\pi$
$677$	−32.2459	+	27.0575i	−1.23931	+	1.03991i	−0.997578	+	0.0695623i	$0.977840\pi$
$678$		0			0
$679$	−4.06720	−	0.717158i	−0.156085	−	0.0275220i
$680$	37.4081	−	19.4813i	1.43453	−	0.747075i
$681$		0			0
$682$	9.71108	−	2.15346i	0.371857	−	0.0824603i
$683$	−34.0757	+	19.6736i	−1.30387	+	0.752789i	−0.981065	−	0.193676i	$-0.937959\pi$
$683$	−34.0757	+	19.6736i	−1.30387	+	0.752789i	−0.322804	+	0.946466i	$0.604625\pi$
$684$		0			0
$685$	36.5130	+	21.0808i	1.39509	+	0.805456i
$686$	−48.2804	−	15.2198i	−1.84336	−	0.581095i
$687$		0			0
$688$	10.5414	+	6.08294i	0.401886	+	0.231910i
$689$	−1.55518	+	1.85340i	−0.0592478	+	0.0706087i
$690$		0			0
$691$	34.6497	+	12.6115i	1.31814	+	0.479762i	0.902861	−	0.429933i	$-0.141463\pi$
$691$	34.6497	+	12.6115i	1.31814	+	0.479762i	0.415276	+	0.909696i	$0.363685\pi$
$692$	11.9809	−	25.7005i	0.455444	−	0.976986i
$693$		0			0
$694$	−16.4424	−	25.8062i	−0.624145	−	0.979591i
$695$	−6.66949	−	37.8245i	−0.252988	−	1.43477i
$696$		0			0
$697$	−0.236102	+	0.0859340i	−0.00894299	+	0.00325498i
$698$	3.90672	−	29.6872i	0.147872	−	1.12368i
$699$		0			0
$700$	34.6189	+	34.6113i	1.30847	+	1.30818i
$701$	6.58502			0.248713			0.124356	−	0.992238i	$-0.460313\pi$
$701$	6.58502			0.248713			0.124356	+	0.992238i	$0.460313\pi$
$702$		0			0
$703$		−	0.917317i		−	0.0345973i
$704$	−5.81481	−	4.06869i	−0.219154	−	0.153344i
$705$		0			0
$706$	2.87988	−	21.8843i	0.108386	−	0.823625i
$707$	10.0443	+	27.5965i	0.377755	+	1.03787i
$708$		0			0
$709$	−11.2866	+	1.99013i	−0.423876	+	0.0747408i	−0.381517	−	0.924362i	$-0.624598\pi$
$709$	−11.2866	+	1.99013i	−0.423876	+	0.0747408i	−0.0423588	+	0.999102i	$0.513487\pi$
$710$	1.42691	−	0.909153i	0.0535510	−	0.0341199i
$711$		0			0
$712$	7.93343	−	19.1620i	0.297318	−	0.718127i
$713$	15.6406	−	42.9723i	0.585746	−	1.60932i
$714$		0			0
$715$	4.13252	+	3.46760i	0.154548	+	0.129681i
$716$	−6.98163	+	9.97316i	−0.260916	+	0.372715i
$717$		0			0
$718$	−2.07588	+	6.58513i	−0.0774712	+	0.245755i
$719$	−14.6250	+	25.3313i	−0.545421	+	0.944697i	0.453159	+	0.891430i	$0.350297\pi$
$719$	−14.6250	+	25.3313i	−0.545421	+	0.944697i	−0.998580	+	0.0532673i	$0.983036\pi$
$720$		0			0
$721$	20.3569	+	35.2591i	0.758129	+	1.31312i
$722$	−26.0707	+	5.78125i	−0.970249	+	0.215156i
$723$		0			0
$724$	−11.1348	−	23.8717i	−0.413820	−	0.887183i
$725$	−4.96752	+	28.1722i	−0.184489	+	1.04629i
$726$		0			0
$727$	−32.7533	−	39.0339i	−1.21475	−	1.44769i	−0.858125	−	0.513440i	$-0.828371\pi$
$727$	−32.7533	−	39.0339i	−1.21475	−	1.44769i	−0.356628	−	0.934246i	$-0.616074\pi$
$728$	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	$-0.429271\pi$
$733$	2.54100	+	0.448046i	0.0938538	+	0.0165490i	−0.126524	+	0.991964i	$0.540382\pi$
$734$	13.1497	−	5.44766i	0.485366	−	0.201077i
$735$		0			0
$736$	−30.1402	+	12.4943i	−1.11098	+	0.460546i
$737$	−6.33034	+	3.65482i	−0.233181	+	0.134627i
$738$		0			0
$739$	3.86165	−	6.68857i	0.142053	−	0.246043i	−0.786217	−	0.617951i	$-0.787963\pi$
$739$	3.86165	−	6.68857i	0.142053	−	0.246043i	0.928270	+	0.371908i	$0.121296\pi$
$740$	−4.43548	+	16.5608i	−0.163051	+	0.608787i
$741$		0			0
$742$	−6.65760	−	5.10797i	−0.244408	−	0.187519i
$743$	9.80501	+	8.22738i	0.359711	+	0.301833i	0.804676	−	0.593715i	$-0.202339\pi$
$743$	9.80501	+	8.22738i	0.359711	+	0.301833i	−0.444965	+	0.895548i	$0.646784\pi$
$744$		0			0
$745$	−26.6479	−	9.69906i	−0.976305	−	0.355346i
$746$	−0.976574	+	1.87624i	−0.0357549	+	0.0686939i
$747$		0			0
$748$	4.73926	+	6.76676i	0.173284	+	0.247417i
$749$	−2.61279	−	14.8179i	−0.0954693	−	0.541433i
$750$		0			0
$751$	−15.0834	−	41.4413i	−0.550401	−	1.51221i	−0.833165	−	0.553025i	$-0.813473\pi$
$751$	−15.0834	−	41.4413i	−0.550401	−	1.51221i	0.282763	−	0.959190i	$-0.408749\pi$
$752$	0.00973759	+	43.8079i	0.000355093	+	1.59751i
$753$		0			0
$754$	−10.7753	+	9.87487i	−0.392414	+	0.359622i
$755$		−	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	$-0.169316\pi$
$758$	−25.2281	−	27.5286i	−0.916326	−	0.999883i
$759$		0			0
$760$	−3.10126	−	0.134886i	−0.112494	−	0.00489282i
$761$	7.20399	+	19.7928i	0.261145	+	0.717489i	0.999091	+	0.0426294i	$0.0135735\pi$
$761$	7.20399	+	19.7928i	0.261145	+	0.717489i	−0.737946	+	0.674859i	$0.764204\pi$
$762$		0			0
$763$	−8.78916	−	49.8458i	−0.318189	−	1.80454i
$764$	−24.5309	−	35.0255i	−0.887498	−	1.26718i
$765$		0			0
$766$	−19.7128	−	10.2604i	−0.712251	−	0.370724i
$767$	12.6983	+	4.62181i	0.458509	+	0.166884i
$768$		0			0
$769$	−9.76794	−	8.19627i	−0.352241	−	0.295565i	0.449448	−	0.893306i	$-0.351621\pi$
$769$	−9.76794	−	8.19627i	−0.352241	−	0.295565i	−0.801689	+	0.597741i	$0.796065\pi$
$770$	−11.3893	+	14.8445i	−0.410440	+	0.534958i
$771$		0			0
$772$	40.5574	+	10.8625i	1.45969	+	0.390950i
$773$	−24.3894	+	42.2437i	−0.877226	+	1.51940i	−0.0228536	+	0.999739i	$0.507275\pi$
$773$	−24.3894	+	42.2437i	−0.877226	+	1.51940i	−0.854372	+	0.519661i	$0.826058\pi$
$774$		0			0
$775$	−36.0896	+	20.8363i	−1.29638	+	0.748463i
$776$	−2.39216	+	0.754684i	−0.0858736	+	0.0270916i
$777$		0			0
$778$	10.9561	+	26.4462i	0.392795	+	0.948142i
$779$	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	0.788532	+	0.614994i	$0.210841\pi$
$787$	−4.56672	+	25.8991i	−0.162786	+	0.923205i	−0.951318	+	0.308211i	$0.900270\pi$
$788$	−18.9692	+	8.84803i	−0.675749	+	0.315198i
$789$		0			0
$790$	−3.88226	−	17.5071i	−0.138125	−	0.622876i
$791$	−25.3209	−	43.8570i	−0.900306	−	1.55938i
$792$		0			0
$793$	7.89615	−	13.6765i	0.280401	−	0.485668i
$794$	−37.1728	−	11.7183i	−1.31921	−	0.415865i
$795$		0			0
$796$	−19.0297	+	27.1837i	−0.674491	+	0.963501i
$797$	27.3124	+	22.9179i	0.967456	+	0.811792i	0.982150	−	0.188100i	$-0.0602328\pi$
$797$	27.3124	+	22.9179i	0.967456	+	0.811792i	−0.0146935	+	0.999892i	$0.504677\pi$
$798$		0			0
$799$	17.4415	−	47.9201i	0.617036	−	1.69529i
$800$	28.3588	+	8.93283i	1.00263	+	0.315823i
$801$		0			0
$802$	−5.15743	−	8.09456i	−0.182115	−	0.285829i
$803$	11.0000	−	1.93959i	0.388180	−	0.0684467i
$804$		0			0
$805$	29.4200	+	80.8307i	1.03692	+	2.84891i
$806$	−21.1094	−	2.77791i	−0.743546	−	0.0978477i
$807$		0			0
$808$	13.1527	+	12.0482i	0.462710	+	0.423854i
$809$		−	41.4917i		−	1.45877i	−0.684103	−	0.729385i	$-0.739806\pi$
$809$		−	41.4917i		−	1.45877i	0.684103	−	0.729385i	$-0.260194\pi$
$810$		0			0
$811$	29.0442			1.01988			0.509940	−	0.860210i	$-0.329667\pi$
$811$	29.0442			1.01988			0.509940	+	0.860210i	$0.329667\pi$
$812$	−35.8487	−	35.8407i	−1.25804	−	1.25776i
$813$		0			0
$814$	−3.32945	−	0.438142i	−0.116697	−	0.0153569i
$815$	−2.95951	+	1.07717i	−0.103667	+	0.0377318i
$816$		0			0
$817$	0.181065	+	1.02687i	0.00633467	+	0.0359257i
$818$	20.4181	−	13.0094i	0.713902	−	0.454862i
$819$		0			0
$820$	−0.313249	−	0.146028i	−0.0109391	−	0.00509953i
$821$	47.7187	+	17.3682i	1.66539	+	0.606153i	0.991197	−	0.132399i	$-0.0422679\pi$
$821$	47.7187	+	17.3682i	1.66539	+	0.606153i	0.674196	+	0.738552i	$0.264490\pi$
$822$		0			0
$823$	−10.2372	+	12.2002i	−0.356847	+	0.425274i	−0.914365	−	0.404891i	$-0.867309\pi$
$823$	−10.2372	+	12.2002i	−0.356847	+	0.425274i	0.557518	+	0.830165i	$0.311754\pi$
$824$	20.8577	+	13.2829i	0.726611	+	0.462732i
$825$		0			0
$826$	−14.0911	+	44.6998i	−0.490291	+	1.55530i
$827$	−26.8166	−	15.4826i	−0.932504	−	0.538381i	−0.0449012	−	0.998991i	$-0.514297\pi$
$827$	−26.8166	−	15.4826i	−0.932504	−	0.538381i	−0.887603	+	0.460610i	$0.847631\pi$
$828$		0			0
$829$	−5.02207	+	2.89949i	−0.174424	+	0.100704i	−0.584670	−	0.811271i	$-0.698776\pi$
$829$	−5.02207	+	2.89949i	−0.174424	+	0.100704i	0.410246	+	0.911975i	$0.365443\pi$
$830$	13.5912	+	61.2898i	0.471758	+	2.12740i
$831$		0			0
$832$	8.71726	+	12.4407i	0.302217	+	0.431304i
$833$	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	$-0.635781\pi$
$839$	11.9037	−	9.98841i	0.410962	−	0.344838i	0.824712	+	0.565552i	$0.191337\pi$
$840$		0			0
$841$	0.108181	−	0.613526i	0.00373038	−	0.0211561i
$842$	−17.6325	+	7.30477i	−0.607656	+	0.251739i
$843$		0			0
$844$	−4.83041	−	18.0193i	−0.166269	−	0.620250i
$845$	15.0427	+	26.0547i	0.517484	+	0.896309i
$846$		0			0
$847$	41.1889	+	23.7804i	1.41527	+	0.817106i
$848$	−5.01938	−	0.883902i	−0.172366	−	0.0303533i
$849$		0			0
$850$	−27.4597	−	21.0681i	−0.941859	−	0.722631i
$851$	−9.92382	+	11.8268i	−0.340184	+	0.405416i
$852$		0			0
$853$	5.27000	−	14.4792i	0.180441	−	0.495758i	−0.816189	−	0.577785i	$-0.803917\pi$
$853$	5.27000	−	14.4792i	0.180441	−	0.495758i	0.996630	+	0.0820269i	$0.0261393\pi$
$854$	48.5854	+	25.2885i	1.66256	+	0.865355i
$855$		0			0
$856$	−5.56449	−	7.24928i	−0.190190	−	0.247775i
$857$	43.4090	−	7.65418i	1.48282	−	0.261462i	0.627118	−	0.778924i	$-0.284234\pi$
$857$	43.4090	−	7.65418i	1.48282	−	0.261462i	0.855706	+	0.517463i	$0.173123\pi$
$858$		0			0
$859$	49.6251	−	18.0621i	1.69319	−	0.616270i	0.698166	−	0.715936i	$-0.254000\pi$
$859$	49.6251	−	18.0621i	1.69319	−	0.616270i	0.995021	+	0.0996665i	$0.0317776\pi$
$860$	1.69634	−	19.4141i	0.0578448	−	0.662016i
$861$		0			0
$862$	−31.1698	−	34.0121i	−1.06165	−	1.15846i
$863$	−51.1622			−1.74158			−0.870791	−	0.491653i	$-0.836393\pi$
$863$	−51.1622			−1.74158			−0.870791	+	0.491653i	$0.836393\pi$
$864$		0			0
$865$	−45.4048			−1.54381
$866$	19.5085	+	21.2874i	0.662924	+	0.723374i
$867$		0			0
$868$	6.42785	−	73.5649i	0.218176	−	2.49695i
$869$	3.30066	−	1.20134i	0.111967	−	0.0407527i
$870$		0			0
$871$	15.4085	−	2.71693i	0.522097	−	0.0920597i
$872$	−18.7184	−	24.3858i	−0.633884	−	0.825808i
$873$		0			0
$874$	−2.47957	−	1.29061i	−0.0838728	−	0.0436555i
$875$	1.30578	−	3.58759i	0.0441433	−	0.121283i
$876$		0			0
$877$	−21.3535	+	25.4481i	−0.721055	+	0.859320i	−0.994733	−	0.102501i	$-0.967315\pi$
$877$	−21.3535	+	25.4481i	−0.721055	+	0.859320i	0.273678	+	0.961822i	$0.411760\pi$
$878$	−5.71843	−	4.38740i	−0.192988	−	0.148067i
$879$		0			0
$880$	−1.97084	+	11.1917i	−0.0664370	+	0.377273i
$881$	24.0135	+	13.8642i	0.809034	+	0.467096i	0.846620	−	0.532197i	$-0.178634\pi$
$881$	24.0135	+	13.8642i	0.809034	+	0.467096i	−0.0375862	+	0.999293i	$0.511967\pi$
$882$		0			0
$883$	7.38127	+	12.7847i	0.248400	+	0.430241i	0.963082	−	0.269208i	$-0.0867621\pi$
$883$	7.38127	+	12.7847i	0.248400	+	0.430241i	−0.714682	+	0.699449i	$0.753429\pi$
$884$	−4.57866	−	17.0802i	−0.153997	−	0.574470i
$885$		0			0
$886$	24.2029	−	10.0268i	0.813114	−	0.336856i
$887$	3.08832	−	17.5147i	0.103695	−	0.588086i	−0.888038	−	0.459770i	$-0.847932\pi$
$887$	3.08832	−	17.5147i	0.103695	−	0.588086i	0.991733	−	0.128316i	$-0.0409572\pi$
$888$		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
$896$	−41.7866	+	32.0899i	−1.39599	+	1.07205i
$897$		0			0
$898$	5.79860	+	26.1489i	0.193502	+	0.872600i
$899$	37.3716	−	21.5765i	1.24641	−	0.719616i
$900$		0			0
$901$	5.13798	+	2.96642i	0.171171	+	0.0988256i
$902$	0.0203532	−	0.0645647i	0.000677689	−	0.00214977i
$903$		0			0
$904$	−25.9438	−	16.5219i	−0.862877	−	0.549511i
$905$	−27.1116	+	32.3104i	−0.901221	+	1.07403i
$906$		0			0
$907$	−33.8368	−	12.3156i	−1.12353	−	0.408932i	−0.287591	−	0.957753i	$-0.592854\pi$
$907$	−33.8368	−	12.3156i	−1.12353	−	0.408932i	−0.835940	+	0.548821i	$0.815077\pi$
$908$	−9.18612	−	4.28232i	−0.304852	−	0.142114i
$909$		0			0
$910$	33.7758	−	21.5202i	1.11966	−	0.713387i
$911$	−0.0484884	−	0.274992i	−0.00160649	−	0.00911088i	0.983994	−	0.178202i	$-0.0570280\pi$
$911$	−0.0484884	−	0.274992i	−0.00160649	−	0.00911088i	−0.985600	+	0.169091i	$0.945917\pi$
$912$		0			0
$913$	−11.5551	+	4.20572i	−0.382418	+	0.139189i
$914$	14.6798	+	1.93181i	0.485565	+	0.0638985i
$915$		0			0
$916$	−31.8845	−	31.8774i	−1.05349	−	1.05326i
$917$	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	$0.895642\pi$
$920$	38.5245	+	35.2894i	1.27012	+	1.16346i
$921$		0			0
$922$	34.1967	+	4.50014i	1.12621	+	0.148204i
$923$	−0.242618	−	0.666587i	−0.00798586	−	0.0219410i
$924$		0			0
$925$	13.8552	−	2.44304i	0.455555	−	0.0803267i
$926$	−11.9720	−	18.7900i	−0.393425	−	0.617477i
$927$		0			0
$928$	−29.3661	−	9.25014i	−0.963991	−	0.303651i
$929$	12.7507	−	35.0323i	0.418338	−	1.14937i	−0.534308	−	0.845290i	$-0.679428\pi$
$929$	12.7507	−	35.0323i	0.418338	−	1.14937i	0.952645	−	0.304083i	$-0.0983502\pi$
$930$		0			0
$931$	−3.85557	−	3.23521i	−0.126361	−	0.106030i
$932$	6.53860	−	9.34030i	0.214179	−	0.305952i
$933$		0			0
$934$	−10.3526	−	3.26353i	−0.338747	−	0.106786i
$935$	6.61423	−	11.4562i	0.216308	−	0.374657i
$936$		0			0
$937$	−1.65449	−	2.86566i	−0.0540499	−	0.0936171i	0.837735	−	0.546078i	$-0.183880\pi$
$937$	−1.65449	−	2.86566i	−0.0540499	−	0.0936171i	−0.891784	+	0.452461i	$0.850546\pi$
$938$	11.7482	+	52.9789i	0.383593	+	1.72982i
$939$		0			0
$940$	63.5718	−	29.6526i	2.07348	−	0.967161i
$941$	8.25196	−	46.7992i	0.269006	−	1.52561i	−0.488373	−	0.872635i	$-0.662409\pi$
$941$	8.25196	−	46.7992i	0.269006	−	1.52561i	0.757379	−	0.652975i	$-0.226479\pi$
$942$		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	0.445863	−	0.895101i	$-0.352897\pi$
$947$	−15.7887	−	18.8162i	−0.513063	−	0.611444i	−0.958926	+	0.283657i	$0.908452\pi$
$948$		0			0
$949$	−23.5453	−	4.15167i	−0.764312	−	0.134769i
$950$	0.974949	+	2.35337i	0.0316315	+	0.0763533i
$951$		0			0
$952$	58.4894	−	18.4524i	1.89565	−	0.598045i
$953$	5.53399	−	3.19505i	0.179264	−	0.103498i	−0.407683	−	0.913124i	$-0.633663\pi$
$953$	5.53399	−	3.19505i	0.179264	−	0.103498i	0.586947	+	0.809626i	$0.300330\pi$
$954$		0			0
$955$	−34.2360	+	59.2984i	−1.10785	+	1.91885i
$956$	44.4963	+	11.9174i	1.43911	+	0.385438i
$957$		0			0
$958$	26.8493	−	34.9947i	0.867461	−	1.13063i
$959$	46.9654	+	39.4086i	1.51659	+	1.27257i
$960$		0			0
$961$	29.9411	+	10.8977i	0.965843	+	0.351538i
$962$	6.37608	+	3.31873i	0.205573	+	0.107000i
$963$		0			0
$964$	24.8871	+	35.5340i	0.801559	+	1.14447i
$965$	−11.6746	−	66.2101i	−0.375819	−	2.13138i
$966$		0			0
$967$	−7.29798	−	20.0510i	−0.234687	−	0.644798i	−0.999999	−	0.00113855i	$-0.999638\pi$
$967$	−7.29798	−	20.0510i	−0.234687	−	0.644798i	0.765312	−	0.643659i	$-0.222585\pi$
$968$	28.8595	+	1.25521i	0.927580	+	0.0403441i
$969$		0			0
$970$	2.71370	+	2.96116i	0.0871318	+	0.0950771i
$971$			18.8858i			0.606074i	0.952979	+	0.303037i	$0.0980006\pi$
$971$			18.8858i			0.606074i	−0.952979	+	0.303037i	$0.901999\pi$
$972$		0			0
$973$		−	55.8507i		−	1.79049i
$974$	14.8235	−	13.5848i	0.474976	−	0.435284i
$975$		0			0
$976$	33.2670	−	0.00739456i	1.06485	−	0.000236694i
$977$	12.8528	+	35.3129i	0.411199	+	1.12976i	0.956554	+	0.291555i	$0.0941726\pi$
$977$	12.8528	+	35.3129i	0.411199	+	1.12976i	−0.545355	+	0.838205i	$0.683605\pi$
$978$		0			0
$979$	−1.12954	−	6.40593i	−0.0361002	−	0.204735i
$980$	53.9635	+	77.0496i	1.72380	+	2.46126i
$981$		0			0
$982$	−0.922188	+	1.77175i	−0.0294282	+	0.0565387i
$983$	0.0615360	+	0.0223973i	0.00196269	+	0.000714362i	0.343001	−	0.939335i	$-0.388556\pi$
$983$	0.0615360	+	0.0223973i	0.00196269	+	0.000714362i	−0.341039	+	0.940049i	$0.610779\pi$
$984$		0			0
$985$	25.6749	+	21.5438i	0.818069	+	0.686441i
$986$	28.4351	+	21.8165i	0.905558	+	0.694779i
$987$		0			0
$988$	−0.336707	+	1.25717i	−0.0107121	+	0.0399958i
$989$	8.77459	−	15.1980i	0.279016	−	0.483269i
$990$		0			0
$991$	2.32285	−	1.34110i	0.0737876	−	0.0426013i	−0.462652	−	0.886540i	$-0.653102\pi$
$991$	2.32285	−	1.34110i	0.0737876	−	0.0426013i	0.536440	+	0.843939i	$0.319769\pi$
$992$	−17.1752	−	41.4321i	−0.545314	−	1.31547i
$993$		0			0
$994$	2.27297	−	0.941645i	0.0720944	−	0.0298672i
$995$	52.3264	+	9.22655i	1.65886	+	0.292501i
$996$		0			0
$997$	6.81445	+	8.12114i	0.215816	+	0.257199i	0.863081	−	0.505066i	$-0.168532\pi$
$997$	6.81445	+	8.12114i	0.215816	+	0.257199i	−0.647265	+	0.762265i	$0.724087\pi$
$998$	−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.611.8		192
3.2	odd	2		216.2.v.b.59.25	yes	192
8.3	odd	2	inner	648.2.v.b.611.9		192
12.11	even	2		864.2.bh.b.815.3		192
24.5	odd	2		864.2.bh.b.815.4		192
24.11	even	2		216.2.v.b.59.24	yes	192
27.11	odd	18	inner	648.2.v.b.35.9		192
27.16	even	9		216.2.v.b.11.24	✓	192
108.43	odd	18		864.2.bh.b.335.4		192
216.11	even	18	inner	648.2.v.b.35.8		192
216.43	odd	18		216.2.v.b.11.25	yes	192
216.205	even	18		864.2.bh.b.335.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.24	✓	192	27.16	even	9
216.2.v.b.11.25	yes	192	216.43	odd	18
216.2.v.b.59.24	yes	192	24.11	even	2
216.2.v.b.59.25	yes	192	3.2	odd	2
648.2.v.b.35.8		192	216.11	even	18	inner
648.2.v.b.35.9		192	27.11	odd	18	inner
648.2.v.b.611.8		192	1.1	even	1	trivial
648.2.v.b.611.9		192	8.3	odd	2	inner
864.2.bh.b.335.3		192	216.205	even	18
864.2.bh.b.335.4		192	108.43	odd	18
864.2.bh.b.815.3		192	12.11	even	2
864.2.bh.b.815.4		192	24.5	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.955487 - 1.04261i) q^{2} +(-0.174090 + 1.99241i) q^{4} +(3.00936 - 1.09532i) q^{5} +(4.58614 - 0.808660i) q^{7} +(2.24366 - 1.72221i) q^{8} +(-4.01740 - 2.09104i) q^{10} +(0.303411 - 0.833616i) q^{11} +(-1.22056 + 1.45461i) q^{13} +(-5.22511 - 4.00891i) q^{14} +(-3.93939 - 0.693717i) q^{16} +(4.03247 + 2.32815i) q^{17} +(-0.171350 - 0.296787i) q^{19} +(1.65842 + 6.18657i) q^{20} +(-1.15905 + 0.480168i) q^{22} +(-1.00156 + 5.68012i) q^{23} +(4.02633 - 3.37849i) q^{25} +(2.68283 - 0.117284i) q^{26} +(0.812780 + 9.27824i) q^{28} +(-4.16935 + 3.49850i) q^{29} +(-7.80815 - 1.37679i) q^{31} +(3.04075 + 4.77010i) q^{32} +(-1.42561 - 6.42882i) q^{34} +(12.9156 - 7.45683i) q^{35} +(2.31812 + 1.33837i) q^{37} +(-0.145712 + 0.462228i) q^{38} +(4.86560 - 7.64028i) q^{40} +(-0.0346849 + 0.0413359i) q^{41} +(-2.85915 - 1.04064i) q^{43} +(1.60808 + 0.749643i) q^{44} +(6.87915 - 4.38304i) q^{46} +(-1.90179 - 10.7856i) q^{47} +(13.8009 - 5.02311i) q^{49} +(-7.36956 - 0.969805i) q^{50} +(-2.68569 - 2.68509i) q^{52} +1.27415 q^{53} -2.84099i q^{55} +(8.89703 - 9.71265i) q^{56} +(7.63135 + 1.00425i) q^{58} +(-2.43399 - 6.68734i) q^{59} +(-8.19039 + 1.44419i) q^{61} +(6.02512 + 9.45639i) q^{62} +(2.06798 - 7.72810i) q^{64} +(-2.07985 + 5.71435i) q^{65} +(-6.31205 - 5.29644i) q^{67} +(-5.34063 + 7.62901i) q^{68} +(-20.1153 - 6.34110i) q^{70} +(-0.186788 + 0.323526i) q^{71} +(6.29550 + 10.9041i) q^{73} +(-0.819532 - 3.69570i) q^{74} +(0.621151 - 0.289732i) q^{76} +(0.717374 - 4.06843i) q^{77} +(2.54509 + 3.03312i) q^{79} +(-12.6149 + 2.22724i) q^{80} +(0.0762384 - 0.00333288i) q^{82} +(-8.90996 - 10.6185i) q^{83} +(14.6852 + 2.58940i) q^{85} +(1.64689 + 3.97531i) q^{86} +(-0.754912 - 2.39288i) q^{88} +(6.35012 - 3.66624i) q^{89} +(-4.42138 + 7.65805i) q^{91} +(-11.1428 - 2.98437i) q^{92} +(-9.42807 + 12.2883i) q^{94} +(-0.840731 - 0.705457i) q^{95} +(-0.833364 - 0.303320i) q^{97} +(-18.4237 - 9.58948i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40}+ \cdots - 162 q^{98}+O(q^{100}) \) 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

L-functions

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