LMFDB - Embedded newform 297.2.f.a.82.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 8 x^{14} - 22 x^{13} + 62 x^{12} - 24 x^{11} + 152 x^{10} - 161 x^{9} + 552 x^{8} + \cdots + 25 $ x^16 - 2x^15 + 8x^14 - 22x^13 + 62x^12 - 24x^11 + 152x^10 - 161x^9 + 552x^8 - 609x^7 + 1150x^6 - 862x^5 + 1346x^4 - 235x^3 + 340x^2 + 150*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.3
Root			$0.231171 - 0.711471i$ of defining polynomial
Character	$\chi$	$=$	297.82
Dual form			297.2.f.a.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540188 + 1.66253i) q^{2} +(-0.854162 + 0.620585i) q^{4} +(1.19305 - 3.67184i) q^{5} +(-0.710219 + 0.516004i) q^{7} +(1.33531 + 0.970162i) q^{8} +O(q^{10})$	\(q+(0.540188 + 1.66253i) q^{2} +(-0.854162 + 0.620585i) q^{4} +(1.19305 - 3.67184i) q^{5} +(-0.710219 + 0.516004i) q^{7} +(1.33531 + 0.970162i) q^{8} +6.74902 q^{10} +(1.60148 - 2.90435i) q^{11} +(1.15295 + 3.54840i) q^{13} +(-1.24152 - 0.902019i) q^{14} +(-1.54412 + 4.75232i) q^{16} +(0.595090 - 1.83150i) q^{17} +(2.27654 + 1.65401i) q^{19} +(1.25963 + 3.87674i) q^{20} +(5.69367 + 1.09360i) q^{22} +0.221568 q^{23} +(-8.01398 - 5.82250i) q^{25} +(-5.27651 + 3.83361i) q^{26} +(0.286418 - 0.881503i) q^{28} +(-6.81303 + 4.94996i) q^{29} +(-1.95486 - 6.01645i) q^{31} -5.43391 q^{32} +3.36638 q^{34} +(1.04736 + 3.22343i) q^{35} +(-8.84860 + 6.42888i) q^{37} +(-1.52007 + 4.67829i) q^{38} +(5.15538 - 3.74561i) q^{40} +(-4.47217 - 3.24922i) q^{41} +4.57724 q^{43} +(0.434478 + 3.47464i) q^{44} +(0.119688 + 0.368363i) q^{46} +(9.12925 + 6.63279i) q^{47} +(-1.92497 + 5.92444i) q^{49} +(5.35101 - 16.4687i) q^{50} +(-3.18689 - 2.31541i) q^{52} +(-3.19914 - 9.84594i) q^{53} +(-8.75369 - 9.34543i) q^{55} -1.44897 q^{56} +(-11.9098 - 8.65295i) q^{58} +(-1.88586 + 1.37016i) q^{59} +(2.03196 - 6.25374i) q^{61} +(8.94652 - 6.50002i) q^{62} +(0.152913 + 0.470618i) q^{64} +14.4047 q^{65} +3.06382 q^{67} +(0.628297 + 1.93370i) q^{68} +(-4.79328 + 3.48252i) q^{70} +(0.354219 - 1.09017i) q^{71} +(-0.953826 + 0.692995i) q^{73} +(-15.4681 - 11.2382i) q^{74} -2.97099 q^{76} +(0.361260 + 2.88910i) q^{77} +(3.43768 + 10.5801i) q^{79} +(15.6076 + 11.3396i) q^{80} +(2.98611 - 9.19029i) q^{82} +(-1.55442 + 4.78403i) q^{83} +(-6.01500 - 4.37015i) q^{85} +(2.47257 + 7.60979i) q^{86} +(4.95617 - 2.32453i) q^{88} -9.74600 q^{89} +(-2.64984 - 1.92522i) q^{91} +(-0.189255 + 0.137502i) q^{92} +(-6.09568 + 18.7606i) q^{94} +(8.78930 - 6.38580i) q^{95} +(-0.125760 - 0.387049i) q^{97} -10.8894 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7	$ 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7} + 6 q^{10} - 13 q^{11} - 2 q^{13} + 22 q^{14} - 24 q^{16} + 2 q^{17} - 2 q^{19} + 15 q^{22} - 14 q^{23} - 19 q^{25} - 21 q^{26} + 15 q^{28} - q^{29} + 14 q^{31} + 48 q^{32} + 10 q^{34} + 18 q^{35} + 9 q^{37} - 11 q^{38} + 33 q^{40} - 25 q^{41} + 14 q^{43} - 14 q^{44} + 4 q^{46} + 28 q^{47} - 4 q^{49} + 63 q^{50} + 10 q^{52} - q^{53} - 40 q^{55} - 96 q^{56} - 20 q^{58} - 41 q^{59} + 5 q^{62} - 92 q^{64} + 60 q^{65} - 48 q^{67} - 25 q^{68} - 31 q^{70} - 3 q^{71} - 13 q^{73} - 29 q^{74} - 58 q^{76} + 2 q^{77} + 83 q^{80} + 41 q^{82} + 14 q^{83} - 10 q^{85} + 56 q^{86} + 86 q^{88} - 82 q^{89} + 14 q^{91} - 74 q^{92} - 2 q^{94} + 56 q^{95} + 12 q^{97} - 26 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7 + 6 * q^10 - 13 * q^11 - 2 * q^13 + 22 * q^14 - 24 * q^16 + 2 * q^17 - 2 * q^19 + 15 * q^22 - 14 * q^23 - 19 * q^25 - 21 * q^26 + 15 * q^28 - q^29 + 14 * q^31 + 48 * q^32 + 10 * q^34 + 18 * q^35 + 9 * q^37 - 11 * q^38 + 33 * q^40 - 25 * q^41 + 14 * q^43 - 14 * q^44 + 4 * q^46 + 28 * q^47 - 4 * q^49 + 63 * q^50 + 10 * q^52 - q^53 - 40 * q^55 - 96 * q^56 - 20 * q^58 - 41 * q^59 + 5 * q^62 - 92 * q^64 + 60 * q^65 - 48 * q^67 - 25 * q^68 - 31 * q^70 - 3 * q^71 - 13 * q^73 - 29 * q^74 - 58 * q^76 + 2 * q^77 + 83 * q^80 + 41 * q^82 + 14 * q^83 - 10 * q^85 + 56 * q^86 + 86 * q^88 - 82 * q^89 + 14 * q^91 - 74 * q^92 - 2 * q^94 + 56 * q^95 + 12 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.540188	+	1.66253i	0.381971	+	1.17558i	0.938654	+	0.344860i	$0.112074\pi$
$2$	0.540188	+	1.66253i	0.381971	+	1.17558i	−0.556683	+	0.830725i	$0.687926\pi$
$3$		0			0
$3$		0			0
$4$	−0.854162	+	0.620585i	−0.427081	+	0.310293i
$5$	1.19305	−	3.67184i	0.533550	−	1.64210i	−0.213211	−	0.977006i	$-0.568392\pi$
$5$	1.19305	−	3.67184i	0.533550	−	1.64210i	0.746761	−	0.665093i	$-0.231608\pi$
$6$		0			0
$7$	−0.710219	+	0.516004i	−0.268437	+	0.195031i	−0.713858	−	0.700290i	$-0.753054\pi$
$7$	−0.710219	+	0.516004i	−0.268437	+	0.195031i	0.445421	+	0.895321i	$0.353054\pi$
$8$	1.33531	+	0.970162i	0.472104	+	0.343004i
$9$		0			0
$10$	6.74902			2.13423
$11$	1.60148	−	2.90435i	0.482863	−	0.875696i
$11$	1.60148	−	2.90435i	0.482863	−	0.875696i
$12$		0			0
$13$	1.15295	+	3.54840i	0.319770	+	0.984150i	0.973746	+	0.227635i	$0.0730994\pi$
$13$	1.15295	+	3.54840i	0.319770	+	0.984150i	−0.653977	+	0.756515i	$0.726901\pi$
$14$	−1.24152	−	0.902019i	−0.331811	−	0.241075i
$15$		0			0
$16$	−1.54412	+	4.75232i	−0.386031	+	1.18808i
$17$	0.595090	−	1.83150i	0.144330	−	0.444204i	−0.852594	−	0.522574i	$-0.824972\pi$
$17$	0.595090	−	1.83150i	0.144330	−	0.444204i	0.996924	+	0.0783707i	$0.0249718\pi$
$18$		0			0
$19$	2.27654	+	1.65401i	0.522275	+	0.379455i	0.817460	−	0.575985i	$-0.195381\pi$
$19$	2.27654	+	1.65401i	0.522275	+	0.379455i	−0.295185	+	0.955440i	$0.595381\pi$
$20$	1.25963	+	3.87674i	0.281662	+	0.866866i
$21$		0			0
$22$	5.69367	+	1.09360i	1.21389	+	0.233157i
$23$	0.221568			0.0462001			0.0231001	−	0.999733i	$-0.492646\pi$
$23$	0.221568			0.0462001			0.0231001	+	0.999733i	$0.492646\pi$
$24$		0			0
$25$	−8.01398	−	5.82250i	−1.60280	−	1.16450i
$26$	−5.27651	+	3.83361i	−1.03481	+	0.751833i
$27$		0			0
$28$	0.286418	−	0.881503i	0.0541278	−	0.166588i
$29$	−6.81303	+	4.94996i	−1.26515	+	0.919184i	−0.998998	−	0.0447479i	$-0.985752\pi$
$29$	−6.81303	+	4.94996i	−1.26515	+	0.919184i	−0.266150	+	0.963932i	$0.585752\pi$
$30$		0			0
$31$	−1.95486	−	6.01645i	−0.351104	−	1.08059i	−0.958234	−	0.285984i	$-0.907680\pi$
$31$	−1.95486	−	6.01645i	−0.351104	−	1.08059i	0.607131	−	0.794602i	$-0.292320\pi$
$32$	−5.43391			−0.960588
$33$		0			0
$34$	3.36638			0.577329
$35$	1.04736	+	3.22343i	0.177036	+	0.544860i
$36$		0			0
$37$	−8.84860	+	6.42888i	−1.45470	+	1.05690i	−0.469997	+	0.882668i	$0.655745\pi$
$37$	−8.84860	+	6.42888i	−1.45470	+	1.05690i	−0.984704	+	0.174234i	$0.944255\pi$
$38$	−1.52007	+	4.67829i	−0.246588	+	0.758919i
$39$		0			0
$40$	5.15538	−	3.74561i	0.815138	−	0.592232i
$41$	−4.47217	−	3.24922i	−0.698435	−	0.507443i	0.180987	−	0.983485i	$-0.442071\pi$
$41$	−4.47217	−	3.24922i	−0.698435	−	0.507443i	−0.879422	+	0.476043i	$0.842071\pi$
$42$		0			0
$43$	4.57724			0.698023			0.349011	−	0.937118i	$-0.386517\pi$
$43$	4.57724			0.698023			0.349011	+	0.937118i	$0.386517\pi$
$44$	0.434478	+	3.47464i	0.0655000	+	0.523822i
$45$		0			0
$46$	0.119688	+	0.368363i	0.0176471	+	0.0543122i
$47$	9.12925	+	6.63279i	1.33164	+	0.967492i	0.999707	+	0.0241878i	$0.00769996\pi$
$47$	9.12925	+	6.63279i	1.33164	+	0.967492i	0.331931	+	0.943304i	$0.392300\pi$
$48$		0			0
$49$	−1.92497	+	5.92444i	−0.274995	+	0.846349i
$50$	5.35101	−	16.4687i	0.756747	−	2.32903i
$51$		0			0
$52$	−3.18689	−	2.31541i	−0.441942	−	0.321090i
$53$	−3.19914	−	9.84594i	−0.439436	−	1.35244i	−0.888472	−	0.458931i	$-0.848233\pi$
$53$	−3.19914	−	9.84594i	−0.439436	−	1.35244i	0.449036	−	0.893514i	$-0.351767\pi$
$54$		0			0
$55$	−8.75369	−	9.34543i	−1.18035	−	1.26014i
$56$	−1.44897			−0.193627
$57$		0			0
$58$	−11.9098	−	8.65295i	−1.56383	−	1.13619i
$59$	−1.88586	+	1.37016i	−0.245519	+	0.178380i	−0.703738	−	0.710459i	$-0.748487\pi$
$59$	−1.88586	+	1.37016i	−0.245519	+	0.178380i	0.458220	+	0.888839i	$0.348487\pi$
$60$		0			0
$61$	2.03196	−	6.25374i	0.260166	−	0.800710i	−0.732601	−	0.680658i	$-0.761694\pi$
$61$	2.03196	−	6.25374i	0.260166	−	0.800710i	0.992768	−	0.120052i	$-0.0383060\pi$
$62$	8.94652	−	6.50002i	1.13621	−	0.825504i
$63$		0			0
$64$	0.152913	+	0.470618i	0.0191141	+	0.0588273i
$65$	14.4047			1.78669
$66$		0			0
$67$	3.06382			0.374305			0.187152	−	0.982331i	$-0.440074\pi$
$67$	3.06382			0.374305			0.187152	+	0.982331i	$0.440074\pi$
$68$	0.628297	+	1.93370i	0.0761922	+	0.234496i
$69$		0			0
$70$	−4.79328	+	3.48252i	−0.572907	+	0.416241i
$71$	0.354219	−	1.09017i	0.0420380	−	0.129380i	−0.927835	−	0.372991i	$-0.878332\pi$
$71$	0.354219	−	1.09017i	0.0420380	−	0.129380i	0.969873	+	0.243611i	$0.0783322\pi$
$72$		0			0
$73$	−0.953826	+	0.692995i	−0.111637	+	0.0811089i	−0.642203	−	0.766535i	$-0.721979\pi$
$73$	−0.953826	+	0.692995i	−0.111637	+	0.0811089i	0.530566	+	0.847644i	$0.321979\pi$
$74$	−15.4681	−	11.2382i	−1.79813	−	1.30642i
$75$		0			0
$76$	−2.97099			−0.340796
$77$	0.361260	+	2.88910i	0.0411694	+	0.329243i
$78$		0			0
$79$	3.43768	+	10.5801i	0.386769	+	1.19035i	0.935189	+	0.354149i	$0.115229\pi$
$79$	3.43768	+	10.5801i	0.386769	+	1.19035i	−0.548420	+	0.836203i	$0.684771\pi$
$80$	15.6076	+	11.3396i	1.74498	+	1.26780i
$81$		0			0
$82$	2.98611	−	9.19029i	0.329760	−	1.01490i
$83$	−1.55442	+	4.78403i	−0.170620	+	0.525115i	−0.999406	−	0.0344503i	$-0.989032\pi$
$83$	−1.55442	+	4.78403i	−0.170620	+	0.525115i	0.828786	+	0.559565i	$0.189032\pi$
$84$		0			0
$85$	−6.01500	−	4.37015i	−0.652419	−	0.474010i
$86$	2.47257	+	7.60979i	0.266624	+	0.820585i
$87$		0			0
$88$	4.95617	−	2.32453i	0.528329	−	0.247796i
$89$	−9.74600			−1.03307			−0.516537	−	0.856265i	$-0.672779\pi$
$89$	−9.74600			−1.03307			−0.516537	+	0.856265i	$0.672779\pi$
$90$		0			0
$91$	−2.64984	−	1.92522i	−0.277778	−	0.201818i
$92$	−0.189255	+	0.137502i	−0.0197312	+	0.0143356i
$93$		0			0
$94$	−6.09568	+	18.7606i	−0.628722	+	1.93501i
$95$	8.78930	−	6.38580i	0.901763	−	0.655169i
$96$		0			0
$97$	−0.125760	−	0.387049i	−0.0127690	−	0.0392989i	0.944469	−	0.328600i	$-0.106577\pi$
$97$	−0.125760	−	0.387049i	−0.0127690	−	0.0392989i	−0.957238	+	0.289302i	$0.906577\pi$
$98$	−10.8894			−1.10000
$99$		0			0
$100$	10.4586			1.04586
$101$	2.19151	+	6.74478i	0.218064	+	0.671131i	0.998922	+	0.0464227i	$0.0147821\pi$
$101$	2.19151	+	6.74478i	0.218064	+	0.671131i	−0.780858	+	0.624708i	$0.785218\pi$
$102$		0			0
$103$	2.02450	−	1.47089i	0.199480	−	0.144931i	−0.483561	−	0.875311i	$-0.660657\pi$
$103$	2.02450	−	1.47089i	0.199480	−	0.144931i	0.683041	+	0.730380i	$0.260657\pi$
$104$	−1.90298	+	5.85677i	−0.186603	+	0.574304i
$105$		0			0
$106$	14.6410	−	10.6373i	1.42206	−	1.03319i
$107$	−1.29033	−	0.937478i	−0.124741	−	0.0906294i	0.523666	−	0.851924i	$-0.324564\pi$
$107$	−1.29033	−	0.937478i	−0.124741	−	0.0906294i	−0.648406	+	0.761295i	$0.724564\pi$
$108$		0			0
$109$	−15.6313			−1.49720			−0.748602	−	0.663020i	$-0.769275\pi$
$109$	−15.6313			−1.49720			−0.748602	+	0.663020i	$0.769275\pi$
$110$	10.8084	−	19.6015i	1.03054	−	1.86893i
$111$		0			0
$112$	−1.35555	−	4.17196i	−0.128088	−	0.394213i
$113$	−1.99094	−	1.44650i	−0.187291	−	0.136075i	0.490188	−	0.871616i	$-0.336928\pi$
$113$	−1.99094	−	1.44650i	−0.187291	−	0.136075i	−0.677480	+	0.735541i	$0.736928\pi$
$114$		0			0
$115$	0.264343	−	0.813563i	0.0246501	−	0.0758652i
$116$	2.74756	−	8.45613i	0.255105	−	0.785132i
$117$		0			0
$118$	−3.29665	−	2.39516i	−0.303481	−	0.220492i
$119$	0.522417	+	1.60783i	0.0478899	+	0.147390i
$120$		0			0
$121$	−5.87054	−	9.30251i	−0.533686	−	0.845683i
$122$	11.4947			1.04068
$123$		0			0
$124$	5.40349	+	3.92586i	0.485247	+	0.352553i
$125$	−15.3231	+	11.1329i	−1.37054	+	0.995757i
$126$		0			0
$127$	−0.816614	+	2.51328i	−0.0724628	+	0.223017i	−0.980728	−	0.195377i	$-0.937407\pi$
$127$	−0.816614	+	2.51328i	−0.0724628	+	0.223017i	0.908265	+	0.418394i	$0.137407\pi$
$128$	−9.49206	+	6.89639i	−0.838988	+	0.609560i
$129$		0			0
$130$	7.78126	+	23.9482i	0.682461	+	2.10040i
$131$	−20.0525			−1.75200			−0.876000	−	0.482312i	$-0.839797\pi$
$131$	−20.0525			−1.75200			−0.876000	+	0.482312i	$0.839797\pi$
$132$		0			0
$133$	−2.47032			−0.214204
$134$	1.65504	+	5.09368i	0.142973	+	0.440027i
$135$		0			0
$136$	2.57148	−	1.86829i	0.220503	−	0.160205i
$137$	1.49119	−	4.58941i	0.127401	−	0.392100i	−0.866930	−	0.498430i	$-0.833910\pi$
$137$	1.49119	−	4.58941i	0.127401	−	0.392100i	0.994331	+	0.106330i	$0.0339100\pi$
$138$		0			0
$139$	14.2728	−	10.3698i	1.21060	−	0.879556i	0.215319	−	0.976544i	$-0.430921\pi$
$139$	14.2728	−	10.3698i	1.21060	−	0.879556i	0.995286	+	0.0969882i	$0.0309209\pi$
$140$	−2.89503	−	2.10336i	−0.244675	−	0.177766i
$141$		0			0
$142$	2.00379			0.168154
$143$	12.1522	+	2.33412i	1.01622	+	0.195189i
$144$		0			0
$145$	10.0472	+	30.9220i	0.834371	+	2.56793i
$146$	−1.66737	−	1.21141i	−0.137992	−	0.100257i
$147$		0			0
$148$	3.56847	−	10.9826i	0.293326	−	0.902766i
$149$	3.21492	−	9.89451i	0.263377	−	0.810590i	−0.728686	−	0.684848i	$-0.759869\pi$
$149$	3.21492	−	9.89451i	0.263377	−	0.810590i	0.992063	−	0.125742i	$-0.0401312\pi$
$150$		0			0
$151$	16.9282	+	12.2990i	1.37759	+	1.00088i	0.997100	+	0.0760980i	$0.0242462\pi$
$151$	16.9282	+	12.2990i	1.37759	+	1.00088i	0.380494	+	0.924783i	$0.375754\pi$
$152$	1.43525	+	4.41723i	0.116414	+	0.358285i
$153$		0			0
$154$	−4.60805	+	2.16126i	−0.371328	+	0.174159i
$155$	−24.4237			−1.96176
$156$		0			0
$157$	16.3735	+	11.8960i	1.30674	+	0.949405i	0.999997	−	0.00238649i	$-0.000759644\pi$
$157$	16.3735	+	11.8960i	1.30674	+	0.949405i	0.306746	+	0.951791i	$0.400760\pi$
$158$	−15.7327	+	11.4305i	−1.25163	+	0.909359i
$159$		0			0
$160$	−6.48295	+	19.9525i	−0.512522	+	1.57738i
$161$	−0.157362	+	0.114330i	−0.0124018	+	0.00901047i
$162$		0			0
$163$	−3.71038	−	11.4194i	−0.290620	−	0.894435i	−0.984658	−	0.174497i	$-0.944170\pi$
$163$	−3.71038	−	11.4194i	−0.290620	−	0.894435i	0.694038	−	0.719938i	$-0.255830\pi$
$164$	5.83637			0.455744
$165$		0			0
$166$	−8.79326			−0.682489
$167$	5.69731	+	17.5345i	0.440871	+	1.35686i	0.886949	+	0.461868i	$0.152821\pi$
$167$	5.69731	+	17.5345i	0.440871	+	1.35686i	−0.446077	+	0.894994i	$0.647179\pi$
$168$		0			0
$169$	−0.744663	+	0.541030i	−0.0572818	+	0.0416177i
$170$	4.01627	−	12.3608i	0.308034	−	0.948031i
$171$		0			0
$172$	−3.90971	+	2.84057i	−0.298112	+	0.216591i
$173$	−1.59760	−	1.16072i	−0.121463	−	0.0882481i	0.525395	−	0.850858i	$-0.323917\pi$
$173$	−1.59760	−	1.16072i	−0.121463	−	0.0882481i	−0.646858	+	0.762610i	$0.723917\pi$
$174$		0			0
$175$	8.69611			0.657364
$176$	11.3295	+	12.0954i	0.853997	+	0.911726i
$177$		0			0
$178$	−5.26467	−	16.2030i	−0.394604	−	1.21447i
$179$	−14.8602	−	10.7966i	−1.11070	−	0.806973i	−0.127929	−	0.991783i	$-0.540833\pi$
$179$	−14.8602	−	10.7966i	−1.11070	−	0.806973i	−0.982774	+	0.184810i	$0.940833\pi$
$180$		0			0
$181$	0.143613	−	0.441995i	0.0106747	−	0.0328532i	−0.945577	−	0.325398i	$-0.894502\pi$
$181$	0.143613	−	0.441995i	0.0106747	−	0.0328532i	0.956252	+	0.292544i	$0.0945019\pi$
$182$	1.76932	−	5.44541i	0.131151	−	0.403640i
$183$		0			0
$184$	0.295863	+	0.214957i	0.0218113	+	0.0158468i
$185$	13.0490	+	40.1607i	0.959382	+	2.95267i
$186$		0			0
$187$	−4.36630	−	4.66145i	−0.319295	−	0.340879i
$188$	−11.9141			−0.868923
$189$		0			0
$190$	15.3644	+	11.1629i	1.11465	+	0.809843i
$191$	8.39115	−	6.09653i	0.607162	−	0.441129i	−0.241252	−	0.970463i	$-0.577558\pi$
$191$	8.39115	−	6.09653i	0.607162	−	0.441129i	0.848414	+	0.529333i	$0.177558\pi$
$192$		0			0
$193$	3.87057	−	11.9124i	0.278610	−	0.857472i	−0.709632	−	0.704572i	$-0.751139\pi$
$193$	3.87057	−	11.9124i	0.278610	−	0.857472i	0.988242	−	0.152900i	$-0.0488612\pi$
$194$	0.575546	−	0.418159i	0.0413218	−	0.0300221i
$195$		0			0
$196$	−2.03239	−	6.25504i	−0.145170	−	0.446789i
$197$	15.6650			1.11609			0.558043	−	0.829812i	$-0.311552\pi$
$197$	15.6650			1.11609			0.558043	+	0.829812i	$0.311552\pi$
$198$		0			0
$199$	15.9645			1.13170			0.565848	−	0.824509i	$-0.308549\pi$
$199$	15.9645			1.13170			0.565848	+	0.824509i	$0.308549\pi$
$200$	−5.05241	−	15.5497i	−0.357259	−	1.09953i
$201$		0			0
$202$	−10.0296	+	7.28690i	−0.705677	+	0.512705i
$203$	2.28454	−	7.03110i	0.160344	−	0.493487i
$204$		0			0
$205$	−17.2662	+	12.5446i	−1.20592	+	0.876153i
$206$	3.53900	+	2.57123i	0.246574	+	0.179146i
$207$		0			0
$208$	−18.6434			−1.29269
$209$	8.44965	−	3.96304i	0.584475	−	0.274129i
$210$		0			0
$211$	−5.76824	−	17.7528i	−0.397102	−	1.22215i	−0.927312	−	0.374288i	$-0.877887\pi$
$211$	−5.76824	−	17.7528i	−0.397102	−	1.22215i	0.530210	−	0.847866i	$-0.322113\pi$
$212$	8.84283	+	6.42469i	0.607328	+	0.441250i
$213$		0			0
$214$	0.861563	−	2.65162i	0.0588953	−	0.181261i
$215$	5.46090	−	16.8069i	0.372430	−	1.14622i
$216$		0			0
$217$	4.49289	+	3.26428i	0.304997	+	0.221594i
$218$	−8.44383	−	25.9874i	−0.571888	−	1.76009i
$219$		0			0
$220$	13.2767	+	2.55010i	0.895115	+	0.171928i
$221$	7.18500			0.483316
$222$		0			0
$223$	−5.57178	−	4.04813i	−0.373114	−	0.271083i	0.385387	−	0.922755i	$-0.374068\pi$
$223$	−5.57178	−	4.04813i	−0.373114	−	0.271083i	−0.758501	+	0.651672i	$0.774068\pi$
$224$	3.85926	−	2.80392i	0.257858	−	0.187345i
$225$		0			0
$226$	1.32937	−	4.09137i	0.0884281	−	0.272154i
$227$	5.39418	−	3.91910i	0.358024	−	0.260120i	−0.394203	−	0.919023i	$-0.628979\pi$
$227$	5.39418	−	3.91910i	0.358024	−	0.260120i	0.752228	+	0.658903i	$0.228979\pi$
$228$		0			0
$229$	5.61856	+	17.2921i	0.371285	+	1.14270i	0.945951	+	0.324309i	$0.105132\pi$
$229$	5.61856	+	17.2921i	0.371285	+	1.14270i	−0.574666	+	0.818388i	$0.694868\pi$
$230$	1.49537			0.0986015
$231$		0			0
$232$	−13.8998			−0.912566
$233$	−0.569063	−	1.75139i	−0.0372805	−	0.114738i	0.930684	−	0.365823i	$-0.119212\pi$
$233$	−0.569063	−	1.75139i	−0.0372805	−	0.114738i	−0.967965	+	0.251085i	$0.919212\pi$
$234$		0			0
$235$	35.2463	−	25.6079i	2.29921	−	1.67048i
$236$	0.760533	−	2.34068i	0.0495065	−	0.152365i
$237$		0			0
$238$	−2.39086	+	1.73706i	−0.154977	+	0.112597i
$239$	−16.4897	−	11.9805i	−1.06663	−	0.774953i	−0.0913272	−	0.995821i	$-0.529111\pi$
$239$	−16.4897	−	11.9805i	−1.06663	−	0.774953i	−0.975304	+	0.220868i	$0.929111\pi$
$240$		0			0
$241$	−0.762352			−0.0491074			−0.0245537	−	0.999699i	$-0.507816\pi$
$241$	−0.762352			−0.0491074			−0.0245537	+	0.999699i	$0.507816\pi$
$242$	12.2945	−	14.7850i	0.790320	−	0.950419i
$243$		0			0
$244$	2.14535	+	6.60272i	0.137342	+	0.422696i
$245$	19.4570	+	14.1364i	1.24306	+	0.903140i
$246$		0			0
$247$	−3.24435	+	9.98508i	−0.206433	+	0.635335i
$248$	3.22657	−	9.93037i	0.204888	−	0.630579i
$249$		0			0
$250$	−26.7861	−	19.4613i	−1.69410	−	1.23084i
$251$	−0.176045	−	0.541812i	−0.0111119	−	0.0341989i	0.945347	−	0.326066i	$-0.105723\pi$
$251$	−0.176045	−	0.541812i	−0.0111119	−	0.0341989i	−0.956459	+	0.291868i	$0.905723\pi$
$252$		0			0
$253$	0.354836	−	0.643512i	0.0223083	−	0.0404572i
$254$	−4.61952			−0.289855
$255$		0			0
$256$	−15.7923	−	11.4738i	−0.987017	−	0.717110i
$257$	13.3708	−	9.71445i	0.834047	−	0.605971i	−0.0866544	−	0.996238i	$-0.527618\pi$
$257$	13.3708	−	9.71445i	0.834047	−	0.605971i	0.920701	+	0.390268i	$0.127618\pi$
$258$		0			0
$259$	2.96711	−	9.13183i	0.184367	−	0.567424i
$260$	−12.3040	+	8.93935i	−0.763059	+	0.554395i
$261$		0			0
$262$	−10.8321	−	33.3379i	−0.669212	−	2.05962i
$263$	2.41867			0.149142			0.0745709	−	0.997216i	$-0.476241\pi$
$263$	2.41867			0.149142			0.0745709	+	0.997216i	$0.476241\pi$
$264$		0			0
$265$	−39.9695			−2.45531
$266$	−1.33444	−	4.10697i	−0.0818196	−	0.251815i
$267$		0			0
$268$	−2.61700	+	1.90136i	−0.159859	+	0.116144i
$269$	−3.76657	+	11.5923i	−0.229652	+	0.706795i	0.768134	+	0.640289i	$0.221185\pi$
$269$	−3.76657	+	11.5923i	−0.229652	+	0.706795i	−0.997786	+	0.0665066i	$0.978815\pi$
$270$		0			0
$271$	−16.4142	+	11.9256i	−0.997093	+	0.724431i	−0.961463	−	0.274934i	$-0.911344\pi$
$271$	−16.4142	+	11.9256i	−0.997093	+	0.724431i	−0.0356304	+	0.999365i	$0.511344\pi$
$272$	7.78498	+	5.65612i	0.472033	+	0.342952i
$273$		0			0
$274$	8.43555			0.509610
$275$	−29.7448	+	13.9508i	−1.79368	+	0.841267i
$276$		0			0
$277$	−5.93364	−	18.2619i	−0.356518	−	1.09725i	−0.955124	−	0.296206i	$-0.904278\pi$
$277$	−5.93364	−	18.2619i	−0.356518	−	1.09725i	0.598606	−	0.801044i	$-0.295722\pi$
$278$	24.9501	+	18.1273i	1.49641	+	1.08720i
$279$		0			0
$280$	−1.72870	+	5.32040i	−0.103310	+	0.317955i
$281$	−1.83037	+	5.63331i	−0.109191	+	0.336055i	−0.990691	−	0.136128i	$-0.956534\pi$
$281$	−1.83037	+	5.63331i	−0.109191	+	0.336055i	0.881500	+	0.472183i	$0.156534\pi$
$282$		0			0
$283$	11.1334	+	8.08889i	0.661812	+	0.480835i	0.867274	−	0.497830i	$-0.165870\pi$
$283$	11.1334	+	8.08889i	0.661812	+	0.480835i	−0.205462	+	0.978665i	$0.565870\pi$
$284$	0.373985	+	1.15101i	0.0221919	+	0.0682997i
$285$		0			0
$286$	2.68395	+	21.4643i	0.158705	+	1.26921i
$287$	4.85283			0.286453
$288$		0			0
$289$	10.7530	+	7.81254i	0.632531	+	0.459561i
$290$	−45.9813	+	33.4073i	−2.70011	+	1.96175i
$291$		0			0
$292$	0.384660	−	1.18386i	0.0225105	−	0.0692802i
$293$	16.2270	−	11.7896i	0.947992	−	0.688756i	−0.00233910	−	0.999997i	$-0.500745\pi$
$293$	16.2270	−	11.7896i	0.947992	−	0.688756i	0.950331	+	0.311241i	$0.100745\pi$
$294$		0			0
$295$	2.78108	+	8.55928i	0.161921	+	0.498340i
$296$	−18.0527			−1.04929
$297$		0			0
$298$	18.1866			1.05352
$299$	0.255456	+	0.786213i	0.0147734	+	0.0454679i
$300$		0			0
$301$	−3.25084	+	2.36188i	−0.187375	+	0.136136i
$302$	−11.3031	+	34.7873i	−0.650420	+	2.00179i
$303$		0			0
$304$	−11.3756	+	8.26488i	−0.652437	+	0.474023i
$305$	−20.5385	−	14.9221i	−1.17603	−	0.854438i
$306$		0			0
$307$	16.4473			0.938694			0.469347	−	0.883014i	$-0.344489\pi$
$307$	16.4473			0.938694			0.469347	+	0.883014i	$0.344489\pi$
$308$	−2.10150	−	2.24356i	−0.119744	−	0.127839i
$309$		0			0
$310$	−13.1934	−	40.6051i	−0.749335	−	2.30621i
$311$	−1.80172	−	1.30903i	−0.102166	−	0.0742281i	0.535529	−	0.844517i	$-0.320112\pi$
$311$	−1.80172	−	1.30903i	−0.102166	−	0.0742281i	−0.637695	+	0.770289i	$0.720112\pi$
$312$		0			0
$313$	−1.05993	+	3.26213i	−0.0599108	+	0.184386i	−0.976533	−	0.215368i	$-0.930905\pi$
$313$	−1.05993	+	3.26213i	−0.0599108	+	0.184386i	0.916622	+	0.399755i	$0.130905\pi$
$314$	−10.9327	+	33.6474i	−0.616968	+	1.89883i
$315$		0			0
$316$	−9.50217	−	6.90373i	−0.534539	−	0.388365i
$317$	−4.86235	−	14.9648i	−0.273097	−	0.840505i	−0.989717	−	0.143041i	$-0.954312\pi$
$317$	−4.86235	−	14.9648i	−0.273097	−	0.840505i	0.716620	−	0.697464i	$-0.245688\pi$
$318$		0			0
$319$	3.46552	+	27.7147i	0.194032	+	1.55172i
$320$	1.91047			0.106799
$321$		0			0
$322$	−0.275082	−	0.199859i	−0.0153297	−	0.0111377i
$323$	4.38406	−	3.18520i	0.243936	−	0.177230i
$324$		0			0
$325$	11.4209	−	35.1499i	0.633517	−	1.94976i
$326$	16.9807	−	12.3372i	0.940477	−	0.683296i
$327$		0			0
$328$	−2.81948	−	8.67745i	−0.155679	−	0.479132i
$329$	−9.90631			−0.546153
$330$		0			0
$331$	−4.76189			−0.261737			−0.130869	−	0.991400i	$-0.541777\pi$
$331$	−4.76189			−0.261737			−0.130869	+	0.991400i	$0.541777\pi$
$332$	−1.64117	−	5.05099i	−0.0900706	−	0.277209i
$333$		0			0
$334$	−26.0740	+	18.9439i	−1.42671	+	1.03656i
$335$	3.65530	−	11.2499i	0.199710	−	0.614645i
$336$		0			0
$337$	7.65952	−	5.56497i	0.417241	−	0.303143i	−0.359286	−	0.933228i	$-0.616980\pi$
$337$	7.65952	−	5.56497i	0.417241	−	0.303143i	0.776527	+	0.630084i	$0.216980\pi$
$338$	−1.30174	−	0.945766i	−0.0708051	−	0.0514429i
$339$		0			0
$340$	7.84984			0.425717
$341$	−20.6046	−	3.95759i	−1.11580	−	0.214315i
$342$		0			0
$343$	−3.58885	−	11.0453i	−0.193779	−	0.596392i
$344$	6.11205	+	4.44066i	0.329540	+	0.239425i
$345$		0			0
$346$	1.06673	−	3.28306i	0.0573478	−	0.176498i
$347$	6.53867	−	20.1240i	0.351014	−	1.08031i	−0.607270	−	0.794495i	$-0.707735\pi$
$347$	6.53867	−	20.1240i	0.351014	−	1.08031i	0.958285	−	0.285816i	$-0.0922646\pi$
$348$		0			0
$349$	7.68176	+	5.58112i	0.411195	+	0.298751i	0.774085	−	0.633081i	$-0.218210\pi$
$349$	7.68176	+	5.58112i	0.411195	+	0.298751i	−0.362890	+	0.931832i	$0.618210\pi$
$350$	4.69754	+	14.4575i	0.251094	+	0.772787i
$351$		0			0
$352$	−8.70228	+	15.7820i	−0.463833	+	0.841183i
$353$	−8.71026			−0.463600			−0.231800	−	0.972763i	$-0.574462\pi$
$353$	−8.71026			−0.463600			−0.231800	+	0.972763i	$0.574462\pi$
$354$		0			0
$355$	−3.58034	−	2.60127i	−0.190025	−	0.138061i
$356$	8.32467	−	6.04822i	0.441206	−	0.320555i
$357$		0			0
$358$	9.92229	−	30.5377i	0.524409	−	1.61397i
$359$	0.422685	−	0.307099i	0.0223085	−	0.0162080i	−0.576575	−	0.817044i	$-0.695611\pi$
$359$	0.422685	−	0.307099i	0.0223085	−	0.0162080i	0.598884	+	0.800836i	$0.295611\pi$
$360$		0			0
$361$	−3.42441	−	10.5392i	−0.180232	−	0.554697i
$362$	0.812407			0.0426992
$363$		0			0
$364$	3.45815			0.181256
$365$	1.40660	+	4.32908i	0.0736250	+	0.226595i
$366$		0			0
$367$	26.9606	−	19.5880i	1.40733	−	1.02249i	0.413627	−	0.910447i	$-0.364262\pi$
$367$	26.9606	−	19.5880i	1.40733	−	1.02249i	0.993704	−	0.112039i	$-0.0357382\pi$
$368$	−0.342128	+	1.05296i	−0.0178347	+	0.0548894i
$369$		0			0
$370$	−59.7194	+	43.3887i	−3.10466	+	2.25567i
$371$	7.35264	+	5.34200i	0.381730	+	0.277343i
$372$		0			0
$373$	−8.31725			−0.430651			−0.215325	−	0.976542i	$-0.569081\pi$
$373$	−8.31725			−0.430651			−0.215325	+	0.976542i	$0.569081\pi$
$374$	5.39118	−	9.77715i	0.278771	−	0.505564i
$375$		0			0
$376$	5.75553	+	17.7137i	0.296819	+	0.913514i
$377$	−25.4195	−	18.4683i	−1.30917	−	0.951168i
$378$		0			0
$379$	−1.99966	+	6.15433i	−0.102716	+	0.316127i	−0.989188	−	0.146656i	$-0.953149\pi$
$379$	−1.99966	+	6.15433i	−0.102716	+	0.316127i	0.886472	+	0.462783i	$0.153149\pi$
$380$	−3.54455	+	10.9090i	−0.181832	+	0.559621i
$381$		0			0
$382$	14.6684	+	10.6572i	0.750503	+	0.545272i
$383$	−4.73079	−	14.5599i	−0.241732	−	0.743975i	−0.996157	−	0.0875880i	$-0.972084\pi$
$383$	−4.73079	−	14.5599i	−0.241732	−	0.743975i	0.754425	−	0.656386i	$-0.227916\pi$
$384$		0			0
$385$	11.0393	+	2.12036i	0.562615	+	0.108064i
$386$	21.8955			1.11445
$387$		0			0
$388$	0.347616	+	0.252558i	0.0176476	+	0.0128217i
$389$	11.6490	−	8.46346i	0.590625	−	0.429114i	−0.251914	−	0.967750i	$-0.581060\pi$
$389$	11.6490	−	8.46346i	0.590625	−	0.429114i	0.842539	+	0.538635i	$0.181060\pi$
$390$		0			0
$391$	0.131853	−	0.405801i	0.00666809	−	0.0205223i
$392$	−8.31810	+	6.04346i	−0.420128	+	0.305241i
$393$		0			0
$394$	8.46206	+	26.0435i	0.426312	+	1.31205i
$395$	42.9497			2.16104
$396$		0			0
$397$	−25.8637			−1.29806			−0.649030	−	0.760763i	$-0.724825\pi$
$397$	−25.8637			−1.29806			−0.649030	+	0.760763i	$0.724825\pi$
$398$	8.62386	+	26.5415i	0.432275	+	1.33041i
$399$		0			0
$400$	40.0449	−	29.0944i	2.00225	−	1.45472i
$401$	7.99826	−	24.6161i	0.399414	−	1.22927i	−0.526056	−	0.850450i	$-0.676330\pi$
$401$	7.99826	−	24.6161i	0.399414	−	1.22927i	0.925470	−	0.378820i	$-0.123670\pi$
$402$		0			0
$403$	19.0949	−	13.8733i	0.951186	−	0.691077i
$404$	−6.05762	−	4.40112i	−0.301378	−	0.218964i
$405$		0			0
$406$	12.9235			0.641382
$407$	4.50093	+	35.9952i	0.223103	+	1.78421i
$408$		0			0
$409$	3.49302	+	10.7504i	0.172719	+	0.531573i	0.999522	−	0.0309179i	$-0.00984305\pi$
$409$	3.49302	+	10.7504i	0.172719	+	0.531573i	−0.826803	+	0.562491i	$0.809843\pi$
$410$	−30.1827	−	21.9290i	−1.49062	−	1.08300i
$411$		0			0
$412$	−0.816442	+	2.51275i	−0.0402232	+	0.123794i
$413$	0.632368	−	1.94623i	0.0311168	−	0.0957676i
$414$		0			0
$415$	15.7117	+	11.4152i	0.771256	+	0.560351i
$416$	−6.26500	−	19.2817i	−0.307167	−	0.945363i
$417$		0			0
$418$	11.1531	+	11.9070i	0.545514	+	0.582390i
$419$	22.3125			1.09004			0.545018	−	0.838424i	$-0.316523\pi$
$419$	22.3125			1.09004			0.545018	+	0.838424i	$0.316523\pi$
$420$		0			0
$421$	23.7495	+	17.2551i	1.15748	+	0.840960i	0.989458	−	0.144823i	$-0.0462612\pi$
$421$	23.7495	+	17.2551i	1.15748	+	0.840960i	0.168025	+	0.985783i	$0.446261\pi$
$422$	26.3986	−	19.1797i	1.28506	−	0.933654i
$423$		0			0
$424$	5.28030	−	16.2511i	0.256434	−	0.789223i
$425$	−15.4329	+	11.2127i	−0.748607	+	0.543895i
$426$		0			0
$427$	1.78382	+	5.49003i	0.0863250	+	0.265681i
$428$	1.68393			0.0813960
$429$		0			0
$430$	30.8919			1.48974
$431$	11.1514	+	34.3205i	0.537145	+	1.65316i	0.738968	+	0.673741i	$0.235313\pi$
$431$	11.1514	+	34.3205i	0.537145	+	1.65316i	−0.201823	+	0.979422i	$0.564687\pi$
$432$		0			0
$433$	−14.2958	+	10.3865i	−0.687014	+	0.499145i	−0.875677	−	0.482897i	$-0.839585\pi$
$433$	−14.2958	+	10.3865i	−0.687014	+	0.499145i	0.188663	+	0.982042i	$0.439585\pi$
$434$	−2.99994	+	9.23288i	−0.144002	+	0.443192i
$435$		0			0
$436$	13.3516	−	9.70053i	0.639428	−	0.464571i
$437$	0.504409	+	0.366475i	0.0241292	+	0.0175309i
$438$		0			0
$439$	−17.5146			−0.835925			−0.417962	−	0.908464i	$-0.637256\pi$
$439$	−17.5146			−0.835925			−0.417962	+	0.908464i	$0.637256\pi$
$440$	−2.62234	−	20.9716i	−0.125015	−	0.999780i
$441$		0			0
$442$	3.88125	+	11.9453i	0.184612	+	0.568178i
$443$	1.52844	+	1.11047i	0.0726181	+	0.0527602i	0.623502	−	0.781822i	$-0.285709\pi$
$443$	1.52844	+	1.11047i	0.0726181	+	0.0527602i	−0.550884	+	0.834582i	$0.685709\pi$
$444$		0			0
$445$	−11.6275	+	35.7858i	−0.551197	+	1.69641i
$446$	3.72033	−	11.4500i	0.176163	−	0.542173i
$447$		0			0
$448$	−0.351443	−	0.255338i	−0.0166041	−	0.0120636i
$449$	2.93945	+	9.04671i	0.138721	+	0.426941i	0.996150	−	0.0876619i	$-0.0279395\pi$
$449$	2.93945	+	9.04671i	0.138721	+	0.426941i	−0.857429	+	0.514602i	$0.827940\pi$
$450$		0			0
$451$	−16.5990	+	7.78521i	−0.781614	+	0.366591i
$452$	2.59826			0.122212
$453$		0			0
$454$	9.42949	+	6.85092i	0.442548	+	0.321530i
$455$	−10.2305	+	7.43289i	−0.479613	+	0.348459i
$456$		0			0
$457$	−5.69545	+	17.5288i	−0.266422	+	0.819962i	0.724940	+	0.688812i	$0.241867\pi$
$457$	−5.69545	+	17.5288i	−0.266422	+	0.819962i	−0.991362	+	0.131151i	$0.958133\pi$
$458$	−25.7136	+	18.6820i	−1.20152	+	0.872953i
$459$		0			0
$460$	0.279094	+	0.858962i	0.0130128	+	0.0400493i
$461$	−13.0616			−0.608338			−0.304169	−	0.952618i	$-0.598379\pi$
$461$	−13.0616			−0.608338			−0.304169	+	0.952618i	$0.598379\pi$
$462$		0			0
$463$	−19.3337			−0.898514			−0.449257	−	0.893403i	$-0.648311\pi$
$463$	−19.3337			−0.898514			−0.449257	+	0.893403i	$0.648311\pi$
$464$	−13.0036	−	40.0210i	−0.603678	−	1.85793i
$465$		0			0
$466$	2.60434	−	1.89217i	0.120644	−	0.0876529i
$467$	0.713438	−	2.19574i	0.0330140	−	0.101607i	−0.933192	−	0.359379i	$-0.882989\pi$
$467$	0.713438	−	2.19574i	0.0330140	−	0.101607i	0.966206	+	0.257773i	$0.0829885\pi$
$468$		0			0
$469$	−2.17598	+	1.58094i	−0.100477	+	0.0730011i
$470$	61.6135	+	44.7648i	2.84202	+	2.06485i
$471$		0			0
$472$	−3.84750			−0.177095
$473$	7.33035	−	13.2939i	0.337050	−	0.611256i
$474$		0			0
$475$	−8.61373	−	26.5103i	−0.395225	−	1.21638i
$476$	−1.44403	−	1.04915i	−0.0661868	−	0.0480875i
$477$		0			0
$478$	11.0103	−	33.8863i	0.503601	−	1.54992i
$479$	−0.861057	+	2.65006i	−0.0393427	+	0.121084i	−0.968799	−	0.247848i	$-0.920277\pi$
$479$	−0.861057	+	2.65006i	−0.0393427	+	0.121084i	0.929456	+	0.368932i	$0.120277\pi$
$480$		0			0
$481$	−33.0142	−	23.9862i	−1.50532	−	1.09368i
$482$	−0.411813	−	1.26743i	−0.0187576	−	0.0577299i
$483$		0			0
$484$	10.7874	+	4.30268i	0.490336	+	0.195576i
$485$	−1.57122			−0.0713456
$486$		0			0
$487$	5.52551	+	4.01452i	0.250385	+	0.181915i	0.705897	−	0.708314i	$-0.250544\pi$
$487$	5.52551	+	4.01452i	0.250385	+	0.181915i	−0.455513	+	0.890229i	$0.650544\pi$
$488$	8.78045	−	6.37937i	0.397472	−	0.288781i
$489$		0			0
$490$	−12.9916	+	39.9842i	−0.586903	+	1.80630i
$491$	−13.7421	+	9.98425i	−0.620174	+	0.450583i	−0.852982	−	0.521940i	$-0.825209\pi$
$491$	−13.7421	+	9.98425i	−0.620174	+	0.450583i	0.232808	+	0.972523i	$0.425209\pi$
$492$		0			0
$493$	5.01147	+	15.4237i	0.225705	+	0.694649i
$494$	−18.3530			−0.825742
$495$		0			0
$496$	31.6106			1.41936
$497$	0.310961	+	0.957039i	0.0139485	+	0.0429291i
$498$		0			0
$499$	5.14267	−	3.73637i	0.230218	−	0.167263i	−0.466696	−	0.884418i	$-0.654556\pi$
$499$	5.14267	−	3.73637i	0.230218	−	0.167263i	0.696914	+	0.717155i	$0.254556\pi$
$500$	6.17952	−	19.0186i	0.276357	−	0.850538i
$501$		0			0
$502$	0.805680	−	0.585361i	0.0359592	−	0.0261259i
$503$	19.4494	+	14.1308i	0.867205	+	0.630061i	0.929835	−	0.367976i	$-0.119949\pi$
$503$	19.4494	+	14.1308i	0.867205	+	0.630061i	−0.0626305	+	0.998037i	$0.519949\pi$
$504$		0			0
$505$	27.3804			1.21841
$506$	1.26153	+	0.242307i	0.0560821	+	0.0107719i
$507$		0			0
$508$	−0.862183	−	2.65353i	−0.0382532	−	0.117731i
$509$	1.76950	+	1.28562i	0.0784317	+	0.0569840i	0.626310	−	0.779574i	$-0.284564\pi$
$509$	1.76950	+	1.28562i	0.0784317	+	0.0569840i	−0.547878	+	0.836558i	$0.684564\pi$
$510$		0			0
$511$	0.319837	−	0.984356i	0.0141487	−	0.0435454i
$512$	3.29335	−	10.1359i	0.145547	−	0.447948i
$513$		0			0
$514$	23.3733	+	16.9817i	1.03095	+	0.749030i
$515$	−2.98552	−	9.18850i	−0.131558	−	0.404894i
$516$		0			0
$517$	33.8842	−	15.8923i	1.49023	−	0.698943i
$518$	16.7847			0.737478
$519$		0			0
$520$	19.2348	+	13.9749i	0.843502	+	0.612840i
$521$	6.32373	−	4.59446i	0.277048	−	0.201287i	−0.440581	−	0.897713i	$-0.645228\pi$
$521$	6.32373	−	4.59446i	0.277048	−	0.201287i	0.717629	+	0.696426i	$0.245228\pi$
$522$		0			0
$523$	1.19774	−	3.68626i	0.0523735	−	0.161189i	−0.921449	−	0.388500i	$-0.872993\pi$
$523$	1.19774	−	3.68626i	0.0523735	−	0.161189i	0.973822	+	0.227311i	$0.0729934\pi$
$524$	17.1281	−	12.4443i	0.748246	−	0.543632i
$525$		0			0
$526$	1.30654	+	4.02111i	0.0569678	+	0.175329i
$527$	−12.1824			−0.530675
$528$		0			0
$529$	−22.9509			−0.997866
$530$	−21.5911	−	66.4504i	−0.937856	−	2.88642i
$531$		0			0
$532$	2.11005	−	1.53304i	0.0914824	−	0.0664659i
$533$	6.37338	−	19.6152i	0.276062	−	0.849630i
$534$		0			0
$535$	−4.98170	+	3.61942i	−0.215378	+	0.156481i
$536$	4.09115	+	2.97240i	0.176711	+	0.128388i
$537$		0			0
$538$	−21.3072			−0.918618
$539$	14.1239	+	15.0786i	0.608359	+	0.649483i
$540$		0			0
$541$	−6.73051	−	20.7144i	−0.289367	−	0.890580i	−0.985056	−	0.172237i	$-0.944901\pi$
$541$	−6.73051	−	20.7144i	−0.289367	−	0.890580i	0.695689	−	0.718344i	$-0.255099\pi$
$542$	−28.6935	−	20.8470i	−1.23249	−	0.895457i
$543$		0			0
$544$	−3.23366	+	9.95219i	−0.138642	+	0.426697i
$545$	−18.6490	+	57.3956i	−0.798834	+	2.45856i
$546$		0			0
$547$	10.7562	+	7.81480i	0.459900	+	0.334137i	0.793492	−	0.608581i	$-0.208261\pi$
$547$	10.7562	+	7.81480i	0.459900	+	0.334137i	−0.333592	+	0.942718i	$0.608261\pi$
$548$	1.57440	+	4.84551i	0.0672552	+	0.206990i
$549$		0			0
$550$	−39.2614	−	41.9155i	−1.67411	−	1.78728i
$551$	−23.6974			−1.00954
$552$		0			0
$553$	−7.90087	−	5.74032i	−0.335979	−	0.244103i
$554$	27.1556	−	19.7297i	1.15373	−	0.838235i
$555$		0			0
$556$	−5.75595	+	17.7150i	−0.244107	+	0.751283i
$557$	−21.6884	+	15.7575i	−0.918966	+	0.667668i	−0.943266	−	0.332037i	$-0.892264\pi$
$557$	−21.6884	+	15.7575i	−0.918966	+	0.667668i	0.0243004	+	0.999705i	$0.492264\pi$
$558$		0			0
$559$	5.27731	+	16.2419i	0.223207	+	0.686959i
$560$	−16.9360			−0.715678
$561$		0			0
$562$	−10.3543			−0.436769
$563$	4.58868	+	14.1225i	0.193390	+	0.595193i	0.999992	+	0.00409776i	$0.00130436\pi$
$563$	4.58868	+	14.1225i	0.193390	+	0.595193i	−0.806602	+	0.591095i	$0.798696\pi$
$564$		0			0
$565$	−7.68662	+	5.58465i	−0.323378	+	0.234948i
$566$	−7.43388	+	22.8791i	−0.312469	+	0.961681i
$567$		0			0
$568$	1.53064	−	1.11207i	0.0642241	−	0.0466615i
$569$	0.889133	+	0.645993i	0.0372744	+	0.0270814i	0.606266	−	0.795262i	$-0.292666\pi$
$569$	0.889133	+	0.645993i	0.0372744	+	0.0270814i	−0.568992	+	0.822343i	$0.692666\pi$
$570$		0			0
$571$	−30.6361			−1.28208			−0.641040	−	0.767507i	$-0.721497\pi$
$571$	−30.6361			−1.28208			−0.641040	+	0.767507i	$0.721497\pi$
$572$	−11.8285	+	5.54778i	−0.494575	+	0.231964i
$573$		0			0
$574$	2.62144	+	8.06796i	0.109417	+	0.336750i
$575$	−1.77564	−	1.29008i	−0.0740494	−	0.0538000i
$576$		0			0
$577$	8.69916	−	26.7733i	0.362151	−	1.11459i	−0.589595	−	0.807699i	$-0.700713\pi$
$577$	8.69916	−	26.7733i	0.362151	−	1.11459i	0.951746	−	0.306887i	$-0.0992874\pi$
$578$	−7.17990	+	22.0975i	−0.298644	+	0.919133i
$579$		0			0
$580$	−27.7716	−	20.1773i	−1.15315	−	0.837815i
$581$	−1.36460	−	4.19980i	−0.0566130	−	0.174237i
$582$		0			0
$583$	−33.7195	−	6.47661i	−1.39652	−	0.268234i
$584$	−1.94597			−0.0805250
$585$		0			0
$586$	28.3662	+	20.6092i	1.17180	+	0.851360i
$587$	−19.2293	+	13.9709i	−0.793678	+	0.576641i	−0.909053	−	0.416681i	$-0.863193\pi$
$587$	−19.2293	+	13.9709i	−0.793678	+	0.576641i	0.115374	+	0.993322i	$0.463193\pi$
$588$		0			0
$589$	5.50091	−	16.9301i	0.226661	−	0.697591i
$590$	−12.7277	+	9.24724i	−0.523992	+	0.380703i
$591$		0			0
$592$	−16.8888	−	51.9784i	−0.694125	−	2.13630i
$593$	19.9552			0.819463			0.409732	−	0.912206i	$-0.365622\pi$
$593$	19.9552			0.819463			0.409732	+	0.912206i	$0.365622\pi$
$594$		0			0
$595$	6.52699			0.267580
$596$	3.39432	+	10.4466i	0.139037	+	0.427911i
$597$		0			0
$598$	−1.16911	+	0.849405i	−0.0478083	+	0.0347348i
$599$	2.58298	−	7.94959i	0.105538	−	0.324811i	−0.884319	−	0.466884i	$-0.845377\pi$
$599$	2.58298	−	7.94959i	0.105538	−	0.324811i	0.989856	+	0.142072i	$0.0453766\pi$
$600$		0			0
$601$	23.2621	−	16.9009i	0.948882	−	0.689403i	−0.00165981	−	0.999999i	$-0.500528\pi$
$601$	23.2621	−	16.9009i	0.948882	−	0.689403i	0.950542	+	0.310595i	$0.100528\pi$
$602$	−5.68275	−	4.12876i	−0.231612	−	0.168276i
$603$		0			0
$604$	−22.0920			−0.898911
$605$	−41.1613	+	10.4573i	−1.67344	+	0.425151i
$606$		0			0
$607$	2.20564	+	6.78826i	0.0895241	+	0.275527i	0.985788	−	0.167994i	$-0.0537291\pi$
$607$	2.20564	+	6.78826i	0.0895241	+	0.275527i	−0.896264	+	0.443521i	$0.853729\pi$
$608$	−12.3705	−	8.98772i	−0.501691	−	0.364500i
$609$		0			0
$610$	13.7138	−	42.2066i	0.555254	−	1.70890i
$611$	−13.0103	+	40.0415i	−0.526339	+	1.61991i
$612$		0			0
$613$	−4.08413	−	2.96729i	−0.164956	−	0.119848i	0.502245	−	0.864726i	$-0.332508\pi$
$613$	−4.08413	−	2.96729i	−0.164956	−	0.119848i	−0.667201	+	0.744878i	$0.732508\pi$
$614$	8.88461	+	27.3440i	0.358554	+	1.10351i
$615$		0			0
$616$	−2.32050	+	4.20833i	−0.0934954	+	0.169558i
$617$	−44.1679			−1.77813			−0.889066	−	0.457780i	$-0.848645\pi$
$617$	−44.1679			−1.77813			−0.889066	+	0.457780i	$0.848645\pi$
$618$		0			0
$619$	−37.2714	−	27.0793i	−1.49806	−	1.08841i	−0.971144	−	0.238492i	$-0.923347\pi$
$619$	−37.2714	−	27.0793i	−1.49806	−	1.08841i	−0.526920	−	0.849915i	$-0.676653\pi$
$620$	20.8618	−	15.1570i	0.837830	−	0.608719i
$621$		0			0
$622$	1.20303	−	3.70253i	0.0482370	−	0.148458i
$623$	6.92179	−	5.02898i	0.277316	−	0.201482i
$624$		0			0
$625$	7.29163	+	22.4413i	0.291665	+	0.897653i
$626$	−5.99594			−0.239646
$627$		0			0
$628$	−21.3681			−0.852679
$629$	6.50878	+	20.0320i	0.259522	+	0.798727i
$630$		0			0
$631$	−14.4522	+	10.5002i	−0.575335	+	0.418005i	−0.837039	−	0.547143i	$-0.815715\pi$
$631$	−14.4522	+	10.5002i	−0.575335	+	0.418005i	0.261704	+	0.965148i	$0.415715\pi$
$632$	−5.67401	+	17.4628i	−0.225700	+	0.694634i
$633$		0			0
$634$	22.2528	−	16.1676i	0.883770	−	0.642096i
$635$	8.25410	+	5.99696i	0.327554	+	0.237982i
$636$		0			0
$637$	−23.2417			−0.920870
$638$	−44.2044	+	20.7327i	−1.75007	+	0.820814i
$639$		0			0
$640$	13.9979	+	43.0811i	0.553316	+	1.70293i
$641$	12.1608	+	8.83537i	0.480325	+	0.348976i	0.801451	−	0.598060i	$-0.204062\pi$
$641$	12.1608	+	8.83537i	0.480325	+	0.348976i	−0.321127	+	0.947036i	$0.604062\pi$
$642$		0			0
$643$	11.2514	−	34.6281i	0.443711	−	1.36560i	−0.440181	−	0.897909i	$-0.645086\pi$
$643$	11.2514	−	34.6281i	0.443711	−	1.36560i	0.883892	−	0.467692i	$-0.154914\pi$
$644$	0.0634610	−	0.195313i	0.00250071	−	0.00769640i
$645$		0			0
$646$	7.66371	+	5.56801i	0.301525	+	0.219070i
$647$	−6.54099	−	20.1311i	−0.257153	−	0.791435i	−0.993398	−	0.114720i	$-0.963403\pi$
$647$	−6.54099	−	20.1311i	−0.257153	−	0.791435i	0.736245	−	0.676715i	$-0.236597\pi$
$648$		0			0
$649$	0.959263	+	7.67150i	0.0376544	+	0.301133i
$650$	64.6070			2.53410
$651$		0			0
$652$	10.2560	+	7.45140i	0.401655	+	0.291819i
$653$	30.3759	−	22.0694i	1.18870	−	0.863641i	0.195574	−	0.980689i	$-0.437343\pi$
$653$	30.3759	−	22.0694i	1.18870	−	0.863641i	0.993126	+	0.117048i	$0.0373431\pi$
$654$		0			0
$655$	−23.9238	+	73.6298i	−0.934780	+	2.87696i
$656$	22.3469	−	16.2360i	0.872500	−	0.633909i
$657$		0			0
$658$	−5.35127	−	16.4695i	−0.208614	−	0.642049i
$659$	17.4501			0.679760			0.339880	−	0.940469i	$-0.389613\pi$
$659$	17.4501			0.679760			0.339880	+	0.940469i	$0.389613\pi$
$660$		0			0
$661$	−2.02130			−0.0786195			−0.0393098	−	0.999227i	$-0.512516\pi$
$661$	−2.02130			−0.0786195			−0.0393098	+	0.999227i	$0.512516\pi$
$662$	−2.57232	−	7.91678i	−0.0999759	−	0.307694i
$663$		0			0
$664$	−6.71692	+	4.88013i	−0.260667	+	0.189386i
$665$	−2.94723	+	9.07063i	−0.114289	+	0.351744i
$666$		0			0
$667$	−1.50955	+	1.09675i	−0.0584500	+	0.0424664i
$668$	−15.7481	−	11.4417i	−0.609312	−	0.442691i
$669$		0			0
$670$	20.6778			0.798851
$671$	−14.9089	−	15.9168i	−0.575553	−	0.614460i
$672$		0			0
$673$	5.60714	+	17.2570i	0.216140	+	0.665209i	0.999071	+	0.0431008i	$0.0137237\pi$
$673$	5.60714	+	17.2570i	0.216140	+	0.665209i	−0.782931	+	0.622108i	$0.786276\pi$
$674$	13.3895	+	9.72804i	0.515744	+	0.374710i
$675$		0			0
$676$	0.300308	−	0.924254i	0.0115503	−	0.0355482i
$677$	1.08583	−	3.34184i	0.0417319	−	0.128437i	−0.928020	−	0.372530i	$-0.878490\pi$
$677$	1.08583	−	3.34184i	0.0417319	−	0.128437i	0.969752	+	0.244093i	$0.0784902\pi$
$678$		0			0
$679$	0.289036	+	0.209997i	0.0110922	+	0.00805895i
$680$	−3.79215	−	11.6711i	−0.145422	−	0.447564i
$681$		0			0
$682$	−4.55073	−	36.3935i	−0.174257	−	1.39358i
$683$	17.9689			0.687562			0.343781	−	0.939050i	$-0.388292\pi$
$683$	17.9689			0.687562			0.343781	+	0.939050i	$0.388292\pi$
$684$		0			0
$685$	−15.0725	−	10.9508i	−0.575892	−	0.418410i
$686$	16.4245	−	11.9331i	0.627091	−	0.455608i
$687$		0			0
$688$	−7.06782	+	21.7525i	−0.269458	+	0.829307i
$689$	31.2489	−	22.7037i	1.19049	−	0.864942i
$690$		0			0
$691$	−7.03498	−	21.6514i	−0.267623	−	0.823660i	−0.991077	−	0.133287i	$-0.957447\pi$
$691$	−7.03498	−	21.6514i	−0.267623	−	0.823660i	0.723454	−	0.690372i	$-0.242553\pi$
$692$	2.08493			0.0792573
$693$		0			0
$694$	36.9888			1.40407
$695$	−21.0481	−	64.7793i	−0.798399	−	2.45722i
$696$		0			0
$697$	−8.61228	+	6.25719i	−0.326213	+	0.237008i
$698$	−5.12918	+	15.7860i	−0.194142	+	0.597509i
$699$		0			0
$700$	−7.42789	+	5.39668i	−0.280748	+	0.203975i
$701$	−28.5010	−	20.7072i	−1.07647	−	0.782101i	−0.0994053	−	0.995047i	$-0.531694\pi$
$701$	−28.5010	−	20.7072i	−1.07647	−	0.782101i	−0.977064	+	0.212946i	$0.931694\pi$
$702$		0			0
$703$	−30.7776			−1.16080
$704$	1.61173	+	0.309570i	0.0607443	+	0.0116674i
$705$		0			0
$706$	−4.70518	−	14.4810i	−0.177082	−	0.545001i
$707$	−5.03679	−	3.65944i	−0.189428	−	0.137627i
$708$		0			0
$709$	−6.21530	+	19.1287i	−0.233421	+	0.718395i	0.763906	+	0.645327i	$0.223279\pi$
$709$	−6.21530	+	19.1287i	−0.233421	+	0.718395i	−0.997327	+	0.0730677i	$0.976721\pi$
$710$	2.39063	−	7.35760i	0.0897187	−	0.276126i
$711$		0			0
$712$	−13.0140	−	9.45520i	−0.487719	−	0.354349i
$713$	−0.433135	−	1.33305i	−0.0162210	−	0.0499232i
$714$		0			0
$715$	23.0688	−	41.8364i	0.862725	−	1.56459i
$716$	19.3932			0.724758
$717$		0			0
$718$	0.738889	+	0.536834i	0.0275751	+	0.0200345i
$719$	−13.8307	+	10.0486i	−0.515798	+	0.374749i	−0.815018	−	0.579435i	$-0.803273\pi$
$719$	−13.8307	+	10.0486i	−0.515798	+	0.374749i	0.299221	+	0.954184i	$0.403273\pi$
$720$		0			0
$721$	−0.678855	+	2.08930i	−0.0252819	+	0.0778097i
$722$	15.6720	−	11.3863i	0.583250	−	0.423756i
$723$		0			0
$724$	0.151627	+	0.466659i	0.00563517	+	0.0173433i
$725$	83.4206			3.09816
$726$		0			0
$727$	−33.3798			−1.23799			−0.618993	−	0.785396i	$-0.712459\pi$
$727$	−33.3798			−1.23799			−0.618993	+	0.785396i	$0.712459\pi$
$728$	−1.67059	−	5.14154i	−0.0619161	−	0.190558i
$729$		0			0
$730$	−6.43739	+	4.67704i	−0.238258	+	0.173105i
$731$	2.72387	−	8.38321i	0.100746	−	0.310064i
$732$		0			0
$733$	32.9645	−	23.9501i	1.21757	−	0.884616i	0.221674	−	0.975121i	$-0.428848\pi$
$733$	32.9645	−	23.9501i	1.21757	−	0.884616i	0.995896	+	0.0905044i	$0.0288479\pi$
$734$	47.1294	+	34.2415i	1.73958	+	1.26388i
$735$		0			0
$736$	−1.20398			−0.0443793
$737$	4.90663	−	8.89841i	0.180738	−	0.327777i
$738$		0			0
$739$	2.82810	+	8.70398i	0.104033	+	0.320181i	0.989502	−	0.144517i	$-0.0461628\pi$
$739$	2.82810	+	8.70398i	0.104033	+	0.320181i	−0.885469	+	0.464698i	$0.846163\pi$
$740$	−36.0691	−	26.2057i	−1.32593	−	0.963342i
$741$		0			0
$742$	−4.90942	+	15.1097i	−0.180231	+	0.554693i
$743$	−10.0886	+	31.0495i	−0.370115	+	1.13910i	0.576601	+	0.817026i	$0.304379\pi$
$743$	−10.0886	+	31.0495i	−0.370115	+	1.13910i	−0.946716	+	0.322070i	$0.895621\pi$
$744$		0			0
$745$	−32.4955	−	23.6094i	−1.19054	−	0.864981i
$746$	−4.49288	−	13.8277i	−0.164496	−	0.506267i
$747$		0			0
$748$	6.62235	+	1.27198i	0.242137	+	0.0465081i
$749$	1.40016			0.0511606
$750$		0			0
$751$	−32.0338	−	23.2739i	−1.16893	−	0.849278i	−0.178050	−	0.984021i	$-0.556979\pi$
$751$	−32.0338	−	23.2739i	−1.16893	−	0.849278i	−0.990881	+	0.134743i	$0.956979\pi$
$752$	−45.6178	+	33.1433i	−1.66351	+	1.20861i
$753$		0			0
$754$	16.9728	−	52.2370i	0.618114	−	1.90236i
$755$	65.3564	−	47.4842i	2.37856	−	1.72813i
$756$		0			0
$757$	−7.54729	−	23.2282i	−0.274311	−	0.844242i	−0.989401	−	0.145210i	$-0.953614\pi$
$757$	−7.54729	−	23.2282i	−0.274311	−	0.844242i	0.715090	−	0.699032i	$-0.246386\pi$
$758$	−11.3119			−0.410868
$759$		0			0
$760$	17.9317			0.650452
$761$	−1.08662	−	3.34427i	−0.0393900	−	0.121230i	0.929428	−	0.369004i	$-0.120301\pi$
$761$	−1.08662	−	3.34427i	−0.0393900	−	0.121230i	−0.968818	+	0.247774i	$0.920301\pi$
$762$		0			0
$763$	11.1016	−	8.06580i	0.401906	−	0.292002i
$764$	−3.38399	+	10.4148i	−0.122428	+	0.376796i
$765$		0			0
$766$	21.6507	−	15.7301i	0.782271	−	0.568353i
$767$	−7.03618	−	5.11209i	−0.254062	−	0.184587i
$768$		0			0
$769$	15.8851			0.572833			0.286416	−	0.958105i	$-0.407536\pi$
$769$	15.8851			0.572833			0.286416	+	0.958105i	$0.407536\pi$
$770$	2.43815	+	19.4986i	0.0878648	+	0.702679i
$771$		0			0
$772$	4.08656	+	12.5771i	0.147078	+	0.452661i
$773$	−29.4747	−	21.4146i	−1.06013	−	0.770230i	−0.0860181	−	0.996294i	$-0.527414\pi$
$773$	−29.4747	−	21.4146i	−1.06013	−	0.770230i	−0.974113	+	0.226064i	$0.927414\pi$
$774$		0			0
$775$	−19.3645	+	59.5978i	−0.695594	+	2.14082i
$776$	0.207572	−	0.638840i	0.00745138	−	0.0229330i
$777$		0			0
$778$	20.3634	+	14.7948i	0.730062	+	0.530421i
$779$	−4.80686	−	14.7940i	−0.172224	−	0.530050i
$780$		0			0
$781$	−2.59897	−	2.77466i	−0.0929986	−	0.0992852i
$782$	0.745881			0.0266727
$783$		0			0
$784$	−25.1825	−	18.2961i	−0.899374	−	0.653433i
$785$	63.2147	−	45.9282i	2.25623	−	1.63925i
$786$		0			0
$787$	−10.6356	+	32.7329i	−0.379117	+	1.16680i	0.561543	+	0.827448i	$0.310208\pi$
$787$	−10.6356	+	32.7329i	−0.379117	+	1.16680i	−0.940659	+	0.339353i	$0.889792\pi$
$788$	−13.3805	+	9.72148i	−0.476659	+	0.346313i
$789$		0			0
$790$	23.2009	+	71.4051i	0.825452	+	2.54048i
$791$	2.16040			0.0768150
$792$		0			0
$793$	24.5336			0.871212
$794$	−13.9712	−	42.9991i	−0.495821	−	1.52598i
$795$		0			0
$796$	−13.6363	+	9.90736i	−0.483326	+	0.351157i
$797$	−14.0495	+	43.2399i	−0.497659	+	1.53164i	0.315112	+	0.949054i	$0.397958\pi$
$797$	−14.0495	+	43.2399i	−0.497659	+	1.53164i	−0.812771	+	0.582583i	$0.802042\pi$
$798$		0			0
$799$	17.5807	−	12.7731i	0.621959	−	0.451880i
$800$	43.5472	+	31.6389i	1.53963	+	1.11860i
$801$		0			0
$802$	45.2455			1.59768
$803$	0.485173	+	3.88006i	0.0171214	+	0.136924i
$804$		0			0
$805$	0.232061	+	0.714210i	0.00817907	+	0.0251726i
$806$	33.3796	+	24.2517i	1.17574	+	0.854229i
$807$		0			0
$808$	−3.61717	+	11.1325i	−0.127252	+	0.391641i
$809$	−5.98534	+	18.4210i	−0.210433	+	0.647648i	0.789013	+	0.614377i	$0.210592\pi$
$809$	−5.98534	+	18.4210i	−0.210433	+	0.647648i	−0.999446	+	0.0332710i	$0.989408\pi$
$810$		0			0
$811$	2.82641	+	2.05351i	0.0992486	+	0.0721083i	0.636303	−	0.771439i	$-0.280463\pi$
$811$	2.82641	+	2.05351i	0.0992486	+	0.0721083i	−0.537054	+	0.843548i	$0.680463\pi$
$812$	2.41203	+	7.42346i	0.0846456	+	0.260512i
$813$		0			0
$814$	−57.4116	+	26.9271i	−2.01228	+	0.943794i
$815$	−46.3569			−1.62381
$816$		0			0
$817$	10.4203	+	7.57079i	0.364560	+	0.264868i
$818$	−15.9860	+	11.6145i	−0.558936	+	0.406091i
$819$		0			0
$820$	6.96311	−	21.4303i	0.243162	−	0.748377i
$821$	−41.7441	+	30.3289i	−1.45688	+	1.05849i	−0.472719	+	0.881213i	$0.656727\pi$
$821$	−41.7441	+	30.3289i	−1.45688	+	1.05849i	−0.984162	+	0.177273i	$0.943273\pi$
$822$		0			0
$823$	9.85022	+	30.3159i	0.343357	+	1.05674i	0.962457	+	0.271433i	$0.0874975\pi$
$823$	9.85022	+	30.3159i	0.343357	+	1.05674i	−0.619100	+	0.785312i	$0.712502\pi$
$824$	4.13034			0.143887
$825$		0			0
$826$	3.57726			0.124469
$827$	−4.11030	−	12.6502i	−0.142929	−	0.439890i	0.853810	−	0.520585i	$-0.174286\pi$
$827$	−4.11030	−	12.6502i	−0.142929	−	0.439890i	−0.996739	+	0.0806946i	$0.974286\pi$
$828$		0			0
$829$	13.3163	−	9.67486i	0.462494	−	0.336022i	−0.332015	−	0.943274i	$-0.607728\pi$
$829$	13.3163	−	9.67486i	0.462494	−	0.336022i	0.794509	+	0.607253i	$0.207728\pi$
$830$	−10.4908	+	32.2875i	−0.364142	+	1.12071i
$831$		0			0
$832$	−1.49364	+	1.08519i	−0.0517827	+	0.0376224i
$833$	9.70508	+	7.05115i	0.336261	+	0.244308i
$834$		0			0
$835$	71.1813			2.46333
$836$	−4.75797	+	8.62881i	−0.164558	+	0.298434i
$837$		0			0
$838$	12.0529	+	37.0951i	0.416362	+	1.28143i
$839$	−41.3931	−	30.0739i	−1.42905	−	1.03827i	−0.990193	−	0.139708i	$-0.955383\pi$
$839$	−41.3931	−	30.0739i	−1.42905	−	1.03827i	−0.438857	−	0.898557i	$-0.644617\pi$
$840$		0			0
$841$	12.9538	−	39.8678i	0.446684	−	1.37475i
$842$	−15.8578	+	48.8053i	−0.546496	+	1.68194i
$843$		0			0
$844$	15.9441	+	11.5841i	0.548820	+	0.398741i
$845$	1.09815	+	3.37977i	0.0377776	+	0.116268i
$846$		0			0
$847$	8.96951	+	3.57759i	0.308196	+	0.122928i
$848$	51.7309			1.77645
$849$		0			0
$850$	−26.9781	−	19.6007i	−0.925340	−	0.672299i
$851$	−1.96057	+	1.42444i	−0.0672074	+	0.0488290i
$852$		0			0
$853$	3.98393	−	12.2613i	0.136407	−	0.419818i	−0.859399	−	0.511305i	$-0.829162\pi$
$853$	3.98393	−	12.2613i	0.136407	−	0.419818i	0.995806	+	0.0914875i	$0.0291622\pi$
$854$	−8.16373	+	5.93130i	−0.279357	+	0.202965i
$855$		0			0
$856$	−0.813486	−	2.50365i	−0.0278044	−	0.0855731i
$857$	−8.46528			−0.289169			−0.144584	−	0.989492i	$-0.546184\pi$
$857$	−8.46528			−0.289169			−0.144584	+	0.989492i	$0.546184\pi$
$858$		0			0
$859$	25.2349			0.861004			0.430502	−	0.902590i	$-0.358337\pi$
$859$	25.2349			0.861004			0.430502	+	0.902590i	$0.358337\pi$
$860$	5.76563	+	17.7448i	0.196606	+	0.605092i
$861$		0			0
$862$	−51.0350	+	37.0791i	−1.73826	+	1.26292i
$863$	6.65244	−	20.4741i	0.226452	−	0.696947i	−0.771689	−	0.636000i	$-0.780588\pi$
$863$	6.65244	−	20.4741i	0.226452	−	0.696947i	0.998141	−	0.0609470i	$-0.0194121\pi$
$864$		0			0
$865$	−6.16801	+	4.48132i	−0.209719	+	0.152370i
$866$	−24.9903	−	18.1565i	−0.849206	−	0.616984i
$867$		0			0
$868$	−5.86342			−0.199017
$869$	36.2336	+	6.95952i	1.22914	+	0.236086i
$870$		0			0
$871$	3.53242	+	10.8717i	0.119691	+	0.368372i
$872$	−20.8726	−	15.1649i	−0.706837	−	0.513547i
$873$		0			0
$874$	−0.336799	+	1.03656i	−0.0113924	+	0.0350622i
$875$	5.13815	−	15.8136i	0.173701	−	0.534597i
$876$		0			0
$877$	30.8763	+	22.4330i	1.04262	+	0.757508i	0.970795	−	0.239909i	$-0.0771177\pi$
$877$	30.8763	+	22.4330i	1.04262	+	0.757508i	0.0718248	+	0.997417i	$0.477118\pi$
$878$	−9.46116	−	29.1185i	−0.319299	−	0.982701i
$879$		0			0
$880$	57.9292	−	27.1698i	1.95279	−	0.915895i
$881$	11.9022			0.400996			0.200498	−	0.979694i	$-0.435744\pi$
$881$	11.9022			0.400996			0.200498	+	0.979694i	$0.435744\pi$
$882$		0			0
$883$	−13.0075	−	9.45048i	−0.437736	−	0.318034i	0.346998	−	0.937866i	$-0.387201\pi$
$883$	−13.0075	−	9.45048i	−0.437736	−	0.318034i	−0.784735	+	0.619832i	$0.787201\pi$
$884$	−6.13716	+	4.45891i	−0.206415	+	0.149969i
$885$		0			0
$886$	−1.02055	+	3.14093i	−0.0342861	+	0.105522i
$887$	−40.8231	+	29.6597i	−1.37070	+	0.995875i	−0.373023	+	0.927822i	$0.621679\pi$
$887$	−40.8231	+	29.6597i	−1.37070	+	0.995875i	−0.997682	+	0.0680528i	$0.978321\pi$
$888$		0			0
$889$	−0.716888	−	2.20635i	−0.0240436	−	0.0739987i
$890$	−65.7760			−2.20481
$891$		0			0
$892$	7.27142			0.243465
$893$	9.81247	+	30.1997i	0.328362	+	1.01059i
$894$		0			0
$895$	−57.3723	+	41.6834i	−1.91775	+	1.39332i
$896$	3.18288	−	9.79589i	0.106332	−	0.327258i
$897$		0			0
$898$	−13.4525	+	9.77385i	−0.448917	+	0.326158i
$899$	43.0997	+	31.3137i	1.43745	+	1.04437i
$900$		0			0
$901$	−19.9366			−0.664184
$902$	−21.9097	−	23.3908i	−0.729513	−	0.778827i
$903$		0			0
$904$	−1.25518	−	3.86306i	−0.0417468	−	0.128483i
$905$	−1.45160	−	1.05465i	−0.0482528	−	0.0350577i
$906$		0			0
$907$	−5.09517	+	15.6813i	−0.169182	+	0.520690i	−0.999320	−	0.0368686i	$-0.988262\pi$
$907$	−5.09517	+	15.6813i	−0.169182	+	0.520690i	0.830138	+	0.557558i	$0.188262\pi$
$908$	−2.17537	+	6.69510i	−0.0721921	+	0.222185i
$909$		0			0
$910$	−17.8838	−	12.9933i	−0.592842	−	0.430725i
$911$	15.6143	+	48.0560i	0.517326	+	1.59217i	0.779010	+	0.627012i	$0.215722\pi$
$911$	15.6143	+	48.0560i	0.517326	+	1.59217i	−0.261684	+	0.965154i	$0.584278\pi$
$912$		0			0
$913$	11.4051	+	12.1761i	0.377455	+	0.402970i
$914$	−32.2187			−1.06570
$915$		0			0
$916$	−15.5304	−	11.2835i	−0.513139	−	0.372817i
$917$	14.2417	−	10.3472i	0.470302	−	0.341695i
$918$		0			0
$919$	−6.74826	+	20.7690i	−0.222605	+	0.685106i	0.775921	+	0.630830i	$0.217285\pi$
$919$	−6.74826	+	20.7690i	−0.222605	+	0.685106i	−0.998526	+	0.0542767i	$0.982715\pi$
$920$	1.14227	−	0.829906i	0.0376595	−	0.0273612i
$921$		0			0
$922$	−7.05571	−	21.7152i	−0.232367	−	0.715153i
$923$	4.27677			0.140772
$924$		0			0
$925$	108.345			3.56235
$926$	−10.4438	−	32.1428i	−0.343206	−	1.05628i
$927$		0			0
$928$	37.0214	−	26.8976i	1.21529	−	0.882957i
$929$	6.33735	−	19.5043i	0.207922	−	0.639917i	−0.791659	−	0.610963i	$-0.790782\pi$
$929$	6.33735	−	19.5043i	0.207922	−	0.639917i	0.999581	−	0.0289538i	$-0.00921758\pi$
$930$		0			0
$931$	−14.1813	+	10.3033i	−0.464775	+	0.337679i
$932$	1.57296	+	1.14282i	0.0515241	+	0.0374344i
$933$		0			0
$934$	4.03586			0.132058
$935$	−22.3254	+	10.4710i	−0.730117	+	0.342438i
$936$		0			0
$937$	13.0605	+	40.1959i	0.426666	+	1.31314i	0.901390	+	0.433009i	$0.142548\pi$
$937$	13.0605	+	40.1959i	0.426666	+	1.31314i	−0.474723	+	0.880135i	$0.657452\pi$
$938$	−3.80380	−	2.76362i	−0.124198	−	0.0902355i
$939$		0			0
$940$	−14.2141	+	43.7466i	−0.463614	+	1.42686i
$941$	−2.43535	+	7.49524i	−0.0793902	+	0.244338i	−0.982872	−	0.184288i	$-0.941002\pi$
$941$	−2.43535	+	7.49524i	−0.0793902	+	0.244338i	0.903482	+	0.428626i	$0.141002\pi$
$942$		0			0
$943$	−0.990889	−	0.719923i	−0.0322678	−	0.0234439i
$944$	−3.59944	−	11.0779i	−0.117152	−	0.360556i
$945$		0			0
$946$	26.0613	+	5.00568i	0.847326	+	0.162749i
$947$	−30.1367			−0.979310			−0.489655	−	0.871916i	$-0.662877\pi$
$947$	−30.1367			−0.979310			−0.489655	+	0.871916i	$0.662877\pi$
$948$		0			0
$949$	−3.55874	−	2.58557i	−0.115521	−	0.0839313i
$950$	39.4212	−	28.6411i	1.27899	−	0.929241i
$951$		0			0
$952$	−0.862269	+	2.65379i	−0.0279463	+	0.0860098i
$953$	−24.5794	+	17.8580i	−0.796206	+	0.578477i	−0.909799	−	0.415050i	$-0.863764\pi$
$953$	−24.5794	+	17.8580i	−0.796206	+	0.578477i	0.113593	+	0.993527i	$0.463764\pi$
$954$		0			0
$955$	−12.3744	−	38.0845i	−0.400426	−	1.23238i
$956$	21.5198			0.696000
$957$		0			0
$958$	−4.87093			−0.157373
$959$	1.30908	+	4.02895i	0.0422725	+	0.130102i
$960$		0			0
$961$	−7.29661	+	5.30129i	−0.235374	+	0.171009i
$962$	22.0439	−	67.8442i	0.710724	−	2.18738i
$963$		0			0
$964$	0.651172	−	0.473104i	0.0209728	−	0.0152377i
$965$	−39.1226	−	28.4243i	−1.25940	−	0.915009i
$966$		0			0
$967$	51.6795			1.66190			0.830951	−	0.556346i	$-0.187797\pi$
$967$	51.6795			1.66190			0.830951	+	0.556346i	$0.187797\pi$
$968$	1.18593	−	18.1171i	0.0381171	−	0.582307i
$969$		0			0
$970$	−0.848756	−	2.61220i	−0.0272519	−	0.0838728i
$971$	6.80481	+	4.94398i	0.218377	+	0.158660i	0.691596	−	0.722285i	$-0.256908\pi$
$971$	6.80481	+	4.94398i	0.218377	+	0.158660i	−0.473219	+	0.880945i	$0.656908\pi$
$972$		0			0
$973$	−4.78596	+	14.7297i	−0.153431	+	0.472211i
$974$	−3.68943	+	11.3549i	−0.118217	+	0.363835i
$975$		0			0
$976$	26.5822	+	19.3131i	0.850875	+	0.618197i
$977$	0.703653	+	2.16562i	0.0225118	+	0.0692843i	0.961681	−	0.274170i	$-0.0884030\pi$
$977$	0.703653	+	2.16562i	0.0225118	+	0.0692843i	−0.939169	+	0.343454i	$0.888403\pi$
$978$		0			0
$979$	−15.6080	+	28.3058i	−0.498834	+	0.904659i
$980$	−25.3923			−0.811127
$981$		0			0
$982$	−24.0224	−	17.4533i	−0.766586	−	0.556958i
$983$	31.5418	−	22.9164i	1.00603	−	0.730921i	0.0426547	−	0.999090i	$-0.486418\pi$
$983$	31.5418	−	22.9164i	1.00603	−	0.730921i	0.963372	+	0.268169i	$0.0864185\pi$
$984$		0			0
$985$	18.6892	−	57.5195i	0.595488	−	1.83272i
$986$	−22.9352	+	16.6634i	−0.730407	+	0.530671i
$987$		0			0
$988$	−3.42539	−	10.5423i	−0.108976	−	0.335394i
$989$	1.01417			0.0322487
$990$		0			0
$991$	5.27167			0.167460			0.0837300	−	0.996488i	$-0.473317\pi$
$991$	5.27167			0.167460			0.0837300	+	0.996488i	$0.473317\pi$
$992$	10.6225	+	32.6928i	0.337266	+	1.03800i
$993$		0			0
$994$	−1.42313	+	1.03396i	−0.0451389	+	0.0327953i
$995$	19.0466	−	58.6193i	0.603817	−	1.85836i
$996$		0			0
$997$	16.1875	−	11.7609i	0.512662	−	0.372471i	−0.301170	−	0.953570i	$-0.597377\pi$
$997$	16.1875	−	11.7609i	0.512662	−	0.372471i	0.813833	+	0.581099i	$0.197377\pi$
$998$	8.98983	+	6.53149i	0.284568	+	0.206751i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.a.82.3	✓	16
3.2	odd	2		297.2.f.d.82.2	yes	16
9.2	odd	6		891.2.n.f.676.2		32
9.4	even	3		891.2.n.i.379.2		32
9.5	odd	6		891.2.n.f.379.3		32
9.7	even	3		891.2.n.i.676.3		32
11.3	even	5		3267.2.a.bm.1.6		8
11.8	odd	10		3267.2.a.bf.1.3		8
11.9	even	5	inner	297.2.f.a.163.3	yes	16
33.8	even	10		3267.2.a.bl.1.6		8
33.14	odd	10		3267.2.a.be.1.3		8
33.20	odd	10		297.2.f.d.163.2	yes	16
99.20	odd	30		891.2.n.f.757.3		32
99.31	even	15		891.2.n.i.460.3		32
99.86	odd	30		891.2.n.f.460.2		32
99.97	even	15		891.2.n.i.757.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.82.3	✓	16	1.1	even	1	trivial
297.2.f.a.163.3	yes	16	11.9	even	5	inner
297.2.f.d.82.2	yes	16	3.2	odd	2
297.2.f.d.163.2	yes	16	33.20	odd	10
891.2.n.f.379.3		32	9.5	odd	6
891.2.n.f.460.2		32	99.86	odd	30
891.2.n.f.676.2		32	9.2	odd	6
891.2.n.f.757.3		32	99.20	odd	30
891.2.n.i.379.2		32	9.4	even	3
891.2.n.i.460.3		32	99.31	even	15
891.2.n.i.676.3		32	9.7	even	3
891.2.n.i.757.2		32	99.97	even	15
3267.2.a.be.1.3		8	33.14	odd	10
3267.2.a.bf.1.3		8	11.8	odd	10
3267.2.a.bl.1.6		8	33.8	even	10
3267.2.a.bm.1.6		8	11.3	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540188 + 1.66253i) q^{2} +(-0.854162 + 0.620585i) q^{4} +(1.19305 - 3.67184i) q^{5} +(-0.710219 + 0.516004i) q^{7} +(1.33531 + 0.970162i) q^{8} +O(q^{10})\)	\(q+(0.540188 + 1.66253i) q^{2} +(-0.854162 + 0.620585i) q^{4} +(1.19305 - 3.67184i) q^{5} +(-0.710219 + 0.516004i) q^{7} +(1.33531 + 0.970162i) q^{8} +6.74902 q^{10} +(1.60148 - 2.90435i) q^{11} +(1.15295 + 3.54840i) q^{13} +(-1.24152 - 0.902019i) q^{14} +(-1.54412 + 4.75232i) q^{16} +(0.595090 - 1.83150i) q^{17} +(2.27654 + 1.65401i) q^{19} +(1.25963 + 3.87674i) q^{20} +(5.69367 + 1.09360i) q^{22} +0.221568 q^{23} +(-8.01398 - 5.82250i) q^{25} +(-5.27651 + 3.83361i) q^{26} +(0.286418 - 0.881503i) q^{28} +(-6.81303 + 4.94996i) q^{29} +(-1.95486 - 6.01645i) q^{31} -5.43391 q^{32} +3.36638 q^{34} +(1.04736 + 3.22343i) q^{35} +(-8.84860 + 6.42888i) q^{37} +(-1.52007 + 4.67829i) q^{38} +(5.15538 - 3.74561i) q^{40} +(-4.47217 - 3.24922i) q^{41} +4.57724 q^{43} +(0.434478 + 3.47464i) q^{44} +(0.119688 + 0.368363i) q^{46} +(9.12925 + 6.63279i) q^{47} +(-1.92497 + 5.92444i) q^{49} +(5.35101 - 16.4687i) q^{50} +(-3.18689 - 2.31541i) q^{52} +(-3.19914 - 9.84594i) q^{53} +(-8.75369 - 9.34543i) q^{55} -1.44897 q^{56} +(-11.9098 - 8.65295i) q^{58} +(-1.88586 + 1.37016i) q^{59} +(2.03196 - 6.25374i) q^{61} +(8.94652 - 6.50002i) q^{62} +(0.152913 + 0.470618i) q^{64} +14.4047 q^{65} +3.06382 q^{67} +(0.628297 + 1.93370i) q^{68} +(-4.79328 + 3.48252i) q^{70} +(0.354219 - 1.09017i) q^{71} +(-0.953826 + 0.692995i) q^{73} +(-15.4681 - 11.2382i) q^{74} -2.97099 q^{76} +(0.361260 + 2.88910i) q^{77} +(3.43768 + 10.5801i) q^{79} +(15.6076 + 11.3396i) q^{80} +(2.98611 - 9.19029i) q^{82} +(-1.55442 + 4.78403i) q^{83} +(-6.01500 - 4.37015i) q^{85} +(2.47257 + 7.60979i) q^{86} +(4.95617 - 2.32453i) q^{88} -9.74600 q^{89} +(-2.64984 - 1.92522i) q^{91} +(-0.189255 + 0.137502i) q^{92} +(-6.09568 + 18.7606i) q^{94} +(8.78930 - 6.38580i) q^{95} +(-0.125760 - 0.387049i) q^{97} -10.8894 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7	\( 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7} + 6 q^{10} - 13 q^{11} - 2 q^{13} + 22 q^{14} - 24 q^{16} + 2 q^{17} - 2 q^{19} + 15 q^{22} - 14 q^{23} - 19 q^{25} - 21 q^{26} + 15 q^{28} - q^{29} + 14 q^{31} + 48 q^{32} + 10 q^{34} + 18 q^{35} + 9 q^{37} - 11 q^{38} + 33 q^{40} - 25 q^{41} + 14 q^{43} - 14 q^{44} + 4 q^{46} + 28 q^{47} - 4 q^{49} + 63 q^{50} + 10 q^{52} - q^{53} - 40 q^{55} - 96 q^{56} - 20 q^{58} - 41 q^{59} + 5 q^{62} - 92 q^{64} + 60 q^{65} - 48 q^{67} - 25 q^{68} - 31 q^{70} - 3 q^{71} - 13 q^{73} - 29 q^{74} - 58 q^{76} + 2 q^{77} + 83 q^{80} + 41 q^{82} + 14 q^{83} - 10 q^{85} + 56 q^{86} + 86 q^{88} - 82 q^{89} + 14 q^{91} - 74 q^{92} - 2 q^{94} + 56 q^{95} + 12 q^{97} - 26 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7 + 6 * q^10 - 13 * q^11 - 2 * q^13 + 22 * q^14 - 24 * q^16 + 2 * q^17 - 2 * q^19 + 15 * q^22 - 14 * q^23 - 19 * q^25 - 21 * q^26 + 15 * q^28 - q^29 + 14 * q^31 + 48 * q^32 + 10 * q^34 + 18 * q^35 + 9 * q^37 - 11 * q^38 + 33 * q^40 - 25 * q^41 + 14 * q^43 - 14 * q^44 + 4 * q^46 + 28 * q^47 - 4 * q^49 + 63 * q^50 + 10 * q^52 - q^53 - 40 * q^55 - 96 * q^56 - 20 * q^58 - 41 * q^59 + 5 * q^62 - 92 * q^64 + 60 * q^65 - 48 * q^67 - 25 * q^68 - 31 * q^70 - 3 * q^71 - 13 * q^73 - 29 * q^74 - 58 * q^76 + 2 * q^77 + 83 * q^80 + 41 * q^82 + 14 * q^83 - 10 * q^85 + 56 * q^86 + 86 * q^88 - 82 * q^89 + 14 * q^91 - 74 * q^92 - 2 * q^94 + 56 * q^95 + 12 * q^97 - 26 * q^98

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