LMFDB - Embedded newform 441.2.u.d.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	441.127
Dual form			441.2.u.d.316.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.402966 - 0.194058i) q^{2} +(-1.12226 - 1.40727i) q^{4} +(0.162101 + 0.710213i) q^{5} +(-1.42812 - 2.22721i) q^{7} +(0.378189 + 1.65695i) q^{8} +O(q^{10})$	\(q+(-0.402966 - 0.194058i) q^{2} +(-1.12226 - 1.40727i) q^{4} +(0.162101 + 0.710213i) q^{5} +(-1.42812 - 2.22721i) q^{7} +(0.378189 + 1.65695i) q^{8} +(0.0725012 - 0.317649i) q^{10} +(-3.11871 - 1.50189i) q^{11} +(2.26731 + 1.09188i) q^{13} +(0.143273 + 1.17463i) q^{14} +(-0.631909 + 2.76858i) q^{16} +(-3.59992 + 4.51416i) q^{17} -5.20820 q^{19} +(0.817538 - 1.02516i) q^{20} +(0.965280 + 1.21042i) q^{22} +(-5.47218 - 6.86189i) q^{23} +(4.02672 - 1.93917i) q^{25} +(-0.701761 - 0.879980i) q^{26} +(-1.53157 + 4.50924i) q^{28} +(-2.54566 + 3.19216i) q^{29} -4.41702 q^{31} +(2.91122 - 3.65056i) q^{32} +(2.32666 - 1.12046i) q^{34} +(1.35030 - 1.37530i) q^{35} +(-4.34155 + 5.44413i) q^{37} +(2.09873 + 1.01069i) q^{38} +(-1.11548 + 0.537189i) q^{40} +(0.150003 + 0.657205i) q^{41} +(1.08661 - 4.76076i) q^{43} +(1.38643 + 6.07436i) q^{44} +(0.873495 + 3.82703i) q^{46} +(2.54224 + 1.22428i) q^{47} +(-2.92097 + 6.36144i) q^{49} -1.99894 q^{50} +(-1.00794 - 4.41608i) q^{52} +(-8.42389 - 10.5632i) q^{53} +(0.561115 - 2.45841i) q^{55} +(3.15029 - 3.20863i) q^{56} +(1.64528 - 0.792324i) q^{58} +(-0.598629 + 2.62276i) q^{59} +(8.78325 - 11.0139i) q^{61} +(1.77991 + 0.857158i) q^{62} +(3.23555 - 1.55816i) q^{64} +(-0.407932 + 1.78727i) q^{65} -4.28478 q^{67} +10.3927 q^{68} +(-0.811012 + 0.292163i) q^{70} +(2.84281 + 3.56477i) q^{71} +(0.515660 - 0.248329i) q^{73} +(2.80597 - 1.35129i) q^{74} +(5.84494 + 7.32933i) q^{76} +(1.10885 + 9.09091i) q^{77} +4.07622 q^{79} -2.06871 q^{80} +(0.0670900 - 0.293941i) q^{82} +(4.48757 - 2.16110i) q^{83} +(-3.78957 - 1.82496i) q^{85} +(-1.36173 + 1.70756i) q^{86} +(1.30910 - 5.73555i) q^{88} +(6.71020 - 3.23146i) q^{89} +(-0.806134 - 6.60912i) q^{91} +(-3.51532 + 15.4016i) q^{92} +(-0.786854 - 0.986684i) q^{94} +(-0.844257 - 3.69893i) q^{95} +3.17139 q^{97} +(2.41154 - 1.99661i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

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 $

$2$	−0.402966	−	0.194058i	−0.284940	−	0.137220i	0.285955	−	0.958243i	$-0.407689\pi$
$2$	−0.402966	−	0.194058i	−0.284940	−	0.137220i	−0.570895	+	0.821023i	$0.693404\pi$
$3$		0			0
$3$		0			0
$4$	−1.12226	−	1.40727i	−0.561128	−	0.703633i
$5$	0.162101	+	0.710213i	0.0724940	+	0.317617i	0.998154	−	0.0607405i	$-0.0193462\pi$
$5$	0.162101	+	0.710213i	0.0724940	+	0.317617i	−0.925660	+	0.378357i	$0.876489\pi$
$6$		0			0
$7$	−1.42812	−	2.22721i	−0.539777	−	0.841808i
$7$	−1.42812	−	2.22721i	−0.539777	−	0.841808i
$8$	0.378189	+	1.65695i	0.133710	+	0.585821i
$9$		0			0
$10$	0.0725012	−	0.317649i	0.0229269	−	0.100449i
$11$	−3.11871	−	1.50189i	−0.940326	−	0.452837i	−0.100042	−	0.994983i	$-0.531898\pi$
$11$	−3.11871	−	1.50189i	−0.940326	−	0.452837i	−0.840284	+	0.542146i	$0.817612\pi$
$12$		0			0
$13$	2.26731	+	1.09188i	0.628839	+	0.302833i	0.721025	−	0.692909i	$-0.243671\pi$
$13$	2.26731	+	1.09188i	0.628839	+	0.302833i	−0.0921863	+	0.995742i	$0.529386\pi$
$14$	0.143273	+	1.17463i	0.0382913	+	0.313933i
$15$		0			0
$16$	−0.631909	+	2.76858i	−0.157977	+	0.692144i
$17$	−3.59992	+	4.51416i	−0.873110	+	1.09485i	0.121647	+	0.992573i	$0.461183\pi$
$17$	−3.59992	+	4.51416i	−0.873110	+	1.09485i	−0.994756	+	0.102272i	$0.967389\pi$
$18$		0			0
$19$	−5.20820			−1.19484			−0.597422	−	0.801927i	$-0.703808\pi$
$19$	−5.20820			−1.19484			−0.597422	+	0.801927i	$0.703808\pi$
$20$	0.817538	−	1.02516i	0.182807	−	0.229233i
$21$		0			0
$22$	0.965280	+	1.21042i	0.205798	+	0.258063i
$23$	−5.47218	−	6.86189i	−1.14103	−	1.43080i	−0.885888	−	0.463900i	$-0.846450\pi$
$23$	−5.47218	−	6.86189i	−1.14103	−	1.43080i	−0.255140	−	0.966904i	$-0.582122\pi$
$24$		0			0
$25$	4.02672	−	1.93917i	0.805344	−	0.387833i
$26$	−0.701761	−	0.879980i	−0.137627	−	0.172578i
$27$		0			0
$28$	−1.53157	+	4.50924i	−0.289439	+	0.852167i
$29$	−2.54566	+	3.19216i	−0.472717	+	0.592769i	−0.959834	−	0.280568i	$-0.909477\pi$
$29$	−2.54566	+	3.19216i	−0.472717	+	0.592769i	0.487117	+	0.873337i	$0.338049\pi$
$30$		0			0
$31$	−4.41702			−0.793320			−0.396660	−	0.917966i	$-0.629831\pi$
$31$	−4.41702			−0.793320			−0.396660	+	0.917966i	$0.629831\pi$
$32$	2.91122	−	3.65056i	0.514637	−	0.645334i
$33$		0			0
$34$	2.32666	−	1.12046i	0.399018	−	0.192157i
$35$	1.35030	−	1.37530i	0.228242	−	0.232468i
$36$		0			0
$37$	−4.34155	+	5.44413i	−0.713746	+	0.895009i	−0.997966	−	0.0637502i	$-0.979694\pi$
$37$	−4.34155	+	5.44413i	−0.713746	+	0.895009i	0.284220	+	0.958759i	$0.408265\pi$
$38$	2.09873	+	1.01069i	0.340459	+	0.163956i
$39$		0			0
$40$	−1.11548	+	0.537189i	−0.176373	+	0.0849370i
$41$	0.150003	+	0.657205i	0.0234265	+	0.102638i	0.985290	−	0.170893i	$-0.0546654\pi$
$41$	0.150003	+	0.657205i	0.0234265	+	0.102638i	−0.961863	+	0.273532i	$0.911808\pi$
$42$		0			0
$43$	1.08661	−	4.76076i	0.165707	−	0.726009i	−0.821974	−	0.569525i	$-0.807127\pi$
$43$	1.08661	−	4.76076i	0.165707	−	0.726009i	0.987681	−	0.156483i	$-0.0500158\pi$
$44$	1.38643	+	6.07436i	0.209013	+	0.915744i
$45$		0			0
$46$	0.873495	+	3.82703i	0.128790	+	0.564265i
$47$	2.54224	+	1.22428i	0.370823	+	0.178579i	0.610009	−	0.792395i	$-0.291166\pi$
$47$	2.54224	+	1.22428i	0.370823	+	0.178579i	−0.239185	+	0.970974i	$0.576880\pi$
$48$		0			0
$49$	−2.92097	+	6.36144i	−0.417281	+	0.908777i
$50$	−1.99894			−0.282693
$51$		0			0
$52$	−1.00794	−	4.41608i	−0.139776	−	0.612399i
$53$	−8.42389	−	10.5632i	−1.15711	−	1.45097i	−0.869986	−	0.493077i	$-0.835872\pi$
$53$	−8.42389	−	10.5632i	−1.15711	−	1.45097i	−0.287124	−	0.957893i	$-0.592699\pi$
$54$		0			0
$55$	0.561115	−	2.45841i	0.0756608	−	0.331491i
$56$	3.15029	−	3.20863i	0.420975	−	0.428771i
$57$		0			0
$58$	1.64528	−	0.792324i	0.216036	−	0.104037i
$59$	−0.598629	+	2.62276i	−0.0779348	+	0.341455i	−0.998830	−	0.0483551i	$-0.984602\pi$
$59$	−0.598629	+	2.62276i	−0.0779348	+	0.341455i	0.920895	+	0.389810i	$0.127459\pi$
$60$		0			0
$61$	8.78325	−	11.0139i	1.12458	−	1.41018i	0.224490	−	0.974476i	$-0.427929\pi$
$61$	8.78325	−	11.0139i	1.12458	−	1.41018i	0.900091	−	0.435703i	$-0.143500\pi$
$62$	1.77991	+	0.857158i	0.226048	+	0.108859i
$63$		0			0
$64$	3.23555	−	1.55816i	0.404444	−	0.194770i
$65$	−0.407932	+	1.78727i	−0.0505978	+	0.221683i
$66$		0			0
$67$	−4.28478			−0.523470			−0.261735	−	0.965140i	$-0.584295\pi$
$67$	−4.28478			−0.523470			−0.261735	+	0.965140i	$0.584295\pi$
$68$	10.3927			1.26030
$69$		0			0
$70$	−0.811012	+	0.292163i	−0.0969345	+	0.0349202i
$71$	2.84281	+	3.56477i	0.337379	+	0.423060i	0.921362	−	0.388706i	$-0.127078\pi$
$71$	2.84281	+	3.56477i	0.337379	+	0.423060i	−0.583983	+	0.811766i	$0.698506\pi$
$72$		0			0
$73$	0.515660	−	0.248329i	0.0603535	−	0.0290647i	−0.403464	−	0.914996i	$-0.632194\pi$
$73$	0.515660	−	0.248329i	0.0603535	−	0.0290647i	0.463817	+	0.885931i	$0.346480\pi$
$74$	2.80597	−	1.35129i	0.326188	−	0.157084i
$75$		0			0
$76$	5.84494	+	7.32933i	0.670461	+	0.840731i
$77$	1.10885	+	9.09091i	0.126365	+	1.03601i
$78$		0			0
$79$	4.07622			0.458610			0.229305	−	0.973355i	$-0.426355\pi$
$79$	4.07622			0.458610			0.229305	+	0.973355i	$0.426355\pi$
$80$	−2.06871			−0.231289
$81$		0			0
$82$	0.0670900	−	0.293941i	0.00740885	−	0.0324603i
$83$	4.48757	−	2.16110i	0.492574	−	0.237211i	−0.171071	−	0.985259i	$-0.554723\pi$
$83$	4.48757	−	2.16110i	0.492574	−	0.237211i	0.663645	+	0.748047i	$0.269008\pi$
$84$		0			0
$85$	−3.78957	−	1.82496i	−0.411036	−	0.197945i
$86$	−1.36173	+	1.70756i	−0.146839	+	0.184131i
$87$		0			0
$88$	1.30910	−	5.73555i	0.139551	−	0.611412i
$89$	6.71020	−	3.23146i	0.711280	−	0.342534i	−0.0430109	−	0.999075i	$-0.513695\pi$
$89$	6.71020	−	3.23146i	0.711280	−	0.342534i	0.754291	+	0.656540i	$0.227981\pi$
$90$		0			0
$91$	−0.806134	−	6.60912i	−0.0845058	−	0.692824i
$92$	−3.51532	+	15.4016i	−0.366497	+	1.60573i
$93$		0			0
$94$	−0.786854	−	0.986684i	−0.0811578	−	0.101769i
$95$	−0.844257	−	3.69893i	−0.0866190	−	0.379503i
$96$		0			0
$97$	3.17139			0.322006			0.161003	−	0.986954i	$-0.448527\pi$
$97$	3.17139			0.322006			0.161003	+	0.986954i	$0.448527\pi$
$98$	2.41154	−	1.99661i	0.243602	−	0.201688i
$99$		0			0
$100$	−7.24793	−	3.49042i	−0.724793	−	0.349042i
$101$	−3.43140	−	15.0339i	−0.341437	−	1.49593i	−0.796043	−	0.605240i	$-0.793077\pi$
$101$	−3.43140	−	15.0339i	−0.341437	−	1.49593i	0.454607	−	0.890692i	$-0.349780\pi$
$102$		0			0
$103$	0.954437	+	4.18166i	0.0940434	+	0.412031i	0.999934	−	0.0114804i	$-0.00365442\pi$
$103$	0.954437	+	4.18166i	0.0940434	+	0.412031i	−0.905891	+	0.423512i	$0.860797\pi$
$104$	−0.951721	+	4.16976i	−0.0933239	+	0.408879i
$105$		0			0
$106$	1.34466	+	5.89134i	0.130605	+	0.572218i
$107$	3.41470	−	1.64443i	0.330111	−	0.158973i	−0.261485	−	0.965208i	$-0.584212\pi$
$107$	3.41470	−	1.64443i	0.330111	−	0.158973i	0.591596	+	0.806234i	$0.298498\pi$
$108$		0			0
$109$	2.99937	+	1.44442i	0.287287	+	0.138350i	0.571977	−	0.820269i	$-0.306176\pi$
$109$	2.99937	+	1.44442i	0.287287	+	0.138350i	−0.284690	+	0.958620i	$0.591891\pi$
$110$	−0.703184	+	0.881765i	−0.0670460	+	0.0840730i
$111$		0			0
$112$	7.06865	−	2.54645i	0.667925	−	0.240617i
$113$	6.82116	−	3.28490i	0.641681	−	0.309017i	−0.0846005	−	0.996415i	$-0.526961\pi$
$113$	6.82116	−	3.28490i	0.641681	−	0.309017i	0.726281	+	0.687398i	$0.241247\pi$
$114$		0			0
$115$	3.98636	−	4.99873i	0.371730	−	0.466134i
$116$	7.34909			0.682346
$117$		0			0
$118$	0.750196	−	0.940716i	0.0690611	−	0.0865999i
$119$	15.1951	+	1.57105i	1.39293	+	0.144018i
$120$		0			0
$121$	0.612285	+	0.767781i	0.0556623	+	0.0697983i
$122$	−5.67668	+	2.73374i	−0.513942	+	0.247502i
$123$		0			0
$124$	4.95703	+	6.21591i	0.445154	+	0.558206i
$125$	4.30095	+	5.39322i	0.384688	+	0.482384i
$126$		0			0
$127$	−8.38014	+	10.5084i	−0.743617	+	0.932467i	−0.999413	−	0.0342644i	$-0.989091\pi$
$127$	−8.38014	+	10.5084i	−0.743617	+	0.932467i	0.255796	+	0.966731i	$0.417663\pi$
$128$	−10.9447			−0.967382
$129$		0			0
$130$	0.511217	−	0.641045i	0.0448367	−	0.0562234i
$131$	2.87554	−	12.5986i	0.251237	−	1.10074i	−0.679103	−	0.734043i	$-0.737631\pi$
$131$	2.87554	−	12.5986i	0.251237	−	1.10074i	0.930340	−	0.366699i	$-0.119512\pi$
$132$		0			0
$133$	7.43792	+	11.5998i	0.644950	+	1.00583i
$134$	1.72662	+	0.831497i	0.149157	+	0.0718304i
$135$		0			0
$136$	−8.84120	−	4.25770i	−0.758127	−	0.365095i
$137$	−0.107338	+	0.470276i	−0.00917046	+	0.0401784i	−0.979306	−	0.202384i	$-0.935131\pi$
$137$	−0.107338	+	0.470276i	−0.00917046	+	0.0401784i	0.970136	+	0.242563i	$0.0779881\pi$
$138$		0			0
$139$	−1.15982	−	5.08151i	−0.0983748	−	0.431008i	0.901624	−	0.432521i	$-0.142376\pi$
$139$	−1.15982	−	5.08151i	−0.0983748	−	0.431008i	−0.999999	+	0.00151250i	$0.999519\pi$
$140$	−3.45079	−	0.356785i	−0.291645	−	0.0301538i
$141$		0			0
$142$	−0.453782	−	1.98815i	−0.0380806	−	0.166842i
$143$	−5.43120	−	6.81051i	−0.454180	−	0.569523i
$144$		0			0
$145$	−2.67977	−	1.29051i	−0.222542	−	0.107171i
$146$	−0.255984			−0.0211854
$147$		0			0
$148$	12.5337			1.03026
$149$	0.0416240	+	0.0200451i	0.00340997	+	0.00164216i	0.435588	−	0.900146i	$-0.356540\pi$
$149$	0.0416240	+	0.0200451i	0.00340997	+	0.00164216i	−0.432178	+	0.901788i	$0.642255\pi$
$150$		0			0
$151$	−1.51799	−	1.90351i	−0.123533	−	0.154905i	0.716219	−	0.697875i	$-0.245871\pi$
$151$	−1.51799	−	1.90351i	−0.123533	−	0.154905i	−0.839752	+	0.542970i	$0.817300\pi$
$152$	−1.96968	−	8.62975i	−0.159762	−	0.699965i
$153$		0			0
$154$	1.31734	−	3.87851i	0.106154	−	0.312539i
$155$	−0.716005	−	3.13702i	−0.0575109	−	0.251972i
$156$		0			0
$157$	−4.96232	+	21.7413i	−0.396036	+	1.73515i	0.246729	+	0.969085i	$0.420644\pi$
$157$	−4.96232	+	21.7413i	−0.396036	+	1.73515i	−0.642765	+	0.766063i	$0.722213\pi$
$158$	−1.64258	−	0.791023i	−0.130676	−	0.0629304i
$159$		0			0
$160$	3.06459	+	1.47583i	0.242277	+	0.116674i
$161$	−7.46800	+	21.9873i	−0.588561	+	1.73284i
$162$		0			0
$163$	−3.35744	+	14.7099i	−0.262975	+	1.15217i	0.655031	+	0.755602i	$0.272656\pi$
$163$	−3.35744	+	14.7099i	−0.262975	+	1.15217i	−0.918006	+	0.396567i	$0.870201\pi$
$164$	0.756520	−	0.948647i	0.0590743	−	0.0740769i
$165$		0			0
$166$	−2.22772			−0.172904
$167$	11.4013	−	14.2968i	0.882258	−	1.10632i	−0.111390	−	0.993777i	$-0.535530\pi$
$167$	11.4013	−	14.2968i	0.882258	−	1.10632i	0.993647	−	0.112539i	$-0.0358984\pi$
$168$		0			0
$169$	−4.15687	−	5.21255i	−0.319759	−	0.400966i
$170$	1.17292	+	1.47079i	0.0899588	+	0.112805i
$171$		0			0
$172$	−7.91911	+	3.81364i	−0.603826	+	0.290787i
$173$	−10.2165	−	12.8111i	−0.776749	−	0.974013i	0.223250	−	0.974761i	$-0.428333\pi$
$173$	−10.2165	−	12.8111i	−0.776749	−	0.974013i	−1.00000		0.000748328i	$0.999762\pi$
$174$		0			0
$175$	−10.0696	−	6.19901i	−0.761187	−	0.468601i
$176$	6.12884	−	7.68533i	0.461979	−	0.579303i
$177$		0			0
$178$	−3.33108			−0.249675
$179$	−3.77527	+	4.73404i	−0.282177	+	0.353839i	−0.902640	−	0.430397i	$-0.858373\pi$
$179$	−3.77527	+	4.73404i	−0.282177	+	0.353839i	0.620463	+	0.784236i	$0.286945\pi$
$180$		0			0
$181$	−4.31600	+	2.07848i	−0.320806	+	0.154492i	−0.587355	−	0.809329i	$-0.699831\pi$
$181$	−4.31600	+	2.07848i	−0.320806	+	0.154492i	0.266549	+	0.963821i	$0.414117\pi$
$182$	−0.957709	+	2.81969i	−0.0709901	+	0.209009i
$183$		0			0
$184$	9.30032	−	11.6622i	0.685629	−	0.859751i
$185$	−4.57026	−	2.20092i	−0.336012	−	0.161815i
$186$		0			0
$187$	18.0069	−	8.67167i	1.31680	−	0.634135i
$188$	−1.13016	−	4.95155i	−0.0824254	−	0.361129i
$189$		0			0
$190$	−0.377601	+	1.65438i	−0.0273941	+	0.120021i
$191$	2.26309	+	9.91523i	0.163751	+	0.717441i	0.988410	+	0.151810i	$0.0485102\pi$
$191$	2.26309	+	9.91523i	0.163751	+	0.717441i	−0.824658	+	0.565631i	$0.808633\pi$
$192$		0			0
$193$	−5.30033	−	23.2223i	−0.381526	−	1.67158i	−0.692702	−	0.721223i	$-0.743580\pi$
$193$	−5.30033	−	23.2223i	−0.381526	−	1.67158i	0.311176	−	0.950352i	$-0.399277\pi$
$194$	−1.27796	−	0.615435i	−0.0917524	−	0.0441856i
$195$		0			0
$196$	12.2303	−	3.02859i	0.873594	−	0.216328i
$197$	−25.2158			−1.79655			−0.898274	−	0.439436i	$-0.855178\pi$
$197$	−25.2158			−1.79655			−0.898274	+	0.439436i	$0.855178\pi$
$198$		0			0
$199$	−3.16846	−	13.8819i	−0.224606	−	0.984065i	−0.953961	−	0.299930i	$-0.903037\pi$
$199$	−3.16846	−	13.8819i	−0.224606	−	0.984065i	0.729355	−	0.684136i	$-0.239820\pi$
$200$	4.73597	+	5.93871i	0.334883	+	0.419930i
$201$		0			0
$202$	−1.53472	+	6.72405i	−0.107983	+	0.473103i
$203$	10.7451	+	1.11096i	0.754159	+	0.0779741i
$204$		0			0
$205$	−0.442440	+	0.213068i	−0.0309013	+	0.0148813i
$206$	0.426880	−	1.87028i	0.0297421	−	0.130309i
$207$		0			0
$208$	−4.45569	+	5.58725i	−0.308946	+	0.387406i
$209$	16.2429	+	7.82216i	1.12354	+	0.541070i
$210$		0			0
$211$	−15.1682	+	7.30461i	−1.04422	+	0.502870i	−0.875714	−	0.482831i	$-0.839609\pi$
$211$	−15.1682	+	7.30461i	−1.04422	+	0.502870i	−0.168506	+	0.985701i	$0.553894\pi$
$212$	−5.41149	+	23.7093i	−0.371663	+	1.62836i
$213$		0			0
$214$	−1.69512			−0.115876
$215$	3.55729			0.242605
$216$		0			0
$217$	6.30801	+	9.83764i	0.428216	+	0.667823i
$218$	−0.928341	−	1.16410i	−0.0628752	−	0.0788430i
$219$		0			0
$220$	−4.08934	+	1.96932i	−0.275704	+	0.132772i
$221$	−13.0911	+	6.30432i	−0.880600	+	0.424075i
$222$		0			0
$223$	−8.17696	−	10.2536i	−0.547570	−	0.686631i	0.428636	−	0.903477i	$-0.358994\pi$
$223$	−8.17696	−	10.2536i	−0.547570	−	0.686631i	−0.976206	+	0.216847i	$0.930423\pi$
$224$	−12.2881	−	1.27050i	−0.821036	−	0.0848887i
$225$		0			0
$226$	−3.38616			−0.225244
$227$	−27.3303			−1.81397			−0.906987	−	0.421159i	$-0.861623\pi$
$227$	−27.3303			−1.81397			−0.906987	+	0.421159i	$0.861623\pi$
$228$		0			0
$229$	4.02966	−	17.6551i	0.266288	−	1.16668i	−0.648008	−	0.761634i	$-0.724397\pi$
$229$	4.02966	−	17.6551i	0.266288	−	1.16668i	0.914295	−	0.405049i	$-0.132745\pi$
$230$	−2.57641	+	1.24073i	−0.169884	+	0.0818116i
$231$		0			0
$232$	−6.25199	−	3.01080i	−0.410463	−	0.197669i
$233$	−6.73423	+	8.44445i	−0.441174	+	0.553215i	−0.951852	−	0.306557i	$-0.900823\pi$
$233$	−6.73423	+	8.44445i	−0.441174	+	0.553215i	0.510678	+	0.859772i	$0.329394\pi$
$234$		0			0
$235$	−0.457397	+	2.00399i	−0.0298373	+	0.130726i
$236$	4.36274	−	2.10098i	0.283990	−	0.136762i
$237$		0			0
$238$	−5.81824	−	3.58182i	−0.377140	−	0.232175i
$239$	−3.85327	+	16.8823i	−0.249247	+	1.09202i	0.683062	+	0.730361i	$0.260648\pi$
$239$	−3.85327	+	16.8823i	−0.249247	+	1.09202i	−0.932309	+	0.361663i	$0.882209\pi$
$240$		0			0
$241$	6.31357	+	7.91697i	0.406693	+	0.509977i	0.942428	−	0.334409i	$-0.108537\pi$
$241$	6.31357	+	7.91697i	0.406693	+	0.509977i	−0.535735	+	0.844386i	$0.679965\pi$
$242$	−0.0977358	−	0.428209i	−0.00628270	−	0.0275263i
$243$		0			0
$244$	−25.3565			−1.62328
$245$	−4.99147	−	1.04331i	−0.318893	−	0.0666546i
$246$		0			0
$247$	−11.8086	−	5.68673i	−0.751364	−	0.361838i
$248$	−1.67047	−	7.31879i	−0.106075	−	0.464743i
$249$		0			0
$250$	−0.686537	−	3.00792i	−0.0434204	−	0.190237i
$251$	−4.51120	+	19.7648i	−0.284744	+	1.24755i	0.606889	+	0.794787i	$0.292417\pi$
$251$	−4.51120	+	19.7648i	−0.284744	+	1.24755i	−0.891633	+	0.452759i	$0.850440\pi$
$252$		0			0
$253$	6.76031	+	29.6189i	0.425017	+	1.86212i
$254$	5.41615	−	2.60828i	0.339839	−	0.163658i
$255$		0			0
$256$	−2.06077	−	0.992416i	−0.128798	−	0.0620260i
$257$	−17.7404	+	22.2458i	−1.10662	+	1.38766i	−0.192943	+	0.981210i	$0.561803\pi$
$257$	−17.7404	+	22.2458i	−1.10662	+	1.38766i	−0.913675	+	0.406445i	$0.866768\pi$
$258$		0			0
$259$	18.3255	+	1.89471i	1.13869	+	0.117731i
$260$	2.97296	−	1.43170i	0.184375	−	0.0887905i
$261$		0			0
$262$	−3.60360	+	4.51877i	−0.222631	+	0.279171i
$263$	−3.67291			−0.226481			−0.113241	−	0.993568i	$-0.536123\pi$
$263$	−3.67291			−0.226481			−0.113241	+	0.993568i	$0.536123\pi$
$264$		0			0
$265$	6.13661	−	7.69507i	0.376969	−	0.472704i
$266$	−0.746195	−	6.11771i	−0.0457522	−	0.375101i
$267$		0			0
$268$	4.80863	+	6.02983i	0.293734	+	0.368330i
$269$	25.9348	−	12.4895i	1.58127	−	0.761501i	0.582588	−	0.812767i	$-0.302040\pi$
$269$	25.9348	−	12.4895i	1.58127	−	0.761501i	0.998685	+	0.0512663i	$0.0163257\pi$
$270$		0			0
$271$	11.1789	+	14.0179i	0.679072	+	0.851529i	0.995268	−	0.0971646i	$-0.0309773\pi$
$271$	11.1789	+	14.0179i	0.679072	+	0.851529i	−0.316197	+	0.948694i	$0.602406\pi$
$272$	−10.2230	−	12.8192i	−0.619859	−	0.777279i
$273$		0			0
$274$	0.134514	−	0.168676i	0.00812631	−	0.0101901i
$275$	−15.4706			−0.932911
$276$		0			0
$277$	−11.2890	+	14.1560i	−0.678290	+	0.850549i	−0.995195	−	0.0979080i	$-0.968785\pi$
$277$	−11.2890	+	14.1560i	−0.678290	+	0.850549i	0.316905	+	0.948457i	$0.397356\pi$
$278$	−0.518740	+	2.27275i	−0.0311120	+	0.136310i
$279$		0			0
$280$	2.78948	+	1.71725i	0.166703	+	0.102626i
$281$	0.962940	+	0.463727i	0.0574442	+	0.0276637i	0.462385	−	0.886679i	$-0.346994\pi$
$281$	0.962940	+	0.463727i	0.0574442	+	0.0276637i	−0.404941	+	0.914343i	$0.632708\pi$
$282$		0			0
$283$	16.5163	+	7.95383i	0.981792	+	0.472806i	0.854721	−	0.519087i	$-0.173728\pi$
$283$	16.5163	+	7.95383i	0.981792	+	0.472806i	0.127071	+	0.991894i	$0.459442\pi$
$284$	1.82622	−	8.00117i	0.108366	−	0.474782i
$285$		0			0
$286$	0.866954	+	3.79837i	0.0512640	+	0.224602i
$287$	1.24952	−	1.27265i	0.0737566	−	0.0751224i
$288$		0			0
$289$	−3.63535	−	15.9275i	−0.213844	−	0.936913i
$290$	0.829421	+	1.04006i	0.0487053	+	0.0610745i
$291$		0			0
$292$	−0.928168	−	0.446982i	−0.0543169	−	0.0261576i
$293$	21.7500			1.27065			0.635325	−	0.772245i	$-0.280866\pi$
$293$	21.7500			1.27065			0.635325	+	0.772245i	$0.280866\pi$
$294$		0			0
$295$	−1.95976			−0.114102
$296$	−10.6626	−	5.13483i	−0.619750	−	0.298456i
$297$		0			0
$298$	−0.0128831	−	0.0161550i	−0.000746301	−	0.000935831i
$299$	−4.91477	−	21.5330i	−0.284228	−	1.24529i
$300$		0			0
$301$	−12.1550	+	4.37880i	−0.700605	+	0.252390i
$302$	0.242309	+	1.06163i	0.0139433	+	0.0610898i
$303$		0			0
$304$	3.29111	−	14.4193i	0.188758	−	0.827004i
$305$	9.24595	+	4.45262i	0.529422	+	0.254956i
$306$		0			0
$307$	0.813338	+	0.391683i	0.0464197	+	0.0223545i	0.456950	−	0.889493i	$-0.348942\pi$
$307$	0.813338	+	0.391683i	0.0464197	+	0.0223545i	−0.410530	+	0.911847i	$0.634656\pi$
$308$	11.5489	−	11.7628i	0.658060	−	0.670246i
$309$		0			0
$310$	−0.320239	+	1.40306i	−0.0181884	+	0.0796884i
$311$	8.66292	−	10.8630i	0.491229	−	0.615982i	−0.472997	−	0.881064i	$-0.656828\pi$
$311$	8.66292	−	10.8630i	0.491229	−	0.615982i	0.964226	+	0.265082i	$0.0853991\pi$
$312$		0			0
$313$	−18.5139			−1.04647			−0.523233	−	0.852190i	$-0.675274\pi$
$313$	−18.5139			−1.04647			−0.523233	+	0.852190i	$0.675274\pi$
$314$	6.21873	−	7.79804i	0.350943	−	0.440069i
$315$		0			0
$316$	−4.57456	−	5.73632i	−0.257339	−	0.322693i
$317$	−3.11259	−	3.90306i	−0.174820	−	0.219218i	0.686700	−	0.726941i	$-0.259059\pi$
$317$	−3.11259	−	3.90306i	−0.174820	−	0.219218i	−0.861520	+	0.507723i	$0.830487\pi$
$318$		0			0
$319$	12.7334	−	6.13210i	0.712936	−	0.343332i
$320$	1.63111	+	2.04535i	0.0911820	+	0.114339i
$321$		0			0
$322$	7.27617	−	7.41090i	0.405485	−	0.412994i
$323$	18.7491	−	23.5107i	1.04323	−	1.30817i
$324$		0			0
$325$	11.2472			0.623880
$326$	4.20751	−	5.27606i	0.233033	−	0.292214i
$327$		0			0
$328$	−1.03223	+	0.497095i	−0.0569953	+	0.0274475i
$329$	−0.903883	−	7.41052i	−0.0498327	−	0.408555i
$330$		0			0
$331$	10.9572	−	13.7399i	0.602264	−	0.755215i	−0.383465	−	0.923556i	$-0.625269\pi$
$331$	10.9572	−	13.7399i	0.602264	−	0.755215i	0.985729	+	0.168340i	$0.0538407\pi$
$332$	−8.07744	−	3.88989i	−0.443307	−	0.213485i
$333$		0			0
$334$	−7.36873	+	3.54859i	−0.403199	+	0.194170i
$335$	−0.694570	−	3.04311i	−0.0379484	−	0.166263i
$336$		0			0
$337$	1.99186	−	8.72692i	0.108504	−	0.475385i	−0.891257	−	0.453499i	$-0.850176\pi$
$337$	1.99186	−	8.72692i	0.108504	−	0.475385i	0.999760	−	0.0218865i	$-0.00696726\pi$
$338$	0.663539	+	2.90716i	0.0360918	+	0.158128i
$339$		0			0
$340$	1.68467	+	7.38100i	0.0913638	+	0.400291i
$341$	13.7754	+	6.63388i	0.745979	+	0.359245i
$342$		0			0
$343$	18.3398	−	2.57926i	0.990255	−	0.139267i
$344$	8.29929			0.447468
$345$		0			0
$346$	1.63081	+	7.14506i	0.0876730	+	0.384121i
$347$	0.973341	+	1.22053i	0.0522517	+	0.0655215i	0.807271	−	0.590181i	$-0.200944\pi$
$347$	0.973341	+	1.22053i	0.0522517	+	0.0655215i	−0.755019	+	0.655703i	$0.772372\pi$
$348$		0			0
$349$	−1.63426	+	7.16017i	−0.0874801	+	0.383275i	−0.999648	−	0.0265421i	$-0.991550\pi$
$349$	−1.63426	+	7.16017i	−0.0874801	+	0.383275i	0.912168	+	0.409817i	$0.134408\pi$
$350$	2.85472	+	4.45207i	0.152591	+	0.237973i
$351$		0			0
$352$	−14.5620	+	7.01269i	−0.776158	+	0.373778i
$353$	−7.82159	+	34.2686i	−0.416301	+	1.82393i	0.136524	+	0.990637i	$0.456407\pi$
$353$	−7.82159	+	34.2686i	−0.416301	+	1.82393i	−0.552825	+	0.833297i	$0.686450\pi$
$354$		0			0
$355$	−2.07092	+	2.59685i	−0.109913	+	0.137827i
$356$	−12.0781	−	5.81651i	−0.640138	−	0.308274i
$357$		0			0
$358$	2.43999	−	1.17504i	0.128957	−	0.0621025i
$359$	7.45672	−	32.6700i	0.393551	−	1.72426i	−0.258437	−	0.966028i	$-0.583208\pi$
$359$	7.45672	−	32.6700i	0.393551	−	1.72426i	0.651988	−	0.758229i	$-0.273935\pi$
$360$		0			0
$361$	8.12540			0.427653
$362$	2.14255			0.112610
$363$		0			0
$364$	−8.39609	+	8.55157i	−0.440075	+	0.448224i
$365$	0.259956	+	0.325974i	0.0136067	+	0.0170623i
$366$		0			0
$367$	12.3532	−	5.94899i	0.644832	−	0.310535i	−0.0827348	−	0.996572i	$-0.526365\pi$
$367$	12.3532	−	5.94899i	0.644832	−	0.310535i	0.727567	+	0.686037i	$0.240651\pi$
$368$	22.4556	−	10.8140i	1.17058	−	0.563721i
$369$		0			0
$370$	1.41455	+	1.77379i	0.0735391	+	0.0922151i
$371$	−11.4963	+	33.8473i	−0.596856	+	1.75726i
$372$		0			0
$373$	0.547746			0.0283612			0.0141806	−	0.999899i	$-0.495486\pi$
$373$	0.547746			0.0283612			0.0141806	+	0.999899i	$0.495486\pi$
$374$	−8.93898			−0.462223
$375$		0			0
$376$	−1.06712	+	4.67537i	−0.0550327	+	0.241114i
$377$	−9.25725	+	4.45806i	−0.476773	+	0.229602i
$378$		0			0
$379$	−21.7210	−	10.4603i	−1.11573	−	0.537309i	−0.217162	−	0.976136i	$-0.569680\pi$
$379$	−21.7210	−	10.4603i	−1.11573	−	0.537309i	−0.898572	+	0.438826i	$0.855394\pi$
$380$	−4.25791	+	5.33925i	−0.218426	+	0.273898i
$381$		0			0
$382$	1.01218	−	4.43467i	0.0517879	−	0.226898i
$383$	9.30259	−	4.47989i	0.475340	−	0.228912i	−0.180845	−	0.983512i	$-0.557883\pi$
$383$	9.30259	−	4.47989i	0.475340	−	0.228912i	0.656185	+	0.754600i	$0.272169\pi$
$384$		0			0
$385$	−6.27674	+	2.26117i	−0.319892	+	0.115240i
$386$	−2.37062	+	10.3864i	−0.120661	+	0.528652i
$387$		0			0
$388$	−3.55912	−	4.46299i	−0.180687	−	0.226574i
$389$	0.427243	+	1.87188i	0.0216621	+	0.0949078i	0.984603	−	0.174803i	$-0.0559289\pi$
$389$	0.427243	+	1.87188i	0.0216621	+	0.0949078i	−0.962941	+	0.269711i	$0.913072\pi$
$390$		0			0
$391$	50.6751			2.56275
$392$	−11.6453	−	2.43408i	−0.588176	−	0.122940i
$393$		0			0
$394$	10.1611	+	4.89332i	0.511908	+	0.246522i
$395$	0.660761	+	2.89498i	0.0332465	+	0.145662i
$396$		0			0
$397$	2.98564	+	13.0810i	0.149845	+	0.656515i	0.992927	+	0.118729i	$0.0378819\pi$
$397$	2.98564	+	13.0810i	0.149845	+	0.656515i	−0.843082	+	0.537786i	$0.819261\pi$
$398$	−1.41712	+	6.20882i	−0.0710339	+	0.311220i
$399$		0			0
$400$	2.82421	+	12.3737i	0.141210	+	0.618683i
$401$	28.3903	−	13.6720i	1.41774	−	0.682749i	0.441069	−	0.897473i	$-0.354599\pi$
$401$	28.3903	−	13.6720i	1.41774	−	0.682749i	0.976675	+	0.214724i	$0.0688852\pi$
$402$		0			0
$403$	−10.0147	−	4.82285i	−0.498870	−	0.240243i
$404$	−17.3058	+	21.7008i	−0.860997	+	1.07966i
$405$		0			0
$406$	−4.11432	−	2.53286i	−0.204191	−	0.125704i
$407$	21.7165	−	10.4581i	1.07645	−	0.518390i
$408$		0			0
$409$	−10.0320	+	12.5797i	−0.496051	+	0.622029i	−0.965333	−	0.261020i	$-0.915941\pi$
$409$	−10.0320	+	12.5797i	−0.496051	+	0.622029i	0.469282	+	0.883048i	$0.344513\pi$
$410$	0.219636			0.0108470
$411$		0			0
$412$	4.81358	−	6.03604i	0.237148	−	0.297374i
$413$	6.69637	−	2.41234i	0.329507	−	0.118703i
$414$		0			0
$415$	2.26228	+	2.83681i	0.111051	+	0.139254i
$416$	10.5866	−	5.09825i	0.519052	−	0.249962i
$417$		0			0
$418$	−5.02737	−	6.30413i	−0.245897	−	0.308345i
$419$	6.08727	+	7.63319i	0.297383	+	0.372906i	0.907964	−	0.419047i	$-0.137636\pi$
$419$	6.08727	+	7.63319i	0.297383	+	0.372906i	−0.610582	+	0.791953i	$0.709064\pi$
$420$		0			0
$421$	22.8212	−	28.6168i	1.11224	−	1.39470i	0.202615	−	0.979259i	$-0.435056\pi$
$421$	22.8212	−	28.6168i	1.11224	−	1.39470i	0.909620	−	0.415440i	$-0.136372\pi$
$422$	7.52978			0.366544
$423$		0			0
$424$	14.3169	−	17.9529i	0.695292	−	0.871869i
$425$	−5.74218	+	25.1581i	−0.278536	+	1.22035i
$426$		0			0
$427$	−37.0737	−	3.83313i	−1.79412	−	0.185498i
$428$	−6.14632	−	2.95991i	−0.297094	−	0.143073i
$429$		0			0
$430$	−1.43347	−	0.690322i	−0.0691279	−	0.0332903i
$431$	0.349675	−	1.53203i	0.0168433	−	0.0737951i	−0.965808	−	0.259259i	$-0.916522\pi$
$431$	0.349675	−	1.53203i	0.0168433	−	0.0737951i	0.982651	+	0.185464i	$0.0593788\pi$
$432$		0			0
$433$	−2.15350	−	9.43508i	−0.103490	−	0.453421i	−0.999947	−	0.0102897i	$-0.996725\pi$
$433$	−2.15350	−	9.43508i	−0.103490	−	0.453421i	0.896457	−	0.443131i	$-0.146133\pi$
$434$	−0.632839	−	5.18836i	−0.0303773	−	0.249049i
$435$		0			0
$436$	−1.33338	−	5.84191i	−0.0638573	−	0.279777i
$437$	28.5002	+	35.7382i	1.36335	+	1.70959i
$438$		0			0
$439$	−2.56377	−	1.23464i	−0.122362	−	0.0589264i	0.371701	−	0.928352i	$-0.378775\pi$
$439$	−2.56377	−	1.23464i	−0.122362	−	0.0589264i	−0.494063	+	0.869426i	$0.664489\pi$
$440$	4.28567			0.204311
$441$		0			0
$442$	6.49866			0.309110
$443$	6.24787	+	3.00881i	0.296845	+	0.142953i	0.576378	−	0.817183i	$-0.304465\pi$
$443$	6.24787	+	3.00881i	0.296845	+	0.142953i	−0.279533	+	0.960136i	$0.590180\pi$
$444$		0			0
$445$	3.38276	+	4.24185i	0.160358	+	0.201083i
$446$	1.30524	+	5.71865i	0.0618051	+	0.270786i
$447$		0			0
$448$	−8.09110	−	4.98104i	−0.382269	−	0.235332i
$449$	4.35675	+	19.0882i	0.205608	+	0.900827i	0.967450	+	0.253064i	$0.0814383\pi$
$449$	4.35675	+	19.0882i	0.205608	+	0.900827i	−0.761842	+	0.647763i	$0.775705\pi$
$450$		0			0
$451$	0.519236	−	2.27492i	0.0244499	−	0.107122i
$452$	−12.2778	−	5.91268i	−0.577500	−	0.278109i
$453$		0			0
$454$	11.0132	+	5.30366i	0.516874	+	0.248913i
$455$	4.56320	−	1.64387i	0.213926	−	0.0770660i
$456$		0			0
$457$	−2.37239	+	10.3941i	−0.110976	+	0.486217i	0.888643	+	0.458600i	$0.151649\pi$
$457$	−2.37239	+	10.3941i	−0.110976	+	0.486217i	−0.999619	+	0.0276171i	$0.991208\pi$
$458$	−5.04994	+	6.33242i	−0.235968	+	0.295894i
$459$		0			0
$460$	−11.5083			−0.536575
$461$	9.30604	−	11.6694i	0.433425	−	0.543498i	−0.516372	−	0.856364i	$-0.672718\pi$
$461$	9.30604	−	11.6694i	0.433425	−	0.543498i	0.949797	+	0.312866i	$0.101289\pi$
$462$		0			0
$463$	9.61217	+	12.0533i	0.446716	+	0.560164i	0.953299	−	0.302027i	$-0.0976633\pi$
$463$	9.61217	+	12.0533i	0.446716	+	0.560164i	−0.506584	+	0.862191i	$0.669092\pi$
$464$	−7.22910	−	9.06501i	−0.335603	−	0.420832i
$465$		0			0
$466$	4.35238	−	2.09600i	0.201620	−	0.0970951i
$467$	−17.1455	−	21.4998i	−0.793400	−	0.994892i	−0.999865	−	0.0164379i	$-0.994767\pi$
$467$	−17.1455	−	21.4998i	−0.793400	−	0.994892i	0.206465	−	0.978454i	$-0.433804\pi$
$468$		0			0
$469$	6.11917	+	9.54313i	0.282557	+	0.440661i
$470$	0.573205	−	0.718777i	0.0264400	−	0.0331547i
$471$		0			0
$472$	−4.57219			−0.210452
$473$	−10.5390	+	13.2154i	−0.484582	+	0.607647i
$474$		0			0
$475$	−20.9720	+	10.0996i	−0.962260	+	0.463400i
$476$	−14.8419	−	23.1467i	−0.680279	−	1.06093i
$477$		0			0
$478$	4.82888	−	6.05522i	0.220868	−	0.276959i
$479$	26.5714	+	12.7961i	1.21408	+	0.584669i	0.927656	−	0.373435i	$-0.121820\pi$
$479$	26.5714	+	12.7961i	1.21408	+	0.584669i	0.286421	+	0.958104i	$0.407534\pi$
$480$		0			0
$481$	−15.7880	+	7.60308i	−0.719869	+	0.346671i
$482$	−1.00780	−	4.41547i	−0.0459041	−	0.201119i
$483$		0			0
$484$	0.393331	−	1.72330i	0.0178787	−	0.0783316i
$485$	0.514087	+	2.25236i	0.0233435	+	0.102275i
$486$		0			0
$487$	4.99317	+	21.8765i	0.226262	+	0.991320i	0.952658	+	0.304043i	$0.0983368\pi$
$487$	4.99317	+	21.8765i	0.226262	+	0.991320i	−0.726396	+	0.687277i	$0.758806\pi$
$488$	21.5712	+	10.3881i	0.976480	+	0.470248i
$489$		0			0
$490$	1.80893	+	1.38905i	0.0817191	+	0.0627511i
$491$	−37.7619			−1.70417			−0.852085	−	0.523403i	$-0.824662\pi$
$491$	−37.7619			−1.70417			−0.852085	+	0.523403i	$0.824662\pi$
$492$		0			0
$493$	−5.24573	−	22.9830i	−0.236256	−	1.03510i
$494$	3.65491	+	4.58312i	0.164442	+	0.206204i
$495$		0			0
$496$	2.79115	−	12.2288i	0.125327	−	0.549091i
$497$	3.87964	−	11.4224i	0.174026	−	0.512367i
$498$		0			0
$499$	−1.28592	+	0.619265i	−0.0575656	+	0.0277221i	−0.462445	−	0.886648i	$-0.653028\pi$
$499$	−1.28592	+	0.619265i	−0.0575656	+	0.0277221i	0.404879	+	0.914370i	$0.367313\pi$
$500$	2.76292	−	12.1051i	0.123562	−	0.541359i
$501$		0			0
$502$	5.65339	−	7.08912i	0.252323	−	0.316403i
$503$	−26.3745	−	12.7013i	−1.17598	−	0.566321i	−0.259242	−	0.965813i	$-0.583473\pi$
$503$	−26.3745	−	12.7013i	−1.17598	−	0.566321i	−0.916737	+	0.399491i	$0.869187\pi$
$504$		0			0
$505$	10.1211	−	4.87404i	0.450381	−	0.216892i
$506$	3.02361	−	13.2473i	0.134416	−	0.588914i
$507$		0			0
$508$	24.1927			1.07338
$509$	−4.27049			−0.189286			−0.0946430	−	0.995511i	$-0.530171\pi$
$509$	−4.27049			−0.189286			−0.0946430	+	0.995511i	$0.530171\pi$
$510$		0			0
$511$	−1.28950	−	0.793843i	−0.0570443	−	0.0351176i
$512$	14.2856	+	17.9136i	0.631341	+	0.791677i
$513$		0			0
$514$	11.4658	−	5.52163i	0.505734	−	0.243548i
$515$	−2.81515	+	1.35571i	−0.124050	+	0.0597395i
$516$		0			0
$517$	−6.08977	−	7.63633i	−0.267828	−	0.335845i
$518$	−7.01686	−	4.31971i	−0.308303	−	0.189797i
$519$		0			0
$520$	−3.11569			−0.136632
$521$	31.2794			1.37038			0.685188	−	0.728366i	$-0.259720\pi$
$521$	31.2794			1.37038			0.685188	+	0.728366i	$0.259720\pi$
$522$		0			0
$523$	4.05076	−	17.7475i	0.177127	−	0.776045i	−0.805821	−	0.592160i	$-0.798275\pi$
$523$	4.05076	−	17.7475i	0.177127	−	0.776045i	0.982948	−	0.183885i	$-0.0588675\pi$
$524$	−20.9566	+	10.0922i	−0.915494	+	0.440879i
$525$		0			0
$526$	1.48006	+	0.712759i	0.0645336	+	0.0310778i
$527$	15.9009	−	19.9391i	0.692655	−	0.868562i
$528$		0			0
$529$	−12.0229	+	52.6757i	−0.522734	+	2.29025i
$530$	−3.96614	+	1.90999i	−0.172278	+	0.0829647i
$531$		0			0
$532$	7.97672	−	23.4851i	0.345835	−	1.01821i
$533$	−0.377486	+	1.65387i	−0.0163507	+	0.0716372i
$534$		0			0
$535$	1.72142	+	2.15860i	0.0744237	+	0.0933243i
$536$	−1.62046	−	7.09968i	−0.0699931	−	0.306660i
$537$		0			0
$538$	−12.8745			−0.555061
$539$	18.6638	−	15.4525i	0.803909	−	0.665587i
$540$		0			0
$541$	−14.3645	−	6.91758i	−0.617578	−	0.297410i	0.0988160	−	0.995106i	$-0.468494\pi$
$541$	−14.3645	−	6.91758i	−0.617578	−	0.297410i	−0.716394	+	0.697696i	$0.754209\pi$
$542$	−1.78443	−	7.81812i	−0.0766480	−	0.335817i
$543$		0			0
$544$	5.99903	+	26.2835i	0.257206	+	1.12690i
$545$	−0.539643	+	2.36433i	−0.0231158	+	0.101277i
$546$		0			0
$547$	−2.23657	−	9.79905i	−0.0956288	−	0.418977i	0.904340	−	0.426812i	$-0.140363\pi$
$547$	−2.23657	−	9.79905i	−0.0956288	−	0.418977i	−0.999969	+	0.00783452i	$0.997506\pi$
$548$	0.782264	−	0.376718i	0.0334167	−	0.0160926i
$549$		0			0
$550$	6.23412	+	3.00219i	0.265824	+	0.128014i
$551$	13.2583	−	16.6254i	0.564823	−	0.708266i
$552$		0			0
$553$	−5.82131	−	9.07861i	−0.247547	−	0.386062i
$554$	7.29616	−	3.51365i	0.309984	−	0.149281i
$555$		0			0
$556$	−5.84941	+	7.33493i	−0.248070	+	0.311071i
$557$	−18.5465			−0.785842			−0.392921	−	0.919572i	$-0.628535\pi$
$557$	−18.5465			−0.785842			−0.392921	+	0.919572i	$0.628535\pi$
$558$		0			0
$559$	7.66186	−	9.60767i	0.324062	−	0.406361i
$560$	2.95436	+	4.60746i	0.124845	+	0.194701i
$561$		0			0
$562$	−0.298042	−	0.373733i	−0.0125721	−	0.0157650i
$563$	−6.64188	+	3.19856i	−0.279922	+	0.134803i	−0.568577	−	0.822630i	$-0.692506\pi$
$563$	−6.64188	+	3.19856i	−0.279922	+	0.134803i	0.288656	+	0.957433i	$0.406792\pi$
$564$		0			0
$565$	3.43869	+	4.31199i	0.144667	+	0.181407i
$566$	−5.11200	−	6.41025i	−0.214873	−	0.269443i
$567$		0			0
$568$	−4.83154	+	6.05855i	−0.202727	+	0.254211i
$569$	7.91372			0.331760			0.165880	−	0.986146i	$-0.446953\pi$
$569$	7.91372			0.331760			0.165880	+	0.986146i	$0.446953\pi$
$570$		0			0
$571$	−13.4700	+	16.8909i	−0.563704	+	0.706862i	−0.979238	−	0.202715i	$-0.935023\pi$
$571$	−13.4700	+	16.8909i	−0.563704	+	0.706862i	0.415534	+	0.909578i	$0.363595\pi$
$572$	−3.48899	+	15.2863i	−0.145882	+	0.639151i
$573$		0			0
$574$	−0.750481	+	0.270357i	−0.0313245	+	0.0112845i
$575$	−35.3413	−	17.0195i	−1.47383	−	0.709761i
$576$		0			0
$577$	−0.772776	−	0.372149i	−0.0321711	−	0.0154928i	0.417729	−	0.908572i	$-0.362826\pi$
$577$	−0.772776	−	0.372149i	−0.0321711	−	0.0154928i	−0.449900	+	0.893079i	$0.648540\pi$
$578$	−1.62594	+	7.12372i	−0.0676302	+	0.296307i
$579$		0			0
$580$	1.19130	+	5.21942i	0.0494660	+	0.216725i
$581$	−11.2220	−	6.90847i	−0.465567	−	0.286612i
$582$		0			0
$583$	10.4068	+	45.5954i	0.431008	+	1.88837i
$584$	0.606486	+	0.760509i	0.0250966	+	0.0314701i
$585$		0			0
$586$	−8.76452	−	4.22077i	−0.362059	−	0.174358i
$587$	−24.0778			−0.993796			−0.496898	−	0.867809i	$-0.665528\pi$
$587$	−24.0778			−0.993796			−0.496898	+	0.867809i	$0.665528\pi$
$588$		0			0
$589$	23.0047			0.947893
$590$	0.789716	+	0.380307i	0.0325121	+	0.0156570i
$591$		0			0
$592$	−12.3290	−	15.4601i	−0.506719	−	0.635406i
$593$	5.81912	+	25.4952i	0.238963	+	1.04696i	0.941948	+	0.335759i	$0.108993\pi$
$593$	5.81912	+	25.4952i	0.238963	+	1.04696i	−0.702985	+	0.711205i	$0.748150\pi$
$594$		0			0
$595$	1.34737	+	11.0464i	0.0552367	+	0.452860i
$596$	−0.0185041	−	0.0810717i	−0.000757957	−	0.00332083i
$597$		0			0
$598$	−2.19817	+	9.63082i	−0.0898899	+	0.393833i
$599$	24.5637	+	11.8292i	1.00365	+	0.483330i	0.862174	−	0.506612i	$-0.169102\pi$
$599$	24.5637	+	11.8292i	1.00365	+	0.483330i	0.141471	+	0.989942i	$0.454817\pi$
$600$		0			0
$601$	−24.3305	−	11.7170i	−0.992462	−	0.477945i	−0.134088	−	0.990969i	$-0.542811\pi$
$601$	−24.3305	−	11.7170i	−0.992462	−	0.477945i	−0.858374	+	0.513025i	$0.828525\pi$
$602$	5.74781	+	0.594278i	0.234263	+	0.0242210i
$603$		0			0
$604$	−0.975157	+	4.27244i	−0.0396786	+	0.173843i
$605$	−0.446036	+	0.559311i	−0.0181339	+	0.0227392i
$606$		0			0
$607$	−33.6058			−1.36402			−0.682009	−	0.731344i	$-0.738893\pi$
$607$	−33.6058			−1.36402			−0.682009	+	0.731344i	$0.738893\pi$
$608$	−15.1623	+	19.0129i	−0.614911	+	0.771074i
$609$		0			0
$610$	−2.86174	−	3.58851i	−0.115868	−	0.145294i
$611$	4.42728	+	5.55163i	0.179108	+	0.224595i
$612$		0			0
$613$	1.24231	−	0.598264i	0.0501763	−	0.0241636i	−0.408627	−	0.912701i	$-0.633992\pi$
$613$	1.24231	−	0.598264i	0.0501763	−	0.0241636i	0.458804	+	0.888538i	$0.348278\pi$
$614$	−0.251738	−	0.315670i	−0.0101593	−	0.0127394i
$615$		0			0
$616$	−14.6439	+	5.27538i	−0.590018	+	0.212551i
$617$	12.8926	−	16.1668i	0.519038	−	0.650852i	−0.451367	−	0.892339i	$-0.649063\pi$
$617$	12.8926	−	16.1668i	0.519038	−	0.650852i	0.970404	+	0.241486i	$0.0776348\pi$
$618$		0			0
$619$	−8.07714			−0.324648			−0.162324	−	0.986738i	$-0.551899\pi$
$619$	−8.07714			−0.324648			−0.162324	+	0.986738i	$0.551899\pi$
$620$	−3.61108	+	4.52815i	−0.145024	+	0.181855i
$621$		0			0
$622$	−5.59891	+	2.69629i	−0.224496	+	0.108111i
$623$	−16.7801	−	10.3302i	−0.672281	−	0.413869i
$624$		0			0
$625$	10.7997	−	13.5424i	0.431990	−	0.541698i
$626$	7.46046	+	3.59277i	0.298180	+	0.143596i
$627$		0			0
$628$	36.1648	−	17.4161i	1.44313	−	0.694977i
$629$	−8.94643	−	39.1969i	−0.356718	−	1.56288i
$630$		0			0
$631$	6.71216	−	29.4079i	0.267207	−	1.17071i	−0.646040	−	0.763304i	$-0.723576\pi$
$631$	6.71216	−	29.4079i	0.267207	−	1.17071i	0.913247	−	0.407407i	$-0.133567\pi$
$632$	1.54158	+	6.75410i	0.0613207	+	0.268664i
$633$		0			0
$634$	0.496846	+	2.17682i	0.0197323	+	0.0864527i
$635$	−8.82161	−	4.24826i	−0.350075	−	0.168587i
$636$		0			0
$637$	−13.5687	+	11.2340i	−0.537610	+	0.445108i
$638$	−6.32113			−0.250256
$639$		0			0
$640$	−1.77415	−	7.77305i	−0.0701293	−	0.307257i
$641$	−15.3257	−	19.2178i	−0.605328	−	0.759057i	0.380870	−	0.924629i	$-0.375625\pi$
$641$	−15.3257	−	19.2178i	−0.605328	−	0.759057i	−0.986198	+	0.165571i	$0.947053\pi$
$642$		0			0
$643$	−9.17060	+	40.1790i	−0.361653	+	1.58451i	0.387346	+	0.921935i	$0.373392\pi$
$643$	−9.17060	+	40.1790i	−0.361653	+	1.58451i	−0.748999	+	0.662571i	$0.769465\pi$
$644$	39.3230	−	14.1659i	1.54954	−	0.558216i
$645$		0			0
$646$	−12.1177	+	5.83558i	−0.476765	+	0.229598i
$647$	−6.24824	+	27.3753i	−0.245644	+	1.07623i	0.690144	+	0.723672i	$0.257547\pi$
$647$	−6.24824	+	27.3753i	−0.245644	+	1.07623i	−0.935788	+	0.352563i	$0.885310\pi$
$648$		0			0
$649$	5.80605	−	7.28056i	0.227908	−	0.285787i
$650$	−4.53222	−	2.18260i	−0.177768	−	0.0856087i
$651$		0			0
$652$	24.4687	−	11.7835i	0.958267	−	0.461477i
$653$	0.899603	−	3.94142i	0.0352042	−	0.154240i	−0.954271	−	0.298943i	$-0.903366\pi$
$653$	0.899603	−	3.94142i	0.0352042	−	0.154240i	0.989475	+	0.144704i	$0.0462229\pi$
$654$		0			0
$655$	9.41379			0.367827
$656$	−1.91431			−0.0747413
$657$		0			0
$658$	−1.07384	+	3.16159i	−0.0418625	+	0.123252i
$659$	−20.1268	−	25.2382i	−0.784029	−	0.983141i	−0.999977	−	0.00673639i	$-0.997856\pi$
$659$	−20.1268	−	25.2382i	−0.784029	−	0.983141i	0.215948	−	0.976405i	$-0.430716\pi$
$660$		0			0
$661$	−13.8955	+	6.69174i	−0.540474	+	0.260278i	−0.684144	−	0.729347i	$-0.739824\pi$
$661$	−13.8955	+	6.69174i	−0.540474	+	0.260278i	0.143670	+	0.989626i	$0.454110\pi$
$662$	−7.08174	+	3.41039i	−0.275240	+	0.132548i
$663$		0			0
$664$	5.27798	+	6.61838i	0.204826	+	0.256843i
$665$	−7.03262	+	7.16285i	−0.272713	+	0.277763i
$666$		0			0
$667$	35.8345			1.38752
$668$	−32.9145			−1.27350
$669$		0			0
$670$	−0.310652	+	1.36106i	−0.0120015	+	0.0525822i
$671$	−43.9340	+	21.1575i	−1.69605	+	0.816777i
$672$		0			0
$673$	−39.7598	−	19.1473i	−1.53263	−	0.738074i	−0.538132	−	0.842861i	$-0.680870\pi$
$673$	−39.7598	−	19.1473i	−1.53263	−	0.738074i	−0.994495	+	0.104787i	$0.966584\pi$
$674$	−2.49618	+	3.13011i	−0.0961493	+	0.120567i
$675$		0			0
$676$	−2.67037	+	11.6996i	−0.102706	+	0.449986i
$677$	−12.6033	+	6.06942i	−0.484383	+	0.233267i	−0.660105	−	0.751173i	$-0.729488\pi$
$677$	−12.6033	+	6.06942i	−0.484383	+	0.233267i	0.175722	+	0.984440i	$0.443774\pi$
$678$		0			0
$679$	−4.52912	−	7.06337i	−0.173812	−	0.271067i
$680$	1.59070	−	6.96931i	0.0610006	−	0.267261i
$681$		0			0
$682$	−4.26366	−	5.34646i	−0.163264	−	0.204726i
$683$	8.74138	+	38.2985i	0.334480	+	1.46545i	0.810356	+	0.585938i	$0.199274\pi$
$683$	8.74138	+	38.2985i	0.334480	+	1.46545i	−0.475876	+	0.879512i	$0.657869\pi$
$684$		0			0
$685$	−0.351396			−0.0134261
$686$	−7.89083	−	2.51963i	−0.301273	−	0.0962000i
$687$		0			0
$688$	12.4939	+	6.01674i	0.476325	+	0.229386i
$689$	−7.56581	−	33.1480i	−0.288234	−	1.26284i
$690$		0			0
$691$	−1.52303	−	6.67284i	−0.0579389	−	0.253847i	0.937661	−	0.347551i	$-0.112986\pi$
$691$	−1.52303	−	6.67284i	−0.0579389	−	0.253847i	−0.995600	+	0.0937038i	$0.970129\pi$
$692$	−6.56309	+	28.7548i	−0.249491	+	1.09309i
$693$		0			0
$694$	−0.155369	−	0.680717i	−0.00589773	−	0.0258397i
$695$	3.42094	−	1.64744i	0.129764	−	0.0624910i
$696$		0			0
$697$	−3.50673	−	1.68875i	−0.132827	−	0.0639660i
$698$	2.04804	−	2.56816i	0.0775195	−	0.0972064i
$699$		0			0
$700$	2.57698	+	21.1274i	0.0974005	+	0.798542i
$701$	23.5538	−	11.3429i	0.889615	−	0.428416i	0.0674882	−	0.997720i	$-0.478501\pi$
$701$	23.5538	−	11.3429i	0.889615	−	0.428416i	0.822127	+	0.569304i	$0.192787\pi$
$702$		0			0
$703$	22.6117	−	28.3541i	0.852815	−	1.06940i
$704$	−12.4309			−0.468509
$705$		0			0
$706$	9.80194	−	12.2912i	0.368901	−	0.462587i
$707$	−28.5834	+	29.1127i	−1.07499	+	1.09489i
$708$		0			0
$709$	3.60042	+	4.51479i	0.135217	+	0.169556i	0.844830	−	0.535035i	$-0.179702\pi$
$709$	3.60042	+	4.51479i	0.135217	+	0.169556i	−0.709613	+	0.704592i	$0.751130\pi$
$710$	1.33845	−	0.644564i	0.0502312	−	0.0241901i
$711$		0			0
$712$	7.89211	+	9.89639i	0.295769	+	0.370883i
$713$	24.1707	+	30.3091i	0.905200	+	1.13508i
$714$		0			0
$715$	3.95650	−	4.96130i	0.147965	−	0.185542i
$716$	10.8989			0.407310
$717$		0			0
$718$	−9.34469	+	11.7179i	−0.348741	+	0.437307i
$719$	0.462515	−	2.02641i	0.0172489	−	0.0755723i	−0.965571	−	0.260140i	$-0.916231\pi$
$719$	0.462515	−	2.02641i	0.0172489	−	0.0755723i	0.982820	+	0.184568i	$0.0590885\pi$
$720$		0			0
$721$	7.95041	−	8.09763i	0.296089	−	0.301572i
$722$	−3.27426	−	1.57680i	−0.121855	−	0.0586824i
$723$		0			0
$724$	7.76863	+	3.74118i	0.288719	+	0.139040i
$725$	−4.06054	+	17.7904i	−0.150805	+	0.660718i
$726$		0			0
$727$	−2.05743	−	9.01420i	−0.0763060	−	0.334318i	0.922338	−	0.386385i	$-0.126276\pi$
$727$	−2.05743	−	9.01420i	−0.0763060	−	0.334318i	−0.998644	+	0.0520666i	$0.983419\pi$
$728$	10.6461	−	3.83522i	0.394572	−	0.142143i
$729$		0			0
$730$	−0.0414953	−	0.181803i	−0.00153581	−	0.00672883i
$731$	17.5791	+	22.0435i	0.650187	+	0.815309i
$732$		0			0
$733$	−27.1023	−	13.0518i	−1.00104	−	0.482078i	−0.139752	−	0.990187i	$-0.544630\pi$
$733$	−27.1023	−	13.0518i	−1.00104	−	0.482078i	−0.861293	+	0.508109i	$0.830345\pi$
$734$	−6.13237			−0.226350
$735$		0			0
$736$	−40.9805			−1.51056
$737$	13.3630	+	6.43528i	0.492232	+	0.237047i
$738$		0			0
$739$	−4.67111	−	5.85739i	−0.171830	−	0.215467i	0.688458	−	0.725276i	$-0.258288\pi$
$739$	−4.67111	−	5.85739i	−0.171830	−	0.215467i	−0.860288	+	0.509808i	$0.829716\pi$
$740$	2.03172	+	8.90156i	0.0746877	+	0.327228i
$741$		0			0
$742$	11.2010	−	11.4084i	0.411200	−	0.418814i
$743$	0.878113	+	3.84727i	0.0322149	+	0.141143i	0.988478	−	0.151366i	$-0.0483672\pi$
$743$	0.878113	+	3.84727i	0.0322149	+	0.141143i	−0.956263	+	0.292508i	$0.905510\pi$
$744$		0			0
$745$	−0.00748895	+	0.0328112i	−0.000274374	+	0.00120211i
$746$	−0.220723	−	0.106295i	−0.00808125	−	0.00389172i
$747$		0			0
$748$	−32.4117	−	15.6087i	−1.18509	−	0.570709i
$749$	−8.53909	−	5.25683i	−0.312012	−	0.192080i
$750$		0			0
$751$	11.4556	−	50.1901i	0.418019	−	1.83146i	−0.125538	−	0.992089i	$-0.540066\pi$
$751$	11.4556	−	50.1901i	0.418019	−	1.83146i	0.543557	−	0.839372i	$-0.317077\pi$
$752$	−4.99597	+	6.26474i	−0.182184	+	0.228452i
$753$		0			0
$754$	4.59548			0.167357
$755$	1.10582	−	1.38666i	0.0402451	−	0.0504657i
$756$		0			0
$757$	11.9567	+	14.9932i	0.434572	+	0.544936i	0.950104	−	0.311935i	$-0.100977\pi$
$757$	11.9567	+	14.9932i	0.434572	+	0.544936i	−0.515532	+	0.856871i	$0.672406\pi$
$758$	6.72293	+	8.43029i	0.244188	+	0.306202i
$759$		0			0
$760$	5.80967	−	2.79779i	0.210739	−	0.101486i
$761$	16.3060	+	20.4471i	0.591092	+	0.741206i	0.983960	−	0.178389i	$-0.0570885\pi$
$761$	16.3060	+	20.4471i	0.591092	+	0.741206i	−0.392868	+	0.919595i	$0.628517\pi$
$762$		0			0
$763$	−1.06641	−	8.74303i	−0.0386068	−	0.316519i
$764$	11.4136	−	14.3122i	0.412929	−	0.517797i
$765$		0			0
$766$	−4.61798			−0.166855
$767$	−4.22102	+	5.29299i	−0.152412	+	0.191119i
$768$		0			0
$769$	16.4615	−	7.92744i	0.593617	−	0.285871i	−0.112856	−	0.993611i	$-0.536000\pi$
$769$	16.4615	−	7.92744i	0.593617	−	0.285871i	0.706472	+	0.707741i	$0.250285\pi$
$770$	2.96811	+	0.306879i	0.106963	+	0.0110591i
$771$		0			0
$772$	−26.7316	+	33.5203i	−0.962090	+	1.20642i
$773$	3.27997	+	1.57955i	0.117972	+	0.0568124i	0.491939	−	0.870630i	$-0.336288\pi$
$773$	3.27997	+	1.57955i	0.117972	+	0.0568124i	−0.373967	+	0.927442i	$0.622003\pi$
$774$		0			0
$775$	−17.7861	+	8.56533i	−0.638895	+	0.307676i
$776$	1.19938	+	5.25485i	0.0430554	+	0.188638i
$777$		0			0
$778$	0.191088	−	0.837212i	0.00685084	−	0.0300155i
$779$	−0.781245	−	3.42286i	−0.0279910	−	0.122637i
$780$		0			0
$781$	−3.51200	−	15.3871i	−0.125669	−	0.550593i
$782$	−20.4204	−	9.83392i	−0.730230	−	0.351660i
$783$		0			0
$784$	−15.7663	−	12.1068i	−0.563084	−	0.432385i
$785$	−16.2454			−0.579822
$786$		0			0
$787$	4.24042	+	18.5785i	0.151155	+	0.662251i	0.992551	+	0.121832i	$0.0388770\pi$
$787$	4.24042	+	18.5785i	0.151155	+	0.662251i	−0.841396	+	0.540419i	$0.818266\pi$
$788$	28.2985	+	35.4853i	1.00809	+	1.26411i
$789$		0			0
$790$	0.295531	−	1.29480i	0.0105145	−	0.0460671i
$791$	−17.0576	−	10.5010i	−0.606498	−	0.373371i
$792$		0			0
$793$	31.9402	−	15.3816i	1.13423	−	0.546215i
$794$	1.33535	−	5.85057i	0.0473900	−	0.207629i
$795$		0			0
$796$	−15.9798	+	20.0380i	−0.566387	+	0.710227i
$797$	−12.0106	−	5.78398i	−0.425436	−	0.204879i	0.208899	−	0.977937i	$-0.433012\pi$
$797$	−12.0106	−	5.78398i	−0.425436	−	0.204879i	−0.634335	+	0.773058i	$0.718726\pi$
$798$		0			0
$799$	−14.6784	+	7.06877i	−0.519286	+	0.250075i
$800$	4.64364	−	20.3451i	0.164178	−	0.719309i
$801$		0			0
$802$	−14.0935			−0.497659
$803$	−1.98116			−0.0699135
$804$		0			0
$805$	−16.8262	−	1.73970i	−0.593047	−	0.0613163i
$806$	3.09969	+	3.88689i	0.109182	+	0.136910i
$807$		0			0
$808$	23.6128	−	11.3713i	0.830695	−	0.400042i
$809$	−13.9533	+	6.71953i	−0.490570	+	0.236246i	−0.662780	−	0.748814i	$-0.730624\pi$
$809$	−13.9533	+	6.71953i	−0.490570	+	0.236246i	0.172210	+	0.985060i	$0.444909\pi$
$810$		0			0
$811$	27.4607	+	34.4347i	0.964276	+	1.20916i	0.977861	+	0.209257i	$0.0671044\pi$
$811$	27.4607	+	34.4347i	0.964276	+	1.20916i	−0.0135843	+	0.999908i	$0.504324\pi$
$812$	−10.4954	−	16.3680i	−0.368315	−	0.574405i
$813$		0			0
$814$	−10.7805			−0.377856
$815$	−10.9914			−0.385012
$816$		0			0
$817$	−5.65930	+	24.7950i	−0.197994	+	0.867467i
$818$	6.48376	−	3.12242i	0.226699	−	0.109173i
$819$		0			0
$820$	0.796374	+	0.383513i	0.0278106	+	0.0133929i
$821$	2.73128	−	3.42491i	0.0953223	−	0.119530i	−0.731883	−	0.681431i	$-0.761358\pi$
$821$	2.73128	−	3.42491i	0.0953223	−	0.119530i	0.827205	+	0.561900i	$0.189930\pi$
$822$		0			0
$823$	11.8352	−	51.8534i	0.412549	−	1.80750i	−0.159409	−	0.987213i	$-0.550959\pi$
$823$	11.8352	−	51.8534i	0.412549	−	1.80750i	0.571958	−	0.820283i	$-0.306184\pi$
$824$	−6.56786	+	3.16291i	−0.228802	+	0.110185i
$825$		0			0
$826$	−3.16654	−	0.327395i	−0.110178	−	0.0113915i
$827$	0.819506	−	3.59049i	0.0284970	−	0.124854i	−0.958679	−	0.284491i	$-0.908175\pi$
$827$	0.819506	−	3.59049i	0.0284970	−	0.124854i	0.987176	+	0.159637i	$0.0510325\pi$
$828$		0			0
$829$	26.7900	+	33.5936i	0.930456	+	1.16676i	0.985738	+	0.168285i	$0.0538228\pi$
$829$	26.7900	+	33.5936i	0.930456	+	1.16676i	−0.0552819	+	0.998471i	$0.517606\pi$
$830$	−0.361116	−	1.58215i	−0.0125345	−	0.0549173i
$831$		0			0
$832$	9.03732			0.313313
$833$	−18.2013	−	36.0864i	−0.630638	−	1.25032i
$834$		0			0
$835$	12.0019	+	5.77981i	0.415343	+	0.200019i
$836$	−7.22083	−	31.6365i	−0.249738	−	1.09417i
$837$		0			0
$838$	−0.971678	−	4.25720i	−0.0335661	−	0.147063i
$839$	8.64414	−	37.8724i	0.298429	−	1.30750i	−0.574038	−	0.818828i	$-0.694624\pi$
$839$	8.64414	−	37.8724i	0.298429	−	1.30750i	0.872467	−	0.488673i	$-0.162519\pi$
$840$		0			0
$841$	2.74363	+	12.0206i	0.0946079	+	0.414504i
$842$	−14.7495	+	7.10297i	−0.508301	+	0.244785i
$843$		0			0
$844$	27.3021	+	13.1480i	0.939777	+	0.452573i
$845$	3.02819	−	3.79723i	0.104173	−	0.130629i
$846$		0			0
$847$	0.835599	−	2.46017i	0.0287115	−	0.0845325i
$848$	34.5682	−	16.6472i	1.18708	−	0.571666i
$849$		0			0
$850$	7.19604	−	9.02355i	0.246822	−	0.309505i
$851$	61.1147			2.09499
$852$		0			0
$853$	−31.8618	+	39.9534i	−1.09093	+	1.36798i	−0.166758	+	0.985998i	$0.553330\pi$
$853$	−31.8618	+	39.9534i	−1.09093	+	1.36798i	−0.924170	+	0.381982i	$0.875242\pi$
$854$	14.1956	+	8.73908i	0.485763	+	0.299045i
$855$		0			0
$856$	4.01615	+	5.03609i	0.137269	+	0.172130i
$857$	34.7896	−	16.7538i	1.18839	−	0.572298i	0.268045	−	0.963407i	$-0.413623\pi$
$857$	34.7896	−	16.7538i	1.18839	−	0.572298i	0.920345	+	0.391109i	$0.127908\pi$
$858$		0			0
$859$	11.9104	+	14.9352i	0.406378	+	0.509581i	0.942338	−	0.334662i	$-0.108622\pi$
$859$	11.9104	+	14.9352i	0.406378	+	0.509581i	−0.535961	+	0.844243i	$0.680051\pi$
$860$	−3.99219	−	5.00605i	−0.136133	−	0.170705i
$861$		0			0
$862$	−0.438209	+	0.549497i	−0.0149255	+	0.0187159i
$863$	14.8071			0.504039			0.252020	−	0.967722i	$-0.418905\pi$
$863$	14.8071			0.504039			0.252020	+	0.967722i	$0.418905\pi$
$864$		0			0
$865$	7.44252	−	9.33262i	0.253053	−	0.317319i
$866$	−0.963169	+	4.21992i	−0.0327298	+	0.143399i
$867$		0			0
$868$	6.76496	−	19.9174i	0.229618	−	0.676041i
$869$	−12.7125	−	6.12204i	−0.431243	−	0.207676i
$870$		0			0
$871$	−9.71494	−	4.67847i	−0.329178	−	0.158524i
$872$	−1.25901	+	5.51607i	−0.0426354	+	0.186798i
$873$		0			0
$874$	−4.54934	−	19.9320i	−0.153884	−	0.674209i
$875$	5.86960	−	17.2813i	0.198429	−	0.584214i
$876$		0			0
$877$	−12.1382	−	53.1808i	−0.409877	−	1.79579i	−0.584767	−	0.811201i	$-0.698814\pi$
$877$	−12.1382	−	53.1808i	−0.409877	−	1.79579i	0.174890	−	0.984588i	$-0.444043\pi$
$878$	0.793518	+	0.995040i	0.0267799	+	0.0335810i
$879$		0			0
$880$	6.45171	+	3.10698i	0.217487	+	0.104736i
$881$	5.97332			0.201246			0.100623	−	0.994925i	$-0.467916\pi$
$881$	5.97332			0.201246			0.100623	+	0.994925i	$0.467916\pi$
$882$		0			0
$883$	−11.7330			−0.394848			−0.197424	−	0.980318i	$-0.563258\pi$
$883$	−11.7330			−0.394848			−0.197424	+	0.980318i	$0.563258\pi$
$884$	23.5634	+	11.3475i	0.792523	+	0.381659i
$885$		0			0
$886$	−1.93379	−	2.42490i	−0.0649670	−	0.0814661i
$887$	−10.5123	−	46.0574i	−0.352968	−	1.54646i	−0.770288	−	0.637696i	$-0.779888\pi$
$887$	−10.5123	−	46.0574i	−0.352968	−	1.54646i	0.417320	−	0.908760i	$-0.362970\pi$
$888$		0			0
$889$	35.3722	+	3.65720i	1.18635	+	0.122659i
$890$	−0.539972	−	2.36577i	−0.0180999	−	0.0793009i
$891$		0			0
$892$	−5.25286	+	23.0143i	−0.175879	+	0.770576i
$893$	−13.2405	−	6.37628i	−0.443076	−	0.213374i
$894$		0			0
$895$	−3.97415	−	1.91385i	−0.132841	−	0.0639730i
$896$	15.6303	+	24.3761i	0.522171	+	0.814350i
$897$		0			0
$898$	1.94860	−	8.53735i	0.0650255	−	0.284895i
$899$	11.2442	−	14.0998i	0.375016	−	0.470255i
$900$		0			0
$901$	78.0095			2.59887
$902$	−0.650701	+	0.815953i	−0.0216660	+	0.0271683i
$903$		0			0
$904$	8.02260	+	10.0600i	0.266828	+	0.334591i
$905$	−2.17579	−	2.72836i	−0.0723258	−	0.0906936i
$906$		0			0
$907$	−42.1100	+	20.2791i	−1.39824	+	0.673357i	−0.972804	−	0.231631i	$-0.925594\pi$
$907$	−42.1100	+	20.2791i	−1.39824	+	0.673357i	−0.425437	+	0.904988i	$0.639880\pi$
$908$	30.6716	+	38.4609i	1.01787	+	1.27637i
$909$		0			0
$910$	−2.15782	−	0.223102i	−0.0715311	−	0.00739575i
$911$	9.39835	−	11.7852i	0.311381	−	0.390460i	−0.601373	−	0.798968i	$-0.705380\pi$
$911$	9.39835	−	11.7852i	0.311381	−	0.390460i	0.912755	+	0.408508i	$0.133951\pi$
$912$		0			0
$913$	−17.2412			−0.570599
$914$	2.97306	−	3.72810i	0.0983402	−	0.123315i
$915$		0			0
$916$	−29.3677	+	14.1428i	−0.970337	+	0.467290i
$917$	−32.1663	+	11.5878i	−1.06223	+	0.382662i
$918$		0			0
$919$	−15.1178	+	18.9572i	−0.498691	+	0.625339i	−0.965934	−	0.258790i	$-0.916676\pi$
$919$	−15.1178	+	18.9572i	−0.498691	+	0.625339i	0.467242	+	0.884129i	$0.345248\pi$
$920$	9.79026	+	4.71474i	0.322775	+	0.155440i
$921$		0			0
$922$	−6.01456	+	2.89646i	−0.198079	+	0.0953898i
$923$	2.55323	+	11.1864i	0.0840407	+	0.368206i
$924$		0			0
$925$	−6.92512	+	30.3409i	−0.227697	+	0.997604i
$926$	−1.53434	−	6.72238i	−0.0504215	−	0.220911i
$927$		0			0
$928$	4.24217	+	18.5862i	0.139256	+	0.610121i
$929$	−20.0259	−	9.64397i	−0.657029	−	0.316408i	0.0754987	−	0.997146i	$-0.475945\pi$
$929$	−20.0259	−	9.64397i	−0.657029	−	0.316408i	−0.732527	+	0.680738i	$0.761659\pi$
$930$		0			0
$931$	15.2130	−	33.1317i	0.498586	−	1.08585i
$932$	19.4411			0.636815
$933$		0			0
$934$	2.73685	+	11.9909i	0.0895524	+	0.392355i
$935$	9.07767	+	11.3830i	0.296872	+	0.372265i
$936$		0			0
$937$	−2.64108	+	11.5713i	−0.0862803	+	0.378019i	−0.999571	−	0.0292897i	$-0.990675\pi$
$937$	−2.64108	+	11.5713i	−0.0862803	+	0.378019i	0.913291	+	0.407308i	$0.133533\pi$
$938$	−0.613894	−	5.03303i	−0.0200444	−	0.164334i
$939$		0			0
$940$	3.33346	−	1.60531i	0.108725	−	0.0523594i
$941$	−6.23981	+	27.3384i	−0.203412	+	0.891207i	0.765428	+	0.643521i	$0.222527\pi$
$941$	−6.23981	+	27.3384i	−0.203412	+	0.891207i	−0.968840	+	0.247686i	$0.920330\pi$
$942$		0			0
$943$	3.68883	−	4.62565i	0.120125	−	0.150632i
$944$	−6.88304	−	3.31470i	−0.224024	−	0.107884i
$945$		0			0
$946$	6.81141	−	3.28020i	0.221458	−	0.106649i
$947$	−8.87735	+	38.8942i	−0.288475	+	1.26389i	0.598143	+	0.801390i	$0.295906\pi$
$947$	−8.87735	+	38.8942i	−0.288475	+	1.26389i	−0.886618	+	0.462503i	$0.846952\pi$
$948$		0			0
$949$	1.44031			0.0467543
$950$	10.4109			0.337774
$951$		0			0
$952$	3.14346	+	25.7717i	0.101880	+	0.835267i
$953$	−28.7567	−	36.0597i	−0.931519	−	1.16809i	−0.985522	−	0.169548i	$-0.945769\pi$
$953$	−28.7567	−	36.0597i	−0.931519	−	1.16809i	0.0540026	−	0.998541i	$-0.482802\pi$
$954$		0			0
$955$	−6.67507	+	3.21455i	−0.216000	+	0.104020i
$956$	28.0822	−	13.5237i	0.908243	−	0.437387i
$957$		0			0
$958$	−8.22417	−	10.3128i	−0.265711	−	0.333191i
$959$	1.20070	−	0.432546i	0.0387725	−	0.0139676i
$960$		0			0
$961$	−11.4900			−0.370644
$962$	7.83745			0.252690
$963$		0			0
$964$	4.05583	−	17.7697i	0.130629	−	0.572325i
$965$	15.6336	−	7.52873i	0.503262	−	0.242358i
$966$		0			0
$967$	10.3634	+	4.99076i	0.333265	+	0.160492i	0.593031	−	0.805180i	$-0.297931\pi$
$967$	10.3634	+	4.99076i	0.333265	+	0.160492i	−0.259766	+	0.965672i	$0.583645\pi$
$968$	−1.04062	+	1.30489i	−0.0334467	+	0.0419409i
$969$		0			0
$970$	0.229930	−	1.00739i	0.00738260	−	0.0323453i
$971$	−21.3086	+	10.2617i	−0.683826	+	0.329313i	−0.743340	−	0.668914i	$-0.766759\pi$
$971$	−21.3086	+	10.2617i	−0.683826	+	0.329313i	0.0595133	+	0.998228i	$0.481045\pi$
$972$		0			0
$973$	−9.66125	+	9.84016i	−0.309726	+	0.315461i
$974$	2.23324	−	9.78446i	0.0715576	−	0.313514i
$975$		0			0
$976$	24.9425	+	31.2769i	0.798389	+	1.00115i
$977$	−9.06810	−	39.7299i	−0.290114	−	1.27107i	−0.884366	−	0.466794i	$-0.845409\pi$
$977$	−9.06810	−	39.7299i	−0.290114	−	1.27107i	0.594252	−	0.804279i	$-0.297448\pi$
$978$		0			0
$979$	−25.7805			−0.823948
$980$	4.13350	+	8.19518i	0.132040	+	0.261786i
$981$		0			0
$982$	15.2168	+	7.32800i	0.485586	+	0.233846i
$983$	−2.20426	−	9.65747i	−0.0703048	−	0.308026i	0.927534	−	0.373740i	$-0.121925\pi$
$983$	−2.20426	−	9.65747i	−0.0703048	−	0.308026i	−0.997838	+	0.0657140i	$0.979067\pi$
$984$		0			0
$985$	−4.08751	−	17.9085i	−0.130239	−	0.570614i
$986$	−2.34620	+	10.2794i	−0.0747181	+	0.327362i
$987$		0			0
$988$	5.24956	+	22.9998i	0.167011	+	0.731722i
$989$	−38.6140	+	18.5955i	−1.22785	+	0.591302i
$990$		0			0
$991$	−11.9868	−	5.77253i	−0.380773	−	0.183371i	0.233700	−	0.972309i	$-0.424917\pi$
$991$	−11.9868	−	5.77253i	−0.380773	−	0.183371i	−0.614472	+	0.788938i	$0.710631\pi$
$992$	−12.8589	+	16.1246i	−0.408271	+	0.511956i
$993$		0			0
$994$	−3.77998	+	3.84998i	−0.119894	+	0.122114i
$995$	9.34552	−	4.50057i	0.296273	−	0.142678i
$996$		0			0
$997$	1.30418	−	1.63538i	0.0413036	−	0.0517931i	−0.760751	−	0.649044i	$-0.775169\pi$
$997$	1.30418	−	1.63538i	0.0413036	−	0.0517931i	0.802054	+	0.597251i	$0.203740\pi$
$998$	0.638354			0.0202068
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.127.3		36
3.2	odd	2		147.2.i.b.127.4	yes	36
49.22	even	7	inner	441.2.u.d.316.3		36
147.62	even	14		7203.2.a.g.1.8		18
147.71	odd	14		147.2.i.b.22.4	✓	36
147.134	odd	14		7203.2.a.h.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.22.4	✓	36	147.71	odd	14
147.2.i.b.127.4	yes	36	3.2	odd	2
441.2.u.d.127.3		36	1.1	even	1	trivial
441.2.u.d.316.3		36	49.22	even	7	inner
7203.2.a.g.1.8		18	147.62	even	14
7203.2.a.h.1.8		18	147.134	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.402966 - 0.194058i) q^{2} +(-1.12226 - 1.40727i) q^{4} +(0.162101 + 0.710213i) q^{5} +(-1.42812 - 2.22721i) q^{7} +(0.378189 + 1.65695i) q^{8} +O(q^{10})\)	\(q+(-0.402966 - 0.194058i) q^{2} +(-1.12226 - 1.40727i) q^{4} +(0.162101 + 0.710213i) q^{5} +(-1.42812 - 2.22721i) q^{7} +(0.378189 + 1.65695i) q^{8} +(0.0725012 - 0.317649i) q^{10} +(-3.11871 - 1.50189i) q^{11} +(2.26731 + 1.09188i) q^{13} +(0.143273 + 1.17463i) q^{14} +(-0.631909 + 2.76858i) q^{16} +(-3.59992 + 4.51416i) q^{17} -5.20820 q^{19} +(0.817538 - 1.02516i) q^{20} +(0.965280 + 1.21042i) q^{22} +(-5.47218 - 6.86189i) q^{23} +(4.02672 - 1.93917i) q^{25} +(-0.701761 - 0.879980i) q^{26} +(-1.53157 + 4.50924i) q^{28} +(-2.54566 + 3.19216i) q^{29} -4.41702 q^{31} +(2.91122 - 3.65056i) q^{32} +(2.32666 - 1.12046i) q^{34} +(1.35030 - 1.37530i) q^{35} +(-4.34155 + 5.44413i) q^{37} +(2.09873 + 1.01069i) q^{38} +(-1.11548 + 0.537189i) q^{40} +(0.150003 + 0.657205i) q^{41} +(1.08661 - 4.76076i) q^{43} +(1.38643 + 6.07436i) q^{44} +(0.873495 + 3.82703i) q^{46} +(2.54224 + 1.22428i) q^{47} +(-2.92097 + 6.36144i) q^{49} -1.99894 q^{50} +(-1.00794 - 4.41608i) q^{52} +(-8.42389 - 10.5632i) q^{53} +(0.561115 - 2.45841i) q^{55} +(3.15029 - 3.20863i) q^{56} +(1.64528 - 0.792324i) q^{58} +(-0.598629 + 2.62276i) q^{59} +(8.78325 - 11.0139i) q^{61} +(1.77991 + 0.857158i) q^{62} +(3.23555 - 1.55816i) q^{64} +(-0.407932 + 1.78727i) q^{65} -4.28478 q^{67} +10.3927 q^{68} +(-0.811012 + 0.292163i) q^{70} +(2.84281 + 3.56477i) q^{71} +(0.515660 - 0.248329i) q^{73} +(2.80597 - 1.35129i) q^{74} +(5.84494 + 7.32933i) q^{76} +(1.10885 + 9.09091i) q^{77} +4.07622 q^{79} -2.06871 q^{80} +(0.0670900 - 0.293941i) q^{82} +(4.48757 - 2.16110i) q^{83} +(-3.78957 - 1.82496i) q^{85} +(-1.36173 + 1.70756i) q^{86} +(1.30910 - 5.73555i) q^{88} +(6.71020 - 3.23146i) q^{89} +(-0.806134 - 6.60912i) q^{91} +(-3.51532 + 15.4016i) q^{92} +(-0.786854 - 0.986684i) q^{94} +(-0.844257 - 3.69893i) q^{95} +3.17139 q^{97} +(2.41154 - 1.99661i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Introduction

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