LMFDB - Embedded newform 441.2.u.d.127.5

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			127.5
Character	$\chi$	$=$	441.127
Dual form			441.2.u.d.316.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60360 + 0.772253i) q^{2} +(0.728177 + 0.913105i) q^{4} +(-0.987738 - 4.32756i) q^{5} +(-2.63181 + 0.271221i) q^{7} +(-0.329556 - 1.44388i) q^{8} +O(q^{10})$	\(q+(1.60360 + 0.772253i) q^{2} +(0.728177 + 0.913105i) q^{4} +(-0.987738 - 4.32756i) q^{5} +(-2.63181 + 0.271221i) q^{7} +(-0.329556 - 1.44388i) q^{8} +(1.75804 - 7.70246i) q^{10} +(-0.951225 - 0.458086i) q^{11} +(4.24896 + 2.04619i) q^{13} +(-4.42982 - 1.59749i) q^{14} +(1.10633 - 4.84715i) q^{16} +(2.95622 - 3.70698i) q^{17} +2.09671 q^{19} +(3.23227 - 4.05314i) q^{20} +(-1.17163 - 1.46917i) q^{22} +(0.565574 + 0.709207i) q^{23} +(-13.2473 + 6.37957i) q^{25} +(5.23345 + 6.56254i) q^{26} +(-2.16408 - 2.20562i) q^{28} +(-1.79593 + 2.25202i) q^{29} +1.97581 q^{31} +(3.67055 - 4.60272i) q^{32} +(7.60332 - 3.66156i) q^{34} +(3.77327 + 11.1214i) q^{35} +(0.285021 - 0.357405i) q^{37} +(3.36228 + 1.61919i) q^{38} +(-5.92297 + 2.85235i) q^{40} +(-0.917612 - 4.02032i) q^{41} +(-1.67837 + 7.35342i) q^{43} +(-0.274380 - 1.20214i) q^{44} +(0.359267 + 1.57405i) q^{46} +(7.33253 + 3.53116i) q^{47} +(6.85288 - 1.42761i) q^{49} -26.1700 q^{50} +(1.22561 + 5.36974i) q^{52} +(0.774992 + 0.971809i) q^{53} +(-1.04283 + 4.56895i) q^{55} +(1.25894 + 3.71064i) q^{56} +(-4.61908 + 2.22443i) q^{58} +(-0.293639 + 1.28652i) q^{59} +(7.12459 - 8.93395i) q^{61} +(3.16841 + 1.52583i) q^{62} +(0.481665 - 0.231958i) q^{64} +(4.65816 - 20.4087i) q^{65} +2.75438 q^{67} +5.53752 q^{68} +(-2.53775 + 20.7482i) q^{70} +(2.88977 + 3.62366i) q^{71} +(4.97674 - 2.39667i) q^{73} +(0.733067 - 0.353027i) q^{74} +(1.52677 + 1.91452i) q^{76} +(2.62769 + 0.947604i) q^{77} +8.21672 q^{79} -22.0691 q^{80} +(1.63322 - 7.15562i) q^{82} +(-13.7077 + 6.60126i) q^{83} +(-18.9622 - 9.13169i) q^{85} +(-8.37014 + 10.4958i) q^{86} +(-0.347939 + 1.52442i) q^{88} +(-10.0755 + 4.85213i) q^{89} +(-11.7374 - 4.23278i) q^{91} +(-0.235743 + 1.03286i) q^{92} +(9.03149 + 11.3251i) q^{94} +(-2.07100 - 9.07363i) q^{95} +5.72620 q^{97} +(12.0917 + 3.00284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.60360	+	0.772253i	1.13392	+	0.546065i	0.904165	−	0.427184i	$-0.140494\pi$
$2$	1.60360	+	0.772253i	1.13392	+	0.546065i	0.229751	+	0.973249i	$0.426209\pi$
$3$		0			0
$3$		0			0
$4$	0.728177	+	0.913105i	0.364089	+	0.456553i
$5$	−0.987738	−	4.32756i	−0.441730	−	1.93534i	−0.339588	−	0.940574i	$-0.610288\pi$
$5$	−0.987738	−	4.32756i	−0.441730	−	1.93534i	−0.102141	−	0.994770i	$-0.532569\pi$
$6$		0			0
$7$	−2.63181	+	0.271221i	−0.994732	+	0.102512i
$7$	−2.63181	+	0.271221i	−0.994732	+	0.102512i
$8$	−0.329556	−	1.44388i	−0.116516	−	0.510489i
$9$		0			0
$10$	1.75804	−	7.70246i	0.555940	−	2.43573i
$11$	−0.951225	−	0.458086i	−0.286805	−	0.138118i	0.284950	−	0.958542i	$-0.408023\pi$
$11$	−0.951225	−	0.458086i	−0.286805	−	0.138118i	−0.571755	+	0.820424i	$0.693737\pi$
$12$		0			0
$13$	4.24896	+	2.04619i	1.17845	+	0.567511i	0.917459	−	0.397830i	$-0.130237\pi$
$13$	4.24896	+	2.04619i	1.17845	+	0.567511i	0.260990	+	0.965341i	$0.415951\pi$
$14$	−4.42982	−	1.59749i	−1.18392	−	0.426948i
$15$		0			0
$16$	1.10633	−	4.84715i	0.276583	−	1.21179i
$17$	2.95622	−	3.70698i	0.716988	−	0.899075i	−0.281175	−	0.959657i	$-0.590724\pi$
$17$	2.95622	−	3.70698i	0.716988	−	0.899075i	0.998163	+	0.0605815i	$0.0192955\pi$
$18$		0			0
$19$	2.09671			0.481018			0.240509	−	0.970647i	$-0.422686\pi$
$19$	2.09671			0.481018			0.240509	+	0.970647i	$0.422686\pi$
$20$	3.23227	−	4.05314i	0.722758	−	0.906309i
$21$		0			0
$22$	−1.17163	−	1.46917i	−0.249792	−	0.313229i
$23$	0.565574	+	0.709207i	0.117930	+	0.147880i	0.837292	−	0.546755i	$-0.184137\pi$
$23$	0.565574	+	0.709207i	0.117930	+	0.147880i	−0.719362	+	0.694635i	$0.755566\pi$
$24$		0			0
$25$	−13.2473	+	6.37957i	−2.64946	+	1.27591i
$26$	5.23345	+	6.56254i	1.02636	+	1.28702i
$27$		0			0
$28$	−2.16408	−	2.20562i	−0.408973	−	0.416824i
$29$	−1.79593	+	2.25202i	−0.333495	+	0.418190i	−0.920100	−	0.391684i	$-0.871893\pi$
$29$	−1.79593	+	2.25202i	−0.333495	+	0.418190i	0.586605	+	0.809873i	$0.300464\pi$
$30$		0			0
$31$	1.97581			0.354866			0.177433	−	0.984133i	$-0.443221\pi$
$31$	1.97581			0.354866			0.177433	+	0.984133i	$0.443221\pi$
$32$	3.67055	−	4.60272i	0.648867	−	0.813654i
$33$		0			0
$34$	7.60332	−	3.66156i	1.30396	−	0.627953i
$35$	3.77327	+	11.1214i	0.637799	+	1.87987i
$36$		0			0
$37$	0.285021	−	0.357405i	0.0468572	−	0.0587571i	−0.757851	−	0.652428i	$-0.773750\pi$
$37$	0.285021	−	0.357405i	0.0468572	−	0.0587571i	0.804708	+	0.593671i	$0.202322\pi$
$38$	3.36228	+	1.61919i	0.545434	+	0.262667i
$39$		0			0
$40$	−5.92297	+	2.85235i	−0.936503	+	0.450996i
$41$	−0.917612	−	4.02032i	−0.143307	−	0.627869i	−0.994654	−	0.103266i	$-0.967071\pi$
$41$	−0.917612	−	4.02032i	−0.143307	−	0.627869i	0.851347	−	0.524603i	$-0.175786\pi$
$42$		0			0
$43$	−1.67837	+	7.35342i	−0.255949	+	1.12139i	0.669589	+	0.742732i	$0.266470\pi$
$43$	−1.67837	+	7.35342i	−0.255949	+	1.12139i	−0.925538	+	0.378655i	$0.876387\pi$
$44$	−0.274380	−	1.20214i	−0.0413643	−	0.181229i
$45$		0			0
$46$	0.359267	+	1.57405i	0.0529710	+	0.232081i
$47$	7.33253	+	3.53116i	1.06956	+	0.515073i	0.883965	−	0.467554i	$-0.154864\pi$
$47$	7.33253	+	3.53116i	1.06956	+	0.515073i	0.185595	+	0.982626i	$0.440579\pi$
$48$		0			0
$49$	6.85288	−	1.42761i	0.978983	−	0.203944i
$50$	−26.1700			−3.70100
$51$		0			0
$52$	1.22561	+	5.36974i	0.169961	+	0.744648i
$53$	0.774992	+	0.971809i	0.106453	+	0.133488i	0.832204	−	0.554470i	$-0.187079\pi$
$53$	0.774992	+	0.971809i	0.106453	+	0.133488i	−0.725751	+	0.687958i	$0.758507\pi$
$54$		0			0
$55$	−1.04283	+	4.56895i	−0.140616	+	0.616078i
$56$	1.25894	+	3.71064i	0.168233	+	0.495855i
$57$		0			0
$58$	−4.61908	+	2.22443i	−0.606514	+	0.292082i
$59$	−0.293639	+	1.28652i	−0.0382286	+	0.167490i	−0.990439	−	0.137953i	$-0.955948\pi$
$59$	−0.293639	+	1.28652i	−0.0382286	+	0.167490i	0.952210	+	0.305444i	$0.0988047\pi$
$60$		0			0
$61$	7.12459	−	8.93395i	0.912210	−	1.14388i	−0.0769500	−	0.997035i	$-0.524518\pi$
$61$	7.12459	−	8.93395i	0.912210	−	1.14388i	0.989160	−	0.146840i	$-0.0469104\pi$
$62$	3.16841	+	1.52583i	0.402388	+	0.193780i
$63$		0			0
$64$	0.481665	−	0.231958i	0.0602081	−	0.0289947i
$65$	4.65816	−	20.4087i	0.577774	−	2.53139i
$66$		0			0
$67$	2.75438			0.336502			0.168251	−	0.985744i	$-0.446188\pi$
$67$	2.75438			0.336502			0.168251	+	0.985744i	$0.446188\pi$
$68$	5.53752			0.671522
$69$		0			0
$70$	−2.53775	+	20.7482i	−0.303319	+	2.47989i
$71$	2.88977	+	3.62366i	0.342953	+	0.430049i	0.923158	−	0.384421i	$-0.125599\pi$
$71$	2.88977	+	3.62366i	0.342953	+	0.430049i	−0.580205	+	0.814470i	$0.697028\pi$
$72$		0			0
$73$	4.97674	−	2.39667i	0.582483	−	0.280509i	−0.119348	−	0.992852i	$-0.538080\pi$
$73$	4.97674	−	2.39667i	0.582483	−	0.280509i	0.701831	+	0.712343i	$0.252366\pi$
$74$	0.733067	−	0.353027i	0.0852173	−	0.0410385i
$75$		0			0
$76$	1.52677	+	1.91452i	0.175133	+	0.219610i
$77$	2.62769	+	0.947604i	0.299453	+	0.107990i
$78$		0			0
$79$	8.21672			0.924453			0.462226	−	0.886762i	$-0.347051\pi$
$79$	8.21672			0.924453			0.462226	+	0.886762i	$0.347051\pi$
$80$	−22.0691			−2.46740
$81$		0			0
$82$	1.63322	−	7.15562i	0.180359	−	0.790206i
$83$	−13.7077	+	6.60126i	−1.50461	+	0.724583i	−0.991053	−	0.133471i	$-0.957388\pi$
$83$	−13.7077	+	6.60126i	−1.50461	+	0.724583i	−0.513559	+	0.858054i	$0.671673\pi$
$84$		0			0
$85$	−18.9622	−	9.13169i	−2.05673	−	0.990471i
$86$	−8.37014	+	10.4958i	−0.902575	+	1.13179i
$87$		0			0
$88$	−0.347939	+	1.52442i	−0.0370904	+	0.162504i
$89$	−10.0755	+	4.85213i	−1.06801	+	0.514324i	−0.883463	−	0.468500i	$-0.844794\pi$
$89$	−10.0755	+	4.85213i	−1.06801	+	0.514324i	−0.184542	+	0.982825i	$0.559080\pi$
$90$		0			0
$91$	−11.7374	−	4.23278i	−1.23042	−	0.443716i
$92$	−0.235743	+	1.03286i	−0.0245779	+	0.107683i
$93$		0			0
$94$	9.03149	+	11.3251i	0.931528	+	1.16810i
$95$	−2.07100	−	9.07363i	−0.212480	−	0.930935i
$96$		0			0
$97$	5.72620			0.581408			0.290704	−	0.956813i	$-0.406111\pi$
$97$	5.72620			0.581408			0.290704	+	0.956813i	$0.406111\pi$
$98$	12.0917	+	3.00284i	1.22145	+	0.303333i
$99$		0			0
$100$	−15.4716	−	7.45073i	−1.54716	−	0.745073i
$101$	0.638061	+	2.79553i	0.0634894	+	0.278165i	0.996701	−	0.0811623i	$-0.0258632\pi$
$101$	0.638061	+	2.79553i	0.0634894	+	0.278165i	−0.933211	+	0.359328i	$0.883006\pi$
$102$		0			0
$103$	−3.11171	−	13.6333i	−0.306606	−	1.34333i	−0.859951	−	0.510377i	$-0.829506\pi$
$103$	−3.11171	−	13.6333i	−0.306606	−	1.34333i	0.553345	−	0.832952i	$-0.313351\pi$
$104$	1.55418	−	6.80932i	0.152400	−	0.667709i
$105$		0			0
$106$	0.492294	+	2.15688i	0.0478158	+	0.209495i
$107$	2.49968	−	1.20378i	0.241654	−	0.116374i	−0.309138	−	0.951017i	$-0.600040\pi$
$107$	2.49968	−	1.20378i	0.241654	−	0.116374i	0.550791	+	0.834643i	$0.314326\pi$
$108$		0			0
$109$	0.0742165	+	0.0357408i	0.00710865	+	0.00342335i	0.437435	−	0.899250i	$-0.355887\pi$
$109$	0.0742165	+	0.0357408i	0.00710865	+	0.00342335i	−0.430326	+	0.902674i	$0.641601\pi$
$110$	−5.20068	+	6.52144i	−0.495865	+	0.621795i
$111$		0			0
$112$	−1.59701	+	13.0569i	−0.150903	+	1.23376i
$113$	12.7135	−	6.12248i	1.19598	−	0.575954i	0.273454	−	0.961885i	$-0.411834\pi$
$113$	12.7135	−	6.12248i	1.19598	−	0.575954i	0.922528	+	0.385931i	$0.126120\pi$
$114$		0			0
$115$	2.51050	−	3.14807i	0.234105	−	0.293559i
$116$	−3.36408			−0.312347
$117$		0			0
$118$	−1.46440	+	1.83629i	−0.134809	+	0.169045i
$119$	−6.77480	+	10.5579i	−0.621045	+	0.967838i
$120$		0			0
$121$	−6.16340	−	7.72866i	−0.560309	−	0.702605i
$122$	18.3243	−	8.82450i	1.65900	−	0.798932i
$123$		0			0
$124$	1.43874	+	1.80412i	0.129203	+	0.162015i
$125$	26.8550	+	33.6750i	2.40198	+	3.01199i
$126$		0			0
$127$	−0.699528	+	0.877180i	−0.0620731	+	0.0778372i	−0.811899	−	0.583798i	$-0.801566\pi$
$127$	−0.699528	+	0.877180i	−0.0620731	+	0.0778372i	0.749826	+	0.661635i	$0.230137\pi$
$128$	−10.8227			−0.956598
$129$		0			0
$130$	23.2305	−	29.1301i	2.03745	−	2.55488i
$131$	3.68194	−	16.1316i	0.321692	−	1.40943i	−0.512848	−	0.858480i	$-0.671409\pi$
$131$	3.68194	−	16.1316i	0.321692	−	1.40943i	0.834540	−	0.550947i	$-0.185733\pi$
$132$		0			0
$133$	−5.51814	+	0.568672i	−0.478484	+	0.0493101i
$134$	4.41693	+	2.12708i	0.381564	+	0.183752i
$135$		0			0
$136$	−6.32668	−	3.04677i	−0.542508	−	0.261258i
$137$	0.272365	−	1.19331i	0.0232697	−	0.101951i	−0.961959	−	0.273192i	$-0.911920\pi$
$137$	0.272365	−	1.19331i	0.0232697	−	0.101951i	0.985229	+	0.171241i	$0.0547776\pi$
$138$		0			0
$139$	2.53972	+	11.1272i	0.215416	+	0.943801i	0.960817	+	0.277184i	$0.0894011\pi$
$139$	2.53972	+	11.1272i	0.215416	+	0.943801i	−0.745401	+	0.666617i	$0.767742\pi$
$140$	−7.40743	+	11.5438i	−0.626042	+	0.975626i
$141$		0			0
$142$	1.83565	+	8.04253i	0.154045	+	0.674914i
$143$	−3.10439	−	3.89278i	−0.259602	−	0.325530i
$144$		0			0
$145$	11.5197	+	5.54758i	0.956656	+	0.460701i
$146$	9.83153			0.813663
$147$		0			0
$148$	0.533895			0.0438859
$149$	−2.67461	−	1.28802i	−0.219112	−	0.105519i	0.321108	−	0.947043i	$-0.395945\pi$
$149$	−2.67461	−	1.28802i	−0.219112	−	0.105519i	−0.540220	+	0.841524i	$0.681659\pi$
$150$		0			0
$151$	10.4934	+	13.1583i	0.853937	+	1.07080i	0.996710	+	0.0810482i	$0.0258268\pi$
$151$	10.4934	+	13.1583i	0.853937	+	1.07080i	−0.142773	+	0.989755i	$0.545602\pi$
$152$	−0.690983	−	3.02740i	−0.0560462	−	0.245554i
$153$		0			0
$154$	3.48197	+	3.54882i	0.280585	+	0.285972i
$155$	−1.95158	−	8.55044i	−0.156755	−	0.686788i
$156$		0			0
$157$	0.502985	−	2.20372i	0.0401426	−	0.175876i	−0.950883	−	0.309552i	$-0.899821\pi$
$157$	0.502985	−	2.20372i	0.0401426	−	0.175876i	0.991025	+	0.133676i	$0.0426781\pi$
$158$	13.1763	+	6.34538i	1.04825	+	0.504811i
$159$		0			0
$160$	−23.5441	−	11.3382i	−1.86132	−	0.896366i
$161$	−1.68084	−	1.71311i	−0.132469	−	0.135012i
$162$		0			0
$163$	1.94093	−	8.50376i	0.152025	−	0.666066i	−0.840270	−	0.542168i	$-0.817604\pi$
$163$	1.94093	−	8.50376i	0.152025	−	0.666066i	0.992295	−	0.123897i	$-0.0395393\pi$
$164$	3.00279	−	3.76538i	0.234479	−	0.294027i
$165$		0			0
$166$	−27.0794			−2.10177
$167$	−9.43677	+	11.8333i	−0.730239	+	0.915691i	−0.998869	−	0.0475523i	$-0.984858\pi$
$167$	−9.43677	+	11.8333i	−0.730239	+	0.915691i	0.268629	+	0.963244i	$0.413429\pi$
$168$		0			0
$169$	5.76139	+	7.22455i	0.443184	+	0.555735i
$170$	−23.3557	−	29.2872i	−1.79130	−	2.24622i
$171$		0			0
$172$	−7.93660	+	3.82207i	−0.605160	+	0.291430i
$173$	−13.2846	−	16.6583i	−1.01001	−	1.26651i	−0.963533	−	0.267588i	$-0.913773\pi$
$173$	−13.2846	−	16.6583i	−1.01001	−	1.26651i	−0.0464724	−	0.998920i	$-0.514798\pi$
$174$		0			0
$175$	33.1342	−	20.3828i	2.50471	−	1.54079i
$176$	−3.27278	+	4.10394i	−0.246695	+	0.309346i
$177$		0			0
$178$	−19.9042			−1.49188
$179$	−3.17234	+	3.97799i	−0.237112	+	0.297329i	−0.886123	−	0.463450i	$-0.846611\pi$
$179$	−3.17234	+	3.97799i	−0.237112	+	0.297329i	0.649011	+	0.760779i	$0.275183\pi$
$180$		0			0
$181$	1.65415	−	0.796597i	0.122952	−	0.0592106i	−0.371397	−	0.928474i	$-0.621121\pi$
$181$	1.65415	−	0.796597i	0.122952	−	0.0592106i	0.494349	+	0.869264i	$0.335407\pi$
$182$	−15.5534	−	15.8520i	−1.15289	−	1.17503i
$183$		0			0
$184$	0.837622	−	1.05035i	0.0617503	−	0.0774325i
$185$	−1.82822	−	0.880424i	−0.134413	−	0.0647301i
$186$		0			0
$187$	−4.51015	+	2.17197i	−0.329815	+	0.158830i
$188$	2.11506	+	9.26668i	0.154257	+	0.675842i
$189$		0			0
$190$	3.68609	−	16.1498i	0.267417	−	1.17163i
$191$	2.95936	+	12.9658i	0.214131	+	0.938171i	0.961725	+	0.274015i	$0.0883518\pi$
$191$	2.95936	+	12.9658i	0.214131	+	0.938171i	−0.747594	+	0.664156i	$0.768791\pi$
$192$		0			0
$193$	3.35030	+	14.6786i	0.241160	+	1.05659i	0.939963	+	0.341277i	$0.110859\pi$
$193$	3.35030	+	14.6786i	0.241160	+	1.05659i	−0.698802	+	0.715315i	$0.746283\pi$
$194$	9.18254	+	4.42208i	0.659268	+	0.317487i
$195$		0			0
$196$	6.29366	+	5.21785i	0.449547	+	0.372703i
$197$	−11.2917			−0.804498			−0.402249	−	0.915530i	$-0.631771\pi$
$197$	−11.2917			−0.804498			−0.402249	+	0.915530i	$0.631771\pi$
$198$		0			0
$199$	5.34073	+	23.3992i	0.378594	+	1.65873i	0.701780	+	0.712393i	$0.252389\pi$
$199$	5.34073	+	23.3992i	0.378594	+	1.65873i	−0.323186	+	0.946335i	$0.604754\pi$
$200$	13.5771	+	17.0251i	0.960044	+	1.20386i
$201$		0			0
$202$	−1.13566	+	4.97565i	−0.0799047	+	0.350085i
$203$	4.11575	−	6.41399i	0.288869	−	0.450174i
$204$		0			0
$205$	−16.4918	+	7.94205i	−1.15184	+	0.554697i
$206$	5.53841	−	24.2654i	0.385880	−	1.69065i
$207$		0			0
$208$	14.6190	−	18.3316i	1.01364	−	1.27107i
$209$	−1.99444	−	0.960473i	−0.137958	−	0.0664373i
$210$		0			0
$211$	−13.1458	+	6.33066i	−0.904991	+	0.435821i	−0.827689	−	0.561187i	$-0.810345\pi$
$211$	−13.1458	+	6.33066i	−0.904991	+	0.435821i	−0.0773021	+	0.997008i	$0.524631\pi$
$212$	−0.323033	+	1.41530i	−0.0221860	+	0.0972031i
$213$		0			0
$214$	4.93812			0.337563
$215$	33.4802			2.28333
$216$		0			0
$217$	−5.19996	+	0.535882i	−0.352997	+	0.0363780i
$218$	0.0914126	+	0.114628i	0.00619124	+	0.00776358i
$219$		0			0
$220$	−4.93130	+	2.37479i	−0.332468	+	0.160108i
$221$	20.1460	−	9.70182i	1.35517	−	0.652615i
$222$		0			0
$223$	0.163765	+	0.205355i	0.0109665	+	0.0137516i	0.787284	−	0.616590i	$-0.211486\pi$
$223$	0.163765	+	0.205355i	0.0109665	+	0.0137516i	−0.776318	+	0.630341i	$0.782915\pi$
$224$	−8.41184	+	13.1090i	−0.562040	+	0.875884i
$225$		0			0
$226$	25.1154			1.67065
$227$	6.43940			0.427398			0.213699	−	0.976900i	$-0.431449\pi$
$227$	6.43940			0.427398			0.213699	+	0.976900i	$0.431449\pi$
$228$		0			0
$229$	−2.37820	+	10.4196i	−0.157156	+	0.688545i	0.833541	+	0.552458i	$0.186310\pi$
$229$	−2.37820	+	10.4196i	−0.157156	+	0.688545i	−0.990697	+	0.136087i	$0.956547\pi$
$230$	6.45694	−	3.10950i	0.425758	−	0.205034i
$231$		0			0
$232$	3.84351	+	1.85094i	0.252339	+	0.121520i
$233$	−7.86250	+	9.85926i	−0.515089	+	0.645902i	−0.969558	−	0.244861i	$-0.921258\pi$
$233$	−7.86250	+	9.85926i	−0.515089	+	0.645902i	0.454469	+	0.890763i	$0.349829\pi$
$234$		0			0
$235$	8.03870	−	35.2198i	0.524387	−	2.29749i
$236$	−1.38855	+	0.668689i	−0.0903867	+	0.0435279i
$237$		0			0
$238$	−19.0174	+	11.6987i	−1.23272	+	0.758316i
$239$	−5.59499	+	24.5133i	−0.361910	+	1.58563i	0.386432	+	0.922318i	$0.373708\pi$
$239$	−5.59499	+	24.5133i	−0.361910	+	1.58563i	−0.748342	+	0.663313i	$0.769150\pi$
$240$		0			0
$241$	−10.0426	−	12.5930i	−0.646900	−	0.811187i	0.344947	−	0.938622i	$-0.387897\pi$
$241$	−10.0426	−	12.5930i	−0.646900	−	0.811187i	−0.991847	+	0.127435i	$0.959326\pi$
$242$	−3.91515	−	17.1534i	−0.251675	−	1.10266i
$243$		0			0
$244$	13.3456			0.854365
$245$	−12.9469	−	28.2461i	−0.827147	−	1.80458i
$246$		0			0
$247$	8.90883	+	4.29026i	0.566855	+	0.272983i
$248$	−0.651141	−	2.85284i	−0.0413475	−	0.181155i
$249$		0			0
$250$	17.0589	+	74.7401i	1.07890	+	4.72698i
$251$	2.71050	−	11.8755i	0.171085	−	0.749574i	−0.814468	−	0.580209i	$-0.802971\pi$
$251$	2.71050	−	11.8755i	0.171085	−	0.749574i	0.985553	−	0.169366i	$-0.0541719\pi$
$252$		0			0
$253$	−0.213110	−	0.933698i	−0.0133981	−	0.0587011i
$254$	−1.79917	+	0.866433i	−0.112890	+	0.0543649i
$255$		0			0
$256$	−18.3186	−	8.82176i	−1.14491	−	0.551360i
$257$	10.2907	−	12.9042i	0.641919	−	0.804940i	−0.349323	−	0.937002i	$-0.613588\pi$
$257$	10.2907	−	12.9042i	0.641919	−	0.804940i	0.991241	+	0.132062i	$0.0421598\pi$
$258$		0			0
$259$	−0.653187	+	1.01793i	−0.0405870	+	0.0632510i
$260$	22.0273	−	10.6078i	1.36607	−	0.657867i
$261$		0			0
$262$	18.3620	−	23.0253i	1.13441	−	1.42251i
$263$	5.58393			0.344320			0.172160	−	0.985069i	$-0.444925\pi$
$263$	5.58393			0.344320			0.172160	+	0.985069i	$0.444925\pi$
$264$		0			0
$265$	3.44007	−	4.31372i	0.211322	−	0.264990i
$266$	−9.28805	−	3.34948i	−0.569487	−	0.205370i
$267$		0			0
$268$	2.00568	+	2.51504i	0.122516	+	0.153631i
$269$	−10.3472	+	4.98296i	−0.630882	+	0.303817i	−0.721863	−	0.692036i	$-0.756714\pi$
$269$	−10.3472	+	4.98296i	−0.630882	+	0.303817i	0.0909812	+	0.995853i	$0.471000\pi$
$270$		0			0
$271$	2.07215	+	2.59840i	0.125874	+	0.157841i	0.840775	−	0.541384i	$-0.182100\pi$
$271$	2.07215	+	2.59840i	0.125874	+	0.157841i	−0.714901	+	0.699226i	$0.753528\pi$
$272$	−14.6978	−	18.4304i	−0.891182	−	1.11751i
$273$		0			0
$274$	1.35830	−	1.70326i	0.0820580	−	0.102897i
$275$	15.5236			0.936107
$276$		0			0
$277$	−1.61162	+	2.02091i	−0.0968328	+	0.121424i	−0.827887	−	0.560895i	$-0.810457\pi$
$277$	−1.61162	+	2.02091i	−0.0968328	+	0.121424i	0.731054	+	0.682319i	$0.239029\pi$
$278$	−4.52035	+	19.8050i	−0.271113	+	1.18782i
$279$		0			0
$280$	14.8145	−	9.11329i	0.885337	−	0.544623i
$281$	−11.8811	−	5.72163i	−0.708766	−	0.341324i	0.0445277	−	0.999008i	$-0.485822\pi$
$281$	−11.8811	−	5.72163i	−0.708766	−	0.341324i	−0.753293	+	0.657685i	$0.771536\pi$
$282$		0			0
$283$	−5.13752	−	2.47410i	−0.305394	−	0.147070i	0.274910	−	0.961470i	$-0.411352\pi$
$283$	−5.13752	−	2.47410i	−0.305394	−	0.147070i	−0.580304	+	0.814400i	$0.697066\pi$
$284$	−1.20452	+	5.27733i	−0.0714749	+	0.313152i
$285$		0			0
$286$	−1.97198	−	8.63983i	−0.116606	−	0.510884i
$287$	3.50538	+	10.3319i	0.206916	+	0.609870i
$288$		0			0
$289$	−1.21962	−	5.34352i	−0.0717426	−	0.314325i
$290$	14.1888	+	17.7922i	0.833194	+	1.04479i
$291$		0			0
$292$	5.81236	+	2.79908i	0.340143	+	0.163804i
$293$	−1.16842			−0.0682596			−0.0341298	−	0.999417i	$-0.510866\pi$
$293$	−1.16842			−0.0682596			−0.0341298	+	0.999417i	$0.510866\pi$
$294$		0			0
$295$	5.85752			0.341038
$296$	−0.609981	−	0.293751i	−0.0354544	−	0.0170740i
$297$		0			0
$298$	−3.29432	−	4.13095i	−0.190835	−	0.239299i
$299$	0.951927	+	4.17067i	0.0550514	+	0.241196i
$300$		0			0
$301$	2.42275	−	19.8080i	0.139645	−	1.14172i
$302$	6.66564	+	29.2041i	0.383565	+	1.68051i
$303$		0			0
$304$	2.31965	−	10.1631i	0.133041	−	0.582892i
$305$	−45.6994	−	22.0077i	−2.61674	−	1.26016i
$306$		0			0
$307$	−13.6585	−	6.57757i	−0.779530	−	0.375402i	0.00141723	−	0.999999i	$-0.499549\pi$
$307$	−13.6585	−	6.57757i	−0.779530	−	0.375402i	−0.780947	+	0.624597i	$0.785263\pi$
$308$	1.04816	+	3.08938i	0.0597245	+	0.176034i
$309$		0			0
$310$	3.47355	−	15.2186i	0.197284	−	0.864358i
$311$	−0.334482	+	0.419427i	−0.0189667	+	0.0237835i	−0.791224	−	0.611526i	$-0.790556\pi$
$311$	−0.334482	+	0.419427i	−0.0189667	+	0.0237835i	0.772258	+	0.635309i	$0.219127\pi$
$312$		0			0
$313$	29.7171			1.67971			0.839854	−	0.542813i	$-0.182641\pi$
$313$	29.7171			1.67971			0.839854	+	0.542813i	$0.182641\pi$
$314$	2.50842	−	3.14546i	0.141558	−	0.177508i
$315$		0			0
$316$	5.98322	+	7.50273i	0.336583	+	0.422061i
$317$	17.5060	+	21.9518i	0.983235	+	1.23294i	0.972478	+	0.232996i	$0.0748529\pi$
$317$	17.5060	+	21.9518i	0.983235	+	1.23294i	0.0107577	+	0.999942i	$0.496576\pi$
$318$		0			0
$319$	2.73995	−	1.31949i	0.153408	−	0.0738773i
$320$	−1.47957	−	1.85532i	−0.0827104	−	0.103716i
$321$		0			0
$322$	−1.37244	−	4.04517i	−0.0764830	−	0.225428i
$323$	6.19833	−	7.77246i	0.344884	−	0.432471i
$324$		0			0
$325$	−69.3411			−3.84635
$326$	9.67952	−	12.1377i	0.536099	−	0.672247i
$327$		0			0
$328$	−5.50246	+	2.64985i	−0.303823	+	0.146313i
$329$	−20.2556	−	7.30462i	−1.11673	−	0.402717i
$330$		0			0
$331$	−3.87933	+	4.86453i	−0.213227	+	0.267379i	−0.876930	−	0.480618i	$-0.840412\pi$
$331$	−3.87933	+	4.86453i	−0.213227	+	0.267379i	0.663703	+	0.747996i	$0.268984\pi$
$332$	−16.0093	−	7.70965i	−0.878622	−	0.423122i
$333$		0			0
$334$	−24.2711	+	11.6884i	−1.32806	+	0.639559i
$335$	−2.72061	−	11.9198i	−0.148643	−	0.651246i
$336$		0			0
$337$	2.98668	−	13.0855i	0.162695	−	0.712812i	−0.826099	−	0.563525i	$-0.809445\pi$
$337$	2.98668	−	13.0855i	0.162695	−	0.712812i	0.988794	−	0.149287i	$-0.0476980\pi$
$338$	3.65978	+	16.0345i	0.199066	+	0.872164i
$339$		0			0
$340$	−5.46961	−	23.9639i	−0.296631	−	1.29963i
$341$	−1.87944	−	0.905091i	−0.101777	−	0.0490134i
$342$		0			0
$343$	−17.6483	+	5.61584i	−0.952918	+	0.303227i
$344$	11.1706			0.602277
$345$		0			0
$346$	−8.43868	−	36.9723i	−0.453666	−	1.98764i
$347$	9.30336	+	11.6660i	0.499430	+	0.626266i	0.966101	−	0.258165i	$-0.0831180\pi$
$347$	9.30336	+	11.6660i	0.499430	+	0.626266i	−0.466670	+	0.884431i	$0.654547\pi$
$348$		0			0
$349$	−5.49929	+	24.0939i	−0.294370	+	1.28972i	0.584006	+	0.811749i	$0.301484\pi$
$349$	−5.49929	+	24.0939i	−0.294370	+	1.28972i	−0.878376	+	0.477970i	$0.841373\pi$
$350$	68.8746	−	7.09787i	3.68150	−	0.379397i
$351$		0			0
$352$	−5.59996	+	2.69680i	−0.298479	+	0.143740i
$353$	−0.741409	+	3.24833i	−0.0394612	+	0.172891i	−0.990818	−	0.135199i	$-0.956833\pi$
$353$	−0.741409	+	3.24833i	−0.0394612	+	0.172891i	0.951357	+	0.308090i	$0.0996898\pi$
$354$		0			0
$355$	12.8273	−	16.0849i	0.680800	−	0.853697i
$356$	−11.7673	−	5.66682i	−0.623665	−	0.300341i
$357$		0			0
$358$	−8.15918	+	3.92925i	−0.431226	+	0.207667i
$359$	2.08440	−	9.13234i	0.110010	−	0.481987i	−0.889668	−	0.456609i	$-0.849064\pi$
$359$	2.08440	−	9.13234i	0.110010	−	0.481987i	0.999678	−	0.0253779i	$-0.00807892\pi$
$360$		0			0
$361$	−14.6038			−0.768622
$362$	3.26777			0.171750
$363$		0			0
$364$	−4.68196	−	13.7997i	−0.245401	−	0.723302i
$365$	−15.2874	−	19.1699i	−0.800182	−	1.00340i
$366$		0			0
$367$	27.8010	−	13.3883i	1.45120	−	0.698862i	0.468399	−	0.883517i	$-0.344831\pi$
$367$	27.8010	−	13.3883i	1.45120	−	0.698862i	0.982803	+	0.184655i	$0.0591166\pi$
$368$	4.06335	−	1.95681i	0.211817	−	0.102006i
$369$		0			0
$370$	−2.25182	−	2.82370i	−0.117067	−	0.146797i
$371$	−2.30321	−	2.34743i	−0.119577	−	0.121872i
$372$		0			0
$373$	14.0696			0.728496			0.364248	−	0.931302i	$-0.381326\pi$
$373$	14.0696			0.728496			0.364248	+	0.931302i	$0.381326\pi$
$374$	−8.90978			−0.460714
$375$		0			0
$376$	2.68209	−	11.7510i	0.138318	−	0.606012i
$377$	−12.2389	+	5.89393i	−0.630334	+	0.303553i
$378$		0			0
$379$	−28.4035	−	13.6784i	−1.45899	−	0.702611i	−0.474858	−	0.880062i	$-0.657501\pi$
$379$	−28.4035	−	13.6784i	−1.45899	−	0.702611i	−0.984130	+	0.177451i	$0.943215\pi$
$380$	6.77713	−	8.49825i	0.347659	−	0.435951i
$381$		0			0
$382$	−5.26724	+	23.0773i	−0.269496	+	1.18074i
$383$	0.793314	−	0.382040i	0.0405365	−	0.0195213i	−0.413506	−	0.910502i	$-0.635696\pi$
$383$	0.793314	−	0.382040i	0.0405365	−	0.0195213i	0.454042	+	0.890980i	$0.349982\pi$
$384$		0			0
$385$	1.50535	−	12.3075i	0.0767196	−	0.627247i
$386$	−5.96308	+	26.1259i	−0.303513	+	1.32978i
$387$		0			0
$388$	4.16969	+	5.22863i	0.211684	+	0.265443i
$389$	6.50001	+	28.4784i	0.329563	+	1.44391i	0.819964	+	0.572415i	$0.193993\pi$
$389$	6.50001	+	28.4784i	0.329563	+	1.44391i	−0.490401	+	0.871497i	$0.663150\pi$
$390$		0			0
$391$	4.30098			0.217510
$392$	−4.31970	−	9.42426i	−0.218178	−	0.475997i
$393$		0			0
$394$	−18.1073	−	8.72002i	−0.912233	−	0.439308i
$395$	−8.11596	−	35.5583i	−0.408358	−	1.78913i
$396$		0			0
$397$	2.48669	+	10.8949i	0.124804	+	0.546800i	0.998210	+	0.0598080i	$0.0190488\pi$
$397$	2.48669	+	10.8949i	0.124804	+	0.546800i	−0.873406	+	0.486992i	$0.838094\pi$
$398$	−9.50575	+	41.6474i	−0.476480	+	2.08760i
$399$		0			0
$400$	16.2668	+	71.2697i	0.813342	+	3.56348i
$401$	−28.7143	+	13.8281i	−1.43392	+	0.690542i	−0.979723	−	0.200358i	$-0.935790\pi$
$401$	−28.7143	+	13.8281i	−1.43392	+	0.690542i	−0.454201	+	0.890899i	$0.650075\pi$
$402$		0			0
$403$	8.39514	+	4.04289i	0.418192	+	0.201390i
$404$	−2.08799	+	2.61825i	−0.103881	+	0.130263i
$405$		0			0
$406$	11.5532	−	7.10707i	0.573377	−	0.352718i
$407$	−0.434842	+	0.209409i	−0.0215543	+	0.0103800i
$408$		0			0
$409$	−20.2302	+	25.3679i	−1.00032	+	1.25436i	−0.0333591	+	0.999443i	$0.510621\pi$
$409$	−20.2302	+	25.3679i	−1.00032	+	1.25436i	−0.966962	+	0.254920i	$0.917951\pi$
$410$	−32.5796			−1.60899
$411$		0			0
$412$	10.1828	−	12.7688i	0.501669	−	0.629073i
$413$	0.423872	−	3.46551i	0.0208574	−	0.170527i
$414$		0			0
$415$	42.1069	+	52.8004i	2.06695	+	2.59187i
$416$	25.0141	−	12.0461i	1.22641	−	0.590610i
$417$		0			0
$418$	−2.45656	−	3.08043i	−0.120154	−	0.150669i
$419$	−6.05176	−	7.58867i	−0.295648	−	0.370731i	0.611716	−	0.791078i	$-0.290480\pi$
$419$	−6.05176	−	7.58867i	−0.295648	−	0.370731i	−0.907363	+	0.420347i	$0.861908\pi$
$420$		0			0
$421$	12.5823	−	15.7777i	0.613224	−	0.768958i	−0.374149	−	0.927368i	$-0.622065\pi$
$421$	12.5823	−	15.7777i	0.613224	−	0.768958i	0.987373	+	0.158410i	$0.0506367\pi$
$422$	−25.9694			−1.26417
$423$		0			0
$424$	1.14777	−	1.43926i	0.0557408	−	0.0698967i
$425$	−15.5130	+	67.9670i	−0.752492	+	3.29688i
$426$		0			0
$427$	−16.3275	+	25.4448i	−0.790143	+	1.23136i
$428$	2.91939	+	1.40591i	0.141114	+	0.0679570i
$429$		0			0
$430$	53.6888	+	25.8552i	2.58910	+	1.24685i
$431$	2.20568	−	9.66374i	0.106244	−	0.465486i	−0.893617	−	0.448830i	$-0.851841\pi$
$431$	2.20568	−	9.66374i	0.106244	−	0.465486i	0.999861	−	0.0166558i	$-0.00530196\pi$
$432$		0			0
$433$	−4.44868	−	19.4909i	−0.213790	−	0.936674i	−0.961965	−	0.273173i	$-0.911927\pi$
$433$	−4.44868	−	19.4909i	−0.213790	−	0.936674i	0.748175	−	0.663501i	$-0.230930\pi$
$434$	−8.75250	−	3.15635i	−0.420133	−	0.151510i
$435$		0			0
$436$	0.0214077	+	0.0937931i	0.00102524	+	0.00449188i
$437$	1.18584	+	1.48700i	0.0567266	+	0.0711329i
$438$		0			0
$439$	−30.0813	−	14.4864i	−1.43570	−	0.691399i	−0.455656	−	0.890156i	$-0.650595\pi$
$439$	−30.0813	−	14.4864i	−1.43570	−	0.691399i	−0.980049	+	0.198757i	$0.936309\pi$
$440$	6.94070			0.330885
$441$		0			0
$442$	39.7984			1.89302
$443$	19.8332	+	9.55118i	0.942306	+	0.453790i	0.840982	−	0.541063i	$-0.181978\pi$
$443$	19.8332	+	9.55118i	0.942306	+	0.453790i	0.101324	+	0.994854i	$0.467692\pi$
$444$		0			0
$445$	30.9499	+	38.8099i	1.46716	+	1.83977i
$446$	0.104028	+	0.455774i	0.00492585	+	0.0215815i
$447$		0			0
$448$	−1.20474	+	0.741107i	−0.0569186	+	0.0350140i
$449$	1.68875	+	7.39891i	0.0796972	+	0.349176i	0.999017	−	0.0443357i	$-0.0141171\pi$
$449$	1.68875	+	7.39891i	0.0796972	+	0.349176i	−0.919319	+	0.393512i	$0.871260\pi$
$450$		0			0
$451$	−0.968797	+	4.24458i	−0.0456189	+	0.199869i
$452$	14.8481	+	7.15048i	0.698397	+	0.336330i
$453$		0			0
$454$	10.3262	+	4.97284i	0.484633	+	0.233387i
$455$	−6.72412	+	54.9753i	−0.315232	+	2.57728i
$456$		0			0
$457$	−6.05373	+	26.5231i	−0.283182	+	1.24070i	0.610506	+	0.792011i	$0.290966\pi$
$457$	−6.05373	+	26.5231i	−0.283182	+	1.24070i	−0.893688	+	0.448689i	$0.851891\pi$
$458$	−11.8602	+	14.8722i	−0.554192	+	0.694935i
$459$		0			0
$460$	4.70260			0.219260
$461$	−1.31974	+	1.65490i	−0.0614664	+	0.0770764i	−0.811614	−	0.584194i	$-0.801411\pi$
$461$	−1.31974	+	1.65490i	−0.0614664	+	0.0770764i	0.750148	+	0.661270i	$0.229982\pi$
$462$		0			0
$463$	16.9110	+	21.2058i	0.785923	+	0.985516i	0.999962	+	0.00869098i	$0.00276646\pi$
$463$	16.9110	+	21.2058i	0.785923	+	0.985516i	−0.214039	+	0.976825i	$0.568662\pi$
$464$	8.92900	+	11.1966i	0.414518	+	0.519790i
$465$		0			0
$466$	−20.2221	+	9.73847i	−0.936772	+	0.451126i
$467$	−21.7853	−	27.3179i	−1.00810	−	1.26412i	−0.964225	−	0.265084i	$-0.914600\pi$
$467$	−21.7853	−	27.3179i	−1.00810	−	1.26412i	−0.0438778	−	0.999037i	$-0.513971\pi$
$468$		0			0
$469$	−7.24902	+	0.747047i	−0.334729	+	0.0344954i
$470$	40.0895	−	50.2706i	1.84919	−	2.31881i
$471$		0			0
$472$	1.95435			0.0899561
$473$	4.96501	−	6.22592i	0.228291	−	0.286268i
$474$		0			0
$475$	−27.7757	+	13.3761i	−1.27444	+	0.613737i
$476$	−14.5737	+	1.50189i	−0.667985	+	0.0688391i
$477$		0			0
$478$	−27.9026	+	34.9887i	−1.27623	+	1.60035i
$479$	16.0365	+	7.72275i	0.732725	+	0.352862i	0.762755	−	0.646687i	$-0.223846\pi$
$479$	16.0365	+	7.72275i	0.732725	+	0.352862i	−0.0300304	+	0.999549i	$0.509560\pi$
$480$		0			0
$481$	1.94236	−	0.935393i	0.0885641	−	0.0426502i
$482$	−6.37930	−	27.9496i	−0.290569	−	1.27307i
$483$		0			0
$484$	2.56903	−	11.2557i	0.116774	−	0.511621i
$485$	−5.65599	−	24.7805i	−0.256825	−	1.12522i
$486$		0			0
$487$	0.502855	+	2.20315i	0.0227865	+	0.0998343i	0.985042	−	0.172312i	$-0.0551237\pi$
$487$	0.502855	+	2.20315i	0.0227865	+	0.0998343i	−0.962256	+	0.272146i	$0.912267\pi$
$488$	−15.2475	−	7.34282i	−0.690223	−	0.332394i
$489$		0			0
$490$	1.05152	−	55.2938i	0.0475028	−	2.49792i
$491$	1.77691			0.0801910			0.0400955	−	0.999196i	$-0.487234\pi$
$491$	1.77691			0.0801910			0.0400955	+	0.999196i	$0.487234\pi$
$492$		0			0
$493$	3.03905	+	13.3149i	0.136872	+	0.599674i
$494$	10.9730	+	13.7597i	0.493700	+	0.619080i
$495$		0			0
$496$	2.18590	−	9.57706i	0.0981499	−	0.430023i
$497$	−8.58815	−	8.75302i	−0.385231	−	0.392627i
$498$		0			0
$499$	−22.9011	+	11.0286i	−1.02519	+	0.493708i	−0.869414	−	0.494084i	$-0.835504\pi$
$499$	−22.9011	+	11.0286i	−1.02519	+	0.493708i	−0.155780	+	0.987792i	$0.549789\pi$
$500$	−11.1937	+	49.0428i	−0.500597	+	2.19326i
$501$		0			0
$502$	13.5174	−	16.9503i	0.603313	−	0.756531i
$503$	28.2066	+	13.5836i	1.25767	+	0.605661i	0.939557	−	0.342392i	$-0.111237\pi$
$503$	28.2066	+	13.5836i	1.25767	+	0.605661i	0.318111	+	0.948053i	$0.396952\pi$
$504$		0			0
$505$	11.4676	−	5.52249i	0.510300	−	0.245748i
$506$	0.379307	−	1.66185i	0.0168622	−	0.0738783i
$507$		0			0
$508$	−1.31034			−0.0581369
$509$	11.6124			0.514712			0.257356	−	0.966317i	$-0.417149\pi$
$509$	11.6124			0.514712			0.257356	+	0.966317i	$0.417149\pi$
$510$		0			0
$511$	−12.4478	+	7.65739i	−0.550659	+	0.338743i
$512$	−9.06736	−	11.3701i	−0.400724	−	0.502493i
$513$		0			0
$514$	26.4675	−	12.7461i	1.16743	−	0.562205i
$515$	−55.9254	+	26.9322i	−2.46437	+	1.18678i
$516$		0			0
$517$	−5.35732	−	6.71786i	−0.235614	−	0.295451i
$518$	−1.83355	+	1.12792i	−0.0805614	+	0.0495581i
$519$		0			0
$520$	−31.0029			−1.35957
$521$	−36.5984			−1.60340			−0.801702	−	0.597724i	$-0.796072\pi$
$521$	−36.5984			−1.60340			−0.801702	+	0.597724i	$0.796072\pi$
$522$		0			0
$523$	−3.55728	+	15.5855i	−0.155549	+	0.681505i	0.835665	+	0.549239i	$0.185082\pi$
$523$	−3.55728	+	15.5855i	−0.155549	+	0.681505i	−0.991214	+	0.132266i	$0.957775\pi$
$524$	17.4110	−	8.38468i	0.760602	−	0.366287i
$525$		0			0
$526$	8.95438	+	4.31220i	0.390430	+	0.188021i
$527$	5.84093	−	7.32429i	0.254435	−	0.319051i
$528$		0			0
$529$	4.93488	−	21.6211i	0.214560	−	0.940049i
$530$	8.84778	−	4.26087i	0.384323	−	0.185080i
$531$		0			0
$532$	−4.53744	−	4.62455i	−0.196723	−	0.200500i
$533$	4.32745	−	18.9598i	0.187443	−	0.821240i
$534$		0			0
$535$	−7.67848	−	9.62851i	−0.331970	−	0.416277i
$536$	−0.907725	−	3.97700i	−0.0392077	−	0.171780i
$537$		0			0
$538$	−20.4409			−0.881271
$539$	−7.17260	−	1.78123i	−0.308946	−	0.0767231i
$540$		0			0
$541$	−33.8972	−	16.3240i	−1.45735	−	0.701824i	−0.473499	−	0.880795i	$-0.657009\pi$
$541$	−33.8972	−	16.3240i	−1.45735	−	0.701824i	−0.983854	+	0.178970i	$0.942723\pi$
$542$	1.31628	+	5.76701i	0.0565392	+	0.247714i
$543$		0			0
$544$	−6.21126	−	27.2133i	−0.266306	−	1.16676i
$545$	0.0813640	−	0.356479i	0.00348525	−	0.0152699i
$546$		0			0
$547$	−8.76534	−	38.4034i	−0.374779	−	1.64201i	−0.713158	−	0.701003i	$-0.752736\pi$
$547$	−8.76534	−	38.4034i	−0.374779	−	1.64201i	0.338379	−	0.941010i	$-0.390121\pi$
$548$	1.28795	−	0.620243i	0.0550184	−	0.0264955i
$549$		0			0
$550$	24.8936	+	11.9881i	1.06147	+	0.511175i
$551$	−3.76553	+	4.72183i	−0.160417	+	0.201157i
$552$		0			0
$553$	−21.6249	+	2.22855i	−0.919583	+	0.0947675i
$554$	−4.14504	+	1.99615i	−0.176106	+	0.0848081i
$555$		0			0
$556$	−8.31098	+	10.4216i	−0.352464	+	0.441976i
$557$	2.56930			0.108865			0.0544323	−	0.998517i	$-0.482665\pi$
$557$	2.56930			0.108865			0.0544323	+	0.998517i	$0.482665\pi$
$558$		0			0
$559$	−22.1778	+	27.8101i	−0.938022	+	1.17624i
$560$	58.0818	−	5.98561i	2.45440	−	0.252938i
$561$		0			0
$562$	−14.6339	−	18.3504i	−0.617296	−	0.774065i
$563$	−10.2219	+	4.92262i	−0.430802	+	0.207464i	−0.636703	−	0.771109i	$-0.719702\pi$
$563$	−10.2219	+	4.92262i	−0.430802	+	0.207464i	0.205900	+	0.978573i	$0.433988\pi$
$564$		0			0
$565$	−39.0530	−	48.9709i	−1.64297	−	2.06022i
$566$	−6.32789	−	7.93493i	−0.265981	−	0.333530i
$567$		0			0
$568$	4.27979	−	5.36668i	0.179576	−	0.225181i
$569$	42.9685			1.80133			0.900666	−	0.434512i	$-0.143079\pi$
$569$	42.9685			1.80133			0.900666	+	0.434512i	$0.143079\pi$
$570$		0			0
$571$	5.03117	−	6.30888i	0.210548	−	0.264019i	−0.665332	−	0.746547i	$-0.731710\pi$
$571$	5.03117	−	6.30888i	0.210548	−	0.264019i	0.875880	+	0.482529i	$0.160282\pi$
$572$	1.29397	−	5.66926i	0.0541037	−	0.237044i
$573$		0			0
$574$	−2.35758	+	19.2752i	−0.0984035	+	0.804532i
$575$	−12.0168	−	5.78697i	−0.501134	−	0.241333i
$576$		0			0
$577$	−9.01622	−	4.34198i	−0.375350	−	0.180759i	0.236691	−	0.971585i	$-0.423937\pi$
$577$	−9.01622	−	4.34198i	−0.375350	−	0.180759i	−0.612041	+	0.790826i	$0.709651\pi$
$578$	2.17076	−	9.51073i	0.0902918	−	0.395594i
$579$		0			0
$580$	3.32283	+	14.5583i	0.137973	+	0.604500i
$581$	34.2856	−	21.0911i	1.42241	−	0.875006i
$582$		0			0
$583$	−0.292020	−	1.27942i	−0.0120942	−	0.0529883i
$584$	−5.10062	−	6.39598i	−0.211065	−	0.264667i
$585$		0			0
$586$	−1.87367	−	0.902312i	−0.0774006	−	0.0372742i
$587$	−13.7235			−0.566428			−0.283214	−	0.959057i	$-0.591401\pi$
$587$	−13.7235			−0.566428			−0.283214	+	0.959057i	$0.591401\pi$
$588$		0			0
$589$	4.14270			0.170697
$590$	9.39311	+	4.52349i	0.386708	+	0.186229i
$591$		0			0
$592$	−1.41707	−	1.77695i	−0.0582413	−	0.0730322i
$593$	−0.0918112	−	0.402251i	−0.00377023	−	0.0165185i	0.973008	−	0.230772i	$-0.0741252\pi$
$593$	−0.0918112	−	0.402251i	−0.00377023	−	0.0165185i	−0.976778	+	0.214254i	$0.931268\pi$
$594$		0			0
$595$	52.3816	+	18.8900i	2.14743	+	0.774413i
$596$	−0.771487	−	3.38011i	−0.0316014	−	0.138455i
$597$		0			0
$598$	−1.69430	+	7.42320i	−0.0692850	+	0.303557i
$599$	30.2099	+	14.5483i	1.23435	+	0.594429i	0.933272	−	0.359172i	$-0.116941\pi$
$599$	30.2099	+	14.5483i	1.23435	+	0.594429i	0.301074	+	0.953601i	$0.402655\pi$
$600$		0			0
$601$	36.7318	+	17.6891i	1.49832	+	0.721553i	0.990190	−	0.139726i	$-0.0446223\pi$
$601$	36.7318	+	17.6891i	1.49832	+	0.721553i	0.508131	+	0.861280i	$0.330337\pi$
$602$	19.1819	−	29.8932i	0.781798	−	1.21836i
$603$		0			0
$604$	−4.37385	+	19.1631i	−0.177969	+	0.779735i
$605$	−27.3584	+	34.3064i	−1.11228	+	1.39475i
$606$		0			0
$607$	−10.2488			−0.415986			−0.207993	−	0.978130i	$-0.566693\pi$
$607$	−10.2488			−0.415986			−0.207993	+	0.978130i	$0.566693\pi$
$608$	7.69607	−	9.65056i	0.312117	−	0.391382i
$609$		0			0
$610$	−56.2881	−	70.5831i	−2.27904	−	2.85782i
$611$	23.9302	+	30.0075i	0.968112	+	1.21397i
$612$		0			0
$613$	38.6038	−	18.5906i	1.55919	−	0.750867i	0.562099	−	0.827070i	$-0.309994\pi$
$613$	38.6038	−	18.5906i	1.55919	−	0.750867i	0.997092	+	0.0762034i	$0.0242798\pi$
$614$	−16.8232	−	21.0956i	−0.678928	−	0.851348i
$615$		0			0
$616$	0.502255	−	4.10636i	0.0202364	−	0.165450i
$617$	22.1784	−	27.8109i	0.892870	−	1.11962i	−0.0993410	−	0.995053i	$-0.531673\pi$
$617$	22.1784	−	27.8109i	0.892870	−	1.11962i	0.992211	−	0.124570i	$-0.0397551\pi$
$618$		0			0
$619$	43.8561			1.76272			0.881362	−	0.472442i	$-0.156627\pi$
$619$	43.8561			1.76272			0.881362	+	0.472442i	$0.156627\pi$
$620$	6.38636	−	8.00824i	0.256482	−	0.321619i
$621$		0			0
$622$	−0.860279	+	0.414289i	−0.0344941	+	0.0166115i
$623$	25.2009	−	15.5026i	1.00965	−	0.621098i
$624$		0			0
$625$	73.3680	−	92.0006i	2.93472	−	3.68002i
$626$	47.6543	+	22.9491i	1.90465	+	0.917230i
$627$		0			0
$628$	2.37849	−	1.14542i	0.0949122	−	0.0457073i
$629$	−0.482310	−	2.11314i	−0.0192309	−	0.0842563i
$630$		0			0
$631$	1.01075	−	4.42840i	0.0402375	−	0.176292i	−0.950816	−	0.309756i	$-0.899753\pi$
$631$	1.01075	−	4.42840i	0.0402375	−	0.176292i	0.991054	+	0.133464i	$0.0426099\pi$
$632$	−2.70787	−	11.8640i	−0.107713	−	0.471923i
$633$		0			0
$634$	11.1203	+	48.7210i	0.441642	+	1.93496i
$635$	4.48700	+	2.16083i	0.178061	+	0.0857498i
$636$		0			0
$637$	32.0388	+	7.95645i	1.26942	+	0.315246i
$638$	5.41276			0.214293
$639$		0			0
$640$	10.6900	+	46.8358i	0.422558	+	1.85135i
$641$	−23.7547	−	29.7874i	−0.938253	−	1.17653i	−0.984106	−	0.177584i	$-0.943172\pi$
$641$	−23.7547	−	29.7874i	−0.938253	−	1.17653i	0.0458528	−	0.998948i	$-0.485399\pi$
$642$		0			0
$643$	4.49401	−	19.6896i	0.177227	−	0.776480i	−0.805676	−	0.592356i	$-0.798198\pi$
$643$	4.49401	−	19.6896i	0.177227	−	0.776480i	0.982903	−	0.184124i	$-0.0589449\pi$
$644$	0.340298	−	2.78223i	0.0134096	−	0.109635i
$645$		0			0
$646$	15.9419	−	7.67723i	0.627227	−	0.302057i
$647$	−5.86678	+	25.7041i	−0.230647	+	1.01053i	0.718458	+	0.695571i	$0.244848\pi$
$647$	−5.86678	+	25.7041i	−0.230647	+	1.01053i	−0.949105	+	0.314960i	$0.898009\pi$
$648$		0			0
$649$	0.868652	−	1.08926i	0.0340976	−	0.0427570i
$650$	−111.195	−	53.5489i	−4.36144	−	2.10036i
$651$		0			0
$652$	9.17816	−	4.41997i	0.359445	−	0.173099i
$653$	1.23294	−	5.40187i	0.0482487	−	0.211391i	−0.945057	−	0.326905i	$-0.893994\pi$
$653$	1.23294	−	5.40187i	0.0482487	−	0.211391i	0.993306	+	0.115514i	$0.0368514\pi$
$654$		0			0
$655$	−73.4474			−2.86983
$656$	−20.5023			−0.800481
$657$		0			0
$658$	−26.8408	−	27.3561i	−1.04636	−	1.06645i
$659$	23.3548	+	29.2860i	0.909773	+	1.14082i	0.989576	+	0.144009i	$0.0459993\pi$
$659$	23.3548	+	29.2860i	0.909773	+	1.14082i	−0.0798035	+	0.996811i	$0.525429\pi$
$660$		0			0
$661$	−9.44590	+	4.54891i	−0.367403	+	0.176932i	−0.608471	−	0.793576i	$-0.708217\pi$
$661$	−9.44590	+	4.54891i	−0.367403	+	0.176932i	0.241068	+	0.970508i	$0.422502\pi$
$662$	−9.97753	+	4.80493i	−0.387788	+	0.186749i
$663$		0			0
$664$	14.0489	+	17.6167i	0.545202	+	0.683662i
$665$	7.91144	+	23.3184i	0.306792	+	0.904249i
$666$		0			0
$667$	−2.61288			−0.101171
$668$	−17.6767			−0.683933
$669$		0			0
$670$	4.84230	−	21.2155i	0.187075	−	0.819627i
$671$	−10.8696	+	5.23453i	−0.419617	+	0.202077i
$672$		0			0
$673$	21.4344	+	10.3222i	0.826234	+	0.397893i	0.798701	−	0.601728i	$-0.205521\pi$
$673$	21.4344	+	10.3222i	0.826234	+	0.397893i	0.0275325	+	0.999621i	$0.491235\pi$
$674$	14.8947	−	18.6774i	0.573724	−	0.719427i
$675$		0			0
$676$	−2.40147	+	10.5215i	−0.0923640	+	0.404673i
$677$	−15.6971	+	7.55932i	−0.603289	+	0.290528i	−0.710488	−	0.703709i	$-0.751526\pi$
$677$	−15.6971	+	7.55932i	−0.603289	+	0.290528i	0.107200	+	0.994238i	$0.465812\pi$
$678$		0			0
$679$	−15.0703	+	1.55307i	−0.578345	+	0.0596013i
$680$	−6.93598	+	30.3885i	−0.265983	+	1.16535i
$681$		0			0
$682$	−2.31491	−	2.90281i	−0.0886426	−	0.111154i
$683$	−6.07595	−	26.6205i	−0.232490	−	1.01860i	−0.947567	−	0.319559i	$-0.896465\pi$
$683$	−6.07595	−	26.6205i	−0.232490	−	1.01860i	0.715077	−	0.699046i	$-0.246392\pi$
$684$		0			0
$685$	−5.43315			−0.207590
$686$	−32.6376	−	4.62338i	−1.24611	−	0.176522i
$687$		0			0
$688$	33.7863	+	16.2706i	1.28809	+	0.620312i
$689$	1.30440	+	5.71496i	0.0496938	+	0.217723i
$690$		0			0
$691$	−0.113414	−	0.496899i	−0.00431447	−	0.0189029i	0.972725	−	0.231962i	$-0.0745145\pi$
$691$	−0.113414	−	0.496899i	−0.00431447	−	0.0189029i	−0.977039	+	0.213059i	$0.931657\pi$
$692$	5.53728	−	24.2604i	0.210496	−	0.922242i
$693$		0			0
$694$	5.90973	+	25.8922i	0.224330	+	0.982854i
$695$	45.6453	−	21.9816i	1.73142	−	0.833810i
$696$		0			0
$697$	−17.6159	−	8.48338i	−0.667251	−	0.321331i
$698$	−27.4253	+	34.3902i	−1.03806	+	1.30169i
$699$		0			0
$700$	42.7392	+	15.4127i	1.61539	+	0.582546i
$701$	−18.7213	+	9.01569i	−0.707093	+	0.340518i	−0.752629	−	0.658445i	$-0.771215\pi$
$701$	−18.7213	+	9.01569i	−0.707093	+	0.340518i	0.0455362	+	0.998963i	$0.485500\pi$
$702$		0			0
$703$	0.597606	−	0.749375i	0.0225392	−	0.0282632i
$704$	−0.564428			−0.0212727
$705$		0			0
$706$	−3.69745	+	4.63646i	−0.139155	+	0.174495i
$707$	−2.43746	−	7.18425i	−0.0916702	−	0.270191i
$708$		0			0
$709$	−16.4628	−	20.6437i	−0.618274	−	0.775291i	0.369826	−	0.929101i	$-0.379417\pi$
$709$	−16.4628	−	20.6437i	−0.618274	−	0.775291i	−0.988100	+	0.153810i	$0.950846\pi$
$710$	32.9914	−	15.8878i	1.23814	−	0.596259i
$711$		0			0
$712$	10.3263	+	12.9488i	0.386996	+	0.485278i
$713$	1.11747	+	1.40126i	0.0418495	+	0.0524776i
$714$		0			0
$715$	−13.7799	+	17.2795i	−0.515339	+	0.646215i
$716$	−5.94235			−0.222076
$717$		0			0
$718$	10.3950	−	13.0349i	0.387939	−	0.486460i
$719$	8.87998	−	38.9057i	0.331167	−	1.45094i	−0.485706	−	0.874122i	$-0.661438\pi$
$719$	8.87998	−	38.9057i	0.331167	−	1.45094i	0.816874	−	0.576817i	$-0.195705\pi$
$720$		0			0
$721$	11.8871	+	35.0363i	0.442698	+	1.30482i
$722$	−23.4187	−	11.2778i	−0.871553	−	0.419718i
$723$		0			0
$724$	1.93189	+	0.930350i	0.0717982	+	0.0345762i
$725$	9.42428	−	41.2905i	0.350009	−	1.53349i
$726$		0			0
$727$	−7.61269	−	33.3534i	−0.282339	−	1.23701i	−0.894786	−	0.446496i	$-0.852672\pi$
$727$	−7.61269	−	33.3534i	−0.282339	−	1.23701i	0.612447	−	0.790512i	$-0.290185\pi$
$728$	−2.24349	+	18.3424i	−0.0831492	+	0.679814i
$729$		0			0
$730$	−9.71097	−	42.5465i	−0.359419	−	1.57472i
$731$	22.2974	+	27.9600i	0.824698	+	1.03414i
$732$		0			0
$733$	6.93137	+	3.33797i	0.256016	+	0.123291i	0.557490	−	0.830183i	$-0.311764\pi$
$733$	6.93137	+	3.33797i	0.256016	+	0.123291i	−0.301474	+	0.953474i	$0.597479\pi$
$734$	54.9209			2.02717
$735$		0			0
$736$	5.34025			0.196844
$737$	−2.62004	−	1.26174i	−0.0965104	−	0.0464770i
$738$		0			0
$739$	−12.8130	−	16.0670i	−0.471334	−	0.591034i	0.488163	−	0.872752i	$-0.337667\pi$
$739$	−12.8130	−	16.0670i	−0.471334	−	0.591034i	−0.959497	+	0.281718i	$0.909096\pi$
$740$	−0.527348	−	2.31046i	−0.0193857	−	0.0849343i
$741$		0			0
$742$	−1.88062	−	5.54299i	−0.0690397	−	0.203490i
$743$	−0.406060	−	1.77907i	−0.0148969	−	0.0652676i	0.966933	−	0.255030i	$-0.0820854\pi$
$743$	−0.406060	−	1.77907i	−0.0148969	−	0.0652676i	−0.981830	+	0.189762i	$0.939228\pi$
$744$		0			0
$745$	−2.93219	+	12.8468i	−0.107427	+	0.470669i
$746$	22.5620	+	10.8653i	0.826053	+	0.397806i
$747$		0			0
$748$	−5.26743	−	2.53666i	−0.192596	−	0.0927494i
$749$	−6.25221	+	3.84610i	−0.228451	+	0.140533i
$750$		0			0
$751$	−5.31651	+	23.2932i	−0.194002	+	0.849980i	0.780420	+	0.625256i	$0.215005\pi$
$751$	−5.31651	+	23.2932i	−0.194002	+	0.849980i	−0.974422	+	0.224724i	$0.927852\pi$
$752$	25.2283	−	31.6353i	0.919981	−	1.15362i
$753$		0			0
$754$	−24.1779			−0.880506
$755$	46.5785	−	58.4076i	1.69516	−	2.12567i
$756$		0			0
$757$	−8.52170	−	10.6859i	−0.309727	−	0.388385i	0.602467	−	0.798143i	$-0.294184\pi$
$757$	−8.52170	−	10.6859i	−0.309727	−	0.388385i	−0.912194	+	0.409759i	$0.865613\pi$
$758$	−34.9846	−	43.8693i	−1.27070	−	1.59340i
$759$		0			0
$760$	−12.4187	+	5.98055i	−0.450475	+	0.216937i
$761$	−19.7430	−	24.7569i	−0.715682	−	0.897437i	0.282403	−	0.959296i	$-0.408869\pi$
$761$	−19.7430	−	24.7569i	−0.715682	−	0.897437i	−0.998085	+	0.0618589i	$0.980297\pi$
$762$		0			0
$763$	−0.205018	−	0.0739340i	−0.00742214	−	0.00267659i
$764$	−9.68419	+	12.1436i	−0.350362	+	0.439340i
$765$		0			0
$766$	1.56719			0.0566249
$767$	−3.88012	+	4.86552i	−0.140103	+	0.175684i
$768$		0			0
$769$	25.4821	−	12.2715i	0.918908	−	0.442523i	0.0862270	−	0.996276i	$-0.472519\pi$
$769$	25.4821	−	12.2715i	0.918908	−	0.442523i	0.832681	+	0.553753i	$0.186805\pi$
$770$	11.9185	−	18.5737i	0.429511	−	0.669351i
$771$		0			0
$772$	−10.9635	+	13.7478i	−0.394586	+	0.494795i
$773$	35.5234	+	17.1071i	1.27769	+	0.615301i	0.944794	−	0.327664i	$-0.106261\pi$
$773$	35.5234	+	17.1071i	1.27769	+	0.615301i	0.332892	+	0.942965i	$0.391976\pi$
$774$		0			0
$775$	−26.1742	+	12.6048i	−0.940204	+	0.452779i
$776$	−1.88711	−	8.26795i	−0.0677432	−	0.296802i
$777$		0			0
$778$	−11.5691	+	50.6876i	−0.414773	+	1.81724i
$779$	−1.92397	−	8.42944i	−0.0689332	−	0.302016i
$780$		0			0
$781$	−1.08888	−	4.77068i	−0.0389631	−	0.170708i
$782$	6.89705	+	3.32144i	0.246638	+	0.118775i
$783$		0			0
$784$	0.661721	−	34.7964i	0.0236329	−	1.24273i
$785$	−10.0336			−0.358113
$786$		0			0
$787$	−10.3457	−	45.3276i	−0.368785	−	1.61575i	−0.730121	−	0.683317i	$-0.760537\pi$
$787$	−10.3457	−	45.3276i	−0.368785	−	1.61575i	0.361336	−	0.932436i	$-0.382321\pi$
$788$	−8.22233	−	10.3105i	−0.292908	−	0.367296i
$789$		0			0
$790$	14.4453	−	63.2889i	0.513940	−	2.25172i
$791$	−31.7989	+	19.5614i	−1.13064	+	0.695523i
$792$		0			0
$793$	48.5527	−	23.3817i	1.72416	−	0.830310i
$794$	−4.42597	+	19.3914i	−0.157072	+	0.688176i
$795$		0			0
$796$	−17.4770	+	21.9154i	−0.619455	+	0.776772i
$797$	14.1608	+	6.81948i	0.501601	+	0.241558i	0.667535	−	0.744578i	$-0.267349\pi$
$797$	14.1608	+	6.81948i	0.501601	+	0.241558i	−0.165934	+	0.986137i	$0.553064\pi$
$798$		0			0
$799$	34.7665	−	16.7427i	1.22995	−	0.592313i
$800$	−19.2615	+	84.3902i	−0.680997	+	2.98364i
$801$		0			0
$802$	−56.7250			−2.00303
$803$	−5.83188			−0.205803
$804$		0			0
$805$	−5.75334	+	8.96602i	−0.202779	+	0.316011i
$806$	10.3403	+	12.9663i	0.364222	+	0.456720i
$807$		0			0
$808$	3.82613	−	1.84257i	0.134603	−	0.0648213i
$809$	−24.0544	+	11.5840i	−0.845709	+	0.407272i	−0.805983	−	0.591939i	$-0.798363\pi$
$809$	−24.0544	+	11.5840i	−0.845709	+	0.407272i	−0.0397260	+	0.999211i	$0.512649\pi$
$810$		0			0
$811$	23.4997	+	29.4676i	0.825184	+	1.03475i	0.998753	+	0.0499268i	$0.0158988\pi$
$811$	23.4997	+	29.4676i	0.825184	+	1.03475i	−0.173568	+	0.984822i	$0.555530\pi$
$812$	8.85364	−	0.912411i	0.310702	−	0.0320194i
$813$		0			0
$814$	−0.859029			−0.0301089
$815$	−38.7176			−1.35622
$816$		0			0
$817$	−3.51905	+	15.4180i	−0.123116	+	0.539407i
$818$	−52.0317	+	25.0571i	−1.81924	+	0.876102i
$819$		0			0
$820$	−19.2609	−	9.27556i	−0.672620	−	0.323917i
$821$	−15.1994	+	19.0595i	−0.530463	+	0.665180i	−0.972794	−	0.231672i	$-0.925580\pi$
$821$	−15.1994	+	19.0595i	−0.530463	+	0.665180i	0.442331	+	0.896852i	$0.354152\pi$
$822$		0			0
$823$	−1.45249	+	6.36376i	−0.0506305	+	0.221827i	−0.993914	−	0.110163i	$-0.964863\pi$
$823$	−1.45249	+	6.36376i	−0.0506305	+	0.221827i	0.943283	+	0.331990i	$0.107720\pi$
$824$	−18.6594	+	8.98588i	−0.650030	+	0.313038i
$825$		0			0
$826$	3.35597	−	5.22996i	0.116769	−	0.181974i
$827$	8.30420	−	36.3831i	0.288765	−	1.26516i	−0.597456	−	0.801901i	$-0.703822\pi$
$827$	8.30420	−	36.3831i	0.288765	−	1.26516i	0.886222	−	0.463262i	$-0.153321\pi$
$828$		0			0
$829$	9.20208	+	11.5390i	0.319602	+	0.400768i	0.915517	−	0.402280i	$-0.131782\pi$
$829$	9.20208	+	11.5390i	0.319602	+	0.400768i	−0.595915	+	0.803047i	$0.703211\pi$
$830$	26.7474	+	117.188i	0.928415	+	4.06765i
$831$		0			0
$832$	2.52120			0.0874070
$833$	14.9665	−	29.6238i	0.518558	−	1.02640i
$834$		0			0
$835$	60.5306	+	29.1500i	2.09475	+	1.00878i
$836$	−0.575294	−	2.52053i	−0.0198970	−	0.0871743i
$837$		0			0
$838$	−3.84423	−	16.8427i	−0.132797	−	0.581820i
$839$	−9.18022	+	40.2212i	−0.316936	+	1.38859i	0.525958	+	0.850510i	$0.323707\pi$
$839$	−9.18022	+	40.2212i	−0.316936	+	1.38859i	−0.842895	+	0.538079i	$0.819150\pi$
$840$		0			0
$841$	4.60686	+	20.1840i	0.158857	+	0.695999i
$842$	32.3614	−	15.5844i	1.11525	−	0.537074i
$843$		0			0
$844$	−15.3530	−	7.39362i	−0.528472	−	0.254499i
$845$	25.5739	−	32.0687i	0.879771	−	1.10320i
$846$		0			0
$847$	18.3171	+	18.6687i	0.629383	+	0.641466i
$848$	5.56791	−	2.68136i	0.191203	−	0.0920784i
$849$		0			0
$850$	−77.3643	+	97.0118i	−2.65357	+	3.32748i
$851$	0.414675			0.0142149
$852$		0			0
$853$	24.9444	−	31.2793i	0.854082	−	1.07098i	−0.142616	−	0.989778i	$-0.545551\pi$
$853$	24.9444	−	31.2793i	0.854082	−	1.07098i	0.996697	−	0.0812063i	$-0.0258773\pi$
$854$	−45.8326	+	28.1944i	−1.56836	+	0.964791i
$855$		0			0
$856$	−2.56191	−	3.21253i	−0.0875642	−	0.109802i
$857$	45.1751	−	21.7552i	1.54315	−	0.743143i	0.547545	−	0.836776i	$-0.315562\pi$
$857$	45.1751	−	21.7552i	1.54315	−	0.743143i	0.995607	+	0.0936335i	$0.0298482\pi$
$858$		0			0
$859$	−22.6519	−	28.4046i	−0.772874	−	0.969154i	0.227115	−	0.973868i	$-0.427071\pi$
$859$	−22.6519	−	28.4046i	−0.772874	−	0.969154i	−0.999989	+	0.00471448i	$0.998499\pi$
$860$	24.3795	+	30.5709i	0.831334	+	1.04246i
$861$		0			0
$862$	10.9999	−	13.7934i	0.374657	−	0.469806i
$863$	−31.1095			−1.05898			−0.529489	−	0.848317i	$-0.677616\pi$
$863$	−31.1095			−1.05898			−0.529489	+	0.848317i	$0.677616\pi$
$864$		0			0
$865$	−58.9682	+	73.9437i	−2.00498	+	2.51416i
$866$	7.91803	−	34.6911i	0.269065	−	1.17885i
$867$		0			0
$868$	−4.27581	−	4.35790i	−0.145131	−	0.147917i
$869$	−7.81595	−	3.76396i	−0.265138	−	0.127684i
$870$		0			0
$871$	11.7033	+	5.63599i	0.396550	+	0.190968i
$872$	0.0271469	−	0.118938i	0.000919310	−	0.00402776i
$873$		0			0
$874$	0.753278	+	3.30032i	0.0254800	+	0.111635i
$875$	−79.8106	−	81.3428i	−2.69809	−	2.74989i
$876$		0			0
$877$	−3.38184	−	14.8168i	−0.114197	−	0.500329i	−0.999384	−	0.0350938i	$-0.988827\pi$
$877$	−3.38184	−	14.8168i	−0.114197	−	0.500329i	0.885187	−	0.465235i	$-0.154030\pi$
$878$	−37.0513	−	46.4608i	−1.25042	−	1.56798i
$879$		0			0
$880$	20.9927	+	10.1096i	0.707664	+	0.340793i
$881$	31.5540			1.06308			0.531540	−	0.847033i	$-0.321613\pi$
$881$	31.5540			1.06308			0.531540	+	0.847033i	$0.321613\pi$
$882$		0			0
$883$	−39.3376			−1.32382			−0.661908	−	0.749585i	$-0.730253\pi$
$883$	−39.3376			−1.32382			−0.661908	+	0.749585i	$0.730253\pi$
$884$	23.5287	+	11.3308i	0.791355	+	0.381096i
$885$		0			0
$886$	24.4286	+	30.6325i	0.820696	+	1.02912i
$887$	−0.242856	−	1.06402i	−0.00815429	−	0.0357263i	0.970687	−	0.240347i	$-0.0772611\pi$
$887$	−0.242856	−	1.06402i	−0.00815429	−	0.0357263i	−0.978841	+	0.204620i	$0.934404\pi$
$888$		0			0
$889$	1.60312	−	2.49830i	0.0537668	−	0.0837903i
$890$	19.6601	+	86.1366i	0.659009	+	2.88731i
$891$		0			0
$892$	−0.0682606	+	0.299069i	−0.00228553	+	0.0100136i
$893$	15.3742	+	7.40381i	0.514477	+	0.247759i
$894$		0			0
$895$	20.3484	+	9.79929i	0.680173	+	0.327554i
$896$	28.4833	−	2.93534i	0.951559	−	0.0980628i
$897$		0			0
$898$	−3.00575	+	13.1690i	−0.100303	+	0.439457i
$899$	−3.54841	+	4.44957i	−0.118346	+	0.148401i
$900$		0			0
$901$	5.89352			0.196342
$902$	−4.83145	+	6.05845i	−0.160870	+	0.201724i
$903$		0			0
$904$	−13.0299	−	16.3390i	−0.433369	−	0.543427i
$905$	−5.08119	−	6.37161i	−0.168904	−	0.211799i
$906$		0			0
$907$	−4.83211	+	2.32702i	−0.160448	+	0.0772675i	−0.512384	−	0.858756i	$-0.671238\pi$
$907$	−4.83211	+	2.32702i	−0.160448	+	0.0772675i	0.351937	+	0.936024i	$0.385523\pi$
$908$	4.68902	+	5.87985i	0.155611	+	0.195130i
$909$		0			0
$910$	−53.2377	+	82.9657i	−1.76481	+	2.75029i
$911$	2.87417	−	3.60410i	0.0952256	−	0.119409i	−0.731936	−	0.681374i	$-0.761383\pi$
$911$	2.87417	−	3.60410i	0.0952256	−	0.119409i	0.827161	+	0.561965i	$0.189954\pi$
$912$		0			0
$913$	16.0630			0.531609
$914$	−30.1903	+	37.8575i	−0.998607	+	1.25221i
$915$		0			0
$916$	−11.2459	+	5.41575i	−0.371576	+	0.178941i
$917$	−5.31493	+	43.4540i	−0.175515	+	1.43498i
$918$		0			0
$919$	−10.8458	+	13.6002i	−0.357769	+	0.448629i	−0.927846	−	0.372963i	$-0.878342\pi$
$919$	−10.8458	+	13.6002i	−0.357769	+	0.448629i	0.570077	+	0.821591i	$0.306913\pi$
$920$	−5.37278	−	2.58740i	−0.177135	−	0.0853039i
$921$		0			0
$922$	−3.39433	+	1.63463i	−0.111786	+	0.0538335i
$923$	4.86382	+	21.3098i	0.160095	+	0.701420i
$924$		0			0
$925$	−1.49567	+	6.55297i	−0.0491774	+	0.215460i
$926$	10.7423	+	47.0652i	0.353014	+	1.54666i
$927$		0			0
$928$	3.77339	+	16.5323i	0.123868	+	0.542699i
$929$	2.83484	+	1.36518i	0.0930079	+	0.0447903i	0.479809	−	0.877373i	$-0.340706\pi$
$929$	2.83484	+	1.36518i	0.0930079	+	0.0447903i	−0.386801	+	0.922163i	$0.626420\pi$
$930$		0			0
$931$	14.3685	−	2.99328i	0.470908	−	0.0981007i
$932$	−14.7278			−0.482426
$933$		0			0
$934$	−13.8386	−	60.6307i	−0.452812	−	1.98390i
$935$	13.8542	+	17.3726i	0.453080	+	0.568145i
$936$		0			0
$937$	−4.31828	+	18.9196i	−0.141072	+	0.618076i	0.854115	+	0.520084i	$0.174099\pi$
$937$	−4.31828	+	18.9196i	−0.141072	+	0.618076i	−0.995187	+	0.0979926i	$0.968758\pi$
$938$	−12.2014	−	4.40011i	−0.398391	−	0.143669i
$939$		0			0
$940$	38.0130	−	18.3061i	1.23985	−	0.597079i
$941$	−7.00672	+	30.6985i	−0.228413	+	1.00074i	0.722522	+	0.691348i	$0.242983\pi$
$941$	−7.00672	+	30.6985i	−0.228413	+	1.00074i	−0.950934	+	0.309393i	$0.899874\pi$
$942$		0			0
$943$	2.33226	−	2.92457i	0.0759490	−	0.0952370i
$944$	5.91108	+	2.84663i	0.192389	+	0.0926499i
$945$		0			0
$946$	12.7699	−	6.14965i	0.415184	−	0.199942i
$947$	−4.38498	+	19.2119i	−0.142493	+	0.624301i	0.852359	+	0.522957i	$0.175171\pi$
$947$	−4.38498	+	19.2119i	−0.142493	+	0.624301i	−0.994851	+	0.101344i	$0.967686\pi$
$948$		0			0
$949$	26.0500			0.845619
$950$	−54.8709			−1.78025
$951$		0			0
$952$	17.4770	+	6.30259i	0.566432	+	0.204268i
$953$	19.4009	+	24.3279i	0.628456	+	0.788058i	0.989507	−	0.144488i	$-0.0461534\pi$
$953$	19.4009	+	24.3279i	0.628456	+	0.788058i	−0.361051	+	0.932546i	$0.617582\pi$
$954$		0			0
$955$	53.1872	−	25.6136i	1.72110	−	0.828836i
$956$	−26.4573	+	12.7412i	−0.855691	+	0.412079i
$957$		0			0
$958$	19.7521	+	24.7684i	0.638163	+	0.800231i
$959$	−0.393163	+	3.21444i	−0.0126959	+	0.103800i
$960$		0			0
$961$	−27.0962			−0.874070
$962$	3.83713			0.123714
$963$		0			0
$964$	4.18596	−	18.3399i	0.134821	−	0.590688i
$965$	60.2135	−	28.9973i	1.93834	−	0.933456i
$966$		0			0
$967$	−26.4059	−	12.7164i	−0.849157	−	0.408932i	−0.0418923	−	0.999122i	$-0.513339\pi$
$967$	−26.4059	−	12.7164i	−0.849157	−	0.408932i	−0.807265	+	0.590190i	$0.799053\pi$
$968$	−9.12807	+	11.4462i	−0.293387	+	0.367896i
$969$		0			0
$970$	10.0669	−	44.1058i	0.323228	−	1.41615i
$971$	30.2071	−	14.5470i	0.969391	−	0.466834i	0.118947	−	0.992901i	$-0.462048\pi$
$971$	30.2071	−	14.5470i	0.969391	−	0.466834i	0.850443	+	0.526067i	$0.176334\pi$
$972$		0			0
$973$	−9.70202	−	28.5960i	−0.311032	−	0.916746i
$974$	−0.895011	+	3.92130i	−0.0286780	+	0.125647i
$975$		0			0
$976$	−35.4221	−	44.4179i	−1.13383	−	1.42178i
$977$	6.25671	+	27.4124i	0.200170	+	0.877002i	0.970833	+	0.239758i	$0.0770683\pi$
$977$	6.25671	+	27.4124i	0.200170	+	0.877002i	−0.770663	+	0.637243i	$0.780075\pi$
$978$		0			0
$979$	11.8068			0.377347
$980$	16.3641	−	32.3901i	0.522731	−	1.03466i
$981$		0			0
$982$	2.84946	+	1.37223i	0.0909299	+	0.0437895i
$983$	−8.13210	−	35.6290i	−0.259374	−	1.13639i	−0.921923	−	0.387372i	$-0.873383\pi$
$983$	−8.13210	−	35.6290i	−0.259374	−	1.13639i	0.662550	−	0.749018i	$-0.269474\pi$
$984$		0			0
$985$	11.1532	+	48.8654i	0.355371	+	1.55698i
$986$	−5.40908	+	23.6987i	−0.172260	+	0.754721i
$987$		0			0
$988$	2.56974	+	11.2588i	0.0817543	+	0.358189i
$989$	−6.16434	+	2.96859i	−0.196015	+	0.0943957i
$990$		0			0
$991$	21.7661	+	10.4820i	0.691422	+	0.332971i	0.746383	−	0.665517i	$-0.231789\pi$
$991$	21.7661	+	10.4820i	0.691422	+	0.332971i	−0.0549604	+	0.998489i	$0.517503\pi$
$992$	7.25231	−	9.09411i	0.230261	−	0.288738i
$993$		0			0
$994$	−7.01240	−	20.6686i	−0.222420	−	0.655567i
$995$	95.9864	−	46.2246i	3.04297	−	1.46542i
$996$		0			0
$997$	13.2055	−	16.5592i	0.418222	−	0.524434i	−0.527437	−	0.849594i	$-0.676847\pi$
$997$	13.2055	−	16.5592i	0.418222	−	0.524434i	0.945659	+	0.325160i	$0.105418\pi$
$998$	−45.2411			−1.43208
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.127.5		36
3.2	odd	2		147.2.i.b.127.2	yes	36
49.22	even	7	inner	441.2.u.d.316.5		36
147.62	even	14		7203.2.a.g.1.13		18
147.71	odd	14		147.2.i.b.22.2	✓	36
147.134	odd	14		7203.2.a.h.1.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.22.2	✓	36	147.71	odd	14
147.2.i.b.127.2	yes	36	3.2	odd	2
441.2.u.d.127.5		36	1.1	even	1	trivial
441.2.u.d.316.5		36	49.22	even	7	inner
7203.2.a.g.1.13		18	147.62	even	14
7203.2.a.h.1.13		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)

\(f(q)\)	\(=\)	\(q+(1.60360 + 0.772253i) q^{2} +(0.728177 + 0.913105i) q^{4} +(-0.987738 - 4.32756i) q^{5} +(-2.63181 + 0.271221i) q^{7} +(-0.329556 - 1.44388i) q^{8} +O(q^{10})\)	\(q+(1.60360 + 0.772253i) q^{2} +(0.728177 + 0.913105i) q^{4} +(-0.987738 - 4.32756i) q^{5} +(-2.63181 + 0.271221i) q^{7} +(-0.329556 - 1.44388i) q^{8} +(1.75804 - 7.70246i) q^{10} +(-0.951225 - 0.458086i) q^{11} +(4.24896 + 2.04619i) q^{13} +(-4.42982 - 1.59749i) q^{14} +(1.10633 - 4.84715i) q^{16} +(2.95622 - 3.70698i) q^{17} +2.09671 q^{19} +(3.23227 - 4.05314i) q^{20} +(-1.17163 - 1.46917i) q^{22} +(0.565574 + 0.709207i) q^{23} +(-13.2473 + 6.37957i) q^{25} +(5.23345 + 6.56254i) q^{26} +(-2.16408 - 2.20562i) q^{28} +(-1.79593 + 2.25202i) q^{29} +1.97581 q^{31} +(3.67055 - 4.60272i) q^{32} +(7.60332 - 3.66156i) q^{34} +(3.77327 + 11.1214i) q^{35} +(0.285021 - 0.357405i) q^{37} +(3.36228 + 1.61919i) q^{38} +(-5.92297 + 2.85235i) q^{40} +(-0.917612 - 4.02032i) q^{41} +(-1.67837 + 7.35342i) q^{43} +(-0.274380 - 1.20214i) q^{44} +(0.359267 + 1.57405i) q^{46} +(7.33253 + 3.53116i) q^{47} +(6.85288 - 1.42761i) q^{49} -26.1700 q^{50} +(1.22561 + 5.36974i) q^{52} +(0.774992 + 0.971809i) q^{53} +(-1.04283 + 4.56895i) q^{55} +(1.25894 + 3.71064i) q^{56} +(-4.61908 + 2.22443i) q^{58} +(-0.293639 + 1.28652i) q^{59} +(7.12459 - 8.93395i) q^{61} +(3.16841 + 1.52583i) q^{62} +(0.481665 - 0.231958i) q^{64} +(4.65816 - 20.4087i) q^{65} +2.75438 q^{67} +5.53752 q^{68} +(-2.53775 + 20.7482i) q^{70} +(2.88977 + 3.62366i) q^{71} +(4.97674 - 2.39667i) q^{73} +(0.733067 - 0.353027i) q^{74} +(1.52677 + 1.91452i) q^{76} +(2.62769 + 0.947604i) q^{77} +8.21672 q^{79} -22.0691 q^{80} +(1.63322 - 7.15562i) q^{82} +(-13.7077 + 6.60126i) q^{83} +(-18.9622 - 9.13169i) q^{85} +(-8.37014 + 10.4958i) q^{86} +(-0.347939 + 1.52442i) q^{88} +(-10.0755 + 4.85213i) q^{89} +(-11.7374 - 4.23278i) q^{91} +(-0.235743 + 1.03286i) q^{92} +(9.03149 + 11.3251i) q^{94} +(-2.07100 - 9.07363i) q^{95} +5.72620 q^{97} +(12.0917 + 3.00284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 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

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