LMFDB - Embedded newform 441.2.u.d.64.2

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			64.2
Character	$\chi$	$=$	441.64
Dual form			441.2.u.d.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.368659 + 1.61520i) q^{2} +(-0.671021 - 0.323147i) q^{4} +(-0.768029 + 0.963077i) q^{5} +(-1.85883 + 1.88275i) q^{7} +(-1.29659 + 1.62588i) q^{8} +O(q^{10})$	\(q+(-0.368659 + 1.61520i) q^{2} +(-0.671021 - 0.323147i) q^{4} +(-0.768029 + 0.963077i) q^{5} +(-1.85883 + 1.88275i) q^{7} +(-1.29659 + 1.62588i) q^{8} +(-1.27242 - 1.59557i) q^{10} +(0.480814 - 2.10659i) q^{11} +(-0.494793 + 2.16783i) q^{13} +(-2.35573 - 3.69648i) q^{14} +(-3.07684 - 3.85823i) q^{16} +(1.21217 - 0.583750i) q^{17} -1.74215 q^{19} +(0.826579 - 0.398059i) q^{20} +(3.22530 + 1.55322i) q^{22} +(-3.01499 - 1.45194i) q^{23} +(0.774955 + 3.39530i) q^{25} +(-3.31907 - 1.59838i) q^{26} +(1.85572 - 0.662686i) q^{28} +(-6.38940 + 3.07697i) q^{29} -6.80992 q^{31} +(3.61885 - 1.74275i) q^{32} +(0.495996 + 2.17310i) q^{34} +(-0.385592 - 3.23620i) q^{35} +(5.84053 - 2.81265i) q^{37} +(0.642259 - 2.81392i) q^{38} +(-0.570024 - 2.49744i) q^{40} +(-0.915699 + 1.14825i) q^{41} +(5.27379 + 6.61313i) q^{43} +(-1.00337 + 1.25819i) q^{44} +(3.45668 - 4.33454i) q^{46} +(0.595078 - 2.60721i) q^{47} +(-0.0894674 - 6.99943i) q^{49} -5.76978 q^{50} +(1.03254 - 1.29477i) q^{52} +(12.0649 + 5.81015i) q^{53} +(1.65953 + 2.08098i) q^{55} +(-0.650960 - 5.46339i) q^{56} +(-2.61442 - 11.4545i) q^{58} +(3.23073 + 4.05121i) q^{59} +(-14.0088 + 6.74626i) q^{61} +(2.51054 - 10.9994i) q^{62} +(-0.715458 - 3.13463i) q^{64} +(-1.70777 - 2.14148i) q^{65} +4.18684 q^{67} -1.00203 q^{68} +(5.36927 + 0.570247i) q^{70} +(13.7366 + 6.61522i) q^{71} +(-0.565319 - 2.47682i) q^{73} +(2.38983 + 10.4705i) q^{74} +(1.16902 + 0.562971i) q^{76} +(3.07241 + 4.82105i) q^{77} +0.184803 q^{79} +6.07887 q^{80} +(-1.51707 - 1.90235i) q^{82} +(-0.579573 - 2.53927i) q^{83} +(-0.368784 + 1.61575i) q^{85} +(-12.6257 + 6.08024i) q^{86} +(2.80163 + 3.51313i) q^{88} +(3.12670 + 13.6990i) q^{89} +(-3.16173 - 4.96121i) q^{91} +(1.55393 + 1.94857i) q^{92} +(3.99178 + 1.92234i) q^{94} +(1.33802 - 1.67783i) q^{95} +14.7372 q^{97} +(11.3385 + 2.43589i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−0.368659	+	1.61520i	−0.260681	+	1.14212i	0.659834	+	0.751411i	$0.270627\pi$
$2$	−0.368659	+	1.61520i	−0.260681	+	1.14212i	−0.920515	+	0.390707i	$0.872231\pi$
$3$		0			0
$3$		0			0
$4$	−0.671021	−	0.323147i	−0.335511	−	0.161573i
$5$	−0.768029	+	0.963077i	−0.343473	+	0.430701i	−0.923324	−	0.384021i	$-0.874539\pi$
$5$	−0.768029	+	0.963077i	−0.343473	+	0.430701i	0.579852	+	0.814722i	$0.303111\pi$
$6$		0			0
$7$	−1.85883	+	1.88275i	−0.702573	+	0.711611i
$7$	−1.85883	+	1.88275i	−0.702573	+	0.711611i
$8$	−1.29659	+	1.62588i	−0.458415	+	0.574834i
$9$		0			0
$10$	−1.27242	−	1.59557i	−0.402375	−	0.504562i
$11$	0.480814	−	2.10659i	0.144971	−	0.635159i	−0.849267	−	0.527964i	$-0.822956\pi$
$11$	0.480814	−	2.10659i	0.144971	−	0.635159i	0.994238	−	0.107196i	$-0.0341871\pi$
$12$		0			0
$13$	−0.494793	+	2.16783i	−0.137231	+	0.601248i	0.858806	+	0.512302i	$0.171207\pi$
$13$	−0.494793	+	2.16783i	−0.137231	+	0.601248i	−0.996036	+	0.0889460i	$0.971650\pi$
$14$	−2.35573	−	3.69648i	−0.629597	−	0.987926i
$15$		0			0
$16$	−3.07684	−	3.85823i	−0.769209	−	0.964557i
$17$	1.21217	−	0.583750i	0.293994	−	0.141580i	−0.281073	−	0.959686i	$-0.590690\pi$
$17$	1.21217	−	0.583750i	0.293994	−	0.141580i	0.575067	+	0.818106i	$0.304976\pi$
$18$		0			0
$19$	−1.74215			−0.399677			−0.199838	−	0.979829i	$-0.564042\pi$
$19$	−1.74215			−0.399677			−0.199838	+	0.979829i	$0.564042\pi$
$20$	0.826579	−	0.398059i	0.184829	−	0.0890088i
$21$		0			0
$22$	3.22530	+	1.55322i	0.687636	+	0.331148i
$23$	−3.01499	−	1.45194i	−0.628669	−	0.302751i	0.0922864	−	0.995733i	$-0.470582\pi$
$23$	−3.01499	−	1.45194i	−0.628669	−	0.302751i	−0.720955	+	0.692981i	$0.756297\pi$
$24$		0			0
$25$	0.774955	+	3.39530i	0.154991	+	0.679060i
$26$	−3.31907	−	1.59838i	−0.650922	−	0.313468i
$27$		0			0
$28$	1.85572	−	0.662686i	0.350698	−	0.125236i
$29$	−6.38940	+	3.07697i	−1.18648	+	0.571380i	−0.919793	−	0.392403i	$-0.871644\pi$
$29$	−6.38940	+	3.07697i	−1.18648	+	0.571380i	−0.266689	+	0.963783i	$0.585930\pi$
$30$		0			0
$31$	−6.80992			−1.22310			−0.611549	−	0.791206i	$-0.709453\pi$
$31$	−6.80992			−1.22310			−0.611549	+	0.791206i	$0.709453\pi$
$32$	3.61885	−	1.74275i	0.639728	−	0.308077i
$33$		0			0
$34$	0.495996	+	2.17310i	0.0850626	+	0.372684i
$35$	−0.385592	−	3.23620i	−0.0651770	−	0.547018i
$36$		0			0
$37$	5.84053	−	2.81265i	0.960178	−	0.462397i	0.112934	−	0.993602i	$-0.463975\pi$
$37$	5.84053	−	2.81265i	0.960178	−	0.462397i	0.847243	+	0.531205i	$0.178261\pi$
$38$	0.642259	−	2.81392i	0.104188	−	0.456478i
$39$		0			0
$40$	−0.570024	−	2.49744i	−0.0901287	−	0.394880i
$41$	−0.915699	+	1.14825i	−0.143008	+	0.179327i	−0.848177	−	0.529713i	$-0.822300\pi$
$41$	−0.915699	+	1.14825i	−0.143008	+	0.179327i	0.705169	+	0.709039i	$0.250871\pi$
$42$		0			0
$43$	5.27379	+	6.61313i	0.804246	+	1.00849i	0.999615	+	0.0277626i	$0.00883824\pi$
$43$	5.27379	+	6.61313i	0.804246	+	1.00849i	−0.195369	+	0.980730i	$0.562590\pi$
$44$	−1.00337	+	1.25819i	−0.151264	+	0.189679i
$45$		0			0
$46$	3.45668	−	4.33454i	0.509660	−	0.639093i
$47$	0.595078	−	2.60721i	0.0868010	−	0.380300i	−0.912804	−	0.408398i	$-0.866088\pi$
$47$	0.595078	−	2.60721i	0.0868010	−	0.380300i	0.999605	+	0.0280974i	$0.00894485\pi$
$48$		0			0
$49$	−0.0894674	−	6.99943i	−0.0127811	−	0.999918i
$50$	−5.76978			−0.815969
$51$		0			0
$52$	1.03254	−	1.29477i	0.143188	−	0.179552i
$53$	12.0649	+	5.81015i	1.65724	+	0.798086i	0.998973	+	0.0453023i	$0.0144251\pi$
$53$	12.0649	+	5.81015i	1.65724	+	0.798086i	0.658268	+	0.752783i	$0.271289\pi$
$54$		0			0
$55$	1.65953	+	2.08098i	0.223770	+	0.280599i
$56$	−0.650960	−	5.46339i	−0.0869882	−	0.730076i
$57$		0			0
$58$	−2.61442	−	11.4545i	−0.343290	−	1.50405i
$59$	3.23073	+	4.05121i	0.420606	+	0.527423i	0.946317	−	0.323240i	$-0.104772\pi$
$59$	3.23073	+	4.05121i	0.420606	+	0.527423i	−0.525711	+	0.850663i	$0.676201\pi$
$60$		0			0
$61$	−14.0088	+	6.74626i	−1.79364	+	0.863770i	−0.855220	+	0.518265i	$0.826578\pi$
$61$	−14.0088	+	6.74626i	−1.79364	+	0.863770i	−0.938417	+	0.345506i	$0.887707\pi$
$62$	2.51054	−	10.9994i	0.318839	−	1.39692i
$63$		0			0
$64$	−0.715458	−	3.13463i	−0.0894323	−	0.391828i
$65$	−1.70777	−	2.14148i	−0.211823	−	0.265618i
$66$		0			0
$67$	4.18684			0.511504			0.255752	−	0.966742i	$-0.417677\pi$
$67$	4.18684			0.511504			0.255752	+	0.966742i	$0.417677\pi$
$68$	−1.00203			−0.121514
$69$		0			0
$70$	5.36927	+	0.570247i	0.641750	+	0.0681575i
$71$	13.7366	+	6.61522i	1.63024	+	0.785082i	0.999962	+	0.00871138i	$0.00277295\pi$
$71$	13.7366	+	6.61522i	1.63024	+	0.785082i	0.630277	+	0.776370i	$0.282941\pi$
$72$		0			0
$73$	−0.565319	−	2.47682i	−0.0661656	−	0.289890i	0.931010	−	0.364993i	$-0.118929\pi$
$73$	−0.565319	−	2.47682i	−0.0661656	−	0.289890i	−0.997176	+	0.0751028i	$0.976072\pi$
$74$	2.38983	+	10.4705i	0.277812	+	1.21717i
$75$		0			0
$76$	1.16902	+	0.562971i	0.134096	+	0.0645772i
$77$	3.07241	+	4.82105i	0.350134	+	0.549409i
$78$		0			0
$79$	0.184803			0.0207919			0.0103960	−	0.999946i	$-0.496691\pi$
$79$	0.184803			0.0207919			0.0103960	+	0.999946i	$0.496691\pi$
$80$	6.07887			0.679639
$81$		0			0
$82$	−1.51707	−	1.90235i	−0.167533	−	0.210079i
$83$	−0.579573	−	2.53927i	−0.0636163	−	0.278721i	0.933108	−	0.359597i	$-0.117086\pi$
$83$	−0.579573	−	2.53927i	−0.0636163	−	0.278721i	−0.996724	+	0.0808751i	$0.974229\pi$
$84$		0			0
$85$	−0.368784	+	1.61575i	−0.0400003	+	0.175253i
$86$	−12.6257	+	6.08024i	−1.36147	+	0.655649i
$87$		0			0
$88$	2.80163	+	3.51313i	0.298654	+	0.374501i
$89$	3.12670	+	13.6990i	0.331430	+	1.45209i	0.816364	+	0.577538i	$0.195986\pi$
$89$	3.12670	+	13.6990i	0.331430	+	1.45209i	−0.484934	+	0.874551i	$0.661156\pi$
$90$		0			0
$91$	−3.16173	−	4.96121i	−0.331440	−	0.520076i
$92$	1.55393	+	1.94857i	0.162009	+	0.203152i
$93$		0			0
$94$	3.99178	+	1.92234i	0.411720	+	0.198274i
$95$	1.33802	−	1.67783i	0.137278	−	0.172141i
$96$		0			0
$97$	14.7372			1.49633			0.748167	−	0.663511i	$-0.230934\pi$
$97$	14.7372			1.49633			0.748167	+	0.663511i	$0.230934\pi$
$98$	11.3385	+	2.43589i	1.14536	+	0.246062i
$99$		0			0
$100$	0.577169	−	2.52874i	0.0577169	−	0.252874i
$101$	−8.30459	+	10.4136i	−0.826338	+	1.03620i	0.172353	+	0.985035i	$0.444863\pi$
$101$	−8.30459	+	10.4136i	−0.826338	+	1.03620i	−0.998690	+	0.0511597i	$0.983708\pi$
$102$		0			0
$103$	−11.0881	+	13.9040i	−1.09254	+	1.37000i	−0.169398	+	0.985548i	$0.554182\pi$
$103$	−11.0881	+	13.9040i	−1.09254	+	1.37000i	−0.923143	+	0.384456i	$0.874389\pi$
$104$	−2.88308	−	3.61526i	−0.282709	−	0.354506i
$105$		0			0
$106$	−13.8324	+	17.3453i	−1.34352	+	1.68472i
$107$	−2.56792	−	11.2508i	−0.248250	−	1.08765i	−0.933283	−	0.359142i	$-0.883069\pi$
$107$	−2.56792	−	11.2508i	−0.248250	−	1.08765i	0.685033	−	0.728512i	$-0.259788\pi$
$108$		0			0
$109$	−0.0251088	+	0.110009i	−0.00240498	+	0.0105369i	−0.976116	−	0.217249i	$-0.930292\pi$
$109$	−0.0251088	+	0.110009i	−0.00240498	+	0.0105369i	0.973711	+	0.227786i	$0.0731487\pi$
$110$	−3.97299	+	1.91329i	−0.378810	+	0.182425i
$111$		0			0
$112$	12.9834	+	1.37891i	1.22682	+	0.130295i
$113$	3.07054	+	13.4529i	0.288852	+	1.26554i	0.886103	+	0.463488i	$0.153402\pi$
$113$	3.07054	+	13.4529i	0.288852	+	1.26554i	−0.597251	+	0.802054i	$0.703741\pi$
$114$		0			0
$115$	3.71393	−	1.78854i	0.346326	−	0.166782i
$116$	5.28174			0.490397
$117$		0			0
$118$	−7.73455	+	3.72476i	−0.712023	+	0.342892i
$119$	−1.15417	+	3.36730i	−0.105803	+	0.308680i
$120$		0			0
$121$	5.70414	+	2.74697i	0.518558	+	0.249724i
$122$	−5.73210	−	25.1140i	−0.518960	−	2.27371i
$123$		0			0
$124$	4.56960	+	2.20060i	0.410362	+	0.197620i
$125$	−9.41429	−	4.53368i	−0.842040	−	0.405505i
$126$		0			0
$127$	0.978941	−	0.471433i	0.0868670	−	0.0418329i	−0.389946	−	0.920838i	$-0.627506\pi$
$127$	0.978941	−	0.471433i	0.0868670	−	0.0418329i	0.476813	+	0.879005i	$0.341792\pi$
$128$	13.3600			1.18087
$129$		0			0
$130$	4.08850	−	1.96892i	0.358585	−	0.172685i
$131$	−2.54080	−	3.18606i	−0.221991	−	0.278367i	0.658347	−	0.752714i	$-0.271256\pi$
$131$	−2.54080	−	3.18606i	−0.221991	−	0.278367i	−0.880338	+	0.474347i	$0.842684\pi$
$132$		0			0
$133$	3.23837	−	3.28003i	0.280802	−	0.284415i
$134$	−1.54352	+	6.76258i	−0.133339	+	0.584198i
$135$		0			0
$136$	−0.622585	+	2.72772i	−0.0533863	+	0.233900i
$137$	0.643294	+	0.806666i	0.0549603	+	0.0689181i	0.808552	−	0.588425i	$-0.200252\pi$
$137$	0.643294	+	0.806666i	0.0549603	+	0.0689181i	−0.753592	+	0.657343i	$0.771680\pi$
$138$		0			0
$139$	5.20868	−	6.53148i	0.441794	−	0.553993i	−0.510221	−	0.860043i	$-0.670436\pi$
$139$	5.20868	−	6.53148i	0.441794	−	0.553993i	0.952015	+	0.306051i	$0.0990078\pi$
$140$	−0.787028	+	2.29616i	−0.0665160	+	0.194061i
$141$		0			0
$142$	−15.7490	+	19.7486i	−1.32163	+	1.65727i
$143$	4.32881	+	2.08465i	0.361994	+	0.174327i
$144$		0			0
$145$	1.94388	−	8.51669i	0.161430	−	0.707273i
$146$	4.20897			0.348337
$147$		0			0
$148$	−4.82802			−0.396861
$149$	1.30197	−	5.70430i	0.106662	−	0.467315i	−0.893183	−	0.449693i	$-0.851533\pi$
$149$	1.30197	−	5.70430i	0.106662	−	0.467315i	0.999845	−	0.0176217i	$-0.00560947\pi$
$150$		0			0
$151$	−2.66861	−	1.28514i	−0.217169	−	0.104583i	0.322137	−	0.946693i	$-0.395599\pi$
$151$	−2.66861	−	1.28514i	−0.217169	−	0.104583i	−0.539306	+	0.842110i	$0.681313\pi$
$152$	2.25886	−	2.83252i	0.183218	−	0.229748i
$153$		0			0
$154$	−8.91962	+	3.18524i	−0.718763	+	0.256674i
$155$	5.23022	−	6.55848i	0.420101	−	0.526790i
$156$		0			0
$157$	8.91084	+	11.1738i	0.711162	+	0.891769i	0.997802	−	0.0662694i	$-0.0211097\pi$
$157$	8.91084	+	11.1738i	0.711162	+	0.891769i	−0.286640	+	0.958038i	$0.592538\pi$
$158$	−0.0681290	+	0.298493i	−0.00542006	+	0.0237468i
$159$		0			0
$160$	−1.10098	+	4.82371i	−0.0870401	+	0.381348i
$161$	8.33801	−	2.97754i	0.657127	−	0.234663i
$162$		0			0
$163$	4.21912	+	5.29061i	0.330467	+	0.414392i	0.919110	−	0.394000i	$-0.128909\pi$
$163$	4.21912	+	5.29061i	0.330467	+	0.414392i	−0.588643	+	0.808393i	$0.700338\pi$
$164$	0.985507	−	0.474595i	0.0769552	−	0.0370597i
$165$		0			0
$166$	4.31510			0.334916
$167$	−5.48134	+	2.63968i	−0.424159	+	0.204264i	−0.633772	−	0.773520i	$-0.718494\pi$
$167$	−5.48134	+	2.63968i	−0.424159	+	0.204264i	0.209612	+	0.977785i	$0.432780\pi$
$168$		0			0
$169$	7.25793	+	3.49524i	0.558302	+	0.268864i
$170$	−2.47380	−	1.19132i	−0.189732	−	0.0913701i
$171$		0			0
$172$	−1.40182	−	6.14176i	−0.106887	−	0.468305i
$173$	−18.0070	−	8.67170i	−1.36904	−	0.659297i	−0.402411	−	0.915459i	$-0.631828\pi$
$173$	−18.0070	−	8.67170i	−1.36904	−	0.659297i	−0.966634	+	0.256162i	$0.917542\pi$
$174$		0			0
$175$	−7.83300	−	4.85225i	−0.592119	−	0.366796i
$176$	−9.60708	+	4.62652i	−0.724161	+	0.348737i
$177$		0			0
$178$	−23.2793			−1.74485
$179$	2.36211	−	1.13753i	0.176552	−	0.0850231i	−0.343520	−	0.939145i	$-0.611619\pi$
$179$	2.36211	−	1.13753i	0.176552	−	0.0850231i	0.520072	+	0.854122i	$0.325905\pi$
$180$		0			0
$181$	−3.87100	−	16.9600i	−0.287729	−	1.26062i	−0.887633	−	0.460552i	$-0.847652\pi$
$181$	−3.87100	−	16.9600i	−0.287729	−	1.26062i	0.599903	−	0.800072i	$-0.295206\pi$
$182$	9.17894	−	3.27784i	0.680388	−	0.242970i
$183$		0			0
$184$	6.26990	−	3.01942i	0.462223	−	0.222595i
$185$	−1.77689	+	7.78508i	−0.130640	+	0.572371i
$186$		0			0
$187$	−0.646891	−	2.83421i	−0.0473054	−	0.207258i
$188$	−1.24182	+	1.55719i	−0.0905691	+	0.113570i
$189$		0			0
$190$	2.21675	+	2.77972i	0.160820	+	0.201662i
$191$	3.53873	−	4.43743i	0.256054	−	0.321081i	−0.637145	−	0.770744i	$-0.719885\pi$
$191$	3.53873	−	4.43743i	0.256054	−	0.321081i	0.893198	+	0.449663i	$0.148456\pi$
$192$		0			0
$193$	2.36856	−	2.97008i	0.170493	−	0.213791i	−0.689243	−	0.724530i	$-0.742057\pi$
$193$	2.36856	−	2.97008i	0.170493	−	0.213791i	0.859736	+	0.510739i	$0.170628\pi$
$194$	−5.43299	+	23.8035i	−0.390066	+	1.70899i
$195$		0			0
$196$	−2.20181	+	4.72568i	−0.157272	+	0.337548i
$197$	14.2164			1.01288			0.506438	−	0.862276i	$-0.330962\pi$
$197$	14.2164			1.01288			0.506438	+	0.862276i	$0.330962\pi$
$198$		0			0
$199$	15.5833	−	19.5409i	1.10467	−	1.38521i	0.189630	−	0.981856i	$-0.439271\pi$
$199$	15.5833	−	19.5409i	1.10467	−	1.38521i	0.915042	−	0.403359i	$-0.132157\pi$
$200$	−6.52513	−	3.14234i	−0.461397	−	0.222197i
$201$		0			0
$202$	−13.7585	−	17.2526i	−0.968047	−	1.21389i
$203$	6.08368	−	17.7492i	0.426991	−	1.24575i
$204$		0			0
$205$	−0.402571	−	1.76378i	−0.0281168	−	0.123188i
$206$	−18.3700	−	23.0353i	−1.27990	−	1.60495i
$207$		0			0
$208$	9.88638	−	4.76103i	0.685497	−	0.330118i
$209$	−0.837651	+	3.66999i	−0.0579416	+	0.253859i
$210$		0			0
$211$	−3.91013	−	17.1314i	−0.269184	−	1.17937i	−0.910964	−	0.412485i	$-0.864661\pi$
$211$	−3.91013	−	17.1314i	−0.269184	−	1.17937i	0.641780	−	0.766889i	$-0.278196\pi$
$212$	−6.21827	−	7.79747i	−0.427073	−	0.535532i
$213$		0			0
$214$	19.1189			1.30694
$215$	−10.4194			−0.710596
$216$		0			0
$217$	12.6585	−	12.8214i	0.859316	−	0.870370i
$218$	−0.168429	−	0.0811113i	−0.0114075	−	0.00549355i
$219$		0			0
$220$	−0.441115	−	1.93265i	−0.0297400	−	0.130299i
$221$	0.665698	+	2.91661i	0.0447797	+	0.196193i
$222$		0			0
$223$	−21.9508	−	10.5710i	−1.46994	−	0.707884i	−0.484010	−	0.875063i	$-0.660820\pi$
$223$	−21.9508	−	10.5710i	−1.46994	−	0.707884i	−0.985927	+	0.167178i	$0.946534\pi$
$224$	−3.44569	+	10.0529i	−0.230225	+	0.671684i
$225$		0			0
$226$	−22.8611			−1.52070
$227$	10.6371			0.706009			0.353005	−	0.935622i	$-0.385160\pi$
$227$	10.6371			0.706009			0.353005	+	0.935622i	$0.385160\pi$
$228$		0			0
$229$	1.93403	+	2.42520i	0.127805	+	0.160262i	0.841617	−	0.540075i	$-0.181604\pi$
$229$	1.93403	+	2.42520i	0.127805	+	0.160262i	−0.713812	+	0.700337i	$0.753033\pi$
$230$	1.51967	+	6.65810i	0.100204	+	0.439022i
$231$		0			0
$232$	3.28168	−	14.3780i	0.215453	−	0.943960i
$233$	−24.9959	+	12.0374i	−1.63754	+	0.788597i	−0.637707	+	0.770279i	$0.720117\pi$
$233$	−24.9959	+	12.0374i	−1.63754	+	0.788597i	−0.999832	+	0.0183178i	$0.994169\pi$
$234$		0			0
$235$	2.05390	+	2.57552i	0.133982	+	0.168008i
$236$	−0.858754	−	3.76245i	−0.0559002	−	0.244915i
$237$		0			0
$238$	−5.01337	−	3.10560i	−0.324969	−	0.201306i
$239$	−5.01850	−	6.29300i	−0.324620	−	0.407061i	0.592565	−	0.805523i	$-0.298115\pi$
$239$	−5.01850	−	6.29300i	−0.324620	−	0.407061i	−0.917185	+	0.398462i	$0.869544\pi$
$240$		0			0
$241$	4.32377	+	2.08222i	0.278518	+	0.134127i	0.567929	−	0.823078i	$-0.307745\pi$
$241$	4.32377	+	2.08222i	0.278518	+	0.134127i	−0.289410	+	0.957205i	$0.593459\pi$
$242$	−6.53978	+	8.20062i	−0.420393	+	0.527156i
$243$		0			0
$244$	11.5802			0.741346
$245$	6.80970	+	5.28960i	0.435056	+	0.337940i
$246$		0			0
$247$	0.862004	−	3.77669i	0.0548480	−	0.240305i
$248$	8.82970	−	11.0721i	0.560686	−	0.703079i
$249$		0			0
$250$	10.7935	−	13.5346i	0.682638	−	0.856001i
$251$	−6.56292	−	8.22964i	−0.414248	−	0.519450i	0.530306	−	0.847806i	$-0.322077\pi$
$251$	−6.56292	−	8.22964i	−0.414248	−	0.519450i	−0.944554	+	0.328356i	$0.893505\pi$
$252$		0			0
$253$	−4.50829	+	5.65322i	−0.283434	+	0.355415i
$254$	0.400563	+	1.75498i	0.0251336	+	0.110117i
$255$		0			0
$256$	−3.49438	+	15.3099i	−0.218399	+	0.956868i
$257$	−9.71434	+	4.67818i	−0.605964	+	0.291817i	−0.711596	−	0.702588i	$-0.752028\pi$
$257$	−9.71434	+	4.67818i	−0.605964	+	0.291817i	0.105633	+	0.994405i	$0.466313\pi$
$258$		0			0
$259$	−5.56107	+	16.2245i	−0.345548	+	1.00814i
$260$	0.453939	+	1.98884i	0.0281521	+	0.123343i
$261$		0			0
$262$	6.08281	−	2.92933i	0.375797	−	0.180974i
$263$	−25.5829			−1.57751			−0.788756	−	0.614707i	$-0.789274\pi$
$263$	−25.5829			−1.57751			−0.788756	+	0.614707i	$0.789274\pi$
$264$		0			0
$265$	−14.8618	+	7.15707i	−0.912954	+	0.439655i
$266$	4.10405	+	6.43983i	0.251635	+	0.394851i
$267$		0			0
$268$	−2.80946	−	1.35296i	−0.171615	−	0.0826454i
$269$	−2.72216	−	11.9266i	−0.165973	−	0.727176i	−0.987579	−	0.157121i	$-0.949779\pi$
$269$	−2.72216	−	11.9266i	−0.165973	−	0.727176i	0.821606	−	0.570056i	$-0.193078\pi$
$270$		0			0
$271$	7.74581	+	3.73018i	0.470524	+	0.226593i	0.654093	−	0.756414i	$-0.273051\pi$
$271$	7.74581	+	3.73018i	0.470524	+	0.226593i	−0.183568	+	0.983007i	$0.558765\pi$
$272$	−5.98189	−	2.88073i	−0.362705	−	0.174670i
$273$		0			0
$274$	−1.54008	+	0.741664i	−0.0930397	+	0.0448056i
$275$	7.52509			0.453780
$276$		0			0
$277$	−25.9295	+	12.4870i	−1.55795	+	0.750270i	−0.996987	−	0.0775686i	$-0.975284\pi$
$277$	−25.9295	+	12.4870i	−1.55795	+	0.750270i	−0.560966	+	0.827839i	$0.689570\pi$
$278$	8.62941	+	10.8209i	0.517558	+	0.648997i
$279$		0			0
$280$	5.76162	+	3.56912i	0.344323	+	0.213295i
$281$	5.09232	−	22.3109i	0.303782	−	1.33096i	−0.560586	−	0.828097i	$-0.689424\pi$
$281$	5.09232	−	22.3109i	0.303782	−	1.33096i	0.864368	−	0.502860i	$-0.167719\pi$
$282$		0			0
$283$	−5.17253	+	22.6623i	−0.307475	+	1.34714i	0.551096	+	0.834442i	$0.314210\pi$
$283$	−5.17253	+	22.6623i	−0.307475	+	1.34714i	−0.858571	+	0.512694i	$0.828647\pi$
$284$	−7.07989	−	8.87790i	−0.420114	−	0.526806i
$285$		0			0
$286$	−4.96297	+	6.22337i	−0.293467	+	0.367996i
$287$	−0.459731	−	3.85844i	−0.0271371	−	0.227756i
$288$		0			0
$289$	−9.47074	+	11.8759i	−0.557102	+	0.698584i
$290$	13.0395	+	6.27951i	0.765708	+	0.368745i
$291$		0			0
$292$	−0.421037	+	1.84468i	−0.0246393	+	0.107952i
$293$	31.5742			1.84459			0.922293	−	0.386492i	$-0.126313\pi$
$293$	31.5742			1.84459			0.922293	+	0.386492i	$0.126313\pi$
$294$		0			0
$295$	−6.38292			−0.371628
$296$	−2.99977	+	13.1428i	−0.174358	+	0.763913i
$297$		0			0
$298$	8.73360	+	4.20588i	0.505924	+	0.243640i
$299$	4.63936	−	5.81757i	0.268301	−	0.336439i
$300$		0			0
$301$	−22.2540	−	2.36350i	−1.28270	−	0.136230i
$302$	3.05956	−	3.83657i	0.176058	−	0.220770i
$303$		0			0
$304$	5.36031	+	6.72162i	0.307435	+	0.385511i
$305$	4.26195	−	18.6728i	0.244039	−	1.06920i
$306$		0			0
$307$	5.26665	−	23.0747i	0.300583	−	1.31694i	−0.568666	−	0.822568i	$-0.692540\pi$
$307$	5.26665	−	23.0747i	0.300583	−	1.31694i	0.869250	−	0.494373i	$-0.164602\pi$
$308$	−0.503748	−	4.22786i	−0.0287037	−	0.240905i
$309$		0			0
$310$	8.66509	+	10.8657i	0.492144	+	0.617129i
$311$	8.77293	−	4.22482i	0.497467	−	0.239568i	−0.168288	−	0.985738i	$-0.553824\pi$
$311$	8.77293	−	4.22482i	0.497467	−	0.239568i	0.665755	+	0.746170i	$0.268110\pi$
$312$		0			0
$313$	21.9406			1.24015			0.620077	−	0.784541i	$-0.287101\pi$
$313$	21.9406			1.24015			0.620077	+	0.784541i	$0.287101\pi$
$314$	−21.3330	+	10.2734i	−1.20389	+	0.579764i
$315$		0			0
$316$	−0.124006	−	0.0597183i	−0.00697591	−	0.00335942i
$317$	14.8916	+	7.17141i	0.836394	+	0.402786i	0.802509	−	0.596639i	$-0.203498\pi$
$317$	14.8916	+	7.17141i	0.836394	+	0.402786i	0.0338850	+	0.999426i	$0.489212\pi$
$318$		0			0
$319$	3.40979	+	14.9393i	0.190912	+	0.836439i
$320$	3.56838	+	1.71844i	0.199479	+	0.0960638i
$321$		0			0
$322$	1.73544	+	14.5652i	0.0967124	+	0.811689i
$323$	−2.11178	+	1.01698i	−0.117503	+	0.0565863i
$324$		0			0
$325$	−7.74387			−0.429553
$326$	−10.1008	+	4.86429i	−0.559432	+	0.269408i
$327$		0			0
$328$	−0.679624	−	2.97763i	−0.0375260	−	0.164412i
$329$	3.80256	+	5.96675i	0.209642	+	0.328957i
$330$		0			0
$331$	0.0138724	−	0.00668059i	0.000762496	−	0.000367199i	−0.433502	−	0.901152i	$-0.642722\pi$
$331$	0.0138724	−	0.00668059i	0.000762496	−	0.000367199i	0.434265	+	0.900785i	$0.357008\pi$
$332$	−0.431652	+	1.89119i	−0.0236900	+	0.103793i
$333$		0			0
$334$	−2.24286	−	9.82660i	−0.122724	−	0.537688i
$335$	−3.21561	+	4.03225i	−0.175688	+	0.220305i
$336$		0			0
$337$	9.11111	+	11.4250i	0.496314	+	0.622358i	0.965393	−	0.260798i	$-0.0839857\pi$
$337$	9.11111	+	11.4250i	0.496314	+	0.622358i	−0.469080	+	0.883156i	$0.655414\pi$
$338$	−8.32120	+	10.4345i	−0.452614	+	0.567560i
$339$		0			0
$340$	0.769587	−	0.965031i	0.0417367	−	0.0523362i
$341$	−3.27431	+	14.3457i	−0.177314	+	0.776862i
$342$		0			0
$343$	13.3445	+	12.8423i	0.720533	+	0.693421i
$344$	−17.5901			−0.948394
$345$		0			0
$346$	20.6449	−	25.8879i	1.10988	−	1.39174i
$347$	9.32876	+	4.49249i	0.500794	+	0.241170i	0.667188	−	0.744890i	$-0.267498\pi$
$347$	9.32876	+	4.49249i	0.500794	+	0.241170i	−0.166394	+	0.986059i	$0.553212\pi$
$348$		0			0
$349$	21.0055	+	26.3401i	1.12440	+	1.40995i	0.900237	+	0.435400i	$0.143393\pi$
$349$	21.0055	+	26.3401i	1.12440	+	1.40995i	0.224162	+	0.974552i	$0.428036\pi$
$350$	10.7251	−	10.8630i	0.573279	−	0.580653i
$351$		0			0
$352$	−1.93125	−	8.46135i	−0.102936	−	0.450992i
$353$	0.743030	+	0.931730i	0.0395475	+	0.0495910i	0.801212	−	0.598381i	$-0.204189\pi$
$353$	0.743030	+	0.931730i	0.0395475	+	0.0495910i	−0.761664	+	0.647972i	$0.775618\pi$
$354$		0			0
$355$	−16.9211	+	8.14877i	−0.898078	+	0.432492i
$356$	2.32870	−	10.2027i	0.123421	−	0.540741i
$357$		0			0
$358$	0.966528	+	4.23464i	0.0510826	+	0.223807i
$359$	−18.5996	−	23.3232i	−0.981650	−	1.23095i	−0.972957	−	0.230988i	$-0.925804\pi$
$359$	−18.5996	−	23.3232i	−0.981650	−	1.23095i	−0.00869315	−	0.999962i	$-0.502767\pi$
$360$		0			0
$361$	−15.9649			−0.840258
$362$	28.8208			1.51479
$363$		0			0
$364$	0.518393	+	4.35078i	0.0271712	+	0.228043i
$365$	2.81955	+	1.35783i	0.147582	+	0.0710719i
$366$		0			0
$367$	−0.409061	−	1.79221i	−0.0213528	−	0.0935528i	0.963129	−	0.269041i	$-0.0867067\pi$
$367$	−0.409061	−	1.79221i	−0.0213528	−	0.0935528i	−0.984482	+	0.175488i	$0.943850\pi$
$368$	3.67470	+	16.0999i	0.191557	+	0.839266i
$369$		0			0
$370$	−11.9194	−	5.74008i	−0.619660	−	0.298412i
$371$	−33.3657	+	11.9150i	−1.73226	+	0.618598i
$372$		0			0
$373$	2.10248			0.108862			0.0544310	−	0.998518i	$-0.482665\pi$
$373$	2.10248			0.108862			0.0544310	+	0.998518i	$0.482665\pi$
$374$	4.81630			0.249045
$375$		0			0
$376$	3.46742	+	4.34801i	0.178819	+	0.224231i
$377$	−3.50892	−	15.3736i	−0.180719	−	0.791781i
$378$		0			0
$379$	5.28048	−	23.1353i	0.271240	−	1.18838i	−0.637311	−	0.770607i	$-0.719953\pi$
$379$	5.28048	−	23.1353i	0.271240	−	1.18838i	0.908551	−	0.417774i	$-0.137190\pi$
$380$	−1.44003	+	0.693480i	−0.0738717	+	0.0355748i
$381$		0			0
$382$	5.86275	+	7.35165i	0.299964	+	0.376143i
$383$	0.743022	+	3.25539i	0.0379667	+	0.166343i	0.990357	−	0.138538i	$-0.0442404\pi$
$383$	0.743022	+	3.25539i	0.0379667	+	0.166343i	−0.952390	+	0.304881i	$0.901383\pi$
$384$		0			0
$385$	−7.00274	−	0.743731i	−0.356893	−	0.0379040i
$386$	3.92408	+	4.92065i	0.199731	+	0.250454i
$387$		0			0
$388$	−9.88896	−	4.76227i	−0.502036	−	0.241768i
$389$	−1.31930	+	1.65435i	−0.0668911	+	0.0838788i	−0.814151	−	0.580653i	$-0.802797\pi$
$389$	−1.31930	+	1.65435i	−0.0668911	+	0.0838788i	0.747260	+	0.664531i	$0.231369\pi$
$390$		0			0
$391$	−4.50225			−0.227689
$392$	11.4962	+	8.92995i	0.580646	+	0.451030i
$393$		0			0
$394$	−5.24100	+	22.9623i	−0.264038	+	1.15682i
$395$	−0.141934	+	0.177979i	−0.00714146	+	0.00895510i
$396$		0			0
$397$	2.33582	−	2.92902i	0.117231	−	0.147003i	−0.719753	−	0.694230i	$-0.755745\pi$
$397$	2.33582	−	2.92902i	0.117231	−	0.147003i	0.836984	+	0.547227i	$0.184316\pi$
$398$	25.8174	+	32.3741i	1.29411	+	1.62276i
$399$		0			0
$400$	10.7154	−	13.4367i	0.535772	−	0.671836i
$401$	1.97011	+	8.63163i	0.0983827	+	0.431043i	0.999999	−	0.00149414i	$-0.000475600\pi$
$401$	1.97011	+	8.63163i	0.0983827	+	0.431043i	−0.901616	+	0.432537i	$0.857618\pi$
$402$		0			0
$403$	3.36950	−	14.7627i	0.167847	−	0.735385i
$404$	8.93769	−	4.30416i	0.444667	−	0.214140i
$405$		0			0
$406$	26.4257	+	16.3698i	1.31149	+	0.812418i
$407$	−3.11688	−	13.6559i	−0.154498	−	0.676900i
$408$		0			0
$409$	25.3727	−	12.2188i	1.25460	−	0.604183i	0.315858	−	0.948806i	$-0.397708\pi$
$409$	25.3727	−	12.2188i	1.25460	−	0.604183i	0.938741	+	0.344623i	$0.111993\pi$
$410$	2.99726			0.148024
$411$		0			0
$412$	11.9334	−	5.74681i	0.587915	−	0.283125i
$413$	−13.6328	−	1.44788i	−0.670826	−	0.0712456i
$414$		0			0
$415$	2.89064	+	1.39206i	0.141896	+	0.0683336i
$416$	1.98739	+	8.70735i	0.0974400	+	0.426913i
$417$		0			0
$418$	−5.61896	−	2.70595i	−0.274832	−	0.132352i
$419$	−24.0777	−	11.5952i	−1.17627	−	0.566464i	−0.259450	−	0.965756i	$-0.583541\pi$
$419$	−24.0777	−	11.5952i	−1.17627	−	0.566464i	−0.916823	+	0.399293i	$0.869256\pi$
$420$		0			0
$421$	−21.2954	+	10.2553i	−1.03787	+	0.499813i	−0.873622	−	0.486605i	$-0.838235\pi$
$421$	−21.2954	+	10.2553i	−1.03787	+	0.499813i	−0.164251	+	0.986419i	$0.552521\pi$
$422$	29.1121			1.41716
$423$		0			0
$424$	−25.0899	+	12.0826i	−1.21847	+	0.586785i
$425$	2.92138	+	3.66330i	0.141708	+	0.177696i
$426$		0			0
$427$	13.3385	−	38.9151i	0.645493	−	1.88323i
$428$	−1.91253	+	8.37933i	−0.0924455	+	0.405030i
$429$		0			0
$430$	3.84119	−	16.8294i	0.185239	−	0.811584i
$431$	14.6689	+	18.3942i	0.706576	+	0.886018i	0.997496	−	0.0707294i	$-0.0225327\pi$
$431$	14.6689	+	18.3942i	0.706576	+	0.886018i	−0.290920	+	0.956747i	$0.593961\pi$
$432$		0			0
$433$	−5.50526	+	6.90337i	−0.264566	+	0.331755i	−0.896315	−	0.443418i	$-0.853766\pi$
$433$	−5.50526	+	6.90337i	−0.264566	+	0.331755i	0.631749	+	0.775173i	$0.282337\pi$
$434$	16.0424	+	25.1727i	0.770058	+	1.20833i
$435$		0			0
$436$	0.0523975	−	0.0657043i	0.00250938	−	0.00314667i
$437$	5.25257	+	2.52950i	0.251265	+	0.121003i
$438$		0			0
$439$	−0.925534	+	4.05503i	−0.0441733	+	0.193536i	−0.992200	−	0.124654i	$-0.960218\pi$
$439$	−0.925534	+	4.05503i	−0.0441733	+	0.193536i	0.948027	+	0.318190i	$0.103075\pi$
$440$	−5.53514			−0.263878
$441$		0			0
$442$	−4.95633			−0.235748
$443$	3.62098	−	15.8646i	0.172038	−	0.753749i	−0.813120	−	0.582097i	$-0.802232\pi$
$443$	3.62098	−	15.8646i	0.172038	−	0.753749i	0.985158	−	0.171652i	$-0.0549104\pi$
$444$		0			0
$445$	−15.5946	−	7.50995i	−0.739254	−	0.356006i
$446$	25.1666	−	31.5579i	1.19167	−	1.49431i
$447$		0			0
$448$	7.23163	+	4.47973i	0.341662	+	0.211647i
$449$	−10.8528	+	13.6090i	−0.512175	+	0.642247i	−0.968927	−	0.247347i	$-0.920441\pi$
$449$	−10.8528	+	13.6090i	−0.512175	+	0.642247i	0.456752	+	0.889594i	$0.349013\pi$
$450$		0			0
$451$	1.97861	+	2.48109i	0.0931689	+	0.116830i
$452$	2.28687	−	10.0194i	0.107565	−	0.471274i
$453$		0			0
$454$	−3.92146	+	17.1810i	−0.184043	+	0.806346i
$455$	7.20633	+	0.765353i	0.337838	+	0.0358803i
$456$		0			0
$457$	0.0303396	+	0.0380446i	0.00141922	+	0.00177965i	0.782541	−	0.622600i	$-0.213923\pi$
$457$	0.0303396	+	0.0380446i	0.00141922	+	0.00177965i	−0.781121	+	0.624379i	$0.785352\pi$
$458$	−4.63018	+	2.22978i	−0.216354	+	0.104191i
$459$		0			0
$460$	−3.07009			−0.143144
$461$	20.8110	−	10.0221i	0.969266	−	0.466774i	0.118866	−	0.992910i	$-0.462074\pi$
$461$	20.8110	−	10.0221i	0.969266	−	0.466774i	0.850400	+	0.526136i	$0.176360\pi$
$462$		0			0
$463$	11.6076	+	5.58993i	0.539451	+	0.259786i	0.683710	−	0.729754i	$-0.260365\pi$
$463$	11.6076	+	5.58993i	0.539451	+	0.259786i	−0.144259	+	0.989540i	$0.546080\pi$
$464$	31.5308	+	15.1844i	1.46378	+	0.704920i
$465$		0			0
$466$	−10.2278	−	44.8111i	−0.473796	−	2.07584i
$467$	−18.3374	−	8.83082i	−0.848553	−	0.408642i	−0.0415130	−	0.999138i	$-0.513218\pi$
$467$	−18.3374	−	8.83082i	−0.848553	−	0.408642i	−0.807040	+	0.590496i	$0.798932\pi$
$468$		0			0
$469$	−7.78264	+	7.88276i	−0.359369	+	0.363992i
$470$	−4.91716	+	2.36798i	−0.226812	+	0.109227i
$471$		0			0
$472$	−10.7757			−0.495992
$473$	16.4668	−	7.93001i	0.757146	−	0.364622i
$474$		0			0
$475$	−1.35009	−	5.91512i	−0.0619463	−	0.271404i
$476$	1.86261	−	1.88657i	0.0853724	−	0.0864706i
$477$		0			0
$478$	12.0146	−	5.78591i	0.549534	−	0.264641i
$479$	−7.83496	+	34.3272i	−0.357989	+	1.56845i	0.400208	+	0.916424i	$0.368938\pi$
$479$	−7.83496	+	34.3272i	−0.357989	+	1.56845i	−0.758197	+	0.652026i	$0.773919\pi$
$480$		0			0
$481$	3.20750	+	14.0530i	0.146249	+	0.640760i
$482$	−4.95719	+	6.21612i	−0.225794	+	0.283136i
$483$		0			0
$484$	−2.93992	−	3.68655i	−0.133633	−	0.167570i
$485$	−11.3186	+	14.1930i	−0.513950	+	0.644473i
$486$		0			0
$487$	13.4799	−	16.9033i	0.610835	−	0.765962i	−0.376188	−	0.926543i	$-0.622765\pi$
$487$	13.4799	−	16.9033i	0.610835	−	0.765962i	0.987023	+	0.160581i	$0.0513368\pi$
$488$	7.19507	−	31.5237i	0.325705	−	1.42701i
$489$		0			0
$490$	−11.0542	+	9.04897i	−0.499378	+	0.408791i
$491$	30.4474			1.37407			0.687035	−	0.726624i	$-0.258912\pi$
$491$	30.4474			1.37407			0.687035	+	0.726624i	$0.258912\pi$
$492$		0			0
$493$	−5.94886	+	7.45963i	−0.267923	+	0.335965i
$494$	5.78232	+	2.78462i	0.260159	+	0.125286i
$495$		0			0
$496$	20.9530	+	26.2742i	0.940818	+	1.17975i
$497$	−37.9889	+	13.5660i	−1.70404	+	0.608519i
$498$		0			0
$499$	−4.57823	−	20.0585i	−0.204950	−	0.897944i	−0.967870	−	0.251451i	$-0.919092\pi$
$499$	−4.57823	−	20.0585i	−0.204950	−	0.897944i	0.762920	−	0.646493i	$-0.223765\pi$
$500$	4.85214	+	6.08439i	0.216994	+	0.272102i
$501$		0			0
$502$	15.7120	−	7.56649i	0.701260	−	0.337709i
$503$	−1.44720	+	6.34060i	−0.0645274	+	0.282713i	−0.996889	−	0.0788129i	$-0.974887\pi$
$503$	−1.44720	+	6.34060i	−0.0645274	+	0.282713i	0.932362	+	0.361526i	$0.117744\pi$
$504$		0			0
$505$	−3.65097	−	15.9959i	−0.162466	−	0.711810i
$506$	−7.46905	−	9.36590i	−0.332040	−	0.416365i
$507$		0			0
$508$	−0.809232			−0.0359039
$509$	27.1535			1.20356			0.601779	−	0.798663i	$-0.294459\pi$
$509$	27.1535			1.20356			0.601779	+	0.798663i	$0.294459\pi$
$510$		0			0
$511$	5.71407	+	3.53965i	0.252775	+	0.156585i
$512$	0.633702	+	0.305175i	0.0280059	+	0.0134869i
$513$		0			0
$514$	−3.97492	−	17.4152i	−0.175326	−	0.768153i
$515$	−4.87468	−	21.3574i	−0.214804	−	0.941118i
$516$		0			0
$517$	−5.20618	−	2.50716i	−0.228968	−	0.110265i
$518$	−24.1557	−	14.9635i	−1.06134	−	0.657460i
$519$		0			0
$520$	5.69606			0.249789
$521$	−25.5265			−1.11834			−0.559169	−	0.829054i	$-0.688880\pi$
$521$	−25.5265			−1.11834			−0.559169	+	0.829054i	$0.688880\pi$
$522$		0			0
$523$	13.1251	+	16.4584i	0.573922	+	0.719675i	0.981063	−	0.193690i	$-0.0620456\pi$
$523$	13.1251	+	16.4584i	0.573922	+	0.719675i	−0.407141	+	0.913365i	$0.633474\pi$
$524$	0.675365	+	2.95897i	0.0295034	+	0.129263i
$525$		0			0
$526$	9.43137	−	41.3215i	0.411227	−	1.80170i
$527$	−8.25478	+	3.97529i	−0.359584	+	0.173167i
$528$		0			0
$529$	−7.35824	−	9.22694i	−0.319923	−	0.401171i
$530$	−6.08116	−	26.6433i	−0.264149	−	1.15731i
$531$		0			0
$532$	−3.23295	+	1.15450i	−0.140166	+	0.0500539i
$533$	−2.03613	−	2.55323i	−0.0881946	−	0.110592i
$534$		0			0
$535$	12.8076	+	6.16782i	0.553721	+	0.266658i
$536$	−5.42863	+	6.80729i	−0.234481	+	0.294030i
$537$		0			0
$538$	20.2674			0.873788
$539$	−14.7879	−	3.17695i	−0.636960	−	0.136841i
$540$		0			0
$541$	−1.70479	+	7.46918i	−0.0732947	+	0.321125i	−0.998263	−	0.0589199i	$-0.981234\pi$
$541$	−1.70479	+	7.46918i	−0.0732947	+	0.321125i	0.924968	+	0.380045i	$0.124091\pi$
$542$	−8.88055	+	11.1359i	−0.381452	+	0.478326i
$543$		0			0
$544$	3.36933	−	4.22501i	0.144459	−	0.181146i
$545$	−0.0866626	−	0.108671i	−0.00371222	−	0.00465497i
$546$		0			0
$547$	12.2226	−	15.3267i	0.522603	−	0.655323i	−0.448557	−	0.893754i	$-0.648062\pi$
$547$	12.2226	−	15.3267i	0.522603	−	0.655323i	0.971159	+	0.238431i	$0.0766332\pi$
$548$	−0.170993	−	0.749168i	−0.00730445	−	0.0320029i
$549$		0			0
$550$	−2.77419	+	12.1545i	−0.118292	+	0.518271i
$551$	11.1313	−	5.36056i	0.474210	−	0.228367i
$552$		0			0
$553$	−0.343517	+	0.347936i	−0.0146078	+	0.0147958i
$554$	−10.6098	−	46.4847i	−0.450769	−	1.97495i
$555$		0			0
$556$	−5.60576	+	2.69959i	−0.237737	+	0.114488i
$557$	3.82542			0.162088			0.0810441	−	0.996711i	$-0.474175\pi$
$557$	3.82542			0.162088			0.0810441	+	0.996711i	$0.474175\pi$
$558$		0			0
$559$	−16.9456	+	8.16055i	−0.716721	+	0.345155i
$560$	−11.2996	+	11.4450i	−0.477496	+	0.483638i
$561$		0			0
$562$	34.1592	+	16.4502i	1.44092	+	0.693910i
$563$	−0.521570	−	2.28515i	−0.0219816	−	0.0963075i	0.962747	−	0.270403i	$-0.0871570\pi$
$563$	−0.521570	−	2.28515i	−0.0219816	−	0.0963075i	−0.984729	+	0.174096i	$0.944300\pi$
$564$		0			0
$565$	−15.3144	−	7.37505i	−0.644283	−	0.310270i
$566$	−34.6973	−	16.7093i	−1.45844	−	0.702346i
$567$		0			0
$568$	−28.5664	+	13.7568i	−1.19862	+	0.577224i
$569$	17.9204			0.751264			0.375632	−	0.926769i	$-0.377426\pi$
$569$	17.9204			0.751264			0.375632	+	0.926769i	$0.377426\pi$
$570$		0			0
$571$	2.10957	−	1.01592i	0.0882829	−	0.0425148i	−0.389221	−	0.921144i	$-0.627256\pi$
$571$	2.10957	−	1.01592i	0.0882829	−	0.0425148i	0.477504	+	0.878629i	$0.341542\pi$
$572$	−2.23108	−	2.79768i	−0.0932861	−	0.116977i
$573$		0			0
$574$	6.40163	+	0.679889i	0.267199	+	0.0283780i
$575$	2.59330	−	11.3620i	0.108148	−	0.473827i
$576$		0			0
$577$	−4.96586	+	21.7568i	−0.206731	+	0.905749i	0.759994	+	0.649931i	$0.225202\pi$
$577$	−4.96586	+	21.7568i	−0.206731	+	0.905749i	−0.966725	+	0.255818i	$0.917655\pi$
$578$	−15.6905	−	19.6753i	−0.652639	−	0.818384i
$579$		0			0
$580$	−4.05653	+	5.08672i	−0.168438	+	0.211215i
$581$	5.85814	+	3.62890i	0.243036	+	0.150552i
$582$		0			0
$583$	18.0406	−	22.6221i	0.747164	−	0.936913i
$584$	4.76000	+	2.29229i	0.196970	+	0.0948558i
$585$		0			0
$586$	−11.6401	+	50.9986i	−0.480848	+	2.10673i
$587$	31.0873			1.28311			0.641556	−	0.767076i	$-0.278289\pi$
$587$	31.0873			1.28311			0.641556	+	0.767076i	$0.278289\pi$
$588$		0			0
$589$	11.8639			0.488844
$590$	2.35312	−	10.3097i	0.0968764	−	0.424443i
$591$		0			0
$592$	−28.8222	−	13.8800i	−1.18459	−	0.570466i
$593$	−16.7801	+	21.0415i	−0.689074	+	0.864072i	−0.996155	−	0.0876116i	$-0.972077\pi$
$593$	−16.7801	+	21.0415i	−0.689074	+	0.864072i	0.307080	+	0.951684i	$0.400648\pi$
$594$		0			0
$595$	−2.35654	−	3.69774i	−0.0966086	−	0.151593i
$596$	−2.71698	+	3.40698i	−0.111292	+	0.139555i
$597$		0			0
$598$	7.68620	+	9.63819i	0.314312	+	0.394135i
$599$	−2.27560	+	9.97006i	−0.0929786	+	0.407366i	−0.999903	−	0.0139276i	$-0.995567\pi$
$599$	−2.27560	+	9.97006i	−0.0929786	+	0.407366i	0.906924	+	0.421293i	$0.138424\pi$
$600$		0			0
$601$	−1.76604	+	7.73751i	−0.0720381	+	0.315619i	−0.998090	−	0.0617767i	$-0.980323\pi$
$601$	−1.76604	+	7.73751i	−0.0720381	+	0.315619i	0.926052	+	0.377396i	$0.123180\pi$
$602$	12.0216	−	35.0732i	0.489965	−	1.42948i
$603$		0			0
$604$	1.37541	+	1.72471i	0.0559646	+	0.0701774i
$605$	−7.02648	+	3.38378i	−0.285667	+	0.137570i
$606$		0			0
$607$	−36.8885			−1.49726			−0.748630	−	0.662989i	$-0.769288\pi$
$607$	−36.8885			−1.49726			−0.748630	+	0.662989i	$0.769288\pi$
$608$	−6.30458	+	3.03613i	−0.255685	+	0.123131i
$609$		0			0
$610$	28.5891	+	13.7678i	1.15754	+	0.557442i
$611$	5.35754	+	2.58005i	0.216743	+	0.104378i
$612$		0			0
$613$	1.78655	+	7.82737i	0.0721579	+	0.316144i	0.998107	−	0.0615043i	$-0.0195898\pi$
$613$	1.78655	+	7.82737i	0.0721579	+	0.316144i	−0.925949	+	0.377649i	$0.876733\pi$
$614$	35.3286	+	17.0134i	1.42575	+	0.686604i
$615$		0			0
$616$	−11.8221	−	1.25557i	−0.476326	−	0.0505885i
$617$	5.93272	−	2.85705i	0.238843	−	0.115020i	−0.310634	−	0.950530i	$-0.600541\pi$
$617$	5.93272	−	2.85705i	0.238843	−	0.115020i	0.549477	+	0.835509i	$0.314827\pi$
$618$		0			0
$619$	−43.7867			−1.75994			−0.879968	−	0.475032i	$-0.842436\pi$
$619$	−43.7867			−1.75994			−0.879968	+	0.475032i	$0.842436\pi$
$620$	−5.62894	+	2.71075i	−0.226064	+	0.108866i
$621$		0			0
$622$	3.58971	+	15.7276i	0.143934	+	0.630617i
$623$	−31.6037	−	19.5773i	−1.26618	−	0.784350i
$624$		0			0
$625$	−4.09191	+	1.97056i	−0.163676	+	0.0788223i
$626$	−8.08858	+	35.4384i	−0.323285	+	1.41640i
$627$		0			0
$628$	−2.36857	−	10.3774i	−0.0945163	−	0.414103i
$629$	5.43783	−	6.81882i	0.216820	−	0.271884i
$630$		0			0
$631$	−4.31465	−	5.41040i	−0.171763	−	0.215385i	0.688497	−	0.725239i	$-0.258271\pi$
$631$	−4.31465	−	5.41040i	−0.171763	−	0.215385i	−0.860261	+	0.509854i	$0.829699\pi$
$632$	−0.239614	+	0.300466i	−0.00953132	+	0.0119519i
$633$		0			0
$634$	−17.0732	+	21.4091i	−0.678062	+	0.850263i
$635$	−0.297828	+	1.30487i	−0.0118189	+	0.0517822i
$636$		0			0
$637$	15.2178	+	3.26932i	0.602953	+	0.129535i
$638$	−25.3870			−1.00508
$639$		0			0
$640$	−10.2609	+	12.8668i	−0.405598	+	0.508603i
$641$	−12.8369	−	6.18193i	−0.507028	−	0.244172i	0.162840	−	0.986653i	$-0.447935\pi$
$641$	−12.8369	−	6.18193i	−0.507028	−	0.244172i	−0.669867	+	0.742481i	$0.733649\pi$
$642$		0			0
$643$	−1.19555	−	1.49917i	−0.0471477	−	0.0591214i	0.757699	−	0.652605i	$-0.226324\pi$
$643$	−1.19555	−	1.49917i	−0.0471477	−	0.0591214i	−0.804846	+	0.593483i	$0.797752\pi$
$644$	−6.55716	−	0.696408i	−0.258388	−	0.0274423i
$645$		0			0
$646$	−0.864100	−	3.78587i	−0.0339976	−	0.148953i
$647$	12.2764	+	15.3941i	0.482634	+	0.605203i	0.962214	−	0.272295i	$-0.0877825\pi$
$647$	12.2764	+	15.3941i	0.482634	+	0.605203i	−0.479580	+	0.877498i	$0.659211\pi$
$648$		0			0
$649$	10.0876	−	4.85793i	0.395973	−	0.190691i
$650$	2.85484	−	12.5079i	0.111976	−	0.490600i
$651$		0			0
$652$	−1.12148	−	4.91351i	−0.0439204	−	0.192428i
$653$	11.4672	+	14.3794i	0.448745	+	0.562709i	0.953825	−	0.300364i	$-0.0971082\pi$
$653$	11.4672	+	14.3794i	0.448745	+	0.562709i	−0.505079	+	0.863073i	$0.668537\pi$
$654$		0			0
$655$	5.01983			0.196141
$656$	7.24767			0.282974
$657$		0			0
$658$	−11.0393	+	3.94219i	−0.430358	+	0.153683i
$659$	−20.5971	−	9.91905i	−0.802350	−	0.386391i	−0.0126773	−	0.999920i	$-0.504035\pi$
$659$	−20.5971	−	9.91905i	−0.802350	−	0.386391i	−0.789673	+	0.613528i	$0.789750\pi$
$660$		0			0
$661$	4.60016	+	20.1546i	0.178925	+	0.783923i	0.982128	+	0.188217i	$0.0602707\pi$
$661$	4.60016	+	20.1546i	0.178925	+	0.783923i	−0.803202	+	0.595706i	$0.796872\pi$
$662$	0.00567631	+	0.0248695i	0.000220616	+	0.000966582i
$663$		0			0
$664$	4.88001	+	2.35009i	0.189381	+	0.0912012i
$665$	0.671760	+	5.63796i	0.0260497	+	0.218631i
$666$		0			0
$667$	23.7316			0.918891
$668$	4.53110			0.175314
$669$		0			0
$670$	−5.32743	−	6.68038i	−0.205816	−	0.258086i
$671$	7.47596	+	32.7543i	0.288606	+	1.26447i
$672$		0			0
$673$	−6.94559	+	30.4306i	−0.267733	+	1.17301i	0.644911	+	0.764258i	$0.276895\pi$
$673$	−6.94559	+	30.4306i	−0.267733	+	1.17301i	−0.912643	+	0.408757i	$0.865963\pi$
$674$	−21.8125	+	10.5043i	−0.840186	+	0.404612i
$675$		0			0
$676$	−3.74075	−	4.69075i	−0.143875	−	0.180414i
$677$	−9.97577	−	43.7067i	−0.383400	−	1.67978i	−0.686740	−	0.726903i	$-0.740959\pi$
$677$	−9.97577	−	43.7067i	−0.383400	−	1.67978i	0.303341	−	0.952882i	$-0.401898\pi$
$678$		0			0
$679$	−27.3940	+	27.7464i	−1.05128	+	1.06481i
$680$	−2.14885	−	2.69457i	−0.0824045	−	0.103332i
$681$		0			0
$682$	−21.9640	−	10.5773i	−0.841046	−	0.405027i
$683$	9.16714	−	11.4952i	0.350771	−	0.439853i	−0.574876	−	0.818240i	$-0.694950\pi$
$683$	9.16714	−	11.4952i	0.350771	−	0.439853i	0.925647	+	0.378388i	$0.123521\pi$
$684$		0			0
$685$	−1.27095			−0.0485605
$686$	−25.6625	+	16.8195i	−0.979798	+	0.642172i
$687$		0			0
$688$	9.28837	−	40.6950i	0.354116	−	1.55148i
$689$	−18.5650	+	23.2798i	−0.707272	+	0.886891i
$690$		0			0
$691$	13.7987	−	17.3030i	0.524928	−	0.658239i	−0.446719	−	0.894674i	$-0.647408\pi$
$691$	13.7987	−	17.3030i	0.524928	−	0.658239i	0.971647	+	0.236435i	$0.0759792\pi$
$692$	9.28082	+	11.6378i	0.352804	+	0.442402i
$693$		0			0
$694$	−10.6954	+	13.4116i	−0.405992	+	0.509097i
$695$	2.28990	+	10.0327i	0.0868610	+	0.380563i
$696$		0			0
$697$	−0.439691	+	1.92641i	−0.0166545	+	0.0729681i
$698$	−50.2883	+	24.2176i	−1.90344	+	0.916649i
$699$		0			0
$700$	3.68812	+	5.78717i	0.139398	+	0.218735i
$701$	3.54474	+	15.5305i	0.133883	+	0.586579i	0.996708	+	0.0810765i	$0.0258358\pi$
$701$	3.54474	+	15.5305i	0.133883	+	0.586579i	−0.862825	+	0.505503i	$0.831307\pi$
$702$		0			0
$703$	−10.1751	+	4.90007i	−0.383761	+	0.184809i
$704$	−6.94736			−0.261839
$705$		0			0
$706$	−1.77885	+	0.856651i	−0.0669481	+	0.0322405i
$707$	−4.16936	−	34.9927i	−0.156805	−	1.31603i
$708$		0			0
$709$	−44.8463	−	21.5968i	−1.68424	−	0.811086i	−0.996359	−	0.0852593i	$-0.972828\pi$
$709$	−44.8463	−	21.5968i	−1.68424	−	0.811086i	−0.687878	−	0.725826i	$-0.741458\pi$
$710$	−6.92378	−	30.3351i	−0.259845	−	1.13845i
$711$		0			0
$712$	−26.3269	−	12.6784i	−0.986642	−	0.475142i
$713$	20.5319	+	9.88762i	0.768924	+	0.370294i
$714$		0			0
$715$	−5.33233	+	2.56791i	−0.199418	+	0.0960346i
$716$	−1.95261			−0.0729726
$717$		0			0
$718$	44.5285	−	21.4438i	1.66179	−	0.800275i
$719$	22.7950	+	28.5841i	0.850112	+	1.06601i	0.997042	+	0.0768594i	$0.0244893\pi$
$719$	22.7950	+	28.5841i	0.850112	+	1.06601i	−0.146930	+	0.989147i	$0.546939\pi$
$720$		0			0
$721$	−5.56682	−	46.7213i	−0.207319	−	1.73999i
$722$	5.88560	−	25.7865i	0.219039	−	0.959674i
$723$		0			0
$724$	−2.88303	+	12.6314i	−0.107147	+	0.469442i
$725$	−15.3987	−	19.3094i	−0.571895	−	0.717134i
$726$		0			0
$727$	19.5660	−	24.5350i	0.725663	−	0.909953i	−0.272980	−	0.962020i	$-0.588009\pi$
$727$	19.5660	−	24.5350i	0.725663	−	0.909953i	0.998644	+	0.0520668i	$0.0165809\pi$
$728$	12.1658	+	1.29208i	0.450894	+	0.0478875i
$729$		0			0
$730$	−3.23261	+	4.05357i	−0.119644	+	0.150029i
$731$	10.2531	+	4.93766i	0.379226	+	0.182626i
$732$		0			0
$733$	4.12170	−	18.0583i	0.152238	−	0.667000i	−0.839993	−	0.542597i	$-0.817441\pi$
$733$	4.12170	−	18.0583i	0.152238	−	0.667000i	0.992232	−	0.124403i	$-0.0397017\pi$
$734$	3.04558			0.112415
$735$		0			0
$736$	−13.4412			−0.495448
$737$	2.01309	−	8.81994i	0.0741532	−	0.324887i
$738$		0			0
$739$	15.0908	+	7.26733i	0.555123	+	0.267333i	0.690343	−	0.723483i	$-0.257460\pi$
$739$	15.0908	+	7.26733i	0.555123	+	0.267333i	−0.135220	+	0.990816i	$0.543174\pi$
$740$	3.70806	−	4.64976i	0.136311	−	0.170928i
$741$		0			0
$742$	−6.94461	−	58.2848i	−0.254945	−	2.13970i
$743$	−23.4988	+	29.4666i	−0.862088	+	1.08102i	0.133852	+	0.991001i	$0.457265\pi$
$743$	−23.4988	+	29.4666i	−0.862088	+	1.08102i	−0.995940	+	0.0900223i	$0.971306\pi$
$744$		0			0
$745$	4.49374	+	5.63497i	0.164638	+	0.206449i
$746$	−0.775096	+	3.39592i	−0.0283783	+	0.124333i
$747$		0			0
$748$	−0.481790	+	2.11086i	−0.0176160	+	0.0771806i
$749$	25.9557	+	16.0786i	0.948401	+	0.587500i
$750$		0			0
$751$	17.4618	+	21.8964i	0.637190	+	0.799012i	0.990648	−	0.136439i	$-0.0435657\pi$
$751$	17.4618	+	21.8964i	0.637190	+	0.799012i	−0.353458	+	0.935450i	$0.614994\pi$
$752$	−11.8902	+	5.72600i	−0.433590	+	0.208806i
$753$		0			0
$754$	26.1250			0.951417
$755$	3.28726	−	1.58306i	0.119636	−	0.0576135i
$756$		0			0
$757$	48.5506	+	23.3808i	1.76460	+	0.849788i	0.970166	+	0.242442i	$0.0779485\pi$
$757$	48.5506	+	23.3808i	1.76460	+	0.849788i	0.794438	+	0.607346i	$0.207766\pi$
$758$	35.4214	+	17.0581i	1.28656	+	0.619576i
$759$		0			0
$760$	0.993068	+	4.35092i	0.0360224	+	0.157824i
$761$	−11.7567	−	5.66174i	−0.426181	−	0.205238i	0.208483	−	0.978026i	$-0.433147\pi$
$761$	−11.7567	−	5.66174i	−0.426181	−	0.205238i	−0.634664	+	0.772788i	$0.718862\pi$
$762$		0			0
$763$	−0.160445	−	0.251761i	−0.00580851	−	0.00911437i
$764$	−3.80850	+	1.83408i	−0.137787	+	0.0663547i
$765$		0			0
$766$	−5.53203			−0.199880
$767$	−10.3809	+	4.99917i	−0.374832	+	0.180509i
$768$		0			0
$769$	3.80201	+	16.6577i	0.137104	+	0.600691i	0.996063	+	0.0886474i	$0.0282544\pi$
$769$	3.80201	+	16.6577i	0.137104	+	0.600691i	−0.858959	+	0.512044i	$0.828888\pi$
$770$	3.78289	−	11.0366i	0.136326	−	0.397733i
$771$		0			0
$772$	−2.54913	+	1.22760i	−0.0917451	+	0.0441821i
$773$	2.44479	−	10.7113i	0.0879330	−	0.385259i	−0.911742	−	0.410764i	$-0.865262\pi$
$773$	2.44479	−	10.7113i	0.0879330	−	0.385259i	0.999675	+	0.0255044i	$0.00811919\pi$
$774$		0			0
$775$	−5.27738	−	23.1217i	−0.189569	−	0.830557i
$776$	−19.1081	+	23.9608i	−0.685942	+	0.860144i
$777$		0			0
$778$	−2.18573	−	2.74082i	−0.0783622	−	0.0982631i
$779$	1.59529	−	2.00043i	0.0571571	−	0.0716727i
$780$		0			0
$781$	20.5403	−	25.7567i	0.734989	−	0.921648i
$782$	1.65979	−	7.27203i	0.0593541	−	0.260047i
$783$		0			0
$784$	−26.7301	+	21.8813i	−0.954647	+	0.781474i
$785$	−17.6050			−0.628351
$786$		0			0
$787$	−26.0272	+	32.6371i	−0.927769	+	1.16339i	0.0585080	+	0.998287i	$0.481366\pi$
$787$	−26.0272	+	32.6371i	−0.927769	+	1.16339i	−0.986277	+	0.165099i	$0.947206\pi$
$788$	−9.53950	−	4.59398i	−0.339831	−	0.163654i
$789$		0			0
$790$	−0.235147	−	0.294865i	−0.00836614	−	0.0104908i
$791$	−31.0360	−	19.2257i	−1.10351	−	0.683586i
$792$		0			0
$793$	−7.69331	−	33.7066i	−0.273197	−	1.19696i
$794$	3.86984	+	4.85262i	0.137335	+	0.172213i
$795$		0			0
$796$	−16.7713	+	8.07663i	−0.594443	+	0.286269i
$797$	8.93976	−	39.1676i	0.316662	−	1.38739i	−0.526704	−	0.850049i	$-0.676572\pi$
$797$	8.93976	−	39.1676i	0.316662	−	1.38739i	0.843366	−	0.537340i	$-0.180571\pi$
$798$		0			0
$799$	−0.800622	−	3.50775i	−0.0283240	−	0.124095i
$800$	8.72159	+	10.9365i	0.308355	+	0.386664i
$801$		0			0
$802$	−14.6681			−0.517949
$803$	−5.48946			−0.193719
$804$		0			0
$805$	−3.53623	+	10.3170i	−0.124636	+	0.363626i
$806$	22.6026	+	10.8848i	0.796142	+	0.383402i
$807$		0			0
$808$	−6.16360	−	27.0045i	−0.216835	−	0.950014i
$809$	−9.32334	−	40.8482i	−0.327791	−	1.43615i	−0.823331	−	0.567561i	$-0.807887\pi$
$809$	−9.32334	−	40.8482i	−0.327791	−	1.43615i	0.495540	−	0.868585i	$-0.334970\pi$
$810$		0			0
$811$	15.8105	+	7.61394i	0.555182	+	0.267362i	0.690368	−	0.723459i	$-0.257449\pi$
$811$	15.8105	+	7.61394i	0.555182	+	0.267362i	−0.135185	+	0.990820i	$0.543163\pi$
$812$	−9.81788	+	9.94418i	−0.344540	+	0.348972i
$813$		0			0
$814$	23.2061			0.813375
$815$	−8.33567			−0.291986
$816$		0			0
$817$	−9.18775	−	11.5211i	−0.321439	−	0.403071i
$818$	10.3820	+	45.4865i	0.362998	+	1.59040i
$819$		0			0
$820$	−0.299826	+	1.31362i	−0.0104704	+	0.0458737i
$821$	44.9579	−	21.6506i	1.56904	−	0.755610i	0.571170	−	0.820832i	$-0.306490\pi$
$821$	44.9579	−	21.6506i	1.56904	−	0.755610i	0.997871	+	0.0652212i	$0.0207753\pi$
$822$		0			0
$823$	29.3286	+	36.7769i	1.02233	+	1.28196i	0.958830	+	0.283980i	$0.0916549\pi$
$823$	29.3286	+	36.7769i	1.02233	+	1.28196i	0.0635000	+	0.997982i	$0.479774\pi$
$824$	−8.22948	−	36.0557i	−0.286688	−	1.25606i
$825$		0			0
$826$	7.36447	−	21.4859i	0.256243	−	0.747591i
$827$	21.1501	+	26.5214i	0.735460	+	0.922238i	0.999101	−	0.0423827i	$-0.0134949\pi$
$827$	21.1501	+	26.5214i	0.735460	+	0.922238i	−0.263641	+	0.964621i	$0.584923\pi$
$828$		0			0
$829$	3.96883	+	1.91129i	0.137843	+	0.0663818i	0.501534	−	0.865138i	$-0.332769\pi$
$829$	3.96883	+	1.91129i	0.137843	+	0.0663818i	−0.363691	+	0.931520i	$0.618483\pi$
$830$	−3.31412	+	4.15577i	−0.115035	+	0.144249i
$831$		0			0
$832$	7.14934			0.247859
$833$	−4.19437	−	8.43227i	−0.145326	−	0.292161i
$834$		0			0
$835$	1.66762	−	7.30630i	0.0577102	−	0.252845i
$836$	1.74803	−	2.19196i	0.0604568	−	0.0758104i
$837$		0			0
$838$	27.6051	−	34.6156i	0.953601	−	1.19578i
$839$	25.3351	+	31.7692i	0.874664	+	1.09679i	0.994576	+	0.104010i	$0.0331674\pi$
$839$	25.3351	+	31.7692i	0.874664	+	1.09679i	−0.119912	+	0.992785i	$0.538261\pi$
$840$		0			0
$841$	13.2755	−	16.6470i	0.457776	−	0.574033i
$842$	−8.71365	−	38.1770i	−0.300292	−	1.31567i
$843$		0			0
$844$	−2.91218	+	12.7591i	−0.100241	+	0.439185i
$845$	−8.94048	+	4.30551i	−0.307562	+	0.148114i
$846$		0			0
$847$	−15.7749	+	5.63329i	−0.542032	+	0.193562i
$848$	−14.7048	−	64.4260i	−0.504966	−	2.21240i
$849$		0			0
$850$	−6.99395	+	3.36811i	−0.239890	+	0.115525i
$851$	−21.6930			−0.743625
$852$		0			0
$853$	24.2760	−	11.6907i	0.831194	−	0.400282i	0.0306313	−	0.999531i	$-0.490248\pi$
$853$	24.2760	−	11.6907i	0.831194	−	0.400282i	0.800563	+	0.599249i	$0.204534\pi$
$854$	57.9383	+	35.8907i	1.98261	+	1.22815i
$855$		0			0
$856$	21.6219	+	10.4126i	0.739022	+	0.355894i
$857$	4.53501	+	19.8692i	0.154913	+	0.678718i	0.991415	+	0.130754i	$0.0417398\pi$
$857$	4.53501	+	19.8692i	0.154913	+	0.678718i	−0.836502	+	0.547964i	$0.815403\pi$
$858$		0			0
$859$	−20.4616	−	9.85379i	−0.698141	−	0.336207i	0.0509250	−	0.998702i	$-0.483783\pi$
$859$	−20.4616	−	9.85379i	−0.698141	−	0.336207i	−0.749066	+	0.662496i	$0.769497\pi$
$860$	6.99162	+	3.36699i	0.238412	+	0.114813i
$861$		0			0
$862$	−35.1181	+	16.9120i	−1.19613	+	0.576025i
$863$	−0.946075			−0.0322048			−0.0161024	−	0.999870i	$-0.505126\pi$
$863$	−0.946075			−0.0322048			−0.0161024	+	0.999870i	$0.505126\pi$
$864$		0			0
$865$	22.1814	−	10.6820i	0.754190	−	0.363199i
$866$	−9.12076	−	11.4371i	−0.309936	−	0.388648i
$867$		0			0
$868$	−12.6373	+	4.51284i	−0.428938	+	0.153176i
$869$	0.0888557	−	0.389302i	0.00301422	−	0.0132062i
$870$		0			0
$871$	−2.07162	+	9.07636i	−0.0701941	+	0.307541i
$872$	−0.146305	−	0.183460i	−0.00495450	−	0.00621275i
$873$		0			0
$874$	−6.02206	+	7.55142i	−0.203699	+	0.255431i
$875$	26.0354	−	9.29735i	0.880156	−	0.314308i
$876$		0			0
$877$	4.94505	−	6.20090i	0.166983	−	0.209390i	−0.691299	−	0.722569i	$-0.742961\pi$
$877$	4.94505	−	6.20090i	0.166983	−	0.209390i	0.858281	+	0.513180i	$0.171533\pi$
$878$	−6.20847	−	2.98984i	−0.209526	−	0.100902i
$879$		0			0
$880$	2.92281	−	12.8057i	0.0985279	−	0.431679i
$881$	47.7320			1.60813			0.804066	−	0.594540i	$-0.202666\pi$
$881$	47.7320			1.60813			0.804066	+	0.594540i	$0.202666\pi$
$882$		0			0
$883$	15.5733			0.524083			0.262042	−	0.965057i	$-0.415604\pi$
$883$	15.5733			0.524083			0.262042	+	0.965057i	$0.415604\pi$
$884$	0.495797	−	2.17223i	0.0166754	−	0.0730599i
$885$		0			0
$886$	24.2895	+	11.6972i	0.816023	+	0.392976i
$887$	−0.571386	+	0.716495i	−0.0191853	+	0.0240576i	−0.791332	−	0.611387i	$-0.790612\pi$
$887$	−0.571386	+	0.716495i	−0.0191853	+	0.0240576i	0.772146	+	0.635445i	$0.219183\pi$
$888$		0			0
$889$	−0.932100	+	2.71941i	−0.0312616	+	0.0912062i
$890$	17.8791	−	22.4197i	0.599310	−	0.751511i
$891$		0			0
$892$	11.3135	+	14.1867i	0.378804	+	0.475005i
$893$	−1.03672	+	4.54215i	−0.0346924	+	0.151997i
$894$		0			0
$895$	−0.718636	+	3.14855i	−0.0240213	+	0.105244i
$896$	−24.8341	+	25.1536i	−0.829650	+	0.840322i
$897$		0			0
$898$	−17.9802	−	22.5465i	−0.600008	−	0.752386i
$899$	43.5113	−	20.9540i	1.45118	−	0.698854i
$900$		0			0
$901$	18.0164			0.600213
$902$	−4.73689	+	2.28117i	−0.157721	+	0.0759545i
$903$		0			0
$904$	−25.8540	−	12.4506i	−0.859891	−	0.414101i
$905$	19.3068	+	9.29766i	0.641780	+	0.309065i
$906$		0			0
$907$	2.19165	+	9.60225i	0.0727726	+	0.318837i	0.998192	−	0.0601072i	$-0.0191442\pi$
$907$	2.19165	+	9.60225i	0.0727726	+	0.318837i	−0.925419	+	0.378945i	$0.876287\pi$
$908$	−7.13772	−	3.43734i	−0.236874	−	0.114072i
$909$		0			0
$910$	−3.89287	+	11.3575i	−0.129047	+	0.376497i
$911$	27.2653	−	13.1303i	0.903340	−	0.435026i	0.0762459	−	0.997089i	$-0.475707\pi$
$911$	27.2653	−	13.1303i	0.903340	−	0.435026i	0.827094	+	0.562063i	$0.189992\pi$
$912$		0			0
$913$	−5.62786			−0.186255
$914$	−0.0726345	+	0.0349790i	−0.00240254	+	0.00115700i
$915$		0			0
$916$	−0.514082	−	2.25234i	−0.0169857	−	0.0744194i
$917$	10.7215	+	1.13868i	0.354054	+	0.0376026i
$918$		0			0
$919$	−34.5316	+	16.6296i	−1.13909	+	0.548558i	−0.905740	−	0.423834i	$-0.860684\pi$
$919$	−34.5316	+	16.6296i	−1.13909	+	0.548558i	−0.233353	+	0.972392i	$0.574970\pi$
$920$	−1.90752	+	8.35740i	−0.0628891	+	0.275535i
$921$		0			0
$922$	8.51546	+	37.3087i	0.280442	+	1.22870i
$923$	−21.1375	+	26.5055i	−0.695748	+	0.872440i
$924$		0			0
$925$	14.0759	+	17.6507i	0.462814	+	0.580350i
$926$	−13.3081	+	16.6878i	−0.437331	+	0.548396i
$927$		0			0
$928$	−17.7599	+	22.2702i	−0.582997	+	0.731056i
$929$	−3.14337	+	13.7720i	−0.103130	+	0.451844i	0.896825	+	0.442386i	$0.145868\pi$
$929$	−3.14337	+	13.7720i	−0.103130	+	0.451844i	−0.999955	+	0.00945827i	$0.996989\pi$
$930$		0			0
$931$	0.155866	+	12.1941i	0.00510829	+	0.399644i
$932$	20.6627			0.676828
$933$		0			0
$934$	21.0238	−	26.3630i	0.687919	−	0.862623i
$935$	3.22640	+	1.55375i	0.105515	+	0.0508131i
$936$		0			0
$937$	8.71274	+	10.9254i	0.284633	+	0.356918i	0.903508	−	0.428571i	$-0.140983\pi$
$937$	8.71274	+	10.9254i	0.284633	+	0.356918i	−0.618875	+	0.785489i	$0.712411\pi$
$938$	−9.86309	−	15.4766i	−0.322041	−	0.505328i
$939$		0			0
$940$	−0.545944	−	2.39194i	−0.0178067	−	0.0780164i
$941$	−13.0591	−	16.3756i	−0.425714	−	0.533829i	0.522002	−	0.852945i	$-0.325186\pi$
$941$	−13.0591	−	16.3756i	−0.425714	−	0.533829i	−0.947716	+	0.319116i	$0.896614\pi$
$942$		0			0
$943$	4.42802	−	2.13242i	0.144196	−	0.0694412i
$944$	5.69007	−	24.9298i	0.185196	−	0.811397i
$945$		0			0
$946$	6.73790	+	29.5207i	0.219068	+	0.959800i
$947$	−26.7973	−	33.6028i	−0.870796	−	1.09194i	−0.995019	−	0.0996887i	$-0.968215\pi$
$947$	−26.7973	−	33.6028i	−0.870796	−	1.09194i	0.124223	−	0.992254i	$-0.460356\pi$
$948$		0			0
$949$	5.64905			0.183376
$950$	10.0518			0.326124
$951$		0			0
$952$	−3.97833	−	6.24256i	−0.128938	−	0.202323i
$953$	18.2193	+	8.77394i	0.590180	+	0.284216i	0.705042	−	0.709166i	$-0.250928\pi$
$953$	18.2193	+	8.77394i	0.590180	+	0.284216i	−0.114862	+	0.993381i	$0.536643\pi$
$954$		0			0
$955$	1.55574	+	6.81614i	0.0503426	+	0.220565i
$956$	1.33396	+	5.84445i	0.0431433	+	0.189023i
$957$		0			0
$958$	−52.5569	−	25.3100i	−1.69804	−	0.817731i
$959$	−2.71452	−	0.288298i	−0.0876566	−	0.00930963i
$960$		0			0
$961$	15.3750			0.495969
$962$	−23.8808			−0.769948
$963$		0			0
$964$	−2.22848	−	2.79442i	−0.0717744	−	0.0900023i
$965$	1.04130	+	4.56222i	0.0335205	+	0.146863i
$966$		0			0
$967$	−3.52113	+	15.4271i	−0.113232	+	0.496102i	0.886228	+	0.463249i	$0.153316\pi$
$967$	−3.52113	+	15.4271i	−0.113232	+	0.496102i	−0.999460	+	0.0328530i	$0.989541\pi$
$968$	−11.8622	+	5.71252i	−0.381265	+	0.183607i
$969$		0			0
$970$	−18.7519	−	23.5141i	−0.602087	−	0.754994i
$971$	5.47183	+	23.9737i	0.175599	+	0.769352i	0.983628	+	0.180209i	$0.0576773\pi$
$971$	5.47183	+	23.9737i	0.175599	+	0.769352i	−0.808029	+	0.589143i	$0.799466\pi$
$972$		0			0
$973$	2.61504	+	21.9476i	0.0838343	+	0.703606i
$974$	22.3327	+	28.0043i	0.715587	+	0.897317i
$975$		0			0
$976$	69.1313	+	33.2919i	2.21284	+	1.06565i
$977$	−1.66127	+	2.08317i	−0.0531489	+	0.0666466i	−0.807695	−	0.589600i	$-0.799285\pi$
$977$	−1.66127	+	2.08317i	−0.0531489	+	0.0666466i	0.754547	+	0.656247i	$0.227857\pi$
$978$		0			0
$979$	30.3614			0.970355
$980$	−2.86014	−	5.74997i	−0.0913638	−	0.183676i
$981$		0			0
$982$	−11.2247	+	49.1786i	−0.358194	+	1.56935i
$983$	1.84356	−	2.31175i	0.0588005	−	0.0737335i	−0.751562	−	0.659663i	$-0.770699\pi$
$983$	1.84356	−	2.31175i	0.0588005	−	0.0737335i	0.810362	+	0.585929i	$0.199270\pi$
$984$		0			0
$985$	−10.9186	+	13.6915i	−0.347895	+	0.436247i
$986$	−9.85569	−	12.3586i	−0.313869	−	0.393580i
$987$		0			0
$988$	−1.79885	+	2.25568i	−0.0572290	+	0.0717628i
$989$	−6.29855	−	27.5958i	−0.200282	−	0.877494i
$990$		0			0
$991$	11.4643	−	50.2283i	0.364175	−	1.59555i	−0.378302	−	0.925682i	$-0.623492\pi$
$991$	11.4643	−	50.2283i	0.364175	−	1.59555i	0.742477	−	0.669872i	$-0.233651\pi$
$992$	−24.6441	+	11.8680i	−0.782450	+	0.376808i
$993$		0			0
$994$	−7.90687	−	66.3609i	−0.250791	−	2.10484i
$995$	6.85093	+	30.0159i	0.217189	+	0.951567i
$996$		0			0
$997$	22.5653	−	10.8669i	0.714651	−	0.344158i	−0.0409756	−	0.999160i	$-0.513047\pi$
$997$	22.5653	−	10.8669i	0.714651	−	0.344158i	0.755627	+	0.655002i	$0.227332\pi$
$998$	34.0863			1.07898
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.64.2		36
3.2	odd	2		147.2.i.b.64.5	✓	36
49.36	even	7	inner	441.2.u.d.379.2		36
147.92	odd	14		7203.2.a.h.1.5		18
147.104	even	14		7203.2.a.g.1.5		18
147.134	odd	14		147.2.i.b.85.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.64.5	✓	36	3.2	odd	2
147.2.i.b.85.5	yes	36	147.134	odd	14
441.2.u.d.64.2		36	1.1	even	1	trivial
441.2.u.d.379.2		36	49.36	even	7	inner
7203.2.a.g.1.5		18	147.104	even	14
7203.2.a.h.1.5		18	147.92	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)

\(f(q)\)	\(=\)	\(q+(-0.368659 + 1.61520i) q^{2} +(-0.671021 - 0.323147i) q^{4} +(-0.768029 + 0.963077i) q^{5} +(-1.85883 + 1.88275i) q^{7} +(-1.29659 + 1.62588i) q^{8} +O(q^{10})\)	\(q+(-0.368659 + 1.61520i) q^{2} +(-0.671021 - 0.323147i) q^{4} +(-0.768029 + 0.963077i) q^{5} +(-1.85883 + 1.88275i) q^{7} +(-1.29659 + 1.62588i) q^{8} +(-1.27242 - 1.59557i) q^{10} +(0.480814 - 2.10659i) q^{11} +(-0.494793 + 2.16783i) q^{13} +(-2.35573 - 3.69648i) q^{14} +(-3.07684 - 3.85823i) q^{16} +(1.21217 - 0.583750i) q^{17} -1.74215 q^{19} +(0.826579 - 0.398059i) q^{20} +(3.22530 + 1.55322i) q^{22} +(-3.01499 - 1.45194i) q^{23} +(0.774955 + 3.39530i) q^{25} +(-3.31907 - 1.59838i) q^{26} +(1.85572 - 0.662686i) q^{28} +(-6.38940 + 3.07697i) q^{29} -6.80992 q^{31} +(3.61885 - 1.74275i) q^{32} +(0.495996 + 2.17310i) q^{34} +(-0.385592 - 3.23620i) q^{35} +(5.84053 - 2.81265i) q^{37} +(0.642259 - 2.81392i) q^{38} +(-0.570024 - 2.49744i) q^{40} +(-0.915699 + 1.14825i) q^{41} +(5.27379 + 6.61313i) q^{43} +(-1.00337 + 1.25819i) q^{44} +(3.45668 - 4.33454i) q^{46} +(0.595078 - 2.60721i) q^{47} +(-0.0894674 - 6.99943i) q^{49} -5.76978 q^{50} +(1.03254 - 1.29477i) q^{52} +(12.0649 + 5.81015i) q^{53} +(1.65953 + 2.08098i) q^{55} +(-0.650960 - 5.46339i) q^{56} +(-2.61442 - 11.4545i) q^{58} +(3.23073 + 4.05121i) q^{59} +(-14.0088 + 6.74626i) q^{61} +(2.51054 - 10.9994i) q^{62} +(-0.715458 - 3.13463i) q^{64} +(-1.70777 - 2.14148i) q^{65} +4.18684 q^{67} -1.00203 q^{68} +(5.36927 + 0.570247i) q^{70} +(13.7366 + 6.61522i) q^{71} +(-0.565319 - 2.47682i) q^{73} +(2.38983 + 10.4705i) q^{74} +(1.16902 + 0.562971i) q^{76} +(3.07241 + 4.82105i) q^{77} +0.184803 q^{79} +6.07887 q^{80} +(-1.51707 - 1.90235i) q^{82} +(-0.579573 - 2.53927i) q^{83} +(-0.368784 + 1.61575i) q^{85} +(-12.6257 + 6.08024i) q^{86} +(2.80163 + 3.51313i) q^{88} +(3.12670 + 13.6990i) q^{89} +(-3.16173 - 4.96121i) q^{91} +(1.55393 + 1.94857i) q^{92} +(3.99178 + 1.92234i) q^{94} +(1.33802 - 1.67783i) q^{95} +14.7372 q^{97} +(11.3385 + 2.43589i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 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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