LMFDB - Embedded newform 441.2.u.d.127.4

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			127.4
Character	$\chi$	$=$	441.127
Dual form			441.2.u.d.316.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11145 + 0.535248i) q^{2} +(-0.298141 - 0.373858i) q^{4} +(0.661767 + 2.89939i) q^{5} +(-0.553581 + 2.58719i) q^{7} +(-0.680276 - 2.98049i) q^{8} +O(q^{10})$	\(q+(1.11145 + 0.535248i) q^{2} +(-0.298141 - 0.373858i) q^{4} +(0.661767 + 2.89939i) q^{5} +(-0.553581 + 2.58719i) q^{7} +(-0.680276 - 2.98049i) q^{8} +(-0.816369 + 3.57675i) q^{10} +(4.64641 + 2.23759i) q^{11} +(-0.946677 - 0.455895i) q^{13} +(-2.00007 + 2.57924i) q^{14} +(0.626392 - 2.74440i) q^{16} +(-3.51495 + 4.40761i) q^{17} -1.28450 q^{19} +(0.886660 - 1.11184i) q^{20} +(3.96660 + 4.97396i) q^{22} +(2.10843 + 2.64389i) q^{23} +(-3.46370 + 1.66803i) q^{25} +(-0.808170 - 1.01341i) q^{26} +(1.13229 - 0.564388i) q^{28} +(1.82069 - 2.28308i) q^{29} +4.40683 q^{31} +(-1.64705 + 2.06533i) q^{32} +(-6.26587 + 3.01748i) q^{34} +(-7.86762 + 0.107068i) q^{35} +(5.04275 - 6.32340i) q^{37} +(-1.42766 - 0.687526i) q^{38} +(8.19141 - 3.94478i) q^{40} +(0.169625 + 0.743175i) q^{41} +(2.19253 - 9.60612i) q^{43} +(-0.548746 - 2.40421i) q^{44} +(0.928289 + 4.06710i) q^{46} +(-1.72772 - 0.832026i) q^{47} +(-6.38710 - 2.86444i) q^{49} -4.74254 q^{50} +(0.111804 + 0.489844i) q^{52} +(3.32088 + 4.16425i) q^{53} +(-3.41282 + 14.9525i) q^{55} +(8.08767 - 0.110063i) q^{56} +(3.24563 - 1.56301i) q^{58} +(2.34804 - 10.2874i) q^{59} +(7.10157 - 8.90508i) q^{61} +(4.89798 + 2.35874i) q^{62} +(-8.00849 + 3.85669i) q^{64} +(0.695340 - 3.04648i) q^{65} -9.22571 q^{67} +2.69577 q^{68} +(-8.80180 - 4.09212i) q^{70} +(-8.91802 - 11.1828i) q^{71} +(1.30092 - 0.626491i) q^{73} +(8.98936 - 4.32905i) q^{74} +(0.382963 + 0.480221i) q^{76} +(-8.36124 + 10.7825i) q^{77} -10.9623 q^{79} +8.37162 q^{80} +(-0.209253 + 0.916796i) q^{82} +(-13.8192 + 6.65499i) q^{83} +(-15.1055 - 7.27441i) q^{85} +(7.57855 - 9.50320i) q^{86} +(3.50827 - 15.3707i) q^{88} +(5.81162 - 2.79873i) q^{89} +(1.70355 - 2.19686i) q^{91} +(0.359828 - 1.57651i) q^{92} +(-1.47494 - 1.84952i) q^{94} +(-0.850041 - 3.72427i) q^{95} +11.8568 q^{97} +(-5.56577 - 6.60237i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.11145	+	0.535248i	0.785916	+	0.378477i	0.783399	−	0.621520i	$-0.213484\pi$
$2$	1.11145	+	0.535248i	0.785916	+	0.378477i	0.00251746	+	0.999997i	$0.499199\pi$
$3$		0			0
$3$		0			0
$4$	−0.298141	−	0.373858i	−0.149071	−	0.186929i
$5$	0.661767	+	2.89939i	0.295951	+	1.29665i	0.876097	+	0.482135i	$0.160138\pi$
$5$	0.661767	+	2.89939i	0.295951	+	1.29665i	−0.580146	+	0.814513i	$0.697004\pi$
$6$		0			0
$7$	−0.553581	+	2.58719i	−0.209234	+	0.977866i
$7$	−0.553581	+	2.58719i	−0.209234	+	0.977866i
$8$	−0.680276	−	2.98049i	−0.240514	−	1.05376i
$9$		0			0
$10$	−0.816369	+	3.57675i	−0.258159	+	1.13107i
$11$	4.64641	+	2.23759i	1.40095	+	0.674660i	0.973353	−	0.229312i	$-0.0736477\pi$
$11$	4.64641	+	2.23759i	1.40095	+	0.674660i	0.427592	+	0.903972i	$0.359362\pi$
$12$		0			0
$13$	−0.946677	−	0.455895i	−0.262561	−	0.126443i	0.297973	−	0.954574i	$-0.403690\pi$
$13$	−0.946677	−	0.455895i	−0.262561	−	0.126443i	−0.560533	+	0.828132i	$0.689404\pi$
$14$	−2.00007	+	2.57924i	−0.534540	+	0.689330i
$15$		0			0
$16$	0.626392	−	2.74440i	0.156598	−	0.686100i
$17$	−3.51495	+	4.40761i	−0.852501	+	1.06900i	0.144336	+	0.989529i	$0.453896\pi$
$17$	−3.51495	+	4.40761i	−0.852501	+	1.06900i	−0.996837	+	0.0794741i	$0.974676\pi$
$18$		0			0
$19$	−1.28450			−0.294685			−0.147342	−	0.989086i	$-0.547072\pi$
$19$	−1.28450			−0.294685			−0.147342	+	0.989086i	$0.547072\pi$
$20$	0.886660	−	1.11184i	0.198263	−	0.248614i
$21$		0			0
$22$	3.96660	+	4.97396i	0.845682	+	1.06045i
$23$	2.10843	+	2.64389i	0.439639	+	0.551290i	0.951448	−	0.307809i	$-0.0995959\pi$
$23$	2.10843	+	2.64389i	0.439639	+	0.551290i	−0.511809	+	0.859099i	$0.671024\pi$
$24$		0			0
$25$	−3.46370	+	1.66803i	−0.692739	+	0.333606i
$26$	−0.808170	−	1.01341i	−0.158495	−	0.198747i
$27$		0			0
$28$	1.13229	−	0.564388i	0.213982	−	0.106659i
$29$	1.82069	−	2.28308i	0.338094	−	0.423957i	−0.583499	−	0.812114i	$-0.698317\pi$
$29$	1.82069	−	2.28308i	0.338094	−	0.423957i	0.921593	+	0.388157i	$0.126888\pi$
$30$		0			0
$31$	4.40683			0.791490			0.395745	−	0.918361i	$-0.370486\pi$
$31$	4.40683			0.791490			0.395745	+	0.918361i	$0.370486\pi$
$32$	−1.64705	+	2.06533i	−0.291159	+	0.365102i
$33$		0			0
$34$	−6.26587	+	3.01748i	−1.07459	+	0.517494i
$35$	−7.86762	+	0.107068i	−1.32987	+	0.0180979i
$36$		0			0
$37$	5.04275	−	6.32340i	0.829023	−	1.03956i	−0.169517	−	0.985527i	$-0.554221\pi$
$37$	5.04275	−	6.32340i	0.829023	−	1.03956i	0.998539	−	0.0540340i	$-0.0172079\pi$
$38$	−1.42766	−	0.687526i	−0.231598	−	0.111532i
$39$		0			0
$40$	8.19141	−	3.94478i	1.29518	−	0.623724i
$41$	0.169625	+	0.743175i	0.0264910	+	0.116064i	0.986445	−	0.164094i	$-0.0524701\pi$
$41$	0.169625	+	0.743175i	0.0264910	+	0.116064i	−0.959954	+	0.280159i	$0.909613\pi$
$42$		0			0
$43$	2.19253	−	9.60612i	0.334358	−	1.46492i	−0.476239	−	0.879316i	$-0.658000\pi$
$43$	2.19253	−	9.60612i	0.334358	−	1.46492i	0.810597	−	0.585604i	$-0.199143\pi$
$44$	−0.548746	−	2.40421i	−0.0827266	−	0.362449i
$45$		0			0
$46$	0.928289	+	4.06710i	0.136869	+	0.599661i
$47$	−1.72772	−	0.832026i	−0.252014	−	0.121363i	0.303613	−	0.952796i	$-0.401807\pi$
$47$	−1.72772	−	0.832026i	−0.252014	−	0.121363i	−0.555626	+	0.831432i	$0.687521\pi$
$48$		0			0
$49$	−6.38710	−	2.86444i	−0.912442	−	0.409205i
$50$	−4.74254			−0.670697
$51$		0			0
$52$	0.111804	+	0.489844i	0.0155044	+	0.0679291i
$53$	3.32088	+	4.16425i	0.456158	+	0.572004i	0.955721	−	0.294274i	$-0.0950777\pi$
$53$	3.32088	+	4.16425i	0.456158	+	0.572004i	−0.499564	+	0.866277i	$0.666506\pi$
$54$		0			0
$55$	−3.41282	+	14.9525i	−0.460184	+	2.01620i
$56$	8.08767	−	0.110063i	1.08076	−	0.0147078i
$57$		0			0
$58$	3.24563	−	1.56301i	0.426172	−	0.205234i
$59$	2.34804	−	10.2874i	0.305689	−	1.33931i	−0.555708	−	0.831378i	$-0.687553\pi$
$59$	2.34804	−	10.2874i	0.305689	−	1.33931i	0.861397	−	0.507933i	$-0.169590\pi$
$60$		0			0
$61$	7.10157	−	8.90508i	0.909263	−	1.14018i	−0.0803999	−	0.996763i	$-0.525620\pi$
$61$	7.10157	−	8.90508i	0.909263	−	1.14018i	0.989662	−	0.143416i	$-0.0458088\pi$
$62$	4.89798	+	2.35874i	0.622044	+	0.299561i
$63$		0			0
$64$	−8.00849	+	3.85669i	−1.00106	+	0.482086i
$65$	0.695340	−	3.04648i	0.0862463	−	0.377870i
$66$		0			0
$67$	−9.22571			−1.12710			−0.563550	−	0.826082i	$-0.690565\pi$
$67$	−9.22571			−1.12710			−0.563550	+	0.826082i	$0.690565\pi$
$68$	2.69577			0.326910
$69$		0			0
$70$	−8.80180	−	4.09212i	−1.05202	−	0.489102i
$71$	−8.91802	−	11.1828i	−1.05837	−	1.32716i	−0.942615	−	0.333883i	$-0.891641\pi$
$71$	−8.91802	−	11.1828i	−1.05837	−	1.32716i	−0.115760	−	0.993277i	$-0.536930\pi$
$72$		0			0
$73$	1.30092	−	0.626491i	0.152261	−	0.0733252i	−0.356201	−	0.934409i	$-0.615928\pi$
$73$	1.30092	−	0.626491i	0.152261	−	0.0733252i	0.508463	+	0.861084i	$0.330214\pi$
$74$	8.98936	−	4.32905i	1.04499	−	0.503242i
$75$		0			0
$76$	0.382963	+	0.480221i	0.0439289	+	0.0550851i
$77$	−8.36124	+	10.7825i	−0.952852	+	1.22877i
$78$		0			0
$79$	−10.9623			−1.23336			−0.616680	−	0.787214i	$-0.711523\pi$
$79$	−10.9623			−1.23336			−0.616680	+	0.787214i	$0.711523\pi$
$80$	8.37162			0.935976
$81$		0			0
$82$	−0.209253	+	0.916796i	−0.0231081	+	0.101243i
$83$	−13.8192	+	6.65499i	−1.51686	+	0.730480i	−0.992640	−	0.121104i	$-0.961356\pi$
$83$	−13.8192	+	6.65499i	−1.51686	+	0.730480i	−0.524218	+	0.851584i	$0.675642\pi$
$84$		0			0
$85$	−15.1055	−	7.27441i	−1.63842	−	0.789021i
$86$	7.57855	−	9.50320i	0.817216	−	1.02476i
$87$		0			0
$88$	3.50827	−	15.3707i	0.373983	−	1.63853i
$89$	5.81162	−	2.79873i	0.616030	−	0.296665i	−0.0997258	−	0.995015i	$-0.531797\pi$
$89$	5.81162	−	2.79873i	0.616030	−	0.296665i	0.715756	+	0.698350i	$0.246082\pi$
$90$		0			0
$91$	1.70355	−	2.19686i	0.178581	−	0.230293i
$92$	0.359828	−	1.57651i	0.0375146	−	0.164362i
$93$		0			0
$94$	−1.47494	−	1.84952i	−0.152128	−	0.190763i
$95$	−0.850041	−	3.72427i	−0.0872124	−	0.382102i
$96$		0			0
$97$	11.8568			1.20388			0.601939	−	0.798542i	$-0.294395\pi$
$97$	11.8568			1.20388			0.601939	+	0.798542i	$0.294395\pi$
$98$	−5.56577	−	6.60237i	−0.562228	−	0.666940i
$99$		0			0
$100$	1.65628	+	0.797621i	0.165628	+	0.0797621i
$101$	−0.0319674	−	0.140059i	−0.00318088	−	0.0139363i	0.973313	−	0.229483i	$-0.0737037\pi$
$101$	−0.0319674	−	0.140059i	−0.00318088	−	0.0139363i	−0.976493	+	0.215547i	$0.930847\pi$
$102$		0			0
$103$	4.17449	+	18.2896i	0.411325	+	1.80213i	0.577907	+	0.816103i	$0.303870\pi$
$103$	4.17449	+	18.2896i	0.411325	+	1.80213i	−0.166582	+	0.986028i	$0.553273\pi$
$104$	−0.714788	+	3.13169i	−0.0700907	+	0.307088i
$105$		0			0
$106$	1.46210	+	6.40586i	0.142011	+	0.622192i
$107$	5.88459	−	2.83387i	0.568885	−	0.273960i	−0.127251	−	0.991871i	$-0.540615\pi$
$107$	5.88459	−	2.83387i	0.568885	−	0.273960i	0.696136	+	0.717910i	$0.254901\pi$
$108$		0			0
$109$	7.99185	+	3.84867i	0.765481	+	0.368636i	0.775528	−	0.631313i	$-0.217484\pi$
$109$	7.99185	+	3.84867i	0.765481	+	0.368636i	−0.0100471	+	0.999950i	$0.503198\pi$
$110$	−11.7965	+	14.7923i	−1.12475	+	1.41039i
$111$		0			0
$112$	6.75353	+	3.13984i	0.638148	+	0.296687i
$113$	10.3357	−	4.97742i	0.972302	−	0.468236i	0.120851	−	0.992671i	$-0.461438\pi$
$113$	10.3357	−	4.97742i	0.972302	−	0.468236i	0.851451	+	0.524435i	$0.175723\pi$
$114$		0			0
$115$	−6.27039	+	7.86282i	−0.584717	+	0.733212i
$116$	−1.39637			−0.129650
$117$		0			0
$118$	8.11607	−	10.1772i	0.747144	−	0.936889i
$119$	−9.45751	−	11.5338i	−0.866969	−	1.05730i
$120$		0			0
$121$	9.72391	+	12.1934i	0.883992	+	1.10849i
$122$	12.6595	−	6.09649i	1.14614	−	0.551950i
$123$		0			0
$124$	−1.31386	−	1.64753i	−0.117988	−	0.147952i
$125$	2.14273	+	2.68690i	0.191651	+	0.240323i
$126$		0			0
$127$	10.6025	−	13.2952i	0.940823	−	1.17975i	−0.0427210	−	0.999087i	$-0.513603\pi$
$127$	10.6025	−	13.2952i	0.940823	−	1.17975i	0.983544	−	0.180668i	$-0.0578259\pi$
$128$	−5.68204			−0.502226
$129$		0			0
$130$	2.40346	−	3.01385i	0.210798	−	0.264332i
$131$	−2.62632	+	11.5067i	−0.229463	+	1.00534i	0.720617	+	0.693334i	$0.243859\pi$
$131$	−2.62632	+	11.5067i	−0.229463	+	1.00534i	−0.950079	+	0.312008i	$0.898998\pi$
$132$		0			0
$133$	0.711076	−	3.32325i	0.0616581	−	0.288162i
$134$	−10.2539	−	4.93804i	−0.885806	−	0.426582i
$135$		0			0
$136$	15.5280	+	7.47787i	1.33151	+	0.641222i
$137$	−0.220816	+	0.967457i	−0.0188656	+	0.0826555i	−0.983484	−	0.180993i	$-0.942069\pi$
$137$	−0.220816	+	0.967457i	−0.0188656	+	0.0826555i	0.964619	+	0.263649i	$0.0849259\pi$
$138$		0			0
$139$	1.88930	+	8.27755i	0.160248	+	0.702093i	0.989657	+	0.143451i	$0.0458201\pi$
$139$	1.88930	+	8.27755i	0.160248	+	0.702093i	−0.829409	+	0.558642i	$0.811323\pi$
$140$	2.38569	+	2.90945i	0.201628	+	0.245893i
$141$		0			0
$142$	−3.92637	−	17.2026i	−0.329494	−	1.44361i
$143$	−3.37854	−	4.23655i	−0.282528	−	0.354278i
$144$		0			0
$145$	7.82441	+	3.76804i	0.649782	+	0.312919i
$146$	1.78124			0.147417
$147$		0			0
$148$	−3.86750			−0.317907
$149$	9.65485	+	4.64953i	0.790956	+	0.380904i	0.785328	−	0.619080i	$-0.212494\pi$
$149$	9.65485	+	4.64953i	0.790956	+	0.380904i	0.00562786	+	0.999984i	$0.498209\pi$
$150$		0			0
$151$	−1.00280	−	1.25747i	−0.0816064	−	0.102331i	0.739352	−	0.673319i	$-0.235132\pi$
$151$	−1.00280	−	1.25747i	−0.0816064	−	0.102331i	−0.820959	+	0.570988i	$0.806560\pi$
$152$	0.873816	+	3.82844i	0.0708759	+	0.310527i
$153$		0			0
$154$	−15.0644	+	7.50885i	−1.21392	+	0.605081i
$155$	2.91629	+	12.7771i	0.234242	+	1.02628i
$156$		0			0
$157$	2.30983	−	10.1200i	0.184345	−	0.807666i	−0.795185	−	0.606367i	$-0.792626\pi$
$157$	2.30983	−	10.1200i	0.184345	−	0.807666i	0.979530	−	0.201300i	$-0.0645165\pi$
$158$	−12.1841	−	5.86757i	−0.969317	−	0.466799i
$159$		0			0
$160$	−7.07816	−	3.40866i	−0.559578	−	0.269478i
$161$	−8.00744	+	3.99131i	−0.631075	+	0.314559i
$162$		0			0
$163$	−4.57501	+	20.0444i	−0.358342	+	1.57000i	0.398980	+	0.916959i	$0.369364\pi$
$163$	−4.57501	+	20.0444i	−0.358342	+	1.57000i	−0.757323	+	0.653041i	$0.773493\pi$
$164$	0.227269	−	0.284987i	0.0177468	−	0.0222537i
$165$		0			0
$166$	−18.9215			−1.46859
$167$	−3.91182	+	4.90527i	−0.302706	+	0.379581i	−0.909799	−	0.415050i	$-0.863764\pi$
$167$	−3.91182	+	4.90527i	−0.302706	+	0.379581i	0.607093	+	0.794631i	$0.292336\pi$
$168$		0			0
$169$	−7.41701	−	9.30064i	−0.570539	−	0.715434i
$170$	−12.8954	−	16.1703i	−0.989033	−	1.24021i
$171$		0			0
$172$	−4.24501	+	2.04429i	−0.323679	+	0.155875i
$173$	−7.29471	−	9.14727i	−0.554606	−	0.695454i	0.422944	−	0.906156i	$-0.360997\pi$
$173$	−7.29471	−	9.14727i	−0.554606	−	0.695454i	−0.977550	+	0.210702i	$0.932425\pi$
$174$		0			0
$175$	−2.39807	−	9.88462i	−0.181277	−	0.747207i
$176$	9.05132	−	11.3500i	0.682269	−	0.855539i
$177$		0			0
$178$	7.95735			0.596429
$179$	2.83095	−	3.54989i	0.211595	−	0.265332i	−0.664696	−	0.747114i	$-0.731439\pi$
$179$	2.83095	−	3.54989i	0.211595	−	0.265332i	0.876291	+	0.481782i	$0.160010\pi$
$180$		0			0
$181$	6.85371	−	3.30057i	0.509432	−	0.245330i	−0.161467	−	0.986878i	$-0.551623\pi$
$181$	6.85371	−	3.30057i	0.509432	−	0.245330i	0.670899	+	0.741549i	$0.265908\pi$
$182$	3.06928	−	1.52988i	0.227510	−	0.113402i
$183$		0			0
$184$	6.44577	−	8.08274i	0.475188	−	0.595867i
$185$	21.6712	+	10.4363i	1.59330	+	0.767290i
$186$		0			0
$187$	−26.1944	+	12.6145i	−1.91552	+	0.922466i
$188$	0.204046	+	0.893982i	0.0148816	+	0.0652004i
$189$		0			0
$190$	1.04863	−	4.59434i	0.0760755	−	0.333308i
$191$	0.521536	+	2.28500i	0.0377370	+	0.165337i	0.990285	−	0.139051i	$-0.0444053\pi$
$191$	0.521536	+	2.28500i	0.0377370	+	0.165337i	−0.952548	+	0.304388i	$0.901548\pi$
$192$		0			0
$193$	5.15094	+	22.5678i	0.370773	+	1.62446i	0.724613	+	0.689156i	$0.242019\pi$
$193$	5.15094	+	22.5678i	0.370773	+	1.62446i	−0.353840	+	0.935306i	$0.615124\pi$
$194$	13.1783	+	6.34633i	0.946147	+	0.455640i
$195$		0			0
$196$	0.833366	+	3.24187i	0.0595261	+	0.231562i
$197$	−22.7707			−1.62234			−0.811172	−	0.584808i	$-0.801170\pi$
$197$	−22.7707			−1.62234			−0.811172	+	0.584808i	$0.801170\pi$
$198$		0			0
$199$	−1.84453	−	8.08141i	−0.130755	−	0.572876i	−0.997278	−	0.0737379i	$-0.976507\pi$
$199$	−1.84453	−	8.08141i	−0.130755	−	0.572876i	0.866522	−	0.499138i	$-0.166350\pi$
$200$	7.32780	+	9.18877i	0.518154	+	0.649744i
$201$		0			0
$202$	0.0394357	−	0.172779i	0.00277468	−	0.0121567i
$203$	4.89885	+	5.97435i	0.343832	+	0.419317i
$204$		0			0
$205$	−2.04250	+	0.983618i	−0.142655	+	0.0686989i
$206$	−5.14973	+	22.5624i	−0.358799	+	1.57200i
$207$		0			0
$208$	−1.84415	+	2.31249i	−0.127869	+	0.160342i
$209$	−5.96832	−	2.87419i	−0.412837	−	0.198812i
$210$		0			0
$211$	1.02985	−	0.495949i	0.0708978	−	0.0341426i	−0.398099	−	0.917343i	$-0.630330\pi$
$211$	1.02985	−	0.495949i	0.0708978	−	0.0341426i	0.468997	+	0.883200i	$0.344616\pi$
$212$	0.566745	−	2.48307i	0.0389242	−	0.170538i
$213$		0			0
$214$	8.05727			0.550783
$215$	29.3029			1.99844
$216$		0			0
$217$	−2.43954	+	11.4013i	−0.165607	+	0.773970i
$218$	6.82258	+	8.55524i	0.462083	+	0.579434i
$219$		0			0
$220$	6.60762	−	3.18206i	0.445486	−	0.214535i
$221$	5.33693	−	2.57013i	0.359001	−	0.172886i
$222$		0			0
$223$	−11.9863	−	15.0303i	−0.802660	−	1.00650i	−0.999659	−	0.0261006i	$-0.991691\pi$
$223$	−11.9863	−	15.0303i	−0.802660	−	1.00650i	0.196999	−	0.980404i	$-0.436880\pi$
$224$	−4.43162	−	5.40454i	−0.296100	−	0.361106i
$225$		0			0
$226$	14.1518			0.941365
$227$	−3.61041			−0.239631			−0.119816	−	0.992796i	$-0.538230\pi$
$227$	−3.61041			−0.239631			−0.119816	+	0.992796i	$0.538230\pi$
$228$		0			0
$229$	1.04840	−	4.59334i	0.0692802	−	0.303536i	−0.928402	−	0.371576i	$-0.878817\pi$
$229$	1.04840	−	4.59334i	0.0692802	−	0.303536i	0.997683	+	0.0680401i	$0.0216746\pi$
$230$	−11.1778	+	5.38295i	−0.737043	+	0.354941i
$231$		0			0
$232$	−8.04326	−	3.87343i	−0.528066	−	0.254303i
$233$	−8.36676	+	10.4916i	−0.548125	+	0.687327i	−0.976313	−	0.216363i	$-0.930581\pi$
$233$	−8.36676	+	10.4916i	−0.548125	+	0.687327i	0.428188	+	0.903690i	$0.359152\pi$
$234$		0			0
$235$	1.26902	−	5.55994i	0.0827818	−	0.362691i
$236$	−4.54609	+	2.18928i	−0.295925	+	0.142510i
$237$		0			0
$238$	−4.33813	−	17.8814i	−0.281199	−	1.15908i
$239$	−2.49858	+	10.9470i	−0.161620	+	0.708102i	0.827558	+	0.561380i	$0.189729\pi$
$239$	−2.49858	+	10.9470i	−0.161620	+	0.708102i	−0.989178	+	0.146722i	$0.953128\pi$
$240$		0			0
$241$	−12.2167	−	15.3192i	−0.786944	−	0.986797i	−0.999953	−	0.00974662i	$-0.996898\pi$
$241$	−12.2167	−	15.3192i	−0.786944	−	0.986797i	0.213008	−	0.977050i	$-0.431674\pi$
$242$	4.28118	+	18.7571i	0.275205	+	1.20575i
$243$		0			0
$244$	−5.44651			−0.348677
$245$	4.07836	−	20.4143i	0.260557	−	1.30422i
$246$		0			0
$247$	1.21601	+	0.585599i	0.0773727	+	0.0372607i
$248$	−2.99786	−	13.1345i	−0.190364	−	0.834041i
$249$		0			0
$250$	0.943387	+	4.13325i	0.0596650	+	0.261410i
$251$	−2.52197	+	11.0495i	−0.159185	+	0.697437i	0.830836	+	0.556518i	$0.187863\pi$
$251$	−2.52197	+	11.0495i	−0.159185	+	0.697437i	−0.990021	+	0.140919i	$0.954994\pi$
$252$		0			0
$253$	3.88069	+	17.0024i	0.243977	+	1.06893i
$254$	18.9004	−	9.10197i	1.18592	−	0.571108i
$255$		0			0
$256$	9.70167	+	4.67208i	0.606354	+	0.292005i
$257$	2.53140	−	3.17427i	0.157904	−	0.198006i	−0.696586	−	0.717474i	$-0.745298\pi$
$257$	2.53140	−	3.17427i	0.157904	−	0.198006i	0.854490	+	0.519468i	$0.173870\pi$
$258$		0			0
$259$	13.5683	+	16.5471i	0.843092	+	1.02818i
$260$	−1.34626	+	0.648325i	−0.0834916	+	0.0402074i
$261$		0			0
$262$	−9.07795	+	11.3834i	−0.560838	+	0.703268i
$263$	−14.5546			−0.897472			−0.448736	−	0.893664i	$-0.648126\pi$
$263$	−14.5546			−0.897472			−0.448736	+	0.893664i	$0.648126\pi$
$264$		0			0
$265$	−9.87614	+	12.3843i	−0.606687	+	0.760761i
$266$	2.56909	−	3.31303i	0.157521	−	0.203135i
$267$		0			0
$268$	2.75057	+	3.44910i	0.168018	+	0.210688i
$269$	13.3318	−	6.42025i	0.812854	−	0.391450i	0.0191972	−	0.999816i	$-0.493889\pi$
$269$	13.3318	−	6.42025i	0.812854	−	0.391450i	0.793657	+	0.608366i	$0.208175\pi$
$270$		0			0
$271$	0.525477	+	0.658927i	0.0319205	+	0.0400270i	0.797536	−	0.603272i	$-0.206137\pi$
$271$	0.525477	+	0.658927i	0.0319205	+	0.0400270i	−0.765615	+	0.643299i	$0.777565\pi$
$272$	9.89452	+	12.4073i	0.599943	+	0.752305i
$273$		0			0
$274$	−0.763256	+	0.957092i	−0.0461100	+	0.0578201i
$275$	−19.8261			−1.19556
$276$		0			0
$277$	5.62720	−	7.05629i	0.338106	−	0.423971i	−0.583491	−	0.812120i	$-0.698314\pi$
$277$	5.62720	−	7.05629i	0.338106	−	0.423971i	0.921597	+	0.388148i	$0.126885\pi$
$278$	−2.33068	+	10.2114i	−0.139785	+	0.612436i
$279$		0			0
$280$	5.67127	+	23.3765i	0.338923	+	1.39701i
$281$	16.8355	+	8.10755i	1.00432	+	0.483656i	0.862403	−	0.506222i	$-0.168958\pi$
$281$	16.8355	+	8.10755i	1.00432	+	0.483656i	0.141919	+	0.989878i	$0.454673\pi$
$282$		0			0
$283$	−25.4710	−	12.2662i	−1.51409	−	0.729149i	−0.521801	−	0.853067i	$-0.674740\pi$
$283$	−25.4710	−	12.2662i	−1.51409	−	0.729149i	−0.992292	+	0.123918i	$0.960454\pi$
$284$	−1.52196	+	6.66814i	−0.0903117	+	0.395681i
$285$		0			0
$286$	−1.48748	−	6.51709i	−0.0879567	−	0.385363i
$287$	−2.01664	+	0.0274439i	−0.119038	+	0.00161996i
$288$		0			0
$289$	−3.28929	−	14.4113i	−0.193488	−	0.847725i
$290$	6.67964	+	8.37600i	0.392242	+	0.491856i
$291$		0			0
$292$	−0.622077	−	0.299577i	−0.0364043	−	0.0175314i
$293$	−24.4581			−1.42886			−0.714428	−	0.699709i	$-0.753313\pi$
$293$	−24.4581			−1.42886			−0.714428	+	0.699709i	$0.753313\pi$
$294$		0			0
$295$	31.3812			1.82708
$296$	−22.2773	−	10.7282i	−1.29484	−	0.623562i
$297$		0			0
$298$	8.24226	+	10.3355i	0.477461	+	0.598718i
$299$	−0.790667	−	3.46414i	−0.0457255	−	0.200336i
$300$		0			0
$301$	23.6391	+	10.9903i	1.36254	+	0.633468i
$302$	−0.441505	−	1.93436i	−0.0254058	−	0.111310i
$303$		0			0
$304$	−0.804601	+	3.52519i	−0.0461470	+	0.202183i
$305$	30.5189	+	14.6971i	1.74751	+	0.841556i
$306$		0			0
$307$	−7.17208	−	3.45389i	−0.409332	−	0.197124i	0.217875	−	0.975977i	$-0.430088\pi$
$307$	−7.17208	−	3.45389i	−0.409332	−	0.197124i	−0.627207	+	0.778853i	$0.715802\pi$
$308$	6.52393	−	0.0887825i	0.371736	−	0.00505885i
$309$		0			0
$310$	−3.59760	+	15.7621i	−0.204330	+	0.895228i
$311$	3.61484	−	4.53286i	0.204979	−	0.257035i	−0.668707	−	0.743526i	$-0.733152\pi$
$311$	3.61484	−	4.53286i	0.204979	−	0.257035i	0.873686	+	0.486491i	$0.161723\pi$
$312$		0			0
$313$	4.76595			0.269387			0.134694	−	0.990887i	$-0.456995\pi$
$313$	4.76595			0.269387			0.134694	+	0.990887i	$0.456995\pi$
$314$	7.98399	−	10.0116i	0.450563	−	0.564988i
$315$		0			0
$316$	3.26833	+	4.09835i	0.183858	+	0.230550i
$317$	3.07314	+	3.85359i	0.172605	+	0.216439i	0.860608	−	0.509268i	$-0.170084\pi$
$317$	3.07314	+	3.85359i	0.172605	+	0.216439i	−0.688003	+	0.725708i	$0.741513\pi$
$318$		0			0
$319$	13.5683	−	6.53414i	0.759678	−	0.365842i
$320$	−16.4818	−	20.6675i	−0.921361	−	1.15535i
$321$		0			0
$322$	−11.0362	+	0.150189i	−0.615025	+	0.00836972i
$323$	4.51496	−	5.66158i	0.251219	−	0.315019i
$324$		0			0
$325$	4.03945			0.224068
$326$	−15.8136	+	19.8297i	−0.875836	+	1.09826i
$327$		0			0
$328$	2.09963	−	1.01113i	0.115933	−	0.0558303i
$329$	3.10904	−	4.00934i	0.171407	−	0.221042i
$330$		0			0
$331$	3.97748	−	4.98760i	0.218622	−	0.274143i	−0.660411	−	0.750904i	$-0.729618\pi$
$331$	3.97748	−	4.98760i	0.218622	−	0.274143i	0.879033	+	0.476761i	$0.158189\pi$
$332$	6.60810	+	3.18229i	0.362667	+	0.174651i
$333$		0			0
$334$	−6.97334	+	3.35818i	−0.381564	+	0.183752i
$335$	−6.10528	−	26.7490i	−0.333567	−	1.46145i
$336$		0			0
$337$	−3.88752	+	17.0324i	−0.211767	+	0.927811i	0.751599	+	0.659620i	$0.229283\pi$
$337$	−3.88752	+	17.0324i	−0.211767	+	0.927811i	−0.963366	+	0.268191i	$0.913574\pi$
$338$	−3.26552	−	14.3072i	−0.177621	−	0.778207i
$339$		0			0
$340$	1.78397	+	7.81610i	0.0967496	+	0.423888i
$341$	20.4759	+	9.86068i	1.10883	+	0.533986i
$342$		0			0
$343$	10.9466	−	14.9389i	0.591062	−	0.806626i
$344$	−30.1224			−1.62409
$345$		0			0
$346$	−3.21167	−	14.0712i	−0.172660	−	0.756474i
$347$	−4.32195	−	5.41956i	−0.232015	−	0.290937i	0.652172	−	0.758071i	$-0.273858\pi$
$347$	−4.32195	−	5.41956i	−0.232015	−	0.290937i	−0.884187	+	0.467134i	$0.845287\pi$
$348$		0			0
$349$	2.03383	−	8.91077i	0.108868	−	0.476983i	−0.890873	−	0.454252i	$-0.849907\pi$
$349$	2.03383	−	8.91077i	0.108868	−	0.476983i	0.999742	−	0.0227312i	$-0.00723617\pi$
$350$	2.62538	−	12.2699i	0.140333	−	0.655851i
$351$		0			0
$352$	−12.2742	+	5.91095i	−0.654218	+	0.315055i
$353$	−1.82755	+	8.00703i	−0.0972708	+	0.426171i	−0.999992	−	0.00405525i	$-0.998709\pi$
$353$	−1.82755	+	8.00703i	−0.0972708	+	0.426171i	0.902721	+	0.430227i	$0.141566\pi$
$354$		0			0
$355$	26.5218	−	33.2573i	1.40763	−	1.76511i
$356$	−2.77901	−	1.33830i	−0.147287	−	0.0709298i
$357$		0			0
$358$	5.04654	−	2.43028i	0.266718	−	0.128444i
$359$	0.935689	−	4.09952i	0.0493838	−	0.216364i	−0.944215	−	0.329329i	$-0.893177\pi$
$359$	0.935689	−	4.09952i	0.0493838	−	0.216364i	0.993599	+	0.112965i	$0.0360346\pi$
$360$		0			0
$361$	−17.3501			−0.913161
$362$	9.38420			0.493223
$363$		0			0
$364$	−1.32921	+	0.0180889i	−0.0696696	+	0.000948115i
$365$	2.67735	+	3.35729i	0.140139	+	0.175729i
$366$		0			0
$367$	18.9891	−	9.14468i	0.991224	−	0.477348i	0.133273	−	0.991079i	$-0.457451\pi$
$367$	18.9891	−	9.14468i	0.991224	−	0.477348i	0.857951	+	0.513731i	$0.171737\pi$
$368$	8.57661	−	4.13028i	0.447087	−	0.215306i
$369$		0			0
$370$	18.5005	+	23.1989i	0.961794	+	1.20605i
$371$	−12.6121	+	6.28649i	−0.654786	+	0.326378i
$372$		0			0
$373$	1.10251			0.0570861			0.0285430	−	0.999593i	$-0.490913\pi$
$373$	1.10251			0.0570861			0.0285430	+	0.999593i	$0.490913\pi$
$374$	−35.8657			−1.85457
$375$		0			0
$376$	−1.30451	+	5.71545i	−0.0672752	+	0.294752i
$377$	−2.76445	+	1.33129i	−0.142377	+	0.0685649i
$378$		0			0
$379$	−6.21884	−	2.99484i	−0.319440	−	0.153834i	0.267291	−	0.963616i	$-0.413871\pi$
$379$	−6.21884	−	2.99484i	−0.319440	−	0.153834i	−0.586732	+	0.809781i	$0.699586\pi$
$380$	−1.13892	+	1.42816i	−0.0584251	+	0.0732628i
$381$		0			0
$382$	−0.643377	+	2.81882i	−0.0329180	+	0.144223i
$383$	−27.6811	+	13.3305i	−1.41444	+	0.681158i	−0.976034	−	0.217619i	$-0.930171\pi$
$383$	−27.6811	+	13.3305i	−1.41444	+	0.681158i	−0.438406	+	0.898777i	$0.644457\pi$
$384$		0			0
$385$	−36.7958	−	17.1070i	−1.87529	−	0.871856i
$386$	−6.35431	+	27.8400i	−0.323426	+	1.41702i
$387$		0			0
$388$	−3.53501	−	4.43276i	−0.179463	−	0.225039i
$389$	−5.85727	−	25.6624i	−0.296975	−	1.30113i	−0.874606	−	0.484835i	$-0.838880\pi$
$389$	−5.85727	−	25.6624i	−0.296975	−	1.30113i	0.577630	−	0.816299i	$-0.303978\pi$
$390$		0			0
$391$	−19.0643			−0.964123
$392$	−4.19243	+	20.9853i	−0.211750	+	1.05992i
$393$		0			0
$394$	−25.3085	−	12.1880i	−1.27503	−	0.614020i
$395$	−7.25452	−	31.7841i	−0.365015	−	1.59923i
$396$		0			0
$397$	4.99215	+	21.8720i	0.250549	+	1.09773i	0.931025	+	0.364955i	$0.118916\pi$
$397$	4.99215	+	21.8720i	0.250549	+	1.09773i	−0.680476	+	0.732770i	$0.738227\pi$
$398$	2.27545	−	9.96939i	0.114058	−	0.499720i
$399$		0			0
$400$	2.40811	+	10.5506i	0.120405	+	0.527530i
$401$	0.750294	−	0.361323i	0.0374679	−	0.0180436i	−0.415056	−	0.909796i	$-0.636238\pi$
$401$	0.750294	−	0.361323i	0.0374679	−	0.0180436i	0.452524	+	0.891752i	$0.350524\pi$
$402$		0			0
$403$	−4.17184	−	2.00905i	−0.207814	−	0.100078i
$404$	−0.0428311	+	0.0537085i	−0.00213093	+	0.00267210i
$405$		0			0
$406$	2.24709	+	9.26231i	0.111521	+	0.459681i
$407$	37.5799	−	18.0975i	1.86277	−	0.897060i
$408$		0			0
$409$	−4.18293	+	5.24523i	−0.206833	+	0.259360i	−0.874418	−	0.485173i	$-0.838756\pi$
$409$	−4.18293	+	5.24523i	−0.206833	+	0.259360i	0.667585	+	0.744533i	$0.267328\pi$
$410$	−2.79663			−0.138116
$411$		0			0
$412$	5.59313	−	7.01356i	0.275554	−	0.345533i
$413$	25.3157	+	11.7698i	1.24571	+	0.579152i
$414$		0			0
$415$	−28.4405	−	35.6633i	−1.39609	−	1.75064i
$416$	2.50079	−	1.20432i	0.122611	−	0.0590466i
$417$		0			0
$418$	−5.09510	−	6.38906i	−0.249210	−	0.312499i
$419$	13.0872	+	16.4108i	0.639352	+	0.801722i	0.990922	−	0.134439i	$-0.0429234\pi$
$419$	13.0872	+	16.4108i	0.639352	+	0.801722i	−0.351570	+	0.936162i	$0.614352\pi$
$420$		0			0
$421$	−8.66945	+	10.8711i	−0.422523	+	0.529827i	−0.946844	−	0.321694i	$-0.895748\pi$
$421$	−8.66945	+	10.8711i	−0.422523	+	0.529827i	0.524321	+	0.851521i	$0.324319\pi$
$422$	1.41009			0.0686419
$423$		0			0
$424$	10.1524	−	12.7307i	0.493043	−	0.618256i
$425$	4.82271	−	21.1297i	0.233936	−	1.02494i
$426$		0			0
$427$	19.1078	+	23.3028i	0.924693	+	1.12770i
$428$	−2.81390	−	1.35510i	−0.136015	−	0.0655015i
$429$		0			0
$430$	32.5688	+	15.6843i	1.57060	+	0.756363i
$431$	6.29114	−	27.5633i	0.303034	−	1.32768i	−0.562488	−	0.826806i	$-0.690156\pi$
$431$	6.29114	−	27.5633i	0.303034	−	1.32768i	0.865521	−	0.500872i	$-0.166987\pi$
$432$		0			0
$433$	−4.99627	−	21.8901i	−0.240105	−	1.05197i	−0.940921	−	0.338627i	$-0.890037\pi$
$433$	−4.99627	−	21.8901i	−0.240105	−	1.05197i	0.700815	−	0.713343i	$-0.252820\pi$
$434$	−8.81395	+	11.3663i	−0.423083	+	0.545597i
$435$		0			0
$436$	−0.943847	−	4.13526i	−0.0452021	−	0.198043i
$437$	−2.70829	−	3.39609i	−0.129555	−	0.162457i
$438$		0			0
$439$	−4.06481	−	1.95751i	−0.194003	−	0.0934269i	0.334360	−	0.942445i	$-0.391480\pi$
$439$	−4.06481	−	1.95751i	−0.194003	−	0.0934269i	−0.528363	+	0.849018i	$0.677194\pi$
$440$	46.8875			2.23527
$441$		0			0
$442$	7.30741			0.347578
$443$	28.9838	+	13.9579i	1.37706	+	0.663159i	0.968371	−	0.249514i	$-0.0802709\pi$
$443$	28.9838	+	13.9579i	1.37706	+	0.663159i	0.408692	+	0.912673i	$0.365985\pi$
$444$		0			0
$445$	11.9605	+	14.9981i	0.566984	+	0.710976i
$446$	−5.27724	−	23.1211i	−0.249885	−	1.09482i
$447$		0			0
$448$	−5.54463	−	22.8545i	−0.261959	−	1.07977i
$449$	−3.19454	−	13.9962i	−0.150760	−	0.660522i	−0.992665	−	0.120897i	$-0.961423\pi$
$449$	−3.19454	−	13.9962i	−0.150760	−	0.660522i	0.841905	−	0.539625i	$-0.181434\pi$
$450$		0			0
$451$	−0.874777	+	3.83265i	−0.0411916	+	0.180472i
$452$	−4.94235	−	2.38011i	−0.232469	−	0.111951i
$453$		0			0
$454$	−4.01280	−	1.93246i	−0.188330	−	0.0906950i
$455$	7.49690	+	3.48545i	0.351460	+	0.163401i
$456$		0			0
$457$	−0.844287	+	3.69906i	−0.0394941	+	0.173035i	−0.990828	−	0.135126i	$-0.956856\pi$
$457$	−0.844287	+	3.69906i	−0.0394941	+	0.173035i	0.951334	+	0.308160i	$0.0997134\pi$
$458$	3.62382	−	4.54413i	0.169330	−	0.212333i
$459$		0			0
$460$	4.80904			0.224223
$461$	16.4244	−	20.5956i	0.764963	−	0.959233i	−0.234956	−	0.972006i	$-0.575494\pi$
$461$	16.4244	−	20.5956i	0.764963	−	0.959233i	0.999918	+	0.0127730i	$0.00406589\pi$
$462$		0			0
$463$	−11.0811	−	13.8953i	−0.514984	−	0.645769i	0.454552	−	0.890720i	$-0.349799\pi$
$463$	−11.0811	−	13.8953i	−0.514984	−	0.645769i	−0.969535	+	0.244951i	$0.921228\pi$
$464$	−5.12521	−	6.42681i	−0.237932	−	0.298357i
$465$		0			0
$466$	−14.9149	+	7.18262i	−0.690918	+	0.332728i
$467$	11.6116	+	14.5605i	0.537322	+	0.673781i	0.974186	−	0.225747i	$-0.0724823\pi$
$467$	11.6116	+	14.5605i	0.537322	+	0.673781i	−0.436864	+	0.899528i	$0.643911\pi$
$468$		0			0
$469$	5.10718	−	23.8687i	0.235828	−	1.10215i
$470$	4.38640	−	5.50038i	0.202330	−	0.253713i
$471$		0			0
$472$	−32.2589			−1.48484
$473$	31.6820	−	39.7280i	1.45674	−	1.82669i
$474$		0			0
$475$	4.44912	−	2.14258i	0.204140	−	0.0983085i
$476$	−1.49233	+	6.97447i	−0.0684008	+	0.319674i
$477$		0			0
$478$	−8.63640	+	10.8297i	−0.395020	+	0.495339i
$479$	−15.6871	−	7.55451i	−0.716762	−	0.345175i	0.0397001	−	0.999212i	$-0.487360\pi$
$479$	−15.6871	−	7.55451i	−0.716762	−	0.345175i	−0.756462	+	0.654037i	$0.773074\pi$
$480$		0			0
$481$	−7.65666	+	3.68725i	−0.349114	+	0.168124i
$482$	−5.37868	−	23.5655i	−0.244992	−	1.07338i
$483$		0			0
$484$	1.65949	−	7.27071i	0.0754315	−	0.330487i
$485$	7.84646	+	34.3776i	0.356289	+	1.56101i
$486$		0			0
$487$	−3.89419	−	17.0615i	−0.176462	−	0.773132i	−0.983246	−	0.182285i	$-0.941651\pi$
$487$	−3.89419	−	17.0615i	−0.176462	−	0.773132i	0.806783	−	0.590847i	$-0.201206\pi$
$488$	−31.3725	−	15.1082i	−1.42017	−	0.683916i
$489$		0			0
$490$	15.4596	−	20.5066i	0.698394	−	0.926393i
$491$	−10.6417			−0.480254			−0.240127	−	0.970741i	$-0.577189\pi$
$491$	−10.6417			−0.480254			−0.240127	+	0.970741i	$0.577189\pi$
$492$		0			0
$493$	3.66327	+	16.0498i	0.164985	+	0.722848i
$494$	1.03810	+	1.30173i	0.0467061	+	0.0585676i
$495$		0			0
$496$	2.76040	−	12.0941i	0.123946	−	0.543041i
$497$	33.8690	−	16.8820i	1.51923	−	0.757261i
$498$		0			0
$499$	6.71375	−	3.23317i	0.300549	−	0.144737i	−0.277532	−	0.960717i	$-0.589516\pi$
$499$	6.71375	−	3.23317i	0.300549	−	0.144737i	0.578080	+	0.815980i	$0.303802\pi$
$500$	0.365680	−	1.60215i	0.0163537	−	0.0716503i
$501$		0			0
$502$	−8.71726	+	10.9311i	−0.389070	+	0.487879i
$503$	−24.0479	−	11.5809i	−1.07224	−	0.516365i	−0.187414	−	0.982281i	$-0.560011\pi$
$503$	−24.0479	−	11.5809i	−1.07224	−	0.516365i	−0.884829	+	0.465916i	$0.845725\pi$
$504$		0			0
$505$	0.384930	−	0.185372i	0.0171291	−	0.00824896i
$506$	−4.78730	+	20.9745i	−0.212822	+	0.932432i
$507$		0			0
$508$	−8.13155			−0.360779
$509$	−32.4950			−1.44031			−0.720157	−	0.693811i	$-0.755930\pi$
$509$	−32.4950			−1.44031			−0.720157	+	0.693811i	$0.755930\pi$
$510$		0			0
$511$	0.900685	+	3.71255i	0.0398440	+	0.164233i
$512$	15.3676	+	19.2704i	0.679159	+	0.851638i
$513$		0			0
$514$	4.51255	−	2.17313i	0.199040	−	0.0958527i
$515$	−50.2663	+	24.2070i	−2.21500	+	1.06669i
$516$		0			0
$517$	−6.16596	−	7.73187i	−0.271178	−	0.340047i
$518$	6.22373	+	25.6537i	0.273455	+	1.12716i
$519$		0			0
$520$	−9.55303			−0.418928
$521$	−29.7326			−1.30261			−0.651303	−	0.758817i	$-0.725778\pi$
$521$	−29.7326			−1.30261			−0.651303	+	0.758817i	$0.725778\pi$
$522$		0			0
$523$	3.06418	−	13.4250i	0.133987	−	0.587036i	−0.862701	−	0.505715i	$-0.831229\pi$
$523$	3.06418	−	13.4250i	0.133987	−	0.587036i	0.996688	−	0.0813213i	$-0.0259140\pi$
$524$	5.08487	−	2.44874i	0.222134	−	0.106974i
$525$		0			0
$526$	−16.1767	−	7.79029i	−0.705338	−	0.339673i
$527$	−15.4898	+	19.4236i	−0.674746	+	0.846105i
$528$		0			0
$529$	2.57330	−	11.2744i	0.111883	−	0.490191i
$530$	−17.6055	+	8.47838i	−0.764735	+	0.368277i
$531$		0			0
$532$	−1.45442	+	0.724957i	−0.0630572	+	0.0314309i
$533$	0.178230	−	0.780878i	0.00772001	−	0.0338236i
$534$		0			0
$535$	12.1107	+	15.1864i	0.523592	+	0.656564i
$536$	6.27604	+	27.4971i	0.271083	+	1.18769i
$537$		0			0
$538$	18.2541			0.786990
$539$	−23.2676	−	27.6011i	−1.00221	−	1.18886i
$540$		0			0
$541$	33.8804	+	16.3159i	1.45663	+	0.701476i	0.983732	−	0.179641i	$-0.0574936\pi$
$541$	33.8804	+	16.3159i	1.45663	+	0.701476i	0.472898	+	0.881117i	$0.343208\pi$
$542$	0.231354	+	1.01363i	0.00993750	+	0.0435390i
$543$		0			0
$544$	−3.31388	−	14.5191i	−0.142082	−	0.622500i
$545$	−5.87007	+	25.7184i	−0.251446	+	1.10166i
$546$		0			0
$547$	3.51386	+	15.3952i	0.150242	+	0.658252i	0.992814	+	0.119668i	$0.0381832\pi$
$547$	3.51386	+	15.3952i	0.150242	+	0.658252i	−0.842572	+	0.538583i	$0.818960\pi$
$548$	0.427526	−	0.205886i	0.0182630	−	0.00879499i
$549$		0			0
$550$	−22.0358	−	10.6119i	−0.939609	−	0.452492i
$551$	−2.33868	+	2.93262i	−0.0996313	+	0.124934i
$552$		0			0
$553$	6.06855	−	28.3617i	0.258061	−	1.20606i
$554$	10.0312	−	4.83079i	0.426186	−	0.205241i
$555$		0			0
$556$	2.53135	−	3.17421i	0.107353	−	0.134616i
$557$	9.87986			0.418623			0.209311	−	0.977849i	$-0.432878\pi$
$557$	9.87986			0.418623			0.209311	+	0.977849i	$0.432878\pi$
$558$		0			0
$559$	−6.45501	+	8.09432i	−0.273018	+	0.342353i
$560$	−4.63437	+	21.6590i	−0.195838	+	0.915258i
$561$		0			0
$562$	14.3723	+	18.0223i	0.606260	+	0.760226i
$563$	−3.72115	+	1.79201i	−0.156828	+	0.0755242i	−0.510651	−	0.859788i	$-0.670596\pi$
$563$	−3.72115	+	1.79201i	−0.156828	+	0.0755242i	0.353824	+	0.935312i	$0.384881\pi$
$564$		0			0
$565$	21.2713	+	26.6734i	0.894891	+	1.12216i
$566$	−21.7444	−	27.2666i	−0.913984	−	1.14610i
$567$		0			0
$568$	−27.2636	+	34.1875i	−1.14396	+	1.43447i
$569$	13.2235			0.554359			0.277180	−	0.960818i	$-0.410600\pi$
$569$	13.2235			0.554359			0.277180	+	0.960818i	$0.410600\pi$
$570$		0			0
$571$	−15.7223	+	19.7152i	−0.657959	+	0.825055i	−0.993119	−	0.117106i	$-0.962638\pi$
$571$	−15.7223	+	19.7152i	−0.657959	+	0.825055i	0.335160	+	0.942161i	$0.391210\pi$
$572$	−0.576585	+	2.52618i	−0.0241082	+	0.105625i
$573$		0			0
$574$	−2.25609	−	1.04890i	−0.0941672	−	0.0437801i
$575$	−11.7131	−	5.64071i	−0.488469	−	0.235234i
$576$		0			0
$577$	29.9662	+	14.4310i	1.24751	+	0.600769i	0.936843	−	0.349750i	$-0.113733\pi$
$577$	29.9662	+	14.4310i	1.24751	+	0.600769i	0.310666	+	0.950519i	$0.399448\pi$
$578$	4.05773	−	17.7781i	0.168780	−	0.739471i
$579$		0			0
$580$	−0.924072	−	4.04863i	−0.0383700	−	0.168110i
$581$	−9.56765	−	39.4370i	−0.396933	−	1.63612i
$582$		0			0
$583$	6.11226	+	26.7796i	0.253144	+	1.10910i
$584$	−2.75223	−	3.45119i	−0.113888	−	0.142811i
$585$		0			0
$586$	−27.1840	−	13.0911i	−1.12296	−	0.540790i
$587$	5.62433			0.232141			0.116070	−	0.993241i	$-0.462970\pi$
$587$	5.62433			0.232141			0.116070	+	0.993241i	$0.462970\pi$
$588$		0			0
$589$	−5.66058			−0.233240
$590$	34.8787	+	16.7967i	1.43593	+	0.691509i
$591$		0			0
$592$	−14.1952	−	17.8002i	−0.583420	−	0.731586i
$593$	−3.52418	−	15.4404i	−0.144721	−	0.634063i	−0.994302	−	0.106604i	$-0.966002\pi$
$593$	−3.52418	−	15.4404i	−0.144721	−	0.634063i	0.849581	−	0.527458i	$-0.176855\pi$
$594$		0			0
$595$	27.1824	−	35.0537i	1.11437	−	1.43706i
$596$	−1.14025	−	4.99576i	−0.0467064	−	0.204634i
$597$		0			0
$598$	0.975383	−	4.27343i	0.0398864	−	0.174754i
$599$	−33.7420	−	16.2493i	−1.37866	−	0.663928i	−0.409948	−	0.912109i	$-0.634453\pi$
$599$	−33.7420	−	16.2493i	−1.37866	−	0.663928i	−0.968714	+	0.248181i	$0.920167\pi$
$600$		0			0
$601$	15.6904	+	7.55608i	0.640024	+	0.308219i	0.725604	−	0.688112i	$-0.241560\pi$
$601$	15.6904	+	7.55608i	0.640024	+	0.308219i	−0.0855808	+	0.996331i	$0.527275\pi$
$602$	20.3912	+	24.8679i	0.831085	+	1.01354i
$603$		0			0
$604$	−0.171138	+	0.749806i	−0.00696352	+	0.0305092i
$605$	−28.9185	+	36.2626i	−1.17570	+	1.47429i
$606$		0			0
$607$	11.0878			0.450041			0.225021	−	0.974354i	$-0.427755\pi$
$607$	11.0878			0.450041			0.225021	+	0.974354i	$0.427755\pi$
$608$	2.11563	−	2.65292i	0.0858002	−	0.107590i
$609$		0			0
$610$	26.0537	+	32.6704i	1.05489	+	1.32278i
$611$	1.25627	+	1.57532i	0.0508234	+	0.0637306i
$612$		0			0
$613$	−11.6730	+	5.62142i	−0.471468	+	0.227047i	−0.654503	−	0.756059i	$-0.727122\pi$
$613$	−11.6730	+	5.62142i	−0.471468	+	0.227047i	0.183035	+	0.983106i	$0.441408\pi$
$614$	−6.12274	−	7.67768i	−0.247094	−	0.309846i
$615$		0			0
$616$	37.8249	+	17.5855i	1.52401	+	0.708540i
$617$	6.34070	−	7.95099i	0.255267	−	0.320095i	−0.637641	−	0.770333i	$-0.720090\pi$
$617$	6.34070	−	7.95099i	0.255267	−	0.320095i	0.892908	+	0.450239i	$0.148661\pi$
$618$		0			0
$619$	−43.4925			−1.74811			−0.874055	−	0.485827i	$-0.838519\pi$
$619$	−43.4925			−1.74811			−0.874055	+	0.485827i	$0.838519\pi$
$620$	3.90736	−	4.89967i	0.156923	−	0.196775i
$621$		0			0
$622$	6.44393	−	3.10323i	0.258378	−	0.124428i
$623$	4.02364	+	16.5851i	0.161204	+	0.664467i
$624$		0			0
$625$	−18.3571	+	23.0191i	−0.734285	+	0.920765i
$626$	5.29713	+	2.55096i	0.211716	+	0.101957i
$627$		0			0
$628$	−4.47211	+	2.15365i	−0.178456	+	0.0859401i
$629$	10.1461	+	44.4529i	0.404551	+	1.77245i
$630$		0			0
$631$	2.60596	−	11.4175i	0.103742	−	0.454522i	−0.896199	−	0.443652i	$-0.853683\pi$
$631$	2.60596	−	11.4175i	0.103742	−	0.454522i	0.999941	−	0.0108703i	$-0.00346019\pi$
$632$	7.45742	+	32.6731i	0.296640	+	1.29967i
$633$		0			0
$634$	1.35302	+	5.92797i	0.0537353	+	0.235430i
$635$	45.5643	+	21.9426i	1.80816	+	0.870766i
$636$		0			0
$637$	4.74063	+	5.62355i	0.187831	+	0.222813i
$638$	18.5779			0.735506
$639$		0			0
$640$	−3.76019	−	16.4745i	−0.148634	−	0.651210i
$641$	7.30584	+	9.16123i	0.288563	+	0.361847i	0.904891	−	0.425643i	$-0.139952\pi$
$641$	7.30584	+	9.16123i	0.288563	+	0.361847i	−0.616328	+	0.787489i	$0.711380\pi$
$642$		0			0
$643$	−9.15257	+	40.1000i	−0.360942	+	1.58139i	0.389866	+	0.920871i	$0.372521\pi$
$643$	−9.15257	+	40.1000i	−0.360942	+	1.58139i	−0.750809	+	0.660520i	$0.770336\pi$
$644$	3.87953	+	1.80367i	0.152875	+	0.0710745i
$645$		0			0
$646$	8.04852	−	3.87596i	0.316665	−	0.152498i
$647$	−3.67409	+	16.0972i	−0.144443	+	0.632847i	0.849928	+	0.526898i	$0.176645\pi$
$647$	−3.67409	+	16.0972i	−0.144443	+	0.632847i	−0.994372	+	0.105949i	$0.966212\pi$
$648$		0			0
$649$	33.9291	−	42.5457i	1.33183	−	1.67006i
$650$	4.48966	+	2.16210i	0.176099	+	0.0848047i
$651$		0			0
$652$	8.85776	−	4.26567i	0.346897	−	0.167057i
$653$	4.12713	−	18.0821i	0.161507	−	0.707609i	−0.827710	−	0.561155i	$-0.810357\pi$
$653$	4.12713	−	18.0821i	0.161507	−	0.707609i	0.989218	−	0.146453i	$-0.0467859\pi$
$654$		0			0
$655$	−35.1004			−1.37148
$656$	2.14582			0.0837803
$657$		0			0
$658$	5.60155	−	2.79209i	0.218371	−	0.108847i
$659$	−4.77391	−	5.98629i	−0.185965	−	0.233193i	0.680106	−	0.733114i	$-0.261934\pi$
$659$	−4.77391	−	5.98629i	−0.185965	−	0.233193i	−0.866071	+	0.499921i	$0.833362\pi$
$660$		0			0
$661$	23.5856	−	11.3582i	0.917375	−	0.441784i	0.0852417	−	0.996360i	$-0.472834\pi$
$661$	23.5856	−	11.3582i	0.917375	−	0.441784i	0.832133	+	0.554576i	$0.187119\pi$
$662$	7.09038	−	3.41455i	0.275575	−	0.132710i
$663$		0			0
$664$	29.2360	+	36.6608i	1.13458	+	1.42271i
$665$	10.1060	−	0.137530i	0.391893	−	0.00533317i
$666$		0			0
$667$	9.87503			0.382363
$668$	3.00015			0.116079
$669$		0			0
$670$	7.53159	−	32.9981i	0.290971	−	1.27483i
$671$	52.9227	−	25.4862i	2.04306	−	0.983886i
$672$		0			0
$673$	15.4940	+	7.46150i	0.597249	+	0.287620i	0.707982	−	0.706230i	$-0.249606\pi$
$673$	15.4940	+	7.46150i	0.597249	+	0.287620i	−0.110734	+	0.993850i	$0.535320\pi$
$674$	−13.4373	+	16.8499i	−0.517586	+	0.649033i
$675$		0			0
$676$	−1.26580	+	5.54581i	−0.0486844	+	0.213300i
$677$	16.0190	−	7.71433i	0.615659	−	0.296486i	−0.0999440	−	0.994993i	$-0.531866\pi$
$677$	16.0190	−	7.71433i	0.615659	−	0.296486i	0.715603	+	0.698507i	$0.246152\pi$
$678$		0			0
$679$	−6.56371	+	30.6758i	−0.251892	+	1.17723i
$680$	−11.4054	+	49.9703i	−0.437377	+	1.91627i
$681$		0			0
$682$	17.4801	+	21.9194i	0.669348	+	0.839336i
$683$	3.44839	+	15.1084i	0.131949	+	0.578105i	0.997067	+	0.0765370i	$0.0243863\pi$
$683$	3.44839	+	15.1084i	0.131949	+	0.578105i	−0.865118	+	0.501568i	$0.832757\pi$
$684$		0			0
$685$	−2.95117			−0.112758
$686$	20.1627	−	10.7448i	0.769815	−	0.410237i
$687$		0			0
$688$	−24.9897	−	12.0344i	−0.952722	−	0.458807i
$689$	−1.24534	−	5.45617i	−0.0474435	−	0.207864i
$690$		0			0
$691$	5.14623	+	22.5471i	0.195772	+	0.857732i	0.973419	+	0.229031i	$0.0735559\pi$
$691$	5.14623	+	22.5471i	0.195772	+	0.857732i	−0.777647	+	0.628701i	$0.783587\pi$
$692$	−1.24492	+	5.45436i	−0.0473249	+	0.207344i
$693$		0			0
$694$	−1.90284	−	8.33690i	−0.0722309	−	0.316464i
$695$	−22.7496	+	10.9556i	−0.862941	+	0.415571i
$696$		0			0
$697$	−3.87185	−	1.86459i	−0.146657	−	0.0706262i
$698$	7.02997	−	8.81531i	0.266088	−	0.333664i
$699$		0			0
$700$	−2.98048	+	3.84355i	−0.112651	+	0.145273i
$701$	4.77069	−	2.29744i	0.180186	−	0.0867732i	−0.341616	−	0.939840i	$-0.610974\pi$
$701$	4.77069	−	2.29744i	0.180186	−	0.0867732i	0.521802	+	0.853066i	$0.325260\pi$
$702$		0			0
$703$	−6.47742	+	8.12242i	−0.244300	+	0.306343i
$704$	−45.8404			−1.72768
$705$		0			0
$706$	−6.31698	+	7.92125i	−0.237743	+	0.298120i
$707$	0.380054	−	0.00517206i	0.0142934	−	0.000194515i
$708$		0			0
$709$	14.1199	+	17.7057i	0.530282	+	0.664953i	0.972757	−	0.231828i	$-0.0744706\pi$
$709$	14.1199	+	17.7057i	0.530282	+	0.664953i	−0.442474	+	0.896781i	$0.645899\pi$
$710$	47.2786	−	22.7682i	1.77434	−	0.854475i
$711$		0			0
$712$	−12.2951	−	15.4175i	−0.460777	−	0.577797i
$713$	9.29151	+	11.6512i	0.347970	+	0.436340i
$714$		0			0
$715$	10.0476	−	12.5993i	0.375760	−	0.471188i
$716$	−2.17118			−0.0811407
$717$		0			0
$718$	3.23423	−	4.05560i	0.120701	−	0.151354i
$719$	−3.97112	+	17.3986i	−0.148098	+	0.648859i	0.845315	+	0.534268i	$0.179413\pi$
$719$	−3.97112	+	17.3986i	−0.148098	+	0.648859i	−0.993413	+	0.114591i	$0.963444\pi$
$720$		0			0
$721$	−49.6296	+	0.675397i	−1.84830	+	0.0251531i
$722$	−19.2838	−	9.28658i	−0.717668	−	0.345611i
$723$		0			0
$724$	−3.27732	−	1.57827i	−0.121801	−	0.0586561i
$725$	−2.49809	+	10.9449i	−0.0927768	+	0.406482i
$726$		0			0
$727$	0.498257	+	2.18301i	0.0184793	+	0.0809632i	0.983327	−	0.181847i	$-0.0582077\pi$
$727$	0.498257	+	2.18301i	0.0184793	+	0.0809632i	−0.964847	+	0.262811i	$0.915351\pi$
$728$	−7.70659	−	3.58294i	−0.285625	−	0.132793i
$729$		0			0
$730$	1.17877	+	5.16452i	0.0436282	+	0.191147i
$731$	34.6334	+	43.4289i	1.28096	+	1.60628i
$732$		0			0
$733$	7.26142	+	3.49691i	0.268207	+	0.129161i	0.563154	−	0.826352i	$-0.309588\pi$
$733$	7.26142	+	3.49691i	0.268207	+	0.129161i	−0.294947	+	0.955514i	$0.595302\pi$
$734$	26.0002			0.959684
$735$		0			0
$736$	−8.93320			−0.329282
$737$	−42.8664	−	20.6434i	−1.57901	−	0.760409i
$738$		0			0
$739$	7.91010	+	9.91896i	0.290978	+	0.364875i	0.905737	−	0.423840i	$-0.139318\pi$
$739$	7.91010	+	9.91896i	0.290978	+	0.364875i	−0.614759	+	0.788715i	$0.710747\pi$
$740$	−2.55939	−	11.2134i	−0.0940850	−	0.412213i
$741$		0			0
$742$	−17.3826	+	0.236555i	−0.638134	+	0.00868420i
$743$	10.7100	+	46.9236i	0.392912	+	1.72146i	0.654308	+	0.756228i	$0.272960\pi$
$743$	10.7100	+	46.9236i	0.392912	+	1.72146i	−0.261396	+	0.965232i	$0.584183\pi$
$744$		0			0
$745$	−7.09155	+	31.0701i	−0.259814	+	1.13832i
$746$	1.22539	+	0.590118i	0.0448648	+	0.0216058i
$747$		0			0
$748$	12.5257	+	6.03204i	0.457984	+	0.220553i
$749$	4.07416	+	16.7933i	0.148866	+	0.613615i
$750$		0			0
$751$	7.18712	−	31.4888i	0.262262	−	1.14904i	−0.656530	−	0.754300i	$-0.727976\pi$
$751$	7.18712	−	31.4888i	0.262262	−	1.14904i	0.918792	−	0.394743i	$-0.129166\pi$
$752$	−3.36564	+	4.22038i	−0.122732	+	0.153901i
$753$		0			0
$754$	−3.78513			−0.137846
$755$	2.98227	−	3.73965i	0.108536	−	0.136100i
$756$		0			0
$757$	−2.75792	−	3.45832i	−0.100238	−	0.125695i	0.729182	−	0.684319i	$-0.239901\pi$
$757$	−2.75792	−	3.45832i	−0.100238	−	0.125695i	−0.829420	+	0.558625i	$0.811329\pi$
$758$	−5.30897	−	6.65724i	−0.192831	−	0.241802i
$759$		0			0
$760$	−10.5219	+	5.06707i	−0.381669	+	0.183802i
$761$	−23.8152	−	29.8634i	−0.863301	−	1.08255i	−0.995817	−	0.0913648i	$-0.970877\pi$
$761$	−23.8152	−	29.8634i	−0.863301	−	1.08255i	0.132516	−	0.991181i	$-0.457694\pi$
$762$		0			0
$763$	−14.3814	+	18.5459i	−0.520641	+	0.671406i
$764$	0.698772	−	0.876232i	0.0252807	−	0.0317010i
$765$		0			0
$766$	−37.9014			−1.36943
$767$	−6.91283	+	8.66842i	−0.249608	+	0.312998i
$768$		0			0
$769$	−43.4807	+	20.9392i	−1.56796	+	0.755088i	−0.997790	−	0.0664425i	$-0.978835\pi$
$769$	−43.4807	+	20.9392i	−1.56796	+	0.755088i	−0.570165	+	0.821530i	$0.693121\pi$
$770$	−31.7402	−	38.7085i	−1.14384	−	1.39496i
$771$		0			0
$772$	6.90142	−	8.65410i	0.248387	−	0.311468i
$773$	−27.2954	−	13.1448i	−0.981747	−	0.472784i	−0.127041	−	0.991897i	$-0.540548\pi$
$773$	−27.2954	−	13.1448i	−0.981747	−	0.472784i	−0.854706	+	0.519113i	$0.826262\pi$
$774$		0			0
$775$	−15.2639	+	7.35071i	−0.548296	+	0.264045i
$776$	−8.06591	−	35.3391i	−0.289549	−	1.26860i
$777$		0			0
$778$	7.22564	−	31.6576i	0.259052	−	1.13498i
$779$	−0.217883	−	0.954610i	−0.00780648	−	0.0342024i
$780$		0			0
$781$	−16.4141	−	71.9150i	−0.587344	−	2.57332i
$782$	−21.1891	−	10.2041i	−0.757720	−	0.364899i
$783$		0			0
$784$	−11.8620	+	15.7345i	−0.423643	+	0.561946i
$785$	30.8705			1.10182
$786$		0			0
$787$	0.771904	+	3.38193i	0.0275154	+	0.120553i	0.986820	−	0.161819i	$-0.0517360\pi$
$787$	0.771904	+	3.38193i	0.0275154	+	0.120553i	−0.959305	+	0.282372i	$0.908879\pi$
$788$	6.78889	+	8.51299i	0.241844	+	0.303263i
$789$		0			0
$790$	8.94932	−	39.2095i	0.318403	−	1.39501i
$791$	7.15586	+	29.4959i	0.254433	+	1.04875i
$792$		0			0
$793$	−10.7827	+	5.19266i	−0.382904	+	0.184397i
$794$	−6.15841	+	26.9818i	−0.218554	+	0.957547i
$795$		0			0
$796$	−2.47137	+	3.09899i	−0.0875952	+	0.109841i
$797$	10.6816	+	5.14401i	0.378363	+	0.182210i	0.613393	−	0.789778i	$-0.289804\pi$
$797$	10.6816	+	5.14401i	0.378363	+	0.182210i	−0.235029	+	0.971988i	$0.575519\pi$
$798$		0			0
$799$	9.74010	−	4.69058i	0.344580	−	0.165941i
$800$	2.25984	−	9.90099i	0.0798973	−	0.350053i
$801$		0			0
$802$	1.02731			0.0362757
$803$	7.44645			0.262779
$804$		0			0
$805$	−16.8714	−	20.5754i	−0.594640	−	0.725188i
$806$	−3.56147	−	4.46594i	−0.125447	−	0.157306i
$807$		0			0
$808$	−0.395696	+	0.190557i	−0.0139205	+	0.00670377i
$809$	−32.0177	+	15.4189i	−1.12568	+	0.542101i	−0.901644	−	0.432479i	$-0.857639\pi$
$809$	−32.0177	+	15.4189i	−1.12568	+	0.542101i	−0.224040	+	0.974580i	$0.571925\pi$
$810$		0			0
$811$	−6.70537	−	8.40826i	−0.235457	−	0.295254i	0.650039	−	0.759901i	$-0.274753\pi$
$811$	−6.70537	−	8.40826i	−0.235457	−	0.295254i	−0.885496	+	0.464647i	$0.846181\pi$
$812$	0.773004	−	3.61267i	0.0271271	−	0.126780i
$813$		0			0
$814$	51.4549			1.80349
$815$	−61.1442			−2.14179
$816$		0			0
$817$	−2.81631	+	12.3391i	−0.0985303	+	0.431690i
$818$	−7.45663	+	3.59092i	−0.260715	+	0.125554i
$819$		0			0
$820$	0.976688	+	0.470348i	0.0341074	+	0.0164253i
$821$	−12.8698	+	16.1382i	−0.449160	+	0.563229i	−0.953932	−	0.300024i	$-0.903005\pi$
$821$	−12.8698	+	16.1382i	−0.449160	+	0.563229i	0.504772	+	0.863253i	$0.331577\pi$
$822$		0			0
$823$	4.33348	−	18.9862i	0.151056	−	0.661818i	−0.841524	−	0.540220i	$-0.818341\pi$
$823$	4.33348	−	18.9862i	0.151056	−	0.661818i	0.992579	−	0.121598i	$-0.0388019\pi$
$824$	51.6722	−	24.8840i	1.80009	−	0.866875i
$825$		0			0
$826$	21.8375	+	26.6317i	0.759824	+	0.926636i
$827$	−1.87421	+	8.21146i	−0.0651728	+	0.285540i	−0.997004	−	0.0773517i	$-0.975354\pi$
$827$	−1.87421	+	8.21146i	−0.0651728	+	0.285540i	0.931831	+	0.362892i	$0.118211\pi$
$828$		0			0
$829$	−11.2163	−	14.0648i	−0.389559	−	0.488491i	0.547922	−	0.836530i	$-0.315419\pi$
$829$	−11.2163	−	14.0648i	−0.389559	−	0.488491i	−0.937480	+	0.348039i	$0.886848\pi$
$830$	−12.5216	−	54.8608i	−0.434632	−	1.90425i
$831$		0			0
$832$	9.33970			0.323796
$833$	35.0757	−	18.0835i	1.21530	−	0.626555i
$834$		0			0
$835$	−16.8110	−	8.09576i	−0.581769	−	0.280165i
$836$	0.704866	+	3.08822i	0.0243783	+	0.106808i
$837$		0			0
$838$	5.76196	+	25.2448i	0.199044	+	0.872067i
$839$	9.37250	−	41.0636i	0.323575	−	1.41767i	−0.507567	−	0.861612i	$-0.669455\pi$
$839$	9.37250	−	41.0636i	0.323575	−	1.41767i	0.831142	−	0.556061i	$-0.187688\pi$
$840$		0			0
$841$	4.55559	+	19.9593i	0.157089	+	0.688253i
$842$	−15.4544	+	7.44247i	−0.532595	+	0.256484i
$843$		0			0
$844$	−0.492455	−	0.237154i	−0.0169510	−	0.00816318i
$845$	22.0579	−	27.6597i	0.758814	−	0.951522i
$846$		0			0
$847$	−36.9296	+	18.4076i	−1.26892	+	0.632491i
$848$	13.5085	−	6.50537i	0.463885	−	0.223395i
$849$		0			0
$850$	16.6698	−	20.9033i	0.571770	−	0.716977i
$851$	27.3507			0.937570
$852$		0			0
$853$	32.8153	−	41.1491i	1.12357	−	1.40892i	0.222674	−	0.974893i	$-0.428521\pi$
$853$	32.8153	−	41.1491i	1.12357	−	1.40892i	0.900901	−	0.434026i	$-0.142907\pi$
$854$	8.76471	+	36.1274i	0.299922	+	1.23625i
$855$		0			0
$856$	−12.4495	−	15.6111i	−0.425514	−	0.533577i
$857$	−27.6171	+	13.2997i	−0.943381	+	0.454308i	−0.841361	−	0.540474i	$-0.818245\pi$
$857$	−27.6171	+	13.2997i	−0.943381	+	0.454308i	−0.102020	+	0.994782i	$0.532531\pi$
$858$		0			0
$859$	−28.5614	−	35.8149i	−0.974504	−	1.22199i	−0.975049	−	0.221989i	$-0.928745\pi$
$859$	−28.5614	−	35.8149i	−0.974504	−	1.22199i	0.000545133	−	1.00000i	$-0.499826\pi$
$860$	−8.73640	−	10.9551i	−0.297909	−	0.373566i
$861$		0			0
$862$	21.7455	−	27.2680i	0.740655	−	0.928752i
$863$	5.55423			0.189068			0.0945341	−	0.995522i	$-0.469864\pi$
$863$	5.55423			0.189068			0.0945341	+	0.995522i	$0.469864\pi$
$864$		0			0
$865$	21.6941	−	27.2036i	0.737623	−	0.924949i
$866$	6.16350	−	27.0040i	0.209444	−	0.917635i
$867$		0			0
$868$	4.98979	−	2.48716i	0.169364	−	0.0844197i
$869$	−50.9355	−	24.5293i	−1.72787	−	0.832098i
$870$		0			0
$871$	8.73377	+	4.20596i	0.295932	+	0.142514i
$872$	6.03425	−	26.4378i	0.204345	−	0.895296i
$873$		0			0
$874$	−1.19239	−	5.22420i	−0.0403331	−	0.176711i
$875$	−8.13768	+	4.05623i	−0.275104	+	0.137125i
$876$		0			0
$877$	7.21261	+	31.6005i	0.243552	+	1.06707i	0.937756	+	0.347294i	$0.112899\pi$
$877$	7.21261	+	31.6005i	0.243552	+	1.06707i	−0.694204	+	0.719778i	$0.744243\pi$
$878$	−3.47010	−	4.35136i	−0.117110	−	0.146851i
$879$		0			0
$880$	38.8980	+	18.7323i	1.31125	+	0.631465i
$881$	2.36116			0.0795496			0.0397748	−	0.999209i	$-0.487336\pi$
$881$	2.36116			0.0795496			0.0397748	+	0.999209i	$0.487336\pi$
$882$		0			0
$883$	−12.4422			−0.418712			−0.209356	−	0.977839i	$-0.567137\pi$
$883$	−12.4422			−0.418712			−0.209356	+	0.977839i	$0.567137\pi$
$884$	−2.55203	−	1.22899i	−0.0858339	−	0.0413354i
$885$		0			0
$886$	24.7432	+	31.0270i	0.831265	+	1.04237i
$887$	9.86596	+	43.2256i	0.331267	+	1.45137i	0.816681	+	0.577089i	$0.195812\pi$
$887$	9.86596	+	43.2256i	0.331267	+	1.45137i	−0.485415	+	0.874284i	$0.661331\pi$
$888$		0			0
$889$	28.5277	+	34.7907i	0.956790	+	1.16684i
$890$	5.26592	+	23.0715i	0.176514	+	0.773358i
$891$		0			0
$892$	−2.04559	+	8.96232i	−0.0684915	+	0.300081i
$893$	2.21926	+	1.06874i	0.0742647	+	0.0357640i
$894$		0			0
$895$	12.1660	+	5.85882i	0.406663	+	0.195839i
$896$	3.14547	−	14.7005i	0.105083	−	0.491109i
$897$		0			0
$898$	3.94085	−	17.2660i	0.131508	−	0.576174i
$899$	8.02348	−	10.0611i	0.267598	−	0.335557i
$900$		0			0
$901$	−30.0271			−1.00035
$902$	−3.02369	+	3.79159i	−0.100678	+	0.126246i
$903$		0			0
$904$	−21.8663	−	27.4194i	−0.727261	−	0.911957i
$905$	14.1052	+	17.6874i	0.468873	+	0.587948i
$906$		0			0
$907$	46.9278	−	22.5992i	1.55821	−	0.750396i	0.561203	−	0.827678i	$-0.310339\pi$
$907$	46.9278	−	22.5992i	1.55821	−	0.750396i	0.997009	+	0.0772825i	$0.0246243\pi$
$908$	1.07641	+	1.34978i	0.0357220	+	0.0447940i
$909$		0			0
$910$	6.46688	+	7.88662i	0.214375	+	0.261439i
$911$	17.8401	−	22.3707i	0.591068	−	0.741176i	−0.392888	−	0.919586i	$-0.628524\pi$
$911$	17.8401	−	22.3707i	0.591068	−	0.741176i	0.983956	+	0.178411i	$0.0570955\pi$
$912$		0			0
$913$	−79.1009			−2.61786
$914$	−2.91830	+	3.65943i	−0.0965288	+	0.121043i
$915$		0			0
$916$	−2.02982	+	0.977512i	−0.0670673	+	0.0322979i
$917$	−28.3160	−	13.1647i	−0.935078	−	0.434735i
$918$		0			0
$919$	14.7853	−	18.5402i	0.487724	−	0.611586i	−0.475687	−	0.879614i	$-0.657801\pi$
$919$	14.7853	−	18.5402i	0.487724	−	0.611586i	0.963411	+	0.268028i	$0.0863721\pi$
$920$	27.7006	+	13.3399i	0.913263	+	0.439804i
$921$		0			0
$922$	29.2788	−	14.0999i	0.964245	−	0.464356i
$923$	3.34428	+	14.6522i	0.110078	+	0.482284i
$924$		0			0
$925$	−6.91892	+	30.3138i	−0.227493	+	0.996711i
$926$	−4.87873	−	21.3751i	−0.160325	−	0.702430i
$927$		0			0
$928$	1.71654	+	7.52066i	0.0563483	+	0.246878i
$929$	−9.86015	−	4.74840i	−0.323501	−	0.155790i	0.265084	−	0.964225i	$-0.414600\pi$
$929$	−9.86015	−	4.74840i	−0.323501	−	0.155790i	−0.588585	+	0.808435i	$0.700315\pi$
$930$		0			0
$931$	8.20424	+	3.67938i	0.268883	+	0.120587i
$932$	6.41684			0.210191
$933$		0			0
$934$	5.11230	+	22.3984i	0.167279	+	0.732899i
$935$	−53.9091	−	67.5998i	−1.76301	−	2.21075i
$936$		0			0
$937$	4.23074	−	18.5361i	0.138212	−	0.605547i	−0.857615	−	0.514292i	$-0.828055\pi$
$937$	4.23074	−	18.5361i	0.138212	−	0.605547i	0.995828	−	0.0912556i	$-0.0290880\pi$
$938$	18.4520	−	23.7953i	0.602481	−	0.776944i
$939$		0			0
$940$	−2.45698	+	1.18322i	−0.0801377	+	0.0385923i
$941$	−5.55962	+	24.3583i	−0.181239	+	0.794058i	0.799803	+	0.600262i	$0.204937\pi$
$941$	−5.55962	+	24.3583i	−0.181239	+	0.794058i	−0.981042	+	0.193796i	$0.937920\pi$
$942$		0			0
$943$	−1.60723	+	2.01541i	−0.0523387	+	0.0656307i
$944$	−26.7621	−	12.8879i	−0.871031	−	0.419467i
$945$		0			0
$946$	56.4774	−	27.1981i	1.83624	−	0.884285i
$947$	1.77241	−	7.76546i	0.0575957	−	0.252343i	−0.937931	−	0.346821i	$-0.887261\pi$
$947$	1.77241	−	7.76546i	0.0575957	−	0.252343i	0.995527	+	0.0944779i	$0.0301182\pi$
$948$		0			0
$949$	−1.51717			−0.0492493
$950$	6.09180			0.197644
$951$		0			0
$952$	−27.9427	+	36.0342i	−0.905627	+	1.16787i
$953$	6.38288	+	8.00388i	0.206762	+	0.259271i	0.874390	−	0.485224i	$-0.161262\pi$
$953$	6.38288	+	8.00388i	0.206762	+	0.259271i	−0.667628	+	0.744495i	$0.732690\pi$
$954$		0			0
$955$	−6.27997	+	3.02427i	−0.203215	+	0.0978632i
$956$	4.83754	−	2.32964i	0.156457	−	0.0753459i
$957$		0			0
$958$	−13.3920	−	16.7930i	−0.432674	−	0.542556i
$959$	−2.38076	−	1.10686i	−0.0768786	−	0.0357423i
$960$		0			0
$961$	−11.5799			−0.373544
$962$	−10.4836			−0.338005
$963$		0			0
$964$	−2.08491	+	9.13458i	−0.0671504	+	0.294205i
$965$	−62.0240	+	29.8692i	−1.99662	+	0.961524i
$966$		0			0
$967$	−4.38024	−	2.10941i	−0.140859	−	0.0678341i	0.362127	−	0.932129i	$-0.382051\pi$
$967$	−4.38024	−	2.10941i	−0.140859	−	0.0678341i	−0.502985	+	0.864295i	$0.667765\pi$
$968$	29.7273	−	37.2769i	0.955472	−	1.19812i
$969$		0			0
$970$	−9.67954	+	42.4089i	−0.310791	+	1.36167i
$971$	−1.17863	+	0.567597i	−0.0378239	+	0.0182150i	−0.452700	−	0.891663i	$-0.649539\pi$
$971$	−1.17863	+	0.567597i	−0.0378239	+	0.0182150i	0.414876	+	0.909878i	$0.363825\pi$
$972$		0			0
$973$	−22.4615	+	0.305672i	−0.720082	+	0.00979941i
$974$	4.80394	−	21.0475i	0.153928	−	0.674404i
$975$		0			0
$976$	−19.9908	−	25.0676i	−0.639889	−	0.802395i
$977$	6.70498	+	29.3764i	0.214511	+	0.939836i	0.961458	+	0.274952i	$0.0886619\pi$
$977$	6.70498	+	29.3764i	0.214511	+	0.939836i	−0.746947	+	0.664884i	$0.768481\pi$
$978$		0			0
$979$	33.2656			1.06317
$980$	−8.84796	+	4.56162i	−0.282638	+	0.145716i
$981$		0			0
$982$	−11.8278	−	5.69596i	−0.377440	−	0.181765i
$983$	−9.73927	−	42.6705i	−0.310634	−	1.36098i	−0.853471	−	0.521140i	$-0.825507\pi$
$983$	−9.73927	−	42.6705i	−0.310634	−	1.36098i	0.542837	−	0.839838i	$-0.317350\pi$
$984$		0			0
$985$	−15.0689	−	66.0211i	−0.480135	−	2.10361i
$986$	−4.51908	+	19.7994i	−0.143917	+	0.630541i
$987$		0			0
$988$	−0.143612	−	0.629205i	−0.00456890	−	0.0200177i
$989$	30.0204	−	14.4571i	0.954592	−	0.459707i
$990$		0			0
$991$	−28.3739	−	13.6641i	−0.901326	−	0.434056i	−0.0749584	−	0.997187i	$-0.523882\pi$
$991$	−28.3739	−	13.6641i	−0.901326	−	0.434056i	−0.826368	+	0.563131i	$0.809597\pi$
$992$	−7.25824	+	9.10155i	−0.230449	+	0.288974i
$993$		0			0
$994$	46.6799	−	0.635254i	1.48059	−	0.0201490i
$995$	22.2105	−	10.6960i	0.704121	−	0.339087i
$996$		0			0
$997$	15.6960	−	19.6822i	0.497099	−	0.623342i	−0.468474	−	0.883478i	$-0.655196\pi$
$997$	15.6960	−	19.6822i	0.497099	−	0.623342i	0.965572	+	0.260136i	$0.0837673\pi$
$998$	9.19257			0.290986
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.127.4		36
3.2	odd	2		147.2.i.b.127.3	yes	36
49.22	even	7	inner	441.2.u.d.316.4		36
147.62	even	14		7203.2.a.g.1.12		18
147.71	odd	14		147.2.i.b.22.3	✓	36
147.134	odd	14		7203.2.a.h.1.12		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.22.3	✓	36	147.71	odd	14
147.2.i.b.127.3	yes	36	3.2	odd	2
441.2.u.d.127.4		36	1.1	even	1	trivial
441.2.u.d.316.4		36	49.22	even	7	inner
7203.2.a.g.1.12		18	147.62	even	14
7203.2.a.h.1.12		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)

\(f(q)\)	\(=\)	\(q+(1.11145 + 0.535248i) q^{2} +(-0.298141 - 0.373858i) q^{4} +(0.661767 + 2.89939i) q^{5} +(-0.553581 + 2.58719i) q^{7} +(-0.680276 - 2.98049i) q^{8} +O(q^{10})\)	\(q+(1.11145 + 0.535248i) q^{2} +(-0.298141 - 0.373858i) q^{4} +(0.661767 + 2.89939i) q^{5} +(-0.553581 + 2.58719i) q^{7} +(-0.680276 - 2.98049i) q^{8} +(-0.816369 + 3.57675i) q^{10} +(4.64641 + 2.23759i) q^{11} +(-0.946677 - 0.455895i) q^{13} +(-2.00007 + 2.57924i) q^{14} +(0.626392 - 2.74440i) q^{16} +(-3.51495 + 4.40761i) q^{17} -1.28450 q^{19} +(0.886660 - 1.11184i) q^{20} +(3.96660 + 4.97396i) q^{22} +(2.10843 + 2.64389i) q^{23} +(-3.46370 + 1.66803i) q^{25} +(-0.808170 - 1.01341i) q^{26} +(1.13229 - 0.564388i) q^{28} +(1.82069 - 2.28308i) q^{29} +4.40683 q^{31} +(-1.64705 + 2.06533i) q^{32} +(-6.26587 + 3.01748i) q^{34} +(-7.86762 + 0.107068i) q^{35} +(5.04275 - 6.32340i) q^{37} +(-1.42766 - 0.687526i) q^{38} +(8.19141 - 3.94478i) q^{40} +(0.169625 + 0.743175i) q^{41} +(2.19253 - 9.60612i) q^{43} +(-0.548746 - 2.40421i) q^{44} +(0.928289 + 4.06710i) q^{46} +(-1.72772 - 0.832026i) q^{47} +(-6.38710 - 2.86444i) q^{49} -4.74254 q^{50} +(0.111804 + 0.489844i) q^{52} +(3.32088 + 4.16425i) q^{53} +(-3.41282 + 14.9525i) q^{55} +(8.08767 - 0.110063i) q^{56} +(3.24563 - 1.56301i) q^{58} +(2.34804 - 10.2874i) q^{59} +(7.10157 - 8.90508i) q^{61} +(4.89798 + 2.35874i) q^{62} +(-8.00849 + 3.85669i) q^{64} +(0.695340 - 3.04648i) q^{65} -9.22571 q^{67} +2.69577 q^{68} +(-8.80180 - 4.09212i) q^{70} +(-8.91802 - 11.1828i) q^{71} +(1.30092 - 0.626491i) q^{73} +(8.98936 - 4.32905i) q^{74} +(0.382963 + 0.480221i) q^{76} +(-8.36124 + 10.7825i) q^{77} -10.9623 q^{79} +8.37162 q^{80} +(-0.209253 + 0.916796i) q^{82} +(-13.8192 + 6.65499i) q^{83} +(-15.1055 - 7.27441i) q^{85} +(7.57855 - 9.50320i) q^{86} +(3.50827 - 15.3707i) q^{88} +(5.81162 - 2.79873i) q^{89} +(1.70355 - 2.19686i) q^{91} +(0.359828 - 1.57651i) q^{92} +(-1.47494 - 1.84952i) q^{94} +(-0.850041 - 3.72427i) q^{95} +11.8568 q^{97} +(-5.56577 - 6.60237i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 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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