LMFDB - Embedded newform 261.2.k.b.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(82,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			199.1
Root			$2.41546 + 1.16323i$ of defining polynomial
Character	$\chi$	$=$	261.199
Dual form			261.2.k.b.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.596570 + 2.61374i) q^{2} +(-4.67383 - 2.25080i) q^{4} +(0.692177 - 3.03263i) q^{5} +(2.13550 - 1.02840i) q^{7} +(5.32817 - 6.68131i) q^{8} +(7.51358 + 3.61835i) q^{10} +(-1.62277 - 2.03489i) q^{11} +(-1.43935 - 1.80488i) q^{13} +(1.41401 + 6.19518i) q^{14} +(7.81583 + 9.80074i) q^{16} +4.83107 q^{17} +(-1.47595 - 0.710781i) q^{19} +(-10.0609 + 12.6160i) q^{20} +(6.28677 - 3.02755i) q^{22} +(-0.263303 - 1.15361i) q^{23} +(-4.21288 - 2.02881i) q^{25} +(5.57617 - 2.68534i) q^{26} -12.2957 q^{28} +(-5.05191 - 1.86501i) q^{29} +(-1.28688 + 5.63821i) q^{31} +(-14.8805 + 7.16606i) q^{32} +(-2.88207 + 12.6272i) q^{34} +(-1.64062 - 7.18803i) q^{35} +(4.30094 - 5.39321i) q^{37} +(2.73831 - 3.43373i) q^{38} +(-16.5739 - 20.7830i) q^{40} +7.66791 q^{41} +(-0.419989 - 1.84009i) q^{43} +(3.00442 + 13.1632i) q^{44} +3.17231 q^{46} +(5.79950 + 7.27234i) q^{47} +(-0.861665 + 1.08049i) q^{49} +(7.81608 - 9.80105i) q^{50} +(2.66483 + 11.6754i) q^{52} +(-1.15113 + 5.04343i) q^{53} +(-7.29430 + 3.51275i) q^{55} +(4.50723 - 19.7475i) q^{56} +(7.88847 - 12.0918i) q^{58} +4.90494 q^{59} +(10.3934 - 5.00522i) q^{61} +(-13.9691 - 6.72717i) q^{62} +(-4.27413 - 18.7262i) q^{64} +(-6.46982 + 3.11570i) q^{65} +(-4.34830 + 5.45260i) q^{67} +(-22.5796 - 10.8738i) q^{68} +19.7664 q^{70} +(-2.32918 - 2.92070i) q^{71} +(-0.532592 - 2.33344i) q^{73} +(11.5306 + 14.4590i) q^{74} +(5.29852 + 6.64413i) q^{76} +(-5.55812 - 2.67665i) q^{77} +(2.34395 - 2.93923i) q^{79} +(35.1319 - 16.9187i) q^{80} +(-4.57445 + 20.0420i) q^{82} +(-9.54570 - 4.59697i) q^{83} +(3.34396 - 14.6508i) q^{85} +5.06009 q^{86} -22.2421 q^{88} +(-1.26895 + 5.55963i) q^{89} +(-4.92988 - 2.37411i) q^{91} +(-1.36590 + 5.98440i) q^{92} +(-22.4678 + 10.8199i) q^{94} +(-3.17715 + 3.98402i) q^{95} +(-15.1300 - 7.28624i) q^{97} +(-2.31009 - 2.89676i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} - 11 q^{13} + 2 q^{14} + 18 q^{16} + 32 q^{17} + 2 q^{19} - 51 q^{20} + 20 q^{22} + 6 q^{23} + 4 q^{25} + 3 q^{26} - 48 q^{28}+ \cdots + 11 q^{98}+O(q^{100}) $ 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 - 11 * q^13 + 2 * q^14 + 18 * q^16 + 32 * q^17 + 2 * q^19 - 51 * q^20 + 20 * q^22 + 6 * q^23 + 4 * q^25 + 3 * q^26 - 48 * q^28 + 10 * q^29 + 8 * q^31 - 55 * q^32 + 6 * q^34 - 31 * q^35 + 20 * q^37 + 20 * q^38 - 59 * q^40 + 68 * q^41 - 3 * q^43 + 10 * q^44 - 12 * q^46 - 19 * q^47 + 17 * q^49 - 23 * q^50 - 4 * q^52 + q^53 + 3 * q^55 - 7 * q^56 - 30 * q^58 - 20 * q^59 + 24 * q^61 - 79 * q^62 - 23 * q^64 - 6 * q^65 - 14 * q^67 + 8 * q^68 + 28 * q^70 + 28 * q^71 + 43 * q^73 + 47 * q^74 + 19 * q^76 - 26 * q^77 + 9 * q^79 + 74 * q^80 - 17 * q^82 - 8 * q^83 - 21 * q^85 + 140 * q^86 - 58 * q^88 + 6 * q^89 - 15 * q^91 - 11 * q^92 + 6 * q^94 + 16 * q^95 - 81 * q^97 + 11 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

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 $

$2$	−0.596570	+	2.61374i	−0.421839	+	1.84820i	0.0997685	+	0.995011i	$0.468190\pi$
$2$	−0.596570	+	2.61374i	−0.421839	+	1.84820i	−0.521607	+	0.853186i	$0.674667\pi$
$3$		0			0
$3$		0			0
$4$	−4.67383	−	2.25080i	−2.33691	−	1.12540i
$5$	0.692177	−	3.03263i	0.309551	−	1.35623i	−0.545684	−	0.837991i	$-0.683730\pi$
$5$	0.692177	−	3.03263i	0.309551	−	1.35623i	0.855235	−	0.518241i	$-0.173413\pi$
$6$		0			0
$7$	2.13550	−	1.02840i	0.807145	−	0.388701i	0.0156510	−	0.999878i	$-0.495018\pi$
$7$	2.13550	−	1.02840i	0.807145	−	0.388701i	0.791494	+	0.611177i	$0.209304\pi$
$8$	5.32817	−	6.68131i	1.88379	−	2.36220i
$9$		0			0
$10$	7.51358	+	3.61835i	2.37600	+	1.14422i
$11$	−1.62277	−	2.03489i	−0.489283	−	0.613542i	0.474491	−	0.880260i	$-0.342632\pi$
$11$	−1.62277	−	2.03489i	−0.489283	−	0.613542i	−0.963774	+	0.266719i	$0.914061\pi$
$12$		0			0
$13$	−1.43935	−	1.80488i	−0.399203	−	0.500584i	0.541084	−	0.840969i	$-0.318014\pi$
$13$	−1.43935	−	1.80488i	−0.399203	−	0.500584i	−0.940286	+	0.340384i	$0.889443\pi$
$14$	1.41401	+	6.19518i	0.377910	+	1.65573i
$15$		0			0
$16$	7.81583	+	9.80074i	1.95396	+	2.45019i
$17$	4.83107			1.17171			0.585854	−	0.810417i	$-0.300759\pi$
$17$	4.83107			1.17171			0.585854	+	0.810417i	$0.300759\pi$
$18$		0			0
$19$	−1.47595	−	0.710781i	−0.338606	−	0.163064i	0.256851	−	0.966451i	$-0.417315\pi$
$19$	−1.47595	−	0.710781i	−0.338606	−	0.163064i	−0.595458	+	0.803387i	$0.703029\pi$
$20$	−10.0609	+	12.6160i	−2.24970	+	2.82103i
$21$		0			0
$22$	6.28677	−	3.02755i	1.34034	−	0.645476i
$23$	−0.263303	−	1.15361i	−0.0549025	−	0.240544i	0.940030	−	0.341093i	$-0.110797\pi$
$23$	−0.263303	−	1.15361i	−0.0549025	−	0.240544i	−0.994932	+	0.100549i	$0.967940\pi$
$24$		0			0
$25$	−4.21288	−	2.02881i	−0.842575	−	0.405763i
$26$	5.57617	−	2.68534i	1.09358	−	0.526639i
$27$		0			0
$28$	−12.2957			−2.32367
$29$	−5.05191	−	1.86501i	−0.938115	−	0.346323i
$29$	−5.05191	−	1.86501i	−0.938115	−	0.346323i
$30$		0			0
$31$	−1.28688	+	5.63821i	−0.231131	+	1.01265i	0.717572	+	0.696484i	$0.245253\pi$
$31$	−1.28688	+	5.63821i	−0.231131	+	1.01265i	−0.948703	+	0.316168i	$0.897604\pi$
$32$	−14.8805	+	7.16606i	−2.63052	+	1.26679i
$33$		0			0
$34$	−2.88207	+	12.6272i	−0.494272	+	2.16555i
$35$	−1.64062	−	7.18803i	−0.277316	−	1.21500i
$36$		0			0
$37$	4.30094	−	5.39321i	0.707070	−	0.886637i	−0.290460	−	0.956887i	$-0.593808\pi$
$37$	4.30094	−	5.39321i	0.707070	−	0.886637i	0.997529	+	0.0702498i	$0.0223796\pi$
$38$	2.73831	−	3.43373i	0.444212	−	0.557024i
$39$		0			0
$40$	−16.5739	−	20.7830i	−2.62056	−	3.28608i
$41$	7.66791			1.19753			0.598763	−	0.800926i	$-0.295659\pi$
$41$	7.66791			1.19753			0.598763	+	0.800926i	$0.295659\pi$
$42$		0			0
$43$	−0.419989	−	1.84009i	−0.0640478	−	0.280612i	0.932755	−	0.360510i	$-0.117397\pi$
$43$	−0.419989	−	1.84009i	−0.0640478	−	0.280612i	−0.996803	+	0.0798987i	$0.974540\pi$
$44$	3.00442	+	13.1632i	0.452934	+	1.98443i
$45$		0			0
$46$	3.17231			0.467732
$47$	5.79950	+	7.27234i	0.845944	+	1.06078i	0.997382	+	0.0723132i	$0.0230381\pi$
$47$	5.79950	+	7.27234i	0.845944	+	1.06078i	−0.151438	+	0.988467i	$0.548390\pi$
$48$		0			0
$49$	−0.861665	+	1.08049i	−0.123095	+	0.154356i
$50$	7.81608	−	9.80105i	1.10536	−	1.38608i
$51$		0			0
$52$	2.66483	+	11.6754i	0.369545	+	1.61908i
$53$	−1.15113	+	5.04343i	−0.158120	+	0.692768i	0.832259	+	0.554387i	$0.187047\pi$
$53$	−1.15113	+	5.04343i	−0.158120	+	0.692768i	−0.990379	+	0.138381i	$0.955810\pi$
$54$		0			0
$55$	−7.29430	+	3.51275i	−0.983563	+	0.473659i
$56$	4.50723	−	19.7475i	0.602304	−	2.63887i
$57$		0			0
$58$	7.88847	−	12.0918i	1.03581	−	1.58773i
$59$	4.90494			0.638569			0.319285	−	0.947659i	$-0.396557\pi$
$59$	4.90494			0.638569			0.319285	+	0.947659i	$0.396557\pi$
$60$		0			0
$61$	10.3934	−	5.00522i	1.33074	−	0.640852i	0.372828	−	0.927901i	$-0.378388\pi$
$61$	10.3934	−	5.00522i	1.33074	−	0.640852i	0.957916	+	0.287048i	$0.0926740\pi$
$62$	−13.9691	−	6.72717i	−1.77408	−	0.854352i
$63$		0			0
$64$	−4.27413	−	18.7262i	−0.534266	−	2.34077i
$65$	−6.46982	+	3.11570i	−0.802482	+	0.386455i
$66$		0			0
$67$	−4.34830	+	5.45260i	−0.531229	+	0.666141i	−0.972951	−	0.231012i	$-0.925796\pi$
$67$	−4.34830	+	5.45260i	−0.531229	+	0.666141i	0.441722	+	0.897152i	$0.354368\pi$
$68$	−22.5796	−	10.8738i	−2.73818	−	1.31864i
$69$		0			0
$70$	19.7664			2.36254
$71$	−2.32918	−	2.92070i	−0.276423	−	0.346623i	0.624169	−	0.781289i	$-0.285438\pi$
$71$	−2.32918	−	2.92070i	−0.276423	−	0.346623i	−0.900592	+	0.434666i	$0.856866\pi$
$72$		0			0
$73$	−0.532592	−	2.33344i	−0.0623351	−	0.273108i	0.934150	−	0.356881i	$-0.116160\pi$
$73$	−0.532592	−	2.33344i	−0.0623351	−	0.273108i	−0.996485	+	0.0837733i	$0.973303\pi$
$74$	11.5306	+	14.4590i	1.34041	+	1.68082i
$75$		0			0
$76$	5.29852	+	6.64413i	0.607782	+	0.762134i
$77$	−5.55812	−	2.67665i	−0.633406	−	0.305032i
$78$		0			0
$79$	2.34395	−	2.93923i	0.263716	−	0.330689i	−0.632290	−	0.774732i	$-0.717885\pi$
$79$	2.34395	−	2.93923i	0.263716	−	0.330689i	0.896005	+	0.444043i	$0.146456\pi$
$80$	35.1319	−	16.9187i	3.92787	−	1.89156i
$81$		0			0
$82$	−4.57445	+	20.0420i	−0.505163	+	2.21326i
$83$	−9.54570	−	4.59697i	−1.04778	−	0.504583i	−0.170895	−	0.985289i	$-0.554666\pi$
$83$	−9.54570	−	4.59697i	−1.04778	−	0.504583i	−0.876882	+	0.480707i	$0.840380\pi$
$84$		0			0
$85$	3.34396	−	14.6508i	0.362703	−	1.58911i
$86$	5.06009			0.545643
$87$		0			0
$88$	−22.2421			−2.37101
$89$	−1.26895	+	5.55963i	−0.134508	+	0.589320i	0.862079	+	0.506774i	$0.169162\pi$
$89$	−1.26895	+	5.55963i	−0.134508	+	0.589320i	−0.996587	+	0.0825457i	$0.973695\pi$
$90$		0			0
$91$	−4.92988	−	2.37411i	−0.516792	−	0.248874i
$92$	−1.36590	+	5.98440i	−0.142405	+	0.623917i
$93$		0			0
$94$	−22.4678	+	10.8199i	−2.31738	+	1.11599i
$95$	−3.17715	+	3.98402i	−0.325969	+	0.408752i
$96$		0			0
$97$	−15.1300	−	7.28624i	−1.53622	−	0.739806i	−0.541337	−	0.840806i	$-0.682082\pi$
$97$	−15.1300	−	7.28624i	−1.53622	−	0.739806i	−0.994886	+	0.101000i	$0.967796\pi$
$98$	−2.31009	−	2.89676i	−0.233354	−	0.292617i
$99$		0			0
$100$	15.1238	+	18.9646i	1.51238	+	1.89646i
$101$	1.01964	+	4.46734i	0.101458	+	0.444517i	0.999984	+	0.00559720i	$0.00178165\pi$
$101$	1.01964	+	4.46734i	0.101458	+	0.444517i	−0.898526	+	0.438920i	$0.855361\pi$
$102$		0			0
$103$	6.56608	+	8.23361i	0.646975	+	0.811281i	0.991856	−	0.127365i	$-0.0406521\pi$
$103$	6.56608	+	8.23361i	0.646975	+	0.811281i	−0.344881	+	0.938647i	$0.612081\pi$
$104$	−19.7281			−1.93449
$105$		0			0
$106$	−12.4955	−	6.01751i	−1.21367	−	0.584473i
$107$	−8.57509	+	10.7528i	−0.828985	+	1.03951i	0.169556	+	0.985520i	$0.445767\pi$
$107$	−8.57509	+	10.7528i	−0.828985	+	1.03951i	−0.998541	+	0.0539937i	$0.982805\pi$
$108$		0			0
$109$	4.82225	−	2.32227i	0.461888	−	0.222434i	−0.188444	−	0.982084i	$-0.560344\pi$
$109$	4.82225	−	2.32227i	0.461888	−	0.222434i	0.650332	+	0.759650i	$0.274630\pi$
$110$	−4.82987	−	21.1610i	−0.460510	−	2.01763i
$111$		0			0
$112$	26.7699	+	12.8917i	2.52952	+	1.21815i
$113$	−9.72860	+	4.68504i	−0.915189	+	0.440732i	−0.831351	−	0.555747i	$-0.812432\pi$
$113$	−9.72860	+	4.68504i	−0.915189	+	0.440732i	−0.0838381	+	0.996479i	$0.526718\pi$
$114$		0			0
$115$	−3.68071			−0.343228
$116$	19.4140	+	20.0875i	1.80254	+	1.86508i
$117$		0			0
$118$	−2.92614	+	12.8203i	−0.269373	+	1.18020i
$119$	10.3168	−	4.96830i	0.945738	−	0.455443i
$120$		0			0
$121$	0.940341	−	4.11990i	0.0854856	−	0.374537i
$122$	6.88194	+	30.1518i	0.623062	+	2.72981i
$123$		0			0
$124$	18.7051	−	23.4555i	1.67977	−	2.10637i
$125$	0.628496	−	0.788109i	0.0562144	−	0.0704906i
$126$		0			0
$127$	10.5127	+	13.1825i	0.932851	+	1.16976i	0.985248	+	0.171132i	$0.0547423\pi$
$127$	10.5127	+	13.1825i	0.932851	+	1.16976i	−0.0523973	+	0.998626i	$0.516686\pi$
$128$	18.4631			1.63192
$129$		0			0
$130$	−4.28394	−	18.7692i	−0.375727	−	1.64617i
$131$	1.01316	+	4.43896i	0.0885206	+	0.387834i	0.999708	−	0.0241577i	$-0.00769039\pi$
$131$	1.01316	+	4.43896i	0.0885206	+	0.387834i	−0.911188	+	0.411992i	$0.864833\pi$
$132$		0			0
$133$	−3.88287			−0.336688
$134$	−11.6576	−	14.6182i	−1.00707	−	1.26282i
$135$		0			0
$136$	25.7408	−	32.2779i	2.20725	−	2.76781i
$137$	13.7225	−	17.2075i	1.17239	−	1.47014i	0.319861	−	0.947465i	$-0.396364\pi$
$137$	13.7225	−	17.2075i	1.17239	−	1.47014i	0.852534	−	0.522672i	$-0.175065\pi$
$138$		0			0
$139$	1.80101	+	7.89075i	0.152760	+	0.669284i	0.992076	+	0.125641i	$0.0400986\pi$
$139$	1.80101	+	7.89075i	0.152760	+	0.669284i	−0.839316	+	0.543644i	$0.817044\pi$
$140$	−8.51081	+	37.2883i	−0.719295	+	3.15144i
$141$		0			0
$142$	9.02347	−	4.34548i	0.757233	−	0.364664i
$143$	−1.33701	+	5.85781i	−0.111806	+	0.489855i
$144$		0			0
$145$	−9.15269	+	14.0296i	−0.760089	+	1.16510i
$146$	6.41673			0.531053
$147$		0			0
$148$	−32.2408	+	15.5264i	−2.65018	+	1.27626i
$149$	0.670037	+	0.322673i	0.0548916	+	0.0264344i	0.461128	−	0.887334i	$-0.347445\pi$
$149$	0.670037	+	0.322673i	0.0548916	+	0.0264344i	−0.406237	+	0.913768i	$0.633159\pi$
$150$		0			0
$151$	3.84695	+	16.8546i	0.313060	+	1.37161i	0.849465	+	0.527646i	$0.176925\pi$
$151$	3.84695	+	16.8546i	0.313060	+	1.37161i	−0.536404	+	0.843961i	$0.680218\pi$
$152$	−12.6131	+	6.07413i	−1.02305	+	0.492677i
$153$		0			0
$154$	10.3119	−	12.9307i	0.830955	−	1.04198i
$155$	16.2078	+	7.80528i	1.30184	+	0.626935i
$156$		0			0
$157$	−0.399286			−0.0318665			−0.0159332	−	0.999873i	$-0.505072\pi$
$157$	−0.399286			−0.0318665			−0.0159332	+	0.999873i	$0.505072\pi$
$158$	6.28405	+	7.87995i	0.499932	+	0.626895i
$159$		0			0
$160$	11.4321	+	50.0872i	0.903784	+	3.95974i
$161$	−1.74866	−	2.19275i	−0.137814	−	0.172813i
$162$		0			0
$163$	6.18092	+	7.75063i	0.484127	+	0.607076i	0.962567	−	0.271044i	$-0.0873690\pi$
$163$	6.18092	+	7.75063i	0.484127	+	0.607076i	−0.478440	+	0.878120i	$0.658798\pi$
$164$	−35.8385	−	17.2589i	−2.79852	−	1.34769i
$165$		0			0
$166$	17.7100	−	22.2076i	1.37456	−	1.72364i
$167$	−10.5584	+	5.08467i	−0.817036	+	0.393464i	−0.795237	−	0.606298i	$-0.792654\pi$
$167$	−10.5584	+	5.08467i	−0.817036	+	0.393464i	−0.0217990	+	0.999762i	$0.506939\pi$
$168$		0			0
$169$	1.70689	−	7.47836i	0.131299	−	0.575259i
$170$	36.2987	+	17.4805i	2.78398	+	1.34069i
$171$		0			0
$172$	−2.17872	+	9.54559i	−0.166126	+	0.727844i
$173$	−8.14339			−0.619131			−0.309565	−	0.950878i	$-0.600184\pi$
$173$	−8.14339			−0.619131			−0.309565	+	0.950878i	$0.600184\pi$
$174$		0			0
$175$	−11.0831			−0.837800
$176$	7.26012	−	31.8087i	0.547252	−	2.39767i
$177$		0			0
$178$	−13.7744	−	6.63342i	−1.03244	−	0.497196i
$179$	2.39845	−	10.5083i	0.179268	−	0.785426i	−0.802700	−	0.596383i	$-0.796604\pi$
$179$	2.39845	−	10.5083i	0.179268	−	0.785426i	0.981969	−	0.189044i	$-0.0605387\pi$
$180$		0			0
$181$	−18.5712	+	8.94342i	−1.38039	+	0.664759i	−0.969082	−	0.246738i	$-0.920641\pi$
$181$	−18.5712	+	8.94342i	−1.38039	+	0.664759i	−0.411305	+	0.911498i	$0.634927\pi$
$182$	9.14632	−	11.4691i	0.677971	−	0.850148i
$183$		0			0
$184$	−9.11053	−	4.38740i	−0.671637	−	0.323443i
$185$	−13.3786	−	16.7762i	−0.983612	−	1.23341i
$186$		0			0
$187$	−7.83972	−	9.83069i	−0.573297	−	0.718891i
$188$	−10.7373	−	47.0431i	−0.783097	−	3.43097i
$189$		0			0
$190$	−8.51782	−	10.6810i	−0.617948	−	0.774882i
$191$	24.4869			1.77181			0.885906	−	0.463865i	$-0.153538\pi$
$191$	24.4869			1.77181			0.885906	+	0.463865i	$0.153538\pi$
$192$		0			0
$193$	14.2742	+	6.87409i	1.02748	+	0.494808i	0.870175	−	0.492743i	$-0.164006\pi$
$193$	14.2742	+	6.87409i	1.02748	+	0.494808i	0.157303	+	0.987550i	$0.449720\pi$
$194$	28.0705	−	35.1993i	2.01535	−	2.52716i
$195$		0			0
$196$	6.45924	−	3.11061i	0.461374	−	0.222186i
$197$	2.83725	+	12.4308i	0.202146	+	0.885660i	0.969627	+	0.244588i	$0.0786527\pi$
$197$	2.83725	+	12.4308i	0.202146	+	0.885660i	−0.767481	+	0.641072i	$0.778490\pi$
$198$		0			0
$199$	7.32020	+	3.52522i	0.518915	+	0.249896i	0.674961	−	0.737853i	$-0.264160\pi$
$199$	7.32020	+	3.52522i	0.518915	+	0.249896i	−0.156046	+	0.987750i	$0.549875\pi$
$200$	−36.0020	+	17.3377i	−2.54573	+	1.22596i
$201$		0			0
$202$	−12.2848			−0.864354
$203$	−12.7064	+	1.21267i	−0.891811	+	0.0851129i
$204$		0			0
$205$	5.30756	−	23.2539i	0.370696	−	1.62412i
$206$	−25.4377	+	12.2501i	−1.77233	+	0.853507i
$207$		0			0
$208$	6.43951	−	28.2133i	0.446499	−	1.95624i
$209$	0.948769	+	4.15683i	0.0656277	+	0.287534i
$210$		0			0
$211$	−13.0904	+	16.4149i	−0.901183	+	1.13005i	0.0897871	+	0.995961i	$0.471381\pi$
$211$	−13.0904	+	16.4149i	−0.901183	+	1.13005i	−0.990970	+	0.134086i	$0.957190\pi$
$212$	16.7319	−	20.9811i	1.14915	−	1.44099i
$213$		0			0
$214$	−22.9895	−	28.8279i	−1.57153	−	1.97063i
$215$	−5.87102			−0.400401
$216$		0			0
$217$	3.05021	+	13.3639i	0.207062	+	0.907198i
$218$	3.19302	+	13.9895i	0.216259	+	0.947491i
$219$		0			0
$220$	41.9988			2.83156
$221$	−6.95359	−	8.71952i	−0.467749	−	0.586538i
$222$		0			0
$223$	13.2224	−	16.5803i	0.885436	−	1.11030i	−0.107799	−	0.994173i	$-0.534380\pi$
$223$	13.2224	−	16.5803i	0.885436	−	1.11030i	0.993234	−	0.116128i	$-0.0370484\pi$
$224$	−24.4077	+	30.6063i	−1.63081	+	2.04497i
$225$		0			0
$226$	−6.44172	−	28.2230i	−0.428497	−	1.87737i
$227$	2.38193	−	10.4359i	0.158094	−	0.692656i	−0.832293	−	0.554335i	$-0.812972\pi$
$227$	2.38193	−	10.4359i	0.158094	−	0.692656i	0.990388	−	0.138320i	$-0.0441704\pi$
$228$		0			0
$229$	12.6188	−	6.07690i	0.833875	−	0.401573i	0.0323077	−	0.999478i	$-0.489714\pi$
$229$	12.6188	−	6.07690i	0.833875	−	0.401573i	0.801567	+	0.597905i	$0.204000\pi$
$230$	2.19580	−	9.62044i	0.144787	−	0.634353i
$231$		0			0
$232$	−39.3781	+	23.8163i	−2.58530	+	1.56361i
$233$	12.3851			0.811377			0.405688	−	0.914011i	$-0.367032\pi$
$233$	12.3851			0.811377			0.405688	+	0.914011i	$0.367032\pi$
$234$		0			0
$235$	26.0686	−	12.5540i	1.70053	−	0.818931i
$236$	−22.9249	−	11.0400i	−1.49228	−	0.718645i
$237$		0			0
$238$	6.83118	+	29.9294i	0.442800	+	1.94003i
$239$	8.02168	−	3.86304i	0.518879	−	0.249879i	−0.156066	−	0.987747i	$-0.549881\pi$
$239$	8.02168	−	3.86304i	0.518879	−	0.249879i	0.674946	+	0.737867i	$0.264167\pi$
$240$		0			0
$241$	−16.3041	+	20.4447i	−1.05024	+	1.31696i	−0.103619	+	0.994617i	$0.533042\pi$
$241$	−16.3041	+	20.4447i	−1.05024	+	1.31696i	−0.946623	+	0.322344i	$0.895529\pi$
$242$	10.2074	+	4.91562i	0.656156	+	0.315988i
$243$		0			0
$244$	−59.8429			−3.83105
$245$	2.68031	+	3.36100i	0.171239	+	0.214726i
$246$		0			0
$247$	0.841529	+	3.68698i	0.0535452	+	0.234597i
$248$	30.8139	+	38.6394i	1.95668	+	2.45360i
$249$		0			0
$250$	1.68497	+	2.11289i	0.106567	+	0.133631i
$251$	3.49262	+	1.68196i	0.220452	+	0.106164i	0.540851	−	0.841119i	$-0.318102\pi$
$251$	3.49262	+	1.68196i	0.220452	+	0.106164i	−0.320398	+	0.947283i	$0.603817\pi$
$252$		0			0
$253$	−1.92018	+	2.40783i	−0.120721	+	0.151379i
$254$	−40.7273	+	19.6132i	−2.55546	+	1.23064i
$255$		0			0
$256$	−2.46628	+	10.8055i	−0.154142	+	0.675341i
$257$	−1.45625	−	0.701292i	−0.0908383	−	0.0437454i	0.387913	−	0.921696i	$-0.373196\pi$
$257$	−1.45625	−	0.701292i	−0.0908383	−	0.0437454i	−0.478751	+	0.877951i	$0.658910\pi$
$258$		0			0
$259$	3.63827	−	15.9403i	0.226071	−	0.990483i
$260$	37.2516			2.31025
$261$		0			0
$262$	−12.2067			−0.754135
$263$	−5.04283	+	22.0941i	−0.310954	+	1.36238i	0.541994	+	0.840382i	$0.317669\pi$
$263$	−5.04283	+	22.0941i	−0.310954	+	1.36238i	−0.852948	+	0.521996i	$0.825188\pi$
$264$		0			0
$265$	14.4980	+	6.98189i	0.890608	+	0.428894i
$266$	2.31640	−	10.1488i	0.142028	−	0.622265i
$267$		0			0
$268$	32.5959	−	15.6973i	1.99111	−	0.958868i
$269$	3.25476	−	4.08133i	0.198446	−	0.248843i	−0.672645	−	0.739966i	$-0.734842\pi$
$269$	3.25476	−	4.08133i	0.198446	−	0.248843i	0.871091	+	0.491122i	$0.163413\pi$
$270$		0			0
$271$	−1.35089	−	0.650556i	−0.0820610	−	0.0395185i	0.392403	−	0.919793i	$-0.371644\pi$
$271$	−1.35089	−	0.650556i	−0.0820610	−	0.0395185i	−0.474464	+	0.880275i	$0.657358\pi$
$272$	37.7589	+	47.3481i	2.28947	+	2.87090i
$273$		0			0
$274$	36.7896	+	46.1327i	2.22254	+	2.78698i
$275$	2.70811	+	11.8650i	0.163305	+	0.715488i
$276$		0			0
$277$	1.35995	+	1.70532i	0.0817112	+	0.102463i	0.821007	−	0.570918i	$-0.193413\pi$
$277$	1.35995	+	1.70532i	0.0817112	+	0.102463i	−0.739296	+	0.673381i	$0.764841\pi$
$278$	−21.6988			−1.30141
$279$		0			0
$280$	−56.7669	−	27.3375i	−3.39247	−	1.63373i
$281$	10.7411	−	13.4689i	0.640761	−	0.803489i	−0.350337	−	0.936624i	$-0.613933\pi$
$281$	10.7411	−	13.4689i	0.640761	−	0.803489i	0.991098	+	0.133135i	$0.0425044\pi$
$282$		0			0
$283$	10.2985	−	4.95949i	0.612182	−	0.294811i	−0.101986	−	0.994786i	$-0.532520\pi$
$283$	10.2985	−	4.95949i	0.612182	−	0.294811i	0.714168	+	0.699975i	$0.246805\pi$
$284$	4.31228	+	18.8933i	0.255887	+	1.12111i
$285$		0			0
$286$	−14.5132	−	6.98919i	−0.858184	−	0.413280i
$287$	16.3749	−	7.88572i	0.966578	−	0.465479i
$288$		0			0
$289$	6.33927			0.372898
$290$	−31.2097	−	32.2924i	−1.83269	−	1.89628i
$291$		0			0
$292$	−2.76285	+	12.1048i	−0.161683	+	0.708382i
$293$	−4.61704	+	2.22345i	−0.269730	+	0.129895i	−0.563860	−	0.825870i	$-0.690684\pi$
$293$	−4.61704	+	2.22345i	−0.269730	+	0.129895i	0.294130	+	0.955765i	$0.404970\pi$
$294$		0			0
$295$	3.39509	−	14.8749i	0.197670	−	0.866048i
$296$	−13.1176	−	57.4718i	−0.762443	−	3.34048i
$297$		0			0
$298$	−1.24311	+	1.55881i	−0.0720114	+	0.0902994i
$299$	−1.70314	+	2.13567i	−0.0984952	+	0.123509i
$300$		0			0
$301$	−2.78925	−	3.49761i	−0.160770	−	0.201599i
$302$	−46.3486			−2.66706
$303$		0			0
$304$	−4.56961	−	20.0208i	−0.262085	−	1.14827i
$305$	−7.98485	−	34.9839i	−0.457211	−	2.00317i
$306$		0			0
$307$	3.39033			0.193496			0.0967482	−	0.995309i	$-0.469156\pi$
$307$	3.39033			0.193496			0.0967482	+	0.995309i	$0.469156\pi$
$308$	19.9531	+	25.0204i	1.13693	+	1.42567i
$309$		0			0
$310$	−30.0701	+	37.7067i	−1.70787	+	2.14160i
$311$	−10.6731	+	13.3836i	−0.605213	+	0.758913i	−0.986180	−	0.165675i	$-0.947020\pi$
$311$	−10.6731	+	13.3836i	−0.605213	+	0.758913i	0.380967	+	0.924589i	$0.375591\pi$
$312$		0			0
$313$	0.322250	+	1.41187i	0.0182147	+	0.0798036i	0.983218	−	0.182433i	$-0.0583972\pi$
$313$	0.322250	+	1.41187i	0.0182147	+	0.0798036i	−0.965004	+	0.262236i	$0.915540\pi$
$314$	0.238202	−	1.04363i	0.0134425	−	0.0588955i
$315$		0			0
$316$	−17.5708	+	8.46167i	−0.988437	+	0.476006i
$317$	−3.89788	+	17.0777i	−0.218927	+	0.959182i	0.739346	+	0.673326i	$0.235135\pi$
$317$	−3.89788	+	17.0777i	−0.218927	+	0.959182i	−0.958273	+	0.285856i	$0.907722\pi$
$318$		0			0
$319$	4.40299	+	13.3065i	0.246520	+	0.745023i
$320$	−59.7480			−3.34002
$321$		0			0
$322$	6.77449	−	3.26242i	0.377528	−	0.181808i
$323$	−7.13043	−	3.43383i	−0.396748	−	0.191064i
$324$		0			0
$325$	2.40201	+	10.5239i	0.133240	+	0.583762i
$326$	−23.9455	+	11.5316i	−1.32622	+	0.638674i
$327$		0			0
$328$	40.8559	−	51.2317i	2.25589	−	2.82880i
$329$	19.8638	+	9.56589i	1.09512	+	0.527384i
$330$		0			0
$331$	10.4276			0.573155			0.286577	−	0.958057i	$-0.407482\pi$
$331$	10.4276			0.573155			0.286577	+	0.958057i	$0.407482\pi$
$332$	34.2681	+	42.9708i	1.88071	+	2.35833i
$333$		0			0
$334$	−6.99119	−	30.6304i	−0.382541	−	1.67602i
$335$	13.5259	+	16.9609i	0.738999	+	0.926675i
$336$		0			0
$337$	−20.0771	−	25.1759i	−1.09367	−	1.37142i	−0.922418	−	0.386194i	$-0.873790\pi$
$337$	−20.0771	−	25.1759i	−1.09367	−	1.37142i	−0.171254	−	0.985227i	$-0.554782\pi$
$338$	18.5282	+	8.92273i	1.00780	+	0.485333i
$339$		0			0
$340$	−48.6052	+	60.9489i	−2.63598	+	3.30542i
$341$	13.5614	−	6.53084i	0.734393	−	0.353665i
$342$		0			0
$343$	−4.42089	+	19.3692i	−0.238705	+	1.04584i
$344$	−14.5320	−	6.99824i	−0.783513	−	0.377320i
$345$		0			0
$346$	4.85811	−	21.2848i	0.261173	−	1.14428i
$347$	−6.96578			−0.373942			−0.186971	−	0.982365i	$-0.559867\pi$
$347$	−6.96578			−0.373942			−0.186971	+	0.982365i	$0.559867\pi$
$348$		0			0
$349$	13.9714			0.747871			0.373935	−	0.927455i	$-0.378008\pi$
$349$	13.9714			0.747871			0.373935	+	0.927455i	$0.378008\pi$
$350$	6.61182	−	28.9683i	0.353417	−	1.54842i
$351$		0			0
$352$	38.7297	+	18.6513i	2.06430	+	0.994115i
$353$	5.75044	−	25.1943i	0.306065	−	1.34096i	−0.554740	−	0.832024i	$-0.687182\pi$
$353$	5.75044	−	25.1943i	0.306065	−	1.34096i	0.860805	−	0.508935i	$-0.169961\pi$
$354$		0			0
$355$	−10.4696	+	5.04189i	−0.555668	+	0.267596i
$356$	18.4444	−	23.1286i	0.977554	−	1.22581i
$357$		0			0
$358$	26.0351	+	12.5379i	1.37600	+	0.662646i
$359$	10.9382	+	13.7160i	0.577295	+	0.723905i	0.981649	−	0.190698i	$-0.0610750\pi$
$359$	10.9382	+	13.7160i	0.577295	+	0.723905i	−0.404354	+	0.914603i	$0.632504\pi$
$360$		0			0
$361$	−10.1731	−	12.7566i	−0.535425	−	0.671402i
$362$	−12.2968	−	53.8758i	−0.646305	−	2.83165i
$363$		0			0
$364$	17.6978	+	22.1923i	0.927616	+	1.16319i
$365$	−7.44509			−0.389694
$366$		0			0
$367$	−26.8154	−	12.9136i	−1.39975	−	0.674086i	−0.426643	−	0.904420i	$-0.640304\pi$
$367$	−26.8154	−	12.9136i	−1.39975	−	0.674086i	−0.973112	+	0.230334i	$0.926018\pi$
$368$	9.24827	−	11.5970i	0.482100	−	0.604534i
$369$		0			0
$370$	51.8299	−	24.9600i	2.69451	−	1.29761i
$371$	2.72844	+	11.9541i	0.141654	+	0.620625i
$372$		0			0
$373$	−17.3846	−	8.37200i	−0.900142	−	0.433485i	−0.0742017	−	0.997243i	$-0.523641\pi$
$373$	−17.3846	−	8.37200i	−0.900142	−	0.433485i	−0.825940	+	0.563758i	$0.809355\pi$
$374$	30.3719	−	14.6263i	1.57049	−	0.756309i
$375$		0			0
$376$	79.4894			4.09936
$377$	3.90532	+	11.8025i	0.201134	+	0.607859i
$378$		0			0
$379$	1.91129	−	8.37391i	0.0981763	−	0.430139i	−0.901822	−	0.432108i	$-0.857770\pi$
$379$	1.91129	−	8.37391i	0.0981763	−	0.430139i	0.999998	+	0.00196965i	$0.000626959\pi$
$380$	23.8167	−	11.4695i	1.22177	−	0.588373i
$381$		0			0
$382$	−14.6082	+	64.0026i	−0.747419	+	3.27466i
$383$	−6.29552	−	27.5825i	−0.321686	−	1.40940i	−0.834552	−	0.550930i	$-0.814273\pi$
$383$	−6.29552	−	27.5825i	−0.321686	−	1.40940i	0.512865	−	0.858469i	$-0.328584\pi$
$384$		0			0
$385$	−11.9645	+	15.0030i	−0.609767	+	0.764623i
$386$	−26.4827	+	33.2082i	−1.34793	+	1.69025i
$387$		0			0
$388$	54.3153	+	68.1093i	2.75744	+	3.45772i
$389$	27.1843			1.37830			0.689149	−	0.724619i	$-0.257984\pi$
$389$	27.1843			1.37830			0.689149	+	0.724619i	$0.257984\pi$
$390$		0			0
$391$	−1.27204	−	5.57316i	−0.0643297	−	0.281847i
$392$	2.62802	+	11.5141i	0.132735	+	0.581550i
$393$		0			0
$394$	−34.1836			−1.72215
$395$	−7.29115	−	9.14281i	−0.366857	−	0.460025i
$396$		0			0
$397$	3.09017	−	3.87495i	0.155091	−	0.194478i	−0.698215	−	0.715888i	$-0.746022\pi$
$397$	3.09017	−	3.87495i	0.155091	−	0.194478i	0.853306	+	0.521410i	$0.174594\pi$
$398$	−13.5810	+	17.0301i	−0.680756	+	0.853641i
$399$		0			0
$400$	−13.0432	−	57.1462i	−0.652162	−	2.85731i
$401$	1.38397	−	6.06358i	0.0691123	−	0.302801i	−0.928544	−	0.371222i	$-0.878939\pi$
$401$	1.38397	−	6.06358i	0.0691123	−	0.302801i	0.997657	+	0.0684210i	$0.0217961\pi$
$402$		0			0
$403$	12.0286	−	5.79266i	0.599186	−	0.288553i
$404$	5.28945	−	23.1746i	0.263160	−	1.15298i
$405$		0			0
$406$	4.41061	−	33.9346i	0.218895	−	1.68415i
$407$	−17.9540			−0.889946
$408$		0			0
$409$	−4.17933	+	2.01266i	−0.206655	+	0.0995196i	−0.534348	−	0.845264i	$-0.679443\pi$
$409$	−4.17933	+	2.01266i	−0.206655	+	0.0995196i	0.327694	+	0.944784i	$0.393729\pi$
$410$	57.6135	+	27.7452i	2.84533	+	1.37024i
$411$		0			0
$412$	−12.1566	−	53.2613i	−0.598910	−	2.62400i
$413$	10.4745	−	5.04427i	0.515418	−	0.248212i
$414$		0			0
$415$	−20.5482	+	25.7666i	−1.00867	+	1.26483i
$416$	34.3521	+	16.5431i	1.68425	+	0.811092i
$417$		0			0
$418$	−11.4309			−0.559103
$419$	−8.52181	−	10.6860i	−0.416318	−	0.522046i	0.528813	−	0.848738i	$-0.322637\pi$
$419$	−8.52181	−	10.6860i	−0.416318	−	0.522046i	−0.945131	+	0.326693i	$0.894066\pi$
$420$		0			0
$421$	2.64867	+	11.6046i	0.129088	+	0.565573i	0.997559	+	0.0698322i	$0.0222464\pi$
$421$	2.64867	+	11.6046i	0.129088	+	0.565573i	−0.868470	+	0.495741i	$0.834896\pi$
$422$	−35.0949	−	44.0077i	−1.70840	−	2.14226i
$423$		0			0
$424$	27.5633	+	34.5633i	1.33859	+	1.67854i
$425$	−20.3527	−	9.80135i	−0.987252	−	0.475435i
$426$		0			0
$427$	17.0479	−	21.3773i	0.825003	−	1.03452i
$428$	64.2809	−	30.9560i	3.10713	−	1.49632i
$429$		0			0
$430$	3.50248	−	15.3454i	0.168904	−	0.740019i
$431$	−20.4808	−	9.86302i	−0.986524	−	0.475085i	−0.130180	−	0.991490i	$-0.541556\pi$
$431$	−20.4808	−	9.86302i	−0.986524	−	0.475085i	−0.856344	+	0.516405i	$0.827270\pi$
$432$		0			0
$433$	1.22623	−	5.37245i	0.0589287	−	0.258184i	−0.936879	−	0.349653i	$-0.886299\pi$
$433$	1.22623	−	5.37245i	0.0589287	−	0.258184i	0.995808	+	0.0914698i	$0.0291565\pi$
$434$	−36.7494			−1.76403
$435$		0			0
$436$	−27.7653			−1.32972
$437$	−0.431339	+	1.88982i	−0.0206337	+	0.0904023i
$438$		0			0
$439$	−18.2571	−	8.79215i	−0.871363	−	0.419626i	−0.0559006	−	0.998436i	$-0.517803\pi$
$439$	−18.2571	−	8.79215i	−0.871363	−	0.419626i	−0.815462	+	0.578810i	$0.803517\pi$
$440$	−15.3955	+	67.4520i	−0.733950	+	3.21565i
$441$		0			0
$442$	26.9389	−	12.9731i	1.28135	−	0.617067i
$443$	−21.1350	+	26.5024i	−1.00415	+	1.25917i	−0.0385212	+	0.999258i	$0.512265\pi$
$443$	−21.1350	+	26.5024i	−1.00415	+	1.25917i	−0.965633	+	0.259911i	$0.916307\pi$
$444$		0			0
$445$	15.9820	+	7.69650i	0.757617	+	0.364849i
$446$	35.4487	+	44.4512i	1.67854	+	2.10483i
$447$		0			0
$448$	−28.3855	−	35.5943i	−1.34109	−	1.68167i
$449$	7.17733	+	31.4459i	0.338719	+	1.48403i	0.801737	+	0.597677i	$0.203909\pi$
$449$	7.17733	+	31.4459i	0.338719	+	1.48403i	−0.463018	+	0.886349i	$0.653234\pi$
$450$		0			0
$451$	−12.4432	−	15.6033i	−0.585930	−	0.734733i
$452$	56.0148			2.63472
$453$		0			0
$454$	25.8558	+	12.4515i	1.21347	+	0.584378i
$455$	−10.6121	+	13.3072i	−0.497504	+	0.623851i
$456$		0			0
$457$	23.5438	−	11.3381i	1.10133	−	0.530375i	0.207257	−	0.978287i	$-0.433546\pi$
$457$	23.5438	−	11.3381i	1.10133	−	0.530375i	0.894078	+	0.447912i	$0.147832\pi$
$458$	8.35546	+	36.6076i	0.390425	+	1.71056i
$459$		0			0
$460$	17.2030	+	8.28453i	0.802095	+	0.386268i
$461$	−11.2947	+	5.43923i	−0.526046	+	0.253330i	−0.678006	−	0.735056i	$-0.737156\pi$
$461$	−11.2947	+	5.43923i	−0.526046	+	0.253330i	0.151960	+	0.988387i	$0.451441\pi$
$462$		0			0
$463$	−38.0989			−1.77061			−0.885303	−	0.465014i	$-0.846049\pi$
$463$	−38.0989			−1.77061			−0.885303	+	0.465014i	$0.846049\pi$
$464$	−21.2064	−	64.0890i	−0.984482	−	2.97526i
$465$		0			0
$466$	−7.38860	+	32.3716i	−0.342270	+	1.49958i
$467$	−6.22496	+	2.99778i	−0.288057	+	0.138721i	−0.572332	−	0.820022i	$-0.693961\pi$
$467$	−6.22496	+	2.99778i	−0.288057	+	0.138721i	0.284276	+	0.958743i	$0.408247\pi$
$468$		0			0
$469$	−3.67834	+	16.1159i	−0.169850	+	0.744161i
$470$	17.2611	+	75.6259i	0.796196	+	3.48836i
$471$		0			0
$472$	26.1344	−	32.7714i	1.20293	−	1.50843i
$473$	−3.06284	+	3.84068i	−0.140829	+	0.176595i
$474$		0			0
$475$	4.77596	+	5.98886i	0.219136	+	0.274788i
$476$	−59.4015			−2.72266
$477$		0			0
$478$	5.31150	+	23.2712i	0.242942	+	1.06440i
$479$	−3.38908	−	14.8485i	−0.154851	−	0.678446i	−0.991434	−	0.130607i	$-0.958308\pi$
$479$	−3.38908	−	14.8485i	−0.154851	−	0.678446i	0.836583	−	0.547840i	$-0.184550\pi$
$480$		0			0
$481$	−15.9246			−0.726101
$482$	−43.7108	−	54.8116i	−1.99097	−	2.49660i
$483$		0			0
$484$	−13.6681	+	17.1392i	−0.621275	+	0.779054i
$485$	−32.5691	+	40.8404i	−1.47889	+	1.85447i
$486$		0			0
$487$	7.04525	+	30.8672i	0.319251	+	1.39873i	0.838871	+	0.544331i	$0.183216\pi$
$487$	7.04525	+	30.8672i	0.319251	+	1.39873i	−0.519620	+	0.854397i	$0.673927\pi$
$488$	21.9366	−	96.1104i	0.993022	−	4.35071i
$489$		0			0
$490$	−10.3838	+	5.00057i	−0.469092	+	0.225903i
$491$	2.38715	−	10.4588i	0.107731	−	0.471998i	−0.892067	−	0.451902i	$-0.850746\pi$
$491$	2.38715	−	10.4588i	0.107731	−	0.471998i	0.999798	−	0.0200962i	$-0.00639726\pi$
$492$		0			0
$493$	−24.4061	−	9.00999i	−1.09920	−	0.405789i
$494$	−10.1388			−0.456168
$495$		0			0
$496$	−65.3167	+	31.4549i	−2.93281	+	1.41237i
$497$	−7.97763	−	3.84182i	−0.357846	−	0.172329i
$498$		0			0
$499$	2.17395	+	9.52472i	0.0973196	+	0.426385i	0.999992	−	0.00394299i	$-0.00125509\pi$
$499$	2.17395	+	9.52472i	0.0973196	+	0.426385i	−0.902673	+	0.430328i	$0.858398\pi$
$500$	−4.71135	+	2.26887i	−0.210698	+	0.101467i
$501$		0			0
$502$	−6.47980	+	8.12541i	−0.289208	+	0.362655i
$503$	−21.8843	−	10.5389i	−0.975771	−	0.469907i	−0.123123	−	0.992391i	$-0.539291\pi$
$503$	−21.8843	−	10.5389i	−0.975771	−	0.469907i	−0.852649	+	0.522485i	$0.825005\pi$
$504$		0			0
$505$	14.2536			0.634275
$506$	−5.14793	−	6.45530i	−0.228853	−	0.286973i
$507$		0			0
$508$	−19.4634	−	85.2747i	−0.863548	−	3.78345i
$509$	2.52048	+	3.16058i	0.111718	+	0.140090i	0.834547	−	0.550937i	$-0.185730\pi$
$509$	2.52048	+	3.16058i	0.111718	+	0.140090i	−0.722828	+	0.691028i	$0.757158\pi$
$510$		0			0
$511$	−3.53707	−	4.43534i	−0.156471	−	0.196208i
$512$	6.49796	+	3.12925i	0.287172	+	0.138295i
$513$		0			0
$514$	2.70175	−	3.38789i	0.119169	−	0.149433i
$515$	29.5144	−	14.2134i	1.30056	−	0.626316i
$516$		0			0
$517$	5.38715	−	23.6027i	0.236927	−	1.03804i
$518$	39.4934	+	19.0190i	1.73524	+	0.835649i
$519$		0			0
$520$	−13.6553	+	59.8278i	−0.598825	+	2.62362i
$521$	20.3240			0.890412			0.445206	−	0.895428i	$-0.353130\pi$
$521$	20.3240			0.890412			0.445206	+	0.895428i	$0.353130\pi$
$522$		0			0
$523$	0.181906			0.00795418			0.00397709	−	0.999992i	$-0.498734\pi$
$523$	0.181906			0.00795418			0.00397709	+	0.999992i	$0.498734\pi$
$524$	5.25585	−	23.0274i	0.229603	−	1.00596i
$525$		0			0
$526$	−54.7398	−	26.3613i	−2.38677	−	1.14941i
$527$	−6.21703	+	27.2386i	−0.270818	+	1.18653i
$528$		0			0
$529$	19.4608	−	9.37183i	0.846122	−	0.407471i
$530$	−26.8980	+	33.7290i	−1.16837	+	1.46509i
$531$		0			0
$532$	18.1479	+	8.73955i	0.786810	+	0.378908i
$533$	−11.0368	−	13.8397i	−0.478056	−	0.599463i
$534$		0			0
$535$	26.6738	+	33.4479i	1.15321	+	1.44608i
$536$	13.2620	+	58.1047i	0.572832	+	2.50974i
$537$		0			0
$538$	8.72587	+	10.9419i	0.376199	+	0.471739i
$539$	3.59696			0.154932
$540$		0			0
$541$	24.3124	+	11.7082i	1.04527	+	0.503376i	0.876059	−	0.482203i	$-0.160163\pi$
$541$	24.3124	+	11.7082i	1.04527	+	0.503376i	0.169212	+	0.985580i	$0.445878\pi$
$542$	2.50629	−	3.14279i	0.107654	−	0.134994i
$543$		0			0
$544$	−71.8887	+	34.6198i	−3.08220	+	1.48431i
$545$	−3.70474	−	16.2315i	−0.158694	−	0.695282i
$546$		0			0
$547$	−7.87494	−	3.79237i	−0.336708	−	0.162150i	0.257887	−	0.966175i	$-0.416974\pi$
$547$	−7.87494	−	3.79237i	−0.336708	−	0.162150i	−0.594596	+	0.804025i	$0.702688\pi$
$548$	−102.867	+	49.5383i	−4.39427	+	2.11617i
$549$		0			0
$550$	−32.6277			−1.39125
$551$	6.13075	+	6.34346i	0.261179	+	0.270240i
$552$		0			0
$553$	1.98281	−	8.68727i	0.0843177	−	0.369420i
$554$	−5.26857	+	2.53721i	−0.223840	+	0.107796i
$555$		0			0
$556$	9.34285	−	40.9337i	0.396225	−	1.73598i
$557$	−6.30376	−	27.6186i	−0.267099	−	1.17024i	−0.913371	−	0.407129i	$-0.866530\pi$
$557$	−6.30376	−	27.6186i	−0.267099	−	1.17024i	0.646272	−	0.763107i	$-0.276327\pi$
$558$		0			0
$559$	−2.71664	+	3.40656i	−0.114902	+	0.144082i
$560$	57.6252	−	72.2597i	2.43511	−	3.05353i
$561$		0			0
$562$	28.7965	+	36.1097i	1.21471	+	1.52319i
$563$	1.24481			0.0524623			0.0262312	−	0.999656i	$-0.491649\pi$
$563$	1.24481			0.0524623			0.0262312	+	0.999656i	$0.491649\pi$
$564$		0			0
$565$	7.47408	+	32.7461i	0.314437	+	1.37764i
$566$	6.81907	+	29.8763i	0.286627	+	1.25579i
$567$		0			0
$568$	−31.9243			−1.33951
$569$	5.14541	+	6.45214i	0.215707	+	0.270488i	0.877899	−	0.478847i	$-0.158945\pi$
$569$	5.14541	+	6.45214i	0.215707	+	0.270488i	−0.662192	+	0.749334i	$0.730374\pi$
$570$		0			0
$571$	17.3342	−	21.7364i	0.725415	−	0.909642i	−0.273216	−	0.961953i	$-0.588087\pi$
$571$	17.3342	−	21.7364i	0.725415	−	0.909642i	0.998631	+	0.0523110i	$0.0166587\pi$
$572$	19.4337	−	24.3691i	0.812563	−	1.01892i
$573$		0			0
$574$	10.8425	+	47.5041i	0.452557	+	1.98278i
$575$	−1.23119	+	5.39420i	−0.0513442	+	0.224954i
$576$		0			0
$577$	−6.48400	+	3.12253i	−0.269932	+	0.129993i	−0.563954	−	0.825806i	$-0.690721\pi$
$577$	−6.48400	+	3.12253i	−0.269932	+	0.129993i	0.294022	+	0.955799i	$0.405006\pi$
$578$	−3.78182	+	16.5692i	−0.157303	+	0.689190i
$579$		0			0
$580$	74.3559	−	44.9712i	3.08746	−	1.86733i
$581$	−25.1124			−1.04184
$582$		0			0
$583$	12.1308	−	5.84190i	0.502407	−	0.241947i
$584$	−18.4281	−	8.87453i	−0.762562	−	0.367231i
$585$		0			0
$586$	−3.05714	−	13.3942i	−0.126289	−	0.553310i
$587$	7.62256	−	3.67083i	0.314617	−	0.151511i	−0.269911	−	0.962885i	$-0.586994\pi$
$587$	7.62256	−	3.67083i	0.314617	−	0.151511i	0.584527	+	0.811374i	$0.301280\pi$
$588$		0			0
$589$	5.90691	−	7.40703i	0.243390	−	0.305201i
$590$	36.8537	+	17.7478i	1.51724	+	0.730666i
$591$		0			0
$592$	86.4728			3.55401
$593$	17.9522	+	22.5114i	0.737210	+	0.924433i	0.999174	−	0.0406452i	$-0.0129413\pi$
$593$	17.9522	+	22.5114i	0.737210	+	0.924433i	−0.261963	+	0.965078i	$0.584370\pi$
$594$		0			0
$595$	−7.92596	−	34.7259i	−0.324933	−	1.42362i
$596$	−2.40537	−	3.01623i	−0.0985277	−	0.123550i
$597$		0			0
$598$	−4.56606	−	5.72565i	−0.186720	−	0.234139i
$599$	−2.23432	−	1.07599i	−0.0912920	−	0.0439639i	0.387681	−	0.921794i	$-0.373276\pi$
$599$	−2.23432	−	1.07599i	−0.0912920	−	0.0439639i	−0.478973	+	0.877830i	$0.658991\pi$
$600$		0			0
$601$	−24.7528	+	31.0390i	−1.00969	+	1.26611i	−0.0460366	+	0.998940i	$0.514659\pi$
$601$	−24.7528	+	31.0390i	−1.00969	+	1.26611i	−0.963650	+	0.267167i	$0.913912\pi$
$602$	10.8058	−	5.20382i	0.440413	−	0.212092i
$603$		0			0
$604$	19.9563	−	87.4341i	0.812009	−	3.55764i
$605$	−11.8433	−	5.70341i	−0.481497	−	0.231877i
$606$		0			0
$607$	−7.86688	+	34.4671i	−0.319307	+	1.39898i	0.519465	+	0.854492i	$0.326131\pi$
$607$	−7.86688	+	34.4671i	−0.319307	+	1.39898i	−0.838772	+	0.544483i	$0.816726\pi$
$608$	27.0564			1.09728
$609$		0			0
$610$	96.2026			3.89513
$611$	4.77824	−	20.9348i	0.193307	−	0.846933i
$612$		0			0
$613$	−7.29240	−	3.51183i	−0.294537	−	0.141842i	0.280780	−	0.959772i	$-0.409407\pi$
$613$	−7.29240	−	3.51183i	−0.294537	−	0.141842i	−0.575317	+	0.817931i	$0.695121\pi$
$614$	−2.02257	+	8.86146i	−0.0816243	+	0.357619i
$615$		0			0
$616$	−47.4981	+	22.8739i	−1.91375	+	0.921615i
$617$	−17.0599	+	21.3924i	−0.686805	+	0.861227i	−0.995961	−	0.0897847i	$-0.971382\pi$
$617$	−17.0599	+	21.3924i	−0.686805	+	0.861227i	0.309156	+	0.951011i	$0.399954\pi$
$618$		0			0
$619$	−24.4911	−	11.7943i	−0.984382	−	0.474053i	−0.128772	−	0.991674i	$-0.541103\pi$
$619$	−24.4911	−	11.7943i	−0.984382	−	0.474053i	−0.855610	+	0.517621i	$0.826818\pi$
$620$	−58.1845	−	72.9611i	−2.33675	−	2.93019i
$621$		0			0
$622$	−28.6140	−	35.8809i	−1.14732	−	1.43869i
$623$	3.00770	+	13.1776i	0.120501	+	0.527950i
$624$		0			0
$625$	−16.5320	−	20.7305i	−0.661280	−	0.829219i
$626$	−3.88251			−0.155176
$627$		0			0
$628$	1.86619	+	0.898710i	0.0744691	+	0.0358624i
$629$	20.7781	−	26.0550i	0.828479	−	1.03888i
$630$		0			0
$631$	−17.7488	+	8.54737i	−0.706568	+	0.340265i	−0.752421	−	0.658683i	$-0.771114\pi$
$631$	−17.7488	+	8.54737i	−0.706568	+	0.340265i	0.0458525	+	0.998948i	$0.485400\pi$
$632$	−7.14890	−	31.3214i	−0.284368	−	1.24590i
$633$		0			0
$634$	−42.3115	−	20.3761i	−1.68040	−	0.809240i
$635$	47.2543	−	22.7565i	1.87523	−	0.903062i
$636$		0			0
$637$	3.19040			0.126408
$638$	−37.4066	+	3.57002i	−1.48094	+	0.141338i
$639$		0			0
$640$	12.7797	−	55.9917i	0.505164	−	2.21327i
$641$	0.252515	−	0.121605i	0.00997374	−	0.00480310i	−0.428890	−	0.903357i	$-0.641095\pi$
$641$	0.252515	−	0.121605i	0.00997374	−	0.00480310i	0.438864	+	0.898554i	$0.355381\pi$
$642$		0			0
$643$	10.4808	−	45.9192i	0.413321	−	1.81088i	−0.154817	−	0.987943i	$-0.549479\pi$
$643$	10.4808	−	45.9192i	0.413321	−	1.81088i	0.568137	−	0.822934i	$-0.307664\pi$
$644$	3.23750	+	14.1844i	0.127575	+	0.558944i
$645$		0			0
$646$	13.2290	−	16.5886i	0.520487	−	0.652670i
$647$	0.681877	−	0.855046i	0.0268073	−	0.0336153i	−0.768247	−	0.640153i	$-0.778871\pi$
$647$	0.681877	−	0.855046i	0.0268073	−	0.0336153i	0.795054	+	0.606538i	$0.207442\pi$
$648$		0			0
$649$	−7.95959	−	9.98101i	−0.312441	−	0.391789i
$650$	−28.9398			−1.13511
$651$		0			0
$652$	−11.4435	−	50.1371i	−0.448161	−	1.96352i
$653$	−6.63281	−	29.0602i	−0.259562	−	1.13722i	−0.921721	−	0.387852i	$-0.873217\pi$
$653$	−6.63281	−	29.0602i	−0.259562	−	1.13722i	0.662160	−	0.749363i	$-0.269640\pi$
$654$		0			0
$655$	14.1630			0.553395
$656$	59.9311	+	75.1513i	2.33992	+	2.93416i
$657$		0			0
$658$	−36.8529	+	46.2121i	−1.43668	+	1.80153i
$659$	20.7854	−	26.0640i	0.809683	−	1.01531i	−0.189756	−	0.981831i	$-0.560770\pi$
$659$	20.7854	−	26.0640i	0.809683	−	1.01531i	0.999439	−	0.0334791i	$-0.0106587\pi$
$660$		0			0
$661$	−0.544903	−	2.38738i	−0.0211943	−	0.0928581i	0.963225	−	0.268698i	$-0.0865932\pi$
$661$	−0.544903	−	2.38738i	−0.0211943	−	0.0928581i	−0.984419	+	0.175839i	$0.943736\pi$
$662$	−6.22082	+	27.2552i	−0.241779	+	1.05930i
$663$		0			0
$664$	−81.5748	+	39.2844i	−3.16572	+	1.52453i
$665$	−2.68764	+	11.7753i	−0.104222	+	0.456627i
$666$		0			0
$667$	−0.821302	+	6.31898i	−0.0318009	+	0.244672i
$668$	60.7929			2.35215
$669$		0			0
$670$	−52.4007	+	25.2348i	−2.02442	+	0.974907i
$671$	−27.0512	−	13.0272i	−1.04430	−	0.502908i
$672$		0			0
$673$	−2.49804	−	10.9446i	−0.0962924	−	0.421884i	0.903688	−	0.428192i	$-0.140849\pi$
$673$	−2.49804	−	10.9446i	−0.0962924	−	0.421884i	−0.999980	+	0.00630766i	$0.997992\pi$
$674$	77.7809	−	37.4573i	2.99601	−	1.44280i
$675$		0			0
$676$	−24.8100	+	31.1107i	−0.954229	+	1.19657i
$677$	−4.61715	−	2.22350i	−0.177451	−	0.0854561i	0.343049	−	0.939318i	$-0.388540\pi$
$677$	−4.61715	−	2.22350i	−0.177451	−	0.0854561i	−0.520500	+	0.853861i	$0.674255\pi$
$678$		0			0
$679$	−39.8035			−1.52752
$680$	−80.0697	−	100.404i	−3.07053	−	3.85032i
$681$		0			0
$682$	8.97961	+	39.3422i	0.343847	+	1.50649i
$683$	−18.4315	−	23.1123i	−0.705260	−	0.884368i	0.292144	−	0.956374i	$-0.405631\pi$
$683$	−18.4315	−	23.1123i	−0.705260	−	0.884368i	−0.997404	+	0.0720063i	$0.977060\pi$
$684$		0			0
$685$	−42.6855	−	53.5260i	−1.63093	−	2.04512i
$686$	−47.9887	−	23.1101i	−1.83222	−	0.882349i
$687$		0			0
$688$	14.7517	−	18.4981i	0.562404	−	0.705232i
$689$	10.7597	−	5.18158i	0.409911	−	0.197403i
$690$		0			0
$691$	−9.83685	+	43.0981i	−0.374211	+	1.63953i	0.340599	+	0.940209i	$0.389370\pi$
$691$	−9.83685	+	43.0981i	−0.374211	+	1.63953i	−0.714810	+	0.699319i	$0.753487\pi$
$692$	38.0608	+	18.3291i	1.44685	+	0.696769i
$693$		0			0
$694$	4.15557	−	18.2068i	0.157743	−	0.691119i
$695$	25.1763			0.954992
$696$		0			0
$697$	37.0443			1.40315
$698$	−8.33491	+	36.5176i	−0.315481	+	1.38221i
$699$		0			0
$700$	51.8003	+	24.9457i	1.95787	+	0.942859i
$701$	−5.71682	+	25.0470i	−0.215921	+	0.946013i	0.744535	+	0.667583i	$0.232671\pi$
$701$	−5.71682	+	25.0470i	−0.215921	+	0.946013i	−0.960457	+	0.278430i	$0.910186\pi$
$702$		0			0
$703$	−10.1814	+	4.90308i	−0.383997	+	0.184923i
$704$	−31.1698	+	39.0857i	−1.17475	+	1.47310i
$705$		0			0
$706$	62.4210	+	30.0604i	2.34925	+	1.13134i
$707$	6.77168	+	8.49142i	0.254675	+	0.319353i
$708$		0			0
$709$	11.3053	+	14.1764i	0.424579	+	0.532405i	0.947406	−	0.320033i	$-0.103694\pi$
$709$	11.3053	+	14.1764i	0.424579	+	0.532405i	−0.522827	+	0.852439i	$0.675123\pi$
$710$	−6.93236	−	30.3727i	−0.260167	−	1.13987i
$711$		0			0
$712$	30.3844	+	38.1009i	1.13871	+	1.42789i
$713$	6.84312			0.256277
$714$		0			0
$715$	16.8391	+	8.10929i	0.629747	+	0.303270i
$716$	−34.8619	+	43.7155i	−1.30285	+	1.63372i
$717$		0			0
$718$	−42.3756	+	20.4070i	−1.58144	+	0.761583i
$719$	1.22528	+	5.36832i	0.0456954	+	0.200205i	0.992623	−	0.121243i	$-0.0386879\pi$
$719$	1.22528	+	5.36832i	0.0456954	+	0.200205i	−0.946928	+	0.321447i	$0.895831\pi$
$720$		0			0
$721$	22.4894	+	10.8303i	0.837548	+	0.403342i
$722$	39.4116	−	18.9796i	1.46675	−	0.706348i
$723$		0			0
$724$	106.928			3.97396
$725$	17.4993	+	18.1064i	0.649908	+	0.672456i
$726$		0			0
$727$	6.13737	−	26.8896i	0.227622	−	0.997279i	−0.723950	−	0.689853i	$-0.757675\pi$
$727$	6.13737	−	26.8896i	0.227622	−	0.997279i	0.951572	−	0.307426i	$-0.0994677\pi$
$728$	−42.1293	+	20.2884i	−1.56142	+	0.751939i
$729$		0			0
$730$	4.44152	−	19.4596i	0.164388	−	0.720231i
$731$	−2.02900	−	8.88963i	−0.0750453	−	0.328795i
$732$		0			0
$733$	−26.6783	+	33.4535i	−0.985384	+	1.23563i	−0.0135639	+	0.999908i	$0.504318\pi$
$733$	−26.6783	+	33.4535i	−0.985384	+	1.23563i	−0.971820	+	0.235724i	$0.924254\pi$
$734$	49.7502	−	62.3848i	1.83631	−	2.30267i
$735$		0			0
$736$	12.1849	+	15.2794i	0.449142	+	0.563206i
$737$	18.1517			0.668627
$738$		0			0
$739$	−6.66662	−	29.2084i	−0.245236	−	1.07445i	−0.936175	−	0.351535i	$-0.885660\pi$
$739$	−6.66662	−	29.2084i	−0.245236	−	1.07445i	0.690939	−	0.722913i	$-0.257197\pi$
$740$	24.7693	+	108.521i	0.910538	+	3.98933i
$741$		0			0
$742$	−32.8726			−1.20679
$743$	−0.969337	−	1.21551i	−0.0355615	−	0.0445928i	0.763733	−	0.645533i	$-0.223365\pi$
$743$	−0.969337	−	1.21551i	−0.0355615	−	0.0445928i	−0.799294	+	0.600940i	$0.794793\pi$
$744$		0			0
$745$	1.44233	−	1.80863i	0.0528429	−	0.0662630i
$746$	32.2534	−	40.4445i	1.18088	−	1.48078i
$747$		0			0
$748$	14.5146	+	63.5925i	0.530706	+	2.32517i
$749$	−7.25389	+	31.7814i	−0.265051	+	1.16127i
$750$		0			0
$751$	37.8839	−	18.2439i	1.38240	−	0.665731i	0.412894	−	0.910779i	$-0.364518\pi$
$751$	37.8839	−	18.2439i	1.38240	−	0.665731i	0.969511	+	0.245048i	$0.0788037\pi$
$752$	−25.9464	+	113.679i	−0.946169	+	4.14544i
$753$		0			0
$754$	−33.1785	+	3.16650i	−1.20829	+	0.115317i
$755$	53.7765			1.95713
$756$		0			0
$757$	24.4696	−	11.7839i	0.889362	−	0.428294i	0.0673267	−	0.997731i	$-0.478553\pi$
$757$	24.4696	−	11.7839i	0.889362	−	0.428294i	0.822035	+	0.569437i	$0.192839\pi$
$758$	20.7470	+	9.99124i	0.753566	+	0.362898i
$759$		0			0
$760$	9.69009	+	42.4551i	0.351497	+	1.54001i
$761$	−31.5591	+	15.1980i	−1.14402	+	0.550929i	−0.907231	−	0.420633i	$-0.861808\pi$
$761$	−31.5591	+	15.1980i	−1.14402	+	0.550929i	−0.236785	+	0.971562i	$0.576094\pi$
$762$		0			0
$763$	7.90970	−	9.91846i	0.286351	−	0.359072i
$764$	−114.448	−	55.1151i	−4.14057	−	1.99399i
$765$		0			0
$766$	75.8493			2.74055
$767$	−7.05991	−	8.85285i	−0.254919	−	0.319658i
$768$		0			0
$769$	−4.80403	−	21.0478i	−0.173238	−	0.759004i	−0.984652	−	0.174532i	$-0.944159\pi$
$769$	−4.80403	−	21.0478i	−0.173238	−	0.759004i	0.811414	−	0.584472i	$-0.198698\pi$
$770$	−32.0763	−	40.2224i	−1.15595	−	1.44952i
$771$		0			0
$772$	−51.2429	−	64.2566i	−1.84427	−	2.31264i
$773$	39.9923	+	19.2593i	1.43842	+	0.692709i	0.980543	−	0.196304i	$-0.0628941\pi$
$773$	39.9923	+	19.2593i	1.43842	+	0.692709i	0.457882	+	0.889013i	$0.348608\pi$
$774$		0			0
$775$	16.8604	−	21.1422i	0.605642	−	0.759451i
$776$	−129.297	+	62.2662i	−4.64149	+	2.23523i
$777$		0			0
$778$	−16.2173	+	71.0528i	−0.581420	+	2.54737i
$779$	−11.3175	−	5.45020i	−0.405490	−	0.195274i
$780$		0			0
$781$	−2.16357	+	9.47923i	−0.0774187	+	0.339194i
$782$	15.3257			0.548045
$783$		0			0
$784$	−17.3243			−0.618724
$785$	−0.276376	+	1.21088i	−0.00986430	+	0.0432183i
$786$		0			0
$787$	−18.6719	−	8.99190i	−0.665580	−	0.320527i	0.0704104	−	0.997518i	$-0.477569\pi$
$787$	−18.6719	−	8.99190i	−0.665580	−	0.320527i	−0.735991	+	0.676991i	$0.763283\pi$
$788$	14.7184	−	64.4856i	0.524322	−	2.29720i
$789$		0			0
$790$	28.2466	−	13.6029i	1.00497	−	0.483968i
$791$	−15.9573	+	20.0099i	−0.567378	+	0.711469i
$792$		0			0
$793$	−23.9936	−	11.5547i	−0.852037	−	0.410319i
$794$	8.28462	+	10.3886i	0.294010	+	0.368677i
$795$		0			0
$796$	−26.2788	−	32.9525i	−0.931427	−	1.16797i
$797$	−1.09838	−	4.81233i	−0.0389068	−	0.170462i	0.951742	−	0.306900i	$-0.0992916\pi$
$797$	−1.09838	−	4.81233i	−0.0389068	−	0.170462i	−0.990649	+	0.136438i	$0.956435\pi$
$798$		0			0
$799$	28.0178	+	35.1332i	0.991199	+	1.24292i
$800$	77.2282			2.73043
$801$		0			0
$802$	15.0230	+	7.23470i	0.530481	+	0.255466i
$803$	−3.88401	+	4.87039i	−0.137064	+	0.171872i
$804$		0			0
$805$	−7.86018	+	3.78526i	−0.277035	+	0.133413i
$806$	7.96464	+	34.8954i	0.280542	+	1.22914i
$807$		0			0
$808$	35.2805	+	16.9902i	1.24116	+	0.597713i
$809$	1.07371	−	0.517072i	0.0377497	−	0.0181793i	−0.414914	−	0.909861i	$-0.636188\pi$
$809$	1.07371	−	0.517072i	0.0377497	−	0.0181793i	0.452663	+	0.891681i	$0.350474\pi$
$810$		0			0
$811$	46.6639			1.63859			0.819296	−	0.573370i	$-0.194364\pi$
$811$	46.6639			1.63859			0.819296	+	0.573370i	$0.194364\pi$
$812$	62.1168	+	22.9316i	2.17987	+	0.804741i
$813$		0			0
$814$	10.7108	−	46.9271i	0.375414	−	1.64480i
$815$	27.7831	−	13.3796i	0.973198	−	0.468668i
$816$		0			0
$817$	−0.688019	+	3.01441i	−0.0240707	+	0.105461i
$818$	−2.76731	−	12.1244i	−0.0967569	−	0.423920i
$819$		0			0
$820$	−77.1464	+	96.7386i	−2.69407	+	3.37826i
$821$	−19.7875	+	24.8127i	−0.690588	+	0.865970i	−0.996281	−	0.0861603i	$-0.972540\pi$
$821$	−19.7875	+	24.8127i	−0.690588	+	0.865970i	0.305694	+	0.952130i	$0.401112\pi$
$822$		0			0
$823$	−23.9132	−	29.9862i	−0.833561	−	1.04525i	−0.998263	−	0.0589096i	$-0.981238\pi$
$823$	−23.9132	−	29.9862i	−0.833561	−	1.04525i	0.164702	−	0.986343i	$-0.447334\pi$
$824$	89.9964			3.13517
$825$		0			0
$826$	6.93564	+	30.3870i	0.241322	+	1.05730i
$827$	−3.81065	−	16.6955i	−0.132509	−	0.580561i	−0.996965	−	0.0778518i	$-0.975194\pi$
$827$	−3.81065	−	16.6955i	−0.132509	−	0.580561i	0.864456	−	0.502709i	$-0.167663\pi$
$828$		0			0
$829$	50.9294			1.76885			0.884425	−	0.466682i	$-0.154551\pi$
$829$	50.9294			1.76885			0.884425	+	0.466682i	$0.154551\pi$
$830$	−55.0890	−	69.0794i	−1.91217	−	2.39778i
$831$		0			0
$832$	−27.6466	+	34.6678i	−0.958474	+	1.20189i
$833$	−4.16277	+	5.21994i	−0.144231	+	0.180860i
$834$		0			0
$835$	8.11161	+	35.5393i	0.280714	+	1.22989i
$836$	4.92179	−	21.5638i	0.170224	−	0.745799i
$837$		0			0
$838$	33.0144	−	15.8989i	1.14046	−	0.549218i
$839$	8.56685	−	37.5338i	0.295760	−	1.29581i	−0.580613	−	0.814179i	$-0.697187\pi$
$839$	8.56685	−	37.5338i	0.295760	−	1.29581i	0.876374	−	0.481632i	$-0.159956\pi$
$840$		0			0
$841$	22.0435	+	18.8437i	0.760121	+	0.649782i
$842$	−31.9116			−1.09974
$843$		0			0
$844$	98.1290	−	47.2564i	3.37774	−	1.62663i
$845$	−21.4976	−	10.3527i	−0.739540	−	0.356144i
$846$		0			0
$847$	−2.22883	−	9.76513i	−0.0765834	−	0.335534i
$848$	−58.4264	+	28.1367i	−2.00637	+	0.966217i
$849$		0			0
$850$	37.7600	−	47.3496i	1.29516	−	1.62408i
$851$	−7.35409	−	3.54154i	−0.252095	−	0.121403i
$852$		0			0
$853$	−19.5496			−0.669364			−0.334682	−	0.942331i	$-0.608629\pi$
$853$	−19.5496			−0.669364			−0.334682	+	0.942331i	$0.608629\pi$
$854$	45.7046	+	57.3118i	1.56398	+	1.96117i
$855$		0			0
$856$	26.1534	+	114.586i	0.893905	+	3.91646i
$857$	3.75869	+	4.71325i	0.128394	+	0.161002i	0.841873	−	0.539675i	$-0.181453\pi$
$857$	3.75869	+	4.71325i	0.128394	+	0.161002i	−0.713479	+	0.700677i	$0.752882\pi$
$858$		0			0
$859$	9.53742	+	11.9596i	0.325413	+	0.408055i	0.917447	−	0.397858i	$-0.130246\pi$
$859$	9.53742	+	11.9596i	0.325413	+	0.408055i	−0.592034	+	0.805913i	$0.701675\pi$
$860$	27.4401	+	13.2145i	0.935701	+	0.450610i
$861$		0			0
$862$	37.9976	−	47.6475i	1.29420	−	1.62288i
$863$	−4.59289	+	2.21182i	−0.156344	+	0.0752913i	−0.510419	−	0.859926i	$-0.670510\pi$
$863$	−4.59289	+	2.21182i	−0.156344	+	0.0752913i	0.354076	+	0.935217i	$0.384796\pi$
$864$		0			0
$865$	−5.63667	+	24.6959i	−0.191653	+	0.839685i
$866$	13.3107	+	6.41009i	0.452315	+	0.217824i
$867$		0			0
$868$	15.8232	−	69.3258i	0.537073	−	2.35307i
$869$	−9.78469			−0.331923
$870$		0			0
$871$	16.1000			0.545528
$872$	10.1779	−	44.5924i	0.344668	−	1.51009i
$873$		0			0
$874$	−4.68218	−	2.25482i	−0.158377	−	0.0762704i
$875$	0.531661	−	2.32936i	0.0179734	−	0.0787467i
$876$		0			0
$877$	−50.7911	+	24.4597i	−1.71509	+	0.825945i	−0.724473	+	0.689303i	$0.757917\pi$
$877$	−50.7911	+	24.4597i	−1.71509	+	0.825945i	−0.990621	+	0.136642i	$0.956369\pi$
$878$	33.8721	−	42.4742i	1.14313	−	1.43344i
$879$		0			0
$880$	−91.4386	−	44.0345i	−3.08239	−	1.48440i
$881$	−5.46459	−	6.85238i	−0.184107	−	0.230863i	0.681210	−	0.732088i	$-0.261454\pi$
$881$	−5.46459	−	6.85238i	−0.184107	−	0.230863i	−0.865317	+	0.501226i	$0.832883\pi$
$882$		0			0
$883$	−27.7872	−	34.8440i	−0.935112	−	1.17259i	−0.984776	−	0.173828i	$-0.944386\pi$
$883$	−27.7872	−	34.8440i	−0.935112	−	1.17259i	0.0496640	−	0.998766i	$-0.484185\pi$
$884$	12.8740	+	56.4046i	0.432999	+	1.89709i
$885$		0			0
$886$	−56.6621	−	71.0520i	−1.90360	−	2.38704i
$887$	−50.8916			−1.70877			−0.854386	−	0.519639i	$-0.826067\pi$
$887$	−50.8916			−1.70877			−0.854386	+	0.519639i	$0.826067\pi$
$888$		0			0
$889$	36.0069	+	17.3400i	1.20763	+	0.581565i
$890$	−29.6511	+	37.1812i	−0.993905	+	1.24632i
$891$		0			0
$892$	−99.1180	+	47.7327i	−3.31872	+	1.59821i
$893$	−3.39074	−	14.8558i	−0.113467	−	0.497130i
$894$		0			0
$895$	−30.2076	−	14.5472i	−1.00973	−	0.486259i
$896$	39.4281	−	18.9876i	1.31720	−	0.634330i
$897$		0			0
$898$	−86.4734			−2.88566
$899$	17.0165	−	26.0836i	0.567533	−	0.869938i
$900$		0			0
$901$	−5.56119	+	24.3652i	−0.185270	+	0.811721i
$902$	48.2064	−	23.2150i	1.60510	−	0.772974i
$903$		0			0
$904$	−20.5333	+	89.9624i	−0.682929	+	2.99211i
$905$	14.2675	+	62.5100i	0.474268	+	2.07790i
$906$		0			0
$907$	−13.8142	+	17.3225i	−0.458695	+	0.575185i	−0.956362	−	0.292183i	$-0.905618\pi$
$907$	−13.8142	+	17.3225i	−0.458695	+	0.575185i	0.497668	+	0.867368i	$0.334190\pi$
$908$	−34.6218	+	43.4144i	−1.14897	+	1.44076i
$909$		0			0
$910$	−28.4507	−	35.6761i	−0.943132	−	1.18265i
$911$	−2.98463			−0.0988851			−0.0494425	−	0.998777i	$-0.515744\pi$
$911$	−2.98463			−0.0988851			−0.0494425	+	0.998777i	$0.515744\pi$
$912$		0			0
$913$	6.13615	+	26.8842i	0.203077	+	0.889738i
$914$	15.5894	+	68.3016i	0.515651	+	2.25921i
$915$		0			0
$916$	−72.6560			−2.40062
$917$	6.72867	+	8.43748i	0.222200	+	0.278630i
$918$		0			0
$919$	−2.67826	+	3.35843i	−0.0883475	+	0.110784i	−0.824041	−	0.566531i	$-0.808285\pi$
$919$	−2.67826	+	3.35843i	−0.0883475	+	0.110784i	0.735693	+	0.677315i	$0.236857\pi$
$920$	−19.6115	+	24.5920i	−0.646570	+	0.810774i
$921$		0			0
$922$	−7.47869	−	32.7663i	−0.246298	−	1.07910i
$923$	−1.91902	+	8.40779i	−0.0631654	+	0.276746i
$924$		0			0
$925$	−29.0611	+	13.9951i	−0.955524	+	0.460156i
$926$	22.7287	−	99.5808i	0.746911	−	3.27243i
$927$		0			0
$928$	88.5396	−	8.45007i	2.90645	−	0.277387i
$929$	−33.6586			−1.10430			−0.552152	−	0.833743i	$-0.686193\pi$
$929$	−33.6586			−1.10430			−0.552152	+	0.833743i	$0.686193\pi$
$930$		0			0
$931$	2.03977	−	0.982301i	0.0668507	−	0.0321936i
$932$	−57.8859	−	27.8764i	−1.89612	−	0.913122i
$933$		0			0
$934$	−4.12181	−	18.0588i	−0.134870	−	0.590903i
$935$	−35.2393	+	16.9704i	−1.15245	+	0.554990i
$936$		0			0
$937$	15.0681	−	18.8947i	0.492252	−	0.617264i	−0.472210	−	0.881486i	$-0.656544\pi$
$937$	15.0681	−	18.8947i	0.492252	−	0.617264i	0.964462	+	0.264222i	$0.0851151\pi$
$938$	−39.9283	−	19.2285i	−1.30371	−	0.627832i
$939$		0			0
$940$	−150.096			−4.89561
$941$	15.7291	+	19.7237i	0.512755	+	0.642974i	0.969053	−	0.246853i	$-0.0793964\pi$
$941$	15.7291	+	19.7237i	0.512755	+	0.642974i	−0.456298	+	0.889827i	$0.650825\pi$
$942$		0			0
$943$	−2.01899	−	8.84576i	−0.0657473	−	0.288058i
$944$	38.3362	+	48.0721i	1.24774	+	1.56461i
$945$		0			0
$946$	−8.21135	−	10.2967i	−0.266974	−	0.334775i
$947$	43.3634	+	20.8827i	1.40912	+	0.678597i	0.974989	−	0.222251i	$-0.0713406\pi$
$947$	43.3634	+	20.8827i	1.40912	+	0.678597i	0.434133	+	0.900849i	$0.357055\pi$
$948$		0			0
$949$	−3.44500	+	4.31989i	−0.111829	+	0.140229i
$950$	−18.5025	+	8.91035i	−0.600302	+	0.289090i
$951$		0			0
$952$	21.7748	−	95.4015i	0.705725	−	3.09198i
$953$	9.31899	+	4.48779i	0.301872	+	0.145374i	0.578688	−	0.815549i	$-0.303565\pi$
$953$	9.31899	+	4.48779i	0.301872	+	0.145374i	−0.276816	+	0.960923i	$0.589279\pi$
$954$		0			0
$955$	16.9493	−	74.2597i	0.548466	−	2.40299i
$956$	−46.1869			−1.49379
$957$		0			0
$958$	40.8321			1.31922
$959$	11.6082	−	50.8590i	0.374850	−	1.64232i
$960$		0			0
$961$	−2.20329	−	1.06105i	−0.0710740	−	0.0342274i
$962$	9.50016	−	41.6229i	0.306298	−	1.34198i
$963$		0			0
$964$	122.220	−	58.8579i	3.93643	−	1.89568i
$965$	30.7268	−	38.5302i	0.989131	−	1.24033i
$966$		0			0
$967$	17.7741	+	8.55958i	0.571578	+	0.275257i	0.697266	−	0.716812i	$-0.254400\pi$
$967$	17.7741	+	8.55958i	0.571578	+	0.275257i	−0.125688	+	0.992070i	$0.540114\pi$
$968$	−22.5161	−	28.2342i	−0.723693	−	0.907483i
$969$		0			0
$970$	−87.3166	−	109.492i	−2.80357	−	3.51556i
$971$	−1.86443	−	8.16861i	−0.0598325	−	0.262143i	0.936161	−	0.351572i	$-0.114353\pi$
$971$	−1.86443	−	8.16861i	−0.0598325	−	0.262143i	−0.995993	+	0.0894292i	$0.971496\pi$
$972$		0			0
$973$	11.9610	+	14.9986i	0.383451	+	0.480832i
$974$	−84.8821			−2.71980
$975$		0			0
$976$	130.288	+	62.7435i	4.17042	+	2.00837i
$977$	−17.2562	+	21.6385i	−0.552073	+	0.692278i	−0.977070	−	0.212917i	$-0.931704\pi$
$977$	−17.2562	+	21.6385i	−0.552073	+	0.692278i	0.424997	+	0.905195i	$0.360275\pi$
$978$		0			0
$979$	13.3724	−	6.43983i	0.427385	−	0.205818i
$980$	−4.96237	−	21.7416i	−0.158517	−	0.694509i
$981$		0			0
$982$	25.9125	+	12.4788i	0.826901	+	0.398214i
$983$	−1.62240	+	0.781309i	−0.0517466	+	0.0249199i	−0.459578	−	0.888137i	$-0.651999\pi$
$983$	−1.62240	+	0.781309i	−0.0517466	+	0.0249199i	0.407831	+	0.913057i	$0.366285\pi$
$984$		0			0
$985$	39.6619			1.26373
$986$	38.1098	−	58.4163i	1.21366	−	1.86035i
$987$		0			0
$988$	4.36548	−	19.1264i	0.138884	−	0.608492i
$989$	−2.01216	+	0.969005i	−0.0639830	+	0.0308126i
$990$		0			0
$991$	−3.73734	+	16.3743i	−0.118720	+	0.520148i	0.880239	+	0.474531i	$0.157382\pi$
$991$	−3.73734	+	16.3743i	−0.118720	+	0.520148i	−0.998959	+	0.0456167i	$0.985475\pi$
$992$	−21.2543	−	93.1212i	−0.674825	−	2.95660i
$993$		0			0
$994$	14.8008	−	18.5596i	0.469452	−	0.588674i
$995$	15.7576	−	19.7594i	0.499548	−	0.626414i
$996$		0			0
$997$	16.6174	+	20.8376i	0.526280	+	0.659934i	0.971929	−	0.235274i	$-0.0755987\pi$
$997$	16.6174	+	20.8376i	0.526280	+	0.659934i	−0.445650	+	0.895208i	$0.647027\pi$
$998$	−26.1921			−0.829096
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.b.199.1		18
3.2	odd	2		87.2.g.b.25.3	yes	18
29.6	even	14		7569.2.a.bk.1.1		9
29.7	even	7	inner	261.2.k.b.181.1		18
29.23	even	7		7569.2.a.bl.1.9		9
87.23	odd	14		2523.2.a.p.1.1		9
87.35	odd	14		2523.2.a.q.1.9		9
87.65	odd	14		87.2.g.b.7.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.7.3	✓	18	87.65	odd	14
87.2.g.b.25.3	yes	18	3.2	odd	2
261.2.k.b.181.1		18	29.7	even	7	inner
261.2.k.b.199.1		18	1.1	even	1	trivial
2523.2.a.p.1.1		9	87.23	odd	14
2523.2.a.q.1.9		9	87.35	odd	14
7569.2.a.bk.1.1		9	29.6	even	14
7569.2.a.bl.1.9		9	29.23	even	7

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.596570 + 2.61374i) q^{2} +(-4.67383 - 2.25080i) q^{4} +(0.692177 - 3.03263i) q^{5} +(2.13550 - 1.02840i) q^{7} +(5.32817 - 6.68131i) q^{8} +(7.51358 + 3.61835i) q^{10} +(-1.62277 - 2.03489i) q^{11} +(-1.43935 - 1.80488i) q^{13} +(1.41401 + 6.19518i) q^{14} +(7.81583 + 9.80074i) q^{16} +4.83107 q^{17} +(-1.47595 - 0.710781i) q^{19} +(-10.0609 + 12.6160i) q^{20} +(6.28677 - 3.02755i) q^{22} +(-0.263303 - 1.15361i) q^{23} +(-4.21288 - 2.02881i) q^{25} +(5.57617 - 2.68534i) q^{26} -12.2957 q^{28} +(-5.05191 - 1.86501i) q^{29} +(-1.28688 + 5.63821i) q^{31} +(-14.8805 + 7.16606i) q^{32} +(-2.88207 + 12.6272i) q^{34} +(-1.64062 - 7.18803i) q^{35} +(4.30094 - 5.39321i) q^{37} +(2.73831 - 3.43373i) q^{38} +(-16.5739 - 20.7830i) q^{40} +7.66791 q^{41} +(-0.419989 - 1.84009i) q^{43} +(3.00442 + 13.1632i) q^{44} +3.17231 q^{46} +(5.79950 + 7.27234i) q^{47} +(-0.861665 + 1.08049i) q^{49} +(7.81608 - 9.80105i) q^{50} +(2.66483 + 11.6754i) q^{52} +(-1.15113 + 5.04343i) q^{53} +(-7.29430 + 3.51275i) q^{55} +(4.50723 - 19.7475i) q^{56} +(7.88847 - 12.0918i) q^{58} +4.90494 q^{59} +(10.3934 - 5.00522i) q^{61} +(-13.9691 - 6.72717i) q^{62} +(-4.27413 - 18.7262i) q^{64} +(-6.46982 + 3.11570i) q^{65} +(-4.34830 + 5.45260i) q^{67} +(-22.5796 - 10.8738i) q^{68} +19.7664 q^{70} +(-2.32918 - 2.92070i) q^{71} +(-0.532592 - 2.33344i) q^{73} +(11.5306 + 14.4590i) q^{74} +(5.29852 + 6.64413i) q^{76} +(-5.55812 - 2.67665i) q^{77} +(2.34395 - 2.93923i) q^{79} +(35.1319 - 16.9187i) q^{80} +(-4.57445 + 20.0420i) q^{82} +(-9.54570 - 4.59697i) q^{83} +(3.34396 - 14.6508i) q^{85} +5.06009 q^{86} -22.2421 q^{88} +(-1.26895 + 5.55963i) q^{89} +(-4.92988 - 2.37411i) q^{91} +(-1.36590 + 5.98440i) q^{92} +(-22.4678 + 10.8199i) q^{94} +(-3.17715 + 3.98402i) q^{95} +(-15.1300 - 7.28624i) q^{97} +(-2.31009 - 2.89676i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} - 11 q^{13} + 2 q^{14} + 18 q^{16} + 32 q^{17} + 2 q^{19} - 51 q^{20} + 20 q^{22} + 6 q^{23} + 4 q^{25} + 3 q^{26} - 48 q^{28}+ \cdots + 11 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 - 11 * q^13 + 2 * q^14 + 18 * q^16 + 32 * q^17 + 2 * q^19 - 51 * q^20 + 20 * q^22 + 6 * q^23 + 4 * q^25 + 3 * q^26 - 48 * q^28 + 10 * q^29 + 8 * q^31 - 55 * q^32 + 6 * q^34 - 31 * q^35 + 20 * q^37 + 20 * q^38 - 59 * q^40 + 68 * q^41 - 3 * q^43 + 10 * q^44 - 12 * q^46 - 19 * q^47 + 17 * q^49 - 23 * q^50 - 4 * q^52 + q^53 + 3 * q^55 - 7 * q^56 - 30 * q^58 - 20 * q^59 + 24 * q^61 - 79 * q^62 - 23 * q^64 - 6 * q^65 - 14 * q^67 + 8 * q^68 + 28 * q^70 + 28 * q^71 + 43 * q^73 + 47 * q^74 + 19 * q^76 - 26 * q^77 + 9 * q^79 + 74 * q^80 - 17 * q^82 - 8 * q^83 - 21 * q^85 + 140 * q^86 - 58 * q^88 + 6 * q^89 - 15 * q^91 - 11 * q^92 + 6 * q^94 + 16 * q^95 - 81 * q^97 + 11 * q^98

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